diff --git a/-sfaHVFWBU8.txt b/-sfaHVFWBU8.txt
new file mode 100644
index 0000000000000000000000000000000000000000..f3f36f45cfe7288252eb66d1071c5c02a51d1df2
--- /dev/null
+++ b/-sfaHVFWBU8.txt
@@ -0,0 +1,12755 @@
+align:start position:0%
+ 
+foreign
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so let's continue our discussion about
+
+ align:start position:0%
+so let's continue our discussion about
+ 
+
+ align:start position:0%
+so let's continue our discussion about
+spectral theory for self-adjoint compact
+
+ align:start position:0%
+spectral theory for self-adjoint compact
+ 
+
+ align:start position:0%
+spectral theory for self-adjoint compact
+operators so let me just briefly recall
+
+ align:start position:0%
+operators so let me just briefly recall
+ 
+
+ align:start position:0%
+operators so let me just briefly recall
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+the spectrum of a bounded operator which
+
+ align:start position:0%
+the spectrum of a bounded operator which
+ 
+
+ align:start position:0%
+the spectrum of a bounded operator which
+was supposed to be a generalization
+
+ align:start position:0%
+was supposed to be a generalization
+ 
+
+ align:start position:0%
+was supposed to be a generalization
+of the eigenvalues of a matrix so we
+
+ align:start position:0%
+of the eigenvalues of a matrix so we
+ 
+
+ align:start position:0%
+of the eigenvalues of a matrix so we
+defined
+
+ align:start position:0%
+defined
+ 
+
+ align:start position:0%
+defined
+the resolvance set of a to B
+
+ align:start position:0%
+the resolvance set of a to B
+ 
+
+ align:start position:0%
+the resolvance set of a to B
+those complex numbers such that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+a minus Lambda times the identity which
+
+ align:start position:0%
+a minus Lambda times the identity which
+ 
+
+ align:start position:0%
+a minus Lambda times the identity which
+I just write as a minus Lambda is an
+
+ align:start position:0%
+I just write as a minus Lambda is an
+ 
+
+ align:start position:0%
+I just write as a minus Lambda is an
+invertible uh
+
+ align:start position:0%
+invertible uh
+ 
+
+ align:start position:0%
+invertible uh
+bounded linear operator meaning it is
+
+ align:start position:0%
+bounded linear operator meaning it is
+ 
+
+ align:start position:0%
+bounded linear operator meaning it is
+um bijective and which by the open
+
+ align:start position:0%
+um bijective and which by the open
+ 
+
+ align:start position:0%
+um bijective and which by the open
+mapping theorem tells you that the
+
+ align:start position:0%
+mapping theorem tells you that the
+ 
+
+ align:start position:0%
+mapping theorem tells you that the
+inverse is also continuous
+
+ align:start position:0%
+inverse is also continuous
+ 
+
+ align:start position:0%
+inverse is also continuous
+um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and the Spectrum
+
+ align:start position:0%
+and the Spectrum
+ 
+
+ align:start position:0%
+and the Spectrum
+of a is simply those Lambda so that a
+
+ align:start position:0%
+of a is simply those Lambda so that a
+ 
+
+ align:start position:0%
+of a is simply those Lambda so that a
+minus Lambda is not invertible so the
+
+ align:start position:0%
+minus Lambda is not invertible so the
+ 
+
+ align:start position:0%
+minus Lambda is not invertible so the
+complement
+
+ align:start position:0%
+complement
+ 
+
+ align:start position:0%
+complement
+of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+resolve instead of a
+
+ align:start position:0%
+resolve instead of a
+ 
+
+ align:start position:0%
+resolve instead of a
+okay and so
+
+ align:start position:0%
+okay and so
+ 
+
+ align:start position:0%
+okay and so
+you know from
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+linear algebra
+
+ align:start position:0%
+linear algebra
+ 
+
+ align:start position:0%
+linear algebra
+you have the following uh
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+characterization of what the spectrum is
+
+ align:start position:0%
+characterization of what the spectrum is
+ 
+
+ align:start position:0%
+characterization of what the spectrum is
+that uh
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+if H is c n and a is just therefore a
+
+ align:start position:0%
+if H is c n and a is just therefore a
+ 
+
+ align:start position:0%
+if H is c n and a is just therefore a
+matrix on c n or RN if you like then the
+
+ align:start position:0%
+matrix on c n or RN if you like then the
+ 
+
+ align:start position:0%
+matrix on c n or RN if you like then the
+spectrum is just simply the set of
+
+ align:start position:0%
+spectrum is just simply the set of
+ 
+
+ align:start position:0%
+spectrum is just simply the set of
+eigenvalues
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+of a
+
+ align:start position:0%
+of a
+ 
+
+ align:start position:0%
+of a
+okay and if we restrict our attention to
+
+ align:start position:0%
+okay and if we restrict our attention to
+ 
+
+ align:start position:0%
+okay and if we restrict our attention to
+hermitian matrices
+
+ align:start position:0%
+hermitian matrices
+ 
+
+ align:start position:0%
+hermitian matrices
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+meaning which are referred to as which
+
+ align:start position:0%
+meaning which are referred to as which
+ 
+
+ align:start position:0%
+meaning which are referred to as which
+are also
+
+ align:start position:0%
+are also
+ 
+
+ align:start position:0%
+are also
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+referred to as self-adjoint also in in
+
+ align:start position:0%
+referred to as self-adjoint also in in
+ 
+
+ align:start position:0%
+referred to as self-adjoint also in in
+linear algebra or symmetric if we're
+
+ align:start position:0%
+linear algebra or symmetric if we're
+ 
+
+ align:start position:0%
+linear algebra or symmetric if we're
+just looking at
+
+ align:start position:0%
+just looking at
+ 
+
+ align:start position:0%
+just looking at
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+real Vector spaces are in
+
+ align:start position:0%
+real Vector spaces are in
+ 
+
+ align:start position:0%
+real Vector spaces are in
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+then the eigenvalues are real
+
+ align:start position:0%
+then the eigenvalues are real
+ 
+
+ align:start position:0%
+then the eigenvalues are real
+and you can find an orthonormal basis of
+
+ align:start position:0%
+and you can find an orthonormal basis of
+ 
+
+ align:start position:0%
+and you can find an orthonormal basis of
+the space CN or RN depending on what
+
+ align:start position:0%
+the space CN or RN depending on what
+ 
+
+ align:start position:0%
+the space CN or RN depending on what
+you're looking at
+
+ align:start position:0%
+you're looking at
+ 
+
+ align:start position:0%
+you're looking at
+for this
+
+ align:start position:0%
+for this
+ 
+
+ align:start position:0%
+for this
+symmetric Matrix so that a complete in
+
+ align:start position:0%
+symmetric Matrix so that a complete in
+ 
+
+ align:start position:0%
+symmetric Matrix so that a complete in
+that Matrix The Matrix in that basis The
+
+ align:start position:0%
+that Matrix The Matrix in that basis The
+ 
+
+ align:start position:0%
+that Matrix The Matrix in that basis The
+Matrix is completely diagonalized okay
+
+ align:start position:0%
+Matrix is completely diagonalized okay
+ 
+
+ align:start position:0%
+Matrix is completely diagonalized okay
+and what are the diagonal elements there
+
+ align:start position:0%
+and what are the diagonal elements there
+ 
+
+ align:start position:0%
+and what are the diagonal elements there
+the eigenvalues of the Matrix okay and
+
+ align:start position:0%
+the eigenvalues of the Matrix okay and
+ 
+
+ align:start position:0%
+the eigenvalues of the Matrix okay and
+what we're going to end up proving is
+
+ align:start position:0%
+what we're going to end up proving is
+ 
+
+ align:start position:0%
+what we're going to end up proving is
+that that picture this kind of picture
+
+ align:start position:0%
+that that picture this kind of picture
+ 
+
+ align:start position:0%
+that that picture this kind of picture
+where the
+
+ align:start position:0%
+where the
+ 
+
+ align:start position:0%
+where the
+um for a
+
+ align:start position:0%
+um for a
+ 
+
+ align:start position:0%
+um for a
+you know self-adjoined Matrix on CN that
+
+ align:start position:0%
+you know self-adjoined Matrix on CN that
+ 
+
+ align:start position:0%
+you know self-adjoined Matrix on CN that
+the spectrum is given by the eigenvalues
+
+ align:start position:0%
+the spectrum is given by the eigenvalues
+ 
+
+ align:start position:0%
+the spectrum is given by the eigenvalues
+and you can diagonalize essentially
+
+ align:start position:0%
+and you can diagonalize essentially
+ 
+
+ align:start position:0%
+and you can diagonalize essentially
+diagonalize this operator meaning you
+
+ align:start position:0%
+diagonalize this operator meaning you
+ 
+
+ align:start position:0%
+diagonalize this operator meaning you
+can form find a orthonormal basis
+
+ align:start position:0%
+can form find a orthonormal basis
+ 
+
+ align:start position:0%
+can form find a orthonormal basis
+consisting entirely of eigenvectors of
+
+ align:start position:0%
+consisting entirely of eigenvectors of
+ 
+
+ align:start position:0%
+consisting entirely of eigenvectors of
+the operator is also true for uh
+
+ align:start position:0%
+the operator is also true for uh
+ 
+
+ align:start position:0%
+the operator is also true for uh
+self-ajoint compact operators okay this
+
+ align:start position:0%
+self-ajoint compact operators okay this
+ 
+
+ align:start position:0%
+self-ajoint compact operators okay this
+shouldn't come too much of a surprise as
+
+ align:start position:0%
+shouldn't come too much of a surprise as
+ 
+
+ align:start position:0%
+shouldn't come too much of a surprise as
+too much of a surprise since compact
+
+ align:start position:0%
+too much of a surprise since compact
+ 
+
+ align:start position:0%
+too much of a surprise since compact
+operators are limits of finite rank I.E
+
+ align:start position:0%
+operators are limits of finite rank I.E
+ 
+
+ align:start position:0%
+operators are limits of finite rank I.E
+Matrix matrices uh
+
+ align:start position:0%
+Matrix matrices uh
+ 
+
+ align:start position:0%
+Matrix matrices uh
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+in the space of bounded linear operators
+
+ align:start position:0%
+in the space of bounded linear operators
+ 
+
+ align:start position:0%
+in the space of bounded linear operators
+okay so that's where we're headed
+
+ align:start position:0%
+okay so that's where we're headed
+ 
+
+ align:start position:0%
+okay so that's where we're headed
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+now
+
+ align:start position:0%
+now
+ 
+
+ align:start position:0%
+now
+so just to
+
+ align:start position:0%
+so just to
+ 
+
+ align:start position:0%
+so just to
+follow up on this
+
+ align:start position:0%
+follow up on this
+ 
+
+ align:start position:0%
+follow up on this
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+for a little bit of review so you know
+
+ align:start position:0%
+for a little bit of review so you know
+ 
+
+ align:start position:0%
+for a little bit of review so you know
+in the finite dimensional space in the
+
+ align:start position:0%
+in the finite dimensional space in the
+ 
+
+ align:start position:0%
+in the finite dimensional space in the
+finite dimensional case the Spectrum can
+
+ align:start position:0%
+finite dimensional case the Spectrum can
+ 
+
+ align:start position:0%
+finite dimensional case the Spectrum can
+be or the spectrum is always just the
+
+ align:start position:0%
+be or the spectrum is always just the
+ 
+
+ align:start position:0%
+be or the spectrum is always just the
+eigenvalues of the Matrix a not so in
+
+ align:start position:0%
+eigenvalues of the Matrix a not so in
+ 
+
+ align:start position:0%
+eigenvalues of the Matrix a not so in
+the infinite dimensional
+
+ align:start position:0%
+the infinite dimensional
+ 
+
+ align:start position:0%
+the infinite dimensional
+setting for example if we're looking at
+
+ align:start position:0%
+setting for example if we're looking at
+ 
+
+ align:start position:0%
+setting for example if we're looking at
+little L2 and then a
+
+ align:start position:0%
+little L2 and then a
+ 
+
+ align:start position:0%
+little L2 and then a
+times a is equal to let's say A1 over
+
+ align:start position:0%
+times a is equal to let's say A1 over
+ 
+
+ align:start position:0%
+times a is equal to let's say A1 over
+one a two over two
+
+ align:start position:0%
+one a two over two
+ 
+
+ align:start position:0%
+one a two over two
+and so on
+
+ align:start position:0%
+and so on
+ 
+
+ align:start position:0%
+and so on
+for a
+
+ align:start position:0%
+for a
+ 
+
+ align:start position:0%
+for a
+sequence in L2 then
+
+ align:start position:0%
+sequence in L2 then
+ 
+
+ align:start position:0%
+sequence in L2 then
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+which we can prove is that 0 is in
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the spectrum of a
+
+ align:start position:0%
+the spectrum of a
+ 
+
+ align:start position:0%
+the spectrum of a
+all right one way to see that is that uh
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+each of the if you like basis vectors of
+
+ align:start position:0%
+each of the if you like basis vectors of
+ 
+
+ align:start position:0%
+each of the if you like basis vectors of
+H given where you just have one in the
+
+ align:start position:0%
+H given where you just have one in the
+ 
+
+ align:start position:0%
+H given where you just have one in the
+nth slot and 0 otherwise each of those
+
+ align:start position:0%
+nth slot and 0 otherwise each of those
+ 
+
+ align:start position:0%
+nth slot and 0 otherwise each of those
+is an eigenvector of this operator a
+
+ align:start position:0%
+is an eigenvector of this operator a
+ 
+
+ align:start position:0%
+is an eigenvector of this operator a
+with eigenvalue 1 over n where the N
+
+ align:start position:0%
+with eigenvalue 1 over n where the N
+ 
+
+ align:start position:0%
+with eigenvalue 1 over n where the N
+tells you where the one is and zero
+
+ align:start position:0%
+tells you where the one is and zero
+ 
+
+ align:start position:0%
+tells you where the one is and zero
+otherwise so 1 over n is in is an
+
+ align:start position:0%
+otherwise so 1 over n is in is an
+ 
+
+ align:start position:0%
+otherwise so 1 over n is in is an
+eigenvalue
+
+ align:start position:0%
+eigenvalue
+ 
+
+ align:start position:0%
+eigenvalue
+of this operator for each n
+
+ align:start position:0%
+of this operator for each n
+ 
+
+ align:start position:0%
+of this operator for each n
+and one over n converges to zero
+
+ align:start position:0%
+and one over n converges to zero
+ 
+
+ align:start position:0%
+and one over n converges to zero
+and since the spectrum of a bounded
+
+ align:start position:0%
+and since the spectrum of a bounded
+ 
+
+ align:start position:0%
+and since the spectrum of a bounded
+linear operator is a compact set in
+
+ align:start position:0%
+linear operator is a compact set in
+ 
+
+ align:start position:0%
+linear operator is a compact set in
+particular closed zero which is the
+
+ align:start position:0%
+particular closed zero which is the
+ 
+
+ align:start position:0%
+particular closed zero which is the
+limit of that sequence has to also be in
+
+ align:start position:0%
+limit of that sequence has to also be in
+ 
+
+ align:start position:0%
+limit of that sequence has to also be in
+the Spectrum
+
+ align:start position:0%
+the Spectrum
+ 
+
+ align:start position:0%
+the Spectrum
+okay and in fact what we're going to
+
+ align:start position:0%
+okay and in fact what we're going to
+ 
+
+ align:start position:0%
+okay and in fact what we're going to
+show is that you know kind of in the
+
+ align:start position:0%
+show is that you know kind of in the
+ 
+
+ align:start position:0%
+show is that you know kind of in the
+non-degenerate case what we see here is
+
+ align:start position:0%
+non-degenerate case what we see here is
+ 
+
+ align:start position:0%
+non-degenerate case what we see here is
+what in general happens for compact
+
+ align:start position:0%
+what in general happens for compact
+ 
+
+ align:start position:0%
+what in general happens for compact
+self-ajoint operators that
+
+ align:start position:0%
+self-ajoint operators that
+ 
+
+ align:start position:0%
+self-ajoint operators that
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+if it's not a finite rank operator then
+
+ align:start position:0%
+if it's not a finite rank operator then
+ 
+
+ align:start position:0%
+if it's not a finite rank operator then
+it has countably many
+
+ align:start position:0%
+it has countably many
+ 
+
+ align:start position:0%
+it has countably many
+uh accountably infinite many that's not
+
+ align:start position:0%
+uh accountably infinite many that's not
+ 
+
+ align:start position:0%
+uh accountably infinite many that's not
+a very good string of words accountably
+
+ align:start position:0%
+a very good string of words accountably
+ 
+
+ align:start position:0%
+a very good string of words accountably
+infinite eigenvalues which converge to
+
+ align:start position:0%
+infinite eigenvalues which converge to
+ 
+
+ align:start position:0%
+infinite eigenvalues which converge to
+zero okay and zero maybe an eigenvalue
+
+ align:start position:0%
+zero okay and zero maybe an eigenvalue
+ 
+
+ align:start position:0%
+zero okay and zero maybe an eigenvalue
+may not be okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+what's more that's going to be the only
+
+ align:start position:0%
+what's more that's going to be the only
+ 
+
+ align:start position:0%
+what's more that's going to be the only
+uh
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that completely characterizes the
+
+ align:start position:0%
+that completely characterizes the
+ 
+
+ align:start position:0%
+that completely characterizes the
+Spectrum so let me just write here for
+
+ align:start position:0%
+Spectrum so let me just write here for
+ 
+
+ align:start position:0%
+Spectrum so let me just write here for
+this example
+
+ align:start position:0%
+this example
+ 
+
+ align:start position:0%
+this example
+that in fact the spectrum of a is equal
+
+ align:start position:0%
+that in fact the spectrum of a is equal
+ 
+
+ align:start position:0%
+that in fact the spectrum of a is equal
+to
+
+ align:start position:0%
+to
+ 
+
+ align:start position:0%
+to
+0.0 Union
+
+ align:start position:0%
+0.0 Union
+ 
+
+ align:start position:0%
+0.0 Union
+1 over n
+
+ align:start position:0%
+1 over n
+ 
+
+ align:start position:0%
+1 over n
+in a natural number
+
+ align:start position:0%
+in a natural number
+ 
+
+ align:start position:0%
+in a natural number
+and these are again for this operator
+
+ align:start position:0%
+and these are again for this operator
+ 
+
+ align:start position:0%
+and these are again for this operator
+here these are the eigenvalues
+
+ align:start position:0%
+here these are the eigenvalues
+ 
+
+ align:start position:0%
+here these are the eigenvalues
+and this is just well zero is zero but
+
+ align:start position:0%
+and this is just well zero is zero but
+ 
+
+ align:start position:0%
+and this is just well zero is zero but
+zero is not
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+an eigenvalue okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+now this is not the general picture
+
+ align:start position:0%
+now this is not the general picture
+ 
+
+ align:start position:0%
+now this is not the general picture
+meaning that for a compact self-adjoin
+
+ align:start position:0%
+meaning that for a compact self-adjoin
+ 
+
+ align:start position:0%
+meaning that for a compact self-adjoin
+operator you'll have infinitely many
+
+ align:start position:0%
+operator you'll have infinitely many
+ 
+
+ align:start position:0%
+operator you'll have infinitely many
+eigenvalues and then zero will not be an
+
+ align:start position:0%
+eigenvalues and then zero will not be an
+ 
+
+ align:start position:0%
+eigenvalues and then zero will not be an
+eigenvalue you could have zero and
+
+ align:start position:0%
+eigenvalue you could have zero and
+ 
+
+ align:start position:0%
+eigenvalue you could have zero and
+eigenvalue as well but in general what
+
+ align:start position:0%
+eigenvalue as well but in general what
+ 
+
+ align:start position:0%
+eigenvalue as well but in general what
+the picture is is that anything in the
+
+ align:start position:0%
+the picture is is that anything in the
+ 
+
+ align:start position:0%
+the picture is is that anything in the
+Spectrum that's not zero has to be an
+
+ align:start position:0%
+Spectrum that's not zero has to be an
+ 
+
+ align:start position:0%
+Spectrum that's not zero has to be an
+eigenvalue
+
+ align:start position:0%
+eigenvalue
+ 
+
+ align:start position:0%
+eigenvalue
+okay and that's essentially what will
+
+ align:start position:0%
+okay and that's essentially what will
+ 
+
+ align:start position:0%
+okay and that's essentially what will
+prove
+
+ align:start position:0%
+prove
+ 
+
+ align:start position:0%
+prove
+our first result
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+of
+
+ align:start position:0%
+of
+ 
+
+ align:start position:0%
+of
+this lecture is that is following so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this is the Fred home
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+alternative
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so let
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+a b itself a joint compact operator
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and uh
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Lambda be a non-zero real number
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+then
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the range of a minus Lambda
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+is closed
+
+ align:start position:0%
+is closed
+ 
+
+ align:start position:0%
+is closed
+so this is the conclusion
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and thus
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the range of a minus Lambda is equal to
+
+ align:start position:0%
+the range of a minus Lambda is equal to
+ 
+
+ align:start position:0%
+the range of a minus Lambda is equal to
+the orthogonal complement of the
+
+ align:start position:0%
+the orthogonal complement of the
+ 
+
+ align:start position:0%
+the orthogonal complement of the
+orthogonal complement of itself
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+which
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the orthogonal complement of the range
+
+ align:start position:0%
+the orthogonal complement of the range
+ 
+
+ align:start position:0%
+the orthogonal complement of the range
+of a minus Lambda is equal to the null
+
+ align:start position:0%
+of a minus Lambda is equal to the null
+ 
+
+ align:start position:0%
+of a minus Lambda is equal to the null
+space of the adjoint and since a is sulf
+
+ align:start position:0%
+space of the adjoint and since a is sulf
+ 
+
+ align:start position:0%
+space of the adjoint and since a is sulf
+a joint and Lambda is a real number the
+
+ align:start position:0%
+a joint and Lambda is a real number the
+ 
+
+ align:start position:0%
+a joint and Lambda is a real number the
+adjoint is just a minus Lambda
+
+ align:start position:0%
+adjoint is just a minus Lambda
+ 
+
+ align:start position:0%
+adjoint is just a minus Lambda
+okay so this right here is the
+
+ align:start position:0%
+okay so this right here is the
+ 
+
+ align:start position:0%
+okay so this right here is the
+main conclusion from which you get this
+
+ align:start position:0%
+main conclusion from which you get this
+ 
+
+ align:start position:0%
+main conclusion from which you get this
+and therefore
+
+ align:start position:0%
+and therefore
+ 
+
+ align:start position:0%
+and therefore
+just to spell out
+
+ align:start position:0%
+just to spell out
+ 
+
+ align:start position:0%
+just to spell out
+uh the conclusion of
+
+ align:start position:0%
+uh the conclusion of
+ 
+
+ align:start position:0%
+uh the conclusion of
+this equality therefore
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+either uh
+
+ align:start position:0%
+either uh
+ 
+
+ align:start position:0%
+either uh
+one of two Alternatives happens so
+
+ align:start position:0%
+one of two Alternatives happens so
+ 
+
+ align:start position:0%
+one of two Alternatives happens so
+that's the name alternative either
+
+ align:start position:0%
+that's the name alternative either
+ 
+
+ align:start position:0%
+that's the name alternative either
+um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+a minus Lambda is
+
+ align:start position:0%
+a minus Lambda is
+ 
+
+ align:start position:0%
+a minus Lambda is
+by objective
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+or
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the null space of a minus Lambda which
+
+ align:start position:0%
+the null space of a minus Lambda which
+ 
+
+ align:start position:0%
+the null space of a minus Lambda which
+is just the eigenspace of a minus Lambda
+
+ align:start position:0%
+is just the eigenspace of a minus Lambda
+ 
+
+ align:start position:0%
+is just the eigenspace of a minus Lambda
+or I should say the eigenspace
+
+ align:start position:0%
+or I should say the eigenspace
+ 
+
+ align:start position:0%
+or I should say the eigenspace
+corresponding to uh
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Lambda is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+non-trivial
+
+ align:start position:0%
+non-trivial
+ 
+
+ align:start position:0%
+non-trivial
+foreign
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and finite dimensional
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+moreover this equality here tells you
+
+ align:start position:0%
+moreover this equality here tells you
+ 
+
+ align:start position:0%
+moreover this equality here tells you
+when you can solve the equation a minus
+
+ align:start position:0%
+when you can solve the equation a minus
+ 
+
+ align:start position:0%
+when you can solve the equation a minus
+Lambda U equals F right
+
+ align:start position:0%
+Lambda U equals F right
+ 
+
+ align:start position:0%
+Lambda U equals F right
+you can solve a minus Lambda U equals F
+
+ align:start position:0%
+you can solve a minus Lambda U equals F
+ 
+
+ align:start position:0%
+you can solve a minus Lambda U equals F
+if and only if f is in the range of a
+
+ align:start position:0%
+if and only if f is in the range of a
+ 
+
+ align:start position:0%
+if and only if f is in the range of a
+minus Lambda which is if and only if f
+
+ align:start position:0%
+minus Lambda which is if and only if f
+ 
+
+ align:start position:0%
+minus Lambda which is if and only if f
+is orthogonal to the null space of a
+
+ align:start position:0%
+is orthogonal to the null space of a
+ 
+
+ align:start position:0%
+is orthogonal to the null space of a
+minus Lambda so let me make a little
+
+ align:start position:0%
+minus Lambda so let me make a little
+ 
+
+ align:start position:0%
+minus Lambda so let me make a little
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+remark here so first off
+
+ align:start position:0%
+remark here so first off
+ 
+
+ align:start position:0%
+remark here so first off
+um the fact that this space has to be
+
+ align:start position:0%
+um the fact that this space has to be
+ 
+
+ align:start position:0%
+um the fact that this space has to be
+finite dimensional we proved last time
+
+ align:start position:0%
+finite dimensional we proved last time
+ 
+
+ align:start position:0%
+finite dimensional we proved last time
+right we proved at the end of uh
+
+ align:start position:0%
+right we proved at the end of uh
+ 
+
+ align:start position:0%
+right we proved at the end of uh
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+lecture the last lecture that for a
+
+ align:start position:0%
+lecture the last lecture that for a
+ 
+
+ align:start position:0%
+lecture the last lecture that for a
+compact self-adjoined operator
+
+ align:start position:0%
+compact self-adjoined operator
+ 
+
+ align:start position:0%
+compact self-adjoined operator
+the null space the eigenspace
+
+ align:start position:0%
+the null space the eigenspace
+ 
+
+ align:start position:0%
+the null space the eigenspace
+corresponding to a given non-zero
+
+ align:start position:0%
+corresponding to a given non-zero
+ 
+
+ align:start position:0%
+corresponding to a given non-zero
+eigenvalue
+
+ align:start position:0%
+eigenvalue
+ 
+
+ align:start position:0%
+eigenvalue
+is finite dimensional right and then we
+
+ align:start position:0%
+is finite dimensional right and then we
+ 
+
+ align:start position:0%
+is finite dimensional right and then we
+also proved the eigenspaces
+
+ align:start position:0%
+also proved the eigenspaces
+ 
+
+ align:start position:0%
+also proved the eigenspaces
+corresponding to two different
+
+ align:start position:0%
+corresponding to two different
+ 
+
+ align:start position:0%
+corresponding to two different
+eigenvalues or orthogonal and we also
+
+ align:start position:0%
+eigenvalues or orthogonal and we also
+ 
+
+ align:start position:0%
+eigenvalues or orthogonal and we also
+prove that the eigenvalues that are
+
+ align:start position:0%
+prove that the eigenvalues that are
+ 
+
+ align:start position:0%
+prove that the eigenvalues that are
+non-zero or any eigenvalue has to be
+
+ align:start position:0%
+non-zero or any eigenvalue has to be
+ 
+
+ align:start position:0%
+non-zero or any eigenvalue has to be
+real okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so now let me make a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+couple of remarks the first is just a
+
+ align:start position:0%
+couple of remarks the first is just a
+ 
+
+ align:start position:0%
+couple of remarks the first is just a
+rephrasing of what's in the theorem that
+
+ align:start position:0%
+rephrasing of what's in the theorem that
+ 
+
+ align:start position:0%
+rephrasing of what's in the theorem that
+therefore um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+f
+
+ align:start position:0%
+f
+ 
+
+ align:start position:0%
+f
+is in the range of a minus Lambda
+
+ align:start position:0%
+is in the range of a minus Lambda
+ 
+
+ align:start position:0%
+is in the range of a minus Lambda
+meaning you can solve the equation a
+
+ align:start position:0%
+meaning you can solve the equation a
+ 
+
+ align:start position:0%
+meaning you can solve the equation a
+minus Lambda U equals f
+
+ align:start position:0%
+minus Lambda U equals f
+ 
+
+ align:start position:0%
+minus Lambda U equals f
+if and only if
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+f is in the null space of
+
+ align:start position:0%
+f is in the null space of
+ 
+
+ align:start position:0%
+f is in the null space of
+you're the orthogonal complement of a
+
+ align:start position:0%
+you're the orthogonal complement of a
+ 
+
+ align:start position:0%
+you're the orthogonal complement of a
+minus uh of the null space of a minus
+
+ align:start position:0%
+minus uh of the null space of a minus
+ 
+
+ align:start position:0%
+minus uh of the null space of a minus
+Lambda okay so what this says is that uh
+
+ align:start position:0%
+Lambda okay so what this says is that uh
+ 
+
+ align:start position:0%
+Lambda okay so what this says is that uh
+you can solve for f given that F
+
+ align:start position:0%
+you can solve for f given that F
+ 
+
+ align:start position:0%
+you can solve for f given that F
+satisfies finitely many uh linear
+
+ align:start position:0%
+satisfies finitely many uh linear
+ 
+
+ align:start position:0%
+satisfies finitely many uh linear
+conditions okay right because the null
+
+ align:start position:0%
+conditions okay right because the null
+ 
+
+ align:start position:0%
+conditions okay right because the null
+space of a minus Lambda is finite
+
+ align:start position:0%
+space of a minus Lambda is finite
+ 
+
+ align:start position:0%
+space of a minus Lambda is finite
+dimensional so F being orthogonal to
+
+ align:start position:0%
+dimensional so F being orthogonal to
+ 
+
+ align:start position:0%
+dimensional so F being orthogonal to
+that means pick a finite base a finite
+
+ align:start position:0%
+that means pick a finite base a finite
+ 
+
+ align:start position:0%
+that means pick a finite base a finite
+or orthonormal basis of a minus null
+
+ align:start position:0%
+or orthonormal basis of a minus null
+ 
+
+ align:start position:0%
+or orthonormal basis of a minus null
+space of a minus Lambda then F in a
+
+ align:start position:0%
+space of a minus Lambda then F in a
+ 
+
+ align:start position:0%
+space of a minus Lambda then F in a
+product with those finitely many vectors
+
+ align:start position:0%
+product with those finitely many vectors
+ 
+
+ align:start position:0%
+product with those finitely many vectors
+has to be zero so you have finitely many
+
+ align:start position:0%
+has to be zero so you have finitely many
+ 
+
+ align:start position:0%
+has to be zero so you have finitely many
+conditions on F to be able to solve for
+
+ align:start position:0%
+conditions on F to be able to solve for
+ 
+
+ align:start position:0%
+conditions on F to be able to solve for
+f and not only that this solution that
+
+ align:start position:0%
+f and not only that this solution that
+ 
+
+ align:start position:0%
+f and not only that this solution that
+you compute is also unique of two
+
+ align:start position:0%
+you compute is also unique of two
+ 
+
+ align:start position:0%
+you compute is also unique of two
+finitely many conditions because again
+
+ align:start position:0%
+finitely many conditions because again
+ 
+
+ align:start position:0%
+finitely many conditions because again
+the null space of a minus Lambda is
+
+ align:start position:0%
+the null space of a minus Lambda is
+ 
+
+ align:start position:0%
+the null space of a minus Lambda is
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+or unique up to a finite dimensional
+
+ align:start position:0%
+or unique up to a finite dimensional
+ 
+
+ align:start position:0%
+or unique up to a finite dimensional
+Subspace again because the null space of
+
+ align:start position:0%
+Subspace again because the null space of
+ 
+
+ align:start position:0%
+Subspace again because the null space of
+a minus Lambda is finite dimensional and
+
+ align:start position:0%
+a minus Lambda is finite dimensional and
+ 
+
+ align:start position:0%
+a minus Lambda is finite dimensional and
+the second is uh that uh
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+since uh for a self-adjoint uh operator
+
+ align:start position:0%
+since uh for a self-adjoint uh operator
+ 
+
+ align:start position:0%
+since uh for a self-adjoint uh operator
+we have at
+
+ align:start position:0%
+we have at
+ 
+
+ align:start position:0%
+we have at
+the spectrum is
+
+ align:start position:0%
+the spectrum is
+ 
+
+ align:start position:0%
+the spectrum is
+a subset of the real numbers right for a
+
+ align:start position:0%
+a subset of the real numbers right for a
+ 
+
+ align:start position:0%
+a subset of the real numbers right for a
+self-adjoin operator this is something
+
+ align:start position:0%
+self-adjoin operator this is something
+ 
+
+ align:start position:0%
+self-adjoin operator this is something
+we proved uh last lecture it doesn't
+
+ align:start position:0%
+we proved uh last lecture it doesn't
+ 
+
+ align:start position:0%
+we proved uh last lecture it doesn't
+have to be compact just a self-adjoin
+
+ align:start position:0%
+have to be compact just a self-adjoin
+ 
+
+ align:start position:0%
+have to be compact just a self-adjoin
+operator so since the spectrum is a
+
+ align:start position:0%
+operator so since the spectrum is a
+ 
+
+ align:start position:0%
+operator so since the spectrum is a
+subset of the reals this proves that for
+
+ align:start position:0%
+subset of the reals this proves that for
+ 
+
+ align:start position:0%
+subset of the reals this proves that for
+a compact
+
+ align:start position:0%
+a compact
+ 
+
+ align:start position:0%
+a compact
+self-adjoin operator the spectrum of a
+
+ align:start position:0%
+self-adjoin operator the spectrum of a
+ 
+
+ align:start position:0%
+self-adjoin operator the spectrum of a
+is equal to the set of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+eigenvalues of a or I should say
+
+ align:start position:0%
+eigenvalues of a or I should say
+ 
+
+ align:start position:0%
+eigenvalues of a or I should say
+non-zero eigenvalues of a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+or let's let's let's write it this way
+
+ align:start position:0%
+or let's let's let's write it this way
+ 
+
+ align:start position:0%
+or let's let's let's write it this way
+if I look at what's in the spec Spectrum
+
+ align:start position:0%
+if I look at what's in the spec Spectrum
+ 
+
+ align:start position:0%
+if I look at what's in the spec Spectrum
+other than 0 possibly
+
+ align:start position:0%
+other than 0 possibly
+ 
+
+ align:start position:0%
+other than 0 possibly
+then the non-zero numbers that are in
+
+ align:start position:0%
+then the non-zero numbers that are in
+ 
+
+ align:start position:0%
+then the non-zero numbers that are in
+the Spectrum have to be eigenvalues
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so for a compact self-adjoint
+
+ align:start position:0%
+okay so for a compact self-adjoint
+ 
+
+ align:start position:0%
+okay so for a compact self-adjoint
+operator
+
+ align:start position:0%
+operator
+ 
+
+ align:start position:0%
+operator
+and adjusting the case of matrices the
+
+ align:start position:0%
+and adjusting the case of matrices the
+ 
+
+ align:start position:0%
+and adjusting the case of matrices the
+Spectrum
+
+ align:start position:0%
+Spectrum
+ 
+
+ align:start position:0%
+Spectrum
+the non-zero Spectrum has to be are
+
+ align:start position:0%
+the non-zero Spectrum has to be are
+ 
+
+ align:start position:0%
+the non-zero Spectrum has to be are
+nothing but eigenvalues okay and last
+
+ align:start position:0%
+nothing but eigenvalues okay and last
+ 
+
+ align:start position:0%
+nothing but eigenvalues okay and last
+time remember we proved that the
+
+ align:start position:0%
+time remember we proved that the
+ 
+
+ align:start position:0%
+time remember we proved that the
+eigenvalues are accountably infinite
+
+ align:start position:0%
+eigenvalues are accountably infinite
+ 
+
+ align:start position:0%
+eigenvalues are accountably infinite
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+or countable they're either finite or
+
+ align:start position:0%
+or countable they're either finite or
+ 
+
+ align:start position:0%
+or countable they're either finite or
+countably infinite and if they're
+
+ align:start position:0%
+countably infinite and if they're
+ 
+
+ align:start position:0%
+countably infinite and if they're
+countably infinite they converge to zero
+
+ align:start position:0%
+countably infinite they converge to zero
+ 
+
+ align:start position:0%
+countably infinite they converge to zero
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+Again by last lecture
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+we conclude again that
+
+ align:start position:0%
+we conclude again that
+ 
+
+ align:start position:0%
+we conclude again that
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+the spectrum of a
+
+ align:start position:0%
+the spectrum of a
+ 
+
+ align:start position:0%
+the spectrum of a
+take away zero
+
+ align:start position:0%
+take away zero
+ 
+
+ align:start position:0%
+take away zero
+equals either
+
+ align:start position:0%
+equals either
+ 
+
+ align:start position:0%
+equals either
+finitely many
+
+ align:start position:0%
+finitely many
+ 
+
+ align:start position:0%
+finitely many
+eigenvalues
+
+ align:start position:0%
+eigenvalues
+ 
+
+ align:start position:0%
+eigenvalues
+or
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+accountably infinite
+
+ align:start position:0%
+accountably infinite
+ 
+
+ align:start position:0%
+accountably infinite
+eigenvalues
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+with that are converging to zero
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so from the Fred home alternative you
+
+ align:start position:0%
+so from the Fred home alternative you
+ 
+
+ align:start position:0%
+so from the Fred home alternative you
+know we get a lot of information about
+
+ align:start position:0%
+know we get a lot of information about
+ 
+
+ align:start position:0%
+know we get a lot of information about
+when we can solve equations but it also
+
+ align:start position:0%
+when we can solve equations but it also
+ 
+
+ align:start position:0%
+when we can solve equations but it also
+tells us I mean from that ability to say
+
+ align:start position:0%
+tells us I mean from that ability to say
+ 
+
+ align:start position:0%
+tells us I mean from that ability to say
+when we can solve equations we can also
+
+ align:start position:0%
+when we can solve equations we can also
+ 
+
+ align:start position:0%
+when we can solve equations we can also
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+characterize the non-zero spectrum of a
+
+ align:start position:0%
+characterize the non-zero spectrum of a
+ 
+
+ align:start position:0%
+characterize the non-zero spectrum of a
+self-adjoined compact operator
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so we need to prove that so remember all
+
+ align:start position:0%
+so we need to prove that so remember all
+ 
+
+ align:start position:0%
+so we need to prove that so remember all
+of this just followed from you know
+
+ align:start position:0%
+of this just followed from you know
+ 
+
+ align:start position:0%
+of this just followed from you know
+stuff we had proven and the main result
+
+ align:start position:0%
+stuff we had proven and the main result
+ 
+
+ align:start position:0%
+stuff we had proven and the main result
+the main conclusion of the theorem which
+
+ align:start position:0%
+the main conclusion of the theorem which
+ 
+
+ align:start position:0%
+the main conclusion of the theorem which
+is that the range of a minus Lambda is
+
+ align:start position:0%
+is that the range of a minus Lambda is
+ 
+
+ align:start position:0%
+is that the range of a minus Lambda is
+closed so we need to prove that the
+
+ align:start position:0%
+closed so we need to prove that the
+ 
+
+ align:start position:0%
+closed so we need to prove that the
+range of a minus Lambda is closed when
+
+ align:start position:0%
+range of a minus Lambda is closed when
+ 
+
+ align:start position:0%
+range of a minus Lambda is closed when
+Lambda is a non-zero real number so um
+
+ align:start position:0%
+Lambda is a non-zero real number so um
+ 
+
+ align:start position:0%
+Lambda is a non-zero real number so um
+suppose that
+
+ align:start position:0%
+suppose that
+ 
+
+ align:start position:0%
+suppose that
+you have a sequence in the range which
+
+ align:start position:0%
+you have a sequence in the range which
+ 
+
+ align:start position:0%
+you have a sequence in the range which
+I'll write as a minus Lambda times u n
+
+ align:start position:0%
+I'll write as a minus Lambda times u n
+ 
+
+ align:start position:0%
+I'll write as a minus Lambda times u n
+converging to some element f
+
+ align:start position:0%
+converging to some element f
+ 
+
+ align:start position:0%
+converging to some element f
+in H
+
+ align:start position:0%
+in H
+ 
+
+ align:start position:0%
+in H
+okay so what we'd like to be able to
+
+ align:start position:0%
+okay so what we'd like to be able to
+ 
+
+ align:start position:0%
+okay so what we'd like to be able to
+show is that f is in the range
+
+ align:start position:0%
+show is that f is in the range
+ 
+
+ align:start position:0%
+show is that f is in the range
+so uh
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+we want to show
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+f is in the range of H
+
+ align:start position:0%
+f is in the range of H
+ 
+
+ align:start position:0%
+f is in the range of H
+or not range of H range of a
+
+ align:start position:0%
+or not range of H range of a
+ 
+
+ align:start position:0%
+or not range of H range of a
+uh minus Lambda sorry
+
+ align:start position:0%
+uh minus Lambda sorry
+ 
+
+ align:start position:0%
+uh minus Lambda sorry
+I hope I didn't make that mistake
+
+ align:start position:0%
+I hope I didn't make that mistake
+ 
+
+ align:start position:0%
+I hope I didn't make that mistake
+elsewhere no just
+
+ align:start position:0%
+elsewhere no just
+ 
+
+ align:start position:0%
+elsewhere no just
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+now we're only assuming that a minus
+
+ align:start position:0%
+now we're only assuming that a minus
+ 
+
+ align:start position:0%
+now we're only assuming that a minus
+Lambda uh when it hits U sub n converges
+
+ align:start position:0%
+Lambda uh when it hits U sub n converges
+ 
+
+ align:start position:0%
+Lambda uh when it hits U sub n converges
+to F we're not a priori assuming the U
+
+ align:start position:0%
+to F we're not a priori assuming the U
+ 
+
+ align:start position:0%
+to F we're not a priori assuming the U
+sub n's converge okay in fact we can't
+
+ align:start position:0%
+sub n's converge okay in fact we can't
+ 
+
+ align:start position:0%
+sub n's converge okay in fact we can't
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+now but in the end we would like to come
+
+ align:start position:0%
+now but in the end we would like to come
+ 
+
+ align:start position:0%
+now but in the end we would like to come
+up with
+
+ align:start position:0%
+up with
+ 
+
+ align:start position:0%
+up with
+you know maybe a subsequence or or a
+
+ align:start position:0%
+you know maybe a subsequence or or a
+ 
+
+ align:start position:0%
+you know maybe a subsequence or or a
+part of the use of bins up to a
+
+ align:start position:0%
+part of the use of bins up to a
+ 
+
+ align:start position:0%
+part of the use of bins up to a
+subsequence which does converge and then
+
+ align:start position:0%
+subsequence which does converge and then
+ 
+
+ align:start position:0%
+subsequence which does converge and then
+we conclude that f is in the range all
+
+ align:start position:0%
+we conclude that f is in the range all
+ 
+
+ align:start position:0%
+we conclude that f is in the range all
+right so um
+
+ align:start position:0%
+right so um
+ 
+
+ align:start position:0%
+right so um
+first I want to get rid of kind of the
+
+ align:start position:0%
+first I want to get rid of kind of the
+ 
+
+ align:start position:0%
+first I want to get rid of kind of the
+useless part of the use of ends so uh
+
+ align:start position:0%
+useless part of the use of ends so uh
+ 
+
+ align:start position:0%
+useless part of the use of ends so uh
+let W be
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh well I don't need to give it a name
+
+ align:start position:0%
+uh well I don't need to give it a name
+ 
+
+ align:start position:0%
+uh well I don't need to give it a name
+really
+
+ align:start position:0%
+really
+ 
+
+ align:start position:0%
+really
+it's my Eraser
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so let V in
+
+ align:start position:0%
+so let V in
+ 
+
+ align:start position:0%
+so let V in
+be the projection onto
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+orthogonal complement of the null space
+
+ align:start position:0%
+orthogonal complement of the null space
+ 
+
+ align:start position:0%
+orthogonal complement of the null space
+of a minus Lambda of
+
+ align:start position:0%
+of a minus Lambda of
+ 
+
+ align:start position:0%
+of a minus Lambda of
+U sub n
+
+ align:start position:0%
+U sub n
+ 
+
+ align:start position:0%
+U sub n
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+now this is just part of so every use of
+
+ align:start position:0%
+now this is just part of so every use of
+ 
+
+ align:start position:0%
+now this is just part of so every use of
+n is written is you can write as
+
+ align:start position:0%
+n is written is you can write as
+ 
+
+ align:start position:0%
+n is written is you can write as
+something in the null space of a minus
+
+ align:start position:0%
+something in the null space of a minus
+ 
+
+ align:start position:0%
+something in the null space of a minus
+Lambda since uh
+
+ align:start position:0%
+Lambda since uh
+ 
+
+ align:start position:0%
+Lambda since uh
+so since null space of a minus Lambda is
+
+ align:start position:0%
+so since null space of a minus Lambda is
+ 
+
+ align:start position:0%
+so since null space of a minus Lambda is
+a closed Subspace of H
+
+ align:start position:0%
+a closed Subspace of H
+ 
+
+ align:start position:0%
+a closed Subspace of H
+it has an orthogonal complement so that
+
+ align:start position:0%
+it has an orthogonal complement so that
+ 
+
+ align:start position:0%
+it has an orthogonal complement so that
+it's it and its orthogonal complement
+
+ align:start position:0%
+it's it and its orthogonal complement
+ 
+
+ align:start position:0%
+it's it and its orthogonal complement
+gives a direct product uh
+
+ align:start position:0%
+gives a direct product uh
+ 
+
+ align:start position:0%
+gives a direct product uh
+or when you take their direct product
+
+ align:start position:0%
+or when you take their direct product
+ 
+
+ align:start position:0%
+or when you take their direct product
+gives you H right so
+
+ align:start position:0%
+gives you H right so
+ 
+
+ align:start position:0%
+gives you H right so
+um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+why am I saying that because then
+
+ align:start position:0%
+why am I saying that because then
+ 
+
+ align:start position:0%
+why am I saying that because then
+if I take a minus Lambda U sub n this is
+
+ align:start position:0%
+if I take a minus Lambda U sub n this is
+ 
+
+ align:start position:0%
+if I take a minus Lambda U sub n this is
+equal to
+
+ align:start position:0%
+equal to
+ 
+
+ align:start position:0%
+equal to
+a minus Lambda applied to
+
+ align:start position:0%
+a minus Lambda applied to
+ 
+
+ align:start position:0%
+a minus Lambda applied to
+Pi so the
+
+ align:start position:0%
+Pi so the
+ 
+
+ align:start position:0%
+Pi so the
+projection onto the null space of
+
+ align:start position:0%
+projection onto the null space of
+ 
+
+ align:start position:0%
+projection onto the null space of
+U sub n plus the projection onto the
+
+ align:start position:0%
+U sub n plus the projection onto the
+ 
+
+ align:start position:0%
+U sub n plus the projection onto the
+orthogonal complement of the null space
+
+ align:start position:0%
+orthogonal complement of the null space
+ 
+
+ align:start position:0%
+orthogonal complement of the null space
+which I defined as V sub n now this
+
+ align:start position:0%
+which I defined as V sub n now this
+ 
+
+ align:start position:0%
+which I defined as V sub n now this
+element here is in the null space of a
+
+ align:start position:0%
+element here is in the null space of a
+ 
+
+ align:start position:0%
+element here is in the null space of a
+minus Lambda so when a minus Lambda hits
+
+ align:start position:0%
+minus Lambda so when a minus Lambda hits
+ 
+
+ align:start position:0%
+minus Lambda so when a minus Lambda hits
+it I get zero so
+
+ align:start position:0%
+it I get zero so
+ 
+
+ align:start position:0%
+it I get zero so
+I get a minus Lambda applied to V sub n
+
+ align:start position:0%
+I get a minus Lambda applied to V sub n
+ 
+
+ align:start position:0%
+I get a minus Lambda applied to V sub n
+all right
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+then a minus Lambda
+
+ align:start position:0%
+then a minus Lambda
+ 
+
+ align:start position:0%
+then a minus Lambda
+V sub n equals a minus Lambda U sub n
+
+ align:start position:0%
+V sub n equals a minus Lambda U sub n
+ 
+
+ align:start position:0%
+V sub n equals a minus Lambda U sub n
+which converges to F all right so
+
+ align:start position:0%
+which converges to F all right so
+ 
+
+ align:start position:0%
+which converges to F all right so
+basically I've taken away uh some noise
+
+ align:start position:0%
+basically I've taken away uh some noise
+ 
+
+ align:start position:0%
+basically I've taken away uh some noise
+all right all right uh the part that
+
+ align:start position:0%
+all right all right uh the part that
+ 
+
+ align:start position:0%
+all right all right uh the part that
+when it hits a minus Lambda I get zero
+
+ align:start position:0%
+when it hits a minus Lambda I get zero
+ 
+
+ align:start position:0%
+when it hits a minus Lambda I get zero
+so now I just have these Visa bins uh
+
+ align:start position:0%
+so now I just have these Visa bins uh
+ 
+
+ align:start position:0%
+so now I just have these Visa bins uh
+which lie in uh
+
+ align:start position:0%
+which lie in uh
+ 
+
+ align:start position:0%
+which lie in uh
+in the orthogonal complement
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+of the null space of a minus Lambda
+
+ align:start position:0%
+of the null space of a minus Lambda
+ 
+
+ align:start position:0%
+of the null space of a minus Lambda
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+my claim is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+first is that the sequence V sub n
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+is bounded
+
+ align:start position:0%
+is bounded
+ 
+
+ align:start position:0%
+is bounded
+right basically once I can show this
+
+ align:start position:0%
+right basically once I can show this
+ 
+
+ align:start position:0%
+right basically once I can show this
+then I'm kind of done because if I can
+
+ align:start position:0%
+then I'm kind of done because if I can
+ 
+
+ align:start position:0%
+then I'm kind of done because if I can
+show V sub n is bounded then since a is
+
+ align:start position:0%
+show V sub n is bounded then since a is
+ 
+
+ align:start position:0%
+show V sub n is bounded then since a is
+a compact operator when a hits V sub n
+
+ align:start position:0%
+a compact operator when a hits V sub n
+ 
+
+ align:start position:0%
+a compact operator when a hits V sub n
+up to subsequence that converges okay
+
+ align:start position:0%
+up to subsequence that converges okay
+ 
+
+ align:start position:0%
+up to subsequence that converges okay
+now this whole expression converges and
+
+ align:start position:0%
+now this whole expression converges and
+ 
+
+ align:start position:0%
+now this whole expression converges and
+therefore Lambda times V sub n converges
+
+ align:start position:0%
+therefore Lambda times V sub n converges
+ 
+
+ align:start position:0%
+therefore Lambda times V sub n converges
+Lambda is non-zero so then V sub n
+
+ align:start position:0%
+Lambda is non-zero so then V sub n
+ 
+
+ align:start position:0%
+Lambda is non-zero so then V sub n
+converges up to a subsequence to
+
+ align:start position:0%
+converges up to a subsequence to
+ 
+
+ align:start position:0%
+converges up to a subsequence to
+something and therefore a minus Lambda V
+
+ align:start position:0%
+something and therefore a minus Lambda V
+ 
+
+ align:start position:0%
+something and therefore a minus Lambda V
+sub n converges to a minus Lambda of V
+
+ align:start position:0%
+sub n converges to a minus Lambda of V
+ 
+
+ align:start position:0%
+sub n converges to a minus Lambda of V
+for some V which shows that f is in the
+
+ align:start position:0%
+for some V which shows that f is in the
+ 
+
+ align:start position:0%
+for some V which shows that f is in the
+range of a minus Lambda so this is
+
+ align:start position:0%
+range of a minus Lambda so this is
+ 
+
+ align:start position:0%
+range of a minus Lambda so this is
+really the whole ball game
+
+ align:start position:0%
+really the whole ball game
+ 
+
+ align:start position:0%
+really the whole ball game
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+and we'll use here kind of crucially as
+
+ align:start position:0%
+and we'll use here kind of crucially as
+ 
+
+ align:start position:0%
+and we'll use here kind of crucially as
+well that we threw away useless parts of
+
+ align:start position:0%
+well that we threw away useless parts of
+ 
+
+ align:start position:0%
+well that we threw away useless parts of
+use of in useless at least to this
+
+ align:start position:0%
+use of in useless at least to this
+ 
+
+ align:start position:0%
+use of in useless at least to this
+argument
+
+ align:start position:0%
+argument
+ 
+
+ align:start position:0%
+argument
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+Okay so
+
+ align:start position:0%
+Okay so
+ 
+
+ align:start position:0%
+Okay so
+I claim uh this is bounded so suppose
+
+ align:start position:0%
+I claim uh this is bounded so suppose
+ 
+
+ align:start position:0%
+I claim uh this is bounded so suppose
+not
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+then there exists
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+subsequence call it V sub N Sub J
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+such that uh
+
+ align:start position:0%
+such that uh
+ 
+
+ align:start position:0%
+such that uh
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+B sub N Sub J
+
+ align:start position:0%
+B sub N Sub J
+ 
+
+ align:start position:0%
+B sub N Sub J
+goes to Infinity
+
+ align:start position:0%
+goes to Infinity
+ 
+
+ align:start position:0%
+goes to Infinity
+okay as J goes to Infinity
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+all right
+
+ align:start position:0%
+all right
+ 
+
+ align:start position:0%
+all right
+now if I look at a minus Lambda
+
+ align:start position:0%
+now if I look at a minus Lambda
+ 
+
+ align:start position:0%
+now if I look at a minus Lambda
+applied to V sub N Sub J
+
+ align:start position:0%
+applied to V sub N Sub J
+ 
+
+ align:start position:0%
+applied to V sub N Sub J
+over Norm of V sub N Sub J
+
+ align:start position:0%
+over Norm of V sub N Sub J
+ 
+
+ align:start position:0%
+over Norm of V sub N Sub J
+this converges so first off
+
+ align:start position:0%
+this converges so first off
+ 
+
+ align:start position:0%
+this converges so first off
+since a is a linear operator this is
+
+ align:start position:0%
+since a is a linear operator this is
+ 
+
+ align:start position:0%
+since a is a linear operator this is
+equal to 1 over Norm V and sub J times a
+
+ align:start position:0%
+equal to 1 over Norm V and sub J times a
+ 
+
+ align:start position:0%
+equal to 1 over Norm V and sub J times a
+minus Lambda applied to V sub N Sub J
+
+ align:start position:0%
+minus Lambda applied to V sub N Sub J
+ 
+
+ align:start position:0%
+minus Lambda applied to V sub N Sub J
+and so this scalar one over Norm v n sub
+
+ align:start position:0%
+and so this scalar one over Norm v n sub
+ 
+
+ align:start position:0%
+and so this scalar one over Norm v n sub
+J converges to zero this converges to f
+
+ align:start position:0%
+J converges to zero this converges to f
+ 
+
+ align:start position:0%
+J converges to zero this converges to f
+so I get the zero vector
+
+ align:start position:0%
+so I get the zero vector
+ 
+
+ align:start position:0%
+so I get the zero vector
+and H okay so
+
+ align:start position:0%
+and H okay so
+ 
+
+ align:start position:0%
+and H okay so
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+this thing converges to zero in the
+
+ align:start position:0%
+this thing converges to zero in the
+ 
+
+ align:start position:0%
+this thing converges to zero in the
+Hilbert space h
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+now why is that bad because
+
+ align:start position:0%
+now why is that bad because
+ 
+
+ align:start position:0%
+now why is that bad because
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+essentially what this is going to say is
+
+ align:start position:0%
+essentially what this is going to say is
+ 
+
+ align:start position:0%
+essentially what this is going to say is
+that there exists some element
+
+ align:start position:0%
+that there exists some element
+ 
+
+ align:start position:0%
+that there exists some element
+or that this sequence converges at least
+
+ align:start position:0%
+or that this sequence converges at least
+ 
+
+ align:start position:0%
+or that this sequence converges at least
+up to a subsequence to an element V with
+
+ align:start position:0%
+up to a subsequence to an element V with
+ 
+
+ align:start position:0%
+up to a subsequence to an element V with
+Norm one because they all have Norm one
+
+ align:start position:0%
+Norm one because they all have Norm one
+ 
+
+ align:start position:0%
+Norm one because they all have Norm one
+so that a minus Lambda V equals zero but
+
+ align:start position:0%
+so that a minus Lambda V equals zero but
+ 
+
+ align:start position:0%
+so that a minus Lambda V equals zero but
+all of these are in the null space of a
+
+ align:start position:0%
+all of these are in the null space of a
+ 
+
+ align:start position:0%
+all of these are in the null space of a
+minus Lambda and we get a contradiction
+
+ align:start position:0%
+minus Lambda and we get a contradiction
+ 
+
+ align:start position:0%
+minus Lambda and we get a contradiction
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+right so
+
+ align:start position:0%
+right so
+ 
+
+ align:start position:0%
+right so
+we have that
+
+ align:start position:0%
+we have that
+ 
+
+ align:start position:0%
+we have that
+a minus Lambda
+
+ align:start position:0%
+a minus Lambda
+ 
+
+ align:start position:0%
+a minus Lambda
+okay so we have that part
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+since a is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+a compact operator
+
+ align:start position:0%
+a compact operator
+ 
+
+ align:start position:0%
+a compact operator
+uh
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+exists the subsequence so a further
+
+ align:start position:0%
+exists the subsequence so a further
+ 
+
+ align:start position:0%
+exists the subsequence so a further
+subsequence I'm just going to call it N
+
+ align:start position:0%
+subsequence I'm just going to call it N
+ 
+
+ align:start position:0%
+subsequence I'm just going to call it N
+Sub K instead of N Sub J sub k
+
+ align:start position:0%
+Sub K instead of N Sub J sub k
+ 
+
+ align:start position:0%
+Sub K instead of N Sub J sub k
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+B sub N Sub k
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+of
+
+ align:start position:0%
+of
+ 
+
+ align:start position:0%
+of
+B sub N Sub J
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+such that the sequence a sub V sub N Sub
+
+ align:start position:0%
+such that the sequence a sub V sub N Sub
+ 
+
+ align:start position:0%
+such that the sequence a sub V sub N Sub
+k
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+converges
+
+ align:start position:0%
+converges
+ 
+
+ align:start position:0%
+converges
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+but then I get that
+
+ align:start position:0%
+but then I get that
+ 
+
+ align:start position:0%
+but then I get that
+B sub N Sub K or I should say uh
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+B sub N Sub K Over Norm or B sub N Sub k
+
+ align:start position:0%
+B sub N Sub K Over Norm or B sub N Sub k
+ 
+
+ align:start position:0%
+B sub N Sub K Over Norm or B sub N Sub k
+okay so these all have Norm one and a
+
+ align:start position:0%
+okay so these all have Norm one and a
+ 
+
+ align:start position:0%
+okay so these all have Norm one and a
+applied to something that has unit
+
+ align:start position:0%
+applied to something that has unit
+ 
+
+ align:start position:0%
+applied to something that has unit
+length uh
+
+ align:start position:0%
+length uh
+ 
+
+ align:start position:0%
+length uh
+or the image of by a of the closed unit
+
+ align:start position:0%
+or the image of by a of the closed unit
+ 
+
+ align:start position:0%
+or the image of by a of the closed unit
+ball is a pre-compact or the closure of
+
+ align:start position:0%
+ball is a pre-compact or the closure of
+ 
+
+ align:start position:0%
+ball is a pre-compact or the closure of
+it is Compact and therefore every
+
+ align:start position:0%
+it is Compact and therefore every
+ 
+
+ align:start position:0%
+it is Compact and therefore every
+sequence has a convergent subsequence
+
+ align:start position:0%
+sequence has a convergent subsequence
+ 
+
+ align:start position:0%
+sequence has a convergent subsequence
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+then B sub N Sub K Over Norm of V sub N
+
+ align:start position:0%
+then B sub N Sub K Over Norm of V sub N
+ 
+
+ align:start position:0%
+then B sub N Sub K Over Norm of V sub N
+Sub k
+
+ align:start position:0%
+Sub k
+ 
+
+ align:start position:0%
+Sub k
+this is equal to 1 over Lambda times
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+a applied to V sub N Sub K over
+
+ align:start position:0%
+a applied to V sub N Sub K over
+ 
+
+ align:start position:0%
+a applied to V sub N Sub K over
+Norm of V sub N Sub K minus
+
+ align:start position:0%
+Norm of V sub N Sub K minus
+ 
+
+ align:start position:0%
+Norm of V sub N Sub K minus
+a minus Lambda Phi to V sub N Sub k
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+now this
+
+ align:start position:0%
+now this
+ 
+
+ align:start position:0%
+now this
+sequence of elements converges to zero
+
+ align:start position:0%
+sequence of elements converges to zero
+ 
+
+ align:start position:0%
+sequence of elements converges to zero
+that's in fact what we just proved
+
+ align:start position:0%
+that's in fact what we just proved
+ 
+
+ align:start position:0%
+that's in fact what we just proved
+and this converges uh by how we've taken
+
+ align:start position:0%
+and this converges uh by how we've taken
+ 
+
+ align:start position:0%
+and this converges uh by how we've taken
+this subsequence because a is a compact
+
+ align:start position:0%
+this subsequence because a is a compact
+ 
+
+ align:start position:0%
+this subsequence because a is a compact
+operator so I have this sequence of
+
+ align:start position:0%
+operator so I have this sequence of
+ 
+
+ align:start position:0%
+operator so I have this sequence of
+vectors is equal to and here we can
+
+ align:start position:0%
+vectors is equal to and here we can
+ 
+
+ align:start position:0%
+vectors is equal to and here we can
+divide by Lambda because Lambda is
+
+ align:start position:0%
+divide by Lambda because Lambda is
+ 
+
+ align:start position:0%
+divide by Lambda because Lambda is
+non-zero
+
+ align:start position:0%
+non-zero
+ 
+
+ align:start position:0%
+non-zero
+it's equal to
+
+ align:start position:0%
+it's equal to
+ 
+
+ align:start position:0%
+it's equal to
+you know a linear combination of two
+
+ align:start position:0%
+you know a linear combination of two
+ 
+
+ align:start position:0%
+you know a linear combination of two
+sequences which converge
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and therefore we get that V sub N Sub k
+
+ align:start position:0%
+and therefore we get that V sub N Sub k
+ 
+
+ align:start position:0%
+and therefore we get that V sub N Sub k
+over Norm of
+
+ align:start position:0%
+over Norm of
+ 
+
+ align:start position:0%
+over Norm of
+P sub N Sub k k
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+converges to
+
+ align:start position:0%
+converges to
+ 
+
+ align:start position:0%
+converges to
+uh
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+an element B and
+
+ align:start position:0%
+an element B and
+ 
+
+ align:start position:0%
+an element B and
+now the null space or the orthogonal
+
+ align:start position:0%
+now the null space or the orthogonal
+ 
+
+ align:start position:0%
+now the null space or the orthogonal
+complement of the null space of a minus
+
+ align:start position:0%
+complement of the null space of a minus
+ 
+
+ align:start position:0%
+complement of the null space of a minus
+Lambda each of these is in
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+remember the note the
+
+ align:start position:0%
+remember the note the
+ 
+
+ align:start position:0%
+remember the note the
+orthogonal complement of the null space
+
+ align:start position:0%
+orthogonal complement of the null space
+ 
+
+ align:start position:0%
+orthogonal complement of the null space
+and since it's converging to an element
+
+ align:start position:0%
+and since it's converging to an element
+ 
+
+ align:start position:0%
+and since it's converging to an element
+and this is closed
+
+ align:start position:0%
+and this is closed
+ 
+
+ align:start position:0%
+and this is closed
+this element has to be in the same
+
+ align:start position:0%
+this element has to be in the same
+ 
+
+ align:start position:0%
+this element has to be in the same
+set
+
+ align:start position:0%
+set
+ 
+
+ align:start position:0%
+set
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+all right so again this follows from uh
+
+ align:start position:0%
+all right so again this follows from uh
+ 
+
+ align:start position:0%
+all right so again this follows from uh
+the fact that V is in here is because
+
+ align:start position:0%
+the fact that V is in here is because
+ 
+
+ align:start position:0%
+the fact that V is in here is because
+this set is closed all right the
+
+ align:start position:0%
+this set is closed all right the
+ 
+
+ align:start position:0%
+this set is closed all right the
+orthogonal complement of any subset of a
+
+ align:start position:0%
+orthogonal complement of any subset of a
+ 
+
+ align:start position:0%
+orthogonal complement of any subset of a
+Hilbert space is closed
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+all right
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+then
+
+ align:start position:0%
+then
+ 
+
+ align:start position:0%
+then
+by continuity of the norm basically the
+
+ align:start position:0%
+by continuity of the norm basically the
+ 
+
+ align:start position:0%
+by continuity of the norm basically the
+norm of V has to be equal to
+
+ align:start position:0%
+norm of V has to be equal to
+ 
+
+ align:start position:0%
+norm of V has to be equal to
+limit as K goes to Infinity of the norm
+
+ align:start position:0%
+limit as K goes to Infinity of the norm
+ 
+
+ align:start position:0%
+limit as K goes to Infinity of the norm
+of the elements
+
+ align:start position:0%
+of the elements
+ 
+
+ align:start position:0%
+of the elements
+converging to it
+
+ align:start position:0%
+converging to it
+ 
+
+ align:start position:0%
+converging to it
+which all equal one
+
+ align:start position:0%
+which all equal one
+ 
+
+ align:start position:0%
+which all equal one
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+if I compute a minus Lambda applied to V
+
+ align:start position:0%
+if I compute a minus Lambda applied to V
+ 
+
+ align:start position:0%
+if I compute a minus Lambda applied to V
+this is equal to since the V sub N Sub K
+
+ align:start position:0%
+this is equal to since the V sub N Sub K
+ 
+
+ align:start position:0%
+this is equal to since the V sub N Sub K
+is over Norm V sub N Sub K's are
+
+ align:start position:0%
+is over Norm V sub N Sub K's are
+ 
+
+ align:start position:0%
+is over Norm V sub N Sub K's are
+converging to V
+
+ align:start position:0%
+converging to V
+ 
+
+ align:start position:0%
+converging to V
+a minus Lambda
+
+ align:start position:0%
+a minus Lambda
+ 
+
+ align:start position:0%
+a minus Lambda
+applied to V sub N Sub K Over Norm V sub
+
+ align:start position:0%
+applied to V sub N Sub K Over Norm V sub
+ 
+
+ align:start position:0%
+applied to V sub N Sub K Over Norm V sub
+N Sub K and remember this is a
+
+ align:start position:0%
+N Sub K and remember this is a
+ 
+
+ align:start position:0%
+N Sub K and remember this is a
+subsequence of V sub N Sub JS and when a
+
+ align:start position:0%
+subsequence of V sub N Sub JS and when a
+ 
+
+ align:start position:0%
+subsequence of V sub N Sub JS and when a
+minus Lambda hits that they're
+
+ align:start position:0%
+minus Lambda hits that they're
+ 
+
+ align:start position:0%
+minus Lambda hits that they're
+converging to zero so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+all right
+
+ align:start position:0%
+all right
+ 
+
+ align:start position:0%
+all right
+all of that predicated upon the
+
+ align:start position:0%
+all of that predicated upon the
+ 
+
+ align:start position:0%
+all of that predicated upon the
+assumption that the norm of V sub N Sub
+
+ align:start position:0%
+assumption that the norm of V sub N Sub
+ 
+
+ align:start position:0%
+assumption that the norm of V sub N Sub
+K's converges to uh infinity or that
+
+ align:start position:0%
+K's converges to uh infinity or that
+ 
+
+ align:start position:0%
+K's converges to uh infinity or that
+um right that the sequence is unbounded
+
+ align:start position:0%
+um right that the sequence is unbounded
+ 
+
+ align:start position:0%
+um right that the sequence is unbounded
+okay so we have this element uh in the
+
+ align:start position:0%
+okay so we have this element uh in the
+ 
+
+ align:start position:0%
+okay so we have this element uh in the
+null space
+
+ align:start position:0%
+null space
+ 
+
+ align:start position:0%
+null space
+that has uh or the orthogonal complement
+
+ align:start position:0%
+that has uh or the orthogonal complement
+ 
+
+ align:start position:0%
+that has uh or the orthogonal complement
+of the null space
+
+ align:start position:0%
+of the null space
+ 
+
+ align:start position:0%
+of the null space
+that has Norm one
+
+ align:start position:0%
+that has Norm one
+ 
+
+ align:start position:0%
+that has Norm one
+but also gives you zero
+
+ align:start position:0%
+but also gives you zero
+ 
+
+ align:start position:0%
+but also gives you zero
+and therefore
+
+ align:start position:0%
+and therefore
+ 
+
+ align:start position:0%
+and therefore
+we get that
+
+ align:start position:0%
+we get that
+ 
+
+ align:start position:0%
+we get that
+V is in
+
+ align:start position:0%
+V is in
+ 
+
+ align:start position:0%
+V is in
+the null space of a minus Lambda from
+
+ align:start position:0%
+the null space of a minus Lambda from
+ 
+
+ align:start position:0%
+the null space of a minus Lambda from
+this computation
+
+ align:start position:0%
+this computation
+ 
+
+ align:start position:0%
+this computation
+and uh
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+it's orthogonal complement
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+but the only possible Vector that's in a
+
+ align:start position:0%
+but the only possible Vector that's in a
+ 
+
+ align:start position:0%
+but the only possible Vector that's in a
+space and its orthogonal complement is
+
+ align:start position:0%
+space and its orthogonal complement is
+ 
+
+ align:start position:0%
+space and its orthogonal complement is
+the zero vector or the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+only Vector in a Subspace and its
+
+ align:start position:0%
+only Vector in a Subspace and its
+ 
+
+ align:start position:0%
+only Vector in a Subspace and its
+orthogonal complement is the zero vector
+
+ align:start position:0%
+orthogonal complement is the zero vector
+ 
+
+ align:start position:0%
+orthogonal complement is the zero vector
+and therefore
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+b equals zero which this is a
+
+ align:start position:0%
+b equals zero which this is a
+ 
+
+ align:start position:0%
+b equals zero which this is a
+contradiction to the fact that the norm
+
+ align:start position:0%
+contradiction to the fact that the norm
+ 
+
+ align:start position:0%
+contradiction to the fact that the norm
+of V equals one
+
+ align:start position:0%
+of V equals one
+ 
+
+ align:start position:0%
+of V equals one
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+so uh we started off with the sequence
+
+ align:start position:0%
+so uh we started off with the sequence
+ 
+
+ align:start position:0%
+so uh we started off with the sequence
+Visa bins assuming that they are
+
+ align:start position:0%
+Visa bins assuming that they are
+ 
+
+ align:start position:0%
+Visa bins assuming that they are
+unbounded V sub n over Norm V sub N is a
+
+ align:start position:0%
+unbounded V sub n over Norm V sub N is a
+ 
+
+ align:start position:0%
+unbounded V sub n over Norm V sub N is a
+sequence of
+
+ align:start position:0%
+sequence of
+ 
+
+ align:start position:0%
+sequence of
+essentially um so maybe you got lost in
+
+ align:start position:0%
+essentially um so maybe you got lost in
+ 
+
+ align:start position:0%
+essentially um so maybe you got lost in
+the subsequences but let's just assume
+
+ align:start position:0%
+the subsequences but let's just assume
+ 
+
+ align:start position:0%
+the subsequences but let's just assume
+I'm talking about the entire sequence
+
+ align:start position:0%
+I'm talking about the entire sequence
+ 
+
+ align:start position:0%
+I'm talking about the entire sequence
+then
+
+ align:start position:0%
+then
+ 
+
+ align:start position:0%
+then
+then V sub n over Norm V sub n uh when a
+
+ align:start position:0%
+then V sub n over Norm V sub n uh when a
+ 
+
+ align:start position:0%
+then V sub n over Norm V sub n uh when a
+minus Lambda hits it converges to zero
+
+ align:start position:0%
+minus Lambda hits it converges to zero
+ 
+
+ align:start position:0%
+minus Lambda hits it converges to zero
+since a is a compact operator we can
+
+ align:start position:0%
+since a is a compact operator we can
+ 
+
+ align:start position:0%
+since a is a compact operator we can
+choose a sub we can show essentially
+
+ align:start position:0%
+choose a sub we can show essentially
+ 
+
+ align:start position:0%
+choose a sub we can show essentially
+that a applied to V sub n over Norm V
+
+ align:start position:0%
+that a applied to V sub n over Norm V
+ 
+
+ align:start position:0%
+that a applied to V sub n over Norm V
+sub n because those things have unit
+
+ align:start position:0%
+sub n because those things have unit
+ 
+
+ align:start position:0%
+sub n because those things have unit
+length converges to something
+
+ align:start position:0%
+length converges to something
+ 
+
+ align:start position:0%
+length converges to something
+and since Lambda is non-zero we can then
+
+ align:start position:0%
+and since Lambda is non-zero we can then
+ 
+
+ align:start position:0%
+and since Lambda is non-zero we can then
+conclude that
+
+ align:start position:0%
+conclude that
+ 
+
+ align:start position:0%
+conclude that
+uh those vectors converge uh in fact to
+
+ align:start position:0%
+uh those vectors converge uh in fact to
+ 
+
+ align:start position:0%
+uh those vectors converge uh in fact to
+something not just their images by a or
+
+ align:start position:0%
+something not just their images by a or
+ 
+
+ align:start position:0%
+something not just their images by a or
+their images by a minus Lambda again
+
+ align:start position:0%
+their images by a minus Lambda again
+ 
+
+ align:start position:0%
+their images by a minus Lambda again
+because Lambda is non-zero all right and
+
+ align:start position:0%
+because Lambda is non-zero all right and
+ 
+
+ align:start position:0%
+because Lambda is non-zero all right and
+since they all have unit length
+
+ align:start position:0%
+since they all have unit length
+ 
+
+ align:start position:0%
+since they all have unit length
+their limit must have unit length
+
+ align:start position:0%
+their limit must have unit length
+ 
+
+ align:start position:0%
+their limit must have unit length
+and since when a minus Lambda hits these
+
+ align:start position:0%
+and since when a minus Lambda hits these
+ 
+
+ align:start position:0%
+and since when a minus Lambda hits these
+guys they go to zero
+
+ align:start position:0%
+guys they go to zero
+ 
+
+ align:start position:0%
+guys they go to zero
+the limit must also when a minus Lambda
+
+ align:start position:0%
+the limit must also when a minus Lambda
+ 
+
+ align:start position:0%
+the limit must also when a minus Lambda
+hit it equals zero and that gives us our
+
+ align:start position:0%
+hit it equals zero and that gives us our
+ 
+
+ align:start position:0%
+hit it equals zero and that gives us our
+contradiction because this limit V had
+
+ align:start position:0%
+contradiction because this limit V had
+ 
+
+ align:start position:0%
+contradiction because this limit V had
+to be in the null the orthogonal
+
+ align:start position:0%
+to be in the null the orthogonal
+ 
+
+ align:start position:0%
+to be in the null the orthogonal
+complement of the null space but then
+
+ align:start position:0%
+complement of the null space but then
+ 
+
+ align:start position:0%
+complement of the null space but then
+also in the null space and have unit
+
+ align:start position:0%
+also in the null space and have unit
+ 
+
+ align:start position:0%
+also in the null space and have unit
+length uh those three things can all
+
+ align:start position:0%
+length uh those three things can all
+ 
+
+ align:start position:0%
+length uh those three things can all
+happen at once
+
+ align:start position:0%
+happen at once
+ 
+
+ align:start position:0%
+happen at once
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+so uh
+
+ align:start position:0%
+so uh
+ 
+
+ align:start position:0%
+so uh
+thus
+
+ align:start position:0%
+thus
+ 
+
+ align:start position:0%
+thus
+this sequence V sub n
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+is bounded okay so remember how was the
+
+ align:start position:0%
+is bounded okay so remember how was the
+ 
+
+ align:start position:0%
+is bounded okay so remember how was the
+V what were the Visa bins uh to start
+
+ align:start position:0%
+V what were the Visa bins uh to start
+ 
+
+ align:start position:0%
+V what were the Visa bins uh to start
+with they were so that a minus Lambda V
+
+ align:start position:0%
+with they were so that a minus Lambda V
+ 
+
+ align:start position:0%
+with they were so that a minus Lambda V
+sub n is converge to this element F and
+
+ align:start position:0%
+sub n is converge to this element F and
+ 
+
+ align:start position:0%
+sub n is converge to this element F and
+we wanted to show that f
+
+ align:start position:0%
+we wanted to show that f
+ 
+
+ align:start position:0%
+we wanted to show that f
+is in the range right so we
+
+ align:start position:0%
+is in the range right so we
+ 
+
+ align:start position:0%
+is in the range right so we
+coming back over here
+
+ align:start position:0%
+coming back over here
+ 
+
+ align:start position:0%
+coming back over here
+we had these Visa bins so that a minus
+
+ align:start position:0%
+we had these Visa bins so that a minus
+ 
+
+ align:start position:0%
+we had these Visa bins so that a minus
+Lambda V sub n converges to F and we
+
+ align:start position:0%
+Lambda V sub n converges to F and we
+ 
+
+ align:start position:0%
+Lambda V sub n converges to F and we
+want to show f is in the range to
+
+ align:start position:0%
+want to show f is in the range to
+ 
+
+ align:start position:0%
+want to show f is in the range to
+conclude that the range of a minus
+
+ align:start position:0%
+conclude that the range of a minus
+ 
+
+ align:start position:0%
+conclude that the range of a minus
+Lambda is closed
+
+ align:start position:0%
+Lambda is closed
+ 
+
+ align:start position:0%
+Lambda is closed
+but now that since it's bounded and
+
+ align:start position:0%
+but now that since it's bounded and
+ 
+
+ align:start position:0%
+but now that since it's bounded and
+we've kind of done this argument already
+
+ align:start position:0%
+we've kind of done this argument already
+ 
+
+ align:start position:0%
+we've kind of done this argument already
+this is essentially the whole ball game
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+since the sequence V sub n is bounded
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+a
+
+ align:start position:0%
+a
+ 
+
+ align:start position:0%
+a
+is a
+
+ align:start position:0%
+is a
+ 
+
+ align:start position:0%
+is a
+compact operator
+
+ align:start position:0%
+compact operator
+ 
+
+ align:start position:0%
+compact operator
+we conclude that
+
+ align:start position:0%
+we conclude that
+ 
+
+ align:start position:0%
+we conclude that
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+there exists a subsequence
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+B sub N Sub J
+
+ align:start position:0%
+B sub N Sub J
+ 
+
+ align:start position:0%
+B sub N Sub J
+such that so this has nothing to do with
+
+ align:start position:0%
+such that so this has nothing to do with
+ 
+
+ align:start position:0%
+such that so this has nothing to do with
+the previous argument now but I just
+
+ align:start position:0%
+the previous argument now but I just
+ 
+
+ align:start position:0%
+the previous argument now but I just
+don't feel like using different letters
+
+ align:start position:0%
+don't feel like using different letters
+ 
+
+ align:start position:0%
+don't feel like using different letters
+such that a applied to V sub N Sub J
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+converges
+
+ align:start position:0%
+converges
+ 
+
+ align:start position:0%
+converges
+so remember a is a compact operator
+
+ align:start position:0%
+so remember a is a compact operator
+ 
+
+ align:start position:0%
+so remember a is a compact operator
+which
+
+ align:start position:0%
+which
+ 
+
+ align:start position:0%
+which
+you know we stated in it in terms of the
+
+ align:start position:0%
+you know we stated in it in terms of the
+ 
+
+ align:start position:0%
+you know we stated in it in terms of the
+closure of the image of the closed unit
+
+ align:start position:0%
+closure of the image of the closed unit
+ 
+
+ align:start position:0%
+closure of the image of the closed unit
+ball being compact equivalently
+
+ align:start position:0%
+ball being compact equivalently
+ 
+
+ align:start position:0%
+ball being compact equivalently
+by scaling the unit ball
+
+ align:start position:0%
+by scaling the unit ball
+ 
+
+ align:start position:0%
+by scaling the unit ball
+it means that a takes any bounded
+
+ align:start position:0%
+it means that a takes any bounded
+ 
+
+ align:start position:0%
+it means that a takes any bounded
+sequence to
+
+ align:start position:0%
+sequence to
+ 
+
+ align:start position:0%
+sequence to
+a sequence that has a convergence
+
+ align:start position:0%
+a sequence that has a convergence
+ 
+
+ align:start position:0%
+a sequence that has a convergence
+subsequence okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so we showed V sub n is bounded and
+
+ align:start position:0%
+so we showed V sub n is bounded and
+ 
+
+ align:start position:0%
+so we showed V sub n is bounded and
+therefore since a is a compact operator
+
+ align:start position:0%
+therefore since a is a compact operator
+ 
+
+ align:start position:0%
+therefore since a is a compact operator
+we can find a subsequent so that when a
+
+ align:start position:0%
+we can find a subsequent so that when a
+ 
+
+ align:start position:0%
+we can find a subsequent so that when a
+hits it we have a convergent sequence
+
+ align:start position:0%
+hits it we have a convergent sequence
+ 
+
+ align:start position:0%
+hits it we have a convergent sequence
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+and by that same trick we used a minute
+
+ align:start position:0%
+and by that same trick we used a minute
+ 
+
+ align:start position:0%
+and by that same trick we used a minute
+ago we conclude that V sub N Sub J which
+
+ align:start position:0%
+ago we conclude that V sub N Sub J which
+ 
+
+ align:start position:0%
+ago we conclude that V sub N Sub J which
+is
+
+ align:start position:0%
+is
+ 
+
+ align:start position:0%
+is
+and we can do this because Lambda is
+
+ align:start position:0%
+and we can do this because Lambda is
+ 
+
+ align:start position:0%
+and we can do this because Lambda is
+non-zero we can divide by it
+
+ align:start position:0%
+non-zero we can divide by it
+ 
+
+ align:start position:0%
+non-zero we can divide by it
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+so a
+
+ align:start position:0%
+so a
+ 
+
+ align:start position:0%
+so a
+B sub N Sub J minus a minus Lambda V sub
+
+ align:start position:0%
+B sub N Sub J minus a minus Lambda V sub
+ 
+
+ align:start position:0%
+B sub N Sub J minus a minus Lambda V sub
+N Sub J now again this here is
+
+ align:start position:0%
+N Sub J now again this here is
+ 
+
+ align:start position:0%
+N Sub J now again this here is
+converging to something
+
+ align:start position:0%
+converging to something
+ 
+
+ align:start position:0%
+converging to something
+this here is converging to F right
+
+ align:start position:0%
+this here is converging to F right
+ 
+
+ align:start position:0%
+this here is converging to F right
+so this linear combination of convergent
+
+ align:start position:0%
+so this linear combination of convergent
+ 
+
+ align:start position:0%
+so this linear combination of convergent
+sequences is convergent
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+converges
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+to
+
+ align:start position:0%
+to
+ 
+
+ align:start position:0%
+to
+uh
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+in element V
+
+ align:start position:0%
+in element V
+ 
+
+ align:start position:0%
+in element V
+and therefore I get that f
+
+ align:start position:0%
+and therefore I get that f
+ 
+
+ align:start position:0%
+and therefore I get that f
+which is
+
+ align:start position:0%
+which is
+ 
+
+ align:start position:0%
+which is
+the limit as n goes to Infinity of the V
+
+ align:start position:0%
+the limit as n goes to Infinity of the V
+ 
+
+ align:start position:0%
+the limit as n goes to Infinity of the V
+sub NS but
+
+ align:start position:0%
+sub NS but
+ 
+
+ align:start position:0%
+sub NS but
+convergence still holds if I look at a
+
+ align:start position:0%
+convergence still holds if I look at a
+ 
+
+ align:start position:0%
+convergence still holds if I look at a
+subsequence a minus Lambda
+
+ align:start position:0%
+subsequence a minus Lambda
+ 
+
+ align:start position:0%
+subsequence a minus Lambda
+V sub N Sub J equals and since a minus
+
+ align:start position:0%
+V sub N Sub J equals and since a minus
+ 
+
+ align:start position:0%
+V sub N Sub J equals and since a minus
+lamb so a is a bounded linear operator
+
+ align:start position:0%
+lamb so a is a bounded linear operator
+ 
+
+ align:start position:0%
+lamb so a is a bounded linear operator
+Lambda times the identity is a bounded
+
+ align:start position:0%
+Lambda times the identity is a bounded
+ 
+
+ align:start position:0%
+Lambda times the identity is a bounded
+linear operator this is equal to a minus
+
+ align:start position:0%
+linear operator this is equal to a minus
+ 
+
+ align:start position:0%
+linear operator this is equal to a minus
+Lambda
+
+ align:start position:0%
+Lambda
+ 
+
+ align:start position:0%
+Lambda
+V and therefore f is in the range
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+of a minus Lambda
+
+ align:start position:0%
+of a minus Lambda
+ 
+
+ align:start position:0%
+of a minus Lambda
+Okay so
+
+ align:start position:0%
+Okay so
+ 
+
+ align:start position:0%
+Okay so
+uh Fred home alternative tells you that
+
+ align:start position:0%
+uh Fred home alternative tells you that
+ 
+
+ align:start position:0%
+uh Fred home alternative tells you that
+the range of a minus Lambda for a
+
+ align:start position:0%
+the range of a minus Lambda for a
+ 
+
+ align:start position:0%
+the range of a minus Lambda for a
+compact self-adjoined operator is closed
+
+ align:start position:0%
+compact self-adjoined operator is closed
+ 
+
+ align:start position:0%
+compact self-adjoined operator is closed
+um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so you know where did we
+
+ align:start position:0%
+so you know where did we
+ 
+
+ align:start position:0%
+so you know where did we
+really use the fact that it was
+
+ align:start position:0%
+really use the fact that it was
+ 
+
+ align:start position:0%
+really use the fact that it was
+self-adjoint nowhere in this argument so
+
+ align:start position:0%
+self-adjoint nowhere in this argument so
+ 
+
+ align:start position:0%
+self-adjoint nowhere in this argument so
+this uh
+
+ align:start position:0%
+this uh
+ 
+
+ align:start position:0%
+this uh
+fact that the range of a minus Lambda is
+
+ align:start position:0%
+fact that the range of a minus Lambda is
+ 
+
+ align:start position:0%
+fact that the range of a minus Lambda is
+closed is still true if um you know a is
+
+ align:start position:0%
+closed is still true if um you know a is
+ 
+
+ align:start position:0%
+closed is still true if um you know a is
+just a compact operator and lambda's
+
+ align:start position:0%
+just a compact operator and lambda's
+ 
+
+ align:start position:0%
+just a compact operator and lambda's
+just some non-zero uh complex number
+
+ align:start position:0%
+just some non-zero uh complex number
+ 
+
+ align:start position:0%
+just some non-zero uh complex number
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+but where we use that itself a joint is
+
+ align:start position:0%
+but where we use that itself a joint is
+ 
+
+ align:start position:0%
+but where we use that itself a joint is
+kind of I guess in in the rest of the
+
+ align:start position:0%
+kind of I guess in in the rest of the
+ 
+
+ align:start position:0%
+kind of I guess in in the rest of the
+conclusion that the range of a minus
+
+ align:start position:0%
+conclusion that the range of a minus
+ 
+
+ align:start position:0%
+conclusion that the range of a minus
+Lambda is therefore equal to the null
+
+ align:start position:0%
+Lambda is therefore equal to the null
+ 
+
+ align:start position:0%
+Lambda is therefore equal to the null
+space of a minus Lambda and therefore
+
+ align:start position:0%
+space of a minus Lambda and therefore
+ 
+
+ align:start position:0%
+space of a minus Lambda and therefore
+either a minus Lambda is bijective or
+
+ align:start position:0%
+either a minus Lambda is bijective or
+ 
+
+ align:start position:0%
+either a minus Lambda is bijective or
+the null space of a minus Lambda is
+
+ align:start position:0%
+the null space of a minus Lambda is
+ 
+
+ align:start position:0%
+the null space of a minus Lambda is
+non-trivial and finite dimensional by
+
+ align:start position:0%
+non-trivial and finite dimensional by
+ 
+
+ align:start position:0%
+non-trivial and finite dimensional by
+what we did in the previous lecture
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+foreign
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+[Applause]
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+very
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+powerful theorem
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and again what this says is that if I
+
+ align:start position:0%
+and again what this says is that if I
+ 
+
+ align:start position:0%
+and again what this says is that if I
+look at the non-zero spectrum of a
+
+ align:start position:0%
+look at the non-zero spectrum of a
+ 
+
+ align:start position:0%
+look at the non-zero spectrum of a
+compact self-adjoined operator then that
+
+ align:start position:0%
+compact self-adjoined operator then that
+ 
+
+ align:start position:0%
+compact self-adjoined operator then that
+consists entirely of eigenvalues of a
+
+ align:start position:0%
+consists entirely of eigenvalues of a
+ 
+
+ align:start position:0%
+consists entirely of eigenvalues of a
+right now earlier we proved that plus or
+
+ align:start position:0%
+right now earlier we proved that plus or
+ 
+
+ align:start position:0%
+right now earlier we proved that plus or
+minus the norm of a has to be in the
+
+ align:start position:0%
+minus the norm of a has to be in the
+ 
+
+ align:start position:0%
+minus the norm of a has to be in the
+Spectrum
+
+ align:start position:0%
+Spectrum
+ 
+
+ align:start position:0%
+Spectrum
+right of a self-adjoin operator
+
+ align:start position:0%
+right of a self-adjoin operator
+ 
+
+ align:start position:0%
+right of a self-adjoin operator
+and therefore what we can conclude is
+
+ align:start position:0%
+and therefore what we can conclude is
+ 
+
+ align:start position:0%
+and therefore what we can conclude is
+that if we have a non-trivial
+
+ align:start position:0%
+that if we have a non-trivial
+ 
+
+ align:start position:0%
+that if we have a non-trivial
+self-adjoint compact operator then it
+
+ align:start position:0%
+self-adjoint compact operator then it
+ 
+
+ align:start position:0%
+self-adjoint compact operator then it
+has a at least one eigenvalue
+
+ align:start position:0%
+has a at least one eigenvalue
+ 
+
+ align:start position:0%
+has a at least one eigenvalue
+and we can characterize that eigenvalue
+
+ align:start position:0%
+and we can characterize that eigenvalue
+ 
+
+ align:start position:0%
+and we can characterize that eigenvalue
+so this uh has a following theorem let
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+a be a non-trivial uh
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+compact self-adjoined operator a equals
+
+ align:start position:0%
+compact self-adjoined operator a equals
+ 
+
+ align:start position:0%
+compact self-adjoined operator a equals
+a star
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+then
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+as a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+non-trivial
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+eigenvalue Lambda 1
+
+ align:start position:0%
+eigenvalue Lambda 1
+ 
+
+ align:start position:0%
+eigenvalue Lambda 1
+and we can characterize Lambda one
+
+ align:start position:0%
+and we can characterize Lambda one
+ 
+
+ align:start position:0%
+and we can characterize Lambda one
+or at least the absolute value of Lambda
+
+ align:start position:0%
+or at least the absolute value of Lambda
+ 
+
+ align:start position:0%
+or at least the absolute value of Lambda
+1 as the supremum over
+
+ align:start position:0%
+1 as the supremum over
+ 
+
+ align:start position:0%
+1 as the supremum over
+Norm U equals one
+
+ align:start position:0%
+Norm U equals one
+ 
+
+ align:start position:0%
+Norm U equals one
+a u
+
+ align:start position:0%
+a u
+ 
+
+ align:start position:0%
+a u
+U
+
+ align:start position:0%
+U
+ 
+
+ align:start position:0%
+U
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+equals and this supremum is actually
+
+ align:start position:0%
+equals and this supremum is actually
+ 
+
+ align:start position:0%
+equals and this supremum is actually
+achieved
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+where U1
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+is a normalized eigenvector
+
+ align:start position:0%
+is a normalized eigenvector
+ 
+
+ align:start position:0%
+is a normalized eigenvector
+corresponding to Lambda 1.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+all right so
+
+ align:start position:0%
+all right so
+ 
+
+ align:start position:0%
+all right so
+um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+why do we have or
+
+ align:start position:0%
+why do we have or
+ 
+
+ align:start position:0%
+why do we have or
+so I should say let me make sure I have
+
+ align:start position:0%
+so I should say let me make sure I have
+ 
+
+ align:start position:0%
+so I should say let me make sure I have
+everything here okay
+
+ align:start position:0%
+everything here okay
+ 
+
+ align:start position:0%
+everything here okay
+so why is this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so first off we've shown that plus or
+
+ align:start position:0%
+so first off we've shown that plus or
+ 
+
+ align:start position:0%
+so first off we've shown that plus or
+minus
+
+ align:start position:0%
+minus
+ 
+
+ align:start position:0%
+minus
+the norm of a
+
+ align:start position:0%
+the norm of a
+ 
+
+ align:start position:0%
+the norm of a
+is in fact in
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the spectrum of a
+
+ align:start position:0%
+the spectrum of a
+ 
+
+ align:start position:0%
+the spectrum of a
+all right for any self-adjoint uh
+
+ align:start position:0%
+all right for any self-adjoint uh
+ 
+
+ align:start position:0%
+all right for any self-adjoint uh
+bounded linear operator not necessarily
+
+ align:start position:0%
+bounded linear operator not necessarily
+ 
+
+ align:start position:0%
+bounded linear operator not necessarily
+compact uh
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that plus or minus
+
+ align:start position:0%
+that plus or minus
+ 
+
+ align:start position:0%
+that plus or minus
+not necessarily both of them but plus or
+
+ align:start position:0%
+not necessarily both of them but plus or
+ 
+
+ align:start position:0%
+not necessarily both of them but plus or
+minus one of these
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+at least one
+
+ align:start position:0%
+at least one
+ 
+
+ align:start position:0%
+at least one
+of plus or minus
+
+ align:start position:0%
+of plus or minus
+ 
+
+ align:start position:0%
+of plus or minus
+since a is self a joint meaning a star
+
+ align:start position:0%
+since a is self a joint meaning a star
+ 
+
+ align:start position:0%
+since a is self a joint meaning a star
+equals a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+then Lambda one
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+then I'm going to say plus or minus
+
+ align:start position:0%
+then I'm going to say plus or minus
+ 
+
+ align:start position:0%
+then I'm going to say plus or minus
+meaning not both actually at least one
+
+ align:start position:0%
+meaning not both actually at least one
+ 
+
+ align:start position:0%
+meaning not both actually at least one
+of these uh
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+is an eigenvalue of a
+
+ align:start position:0%
+is an eigenvalue of a
+ 
+
+ align:start position:0%
+is an eigenvalue of a
+by the Fret home alternative
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the Fred home alternative
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the fact that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so Lambda 1 is going to be
+
+ align:start position:0%
+so Lambda 1 is going to be
+ 
+
+ align:start position:0%
+so Lambda 1 is going to be
+you know either
+
+ align:start position:0%
+you know either
+ 
+
+ align:start position:0%
+you know either
+plus Norm of a or minus Norm of a uh
+
+ align:start position:0%
+plus Norm of a or minus Norm of a uh
+ 
+
+ align:start position:0%
+plus Norm of a or minus Norm of a uh
+depending on whether which one is in the
+
+ align:start position:0%
+depending on whether which one is in the
+ 
+
+ align:start position:0%
+depending on whether which one is in the
+Spectrum let's say plus if it's in the
+
+ align:start position:0%
+Spectrum let's say plus if it's in the
+ 
+
+ align:start position:0%
+Spectrum let's say plus if it's in the
+Spectrum minus if plus is not and the
+
+ align:start position:0%
+Spectrum minus if plus is not and the
+ 
+
+ align:start position:0%
+Spectrum minus if plus is not and the
+fact that we can identify it as this
+
+ align:start position:0%
+fact that we can identify it as this
+ 
+
+ align:start position:0%
+fact that we can identify it as this
+quantity here is because
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+we have that for self-adjoint operators
+
+ align:start position:0%
+we have that for self-adjoint operators
+ 
+
+ align:start position:0%
+we have that for self-adjoint operators
+Norm of a which is
+
+ align:start position:0%
+Norm of a which is
+ 
+
+ align:start position:0%
+Norm of a which is
+the absolute value of
+
+ align:start position:0%
+the absolute value of
+ 
+
+ align:start position:0%
+the absolute value of
+one of those plus or minuses that are in
+
+ align:start position:0%
+one of those plus or minuses that are in
+ 
+
+ align:start position:0%
+one of those plus or minuses that are in
+the spectrum is equal to so this is
+
+ align:start position:0%
+the spectrum is equal to so this is
+ 
+
+ align:start position:0%
+the spectrum is equal to so this is
+where
+
+ align:start position:0%
+where
+ 
+
+ align:start position:0%
+where
+so this is equal to
+
+ align:start position:0%
+so this is equal to
+ 
+
+ align:start position:0%
+so this is equal to
+um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+soup U equals one
+
+ align:start position:0%
+soup U equals one
+ 
+
+ align:start position:0%
+soup U equals one
+a u equals U
+
+ align:start position:0%
+a u equals U
+ 
+
+ align:start position:0%
+a u equals U
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+all right
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so that's uh end of the proof
+
+ align:start position:0%
+so that's uh end of the proof
+ 
+
+ align:start position:0%
+so that's uh end of the proof
+and now what we're going to do is we are
+
+ align:start position:0%
+and now what we're going to do is we are
+ 
+
+ align:start position:0%
+and now what we're going to do is we are
+going to keep going all right
+
+ align:start position:0%
+going to keep going all right
+ 
+
+ align:start position:0%
+going to keep going all right
+um so the end result will be that
+
+ align:start position:0%
+um so the end result will be that
+ 
+
+ align:start position:0%
+um so the end result will be that
+we can
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+determine all of the eigenvalues Via a
+
+ align:start position:0%
+determine all of the eigenvalues Via a
+ 
+
+ align:start position:0%
+determine all of the eigenvalues Via a
+certain maximum principle and build up a
+
+ align:start position:0%
+certain maximum principle and build up a
+ 
+
+ align:start position:0%
+certain maximum principle and build up a
+sequence of eigenvectors normalize
+
+ align:start position:0%
+sequence of eigenvectors normalize
+ 
+
+ align:start position:0%
+sequence of eigenvectors normalize
+eigenvectors which are pairwise
+
+ align:start position:0%
+eigenvectors which are pairwise
+ 
+
+ align:start position:0%
+eigenvectors which are pairwise
+orthogonal simply because they come from
+
+ align:start position:0%
+orthogonal simply because they come from
+ 
+
+ align:start position:0%
+orthogonal simply because they come from
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+how they're built up we'll see
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and what and then we'll show that
+
+ align:start position:0%
+and what and then we'll show that
+ 
+
+ align:start position:0%
+and what and then we'll show that
+essentially that set of eigenvectors
+
+ align:start position:0%
+essentially that set of eigenvectors
+ 
+
+ align:start position:0%
+essentially that set of eigenvectors
+that we get along with a set of or an
+
+ align:start position:0%
+that we get along with a set of or an
+ 
+
+ align:start position:0%
+that we get along with a set of or an
+orthonormal basis chosen for the null
+
+ align:start position:0%
+orthonormal basis chosen for the null
+ 
+
+ align:start position:0%
+orthonormal basis chosen for the null
+space of a uh form an orthonormal basis
+
+ align:start position:0%
+space of a uh form an orthonormal basis
+ 
+
+ align:start position:0%
+space of a uh form an orthonormal basis
+for a separable Hilbert space h
+
+ align:start position:0%
+for a separable Hilbert space h
+ 
+
+ align:start position:0%
+for a separable Hilbert space h
+okay so that's where we're going but we
+
+ align:start position:0%
+okay so that's where we're going but we
+ 
+
+ align:start position:0%
+okay so that's where we're going but we
+can basically
+
+ align:start position:0%
+can basically
+ 
+
+ align:start position:0%
+can basically
+take this theorem and keep applying it
+
+ align:start position:0%
+take this theorem and keep applying it
+ 
+
+ align:start position:0%
+take this theorem and keep applying it
+so we have the following maximum
+
+ align:start position:0%
+so we have the following maximum
+ 
+
+ align:start position:0%
+so we have the following maximum
+principle
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+if you like this is the first step in a
+
+ align:start position:0%
+if you like this is the first step in a
+ 
+
+ align:start position:0%
+if you like this is the first step in a
+maximum principle this says if you want
+
+ align:start position:0%
+maximum principle this says if you want
+ 
+
+ align:start position:0%
+maximum principle this says if you want
+to find the largest eigenvalue Lambda 1.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+I should say I can even say largest
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+eigenvalue
+
+ align:start position:0%
+eigenvalue
+ 
+
+ align:start position:0%
+eigenvalue
+largest in the sense of uh
+
+ align:start position:0%
+largest in the sense of uh
+ 
+
+ align:start position:0%
+largest in the sense of uh
+absolute value
+
+ align:start position:0%
+absolute value
+ 
+
+ align:start position:0%
+absolute value
+why because remember the spectrum is
+
+ align:start position:0%
+why because remember the spectrum is
+ 
+
+ align:start position:0%
+why because remember the spectrum is
+contained in the interval
+
+ align:start position:0%
+contained in the interval
+ 
+
+ align:start position:0%
+contained in the interval
+minus Norm a plus Norm of a okay so
+
+ align:start position:0%
+minus Norm a plus Norm of a okay so
+ 
+
+ align:start position:0%
+minus Norm a plus Norm of a okay so
+anything in the Spectrum has to have
+
+ align:start position:0%
+anything in the Spectrum has to have
+ 
+
+ align:start position:0%
+anything in the Spectrum has to have
+absolute value less than or equal to
+
+ align:start position:0%
+absolute value less than or equal to
+ 
+
+ align:start position:0%
+absolute value less than or equal to
+uh the norm of a
+
+ align:start position:0%
+uh the norm of a
+ 
+
+ align:start position:0%
+uh the norm of a
+and if it's a eigenvalue it's or if it's
+
+ align:start position:0%
+and if it's a eigenvalue it's or if it's
+ 
+
+ align:start position:0%
+and if it's a eigenvalue it's or if it's
+a
+
+ align:start position:0%
+a
+ 
+
+ align:start position:0%
+a
+right anything other than zero has to be
+
+ align:start position:0%
+right anything other than zero has to be
+ 
+
+ align:start position:0%
+right anything other than zero has to be
+an eigenvalue so we get uh get this
+
+ align:start position:0%
+an eigenvalue so we get uh get this
+ 
+
+ align:start position:0%
+an eigenvalue so we get uh get this
+okay so what's this maximum principle
+
+ align:start position:0%
+okay so what's this maximum principle
+ 
+
+ align:start position:0%
+okay so what's this maximum principle
+um and why was I saying all that oh so
+
+ align:start position:0%
+um and why was I saying all that oh so
+ 
+
+ align:start position:0%
+um and why was I saying all that oh so
+this gives you a way to to if you'd like
+
+ align:start position:0%
+this gives you a way to to if you'd like
+ 
+
+ align:start position:0%
+this gives you a way to to if you'd like
+try and find or at least approximate the
+
+ align:start position:0%
+try and find or at least approximate the
+ 
+
+ align:start position:0%
+try and find or at least approximate the
+first eigenvalue
+
+ align:start position:0%
+first eigenvalue
+ 
+
+ align:start position:0%
+first eigenvalue
+of a bounded linear operator right this
+
+ align:start position:0%
+of a bounded linear operator right this
+ 
+
+ align:start position:0%
+of a bounded linear operator right this
+is a maximization problem with a
+
+ align:start position:0%
+is a maximization problem with a
+ 
+
+ align:start position:0%
+is a maximization problem with a
+constraint yeah so you could use the
+
+ align:start position:0%
+constraint yeah so you could use the
+ 
+
+ align:start position:0%
+constraint yeah so you could use the
+method of LaGrange multipliers
+
+ align:start position:0%
+method of LaGrange multipliers
+ 
+
+ align:start position:0%
+method of LaGrange multipliers
+um you know
+
+ align:start position:0%
+um you know
+ 
+
+ align:start position:0%
+um you know
+that doesn't
+
+ align:start position:0%
+that doesn't
+ 
+
+ align:start position:0%
+that doesn't
+maybe make sense to you to be able to do
+
+ align:start position:0%
+maybe make sense to you to be able to do
+ 
+
+ align:start position:0%
+maybe make sense to you to be able to do
+on an infinite dimensional Hilbert space
+
+ align:start position:0%
+on an infinite dimensional Hilbert space
+ 
+
+ align:start position:0%
+on an infinite dimensional Hilbert space
+but let's say you choose a big basis uh
+
+ align:start position:0%
+but let's say you choose a big basis uh
+ 
+
+ align:start position:0%
+but let's say you choose a big basis uh
+of your Hilbert space and you just
+
+ align:start position:0%
+of your Hilbert space and you just
+ 
+
+ align:start position:0%
+of your Hilbert space and you just
+restrict to looking at that uh big but
+
+ align:start position:0%
+restrict to looking at that uh big but
+ 
+
+ align:start position:0%
+restrict to looking at that uh big but
+finite dimensional or finite basis uh
+
+ align:start position:0%
+finite dimensional or finite basis uh
+ 
+
+ align:start position:0%
+finite dimensional or finite basis uh
+or span of that finite basis and try to
+
+ align:start position:0%
+or span of that finite basis and try to
+ 
+
+ align:start position:0%
+or span of that finite basis and try to
+solve the approximate problem then you
+
+ align:start position:0%
+solve the approximate problem then you
+ 
+
+ align:start position:0%
+solve the approximate problem then you
+should get close to
+
+ align:start position:0%
+should get close to
+ 
+
+ align:start position:0%
+should get close to
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+the eigenvalue
+
+ align:start position:0%
+the eigenvalue
+ 
+
+ align:start position:0%
+the eigenvalue
+okay and get an approximate eigenvector
+
+ align:start position:0%
+okay and get an approximate eigenvector
+ 
+
+ align:start position:0%
+okay and get an approximate eigenvector
+because as I've said the eigenvector
+
+ align:start position:0%
+because as I've said the eigenvector
+ 
+
+ align:start position:0%
+because as I've said the eigenvector
+will be
+
+ align:start position:0%
+will be
+ 
+
+ align:start position:0%
+will be
+achieved
+
+ align:start position:0%
+achieved
+ 
+
+ align:start position:0%
+achieved
+or I should say the the eigenvector
+
+ align:start position:0%
+or I should say the the eigenvector
+ 
+
+ align:start position:0%
+or I should say the the eigenvector
+achieves this maximum here
+
+ align:start position:0%
+achieves this maximum here
+ 
+
+ align:start position:0%
+achieves this maximum here
+or the suprema okay so uh the maximum
+
+ align:start position:0%
+or the suprema okay so uh the maximum
+ 
+
+ align:start position:0%
+or the suprema okay so uh the maximum
+principle is the following so let a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+again we're only looking at compact
+
+ align:start position:0%
+again we're only looking at compact
+ 
+
+ align:start position:0%
+again we're only looking at compact
+self-adjoined operators
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+compact
+
+ align:start position:0%
+compact
+ 
+
+ align:start position:0%
+compact
+operator
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+then
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the non-zero eigenvalues
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+of a
+
+ align:start position:0%
+of a
+ 
+
+ align:start position:0%
+of a
+can be ordered
+
+ align:start position:0%
+can be ordered
+ 
+
+ align:start position:0%
+can be ordered
+now this we kind of this part we already
+
+ align:start position:0%
+now this we kind of this part we already
+ 
+
+ align:start position:0%
+now this we kind of this part we already
+know they can be ordered
+
+ align:start position:0%
+know they can be ordered
+ 
+
+ align:start position:0%
+know they can be ordered
+Lambda 1 less than or equal to Lambda 2
+
+ align:start position:0%
+Lambda 1 less than or equal to Lambda 2
+ 
+
+ align:start position:0%
+Lambda 1 less than or equal to Lambda 2
+less than or equal to Lambda 3.
+
+ align:start position:0%
+less than or equal to Lambda 3.
+ 
+
+ align:start position:0%
+less than or equal to Lambda 3.
+counted with multiplicity meaning
+
+ align:start position:0%
+counted with multiplicity meaning
+ 
+
+ align:start position:0%
+counted with multiplicity meaning
+uh if Lambda 1 has a two-dimensional
+
+ align:start position:0%
+uh if Lambda 1 has a two-dimensional
+ 
+
+ align:start position:0%
+uh if Lambda 1 has a two-dimensional
+eigenspace then Lambda 2 or the absolute
+
+ align:start position:0%
+eigenspace then Lambda 2 or the absolute
+ 
+
+ align:start position:0%
+eigenspace then Lambda 2 or the absolute
+value of or Lambda 2 will be Lambda 1 so
+
+ align:start position:0%
+value of or Lambda 2 will be Lambda 1 so
+ 
+
+ align:start position:0%
+value of or Lambda 2 will be Lambda 1 so
+we're we'll repeat it according to
+
+ align:start position:0%
+we're we'll repeat it according to
+ 
+
+ align:start position:0%
+we're we'll repeat it according to
+multiple Multiplicity
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+so we know that there's finitely many
+
+ align:start position:0%
+so we know that there's finitely many
+ 
+
+ align:start position:0%
+so we know that there's finitely many
+distinct eigenvalues that was the part
+
+ align:start position:0%
+distinct eigenvalues that was the part
+ 
+
+ align:start position:0%
+distinct eigenvalues that was the part
+that I was saying we know we can order
+
+ align:start position:0%
+that I was saying we know we can order
+ 
+
+ align:start position:0%
+that I was saying we know we can order
+them but uh you know
+
+ align:start position:0%
+them but uh you know
+ 
+
+ align:start position:0%
+them but uh you know
+maybe it's it's uh not clear that you
+
+ align:start position:0%
+maybe it's it's uh not clear that you
+ 
+
+ align:start position:0%
+maybe it's it's uh not clear that you
+can order them with Multiplicity
+
+ align:start position:0%
+can order them with Multiplicity
+ 
+
+ align:start position:0%
+can order them with Multiplicity
+um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+with corresponding
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+orthonormal
+
+ align:start position:0%
+orthonormal
+ 
+
+ align:start position:0%
+orthonormal
+eigenfunctions
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+UK so U1 is a
+
+ align:start position:0%
+UK so U1 is a
+ 
+
+ align:start position:0%
+UK so U1 is a
+normalized eigenfunction for Lambda 1.
+
+ align:start position:0%
+normalized eigenfunction for Lambda 1.
+ 
+
+ align:start position:0%
+normalized eigenfunction for Lambda 1.
+U2 will be a normalized eigenfunction
+
+ align:start position:0%
+U2 will be a normalized eigenfunction
+ 
+
+ align:start position:0%
+U2 will be a normalized eigenfunction
+for Lambda 2 which is orthogonal to U1
+
+ align:start position:0%
+for Lambda 2 which is orthogonal to U1
+ 
+
+ align:start position:0%
+for Lambda 2 which is orthogonal to U1
+so these are pairwise orthonormal
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and how do we obtain
+
+ align:start position:0%
+and how do we obtain
+ 
+
+ align:start position:0%
+and how do we obtain
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+the eigenvalues in this order and these
+
+ align:start position:0%
+the eigenvalues in this order and these
+ 
+
+ align:start position:0%
+the eigenvalues in this order and these
+eigenfunctions via the following process
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so that Lambda
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+J is equal to the supremum Over All
+
+ align:start position:0%
+J is equal to the supremum Over All
+ 
+
+ align:start position:0%
+J is equal to the supremum Over All
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+unit vectors
+
+ align:start position:0%
+unit vectors
+ 
+
+ align:start position:0%
+unit vectors
+that or are orthogonal to the first
+
+ align:start position:0%
+that or are orthogonal to the first
+ 
+
+ align:start position:0%
+that or are orthogonal to the first
+J minus one
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and this is equal to this will be
+
+ align:start position:0%
+and this is equal to this will be
+ 
+
+ align:start position:0%
+and this is equal to this will be
+achieved on the U sub J
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+so we have the first one if you like we
+
+ align:start position:0%
+so we have the first one if you like we
+ 
+
+ align:start position:0%
+so we have the first one if you like we
+built up Lambda one U1 and now what this
+
+ align:start position:0%
+built up Lambda one U1 and now what this
+ 
+
+ align:start position:0%
+built up Lambda one U1 and now what this
+maximum principle theorem is saying is
+
+ align:start position:0%
+maximum principle theorem is saying is
+ 
+
+ align:start position:0%
+maximum principle theorem is saying is
+that we can kind of repeat this okay is
+
+ align:start position:0%
+that we can kind of repeat this okay is
+ 
+
+ align:start position:0%
+that we can kind of repeat this okay is
+that if we now look at
+
+ align:start position:0%
+that if we now look at
+ 
+
+ align:start position:0%
+that if we now look at
+um this quantity here the supremum over
+
+ align:start position:0%
+um this quantity here the supremum over
+ 
+
+ align:start position:0%
+um this quantity here the supremum over
+all Norm one uh vectors that are
+
+ align:start position:0%
+all Norm one uh vectors that are
+ 
+
+ align:start position:0%
+all Norm one uh vectors that are
+orthogonal to U1
+
+ align:start position:0%
+orthogonal to U1
+ 
+
+ align:start position:0%
+orthogonal to U1
+then we're going to pick up uh
+
+ align:start position:0%
+then we're going to pick up uh
+ 
+
+ align:start position:0%
+then we're going to pick up uh
+the next largest eigenvalue counted with
+
+ align:start position:0%
+the next largest eigenvalue counted with
+ 
+
+ align:start position:0%
+the next largest eigenvalue counted with
+multiplicity meaning uh it'll be the
+
+ align:start position:0%
+multiplicity meaning uh it'll be the
+ 
+
+ align:start position:0%
+multiplicity meaning uh it'll be the
+absolute value of Lambda 2 which will be
+
+ align:start position:0%
+absolute value of Lambda 2 which will be
+ 
+
+ align:start position:0%
+absolute value of Lambda 2 which will be
+less than Lambda 1 if you know Lambda 1
+
+ align:start position:0%
+less than Lambda 1 if you know Lambda 1
+ 
+
+ align:start position:0%
+less than Lambda 1 if you know Lambda 1
+is uh only has a one-dimensional
+
+ align:start position:0%
+is uh only has a one-dimensional
+ 
+
+ align:start position:0%
+is uh only has a one-dimensional
+eigenspace
+
+ align:start position:0%
+eigenspace
+ 
+
+ align:start position:0%
+eigenspace
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+or it'll be Lambda or that absolute
+
+ align:start position:0%
+or it'll be Lambda or that absolute
+ 
+
+ align:start position:0%
+or it'll be Lambda or that absolute
+value of Lambda 2 will be Lambda
+
+ align:start position:0%
+value of Lambda 2 will be Lambda
+ 
+
+ align:start position:0%
+value of Lambda 2 will be Lambda
+absolute value of Lambda 1 again if
+
+ align:start position:0%
+absolute value of Lambda 1 again if
+ 
+
+ align:start position:0%
+absolute value of Lambda 1 again if
+Lambda 1 has a let's say two dimensional
+
+ align:start position:0%
+Lambda 1 has a let's say two dimensional
+ 
+
+ align:start position:0%
+Lambda 1 has a let's say two dimensional
+eigenspace okay
+
+ align:start position:0%
+eigenspace okay
+ 
+
+ align:start position:0%
+eigenspace okay
+and if it had a three-dimensional
+
+ align:start position:0%
+and if it had a three-dimensional
+ 
+
+ align:start position:0%
+and if it had a three-dimensional
+eigenspace we would get the absolute
+
+ align:start position:0%
+eigenspace we would get the absolute
+ 
+
+ align:start position:0%
+eigenspace we would get the absolute
+value of Lambda 1 for
+
+ align:start position:0%
+value of Lambda 1 for
+ 
+
+ align:start position:0%
+value of Lambda 1 for
+um it would equal this number and this
+
+ align:start position:0%
+um it would equal this number and this
+ 
+
+ align:start position:0%
+um it would equal this number and this
+number as well okay so again these these
+
+ align:start position:0%
+number as well okay so again these these
+ 
+
+ align:start position:0%
+number as well okay so again these these
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+non-zero eigenvalues are
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+can be ordered in this way
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+oh and I left off one
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and the Lambda J is going to zero okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay so
+
+ align:start position:0%
+Okay so
+ 
+
+ align:start position:0%
+Okay so
+we have the first one uh the absolute
+
+ align:start position:0%
+we have the first one uh the absolute
+ 
+
+ align:start position:0%
+we have the first one uh the absolute
+value of Lambda 1 and the first
+
+ align:start position:0%
+value of Lambda 1 and the first
+ 
+
+ align:start position:0%
+value of Lambda 1 and the first
+eigenvector U1 and now we're just gonna
+
+ align:start position:0%
+eigenvector U1 and now we're just gonna
+ 
+
+ align:start position:0%
+eigenvector U1 and now we're just gonna
+basically repeat
+
+ align:start position:0%
+basically repeat
+ 
+
+ align:start position:0%
+basically repeat
+or apply the previous theorem
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+to a modification of a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+now
+
+ align:start position:0%
+now
+ 
+
+ align:start position:0%
+now
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+I should say
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this is not entirely true because there
+
+ align:start position:0%
+this is not entirely true because there
+ 
+
+ align:start position:0%
+this is not entirely true because there
+may only be finitely many
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so really this should be a remark
+
+ align:start position:0%
+so really this should be a remark
+ 
+
+ align:start position:0%
+so really this should be a remark
+if
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the decreasing sequence
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+does not terminate
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+then uh
+
+ align:start position:0%
+then uh
+ 
+
+ align:start position:0%
+then uh
+the absolute value of the Lambda JS goes
+
+ align:start position:0%
+the absolute value of the Lambda JS goes
+ 
+
+ align:start position:0%
+the absolute value of the Lambda JS goes
+to zero
+
+ align:start position:0%
+to zero
+ 
+
+ align:start position:0%
+to zero
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+now
+
+ align:start position:0%
+now
+ 
+
+ align:start position:0%
+now
+Okay so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+what's what's kind of the new bit
+
+ align:start position:0%
+what's what's kind of the new bit
+ 
+
+ align:start position:0%
+what's what's kind of the new bit
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+of information here you know we do know
+
+ align:start position:0%
+of information here you know we do know
+ 
+
+ align:start position:0%
+of information here you know we do know
+that we can
+
+ align:start position:0%
+that we can
+ 
+
+ align:start position:0%
+that we can
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+you know for each
+
+ align:start position:0%
+you know for each
+ 
+
+ align:start position:0%
+you know for each
+let's say capital N the number of
+
+ align:start position:0%
+let's say capital N the number of
+ 
+
+ align:start position:0%
+let's say capital N the number of
+eigenvalues outside of uh or with
+
+ align:start position:0%
+eigenvalues outside of uh or with
+ 
+
+ align:start position:0%
+eigenvalues outside of uh or with
+absolute value bigger than 1 over n
+
+ align:start position:0%
+absolute value bigger than 1 over n
+ 
+
+ align:start position:0%
+absolute value bigger than 1 over n
+um has to be finite so you know
+
+ align:start position:0%
+um has to be finite so you know
+ 
+
+ align:start position:0%
+um has to be finite so you know
+the fact that we can order them is not
+
+ align:start position:0%
+the fact that we can order them is not
+ 
+
+ align:start position:0%
+the fact that we can order them is not
+really
+
+ align:start position:0%
+really
+ 
+
+ align:start position:0%
+really
+that much new information in the fact
+
+ align:start position:0%
+that much new information in the fact
+ 
+
+ align:start position:0%
+that much new information in the fact
+that they have to go to zero if this
+
+ align:start position:0%
+that they have to go to zero if this
+ 
+
+ align:start position:0%
+that they have to go to zero if this
+sequence is infinite that's also not new
+
+ align:start position:0%
+sequence is infinite that's also not new
+ 
+
+ align:start position:0%
+sequence is infinite that's also not new
+information I mean we did prove that uh
+
+ align:start position:0%
+information I mean we did prove that uh
+ 
+
+ align:start position:0%
+information I mean we did prove that uh
+in a previous lecture that if you have
+
+ align:start position:0%
+in a previous lecture that if you have
+ 
+
+ align:start position:0%
+in a previous lecture that if you have
+um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so there we proved it for a sequence of
+
+ align:start position:0%
+so there we proved it for a sequence of
+ 
+
+ align:start position:0%
+so there we proved it for a sequence of
+distinct eigenvalues but because we now
+
+ align:start position:0%
+distinct eigenvalues but because we now
+ 
+
+ align:start position:0%
+distinct eigenvalues but because we now
+know that each of these has a finite
+
+ align:start position:0%
+know that each of these has a finite
+ 
+
+ align:start position:0%
+know that each of these has a finite
+dimensional uh eigenspace you know if
+
+ align:start position:0%
+dimensional uh eigenspace you know if
+ 
+
+ align:start position:0%
+dimensional uh eigenspace you know if
+you just look back at the same proof or
+
+ align:start position:0%
+you just look back at the same proof or
+ 
+
+ align:start position:0%
+you just look back at the same proof or
+that proof you can make a small
+
+ align:start position:0%
+that proof you can make a small
+ 
+
+ align:start position:0%
+that proof you can make a small
+adjustment to be able to say that if you
+
+ align:start position:0%
+adjustment to be able to say that if you
+ 
+
+ align:start position:0%
+adjustment to be able to say that if you
+count the eigenvalues with multiplicity
+
+ align:start position:0%
+count the eigenvalues with multiplicity
+ 
+
+ align:start position:0%
+count the eigenvalues with multiplicity
+then also the sequence has to go to zero
+
+ align:start position:0%
+then also the sequence has to go to zero
+ 
+
+ align:start position:0%
+then also the sequence has to go to zero
+okay not just necessarily the sequence
+
+ align:start position:0%
+okay not just necessarily the sequence
+ 
+
+ align:start position:0%
+okay not just necessarily the sequence
+consisting of the distinct eigenvalues
+
+ align:start position:0%
+consisting of the distinct eigenvalues
+ 
+
+ align:start position:0%
+consisting of the distinct eigenvalues
+okay so let me make that small
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+remark
+
+ align:start position:0%
+remark
+ 
+
+ align:start position:0%
+remark
+what the new piece is is that we can
+
+ align:start position:0%
+what the new piece is is that we can
+ 
+
+ align:start position:0%
+what the new piece is is that we can
+compute the eigenvalues in this way and
+
+ align:start position:0%
+compute the eigenvalues in this way and
+ 
+
+ align:start position:0%
+compute the eigenvalues in this way and
+choose the eigenvectors in this way
+
+ align:start position:0%
+choose the eigenvectors in this way
+ 
+
+ align:start position:0%
+choose the eigenvectors in this way
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+that's the new piece and that's kind of
+
+ align:start position:0%
+that's the new piece and that's kind of
+ 
+
+ align:start position:0%
+that's the new piece and that's kind of
+what
+
+ align:start position:0%
+what
+ 
+
+ align:start position:0%
+what
+in the end we'll we'll
+
+ align:start position:0%
+in the end we'll we'll
+ 
+
+ align:start position:0%
+in the end we'll we'll
+use to be able to show that H can be or
+
+ align:start position:0%
+use to be able to show that H can be or
+ 
+
+ align:start position:0%
+use to be able to show that H can be or
+that a can basically be diagonalized or
+
+ align:start position:0%
+that a can basically be diagonalized or
+ 
+
+ align:start position:0%
+that a can basically be diagonalized or
+that you can find an orthonormal basis
+
+ align:start position:0%
+that you can find an orthonormal basis
+ 
+
+ align:start position:0%
+that you can find an orthonormal basis
+of a Hilbert space separable Hilbert
+
+ align:start position:0%
+of a Hilbert space separable Hilbert
+ 
+
+ align:start position:0%
+of a Hilbert space separable Hilbert
+space consisting entirely of
+
+ align:start position:0%
+space consisting entirely of
+ 
+
+ align:start position:0%
+space consisting entirely of
+eigenvectors of a
+
+ align:start position:0%
+eigenvectors of a
+ 
+
+ align:start position:0%
+eigenvectors of a
+okay all right so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the construction
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+proceeds
+
+ align:start position:0%
+proceeds
+ 
+
+ align:start position:0%
+proceeds
+inductively so you know at one point I
+
+ align:start position:0%
+inductively so you know at one point I
+ 
+
+ align:start position:0%
+inductively so you know at one point I
+said you know if you can do it for one
+
+ align:start position:0%
+said you know if you can do it for one
+ 
+
+ align:start position:0%
+said you know if you can do it for one
+then you can do it for the next and then
+
+ align:start position:0%
+then you can do it for the next and then
+ 
+
+ align:start position:0%
+then you can do it for the next and then
+I won't be so formal every time I do a
+
+ align:start position:0%
+I won't be so formal every time I do a
+ 
+
+ align:start position:0%
+I won't be so formal every time I do a
+kind of an inductive uh construction and
+
+ align:start position:0%
+kind of an inductive uh construction and
+ 
+
+ align:start position:0%
+kind of an inductive uh construction and
+but in this case it pays to be careful
+
+ align:start position:0%
+but in this case it pays to be careful
+ 
+
+ align:start position:0%
+but in this case it pays to be careful
+so um
+
+ align:start position:0%
+so um
+ 
+
+ align:start position:0%
+so um
+you know we'll construct the
+
+ align:start position:0%
+you know we'll construct the
+ 
+
+ align:start position:0%
+you know we'll construct the
+sequence of uh Lambda J's in New in new
+
+ align:start position:0%
+sequence of uh Lambda J's in New in new
+ 
+
+ align:start position:0%
+sequence of uh Lambda J's in New in new
+case in this way all right
+
+ align:start position:0%
+case in this way all right
+ 
+
+ align:start position:0%
+case in this way all right
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+uh via an inductive argument Okay so
+
+ align:start position:0%
+uh via an inductive argument Okay so
+ 
+
+ align:start position:0%
+uh via an inductive argument Okay so
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+coming up with k equals one that was the
+
+ align:start position:0%
+coming up with k equals one that was the
+ 
+
+ align:start position:0%
+coming up with k equals one that was the
+previous theorem right so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+previous or I should say uh
+
+ align:start position:0%
+previous or I should say uh
+ 
+
+ align:start position:0%
+previous or I should say uh
+J equals one that's the previous
+
+ align:start position:0%
+J equals one that's the previous
+ 
+
+ align:start position:0%
+J equals one that's the previous
+theorem right we defined we found the
+
+ align:start position:0%
+theorem right we defined we found the
+ 
+
+ align:start position:0%
+theorem right we defined we found the
+largest eigenvalue or the eigenvalue
+
+ align:start position:0%
+largest eigenvalue or the eigenvalue
+ 
+
+ align:start position:0%
+largest eigenvalue or the eigenvalue
+with the N eigenvalue with the largest
+
+ align:start position:0%
+with the N eigenvalue with the largest
+ 
+
+ align:start position:0%
+with the N eigenvalue with the largest
+absolute value
+
+ align:start position:0%
+absolute value
+ 
+
+ align:start position:0%
+absolute value
+via this theorem okay and then we
+
+ align:start position:0%
+via this theorem okay and then we
+ 
+
+ align:start position:0%
+via this theorem okay and then we
+obtained an eigenvector this way
+
+ align:start position:0%
+obtained an eigenvector this way
+ 
+
+ align:start position:0%
+obtained an eigenvector this way
+just basically as a consequence of the
+
+ align:start position:0%
+just basically as a consequence of the
+ 
+
+ align:start position:0%
+just basically as a consequence of the
+Fred home alternative and then that we
+
+ align:start position:0%
+Fred home alternative and then that we
+ 
+
+ align:start position:0%
+Fred home alternative and then that we
+know that plus or minus the norm of a
+
+ align:start position:0%
+know that plus or minus the norm of a
+ 
+
+ align:start position:0%
+know that plus or minus the norm of a
+has to be in the Spectrum Okay so
+
+ align:start position:0%
+has to be in the Spectrum Okay so
+ 
+
+ align:start position:0%
+has to be in the Spectrum Okay so
+the fact that we can find the first
+
+ align:start position:0%
+the fact that we can find the first
+ 
+
+ align:start position:0%
+the fact that we can find the first
+eigenvalued Lambda 1 that follows from
+
+ align:start position:0%
+eigenvalued Lambda 1 that follows from
+ 
+
+ align:start position:0%
+eigenvalued Lambda 1 that follows from
+the previous theorem so now we want to
+
+ align:start position:0%
+the previous theorem so now we want to
+ 
+
+ align:start position:0%
+the previous theorem so now we want to
+do the inductive step
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+I.E we want to suppose
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+we have
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+found
+
+ align:start position:0%
+found
+ 
+
+ align:start position:0%
+found
+Lambda 1 up to Lambda
+
+ align:start position:0%
+Lambda 1 up to Lambda
+ 
+
+ align:start position:0%
+Lambda 1 up to Lambda
+say what did I use here
+
+ align:start position:0%
+say what did I use here
+ 
+
+ align:start position:0%
+say what did I use here
+Lambda n so J equals in
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+along with
+
+ align:start position:0%
+along with
+ 
+
+ align:start position:0%
+along with
+uh
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+what the normal
+
+ align:start position:0%
+what the normal
+ 
+
+ align:start position:0%
+what the normal
+eigen
+
+ align:start position:0%
+eigen
+ 
+
+ align:start position:0%
+eigen
+vectors
+
+ align:start position:0%
+vectors
+ 
+
+ align:start position:0%
+vectors
+U1 up to u n
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+satisfying
+
+ align:start position:0%
+satisfying
+ 
+
+ align:start position:0%
+satisfying
+um this uh
+
+ align:start position:0%
+um this uh
+ 
+
+ align:start position:0%
+um this uh
+maximum principle Okay so
+
+ align:start position:0%
+maximum principle Okay so
+ 
+
+ align:start position:0%
+maximum principle Okay so
+for J up to from J starting from
+
+ align:start position:0%
+for J up to from J starting from
+ 
+
+ align:start position:0%
+for J up to from J starting from
+starting at one up to n we've
+
+ align:start position:0%
+starting at one up to n we've
+ 
+
+ align:start position:0%
+starting at one up to n we've
+constructed or found the Lambda 2 Lambda
+
+ align:start position:0%
+constructed or found the Lambda 2 Lambda
+ 
+
+ align:start position:0%
+constructed or found the Lambda 2 Lambda
+3 up to Lambda n and the U1 up to U in
+
+ align:start position:0%
+3 up to Lambda n and the U1 up to U in
+ 
+
+ align:start position:0%
+3 up to Lambda n and the U1 up to U in
+satisfying that maximum property
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+all right so
+
+ align:start position:0%
+all right so
+ 
+
+ align:start position:0%
+all right so
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+then there's two cases
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+case one is
+
+ align:start position:0%
+case one is
+ 
+
+ align:start position:0%
+case one is
+the fact that a minus
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+a is equal to the sum from k equals 1 to
+
+ align:start position:0%
+a is equal to the sum from k equals 1 to
+ 
+
+ align:start position:0%
+a is equal to the sum from k equals 1 to
+n
+
+ align:start position:0%
+n
+ 
+
+ align:start position:0%
+n
+of
+
+ align:start position:0%
+of
+ 
+
+ align:start position:0%
+of
+Lambda k u
+
+ align:start position:0%
+Lambda k u
+ 
+
+ align:start position:0%
+Lambda k u
+inner product UK UK
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and therefore
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+what this shows is that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+we found all the
+
+ align:start position:0%
+we found all the
+ 
+
+ align:start position:0%
+we found all the
+eigenvalues
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and the process terminates
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so this is kind of the degenerate
+
+ align:start position:0%
+okay so this is kind of the degenerate
+ 
+
+ align:start position:0%
+okay so this is kind of the degenerate
+case that a is a finite rank operator
+
+ align:start position:0%
+case that a is a finite rank operator
+ 
+
+ align:start position:0%
+case that a is a finite rank operator
+okay so I could have started this whole
+
+ align:start position:0%
+okay so I could have started this whole
+ 
+
+ align:start position:0%
+okay so I could have started this whole
+theorem off with let's assume a is not a
+
+ align:start position:0%
+theorem off with let's assume a is not a
+ 
+
+ align:start position:0%
+theorem off with let's assume a is not a
+finite rank operator and therefore we
+
+ align:start position:0%
+finite rank operator and therefore we
+ 
+
+ align:start position:0%
+finite rank operator and therefore we
+wouldn't have to deal with this case but
+
+ align:start position:0%
+wouldn't have to deal with this case but
+ 
+
+ align:start position:0%
+wouldn't have to deal with this case but
+I just stated it for an arbitrary a so
+
+ align:start position:0%
+I just stated it for an arbitrary a so
+ 
+
+ align:start position:0%
+I just stated it for an arbitrary a so
+there is the possibility that that
+
+ align:start position:0%
+there is the possibility that that
+ 
+
+ align:start position:0%
+there is the possibility that that
+sequence stopped okay we found all of
+
+ align:start position:0%
+sequence stopped okay we found all of
+ 
+
+ align:start position:0%
+sequence stopped okay we found all of
+the eigenvalues
+
+ align:start position:0%
+the eigenvalues
+ 
+
+ align:start position:0%
+the eigenvalues
+with multiplicity in this in this
+
+ align:start position:0%
+with multiplicity in this in this
+ 
+
+ align:start position:0%
+with multiplicity in this in this
+process
+
+ align:start position:0%
+process
+ 
+
+ align:start position:0%
+process
+and then the theorem or construction is
+
+ align:start position:0%
+and then the theorem or construction is
+ 
+
+ align:start position:0%
+and then the theorem or construction is
+done in that case
+
+ align:start position:0%
+done in that case
+ 
+
+ align:start position:0%
+done in that case
+in the case two
+
+ align:start position:0%
+in the case two
+ 
+
+ align:start position:0%
+in the case two
+is that it is not a finite rank operator
+
+ align:start position:0%
+is that it is not a finite rank operator
+ 
+
+ align:start position:0%
+is that it is not a finite rank operator
+so it's not equal to k equals 1 to n
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay now we have to show how can we find
+
+ align:start position:0%
+okay now we have to show how can we find
+ 
+
+ align:start position:0%
+okay now we have to show how can we find
+uh Lambda sub n plus one okay and the
+
+ align:start position:0%
+uh Lambda sub n plus one okay and the
+ 
+
+ align:start position:0%
+uh Lambda sub n plus one okay and the
+eigenvector U sub n plus one
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+let a sub n
+
+ align:start position:0%
+let a sub n
+ 
+
+ align:start position:0%
+let a sub n
+B
+
+ align:start position:0%
+B
+ 
+
+ align:start position:0%
+B
+the operator A minus
+
+ align:start position:0%
+the operator A minus
+ 
+
+ align:start position:0%
+the operator A minus
+k equals 1 to n Lambda K inner product U
+
+ align:start position:0%
+k equals 1 to n Lambda K inner product U
+ 
+
+ align:start position:0%
+k equals 1 to n Lambda K inner product U
+so should say a
+
+ align:start position:0%
+so should say a
+ 
+
+ align:start position:0%
+so should say a
+U
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+sub k
+
+ align:start position:0%
+sub k
+ 
+
+ align:start position:0%
+sub k
+all right
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+now note since we are in case two this
+
+ align:start position:0%
+now note since we are in case two this
+ 
+
+ align:start position:0%
+now note since we are in case two this
+operator is non-zero okay so we're
+
+ align:start position:0%
+operator is non-zero okay so we're
+ 
+
+ align:start position:0%
+operator is non-zero okay so we're
+basically going to apply the previous
+
+ align:start position:0%
+basically going to apply the previous
+ 
+
+ align:start position:0%
+basically going to apply the previous
+theorem now to this operator okay but
+
+ align:start position:0%
+theorem now to this operator okay but
+ 
+
+ align:start position:0%
+theorem now to this operator okay but
+let me first make a few remarks
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+then a is
+
+ align:start position:0%
+then a is
+ 
+
+ align:start position:0%
+then a is
+a sub N is a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this is something you can check it's a
+
+ align:start position:0%
+this is something you can check it's a
+ 
+
+ align:start position:0%
+this is something you can check it's a
+self itself a joint
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+compact operator
+
+ align:start position:0%
+compact operator
+ 
+
+ align:start position:0%
+compact operator
+so why is itself a joint basically
+
+ align:start position:0%
+so why is itself a joint basically
+ 
+
+ align:start position:0%
+so why is itself a joint basically
+because a is Alpha joint
+
+ align:start position:0%
+because a is Alpha joint
+ 
+
+ align:start position:0%
+because a is Alpha joint
+and these Lambda K's are real numbers
+
+ align:start position:0%
+and these Lambda K's are real numbers
+ 
+
+ align:start position:0%
+and these Lambda K's are real numbers
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+all right because eigenvalues have to be
+
+ align:start position:0%
+all right because eigenvalues have to be
+ 
+
+ align:start position:0%
+all right because eigenvalues have to be
+real because a is self a joint
+
+ align:start position:0%
+real because a is self a joint
+ 
+
+ align:start position:0%
+real because a is self a joint
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+and these are orthonormal
+
+ align:start position:0%
+and these are orthonormal
+ 
+
+ align:start position:0%
+and these are orthonormal
+um so
+
+ align:start position:0%
+um so
+ 
+
+ align:start position:0%
+um so
+that is why they're self-adjoint why is
+
+ align:start position:0%
+that is why they're self-adjoint why is
+ 
+
+ align:start position:0%
+that is why they're self-adjoint why is
+it a compact operator well it's the sum
+
+ align:start position:0%
+it a compact operator well it's the sum
+ 
+
+ align:start position:0%
+it a compact operator well it's the sum
+of a compact operator a in a finite rank
+
+ align:start position:0%
+of a compact operator a in a finite rank
+ 
+
+ align:start position:0%
+of a compact operator a in a finite rank
+operator here so it's also a compact
+
+ align:start position:0%
+operator here so it's also a compact
+ 
+
+ align:start position:0%
+operator here so it's also a compact
+operator
+
+ align:start position:0%
+operator
+ 
+
+ align:start position:0%
+operator
+uh and it's a non-trivial one because
+
+ align:start position:0%
+uh and it's a non-trivial one because
+ 
+
+ align:start position:0%
+uh and it's a non-trivial one because
+it's not identically equal to zero
+
+ align:start position:0%
+it's not identically equal to zero
+ 
+
+ align:start position:0%
+it's not identically equal to zero
+so I shouldn't say not equal to zero but
+
+ align:start position:0%
+so I shouldn't say not equal to zero but
+ 
+
+ align:start position:0%
+so I shouldn't say not equal to zero but
+which is not identically the zero
+
+ align:start position:0%
+which is not identically the zero
+ 
+
+ align:start position:0%
+which is not identically the zero
+operator
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+all right so here's a couple of facts uh
+
+ align:start position:0%
+all right so here's a couple of facts uh
+ 
+
+ align:start position:0%
+all right so here's a couple of facts uh
+that if you
+
+ align:start position:0%
+that if you
+ 
+
+ align:start position:0%
+that if you
+is in the span of U1 up to you in
+
+ align:start position:0%
+is in the span of U1 up to you in
+ 
+
+ align:start position:0%
+is in the span of U1 up to you in
+then
+
+ align:start position:0%
+then
+ 
+
+ align:start position:0%
+then
+I get that a sub n
+
+ align:start position:0%
+I get that a sub n
+ 
+
+ align:start position:0%
+I get that a sub n
+applied to U is the zero vector
+
+ align:start position:0%
+applied to U is the zero vector
+ 
+
+ align:start position:0%
+applied to U is the zero vector
+okay why is that so it suffices to check
+
+ align:start position:0%
+okay why is that so it suffices to check
+ 
+
+ align:start position:0%
+okay why is that so it suffices to check
+that this gives me this formula gives me
+
+ align:start position:0%
+that this gives me this formula gives me
+ 
+
+ align:start position:0%
+that this gives me this formula gives me
+zero When U is one of the uks now if you
+
+ align:start position:0%
+zero When U is one of the uks now if you
+ 
+
+ align:start position:0%
+zero When U is one of the uks now if you
+as one of the uks then this will be
+
+ align:start position:0%
+as one of the uks then this will be
+ 
+
+ align:start position:0%
+as one of the uks then this will be
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+one only when or let's say it's one of
+
+ align:start position:0%
+one only when or let's say it's one of
+ 
+
+ align:start position:0%
+one only when or let's say it's one of
+the U JS I need a different letter so if
+
+ align:start position:0%
+the U JS I need a different letter so if
+ 
+
+ align:start position:0%
+the U JS I need a different letter so if
+you is one of these UJS
+
+ align:start position:0%
+you is one of these UJS
+ 
+
+ align:start position:0%
+you is one of these UJS
+then this will give me one only when J
+
+ align:start position:0%
+then this will give me one only when J
+ 
+
+ align:start position:0%
+then this will give me one only when J
+equals K and I pick up Lambda J times u
+
+ align:start position:0%
+equals K and I pick up Lambda J times u
+ 
+
+ align:start position:0%
+equals K and I pick up Lambda J times u
+j and then I have a hitting U sub J and
+
+ align:start position:0%
+j and then I have a hitting U sub J and
+ 
+
+ align:start position:0%
+j and then I have a hitting U sub J and
+that spits out Lambda J times U sub J
+
+ align:start position:0%
+that spits out Lambda J times U sub J
+ 
+
+ align:start position:0%
+that spits out Lambda J times U sub J
+because U sub J is an eigenvector of a
+
+ align:start position:0%
+because U sub J is an eigenvector of a
+ 
+
+ align:start position:0%
+because U sub J is an eigenvector of a
+so then I get the same thing here and
+
+ align:start position:0%
+so then I get the same thing here and
+ 
+
+ align:start position:0%
+so then I get the same thing here and
+there and subtracting them gives me zero
+
+ align:start position:0%
+there and subtracting them gives me zero
+ 
+
+ align:start position:0%
+there and subtracting them gives me zero
+um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+now if U is orthogonal to
+
+ align:start position:0%
+now if U is orthogonal to
+ 
+
+ align:start position:0%
+now if U is orthogonal to
+uh the span of the U1 up to u n then I
+
+ align:start position:0%
+uh the span of the U1 up to u n then I
+ 
+
+ align:start position:0%
+uh the span of the U1 up to u n then I
+get
+
+ align:start position:0%
+get
+ 
+
+ align:start position:0%
+get
+a in a view
+
+ align:start position:0%
+a in a view
+ 
+
+ align:start position:0%
+a in a view
+equals a u
+
+ align:start position:0%
+equals a u
+ 
+
+ align:start position:0%
+equals a u
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+so you just see this If U is orthogonal
+
+ align:start position:0%
+so you just see this If U is orthogonal
+ 
+
+ align:start position:0%
+so you just see this If U is orthogonal
+to these then this whole term is zero
+
+ align:start position:0%
+to these then this whole term is zero
+ 
+
+ align:start position:0%
+to these then this whole term is zero
+okay and I just pick up a n u equals a u
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+for All U in H
+
+ align:start position:0%
+for All U in H
+ 
+
+ align:start position:0%
+for All U in H
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+the span of U1 up to u n
+
+ align:start position:0%
+the span of U1 up to u n
+ 
+
+ align:start position:0%
+the span of U1 up to u n
+if I compute
+
+ align:start position:0%
+if I compute
+ 
+
+ align:start position:0%
+if I compute
+a and u inner product
+
+ align:start position:0%
+a and u inner product
+ 
+
+ align:start position:0%
+a and u inner product
+V this is equal to U
+
+ align:start position:0%
+V this is equal to U
+ 
+
+ align:start position:0%
+V this is equal to U
+a and v since a n is Alpha joint and
+
+ align:start position:0%
+a and v since a n is Alpha joint and
+ 
+
+ align:start position:0%
+a and v since a n is Alpha joint and
+since V is in the span of the u1s up to
+
+ align:start position:0%
+since V is in the span of the u1s up to
+ 
+
+ align:start position:0%
+since V is in the span of the u1s up to
+U Ends by the first property that's
+
+ align:start position:0%
+U Ends by the first property that's
+ 
+
+ align:start position:0%
+U Ends by the first property that's
+going to be zero so this equals zero and
+
+ align:start position:0%
+going to be zero so this equals zero and
+ 
+
+ align:start position:0%
+going to be zero so this equals zero and
+therefore
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um what have I shown I've shown that a
+
+ align:start position:0%
+um what have I shown I've shown that a
+ 
+
+ align:start position:0%
+um what have I shown I've shown that a
+and u inner product V is zero no matter
+
+ align:start position:0%
+and u inner product V is zero no matter
+ 
+
+ align:start position:0%
+and u inner product V is zero no matter
+what uh U is an h and therefore that
+
+ align:start position:0%
+what uh U is an h and therefore that
+ 
+
+ align:start position:0%
+what uh U is an h and therefore that
+means that V has to be in the orthogonal
+
+ align:start position:0%
+means that V has to be in the orthogonal
+ 
+
+ align:start position:0%
+means that V has to be in the orthogonal
+complement of the range
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so I said that backwards so anyways
+
+ align:start position:0%
+okay so I said that backwards so anyways
+ 
+
+ align:start position:0%
+okay so I said that backwards so anyways
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+here U is fixed V is the thing that's
+
+ align:start position:0%
+here U is fixed V is the thing that's
+ 
+
+ align:start position:0%
+here U is fixed V is the thing that's
+changing so what does this say U is
+
+ align:start position:0%
+changing so what does this say U is
+ 
+
+ align:start position:0%
+changing so what does this say U is
+fixed a and u inner product V when V is
+
+ align:start position:0%
+fixed a and u inner product V when V is
+ 
+
+ align:start position:0%
+fixed a and u inner product V when V is
+in the span has to be zero this holds
+
+ align:start position:0%
+in the span has to be zero this holds
+ 
+
+ align:start position:0%
+in the span has to be zero this holds
+for all V in the span
+
+ align:start position:0%
+for all V in the span
+ 
+
+ align:start position:0%
+for all V in the span
+and therefore Anu has to be in the
+
+ align:start position:0%
+and therefore Anu has to be in the
+ 
+
+ align:start position:0%
+and therefore Anu has to be in the
+orthogonal complement of the span of
+
+ align:start position:0%
+orthogonal complement of the span of
+ 
+
+ align:start position:0%
+orthogonal complement of the span of
+these guys so this proves that the range
+
+ align:start position:0%
+these guys so this proves that the range
+ 
+
+ align:start position:0%
+these guys so this proves that the range
+of a n
+
+ align:start position:0%
+of a n
+ 
+
+ align:start position:0%
+of a n
+is a subset of
+
+ align:start position:0%
+is a subset of
+ 
+
+ align:start position:0%
+is a subset of
+the orthogonal complement
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+of U1 up to u n
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and okay so from this previous property
+
+ align:start position:0%
+and okay so from this previous property
+ 
+
+ align:start position:0%
+and okay so from this previous property
+we get one last property
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that if
+
+ align:start position:0%
+that if
+ 
+
+ align:start position:0%
+that if
+a Anu
+
+ align:start position:0%
+a Anu
+ 
+
+ align:start position:0%
+a Anu
+equals Lambda U
+
+ align:start position:0%
+equals Lambda U
+ 
+
+ align:start position:0%
+equals Lambda U
+is non-zero meaning we have a non-zero
+
+ align:start position:0%
+is non-zero meaning we have a non-zero
+ 
+
+ align:start position:0%
+is non-zero meaning we have a non-zero
+eigenvalue of a sub n
+
+ align:start position:0%
+eigenvalue of a sub n
+ 
+
+ align:start position:0%
+eigenvalue of a sub n
+uh then
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that implies that U
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so U is equal to one over Lambda a sub n
+
+ align:start position:0%
+so U is equal to one over Lambda a sub n
+ 
+
+ align:start position:0%
+so U is equal to one over Lambda a sub n
+applied to U in other words U is equal
+
+ align:start position:0%
+applied to U in other words U is equal
+ 
+
+ align:start position:0%
+applied to U in other words U is equal
+to a sub n applied to U over Lambda so
+
+ align:start position:0%
+to a sub n applied to U over Lambda so
+ 
+
+ align:start position:0%
+to a sub n applied to U over Lambda so
+that implies U is in the range of a sub
+
+ align:start position:0%
+that implies U is in the range of a sub
+ 
+
+ align:start position:0%
+that implies U is in the range of a sub
+n
+
+ align:start position:0%
+n
+ 
+
+ align:start position:0%
+n
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+which again is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+contained in the orthogonal complement
+
+ align:start position:0%
+contained in the orthogonal complement
+ 
+
+ align:start position:0%
+contained in the orthogonal complement
+of U1 up to U sub n and since it's in
+
+ align:start position:0%
+of U1 up to U sub n and since it's in
+ 
+
+ align:start position:0%
+of U1 up to U sub n and since it's in
+the orthogonal complement that means a
+
+ align:start position:0%
+the orthogonal complement that means a
+ 
+
+ align:start position:0%
+the orthogonal complement that means a
+sub n u equals a u
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so any non-zero eigenvalue of a sub n
+
+ align:start position:0%
+so any non-zero eigenvalue of a sub n
+ 
+
+ align:start position:0%
+so any non-zero eigenvalue of a sub n
+has to be a non-zero eigenvalue of a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+now we just apply the previous theorem
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+to um
+
+ align:start position:0%
+to um
+ 
+
+ align:start position:0%
+to um
+to a sub n to get the next eigen or next
+
+ align:start position:0%
+to a sub n to get the next eigen or next
+ 
+
+ align:start position:0%
+to a sub n to get the next eigen or next
+uh eigenvalue a sub n Plus or Lambda sub
+
+ align:start position:0%
+uh eigenvalue a sub n Plus or Lambda sub
+ 
+
+ align:start position:0%
+uh eigenvalue a sub n Plus or Lambda sub
+n plus 1 and eigenvector U sub n plus
+
+ align:start position:0%
+n plus 1 and eigenvector U sub n plus
+ 
+
+ align:start position:0%
+n plus 1 and eigenvector U sub n plus
+one
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+all right the previous theorem
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+a sub n
+
+ align:start position:0%
+a sub n
+ 
+
+ align:start position:0%
+a sub n
+has a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+non-zero eigenvalue
+
+ align:start position:0%
+non-zero eigenvalue
+ 
+
+ align:start position:0%
+non-zero eigenvalue
+which I will call Lambda n plus one
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+with
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+unit
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+eigenvector
+
+ align:start position:0%
+eigenvector
+ 
+
+ align:start position:0%
+eigenvector
+U sub n plus one
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so that Lambda n plus one
+
+ align:start position:0%
+so that Lambda n plus one
+ 
+
+ align:start position:0%
+so that Lambda n plus one
+is equal to
+
+ align:start position:0%
+is equal to
+ 
+
+ align:start position:0%
+is equal to
+the soup over
+
+ align:start position:0%
+the soup over
+ 
+
+ align:start position:0%
+the soup over
+all uh
+
+ align:start position:0%
+all uh
+ 
+
+ align:start position:0%
+all uh
+Norm
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+ah okay soup overall Norm uh or unit
+
+ align:start position:0%
+ah okay soup overall Norm uh or unit
+ 
+
+ align:start position:0%
+ah okay soup overall Norm uh or unit
+length vectors of absolute value of a
+
+ align:start position:0%
+length vectors of absolute value of a
+ 
+
+ align:start position:0%
+length vectors of absolute value of a
+sub n applied to U in a product U now
+
+ align:start position:0%
+sub n applied to U in a product U now
+ 
+
+ align:start position:0%
+sub n applied to U in a product U now
+this soup is overalls is the same uh
+
+ align:start position:0%
+this soup is overalls is the same uh
+ 
+
+ align:start position:0%
+this soup is overalls is the same uh
+soup overall
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+one so that a sub n u is non-zero so
+
+ align:start position:0%
+one so that a sub n u is non-zero so
+ 
+
+ align:start position:0%
+one so that a sub n u is non-zero so
+that in particular includes
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+right so if U is in the span of U1 up to
+
+ align:start position:0%
+right so if U is in the span of U1 up to
+ 
+
+ align:start position:0%
+right so if U is in the span of U1 up to
+U in then a and u equals zero so the
+
+ align:start position:0%
+U in then a and u equals zero so the
+ 
+
+ align:start position:0%
+U in then a and u equals zero so the
+supremum overall unit length is the same
+
+ align:start position:0%
+supremum overall unit length is the same
+ 
+
+ align:start position:0%
+supremum overall unit length is the same
+as uh the supremum over everything in
+
+ align:start position:0%
+as uh the supremum over everything in
+ 
+
+ align:start position:0%
+as uh the supremum over everything in
+the orthogonal complement of these guys
+
+ align:start position:0%
+the orthogonal complement of these guys
+ 
+
+ align:start position:0%
+the orthogonal complement of these guys
+because these guys when you stick them
+
+ align:start position:0%
+because these guys when you stick them
+ 
+
+ align:start position:0%
+because these guys when you stick them
+into a in gives me uh zero so that's the
+
+ align:start position:0%
+into a in gives me uh zero so that's the
+ 
+
+ align:start position:0%
+into a in gives me uh zero so that's the
+same supremum but now also
+
+ align:start position:0%
+same supremum but now also
+ 
+
+ align:start position:0%
+same supremum but now also
+when you is in the orthogonal complement
+
+ align:start position:0%
+when you is in the orthogonal complement
+ 
+
+ align:start position:0%
+when you is in the orthogonal complement
+of these u1s up to u n this is equal to
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+soup of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+U
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+on the orthogonal complement of the U1
+
+ align:start position:0%
+on the orthogonal complement of the U1
+ 
+
+ align:start position:0%
+on the orthogonal complement of the U1
+up to you ends a and u remember equals
+
+ align:start position:0%
+up to you ends a and u remember equals
+ 
+
+ align:start position:0%
+up to you ends a and u remember equals
+a u
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+so that uh
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+gives us you know the fact that I can
+
+ align:start position:0%
+gives us you know the fact that I can
+ 
+
+ align:start position:0%
+gives us you know the fact that I can
+find this from this uh
+
+ align:start position:0%
+find this from this uh
+ 
+
+ align:start position:0%
+find this from this uh
+supremum
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and so why okay so why does
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this eigenvector have to be in the
+
+ align:start position:0%
+this eigenvector have to be in the
+ 
+
+ align:start position:0%
+this eigenvector have to be in the
+orthogonal complement of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh U1 up to u n it's because I can
+
+ align:start position:0%
+uh U1 up to u n it's because I can
+ 
+
+ align:start position:0%
+uh U1 up to u n it's because I can
+choose it that way because again when a
+
+ align:start position:0%
+choose it that way because again when a
+ 
+
+ align:start position:0%
+choose it that way because again when a
+sub n hits any of anything in here I get
+
+ align:start position:0%
+sub n hits any of anything in here I get
+ 
+
+ align:start position:0%
+sub n hits any of anything in here I get
+zero okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+I should say this is also equal to
+
+ align:start position:0%
+I should say this is also equal to
+ 
+
+ align:start position:0%
+I should say this is also equal to
+a n applied to u n plus one but it's uh
+
+ align:start position:0%
+a n applied to u n plus one but it's uh
+ 
+
+ align:start position:0%
+a n applied to u n plus one but it's uh
+that's the same as a applied to u n plus
+
+ align:start position:0%
+that's the same as a applied to u n plus
+ 
+
+ align:start position:0%
+that's the same as a applied to u n plus
+one
+
+ align:start position:0%
+one
+ 
+
+ align:start position:0%
+one
+u n plus one
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+right okay and this is less than or
+
+ align:start position:0%
+right okay and this is less than or
+ 
+
+ align:start position:0%
+right okay and this is less than or
+equal to the soup over Norm U equals one
+
+ align:start position:0%
+equal to the soup over Norm U equals one
+ 
+
+ align:start position:0%
+equal to the soup over Norm U equals one
+U and
+
+ align:start position:0%
+U and
+ 
+
+ align:start position:0%
+U and
+span U1 up to U
+
+ align:start position:0%
+span U1 up to U
+ 
+
+ align:start position:0%
+span U1 up to U
+n minus 1 orthogonal complement
+
+ align:start position:0%
+n minus 1 orthogonal complement
+ 
+
+ align:start position:0%
+n minus 1 orthogonal complement
+a u applied to U which equals uh
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the absolute value of the nth eigenvalue
+
+ align:start position:0%
+the absolute value of the nth eigenvalue
+ 
+
+ align:start position:0%
+the absolute value of the nth eigenvalue
+counted with multiple multiplicity okay
+
+ align:start position:0%
+counted with multiple multiplicity okay
+ 
+
+ align:start position:0%
+counted with multiple multiplicity okay
+so we found uh
+
+ align:start position:0%
+so we found uh
+ 
+
+ align:start position:0%
+so we found uh
+the next eigenvalue in the sequence
+
+ align:start position:0%
+the next eigenvalue in the sequence
+ 
+
+ align:start position:0%
+the next eigenvalue in the sequence
+again of eigenvalues counted with
+
+ align:start position:0%
+again of eigenvalues counted with
+ 
+
+ align:start position:0%
+again of eigenvalues counted with
+Multiplicity
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so now we have uh we can conclude
+
+ align:start position:0%
+okay so now we have uh we can conclude
+ 
+
+ align:start position:0%
+okay so now we have uh we can conclude
+the following spectral theorem
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+for compact self-adjoined operators uh
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+let
+
+ align:start position:0%
+let
+ 
+
+ align:start position:0%
+let
+a be a
+
+ align:start position:0%
+a be a
+ 
+
+ align:start position:0%
+a be a
+self-adjoint compact operator
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+on a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+separable
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Hilbert space h
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+let
+
+ align:start position:0%
+let
+ 
+
+ align:start position:0%
+let
+M to 1 bigger than or equal to Lambda 2.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+corresponding eigenvalues
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+be the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+eigenvalues or I should say non-zero
+
+ align:start position:0%
+eigenvalues or I should say non-zero
+ 
+
+ align:start position:0%
+eigenvalues or I should say non-zero
+eigenvalues
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+a counted again with multiplicity so uh
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+counted with multiplicity as we've
+
+ align:start position:0%
+counted with multiplicity as we've
+ 
+
+ align:start position:0%
+counted with multiplicity as we've
+constructed in this uh theorem of which
+
+ align:start position:0%
+constructed in this uh theorem of which
+ 
+
+ align:start position:0%
+constructed in this uh theorem of which
+I call the maximum principle
+
+ align:start position:0%
+I call the maximum principle
+ 
+
+ align:start position:0%
+I call the maximum principle
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+with
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+corresponding
+
+ align:start position:0%
+corresponding
+ 
+
+ align:start position:0%
+corresponding
+um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+orthonormal
+
+ align:start position:0%
+orthonormal
+ 
+
+ align:start position:0%
+orthonormal
+eigenvectors
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+UK so we have these eigenvectors
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+coming from this process
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and the conclusion is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this uh
+
+ align:start position:0%
+this uh
+ 
+
+ align:start position:0%
+this uh
+subset of eigenvectors or orthonormal
+
+ align:start position:0%
+subset of eigenvectors or orthonormal
+ 
+
+ align:start position:0%
+subset of eigenvectors or orthonormal
+eigenvectors is
+
+ align:start position:0%
+eigenvectors is
+ 
+
+ align:start position:0%
+eigenvectors is
+and
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+orthonormal basis
+
+ align:start position:0%
+orthonormal basis
+ 
+
+ align:start position:0%
+orthonormal basis
+for
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the closure or for the range of a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+in fact we can upgrade that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+UK is in fact
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+not the normal basis for
+
+ align:start position:0%
+not the normal basis for
+ 
+
+ align:start position:0%
+not the normal basis for
+the range of a closure
+
+ align:start position:0%
+the range of a closure
+ 
+
+ align:start position:0%
+the range of a closure
+and
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+there exists
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+North the normal
+
+ align:start position:0%
+North the normal
+ 
+
+ align:start position:0%
+North the normal
+basis
+
+ align:start position:0%
+basis
+ 
+
+ align:start position:0%
+basis
+call it
+
+ align:start position:0%
+call it
+ 
+
+ align:start position:0%
+call it
+uh F sub J
+
+ align:start position:0%
+uh F sub J
+ 
+
+ align:start position:0%
+uh F sub J
+of the null space
+
+ align:start position:0%
+of the null space
+ 
+
+ align:start position:0%
+of the null space
+of a if it's non-zero
+
+ align:start position:0%
+of a if it's non-zero
+ 
+
+ align:start position:0%
+of a if it's non-zero
+such that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+you
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+FJ
+
+ align:start position:0%
+FJ
+ 
+
+ align:start position:0%
+FJ
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+so first off
+
+ align:start position:0%
+so first off
+ 
+
+ align:start position:0%
+so first off
+the union of these two
+
+ align:start position:0%
+the union of these two
+ 
+
+ align:start position:0%
+the union of these two
+sets of orthonormal vectors is then
+
+ align:start position:0%
+sets of orthonormal vectors is then
+ 
+
+ align:start position:0%
+sets of orthonormal vectors is then
+going to be again a subset of
+
+ align:start position:0%
+going to be again a subset of
+ 
+
+ align:start position:0%
+going to be again a subset of
+orthonormal vectors because all the fjs
+
+ align:start position:0%
+orthonormal vectors because all the fjs
+ 
+
+ align:start position:0%
+orthonormal vectors because all the fjs
+would correspond to the eigenvalue 0
+
+ align:start position:0%
+would correspond to the eigenvalue 0
+ 
+
+ align:start position:0%
+would correspond to the eigenvalue 0
+and these uks would correspond to
+
+ align:start position:0%
+and these uks would correspond to
+ 
+
+ align:start position:0%
+and these uks would correspond to
+eigenvalues that are non-zero
+
+ align:start position:0%
+eigenvalues that are non-zero
+ 
+
+ align:start position:0%
+eigenvalues that are non-zero
+and by what we proved last time uh any
+
+ align:start position:0%
+and by what we proved last time uh any
+ 
+
+ align:start position:0%
+and by what we proved last time uh any
+eigenvector for two distinct eigenvalues
+
+ align:start position:0%
+eigenvector for two distinct eigenvalues
+ 
+
+ align:start position:0%
+eigenvector for two distinct eigenvalues
+would have to be orthonormal so this
+
+ align:start position:0%
+would have to be orthonormal so this
+ 
+
+ align:start position:0%
+would have to be orthonormal so this
+subset is orthonormal from this subset
+
+ align:start position:0%
+subset is orthonormal from this subset
+ 
+
+ align:start position:0%
+subset is orthonormal from this subset
+but moreover
+
+ align:start position:0%
+but moreover
+ 
+
+ align:start position:0%
+but moreover
+is
+
+ align:start position:0%
+is
+ 
+
+ align:start position:0%
+is
+worth the normal like I said but also an
+
+ align:start position:0%
+worth the normal like I said but also an
+ 
+
+ align:start position:0%
+worth the normal like I said but also an
+orthonormal basis
+
+ align:start position:0%
+orthonormal basis
+ 
+
+ align:start position:0%
+orthonormal basis
+for H okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so in other words I can find
+
+ align:start position:0%
+so in other words I can find
+ 
+
+ align:start position:0%
+so in other words I can find
+an orthonormal basis 4-H consisting
+
+ align:start position:0%
+an orthonormal basis 4-H consisting
+ 
+
+ align:start position:0%
+an orthonormal basis 4-H consisting
+entirely of eigenvectors of this uh
+
+ align:start position:0%
+entirely of eigenvectors of this uh
+ 
+
+ align:start position:0%
+entirely of eigenvectors of this uh
+self-adjoint compact operator
+
+ align:start position:0%
+self-adjoint compact operator
+ 
+
+ align:start position:0%
+self-adjoint compact operator
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+so I will have one piece of this basis
+
+ align:start position:0%
+so I will have one piece of this basis
+ 
+
+ align:start position:0%
+so I will have one piece of this basis
+coming from the null space and the other
+
+ align:start position:0%
+coming from the null space and the other
+ 
+
+ align:start position:0%
+coming from the null space and the other
+piece uh corresponding to
+
+ align:start position:0%
+piece uh corresponding to
+ 
+
+ align:start position:0%
+piece uh corresponding to
+non-zero eigenvalues
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so really two follows from one
+
+ align:start position:0%
+so really two follows from one
+ 
+
+ align:start position:0%
+so really two follows from one
+um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+not sure why I decided to State them
+
+ align:start position:0%
+not sure why I decided to State them
+ 
+
+ align:start position:0%
+not sure why I decided to State them
+separately but here we are
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so proof of one will show that UK is an
+
+ align:start position:0%
+so proof of one will show that UK is an
+ 
+
+ align:start position:0%
+so proof of one will show that UK is an
+orthonormal basis for the range of a
+
+ align:start position:0%
+orthonormal basis for the range of a
+ 
+
+ align:start position:0%
+orthonormal basis for the range of a
+so first off Note as we did in the
+
+ align:start position:0%
+so first off Note as we did in the
+ 
+
+ align:start position:0%
+so first off Note as we did in the
+previous proof that the process
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+obtaining the
+
+ align:start position:0%
+obtaining the
+ 
+
+ align:start position:0%
+obtaining the
+Lambda 1 or the eigenvalues
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and eigenvectors
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+or the normal eigenvectors
+
+ align:start position:0%
+or the normal eigenvectors
+ 
+
+ align:start position:0%
+or the normal eigenvectors
+uh
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+terminates
+
+ align:start position:0%
+terminates
+ 
+
+ align:start position:0%
+terminates
+if and only if
+
+ align:start position:0%
+if and only if
+ 
+
+ align:start position:0%
+if and only if
+um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+a was finite rank in other words there
+
+ align:start position:0%
+a was finite rank in other words there
+ 
+
+ align:start position:0%
+a was finite rank in other words there
+exists an N so that
+
+ align:start position:0%
+exists an N so that
+ 
+
+ align:start position:0%
+exists an N so that
+Au is this finite rink
+
+ align:start position:0%
+Au is this finite rink
+ 
+
+ align:start position:0%
+Au is this finite rink
+operator
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+you and a product
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+UK UK
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+in this case if it's a finite rank
+
+ align:start position:0%
+in this case if it's a finite rank
+ 
+
+ align:start position:0%
+in this case if it's a finite rank
+operator then the range is contained in
+
+ align:start position:0%
+operator then the range is contained in
+ 
+
+ align:start position:0%
+operator then the range is contained in
+UK the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+which is what we wanted to prove for
+
+ align:start position:0%
+which is what we wanted to prove for
+ 
+
+ align:start position:0%
+which is what we wanted to prove for
+this case that a is this finite rank
+
+ align:start position:0%
+this case that a is this finite rank
+ 
+
+ align:start position:0%
+this case that a is this finite rank
+operator
+
+ align:start position:0%
+operator
+ 
+
+ align:start position:0%
+operator
+so suppose otherwise
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+in other words the process does not
+
+ align:start position:0%
+in other words the process does not
+ 
+
+ align:start position:0%
+in other words the process does not
+terminate
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so that we have countably infinite many
+
+ align:start position:0%
+so that we have countably infinite many
+ 
+
+ align:start position:0%
+so that we have countably infinite many
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+non-zero eigenvalues counted with
+
+ align:start position:0%
+non-zero eigenvalues counted with
+ 
+
+ align:start position:0%
+non-zero eigenvalues counted with
+multiplicity and uh and corresponding
+
+ align:start position:0%
+multiplicity and uh and corresponding
+ 
+
+ align:start position:0%
+multiplicity and uh and corresponding
+orthonormal eigenvectors U sub K all
+
+ align:start position:0%
+orthonormal eigenvectors U sub K all
+ 
+
+ align:start position:0%
+orthonormal eigenvectors U sub K all
+right
+
+ align:start position:0%
+right
+ 
+
+ align:start position:0%
+right
+so this is a more interesting
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so the eigenvalues are countably
+
+ align:start position:0%
+so the eigenvalues are countably
+ 
+
+ align:start position:0%
+so the eigenvalues are countably
+intimate
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so now we want to show so as in the
+
+ align:start position:0%
+okay so now we want to show so as in the
+ 
+
+ align:start position:0%
+okay so now we want to show so as in the
+remark
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that I made afterwards
+
+ align:start position:0%
+that I made afterwards
+ 
+
+ align:start position:0%
+that I made afterwards
+you know that
+
+ align:start position:0%
+you know that
+ 
+
+ align:start position:0%
+you know that
+these Lambda Kays have to go to zero
+
+ align:start position:0%
+these Lambda Kays have to go to zero
+ 
+
+ align:start position:0%
+these Lambda Kays have to go to zero
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+now
+
+ align:start position:0%
+now
+ 
+
+ align:start position:0%
+now
+we want to prove that the uks are an
+
+ align:start position:0%
+we want to prove that the uks are an
+ 
+
+ align:start position:0%
+we want to prove that the uks are an
+orthodontal basis for the range of a
+
+ align:start position:0%
+orthodontal basis for the range of a
+ 
+
+ align:start position:0%
+orthodontal basis for the range of a
+what does that mean by definition that
+
+ align:start position:0%
+what does that mean by definition that
+ 
+
+ align:start position:0%
+what does that mean by definition that
+means that they're in maximal
+
+ align:start position:0%
+means that they're in maximal
+ 
+
+ align:start position:0%
+means that they're in maximal
+orthonormal subset of the range of a so
+
+ align:start position:0%
+orthonormal subset of the range of a so
+ 
+
+ align:start position:0%
+orthonormal subset of the range of a so
+we have to show that if something's in
+
+ align:start position:0%
+we have to show that if something's in
+ 
+
+ align:start position:0%
+we have to show that if something's in
+the range and it's orthogonal to every
+
+ align:start position:0%
+the range and it's orthogonal to every
+ 
+
+ align:start position:0%
+the range and it's orthogonal to every
+uh one of these eigenvectors then that
+
+ align:start position:0%
+uh one of these eigenvectors then that
+ 
+
+ align:start position:0%
+uh one of these eigenvectors then that
+thing has to be zero okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so the claim
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+if f is in the range of a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and for all k
+
+ align:start position:0%
+and for all k
+ 
+
+ align:start position:0%
+and for all k
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+F inner product u k equals zero
+
+ align:start position:0%
+F inner product u k equals zero
+ 
+
+ align:start position:0%
+F inner product u k equals zero
+then
+
+ align:start position:0%
+then
+ 
+
+ align:start position:0%
+then
+f is a zero vector
+
+ align:start position:0%
+f is a zero vector
+ 
+
+ align:start position:0%
+f is a zero vector
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so this is the claim we want to prove so
+
+ align:start position:0%
+so this is the claim we want to prove so
+ 
+
+ align:start position:0%
+so this is the claim we want to prove so
+suppose we have something in the range
+
+ align:start position:0%
+suppose we have something in the range
+ 
+
+ align:start position:0%
+suppose we have something in the range
+that means we can write it as a times U
+
+ align:start position:0%
+that means we can write it as a times U
+ 
+
+ align:start position:0%
+that means we can write it as a times U
+and uh
+
+ align:start position:0%
+and uh
+ 
+
+ align:start position:0%
+and uh
+F inner product UK equals zero
+
+ align:start position:0%
+F inner product UK equals zero
+ 
+
+ align:start position:0%
+F inner product UK equals zero
+for all k
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+it's in for all K uh if I
+
+ align:start position:0%
+it's in for all K uh if I
+ 
+
+ align:start position:0%
+it's in for all K uh if I
+look at Lambda k u inner product UK this
+
+ align:start position:0%
+look at Lambda k u inner product UK this
+ 
+
+ align:start position:0%
+look at Lambda k u inner product UK this
+is equal to
+
+ align:start position:0%
+is equal to
+ 
+
+ align:start position:0%
+is equal to
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+Lambda K is a real number so I can bring
+
+ align:start position:0%
+Lambda K is a real number so I can bring
+ 
+
+ align:start position:0%
+Lambda K is a real number so I can bring
+it all the way in
+
+ align:start position:0%
+it all the way in
+ 
+
+ align:start position:0%
+it all the way in
+get Lambda k u k and this is equal to U
+
+ align:start position:0%
+get Lambda k u k and this is equal to U
+ 
+
+ align:start position:0%
+get Lambda k u k and this is equal to U
+a applied to UK now a itself a joint so
+
+ align:start position:0%
+a applied to UK now a itself a joint so
+ 
+
+ align:start position:0%
+a applied to UK now a itself a joint so
+I can move this a over here to U
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and this is equal to f
+
+ align:start position:0%
+and this is equal to f
+ 
+
+ align:start position:0%
+and this is equal to f
+in a product UK equals zero for all k
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+right
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so by this uh
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+maximum principle which we proved just a
+
+ align:start position:0%
+maximum principle which we proved just a
+ 
+
+ align:start position:0%
+maximum principle which we proved just a
+minute ago
+
+ align:start position:0%
+minute ago
+ 
+
+ align:start position:0%
+minute ago
+we conclude that the norm of f
+
+ align:start position:0%
+we conclude that the norm of f
+ 
+
+ align:start position:0%
+we conclude that the norm of f
+which is equal to the norm of
+
+ align:start position:0%
+which is equal to the norm of
+ 
+
+ align:start position:0%
+which is equal to the norm of
+a u which is equal to the norm of A
+
+ align:start position:0%
+a u which is equal to the norm of A
+ 
+
+ align:start position:0%
+a u which is equal to the norm of A
+minus
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+sum from k equals 1 to n of Lambda k
+
+ align:start position:0%
+sum from k equals 1 to n of Lambda k
+ 
+
+ align:start position:0%
+sum from k equals 1 to n of Lambda k
+U
+
+ align:start position:0%
+U
+ 
+
+ align:start position:0%
+U
+k
+
+ align:start position:0%
+k
+ 
+
+ align:start position:0%
+k
+um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+UK applied to you
+
+ align:start position:0%
+UK applied to you
+ 
+
+ align:start position:0%
+UK applied to you
+right because every one of these numbers
+
+ align:start position:0%
+right because every one of these numbers
+ 
+
+ align:start position:0%
+right because every one of these numbers
+is zero so I haven't
+
+ align:start position:0%
+is zero so I haven't
+ 
+
+ align:start position:0%
+is zero so I haven't
+subtracted off anything
+
+ align:start position:0%
+subtracted off anything
+ 
+
+ align:start position:0%
+subtracted off anything
+right
+
+ align:start position:0%
+right
+ 
+
+ align:start position:0%
+right
+this is
+
+ align:start position:0%
+this is
+ 
+
+ align:start position:0%
+this is
+uh
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+I can write this in terms of
+
+ align:start position:0%
+I can write this in terms of
+ 
+
+ align:start position:0%
+I can write this in terms of
+this a sub n
+
+ align:start position:0%
+this a sub n
+ 
+
+ align:start position:0%
+this a sub n
+applied to U where a sub n was this
+
+ align:start position:0%
+applied to U where a sub n was this
+ 
+
+ align:start position:0%
+applied to U where a sub n was this
+thing that or a sub n is this thing
+
+ align:start position:0%
+thing that or a sub n is this thing
+ 
+
+ align:start position:0%
+thing that or a sub n is this thing
+which
+
+ align:start position:0%
+which
+ 
+
+ align:start position:0%
+which
+by the previous uh
+
+ align:start position:0%
+by the previous uh
+ 
+
+ align:start position:0%
+by the previous uh
+or the proof of the maximization or the
+
+ align:start position:0%
+or the proof of the maximization or the
+ 
+
+ align:start position:0%
+or the proof of the maximization or the
+maximum principle is less than or equal
+
+ align:start position:0%
+maximum principle is less than or equal
+ 
+
+ align:start position:0%
+maximum principle is less than or equal
+to
+
+ align:start position:0%
+to
+ 
+
+ align:start position:0%
+to
+Lambda plus one n plus one of
+
+ align:start position:0%
+Lambda plus one n plus one of
+ 
+
+ align:start position:0%
+Lambda plus one n plus one of
+U because again
+
+ align:start position:0%
+U because again
+ 
+
+ align:start position:0%
+U because again
+um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+remember this
+
+ align:start position:0%
+remember this
+ 
+
+ align:start position:0%
+remember this
+thing here is the supremum overall use
+
+ align:start position:0%
+thing here is the supremum overall use
+ 
+
+ align:start position:0%
+thing here is the supremum overall use
+of unit length of a sub n applied to U
+
+ align:start position:0%
+of unit length of a sub n applied to U
+ 
+
+ align:start position:0%
+of unit length of a sub n applied to U
+so uh Lambda n plus 1 is less than or or
+
+ align:start position:0%
+so uh Lambda n plus 1 is less than or or
+ 
+
+ align:start position:0%
+so uh Lambda n plus 1 is less than or or
+this quantity here divided by the norm
+
+ align:start position:0%
+this quantity here divided by the norm
+ 
+
+ align:start position:0%
+this quantity here divided by the norm
+of U so that U is a unit length is
+
+ align:start position:0%
+of U so that U is a unit length is
+ 
+
+ align:start position:0%
+of U so that U is a unit length is
+always less than or equal to this
+
+ align:start position:0%
+always less than or equal to this
+ 
+
+ align:start position:0%
+always less than or equal to this
+quantity here
+
+ align:start position:0%
+quantity here
+ 
+
+ align:start position:0%
+quantity here
+but now Lambda so this I had a fixed
+
+ align:start position:0%
+but now Lambda so this I had a fixed
+ 
+
+ align:start position:0%
+but now Lambda so this I had a fixed
+thing here Norm of F and I've shown it's
+
+ align:start position:0%
+thing here Norm of F and I've shown it's
+ 
+
+ align:start position:0%
+thing here Norm of F and I've shown it's
+less than or equal to Lambda n plus 1
+
+ align:start position:0%
+less than or equal to Lambda n plus 1
+ 
+
+ align:start position:0%
+less than or equal to Lambda n plus 1
+times the norm of U this is a fixed
+
+ align:start position:0%
+times the norm of U this is a fixed
+ 
+
+ align:start position:0%
+times the norm of U this is a fixed
+thing and the Lambda ends are converging
+
+ align:start position:0%
+thing and the Lambda ends are converging
+ 
+
+ align:start position:0%
+thing and the Lambda ends are converging
+to zero
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay and thus
+
+ align:start position:0%
+okay and thus
+ 
+
+ align:start position:0%
+okay and thus
+I started off with something
+
+ align:start position:0%
+I started off with something
+ 
+
+ align:start position:0%
+I started off with something
+non-negative less than or equal to
+
+ align:start position:0%
+non-negative less than or equal to
+ 
+
+ align:start position:0%
+non-negative less than or equal to
+something converging to zero and
+
+ align:start position:0%
+something converging to zero and
+ 
+
+ align:start position:0%
+something converging to zero and
+therefore that
+
+ align:start position:0%
+therefore that
+ 
+
+ align:start position:0%
+therefore that
+thing had to be zero
+
+ align:start position:0%
+thing had to be zero
+ 
+
+ align:start position:0%
+thing had to be zero
+therefore f is zero Okay so
+
+ align:start position:0%
+therefore f is zero Okay so
+ 
+
+ align:start position:0%
+therefore f is zero Okay so
+um this proves one that these
+
+ align:start position:0%
+um this proves one that these
+ 
+
+ align:start position:0%
+um this proves one that these
+eigenvectors are
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+a maximal orthonormal
+
+ align:start position:0%
+a maximal orthonormal
+ 
+
+ align:start position:0%
+a maximal orthonormal
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+subset of the range of a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and for two we simply note uh
+
+ align:start position:0%
+and for two we simply note uh
+ 
+
+ align:start position:0%
+and for two we simply note uh
+that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+by one we have that the range
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+today closure this is since the
+
+ align:start position:0%
+today closure this is since the
+ 
+
+ align:start position:0%
+today closure this is since the
+um eigenvectors are an orthonormal basis
+
+ align:start position:0%
+um eigenvectors are an orthonormal basis
+ 
+
+ align:start position:0%
+um eigenvectors are an orthonormal basis
+for the range of a the closure is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+contained in
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+closure of the spans of the uks here
+
+ align:start position:0%
+closure of the spans of the uks here
+ 
+
+ align:start position:0%
+closure of the spans of the uks here
+this is a finite span
+
+ align:start position:0%
+this is a finite span
+ 
+
+ align:start position:0%
+this is a finite span
+um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+which remember this is by uh an
+
+ align:start position:0%
+which remember this is by uh an
+ 
+
+ align:start position:0%
+which remember this is by uh an
+assignment exercise this is equal to k c
+
+ align:start position:0%
+assignment exercise this is equal to k c
+ 
+
+ align:start position:0%
+assignment exercise this is equal to k c
+k u k such that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and therefore
+
+ align:start position:0%
+and therefore
+ 
+
+ align:start position:0%
+and therefore
+this implies that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+is an orthonormal basis
+
+ align:start position:0%
+is an orthonormal basis
+ 
+
+ align:start position:0%
+is an orthonormal basis
+for
+
+ align:start position:0%
+for
+ 
+
+ align:start position:0%
+for
+the range of a
+
+ align:start position:0%
+the range of a
+ 
+
+ align:start position:0%
+the range of a
+closure
+
+ align:start position:0%
+closure
+ 
+
+ align:start position:0%
+closure
+and this is equal to
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+range of a
+
+ align:start position:0%
+range of a
+ 
+
+ align:start position:0%
+range of a
+orthogonal complement orthogonal
+
+ align:start position:0%
+orthogonal complement orthogonal
+ 
+
+ align:start position:0%
+orthogonal complement orthogonal
+complement
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+which is equal to the null space
+
+ align:start position:0%
+which is equal to the null space
+ 
+
+ align:start position:0%
+which is equal to the null space
+of
+
+ align:start position:0%
+of
+ 
+
+ align:start position:0%
+of
+the orthogonal complement of the null
+
+ align:start position:0%
+the orthogonal complement of the null
+ 
+
+ align:start position:0%
+the orthogonal complement of the null
+space of a star a star equals a so we
+
+ align:start position:0%
+space of a star a star equals a so we
+ 
+
+ align:start position:0%
+space of a star a star equals a so we
+get that so the UK's the eigenvectors
+
+ align:start position:0%
+get that so the UK's the eigenvectors
+ 
+
+ align:start position:0%
+get that so the UK's the eigenvectors
+form an orthogonal or an orthonormal
+
+ align:start position:0%
+form an orthogonal or an orthonormal
+ 
+
+ align:start position:0%
+form an orthogonal or an orthonormal
+basis for the orthogonal complement of
+
+ align:start position:0%
+basis for the orthogonal complement of
+ 
+
+ align:start position:0%
+basis for the orthogonal complement of
+the null space of a so once we've chosen
+
+ align:start position:0%
+the null space of a so once we've chosen
+ 
+
+ align:start position:0%
+the null space of a so once we've chosen
+an orthonormal basis for
+
+ align:start position:0%
+an orthonormal basis for
+ 
+
+ align:start position:0%
+an orthonormal basis for
+uh null space of a that's it
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+H is
+
+ align:start position:0%
+H is
+ 
+
+ align:start position:0%
+H is
+separable and the null space of a is a
+
+ align:start position:0%
+separable and the null space of a is a
+ 
+
+ align:start position:0%
+separable and the null space of a is a
+closed Subspace of H
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+on no space of a
+
+ align:start position:0%
+on no space of a
+ 
+
+ align:start position:0%
+on no space of a
+separable and we've proven that every
+
+ align:start position:0%
+separable and we've proven that every
+ 
+
+ align:start position:0%
+separable and we've proven that every
+separable Hilbert space or
+
+ align:start position:0%
+separable Hilbert space or
+ 
+
+ align:start position:0%
+separable Hilbert space or
+even just uh okay so this is a closed
+
+ align:start position:0%
+even just uh okay so this is a closed
+ 
+
+ align:start position:0%
+even just uh okay so this is a closed
+one so it's a Hilbert space anyways but
+
+ align:start position:0%
+one so it's a Hilbert space anyways but
+ 
+
+ align:start position:0%
+one so it's a Hilbert space anyways but
+every separable Hilbert space has an
+
+ align:start position:0%
+every separable Hilbert space has an
+ 
+
+ align:start position:0%
+every separable Hilbert space has an
+orthonormal basis
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and therefore again so we
+
+ align:start position:0%
+and therefore again so we
+ 
+
+ align:start position:0%
+and therefore again so we
+uh since these two
+
+ align:start position:0%
+uh since these two
+ 
+
+ align:start position:0%
+uh since these two
+call this
+
+ align:start position:0%
+call this
+ 
+
+ align:start position:0%
+call this
+FJ
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this is an orthonormal basis
+
+ align:start position:0%
+this is an orthonormal basis
+ 
+
+ align:start position:0%
+this is an orthonormal basis
+for
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the null space of a direct products
+
+ align:start position:0%
+the null space of a direct products
+ 
+
+ align:start position:0%
+the null space of a direct products
+null space of a
+
+ align:start position:0%
+null space of a
+ 
+
+ align:start position:0%
+null space of a
+orthogonal complement
+
+ align:start position:0%
+orthogonal complement
+ 
+
+ align:start position:0%
+orthogonal complement
+that equals h
+
+ align:start position:0%
+that equals h
+ 
+
+ align:start position:0%
+that equals h
+all right and just in the nick of time
+
+ align:start position:0%
+all right and just in the nick of time
+ 
+
+ align:start position:0%
+all right and just in the nick of time
+I'm finished
+
+ align:start position:0%
+I'm finished
+ 
+
+ align:start position:0%
+I'm finished
+so next time
+
+ align:start position:0%
+so next time
+ 
+
+ align:start position:0%
+so next time
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+where do we go from here we'll see some
+
+ align:start position:0%
+where do we go from here we'll see some
+ 
+
+ align:start position:0%
+where do we go from here we'll see some
+of this applied in a concrete setting of
+
+ align:start position:0%
+of this applied in a concrete setting of
+ 
+
+ align:start position:0%
+of this applied in a concrete setting of
+differential equations and also discuss
+
+ align:start position:0%
+differential equations and also discuss
+ 
+
+ align:start position:0%
+differential equations and also discuss
+the functional calculus
\ No newline at end of file
diff --git a/00PK6cUCbnU.txt b/00PK6cUCbnU.txt
new file mode 100644
index 0000000000000000000000000000000000000000..5d101fa589637e5ffdbe24e9d3e1412c8c06bfe7
--- /dev/null
+++ b/00PK6cUCbnU.txt
@@ -0,0 +1,2998 @@
+The following
+content is provided
+
+under a Creative
+Commons license.
+
+Your support will help MIT
+OpenCourseWare continue
+
+to offer high-quality
+educational resources for free.
+
+To make a donation, or
+view additional materials
+
+from hundreds of MIT courses,
+visit MIT OpenCourseWare
+
+at ocw.mit.edu.
+
+PROFESSOR: OK.
+
+Let's start with our
+standard starting
+
+point of the last few lectures.
+
+That is, we are
+looking at some system.
+
+We tried to describe
+it by some kind
+
+of a field, statistical
+field after some averaging.
+
+That is, a function of position.
+
+And we are interested
+in calculating something
+
+like a partition function
+by integrating over
+
+all configurations of
+the statistical field.
+
+And these configurations
+have some kind of a weight.
+
+This weight we choose
+to write as exponential
+
+of some kind of a-- something
+like an effective Hamiltonian
+
+that depends on
+the configuration
+
+that you're looking at.
+
+And of course, the main
+thing faced with a problem
+
+that you haven't seen before is
+to decide on what the field is
+
+that you are looking
+at to average.
+
+And what kind of
+symmetries and constraints
+
+you want to construct in
+this form of the weight.
+
+In particular, we
+are sort of focusing
+
+on this Landau-Ginzburg
+model that
+
+describes phase transitions.
+
+And let's say in the
+absence of magnetic field,
+
+we are interested in a system
+that is rotationally symmetric.
+
+But the procedure is
+reasonably standard.
+
+Maybe in some
+cases you can solve
+
+a particular part of this.
+
+Let's call that part beta H0.
+
+In the context that
+we are working with,
+
+it's the Gaussian part that
+we have looked at before.
+
+So that's the
+integral over space.
+
+We used this idea of locality.
+
+We had an expansion
+in all things
+
+that are consistent with this.
+
+But for the purposes of
+the exactly solvable part,
+
+we focus on the Gaussian.
+
+So there is a term that is
+proportional to m squared,
+
+gradient of m squared
+and higher-order terms.
+
+So clearly for the
+time being, I'm
+
+ignoring the magnetic field.
+
+So let's say in this
+formulation the problem that we
+
+are interested is how our
+partition function depends
+
+on this coefficient,
+which where it goes to 0,
+
+the Gaussian weight becomes
+kind of unsustainable.
+
+Now, of course, we said that the
+full problem has, in addition
+
+to this beta H0, a part that
+involves the interaction.
+
+So what I have done is I
+have written the weight
+
+as beta H0 and a part
+that is an interaction.
+
+By interaction, I
+really mean something
+
+that is not solvable within
+the framework of Gaussian.
+
+In our case, what was
+non-solvable is essentially
+
+anything-- and there
+is infinity of terms--
+
+that don't have
+second-order powers of m.
+
+So we wrote terms like m to
+the fourth, m to the sixth,
+
+and so forth.
+
+Now, the key to being
+able to solve this problem
+
+was to make a transformation
+to Fourier modes.
+
+So essentially, what
+we did was to write
+
+our m of x as a sum
+over Fourier modes.
+
+You could write it, let's
+say, in the discrete form as e
+
+to the i q dot x.
+
+And whether I write e to
+the i q dot x or minus i q
+
+dot x is not as
+important as long as I'm
+
+consistent within
+one session at least.
+
+And the normalization
+that I used was 1 over V.
+
+And the reason I used
+this normalization was
+
+that if I went to the
+continuum, I could write it
+
+nicely as an integral
+over q divided
+
+by the density of states.
+
+The V would disappear.
+
+e to the i q x m tilde of q.
+
+Now in particular if I
+do that transformation,
+
+the Gaussian part simply
+becomes 1 over V sum over q.
+
+Then the Fourier
+transform of this kernel t
+
+plus k q squared and so forth
+divided by 2 m of q discrete
+
+squared.
+
+Which if I go to the
+continuum limit simply
+
+becomes an integral
+over q t plus k q
+
+squared and so forth
+over 2 m of q squared.
+
+Now, once I have the Gaussian
+weight, from the Gaussian
+
+weight I can calculate
+various averages.
+
+And the averages
+are best described
+
+by noting that essentially
+after this transformation
+
+I can also write my weight as a
+product over the contributions
+
+of the different modes of
+something that is of this form,
+
+e to the minus beta H0.
+
+Now written in terms
+of these q modes,
+
+clearly it's a product of
+independent contributions.
+
+And then of course, there will
+be the u to be added later on.
+
+But when I have a product
+of independent contributions
+
+for each q, I can immediately
+see that if I look at,
+
+say, m evaluated for
+some q, m evaluated
+
+for some different q
+with the Gaussian weight.
+
+And when I calculate things
+with the Gaussian weight,
+
+I put this index 0.
+
+So that's my 0 to order or
+exactly solvable theory.
+
+And of course, we are
+dealing here with a vector.
+
+So these things have
+indices alpha and beta
+
+associated with them.
+
+And if I look at the
+discrete version,
+
+I have a product over
+Gaussians for each one of them.
+
+Clearly, I will
+get 0 unless I am
+
+looking at the same components.
+
+And I'm looking at the same q.
+
+And in particular,
+the constraint really
+
+is that q plus q prime
+should add up to 0.
+
+And if those constraints
+are satisfied,
+
+then I am looking at
+the particular term
+
+in this Gaussian.
+
+And the expectation
+value of m squared
+
+is simply the variance
+that we can see
+
+is V divided by t plus k q
+squared, q to the fourth,
+
+and so forth.
+
+And the thing is that most
+of the time we will actually
+
+be looking at things directly
+in the limit of the continuum
+
+where we replace sums q's
+with integrals over q.
+
+And then we have to replace
+this discrete delta function
+
+with a continuum delta function.
+
+And the procedure to
+do that is that this
+
+becomes delta alpha beta.
+
+This combination
+gets replaced by 2 pi
+
+to the d delta function
+q plus q prime,
+
+where this is now a
+direct delta function
+
+t plus k q squared plus l q
+to the fourth and so forth.
+
+And the justification
+for doing that is simply
+
+that the Kronecker
+delta is defined such
+
+that if I sum over, let's
+say, all q, the delta that
+
+is Kronecker, the
+answer would be 0.
+
+Now, if I go to the
+continuum limit,
+
+the sum over q I have to
+replace with integral over q
+
+with a density of states, which
+is V divided by 2 pi to the d.
+
+So if I want to replace
+this with a continuum delta
+
+function of q, I have to get rid
+of this 2 pi to the d over V.
+
+And that's what I have done.
+
+So basically, you
+replace-- hopefully I
+
+didn't make a mistake.
+
+Yes.
+
+So the discrete delta I
+replace with 1 over V. The V
+
+disappears and the 2
+pi to the d appears.
+
+OK?
+
+Now, the thing that
+makes some difficulty
+
+is that whereas the rest of
+these things that we have not
+
+included as part
+of the Gaussian,
+
+because of the locality I
+could write reasonably simply
+
+in the space x.
+
+When I go to the space q,
+it becomes complicated.
+
+Because each m of x
+here I have to replace
+
+with a sum or an integral.
+
+And I have four of those m's.
+
+So here, let's say for the
+first term that involves u,
+
+I have in principle to go
+over an integral associated
+
+with conversion of the first
+m, conversion of the second m,
+
+third m.
+
+Each one of them will carry
+a factor of 2 pi to the d.
+
+So there will be three of them.
+
+And the reason I didn't
+write the fourth one
+
+is because after I do all
+of that transformation,
+
+I will have an integral
+over x of e to the i q1
+
+dot x plus q2 dot x plus
+q3 dot x plus q4 dot x.
+
+So I have an integral
+of e to the i q
+
+dot x where q is the sum
+of the four of them over x.
+
+And that gives me
+a delta function
+
+that ensures the sum of
+the four q's have to be 0.
+
+So basically, one of the
+m's will carry now index q1.
+
+The other will carry index q2.
+
+The third will carry index q3.
+
+The fourth will carry index that
+is minus q1 minus q2 minus q3.
+
+Yes?
+
+AUDIENCE: Does it matter
+which indices for squaring it,
+
+or whatever?
+
+Sorry.
+
+Do you need a subscript
+for alpha and beta?
+
+PROFESSOR: OK.
+
+That's what I was [INAUDIBLE].
+
+So this m to the fourth is
+really m squared m squared,
+
+where m squared is a
+vector that is squared.
+
+So I have to put the indices--
+let's say alpha alpha--
+
+that are summed
+over all possibility
+
+to get the dot product here.
+
+And I have to put
+the indices beta
+
+beta to have the
+dot products here.
+
+OK?
+
+Now when I go to the
+next term, clearly I
+
+will have a whole bunch more
+integrals and things like that.
+
+So the e u terms do not
+look as nice and clean.
+
+They were local in real space.
+
+But when I go to this Fourier
+space, they become non-local.
+
+q's that are all
+over this [INAUDIBLE]
+
+are going to be coupled to each
+other through this expression.
+
+And that's also why it
+is called interaction.
+
+Because in some sense,
+previously each q was a mode
+
+by itself and these terms give
+interactions between modes that
+
+have different q's.
+
+Yes?
+
+AUDIENCE: Is there
+a way to understand
+
+that physically of why you
+get coupling in Fourier space?
+
+[INAUDIBLE] higher
+than [INAUDIBLE].
+
+PROFESSOR: OK.
+
+So essentially, we
+have a system that
+
+has translational symmetry.
+
+So when you have
+translational symmetry,
+
+this Fourier vector q is
+a good conserved quantity.
+
+It's like a momentum.
+
+So one thing that we have
+is, in some sense, a particle
+
+or an excitation that
+is going by itself
+
+with some particular momentum.
+
+But what these terms represent
+is the possibility that you
+
+have, let's say,
+two of these momenta
+
+coming and interacting
+with each other
+
+and getting two
+that are going out.
+
+Why is it [INAUDIBLE]?
+
+It's partly because
+of the symmetries
+
+that we built into the problem.
+
+If I had written something
+that was m cubed,
+
+I had the possibility
+of 2 going to, 1 or 1
+
+going to 2, et cetera.
+
+All right.
+
+I forgot to say one
+more thing, which
+
+is that for the Gaussian theory,
+I can calculate essentially
+
+all expectation values
+most [INAUDIBLE]
+
+in this context of the
+Fourier representation.
+
+So this was an
+example of something
+
+that had two factors of m.
+
+But very soon, we will see
+that we would need terms
+
+that, let's say, involve
+m factors of n that
+
+are multiplied each other.
+
+So I have m alpha i of
+qi-- something like that.
+
+And again, 0 for the
+Gaussian expectation value.
+
+And if I have written things
+the way that I have-- that is,
+
+I have no magnetic field.
+
+So I have m2 minus
+m symmetry, clearly
+
+the answer is going
+to be 0 if l is odd.
+
+If l is even, we have this
+nice property of Gaussians
+
+that we described
+in 8.333, which
+
+is that this will be the sum
+over all pairs of averages.
+
+So something like
+m1, m2, m3, m4.
+
+You can have m1 m2
+multiplying by m3 m4 average.
+
+m1 m3 average multiply
+m2 m4 average.
+
+m1 m4 average multiplied
+by m2 m3 average.
+
+And this is what's called
+a Wick's theorem, which
+
+is an important property of
+the Gaussian that we will use.
+
+So we know how to calculate
+averages of things of interest,
+
+which are essentially product
+of these factors of m,
+
+in the Gaussian theory.
+
+Now let's calculate
+these averages
+
+in perturbation theory.
+
+So quite generally, if I want to
+calculate the average of some O
+
+in a theory that involves
+averaging over some function
+
+l-- so this could be some
+trace, some completely
+
+unspecified things-- of a
+weight that is like, say,
+
+e to the minus beta H0.
+
+A part that I can
+do and a part that I
+
+want to treat as a small
+change to what I can do.
+
+The procedure of
+calculating the average
+
+is to multiply the
+probability by the quantity
+
+that I want to average.
+
+And of course, the whole thing
+has to be properly normalized.
+
+And this is the normalization,
+which is the partition function
+
+that we had previously.
+
+Now, the whole idea
+of perturbation
+
+is to assume that this
+quantity u is small.
+
+So we start to expand
+e to the minus u.
+
+I can certainly do
+that very easily,
+
+let's say, in the denominator.
+
+I have e to the minus
+beta H0, and then I
+
+have 1 minus u plus u squared
+over 2 minus u cubed over 6.
+
+Basically, the usual
+expansion of the exponential.
+
+In the numerator, I
+have the same thing,
+
+except that there is an
+I that is multiplying
+
+this expansion for the
+operator, or the object that I
+
+want to calculate the average.
+
+Now, the first term that I
+have in the denominator here,
+
+1 multiplied by all integrals
+of e to the minus H0
+
+is clearly what I would
+call the partition function,
+
+or the normalization
+that I would
+
+have for the Gaussian weight.
+
+So that's the first term.
+
+If I factor that out,
+then the next term
+
+is u integrated against
+the Gaussian weight
+
+and then properly normalized.
+
+So the next term will be the
+average of u with the Gaussian
+
+or whatever other
+0 to order weight
+
+is that I can calculate things
+and I have indicated that by 0.
+
+And then I would
+have 1/2 average
+
+of u squared 0 and so forth.
+
+And the series in the numerator
+once I factor out the Z0
+
+is pretty much the same except
+that every term will have an o.
+
+The Z 0's naturally
+I can cancel out.
+
+So what I have is
+from the numerator o
+
+minus ou plus 1/2 ou squared.
+
+What I will do with
+the denominator
+
+is to bring it in the
+numerator regarding
+
+all of these as
+a small quantity.
+
+So if I were to essentially
+write this expression raised
+
+to the minus 1 power, I
+can make a series expansion
+
+of all of these terms.
+
+So the first thing, if I
+just had one over 1 minus u
+
+in the denominator,
+it would come
+
+from 1 plus u plus u squared
+and u cubed, et cetera.
+
+But I've only kept thing
+to order of u squared.
+
+So when I then
+correct it because
+
+of this thing in
+the denominator,
+
+the 1/2 becomes minus
+1/2 u squared 0.
+
+And then, there will be
+order of u cubed terms.
+
+So the answer is the
+product of two brackets.
+
+And I can reorganize that
+product, again, in powers of u.
+
+The lowest-order term
+is the 0 to order,
+
+or unperturbed average.
+
+And the first correction
+comes from ou average.
+
+And then I have the
+average of u average of u.
+
+You can see that something
+like a variance or connected
+
+correlation or cumulant
+appears because I
+
+have to subtract
+out the averages.
+
+And then the next order
+term, what will I have?
+
+I will write it as 1/2.
+
+I start with ou squared 0.
+
+Then I can multiply
+this with this,
+
+so I will get minus 2 o u0 u0.
+
+And then I can multiply
+o0 with those two terms.
+
+So I will have minus o0
+u squared 0 plus 2 o0--
+
+this is over here.
+
+u0 squared and
+higher-order terms.
+
+So basically, we can see
+that the coefficients,
+
+as I have written, are going to
+be essentially the coefficients
+
+that I would have if I were
+to expand the exponential.
+
+So things like minus 1 to
+the n over n factorial.
+
+And the leading
+term in all cases
+
+is o u raised to
+the n-th power 0,
+
+out of which are
+subtracted various things.
+
+And the effect of
+those subtractions,
+
+let's say we define
+a quantity which
+
+is likely cumulants that we were
+using in 8.333, which describe
+
+the subtractions that you would
+have to define such an average.
+
+So that's the general structure.
+
+What this really
+means-- and I sometimes
+
+call it cumulant or connected--
+will become apparent
+
+very shortly.
+
+This is the general result.
+
+We have a particular
+case above, which
+
+is this Landau-Ginzburg theory
+perturbed around the Gaussian.
+
+So let's calculate the simplest
+one of our averages, this m
+
+alpha of q m beta of q prime,
+not at the Gaussian level,
+
+but as a perturbation.
+
+And actually, for
+practical reasons,
+
+I will just calculate the
+effect of the first term, which
+
+is u m to the fourth.
+
+So I will expand in powers of u.
+
+But once you see
+that, you would know
+
+how to do it for m to the sixth
+and all the higher powers.
+
+So according to
+what we have here,
+
+the first term is
+m alpha of q m beta
+
+of q prime evaluated
+with the Gaussian theory.
+
+The next term, this one,
+involves the average
+
+of this entity and the u.
+
+So our u I have
+written up there.
+
+So I have minus
+from the first term.
+
+The terms that are
+proportional to u,
+
+I will group together
+coming from here.
+
+u itself involved this
+integration over q1 q2 q3.
+
+And u involves
+this m i of q1 m i
+
+of q2 mj of q3 mj of minus
+q1 minus q2 minus q3.
+
+And I have to multiply it.
+
+So this is u.
+
+I have to multiply it by o.
+
+So I have m alpha of
+q m beta of q prime.
+
+So this is my o.
+
+This is my u.
+
+And I have to take the
+average of this term.
+
+But really, the average
+operates on the m's,
+
+so it will go over here.
+
+So that's the average of ou.
+
+I have to subtract from that
+the average of o average of u.
+
+So let me, again,
+write the next term.
+
+u will be the same
+bunch of integrations.
+
+I have to do average of
+o and then average of u.
+
+This completes my first
+correction coming from u,
+
+and then there will be
+corrections to first order
+
+coming from V. There will be
+second-order corrections coming
+
+from u squared,
+all kinds of things
+
+that will come into play.
+
+But the important thing, again,
+to realize is the structure.
+
+u is this thing that
+involves four factors of m.
+
+The averages are
+over the m, so I
+
+can take them
+within the integral.
+
+And so I have one case which
+is an expectation value of six
+
+m's.
+
+Another case, a product of
+two and a product of four.
+
+So that's why I
+said I would need
+
+to know how to calculate
+in the Gaussian theory
+
+product of various factors
+of m because my interaction
+
+term involves various powers
+of m that will be added
+
+to whatever expectation value
+I'm calculating perturbation
+
+theory.
+
+So how do I calculate
+an expectation
+
+that involves six factors--
+certainly, it's even-- of m?
+
+I have to group-- make
+all possible pairings.
+
+So this, for example,
+can be paired to this.
+
+This can be paired to this.
+
+This can be paired to this.
+
+That's a perfectly
+well-defined average.
+
+But you can see
+that if I do this,
+
+if I pair this one,
+this one, this one,
+
+I will get something that will
+cancel out against this one.
+
+So basically, you can
+see that any way that I
+
+do averaging that involves only
+things that are coming from o
+
+and separately the
+things that come from u
+
+will cancel out with the
+corresponding-- oops.
+
+With the corresponding
+averages that I do over here.
+
+That c stands for connected.
+
+So the only things that survive
+are pairings or contractions
+
+that pick something
+that is from o
+
+and connect it to
+something that is from u.
+
+And the purpose of all of
+these other terms at all higher
+
+orders is precisely
+to remove pieces
+
+where you don't have full
+connections among all
+
+of the o's and the u's
+that you are dealing with.
+
+So let's see what this is.
+
+So I will show you that using
+connections that involve both o
+
+and u, I will have two types of
+contractions joining o and u.
+
+The first type is
+something like this.
+
+I will, again, draw all-- or
+write down all of the fours.
+
+So I have m alpha of q m beta of
+q prime m i of q1 m i of q2 mj
+
+of q3 mj of minus q1
+minus q2 minus q3.
+
+I have to take that average.
+
+And I do that the
+average according
+
+to Wick's theorem as a
+product of contractions.
+
+So let's pick this m alpha.
+
+It has to ultimately be
+paired with somebody.
+
+I can't pair it with
+m beta because that's
+
+a self-contraction and
+will get subtracted out.
+
+So I can pick any
+one of these fours.
+
+As far as I'm concerned,
+all four are the same,
+
+so I have a choice of four
+as to which one of these four
+
+operators from u I connect to.
+
+So that 4 is one of
+the numerical factors
+
+that ultimately we
+have to take care of.
+
+Then, the two types
+comes because the next m
+
+that I pick from o I
+have two possibilities.
+
+I can connect it either with the
+partner of the first one that
+
+also carries index
+i or I can connect
+
+to one of the things that
+carries the opposite index j.
+
+So let's call type 1 where
+I make the choice that I
+
+connect to the partner.
+
+And once I do that,
+then I am forced
+
+to connect these two together.
+
+Now, each one of these pairings
+connects one of these averages.
+
+So I can write
+down what that is.
+
+So the first one connected an
+alpha to an i as far as indices
+
+were concerned.
+
+It connected q to q1, so I have
+2 pi to the d a delta function
+
+q plus q1.
+
+And the variance
+associated with that,
+
+which is t plus k q
+squared, et cetera.
+
+The second pairing
+connects a beta to an i.
+
+So that's a delta beta i.
+
+And it connects q prime to q2.
+
+And so the variance
+associated with that
+
+is t plus k q prime
+squared and so forth.
+
+And finally, the third pairing
+connects j to itself j.
+
+So I will get a delta jj.
+
+And then I have 2 pi to the d.
+
+q3 to minus q1
+minus q2 minus q3.
+
+So I will get minus
+q1 minus q2, and then
+
+I have t plus, say, k
+q3 squared and so forth.
+
+Now, what I am supposed to
+do is at the next stage,
+
+I have to sum over indices i and
+j and integrate over q1 q2 q3.
+
+So when I do that,
+what do I get?
+
+There is an overall
+factor of minus u.
+
+Let's do the indices.
+
+When I sum over i, delta
+alpha i delta beta i
+
+becomes-- actually, let
+me put the factor of 4
+
+before I forget it.
+
+There is a factor
+of 4 numerically.
+
+Delta alpha i delta beta i will
+give me a delta alpha beta.
+
+When I integrate over
+q1, q1 is set to minus q.
+
+So this after the
+integration becomes q.
+
+When I integrate
+over q2, the delta
+
+function q2 forces
+minus q2 to be q prime.
+
+And through the process, two of
+these factors of 2 pi to the d
+
+disappear.
+
+So what I'm left with
+is 2 pi to the d.
+
+This delta function now
+involves q plus q prime.
+
+And then in the denominator,
+I have this factor of t
+
+plus k q squared.
+
+I have t plus k q prime squared.
+
+Although, q prime squared
+and q squared are the same.
+
+I could have collapsed
+these things together.
+
+I have one integration
+left over q3.
+
+And these two
+factors went outside
+
+the integral [INAUDIBLE]
+independent q3.
+
+The only thing
+that depends on q3
+
+is t plus k q3
+squared and so forth.
+
+So that was easy.
+
+AUDIENCE: I have a question.
+
+PROFESSOR: Yes.
+
+AUDIENCE: If you're summing
+over j, won't you get an n?
+
+PROFESSOR: Thank you very much.
+
+I forgot the delta jj.
+
+Summing over j, I will
+get a factor of n.
+
+So what I had written
+here as 4 should be 4n.
+
+Yes.
+
+AUDIENCE: This may be a
+question too far back.
+
+But when you write a correlation
+between two different m's,
+
+why do you write
+delta function of q
+
+plus q prime instead
+of q minus q prime?
+
+PROFESSOR: OK.
+
+Again, go back all
+the way to here
+
+when we were doing
+the Gaussian integral.
+
+I will have for
+the first one, q1.
+
+For the second m,
+I will write q2.
+
+So when I Fourier
+transform this term,
+
+I will have e to the
+i q1 plus q2 dot x.
+
+And then when I
+integrate over x,
+
+I will get a delta
+function q1 plus q2.
+
+So that's why I write all
+of these as absolute value
+
+squared because I
+could have written this
+
+as m of q m of minus q, but
+I realized that m of minus q
+
+is the complex
+conjugate of m of q.
+
+So all of these are
+absolute values squared.
+
+Now, the second class of
+contraction is-- again,
+
+write the same thing, m alpha of
+q m beta of q prime m i of q1 m
+
+i of q2, mj of q3 mj of
+minus q1 minus q2 minus q3.
+
+The first step is the same.
+
+I pick m alpha of q and I
+have no choice but to pick
+
+one of the four
+possibilities that I have
+
+for the operators
+that appear in u.
+
+But for the second
+one, previously I
+
+chose to connect it
+to something that
+
+was carrying the same index.
+
+Now I choose to
+carry it to something
+
+that carries the other
+index, j in this case.
+
+And there are two things
+that carry index j,
+
+so I have two choices there.
+
+And then I have the remaining
+two have to be connected.
+
+Yes?
+
+AUDIENCE: Just going
+back a little bit.
+
+Are you assuming that
+your integral over q3
+
+converges because you're
+only integrating over
+
+the [INAUDIBLE] zone?
+
+PROFESSOR: Yes.
+
+AUDIENCE: OK.
+
+PROFESSOR: That's right.
+
+Any time I see a
+divergent integral,
+
+I have a reason to
+go back to my physics
+
+and see why physics
+will avoid infinities.
+
+And in this case, because
+all of my theories
+
+have an underlying length
+scale associated with them
+
+and there is an
+associated maximum value
+
+that I can go in Fourier space.
+
+The only possible
+singularities that I
+
+want to get are coming
+from q goes to 0.
+
+And again, if I really want
+to physically cut that off,
+
+I would put the
+size of the system.
+
+But I'm interested in systems
+that become infinite in size.
+
+So the first term for this
+way of contracting things
+
+is as follows.
+
+There are eight such terms.
+
+I should have really
+put the four here.
+
+There are eight such
+types of contractions.
+
+Then I have a delta alpha
+i 2 pi to the d delta
+
+function q plus q1 divided by t
+plus k q squared and so forth.
+
+The first contraction is
+exactly the same as before.
+
+The next contraction I connect
+i to j and q prime to q3.
+
+So I have a delta beta j 2
+pi to the d delta function q
+
+prime going to q3 divided
+by t plus k q prime squared
+
+and so forth.
+
+And the last contraction
+connects an i to a j.
+
+Delta ij.
+
+I have 2 pi to the d.
+
+Connecting q2 to minus
+q1 minus q2 minus q3
+
+will give me a delta function
+which is minus q1 minus q3.
+
+And then I have t plus k-- I
+guess in this case-- q2 squared
+
+and so forth.
+
+So once more sum ij.
+
+Integrate q1 q2 q3 and
+let's see what happens.
+
+So again, it's a term that
+is proportional to minus u.
+
+The numerical coefficient
+that it carries is 8.
+
+And there is no n here
+because when I sum over i,
+
+you can see that j is set
+to be the same as alpha.
+
+Then when I sum over j, I set
+alpha to be the same as beta.
+
+So there is just a
+delta alpha beta.
+
+When I integrate over
+q1, q1 is set to minus q.
+
+q3 is set to minus q prime.
+
+So this factor becomes the
+same as q plus q prime.
+
+And the two variances,
+which are in fact the same,
+
+I can continue to write
+as separate entities
+
+but they're really
+the same thing.
+
+And then the one
+integral that is
+
+left-- I did q1 and Q3--
+it's the integral over q2,
+
+2 pi to the d 1 over t plus
+K q2 squared and so forth.
+
+It is, in fact, exactly
+the same integral
+
+as before, except that the
+name of the dummy integration
+
+variable has changed from
+q2 to q3, or q3 to q2.
+
+So we have calculated m
+alpha of q m beta of q prime
+
+to the lowest order in
+perturbation theory.
+
+To the first order, what I
+had was a delta alpha beta 2
+
+pi to the d delta function
+q plus q prime divided by t
+
+plus k q squared.
+
+Now, note that all
+of these factors
+
+are present in the
+two terms that I
+
+had calculated as corrections.
+
+So I can factor this
+out and write it
+
+as the correction as 1
+plus or minus something.
+
+It is proportional to u.
+
+The coefficient is
+4n plus 8, which
+
+I will write as 4 n plus 2.
+
+I took out one factor
+of t plus k q squared.
+
+There is one factor
+that's will be remaining.
+
+Therefore, t plus k q squared.
+
+And then I have one
+integration over some variable.
+
+Let's call it k.
+
+It doesn't matter what I call
+the integration variable.
+
+1 over t plus k, k
+squared, and so forth.
+
+And presumably, there will
+be higher-order terms.
+
+Now again, I did the
+calculation specifically
+
+for the Landau-Ginzburg,
+but the procedure you
+
+would have been able to
+do for any field theory.
+
+You could have
+started with a part
+
+that you can solve
+exactly and then
+
+look at perturbations
+and corrections.
+
+Now, there is, in
+fact, a reason why
+
+this correction
+that we calculated
+
+had exactly the same
+structure of delta functions
+
+as the original one.
+
+And why I anticipate that
+higher-order terms, if I were
+
+to calculate, will
+preserve that structure.
+
+And the reason has to
+do with symmetries.
+
+Because quite generally, I
+can write for anything-- m
+
+alpha m beta of q prime without
+doing perturbation theory.
+
+Again, let's remember
+m alphas of q
+
+are going to be related to
+m of x by inverse Fourier
+
+transformation.
+
+So m alpha of q I can write
+an integral d dx e to the-- I
+
+guess by that convention, it
+has to be minus i q dot x.
+
+m alpha of x.
+
+And again, m beta
+of q prime I can
+
+write as minus i q
+prime dot x prime.
+
+And I integrate
+also over an x prime
+
+of m alpha of x m
+beta of x prime.
+
+Now, these are evaluated in
+real space as opposed to Fourier
+
+space.
+
+And the average goes over here.
+
+At this stage, I
+don't say anything
+
+about perturbation theory,
+Gaussian, et cetera.
+
+What I expect is that
+this is a function,
+
+that in a system that has
+translational symmetry, only
+
+depends on x minus x prime.
+
+m beta.
+
+Furthermore, in a system that
+has rotational symmetry that
+
+is not spontaneously
+broken, that
+
+is approaching from the
+high temperature side,
+
+then just rotational
+symmetry forces you
+
+that-- the only
+tensor that you have
+
+has to be proportional
+to delta alpha beta.
+
+So I can pick some particular
+component-- let's say m1--
+
+and I can write it
+in this fashion.
+
+So the rotational symmetry
+explains the delta alpha beta.
+
+Now, knowing that the function
+that I'm integrating over two
+
+variables actually only depends
+on the relative position
+
+means that I can re-express
+this in terms of the relative
+
+and center of mass coordinates.
+
+So I can express
+that expression as e
+
+to the minus i q minus q
+prime x minus x prime over 2.
+
+And then I will
+write it as minus i
+
+q plus q prime x
+plus x prime over 2.
+
+If you expand those, you will
+see that all of the cross terms
+
+will vanish and I will get q
+dot x and q prime dot x prime.
+
+Yes.
+
+AUDIENCE: [INAUDIBLE]?
+
+PROFESSOR: Yes.
+
+Thank you.
+
+So now I can change
+integration variables
+
+to the relative coordinate and
+the center of mass coordinate
+
+rather than integrating
+over x and x prime.
+
+The integration over the
+center of mass, the x plus x
+
+prime variable, couples
+to q plus q prime.
+
+So it will immediately
+tell me that the answer has
+
+to be proportional
+to q plus q prime.
+
+I had already established that
+there is a delta alpha beta.
+
+So the only thing that is
+left is the integration
+
+over the relative coordinate
+of e to the minus i
+
+some q-- either one of them.
+
+q dot r.
+
+Since q prime is minus q,
+I can replace it with e
+
+to the i q dot the
+relative coordinate.
+
+m1 of r m1 of 0.
+
+So that's why for a system
+that has translational symmetry
+
+and rotational
+symmetry, this structure
+
+of the delta functions
+is really imposed
+
+for this type of
+expectation value.
+
+Naturally, perturbation
+theory has to obey that.
+
+But then, this is a quantity
+that we had encountered before.
+
+If you recall when
+we were scattering
+
+light out of the
+system, the amplitude
+
+of something that was
+scattered was proportional
+
+to the Fourier transform of
+the correlation function.
+
+And furthermore,
+in the limit where
+
+S is evaluated for q equal
+to 0, what we are doing
+
+is we're essentially integrating
+the correlation function.
+
+We've seen that the integrals
+of correlation function
+
+correspond to the
+susceptibilities.
+
+So you may have thought
+that what I was calculating
+
+was a two-point correlation
+function in perturbation
+
+theory.
+
+But what I was
+actually leading up to
+
+is to know what the
+result is for scattering
+
+from this theory.
+
+And in some limit
+of it, I've also
+
+calculated what the
+susceptibility is,
+
+how the susceptibility
+is corrected.
+
+And again, if you recall
+the typical structure
+
+that people see for
+S of q is that S of q
+
+is something like 1 over
+something like this.
+
+This is the
+Lorentzian line shapes
+
+that we had in scattering.
+
+And clearly, the
+Lorentzian line shape
+
+is obtained by Fourier
+transformation and expectation
+
+values of these
+expansions that we make.
+
+So it kind of makes
+sense that rather
+
+than looking at this quantity,
+I should look at its inverse.
+
+So I have calculated
+s of q, which
+
+is the formula that
+I have up there.
+
+So this whole thing
+here is S of q.
+
+If I calculate its
+inverse, what do I get?
+
+First of all, I
+have to invert this.
+
+I have t plus k q squared, which
+is what would have given me
+
+the Lorentzian if I
+were to invert it.
+
+And now we have found the
+correction to the Lorentzian
+
+if you like, which
+is this object raised
+
+to the power of minus 1.
+
+But recall that I've
+only calculated things
+
+to lowest order in u.
+
+So whenever I see something
+and I'm inverting it
+
+just like I did
+over here, I better
+
+be consistent to order of u.
+
+So to order of u, I can take
+this thing from the numerator,
+
+bring it to the num--
+from denominator
+
+to numerator at the expense
+of just changing the sign.
+
+Order of u squared
+that we haven't really
+
+bothered to calculate.
+
+So now it's nice because you
+can see that when I expand this,
+
+this factor will
+cancel that factor.
+
+So the inverse has the
+structure that we would like.
+
+It is t plus something
+that is a constant,
+
+doesn't depend on
+q, 4 n plus 2 u.
+
+Well, actually, no.
+
+Yeah.
+
+Because this denominator
+gets canceled.
+
+I will get 4 n plus 2
+u integral over k 2 pi
+
+to the d 1 over t plus k
+k squared and so forth.
+
+And then I have my k q squared.
+
+And presumably, I will
+have higher-order terms
+
+both in u and higher
+powers of q, et cetera.
+
+And in particular, the
+inverse of the susceptibility
+
+is simply the first part.
+
+Forget about the k q squared.
+
+So the inverse of
+susceptibility is
+
+t plus 4 n plus 2 u integral
+d dk 2 pi to the d 1 over t
+
+plus k k squared and so forth.
+
+Plus order of things
+that we haven't computed.
+
+So why is it interesting
+to look at susceptibility?
+
+Because susceptibility is
+one of the quantities--
+
+it always has to be positive--
+that we were associating
+
+previously with
+singular behavior.
+
+And in the absence of the
+perturbative correction
+
+from the Gaussian,
+the susceptibility
+
+we calculated many times.
+
+It was simply 1 over t.
+
+If I had added a
+field, the field h
+
+would have changed
+the free energy
+
+by an amount that would be
+h squared over 2t as we saw.
+
+Take two derivatives,
+I will get 1
+
+over t for the susceptibility.
+
+So the 0 order sustainability
+that I will indicate by chi sub
+
+0 was something that was
+diverging at t equals to 0.
+
+And we were identifying
+the critical exponent
+
+of the divergence as
+gamma equals to 1.
+
+So here, I would have
+added gamma 0 equals to 1.
+
+Because of the
+linear divergence--
+
+and the linear divergence
+can be traced back
+
+to the linearity
+of the vanishing
+
+of the inverse susceptibility
+at temperature.
+
+Now, let's see whether we
+have calculated a correction
+
+to gamma.
+
+Well, the first
+thing that you notice
+
+that if I evaluated the new chi
+inverse at 0, all I need to do
+
+is to put 0 in this formula.
+
+I will get 4 n plus 2 u.
+
+This integral d dk 2 pi to
+the d 1 over k k squared.
+
+I set t equals to 0 here.
+
+Now this is, indeed, an integral
+that if I integrate all the ay
+
+to infinity would diverge on me.
+
+I have to put an upper cutoff.
+
+It's a simple integral.
+
+I can write it as
+integral 0 to lambda dk
+
+k to the d minus 1 with some
+surface of a d dimensional
+
+sphere.
+
+I have this 2 pi
+to the d out front
+
+and I have a k squared here.
+
+I can put the k out here.
+
+So you can see that this is an
+integral that's just a power.
+
+I can simply do that.
+
+The answer ultimately will be
+4 n plus 2 u Sd 2 pi to the d.
+
+There is a factor of 1 over
+k that comes into play.
+
+The integral of
+this will give me
+
+the upper cutoff to the d
+minus 2 divided by d minus 2.
+
+So what we find is that the
+corrected susceptibility
+
+to lowest order does not
+diverge at t equals to 0.
+
+Its inverse is a finite value.
+
+So actually, you
+can see that I've
+
+added something positive
+to the denominator
+
+so the value of susceptibility
+is always reduced.
+
+So what does that mean?
+
+Does that mean that the
+susceptibility does not
+
+have a singularity anymore?
+
+The answer is no.
+
+It's just that the location of
+the singularity has changed.
+
+The presence of
+u m to the fourth
+
+gives some additional stiffness
+that you have to overcome.
+
+t equals to 0 is not
+sufficient for you.
+
+You have to go to
+some other point tc.
+
+So I expect that this
+thing will actually
+
+diverge at a new point
+tc that is negative.
+
+And if it diverges, then
+its inverse will be 0.
+
+So I have to solve the
+equation tc plus 4 n
+
+plus 2 u integral d dk 2 pi
+to the d of 1 over tc plus k
+
+k squared and so forth.
+
+So this seems like an implicit
+[INAUDIBLE] equation in tc
+
+because I have to evaluate the
+integral that depends on tc,
+
+and then have to set
+that function to 0.
+
+But again, we have calculated
+things only correctly
+
+to order of u.
+
+And you can see already that
+tc is proportional to u.
+
+So this answer here is something
+that is order of u presumably.
+
+And a u compared
+to the u out front
+
+will give me a correction
+that is order of u squared.
+
+So I can ignore this
+thing that is over here.
+
+So to order of u, I know
+that tc is actually minus
+
+what I had calculated before.
+
+So I get that tc is
+minus this 4 n plus 2 u k
+
+Sd lambda to the d minus
+2 2 pi to the d d minus 2.
+
+It doesn't matter what it is,
+it's some non-universal value.
+
+Point is that, again,
+the location of the phase
+
+transition certainly will
+depend on the parameters
+
+that you put in your theory.
+
+We readjusted our theory
+by putting m to the fourth.
+
+And certainly, that will change
+the location of the transition.
+
+So this is what we found.
+
+The location of the
+transition is not universal.
+
+However, we kind
+of hope and expect
+
+that the singularity, the
+divergence of susceptibility
+
+has a form that is universal.
+
+There is an exponent that
+is characteristic of that.
+
+So asking the question of
+how these corrected chi
+
+divergence diverges
+at this tc is the same
+
+as asking the question of how
+its inverse vanishes at tc.
+
+So what I am interested
+is to find out
+
+what the behavior of chi inverse
+is in the vicinity of the point
+
+that it goes to 0.
+
+So basically, what
+this singularity is.
+
+This is, of course, 0.
+
+By definition, chi
+inverse of tc is 0.
+
+So I am asking how chi vanishes
+its inverse when I approach tc.
+
+So I have the formula for
+chi once I substitute t,
+
+once I substitute tc
+and I subtract them.
+
+To lowest order I
+have t minus tc.
+
+To next order, I have this 4 u
+n plus 2 integral over k 2 pi
+
+to the d.
+
+I have for chi inverse of t 1
+over t plus k k squared minus 1
+
+over tc plus k k squared.
+
+And terms that I
+have not calculated
+
+are certainly
+order of u squared.
+
+Now, you can see that
+if I combine these two
+
+into the same denominator
+that is the product,
+
+in the numerator I will
+get a factor of t minus tc.
+
+The k q squareds cancel.
+
+So I can factor out this t
+minus tc between the two terms.
+
+Both terms vanish
+at t equals to tc.
+
+And then I can look at
+what the correction is
+
+to one, just like I did before.
+
+The correction is going
+to-- actually, this
+
+will give me tc minus t,
+so I will have a minus 4 u
+
+n plus 2 integral
+d dk 2 pi to the d.
+
+The product of two of these
+factors, t plus k-- tc plus k k
+
+squared t plus k k squared,
+and then order of u squared.
+
+OK?
+
+Happy with that?
+
+Now again, this tc we've
+calculated is order of u.
+
+And consistently, to calculate
+things to order of u,
+
+I can drop that.
+
+And again, consistently to
+doing things to order of u,
+
+I can add a tc here.
+
+And that's also a correction
+that is order of u.
+
+And this answer
+would not change.
+
+The justification of
+why I choose to do that
+
+will become apparent
+shortly, but it's consistent
+
+that this is left.
+
+So what I find at
+this stage is that I
+
+need to evaluate an
+integral of this form.
+
+And again, with all
+of these integrals,
+
+we better take a look as to
+what the most significant
+
+contribution to the integral is.
+
+And clearly, if I
+look at k goes to 0,
+
+there are various
+factors out there
+
+that as long as t
+minus tc is positive,
+
+I will have no worries
+because this k squared
+
+will be killed off
+by factors of k
+
+to the d minus 1 in
+dimensions above 2.
+
+But if I go to large
+k-values, I find
+
+that large k-values,
+the singularity
+
+is governed by k to
+the power of d minus 4.
+
+So as long as I'm
+dealing with things
+
+that have some upper
+cutoff, I don't
+
+have to worry about it even
+in dimensions greater than 4.
+
+In dimensions
+greater than 4, what
+
+happens is that the
+integral is going
+
+to be dominated by the
+largest values of k.
+
+But those largest values of
+k will be cutoff by lambda.
+
+The answer ultimately
+will be proportional to 1
+
+over k squared, and then k
+to the power of d minus 4
+
+replaced by lambda
+to the d minus 4--
+
+various overall coefficient
+of d minus 4 or whatever.
+
+It doesn't matter.
+
+On the other hand, if you go
+to dimensions less than 4--
+
+again, larger than
+2, but I won't
+
+write that for the time being--
+then the behavior at large k
+
+is perfectly convergent.
+
+So you are integrating
+a function that goes up,
+
+comes down.
+
+You can extend the integration
+all the way to infinity,
+
+end up with a definite integral.
+
+We can rescale all
+of our factors of k
+
+to find out what that definite
+integral is dependent on.
+
+And essentially, what it does
+is it replaces this lambda
+
+with the characteristic value
+of k that corresponds roughly
+
+to the maximum.
+
+And that's going to
+occur at something
+
+like t minus tc over
+k to the power of 1/2.
+
+So I will get d minus 4 over 2.
+
+There is some overall definite
+integral that I have to do,
+
+which will give me some
+numerical coefficient.
+
+But at this time,
+let's forget about
+
+the numerical coefficient.
+
+Let's see what the structure is.
+
+So the structure then
+is that chi inverse
+
+of t, the singularity
+that it has
+
+is t minus tc to the 0 order.
+
+Same thing as you would have
+predicted for the Gaussian.
+
+And then we have a
+correction, which
+
+is this minus something that
+goes after all of these things
+
+with some coefficient.
+
+I don't care what
+that coefficient is.
+
+u n plus 2 divided by k squared.
+
+And then multiplied by lambda
+to the power of d minus 4,
+
+or t minus tc over k to the
+power of d minus 4 over 2.
+
+And then presumably,
+higher-order terms.
+
+And whether you have
+the top or the bottom
+
+will depend on d greater
+than 4 or d less than 4.
+
+So you see the problem.
+
+If I'm above four
+dimensions, this term
+
+is governed by the upper cutoff.
+
+But the upper cutoff
+is just some constant.
+
+So all that happens
+is that the dependence
+
+remains as being
+proportional to t minus tc.
+
+The overall amplitude
+is corrected
+
+by something that depends on u.
+
+You are not worried.
+
+You say that the leading
+singularity is the same thing
+
+as I had before.
+
+Gamma will stay to be 1.
+
+I try to do that in less
+than four dimensions
+
+and I find that as I approach
+tc, the correction that I had
+
+actually itself
+becomes divergent.
+
+So now I have to throw out
+my entire perturbation theory
+
+because I thought I was making
+an expansion in quantity
+
+that I can make
+sufficiently small.
+
+So in usual perturbation
+theory, you say
+
+choose epsilon less than 10
+to the minus 100, or whatever,
+
+and then things will
+be small correction
+
+to what you had at 0 order.
+
+Here, I can choose my u
+to be as small as I like.
+
+Once I approach tc, the
+correction will blow up.
+
+So this is called a divergent
+perturbation theory.
+
+Yes.
+
+AUDIENCE: So could we have
+known a priori that we couldn't
+
+get a correction to gamma
+from the perturbation theory
+
+because the only way
+for gamma to change
+
+is for the correction
+to have a divergence?
+
+PROFESSOR: You are presuming
+that that's what happens.
+
+So indeed, if you
+knew that there
+
+is a divergence with an exponent
+that is larger than gamma,
+
+you probably could
+have guessed that you
+
+wouldn't get it this way.
+
+Let's say that we are choosing
+to proceed mathematically
+
+without prior knowledge of what
+the experimentalists have told
+
+us, then we can
+discover it this way.
+
+AUDIENCE: I was
+thinking if you're
+
+looking for how gamma changes
+due to the higher-order things,
+
+if we found that our
+perturbation diverged
+
+with a lower
+exponent than gamma,
+
+then the leading one
+would still be there,
+
+original gamma would be gone.
+
+PROFESSOR: Yes.
+
+AUDIENCE: And then
+if it's higher,
+
+then we have the same problem.
+
+PROFESSOR: That's right.
+
+So the problem that
+we have is actually
+
+to somehow make sense of this
+type of perturbation theory.
+
+And as you say, it's correct.
+
+We could have actually guessed.
+
+And I'll give you another
+reason why the perturbation
+
+theory would not have worked.
+
+But the only thing
+that we can really do
+
+is perturbation
+theory, so we have
+
+to be clever and figure
+out a way of making sense
+
+of this perturbation theory,
+which we will do by combining
+
+it with the normalization group.
+
+But a better way or another
+way to have seen maybe
+
+why this does not work is
+good old-fashioned dimensional
+
+analysis.
+
+I have within the exponent of
+the weight that I wrote down
+
+terms that are of this formula,
+t m squared k gradient of m
+
+squared u m to the
+fourth and so forth.
+
+Since whatever is in
+the exponent should
+
+be dimensionless-- I usually
+write beta H for example--
+
+we know that this t
+has some dimension.
+
+Square the dimension of m
+multiplied by length to the d.
+
+This should be dimensionless.
+
+Similarly, k m squared again.
+
+Because of the gradient
+l to the d minus 2,
+
+that combination should
+be dimensionless.
+
+And my u m to the fourth l to
+the d should be dimensionless.
+
+So we can get rid of the
+dimensions of m by dividing,
+
+let's say, u m to the fourth
+with the square of k m squared.
+
+So we can immediately
+see that u divided by k
+
+squared, I get rid of
+the dimensions of m.
+
+l to the power of d
+l to the 2d minus 4,
+
+giving me l to the 4
+minus d is dimensionless.
+
+So any perturbation theory that
+I write down ultimately where
+
+I have some quantity x,
+which is at 0 order 1,
+
+and then I want to make a
+correction where u appears,
+
+I should have
+something, u over k
+
+squared, and then some power of
+length to make the dimensions
+
+work out.
+
+So what lengths do I
+have available to me?
+
+One length that I have is
+my microscopic length a.
+
+So I could have put here a
+to the power of 4 minus d.
+
+But there is also
+an emergent length
+
+in the problem, which is
+the correlation length.
+
+And there is no reason why
+the dimensionless form that
+
+involves the correlation
+length should not appear.
+
+And indeed, what we have
+over here to 0 order,
+
+our correlation length had
+the exponent 1/2 divergence.
+
+So this is really the 0
+order correlation length
+
+that is raised to the
+power of 4 minus d.
+
+So even before doing
+the calculation,
+
+we could have guessed
+on dimensional ground
+
+that it is quite possible
+that we are expanding in u,
+
+we think.
+
+But at the end of the day,
+we are expanding in u c
+
+to the power of 4 minus d.
+
+And there is no way that that's
+a small quantity on approaching
+
+the phase transition.
+
+And that hit us on
+the face and also is
+
+the reason why I replaced this
+t over here with t minus tc
+
+because the only place where I
+expect singularities to emerge
+
+in any of these
+expansions is at tc.
+
+I arranged things so they would
+appear at the right place.
+
+So should we throw out
+perturbation theory completely
+
+since the only
+thing that we can do
+
+is really perturbation theory?
+
+Well, we have to
+be clever about it.
+
+And that's what we
+will do next lectures.
\ No newline at end of file
diff --git a/0OX-DkYPB3c.txt b/0OX-DkYPB3c.txt
new file mode 100644
index 0000000000000000000000000000000000000000..edb4ac12ba30422b68f366499e686d96d502db34
--- /dev/null
+++ b/0OX-DkYPB3c.txt
@@ -0,0 +1,228 @@
+One of the biggest and slowest circuits in
+an arithmetic and logic unit is the multiplier.
+
+We'll start by developing a straightforward
+implementation and then, in the next section,
+
+look into tradeoffs to make it either smaller
+or faster.
+
+Here's the multiplication operation for two
+unsigned 4-bit operands broken down into its
+
+component operations.
+
+This is exactly how we learned to do it in
+primary school.
+
+We take each digit of the multiplier (the
+B operand) and use our memorized multiplication
+
+tables to multiply it with each digit of the
+multiplicand (the A operand),
+
+dealing with any carries into the next column
+as we process the multiplicand right-to-left.
+
+The output from this step is called a partial
+product and then we repeat the step for the
+
+remaining bits of the multiplier.
+
+Each partial product is shifted one digit
+to the left, reflecting the increasing weight
+
+of the multiplier digits.
+
+In our case the digits are just single bits,
+i.e., they're 0 or 1 and the multiplication
+
+table is pretty simple!
+
+In fact, the 1-bit-by-1-bit binary multiplication
+circuit is just a 2-input AND gate.
+
+And look Mom, no carries!
+
+The partial products are N bits wide since
+there are no carries.
+
+If the multiplier has M bits, there will be
+M partial products.
+
+And when we add the partial products together,
+we'll get an N+M bit result if we account
+
+for the possible carry-out from the high-order
+bit.
+
+The easy part of the multiplication is forming
+the partial products - it just requires some
+
+AND gates.
+
+The more expensive operation is adding together
+the M N-bit partial products.
+
+Here's the schematic for the combinational
+logic needed to implement the 4x4 multiplication,
+
+which would be easy to extend for larger multipliers
+(we'd need more rows) or larger multiplicands
+
+(we'd need more columns).
+
+The M*N 2-input AND gates compute the bits
+of the M partial products.
+
+The adder modules add the current row's partial
+product with the sum of the partial products
+
+from the earlier rows.
+
+Actually there are two types of adder modules.
+
+The full adder is used when the modules needs
+three inputs.
+
+The simpler half adder is used when only two
+inputs are needed.
+
+The longest path through this circuit takes
+a moment to figure out.
+
+Information is always moving either down a
+row or left to the adjacent column.
+
+Since there are M rows and, in any particular
+row, N columns, there are at most N+M modules
+
+along any path from input to output.
+
+So the latency is order N, since M and N differ
+by just some constant factor.
+
+Since this is a combinational circuit, the
+throughput is just 1/latency.
+
+And the total amount of hardware is order
+N^2.
+
+In the next section, we'll investigate how
+to reduce the hardware costs, or, separately,
+
+how to increase the throughput.
+
+But before we do that, let's take a moment
+to see how the circuit would change if the
+
+operands were two's complement integers instead
+of unsigned integers.
+
+With a two's complement multiplier and multiplicand,
+the high-order bit of each has negative weight.
+
+So when adding together the partial products,
+we'll need to sign-extend each of the N-bit
+
+partial products to the full N+M-bit width
+of the addition.
+
+This will ensure that a negative partial product
+is properly treated when doing the addition.
+
+And, of course, since the high-order bit of
+the multiplier has a negative weight, we'd
+
+subtract instead of add the last partial product.
+
+Now for the clever bit.
+
+We'll add 1's to various of the columns and
+then subtract them later, with the goal of
+
+eliminating all the extra additions caused
+by the sign-extension.
+
+We'll also rewrite the subtraction of the
+last partial product as first complementing
+
+the partial product and then adding 1.
+
+This is all a bit mysterious but…
+
+Here in step 3 we see the effect of all the
+step 2 machinations.
+
+Let's look at the high order bit of the first
+partial product X3Y0.
+
+If that partial product is non-negative, X3Y0
+is a 0, so all the sign-extension bits are
+
+0 and can be removed.
+
+The effect of adding a 1 in that position
+is to simply complement X3Y0.
+
+On the other hand, if that partial product
+is negative, X3Y0 is 1, and all the sign-extension
+
+bits are 1.
+
+Now when we add a 1 in that position, we complement
+the X3Y0 bit back to 0, but we also get a
+
+carry-out.
+
+When that's added to the first sign-extension
+bit (which is itself a 1), we get zero with
+
+another carry-out.
+
+And so on, with all the sign-extension bits
+eventually getting flipped to 0 as the carry
+
+ripples to the end.
+
+Again the net effect of adding a 1 in that
+position is to simply complement X3Y0.
+
+We do the same for all the other sign-extended
+partial products, leaving us with the results
+
+shown here.
+
+In the final step we do a bit of arithmetic
+on the remaining constants to end up with
+
+this table of work to be done.
+
+Somewhat to our surprise, this isn't much
+different than the original table for the
+
+unsigned multiplication.
+
+There are a few partial product bits that
+need to be complemented, and two 1-bits that
+
+need to be added to particular columns.
+
+The resulting circuitry is shown here.
+
+We've changed some of the AND gates to NAND
+gates to perform the necessary complements.
+
+And we've changed the logic necessary to deal
+with the two 1-bits that needed to be added
+
+in.
+
+The colored elements show the changes made
+from the original unsigned multiplier circuitry.
+
+Basically, the circuit for multiplying two's
+complement operands has the same latency,
+
+throughput and hardware costs as the original
+circuitry.
\ No newline at end of file
diff --git a/0UFwGJe6ubg.txt b/0UFwGJe6ubg.txt
new file mode 100644
index 0000000000000000000000000000000000000000..15b7ef563766db52449152cc969bd69260382ce3
--- /dev/null
+++ b/0UFwGJe6ubg.txt
@@ -0,0 +1,12499 @@
+align:start position:0%
+ 
+so last time we talked about
+
+ align:start position:0%
+so last time we talked about
+ 
+
+ align:start position:0%
+so last time we talked about
+medicine does and today I want to take a
+
+ align:start position:0%
+medicine does and today I want to take a
+ 
+
+ align:start position:0%
+medicine does and today I want to take a
+deep dive into medical data and I'm
+
+ align:start position:0%
+deep dive into medical data and I'm
+ 
+
+ align:start position:0%
+deep dive into medical data and I'm
+going to use as examples a lot of stuff
+
+ align:start position:0%
+going to use as examples a lot of stuff
+ 
+
+ align:start position:0%
+going to use as examples a lot of stuff
+from the mimic database which is one of
+
+ align:start position:0%
+from the mimic database which is one of
+ 
+
+ align:start position:0%
+from the mimic database which is one of
+the databases that we're going to be
+
+ align:start position:0%
+the databases that we're going to be
+ 
+
+ align:start position:0%
+the databases that we're going to be
+using in this class some of you are
+
+ align:start position:0%
+using in this class some of you are
+ 
+
+ align:start position:0%
+using in this class some of you are
+probably familiar with it and some of
+
+ align:start position:0%
+probably familiar with it and some of
+ 
+
+ align:start position:0%
+probably familiar with it and some of
+you or not and there are I hope some
+
+ align:start position:0%
+you or not and there are I hope some
+ 
+
+ align:start position:0%
+you or not and there are I hope some
+takeaway lessons from this discussion so
+
+ align:start position:0%
+takeaway lessons from this discussion so
+ 
+
+ align:start position:0%
+takeaway lessons from this discussion so
+for example a few years ago when mimic 3
+
+ align:start position:0%
+for example a few years ago when mimic 3
+ 
+
+ align:start position:0%
+for example a few years ago when mimic 3
+was about to be released I was playing
+
+ align:start position:0%
+was about to be released I was playing
+ 
+
+ align:start position:0%
+was about to be released I was playing
+with the data and I looked at the
+
+ align:start position:0%
+with the data and I looked at the
+ 
+
+ align:start position:0%
+with the data and I looked at the
+distribution of heart rates in the care
+
+ align:start position:0%
+distribution of heart rates in the care
+ 
+
+ align:start position:0%
+distribution of heart rates in the care
+view part of the database so mimic for
+
+ align:start position:0%
+view part of the database so mimic for
+ 
+
+ align:start position:0%
+view part of the database so mimic for
+those of you who don't know has
+
+ align:start position:0%
+those of you who don't know has
+ 
+
+ align:start position:0%
+those of you who don't know has
+intensive care data from about 60
+
+ align:start position:0%
+intensive care data from about 60
+ 
+
+ align:start position:0%
+intensive care data from about 60
+something thousand admissions to
+
+ align:start position:0%
+something thousand admissions to
+ 
+
+ align:start position:0%
+something thousand admissions to
+intensive care units at the Beth Israel
+
+ align:start position:0%
+intensive care units at the Beth Israel
+ 
+
+ align:start position:0%
+intensive care units at the Beth Israel
+Deaconess Medical Center over a period
+
+ align:start position:0%
+Deaconess Medical Center over a period
+ 
+
+ align:start position:0%
+Deaconess Medical Center over a period
+of about twelve years and one of the
+
+ align:start position:0%
+of about twelve years and one of the
+ 
+
+ align:start position:0%
+of about twelve years and one of the
+technical difficulties that we
+
+ align:start position:0%
+technical difficulties that we
+ 
+
+ align:start position:0%
+technical difficulties that we
+encountered is that in the middle of
+
+ align:start position:0%
+encountered is that in the middle of
+ 
+
+ align:start position:0%
+encountered is that in the middle of
+that time period the hospital shifted
+
+ align:start position:0%
+that time period the hospital shifted
+ 
+
+ align:start position:0%
+that time period the hospital shifted
+from one information system that they
+
+ align:start position:0%
+from one information system that they
+ 
+
+ align:start position:0%
+from one information system that they
+used in their intensive care unit to
+
+ align:start position:0%
+used in their intensive care unit to
+ 
+
+ align:start position:0%
+used in their intensive care unit to
+another care view as the old one meta
+
+ align:start position:0%
+another care view as the old one meta
+ 
+
+ align:start position:0%
+another care view as the old one meta
+vision is the new one and of course
+
+ align:start position:0%
+vision is the new one and of course
+ 
+
+ align:start position:0%
+vision is the new one and of course
+they're not exactly compatible so we'll
+
+ align:start position:0%
+they're not exactly compatible so we'll
+ 
+
+ align:start position:0%
+they're not exactly compatible so we'll
+say that we'll see some examples of that
+
+ align:start position:0%
+say that we'll see some examples of that
+ 
+
+ align:start position:0%
+say that we'll see some examples of that
+so this is the old data so this is from
+
+ align:start position:0%
+so this is the old data so this is from
+ 
+
+ align:start position:0%
+so this is the old data so this is from
+care view and you look at that and say
+
+ align:start position:0%
+care view and you look at that and say
+ 
+
+ align:start position:0%
+care view and you look at that and say
+well heart rates range from you know 40
+
+ align:start position:0%
+well heart rates range from you know 40
+ 
+
+ align:start position:0%
+well heart rates range from you know 40
+to 200 roughly which is okay but then
+
+ align:start position:0%
+to 200 roughly which is okay but then
+ 
+
+ align:start position:0%
+to 200 roughly which is okay but then
+there's this funny thing there are two
+
+ align:start position:0%
+there's this funny thing there are two
+ 
+
+ align:start position:0%
+there's this funny thing there are two
+peaks so where if ever do you see two
+
+ align:start position:0%
+peaks so where if ever do you see two
+ 
+
+ align:start position:0%
+peaks so where if ever do you see two
+peaks in physiological data not typical
+
+ align:start position:0%
+peaks in physiological data not typical
+ 
+
+ align:start position:0%
+peaks in physiological data not typical
+and so my initial reaction was
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so then I looked a little little closer
+
+ align:start position:0%
+so then I looked a little little closer
+ 
+
+ align:start position:0%
+so then I looked a little little closer
+and I said hmm
+
+ align:start position:0%
+and I said hmm
+ 
+
+ align:start position:0%
+and I said hmm
+what are the heart rates look like from
+
+ align:start position:0%
+what are the heart rates look like from
+ 
+
+ align:start position:0%
+what are the heart rates look like from
+these two systems and if you look in
+
+ align:start position:0%
+these two systems and if you look in
+ 
+
+ align:start position:0%
+these two systems and if you look in
+care of you you see the picture that I
+
+ align:start position:0%
+care of you you see the picture that I
+ 
+
+ align:start position:0%
+care of you you see the picture that I
+just showed you and if you look in meta
+
+ align:start position:0%
+just showed you and if you look in meta
+ 
+
+ align:start position:0%
+just showed you and if you look in meta
+vision you see this other picture which
+
+ align:start position:0%
+vision you see this other picture which
+ 
+
+ align:start position:0%
+vision you see this other picture which
+looks more like what you would normally
+
+ align:start position:0%
+looks more like what you would normally
+ 
+
+ align:start position:0%
+looks more like what you would normally
+expect and so I'm sitting there
+
+ align:start position:0%
+expect and so I'm sitting there
+ 
+
+ align:start position:0%
+expect and so I'm sitting there
+scratching my head going okay there must
+
+ align:start position:0%
+scratching my head going okay there must
+ 
+
+ align:start position:0%
+scratching my head going okay there must
+be some difference between these it's
+
+ align:start position:0%
+be some difference between these it's
+ 
+
+ align:start position:0%
+be some difference between these it's
+not that simultaneous with the
+
+ align:start position:0%
+not that simultaneous with the
+ 
+
+ align:start position:0%
+not that simultaneous with the
+switchover of the hospital from one
+
+ align:start position:0%
+switchover of the hospital from one
+ 
+
+ align:start position:0%
+switchover of the hospital from one
+information system to another physiology
+
+ align:start position:0%
+information system to another physiology
+ 
+
+ align:start position:0%
+information system to another physiology
+of people changed and all of a sudden
+
+ align:start position:0%
+of people changed and all of a sudden
+ 
+
+ align:start position:0%
+of people changed and all of a sudden
+some subset of people started having
+
+ align:start position:0%
+some subset of people started having
+ 
+
+ align:start position:0%
+some subset of people started having
+faster heart rates right but if you
+
+ align:start position:0%
+faster heart rates right but if you
+ 
+
+ align:start position:0%
+faster heart rates right but if you
+think about that what subset of people
+
+ align:start position:0%
+think about that what subset of people
+ 
+
+ align:start position:0%
+think about that what subset of people
+have faster heart rates yeah kids right
+
+ align:start position:0%
+have faster heart rates yeah kids right
+ 
+
+ align:start position:0%
+have faster heart rates yeah kids right
+so I said hmm interesting so anyway if
+
+ align:start position:0%
+so I said hmm interesting so anyway if
+ 
+
+ align:start position:0%
+so I said hmm interesting so anyway if
+you look at the statistics you see that
+
+ align:start position:0%
+you look at the statistics you see that
+ 
+
+ align:start position:0%
+you look at the statistics you see that
+the mean heart rate in care view is a
+
+ align:start position:0%
+the mean heart rate in care view is a
+ 
+
+ align:start position:0%
+the mean heart rate in care view is a
+hundred and eight heart heart rate and
+
+ align:start position:0%
+hundred and eight heart heart rate and
+ 
+
+ align:start position:0%
+hundred and eight heart heart rate and
+meta vision is is 87
+
+ align:start position:0%
+meta vision is is 87
+ 
+
+ align:start position:0%
+meta vision is is 87
+but of course means are not that
+
+ align:start position:0%
+but of course means are not that
+ 
+
+ align:start position:0%
+but of course means are not that
+meaningful when you look at at these
+
+ align:start position:0%
+meaningful when you look at at these
+ 
+
+ align:start position:0%
+meaningful when you look at at these
+bimodal distributions so then I said
+
+ align:start position:0%
+bimodal distributions so then I said
+ 
+
+ align:start position:0%
+bimodal distributions so then I said
+well what if we just look at adults so
+
+ align:start position:0%
+well what if we just look at adults so
+ 
+
+ align:start position:0%
+well what if we just look at adults so
+we look at people from age greater than
+
+ align:start position:0%
+we look at people from age greater than
+ 
+
+ align:start position:0%
+we look at people from age greater than
+one up to age 90 and I'll say a word
+
+ align:start position:0%
+one up to age 90 and I'll say a word
+ 
+
+ align:start position:0%
+one up to age 90 and I'll say a word
+about that in a minute
+
+ align:start position:0%
+about that in a minute
+ 
+
+ align:start position:0%
+about that in a minute
+and I look at those two distributions
+
+ align:start position:0%
+and I look at those two distributions
+ 
+
+ align:start position:0%
+and I look at those two distributions
+they look pretty close they look pretty
+
+ align:start position:0%
+they look pretty close they look pretty
+ 
+
+ align:start position:0%
+they look pretty close they look pretty
+similar so that means that the number of
+
+ align:start position:0%
+similar so that means that the number of
+ 
+
+ align:start position:0%
+similar so that means that the number of
+patients of different ages in the adult
+
+ align:start position:0%
+patients of different ages in the adult
+ 
+
+ align:start position:0%
+patients of different ages in the adult
+group is similar in the two data sets
+
+ align:start position:0%
+group is similar in the two data sets
+ 
+
+ align:start position:0%
+group is similar in the two data sets
+but if I don't exclude the very young or
+
+ align:start position:0%
+but if I don't exclude the very young or
+ 
+
+ align:start position:0%
+but if I don't exclude the very young or
+the very old then I see this funny
+
+ align:start position:0%
+the very old then I see this funny
+ 
+
+ align:start position:0%
+the very old then I see this funny
+distribution where I have suppressed
+
+ align:start position:0%
+distribution where I have suppressed
+ 
+
+ align:start position:0%
+distribution where I have suppressed
+ages greater than 90 but not the young
+
+ align:start position:0%
+ages greater than 90 but not the young
+ 
+
+ align:start position:0%
+ages greater than 90 but not the young
+and what you see is that in care view
+
+ align:start position:0%
+and what you see is that in care view
+ 
+
+ align:start position:0%
+and what you see is that in care view
+there's this giant spike at age
+
+ align:start position:0%
+there's this giant spike at age
+ 
+
+ align:start position:0%
+there's this giant spike at age
+zero right so what happened at the
+
+ align:start position:0%
+zero right so what happened at the
+ 
+
+ align:start position:0%
+zero right so what happened at the
+hospital is that under the old system it
+
+ align:start position:0%
+hospital is that under the old system it
+ 
+
+ align:start position:0%
+hospital is that under the old system it
+was also being used in the NICU the
+
+ align:start position:0%
+was also being used in the NICU the
+ 
+
+ align:start position:0%
+was also being used in the NICU the
+neonatal intensive care unit the new
+
+ align:start position:0%
+neonatal intensive care unit the new
+ 
+
+ align:start position:0%
+neonatal intensive care unit the new
+system was not being used in the NICU
+
+ align:start position:0%
+system was not being used in the NICU
+ 
+
+ align:start position:0%
+system was not being used in the NICU
+and therefore they didn't capture data
+
+ align:start position:0%
+and therefore they didn't capture data
+ 
+
+ align:start position:0%
+and therefore they didn't capture data
+about babies all right and in fact if
+
+ align:start position:0%
+about babies all right and in fact if
+ 
+
+ align:start position:0%
+about babies all right and in fact if
+you look at age versus heart rate of the
+
+ align:start position:0%
+you look at age versus heart rate of the
+ 
+
+ align:start position:0%
+you look at age versus heart rate of the
+entire population you see two very
+
+ align:start position:0%
+entire population you see two very
+ 
+
+ align:start position:0%
+entire population you see two very
+peculiar things so here are the adults
+
+ align:start position:0%
+peculiar things so here are the adults
+ 
+
+ align:start position:0%
+peculiar things so here are the adults
+that we've been talking about and here
+
+ align:start position:0%
+that we've been talking about and here
+ 
+
+ align:start position:0%
+that we've been talking about and here
+are the babies and sure enough they have
+
+ align:start position:0%
+are the babies and sure enough they have
+ 
+
+ align:start position:0%
+are the babies and sure enough they have
+higher heart rates and then here are
+
+ align:start position:0%
+higher heart rates and then here are
+ 
+
+ align:start position:0%
+higher heart rates and then here are
+these 300 year old people oh wow I don't
+
+ align:start position:0%
+these 300 year old people oh wow I don't
+ 
+
+ align:start position:0%
+these 300 year old people oh wow I don't
+think I'm going to have a heart rate
+
+ align:start position:0%
+think I'm going to have a heart rate
+ 
+
+ align:start position:0%
+think I'm going to have a heart rate
+when I'm slow
+
+ align:start position:0%
+when I'm slow
+ 
+
+ align:start position:0%
+when I'm slow
+so who are those people anybody have a
+
+ align:start position:0%
+so who are those people anybody have a
+ 
+
+ align:start position:0%
+so who are those people anybody have a
+clue yeah sorry there are too many of
+
+ align:start position:0%
+clue yeah sorry there are too many of
+ 
+
+ align:start position:0%
+clue yeah sorry there are too many of
+them yeah entry errors is always a
+
+ align:start position:0%
+them yeah entry errors is always a
+ 
+
+ align:start position:0%
+them yeah entry errors is always a
+possibility but there's quite a few data
+
+ align:start position:0%
+possibility but there's quite a few data
+ 
+
+ align:start position:0%
+possibility but there's quite a few data
+points there yeah
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+close it's not quite missing data so
+
+ align:start position:0%
+close it's not quite missing data so
+ 
+
+ align:start position:0%
+close it's not quite missing data so
+HIPAA the Health Insurance Portability
+
+ align:start position:0%
+HIPAA the Health Insurance Portability
+ 
+
+ align:start position:0%
+HIPAA the Health Insurance Portability
+and Accountability Act defines a set of
+
+ align:start position:0%
+and Accountability Act defines a set of
+ 
+
+ align:start position:0%
+and Accountability Act defines a set of
+criteria about protecting personal
+
+ align:start position:0%
+criteria about protecting personal
+ 
+
+ align:start position:0%
+criteria about protecting personal
+health information and one of the things
+
+ align:start position:0%
+health information and one of the things
+ 
+
+ align:start position:0%
+health information and one of the things
+you are not allowed to do is to specify
+
+ align:start position:0%
+you are not allowed to do is to specify
+ 
+
+ align:start position:0%
+you are not allowed to do is to specify
+the age of somebody who is 90 years old
+
+ align:start position:0%
+the age of somebody who is 90 years old
+ 
+
+ align:start position:0%
+the age of somebody who is 90 years old
+or older and the reason is because the
+
+ align:start position:0%
+or older and the reason is because the
+ 
+
+ align:start position:0%
+or older and the reason is because the
+number of 97 year olds is pretty small
+
+ align:start position:0%
+number of 97 year olds is pretty small
+ 
+
+ align:start position:0%
+number of 97 year olds is pretty small
+and so if I tell you that Willie is 97
+
+ align:start position:0%
+and so if I tell you that Willie is 97
+ 
+
+ align:start position:0%
+and so if I tell you that Willie is 97
+years old then you're going to be able
+
+ align:start position:0%
+years old then you're going to be able
+ 
+
+ align:start position:0%
+years old then you're going to be able
+to pick them out of a population
+
+ align:start position:0%
+to pick them out of a population
+ 
+
+ align:start position:0%
+to pick them out of a population
+relatively easily and so it's prohibited
+
+ align:start position:0%
+relatively easily and so it's prohibited
+ 
+
+ align:start position:0%
+relatively easily and so it's prohibited
+to say that okay so as a result
+
+ align:start position:0%
+to say that okay so as a result
+ 
+
+ align:start position:0%
+to say that okay so as a result
+everybody who's 90 or older
+
+ align:start position:0%
+everybody who's 90 or older
+ 
+
+ align:start position:0%
+everybody who's 90 or older
+gets labeled as being 300 years old in
+
+ align:start position:0%
+gets labeled as being 300 years old in
+ 
+
+ align:start position:0%
+gets labeled as being 300 years old in
+the database it's an artifact right it's
+
+ align:start position:0%
+the database it's an artifact right it's
+ 
+
+ align:start position:0%
+the database it's an artifact right it's
+like back in
+
+ align:start position:0%
+like back in
+ 
+
+ align:start position:0%
+like back in
+very in my in my youth I worked as a
+
+ align:start position:0%
+very in my in my youth I worked as a
+ 
+
+ align:start position:0%
+very in my in my youth I worked as a
+computer programmer at a health sciences
+
+ align:start position:0%
+computer programmer at a health sciences
+ 
+
+ align:start position:0%
+computer programmer at a health sciences
+computing facility at UCLA and we used
+
+ align:start position:0%
+computing facility at UCLA and we used
+ 
+
+ align:start position:0%
+computing facility at UCLA and we used
+to have a convention that missing data
+
+ align:start position:0%
+to have a convention that missing data
+ 
+
+ align:start position:0%
+to have a convention that missing data
+was represented by nine nine nine nine
+
+ align:start position:0%
+was represented by nine nine nine nine
+ 
+
+ align:start position:0%
+was represented by nine nine nine nine
+nine okay and of course if you average
+
+ align:start position:0%
+nine okay and of course if you average
+ 
+
+ align:start position:0%
+nine okay and of course if you average
+that into a real data set you get
+
+ align:start position:0%
+that into a real data set you get
+ 
+
+ align:start position:0%
+that into a real data set you get
+garbage which people did regularly so
+
+ align:start position:0%
+garbage which people did regularly so
+ 
+
+ align:start position:0%
+garbage which people did regularly so
+there there are problems with this and
+
+ align:start position:0%
+there there are problems with this and
+ 
+
+ align:start position:0%
+there there are problems with this and
+we're running into one of those if you
+
+ align:start position:0%
+we're running into one of those if you
+ 
+
+ align:start position:0%
+we're running into one of those if you
+look at the at just the adults the two
+
+ align:start position:0%
+look at the at just the adults the two
+ 
+
+ align:start position:0%
+look at the at just the adults the two
+systems actually look very similar so
+
+ align:start position:0%
+systems actually look very similar so
+ 
+
+ align:start position:0%
+systems actually look very similar so
+the blue and red dots or the two systems
+
+ align:start position:0%
+the blue and red dots or the two systems
+ 
+
+ align:start position:0%
+the blue and red dots or the two systems
+and I've drawn the trend lines between
+
+ align:start position:0%
+and I've drawn the trend lines between
+ 
+
+ align:start position:0%
+and I've drawn the trend lines between
+them and you can see that they're very
+
+ align:start position:0%
+them and you can see that they're very
+ 
+
+ align:start position:0%
+them and you can see that they're very
+similar so it looks like as you get
+
+ align:start position:0%
+similar so it looks like as you get
+ 
+
+ align:start position:0%
+similar so it looks like as you get
+older your heart rate declines very
+
+ align:start position:0%
+older your heart rate declines very
+ 
+
+ align:start position:0%
+older your heart rate declines very
+slightly but it does so equally in the
+
+ align:start position:0%
+slightly but it does so equally in the
+ 
+
+ align:start position:0%
+slightly but it does so equally in the
+to date a bit datasets yeah well that's
+
+ align:start position:0%
+to date a bit datasets yeah well that's
+ 
+
+ align:start position:0%
+to date a bit datasets yeah well that's
+because the ages there are computed at
+
+ align:start position:0%
+because the ages there are computed at
+ 
+
+ align:start position:0%
+because the ages there are computed at
+the time that the heart rate is measured
+
+ align:start position:0%
+the time that the heart rate is measured
+ 
+
+ align:start position:0%
+the time that the heart rate is measured
+and so if you are 300 years old when you
+
+ align:start position:0%
+and so if you are 300 years old when you
+ 
+
+ align:start position:0%
+and so if you are 300 years old when you
+admitted to the hospital if you stay in
+
+ align:start position:0%
+admitted to the hospital if you stay in
+ 
+
+ align:start position:0%
+admitted to the hospital if you stay in
+the hospital for six months then you're
+
+ align:start position:0%
+the hospital for six months then you're
+ 
+
+ align:start position:0%
+the hospital for six months then you're
+300 and a half years old by the time of
+
+ align:start position:0%
+300 and a half years old by the time of
+ 
+
+ align:start position:0%
+300 and a half years old by the time of
+that measurement so that's why there are
+
+ align:start position:0%
+that measurement so that's why there are
+ 
+
+ align:start position:0%
+that measurement so that's why there are
+data points to the right of 300 yeah
+
+ align:start position:0%
+data points to the right of 300 yeah
+ 
+
+ align:start position:0%
+data points to the right of 300 yeah
+good good catch okay and then this is
+
+ align:start position:0%
+good good catch okay and then this is
+ 
+
+ align:start position:0%
+good good catch okay and then this is
+what the babies look like and of course
+
+ align:start position:0%
+what the babies look like and of course
+ 
+
+ align:start position:0%
+what the babies look like and of course
+they do have higher heart rates and here
+
+ align:start position:0%
+they do have higher heart rates and here
+ 
+
+ align:start position:0%
+they do have higher heart rates and here
+here are the oldsters so actually there
+
+ align:start position:0%
+here are the oldsters so actually there
+ 
+
+ align:start position:0%
+here are the oldsters so actually there
+are people out to 310 years old because
+
+ align:start position:0%
+are people out to 310 years old because
+ 
+
+ align:start position:0%
+are people out to 310 years old because
+maybe they were discharged from the
+
+ align:start position:0%
+maybe they were discharged from the
+ 
+
+ align:start position:0%
+maybe they were discharged from the
+hospital and then at age 100 they came
+
+ align:start position:0%
+hospital and then at age 100 they came
+ 
+
+ align:start position:0%
+hospital and then at age 100 they came
+back you know maybe there were 90 years
+
+ align:start position:0%
+back you know maybe there were 90 years
+ 
+
+ align:start position:0%
+back you know maybe there were 90 years
+old at the time they were initially
+
+ align:start position:0%
+old at the time they were initially
+ 
+
+ align:start position:0%
+old at the time they were initially
+admitted ten years later they came back
+
+ align:start position:0%
+admitted ten years later they came back
+ 
+
+ align:start position:0%
+admitted ten years later they came back
+and we recorded more data about them so
+
+ align:start position:0%
+and we recorded more data about them so
+ 
+
+ align:start position:0%
+and we recorded more data about them so
+this is all relative to to that 300 okay
+
+ align:start position:0%
+this is all relative to to that 300 okay
+ 
+
+ align:start position:0%
+this is all relative to to that 300 okay
+so that's just one example and the
+
+ align:start position:0%
+so that's just one example and the
+ 
+
+ align:start position:0%
+so that's just one example and the
+lesson there is be careful when you look
+
+ align:start position:0%
+lesson there is be careful when you look
+ 
+
+ align:start position:0%
+lesson there is be careful when you look
+at data because it can really easily
+
+ align:start position:0%
+at data because it can really easily
+ 
+
+ align:start position:0%
+at data because it can really easily
+fool you because there are all kinds of
+
+ align:start position:0%
+fool you because there are all kinds of
+ 
+
+ align:start position:0%
+fool you because there are all kinds of
+funny things about the way it's
+
+ align:start position:0%
+funny things about the way it's
+ 
+
+ align:start position:0%
+funny things about the way it's
+collected about these artefactual things
+
+ align:start position:0%
+collected about these artefactual things
+ 
+
+ align:start position:0%
+collected about these artefactual things
+like 300
+
+ align:start position:0%
+like 300
+ 
+
+ align:start position:0%
+like 300
+patience and so on okay so here's a
+
+ align:start position:0%
+patience and so on okay so here's a
+ 
+
+ align:start position:0%
+patience and so on okay so here's a
+catalog of the types of data that are
+
+ align:start position:0%
+catalog of the types of data that are
+ 
+
+ align:start position:0%
+catalog of the types of data that are
+available to us so we have a typical
+
+ align:start position:0%
+available to us so we have a typical
+ 
+
+ align:start position:0%
+available to us so we have a typical
+kind of electronic health record data
+
+ align:start position:0%
+kind of electronic health record data
+ 
+
+ align:start position:0%
+kind of electronic health record data
+from hospitals demographics age sex
+
+ align:start position:0%
+from hospitals demographics age sex
+ 
+
+ align:start position:0%
+from hospitals demographics age sex
+socioeconomic status insurance type
+
+ align:start position:0%
+socioeconomic status insurance type
+ 
+
+ align:start position:0%
+socioeconomic status insurance type
+language religion living situation
+
+ align:start position:0%
+language religion living situation
+ 
+
+ align:start position:0%
+language religion living situation
+family structure location work etc we
+
+ align:start position:0%
+family structure location work etc we
+ 
+
+ align:start position:0%
+family structure location work etc we
+have vital signs your weight your height
+
+ align:start position:0%
+have vital signs your weight your height
+ 
+
+ align:start position:0%
+have vital signs your weight your height
+your pulse respiration rate body
+
+ align:start position:0%
+your pulse respiration rate body
+ 
+
+ align:start position:0%
+your pulse respiration rate body
+temperature etc so these are typically
+
+ align:start position:0%
+temperature etc so these are typically
+ 
+
+ align:start position:0%
+temperature etc so these are typically
+the things that if you ever go to a
+
+ align:start position:0%
+the things that if you ever go to a
+ 
+
+ align:start position:0%
+the things that if you ever go to a
+doctor's office or you go into a
+
+ align:start position:0%
+doctor's office or you go into a
+ 
+
+ align:start position:0%
+doctor's office or you go into a
+hospital nurse will take you aside and
+
+ align:start position:0%
+hospital nurse will take you aside and
+ 
+
+ align:start position:0%
+hospital nurse will take you aside and
+weigh you and measure your height and
+
+ align:start position:0%
+weigh you and measure your height and
+ 
+
+ align:start position:0%
+weigh you and measure your height and
+check your blood pressure and take your
+
+ align:start position:0%
+check your blood pressure and take your
+ 
+
+ align:start position:0%
+check your blood pressure and take your
+temperature and stuff like that these
+
+ align:start position:0%
+temperature and stuff like that these
+ 
+
+ align:start position:0%
+temperature and stuff like that these
+are standard vital signs and so we have
+
+ align:start position:0%
+are standard vital signs and so we have
+ 
+
+ align:start position:0%
+are standard vital signs and so we have
+lots of those recorded medications
+
+ align:start position:0%
+lots of those recorded medications
+ 
+
+ align:start position:0%
+lots of those recorded medications
+prescription medications
+
+ align:start position:0%
+prescription medications
+ 
+
+ align:start position:0%
+prescription medications
+over-the-counter drugs illegal drugs if
+
+ align:start position:0%
+over-the-counter drugs illegal drugs if
+ 
+
+ align:start position:0%
+over-the-counter drugs illegal drugs if
+you're willing not to lie to your
+
+ align:start position:0%
+you're willing not to lie to your
+ 
+
+ align:start position:0%
+you're willing not to lie to your
+healthcare provider alcohol again one of
+
+ align:start position:0%
+healthcare provider alcohol again one of
+ 
+
+ align:start position:0%
+healthcare provider alcohol again one of
+my earliest days I was hanging out with
+
+ align:start position:0%
+my earliest days I was hanging out with
+ 
+
+ align:start position:0%
+my earliest days I was hanging out with
+the cardiologist at Tufts Medical Center
+
+ align:start position:0%
+the cardiologist at Tufts Medical Center
+ 
+
+ align:start position:0%
+the cardiologist at Tufts Medical Center
+and we see this elderly lady who looks
+
+ align:start position:0%
+and we see this elderly lady who looks
+ 
+
+ align:start position:0%
+and we see this elderly lady who looks
+kind of terrible and and we're talking
+
+ align:start position:0%
+kind of terrible and and we're talking
+ 
+
+ align:start position:0%
+kind of terrible and and we're talking
+to her well the doctor is talking to her
+
+ align:start position:0%
+to her well the doctor is talking to her
+ 
+
+ align:start position:0%
+to her well the doctor is talking to her
+I'm trying to stay out of the way and
+
+ align:start position:0%
+I'm trying to stay out of the way and
+ 
+
+ align:start position:0%
+I'm trying to stay out of the way and
+and he says so you know do you drink
+
+ align:start position:0%
+and he says so you know do you drink
+ 
+
+ align:start position:0%
+and he says so you know do you drink
+alcohol and she says oh no never touch
+
+ align:start position:0%
+alcohol and she says oh no never touch
+ 
+
+ align:start position:0%
+alcohol and she says oh no never touch
+the stuff
+
+ align:start position:0%
+the stuff
+ 
+
+ align:start position:0%
+the stuff
+and and then we talked some more and we
+
+ align:start position:0%
+and and then we talked some more and we
+ 
+
+ align:start position:0%
+and and then we talked some more and we
+go out of the out of the patients room
+
+ align:start position:0%
+go out of the out of the patients room
+ 
+
+ align:start position:0%
+go out of the out of the patients room
+and and the doctor turns to me out of
+
+ align:start position:0%
+and and the doctor turns to me out of
+ 
+
+ align:start position:0%
+and and the doctor turns to me out of
+earshot of the patient and says oh she's
+
+ align:start position:0%
+earshot of the patient and says oh she's
+ 
+
+ align:start position:0%
+earshot of the patient and says oh she's
+a chronic drunk I said well how do you
+
+ align:start position:0%
+a chronic drunk I said well how do you
+ 
+
+ align:start position:0%
+a chronic drunk I said well how do you
+know and he says well from lab tests
+
+ align:start position:0%
+know and he says well from lab tests
+ 
+
+ align:start position:0%
+know and he says well from lab tests
+from the appearance of her skin from her
+
+ align:start position:0%
+from the appearance of her skin from her
+ 
+
+ align:start position:0%
+from the appearance of her skin from her
+general demeanor from you know various
+
+ align:start position:0%
+general demeanor from you know various
+ 
+
+ align:start position:0%
+general demeanor from you know various
+sort of ineffable factors and so
+
+ align:start position:0%
+sort of ineffable factors and so
+ 
+
+ align:start position:0%
+sort of ineffable factors and so
+patients lie okay they really do because
+
+ align:start position:0%
+patients lie okay they really do because
+ 
+
+ align:start position:0%
+patients lie okay they really do because
+they don't want to tell you things
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay medications by the way is a big
+
+ align:start position:0%
+okay medications by the way is a big
+ 
+
+ align:start position:0%
+okay medications by the way is a big
+deal so there's this whole field called
+
+ align:start position:0%
+deal so there's this whole field called
+ 
+
+ align:start position:0%
+deal so there's this whole field called
+mad wreck medication reconciliation
+
+ align:start position:0%
+mad wreck medication reconciliation
+ 
+
+ align:start position:0%
+mad wreck medication reconciliation
+which is the hospitals or the doctors
+
+ align:start position:0%
+which is the hospitals or the doctors
+ 
+
+ align:start position:0%
+which is the hospitals or the doctors
+offices attempt to figure out what
+
+ align:start position:0%
+offices attempt to figure out what
+ 
+
+ align:start position:0%
+offices attempt to figure out what
+medications you're actually taking so
+
+ align:start position:0%
+medications you're actually taking so
+ 
+
+ align:start position:0%
+medications you're actually taking so
+I'm a member of the MIT health plan and
+
+ align:start position:0%
+I'm a member of the MIT health plan and
+ 
+
+ align:start position:0%
+I'm a member of the MIT health plan and
+if I sign into my health plan account it
+
+ align:start position:0%
+if I sign into my health plan account it
+ 
+
+ align:start position:0%
+if I sign into my health plan account it
+tells me that I'm taking some pills that
+
+ align:start position:0%
+tells me that I'm taking some pills that
+ 
+
+ align:start position:0%
+tells me that I'm taking some pills that
+I got 12 years ago as part of a
+
+ align:start position:0%
+I got 12 years ago as part of a
+ 
+
+ align:start position:0%
+I got 12 years ago as part of a
+laboratory test but we were you know I
+
+ align:start position:0%
+laboratory test but we were you know I
+ 
+
+ align:start position:0%
+laboratory test but we were you know I
+took two pills which were supposed to
+
+ align:start position:0%
+took two pills which were supposed to
+ 
+
+ align:start position:0%
+took two pills which were supposed to
+have some physiological effect and then
+
+ align:start position:0%
+have some physiological effect and then
+ 
+
+ align:start position:0%
+have some physiological effect and then
+they measured that and I've never gotten
+
+ align:start position:0%
+they measured that and I've never gotten
+ 
+
+ align:start position:0%
+they measured that and I've never gotten
+another pill and never taken one since
+
+ align:start position:0%
+another pill and never taken one since
+ 
+
+ align:start position:0%
+another pill and never taken one since
+then nor would it be particularly good
+
+ align:start position:0%
+then nor would it be particularly good
+ 
+
+ align:start position:0%
+then nor would it be particularly good
+for me but it's still on my record and
+
+ align:start position:0%
+for me but it's still on my record and
+ 
+
+ align:start position:0%
+for me but it's still on my record and
+there's no notice of it ever having been
+
+ align:start position:0%
+there's no notice of it ever having been
+ 
+
+ align:start position:0%
+there's no notice of it ever having been
+discontinued and that's a real problem
+
+ align:start position:0%
+discontinued and that's a real problem
+ 
+
+ align:start position:0%
+discontinued and that's a real problem
+because if you're taking care of a
+
+ align:start position:0%
+because if you're taking care of a
+ 
+
+ align:start position:0%
+because if you're taking care of a
+patient you'd like to understand what
+
+ align:start position:0%
+patient you'd like to understand what
+ 
+
+ align:start position:0%
+patient you'd like to understand what
+drugs they're actually taking it's hard
+
+ align:start position:0%
+drugs they're actually taking it's hard
+ 
+
+ align:start position:0%
+drugs they're actually taking it's hard
+to know okay that lab tests so this is
+
+ align:start position:0%
+to know okay that lab tests so this is
+ 
+
+ align:start position:0%
+to know okay that lab tests so this is
+the things that you you imagine that we
+
+ align:start position:0%
+the things that you you imagine that we
+ 
+
+ align:start position:0%
+the things that you you imagine that we
+do a lot of and these are components of
+
+ align:start position:0%
+do a lot of and these are components of
+ 
+
+ align:start position:0%
+do a lot of and these are components of
+the blood and the urine mainly but also
+
+ align:start position:0%
+the blood and the urine mainly but also
+ 
+
+ align:start position:0%
+the blood and the urine mainly but also
+of the stool saliva spinal fluid fluid
+
+ align:start position:0%
+of the stool saliva spinal fluid fluid
+ 
+
+ align:start position:0%
+of the stool saliva spinal fluid fluid
+taken off the belly joint fluid bone
+
+ align:start position:0%
+taken off the belly joint fluid bone
+ 
+
+ align:start position:0%
+taken off the belly joint fluid bone
+marrow stuff coming out of your lungs
+
+ align:start position:0%
+marrow stuff coming out of your lungs
+ 
+
+ align:start position:0%
+marrow stuff coming out of your lungs
+it's all anything right and any place
+
+ align:start position:0%
+it's all anything right and any place
+ 
+
+ align:start position:0%
+it's all anything right and any place
+where you can produce something some
+
+ align:start position:0%
+where you can produce something some
+ 
+
+ align:start position:0%
+where you can produce something some
+specimen they can send it to a lab and
+
+ align:start position:0%
+specimen they can send it to a lab and
+ 
+
+ align:start position:0%
+specimen they can send it to a lab and
+measure things in it and they measure
+
+ align:start position:0%
+measure things in it and they measure
+ 
+
+ align:start position:0%
+measure things in it and they measure
+lots and lots of different kinds of
+
+ align:start position:0%
+lots and lots of different kinds of
+ 
+
+ align:start position:0%
+lots and lots of different kinds of
+things and these are often useful
+
+ align:start position:0%
+things and these are often useful
+ 
+
+ align:start position:0%
+things and these are often useful
+pathology qualitative and quantitative
+
+ align:start position:0%
+pathology qualitative and quantitative
+ 
+
+ align:start position:0%
+pathology qualitative and quantitative
+examination of any body tissue for
+
+ align:start position:0%
+examination of any body tissue for
+ 
+
+ align:start position:0%
+examination of any body tissue for
+example biopsy samples or surgical
+
+ align:start position:0%
+example biopsy samples or surgical
+ 
+
+ align:start position:0%
+example biopsy samples or surgical
+scraps you know if they do an operation
+
+ align:start position:0%
+scraps you know if they do an operation
+ 
+
+ align:start position:0%
+scraps you know if they do an operation
+they cut something out of you
+
+ align:start position:0%
+they cut something out of you
+ 
+
+ align:start position:0%
+they cut something out of you
+that typically winds up on a pathologist
+
+ align:start position:0%
+that typically winds up on a pathologist
+ 
+
+ align:start position:0%
+that typically winds up on a pathologist
+bench who then tries to figure out what
+
+ align:start position:0%
+bench who then tries to figure out what
+ 
+
+ align:start position:0%
+bench who then tries to figure out what
+its characteristics are and that's again
+
+ align:start position:0%
+its characteristics are and that's again
+ 
+
+ align:start position:0%
+its characteristics are and that's again
+useful information okay
+
+ align:start position:0%
+useful information okay
+ 
+
+ align:start position:0%
+useful information okay
+microbiology ever since Pasteur we know
+
+ align:start position:0%
+microbiology ever since Pasteur we know
+ 
+
+ align:start position:0%
+microbiology ever since Pasteur we know
+that organisms cause disease and so we
+
+ align:start position:0%
+that organisms cause disease and so we
+ 
+
+ align:start position:0%
+that organisms cause disease and so we
+are quite interested in knowing what
+
+ align:start position:0%
+are quite interested in knowing what
+ 
+
+ align:start position:0%
+are quite interested in knowing what
+organisms are growing inside your body
+
+ align:start position:0%
+organisms are growing inside your body
+ 
+
+ align:start position:0%
+organisms are growing inside your body
+and and typically testing is not only to
+
+ align:start position:0%
+and and typically testing is not only to
+ 
+
+ align:start position:0%
+and and typically testing is not only to
+identify the organism but also to figure
+
+ align:start position:0%
+identify the organism but also to figure
+ 
+
+ align:start position:0%
+identify the organism but also to figure
+out which antibiotics it's sensitive to
+
+ align:start position:0%
+out which antibiotics it's sensitive to
+ 
+
+ align:start position:0%
+out which antibiotics it's sensitive to
+and insensitive to and so you'll see
+
+ align:start position:0%
+and insensitive to and so you'll see
+ 
+
+ align:start position:0%
+and insensitive to and so you'll see
+things like reports of sensitivity
+
+ align:start position:0%
+things like reports of sensitivity
+ 
+
+ align:start position:0%
+things like reports of sensitivity
+testing at various delusions in other
+
+ align:start position:0%
+testing at various delusions in other
+ 
+
+ align:start position:0%
+testing at various delusions in other
+words they try to give a strong dose of
+
+ align:start position:0%
+words they try to give a strong dose of
+ 
+
+ align:start position:0%
+words they try to give a strong dose of
+an antibiotic or weaker dose a weaker
+
+ align:start position:0%
+an antibiotic or weaker dose a weaker
+ 
+
+ align:start position:0%
+an antibiotic or weaker dose a weaker
+dose a weaker dose a weaker dose to see
+
+ align:start position:0%
+dose a weaker dose a weaker dose to see
+ 
+
+ align:start position:0%
+dose a weaker dose a weaker dose to see
+which is the minimum level of dosing
+
+ align:start position:0%
+which is the minimum level of dosing
+ 
+
+ align:start position:0%
+which is the minimum level of dosing
+that's enough to kill the bacteria
+
+ align:start position:0%
+that's enough to kill the bacteria
+ 
+
+ align:start position:0%
+that's enough to kill the bacteria
+there's a comma missing there but input
+
+ align:start position:0%
+there's a comma missing there but input
+ 
+
+ align:start position:0%
+there's a comma missing there but input
+output of fluids is another important
+
+ align:start position:0%
+output of fluids is another important
+ 
+
+ align:start position:0%
+output of fluids is another important
+thing because people especially in the
+
+ align:start position:0%
+thing because people especially in the
+ 
+
+ align:start position:0%
+thing because people especially in the
+hospital often get either dehydrated or
+
+ align:start position:0%
+hospital often get either dehydrated or
+ 
+
+ align:start position:0%
+hospital often get either dehydrated or
+over hydrated and neither of those is
+
+ align:start position:0%
+over hydrated and neither of those is
+ 
+
+ align:start position:0%
+over hydrated and neither of those is
+good for you and so trying to keep track
+
+ align:start position:0%
+good for you and so trying to keep track
+ 
+
+ align:start position:0%
+good for you and so trying to keep track
+of what's going into you and what's
+
+ align:start position:0%
+of what's going into you and what's
+ 
+
+ align:start position:0%
+of what's going into you and what's
+coming out of you is important then
+
+ align:start position:0%
+coming out of you is important then
+ 
+
+ align:start position:0%
+coming out of you is important then
+there are tons of notes so an important
+
+ align:start position:0%
+there are tons of notes so an important
+ 
+
+ align:start position:0%
+there are tons of notes so an important
+one that we're going to look at in this
+
+ align:start position:0%
+one that we're going to look at in this
+ 
+
+ align:start position:0%
+one that we're going to look at in this
+class is discharge summaries so these
+
+ align:start position:0%
+class is discharge summaries so these
+ 
+
+ align:start position:0%
+class is discharge summaries so these
+are the typically long notes that are
+
+ align:start position:0%
+are the typically long notes that are
+ 
+
+ align:start position:0%
+are the typically long notes that are
+written at the end of a hospitalization
+
+ align:start position:0%
+written at the end of a hospitalization
+ 
+
+ align:start position:0%
+written at the end of a hospitalization
+so this is a summary of why you came in
+
+ align:start position:0%
+so this is a summary of why you came in
+ 
+
+ align:start position:0%
+so this is a summary of why you came in
+what they did to you the main things
+
+ align:start position:0%
+what they did to you the main things
+ 
+
+ align:start position:0%
+what they did to you the main things
+they discovered about you and then plans
+
+ align:start position:0%
+they discovered about you and then plans
+ 
+
+ align:start position:0%
+they discovered about you and then plans
+for what to do after your discharge
+
+ align:start position:0%
+for what to do after your discharge
+ 
+
+ align:start position:0%
+for what to do after your discharge
+where are you going to go what drugs are
+
+ align:start position:0%
+where are you going to go what drugs are
+ 
+
+ align:start position:0%
+where are you going to go what drugs are
+you going to be taking when are you
+
+ align:start position:0%
+you going to be taking when are you
+ 
+
+ align:start position:0%
+you going to be taking when are you
+supposed to come back for follow-up etc
+
+ align:start position:0%
+supposed to come back for follow-up etc
+ 
+
+ align:start position:0%
+supposed to come back for follow-up etc
+I'll show you a excruciating Lee long
+
+ align:start position:0%
+I'll show you a excruciating Lee long
+ 
+
+ align:start position:0%
+I'll show you a excruciating Lee long
+one of those later in the lecture today
+
+ align:start position:0%
+one of those later in the lecture today
+ 
+
+ align:start position:0%
+one of those later in the lecture today
+but we also have notes from attendings
+
+ align:start position:0%
+but we also have notes from attendings
+ 
+
+ align:start position:0%
+but we also have notes from attendings
+under residents nurses various
+
+ align:start position:0%
+under residents nurses various
+ 
+
+ align:start position:0%
+under residents nurses various
+specialties consultants the referring
+
+ align:start position:0%
+specialties consultants the referring
+ 
+
+ align:start position:0%
+specialties consultants the referring
+physician if somebody sends you to the
+
+ align:start position:0%
+physician if somebody sends you to the
+ 
+
+ align:start position:0%
+physician if somebody sends you to the
+hospital that doctor will usually write
+
+ align:start position:0%
+hospital that doctor will usually write
+ 
+
+ align:start position:0%
+hospital that doctor will usually write
+a note saying this is what I'm
+
+ align:start position:0%
+a note saying this is what I'm
+ 
+
+ align:start position:0%
+a note saying this is what I'm
+interested in here's why I'm sending in
+
+ align:start position:0%
+interested in here's why I'm sending in
+ 
+
+ align:start position:0%
+interested in here's why I'm sending in
+the patient there are letters back to
+
+ align:start position:0%
+the patient there are letters back to
+ 
+
+ align:start position:0%
+the patient there are letters back to
+the referring physician saying okay this
+
+ align:start position:0%
+the referring physician saying okay this
+ 
+
+ align:start position:0%
+the referring physician saying okay this
+is what we found out here's the answer
+
+ align:start position:0%
+is what we found out here's the answer
+ 
+
+ align:start position:0%
+is what we found out here's the answer
+to the question you were asking their
+
+ align:start position:0%
+to the question you were asking their
+ 
+
+ align:start position:0%
+to the question you were asking their
+emergency department notes so that's
+
+ align:start position:0%
+emergency department notes so that's
+ 
+
+ align:start position:0%
+emergency department notes so that's
+often the first contact between the
+
+ align:start position:0%
+often the first contact between the
+ 
+
+ align:start position:0%
+often the first contact between the
+patient and the healthcare system so
+
+ align:start position:0%
+patient and the healthcare system so
+ 
+
+ align:start position:0%
+patient and the healthcare system so
+these are all important and then there's
+
+ align:start position:0%
+these are all important and then there's
+ 
+
+ align:start position:0%
+these are all important and then there's
+tons and tons of billing data so
+
+ align:start position:0%
+tons and tons of billing data so
+ 
+
+ align:start position:0%
+tons and tons of billing data so
+remember the EHR systems were initially
+
+ align:start position:0%
+remember the EHR systems were initially
+ 
+
+ align:start position:0%
+remember the EHR systems were initially
+designed by accountants and they were
+
+ align:start position:0%
+designed by accountants and they were
+ 
+
+ align:start position:0%
+designed by accountants and they were
+designed for the purpose of billing and
+
+ align:start position:0%
+designed for the purpose of billing and
+ 
+
+ align:start position:0%
+designed for the purpose of billing and
+so we capture a lot of data about
+
+ align:start position:0%
+so we capture a lot of data about
+ 
+
+ align:start position:0%
+so we capture a lot of data about
+formalized ways of describing the
+
+ align:start position:0%
+formalized ways of describing the
+ 
+
+ align:start position:0%
+formalized ways of describing the
+condition of the patient and what was
+
+ align:start position:0%
+condition of the patient and what was
+ 
+
+ align:start position:0%
+condition of the patient and what was
+done to the patient in order to submit
+
+ align:start position:0%
+done to the patient in order to submit
+ 
+
+ align:start position:0%
+done to the patient in order to submit
+the right bills you obviously want to
+
+ align:start position:0%
+the right bills you obviously want to
+ 
+
+ align:start position:0%
+the right bills you obviously want to
+bill for it as much as possible but you
+
+ align:start position:0%
+bill for it as much as possible but you
+ 
+
+ align:start position:0%
+bill for it as much as possible but you
+have to be able to justify the bills
+
+ align:start position:0%
+have to be able to justify the bills
+ 
+
+ align:start position:0%
+have to be able to justify the bills
+that you submit because insurance
+
+ align:start position:0%
+that you submit because insurance
+ 
+
+ align:start position:0%
+that you submit because insurance
+companies and Medicare and Medicaid
+
+ align:start position:0%
+companies and Medicare and Medicaid
+ 
+
+ align:start position:0%
+companies and Medicare and Medicaid
+don't have a good sense of humor and if
+
+ align:start position:0%
+don't have a good sense of humor and if
+ 
+
+ align:start position:0%
+don't have a good sense of humor and if
+you submit bills for things that you
+
+ align:start position:0%
+you submit bills for things that you
+ 
+
+ align:start position:0%
+you submit bills for things that you
+can't justify then you get penalized
+
+ align:start position:0%
+can't justify then you get penalized
+ 
+
+ align:start position:0%
+can't justify then you get penalized
+okay and then there are administrative
+
+ align:start position:0%
+okay and then there are administrative
+ 
+
+ align:start position:0%
+okay and then there are administrative
+data like which service are you on so
+
+ align:start position:0%
+data like which service are you on so
+ 
+
+ align:start position:0%
+data like which service are you on so
+this this is occasionally a confusing
+
+ align:start position:0%
+this this is occasionally a confusing
+ 
+
+ align:start position:0%
+this this is occasionally a confusing
+thing you can go into the hospital and
+
+ align:start position:0%
+thing you can go into the hospital and
+ 
+
+ align:start position:0%
+thing you can go into the hospital and
+have heart problems but it turns out
+
+ align:start position:0%
+have heart problems but it turns out
+ 
+
+ align:start position:0%
+have heart problems but it turns out
+that the heart intensive care unit the
+
+ align:start position:0%
+that the heart intensive care unit the
+ 
+
+ align:start position:0%
+that the heart intensive care unit the
+cardiac intensive care unit is full up
+
+ align:start position:0%
+cardiac intensive care unit is full up
+ 
+
+ align:start position:0%
+cardiac intensive care unit is full up
+with patients but there's an extra bed
+
+ align:start position:0%
+with patients but there's an extra bed
+ 
+
+ align:start position:0%
+with patients but there's an extra bed
+in the pulmonary intensive care unit and
+
+ align:start position:0%
+in the pulmonary intensive care unit and
+ 
+
+ align:start position:0%
+in the pulmonary intensive care unit and
+so they stick you in that unit but
+
+ align:start position:0%
+so they stick you in that unit but
+ 
+
+ align:start position:0%
+so they stick you in that unit but
+you're still on the cardiology service
+
+ align:start position:0%
+you're still on the cardiology service
+ 
+
+ align:start position:0%
+you're still on the cardiology service
+and so there are these sort of mixture
+
+ align:start position:0%
+and so there are these sort of mixture
+ 
+
+ align:start position:0%
+and so there are these sort of mixture
+kinds of cases that you still have to
+
+ align:start position:0%
+kinds of cases that you still have to
+ 
+
+ align:start position:0%
+kinds of cases that you still have to
+take care of transfers are when you get
+
+ align:start position:0%
+take care of transfers are when you get
+ 
+
+ align:start position:0%
+take care of transfers are when you get
+transferred from one place to another in
+
+ align:start position:0%
+transferred from one place to another in
+ 
+
+ align:start position:0%
+transferred from one place to another in
+the hospital imaging data so I'm not
+
+ align:start position:0%
+the hospital imaging data so I'm not
+ 
+
+ align:start position:0%
+the hospital imaging data so I'm not
+going to talk about that much today but
+
+ align:start position:0%
+going to talk about that much today but
+ 
+
+ align:start position:0%
+going to talk about that much today but
+there are x-rays ultrasound CT MRI PET
+
+ align:start position:0%
+there are x-rays ultrasound CT MRI PET
+ 
+
+ align:start position:0%
+there are x-rays ultrasound CT MRI PET
+scans retinal scans endoscopy
+
+ align:start position:0%
+scans retinal scans endoscopy
+ 
+
+ align:start position:0%
+scans retinal scans endoscopy
+photographs of like your skin and stuff
+
+ align:start position:0%
+photographs of like your skin and stuff
+ 
+
+ align:start position:0%
+photographs of like your skin and stuff
+like that so this is all imaging data
+
+ align:start position:0%
+like that so this is all imaging data
+ 
+
+ align:start position:0%
+like that so this is all imaging data
+and there's been a tremendous amount of
+
+ align:start position:0%
+and there's been a tremendous amount of
+ 
+
+ align:start position:0%
+and there's been a tremendous amount of
+progress recently in applying machine
+
+ align:start position:0%
+progress recently in applying machine
+ 
+
+ align:start position:0%
+progress recently in applying machine
+learning technique
+
+ align:start position:0%
+learning technique
+ 
+
+ align:start position:0%
+learning technique
+to try to interpret the contents of
+
+ align:start position:0%
+to try to interpret the contents of
+ 
+
+ align:start position:0%
+to try to interpret the contents of
+these data so these are also very
+
+ align:start position:0%
+these data so these are also very
+ 
+
+ align:start position:0%
+these data so these are also very
+important and then there's the whole
+
+ align:start position:0%
+important and then there's the whole
+ 
+
+ align:start position:0%
+important and then there's the whole
+quantified self-movement
+
+ align:start position:0%
+quantified self-movement
+ 
+
+ align:start position:0%
+quantified self-movement
+I mean how many of you wear a activity
+
+ align:start position:0%
+I mean how many of you wear a activity
+ 
+
+ align:start position:0%
+I mean how many of you wear a activity
+tracker only about a third I'm surprised
+
+ align:start position:0%
+tracker only about a third I'm surprised
+ 
+
+ align:start position:0%
+tracker only about a third I'm surprised
+that the place like MIT so you know we
+
+ align:start position:0%
+that the place like MIT so you know we
+ 
+
+ align:start position:0%
+that the place like MIT so you know we
+measure steps and elevation change and
+
+ align:start position:0%
+measure steps and elevation change and
+ 
+
+ align:start position:0%
+measure steps and elevation change and
+workouts and you can record vital signs
+
+ align:start position:0%
+workouts and you can record vital signs
+ 
+
+ align:start position:0%
+workouts and you can record vital signs
+and diet and your blood sugar especially
+
+ align:start position:0%
+and diet and your blood sugar especially
+ 
+
+ align:start position:0%
+and diet and your blood sugar especially
+if you're diabetic allergies allergic
+
+ align:start position:0%
+if you're diabetic allergies allergic
+ 
+
+ align:start position:0%
+if you're diabetic allergies allergic
+incidents there's all this mindfulness
+
+ align:start position:0%
+incidents there's all this mindfulness
+ 
+
+ align:start position:0%
+incidents there's all this mindfulness
+mood sleep pain sexual activity and then
+
+ align:start position:0%
+mood sleep pain sexual activity and then
+ 
+
+ align:start position:0%
+mood sleep pain sexual activity and then
+people have developed this idea of n of
+
+ align:start position:0%
+people have developed this idea of n of
+ 
+
+ align:start position:0%
+people have developed this idea of n of
+one experiments where for example I had
+
+ align:start position:0%
+one experiments where for example I had
+ 
+
+ align:start position:0%
+one experiments where for example I had
+a student some years ago who was
+
+ align:start position:0%
+a student some years ago who was
+ 
+
+ align:start position:0%
+a student some years ago who was
+suffered from psoriasis
+
+ align:start position:0%
+suffered from psoriasis
+ 
+
+ align:start position:0%
+suffered from psoriasis
+it's a Brodie condition of the skin and
+
+ align:start position:0%
+it's a Brodie condition of the skin and
+ 
+
+ align:start position:0%
+it's a Brodie condition of the skin and
+the problem is there are no good cures
+
+ align:start position:0%
+the problem is there are no good cures
+ 
+
+ align:start position:0%
+the problem is there are no good cures
+for it and so people who suffer from
+
+ align:start position:0%
+for it and so people who suffer from
+ 
+
+ align:start position:0%
+for it and so people who suffer from
+psoriasis try all kinds of things you
+
+ align:start position:0%
+psoriasis try all kinds of things you
+ 
+
+ align:start position:0%
+psoriasis try all kinds of things you
+know they stop eating nuts for a while
+
+ align:start position:0%
+know they stop eating nuts for a while
+ 
+
+ align:start position:0%
+know they stop eating nuts for a while
+or they douse themselves with vinegar or
+
+ align:start position:0%
+or they douse themselves with vinegar or
+ 
+
+ align:start position:0%
+or they douse themselves with vinegar or
+they do you know whatever crazy thing
+
+ align:start position:0%
+they do you know whatever crazy thing
+ 
+
+ align:start position:0%
+they do you know whatever crazy thing
+comes to mind and we don't have a good
+
+ align:start position:0%
+comes to mind and we don't have a good
+ 
+
+ align:start position:0%
+comes to mind and we don't have a good
+theory for how to treat this disease but
+
+ align:start position:0%
+theory for how to treat this disease but
+ 
+
+ align:start position:0%
+theory for how to treat this disease but
+on the other hand some things work for
+
+ align:start position:0%
+on the other hand some things work for
+ 
+
+ align:start position:0%
+on the other hand some things work for
+some people and so there's a whole
+
+ align:start position:0%
+some people and so there's a whole
+ 
+
+ align:start position:0%
+some people and so there's a whole
+methodology that has been developed that
+
+ align:start position:0%
+methodology that has been developed that
+ 
+
+ align:start position:0%
+methodology that has been developed that
+says when you try these things act like
+
+ align:start position:0%
+says when you try these things act like
+ 
+
+ align:start position:0%
+says when you try these things act like
+a scientist have hypotheses take good
+
+ align:start position:0%
+a scientist have hypotheses take good
+ 
+
+ align:start position:0%
+a scientist have hypotheses take good
+notes collect good data be cognizant of
+
+ align:start position:0%
+notes collect good data be cognizant of
+ 
+
+ align:start position:0%
+notes collect good data be cognizant of
+things like onset periods where you know
+
+ align:start position:0%
+things like onset periods where you know
+ 
+
+ align:start position:0%
+things like onset periods where you know
+you may have to drip vinegar on yourself
+
+ align:start position:0%
+you may have to drip vinegar on yourself
+ 
+
+ align:start position:0%
+you may have to drip vinegar on yourself
+for a week before you see any effect so
+
+ align:start position:0%
+for a week before you see any effect so
+ 
+
+ align:start position:0%
+for a week before you see any effect so
+if it doesn't do anything after one day
+
+ align:start position:0%
+if it doesn't do anything after one day
+ 
+
+ align:start position:0%
+if it doesn't do anything after one day
+don't stop and furthermore if you stop
+
+ align:start position:0%
+don't stop and furthermore if you stop
+ 
+
+ align:start position:0%
+don't stop and furthermore if you stop
+then don't start something new
+
+ align:start position:0%
+then don't start something new
+ 
+
+ align:start position:0%
+then don't start something new
+immediately because you will then be
+
+ align:start position:0%
+immediately because you will then be
+ 
+
+ align:start position:0%
+immediately because you will then be
+confused about whether this is the
+
+ align:start position:0%
+confused about whether this is the
+ 
+
+ align:start position:0%
+confused about whether this is the
+effect of the thing you were on before
+
+ align:start position:0%
+effect of the thing you were on before
+ 
+
+ align:start position:0%
+effect of the thing you were on before
+or the new thing that you're trying so
+
+ align:start position:0%
+or the new thing that you're trying so
+ 
+
+ align:start position:0%
+or the new thing that you're trying so
+there's all sorts of ideas like that
+
+ align:start position:0%
+there's all sorts of ideas like that
+ 
+
+ align:start position:0%
+there's all sorts of ideas like that
+okay so this is a slide from our paper
+
+ align:start position:0%
+okay so this is a slide from our paper
+ 
+
+ align:start position:0%
+okay so this is a slide from our paper
+on on mimic three and it gives you a
+
+ align:start position:0%
+on on mimic three and it gives you a
+ 
+
+ align:start position:0%
+on on mimic three and it gives you a
+kind of overview of what's going on with
+
+ align:start position:0%
+kind of overview of what's going on with
+ 
+
+ align:start position:0%
+kind of overview of what's going on with
+the patient so if you look at this I'm
+
+ align:start position:0%
+the patient so if you look at this I'm
+ 
+
+ align:start position:0%
+the patient so if you look at this I'm
+gonna point with my hands at the top is
+
+ align:start position:0%
+gonna point with my hands at the top is
+ 
+
+ align:start position:0%
+gonna point with my hands at the top is
+something very important this patient
+
+ align:start position:0%
+something very important this patient
+ 
+
+ align:start position:0%
+something very important this patient
+starts off at full code that means that
+
+ align:start position:0%
+starts off at full code that means that
+ 
+
+ align:start position:0%
+starts off at full code that means that
+if something bad happens to him he wants
+
+ align:start position:0%
+if something bad happens to him he wants
+ 
+
+ align:start position:0%
+if something bad happens to him he wants
+everything to be done to try to save him
+
+ align:start position:0%
+everything to be done to try to save him
+ 
+
+ align:start position:0%
+everything to be done to try to save him
+and he winds up in comfort measures only
+
+ align:start position:0%
+and he winds up in comfort measures only
+ 
+
+ align:start position:0%
+and he winds up in comfort measures only
+which means that if something bad
+
+ align:start position:0%
+which means that if something bad
+ 
+
+ align:start position:0%
+which means that if something bad
+happens to him he wants to die where his
+
+ align:start position:0%
+happens to him he wants to die where his
+ 
+
+ align:start position:0%
+happens to him he wants to die where his
+family does if if he's unconscious
+
+ align:start position:0%
+family does if if he's unconscious
+ 
+
+ align:start position:0%
+family does if if he's unconscious
+right so what else do we know about this
+
+ align:start position:0%
+right so what else do we know about this
+ 
+
+ align:start position:0%
+right so what else do we know about this
+guy well GCS is the Glasgow Coma score
+
+ align:start position:0%
+guy well GCS is the Glasgow Coma score
+ 
+
+ align:start position:0%
+guy well GCS is the Glasgow Coma score
+and it's a way of quantifying people's
+
+ align:start position:0%
+and it's a way of quantifying people's
+ 
+
+ align:start position:0%
+and it's a way of quantifying people's
+level of consciousness and you see that
+
+ align:start position:0%
+level of consciousness and you see that
+ 
+
+ align:start position:0%
+level of consciousness and you see that
+at the beginning this patient is
+
+ align:start position:0%
+at the beginning this patient is
+ 
+
+ align:start position:0%
+at the beginning this patient is
+oriented and then gets confused and
+
+ align:start position:0%
+oriented and then gets confused and
+ 
+
+ align:start position:0%
+oriented and then gets confused and
+finally as only making incomprehensible
+
+ align:start position:0%
+finally as only making incomprehensible
+ 
+
+ align:start position:0%
+finally as only making incomprehensible
+words or sounds motor is able to obey
+
+ align:start position:0%
+words or sounds motor is able to obey
+ 
+
+ align:start position:0%
+words or sounds motor is able to obey
+commands eventually he's only able to
+
+ align:start position:0%
+commands eventually he's only able to
+ 
+
+ align:start position:0%
+commands eventually he's only able to
+flex when you stimulate his muscles so
+
+ align:start position:0%
+flex when you stimulate his muscles so
+ 
+
+ align:start position:0%
+flex when you stimulate his muscles so
+he's no longer conscious high movements
+
+ align:start position:0%
+he's no longer conscious high movements
+ 
+
+ align:start position:0%
+he's no longer conscious high movements
+he's able to follow you spontaneously
+
+ align:start position:0%
+he's able to follow you spontaneously
+ 
+
+ align:start position:0%
+he's able to follow you spontaneously
+he's able to orient to speech and
+
+ align:start position:0%
+he's able to orient to speech and
+ 
+
+ align:start position:0%
+he's able to orient to speech and
+eventually no more intuition at all so
+
+ align:start position:0%
+eventually no more intuition at all so
+ 
+
+ align:start position:0%
+eventually no more intuition at all so
+this is clearly somebody who's going
+
+ align:start position:0%
+this is clearly somebody who's going
+ 
+
+ align:start position:0%
+this is clearly somebody who's going
+downhill quickly and in fact dies at the
+
+ align:start position:0%
+downhill quickly and in fact dies at the
+ 
+
+ align:start position:0%
+downhill quickly and in fact dies at the
+end of this of this episode
+
+ align:start position:0%
+end of this of this episode
+ 
+
+ align:start position:0%
+end of this of this episode
+now we then look at labs so we can see
+
+ align:start position:0%
+now we then look at labs so we can see
+ 
+
+ align:start position:0%
+now we then look at labs so we can see
+what is their level of platelets at
+
+ align:start position:0%
+what is their level of platelets at
+ 
+
+ align:start position:0%
+what is their level of platelets at
+about the time that they're measured
+
+ align:start position:0%
+about the time that they're measured
+ 
+
+ align:start position:0%
+about the time that they're measured
+their creatinine level their white blood
+
+ align:start position:0%
+their creatinine level their white blood
+ 
+
+ align:start position:0%
+their creatinine level their white blood
+cell count the neutrophil percentage etc
+
+ align:start position:0%
+cell count the neutrophil percentage etc
+ 
+
+ align:start position:0%
+cell count the neutrophil percentage etc
+and there's not every possible data
+
+ align:start position:0%
+and there's not every possible data
+ 
+
+ align:start position:0%
+and there's not every possible data
+point on the slide this is just
+
+ align:start position:0%
+point on the slide this is just
+ 
+
+ align:start position:0%
+point on the slide this is just
+illustrative the next section is
+
+ align:start position:0%
+illustrative the next section is
+ 
+
+ align:start position:0%
+illustrative the next section is
+medications so the person is on morphine
+
+ align:start position:0%
+medications so the person is on morphine
+ 
+
+ align:start position:0%
+medications so the person is on morphine
+of they're on vancomycin which is an
+
+ align:start position:0%
+of they're on vancomycin which is an
+ 
+
+ align:start position:0%
+of they're on vancomycin which is an
+antibiotic Pipper asila and I don't know
+
+ align:start position:0%
+antibiotic Pipper asila and I don't know
+ 
+
+ align:start position:0%
+antibiotic Pipper asila and I don't know
+that is somebody no that's what okay
+
+ align:start position:0%
+that is somebody no that's what okay
+ 
+
+ align:start position:0%
+that is somebody no that's what okay
+sodium chloride 9% so that's just
+
+ align:start position:0%
+sodium chloride 9% so that's just
+ 
+
+ align:start position:0%
+sodium chloride 9% so that's just
+keeping him hydrated amiodarone and
+
+ align:start position:0%
+keeping him hydrated amiodarone and
+ 
+
+ align:start position:0%
+keeping him hydrated amiodarone and
+dextrose or dextrose is giving him some
+
+ align:start position:0%
+dextrose or dextrose is giving him some
+ 
+
+ align:start position:0%
+dextrose or dextrose is giving him some
+energy and then these are the various
+
+ align:start position:0%
+energy and then these are the various
+ 
+
+ align:start position:0%
+energy and then these are the various
+measurements so you see the heart rate
+
+ align:start position:0%
+measurements so you see the heart rate
+ 
+
+ align:start position:0%
+measurements so you see the heart rate
+for example is up pretty high and is
+
+ align:start position:0%
+for example is up pretty high and is
+ 
+
+ align:start position:0%
+for example is up pretty high and is
+going up near the end the oxygen
+
+ align:start position:0%
+going up near the end the oxygen
+ 
+
+ align:start position:0%
+going up near the end the oxygen
+saturation starts off pretty good but
+
+ align:start position:0%
+saturation starts off pretty good but
+ 
+
+ align:start position:0%
+saturation starts off pretty good but
+here we're down to you know sixty
+
+ align:start position:0%
+here we're down to you know sixty
+ 
+
+ align:start position:0%
+here we're down to you know sixty
+percent or fifty percent o2 sat which is
+
+ align:start position:0%
+percent or fifty percent o2 sat which is
+ 
+
+ align:start position:0%
+percent or fifty percent o2 sat which is
+supposed to be above about 92 in order
+
+ align:start position:0%
+supposed to be above about 92 in order
+ 
+
+ align:start position:0%
+supposed to be above about 92 in order
+to be considered reasonable so again
+
+ align:start position:0%
+to be considered reasonable so again
+ 
+
+ align:start position:0%
+to be considered reasonable so again
+this is a very consistent picture of
+
+ align:start position:0%
+this is a very consistent picture of
+ 
+
+ align:start position:0%
+this is a very consistent picture of
+things going very badly wrong for this
+
+ align:start position:0%
+things going very badly wrong for this
+ 
+
+ align:start position:0%
+things going very badly wrong for this
+particular patient so this is all the
+
+ align:start position:0%
+particular patient so this is all the
+ 
+
+ align:start position:0%
+particular patient so this is all the
+data in the database now if you want to
+
+ align:start position:0%
+data in the database now if you want to
+ 
+
+ align:start position:0%
+data in the database now if you want to
+try to analyze some of this stuff you
+
+ align:start position:0%
+try to analyze some of this stuff you
+ 
+
+ align:start position:0%
+try to analyze some of this stuff you
+can say well let's look at the ages at
+
+ align:start position:0%
+can say well let's look at the ages at
+ 
+
+ align:start position:0%
+can say well let's look at the ages at
+the time of the last lab measurement in
+
+ align:start position:0%
+the time of the last lab measurement in
+ 
+
+ align:start position:0%
+the time of the last lab measurement in
+the database so we have the times of all
+
+ align:start position:0%
+the database so we have the times of all
+ 
+
+ align:start position:0%
+the database so we have the times of all
+the lab measurements so we can see that
+
+ align:start position:0%
+the lab measurements so we can see that
+ 
+
+ align:start position:0%
+the lab measurements so we can see that
+many of the ICU population are fairly
+
+ align:start position:0%
+many of the ICU population are fairly
+ 
+
+ align:start position:0%
+many of the ICU population are fairly
+old right there's a relatively small
+
+ align:start position:0%
+old right there's a relatively small
+ 
+
+ align:start position:0%
+old right there's a relatively small
+number of young people and then a
+
+ align:start position:0%
+number of young people and then a
+ 
+
+ align:start position:0%
+number of young people and then a
+growing number of older people in both
+
+ align:start position:0%
+growing number of older people in both
+ 
+
+ align:start position:0%
+growing number of older people in both
+both females and males if we look at age
+
+ align:start position:0%
+both females and males if we look at age
+ 
+
+ align:start position:0%
+both females and males if we look at age
+8 admission by gender so this is age at
+
+ align:start position:0%
+8 admission by gender so this is age at
+ 
+
+ align:start position:0%
+8 admission by gender so this is age at
+admission not age at the time the last
+
+ align:start position:0%
+admission not age at the time the last
+ 
+
+ align:start position:0%
+admission not age at the time the last
+lab measurement was done it's pretty
+
+ align:start position:0%
+lab measurement was done it's pretty
+ 
+
+ align:start position:0%
+lab measurement was done it's pretty
+similar curve so we see that you know
+
+ align:start position:0%
+similar curve so we see that you know
+ 
+
+ align:start position:0%
+similar curve so we see that you know
+females were sixty four point two one at
+
+ align:start position:0%
+females were sixty four point two one at
+ 
+
+ align:start position:0%
+females were sixty four point two one at
+time of last measurement lab measurement
+
+ align:start position:0%
+time of last measurement lab measurement
+ 
+
+ align:start position:0%
+time of last measurement lab measurement
+sixty three point five at the time of
+
+ align:start position:0%
+sixty three point five at the time of
+ 
+
+ align:start position:0%
+sixty three point five at the time of
+admission so we can look at demographics
+
+ align:start position:0%
+admission so we can look at demographics
+ 
+
+ align:start position:0%
+admission so we can look at demographics
+and demographics typically includes
+
+ align:start position:0%
+and demographics typically includes
+ 
+
+ align:start position:0%
+and demographics typically includes
+these kinds of factors which I mentioned
+
+ align:start position:0%
+these kinds of factors which I mentioned
+ 
+
+ align:start position:0%
+these kinds of factors which I mentioned
+before and again if we're interested in
+
+ align:start position:0%
+before and again if we're interested in
+ 
+
+ align:start position:0%
+before and again if we're interested in
+the relationship between this and for
+
+ align:start position:0%
+the relationship between this and for
+ 
+
+ align:start position:0%
+the relationship between this and for
+example the age distribution we see that
+
+ align:start position:0%
+example the age distribution we see that
+ 
+
+ align:start position:0%
+example the age distribution we see that
+if you look at the
+
+ align:start position:0%
+if you look at the
+ 
+
+ align:start position:0%
+if you look at the
+different admission types so you can be
+
+ align:start position:0%
+different admission types so you can be
+ 
+
+ align:start position:0%
+different admission types so you can be
+either admitted through before an
+
+ align:start position:0%
+either admitted through before an
+ 
+
+ align:start position:0%
+either admitted through before an
+emergency for some urgent care or
+
+ align:start position:0%
+emergency for some urgent care or
+ 
+
+ align:start position:0%
+emergency for some urgent care or
+electively
+
+ align:start position:0%
+electively
+ 
+
+ align:start position:0%
+electively
+and it doesn't seem to make a whole lot
+
+ align:start position:0%
+and it doesn't seem to make a whole lot
+ 
+
+ align:start position:0%
+and it doesn't seem to make a whole lot
+of difference at least in the means of
+
+ align:start position:0%
+of difference at least in the means of
+ 
+
+ align:start position:0%
+of difference at least in the means of
+the population age distribution on the
+
+ align:start position:0%
+the population age distribution on the
+ 
+
+ align:start position:0%
+the population age distribution on the
+other hand if you look at insurance type
+
+ align:start position:0%
+other hand if you look at insurance type
+ 
+
+ align:start position:0%
+other hand if you look at insurance type
+and say what who's paying the bills
+
+ align:start position:0%
+and say what who's paying the bills
+ 
+
+ align:start position:0%
+and say what who's paying the bills
+there's a big difference in the age
+
+ align:start position:0%
+there's a big difference in the age
+ 
+
+ align:start position:0%
+there's a big difference in the age
+distributions now why do you think that
+
+ align:start position:0%
+distributions now why do you think that
+ 
+
+ align:start position:0%
+distributions now why do you think that
+private insurance drops way off at about
+
+ align:start position:0%
+private insurance drops way off at about
+ 
+
+ align:start position:0%
+private insurance drops way off at about
+65 it's because of Medicare so Medicare
+
+ align:start position:0%
+65 it's because of Medicare so Medicare
+ 
+
+ align:start position:0%
+65 it's because of Medicare so Medicare
+covers people over 65 years old there's
+
+ align:start position:0%
+covers people over 65 years old there's
+ 
+
+ align:start position:0%
+covers people over 65 years old there's
+a terrible story I have to tell you I
+
+ align:start position:0%
+a terrible story I have to tell you I
+ 
+
+ align:start position:0%
+a terrible story I have to tell you I
+was talking to somebody at an insurance
+
+ align:start position:0%
+was talking to somebody at an insurance
+ 
+
+ align:start position:0%
+was talking to somebody at an insurance
+company it's a bit cynical and he said
+
+ align:start position:0%
+company it's a bit cynical and he said
+ 
+
+ align:start position:0%
+company it's a bit cynical and he said
+suppose that you see a 63 year old
+
+ align:start position:0%
+suppose that you see a 63 year old
+ 
+
+ align:start position:0%
+suppose that you see a 63 year old
+patient who's developing type 2 diabetes
+
+ align:start position:0%
+patient who's developing type 2 diabetes
+ 
+
+ align:start position:0%
+patient who's developing type 2 diabetes
+what should you do for him well there
+
+ align:start position:0%
+what should you do for him well there
+ 
+
+ align:start position:0%
+what should you do for him well there
+are standard things you should do for
+
+ align:start position:0%
+are standard things you should do for
+ 
+
+ align:start position:0%
+are standard things you should do for
+somebody developing type 2 diabetes like
+
+ align:start position:0%
+somebody developing type 2 diabetes like
+ 
+
+ align:start position:0%
+somebody developing type 2 diabetes like
+get him to eat better again him to lose
+
+ align:start position:0%
+get him to eat better again him to lose
+ 
+
+ align:start position:0%
+get him to eat better again him to lose
+weight get him to exercise more etc etc
+
+ align:start position:0%
+weight get him to exercise more etc etc
+ 
+
+ align:start position:0%
+weight get him to exercise more etc etc
+but his cynical answer was absolutely
+
+ align:start position:0%
+but his cynical answer was absolutely
+ 
+
+ align:start position:0%
+but his cynical answer was absolutely
+nothing okay why well it's very cheap to
+
+ align:start position:0%
+nothing okay why well it's very cheap to
+ 
+
+ align:start position:0%
+nothing okay why well it's very cheap to
+do nothing most people who develop type
+
+ align:start position:0%
+do nothing most people who develop type
+ 
+
+ align:start position:0%
+do nothing most people who develop type
+2 diabetes don't get real sick in the
+
+ align:start position:0%
+2 diabetes don't get real sick in the
+ 
+
+ align:start position:0%
+2 diabetes don't get real sick in the
+next two years and by the time this
+
+ align:start position:0%
+next two years and by the time this
+ 
+
+ align:start position:0%
+next two years and by the time this
+patient is 65 he'll be the government's
+
+ align:start position:0%
+patient is 65 he'll be the government's
+ 
+
+ align:start position:0%
+patient is 65 he'll be the government's
+responsibility not the insurance
+
+ align:start position:0%
+responsibility not the insurance
+ 
+
+ align:start position:0%
+responsibility not the insurance
+companies okay nice
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so of course a lot of the elderly
+
+ align:start position:0%
+okay so of course a lot of the elderly
+ 
+
+ align:start position:0%
+okay so of course a lot of the elderly
+are insured by Medicare or Medicaid not
+
+ align:start position:0%
+are insured by Medicare or Medicaid not
+ 
+
+ align:start position:0%
+are insured by Medicare or Medicaid not
+that surprising self-pay is a pretty
+
+ align:start position:0%
+that surprising self-pay is a pretty
+ 
+
+ align:start position:0%
+that surprising self-pay is a pretty
+small number because it's insanely
+
+ align:start position:0%
+small number because it's insanely
+ 
+
+ align:start position:0%
+small number because it's insanely
+expensive to pay for your own health
+
+ align:start position:0%
+expensive to pay for your own health
+ 
+
+ align:start position:0%
+expensive to pay for your own health
+care what about where you came from
+
+ align:start position:0%
+care what about where you came from
+ 
+
+ align:start position:0%
+care what about where you came from
+right were you referred from a clinic or
+
+ align:start position:0%
+right were you referred from a clinic or
+ 
+
+ align:start position:0%
+right were you referred from a clinic or
+were you an emergency room admit or were
+
+ align:start position:0%
+were you an emergency room admit or were
+ 
+
+ align:start position:0%
+were you an emergency room admit or were
+you referred from an HMO or etc and
+
+ align:start position:0%
+you referred from an HMO or etc and
+ 
+
+ align:start position:0%
+you referred from an HMO or etc and
+other than transfer from a skilled
+
+ align:start position:0%
+other than transfer from a skilled
+ 
+
+ align:start position:0%
+other than transfer from a skilled
+nursing facility were transferred within
+
+ align:start position:0%
+nursing facility were transferred within
+ 
+
+ align:start position:0%
+nursing facility were transferred within
+the facility within the hospital it
+
+ align:start position:0%
+the facility within the hospital it
+ 
+
+ align:start position:0%
+the facility within the hospital it
+doesn't make much difference the
+
+ align:start position:0%
+doesn't make much difference the
+ 
+
+ align:start position:0%
+doesn't make much difference the
+averages there and the distributions
+
+ align:start position:0%
+averages there and the distributions
+ 
+
+ align:start position:0%
+averages there and the distributions
+look moderately similar if you're coming
+
+ align:start position:0%
+look moderately similar if you're coming
+ 
+
+ align:start position:0%
+look moderately similar if you're coming
+from a skilled nursing facility if you
+
+ align:start position:0%
+from a skilled nursing facility if you
+ 
+
+ align:start position:0%
+from a skilled nursing facility if you
+are in a skilled nursing facility you're
+
+ align:start position:0%
+are in a skilled nursing facility you're
+ 
+
+ align:start position:0%
+are in a skilled nursing facility you're
+probably old because younger people
+
+ align:start position:0%
+probably old because younger people
+ 
+
+ align:start position:0%
+probably old because younger people
+don't typically know need skilled
+
+ align:start position:0%
+don't typically know need skilled
+ 
+
+ align:start position:0%
+don't typically know need skilled
+nursing care and I'm not sure why
+
+ align:start position:0%
+nursing care and I'm not sure why
+ 
+
+ align:start position:0%
+nursing care and I'm not sure why
+transfers within the facility are
+
+ align:start position:0%
+transfers within the facility are
+ 
+
+ align:start position:0%
+transfers within the facility are
+significantly younger ages but it's true
+
+ align:start position:0%
+significantly younger ages but it's true
+ 
+
+ align:start position:0%
+significantly younger ages but it's true
+in from the mimic data what about H of
+
+ align:start position:0%
+in from the mimic data what about H of
+ 
+
+ align:start position:0%
+in from the mimic data what about H of
+add admission by language so some people
+
+ align:start position:0%
+add admission by language so some people
+ 
+
+ align:start position:0%
+add admission by language so some people
+speak English some speak people speak
+
+ align:start position:0%
+speak English some speak people speak
+ 
+
+ align:start position:0%
+speak English some speak people speak
+not available some people speak Spanish
+
+ align:start position:0%
+not available some people speak Spanish
+ 
+
+ align:start position:0%
+not available some people speak Spanish
+it's not a row so it turns out the
+
+ align:start position:0%
+it's not a row so it turns out the
+ 
+
+ align:start position:0%
+it's not a row so it turns out the
+Russians are the oldest right and that
+
+ align:start position:0%
+Russians are the oldest right and that
+ 
+
+ align:start position:0%
+Russians are the oldest right and that
+may have to do with immigration patterns
+
+ align:start position:0%
+may have to do with immigration patterns
+ 
+
+ align:start position:0%
+may have to do with immigration patterns
+or I don't know exactly why but that's
+
+ align:start position:0%
+or I don't know exactly why but that's
+ 
+
+ align:start position:0%
+or I don't know exactly why but that's
+that's the data that's what the data
+
+ align:start position:0%
+that's the data that's what the data
+ 
+
+ align:start position:0%
+that's the data that's what the data
+show if you do it by ethnicity it turns
+
+ align:start position:0%
+show if you do it by ethnicity it turns
+ 
+
+ align:start position:0%
+show if you do it by ethnicity it turns
+out that African Americans on the whole
+
+ align:start position:0%
+out that African Americans on the whole
+ 
+
+ align:start position:0%
+out that African Americans on the whole
+are somewhat younger than whites and
+
+ align:start position:0%
+are somewhat younger than whites and
+ 
+
+ align:start position:0%
+are somewhat younger than whites and
+Hispanics are somewhat younger yet so
+
+ align:start position:0%
+Hispanics are somewhat younger yet so
+ 
+
+ align:start position:0%
+Hispanics are somewhat younger yet so
+that means that those subpopulations
+
+ align:start position:0%
+that means that those subpopulations
+ 
+
+ align:start position:0%
+that means that those subpopulations
+apparently need
+
+ align:start position:0%
+apparently need
+ 
+
+ align:start position:0%
+apparently need
+tensive care earlier in life than than
+
+ align:start position:0%
+tensive care earlier in life than than
+ 
+
+ align:start position:0%
+tensive care earlier in life than than
+whites so this is a topic that's very
+
+ align:start position:0%
+whites so this is a topic that's very
+ 
+
+ align:start position:0%
+whites so this is a topic that's very
+hot right now
+
+ align:start position:0%
+hot right now
+ 
+
+ align:start position:0%
+hot right now
+discussions about how bias might play
+
+ align:start position:0%
+discussions about how bias might play
+ 
+
+ align:start position:0%
+discussions about how bias might play
+into healthcare yeah it just means that
+
+ align:start position:0%
+into healthcare yeah it just means that
+ 
+
+ align:start position:0%
+into healthcare yeah it just means that
+you know somebody refused to say what
+
+ align:start position:0%
+you know somebody refused to say what
+ 
+
+ align:start position:0%
+you know somebody refused to say what
+their ethnicity was yeah I think I'm not
+
+ align:start position:0%
+their ethnicity was yeah I think I'm not
+ 
+
+ align:start position:0%
+their ethnicity was yeah I think I'm not
+positive just this also represents like
+
+ align:start position:0%
+positive just this also represents like
+ 
+
+ align:start position:0%
+positive just this also represents like
+Boston's it's the catchment basin of the
+
+ align:start position:0%
+Boston's it's the catchment basin of the
+ 
+
+ align:start position:0%
+Boston's it's the catchment basin of the
+Beth Israel Deaconess Hospital which is
+
+ align:start position:0%
+Beth Israel Deaconess Hospital which is
+ 
+
+ align:start position:0%
+Beth Israel Deaconess Hospital which is
+Boston clearly but but they're all you
+
+ align:start position:0%
+Boston clearly but but they're all you
+ 
+
+ align:start position:0%
+Boston clearly but but they're all you
+know it turns out that like a lot of
+
+ align:start position:0%
+know it turns out that like a lot of
+ 
+
+ align:start position:0%
+know it turns out that like a lot of
+North Shore people go to Mass General
+
+ align:start position:0%
+North Shore people go to Mass General
+ 
+
+ align:start position:0%
+North Shore people go to Mass General
+and and so different hospitals have
+
+ align:start position:0%
+and and so different hospitals have
+ 
+
+ align:start position:0%
+and and so different hospitals have
+different catchment basins everybody
+
+ align:start position:0%
+different catchment basins everybody
+ 
+
+ align:start position:0%
+different catchment basins everybody
+these are all people who at some point
+
+ align:start position:0%
+these are all people who at some point
+ 
+
+ align:start position:0%
+these are all people who at some point
+were in the ICU so these are the sicker
+
+ align:start position:0%
+were in the ICU so these are the sicker
+ 
+
+ align:start position:0%
+were in the ICU so these are the sicker
+patients yeah so that is a higher
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+no actually I don't remember if I have
+
+ align:start position:0%
+no actually I don't remember if I have
+ 
+
+ align:start position:0%
+no actually I don't remember if I have
+that graph I think this is cumulative
+
+ align:start position:0%
+that graph I think this is cumulative
+ 
+
+ align:start position:0%
+that graph I think this is cumulative
+okay so so the most most people are are
+
+ align:start position:0%
+okay so so the most most people are are
+ 
+
+ align:start position:0%
+okay so so the most most people are are
+white for whatever the definition of
+
+ align:start position:0%
+white for whatever the definition of
+ 
+
+ align:start position:0%
+white for whatever the definition of
+white we're using and I think it's only
+
+ align:start position:0%
+white we're using and I think it's only
+ 
+
+ align:start position:0%
+white we're using and I think it's only
+the increment that you see on top okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+all right how about marital status well
+
+ align:start position:0%
+all right how about marital status well
+ 
+
+ align:start position:0%
+all right how about marital status well
+according to this it's bad to be single
+
+ align:start position:0%
+according to this it's bad to be single
+ 
+
+ align:start position:0%
+according to this it's bad to be single
+right so I could sort of see that for
+
+ align:start position:0%
+right so I could sort of see that for
+ 
+
+ align:start position:0%
+right so I could sort of see that for
+hospitalization I'm not sure why it's
+
+ align:start position:0%
+hospitalization I'm not sure why it's
+ 
+
+ align:start position:0%
+hospitalization I'm not sure why it's
+true for the ICU because if you don't
+
+ align:start position:0%
+true for the ICU because if you don't
+ 
+
+ align:start position:0%
+true for the ICU because if you don't
+have anybody at home to take care of you
+
+ align:start position:0%
+have anybody at home to take care of you
+ 
+
+ align:start position:0%
+have anybody at home to take care of you
+and you get sick it seems reasonable
+
+ align:start position:0%
+and you get sick it seems reasonable
+ 
+
+ align:start position:0%
+and you get sick it seems reasonable
+that you'd be more likely to wind up in
+
+ align:start position:0%
+that you'd be more likely to wind up in
+ 
+
+ align:start position:0%
+that you'd be more likely to wind up in
+the hospital but I don't know why you'd
+
+ align:start position:0%
+the hospital but I don't know why you'd
+ 
+
+ align:start position:0%
+the hospital but I don't know why you'd
+wind up in intensive care
+
+ align:start position:0%
+wind up in intensive care
+ 
+
+ align:start position:0%
+wind up in intensive care
+yeah probably younger and those are
+
+ align:start position:0%
+yeah probably younger and those are
+ 
+
+ align:start position:0%
+yeah probably younger and those are
+probably younger yes yeah yeah that's
+
+ align:start position:0%
+probably younger yes yeah yeah that's
+ 
+
+ align:start position:0%
+probably younger yes yeah yeah that's
+probably also right yep
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so here's an interesting question a
+
+ align:start position:0%
+okay so here's an interesting question a
+ 
+
+ align:start position:0%
+okay so here's an interesting question a
+little bit related to something you'll
+
+ align:start position:0%
+little bit related to something you'll
+ 
+
+ align:start position:0%
+little bit related to something you'll
+see on the next problem set so could we
+
+ align:start position:0%
+see on the next problem set so could we
+ 
+
+ align:start position:0%
+see on the next problem set so could we
+predict in hospital mortality from just
+
+ align:start position:0%
+predict in hospital mortality from just
+ 
+
+ align:start position:0%
+predict in hospital mortality from just
+these demographic features so I'm using
+
+ align:start position:0%
+these demographic features so I'm using
+ 
+
+ align:start position:0%
+these demographic features so I'm using
+a tool in in language called R this is a
+
+ align:start position:0%
+a tool in in language called R this is a
+ 
+
+ align:start position:0%
+a tool in in language called R this is a
+general linear model and I've set it up
+
+ align:start position:0%
+general linear model and I've set it up
+ 
+
+ align:start position:0%
+general linear model and I've set it up
+to do basically logistic regression and
+
+ align:start position:0%
+to do basically logistic regression and
+ 
+
+ align:start position:0%
+to do basically logistic regression and
+it says I'm predicting whether you die
+
+ align:start position:0%
+it says I'm predicting whether you die
+ 
+
+ align:start position:0%
+it says I'm predicting whether you die
+in the hospital based on these
+
+ align:start position:0%
+in the hospital based on these
+ 
+
+ align:start position:0%
+in the hospital based on these
+demographic factors and it turns out
+
+ align:start position:0%
+demographic factors and it turns out
+ 
+
+ align:start position:0%
+demographic factors and it turns out
+that the only ones that are highly
+
+ align:start position:0%
+that the only ones that are highly
+ 
+
+ align:start position:0%
+that the only ones that are highly
+significant are age so that's not
+
+ align:start position:0%
+significant are age so that's not
+ 
+
+ align:start position:0%
+significant are age so that's not
+surprising that older people are more
+
+ align:start position:0%
+surprising that older people are more
+ 
+
+ align:start position:0%
+surprising that older people are more
+likely to die than younger people it's
+
+ align:start position:0%
+likely to die than younger people it's
+ 
+
+ align:start position:0%
+likely to die than younger people it's
+generally true and if I'm unable to
+
+ align:start position:0%
+generally true and if I'm unable to
+ 
+
+ align:start position:0%
+generally true and if I'm unable to
+obtain your ethnicity or I don't know
+
+ align:start position:0%
+obtain your ethnicity or I don't know
+ 
+
+ align:start position:0%
+obtain your ethnicity or I don't know
+your ethnicity then you're more likely
+
+ align:start position:0%
+your ethnicity then you're more likely
+ 
+
+ align:start position:0%
+your ethnicity then you're more likely
+to die I've no clue why that might be
+
+ align:start position:0%
+to die I've no clue why that might be
+ 
+
+ align:start position:0%
+to die I've no clue why that might be
+the case and other things are not as
+
+ align:start position:0%
+the case and other things are not as
+ 
+
+ align:start position:0%
+the case and other things are not as
+significant so if you speak Spanish or
+
+ align:start position:0%
+significant so if you speak Spanish or
+ 
+
+ align:start position:0%
+significant so if you speak Spanish or
+English you're slightly less likely to
+
+ align:start position:0%
+English you're slightly less likely to
+ 
+
+ align:start position:0%
+English you're slightly less likely to
+die you see a negative contribution here
+
+ align:start position:0%
+die you see a negative contribution here
+ 
+
+ align:start position:0%
+die you see a negative contribution here
+and if your if you speak Russian you're
+
+ align:start position:0%
+and if your if you speak Russian you're
+ 
+
+ align:start position:0%
+and if your if you speak Russian you're
+slightly less likely to die but it's
+
+ align:start position:0%
+slightly less likely to die but it's
+ 
+
+ align:start position:0%
+slightly less likely to die but it's
+significant not at the P equal point oh
+
+ align:start position:0%
+significant not at the P equal point oh
+ 
+
+ align:start position:0%
+significant not at the P equal point oh
+five level but it is at the P equal
+
+ align:start position:0%
+five level but it is at the P equal
+ 
+
+ align:start position:0%
+five level but it is at the P equal
+point oh six level and marriage doesn't
+
+ align:start position:0%
+point oh six level and marriage doesn't
+ 
+
+ align:start position:0%
+point oh six level and marriage doesn't
+seem to make much difference in
+
+ align:start position:0%
+seem to make much difference in
+ 
+
+ align:start position:0%
+seem to make much difference in
+predicting whether you're gonna die or
+
+ align:start position:0%
+predicting whether you're gonna die or
+ 
+
+ align:start position:0%
+predicting whether you're gonna die or
+not
+
+ align:start position:0%
+not
+ 
+
+ align:start position:0%
+not
+now remember this is ICU patients and
+
+ align:start position:0%
+now remember this is ICU patients and
+ 
+
+ align:start position:0%
+now remember this is ICU patients and
+we're looking at in hospital mortality
+
+ align:start position:0%
+we're looking at in hospital mortality
+ 
+
+ align:start position:0%
+we're looking at in hospital mortality
+yeah I don't know because it could be
+
+ align:start position:0%
+yeah I don't know because it could be
+ 
+
+ align:start position:0%
+yeah I don't know because it could be
+that unable to obtain means that they
+
+ align:start position:0%
+that unable to obtain means that they
+ 
+
+ align:start position:0%
+that unable to obtain means that they
+died before we could ask them no cuz
+
+ align:start position:0%
+died before we could ask them no cuz
+ 
+
+ align:start position:0%
+died before we could ask them no cuz
+though there wouldn't be that many of
+
+ align:start position:0%
+though there wouldn't be that many of
+ 
+
+ align:start position:0%
+though there wouldn't be that many of
+those people I think there are not that
+
+ align:start position:0%
+those people I think there are not that
+ 
+
+ align:start position:0%
+those people I think there are not that
+many people who don't live past the
+
+ align:start position:0%
+many people who don't live past the
+ 
+
+ align:start position:0%
+many people who don't live past the
+intake interview and they do ask them
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah that would that would be an example
+
+ align:start position:0%
+yeah that would that would be an example
+ 
+
+ align:start position:0%
+yeah that would that would be an example
+but I don't think you'd see enough such
+
+ align:start position:0%
+but I don't think you'd see enough such
+ 
+
+ align:start position:0%
+but I don't think you'd see enough such
+people to show up statistically okay
+
+ align:start position:0%
+people to show up statistically okay
+ 
+
+ align:start position:0%
+people to show up statistically okay
+well so I've already mentioned that
+
+ align:start position:0%
+well so I've already mentioned that
+ 
+
+ align:start position:0%
+well so I've already mentioned that
+there's this problem of having moved
+
+ align:start position:0%
+there's this problem of having moved
+ 
+
+ align:start position:0%
+there's this problem of having moved
+from care view to meta vision just in
+
+ align:start position:0%
+from care view to meta vision just in
+ 
+
+ align:start position:0%
+from care view to meta vision just in
+the mimic database but of course this is
+
+ align:start position:0%
+the mimic database but of course this is
+ 
+
+ align:start position:0%
+the mimic database but of course this is
+a much bigger problem around the country
+
+ align:start position:0%
+a much bigger problem around the country
+ 
+
+ align:start position:0%
+a much bigger problem around the country
+and around the world because every
+
+ align:start position:0%
+and around the world because every
+ 
+
+ align:start position:0%
+and around the world because every
+hospital has its own way of keeping
+
+ align:start position:0%
+hospital has its own way of keeping
+ 
+
+ align:start position:0%
+hospital has its own way of keeping
+records and wouldn't it be nice if we
+
+ align:start position:0%
+records and wouldn't it be nice if we
+ 
+
+ align:start position:0%
+records and wouldn't it be nice if we
+had standards and of course there's this
+
+ align:start position:0%
+had standards and of course there's this
+ 
+
+ align:start position:0%
+had standards and of course there's this
+funny phrase the wonderful thing about
+
+ align:start position:0%
+funny phrase the wonderful thing about
+ 
+
+ align:start position:0%
+funny phrase the wonderful thing about
+standards is that there's so many to
+
+ align:start position:0%
+standards is that there's so many to
+ 
+
+ align:start position:0%
+standards is that there's so many to
+choose from so for example if you look
+
+ align:start position:0%
+choose from so for example if you look
+ 
+
+ align:start position:0%
+choose from so for example if you look
+at prescriptions in the mimic database
+
+ align:start position:0%
+at prescriptions in the mimic database
+ 
+
+ align:start position:0%
+at prescriptions in the mimic database
+here are two particular prescriptions
+
+ align:start position:0%
+here are two particular prescriptions
+ 
+
+ align:start position:0%
+here are two particular prescriptions
+for subject number 57 139 admitted on
+
+ align:start position:0%
+for subject number 57 139 admitted on
+ 
+
+ align:start position:0%
+for subject number 57 139 admitted on
+admission ID 155 for 7 oh and so they're
+
+ align:start position:0%
+admission ID 155 for 7 oh and so they're
+ 
+
+ align:start position:0%
+admission ID 155 for 7 oh and so they're
+they have the same start date but
+
+ align:start position:0%
+they have the same start date but
+ 
+
+ align:start position:0%
+they have the same start date but
+different end dates one is a
+
+ align:start position:0%
+different end dates one is a
+ 
+
+ align:start position:0%
+different end dates one is a
+prescription for tylenol acetaminophen
+
+ align:start position:0%
+prescription for tylenol acetaminophen
+ 
+
+ align:start position:0%
+prescription for tylenol acetaminophen
+and the other is for through beta salt
+
+ align:start position:0%
+and the other is for through beta salt
+ 
+
+ align:start position:0%
+and the other is for through beta salt
+propionate 0.05% cream that's a skin
+
+ align:start position:0%
+propionate 0.05% cream that's a skin
+ 
+
+ align:start position:0%
+propionate 0.05% cream that's a skin
+lotion thing for I think it's a steroid
+
+ align:start position:0%
+lotion thing for I think it's a steroid
+ 
+
+ align:start position:0%
+lotion thing for I think it's a steroid
+skin skin cream so if you look in the B
+
+ align:start position:0%
+skin skin cream so if you look in the B
+ 
+
+ align:start position:0%
+skin skin cream so if you look in the B
+eyes database they have their own
+
+ align:start position:0%
+eyes database they have their own
+ 
+
+ align:start position:0%
+eyes database they have their own
+private formulary code where this thing
+
+ align:start position:0%
+private formulary code where this thing
+ 
+
+ align:start position:0%
+private formulary code where this thing
+is a set 325 and this thing is Club dot
+
+ align:start position:0%
+is a set 325 and this thing is Club dot
+ 
+
+ align:start position:0%
+is a set 325 and this thing is Club dot
+zero five C 30 right and if you look
+
+ align:start position:0%
+zero five C 30 right and if you look
+ 
+
+ align:start position:0%
+zero five C 30 right and if you look
+there's also something called a GSN
+
+ align:start position:0%
+there's also something called a GSN
+ 
+
+ align:start position:0%
+there's also something called a GSN
+which is some commercial coding system
+
+ align:start position:0%
+which is some commercial coding system
+ 
+
+ align:start position:0%
+which is some commercial coding system
+for drugs maybe having to do with who
+
+ align:start position:0%
+for drugs maybe having to do with who
+ 
+
+ align:start position:0%
+for drugs maybe having to do with who
+their drug supplier is at the hospital
+
+ align:start position:0%
+their drug supplier is at the hospital
+ 
+
+ align:start position:0%
+their drug supplier is at the hospital
+and these have different codes
+
+ align:start position:0%
+and these have different codes
+ 
+
+ align:start position:0%
+and these have different codes
+there's the national drug code which is
+
+ align:start position:0%
+there's the national drug code which is
+ 
+
+ align:start position:0%
+there's the national drug code which is
+an FDA
+
+ align:start position:0%
+an FDA
+ 
+
+ align:start position:0%
+an FDA
+assigned nine digit code that specifies
+
+ align:start position:0%
+assigned nine digit code that specifies
+ 
+
+ align:start position:0%
+assigned nine digit code that specifies
+who made the drug what form it's in and
+
+ align:start position:0%
+who made the drug what form it's in and
+ 
+
+ align:start position:0%
+who made the drug what form it's in and
+what's its strength and so you get these
+
+ align:start position:0%
+what's its strength and so you get these
+ 
+
+ align:start position:0%
+what's its strength and so you get these
+then there's a human readable
+
+ align:start position:0%
+then there's a human readable
+ 
+
+ align:start position:0%
+then there's a human readable
+description that says tylenol comes in
+
+ align:start position:0%
+description that says tylenol comes in
+ 
+
+ align:start position:0%
+description that says tylenol comes in
+three hundred twenty five milligram
+
+ align:start position:0%
+three hundred twenty five milligram
+ 
+
+ align:start position:0%
+three hundred twenty five milligram
+tablets and this club a dose all comes
+
+ align:start position:0%
+tablets and this club a dose all comes
+ 
+
+ align:start position:0%
+tablets and this club a dose all comes
+in 30 gram tubes and the dose is
+
+ align:start position:0%
+in 30 gram tubes and the dose is
+ 
+
+ align:start position:0%
+in 30 gram tubes and the dose is
+supposed to be three twenty five to six
+
+ align:start position:0%
+supposed to be three twenty five to six
+ 
+
+ align:start position:0%
+supposed to be three twenty five to six
+fifty ie one to two tablets measured in
+
+ align:start position:0%
+fifty ie one to two tablets measured in
+ 
+
+ align:start position:0%
+fifty ie one to two tablets measured in
+milligrams the dose here is one
+
+ align:start position:0%
+milligrams the dose here is one
+ 
+
+ align:start position:0%
+milligrams the dose here is one
+application whatever that is I don't
+
+ align:start position:0%
+application whatever that is I don't
+ 
+
+ align:start position:0%
+application whatever that is I don't
+know what the point of one means and
+
+ align:start position:0%
+know what the point of one means and
+ 
+
+ align:start position:0%
+know what the point of one means and
+this is a tablet and that's a tube and
+
+ align:start position:0%
+this is a tablet and that's a tube and
+ 
+
+ align:start position:0%
+this is a tablet and that's a tube and
+this is taken orally and that's
+
+ align:start position:0%
+this is taken orally and that's
+ 
+
+ align:start position:0%
+this is taken orally and that's
+administered on the skin right so this
+
+ align:start position:0%
+administered on the skin right so this
+ 
+
+ align:start position:0%
+administered on the skin right so this
+is a local database for doctor the
+
+ align:start position:0%
+is a local database for doctor the
+ 
+
+ align:start position:0%
+is a local database for doctor the
+package
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+at most hospitals that's true now it
+
+ align:start position:0%
+at most hospitals that's true now it
+ 
+
+ align:start position:0%
+at most hospitals that's true now it
+wasn't true when the mimic database
+
+ align:start position:0%
+wasn't true when the mimic database
+ 
+
+ align:start position:0%
+wasn't true when the mimic database
+started being collected and the BI was
+
+ align:start position:0%
+started being collected and the BI was
+ 
+
+ align:start position:0%
+started being collected and the BI was
+relatively late in moving to that
+
+ align:start position:0%
+relatively late in moving to that
+ 
+
+ align:start position:0%
+relatively late in moving to that
+compared to some of the other hospitals
+
+ align:start position:0%
+compared to some of the other hospitals
+ 
+
+ align:start position:0%
+compared to some of the other hospitals
+in the Boston area I mean each hospital
+
+ align:start position:0%
+in the Boston area I mean each hospital
+ 
+
+ align:start position:0%
+in the Boston area I mean each hospital
+has its own digital or what it thinks is
+
+ align:start position:0%
+has its own digital or what it thinks is
+ 
+
+ align:start position:0%
+has its own digital or what it thinks is
+most important and and I think the B I
+
+ align:start position:0%
+most important and and I think the B I
+ 
+
+ align:start position:0%
+most important and and I think the B I
+just didn't prioritize it as much as
+
+ align:start position:0%
+just didn't prioritize it as much as
+ 
+
+ align:start position:0%
+just didn't prioritize it as much as
+some of the other hospitals okay so then
+
+ align:start position:0%
+some of the other hospitals okay so then
+ 
+
+ align:start position:0%
+some of the other hospitals okay so then
+I said well if you look at prescriptions
+
+ align:start position:0%
+I said well if you look at prescriptions
+ 
+
+ align:start position:0%
+I said well if you look at prescriptions
+how often are they given so remember we
+
+ align:start position:0%
+how often are they given so remember we
+ 
+
+ align:start position:0%
+how often are they given so remember we
+have about 60,000 ICU stays and so I so
+
+ align:start position:0%
+have about 60,000 ICU stays and so I so
+ 
+
+ align:start position:0%
+have about 60,000 ICU stays and so I so
+osmotic dextrose was given eighty seven
+
+ align:start position:0%
+osmotic dextrose was given eighty seven
+ 
+
+ align:start position:0%
+osmotic dextrose was given eighty seven
+thousand times to various people sodium
+
+ align:start position:0%
+thousand times to various people sodium
+ 
+
+ align:start position:0%
+thousand times to various people sodium
+chloride point nine percent flush do you
+
+ align:start position:0%
+chloride point nine percent flush do you
+ 
+
+ align:start position:0%
+chloride point nine percent flush do you
+know what that is
+
+ align:start position:0%
+know what that is
+ 
+
+ align:start position:0%
+know what that is
+have you ever had an IV so periodically
+
+ align:start position:0%
+have you ever had an IV so periodically
+ 
+
+ align:start position:0%
+have you ever had an IV so periodically
+the nurse comes by and squirts a little
+
+ align:start position:0%
+the nurse comes by and squirts a little
+ 
+
+ align:start position:0%
+the nurse comes by and squirts a little
+bit of stuff in in the IV to make sure
+
+ align:start position:0%
+bit of stuff in in the IV to make sure
+ 
+
+ align:start position:0%
+bit of stuff in in the IV to make sure
+that it hasn't clogged up that's what
+
+ align:start position:0%
+that it hasn't clogged up that's what
+ 
+
+ align:start position:0%
+that it hasn't clogged up that's what
+that is
+
+ align:start position:0%
+that is
+ 
+
+ align:start position:0%
+that is
+insulin SW I don't know salt water
+
+ align:start position:0%
+insulin SW I don't know salt water
+ 
+
+ align:start position:0%
+insulin SW I don't know salt water
+I don't know what s W is magnesium
+
+ align:start position:0%
+I don't know what s W is magnesium
+ 
+
+ align:start position:0%
+I don't know what s W is magnesium
+sulfate dextrose v in water
+
+ align:start position:0%
+sulfate dextrose v in water
+ 
+
+ align:start position:0%
+sulfate dextrose v in water
+furosemide is a diuretic potassium
+
+ align:start position:0%
+furosemide is a diuretic potassium
+ 
+
+ align:start position:0%
+furosemide is a diuretic potassium
+chloride replenishes potassium that
+
+ align:start position:0%
+chloride replenishes potassium that
+ 
+
+ align:start position:0%
+chloride replenishes potassium that
+people are often low on and then you go
+
+ align:start position:0%
+people are often low on and then you go
+ 
+
+ align:start position:0%
+people are often low on and then you go
+so why is there this d5w and that d5w
+
+ align:start position:0%
+so why is there this d5w and that d5w
+ 
+
+ align:start position:0%
+so why is there this d5w and that d5w
+and that's probably some data or in the
+
+ align:start position:0%
+and that's probably some data or in the
+ 
+
+ align:start position:0%
+and that's probably some data or in the
+system okay they one of them has an NDC
+
+ align:start position:0%
+system okay they one of them has an NDC
+ 
+
+ align:start position:0%
+system okay they one of them has an NDC
+code associated with it and the other
+
+ align:start position:0%
+code associated with it and the other
+ 
+
+ align:start position:0%
+code associated with it and the other
+one doesn't but probably should yeah the
+
+ align:start position:0%
+one doesn't but probably should yeah the
+ 
+
+ align:start position:0%
+one doesn't but probably should yeah the
+NDC code should be standard across the
+
+ align:start position:0%
+NDC code should be standard across the
+ 
+
+ align:start position:0%
+NDC code should be standard across the
+country because those are FDA assigned
+
+ align:start position:0%
+country because those are FDA assigned
+ 
+
+ align:start position:0%
+country because those are FDA assigned
+codes but not every hospital uses them
+
+ align:start position:0%
+codes but not every hospital uses them
+ 
+
+ align:start position:0%
+codes but not every hospital uses them
+okay and for the ones that say zero I'm
+
+ align:start position:0%
+okay and for the ones that say zero I'm
+ 
+
+ align:start position:0%
+okay and for the ones that say zero I'm
+not sure why they're not associated with
+
+ align:start position:0%
+not sure why they're not associated with
+ 
+
+ align:start position:0%
+not sure why they're not associated with
+the code in this this hospitals database
+
+ align:start position:0%
+the code in this this hospitals database
+ 
+
+ align:start position:0%
+the code in this this hospitals database
+okay next most common you see normal
+
+ align:start position:0%
+okay next most common you see normal
+ 
+
+ align:start position:0%
+okay next most common you see normal
+saline 0.9% sodium chloride so that was
+
+ align:start position:0%
+saline 0.9% sodium chloride so that was
+ 
+
+ align:start position:0%
+saline 0.9% sodium chloride so that was
+the same stuff as the flush solution but
+
+ align:start position:0%
+the same stuff as the flush solution but
+ 
+
+ align:start position:0%
+the same stuff as the flush solution but
+this time not being used for flush
+
+ align:start position:0%
+this time not being used for flush
+ 
+
+ align:start position:0%
+this time not being used for flush
+metoprolol is a beta blocker
+
+ align:start position:0%
+metoprolol is a beta blocker
+ 
+
+ align:start position:0%
+metoprolol is a beta blocker
+here's another insulin this time with an
+
+ align:start position:0%
+here's another insulin this time with an
+ 
+
+ align:start position:0%
+here's another insulin this time with an
+NDC code etc I love bag and vial okay so
+
+ align:start position:0%
+NDC code etc I love bag and vial okay so
+ 
+
+ align:start position:0%
+NDC code etc I love bag and vial okay so
+these are not exactly medications a bag
+
+ align:start position:0%
+these are not exactly medications a bag
+ 
+
+ align:start position:0%
+these are not exactly medications a bag
+is literally like a baggie that they put
+
+ align:start position:0%
+is literally like a baggie that they put
+ 
+
+ align:start position:0%
+is literally like a baggie that they put
+something into and a vial is literally
+
+ align:start position:0%
+something into and a vial is literally
+ 
+
+ align:start position:0%
+something into and a vial is literally
+something that they put pills in and why
+
+ align:start position:0%
+something that they put pills in and why
+ 
+
+ align:start position:0%
+something that they put pills in and why
+is that in the database because they get
+
+ align:start position:0%
+is that in the database because they get
+ 
+
+ align:start position:0%
+is that in the database because they get
+to charge for it okay and I don't know
+
+ align:start position:0%
+to charge for it okay and I don't know
+ 
+
+ align:start position:0%
+to charge for it okay and I don't know
+what the charges but it wouldn't
+
+ align:start position:0%
+what the charges but it wouldn't
+ 
+
+ align:start position:0%
+what the charges but it wouldn't
+surprise me if you're paying five bucks
+
+ align:start position:0%
+surprise me if you're paying five bucks
+ 
+
+ align:start position:0%
+surprise me if you're paying five bucks
+for a plastic bag to put something in
+
+ align:start position:0%
+for a plastic bag to put something in
+ 
+
+ align:start position:0%
+for a plastic bag to put something in
+okay so if we say well how many pharmacy
+
+ align:start position:0%
+okay so if we say well how many pharmacy
+ 
+
+ align:start position:0%
+okay so if we say well how many pharmacy
+orders are there for admission at this
+
+ align:start position:0%
+orders are there for admission at this
+ 
+
+ align:start position:0%
+orders are there for admission at this
+hospital and the answer is a lot so if
+
+ align:start position:0%
+hospital and the answer is a lot so if
+ 
+
+ align:start position:0%
+hospital and the answer is a lot so if
+you look at it's a very long tailed
+
+ align:start position:0%
+you look at it's a very long tailed
+ 
+
+ align:start position:0%
+you look at it's a very long tailed
+distribution goes out to about 2,500 but
+
+ align:start position:0%
+distribution goes out to about 2,500 but
+ 
+
+ align:start position:0%
+distribution goes out to about 2,500 but
+you see if I blow up just the numbers up
+
+ align:start position:0%
+you see if I blow up just the numbers up
+ 
+
+ align:start position:0%
+you see if I blow up just the numbers up
+to about two hundred there's a very
+
+ align:start position:0%
+to about two hundred there's a very
+ 
+
+ align:start position:0%
+to about two hundred there's a very
+large number of people with like two
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+prescriptions filled and then a fairly
+
+ align:start position:0%
+prescriptions filled and then a fairly
+ 
+
+ align:start position:0%
+prescriptions filled and then a fairly
+declining number with with more and then
+
+ align:start position:0%
+declining number with with more and then
+ 
+
+ align:start position:0%
+declining number with with more and then
+it's a very long tail so can you imagine
+
+ align:start position:0%
+it's a very long tail so can you imagine
+ 
+
+ align:start position:0%
+it's a very long tail so can you imagine
+you know twenty five hundred things
+
+ align:start position:0%
+you know twenty five hundred things
+ 
+
+ align:start position:0%
+you know twenty five hundred things
+prescribed for you during a hospital
+
+ align:start position:0%
+prescribed for you during a hospital
+ 
+
+ align:start position:0%
+prescribed for you during a hospital
+stay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+well a little more about standards so
+
+ align:start position:0%
+well a little more about standards so
+ 
+
+ align:start position:0%
+well a little more about standards so
+NDC is probably the best of the coding
+
+ align:start position:0%
+NDC is probably the best of the coding
+ 
+
+ align:start position:0%
+NDC is probably the best of the coding
+systems and it's developed by the FDA
+
+ align:start position:0%
+systems and it's developed by the FDA
+ 
+
+ align:start position:0%
+systems and it's developed by the FDA
+the picture up on the top right shows
+
+ align:start position:0%
+the picture up on the top right shows
+ 
+
+ align:start position:0%
+the picture up on the top right shows
+that the first four digits are the
+
+ align:start position:0%
+that the first four digits are the
+ 
+
+ align:start position:0%
+that the first four digits are the
+so-called label er that's usually the
+
+ align:start position:0%
+so-called label er that's usually the
+ 
+
+ align:start position:0%
+so-called label er that's usually the
+person who produced the drugs or at
+
+ align:start position:0%
+person who produced the drugs or at
+ 
+
+ align:start position:0%
+person who produced the drugs or at
+least the person who distributes them
+
+ align:start position:0%
+least the person who distributes them
+ 
+
+ align:start position:0%
+least the person who distributes them
+the second four digit number is the form
+
+ align:start position:0%
+the second four digit number is the form
+ 
+
+ align:start position:0%
+the second four digit number is the form
+of the drug so whether it's capsules or
+
+ align:start position:0%
+of the drug so whether it's capsules or
+ 
+
+ align:start position:0%
+of the drug so whether it's capsules or
+tablets or liquid or whatever and the
+
+ align:start position:0%
+tablets or liquid or whatever and the
+ 
+
+ align:start position:0%
+tablets or liquid or whatever and the
+dose and then the the last two digits
+
+ align:start position:0%
+dose and then the the last two digits
+ 
+
+ align:start position:0%
+dose and then the the last two digits
+are a package code which translates into
+
+ align:start position:0%
+are a package code which translates into
+ 
+
+ align:start position:0%
+are a package code which translates into
+the total number of doses that are in a
+
+ align:start position:0%
+the total number of doses that are in a
+ 
+
+ align:start position:0%
+the total number of doses that are in a
+package right so this is a godsend and
+
+ align:start position:0%
+package right so this is a godsend and
+ 
+
+ align:start position:0%
+package right so this is a godsend and
+all of the robotic pharmacies and so on
+
+ align:start position:0%
+all of the robotic pharmacies and so on
+ 
+
+ align:start position:0%
+all of the robotic pharmacies and so on
+rely on using this kind of information
+
+ align:start position:0%
+rely on using this kind of information
+ 
+
+ align:start position:0%
+rely on using this kind of information
+nowadays unfortunately they ran out of
+
+ align:start position:0%
+nowadays unfortunately they ran out of
+ 
+
+ align:start position:0%
+nowadays unfortunately they ran out of
+four-digit numbers and so there's now a
+
+ align:start position:0%
+four-digit numbers and so there's now a
+ 
+
+ align:start position:0%
+four-digit numbers and so there's now a
+they added an extra digit but they
+
+ align:start position:0%
+they added an extra digit but they
+ 
+
+ align:start position:0%
+they added an extra digit but they
+didn't do it systematically and so
+
+ align:start position:0%
+didn't do it systematically and so
+ 
+
+ align:start position:0%
+didn't do it systematically and so
+sometimes they added an extra digit to
+
+ align:start position:0%
+sometimes they added an extra digit to
+ 
+
+ align:start position:0%
+sometimes they added an extra digit to
+the label or and sometimes to the
+
+ align:start position:0%
+the label or and sometimes to the
+ 
+
+ align:start position:0%
+the label or and sometimes to the
+product code and so there's a nightmare
+
+ align:start position:0%
+product code and so there's a nightmare
+ 
+
+ align:start position:0%
+product code and so there's a nightmare
+of translations between the old codes
+
+ align:start position:0%
+of translations between the old codes
+ 
+
+ align:start position:0%
+of translations between the old codes
+and the new codes and you have to have a
+
+ align:start position:0%
+and the new codes and you have to have a
+ 
+
+ align:start position:0%
+and the new codes and you have to have a
+code dictionary in order to do it
+
+ align:start position:0%
+code dictionary in order to do it
+ 
+
+ align:start position:0%
+code dictionary in order to do it
+properly and so on okay well if that
+
+ align:start position:0%
+properly and so on okay well if that
+ 
+
+ align:start position:0%
+properly and so on okay well if that
+weren't good enough the International
+
+ align:start position:0%
+weren't good enough the International
+ 
+
+ align:start position:0%
+weren't good enough the International
+Council for the harmonization of
+
+ align:start position:0%
+Council for the harmonization of
+ 
+
+ align:start position:0%
+Council for the harmonization of
+technical requirements for
+
+ align:start position:0%
+technical requirements for
+ 
+
+ align:start position:0%
+technical requirements for
+pharmaceuticals for human use developed
+
+ align:start position:0%
+pharmaceuticals for human use developed
+ 
+
+ align:start position:0%
+pharmaceuticals for human use developed
+another coding system called meddra
+
+ align:start position:0%
+another coding system called meddra
+ 
+
+ align:start position:0%
+another coding system called meddra
+which is also used in various places and
+
+ align:start position:0%
+which is also used in various places and
+ 
+
+ align:start position:0%
+which is also used in various places and
+this is an international standard which
+
+ align:start position:0%
+this is an international standard which
+ 
+
+ align:start position:0%
+this is an international standard which
+is of course incompatible with the NDC
+
+ align:start position:0%
+is of course incompatible with the NDC
+ 
+
+ align:start position:0%
+is of course incompatible with the NDC
+there are also CPT is the common
+
+ align:start position:0%
+there are also CPT is the common
+ 
+
+ align:start position:0%
+there are also CPT is the common
+procedural terminology which we'll talk
+
+ align:start position:0%
+procedural terminology which we'll talk
+ 
+
+ align:start position:0%
+procedural terminology which we'll talk
+about in a little bit and they have a
+
+ align:start position:0%
+about in a little bit and they have a
+ 
+
+ align:start position:0%
+about in a little bit and they have a
+sub range of their codes which also
+
+ align:start position:0%
+sub range of their codes which also
+ 
+
+ align:start position:0%
+sub range of their codes which also
+correspond to medication administration
+
+ align:start position:0%
+correspond to medication administration
+ 
+
+ align:start position:0%
+correspond to medication administration
+and so this is yet another way of
+
+ align:start position:0%
+and so this is yet another way of
+ 
+
+ align:start position:0%
+and so this is yet another way of
+coding giving medicines and then the
+
+ align:start position:0%
+coding giving medicines and then the
+ 
+
+ align:start position:0%
+coding giving medicines and then the
+HCPCS is yet another set of codes for
+
+ align:start position:0%
+HCPCS is yet another set of codes for
+ 
+
+ align:start position:0%
+HCPCS is yet another set of codes for
+specifying what medicines you've given
+
+ align:start position:0%
+specifying what medicines you've given
+ 
+
+ align:start position:0%
+specifying what medicines you've given
+to somebody and then I had mentioned
+
+ align:start position:0%
+to somebody and then I had mentioned
+ 
+
+ align:start position:0%
+to somebody and then I had mentioned
+this GSN number which apparently the
+
+ align:start position:0%
+this GSN number which apparently the
+ 
+
+ align:start position:0%
+this GSN number which apparently the
+Beth Israel uses this is a commercial
+
+ align:start position:0%
+Beth Israel uses this is a commercial
+ 
+
+ align:start position:0%
+Beth Israel uses this is a commercial
+coding system from a company called
+
+ align:start position:0%
+coding system from a company called
+ 
+
+ align:start position:0%
+coding system from a company called
+First Data Bank that is in the business
+
+ align:start position:0%
+First Data Bank that is in the business
+ 
+
+ align:start position:0%
+First Data Bank that is in the business
+of trying to produce standards but in
+
+ align:start position:0%
+of trying to produce standards but in
+ 
+
+ align:start position:0%
+of trying to produce standards but in
+this case they're producing ones that
+
+ align:start position:0%
+this case they're producing ones that
+ 
+
+ align:start position:0%
+this case they're producing ones that
+are pretty redundant with other existing
+
+ align:start position:0%
+are pretty redundant with other existing
+ 
+
+ align:start position:0%
+are pretty redundant with other existing
+standards but nevertheless for
+
+ align:start position:0%
+standards but nevertheless for
+ 
+
+ align:start position:0%
+standards but nevertheless for
+historical reasons or for whatever
+
+ align:start position:0%
+historical reasons or for whatever
+ 
+
+ align:start position:0%
+historical reasons or for whatever
+reasons people are using these okay
+
+ align:start position:0%
+reasons people are using these okay
+ 
+
+ align:start position:0%
+reasons people are using these okay
+enough of drugs so what procedures were
+
+ align:start position:0%
+enough of drugs so what procedures were
+ 
+
+ align:start position:0%
+enough of drugs so what procedures were
+done to a patient if you look in mimic
+
+ align:start position:0%
+done to a patient if you look in mimic
+ 
+
+ align:start position:0%
+done to a patient if you look in mimic
+there are three tables there's
+
+ align:start position:0%
+there are three tables there's
+ 
+
+ align:start position:0%
+there are three tables there's
+procedures ICD which has icd-9 codes for
+
+ align:start position:0%
+procedures ICD which has icd-9 codes for
+ 
+
+ align:start position:0%
+procedures ICD which has icd-9 codes for
+about a quarter million procedures
+
+ align:start position:0%
+about a quarter million procedures
+ 
+
+ align:start position:0%
+about a quarter million procedures
+there's CPT events which has about half
+
+ align:start position:0%
+there's CPT events which has about half
+ 
+
+ align:start position:0%
+there's CPT events which has about half
+a million six hundred thousand events
+
+ align:start position:0%
+a million six hundred thousand events
+ 
+
+ align:start position:0%
+a million six hundred thousand events
+that are coded in the CPT terminology
+
+ align:start position:0%
+that are coded in the CPT terminology
+ 
+
+ align:start position:0%
+that are coded in the CPT terminology
+and then meta vision the newer of the
+
+ align:start position:0%
+and then meta vision the newer of the
+ 
+
+ align:start position:0%
+and then meta vision the newer of the
+two systems has about a quarter million
+
+ align:start position:0%
+two systems has about a quarter million
+ 
+
+ align:start position:0%
+two systems has about a quarter million
+procedure events that are coded in that
+
+ align:start position:0%
+procedure events that are coded in that
+ 
+
+ align:start position:0%
+procedure events that are coded in that
+system so some examples here's the most
+
+ align:start position:0%
+system so some examples here's the most
+ 
+
+ align:start position:0%
+system so some examples here's the most
+common icd-9 procedure codes so icd-9
+
+ align:start position:0%
+common icd-9 procedure codes so icd-9
+ 
+
+ align:start position:0%
+common icd-9 procedure codes so icd-9
+code 38 93 of which there are 14,000
+
+ align:start position:0%
+code 38 93 of which there are 14,000
+ 
+
+ align:start position:0%
+code 38 93 of which there are 14,000
+instances is venous catheterization not
+
+ align:start position:0%
+instances is venous catheterization not
+ 
+
+ align:start position:0%
+instances is venous catheterization not
+elsewhere classified
+
+ align:start position:0%
+elsewhere classified
+ 
+
+ align:start position:0%
+elsewhere classified
+so what's venous catheterization it's
+
+ align:start position:0%
+so what's venous catheterization it's
+ 
+
+ align:start position:0%
+so what's venous catheterization it's
+when somebody sticks on IV in your vein
+
+ align:start position:0%
+when somebody sticks on IV in your vein
+ 
+
+ align:start position:0%
+when somebody sticks on IV in your vein
+okay very common you show up at a
+
+ align:start position:0%
+okay very common you show up at a
+ 
+
+ align:start position:0%
+okay very common you show up at a
+hospital before they ask you your name
+
+ align:start position:0%
+hospital before they ask you your name
+ 
+
+ align:start position:0%
+hospital before they ask you your name
+they stick an IV in here
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that's a buildable event - insertion of
+
+ align:start position:0%
+that's a buildable event - insertion of
+ 
+
+ align:start position:0%
+that's a buildable event - insertion of
+an endotracheal tube you know if you're
+
+ align:start position:0%
+an endotracheal tube you know if you're
+ 
+
+ align:start position:0%
+an endotracheal tube you know if you're
+having any problems like that they stick
+
+ align:start position:0%
+having any problems like that they stick
+ 
+
+ align:start position:0%
+having any problems like that they stick
+it out stick something down your throat
+
+ align:start position:0%
+it out stick something down your throat
+ 
+
+ align:start position:0%
+it out stick something down your throat
+ntral infusion of concentrated
+
+ align:start position:0%
+ntral infusion of concentrated
+ 
+
+ align:start position:0%
+ntral infusion of concentrated
+nutritional substances so if you're not
+
+ align:start position:0%
+nutritional substances so if you're not
+ 
+
+ align:start position:0%
+nutritional substances so if you're not
+able to eat then they feed you through a
+
+ align:start position:0%
+able to eat then they feed you through a
+ 
+
+ align:start position:0%
+able to eat then they feed you through a
+stomach tube okay so that's what that is
+
+ align:start position:0%
+stomach tube okay so that's what that is
+ 
+
+ align:start position:0%
+stomach tube okay so that's what that is
+continuous invasive mechanical
+
+ align:start position:0%
+continuous invasive mechanical
+ 
+
+ align:start position:0%
+continuous invasive mechanical
+ventilation for less than 96 consecutive
+
+ align:start position:0%
+ventilation for less than 96 consecutive
+ 
+
+ align:start position:0%
+ventilation for less than 96 consecutive
+hours so this is being put on a on a
+
+ align:start position:0%
+hours so this is being put on a on a
+ 
+
+ align:start position:0%
+hours so this is being put on a on a
+ventilator that's breathing for you
+
+ align:start position:0%
+ventilator that's breathing for you
+ 
+
+ align:start position:0%
+ventilator that's breathing for you
+etc so you see that there's a very long
+
+ align:start position:0%
+etc so you see that there's a very long
+ 
+
+ align:start position:0%
+etc so you see that there's a very long
+tail of these so those are the icd-9
+
+ align:start position:0%
+tail of these so those are the icd-9
+ 
+
+ align:start position:0%
+tail of these so those are the icd-9
+codes now CPT has its own procedure
+
+ align:start position:0%
+codes now CPT has its own procedure
+ 
+
+ align:start position:0%
+codes now CPT has its own procedure
+codes that go into tremendous amount of
+
+ align:start position:0%
+codes that go into tremendous amount of
+ 
+
+ align:start position:0%
+codes that go into tremendous amount of
+detail so for example this is the
+
+ align:start position:0%
+detail so for example this is the
+ 
+
+ align:start position:0%
+detail so for example this is the
+medicine subsection and it shows you the
+
+ align:start position:0%
+medicine subsection and it shows you the
+ 
+
+ align:start position:0%
+medicine subsection and it shows you the
+kinds of drugs that you're being
+
+ align:start position:0%
+kinds of drugs that you're being
+ 
+
+ align:start position:0%
+kinds of drugs that you're being
+administered that are involved in
+
+ align:start position:0%
+administered that are involved in
+ 
+
+ align:start position:0%
+administered that are involved in
+dialysis or psychiatry or vaccines or
+
+ align:start position:0%
+dialysis or psychiatry or vaccines or
+ 
+
+ align:start position:0%
+dialysis or psychiatry or vaccines or
+whatever and then here are the surgical
+
+ align:start position:0%
+whatever and then here are the surgical
+ 
+
+ align:start position:0%
+whatever and then here are the surgical
+and the radiological codes and there's
+
+ align:start position:0%
+and the radiological codes and there's
+ 
+
+ align:start position:0%
+and the radiological codes and there's
+tons and tons of detail on these yeah no
+
+ align:start position:0%
+tons and tons of detail on these yeah no
+ 
+
+ align:start position:0%
+tons and tons of detail on these yeah no
+these are categories so if if you drill
+
+ align:start position:0%
+these are categories so if if you drill
+ 
+
+ align:start position:0%
+these are categories so if if you drill
+down there's a there's a fan out of that
+
+ align:start position:0%
+down there's a there's a fan out of that
+ 
+
+ align:start position:0%
+down there's a there's a fan out of that
+tree and you get down to individual
+
+ align:start position:0%
+tree and you get down to individual
+ 
+
+ align:start position:0%
+tree and you get down to individual
+codes just as as a nasty surprise CPT is
+
+ align:start position:0%
+codes just as as a nasty surprise CPT is
+ 
+
+ align:start position:0%
+codes just as as a nasty surprise CPT is
+owned by the American College of
+
+ align:start position:0%
+owned by the American College of
+ 
+
+ align:start position:0%
+owned by the American College of
+Physicians and if they they could sue me
+
+ align:start position:0%
+Physicians and if they they could sue me
+ 
+
+ align:start position:0%
+Physicians and if they they could sue me
+if I showed you the actual codes because
+
+ align:start position:0%
+if I showed you the actual codes because
+ 
+
+ align:start position:0%
+if I showed you the actual codes because
+they're copyrighted and you have to pay
+
+ align:start position:0%
+they're copyrighted and you have to pay
+ 
+
+ align:start position:0%
+they're copyrighted and you have to pay
+them if you if you use those codes it's
+
+ align:start position:0%
+them if you if you use those codes it's
+ 
+
+ align:start position:0%
+them if you if you use those codes it's
+crazy
+
+ align:start position:0%
+crazy
+ 
+
+ align:start position:0%
+crazy
+okay so if you look at the number of all
+
+ align:start position:0%
+okay so if you look at the number of all
+ 
+
+ align:start position:0%
+okay so if you look at the number of all
+of these codes per admission you see a
+
+ align:start position:0%
+of these codes per admission you see a
+ 
+
+ align:start position:0%
+of these codes per admission you see a
+distribution like this or if I separate
+
+ align:start position:0%
+distribution like this or if I separate
+ 
+
+ align:start position:0%
+distribution like this or if I separate
+them out you see that there are more
+
+ align:start position:0%
+them out you see that there are more
+ 
+
+ align:start position:0%
+them out you see that there are more
+icd-9 codes and fewer of the cpt and the
+
+ align:start position:0%
+icd-9 codes and fewer of the cpt and the
+ 
+
+ align:start position:0%
+icd-9 codes and fewer of the cpt and the
+codes that are in meta vision but they
+
+ align:start position:0%
+codes that are in meta vision but they
+ 
+
+ align:start position:0%
+codes that are in meta vision but they
+look somewhat similar in their
+
+ align:start position:0%
+look somewhat similar in their
+ 
+
+ align:start position:0%
+look somewhat similar in their
+distributions okay
+
+ align:start position:0%
+distributions okay
+ 
+
+ align:start position:0%
+distributions okay
+lab measurements so you send off a
+
+ align:start position:0%
+lab measurements so you send off a
+ 
+
+ align:start position:0%
+lab measurements so you send off a
+sputum sample blood urine a piece of
+
+ align:start position:0%
+sputum sample blood urine a piece of
+ 
+
+ align:start position:0%
+sputum sample blood urine a piece of
+your brain something they stick it in
+
+ align:start position:0%
+your brain something they stick it in
+ 
+
+ align:start position:0%
+your brain something they stick it in
+some goo and measure something about it
+
+ align:start position:0%
+some goo and measure something about it
+ 
+
+ align:start position:0%
+some goo and measure something about it
+so what is it that they're measuring
+
+ align:start position:0%
+so what is it that they're measuring
+ 
+
+ align:start position:0%
+so what is it that they're measuring
+well it turns out that hematocrit is the
+
+ align:start position:0%
+well it turns out that hematocrit is the
+ 
+
+ align:start position:0%
+well it turns out that hematocrit is the
+most common measurement so this is how
+
+ align:start position:0%
+most common measurement so this is how
+ 
+
+ align:start position:0%
+most common measurement so this is how
+much hemoglobin is in your blood or what
+
+ align:start position:0%
+much hemoglobin is in your blood or what
+ 
+
+ align:start position:0%
+much hemoglobin is in your blood or what
+fraction in your blood and is very
+
+ align:start position:0%
+fraction in your blood and is very
+ 
+
+ align:start position:0%
+fraction in your blood and is very
+important for sick people and the second
+
+ align:start position:0%
+important for sick people and the second
+ 
+
+ align:start position:0%
+important for sick people and the second
+most important is potassium than sodium
+
+ align:start position:0%
+most important is potassium than sodium
+ 
+
+ align:start position:0%
+most important is potassium than sodium
+creatinine chloride urea nitrogen
+
+ align:start position:0%
+creatinine chloride urea nitrogen
+ 
+
+ align:start position:0%
+creatinine chloride urea nitrogen
+bicarbonate etc so this is a long long
+
+ align:start position:0%
+bicarbonate etc so this is a long long
+ 
+
+ align:start position:0%
+bicarbonate etc so this is a long long
+list of different things that can be
+
+ align:start position:0%
+list of different things that can be
+ 
+
+ align:start position:0%
+list of different things that can be
+measured and all the stuff is in the
+
+ align:start position:0%
+measured and all the stuff is in the
+ 
+
+ align:start position:0%
+measured and all the stuff is in the
+database so for example here is patient
+
+ align:start position:0%
+database so for example here is patient
+ 
+
+ align:start position:0%
+database so for example here is patient
+number two in the database and in on
+
+ align:start position:0%
+number two in the database and in on
+ 
+
+ align:start position:0%
+number two in the database and in on
+July 17th of 21:38 this is part of the D
+
+ align:start position:0%
+July 17th of 21:38 this is part of the D
+ 
+
+ align:start position:0%
+July 17th of 21:38 this is part of the D
+identification process to make it
+
+ align:start position:0%
+identification process to make it
+ 
+
+ align:start position:0%
+identification process to make it
+difficult to figure out who the patient
+
+ align:start position:0%
+difficult to figure out who the patient
+ 
+
+ align:start position:0%
+difficult to figure out who the patient
+actually is this person got a test for
+
+ align:start position:0%
+actually is this person got a test for
+ 
+
+ align:start position:0%
+actually is this person got a test for
+their blood and they reported atypical
+
+ align:start position:0%
+their blood and they reported atypical
+ 
+
+ align:start position:0%
+their blood and they reported atypical
+lymphocytes so there are a couple of
+
+ align:start position:0%
+lymphocytes so there are a couple of
+ 
+
+ align:start position:0%
+lymphocytes so there are a couple of
+interesting things to note here one is
+
+ align:start position:0%
+interesting things to note here one is
+ 
+
+ align:start position:0%
+interesting things to note here one is
+that some things have a value and others
+
+ align:start position:0%
+that some things have a value and others
+ 
+
+ align:start position:0%
+that some things have a value and others
+don't so this is a qualitative measure
+
+ align:start position:0%
+don't so this is a qualitative measure
+ 
+
+ align:start position:0%
+don't so this is a qualitative measure
+so there's no value associated with it
+
+ align:start position:0%
+so there's no value associated with it
+ 
+
+ align:start position:0%
+so there's no value associated with it
+just the fact of the label tells you
+
+ align:start position:0%
+just the fact of the label tells you
+ 
+
+ align:start position:0%
+just the fact of the label tells you
+what the result of the test was the
+
+ align:start position:0%
+what the result of the test was the
+ 
+
+ align:start position:0%
+what the result of the test was the
+other thing that's interesting is this
+
+ align:start position:0%
+other thing that's interesting is this
+ 
+
+ align:start position:0%
+other thing that's interesting is this
+last column which is linked and I'll say
+
+ align:start position:0%
+last column which is linked and I'll say
+ 
+
+ align:start position:0%
+last column which is linked and I'll say
+a word about that in a minute
+
+ align:start position:0%
+a word about that in a minute
+ 
+
+ align:start position:0%
+a word about that in a minute
+actually right now so link is the
+
+ align:start position:0%
+actually right now so link is the
+ 
+
+ align:start position:0%
+actually right now so link is the
+logical observation identifier name
+
+ align:start position:0%
+logical observation identifier name
+ 
+
+ align:start position:0%
+logical observation identifier name
+and codes it was developed by our
+
+ align:start position:0%
+and codes it was developed by our
+ 
+
+ align:start position:0%
+and codes it was developed by our
+colleagues at Reagan Street clinic in
+
+ align:start position:0%
+colleagues at Reagan Street clinic in
+ 
+
+ align:start position:0%
+colleagues at Reagan Street clinic in
+Indiana about 15 years ago maybe 20
+
+ align:start position:0%
+Indiana about 15 years ago maybe 20
+ 
+
+ align:start position:0%
+Indiana about 15 years ago maybe 20
+years ago at this point and the attempt
+
+ align:start position:0%
+years ago at this point and the attempt
+ 
+
+ align:start position:0%
+years ago at this point and the attempt
+was to say every different type of
+
+ align:start position:0%
+was to say every different type of
+ 
+
+ align:start position:0%
+was to say every different type of
+laboratory test ought to have a unique
+
+ align:start position:0%
+laboratory test ought to have a unique
+ 
+
+ align:start position:0%
+laboratory test ought to have a unique
+name and they ought to be hierarchical
+
+ align:start position:0%
+name and they ought to be hierarchical
+ 
+
+ align:start position:0%
+name and they ought to be hierarchical
+so that if you have for example three
+
+ align:start position:0%
+so that if you have for example three
+ 
+
+ align:start position:0%
+so that if you have for example three
+different ways of measuring serum
+
+ align:start position:0%
+different ways of measuring serum
+ 
+
+ align:start position:0%
+different ways of measuring serum
+potassium that they're related to each
+
+ align:start position:0%
+potassium that they're related to each
+ 
+
+ align:start position:0%
+potassium that they're related to each
+other but that they're distinct from
+
+ align:start position:0%
+other but that they're distinct from
+ 
+
+ align:start position:0%
+other but that they're distinct from
+each other because there may be
+
+ align:start position:0%
+each other because there may be
+ 
+
+ align:start position:0%
+each other because there may be
+circumstances under which the errors
+
+ align:start position:0%
+circumstances under which the errors
+ 
+
+ align:start position:0%
+circumstances under which the errors
+that you get from one measurement versus
+
+ align:start position:0%
+that you get from one measurement versus
+ 
+
+ align:start position:0%
+that you get from one measurement versus
+another are different and so this is the
+
+ align:start position:0%
+another are different and so this is the
+ 
+
+ align:start position:0%
+another are different and so this is the
+standard way if you send off your blood
+
+ align:start position:0%
+standard way if you send off your blood
+ 
+
+ align:start position:0%
+standard way if you send off your blood
+sample to a lab they send back a string
+
+ align:start position:0%
+sample to a lab they send back a string
+ 
+
+ align:start position:0%
+sample to a lab they send back a string
+like this to the hospital or to your
+
+ align:start position:0%
+like this to the hospital or to your
+ 
+
+ align:start position:0%
+like this to the hospital or to your
+doctor's office that says it's coded in
+
+ align:start position:0%
+doctor's office that says it's coded in
+ 
+
+ align:start position:0%
+doctor's office that says it's coded in
+this OBX coding system and here is the
+
+ align:start position:0%
+this OBX coding system and here is the
+ 
+
+ align:start position:0%
+this OBX coding system and here is the
+link code and this is the sno-med
+
+ align:start position:0%
+link code and this is the sno-med
+ 
+
+ align:start position:0%
+link code and this is the sno-med
+interpretation and so this string is the
+
+ align:start position:0%
+interpretation and so this string is the
+ 
+
+ align:start position:0%
+interpretation and so this string is the
+way that your hospitals EHR or your
+
+ align:start position:0%
+way that your hospitals EHR or your
+ 
+
+ align:start position:0%
+way that your hospitals EHR or your
+doctor's office system figures out what
+
+ align:start position:0%
+doctor's office system figures out what
+ 
+
+ align:start position:0%
+doctor's office system figures out what
+the result of the test was hl7 is this
+
+ align:start position:0%
+the result of the test was hl7 is this
+ 
+
+ align:start position:0%
+the result of the test was hl7 is this
+30 something year old organization that
+
+ align:start position:0%
+30 something year old organization that
+ 
+
+ align:start position:0%
+30 something year old organization that
+has been working on standardizing stuff
+
+ align:start position:0%
+has been working on standardizing stuff
+ 
+
+ align:start position:0%
+has been working on standardizing stuff
+like this and linked as part of their of
+
+ align:start position:0%
+like this and linked as part of their of
+ 
+
+ align:start position:0%
+like this and linked as part of their of
+their standardization so if you look at
+
+ align:start position:0%
+their standardization so if you look at
+ 
+
+ align:start position:0%
+their standardization so if you look at
+these you say well again how many tests
+
+ align:start position:0%
+these you say well again how many tests
+ 
+
+ align:start position:0%
+these you say well again how many tests
+per admission again a huge longtail up
+
+ align:start position:0%
+per admission again a huge longtail up
+ 
+
+ align:start position:0%
+per admission again a huge longtail up
+to about 15,000 for a very small number
+
+ align:start position:0%
+to about 15,000 for a very small number
+ 
+
+ align:start position:0%
+to about 15,000 for a very small number
+of patients if you look at lab tests per
+
+ align:start position:0%
+of patients if you look at lab tests per
+ 
+
+ align:start position:0%
+of patients if you look at lab tests per
+admission you can do a log transform and
+
+ align:start position:0%
+admission you can do a log transform and
+ 
+
+ align:start position:0%
+admission you can do a log transform and
+get something that looks like a more
+
+ align:start position:0%
+get something that looks like a more
+ 
+
+ align:start position:0%
+get something that looks like a more
+reasonable distribution by the way
+
+ align:start position:0%
+reasonable distribution by the way
+ 
+
+ align:start position:0%
+reasonable distribution by the way
+that's a very generic lesson when we're
+
+ align:start position:0%
+that's a very generic lesson when we're
+ 
+
+ align:start position:0%
+that's a very generic lesson when we're
+going to do analyses of these data is
+
+ align:start position:0%
+going to do analyses of these data is
+ 
+
+ align:start position:0%
+going to do analyses of these data is
+that often doing a transform of some
+
+ align:start position:0%
+that often doing a transform of some
+ 
+
+ align:start position:0%
+that often doing a transform of some
+sort like in this case a log takes some
+
+ align:start position:0%
+sort like in this case a log takes some
+ 
+
+ align:start position:0%
+sort like in this case a log takes some
+funny-looking distribution and turns it
+
+ align:start position:0%
+funny-looking distribution and turns it
+ 
+
+ align:start position:0%
+funny-looking distribution and turns it
+into something that looks plausibly
+
+ align:start position:0%
+into something that looks plausibly
+ 
+
+ align:start position:0%
+into something that looks plausibly
+normal which is better for a lot of the
+
+ align:start position:0%
+normal which is better for a lot of the
+ 
+
+ align:start position:0%
+normal which is better for a lot of the
+tech
+
+ align:start position:0%
+tech
+ 
+
+ align:start position:0%
+tech
+yeah those dudes means the same thing
+
+ align:start position:0%
+yeah those dudes means the same thing
+ 
+
+ align:start position:0%
+yeah those dudes means the same thing
+yes I met the great at once - and yes
+
+ align:start position:0%
+yes I met the great at once - and yes
+ 
+
+ align:start position:0%
+yes I met the great at once - and yes
+yes yes that's the whole idea of
+
+ align:start position:0%
+yes yes that's the whole idea of
+ 
+
+ align:start position:0%
+yes yes that's the whole idea of
+creating the standard and that has been
+
+ align:start position:0%
+creating the standard and that has been
+ 
+
+ align:start position:0%
+creating the standard and that has been
+pretty successful pretty successfully
+
+ align:start position:0%
+pretty successful pretty successfully
+ 
+
+ align:start position:0%
+pretty successful pretty successfully
+adopted ok chart events so these are the
+
+ align:start position:0%
+adopted ok chart events so these are the
+ 
+
+ align:start position:0%
+adopted ok chart events so these are the
+things that nurses typically enter at
+
+ align:start position:0%
+things that nurses typically enter at
+ 
+
+ align:start position:0%
+things that nurses typically enter at
+the bedside and so there are 5.1 5.2
+
+ align:start position:0%
+the bedside and so there are 5.1 5.2
+ 
+
+ align:start position:0%
+the bedside and so there are 5.1 5.2
+million heart rates measured in the
+
+ align:start position:0%
+million heart rates measured in the
+ 
+
+ align:start position:0%
+million heart rates measured in the
+mimic database and a Cal previs League
+
+ align:start position:0%
+mimic database and a Cal previs League
+ 
+
+ align:start position:0%
+mimic database and a Cal previs League
+is is an artifact it exists in every
+
+ align:start position:0%
+is is an artifact it exists in every
+ 
+
+ align:start position:0%
+is is an artifact it exists in every
+record and it's some calibration
+
+ align:start position:0%
+record and it's some calibration
+ 
+
+ align:start position:0%
+record and it's some calibration
+something or other that doesn't mean
+
+ align:start position:0%
+something or other that doesn't mean
+ 
+
+ align:start position:0%
+something or other that doesn't mean
+anything I've never been able to figure
+
+ align:start position:0%
+anything I've never been able to figure
+ 
+
+ align:start position:0%
+anything I've never been able to figure
+out exactly what it is
+
+ align:start position:0%
+out exactly what it is
+ 
+
+ align:start position:0%
+out exactly what it is
+spo2 is is the partial pressure of
+
+ align:start position:0%
+spo2 is is the partial pressure of
+ 
+
+ align:start position:0%
+spo2 is is the partial pressure of
+oxygen in your blood if use a pulse
+
+ align:start position:0%
+oxygen in your blood if use a pulse
+ 
+
+ align:start position:0%
+oxygen in your blood if use a pulse
+oximeter that's what that's measuring
+
+ align:start position:0%
+oximeter that's what that's measuring
+ 
+
+ align:start position:0%
+oximeter that's what that's measuring
+respiratory rate heart rhythm active
+
+ align:start position:0%
+respiratory rate heart rhythm active
+ 
+
+ align:start position:0%
+respiratory rate heart rhythm active
+p-type dot dot dot now you might be
+
+ align:start position:0%
+p-type dot dot dot now you might be
+ 
+
+ align:start position:0%
+p-type dot dot dot now you might be
+troubled by the fact that here's heart
+
+ align:start position:0%
+troubled by the fact that here's heart
+ 
+
+ align:start position:0%
+troubled by the fact that here's heart
+rate again right but I've already shown
+
+ align:start position:0%
+rate again right but I've already shown
+ 
+
+ align:start position:0%
+rate again right but I've already shown
+you this that heart rate in care view
+
+ align:start position:0%
+you this that heart rate in care view
+ 
+
+ align:start position:0%
+you this that heart rate in care view
+and heart rate and meta vision were
+
+ align:start position:0%
+and heart rate and meta vision were
+ 
+
+ align:start position:0%
+and heart rate and meta vision were
+coded under different codes in the joint
+
+ align:start position:0%
+coded under different codes in the joint
+ 
+
+ align:start position:0%
+coded under different codes in the joint
+system that we created out of those two
+
+ align:start position:0%
+system that we created out of those two
+ 
+
+ align:start position:0%
+system that we created out of those two
+databases and so you have to take care
+
+ align:start position:0%
+databases and so you have to take care
+ 
+
+ align:start position:0%
+databases and so you have to take care
+of figuring out what's what if you're
+
+ align:start position:0%
+of figuring out what's what if you're
+ 
+
+ align:start position:0%
+of figuring out what's what if you're
+trying to analyze this data not only do
+
+ align:start position:0%
+trying to analyze this data not only do
+ 
+
+ align:start position:0%
+trying to analyze this data not only do
+we have that problem of different age
+
+ align:start position:0%
+we have that problem of different age
+ 
+
+ align:start position:0%
+we have that problem of different age
+distributions across the two different
+
+ align:start position:0%
+distributions across the two different
+ 
+
+ align:start position:0%
+distributions across the two different
+data sets but we also just have the
+
+ align:start position:0%
+data sets but we also just have the
+ 
+
+ align:start position:0%
+data sets but we also just have the
+mechanical problem that there will be
+
+ align:start position:0%
+mechanical problem that there will be
+ 
+
+ align:start position:0%
+mechanical problem that there will be
+things with the same label that may or
+
+ align:start position:0%
+things with the same label that may or
+ 
+
+ align:start position:0%
+things with the same label that may or
+may not represent the same measurement
+
+ align:start position:0%
+may not represent the same measurement
+ 
+
+ align:start position:0%
+may not represent the same measurement
+at different times in the system okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this is the number of chart entries per
+
+ align:start position:0%
+this is the number of chart entries per
+ 
+
+ align:start position:0%
+this is the number of chart entries per
+admission again on a log scale so you
+
+ align:start position:0%
+admission again on a log scale so you
+ 
+
+ align:start position:0%
+admission again on a log scale so you
+see that there are about 10 to the 3.5
+
+ align:start position:0%
+see that there are about 10 to the 3.5
+ 
+
+ align:start position:0%
+see that there are about 10 to the 3.5
+chart entries per admission so you know
+
+ align:start position:0%
+chart entries per admission so you know
+ 
+
+ align:start position:0%
+chart entries per admission so you know
+thousands of of Admissions of chart
+
+ align:start position:0%
+thousands of of Admissions of chart
+ 
+
+ align:start position:0%
+thousands of of Admissions of chart
+events for admission we also track
+
+ align:start position:0%
+events for admission we also track
+ 
+
+ align:start position:0%
+events for admission we also track
+outputs so Foley catheter allows your
+
+ align:start position:0%
+outputs so Foley catheter allows your
+ 
+
+ align:start position:0%
+outputs so Foley catheter allows your
+your bladder to drain without your
+
+ align:start position:0%
+your bladder to drain without your
+ 
+
+ align:start position:0%
+your bladder to drain without your
+having consciously to go to the bathroom
+
+ align:start position:0%
+having consciously to go to the bathroom
+ 
+
+ align:start position:0%
+having consciously to go to the bathroom
+so they collect that information there
+
+ align:start position:0%
+so they collect that information there
+ 
+
+ align:start position:0%
+so they collect that information there
+are 1.9 million
+
+ align:start position:0%
+are 1.9 million
+ 
+
+ align:start position:0%
+are 1.9 million
+recordings of how much fluid came out of
+
+ align:start position:0%
+recordings of how much fluid came out of
+ 
+
+ align:start position:0%
+recordings of how much fluid came out of
+your bladder chest tubes will drain
+
+ align:start position:0%
+your bladder chest tubes will drain
+ 
+
+ align:start position:0%
+your bladder chest tubes will drain
+stuff out of your chest if you have
+
+ align:start position:0%
+stuff out of your chest if you have
+ 
+
+ align:start position:0%
+stuff out of your chest if you have
+congestion urine is if you pee regularly
+
+ align:start position:0%
+congestion urine is if you pee regularly
+ 
+
+ align:start position:0%
+congestion urine is if you pee regularly
+stool out etc and again I'm not sure I
+
+ align:start position:0%
+stool out etc and again I'm not sure I
+ 
+
+ align:start position:0%
+stool out etc and again I'm not sure I
+understand what the difference is
+
+ align:start position:0%
+understand what the difference is
+ 
+
+ align:start position:0%
+understand what the difference is
+between urine out Foley versus fully
+
+ align:start position:0%
+between urine out Foley versus fully
+ 
+
+ align:start position:0%
+between urine out Foley versus fully
+explained thing but one from care view
+
+ align:start position:0%
+explained thing but one from care view
+ 
+
+ align:start position:0%
+explained thing but one from care view
+and one from meta vision so again
+
+ align:start position:0%
+and one from meta vision so again
+ 
+
+ align:start position:0%
+and one from meta vision so again
+typical kinds of problems if you look at
+
+ align:start position:0%
+typical kinds of problems if you look at
+ 
+
+ align:start position:0%
+typical kinds of problems if you look at
+the number of output events per
+
+ align:start position:0%
+the number of output events per
+ 
+
+ align:start position:0%
+the number of output events per
+admission you're seeing on the order of
+
+ align:start position:0%
+admission you're seeing on the order of
+ 
+
+ align:start position:0%
+admission you're seeing on the order of
+a hundred roughly
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+well if you're tracking outputs you
+
+ align:start position:0%
+well if you're tracking outputs you
+ 
+
+ align:start position:0%
+well if you're tracking outputs you
+should also track inputs and so they do
+
+ align:start position:0%
+should also track inputs and so they do
+ 
+
+ align:start position:0%
+should also track inputs and so they do
+and so d5w is this dextrose in water
+
+ align:start position:0%
+and so d5w is this dextrose in water
+ 
+
+ align:start position:0%
+and so d5w is this dextrose in water
+0.9% normal saline propofol is an
+
+ align:start position:0%
+0.9% normal saline propofol is an
+ 
+
+ align:start position:0%
+0.9% normal saline propofol is an
+anesthetic insulin heparin blood thinner
+
+ align:start position:0%
+anesthetic insulin heparin blood thinner
+ 
+
+ align:start position:0%
+anesthetic insulin heparin blood thinner
+etc fentanyl's of I think an opioid if I
+
+ align:start position:0%
+etc fentanyl's of I think an opioid if I
+ 
+
+ align:start position:0%
+etc fentanyl's of I think an opioid if I
+remember right
+
+ align:start position:0%
+remember right
+ 
+
+ align:start position:0%
+remember right
+so these are various things that are
+
+ align:start position:0%
+so these are various things that are
+ 
+
+ align:start position:0%
+so these are various things that are
+given to people and they affect the
+
+ align:start position:0%
+given to people and they affect the
+ 
+
+ align:start position:0%
+given to people and they affect the
+volume of the person so this is an
+
+ align:start position:0%
+volume of the person so this is an
+ 
+
+ align:start position:0%
+volume of the person so this is an
+attempt to keep the person in balance
+
+ align:start position:0%
+attempt to keep the person in balance
+ 
+
+ align:start position:0%
+attempt to keep the person in balance
+and keep track of that meta vision
+
+ align:start position:0%
+and keep track of that meta vision
+ 
+
+ align:start position:0%
+and keep track of that meta vision
+inputs are classified somewhat
+
+ align:start position:0%
+inputs are classified somewhat
+ 
+
+ align:start position:0%
+inputs are classified somewhat
+differently but they have similar kinds
+
+ align:start position:0%
+differently but they have similar kinds
+ 
+
+ align:start position:0%
+differently but they have similar kinds
+of data and if you combine them you get
+
+ align:start position:0%
+of data and if you combine them you get
+ 
+
+ align:start position:0%
+of data and if you combine them you get
+again a distribution on a log scale that
+
+ align:start position:0%
+again a distribution on a log scale that
+ 
+
+ align:start position:0%
+again a distribution on a log scale that
+shows that there are on the order of 10
+
+ align:start position:0%
+shows that there are on the order of 10
+ 
+
+ align:start position:0%
+shows that there are on the order of 10
+to the fifth input events so quite a few
+
+ align:start position:0%
+to the fifth input events so quite a few
+ 
+
+ align:start position:0%
+to the fifth input events so quite a few
+input events because this is recorded
+
+ align:start position:0%
+input events because this is recorded
+ 
+
+ align:start position:0%
+input events because this is recorded
+periodically now the paper that I yeah
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+no no it's it's an input into you so
+
+ align:start position:0%
+no no it's it's an input into you so
+ 
+
+ align:start position:0%
+no no it's it's an input into you so
+it's like you drink a glass of water the
+
+ align:start position:0%
+it's like you drink a glass of water the
+ 
+
+ align:start position:0%
+it's like you drink a glass of water the
+nurse is supposed to record it although
+
+ align:start position:0%
+nurse is supposed to record it although
+ 
+
+ align:start position:0%
+nurse is supposed to record it although
+she doesn't always because she may not
+
+ align:start position:0%
+she doesn't always because she may not
+ 
+
+ align:start position:0%
+she doesn't always because she may not
+notice it but if they hang an IV bag and
+
+ align:start position:0%
+notice it but if they hang an IV bag and
+ 
+
+ align:start position:0%
+notice it but if they hang an IV bag and
+pour a liter of liquid into you they do
+
+ align:start position:0%
+pour a liter of liquid into you they do
+ 
+
+ align:start position:0%
+pour a liter of liquid into you they do
+record that okay all right so I I had
+
+ align:start position:0%
+record that okay all right so I I had
+ 
+
+ align:start position:0%
+record that okay all right so I I had
+you read this interesting paper and a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+discussion prior to that paper because
+
+ align:start position:0%
+discussion prior to that paper because
+ 
+
+ align:start position:0%
+discussion prior to that paper because
+one of the authors as a former student
+
+ align:start position:0%
+one of the authors as a former student
+ 
+
+ align:start position:0%
+one of the authors as a former student
+of mine and I know the one of the other
+
+ align:start position:0%
+of mine and I know the one of the other
+ 
+
+ align:start position:0%
+of mine and I know the one of the other
+guys pretty well and the former students
+
+ align:start position:0%
+guys pretty well and the former students
+ 
+
+ align:start position:0%
+guys pretty well and the former students
+at Kohana came back some years ago from
+
+ align:start position:0%
+at Kohana came back some years ago from
+ 
+
+ align:start position:0%
+at Kohana came back some years ago from
+a conference in California and was
+
+ align:start position:0%
+a conference in California and was
+ 
+
+ align:start position:0%
+a conference in California and was
+explaining to me that he ran into a
+
+ align:start position:0%
+explaining to me that he ran into a
+ 
+
+ align:start position:0%
+explaining to me that he ran into a
+venture capitalist who discovered that
+
+ align:start position:0%
+venture capitalist who discovered that
+ 
+
+ align:start position:0%
+venture capitalist who discovered that
+there's an interesting physiological
+
+ align:start position:0%
+there's an interesting physiological
+ 
+
+ align:start position:0%
+there's an interesting physiological
+variation in the epiderm allottee of lab
+
+ align:start position:0%
+variation in the epiderm allottee of lab
+ 
+
+ align:start position:0%
+variation in the epiderm allottee of lab
+tests that are done at night and he
+
+ align:start position:0%
+tests that are done at night and he
+ 
+
+ align:start position:0%
+tests that are done at night and he
+suspected that there's a diurnal
+
+ align:start position:0%
+suspected that there's a diurnal
+ 
+
+ align:start position:0%
+suspected that there's a diurnal
+variation that lab tests actually become
+
+ align:start position:0%
+variation that lab tests actually become
+ 
+
+ align:start position:0%
+variation that lab tests actually become
+more abnormal at night than they do
+
+ align:start position:0%
+more abnormal at night than they do
+ 
+
+ align:start position:0%
+more abnormal at night than they do
+during the day
+
+ align:start position:0%
+during the day
+ 
+
+ align:start position:0%
+during the day
+and Zach who is not only a computer
+
+ align:start position:0%
+and Zach who is not only a computer
+ 
+
+ align:start position:0%
+and Zach who is not only a computer
+science PhD but also a practicing doctor
+
+ align:start position:0%
+science PhD but also a practicing doctor
+ 
+
+ align:start position:0%
+science PhD but also a practicing doctor
+turns to him Francis you're an idiot
+
+ align:start position:0%
+turns to him Francis you're an idiot
+ 
+
+ align:start position:0%
+turns to him Francis you're an idiot
+right who has their blood drawn at 3
+
+ align:start position:0%
+right who has their blood drawn at 3
+ 
+
+ align:start position:0%
+right who has their blood drawn at 3
+o'clock in the morning it's typically
+
+ align:start position:0%
+o'clock in the morning it's typically
+ 
+
+ align:start position:0%
+o'clock in the morning it's typically
+not healthy people right so this is
+
+ align:start position:0%
+not healthy people right so this is
+ 
+
+ align:start position:0%
+not healthy people right so this is
+another of these nice confounding
+
+ align:start position:0%
+another of these nice confounding
+ 
+
+ align:start position:0%
+another of these nice confounding
+stories where if you have a test done in
+
+ align:start position:0%
+stories where if you have a test done in
+ 
+
+ align:start position:0%
+stories where if you have a test done in
+the middle of the night it probably
+
+ align:start position:0%
+the middle of the night it probably
+ 
+
+ align:start position:0%
+the middle of the night it probably
+indicates that you're sicker so he and
+
+ align:start position:0%
+indicates that you're sicker so he and
+ 
+
+ align:start position:0%
+indicates that you're sicker so he and
+Griffin recruited their third author and
+
+ align:start position:0%
+Griffin recruited their third author and
+ 
+
+ align:start position:0%
+Griffin recruited their third author and
+went off and did a very large-scale
+
+ align:start position:0%
+went off and did a very large-scale
+ 
+
+ align:start position:0%
+went off and did a very large-scale
+study of this question which is what the
+
+ align:start position:0%
+study of this question which is what the
+ 
+
+ align:start position:0%
+study of this question which is what the
+paper that I asked you to read reports
+
+ align:start position:0%
+paper that I asked you to read reports
+ 
+
+ align:start position:0%
+paper that I asked you to read reports
+on and so I said well I wonder if I
+
+ align:start position:0%
+on and so I said well I wonder if I
+ 
+
+ align:start position:0%
+on and so I said well I wonder if I
+could reproduce that study in the mimic
+
+ align:start position:0%
+could reproduce that study in the mimic
+ 
+
+ align:start position:0%
+could reproduce that study in the mimic
+database
+
+ align:start position:0%
+database
+ 
+
+ align:start position:0%
+database
+and the answer just in case you get your
+
+ align:start position:0%
+and the answer just in case you get your
+ 
+
+ align:start position:0%
+and the answer just in case you get your
+hopes up was no in large part because we
+
+ align:start position:0%
+hopes up was no in large part because we
+ 
+
+ align:start position:0%
+hopes up was no in large part because we
+just don't have the right kind of data
+
+ align:start position:0%
+just don't have the right kind of data
+ 
+
+ align:start position:0%
+just don't have the right kind of data
+so they're not not that many white blood
+
+ align:start position:0%
+so they're not not that many white blood
+ 
+
+ align:start position:0%
+so they're not not that many white blood
+counts that were measured in the mimic
+
+ align:start position:0%
+counts that were measured in the mimic
+ 
+
+ align:start position:0%
+counts that were measured in the mimic
+database for example but if you look at
+
+ align:start position:0%
+database for example but if you look at
+ 
+
+ align:start position:0%
+database for example but if you look at
+the this is mimic data and if you say
+
+ align:start position:0%
+the this is mimic data and if you say
+ 
+
+ align:start position:0%
+the this is mimic data and if you say
+what's the fraction of abnormal white
+
+ align:start position:0%
+what's the fraction of abnormal white
+ 
+
+ align:start position:0%
+what's the fraction of abnormal white
+blood count values by our so this is
+
+ align:start position:0%
+blood count values by our so this is
+ 
+
+ align:start position:0%
+blood count values by our so this is
+midnight to midnight and each hour
+
+ align:start position:0%
+midnight to midnight and each hour
+ 
+
+ align:start position:0%
+midnight to midnight and each hour
+there's some fraction of these test
+
+ align:start position:0%
+there's some fraction of these test
+ 
+
+ align:start position:0%
+there's some fraction of these test
+results that are abnormal and sure
+
+ align:start position:0%
+results that are abnormal and sure
+ 
+
+ align:start position:0%
+results that are abnormal and sure
+enough what you see is that at five
+
+ align:start position:0%
+enough what you see is that at five
+ 
+
+ align:start position:0%
+enough what you see is that at five
+o'clock in the morning much higher
+
+ align:start position:0%
+o'clock in the morning much higher
+ 
+
+ align:start position:0%
+o'clock in the morning much higher
+fraction of them is abnormal than at 3
+
+ align:start position:0%
+fraction of them is abnormal than at 3
+ 
+
+ align:start position:0%
+fraction of them is abnormal than at 3
+o'clock in the afternoon okay which is
+
+ align:start position:0%
+o'clock in the afternoon okay which is
+ 
+
+ align:start position:0%
+o'clock in the afternoon okay which is
+consistent with Zak's peremptory comment
+
+ align:start position:0%
+consistent with Zak's peremptory comment
+ 
+
+ align:start position:0%
+consistent with Zak's peremptory comment
+about the guy being an idiot so once
+
+ align:start position:0%
+about the guy being an idiot so once
+ 
+
+ align:start position:0%
+about the guy being an idiot so once
+again I said well can we build a really
+
+ align:start position:0%
+again I said well can we build a really
+ 
+
+ align:start position:0%
+again I said well can we build a really
+simple model that predicts who's going
+
+ align:start position:0%
+simple model that predicts who's going
+ 
+
+ align:start position:0%
+simple model that predicts who's going
+to die in the hospital in this case
+
+ align:start position:0%
+to die in the hospital in this case
+ 
+
+ align:start position:0%
+to die in the hospital in this case
+that's the easiest one to predict
+
+ align:start position:0%
+that's the easiest one to predict
+ 
+
+ align:start position:0%
+that's the easiest one to predict
+because I have that data we we could get
+
+ align:start position:0%
+because I have that data we we could get
+ 
+
+ align:start position:0%
+because I have that data we we could get
+three year survival data which is what
+
+ align:start position:0%
+three year survival data which is what
+ 
+
+ align:start position:0%
+three year survival data which is what
+they were looking at but it's harder and
+
+ align:start position:0%
+they were looking at but it's harder and
+ 
+
+ align:start position:0%
+they were looking at but it's harder and
+it runs into sensoring problems of what
+
+ align:start position:0%
+it runs into sensoring problems of what
+ 
+
+ align:start position:0%
+it runs into sensoring problems of what
+happens if the person was hospitalized
+
+ align:start position:0%
+happens if the person was hospitalized
+ 
+
+ align:start position:0%
+happens if the person was hospitalized
+less than three years before the end of
+
+ align:start position:0%
+less than three years before the end of
+ 
+
+ align:start position:0%
+less than three years before the end of
+our data collection period and so on and
+
+ align:start position:0%
+our data collection period and so on and
+ 
+
+ align:start position:0%
+our data collection period and so on and
+so I avoided that but what this is
+
+ align:start position:0%
+so I avoided that but what this is
+ 
+
+ align:start position:0%
+so I avoided that but what this is
+showing you is for each of the hours 0
+
+ align:start position:0%
+showing you is for each of the hours 0
+ 
+
+ align:start position:0%
+showing you is for each of the hours 0
+to 24 what is the the number of
+
+ align:start position:0%
+to 24 what is the the number of
+ 
+
+ align:start position:0%
+to 24 what is the the number of
+measurements and for each of those hours
+
+ align:start position:0%
+measurements and for each of those hours
+ 
+
+ align:start position:0%
+measurements and for each of those hours
+what is the number what is the fraction
+
+ align:start position:0%
+what is the number what is the fraction
+ 
+
+ align:start position:0%
+what is the number what is the fraction
+of those measurements that's abnormal
+
+ align:start position:0%
+of those measurements that's abnormal
+ 
+
+ align:start position:0%
+of those measurements that's abnormal
+okay so I said well let's just throw it
+
+ align:start position:0%
+okay so I said well let's just throw it
+ 
+
+ align:start position:0%
+okay so I said well let's just throw it
+into logistic regression model and what
+
+ align:start position:0%
+into logistic regression model and what
+ 
+
+ align:start position:0%
+into logistic regression model and what
+comes out is something really weird
+
+ align:start position:0%
+comes out is something really weird
+ 
+
+ align:start position:0%
+comes out is something really weird
+which is that a few particular hours are
+
+ align:start position:0%
+which is that a few particular hours are
+ 
+
+ align:start position:0%
+which is that a few particular hours are
+significant but most of them are not and
+
+ align:start position:0%
+significant but most of them are not and
+ 
+
+ align:start position:0%
+significant but most of them are not and
+that looks like noise to me
+
+ align:start position:0%
+that looks like noise to me
+ 
+
+ align:start position:0%
+that looks like noise to me
+right because you wouldn't expect that
+
+ align:start position:0%
+right because you wouldn't expect that
+ 
+
+ align:start position:0%
+right because you wouldn't expect that
+that at at eight o'clock in the morning
+
+ align:start position:0%
+that at at eight o'clock in the morning
+ 
+
+ align:start position:0%
+that at at eight o'clock in the morning
+the the fact that you had something
+
+ align:start position:0%
+the the fact that you had something
+ 
+
+ align:start position:0%
+the the fact that you had something
+measured matters but at nine o'clock in
+
+ align:start position:0%
+measured matters but at nine o'clock in
+ 
+
+ align:start position:0%
+measured matters but at nine o'clock in
+the morning it doesn't that doesn't seem
+
+ align:start position:0%
+the morning it doesn't that doesn't seem
+ 
+
+ align:start position:0%
+the morning it doesn't that doesn't seem
+sensible so I don't think there's enough
+
+ align:start position:0%
+sensible so I don't think there's enough
+ 
+
+ align:start position:0%
+sensible so I don't think there's enough
+signal here and in fact when I looked at
+
+ align:start position:0%
+signal here and in fact when I looked at
+ 
+
+ align:start position:0%
+signal here and in fact when I looked at
+the number of white blood count
+
+ align:start position:0%
+the number of white blood count
+ 
+
+ align:start position:0%
+the number of white blood count
+measurements at night and related to
+
+ align:start position:0%
+measurements at night and related to
+ 
+
+ align:start position:0%
+measurements at night and related to
+mortality so false means people lived
+
+ align:start position:0%
+mortality so false means people lived
+ 
+
+ align:start position:0%
+mortality so false means people lived
+and true means they died but you see
+
+ align:start position:0%
+and true means they died but you see
+ 
+
+ align:start position:0%
+and true means they died but you see
+that there's not a whole lot of
+
+ align:start position:0%
+that there's not a whole lot of
+ 
+
+ align:start position:0%
+that there's not a whole lot of
+difference between the distributions but
+
+ align:start position:0%
+difference between the distributions but
+ 
+
+ align:start position:0%
+difference between the distributions but
+you also see that the number of white
+
+ align:start position:0%
+you also see that the number of white
+ 
+
+ align:start position:0%
+you also see that the number of white
+blood counts is relatively small in this
+
+ align:start position:0%
+blood counts is relatively small in this
+ 
+
+ align:start position:0%
+blood counts is relatively small in this
+database and so I think we just don't
+
+ align:start position:0%
+database and so I think we just don't
+ 
+
+ align:start position:0%
+database and so I think we just don't
+have enough data to take to do it on the
+
+ align:start position:0%
+have enough data to take to do it on the
+ 
+
+ align:start position:0%
+have enough data to take to do it on the
+other hand if you look at a panel of
+
+ align:start position:0%
+other hand if you look at a panel of
+ 
+
+ align:start position:0%
+other hand if you look at a panel of
+different drugs you look at mean values
+
+ align:start position:0%
+different drugs you look at mean values
+ 
+
+ align:start position:0%
+different drugs you look at mean values
+of blood urea nitrogen or calcium
+
+ align:start position:0%
+of blood urea nitrogen or calcium
+ 
+
+ align:start position:0%
+of blood urea nitrogen or calcium
+chloride co2 etc you see that there is
+
+ align:start position:0%
+chloride co2 etc you see that there is
+ 
+
+ align:start position:0%
+chloride co2 etc you see that there is
+variation across time so the there is
+
+ align:start position:0%
+variation across time so the there is
+ 
+
+ align:start position:0%
+variation across time so the there is
+some some sort of variance that's either
+
+ align:start position:0%
+some some sort of variance that's either
+ 
+
+ align:start position:0%
+some some sort of variance that's either
+caused by the diurnal physiology of the
+
+ align:start position:0%
+caused by the diurnal physiology of the
+ 
+
+ align:start position:0%
+caused by the diurnal physiology of the
+human body or by the routine practice of
+
+ align:start position:0%
+human body or by the routine practice of
+ 
+
+ align:start position:0%
+human body or by the routine practice of
+medicine about when people choose to
+
+ align:start position:0%
+medicine about when people choose to
+ 
+
+ align:start position:0%
+medicine about when people choose to
+take lab measurements and in fact if you
+
+ align:start position:0%
+take lab measurements and in fact if you
+ 
+
+ align:start position:0%
+take lab measurements and in fact if you
+look at the fraction of high and low lab
+
+ align:start position:0%
+look at the fraction of high and low lab
+ 
+
+ align:start position:0%
+look at the fraction of high and low lab
+values they do vary by hour and in
+
+ align:start position:0%
+values they do vary by hour and in
+ 
+
+ align:start position:0%
+values they do vary by hour and in
+particular if you look at white blood
+
+ align:start position:0%
+particular if you look at white blood
+ 
+
+ align:start position:0%
+particular if you look at white blood
+counts you see that the fraction of high
+
+ align:start position:0%
+counts you see that the fraction of high
+ 
+
+ align:start position:0%
+counts you see that the fraction of high
+values goes up at night and the fraction
+
+ align:start position:0%
+values goes up at night and the fraction
+ 
+
+ align:start position:0%
+values goes up at night and the fraction
+of low values goes down at night which
+
+ align:start position:0%
+of low values goes down at night which
+ 
+
+ align:start position:0%
+of low values goes down at night which
+is consistent with what they saw as well
+
+ align:start position:0%
+is consistent with what they saw as well
+ 
+
+ align:start position:0%
+is consistent with what they saw as well
+there's another way to measure it which
+
+ align:start position:0%
+there's another way to measure it which
+ 
+
+ align:start position:0%
+there's another way to measure it which
+is the instead of using normal ranges
+
+ align:start position:0%
+is the instead of using normal ranges
+ 
+
+ align:start position:0%
+is the instead of using normal ranges
+the lab actually gives you a call that
+
+ align:start position:0%
+the lab actually gives you a call that
+ 
+
+ align:start position:0%
+the lab actually gives you a call that
+says is this value normal
+
+ align:start position:0%
+says is this value normal
+ 
+
+ align:start position:0%
+says is this value normal
+low or high and we can use that that's a
+
+ align:start position:0%
+low or high and we can use that that's a
+ 
+
+ align:start position:0%
+low or high and we can use that that's a
+little bit more subtle because it
+
+ align:start position:0%
+little bit more subtle because it
+ 
+
+ align:start position:0%
+little bit more subtle because it
+depends on on calibration of the
+
+ align:start position:0%
+depends on on calibration of the
+ 
+
+ align:start position:0%
+depends on on calibration of the
+equipment and is updated as the
+
+ align:start position:0%
+equipment and is updated as the
+ 
+
+ align:start position:0%
+equipment and is updated as the
+calibration changes so that's probably a
+
+ align:start position:0%
+calibration changes so that's probably a
+ 
+
+ align:start position:0%
+calibration changes so that's probably a
+little bit more accurate but you see
+
+ align:start position:0%
+little bit more accurate but you see
+ 
+
+ align:start position:0%
+little bit more accurate but you see
+essentially the same phenomenon here but
+
+ align:start position:0%
+essentially the same phenomenon here but
+ 
+
+ align:start position:0%
+essentially the same phenomenon here but
+if you look at the distributions of when
+
+ align:start position:0%
+if you look at the distributions of when
+ 
+
+ align:start position:0%
+if you look at the distributions of when
+measurements are done that turn out to
+
+ align:start position:0%
+measurements are done that turn out to
+ 
+
+ align:start position:0%
+measurements are done that turn out to
+be normal versus when they turn out to
+
+ align:start position:0%
+be normal versus when they turn out to
+ 
+
+ align:start position:0%
+be normal versus when they turn out to
+be abnormal there's a lot of similarity
+
+ align:start position:0%
+be abnormal there's a lot of similarity
+ 
+
+ align:start position:0%
+be abnormal there's a lot of similarity
+between the normal and the abnormal
+
+ align:start position:0%
+between the normal and the abnormal
+ 
+
+ align:start position:0%
+between the normal and the abnormal
+curves of when those measurements are
+
+ align:start position:0%
+curves of when those measurements are
+ 
+
+ align:start position:0%
+curves of when those measurements are
+taken so we're not seeing that okay let
+
+ align:start position:0%
+taken so we're not seeing that okay let
+ 
+
+ align:start position:0%
+taken so we're not seeing that okay let
+me race through to the end this is my
+
+ align:start position:0%
+me race through to the end this is my
+ 
+
+ align:start position:0%
+me race through to the end this is my
+heartbeat from my watch you can actually
+
+ align:start position:0%
+heartbeat from my watch you can actually
+ 
+
+ align:start position:0%
+heartbeat from my watch you can actually
+download the stuff and put it in your
+
+ align:start position:0%
+download the stuff and put it in your
+ 
+
+ align:start position:0%
+download the stuff and put it in your
+favorite analysis engine and take a look
+
+ align:start position:0%
+favorite analysis engine and take a look
+ 
+
+ align:start position:0%
+favorite analysis engine and take a look
+so here I was running across the Harvard
+
+ align:start position:0%
+so here I was running across the Harvard
+ 
+
+ align:start position:0%
+so here I was running across the Harvard
+bridge and if you look at my heart rate
+
+ align:start position:0%
+bridge and if you look at my heart rate
+ 
+
+ align:start position:0%
+bridge and if you look at my heart rate
+variability over the 30 seconds or so
+
+ align:start position:0%
+variability over the 30 seconds or so
+ 
+
+ align:start position:0%
+variability over the 30 seconds or so
+you see that the intra beat interval
+
+ align:start position:0%
+you see that the intra beat interval
+ 
+
+ align:start position:0%
+you see that the intra beat interval
+ranges from about 550 to about six
+
+ align:start position:0%
+ranges from about 550 to about six
+ 
+
+ align:start position:0%
+ranges from about 550 to about six
+hundred and thirty six hundred and
+
+ align:start position:0%
+hundred and thirty six hundred and
+ 
+
+ align:start position:0%
+hundred and thirty six hundred and
+whatever 20 milliseconds and so you
+
+ align:start position:0%
+whatever 20 milliseconds and so you
+ 
+
+ align:start position:0%
+whatever 20 milliseconds and so you
+could calculate my heart rate
+
+ align:start position:0%
+could calculate my heart rate
+ 
+
+ align:start position:0%
+could calculate my heart rate
+variability which is thought to be an
+
+ align:start position:0%
+variability which is thought to be an
+ 
+
+ align:start position:0%
+variability which is thought to be an
+indicator of heart health and so on you
+
+ align:start position:0%
+indicator of heart health and so on you
+ 
+
+ align:start position:0%
+indicator of heart health and so on you
+can calculate that I was running at a
+
+ align:start position:0%
+can calculate that I was running at a
+ 
+
+ align:start position:0%
+can calculate that I was running at a
+pace of about a hundred my heart was
+
+ align:start position:0%
+pace of about a hundred my heart was
+ 
+
+ align:start position:0%
+pace of about a hundred my heart was
+beating at a pace of about a hundred
+
+ align:start position:0%
+beating at a pace of about a hundred
+ 
+
+ align:start position:0%
+beating at a pace of about a hundred
+beats per minute so you know there's all
+
+ align:start position:0%
+beats per minute so you know there's all
+ 
+
+ align:start position:0%
+beats per minute so you know there's all
+sorts of information like that available
+
+ align:start position:0%
+sorts of information like that available
+ 
+
+ align:start position:0%
+sorts of information like that available
+now as I said I'm not going to get into
+
+ align:start position:0%
+now as I said I'm not going to get into
+ 
+
+ align:start position:0%
+now as I said I'm not going to get into
+this today but this was a very
+
+ align:start position:0%
+this today but this was a very
+ 
+
+ align:start position:0%
+this today but this was a very
+successful recently published paper
+
+ align:start position:0%
+successful recently published paper
+ 
+
+ align:start position:0%
+successful recently published paper
+where they're able to take a look at at
+
+ align:start position:0%
+where they're able to take a look at at
+ 
+
+ align:start position:0%
+where they're able to take a look at at
+images of the lung so this is a
+
+ align:start position:0%
+images of the lung so this is a
+ 
+
+ align:start position:0%
+images of the lung so this is a
+transverse scan of the of the lung and
+
+ align:start position:0%
+transverse scan of the of the lung and
+ 
+
+ align:start position:0%
+transverse scan of the of the lung and
+they have a deep learning machine that
+
+ align:start position:0%
+they have a deep learning machine that
+ 
+
+ align:start position:0%
+they have a deep learning machine that
+is able to identify these two yellow
+
+ align:start position:0%
+is able to identify these two yellow
+ 
+
+ align:start position:0%
+is able to identify these two yellow
+mark things as pulmonary emboli as
+
+ align:start position:0%
+mark things as pulmonary emboli as
+ 
+
+ align:start position:0%
+mark things as pulmonary emboli as
+opposed to these other things that are
+
+ align:start position:0%
+opposed to these other things that are
+ 
+
+ align:start position:0%
+opposed to these other things that are
+just random flecks in the tissue and I
+
+ align:start position:0%
+just random flecks in the tissue and I
+ 
+
+ align:start position:0%
+just random flecks in the tissue and I
+can't do that
+
+ align:start position:0%
+can't do that
+ 
+
+ align:start position:0%
+can't do that
+my eyeball maybe a good radiologist
+
+ align:start position:0%
+my eyeball maybe a good radiologist
+ 
+
+ align:start position:0%
+my eyeball maybe a good radiologist
+might be able to but this is claimed in
+
+ align:start position:0%
+might be able to but this is claimed in
+ 
+
+ align:start position:0%
+might be able to but this is claimed in
+the paper to outperform decent
+
+ align:start position:0%
+the paper to outperform decent
+ 
+
+ align:start position:0%
+the paper to outperform decent
+radiologists already this was one of the
+
+ align:start position:0%
+radiologists already this was one of the
+ 
+
+ align:start position:0%
+radiologists already this was one of the
+articles that led geoff hinton to make
+
+ align:start position:0%
+articles that led geoff hinton to make
+ 
+
+ align:start position:0%
+articles that led geoff hinton to make
+this rather stupid pronouncement that
+
+ align:start position:0%
+this rather stupid pronouncement that
+ 
+
+ align:start position:0%
+this rather stupid pronouncement that
+said tell your children not to become
+
+ align:start position:0%
+said tell your children not to become
+ 
+
+ align:start position:0%
+said tell your children not to become
+radiologists because the profession will
+
+ align:start position:0%
+radiologists because the profession will
+ 
+
+ align:start position:0%
+radiologists because the profession will
+be over by the time they get fully
+
+ align:start position:0%
+be over by the time they get fully
+ 
+
+ align:start position:0%
+be over by the time they get fully
+trained which i don't believe they may
+
+ align:start position:0%
+trained which i don't believe they may
+ 
+
+ align:start position:0%
+trained which i don't believe they may
+do different things but but they won't
+
+ align:start position:0%
+do different things but but they won't
+ 
+
+ align:start position:0%
+do different things but but they won't
+go away this was a slide from ron
+
+ align:start position:0%
+go away this was a slide from ron
+ 
+
+ align:start position:0%
+go away this was a slide from ron
+kookiness at the Brigham and they're
+
+ align:start position:0%
+kookiness at the Brigham and they're
+ 
+
+ align:start position:0%
+kookiness at the Brigham and they're
+using automated techniques of analyzing
+
+ align:start position:0%
+using automated techniques of analyzing
+ 
+
+ align:start position:0%
+using automated techniques of analyzing
+white matter in order to identify lupus
+
+ align:start position:0%
+white matter in order to identify lupus
+ 
+
+ align:start position:0%
+white matter in order to identify lupus
+lesions so lupus is a bad disease that
+
+ align:start position:0%
+lesions so lupus is a bad disease that
+ 
+
+ align:start position:0%
+lesions so lupus is a bad disease that
+shows up in these magnetic resonance
+
+ align:start position:0%
+shows up in these magnetic resonance
+ 
+
+ align:start position:0%
+shows up in these magnetic resonance
+images in certain ways the last thing I
+
+ align:start position:0%
+images in certain ways the last thing I
+ 
+
+ align:start position:0%
+images in certain ways the last thing I
+want to talk about today is notes so my
+
+ align:start position:0%
+want to talk about today is notes so my
+ 
+
+ align:start position:0%
+want to talk about today is notes so my
+students stood a little exercise last
+
+ align:start position:0%
+students stood a little exercise last
+ 
+
+ align:start position:0%
+students stood a little exercise last
+semester where we tried to see how good
+
+ align:start position:0%
+semester where we tried to see how good
+ 
+
+ align:start position:0%
+semester where we tried to see how good
+is the average ape namely a member of my
+
+ align:start position:0%
+is the average ape namely a member of my
+ 
+
+ align:start position:0%
+is the average ape namely a member of my
+research group at predicting mortality
+
+ align:start position:0%
+research group at predicting mortality
+ 
+
+ align:start position:0%
+research group at predicting mortality
+okay and so we took a bunch of cases
+
+ align:start position:0%
+okay and so we took a bunch of cases
+ 
+
+ align:start position:0%
+okay and so we took a bunch of cases
+from the mimic data set blind it to the
+
+ align:start position:0%
+from the mimic data set blind it to the
+ 
+
+ align:start position:0%
+from the mimic data set blind it to the
+question of whether the person lived or
+
+ align:start position:0%
+question of whether the person lived or
+ 
+
+ align:start position:0%
+question of whether the person lived or
+died we gave the data to people in a
+
+ align:start position:0%
+died we gave the data to people in a
+ 
+
+ align:start position:0%
+died we gave the data to people in a
+kind of visualization tool sort of like
+
+ align:start position:0%
+kind of visualization tool sort of like
+ 
+
+ align:start position:0%
+kind of visualization tool sort of like
+the one that I showed you earlier that
+
+ align:start position:0%
+the one that I showed you earlier that
+ 
+
+ align:start position:0%
+the one that I showed you earlier that
+summarizes the case and then also gave
+
+ align:start position:0%
+summarizes the case and then also gave
+ 
+
+ align:start position:0%
+summarizes the case and then also gave
+people access to the notes the
+
+ align:start position:0%
+people access to the notes the
+ 
+
+ align:start position:0%
+people access to the notes the
+de-identified notes about those cases to
+
+ align:start position:0%
+de-identified notes about those cases to
+ 
+
+ align:start position:0%
+de-identified notes about those cases to
+see whether people could predict better
+
+ align:start position:0%
+see whether people could predict better
+ 
+
+ align:start position:0%
+see whether people could predict better
+than a coin flip whether somebody was
+
+ align:start position:0%
+than a coin flip whether somebody was
+ 
+
+ align:start position:0%
+than a coin flip whether somebody was
+going to live or die and the answer is
+
+ align:start position:0%
+going to live or die and the answer is
+ 
+
+ align:start position:0%
+going to live or die and the answer is
+yes slightly better okay not immensely
+
+ align:start position:0%
+yes slightly better okay not immensely
+ 
+
+ align:start position:0%
+yes slightly better okay not immensely
+better but slightly better and
+
+ align:start position:0%
+better but slightly better and
+ 
+
+ align:start position:0%
+better but slightly better and
+furthermore it looks like by giving them
+
+ align:start position:0%
+furthermore it looks like by giving them
+ 
+
+ align:start position:0%
+furthermore it looks like by giving them
+feedback so as they're looking at these
+
+ align:start position:0%
+feedback so as they're looking at these
+ 
+
+ align:start position:0%
+feedback so as they're looking at these
+cases and trying
+
+ align:start position:0%
+cases and trying
+ 
+
+ align:start position:0%
+cases and trying
+to make the prediction they make a
+
+ align:start position:0%
+to make the prediction they make a
+ 
+
+ align:start position:0%
+to make the prediction they make a
+prediction you tell them if they were
+
+ align:start position:0%
+prediction you tell them if they were
+ 
+
+ align:start position:0%
+prediction you tell them if they were
+right or wrong we learn and so we get
+
+ align:start position:0%
+right or wrong we learn and so we get
+ 
+
+ align:start position:0%
+right or wrong we learn and so we get
+slightly better than slightly better
+
+ align:start position:0%
+slightly better than slightly better
+ 
+
+ align:start position:0%
+slightly better than slightly better
+than random right it's kind of
+
+ align:start position:0%
+than random right it's kind of
+ 
+
+ align:start position:0%
+than random right it's kind of
+interesting okay
+
+ align:start position:0%
+interesting okay
+ 
+
+ align:start position:0%
+interesting okay
+so one of the things I discovered is
+
+ align:start position:0%
+so one of the things I discovered is
+ 
+
+ align:start position:0%
+so one of the things I discovered is
+that at least when I was playing the
+
+ align:start position:0%
+that at least when I was playing the
+ 
+
+ align:start position:0%
+that at least when I was playing the
+monkey in this exercise I found the
+
+ align:start position:0%
+monkey in this exercise I found the
+ 
+
+ align:start position:0%
+monkey in this exercise I found the
+notes to be immensely useful much more
+
+ align:start position:0%
+notes to be immensely useful much more
+ 
+
+ align:start position:0%
+notes to be immensely useful much more
+useful than the trendlines of laboratory
+
+ align:start position:0%
+useful than the trendlines of laboratory
+ 
+
+ align:start position:0%
+useful than the trendlines of laboratory
+data partly it's because I'm used to
+
+ align:start position:0%
+data partly it's because I'm used to
+ 
+
+ align:start position:0%
+data partly it's because I'm used to
+reading English I'm not so used to
+
+ align:start position:0%
+reading English I'm not so used to
+ 
+
+ align:start position:0%
+reading English I'm not so used to
+reading graphs of laboratory data but
+
+ align:start position:0%
+reading graphs of laboratory data but
+ 
+
+ align:start position:0%
+reading graphs of laboratory data but
+part of it is that there's a level of
+
+ align:start position:0%
+part of it is that there's a level of
+ 
+
+ align:start position:0%
+part of it is that there's a level of
+human understanding that is transmitted
+
+ align:start position:0%
+human understanding that is transmitted
+ 
+
+ align:start position:0%
+human understanding that is transmitted
+in the nursing notes and in the
+
+ align:start position:0%
+in the nursing notes and in the
+ 
+
+ align:start position:0%
+in the nursing notes and in the
+discharge summaries and so on that you
+
+ align:start position:0%
+discharge summaries and so on that you
+ 
+
+ align:start position:0%
+discharge summaries and so on that you
+don't get from just looking at raw data
+
+ align:start position:0%
+don't get from just looking at raw data
+ 
+
+ align:start position:0%
+don't get from just looking at raw data
+and so there is very much the sense
+
+ align:start position:0%
+and so there is very much the sense
+ 
+
+ align:start position:0%
+and so there is very much the sense
+which we're going to talk about in a
+
+ align:start position:0%
+which we're going to talk about in a
+ 
+
+ align:start position:0%
+which we're going to talk about in a
+couple of weeks of how can we take take
+
+ align:start position:0%
+couple of weeks of how can we take take
+ 
+
+ align:start position:0%
+couple of weeks of how can we take take
+advantage of that information extract it
+
+ align:start position:0%
+advantage of that information extract it
+ 
+
+ align:start position:0%
+advantage of that information extract it
+and use it in the kinds of modeling that
+
+ align:start position:0%
+and use it in the kinds of modeling that
+ 
+
+ align:start position:0%
+and use it in the kinds of modeling that
+we want to do so in mimic if you look we
+
+ align:start position:0%
+we want to do so in mimic if you look we
+ 
+
+ align:start position:0%
+we want to do so in mimic if you look we
+have nursing notes and radiology reports
+
+ align:start position:0%
+have nursing notes and radiology reports
+ 
+
+ align:start position:0%
+have nursing notes and radiology reports
+and more nursing notes and
+
+ align:start position:0%
+and more nursing notes and
+ 
+
+ align:start position:0%
+and more nursing notes and
+electrocardiogram reports and doctors
+
+ align:start position:0%
+electrocardiogram reports and doctors
+ 
+
+ align:start position:0%
+electrocardiogram reports and doctors
+notes and discharge some reason
+
+ align:start position:0%
+notes and discharge some reason
+ 
+
+ align:start position:0%
+notes and discharge some reason
+echocardiogram is respiratory etc and if
+
+ align:start position:0%
+echocardiogram is respiratory etc and if
+ 
+
+ align:start position:0%
+echocardiogram is respiratory etc and if
+you look at the distribution of the
+
+ align:start position:0%
+you look at the distribution of the
+ 
+
+ align:start position:0%
+you look at the distribution of the
+length of these these are unfortunately
+
+ align:start position:0%
+length of these these are unfortunately
+ 
+
+ align:start position:0%
+length of these these are unfortunately
+not on the same scale but the discharge
+
+ align:start position:0%
+not on the same scale but the discharge
+ 
+
+ align:start position:0%
+not on the same scale but the discharge
+summary is the thing that's written at
+
+ align:start position:0%
+summary is the thing that's written at
+ 
+
+ align:start position:0%
+summary is the thing that's written at
+the time you leave the hospital so this
+
+ align:start position:0%
+the time you leave the hospital so this
+ 
+
+ align:start position:0%
+the time you leave the hospital so this
+is sort of the summary of everything
+
+ align:start position:0%
+is sort of the summary of everything
+ 
+
+ align:start position:0%
+is sort of the summary of everything
+that happened to you during your
+
+ align:start position:0%
+that happened to you during your
+ 
+
+ align:start position:0%
+that happened to you during your
+hospitalization and it's long so you
+
+ align:start position:0%
+hospitalization and it's long so you
+ 
+
+ align:start position:0%
+hospitalization and it's long so you
+know it goes up to like 30,000
+
+ align:start position:0%
+know it goes up to like 30,000
+ 
+
+ align:start position:0%
+know it goes up to like 30,000
+characters you know it's a small it's a
+
+ align:start position:0%
+characters you know it's a small it's a
+ 
+
+ align:start position:0%
+characters you know it's a small it's a
+short story not not so short short story
+
+ align:start position:0%
+short story not not so short short story
+ 
+
+ align:start position:0%
+short story not not so short short story
+nursing notes tend to be shorter they
+
+ align:start position:0%
+nursing notes tend to be shorter they
+ 
+
+ align:start position:0%
+nursing notes tend to be shorter they
+run up to about 3,000 characters this
+
+ align:start position:0%
+run up to about 3,000 characters this
+ 
+
+ align:start position:0%
+run up to about 3,000 characters this
+other set of nursing notes which I think
+
+ align:start position:0%
+other set of nursing notes which I think
+ 
+
+ align:start position:0%
+other set of nursing notes which I think
+is comes from the other system is a
+
+ align:start position:0%
+is comes from the other system is a
+ 
+
+ align:start position:0%
+is comes from the other system is a
+little bit longer it goes up to about
+
+ align:start position:0%
+little bit longer it goes up to about
+ 
+
+ align:start position:0%
+little bit longer it goes up to about
+5,000 doctor's notes are a little bit
+
+ align:start position:0%
+5,000 doctor's notes are a little bit
+ 
+
+ align:start position:0%
+5,000 doctor's notes are a little bit
+longer yet they go up to about 10:15
+
+ align:start position:0%
+longer yet they go up to about 10:15
+ 
+
+ align:start position:0%
+longer yet they go up to about 10:15
+thousand characters typically and there
+
+ align:start position:0%
+thousand characters typically and there
+ 
+
+ align:start position:0%
+thousand characters typically and there
+are various other kinds of notes so I
+
+ align:start position:0%
+are various other kinds of notes so I
+ 
+
+ align:start position:0%
+are various other kinds of notes so I
+just wanted to show you a few of these
+
+ align:start position:0%
+just wanted to show you a few of these
+ 
+
+ align:start position:0%
+just wanted to show you a few of these
+here's a brief nursing note so this is a
+
+ align:start position:0%
+here's a brief nursing note so this is a
+ 
+
+ align:start position:0%
+here's a brief nursing note so this is a
+patient who is hypotensive but not in
+
+ align:start position:0%
+patient who is hypotensive but not in
+ 
+
+ align:start position:0%
+patient who is hypotensive but not in
+shock patient remains on this drug drip
+
+ align:start position:0%
+shock patient remains on this drug drip
+ 
+
+ align:start position:0%
+shock patient remains on this drug drip
+at point 75 micrograms per kilogram per
+
+ align:start position:0%
+at point 75 micrograms per kilogram per
+ 
+
+ align:start position:0%
+at point 75 micrograms per kilogram per
+minute
+
+ align:start position:0%
+minute
+ 
+
+ align:start position:0%
+minute
+no titration needed at this time their
+
+ align:start position:0%
+no titration needed at this time their
+ 
+
+ align:start position:0%
+no titration needed at this time their
+blood pressure is stable at more than a
+
+ align:start position:0%
+blood pressure is stable at more than a
+ 
+
+ align:start position:0%
+blood pressure is stable at more than a
+hundred the mean arterial pressure is 65
+
+ align:start position:0%
+hundred the mean arterial pressure is 65
+ 
+
+ align:start position:0%
+hundred the mean arterial pressure is 65
+greater than 65 weaned them from this
+
+ align:start position:0%
+greater than 65 weaned them from this
+ 
+
+ align:start position:0%
+greater than 65 weaned them from this
+drug presumably if if it's tolerated a
+
+ align:start position:0%
+drug presumably if if it's tolerated a
+ 
+
+ align:start position:0%
+drug presumably if if it's tolerated a
+wound infection so anterior groin area
+
+ align:start position:0%
+wound infection so anterior groin area
+ 
+
+ align:start position:0%
+wound infection so anterior groin area
+open and losing moderate amounts of thin
+
+ align:start position:0%
+open and losing moderate amounts of thin
+ 
+
+ align:start position:0%
+open and losing moderate amounts of thin
+pink pink tinged serous fluid patients
+
+ align:start position:0%
+pink pink tinged serous fluid patients
+ 
+
+ align:start position:0%
+pink pink tinged serous fluid patients
+tooling with small amounts of stool on
+
+ align:start position:0%
+tooling with small amounts of stool on
+ 
+
+ align:start position:0%
+tooling with small amounts of stool on
+something and dangerously close to the
+
+ align:start position:0%
+something and dangerously close to the
+ 
+
+ align:start position:0%
+something and dangerously close to the
+open wound etc so this is sort of the
+
+ align:start position:0%
+open wound etc so this is sort of the
+ 
+
+ align:start position:0%
+open wound etc so this is sort of the
+nurse's snapshot she just went in saw
+
+ align:start position:0%
+nurse's snapshot she just went in saw
+ 
+
+ align:start position:0%
+nurse's snapshot she just went in saw
+the patient by the way I say she but you
+
+ align:start position:0%
+the patient by the way I say she but you
+ 
+
+ align:start position:0%
+the patient by the way I say she but you
+know probably a vast majority of nurses
+
+ align:start position:0%
+know probably a vast majority of nurses
+ 
+
+ align:start position:0%
+know probably a vast majority of nurses
+in Boston area hospitals really are
+
+ align:start position:0%
+in Boston area hospitals really are
+ 
+
+ align:start position:0%
+in Boston area hospitals really are
+women but there are some male nurses and
+
+ align:start position:0%
+women but there are some male nurses and
+ 
+
+ align:start position:0%
+women but there are some male nurses and
+we'll record sort of a snapshot of
+
+ align:start position:0%
+we'll record sort of a snapshot of
+ 
+
+ align:start position:0%
+we'll record sort of a snapshot of
+what's going on with the patient what
+
+ align:start position:0%
+what's going on with the patient what
+ 
+
+ align:start position:0%
+what's going on with the patient what
+are the concerns in principle this is
+
+ align:start position:0%
+are the concerns in principle this is
+ 
+
+ align:start position:0%
+are the concerns in principle this is
+going to be useful not only as a part of
+
+ align:start position:0%
+going to be useful not only as a part of
+ 
+
+ align:start position:0%
+going to be useful not only as a part of
+the medical record but also when this
+
+ align:start position:0%
+the medical record but also when this
+ 
+
+ align:start position:0%
+the medical record but also when this
+nurse goes off shift and the next nurse
+
+ align:start position:0%
+nurse goes off shift and the next nurse
+ 
+
+ align:start position:0%
+nurse goes off shift and the next nurse
+comes on shift then this is a recording
+
+ align:start position:0%
+comes on shift then this is a recording
+ 
+
+ align:start position:0%
+comes on shift then this is a recording
+of what the state of the patient was the
+
+ align:start position:0%
+of what the state of the patient was the
+ 
+
+ align:start position:0%
+of what the state of the patient was the
+last time they were seen by by the nurse
+
+ align:start position:0%
+last time they were seen by by the nurse
+ 
+
+ align:start position:0%
+last time they were seen by by the nurse
+in reality the nurses tend to tell each
+
+ align:start position:0%
+in reality the nurses tend to tell each
+ 
+
+ align:start position:0%
+in reality the nurses tend to tell each
+other verbally rather than relying on
+
+ align:start position:0%
+other verbally rather than relying on
+ 
+
+ align:start position:0%
+other verbally rather than relying on
+the written version I remember one time
+
+ align:start position:0%
+the written version I remember one time
+ 
+
+ align:start position:0%
+the written version I remember one time
+talking to a nurse in an intensive care
+
+ align:start position:0%
+talking to a nurse in an intensive care
+ 
+
+ align:start position:0%
+talking to a nurse in an intensive care
+unit in another part of the country and
+
+ align:start position:0%
+unit in another part of the country and
+ 
+
+ align:start position:0%
+unit in another part of the country and
+I said so whoever reads your notes and
+
+ align:start position:0%
+I said so whoever reads your notes and
+ 
+
+ align:start position:0%
+I said so whoever reads your notes and
+she says quality assurance officers so
+
+ align:start position:0%
+she says quality assurance officers so
+ 
+
+ align:start position:0%
+she says quality assurance officers so
+the hospital has people responsible for
+
+ align:start position:0%
+the hospital has people responsible for
+ 
+
+ align:start position:0%
+the hospital has people responsible for
+trying to assess the quality of care
+
+ align:start position:0%
+trying to assess the quality of care
+ 
+
+ align:start position:0%
+trying to assess the quality of care
+they're giving and lawyers when there's
+
+ align:start position:0%
+they're giving and lawyers when there's
+ 
+
+ align:start position:0%
+they're giving and lawyers when there's
+a lawsuit
+
+ align:start position:0%
+a lawsuit
+ 
+
+ align:start position:0%
+a lawsuit
+and she was very happy because she had
+
+ align:start position:0%
+and she was very happy because she had
+ 
+
+ align:start position:0%
+and she was very happy because she had
+saved the hospital ten million dollars
+
+ align:start position:0%
+saved the hospital ten million dollars
+ 
+
+ align:start position:0%
+saved the hospital ten million dollars
+by having carefully recorded that some
+
+ align:start position:0%
+by having carefully recorded that some
+ 
+
+ align:start position:0%
+by having carefully recorded that some
+procedure had been done to a patient who
+
+ align:start position:0%
+procedure had been done to a patient who
+ 
+
+ align:start position:0%
+procedure had been done to a patient who
+then had a bad outcome and was suing the
+
+ align:start position:0%
+then had a bad outcome and was suing the
+ 
+
+ align:start position:0%
+then had a bad outcome and was suing the
+hospital for their neglect and not
+
+ align:start position:0%
+hospital for their neglect and not
+ 
+
+ align:start position:0%
+hospital for their neglect and not
+having done this but because it was in
+
+ align:start position:0%
+having done this but because it was in
+ 
+
+ align:start position:0%
+having done this but because it was in
+the note that was proof that it actually
+
+ align:start position:0%
+the note that was proof that it actually
+ 
+
+ align:start position:0%
+the note that was proof that it actually
+had been done and therefore the hospital
+
+ align:start position:0%
+had been done and therefore the hospital
+ 
+
+ align:start position:0%
+had been done and therefore the hospital
+wasn't liable so but there's a lot of
+
+ align:start position:0%
+wasn't liable so but there's a lot of
+ 
+
+ align:start position:0%
+wasn't liable so but there's a lot of
+information in here now I'm going to
+
+ align:start position:0%
+information in here now I'm going to
+ 
+
+ align:start position:0%
+information in here now I'm going to
+show you many pages of a typical
+
+ align:start position:0%
+show you many pages of a typical
+ 
+
+ align:start position:0%
+show you many pages of a typical
+discharge summary so this is somebody on
+
+ align:start position:0%
+discharge summary so this is somebody on
+ 
+
+ align:start position:0%
+discharge summary so this is somebody on
+the surgery service who came in
+
+ align:start position:0%
+the surgery service who came in
+ 
+
+ align:start position:0%
+the surgery service who came in
+complaining of leg leg pain redness and
+
+ align:start position:0%
+complaining of leg leg pain redness and
+ 
+
+ align:start position:0%
+complaining of leg leg pain redness and
+swelling secondary to infection of the
+
+ align:start position:0%
+swelling secondary to infection of the
+ 
+
+ align:start position:0%
+swelling secondary to infection of the
+left femoral pop pop little bypass so
+
+ align:start position:0%
+left femoral pop pop little bypass so
+ 
+
+ align:start position:0%
+left femoral pop pop little bypass so
+she had surgery I think she now female
+
+ align:start position:0%
+she had surgery I think she now female
+ 
+
+ align:start position:0%
+she had surgery I think she now female
+she had surgery which didn't heal well
+
+ align:start position:0%
+she had surgery which didn't heal well
+ 
+
+ align:start position:0%
+she had surgery which didn't heal well
+so major surgical or invasive procedure
+
+ align:start position:0%
+so major surgical or invasive procedure
+ 
+
+ align:start position:0%
+so major surgical or invasive procedure
+incision and drainage and pulse
+
+ align:start position:0%
+incision and drainage and pulse
+ 
+
+ align:start position:0%
+incision and drainage and pulse
+irrigation of the left groin and left
+
+ align:start position:0%
+irrigation of the left groin and left
+ 
+
+ align:start position:0%
+irrigation of the left groin and left
+above knee popliteal site incisions with
+
+ align:start position:0%
+above knee popliteal site incisions with
+ 
+
+ align:start position:0%
+above knee popliteal site incisions with
+exploration of bypass graft and excision
+
+ align:start position:0%
+exploration of bypass graft and excision
+ 
+
+ align:start position:0%
+exploration of bypass graft and excision
+of the entire left common femoral artery
+
+ align:start position:0%
+of the entire left common femoral artery
+ 
+
+ align:start position:0%
+of the entire left common femoral artery
+- above knee blah blah blah blah blah
+
+ align:start position:0%
+- above knee blah blah blah blah blah
+ 
+
+ align:start position:0%
+- above knee blah blah blah blah blah
+blah so this is what they did history of
+
+ align:start position:0%
+blah so this is what they did history of
+ 
+
+ align:start position:0%
+blah so this is what they did history of
+the present illness she's a 45 year old
+
+ align:start position:0%
+the present illness she's a 45 year old
+ 
+
+ align:start position:0%
+the present illness she's a 45 year old
+woman who underwent a left femoral ache
+
+ align:start position:0%
+woman who underwent a left femoral ache
+ 
+
+ align:start position:0%
+woman who underwent a left femoral ache
+a doctor or something or other with PTFE
+
+ align:start position:0%
+a doctor or something or other with PTFE
+ 
+
+ align:start position:0%
+a doctor or something or other with PTFE
+whatever that is over a month ago on a
+
+ align:start position:0%
+whatever that is over a month ago on a
+ 
+
+ align:start position:0%
+whatever that is over a month ago on a
+certain date by the way these bracket
+
+ align:start position:0%
+certain date by the way these bracket
+ 
+
+ align:start position:0%
+certain date by the way these bracket
+asterisk things are where we've taken
+
+ align:start position:0%
+asterisk things are where we've taken
+ 
+
+ align:start position:0%
+asterisk things are where we've taken
+out identifying information from the
+
+ align:start position:0%
+out identifying information from the
+ 
+
+ align:start position:0%
+out identifying information from the
+record she had been doing well
+
+ align:start position:0%
+record she had been doing well
+ 
+
+ align:start position:0%
+record she had been doing well
+postoperatively and was seen in the
+
+ align:start position:0%
+postoperatively and was seen in the
+ 
+
+ align:start position:0%
+postoperatively and was seen in the
+clinic six days prior to presentation at
+
+ align:start position:0%
+clinic six days prior to presentation at
+ 
+
+ align:start position:0%
+clinic six days prior to presentation at
+this time she acutely developed nausea
+
+ align:start position:0%
+this time she acutely developed nausea
+ 
+
+ align:start position:0%
+this time she acutely developed nausea
+vomiting fevers and progressive redness
+
+ align:start position:0%
+vomiting fevers and progressive redness
+ 
+
+ align:start position:0%
+vomiting fevers and progressive redness
+swelling pain of her left thigh etc okay
+
+ align:start position:0%
+swelling pain of her left thigh etc okay
+ 
+
+ align:start position:0%
+swelling pain of her left thigh etc okay
+so that's just page one of many pages
+
+ align:start position:0%
+so that's just page one of many pages
+ 
+
+ align:start position:0%
+so that's just page one of many pages
+yeah
+
+ align:start position:0%
+yeah
+ 
+
+ align:start position:0%
+yeah
+these information fields there's no help
+
+ align:start position:0%
+these information fields there's no help
+ 
+
+ align:start position:0%
+these information fields there's no help
+is there's no heart of impedes if you
+
+ align:start position:0%
+is there's no heart of impedes if you
+ 
+
+ align:start position:0%
+is there's no heart of impedes if you
+type a patient's name we're not in this
+
+ align:start position:0%
+type a patient's name we're not in this
+ 
+
+ align:start position:0%
+type a patient's name we're not in this
+system there there are people Henrich
+
+ align:start position:0%
+system there there are people Henrich
+ 
+
+ align:start position:0%
+system there there are people Henrich
+way at Mass General spent ten years
+
+ align:start position:0%
+way at Mass General spent ten years
+ 
+
+ align:start position:0%
+way at Mass General spent ten years
+building a system that had autocomplete
+
+ align:start position:0%
+building a system that had autocomplete
+ 
+
+ align:start position:0%
+building a system that had autocomplete
+and so on and some doctors liked it and
+
+ align:start position:0%
+and so on and some doctors liked it and
+ 
+
+ align:start position:0%
+and so on and some doctors liked it and
+some doctors hated it and the MGH threw
+
+ align:start position:0%
+some doctors hated it and the MGH threw
+ 
+
+ align:start position:0%
+some doctors hated it and the MGH threw
+out all of their old systems in order to
+
+ align:start position:0%
+out all of their old systems in order to
+ 
+
+ align:start position:0%
+out all of their old systems in order to
+buy epic and so it's gone was like 10
+
+ align:start position:0%
+buy epic and so it's gone was like 10
+ 
+
+ align:start position:0%
+buy epic and so it's gone was like 10
+years of work down the drain but it was
+
+ align:start position:0%
+years of work down the drain but it was
+ 
+
+ align:start position:0%
+years of work down the drain but it was
+not a spectacular success so because
+
+ align:start position:0%
+not a spectacular success so because
+ 
+
+ align:start position:0%
+not a spectacular success so because
+whenever you have like autocomplete you
+
+ align:start position:0%
+whenever you have like autocomplete you
+ 
+
+ align:start position:0%
+whenever you have like autocomplete you
+have to anticipate every possible answer
+
+ align:start position:0%
+have to anticipate every possible answer
+ 
+
+ align:start position:0%
+have to anticipate every possible answer
+and people are very creative and they
+
+ align:start position:0%
+and people are very creative and they
+ 
+
+ align:start position:0%
+and people are very creative and they
+always want to type something that you
+
+ align:start position:0%
+always want to type something that you
+ 
+
+ align:start position:0%
+always want to type something that you
+didn't anticipate so it's it's hard to
+
+ align:start position:0%
+didn't anticipate so it's it's hard to
+ 
+
+ align:start position:0%
+didn't anticipate so it's it's hard to
+support it epic is a big company that
+
+ align:start position:0%
+support it epic is a big company that
+ 
+
+ align:start position:0%
+support it epic is a big company that
+has been winning all the recent contests
+
+ align:start position:0%
+has been winning all the recent contests
+ 
+
+ align:start position:0%
+has been winning all the recent contests
+for installing electronic medical record
+
+ align:start position:0%
+for installing electronic medical record
+ 
+
+ align:start position:0%
+for installing electronic medical record
+systems remember in my last lecture I
+
+ align:start position:0%
+systems remember in my last lecture I
+ 
+
+ align:start position:0%
+systems remember in my last lecture I
+showed that we're reaching about a
+
+ align:start position:0%
+showed that we're reaching about a
+ 
+
+ align:start position:0%
+showed that we're reaching about a
+hundred percent saturation so they've
+
+ align:start position:0%
+hundred percent saturation so they've
+ 
+
+ align:start position:0%
+hundred percent saturation so they've
+been winning a lot of the of the of the
+
+ align:start position:0%
+been winning a lot of the of the of the
+ 
+
+ align:start position:0%
+been winning a lot of the of the of the
+installation deals and they're getting a
+
+ align:start position:0%
+installation deals and they're getting a
+ 
+
+ align:start position:0%
+installation deals and they're getting a
+lot of the subsidy the estimate I heard
+
+ align:start position:0%
+lot of the subsidy the estimate I heard
+ 
+
+ align:start position:0%
+lot of the subsidy the estimate I heard
+was that Partners HealthCare which is
+
+ align:start position:0%
+was that Partners HealthCare which is
+ 
+
+ align:start position:0%
+was that Partners HealthCare which is
+MGH of the Brigham and a couple of other
+
+ align:start position:0%
+MGH of the Brigham and a couple of other
+ 
+
+ align:start position:0%
+MGH of the Brigham and a couple of other
+hospitals spent somewhere on the order
+
+ align:start position:0%
+hospitals spent somewhere on the order
+ 
+
+ align:start position:0%
+hospitals spent somewhere on the order
+of two billion dollars installing the
+
+ align:start position:0%
+of two billion dollars installing the
+ 
+
+ align:start position:0%
+of two billion dollars installing the
+system so that included all the
+
+ align:start position:0%
+system so that included all the
+ 
+
+ align:start position:0%
+system so that included all the
+customizations and all the training and
+
+ align:start position:0%
+customizations and all the training and
+ 
+
+ align:start position:0%
+customizations and all the training and
+all the administrative stuff that went
+
+ align:start position:0%
+all the administrative stuff that went
+ 
+
+ align:start position:0%
+all the administrative stuff that went
+with it but that's a huge amount of
+
+ align:start position:0%
+with it but that's a huge amount of
+ 
+
+ align:start position:0%
+with it but that's a huge amount of
+money okay so we have past medical
+
+ align:start position:0%
+money okay so we have past medical
+ 
+
+ align:start position:0%
+money okay so we have past medical
+history one pack a day smoker abused
+
+ align:start position:0%
+history one pack a day smoker abused
+ 
+
+ align:start position:0%
+history one pack a day smoker abused
+cocaine but she stopped six months ago
+
+ align:start position:0%
+cocaine but she stopped six months ago
+ 
+
+ align:start position:0%
+cocaine but she stopped six months ago
+has asthma type two diabetes
+
+ align:start position:0%
+has asthma type two diabetes
+ 
+
+ align:start position:0%
+has asthma type two diabetes
+social history family history these are
+
+ align:start position:0%
+social history family history these are
+ 
+
+ align:start position:0%
+social history family history these are
+the physical exam results
+
+ align:start position:0%
+the physical exam results
+ 
+
+ align:start position:0%
+the physical exam results
+so it's giving you a lot of information
+
+ align:start position:0%
+so it's giving you a lot of information
+ 
+
+ align:start position:0%
+so it's giving you a lot of information
+about the person description of the
+
+ align:start position:0%
+about the person description of the
+ 
+
+ align:start position:0%
+about the person description of the
+wound down at the bottom pertinent lab
+
+ align:start position:0%
+wound down at the bottom pertinent lab
+ 
+
+ align:start position:0%
+wound down at the bottom pertinent lab
+results so these are copied out of the
+
+ align:start position:0%
+results so these are copied out of the
+ 
+
+ align:start position:0%
+results so these are copied out of the
+laboratory tables yeah sorry yeah yeah
+
+ align:start position:0%
+laboratory tables yeah sorry yeah yeah
+ 
+
+ align:start position:0%
+laboratory tables yeah sorry yeah yeah
+the the identification technology here
+
+ align:start position:0%
+the the identification technology here
+ 
+
+ align:start position:0%
+the the identification technology here
+maintains the relative dates but not the
+
+ align:start position:0%
+maintains the relative dates but not the
+ 
+
+ align:start position:0%
+maintains the relative dates but not the
+absolute dates so these are results
+
+ align:start position:0%
+absolute dates so these are results
+ 
+
+ align:start position:0%
+absolute dates so these are results
+again copied out of the laboratory
+
+ align:start position:0%
+again copied out of the laboratory
+ 
+
+ align:start position:0%
+again copied out of the laboratory
+database in into the discharge summary
+
+ align:start position:0%
+database in into the discharge summary
+ 
+
+ align:start position:0%
+database in into the discharge summary
+brief Hospital course and then a review
+
+ align:start position:0%
+brief Hospital course and then a review
+ 
+
+ align:start position:0%
+brief Hospital course and then a review
+of systems so what's going on
+
+ align:start position:0%
+of systems so what's going on
+ 
+
+ align:start position:0%
+of systems so what's going on
+neurologically cardiovascular pulmonary
+
+ align:start position:0%
+neurologically cardiovascular pulmonary
+ 
+
+ align:start position:0%
+neurologically cardiovascular pulmonary
+gi/gu etcetera infectious disease
+
+ align:start position:0%
+gi/gu etcetera infectious disease
+ 
+
+ align:start position:0%
+gi/gu etcetera infectious disease
+endocrine hematology prophylaxis and at
+
+ align:start position:0%
+endocrine hematology prophylaxis and at
+ 
+
+ align:start position:0%
+endocrine hematology prophylaxis and at
+the time of discharge the patient was
+
+ align:start position:0%
+the time of discharge the patient was
+ 
+
+ align:start position:0%
+the time of discharge the patient was
+doing well no fever and stable vital
+
+ align:start position:0%
+doing well no fever and stable vital
+ 
+
+ align:start position:0%
+doing well no fever and stable vital
+signs tolerating a regular diet
+
+ align:start position:0%
+signs tolerating a regular diet
+ 
+
+ align:start position:0%
+signs tolerating a regular diet
+ambulating waiting without assistance
+
+ align:start position:0%
+ambulating waiting without assistance
+ 
+
+ align:start position:0%
+ambulating waiting without assistance
+and pain was well controlled medications
+
+ align:start position:0%
+and pain was well controlled medications
+ 
+
+ align:start position:0%
+and pain was well controlled medications
+on admission so this was the medication
+
+ align:start position:0%
+on admission so this was the medication
+ 
+
+ align:start position:0%
+on admission so this was the medication
+reconciliation discharge medications so
+
+ align:start position:0%
+reconciliation discharge medications so
+ 
+
+ align:start position:0%
+reconciliation discharge medications so
+this is what she's being sent home on
+
+ align:start position:0%
+this is what she's being sent home on
+ 
+
+ align:start position:0%
+this is what she's being sent home on
+discharge disposition is to the home
+
+ align:start position:0%
+discharge disposition is to the home
+ 
+
+ align:start position:0%
+discharge disposition is to the home
+with some follow-up service and she's
+
+ align:start position:0%
+with some follow-up service and she's
+ 
+
+ align:start position:0%
+with some follow-up service and she's
+going home and the discharge diagnosis
+
+ align:start position:0%
+going home and the discharge diagnosis
+ 
+
+ align:start position:0%
+going home and the discharge diagnosis
+is infected left femoral popliteal
+
+ align:start position:0%
+is infected left femoral popliteal
+ 
+
+ align:start position:0%
+is infected left femoral popliteal
+bypass graft and the condition and these
+
+ align:start position:0%
+bypass graft and the condition and these
+ 
+
+ align:start position:0%
+bypass graft and the condition and these
+are the instructions to the patient that
+
+ align:start position:0%
+are the instructions to the patient that
+ 
+
+ align:start position:0%
+are the instructions to the patient that
+say you know here's what you can do
+
+ align:start position:0%
+say you know here's what you can do
+ 
+
+ align:start position:0%
+say you know here's what you can do
+here's when you should come back and
+
+ align:start position:0%
+here's when you should come back and
+ 
+
+ align:start position:0%
+here's when you should come back and
+tell us if something is going
+
+ align:start position:0%
+tell us if something is going
+ 
+
+ align:start position:0%
+tell us if something is going
+etc and here's what you should report if
+
+ align:start position:0%
+etc and here's what you should report if
+ 
+
+ align:start position:0%
+etc and here's what you should report if
+if it happens you know if you have
+
+ align:start position:0%
+if it happens you know if you have
+ 
+
+ align:start position:0%
+if it happens you know if you have
+sudden severe bleeding or swelling do
+
+ align:start position:0%
+sudden severe bleeding or swelling do
+ 
+
+ align:start position:0%
+sudden severe bleeding or swelling do
+this follow up with doctor or somebody
+
+ align:start position:0%
+this follow up with doctor or somebody
+ 
+
+ align:start position:0%
+this follow up with doctor or somebody
+or other call his clinic at this number
+
+ align:start position:0%
+or other call his clinic at this number
+ 
+
+ align:start position:0%
+or other call his clinic at this number
+to schedule an appointment and and then
+
+ align:start position:0%
+to schedule an appointment and and then
+ 
+
+ align:start position:0%
+to schedule an appointment and and then
+follow up with doctor somebody else in
+
+ align:start position:0%
+follow up with doctor somebody else in
+ 
+
+ align:start position:0%
+follow up with doctor somebody else in
+two weeks I think this is the same one
+
+ align:start position:0%
+two weeks I think this is the same one
+ 
+
+ align:start position:0%
+two weeks I think this is the same one
+so just a couple of final words about
+
+ align:start position:0%
+so just a couple of final words about
+ 
+
+ align:start position:0%
+so just a couple of final words about
+standards so you saw in David's
+
+ align:start position:0%
+standards so you saw in David's
+ 
+
+ align:start position:0%
+standards so you saw in David's
+introductory lecture a reference to
+
+ align:start position:0%
+introductory lecture a reference to
+ 
+
+ align:start position:0%
+introductory lecture a reference to
+Odyssey which is a standard method of
+
+ align:start position:0%
+Odyssey which is a standard method of
+ 
+
+ align:start position:0%
+Odyssey which is a standard method of
+encoding the kind of data that we're
+
+ align:start position:0%
+encoding the kind of data that we're
+ 
+
+ align:start position:0%
+encoding the kind of data that we're
+talking about today there's a likelihood
+
+ align:start position:0%
+talking about today there's a likelihood
+ 
+
+ align:start position:0%
+talking about today there's a likelihood
+that the next release of the mimic
+
+ align:start position:0%
+that the next release of the mimic
+ 
+
+ align:start position:0%
+that the next release of the mimic
+database will adopt the Odyssey formats
+
+ align:start position:0%
+database will adopt the Odyssey formats
+ 
+
+ align:start position:0%
+database will adopt the Odyssey formats
+rather than the David shaking his head
+
+ align:start position:0%
+rather than the David shaking his head
+ 
+
+ align:start position:0%
+rather than the David shaking his head
+wondering why me too
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+well so you know what always happens as
+
+ align:start position:0%
+well so you know what always happens as
+ 
+
+ align:start position:0%
+well so you know what always happens as
+you say I'm going to adopt the standard
+
+ align:start position:0%
+you say I'm going to adopt the standard
+ 
+
+ align:start position:0%
+you say I'm going to adopt the standard
+asterisk with the following extensions
+
+ align:start position:0%
+asterisk with the following extensions
+ 
+
+ align:start position:0%
+asterisk with the following extensions
+and that's probably what's going to
+
+ align:start position:0%
+and that's probably what's going to
+ 
+
+ align:start position:0%
+and that's probably what's going to
+happen but it means that the the central
+
+ align:start position:0%
+happen but it means that the the central
+ 
+
+ align:start position:0%
+happen but it means that the the central
+tables you know the icd-9 code tables
+
+ align:start position:0%
+tables you know the icd-9 code tables
+ 
+
+ align:start position:0%
+tables you know the icd-9 code tables
+and the drug tables and things like that
+
+ align:start position:0%
+and the drug tables and things like that
+ 
+
+ align:start position:0%
+and the drug tables and things like that
+are likely to wind up adopting the
+
+ align:start position:0%
+are likely to wind up adopting the
+ 
+
+ align:start position:0%
+are likely to wind up adopting the
+format's of the Odyssey database you
+
+ align:start position:0%
+format's of the Odyssey database you
+ 
+
+ align:start position:0%
+format's of the Odyssey database you
+should also know about this thing called
+
+ align:start position:0%
+should also know about this thing called
+ 
+
+ align:start position:0%
+should also know about this thing called
+fire fhir the fast health
+
+ align:start position:0%
+fire fhir the fast health
+ 
+
+ align:start position:0%
+fire fhir the fast health
+interoperability resources so hl7 is the
+
+ align:start position:0%
+interoperability resources so hl7 is the
+ 
+
+ align:start position:0%
+interoperability resources so hl7 is the
+standards organization that had a
+
+ align:start position:0%
+standards organization that had a
+ 
+
+ align:start position:0%
+standards organization that had a
+tremendous success in the early 1990s in
+
+ align:start position:0%
+tremendous success in the early 1990s in
+ 
+
+ align:start position:0%
+tremendous success in the early 1990s in
+solving the problem of how to allow
+
+ align:start position:0%
+solving the problem of how to allow
+ 
+
+ align:start position:0%
+solving the problem of how to allow
+laboratories to report lab data back to
+
+ align:start position:0%
+laboratories to report lab data back to
+ 
+
+ align:start position:0%
+laboratories to report lab data back to
+the hospitals or the clinics that
+
+ align:start position:0%
+the hospitals or the clinics that
+ 
+
+ align:start position:0%
+the hospitals or the clinics that
+ordered the labs and that character
+
+ align:start position:0%
+ordered the labs and that character
+ 
+
+ align:start position:0%
+ordered the labs and that character
+string with the up arrows on the
+
+ align:start position:0%
+string with the up arrows on the
+ 
+
+ align:start position:0%
+string with the up arrows on the
+vertical bars and so on that I showed
+
+ align:start position:0%
+vertical bars and so on that I showed
+ 
+
+ align:start position:0%
+vertical bars and so on that I showed
+you before that had link encoded in it
+
+ align:start position:0%
+you before that had link encoded in it
+ 
+
+ align:start position:0%
+you before that had link encoded in it
+is that standard that's called hl7
+
+ align:start position:0%
+is that standard that's called hl7
+ 
+
+ align:start position:0%
+is that standard that's called hl7
+version 2 it's still in use very widely
+
+ align:start position:0%
+version 2 it's still in use very widely
+ 
+
+ align:start position:0%
+version 2 it's still in use very widely
+they then got ambitious and suffered
+
+ align:start position:0%
+they then got ambitious and suffered
+ 
+
+ align:start position:0%
+they then got ambitious and suffered
+second system syndrome which is they
+
+ align:start position:0%
+second system syndrome which is they
+ 
+
+ align:start position:0%
+second system syndrome which is they
+decided to build hl7 version 3 which I
+
+ align:start position:0%
+decided to build hl7 version 3 which I
+ 
+
+ align:start position:0%
+decided to build hl7 version 3 which I
+used to teach in a class here 10 years
+
+ align:start position:0%
+used to teach in a class here 10 years
+ 
+
+ align:start position:0%
+used to teach in a class here 10 years
+ago but one of my friends who works for
+
+ align:start position:0%
+ago but one of my friends who works for
+ 
+
+ align:start position:0%
+ago but one of my friends who works for
+a company that helps hospitals implement
+
+ align:start position:0%
+a company that helps hospitals implement
+ 
+
+ align:start position:0%
+a company that helps hospitals implement
+that sent me a like a 38 megabyte PDF
+
+ align:start position:0%
+that sent me a like a 38 megabyte PDF
+ 
+
+ align:start position:0%
+that sent me a like a 38 megabyte PDF
+file that describes what you need to
+
+ align:start position:0%
+file that describes what you need to
+ 
+
+ align:start position:0%
+file that describes what you need to
+know in order to implement that system
+
+ align:start position:0%
+know in order to implement that system
+ 
+
+ align:start position:0%
+know in order to implement that system
+and as a result nobody was doing it so
+
+ align:start position:0%
+and as a result nobody was doing it so
+ 
+
+ align:start position:0%
+and as a result nobody was doing it so
+fire is a gross simplification of that
+
+ align:start position:0%
+fire is a gross simplification of that
+ 
+
+ align:start position:0%
+fire is a gross simplification of that
+that starts off and says if a doctor
+
+ align:start position:0%
+that starts off and says if a doctor
+ 
+
+ align:start position:0%
+that starts off and says if a doctor
+refers a new patient to you what is the
+
+ align:start position:0%
+refers a new patient to you what is the
+ 
+
+ align:start position:0%
+refers a new patient to you what is the
+minimum set of data that you need to
+
+ align:start position:0%
+minimum set of data that you need to
+ 
+
+ align:start position:0%
+minimum set of data that you need to
+know in order to take care of that
+
+ align:start position:0%
+know in order to take care of that
+ 
+
+ align:start position:0%
+know in order to take care of that
+person and fire tries to provide just
+
+ align:start position:0%
+person and fire tries to provide just
+ 
+
+ align:start position:0%
+person and fire tries to provide just
+that subset of all the data it has
+
+ align:start position:0%
+that subset of all the data it has
+ 
+
+ align:start position:0%
+that subset of all the data it has
+become a standard mainly because after
+
+ align:start position:0%
+become a standard mainly because after
+ 
+
+ align:start position:0%
+become a standard mainly because after
+Congress spent 42 billion dollars or so
+
+ align:start position:0%
+Congress spent 42 billion dollars or so
+ 
+
+ align:start position:0%
+Congress spent 42 billion dollars or so
+bribing people into buying these
+
+ align:start position:0%
+bribing people into buying these
+ 
+
+ align:start position:0%
+bribing people into buying these
+informations
+
+ align:start position:0%
+informations
+ 
+
+ align:start position:0%
+informations
+they got mad that the information
+
+ align:start position:0%
+they got mad that the information
+ 
+
+ align:start position:0%
+they got mad that the information
+systems they bought couldn't talk to
+
+ align:start position:0%
+systems they bought couldn't talk to
+ 
+
+ align:start position:0%
+systems they bought couldn't talk to
+each other and so they called in on the
+
+ align:start position:0%
+each other and so they called in on the
+ 
+
+ align:start position:0%
+each other and so they called in on the
+carpet the heads of these IT companies
+
+ align:start position:0%
+carpet the heads of these IT companies
+ 
+
+ align:start position:0%
+carpet the heads of these IT companies
+health IT companies and they yelled at
+
+ align:start position:0%
+health IT companies and they yelled at
+ 
+
+ align:start position:0%
+health IT companies and they yelled at
+them and they made them promise that
+
+ align:start position:0%
+them and they made them promise that
+ 
+
+ align:start position:0%
+them and they made them promise that
+there would be interoperability they
+
+ align:start position:0%
+there would be interoperability they
+ 
+
+ align:start position:0%
+there would be interoperability they
+promised and out of that came fire it
+
+ align:start position:0%
+promised and out of that came fire it
+ 
+
+ align:start position:0%
+promised and out of that came fire it
+was probably simultaneously developed
+
+ align:start position:0%
+was probably simultaneously developed
+ 
+
+ align:start position:0%
+was probably simultaneously developed
+but they adopted it and so now in
+
+ align:start position:0%
+but they adopted it and so now in
+ 
+
+ align:start position:0%
+but they adopted it and so now in
+principle it's possible to exchange data
+
+ align:start position:0%
+principle it's possible to exchange data
+ 
+
+ align:start position:0%
+principle it's possible to exchange data
+between different hospitals at least to
+
+ align:start position:0%
+between different hospitals at least to
+ 
+
+ align:start position:0%
+between different hospitals at least to
+the level of that degree of
+
+ align:start position:0%
+the level of that degree of
+ 
+
+ align:start position:0%
+the level of that degree of
+harmonization of the data in reality the
+
+ align:start position:0%
+harmonization of the data in reality the
+ 
+
+ align:start position:0%
+harmonization of the data in reality the
+companies don't want you to do that
+
+ align:start position:0%
+companies don't want you to do that
+ 
+
+ align:start position:0%
+companies don't want you to do that
+because they like there to be friction
+
+ align:start position:0%
+because they like there to be friction
+ 
+
+ align:start position:0%
+because they like there to be friction
+in not being able to take all your data
+
+ align:start position:0%
+in not being able to take all your data
+ 
+
+ align:start position:0%
+in not being able to take all your data
+to a different Hospital because it is
+
+ align:start position:0%
+to a different Hospital because it is
+ 
+
+ align:start position:0%
+to a different Hospital because it is
+more likely to leave you at the one that
+
+ align:start position:0%
+more likely to leave you at the one that
+ 
+
+ align:start position:0%
+more likely to leave you at the one that
+you're at
+
+ align:start position:0%
+you're at
+ 
+
+ align:start position:0%
+you're at
+so there's complicated socio-economic
+
+ align:start position:0%
+so there's complicated socio-economic
+ 
+
+ align:start position:0%
+so there's complicated socio-economic
+kinds of issues in all this but at least
+
+ align:start position:0%
+kinds of issues in all this but at least
+ 
+
+ align:start position:0%
+kinds of issues in all this but at least
+the standard exists and is becoming more
+
+ align:start position:0%
+the standard exists and is becoming more
+ 
+
+ align:start position:0%
+the standard exists and is becoming more
+and more widely deployed as long as
+
+ align:start position:0%
+and more widely deployed as long as
+ 
+
+ align:start position:0%
+and more widely deployed as long as
+Congress pays attention it's ugly
+
+ align:start position:0%
+Congress pays attention it's ugly
+ 
+
+ align:start position:0%
+Congress pays attention it's ugly
+so here's what a patient looks like
+
+ align:start position:0%
+so here's what a patient looks like
+ 
+
+ align:start position:0%
+so here's what a patient looks like
+right it's the usual unreadable XML
+
+ align:start position:0%
+right it's the usual unreadable XML
+ 
+
+ align:start position:0%
+right it's the usual unreadable XML
+garbage but fortunately there are
+
+ align:start position:0%
+garbage but fortunately there are
+ 
+
+ align:start position:0%
+garbage but fortunately there are
+parsers that can turn it into JSON and
+
+ align:start position:0%
+parsers that can turn it into JSON and
+ 
+
+ align:start position:0%
+parsers that can turn it into JSON and
+simpler representations and so that
+
+ align:start position:0%
+simpler representations and so that
+ 
+
+ align:start position:0%
+simpler representations and so that
+that's pretty common so the
+
+ align:start position:0%
+that's pretty common so the
+ 
+
+ align:start position:0%
+that's pretty common so the
+terminologies that exist or loin and NDC
+
+ align:start position:0%
+terminologies that exist or loin and NDC
+ 
+
+ align:start position:0%
+terminologies that exist or loin and NDC
+ICD 9 and 10 sno-med I didn't talk about
+
+ align:start position:0%
+ICD 9 and 10 sno-med I didn't talk about
+ 
+
+ align:start position:0%
+ICD 9 and 10 sno-med I didn't talk about
+today dsm-5 is the Diagnostic and
+
+ align:start position:0%
+today dsm-5 is the Diagnostic and
+ 
+
+ align:start position:0%
+today dsm-5 is the Diagnostic and
+Statistical Manual for psychiatrists
+
+ align:start position:0%
+Statistical Manual for psychiatrists
+ 
+
+ align:start position:0%
+Statistical Manual for psychiatrists
+that's used as a common coding method
+
+ align:start position:0%
+that's used as a common coding method
+ 
+
+ align:start position:0%
+that's used as a common coding method
+for psyche describing psychiatric
+
+ align:start position:0%
+for psyche describing psychiatric
+ 
+
+ align:start position:0%
+for psyche describing psychiatric
+disease and there are many more of these
+
+ align:start position:0%
+disease and there are many more of these
+ 
+
+ align:start position:0%
+disease and there are many more of these
+there's something called the unified
+
+ align:start position:0%
+there's something called the unified
+ 
+
+ align:start position:0%
+there's something called the unified
+medical language systems metaphor Saurus
+
+ align:start position:0%
+medical language systems metaphor Saurus
+ 
+
+ align:start position:0%
+medical language systems metaphor Saurus
+from the National Library of Medicine
+
+ align:start position:0%
+from the National Library of Medicine
+ 
+
+ align:start position:0%
+from the National Library of Medicine
+that integrates about a hundred and
+
+ align:start position:0%
+that integrates about a hundred and
+ 
+
+ align:start position:0%
+that integrates about a hundred and
+eighty of these different terminologies
+
+ align:start position:0%
+eighty of these different terminologies
+ 
+
+ align:start position:0%
+eighty of these different terminologies
+and so there is a nice once one-stop
+
+ align:start position:0%
+and so there is a nice once one-stop
+ 
+
+ align:start position:0%
+and so there is a nice once one-stop
+shop where you can get all these things
+
+ align:start position:0%
+shop where you can get all these things
+ 
+
+ align:start position:0%
+shop where you can get all these things
+from them
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so takeaway lessons know your data
+
+ align:start position:0%
+so takeaway lessons know your data
+ 
+
+ align:start position:0%
+so takeaway lessons know your data
+remember that first example of the heart
+
+ align:start position:0%
+remember that first example of the heart
+ 
+
+ align:start position:0%
+remember that first example of the heart
+rates that comes up over and over again
+
+ align:start position:0%
+rates that comes up over and over again
+ 
+
+ align:start position:0%
+rates that comes up over and over again
+and doing machine learning and analysis
+
+ align:start position:0%
+and doing machine learning and analysis
+ 
+
+ align:start position:0%
+and doing machine learning and analysis
+on data that you don't understand is
+
+ align:start position:0%
+on data that you don't understand is
+ 
+
+ align:start position:0%
+on data that you don't understand is
+likely to lead you to false conclusions
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+harmonization is difficult and
+
+ align:start position:0%
+harmonization is difficult and
+ 
+
+ align:start position:0%
+harmonization is difficult and
+time-consuming and there are lots of
+
+ align:start position:0%
+time-consuming and there are lots of
+ 
+
+ align:start position:0%
+time-consuming and there are lots of
+things for which we just don't have
+
+ align:start position:0%
+things for which we just don't have
+ 
+
+ align:start position:0%
+things for which we just don't have
+standards and so everybody develops
+
+ align:start position:0%
+standards and so everybody develops
+ 
+
+ align:start position:0%
+standards and so everybody develops
+their own representations I had a PhD
+
+ align:start position:0%
+their own representations I had a PhD
+ 
+
+ align:start position:0%
+their own representations I had a PhD
+student about a decade ago who in his
+
+ align:start position:0%
+student about a decade ago who in his
+ 
+
+ align:start position:0%
+student about a decade ago who in his
+thesis wrote that he spent about half
+
+ align:start position:0%
+thesis wrote that he spent about half
+ 
+
+ align:start position:0%
+thesis wrote that he spent about half
+his time cleaning data and I gave that
+
+ align:start position:0%
+his time cleaning data and I gave that
+ 
+
+ align:start position:0%
+his time cleaning data and I gave that
+thesis to another student who started a
+
+ align:start position:0%
+thesis to another student who started a
+ 
+
+ align:start position:0%
+thesis to another student who started a
+few years later who read it and he comes
+
+ align:start position:0%
+few years later who read it and he comes
+ 
+
+ align:start position:0%
+few years later who read it and he comes
+to me with just awestruck and he says
+
+ align:start position:0%
+to me with just awestruck and he says
+ 
+
+ align:start position:0%
+to me with just awestruck and he says
+what he only spent half his time clean
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+unfortunately that's roughly where we
+
+ align:start position:0%
+unfortunately that's roughly where we
+ 
+
+ align:start position:0%
+unfortunately that's roughly where we
+are in this field so sorry to be a
+
+ align:start position:0%
+are in this field so sorry to be a
+ 
+
+ align:start position:0%
+are in this field so sorry to be a
+downer but that's that's the current
+
+ align:start position:0%
+downer but that's that's the current
+ 
+
+ align:start position:0%
+downer but that's that's the current
+state of the art and next time David
+
+ align:start position:0%
+state of the art and next time David
+ 
+
+ align:start position:0%
+state of the art and next time David
+will start by looking at actually
+
+ align:start position:0%
+will start by looking at actually
+ 
+
+ align:start position:0%
+will start by looking at actually
+building some models with these kinds of
+
+ align:start position:0%
+building some models with these kinds of
+ 
+
+ align:start position:0%
+building some models with these kinds of
+data and showing you what what we can
+
+ align:start position:0%
+data and showing you what what we can
+ 
+
+ align:start position:0%
+data and showing you what what we can
+accomplish all right thank you
+
+ align:start position:0%
+accomplish all right thank you
+ 
+
+ align:start position:0%
+accomplish all right thank you
+you
+
+ align:start position:0%
+you
+ 
+
+ align:start position:0%
+you
+[Applause]
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+you
\ No newline at end of file
diff --git a/16Vhe_1b974.txt b/16Vhe_1b974.txt
new file mode 100644
index 0000000000000000000000000000000000000000..3cb7a32fb49f9c84087cf9ee9a6cb2400ba13c25
--- /dev/null
+++ b/16Vhe_1b974.txt
@@ -0,0 +1,3635 @@
+align:start position:0%
+ 
+in this video we'll look at a beautiful
+
+ align:start position:0%
+in this video we'll look at a beautiful
+ 
+
+ align:start position:0%
+in this video we'll look at a beautiful
+result that provides us with the
+
+ align:start position:0%
+result that provides us with the
+ 
+
+ align:start position:0%
+result that provides us with the
+existence of graphs with high girth and
+
+ align:start position:0%
+existence of graphs with high girth and
+ 
+
+ align:start position:0%
+existence of graphs with high girth and
+high chromatic number and it's a very
+
+ align:start position:0%
+high chromatic number and it's a very
+ 
+
+ align:start position:0%
+high chromatic number and it's a very
+nice demonstration of the power of the
+
+ align:start position:0%
+nice demonstration of the power of the
+ 
+
+ align:start position:0%
+nice demonstration of the power of the
+probabilistic
+
+ align:start position:0%
+probabilistic
+ 
+
+ align:start position:0%
+probabilistic
+method we'll recall some definitions
+
+ align:start position:0%
+method we'll recall some definitions
+ 
+
+ align:start position:0%
+method we'll recall some definitions
+given a graph G its chromatic number is
+
+ align:start position:0%
+given a graph G its chromatic number is
+ 
+
+ align:start position:0%
+given a graph G its chromatic number is
+the minimum number of colors we need to
+
+ align:start position:0%
+the minimum number of colors we need to
+ 
+
+ align:start position:0%
+the minimum number of colors we need to
+color the vertices of the graph G so
+
+ align:start position:0%
+color the vertices of the graph G so
+ 
+
+ align:start position:0%
+color the vertices of the graph G so
+that no Edge has both end points
+
+ align:start position:0%
+that no Edge has both end points
+ 
+
+ align:start position:0%
+that no Edge has both end points
+receiving the same
+
+ align:start position:0%
+receiving the same
+ 
+
+ align:start position:0%
+receiving the same
+color the girth of a graph G is the
+
+ align:start position:0%
+color the girth of a graph G is the
+ 
+
+ align:start position:0%
+color the girth of a graph G is the
+length of the shortest cycle for example
+
+ align:start position:0%
+length of the shortest cycle for example
+ 
+
+ align:start position:0%
+length of the shortest cycle for example
+the following
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+graph has scur
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+four because the shortest cycle in this
+
+ align:start position:0%
+four because the shortest cycle in this
+ 
+
+ align:start position:0%
+four because the shortest cycle in this
+graph has length form and there are a
+
+ align:start position:0%
+graph has length form and there are a
+ 
+
+ align:start position:0%
+graph has length form and there are a
+couple of
+
+ align:start position:0%
+couple of
+ 
+
+ align:start position:0%
+couple of
+them another
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+example is this graph
+
+ align:start position:0%
+example is this graph
+ 
+
+ align:start position:0%
+example is this graph
+here there are many cycles but the
+
+ align:start position:0%
+here there are many cycles but the
+ 
+
+ align:start position:0%
+here there are many cycles but the
+shortest one has length three it is this
+
+ align:start position:0%
+shortest one has length three it is this
+ 
+
+ align:start position:0%
+shortest one has length three it is this
+triangle up here so the girth is
+
+ align:start position:0%
+triangle up here so the girth is
+ 
+
+ align:start position:0%
+triangle up here so the girth is
+three if the graph is a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+tree then he has no cycles in which case
+
+ align:start position:0%
+tree then he has no cycles in which case
+ 
+
+ align:start position:0%
+tree then he has no cycles in which case
+we say that its girth is infinite
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so what can we say about girth and
+
+ align:start position:0%
+okay so what can we say about girth and
+ 
+
+ align:start position:0%
+okay so what can we say about girth and
+chromatic number
+
+ align:start position:0%
+chromatic number
+ 
+
+ align:start position:0%
+chromatic number
+well suppose your graph contains a
+
+ align:start position:0%
+well suppose your graph contains a
+ 
+
+ align:start position:0%
+well suppose your graph contains a
+click on K
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+vertices then just to color this click
+
+ align:start position:0%
+vertices then just to color this click
+ 
+
+ align:start position:0%
+vertices then just to color this click
+we need at least K different colors so
+
+ align:start position:0%
+we need at least K different colors so
+ 
+
+ align:start position:0%
+we need at least K different colors so
+then the chromatic number
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+is at least
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+K can we say something in the reverse
+
+ align:start position:0%
+K can we say something in the reverse
+ 
+
+ align:start position:0%
+K can we say something in the reverse
+Direction suppose we have a graph with
+
+ align:start position:0%
+Direction suppose we have a graph with
+ 
+
+ align:start position:0%
+Direction suppose we have a graph with
+high chromatic
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+number would it be possible to deduce
+
+ align:start position:0%
+number would it be possible to deduce
+ 
+
+ align:start position:0%
+number would it be possible to deduce
+some local information
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+about the graph for example would it be
+
+ align:start position:0%
+about the graph for example would it be
+ 
+
+ align:start position:0%
+about the graph for example would it be
+possible to say that if we have very
+
+ align:start position:0%
+possible to say that if we have very
+ 
+
+ align:start position:0%
+possible to say that if we have very
+high chromatic number then there must be
+
+ align:start position:0%
+high chromatic number then there must be
+ 
+
+ align:start position:0%
+high chromatic number then there must be
+a triangle somewhere in the graph or
+
+ align:start position:0%
+a triangle somewhere in the graph or
+ 
+
+ align:start position:0%
+a triangle somewhere in the graph or
+there's some fairly dense structure
+
+ align:start position:0%
+there's some fairly dense structure
+ 
+
+ align:start position:0%
+there's some fairly dense structure
+that's very local in this
+
+ align:start position:0%
+that's very local in this
+ 
+
+ align:start position:0%
+that's very local in this
+graph so the main theorem that we'll
+
+ align:start position:0%
+graph so the main theorem that we'll
+ 
+
+ align:start position:0%
+graph so the main theorem that we'll
+present in this video gives a definitive
+
+ align:start position:0%
+present in this video gives a definitive
+ 
+
+ align:start position:0%
+present in this video gives a definitive
+no to this question
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and it is a classic result due to Paul
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+erish from the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+50s and the statement of theorem is the
+
+ align:start position:0%
+50s and the statement of theorem is the
+ 
+
+ align:start position:0%
+50s and the statement of theorem is the
+following for
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+any positive integers K and
+
+ align:start position:0%
+any positive integers K and
+ 
+
+ align:start position:0%
+any positive integers K and
+L there exists
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+graph there exists a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+graph with
+
+ align:start position:0%
+graph with
+ 
+
+ align:start position:0%
+graph with
+girth
+
+ align:start position:0%
+girth
+ 
+
+ align:start position:0%
+girth
+L girth bigger than L and chromatic
+
+ align:start position:0%
+L girth bigger than L and chromatic
+ 
+
+ align:start position:0%
+L girth bigger than L and chromatic
+number
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+bigger than
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+K okay so let's pause for a moment and
+
+ align:start position:0%
+K okay so let's pause for a moment and
+ 
+
+ align:start position:0%
+K okay so let's pause for a moment and
+think about what this theorem is saying
+
+ align:start position:0%
+think about what this theorem is saying
+ 
+
+ align:start position:0%
+think about what this theorem is saying
+so given any K&L no matter how large we
+
+ align:start position:0%
+so given any K&L no matter how large we
+ 
+
+ align:start position:0%
+so given any K&L no matter how large we
+can find a graph there exists a graph
+
+ align:start position:0%
+can find a graph there exists a graph
+ 
+
+ align:start position:0%
+can find a graph there exists a graph
+for which there are no short Cycles no
+
+ align:start position:0%
+for which there are no short Cycles no
+ 
+
+ align:start position:0%
+for which there are no short Cycles no
+cycles of length and most L and
+
+ align:start position:0%
+cycles of length and most L and
+ 
+
+ align:start position:0%
+cycles of length and most L and
+furthermore to properly color the
+
+ align:start position:0%
+furthermore to properly color the
+ 
+
+ align:start position:0%
+furthermore to properly color the
+vertices of the graph you need at least
+
+ align:start position:0%
+vertices of the graph you need at least
+ 
+
+ align:start position:0%
+vertices of the graph you need at least
+you need strictly more than K colors
+
+ align:start position:0%
+you need strictly more than K colors
+ 
+
+ align:start position:0%
+you need strictly more than K colors
+so even though this graph has very high
+
+ align:start position:0%
+so even though this graph has very high
+ 
+
+ align:start position:0%
+so even though this graph has very high
+chromatic number around every vertex if
+
+ align:start position:0%
+chromatic number around every vertex if
+ 
+
+ align:start position:0%
+chromatic number around every vertex if
+you only look not too far away then the
+
+ align:start position:0%
+you only look not too far away then the
+ 
+
+ align:start position:0%
+you only look not too far away then the
+graph locally looks like a tree because
+
+ align:start position:0%
+graph locally looks like a tree because
+ 
+
+ align:start position:0%
+graph locally looks like a tree because
+there are no short
+
+ align:start position:0%
+there are no short
+ 
+
+ align:start position:0%
+there are no short
+Cycles so in particular having high
+
+ align:start position:0%
+Cycles so in particular having high
+ 
+
+ align:start position:0%
+Cycles so in particular having high
+chromatic number does not give you local
+
+ align:start position:0%
+chromatic number does not give you local
+ 
+
+ align:start position:0%
+chromatic number does not give you local
+information and eror shows that there
+
+ align:start position:0%
+information and eror shows that there
+ 
+
+ align:start position:0%
+information and eror shows that there
+always
+
+ align:start position:0%
+always
+ 
+
+ align:start position:0%
+always
+exists counter examples to such a
+
+ align:start position:0%
+exists counter examples to such a
+ 
+
+ align:start position:0%
+exists counter examples to such a
+statement if we want some local
+
+ align:start position:0%
+statement if we want some local
+ 
+
+ align:start position:0%
+statement if we want some local
+information from High chromatic
+
+ align:start position:0%
+information from High chromatic
+ 
+
+ align:start position:0%
+information from High chromatic
+number okay so the rest of this video
+
+ align:start position:0%
+number okay so the rest of this video
+ 
+
+ align:start position:0%
+number okay so the rest of this video
+will concern the proof of ERS
+
+ align:start position:0%
+will concern the proof of ERS
+ 
+
+ align:start position:0%
+will concern the proof of ERS
+theorem it's quite a miraculous result
+
+ align:start position:0%
+theorem it's quite a miraculous result
+ 
+
+ align:start position:0%
+theorem it's quite a miraculous result
+and certainly before ERS proved this
+
+ align:start position:0%
+and certainly before ERS proved this
+ 
+
+ align:start position:0%
+and certainly before ERS proved this
+result there were other resulting graph
+
+ align:start position:0%
+result there were other resulting graph
+ 
+
+ align:start position:0%
+result there were other resulting graph
+theory that constructed very explicit
+
+ align:start position:0%
+theory that constructed very explicit
+ 
+
+ align:start position:0%
+theory that constructed very explicit
+graphs that have some large chromatic
+
+ align:start position:0%
+graphs that have some large chromatic
+ 
+
+ align:start position:0%
+graphs that have some large chromatic
+number and girth but not for all values
+
+ align:start position:0%
+number and girth but not for all values
+ 
+
+ align:start position:0%
+number and girth but not for all values
+of K and those constructions are in some
+
+ align:start position:0%
+of K and those constructions are in some
+ 
+
+ align:start position:0%
+of K and those constructions are in some
+sense very Hands-On it tells you how
+
+ align:start position:0%
+sense very Hands-On it tells you how
+ 
+
+ align:start position:0%
+sense very Hands-On it tells you how
+exactly how to construct these graphs
+
+ align:start position:0%
+exactly how to construct these graphs
+ 
+
+ align:start position:0%
+exactly how to construct these graphs
+but they were not able to get
+
+ align:start position:0%
+but they were not able to get
+ 
+
+ align:start position:0%
+but they were not able to get
+arbitrarily large girth and chromatic
+
+ align:start position:0%
+arbitrarily large girth and chromatic
+ 
+
+ align:start position:0%
+arbitrarily large girth and chromatic
+number A's Insight is to use Randomness
+
+ align:start position:0%
+number A's Insight is to use Randomness
+ 
+
+ align:start position:0%
+number A's Insight is to use Randomness
+use the probabilistic method and show
+
+ align:start position:0%
+use the probabilistic method and show
+ 
+
+ align:start position:0%
+use the probabilistic method and show
+that by appropriately modifying a random
+
+ align:start position:0%
+that by appropriately modifying a random
+ 
+
+ align:start position:0%
+that by appropriately modifying a random
+graph one can achieve the desired
+
+ align:start position:0%
+graph one can achieve the desired
+ 
+
+ align:start position:0%
+graph one can achieve the desired
+outcome so let's see how this works
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+we'll Begin by taking an random graph
+
+ align:start position:0%
+we'll Begin by taking an random graph
+ 
+
+ align:start position:0%
+we'll Begin by taking an random graph
+GNP so this is the a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+r random
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+graph
+
+ align:start position:0%
+graph
+ 
+
+ align:start position:0%
+graph
+and there nend vertices
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and um The Edge probability is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+p meaning that we flip a probability P
+
+ align:start position:0%
+p meaning that we flip a probability P
+ 
+
+ align:start position:0%
+p meaning that we flip a probability P
+coin for each possible Edge and put down
+
+ align:start position:0%
+coin for each possible Edge and put down
+ 
+
+ align:start position:0%
+coin for each possible Edge and put down
+an edge
+
+ align:start position:0%
+an edge
+ 
+
+ align:start position:0%
+an edge
+independently with probability P between
+
+ align:start position:0%
+independently with probability P between
+ 
+
+ align:start position:0%
+independently with probability P between
+every pair of
+
+ align:start position:0%
+every pair of
+ 
+
+ align:start position:0%
+every pair of
+vertices
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+right so let G be drawn from this
+
+ align:start position:0%
+right so let G be drawn from this
+ 
+
+ align:start position:0%
+right so let G be drawn from this
+distribution so G is this random
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+graph now
+
+ align:start position:0%
+graph now
+ 
+
+ align:start position:0%
+graph now
+let's take a specific choice of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+P being log n^ s Over N turns out other
+
+ align:start position:0%
+P being log n^ s Over N turns out other
+ 
+
+ align:start position:0%
+P being log n^ s Over N turns out other
+choices of P work as long as P Falls in
+
+ align:start position:0%
+choices of P work as long as P Falls in
+ 
+
+ align:start position:0%
+choices of P work as long as P Falls in
+some range but for concreteness we'll
+
+ align:start position:0%
+some range but for concreteness we'll
+ 
+
+ align:start position:0%
+some range but for concreteness we'll
+take this very specific choice of P so
+
+ align:start position:0%
+take this very specific choice of P so
+ 
+
+ align:start position:0%
+take this very specific choice of P so
+this is a random graph and let's
+
+ align:start position:0%
+this is a random graph and let's
+ 
+
+ align:start position:0%
+this is a random graph and let's
+construct the random variable
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+X defined to be the number of
+
+ align:start position:0%
+X defined to be the number of
+ 
+
+ align:start position:0%
+X defined to be the number of
+cycles of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+length at most
+
+ align:start position:0%
+length at most
+ 
+
+ align:start position:0%
+length at most
+l in G okay so these are short Cycles in
+
+ align:start position:0%
+l in G okay so these are short Cycles in
+ 
+
+ align:start position:0%
+l in G okay so these are short Cycles in
+G and these are the cycles that we want
+
+ align:start position:0%
+G and these are the cycles that we want
+ 
+
+ align:start position:0%
+G and these are the cycles that we want
+to avoid because we want to construct a
+
+ align:start position:0%
+to avoid because we want to construct a
+ 
+
+ align:start position:0%
+to avoid because we want to construct a
+graph with girth strictly larger than l
+
+ align:start position:0%
+graph with girth strictly larger than l
+ 
+
+ align:start position:0%
+graph with girth strictly larger than l
+so we really do not like these
+
+ align:start position:0%
+so we really do not like these
+ 
+
+ align:start position:0%
+so we really do not like these
+Cycles it will be nice if there were not
+
+ align:start position:0%
+Cycles it will be nice if there were not
+ 
+
+ align:start position:0%
+Cycles it will be nice if there were not
+too many such Cycles so let's compute
+
+ align:start position:0%
+too many such Cycles so let's compute
+ 
+
+ align:start position:0%
+too many such Cycles so let's compute
+the expected value of
+
+ align:start position:0%
+the expected value of
+ 
+
+ align:start position:0%
+the expected value of
+x for this computation we use linearity
+
+ align:start position:0%
+x for this computation we use linearity
+ 
+
+ align:start position:0%
+x for this computation we use linearity
+of
+
+ align:start position:0%
+of
+ 
+
+ align:start position:0%
+of
+expectations and look over all possible
+
+ align:start position:0%
+expectations and look over all possible
+ 
+
+ align:start position:0%
+expectations and look over all possible
+cycle lengths from 3 to
+
+ align:start position:0%
+cycle lengths from 3 to
+ 
+
+ align:start position:0%
+cycle lengths from 3 to
+L right so I is the target cycle length
+
+ align:start position:0%
+L right so I is the target cycle length
+ 
+
+ align:start position:0%
+L right so I is the target cycle length
+and for cycles of length
+
+ align:start position:0%
+and for cycles of length
+ 
+
+ align:start position:0%
+and for cycles of length
+I there are n choose I different choices
+
+ align:start position:0%
+I there are n choose I different choices
+ 
+
+ align:start position:0%
+I there are n choose I different choices
+of
+
+ align:start position:0%
+of
+ 
+
+ align:start position:0%
+of
+which I vertices the Cycles can
+
+ align:start position:0%
+which I vertices the Cycles can
+ 
+
+ align:start position:0%
+which I vertices the Cycles can
+involve and once you specify those
+
+ align:start position:0%
+involve and once you specify those
+ 
+
+ align:start position:0%
+involve and once you specify those
+vertices there are IUS one factorial
+
+ align:start position:0%
+vertices there are IUS one factorial
+ 
+
+ align:start position:0%
+vertices there are IUS one factorial
+different permutations circular
+
+ align:start position:0%
+different permutations circular
+ 
+
+ align:start position:0%
+different permutations circular
+permutations of these vertices and we
+
+ align:start position:0%
+permutations of these vertices and we
+ 
+
+ align:start position:0%
+permutations of these vertices and we
+divide it by two
+
+ align:start position:0%
+divide it by two
+ 
+
+ align:start position:0%
+divide it by two
+because a cycle could be counted in two
+
+ align:start position:0%
+because a cycle could be counted in two
+ 
+
+ align:start position:0%
+because a cycle could be counted in two
+different directions and they will
+
+ align:start position:0%
+different directions and they will
+ 
+
+ align:start position:0%
+different directions and they will
+correspond to the same
+
+ align:start position:0%
+correspond to the same
+ 
+
+ align:start position:0%
+correspond to the same
+cycle so
+
+ align:start position:0%
+cycle so
+ 
+
+ align:start position:0%
+cycle so
+so this quantity here is the number of
+
+ align:start position:0%
+so this quantity here is the number of
+ 
+
+ align:start position:0%
+so this quantity here is the number of
+cycles of
+
+ align:start position:0%
+cycles of
+ 
+
+ align:start position:0%
+cycles of
+length I in the complete graph on N
+
+ align:start position:0%
+length I in the complete graph on N
+ 
+
+ align:start position:0%
+length I in the complete graph on N
+vertices with all edges
+
+ align:start position:0%
+vertices with all edges
+ 
+
+ align:start position:0%
+vertices with all edges
+present for each such possible cycle the
+
+ align:start position:0%
+present for each such possible cycle the
+ 
+
+ align:start position:0%
+present for each such possible cycle the
+probability that the cycle appears in G
+
+ align:start position:0%
+probability that the cycle appears in G
+ 
+
+ align:start position:0%
+probability that the cycle appears in G
+is p to the I so the second term
+
+ align:start position:0%
+is p to the I so the second term
+ 
+
+ align:start position:0%
+is p to the I so the second term
+here is probability
+
+ align:start position:0%
+here is probability
+ 
+
+ align:start position:0%
+here is probability
+that
+
+ align:start position:0%
+that
+ 
+
+ align:start position:0%
+that
+this
+
+ align:start position:0%
+this
+ 
+
+ align:start position:0%
+this
+cycle
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+appears in
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+GMP okay this is some expression it's a
+
+ align:start position:0%
+GMP okay this is some expression it's a
+ 
+
+ align:start position:0%
+GMP okay this is some expression it's a
+little complicated but we can simplify
+
+ align:start position:0%
+little complicated but we can simplify
+ 
+
+ align:start position:0%
+little complicated but we can simplify
+it and do some approximations to Upper
+
+ align:start position:0%
+it and do some approximations to Upper
+ 
+
+ align:start position:0%
+it and do some approximations to Upper
+bound this
+
+ align:start position:0%
+bound this
+ 
+
+ align:start position:0%
+bound this
+quantity so you see that the
+
+ align:start position:0%
+quantity so you see that the
+ 
+
+ align:start position:0%
+quantity so you see that the
+um n choose I if you expand it in terms
+
+ align:start position:0%
+um n choose I if you expand it in terms
+ 
+
+ align:start position:0%
+um n choose I if you expand it in terms
+of
+
+ align:start position:0%
+of
+ 
+
+ align:start position:0%
+of
+factorials one can upper bound this
+
+ align:start position:0%
+factorials one can upper bound this
+ 
+
+ align:start position:0%
+factorials one can upper bound this
+quantity by n to the I so incorporating
+
+ align:start position:0%
+quantity by n to the I so incorporating
+ 
+
+ align:start position:0%
+quantity by n to the I so incorporating
+the um the first two
+
+ align:start position:0%
+the um the first two
+ 
+
+ align:start position:0%
+the um the first two
+factors and then leaving P to the I
+
+ align:start position:0%
+factors and then leaving P to the I
+ 
+
+ align:start position:0%
+factors and then leaving P to the I
+factor
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+intact
+
+ align:start position:0%
+intact
+ 
+
+ align:start position:0%
+intact
+okay we chose P so that P * n equals to
+
+ align:start position:0%
+okay we chose P so that P * n equals to
+ 
+
+ align:start position:0%
+okay we chose P so that P * n equals to
+log s of M and
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so we can rewrite this quantity
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+here like
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this okay uh there are L terms here so
+
+ align:start position:0%
+this okay uh there are L terms here so
+ 
+
+ align:start position:0%
+this okay uh there are L terms here so
+let
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+me furthermore upper bound this
+
+ align:start position:0%
+me furthermore upper bound this
+ 
+
+ align:start position:0%
+me furthermore upper bound this
+expression by L Times log n to
+
+ align:start position:0%
+expression by L Times log n to
+ 
+
+ align:start position:0%
+expression by L Times log n to
+the 2 L here L is a constant so this
+
+ align:start position:0%
+the 2 L here L is a constant so this
+ 
+
+ align:start position:0%
+the 2 L here L is a constant so this
+quantity here is some growth and the
+
+ align:start position:0%
+quantity here is some growth and the
+ 
+
+ align:start position:0%
+quantity here is some growth and the
+rate of some power of a log and
+
+ align:start position:0%
+rate of some power of a log and
+ 
+
+ align:start position:0%
+rate of some power of a log and
+certainly
+
+ align:start position:0%
+certainly
+ 
+
+ align:start position:0%
+certainly
+much slower growing compared to the
+
+ align:start position:0%
+much slower growing compared to the
+ 
+
+ align:start position:0%
+much slower growing compared to the
+function n so it's little o of n okay
+
+ align:start position:0%
+function n so it's little o of n okay
+ 
+
+ align:start position:0%
+function n so it's little o of n okay
+it's a fairly crude approximation but
+
+ align:start position:0%
+it's a fairly crude approximation but
+ 
+
+ align:start position:0%
+it's a fairly crude approximation but
+will be sufficient for our
+
+ align:start position:0%
+will be sufficient for our
+ 
+
+ align:start position:0%
+will be sufficient for our
+purposes so this is a calculation
+
+ align:start position:0%
+purposes so this is a calculation
+ 
+
+ align:start position:0%
+purposes so this is a calculation
+conclusion can be read as the expected
+
+ align:start position:0%
+conclusion can be read as the expected
+ 
+
+ align:start position:0%
+conclusion can be read as the expected
+number of short Cycles is fairly
+
+ align:start position:0%
+number of short Cycles is fairly
+ 
+
+ align:start position:0%
+number of short Cycles is fairly
+small well if there are few short Cycles
+
+ align:start position:0%
+small well if there are few short Cycles
+ 
+
+ align:start position:0%
+small well if there are few short Cycles
+we
+
+ align:start position:0%
+we
+ 
+
+ align:start position:0%
+we
+can get rid of all of them to get a
+
+ align:start position:0%
+can get rid of all of them to get a
+ 
+
+ align:start position:0%
+can get rid of all of them to get a
+graph without short Cycles so this is
+
+ align:start position:0%
+graph without short Cycles so this is
+ 
+
+ align:start position:0%
+graph without short Cycles so this is
+the basic idea of the alteration method
+
+ align:start position:0%
+the basic idea of the alteration method
+ 
+
+ align:start position:0%
+the basic idea of the alteration method
+in the probabilistic method okay so
+
+ align:start position:0%
+in the probabilistic method okay so
+ 
+
+ align:start position:0%
+in the probabilistic method okay so
+start with this GMP this random
+
+ align:start position:0%
+start with this GMP this random
+ 
+
+ align:start position:0%
+start with this GMP this random
+graph it's not going to get us what we
+
+ align:start position:0%
+graph it's not going to get us what we
+ 
+
+ align:start position:0%
+graph it's not going to get us what we
+want right away but we're going to do
+
+ align:start position:0%
+want right away but we're going to do
+ 
+
+ align:start position:0%
+want right away but we're going to do
+something to fix the defects in this
+
+ align:start position:0%
+something to fix the defects in this
+ 
+
+ align:start position:0%
+something to fix the defects in this
+graph in this case get rid of short
+
+ align:start position:0%
+graph in this case get rid of short
+ 
+
+ align:start position:0%
+graph in this case get rid of short
+Cycles to that end that is known that by
+
+ align:start position:0%
+Cycles to that end that is known that by
+ 
+
+ align:start position:0%
+Cycles to that end that is known that by
+markov's
+
+ align:start position:0%
+markov's
+ 
+
+ align:start position:0%
+markov's
+inequality the
+
+ align:start position:0%
+inequality the
+ 
+
+ align:start position:0%
+inequality the
+probability that the number of short
+
+ align:start position:0%
+probability that the number of short
+ 
+
+ align:start position:0%
+probability that the number of short
+Cycles here short means length and most
+
+ align:start position:0%
+Cycles here short means length and most
+ 
+
+ align:start position:0%
+Cycles here short means length and most
+L the probability that the number of of
+
+ align:start position:0%
+L the probability that the number of of
+ 
+
+ align:start position:0%
+L the probability that the number of of
+short Cycles X is at least n / two is
+
+ align:start position:0%
+short Cycles X is at least n / two is
+ 
+
+ align:start position:0%
+short Cycles X is at least n / two is
+upper bounded by the expectation of x
+
+ align:start position:0%
+upper bounded by the expectation of x
+ 
+
+ align:start position:0%
+upper bounded by the expectation of x
+divided by n /2
+
+ align:start position:0%
+divided by n /2
+ 
+
+ align:start position:0%
+divided by n /2
+and because expectation of X is little o
+
+ align:start position:0%
+and because expectation of X is little o
+ 
+
+ align:start position:0%
+and because expectation of X is little o
+of n this final quantity is little o of
+
+ align:start position:0%
+of n this final quantity is little o of
+ 
+
+ align:start position:0%
+of n this final quantity is little o of
+one is the case to zero as n goes to
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Infinity okay
+
+ align:start position:0%
+Infinity okay
+ 
+
+ align:start position:0%
+Infinity okay
+so this is a good sign right so means
+
+ align:start position:0%
+so this is a good sign right so means
+ 
+
+ align:start position:0%
+so this is a good sign right so means
+that typically the graph does not have
+
+ align:start position:0%
+that typically the graph does not have
+ 
+
+ align:start position:0%
+that typically the graph does not have
+very many short Cycles has fewer than n
+
+ align:start position:0%
+very many short Cycles has fewer than n
+ 
+
+ align:start position:0%
+very many short Cycles has fewer than n
+/ two and then eventually we'll be able
+
+ align:start position:0%
+/ two and then eventually we'll be able
+ 
+
+ align:start position:0%
+/ two and then eventually we'll be able
+to get rid of one Edge from each cycle
+
+ align:start position:0%
+to get rid of one Edge from each cycle
+ 
+
+ align:start position:0%
+to get rid of one Edge from each cycle
+to get us a graph with still fairly
+
+ align:start position:0%
+to get us a graph with still fairly
+ 
+
+ align:start position:0%
+to get us a graph with still fairly
+large number of vertices but there are
+
+ align:start position:0%
+large number of vertices but there are
+ 
+
+ align:start position:0%
+large number of vertices but there are
+no short Cycles left in this after the
+
+ align:start position:0%
+no short Cycles left in this after the
+ 
+
+ align:start position:0%
+no short Cycles left in this after the
+alteration now let's think about
+
+ align:start position:0%
+alteration now let's think about
+ 
+
+ align:start position:0%
+alteration now let's think about
+chromatic number so we want to ensure
+
+ align:start position:0%
+chromatic number so we want to ensure
+ 
+
+ align:start position:0%
+chromatic number so we want to ensure
+that the graph that we end up having has
+
+ align:start position:0%
+that the graph that we end up having has
+ 
+
+ align:start position:0%
+that the graph that we end up having has
+high chromatic
+
+ align:start position:0%
+high chromatic
+ 
+
+ align:start position:0%
+high chromatic
+number to that
+
+ align:start position:0%
+number to that
+ 
+
+ align:start position:0%
+number to that
+end we'll recall the following
+
+ align:start position:0%
+end we'll recall the following
+ 
+
+ align:start position:0%
+end we'll recall the following
+fact if we give you a graph
+
+ align:start position:0%
+fact if we give you a graph
+ 
+
+ align:start position:0%
+fact if we give you a graph
+G then the chromatic number of G so this
+
+ align:start position:0%
+G then the chromatic number of G so this
+ 
+
+ align:start position:0%
+G then the chromatic number of G so this
+is Kai of G so that's the chromatic
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+number well the chromatic number is the
+
+ align:start position:0%
+number well the chromatic number is the
+ 
+
+ align:start position:0%
+number well the chromatic number is the
+minimum number of colors that one need
+
+ align:start position:0%
+minimum number of colors that one need
+ 
+
+ align:start position:0%
+minimum number of colors that one need
+to color the vertices of the graph so
+
+ align:start position:0%
+to color the vertices of the graph so
+ 
+
+ align:start position:0%
+to color the vertices of the graph so
+that no Edge has the same color on both
+
+ align:start position:0%
+that no Edge has the same color on both
+ 
+
+ align:start position:0%
+that no Edge has the same color on both
+sides in particular every color class
+
+ align:start position:0%
+sides in particular every color class
+ 
+
+ align:start position:0%
+sides in particular every color class
+right so if you look at a single color
+
+ align:start position:0%
+right so if you look at a single color
+ 
+
+ align:start position:0%
+right so if you look at a single color
+like red and look at the vertices
+
+ align:start position:0%
+like red and look at the vertices
+ 
+
+ align:start position:0%
+like red and look at the vertices
+colored by that
+
+ align:start position:0%
+colored by that
+ 
+
+ align:start position:0%
+colored by that
+color these vertices have no edges
+
+ align:start position:0%
+color these vertices have no edges
+ 
+
+ align:start position:0%
+color these vertices have no edges
+directly between them and so they form
+
+ align:start position:0%
+directly between them and so they form
+ 
+
+ align:start position:0%
+directly between them and so they form
+an independent set so each color class
+
+ align:start position:0%
+an independent set so each color class
+ 
+
+ align:start position:0%
+an independent set so each color class
+is an independent set and so the number
+
+ align:start position:0%
+is an independent set and so the number
+ 
+
+ align:start position:0%
+is an independent set and so the number
+of color classes you
+
+ align:start position:0%
+of color classes you
+ 
+
+ align:start position:0%
+of color classes you
+need then should be at least the number
+
+ align:start position:0%
+need then should be at least the number
+ 
+
+ align:start position:0%
+need then should be at least the number
+of vertices divided by the independence
+
+ align:start position:0%
+of vertices divided by the independence
+ 
+
+ align:start position:0%
+of vertices divided by the independence
+number this is the size of the largest
+
+ align:start position:0%
+number this is the size of the largest
+ 
+
+ align:start position:0%
+number this is the size of the largest
+independent set so this Alpha of the
+
+ align:start position:0%
+independent set so this Alpha of the
+ 
+
+ align:start position:0%
+independent set so this Alpha of the
+independence number is the
+
+ align:start position:0%
+independence number is the
+ 
+
+ align:start position:0%
+independence number is the
+size of the
+
+ align:start position:0%
+size of the
+ 
+
+ align:start position:0%
+size of the
+largest independent
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+set indeed each color class is
+
+ align:start position:0%
+set indeed each color class is
+ 
+
+ align:start position:0%
+set indeed each color class is
+independent set and each independent set
+
+ align:start position:0%
+independent set and each independent set
+ 
+
+ align:start position:0%
+independent set and each independent set
+has size at most Alpha of G and
+
+ align:start position:0%
+has size at most Alpha of G and
+ 
+
+ align:start position:0%
+has size at most Alpha of G and
+therefore the number of colors you need
+
+ align:start position:0%
+therefore the number of colors you need
+ 
+
+ align:start position:0%
+therefore the number of colors you need
+should be at least the number of
+
+ align:start position:0%
+should be at least the number of
+ 
+
+ align:start position:0%
+should be at least the number of
+vertices divided by the independence
+
+ align:start position:0%
+vertices divided by the independence
+ 
+
+ align:start position:0%
+vertices divided by the independence
+number
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay now for
+
+ align:start position:0%
+okay now for
+ 
+
+ align:start position:0%
+okay now for
+every
+
+ align:start position:0%
+every
+ 
+
+ align:start position:0%
+every
+H the probability that the independence
+
+ align:start position:0%
+H the probability that the independence
+ 
+
+ align:start position:0%
+H the probability that the independence
+number so after here see that it makes
+
+ align:start position:0%
+number so after here see that it makes
+ 
+
+ align:start position:0%
+number so after here see that it makes
+sense to think about the independence
+
+ align:start position:0%
+sense to think about the independence
+ 
+
+ align:start position:0%
+sense to think about the independence
+number the probability that Independence
+
+ align:start position:0%
+number the probability that Independence
+ 
+
+ align:start position:0%
+number the probability that Independence
+number is bigger than
+
+ align:start position:0%
+number is bigger than
+ 
+
+ align:start position:0%
+number is bigger than
+H
+
+ align:start position:0%
+H
+ 
+
+ align:start position:0%
+H
+is and most the following so here we'll
+
+ align:start position:0%
+is and most the following so here we'll
+ 
+
+ align:start position:0%
+is and most the following so here we'll
+use Union
+
+ align:start position:0%
+use Union
+ 
+
+ align:start position:0%
+use Union
+sound for
+
+ align:start position:0%
+sound for
+ 
+
+ align:start position:0%
+sound for
+each H vertex subset of which there are
+
+ align:start position:0%
+each H vertex subset of which there are
+ 
+
+ align:start position:0%
+each H vertex subset of which there are
+n choose H such H vertex subsets the
+
+ align:start position:0%
+n choose H such H vertex subsets the
+ 
+
+ align:start position:0%
+n choose H such H vertex subsets the
+probability that those H vertices from
+
+ align:start position:0%
+probability that those H vertices from
+ 
+
+ align:start position:0%
+probability that those H vertices from
+an independent
+
+ align:start position:0%
+an independent
+ 
+
+ align:start position:0%
+an independent
+set is the probability that there are no
+
+ align:start position:0%
+set is the probability that there are no
+ 
+
+ align:start position:0%
+set is the probability that there are no
+edges appearing among these H vertices
+
+ align:start position:0%
+edges appearing among these H vertices
+ 
+
+ align:start position:0%
+edges appearing among these H vertices
+and that's 1 minus P raised to the power
+
+ align:start position:0%
+and that's 1 minus P raised to the power
+ 
+
+ align:start position:0%
+and that's 1 minus P raised to the power
+H choose
+
+ align:start position:0%
+H choose
+ 
+
+ align:start position:0%
+H choose
+two okay so this is some expression and
+
+ align:start position:0%
+two okay so this is some expression and
+ 
+
+ align:start position:0%
+two okay so this is some expression and
+we can do some manipulations to simplify
+
+ align:start position:0%
+we can do some manipulations to simplify
+ 
+
+ align:start position:0%
+we can do some manipulations to simplify
+this
+
+ align:start position:0%
+this
+ 
+
+ align:start position:0%
+this
+expression yielding an upper bound of n
+
+ align:start position:0%
+expression yielding an upper bound of n
+ 
+
+ align:start position:0%
+expression yielding an upper bound of n
+to the H times so the latter expression
+
+ align:start position:0%
+to the H times so the latter expression
+ 
+
+ align:start position:0%
+to the H times so the latter expression
+we can simplify it as so upper bounded
+
+ align:start position:0%
+we can simplify it as so upper bounded
+ 
+
+ align:start position:0%
+we can simplify it as so upper bounded
+by e to the minus
+
+ align:start position:0%
+by e to the minus
+ 
+
+ align:start position:0%
+by e to the minus
+p h h -1 / 2 right so 1 minus
+
+ align:start position:0%
+p h h -1 / 2 right so 1 minus
+ 
+
+ align:start position:0%
+p h h -1 / 2 right so 1 minus
+p
+
+ align:start position:0%
+p
+ 
+
+ align:start position:0%
+p
+is less than e to the minus p
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay simplifying further we see that
+
+ align:start position:0%
+okay simplifying further we see that
+ 
+
+ align:start position:0%
+okay simplifying further we see that
+this expression can be
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Rewritten this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+way and now let's make a choice for what
+
+ align:start position:0%
+way and now let's make a choice for what
+ 
+
+ align:start position:0%
+way and now let's make a choice for what
+H I want to set so let's set H to be the
+
+ align:start position:0%
+H I want to set so let's set H to be the
+ 
+
+ align:start position:0%
+H I want to set so let's set H to be the
+quantity which for now seems a little
+
+ align:start position:0%
+quantity which for now seems a little
+ 
+
+ align:start position:0%
+quantity which for now seems a little
+mysterious but it turns out to be a
+
+ align:start position:0%
+mysterious but it turns out to be a
+ 
+
+ align:start position:0%
+mysterious but it turns out to be a
+natural thing to set after we see what
+
+ align:start position:0%
+natural thing to set after we see what
+ 
+
+ align:start position:0%
+natural thing to set after we see what
+the calculation looks like so we set H
+
+ align:start position:0%
+the calculation looks like so we set H
+ 
+
+ align:start position:0%
+the calculation looks like so we set H
+to be this quantity three * log n over p
+
+ align:start position:0%
+to be this quantity three * log n over p
+ 
+
+ align:start position:0%
+to be this quantity three * log n over p
+and knowing what P was from earlier uh
+
+ align:start position:0%
+and knowing what P was from earlier uh
+ 
+
+ align:start position:0%
+and knowing what P was from earlier uh
+this quantity is 3 n
+
+ align:start position:0%
+this quantity is 3 n
+ 
+
+ align:start position:0%
+this quantity is 3 n
+over log
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+n if we set H to be this quantity here
+
+ align:start position:0%
+n if we set H to be this quantity here
+ 
+
+ align:start position:0%
+n if we set H to be this quantity here
+then you see that here in this
+
+ align:start position:0%
+then you see that here in this
+ 
+
+ align:start position:0%
+then you see that here in this
+expression the numerator here um can be
+
+ align:start position:0%
+expression the numerator here um can be
+ 
+
+ align:start position:0%
+expression the numerator here um can be
+simplified and the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+result is that this expression de
+
+ align:start position:0%
+result is that this expression de
+ 
+
+ align:start position:0%
+result is that this expression de
+case According to some rate which is n
+
+ align:start position:0%
+case According to some rate which is n
+ 
+
+ align:start position:0%
+case According to some rate which is n
+to something that is a minus
+
+ align:start position:0%
+to something that is a minus
+ 
+
+ align:start position:0%
+to something that is a minus
+constant something on a constant word in
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+particular it goes to zero as n goes to
+
+ align:start position:0%
+particular it goes to zero as n goes to
+ 
+
+ align:start position:0%
+particular it goes to zero as n goes to
+infinity and that's really the only
+
+ align:start position:0%
+infinity and that's really the only
+ 
+
+ align:start position:0%
+infinity and that's really the only
+thing that we need for uh that we need
+
+ align:start position:0%
+thing that we need for uh that we need
+ 
+
+ align:start position:0%
+thing that we need for uh that we need
+out of this
+
+ align:start position:0%
+out of this
+ 
+
+ align:start position:0%
+out of this
+calculation so if we set H to be of an
+
+ align:start position:0%
+calculation so if we set H to be of an
+ 
+
+ align:start position:0%
+calculation so if we set H to be of an
+appropriate quantity then typically one
+
+ align:start position:0%
+appropriate quantity then typically one
+ 
+
+ align:start position:0%
+appropriate quantity then typically one
+does not have independent sets of size
+
+ align:start position:0%
+does not have independent sets of size
+ 
+
+ align:start position:0%
+does not have independent sets of size
+at least H in the
+
+ align:start position:0%
+at least H in the
+ 
+
+ align:start position:0%
+at least H in the
+graph
+
+ align:start position:0%
+graph
+ 
+
+ align:start position:0%
+graph
+okay so let's regroup so we proved a
+
+ align:start position:0%
+okay so let's regroup so we proved a
+ 
+
+ align:start position:0%
+okay so let's regroup so we proved a
+couple of
+
+ align:start position:0%
+couple of
+ 
+
+ align:start position:0%
+couple of
+things first we show that typically so
+
+ align:start position:0%
+things first we show that typically so
+ 
+
+ align:start position:0%
+things first we show that typically so
+when I say typically I mean with
+
+ align:start position:0%
+when I say typically I mean with
+ 
+
+ align:start position:0%
+when I say typically I mean with
+probability approaching one as Ang goes
+
+ align:start position:0%
+probability approaching one as Ang goes
+ 
+
+ align:start position:0%
+probability approaching one as Ang goes
+to Infinity so typically this graph does
+
+ align:start position:0%
+to Infinity so typically this graph does
+ 
+
+ align:start position:0%
+to Infinity so typically this graph does
+not
+
+ align:start position:0%
+not
+ 
+
+ align:start position:0%
+not
+have short Cycles meaning cycles of
+
+ align:start position:0%
+have short Cycles meaning cycles of
+ 
+
+ align:start position:0%
+have short Cycles meaning cycles of
+length and most L and also typically
+
+ align:start position:0%
+length and most L and also typically
+ 
+
+ align:start position:0%
+length and most L and also typically
+this graph does not have large
+
+ align:start position:0%
+this graph does not have large
+ 
+
+ align:start position:0%
+this graph does not have large
+independent
+
+ align:start position:0%
+independent
+ 
+
+ align:start position:0%
+independent
+sets okay now let us put everything
+
+ align:start position:0%
+sets okay now let us put everything
+ 
+
+ align:start position:0%
+sets okay now let us put everything
+together
+
+ align:start position:0%
+together
+ 
+
+ align:start position:0%
+together
+so by
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+choosing and sufficiently large
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+we can
+
+ align:start position:0%
+we can
+ 
+
+ align:start position:0%
+we can
+simultaneously ensure that the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+probability that X the number of short
+
+ align:start position:0%
+probability that X the number of short
+ 
+
+ align:start position:0%
+probability that X the number of short
+Cycles exceeds n /2 is strictly less
+
+ align:start position:0%
+Cycles exceeds n /2 is strictly less
+ 
+
+ align:start position:0%
+Cycles exceeds n /2 is strictly less
+than
+
+ align:start position:0%
+than
+ 
+
+ align:start position:0%
+than
+half and the probability that the
+
+ align:start position:0%
+half and the probability that the
+ 
+
+ align:start position:0%
+half and the probability that the
+independence number
+
+ align:start position:0%
+independence number
+ 
+
+ align:start position:0%
+independence number
+exceeds H is also strictly less than
+
+ align:start position:0%
+exceeds H is also strictly less than
+ 
+
+ align:start position:0%
+exceeds H is also strictly less than
+half okay so both of these are quantity
+
+ align:start position:0%
+half okay so both of these are quantity
+ 
+
+ align:start position:0%
+half okay so both of these are quantity
+quantities that decay to zero as n goes
+
+ align:start position:0%
+quantities that decay to zero as n goes
+ 
+
+ align:start position:0%
+quantities that decay to zero as n goes
+to Infinity so by choosing sufficiently
+
+ align:start position:0%
+to Infinity so by choosing sufficiently
+ 
+
+ align:start position:0%
+to Infinity so by choosing sufficiently
+r n we can make sure both probabilities
+
+ align:start position:0%
+r n we can make sure both probabilities
+ 
+
+ align:start position:0%
+r n we can make sure both probabilities
+are strictly less than 1/2 and therefore
+
+ align:start position:0%
+are strictly less than 1/2 and therefore
+ 
+
+ align:start position:0%
+are strictly less than 1/2 and therefore
+there is some possibility that lie
+
+ align:start position:0%
+there is some possibility that lie
+ 
+
+ align:start position:0%
+there is some possibility that lie
+outside both
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+events thus there
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+exists a graph
+
+ align:start position:0%
+exists a graph
+ 
+
+ align:start position:0%
+exists a graph
+G
+
+ align:start position:0%
+G
+ 
+
+ align:start position:0%
+G
+with
+
+ align:start position:0%
+with
+ 
+
+ align:start position:0%
+with
+fewer
+
+ align:start position:0%
+fewer
+ 
+
+ align:start position:0%
+fewer
+than n / two
+
+ align:start position:0%
+than n / two
+ 
+
+ align:start position:0%
+than n / two
+cycles of
+
+ align:start position:0%
+cycles of
+ 
+
+ align:start position:0%
+cycles of
+length at most
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+L
+
+ align:start position:0%
+L
+ 
+
+ align:start position:0%
+L
+and furthermore its independent number
+
+ align:start position:0%
+and furthermore its independent number
+ 
+
+ align:start position:0%
+and furthermore its independent number
+the size of the largest independent set
+
+ align:start position:0%
+the size of the largest independent set
+ 
+
+ align:start position:0%
+the size of the largest independent set
+is at
+
+ align:start position:0%
+is at
+ 
+
+ align:start position:0%
+is at
+most H which we said earlier to be 3n
+
+ align:start position:0%
+most H which we said earlier to be 3n
+ 
+
+ align:start position:0%
+most H which we said earlier to be 3n
+over log
+
+ align:start position:0%
+over log
+ 
+
+ align:start position:0%
+over log
+n okay so we have such a graph G that
+
+ align:start position:0%
+n okay so we have such a graph G that
+ 
+
+ align:start position:0%
+n okay so we have such a graph G that
+has these nice
+
+ align:start position:0%
+has these nice
+ 
+
+ align:start position:0%
+has these nice
+properties well we're looking for a
+
+ align:start position:0%
+properties well we're looking for a
+ 
+
+ align:start position:0%
+properties well we're looking for a
+graph with high girth well here G has
+
+ align:start position:0%
+graph with high girth well here G has
+ 
+
+ align:start position:0%
+graph with high girth well here G has
+not too many short Cycles so we can get
+
+ align:start position:0%
+not too many short Cycles so we can get
+ 
+
+ align:start position:0%
+not too many short Cycles so we can get
+rid of one vertex from each short
+
+ align:start position:0%
+rid of one vertex from each short
+ 
+
+ align:start position:0%
+rid of one vertex from each short
+cycle to remove all the short Cycles so
+
+ align:start position:0%
+cycle to remove all the short Cycles so
+ 
+
+ align:start position:0%
+cycle to remove all the short Cycles so
+remove a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Vertex from each short cycle the each
+
+ align:start position:0%
+Vertex from each short cycle the each
+ 
+
+ align:start position:0%
+Vertex from each short cycle the each
+cycle of
+
+ align:start position:0%
+cycle of
+ 
+
+ align:start position:0%
+cycle of
+length at
+
+ align:start position:0%
+length at
+ 
+
+ align:start position:0%
+length at
+most
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+l so remove one vertex from each such
+
+ align:start position:0%
+l so remove one vertex from each such
+ 
+
+ align:start position:0%
+l so remove one vertex from each such
+cycle and
+
+ align:start position:0%
+cycle and
+ 
+
+ align:start position:0%
+cycle and
+doing so results in a subgraph g
+
+ align:start position:0%
+doing so results in a subgraph g
+ 
+
+ align:start position:0%
+doing so results in a subgraph g
+Prime and then we know that the girth of
+
+ align:start position:0%
+Prime and then we know that the girth of
+ 
+
+ align:start position:0%
+Prime and then we know that the girth of
+G
+
+ align:start position:0%
+G
+ 
+
+ align:start position:0%
+G
+Prime is strictly larger than L because
+
+ align:start position:0%
+Prime is strictly larger than L because
+ 
+
+ align:start position:0%
+Prime is strictly larger than L because
+we got rid of all the short
+
+ align:start position:0%
+we got rid of all the short
+ 
+
+ align:start position:0%
+we got rid of all the short
+cycles and furthermore the chromatic
+
+ align:start position:0%
+cycles and furthermore the chromatic
+ 
+
+ align:start position:0%
+cycles and furthermore the chromatic
+number of G
+
+ align:start position:0%
+number of G
+ 
+
+ align:start position:0%
+number of G
+Prime is by what we saw earlier at least
+
+ align:start position:0%
+Prime is by what we saw earlier at least
+ 
+
+ align:start position:0%
+Prime is by what we saw earlier at least
+the number of vertices of G Prime
+
+ align:start position:0%
+the number of vertices of G Prime
+ 
+
+ align:start position:0%
+the number of vertices of G Prime
+divided by its independ
+
+ align:start position:0%
+divided by its independ
+ 
+
+ align:start position:0%
+divided by its independ
+number well the number of vertices is at
+
+ align:start position:0%
+number well the number of vertices is at
+ 
+
+ align:start position:0%
+number well the number of vertices is at
+least n / two because we removed at most
+
+ align:start position:0%
+least n / two because we removed at most
+ 
+
+ align:start position:0%
+least n / two because we removed at most
+n /2 vertices from G to obtain G
+
+ align:start position:0%
+n /2 vertices from G to obtain G
+ 
+
+ align:start position:0%
+n /2 vertices from G to obtain G
+Prime the independence number of G Prime
+
+ align:start position:0%
+Prime the independence number of G Prime
+ 
+
+ align:start position:0%
+Prime the independence number of G Prime
+well the independence number of G
+
+ align:start position:0%
+well the independence number of G
+ 
+
+ align:start position:0%
+well the independence number of G
+Prime is at most the independence number
+
+ align:start position:0%
+Prime is at most the independence number
+ 
+
+ align:start position:0%
+Prime is at most the independence number
+of G because any independent set in G
+
+ align:start position:0%
+of G because any independent set in G
+ 
+
+ align:start position:0%
+of G because any independent set in G
+Prime is automatically independent set
+
+ align:start position:0%
+Prime is automatically independent set
+ 
+
+ align:start position:0%
+Prime is automatically independent set
+in G and here we saw that
+
+ align:start position:0%
+in G and here we saw that
+ 
+
+ align:start position:0%
+in G and here we saw that
+the independent number of G Prime is at
+
+ align:start position:0%
+the independent number of G Prime is at
+ 
+
+ align:start position:0%
+the independent number of G Prime is at
+most H which is three log n over 3 n
+
+ align:start position:0%
+most H which is three log n over 3 n
+ 
+
+ align:start position:0%
+most H which is three log n over 3 n
+over log
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+n so we have in the denominator 3n
+
+ align:start position:0%
+n so we have in the denominator 3n
+ 
+
+ align:start position:0%
+n so we have in the denominator 3n
+over
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+login
+
+ align:start position:0%
+login
+ 
+
+ align:start position:0%
+login
+and whole expression simplifies to log n
+
+ align:start position:0%
+and whole expression simplifies to log n
+ 
+
+ align:start position:0%
+and whole expression simplifies to log n
+/ 6
+
+ align:start position:0%
+/ 6
+ 
+
+ align:start position:0%
+/ 6
+which is bigger than the constant that
+
+ align:start position:0%
+which is bigger than the constant that
+ 
+
+ align:start position:0%
+which is bigger than the constant that
+we were given K as
+
+ align:start position:0%
+we were given K as
+ 
+
+ align:start position:0%
+we were given K as
+long as n is sufficiently
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+large
+
+ align:start position:0%
+large
+ 
+
+ align:start position:0%
+large
+and thus G Prime
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+satisfies the desired
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+requirements okay this finishes the
+
+ align:start position:0%
+requirements okay this finishes the
+ 
+
+ align:start position:0%
+requirements okay this finishes the
+proof of this theorem of airush that
+
+ align:start position:0%
+proof of this theorem of airush that
+ 
+
+ align:start position:0%
+proof of this theorem of airush that
+there exists graphs with arbitrarily
+
+ align:start position:0%
+there exists graphs with arbitrarily
+ 
+
+ align:start position:0%
+there exists graphs with arbitrarily
+large girth and arbitrarily large
+
+ align:start position:0%
+large girth and arbitrarily large
+ 
+
+ align:start position:0%
+large girth and arbitrarily large
+chromatic
+
+ align:start position:0%
+chromatic
+ 
+
+ align:start position:0%
+chromatic
+number to review some of the key ideas
+
+ align:start position:0%
+number to review some of the key ideas
+ 
+
+ align:start position:0%
+number to review some of the key ideas
+in this proof we use the probabilistic
+
+ align:start position:0%
+in this proof we use the probabilistic
+ 
+
+ align:start position:0%
+in this proof we use the probabilistic
+method with alterations to construct
+
+ align:start position:0%
+method with alterations to construct
+ 
+
+ align:start position:0%
+method with alterations to construct
+first a random
+
+ align:start position:0%
+first a random
+ 
+
+ align:start position:0%
+first a random
+graph with various parameters so that
+
+ align:start position:0%
+graph with various parameters so that
+ 
+
+ align:start position:0%
+graph with various parameters so that
+this random graph typically has very few
+
+ align:start position:0%
+this random graph typically has very few
+ 
+
+ align:start position:0%
+this random graph typically has very few
+short
+
+ align:start position:0%
+short
+ 
+
+ align:start position:0%
+short
+Cycles so that we can then remove one
+
+ align:start position:0%
+Cycles so that we can then remove one
+ 
+
+ align:start position:0%
+Cycles so that we can then remove one
+vertex from each short
+
+ align:start position:0%
+vertex from each short
+ 
+
+ align:start position:0%
+vertex from each short
+cycle and get rid of all the short
+
+ align:start position:0%
+cycle and get rid of all the short
+ 
+
+ align:start position:0%
+cycle and get rid of all the short
+cycles and this is a way to ensure large
+
+ align:start position:0%
+cycles and this is a way to ensure large
+ 
+
+ align:start position:0%
+cycles and this is a way to ensure large
+growth to obtain High chromatic number
+
+ align:start position:0%
+growth to obtain High chromatic number
+ 
+
+ align:start position:0%
+growth to obtain High chromatic number
+we note that this graph typically
+
+ align:start position:0%
+we note that this graph typically
+ 
+
+ align:start position:0%
+we note that this graph typically
+has typically does not have large
+
+ align:start position:0%
+has typically does not have large
+ 
+
+ align:start position:0%
+has typically does not have large
+independent
+
+ align:start position:0%
+independent
+ 
+
+ align:start position:0%
+independent
+sets and so its independence number is
+
+ align:start position:0%
+sets and so its independence number is
+ 
+
+ align:start position:0%
+sets and so its independence number is
+typically small and therefore the
+
+ align:start position:0%
+typically small and therefore the
+ 
+
+ align:start position:0%
+typically small and therefore the
+independence number of the subgraph must
+
+ align:start position:0%
+independence number of the subgraph must
+ 
+
+ align:start position:0%
+independence number of the subgraph must
+be typically small as well and having
+
+ align:start position:0%
+be typically small as well and having
+ 
+
+ align:start position:0%
+be typically small as well and having
+small Independence number implies High
+
+ align:start position:0%
+small Independence number implies High
+ 
+
+ align:start position:0%
+small Independence number implies High
+chromatic
+
+ align:start position:0%
+chromatic
+ 
+
+ align:start position:0%
+chromatic
+number okay so it's a beautiful
+
+ align:start position:0%
+number okay so it's a beautiful
+ 
+
+ align:start position:0%
+number okay so it's a beautiful
+illustration of the probabilistic method
+
+ align:start position:0%
+illustration of the probabilistic method
+ 
+
+ align:start position:0%
+illustration of the probabilistic method
+with alterations that allows us to
+
+ align:start position:0%
+with alterations that allows us to
+ 
+
+ align:start position:0%
+with alterations that allows us to
+deduce this highly counterintuitive
+
+ align:start position:0%
+deduce this highly counterintuitive
+ 
+
+ align:start position:0%
+deduce this highly counterintuitive
+result
+
+ align:start position:0%
+result
+ 
+
+ align:start position:0%
+result
+which was U quite surprising because in
+
+ align:start position:0%
+which was U quite surprising because in
+ 
+
+ align:start position:0%
+which was U quite surprising because in
+previously various researchers have
+
+ align:start position:0%
+previously various researchers have
+ 
+
+ align:start position:0%
+previously various researchers have
+tried to construct such examples of
+
+ align:start position:0%
+tried to construct such examples of
+ 
+
+ align:start position:0%
+tried to construct such examples of
+graphs by hand explicitly but
+
+ align:start position:0%
+graphs by hand explicitly but
+ 
+
+ align:start position:0%
+graphs by hand explicitly but
+successfully and ERS brought this
+
+ align:start position:0%
+successfully and ERS brought this
+ 
+
+ align:start position:0%
+successfully and ERS brought this
+beautiful Insight that introducing
+
+ align:start position:0%
+beautiful Insight that introducing
+ 
+
+ align:start position:0%
+beautiful Insight that introducing
+Randomness by looking at random graphs
+
+ align:start position:0%
+Randomness by looking at random graphs
+ 
+
+ align:start position:0%
+Randomness by looking at random graphs
+one can indeed prove the existence of
+
+ align:start position:0%
+one can indeed prove the existence of
+ 
+
+ align:start position:0%
+one can indeed prove the existence of
+graphs with highly counterintuitive
+
+ align:start position:0%
+graphs with highly counterintuitive
+ 
+
+ align:start position:0%
+graphs with highly counterintuitive
+properties
\ No newline at end of file
diff --git a/1KcxRSsHrcI.txt b/1KcxRSsHrcI.txt
new file mode 100644
index 0000000000000000000000000000000000000000..78304a2741ed3099c09b3c719bf0180e00764b9d
--- /dev/null
+++ b/1KcxRSsHrcI.txt
@@ -0,0 +1,7883 @@
+align:start position:0%
+ 
+so uh last in the last lecture I spent
+
+ align:start position:0%
+so uh last in the last lecture I spent
+ 
+
+ align:start position:0%
+so uh last in the last lecture I spent
+quite a while trying to convey uh a
+
+ align:start position:0%
+quite a while trying to convey uh a
+ 
+
+ align:start position:0%
+quite a while trying to convey uh a
+sense of how the structure of DNA was uh
+
+ align:start position:0%
+sense of how the structure of DNA was uh
+ 
+
+ align:start position:0%
+sense of how the structure of DNA was uh
+discovered um I the data that led the
+
+ align:start position:0%
+discovered um I the data that led the
+ 
+
+ align:start position:0%
+discovered um I the data that led the
+crystalographic data that led to it as I
+
+ align:start position:0%
+crystalographic data that led to it as I
+ 
+
+ align:start position:0%
+crystalographic data that led to it as I
+said was collected by Roslin Franklin
+
+ align:start position:0%
+said was collected by Roslin Franklin
+ 
+
+ align:start position:0%
+said was collected by Roslin Franklin
+and I saw there there's some confusion
+
+ align:start position:0%
+and I saw there there's some confusion
+ 
+
+ align:start position:0%
+and I saw there there's some confusion
+about this picture that I showed you
+
+ align:start position:0%
+about this picture that I showed you
+ 
+
+ align:start position:0%
+about this picture that I showed you
+next this is not a photograph of a
+
+ align:start position:0%
+next this is not a photograph of a
+ 
+
+ align:start position:0%
+next this is not a photograph of a
+double helix this is what happened when
+
+ align:start position:0%
+double helix this is what happened when
+ 
+
+ align:start position:0%
+double helix this is what happened when
+she bounced electron um x-ray off the
+
+ align:start position:0%
+she bounced electron um x-ray off the
+ 
+
+ align:start position:0%
+she bounced electron um x-ray off the
+crystal of DNA this is the defraction
+
+ align:start position:0%
+crystal of DNA this is the defraction
+ 
+
+ align:start position:0%
+crystal of DNA this is the defraction
+pattern that she saw and then one works
+
+ align:start position:0%
+pattern that she saw and then one works
+ 
+
+ align:start position:0%
+pattern that she saw and then one works
+backwards from that trying to figure out
+
+ align:start position:0%
+backwards from that trying to figure out
+ 
+
+ align:start position:0%
+backwards from that trying to figure out
+what kind of structure it was that would
+
+ align:start position:0%
+what kind of structure it was that would
+ 
+
+ align:start position:0%
+what kind of structure it was that would
+have caused that defraction pattern you
+
+ align:start position:0%
+have caused that defraction pattern you
+ 
+
+ align:start position:0%
+have caused that defraction pattern you
+have to be a pretty good ex uh x-ray
+
+ align:start position:0%
+have to be a pretty good ex uh x-ray
+ 
+
+ align:start position:0%
+have to be a pretty good ex uh x-ray
+crystallographer to draw any kind of
+
+ align:start position:0%
+crystallographer to draw any kind of
+ 
+
+ align:start position:0%
+crystallographer to draw any kind of
+inferences from that and there were
+
+ align:start position:0%
+inferences from that and there were
+ 
+
+ align:start position:0%
+inferences from that and there were
+people including uh Francis Crick who
+
+ align:start position:0%
+people including uh Francis Crick who
+ 
+
+ align:start position:0%
+people including uh Francis Crick who
+saw the implications of it right away
+
+ align:start position:0%
+saw the implications of it right away
+ 
+
+ align:start position:0%
+saw the implications of it right away
+but the point was she she collected the
+
+ align:start position:0%
+but the point was she she collected the
+ 
+
+ align:start position:0%
+but the point was she she collected the
+data and then uh the two people that I
+
+ align:start position:0%
+data and then uh the two people that I
+ 
+
+ align:start position:0%
+data and then uh the two people that I
+told you about then who whose names you
+
+ align:start position:0%
+told you about then who whose names you
+ 
+
+ align:start position:0%
+told you about then who whose names you
+know so well Jim Watson and Francis
+
+ align:start position:0%
+know so well Jim Watson and Francis
+ 
+
+ align:start position:0%
+know so well Jim Watson and Francis
+Crick were the two individuals that uh
+
+ align:start position:0%
+Crick were the two individuals that uh
+ 
+
+ align:start position:0%
+Crick were the two individuals that uh
+then solved the uh came up with the
+
+ align:start position:0%
+then solved the uh came up with the
+ 
+
+ align:start position:0%
+then solved the uh came up with the
+model that explained the the defraction
+
+ align:start position:0%
+model that explained the the defraction
+ 
+
+ align:start position:0%
+model that explained the the defraction
+pattern and therefore we learned the the
+
+ align:start position:0%
+pattern and therefore we learned the the
+ 
+
+ align:start position:0%
+pattern and therefore we learned the the
+structure of DNA as a double stranded
+
+ align:start position:0%
+structure of DNA as a double stranded
+ 
+
+ align:start position:0%
+structure of DNA as a double stranded
+Helix I also tried to make the case that
+
+ align:start position:0%
+Helix I also tried to make the case that
+ 
+
+ align:start position:0%
+Helix I also tried to make the case that
+it wasn't two Geniuses who sat down in a
+
+ align:start position:0%
+it wasn't two Geniuses who sat down in a
+ 
+
+ align:start position:0%
+it wasn't two Geniuses who sat down in a
+room took a look at this and popped up
+
+ align:start position:0%
+room took a look at this and popped up
+ 
+
+ align:start position:0%
+room took a look at this and popped up
+with the model it was a story of real
+
+ align:start position:0%
+with the model it was a story of real
+ 
+
+ align:start position:0%
+with the model it was a story of real
+people with Misadventures and mistakes
+
+ align:start position:0%
+people with Misadventures and mistakes
+ 
+
+ align:start position:0%
+people with Misadventures and mistakes
+and recovery from mistakes and so on
+
+ align:start position:0%
+and recovery from mistakes and so on
+ 
+
+ align:start position:0%
+and recovery from mistakes and so on
+getting it it was also uh a very small
+
+ align:start position:0%
+getting it it was also uh a very small
+ 
+
+ align:start position:0%
+getting it it was also uh a very small
+group and I'm going to take just a very
+
+ align:start position:0%
+group and I'm going to take just a very
+ 
+
+ align:start position:0%
+group and I'm going to take just a very
+small minute it's the beginning of the
+
+ align:start position:0%
+small minute it's the beginning of the
+ 
+
+ align:start position:0%
+small minute it's the beginning of the
+uh class because there's I have uh a
+
+ align:start position:0%
+uh class because there's I have uh a
+ 
+
+ align:start position:0%
+uh class because there's I have uh a
+colleague Vernon Ingram who's sitting
+
+ align:start position:0%
+colleague Vernon Ingram who's sitting
+ 
+
+ align:start position:0%
+colleague Vernon Ingram who's sitting
+down here in the front who was in a
+
+ align:start position:0%
+down here in the front who was in a
+ 
+
+ align:start position:0%
+down here in the front who was in a
+member of this very small group of with
+
+ align:start position:0%
+member of this very small group of with
+ 
+
+ align:start position:0%
+member of this very small group of with
+with uh Jim Watson and Francis Crick so
+
+ align:start position:0%
+with uh Jim Watson and Francis Crick so
+ 
+
+ align:start position:0%
+with uh Jim Watson and Francis Crick so
+he was there well where all this
+
+ align:start position:0%
+he was there well where all this
+ 
+
+ align:start position:0%
+he was there well where all this
+happened and almost nobody in the world
+
+ align:start position:0%
+happened and almost nobody in the world
+ 
+
+ align:start position:0%
+happened and almost nobody in the world
+has had a chance in your generation has
+
+ align:start position:0%
+has had a chance in your generation has
+ 
+
+ align:start position:0%
+has had a chance in your generation has
+heard a chance to hear directly from
+
+ align:start position:0%
+heard a chance to hear directly from
+ 
+
+ align:start position:0%
+heard a chance to hear directly from
+somebody who was there when it happened
+
+ align:start position:0%
+somebody who was there when it happened
+ 
+
+ align:start position:0%
+somebody who was there when it happened
+so I ask Vernon if he'd come and just
+
+ align:start position:0%
+so I ask Vernon if he'd come and just
+ 
+
+ align:start position:0%
+so I ask Vernon if he'd come and just
+talk to you for a little bit just what
+
+ align:start position:0%
+talk to you for a little bit just what
+ 
+
+ align:start position:0%
+talk to you for a little bit just what
+it was like to be
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+there put these onto your sweater
+
+ align:start position:0%
+there put these onto your sweater
+ 
+
+ align:start position:0%
+there put these onto your sweater
+anywhere I guess this I'll
+
+ align:start position:0%
+anywhere I guess this I'll
+ 
+
+ align:start position:0%
+anywhere I guess this I'll
+put pinch it on but
+
+ align:start position:0%
+put pinch it on but
+ 
+
+ align:start position:0%
+put pinch it on but
+there
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+you want come
+
+ align:start position:0%
+you want come
+ 
+
+ align:start position:0%
+you want come
+back
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+eventually well thanks Graham um you
+
+ align:start position:0%
+eventually well thanks Graham um you
+ 
+
+ align:start position:0%
+eventually well thanks Graham um you
+seem to be at a very exciting stage in
+
+ align:start position:0%
+seem to be at a very exciting stage in
+ 
+
+ align:start position:0%
+seem to be at a very exciting stage in
+7014 this structure of the secret of
+
+ align:start position:0%
+7014 this structure of the secret of
+ 
+
+ align:start position:0%
+7014 this structure of the secret of
+life no
+
+ align:start position:0%
+life no
+ 
+
+ align:start position:0%
+life no
+less and it's interesting that
+
+ align:start position:0%
+less and it's interesting that
+ 
+
+ align:start position:0%
+less and it's interesting that
+immediately uh when Watson and cck
+
+ align:start position:0%
+immediately uh when Watson and cck
+ 
+
+ align:start position:0%
+immediately uh when Watson and cck
+um put together a
+
+ align:start position:0%
+um put together a
+ 
+
+ align:start position:0%
+um put together a
+model of the DNA
+
+ align:start position:0%
+model of the DNA
+ 
+
+ align:start position:0%
+model of the DNA
+molecule that fit the X-ray data that
+
+ align:start position:0%
+molecule that fit the X-ray data that
+ 
+
+ align:start position:0%
+molecule that fit the X-ray data that
+was the point how do you know a model is
+
+ align:start position:0%
+was the point how do you know a model is
+ 
+
+ align:start position:0%
+was the point how do you know a model is
+correct
+
+ align:start position:0%
+correct
+ 
+
+ align:start position:0%
+correct
+because there are certain distances in
+
+ align:start position:0%
+because there are certain distances in
+ 
+
+ align:start position:0%
+because there are certain distances in
+the model and
+
+ align:start position:0%
+the model and
+ 
+
+ align:start position:0%
+the model and
+those have to correlate
+
+ align:start position:0%
+those have to correlate
+ 
+
+ align:start position:0%
+those have to correlate
+exactly with the
+
+ align:start position:0%
+exactly with the
+ 
+
+ align:start position:0%
+exactly with the
+distances of the X-ray spots in the
+
+ align:start position:0%
+distances of the X-ray spots in the
+ 
+
+ align:start position:0%
+distances of the X-ray spots in the
+defraction pattern that you saw that's
+
+ align:start position:0%
+defraction pattern that you saw that's
+ 
+
+ align:start position:0%
+defraction pattern that you saw that's
+how you know that a model that you've
+
+ align:start position:0%
+how you know that a model that you've
+ 
+
+ align:start position:0%
+how you know that a model that you've
+built to certain
+
+ align:start position:0%
+built to certain
+ 
+
+ align:start position:0%
+built to certain
+specifications corresponds to what the
+
+ align:start position:0%
+specifications corresponds to what the
+ 
+
+ align:start position:0%
+specifications corresponds to what the
+molecule itself in the crystal that
+
+ align:start position:0%
+molecule itself in the crystal that
+ 
+
+ align:start position:0%
+molecule itself in the crystal that
+you're examining
+
+ align:start position:0%
+you're examining
+ 
+
+ align:start position:0%
+you're examining
+actually
+
+ align:start position:0%
+actually
+ 
+
+ align:start position:0%
+actually
+uh is composed
+
+ align:start position:0%
+uh is composed
+ 
+
+ align:start position:0%
+uh is composed
+of it was by sheer accident that I
+
+ align:start position:0%
+of it was by sheer accident that I
+ 
+
+ align:start position:0%
+of it was by sheer accident that I
+happened to be working as a
+
+ align:start position:0%
+happened to be working as a
+ 
+
+ align:start position:0%
+happened to be working as a
+biochemist in uh the MRC medical
+
+ align:start position:0%
+biochemist in uh the MRC medical
+ 
+
+ align:start position:0%
+biochemist in uh the MRC medical
+research Council Lab at the Cavendish
+
+ align:start position:0%
+research Council Lab at the Cavendish
+ 
+
+ align:start position:0%
+research Council Lab at the Cavendish
+laboratory where Watson and Crick um
+
+ align:start position:0%
+laboratory where Watson and Crick um
+ 
+
+ align:start position:0%
+laboratory where Watson and Crick um
+were working sheer accident it was a
+
+ align:start position:0%
+were working sheer accident it was a
+ 
+
+ align:start position:0%
+were working sheer accident it was a
+very crowed lab as Graham
+
+ align:start position:0%
+very crowed lab as Graham
+ 
+
+ align:start position:0%
+very crowed lab as Graham
+said and that's something that you
+
+ align:start position:0%
+said and that's something that you
+ 
+
+ align:start position:0%
+said and that's something that you
+should
+
+ align:start position:0%
+should
+ 
+
+ align:start position:0%
+should
+remember when you're choosing a lab to
+
+ align:start position:0%
+remember when you're choosing a lab to
+ 
+
+ align:start position:0%
+remember when you're choosing a lab to
+work
+
+ align:start position:0%
+work
+ 
+
+ align:start position:0%
+work
+in always go to a lab that's
+
+ align:start position:0%
+in always go to a lab that's
+ 
+
+ align:start position:0%
+in always go to a lab that's
+overcrowded never go to a lab where
+
+ align:start position:0%
+overcrowded never go to a lab where
+ 
+
+ align:start position:0%
+overcrowded never go to a lab where
+there's lots of
+
+ align:start position:0%
+there's lots of
+ 
+
+ align:start position:0%
+there's lots of
+space
+
+ align:start position:0%
+space
+ 
+
+ align:start position:0%
+space
+because a really successful lab attracts
+
+ align:start position:0%
+because a really successful lab attracts
+ 
+
+ align:start position:0%
+because a really successful lab attracts
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+many co-workers visitors that it rapidly
+
+ align:start position:0%
+many co-workers visitors that it rapidly
+ 
+
+ align:start position:0%
+many co-workers visitors that it rapidly
+gets overcrowded and that was the case
+
+ align:start position:0%
+gets overcrowded and that was the case
+ 
+
+ align:start position:0%
+gets overcrowded and that was the case
+in this uh in this
+
+ align:start position:0%
+in this uh in this
+ 
+
+ align:start position:0%
+in this uh in this
+laboratory the director was Max perutz
+
+ align:start position:0%
+laboratory the director was Max perutz
+ 
+
+ align:start position:0%
+laboratory the director was Max perutz
+co-director John kendrew doing x-ray
+
+ align:start position:0%
+co-director John kendrew doing x-ray
+ 
+
+ align:start position:0%
+co-director John kendrew doing x-ray
+crystallography of uh proteins for
+
+ align:start position:0%
+crystallography of uh proteins for
+ 
+
+ align:start position:0%
+crystallography of uh proteins for
+almost the first time and solving the
+
+ align:start position:0%
+almost the first time and solving the
+ 
+
+ align:start position:0%
+almost the first time and solving the
+protein
+
+ align:start position:0%
+protein
+ 
+
+ align:start position:0%
+protein
+structure uh Francis criek was a
+
+ align:start position:0%
+structure uh Francis criek was a
+ 
+
+ align:start position:0%
+structure uh Francis criek was a
+graduate student of U Max perutz doing
+
+ align:start position:0%
+graduate student of U Max perutz doing
+ 
+
+ align:start position:0%
+graduate student of U Max perutz doing
+PhD work and the first thing I remember
+
+ align:start position:0%
+PhD work and the first thing I remember
+ 
+
+ align:start position:0%
+PhD work and the first thing I remember
+about
+
+ align:start position:0%
+about
+ 
+
+ align:start position:0%
+about
+Francis was when I went there as a
+
+ align:start position:0%
+Francis was when I went there as a
+ 
+
+ align:start position:0%
+Francis was when I went there as a
+biochemist to work with Max PRS when I
+
+ align:start position:0%
+biochemist to work with Max PRS when I
+ 
+
+ align:start position:0%
+biochemist to work with Max PRS when I
+went there there was this tall gangling
+
+ align:start position:0%
+went there there was this tall gangling
+ 
+
+ align:start position:0%
+went there there was this tall gangling
+guy constantly circulating between the
+
+ align:start position:0%
+guy constantly circulating between the
+ 
+
+ align:start position:0%
+guy constantly circulating between the
+top floor of the
+
+ align:start position:0%
+top floor of the
+ 
+
+ align:start position:0%
+top floor of the
+building his office in the middle and
+
+ align:start position:0%
+building his office in the middle and
+ 
+
+ align:start position:0%
+building his office in the middle and
+the X-ray machines at the bottom is
+
+ align:start position:0%
+the X-ray machines at the bottom is
+ 
+
+ align:start position:0%
+the X-ray machines at the bottom is
+constantly going up and down and in
+
+ align:start position:0%
+constantly going up and down and in
+ 
+
+ align:start position:0%
+constantly going up and down and in
+those days the buildings didn't have any
+
+ align:start position:0%
+those days the buildings didn't have any
+ 
+
+ align:start position:0%
+those days the buildings didn't have any
+elevators or lifts as the English call
+
+ align:start position:0%
+elevators or lifts as the English call
+ 
+
+ align:start position:0%
+elevators or lifts as the English call
+them so he was in excellent physical
+
+ align:start position:0%
+them so he was in excellent physical
+ 
+
+ align:start position:0%
+them so he was in excellent physical
+shape
+
+ align:start position:0%
+shape
+ 
+
+ align:start position:0%
+shape
+uh very crowded a very modest lab and
+
+ align:start position:0%
+uh very crowded a very modest lab and
+ 
+
+ align:start position:0%
+uh very crowded a very modest lab and
+what's usually
+
+ align:start position:0%
+what's usually
+ 
+
+ align:start position:0%
+what's usually
+forgotten is a key member of that group
+
+ align:start position:0%
+forgotten is a key member of that group
+ 
+
+ align:start position:0%
+forgotten is a key member of that group
+an engineer Tony
+
+ align:start position:0%
+an engineer Tony
+ 
+
+ align:start position:0%
+an engineer Tony
+broad key person because he invented
+
+ align:start position:0%
+broad key person because he invented
+ 
+
+ align:start position:0%
+broad key person because he invented
+what was then the world's best and most
+
+ align:start position:0%
+what was then the world's best and most
+ 
+
+ align:start position:0%
+what was then the world's best and most
+efficient x-ray machine a rotating anode
+
+ align:start position:0%
+efficient x-ray machine a rotating anode
+ 
+
+ align:start position:0%
+efficient x-ray machine a rotating anode
+x-ray machine and it because to the
+
+ align:start position:0%
+x-ray machine and it because to the
+ 
+
+ align:start position:0%
+x-ray machine and it because to the
+X-ray crystallographers in that group
+
+ align:start position:0%
+X-ray crystallographers in that group
+ 
+
+ align:start position:0%
+X-ray crystallographers in that group
+this machine was
+
+ align:start position:0%
+this machine was
+ 
+
+ align:start position:0%
+this machine was
+available because of that they were the
+
+ align:start position:0%
+available because of that they were the
+ 
+
+ align:start position:0%
+available because of that they were the
+preeminent x-ray structure group in the
+
+ align:start position:0%
+preeminent x-ray structure group in the
+ 
+
+ align:start position:0%
+preeminent x-ray structure group in the
+world my job was as a bi biochemist
+
+ align:start position:0%
+world my job was as a bi biochemist
+ 
+
+ align:start position:0%
+world my job was as a bi biochemist
+protein
+
+ align:start position:0%
+protein
+ 
+
+ align:start position:0%
+protein
+biochemist uh putting a heavy atom
+
+ align:start position:0%
+biochemist uh putting a heavy atom
+ 
+
+ align:start position:0%
+biochemist uh putting a heavy atom
+Mercury very heavy atom into max
+
+ align:start position:0%
+Mercury very heavy atom into max
+ 
+
+ align:start position:0%
+Mercury very heavy atom into max
+perutz's hemoglobin crystals in specific
+
+ align:start position:0%
+perutz's hemoglobin crystals in specific
+ 
+
+ align:start position:0%
+perutz's hemoglobin crystals in specific
+places that has a predictable effect on
+
+ align:start position:0%
+places that has a predictable effect on
+ 
+
+ align:start position:0%
+places that has a predictable effect on
+the X-ray pattern and that enables the
+
+ align:start position:0%
+the X-ray pattern and that enables the
+ 
+
+ align:start position:0%
+the X-ray pattern and that enables the
+FIA diagram to be uh constructed with
+
+ align:start position:0%
+FIA diagram to be uh constructed with
+ 
+
+ align:start position:0%
+FIA diagram to be uh constructed with
+real phase values for the X-ray
+
+ align:start position:0%
+real phase values for the X-ray
+ 
+
+ align:start position:0%
+real phase values for the X-ray
+diffractions um for the physicists among
+
+ align:start position:0%
+diffractions um for the physicists among
+ 
+
+ align:start position:0%
+diffractions um for the physicists among
+you here are there any physicists here
+
+ align:start position:0%
+you here are there any physicists here
+ 
+
+ align:start position:0%
+you here are there any physicists here
+yeah thought
+
+ align:start position:0%
+yeah thought
+ 
+
+ align:start position:0%
+yeah thought
+so um that was a big step
+
+ align:start position:0%
+so um that was a big step
+ 
+
+ align:start position:0%
+so um that was a big step
+forward and that was also a big step in
+
+ align:start position:0%
+forward and that was also a big step in
+ 
+
+ align:start position:0%
+forward and that was also a big step in
+uh figuring out um the structure of the
+
+ align:start position:0%
+uh figuring out um the structure of the
+ 
+
+ align:start position:0%
+uh figuring out um the structure of the
+DNA uh
+
+ align:start position:0%
+DNA uh
+ 
+
+ align:start position:0%
+DNA uh
+samples semi
+
+ align:start position:0%
+samples semi
+ 
+
+ align:start position:0%
+samples semi
+crystals that uh Professor walker uh
+
+ align:start position:0%
+crystals that uh Professor walker uh
+ 
+
+ align:start position:0%
+crystals that uh Professor walker uh
+just referred
+
+ align:start position:0%
+just referred
+ 
+
+ align:start position:0%
+just referred
+to all dependent on the engineer Tony
+
+ align:start position:0%
+to all dependent on the engineer Tony
+ 
+
+ align:start position:0%
+to all dependent on the engineer Tony
+broad who's never mentioned in any of
+
+ align:start position:0%
+broad who's never mentioned in any of
+ 
+
+ align:start position:0%
+broad who's never mentioned in any of
+these histories but without him this
+
+ align:start position:0%
+these histories but without him this
+ 
+
+ align:start position:0%
+these histories but without him this
+would not have happened so it was an
+
+ align:start position:0%
+would not have happened so it was an
+ 
+
+ align:start position:0%
+would not have happened so it was an
+exciting place to work in very exciting
+
+ align:start position:0%
+exciting place to work in very exciting
+ 
+
+ align:start position:0%
+exciting place to work in very exciting
+we were all young in those
+
+ align:start position:0%
+we were all young in those
+ 
+
+ align:start position:0%
+we were all young in those
+days and living the lives of young men
+
+ align:start position:0%
+days and living the lives of young men
+ 
+
+ align:start position:0%
+days and living the lives of young men
+and young
+
+ align:start position:0%
+and young
+ 
+
+ align:start position:0%
+and young
+women with all the
+
+ align:start position:0%
+women with all the
+ 
+
+ align:start position:0%
+women with all the
+complications that arise when you put a
+
+ align:start position:0%
+complications that arise when you put a
+ 
+
+ align:start position:0%
+complications that arise when you put a
+whole bunch of very energetic young men
+
+ align:start position:0%
+whole bunch of very energetic young men
+ 
+
+ align:start position:0%
+whole bunch of very energetic young men
+very energetic young women together and
+
+ align:start position:0%
+very energetic young women together and
+ 
+
+ align:start position:0%
+very energetic young women together and
+by that I mean the
+
+ align:start position:0%
+by that I mean the
+ 
+
+ align:start position:0%
+by that I mean the
+interpersonal
+
+ align:start position:0%
+interpersonal
+ 
+
+ align:start position:0%
+interpersonal
+relationships which when you're in a
+
+ align:start position:0%
+relationships which when you're in a
+ 
+
+ align:start position:0%
+relationships which when you're in a
+crowded very active
+
+ align:start position:0%
+crowded very active
+ 
+
+ align:start position:0%
+crowded very active
+situation um can sometimes
+
+ align:start position:0%
+situation um can sometimes
+ 
+
+ align:start position:0%
+situation um can sometimes
+interfere and we're always very
+
+ align:start position:0%
+interfere and we're always very
+ 
+
+ align:start position:0%
+interfere and we're always very
+entertaining I can tell you that I could
+
+ align:start position:0%
+entertaining I can tell you that I could
+ 
+
+ align:start position:0%
+entertaining I can tell you that I could
+tell you give you a chapter and verse
+
+ align:start position:0%
+tell you give you a chapter and verse
+ 
+
+ align:start position:0%
+tell you give you a chapter and verse
+but it isn't really so very different
+
+ align:start position:0%
+but it isn't really so very different
+ 
+
+ align:start position:0%
+but it isn't really so very different
+from people your age now right I mean
+
+ align:start position:0%
+from people your age now right I mean
+ 
+
+ align:start position:0%
+from people your age now right I mean
+that I'm not saying it interferes with
+
+ align:start position:0%
+that I'm not saying it interferes with
+ 
+
+ align:start position:0%
+that I'm not saying it interferes with
+you sometimes it might there an exciting
+
+ align:start position:0%
+you sometimes it might there an exciting
+ 
+
+ align:start position:0%
+you sometimes it might there an exciting
+lab an exciting time to be there
+
+ align:start position:0%
+lab an exciting time to be there
+ 
+
+ align:start position:0%
+lab an exciting time to be there
+because we were not the only
+
+ align:start position:0%
+because we were not the only
+ 
+
+ align:start position:0%
+because we were not the only
+group uh trying to figure out the
+
+ align:start position:0%
+group uh trying to figure out the
+ 
+
+ align:start position:0%
+group uh trying to figure out the
+structure of
+
+ align:start position:0%
+structure of
+ 
+
+ align:start position:0%
+structure of
+DNA a huge competitor was lonus Pauling
+
+ align:start position:0%
+DNA a huge competitor was lonus Pauling
+ 
+
+ align:start position:0%
+DNA a huge competitor was lonus Pauling
+at
+
+ align:start position:0%
+at
+ 
+
+ align:start position:0%
+at
+Caltech who had beaten that same group
+
+ align:start position:0%
+Caltech who had beaten that same group
+ 
+
+ align:start position:0%
+Caltech who had beaten that same group
+once before quite recently over the
+
+ align:start position:0%
+once before quite recently over the
+ 
+
+ align:start position:0%
+once before quite recently over the
+alpha Helix the component of the crucial
+
+ align:start position:0%
+alpha Helix the component of the crucial
+ 
+
+ align:start position:0%
+alpha Helix the component of the crucial
+component of protein structure he got
+
+ align:start position:0%
+component of protein structure he got
+ 
+
+ align:start position:0%
+component of protein structure he got
+the right answer first 1.5 angstrom
+
+ align:start position:0%
+the right answer first 1.5 angstrom
+ 
+
+ align:start position:0%
+the right answer first 1.5 angstrom
+reflection the alpha Helix but and our
+
+ align:start position:0%
+reflection the alpha Helix but and our
+ 
+
+ align:start position:0%
+reflection the alpha Helix but and our
+group Max perut and our group had been
+
+ align:start position:0%
+group Max perut and our group had been
+ 
+
+ align:start position:0%
+group Max perut and our group had been
+wrong so the group was smarting under
+
+ align:start position:0%
+wrong so the group was smarting under
+ 
+
+ align:start position:0%
+wrong so the group was smarting under
+that kind of defeat if you like and
+
+ align:start position:0%
+that kind of defeat if you like and
+ 
+
+ align:start position:0%
+that kind of defeat if you like and
+competition uh is a wonderful SP spur as
+
+ align:start position:0%
+competition uh is a wonderful SP spur as
+ 
+
+ align:start position:0%
+competition uh is a wonderful SP spur as
+long as you don't let it get out of hand
+
+ align:start position:0%
+long as you don't let it get out of hand
+ 
+
+ align:start position:0%
+long as you don't let it get out of hand
+well needless to say we didn't but uh
+
+ align:start position:0%
+well needless to say we didn't but uh
+ 
+
+ align:start position:0%
+well needless to say we didn't but uh
+the the competition with the with the um
+
+ align:start position:0%
+the the competition with the with the um
+ 
+
+ align:start position:0%
+the the competition with the with the um
+uh polling lab was certainly so severe
+
+ align:start position:0%
+uh polling lab was certainly so severe
+ 
+
+ align:start position:0%
+uh polling lab was certainly so severe
+that we awaited the next letter you see
+
+ align:start position:0%
+that we awaited the next letter you see
+ 
+
+ align:start position:0%
+that we awaited the next letter you see
+in those days new scientific
+
+ align:start position:0%
+in those days new scientific
+ 
+
+ align:start position:0%
+in those days new scientific
+information arrived not by Publications
+
+ align:start position:0%
+information arrived not by Publications
+ 
+
+ align:start position:0%
+information arrived not by Publications
+that took much too long but by personal
+
+ align:start position:0%
+that took much too long but by personal
+ 
+
+ align:start position:0%
+that took much too long but by personal
+letter and in fact the NIH has put
+
+ align:start position:0%
+letter and in fact the NIH has put
+ 
+
+ align:start position:0%
+letter and in fact the NIH has put
+together all these various letters in
+
+ align:start position:0%
+together all these various letters in
+ 
+
+ align:start position:0%
+together all these various letters in
+the Francis criek
+
+ align:start position:0%
+the Francis criek
+ 
+
+ align:start position:0%
+the Francis criek
+collection and when you have time you
+
+ align:start position:0%
+collection and when you have time you
+ 
+
+ align:start position:0%
+collection and when you have time you
+should look at those they're quite
+
+ align:start position:0%
+should look at those they're quite
+ 
+
+ align:start position:0%
+should look at those they're quite
+interesting because they tell you in a
+
+ align:start position:0%
+interesting because they tell you in a
+ 
+
+ align:start position:0%
+interesting because they tell you in a
+way a scientific paper does not tell
+
+ align:start position:0%
+way a scientific paper does not tell
+ 
+
+ align:start position:0%
+way a scientific paper does not tell
+you what I feel about my experimental
+
+ align:start position:0%
+you what I feel about my experimental
+ 
+
+ align:start position:0%
+you what I feel about my experimental
+result what she feels about her
+
+ align:start position:0%
+result what she feels about her
+ 
+
+ align:start position:0%
+result what she feels about her
+experimental results what it means to me
+
+ align:start position:0%
+experimental results what it means to me
+ 
+
+ align:start position:0%
+experimental results what it means to me
+as a person to her as a person to him as
+
+ align:start position:0%
+as a person to her as a person to him as
+ 
+
+ align:start position:0%
+as a person to her as a person to him as
+a
+
+ align:start position:0%
+a
+ 
+
+ align:start position:0%
+a
+person so we were constantly watching
+
+ align:start position:0%
+person so we were constantly watching
+ 
+
+ align:start position:0%
+person so we were constantly watching
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+mail and discussing the news as it came
+
+ align:start position:0%
+mail and discussing the news as it came
+ 
+
+ align:start position:0%
+mail and discussing the news as it came
+in mostly over a beer at the pub next
+
+ align:start position:0%
+in mostly over a beer at the pub next
+ 
+
+ align:start position:0%
+in mostly over a beer at the pub next
+door it was very conveniently Lo
+
+ align:start position:0%
+door it was very conveniently Lo
+ 
+
+ align:start position:0%
+door it was very conveniently Lo
+located but being a small group crowded
+
+ align:start position:0%
+located but being a small group crowded
+ 
+
+ align:start position:0%
+located but being a small group crowded
+Together made communication within our
+
+ align:start position:0%
+Together made communication within our
+ 
+
+ align:start position:0%
+Together made communication within our
+group very easy indeed and we had fights
+
+ align:start position:0%
+group very easy indeed and we had fights
+ 
+
+ align:start position:0%
+group very easy indeed and we had fights
+I don't mean physical fights we had
+
+ align:start position:0%
+I don't mean physical fights we had
+ 
+
+ align:start position:0%
+I don't mean physical fights we had
+fights scientific fights and
+
+ align:start position:0%
+fights scientific fights and
+ 
+
+ align:start position:0%
+fights scientific fights and
+um as a biochemist I was able to settle
+
+ align:start position:0%
+um as a biochemist I was able to settle
+ 
+
+ align:start position:0%
+um as a biochemist I was able to settle
+a crucial fight among the
+
+ align:start position:0%
+a crucial fight among the
+ 
+
+ align:start position:0%
+a crucial fight among the
+crystallographers Crick and Watson who
+
+ align:start position:0%
+crystallographers Crick and Watson who
+ 
+
+ align:start position:0%
+crystallographers Crick and Watson who
+were building the model because quite
+
+ align:start position:0%
+were building the model because quite
+ 
+
+ align:start position:0%
+were building the model because quite
+frankly they didn't do Know Much
+
+ align:start position:0%
+frankly they didn't do Know Much
+ 
+
+ align:start position:0%
+frankly they didn't do Know Much
+Chemistry and we're trying to build a
+
+ align:start position:0%
+Chemistry and we're trying to build a
+ 
+
+ align:start position:0%
+Chemistry and we're trying to build a
+model with a wrong confirmation of the
+
+ align:start position:0%
+model with a wrong confirmation of the
+ 
+
+ align:start position:0%
+model with a wrong confirmation of the
+peptide bond they didn't realize that a
+
+ align:start position:0%
+peptide bond they didn't realize that a
+ 
+
+ align:start position:0%
+peptide bond they didn't realize that a
+peptide bond has two possible
+
+ align:start position:0%
+peptide bond has two possible
+ 
+
+ align:start position:0%
+peptide bond has two possible
+confirmations and they had at one point
+
+ align:start position:0%
+confirmations and they had at one point
+ 
+
+ align:start position:0%
+confirmations and they had at one point
+a terrible time
+
+ align:start position:0%
+a terrible time
+ 
+
+ align:start position:0%
+a terrible time
+um uh trying to fit everything together
+
+ align:start position:0%
+um uh trying to fit everything together
+ 
+
+ align:start position:0%
+um uh trying to fit everything together
+because they were using the wrong
+
+ align:start position:0%
+because they were using the wrong
+ 
+
+ align:start position:0%
+because they were using the wrong
+confirmation I'm talking about laam
+
+ align:start position:0%
+confirmation I'm talking about laam
+ 
+
+ align:start position:0%
+confirmation I'm talking about laam
+latim uh for those of you who are
+
+ align:start position:0%
+latim uh for those of you who are
+ 
+
+ align:start position:0%
+latim uh for those of you who are
+organic chemists that mean something
+
+ align:start position:0%
+organic chemists that mean something
+ 
+
+ align:start position:0%
+organic chemists that mean something
+confirmation and once they got the right
+
+ align:start position:0%
+confirmation and once they got the right
+ 
+
+ align:start position:0%
+confirmation and once they got the right
+confirmation then the model clicked into
+
+ align:start position:0%
+confirmation then the model clicked into
+ 
+
+ align:start position:0%
+confirmation then the model clicked into
+place so we all helped that's what I'm
+
+ align:start position:0%
+place so we all helped that's what I'm
+ 
+
+ align:start position:0%
+place so we all helped that's what I'm
+trying to say we all helped with one
+
+ align:start position:0%
+trying to say we all helped with one
+ 
+
+ align:start position:0%
+trying to say we all helped with one
+great aim in mind it was clear and you
+
+ align:start position:0%
+great aim in mind it was clear and you
+ 
+
+ align:start position:0%
+great aim in mind it was clear and you
+know from what Professor Walker said
+
+ align:start position:0%
+know from what Professor Walker said
+ 
+
+ align:start position:0%
+know from what Professor Walker said
+that the DNA structure
+
+ align:start position:0%
+that the DNA structure
+ 
+
+ align:start position:0%
+that the DNA structure
+in its structure held the clue to
+
+ align:start position:0%
+in its structure held the clue to
+ 
+
+ align:start position:0%
+in its structure held the clue to
+crucial physiological behavior of
+
+ align:start position:0%
+crucial physiological behavior of
+ 
+
+ align:start position:0%
+crucial physiological behavior of
+DNA
+
+ align:start position:0%
+DNA
+ 
+
+ align:start position:0%
+DNA
+and um KCK and Watson said this in their
+
+ align:start position:0%
+and um KCK and Watson said this in their
+ 
+
+ align:start position:0%
+and um KCK and Watson said this in their
+first paper the structure itself because
+
+ align:start position:0%
+first paper the structure itself because
+ 
+
+ align:start position:0%
+first paper the structure itself because
+of its
+
+ align:start position:0%
+of its
+ 
+
+ align:start position:0%
+of its
+complementarity gives you an immediate
+
+ align:start position:0%
+complementarity gives you an immediate
+ 
+
+ align:start position:0%
+complementarity gives you an immediate
+clue as to how it
+
+ align:start position:0%
+clue as to how it
+ 
+
+ align:start position:0%
+clue as to how it
+replicates and replication of DNA
+
+ align:start position:0%
+replicates and replication of DNA
+ 
+
+ align:start position:0%
+replicates and replication of DNA
+structure from generation to
+
+ align:start position:0%
+structure from generation to
+ 
+
+ align:start position:0%
+structure from generation to
+generation is
+
+ align:start position:0%
+generation is
+ 
+
+ align:start position:0%
+generation is
+um of course the crucial thing about
+
+ align:start position:0%
+um of course the crucial thing about
+ 
+
+ align:start position:0%
+um of course the crucial thing about
+DNA the copying the precise copying from
+
+ align:start position:0%
+DNA the copying the precise copying from
+ 
+
+ align:start position:0%
+DNA the copying the precise copying from
+generation to generation and that fell
+
+ align:start position:0%
+generation to generation and that fell
+ 
+
+ align:start position:0%
+generation to generation and that fell
+out of the X-ray structure that's why
+
+ align:start position:0%
+out of the X-ray structure that's why
+ 
+
+ align:start position:0%
+out of the X-ray structure that's why
+the X-ray structure was so very
+
+ align:start position:0%
+the X-ray structure was so very
+ 
+
+ align:start position:0%
+the X-ray structure was so very
+important because it gave you an
+
+ align:start position:0%
+important because it gave you an
+ 
+
+ align:start position:0%
+important because it gave you an
+immediate understanding of uh the role
+
+ align:start position:0%
+immediate understanding of uh the role
+ 
+
+ align:start position:0%
+immediate understanding of uh the role
+of DNA in Modern Biology so that's what
+
+ align:start position:0%
+of DNA in Modern Biology so that's what
+ 
+
+ align:start position:0%
+of DNA in Modern Biology so that's what
+we did and eventually um the people in
+
+ align:start position:0%
+we did and eventually um the people in
+ 
+
+ align:start position:0%
+we did and eventually um the people in
+the group the group got so overcrowded
+
+ align:start position:0%
+the group the group got so overcrowded
+ 
+
+ align:start position:0%
+the group the group got so overcrowded
+they built a huge lab and that's very
+
+ align:start position:0%
+they built a huge lab and that's very
+ 
+
+ align:start position:0%
+they built a huge lab and that's very
+beautiful like any new lab is but the
+
+ align:start position:0%
+beautiful like any new lab is but the
+ 
+
+ align:start position:0%
+beautiful like any new lab is but the
+thing I remember most of all was the
+
+ align:start position:0%
+thing I remember most of all was the
+ 
+
+ align:start position:0%
+thing I remember most of all was the
+atmosphere in that place so remember
+
+ align:start position:0%
+atmosphere in that place so remember
+ 
+
+ align:start position:0%
+atmosphere in that place so remember
+when you go and choose a lab choose one
+
+ align:start position:0%
+when you go and choose a lab choose one
+ 
+
+ align:start position:0%
+when you go and choose a lab choose one
+that's overcrowded it'll pay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+off
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so much that was really wonderful thank
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+you
+
+ align:start position:0%
+you
+ 
+
+ align:start position:0%
+you
+I don't know if some of you realize
+
+ align:start position:0%
+I don't know if some of you realize
+ 
+
+ align:start position:0%
+I don't know if some of you realize
+quite how rare that was this discovery
+
+ align:start position:0%
+quite how rare that was this discovery
+ 
+
+ align:start position:0%
+quite how rare that was this discovery
+of the structure of DNA as I said
+
+ align:start position:0%
+of the structure of DNA as I said
+ 
+
+ align:start position:0%
+of the structure of DNA as I said
+probably one of the big discoveries of
+
+ align:start position:0%
+probably one of the big discoveries of
+ 
+
+ align:start position:0%
+probably one of the big discoveries of
+mankind because as Vernon said so much
+
+ align:start position:0%
+mankind because as Vernon said so much
+ 
+
+ align:start position:0%
+mankind because as Vernon said so much
+it was you could see so many of the
+
+ align:start position:0%
+it was you could see so many of the
+ 
+
+ align:start position:0%
+it was you could see so many of the
+secrets of life as soon as you saw that
+
+ align:start position:0%
+secrets of life as soon as you saw that
+ 
+
+ align:start position:0%
+secrets of life as soon as you saw that
+structure very few people have ever
+
+ align:start position:0%
+structure very few people have ever
+ 
+
+ align:start position:0%
+structure very few people have ever
+heard from someone who was there at the
+
+ align:start position:0%
+heard from someone who was there at the
+ 
+
+ align:start position:0%
+heard from someone who was there at the
+time maybe you'll forget a bunch of
+
+ align:start position:0%
+time maybe you'll forget a bunch of
+ 
+
+ align:start position:0%
+time maybe you'll forget a bunch of
+stuff down the line I hope you'll
+
+ align:start position:0%
+stuff down the line I hope you'll
+ 
+
+ align:start position:0%
+stuff down the line I hope you'll
+remember you heard somebody was there
+
+ align:start position:0%
+remember you heard somebody was there
+ 
+
+ align:start position:0%
+remember you heard somebody was there
+when won and Crick were there and maybe
+
+ align:start position:0%
+when won and Crick were there and maybe
+ 
+
+ align:start position:0%
+when won and Crick were there and maybe
+his extra piece advice about choosing a
+
+ align:start position:0%
+his extra piece advice about choosing a
+ 
+
+ align:start position:0%
+his extra piece advice about choosing a
+lab um just say one thing quickly some
+
+ align:start position:0%
+lab um just say one thing quickly some
+ 
+
+ align:start position:0%
+lab um just say one thing quickly some
+of you I think understood what I've been
+
+ align:start position:0%
+of you I think understood what I've been
+ 
+
+ align:start position:0%
+of you I think understood what I've been
+trying to do I spent quite a bit of time
+
+ align:start position:0%
+trying to do I spent quite a bit of time
+ 
+
+ align:start position:0%
+trying to do I spent quite a bit of time
+talking about science being done by real
+
+ align:start position:0%
+talking about science being done by real
+ 
+
+ align:start position:0%
+talking about science being done by real
+people real uh doing real
+
+ align:start position:0%
+people real uh doing real
+ 
+
+ align:start position:0%
+people real uh doing real
+experiments uh thanks for your comments
+
+ align:start position:0%
+experiments uh thanks for your comments
+ 
+
+ align:start position:0%
+experiments uh thanks for your comments
+a few of you have gone out of your way
+
+ align:start position:0%
+a few of you have gone out of your way
+ 
+
+ align:start position:0%
+a few of you have gone out of your way
+to say that this was a total waste of
+
+ align:start position:0%
+to say that this was a total waste of
+ 
+
+ align:start position:0%
+to say that this was a total waste of
+time and you didn't understand why I
+
+ align:start position:0%
+time and you didn't understand why I
+ 
+
+ align:start position:0%
+time and you didn't understand why I
+didn't teach you something instead of
+
+ align:start position:0%
+didn't teach you something instead of
+ 
+
+ align:start position:0%
+didn't teach you something instead of
+doing something on the test well I'm
+
+ align:start position:0%
+doing something on the test well I'm
+ 
+
+ align:start position:0%
+doing something on the test well I'm
+making up the test and if you don't
+
+ align:start position:0%
+making up the test and if you don't
+ 
+
+ align:start position:0%
+making up the test and if you don't
+think there'll be something on
+
+ align:start position:0%
+think there'll be something on
+ 
+
+ align:start position:0%
+think there'll be something on
+scientific process on the the second
+
+ align:start position:0%
+scientific process on the the second
+ 
+
+ align:start position:0%
+scientific process on the the second
+exam you'll be surprised so uh I'm I'm
+
+ align:start position:0%
+exam you'll be surprised so uh I'm I'm
+ 
+
+ align:start position:0%
+exam you'll be surprised so uh I'm I'm
+spending a lot of time on this and the
+
+ align:start position:0%
+spending a lot of time on this and the
+ 
+
+ align:start position:0%
+spending a lot of time on this and the
+reason is because you're MIT students
+
+ align:start position:0%
+reason is because you're MIT students
+ 
+
+ align:start position:0%
+reason is because you're MIT students
+you know you can go many places in the
+
+ align:start position:0%
+you know you can go many places in the
+ 
+
+ align:start position:0%
+you know you can go many places in the
+country many high school biology courses
+
+ align:start position:0%
+country many high school biology courses
+ 
+
+ align:start position:0%
+country many high school biology courses
+and you can memorize all the someone
+
+ align:start position:0%
+and you can memorize all the someone
+ 
+
+ align:start position:0%
+and you can memorize all the someone
+will tell you to memorize everything
+
+ align:start position:0%
+will tell you to memorize everything
+ 
+
+ align:start position:0%
+will tell you to memorize everything
+that's in the book and you'll get tested
+
+ align:start position:0%
+that's in the book and you'll get tested
+ 
+
+ align:start position:0%
+that's in the book and you'll get tested
+whether you can memorize it if you guys
+
+ align:start position:0%
+whether you can memorize it if you guys
+ 
+
+ align:start position:0%
+whether you can memorize it if you guys
+are at MIT because you have the
+
+ align:start position:0%
+are at MIT because you have the
+ 
+
+ align:start position:0%
+are at MIT because you have the
+potential to be leaders in whatever you
+
+ align:start position:0%
+potential to be leaders in whatever you
+ 
+
+ align:start position:0%
+potential to be leaders in whatever you
+do I've made the transition from being
+
+ align:start position:0%
+do I've made the transition from being
+ 
+
+ align:start position:0%
+do I've made the transition from being
+an undergrad sort of trying to memorize
+
+ align:start position:0%
+an undergrad sort of trying to memorize
+ 
+
+ align:start position:0%
+an undergrad sort of trying to memorize
+stuff in a textbook to working on a
+
+ align:start position:0%
+stuff in a textbook to working on a
+ 
+
+ align:start position:0%
+stuff in a textbook to working on a
+Cutting Edge I've made some reasonably
+
+ align:start position:0%
+Cutting Edge I've made some reasonably
+ 
+
+ align:start position:0%
+Cutting Edge I've made some reasonably
+significant discoveries in science as
+
+ align:start position:0%
+significant discoveries in science as
+ 
+
+ align:start position:0%
+significant discoveries in science as
+have my other colleagues in the
+
+ align:start position:0%
+have my other colleagues in the
+ 
+
+ align:start position:0%
+have my other colleagues in the
+department some of them making greater
+
+ align:start position:0%
+department some of them making greater
+ 
+
+ align:start position:0%
+department some of them making greater
+than I but nevertheless if you're on
+
+ align:start position:0%
+than I but nevertheless if you're on
+ 
+
+ align:start position:0%
+than I but nevertheless if you're on
+that Cutting Edge then you're dealing
+
+ align:start position:0%
+that Cutting Edge then you're dealing
+ 
+
+ align:start position:0%
+that Cutting Edge then you're dealing
+with all the stuff I'm trying to tell
+
+ align:start position:0%
+with all the stuff I'm trying to tell
+ 
+
+ align:start position:0%
+with all the stuff I'm trying to tell
+you about in in in this thing you're
+
+ align:start position:0%
+you about in in in this thing you're
+ 
+
+ align:start position:0%
+you about in in in this thing you're
+working as part of a groups there's
+
+ align:start position:0%
+working as part of a groups there's
+ 
+
+ align:start position:0%
+working as part of a groups there's
+competition there's interpersonal
+
+ align:start position:0%
+competition there's interpersonal
+ 
+
+ align:start position:0%
+competition there's interpersonal
+relationship you make mistakes you
+
+ align:start position:0%
+relationship you make mistakes you
+ 
+
+ align:start position:0%
+relationship you make mistakes you
+recover from them you're making
+
+ align:start position:0%
+recover from them you're making
+ 
+
+ align:start position:0%
+recover from them you're making
+inferences you're testing models it's a
+
+ align:start position:0%
+inferences you're testing models it's a
+ 
+
+ align:start position:0%
+inferences you're testing models it's a
+very complex very real very Dynamic very
+
+ align:start position:0%
+very complex very real very Dynamic very
+ 
+
+ align:start position:0%
+very complex very real very Dynamic very
+human uh interaction I hope you caught a
+
+ align:start position:0%
+human uh interaction I hope you caught a
+ 
+
+ align:start position:0%
+human uh interaction I hope you caught a
+little bit of a whiff of that that from
+
+ align:start position:0%
+little bit of a whiff of that that from
+ 
+
+ align:start position:0%
+little bit of a whiff of that that from
+uh from uh from Vernon and I wouldn't be
+
+ align:start position:0%
+uh from uh from Vernon and I wouldn't be
+ 
+
+ align:start position:0%
+uh from uh from Vernon and I wouldn't be
+I I'm quite capable of reproducing
+
+ align:start position:0%
+I I'm quite capable of reproducing
+ 
+
+ align:start position:0%
+I I'm quite capable of reproducing
+diagrams from the textbook without
+
+ align:start position:0%
+diagrams from the textbook without
+ 
+
+ align:start position:0%
+diagrams from the textbook without
+trying to give you a deeper
+
+ align:start position:0%
+trying to give you a deeper
+ 
+
+ align:start position:0%
+trying to give you a deeper
+understanding and that's what I'm trying
+
+ align:start position:0%
+understanding and that's what I'm trying
+ 
+
+ align:start position:0%
+understanding and that's what I'm trying
+to do here and I hope uh if it hasn't
+
+ align:start position:0%
+to do here and I hope uh if it hasn't
+ 
+
+ align:start position:0%
+to do here and I hope uh if it hasn't
+made sense to you by the end is at least
+
+ align:start position:0%
+made sense to you by the end is at least
+ 
+
+ align:start position:0%
+made sense to you by the end is at least
+a few more of you will will get it and
+
+ align:start position:0%
+a few more of you will will get it and
+ 
+
+ align:start position:0%
+a few more of you will will get it and
+those of you who I think saw what I was
+
+ align:start position:0%
+those of you who I think saw what I was
+ 
+
+ align:start position:0%
+those of you who I think saw what I was
+doing um I appreciate your your uh
+
+ align:start position:0%
+doing um I appreciate your your uh
+ 
+
+ align:start position:0%
+doing um I appreciate your your uh
+you're telling me that in the in the
+
+ align:start position:0%
+you're telling me that in the in the
+ 
+
+ align:start position:0%
+you're telling me that in the in the
+things these are Anonymous so I don't
+
+ align:start position:0%
+things these are Anonymous so I don't
+ 
+
+ align:start position:0%
+things these are Anonymous so I don't
+know but you know a couple of you are
+
+ align:start position:0%
+know but you know a couple of you are
+ 
+
+ align:start position:0%
+know but you know a couple of you are
+certainly trying to to make it clear
+
+ align:start position:0%
+certainly trying to to make it clear
+ 
+
+ align:start position:0%
+certainly trying to to make it clear
+that you didn't think it was um uh was
+
+ align:start position:0%
+that you didn't think it was um uh was
+ 
+
+ align:start position:0%
+that you didn't think it was um uh was
+worth your time coming to lecture I'm
+
+ align:start position:0%
+worth your time coming to lecture I'm
+ 
+
+ align:start position:0%
+worth your time coming to lecture I'm
+trying to tell you why I'm trying to do
+
+ align:start position:0%
+trying to tell you why I'm trying to do
+ 
+
+ align:start position:0%
+trying to tell you why I'm trying to do
+it I'm trying to te Teach You in a
+
+ align:start position:0%
+it I'm trying to te Teach You in a
+ 
+
+ align:start position:0%
+it I'm trying to te Teach You in a
+deeper way that's what I'm this is a
+
+ align:start position:0%
+deeper way that's what I'm this is a
+ 
+
+ align:start position:0%
+deeper way that's what I'm this is a
+required course it's important for your
+
+ align:start position:0%
+required course it's important for your
+ 
+
+ align:start position:0%
+required course it's important for your
+life I hope some of you will see that or
+
+ align:start position:0%
+life I hope some of you will see that or
+ 
+
+ align:start position:0%
+life I hope some of you will see that or
+if you don't see it now you'll see it
+
+ align:start position:0%
+if you don't see it now you'll see it
+ 
+
+ align:start position:0%
+if you don't see it now you'll see it
+later in your career okay now we're
+
+ align:start position:0%
+later in your career okay now we're
+ 
+
+ align:start position:0%
+later in your career okay now we're
+going to talk about uh DNA replication
+
+ align:start position:0%
+going to talk about uh DNA replication
+ 
+
+ align:start position:0%
+going to talk about uh DNA replication
+I'm going to start to drive into some of
+
+ align:start position:0%
+I'm going to start to drive into some of
+ 
+
+ align:start position:0%
+I'm going to start to drive into some of
+the details that maybe are more of the
+
+ align:start position:0%
+the details that maybe are more of the
+ 
+
+ align:start position:0%
+the details that maybe are more of the
+kind of things you're expecting just
+
+ align:start position:0%
+kind of things you're expecting just
+ 
+
+ align:start position:0%
+kind of things you're expecting just
+want to make one quick Point here I've
+
+ align:start position:0%
+want to make one quick Point here I've
+ 
+
+ align:start position:0%
+want to make one quick Point here I've
+talked about cell division we saw this
+
+ align:start position:0%
+talked about cell division we saw this
+ 
+
+ align:start position:0%
+talked about cell division we saw this
+how cells come from other cells go on to
+
+ align:start position:0%
+how cells come from other cells go on to
+ 
+
+ align:start position:0%
+how cells come from other cells go on to
+make more cells I showed you this little
+
+ align:start position:0%
+make more cells I showed you this little
+ 
+
+ align:start position:0%
+make more cells I showed you this little
+movie you've seen a few times of a of a
+
+ align:start position:0%
+movie you've seen a few times of a of a
+ 
+
+ align:start position:0%
+movie you've seen a few times of a of a
+yeast cell dividing but all cells divide
+
+ align:start position:0%
+yeast cell dividing but all cells divide
+ 
+
+ align:start position:0%
+yeast cell dividing but all cells divide
+here's a cancer cell
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+dividing if you get a cancer it's a cell
+
+ align:start position:0%
+dividing if you get a cancer it's a cell
+ 
+
+ align:start position:0%
+dividing if you get a cancer it's a cell
+that's forgotten how to stop dividing
+
+ align:start position:0%
+that's forgotten how to stop dividing
+ 
+
+ align:start position:0%
+that's forgotten how to stop dividing
+and it's growing to make a tumor there's
+
+ align:start position:0%
+and it's growing to make a tumor there's
+ 
+
+ align:start position:0%
+and it's growing to make a tumor there's
+a cancer cell dividing looks not unlike
+
+ align:start position:0%
+a cancer cell dividing looks not unlike
+ 
+
+ align:start position:0%
+a cancer cell dividing looks not unlike
+a yeast and very molecular level very
+
+ align:start position:0%
+a yeast and very molecular level very
+ 
+
+ align:start position:0%
+a yeast and very molecular level very
+very similar but there's another point I
+
+ align:start position:0%
+very similar but there's another point I
+ 
+
+ align:start position:0%
+very similar but there's another point I
+told you the how the structure of DNA
+
+ align:start position:0%
+told you the how the structure of DNA
+ 
+
+ align:start position:0%
+told you the how the structure of DNA
+with the complimentary strands with G
+
+ align:start position:0%
+with the complimentary strands with G
+ 
+
+ align:start position:0%
+with the complimentary strands with G
+pairing with c and a pairing with t
+
+ align:start position:0%
+pairing with c and a pairing with t
+ 
+
+ align:start position:0%
+pairing with c and a pairing with t
+immediately gave rise to an insight as
+
+ align:start position:0%
+immediately gave rise to an insight as
+ 
+
+ align:start position:0%
+immediately gave rise to an insight as
+to how the the genetic material could be
+
+ align:start position:0%
+to how the the genetic material could be
+ 
+
+ align:start position:0%
+to how the the genetic material could be
+replicated and you guys know that it's
+
+ align:start position:0%
+replicated and you guys know that it's
+ 
+
+ align:start position:0%
+replicated and you guys know that it's
+held together by hydrogen bonds between
+
+ align:start position:0%
+held together by hydrogen bonds between
+ 
+
+ align:start position:0%
+held together by hydrogen bonds between
+the base pairs which are about 12/ 12th
+
+ align:start position:0%
+the base pairs which are about 12/ 12th
+ 
+
+ align:start position:0%
+the base pairs which are about 12/ 12th
+the strength of the calent bonds so
+
+ align:start position:0%
+the strength of the calent bonds so
+ 
+
+ align:start position:0%
+the strength of the calent bonds so
+you're able to peel the strands apart
+
+ align:start position:0%
+you're able to peel the strands apart
+ 
+
+ align:start position:0%
+you're able to peel the strands apart
+without breaking the bonds the calent
+
+ align:start position:0%
+without breaking the bonds the calent
+ 
+
+ align:start position:0%
+without breaking the bonds the calent
+bonds and then by pairing a with T and G
+
+ align:start position:0%
+bonds and then by pairing a with T and G
+ 
+
+ align:start position:0%
+bonds and then by pairing a with T and G
+with c and doing that on both strings
+
+ align:start position:0%
+with c and doing that on both strings
+ 
+
+ align:start position:0%
+with c and doing that on both strings
+then you can end up with two identical
+
+ align:start position:0%
+then you can end up with two identical
+ 
+
+ align:start position:0%
+then you can end up with two identical
+copies and so if you do two identical
+
+ align:start position:0%
+copies and so if you do two identical
+ 
+
+ align:start position:0%
+copies and so if you do two identical
+copies they do it again you get eight
+
+ align:start position:0%
+copies they do it again you get eight
+ 
+
+ align:start position:0%
+copies they do it again you get eight
+one of the things we've we've realized
+
+ align:start position:0%
+one of the things we've we've realized
+ 
+
+ align:start position:0%
+one of the things we've we've realized
+over the last few last two or three
+
+ align:start position:0%
+over the last few last two or three
+ 
+
+ align:start position:0%
+over the last few last two or three
+years in looking through the exams is
+
+ align:start position:0%
+years in looking through the exams is
+ 
+
+ align:start position:0%
+years in looking through the exams is
+somehow at least some of the class
+
+ align:start position:0%
+somehow at least some of the class
+ 
+
+ align:start position:0%
+somehow at least some of the class
+didn't connect the business about cells
+
+ align:start position:0%
+didn't connect the business about cells
+ 
+
+ align:start position:0%
+didn't connect the business about cells
+coming from other cells and DNA
+
+ align:start position:0%
+coming from other cells and DNA
+ 
+
+ align:start position:0%
+coming from other cells and DNA
+duplicating to give daughter DNA and I'm
+
+ align:start position:0%
+duplicating to give daughter DNA and I'm
+ 
+
+ align:start position:0%
+duplicating to give daughter DNA and I'm
+just trying to hammer home the point the
+
+ align:start position:0%
+just trying to hammer home the point the
+ 
+
+ align:start position:0%
+just trying to hammer home the point the
+these are related every time a cell
+
+ align:start position:0%
+these are related every time a cell
+ 
+
+ align:start position:0%
+these are related every time a cell
+divides it has to duplicate it genetic
+
+ align:start position:0%
+divides it has to duplicate it genetic
+ 
+
+ align:start position:0%
+divides it has to duplicate it genetic
+information that's why I'm going to be
+
+ align:start position:0%
+information that's why I'm going to be
+ 
+
+ align:start position:0%
+information that's why I'm going to be
+telling you about DNA replication here's
+
+ align:start position:0%
+telling you about DNA replication here's
+ 
+
+ align:start position:0%
+telling you about DNA replication here's
+a picture of that same cancer cell but
+
+ align:start position:0%
+a picture of that same cancer cell but
+ 
+
+ align:start position:0%
+a picture of that same cancer cell but
+watch over here this is the DNA and you
+
+ align:start position:0%
+watch over here this is the DNA and you
+ 
+
+ align:start position:0%
+watch over here this is the DNA and you
+see it's doubled and see how the the DNA
+
+ align:start position:0%
+see it's doubled and see how the the DNA
+ 
+
+ align:start position:0%
+see it's doubled and see how the the DNA
+which is in chromosomes has pulled apart
+
+ align:start position:0%
+which is in chromosomes has pulled apart
+ 
+
+ align:start position:0%
+which is in chromosomes has pulled apart
+so that at the end you now have two
+
+ align:start position:0%
+so that at the end you now have two
+ 
+
+ align:start position:0%
+so that at the end you now have two
+cells and you've got identical copies of
+
+ align:start position:0%
+cells and you've got identical copies of
+ 
+
+ align:start position:0%
+cells and you've got identical copies of
+of DNA so if you're studying cancer for
+
+ align:start position:0%
+of DNA so if you're studying cancer for
+ 
+
+ align:start position:0%
+of DNA so if you're studying cancer for
+example there's this this sort of thing
+
+ align:start position:0%
+example there's this this sort of thing
+ 
+
+ align:start position:0%
+example there's this this sort of thing
+is relevant to
+
+ align:start position:0%
+is relevant to
+ 
+
+ align:start position:0%
+is relevant to
+you okay so um the issue of how oh
+
+ align:start position:0%
+you okay so um the issue of how oh
+ 
+
+ align:start position:0%
+you okay so um the issue of how oh
+before I do that sorry just a couple of
+
+ align:start position:0%
+before I do that sorry just a couple of
+ 
+
+ align:start position:0%
+before I do that sorry just a couple of
+things about DNA replication before I
+
+ align:start position:0%
+things about DNA replication before I
+ 
+
+ align:start position:0%
+things about DNA replication before I
+dive into this so we all started as a
+
+ align:start position:0%
+dive into this so we all started as a
+ 
+
+ align:start position:0%
+dive into this so we all started as a
+single
+
+ align:start position:0%
+single
+ 
+
+ align:start position:0%
+single
+cell uh I've got a lot more obviously
+
+ align:start position:0%
+cell uh I've got a lot more obviously
+ 
+
+ align:start position:0%
+cell uh I've got a lot more obviously
+because I'm made up of a lot of
+
+ align:start position:0%
+because I'm made up of a lot of
+ 
+
+ align:start position:0%
+because I'm made up of a lot of
+cells if I took all the DNA in my body
+
+ align:start position:0%
+cells if I took all the DNA in my body
+ 
+
+ align:start position:0%
+cells if I took all the DNA in my body
+and I lined up all the molecules in
+
+ align:start position:0%
+and I lined up all the molecules in
+ 
+
+ align:start position:0%
+and I lined up all the molecules in
+it you guys any got any idea how long
+
+ align:start position:0%
+it you guys any got any idea how long
+ 
+
+ align:start position:0%
+it you guys any got any idea how long
+that would
+
+ align:start position:0%
+that would
+ 
+
+ align:start position:0%
+that would
+be who thinks it would reach let's say
+
+ align:start position:0%
+be who thinks it would reach let's say
+ 
+
+ align:start position:0%
+be who thinks it would reach let's say
+across the room
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay choss
+
+ align:start position:0%
+okay choss
+ 
+
+ align:start position:0%
+okay choss
+campus chross
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Cambridge round round the
+
+ align:start position:0%
+Cambridge round round the
+ 
+
+ align:start position:0%
+Cambridge round round the
+world to the
+
+ align:start position:0%
+world to the
+ 
+
+ align:start position:0%
+world to the
+Moon anybody left to the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+sun I got 10 to the 14 cells there's
+
+ align:start position:0%
+sun I got 10 to the 14 cells there's
+ 
+
+ align:start position:0%
+sun I got 10 to the 14 cells there's
+about meter two in each cell 10 to 20
+
+ align:start position:0%
+about meter two in each cell 10 to 20
+ 
+
+ align:start position:0%
+about meter two in each cell 10 to 20
+billion miles of
+
+ align:start position:0%
+billion miles of
+ 
+
+ align:start position:0%
+billion miles of
+DNA in each of our bodies human DNA they
+
+ align:start position:0%
+DNA in each of our bodies human DNA they
+ 
+
+ align:start position:0%
+DNA in each of our bodies human DNA they
+would go back and forth to the sun
+
+ align:start position:0%
+would go back and forth to the sun
+ 
+
+ align:start position:0%
+would go back and forth to the sun
+multiple times so that much DNA had to
+
+ align:start position:0%
+multiple times so that much DNA had to
+ 
+
+ align:start position:0%
+multiple times so that much DNA had to
+get
+
+ align:start position:0%
+get
+ 
+
+ align:start position:0%
+get
+replicated in order for the fertilized
+
+ align:start position:0%
+replicated in order for the fertilized
+ 
+
+ align:start position:0%
+replicated in order for the fertilized
+EG we all started it as to become
+
+ align:start position:0%
+EG we all started it as to become
+ 
+
+ align:start position:0%
+EG we all started it as to become
+you another thing the accuracy of
+
+ align:start position:0%
+you another thing the accuracy of
+ 
+
+ align:start position:0%
+you another thing the accuracy of
+replication is about 10 Theus
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+10th most people including myself don't
+
+ align:start position:0%
+10th most people including myself don't
+ 
+
+ align:start position:0%
+10th most people including myself don't
+have a very good feel for exponents so
+
+ align:start position:0%
+have a very good feel for exponents so
+ 
+
+ align:start position:0%
+have a very good feel for exponents so
+that's one mistake in 10 billion
+
+ align:start position:0%
+that's one mistake in 10 billion
+ 
+
+ align:start position:0%
+that's one mistake in 10 billion
+can we you know could be one mistake in
+
+ align:start position:0%
+can we you know could be one mistake in
+ 
+
+ align:start position:0%
+can we you know could be one mistake in
+10 to the 99th what does one mistake in
+
+ align:start position:0%
+10 to the 99th what does one mistake in
+ 
+
+ align:start position:0%
+10 to the 99th what does one mistake in
+10 billion mean so it is uh let's relate
+
+ align:start position:0%
+10 billion mean so it is uh let's relate
+ 
+
+ align:start position:0%
+10 billion mean so it is uh let's relate
+it to something we know if I was
+
+ align:start position:0%
+it to something we know if I was
+ 
+
+ align:start position:0%
+it to something we know if I was
+typing let's say eight-letter words 60
+
+ align:start position:0%
+typing let's say eight-letter words 60
+ 
+
+ align:start position:0%
+typing let's say eight-letter words 60
+words a
+
+ align:start position:0%
+words a
+ 
+
+ align:start position:0%
+words a
+minute 24 hours a day 7 days a week and
+
+ align:start position:0%
+minute 24 hours a day 7 days a week and
+ 
+
+ align:start position:0%
+minute 24 hours a day 7 days a week and
+I was as good as DNA
+
+ align:start position:0%
+I was as good as DNA
+ 
+
+ align:start position:0%
+I was as good as DNA
+replication how often would I make a
+
+ align:start position:0%
+replication how often would I make a
+ 
+
+ align:start position:0%
+replication how often would I make a
+mistake so you can each think of how
+
+ align:start position:0%
+mistake so you can each think of how
+ 
+
+ align:start position:0%
+mistake so you can each think of how
+long you think that is but if I was good
+
+ align:start position:0%
+long you think that is but if I was good
+ 
+
+ align:start position:0%
+long you think that is but if I was good
+at that on on average I would make a
+
+ align:start position:0%
+at that on on average I would make a
+ 
+
+ align:start position:0%
+at that on on average I would make a
+mistake once every 38
+
+ align:start position:0%
+mistake once every 38
+ 
+
+ align:start position:0%
+mistake once every 38
+years so I'm about to tell you about a
+
+ align:start position:0%
+years so I'm about to tell you about a
+ 
+
+ align:start position:0%
+years so I'm about to tell you about a
+process that's absolutely astonishing in
+
+ align:start position:0%
+process that's absolutely astonishing in
+ 
+
+ align:start position:0%
+process that's absolutely astonishing in
+terms of how you know how fast and how
+
+ align:start position:0%
+terms of how you know how fast and how
+ 
+
+ align:start position:0%
+terms of how you know how fast and how
+much you can do and with an accuracy
+
+ align:start position:0%
+much you can do and with an accuracy
+ 
+
+ align:start position:0%
+much you can do and with an accuracy
+that goes beyond what we're used to in
+
+ align:start position:0%
+that goes beyond what we're used to in
+ 
+
+ align:start position:0%
+that goes beyond what we're used to in
+our our ordinary ordinary life so how
+
+ align:start position:0%
+our our ordinary ordinary life so how
+ 
+
+ align:start position:0%
+our our ordinary ordinary life so how
+does it do this it has to be more than
+
+ align:start position:0%
+does it do this it has to be more than
+ 
+
+ align:start position:0%
+does it do this it has to be more than
+just pulling the the strands apart and
+
+ align:start position:0%
+just pulling the the strands apart and
+ 
+
+ align:start position:0%
+just pulling the the strands apart and
+there's been some confusion as to why
+
+ align:start position:0%
+there's been some confusion as to why
+ 
+
+ align:start position:0%
+there's been some confusion as to why
+I'm emphasizing 5 Prime and 3 Prime well
+
+ align:start position:0%
+I'm emphasizing 5 Prime and 3 Prime well
+ 
+
+ align:start position:0%
+I'm emphasizing 5 Prime and 3 Prime well
+each of these subunits each
+
+ align:start position:0%
+each of these subunits each
+ 
+
+ align:start position:0%
+each of these subunits each
+nucleotide this is a thre Prime
+
+ align:start position:0%
+nucleotide this is a thre Prime
+ 
+
+ align:start position:0%
+nucleotide this is a thre Prime
+hydroxy this is the five Prime position
+
+ align:start position:0%
+hydroxy this is the five Prime position
+ 
+
+ align:start position:0%
+hydroxy this is the five Prime position
+if we were joining together subunits
+
+ align:start position:0%
+if we were joining together subunits
+ 
+
+ align:start position:0%
+if we were joining together subunits
+that had a hook and an eye it would make
+
+ align:start position:0%
+that had a hook and an eye it would make
+ 
+
+ align:start position:0%
+that had a hook and an eye it would make
+a difference because it's not the same
+
+ align:start position:0%
+a difference because it's not the same
+ 
+
+ align:start position:0%
+a difference because it's not the same
+on both ends if we're going to start
+
+ align:start position:0%
+on both ends if we're going to start
+ 
+
+ align:start position:0%
+on both ends if we're going to start
+hooking together it's it's exactly the
+
+ align:start position:0%
+hooking together it's it's exactly the
+ 
+
+ align:start position:0%
+hooking together it's it's exactly the
+same thing when we get to a biochemical
+
+ align:start position:0%
+same thing when we get to a biochemical
+ 
+
+ align:start position:0%
+same thing when we get to a biochemical
+level hydroxy the five Prime n is not
+
+ align:start position:0%
+level hydroxy the five Prime n is not
+ 
+
+ align:start position:0%
+level hydroxy the five Prime n is not
+the same as hydroxy the three prime in
+
+ align:start position:0%
+the same as hydroxy the three prime in
+ 
+
+ align:start position:0%
+the same as hydroxy the three prime in
+because the it's an asymmetric um the
+
+ align:start position:0%
+because the it's an asymmetric um the
+ 
+
+ align:start position:0%
+because the it's an asymmetric um the
+whole thing is is asymmetric so uh
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the enzymes that copy
+
+ align:start position:0%
+the enzymes that copy
+ 
+
+ align:start position:0%
+the enzymes that copy
+DNA are known as as DNA U
+
+ align:start position:0%
+DNA are known as as DNA U
+ 
+
+ align:start position:0%
+DNA are known as as DNA U
+polymerases and it was very difficult
+
+ align:start position:0%
+polymerases and it was very difficult
+ 
+
+ align:start position:0%
+polymerases and it was very difficult
+challenge to uh figure out how they um
+
+ align:start position:0%
+challenge to uh figure out how they um
+ 
+
+ align:start position:0%
+challenge to uh figure out how they um
+how how they operated but Arthur
+
+ align:start position:0%
+how how they operated but Arthur
+ 
+
+ align:start position:0%
+how how they operated but Arthur
+cornberg
+
+ align:start position:0%
+cornberg
+ 
+
+ align:start position:0%
+cornberg
+was the P first person to solve this
+
+ align:start position:0%
+was the P first person to solve this
+ 
+
+ align:start position:0%
+was the P first person to solve this
+problem he was an EXT
+
+ align:start position:0%
+problem he was an EXT
+ 
+
+ align:start position:0%
+problem he was an EXT
+extraordinarily gifted biochemist he's
+
+ align:start position:0%
+extraordinarily gifted biochemist he's
+ 
+
+ align:start position:0%
+extraordinarily gifted biochemist he's
+still at uh he's still at uh Stanford
+
+ align:start position:0%
+still at uh he's still at uh Stanford
+ 
+
+ align:start position:0%
+still at uh he's still at uh Stanford
+and what he found was I'm if we have a
+
+ align:start position:0%
+and what he found was I'm if we have a
+ 
+
+ align:start position:0%
+and what he found was I'm if we have a
+five Prime end this would then be the
+
+ align:start position:0%
+five Prime end this would then be the
+ 
+
+ align:start position:0%
+five Prime end this would then be the
+three prime end and there's a three
+
+ align:start position:0%
+three prime end and there's a three
+ 
+
+ align:start position:0%
+three prime end and there's a three
+prime hydroxy which is this one right
+
+ align:start position:0%
+prime hydroxy which is this one right
+ 
+
+ align:start position:0%
+prime hydroxy which is this one right
+here and this was paired say with a c
+
+ align:start position:0%
+here and this was paired say with a c
+ 
+
+ align:start position:0%
+here and this was paired say with a c
+and an a paired with a uh
+
+ align:start position:0%
+and an a paired with a uh
+ 
+
+ align:start position:0%
+and an a paired with a uh
+a t and let's say a g paired with a a c
+
+ align:start position:0%
+a t and let's say a g paired with a a c
+ 
+
+ align:start position:0%
+a t and let's say a g paired with a a c
+here and let's say the next template
+
+ align:start position:0%
+here and let's say the next template
+ 
+
+ align:start position:0%
+here and let's say the next template
+base
+
+ align:start position:0%
+base
+ 
+
+ align:start position:0%
+base
+was uh let's make it a
+
+ align:start position:0%
+was uh let's make it a
+ 
+
+ align:start position:0%
+was uh let's make it a
+t what Arthur cornberg was able to find
+
+ align:start position:0%
+t what Arthur cornberg was able to find
+ 
+
+ align:start position:0%
+t what Arthur cornberg was able to find
+was an enzyme activity that catalyzed a
+
+ align:start position:0%
+was an enzyme activity that catalyzed a
+ 
+
+ align:start position:0%
+was an enzyme activity that catalyzed a
+template
+
+ align:start position:0%
+template
+ 
+
+ align:start position:0%
+template
+dependent replication of DNA that was
+
+ align:start position:0%
+dependent replication of DNA that was
+ 
+
+ align:start position:0%
+dependent replication of DNA that was
+critical because he had to find
+
+ align:start position:0%
+critical because he had to find
+ 
+
+ align:start position:0%
+critical because he had to find
+somewhere if he broke the cells open
+
+ align:start position:0%
+somewhere if he broke the cells open
+ 
+
+ align:start position:0%
+somewhere if he broke the cells open
+somewhere in that Commish
+
+ align:start position:0%
+somewhere in that Commish
+ 
+
+ align:start position:0%
+somewhere in that Commish
+of uh enzymes and and things from inside
+
+ align:start position:0%
+of uh enzymes and and things from inside
+ 
+
+ align:start position:0%
+of uh enzymes and and things from inside
+a cell there had to be something that
+
+ align:start position:0%
+a cell there had to be something that
+ 
+
+ align:start position:0%
+a cell there had to be something that
+was able to copy DNA so in order to do
+
+ align:start position:0%
+was able to copy DNA so in order to do
+ 
+
+ align:start position:0%
+was able to copy DNA so in order to do
+that he had to work out an assay and he
+
+ align:start position:0%
+that he had to work out an assay and he
+ 
+
+ align:start position:0%
+that he had to work out an assay and he
+also had to have some kind of guess as
+
+ align:start position:0%
+also had to have some kind of guess as
+ 
+
+ align:start position:0%
+also had to have some kind of guess as
+to what the the cell would be using in
+
+ align:start position:0%
+to what the the cell would be using in
+ 
+
+ align:start position:0%
+to what the the cell would be using in
+order to carry out the synthesis well
+
+ align:start position:0%
+order to carry out the synthesis well
+ 
+
+ align:start position:0%
+order to carry out the synthesis well
+one thing was sort of obvious was a was
+
+ align:start position:0%
+one thing was sort of obvious was a was
+ 
+
+ align:start position:0%
+one thing was sort of obvious was a was
+a DNA template because that was being
+
+ align:start position:0%
+a DNA template because that was being
+ 
+
+ align:start position:0%
+a DNA template because that was being
+copied but the other part was you had to
+
+ align:start position:0%
+copied but the other part was you had to
+ 
+
+ align:start position:0%
+copied but the other part was you had to
+have energy to form a Cove valent Bond
+
+ align:start position:0%
+have energy to form a Cove valent Bond
+ 
+
+ align:start position:0%
+have energy to form a Cove valent Bond
+Bond so somehow there had to be
+
+ align:start position:0%
+Bond so somehow there had to be
+ 
+
+ align:start position:0%
+Bond so somehow there had to be
+something that was sort of activated
+
+ align:start position:0%
+something that was sort of activated
+ 
+
+ align:start position:0%
+something that was sort of activated
+with the energy built into the molecule
+
+ align:start position:0%
+with the energy built into the molecule
+ 
+
+ align:start position:0%
+with the energy built into the molecule
+so that thermodynamically the whole
+
+ align:start position:0%
+so that thermodynamically the whole
+ 
+
+ align:start position:0%
+so that thermodynamically the whole
+thing would slide downhill when you made
+
+ align:start position:0%
+thing would slide downhill when you made
+ 
+
+ align:start position:0%
+thing would slide downhill when you made
+a when you made a bond and he knew that
+
+ align:start position:0%
+a when you made a bond and he knew that
+ 
+
+ align:start position:0%
+a when you made a bond and he knew that
+the cell
+
+ align:start position:0%
+the cell
+ 
+
+ align:start position:0%
+the cell
+had triphosphates just the same type
+
+ align:start position:0%
+had triphosphates just the same type
+ 
+
+ align:start position:0%
+had triphosphates just the same type
+that we talked about with when we talked
+
+ align:start position:0%
+that we talked about with when we talked
+ 
+
+ align:start position:0%
+that we talked about with when we talked
+about
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+ATP
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so this would
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+be a deoxy Riu uh
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+nucleotide
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+triphosphate and he was able to uh make
+
+ align:start position:0%
+triphosphate and he was able to uh make
+ 
+
+ align:start position:0%
+triphosphate and he was able to uh make
+a guess cuz he had to try things until
+
+ align:start position:0%
+a guess cuz he had to try things until
+ 
+
+ align:start position:0%
+a guess cuz he had to try things until
+he found something was work that would
+
+ align:start position:0%
+he found something was work that would
+ 
+
+ align:start position:0%
+he found something was work that would
+work that this was what's used in DNA
+
+ align:start position:0%
+work that this was what's used in DNA
+ 
+
+ align:start position:0%
+work that this was what's used in DNA
+synthesis so this
+
+ align:start position:0%
+synthesis so this
+ 
+
+ align:start position:0%
+synthesis so this
+hydroxy ultimately attacks this uh
+
+ align:start position:0%
+hydroxy ultimately attacks this uh
+ 
+
+ align:start position:0%
+hydroxy ultimately attacks this uh
+phosphate here and these two other
+
+ align:start position:0%
+phosphate here and these two other
+ 
+
+ align:start position:0%
+phosphate here and these two other
+phosphates then come off as a as a
+
+ align:start position:0%
+phosphates then come off as a as a
+ 
+
+ align:start position:0%
+phosphates then come off as a as a
+leaving group so if we thought of it as
+
+ align:start position:0%
+leaving group so if we thought of it as
+ 
+
+ align:start position:0%
+leaving group so if we thought of it as
+a a
+
+ align:start position:0%
+a a
+ 
+
+ align:start position:0%
+a a
+p like this with two more PS here these
+
+ align:start position:0%
+p like this with two more PS here these
+ 
+
+ align:start position:0%
+p like this with two more PS here these
+two come off and you get a a new bond
+
+ align:start position:0%
+two come off and you get a a new bond
+ 
+
+ align:start position:0%
+two come off and you get a a new bond
+form
+
+ align:start position:0%
+form
+ 
+
+ align:start position:0%
+form
+to
+
+ align:start position:0%
+to
+ 
+
+ align:start position:0%
+to
+the to the phosphate and so what
+
+ align:start position:0%
+the to the phosphate and so what
+ 
+
+ align:start position:0%
+the to the phosphate and so what
+cornberg then was able to find by using
+
+ align:start position:0%
+cornberg then was able to find by using
+ 
+
+ align:start position:0%
+cornberg then was able to find by using
+a DNA template that had this sort
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+of structure
+
+ align:start position:0%
+of structure
+ 
+
+ align:start position:0%
+of structure
+and PP
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+p a like this that he was now able to
+
+ align:start position:0%
+p a like this that he was now able to
+ 
+
+ align:start position:0%
+p a like this that he was now able to
+get an A added here here this new this
+
+ align:start position:0%
+get an A added here here this new this
+ 
+
+ align:start position:0%
+get an A added here here this new this
+hydroxy here became the new uh hydroxy
+
+ align:start position:0%
+hydroxy here became the new uh hydroxy
+ 
+
+ align:start position:0%
+hydroxy here became the new uh hydroxy
+and so the the the direction of
+
+ align:start position:0%
+and so the the the direction of
+ 
+
+ align:start position:0%
+and so the the the direction of
+synthesis this strand is the other way
+
+ align:start position:0%
+synthesis this strand is the other way
+ 
+
+ align:start position:0%
+synthesis this strand is the other way
+so the direction of
+
+ align:start position:0%
+so the direction of
+ 
+
+ align:start position:0%
+so the direction of
+synthesis of a DNA polymerize polymerase
+
+ align:start position:0%
+synthesis of a DNA polymerize polymerase
+ 
+
+ align:start position:0%
+synthesis of a DNA polymerize polymerase
+it's polymerizing in the five Prime to 2
+
+ align:start position:0%
+it's polymerizing in the five Prime to 2
+ 
+
+ align:start position:0%
+it's polymerizing in the five Prime to 2
+three prime Direction This was again an
+
+ align:start position:0%
+three prime Direction This was again an
+ 
+
+ align:start position:0%
+three prime Direction This was again an
+amazing Discovery because it was the
+
+ align:start position:0%
+amazing Discovery because it was the
+ 
+
+ align:start position:0%
+amazing Discovery because it was the
+first time that anyone had found an
+
+ align:start position:0%
+first time that anyone had found an
+ 
+
+ align:start position:0%
+first time that anyone had found an
+enzyme that could copy copy DNA Arthur
+
+ align:start position:0%
+enzyme that could copy copy DNA Arthur
+ 
+
+ align:start position:0%
+enzyme that could copy copy DNA Arthur
+cornberg got a Nobel Prize for it but at
+
+ align:start position:0%
+cornberg got a Nobel Prize for it but at
+ 
+
+ align:start position:0%
+cornberg got a Nobel Prize for it but at
+this point um actually genetics came in
+
+ align:start position:0%
+this point um actually genetics came in
+ 
+
+ align:start position:0%
+this point um actually genetics came in
+because there was a scientist John Karn
+
+ align:start position:0%
+because there was a scientist John Karn
+ 
+
+ align:start position:0%
+because there was a scientist John Karn
+who was at that point down in Cold
+
+ align:start position:0%
+who was at that point down in Cold
+ 
+
+ align:start position:0%
+who was at that point down in Cold
+Spring Harbor they told you the other
+
+ align:start position:0%
+Spring Harbor they told you the other
+ 
+
+ align:start position:0%
+Spring Harbor they told you the other
+day and uh John didn't think that in
+
+ align:start position:0%
+day and uh John didn't think that in
+ 
+
+ align:start position:0%
+day and uh John didn't think that in
+spite of the fact that uh Arthur had
+
+ align:start position:0%
+spite of the fact that uh Arthur had
+ 
+
+ align:start position:0%
+spite of the fact that uh Arthur had
+found a DN a DNA plase that had all the
+
+ align:start position:0%
+found a DN a DNA plase that had all the
+ 
+
+ align:start position:0%
+found a DN a DNA plase that had all the
+properties that you'd expect for copying
+
+ align:start position:0%
+properties that you'd expect for copying
+ 
+
+ align:start position:0%
+properties that you'd expect for copying
+uh DNA he didn't think that was the the
+
+ align:start position:0%
+uh DNA he didn't think that was the the
+ 
+
+ align:start position:0%
+uh DNA he didn't think that was the the
+one that actually copied the DNA
+
+ align:start position:0%
+one that actually copied the DNA
+ 
+
+ align:start position:0%
+one that actually copied the DNA
+necessary for cellular replication so he
+
+ align:start position:0%
+necessary for cellular replication so he
+ 
+
+ align:start position:0%
+necessary for cellular replication so he
+reasoned if he was right he'd be able to
+
+ align:start position:0%
+reasoned if he was right he'd be able to
+ 
+
+ align:start position:0%
+reasoned if he was right he'd be able to
+find a mutation that would eliminate the
+
+ align:start position:0%
+find a mutation that would eliminate the
+ 
+
+ align:start position:0%
+find a mutation that would eliminate the
+activity of that enzyme in the cell
+
+ align:start position:0%
+activity of that enzyme in the cell
+ 
+
+ align:start position:0%
+activity of that enzyme in the cell
+would still live and so they did a
+
+ align:start position:0%
+would still live and so they did a
+ 
+
+ align:start position:0%
+would still live and so they did a
+screening and they was a lot of work but
+
+ align:start position:0%
+screening and they was a lot of work but
+ 
+
+ align:start position:0%
+screening and they was a lot of work but
+they eventually found a mutant of ecoli
+
+ align:start position:0%
+they eventually found a mutant of ecoli
+ 
+
+ align:start position:0%
+they eventually found a mutant of ecoli
+that lacked this DNA polymerase that
+
+ align:start position:0%
+that lacked this DNA polymerase that
+ 
+
+ align:start position:0%
+that lacked this DNA polymerase that
+Arthur cornberg discovered and the Stell
+
+ align:start position:0%
+Arthur cornberg discovered and the Stell
+ 
+
+ align:start position:0%
+Arthur cornberg discovered and the Stell
+was still alive was still replicating
+
+ align:start position:0%
+was still alive was still replicating
+ 
+
+ align:start position:0%
+was still alive was still replicating
+its DNA so it told both John and then
+
+ align:start position:0%
+its DNA so it told both John and then
+ 
+
+ align:start position:0%
+its DNA so it told both John and then
+Arthur there must be another enzyme in
+
+ align:start position:0%
+Arthur there must be another enzyme in
+ 
+
+ align:start position:0%
+Arthur there must be another enzyme in
+the cell and so Arthur went back and now
+
+ align:start position:0%
+the cell and so Arthur went back and now
+ 
+
+ align:start position:0%
+the cell and so Arthur went back and now
+working in a mutant that was missing
+
+ align:start position:0%
+working in a mutant that was missing
+ 
+
+ align:start position:0%
+working in a mutant that was missing
+this first plase he discovered he found
+
+ align:start position:0%
+this first plase he discovered he found
+ 
+
+ align:start position:0%
+this first plase he discovered he found
+the one that really replicates the DNA
+
+ align:start position:0%
+the one that really replicates the DNA
+ 
+
+ align:start position:0%
+the one that really replicates the DNA
+the first one's important too it's
+
+ align:start position:0%
+the first one's important too it's
+ 
+
+ align:start position:0%
+the first one's important too it's
+needed for DNA repair I'm going to talk
+
+ align:start position:0%
+needed for DNA repair I'm going to talk
+ 
+
+ align:start position:0%
+needed for DNA repair I'm going to talk
+to you about that in next lecture but
+
+ align:start position:0%
+to you about that in next lecture but
+ 
+
+ align:start position:0%
+to you about that in next lecture but
+it's not absolutely crucial for life and
+
+ align:start position:0%
+it's not absolutely crucial for life and
+ 
+
+ align:start position:0%
+it's not absolutely crucial for life and
+there's an interplay of genetics and
+
+ align:start position:0%
+there's an interplay of genetics and
+ 
+
+ align:start position:0%
+there's an interplay of genetics and
+biochemistry and you'll see I'm just
+
+ align:start position:0%
+biochemistry and you'll see I'm just
+ 
+
+ align:start position:0%
+biochemistry and you'll see I'm just
+sort of foreshadowing what we're going
+
+ align:start position:0%
+sort of foreshadowing what we're going
+ 
+
+ align:start position:0%
+sort of foreshadowing what we're going
+to get to when we talk about the
+
+ align:start position:0%
+to get to when we talk about the
+ 
+
+ align:start position:0%
+to get to when we talk about the
+genetics uh of this and I know a couple
+
+ align:start position:0%
+genetics uh of this and I know a couple
+ 
+
+ align:start position:0%
+genetics uh of this and I know a couple
+of you clearly were frustrated about me
+
+ align:start position:0%
+of you clearly were frustrated about me
+ 
+
+ align:start position:0%
+of you clearly were frustrated about me
+showing you pictures of the people who
+
+ align:start position:0%
+showing you pictures of the people who
+ 
+
+ align:start position:0%
+showing you pictures of the people who
+did this but nevertheless since this was
+
+ align:start position:0%
+did this but nevertheless since this was
+ 
+
+ align:start position:0%
+did this but nevertheless since this was
+such a historic event a couple of years
+
+ align:start position:0%
+such a historic event a couple of years
+ 
+
+ align:start position:0%
+such a historic event a couple of years
+ago uh at Cold Spring Harbor this you
+
+ align:start position:0%
+ago uh at Cold Spring Harbor this you
+ 
+
+ align:start position:0%
+ago uh at Cold Spring Harbor this you
+see the the Helix model down there there
+
+ align:start position:0%
+see the the Helix model down there there
+ 
+
+ align:start position:0%
+see the the Helix model down there there
+was Jim Watson opening the Symposium
+
+ align:start position:0%
+was Jim Watson opening the Symposium
+ 
+
+ align:start position:0%
+was Jim Watson opening the Symposium
+when I got up to talk I said well I'm
+
+ align:start position:0%
+when I got up to talk I said well I'm
+ 
+
+ align:start position:0%
+when I got up to talk I said well I'm
+going to take I told my students I'd let
+
+ align:start position:0%
+going to take I told my students I'd let
+ 
+
+ align:start position:0%
+going to take I told my students I'd let
+them know what it was like when it was
+
+ align:start position:0%
+them know what it was like when it was
+ 
+
+ align:start position:0%
+them know what it was like when it was
+there so I took out a camera and I took
+
+ align:start position:0%
+there so I took out a camera and I took
+ 
+
+ align:start position:0%
+there so I took out a camera and I took
+a picture of the audience and so there
+
+ align:start position:0%
+a picture of the audience and so there
+ 
+
+ align:start position:0%
+a picture of the audience and so there
+are a bunch of Nobel laurates and types
+
+ align:start position:0%
+are a bunch of Nobel laurates and types
+ 
+
+ align:start position:0%
+are a bunch of Nobel laurates and types
+here who are sitting there smiling for
+
+ align:start position:0%
+here who are sitting there smiling for
+ 
+
+ align:start position:0%
+here who are sitting there smiling for
+you guys in in the and there was Arthur
+
+ align:start position:0%
+you guys in in the and there was Arthur
+ 
+
+ align:start position:0%
+you guys in in the and there was Arthur
+cornberg giving his talk now
+
+ align:start position:0%
+cornberg giving his talk now
+ 
+
+ align:start position:0%
+cornberg giving his talk now
+um these DNA U plases are incredible
+
+ align:start position:0%
+um these DNA U plases are incredible
+ 
+
+ align:start position:0%
+um these DNA U plases are incredible
+protein machines the crystal structures
+
+ align:start position:0%
+protein machines the crystal structures
+ 
+
+ align:start position:0%
+protein machines the crystal structures
+of a DNA plase operating plases
+
+ align:start position:0%
+of a DNA plase operating plases
+ 
+
+ align:start position:0%
+of a DNA plase operating plases
+operating their template have been
+
+ align:start position:0%
+operating their template have been
+ 
+
+ align:start position:0%
+operating their template have been
+solved and you can solve depending on
+
+ align:start position:0%
+solved and you can solve depending on
+ 
+
+ align:start position:0%
+solved and you can solve depending on
+how many diffractions you can get you
+
+ align:start position:0%
+how many diffractions you can get you
+ 
+
+ align:start position:0%
+how many diffractions you can get you
+can get a model that's more or more
+
+ align:start position:0%
+can get a model that's more or more
+ 
+
+ align:start position:0%
+can get a model that's more or more
+detailed and there have been some very
+
+ align:start position:0%
+detailed and there have been some very
+ 
+
+ align:start position:0%
+detailed and there have been some very
+high resolution models of DNA plases
+
+ align:start position:0%
+high resolution models of DNA plases
+ 
+
+ align:start position:0%
+high resolution models of DNA plases
+this blue and white stuff is the surface
+
+ align:start position:0%
+this blue and white stuff is the surface
+ 
+
+ align:start position:0%
+this blue and white stuff is the surface
+of the protein and this is sort of the
+
+ align:start position:0%
+of the protein and this is sort of the
+ 
+
+ align:start position:0%
+of the protein and this is sort of the
+template and the and the the various
+
+ align:start position:0%
+template and the and the the various
+ 
+
+ align:start position:0%
+template and the and the the various
+parts I'm just uh to give you an idea
+
+ align:start position:0%
+parts I'm just uh to give you an idea
+ 
+
+ align:start position:0%
+parts I'm just uh to give you an idea
+here these tracings of the of the shapes
+
+ align:start position:0%
+here these tracings of the of the shapes
+ 
+
+ align:start position:0%
+here these tracings of the of the shapes
+of the the electron density and you can
+
+ align:start position:0%
+of the the electron density and you can
+ 
+
+ align:start position:0%
+of the the electron density and you can
+see how the crystallographers have fit
+
+ align:start position:0%
+see how the crystallographers have fit
+ 
+
+ align:start position:0%
+see how the crystallographers have fit
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+nucleotides uh into these uh in the
+
+ align:start position:0%
+nucleotides uh into these uh in the
+ 
+
+ align:start position:0%
+nucleotides uh into these uh in the
+right in the right in the crystal into
+
+ align:start position:0%
+right in the right in the crystal into
+ 
+
+ align:start position:0%
+right in the right in the crystal into
+these electron densities and here
+
+ align:start position:0%
+these electron densities and here
+ 
+
+ align:start position:0%
+these electron densities and here
+putting it together a bit is in the blue
+
+ align:start position:0%
+putting it together a bit is in the blue
+ 
+
+ align:start position:0%
+putting it together a bit is in the blue
+is the secondary structure of the
+
+ align:start position:0%
+is the secondary structure of the
+ 
+
+ align:start position:0%
+is the secondary structure of the
+protein and and the templates and
+
+ align:start position:0%
+protein and and the templates and
+ 
+
+ align:start position:0%
+protein and and the templates and
+whatnot and I don't expect you see very
+
+ align:start position:0%
+whatnot and I don't expect you see very
+ 
+
+ align:start position:0%
+whatnot and I don't expect you see very
+much in that but the point I want to
+
+ align:start position:0%
+much in that but the point I want to
+ 
+
+ align:start position:0%
+much in that but the point I want to
+tell you I want to sort of just set you
+
+ align:start position:0%
+tell you I want to sort of just set you
+ 
+
+ align:start position:0%
+tell you I want to sort of just set you
+up to show you this little movie because
+
+ align:start position:0%
+up to show you this little movie because
+ 
+
+ align:start position:0%
+up to show you this little movie because
+this is an DNA polymerase is a
+
+ align:start position:0%
+this is an DNA polymerase is a
+ 
+
+ align:start position:0%
+this is an DNA polymerase is a
+incredible machines they copy at about a
+
+ align:start position:0%
+incredible machines they copy at about a
+ 
+
+ align:start position:0%
+incredible machines they copy at about a
+thousand nucleotides a second and their
+
+ align:start position:0%
+thousand nucleotides a second and their
+ 
+
+ align:start position:0%
+thousand nucleotides a second and their
+accuracy is is really amazing and I'll
+
+ align:start position:0%
+accuracy is is really amazing and I'll
+ 
+
+ align:start position:0%
+accuracy is is really amazing and I'll
+tell you all the tricks to the accuracy
+
+ align:start position:0%
+tell you all the tricks to the accuracy
+ 
+
+ align:start position:0%
+tell you all the tricks to the accuracy
+in the next lecture but I want to show
+
+ align:start position:0%
+in the next lecture but I want to show
+ 
+
+ align:start position:0%
+in the next lecture but I want to show
+you this little movie because it this is
+
+ align:start position:0%
+you this little movie because it this is
+ 
+
+ align:start position:0%
+you this little movie because it this is
+a a little s sort of a simulation of
+
+ align:start position:0%
+a a little s sort of a simulation of
+ 
+
+ align:start position:0%
+a a little s sort of a simulation of
+what must happen every time a nucleotide
+
+ align:start position:0%
+what must happen every time a nucleotide
+ 
+
+ align:start position:0%
+what must happen every time a nucleotide
+is added now the yellow here is the
+
+ align:start position:0%
+is added now the yellow here is the
+ 
+
+ align:start position:0%
+is added now the yellow here is the
+we'll see this over and over again so uh
+
+ align:start position:0%
+we'll see this over and over again so uh
+ 
+
+ align:start position:0%
+we'll see this over and over again so uh
+I'll take it in pieces the yellow and
+
+ align:start position:0%
+I'll take it in pieces the yellow and
+ 
+
+ align:start position:0%
+I'll take it in pieces the yellow and
+the orange are the are the secondary
+
+ align:start position:0%
+the orange are the are the secondary
+ 
+
+ align:start position:0%
+the orange are the are the secondary
+structures that's an alpha Helix and
+
+ align:start position:0%
+structures that's an alpha Helix and
+ 
+
+ align:start position:0%
+structures that's an alpha Helix and
+certainly one thing you can see is
+
+ align:start position:0%
+certainly one thing you can see is
+ 
+
+ align:start position:0%
+certainly one thing you can see is
+happening as I'm sure as we're looking
+
+ align:start position:0%
+happening as I'm sure as we're looking
+ 
+
+ align:start position:0%
+happening as I'm sure as we're looking
+at this is this the parts of the protein
+
+ align:start position:0%
+at this is this the parts of the protein
+ 
+
+ align:start position:0%
+at this is this the parts of the protein
+are moving during this you can see this
+
+ align:start position:0%
+are moving during this you can see this
+ 
+
+ align:start position:0%
+are moving during this you can see this
+Alpha Helix is sort of swinging up and
+
+ align:start position:0%
+Alpha Helix is sort of swinging up and
+ 
+
+ align:start position:0%
+Alpha Helix is sort of swinging up and
+Swinging back down now what's what's
+
+ align:start position:0%
+Swinging back down now what's what's
+ 
+
+ align:start position:0%
+Swinging back down now what's what's
+over here is the over on this over here
+
+ align:start position:0%
+over here is the over on this over here
+ 
+
+ align:start position:0%
+over here is the over on this over here
+is the template base that's the base
+
+ align:start position:0%
+is the template base that's the base
+ 
+
+ align:start position:0%
+is the template base that's the base
+that's that corresponds to the T that I
+
+ align:start position:0%
+that's that corresponds to the T that I
+ 
+
+ align:start position:0%
+that's that corresponds to the T that I
+was just showing you here this is the
+
+ align:start position:0%
+was just showing you here this is the
+ 
+
+ align:start position:0%
+was just showing you here this is the
+incoming nucleotide there is the
+
+ align:start position:0%
+incoming nucleotide there is the
+ 
+
+ align:start position:0%
+incoming nucleotide there is the
+triphosphate coming down here and in
+
+ align:start position:0%
+triphosphate coming down here and in
+ 
+
+ align:start position:0%
+triphosphate coming down here and in
+fact you just see those two phosphates
+
+ align:start position:0%
+fact you just see those two phosphates
+ 
+
+ align:start position:0%
+fact you just see those two phosphates
+going so what's happening here here this
+
+ align:start position:0%
+going so what's happening here here this
+ 
+
+ align:start position:0%
+going so what's happening here here this
+is going to be the end of the the
+
+ align:start position:0%
+is going to be the end of the the
+ 
+
+ align:start position:0%
+is going to be the end of the the
+growing chain it's going to attack right
+
+ align:start position:0%
+growing chain it's going to attack right
+ 
+
+ align:start position:0%
+growing chain it's going to attack right
+there join the phosphate and the
+
+ align:start position:0%
+there join the phosphate and the
+ 
+
+ align:start position:0%
+there join the phosphate and the
+pyrophosphate will leave and when the if
+
+ align:start position:0%
+pyrophosphate will leave and when the if
+ 
+
+ align:start position:0%
+pyrophosphate will leave and when the if
+you'll take a look when you see this
+
+ align:start position:0%
+you'll take a look when you see this
+ 
+
+ align:start position:0%
+you'll take a look when you see this
+movement of this this Helix from the
+
+ align:start position:0%
+movement of this this Helix from the
+ 
+
+ align:start position:0%
+movement of this this Helix from the
+beginning state to up to here you'll see
+
+ align:start position:0%
+beginning state to up to here you'll see
+ 
+
+ align:start position:0%
+beginning state to up to here you'll see
+what happens is it's squeezing the
+
+ align:start position:0%
+what happens is it's squeezing the
+ 
+
+ align:start position:0%
+what happens is it's squeezing the
+template base and
+
+ align:start position:0%
+template base and
+ 
+
+ align:start position:0%
+template base and
+the uh incoming nucleotide together what
+
+ align:start position:0%
+the uh incoming nucleotide together what
+ 
+
+ align:start position:0%
+the uh incoming nucleotide together what
+it's really doing is testing for the
+
+ align:start position:0%
+it's really doing is testing for the
+ 
+
+ align:start position:0%
+it's really doing is testing for the
+correct shape remember the shape of an
+
+ align:start position:0%
+correct shape remember the shape of an
+ 
+
+ align:start position:0%
+correct shape remember the shape of an
+at base pair and a GC based pair is the
+
+ align:start position:0%
+at base pair and a GC based pair is the
+ 
+
+ align:start position:0%
+at base pair and a GC based pair is the
+same and if those of you who are
+
+ align:start position:0%
+same and if those of you who are
+ 
+
+ align:start position:0%
+same and if those of you who are
+confused about guanine and the keto enol
+
+ align:start position:0%
+confused about guanine and the keto enol
+ 
+
+ align:start position:0%
+confused about guanine and the keto enol
+thing try to draw hydrogen bonds with
+
+ align:start position:0%
+thing try to draw hydrogen bonds with
+ 
+
+ align:start position:0%
+thing try to draw hydrogen bonds with
+the enol form of of guanine and see how
+
+ align:start position:0%
+the enol form of of guanine and see how
+ 
+
+ align:start position:0%
+the enol form of of guanine and see how
+and see how you do I think he'll you'll
+
+ align:start position:0%
+and see how you do I think he'll you'll
+ 
+
+ align:start position:0%
+and see how you do I think he'll you'll
+begin to understand of it so this is one
+
+ align:start position:0%
+begin to understand of it so this is one
+ 
+
+ align:start position:0%
+begin to understand of it so this is one
+of the so at the heart of life is
+
+ align:start position:0%
+of the so at the heart of life is
+ 
+
+ align:start position:0%
+of the so at the heart of life is
+something that can copy DNA and there
+
+ align:start position:0%
+something that can copy DNA and there
+ 
+
+ align:start position:0%
+something that can copy DNA and there
+are these exquisitely beautiful machines
+
+ align:start position:0%
+are these exquisitely beautiful machines
+ 
+
+ align:start position:0%
+are these exquisitely beautiful machines
+uh the replicative machine in in E coli
+
+ align:start position:0%
+uh the replicative machine in in E coli
+ 
+
+ align:start position:0%
+uh the replicative machine in in E coli
+has 18 proteins and the ones and our
+
+ align:start position:0%
+has 18 proteins and the ones and our
+ 
+
+ align:start position:0%
+has 18 proteins and the ones and our
+bodies are even more sophisticated with
+
+ align:start position:0%
+bodies are even more sophisticated with
+ 
+
+ align:start position:0%
+bodies are even more sophisticated with
+even more with more parts
+
+ align:start position:0%
+even more with more parts
+ 
+
+ align:start position:0%
+even more with more parts
+um okay but
+
+ align:start position:0%
+um okay but
+ 
+
+ align:start position:0%
+um okay but
+to to replicate a DNA molecule there's
+
+ align:start position:0%
+to to replicate a DNA molecule there's
+ 
+
+ align:start position:0%
+to to replicate a DNA molecule there's
+an another problem that comes up because
+
+ align:start position:0%
+an another problem that comes up because
+ 
+
+ align:start position:0%
+an another problem that comes up because
+DNA polymerases
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+copy see grow let's
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+see grow
+
+ align:start position:0%
+see grow
+ 
+
+ align:start position:0%
+see grow
+chains in a five Prime to three prime
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Direction
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and they
+
+ align:start position:0%
+and they
+ 
+
+ align:start position:0%
+and they
+need a thre Prime hydroxy
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Terminus so they won't work if you just
+
+ align:start position:0%
+Terminus so they won't work if you just
+ 
+
+ align:start position:0%
+Terminus so they won't work if you just
+gave it a single strand of of
+
+ align:start position:0%
+gave it a single strand of of
+ 
+
+ align:start position:0%
+gave it a single strand of of
+DNA no DNA polymerase can handle that it
+
+ align:start position:0%
+DNA no DNA polymerase can handle that it
+ 
+
+ align:start position:0%
+DNA no DNA polymerase can handle that it
+has to have something like this where
+
+ align:start position:0%
+has to have something like this where
+ 
+
+ align:start position:0%
+has to have something like this where
+there's a template
+
+ align:start position:0%
+there's a template
+ 
+
+ align:start position:0%
+there's a template
+strand
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and there's what's known as the primer
+
+ align:start position:0%
+and there's what's known as the primer
+ 
+
+ align:start position:0%
+and there's what's known as the primer
+strand so there has to be something that
+
+ align:start position:0%
+strand so there has to be something that
+ 
+
+ align:start position:0%
+strand so there has to be something that
+has the three prime hydroxy and there
+
+ align:start position:0%
+has the three prime hydroxy and there
+ 
+
+ align:start position:0%
+has the three prime hydroxy and there
+has to be something that's going to
+
+ align:start position:0%
+has to be something that's going to
+ 
+
+ align:start position:0%
+has to be something that's going to
+provide the template that's going to be
+
+ align:start position:0%
+provide the template that's going to be
+ 
+
+ align:start position:0%
+provide the template that's going to be
+copied so if we pull strands apart like
+
+ align:start position:0%
+copied so if we pull strands apart like
+ 
+
+ align:start position:0%
+copied so if we pull strands apart like
+this with five Prime to 3 Prime then
+
+ align:start position:0%
+this with five Prime to 3 Prime then
+ 
+
+ align:start position:0%
+this with five Prime to 3 Prime then
+this will be five Prime to 3 Prime
+
+ align:start position:0%
+this will be five Prime to 3 Prime
+ 
+
+ align:start position:0%
+this will be five Prime to 3 Prime
+running in the opposite direction
+
+ align:start position:0%
+running in the opposite direction
+ 
+
+ align:start position:0%
+running in the opposite direction
+if we
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+have uh template like this this is okay
+
+ align:start position:0%
+have uh template like this this is okay
+ 
+
+ align:start position:0%
+have uh template like this this is okay
+because the Strand here can be copied
+
+ align:start position:0%
+because the Strand here can be copied
+ 
+
+ align:start position:0%
+because the Strand here can be copied
+five Prime to three prime
+
+ align:start position:0%
+five Prime to three prime
+ 
+
+ align:start position:0%
+five Prime to three prime
+the this is the New
+
+ align:start position:0%
+the this is the New
+ 
+
+ align:start position:0%
+the this is the New
+Strand being
+
+ align:start position:0%
+Strand being
+ 
+
+ align:start position:0%
+Strand being
+synthesized by the DNA
+
+ align:start position:0%
+synthesized by the DNA
+ 
+
+ align:start position:0%
+synthesized by the DNA
+polymerase but what about the other
+
+ align:start position:0%
+polymerase but what about the other
+ 
+
+ align:start position:0%
+polymerase but what about the other
+strand the replication fork is moving in
+
+ align:start position:0%
+strand the replication fork is moving in
+ 
+
+ align:start position:0%
+strand the replication fork is moving in
+this
+
+ align:start position:0%
+this
+ 
+
+ align:start position:0%
+this
+direction but if the so here is the 3 to
+
+ align:start position:0%
+direction but if the so here is the 3 to
+ 
+
+ align:start position:0%
+direction but if the so here is the 3 to
+five Prime Direction here so if the DNA
+
+ align:start position:0%
+five Prime Direction here so if the DNA
+ 
+
+ align:start position:0%
+five Prime Direction here so if the DNA
+polymerase is going to be copying this
+
+ align:start position:0%
+polymerase is going to be copying this
+ 
+
+ align:start position:0%
+polymerase is going to be copying this
+strand it's going to be moving backwards
+
+ align:start position:0%
+strand it's going to be moving backwards
+ 
+
+ align:start position:0%
+strand it's going to be moving backwards
+to the
+
+ align:start position:0%
+to the
+ 
+
+ align:start position:0%
+to the
+direction of the replication fork now I
+
+ align:start position:0%
+direction of the replication fork now I
+ 
+
+ align:start position:0%
+direction of the replication fork now I
+guess Evolution nature could have
+
+ align:start position:0%
+guess Evolution nature could have
+ 
+
+ align:start position:0%
+guess Evolution nature could have
+selected for two types of DNA
+
+ align:start position:0%
+selected for two types of DNA
+ 
+
+ align:start position:0%
+selected for two types of DNA
+polymerases one that copies 5 Prime to 3
+
+ align:start position:0%
+polymerases one that copies 5 Prime to 3
+ 
+
+ align:start position:0%
+polymerases one that copies 5 Prime to 3
+Prime and one that cop copies in the in
+
+ align:start position:0%
+Prime and one that cop copies in the in
+ 
+
+ align:start position:0%
+Prime and one that cop copies in the in
+the opposite direction but it didn't and
+
+ align:start position:0%
+the opposite direction but it didn't and
+ 
+
+ align:start position:0%
+the opposite direction but it didn't and
+there are a number of theoretical
+
+ align:start position:0%
+there are a number of theoretical
+ 
+
+ align:start position:0%
+there are a number of theoretical
+reasons that we could discuss in more
+
+ align:start position:0%
+reasons that we could discuss in more
+ 
+
+ align:start position:0%
+reasons that we could discuss in more
+advanced course perhaps for why that's
+
+ align:start position:0%
+advanced course perhaps for why that's
+ 
+
+ align:start position:0%
+advanced course perhaps for why that's
+true but in fact what it does is it uses
+
+ align:start position:0%
+true but in fact what it does is it uses
+ 
+
+ align:start position:0%
+true but in fact what it does is it uses
+the same pimas so as these things peel
+
+ align:start position:0%
+the same pimas so as these things peel
+ 
+
+ align:start position:0%
+the same pimas so as these things peel
+apart the plas works in the other
+
+ align:start position:0%
+apart the plas works in the other
+ 
+
+ align:start position:0%
+apart the plas works in the other
+direction but there's another problem
+
+ align:start position:0%
+direction but there's another problem
+ 
+
+ align:start position:0%
+direction but there's another problem
+there's no if I just peel it apart like
+
+ align:start position:0%
+there's no if I just peel it apart like
+ 
+
+ align:start position:0%
+there's no if I just peel it apart like
+this there's no three prime
+
+ align:start position:0%
+this there's no three prime
+ 
+
+ align:start position:0%
+this there's no three prime
+hydroxy so it took people quite a few
+
+ align:start position:0%
+hydroxy so it took people quite a few
+ 
+
+ align:start position:0%
+hydroxy so it took people quite a few
+years to figure fure out the strategy
+
+ align:start position:0%
+years to figure fure out the strategy
+ 
+
+ align:start position:0%
+years to figure fure out the strategy
+that's used in nature nature has a
+
+ align:start position:0%
+that's used in nature nature has a
+ 
+
+ align:start position:0%
+that's used in nature nature has a
+special enzyme that makes a little piece
+
+ align:start position:0%
+special enzyme that makes a little piece
+ 
+
+ align:start position:0%
+special enzyme that makes a little piece
+of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+RNA it's called
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+a an RNA primer what it does is it
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+provides a three prime
+
+ align:start position:0%
+provides a three prime
+ 
+
+ align:start position:0%
+provides a three prime
+hydroxy and once you have the three
+
+ align:start position:0%
+hydroxy and once you have the three
+ 
+
+ align:start position:0%
+hydroxy and once you have the three
+prime hydroxy at the end of a little RNA
+
+ align:start position:0%
+prime hydroxy at the end of a little RNA
+ 
+
+ align:start position:0%
+prime hydroxy at the end of a little RNA
+chain then the DNA
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+polymerase can be made five Prime to
+
+ align:start position:0%
+polymerase can be made five Prime to
+ 
+
+ align:start position:0%
+polymerase can be made five Prime to
+three prime so as the as you peel open
+
+ align:start position:0%
+three prime so as the as you peel open
+ 
+
+ align:start position:0%
+three prime so as the as you peel open
+the replication fork then you little
+
+ align:start position:0%
+the replication fork then you little
+ 
+
+ align:start position:0%
+the replication fork then you little
+pieces of of RNA are used to make the a
+
+ align:start position:0%
+pieces of of RNA are used to make the a
+ 
+
+ align:start position:0%
+pieces of of RNA are used to make the a
+new strand of DNA and it goes this this
+
+ align:start position:0%
+new strand of DNA and it goes this this
+ 
+
+ align:start position:0%
+new strand of DNA and it goes this this
+way now that obviously doesn't give you
+
+ align:start position:0%
+way now that obviously doesn't give you
+ 
+
+ align:start position:0%
+way now that obviously doesn't give you
+a new intact DNA strand and the part of
+
+ align:start position:0%
+a new intact DNA strand and the part of
+ 
+
+ align:start position:0%
+a new intact DNA strand and the part of
+the clue to this uh working out what was
+
+ align:start position:0%
+the clue to this uh working out what was
+ 
+
+ align:start position:0%
+the clue to this uh working out what was
+going on at DNA replication was the
+
+ align:start position:0%
+going on at DNA replication was the
+ 
+
+ align:start position:0%
+going on at DNA replication was the
+recognition that newly synthesized DNA
+
+ align:start position:0%
+recognition that newly synthesized DNA
+ 
+
+ align:start position:0%
+recognition that newly synthesized DNA
+was made as little pieces and then later
+
+ align:start position:0%
+was made as little pieces and then later
+ 
+
+ align:start position:0%
+was made as little pieces and then later
+it got joined into longer longer
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+pieces and the person who discovered
+
+ align:start position:0%
+pieces and the person who discovered
+ 
+
+ align:start position:0%
+pieces and the person who discovered
+this was okazaki so these fragments of
+
+ align:start position:0%
+this was okazaki so these fragments of
+ 
+
+ align:start position:0%
+this was okazaki so these fragments of
+DNA that are synthesized initially are
+
+ align:start position:0%
+DNA that are synthesized initially are
+ 
+
+ align:start position:0%
+DNA that are synthesized initially are
+called okazaki fragments after the the
+
+ align:start position:0%
+called okazaki fragments after the the
+ 
+
+ align:start position:0%
+called okazaki fragments after the the
+person who discovered this it was it was
+
+ align:start position:0%
+person who discovered this it was it was
+ 
+
+ align:start position:0%
+person who discovered this it was it was
+rather puzzling because little when you
+
+ align:start position:0%
+rather puzzling because little when you
+ 
+
+ align:start position:0%
+rather puzzling because little when you
+tried to look at the synthesis of DNA
+
+ align:start position:0%
+tried to look at the synthesis of DNA
+ 
+
+ align:start position:0%
+tried to look at the synthesis of DNA
+you're looking at a long molecule and
+
+ align:start position:0%
+you're looking at a long molecule and
+ 
+
+ align:start position:0%
+you're looking at a long molecule and
+you found some of the newly synthesized
+
+ align:start position:0%
+you found some of the newly synthesized
+ 
+
+ align:start position:0%
+you found some of the newly synthesized
+material was in short pieces and as you
+
+ align:start position:0%
+material was in short pieces and as you
+ 
+
+ align:start position:0%
+material was in short pieces and as you
+watched over time it got uh it got um
+
+ align:start position:0%
+watched over time it got uh it got um
+ 
+
+ align:start position:0%
+watched over time it got uh it got um
+longer so the the cell I think you can
+
+ align:start position:0%
+longer so the the cell I think you can
+ 
+
+ align:start position:0%
+longer so the the cell I think you can
+sort of see from first principles what
+
+ align:start position:0%
+sort of see from first principles what
+ 
+
+ align:start position:0%
+sort of see from first principles what
+has to happen here then that in order
+
+ align:start position:0%
+has to happen here then that in order
+ 
+
+ align:start position:0%
+has to happen here then that in order
+order to come and
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+make this strand is pretty easy to do
+
+ align:start position:0%
+make this strand is pretty easy to do
+ 
+
+ align:start position:0%
+make this strand is pretty easy to do
+but what the cells have to do now is
+
+ align:start position:0%
+but what the cells have to do now is
+ 
+
+ align:start position:0%
+but what the cells have to do now is
+they put these little RNA
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+primers and then they remove the
+
+ align:start position:0%
+primers and then they remove the
+ 
+
+ align:start position:0%
+primers and then they remove the
+RNA
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+by an enzyme that's capable of of
+
+ align:start position:0%
+by an enzyme that's capable of of
+ 
+
+ align:start position:0%
+by an enzyme that's capable of of
+degrading the DNA or clipping it at the
+
+ align:start position:0%
+degrading the DNA or clipping it at the
+ 
+
+ align:start position:0%
+degrading the DNA or clipping it at the
+junction and that then leaves
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the cell in this sort of situation where
+
+ align:start position:0%
+the cell in this sort of situation where
+ 
+
+ align:start position:0%
+the cell in this sort of situation where
+there are little tiny gaps in between
+
+ align:start position:0%
+there are little tiny gaps in between
+ 
+
+ align:start position:0%
+there are little tiny gaps in between
+these pieces of DNA but at the end of
+
+ align:start position:0%
+these pieces of DNA but at the end of
+ 
+
+ align:start position:0%
+these pieces of DNA but at the end of
+each one of these is a three prime
+
+ align:start position:0%
+each one of these is a three prime
+ 
+
+ align:start position:0%
+each one of these is a three prime
+hydroxy so another polymerase or some
+
+ align:start position:0%
+hydroxy so another polymerase or some
+ 
+
+ align:start position:0%
+hydroxy so another polymerase or some
+one one or another polymerase in the
+
+ align:start position:0%
+one one or another polymerase in the
+ 
+
+ align:start position:0%
+one one or another polymerase in the
+cell can fill those little pieces of uh
+
+ align:start position:0%
+cell can fill those little pieces of uh
+ 
+
+ align:start position:0%
+cell can fill those little pieces of uh
+of DNA out and then there's one little
+
+ align:start position:0%
+of DNA out and then there's one little
+ 
+
+ align:start position:0%
+of DNA out and then there's one little
+Nick that needs to be need to needs to
+
+ align:start position:0%
+Nick that needs to be need to needs to
+ 
+
+ align:start position:0%
+Nick that needs to be need to needs to
+be sealed and so what you finally end up
+
+ align:start position:0%
+be sealed and so what you finally end up
+ 
+
+ align:start position:0%
+be sealed and so what you finally end up
+with is a a three prime hydroxy here a
+
+ align:start position:0%
+with is a a three prime hydroxy here a
+ 
+
+ align:start position:0%
+with is a a three prime hydroxy here a
+five
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Prime
+
+ align:start position:0%
+Prime
+ 
+
+ align:start position:0%
+Prime
+phosphate that's the other end and then
+
+ align:start position:0%
+phosphate that's the other end and then
+ 
+
+ align:start position:0%
+phosphate that's the other end and then
+these are joined together this is one
+
+ align:start position:0%
+these are joined together this is one
+ 
+
+ align:start position:0%
+these are joined together this is one
+nucleotide here and the other here here
+
+ align:start position:0%
+nucleotide here and the other here here
+ 
+
+ align:start position:0%
+nucleotide here and the other here here
+these are then joined
+
+ align:start position:0%
+these are then joined
+ 
+
+ align:start position:0%
+these are then joined
+together to give the
+
+ align:start position:0%
+together to give the
+ 
+
+ align:start position:0%
+together to give the
+ordinary phosphodiester bond that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+links the two
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+nucleotides together like that and the
+
+ align:start position:0%
+nucleotides together like that and the
+ 
+
+ align:start position:0%
+nucleotides together like that and the
+enzyme that does
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that it's an enzyme called DNA ligase
+
+ align:start position:0%
+that it's an enzyme called DNA ligase
+ 
+
+ align:start position:0%
+that it's an enzyme called DNA ligase
+you can almost think about it as as DNA
+
+ align:start position:0%
+you can almost think about it as as DNA
+ 
+
+ align:start position:0%
+you can almost think about it as as DNA
+Scotch tape it will take a little Nick
+
+ align:start position:0%
+Scotch tape it will take a little Nick
+ 
+
+ align:start position:0%
+Scotch tape it will take a little Nick
+in DNA we've got a phosphate and hydroxy
+
+ align:start position:0%
+in DNA we've got a phosphate and hydroxy
+ 
+
+ align:start position:0%
+in DNA we've got a phosphate and hydroxy
+and it'll it'll join them join them
+
+ align:start position:0%
+and it'll it'll join them join them
+ 
+
+ align:start position:0%
+and it'll it'll join them join them
+together so this process of of
+
+ align:start position:0%
+together so this process of of
+ 
+
+ align:start position:0%
+together so this process of of
+replication which can go at about a
+
+ align:start position:0%
+replication which can go at about a
+ 
+
+ align:start position:0%
+replication which can go at about a
+thousand
+
+ align:start position:0%
+thousand
+ 
+
+ align:start position:0%
+thousand
+nucleotides uh a second with this
+
+ align:start position:0%
+nucleotides uh a second with this
+ 
+
+ align:start position:0%
+nucleotides uh a second with this
+amazing degree of of accuracy uses two
+
+ align:start position:0%
+amazing degree of of accuracy uses two
+ 
+
+ align:start position:0%
+amazing degree of of accuracy uses two
+different DNA plases both of which can
+
+ align:start position:0%
+different DNA plases both of which can
+ 
+
+ align:start position:0%
+different DNA plases both of which can
+chem biochemically can only go in One
+
+ align:start position:0%
+chem biochemically can only go in One
+ 
+
+ align:start position:0%
+chem biochemically can only go in One
+Direction but you can see they have to
+
+ align:start position:0%
+Direction but you can see they have to
+ 
+
+ align:start position:0%
+Direction but you can see they have to
+be somehow oriented in um
+
+ align:start position:0%
+be somehow oriented in um
+ 
+
+ align:start position:0%
+be somehow oriented in um
+so that one of them is able to move in
+
+ align:start position:0%
+so that one of them is able to move in
+ 
+
+ align:start position:0%
+so that one of them is able to move in
+this direction and the other one is able
+
+ align:start position:0%
+this direction and the other one is able
+ 
+
+ align:start position:0%
+this direction and the other one is able
+to move in that direction the Strand
+
+ align:start position:0%
+to move in that direction the Strand
+ 
+
+ align:start position:0%
+to move in that direction the Strand
+um the the key part in this sort of the
+
+ align:start position:0%
+um the the key part in this sort of the
+ 
+
+ align:start position:0%
+um the the key part in this sort of the
+course is to try and understand this 5
+
+ align:start position:0%
+course is to try and understand this 5
+ 
+
+ align:start position:0%
+course is to try and understand this 5
+to 3 Prime and to get this basic idea
+
+ align:start position:0%
+to 3 Prime and to get this basic idea
+ 
+
+ align:start position:0%
+to 3 Prime and to get this basic idea
+that nature had to do something it was
+
+ align:start position:0%
+that nature had to do something it was
+ 
+
+ align:start position:0%
+that nature had to do something it was
+fairly easy to copy one strand because
+
+ align:start position:0%
+fairly easy to copy one strand because
+ 
+
+ align:start position:0%
+fairly easy to copy one strand because
+that was sort of the direction of the
+
+ align:start position:0%
+that was sort of the direction of the
+ 
+
+ align:start position:0%
+that was sort of the direction of the
+Pumas movement was the same as the
+
+ align:start position:0%
+Pumas movement was the same as the
+ 
+
+ align:start position:0%
+Pumas movement was the same as the
+replication fork movement but the other
+
+ align:start position:0%
+replication fork movement but the other
+ 
+
+ align:start position:0%
+replication fork movement but the other
+strand had to been much more of a
+
+ align:start position:0%
+strand had to been much more of a
+ 
+
+ align:start position:0%
+strand had to been much more of a
+problem uh and so when you get down to a
+
+ align:start position:0%
+problem uh and so when you get down to a
+ 
+
+ align:start position:0%
+problem uh and so when you get down to a
+biochemical level though it's very
+
+ align:start position:0%
+biochemical level though it's very
+ 
+
+ align:start position:0%
+biochemical level though it's very
+conceptually easy to say oh you've got
+
+ align:start position:0%
+conceptually easy to say oh you've got
+ 
+
+ align:start position:0%
+conceptually easy to say oh you've got
+complimentary strand so we just take it
+
+ align:start position:0%
+complimentary strand so we just take it
+ 
+
+ align:start position:0%
+complimentary strand so we just take it
+apart we make a the take the photograph
+
+ align:start position:0%
+apart we make a the take the photograph
+ 
+
+ align:start position:0%
+apart we make a the take the photograph
+and negative and we make the opposite
+
+ align:start position:0%
+and negative and we make the opposite
+ 
+
+ align:start position:0%
+and negative and we make the opposite
+one and now we've got two copies when we
+
+ align:start position:0%
+one and now we've got two copies when we
+ 
+
+ align:start position:0%
+one and now we've got two copies when we
+get down to the biochemical details uh
+
+ align:start position:0%
+get down to the biochemical details uh
+ 
+
+ align:start position:0%
+get down to the biochemical details uh
+there is this major biochemical issue of
+
+ align:start position:0%
+there is this major biochemical issue of
+ 
+
+ align:start position:0%
+there is this major biochemical issue of
+whether the the plase uh can go in the
+
+ align:start position:0%
+whether the the plase uh can go in the
+ 
+
+ align:start position:0%
+whether the the plase uh can go in the
+three prime or the five Prime Direction
+
+ align:start position:0%
+three prime or the five Prime Direction
+ 
+
+ align:start position:0%
+three prime or the five Prime Direction
+and nature has chosen to do it all or
+
+ align:start position:0%
+and nature has chosen to do it all or
+ 
+
+ align:start position:0%
+and nature has chosen to do it all or
+has been selected to do it all some in
+
+ align:start position:0%
+has been selected to do it all some in
+ 
+
+ align:start position:0%
+has been selected to do it all some in
+with the plase going in one One
+
+ align:start position:0%
+with the plase going in one One
+ 
+
+ align:start position:0%
+with the plase going in one One
+Direction now there many uh many other
+
+ align:start position:0%
+Direction now there many uh many other
+ 
+
+ align:start position:0%
+Direction now there many uh many other
+aspects to this uh to DNA replication
+
+ align:start position:0%
+aspects to this uh to DNA replication
+ 
+
+ align:start position:0%
+aspects to this uh to DNA replication
+and one of the one of the tricks that I
+
+ align:start position:0%
+and one of the one of the tricks that I
+ 
+
+ align:start position:0%
+and one of the one of the tricks that I
+find Most Fascinating is that these
+
+ align:start position:0%
+find Most Fascinating is that these
+ 
+
+ align:start position:0%
+find Most Fascinating is that these
+polymerases once they get on DNA they
+
+ align:start position:0%
+polymerases once they get on DNA they
+ 
+
+ align:start position:0%
+polymerases once they get on DNA they
+stay on and that's part of the secret
+
+ align:start position:0%
+stay on and that's part of the secret
+ 
+
+ align:start position:0%
+stay on and that's part of the secret
+because it takes about a millisecond to
+
+ align:start position:0%
+because it takes about a millisecond to
+ 
+
+ align:start position:0%
+because it takes about a millisecond to
+add a nucleotide but if it comes off the
+
+ align:start position:0%
+add a nucleotide but if it comes off the
+ 
+
+ align:start position:0%
+add a nucleotide but if it comes off the
+DNA and has to get back on then uh it
+
+ align:start position:0%
+DNA and has to get back on then uh it
+ 
+
+ align:start position:0%
+DNA and has to get back on then uh it
+takes about a minute so the whole trick
+
+ align:start position:0%
+takes about a minute so the whole trick
+ 
+
+ align:start position:0%
+takes about a minute so the whole trick
+to being a very very fast DNA polymerase
+
+ align:start position:0%
+to being a very very fast DNA polymerase
+ 
+
+ align:start position:0%
+to being a very very fast DNA polymerase
+is to somehow hang on to the DNA so what
+
+ align:start position:0%
+is to somehow hang on to the DNA so what
+ 
+
+ align:start position:0%
+is to somehow hang on to the DNA so what
+biochemists did was they purified uh the
+
+ align:start position:0%
+biochemists did was they purified uh the
+ 
+
+ align:start position:0%
+biochemists did was they purified uh the
+actual enzymatic activity that could
+
+ align:start position:0%
+actual enzymatic activity that could
+ 
+
+ align:start position:0%
+actual enzymatic activity that could
+carry out this process and then they
+
+ align:start position:0%
+carry out this process and then they
+ 
+
+ align:start position:0%
+carry out this process and then they
+started to look for other protein
+
+ align:start position:0%
+started to look for other protein
+ 
+
+ align:start position:0%
+started to look for other protein
+factors that would help the process to
+
+ align:start position:0%
+factors that would help the process to
+ 
+
+ align:start position:0%
+factors that would help the process to
+work better and they discovered
+
+ align:start position:0%
+work better and they discovered
+ 
+
+ align:start position:0%
+work better and they discovered
+something called a processivity factor
+
+ align:start position:0%
+something called a processivity factor
+ 
+
+ align:start position:0%
+something called a processivity factor
+which made the plase stay on the on the
+
+ align:start position:0%
+which made the plase stay on the on the
+ 
+
+ align:start position:0%
+which made the plase stay on the on the
+DNA and people wondered for a lot of
+
+ align:start position:0%
+DNA and people wondered for a lot of
+ 
+
+ align:start position:0%
+DNA and people wondered for a lot of
+years how that works and why did this
+
+ align:start position:0%
+years how that works and why did this
+ 
+
+ align:start position:0%
+years how that works and why did this
+system work so well and finally the
+
+ align:start position:0%
+system work so well and finally the
+ 
+
+ align:start position:0%
+system work so well and finally the
+crystal structure of a of the
+
+ align:start position:0%
+crystal structure of a of the
+ 
+
+ align:start position:0%
+crystal structure of a of the
+processivity factor was discovered and
+
+ align:start position:0%
+processivity factor was discovered and
+ 
+
+ align:start position:0%
+processivity factor was discovered and
+if I go back to this this sort of
+
+ align:start position:0%
+if I go back to this this sort of
+ 
+
+ align:start position:0%
+if I go back to this this sort of
+diagram where this is the the piece of
+
+ align:start position:0%
+diagram where this is the the piece of
+ 
+
+ align:start position:0%
+diagram where this is the the piece of
+DNA that's copied what what it turned
+
+ align:start position:0%
+DNA that's copied what what it turned
+ 
+
+ align:start position:0%
+DNA that's copied what what it turned
+out was that the processivity factor is
+
+ align:start position:0%
+out was that the processivity factor is
+ 
+
+ align:start position:0%
+out was that the processivity factor is
+basically a donut that kind of gets
+
+ align:start position:0%
+basically a donut that kind of gets
+ 
+
+ align:start position:0%
+basically a donut that kind of gets
+clamped around the DNA like that so it's
+
+ align:start position:0%
+clamped around the DNA like that so it's
+ 
+
+ align:start position:0%
+clamped around the DNA like that so it's
+it's like sort of taking a a washer with
+
+ align:start position:0%
+it's like sort of taking a a washer with
+ 
+
+ align:start position:0%
+it's like sort of taking a a washer with
+a place where you can pry it apart
+
+ align:start position:0%
+a place where you can pry it apart
+ 
+
+ align:start position:0%
+a place where you can pry it apart
+opening it up putting it around the DNA
+
+ align:start position:0%
+opening it up putting it around the DNA
+ 
+
+ align:start position:0%
+opening it up putting it around the DNA
+like this and then the pimas more or
+
+ align:start position:0%
+like this and then the pimas more or
+ 
+
+ align:start position:0%
+like this and then the pimas more or
+less since it's now to this is
+
+ align:start position:0%
+less since it's now to this is
+ 
+
+ align:start position:0%
+less since it's now to this is
+topologically linked to the DNA it's
+
+ align:start position:0%
+topologically linked to the DNA it's
+ 
+
+ align:start position:0%
+topologically linked to the DNA it's
+like a a washer sliding on a wire this
+
+ align:start position:0%
+like a a washer sliding on a wire this
+ 
+
+ align:start position:0%
+like a a washer sliding on a wire this
+DNA polymerase hangs onto that and it
+
+ align:start position:0%
+DNA polymerase hangs onto that and it
+ 
+
+ align:start position:0%
+DNA polymerase hangs onto that and it
+doesn't come off and the I think there's
+
+ align:start position:0%
+doesn't come off and the I think there's
+ 
+
+ align:start position:0%
+doesn't come off and the I think there's
+a little picture of the here's a little
+
+ align:start position:0%
+a little picture of the here's a little
+ 
+
+ align:start position:0%
+a little picture of the here's a little
+movie there's the DNA going through and
+
+ align:start position:0%
+movie there's the DNA going through and
+ 
+
+ align:start position:0%
+movie there's the DNA going through and
+this is one of these uh one of these
+
+ align:start position:0%
+this is one of these uh one of these
+ 
+
+ align:start position:0%
+this is one of these uh one of these
+clamps it's the virtually the same
+
+ align:start position:0%
+clamps it's the virtually the same
+ 
+
+ align:start position:0%
+clamps it's the virtually the same
+structure in a bacterium and inside of
+
+ align:start position:0%
+structure in a bacterium and inside of
+ 
+
+ align:start position:0%
+structure in a bacterium and inside of
+us but in fact the amino acids are
+
+ align:start position:0%
+us but in fact the amino acids are
+ 
+
+ align:start position:0%
+us but in fact the amino acids are
+almost all all different but the the
+
+ align:start position:0%
+almost all all different but the the
+ 
+
+ align:start position:0%
+almost all all different but the the
+underlying structure of the protein is
+
+ align:start position:0%
+underlying structure of the protein is
+ 
+
+ align:start position:0%
+underlying structure of the protein is
+almost identical and there's there are a
+
+ align:start position:0%
+almost identical and there's there are a
+ 
+
+ align:start position:0%
+almost identical and there's there are a
+little special machines that will kind
+
+ align:start position:0%
+little special machines that will kind
+ 
+
+ align:start position:0%
+little special machines that will kind
+of called clamp loaders that pry open
+
+ align:start position:0%
+of called clamp loaders that pry open
+ 
+
+ align:start position:0%
+of called clamp loaders that pry open
+these clamps clamp them around DNA and
+
+ align:start position:0%
+these clamps clamp them around DNA and
+ 
+
+ align:start position:0%
+these clamps clamp them around DNA and
+that's part of the secret to how these
+
+ align:start position:0%
+that's part of the secret to how these
+ 
+
+ align:start position:0%
+that's part of the secret to how these
+uh plases are able to
+
+ align:start position:0%
+uh plases are able to
+ 
+
+ align:start position:0%
+uh plases are able to
+be uh polymerized DNA so fast
+
+ align:start position:0%
+be uh polymerized DNA so fast
+ 
+
+ align:start position:0%
+be uh polymerized DNA so fast
+there are a lot of other pieces of this
+
+ align:start position:0%
+there are a lot of other pieces of this
+ 
+
+ align:start position:0%
+there are a lot of other pieces of this
+Machinery if you go on you'll hear more
+
+ align:start position:0%
+Machinery if you go on you'll hear more
+ 
+
+ align:start position:0%
+Machinery if you go on you'll hear more
+of it I just want to give you one of the
+
+ align:start position:0%
+of it I just want to give you one of the
+ 
+
+ align:start position:0%
+of it I just want to give you one of the
+most recent insights I mean this has
+
+ align:start position:0%
+most recent insights I mean this has
+ 
+
+ align:start position:0%
+most recent insights I mean this has
+been studied in this as you might guess
+
+ align:start position:0%
+been studied in this as you might guess
+ 
+
+ align:start position:0%
+been studied in this as you might guess
+since DNA replication is at the heart of
+
+ align:start position:0%
+since DNA replication is at the heart of
+ 
+
+ align:start position:0%
+since DNA replication is at the heart of
+life it's been studied very very hard
+
+ align:start position:0%
+life it's been studied very very hard
+ 
+
+ align:start position:0%
+life it's been studied very very hard
+ever since the uh discovery of DNA Helix
+
+ align:start position:0%
+ever since the uh discovery of DNA Helix
+ 
+
+ align:start position:0%
+ever since the uh discovery of DNA Helix
+my colleague Alan Gman um made quite a
+
+ align:start position:0%
+my colleague Alan Gman um made quite a
+ 
+
+ align:start position:0%
+my colleague Alan Gman um made quite a
+discovery uh just probably 3 or four
+
+ align:start position:0%
+discovery uh just probably 3 or four
+ 
+
+ align:start position:0%
+discovery uh just probably 3 or four
+years ago uh he was he took that green
+
+ align:start position:0%
+years ago uh he was he took that green
+ 
+
+ align:start position:0%
+years ago uh he was he took that green
+fluorescent protein that we've seen a
+
+ align:start position:0%
+fluorescent protein that we've seen a
+ 
+
+ align:start position:0%
+fluorescent protein that we've seen a
+few times and he actually joined the uh
+
+ align:start position:0%
+few times and he actually joined the uh
+ 
+
+ align:start position:0%
+few times and he actually joined the uh
+the gene en coding green floresent
+
+ align:start position:0%
+the gene en coding green floresent
+ 
+
+ align:start position:0%
+the gene en coding green floresent
+protein to the back end of a piece of
+
+ align:start position:0%
+protein to the back end of a piece of
+ 
+
+ align:start position:0%
+protein to the back end of a piece of
+the DNA plase so wherever the DNA plase
+
+ align:start position:0%
+the DNA plase so wherever the DNA plase
+ 
+
+ align:start position:0%
+the DNA plase so wherever the DNA plase
+went now there was a little
+
+ align:start position:0%
+went now there was a little
+ 
+
+ align:start position:0%
+went now there was a little
+fluorescent molecule and he looked to
+
+ align:start position:0%
+fluorescent molecule and he looked to
+ 
+
+ align:start position:0%
+fluorescent molecule and he looked to
+see where it was in the cell and I like
+
+ align:start position:0%
+see where it was in the cell and I like
+ 
+
+ align:start position:0%
+see where it was in the cell and I like
+many other people had for years taught
+
+ align:start position:0%
+many other people had for years taught
+ 
+
+ align:start position:0%
+many other people had for years taught
+this is why you know I have respect for
+
+ align:start position:0%
+this is why you know I have respect for
+ 
+
+ align:start position:0%
+this is why you know I have respect for
+the fact that I'm just teaching you the
+
+ align:start position:0%
+the fact that I'm just teaching you the
+ 
+
+ align:start position:0%
+the fact that I'm just teaching you the
+current model uh for much of my career I
+
+ align:start position:0%
+current model uh for much of my career I
+ 
+
+ align:start position:0%
+current model uh for much of my career I
+taught so DNA plas is sort of like a
+
+ align:start position:0%
+taught so DNA plas is sort of like a
+ 
+
+ align:start position:0%
+taught so DNA plas is sort of like a
+train going down the tracks th mile
+
+ align:start position:0%
+train going down the tracks th mile
+ 
+
+ align:start position:0%
+train going down the tracks th mile
+molecules per second and we're doing all
+
+ align:start position:0%
+molecules per second and we're doing all
+ 
+
+ align:start position:0%
+molecules per second and we're doing all
+this stuff with the leading and the the
+
+ align:start position:0%
+this stuff with the leading and the the
+ 
+
+ align:start position:0%
+this stuff with the leading and the the
+with the two strands um actually let me
+
+ align:start position:0%
+with the two strands um actually let me
+ 
+
+ align:start position:0%
+with the two strands um actually let me
+just put those words up while I'm up
+
+ align:start position:0%
+just put those words up while I'm up
+ 
+
+ align:start position:0%
+just put those words up while I'm up
+there this
+
+ align:start position:0%
+there this
+ 
+
+ align:start position:0%
+there this
+one this is
+
+ align:start position:0%
+one this is
+ 
+
+ align:start position:0%
+one this is
+called The Strand that's
+
+ align:start position:0%
+called The Strand that's
+ 
+
+ align:start position:0%
+called The Strand that's
+easy easy to replicate is called the
+
+ align:start position:0%
+easy easy to replicate is called the
+ 
+
+ align:start position:0%
+easy easy to replicate is called the
+leading
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Strand and this one you have have to do
+
+ align:start position:0%
+Strand and this one you have have to do
+ 
+
+ align:start position:0%
+Strand and this one you have have to do
+the primer what not is called the
+
+ align:start position:0%
+the primer what not is called the
+ 
+
+ align:start position:0%
+the primer what not is called the
+lagging
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+strand in any case um so what I had
+
+ align:start position:0%
+strand in any case um so what I had
+ 
+
+ align:start position:0%
+strand in any case um so what I had
+taught was the ply was was like a A
+
+ align:start position:0%
+taught was the ply was was like a A
+ 
+
+ align:start position:0%
+taught was the ply was was like a A
+train running on tracks you could even
+
+ align:start position:0%
+train running on tracks you could even
+ 
+
+ align:start position:0%
+train running on tracks you could even
+calculate how fast it would move what
+
+ align:start position:0%
+calculate how fast it would move what
+ 
+
+ align:start position:0%
+calculate how fast it would move what
+alen to his amazement I imagine found
+
+ align:start position:0%
+alen to his amazement I imagine found
+ 
+
+ align:start position:0%
+alen to his amazement I imagine found
+was when he looked to see where the DNA
+
+ align:start position:0%
+was when he looked to see where the DNA
+ 
+
+ align:start position:0%
+was when he looked to see where the DNA
+plase was it wasn't spread out all over
+
+ align:start position:0%
+plase was it wasn't spread out all over
+ 
+
+ align:start position:0%
+plase was it wasn't spread out all over
+the cell as if you thought it was a a
+
+ align:start position:0%
+the cell as if you thought it was a a
+ 
+
+ align:start position:0%
+the cell as if you thought it was a a
+thing running in tracks in fact it was
+
+ align:start position:0%
+thing running in tracks in fact it was
+ 
+
+ align:start position:0%
+thing running in tracks in fact it was
+in the center of the cell and then Laden
+
+ align:start position:0%
+in the center of the cell and then Laden
+ 
+
+ align:start position:0%
+in the center of the cell and then Laden
+cell division it split into two spots
+
+ align:start position:0%
+cell division it split into two spots
+ 
+
+ align:start position:0%
+cell division it split into two spots
+that went to the midpoints of what would
+
+ align:start position:0%
+that went to the midpoints of what would
+ 
+
+ align:start position:0%
+that went to the midpoints of what would
+be the daughter cells and so what he
+
+ align:start position:0%
+be the daughter cells and so what he
+ 
+
+ align:start position:0%
+be the daughter cells and so what he
+ended up realizing from that was that
+
+ align:start position:0%
+ended up realizing from that was that
+ 
+
+ align:start position:0%
+ended up realizing from that was that
+instead it was more as if the Plumas was
+
+ align:start position:0%
+instead it was more as if the Plumas was
+ 
+
+ align:start position:0%
+instead it was more as if the Plumas was
+a a factory and it pulled the DNA
+
+ align:start position:0%
+a a factory and it pulled the DNA
+ 
+
+ align:start position:0%
+a a factory and it pulled the DNA
+through it rather than it traveling down
+
+ align:start position:0%
+through it rather than it traveling down
+ 
+
+ align:start position:0%
+through it rather than it traveling down
+the down the tracks of the of the DNA
+
+ align:start position:0%
+the down the tracks of the of the DNA
+ 
+
+ align:start position:0%
+the down the tracks of the of the DNA
+and that has that was a very surprising
+
+ align:start position:0%
+and that has that was a very surprising
+ 
+
+ align:start position:0%
+and that has that was a very surprising
+discovery that went against all the
+
+ align:start position:0%
+discovery that went against all the
+ 
+
+ align:start position:0%
+discovery that went against all the
+Dogma and all the pictures in the
+
+ align:start position:0%
+Dogma and all the pictures in the
+ 
+
+ align:start position:0%
+Dogma and all the pictures in the
+textbook and it was a discovery made in
+
+ align:start position:0%
+textbook and it was a discovery made in
+ 
+
+ align:start position:0%
+textbook and it was a discovery made in
+MIT that was published in I think it was
+
+ align:start position:0%
+MIT that was published in I think it was
+ 
+
+ align:start position:0%
+MIT that was published in I think it was
+2001 something like that a very recent
+
+ align:start position:0%
+2001 something like that a very recent
+ 
+
+ align:start position:0%
+2001 something like that a very recent
+discovery things keep changing it's
+
+ align:start position:0%
+discovery things keep changing it's
+ 
+
+ align:start position:0%
+discovery things keep changing it's
+again why I keep emphasizing I can I
+
+ align:start position:0%
+again why I keep emphasizing I can I
+ 
+
+ align:start position:0%
+again why I keep emphasizing I can I
+can't teach you a fact in biology I can
+
+ align:start position:0%
+can't teach you a fact in biology I can
+ 
+
+ align:start position:0%
+can't teach you a fact in biology I can
+teach you the best understanding we have
+
+ align:start position:0%
+teach you the best understanding we have
+ 
+
+ align:start position:0%
+teach you the best understanding we have
+that's that's that explains the
+
+ align:start position:0%
+that's that's that explains the
+ 
+
+ align:start position:0%
+that's that's that explains the
+experiments to date but somebody may
+
+ align:start position:0%
+experiments to date but somebody may
+ 
+
+ align:start position:0%
+experiments to date but somebody may
+make a discovery tomorrow that means
+
+ align:start position:0%
+make a discovery tomorrow that means
+ 
+
+ align:start position:0%
+make a discovery tomorrow that means
+we'll have to change your understanding
+
+ align:start position:0%
+we'll have to change your understanding
+ 
+
+ align:start position:0%
+we'll have to change your understanding
+okay so good luck on the exam I'll see
+
+ align:start position:0%
+okay so good luck on the exam I'll see
+ 
+
+ align:start position:0%
+okay so good luck on the exam I'll see
+you on on Monday
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
\ No newline at end of file
diff --git a/2QRfkG7jOfY.txt b/2QRfkG7jOfY.txt
new file mode 100644
index 0000000000000000000000000000000000000000..2b7e7e5d52c7511cbf24d783092ad869328d6836
--- /dev/null
+++ b/2QRfkG7jOfY.txt
@@ -0,0 +1,3813 @@
+We're about ready to get started.
+
+A couple things.
+
+First of all, this is for those of you who
+are working on GN&C for your projects.
+
+I have spoken with Phil Hattis from Draper
+Lab, who is going to be giving the lecture
+
+on GN&C, but he is not giving the lecture
+until the third of November.
+
+Now, that is kind of late.
+
+And so I asked him if he would be willing
+to meet with all of you who are working on
+
+GN&C just so you could talk with him and ask
+questions.
+
+If you want him to give you a short version
+of his presentation that he's going to give
+
+in November, he can do that.
+
+But he is our in-house resident expert.
+
+And I figured it's better if you get a chance
+to talk to him early.
+
+He has some time free tomorrow and he has
+some time next week.
+
+He is out of town through today.
+
+I know we have two teams working on GN&C.
+
+If you guys want to get together and find
+out if there is some time when you could all
+
+meet with Phil, I will give you his contact
+information.
+
+He says he is happy to do it.
+
+It would be much more convenient, from his
+point of view, if you could all see him at
+
+the same time and talk about it together.
+
+Let me know what you come up with.
+
+But, as I say, he is happy to do it.
+
+Second thing.
+
+There was an interview printed in US Today,
+which I have posted on the class website with
+
+Mike Griffin, the administrator.
+
+And it says NASA administrator says space
+shuttle was a mistake.
+
+And so the question was what do we intend
+to do about that in this class?
+
+Well, let me actually read the specific words
+that Griffin uses because I think that's important.
+
+Griffin said my opinion is that the Shuttle
+was a design which was extremely aggressive
+
+and just barely possible.
+
+And that's actually, I think, a slightly different
+way of looking at this.
+
+I mean I would also say that Apollo was a
+project that was extremely aggressive and
+
+just barely possible.
+
+And I think that it is actually NASA's business
+to do things which are aggressive and just
+
+barely possible.
+
+Now, whether it was the right decision for
+the country to abandon the Exploration Program
+
+after Apollo and do the Shuttle and then later
+on the Space Station that's more, I think,
+
+in the political realm.
+
+And, as I think you've heard both from Dale
+Myers and John Logsdon, that, in fact, there
+
+were political determining factors which didn't
+really give NASA a lot of choice.
+
+Just to remind you, the basic point of this
+course is not the political and economic history
+
+of the shuttle.
+
+It's a technical exploration of how we did
+the shuttle.
+
+I think we would all agree that the concept
+of the Shuttle was extremely aggressive and
+
+the technology was being stretched and it
+was just barely possible.
+
+And, yet, we did it.
+
+And the idea of this course is to understand
+how we did it and how the systems work.
+
+I think it will be interesting, when we get
+towards the end of the course, maybe we'll
+
+sit down and relax and instead of having,
+I think there are two kinds of open sessions
+
+towards the end that I've been thinking about
+what we want to do there.
+
+And in one of them I think we may just talk
+a little bit and reflect on what we've learned,
+
+and that will give us an opportunity to discuss
+issues like this.
+
+That's all I'm going to say about this.
+
+I don't propose that we discuss this further
+today because we really are fortunate to have
+
+Bass Redd.
+
+And Aaron Cohen is going to introduce him
+formally.
+
+I will just say that when I was at Johnston
+Space Center last spring and I met one of
+
+the older managers there and I was telling
+him about our plans for this course and how
+
+Aaron was going to be a visiting professor
+here and we were inviting some of the experts
+
+in the early design of the Shuttle, he said,
+well, there is one guy you absolutely have
+
+to get, and that's Bass Redd.
+
+Well, we've got him.
+
+We're very fortunate.
+
+And, Aaron, I will turn it over to you and
+let you explain a little bit more why we're
+
+so fortunate.
+
+Well, first I have to tell you how I found
+Bass.
+
+I had a hard time finding Bass.
+
+He lives in a placed called Smithville, Texas.
+
+And, when people ask him where Smithville,
+Texas is, he said it's about a few minutes
+
+after you pass resume speed.
+
+So, it's not a very well known place.
+
+But I finally found Bass.
+
+And he is truly an outstanding aerodynamicist.
+
+And the thing that is so important is that
+aerodynamics, to me, from my vantage point,
+
+is really the linchpin, you might say, of
+putting a system together.
+
+Aerodynamics makes the system come alive.
+
+And as you could hear from the various speakers,
+from Tom Moser, and we talked a little bit
+
+about the guidance, navigation and control,
+it's important for the structures.
+
+Aerodynamics is important for the structures,
+it's important for the flight control system,
+
+it's important for the hydraulic system and
+it's important for the heating system.
+
+So, you have to understand the aerodynamics
+before you can make the vehicle actually come
+
+alive.
+
+And Bass Redd is the man to do it.
+
+He is absolutely one of the great aerodynamicists
+of our times.
+
+And he started out before there was computational
+fluid dynamics and the old wind tunnel testing.
+
+And now there is computational fluid dynamics,
+so you're going to be in for a real treat
+
+today to hear how Bass Redd put both the Apollo
+together, he did the Apollo aerodynamics,
+
+and he also did the Shuttle aerodynamics.
+
+And he is also now consulting to help NASA
+do their future work.
+
+Let me now turn it over to Bass.
+
+Thank you, Aaron.
+
+It's a great honor to be with you this morning.
+
+And you sure do look young.
+
+[LAUGHTER] We will try to cover basically
+-- [STATIC OBSCURES] And with that overview
+
+then of the Orbiter is how the program requirements
+drove the aerodynamic configuration, probably
+
+the biggest thing in what the aerodynamic
+characteristics are driven by the program
+
+requirements.
+
+And that will make a little more sense after
+we get into the briefing.
+
+Then the aerodynamic considerations, those
+that aren't due to program requirements but
+
+just due to the basic fundamentals of aerodynamics
+and the configuration that is being evaluated.
+
+We will do that for both the Orbiter and the
+Integrated Vehicle.
+
+Then I'll try to tell you how the aerodynamic
+design was accomplished through each of those
+
+phases, a lot of ways to work problems.
+
+Early on having powerful tools or sometimes
+a curse to you because you can produce more
+
+data than the system can consume.
+
+And I remember when we first got started on
+the Shuttle design, the people from structures
+
+had just finished the NASTRAN on the Apollo
+and they immediately wanted enough data to
+
+put into the NASTRAN for every configuration
+that was being conceived.
+
+That's not really a smart thing to do when
+you have literally hundreds of configurations
+
+to be considered.
+
+We will try to talk to you about phases, phase
+A, B and C, and defining the problem areas.
+
+And then defining the aerodynamic characteristics
+and do just a quick summary of the wind tunnel
+
+test program.
+
+And with some comments on how CFD might have
+driven that were it available.
+
+Through the `60s and `80s these design studies
+were accomplished in phases.
+
+Phase A is primarily in-house civil service
+design.
+
+I don't know how well you understand the NASA
+part, what the contractor part, what the civil
+
+service part is, but phase A is primarily
+in-house civil service.
+
+Whenever the contractors began to feel that
+this might be a real program, they began to
+
+do their in-house studies and they began to
+visit and give us recommendations and ideas
+
+on their own to drive that.
+
+None of that is paid for.
+
+That's a gratuitous kind of a thing.
+
+And contractors have a bit of change set aside
+to do those kinds of studies, but it's a freebee
+
+and really a super way to do things.
+
+And that's still going on today.
+
+Phase B is then you give contracts for generic
+studies.
+
+Scopes out the concept feasibilities and the
+program requirements and does those trades,
+
+does projected cost and timelines.
+
+By the way, before I forget it, Humboldt Mandell
+on costing would be excellent.
+
+We worked quite close hand-in-hand on trying
+to get those requirements and cost run together
+
+along with the weight.
+
+NASA then, after they get through this phase
+B, they produce a detailed statement of work
+
+that 
+is required for the phase C and D.
+
+And then phase C and D is the design and development.
+
+The Air Force separated those two.
+
+NASA always sort of put those together.
+
+So the design, development and construction.
+
+And the contractors do the detail work.
+
+NASA manages and checks it.
+
+Usually the way we operate, at least in our
+area, the aerodynamic area, we had a crack
+
+team that would go back in and define the
+problem, a potential solution to that problem
+
+and then suggest to the contractor they might
+look at this way or that way.
+
+But they really put the muscle to it.
+
+They put the final studies.
+
+They have the design documentation.
+
+And we try to steer that train as those things
+happen.
+
+In the Shuttle now, phase A, we started in
+1969, just shortly after the Lunar landing,
+
+they put together a small team.
+
+And this is at Johnson Space Craft Center.
+
+And that's through my knothole and the way
+that I look at things.
+
+But we did end up being the lead center in
+the shuttle.
+
+But we started with a small E&D group that
+was headed by a fellow by the name of Jim
+
+Chamberlain.
+
+Jim Chamberlain was the one that was responsible
+for the Gemini Space Craft, a very unique
+
+individual gone to heaven to be with the Lord
+now, reviewed by Max Faget who was head of
+
+E&D and Bob Gilruth who was center director,
+but that was a real privilege to work with
+
+him.
+
+What came out of that initial phase A study
+is what the vehicle should be, is a small
+
+personnel vehicle with a four man crew, 10k
+payload landing on the runway with about 200
+
+nautical miles cross-range.
+
+Quite different from the shuttle that we have
+today, but that was during the phase A.
+
+Strong design modules in this time were developed.
+
+And, showing how the other program requirements
+go with the design, the size and the program
+
+cost, there were individuals who had in their
+databank, which consisted of books that they
+
+kept on their tables, were all of the aircraft,
+all of the spacecraft, all of the missiles,
+
+what the weight of every individual subsystem
+was based upon plots with ECLS's on how much
+
+heat they took out, on the avionics as to
+how many computations they made.
+
+Well, not to chase that rabbit too far, but
+basically they were down to the subsystem
+
+kind of level.
+
+And then with the primary structure, secondary
+structure, how that was affected by landed
+
+weights or entry weights, the thermal protection
+system.
+
+And it was amazing what a good job that kind
+of approach would do.
+
+And then we had point designs that were being
+looked at both in-house at Johnson Space Craft
+
+Center, at Marshall and by all the contractors.
+
+And then all that data was fed into the system.
+
+So, that was a designed database.
+
+Some of those have been automated now and
+pretty good.
+
+And they don't give you the right answers,
+but the answers they give you aren't very
+
+far wrong either.
+
+They get into the ballpark for you.
+
+Phase B started in 1971.
+
+Something happened.
+
+The requirements were not dictated by NASA.
+
+The requirements were dictated by the Air
+Force, at least the driving requirements.
+
+If we had our own, a small vehicle it would
+have satisfied that.
+
+The Air Force requirements were 55,000 pound
+payload, 60 foot long payload bay, 15 foot
+
+in diameter, it had to be returned with a
+1200 nautical mile cross-range.
+
+At least 32,000 pounds of it had to be returned.
+
+It was classified at that time.
+
+It is no longer classified.
+
+You can use your imagination to figure out
+what kind of payload that you would want to
+
+go up into a high inclination orbit and bring
+back in one pass.
+
+Where that would take you and why you'd have
+to get back that quickly.
+
+But those were the requirements that were
+fed into phase B.
+
+Maximum reusability did not come from the
+Air Force.
+
+That came from the NASA side as that was part
+of technology.
+
+NASA has two basic jobs to do.
+
+One is the design of the vehicle, the delivering
+of the hardware, accomplishing the mission,
+
+but the other requirement for NASA is that
+it increased the technology.
+
+Going where no man has gone before, yes, but
+doing things that man has not done before
+
+in a better, faster way.
+
+And so maximum reusability was a goal that
+the engineers were handed.
+
+Soft ride.
+
+They wanted to be able to a congressman or
+a senator up in it.
+
+[LAUGHTER] A neat thing.
+
+Multi-center participation.
+
+If you ever get Hum up here, that cost you.
+
+Any time you break a job down and give it
+to more than one center or more than one contractor,
+
+it's like Humpty-Dumpty, you break him apart,
+you've got to put him back together again.
+
+And it takes a lot of eyes and elbows on both
+sides to accomplish that.
+
+And basically, once you break something down,
+you've increased your cost by 30% to 40% to
+
+put it back together again.
+
+Now, NASA has to have, under congressional
+mandate, contracts in every state in the union.
+
+Multi-center participation drives a great
+number of things so I felt it needed to be
+
+on the chart.
+
+But the big thing that you need to know as
+engineers, sometimes you cannot set your own
+
+program requirements.
+
+They are dictated to you for strange reasons.
+
+And you have to play the hand that you're
+dealt.
+
+Phase C and D, we had four contractors that
+bid on phase C and D.
+
+The interesting thing is Rockwell was the
+only contractor that bid within the allocated
+
+funds.
+
+They also had the best proposal, but that
+was very interesting.
+
+What they did was use the aerodynamic database
+that was developed in phase A and in phase
+
+B for their design analysis.
+
+They augmented that, they did some in-house
+testing, and Rockwell said we can do it for
+
+that amount of money but only if you don't
+change anything, NASA.
+
+And we changed things.
+
+They had a smaller orbiter, and we rejected
+that very early on.
+
+It had no capability for weight growth.
+
+And we showed that every program that has
+ever existed grew in weight by at least 5%,
+
+10%, 15%.
+
+And so the Orbiter was sized up just a little
+bit larger than the one that they had proposed
+
+with their agreement.
+
+Aaron probably had a contract change authorization
+because of that.
+
+But, anyway, we did that right at the beginning.
+
+What we did also aerodynamically during that
+phase B is we developed a complete database
+
+in the nation's best facility to be used for
+what we call verification analysis.
+
+And that database is very well documented,
+and we will talk about that a little bit more.
+
+Program requirements.
+
+May I ask, before you go onto program requirements,
+could you say something about kind of, you
+
+talked about the aerodynamic database, but
+nowadays we've got a lot of information about
+
+hypersonic aerodynamics?
+
+Can you say a little bit about the state of
+the art?
+
+What did people really know?
+
+Yeah.
+
+As a matter of fact, I'm going to do that
+when we go through it by phases specifically.
+
+I'm kind of telling it to you like a mystery
+story.
+
+[LAUGHTER] The program requirements dictated
+the basic orbiter configuration, payload size,
+
+crew size and returning the payload bay, the
+engine.
+
+Now, if you just visualize in your mind, and
+it's kind of a two-chart thing, let me just
+
+jump over to that since I know how to go back
+now.
+
+If you've got a payload that's got to be that
+long and you've got a crew size and the crew
+
+takes at least one telephone booth's worth
+of volume per crew takes at least one telephone
+
+booths worth of volume per crew, Even Superman
+needed something that big.
+
+[LAUGHTER] You've got the volume of this.
+
+Engines in the back.
+
+You want to return that because engines are
+very, very expensive.
+
+The avionics, of course, you want to bring
+those back.
+
+They are very, very expensive.
+
+And you've got to have it pointy end first.
+
+You looked at that and said, boy, you didn't
+have much choice as far as the fuselage was
+
+concerned.
+
+And that's right, you really don't.
+
+Now, that's pretty well set.
+
+Now, the wing size is required to augment
+the body lift.
+
+Now, if you just had the body on there, it
+would have to land about 300 knots.
+
+We didn't have wheel tires and breaks to land
+at that those speeds so we had to have some
+
+more lift.
+
+And that was accommodated with a wing.
+
+Figure out what CL max is.
+
+They're all about the same.
+
+You like a delta wing because it's a little
+more nice from a heat transfer standpoint.
+
+Sure a whole lot nicer if you've got to go
+through supersonic and transonic conditions
+
+at low angles of attack.
+
+So, you've got a delta wing that you want
+to have on there.
+
+You don't have much choice on the size of
+that.
+
+Airflow by the way 12% thick.
+
+That makes it nice for the structures people.
+
+Still does a super job aerodynamically, too.
+
+And so that's pretty well dictated.
+
+Then the entry angle of attack is dictated
+by the hypersonic L/D required for the cross-range.
+
+And you can go through your equations, Newtonian
+aerodynamics sign or the exposed area, and
+
+the then L/D, the tangents.
+
+And so you've got the hypersonic aerodynamics
+from that angle of attack required for the
+
+cross-range.
+
+The wing shape to balance the configuration
+for the aft CG and acceptable wing leading
+
+edge heating.
+
+In other words, we can position that wing
+at the right place for the center of gravity
+
+that we have which, by the way, even in phase
+A is known pretty well didn't change much.
+
+The control services was the magic thing.
+
+With the payload in and out 1.5% CG changed.
+
+There has only been one other aerodynamic
+vehicle that has ever been built that has
+
+a CG of 1.5% of body length.
+
+That was a B-36.
+
+And this vehicle had to have the 1.5% change
+in the center of gravity because of payload
+
+in/ payload out.
+
+And you can try to stack it together in many
+different ways.
+
+That's just as good as you can do.
+
+That dictated the size of the control services
+to accommodate that.
+
+They are very big.
+
+They are barn doors.
+
+It makes it nice for controlling the vehicle.
+
+Oh, and the vertical tail, we'll talk about
+that.
+
+That's for crosswind landings.
+
+But the way, most all the vehicles that you've
+seen from overseas that have been proposed
+
+cannot land in a crosswind.
+
+I don't know what they are going to do.
+
+They don't have enough control service to
+land in the crosswind.
+
+But that dictated the vertical tail size.
+
+Now, as you kind of go around the loop on
+those things, some potential items that we
+
+probably want to point out here is the body
+shape.
+
+We've already basically talked about it.
+
+Nose shape, that's pretty straight forward.
+
+The basic Orbiter shape didn't really change
+from phase A through phase C and D.
+
+We blended the OMS pot a little bit because
+we didn't want it to interfere with the payload
+
+bay door which was built by a different set
+of groups.
+
+The delta wing, we put a little crank in it,
+a double delta, and got a little more subsonic
+
+lift.
+
+And we didn't have the body flap moving to
+start with, but we found that it was a very
+
+powerful control of which assisted the center
+of gravity movement.
+
+The full-spanned elevons were needed to control
+the center of pressure for hypersonics.
+
+And there are other little things there, and
+you can read those through at your convenience,
+
+but those are just basic things that you have
+to do.
+
+And we will comment on some of those a little
+bit later.
+
+The Integrated Vehicle, the launch vehicle,
+if you please, what do the program requirements
+
+do to it?
+
+Well, the Orbiter was sized for that payload
+bay weight.
+
+It had to land.
+
+It had to enter.
+
+We knew the weights pretty well.
+
+The 150k pound Orbiter, the 65k pound payload
+dictated the requirements of the Orbiter injected
+
+weight.
+
+You add them up.
+
+You've got to get it into orbit.
+
+Once around at the high inclination and return
+to the launch site set the Orbiter performance
+
+requirements.
+
+We had to have a certain amount of energy
+available from the propulsion system.
+
+Maximum hardware reusability mixed with a
+cost consideration yielded a stage and a half
+
+vehicle.
+
+And I will talk to you about that in just
+a minute.
+
+But the cost constraints, there was a great
+move afoot to have a return to the launch
+
+site booster, manned booster, if you please,
+but the cost and constraints and the size
+
+of the vehicle got pretty big.
+
+The wing vehicle loads were significantly
+reduced by the parallel burn.
+
+You've got the orbiter tucked in between the
+solid rocket boosters and the external tank
+
+versus an orbiter that would be on the end.
+
+It makes a great difference in the structural
+loads that the aerodynamics produces.
+
+Solid rocket booster mismatch decreased or
+dictated an increased beta dispersion.
+
+Typically on an end-to-end vehicle you've
+got everything kind of tucked in pretty tightly.
+
+On this one the SRBs are spread, any mismatch
+at burnout and we had some big beta dispersions
+
+that still haunt us a little bit today.
+
+Soft ride requirement.
+
+Yes, I'm sorry.
+
+I just don't know what a beta dispersion is.
+
+You don't know what a beta dispersion is.
+
+All right.
+
+[LAUGHTER] Angle of attack.
+
+Angle the size of it, beta.
+
+Alpha, beta, standard aerodynamic definition.
+
+Which, by the way, brings me to a comment.
+
+We've been asked to chase a rabbit with you
+here.
+
+I would suggest very highly that you get yourself
+a NASA dictionary where standard terms that
+
+your bosses will use because they've been
+using them for years.
+
+[LAUGHTER] That you do that.
+
+And I'm not fussing at you at all.
+
+You can get a little gray book that's called
+the NASA Dictionary.
+
+And you will know what alpha and betas are.
+
+CMQ plus CM alpha dots.
+
+All those standards terms are defined.
+
+Flutter.
+
+Buffet.
+
+And you will really look sharp when you know
+what he's saying.
+
+[LAUGHTER] All right.
+
+Go ahead.
+
+I know there are some people here who didn't
+go through aero-astro, and so may have actually
+
+not had a full course in aerodynamics.
+
+Hopefully most of you have had it.
+
+But any time there are expressions or terms
+you don't understand just do ask and we'll
+
+bring you up to speed.
+
+And that NASA dictionary, by the way, covers
+not just aerodynamics.
+
+It covers all kinds of other vocabulary kinds
+of things that your peers will be using and
+
+your supervisors will be using and you will
+know what they're talking about.
+
+Soft ride requirements, that caused us to
+go to a real low dynamic pressure which is
+
+nice.
+
+Most vehicles are up around 1200 pounds per
+square foot dynamic pressure.
+
+This one is down around 800.
+
+And the reason that came about is lesser G
+loads early on.
+
+SRB flare angle, no big deal there.
+
+Plume effects have really ate up aerodynamics.
+
+To this day that is the only thing aerodynamically
+that we still don't know how to predict or
+
+the base pressure due to plume effects through
+the subsonic and supersonic speed regime.
+
+CFD gets it right every now and then.
+
+Sometimes it doesn't get it right.
+
+And the wind tunnel test still hadn't got
+it right with solid plumes.
+
+All the scaling parameters that you use still
+don't produce, to me, what a real valid answer
+
+is.
+
+The flight data is used, and we update that.
+
+Yes, sir.
+
+When you say flare angle, do you mean like
+in the stack away from the Orbiter?
+
+Yes, sir.
+
+This flare angle right back here.
+
+We found that if you set that right, it pretty
+well sets the flow and the plumes behave themselves.
+
+If you set that too small the plumes will
+change greatly with mach numbers, sometimes
+
+in an unpredictable fashion, so that SRB skirt
+size was primarily from that consideration.
+
+This is real precious to Aaron's heart.
+
+We changed the tank shape early in phase C
+and D.
+
+And remember I told you that we had developed
+a database during phase B that would suffice
+
+and we could go immediately into the design
+and development of the total stack?
+
+By the way, I like the ogive.
+
+It's a lot prettier than the cone that we
+had on the front end.
+
+But basically what that did, that changed
+the aerodynamics of the whole stack.
+
+And the data that was delivered to structure
+for their structural analysis, the data that
+
+was delivered to the heating people for their
+heat transfer analysis had to be done all
+
+over again.
+
+That's a year and a half cycle from the time
+you say let's go build a model, let's get
+
+the data, let's analyze it.
+
+The other thing that happened when we changed
+the tank, everybody took note of that, and
+
+there are all kinds of other small changes
+that jumped on.
+
+[LAUGHTER] On the Orbiter a little bit, on
+the external tank, on the SRBs and on the
+
+inclination that we had between the Orbiter
+and the tank.
+
+Let me just hit some things I think that you
+want to take note of on this one.
+
+I guess the nose shape, we mentioned that
+one already, reduces the drag.
+
+It also reduces the loads.
+
+We have to worry about the punch loads between
+the SRB and the tank.
+
+And those aerodynamics are driven quite a
+bit by that nose shape.
+
+The SRB locations fore and aft, there is some
+adjustment that you can have in that, and
+
+those are all optimized that whenever we do
+the aerodynamics that puts a minimum amount
+
+of load into the system.
+
+Orbiter instance angle, that's the angle between
+the Orbiter and the external tank.
+
+It drives the stability of the configuration
+to some degree.
+
+But, more than that, it drove the loads quite
+a bit into the program.
+
+And that was optimized.
+
+Full span elevators, we use those to adjust
+the pitching moments so we get minimum change
+
+required to trim the vehicle from the SRBs,
+solid rocket boosters, and the SSMEs, the
+
+main shuttle engines.
+
+SSME, plume effects and the plume effects
+from the SRB, that's the only thing that we
+
+got a bad grade on as far as predicting aerodynamics
+on either the Orbiter or the Integrated Vehicle.
+
+All the rest of the stuff came out just about
+as we had predicted.
+
+Now, getting back to where you asked the question.
+
+Phase A.
+
+Go back now.
+
+What is a phase A?
+
+That is the conceptual design.
+
+We had all kinds of configurations because
+we had all kinds of requirements.
+
+We really didn't know what those were, and
+so that analysis had to be done.
+
+Many, many vehicles.
+
+A lot of considerations.
+
+The analytical techniques we used to identify
+problem areas.
+
+Hypersonics, quite frankly in phase A.
+
+Newtonian vehicle shape was approximated with
+flat plates.
+
+Works great on a configuration.
+
+[LAUGHTER] That's pretty much like a vehicle
+that is kind of trimmed out of a piece of
+
+a sphere, if you please.
+
+And those aerodynamic characteristics were
+very good.
+
+As a matter of fact, the thing is laid out
+on graph paper and you counted the squares
+
+and saw where the CG was and what things had
+to be.
+
+And it worked.
+
+It worked.
+
+Now, we didn't know that it was working at
+that time.
+
+But we found out later that it did.
+
+But that's what we used.
+
+[LAUGHTER] NASA documentation.
+
+NASA had pretty good TNs on vehicles that
+were somewhat similar.
+
+And the characteristics of those, we made
+the adjustments because of the difference
+
+in configuration.
+
+The Air Force had a document called Dataman.
+
+It was unpublished at that time, but we got
+a preliminary draft that we worked through
+
+by hand.
+
+By the way, this is a published thing.
+
+I would suggest very highly if aerodynamics
+is going to be your forte is that you learn
+
+how to use that program.
+
+It's Dataman Aerodynamics Handbook.
+
+Navel Ordinance had a handbook out.
+
+They've never computerized theirs, but it's
+the Handbook of Supersonic Aerodynamics and
+
+good-old Horner's fluid dynamics lift and
+drag.
+
+It is still around today, still use it, but
+those were the aerodynamic methods that we
+
+used during phase day.
+
+And we also did small scale wind tunnel tests
+and those things that were the problem areas.
+
+And the problem areas were primarily in the
+transition.
+
+Yes, sir.
+
+I can understand how you can do wind tunnel
+testing.
+
+What about plume effects?
+
+You said you didn't understand those.
+
+How do you test that experimentally?
+
+[UNINTELLIGIBLE PHRASE] No, that's done in
+a wind tunnel.
+
+Some people said you need to match momentum
+on a scale vehicle.
+
+Certain other characteristics.
+
+What you'd like to do is be able to simulate
+it with a solid plume, so we did solid plume
+
+testing.
+
+We had method of characteristics back then.
+
+It took it about three weeks to run, to get
+the plume sizes, and they did a pretty good
+
+job.
+
+But when you have the plume sizes you still
+after the base effects change in the pitching
+
+moment.
+
+And so we did the solid plumes.
+
+And we did gaseous plumes at Ames Research
+Center.
+
+We did cold gas and hot gas.
+
+But none of those met all the scaling parameters.
+
+When you rolled all that up and you did the
+best you could, we still missed base pressure.
+
+Base pressure was missed on Saturn 5.
+
+Base pressure was missed on Mercury.
+
+Base pressure was missed on Little Joe II
+and Little Joe I.
+
+Every launch vehicle that I could find we
+missed base pressure on.
+
+We missed base pressure on the Shuttle also.
+
+Not a big effect, but it is embarrassing that
+you cannot get it right.
+
+But this was done primarily more in phase
+C and D than in the phase A time period.
+
+We just kind of said plumes are going to be
+about that much based upon data from other
+
+vehicles.
+
+And then making sure that it was not a design
+driver or design stopper, if you please, that
+
+it wasn't going to be a problem that was so
+big that it changed things so greatly that
+
+your performance wasn't adequate.
+
+And we had margins and everything.
+
+Anyway, we did some small scale testing.
+
+Phase B.
+
+What did we do on the Shuttle on phase B?
+
+We went into phase B with four major configurations.
+
+Three externally identical configurations
+with swing wings.
+
+It was called the Triamese.
+
+And I think General Dynamics was the one that
+proposed that one.
+
+They have all bought on another, and it's
+hard to find out who is who any longer.
+
+But, anyway, that was one of the concepts.
+
+Very, very expensive.
+
+The swing wings, never really solved those
+problems.
+
+Lockheed had a large single stage blended
+body, kind of an HL-10 looking thing with
+
+a flat bottom, and then with a large external
+tank around.
+
+And I couldn't find pictures of all this to
+show you, but that was one that came in.
+
+And then the two-stage fully reusable with
+both the first and the second stages being
+
+runway landers, a very favorite of Marshall.
+
+And then, the one that we called the stage
+and a half where you're literally burning
+
+the first stage boosters and the second stage
+engines at the same time with the external
+
+tank, we referred to that as a stage and a
+half with parallel burn which is the current
+
+shuttle.
+
+But those are the things that we started phase
+B in and did aerodynamic designs on all those.
+
+How did we do that?
+
+Well, we had gotten a little smarter.
+
+A lot of the Newtonian programs had now been
+automated.
+
+It was still pretty much a flat plate kind
+of a program, though, were you divided the
+
+vehicle up into a number of flat plates.
+
+And then there was some contractor in-house
+wind tunnel test.
+
+NASA did some limited tests on potential problem
+areas post phase B and pre phase C and D.
+
+That was a gap between the time we put out
+an RFP, request for proposal, and the time
+
+that the contractors came back with a proposal.
+
+We had narrowed it down that it would be a
+stage and a half.
+
+That would be what we would write the RFP
+for.
+
+We developed a large wind tunnel test program,
+developed a full aerodynamic database and
+
+heating database for that shuttle that was
+there at that time that was delivered to the
+
+contractors that were going to bid on that.
+
+Integrated Vehicle.
+
+We used the USF stability and control datcom.
+
+Some contractor wind tunnel tests were done
+and limited NASA testing and analysis for
+
+potential problem areas.
+
+And also we did a post phase B, full aerodynamic
+database for that vehicle.
+
+Now, with that, what we're trying to do is
+eliminate configuration changes if at all
+
+possible.
+
+And we accomplished that to some degree, but
+the change to the tank and other changes came
+
+back in that caused us some delay.
+
+But it was minimized.
+
+Phase C and D, configuration was baseline.
+
+A big word here, make work changes only.
+
+Nothing has changed because it looks better,
+works better.
+
+You've got to change it or it will crash.
+
+That's what we said.
+
+That's not what we did.
+
+We made some changes because they were nice.
+
+Theoretical aerodynamic techniques were employed
+to ensure you never get to test the right
+
+Reynolds number.
+
+Henceforth, your boundary layer is a little
+bit wrong.
+
+Plume effects, they've got to be corrected.
+
+So there was a lot of analytical work that
+was done during that phase C and D.
+
+Let me say this.
+
+That area of our technology was really improved.
+
+A lot of dollars that went into that, Aaron's
+courtesy, that the program probably didn't
+
+need to fly the shuttle.
+
+Now I tell him.
+
+I didn't tell him back then, you're right.
+
+[LAUGHTER] But, for the benefit of technology,
+we did that.
+
+We pumped great money into CFD, great money
+into method of characteristics.
+
+A lot of money into other techniques that
+were there.
+
+And once more NASA goal was not only to do
+that mission but to help technology.
+
+And the reason you can do CFD today was because
+the dollars that the shuttle program pumped
+
+into that.
+
+Had they not pumped that in you would still
+be adding up flat plates.
+
+[LAUGHTER] Aerodynamic variations and uncertainty
+were developed for all aerodynamic coefficients.
+
+No other vehicle had really done that.
+
+You sort of did the best that you could and
+said these are my aerodynamics.
+
+This is my normal force versus angle of attack.
+
+This is my side force coefficients, yawing
+moment coefficients versus beta.
+
+And that said you would analyze that, give
+that to the flight control system, give that
+
+to the structures people and they would put
+their margins of safety in and look at it.
+
+We were quite concerned on this vehicle, especially
+when it starts out at a 45 degree angle of
+
+attack.
+
+And sometimes during the supersonic and transonic
+regime it transists down to a low angle of
+
+attack.
+
+Flow is separated.
+
+Some place in there it reattaches.
+
+It cannot always make up its mind.
+
+You've got to be able to control the vehicle,
+even though we weren't intentionally maneuvering
+
+at that time.
+
+And so we developed these variations.
+
+If you go back in the tunnel three times you
+get what?
+
+Four different answers.
+
+[LAUGHTER] And they're all very, very close.
+
+If you change facilities you get slightly
+different answers.
+
+We had some Reynolds level boundary layer
+kinds of problems between the wind tunnel
+
+and the full scale.
+
+And so these uncertainties were developed
+for all the aerodynamic coefficients.
+
+Then this data was delivered to the GN&C people
+where they make for sure that they can fly
+
+their system with the uncertainties.
+
+The CN betas, yawing moment coefficient with
+angle of side slip, the control moment coefficients,
+
+the delta yawing moments and rolling moments
+due to elevon maneuvers, where the errors
+
+on those, that the control system wouldn't
+go berserk with any combination of those.
+
+The same with structures and with flight dynamics.
+
+Now, we're not living with those today.
+
+We did flight tests to reduce the variations.
+
+The astronauts put in PTI, pilot test inputs,
+where they would do it a certain way and we
+
+would pre-predict those characteristics.
+
+Then we'd look at them post-flight.
+
+We would pull the aerodynamic characteristics
+out with regression analysis techniques to
+
+say this is the aerodynamic coefficients that
+had to be there for that maneuver to look
+
+like it looked.
+
+That, within itself, has some plus or minus
+stuff because you can change stuff a little
+
+bit and it still looks pretty good.
+
+Those two then were combined and we had a
+set of reduced aerodynamics.
+
+But today when you go to the aerodynamic data
+book, which we hope to be able to get you
+
+copies of, it will have not only the coefficients
+for all mach numbers, angles of attack, angle
+
+to slide slip, it will tell you what the uncertainty
+as a function of mach number angle of attack
+
+is for that.
+
+And your system should be able to work with
+all those.
+
+I want to mention this aerodynamic design
+substantiation report.
+
+You won't be able to get a copy of that any
+place that I know of but we're going to try
+
+to get a copy to Jeff for you, and it should
+be available in your files.
+
+But what that did, that goes back in, and
+for every coefficient, every angle of attack,
+
+how we arrived at that specific value and
+those specific variations using both wind
+
+tunnel and flight test.
+
+A super document.
+
+Not pretty but an excellent technical document.
+
+And that was done during the flight test program
+and afterwards.
+
+I thought we would stick up there the Wind
+Tunnel Testing Program.
+
+That's primarily the backbone of the aerodynamic
+database of the shuttle both for the Orbiter
+
+and the Integrated Vehicle.
+
+149 entry tests on the entry vehicle.
+
+79 heating.
+
+40 structural.
+
+You can add them up.
+
+Hours of wind tunnel test time 17,000.
+
+Aaron asked me how that compared with the
+Apollo.
+
+As best I remember, we did about 4,000 to
+5,000 hours on the entry vehicle on Apollo.
+
+However, Apollo didn't have all of those moveable
+surfaces.
+
+Moveable surfaces are nice, do a lot of things
+for you, but you've got to test and make sure
+
+they're there.
+
+And those were through various wind tunnels
+throughout the country?
+
+Yes, sir.
+
+These were the best facilities in the country.
+
+Do they still exist?
+
+Far up and away, yes, sir, they still exist.
+
+The ones at Ames are still usable.
+
+The ones at AEDC are still usable.
+
+Unfortunately, those at Langley, even though
+they're there and they work, because of funding
+
+constraints, Langley has a hard time bringing
+them up and using them.
+
+And that's unfortunate because they have some
+excellent facilities there.
+
+And we surely used them.
+
+In this Wind Tunnel Test Program, you can
+find out in a special wind tunnel testing
+
+program summary.
+
+By the way, you can get this document pretty
+straightforwardly.
+
+Ascent vehicle.
+
+A few less hours, and that's because you don't
+move as many surfaces primarily.
+
+Heating.
+
+That's something to work on.
+
+If you want a good project to work on, how
+do you take heating data in a wind tunnel
+
+on a small scale vehicle and make full scale
+predictions?
+
+The reason that's near and dear to my heart,
+they ran a test not too long ago and they
+
+still cannot match those two.
+
+A good PhD thesis.
+
+Maybe you can figure out how to do that and
+how to do it right.
+
+A lot of scaling parameters that are used,
+kind of like plumes.
+
+You're not sure which scaling parameter really
+works, but there is slide test data, calorimeters,
+
+and there is fly test data and wind tunnel
+data.
+
+It doesn't bother us that much because we've
+got enough conservatism in the system and
+
+uncertainties that we know we're safe to fly,
+but it does hurt your pride when you said
+
+hey, that heating rate should be 9 BTU's per
+foot squared per second and the fly test data
+
+said it's not but 2.
+
+You might look good one way, you look bad
+another way, but if I was looking for something
+
+to get my plow into and I was interested in
+theoretical stuff, that's probably what I'd
+
+pick.
+
+Total Wind Tunnel Test Program, Aaron paid
+for that out of his budget, by the way.
+
+It was less than $100 million.
+
+[LAUGHTER] In those year dollars.
+
+But it was an excellent program.
+
+Every test that was conducted was documented,
+analyzed, and we can make that available.
+
+That concludes the things that I had to tell
+you.
+
+And we hit that hour, just about right.
+
+Do you have any questions that you'd like
+to ask?
+
+If not, I'll give you a test.
+
+Yes, sir.
+
+[UNINTELLIGIBLE PHRASE] How do we affect the
+trim?
+
+[UNINTELLIGIBLE PHRASE] Hypersonics, and when
+I say hypersonic, let me take it down to mach
+
+5, was probably the best at prediction that
+we had.
+
+A flat plate which the belly of the orbiter
+has a little bit of surface bending both in
+
+the pitch plane and in the yaw plane for stability.
+
+If you put a big sphere or segment of a sphere,
+you could place the Orbiter on that and you'd
+
+say, hey.
+
+And I know a sphere or segment of a sphere
+has stability.
+
+Now, the uncertainties turn out not to be
+in normal forces or in even side forces.
+
+Pitching moment is the one that you tend to
+miss the most.
+
+And sometimes you don't know if you have a
+wrong pitching moment or a wrong center of
+
+gravity.
+
+They both precipitate a delta pitching moment
+coefficient change.
+
+The big barn doors, we have that into the
+system where we control not only a rate control
+
+system but an attitude control system.
+
+And so it takes, with a 70 square foot, it
+just takes a small amount of change to correct
+
+any error that you might have in either CGR
+pitching moment.
+
+Your control mechanism is with the big elevators
+and also the body flap a little bit, if you
+
+want to use that.
+
+The reaction control system is a rate system.
+
+And I didn't mention that.
+
+And we intentionally put the reaction control
+system in the wake of the vehicle, even though,
+
+for orbital maneuvering, we have jets that
+are the forward firing end.
+
+But so much uncertainty in how that changes
+the aerodynamics in a surface that is not
+
+a hard surface.
+
+And that interaction, you can change things
+in such a way that you amplify it or reduce
+
+it.
+
+And so we elected not to try to grapple with
+that problem and use just the aft jets, but
+
+it's just for a rate control system.
+
+End pitch, that's the distance that separated
+that, and yaw on both sides, and in roll.
+
+[UNINTELLIGIBLE PHRASE] X-15 was a low angle
+of attack airplane type configuration from
+
+mach 25 to mach 5.
+
+You're flying a spacecraft kind of configuration
+where you basically roll about the velocity
+
+vector.
+
+You want to maintain that pitch trim and roll
+about the velocity vector for cross-range
+
+in either direction.
+
+Now, when you begin transition because you've
+got to be down here when you're landing, you
+
+pick the best place to do that.
+
+And the best place to do that is back in the
+mach below 5 and, of course, above the subsonic
+
+regime.
+
+And we try not to have any maneuvers that
+are required during that time period.
+
+Any time you're going from a totally separated
+flow on the back of the vehicle to one that
+
+is now attached, separated flow cannot make
+its mind sometimes.
+
+Does it want to be separated?
+
+Does it want to be attached?
+
+Not only the whole vehicle but even on small
+pieces of the vehicle.
+
+And so there are uncertainties that come in
+there.
+
+But that's the area.
+
+But you've got to be sure.
+
+And that's where we did a lot of our PTIs,
+by the way, as we became more and more brave
+
+to get those coefficients.
+
+And the wind tunnel did a pretty good job
+on them.
+
+Yes.
+
+[UNINTELLIGIBLE PHRASE] What you're doing
+is changing the Newtonian flow now on my flat
+
+plate 70 square foot per surface.
+
+You mean the rear-end?
+
+The rear-end, the big end, yeah.
+
+Now I've got a normal force coefficient sine
+squared to the angle.
+
+Then I just change the angle up and reduce
+the forces on that, and that gives me a nose
+
+up.
+
+I bring it down.
+
+That gives me a nose down.
+
+It works beautifully.
+
+This is the body flap we're talking about.
+
+Body flap and elevators, yeah, both.
+
+Body flap and aft control surfaces.
+
+Yes, sir.
+
+You talked about the flight test portion of
+the aerodynamics.
+
+What sort of planes were you using to do that?
+
+The flight test was the shuttle itself.
+
+After we safely entered and everything then
+we designed these pilot test inputs to extract
+
+aerodynamic characteristics.
+
+The same technique that Edwards developed.
+
+And they did develop that, by the way, on
+the X-15 and on other vehicles, too.
+
+And we used that same technique.
+
+We sent one of our men out and he spent about
+almost a half a year learning all their techniques,
+
+brought that back, developed that and worked
+with the astronauts very, very closely.
+
+They trained for those maneuvers.
+
+We extracted data for those maneuvers.
+
+We would change the aerodynamic characteristics
+and not tell them what they are in the simulators.
+
+And made sure that we didn't get any difficulty
+and made sure that the aero people could extract
+
+that data right and tell us how we changed
+it.
+
+They all got good As.
+
+And it worked very, very well.
+
+[UNINTELLIGIBLE PHRASE] No, sir.
+
+We did that one.
+
+That was for the approach and landing test.
+
+But for the entry vehicle, no, those were
+supersonic.
+
+Yes, and we did hypersonic.
+
+We're talking about tests that were done during
+the flights.
+
+The first four flights were designated orbital
+flight tests.
+
+And I think the PTIs actually continued well
+after that.
+
+Yes.
+
+Actually, what this has given us, in terms
+of a hypersonic database for a winged vehicle,
+
+is incredible.
+
+At first they were called pilot test inputs
+because the pilots were doing them automatically.
+
+And then I remember some of the pilots were
+saying you've got to do it very precisely
+
+and so we really have got to be concentrating
+on that.
+
+And there are so many other things we have
+to concentrate on.
+
+Could we possibly computerize this?
+
+And so I don't remember which flight they
+started doing that, but at that point the
+
+PTIs became known as the program test inputs
+rather than the pilot test inputs.
+
+You basically put in a little pitch up, pitch
+down and see how it affected the roll and
+
+the yaw and all these cross-coupling things
+at lots of different mach numbers.
+
+And, over the course of a bunch of different
+flights and a lot of different PTIs, it really
+
+built up the aerodynamic coefficients at all
+these different mach numbers.
+
+You might say a little bit about how we collected
+hypersonic test data in wind tunnels.
+
+I mean it's not like you can just have a fan
+going and produce a mach 20 airflow for 20
+
+minutes and you can play with your little
+thing.
+
+Hypersonic testing was done primarily at the
+Ames Research Center three and a half foot
+
+facility.
+
+We also did some up at Calspan, also used
+some of the Langley facilities, but the real
+
+workhorse was this three and a half foot hypersonic
+tunnel.
+
+And basically you would have the air coming
+through the tunnel at the required conditions.
+
+You would put the model of the vehicle, which
+is usually a 1.5% to 3% model in the facility.
+
+You have what is called a six component balance
+that fits into the model.
+
+That is a strain gauge relationship.
+
+It gives you force and moments in both directions,
+or forces in both directions and some difference
+
+between the gauges so you can pull the pitching
+moments and the yawing moments and the rolling
+
+moments out of that.
+
+You reduce it based primarily upon dynamic
+pressure or you say CN is equal to the normal
+
+force divided by QS, the dynamic pressure
+times a reference area.
+
+Standard aerodynamics, but once more a language
+kind of thing where if you're in gas dynamics
+
+and not aerodynamics sometimes you don't get
+back over to those coefficients.
+
+By the way, in that same document all of those
+terms are defined pretty well.
+
+But you measure those with a balance.
+
+Then the question happens, well, I wasn't
+at full scale Reynolds number.
+
+And then that's where you come up with your
+theoretical techniques.
+
+And you come back in and you look at it and
+you see that the boundary layer and the Reynolds
+
+number corrections theoretically make a very
+little bit of difference.
+
+And then you go through today the CFD programs.
+
+You say it gets about the same answer.
+
+You go back to the flight test data and it
+gets about the same answer.
+
+Basically, what you conclude is wind tunnels
+do a super job hypersonically for this kind
+
+of a configuration.
+
+Now, it did good on the Apollo, it did good
+on the Gemini, it did good on the Mercury
+
+and it did good on the Shuttle.
+
+Give me that configuration and I'll tell you
+what the hypersonic aerodynamic characteristics
+
+are.
+
+I can tell you in phase A, and it's not going
+to be too much different at the end of phase
+
+B.
+
+And maybe you don't want to hear that because
+maybe you were going to do great things in
+
+the hypersonic area.
+
+But on a blunt body, which is what we're talking
+about, it does a super job now.
+
+X-15, low angles of attack flying like an
+airplane, a different story completely.
+
+[UNINTELLIGIBLE] configuration.
+
+No, I wouldn't want to use just Newtonian
+to predict the aerodynamic characteristics
+
+hypersonically of that vehicle.
+
+On the other hand, I wouldn't want to fly
+it there either.
+
+It would burn up.
+
+Blunt body is good.
+
+98% of the energy goes into the shockwave.
+
+98% of the energy goes into your vehicle when
+you're flying low.
+
+A manned entry vehicle enters the earth's
+atmosphere.
+
+You're going to be flying something like a
+segment of a sphere or at worst a right elliptical
+
+cone.
+
+And Newtonian works good on that one, too,
+by the way.
+
+We wind tunnel tested those for different
+configurations.
+
+That gets your L/D on up to a 1.75 rather
+than 1.5.
+
+Yes, sir.
+
+Why couldn't any sort of straight winged configuration
+make the cross-range requirement?
+
+The cross-range requirement is primarily angle
+of attack oriented.
+
+The relationship between the CG payload in
+and payload out is a pretty good change.
+
+And, if you had a straight wing, your straight
+wing cannot be placed in such a way that it
+
+trims subsonically and trims hypersonically.
+
+Now, it can,at higher angles of attack with
+less L/D, you can make it work.
+
+But down at 45 degrees you end up with a delta
+wing configuration.
+
+Does that answer your question?
+
+And that's a good exercise, though.
+
+But you can go through it on a couple of sheets
+of paper and say ah-ha.
+
+Because hypersonically you've got that CG,
+you've got your CP, you know where it has
+
+got to be placed, you get down to low angles
+of attack, you know where your CP is for that
+
+body, you know your CP is up at the quarter
+card and you know you've got 4.5 CGs.
+
+It doesn't quite work.
+
+It takes a delta to do that.
+
+So it was more CG related than heating?
+
+Yes, sir.
+
+Although, the one that we mentioned, the 200
+nautical mile cross-range with a straight
+
+wing, Langley did some tests on that, even
+at high angle of attack.
+
+And right in where that straight wing ties
+back into the fuselage had super high heating
+
+rates.
+
+But we could put little fillets in there and
+overcome that heating particular thing.
+
+But, if you're going to go real fast, delta
+wings look better.
+
+[LAUGHTER] All right.
+
+Yes, ma'am.
+
+When you were doing all this aerodynamic analysis,
+did you consider a perfect surface, or did
+
+you also do tests or analysis on what if the
+TPS fails?
+
+Good question.
+
+First of all, we have an external insulator.
+
+And Bob Ried will talk to you about that,
+and Tom Moser probably has too.
+
+Which meant that our main aluminum surface,
+which we want to keep quite cool, is different
+
+than the one that we initially designed.
+
+We went back in, made models that simulated
+those differences, made calculations that
+
+simulated those differences.
+
+They were very small corrections that needed
+to be made.
+
+Then the other question that you had was suppose
+you lose a piece of TPS?
+
+Which we did.
+
+We've lost some chunks of TPS early in the
+program.
+
+And you cannot do much testing on that because
+it's so little bitty and it's like a greased
+
+pencil kind of a thing.
+
+But you go back in.
+
+The first approach is we take some maximum
+things.
+
+The pressure cannot be greater than total
+and it cannot be less than zero.
+
+And so let's put those deltas into that area
+and into a nice area around there and see
+
+if it makes any difference to the aerodynamic
+coefficients.
+
+And they're quite small and so we feel quite
+comfortable with that.
+
+Now, from a heating, a different answer.
+
+But, from an aerodynamic standpoint, does
+it affect the aerodynamics?
+
+We scope it in that way.
+
+It's a pretty small area.
+
+Yes, sir.
+
+Where was the greatest risk on the aerodynamic
+design?
+
+During the first flight, was there anything
+you were particularly concerned about?
+
+Oh, yeah.
+
+[LAUGHTER] Getting it right.
+
+I guess my biggest pucker factor is in the
+transitional phase.
+
+I'd just seen so many things go wrong transonically
+that transonic wind tunnels miss.
+
+It's a dynamic situation where you're moving.
+
+And that was, personally, my greatest concern,
+did we get that right?
+
+We did everything we could.
+
+And it turned out that we did a good job,
+but I worried about that more than anything
+
+else.
+
+Launch vehicle.
+
+Primarily did we get the structural loads
+right and did we put enough margin in?
+
+We did not use uncertainties in the pressure
+distributions.
+
+Couldn't really figure out how to do that.
+
+We had to have balance loads.
+
+And if you said my CP can be higher or lower,
+do you put it higher over the whole vehicle
+
+or higher here and lower there?
+
+And then you've got unbalanced loads.
+
+But we did measure the wing bending moments,
+wing shears, wing torsion and also the attached
+
+loads in those.
+
+And so we put some uncertainties on those.
+
+And Tom has already been here.
+
+I don't know if he mentioned how they tried
+to handle those.
+
+But at least they had some of those things.
+
+But we never figured out how to put uncertainties
+and pressure distributions and still be able
+
+to get all the balance loads for NASTRAN.
+
+Maybe one of you all are sharp enough to figure
+out how to do something like that.
+
+But that was the one on the ascent, had we
+adequately covered the uncertainties in pressure
+
+distributions with the way that we accomplished
+that by the uncertainties in the bending moments,
+
+torsion and shear?
+
+Let's take a couple minute break and then
+we can resume with questions.
+
+I am going to go down to my office and get
+one or two things which I think will be interesting
+
+that we can also talk about.
+
+Take a minute or two.
+
+Instead of one configuration, you've got one
+configuration times 5 degrees, 10 degrees,
+
+minus 5 degrees.
+
+These split down the middle.
+
+The same way here, body flap.
+
+You've got one, two, three, four, five times
+five.
+
+You've got 25 different configurations versus
+one.
+
+And so it means more testing, but you're using
+the same facility.
+
+It just means more hours of wind tunnel time,
+more hours of plotting and looking.
+
+Say a few words about how you did the systems
+engineering or the systems integration between
+
+the aerodynamics and the flight control system
+[UNINTELLIGIBLE PHRASE].
+
+All right.
+
+Let's take flight control system.
+
+We, in our division, were responsible for
+aerodynamics and flight dynamics.
+
+And flight dynamics wasn't very well defined.
+
+The Avionics Division was responsible for
+the GN&C system control system and also flight
+
+dynamics.
+
+So, you've got to work together.
+
+And you're going to get in one another's bailiwick.
+
+That's part of good systems engineering.
+
+You're going to do what the other fellow is
+going to redo, and he's going to do what you're
+
+going to redo.
+
+But our responsibility was two-fold.
+
+One is we had to have the right aerodynamic
+characteristics.
+
+But, before we had the right aerodynamic characteristics,
+we had to have a configuration that should
+
+be able to live with a GN&C system.
+
+The way we accomplished that is Ken Cox, is
+Ken going to be here with you?
+
+No, OK.
+
+Ken Cox was head of the Avionics and GN&C
+System.
+
+He gave us a functional GN&C system.
+
+It didn't have all the strings in it, didn't
+have all of the relays and all the stuff there,
+
+but if we gave it a command to change that
+we knew how much it would change and how long
+
+it would take it to change.
+
+An elevator position as a for instance.
+
+And so that was called a functional GN&C system.
+
+It did the right functions but it didn't do
+it the same method that the real GN&C system
+
+did.
+
+We would take our aerodynamics and see that
+it would work.
+
+And we would be able to make the maneuvers
+that were required.
+
+And we would analyze it.
+
+Ad we would be pretty satisfied that with
+those aerodynamics and with the variations
+
+that we were OK.
+
+But that didn't say the system was OK.
+
+That just said that we had a pretty high probability
+of making it work.
+
+Then we sent that aerodynamic database.
+
+And all this is happening not ship it, throw
+it over the fence, but over a period of time
+
+we sent them the aerodynamic characteristics
+with the variations.
+
+And then they beat it bloody flying everything
+they can think of with their GN&C system.
+
+Fortunately, that worked out pretty well.
+
+He would pick up a few things, but not anything
+major.
+
+And, by the way, this is the only vehicle
+I know that happened that way on the Orbiter.
+
+We didn't have any major configuration changes
+that we had to make once we got well into
+
+the program.
+
+It stayed the same.
+
+[UNINTELLIGIBLE PHRASE] That's right, yes.
+
+And that was true.
+
+That whole thing, not only the GN&C system
+but the hydraulics is when you give it the
+
+command, when you say I want a delta theta
+so much or delta E of so much, that it takes
+
+it about a quarter of a second to get there.
+
+And that's a long time on a lag time when
+you pile all those things end to end up.
+
+Now, structure is much the same way.
+
+They gave us load indicators where they said
+we can take so much wing shear, so much wing
+
+torsion, so much wing bending, so much punch
+loads into the tank from the attach point
+
+in the front, so much punch loads into the
+tank on the backend, SRB and we have all the
+
+gimbling.
+
+That's where we're doing the flight performance
+calculations, through the wind shears and
+
+the wind gust.
+
+And we assure ourselves that we don't violate
+any of the load indicators.
+
+But that does not say the vehicle is safe.
+
+Then GN&C flies that one through that and
+gives all those conditions back over to the
+
+structures people, and they analyze the hound
+out of it.
+
+They look at all the cracks and crevices.
+
+And, if you have people that don't have a
+cooperative spirit, it will not work.
+
+It just doesn't work.
+
+So, you've got to learn how to get along with
+your buddies over on the other side.
+
+Don't build your fiefdom up that your wall
+is so big and you control your own destiny
+
+because you don't.
+
+And we had a super group of people to work
+with.
+
+And, to me, that's what really made it work.
+
+The same thing on heating, by the way.
+
+They would give us heating indicators and
+we would fly it because that was a little
+
+more straightforward where they would give
+us the Q dot locals to Q dot references.
+
+And we would look through all the Q dot references.
+
+And we'd give them all the final set of trajectories
+and they would analyze it in detail.
+
+But I look at it as here is a problem and
+I can work it like a piece of pie and go on
+
+this problem, go all the way down to the center,
+then go over and eat this piece and this piece.
+
+It doesn't work that way.
+
+You start around the edges and you cycle in
+on it.
+
+You eat all the pie, but you accomplished
+it around the edges first and work out your
+
+bigger problems and then get down to the smaller
+problems.
+
+Bass, I think the important point, too, is
+that no matter what system you work on, whether
+
+you work on the Apollo or you work on the
+Shuttle or whether you work on the new CEV,
+
+you're going to basically have to go through
+the same process.
+
+It may be simpler or harder but you're going
+to have to go through the same process.
+
+Absolutely.
+
+Yes, sir.
+
+You said there was no major configuration
+changes like around the program, but is there
+
+anything that you felt you were kind of stuck
+with like I wish we could have changed this?
+
+Like not having the OMS pods stick out in
+the back like that?
+
+What that a problem for aerodynamics?
+
+No.
+
+We lost the increased drag a little bit, but
+not enough to hurt anything.
+
+And aerodynamics, it didn't bother me any
+that my L/D went down by 0.001.
+
+But now the fellows that were flying it, they
+got in there, they said I can still go around
+
+the hack and I can still do all the things
+I want to.
+
+But all that was done.
+
+And once more, systems integration, you've
+got to include the crew.
+
+GN&C system, it doesn't bother them in aero,
+it doesn't bother them in structures, but
+
+you've still got to fly.
+
+And Dr.Gilvarry said you don't want the pilots
+talking bad about your airplanes in the bars
+
+so keep your crew happy.
+
+[LAUGHTER] But, to answer your question, no,
+not really.
+
+To meet the requirements, it's going to look
+pretty much the same.
+
+If I designed it today, OK, let's go back,
+the same requirements now.
+
+If you give me a different set of requirements,
+it's not going to look the same.
+
+Bass, some people wanted to put some canards
+[UNINTELLIGIBLE PHRASE].
+
+canards, that's not a joke.
+
+That was done, but it was a big argument.
+
+A canard is an aerodynamic surface part of
+the center of gravity.
+
+And the beneficial part, let me tell you the
+good parts about canards.
+
+canards, subsonically, I can give a pitch
+up moment and increase my lift.
+
+If it's on the aft of the vehicle when I give
+a pitch up moment, I decrease my lift.
+
+So, canards are wonderful.
+
+But what canards do is it fouls up the flow
+over all of the rest of your vehicle.
+
+And so, back to here, I've got one configuration.
+
+Unsteady aerodynamics.
+
+Heating.
+
+Fixed configuration.
+
+I put a canard out there.
+
+Now I've got two more configurations, three
+more configurations, four more, five more,
+
+six more.
+
+And it does a lot of grief with vortexes and
+stuff like that.
+
+Now, if you had to have it, you have to have
+it.
+
+Concorde had to have it, but that didn't mean
+that Shuttle had to have it.
+
+It operated fine without canards.
+
+I sure wouldn't put canards on there, if we
+had another shot at it.
+
+Yes, ma'am.
+
+Would it be easier, faster or cheaper to design
+the Shuttle, the Orbiter [UNINTELLIGIBLE PHRASE]?
+
+You ask good questions, young lady.
+
+[LAUGHTER] Yes and no.
+
+With the tools we have and the foreknowledge
+that we have, having been there before, absolutely
+
+yes.
+
+And I don't want to be negative, but you don't
+have the cooperative spirit going on that
+
+you had then.
+
+I don't know why either.
+
+The young engineers are sharper, no ifs, and
+or buts.
+
+You all know a whole lot more than I ever
+knew, but you don't get along as well.
+
+[LAUGHTER] This is mine.
+
+I don't need you here.
+
+I don't want you here.
+
+Get out of here.
+
+I'm going to do it my way.
+
+And that's just an observation I made.
+
+It might be that my knothole is too restricted.
+
+But it goes up to pretty high management,
+too.
+
+Not just at the working level.
+
+A second thing is they asked me to come in
+and consult with them.
+
+And they had lost technical capability.
+
+Didn't use any engineers much after a certain
+time on the Shuttle.
+
+And then, after the last accident, they had
+to bring the engineers in.
+
+And they said I've never looked at that and
+I'm on the payroll.
+
+The capability was greatly lacking, and so
+we developed some ways to bring them to speed
+
+in about a year and a half period of time
+which happened.
+
+Observation.
+
+By the way, I was pleased that you all got
+to class on time.
+
+I told management to send them to ethics school.
+
+Now, if there is a meeting and you tell somebody
+you will be there at that time, you be there
+
+at that time.
+
+If you tell somebody you will make a deliverable
+at that time, you make a deliverable at that
+
+time.
+
+Be a man or woman of your word.
+
+And I found that lacking.
+
+I don't know that ethics school helped too
+much that we sent them all to.
+
+Well, it did, too, because the second day
+of class there were, I think, ten of them
+
+late.
+
+And he sent them back and wouldn't let them
+in the class.
+
+[LAUGHTER] But learn to get along with folks.
+
+They are your friends.
+
+They're your buddies.
+
+They are going to be there for a lifetime.
+
+And, yeah, you're going to have some grief.
+
+And, yeah, he will give you some headaches
+or she will give you some headaches.
+
+But you're all on the same team, and work
+hard towards that.
+
+I know you've got to grit your teeth and spit
+sometimes, but that's major.
+
+And that didn't cost you anything.
+
+About the wind tunnel testing, firstly, could
+you have reduced that now with CFD?
+
+And, secondly, you showed there were several
+hundred tests.
+
+Yes.
+
+And several tens of thousands of hours.
+
+Yes.
+
+Does that mean each test ran for several hundred
+hours?
+
+Some tests ran for hundreds of hours.
+
+That was the total number of hours for all
+those tests, not a per hour basis.
+
+But, yeah, there were some hundred hour tests
+that went on.
+
+To answer your question, does CFD reduce the
+number of wind tunnel hours?
+
+Three areas that we're working in right now.
+
+One reason is to bring the engineers up to
+technical speed where they can stand up and
+
+be counted.
+
+And you can ask them a technical question,
+they can give you a technical answer and say
+
+this is my analysis and this is how I got
+that.
+
+To do that we recommended back to Johnson
+Spacecraft Center that you better get your
+
+engineers knowing how to do wind tunnel tests
+and you've got to get them to know how to
+
+make the calculations to run these programs.
+
+You've got to be able to do all that.
+
+That's your integration contractor.
+
+They need to have that capability.
+
+And they've done that and they really came
+up to speed.
+
+In the midst of that, they've also increased
+their CFD capabilities.
+
+And I'm very envious of what you can do with
+CFD.
+
+However, it hasn't decreased the amount of
+runs that they're requesting.
+
+It's increasing the amount of runs that they're
+requesting because they will do this little
+
+bitty analysis and here is the cable tray
+going down that, and they'll say does it go
+
+sonic under the cable tray?
+
+Well, I don't know.
+
+What does the wind tunnel test say?
+
+Well, we just have a data point here and a
+data point here and our CFD shows that it
+
+can go sonic under there, we need to test
+that to make sure that's there.
+
+[LAUGHTER] And so it could but I don't think
+it will.
+
+I think the better your tools get you want
+to make sure they're right.
+
+Now, one day I think yes, that's going to
+happen, but right now there is still a lot
+
+of question, even in the CFD-er's mind, am
+I really right?
+
+And they've always been accused of they can
+tell you what the right answer is if you give
+
+it to them.
+
+[LAUGHTER] And that's really not true any
+longer.
+
+That was for a number of years.
+
+But that CFD is so great.
+
+And they used overflow, by the way, is the
+one that's primary to the big workhorse right
+
+now, and it does a super job.
+
+Was there a question?
+
+All right.
+
+Any other question?
+
+I would like to address the question that
+was asked about [UNINTELLIGIBLE PHRASE].
+
+Let me not talk necessarily about the Shuttle,
+but let me talk about Apollo for a moment.
+
+And I mentioned it before.
+
+In Apollo, we went to the moon with a single
+string avionic system.
+
+We had one IMU, one computer on the Command
+and Service Module.
+
+We had one service propulsion system to get
+you out of lunar orbit or to get you into
+
+lunar orbit.
+
+And I think today it would be very difficult
+to do that.
+
+I think you're probably going to have to have
+multiple strings.
+
+You're going to have an escape system.
+
+I think, in that context, it may be more difficult.
+
+I do think the tools you have today will make
+it easier, but I do think what we know today,
+
+just like Bass said on understanding a little
+bit about the aerodynamics, you want more.
+
+I think in some respects -- My comment is
+that the next time we go to the moon we're
+
+going to find out how hard it really was because
+I do think it's going to be hard to do.
+
+At least that's my personal feeling.
+
+And I think a lot of people agree with me.
+
+One of the toughest decisions we ever made
+in the Space Program, and Bass and I were
+
+talking about it at breakfast, is when we
+decided to do Apollo 8.
+
+Apollo 8 was probably the most fantastic mission
+that we ever came up with.
+
+That was the first time we left the influence
+of earth's gravity, we went into orbit around
+
+the moon and we got out of orbit of the moon.
+
+Now, we didn't land on the moon but did everything
+we had to do for the first time.
+
+And I think that was probably the boldest
+decision that NASA and the government ever
+
+made.
+
+Again, I look back, and I'm not sure how we
+would make that decision today.
+
+It was pretty tough.
+
+And, of course, one man led that attack, George
+Low who was Manager of the Apollo Program
+
+Office at Johnson Space Center, then became
+Deputy Administrator and then became President
+
+of Rensselaer Polytechnic Institute.
+
+But that was really a fantastic project.
+
+I will comment on the programs that I worked
+on.
+
+Aerodynamics on Dyna-Soar, which was a defunked
+Air Force manned spacecraft program.
+
+I worked on Mercury, Gemini, Apollo and Blue
+Gemini.
+
+And each time I would go onto the next program
+and learn more, I would say we sure were lucky.
+
+[LAUGHTER] When I was telling you about these
+new young engineers now that are up to speed
+
+where they didn't want to say anything.
+
+Now that they're crunching numbers, they got
+a lot of criticism for the way we did it.
+
+[LAUGHTER] And rightfully so.
+
+A lot of capability that is there.
+
+And you're going to have more capability today
+than you had yesterday, more capability on
+
+the next program than you had on the last
+program.
+
+You're going to find some things to do and
+be able to do it better than the last program
+
+was done.
+
+That's both good news and bad news.
+
+Bad news is it will cost you more to do it
+and the good news is it will be done a whole
+
+lot better.
+
+All right.
+
+Any other question?
+
+I thought it might be interesting, just to
+make sure you really have an understanding
+
+of what the Shuttle has to do, to sort of
+take them through the entry.
+
+And maybe, Bass, you'll make some comments
+about the aerodynamics and I'll talk a little
+
+bit about the operations.
+
+You're in orbit a couple hundred miles above
+the ground, and the first thing that you do
+
+is basically put the Orbiter, after you get
+everything stowed and ready for entry, so
+
+you're essentially going backwards, face to
+the ground.
+
+And you burn the OMS engines.
+
+And just, in terms of redundancy, we've got
+two engines.
+
+You can cross-feed the fuel that is inside
+the OMS pod.
+
+You can cross-feed from one side to the other.
+
+So, even if you lose one OMS engine, you can
+still do a de-orbit burn just on the other
+
+engine.
+
+Of course, you will have to turn a little
+bit so that you can burn through the CG.
+
+If you lose both OMS engines, you can cross-feed
+the propellant into the reaction control system
+
+aft jets and you can come back using those.
+
+And if you're having a real bad day and you
+run out, well, you know, you might have a
+
+fuel leak, for instance, and so you don't
+have enough propellant back there.
+
+Actually, there was a procedure where you
+then would flip over and burn the remainder
+
+of your forward RCS propellant to just slow
+yourself down as much as you could.
+
+We never had to do that.
+
+In fact, I don't think we ever lost an OMS
+engine.
+
+But we practice all these things.
+
+Anyway, the point is, one way or the other,
+you slow yourself down.
+
+Here is the earth and here is your orbit.
+
+This is grossly out of scale.
+
+You realize that on this scale your orbit
+is actually about like that.
+
+In any case, you do your burn just enough
+to lower your perigee just about two ground
+
+level.
+
+And now you're essentially in free-fall.
+
+I mean you're in free-fall in orbit, but now
+you're gradually getting closer to the earth.
+
+And so what you do is you now flip over and
+you put yourself in a position where when
+
+you actually hit the top upper reaches of
+the atmosphere -- And about 400,000 feet is
+
+what we call entry interface.
+
+And, actually, the flight control system changes
+at that point and the computer actually goes
+
+into a different mode.
+
+So, at this point, you're now at a 40 degree
+angle.
+
+And, as Bass said, that gives you your blunt
+surfaces approaching.
+
+And basically the sensors feel the deceleration.
+
+And that's really how you know where you are
+in the entry.
+
+You sense the deceleration.
+
+That tells you what the dynamic pressure is.
+
+During the early part of the entry, all of
+your control is by the reaction control system
+
+because you don't have enough dynamic pressure
+on the aerodynamic surfaces to be effective.
+
+As you get down further and further into the
+atmosphere -- Let's see.
+
+I think the number that comes to mind is ten.
+
+I assume that's ten pounds per square foot
+dynamic pressure.
+
+Yes.
+
+Is when the ailerons become effective.
+
+And so you have what is called a blended control
+system.
+
+The first thing that you can do is actually
+control your roll, and so you disable the
+
+roll jets and you enable the ailerons.
+
+But the pitch and the yaw is still controlled
+by the RCS.
+
+And the critical thing, like Bass was saying,
+is you've got to keep your angle of attack
+
+constant with respect to your velocity vector
+because your aerodynamic heating depends on
+
+that.
+
+If you get down to too low an angle now you're
+going to heat the surfaces, the upper part
+
+of the Orbiter and you're going to burn up.
+
+You're controlling your angle around the velocity
+vector.
+
+And now you can move about that.
+
+You have a lift vector.
+
+And now the whole name of the game, because,
+remember, this is a glider.
+
+And so energy control is what is absolutely
+essential to make sure that you're going to
+
+end up at the threshold of the runway at about
+-- You said we were aiming for 150 knots.
+
+We never actually made it.
+
+Actually, about 200 knots was the touchdown
+speed.
+
+But pretty good anyway.
+
+We got close.
+
+At every phase of your entry, knowing your
+energy and controlling it is critical.
+
+For instance, for whatever reason, if your
+burn didn't go right and you think you're
+
+going to be short of the runway, we notched
+down the angle of attack just a little bit.
+
+I think about 38 degrees was about the lowest
+you could safely go.
+
+And you keep your lift vector.
+
+You basically would fly the entire entry with
+your lift vector going away from the earth,
+
+and that maximizes your range.
+
+But you actually target the entry so that
+you have more energy than you need because
+
+it's a lot easier to bleed off energy than
+somehow to get it back, especially when you
+
+don't have any engines.
+
+What you normally do then is you will basically
+do a roll maneuver.
+
+And you'll be rolling so that your angle of
+attack, with respect to your velocity vector,
+
+is always 40 degrees.
+
+But essentially you're rolling around the
+velocity vector so you can now point your
+
+lift over to the side.
+
+And, for instance, if you didn't have enough
+propellant when you were burning, and so now
+
+you actually have too much energy, what you're
+going to do -- Or, for instance, if you have
+
+a lot of cross-range that you have to make
+up, you could spend your entire entry over
+
+on your side like this.
+
+And, in fact, there was even a case which
+we would simulate if you have an under-burn,
+
+now you have too much energy and you have
+to get really get rid of a lot of energy,
+
+you could actually roll 180 degrees.
+
+And that would be pretty sporty.
+
+[LAUGHTER] Again, nobody has ever had to do
+that.
+
+But we did simulate it.
+
+And I don't know what you would make of the
+aerodynamics coming in, but the point is you
+
+have a basic design that you're working with
+and then you try to develop operational procedures
+
+to make the system work in as many contingencies
+as possible.
+
+Anyway, that's the deal.
+
+You basically are rolling around the velocity
+vector to control both your energy and your
+
+cross-range.
+
+Let's see.
+
+Then at 20 psf the elevons actually get pitch
+affectivity, and so you disable the pitch
+
+jets.
+
+And now both the pitch and the roll are controlled
+by the elevons.
+
+The vertical stabilizer, as you can see, is
+in the shadow.
+
+And so, actually, you don't get yaw affectivity
+out of the vertical stabilizer until just
+
+about transonic and subsonic, when you actually
+do the final pitch-over to get ready for going
+
+into the heading alignment circle.
+
+And that's why sometimes, if you've seen pictures
+of the Shuttle as it approaches the landing
+
+at Kennedy Space Center, you will see little
+plumes come out the side.
+
+And that's the yaw jets and the RCS which
+are still firing, because it's still supersonic
+
+when it gets over the Space Center.
+
+And, if you're on the ground, you can actually
+hear this double sonic boom which is pretty
+
+impressive.
+
+And I guess you get one from the front and
+one from the back of the vehicle, so it's
+
+a boom boom and then it goes around.
+
+And then, of course, you hit the atmosphere
+at mach 25.
+
+And so you're going through this entire aerodynamic
+regime down through hypersonic, supersonic,
+
+transonic, subsonic.
+
+And I remember, Max Faget gave us a little
+talk about how the aerodynamic coefficients,
+
+I mean you were talking about them, but they
+change at different mach numbers, right?
+
+Oh, yes.
+
+And we mentioned this before, you know, why
+you really need a fly-by-wire system on this
+
+vehicle, because the control laws that you're
+using to do a roll maneuver at mach 15 are
+
+different from doing a roll maneuver at mach
+8.
+
+These program test inputs, you can hardly
+see them.
+
+I mean you really didn't feel them.
+
+They were just a couple of degrees that you
+would move the stick, you know, just little
+
+things.
+
+But that collected enough data to get a much
+better determination of these coefficients.
+
+You're very sensitive to things like beta
+angle.
+
+Probably about two degrees.
+
+If you go off more than that.
+
+Actually, when you read the detailed description
+of the loss of Columbia, when they had a penetration
+
+of the forward edge of the wing, that disturbed
+the airflow.
+
+And so the control system was fighting a really
+valiant fight to keep Columbia on target.
+
+And they could see that on the ground.
+
+There was more aerodynamic surface activity
+and the RCS jets kicked in.
+
+In the end, of course, you run out of control
+authority and the vehicle eventually diverged
+
+and it actually broke up aerodynamically.
+
+It was not an explosion.
+
+It just broke up aerodynamically.
+
+The hot gases in the wing were disrupting
+the airflow and eventually the wing was slumping,
+
+and so things were just getting worse and
+worse.
+
+And I don't know exactly what went first.
+
+Pieces were falling off along the way.
+
+The same thing if you read the analysis of
+the Challenger accident on a second-by-second
+
+basis, you'll see the main engines were adjusting
+their thrust and trying to keep it -- The
+
+system was really working hard just doing
+what it was supposed to do.
+
+Essentially the flight control system was
+trying to keep it within the control boundaries,
+
+and eventually it ran out of muscle because
+of the other failures.
+
+And once you go to a bad beta angle or angle
+of attack the vehicle breaks up aerodynamically.
+
+Bass, you might say a word about the aerodynamic
+coefficients and which ones were the hardest
+
+to determine and how big [were the errors?].
+
+OK.
+
+Basically, aerodynamic coefficients are normal
+forces, side forces, rolling moments, yawing
+
+moments, pitching moments and those that change
+that like elevators, body flaps, rudders and
+
+speed breaks.
+
+The coefficients, the biggest variations are
+in the low supersonic to transonic speed regimes
+
+primarily in the control variables.
+
+The biggest ones were just before transition
+or any time that the elevators were in an
+
+up position where the flow couldn't quite
+decide whether to be attached or separated.
+
+And so you want to avoid that.
+
+Digging down, not very much variations in
+those at all, but coming in the up position
+
+pretty big variations in the rolling moments
+and yaw moments due to those.
+
+And we tried to avoid those, of course, and
+henceforth with the CG location.
+
+But those were the ones that probably were
+the toughest and we tried to stay away from.
+
+Overall, hypersonics right on, subsonics second
+best, transonic the most difficult, low supersonic
+
+kind of in between there.
+
+The coefficients, it's hard to talk about
+them on a percentage basis because CM is zero
+
+and the delta CM is an infinite percentage
+so you cannot really talk about them on a
+
+percentage basis.
+
+But, when you look at the plots like CM versus
+alpha, very small variation after we got through
+
+with the flight test program.
+
+Before we got through the flight test program,
+we probably cut the variations in half on
+
+things like pitching moments, yawing moments
+and rolling moments.
+
+We did better than that on the pitching moments,
+yawing moments and rolling moments due to
+
+elevator positions when they were local angles
+of attack.
+
+And those were cut quite significantly with
+the PTIs.
+
+But still, even today, you don't just have
+one coefficient at one angle of attack, one
+
+angle of side slippage.
+
+You evaluate that one plus the variation that's
+about it.
+
+And I remember one of the big activities in
+the simulators before the first flight.
+
+They would have the test flight crews, who
+were going to make these flights, do flying
+
+entries.
+
+And they would actually vary the aerodynamic
+coefficients.
+
+And, if you put in a big enough variation,
+three sigma and all of the parameters and
+
+they went in the wrong direction, you could
+always make it impossible to have a successful
+
+entry.
+
+And so it was a real question where the managers,
+and Aaron, maybe you have something to say
+
+about that, you and Chris Kraft had to really
+make the decision when you knew enough and
+
+when you could fly safely.
+
+You're going to hear Chris Kraft talk shortly.
+
+But I remember after we landed the first mission
+there were a lot of people saying that the
+
+Shuttle wasn't going to work, all the tiles
+were going to come off.
+
+The flight control system was a big issue
+because of the aerodynamics.
+
+The flight control system, the aerodynamics
+wasn't going to work.
+
+I don't know if you've ever been to the Johnson
+Space Center and to the Control Room, but
+
+I was sitting at the consul with Chris Kraft
+and he got on the Net and said -- Because
+
+there was a lot of criticism.
+
+A lot of people wrote letters that the Shuttle
+would crash and wasn't going to make it.
+
+And he got on the Net and said we're infinitely
+smarter today.
+
+And I guess that summarized it, we were infinitely
+smarter and we did design a good system.
+
+And I think that about summed it up, that
+we were infinitely smarter.
+
+Any more questions?
+
+Yeah.
+
+Actually, it's an operational question.
+
+OK.
+
+I'm just wondering if the entire crew is trained
+on the whole landing procedure.
+
+No.
+
+We have two pilots just like in any airplane.
+
+Some of the people who flew center seat as
+flight engineers were trained pilots.
+
+And I would have been quite comfortable if
+they had landed the Shuttle.
+
+But how many failures do you prepare for?
+
+We have two people onboard who are trained
+to land.
+
+I always thought to myself, we also have this
+auto land software which nobody has ever used,
+
+but if somehow all the other six people were
+incapacitated and it was just me, I would
+
+push the auto land sequence.
+
+[LAUGHTER] And all you have to do is put the
+gear down manually, and I know how to do that.
+
+But landing the Shuttle is really very complicated.
+
+And they train hundreds and hundreds of hours
+in the simulator.
+
+Some day we could spend a whole session talking
+about the Shuttle Training Aircraft.
+
+It is one thing to land in the simulator,
+but nobody has ever died in a simulator, number
+
+one.
+
+And, number two, you're looking at a TV screen.
+
+You're not actually looking out at the runway.
+
+You don't feel the bumpy aerodynamics.
+
+And so they developed a Shuttle Training Aircraft,
+which is the Gulfstream II very heavily modified.
+
+It's actually a flying simulator.
+
+Your final approach, because your L/D on this
+vehicle, I don't know what it is exactly,
+
+is about five maybe.
+
+I think five at best, yeah.
+
+You're coming in at about a 20 degree approach
+angle, which may not seem like a lot.
+
+But a commercial airplane comes in at about
+three degrees and the problem is, you take
+
+a regular airplane, and you point it down
+at a 20 degree angle,and your airspeed is
+
+going to go above your redline.
+
+So you've got to make enough drag to simulate
+the Shuttle.
+
+There's computers inside this Shuttle training
+aircraft.
+
+The left seat is set up to be just like the
+Shuttle cockpit, and when the pilot makes
+
+the maneuvers, it basically goes back into
+the computers and they work the flight control
+
+system of the gulf stream, to make the gulf
+stream fly like the Shuttle.
+
+The only way that they can produce enough
+drag to make it go at a constant speed at
+
+a 20 degree angle, is you have full speed
+brakes your gear is down, you have thrust
+
+reverses you run your engines in reverse,
+after your on the runway to slow youself down.
+
+On the gulf stream, they run their engines
+at 90% reverse thrust while they're flying
+
+in the air.
+
+It's an extraodinary vehicle.
+
+I've flown in the center seat just to sit
+in it and you may be flying on this angle
+
+but it looks like your flying like this [LAUGHTER]
+It's really extraodinary.
+
+Just one thing to remind you,a week from today
+we've asked for the initial report outline
+
+plus some reference material.
+
+What we want to get a sense of what is your
+plans, what's the scope of what you're going
+
+to be looking at, what are you going to deal
+with and I hope by this time that you've located
+
+some reference materials you're going to be
+using.
+
+We'll be sort of spiralling in on this so
+the idea is we'll take a look at what your
+
+plans are and then we can work together if
+you have some questions or having difficulties
+
+this gives us some opportunities to talk about
+it to make sure you're on the right track
+
+so you'll be doing something that you can
+be proud of, that you'll actually learn something
+
+from, so that's due a week from today.
+
+It would be useful for me to have those electronically
+so that I can send them to Professor Cohen
+
+for him to look at.
+
+I am happy to accept hard copy as well but
+I want them electronically Any questions?
+
+Have a good weekend.
\ No newline at end of file
diff --git a/3ejfkMHr_DE.txt b/3ejfkMHr_DE.txt
new file mode 100644
index 0000000000000000000000000000000000000000..f177f7c3b21c9aaafd994e6f03b29d68c4adb8f2
--- /dev/null
+++ b/3ejfkMHr_DE.txt
@@ -0,0 +1,7235 @@
+align:start position:0%
+ 
+today is going to be one of the more
+
+ align:start position:0%
+today is going to be one of the more
+ 
+
+ align:start position:0%
+today is going to be one of the more
+difficult lectures of the term so put on
+
+ align:start position:0%
+difficult lectures of the term so put on
+ 
+
+ align:start position:0%
+difficult lectures of the term so put on
+your thinking caps as they say in
+
+ align:start position:0%
+your thinking caps as they say in
+ 
+
+ align:start position:0%
+your thinking caps as they say in
+Elementary School uh the topic is going
+
+ align:start position:0%
+Elementary School uh the topic is going
+ 
+
+ align:start position:0%
+Elementary School uh the topic is going
+to be What's called the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+convolution the convolution is something
+
+ align:start position:0%
+convolution the convolution is something
+ 
+
+ align:start position:0%
+convolution the convolution is something
+very peculiar that you do to two
+
+ align:start position:0%
+very peculiar that you do to two
+ 
+
+ align:start position:0%
+very peculiar that you do to two
+functions to get a third function it has
+
+ align:start position:0%
+functions to get a third function it has
+ 
+
+ align:start position:0%
+functions to get a third function it has
+its own special symbol F of
+
+ align:start position:0%
+its own special symbol F of
+ 
+
+ align:start position:0%
+its own special symbol F of
+T asterisk is the universal symbol
+
+ align:start position:0%
+T asterisk is the universal symbol
+ 
+
+ align:start position:0%
+T asterisk is the universal symbol
+that's used for
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that so this is a new function of T
+
+ align:start position:0%
+that so this is a new function of T
+ 
+
+ align:start position:0%
+that so this is a new function of T
+which Bears very little resemblance to
+
+ align:start position:0%
+which Bears very little resemblance to
+ 
+
+ align:start position:0%
+which Bears very little resemblance to
+the ones F of T that you started with uh
+
+ align:start position:0%
+the ones F of T that you started with uh
+ 
+
+ align:start position:0%
+the ones F of T that you started with uh
+uh I'm going to give you the formula for
+
+ align:start position:0%
+uh I'm going to give you the formula for
+ 
+
+ align:start position:0%
+uh I'm going to give you the formula for
+it but I first there are two ways of
+
+ align:start position:0%
+it but I first there are two ways of
+ 
+
+ align:start position:0%
+it but I first there are two ways of
+motivating it and both are important
+
+ align:start position:0%
+motivating it and both are important
+ 
+
+ align:start position:0%
+motivating it and both are important
+there's a formal motivation which is why
+
+ align:start position:0%
+there's a formal motivation which is why
+ 
+
+ align:start position:0%
+there's a formal motivation which is why
+it's tucked into this section Ono
+
+ align:start position:0%
+it's tucked into this section Ono
+ 
+
+ align:start position:0%
+it's tucked into this section Ono
+transform and the formal motivation is
+
+ align:start position:0%
+transform and the formal motivation is
+ 
+
+ align:start position:0%
+transform and the formal motivation is
+the following suppose we start with a
+
+ align:start position:0%
+the following suppose we start with a
+ 
+
+ align:start position:0%
+the following suppose we start with a
+lus transform of two different fun those
+
+ align:start position:0%
+lus transform of two different fun those
+ 
+
+ align:start position:0%
+lus transform of two different fun those
+two
+
+ align:start position:0%
+two
+ 
+
+ align:start position:0%
+two
+functions uh now the most natural
+
+ align:start position:0%
+functions uh now the most natural
+ 
+
+ align:start position:0%
+functions uh now the most natural
+question to ask is since llao transforms
+
+ align:start position:0%
+question to ask is since llao transforms
+ 
+
+ align:start position:0%
+question to ask is since llao transforms
+are really a pain to calculate is from
+
+ align:start position:0%
+are really a pain to calculate is from
+ 
+
+ align:start position:0%
+are really a pain to calculate is from
+old Lao transforms is it easy to get new
+
+ align:start position:0%
+old Lao transforms is it easy to get new
+ 
+
+ align:start position:0%
+old Lao transforms is it easy to get new
+ones and the first thing one of course
+
+ align:start position:0%
+ones and the first thing one of course
+ 
+
+ align:start position:0%
+ones and the first thing one of course
+summing functions is easy that gives you
+
+ align:start position:0%
+summing functions is easy that gives you
+ 
+
+ align:start position:0%
+summing functions is easy that gives you
+the sum of the transforms but a more
+
+ align:start position:0%
+the sum of the transforms but a more
+ 
+
+ align:start position:0%
+the sum of the transforms but a more
+natural question would be suppose I want
+
+ align:start position:0%
+natural question would be suppose I want
+ 
+
+ align:start position:0%
+natural question would be suppose I want
+to multiply F of T and G of T is there
+
+ align:start position:0%
+to multiply F of T and G of T is there
+ 
+
+ align:start position:0%
+to multiply F of T and G of T is there
+some hopefully some neat formula If I
+
+ align:start position:0%
+some hopefully some neat formula If I
+ 
+
+ align:start position:0%
+some hopefully some neat formula If I
+multiply the product of the take the
+
+ align:start position:0%
+multiply the product of the take the
+ 
+
+ align:start position:0%
+multiply the product of the take the
+product of these two is there some neat
+
+ align:start position:0%
+product of these two is there some neat
+ 
+
+ align:start position:0%
+product of these two is there some neat
+formula for the Lelo transform of that
+
+ align:start position:0%
+formula for the Lelo transform of that
+ 
+
+ align:start position:0%
+formula for the Lelo transform of that
+product that would simplify life greatly
+
+ align:start position:0%
+product that would simplify life greatly
+ 
+
+ align:start position:0%
+product that would simplify life greatly
+and the answer is there is no such
+
+ align:start position:0%
+and the answer is there is no such
+ 
+
+ align:start position:0%
+and the answer is there is no such
+formula and there never will
+
+ align:start position:0%
+formula and there never will
+ 
+
+ align:start position:0%
+formula and there never will
+be well we will not give up entirely
+
+ align:start position:0%
+be well we will not give up entirely
+ 
+
+ align:start position:0%
+be well we will not give up entirely
+suppose we ask the other
+
+ align:start position:0%
+suppose we ask the other
+ 
+
+ align:start position:0%
+suppose we ask the other
+question suppose instead I multiply the
+
+ align:start position:0%
+question suppose instead I multiply the
+ 
+
+ align:start position:0%
+question suppose instead I multiply the
+llao
+
+ align:start position:0%
+llao
+ 
+
+ align:start position:0%
+llao
+transforms could that be related to
+
+ align:start position:0%
+transforms could that be related to
+ 
+
+ align:start position:0%
+transforms could that be related to
+something I cook up out of f of T and G
+
+ align:start position:0%
+something I cook up out of f of T and G
+ 
+
+ align:start position:0%
+something I cook up out of f of T and G
+of T could it be the transform of
+
+ align:start position:0%
+of T could it be the transform of
+ 
+
+ align:start position:0%
+of T could it be the transform of
+something I cook up out of F T and G of
+
+ align:start position:0%
+something I cook up out of F T and G of
+ 
+
+ align:start position:0%
+something I cook up out of F T and G of
+T and that's what the convolution is for
+
+ align:start position:0%
+T and that's what the convolution is for
+ 
+
+ align:start position:0%
+T and that's what the convolution is for
+the answer is that F of s times G of s
+
+ align:start position:0%
+the answer is that F of s times G of s
+ 
+
+ align:start position:0%
+the answer is that F of s times G of s
+turns out to be the llao transform of
+
+ align:start position:0%
+turns out to be the llao transform of
+ 
+
+ align:start position:0%
+turns out to be the llao transform of
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+convolution the convolution and that's
+
+ align:start position:0%
+convolution the convolution and that's
+ 
+
+ align:start position:0%
+convolution the convolution and that's
+one way of defining it is the thing that
+
+ align:start position:0%
+one way of defining it is the thing that
+ 
+
+ align:start position:0%
+one way of defining it is the thing that
+you the function of T that you should
+
+ align:start position:0%
+you the function of T that you should
+ 
+
+ align:start position:0%
+you the function of T that you should
+put in there in order that its llas
+
+ align:start position:0%
+put in there in order that its llas
+ 
+
+ align:start position:0%
+put in there in order that its llas
+transform turn out to be the product of
+
+ align:start position:0%
+transform turn out to be the product of
+ 
+
+ align:start position:0%
+transform turn out to be the product of
+f of s time G of
+
+ align:start position:0%
+f of s time G of
+ 
+
+ align:start position:0%
+f of s time G of
+s
+
+ align:start position:0%
+s
+ 
+
+ align:start position:0%
+s
+now I'll give you in a moment the
+
+ align:start position:0%
+now I'll give you in a moment the
+ 
+
+ align:start position:0%
+now I'll give you in a moment the
+formula for it but I think
+
+ align:start position:0%
+formula for it but I think
+ 
+
+ align:start position:0%
+formula for it but I think
+I'll I'll give you
+
+ align:start position:0%
+I'll I'll give you
+ 
+
+ align:start position:0%
+I'll I'll give you
+one and a quarter minutes of well two
+
+ align:start position:0%
+one and a quarter minutes of well two
+ 
+
+ align:start position:0%
+one and a quarter minutes of well two
+minutes of motivation as to why there
+
+ align:start position:0%
+minutes of motivation as to why there
+ 
+
+ align:start position:0%
+minutes of motivation as to why there
+should be such a
+
+ align:start position:0%
+should be such a
+ 
+
+ align:start position:0%
+should be such a
+formula now I won't calculate this out
+
+ align:start position:0%
+formula now I won't calculate this out
+ 
+
+ align:start position:0%
+formula now I won't calculate this out
+to the end because I don't have time but
+
+ align:start position:0%
+to the end because I don't have time but
+ 
+
+ align:start position:0%
+to the end because I don't have time but
+here's the reason why there should be
+
+ align:start position:0%
+here's the reason why there should be
+ 
+
+ align:start position:0%
+here's the reason why there should be
+such a formula and you might suspect and
+
+ align:start position:0%
+such a formula and you might suspect and
+ 
+
+ align:start position:0%
+such a formula and you might suspect and
+therefore it will be worth looking for
+
+ align:start position:0%
+therefore it will be worth looking for
+ 
+
+ align:start position:0%
+therefore it will be worth looking for
+it's because remember I told you where
+
+ align:start position:0%
+it's because remember I told you where
+ 
+
+ align:start position:0%
+it's because remember I told you where
+the llast transform came from that the
+
+ align:start position:0%
+the llast transform came from that the
+ 
+
+ align:start position:0%
+the llast transform came from that the
+transform was the continuous analog of a
+
+ align:start position:0%
+transform was the continuous analog of a
+ 
+
+ align:start position:0%
+transform was the continuous analog of a
+power Series so that when you ask a
+
+ align:start position:0%
+power Series so that when you ask a
+ 
+
+ align:start position:0%
+power Series so that when you ask a
+general question like that the place to
+
+ align:start position:0%
+general question like that the place to
+ 
+
+ align:start position:0%
+general question like that the place to
+look for is if you know an analogous
+
+ align:start position:0%
+look for is if you know an analogous
+ 
+
+ align:start position:0%
+look for is if you know an analogous
+idea say does it work something like
+
+ align:start position:0%
+idea say does it work something like
+ 
+
+ align:start position:0%
+idea say does it work something like
+that work there so here I have a power
+
+ align:start position:0%
+that work there so here I have a power
+ 
+
+ align:start position:0%
+that work there so here I have a power
+series summation a n x to the N remember
+
+ align:start position:0%
+series summation a n x to the N remember
+ 
+
+ align:start position:0%
+series summation a n x to the N remember
+you can write this in computer notation
+
+ align:start position:0%
+you can write this in computer notation
+ 
+
+ align:start position:0%
+you can write this in computer notation
+as a of n to make it look like f of n f
+
+ align:start position:0%
+as a of n to make it look like f of n f
+ 
+
+ align:start position:0%
+as a of n to make it look like f of n f
+of T and the analog is between n is
+
+ align:start position:0%
+of T and the analog is between n is
+ 
+
+ align:start position:0%
+of T and the analog is between n is
+turned into T when you turn a power
+
+ align:start position:0%
+turned into T when you turn a power
+ 
+
+ align:start position:0%
+turned into T when you turn a power
+series into the plus transform and uh X
+
+ align:start position:0%
+series into the plus transform and uh X
+ 
+
+ align:start position:0%
+series into the plus transform and uh X
+gets turned into e the S and one formula
+
+ align:start position:0%
+gets turned into e the S and one formula
+ 
+
+ align:start position:0%
+gets turned into e the S and one formula
+just turns into the other okay so
+
+ align:start position:0%
+just turns into the other okay so
+ 
+
+ align:start position:0%
+just turns into the other okay so
+there's a formula for F ofx this is the
+
+ align:start position:0%
+there's a formula for F ofx this is the
+ 
+
+ align:start position:0%
+there's a formula for F ofx this is the
+analog of the llas transform and
+
+ align:start position:0%
+analog of the llas transform and
+ 
+
+ align:start position:0%
+analog of the llas transform and
+similarly G of X here is summation BN x
+
+ align:start position:0%
+similarly G of X here is summation BN x
+ 
+
+ align:start position:0%
+similarly G of X here is summation BN x
+to the
+
+ align:start position:0%
+to the
+ 
+
+ align:start position:0%
+to the
+N now again the naive question would be
+
+ align:start position:0%
+N now again the naive question would be
+ 
+
+ align:start position:0%
+N now again the naive question would be
+well suppose I multiply the two
+
+ align:start position:0%
+well suppose I multiply the two
+ 
+
+ align:start position:0%
+well suppose I multiply the two
+coefficient corresponding coefficients
+
+ align:start position:0%
+coefficient corresponding coefficients
+ 
+
+ align:start position:0%
+coefficient corresponding coefficients
+together and add up that power series
+
+ align:start position:0%
+together and add up that power series
+ 
+
+ align:start position:0%
+together and add up that power series
+summation a n b n * X the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+N is that somehow it's some related to f
+
+ align:start position:0%
+N is that somehow it's some related to f
+ 
+
+ align:start position:0%
+N is that somehow it's some related to f
+and g and of course everybody knows the
+
+ align:start position:0%
+and g and of course everybody knows the
+ 
+
+ align:start position:0%
+and g and of course everybody knows the
+answer to that is no has no relation
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+whatever but suppose instead I multiply
+
+ align:start position:0%
+whatever but suppose instead I multiply
+ 
+
+ align:start position:0%
+whatever but suppose instead I multiply
+these two guys well in that case I'll
+
+ align:start position:0%
+these two guys well in that case I'll
+ 
+
+ align:start position:0%
+these two guys well in that case I'll
+get a new power
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+series I don't know what its
+
+ align:start position:0%
+series I don't know what its
+ 
+
+ align:start position:0%
+series I don't know what its
+coefficients are but let's write them
+
+ align:start position:0%
+coefficients are but let's write them
+ 
+
+ align:start position:0%
+coefficients are but let's write them
+down let's just call them CN
+
+ align:start position:0%
+down let's just call them CN
+ 
+
+ align:start position:0%
+down let's just call them CN
+so what I'm asking is if this
+
+ align:start position:0%
+so what I'm asking is if this
+ 
+
+ align:start position:0%
+so what I'm asking is if this
+corresponds to the product of the two
+
+ align:start position:0%
+corresponds to the product of the two
+ 
+
+ align:start position:0%
+corresponds to the product of the two
+llast transforms and what I want to know
+
+ align:start position:0%
+llast transforms and what I want to know
+ 
+
+ align:start position:0%
+llast transforms and what I want to know
+is is there a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+formula which says that CN is equal to
+
+ align:start position:0%
+formula which says that CN is equal to
+ 
+
+ align:start position:0%
+formula which says that CN is equal to
+something that can be calcul calculated
+
+ align:start position:0%
+something that can be calcul calculated
+ 
+
+ align:start position:0%
+something that can be calcul calculated
+out of the AI and the
+
+ align:start position:0%
+out of the AI and the
+ 
+
+ align:start position:0%
+out of the AI and the
+BJ now the answer to that is yes there
+
+ align:start position:0%
+BJ now the answer to that is yes there
+ 
+
+ align:start position:0%
+BJ now the answer to that is yes there
+is and the formula for CN is called the
+
+ align:start position:0%
+is and the formula for CN is called the
+ 
+
+ align:start position:0%
+is and the formula for CN is called the
+convolution
+
+ align:start position:0%
+convolution
+ 
+
+ align:start position:0%
+convolution
+now you could figure out this formula
+
+ align:start position:0%
+now you could figure out this formula
+ 
+
+ align:start position:0%
+now you could figure out this formula
+yourself you figure it
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+out anyone who's smart enough to be
+
+ align:start position:0%
+out anyone who's smart enough to be
+ 
+
+ align:start position:0%
+out anyone who's smart enough to be
+interested in the question in the first
+
+ align:start position:0%
+interested in the question in the first
+ 
+
+ align:start position:0%
+interested in the question in the first
+place is smart enough to figure out what
+
+ align:start position:0%
+place is smart enough to figure out what
+ 
+
+ align:start position:0%
+place is smart enough to figure out what
+that formula is and it will give you
+
+ align:start position:0%
+that formula is and it will give you
+ 
+
+ align:start position:0%
+that formula is and it will give you
+great pleasure to see that it's just
+
+ align:start position:0%
+great pleasure to see that it's just
+ 
+
+ align:start position:0%
+great pleasure to see that it's just
+like the formula for the convolution
+
+ align:start position:0%
+like the formula for the convolution
+ 
+
+ align:start position:0%
+like the formula for the convolution
+that I'm going to give you
+
+ align:start position:0%
+that I'm going to give you
+ 
+
+ align:start position:0%
+that I'm going to give you
+now so what is that formula for the
+
+ align:start position:0%
+now so what is that formula for the
+ 
+
+ align:start position:0%
+now so what is that formula for the
+convolution okay hang
+
+ align:start position:0%
+convolution okay hang
+ 
+
+ align:start position:0%
+convolution okay hang
+on now you're not going to lie like it
+
+ align:start position:0%
+on now you're not going to lie like it
+ 
+
+ align:start position:0%
+on now you're not going to lie like it
+but you didn't like the formula of llast
+
+ align:start position:0%
+but you didn't like the formula of llast
+ 
+
+ align:start position:0%
+but you didn't like the formula of llast
+transform either uh you felt wiser grown
+
+ align:start position:0%
+transform either uh you felt wiser grown
+ 
+
+ align:start position:0%
+transform either uh you felt wiser grown
+up getting it but it it's a mouthful to
+
+ align:start position:0%
+up getting it but it it's a mouthful to
+ 
+
+ align:start position:0%
+up getting it but it it's a mouthful to
+swallow it's something you get used to
+
+ align:start position:0%
+swallow it's something you get used to
+ 
+
+ align:start position:0%
+swallow it's something you get used to
+slowly and you'll get used to the
+
+ align:start position:0%
+slowly and you'll get used to the
+ 
+
+ align:start position:0%
+slowly and you'll get used to the
+convolution equally
+
+ align:start position:0%
+convolution equally
+ 
+
+ align:start position:0%
+convolution equally
+slowly so what is the convolution of f
+
+ align:start position:0%
+slowly so what is the convolution of f
+ 
+
+ align:start position:0%
+slowly so what is the convolution of f
+of T and G of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+T it's a function calculated according
+
+ align:start position:0%
+T it's a function calculated according
+ 
+
+ align:start position:0%
+T it's a function calculated according
+to the corresponding formula it's a
+
+ align:start position:0%
+to the corresponding formula it's a
+ 
+
+ align:start position:0%
+to the corresponding formula it's a
+function of
+
+ align:start position:0%
+function of
+ 
+
+ align:start position:0%
+function of
+T it's the integral from 0 to T
+
+ align:start position:0%
+T it's the integral from 0 to T
+ 
+
+ align:start position:0%
+T it's the integral from 0 to T
+of f of u u is a dummy variable because
+
+ align:start position:0%
+of f of u u is a dummy variable because
+ 
+
+ align:start position:0%
+of f of u u is a dummy variable because
+I'm it's going to be integrated out when
+
+ align:start position:0%
+I'm it's going to be integrated out when
+ 
+
+ align:start position:0%
+I'm it's going to be integrated out when
+I do the integration G of T minus U
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+DT that's it I didn't make it up I'm
+
+ align:start position:0%
+DT that's it I didn't make it up I'm
+ 
+
+ align:start position:0%
+DT that's it I didn't make it up I'm
+just bearing the bad
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+news well what do you do when you see a
+
+ align:start position:0%
+news well what do you do when you see a
+ 
+
+ align:start position:0%
+news well what do you do when you see a
+formula that seems to you know well you
+
+ align:start position:0%
+formula that seems to you know well you
+ 
+
+ align:start position:0%
+formula that seems to you know well you
+know well the first thing to do of
+
+ align:start position:0%
+know well the first thing to do of
+ 
+
+ align:start position:0%
+know well the first thing to do of
+course is try calculating just just to
+
+ align:start position:0%
+course is try calculating just just to
+ 
+
+ align:start position:0%
+course is try calculating just just to
+get some feeling for what kind of a
+
+ align:start position:0%
+get some feeling for what kind of a
+ 
+
+ align:start position:0%
+get some feeling for what kind of a
+thing you know what what's this good
+
+ align:start position:0%
+thing you know what what's this good
+ 
+
+ align:start position:0%
+thing you know what what's this good
+let's try some examples uh let's see
+
+ align:start position:0%
+let's try some examples uh let's see
+ 
+
+ align:start position:0%
+let's try some examples uh let's see
+let's calculate uh what would be a
+
+ align:start position:0%
+let's calculate uh what would be a
+ 
+
+ align:start position:0%
+let's calculate uh what would be a
+modest beginning uh let's calculate the
+
+ align:start position:0%
+modest beginning uh let's calculate the
+ 
+
+ align:start position:0%
+modest beginning uh let's calculate the
+convolution of uh t with
+
+ align:start position:0%
+convolution of uh t with
+ 
+
+ align:start position:0%
+convolution of uh t with
+itself or Betty yet let's calculate the
+
+ align:start position:0%
+itself or Betty yet let's calculate the
+ 
+
+ align:start position:0%
+itself or Betty yet let's calculate the
+convolution just so that you could tell
+
+ align:start position:0%
+convolution just so that you could tell
+ 
+
+ align:start position:0%
+convolution just so that you could tell
+the difference uh t with
+
+ align:start position:0%
+the difference uh t with
+ 
+
+ align:start position:0%
+the difference uh t with
+t2qu a t squ with t make it a little
+
+ align:start position:0%
+t2qu a t squ with t make it a little
+ 
+
+ align:start position:0%
+t2qu a t squ with t make it a little
+easier by the way the convolution is
+
+ align:start position:0%
+easier by the way the convolution is
+ 
+
+ align:start position:0%
+easier by the way the convolution is
+symmetric F star G is the same thing as
+
+ align:start position:0%
+symmetric F star G is the same thing as
+ 
+
+ align:start position:0%
+symmetric F star G is the same thing as
+G starf let's put that down explicitly I
+
+ align:start position:0%
+G starf let's put that down explicitly I
+ 
+
+ align:start position:0%
+G starf let's put that down explicitly I
+forgot to last period so tell all the
+
+ align:start position:0%
+forgot to last period so tell all the
+ 
+
+ align:start position:0%
+forgot to last period so tell all the
+guys who came to the one o'clock lecture
+
+ align:start position:0%
+guys who came to the one o'clock lecture
+ 
+
+ align:start position:0%
+guys who came to the one o'clock lecture
+did you know something that they
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+don't now that's a theory it's
+
+ align:start position:0%
+don't now that's a theory it's
+ 
+
+ align:start position:0%
+don't now that's a theory it's
+commutative this operation is
+
+ align:start position:0%
+commutative this operation is
+ 
+
+ align:start position:0%
+commutative this operation is
+commutative in other words now that has
+
+ align:start position:0%
+commutative in other words now that has
+ 
+
+ align:start position:0%
+commutative in other words now that has
+to be a because the formula is not
+
+ align:start position:0%
+to be a because the formula is not
+ 
+
+ align:start position:0%
+to be a because the formula is not
+symmetric the formula does not treat f
+
+ align:start position:0%
+symmetric the formula does not treat f
+ 
+
+ align:start position:0%
+symmetric the formula does not treat f
+and g
+
+ align:start position:0%
+and g
+ 
+
+ align:start position:0%
+and g
+equally and therefore this is not
+
+ align:start position:0%
+equally and therefore this is not
+ 
+
+ align:start position:0%
+equally and therefore this is not
+obvious it's not it's at least not
+
+ align:start position:0%
+obvious it's not it's at least not
+ 
+
+ align:start position:0%
+obvious it's not it's at least not
+obvious if you look at it that way but
+
+ align:start position:0%
+obvious if you look at it that way but
+ 
+
+ align:start position:0%
+obvious if you look at it that way but
+it is obvious if you look at it that way
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+why in other words F star G is the guy
+
+ align:start position:0%
+why in other words F star G is the guy
+ 
+
+ align:start position:0%
+why in other words F star G is the guy
+whose lass transform is f of s * G of
+
+ align:start position:0%
+whose lass transform is f of s * G of
+ 
+
+ align:start position:0%
+whose lass transform is f of s * G of
+s well what would G Star F be that would
+
+ align:start position:0%
+s well what would G Star F be that would
+ 
+
+ align:start position:0%
+s well what would G Star F be that would
+be the guy whose lass transform is G * F
+
+ align:start position:0%
+be the guy whose lass transform is G * F
+ 
+
+ align:start position:0%
+be the guy whose lass transform is G * F
+but F capital F time capital G is the
+
+ align:start position:0%
+but F capital F time capital G is the
+ 
+
+ align:start position:0%
+but F capital F time capital G is the
+same as capital G * capital
+
+ align:start position:0%
+same as capital G * capital
+ 
+
+ align:start position:0%
+same as capital G * capital
+F so it's because the Lao transforms are
+
+ align:start position:0%
+F so it's because the Lao transforms are
+ 
+
+ align:start position:0%
+F so it's because the Lao transforms are
+commutative ordinary multiplication is
+
+ align:start position:0%
+commutative ordinary multiplication is
+ 
+
+ align:start position:0%
+commutative ordinary multiplication is
+commutative it follows that this has to
+
+ align:start position:0%
+commutative it follows that this has to
+ 
+
+ align:start position:0%
+commutative it follows that this has to
+be comput commutative too so I'll write
+
+ align:start position:0%
+be comput commutative too so I'll write
+ 
+
+ align:start position:0%
+be comput commutative too so I'll write
+that down since f * G is equal to GF and
+
+ align:start position:0%
+that down since f * G is equal to GF and
+ 
+
+ align:start position:0%
+that down since f * G is equal to GF and
+you have to understand that here I mean
+
+ align:start position:0%
+you have to understand that here I mean
+ 
+
+ align:start position:0%
+you have to understand that here I mean
+these are the little transforms of those
+
+ align:start position:0%
+these are the little transforms of those
+ 
+
+ align:start position:0%
+these are the little transforms of those
+guys but it's not obvious from the
+
+ align:start position:0%
+guys but it's not obvious from the
+ 
+
+ align:start position:0%
+guys but it's not obvious from the
+formula okay let's calculate the LL
+
+ align:start position:0%
+formula okay let's calculate the LL
+ 
+
+ align:start position:0%
+formula okay let's calculate the LL
+transform of uh sorry the convolution of
+
+ align:start position:0%
+transform of uh sorry the convolution of
+ 
+
+ align:start position:0%
+transform of uh sorry the convolution of
+tar let's do it by the
+
+ align:start position:0%
+tar let's do it by the
+ 
+
+ align:start position:0%
+tar let's do it by the
+formula all right by the formula I
+
+ align:start position:0%
+formula all right by the formula I
+ 
+
+ align:start position:0%
+formula all right by the formula I
+calculate integral 0 to T now I take the
+
+ align:start position:0%
+calculate integral 0 to T now I take the
+ 
+
+ align:start position:0%
+calculate integral 0 to T now I take the
+first function but I change its variable
+
+ align:start position:0%
+first function but I change its variable
+ 
+
+ align:start position:0%
+first function but I change its variable
+to the dummy variable U so that's u^2 I
+
+ align:start position:0%
+to the dummy variable U so that's u^2 I
+ 
+
+ align:start position:0%
+to the dummy variable U so that's u^2 I
+take the second function and replace its
+
+ align:start position:0%
+take the second function and replace its
+ 
+
+ align:start position:0%
+take the second function and replace its
+variable by uus T so this is
+
+ align:start position:0%
+variable by uus T so this is
+ 
+
+ align:start position:0%
+variable by uus T so this is
+times U T minus U
+
+ align:start position:0%
+times U T minus U
+ 
+
+ align:start position:0%
+times U T minus U
+sorry
+
+ align:start position:0%
+sorry
+ 
+
+ align:start position:0%
+sorry
+okay do you see that this to calculate
+
+ align:start position:0%
+okay do you see that this to calculate
+ 
+
+ align:start position:0%
+okay do you see that this to calculate
+that this is what I have to write down
+
+ align:start position:0%
+that this is what I have to write down
+ 
+
+ align:start position:0%
+that this is what I have to write down
+that's what the formula
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+becomes any question is it anything
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+wrong oh sorry the you the integration
+
+ align:start position:0%
+wrong oh sorry the you the integration
+ 
+
+ align:start position:0%
+wrong oh sorry the you the integration
+respect to you of course this should be
+
+ align:start position:0%
+respect to you of course this should be
+ 
+
+ align:start position:0%
+respect to you of course this should be
+a thanks very
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+much okay let's do it uh so it is U
+
+ align:start position:0%
+much okay let's do it uh so it is U
+ 
+
+ align:start position:0%
+much okay let's do it uh so it is U
+integral of u^2 T is remember it's
+
+ align:start position:0%
+integral of u^2 T is remember it's
+ 
+
+ align:start position:0%
+integral of u^2 T is remember it's
+integrated with respect to U so it's U
+
+ align:start position:0%
+integrated with respect to U so it's U
+ 
+
+ align:start position:0%
+integrated with respect to U so it's U
+cubed over 3 *
+
+ align:start position:0%
+cubed over 3 *
+ 
+
+ align:start position:0%
+cubed over 3 *
+T the rest of it is the integral of U
+
+ align:start position:0%
+T the rest of it is the integral of U
+ 
+
+ align:start position:0%
+T the rest of it is the integral of U
+cubed which is U 4th over 4 all this is
+
+ align:start position:0%
+cubed which is U 4th over 4 all this is
+ 
+
+ align:start position:0%
+cubed which is U 4th over 4 all this is
+to be evaluated between 0 and T at the
+
+ align:start position:0%
+to be evaluated between 0 and T at the
+ 
+
+ align:start position:0%
+to be evaluated between 0 and T at the
+upper limit so I put U equal T I get T
+
+ align:start position:0%
+upper limit so I put U equal T I get T
+ 
+
+ align:start position:0%
+upper limit so I put U equal T I get T
+4th over
+
+ align:start position:0%
+4th over
+ 
+
+ align:start position:0%
+4th over
+3 minus t 4 over four of course at the
+
+ align:start position:0%
+3 minus t 4 over four of course at the
+ 
+
+ align:start position:0%
+3 minus t 4 over four of course at the
+lower limit U is zero so both of these
+
+ align:start position:0%
+lower limit U is zero so both of these
+ 
+
+ align:start position:0%
+lower limit U is zero so both of these
+are terms are zero there's nothing there
+
+ align:start position:0%
+are terms are zero there's nothing there
+ 
+
+ align:start position:0%
+are terms are zero there's nothing there
+and the answer is therefore T 4
+
+ align:start position:0%
+and the answer is therefore T 4
+ 
+
+ align:start position:0%
+and the answer is therefore T 4
+/ a 3 minus A4 is a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+12th so that's doing it from the formula
+
+ align:start position:0%
+12th so that's doing it from the formula
+ 
+
+ align:start position:0%
+12th so that's doing it from the formula
+but of course there's an easier way to
+
+ align:start position:0%
+but of course there's an easier way to
+ 
+
+ align:start position:0%
+but of course there's an easier way to
+do it uh we can I use the LL transform
+
+ align:start position:0%
+do it uh we can I use the LL transform
+ 
+
+ align:start position:0%
+do it uh we can I use the LL transform
+instead uh if I L transform it the L
+
+ align:start position:0%
+instead uh if I L transform it the L
+ 
+
+ align:start position:0%
+instead uh if I L transform it the L
+transform of t^2 is what
+
+ align:start position:0%
+transform of t^2 is what
+ 
+
+ align:start position:0%
+transform of t^2 is what
+is 2 factorial / s
+
+ align:start position:0%
+is 2 factorial / s
+ 
+
+ align:start position:0%
+is 2 factorial / s
+cubed the transform of T is 1 /
+
+ align:start position:0%
+cubed the transform of T is 1 /
+ 
+
+ align:start position:0%
+cubed the transform of T is 1 /
+S2 and so because this is the
+
+ align:start position:0%
+S2 and so because this is the
+ 
+
+ align:start position:0%
+S2 and so because this is the
+convolution of these it should
+
+ align:start position:0%
+convolution of these it should
+ 
+
+ align:start position:0%
+convolution of these it should
+correspond to the product of the Lelo
+
+ align:start position:0%
+correspond to the product of the Lelo
+ 
+
+ align:start position:0%
+correspond to the product of the Lelo
+transforms which is two over s 5th
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+power well is that the same as this
+
+ align:start position:0%
+power well is that the same as this
+ 
+
+ align:start position:0%
+power well is that the same as this
+what's the L transform of in other words
+
+ align:start position:0%
+what's the L transform of in other words
+ 
+
+ align:start position:0%
+what's the L transform of in other words
+what's the inverse LL transform
+
+ align:start position:0%
+what's the inverse LL transform
+ 
+
+ align:start position:0%
+what's the inverse LL transform
+of two over S
+
+ align:start position:0%
+of two over S
+ 
+
+ align:start position:0%
+of two over S
+5 well the inverse lass transform of
+
+ align:start position:0%
+5 well the inverse lass transform of
+ 
+
+ align:start position:0%
+5 well the inverse lass transform of
+four factorial over s the 5th is how
+
+ align:start position:0%
+four factorial over s the 5th is how
+ 
+
+ align:start position:0%
+four factorial over s the 5th is how
+much that's T 4th right
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+now how does this differ well to turn
+
+ align:start position:0%
+now how does this differ well to turn
+ 
+
+ align:start position:0%
+now how does this differ well to turn
+that into that I should divide by four *
+
+ align:start position:0%
+that into that I should divide by four *
+ 
+
+ align:start position:0%
+that into that I should divide by four *
+3 so this should be 112th T 4th 1 over4
+
+ align:start position:0%
+3 so this should be 112th T 4th 1 over4
+ 
+
+ align:start position:0%
+3 so this should be 112th T 4th 1 over4
+* 3 because this is 24 and that's two so
+
+ align:start position:0%
+* 3 because this is 24 and that's two so
+ 
+
+ align:start position:0%
+* 3 because this is 24 and that's two so
+divide by 12 toer what constant
+
+ align:start position:0%
+divide by 12 toer what constant
+ 
+
+ align:start position:0%
+divide by 12 toer what constant
+have so it works at least in that
+
+ align:start position:0%
+have so it works at least in that
+ 
+
+ align:start position:0%
+have so it works at least in that
+case but now notice uh this is not an
+
+ align:start position:0%
+case but now notice uh this is not an
+ 
+
+ align:start position:0%
+case but now notice uh this is not an
+ordinary product the convolution of t^2
+
+ align:start position:0%
+ordinary product the convolution of t^2
+ 
+
+ align:start position:0%
+ordinary product the convolution of t^2
+and T is not something like T Cub is
+
+ align:start position:0%
+and T is not something like T Cub is
+ 
+
+ align:start position:0%
+and T is not something like T Cub is
+something like T 4th power and there's a
+
+ align:start position:0%
+something like T 4th power and there's a
+ 
+
+ align:start position:0%
+something like T 4th power and there's a
+funny constant in there too very
+
+ align:start position:0%
+funny constant in there too very
+ 
+
+ align:start position:0%
+funny constant in there too very
+unpredictable let's look at the
+
+ align:start position:0%
+unpredictable let's look at the
+ 
+
+ align:start position:0%
+unpredictable let's look at the
+convolution let's take another example
+
+ align:start position:0%
+convolution let's take another example
+ 
+
+ align:start position:0%
+convolution let's take another example
+of a convolution
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh let's do something really humble just
+
+ align:start position:0%
+uh let's do something really humble just
+ 
+
+ align:start position:0%
+uh let's do something really humble just
+to show you that this even at the
+
+ align:start position:0%
+to show you that this even at the
+ 
+
+ align:start position:0%
+to show you that this even at the
+simplest example this is not trivial
+
+ align:start position:0%
+simplest example this is not trivial
+ 
+
+ align:start position:0%
+simplest example this is not trivial
+let's take the convolution of f of t
+
+ align:start position:0%
+let's take the convolution of f of t
+ 
+
+ align:start position:0%
+let's take the convolution of f of t
+with
+
+ align:start position:0%
+with
+ 
+
+ align:start position:0%
+with
+one can you take yeah one is a function
+
+ align:start position:0%
+one can you take yeah one is a function
+ 
+
+ align:start position:0%
+one can you take yeah one is a function
+just like any function uh but you mean
+
+ align:start position:0%
+just like any function uh but you mean
+ 
+
+ align:start position:0%
+just like any function uh but you mean
+you get something out of the convolution
+
+ align:start position:0%
+you get something out of the convolution
+ 
+
+ align:start position:0%
+you get something out of the convolution
+yes
+
+ align:start position:0%
+yes
+ 
+
+ align:start position:0%
+yes
+yes let's just write down the formula
+
+ align:start position:0%
+yes let's just write down the formula
+ 
+
+ align:start position:0%
+yes let's just write down the formula
+it's now I can't use the llast transform
+
+ align:start position:0%
+it's now I can't use the llast transform
+ 
+
+ align:start position:0%
+it's now I can't use the llast transform
+here because you won't know what to do
+
+ align:start position:0%
+here because you won't know what to do
+ 
+
+ align:start position:0%
+here because you won't know what to do
+with it uh you don't have that formula
+
+ align:start position:0%
+with it uh you don't have that formula
+ 
+
+ align:start position:0%
+with it uh you don't have that formula
+yet it's a secret one that only I know
+
+ align:start position:0%
+yet it's a secret one that only I know
+ 
+
+ align:start position:0%
+yet it's a secret one that only I know
+so let's so let's do it let's use let's
+
+ align:start position:0%
+so let's so let's do it let's use let's
+ 
+
+ align:start position:0%
+so let's so let's do it let's use let's
+calculate it out the way we're supposed
+
+ align:start position:0%
+calculate it out the way we're supposed
+ 
+
+ align:start position:0%
+calculate it out the way we're supposed
+to so it's the integral from 0er to T of
+
+ align:start position:0%
+to so it's the integral from 0er to T of
+ 
+
+ align:start position:0%
+to so it's the integral from 0er to T of
+f of U and now what do I do with that
+
+ align:start position:0%
+f of U and now what do I do with that
+ 
+
+ align:start position:0%
+f of U and now what do I do with that
+one I'm supposed to take that one is the
+
+ align:start position:0%
+one I'm supposed to take that one is the
+ 
+
+ align:start position:0%
+one I'm supposed to take that one is the
+function G of T and wherever I see a t
+
+ align:start position:0%
+function G of T and wherever I see a t
+ 
+
+ align:start position:0%
+function G of T and wherever I see a t
+I'm supposed to plug in T minus U well I
+
+ align:start position:0%
+I'm supposed to plug in T minus U well I
+ 
+
+ align:start position:0%
+I'm supposed to plug in T minus U well I
+don't see any T
+
+ align:start position:0%
+don't see any T
+ 
+
+ align:start position:0%
+don't see any T
+there but that's something for rejoicing
+
+ align:start position:0%
+there but that's something for rejoicing
+ 
+
+ align:start position:0%
+there but that's something for rejoicing
+there's nothing to do to make the
+
+ align:start position:0%
+there's nothing to do to make the
+ 
+
+ align:start position:0%
+there's nothing to do to make the
+substitution it's just
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+one so the answer is it's the this
+
+ align:start position:0%
+one so the answer is it's the this
+ 
+
+ align:start position:0%
+one so the answer is it's the this
+Curious Thing the convolution of a
+
+ align:start position:0%
+Curious Thing the convolution of a
+ 
+
+ align:start position:0%
+Curious Thing the convolution of a
+function with one you
+
+ align:start position:0%
+function with one you
+ 
+
+ align:start position:0%
+function with one you
+integrated from 0 to T
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+well as they said now Wonderland was it
+
+ align:start position:0%
+well as they said now Wonderland was it
+ 
+
+ align:start position:0%
+well as they said now Wonderland was it
+things are getting curiouser and
+
+ align:start position:0%
+things are getting curiouser and
+ 
+
+ align:start position:0%
+things are getting curiouser and
+curiouser uh I mean what is going on
+
+ align:start position:0%
+curiouser uh I mean what is going on
+ 
+
+ align:start position:0%
+curiouser uh I mean what is going on
+with this crazy function and where are
+
+ align:start position:0%
+with this crazy function and where are
+ 
+
+ align:start position:0%
+with this crazy function and where are
+we supposed to start with it well I'm
+
+ align:start position:0%
+we supposed to start with it well I'm
+ 
+
+ align:start position:0%
+we supposed to start with it well I'm
+going to prove this for you uh mostly
+
+ align:start position:0%
+going to prove this for you uh mostly
+ 
+
+ align:start position:0%
+going to prove this for you uh mostly
+because the proof is easy in other words
+
+ align:start position:0%
+because the proof is easy in other words
+ 
+
+ align:start position:0%
+because the proof is easy in other words
+I'm going to prove prove that that's
+
+ align:start position:0%
+I'm going to prove prove that that's
+ 
+
+ align:start position:0%
+I'm going to prove prove that that's
+true and
+
+ align:start position:0%
+true and
+ 
+
+ align:start position:0%
+true and
+as I give the proof you'll see where the
+
+ align:start position:0%
+as I give the proof you'll see where the
+ 
+
+ align:start position:0%
+as I give the proof you'll see where the
+convolution is coming from that's number
+
+ align:start position:0%
+convolution is coming from that's number
+ 
+
+ align:start position:0%
+convolution is coming from that's number
+one and number two the real reason I'm
+
+ align:start position:0%
+one and number two the real reason I'm
+ 
+
+ align:start position:0%
+one and number two the real reason I'm
+giving you the proof because it's a
+
+ align:start position:0%
+giving you the proof because it's a
+ 
+
+ align:start position:0%
+giving you the proof because it's a
+marvelous it's a marvelous exercise in
+
+ align:start position:0%
+marvelous it's a marvelous exercise in
+ 
+
+ align:start position:0%
+marvelous it's a marvelous exercise in
+changing the variables in a double
+
+ align:start position:0%
+changing the variables in a double
+ 
+
+ align:start position:0%
+changing the variables in a double
+integral now that's something you all
+
+ align:start position:0%
+integral now that's something you all
+ 
+
+ align:start position:0%
+integral now that's something you all
+know how to do even the ones who are
+
+ align:start position:0%
+know how to do even the ones who are
+ 
+
+ align:start position:0%
+know how to do even the ones who are
+taking 1802 concurrently and I didn't
+
+ align:start position:0%
+taking 1802 concurrently and I didn't
+ 
+
+ align:start position:0%
+taking 1802 concurrently and I didn't
+advise you to do that uh but I've
+
+ align:start position:0%
+advise you to do that uh but I've
+ 
+
+ align:start position:0%
+advise you to do that uh but I've
+arranged the course so it's possible to
+
+ align:start position:0%
+arranged the course so it's possible to
+ 
+
+ align:start position:0%
+arranged the course so it's possible to
+do but I knew that by the time we got to
+
+ align:start position:0%
+do but I knew that by the time we got to
+ 
+
+ align:start position:0%
+do but I knew that by the time we got to
+this you would already know how to
+
+ align:start position:0%
+this you would already know how to
+ 
+
+ align:start position:0%
+this you would already know how to
+change variables at a double integral so
+
+ align:start position:0%
+change variables at a double integral so
+ 
+
+ align:start position:0%
+change variables at a double integral so
+and in fact you'll have the advantage of
+
+ align:start position:0%
+and in fact you'll have the advantage of
+ 
+
+ align:start position:0%
+and in fact you'll have the advantage of
+remembering how to do it because you
+
+ align:start position:0%
+remembering how to do it because you
+ 
+
+ align:start position:0%
+remembering how to do it because you
+just had it a week or two ago whereas
+
+ align:start position:0%
+just had it a week or two ago whereas
+ 
+
+ align:start position:0%
+just had it a week or two ago whereas
+all the other guys is something dim in
+
+ align:start position:0%
+all the other guys is something dim in
+ 
+
+ align:start position:0%
+all the other guys is something dim in
+their distance and so I'm reviewing how
+
+ align:start position:0%
+their distance and so I'm reviewing how
+ 
+
+ align:start position:0%
+their distance and so I'm reviewing how
+to change variables at a double
+
+ align:start position:0%
+to change variables at a double
+ 
+
+ align:start position:0%
+to change variables at a double
+integral I'm showing you it's good for
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+something so what we're out to try to
+
+ align:start position:0%
+something so what we're out to try to
+ 
+
+ align:start position:0%
+something so what we're out to try to
+prove is this
+
+ align:start position:0%
+prove is this
+ 
+
+ align:start position:0%
+prove is this
+formula
+
+ align:start position:0%
+formula
+ 
+
+ align:start position:0%
+formula
+let's put that down in so you
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+understand okay let's do
+
+ align:start position:0%
+understand okay let's do
+ 
+
+ align:start position:0%
+understand okay let's do
+it now we'll use the desert island
+
+ align:start position:0%
+it now we'll use the desert island
+ 
+
+ align:start position:0%
+it now we'll use the desert island
+method so you have as much time as you
+
+ align:start position:0%
+method so you have as much time as you
+ 
+
+ align:start position:0%
+method so you have as much time as you
+want your desert island I in fact I'm
+
+ align:start position:0%
+want your desert island I in fact I'm
+ 
+
+ align:start position:0%
+want your desert island I in fact I'm
+going to even go it the opposite
+
+ align:start position:0%
+going to even go it the opposite
+ 
+
+ align:start position:0%
+going to even go it the opposite
+way I'm going to start with you got a
+
+ align:start position:0%
+way I'm going to start with you got a
+ 
+
+ align:start position:0%
+way I'm going to start with you got a
+lot of time on your hand say gee I
+
+ align:start position:0%
+lot of time on your hand say gee I
+ 
+
+ align:start position:0%
+lot of time on your hand say gee I
+wonder if there's a
+
+ align:start position:0%
+wonder if there's a
+ 
+
+ align:start position:0%
+wonder if there's a
+if I take the product of the llast
+
+ align:start position:0%
+if I take the product of the llast
+ 
+
+ align:start position:0%
+if I take the product of the llast
+transforms I wonder if there's some
+
+ align:start position:0%
+transforms I wonder if there's some
+ 
+
+ align:start position:0%
+transforms I wonder if there's some
+crazy function I could put in there
+
+ align:start position:0%
+crazy function I could put in there
+ 
+
+ align:start position:0%
+crazy function I could put in there
+which would make things work you've
+
+ align:start position:0%
+which would make things work you've
+ 
+
+ align:start position:0%
+which would make things work you've
+never heard of the convolution you're
+
+ align:start position:0%
+never heard of the convolution you're
+ 
+
+ align:start position:0%
+never heard of the convolution you're
+going to discover it all by
+
+ align:start position:0%
+going to discover it all by
+ 
+
+ align:start position:0%
+going to discover it all by
+yourself okay so how do you begin so
+
+ align:start position:0%
+yourself okay so how do you begin so
+ 
+
+ align:start position:0%
+yourself okay so how do you begin so
+we'll start with the left hand side
+
+ align:start position:0%
+we'll start with the left hand side
+ 
+
+ align:start position:0%
+we'll start with the left hand side
+we'll looking
+
+ align:start position:0%
+we'll looking
+ 
+
+ align:start position:0%
+we'll looking
+for some nice way of calculating that as
+
+ align:start position:0%
+for some nice way of calculating that as
+ 
+
+ align:start position:0%
+for some nice way of calculating that as
+the llao transform of a single function
+
+ align:start position:0%
+the llao transform of a single function
+ 
+
+ align:start position:0%
+the llao transform of a single function
+so the way to begin is by writing out
+
+ align:start position:0%
+so the way to begin is by writing out
+ 
+
+ align:start position:0%
+so the way to begin is by writing out
+the definitions we couldn't use anything
+
+ align:start position:0%
+the definitions we couldn't use anything
+ 
+
+ align:start position:0%
+the definitions we couldn't use anything
+else since we don't have anything else
+
+ align:start position:0%
+else since we don't have anything else
+ 
+
+ align:start position:0%
+else since we don't have anything else
+to use now looking ahead I'm going to
+
+ align:start position:0%
+to use now looking ahead I'm going to
+ 
+
+ align:start position:0%
+to use now looking ahead I'm going to
+not use T I'm going to use two neutral
+
+ align:start position:0%
+not use T I'm going to use two neutral
+ 
+
+ align:start position:0%
+not use T I'm going to use two neutral
+variables when I calculate after all the
+
+ align:start position:0%
+variables when I calculate after all the
+ 
+
+ align:start position:0%
+variables when I calculate after all the
+t is just a dummy variable anyway you'll
+
+ align:start position:0%
+t is just a dummy variable anyway you'll
+ 
+
+ align:start position:0%
+t is just a dummy variable anyway you'll
+see uh in a minute the wisdom of doing
+
+ align:start position:0%
+see uh in a minute the wisdom of doing
+ 
+
+ align:start position:0%
+see uh in a minute the wisdom of doing
+this so it's this times the integral
+
+ align:start position:0%
+this so it's this times the integral
+ 
+
+ align:start position:0%
+this so it's this times the integral
+which gives the lass transform of G so
+
+ align:start position:0%
+which gives the lass transform of G so
+ 
+
+ align:start position:0%
+which gives the lass transform of G so
+that's e to the S V let's say times G of
+
+ align:start position:0%
+that's e to the S V let's say times G of
+ 
+
+ align:start position:0%
+that's e to the S V let's say times G of
+V
+
+ align:start position:0%
+V
+ 
+
+ align:start position:0%
+V
+DV okay everybody can get that far and
+
+ align:start position:0%
+DV okay everybody can get that far and
+ 
+
+ align:start position:0%
+DV okay everybody can get that far and
+now we have to start looking
+
+ align:start position:0%
+now we have to start looking
+ 
+
+ align:start position:0%
+now we have to start looking
+well this is a single integral an 1801
+
+ align:start position:0%
+well this is a single integral an 1801
+ 
+
+ align:start position:0%
+well this is a single integral an 1801
+integral involving U and this is an 1801
+
+ align:start position:0%
+integral involving U and this is an 1801
+ 
+
+ align:start position:0%
+integral involving U and this is an 1801
+integral involving V but when you take
+
+ align:start position:0%
+integral involving V but when you take
+ 
+
+ align:start position:0%
+integral involving V but when you take
+the product of two integrals like that
+
+ align:start position:0%
+the product of two integrals like that
+ 
+
+ align:start position:0%
+the product of two integrals like that
+remember when you evaluate a double
+
+ align:start position:0%
+remember when you evaluate a double
+ 
+
+ align:start position:0%
+remember when you evaluate a double
+integral there's an easy case where you
+
+ align:start position:0%
+integral there's an easy case where you
+ 
+
+ align:start position:0%
+integral there's an easy case where you
+don't it's much easier than any other
+
+ align:start position:0%
+don't it's much easier than any other
+ 
+
+ align:start position:0%
+don't it's much easier than any other
+case if you could write the inside if
+
+ align:start position:0%
+case if you could write the inside if
+ 
+
+ align:start position:0%
+case if you could write the inside if
+you're integrating over a rectangle for
+
+ align:start position:0%
+you're integrating over a rectangle for
+ 
+
+ align:start position:0%
+you're integrating over a rectangle for
+example and and you can write the
+
+ align:start position:0%
+example and and you can write the
+ 
+
+ align:start position:0%
+example and and you can write the
+integral as product of a function just
+
+ align:start position:0%
+integral as product of a function just
+ 
+
+ align:start position:0%
+integral as product of a function just
+of U and the product of a function just
+
+ align:start position:0%
+of U and the product of a function just
+ 
+
+ align:start position:0%
+of U and the product of a function just
+is V then the integral is very easy to
+
+ align:start position:0%
+is V then the integral is very easy to
+ 
+
+ align:start position:0%
+is V then the integral is very easy to
+evaluate you can forget all the rules
+
+ align:start position:0%
+evaluate you can forget all the rules
+ 
+
+ align:start position:0%
+evaluate you can forget all the rules
+you just take all the U part out all the
+
+ align:start position:0%
+you just take all the U part out all the
+ 
+
+ align:start position:0%
+you just take all the U part out all the
+V part out and integrate them separately
+
+ align:start position:0%
+V part out and integrate them separately
+ 
+
+ align:start position:0%
+V part out and integrate them separately
+A to B C to d That's the easy case of
+
+ align:start position:0%
+A to B C to d That's the easy case of
+ 
+
+ align:start position:0%
+A to B C to d That's the easy case of
+evaluating a double integral it's what
+
+ align:start position:0%
+evaluating a double integral it's what
+ 
+
+ align:start position:0%
+evaluating a double integral it's what
+everybody tries to do even when it's not
+
+ align:start position:0%
+everybody tries to do even when it's not
+ 
+
+ align:start position:0%
+everybody tries to do even when it's not
+appropriate now here it is appropriate
+
+ align:start position:0%
+appropriate now here it is appropriate
+ 
+
+ align:start position:0%
+appropriate now here it is appropriate
+except I'm going to use it backwards
+
+ align:start position:0%
+except I'm going to use it backwards
+ 
+
+ align:start position:0%
+except I'm going to use it backwards
+this is the result of having done that
+
+ align:start position:0%
+this is the result of having done that
+ 
+
+ align:start position:0%
+this is the result of having done that
+if this is the result of having done it
+
+ align:start position:0%
+if this is the result of having done it
+ 
+
+ align:start position:0%
+if this is the result of having done it
+what was the step just before it well I
+
+ align:start position:0%
+what was the step just before it well I
+ 
+
+ align:start position:0%
+what was the step just before it well I
+must have been trying to evaluate a
+
+ align:start position:0%
+must have been trying to evaluate a
+ 
+
+ align:start position:0%
+must have been trying to evaluate a
+double
+
+ align:start position:0%
+double
+ 
+
+ align:start position:0%
+double
+integral as U runs from zero to infinity
+
+ align:start position:0%
+integral as U runs from zero to infinity
+ 
+
+ align:start position:0%
+integral as U runs from zero to infinity
+and V runs from zero to Infinity of what
+
+ align:start position:0%
+and V runs from zero to Infinity of what
+ 
+
+ align:start position:0%
+and V runs from zero to Infinity of what
+well of the product of these two
+
+ align:start position:0%
+well of the product of these two
+ 
+
+ align:start position:0%
+well of the product of these two
+functions now what is that e Theus Su *
+
+ align:start position:0%
+functions now what is that e Theus Su *
+ 
+
+ align:start position:0%
+functions now what is that e Theus Su *
+e Theus SV well I must surely want to
+
+ align:start position:0%
+e Theus SV well I must surely want to
+ 
+
+ align:start position:0%
+e Theus SV well I must surely want to
+combine
+
+ align:start position:0%
+combine
+ 
+
+ align:start position:0%
+combine
+those eus Su * eus s B and what's left
+
+ align:start position:0%
+those eus Su * eus s B and what's left
+ 
+
+ align:start position:0%
+those eus Su * eus s B and what's left
+well what's gets dragged along
+
+ align:start position:0%
+well what's gets dragged along
+ 
+
+ align:start position:0%
+well what's gets dragged along
+DV this is the same as that because of
+
+ align:start position:0%
+DV this is the same as that because of
+ 
+
+ align:start position:0%
+DV this is the same as that because of
+that law I just gave you this is the
+
+ align:start position:0%
+that law I just gave you this is the
+ 
+
+ align:start position:0%
+that law I just gave you this is the
+product of a function just of U and a
+
+ align:start position:0%
+product of a function just of U and a
+ 
+
+ align:start position:0%
+product of a function just of U and a
+function just of v and therefore it's
+
+ align:start position:0%
+function just of v and therefore it's
+ 
+
+ align:start position:0%
+function just of v and therefore it's
+okay to separate the two integrals out
+
+ align:start position:0%
+okay to separate the two integrals out
+ 
+
+ align:start position:0%
+okay to separate the two integrals out
+that way because I'm integrating a sort
+
+ align:start position:0%
+that way because I'm integrating a sort
+ 
+
+ align:start position:0%
+that way because I'm integrating a sort
+of a rectangle it goes to Infinity that
+
+ align:start position:0%
+of a rectangle it goes to Infinity that
+ 
+
+ align:start position:0%
+of a rectangle it goes to Infinity that
+way and infinity that way but what I'm
+
+ align:start position:0%
+way and infinity that way but what I'm
+ 
+
+ align:start position:0%
+way and infinity that way but what I'm
+integrating is over the plane in other
+
+ align:start position:0%
+integrating is over the plane in other
+ 
+
+ align:start position:0%
+integrating is over the plane in other
+words this region of the plane
+
+ align:start position:0%
+words this region of the plane
+ 
+
+ align:start position:0%
+words this region of the plane
+as u v goes from zero to Infinity zero
+
+ align:start position:0%
+as u v goes from zero to Infinity zero
+ 
+
+ align:start position:0%
+as u v goes from zero to Infinity zero
+to
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Infinity
+
+ align:start position:0%
+Infinity
+ 
+
+ align:start position:0%
+Infinity
+now let's take a look what are we
+
+ align:start position:0%
+now let's take a look what are we
+ 
+
+ align:start position:0%
+now let's take a look what are we
+looking for well we're looking for we
+
+ align:start position:0%
+looking for well we're looking for we
+ 
+
+ align:start position:0%
+looking for well we're looking for we
+would be very happy if U plus v were
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+T let's make it
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+t in other words I'm introducing a new
+
+ align:start position:0%
+t in other words I'm introducing a new
+ 
+
+ align:start position:0%
+t in other words I'm introducing a new
+variable t u plus v and it's suggested
+
+ align:start position:0%
+variable t u plus v and it's suggested
+ 
+
+ align:start position:0%
+variable t u plus v and it's suggested
+by the form in which I'm looking for the
+
+ align:start position:0%
+by the form in which I'm looking for the
+ 
+
+ align:start position:0%
+by the form in which I'm looking for the
+answer now you of course you then have
+
+ align:start position:0%
+answer now you of course you then have
+ 
+
+ align:start position:0%
+answer now you of course you then have
+to we need another variable we could
+
+ align:start position:0%
+to we need another variable we could
+ 
+
+ align:start position:0%
+to we need another variable we could
+keep either U or V oh let's keep U that
+
+ align:start position:0%
+keep either U or V oh let's keep U that
+ 
+
+ align:start position:0%
+keep either U or V oh let's keep U that
+means V we this game of musical chairs V
+
+ align:start position:0%
+means V we this game of musical chairs V
+ 
+
+ align:start position:0%
+means V we this game of musical chairs V
+got dropped out uh well we can't have
+
+ align:start position:0%
+got dropped out uh well we can't have
+ 
+
+ align:start position:0%
+got dropped out uh well we can't have
+three variables we only have room for
+
+ align:start position:0%
+three variables we only have room for
+ 
+
+ align:start position:0%
+three variables we only have room for
+two but uh we will remember
+
+ align:start position:0%
+two but uh we will remember
+ 
+
+ align:start position:0%
+two but uh we will remember
+it rest in peace V was equal to T minus
+
+ align:start position:0%
+it rest in peace V was equal to T minus
+ 
+
+ align:start position:0%
+it rest in peace V was equal to T minus
+U in we ever need him
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+again okay let's now put in the limits
+
+ align:start position:0%
+again okay let's now put in the limits
+ 
+
+ align:start position:0%
+again okay let's now put in the limits
+let's put in the integral the rest of
+
+ align:start position:0%
+let's put in the integral the rest of
+ 
+
+ align:start position:0%
+let's put in the integral the rest of
+the change of variable so it's e so I'm
+
+ align:start position:0%
+the change of variable so it's e so I'm
+ 
+
+ align:start position:0%
+the change of variable so it's e so I'm
+now changing it to these new variables T
+
+ align:start position:0%
+now changing it to these new variables T
+ 
+
+ align:start position:0%
+now changing it to these new variables T
+and U so it's e to the negative St well
+
+ align:start position:0%
+and U so it's e to the negative St well
+ 
+
+ align:start position:0%
+and U so it's e to the negative St well
+F of U I don't have to do anything
+
+ align:start position:0%
+F of U I don't have to do anything
+ 
+
+ align:start position:0%
+F of U I don't have to do anything
+to but G of V I'm not allowed to keep V
+
+ align:start position:0%
+to but G of V I'm not allowed to keep V
+ 
+
+ align:start position:0%
+to but G of V I'm not allowed to keep V
+so V has to be changed to T minus U
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+amazing things are
+
+ align:start position:0%
+amazing things are
+ 
+
+ align:start position:0%
+amazing things are
+happening
+
+ align:start position:0%
+happening
+ 
+
+ align:start position:0%
+happening
+du now I want to change this to an
+
+ align:start position:0%
+du now I want to change this to an
+ 
+
+ align:start position:0%
+du now I want to change this to an
+integral du DT now for that you have to
+
+ align:start position:0%
+integral du DT now for that you have to
+ 
+
+ align:start position:0%
+integral du DT now for that you have to
+be a little careful we have two things
+
+ align:start position:0%
+be a little careful we have two things
+ 
+
+ align:start position:0%
+be a little careful we have two things
+to do to figure out this what goes with
+
+ align:start position:0%
+to do to figure out this what goes with
+ 
+
+ align:start position:0%
+to do to figure out this what goes with
+that and we have to put in the limits
+
+ align:start position:0%
+that and we have to put in the limits
+ 
+
+ align:start position:0%
+that and we have to put in the limits
+also now those are the two non-trivial
+
+ align:start position:0%
+also now those are the two non-trivial
+ 
+
+ align:start position:0%
+also now those are the two non-trivial
+operations when you change integrals in
+
+ align:start position:0%
+operations when you change integrals in
+ 
+
+ align:start position:0%
+operations when you change integrals in
+a change variables in a double integral
+
+ align:start position:0%
+a change variables in a double integral
+ 
+
+ align:start position:0%
+a change variables in a double integral
+so let's be really careful let's do the
+
+ align:start position:0%
+so let's be really careful let's do the
+ 
+
+ align:start position:0%
+so let's be really careful let's do the
+easier of the two first I want to change
+
+ align:start position:0%
+easier of the two first I want to change
+ 
+
+ align:start position:0%
+easier of the two first I want to change
+from du DV
+
+ align:start position:0%
+from du DV
+ 
+
+ align:start position:0%
+from du DV
+to duu DT and now to do that you have to
+
+ align:start position:0%
+to duu DT and now to do that you have to
+ 
+
+ align:start position:0%
+to duu DT and now to do that you have to
+put in the Jacobian matrix the Jacobian
+
+ align:start position:0%
+put in the Jacobian matrix the Jacobian
+ 
+
+ align:start position:0%
+put in the Jacobian matrix the Jacobian
+DET ter
+
+ align:start position:0%
+DET ter
+ 
+
+ align:start position:0%
+DET ter
+ah you how many of you forgot that I
+
+ align:start position:0%
+ah you how many of you forgot that I
+ 
+
+ align:start position:0%
+ah you how many of you forgot that I
+won't even bother asking
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh oh come on you only lose two points
+
+ align:start position:0%
+uh oh come on you only lose two points
+ 
+
+ align:start position:0%
+uh oh come on you only lose two points
+what's the it doesn't matter if you put
+
+ align:start position:0%
+what's the it doesn't matter if you put
+ 
+
+ align:start position:0%
+what's the it doesn't matter if you put
+in the Jacobian uh as you see you know
+
+ align:start position:0%
+in the Jacobian uh as you see you know
+ 
+
+ align:start position:0%
+in the Jacobian uh as you see you know
+going forget something you'll lose less
+
+ align:start position:0%
+going forget something you'll lose less
+ 
+
+ align:start position:0%
+going forget something you'll lose less
+credit for forgetting that than anything
+
+ align:start position:0%
+credit for forgetting that than anything
+ 
+
+ align:start position:0%
+credit for forgetting that than anything
+else so it's the Jacobian of u and v
+
+ align:start position:0%
+else so it's the Jacobian of u and v
+ 
+
+ align:start position:0%
+else so it's the Jacobian of u and v
+with respect to U and T So to calculate
+
+ align:start position:0%
+with respect to U and T So to calculate
+ 
+
+ align:start position:0%
+with respect to U and T So to calculate
+that you write U equals u v equals uh T
+
+ align:start position:0%
+that you write U equals u v equals uh T
+ 
+
+ align:start position:0%
+that you write U equals u v equals uh T
+minus
+
+ align:start position:0%
+minus
+ 
+
+ align:start position:0%
+minus
+U and then the Jacobian
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+is the Jacobian is uh blah blah blah
+
+ align:start position:0%
+is the Jacobian is uh blah blah blah
+ 
+
+ align:start position:0%
+is the Jacobian is uh blah blah blah
+blah blah blah
+
+ align:start position:0%
+blah blah blah
+ 
+
+ align:start position:0%
+blah blah blah
+uh the partial The Matrix of the
+
+ align:start position:0%
+uh the partial The Matrix of the
+ 
+
+ align:start position:0%
+uh the partial The Matrix of the
+determinant of partial
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+derivatives so it's the determinant
+
+ align:start position:0%
+derivatives so it's the determinant
+ 
+
+ align:start position:0%
+derivatives so it's the determinant
+whose entries are the partial of U with
+
+ align:start position:0%
+whose entries are the partial of U with
+ 
+
+ align:start position:0%
+whose entries are the partial of U with
+respect to U the partial of U with
+
+ align:start position:0%
+respect to U the partial of U with
+ 
+
+ align:start position:0%
+respect to U the partial of U with
+respect to T but these are independent
+
+ align:start position:0%
+respect to T but these are independent
+ 
+
+ align:start position:0%
+respect to T but these are independent
+variables so that's zero the partial of
+
+ align:start position:0%
+variables so that's zero the partial of
+ 
+
+ align:start position:0%
+variables so that's zero the partial of
+V with respect to U is negative one the
+
+ align:start position:0%
+V with respect to U is negative one the
+ 
+
+ align:start position:0%
+V with respect to U is negative one the
+partial of V with respect to T is one so
+
+ align:start position:0%
+partial of V with respect to T is one so
+ 
+
+ align:start position:0%
+partial of V with respect to T is one so
+the Jacobian is one so if you forgot it
+
+ align:start position:0%
+the Jacobian is one so if you forgot it
+ 
+
+ align:start position:0%
+the Jacobian is one so if you forgot it
+no
+
+ align:start position:0%
+no
+ 
+
+ align:start position:0%
+no
+harm
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so the Jacobian is
+
+ align:start position:0%
+so the Jacobian is
+ 
+
+ align:start position:0%
+so the Jacobian is
+one now more serious and in some ways I
+
+ align:start position:0%
+one now more serious and in some ways I
+ 
+
+ align:start position:0%
+one now more serious and in some ways I
+think for most of you the most difficult
+
+ align:start position:0%
+think for most of you the most difficult
+ 
+
+ align:start position:0%
+think for most of you the most difficult
+part of the operation is putting in the
+
+ align:start position:0%
+part of the operation is putting in the
+ 
+
+ align:start position:0%
+part of the operation is putting in the
+new
+
+ align:start position:0%
+new
+ 
+
+ align:start position:0%
+new
+livits now for that you look at the
+
+ align:start position:0%
+livits now for that you look at the
+ 
+
+ align:start position:0%
+livits now for that you look at the
+region over which you're integrating I
+
+ align:start position:0%
+region over which you're integrating I
+ 
+
+ align:start position:0%
+region over which you're integrating I
+think I better do that carefully uh
+
+ align:start position:0%
+think I better do that carefully uh
+ 
+
+ align:start position:0%
+think I better do that carefully uh
+let's I need a bigger picture that's
+
+ align:start position:0%
+let's I need a bigger picture that's
+ 
+
+ align:start position:0%
+let's I need a bigger picture that's
+really what I'm trying to say so here is
+
+ align:start position:0%
+really what I'm trying to say so here is
+ 
+
+ align:start position:0%
+really what I'm trying to say so here is
+the UV coordinates and I want to change
+
+ align:start position:0%
+the UV coordinates and I want to change
+ 
+
+ align:start position:0%
+the UV coordinates and I want to change
+these to UV to UT coordinates the
+
+ align:start position:0%
+these to UV to UT coordinates the
+ 
+
+ align:start position:0%
+these to UV to UT coordinates the
+integration is over the first
+
+ align:start position:0%
+integration is over the first
+ 
+
+ align:start position:0%
+integration is over the first
+quadrant so what you do is when you do
+
+ align:start position:0%
+quadrant so what you do is when you do
+ 
+
+ align:start position:0%
+quadrant so what you do is when you do
+the integral the first step is U is
+
+ align:start position:0%
+the integral the first step is U is
+ 
+
+ align:start position:0%
+the integral the first step is U is
+varying and T is held fixed so in the
+
+ align:start position:0%
+varying and T is held fixed so in the
+ 
+
+ align:start position:0%
+varying and T is held fixed so in the
+first integration U
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+varies T is held fixed now what is
+
+ align:start position:0%
+varies T is held fixed now what is
+ 
+
+ align:start position:0%
+varies T is held fixed now what is
+holding T fixed in this picture mean
+
+ align:start position:0%
+holding T fixed in this picture mean
+ 
+
+ align:start position:0%
+holding T fixed in this picture mean
+well T is equal to U + V so U plus v is
+
+ align:start position:0%
+well T is equal to U + V so U plus v is
+ 
+
+ align:start position:0%
+well T is equal to U + V so U plus v is
+fixed is a constant in other words now
+
+ align:start position:0%
+fixed is a constant in other words now
+ 
+
+ align:start position:0%
+fixed is a constant in other words now
+where are the curves along which U plus
+
+ align:start position:0%
+where are the curves along which U plus
+ 
+
+ align:start position:0%
+where are the curves along which U plus
+v is a constant well they are these
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+lines these are the lines along which u+
+
+ align:start position:0%
+lines these are the lines along which u+
+ 
+
+ align:start position:0%
+lines these are the lines along which u+
+V equals a constant or t is a constant
+
+ align:start position:0%
+V equals a constant or t is a constant
+ 
+
+ align:start position:0%
+V equals a constant or t is a constant
+the reason I'm holding t a constant is
+
+ align:start position:0%
+the reason I'm holding t a constant is
+ 
+
+ align:start position:0%
+the reason I'm holding t a constant is
+because the first integration only
+
+ align:start position:0%
+because the first integration only
+ 
+
+ align:start position:0%
+because the first integration only
+allows U to change T is held
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+fixed okay you let U
+
+ align:start position:0%
+fixed okay you let U
+ 
+
+ align:start position:0%
+fixed okay you let U
+increase as U increase and T is held
+
+ align:start position:0%
+increase as U increase and T is held
+ 
+
+ align:start position:0%
+increase as U increase and T is held
+fixed I'm traversing these lines in this
+
+ align:start position:0%
+fixed I'm traversing these lines in this
+ 
+
+ align:start position:0%
+fixed I'm traversing these lines in this
+Direction that's the direction on which
+
+ align:start position:0%
+Direction that's the direction on which
+ 
+
+ align:start position:0%
+Direction that's the direction on which
+U is increasing I integrate from the
+
+ align:start position:0%
+U is increasing I integrate from the
+ 
+
+ align:start position:0%
+U is increasing I integrate from the
+point from the U value where they leave
+
+ align:start position:0%
+point from the U value where they leave
+ 
+
+ align:start position:0%
+point from the U value where they leave
+the region into enter the region what's
+
+ align:start position:0%
+the region into enter the region what's
+ 
+
+ align:start position:0%
+the region into enter the region what's
+the U value where they enter the region
+
+ align:start position:0%
+the U value where they enter the region
+ 
+
+ align:start position:0%
+the U value where they enter the region
+U is equal to zero everybody would know
+
+ align:start position:0%
+U is equal to zero everybody would know
+ 
+
+ align:start position:0%
+U is equal to zero everybody would know
+that not so many people would be able to
+
+ align:start position:0%
+that not so many people would be able to
+ 
+
+ align:start position:0%
+that not so many people would be able to
+figure out what to put for where it
+
+ align:start position:0%
+figure out what to put for where it
+ 
+
+ align:start position:0%
+figure out what to put for where it
+leaves the
+
+ align:start position:0%
+leaves the
+ 
+
+ align:start position:0%
+leaves the
+region what's U the value of U when it
+
+ align:start position:0%
+region what's U the value of U when it
+ 
+
+ align:start position:0%
+region what's U the value of U when it
+leaves the region well this is the curve
+
+ align:start position:0%
+leaves the region well this is the curve
+ 
+
+ align:start position:0%
+leaves the region well this is the curve
+v equals 0 but V equals 0 is in another
+
+ align:start position:0%
+v equals 0 but V equals 0 is in another
+ 
+
+ align:start position:0%
+v equals 0 but V equals 0 is in another
+language U equals T T minus U equal 0 or
+
+ align:start position:0%
+language U equals T T minus U equal 0 or
+ 
+
+ align:start position:0%
+language U equals T T minus U equal 0 or
+U equals T in other words they enter the
+
+ align:start position:0%
+U equals T in other words they enter the
+ 
+
+ align:start position:0%
+U equals T in other words they enter the
+region where U equals 0 and they leave
+
+ align:start position:0%
+region where U equals 0 and they leave
+ 
+
+ align:start position:0%
+region where U equals 0 and they leave
+where U is T has the value
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+t
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and how about the other guys for which
+
+ align:start position:0%
+and how about the other guys for which
+ 
+
+ align:start position:0%
+and how about the other guys for which
+T's do I want to do this well I want to
+
+ align:start position:0%
+T's do I want to do this well I want to
+ 
+
+ align:start position:0%
+T's do I want to do this well I want to
+do it for all these T values well now
+
+ align:start position:0%
+do it for all these T values well now
+ 
+
+ align:start position:0%
+do it for all these T values well now
+the T value here that's the starting one
+
+ align:start position:0%
+the T value here that's the starting one
+ 
+
+ align:start position:0%
+the T value here that's the starting one
+here T is zero and here T is not zero
+
+ align:start position:0%
+here T is zero and here T is not zero
+ 
+
+ align:start position:0%
+here T is zero and here T is not zero
+and if I go out and cover the whole
+
+ align:start position:0%
+and if I go out and cover the whole
+ 
+
+ align:start position:0%
+and if I go out and cover the whole
+first quadrant I'll be going letting T
+
+ align:start position:0%
+first quadrant I'll be going letting T
+ 
+
+ align:start position:0%
+first quadrant I'll be going letting T
+increase to Infinity the sum of u and v
+
+ align:start position:0%
+increase to Infinity the sum of u and v
+ 
+
+ align:start position:0%
+increase to Infinity the sum of u and v
+i will be letting increase to Infinity
+
+ align:start position:0%
+i will be letting increase to Infinity
+ 
+
+ align:start position:0%
+i will be letting increase to Infinity
+so it's 0 to Infinity so all this is an
+
+ align:start position:0%
+so it's 0 to Infinity so all this is an
+ 
+
+ align:start position:0%
+so it's 0 to Infinity so all this is an
+exercise in changing taking this double
+
+ align:start position:0%
+exercise in changing taking this double
+ 
+
+ align:start position:0%
+exercise in changing taking this double
+integral in UV coordinates and changing
+
+ align:start position:0%
+integral in UV coordinates and changing
+ 
+
+ align:start position:0%
+integral in UV coordinates and changing
+it to this double integral an equivalent
+
+ align:start position:0%
+it to this double integral an equivalent
+ 
+
+ align:start position:0%
+it to this double integral an equivalent
+double integral over the same region but
+
+ align:start position:0%
+double integral over the same region but
+ 
+
+ align:start position:0%
+double integral over the same region but
+now in ut coordinates and now that's the
+
+ align:start position:0%
+now in ut coordinates and now that's the
+ 
+
+ align:start position:0%
+now in ut coordinates and now that's the
+answer somewhere here is the answer
+
+ align:start position:0%
+answer somewhere here is the answer
+ 
+
+ align:start position:0%
+answer somewhere here is the answer
+because
+
+ align:start position:0%
+because
+ 
+
+ align:start position:0%
+because
+look because look if I
+
+ align:start position:0%
+look because look if I
+ 
+
+ align:start position:0%
+look because look if I
+uh since the first integration is with
+
+ align:start position:0%
+uh since the first integration is with
+ 
+
+ align:start position:0%
+uh since the first integration is with
+respect to you this this guy can migrate
+
+ align:start position:0%
+respect to you this this guy can migrate
+ 
+
+ align:start position:0%
+respect to you this this guy can migrate
+outside because it doesn't involve
+
+ align:start position:0%
+outside because it doesn't involve
+ 
+
+ align:start position:0%
+outside because it doesn't involve
+you that only involves T and T is only
+
+ align:start position:0%
+you that only involves T and T is only
+ 
+
+ align:start position:0%
+you that only involves T and T is only
+caught by the second integration so I
+
+ align:start position:0%
+caught by the second integration so I
+ 
+
+ align:start position:0%
+caught by the second integration so I
+can put this outside and what do I end
+
+ align:start position:0%
+can put this outside and what do I end
+ 
+
+ align:start position:0%
+can put this outside and what do I end
+up with the integral from zero to
+
+ align:start position:0%
+up with the integral from zero to
+ 
+
+ align:start position:0%
+up with the integral from zero to
+Infinity of e to the negative St times
+
+ align:start position:0%
+Infinity of e to the negative St times
+ 
+
+ align:start position:0%
+Infinity of e to the negative St times
+what's left a funny expression but
+
+ align:start position:0%
+what's left a funny expression but
+ 
+
+ align:start position:0%
+what's left a funny expression but
+you're on your desert island and found
+
+ align:start position:0%
+you're on your desert island and found
+ 
+
+ align:start position:0%
+you're on your desert island and found
+it this funny expression integral from 0
+
+ align:start position:0%
+it this funny expression integral from 0
+ 
+
+ align:start position:0%
+it this funny expression integral from 0
+to T F of uu G of T minus U du in short
+
+ align:start position:0%
+to T F of uu G of T minus U du in short
+ 
+
+ align:start position:0%
+to T F of uu G of T minus U du in short
+the convolution exactly the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+convolution so all you have to do is get
+
+ align:start position:0%
+convolution so all you have to do is get
+ 
+
+ align:start position:0%
+convolution so all you have to do is get
+the idea that there might be a formula
+
+ align:start position:0%
+the idea that there might be a formula
+ 
+
+ align:start position:0%
+the idea that there might be a formula
+sit down change variables the double
+
+ align:start position:0%
+sit down change variables the double
+ 
+
+ align:start position:0%
+sit down change variables the double
+integral Echo you got your formula
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+well I would like to spend much of the
+
+ align:start position:0%
+well I would like to spend much of the
+ 
+
+ align:start position:0%
+well I would like to spend much of the
+rest of the
+
+ align:start position:0%
+rest of the
+ 
+
+ align:start position:0%
+rest of the
+period
+
+ align:start position:0%
+period
+ 
+
+ align:start position:0%
+period
+in other words so that's how it relates
+
+ align:start position:0%
+in other words so that's how it relates
+ 
+
+ align:start position:0%
+in other words so that's how it relates
+to the luse transform that's how it
+
+ align:start position:0%
+to the luse transform that's how it
+ 
+
+ align:start position:0%
+to the luse transform that's how it
+comes out of the LL transform here's how
+
+ align:start position:0%
+comes out of the LL transform here's how
+ 
+
+ align:start position:0%
+comes out of the LL transform here's how
+to use it you know calculate it either
+
+ align:start position:0%
+to use it you know calculate it either
+ 
+
+ align:start position:0%
+to use it you know calculate it either
+with a llao transform or directly from
+
+ align:start position:0%
+with a llao transform or directly from
+ 
+
+ align:start position:0%
+with a llao transform or directly from
+the integral and of course you'll solve
+
+ align:start position:0%
+the integral and of course you'll solve
+ 
+
+ align:start position:0%
+the integral and of course you'll solve
+problems llao transform problems
+
+ align:start position:0%
+problems llao transform problems
+ 
+
+ align:start position:0%
+problems llao transform problems
+differential equations using the
+
+ align:start position:0%
+differential equations using the
+ 
+
+ align:start position:0%
+differential equations using the
+convolution but I have to tell you that
+
+ align:start position:0%
+convolution but I have to tell you that
+ 
+
+ align:start position:0%
+convolution but I have to tell you that
+most people convolution is very
+
+ align:start position:0%
+most people convolution is very
+ 
+
+ align:start position:0%
+most people convolution is very
+important and most people who use it
+
+ align:start position:0%
+important and most people who use it
+ 
+
+ align:start position:0%
+important and most people who use it
+don't use it in connection of the llao
+
+ align:start position:0%
+don't use it in connection of the llao
+ 
+
+ align:start position:0%
+don't use it in connection of the llao
+transform they use it for its own
+
+ align:start position:0%
+transform they use it for its own
+ 
+
+ align:start position:0%
+transform they use it for its own
+sake uh the first
+
+ align:start position:0%
+sake uh the first
+ 
+
+ align:start position:0%
+sake uh the first
+place I learned that you know outside of
+
+ align:start position:0%
+place I learned that you know outside of
+ 
+
+ align:start position:0%
+place I learned that you know outside of
+MIT people use the convolution was
+
+ align:start position:0%
+MIT people use the convolution was
+ 
+
+ align:start position:0%
+MIT people use the convolution was
+actually from my daughter who uh you
+
+ align:start position:0%
+actually from my daughter who uh you
+ 
+
+ align:start position:0%
+actually from my daughter who uh you
+know is she's an environmental engineer
+
+ align:start position:0%
+know is she's an environmental engineer
+ 
+
+ align:start position:0%
+know is she's an environmental engineer
+a consultant uh environmental consultant
+
+ align:start position:0%
+a consultant uh environmental consultant
+ 
+
+ align:start position:0%
+a consultant uh environmental consultant
+she does risk assessment stuff like that
+
+ align:start position:0%
+she does risk assessment stuff like that
+ 
+
+ align:start position:0%
+she does risk assessment stuff like that
+but anyway she had this paper on acid
+
+ align:start position:0%
+but anyway she had this paper on acid
+ 
+
+ align:start position:0%
+but anyway she had this paper on acid
+range she was trying to read for a
+
+ align:start position:0%
+range she was trying to read for a
+ 
+
+ align:start position:0%
+range she was trying to read for a
+client and uh she said you know was
+
+ align:start position:0%
+client and uh she said you know was
+ 
+
+ align:start position:0%
+client and uh she said you know was
+something about calculating acid rain
+
+ align:start position:0%
+something about calculating acid rain
+ 
+
+ align:start position:0%
+something about calculating acid rain
+falls on uh soil and then from there the
+
+ align:start position:0%
+falls on uh soil and then from there the
+ 
+
+ align:start position:0%
+falls on uh soil and then from there the
+stuff leeches into a river but uh things
+
+ align:start position:0%
+stuff leeches into a river but uh things
+ 
+
+ align:start position:0%
+stuff leeches into a river but uh things
+happen to it on the way the soil
+
+ align:start position:0%
+happen to it on the way the soil
+ 
+
+ align:start position:0%
+happen to it on the way the soil
+combines with it in various ways reduces
+
+ align:start position:0%
+combines with it in various ways reduces
+ 
+
+ align:start position:0%
+combines with it in various ways reduces
+the acidity and things happen chemical
+
+ align:start position:0%
+the acidity and things happen chemical
+ 
+
+ align:start position:0%
+the acidity and things happen chemical
+reactions take place blah blah blah blah
+
+ align:start position:0%
+reactions take place blah blah blah blah
+ 
+
+ align:start position:0%
+reactions take place blah blah blah blah
+anyway she said well then they
+
+ align:start position:0%
+anyway she said well then they
+ 
+
+ align:start position:0%
+anyway she said well then they
+calculated in the end how much the water
+
+ align:start position:0%
+calculated in the end how much the water
+ 
+
+ align:start position:0%
+calculated in the end how much the water
+get the river gets polluted but she said
+
+ align:start position:0%
+get the river gets polluted but she said
+ 
+
+ align:start position:0%
+get the river gets polluted but she said
+but it's a
+
+ align:start position:0%
+but it's a
+ 
+
+ align:start position:0%
+but it's a
+convolution she said well what's the
+
+ align:start position:0%
+convolution she said well what's the
+ 
+
+ align:start position:0%
+convolution she said well what's the
+convolution so I told her she was too
+
+ align:start position:0%
+convolution so I told her she was too
+ 
+
+ align:start position:0%
+convolution so I told her she was too
+young to learn about the convolution and
+
+ align:start position:0%
+young to learn about the convolution and
+ 
+
+ align:start position:0%
+young to learn about the convolution and
+you know so I thought I'd better look it
+
+ align:start position:0%
+you know so I thought I'd better look it
+ 
+
+ align:start position:0%
+you know so I thought I'd better look it
+up first uh I mean I of course knew what
+
+ align:start position:0%
+up first uh I mean I of course knew what
+ 
+
+ align:start position:0%
+up first uh I mean I of course knew what
+the convolution was but I was a little
+
+ align:start position:0%
+the convolution was but I was a little
+ 
+
+ align:start position:0%
+the convolution was but I was a little
+puzzled at that application of it so I
+
+ align:start position:0%
+puzzled at that application of it so I
+ 
+
+ align:start position:0%
+puzzled at that application of it so I
+read the paper it was interesting and I
+
+ align:start position:0%
+read the paper it was interesting and I
+ 
+
+ align:start position:0%
+read the paper it was interesting and I
+uh in thinking about it uh I then other
+
+ align:start position:0%
+uh in thinking about it uh I then other
+ 
+
+ align:start position:0%
+uh in thinking about it uh I then other
+people have come to me you know some guy
+
+ align:start position:0%
+people have come to me you know some guy
+ 
+
+ align:start position:0%
+people have come to me you know some guy
+with a problem about they drilled ice
+
+ align:start position:0%
+with a problem about they drilled ice
+ 
+
+ align:start position:0%
+with a problem about they drilled ice
+cores in the North Pole and uh from the
+
+ align:start position:0%
+cores in the North Pole and uh from the
+ 
+
+ align:start position:0%
+cores in the North Pole and uh from the
+radioactive carbon and so on they were
+
+ align:start position:0%
+radioactive carbon and so on they were
+ 
+
+ align:start position:0%
+radioactive carbon and so on they were
+deducing various things about the
+
+ align:start position:0%
+deducing various things about the
+ 
+
+ align:start position:0%
+deducing various things about the
+climate you know 60 billion years ago
+
+ align:start position:0%
+climate you know 60 billion years ago
+ 
+
+ align:start position:0%
+climate you know 60 billion years ago
+and it was all convolution he asked me
+
+ align:start position:0%
+and it was all convolution he asked me
+ 
+
+ align:start position:0%
+and it was all convolution he asked me
+if I could explain that to him so let me
+
+ align:start position:0%
+if I could explain that to him so let me
+ 
+
+ align:start position:0%
+if I could explain that to him so let me
+give you uh a sort of an allpurpose
+
+ align:start position:0%
+give you uh a sort of an allpurpose
+ 
+
+ align:start position:0%
+give you uh a sort of an allpurpose
+thing a simple all purpose model which
+
+ align:start position:0%
+thing a simple all purpose model which
+ 
+
+ align:start position:0%
+thing a simple all purpose model which
+can be adapted which is a very good way
+
+ align:start position:0%
+can be adapted which is a very good way
+ 
+
+ align:start position:0%
+can be adapted which is a very good way
+I of thinking of the convolution in my
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+opinion it's a problem of radioactive
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+dumping it's in the notes by the way uh
+
+ align:start position:0%
+dumping it's in the notes by the way uh
+ 
+
+ align:start position:0%
+dumping it's in the notes by the way uh
+so I'm just uh if you want to take a
+
+ align:start position:0%
+so I'm just uh if you want to take a
+ 
+
+ align:start position:0%
+so I'm just uh if you want to take a
+chance uh and just listen to what I'm
+
+ align:start position:0%
+chance uh and just listen to what I'm
+ 
+
+ align:start position:0%
+chance uh and just listen to what I'm
+saying rather than scribbling everything
+
+ align:start position:0%
+saying rather than scribbling everything
+ 
+
+ align:start position:0%
+saying rather than scribbling everything
+down maybe it's a good you'll be able to
+
+ align:start position:0%
+down maybe it's a good you'll be able to
+ 
+
+ align:start position:0%
+down maybe it's a good you'll be able to
+figured out the notes also so the
+
+ align:start position:0%
+figured out the notes also so the
+ 
+
+ align:start position:0%
+figured out the notes also so the
+problem is we have some Factory or some
+
+ align:start position:0%
+problem is we have some Factory or some
+ 
+
+ align:start position:0%
+problem is we have some Factory or some
+a nuclear plant or something like that
+
+ align:start position:0%
+a nuclear plant or something like that
+ 
+
+ align:start position:0%
+a nuclear plant or something like that
+it's producing nuclear material
+
+ align:start position:0%
+it's producing nuclear material
+ 
+
+ align:start position:0%
+it's producing nuclear material
+radioactive waste certain not always at
+
+ align:start position:0%
+radioactive waste certain not always at
+ 
+
+ align:start position:0%
+radioactive waste certain not always at
+the same rate uh and then it carts it
+
+ align:start position:0%
+the same rate uh and then it carts it
+ 
+
+ align:start position:0%
+the same rate uh and then it carts it
+and dumps it on a pile somewhere so
+
+ align:start position:0%
+and dumps it on a pile somewhere so
+ 
+
+ align:start position:0%
+and dumps it on a pile somewhere so
+radioactive
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+waste is dumped and there's a dumping
+
+ align:start position:0%
+waste is dumped and there's a dumping
+ 
+
+ align:start position:0%
+waste is dumped and there's a dumping
+function I'll call that F of T the dump
+
+ align:start position:0%
+function I'll call that F of T the dump
+ 
+
+ align:start position:0%
+function I'll call that F of T the dump
+rate
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+rate That's The Dumping rate let's say t
+
+ align:start position:0%
+rate That's The Dumping rate let's say t
+ 
+
+ align:start position:0%
+rate That's The Dumping rate let's say t
+is in years you like to have units and
+
+ align:start position:0%
+is in years you like to have units and
+ 
+
+ align:start position:0%
+is in years you like to have units and
+quantity kilograms I don't know whatever
+
+ align:start position:0%
+quantity kilograms I don't know whatever
+ 
+
+ align:start position:0%
+quantity kilograms I don't know whatever
+whatever you want uh now what does The
+
+ align:start position:0%
+whatever you want uh now what does The
+ 
+
+ align:start position:0%
+whatever you want uh now what does The
+Dumping rate
+
+ align:start position:0%
+Dumping rate
+ 
+
+ align:start position:0%
+Dumping rate
+mean The Dumping rate
+
+ align:start position:0%
+mean The Dumping rate
+ 
+
+ align:start position:0%
+mean The Dumping rate
+means that if I on the time axis if I
+
+ align:start position:0%
+means that if I on the time axis if I
+ 
+
+ align:start position:0%
+means that if I on the time axis if I
+have two times which are close together
+
+ align:start position:0%
+have two times which are close together
+ 
+
+ align:start position:0%
+have two times which are close together
+for example two successive days a new
+
+ align:start position:0%
+for example two successive days a new
+ 
+
+ align:start position:0%
+for example two successive days a new
+midnight on two successive days then
+
+ align:start position:0%
+midnight on two successive days then
+ 
+
+ align:start position:0%
+midnight on two successive days then
+there's a time interval between them
+
+ align:start position:0%
+there's a time interval between them
+ 
+
+ align:start position:0%
+there's a time interval between them
+I'll call that delta
+
+ align:start position:0%
+I'll call that delta
+ 
+
+ align:start position:0%
+I'll call that delta
+T to say The Dumping rate is f of t
+
+ align:start position:0%
+T to say The Dumping rate is f of t
+ 
+
+ align:start position:0%
+T to say The Dumping rate is f of t
+means that the amount
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+dumped in the in this time interval in
+
+ align:start position:0%
+dumped in the in this time interval in
+ 
+
+ align:start position:0%
+dumped in the in this time interval in
+the time interval from TI to TI + one is
+
+ align:start position:0%
+the time interval from TI to TI + one is
+ 
+
+ align:start position:0%
+the time interval from TI to TI + one is
+approximately not exactly because the
+
+ align:start position:0%
+approximately not exactly because the
+ 
+
+ align:start position:0%
+approximately not exactly because the
+damping The Dumping rate isn't even
+
+ align:start position:0%
+damping The Dumping rate isn't even
+ 
+
+ align:start position:0%
+damping The Dumping rate isn't even
+constant within this time interval uh
+
+ align:start position:0%
+constant within this time interval uh
+ 
+
+ align:start position:0%
+constant within this time interval uh
+but it's approximately The Dumping rate
+
+ align:start position:0%
+but it's approximately The Dumping rate
+ 
+
+ align:start position:0%
+but it's approximately The Dumping rate
+times the
+
+ align:start position:0%
+times the
+ 
+
+ align:start position:0%
+times the
+time over which The Dumping was taking
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+place that's what I mean by The Dump
+
+ align:start position:0%
+place that's what I mean by The Dump
+ 
+
+ align:start position:0%
+place that's what I mean by The Dump
+break and it gets more and more accurate
+
+ align:start position:0%
+break and it gets more and more accurate
+ 
+
+ align:start position:0%
+break and it gets more and more accurate
+the smaller the time interval you
+
+ align:start position:0%
+the smaller the time interval you
+ 
+
+ align:start position:0%
+the smaller the time interval you
+take okay now here's my problem the
+
+ align:start position:0%
+take okay now here's my problem the
+ 
+
+ align:start position:0%
+take okay now here's my problem the
+problem
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+is start
+
+ align:start position:0%
+is start
+ 
+
+ align:start position:0%
+is start
+dumping at time tal
+
+ align:start position:0%
+dumping at time tal
+ 
+
+ align:start position:0%
+dumping at time tal
+0 at time tal
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+T how much radioactive waste is in the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+pile now what makes that problem
+
+ align:start position:0%
+pile now what makes that problem
+ 
+
+ align:start position:0%
+pile now what makes that problem
+slightly complicated is
+
+ align:start position:0%
+slightly complicated is
+ 
+
+ align:start position:0%
+slightly complicated is
+radioactive waste decays if I put some
+
+ align:start position:0%
+radioactive waste decays if I put some
+ 
+
+ align:start position:0%
+radioactive waste decays if I put some
+at at certain day and then go back
+
+ align:start position:0%
+at at certain day and then go back
+ 
+
+ align:start position:0%
+at at certain day and then go back
+several months later I don't and
+
+ align:start position:0%
+several months later I don't and
+ 
+
+ align:start position:0%
+several months later I don't and
+nothing's happened in between I don't
+
+ align:start position:0%
+nothing's happened in between I don't
+ 
+
+ align:start position:0%
+nothing's happened in between I don't
+have the same amount that I dumped
+
+ align:start position:0%
+have the same amount that I dumped
+ 
+
+ align:start position:0%
+have the same amount that I dumped
+because some of a fraction of it decayed
+
+ align:start position:0%
+because some of a fraction of it decayed
+ 
+
+ align:start position:0%
+because some of a fraction of it decayed
+I have less and our answer to the
+
+ align:start position:0%
+I have less and our answer to the
+ 
+
+ align:start position:0%
+I have less and our answer to the
+problem must take account of for each
+
+ align:start position:0%
+problem must take account of for each
+ 
+
+ align:start position:0%
+problem must take account of for each
+piece of waste how long it has been in
+
+ align:start position:0%
+piece of waste how long it has been in
+ 
+
+ align:start position:0%
+piece of waste how long it has been in
+the pile because that takes account of
+
+ align:start position:0%
+the pile because that takes account of
+ 
+
+ align:start position:0%
+the pile because that takes account of
+how long it had to Decay and what ends
+
+ align:start position:0%
+how long it had to Decay and what ends
+ 
+
+ align:start position:0%
+how long it had to Decay and what ends
+up what it ends up as so the
+
+ align:start position:0%
+up what it ends up as so the
+ 
+
+ align:start position:0%
+up what it ends up as so the
+calculation the essential part of the
+
+ align:start position:0%
+calculation the essential part of the
+ 
+
+ align:start position:0%
+calculation the essential part of the
+calculation will be that if you have an
+
+ align:start position:0%
+calculation will be that if you have an
+ 
+
+ align:start position:0%
+calculation will be that if you have an
+initial amount of this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+substance and it decays for a Time
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+T this is the amount left at time
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+t
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+you know this is a law of radioactive
+
+ align:start position:0%
+you know this is a law of radioactive
+ 
+
+ align:start position:0%
+you know this is a law of radioactive
+decay you knew that coming into 1803
+
+ align:start position:0%
+decay you knew that coming into 1803
+ 
+
+ align:start position:0%
+decay you knew that coming into 1803
+although it's of course a simple
+
+ align:start position:0%
+although it's of course a simple
+ 
+
+ align:start position:0%
+although it's of course a simple
+differential equation which produces it
+
+ align:start position:0%
+differential equation which produces it
+ 
+
+ align:start position:0%
+differential equation which produces it
+but I'll assume you simply know the
+
+ align:start position:0%
+but I'll assume you simply know the
+ 
+
+ align:start position:0%
+but I'll assume you simply know the
+answer K depends on the material so I'm
+
+ align:start position:0%
+answer K depends on the material so I'm
+ 
+
+ align:start position:0%
+answer K depends on the material so I'm
+going to assume that the uh nuclear
+
+ align:start position:0%
+going to assume that the uh nuclear
+ 
+
+ align:start position:0%
+going to assume that the uh nuclear
+plant dumps the same radioactive
+
+ align:start position:0%
+plant dumps the same radioactive
+ 
+
+ align:start position:0%
+plant dumps the same radioactive
+substance each time it's only one
+
+ align:start position:0%
+substance each time it's only one
+ 
+
+ align:start position:0%
+substance each time it's only one
+substance I'm calculating and K is it so
+
+ align:start position:0%
+substance I'm calculating and K is it so
+ 
+
+ align:start position:0%
+substance I'm calculating and K is it so
+assume the K is
+
+ align:start position:0%
+assume the K is
+ 
+
+ align:start position:0%
+assume the K is
+fixed I don't have to change from one K
+
+ align:start position:0%
+fixed I don't have to change from one K
+ 
+
+ align:start position:0%
+fixed I don't have to change from one K
+from one material to a k for another
+
+ align:start position:0%
+from one material to a k for another
+ 
+
+ align:start position:0%
+from one material to a k for another
+because it's mixing up the
+
+ align:start position:0%
+because it's mixing up the
+ 
+
+ align:start position:0%
+because it's mixing up the
+stuff just one material okay and now
+
+ align:start position:0%
+stuff just one material okay and now
+ 
+
+ align:start position:0%
+stuff just one material okay and now
+let's calculate it here's the idea I'll
+
+ align:start position:0%
+let's calculate it here's the idea I'll
+ 
+
+ align:start position:0%
+let's calculate it here's the idea I'll
+take the txis but now I'm going to
+
+ align:start position:0%
+take the txis but now I'm going to
+ 
+
+ align:start position:0%
+take the txis but now I'm going to
+change its name to the U axis you'll see
+
+ align:start position:0%
+change its name to the U axis you'll see
+ 
+
+ align:start position:0%
+change its name to the U axis you'll see
+why in just a second starts at
+
+ align:start position:0%
+why in just a second starts at
+ 
+
+ align:start position:0%
+why in just a second starts at
+zero I'm interested in what's happening
+
+ align:start position:0%
+zero I'm interested in what's happening
+ 
+
+ align:start position:0%
+zero I'm interested in what's happening
+at the time T how much is left at time T
+
+ align:start position:0%
+at the time T how much is left at time T
+ 
+
+ align:start position:0%
+at the time T how much is left at time T
+so I'm going to divide up the interval
+
+ align:start position:0%
+so I'm going to divide up the interval
+ 
+
+ align:start position:0%
+so I'm going to divide up the interval
+from 0 to T on this time axis to well
+
+ align:start position:0%
+from 0 to T on this time axis to well
+ 
+
+ align:start position:0%
+from 0 to T on this time axis to well
+here's u0o the starting point U1
+
+ align:start position:0%
+here's u0o the starting point U1
+ 
+
+ align:start position:0%
+here's u0o the starting point U1
+U2 uh let's make this U1
+
+ align:start position:0%
+U2 uh let's make this U1
+ 
+
+ align:start position:0%
+U2 uh let's make this U1
+U oh curses U
+
+ align:start position:0%
+U oh curses U
+ 
+
+ align:start position:0%
+U oh curses U
+Want U two u3 and so on let's call this
+
+ align:start position:0%
+Want U two u3 and so on let's call this
+ 
+
+ align:start position:0%
+Want U two u3 and so on let's call this
+uh
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+U plus it doesn't
+
+ align:start position:0%
+U plus it doesn't
+ 
+
+ align:start position:0%
+U plus it doesn't
+matter okay now the
+
+ align:start position:0%
+matter okay now the
+ 
+
+ align:start position:0%
+matter okay now the
+amount
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so what I'm going to do is look at the
+
+ align:start position:0%
+so what I'm going to do is look at the
+ 
+
+ align:start position:0%
+so what I'm going to do is look at the
+amount uh take a time interval from UI
+
+ align:start position:0%
+amount uh take a time interval from UI
+ 
+
+ align:start position:0%
+amount uh take a time interval from UI
+to UI + 1 this is a time interval delta
+
+ align:start position:0%
+to UI + 1 this is a time interval delta
+ 
+
+ align:start position:0%
+to UI + 1 this is a time interval delta
+T Delta
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+U divide it up into equal time
+
+ align:start position:0%
+U divide it up into equal time
+ 
+
+ align:start position:0%
+U divide it up into equal time
+intervals so the amount
+
+ align:start position:0%
+intervals so the amount
+ 
+
+ align:start position:0%
+intervals so the amount
+dumped in the time interval from UI to
+
+ align:start position:0%
+dumped in the time interval from UI to
+ 
+
+ align:start position:0%
+dumped in the time interval from UI to
+UI + 1 is equal to approximately F of UI
+
+ align:start position:0%
+UI + 1 is equal to approximately F of UI
+ 
+
+ align:start position:0%
+UI + 1 is equal to approximately F of UI
+the dump function there times Delta U we
+
+ align:start position:0%
+the dump function there times Delta U we
+ 
+
+ align:start position:0%
+the dump function there times Delta U we
+calculated that before that's what the
+
+ align:start position:0%
+calculated that before that's what the
+ 
+
+ align:start position:0%
+calculated that before that's what the
+meaning of The Dumping
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+rate by time T how much has it decayed
+
+ align:start position:0%
+rate by time T how much has it decayed
+ 
+
+ align:start position:0%
+rate by time T how much has it decayed
+to it has decayed how much is left in
+
+ align:start position:0%
+to it has decayed how much is left in
+ 
+
+ align:start position:0%
+to it has decayed how much is left in
+other
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+words well this is the starting
+
+ align:start position:0%
+words well this is the starting
+ 
+
+ align:start position:0%
+words well this is the starting
+amount so the answer is going to be it's
+
+ align:start position:0%
+amount so the answer is going to be it's
+ 
+
+ align:start position:0%
+amount so the answer is going to be it's
+F of U
+
+ align:start position:0%
+F of U
+ 
+
+ align:start position:0%
+F of U
+* Delta U
+
+ align:start position:0%
+* Delta U
+ 
+
+ align:start position:0%
+* Delta U
+times this factor which tells how how
+
+ align:start position:0%
+times this factor which tells how how
+ 
+
+ align:start position:0%
+times this factor which tells how how
+much it decay now so times so this is
+
+ align:start position:0%
+much it decay now so times so this is
+ 
+
+ align:start position:0%
+much it decay now so times so this is
+the starting amount at time
+
+ align:start position:0%
+the starting amount at time
+ 
+
+ align:start position:0%
+the starting amount at time
+UI that's what it was first dumped and
+
+ align:start position:0%
+UI that's what it was first dumped and
+ 
+
+ align:start position:0%
+UI that's what it was first dumped and
+this is the amount that was dumped time
+
+ align:start position:0%
+this is the amount that was dumped time
+ 
+
+ align:start position:0%
+this is the amount that was dumped time
+multiply that by e to the minus K times
+
+ align:start position:0%
+multiply that by e to the minus K times
+ 
+
+ align:start position:0%
+multiply that by e to the minus K times
+now what should I put up in there I have
+
+ align:start position:0%
+now what should I put up in there I have
+ 
+
+ align:start position:0%
+now what should I put up in there I have
+to put the length of time that it had to
+
+ align:start position:0%
+to put the length of time that it had to
+ 
+
+ align:start position:0%
+to put the length of time that it had to
+decay
+
+ align:start position:0%
+decay
+ 
+
+ align:start position:0%
+decay
+what is the length of time that it had
+
+ align:start position:0%
+what is the length of time that it had
+ 
+
+ align:start position:0%
+what is the length of time that it had
+to Decay it was dumped at UI I'm looking
+
+ align:start position:0%
+to Decay it was dumped at UI I'm looking
+ 
+
+ align:start position:0%
+to Decay it was dumped at UI I'm looking
+at time T it decayed
+
+ align:start position:0%
+at time T it decayed
+ 
+
+ align:start position:0%
+at time T it decayed
+for the time length T minus
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+UI the length of
+
+ align:start position:0%
+UI the length of
+ 
+
+ align:start position:0%
+UI the length of
+time it
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+had it on the pile
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so the stuff that was dumped in this
+
+ align:start position:0%
+so the stuff that was dumped in this
+ 
+
+ align:start position:0%
+so the stuff that was dumped in this
+time interval when I at time T when I
+
+ align:start position:0%
+time interval when I at time T when I
+ 
+
+ align:start position:0%
+time interval when I at time T when I
+come to look at it this is how much of
+
+ align:start position:0%
+come to look at it this is how much of
+ 
+
+ align:start position:0%
+come to look at it this is how much of
+it is left and now all I have to do is
+
+ align:start position:0%
+it is left and now all I have to do is
+ 
+
+ align:start position:0%
+it is left and now all I have to do is
+add up that that quantity for this time
+
+ align:start position:0%
+add up that that quantity for this time
+ 
+
+ align:start position:0%
+add up that that quantity for this time
+the stuff that was dumped in this time
+
+ align:start position:0%
+the stuff that was dumped in this time
+ 
+
+ align:start position:0%
+the stuff that was dumped in this time
+interval plus the stuff dumped then plus
+
+ align:start position:0%
+interval plus the stuff dumped then plus
+ 
+
+ align:start position:0%
+interval plus the stuff dumped then plus
+and so on all the way up to the stuff
+
+ align:start position:0%
+and so on all the way up to the stuff
+ 
+
+ align:start position:0%
+and so on all the way up to the stuff
+that was dumped yesterday and the answer
+
+ align:start position:0%
+that was dumped yesterday and the answer
+ 
+
+ align:start position:0%
+that was dumped yesterday and the answer
+will be
+
+ align:start position:0%
+will be
+ 
+
+ align:start position:0%
+will be
+therefore
+
+ align:start position:0%
+therefore
+ 
+
+ align:start position:0%
+therefore
+the answer will be the total
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+amount left at time
+
+ align:start position:0%
+amount left at time
+ 
+
+ align:start position:0%
+amount left at time
+T that is that is not yet
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+decayed will be approximately you add up
+
+ align:start position:0%
+decayed will be approximately you add up
+ 
+
+ align:start position:0%
+decayed will be approximately you add up
+the amount coming from the first time
+
+ align:start position:0%
+the amount coming from the first time
+ 
+
+ align:start position:0%
+the amount coming from the first time
+interval plus the amount coming and so
+
+ align:start position:0%
+interval plus the amount coming and so
+ 
+
+ align:start position:0%
+interval plus the amount coming and so
+on so it will be F of UI I'll save the
+
+ align:start position:0%
+on so it will be F of UI I'll save the
+ 
+
+ align:start position:0%
+on so it will be F of UI I'll save the
+Delta U for the n * eus K * tus UI Del
+
+ align:start position:0%
+Delta U for the n * eus K * tus UI Del
+ 
+
+ align:start position:0%
+Delta U for the n * eus K * tus UI Del
+Delta U so these two parts represent the
+
+ align:start position:0%
+Delta U so these two parts represent the
+ 
+
+ align:start position:0%
+Delta U so these two parts represent the
+amount dumped and this is the Decay
+
+ align:start position:0%
+amount dumped and this is the Decay
+ 
+
+ align:start position:0%
+amount dumped and this is the Decay
+factor and I add those up as I runs from
+
+ align:start position:0%
+factor and I add those up as I runs from
+ 
+
+ align:start position:0%
+factor and I add those up as I runs from
+well where did I start from one to then
+
+ align:start position:0%
+well where did I start from one to then
+ 
+
+ align:start position:0%
+well where did I start from one to then
+let's
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+say and now let delta T go to zero in
+
+ align:start position:0%
+say and now let delta T go to zero in
+ 
+
+ align:start position:0%
+say and now let delta T go to zero in
+other words make this more AC Delta U go
+
+ align:start position:0%
+other words make this more AC Delta U go
+ 
+
+ align:start position:0%
+other words make this more AC Delta U go
+to zero make this more accurate by
+
+ align:start position:0%
+to zero make this more accurate by
+ 
+
+ align:start position:0%
+to zero make this more accurate by
+taking finer and finer subdiv in other
+
+ align:start position:0%
+taking finer and finer subdiv in other
+ 
+
+ align:start position:0%
+taking finer and finer subdiv in other
+words instead of looking every month to
+
+ align:start position:0%
+words instead of looking every month to
+ 
+
+ align:start position:0%
+words instead of looking every month to
+see how much was dump let's look every
+
+ align:start position:0%
+see how much was dump let's look every
+ 
+
+ align:start position:0%
+see how much was dump let's look every
+week every day and so on to make this
+
+ align:start position:0%
+week every day and so on to make this
+ 
+
+ align:start position:0%
+week every day and so on to make this
+calculation more accurate and the answer
+
+ align:start position:0%
+calculation more accurate and the answer
+ 
+
+ align:start position:0%
+calculation more accurate and the answer
+is this
+
+ align:start position:0%
+is this
+ 
+
+ align:start position:0%
+is this
+approaches the exact amount which will
+
+ align:start position:0%
+approaches the exact amount which will
+ 
+
+ align:start position:0%
+approaches the exact amount which will
+be the integral this sum is a remon sum
+
+ align:start position:0%
+be the integral this sum is a remon sum
+ 
+
+ align:start position:0%
+be the integral this sum is a remon sum
+it approaches the integral from zero to
+
+ align:start position:0%
+it approaches the integral from zero to
+ 
+
+ align:start position:0%
+it approaches the integral from zero to
+well I'm adding it up from
+
+ align:start position:0%
+well I'm adding it up from
+ 
+
+ align:start position:0%
+well I'm adding it up from
+U 1al 0 to u n = t the final value so it
+
+ align:start position:0%
+U 1al 0 to u n = t the final value so it
+ 
+
+ align:start position:0%
+U 1al 0 to u n = t the final value so it
+will be the integral from the starting
+
+ align:start position:0%
+will be the integral from the starting
+ 
+
+ align:start position:0%
+will be the integral from the starting
+point to the ending point of f of U
+
+ align:start position:0%
+point to the ending point of f of U
+ 
+
+ align:start position:0%
+point to the ending point of f of U
+eus K * tus U
+
+ align:start position:0%
+eus K * tus U
+ 
+
+ align:start position:0%
+eus K * tus U
+du that's the answer to the problem it's
+
+ align:start position:0%
+du that's the answer to the problem it's
+ 
+
+ align:start position:0%
+du that's the answer to the problem it's
+given by this rather funny looking
+
+ align:start position:0%
+given by this rather funny looking
+ 
+
+ align:start position:0%
+given by this rather funny looking
+integral but from this point of view
+
+ align:start position:0%
+integral but from this point of view
+ 
+
+ align:start position:0%
+integral but from this point of view
+it's entirely natural It's a combination
+
+ align:start position:0%
+it's entirely natural It's a combination
+ 
+
+ align:start position:0%
+it's entirely natural It's a combination
+of The Dumping function this doesn't
+
+ align:start position:0%
+of The Dumping function this doesn't
+ 
+
+ align:start position:0%
+of The Dumping function this doesn't
+care what the material was it only wants
+
+ align:start position:0%
+care what the material was it only wants
+ 
+
+ align:start position:0%
+care what the material was it only wants
+to know how much was put on every day
+
+ align:start position:0%
+to know how much was put on every day
+ 
+
+ align:start position:0%
+to know how much was put on every day
+and this part which doesn't care how
+
+ align:start position:0%
+and this part which doesn't care how
+ 
+
+ align:start position:0%
+and this part which doesn't care how
+much was put on each day it just is an
+
+ align:start position:0%
+much was put on each day it just is an
+ 
+
+ align:start position:0%
+much was put on each day it just is an
+intrinsic constant of the materal
+
+ align:start position:0%
+intrinsic constant of the materal
+ 
+
+ align:start position:0%
+intrinsic constant of the materal
+material involving its Decay rate and
+
+ align:start position:0%
+material involving its Decay rate and
+ 
+
+ align:start position:0%
+material involving its Decay rate and
+this total thing represents the total
+
+ align:start position:0%
+this total thing represents the total
+ 
+
+ align:start position:0%
+this total thing represents the total
+amount and that is what is it it's the
+
+ align:start position:0%
+amount and that is what is it it's the
+ 
+
+ align:start position:0%
+amount and that is what is it it's the
+convolution of f of t with what
+
+ align:start position:0%
+convolution of f of t with what
+ 
+
+ align:start position:0%
+convolution of f of t with what
+function e to
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the minus
+
+ align:start position:0%
+the minus
+ 
+
+ align:start position:0%
+the minus
+KT it's the convolution of The Dumping
+
+ align:start position:0%
+KT it's the convolution of The Dumping
+ 
+
+ align:start position:0%
+KT it's the convolution of The Dumping
+function and the Decay function and the
+
+ align:start position:0%
+function and the Decay function and the
+ 
+
+ align:start position:0%
+function and the Decay function and the
+convolution is exactly the operation
+
+ align:start position:0%
+convolution is exactly the operation
+ 
+
+ align:start position:0%
+convolution is exactly the operation
+that you have to have to do that okay
+
+ align:start position:0%
+that you have to have to do that okay
+ 
+
+ align:start position:0%
+that you have to have to do that okay
+okay uh so I think this is the most
+
+ align:start position:0%
+okay uh so I think this is the most
+ 
+
+ align:start position:0%
+okay uh so I think this is the most
+intuitive approach physical approach to
+
+ align:start position:0%
+intuitive approach physical approach to
+ 
+
+ align:start position:0%
+intuitive approach physical approach to
+the meaning of this of the convolution
+
+ align:start position:0%
+the meaning of this of the convolution
+ 
+
+ align:start position:0%
+the meaning of this of the convolution
+in this particular you say well that's
+
+ align:start position:0%
+in this particular you say well that's
+ 
+
+ align:start position:0%
+in this particular you say well that's
+very special okay so it tells me what
+
+ align:start position:0%
+very special okay so it tells me what
+ 
+
+ align:start position:0%
+very special okay so it tells me what
+the meaning of a convolution with a an
+
+ align:start position:0%
+the meaning of a convolution with a an
+ 
+
+ align:start position:0%
+the meaning of a convolution with a an
+exponential is but what about the
+
+ align:start position:0%
+exponential is but what about the
+ 
+
+ align:start position:0%
+exponential is but what about the
+convolution with all the other functions
+
+ align:start position:0%
+convolution with all the other functions
+ 
+
+ align:start position:0%
+convolution with all the other functions
+we're going to have to use in this
+
+ align:start position:0%
+we're going to have to use in this
+ 
+
+ align:start position:0%
+we're going to have to use in this
+course they can all be interpreted just
+
+ align:start position:0%
+course they can all be interpreted just
+ 
+
+ align:start position:0%
+course they can all be interpreted just
+by being a little flexible in your
+
+ align:start position:0%
+by being a little flexible in your
+ 
+
+ align:start position:0%
+by being a little flexible in your
+approach I'll give you two examples of
+
+ align:start position:0%
+approach I'll give you two examples of
+ 
+
+ align:start position:0%
+approach I'll give you two examples of
+this well you'll three first of all uh I
+
+ align:start position:0%
+this well you'll three first of all uh I
+ 
+
+ align:start position:0%
+this well you'll three first of all uh I
+use it for a i in the problem set I
+
+ align:start position:0%
+use it for a i in the problem set I
+ 
+
+ align:start position:0%
+use it for a i in the problem set I
+asked you about a bank account uh that's
+
+ align:start position:0%
+asked you about a bank account uh that's
+ 
+
+ align:start position:0%
+asked you about a bank account uh that's
+not something any of you are interested
+
+ align:start position:0%
+not something any of you are interested
+ 
+
+ align:start position:0%
+not something any of you are interested
+in okay so how about uh suppose I said I
+
+ align:start position:0%
+in okay so how about uh suppose I said I
+ 
+
+ align:start position:0%
+in okay so how about uh suppose I said I
+dump
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+garbage undecayed
+
+ align:start position:0%
+garbage undecayed
+ 
+
+ align:start position:0%
+garbage undecayed
+undecaying so something that doesn't
+
+ align:start position:0%
+undecaying so something that doesn't
+ 
+
+ align:start position:0%
+undecaying so something that doesn't
+Decay at
+
+ align:start position:0%
+Decay at
+ 
+
+ align:start position:0%
+Decay at
+all what's the answer going to be well
+
+ align:start position:0%
+all what's the answer going to be well
+ 
+
+ align:start position:0%
+all what's the answer going to be well
+the calculation will be exactly the same
+
+ align:start position:0%
+the calculation will be exactly the same
+ 
+
+ align:start position:0%
+the calculation will be exactly the same
+there'll be it'll be the convolution of
+
+ align:start position:0%
+there'll be it'll be the convolution of
+ 
+
+ align:start position:0%
+there'll be it'll be the convolution of
+The Dumping function the only difference
+
+ align:start position:0%
+The Dumping function the only difference
+ 
+
+ align:start position:0%
+The Dumping function the only difference
+is that now the garbage isn't going to
+
+ align:start position:0%
+is that now the garbage isn't going to
+ 
+
+ align:start position:0%
+is that now the garbage isn't going to
+Decay so no matter how long it's left
+
+ align:start position:0%
+Decay so no matter how long it's left
+ 
+
+ align:start position:0%
+Decay so no matter how long it's left
+the same amount is going to be left at
+
+ align:start position:0%
+the same amount is going to be left at
+ 
+
+ align:start position:0%
+the same amount is going to be left at
+the end in other words I don't want the
+
+ align:start position:0%
+the end in other words I don't want the
+ 
+
+ align:start position:0%
+the end in other words I don't want the
+an exponential decay function I want the
+
+ align:start position:0%
+an exponential decay function I want the
+ 
+
+ align:start position:0%
+an exponential decay function I want the
+function one the constant function one
+
+ align:start position:0%
+function one the constant function one
+ 
+
+ align:start position:0%
+function one the constant function one
+because once I stick it on the pile
+
+ align:start position:0%
+because once I stick it on the pile
+ 
+
+ align:start position:0%
+because once I stick it on the pile
+nothing happens to it it just stays
+
+ align:start position:0%
+nothing happens to it it just stays
+ 
+
+ align:start position:0%
+nothing happens to it it just stays
+there so it's going to be the
+
+ align:start position:0%
+there so it's going to be the
+ 
+
+ align:start position:0%
+there so it's going to be the
+convolution of this one because this is
+
+ align:start position:0%
+convolution of this one because this is
+ 
+
+ align:start position:0%
+convolution of this one because this is
+constant it's undecayed
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this by The Identical reasoning and so
+
+ align:start position:0%
+this by The Identical reasoning and so
+ 
+
+ align:start position:0%
+this by The Identical reasoning and so
+what's the answer going to be it's going
+
+ align:start position:0%
+what's the answer going to be it's going
+ 
+
+ align:start position:0%
+what's the answer going to be it's going
+to be the integral from0 to T of f of U
+
+ align:start position:0%
+to be the integral from0 to T of f of U
+ 
+
+ align:start position:0%
+to be the integral from0 to T of f of U
+du now that's an 1801 problem if I dump
+
+ align:start position:0%
+du now that's an 1801 problem if I dump
+ 
+
+ align:start position:0%
+du now that's an 1801 problem if I dump
+with a dumping rate F of U and I dump
+
+ align:start position:0%
+with a dumping rate F of U and I dump
+ 
+
+ align:start position:0%
+with a dumping rate F of U and I dump
+from Time Zero to time T how much to is
+
+ align:start position:0%
+from Time Zero to time T how much to is
+ 
+
+ align:start position:0%
+from Time Zero to time T how much to is
+on the pile they don't give it they
+
+ align:start position:0%
+on the pile they don't give it they
+ 
+
+ align:start position:0%
+on the pile they don't give it they
+always give velocity problems and
+
+ align:start position:0%
+always give velocity problems and
+ 
+
+ align:start position:0%
+always give velocity problems and
+problems of how to slice up red lows and
+
+ align:start position:0%
+problems of how to slice up red lows and
+ 
+
+ align:start position:0%
+problems of how to slice up red lows and
+stuff like that but but this is a real
+
+ align:start position:0%
+stuff like that but but this is a real
+ 
+
+ align:start position:0%
+stuff like that but but this is a real
+life problem if that's the dumping rate
+
+ align:start position:0%
+life problem if that's the dumping rate
+ 
+
+ align:start position:0%
+life problem if that's the dumping rate
+and you dump for T days from zero to
+
+ align:start position:0%
+and you dump for T days from zero to
+ 
+
+ align:start position:0%
+and you dump for T days from zero to
+time0 time T how much you have left at
+
+ align:start position:0%
+time0 time T how much you have left at
+ 
+
+ align:start position:0%
+time0 time T how much you have left at
+the end answer the integral of f of U du
+
+ align:start position:0%
+the end answer the integral of f of U du
+ 
+
+ align:start position:0%
+the end answer the integral of f of U du
+from 0 to
+
+ align:start position:0%
+from 0 to
+ 
+
+ align:start position:0%
+from 0 to
+T I'll give you another example suppose
+
+ align:start position:0%
+T I'll give you another example suppose
+ 
+
+ align:start position:0%
+T I'll give you another example suppose
+I wanted a dumping suppose I wanted a
+
+ align:start position:0%
+I wanted a dumping suppose I wanted a
+ 
+
+ align:start position:0%
+I wanted a dumping suppose I wanted a
+function uh wanted to interpret
+
+ align:start position:0%
+function uh wanted to interpret
+ 
+
+ align:start position:0%
+function uh wanted to interpret
+something uh which grows like T for
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+instance or I want is a physical
+
+ align:start position:0%
+instance or I want is a physical
+ 
+
+ align:start position:0%
+instance or I want is a physical
+interpretation well I have to think of
+
+ align:start position:0%
+interpretation well I have to think of
+ 
+
+ align:start position:0%
+interpretation well I have to think of
+I'm making a pile of something you know
+
+ align:start position:0%
+I'm making a pile of something you know
+ 
+
+ align:start position:0%
+I'm making a pile of something you know
+a metaphorical pile we don't actually
+
+ align:start position:0%
+a metaphorical pile we don't actually
+ 
+
+ align:start position:0%
+a metaphorical pile we don't actually
+have to make a physical pile uh and the
+
+ align:start position:0%
+have to make a physical pile uh and the
+ 
+
+ align:start position:0%
+have to make a physical pile uh and the
+things should be growing like tea well
+
+ align:start position:0%
+things should be growing like tea well
+ 
+
+ align:start position:0%
+things should be growing like tea well
+what grows like tea uh not bacteria they
+
+ align:start position:0%
+what grows like tea uh not bacteria they
+ 
+
+ align:start position:0%
+what grows like tea uh not bacteria they
+grow exponentially let's I was before
+
+ align:start position:0%
+grow exponentially let's I was before
+ 
+
+ align:start position:0%
+grow exponentially let's I was before
+the electure I was trying to think
+
+ align:start position:0%
+the electure I was trying to think
+ 
+
+ align:start position:0%
+the electure I was trying to think
+something so I came up with chickens I'm
+
+ align:start position:0%
+something so I came up with chickens I'm
+ 
+
+ align:start position:0%
+something so I came up with chickens I'm
+sure on a chicken farm little baby
+
+ align:start position:0%
+sure on a chicken farm little baby
+ 
+
+ align:start position:0%
+sure on a chicken farm little baby
+chickens grow linearly all little animal
+
+ align:start position:0%
+chickens grow linearly all little animal
+ 
+
+ align:start position:0%
+chickens grow linearly all little animal
+all little animals anyway I've observed
+
+ align:start position:0%
+all little animals anyway I've observed
+ 
+
+ align:start position:0%
+all little animals anyway I've observed
+that babies grow linearly at at least
+
+ align:start position:0%
+that babies grow linearly at at least
+ 
+
+ align:start position:0%
+that babies grow linearly at at least
+for a while thank God after a while they
+
+ align:start position:0%
+for a while thank God after a while they
+ 
+
+ align:start position:0%
+for a while thank God after a while they
+tap her off but uh but but in the
+
+ align:start position:0%
+tap her off but uh but but in the
+ 
+
+ align:start position:0%
+tap her off but uh but but in the
+beginning you know they eat every four
+
+ align:start position:0%
+beginning you know they eat every four
+ 
+
+ align:start position:0%
+beginning you know they eat every four
+hours or whatever and they eat the same
+
+ align:start position:0%
+hours or whatever and they eat the same
+ 
+
+ align:start position:0%
+hours or whatever and they eat the same
+amount pretty much and that adds up uh
+
+ align:start position:0%
+amount pretty much and that adds up uh
+ 
+
+ align:start position:0%
+amount pretty much and that adds up uh
+so it's uh so let's suppose this
+
+ align:start position:0%
+so it's uh so let's suppose this
+ 
+
+ align:start position:0%
+so it's uh so let's suppose this
+represents the growth lyar growth of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+chickens of baby chicks baby chick that
+
+ align:start position:0%
+chickens of baby chicks baby chick that
+ 
+
+ align:start position:0%
+chickens of baby chicks baby chick that
+makes them sound
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+cuter less offensive okay so a farmer a
+
+ align:start position:0%
+cuter less offensive okay so a farmer a
+ 
+
+ align:start position:0%
+cuter less offensive okay so a farmer a
+chicken farmer or whatever they call
+
+ align:start position:0%
+chicken farmer or whatever they call
+ 
+
+ align:start position:0%
+chicken farmer or whatever they call
+them uh is starting a new brood so
+
+ align:start position:0%
+them uh is starting a new brood so
+ 
+
+ align:start position:0%
+them uh is starting a new brood so
+anyway the hens lay at a certain rate
+
+ align:start position:0%
+anyway the hens lay at a certain rate
+ 
+
+ align:start position:0%
+anyway the hens lay at a certain rate
+and each of those are incubated and
+
+ align:start position:0%
+and each of those are incubated and
+ 
+
+ align:start position:0%
+and each of those are incubated and
+after all a couple months they turn into
+
+ align:start position:0%
+after all a couple months they turn into
+ 
+
+ align:start position:0%
+after all a couple months they turn into
+a little baby chicks come out uh so this
+
+ align:start position:0%
+a little baby chicks come out uh so this
+ 
+
+ align:start position:0%
+a little baby chicks come out uh so this
+will be the rate the production rate for
+
+ align:start position:0%
+will be the rate the production rate for
+ 
+
+ align:start position:0%
+will be the rate the production rate for
+new
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+chickens okay and it will be the
+
+ align:start position:0%
+chickens okay and it will be the
+ 
+
+ align:start position:0%
+chickens okay and it will be the
+convolution which will be tell you at
+
+ align:start position:0%
+convolution which will be tell you at
+ 
+
+ align:start position:0%
+convolution which will be tell you at
+time t uh the number of kilograms we
+
+ align:start position:0%
+time t uh the number of kilograms we
+ 
+
+ align:start position:0%
+time t uh the number of kilograms we
+better do this in kilograms I'm afraid
+
+ align:start position:0%
+better do this in kilograms I'm afraid
+ 
+
+ align:start position:0%
+better do this in kilograms I'm afraid
+uh now that's not as heartless as it
+
+ align:start position:0%
+uh now that's not as heartless as it
+ 
+
+ align:start position:0%
+uh now that's not as heartless as it
+seems uh the number of kilograms of
+
+ align:start position:0%
+seems uh the number of kilograms of
+ 
+
+ align:start position:0%
+seems uh the number of kilograms of
+chickens time
+
+ align:start position:0%
+chickens time
+ 
+
+ align:start position:0%
+chickens time
+te it really isn't heartless because
+
+ align:start position:0%
+te it really isn't heartless because
+ 
+
+ align:start position:0%
+te it really isn't heartless because
+after all why does a why would the
+
+ align:start position:0%
+after all why does a why would the
+ 
+
+ align:start position:0%
+after all why does a why would the
+farmer want to know that well because a
+
+ align:start position:0%
+farmer want to know that well because a
+ 
+
+ align:start position:0%
+farmer want to know that well because a
+certain number of pounds of chicken eat
+
+ align:start position:0%
+certain number of pounds of chicken eat
+ 
+
+ align:start position:0%
+certain number of pounds of chicken eat
+a certain number of pounds of chicken
+
+ align:start position:0%
+a certain number of pounds of chicken
+ 
+
+ align:start position:0%
+a certain number of pounds of chicken
+feed and that's how much he has to dump
+
+ align:start position:0%
+feed and that's how much he has to dump
+ 
+
+ align:start position:0%
+feed and that's how much he has to dump
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+bus have to give them every day that's
+
+ align:start position:0%
+bus have to give them every day that's
+ 
+
+ align:start position:0%
+bus have to give them every day that's
+how he calculates his expenses so he
+
+ align:start position:0%
+how he calculates his expenses so he
+ 
+
+ align:start position:0%
+how he calculates his expenses so he
+will have to know what the convolution
+
+ align:start position:0%
+will have to know what the convolution
+ 
+
+ align:start position:0%
+will have to know what the convolution
+is or better yet he will hire you who
+
+ align:start position:0%
+is or better yet he will hire you who
+ 
+
+ align:start position:0%
+is or better yet he will hire you who
+knows what the convolution is and you'll
+
+ align:start position:0%
+knows what the convolution is and you'll
+ 
+
+ align:start position:0%
+knows what the convolution is and you'll
+be able to tell him okay why don't we
+
+ align:start position:0%
+be able to tell him okay why don't we
+ 
+
+ align:start position:0%
+be able to tell him okay why don't we
+stop there and uh uh go to recitation
+
+ align:start position:0%
+stop there and uh uh go to recitation
+ 
+
+ align:start position:0%
+stop there and uh uh go to recitation
+tomorrow because they'll be doing
+
+ align:start position:0%
+tomorrow because they'll be doing
+ 
+
+ align:start position:0%
+tomorrow because they'll be doing
+important
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+things
\ No newline at end of file
diff --git a/3mu47FWEuqA.txt b/3mu47FWEuqA.txt
new file mode 100644
index 0000000000000000000000000000000000000000..6702b714936ba10250d65081196d6fc99d83edc1
--- /dev/null
+++ b/3mu47FWEuqA.txt
@@ -0,0 +1,330 @@
+In this exercise, we'll be
+looking at a problem, also
+
+know as the coupons collector's
+problem.
+
+We have a set of K coupons,
+or grades in our case.
+
+And each time slot
+we're revealed
+
+with one random grade.
+
+And we'd like to know how long
+it would take for us to
+
+collect all K grades.
+
+In our case, K is equal to 6.
+
+Now the key to solving
+the problem
+
+is essentially twofolds.
+
+First, we'll have to find a way
+to intelligently define
+
+sequence random variables that
+captured, essentially,
+
+stopping time of this process.
+
+And then we'll employ the idea
+of linearity of expectations
+
+in breaking down this value
+in simpler terms.
+
+So let's get started.
+
+We'll define Yi as the number
+of papers till we see
+
+the i-th new grade.
+
+ 
+
+What does that mean?
+
+Well, let's take a look
+at an example.
+
+Suppose, here we have a timeline
+from no paper yet,
+
+first paper, second paper,
+third paper,
+
+so on, and so forth.
+
+Now, if we got grade A on the
+first slot, grade A minus on
+
+second slot, A again on the
+third slot, let's say there's
+
+a fourth's slot, we got B.
+
+According to this process, we
+see that Y1 is always 1,
+
+because whatever we got
+on the first slot
+
+will be a new grade.
+
+Now, Y2 is 2, because
+the second paper is,
+
+again, a new grade.
+
+On the third paper we got a
+grade, which is the same as
+
+the first grade.
+
+So that would not
+count as any Yi.
+
+And the third time we saw new
+grade would now be paper four.
+
+According to this notation,
+we're interested in knowing
+
+what is the expected value of E
+of Y6, which is the time it
+
+takes to receive
+all six grades.
+
+So so far this notation isn't
+really helping us in solving
+
+the problem, but kind of just
+staying a different way.
+
+It turns out, it's much easier
+to look at the following
+
+variable derived from the Yis.
+
+We'll define Xi as the
+difference between Yi
+
+plus 1 minus Yi.
+
+And in [? words, ?] it says, Xi
+is a number of papers you
+
+need until you see the i plus
+1-th new grade, after you have
+
+received i new grade so far.
+
+So in this case, X1 will be if
+we call 0, Y0, will be the
+
+difference between Y1 and
+Y0, which is always 1--
+
+that's X1.
+
+And the difference between
+these two will be X2.
+
+And the difference between
+Y3 and Y2--
+
+Sorry.
+
+It should be Y X0,
+1, 2, and so on.
+
+OK?
+
+Through this notation we see
+that Y6 now can be written as
+
+the summation of i equal
+to 0, 2, 5, X, i.
+
+So all I did was to break down
+i6 into a sequence of
+
+summation of the differences,
+like Y. 6 Minus Y5, Y5 minus
+
+Y4, and so on.
+
+It turns out, this expression
+will be very useful.
+
+OK.
+
+So now that we have the two
+variables Y and X, let's see
+
+if it will be easier to look
+at the distribution of X in
+
+studying this process.
+
+Let's say, we have seen
+a new grade so far--
+
+one.
+
+How many trials would it
+take for us to see
+
+the second new grade?
+
+It turns out it's
+not that hard.
+
+In this case, we know there is
+a total of six grades, and we
+
+have seen one of them.
+
+So that leaves us five
+more grades that
+
+we'll potentially see.
+
+And therefore, on any random
+trial after that, there is a
+
+probability of 5 over 6 that
+we'll see a new grade.
+
+And hence, we know that X1 has
+a distribution geometric with
+
+a success probability,
+or a parameter, 5/6.
+
+Now, more generally, if we
+extend this idea further, we
+
+see that Xi will have a
+geometric distribution of
+
+parameter 6 minus i over 6.
+
+And this is due to the fact that
+so far we have already
+
+seen i new grades.
+
+And that will be the success
+probability of seeing a
+
+further new grade.
+
+So from this expression, we know
+that the expected value
+
+of Xi will simply be the inverse
+of the parameter of
+
+the geometric distribution,
+which is 6 over 6 minus i or 6
+
+times 1 over 6 minus i.
+
+ 
+
+And now we're ready to compute
+a final answer.
+
+So from this expression we know
+expected value of Y6 is
+
+equal to the expected value of
+sum of i equal to 0 to 5 Xi.
+
+ 
+
+And by the linearity of
+expectation, we can pull out
+
+the sum and write it as 2,
+5 expected value of Xi.
+
+Now, since we know that
+expective of Xi is the
+
+following expression.
+
+We see that this term is equal
+to 6 times expected value of i
+
+equals 0, 5, 1 over 6 minus i.
+
+Or written in the other way
+this is equal to 6 times i
+
+equal to 0, 2, 5.
+
+In fact, 1, 2, 5, 1 over i.
+
+And all I did here was to,
+essentially, change the
+
+variable, so that these two
+summations contained exactly
+
+the same terms.
+
+And this will give us the
+answer, which is 14.7.
+
+Now, more generally, we can
+see that there's nothing
+
+special about number 6 here.
+
+We could have substituted 6 with
+a number, let's say, K.
+
+And then we'll get E of YK,
+let's say, there's more than
+
+six labels.
+
+And this will give us K times
+summation i equal to 1, so K
+
+minus 1, 1 over i.
+
+Interestingly, it turns out
+this quantity has an
+
+[? asymptotic ?]
+
+expression that, essentially,
+is roughly equal to K times
+
+the natural logarithm of K.
+And this is known as the
+
+scaling [? la ?]
+
+for the coupon collector's
+problem that says,
+
+essentially, takes about
+K times [? la ?]
+
+K many trials until we collect
+all K coupons.
+
+And that'll be the end
+of the problem.
+
+See you next time.
\ No newline at end of file
diff --git a/45X0puB3YK0.txt b/45X0puB3YK0.txt
new file mode 100644
index 0000000000000000000000000000000000000000..4bfb5daa81c5f70ef5379dd645758c14719c1589
--- /dev/null
+++ b/45X0puB3YK0.txt
@@ -0,0 +1,1187 @@
+align:start position:0%
+ 
+the following content is provided under
+
+ align:start position:0%
+the following content is provided under
+ 
+
+ align:start position:0%
+the following content is provided under
+a Creative Commons license your support
+
+ align:start position:0%
+a Creative Commons license your support
+ 
+
+ align:start position:0%
+a Creative Commons license your support
+will help MIT open courseware continue
+
+ align:start position:0%
+will help MIT open courseware continue
+ 
+
+ align:start position:0%
+will help MIT open courseware continue
+to offer highquality educational
+
+ align:start position:0%
+to offer highquality educational
+ 
+
+ align:start position:0%
+to offer highquality educational
+resources for free to make a donation or
+
+ align:start position:0%
+resources for free to make a donation or
+ 
+
+ align:start position:0%
+resources for free to make a donation or
+view additional materials from hundreds
+
+ align:start position:0%
+view additional materials from hundreds
+ 
+
+ align:start position:0%
+view additional materials from hundreds
+of MIT courses visit mitop coreware at
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+ocw.mit.edu in this demonstration we're
+
+ align:start position:0%
+ocw.mit.edu in this demonstration we're
+ 
+
+ align:start position:0%
+ocw.mit.edu in this demonstration we're
+going to illustrate the propagation of
+
+ align:start position:0%
+going to illustrate the propagation of
+ 
+
+ align:start position:0%
+going to illustrate the propagation of
+light in a fiber a glass fiber as we
+
+ align:start position:0%
+light in a fiber a glass fiber as we
+ 
+
+ align:start position:0%
+light in a fiber a glass fiber as we
+know today
+
+ align:start position:0%
+know today
+ 
+
+ align:start position:0%
+know today
+Optical fibers have a lot of low loss
+
+ align:start position:0%
+Optical fibers have a lot of low loss
+ 
+
+ align:start position:0%
+Optical fibers have a lot of low loss
+very low loss of the order of one or two
+
+ align:start position:0%
+very low loss of the order of one or two
+ 
+
+ align:start position:0%
+very low loss of the order of one or two
+DBS per kilometer and of course they're
+
+ align:start position:0%
+DBS per kilometer and of course they're
+ 
+
+ align:start position:0%
+DBS per kilometer and of course they're
+being used for communication as well as
+
+ align:start position:0%
+being used for communication as well as
+ 
+
+ align:start position:0%
+being used for communication as well as
+other applications like
+
+ align:start position:0%
+other applications like
+ 
+
+ align:start position:0%
+other applications like
+sensors so the setup we have is a uh is
+
+ align:start position:0%
+sensors so the setup we have is a uh is
+ 
+
+ align:start position:0%
+sensors so the setup we have is a uh is
+a laser a helium neon laser over here
+
+ align:start position:0%
+a laser a helium neon laser over here
+ 
+
+ align:start position:0%
+a laser a helium neon laser over here
+here's the output from from the laser
+
+ align:start position:0%
+here's the output from from the laser
+ 
+
+ align:start position:0%
+here's the output from from the laser
+we're going to reflect it by this mirror
+
+ align:start position:0%
+we're going to reflect it by this mirror
+ 
+
+ align:start position:0%
+we're going to reflect it by this mirror
+and this
+
+ align:start position:0%
+and this
+ 
+
+ align:start position:0%
+and this
+mirror and then pass it through a lens
+
+ align:start position:0%
+mirror and then pass it through a lens
+ 
+
+ align:start position:0%
+mirror and then pass it through a lens
+this lens over here focuses the light
+
+ align:start position:0%
+this lens over here focuses the light
+ 
+
+ align:start position:0%
+this lens over here focuses the light
+into the fiber end and if we can take a
+
+ align:start position:0%
+into the fiber end and if we can take a
+ 
+
+ align:start position:0%
+into the fiber end and if we can take a
+closeup of what's going on over here
+
+ align:start position:0%
+closeup of what's going on over here
+ 
+
+ align:start position:0%
+closeup of what's going on over here
+what you would see is then a lens this
+
+ align:start position:0%
+what you would see is then a lens this
+ 
+
+ align:start position:0%
+what you would see is then a lens this
+lens then focusing the light and fiber
+
+ align:start position:0%
+lens then focusing the light and fiber
+ 
+
+ align:start position:0%
+lens then focusing the light and fiber
+and the fiber is very close to the
+
+ align:start position:0%
+and the fiber is very close to the
+ 
+
+ align:start position:0%
+and the fiber is very close to the
+lens and then the rest of the fiber is
+
+ align:start position:0%
+lens and then the rest of the fiber is
+ 
+
+ align:start position:0%
+lens and then the rest of the fiber is
+here all right so here is the the rest
+
+ align:start position:0%
+here all right so here is the the rest
+ 
+
+ align:start position:0%
+here all right so here is the the rest
+of the fiber now this fiber uh in fact
+
+ align:start position:0%
+of the fiber now this fiber uh in fact
+ 
+
+ align:start position:0%
+of the fiber now this fiber uh in fact
+what you're seeing over here is the uh
+
+ align:start position:0%
+what you're seeing over here is the uh
+ 
+
+ align:start position:0%
+what you're seeing over here is the uh
+essentially the the plastic jacket the
+
+ align:start position:0%
+essentially the the plastic jacket the
+ 
+
+ align:start position:0%
+essentially the the plastic jacket the
+fiber
+
+ align:start position:0%
+fiber
+ 
+
+ align:start position:0%
+fiber
+core is about four microns in in
+
+ align:start position:0%
+core is about four microns in in
+ 
+
+ align:start position:0%
+core is about four microns in in
+diameter and the cladding is 125 microns
+
+ align:start position:0%
+diameter and the cladding is 125 microns
+ 
+
+ align:start position:0%
+diameter and the cladding is 125 microns
+and the rest that you see here is the is
+
+ align:start position:0%
+and the rest that you see here is the is
+ 
+
+ align:start position:0%
+and the rest that you see here is the is
+the plastic jacket that's why it looks
+
+ align:start position:0%
+the plastic jacket that's why it looks
+ 
+
+ align:start position:0%
+the plastic jacket that's why it looks
+so so visible because it's so thick the
+
+ align:start position:0%
+so so visible because it's so thick the
+ 
+
+ align:start position:0%
+so so visible because it's so thick the
+other end of the fiber then uh goes into
+
+ align:start position:0%
+other end of the fiber then uh goes into
+ 
+
+ align:start position:0%
+other end of the fiber then uh goes into
+this
+
+ align:start position:0%
+this
+ 
+
+ align:start position:0%
+this
+holder and the in a Chuck here it's in a
+
+ align:start position:0%
+holder and the in a Chuck here it's in a
+ 
+
+ align:start position:0%
+holder and the in a Chuck here it's in a
+hole fiber hold in a Chuck and the
+
+ align:start position:0%
+hole fiber hold in a Chuck and the
+ 
+
+ align:start position:0%
+hole fiber hold in a Chuck and the
+output of the
+
+ align:start position:0%
+output of the
+ 
+
+ align:start position:0%
+output of the
+of the fiber then is over here onto this
+
+ align:start position:0%
+of the fiber then is over here onto this
+ 
+
+ align:start position:0%
+of the fiber then is over here onto this
+uh onto this little
+
+ align:start position:0%
+uh onto this little
+ 
+
+ align:start position:0%
+uh onto this little
+screen now if if we can maybe we can
+
+ align:start position:0%
+screen now if if we can maybe we can
+ 
+
+ align:start position:0%
+screen now if if we can maybe we can
+take a close look at the at the fiber
+
+ align:start position:0%
+take a close look at the at the fiber
+ 
+
+ align:start position:0%
+take a close look at the at the fiber
+end
+
+ align:start position:0%
+end
+ 
+
+ align:start position:0%
+end
+here what which
+
+ align:start position:0%
+here what which
+ 
+
+ align:start position:0%
+here what which
+shows that uh what you see over here uh
+
+ align:start position:0%
+shows that uh what you see over here uh
+ 
+
+ align:start position:0%
+shows that uh what you see over here uh
+in fact let me point to it what you see
+
+ align:start position:0%
+in fact let me point to it what you see
+ 
+
+ align:start position:0%
+in fact let me point to it what you see
+over here is the the cladding
+
+ align:start position:0%
+over here is the the cladding
+ 
+
+ align:start position:0%
+over here is the the cladding
+essentially we've stripped the jacket
+
+ align:start position:0%
+essentially we've stripped the jacket
+ 
+
+ align:start position:0%
+essentially we've stripped the jacket
+and what you see here is just the
+
+ align:start position:0%
+and what you see here is just the
+ 
+
+ align:start position:0%
+and what you see here is just the
+clading and this is the 125 microns
+
+ align:start position:0%
+clading and this is the 125 microns
+ 
+
+ align:start position:0%
+clading and this is the 125 microns
+while over here over
+
+ align:start position:0%
+while over here over
+ 
+
+ align:start position:0%
+while over here over
+here is the is the the fiber with the
+
+ align:start position:0%
+here is the is the the fiber with the
+ 
+
+ align:start position:0%
+here is the is the the fiber with the
+plastic with the plastic jacket so when
+
+ align:start position:0%
+plastic with the plastic jacket so when
+ 
+
+ align:start position:0%
+plastic with the plastic jacket so when
+you remove the plastic jacket then you
+
+ align:start position:0%
+you remove the plastic jacket then you
+ 
+
+ align:start position:0%
+you remove the plastic jacket then you
+have essentially what you're seeing is
+
+ align:start position:0%
+have essentially what you're seeing is
+ 
+
+ align:start position:0%
+have essentially what you're seeing is
+the is just the 125 Micron clading all
+
+ align:start position:0%
+the is just the 125 Micron clading all
+ 
+
+ align:start position:0%
+the is just the 125 Micron clading all
+right so this is then uh the fiber and
+
+ align:start position:0%
+right so this is then uh the fiber and
+ 
+
+ align:start position:0%
+right so this is then uh the fiber and
+there's the output of the of the fiber
+
+ align:start position:0%
+there's the output of the of the fiber
+ 
+
+ align:start position:0%
+there's the output of the of the fiber
+now what we see if we can then enhance
+
+ align:start position:0%
+now what we see if we can then enhance
+ 
+
+ align:start position:0%
+now what we see if we can then enhance
+this and bring it bring it in what we
+
+ align:start position:0%
+this and bring it bring it in what we
+ 
+
+ align:start position:0%
+this and bring it bring it in what we
+see is the uh uh is the single mode uh
+
+ align:start position:0%
+see is the uh uh is the single mode uh
+ 
+
+ align:start position:0%
+see is the uh uh is the single mode uh
+behavior of of a
+
+ align:start position:0%
+behavior of of a
+ 
+
+ align:start position:0%
+behavior of of a
+fiber it looks like almost like a gan
+
+ align:start position:0%
+fiber it looks like almost like a gan
+ 
+
+ align:start position:0%
+fiber it looks like almost like a gan
+kind of uh
+
+ align:start position:0%
+kind of uh
+ 
+
+ align:start position:0%
+kind of uh
+spot not quite gaussian but it looks
+
+ align:start position:0%
+spot not quite gaussian but it looks
+ 
+
+ align:start position:0%
+spot not quite gaussian but it looks
+like a gaussian kind of spot now what
+
+ align:start position:0%
+like a gaussian kind of spot now what
+ 
+
+ align:start position:0%
+like a gaussian kind of spot now what
+I'm doing
+
+ align:start position:0%
+I'm doing
+ 
+
+ align:start position:0%
+I'm doing
+now uh is just it just adjusting the the
+
+ align:start position:0%
+now uh is just it just adjusting the the
+ 
+
+ align:start position:0%
+now uh is just it just adjusting the the
+uh coupling into into the fiber and it's
+
+ align:start position:0%
+uh coupling into into the fiber and it's
+ 
+
+ align:start position:0%
+uh coupling into into the fiber and it's
+very touchy because as I said the core
+
+ align:start position:0%
+very touchy because as I said the core
+ 
+
+ align:start position:0%
+very touchy because as I said the core
+is only about four four
+
+ align:start position:0%
+is only about four four
+ 
+
+ align:start position:0%
+is only about four four
+microns all right so this is what then a
+
+ align:start position:0%
+microns all right so this is what then a
+ 
+
+ align:start position:0%
+microns all right so this is what then a
+single mode uh uh fiber the output from
+
+ align:start position:0%
+single mode uh uh fiber the output from
+ 
+
+ align:start position:0%
+single mode uh uh fiber the output from
+a single mode fiber looks like and if as
+
+ align:start position:0%
+a single mode fiber looks like and if as
+ 
+
+ align:start position:0%
+a single mode fiber looks like and if as
+I miss a line here doesn't make any
+
+ align:start position:0%
+I miss a line here doesn't make any
+ 
+
+ align:start position:0%
+I miss a line here doesn't make any
+difference all you get is just a loss in
+
+ align:start position:0%
+difference all you get is just a loss in
+ 
+
+ align:start position:0%
+difference all you get is just a loss in
+intensity the shape of the mode stays
+
+ align:start position:0%
+intensity the shape of the mode stays
+ 
+
+ align:start position:0%
+intensity the shape of the mode stays
+stays the same so remember the core is
+
+ align:start position:0%
+stays the same so remember the core is
+ 
+
+ align:start position:0%
+stays the same so remember the core is
+four microns cladding is 125 the
+
+ align:start position:0%
+four microns cladding is 125 the
+ 
+
+ align:start position:0%
+four microns cladding is 125 the
+wavelength of the light is 6328 anons
+
+ align:start position:0%
+wavelength of the light is 6328 anons
+ 
+
+ align:start position:0%
+wavelength of the light is 6328 anons
+and the core to index uh difference is
+
+ align:start position:0%
+and the core to index uh difference is
+ 
+
+ align:start position:0%
+and the core to index uh difference is
+about one part in in 10 to the 3 so this
+
+ align:start position:0%
+about one part in in 10 to the 3 so this
+ 
+
+ align:start position:0%
+about one part in in 10 to the 3 so this
+way you can show that indeed you get uh
+
+ align:start position:0%
+way you can show that indeed you get uh
+ 
+
+ align:start position:0%
+way you can show that indeed you get uh
+single mode
+
+ align:start position:0%
+single mode
+ 
+
+ align:start position:0%
+single mode
+propagation now I would like to
+
+ align:start position:0%
+propagation now I would like to
+ 
+
+ align:start position:0%
+propagation now I would like to
+illustrate some interesting phenomena
+
+ align:start position:0%
+illustrate some interesting phenomena
+ 
+
+ align:start position:0%
+illustrate some interesting phenomena
+about fibers so if we get the camera to
+
+ align:start position:0%
+about fibers so if we get the camera to
+ 
+
+ align:start position:0%
+about fibers so if we get the camera to
+look over
+
+ align:start position:0%
+look over
+ 
+
+ align:start position:0%
+look over
+here I want to illustrate how touchy uh
+
+ align:start position:0%
+here I want to illustrate how touchy uh
+ 
+
+ align:start position:0%
+here I want to illustrate how touchy uh
+is the propagation of light in a in a
+
+ align:start position:0%
+is the propagation of light in a in a
+ 
+
+ align:start position:0%
+is the propagation of light in a in a
+single mode fiber now here is here's a
+
+ align:start position:0%
+single mode fiber now here is here's a
+ 
+
+ align:start position:0%
+single mode fiber now here is here's a
+piece of fiber and you can see that
+
+ align:start position:0%
+piece of fiber and you can see that
+ 
+
+ align:start position:0%
+piece of fiber and you can see that
+there's no light scattered from the
+
+ align:start position:0%
+there's no light scattered from the
+ 
+
+ align:start position:0%
+there's no light scattered from the
+fiber now all I have to do is bend the
+
+ align:start position:0%
+fiber now all I have to do is bend the
+ 
+
+ align:start position:0%
+fiber now all I have to do is bend the
+fiber bend the F and you're beginning to
+
+ align:start position:0%
+fiber bend the F and you're beginning to
+ 
+
+ align:start position:0%
+fiber bend the F and you're beginning to
+see light that gets gets transmitted out
+
+ align:start position:0%
+see light that gets gets transmitted out
+ 
+
+ align:start position:0%
+see light that gets gets transmitted out
+of the FI gets essentially kicked out
+
+ align:start position:0%
+of the FI gets essentially kicked out
+ 
+
+ align:start position:0%
+of the FI gets essentially kicked out
+the fiber and uh because because of the
+
+ align:start position:0%
+the fiber and uh because because of the
+ 
+
+ align:start position:0%
+the fiber and uh because because of the
+bend now and and and the reason for that
+
+ align:start position:0%
+bend now and and and the reason for that
+ 
+
+ align:start position:0%
+bend now and and and the reason for that
+because it's you start uh going against
+
+ align:start position:0%
+because it's you start uh going against
+ 
+
+ align:start position:0%
+because it's you start uh going against
+the rules of uh propagation of light in
+
+ align:start position:0%
+the rules of uh propagation of light in
+ 
+
+ align:start position:0%
+the rules of uh propagation of light in
+a
+
+ align:start position:0%
+a
+ 
+
+ align:start position:0%
+a
+fiber for example if you take the ray uh
+
+ align:start position:0%
+fiber for example if you take the ray uh
+ 
+
+ align:start position:0%
+fiber for example if you take the ray uh
+explanation is that what you're doing
+
+ align:start position:0%
+explanation is that what you're doing
+ 
+
+ align:start position:0%
+explanation is that what you're doing
+you are exceeding or or you're changing
+
+ align:start position:0%
+you are exceeding or or you're changing
+ 
+
+ align:start position:0%
+you are exceeding or or you're changing
+the angle of
+
+ align:start position:0%
+the angle of
+ 
+
+ align:start position:0%
+the angle of
+light uh with respect to the to the to
+
+ align:start position:0%
+light uh with respect to the to the to
+ 
+
+ align:start position:0%
+light uh with respect to the to the to
+the uh to the fiber which means that if
+
+ align:start position:0%
+the uh to the fiber which means that if
+ 
+
+ align:start position:0%
+the uh to the fiber which means that if
+you're if you're below the critical
+
+ align:start position:0%
+you're if you're below the critical
+ 
+
+ align:start position:0%
+you're if you're below the critical
+angle then you uh the light is no longer
+
+ align:start position:0%
+angle then you uh the light is no longer
+ 
+
+ align:start position:0%
+angle then you uh the light is no longer
+totally internally reflected and
+
+ align:start position:0%
+totally internally reflected and
+ 
+
+ align:start position:0%
+totally internally reflected and
+therefore gets kicked out
+
+ align:start position:0%
+therefore gets kicked out
+ 
+
+ align:start position:0%
+therefore gets kicked out
+all right so here it is it's very
+
+ align:start position:0%
+all right so here it is it's very
+ 
+
+ align:start position:0%
+all right so here it is it's very
+dramatic as soon as you put Little Bend
+
+ align:start position:0%
+dramatic as soon as you put Little Bend
+ 
+
+ align:start position:0%
+dramatic as soon as you put Little Bend
+in this fiber you can you can kick out a
+
+ align:start position:0%
+in this fiber you can you can kick out a
+ 
+
+ align:start position:0%
+in this fiber you can you can kick out a
+lot of light in fact this the glow uh
+
+ align:start position:0%
+lot of light in fact this the glow uh
+ 
+
+ align:start position:0%
+lot of light in fact this the glow uh
+right here now if we can bring in the
+
+ align:start position:0%
+right here now if we can bring in the
+ 
+
+ align:start position:0%
+right here now if we can bring in the
+the output of the fiber into the inset
+
+ align:start position:0%
+the output of the fiber into the inset
+ 
+
+ align:start position:0%
+the output of the fiber into the inset
+over here now you can see that as I
+
+ align:start position:0%
+over here now you can see that as I
+ 
+
+ align:start position:0%
+over here now you can see that as I
+increase the the band all right you can
+
+ align:start position:0%
+increase the the band all right you can
+ 
+
+ align:start position:0%
+increase the the band all right you can
+see that the intensity yeah I'll do it
+
+ align:start position:0%
+see that the intensity yeah I'll do it
+ 
+
+ align:start position:0%
+see that the intensity yeah I'll do it
+even more intensity then drops quite a
+
+ align:start position:0%
+even more intensity then drops quite a
+ 
+
+ align:start position:0%
+even more intensity then drops quite a
+bit which means I've kicked out almost
+
+ align:start position:0%
+bit which means I've kicked out almost
+ 
+
+ align:start position:0%
+bit which means I've kicked out almost
+all all the light by simply putting a
+
+ align:start position:0%
+all all the light by simply putting a
+ 
+
+ align:start position:0%
+all all the light by simply putting a
+Bend into into the fiber so the the
+
+ align:start position:0%
+Bend into into the fiber so the the
+ 
+
+ align:start position:0%
+Bend into into the fiber so the the
+illustration here then shows that if you
+
+ align:start position:0%
+illustration here then shows that if you
+ 
+
+ align:start position:0%
+illustration here then shows that if you
+leave the fiber alone without sharp
+
+ align:start position:0%
+leave the fiber alone without sharp
+ 
+
+ align:start position:0%
+leave the fiber alone without sharp
+bends everything is fine if you put in a
+
+ align:start position:0%
+bends everything is fine if you put in a
+ 
+
+ align:start position:0%
+bends everything is fine if you put in a
+Bend then you can kick out a lot of
+
+ align:start position:0%
+Bend then you can kick out a lot of
+ 
+
+ align:start position:0%
+Bend then you can kick out a lot of
+light and then not much will be will be
+
+ align:start position:0%
+light and then not much will be will be
+ 
+
+ align:start position:0%
+light and then not much will be will be
+will be
+
+ align:start position:0%
+will be
+ 
+
+ align:start position:0%
+will be
+transmitted so you have to be careful
+
+ align:start position:0%
+transmitted so you have to be careful
+ 
+
+ align:start position:0%
+transmitted so you have to be careful
+you don't put it too tight a Bend
+
+ align:start position:0%
+you don't put it too tight a Bend
+ 
+
+ align:start position:0%
+you don't put it too tight a Bend
+otherwise you Fibber brittle and you
+
+ align:start position:0%
+otherwise you Fibber brittle and you
+ 
+
+ align:start position:0%
+otherwise you Fibber brittle and you
+break the fiber so you have to be be
+
+ align:start position:0%
+break the fiber so you have to be be
+ 
+
+ align:start position:0%
+break the fiber so you have to be be
+careful how you how you do this all
+
+ align:start position:0%
+careful how you how you do this all
+ 
+
+ align:start position:0%
+careful how you how you do this all
+right so in this then in this
+
+ align:start position:0%
+right so in this then in this
+ 
+
+ align:start position:0%
+right so in this then in this
+demonstration we've seen how single mode
+
+ align:start position:0%
+demonstration we've seen how single mode
+ 
+
+ align:start position:0%
+demonstration we've seen how single mode
+fiber behaves in the next demonstration
+
+ align:start position:0%
+fiber behaves in the next demonstration
+ 
+
+ align:start position:0%
+fiber behaves in the next demonstration
+we're going to bring a another fiber
+
+ align:start position:0%
+we're going to bring a another fiber
+ 
+
+ align:start position:0%
+we're going to bring a another fiber
+with a different size core and we're
+
+ align:start position:0%
+with a different size core and we're
+ 
+
+ align:start position:0%
+with a different size core and we're
+going to see what comes out from that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+fiber
\ No newline at end of file
diff --git a/5hETv64GIuE.txt b/5hETv64GIuE.txt
new file mode 100644
index 0000000000000000000000000000000000000000..f01d2b113c9cc774a6929731d080041b5b1f0e98
--- /dev/null
+++ b/5hETv64GIuE.txt
@@ -0,0 +1,2403 @@
+align:start position:0%
+ 
+so in this final segment today we're
+
+ align:start position:0%
+so in this final segment today we're
+ 
+
+ align:start position:0%
+so in this final segment today we're
+going to talk about set theory just a
+
+ align:start position:0%
+going to talk about set theory just a
+ 
+
+ align:start position:0%
+going to talk about set theory just a
+little bit
+
+ align:start position:0%
+little bit
+ 
+
+ align:start position:0%
+little bit
+because if you're going to take a math
+
+ align:start position:0%
+because if you're going to take a math
+ 
+
+ align:start position:0%
+because if you're going to take a math
+class if you're going to be exposed to
+
+ align:start position:0%
+class if you're going to be exposed to
+ 
+
+ align:start position:0%
+class if you're going to be exposed to
+math for computer science it's useful to
+
+ align:start position:0%
+math for computer science it's useful to
+ 
+
+ align:start position:0%
+math for computer science it's useful to
+have at least a glimmering of what the
+
+ align:start position:0%
+have at least a glimmering of what the
+ 
+
+ align:start position:0%
+have at least a glimmering of what the
+foundations of math looks like how it
+
+ align:start position:0%
+foundations of math looks like how it
+ 
+
+ align:start position:0%
+foundations of math looks like how it
+starts and how it gets Justified and
+
+ align:start position:0%
+starts and how it gets Justified and
+ 
+
+ align:start position:0%
+starts and how it gets Justified and
+that's what set theory does in addition
+
+ align:start position:0%
+that's what set theory does in addition
+ 
+
+ align:start position:0%
+that's what set theory does in addition
+we will see that um uh the diagonal
+
+ align:start position:0%
+we will see that um uh the diagonal
+ 
+
+ align:start position:0%
+we will see that um uh the diagonal
+argument that we've already made much of
+
+ align:start position:0%
+argument that we've already made much of
+ 
+
+ align:start position:0%
+argument that we've already made much of
+plays a a crucial role in the
+
+ align:start position:0%
+plays a a crucial role in the
+ 
+
+ align:start position:0%
+plays a a crucial role in the
+development and understanding of set
+
+ align:start position:0%
+development and understanding of set
+ 
+
+ align:start position:0%
+development and understanding of set
+theory um so let's begin with an issue
+
+ align:start position:0%
+theory um so let's begin with an issue
+ 
+
+ align:start position:0%
+theory um so let's begin with an issue
+that plays an important role in set
+
+ align:start position:0%
+that plays an important role in set
+ 
+
+ align:start position:0%
+that plays an important role in set
+theory uh and in computer science having
+
+ align:start position:0%
+theory uh and in computer science having
+ 
+
+ align:start position:0%
+theory uh and in computer science having
+to do with the idea of taking a function
+
+ align:start position:0%
+to do with the idea of taking a function
+ 
+
+ align:start position:0%
+to do with the idea of taking a function
+and applying it to itself or or having
+
+ align:start position:0%
+and applying it to itself or or having
+ 
+
+ align:start position:0%
+and applying it to itself or or having
+something refer to itself and this is
+
+ align:start position:0%
+something refer to itself and this is
+ 
+
+ align:start position:0%
+something refer to itself and this is
+one of these things that's notoriously
+
+ align:start position:0%
+one of these things that's notoriously
+ 
+
+ align:start position:0%
+one of these things that's notoriously
+doubtful there's all these paradoxes
+
+ align:start position:0%
+doubtful there's all these paradoxes
+ 
+
+ align:start position:0%
+doubtful there's all these paradoxes
+about it maybe the simplest one is when
+
+ align:start position:0%
+about it maybe the simplest one is when
+ 
+
+ align:start position:0%
+about it maybe the simplest one is when
+I uh assert this statement is false and
+
+ align:start position:0%
+I uh assert this statement is false and
+ 
+
+ align:start position:0%
+I uh assert this statement is false and
+the question is is it true or false well
+
+ align:start position:0%
+the question is is it true or false well
+ 
+
+ align:start position:0%
+the question is is it true or false well
+if it's true then it's false and if it's
+
+ align:start position:0%
+if it's true then it's false and if it's
+ 
+
+ align:start position:0%
+if it's true then it's false and if it's
+false then it's true and we get a kind
+
+ align:start position:0%
+false then it's true and we get a kind
+ 
+
+ align:start position:0%
+false then it's true and we get a kind
+of buzzer uh it's not possible to figure
+
+ align:start position:0%
+of buzzer uh it's not possible to figure
+ 
+
+ align:start position:0%
+of buzzer uh it's not possible to figure
+out whether this statement is true or
+
+ align:start position:0%
+out whether this statement is true or
+ 
+
+ align:start position:0%
+out whether this statement is true or
+false I think we would deny that it was
+
+ align:start position:0%
+false I think we would deny that it was
+ 
+
+ align:start position:0%
+false I think we would deny that it was
+a proposition so that's a hint that
+
+ align:start position:0%
+a proposition so that's a hint that
+ 
+
+ align:start position:0%
+a proposition so that's a hint that
+there's something suspicious about
+
+ align:start position:0%
+there's something suspicious about
+ 
+
+ align:start position:0%
+there's something suspicious about
+self-reference and self-application and
+
+ align:start position:0%
+self-reference and self-application and
+ 
+
+ align:start position:0%
+self-reference and self-application and
+so on on the other hand it's worth
+
+ align:start position:0%
+so on on the other hand it's worth
+ 
+
+ align:start position:0%
+so on on the other hand it's worth
+remembering that in computer science we
+
+ align:start position:0%
+remembering that in computer science we
+ 
+
+ align:start position:0%
+remembering that in computer science we
+take this for granted so let's look at
+
+ align:start position:0%
+take this for granted so let's look at
+ 
+
+ align:start position:0%
+take this for granted so let's look at
+an example um here's a simple example of
+
+ align:start position:0%
+an example um here's a simple example of
+ 
+
+ align:start position:0%
+an example um here's a simple example of
+a list in uh scheme lisp notation um
+
+ align:start position:0%
+a list in uh scheme lisp notation um
+ 
+
+ align:start position:0%
+a list in uh scheme lisp notation um
+meaning it's a list of three things 0o
+
+ align:start position:0%
+meaning it's a list of three things 0o
+ 
+
+ align:start position:0%
+meaning it's a list of three things 0o
+one and two uh and the the black Parn
+
+ align:start position:0%
+one and two uh and the the black Parn
+ 
+
+ align:start position:0%
+one and two uh and the the black Parn
+indicate that we're thinking of it as an
+
+ align:start position:0%
+indicate that we're thinking of it as an
+ 
+
+ align:start position:0%
+indicate that we're thinking of it as an
+ordered list now the way that I would
+
+ align:start position:0%
+ordered list now the way that I would
+ 
+
+ align:start position:0%
+ordered list now the way that I would
+represent a list like that in memory
+
+ align:start position:0%
+represent a list like that in memory
+ 
+
+ align:start position:0%
+represent a list like that in memory
+typically is by using these things that
+
+ align:start position:0%
+typically is by using these things that
+ 
+
+ align:start position:0%
+typically is by using these things that
+are called conell so a conell has these
+
+ align:start position:0%
+are called conell so a conell has these
+ 
+
+ align:start position:0%
+are called conell so a conell has these
+two parts the leftand part points to the
+
+ align:start position:0%
+two parts the leftand part points to the
+ 
+
+ align:start position:0%
+two parts the leftand part points to the
+uh value in that location in the list so
+
+ align:start position:0%
+uh value in that location in the list so
+ 
+
+ align:start position:0%
+uh value in that location in the list so
+this first conell points to zero which
+
+ align:start position:0%
+this first conell points to zero which
+ 
+
+ align:start position:0%
+this first conell points to zero which
+is the first element of the list the
+
+ align:start position:0%
+is the first element of the list the
+ 
+
+ align:start position:0%
+is the first element of the list the
+second component of the conell points to
+
+ align:start position:0%
+second component of the conell points to
+ 
+
+ align:start position:0%
+second component of the conell points to
+the next element of the list and so here
+
+ align:start position:0%
+the next element of the list and so here
+ 
+
+ align:start position:0%
+the next element of the list and so here
+you see one pointing to the third
+
+ align:start position:0%
+you see one pointing to the third
+ 
+
+ align:start position:0%
+you see one pointing to the third
+element of the list and there you see
+
+ align:start position:0%
+element of the list and there you see
+ 
+
+ align:start position:0%
+element of the list and there you see
+two and that little uh nil marker
+
+ align:start position:0%
+two and that little uh nil marker
+ 
+
+ align:start position:0%
+two and that little uh nil marker
+indicates that's the end of the list so
+
+ align:start position:0%
+indicates that's the end of the list so
+ 
+
+ align:start position:0%
+indicates that's the end of the list so
+that's a simple representation of a list
+
+ align:start position:0%
+that's a simple representation of a list
+ 
+
+ align:start position:0%
+that's a simple representation of a list
+of length three with three conell well
+
+ align:start position:0%
+of length three with three conell well
+ 
+
+ align:start position:0%
+of length three with three conell well
+one of the things that um a computer
+
+ align:start position:0%
+one of the things that um a computer
+ 
+
+ align:start position:0%
+one of the things that um a computer
+science lets you do and many languages
+
+ align:start position:0%
+science lets you do and many languages
+ 
+
+ align:start position:0%
+science lets you do and many languages
+let you do is that you can manipulate
+
+ align:start position:0%
+let you do is that you can manipulate
+ 
+
+ align:start position:0%
+let you do is that you can manipulate
+these pointers so using uh the language
+
+ align:start position:0%
+these pointers so using uh the language
+ 
+
+ align:start position:0%
+these pointers so using uh the language
+of scheme what I can do is uh do an
+
+ align:start position:0%
+of scheme what I can do is uh do an
+ 
+
+ align:start position:0%
+of scheme what I can do is uh do an
+operation called set car where I'm
+
+ align:start position:0%
+operation called set car where I'm
+ 
+
+ align:start position:0%
+operation called set car where I'm
+taking in this case I'm setting the
+
+ align:start position:0%
+taking in this case I'm setting the
+ 
+
+ align:start position:0%
+taking in this case I'm setting the
+second element of L that is this conel
+
+ align:start position:0%
+second element of L that is this conel
+ 
+
+ align:start position:0%
+second element of L that is this conel
+to L and set car is saying let's change
+
+ align:start position:0%
+to L and set car is saying let's change
+ 
+
+ align:start position:0%
+to L and set car is saying let's change
+what the element in the uh uh uh in the
+
+ align:start position:0%
+what the element in the uh uh uh in the
+ 
+
+ align:start position:0%
+what the element in the uh uh uh in the
+left hand part of this uh cell is this
+
+ align:start position:0%
+left hand part of this uh cell is this
+ 
+
+ align:start position:0%
+left hand part of this uh cell is this
+is where the value of the second element
+
+ align:start position:0%
+is where the value of the second element
+ 
+
+ align:start position:0%
+is where the value of the second element
+is let's change the value of the second
+
+ align:start position:0%
+is let's change the value of the second
+ 
+
+ align:start position:0%
+is let's change the value of the second
+element to BL l what does that mean as a
+
+ align:start position:0%
+element to BL l what does that mean as a
+ 
+
+ align:start position:0%
+element to BL l what does that mean as a
+pointer manipulation well it's pretty
+
+ align:start position:0%
+pointer manipulation well it's pretty
+ 
+
+ align:start position:0%
+pointer manipulation well it's pretty
+simple I just move this pointer to point
+
+ align:start position:0%
+simple I just move this pointer to point
+ 
+
+ align:start position:0%
+simple I just move this pointer to point
+to the beginning of the list L and now I
+
+ align:start position:0%
+to the beginning of the list L and now I
+ 
+
+ align:start position:0%
+to the beginning of the list L and now I
+have an interesting situation because
+
+ align:start position:0%
+have an interesting situation because
+ 
+
+ align:start position:0%
+have an interesting situation because
+this list uh now is a list that consists
+
+ align:start position:0%
+this list uh now is a list that consists
+ 
+
+ align:start position:0%
+this list uh now is a list that consists
+of of uh zero and L and two it's a list
+
+ align:start position:0%
+of of uh zero and L and two it's a list
+ 
+
+ align:start position:0%
+of of uh zero and L and two it's a list
+that has itself as a member and it makes
+
+ align:start position:0%
+that has itself as a member and it makes
+ 
+
+ align:start position:0%
+that has itself as a member and it makes
+perfect sense um uh and if you sort of
+
+ align:start position:0%
+perfect sense um uh and if you sort of
+ 
+
+ align:start position:0%
+perfect sense um uh and if you sort of
+expand it out L is this list that has
+
+ align:start position:0%
+expand it out L is this list that has
+ 
+
+ align:start position:0%
+expand it out L is this list that has
+begins with zero and then its second
+
+ align:start position:0%
+begins with zero and then its second
+ 
+
+ align:start position:0%
+begins with zero and then its second
+element is a list that begins with zero
+
+ align:start position:0%
+element is a list that begins with zero
+ 
+
+ align:start position:0%
+element is a list that begins with zero
+um and the second element of that list
+
+ align:start position:0%
+um and the second element of that list
+ 
+
+ align:start position:0%
+um and the second element of that list
+is a list that begins with zero and so
+
+ align:start position:0%
+is a list that begins with zero and so
+ 
+
+ align:start position:0%
+is a list that begins with zero and so
+on and then uh the third element of L is
+
+ align:start position:0%
+on and then uh the third element of L is
+ 
+
+ align:start position:0%
+on and then uh the third element of L is
+two and the third element of the second
+
+ align:start position:0%
+two and the third element of the second
+ 
+
+ align:start position:0%
+two and the third element of the second
+element of L is two and so on it's an
+
+ align:start position:0%
+element of L is two and so on it's an
+ 
+
+ align:start position:0%
+element of L is two and so on it's an
+interesting infinite nested structure
+
+ align:start position:0%
+interesting infinite nested structure
+ 
+
+ align:start position:0%
+interesting infinite nested structure
+that's nicely represented by this finite
+
+ align:start position:0%
+that's nicely represented by this finite
+ 
+
+ align:start position:0%
+that's nicely represented by this finite
+um uh circular
+
+ align:start position:0%
+um uh circular
+ 
+
+ align:start position:0%
+um uh circular
+list okay um let's look at another
+
+ align:start position:0%
+list okay um let's look at another
+ 
+
+ align:start position:0%
+list okay um let's look at another
+example Le where in computer science we
+
+ align:start position:0%
+example Le where in computer science we
+ 
+
+ align:start position:0%
+example Le where in computer science we
+actually apply things to themselves so
+
+ align:start position:0%
+actually apply things to themselves so
+ 
+
+ align:start position:0%
+actually apply things to themselves so
+let's define the composition operator
+
+ align:start position:0%
+let's define the composition operator
+ 
+
+ align:start position:0%
+let's define the composition operator
+and again I'm using uh notation from the
+
+ align:start position:0%
+and again I'm using uh notation from the
+ 
+
+ align:start position:0%
+and again I'm using uh notation from the
+language scheme I want to take two
+
+ align:start position:0%
+language scheme I want to take two
+ 
+
+ align:start position:0%
+language scheme I want to take two
+functions f and g that take one argument
+
+ align:start position:0%
+functions f and g that take one argument
+ 
+
+ align:start position:0%
+functions f and g that take one argument
+and I'm going to Define their
+
+ align:start position:0%
+and I'm going to Define their
+ 
+
+ align:start position:0%
+and I'm going to Define their
+composition the way that I compose f and
+
+ align:start position:0%
+composition the way that I compose f and
+ 
+
+ align:start position:0%
+composition the way that I compose f and
+g is I Define a new function H ofx which
+
+ align:start position:0%
+g is I Define a new function H ofx which
+ 
+
+ align:start position:0%
+g is I Define a new function H ofx which
+is going to be the composition of H and
+
+ align:start position:0%
+is going to be the composition of H and
+ 
+
+ align:start position:0%
+is going to be the composition of H and
+G the way I Define h of X is I say apply
+
+ align:start position:0%
+G the way I Define h of X is I say apply
+ 
+
+ align:start position:0%
+G the way I Define h of X is I say apply
+G to F to G apply F to G apply to X and
+
+ align:start position:0%
+G to F to G apply F to G apply to X and
+ 
+
+ align:start position:0%
+G to F to G apply F to G apply to X and
+return the value H so this is a a
+
+ align:start position:0%
+return the value H so this is a a
+ 
+
+ align:start position:0%
+return the value H so this is a a
+compose is a procedure that takes two
+
+ align:start position:0%
+compose is a procedure that takes two
+ 
+
+ align:start position:0%
+compose is a procedure that takes two
+procedures f and g and returns their
+
+ align:start position:0%
+procedures f and g and returns their
+ 
+
+ align:start position:0%
+procedures f and g and returns their
+composition
+
+ align:start position:0%
+composition
+ 
+
+ align:start position:0%
+composition
+H okay let's practice suppose that I
+
+ align:start position:0%
+H okay let's practice suppose that I
+ 
+
+ align:start position:0%
+H okay let's practice suppose that I
+compose the square function that Maps X
+
+ align:start position:0%
+compose the square function that Maps X
+ 
+
+ align:start position:0%
+compose the square function that Maps X
+to x^2 and the add one function that
+
+ align:start position:0%
+to x^2 and the add one function that
+ 
+
+ align:start position:0%
+to x^2 and the add one function that
+Maps X to x + 1 well um if I uh compose
+
+ align:start position:0%
+Maps X to x + 1 well um if I uh compose
+ 
+
+ align:start position:0%
+Maps X to x + 1 well um if I uh compose
+the square of adding one and I it to
+
+ align:start position:0%
+the square of adding one and I it to
+ 
+
+ align:start position:0%
+the square of adding one and I it to
+three what I'm saying is uh let's add
+
+ align:start position:0%
+three what I'm saying is uh let's add
+ 
+
+ align:start position:0%
+three what I'm saying is uh let's add
+one to three and then Square it and I
+
+ align:start position:0%
+one to three and then Square it and I
+ 
+
+ align:start position:0%
+one to three and then Square it and I
+get 3 + 1^ squ or 16 cuz the add one and
+
+ align:start position:0%
+get 3 + 1^ squ or 16 cuz the add one and
+ 
+
+ align:start position:0%
+get 3 + 1^ squ or 16 cuz the add one and
+then Square it is the function that's
+
+ align:start position:0%
+then Square it is the function that's
+ 
+
+ align:start position:0%
+then Square it is the function that's
+the composition of square and add one
+
+ align:start position:0%
+the composition of square and add one
+ 
+
+ align:start position:0%
+the composition of square and add one
+now I can do the following I could
+
+ align:start position:0%
+now I can do the following I could
+ 
+
+ align:start position:0%
+now I can do the following I could
+Square I could compose square with
+
+ align:start position:0%
+Square I could compose square with
+ 
+
+ align:start position:0%
+Square I could compose square with
+itself if I take the function Square it
+
+ align:start position:0%
+itself if I take the function Square it
+ 
+
+ align:start position:0%
+itself if I take the function Square it
+and square that I'm really taking the
+
+ align:start position:0%
+and square that I'm really taking the
+ 
+
+ align:start position:0%
+and square that I'm really taking the
+fourth power so if I apply the function
+
+ align:start position:0%
+fourth power so if I apply the function
+ 
+
+ align:start position:0%
+fourth power so if I apply the function
+composed of square squ to 3 I get 3^ s^
+
+ align:start position:0%
+composed of square squ to 3 I get 3^ s^
+ 
+
+ align:start position:0%
+composed of square squ to 3 I get 3^ s^
+S or 81 or 3 4 all makes perfect sense
+
+ align:start position:0%
+S or 81 or 3 4 all makes perfect sense
+ 
+
+ align:start position:0%
+S or 81 or 3 4 all makes perfect sense
+okay well now let's uh Define a a
+
+ align:start position:0%
+okay well now let's uh Define a a
+ 
+
+ align:start position:0%
+okay well now let's uh Define a a
+composite with itself operation I'm
+
+ align:start position:0%
+composite with itself operation I'm
+ 
+
+ align:start position:0%
+composite with itself operation I'm
+going to call it comp 2 comp 2 takes one
+
+ align:start position:0%
+going to call it comp 2 comp 2 takes one
+ 
+
+ align:start position:0%
+going to call it comp 2 comp 2 takes one
+function f and the definition of comp 2
+
+ align:start position:0%
+function f and the definition of comp 2
+ 
+
+ align:start position:0%
+function f and the definition of comp 2
+is compose f with
+
+ align:start position:0%
+is compose f with
+ 
+
+ align:start position:0%
+is compose f with
+f um and if I uh then apply comp 2 to
+
+ align:start position:0%
+f um and if I uh then apply comp 2 to
+ 
+
+ align:start position:0%
+f um and if I uh then apply comp 2 to
+square and three it's saying okay okay
+
+ align:start position:0%
+square and three it's saying okay okay
+ 
+
+ align:start position:0%
+square and three it's saying okay okay
+compose square and square we just did
+
+ align:start position:0%
+compose square and square we just did
+ 
+
+ align:start position:0%
+compose square and square we just did
+that that was the fourth power apply it
+
+ align:start position:0%
+that that was the fourth power apply it
+ 
+
+ align:start position:0%
+that that was the fourth power apply it
+to three I get
+
+ align:start position:0%
+to three I get
+ 
+
+ align:start position:0%
+to three I get
+81 and now we can do some weird stuff
+
+ align:start position:0%
+81 and now we can do some weird stuff
+ 
+
+ align:start position:0%
+81 and now we can do some weird stuff
+because suppose that I apply comp 2 to
+
+ align:start position:0%
+because suppose that I apply comp 2 to
+ 
+
+ align:start position:0%
+because suppose that I apply comp 2 to
+comp two and then apply that to add one
+
+ align:start position:0%
+comp two and then apply that to add one
+ 
+
+ align:start position:0%
+comp two and then apply that to add one
+and apply that to
+
+ align:start position:0%
+and apply that to
+ 
+
+ align:start position:0%
+and apply that to
+three well that one's a little hard to
+
+ align:start position:0%
+three well that one's a little hard to
+ 
+
+ align:start position:0%
+three well that one's a little hard to
+follow and I'm going to let you think it
+
+ align:start position:0%
+follow and I'm going to let you think it
+ 
+
+ align:start position:0%
+follow and I'm going to let you think it
+through but comp two of comp two is
+
+ align:start position:0%
+through but comp two of comp two is
+ 
+
+ align:start position:0%
+through but comp two of comp two is
+compose something with it four times and
+
+ align:start position:0%
+compose something with it four times and
+ 
+
+ align:start position:0%
+compose something with it four times and
+when you do that with add one what
+
+ align:start position:0%
+when you do that with add one what
+ 
+
+ align:start position:0%
+when you do that with add one what
+happens is that uh you're uh adding one
+
+ align:start position:0%
+happens is that uh you're uh adding one
+ 
+
+ align:start position:0%
+happens is that uh you're uh adding one
+four times to three if I comp two of
+
+ align:start position:0%
+four times to three if I comp two of
+ 
+
+ align:start position:0%
+four times to three if I comp two of
+comp two of square I'm uh composing
+
+ align:start position:0%
+comp two of square I'm uh composing
+ 
+
+ align:start position:0%
+comp two of square I'm uh composing
+square with itself and then composing
+
+ align:start position:0%
+square with itself and then composing
+ 
+
+ align:start position:0%
+square with itself and then composing
+that with itself I'm really squaring
+
+ align:start position:0%
+that with itself I'm really squaring
+ 
+
+ align:start position:0%
+that with itself I'm really squaring
+four times um and I wind up with uh 2 to
+
+ align:start position:0%
+four times um and I wind up with uh 2 to
+ 
+
+ align:start position:0%
+four times um and I wind up with uh 2 to
+the 4th or
+
+ align:start position:0%
+the 4th or
+ 
+
+ align:start position:0%
+the 4th or
+16 uh uh is the power that I'm taking
+
+ align:start position:0%
+16 uh uh is the power that I'm taking
+ 
+
+ align:start position:0%
+16 uh uh is the power that I'm taking
+and so composed to of composed to of
+
+ align:start position:0%
+and so composed to of composed to of
+ 
+
+ align:start position:0%
+and so composed to of composed to of
+square of three is this rather large
+
+ align:start position:0%
+square of three is this rather large
+ 
+
+ align:start position:0%
+square of three is this rather large
+number 3 to the 16th it could be a
+
+ align:start position:0%
+number 3 to the 16th it could be a
+ 
+
+ align:start position:0%
+number 3 to the 16th it could be a
+little bit tricky to think through but
+
+ align:start position:0%
+little bit tricky to think through but
+ 
+
+ align:start position:0%
+little bit tricky to think through but
+it all makes perfect sense and it works
+
+ align:start position:0%
+it all makes perfect sense and it works
+ 
+
+ align:start position:0%
+it all makes perfect sense and it works
+just fine in recursive programming
+
+ align:start position:0%
+just fine in recursive programming
+ 
+
+ align:start position:0%
+just fine in recursive programming
+languages that allow this kind of
+
+ align:start position:0%
+languages that allow this kind of
+ 
+
+ align:start position:0%
+languages that allow this kind of
+untyped uh or generically typed
+
+ align:start position:0%
+untyped uh or generically typed
+ 
+
+ align:start position:0%
+untyped uh or generically typed
+composition okay so why is it that
+
+ align:start position:0%
+composition okay so why is it that
+ 
+
+ align:start position:0%
+composition okay so why is it that
+computer scientists are so daring and
+
+ align:start position:0%
+computer scientists are so daring and
+ 
+
+ align:start position:0%
+computer scientists are so daring and
+mathematicians are so timid about
+
+ align:start position:0%
+mathematicians are so timid about
+ 
+
+ align:start position:0%
+mathematicians are so timid about
+self-reference and the reason is the
+
+ align:start position:0%
+self-reference and the reason is the
+ 
+
+ align:start position:0%
+self-reference and the reason is the
+mathematicians have been traumatized by
+
+ align:start position:0%
+mathematicians have been traumatized by
+ 
+
+ align:start position:0%
+mathematicians have been traumatized by
+ber Russell because of Russell's famous
+
+ align:start position:0%
+ber Russell because of Russell's famous
+ 
+
+ align:start position:0%
+ber Russell because of Russell's famous
+Paradox which we're now ready to look at
+
+ align:start position:0%
+Paradox which we're now ready to look at
+ 
+
+ align:start position:0%
+Paradox which we're now ready to look at
+so um what Russell was proposing uh and
+
+ align:start position:0%
+so um what Russell was proposing uh and
+ 
+
+ align:start position:0%
+so um what Russell was proposing uh and
+it's going to look just like a diagonal
+
+ align:start position:0%
+it's going to look just like a diagonal
+ 
+
+ align:start position:0%
+it's going to look just like a diagonal
+argument is Russell said let's let W be
+
+ align:start position:0%
+argument is Russell said let's let W be
+ 
+
+ align:start position:0%
+argument is Russell said let's let W be
+the collection of
+
+ align:start position:0%
+the collection of
+ 
+
+ align:start position:0%
+the collection of
+sets uh s such that s is not a member of
+
+ align:start position:0%
+sets uh s such that s is not a member of
+ 
+
+ align:start position:0%
+sets uh s such that s is not a member of
+s now let's think about that for a
+
+ align:start position:0%
+s now let's think about that for a
+ 
+
+ align:start position:0%
+s now let's think about that for a
+little bit most sets are not members of
+
+ align:start position:0%
+little bit most sets are not members of
+ 
+
+ align:start position:0%
+little bit most sets are not members of
+themselves like um the set of integers
+
+ align:start position:0%
+themselves like um the set of integers
+ 
+
+ align:start position:0%
+themselves like um the set of integers
+uh is not a member of itself because the
+
+ align:start position:0%
+uh is not a member of itself because the
+ 
+
+ align:start position:0%
+uh is not a member of itself because the
+only thing in it is in it are integers
+
+ align:start position:0%
+only thing in it is in it are integers
+ 
+
+ align:start position:0%
+only thing in it is in it are integers
+um and the set of the power set of the
+
+ align:start position:0%
+um and the set of the power set of the
+ 
+
+ align:start position:0%
+um and the set of the power set of the
+integers is not a member of itself
+
+ align:start position:0%
+integers is not a member of itself
+ 
+
+ align:start position:0%
+integers is not a member of itself
+because every uh member of the power set
+
+ align:start position:0%
+because every uh member of the power set
+ 
+
+ align:start position:0%
+because every uh member of the power set
+of integers is a set of integers whereas
+
+ align:start position:0%
+of integers is a set of integers whereas
+ 
+
+ align:start position:0%
+of integers is a set of integers whereas
+the power set of integers is a set of
+
+ align:start position:0%
+the power set of integers is a set of
+ 
+
+ align:start position:0%
+the power set of integers is a set of
+sets of those things so those familiar
+
+ align:start position:0%
+sets of those things so those familiar
+ 
+
+ align:start position:0%
+sets of those things so those familiar
+sets are typically not members of
+
+ align:start position:0%
+sets are typically not members of
+ 
+
+ align:start position:0%
+sets are typically not members of
+themselves but who knows maybe there are
+
+ align:start position:0%
+themselves but who knows maybe there are
+ 
+
+ align:start position:0%
+themselves but who knows maybe there are
+these weird sets like the uh uh like the
+
+ align:start position:0%
+these weird sets like the uh uh like the
+ 
+
+ align:start position:0%
+these weird sets like the uh uh like the
+circular list or a function that can
+
+ align:start position:0%
+circular list or a function that can
+ 
+
+ align:start position:0%
+circular list or a function that can
+compose with itself that is a member of
+
+ align:start position:0%
+compose with itself that is a member of
+ 
+
+ align:start position:0%
+compose with itself that is a member of
+itself now let me step back for a moment
+
+ align:start position:0%
+itself now let me step back for a moment
+ 
+
+ align:start position:0%
+itself now let me step back for a moment
+and and mention where where did Russell
+
+ align:start position:0%
+and and mention where where did Russell
+ 
+
+ align:start position:0%
+and and mention where where did Russell
+get thinking about this and it it comes
+
+ align:start position:0%
+get thinking about this and it it comes
+ 
+
+ align:start position:0%
+get thinking about this and it it comes
+from the period in the late 19th century
+
+ align:start position:0%
+from the period in the late 19th century
+ 
+
+ align:start position:0%
+from the period in the late 19th century
+when mathematicians and logicians were
+
+ align:start position:0%
+when mathematicians and logicians were
+ 
+
+ align:start position:0%
+when mathematicians and logicians were
+trying to think about uh uh confirming
+
+ align:start position:0%
+trying to think about uh uh confirming
+ 
+
+ align:start position:0%
+trying to think about uh uh confirming
+and establishing the foundations of math
+
+ align:start position:0%
+and establishing the foundations of math
+ 
+
+ align:start position:0%
+and establishing the foundations of math
+what was math absolutely about what were
+
+ align:start position:0%
+what was math absolutely about what were
+ 
+
+ align:start position:0%
+what was math absolutely about what were
+the fundamental objects that uh that
+
+ align:start position:0%
+the fundamental objects that uh that
+ 
+
+ align:start position:0%
+the fundamental objects that uh that
+mathematics could be built from and what
+
+ align:start position:0%
+mathematics could be built from and what
+ 
+
+ align:start position:0%
+mathematics could be built from and what
+would with the rules for understanding
+
+ align:start position:0%
+would with the rules for understanding
+ 
+
+ align:start position:0%
+would with the rules for understanding
+those OB objects and it was pretty well
+
+ align:start position:0%
+those OB objects and it was pretty well
+ 
+
+ align:start position:0%
+those OB objects and it was pretty well
+agreed that sets were it you could build
+
+ align:start position:0%
+agreed that sets were it you could build
+ 
+
+ align:start position:0%
+agreed that sets were it you could build
+everything out of sets and you just need
+
+ align:start position:0%
+everything out of sets and you just need
+ 
+
+ align:start position:0%
+everything out of sets and you just need
+to understand sets and then you were in
+
+ align:start position:0%
+to understand sets and then you were in
+ 
+
+ align:start position:0%
+to understand sets and then you were in
+business uh and there was a German
+
+ align:start position:0%
+business uh and there was a German
+ 
+
+ align:start position:0%
+business uh and there was a German
+mathematician named Fraga uh who tried
+
+ align:start position:0%
+mathematician named Fraga uh who tried
+ 
+
+ align:start position:0%
+mathematician named Fraga uh who tried
+to demonstrate this by developing uh a
+
+ align:start position:0%
+to demonstrate this by developing uh a
+ 
+
+ align:start position:0%
+to demonstrate this by developing uh a
+set theory very carefully giving careful
+
+ align:start position:0%
+set theory very carefully giving careful
+ 
+
+ align:start position:0%
+set theory very carefully giving careful
+axioms for what sets were and he showed
+
+ align:start position:0%
+axioms for what sets were and he showed
+ 
+
+ align:start position:0%
+axioms for what sets were and he showed
+how you could build out of sets you
+
+ align:start position:0%
+how you could build out of sets you
+ 
+
+ align:start position:0%
+how you could build out of sets you
+could build the integers and then you
+
+ align:start position:0%
+could build the integers and then you
+ 
+
+ align:start position:0%
+could build the integers and then you
+could build rationals which are sort of
+
+ align:start position:0%
+could build rationals which are sort of
+ 
+
+ align:start position:0%
+could build rationals which are sort of
+just pairs of integers and then you
+
+ align:start position:0%
+just pairs of integers and then you
+ 
+
+ align:start position:0%
+just pairs of integers and then you
+could build real numbers by taking
+
+ align:start position:0%
+could build real numbers by taking
+ 
+
+ align:start position:0%
+could build real numbers by taking
+collections of rationals that um uh that
+
+ align:start position:0%
+collections of rationals that um uh that
+ 
+
+ align:start position:0%
+collections of rationals that um uh that
+had at least upper bound and uh and then
+
+ align:start position:0%
+had at least upper bound and uh and then
+ 
+
+ align:start position:0%
+had at least upper bound and uh and then
+you can keep going you can build
+
+ align:start position:0%
+you can keep going you can build
+ 
+
+ align:start position:0%
+you can keep going you can build
+functions and continuous functions and
+
+ align:start position:0%
+functions and continuous functions and
+ 
+
+ align:start position:0%
+functions and continuous functions and
+he showed how you could build up um the
+
+ align:start position:0%
+he showed how you could build up um the
+ 
+
+ align:start position:0%
+he showed how you could build up um the
+basic structures of mathematical
+
+ align:start position:0%
+basic structures of mathematical
+ 
+
+ align:start position:0%
+basic structures of mathematical
+analysis and prove their basic theorems
+
+ align:start position:0%
+analysis and prove their basic theorems
+ 
+
+ align:start position:0%
+analysis and prove their basic theorems
+in his formal set theory the problem was
+
+ align:start position:0%
+in his formal set theory the problem was
+ 
+
+ align:start position:0%
+in his formal set theory the problem was
+that Russell came along and looked at
+
+ align:start position:0%
+that Russell came along and looked at
+ 
+
+ align:start position:0%
+that Russell came along and looked at
+fragga set theory and came up with the
+
+ align:start position:0%
+fragga set theory and came up with the
+ 
+
+ align:start position:0%
+fragga set theory and came up with the
+following
+
+ align:start position:0%
+following
+ 
+
+ align:start position:0%
+following
+Paradox he defined W to be the
+
+ align:start position:0%
+Paradox he defined W to be the
+ 
+
+ align:start position:0%
+Paradox he defined W to be the
+collection of s and sets such that s is
+
+ align:start position:0%
+collection of s and sets such that s is
+ 
+
+ align:start position:0%
+collection of s and sets such that s is
+not a member of s fro would certainly
+
+ align:start position:0%
+not a member of s fro would certainly
+ 
+
+ align:start position:0%
+not a member of s fro would certainly
+have said that's a well-defined set and
+
+ align:start position:0%
+have said that's a well-defined set and
+ 
+
+ align:start position:0%
+have said that's a well-defined set and
+and he will acknowledge that W is a set
+
+ align:start position:0%
+and he will acknowledge that W is a set
+ 
+
+ align:start position:0%
+and he will acknowledge that W is a set
+um and let's look at what this means and
+
+ align:start position:0%
+um and let's look at what this means and
+ 
+
+ align:start position:0%
+um and let's look at what this means and
+I mean this is diagonal argument so
+
+ align:start position:0%
+I mean this is diagonal argument so
+ 
+
+ align:start position:0%
+I mean this is diagonal argument so
+let's remember what's the by this
+
+ align:start position:0%
+let's remember what's the by this
+ 
+
+ align:start position:0%
+let's remember what's the by this
+definition of w what we have is that a
+
+ align:start position:0%
+definition of w what we have is that a
+ 
+
+ align:start position:0%
+definition of w what we have is that a
+set s is in W if and only if s is not a
+
+ align:start position:0%
+set s is in W if and only if s is not a
+ 
+
+ align:start position:0%
+set s is in W if and only if s is not a
+member of s okay that's fine then just
+
+ align:start position:0%
+member of s okay that's fine then just
+ 
+
+ align:start position:0%
+member of s okay that's fine then just
+let s be W and we immediately get a
+
+ align:start position:0%
+let s be W and we immediately get a
+ 
+
+ align:start position:0%
+let s be W and we immediately get a
+contradiction that W is in W if and only
+
+ align:start position:0%
+contradiction that W is in W if and only
+ 
+
+ align:start position:0%
+contradiction that W is in W if and only
+if W is not in W poor
+
+ align:start position:0%
+if W is not in W poor
+ 
+
+ align:start position:0%
+if W is not in W poor
+frager his book was a disaster math is
+
+ align:start position:0%
+frager his book was a disaster math is
+ 
+
+ align:start position:0%
+frager his book was a disaster math is
+broken um uh uh you can prove that
+
+ align:start position:0%
+broken um uh uh you can prove that
+ 
+
+ align:start position:0%
+broken um uh uh you can prove that
+you're the pope you can prove the pigs
+
+ align:start position:0%
+you're the pope you can prove the pigs
+ 
+
+ align:start position:0%
+you're the pope you can prove the pigs
+fly verified programs crash math is just
+
+ align:start position:0%
+fly verified programs crash math is just
+ 
+
+ align:start position:0%
+fly verified programs crash math is just
+broken um it's not reliable you can
+
+ align:start position:0%
+broken um it's not reliable you can
+ 
+
+ align:start position:0%
+broken um it's not reliable you can
+prove anything by in frga system because
+
+ align:start position:0%
+prove anything by in frga system because
+ 
+
+ align:start position:0%
+prove anything by in frga system because
+it reached a contradiction and from
+
+ align:start position:0%
+it reached a contradiction and from
+ 
+
+ align:start position:0%
+it reached a contradiction and from
+something false you can prove anything
+
+ align:start position:0%
+something false you can prove anything
+ 
+
+ align:start position:0%
+something false you can prove anything
+well frga
+
+ align:start position:0%
+well frga
+ 
+
+ align:start position:0%
+well frga
+you know had a book it was a vanity
+
+ align:start position:0%
+you know had a book it was a vanity
+ 
+
+ align:start position:0%
+you know had a book it was a vanity
+publication uh and the the preface of it
+
+ align:start position:0%
+publication uh and the the preface of it
+ 
+
+ align:start position:0%
+publication uh and the the preface of it
+had to be Rewritten and he said look um
+
+ align:start position:0%
+had to be Rewritten and he said look um
+ 
+
+ align:start position:0%
+had to be Rewritten and he said look um
+uh my system's broken and I know that
+
+ align:start position:0%
+uh my system's broken and I know that
+ 
+
+ align:start position:0%
+uh my system's broken and I know that
+and Russell showed that unambiguously
+
+ align:start position:0%
+and Russell showed that unambiguously
+ 
+
+ align:start position:0%
+and Russell showed that unambiguously
+but I think that there's still something
+
+ align:start position:0%
+but I think that there's still something
+ 
+
+ align:start position:0%
+but I think that there's still something
+here that's salvageable and so I'm going
+
+ align:start position:0%
+here that's salvageable and so I'm going
+ 
+
+ align:start position:0%
+here that's salvageable and so I'm going
+to publish the book but I apologize for
+
+ align:start position:0%
+to publish the book but I apologize for
+ 
+
+ align:start position:0%
+to publish the book but I apologize for
+the fact that you can't rely on the
+
+ align:start position:0%
+the fact that you can't rely on the
+ 
+
+ align:start position:0%
+the fact that you can't rely on the
+conclusions um poor frago uh that was
+
+ align:start position:0%
+conclusions um poor frago uh that was
+ 
+
+ align:start position:0%
+conclusions um poor frago uh that was
+his life work gone down the
+
+ align:start position:0%
+his life work gone down the
+ 
+
+ align:start position:0%
+his life work gone down the
+drain okay
+
+ align:start position:0%
+drain okay
+ 
+
+ align:start position:0%
+drain okay
+um how do we resolve this what's wrong
+
+ align:start position:0%
+um how do we resolve this what's wrong
+ 
+
+ align:start position:0%
+um how do we resolve this what's wrong
+with this apparent Paradox of Russell's
+
+ align:start position:0%
+with this apparent Paradox of Russell's
+ 
+
+ align:start position:0%
+with this apparent Paradox of Russell's
+well um the Assumption was that W was a
+
+ align:start position:0%
+well um the Assumption was that W was a
+ 
+
+ align:start position:0%
+well um the Assumption was that W was a
+set and that turns out to be what we can
+
+ align:start position:0%
+set and that turns out to be what we can
+ 
+
+ align:start position:0%
+set and that turns out to be what we can
+doubt so the definition of w is that for
+
+ align:start position:0%
+doubt so the definition of w is that for
+ 
+
+ align:start position:0%
+doubt so the definition of w is that for
+all sets w s is in W if and only if s is
+
+ align:start position:0%
+all sets w s is in W if and only if s is
+ 
+
+ align:start position:0%
+all sets w s is in W if and only if s is
+not in s and we got a contradiction by
+
+ align:start position:0%
+not in s and we got a contradiction by
+ 
+
+ align:start position:0%
+not in s and we got a contradiction by
+saying okay um substitute W for S but
+
+ align:start position:0%
+saying okay um substitute W for S but
+ 
+
+ align:start position:0%
+saying okay um substitute W for S but
+that's allowed only if you believe that
+
+ align:start position:0%
+that's allowed only if you believe that
+ 
+
+ align:start position:0%
+that's allowed only if you believe that
+W is a set now it looks like it ought to
+
+ align:start position:0%
+W is a set now it looks like it ought to
+ 
+
+ align:start position:0%
+W is a set now it looks like it ought to
+be because it's certainly well defined
+
+ align:start position:0%
+be because it's certainly well defined
+ 
+
+ align:start position:0%
+be because it's certainly well defined
+by that
+
+ align:start position:0%
+by that
+ 
+
+ align:start position:0%
+by that
+formula uh but it was well understood at
+
+ align:start position:0%
+formula uh but it was well understood at
+ 
+
+ align:start position:0%
+formula uh but it was well understood at
+the time that that was the fix to the
+
+ align:start position:0%
+the time that that was the fix to the
+ 
+
+ align:start position:0%
+the time that that was the fix to the
+Paradox you just can't allow W to be a
+
+ align:start position:0%
+Paradox you just can't allow W to be a
+ 
+
+ align:start position:0%
+Paradox you just can't allow W to be a
+set um the problem was that W was
+
+ align:start position:0%
+set um the problem was that W was
+ 
+
+ align:start position:0%
+set um the problem was that W was
+acknowledged by everybody to be
+
+ align:start position:0%
+acknowledged by everybody to be
+ 
+
+ align:start position:0%
+acknowledged by everybody to be
+absolutely clearly defined
+
+ align:start position:0%
+absolutely clearly defined
+ 
+
+ align:start position:0%
+absolutely clearly defined
+mathematically it was this bunch of sets
+
+ align:start position:0%
+mathematically it was this bunch of sets
+ 
+
+ align:start position:0%
+mathematically it was this bunch of sets
+and yet we're going to say it's not a
+
+ align:start position:0%
+and yet we're going to say it's not a
+ 
+
+ align:start position:0%
+and yet we're going to say it's not a
+set well it's okay that will fix
+
+ align:start position:0%
+set well it's okay that will fix
+ 
+
+ align:start position:0%
+set well it's okay that will fix
+Russell's Paradox but it leaves us with
+
+ align:start position:0%
+Russell's Paradox but it leaves us with
+ 
+
+ align:start position:0%
+Russell's Paradox but it leaves us with
+a much bigger General philosophical
+
+ align:start position:0%
+a much bigger General philosophical
+ 
+
+ align:start position:0%
+a much bigger General philosophical
+question is when is a well-defined
+
+ align:start position:0%
+question is when is a well-defined
+ 
+
+ align:start position:0%
+question is when is a well-defined
+mathematical object a set and when isn't
+
+ align:start position:0%
+mathematical object a set and when isn't
+ 
+
+ align:start position:0%
+mathematical object a set and when isn't
+a set and that's what you need
+
+ align:start position:0%
+a set and that's what you need
+ 
+
+ align:start position:0%
+a set and that's what you need
+sophisticated rules for when is it that
+
+ align:start position:0%
+sophisticated rules for when is it that
+ 
+
+ align:start position:0%
+sophisticated rules for when is it that
+you're going to Define some collection
+
+ align:start position:0%
+you're going to Define some collection
+ 
+
+ align:start position:0%
+you're going to Define some collection
+of elements and you can be sure it's a
+
+ align:start position:0%
+of elements and you can be sure it's a
+ 
+
+ align:start position:0%
+of elements and you can be sure it's a
+set as opposed to something else called
+
+ align:start position:0%
+set as opposed to something else called
+ 
+
+ align:start position:0%
+set as opposed to something else called
+a class by the way uh which is uh
+
+ align:start position:0%
+a class by the way uh which is uh
+ 
+
+ align:start position:0%
+a class by the way uh which is uh
+basically something that's too big to be
+
+ align:start position:0%
+basically something that's too big to be
+ 
+
+ align:start position:0%
+basically something that's too big to be
+a set because if it was a set it would
+
+ align:start position:0%
+a set because if it was a set it would
+ 
+
+ align:start position:0%
+a set because if it was a set it would
+be uh it would contain itself and be
+
+ align:start position:0%
+be uh it would contain itself and be
+ 
+
+ align:start position:0%
+be uh it would contain itself and be
+circular and
+
+ align:start position:0%
+circular and
+ 
+
+ align:start position:0%
+circular and
+self-referential well there's no simple
+
+ align:start position:0%
+self-referential well there's no simple
+ 
+
+ align:start position:0%
+self-referential well there's no simple
+answer to this question about what
+
+ align:start position:0%
+answer to this question about what
+ 
+
+ align:start position:0%
+answer to this question about what
+things are sets and what are not sets
+
+ align:start position:0%
+things are sets and what are not sets
+ 
+
+ align:start position:0%
+things are sets and what are not sets
+but over uh time by the 1930s people had
+
+ align:start position:0%
+but over uh time by the 1930s people had
+ 
+
+ align:start position:0%
+but over uh time by the 1930s people had
+pretty much settled on an very
+
+ align:start position:0%
+pretty much settled on an very
+ 
+
+ align:start position:0%
+pretty much settled on an very
+economical and and persuasive set of
+
+ align:start position:0%
+economical and and persuasive set of
+ 
+
+ align:start position:0%
+economical and and persuasive set of
+axioms for set theory called the zuro
+
+ align:start position:0%
+axioms for set theory called the zuro
+ 
+
+ align:start position:0%
+axioms for set theory called the zuro
+Frankle set theory axioms
\ No newline at end of file
diff --git a/6b9AW6QxXt0.txt b/6b9AW6QxXt0.txt
new file mode 100644
index 0000000000000000000000000000000000000000..61cdb38050934850a3a4569391407f7a16e6ef2c
--- /dev/null
+++ b/6b9AW6QxXt0.txt
@@ -0,0 +1,2371 @@
+align:start position:0%
+ 
+okay uh this video is about one of the
+
+ align:start position:0%
+okay uh this video is about one of the
+ 
+
+ align:start position:0%
+okay uh this video is about one of the
+key applications of ordinary
+
+ align:start position:0%
+key applications of ordinary
+ 
+
+ align:start position:0%
+key applications of ordinary
+differential equations to electrical
+
+ align:start position:0%
+differential equations to electrical
+ 
+
+ align:start position:0%
+differential equations to electrical
+flow flow of currents in a in a network
+
+ align:start position:0%
+flow flow of currents in a in a network
+ 
+
+ align:start position:0%
+flow flow of currents in a in a network
+and so I drew a network a very simple
+
+ align:start position:0%
+and so I drew a network a very simple
+ 
+
+ align:start position:0%
+and so I drew a network a very simple
+Network it's just called an
+
+ align:start position:0%
+Network it's just called an
+ 
+
+ align:start position:0%
+Network it's just called an
+RLC loop it's only got one Loop so it's
+
+ align:start position:0%
+RLC loop it's only got one Loop so it's
+ 
+
+ align:start position:0%
+RLC loop it's only got one Loop so it's
+a really simple Network it's the r
+
+ align:start position:0%
+a really simple Network it's the r
+ 
+
+ align:start position:0%
+a really simple Network it's the r
+stands for a
+
+ align:start position:0%
+stands for a
+ 
+
+ align:start position:0%
+stands for a
+resistance to the flow the L stands for
+
+ align:start position:0%
+resistance to the flow the L stands for
+ 
+
+ align:start position:0%
+resistance to the flow the L stands for
+an
+
+ align:start position:0%
+an
+ 
+
+ align:start position:0%
+an
+inductance and the C is the capacitance
+
+ align:start position:0%
+inductance and the C is the capacitance
+ 
+
+ align:start position:0%
+inductance and the C is the capacitance
+those are the three elements of a simple
+
+ align:start position:0%
+those are the three elements of a simple
+ 
+
+ align:start position:0%
+those are the three elements of a simple
+linear constant
+
+ align:start position:0%
+linear constant
+ 
+
+ align:start position:0%
+linear constant
+coefficient uh uh problem associated
+
+ align:start position:0%
+coefficient uh uh problem associated
+ 
+
+ align:start position:0%
+coefficient uh uh problem associated
+with one Loop and then there's a switch
+
+ align:start position:0%
+with one Loop and then there's a switch
+ 
+
+ align:start position:0%
+with one Loop and then there's a switch
+which I'll close and the flow will begin
+
+ align:start position:0%
+which I'll close and the flow will begin
+ 
+
+ align:start position:0%
+which I'll close and the flow will begin
+and there's a voltage source or like a
+
+ align:start position:0%
+and there's a voltage source or like a
+ 
+
+ align:start position:0%
+and there's a voltage source or like a
+battery that uh or maybe
+
+ align:start position:0%
+battery that uh or maybe
+ 
+
+ align:start position:0%
+battery that uh or maybe
+let's make it an let's make this
+
+ align:start position:0%
+let's make it an let's make this
+ 
+
+ align:start position:0%
+let's make it an let's make this
+alternating current so the voltage
+
+ align:start position:0%
+alternating current so the voltage
+ 
+
+ align:start position:0%
+alternating current so the voltage
+source will be uh some voltage times an
+
+ align:start position:0%
+source will be uh some voltage times an
+ 
+
+ align:start position:0%
+source will be uh some voltage times an
+e to the I Omega
+
+ align:start position:0%
+e to the I Omega
+ 
+
+ align:start position:0%
+e to the I Omega
+T so we're we're going to have
+
+ align:start position:0%
+T so we're we're going to have
+ 
+
+ align:start position:0%
+T so we're we're going to have
+alternating current and the question is
+
+ align:start position:0%
+alternating current and the question is
+ 
+
+ align:start position:0%
+alternating current and the question is
+what
+
+ align:start position:0%
+what
+ 
+
+ align:start position:0%
+what
+is the current the current will we have
+
+ align:start position:0%
+is the current the current will we have
+ 
+
+ align:start position:0%
+is the current the current will we have
+to find the current I so the current is
+
+ align:start position:0%
+to find the current I so the current is
+ 
+
+ align:start position:0%
+to find the current I so the current is
+I of
+
+ align:start position:0%
+I of
+ 
+
+ align:start position:0%
+I of
+T is the
+
+ align:start position:0%
+T is the
+ 
+
+ align:start position:0%
+T is the
+current going around the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+loop and we so our differential equation
+
+ align:start position:0%
+loop and we so our differential equation
+ 
+
+ align:start position:0%
+loop and we so our differential equation
+will have that unknown I of T rather
+
+ align:start position:0%
+will have that unknown I of T rather
+ 
+
+ align:start position:0%
+will have that unknown I of T rather
+than my usual y I'm going to use I for
+
+ align:start position:0%
+than my usual y I'm going to use I for
+ 
+
+ align:start position:0%
+than my usual y I'm going to use I for
+current okay again this is an
+
+ align:start position:0%
+current okay again this is an
+ 
+
+ align:start position:0%
+current okay again this is an
+RLC Loop that
+
+ align:start position:0%
+RLC Loop that
+ 
+
+ align:start position:0%
+RLC Loop that
+everybody has to
+
+ align:start position:0%
+everybody has to
+ 
+
+ align:start position:0%
+everybody has to
+understand as in in the in Electrical uh
+
+ align:start position:0%
+understand as in in the in Electrical uh
+ 
+
+ align:start position:0%
+understand as in in the in Electrical uh
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+engineering okay so I'm going to have a
+
+ align:start position:0%
+engineering okay so I'm going to have a
+ 
+
+ align:start position:0%
+engineering okay so I'm going to have a
+second order differential equation well
+
+ align:start position:0%
+second order differential equation well
+ 
+
+ align:start position:0%
+second order differential equation well
+you'll see what that equation is so the
+
+ align:start position:0%
+you'll see what that equation is so the
+ 
+
+ align:start position:0%
+you'll see what that equation is so the
+you remember ohms law that the voltage
+
+ align:start position:0%
+you remember ohms law that the voltage
+ 
+
+ align:start position:0%
+you remember ohms law that the voltage
+is the current times the resistance so
+
+ align:start position:0%
+is the current times the resistance so
+ 
+
+ align:start position:0%
+is the current times the resistance so
+this is this gives me a a a voltage
+
+ align:start position:0%
+this is this gives me a a a voltage
+ 
+
+ align:start position:0%
+this is this gives me a a a voltage
+across the resistor if the if the
+
+ align:start position:0%
+across the resistor if the if the
+ 
+
+ align:start position:0%
+across the resistor if the if the
+current is I and the resistance is R
+
+ align:start position:0%
+current is I and the resistance is R
+ 
+
+ align:start position:0%
+current is I and the resistance is R
+then the voltage drop from here to here
+
+ align:start position:0%
+then the voltage drop from here to here
+ 
+
+ align:start position:0%
+then the voltage drop from here to here
+is I * R so that's that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+term but now I I have uh also my current
+
+ align:start position:0%
+term but now I I have uh also my current
+ 
+
+ align:start position:0%
+term but now I I have uh also my current
+is changing it with time it's Al this is
+
+ align:start position:0%
+is changing it with time it's Al this is
+ 
+
+ align:start position:0%
+is changing it with time it's Al this is
+alternating current it's going up and
+
+ align:start position:0%
+alternating current it's going up and
+ 
+
+ align:start position:0%
+alternating current it's going up and
+down so there's a the current through is
+
+ align:start position:0%
+down so there's a the current through is
+ 
+
+ align:start position:0%
+down so there's a the current through is
+is also going through the inductance
+
+ align:start position:0%
+is also going through the inductance
+ 
+
+ align:start position:0%
+is also going through the inductance
+and there
+
+ align:start position:0%
+and there
+ 
+
+ align:start position:0%
+and there
+the voltage drop across the inductance
+
+ align:start position:0%
+the voltage drop across the inductance
+ 
+
+ align:start position:0%
+the voltage drop across the inductance
+has this form the derivative of of the
+
+ align:start position:0%
+has this form the derivative of of the
+ 
+
+ align:start position:0%
+has this form the derivative of of the
+current comes into it and in the
+
+ align:start position:0%
+current comes into it and in the
+ 
+
+ align:start position:0%
+current comes into it and in the
+capacitance which is building up charge
+
+ align:start position:0%
+capacitance which is building up charge
+ 
+
+ align:start position:0%
+capacitance which is building up charge
+the integral of the current comes in so
+
+ align:start position:0%
+the integral of the current comes in so
+ 
+
+ align:start position:0%
+the integral of the current comes in so
+that's that's the physical
+
+ align:start position:0%
+that's that's the physical
+ 
+
+ align:start position:0%
+that's that's the physical
+equation that expresses this voltage law
+
+ align:start position:0%
+equation that expresses this voltage law
+ 
+
+ align:start position:0%
+equation that expresses this voltage law
+which says that if I that around a
+
+ align:start position:0%
+which says that if I that around a
+ 
+
+ align:start position:0%
+which says that if I that around a
+closed loop this is a
+
+ align:start position:0%
+closed loop this is a
+ 
+
+ align:start position:0%
+closed loop this is a
+closed Loops are
+
+ align:start position:0%
+closed Loops are
+ 
+
+ align:start position:0%
+closed Loops are
+closed add to zero so I have four terms
+
+ align:start position:0%
+closed add to zero so I have four terms
+ 
+
+ align:start position:0%
+closed add to zero so I have four terms
+and they combine to give zero okay so
+
+ align:start position:0%
+and they combine to give zero okay so
+ 
+
+ align:start position:0%
+and they combine to give zero okay so
+there's an equation I'd like to
+
+ align:start position:0%
+there's an equation I'd like to
+ 
+
+ align:start position:0%
+there's an equation I'd like to
+solve and how am I going to solve that
+
+ align:start position:0%
+solve and how am I going to solve that
+ 
+
+ align:start position:0%
+solve and how am I going to solve that
+equation by the standard idea which
+
+ align:start position:0%
+equation by the standard idea which
+ 
+
+ align:start position:0%
+equation by the standard idea which
+applies when I have constant
+
+ align:start position:0%
+applies when I have constant
+ 
+
+ align:start position:0%
+applies when I have constant
+coefficients and I have a pure
+
+ align:start position:0%
+coefficients and I have a pure
+ 
+
+ align:start position:0%
+coefficients and I have a pure
+exponential
+
+ align:start position:0%
+exponential
+ 
+
+ align:start position:0%
+exponential
+uh forcing term I look for a solution
+
+ align:start position:0%
+uh forcing term I look for a solution
+ 
+
+ align:start position:0%
+uh forcing term I look for a solution
+that is a multiple of that exponential
+
+ align:start position:0%
+that is a multiple of that exponential
+ 
+
+ align:start position:0%
+that is a multiple of that exponential
+right the solution to differential
+
+ align:start position:0%
+right the solution to differential
+ 
+
+ align:start position:0%
+right the solution to differential
+equations with constant coefficients if
+
+ align:start position:0%
+equations with constant coefficients if
+ 
+
+ align:start position:0%
+equations with constant coefficients if
+they have an exponential forcing then
+
+ align:start position:0%
+they have an exponential forcing then
+ 
+
+ align:start position:0%
+they have an exponential forcing then
+the solution is
+
+ align:start position:0%
+the solution is
+ 
+
+ align:start position:0%
+the solution is
+some uh I equals some um shall I say
+
+ align:start position:0%
+some uh I equals some um shall I say
+ 
+
+ align:start position:0%
+some uh I equals some um shall I say
+w e to the I Omega t
+
+ align:start position:0%
+w e to the I Omega t
+ 
+
+ align:start position:0%
+w e to the I Omega t
+some multiple of the of the source gives
+
+ align:start position:0%
+some multiple of the of the source gives
+ 
+
+ align:start position:0%
+some multiple of the of the source gives
+me the solution to that differential
+
+ align:start position:0%
+me the solution to that differential
+ 
+
+ align:start position:0%
+me the solution to that differential
+equation well it's actually a
+
+ align:start position:0%
+equation well it's actually a
+ 
+
+ align:start position:0%
+equation well it's actually a
+differential integral equation I can
+
+ align:start position:0%
+differential integral equation I can
+ 
+
+ align:start position:0%
+differential integral equation I can
+make it a more familiar looking
+
+ align:start position:0%
+make it a more familiar looking
+ 
+
+ align:start position:0%
+make it a more familiar looking
+differential equation by taking the
+
+ align:start position:0%
+differential equation by taking the
+ 
+
+ align:start position:0%
+differential equation by taking the
+derivative of every term suppose I do
+
+ align:start position:0%
+derivative of every term suppose I do
+ 
+
+ align:start position:0%
+derivative of every term suppose I do
+that suppose I take the derivative of
+
+ align:start position:0%
+that suppose I take the derivative of
+ 
+
+ align:start position:0%
+that suppose I take the derivative of
+every term just to make it look really
+
+ align:start position:0%
+every term just to make it look really
+ 
+
+ align:start position:0%
+every term just to make it look really
+familiar that would be L * I prime right
+
+ align:start position:0%
+familiar that would be L * I prime right
+ 
+
+ align:start position:0%
+familiar that would be L * I prime right
+taking the Der ative of the derivative
+
+ align:start position:0%
+taking the Der ative of the derivative
+ 
+
+ align:start position:0%
+taking the Der ative of the derivative
+this would be
+
+ align:start position:0%
+this would be
+ 
+
+ align:start position:0%
+this would be
+r i Prime the derivative of the integral
+
+ align:start position:0%
+r i Prime the derivative of the integral
+ 
+
+ align:start position:0%
+r i Prime the derivative of the integral
+would be just I itself so I'd have 1 / c
+
+ align:start position:0%
+would be just I itself so I'd have 1 / c
+ 
+
+ align:start position:0%
+would be just I itself so I'd have 1 / c
+i and I would have the derivative here I
+
+ align:start position:0%
+i and I would have the derivative here I
+ 
+
+ align:start position:0%
+i and I would have the derivative here I
+Omega v e to the I Omega
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+T so it's just a standard second order
+
+ align:start position:0%
+T so it's just a standard second order
+ 
+
+ align:start position:0%
+T so it's just a standard second order
+constant coefficient linear differential
+
+ align:start position:0%
+constant coefficient linear differential
+ 
+
+ align:start position:0%
+constant coefficient linear differential
+equation equation and in fact you're if
+
+ align:start position:0%
+equation equation and in fact you're if
+ 
+
+ align:start position:0%
+equation equation and in fact you're if
+you were a mechanical engineer you would
+
+ align:start position:0%
+you were a mechanical engineer you would
+ 
+
+ align:start position:0%
+you were a mechanical engineer you would
+look at that and say well I don't know
+
+ align:start position:0%
+look at that and say well I don't know
+ 
+
+ align:start position:0%
+look at that and say well I don't know
+what LR and one over c stand for but I
+
+ align:start position:0%
+what LR and one over c stand for but I
+ 
+
+ align:start position:0%
+what LR and one over c stand for but I
+know that I should see the mass the
+
+ align:start position:0%
+know that I should see the mass the
+ 
+
+ align:start position:0%
+know that I should see the mass the
+damping and the stiffness there so we
+
+ align:start position:0%
+damping and the stiffness there so we
+ 
+
+ align:start position:0%
+damping and the stiffness there so we
+have a complete parallel between two
+
+ align:start position:0%
+have a complete parallel between two
+ 
+
+ align:start position:0%
+have a complete parallel between two
+important fields of engineering the
+
+ align:start position:0%
+important fields of engineering the
+ 
+
+ align:start position:0%
+important fields of engineering the
+electrical engineering with LR and 1
+
+ align:start position:0%
+electrical engineering with LR and 1
+ 
+
+ align:start position:0%
+electrical engineering with LR and 1
+over C mechanical engineering with
+
+ align:start position:0%
+over C mechanical engineering with
+ 
+
+ align:start position:0%
+over C mechanical engineering with
+m B for damping and K for stiffness and
+
+ align:start position:0%
+m B for damping and K for stiffness and
+ 
+
+ align:start position:0%
+m B for damping and K for stiffness and
+actually that parallel allows uh allowed
+
+ align:start position:0%
+actually that parallel allows uh allowed
+ 
+
+ align:start position:0%
+actually that parallel allows uh allowed
+analog
+
+ align:start position:0%
+analog
+ 
+
+ align:start position:0%
+analog
+computers which were which came before
+
+ align:start position:0%
+computers which were which came before
+ 
+
+ align:start position:0%
+computers which were which came before
+uh digital computers and lost out in
+
+ align:start position:0%
+uh digital computers and lost out in
+ 
+
+ align:start position:0%
+uh digital computers and lost out in
+that uh
+
+ align:start position:0%
+that uh
+ 
+
+ align:start position:0%
+that uh
+competition an analog computer was just
+
+ align:start position:0%
+competition an analog computer was just
+ 
+
+ align:start position:0%
+competition an analog computer was just
+solving this
+
+ align:start position:0%
+solving this
+ 
+
+ align:start position:0%
+solving this
+linear equation by actually a opposing
+
+ align:start position:0%
+linear equation by actually a opposing
+ 
+
+ align:start position:0%
+linear equation by actually a opposing
+the voltage and measuring the
+
+ align:start position:0%
+the voltage and measuring the
+ 
+
+ align:start position:0%
+the voltage and measuring the
+current so that an analog computer
+
+ align:start position:0%
+current so that an analog computer
+ 
+
+ align:start position:0%
+current so that an analog computer
+actually solved the equation by creating
+
+ align:start position:0%
+actually solved the equation by creating
+ 
+
+ align:start position:0%
+actually solved the equation by creating
+the model and measuring the answer okay
+
+ align:start position:0%
+the model and measuring the answer okay
+ 
+
+ align:start position:0%
+the model and measuring the answer okay
+but we're not creating an analog
+
+ align:start position:0%
+but we're not creating an analog
+ 
+
+ align:start position:0%
+but we're not creating an analog
+computer here we're just doing just
+
+ align:start position:0%
+computer here we're just doing just
+ 
+
+ align:start position:0%
+computer here we're just doing just
+doing differential equations so why
+
+ align:start position:0%
+doing differential equations so why
+ 
+
+ align:start position:0%
+doing differential equations so why
+don't I figure out what that W is so so
+
+ align:start position:0%
+don't I figure out what that W is so so
+ 
+
+ align:start position:0%
+don't I figure out what that W is so so
+what am I going to do as always as
+
+ align:start position:0%
+what am I going to do as always as
+ 
+
+ align:start position:0%
+what am I going to do as always as
+always I have this equation I have a
+
+ align:start position:0%
+always I have this equation I have a
+ 
+
+ align:start position:0%
+always I have this equation I have a
+pure exponential I look for a solution
+
+ align:start position:0%
+pure exponential I look for a solution
+ 
+
+ align:start position:0%
+pure exponential I look for a solution
+of that same form I plug it in and I get
+
+ align:start position:0%
+of that same form I plug it in and I get
+ 
+
+ align:start position:0%
+of that same form I plug it in and I get
+an equation for w that's exactly what
+
+ align:start position:0%
+an equation for w that's exactly what
+ 
+
+ align:start position:0%
+an equation for w that's exactly what
+I'll do on the next board I'll plug I'll
+
+ align:start position:0%
+I'll do on the next board I'll plug I'll
+ 
+
+ align:start position:0%
+I'll do on the next board I'll plug I'll
+put w e to the I Omega T into this
+
+ align:start position:0%
+put w e to the I Omega T into this
+ 
+
+ align:start position:0%
+put w e to the I Omega T into this
+equation and uh find W okay let's do
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+it okay maybe I bring that down just a
+
+ align:start position:0%
+it okay maybe I bring that down just a
+ 
+
+ align:start position:0%
+it okay maybe I bring that down just a
+hair and you can I'll do it here where
+
+ align:start position:0%
+hair and you can I'll do it here where
+ 
+
+ align:start position:0%
+hair and you can I'll do it here where
+you can watch me do it so I I have L *
+
+ align:start position:0%
+you can watch me do it so I I have L *
+ 
+
+ align:start position:0%
+you can watch me do it so I I have L *
+the derivative so I have
+
+ align:start position:0%
+the derivative so I have
+ 
+
+ align:start position:0%
+the derivative so I have
+L the derivative will bring down an i
+
+ align:start position:0%
+L the derivative will bring down an i
+ 
+
+ align:start position:0%
+L the derivative will bring down an i
+Omega
+
+ align:start position:0%
+Omega
+ 
+
+ align:start position:0%
+Omega
+L everything is going to multiply
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+W and match V that's
+
+ align:start position:0%
+W and match V that's
+ 
+
+ align:start position:0%
+W and match V that's
+that's when I put this into the equation
+
+ align:start position:0%
+that's when I put this into the equation
+ 
+
+ align:start position:0%
+that's when I put this into the equation
+the derivative is is an i Omega
+
+ align:start position:0%
+the derivative is is an i Omega
+ 
+
+ align:start position:0%
+the derivative is is an i Omega
+l w e to the I Omega T and it's matching
+
+ align:start position:0%
+l w e to the I Omega T and it's matching
+ 
+
+ align:start position:0%
+l w e to the I Omega T and it's matching
+v e to the I Omega T now what what
+
+ align:start position:0%
+v e to the I Omega T now what what
+ 
+
+ align:start position:0%
+v e to the I Omega T now what what
+happens when I
+
+ align:start position:0%
+happens when I
+ 
+
+ align:start position:0%
+happens when I
+put I in for that second term r i just
+
+ align:start position:0%
+put I in for that second term r i just
+ 
+
+ align:start position:0%
+put I in for that second term r i just
+get an r r * W * e to the I Omega t no
+
+ align:start position:0%
+get an r r * W * e to the I Omega t no
+ 
+
+ align:start position:0%
+get an r r * W * e to the I Omega t no
+problem and now finally a 1 / C the
+
+ align:start position:0%
+problem and now finally a 1 / C the
+ 
+
+ align:start position:0%
+problem and now finally a 1 / C the
+integral the integral of
+
+ align:start position:0%
+integral the integral of
+ 
+
+ align:start position:0%
+integral the integral of
+the exponential brings down
+
+ align:start position:0%
+the exponential brings down
+ 
+
+ align:start position:0%
+the exponential brings down
+oh let me put it in the denominator
+
+ align:start position:0%
+oh let me put it in the denominator
+ 
+
+ align:start position:0%
+oh let me put it in the denominator
+neatly brings down I divide by I Omega
+
+ align:start position:0%
+neatly brings down I divide by I Omega
+ 
+
+ align:start position:0%
+neatly brings down I divide by I Omega
+when I integrate e to the I Omega T I
+
+ align:start position:0%
+when I integrate e to the I Omega T I
+ 
+
+ align:start position:0%
+when I integrate e to the I Omega T I
+have a division by I
+
+ align:start position:0%
+have a division by I
+ 
+
+ align:start position:0%
+have a division by I
+Omega that's it that's it those are the
+
+ align:start position:0%
+Omega that's it that's it those are the
+ 
+
+ align:start position:0%
+Omega that's it that's it those are the
+three terms that come times W the
+
+ align:start position:0%
+three terms that come times W the
+ 
+
+ align:start position:0%
+three terms that come times W the
+unknown this is to
+
+ align:start position:0%
+unknown this is to
+ 
+
+ align:start position:0%
+unknown this is to
+find
+
+ align:start position:0%
+find
+ 
+
+ align:start position:0%
+find
+and of course we find it right away we
+
+ align:start position:0%
+and of course we find it right away we
+ 
+
+ align:start position:0%
+and of course we find it right away we
+find W is
+
+ align:start position:0%
+find W is
+ 
+
+ align:start position:0%
+find W is
+V over and now we're seeing this I Omega
+
+ align:start position:0%
+V over and now we're seeing this I Omega
+ 
+
+ align:start position:0%
+V over and now we're seeing this I Omega
+l+ R oh let me combine the I Omega the U
+
+ align:start position:0%
+l+ R oh let me combine the I Omega the U
+ 
+
+ align:start position:0%
+l+ R oh let me combine the I Omega the U
+combine the real part and the imaginary
+
+ align:start position:0%
+combine the real part and the imaginary
+ 
+
+ align:start position:0%
+combine the real part and the imaginary
+part the real part is
+
+ align:start position:0%
+part the real part is
+ 
+
+ align:start position:0%
+part the real part is
+r and the imaginary part is I Omega L
+
+ align:start position:0%
+r and the imaginary part is I Omega L
+ 
+
+ align:start position:0%
+r and the imaginary part is I Omega L
+minus 1/ I Omega
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+C
+
+ align:start position:0%
+C
+ 
+
+ align:start position:0%
+C
+straightforward and that has a
+
+ align:start position:0%
+straightforward and that has a
+ 
+
+ align:start position:0%
+straightforward and that has a
+name that is the
+
+ align:start position:0%
+name that is the
+ 
+
+ align:start position:0%
+name that is the
+resistance but when there's also a terms
+
+ align:start position:0%
+resistance but when there's also a terms
+ 
+
+ align:start position:0%
+resistance but when there's also a terms
+coming from an inductance and a
+
+ align:start position:0%
+coming from an inductance and a
+ 
+
+ align:start position:0%
+coming from an inductance and a
+capacitance then the whole thing is
+
+ align:start position:0%
+capacitance then the whole thing is
+ 
+
+ align:start position:0%
+capacitance then the whole thing is
+called the impedance so this whole thing
+
+ align:start position:0%
+called the impedance so this whole thing
+ 
+
+ align:start position:0%
+called the impedance so this whole thing
+this
+
+ align:start position:0%
+this
+ 
+
+ align:start position:0%
+this
+whole
+
+ align:start position:0%
+whole
+ 
+
+ align:start position:0%
+whole
+denominator is called the complex
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+impedance believe me all these ideas are
+
+ align:start position:0%
+impedance believe me all these ideas are
+ 
+
+ align:start position:0%
+impedance believe me all these ideas are
+so important that they're all all
+
+ align:start position:0%
+so important that they're all all
+ 
+
+ align:start position:0%
+so important that they're all all
+there's a whole vocabulary here but you
+
+ align:start position:0%
+there's a whole vocabulary here but you
+ 
+
+ align:start position:0%
+there's a whole vocabulary here but you
+you see we've done exactly the same
+
+ align:start position:0%
+you see we've done exactly the same
+ 
+
+ align:start position:0%
+you see we've done exactly the same
+thing for other constant coefficient
+
+ align:start position:0%
+thing for other constant coefficient
+ 
+
+ align:start position:0%
+thing for other constant coefficient
+equations we just called the
+
+ align:start position:0%
+equations we just called the
+ 
+
+ align:start position:0%
+equations we just called the
+coefficients ABC or maybe MB K and now
+
+ align:start position:0%
+coefficients ABC or maybe MB K and now
+ 
+
+ align:start position:0%
+coefficients ABC or maybe MB K and now
+we have slightly different letters but
+
+ align:start position:0%
+we have slightly different letters but
+ 
+
+ align:start position:0%
+we have slightly different letters but
+we don't have a new idea here the the
+
+ align:start position:0%
+we don't have a new idea here the the
+ 
+
+ align:start position:0%
+we don't have a new idea here the the
+idea is this one over that one over the
+
+ align:start position:0%
+idea is this one over that one over the
+ 
+
+ align:start position:0%
+idea is this one over that one over the
+impedance that will be the transfer
+
+ align:start position:0%
+impedance that will be the transfer
+ 
+
+ align:start position:0%
+impedance that will be the transfer
+function which multiplies the the the um
+
+ align:start position:0%
+function which multiplies the the the um
+ 
+
+ align:start position:0%
+function which multiplies the the the um
+source to give the to give the complex
+
+ align:start position:0%
+source to give the to give the complex
+ 
+
+ align:start position:0%
+source to give the to give the complex
+number W and W is a complex number I
+
+ align:start position:0%
+number W and W is a complex number I
+ 
+
+ align:start position:0%
+number W and W is a complex number I
+have to now think about that what's this
+
+ align:start position:0%
+have to now think about that what's this
+ 
+
+ align:start position:0%
+have to now think about that what's this
+and that impedance is always called
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Z so that we now have a new letter for
+
+ align:start position:0%
+Z so that we now have a new letter for
+ 
+
+ align:start position:0%
+Z so that we now have a new letter for
+the important quantity that shows up in
+
+ align:start position:0%
+the important quantity that shows up in
+ 
+
+ align:start position:0%
+the important quantity that shows up in
+the denominator there and again its real
+
+ align:start position:0%
+the denominator there and again its real
+ 
+
+ align:start position:0%
+the denominator there and again its real
+part is the resistance its imaginary
+
+ align:start position:0%
+part is the resistance its imaginary
+ 
+
+ align:start position:0%
+part is the resistance its imaginary
+part comes from L and C oh so we we can
+
+ align:start position:0%
+part comes from L and C oh so we we can
+ 
+
+ align:start position:0%
+part comes from L and C oh so we we can
+easily see how large what's the size of
+
+ align:start position:0%
+easily see how large what's the size of
+ 
+
+ align:start position:0%
+easily see how large what's the size of
+that
+
+ align:start position:0%
+that
+ 
+
+ align:start position:0%
+that
+impedance what's what's going to be the
+
+ align:start position:0%
+impedance what's what's going to be the
+ 
+
+ align:start position:0%
+impedance what's what's going to be the
+magnitude of this uh
+
+ align:start position:0%
+magnitude of this uh
+ 
+
+ align:start position:0%
+magnitude of this uh
+current we we want the size of that
+
+ align:start position:0%
+current we we want the size of that
+ 
+
+ align:start position:0%
+current we we want the size of that
+number V is the size of the voltage here
+
+ align:start position:0%
+number V is the size of the voltage here
+ 
+
+ align:start position:0%
+number V is the size of the voltage here
+is the size of the impedance and the
+
+ align:start position:0%
+is the size of the impedance and the
+ 
+
+ align:start position:0%
+is the size of the impedance and the
+answer will give us the size of w i I'm
+
+ align:start position:0%
+answer will give us the size of w i I'm
+ 
+
+ align:start position:0%
+answer will give us the size of w i I'm
+using size or magnitude to say that when
+
+ align:start position:0%
+using size or magnitude to say that when
+ 
+
+ align:start position:0%
+using size or magnitude to say that when
+I only do magnitudes you won't be seeing
+
+ align:start position:0%
+I only do magnitudes you won't be seeing
+ 
+
+ align:start position:0%
+I only do magnitudes you won't be seeing
+the phase lag so complex numbers like
+
+ align:start position:0%
+the phase lag so complex numbers like
+ 
+
+ align:start position:0%
+the phase lag so complex numbers like
+this complex number has a magnitude
+
+ align:start position:0%
+this complex number has a magnitude
+ 
+
+ align:start position:0%
+this complex number has a magnitude
+which we're about to write down and also
+
+ align:start position:0%
+which we're about to write down and also
+ 
+
+ align:start position:0%
+which we're about to write down and also
+it has a phase lag that tells that tells
+
+ align:start position:0%
+it has a phase lag that tells that tells
+ 
+
+ align:start position:0%
+it has a phase lag that tells that tells
+us how much is in the imaginary part and
+
+ align:start position:0%
+us how much is in the imaginary part and
+ 
+
+ align:start position:0%
+us how much is in the imaginary part and
+how much is in the real part but the
+
+ align:start position:0%
+how much is in the real part but the
+ 
+
+ align:start position:0%
+how much is in the real part but the
+magnitude is easy What's the magnitude
+
+ align:start position:0%
+magnitude is easy What's the magnitude
+ 
+
+ align:start position:0%
+magnitude is easy What's the magnitude
+of a complex number it's the real part
+
+ align:start position:0%
+of a complex number it's the real part
+ 
+
+ align:start position:0%
+of a complex number it's the real part
+squared and the imaginary part squared
+
+ align:start position:0%
+squared and the imaginary part squared
+ 
+
+ align:start position:0%
+squared and the imaginary part squared
+oh that should have been a plus there I
+
+ align:start position:0%
+oh that should have been a plus there I
+ 
+
+ align:start position:0%
+oh that should have been a plus there I
+think I don't know how it became a minus
+
+ align:start position:0%
+think I don't know how it became a minus
+ 
+
+ align:start position:0%
+think I don't know how it became a minus
+okay uh it will become a minus so I was
+
+ align:start position:0%
+okay uh it will become a minus so I was
+ 
+
+ align:start position:0%
+okay uh it will become a minus so I was
+thinking if I put the I up there let me
+
+ align:start position:0%
+thinking if I put the I up there let me
+ 
+
+ align:start position:0%
+thinking if I put the I up there let me
+show you what I'm saying the imaginary
+
+ align:start position:0%
+show you what I'm saying the imaginary
+ 
+
+ align:start position:0%
+show you what I'm saying the imaginary
+part is Omega
+
+ align:start position:0%
+part is Omega
+ 
+
+ align:start position:0%
+part is Omega
+L minus 1 over Omega
+
+ align:start position:0%
+L minus 1 over Omega
+ 
+
+ align:start position:0%
+L minus 1 over Omega
+C what I'm saying is that if I put the I
+
+ align:start position:0%
+C what I'm saying is that if I put the I
+ 
+
+ align:start position:0%
+C what I'm saying is that if I put the I
+up there
+
+ align:start position:0%
+up there
+ 
+
+ align:start position:0%
+up there
+then 1 over I is minus I that's the
+
+ align:start position:0%
+then 1 over I is minus I that's the
+ 
+
+ align:start position:0%
+then 1 over I is minus I that's the
+brilliant uh step I just took there so
+
+ align:start position:0%
+brilliant uh step I just took there so
+ 
+
+ align:start position:0%
+brilliant uh step I just took there so
+all that squar
+
+ align:start position:0%
+all that squar
+ 
+
+ align:start position:0%
+all that squar
+are you okay with that it's the
+
+ align:start position:0%
+are you okay with that it's the
+ 
+
+ align:start position:0%
+are you okay with that it's the
+imaginary it's the real part squared
+
+ align:start position:0%
+imaginary it's the real part squared
+ 
+
+ align:start position:0%
+imaginary it's the real part squared
+which is the resistance and this
+
+ align:start position:0%
+which is the resistance and this
+ 
+
+ align:start position:0%
+which is the resistance and this
+combination gives the imaginary part we
+
+ align:start position:0%
+combination gives the imaginary part we
+ 
+
+ align:start position:0%
+combination gives the imaginary part we
+square that that's maybe called the
+
+ align:start position:0%
+square that that's maybe called the
+ 
+
+ align:start position:0%
+square that that's maybe called the
+reactants and the sum of those squares
+
+ align:start position:0%
+reactants and the sum of those squares
+ 
+
+ align:start position:0%
+reactants and the sum of those squares
+is the impedance squared the
+
+ align:start position:0%
+is the impedance squared the
+ 
+
+ align:start position:0%
+is the impedance squared the
+magnitude okay so that's
+
+ align:start position:0%
+magnitude okay so that's
+ 
+
+ align:start position:0%
+magnitude okay so that's
+uh we have essentially successfully
+
+ align:start position:0%
+uh we have essentially successfully
+ 
+
+ align:start position:0%
+uh we have essentially successfully
+solved a uh second order constant
+
+ align:start position:0%
+solved a uh second order constant
+ 
+
+ align:start position:0%
+solved a uh second order constant
+coefficient single equation for the
+
+ align:start position:0%
+coefficient single equation for the
+ 
+
+ align:start position:0%
+coefficient single equation for the
+current okay what to do now just let me
+
+ align:start position:0%
+current okay what to do now just let me
+ 
+
+ align:start position:0%
+current okay what to do now just let me
+add a little little bit
+
+ align:start position:0%
+add a little little bit
+ 
+
+ align:start position:0%
+add a little little bit
+more maybe a maybe just a
+
+ align:start position:0%
+more maybe a maybe just a
+ 
+
+ align:start position:0%
+more maybe a maybe just a
+comment that that video was about one
+
+ align:start position:0%
+comment that that video was about one
+ 
+
+ align:start position:0%
+comment that that video was about one
+Loop when I told Dr Mohler that one of
+
+ align:start position:0%
+Loop when I told Dr Mohler that one of
+ 
+
+ align:start position:0%
+Loop when I told Dr Mohler that one of
+the applications one of the real
+
+ align:start position:0%
+the applications one of the real
+ 
+
+ align:start position:0%
+the applications one of the real
+applications in this series of videos
+
+ align:start position:0%
+applications in this series of videos
+ 
+
+ align:start position:0%
+applications in this series of videos
+would be an RL C circuit his reply was
+
+ align:start position:0%
+would be an RL C circuit his reply was
+ 
+
+ align:start position:0%
+would be an RL C circuit his reply was
+an RLC circuit is not an application not
+
+ align:start position:0%
+an RLC circuit is not an application not
+ 
+
+ align:start position:0%
+an RLC circuit is not an application not
+a realistic application one Loop so what
+
+ align:start position:0%
+a realistic application one Loop so what
+ 
+
+ align:start position:0%
+a realistic application one Loop so what
+H how do we proceed with a full scale
+
+ align:start position:0%
+H how do we proceed with a full scale
+ 
+
+ align:start position:0%
+H how do we proceed with a full scale
+circuit with many nodes many resistors
+
+ align:start position:0%
+circuit with many nodes many resistors
+ 
+
+ align:start position:0%
+circuit with many nodes many resistors
+many conductors many many edges well we
+
+ align:start position:0%
+many conductors many many edges well we
+ 
+
+ align:start position:0%
+many conductors many many edges well we
+have a big decision to make and that's
+
+ align:start position:0%
+have a big decision to make and that's
+ 
+
+ align:start position:0%
+have a big decision to make and that's
+the comment I want to make they have a
+
+ align:start position:0%
+the comment I want to make they have a
+ 
+
+ align:start position:0%
+the comment I want to make they have a
+choice they can use Kirk off's current
+
+ align:start position:0%
+choice they can use Kirk off's current
+ 
+
+ align:start position:0%
+choice they can use Kirk off's current
+law at the
+
+ align:start position:0%
+law at the
+ 
+
+ align:start position:0%
+law at the
+nodes and solve for the voltages at
+
+ align:start position:0%
+nodes and solve for the voltages at
+ 
+
+ align:start position:0%
+nodes and solve for the voltages at
+those
+
+ align:start position:0%
+those
+ 
+
+ align:start position:0%
+those
+nodes or they can do as we did for one
+
+ align:start position:0%
+nodes or they can do as we did for one
+ 
+
+ align:start position:0%
+nodes or they can do as we did for one
+Loop use Kirk's voltage law around that
+
+ align:start position:0%
+Loop use Kirk's voltage law around that
+ 
+
+ align:start position:0%
+Loop use Kirk's voltage law around that
+one Loop which said that the total
+
+ align:start position:0%
+one Loop which said that the total
+ 
+
+ align:start position:0%
+one Loop which said that the total
+voltage that the currents in the loop
+
+ align:start position:0%
+voltage that the currents in the loop
+ 
+
+ align:start position:0%
+voltage that the currents in the loop
+gave a total voltage drop adding to zero
+
+ align:start position:0%
+gave a total voltage drop adding to zero
+ 
+
+ align:start position:0%
+gave a total voltage drop adding to zero
+so we we solved the current equation for
+
+ align:start position:0%
+so we we solved the current equation for
+ 
+
+ align:start position:0%
+so we we solved the current equation for
+the unknown I this is what we did for
+
+ align:start position:0%
+the unknown I this is what we did for
+ 
+
+ align:start position:0%
+the unknown I this is what we did for
+one Loop
+
+ align:start position:0%
+one Loop
+ 
+
+ align:start position:0%
+one Loop
+my message is just for a big system this
+
+ align:start position:0%
+my message is just for a big system this
+ 
+
+ align:start position:0%
+my message is just for a big system this
+is the winner so right writing down the
+
+ align:start position:0%
+is the winner so right writing down the
+ 
+
+ align:start position:0%
+is the winner so right writing down the
+equations in terms of Kirk off's current
+
+ align:start position:0%
+equations in terms of Kirk off's current
+ 
+
+ align:start position:0%
+equations in terms of Kirk off's current
+law that the currents at we get the the
+
+ align:start position:0%
+law that the currents at we get the the
+ 
+
+ align:start position:0%
+law that the currents at we get the the
+nodal picture the picture with an
+
+ align:start position:0%
+nodal picture the picture with an
+ 
+
+ align:start position:0%
+nodal picture the picture with an
+equation for every node instead of the
+
+ align:start position:0%
+equation for every node instead of the
+ 
+
+ align:start position:0%
+equation for every node instead of the
+picture for an equation for every Loop
+
+ align:start position:0%
+picture for an equation for every Loop
+ 
+
+ align:start position:0%
+picture for an equation for every Loop
+because it's not so easy to see which
+
+ align:start position:0%
+because it's not so easy to see which
+ 
+
+ align:start position:0%
+because it's not so easy to see which
+are the loops to consider or and which
+
+ align:start position:0%
+are the loops to consider or and which
+ 
+
+ align:start position:0%
+are the loops to consider or and which
+Loops are uh or combinations of other
+
+ align:start position:0%
+Loops are uh or combinations of other
+ 
+
+ align:start position:0%
+Loops are uh or combinations of other
+Loops so this becomes the linear algebra
+
+ align:start position:0%
+Loops so this becomes the linear algebra
+ 
+
+ align:start position:0%
+Loops so this becomes the linear algebra
+is the question and the linear algebra
+
+ align:start position:0%
+is the question and the linear algebra
+ 
+
+ align:start position:0%
+is the question and the linear algebra
+to get the loop picture independent and
+
+ align:start position:0%
+to get the loop picture independent and
+ 
+
+ align:start position:0%
+to get the loop picture independent and
+clear is more difficult than the node
+
+ align:start position:0%
+clear is more difficult than the node
+ 
+
+ align:start position:0%
+clear is more difficult than the node
+picture the node picture with the
+
+ align:start position:0%
+picture the node picture with the
+ 
+
+ align:start position:0%
+picture the node picture with the
+unknown uh
+
+ align:start position:0%
+unknown uh
+ 
+
+ align:start position:0%
+unknown uh
+voltages
+
+ align:start position:0%
+voltages
+ 
+
+ align:start position:0%
+voltages
+V on the at at the
+
+ align:start position:0%
+V on the at at the
+ 
+
+ align:start position:0%
+V on the at at the
+nodes uh is the good one and The Matrix
+
+ align:start position:0%
+nodes uh is the good one and The Matrix
+ 
+
+ align:start position:0%
+nodes uh is the good one and The Matrix
+that comes into that is the incidence
+
+ align:start position:0%
+that comes into that is the incidence
+ 
+
+ align:start position:0%
+that comes into that is the incidence
+Matrix it it connects uh nodes and edges
+
+ align:start position:0%
+Matrix it it connects uh nodes and edges
+ 
+
+ align:start position:0%
+Matrix it it connects uh nodes and edges
+it says how the network is put together
+
+ align:start position:0%
+it says how the network is put together
+ 
+
+ align:start position:0%
+it says how the network is put together
+and that Matrix I'll study with a little
+
+ align:start position:0%
+and that Matrix I'll study with a little
+ 
+
+ align:start position:0%
+and that Matrix I'll study with a little
+bit of linear algebra so that comes in a
+
+ align:start position:0%
+bit of linear algebra so that comes in a
+ 
+
+ align:start position:0%
+bit of linear algebra so that comes in a
+later video if you look for incidence
+
+ align:start position:0%
+later video if you look for incidence
+ 
+
+ align:start position:0%
+later video if you look for incidence
+matrices you'll see probably two videos
+
+ align:start position:0%
+matrices you'll see probably two videos
+ 
+
+ align:start position:0%
+matrices you'll see probably two videos
+about those very very important and
+
+ align:start position:0%
+about those very very important and
+ 
+
+ align:start position:0%
+about those very very important and
+beautiful matrices thank
+
+ align:start position:0%
+beautiful matrices thank
+ 
+
+ align:start position:0%
+beautiful matrices thank
+you
\ No newline at end of file
diff --git a/7c2bwfiDCgs.txt b/7c2bwfiDCgs.txt
new file mode 100644
index 0000000000000000000000000000000000000000..b175addb96e33bc5f66fa7e4982b05ad50448610
--- /dev/null
+++ b/7c2bwfiDCgs.txt
@@ -0,0 +1,123 @@
+align:start position:0%
+ 
+so I decided to uh focus on Italian that
+
+ align:start position:0%
+so I decided to uh focus on Italian that
+ 
+
+ align:start position:0%
+so I decided to uh focus on Italian that
+the students would have a chance to use
+
+ align:start position:0%
+the students would have a chance to use
+ 
+
+ align:start position:0%
+the students would have a chance to use
+every day um but being grammatically
+
+ align:start position:0%
+every day um but being grammatically
+ 
+
+ align:start position:0%
+every day um but being grammatically
+correct
+
+ align:start position:0%
+correct
+ 
+
+ align:start position:0%
+correct
+so it it's not like um we didn't discuss
+
+ align:start position:0%
+so it it's not like um we didn't discuss
+ 
+
+ align:start position:0%
+so it it's not like um we didn't discuss
+literature and when we did some readings
+
+ align:start position:0%
+literature and when we did some readings
+ 
+
+ align:start position:0%
+literature and when we did some readings
+it was very basic readings from example
+
+ align:start position:0%
+it was very basic readings from example
+ 
+
+ align:start position:0%
+it was very basic readings from example
+from um books from children for children
+
+ align:start position:0%
+from um books from children for children
+ 
+
+ align:start position:0%
+from um books from children for children
+um um the basic idea was to give them
+
+ align:start position:0%
+um um the basic idea was to give them
+ 
+
+ align:start position:0%
+um um the basic idea was to give them
+the tools to be able to have a basic um
+
+ align:start position:0%
+the tools to be able to have a basic um
+ 
+
+ align:start position:0%
+the tools to be able to have a basic um
+communication uh so when I was choosing
+
+ align:start position:0%
+communication uh so when I was choosing
+ 
+
+ align:start position:0%
+communication uh so when I was choosing
+the vocabulary I was choosing vocabulary
+
+ align:start position:0%
+the vocabulary I was choosing vocabulary
+ 
+
+ align:start position:0%
+the vocabulary I was choosing vocabulary
+that every Italian would
+
+ align:start position:0%
+that every Italian would
+ 
+
+ align:start position:0%
+that every Italian would
+use in the kitchen daily and outside the
+
+ align:start position:0%
+use in the kitchen daily and outside the
+ 
+
+ align:start position:0%
+use in the kitchen daily and outside the
+kitchen in uh um personal
+
+ align:start position:0%
+kitchen in uh um personal
+ 
+
+ align:start position:0%
+kitchen in uh um personal
+interactions
\ No newline at end of file
diff --git a/7q32Wnm4dEw.txt b/7q32Wnm4dEw.txt
new file mode 100644
index 0000000000000000000000000000000000000000..e19d64bae316ba6746fcbdfe12b16b22fea1d618
--- /dev/null
+++ b/7q32Wnm4dEw.txt
@@ -0,0 +1,2659 @@
+align:start position:0%
+ 
+the beginning of our analysis and still
+
+ align:start position:0%
+the beginning of our analysis and still
+ 
+
+ align:start position:0%
+the beginning of our analysis and still
+not solve differential equations but we
+
+ align:start position:0%
+not solve differential equations but we
+ 
+
+ align:start position:0%
+not solve differential equations but we
+will have now two particles a protein
+
+ align:start position:0%
+will have now two particles a protein
+ 
+
+ align:start position:0%
+will have now two particles a protein
+whose stories are going to be coordinate
+
+ align:start position:0%
+whose stories are going to be coordinate
+ 
+
+ align:start position:0%
+whose stories are going to be coordinate
+of the proton some index key for the
+
+ align:start position:0%
+of the proton some index key for the
+ 
+
+ align:start position:0%
+of the proton some index key for the
+protocol and momentum of the proton and
+
+ align:start position:0%
+protocol and momentum of the proton and
+ 
+
+ align:start position:0%
+protocol and momentum of the proton and
+there's an electron and there's the
+
+ align:start position:0%
+there's an electron and there's the
+ 
+
+ align:start position:0%
+there's an electron and there's the
+coordinates the three coordinates of the
+
+ align:start position:0%
+coordinates the three coordinates of the
+ 
+
+ align:start position:0%
+coordinates the three coordinates of the
+electron and the three components of the
+
+ align:start position:0%
+electron and the three components of the
+ 
+
+ align:start position:0%
+electron and the three components of the
+momentum of the electron and these are
+
+ align:start position:0%
+momentum of the electron and these are
+ 
+
+ align:start position:0%
+momentum of the electron and these are
+your canonical variables this means that
+
+ align:start position:0%
+your canonical variables this means that
+ 
+
+ align:start position:0%
+your canonical variables this means that
+the components of this object satisfy
+
+ align:start position:0%
+the components of this object satisfy
+ 
+
+ align:start position:0%
+the components of this object satisfy
+the standard commutation relations that
+
+ align:start position:0%
+the standard commutation relations that
+ 
+
+ align:start position:0%
+the standard commutation relations that
+is I have to write like this before they
+
+ align:start position:0%
+is I have to write like this before they
+ 
+
+ align:start position:0%
+is I have to write like this before they
+consider the coordinates of the problem
+
+ align:start position:0%
+consider the coordinates of the problem
+ 
+
+ align:start position:0%
+consider the coordinates of the problem
+the I component and the momentum of the
+
+ align:start position:0%
+the I component and the momentum of the
+ 
+
+ align:start position:0%
+the I component and the momentum of the
+problem the J component that's equal to
+
+ align:start position:0%
+problem the J component that's equal to
+ 
+
+ align:start position:0%
+problem the J component that's equal to
+I h-bar Delta I J
+
+ align:start position:0%
+I h-bar Delta I J
+ 
+
+ align:start position:0%
+I h-bar Delta I J
+you see we used to call for its x y&z
+
+ align:start position:0%
+you see we used to call for its x y&z
+ 
+
+ align:start position:0%
+you see we used to call for its x y&z
+and omega p h py PZ you could have
+
+ align:start position:0%
+and omega p h py PZ you could have
+ 
+
+ align:start position:0%
+and omega p h py PZ you could have
+called them x1 x2 x3 Omega P 1 P 2 P 3
+
+ align:start position:0%
+called them x1 x2 x3 Omega P 1 P 2 P 3
+ 
+
+ align:start position:0%
+called them x1 x2 x3 Omega P 1 P 2 P 3
+and in that way you can use a Kronecker
+
+ align:start position:0%
+and in that way you can use a Kronecker
+ 
+
+ align:start position:0%
+and in that way you can use a Kronecker
+Delta over here so this are the
+
+ align:start position:0%
+Delta over here so this are the
+ 
+
+ align:start position:0%
+Delta over here so this are the
+commutation relations of XS FPS but X
+
+ align:start position:0%
+commutation relations of XS FPS but X
+ 
+
+ align:start position:0%
+commutation relations of XS FPS but X
+and P for a proton so the proton has its
+
+ align:start position:0%
+and P for a proton so the proton has its
+ 
+
+ align:start position:0%
+and P for a proton so the proton has its
+X has its peak and it behaves like an X
+
+ align:start position:0%
+X has its peak and it behaves like an X
+ 
+
+ align:start position:0%
+X has its peak and it behaves like an X
+and P this time the electron has its X
+
+ align:start position:0%
+and P this time the electron has its X
+ 
+
+ align:start position:0%
+and P this time the electron has its X
+its p and also behaves the same way as
+
+ align:start position:0%
+its p and also behaves the same way as
+ 
+
+ align:start position:0%
+its p and also behaves the same way as
+Hornets
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+I see this is because X operator y
+
+ align:start position:0%
+I see this is because X operator y
+ 
+
+ align:start position:0%
+I see this is because X operator y
+operators Z operator you can call them X
+
+ align:start position:0%
+operators Z operator you can call them X
+ 
+
+ align:start position:0%
+operators Z operator you can call them X
+I operators with one two three
+
+ align:start position:0%
+I operators with one two three
+ 
+
+ align:start position:0%
+I operators with one two three
+the P X py PZ operators are better
+
+ align:start position:0%
+the P X py PZ operators are better
+ 
+
+ align:start position:0%
+the P X py PZ operators are better
+called P sub i with i running from 1 2 &
+
+ align:start position:0%
+called P sub i with i running from 1 2 &
+ 
+
+ align:start position:0%
+called P sub i with i running from 1 2 &
+3 and X be the first why the seconds
+
+ align:start position:0%
+3 and X be the first why the seconds
+ 
+
+ align:start position:0%
+3 and X be the first why the seconds
+even the left then the fact that the X
+
+ align:start position:0%
+even the left then the fact that the X
+ 
+
+ align:start position:0%
+even the left then the fact that the X
+just fails to compute with P X Y P Y Z
+
+ align:start position:0%
+just fails to compute with P X Y P Y Z
+ 
+
+ align:start position:0%
+just fails to compute with P X Y P Y Z
+first illumine with busy is X I PJ and
+
+ align:start position:0%
+first illumine with busy is X I PJ and
+ 
+
+ align:start position:0%
+first illumine with busy is X I PJ and
+call I h-bar Delta haiji and this is
+
+ align:start position:0%
+call I h-bar Delta haiji and this is
+ 
+
+ align:start position:0%
+call I h-bar Delta haiji and this is
+what I'm saying here this notation
+
+ align:start position:0%
+what I'm saying here this notation
+ 
+
+ align:start position:0%
+what I'm saying here this notation
+because there's too many subscripts
+
+ align:start position:0%
+because there's too many subscripts
+ 
+
+ align:start position:0%
+because there's too many subscripts
+there's a P for proto
+
+ align:start position:0%
+there's a P for proto
+ 
+
+ align:start position:0%
+there's a P for proto
+but there's an eye for the first second
+
+ align:start position:0%
+but there's an eye for the first second
+ 
+
+ align:start position:0%
+but there's an eye for the first second
+and third of all and there's the
+
+ align:start position:0%
+and third of all and there's the
+ 
+
+ align:start position:0%
+and third of all and there's the
+momentum of the proton which has 1 2 3
+
+ align:start position:0%
+momentum of the proton which has 1 2 3
+ 
+
+ align:start position:0%
+momentum of the proton which has 1 2 3
+components so that those are our
+
+ align:start position:0%
+components so that those are our
+ 
+
+ align:start position:0%
+components so that those are our
+dynamical variables and then when we try
+
+ align:start position:0%
+dynamical variables and then when we try
+ 
+
+ align:start position:0%
+dynamical variables and then when we try
+to solve this you have the issue of wave
+
+ align:start position:0%
+to solve this you have the issue of wave
+ 
+
+ align:start position:0%
+to solve this you have the issue of wave
+functions what happens to the wave
+
+ align:start position:0%
+functions what happens to the wave
+ 
+
+ align:start position:0%
+functions what happens to the wave
+function should I invent a wave function
+
+ align:start position:0%
+function should I invent a wave function
+ 
+
+ align:start position:0%
+function should I invent a wave function
+for the electrode and we function for
+
+ align:start position:0%
+for the electrode and we function for
+ 
+
+ align:start position:0%
+for the electrode and we function for
+the proto no that's not good you should
+
+ align:start position:0%
+the proto no that's not good you should
+ 
+
+ align:start position:0%
+the proto no that's not good you should
+invent a wave function for everybody
+
+ align:start position:0%
+invent a wave function for everybody
+ 
+
+ align:start position:0%
+invent a wave function for everybody
+which is a wave function that depends on
+
+ align:start position:0%
+which is a wave function that depends on
+ 
+
+ align:start position:0%
+which is a wave function that depends on
+the coordinates X of the electron and if
+
+ align:start position:0%
+the coordinates X of the electron and if
+ 
+
+ align:start position:0%
+the coordinates X of the electron and if
+you have just an electron you have a
+
+ align:start position:0%
+you have just an electron you have a
+ 
+
+ align:start position:0%
+you have just an electron you have a
+wave function of the
+
+ align:start position:0%
+wave function of the
+ 
+
+ align:start position:0%
+wave function of the
+the Knights of the leg and now wait
+
+ align:start position:0%
+the Knights of the leg and now wait
+ 
+
+ align:start position:0%
+the Knights of the leg and now wait
+function that depends on the coordinates
+
+ align:start position:0%
+function that depends on the coordinates
+ 
+
+ align:start position:0%
+function that depends on the coordinates
+of the probe and how would you normalize
+
+ align:start position:0%
+of the probe and how would you normalize
+ 
+
+ align:start position:0%
+of the probe and how would you normalize
+it well this thing times the cube X e XV
+
+ align:start position:0%
+it well this thing times the cube X e XV
+ 
+
+ align:start position:0%
+it well this thing times the cube X e XV
+q X P is the probability VP to find the
+
+ align:start position:0%
+q X P is the probability VP to find the
+ 
+
+ align:start position:0%
+q X P is the probability VP to find the
+electric around a little Q about the
+
+ align:start position:0%
+electric around a little Q about the
+ 
+
+ align:start position:0%
+electric around a little Q about the
+point XE and the proton around a little
+
+ align:start position:0%
+point XE and the proton around a little
+ 
+
+ align:start position:0%
+point XE and the proton around a little
+cube around X P and then if you want to
+
+ align:start position:0%
+cube around X P and then if you want to
+ 
+
+ align:start position:0%
+cube around X P and then if you want to
+see what is the probability to find the
+
+ align:start position:0%
+see what is the probability to find the
+ 
+
+ align:start position:0%
+see what is the probability to find the
+electron at some point regardless of the
+
+ align:start position:0%
+electron at some point regardless of the
+ 
+
+ align:start position:0%
+electron at some point regardless of the
+product you integrate over the whole
+
+ align:start position:0%
+product you integrate over the whole
+ 
+
+ align:start position:0%
+product you integrate over the whole
+proton and then you should just have a
+
+ align:start position:0%
+proton and then you should just have a
+ 
+
+ align:start position:0%
+proton and then you should just have a
+wave as if you integrate this size
+
+ align:start position:0%
+wave as if you integrate this size
+ 
+
+ align:start position:0%
+wave as if you integrate this size
+squared
+
+ align:start position:0%
+squared
+ 
+
+ align:start position:0%
+squared
+I'm sorry x squared if you integrate
+
+ align:start position:0%
+I'm sorry x squared if you integrate
+ 
+
+ align:start position:0%
+I'm sorry x squared if you integrate
+this size squared over the product
+
+ align:start position:0%
+this size squared over the product
+ 
+
+ align:start position:0%
+this size squared over the product
+you're left with some probability
+
+ align:start position:0%
+you're left with some probability
+ 
+
+ align:start position:0%
+you're left with some probability
+density for the electrode so this is the
+
+ align:start position:0%
+density for the electrode so this is the
+ 
+
+ align:start position:0%
+density for the electrode so this is the
+good thing about having more and more
+
+ align:start position:0%
+good thing about having more and more
+ 
+
+ align:start position:0%
+good thing about having more and more
+particles you still have just one wave
+
+ align:start position:0%
+particles you still have just one wave
+ 
+
+ align:start position:0%
+particles you still have just one wave
+function and one Schroedinger equation
+
+ align:start position:0%
+function and one Schroedinger equation
+ 
+
+ align:start position:0%
+function and one Schroedinger equation
+you have more Cardinal is just one way
+
+ align:start position:0%
+you have more Cardinal is just one way
+ 
+
+ align:start position:0%
+you have more Cardinal is just one way
+function that's why people eventually
+
+ align:start position:0%
+function that's why people eventually
+ 
+
+ align:start position:0%
+function that's why people eventually
+talk about the wave function of the
+
+ align:start position:0%
+talk about the wave function of the
+ 
+
+ align:start position:0%
+talk about the wave function of the
+universe as saying well the whole
+
+ align:start position:0%
+universe as saying well the whole
+ 
+
+ align:start position:0%
+universe as saying well the whole
+universe has one wave function for every
+
+ align:start position:0%
+universe has one wave function for every
+ 
+
+ align:start position:0%
+universe has one wave function for every
+atom for every molecule for every
+
+ align:start position:0%
+atom for every molecule for every
+ 
+
+ align:start position:0%
+atom for every molecule for every
+elementary particle it's just one wave
+
+ align:start position:0%
+elementary particle it's just one wave
+ 
+
+ align:start position:0%
+elementary particle it's just one wave
+function that's nice about the Cheniere
+
+ align:start position:0%
+function that's nice about the Cheniere
+ 
+
+ align:start position:0%
+function that's nice about the Cheniere
+equation and ok so we have this and what
+
+ align:start position:0%
+equation and ok so we have this and what
+ 
+
+ align:start position:0%
+equation and ok so we have this and what
+is the Hamiltonian the Hamiltonian is
+
+ align:start position:0%
+is the Hamiltonian the Hamiltonian is
+ 
+
+ align:start position:0%
+is the Hamiltonian the Hamiltonian is
+the kinetic energy associated to the
+
+ align:start position:0%
+the kinetic energy associated to the
+ 
+
+ align:start position:0%
+the kinetic energy associated to the
+proton close the kinetic energy
+
+ align:start position:0%
+proton close the kinetic energy
+ 
+
+ align:start position:0%
+proton close the kinetic energy
+associated to the electron plus the
+
+ align:start position:0%
+associated to the electron plus the
+ 
+
+ align:start position:0%
+associated to the electron plus the
+potential energy which is depends of the
+
+ align:start position:0%
+potential energy which is depends of the
+ 
+
+ align:start position:0%
+potential energy which is depends of the
+distance between the electron and the
+
+ align:start position:0%
+distance between the electron and the
+ 
+
+ align:start position:0%
+distance between the electron and the
+pro and then you can write a
+
+ align:start position:0%
+pro and then you can write a
+ 
+
+ align:start position:0%
+pro and then you can write a
+differential equation the Schrodinger
+
+ align:start position:0%
+differential equation the Schrodinger
+ 
+
+ align:start position:0%
+differential equation the Schrodinger
+equation and the P of the proton would
+
+ align:start position:0%
+equation and the P of the proton would
+ 
+
+ align:start position:0%
+equation and the P of the proton would
+be thought as maybe X of the problem and
+
+ align:start position:0%
+be thought as maybe X of the problem and
+ 
+
+ align:start position:0%
+be thought as maybe X of the problem and
+the P of the Elector would be like DDX
+
+ align:start position:0%
+the P of the Elector would be like DDX
+ 
+
+ align:start position:0%
+the P of the Elector would be like DDX
+of the electric and that differential
+
+ align:start position:0%
+of the electric and that differential
+ 
+
+ align:start position:0%
+of the electric and that differential
+equation would make sense so what is our
+
+ align:start position:0%
+equation would make sense so what is our
+ 
+
+ align:start position:0%
+equation would make sense so what is our
+problem solving that we have can think
+
+ align:start position:0%
+problem solving that we have can think
+ 
+
+ align:start position:0%
+problem solving that we have can think
+in some way as a potential or a
+
+ align:start position:0%
+in some way as a potential or a
+ 
+
+ align:start position:0%
+in some way as a potential or a
+Schrodinger equation that involves just
+
+ align:start position:0%
+Schrodinger equation that involves just
+ 
+
+ align:start position:0%
+Schrodinger equation that involves just
+some distance that separates the
+
+ align:start position:0%
+some distance that separates the
+ 
+
+ align:start position:0%
+some distance that separates the
+particles and some equation for the rest
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so we have to change various so what is
+
+ align:start position:0%
+so we have to change various so what is
+ 
+
+ align:start position:0%
+so we have to change various so what is
+the change of variables motivate some of
+
+ align:start position:0%
+the change of variables motivate some of
+ 
+
+ align:start position:0%
+the change of variables motivate some of
+that well we have 42 pairs of canonical
+
+ align:start position:0%
+that well we have 42 pairs of canonical
+ 
+
+ align:start position:0%
+that well we have 42 pairs of canonical
+variables we have the proton canonical
+
+ align:start position:0%
+variables we have the proton canonical
+ 
+
+ align:start position:0%
+variables we have the proton canonical
+variables X and P of the proto and the
+
+ align:start position:0%
+variables X and P of the proto and the
+ 
+
+ align:start position:0%
+variables X and P of the proto and the
+electron canonical variables it should
+
+ align:start position:0%
+electron canonical variables it should
+ 
+
+ align:start position:0%
+electron canonical variables it should
+be of the electron so how can we have
+
+ align:start position:0%
+be of the electron so how can we have
+ 
+
+ align:start position:0%
+be of the electron so how can we have
+different kind of variables that will
+
+ align:start position:0%
+different kind of variables that will
+ 
+
+ align:start position:0%
+different kind of variables that will
+lead to a more interesting thing up we
+
+ align:start position:0%
+lead to a more interesting thing up we
+ 
+
+ align:start position:0%
+lead to a more interesting thing up we
+can imagine that maybe we should define
+
+ align:start position:0%
+can imagine that maybe we should define
+ 
+
+ align:start position:0%
+can imagine that maybe we should define
+a new X that is the difference for which
+
+ align:start position:0%
+a new X that is the difference for which
+ 
+
+ align:start position:0%
+a new X that is the difference for which
+of the magnitude of that X will be what
+
+ align:start position:0%
+of the magnitude of that X will be what
+ 
+
+ align:start position:0%
+of the magnitude of that X will be what
+we call our and that's true but it's not
+
+ align:start position:0%
+we call our and that's true but it's not
+ 
+
+ align:start position:0%
+we call our and that's true but it's not
+so easy to do that from the beginning so
+
+ align:start position:0%
+so easy to do that from the beginning so
+ 
+
+ align:start position:0%
+so easy to do that from the beginning so
+let's try to do what most people would
+
+ align:start position:0%
+let's try to do what most people would
+ 
+
+ align:start position:0%
+let's try to do what most people would
+do from experience and say I know
+
+ align:start position:0%
+do from experience and say I know
+ 
+
+ align:start position:0%
+do from experience and say I know
+there's something simple about a system
+
+ align:start position:0%
+there's something simple about a system
+ 
+
+ align:start position:0%
+there's something simple about a system
+of doing the rapping valley's center of
+
+ align:start position:0%
+of doing the rapping valley's center of
+ 
+
+ align:start position:0%
+of doing the rapping valley's center of
+mass if the center of mass moves with
+
+ align:start position:0%
+mass if the center of mass moves with
+ 
+
+ align:start position:0%
+mass if the center of mass moves with
+constant velocity that's what it does
+
+ align:start position:0%
+constant velocity that's what it does
+ 
+
+ align:start position:0%
+constant velocity that's what it does
+always so if classical notions of how
+
+ align:start position:0%
+always so if classical notions of how
+ 
+
+ align:start position:0%
+always so if classical notions of how
+you treat to body system can be used
+
+ align:start position:0%
+you treat to body system can be used
+ 
+
+ align:start position:0%
+you treat to body system can be used
+with prong setting we should be able to
+
+ align:start position:0%
+with prong setting we should be able to
+ 
+
+ align:start position:0%
+with prong setting we should be able to
+define a new quantum coordinate
+
+ align:start position:0%
+define a new quantum coordinate
+ 
+
+ align:start position:0%
+define a new quantum coordinate
+associated to the center of mass and
+
+ align:start position:0%
+associated to the center of mass and
+ 
+
+ align:start position:0%
+associated to the center of mass and
+then the quantum momentum associated
+
+ align:start position:0%
+then the quantum momentum associated
+ 
+
+ align:start position:0%
+then the quantum momentum associated
+percent and the center of mass of
+
+ align:start position:0%
+percent and the center of mass of
+ 
+
+ align:start position:0%
+percent and the center of mass of
+momentum is always the sum of the
+
+ align:start position:0%
+momentum is always the sum of the
+ 
+
+ align:start position:0%
+momentum is always the sum of the
+momenta so we will define a key a
+
+ align:start position:0%
+momenta so we will define a key a
+ 
+
+ align:start position:0%
+momenta so we will define a key a
+capital P a over made pieces will be
+
+ align:start position:0%
+capital P a over made pieces will be
+ 
+
+ align:start position:0%
+capital P a over made pieces will be
+always here
+
+ align:start position:0%
+always here
+ 
+
+ align:start position:0%
+always here
+supposed to have in for this for the
+
+ align:start position:0%
+supposed to have in for this for the
+ 
+
+ align:start position:0%
+supposed to have in for this for the
+little bar below this is the total P and
+
+ align:start position:0%
+little bar below this is the total P and
+ 
+
+ align:start position:0%
+little bar below this is the total P and
+it's going to be the time as the
+
+ align:start position:0%
+it's going to be the time as the
+ 
+
+ align:start position:0%
+it's going to be the time as the
+momentum of the proper flow the momentum
+
+ align:start position:0%
+momentum of the proper flow the momentum
+ 
+
+ align:start position:0%
+momentum of the proper flow the momentum
+of the electrons and now I want to
+
+ align:start position:0%
+of the electrons and now I want to
+ 
+
+ align:start position:0%
+of the electrons and now I want to
+define an X that goes with this P and by
+
+ align:start position:0%
+define an X that goes with this P and by
+ 
+
+ align:start position:0%
+define an X that goes with this P and by
+lad I need that this X must have a
+
+ align:start position:0%
+lad I need that this X must have a
+ 
+
+ align:start position:0%
+lad I need that this X must have a
+commutation relation with this speed
+
+ align:start position:0%
+commutation relation with this speed
+ 
+
+ align:start position:0%
+commutation relation with this speed
+that tells yes you are an X because X
+
+ align:start position:0%
+that tells yes you are an X because X
+ 
+
+ align:start position:0%
+that tells yes you are an X because X
+with P should be IH bar so whatever I
+
+ align:start position:0%
+with P should be IH bar so whatever I
+ 
+
+ align:start position:0%
+with P should be IH bar so whatever I
+define here that should happen now you
+
+ align:start position:0%
+define here that should happen now you
+ 
+
+ align:start position:0%
+define here that should happen now you
+can imagine that we usually do something
+
+ align:start position:0%
+can imagine that we usually do something
+ 
+
+ align:start position:0%
+can imagine that we usually do something
+like this we multiply each particle
+
+ align:start position:0%
+like this we multiply each particle
+ 
+
+ align:start position:0%
+like this we multiply each particle
+according to its mass so we're waiting
+
+ align:start position:0%
+according to its mass so we're waiting
+ 
+
+ align:start position:0%
+according to its mass so we're waiting
+the momentum associated up I'm sorry
+
+ align:start position:0%
+the momentum associated up I'm sorry
+ 
+
+ align:start position:0%
+the momentum associated up I'm sorry
+what are the positions XP x e associated
+
+ align:start position:0%
+what are the positions XP x e associated
+ 
+
+ align:start position:0%
+what are the positions XP x e associated
+to the mass and this of course would not
+
+ align:start position:0%
+to the mass and this of course would not
+ 
+
+ align:start position:0%
+to the mass and this of course would not
+have the right units doesn't have units
+
+ align:start position:0%
+have the right units doesn't have units
+ 
+
+ align:start position:0%
+have the right units doesn't have units
+of corn it so this is the center of mass
+
+ align:start position:0%
+of corn it so this is the center of mass
+ 
+
+ align:start position:0%
+of corn it so this is the center of mass
+so this will be center of mass quantum
+
+ align:start position:0%
+so this will be center of mass quantum
+ 
+
+ align:start position:0%
+so this will be center of mass quantum
+variables and in order to have unit you
+
+ align:start position:0%
+variables and in order to have unit you
+ 
+
+ align:start position:0%
+variables and in order to have unit you
+must divide by n mass so it's not too
+
+ align:start position:0%
+must divide by n mass so it's not too
+ 
+
+ align:start position:0%
+must divide by n mass so it's not too
+reasonable to put the sum of masses here
+
+ align:start position:0%
+reasonable to put the sum of masses here
+ 
+
+ align:start position:0%
+reasonable to put the sum of masses here
+that's how you define it
+
+ align:start position:0%
+that's how you define it
+ 
+
+ align:start position:0%
+that's how you define it
+away in classical mechanics and now we
+
+ align:start position:0%
+away in classical mechanics and now we
+ 
+
+ align:start position:0%
+away in classical mechanics and now we
+must ask is X with P the I component J
+
+ align:start position:0%
+must ask is X with P the I component J
+ 
+
+ align:start position:0%
+must ask is X with P the I component J
+component is it really people to our
+
+ align:start position:0%
+component is it really people to our
+ 
+
+ align:start position:0%
+component is it really people to our
+h-bar down and the answer I would say is
+
+ align:start position:0%
+h-bar down and the answer I would say is
+ 
+
+ align:start position:0%
+h-bar down and the answer I would say is
+yes because here let's do this one you
+
+ align:start position:0%
+yes because here let's do this one you
+ 
+
+ align:start position:0%
+yes because here let's do this one you
+would have MP x p i+ m e XE I over NP
+
+ align:start position:0%
+would have MP x p i+ m e XE I over NP
+ 
+
+ align:start position:0%
+would have MP x p i+ m e XE I over NP
+plus m e is it what you do one all the
+
+ align:start position:0%
+plus m e is it what you do one all the
+ 
+
+ align:start position:0%
+plus m e is it what you do one all the
+rest you should be able to do just
+
+ align:start position:0%
+rest you should be able to do just
+ 
+
+ align:start position:0%
+rest you should be able to do just
+without thinking up P on the other hand
+
+ align:start position:0%
+without thinking up P on the other hand
+ 
+
+ align:start position:0%
+without thinking up P on the other hand
+is P the momentum sub J plus the
+
+ align:start position:0%
+is P the momentum sub J plus the
+ 
+
+ align:start position:0%
+is P the momentum sub J plus the
+momentum of the electron sub J what is
+
+ align:start position:0%
+momentum of the electron sub J what is
+ 
+
+ align:start position:0%
+momentum of the electron sub J what is
+it equal to
+
+ align:start position:0%
+it equal to
+ 
+
+ align:start position:0%
+it equal to
+and then we say look from XP with
+
+ align:start position:0%
+and then we say look from XP with
+ 
+
+ align:start position:0%
+and then we say look from XP with
+momentum sub P yes they give me I h-bar
+
+ align:start position:0%
+momentum sub P yes they give me I h-bar
+ 
+
+ align:start position:0%
+momentum sub P yes they give me I h-bar
+Delta IJ but there will be I h-bar the
+
+ align:start position:0%
+Delta IJ but there will be I h-bar the
+ 
+
+ align:start position:0%
+Delta IJ but there will be I h-bar the
+first factor there will be an extra MP
+
+ align:start position:0%
+first factor there will be an extra MP
+ 
+
+ align:start position:0%
+first factor there will be an extra MP
+over MP plus m e so this contribution
+
+ align:start position:0%
+over MP plus m e so this contribution
+ 
+
+ align:start position:0%
+over MP plus m e so this contribution
+comes from the first term that only
+
+ align:start position:0%
+comes from the first term that only
+ 
+
+ align:start position:0%
+comes from the first term that only
+talks to the momentum of the proton
+
+ align:start position:0%
+talks to the momentum of the proton
+ 
+
+ align:start position:0%
+talks to the momentum of the proton
+doesn't talk to the momentum of the leg
+
+ align:start position:0%
+doesn't talk to the momentum of the leg
+ 
+
+ align:start position:0%
+doesn't talk to the momentum of the leg
+through and the second term for the
+
+ align:start position:0%
+through and the second term for the
+ 
+
+ align:start position:0%
+through and the second term for the
+coordinate of electron only talks to the
+
+ align:start position:0%
+coordinate of electron only talks to the
+ 
+
+ align:start position:0%
+coordinate of electron only talks to the
+momentum of
+
+ align:start position:0%
+momentum of
+ 
+
+ align:start position:0%
+momentum of
+the lectern and it does give you an I
+
+ align:start position:0%
+the lectern and it does give you an I
+ 
+
+ align:start position:0%
+the lectern and it does give you an I
+h-bar Delta IJ but this time will be
+
+ align:start position:0%
+h-bar Delta IJ but this time will be
+ 
+
+ align:start position:0%
+h-bar Delta IJ but this time will be
+with an M e / MP + M II and this factor
+
+ align:start position:0%
+with an M e / MP + M II and this factor
+ 
+
+ align:start position:0%
+with an M e / MP + M II and this factor
+is equal to 1 so yes we can box this
+
+ align:start position:0%
+is equal to 1 so yes we can box this
+ 
+
+ align:start position:0%
+is equal to 1 so yes we can box this
+this is a pair of quantum mechanical
+
+ align:start position:0%
+this is a pair of quantum mechanical
+ 
+
+ align:start position:0%
+this is a pair of quantum mechanical
+canonical variables they have the right
+
+ align:start position:0%
+canonical variables they have the right
+ 
+
+ align:start position:0%
+canonical variables they have the right
+commutator they have the right unit the
+
+ align:start position:0%
+commutator they have the right unit the
+ 
+
+ align:start position:0%
+commutator they have the right unit the
+right comity to write everything so next
+
+ align:start position:0%
+right comity to write everything so next
+ 
+
+ align:start position:0%
+right comity to write everything so next
+time when you see these you will say X
+
+ align:start position:0%
+time when you see these you will say X
+ 
+
+ align:start position:0%
+time when you see these you will say X
+with P you say X P with piece 1 XE with
+
+ align:start position:0%
+with P you say X P with piece 1 XE with
+ 
+
+ align:start position:0%
+with P you say X P with piece 1 XE with
+piece 1 and P + n - 1 yes it works
+
+ align:start position:0%
+piece 1 and P + n - 1 yes it works
+ 
+
+ align:start position:0%
+piece 1 and P + n - 1 yes it works
+you forget I h-bar Delta IJ was sort of
+
+ align:start position:0%
+you forget I h-bar Delta IJ was sort of
+ 
+
+ align:start position:0%
+you forget I h-bar Delta IJ was sort of
+clear that it will work try it up next
+
+ align:start position:0%
+clear that it will work try it up next
+ 
+
+ align:start position:0%
+clear that it will work try it up next
+we need the second pair of canonical
+
+ align:start position:0%
+we need the second pair of canonical
+ 
+
+ align:start position:0%
+we need the second pair of canonical
+variables so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so for the second pair it's reasonable
+
+ align:start position:0%
+so for the second pair it's reasonable
+ 
+
+ align:start position:0%
+so for the second pair it's reasonable
+to use the X that he anticipated so
+
+ align:start position:0%
+to use the X that he anticipated so
+ 
+
+ align:start position:0%
+to use the X that he anticipated so
+we'll have a relative for Nik eggs and I
+
+ align:start position:0%
+we'll have a relative for Nik eggs and I
+ 
+
+ align:start position:0%
+we'll have a relative for Nik eggs and I
+don't know how I call it X relative or
+
+ align:start position:0%
+don't know how I call it X relative or
+ 
+
+ align:start position:0%
+don't know how I call it X relative or
+know just little X little X will be
+
+ align:start position:0%
+know just little X little X will be
+ 
+
+ align:start position:0%
+know just little X little X will be
+defined as X of the electron electron
+
+ align:start position:0%
+defined as X of the electron electron
+ 
+
+ align:start position:0%
+defined as X of the electron electron
+minus X of the probe this is natural we
+
+ align:start position:0%
+minus X of the probe this is natural we
+ 
+
+ align:start position:0%
+minus X of the probe this is natural we
+want a little X like that already at
+
+ align:start position:0%
+want a little X like that already at
+ 
+
+ align:start position:0%
+want a little X like that already at
+this point you could be paralyzed with
+
+ align:start position:0%
+this point you could be paralyzed with
+ 
+
+ align:start position:0%
+this point you could be paralyzed with
+fear something could have gone wrong at
+
+ align:start position:0%
+fear something could have gone wrong at
+ 
+
+ align:start position:0%
+fear something could have gone wrong at
+this moment imagine if this X doesn't
+
+ align:start position:0%
+this moment imagine if this X doesn't
+ 
+
+ align:start position:0%
+this moment imagine if this X doesn't
+compute with this dies then it's all a
+
+ align:start position:0%
+compute with this dies then it's all a
+ 
+
+ align:start position:0%
+compute with this dies then it's all a
+disaster because this should be electron
+
+ align:start position:0%
+disaster because this should be electron
+ 
+
+ align:start position:0%
+disaster because this should be electron
+and proton commute with each other
+
+ align:start position:0%
+and proton commute with each other
+ 
+
+ align:start position:0%
+and proton commute with each other
+action of written there not only those
+
+ align:start position:0%
+action of written there not only those
+ 
+
+ align:start position:0%
+action of written there not only those
+are the commutation relations everything
+
+ align:start position:0%
+are the commutation relations everything
+ 
+
+ align:start position:0%
+are the commutation relations everything
+else is 0 any X of electron with a
+
+ align:start position:0%
+else is 0 any X of electron with a
+ 
+
+ align:start position:0%
+else is 0 any X of electron with a
+momentum of a proton is 0 that's why
+
+ align:start position:0%
+momentum of a proton is 0 that's why
+ 
+
+ align:start position:0%
+momentum of a proton is 0 that's why
+there are two independent pairs of
+
+ align:start position:0%
+there are two independent pairs of
+ 
+
+ align:start position:0%
+there are two independent pairs of
+dynamical variables a week and three in
+
+ align:start position:0%
+dynamical variables a week and three in
+ 
+
+ align:start position:0%
+dynamical variables a week and three in
+better beam and this is an independent
+
+ align:start position:0%
+better beam and this is an independent
+ 
+
+ align:start position:0%
+better beam and this is an independent
+pair of canonical variables so it better
+
+ align:start position:0%
+pair of canonical variables so it better
+ 
+
+ align:start position:0%
+pair of canonical variables so it better
+be that these eggs and whatever P I'm
+
+ align:start position:0%
+be that these eggs and whatever P I'm
+ 
+
+ align:start position:0%
+be that these eggs and whatever P I'm
+going to define here commute with these
+
+ align:start position:0%
+going to define here commute with these
+ 
+
+ align:start position:0%
+going to define here commute with these
+guys and as far as this eggs happy lead
+
+ align:start position:0%
+guys and as far as this eggs happy lead
+ 
+
+ align:start position:0%
+guys and as far as this eggs happy lead
+works out because excess commute with
+
+ align:start position:0%
+works out because excess commute with
+ 
+
+ align:start position:0%
+works out because excess commute with
+any excess here so this little X
+
+ align:start position:0%
+any excess here so this little X
+ 
+
+ align:start position:0%
+any excess here so this little X
+definitely from this with a little egg
+
+ align:start position:0%
+definitely from this with a little egg
+ 
+
+ align:start position:0%
+definitely from this with a little egg
+but the father who commutes with P could
+
+ align:start position:0%
+but the father who commutes with P could
+ 
+
+ align:start position:0%
+but the father who commutes with P could
+have killed it but it doesn't because of
+
+ align:start position:0%
+have killed it but it doesn't because of
+ 
+
+ align:start position:0%
+have killed it but it doesn't because of
+the minus sign one of the company
+
+ align:start position:0%
+the minus sign one of the company
+ 
+
+ align:start position:0%
+the minus sign one of the company
+of the little eggs with a capital P
+
+ align:start position:0%
+of the little eggs with a capital P
+ 
+
+ align:start position:0%
+of the little eggs with a capital P
+would give for the lek Fernand IH bar
+
+ align:start position:0%
+would give for the lek Fernand IH bar
+ 
+
+ align:start position:0%
+would give for the lek Fernand IH bar
+and for the program and minus IH bar the
+
+ align:start position:0%
+and for the program and minus IH bar the
+ 
+
+ align:start position:0%
+and for the program and minus IH bar the
+answer so all is good so far so this is
+
+ align:start position:0%
+answer so all is good so far so this is
+ 
+
+ align:start position:0%
+answer so all is good so far so this is
+so far so good
+
+ align:start position:0%
+so far so good
+ 
+
+ align:start position:0%
+so far so good
+commutes with capital X and capital P so
+
+ align:start position:0%
+commutes with capital X and capital P so
+ 
+
+ align:start position:0%
+commutes with capital X and capital P so
+now we have here something and we could
+
+ align:start position:0%
+now we have here something and we could
+ 
+
+ align:start position:0%
+now we have here something and we could
+put a number alpha P e minus beta P the
+
+ align:start position:0%
+put a number alpha P e minus beta P the
+ 
+
+ align:start position:0%
+put a number alpha P e minus beta P the
+proto and we all know what alpha and
+
+ align:start position:0%
+proto and we all know what alpha and
+ 
+
+ align:start position:0%
+proto and we all know what alpha and
+beta are but now we can more or less be
+
+ align:start position:0%
+beta are but now we can more or less be
+ 
+
+ align:start position:0%
+beta are but now we can more or less be
+confident oh I need that this momentum
+
+ align:start position:0%
+confident oh I need that this momentum
+ 
+
+ align:start position:0%
+confident oh I need that this momentum
+with this X give me one IH bar so that
+
+ align:start position:0%
+with this X give me one IH bar so that
+ 
+
+ align:start position:0%
+with this X give me one IH bar so that
+would put the condition alpha and beta
+
+ align:start position:0%
+would put the condition alpha and beta
+ 
+
+ align:start position:0%
+would put the condition alpha and beta
+in fact the condition that X I with P
+
+ align:start position:0%
+in fact the condition that X I with P
+ 
+
+ align:start position:0%
+in fact the condition that X I with P
+bar J give you I h-bar Delta I J you can
+
+ align:start position:0%
+bar J give you I h-bar Delta I J you can
+ 
+
+ align:start position:0%
+bar J give you I h-bar Delta I J you can
+imagine what it is is that alpha plus
+
+ align:start position:0%
+imagine what it is is that alpha plus
+ 
+
+ align:start position:0%
+imagine what it is is that alpha plus
+beta is equal to 1 and the condition
+
+ align:start position:0%
+beta is equal to 1 and the condition
+ 
+
+ align:start position:0%
+beta is equal to 1 and the condition
+that this momentum commute with the
+
+ align:start position:0%
+that this momentum commute with the
+ 
+
+ align:start position:0%
+that this momentum commute with the
+center of mass position which it can
+
+ align:start position:0%
+center of mass position which it can
+ 
+
+ align:start position:0%
+center of mass position which it can
+fail to do so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+how what can I give well of alpha of the
+
+ align:start position:0%
+how what can I give well of alpha of the
+ 
+
+ align:start position:0%
+how what can I give well of alpha of the
+P of the letter goes with M e so it's
+
+ align:start position:0%
+P of the letter goes with M e so it's
+ 
+
+ align:start position:0%
+P of the letter goes with M e so it's
+something like alpha M e minus beta M P
+
+ align:start position:0%
+something like alpha M e minus beta M P
+ 
+
+ align:start position:0%
+something like alpha M e minus beta M P
+is equal to zero
+
+ align:start position:0%
+is equal to zero
+ 
+
+ align:start position:0%
+is equal to zero
+and please of this commutator should be
+
+ align:start position:0%
+and please of this commutator should be
+ 
+
+ align:start position:0%
+and please of this commutator should be
+zero please make sure you know how to do
+
+ align:start position:0%
+zero please make sure you know how to do
+ 
+
+ align:start position:0%
+zero please make sure you know how to do
+this we can get those conditions and
+
+ align:start position:0%
+this we can get those conditions and
+ 
+
+ align:start position:0%
+this we can get those conditions and
+though maybe a little fast for you to
+
+ align:start position:0%
+though maybe a little fast for you to
+ 
+
+ align:start position:0%
+though maybe a little fast for you to
+just follow it up
+
+ align:start position:0%
+just follow it up
+ 
+
+ align:start position:0%
+just follow it up
+and so at this moment we can solve for
+
+ align:start position:0%
+and so at this moment we can solve for
+ 
+
+ align:start position:0%
+and so at this moment we can solve for
+alpha beta two equations so alpha is
+
+ align:start position:0%
+alpha beta two equations so alpha is
+ 
+
+ align:start position:0%
+alpha beta two equations so alpha is
+equal to NP over m e+ MP and beta is
+
+ align:start position:0%
+equal to NP over m e+ MP and beta is
+ 
+
+ align:start position:0%
+equal to NP over m e+ MP and beta is
+equal to m e / n e + NP and we have a
+
+ align:start position:0%
+equal to m e / n e + NP and we have a
+ 
+
+ align:start position:0%
+equal to m e / n e + NP and we have a
+pair of canonical variables as well here
+
+ align:start position:0%
+pair of canonical variables as well here
+ 
+
+ align:start position:0%
+pair of canonical variables as well here
+therefore the relative coordinate and
+
+ align:start position:0%
+therefore the relative coordinate and
+ 
+
+ align:start position:0%
+therefore the relative coordinate and
+the relative momentum in some sensors
+
+ align:start position:0%
+the relative momentum in some sensors
+ 
+
+ align:start position:0%
+the relative momentum in some sensors
+useful to be fine too simple
+
+ align:start position:0%
+useful to be fine too simple
+ 
+
+ align:start position:0%
+useful to be fine too simple
+newse mass and the MP / MP + MP and the
+
+ align:start position:0%
+newse mass and the MP / MP + MP and the
+ 
+
+ align:start position:0%
+newse mass and the MP / MP + MP and the
+total mass which is an e + MP in the
+
+ align:start position:0%
+total mass which is an e + MP in the
+ 
+
+ align:start position:0%
+total mass which is an e + MP in the
+case of a heavy proton the reduce mass
+
+ align:start position:0%
+case of a heavy proton the reduce mass
+ 
+
+ align:start position:0%
+case of a heavy proton the reduce mass
+the product is heavy compared with
+
+ align:start position:0%
+the product is heavy compared with
+ 
+
+ align:start position:0%
+the product is heavy compared with
+electron you can ignore the electron
+
+ align:start position:0%
+electron you can ignore the electron
+ 
+
+ align:start position:0%
+electron you can ignore the electron
+here cancel an e and the reduced mass is
+
+ align:start position:0%
+here cancel an e and the reduced mass is
+ 
+
+ align:start position:0%
+here cancel an e and the reduced mass is
+called this so with in terms of the
+
+ align:start position:0%
+called this so with in terms of the
+ 
+
+ align:start position:0%
+called this so with in terms of the
+reduced mass F is equal to MU / n E and
+
+ align:start position:0%
+reduced mass F is equal to MU / n E and
+ 
+
+ align:start position:0%
+reduced mass F is equal to MU / n E and
+beta is mu / MP those are unit free
+
+ align:start position:0%
+beta is mu / MP those are unit free
+ 
+
+ align:start position:0%
+beta is mu / MP those are unit free
+concerts so summarizing the second pair
+
+ align:start position:0%
+concerts so summarizing the second pair
+ 
+
+ align:start position:0%
+concerts so summarizing the second pair
+of canonical variables are X D minus x e
+
+ align:start position:0%
+of canonical variables are X D minus x e
+ 
+
+ align:start position:0%
+of canonical variables are X D minus x e
+minus X P and P equals mu P e / m e
+
+ align:start position:0%
+minus X P and P equals mu P e / m e
+ 
+
+ align:start position:0%
+minus X P and P equals mu P e / m e
+minus P sub P / MP
+
+ align:start position:0%
+minus P sub P / MP
+ 
+
+ align:start position:0%
+minus P sub P / MP
+[Applause]
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+all right so so last step that we're
+
+ align:start position:0%
+all right so so last step that we're
+ 
+
+ align:start position:0%
+all right so so last step that we're
+going to follow and after that we'll get
+
+ align:start position:0%
+going to follow and after that we'll get
+ 
+
+ align:start position:0%
+going to follow and after that we'll get
+the Hamiltonian and stop there we'll
+
+ align:start position:0%
+the Hamiltonian and stop there we'll
+ 
+
+ align:start position:0%
+the Hamiltonian and stop there we'll
+discuss solutions next time but though
+
+ align:start position:0%
+discuss solutions next time but though
+ 
+
+ align:start position:0%
+discuss solutions next time but though
+finally we have enough equations to
+
+ align:start position:0%
+finally we have enough equations to
+ 
+
+ align:start position:0%
+finally we have enough equations to
+solve for the momentum we have in the
+
+ align:start position:0%
+solve for the momentum we have in the
+ 
+
+ align:start position:0%
+solve for the momentum we have in the
+Hamiltonian in terms of the center of
+
+ align:start position:0%
+Hamiltonian in terms of the center of
+ 
+
+ align:start position:0%
+Hamiltonian in terms of the center of
+mass momentum and the relative momentum
+
+ align:start position:0%
+mass momentum and the relative momentum
+ 
+
+ align:start position:0%
+mass momentum and the relative momentum
+so from Equation star and double star
+
+ align:start position:0%
+so from Equation star and double star
+ 
+
+ align:start position:0%
+so from Equation star and double star
+here you can solve for this momentous of
+
+ align:start position:0%
+here you can solve for this momentous of
+ 
+
+ align:start position:0%
+here you can solve for this momentous of
+P of the proton will be equal to NP over
+
+ align:start position:0%
+P of the proton will be equal to NP over
+ 
+
+ align:start position:0%
+P of the proton will be equal to NP over
+m big momentum minus little momenta and
+
+ align:start position:0%
+m big momentum minus little momenta and
+ 
+
+ align:start position:0%
+m big momentum minus little momenta and
+P of the electron is an e over capital n
+
+ align:start position:0%
+P of the electron is an e over capital n
+ 
+
+ align:start position:0%
+P of the electron is an e over capital n
+big momentum plus little
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+well one more equation that we have to
+
+ align:start position:0%
+well one more equation that we have to
+ 
+
+ align:start position:0%
+well one more equation that we have to
+write and that's the key to the
+
+ align:start position:0%
+write and that's the key to the
+ 
+
+ align:start position:0%
+write and that's the key to the
+simplicity of all what we've done at
+
+ align:start position:0%
+simplicity of all what we've done at
+ 
+
+ align:start position:0%
+simplicity of all what we've done at
+this moment we have a very good physical
+
+ align:start position:0%
+this moment we have a very good physical
+ 
+
+ align:start position:0%
+this moment we have a very good physical
+insight into what we've done but we want
+
+ align:start position:0%
+insight into what we've done but we want
+ 
+
+ align:start position:0%
+insight into what we've done but we want
+to see the math collaborate and the good
+
+ align:start position:0%
+to see the math collaborate and the good
+ 
+
+ align:start position:0%
+to see the math collaborate and the good
+physical insight has been that center of
+
+ align:start position:0%
+physical insight has been that center of
+ 
+
+ align:start position:0%
+physical insight has been that center of
+mass motion should be independent of the
+
+ align:start position:0%
+mass motion should be independent of the
+ 
+
+ align:start position:0%
+mass motion should be independent of the
+relative motion and we have the right X
+
+ align:start position:0%
+relative motion and we have the right X
+ 
+
+ align:start position:0%
+relative motion and we have the right X
+so the thing that we have to compute is
+
+ align:start position:0%
+so the thing that we have to compute is
+ 
+
+ align:start position:0%
+so the thing that we have to compute is
+the first two terms in the Hamiltonian P
+
+ align:start position:0%
+the first two terms in the Hamiltonian P
+ 
+
+ align:start position:0%
+the first two terms in the Hamiltonian P
+of the proton squared over 2m of the
+
+ align:start position:0%
+of the proton squared over 2m of the
+ 
+
+ align:start position:0%
+of the proton squared over 2m of the
+proton plus P of the electron squared
+
+ align:start position:0%
+proton plus P of the electron squared
+ 
+
+ align:start position:0%
+proton plus P of the electron squared
+over two months of the electron so I
+
+ align:start position:0%
+over two months of the electron so I
+ 
+
+ align:start position:0%
+over two months of the electron so I
+have 1 over 2m of the proton and 1/2 m
+
+ align:start position:0%
+have 1 over 2m of the proton and 1/2 m
+ 
+
+ align:start position:0%
+have 1 over 2m of the proton and 1/2 m
+of the proton over capital and P minus P
+
+ align:start position:0%
+of the proton over capital and P minus P
+ 
+
+ align:start position:0%
+of the proton over capital and P minus P
+and plus 1 over 2m of the electron is
+
+ align:start position:0%
+and plus 1 over 2m of the electron is
+ 
+
+ align:start position:0%
+and plus 1 over 2m of the electron is
+squared M of the electron over capital M
+
+ align:start position:0%
+squared M of the electron over capital M
+ 
+
+ align:start position:0%
+squared M of the electron over capital M
+big P plus little P and the plus and
+
+ align:start position:0%
+big P plus little P and the plus and
+ 
+
+ align:start position:0%
+big P plus little P and the plus and
+minus are extremely reassuring because
+
+ align:start position:0%
+minus are extremely reassuring because
+ 
+
+ align:start position:0%
+minus are extremely reassuring because
+the cross terms at couple the two are
+
+ align:start position:0%
+the cross terms at couple the two are
+ 
+
+ align:start position:0%
+the cross terms at couple the two are
+going to banish you can see the cross
+
+ align:start position:0%
+going to banish you can see the cross
+ 
+
+ align:start position:0%
+going to banish you can see the cross
+term with a minus sign and P will cancel
+
+ align:start position:0%
+term with a minus sign and P will cancel
+ 
+
+ align:start position:0%
+term with a minus sign and P will cancel
+we will they will cancel so at the end
+
+ align:start position:0%
+we will they will cancel so at the end
+ 
+
+ align:start position:0%
+we will they will cancel so at the end
+of this little calculation that takes a
+
+ align:start position:0%
+of this little calculation that takes a
+ 
+
+ align:start position:0%
+of this little calculation that takes a
+couple of lines you get one over to
+
+ align:start position:0%
+couple of lines you get one over to
+ 
+
+ align:start position:0%
+couple of lines you get one over to
+capital M total center of mass of this
+
+ align:start position:0%
+capital M total center of mass of this
+ 
+
+ align:start position:0%
+capital M total center of mass of this
+squared plus one over to you
+
+ align:start position:0%
+squared plus one over to you
+ 
+
+ align:start position:0%
+squared plus one over to you
+little momentum squared this is a
+
+ align:start position:0%
+little momentum squared this is a
+ 
+
+ align:start position:0%
+little momentum squared this is a
+kinetic operator and then you say great
+
+ align:start position:0%
+kinetic operator and then you say great
+ 
+
+ align:start position:0%
+kinetic operator and then you say great
+success the kinetic energy now has
+
+ align:start position:0%
+success the kinetic energy now has
+ 
+
+ align:start position:0%
+success the kinetic energy now has
+separated into a center of mass
+
+ align:start position:0%
+separated into a center of mass
+ 
+
+ align:start position:0%
+separated into a center of mass
+contribution and a relative confident
+
+ align:start position:0%
+contribution and a relative confident
+ 
+
+ align:start position:0%
+contribution and a relative confident
+this will allow us now with a little
+
+ align:start position:0%
+this will allow us now with a little
+ 
+
+ align:start position:0%
+this will allow us now with a little
+step separated total Schrodinger
+
+ align:start position:0%
+step separated total Schrodinger
+ 
+
+ align:start position:0%
+step separated total Schrodinger
+equation into center of mass motion and
+
+ align:start position:0%
+equation into center of mass motion and
+ 
+
+ align:start position:0%
+equation into center of mass motion and
+relative motion and the relative motion
+
+ align:start position:0%
+relative motion and the relative motion
+ 
+
+ align:start position:0%
+relative motion and the relative motion
+will have the center of edge so we'll do
+
+ align:start position:0%
+will have the center of edge so we'll do
+ 
+
+ align:start position:0%
+will have the center of edge so we'll do
+the punchline next
\ No newline at end of file
diff --git a/8PScXRfu2po.txt b/8PScXRfu2po.txt
new file mode 100644
index 0000000000000000000000000000000000000000..4636950186637e0146b169a82775f980bf79161d
--- /dev/null
+++ b/8PScXRfu2po.txt
@@ -0,0 +1,3466 @@
+SPEAKER: The following content
+is provided under a Creative
+
+Commons license.
+
+Your support will help MIT
+OpenCourseWare continue to
+
+offer high quality educational
+resources for free.
+
+To make a donation, or to view
+additional material from
+
+hundreds of MIT courses, visit
+MIT OpenCourseWare at
+
+ocw.mit.edu.
+
+PROFESSOR: OK I want to review
+a little bit what we said
+
+about detection at the end of
+last hour, last hour and a
+
+half, because we were going
+through it relatively quickly.
+
+Detection is a very
+funny subject.
+
+Particularly the way that we
+do it here because we go
+
+through a bunch of very,
+very simple steps.
+
+Everything looks trivial--
+
+I hope it looks trivial-- as
+we go, at least after you
+
+think about it for awhile, and
+you work with it for awhile,
+
+you will come back and look at
+it and you will say, "yes, in
+
+fact that is trivial." Nothing
+when you look at it for the
+
+first time is trivial.
+
+And the kind of detection
+problems that we're
+
+interested in is--
+
+to start out with-- we want to
+look just at binary detection.
+
+We're sending a binary signal,
+it's going to go through some
+
+signal encoder, which is the
+kind of channel encoder we've
+
+been thinking about.
+
+It's going to go through a
+baseband modulator, a baseband
+
+to passband modulator.
+
+It's going to have white
+Gaussian noise, or some kind
+
+of noise, added to it.
+
+It's going to come out
+the other end.
+
+We come back from passband
+to baseband.
+
+We then go through a baseband
+demodulator.
+
+We then sample at that point.
+
+And, the point is, when you're
+all done with all of that,
+
+what you've done is you've
+started out sending either
+
+plus a or minus a as a one-
+dimensional numerical signal.
+
+And when you're all through,
+there's some one- dimensional
+
+number that comes out, v. And
+on the basis of that one-
+
+dimensional number, v, you're
+supposed to guess whether the
+
+output is zero or one.
+
+Now, one of the things that
+we're doing right now is we're
+
+simplifying the problem in the
+sense that we're not looking
+
+at a sequence of inputs coming
+in, and we're not looking at a
+
+sequence of outputs
+coming out.
+
+We're only looking at a single
+input coming in.
+
+In other words, you build this
+piece of communication
+
+equipment, you get it all tuned
+up, you get it into
+
+steady state.
+
+You send one bit.
+
+You receive something.
+
+You try to guess at the
+receiver, what was sent.
+
+And at that point you tear the
+whole thing down and you wait
+
+a year until you've set
+it up perfectly again.
+
+You send another bit.
+
+And we're not going to worry at
+all about what happens with
+
+the sequence, we're only
+going to worry about
+
+this one shot problem.
+
+You sort of have some kind of
+clue that if you send the
+
+whole sequence of bits, in a
+system like this, and you
+
+don't have intersymbol
+interference, and the noise is
+
+white, so it's sort of
+independent from time to time.
+
+You sort of have a clue that
+you're going to get the same
+
+answer whether you send the
+sequence of data or whether
+
+you just send a single bit.
+
+And we're going to show later
+that that, in fact, is true.
+
+But for the time being we want
+to understand what's going on,
+
+and to understand what's going
+on we take this simplest
+
+possible case where there's
+only one bit that's being
+
+transmitted.
+
+It's the question, "Are we going
+to destroy ourselves in
+
+the next five years or not?" And
+this question is important
+
+to most of us, and at the output
+we find out, in fact,
+
+whether we're going to destroy
+ourselves or not.
+
+So it's one bit, but it's
+one important bit.
+
+OK, why are we doing
+things this way?
+
+Want to tell you a little story
+about the first time I
+
+really talked to
+Claude Shannon.
+
+I was a young member of the
+faculty at that time, and I
+
+was working on a problem
+which I thought was
+
+really a neat problem.
+
+It was interesting
+theoretically.
+
+It was important practically.
+
+And I thought, "gee, I finally
+have something I can go to
+
+this great man and talk to him
+about." So I screwed up my
+
+courage for about two days.
+
+Finally I saw his door open and
+him sitting there, so I
+
+went in and started to tell
+him about this problem.
+
+He's a very kind person and he
+listened very patiently.
+
+And after about 15 minutes
+he said, "My god!
+
+I'm just sort of lost
+with all of this.
+
+There's so much stuff going
+on in this problem.
+
+Can't we simplify it a little
+bit by throwing out this kind
+
+of practical constraint you've
+put on it?" I said, "yeah, I
+
+guess so." So we threw that
+out and the we went on for
+
+awhile later, and then he
+said, "My god, I'm still
+
+terribly confused about
+this whole thing.
+
+Why don't we simplify it
+in some other way?"
+
+And this went on for
+about an hour.
+
+As I say, he was a
+very patient guy.
+
+And at the end of an hour I was
+getting really depressed.
+
+Because here was this beautiful
+problem that I
+
+thought was going to make me
+famous, give me tenure, do all
+
+these neat things.
+
+And here he'd reduced
+the thing to a
+
+totally trivial toy problem.
+
+And we looked at it.
+
+And we said, yes this is
+a trivial toy problem.
+
+This is the answer.
+
+The problem is solved.
+
+But so what?
+
+And then he suggested putting
+some of those
+
+constraints back in again.
+
+And as we started putting the
+constraints back in, one- by-
+
+one, we saw that each time we
+put a new constraint in--
+
+since we understood the problem
+and its simplest
+
+form-- putting the constraint
+in, it was still simple.
+
+And by the time we built the
+whole thing back up again, it
+
+was clear what the answer was.
+
+OK, in other words, what theory
+means is really solving
+
+these toy problems.
+
+And solving the toy
+problems first.
+
+And in terms of practice, some
+people think the most
+
+practical thing is
+to be practical.
+
+And the whole point of this
+course, and this particular
+
+subject of detection is a
+wonderful example of this, the
+
+most practical thing is
+to be theoretical.
+
+I mean, you need to add practice
+to the theory, but
+
+the way you do things is you
+start with a theory-- which
+
+means you start with the toy
+problems, you build up from
+
+those toy problems, and after
+you build up for awhile,
+
+understanding what the practical
+problem is also--
+
+you then understand
+how to deal with
+
+the practical problem.
+
+And the practical engineer who
+doesn't have any of that
+
+fundamental knowledge about
+how to deal with these
+
+problems is always submerged
+in a sea of complexity.
+
+Always doing simulations of
+something that he doesn't, he
+
+or she doesn't understand.
+
+Always trying to interpret
+something from it, but with
+
+just too many things going on
+to have any idea of what it
+
+really means.
+
+Ok, so that's why we're making
+this trivial assumption here.
+
+We're only putting one bit in.
+
+We're ignoring what
+happens all the
+
+way through the system.
+
+We only get one number out.
+
+We're going to assume that this
+one number here is either
+
+plus or minus a, plus
+the Gaussian
+
+random noise variable.
+
+And we're not quite sure why
+it's going to be plus or minus
+
+a, plus a Gaussian noise random
+variable, but we're
+
+going to assume that
+for the time being.
+
+OK?
+
+So the detector observes the
+sample values of the random
+
+variable for which this is the
+sample value, and then guesses
+
+what the value of this random
+variable, h, which is what we
+
+call the input now.
+
+Because we view it from the
+standpoint of the detector--
+
+the detector has two possible
+hypotheses--
+
+one is that a zero was
+sent, and the other
+
+that a one was sent.
+
+And on the basis of this
+observation, you take first
+
+the hypothesis zero and you
+say, "Is this a reasonable
+
+hypothesis?" Then you look at
+the hypothesis one, say, "Is
+
+this a reasonable hypothesis?"
+And then you guess whether you
+
+think zero was more likely or
+one is more likely, given this
+
+observation that you've had.
+
+So what they detector has,
+at this point, is a full
+
+statistical characterization
+of the entire problem.
+
+Mainly you have a model
+of the problem.
+
+You understand every probability
+in the universe
+
+that might have any
+effect on this.
+
+And what might have any
+effect on this--
+
+as far as the way we've
+set up the problem--
+
+is only the question of what
+are the probabilities that
+
+you're going to send
+one or the other of
+
+these signals here?
+
+And conditional on each
+of these, what are the
+
+probabilities of this
+random variable
+
+appearing at the output?
+
+Because you have to base your
+decision only on this.
+
+So all of the probabilities
+only give you
+
+this one simple thing.
+
+Hypothesis testing, decision
+making, decoding, all mean the
+
+same thing.
+
+They mean exactly
+the same thing.
+
+And they're just done
+by different people.
+
+OK, so what that says is we're
+assuming the detector uses a
+
+known probability model.
+
+And in designing the detector,
+you know what that
+
+probability model is.
+
+It might not be the right
+probability model, and one of
+
+the things that many people
+interested in detection study
+
+is the question of when you
+think the probability model is
+
+one thing and it's actually
+something else, how well does
+
+the detection work?
+
+It's a little like the
+Lempel-Ziv algorithm that we
+
+studied earlier for doing
+source coding.
+
+Which is, how do you do source
+coding when you don't know
+
+what the probabilities are?
+
+And we found the best way to
+study that, of course, was to
+
+first find out how to do source
+encoding when you did
+
+know what the probabilities
+were.
+
+So we're doing the
+same thing here.
+
+We assume the detector is
+designed to maximize the
+
+probability of guessing
+correctly.
+
+In other words, it's trying
+to minimize the
+
+probability of error.
+
+We call that a MAP detector--
+maximum a posteriori
+
+probability decoding.
+
+You can try to do
+other things.
+
+You can say that there's a cost
+of one kind of error, and
+
+there's another cost of
+another kind of error.
+
+I mean, if you're doing medical
+testing or something.
+
+If you guess wrong in one way,
+you tell the patient there's
+
+nothing wrong with them, the
+patient goes out, drops dead
+
+the next day.
+
+And you don't care about that,
+of course, but you care about
+
+the fact that the patient is
+going to sue the hospital for
+
+100 million dollars and you're
+going to lose your
+
+job because of it.
+
+So there's a big cost to
+guessing wrong in that way.
+
+But for now, we're not going
+to bother about the costs.
+
+One of the things that you'll
+see when we get all done is
+
+that putting in cost
+doesn't make the
+
+problem any harder, really.
+
+You really wind up with the
+same kind of problem.
+
+OK, so h is the random
+variable that will be
+
+detected, and v is the
+random variable
+
+that's going to be observed.
+
+The experiment is performed.
+
+Some sample value of v is
+observed, and some sample
+
+value of the hypothesis
+has actually happened.
+
+In other words, what has
+happened is you prepared the
+
+whole system.
+
+Then at the input end to the
+whole system, the input to the
+
+channel, somebody has chosen
+a one or a zero without the
+
+knowledge of the receiver.
+
+That one or zero has been sent
+through this whole system, the
+
+receiver has observed some
+output, v, so in fact we're
+
+now dealing with the
+sample values of
+
+two different things.
+
+The sample value of the input,
+which is h, the sample value
+
+of the output, which is v, and
+in terms of the sample value
+
+of the output, we're trying to
+guess what the sample value of
+
+the input is.
+
+OK, an error then occurs if,
+after the output chooses a
+
+particular hypothesis as its
+guess, and that hypothesis,
+
+then, is a function of
+what it receives.
+
+In other words, after you
+receive something, what the
+
+detector has to do is somehow
+map what gets received, which
+
+is some number, into
+either zero or one.
+
+It's like what a
+Quantizer does.
+
+Mainly, it maps the whole
+region into two
+
+different sub- regions.
+
+Some things are mapped into
+zero, Some things
+
+are mapped into one.
+
+This H bar then becomes a random
+variable, but is a
+
+random variable that is a
+function of what's received.
+
+So we have one random variable,
+H, which is what
+
+actually happened.
+
+There's another random variable,
+H hat, which is what
+
+the detector guesses
+will happen.
+
+This is an unusual random
+variable, because it's not
+
+determined ahead of time.
+
+It's determined only in terms
+of what you decide your
+
+detection rule is going to be.
+
+This is a random variable that
+you have some control over.
+
+These other random variables
+you have no
+
+control over at all.
+
+So that's the random variable
+we're going to choose.
+
+And, in fact, what we're going
+to do is we're going to say
+
+what we want to do is this MAP
+decoding, maximum a posteriori
+
+probability decoding, where
+we're trying to minimize the
+
+probability of screwing up.
+
+And we don't care whether we
+make an error of one kind or
+
+make an error of
+the other kind.
+
+OK, is that formulation of the
+problem crystal clear?
+
+Anybody have any questions
+about it?
+
+I mean, the easiest way to get
+screwed up with detection is
+
+at a certain point to be going
+through, studying a detection
+
+problem, and then you
+suddenly realize you
+
+don't understand what--
+
+you don't understand what the
+whole problem is about.
+
+OK, let's assume we do know
+what the problem is, then.
+
+In principle it's simple.
+
+Given a particular observed
+value, what we're going to do
+
+is we're going to calculate
+the-- what we call the a
+
+posteriori probability, the
+probability given that
+
+particular sample value
+of the observation--
+
+we're going to calculate the
+probability that what went
+
+into the system is a zero
+and what went into
+
+the system is a one.
+
+OK?
+
+This is the probability that
+j is the sample value of H,
+
+conditional on what
+we observed.
+
+OK, if you can calculate this
+quantity, it tells you if I
+
+decide that--
+
+if I guess that H is equal to
+j-- this in fact tells me that
+
+this is the probability
+that guess is correct.
+
+And if this is the probability
+that guess is correct, and I
+
+want to maximize my probability
+of guessing
+
+correctly, what do I do?
+
+Well, what I do is my MAP
+rule is arg max of this
+
+probability.
+
+And "arg max" means instead
+of trying to maximize this
+
+instead of trying to maximize
+this quantity over something,
+
+what we're doing is trying to
+find the value of j, which
+
+maximizes this.
+
+In other words, we calculate
+this for each value of j, and
+
+then we picked the j for which
+this quantity is largest.
+
+In other words, we maximize this
+but we're not interested
+
+in the maximum value of
+it at this point.
+
+We're interested in it later
+because that's the probability
+
+that we're choosing correctly.
+
+What we're interested in, for
+now, is what is the hypothesis
+
+that we're going to guess.
+
+OK?
+
+So this probability of being
+correct is going to the this
+
+probability for this
+maximal j.
+
+And when we average over v we
+get the overall probability of
+
+being correct.
+
+There's a theorem which is
+stated in the notes, which is
+
+one of the more trivial theorems
+you can think of,
+
+which says that if you do the
+best thing for every sample
+
+point you, in fact, have done
+the best thing on average.
+
+I think that's pretty clear.
+
+If you, well I mean you can read
+it if you want to form a
+
+proof, but if you do the best
+thing all the time, then it's
+
+the overall best thing.
+
+OK, so that's the general
+idea of detection.
+
+And in doing this we have to
+be able to calculate these
+
+probabilities, so that's
+the only constraint.
+
+These are probabilities, which
+means that this set of
+
+hypothesis is discrete.
+
+If you have an uncountable
+infinite number of hypotheses,
+
+at that point you're dealing
+with an estimation problem.
+
+Because you don't have any
+chance in hell of getting the
+
+right answer, exactly
+the right answer.
+
+And therefore you have to
+have some criterion for
+
+how close you are.
+
+And that's what's important
+in estimation.
+
+And here what's important is
+really, do we guess right or
+
+don't we guess right.
+
+And we don't, we don't care.
+
+There aren't any near
+misses here.
+
+You either get it on the
+nose or you don't.
+
+OK, so we want to study
+binary detection now
+
+to start off with.
+
+We want to trivialize the
+problem because even that
+
+problem we just stated
+is too hard.
+
+So we're going to trivialize
+it in two ways.
+
+We're going to assume that there
+are only two hypotheses.
+
+That it's a binary detection
+problem.
+
+And we're also going to assume
+that it's Gaussian noise.
+
+And that will make it sort of
+transparent what's happening.
+
+So H takes the values
+zero or one.
+
+And we'll call the probabilities
+with which it
+
+takes those values
+P zero and P one.
+
+These are called a priori
+probabilities.
+
+In other words, these are the
+probabilities that the
+
+hypothesis takes to value zero
+or one before seeing any
+
+observation.
+
+And the probabilities after you
+see the observation are
+
+called a posteriori
+probabilities.
+
+In other words, probabilities
+after the observation and the
+
+probabilities before
+the observation.
+
+Up until about 1950
+statisticians used to argue
+
+terribly about whether it was
+valid to assume a priori
+
+probabilities.
+
+And as you can see by thinking
+about it a little bit, the
+
+problem they were facing was
+they couldn't separate the
+
+problem of choosing a
+mathematical model and
+
+analyzing it from the problem
+of figuring out whether the
+
+model was valid or not.
+
+And at that point people
+studying in that area had not
+
+gotten to the point where they
+could say, "Well, maybe I
+
+ought to analyze the problem for
+different models, and then
+
+after I understand what happens
+for different models I
+
+then ought to go back because
+I'll know what's important to
+
+find out in the real problem."
+But up until that time, there
+
+was just fighting
+among everyone.
+
+Bayes was the person who decided
+you really ought to
+
+assume that there's a
+model to start with.
+
+And he developed most
+of detection
+
+theory at an early time.
+
+And people used to think that
+Bayes was a terrible fraud.
+
+Because in fact he was using
+models of the problem rather
+
+than nothing.
+
+But anyway, that's
+where we were.
+
+We're also going to assume that,
+after we get all through
+
+with modulation and
+demodulation, and we really
+
+want to look at a general
+problem here.
+
+There's one discrete random
+variable, H, one analog random
+
+variable, which has a
+probability density, v, what
+
+we want to assume is that
+there's a probability density
+
+that we know, which is the
+probability density of the
+
+observation conditional
+on the hypothesis.
+
+We're assuming that we know
+this, and we know this--
+
+we call these things
+likelihoods--
+
+and in most communication
+problems anyway, it's far
+
+easier to get your hand on these
+likelihoods than it is
+
+to get your hand the a
+posteriori probabilities,
+
+which you're really
+interested in.
+
+So we find these likelihoods,
+we can find the marginal
+
+density of the observation.
+
+Which is just the
+weighted sum.
+
+The probability that the
+hypothesis is zero times a
+
+conditional probability of the
+observation and so forth.
+
+So we're going to assume that
+those densities exist.
+
+We're going to assume
+that we know them.
+
+And then with a great feat of
+probability theory, we say the
+
+a posteriori probability is
+equal to the a priori
+
+probability times the likelihood
+divided by the
+
+marginal probability of v. OK?
+
+What was the first thing you
+learn in probability when you
+
+started studying random
+variables?
+
+It was probably this formula,
+which says when you have a
+
+joint density of two random
+variables you can
+
+write it in two ways.
+
+You can either write, "density
+of one times density of two
+
+conditional and one is equal
+to the density of two times
+
+density of one conditional in
+two." And then you think about
+
+it a little bit and you say,
+"A ha!" It doesn't matter
+
+whether the first one is the
+density or whether it's the
+
+probability.
+
+You can deal with it
+in the same way.
+
+And you get this formula,
+which I hope is
+
+not unusual to you.
+
+OK, so our MAP decision rule
+then, our MAP decision rule,
+
+remember, is to pick the more,
+is to find the a posteriori
+
+probability which is
+most probable.
+
+Because that is the probability
+of being correct.
+
+So, in fact, if this probability
+is bigger than
+
+this probability, this is the a
+posteriori probability that
+
+H is equal to zero.
+
+This is the a posteriori
+probability that
+
+H is equal to one.
+
+So we're just going to compare
+those two and pick the larger.
+
+And if this one is larger than
+this one, we pick our choice
+
+equal zero.
+
+And if it's smaller, we pick
+our choice equal to one.
+
+So this is what MAP
+detection is.
+
+Why did I make this greater
+than or equal
+
+and this less than?
+
+Well, if we have densities,
+it doesn't often make any
+
+difference.
+
+Strangely enough, it does
+sometimes make a difference.
+
+Because sometimes you can have
+a density, and the densities
+
+are the same for both of
+these likelihoods.
+
+And you can find situations
+where it's important.
+
+But when the two probabilities
+are the same, the probability
+
+of being correct is the same in
+both cases, so it doesn't
+
+make any difference what
+you do when you
+
+have a quality here.
+
+And therefore we've just
+made a decision.
+
+We've said, OK, what we're going
+to do is whenever this
+
+is equal to this, we're
+going to choose zero.
+
+If you prefer choosing
+one, be my guest.
+
+All of your MAP error
+probabilities will
+
+be exactly the same.
+
+Nothing will change.
+
+It just is easier to do the
+same thing all the time.
+
+OK, well then we look at this
+formula, and we say, "Well, I
+
+can simplify this a little
+bit." If I take this
+
+likelihood and move it over to
+this side, and if I take this
+
+marginal density and move it
+over to this side, and if I
+
+take p zero and move it over
+to this side, then the
+
+marginal densities cancel out.
+
+They had nothing to do
+with the problem.
+
+And I wind up with a ratio
+of the likelihoods.
+
+And what do you think
+the ratio of the
+
+likelihoods is called?
+
+Somebody got the smart
+idea of calling that
+
+a likelihood ratio.
+
+Somehow the people in statistics
+were much better at
+
+generating notation than the
+people in communication theory
+
+who have done just an abominable
+job of choosing
+
+notation for things.
+
+But anyway, they call this
+a likelihood ratio.
+
+And the rule then becomes: if
+the likelihood ratio is
+
+greater than or equal to
+the ratio of p1 to
+
+p0, we choose zero.
+
+And if it's less,
+we choose one.
+
+And we call this ratio
+the threshold.
+
+So in fact what this says is
+binary MAP tests are always
+
+threshold tests.
+
+And by a threshold test I mean
+finds the likelihood ratio,
+
+compare the likelihood ratio
+with the threshold-- the
+
+threshold in fact is this
+ratio of a priori
+
+probabilities--
+
+and at that point you
+have actually
+
+achieved the MAP test.
+
+In other words, you have done
+something which actually, for
+
+real, minimizes the probability
+of error.
+
+Maximizes the probability
+of being correct.
+
+Well because of that, this thing
+here, this likelihood
+
+ratio, is called a sufficient
+statistic.
+
+And it's called a sufficient
+statistic because you can do
+
+math decoding just by
+knowing this number.
+
+OK?
+
+In other words, it says you can
+you can calculate these
+
+likelihoods.
+
+You can find the ratio of
+them-- which is this
+
+likelihood ratio-- and after you
+know the likelihood ratio,
+
+you don't have to worry about
+these likelihoods anymore.
+
+This is the only thing relevant
+to the problem.
+
+Now this doesn't seem to be a
+huge saving, because here
+
+we're dealing with two real
+numbers-- well here we've
+
+reduced it to one real number--
+which is something.
+
+When we start dealing with
+vectors, when we start dealing
+
+with wave forms, this is
+really a big thing.
+
+Because what you're
+doing is reducing
+
+the vectors to numbers.
+
+And when you reduce accountibly
+infinite
+
+dimensional vector to a number,
+
+that's a big advantage.
+
+It also, in terms of the
+communication problems we're
+
+facing, breaks up a detector
+into two pieces in an
+
+interesting way.
+
+Mainly it says there are things
+you do with the wave
+
+form in order to calculate what
+this likelihood ratio is,
+
+and then after you find the
+likelihood ratio you just
+
+forget about what the wave
+form was and you
+
+deal only with that.
+
+What we're going to find out
+is in this problem we were
+
+looking at here--
+
+we're going to find out
+later when we look
+
+at the vector problem--
+
+in fact this thing here is in
+fact the likelihood ratio if
+
+you make an observation out
+at this point here.
+
+In other words, right at the
+front end of the receiver,
+
+that's where you have all
+the information you
+
+can possibly have.
+
+If you calculate likelihood
+ratios at that point what
+
+you're going to do is to find
+the likelihood ratio you're
+
+going to go through all this
+stuff right here and wind up
+
+with that which is work which
+is proportional to the
+
+likelihood ratio right here.
+
+OK, so one of the things we're
+doing right now is we're not
+
+looking at that problem.
+
+We're only looking at the
+simpler problem, assuming a
+
+one dimensional problem.
+
+But the reason we're looking
+at it is that later we're
+
+going to show that this is, in
+fact, the solution to the more
+
+general problem.
+
+Which was Shannon's idea
+in the first place.
+
+Of, how do you solve the trivial
+problem first and then
+
+see what the complicated
+problem is.
+
+OK, so that's what we're trying
+to do, summarized here
+
+for any binary detection problem
+where the observation
+
+has a sample value of
+a random something.
+
+Namely, a random vector, a
+random process, a random
+
+variable, a complex variable,
+a complex anything.
+
+Anything whatsoever, so long
+as you can assign a
+
+probability density to it.
+
+You calculate the likelihood
+ratio, which is this ratio
+
+here, so long as you have then
+cities even talk about.
+
+The MAP rule is to compare this
+likelihood ratio with the
+
+threshold data-- which is just
+the ratio of the a priori
+
+probabilities--
+
+if this is greater
+than or equal to
+
+that, you choose zero.
+
+Otherwise you choose one.
+
+The MAP rule, as I said before,
+partitions this
+
+observation space
+into two pieces.
+
+Into two segments.
+
+And one of those pieces
+gets mapped into zero.
+
+One of the pieces gets
+mapped into one.
+
+It's exactly like a
+binary quanitizer.
+
+Except the rule you use to
+choose the the quantization
+
+regions is different.
+
+But a quanitizer maps a space
+into a finite set of regions.
+
+And this detection rule does
+exactly the same thing.
+
+And since the beginning of
+information theory people have
+
+been puzzling over how to make
+use of the correspondence
+
+between quanitization on one
+hand and detection on the
+
+other hand.
+
+And there are some
+correspondences but they
+
+aren't all that good
+most of the time.
+
+OK, so you get an error when
+the actual hypothesis that
+
+occurred, namely the bit that
+got sent was i and if the
+
+observation landed in
+the other subset.
+
+We know that the MAP rule
+minimizes the error
+
+probability.
+
+So you have a rule which you
+can use for all binary
+
+detection problems so long
+as you have the density.
+
+And if you don't have a density
+you can generalize it
+
+without too much trouble.
+
+OK, so we want to look at the
+problem in Gaussian noise.
+
+In particular we want to
+look at it for 2PAM.
+
+In other words for a standard
+PAM system, where zero gets
+
+mapped into plus a and one
+gets mapped into minus a.
+
+This is often called antipodal
+signaling because you're
+
+sending a plus something
+and a minus something.
+
+They are at opposite ends
+of the spectrum.
+
+You push them as far away as you
+can, because as you push
+
+them further and further
+away it requires
+
+more and more energy.
+
+So you use the energy
+you have.
+
+You get them as far apart as you
+can, and you hope that's
+
+going to help you.
+
+And we'll see that
+it does help you.
+
+OK, so what you receive then,
+we'll assume, is either plus
+
+or minus a--
+
+depending on which hypothesis
+occured--
+
+plus a Gaussian random
+variable.
+
+And here's where the notation
+of communication theorists
+
+rears its ugly head.
+
+We call the variance of this
+random variable n 0 over 2.
+
+I would prefer to call
+it sigma squared but
+
+unfortunately you can't
+fight city hall on
+
+something like this.
+
+And everybody talks about
+n 0 and n 0 over 2.
+
+And you got to get used to it.
+
+So here's where we're starting
+to get used to it.
+
+So that's the variance of this
+noise random variable.
+
+OK, we're only going to send one
+binary digit, H, so this
+
+is the only, this is the sole
+problem we have to deal with.
+
+We've made a binary choice.
+
+Added one Gaussian random
+variable to it.
+
+You observe the sum,
+and you guess.
+
+So what are these likelihoods
+in this case?
+
+Well, the likelihood if H is
+equal zero, in other words if
+
+you're sending a plus a, the
+likelihood is just a Gaussian
+
+density shifted over by a.
+
+And if you're sending, on
+the other hand, a one--
+
+which means you're sending minus
+a-- you have a Gaussian
+
+density shifted over
+the other way.
+
+Let me show you a
+picture of that.
+
+We'll come back to analyze more
+things about the picture
+
+in a little bit, so don't
+worry about most of the
+
+picture at this point.
+
+OK, this is the likelihood
+probability density of the
+
+output given that
+you sent a zero.
+
+Mainly that you sent plus a.
+
+So we have a Gaussian density--
+this bell shaped
+
+curve-- centered
+around plus a.
+
+If you sent a one, you're
+sending minus a-- one gets
+
+mapped into minus a-- and you
+have the same bell shaped
+
+curve centered around minus a.
+
+If you receive any particular
+value of v, mainly suppose you
+
+receive the value of v here,
+you calculate these two
+
+likelihoods.
+
+One of them is this.
+
+One of them is that.
+
+You compare them, the ratio with
+the threshold, and you
+
+make your choice.
+
+OK, so let's go back to do it.
+
+To do the arithmetic.
+
+Here are the two likelihoods.
+
+You take the ratio of
+these two things.
+
+When you take the ratio
+of them, what happens?
+
+And this sort of always
+happens in
+
+these Gaussian problems.
+
+These terms cancel out.
+
+Well it always happens in these
+
+additive Gaussian problems.
+
+These terms cancel out.
+
+You take a ratio of
+two exponents.
+
+You just get the difference.
+
+So the likelihood ratio--
+this divided by this--
+
+is then e to the minus v minus
+a squared over n0.
+
+and v plus a squared over n0.
+
+OK?
+
+Because normally the Gaussian
+density is something divided
+
+by two sigma squared, and sigma
+squared here is n0 over
+
+2, so the 2's cancel out.
+
+One nice thing about the
+notation anyway, you get rid
+
+of one factor of two in it.
+
+Well so you have this
+minus this.
+
+When you take the difference
+of these two things the v
+
+squareds cancel out.
+
+Because one of these things is
+in the numerator, the other
+
+one was in the denominator.
+
+So you have this term
+comes through as is.
+
+This is--
+
+you're dividing by this--
+
+so when you multiply this
+turns into a plus sign.
+
+So the v squared here cancels
+out with the v squared here.
+
+The a squared here cancels out
+with the a squared here.
+
+And it's only the inner product
+term that survives
+
+this whole thing.
+
+And here you have plus 2va.
+
+Here you have plus 2va.
+
+So you wind up with e to
+the 4av divided by n0.
+
+Which is very nice, because
+what it says is this
+
+likelihood, which is what
+determines everything in the
+
+world, is just a scalar in
+multiple of the observation.
+
+And that that's going to
+simplify things a fair amount.
+
+It's why that picture comes
+out as simply is it does.
+
+OK, so to do a little more
+of the arithmetic.
+
+This is the likelihood here,
+e to the 4av over n0.
+
+So our rule is you compare
+this likelihood to the
+
+threshold-- which is p1 over
+p0, which we call eta--
+
+and you look at that for awhile
+and you say, "Gee, this
+
+is going to be much easier
+to deal with.
+
+Instead of looking at the
+likelihood ratio, I look at
+
+the log likelihood ratio."
+
+And people who deal with
+Gaussian problems a lot, you
+
+never hear them talk about
+likelihood ratios, you always
+
+hear them talk about log
+likelihood ratios.
+
+And you can find one from the
+other, so either one is
+
+equally good.
+
+In other words, the log
+likelihood ratio is a
+
+sufficient statistic, because
+you can calculate the
+
+likelihood ratio from it.
+
+So this is a sufficient
+statistic.
+
+It's equal to 4av over n0.
+
+And when this is greater than
+or equal the log of the
+
+threshold, you go this way.
+
+When it's less than,
+you go this way.
+
+So when you then multiply by n0
+over 4a, your decision rule
+
+is you just look at
+the observation.
+
+You compare it with n0 times
+log of eta divided by 4a.
+
+And at this point we can go back
+to this picture and sort
+
+of sort out what all
+of it means.
+
+Because this point here
+is now the threshold.
+
+It's n0 times log of
+eta divided 4eta.
+
+By 4a.
+
+That's what we said the
+threshold had to be.
+
+So we have these two Gaussian
+curves now.
+
+Why do we have to go back and
+look at these Gaussian curves?
+
+I told you that once we
+calculated the likelihood
+
+ratio we could forget
+about the curves.
+
+So why do I want to put
+the curves back in?
+
+Well because I want to calculate
+the probability of
+
+error at this point.
+
+OK?
+
+And it's easier to calculate the
+probability of error if,
+
+in fact, I draw curve for
+myself and I look at
+
+what's going on.
+
+So here's the threshold.
+
+Here's the density when H equals
+one is the correct
+
+hypothesis.
+
+The probability of error is the
+probability that when I
+
+send one, the observation is
+going to be a random variable
+
+with this probability density
+and if it's a wild case, and I
+
+got an enormous value of noise,
+positive noise, the
+
+noise is going to push me over
+that threshold there and I'm
+
+going to make a mistake.
+
+So, in fact, the probability
+of error-- conditional on
+
+sending one--
+
+is just this probability of that
+little space in there.
+
+OK?
+
+Which is the probability that
+I'm going to say that zero
+
+occurred when, in fact,
+one occurred.
+
+So that's my probability of
+error when one occurs.
+
+What's the probability of
+error when zero occurs?
+
+Well it's the same analysis.
+
+When zero occurs--
+
+mainly when the correct
+hypothesis is zero--
+
+the output, v, follows this
+probability density here.
+
+And I'm going to screw up if
+the noise carries me beyond
+
+this point here.
+
+So you can see what the
+threshold is doing now.
+
+I mean, when you choose a
+threshold which is positive it
+
+makes it much harder to screw
+up when you send a minus a.
+
+It makes it much easier
+to screw up when
+
+you send a plus a.
+
+But you see that's what we
+wanted to do, because the
+
+threshold was positive in this
+case, because p1 was so much
+
+larger than p0.
+
+And because p1 is so much
+larger than p0--
+
+p1 happens almost
+all the time--
+
+and therefore you would normally
+almost choose p1
+
+without looking at v. Which says
+you want to push it over
+
+that way a little bit.
+
+OK, when you calculate this
+probability of error, it's the
+
+probability of the tail of a
+Gaussian random variable.
+
+So you define this tail
+variable, q of x, is the
+
+complimentary distribution
+function of a
+
+normal random variable.
+
+It's the integral from x to
+infinity of one over the
+
+square root of 2pi, e to the
+minus c squared over 2.
+
+I guess this would make better
+sense if this were a z--
+
+one and--
+
+oh, no.
+
+No, I did it right
+the first time.
+
+That's an x, because x is the
+limit in there, you see.
+
+So I'm calculating all of the
+probability density that's off
+
+to the right of x.
+
+And the probability of error
+when H is equal to one is this
+
+probability-- which looks like
+it's the tail on the negative
+
+side but if you think about
+it a little bit, since the
+
+Gaussian curve is symmetric, you
+can also look at it as a q
+
+function where now when you have
+this is equal to zero,
+
+this corresponds to changing
+this plus to a minus here and
+
+that's the only change.
+
+OK, so this looks a
+little ugly and it
+
+looks a little strange.
+
+I mean you can sort
+of interpret
+
+this part of it here--
+
+I can interpret this
+part if I'm using
+
+maximum likelihood decoding--
+
+maximum likelihood is mapped
+decoding where the threshold
+
+is equal to one.
+
+In other words, it's where
+you're assuming that the
+
+hypothesis is equally likely to
+be zero or one-- a priori--
+
+which is a good assumption
+almost always in communication
+
+because we work very hard in
+doing source coding to make
+
+those binary digits equally
+likely zero or one.
+
+And there are other reasons
+for choosing maximum
+
+likelihood.
+
+If you don't know anything about
+the probabilities it's a
+
+good assumption in a sort
+of a max/min sense.
+
+It sort of limits how much you
+can screw up by having the
+
+wrong probability, so it's a
+very robust choice also.
+
+OK, but now this, we're taking
+the ratio of a with the square
+
+root of n0.
+
+Well the square root of n0 over
+2 is really the standard
+
+deviation of the noise.
+
+So what we're doing is comparing
+the amount of input
+
+we've put in with the standard
+deviation of the noise.
+
+Now does that make any sense?
+
+The probability of error
+depends on that ratio?
+
+Well yeah, it makes a
+whole lot of sense.
+
+Because if, for example, I
+wanted to look at this problem
+
+in a different scaling
+system--
+
+if this is volts and I want to
+look at it in milli-volts--
+
+I'm going to divide a by, I'm
+going to multiply a by 1000.
+
+I'm going to multiply the
+standard deviation of the
+
+noise by 1000.
+
+Because one of the things we
+always do here-- the way we
+
+choose n0 over 2--
+
+n0 over 2 is sort of a
+meaningless quantity.
+
+It's the noise energy in one
+degree of freedom in the
+
+scaling reference that we're
+using for the data.
+
+OK?
+
+And that's the only definition
+you can come up with that
+
+makes any sense.
+
+I mean you scale the data in
+whatever way you please, and
+
+when we've gone from baseband
+to passband, we in fact have
+
+multiplied the energy in the
+input by a factor of two.
+
+And therefore, because of
+that, we're going to--
+
+n0 at passband is going to be a
+square root of 2 bigger than
+
+it is at baseband.
+
+If you don't like that,
+live with it.
+
+That's the way it is.
+
+Nobody will change n0,
+no matter who wants
+
+them to change it.
+
+OK, so this term make sense.
+
+It's the ratio of the signal
+amplitude to the standard
+
+deviation of the noise.
+
+And that should be the only way
+that the signal amplitude
+
+or the standard deviation of the
+noise enters in, because
+
+it's really the ratio that
+has to be important.
+
+Why this crazy term?
+
+Well if you look at the curve
+you can sort of see why it is.
+
+The threshold test is comparing
+the likelihood ratio
+
+of this curve with
+the likelihood
+
+ratio of this curve.
+
+What's going to happen as
+a gets very, very large?
+
+You move a out, and the thing
+that's happening then is this
+
+curve-- which is now coming down
+in a modest way here-- if
+
+you move a way out here, you're
+going to have almost
+
+nothing there.
+
+And it's going to be going
+down very fast.
+
+It's going to be going
+down very fast
+
+relative to its magnitude.
+
+In other words the bigger
+a gets, the bigger this
+
+difference is going to be
+for any given threshold.
+
+And that's why you get a over
+square root of n0 here.
+
+And here you get exactly
+the opposite thing.
+
+That's because for a given
+threshold, as this signal to
+
+noise ratio gets bigger, this
+threshold term becomes almost
+
+totally unimportant.
+
+I mean you get so much
+information out of the reading
+
+you're making, because it's
+so reliable, that having a
+
+threshold is almost completely
+irrelevant.
+
+And therefore you can sort
+of forget about it.
+
+If a is very large, this
+term is zilch.
+
+OK?
+
+So if you want to have reliable
+communication and you
+
+use a large amount of single
+noise ratio to get it, that's
+
+another reason for forgetting
+about whether the threshold is
+
+one or something else.
+
+And we would certainly like to
+deal with problems where the
+
+threshold is equal to one
+because most people who
+
+remember q of a signal
+to noise ratio.
+
+I don't know anybody who can
+remember this formula.
+
+I'm sure there's some people,
+but I don't think anybody who
+
+works in the communication
+field ever thinks
+
+about this at all.
+
+Except the first time they
+derive it and the say, "Oh,
+
+that's very nice." And then they
+promptly forget about it.
+
+The only reason I think
+about it more is I
+
+teach the course sometimes.
+
+Otherwise I would forget
+about it, too.
+
+OK, which is what this says.
+
+For communication we assume
+p0 is equal to p1.
+
+So we assume that eta
+is equal to one.
+
+So the probability of error,
+which is also the probability
+
+of error when H is equal to
+one-- in other words when a
+
+one actually enters the
+communication system-- is
+
+equal to the probability of
+error when H is equal to 0.
+
+In other words these two tails
+here, when the threshold is
+
+equal to one you set the
+threshold right there.
+
+The probability of this tail
+is clearly equal to the
+
+probability of this tail.
+
+Just by symmetry.
+
+So these two error probabilities
+are the same.
+
+And in fact they are just
+q of a over the square
+
+root of n0 over 2.
+
+It's nice to put this
+in terms of energy.
+
+We said before that energy is
+sort of important in the
+
+communication field.
+
+So we call e sub b the energy
+per bit that we're
+
+spending to send data.
+
+I mean don't worry about the
+fact that we're only sending
+
+one bit and then we're tearing
+the communication system down.
+
+Because pretty soon we're going
+to send multiple bits.
+
+But the amount of energy we're
+spending sending this one bit
+
+is a squared.
+
+At least back in this frame of
+reference that we're looking
+
+at now, where we're just looking
+at this discrete
+
+signal and single
+variable noise.
+
+And n0 over 2 is the noise
+variance of this particular
+
+random variable, z, so when we
+write this out in terms of Eb,
+
+which is a squared, it looks
+like this-- it's 2eb over n0.
+
+So the probability of error for
+this binary communication
+
+problem is just the square
+root of 2Eb over n0.
+
+Which is a formula that
+you want to remember.
+
+It's the error probability for
+binary detection when n0 over
+
+2 is the noise energy on this
+one degree of freedom and Eb
+
+is the amount of energy you're
+spending on this
+
+one degree of freedom.
+
+You will see about
+50 variations of
+
+this as we go on.
+
+If you try to remember this
+fundamental definition, it'll
+
+save you a lot of agony.
+
+Even so, everybody I know who
+deals with this kind of thing
+
+always screws up the
+factors of twos.
+
+And finally when they get all
+done, they try to figure out
+
+from common sense or from
+something else, what the
+
+factors of two ought to be.
+
+And they reduce their
+probability of error to about
+
+a quarter after they're all done
+with doing all of that.
+
+OK, so we spent a lot
+of time analyzing
+
+binary antipodal signals.
+
+What about the binary non
+antipodal signals?
+
+This is beautiful example of
+Shannon's idea of studying the
+
+simplest cases first.
+
+If you have two signals, one of
+which is b and one of which
+
+is b prime, and they can be put
+anywhere on the real line.
+
+And what I've done, because I
+didn't want to plot this whole
+
+picture again, is I just took
+the zero out, and I replaced
+
+the zero by the point halfway
+between these two points which
+
+is b plus b prime over 2.
+
+And then we look at it and we
+say what happens if you have
+
+an arbitrary set of two points
+anywhere on the real line?
+
+Well when I send this point the
+likelihood, conditional on
+
+this point being sent, is
+this Gaussian curve
+
+centered on b prime.
+
+When I send b the likelihood
+is a Gaussian
+
+curve centered on b.
+
+And it is in fact the same curve
+that we drew before.
+
+If in fact I replaced zero with
+a center point between
+
+these two, which is b
+plus b prime over 2.
+
+And if I then define a as this
+distance in here, the
+
+probability of error that I
+calculated before is the same
+
+as it was before.
+
+Now I would suggest to all of
+you that you try to find the
+
+probability of error for this
+system here, just not using
+
+what we've already done, and
+just writing out the
+
+likelihood ratios as a function
+of an arbitrary b
+
+prime and an arbitrary b and
+finding a likelihood ratio,
+
+and calculating through
+all of that.
+
+And most of you are capable of
+calculating through all of it.
+
+But when you do so, you will
+get a god awful looking
+
+formula, which just looks
+totally messy.
+
+And by looking at the formula
+you are not going to be able
+
+to realize that what's going
+on is what we see here from
+
+the picture.
+
+And the only reason we figured
+out what was going like the
+
+picture is we already
+solved the problem
+
+for the Simpson case.
+
+OK so it never makes any sense
+in this problem to look at
+
+this general case.
+
+You always want to say the
+general case is just a special
+
+case of a special case.
+
+Where you just have to define
+things slightly differently.
+
+OK, so we're going to do the
+center point, then, I mean it
+
+might be a pilot tone.
+
+It might be any other non
+information bearing signal.
+
+In other words were sending
+the one bit.
+
+Sometimes for some reason or
+other, you need to get
+
+synchronization.
+
+You need to get other things
+in a communication system.
+
+And for that reason, you
+send other things.
+
+We'll talk about a lot
+of those later.
+
+But they don't change the error
+probability at all.
+
+The error probability is
+determined solely by the
+
+distance between these two
+points which we call 2a.
+
+So probability of error remains
+the same in terms of
+
+this distance.
+
+The energy per bit
+now changes.
+
+The energy per bit is
+the energy here
+
+plus the energy here.
+
+Which in fact is the energy
+in the center
+
+point plus a squared.
+
+I mean we've done that in a
+number of contexts, the way to
+
+find the energy in a binary
+random variable is to take the
+
+energy in the center point
+plus the energy in the
+
+difference.
+
+It's the same as finding the
+fluctuation plus the
+
+square of the mean.
+
+It's that same underlying
+idea.
+
+So any time you use non
+antipodal and you shift things
+
+off the mean, you can
+see what's going
+
+on very, very easily.
+
+You waste energy.
+
+I mean it might not be wasted,
+you might have to waste it for
+
+some reason.
+
+But as far as a communication
+is concerned you're simply
+
+wasting it.
+
+So your energy per bit changes,
+but your probability
+
+of error remains the same.
+
+Because of that, you get a very
+clear cut idea of what
+
+it's costing you to send
+that pilot tone.
+
+Because in fact what you've done
+is to just increase this
+
+energy, which we talk about
+in terms of db.
+
+If c is equal to a in this case
+which, as will see, is a
+
+common thing that happens in a
+lot of systems, what you've
+
+lost is a factor three db.
+
+Because you're using twice as
+much energy which is three db
+
+more energy, than you have
+to use for the pure
+
+communication.
+
+So it's costing you three db to
+do whatever silly thing you
+
+want to do for synchronization
+or something else.
+
+Which is why people work very
+hard to try to send signals
+
+which carry their own
+synchronization
+
+information in them.
+
+And we will talk about that more
+when we get to wireless
+
+and things like that.
+
+OK.
+
+Let's go on to real antipodal
+vectors in
+
+white Gaussian noise.
+
+And again, let me point out to
+you again that one of the
+
+remarkable things about
+detection theory is once you
+
+understand detection for
+antipodal binary signals and
+
+Gaussian noise, everything
+else just follows along.
+
+OK, so here what we're going to
+do is to assume that under
+
+the hypothesis H equals zero--
+in other words conditional on
+
+a zero entering the
+communication system--
+
+what we're going to send is not
+a single degree, is not
+
+something in a single
+degree of freedom.
+
+But we're actually going
+to send a vector.
+
+And you can think of that if you
+want to as sending a way
+
+form and breaking up the
+waveform into an orthonormal
+
+expansion and a1 to
+ak as being the
+
+coefficients in that expansion.
+
+So we're going to use
+several degrees of
+
+freedom to send one signal.
+
+Yes?
+
+AUDIENCE: [INAUDIBLE]
+
+PROFESSOR: I'm only
+sending one bit.
+
+And on Wednesday I'm going to
+talk about what happens when
+
+we want to send multiple bits
+or when we want to send a
+
+large number of signals in one
+degree of freedom, or all
+
+those cases, multiple
+hypotheses.
+
+You know what's going
+to happen?
+
+It's going to turn out to be
+a trivial problem again.
+
+Multiple hypotheses are no
+harder than just binary
+
+hypotheses.
+
+So again, once you understand
+the simplest case, all
+
+Gaussian problems turn
+out to be solved.
+
+Just with minor variations
+and minor tweaks.
+
+OK, so I have antipodal
+vectors.
+
+One vector is a1 to a sub k.
+
+Under the other hypothesis we're
+going to send minus a,
+
+which is the opposite vector.
+
+So if we're dealing with two
+dimensional space with
+
+coordinates here and here,
+if I send this I'm
+
+going to send this.
+
+If I send that I'm going to
+send that, and so forth.
+
+As the opposite alternative.
+
+The likelihood ratio is then,
+the probability of vector v
+
+conditional on sending this.
+
+I'm assuming here that the noise
+is IID and each noise
+
+variable has mean zero and
+variance n0 over 2.
+
+Namely, we're pretending we're
+communication people here,
+
+using and n0 over 2 here.
+
+So the conditional density--
+
+the likelihood of this output
+vector given zero-- is just
+
+this density of z shifted
+over by a.
+
+So it's what we've talked about
+as the Gaussian density.
+
+Just this, which is just the
+energy in v minus a is what
+
+that turns out to be.
+
+So the log likelihood ratio is
+the ratio of this quantity to
+
+the density where H
+is equal to one.
+
+And when H is equal to one, what
+happens is the same thing
+
+as happened before.
+
+One makes this sign turn
+into a plus sign.
+
+So when I look at the log
+likelihood ratio, I want to
+
+take the ratio of this quantity
+to the same quantity
+
+with a plus put into it.
+
+And when I take the log of that,
+what happens is I get
+
+this term minus the opposite
+term of the opposite side.
+
+So I have minus the norm squared
+of v minus a plus the
+
+norm squared of v
+plus a over n0.
+
+And again, if you multiply
+this out, the v squareds
+
+cancel out.
+
+The a squareds cancel out.
+
+And you just get the inner
+product terms.
+
+And strangely enough you get the
+same formula that you got
+
+before, almost, except here you
+have the inner product of
+
+v with a instead of just the
+product of v times a.
+
+So in fact we just have a slight
+generalization of the
+
+thing that we did before.
+
+In other words, the
+scalar product is
+
+a sufficient statistic.
+
+Now what does that tell you?
+
+It tells you how to
+build a detector.
+
+OK?
+
+It tells you when you have a
+vector detection problem, the
+
+thing that you want to do is to
+take this vector, v, that
+
+you have and form the inner
+product of v times a.
+
+If in fact v is a waveform
+and a is a waveform,
+
+what do you do then?
+
+Well the first thing you
+do is to think of
+
+v as being a vector--
+
+where it's the vector of
+coefficients-- in the
+
+expansion for that waveform
+and a in the same way.
+
+You look at what the inner
+product is then, and then you
+
+say, "well what does that
+correspond to when I deal with
+
+L2 waveforms?" What's the inner
+
+product for L2 waveforms?
+
+It's the integral of the product
+of the waveforms.
+
+And how do you form the
+integral of the
+
+product of the waveforms?
+
+You take this waveform here.
+
+You turn it around and you call
+it a matched filter to a.
+
+And you take the received
+waveform.
+
+You pass it through the max
+filter for a, and you look at
+
+the output for it.
+
+Now, let's go back and look at
+what all of this was doing.
+
+And for now let's forget
+about the baseband to
+
+the passband business.
+
+Let's just look at this part
+here because it's a little
+
+easier to see this first.
+
+So this comes in here.
+
+Now remember what
+we were saying
+
+when we studied Nyquist.
+
+We said a neat thing to do was
+to use a square root of the
+
+Nyquist pulse at the
+transmitter.
+
+When you use a square root of
+the Nyquist pulse at the
+
+transmitter, what you have is
+orthogonality between the
+
+pulse and all of its shifts.
+
+Well now we don't much care
+about the orthogonality
+
+between the pulse and all of the
+shifts because we're only
+
+sending this one bit anyway.
+
+But it sort of looks like we're
+going to be able to put
+
+that back in in a nice
+convenient way.
+
+So we're sending this one pulse,
+p of t, city and what
+
+did we do in this baseband
+demodulator?
+
+We passed this through another
+filter, q of t, which was the
+
+matched filter to p of t.
+
+What's our optimal detector
+for maximum likelihood?
+
+It's to take whatever this
+waveform was, pass it through
+
+the matched filter.
+
+In other words, to calculate
+that inner product we just
+
+talked about.
+
+OK?
+
+So in fact when we were looking
+at the Nyquist problem
+
+and worrying about inner symbol
+interference, in fact
+
+what we were doing was also
+doing the first part of an
+
+optimal MAP detector.
+
+And at this point what comes
+out of here is a single
+
+number, v, which in fact now is
+the inner product of this
+
+waveform at this point.
+
+With the waveform,
+a, that we sent.
+
+OK?
+
+In other words, we started out
+by saying, "let's suppose that
+
+what we have here is a number.
+
+What's the optimal detector to
+build?" And then we go on and
+
+say, "OK, let's suppose we
+look at the problem here.
+
+What's the optimal detector to
+build now?" And the optimal
+
+detector to build now at this
+point is this matched filter
+
+to this input waveform.
+
+Followed by the inner product
+here-- which is what the match
+
+filter does for us-- followed
+by our binary antipodal
+
+detector again.
+
+OK?
+
+So by studying the problem at
+this point, we now understand
+
+what happens at this point.
+
+And do I have time to show you
+what happens at this point?
+
+I don't know.
+
+Let me--
+
+let's not do that at
+least right now--
+
+let's look at the picture of
+this that we get when we just
+
+look at the problem when
+we have two dimensions.
+
+So we're either going to
+transmit a vector, a, or we're
+
+going to transmit a
+vector, minus a.
+
+And think of this in
+two dimensions.
+
+When we transmit the
+vector, a, we have
+
+two dimensional noise.
+
+We've already pointed out that
+two dimensional Gaussian noise
+
+has circular symmetry.
+
+Spherical symmetry in an
+arbitrary number of dimension.
+
+So what happens is you get
+these equal probability
+
+regions which are spreading out
+like when you drop a rock
+
+into a pool of water.
+
+You see all of these things
+spreading out in circles.
+
+And you then say, "OK, what's
+this inner product going to
+
+correspond to?" Finding the
+inner product and comparing it
+
+with a threshold.
+
+Well you can see geometrically
+what's going to happen here.
+
+You're trying to do maximum
+likelihood.
+
+And we already know we're
+supposed to calculate the
+
+inner product, so what the inner
+product is going to do
+
+is take whatever v that we
+receive-- it's going to
+
+project it on to this line
+between 0 and a.
+
+So if I got a v here I'm going
+to project it down to here.
+
+And then what I'm going to do
+is I'm going to compare the
+
+distance from here to there
+with the distance
+
+from here to there.
+
+Which says first project, then
+do the old decision in a one
+
+dimensional way.
+
+Now geometrically, this distance
+squared is equal to
+
+this distance squared plus
+this distance squared.
+
+And this distance squared is
+equal to the same distance
+
+squared plus this distance
+squared.
+
+So whatever you decide to do in
+terms of these distances,
+
+you will also decide to do in
+terms of these distances.
+
+Which also means that the
+maximum likelihood regions
+
+that you're going to develop,
+or in fact the maximum a
+
+posteriori probability regions
+are simply planes.
+
+Which are perpendicular
+to the line between
+
+minus a and plus a.
+
+OK?
+
+So if you're doing maximum
+likelihood you just form a
+
+plane halfway between
+these two points.
+
+Yeah?
+
+AUDIENCE: [UNINTELLIGIBLE]
+
+PROFESSOR: We got the error
+probability just by first
+
+doing the projection and then
+turning it into this scale or
+
+problem again.
+
+So in fact the error
+probability--
+
+What?
+
+AUDIENCE: [UNINTELLIGIBLE]
+
+PROFESSOR: The probability of
+error is just the probability
+
+of error in the projection.
+
+Did I write it down someplace?
+
+Oh yeah, I did write it down.
+
+But I wrote it down, well
+I sort of cheated.
+
+It's in the notes.
+
+I mean the likelihood ratio is
+just a center product here
+
+which is a number.
+
+And when you find the error
+probability, you just use the
+
+same q formula that
+we used before.
+
+And in place of a
+you substitute--
+
+in place of a you substitute the
+inner product of v with a.
+
+Which is the corresponding
+quantity.
+
+So it's q of 4va
+divided by n0.
+
+OK?
+
+So that's the maximum likelihood
+error probability.
+
+OK?
+
+In other words, nothing
+new has happened here.
+
+You just go through the match
+filter and then you do this
+
+same one dimensional problem
+that we've already
+
+figured out how to do.
+
+I think I'm going to stop there
+and we'll do the complex
+
+case which really corresponds to
+what happens after baseband
+
+to passband then passband
+to baseband.
\ No newline at end of file
diff --git a/8gGbViZjoRw.txt b/8gGbViZjoRw.txt
new file mode 100644
index 0000000000000000000000000000000000000000..f2598c0fe81de5b8dab67c8a848759674c47be2a
--- /dev/null
+++ b/8gGbViZjoRw.txt
@@ -0,0 +1,1811 @@
+align:start position:0%
+ 
+hi welcome back to recitation in lecture
+
+ align:start position:0%
+hi welcome back to recitation in lecture
+ 
+
+ align:start position:0%
+hi welcome back to recitation in lecture
+you've been talking about implicitly
+
+ align:start position:0%
+you've been talking about implicitly
+ 
+
+ align:start position:0%
+you've been talking about implicitly
+defined functions and and implicit
+
+ align:start position:0%
+defined functions and and implicit
+ 
+
+ align:start position:0%
+defined functions and and implicit
+differentiation um so one of the reasons
+
+ align:start position:0%
+differentiation um so one of the reasons
+ 
+
+ align:start position:0%
+differentiation um so one of the reasons
+that these are important is or or that
+
+ align:start position:0%
+that these are important is or or that
+ 
+
+ align:start position:0%
+that these are important is or or that
+that implicit different differentiation
+
+ align:start position:0%
+that implicit different differentiation
+ 
+
+ align:start position:0%
+that implicit different differentiation
+is important is that sometimes you have
+
+ align:start position:0%
+is important is that sometimes you have
+ 
+
+ align:start position:0%
+is important is that sometimes you have
+a function defined implicitly and you
+
+ align:start position:0%
+a function defined implicitly and you
+ 
+
+ align:start position:0%
+a function defined implicitly and you
+can't solve for it you don't have any
+
+ align:start position:0%
+can't solve for it you don't have any
+ 
+
+ align:start position:0%
+can't solve for it you don't have any
+algebraic method for for computing the
+
+ align:start position:0%
+algebraic method for for computing the
+ 
+
+ align:start position:0%
+algebraic method for for computing the
+function values um as a formula say so
+
+ align:start position:0%
+function values um as a formula say so
+ 
+
+ align:start position:0%
+function values um as a formula say so
+for example um this function that I've
+
+ align:start position:0%
+for example um this function that I've
+ 
+
+ align:start position:0%
+for example um this function that I've
+written on the board that I've called W
+
+ align:start position:0%
+written on the board that I've called W
+ 
+
+ align:start position:0%
+written on the board that I've called W
+of X is is defined implicitly by the
+
+ align:start position:0%
+of X is is defined implicitly by the
+ 
+
+ align:start position:0%
+of X is is defined implicitly by the
+equation that W of x + 1 quantity time e
+
+ align:start position:0%
+equation that W of x + 1 quantity time e
+ 
+
+ align:start position:0%
+equation that W of x + 1 quantity time e
+to the W ofx is equal to X for all X so
+
+ align:start position:0%
+to the W ofx is equal to X for all X so
+ 
+
+ align:start position:0%
+to the W ofx is equal to X for all X so
+this this function um some of its values
+
+ align:start position:0%
+this this function um some of its values
+ 
+
+ align:start position:0%
+this this function um some of its values
+you can you can guess like like at x
+
+ align:start position:0%
+you can you can guess like like at x
+ 
+
+ align:start position:0%
+you can you can guess like like at x
+equals zero the function value is going
+
+ align:start position:0%
+equals zero the function value is going
+ 
+
+ align:start position:0%
+equals zero the function value is going
+to be negative one and the reason is
+
+ align:start position:0%
+to be negative one and the reason is
+ 
+
+ align:start position:0%
+to be negative one and the reason is
+that this can't ever be zero so the only
+
+ align:start position:0%
+that this can't ever be zero so the only
+ 
+
+ align:start position:0%
+that this can't ever be zero so the only
+way to get this side to be zero is if W
+
+ align:start position:0%
+way to get this side to be zero is if W
+ 
+
+ align:start position:0%
+way to get this side to be zero is if W
+is negative 1 if this term is zero so
+
+ align:start position:0%
+is negative 1 if this term is zero so
+ 
+
+ align:start position:0%
+is negative 1 if this term is zero so
+some of its some of its values are are
+
+ align:start position:0%
+some of its some of its values are are
+ 
+
+ align:start position:0%
+some of its some of its values are are
+easy to compute but some of its values
+
+ align:start position:0%
+easy to compute but some of its values
+ 
+
+ align:start position:0%
+easy to compute but some of its values
+aren't so for example if I asked you
+
+ align:start position:0%
+aren't so for example if I asked you
+ 
+
+ align:start position:0%
+aren't so for example if I asked you
+what w of three Hales is it's it's very
+
+ align:start position:0%
+what w of three Hales is it's it's very
+ 
+
+ align:start position:0%
+what w of three Hales is it's it's very
+hard there there's no algebraic way you
+
+ align:start position:0%
+hard there there's no algebraic way you
+ 
+
+ align:start position:0%
+hard there there's no algebraic way you
+can manipulate this equation that will
+
+ align:start position:0%
+can manipulate this equation that will
+ 
+
+ align:start position:0%
+can manipulate this equation that will
+let you figure that out um so in that
+
+ align:start position:0%
+let you figure that out um so in that
+ 
+
+ align:start position:0%
+let you figure that out um so in that
+situation you might still care about
+
+ align:start position:0%
+situation you might still care about
+ 
+
+ align:start position:0%
+situation you might still care about
+what what the function value is um so
+
+ align:start position:0%
+what what the function value is um so
+ 
+
+ align:start position:0%
+what what the function value is um so
+what can you do well you can you can try
+
+ align:start position:0%
+what can you do well you can you can try
+ 
+
+ align:start position:0%
+what can you do well you can you can try
+and find a numerical approximation so in
+
+ align:start position:0%
+and find a numerical approximation so in
+ 
+
+ align:start position:0%
+and find a numerical approximation so in
+this problem I'd like you to try and
+
+ align:start position:0%
+this problem I'd like you to try and
+ 
+
+ align:start position:0%
+this problem I'd like you to try and
+estimate the value W of 3 by using a
+
+ align:start position:0%
+estimate the value W of 3 by using a
+ 
+
+ align:start position:0%
+estimate the value W of 3 by using a
+linear approximation to to the function
+
+ align:start position:0%
+linear approximation to to the function
+ 
+
+ align:start position:0%
+linear approximation to to the function
+to the to the to the curve yeah a linear
+
+ align:start position:0%
+to the to the to the curve yeah a linear
+ 
+
+ align:start position:0%
+to the to the to the curve yeah a linear
+approximation of the function W ofx
+
+ align:start position:0%
+approximation of the function W ofx
+ 
+
+ align:start position:0%
+approximation of the function W ofx
+um in order in order to compute this
+
+ align:start position:0%
+um in order in order to compute this
+ 
+
+ align:start position:0%
+um in order in order to compute this
+value so as a hint I've given you so
+
+ align:start position:0%
+value so as a hint I've given you so
+ 
+
+ align:start position:0%
+value so as a hint I've given you so
+you're trying to compute W of three
+
+ align:start position:0%
+you're trying to compute W of three
+ 
+
+ align:start position:0%
+you're trying to compute W of three
+Hales as a hint I I'm pointing out to
+
+ align:start position:0%
+Hales as a hint I I'm pointing out to
+ 
+
+ align:start position:0%
+Hales as a hint I I'm pointing out to
+you that that W of one is zero right if
+
+ align:start position:0%
+you that that W of one is zero right if
+ 
+
+ align:start position:0%
+you that that W of one is zero right if
+if you put in x equal Z and W of 0
+
+ align:start position:0%
+if you put in x equal Z and W of 0
+ 
+
+ align:start position:0%
+if you put in x equal Z and W of 0
+equals uh sorry if you put an xals 1 and
+
+ align:start position:0%
+equals uh sorry if you put an xals 1 and
+ 
+
+ align:start position:0%
+equals uh sorry if you put an xals 1 and
+W 1 equals 0 on the left hand side you
+
+ align:start position:0%
+W 1 equals 0 on the left hand side you
+ 
+
+ align:start position:0%
+W 1 equals 0 on the left hand side you
+do indeed get get one as as you should
+
+ align:start position:0%
+do indeed get get one as as you should
+ 
+
+ align:start position:0%
+do indeed get get one as as you should
+so okay
+
+ align:start position:0%
+so okay
+ 
+
+ align:start position:0%
+so okay
+so um good so so that that that'll give
+
+ align:start position:0%
+so um good so so that that that'll give
+ 
+
+ align:start position:0%
+so um good so so that that that'll give
+you a hint about where you could base
+
+ align:start position:0%
+you a hint about where you could base
+ 
+
+ align:start position:0%
+you a hint about where you could base
+your your linear approximation so why
+
+ align:start position:0%
+your your linear approximation so why
+ 
+
+ align:start position:0%
+your your linear approximation so why
+don't you pause the video take a few
+
+ align:start position:0%
+don't you pause the video take a few
+ 
+
+ align:start position:0%
+don't you pause the video take a few
+minutes to work this out come back and
+
+ align:start position:0%
+minutes to work this out come back and
+ 
+
+ align:start position:0%
+minutes to work this out come back and
+we can work it out
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+together
+
+ align:start position:0%
+together
+ 
+
+ align:start position:0%
+together
+all right welcome back so hopefully
+
+ align:start position:0%
+all right welcome back so hopefully
+ 
+
+ align:start position:0%
+all right welcome back so hopefully
+you've had a chance to uh to work on
+
+ align:start position:0%
+you've had a chance to uh to work on
+ 
+
+ align:start position:0%
+you've had a chance to uh to work on
+this question a little bit so uh in
+
+ align:start position:0%
+this question a little bit so uh in
+ 
+
+ align:start position:0%
+this question a little bit so uh in
+order to do this linear approximation
+
+ align:start position:0%
+order to do this linear approximation
+ 
+
+ align:start position:0%
+order to do this linear approximation
+that we want what we need to know or we
+
+ align:start position:0%
+that we want what we need to know or we
+ 
+
+ align:start position:0%
+that we want what we need to know or we
+need to know a base point and we need to
+
+ align:start position:0%
+need to know a base point and we need to
+ 
+
+ align:start position:0%
+need to know a base point and we need to
+know the derivative of the function at
+
+ align:start position:0%
+know the derivative of the function at
+ 
+
+ align:start position:0%
+know the derivative of the function at
+that base point and those those are the
+
+ align:start position:0%
+that base point and those those are the
+ 
+
+ align:start position:0%
+that base point and those those are the
+the two pieces of data you need in order
+
+ align:start position:0%
+the two pieces of data you need in order
+ 
+
+ align:start position:0%
+the two pieces of data you need in order
+to construct a linear approximation so
+
+ align:start position:0%
+to construct a linear approximation so
+ 
+
+ align:start position:0%
+to construct a linear approximation so
+we we have we have a good candidate for
+
+ align:start position:0%
+we we have we have a good candidate for
+ 
+
+ align:start position:0%
+we we have we have a good candidate for
+a base Point here which is the point 1 Z
+
+ align:start position:0%
+a base Point here which is the point 1 Z
+ 
+
+ align:start position:0%
+a base Point here which is the point 1 Z
+so this this curve whatever it looks
+
+ align:start position:0%
+so this this curve whatever it looks
+ 
+
+ align:start position:0%
+so this this curve whatever it looks
+like it passes through the point 1 Z and
+
+ align:start position:0%
+like it passes through the point 1 Z and
+ 
+
+ align:start position:0%
+like it passes through the point 1 Z and
+that's the point we're going to use for
+
+ align:start position:0%
+that's the point we're going to use for
+ 
+
+ align:start position:0%
+that's the point we're going to use for
+our for our approximation so we're going
+
+ align:start position:0%
+our for our approximation so we're going
+ 
+
+ align:start position:0%
+our for our approximation so we're going
+to
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+use the linear
+
+ align:start position:0%
+use the linear
+ 
+
+ align:start position:0%
+use the linear
+approximation W of
+
+ align:start position:0%
+approximation W of
+ 
+
+ align:start position:0%
+approximation W of
+X is approximately equal
+
+ align:start position:0%
+X is approximately equal
+ 
+
+ align:start position:0%
+X is approximately equal
+to
+
+ align:start position:0%
+to
+ 
+
+ align:start position:0%
+to
+W Prime of 1
+
+ align:start position:0%
+W Prime of 1
+ 
+
+ align:start position:0%
+W Prime of 1
+* x
+
+ align:start position:0%
+* x
+ 
+
+ align:start position:0%
+* x
+-1 + W of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+1 when X is approximately equal to one
+
+ align:start position:0%
+1 when X is approximately equal to one
+ 
+
+ align:start position:0%
+1 when X is approximately equal to one
+so this is the linear approximation
+
+ align:start position:0%
+so this is the linear approximation
+ 
+
+ align:start position:0%
+so this is the linear approximation
+we're going to use and and we have that
+
+ align:start position:0%
+we're going to use and and we have that
+ 
+
+ align:start position:0%
+we're going to use and and we have that
+W of 1 here is zero so this is this is
+
+ align:start position:0%
+W of 1 here is zero so this is this is
+ 
+
+ align:start position:0%
+W of 1 here is zero so this is this is
+equal
+
+ align:start position:0%
+equal
+ 
+
+ align:start position:0%
+equal
+to W Prime of 1
+
+ align:start position:0%
+to W Prime of 1
+ 
+
+ align:start position:0%
+to W Prime of 1
+time x minus one just the the W of one
+
+ align:start position:0%
+time x minus one just the the W of one
+ 
+
+ align:start position:0%
+time x minus one just the the W of one
+is zero it just goes away so in order to
+
+ align:start position:0%
+is zero it just goes away so in order to
+ 
+
+ align:start position:0%
+is zero it just goes away so in order to
+estimate W of X and in particular W of
+
+ align:start position:0%
+estimate W of X and in particular W of
+ 
+
+ align:start position:0%
+estimate W of X and in particular W of
+three halves uh what we need to know is
+
+ align:start position:0%
+three halves uh what we need to know is
+ 
+
+ align:start position:0%
+three halves uh what we need to know is
+we need to know the derivative of w
+
+ align:start position:0%
+we need to know the derivative of w
+ 
+
+ align:start position:0%
+we need to know the derivative of w
+okay um and to get the derivative of w
+
+ align:start position:0%
+okay um and to get the derivative of w
+ 
+
+ align:start position:0%
+okay um and to get the derivative of w
+we need to use well we have only one
+
+ align:start position:0%
+we need to use well we have only one
+ 
+
+ align:start position:0%
+we need to use well we have only one
+piece of information about W which is we
+
+ align:start position:0%
+piece of information about W which is we
+ 
+
+ align:start position:0%
+piece of information about W which is we
+have that that it that it's defined by
+
+ align:start position:0%
+have that that it that it's defined by
+ 
+
+ align:start position:0%
+have that that it that it's defined by
+this implicit equation so in order to to
+
+ align:start position:0%
+this implicit equation so in order to to
+ 
+
+ align:start position:0%
+this implicit equation so in order to to
+get the derivative of w we have to use
+
+ align:start position:0%
+get the derivative of w we have to use
+ 
+
+ align:start position:0%
+get the derivative of w we have to use
+implicit differentiation okay so let's
+
+ align:start position:0%
+implicit differentiation okay so let's
+ 
+
+ align:start position:0%
+implicit differentiation okay so let's
+let's do that um so if we if we
+
+ align:start position:0%
+let's do that um so if we if we
+ 
+
+ align:start position:0%
+let's do that um so if we if we
+implicitly differentiate this equation
+
+ align:start position:0%
+implicitly differentiate this equation
+ 
+
+ align:start position:0%
+implicitly differentiate this equation
+so let's let's start with the the right
+
+ align:start position:0%
+so let's let's start with the the right
+ 
+
+ align:start position:0%
+so let's let's start with the the right
+hand side's going to be really easy
+
+ align:start position:0%
+hand side's going to be really easy
+ 
+
+ align:start position:0%
+hand side's going to be really easy
+right we're going to differentiate with
+
+ align:start position:0%
+right we're going to differentiate with
+ 
+
+ align:start position:0%
+right we're going to differentiate with
+respect to X the right hand side's going
+
+ align:start position:0%
+respect to X the right hand side's going
+ 
+
+ align:start position:0%
+respect to X the right hand side's going
+to be one on the left hand side is going
+
+ align:start position:0%
+to be one on the left hand side is going
+ 
+
+ align:start position:0%
+to be one on the left hand side is going
+to be a little more complicated we have
+
+ align:start position:0%
+to be a little more complicated we have
+ 
+
+ align:start position:0%
+to be a little more complicated we have
+a product and then this piece we're
+
+ align:start position:0%
+a product and then this piece we're
+ 
+
+ align:start position:0%
+a product and then this piece we're
+going to we're going to have a chain
+
+ align:start position:0%
+going to we're going to have a chain
+ 
+
+ align:start position:0%
+going to we're going to have a chain
+rule situation right we have e to the W
+
+ align:start position:0%
+rule situation right we have e to the W
+ 
+
+ align:start position:0%
+rule situation right we have e to the W
+of X so so okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so so we're going to take an implicit
+
+ align:start position:0%
+so so we're going to take an implicit
+ 
+
+ align:start position:0%
+so so we're going to take an implicit
+derivative and on the left so okay so
+
+ align:start position:0%
+derivative and on the left so okay so
+ 
+
+ align:start position:0%
+derivative and on the left so okay so
+from the product rule First We Take the
+
+ align:start position:0%
+from the product rule First We Take the
+ 
+
+ align:start position:0%
+from the product rule First We Take the
+derivative of the first part so that's
+
+ align:start position:0%
+derivative of the first part so that's
+ 
+
+ align:start position:0%
+derivative of the first part so that's
+just
+
+ align:start position:0%
+just
+ 
+
+ align:start position:0%
+just
+W Prime of X time the second part that's
+
+ align:start position:0%
+W Prime of X time the second part that's
+ 
+
+ align:start position:0%
+W Prime of X time the second part that's
+e to the W of
+
+ align:start position:0%
+e to the W of
+ 
+
+ align:start position:0%
+e to the W of
+X plus the first part that's W ofx + 1
+
+ align:start position:0%
+X plus the first part that's W ofx + 1
+ 
+
+ align:start position:0%
+X plus the first part that's W ofx + 1
+times the derivative of the second part
+
+ align:start position:0%
+times the derivative of the second part
+ 
+
+ align:start position:0%
+times the derivative of the second part
+so the second part is e to the W of X so
+
+ align:start position:0%
+so the second part is e to the W of X so
+ 
+
+ align:start position:0%
+so the second part is e to the W of X so
+that gives me an e to the W of x
+
+ align:start position:0%
+that gives me an e to the W of x
+ 
+
+ align:start position:0%
+that gives me an e to the W of x
+times W Prime of X that's the that's the
+
+ align:start position:0%
+times W Prime of X that's the that's the
+ 
+
+ align:start position:0%
+times W Prime of X that's the that's the
+chain rule so that's what happens when I
+
+ align:start position:0%
+chain rule so that's what happens when I
+ 
+
+ align:start position:0%
+chain rule so that's what happens when I
+differentiate the left hand side and on
+
+ align:start position:0%
+differentiate the left hand side and on
+ 
+
+ align:start position:0%
+differentiate the left hand side and on
+the right hand side
+
+ align:start position:0%
+the right hand side
+ 
+
+ align:start position:0%
+the right hand side
+I take the derivative of x and I get one
+
+ align:start position:0%
+I take the derivative of x and I get one
+ 
+
+ align:start position:0%
+I take the derivative of x and I get one
+okay good um so now I've got this
+
+ align:start position:0%
+okay good um so now I've got this
+ 
+
+ align:start position:0%
+okay good um so now I've got this
+equation and I need to solve this
+
+ align:start position:0%
+equation and I need to solve this
+ 
+
+ align:start position:0%
+equation and I need to solve this
+equation for w Prime because if you look
+
+ align:start position:0%
+equation for w Prime because if you look
+ 
+
+ align:start position:0%
+equation for w Prime because if you look
+up here that's what I want I want a a
+
+ align:start position:0%
+up here that's what I want I want a a
+ 
+
+ align:start position:0%
+up here that's what I want I want a a
+particular value of w Prime and as
+
+ align:start position:0%
+particular value of w Prime and as
+ 
+
+ align:start position:0%
+particular value of w Prime and as
+always happens in implicit
+
+ align:start position:0%
+always happens in implicit
+ 
+
+ align:start position:0%
+always happens in implicit
+differentiation from the point of view
+
+ align:start position:0%
+differentiation from the point of view
+ 
+
+ align:start position:0%
+differentiation from the point of view
+of this W Prime it's only involved in
+
+ align:start position:0%
+of this W Prime it's only involved in
+ 
+
+ align:start position:0%
+of this W Prime it's only involved in
+the in the equation in a very simple way
+
+ align:start position:0%
+the in the equation in a very simple way
+ 
+
+ align:start position:0%
+the in the equation in a very simple way
+so there's it multiplied by functions of
+
+ align:start position:0%
+so there's it multiplied by functions of
+ 
+
+ align:start position:0%
+so there's it multiplied by functions of
+X and W of X but not there it's just you
+
+ align:start position:0%
+X and W of X but not there it's just you
+ 
+
+ align:start position:0%
+X and W of X but not there it's just you
+know it's just multiplied by something
+
+ align:start position:0%
+know it's just multiplied by something
+ 
+
+ align:start position:0%
+know it's just multiplied by something
+that doesn't involve W Prime at all and
+
+ align:start position:0%
+that doesn't involve W Prime at all and
+ 
+
+ align:start position:0%
+that doesn't involve W Prime at all and
+then here it's multiplied by something
+
+ align:start position:0%
+then here it's multiplied by something
+ 
+
+ align:start position:0%
+then here it's multiplied by something
+that doesn't involve W Prime at all so
+
+ align:start position:0%
+that doesn't involve W Prime at all so
+ 
+
+ align:start position:0%
+that doesn't involve W Prime at all so
+you can just collect your W primes and
+
+ align:start position:0%
+you can just collect your W primes and
+ 
+
+ align:start position:0%
+you can just collect your W primes and
+divide through you know it's it's just
+
+ align:start position:0%
+divide through you know it's it's just
+ 
+
+ align:start position:0%
+divide through you know it's it's just
+like solving a linear equation um so
+
+ align:start position:0%
+like solving a linear equation um so
+ 
+
+ align:start position:0%
+like solving a linear equation um so
+here if we collect our W primes this is
+
+ align:start position:0%
+here if we collect our W primes this is
+ 
+
+ align:start position:0%
+here if we collect our W primes this is
+W Prime of x
+
+ align:start position:0%
+W Prime of x
+ 
+
+ align:start position:0%
+W Prime of x
+times looks like w of
+
+ align:start position:0%
+times looks like w of
+ 
+
+ align:start position:0%
+times looks like w of
+x + 2 time e to the
+
+ align:start position:0%
+x + 2 time e to the
+ 
+
+ align:start position:0%
+x + 2 time e to the
+W of X did I get that
+
+ align:start position:0%
+W of X did I get that
+ 
+
+ align:start position:0%
+W of X did I get that
+right looks good okay so that's still
+
+ align:start position:0%
+right looks good okay so that's still
+ 
+
+ align:start position:0%
+right looks good okay so that's still
+equal to one and so that means that W
+
+ align:start position:0%
+equal to one and so that means that W
+ 
+
+ align:start position:0%
+equal to one and so that means that W
+Prime of X is just well just you know
+
+ align:start position:0%
+Prime of X is just well just you know
+ 
+
+ align:start position:0%
+Prime of X is just well just you know
+it's equal to one
+
+ align:start position:0%
+it's equal to one
+ 
+
+ align:start position:0%
+it's equal to one
+over W of
+
+ align:start position:0%
+over W of
+ 
+
+ align:start position:0%
+over W of
+X+ 2 * e to W of X okay so this is true
+
+ align:start position:0%
+X+ 2 * e to W of X okay so this is true
+ 
+
+ align:start position:0%
+X+ 2 * e to W of X okay so this is true
+for every X but I don't need this
+
+ align:start position:0%
+for every X but I don't need this
+ 
+
+ align:start position:0%
+for every X but I don't need this
+equation for every X I just need the
+
+ align:start position:0%
+equation for every X I just need the
+ 
+
+ align:start position:0%
+equation for every X I just need the
+particular value of w Prime at one so
+
+ align:start position:0%
+particular value of w Prime at one so
+ 
+
+ align:start position:0%
+particular value of w Prime at one so
+that's so so I'm going to take this
+
+ align:start position:0%
+that's so so I'm going to take this
+ 
+
+ align:start position:0%
+that's so so I'm going to take this
+equation then and I'm just going to put
+
+ align:start position:0%
+equation then and I'm just going to put
+ 
+
+ align:start position:0%
+equation then and I'm just going to put
+in xals 1 so I put in xals 1 let me do
+
+ align:start position:0%
+in xals 1 so I put in xals 1 let me do
+ 
+
+ align:start position:0%
+in xals 1 so I put in xals 1 let me do
+it over here so I get W Prime of one and
+
+ align:start position:0%
+it over here so I get W Prime of one and
+ 
+
+ align:start position:0%
+it over here so I get W Prime of one and
+I just everywhere I had an X I put in a
+
+ align:start position:0%
+I just everywhere I had an X I put in a
+ 
+
+ align:start position:0%
+I just everywhere I had an X I put in a
+one so actually in this equation the
+
+ align:start position:0%
+one so actually in this equation the
+ 
+
+ align:start position:0%
+one so actually in this equation the
+only place X appears is in the argument
+
+ align:start position:0%
+only place X appears is in the argument
+ 
+
+ align:start position:0%
+only place X appears is in the argument
+of w so this is W of 1 plus 2 * e to the
+
+ align:start position:0%
+of w so this is W of 1 plus 2 * e to the
+ 
+
+ align:start position:0%
+of w so this is W of 1 plus 2 * e to the
+W of 1 okay so in order to get W Prime
+
+ align:start position:0%
+W of 1 okay so in order to get W Prime
+ 
+
+ align:start position:0%
+W of 1 okay so in order to get W Prime
+of 1 I need to know what w of one is but
+
+ align:start position:0%
+of 1 I need to know what w of one is but
+ 
+
+ align:start position:0%
+of 1 I need to know what w of one is but
+I had that I had it was right back here
+
+ align:start position:0%
+I had that I had it was right back here
+ 
+
+ align:start position:0%
+I had that I had it was right back here
+that was the that was my hint to you
+
+ align:start position:0%
+that was the that was my hint to you
+ 
+
+ align:start position:0%
+that was the that was my hint to you
+right this is why we're using this point
+
+ align:start position:0%
+right this is why we're using this point
+ 
+
+ align:start position:0%
+right this is why we're using this point
+as a base point which is we know the
+
+ align:start position:0%
+as a base point which is we know the
+ 
+
+ align:start position:0%
+as a base point which is we know the
+value of W uh for this value of x so we
+
+ align:start position:0%
+value of W uh for this value of x so we
+ 
+
+ align:start position:0%
+value of W uh for this value of x so we
+we take that value so w of one is zero
+
+ align:start position:0%
+we take that value so w of one is zero
+ 
+
+ align:start position:0%
+we take that value so w of one is zero
+so this is just 1 over well 0 + 2 is 2
+
+ align:start position:0%
+so this is just 1 over well 0 + 2 is 2
+ 
+
+ align:start position:0%
+so this is just 1 over well 0 + 2 is 2
+and E to the 0 is one so it's just one
+
+ align:start position:0%
+and E to the 0 is one so it's just one
+ 
+
+ align:start position:0%
+and E to the 0 is one so it's just one
+over two sorry that's written a little
+
+ align:start position:0%
+over two sorry that's written a little
+ 
+
+ align:start position:0%
+over two sorry that's written a little
+oddly we can make it two * one all right
+
+ align:start position:0%
+oddly we can make it two * one all right
+ 
+
+ align:start position:0%
+oddly we can make it two * one all right
+so one over
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+two okay so I take that back upstairs to
+
+ align:start position:0%
+two okay so I take that back upstairs to
+ 
+
+ align:start position:0%
+two okay so I take that back upstairs to
+this equation that I had here and I have
+
+ align:start position:0%
+this equation that I had here and I have
+ 
+
+ align:start position:0%
+this equation that I had here and I have
+that W of X is approximately equal to W
+
+ align:start position:0%
+that W of X is approximately equal to W
+ 
+
+ align:start position:0%
+that W of X is approximately equal to W
+Prime of 1 * x
+
+ align:start position:0%
+Prime of 1 * x
+ 
+
+ align:start position:0%
+Prime of 1 * x
+-1
+
+ align:start position:0%
+-1
+ 
+
+ align:start position:0%
+-1
+so w of X is approximately equal to W
+
+ align:start position:0%
+so w of X is approximately equal to W
+ 
+
+ align:start position:0%
+so w of X is approximately equal to W
+Prime of 1 we saw
+
+ align:start position:0%
+Prime of 1 we saw
+ 
+
+ align:start position:0%
+Prime of 1 we saw
+is 12 * X -
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+1 and that approximation was good near
+
+ align:start position:0%
+1 and that approximation was good near
+ 
+
+ align:start position:0%
+1 and that approximation was good near
+our base point so that's that's good
+
+ align:start position:0%
+our base point so that's that's good
+ 
+
+ align:start position:0%
+our base point so that's that's good
+when X is near
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+one all right and then so this is this
+
+ align:start position:0%
+one all right and then so this is this
+ 
+
+ align:start position:0%
+one all right and then so this is this
+is the linear approximation and I asked
+
+ align:start position:0%
+is the linear approximation and I asked
+ 
+
+ align:start position:0%
+is the linear approximation and I asked
+for for the linear approximation its
+
+ align:start position:0%
+for for the linear approximation its
+ 
+
+ align:start position:0%
+for for the linear approximation its
+value at the particular point xal
+
+ align:start position:0%
+value at the particular point xal
+ 
+
+ align:start position:0%
+value at the particular point xal
+3es so w of 3es
+
+ align:start position:0%
+3es so w of 3es
+ 
+
+ align:start position:0%
+3es so w of 3es
+is
+
+ align:start position:0%
+is
+ 
+
+ align:start position:0%
+is
+approximately 12 time
+
+ align:start position:0%
+approximately 12 time
+ 
+
+ align:start position:0%
+approximately 12 time
+well 3es minus 1 is also a
+
+ align:start position:0%
+well 3es minus 1 is also a
+ 
+
+ align:start position:0%
+well 3es minus 1 is also a
+half so this is a quarter okay so this
+
+ align:start position:0%
+half so this is a quarter okay so this
+ 
+
+ align:start position:0%
+half so this is a quarter okay so this
+is our estimate for w of three Hales W
+
+ align:start position:0%
+is our estimate for w of three Hales W
+ 
+
+ align:start position:0%
+is our estimate for w of three Hales W
+of three halves is approximately 1/4 if
+
+ align:start position:0%
+of three halves is approximately 1/4 if
+ 
+
+ align:start position:0%
+of three halves is approximately 1/4 if
+you wanted a better estimate you could
+
+ align:start position:0%
+you wanted a better estimate you could
+ 
+
+ align:start position:0%
+you wanted a better estimate you could
+try iterating this process now now you
+
+ align:start position:0%
+try iterating this process now now you
+ 
+
+ align:start position:0%
+try iterating this process now now you
+might have a a you know you could or
+
+ align:start position:0%
+might have a a you know you could or
+ 
+
+ align:start position:0%
+might have a a you know you could or
+choosing some base Point even closer if
+
+ align:start position:0%
+choosing some base Point even closer if
+ 
+
+ align:start position:0%
+choosing some base Point even closer if
+you could figure out the the value of w
+
+ align:start position:0%
+you could figure out the the value of w
+ 
+
+ align:start position:0%
+you could figure out the the value of w
+and X near near that um near this this
+
+ align:start position:0%
+and X near near that um near this this
+ 
+
+ align:start position:0%
+and X near near that um near this this
+point that you're interested in three
+
+ align:start position:0%
+point that you're interested in three
+ 
+
+ align:start position:0%
+point that you're interested in three
+halves um so just to to sum up what we
+
+ align:start position:0%
+halves um so just to to sum up what we
+ 
+
+ align:start position:0%
+halves um so just to to sum up what we
+did was we had this implicitly defined
+
+ align:start position:0%
+did was we had this implicitly defined
+ 
+
+ align:start position:0%
+did was we had this implicitly defined
+function w we wanted to estimate its
+
+ align:start position:0%
+function w we wanted to estimate its
+ 
+
+ align:start position:0%
+function w we wanted to estimate its
+value at a point where we couldn't
+
+ align:start position:0%
+value at a point where we couldn't
+ 
+
+ align:start position:0%
+value at a point where we couldn't
+compute it explicitly so what we did was
+
+ align:start position:0%
+compute it explicitly so what we did was
+ 
+
+ align:start position:0%
+compute it explicitly so what we did was
+we did our normal linear approximation
+
+ align:start position:0%
+we did our normal linear approximation
+ 
+
+ align:start position:0%
+we did our normal linear approximation
+method right so we we wrote down our our
+
+ align:start position:0%
+method right so we we wrote down our our
+ 
+
+ align:start position:0%
+method right so we we wrote down our our
+normal linear approximation formula the
+
+ align:start position:0%
+normal linear approximation formula the
+ 
+
+ align:start position:0%
+normal linear approximation formula the
+only thing that was slightly unusual is
+
+ align:start position:0%
+only thing that was slightly unusual is
+ 
+
+ align:start position:0%
+only thing that was slightly unusual is
+that we had to use implicit
+
+ align:start position:0%
+that we had to use implicit
+ 
+
+ align:start position:0%
+that we had to use implicit
+differentiation in order to compute the
+
+ align:start position:0%
+differentiation in order to compute the
+ 
+
+ align:start position:0%
+differentiation in order to compute the
+derivative that appears in the linear
+
+ align:start position:0%
+derivative that appears in the linear
+ 
+
+ align:start position:0%
+derivative that appears in the linear
+approximation we implicitly
+
+ align:start position:0%
+approximation we implicitly
+ 
+
+ align:start position:0%
+approximation we implicitly
+differentiated okay so that that
+
+ align:start position:0%
+differentiated okay so that that
+ 
+
+ align:start position:0%
+differentiated okay so that that
+happened just like normal and then at
+
+ align:start position:0%
+happened just like normal and then at
+ 
+
+ align:start position:0%
+happened just like normal and then at
+the end we plugged in the values that we
+
+ align:start position:0%
+the end we plugged in the values that we
+ 
+
+ align:start position:0%
+the end we plugged in the values that we
+were interested in to actually compute
+
+ align:start position:0%
+were interested in to actually compute
+ 
+
+ align:start position:0%
+were interested in to actually compute
+the the the particular value of that
+
+ align:start position:0%
+the the the particular value of that
+ 
+
+ align:start position:0%
+the the the particular value of that
+approximation so I'll end there
\ No newline at end of file
diff --git a/8sgl_wzzQUY.txt b/8sgl_wzzQUY.txt
new file mode 100644
index 0000000000000000000000000000000000000000..7efe6d82eb15a964416d0110f3f3e867b3bff5ad
--- /dev/null
+++ b/8sgl_wzzQUY.txt
@@ -0,0 +1,9523 @@
+align:start position:0%
+ 
+today and next lecture we are going to
+
+ align:start position:0%
+today and next lecture we are going to
+ 
+
+ align:start position:0%
+today and next lecture we are going to
+turn to a topic that's as I've
+
+ align:start position:0%
+turn to a topic that's as I've
+ 
+
+ align:start position:0%
+turn to a topic that's as I've
+highlighted previously woefully missing
+
+ align:start position:0%
+highlighted previously woefully missing
+ 
+
+ align:start position:0%
+highlighted previously woefully missing
+from this class and from Bas a lot of
+
+ align:start position:0%
+from this class and from Bas a lot of
+ 
+
+ align:start position:0%
+from this class and from Bas a lot of
+basic economics which is we're going to
+
+ align:start position:0%
+basic economics which is we're going to
+ 
+
+ align:start position:0%
+basic economics which is we're going to
+start talking about Equity this class
+
+ align:start position:0%
+start talking about Equity this class
+ 
+
+ align:start position:0%
+start talking about Equity this class
+has been totally focused on efficiency
+
+ align:start position:0%
+has been totally focused on efficiency
+ 
+
+ align:start position:0%
+has been totally focused on efficiency
+we've come back and back again to ever
+
+ align:start position:0%
+we've come back and back again to ever
+ 
+
+ align:start position:0%
+we've come back and back again to ever
+since we did the lecture on consumer and
+
+ align:start position:0%
+since we did the lecture on consumer and
+ 
+
+ align:start position:0%
+since we did the lecture on consumer and
+producer Surplus we've talked about a
+
+ align:start position:0%
+producer Surplus we've talked about a
+ 
+
+ align:start position:0%
+producer Surplus we've talked about a
+particular normative perspective which
+
+ align:start position:0%
+particular normative perspective which
+ 
+
+ align:start position:0%
+particular normative perspective which
+is the goal of society is to basically
+
+ align:start position:0%
+is the goal of society is to basically
+ 
+
+ align:start position:0%
+is the goal of society is to basically
+maximize total social surplus the goal
+
+ align:start position:0%
+maximize total social surplus the goal
+ 
+
+ align:start position:0%
+maximize total social surplus the goal
+of societ is really to maximize the pi
+
+ align:start position:0%
+of societ is really to maximize the pi
+ 
+
+ align:start position:0%
+of societ is really to maximize the pi
+and we don't really care how it's
+
+ align:start position:0%
+and we don't really care how it's
+ 
+
+ align:start position:0%
+and we don't really care how it's
+distributed and this is Illustrated as I
+
+ align:start position:0%
+distributed and this is Illustrated as I
+ 
+
+ align:start position:0%
+distributed and this is Illustrated as I
+mentioned before nowhere more starkly
+
+ align:start position:0%
+mentioned before nowhere more starkly
+ 
+
+ align:start position:0%
+mentioned before nowhere more starkly
+than the fact that two different Market
+
+ align:start position:0%
+than the fact that two different Market
+ 
+
+ align:start position:0%
+than the fact that two different Market
+outcomes have the exact same welfare
+
+ align:start position:0%
+outcomes have the exact same welfare
+ 
+
+ align:start position:0%
+outcomes have the exact same welfare
+consequences one is a perfectly
+
+ align:start position:0%
+consequences one is a perfectly
+ 
+
+ align:start position:0%
+consequences one is a perfectly
+competitive
+
+ align:start position:0%
+competitive
+ 
+
+ align:start position:0%
+competitive
+market and one is a perfectly price
+
+ align:start position:0%
+market and one is a perfectly price
+ 
+
+ align:start position:0%
+market and one is a perfectly price
+discriminating
+
+ align:start position:0%
+discriminating
+ 
+
+ align:start position:0%
+discriminating
+monopolist both of those Market outcomes
+
+ align:start position:0%
+monopolist both of those Market outcomes
+ 
+
+ align:start position:0%
+monopolist both of those Market outcomes
+yield maximum social
+
+ align:start position:0%
+yield maximum social
+ 
+
+ align:start position:0%
+yield maximum social
+surplus yet they feel very different and
+
+ align:start position:0%
+surplus yet they feel very different and
+ 
+
+ align:start position:0%
+surplus yet they feel very different and
+outcome where consumers and producers
+
+ align:start position:0%
+outcome where consumers and producers
+ 
+
+ align:start position:0%
+outcome where consumers and producers
+split the pie feels to us innately very
+
+ align:start position:0%
+split the pie feels to us innately very
+ 
+
+ align:start position:0%
+split the pie feels to us innately very
+different than an outcome where
+
+ align:start position:0%
+different than an outcome where
+ 
+
+ align:start position:0%
+different than an outcome where
+producers get to keep it all and that's
+
+ align:start position:0%
+producers get to keep it all and that's
+ 
+
+ align:start position:0%
+producers get to keep it all and that's
+because innately we as humans care not
+
+ align:start position:0%
+because innately we as humans care not
+ 
+
+ align:start position:0%
+because innately we as humans care not
+just about efficiency but fairness about
+
+ align:start position:0%
+just about efficiency but fairness about
+ 
+
+ align:start position:0%
+just about efficiency but fairness about
+equity and we actually care about not
+
+ align:start position:0%
+equity and we actually care about not
+ 
+
+ align:start position:0%
+equity and we actually care about not
+just how much stuff gets produced but
+
+ align:start position:0%
+just how much stuff gets produced but
+ 
+
+ align:start position:0%
+just how much stuff gets produced but
+who gets
+
+ align:start position:0%
+who gets
+ 
+
+ align:start position:0%
+who gets
+it now in that particular
+
+ align:start position:0%
+it now in that particular
+ 
+
+ align:start position:0%
+it now in that particular
+example you get two very different
+
+ align:start position:0%
+example you get two very different
+ 
+
+ align:start position:0%
+example you get two very different
+distributional outcomes with the same
+
+ align:start position:0%
+distributional outcomes with the same
+ 
+
+ align:start position:0%
+distributional outcomes with the same
+level of efficiency but that's actually
+
+ align:start position:0%
+level of efficiency but that's actually
+ 
+
+ align:start position:0%
+level of efficiency but that's actually
+pretty unique it turns out generally
+
+ align:start position:0%
+pretty unique it turns out generally
+ 
+
+ align:start position:0%
+pretty unique it turns out generally
+that different distributional outcomes
+
+ align:start position:0%
+that different distributional outcomes
+ 
+
+ align:start position:0%
+that different distributional outcomes
+different levels of fairness come at
+
+ align:start position:0%
+different levels of fairness come at
+ 
+
+ align:start position:0%
+different levels of fairness come at
+different levels of efficiency and that
+
+ align:start position:0%
+different levels of efficiency and that
+ 
+
+ align:start position:0%
+different levels of efficiency and that
+we leads to what we fundamentally call
+
+ align:start position:0%
+we leads to what we fundamentally call
+ 
+
+ align:start position:0%
+we leads to what we fundamentally call
+the equity efficiency
+
+ align:start position:0%
+the equity efficiency
+ 
+
+ align:start position:0%
+the equity efficiency
+tradeoff that basically to get more
+
+ align:start position:0%
+tradeoff that basically to get more
+ 
+
+ align:start position:0%
+tradeoff that basically to get more
+Equitable outcomes often requires less
+
+ align:start position:0%
+Equitable outcomes often requires less
+ 
+
+ align:start position:0%
+Equitable outcomes often requires less
+efficient
+
+ align:start position:0%
+efficient
+ 
+
+ align:start position:0%
+efficient
+outcomes and our goal as economists is
+
+ align:start position:0%
+outcomes and our goal as economists is
+ 
+
+ align:start position:0%
+outcomes and our goal as economists is
+to decide is it worth it how do we think
+
+ align:start position:0%
+to decide is it worth it how do we think
+ 
+
+ align:start position:0%
+to decide is it worth it how do we think
+about whether a potential sacrifice in
+
+ align:start position:0%
+about whether a potential sacrifice in
+ 
+
+ align:start position:0%
+about whether a potential sacrifice in
+efficiency is worth a gain in equity
+
+ align:start position:0%
+efficiency is worth a gain in equity
+ 
+
+ align:start position:0%
+efficiency is worth a gain in equity
+your fairness and the best way to think
+
+ align:start position:0%
+your fairness and the best way to think
+ 
+
+ align:start position:0%
+your fairness and the best way to think
+about this was posed by The Economist
+
+ align:start position:0%
+about this was posed by The Economist
+ 
+
+ align:start position:0%
+about this was posed by The Economist
+Arthur
+
+ align:start position:0%
+Arthur
+ 
+
+ align:start position:0%
+Arthur
+Oaken about 40 50 years ago God it must
+
+ align:start position:0%
+Oaken about 40 50 years ago God it must
+ 
+
+ align:start position:0%
+Oaken about 40 50 years ago God it must
+be 50 years ago
+
+ align:start position:0%
+be 50 years ago
+ 
+
+ align:start position:0%
+be 50 years ago
+now Arthur Oaken
+
+ align:start position:0%
+now Arthur Oaken
+ 
+
+ align:start position:0%
+now Arthur Oaken
+OK posed the example of the Leaky bucket
+
+ align:start position:0%
+OK posed the example of the Leaky bucket
+ 
+
+ align:start position:0%
+OK posed the example of the Leaky bucket
+which is the best way to think about
+
+ align:start position:0%
+which is the best way to think about
+ 
+
+ align:start position:0%
+which is the best way to think about
+redistribution he said imagine the way
+
+ align:start position:0%
+redistribution he said imagine the way
+ 
+
+ align:start position:0%
+redistribution he said imagine the way
+imagine a society with the rich people
+
+ align:start position:0%
+imagine a society with the rich people
+ 
+
+ align:start position:0%
+imagine a society with the rich people
+and poor people and imagine the way we
+
+ align:start position:0%
+and poor people and imagine the way we
+ 
+
+ align:start position:0%
+and poor people and imagine the way we
+redistributed from rich people to poor
+
+ align:start position:0%
+redistributed from rich people to poor
+ 
+
+ align:start position:0%
+redistributed from rich people to poor
+people was by literally the rich people
+
+ align:start position:0%
+people was by literally the rich people
+ 
+
+ align:start position:0%
+people was by literally the rich people
+putting money in a bucket then someone
+
+ align:start position:0%
+putting money in a bucket then someone
+ 
+
+ align:start position:0%
+putting money in a bucket then someone
+carries that bucket and dumps it out in
+
+ align:start position:0%
+carries that bucket and dumps it out in
+ 
+
+ align:start position:0%
+carries that bucket and dumps it out in
+front of the poor people the simplest
+
+ align:start position:0%
+front of the poor people the simplest
+ 
+
+ align:start position:0%
+front of the poor people the simplest
+possible view of distribution and we
+
+ align:start position:0%
+possible view of distribution and we
+ 
+
+ align:start position:0%
+possible view of distribution and we
+probably and so Arthur Oak's question
+
+ align:start position:0%
+probably and so Arthur Oak's question
+ 
+
+ align:start position:0%
+probably and so Arthur Oak's question
+was imagine simple world where a rich
+
+ align:start position:0%
+was imagine simple world where a rich
+ 
+
+ align:start position:0%
+was imagine simple world where a rich
+person puts in a dollar someone carries
+
+ align:start position:0%
+person puts in a dollar someone carries
+ 
+
+ align:start position:0%
+person puts in a dollar someone carries
+over and gives that dollar to a poor
+
+ align:start position:0%
+over and gives that dollar to a poor
+ 
+
+ align:start position:0%
+over and gives that dollar to a poor
+person how many of us would favor that
+
+ align:start position:0%
+person how many of us would favor that
+ 
+
+ align:start position:0%
+person how many of us would favor that
+probably most of us probably most of us
+
+ align:start position:0%
+probably most of us probably most of us
+ 
+
+ align:start position:0%
+probably most of us probably most of us
+would think that the rich person would
+
+ align:start position:0%
+would think that the rich person would
+ 
+
+ align:start position:0%
+would think that the rich person would
+miss the dollar
+
+ align:start position:0%
+miss the dollar
+ 
+
+ align:start position:0%
+miss the dollar
+less than the poor person would value
+
+ align:start position:0%
+less than the poor person would value
+ 
+
+ align:start position:0%
+less than the poor person would value
+the dollar so probably most of us would
+
+ align:start position:0%
+the dollar so probably most of us would
+ 
+
+ align:start position:0%
+the dollar so probably most of us would
+think that if you could take a dollar
+
+ align:start position:0%
+think that if you could take a dollar
+ 
+
+ align:start position:0%
+think that if you could take a dollar
+from the rich and give it to the poor
+
+ align:start position:0%
+from the rich and give it to the poor
+ 
+
+ align:start position:0%
+from the rich and give it to the poor
+that's a good thing to
+
+ align:start position:0%
+that's a good thing to
+ 
+
+ align:start position:0%
+that's a good thing to
+do now Oak can ask but what if the
+
+ align:start position:0%
+do now Oak can ask but what if the
+ 
+
+ align:start position:0%
+do now Oak can ask but what if the
+bucket was leaky what if along the money
+
+ align:start position:0%
+bucket was leaky what if along the money
+ 
+
+ align:start position:0%
+bucket was leaky what if along the money
+along the way some of the money leaked
+
+ align:start position:0%
+along the way some of the money leaked
+ 
+
+ align:start position:0%
+along the way some of the money leaked
+out so the dollar you took from the rich
+
+ align:start position:0%
+out so the dollar you took from the rich
+ 
+
+ align:start position:0%
+out so the dollar you took from the rich
+became less than a Dollar by time I got
+
+ align:start position:0%
+became less than a Dollar by time I got
+ 
+
+ align:start position:0%
+became less than a Dollar by time I got
+to the
+
+ align:start position:0%
+to the
+ 
+
+ align:start position:0%
+to the
+poor what if it was 90 cents 70 cents 50
+
+ align:start position:0%
+poor what if it was 90 cents 70 cents 50
+ 
+
+ align:start position:0%
+poor what if it was 90 cents 70 cents 50
+cents 30 Cent 10 cents or Nothing At
+
+ align:start position:0%
+cents 30 Cent 10 cents or Nothing At
+ 
+
+ align:start position:0%
+cents 30 Cent 10 cents or Nothing At
+what point do you stop wanting to make
+
+ align:start position:0%
+what point do you stop wanting to make
+ 
+
+ align:start position:0%
+what point do you stop wanting to make
+that
+
+ align:start position:0%
+that
+ 
+
+ align:start position:0%
+that
+transfer like I said for most of us if I
+
+ align:start position:0%
+transfer like I said for most of us if I
+ 
+
+ align:start position:0%
+transfer like I said for most of us if I
+said to you you could take a dollar from
+
+ align:start position:0%
+said to you you could take a dollar from
+ 
+
+ align:start position:0%
+said to you you could take a dollar from
+a very rich person give to a very poor
+
+ align:start position:0%
+a very rich person give to a very poor
+ 
+
+ align:start position:0%
+a very rich person give to a very poor
+person you'd say well that seems like a
+
+ align:start position:0%
+person you'd say well that seems like a
+ 
+
+ align:start position:0%
+person you'd say well that seems like a
+good deal what if I say get a dollar for
+
+ align:start position:0%
+good deal what if I say get a dollar for
+ 
+
+ align:start position:0%
+good deal what if I say get a dollar for
+a very rich person and give 50 cents to
+
+ align:start position:0%
+a very rich person and give 50 cents to
+ 
+
+ align:start position:0%
+a very rich person and give 50 cents to
+a very poor person is that a good deal
+
+ align:start position:0%
+a very poor person is that a good deal
+ 
+
+ align:start position:0%
+a very poor person is that a good deal
+that depends that depends on how you
+
+ align:start position:0%
+that depends that depends on how you
+ 
+
+ align:start position:0%
+that depends that depends on how you
+feel about the relative value of money
+
+ align:start position:0%
+feel about the relative value of money
+ 
+
+ align:start position:0%
+feel about the relative value of money
+in the hands of the rich and the poor it
+
+ align:start position:0%
+in the hands of the rich and the poor it
+ 
+
+ align:start position:0%
+in the hands of the rich and the poor it
+becomes a harder question and and that
+
+ align:start position:0%
+becomes a harder question and and that
+ 
+
+ align:start position:0%
+becomes a harder question and and that
+is the equity efficiency tradeoff if you
+
+ align:start position:0%
+is the equity efficiency tradeoff if you
+ 
+
+ align:start position:0%
+is the equity efficiency tradeoff if you
+can redistribute shares of the pie
+
+ align:start position:0%
+can redistribute shares of the pie
+ 
+
+ align:start position:0%
+can redistribute shares of the pie
+without shrinking the pie we probably
+
+ align:start position:0%
+without shrinking the pie we probably
+ 
+
+ align:start position:0%
+without shrinking the pie we probably
+would be in favor of that but once it
+
+ align:start position:0%
+would be in favor of that but once it
+ 
+
+ align:start position:0%
+would be in favor of that but once it
+involves shrinking the
+
+ align:start position:0%
+involves shrinking the
+ 
+
+ align:start position:0%
+involves shrinking the
+pie maybe it's not such a good idea or
+
+ align:start position:0%
+pie maybe it's not such a good idea or
+ 
+
+ align:start position:0%
+pie maybe it's not such a good idea or
+maybe it is maybe even if the dollar
+
+ align:start position:0%
+maybe it is maybe even if the dollar
+ 
+
+ align:start position:0%
+maybe it is maybe even if the dollar
+from the rich becomes nothing to the
+
+ align:start position:0%
+from the rich becomes nothing to the
+ 
+
+ align:start position:0%
+from the rich becomes nothing to the
+poor you'll still favor it because you
+
+ align:start position:0%
+poor you'll still favor it because you
+ 
+
+ align:start position:0%
+poor you'll still favor it because you
+think inherently there's uh there's a
+
+ align:start position:0%
+think inherently there's uh there's a
+ 
+
+ align:start position:0%
+think inherently there's uh there's a
+problem with
+
+ align:start position:0%
+problem with
+ 
+
+ align:start position:0%
+problem with
+inequality so ultimately the question we
+
+ align:start position:0%
+inequality so ultimately the question we
+ 
+
+ align:start position:0%
+inequality so ultimately the question we
+want to think about is where what's the
+
+ align:start position:0%
+want to think about is where what's the
+ 
+
+ align:start position:0%
+want to think about is where what's the
+leak that you accept in your bucket
+
+ align:start position:0%
+leak that you accept in your bucket
+ 
+
+ align:start position:0%
+leak that you accept in your bucket
+what's the leak that you're willing to
+
+ align:start position:0%
+what's the leak that you're willing to
+ 
+
+ align:start position:0%
+what's the leak that you're willing to
+accept to transfer money and we're going
+
+ align:start position:0%
+accept to transfer money and we're going
+ 
+
+ align:start position:0%
+accept to transfer money and we're going
+to discuss that issue in four steps in
+
+ align:start position:0%
+to discuss that issue in four steps in
+ 
+
+ align:start position:0%
+to discuss that issue in four steps in
+the next two
+
+ align:start position:0%
+the next two
+ 
+
+ align:start position:0%
+the next two
+lectures the first step is we're going
+
+ align:start position:0%
+lectures the first step is we're going
+ 
+
+ align:start position:0%
+lectures the first step is we're going
+to ask about social
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+valuation of
+
+ align:start position:0%
+valuation of
+ 
+
+ align:start position:0%
+valuation of
+transfers how does how do we
+
+ align:start position:0%
+transfers how does how do we
+ 
+
+ align:start position:0%
+transfers how does how do we
+think the issue we've avoided through
+
+ align:start position:0%
+think the issue we've avoided through
+ 
+
+ align:start position:0%
+think the issue we've avoided through
+this whole course how do we think within
+
+ align:start position:0%
+this whole course how do we think within
+ 
+
+ align:start position:0%
+this whole course how do we think within
+our base economic framework about how
+
+ align:start position:0%
+our base economic framework about how
+ 
+
+ align:start position:0%
+our base economic framework about how
+Society feels about taking money from a
+
+ align:start position:0%
+Society feels about taking money from a
+ 
+
+ align:start position:0%
+Society feels about taking money from a
+and giving it to
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+B the Second Step we're going to ask is
+
+ align:start position:0%
+B the Second Step we're going to ask is
+ 
+
+ align:start position:0%
+B the Second Step we're going to ask is
+what is the actual inequality that
+
+ align:start position:0%
+what is the actual inequality that
+ 
+
+ align:start position:0%
+what is the actual inequality that
+exists in
+
+ align:start position:0%
+exists in
+ 
+
+ align:start position:0%
+exists in
+society what are the facts on who has
+
+ align:start position:0%
+society what are the facts on who has
+ 
+
+ align:start position:0%
+society what are the facts on who has
+the dollars what are the motivations for
+
+ align:start position:0%
+the dollars what are the motivations for
+ 
+
+ align:start position:0%
+the dollars what are the motivations for
+potentially addressing these
+
+ align:start position:0%
+potentially addressing these
+ 
+
+ align:start position:0%
+potentially addressing these
+distributional
+
+ align:start position:0%
+distributional
+ 
+
+ align:start position:0%
+distributional
+issues the third thing we're to ask is
+
+ align:start position:0%
+issues the third thing we're to ask is
+ 
+
+ align:start position:0%
+issues the third thing we're to ask is
+where does the leakage what are the
+
+ align:start position:0%
+where does the leakage what are the
+ 
+
+ align:start position:0%
+where does the leakage what are the
+sources of leak
+
+ align:start position:0%
+sources of leak
+ 
+
+ align:start position:0%
+sources of leak
+leakage where does the leakage come
+
+ align:start position:0%
+leakage where does the leakage come
+ 
+
+ align:start position:0%
+leakage where does the leakage come
+from where do the leaks that where do
+
+ align:start position:0%
+from where do the leaks that where do
+ 
+
+ align:start position:0%
+from where do the leaks that where do
+the leaks that that leaky bucket come
+
+ align:start position:0%
+the leaks that that leaky bucket come
+ 
+
+ align:start position:0%
+the leaks that that leaky bucket come
+from why is it
+
+ align:start position:0%
+from why is it
+ 
+
+ align:start position:0%
+from why is it
+leaky and then finally we're going to
+
+ align:start position:0%
+leaky and then finally we're going to
+ 
+
+ align:start position:0%
+leaky and then finally we're going to
+ask about transfer
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+policy how does government actually go
+
+ align:start position:0%
+policy how does government actually go
+ 
+
+ align:start position:0%
+policy how does government actually go
+about taking money from some people and
+
+ align:start position:0%
+about taking money from some people and
+ 
+
+ align:start position:0%
+about taking money from some people and
+giving it to
+
+ align:start position:0%
+giving it to
+ 
+
+ align:start position:0%
+giving it to
+others those are the four steps we're
+
+ align:start position:0%
+others those are the four steps we're
+ 
+
+ align:start position:0%
+others those are the four steps we're
+going to go through we'll get through
+
+ align:start position:0%
+going to go through we'll get through
+ 
+
+ align:start position:0%
+going to go through we'll get through
+the first three today and F focus on the
+
+ align:start position:0%
+the first three today and F focus on the
+ 
+
+ align:start position:0%
+the first three today and F focus on the
+last one on
+
+ align:start position:0%
+last one on
+ 
+
+ align:start position:0%
+last one on
+Monday so let's start with the first one
+
+ align:start position:0%
+Monday so let's start with the first one
+ 
+
+ align:start position:0%
+Monday so let's start with the first one
+which
+
+ align:start position:0%
+which
+ 
+
+ align:start position:0%
+which
+is how do we think
+
+ align:start position:0%
+is how do we think
+ 
+
+ align:start position:0%
+is how do we think
+about
+
+ align:start position:0%
+about
+ 
+
+ align:start position:0%
+about
+social
+
+ align:start position:0%
+social
+ 
+
+ align:start position:0%
+social
+welfare of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+allocation so far we've just thought
+
+ align:start position:0%
+allocation so far we've just thought
+ 
+
+ align:start position:0%
+allocation so far we've just thought
+about the social welfare of total if
+
+ align:start position:0%
+about the social welfare of total if
+ 
+
+ align:start position:0%
+about the social welfare of total if
+total efficiency we haven't thought
+
+ align:start position:0%
+total efficiency we haven't thought
+ 
+
+ align:start position:0%
+total efficiency we haven't thought
+about
+
+ align:start position:0%
+about
+ 
+
+ align:start position:0%
+about
+allocation imagine we with many
+
+ align:start position:0%
+allocation imagine we with many
+ 
+
+ align:start position:0%
+allocation imagine we with many
+different
+
+ align:start position:0%
+different
+ 
+
+ align:start position:0%
+different
+outcomes different levels of efficiency
+
+ align:start position:0%
+outcomes different levels of efficiency
+ 
+
+ align:start position:0%
+outcomes different levels of efficiency
+but also different levels of equity a
+
+ align:start position:0%
+but also different levels of equity a
+ 
+
+ align:start position:0%
+but also different levels of equity a
+world with different with with buckets
+
+ align:start position:0%
+world with different with with buckets
+ 
+
+ align:start position:0%
+world with different with with buckets
+that are different leakages and
+
+ align:start position:0%
+that are different leakages and
+ 
+
+ align:start position:0%
+that are different leakages and
+different amounts of money going to
+
+ align:start position:0%
+different amounts of money going to
+ 
+
+ align:start position:0%
+different amounts of money going to
+different people how would we compare
+
+ align:start position:0%
+different people how would we compare
+ 
+
+ align:start position:0%
+different people how would we compare
+them well here we're going to use the
+
+ align:start position:0%
+them well here we're going to use the
+ 
+
+ align:start position:0%
+them well here we're going to use the
+same tool we started with in lecture
+
+ align:start position:0%
+same tool we started with in lecture
+ 
+
+ align:start position:0%
+same tool we started with in lecture
+two how do we think about any valuing
+
+ align:start position:0%
+two how do we think about any valuing
+ 
+
+ align:start position:0%
+two how do we think about any valuing
+any combination of goods from a consumer
+
+ align:start position:0%
+any combination of goods from a consumer
+ 
+
+ align:start position:0%
+any combination of goods from a consumer
+well we say they have utility function
+
+ align:start position:0%
+well we say they have utility function
+ 
+
+ align:start position:0%
+well we say they have utility function
+and we say how do those different
+
+ align:start position:0%
+and we say how do those different
+ 
+
+ align:start position:0%
+and we say how do those different
+combinations of good enter the
+
+ align:start position:0%
+combinations of good enter the
+ 
+
+ align:start position:0%
+combinations of good enter the
+utility well to think about socially
+
+ align:start position:0%
+utility well to think about socially
+ 
+
+ align:start position:0%
+utility well to think about socially
+optimal
+
+ align:start position:0%
+optimal
+ 
+
+ align:start position:0%
+optimal
+allocation we're going to think about a
+
+ align:start position:0%
+allocation we're going to think about a
+ 
+
+ align:start position:0%
+allocation we're going to think about a
+social utility function or what we're
+
+ align:start position:0%
+social utility function or what we're
+ 
+
+ align:start position:0%
+social utility function or what we're
+going to call a social welfare function
+
+ align:start position:0%
+going to call a social welfare function
+ 
+
+ align:start position:0%
+going to call a social welfare function
+we're going to say look if we want to
+
+ align:start position:0%
+we're going to say look if we want to
+ 
+
+ align:start position:0%
+we're going to say look if we want to
+think about the value of goods in the
+
+ align:start position:0%
+think about the value of goods in the
+ 
+
+ align:start position:0%
+think about the value of goods in the
+hands of person a versus B we have to
+
+ align:start position:0%
+hands of person a versus B we have to
+ 
+
+ align:start position:0%
+hands of person a versus B we have to
+write down a mathematical function for
+
+ align:start position:0%
+write down a mathematical function for
+ 
+
+ align:start position:0%
+write down a mathematical function for
+how Society feels about the value of
+
+ align:start position:0%
+how Society feels about the value of
+ 
+
+ align:start position:0%
+how Society feels about the value of
+goods in the hands of person A or B that
+
+ align:start position:0%
+goods in the hands of person A or B that
+ 
+
+ align:start position:0%
+goods in the hands of person A or B that
+is Loosely a utility function for
+
+ align:start position:0%
+is Loosely a utility function for
+ 
+
+ align:start position:0%
+is Loosely a utility function for
+society essentially
+
+ align:start position:0%
+society essentially
+ 
+
+ align:start position:0%
+society essentially
+aggregation of each individual's utility
+
+ align:start position:0%
+aggregation of each individual's utility
+ 
+
+ align:start position:0%
+aggregation of each individual's utility
+so the function per utility one utility
+
+ align:start position:0%
+so the function per utility one utility
+ 
+
+ align:start position:0%
+so the function per utility one utility
+two all the way up to utility 3 150
+
+ align:start position:0%
+two all the way up to utility 3 150
+ 
+
+ align:start position:0%
+two all the way up to utility 3 150
+million okay so this the social welfare
+
+ align:start position:0%
+million okay so this the social welfare
+ 
+
+ align:start position:0%
+million okay so this the social welfare
+function for the United States is
+
+ align:start position:0%
+function for the United States is
+ 
+
+ align:start position:0%
+function for the United States is
+literally some aggregation some
+
+ align:start position:0%
+literally some aggregation some
+ 
+
+ align:start position:0%
+literally some aggregation some
+mathematical function of everyone's
+
+ align:start position:0%
+mathematical function of everyone's
+ 
+
+ align:start position:0%
+mathematical function of everyone's
+utility and you should be able to see
+
+ align:start position:0%
+utility and you should be able to see
+ 
+
+ align:start position:0%
+utility and you should be able to see
+for a given mathematical
+
+ align:start position:0%
+for a given mathematical
+ 
+
+ align:start position:0%
+for a given mathematical
+function I can then evaluate how I feel
+
+ align:start position:0%
+function I can then evaluate how I feel
+ 
+
+ align:start position:0%
+function I can then evaluate how I feel
+about transfers because I can look at
+
+ align:start position:0%
+about transfers because I can look at
+ 
+
+ align:start position:0%
+about transfers because I can look at
+what those transfers done each person's
+
+ align:start position:0%
+what those transfers done each person's
+ 
+
+ align:start position:0%
+what those transfers done each person's
+utility I can use this function to
+
+ align:start position:0%
+utility I can use this function to
+ 
+
+ align:start position:0%
+utility I can use this function to
+translate to new social
+
+ align:start position:0%
+translate to new social
+ 
+
+ align:start position:0%
+translate to new social
+allocation okay so to see that let's
+
+ align:start position:0%
+allocation okay so to see that let's
+ 
+
+ align:start position:0%
+allocation okay so to see that let's
+look at figure
+
+ align:start position:0%
+look at figure
+ 
+
+ align:start position:0%
+look at figure
+231 these draw what we call isow welfare
+
+ align:start position:0%
+231 these draw what we call isow welfare
+ 
+
+ align:start position:0%
+231 these draw what we call isow welfare
+curves now in our two-dimensional graph
+
+ align:start position:0%
+curves now in our two-dimensional graph
+ 
+
+ align:start position:0%
+curves now in our two-dimensional graph
+the trade-off is between goods to two
+
+ align:start position:0%
+the trade-off is between goods to two
+ 
+
+ align:start position:0%
+the trade-off is between goods to two
+people Homer and Ned okay we have Homer
+
+ align:start position:0%
+people Homer and Ned okay we have Homer
+ 
+
+ align:start position:0%
+people Homer and Ned okay we have Homer
+and Ned Society consists of these two
+
+ align:start position:0%
+and Ned Society consists of these two
+ 
+
+ align:start position:0%
+and Ned Society consists of these two
+people and we want to think about how do
+
+ align:start position:0%
+people and we want to think about how do
+ 
+
+ align:start position:0%
+people and we want to think about how do
+we feel about resources in the hand of
+
+ align:start position:0%
+we feel about resources in the hand of
+ 
+
+ align:start position:0%
+we feel about resources in the hand of
+Homer versus Ned and we could say for
+
+ align:start position:0%
+Homer versus Ned and we could say for
+ 
+
+ align:start position:0%
+Homer versus Ned and we could say for
+example that we're indifferent between
+
+ align:start position:0%
+example that we're indifferent between
+ 
+
+ align:start position:0%
+example that we're indifferent between
+the allocations u1h
+
+ align:start position:0%
+the allocations u1h
+ 
+
+ align:start position:0%
+the allocations u1h
+u1n and u2h u2n say we're a different
+
+ align:start position:0%
+u1n and u2h u2n say we're a different
+ 
+
+ align:start position:0%
+u1n and u2h u2n say we're a different
+between Ned having a lot and Homer
+
+ align:start position:0%
+between Ned having a lot and Homer
+ 
+
+ align:start position:0%
+between Ned having a lot and Homer
+having a little or Homer having a lot
+
+ align:start position:0%
+having a little or Homer having a lot
+ 
+
+ align:start position:0%
+having a little or Homer having a lot
+net having a little then they'd be on
+
+ align:start position:0%
+net having a little then they'd be on
+ 
+
+ align:start position:0%
+net having a little then they'd be on
+the same isow welfare curve but by the
+
+ align:start position:0%
+the same isow welfare curve but by the
+ 
+
+ align:start position:0%
+the same isow welfare curve but by the
+Moors better principle we're certainly
+
+ align:start position:0%
+Moors better principle we're certainly
+ 
+
+ align:start position:0%
+Moors better principle we're certainly
+happy as a society with both having
+
+ align:start position:0%
+happy as a society with both having
+ 
+
+ align:start position:0%
+happy as a society with both having
+more just like any indifference curve
+
+ align:start position:0%
+more just like any indifference curve
+ 
+
+ align:start position:0%
+more just like any indifference curve
+the ISO Wells our curves the further out
+
+ align:start position:0%
+the ISO Wells our curves the further out
+ 
+
+ align:start position:0%
+the ISO Wells our curves the further out
+the better off we
+
+ align:start position:0%
+the better off we
+ 
+
+ align:start position:0%
+the better off we
+are okay so basically um this is
+
+ align:start position:0%
+are okay so basically um this is
+ 
+
+ align:start position:0%
+are okay so basically um this is
+essentially a
+
+ align:start position:0%
+essentially a
+ 
+
+ align:start position:0%
+essentially a
+mapping of a social welfare curve of a
+
+ align:start position:0%
+mapping of a social welfare curve of a
+ 
+
+ align:start position:0%
+mapping of a social welfare curve of a
+social welfare function just like
+
+ align:start position:0%
+social welfare function just like
+ 
+
+ align:start position:0%
+social welfare function just like
+utility function gives us an
+
+ align:start position:0%
+utility function gives us an
+ 
+
+ align:start position:0%
+utility function gives us an
+indifference curve
+
+ align:start position:0%
+indifference curve
+ 
+
+ align:start position:0%
+indifference curve
+mapping a social welfare function gives
+
+ align:start position:0%
+mapping a social welfare function gives
+ 
+
+ align:start position:0%
+mapping a social welfare function gives
+us an isow welfare curve
+
+ align:start position:0%
+us an isow welfare curve
+ 
+
+ align:start position:0%
+us an isow welfare curve
+mapping so then we just simply have to
+
+ align:start position:0%
+mapping so then we just simply have to
+ 
+
+ align:start position:0%
+mapping so then we just simply have to
+ask what does a social welfare function
+
+ align:start position:0%
+ask what does a social welfare function
+ 
+
+ align:start position:0%
+ask what does a social welfare function
+look like we talked about what utility
+
+ align:start position:0%
+look like we talked about what utility
+ 
+
+ align:start position:0%
+look like we talked about what utility
+functions look like we talked about
+
+ align:start position:0%
+functions look like we talked about
+ 
+
+ align:start position:0%
+functions look like we talked about
+their General print properties and that
+
+ align:start position:0%
+their General print properties and that
+ 
+
+ align:start position:0%
+their General print properties and that
+common example we use of the square root
+
+ align:start position:0%
+common example we use of the square root
+ 
+
+ align:start position:0%
+common example we use of the square root
+utility function but we said basically
+
+ align:start position:0%
+utility function but we said basically
+ 
+
+ align:start position:0%
+utility function but we said basically
+we can use a broad class of functions
+
+ align:start position:0%
+we can use a broad class of functions
+ 
+
+ align:start position:0%
+we can use a broad class of functions
+you've seen on problem sets and exams a
+
+ align:start position:0%
+you've seen on problem sets and exams a
+ 
+
+ align:start position:0%
+you've seen on problem sets and exams a
+broad class utility
+
+ align:start position:0%
+broad class utility
+ 
+
+ align:start position:0%
+broad class utility
+functions what about social welfare
+
+ align:start position:0%
+functions what about social welfare
+ 
+
+ align:start position:0%
+functions what about social welfare
+function social welfare functions
+
+ align:start position:0%
+function social welfare functions
+ 
+
+ align:start position:0%
+function social welfare functions
+typically we work in economics with a
+
+ align:start position:0%
+typically we work in economics with a
+ 
+
+ align:start position:0%
+typically we work in economics with a
+couple of different forms of social
+
+ align:start position:0%
+couple of different forms of social
+ 
+
+ align:start position:0%
+couple of different forms of social
+welfare
+
+ align:start position:0%
+welfare
+ 
+
+ align:start position:0%
+welfare
+functions the most common form of social
+
+ align:start position:0%
+functions the most common form of social
+ 
+
+ align:start position:0%
+functions the most common form of social
+welfare function is what we call
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+utilitarian social welfare function the
+
+ align:start position:0%
+utilitarian social welfare function the
+ 
+
+ align:start position:0%
+utilitarian social welfare function the
+utilitarian social welfare function
+
+ align:start position:0%
+utilitarian social welfare function
+ 
+
+ align:start position:0%
+utilitarian social welfare function
+simply poses that social
+
+ align:start position:0%
+simply poses that social
+ 
+
+ align:start position:0%
+simply poses that social
+welfare is simply the linear sum of
+
+ align:start position:0%
+welfare is simply the linear sum of
+ 
+
+ align:start position:0%
+welfare is simply the linear sum of
+utilities U1 plus U2 plus dot do D plus
+
+ align:start position:0%
+utilities U1 plus U2 plus dot do D plus
+ 
+
+ align:start position:0%
+utilities U1 plus U2 plus dot do D plus
+u350
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+million that is utilitarian it's
+
+ align:start position:0%
+million that is utilitarian it's
+ 
+
+ align:start position:0%
+million that is utilitarian it's
+literally I I don't know I don't I have
+
+ align:start position:0%
+literally I I don't know I don't I have
+ 
+
+ align:start position:0%
+literally I I don't know I don't I have
+no base Society for caring any more
+
+ align:start position:0%
+no base Society for caring any more
+ 
+
+ align:start position:0%
+no base Society for caring any more
+about one person than anyone else just
+
+ align:start position:0%
+about one person than anyone else just
+ 
+
+ align:start position:0%
+about one person than anyone else just
+going to add their
+
+ align:start position:0%
+going to add their
+ 
+
+ align:start position:0%
+going to add their
+utilities the person this guy named
+
+ align:start position:0%
+utilities the person this guy named
+ 
+
+ align:start position:0%
+utilities the person this guy named
+Jeremy Bentham a famous British
+
+ align:start position:0%
+Jeremy Bentham a famous British
+ 
+
+ align:start position:0%
+Jeremy Bentham a famous British
+philosopher uh couple things to not
+
+ align:start position:0%
+philosopher uh couple things to not
+ 
+
+ align:start position:0%
+philosopher uh couple things to not
+about Jeremy Bentham first of all he
+
+ align:start position:0%
+about Jeremy Bentham first of all he
+ 
+
+ align:start position:0%
+about Jeremy Bentham first of all he
+also invented the modern he invented a
+
+ align:start position:0%
+also invented the modern he invented a
+ 
+
+ align:start position:0%
+also invented the modern he invented a
+modern design of Prisons which is quite
+
+ align:start position:0%
+modern design of Prisons which is quite
+ 
+
+ align:start position:0%
+modern design of Prisons which is quite
+interesting he was a broad thinkinking
+
+ align:start position:0%
+interesting he was a broad thinkinking
+ 
+
+ align:start position:0%
+interesting he was a broad thinkinking
+philosopher he also um when he died his
+
+ align:start position:0%
+philosopher he also um when he died his
+ 
+
+ align:start position:0%
+philosopher he also um when he died his
+stuffed body with the head separated was
+
+ align:start position:0%
+stuffed body with the head separated was
+ 
+
+ align:start position:0%
+stuffed body with the head separated was
+on display at University College London
+
+ align:start position:0%
+on display at University College London
+ 
+
+ align:start position:0%
+on display at University College London
+um until it turned out students would
+
+ align:start position:0%
+um until it turned out students would
+ 
+
+ align:start position:0%
+um until it turned out students would
+take the head out and play soccer with
+
+ align:start position:0%
+take the head out and play soccer with
+ 
+
+ align:start position:0%
+take the head out and play soccer with
+it so they no longer do that so um he's
+
+ align:start position:0%
+it so they no longer do that so um he's
+ 
+
+ align:start position:0%
+it so they no longer do that so um he's
+a famous philosopher cample the
+
+ align:start position:0%
+a famous philosopher cample the
+ 
+
+ align:start position:0%
+a famous philosopher cample the
+utilitarian social war function it's
+
+ align:start position:0%
+utilitarian social war function it's
+ 
+
+ align:start position:0%
+utilitarian social war function it's
+sort of a natural starting
+
+ align:start position:0%
+sort of a natural starting
+ 
+
+ align:start position:0%
+sort of a natural starting
+point and if you think about it it's not
+
+ align:start position:0%
+point and if you think about it it's not
+ 
+
+ align:start position:0%
+point and if you think about it it's not
+really sort of cons you wouldn't look at
+
+ align:start position:0%
+really sort of cons you wouldn't look at
+ 
+
+ align:start position:0%
+really sort of cons you wouldn't look at
+this this is conservative or liberal
+
+ align:start position:0%
+this this is conservative or liberal
+ 
+
+ align:start position:0%
+this this is conservative or liberal
+right you look at to say oh that's a
+
+ align:start position:0%
+right you look at to say oh that's a
+ 
+
+ align:start position:0%
+right you look at to say oh that's a
+lefty or righty it's just it's neutral
+
+ align:start position:0%
+lefty or righty it's just it's neutral
+ 
+
+ align:start position:0%
+lefty or righty it's just it's neutral
+it's just saying look I care about
+
+ align:start position:0%
+it's just saying look I care about
+ 
+
+ align:start position:0%
+it's just saying look I care about
+everyone equally that seems pretty
+
+ align:start position:0%
+everyone equally that seems pretty
+ 
+
+ align:start position:0%
+everyone equally that seems pretty
+neutral and yet this neutral social
+
+ align:start position:0%
+neutral and yet this neutral social
+ 
+
+ align:start position:0%
+neutral and yet this neutral social
+utility function has radical
+
+ align:start position:0%
+utility function has radical
+ 
+
+ align:start position:0%
+utility function has radical
+implications for
+
+ align:start position:0%
+implications for
+ 
+
+ align:start position:0%
+implications for
+distribution in particular it says we
+
+ align:start position:0%
+distribution in particular it says we
+ 
+
+ align:start position:0%
+distribution in particular it says we
+should always
+
+ align:start position:0%
+should always
+ 
+
+ align:start position:0%
+should always
+transfer between any two
+
+ align:start position:0%
+transfer between any two
+ 
+
+ align:start position:0%
+transfer between any two
+people if the transfer makes person two
+
+ align:start position:0%
+people if the transfer makes person two
+ 
+
+ align:start position:0%
+people if the transfer makes person two
+happier than it makes person one
+
+ align:start position:0%
+happier than it makes person one
+ 
+
+ align:start position:0%
+happier than it makes person one
+sad that means we're indifferent between
+
+ align:start position:0%
+sad that means we're indifferent between
+ 
+
+ align:start position:0%
+sad that means we're indifferent between
+one udle to you and to Bill
+
+ align:start position:0%
+one udle to you and to Bill
+ 
+
+ align:start position:0%
+one udle to you and to Bill
+Gates now that sounds kind of
+
+ align:start position:0%
+Gates now that sounds kind of
+ 
+
+ align:start position:0%
+Gates now that sounds kind of
+conservative we're indifferent like
+
+ align:start position:0%
+conservative we're indifferent like
+ 
+
+ align:start position:0%
+conservative we're indifferent like
+you're poor than Bill Gates we should
+
+ align:start position:0%
+you're poor than Bill Gates we should
+ 
+
+ align:start position:0%
+you're poor than Bill Gates we should
+care more about you but remember I said
+
+ align:start position:0%
+care more about you but remember I said
+ 
+
+ align:start position:0%
+care more about you but remember I said
+we're indiff in one udle between you and
+
+ align:start position:0%
+we're indiff in one udle between you and
+ 
+
+ align:start position:0%
+we're indiff in one udle between you and
+Bill Gates that doesn't mean we're
+
+ align:start position:0%
+Bill Gates that doesn't mean we're
+ 
+
+ align:start position:0%
+Bill Gates that doesn't mean we're
+differing than $1 doll between you and
+
+ align:start position:0%
+differing than $1 doll between you and
+ 
+
+ align:start position:0%
+differing than $1 doll between you and
+Bill
+
+ align:start position:0%
+Bill
+ 
+
+ align:start position:0%
+Bill
+Gates okay indeed who would we rather
+
+ align:start position:0%
+Gates okay indeed who would we rather
+ 
+
+ align:start position:0%
+Gates okay indeed who would we rather
+with this social work function who would
+
+ align:start position:0%
+with this social work function who would
+ 
+
+ align:start position:0%
+with this social work function who would
+we rather have the dollar you or Bill
+
+ align:start position:0%
+we rather have the dollar you or Bill
+ 
+
+ align:start position:0%
+we rather have the dollar you or Bill
+Gates and why let's say there's a dollar
+
+ align:start position:0%
+Gates and why let's say there's a dollar
+ 
+
+ align:start position:0%
+Gates and why let's say there's a dollar
+up for grabs with the utilit social
+
+ align:start position:0%
+up for grabs with the utilit social
+ 
+
+ align:start position:0%
+up for grabs with the utilit social
+welfare function would social welfare be
+
+ align:start position:0%
+welfare function would social welfare be
+ 
+
+ align:start position:0%
+welfare function would social welfare be
+higher if you got the dollar or Bill
+
+ align:start position:0%
+higher if you got the dollar or Bill
+ 
+
+ align:start position:0%
+higher if you got the dollar or Bill
+Gates got the dollar and
+
+ align:start position:0%
+Gates got the dollar and
+ 
+
+ align:start position:0%
+Gates got the dollar and
+Y
+
+ align:start position:0%
+Y
+ 
+
+ align:start position:0%
+Y
+yeah L the margin of dollars higher to
+
+ align:start position:0%
+yeah L the margin of dollars higher to
+ 
+
+ align:start position:0%
+yeah L the margin of dollars higher to
+you to you and less to Bill Gates what
+
+ align:start position:0%
+you to you and less to Bill Gates what
+ 
+
+ align:start position:0%
+you to you and less to Bill Gates what
+this says if you maximize this if you
+
+ align:start position:0%
+this says if you maximize this if you
+ 
+
+ align:start position:0%
+this says if you maximize this if you
+maximize this this implies you should
+
+ align:start position:0%
+maximize this this implies you should
+ 
+
+ align:start position:0%
+maximize this this implies you should
+set the Marge utility of all individuals
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+equal I'm put 350 million because 350
+
+ align:start position:0%
+equal I'm put 350 million because 350
+ 
+
+ align:start position:0%
+equal I'm put 350 million because 350
+million people in America okay this
+
+ align:start position:0%
+million people in America okay this
+ 
+
+ align:start position:0%
+million people in America okay this
+implies you should put the margin
+
+ align:start position:0%
+implies you should put the margin
+ 
+
+ align:start position:0%
+implies you should put the margin
+utility of every person equal that's a
+
+ align:start position:0%
+utility of every person equal that's a
+ 
+
+ align:start position:0%
+utility of every person equal that's a
+pretty radical implication
+
+ align:start position:0%
+pretty radical implication
+ 
+
+ align:start position:0%
+pretty radical implication
+that says literally you should reute
+
+ align:start position:0%
+that says literally you should reute
+ 
+
+ align:start position:0%
+that says literally you should reute
+money until everybody values the dollar
+
+ align:start position:0%
+money until everybody values the dollar
+ 
+
+ align:start position:0%
+money until everybody values the dollar
+the next dollar the same that say you
+
+ align:start position:0%
+the next dollar the same that say you
+ 
+
+ align:start position:0%
+the next dollar the same that say you
+should massively redistribute from the
+
+ align:start position:0%
+should massively redistribute from the
+ 
+
+ align:start position:0%
+should massively redistribute from the
+rich to the
+
+ align:start position:0%
+rich to the
+ 
+
+ align:start position:0%
+rich to the
+poor right because the rich value the
+
+ align:start position:0%
+poor right because the rich value the
+ 
+
+ align:start position:0%
+poor right because the rich value the
+next dollar way less than the poor Bill
+
+ align:start position:0%
+next dollar way less than the poor Bill
+ 
+
+ align:start position:0%
+next dollar way less than the poor Bill
+Gates couldn't give a about the
+
+ align:start position:0%
+Gates couldn't give a about the
+ 
+
+ align:start position:0%
+Gates couldn't give a about the
+next dollar where some poor homeless guy
+
+ align:start position:0%
+next dollar where some poor homeless guy
+ 
+
+ align:start position:0%
+next dollar where some poor homeless guy
+mean could be difference between a hot
+
+ align:start position:0%
+mean could be difference between a hot
+ 
+
+ align:start position:0%
+mean could be difference between a hot
+meal and not having a hot meal today on
+
+ align:start position:0%
+meal and not having a hot meal today on
+ 
+
+ align:start position:0%
+meal and not having a hot meal today on
+a cold day so clearly this is fairly
+
+ align:start position:0%
+a cold day so clearly this is fairly
+ 
+
+ align:start position:0%
+a cold day so clearly this is fairly
+this suggests that we dimin as long as
+
+ align:start position:0%
+this suggests that we dimin as long as
+ 
+
+ align:start position:0%
+this suggests that we dimin as long as
+there's diminishing margin
+
+ align:start position:0%
+there's diminishing margin
+ 
+
+ align:start position:0%
+there's diminishing margin
+utility you should have fairly strong
+
+ align:start position:0%
+utility you should have fairly strong
+ 
+
+ align:start position:0%
+utility you should have fairly strong
+preferences to redistribute from the
+
+ align:start position:0%
+preferences to redistribute from the
+ 
+
+ align:start position:0%
+preferences to redistribute from the
+rich to the poor despite the fact that
+
+ align:start position:0%
+rich to the poor despite the fact that
+ 
+
+ align:start position:0%
+rich to the poor despite the fact that
+when I wrote this you didn't look at it
+
+ align:start position:0%
+when I wrote this you didn't look at it
+ 
+
+ align:start position:0%
+when I wrote this you didn't look at it
+and say wow this is some Lefty crazy
+
+ align:start position:0%
+and say wow this is some Lefty crazy
+ 
+
+ align:start position:0%
+and say wow this is some Lefty crazy
+utility function it has sort of Lefty
+
+ align:start position:0%
+utility function it has sort of Lefty
+ 
+
+ align:start position:0%
+utility function it has sort of Lefty
+implications right it says we should
+
+ align:start position:0%
+implications right it says we should
+ 
+
+ align:start position:0%
+implications right it says we should
+redistribute strongly from the rich to
+
+ align:start position:0%
+redistribute strongly from the rich to
+ 
+
+ align:start position:0%
+redistribute strongly from the rich to
+the poor it sort of makes sense the rich
+
+ align:start position:0%
+the poor it sort of makes sense the rich
+ 
+
+ align:start position:0%
+the poor it sort of makes sense the rich
+care about the money less than the poor
+
+ align:start position:0%
+care about the money less than the poor
+ 
+
+ align:start position:0%
+care about the money less than the poor
+care about and that's your sort of
+
+ align:start position:0%
+care about and that's your sort of
+ 
+
+ align:start position:0%
+care about and that's your sort of
+underlying intuition why we all start
+
+ align:start position:0%
+underlying intuition why we all start
+ 
+
+ align:start position:0%
+underlying intuition why we all start
+with this notion that redistribution
+
+ align:start position:0%
+with this notion that redistribution
+ 
+
+ align:start position:0%
+with this notion that redistribution
+makes sense indeed this goes further if
+
+ align:start position:0%
+makes sense indeed this goes further if
+ 
+
+ align:start position:0%
+makes sense indeed this goes further if
+individuals are all
+
+ align:start position:0%
+individuals are all
+ 
+
+ align:start position:0%
+individuals are all
+identical this if individual are all
+
+ align:start position:0%
+identical this if individual are all
+ 
+
+ align:start position:0%
+identical this if individual are all
+this suggests we should have an equal
+
+ align:start position:0%
+this suggests we should have an equal
+ 
+
+ align:start position:0%
+this suggests we should have an equal
+distribution of income a pretty radical
+
+ align:start position:0%
+distribution of income a pretty radical
+ 
+
+ align:start position:0%
+distribution of income a pretty radical
+concept that's never been achieved
+
+ align:start position:0%
+concept that's never been achieved
+ 
+
+ align:start position:0%
+concept that's never been achieved
+anywhere in history by any
+
+ align:start position:0%
+anywhere in history by any
+ 
+
+ align:start position:0%
+anywhere in history by any
+society if individuals are all identical
+
+ align:start position:0%
+society if individuals are all identical
+ 
+
+ align:start position:0%
+society if individuals are all identical
+this says we should have an equal
+
+ align:start position:0%
+this says we should have an equal
+ 
+
+ align:start position:0%
+this says we should have an equal
+distribution of income pretty radical
+
+ align:start position:0%
+distribution of income pretty radical
+ 
+
+ align:start position:0%
+distribution of income pretty radical
+from a pretty straightforward
+
+ align:start position:0%
+from a pretty straightforward
+ 
+
+ align:start position:0%
+from a pretty straightforward
+concept now in fact to many
+
+ align:start position:0%
+concept now in fact to many
+ 
+
+ align:start position:0%
+concept now in fact to many
+people this is actually a very
+
+ align:start position:0%
+people this is actually a very
+ 
+
+ align:start position:0%
+people this is actually a very
+conservative approach to think about
+
+ align:start position:0%
+conservative approach to think about
+ 
+
+ align:start position:0%
+conservative approach to think about
+about income distribution indeed
+
+ align:start position:0%
+about income distribution indeed
+ 
+
+ align:start position:0%
+about income distribution indeed
+typically conservatives often start with
+
+ align:start position:0%
+typically conservatives often start with
+ 
+
+ align:start position:0%
+typically conservatives often start with
+this point many people on the left start
+
+ align:start position:0%
+this point many people on the left start
+ 
+
+ align:start position:0%
+this point many people on the left start
+with an alternative approach what's
+
+ align:start position:0%
+with an alternative approach what's
+ 
+
+ align:start position:0%
+with an alternative approach what's
+called a rollan w r awl rollan social
+
+ align:start position:0%
+called a rollan w r awl rollan social
+ 
+
+ align:start position:0%
+called a rollan w r awl rollan social
+welfare function named up philosopher
+
+ align:start position:0%
+welfare function named up philosopher
+ 
+
+ align:start position:0%
+welfare function named up philosopher
+John rolls famous philosopher at
+
+ align:start position:0%
+John rolls famous philosopher at
+ 
+
+ align:start position:0%
+John rolls famous philosopher at
+Harvard RS said that utility that the
+
+ align:start position:0%
+Harvard RS said that utility that the
+ 
+
+ align:start position:0%
+Harvard RS said that utility that the
+social welfare of society should be
+
+ align:start position:0%
+social welfare of society should be
+ 
+
+ align:start position:0%
+social welfare of society should be
+measured as the men of everyone's
+
+ align:start position:0%
+measured as the men of everyone's
+ 
+
+ align:start position:0%
+measured as the men of everyone's
+utility that a society should be
+
+ align:start position:0%
+utility that a society should be
+ 
+
+ align:start position:0%
+utility that a society should be
+measured by the living standards of its
+
+ align:start position:0%
+measured by the living standards of its
+ 
+
+ align:start position:0%
+measured by the living standards of its
+worst off
+
+ align:start position:0%
+worst off
+ 
+
+ align:start position:0%
+worst off
+member that as Society we should care
+
+ align:start position:0%
+member that as Society we should care
+ 
+
+ align:start position:0%
+member that as Society we should care
+about those who are poorly off and
+
+ align:start position:0%
+about those who are poorly off and
+ 
+
+ align:start position:0%
+about those who are poorly off and
+Society should be measured by the
+
+ align:start position:0%
+Society should be measured by the
+ 
+
+ align:start position:0%
+Society should be measured by the
+utility of the worst off member that
+
+ align:start position:0%
+utility of the worst off member that
+ 
+
+ align:start position:0%
+utility of the worst off member that
+sort of has some appeal okay we should
+
+ align:start position:0%
+sort of has some appeal okay we should
+ 
+
+ align:start position:0%
+sort of has some appeal okay we should
+care about these people but it's
+
+ align:start position:0%
+care about these people but it's
+ 
+
+ align:start position:0%
+care about these people but it's
+incredibly extreme in its implications
+
+ align:start position:0%
+incredibly extreme in its implications
+ 
+
+ align:start position:0%
+incredibly extreme in its implications
+think about it for a second let's say
+
+ align:start position:0%
+think about it for a second let's say
+ 
+
+ align:start position:0%
+think about it for a second let's say
+say there's a society consists of
+
+ align:start position:0%
+say there's a society consists of
+ 
+
+ align:start position:0%
+say there's a society consists of
+everyone in the world everyone in the US
+
+ align:start position:0%
+everyone in the world everyone in the US
+ 
+
+ align:start position:0%
+everyone in the world everyone in the US
+has
+
+ align:start position:0%
+has
+ 
+
+ align:start position:0%
+has
+$40,000 except one guy has a billion
+
+ align:start position:0%
+$40,000 except one guy has a billion
+ 
+
+ align:start position:0%
+$40,000 except one guy has a billion
+dollar and one guy has
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+$39,000 this says that we should be
+
+ align:start position:0%
+$39,000 this says that we should be
+ 
+
+ align:start position:0%
+$39,000 this says that we should be
+willing to take the billionaire all the
+
+ align:start position:0%
+willing to take the billionaire all the
+ 
+
+ align:start position:0%
+willing to take the billionaire all the
+way down to
+
+ align:start position:0%
+way down to
+ 
+
+ align:start position:0%
+way down to
+40,000 just to get the 39,000 guy up to
+
+ align:start position:0%
+40,000 just to get the 39,000 guy up to
+ 
+
+ align:start position:0%
+40,000 just to get the 39,000 guy up to
+40,000 that's pretty radical it says
+
+ align:start position:0%
+40,000 that's pretty radical it says
+ 
+
+ align:start position:0%
+40,000 that's pretty radical it says
+that basically we don't care about any
+
+ align:start position:0%
+that basically we don't care about any
+ 
+
+ align:start position:0%
+that basically we don't care about any
+anything people have about the minimum
+
+ align:start position:0%
+anything people have about the minimum
+ 
+
+ align:start position:0%
+anything people have about the minimum
+we just care about making sure everybody
+
+ align:start position:0%
+we just care about making sure everybody
+ 
+
+ align:start position:0%
+we just care about making sure everybody
+gets to that
+
+ align:start position:0%
+gets to that
+ 
+
+ align:start position:0%
+gets to that
+minimum so that is very that makes this
+
+ align:start position:0%
+minimum so that is very that makes this
+ 
+
+ align:start position:0%
+minimum so that is very that makes this
+look like a conservative fantasy this is
+
+ align:start position:0%
+look like a conservative fantasy this is
+ 
+
+ align:start position:0%
+look like a conservative fantasy this is
+an incredibly radical approach which
+
+ align:start position:0%
+an incredibly radical approach which
+ 
+
+ align:start position:0%
+an incredibly radical approach which
+says we should take everything from the
+
+ align:start position:0%
+says we should take everything from the
+ 
+
+ align:start position:0%
+says we should take everything from the
+rich just to make sure the poor have
+
+ align:start position:0%
+rich just to make sure the poor have
+ 
+
+ align:start position:0%
+rich just to make sure the poor have
+enough
+
+ align:start position:0%
+enough
+ 
+
+ align:start position:0%
+enough
+okay but that's that's um clearly under
+
+ align:start position:0%
+okay but that's that's um clearly under
+ 
+
+ align:start position:0%
+okay but that's that's um clearly under
+utilitarian social war function that
+
+ align:start position:0%
+utilitarian social war function that
+ 
+
+ align:start position:0%
+utilitarian social war function that
+make us bad off clearly Bill clearly is
+
+ align:start position:0%
+make us bad off clearly Bill clearly is
+ 
+
+ align:start position:0%
+make us bad off clearly Bill clearly is
+the guy who goes from a billion to
+
+ align:start position:0%
+the guy who goes from a billion to
+ 
+
+ align:start position:0%
+the guy who goes from a billion to
+40,000 is made sad than the guy goes to
+
+ align:start position:0%
+40,000 is made sad than the guy goes to
+ 
+
+ align:start position:0%
+40,000 is made sad than the guy goes to
+39 to 40,000 is made happier so clearly
+
+ align:start position:0%
+39 to 40,000 is made happier so clearly
+ 
+
+ align:start position:0%
+39 to 40,000 is made happier so clearly
+that would not be a proper thing to do
+
+ align:start position:0%
+that would not be a proper thing to do
+ 
+
+ align:start position:0%
+that would not be a proper thing to do
+under utilitarian social welfare
+
+ align:start position:0%
+under utilitarian social welfare
+ 
+
+ align:start position:0%
+under utilitarian social welfare
+function but it would under
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Ry now of course on the right there's a
+
+ align:start position:0%
+Ry now of course on the right there's a
+ 
+
+ align:start position:0%
+Ry now of course on the right there's a
+on the on the conservative right there's
+
+ align:start position:0%
+on the on the conservative right there's
+ 
+
+ align:start position:0%
+on the on the conservative right there's
+a crism that of both of these approaches
+
+ align:start position:0%
+a crism that of both of these approaches
+ 
+
+ align:start position:0%
+a crism that of both of these approaches
+and that
+
+ align:start position:0%
+and that
+ 
+
+ align:start position:0%
+and that
+view there's there's a criticism on the
+
+ align:start position:0%
+view there's there's a criticism on the
+ 
+
+ align:start position:0%
+view there's there's a criticism on the
+uh uh which is that basically uh the
+
+ align:start position:0%
+uh uh which is that basically uh the
+ 
+
+ align:start position:0%
+uh uh which is that basically uh the
+conservative criticism
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+criticism says that
+
+ align:start position:0%
+criticism says that
+ 
+
+ align:start position:0%
+criticism says that
+basically look this whole discussion is
+
+ align:start position:0%
+basically look this whole discussion is
+ 
+
+ align:start position:0%
+basically look this whole discussion is
+misguided it says look let's say we
+
+ align:start position:0%
+misguided it says look let's say we
+ 
+
+ align:start position:0%
+misguided it says look let's say we
+started in society with everyone having
+
+ align:start position:0%
+started in society with everyone having
+ 
+
+ align:start position:0%
+started in society with everyone having
+the same amount of
+
+ align:start position:0%
+the same amount of
+ 
+
+ align:start position:0%
+the same amount of
+money let's say start everyone you and I
+
+ align:start position:0%
+money let's say start everyone you and I
+ 
+
+ align:start position:0%
+money let's say start everyone you and I
+have the same amount of money and let's
+
+ align:start position:0%
+have the same amount of money and let's
+ 
+
+ align:start position:0%
+have the same amount of money and let's
+say that you were willing as you should
+
+ align:start position:0%
+say that you were willing as you should
+ 
+
+ align:start position:0%
+say that you were willing as you should
+be willing to pay $100 to hear me
+
+ align:start position:0%
+be willing to pay $100 to hear me
+ 
+
+ align:start position:0%
+be willing to pay $100 to hear me
+lecture and so so you come in every day
+
+ align:start position:0%
+lecture and so so you come in every day
+ 
+
+ align:start position:0%
+lecture and so so you come in every day
+and you give me a $100 to you hear me
+
+ align:start position:0%
+and you give me a $100 to you hear me
+ 
+
+ align:start position:0%
+and you give me a $100 to you hear me
+lecture a
+
+ align:start position:0%
+lecture a
+ 
+
+ align:start position:0%
+lecture a
+bargain okay at the end of the semester
+
+ align:start position:0%
+bargain okay at the end of the semester
+ 
+
+ align:start position:0%
+bargain okay at the end of the semester
+I am richer or you are poorer is that
+
+ align:start position:0%
+I am richer or you are poorer is that
+ 
+
+ align:start position:0%
+I am richer or you are poorer is that
+unfair what's unfair about that you paid
+
+ align:start position:0%
+unfair what's unfair about that you paid
+ 
+
+ align:start position:0%
+unfair what's unfair about that you paid
+for something you
+
+ align:start position:0%
+for something you
+ 
+
+ align:start position:0%
+for something you
+wanted I had something you wanted and I
+
+ align:start position:0%
+wanted I had something you wanted and I
+ 
+
+ align:start position:0%
+wanted I had something you wanted and I
+end up richer how yet under utilitarian
+
+ align:start position:0%
+end up richer how yet under utilitarian
+ 
+
+ align:start position:0%
+end up richer how yet under utilitarian
+social Ware function we'd call that
+
+ align:start position:0%
+social Ware function we'd call that
+ 
+
+ align:start position:0%
+social Ware function we'd call that
+bad we'd say wait a second John's rich
+
+ align:start position:0%
+bad we'd say wait a second John's rich
+ 
+
+ align:start position:0%
+bad we'd say wait a second John's rich
+or you're poor John should give that
+
+ align:start position:0%
+or you're poor John should give that
+ 
+
+ align:start position:0%
+or you're poor John should give that
+money back to you but why you gave that
+
+ align:start position:0%
+money back to you but why you gave that
+ 
+
+ align:start position:0%
+money back to you but why you gave that
+money to me voluntarily
+
+ align:start position:0%
+money to me voluntarily
+ 
+
+ align:start position:0%
+money to me voluntarily
+so conservative criticism says that
+
+ align:start position:0%
+so conservative criticism says that
+ 
+
+ align:start position:0%
+so conservative criticism says that
+look as long as everyone has equal
+
+ align:start position:0%
+look as long as everyone has equal
+ 
+
+ align:start position:0%
+look as long as everyone has equal
+opportunity we shouldn't care about
+
+ align:start position:0%
+opportunity we shouldn't care about
+ 
+
+ align:start position:0%
+opportunity we shouldn't care about
+outcomes that what matters is
+
+ align:start position:0%
+outcomes that what matters is
+ 
+
+ align:start position:0%
+outcomes that what matters is
+opportunities not outcomes as long as
+
+ align:start position:0%
+opportunities not outcomes as long as
+ 
+
+ align:start position:0%
+opportunities not outcomes as long as
+has equal opportunities then let people
+
+ align:start position:0%
+has equal opportunities then let people
+ 
+
+ align:start position:0%
+has equal opportunities then let people
+spend their money as they want and let
+
+ align:start position:0%
+spend their money as they want and let
+ 
+
+ align:start position:0%
+spend their money as they want and let
+people end up and whatever income
+
+ align:start position:0%
+people end up and whatever income
+ 
+
+ align:start position:0%
+people end up and whatever income
+distribution results if Michael Jordan
+
+ align:start position:0%
+distribution results if Michael Jordan
+ 
+
+ align:start position:0%
+distribution results if Michael Jordan
+ends up rich he's the best at basketball
+
+ align:start position:0%
+ends up rich he's the best at basketball
+ 
+
+ align:start position:0%
+ends up rich he's the best at basketball
+so be it as long as everyone has equal
+
+ align:start position:0%
+so be it as long as everyone has equal
+ 
+
+ align:start position:0%
+so be it as long as everyone has equal
+opportunities this is a theory which
+
+ align:start position:0%
+opportunities this is a theory which
+ 
+
+ align:start position:0%
+opportunities this is a theory which
+says worry about
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+opportunities not
+
+ align:start position:0%
+opportunities not
+ 
+
+ align:start position:0%
+opportunities not
+outcomes
+
+ align:start position:0%
+outcomes
+ 
+
+ align:start position:0%
+outcomes
+now this
+
+ align:start position:0%
+now this
+ 
+
+ align:start position:0%
+now this
+approach has two fundamental flaws it's
+
+ align:start position:0%
+approach has two fundamental flaws it's
+ 
+
+ align:start position:0%
+approach has two fundamental flaws it's
+pretty compelling the story I told is
+
+ align:start position:0%
+pretty compelling the story I told is
+ 
+
+ align:start position:0%
+pretty compelling the story I told is
+pretty compelling except for two
+
+ align:start position:0%
+pretty compelling except for two
+ 
+
+ align:start position:0%
+pretty compelling except for two
+fundamental
+
+ align:start position:0%
+fundamental
+ 
+
+ align:start position:0%
+fundamental
+problems okay the first problem with
+
+ align:start position:0%
+problems okay the first problem with
+ 
+
+ align:start position:0%
+problems okay the first problem with
+this
+
+ align:start position:0%
+this
+ 
+
+ align:start position:0%
+this
+approach is what does opportunities
+
+ align:start position:0%
+approach is what does opportunities
+ 
+
+ align:start position:0%
+approach is what does opportunities
+mean by definition my kids have better
+
+ align:start position:0%
+mean by definition my kids have better
+ 
+
+ align:start position:0%
+mean by definition my kids have better
+opportunities than the kids born to a
+
+ align:start position:0%
+opportunities than the kids born to a
+ 
+
+ align:start position:0%
+opportunities than the kids born to a
+poor single mother living in a poor part
+
+ align:start position:0%
+poor single mother living in a poor part
+ 
+
+ align:start position:0%
+poor single mother living in a poor part
+of
+
+ align:start position:0%
+of
+ 
+
+ align:start position:0%
+of
+Boston they have more resources there
+
+ align:start position:0%
+Boston they have more resources there
+ 
+
+ align:start position:0%
+Boston they have more resources there
+are better schools things like that so
+
+ align:start position:0%
+are better schools things like that so
+ 
+
+ align:start position:0%
+are better schools things like that so
+in subsense equalizing opportunities is
+
+ align:start position:0%
+in subsense equalizing opportunities is
+ 
+
+ align:start position:0%
+in subsense equalizing opportunities is
+actually by itself pretty radical that
+
+ align:start position:0%
+actually by itself pretty radical that
+ 
+
+ align:start position:0%
+actually by itself pretty radical that
+would involve a large social structural
+
+ align:start position:0%
+would involve a large social structural
+ 
+
+ align:start position:0%
+would involve a large social structural
+change okay so first of all equalizing
+
+ align:start position:0%
+change okay so first of all equalizing
+ 
+
+ align:start position:0%
+change okay so first of all equalizing
+opportunity is not as easy as it sounds
+
+ align:start position:0%
+opportunity is not as easy as it sounds
+ 
+
+ align:start position:0%
+opportunity is not as easy as it sounds
+we don't all start equal it a large
+
+ align:start position:0%
+we don't all start equal it a large
+ 
+
+ align:start position:0%
+we don't all start equal it a large
+social upheaval to get us to that point
+
+ align:start position:0%
+social upheaval to get us to that point
+ 
+
+ align:start position:0%
+social upheaval to get us to that point
+we started equal
+
+ align:start position:0%
+we started equal
+ 
+
+ align:start position:0%
+we started equal
+the second problem with it is it turns
+
+ align:start position:0%
+the second problem with it is it turns
+ 
+
+ align:start position:0%
+the second problem with it is it turns
+out that much of what accounts for
+
+ align:start position:0%
+out that much of what accounts for
+ 
+
+ align:start position:0%
+out that much of what accounts for
+success in life is not skill or hard
+
+ align:start position:0%
+success in life is not skill or hard
+ 
+
+ align:start position:0%
+success in life is not skill or hard
+work but
+
+ align:start position:0%
+work but
+ 
+
+ align:start position:0%
+work but
+luck and in that
+
+ align:start position:0%
+luck and in that
+ 
+
+ align:start position:0%
+luck and in that
+case it's not true that rich people are
+
+ align:start position:0%
+case it's not true that rich people are
+ 
+
+ align:start position:0%
+case it's not true that rich people are
+rich because they deserve it or because
+
+ align:start position:0%
+rich because they deserve it or because
+ 
+
+ align:start position:0%
+rich because they deserve it or because
+they have skills or or they're
+
+ align:start position:0%
+they have skills or or they're
+ 
+
+ align:start position:0%
+they have skills or or they're
+just lucky and why do we necessarily
+
+ align:start position:0%
+just lucky and why do we necessarily
+ 
+
+ align:start position:0%
+just lucky and why do we necessarily
+want to reward luck indeed can't we
+
+ align:start position:0%
+want to reward luck indeed can't we
+ 
+
+ align:start position:0%
+want to reward luck indeed can't we
+think a redistribution is kind of luck
+
+ align:start position:0%
+think a redistribution is kind of luck
+ 
+
+ align:start position:0%
+think a redistribution is kind of luck
+Insurance imagine a world where random
+
+ align:start position:0%
+Insurance imagine a world where random
+ 
+
+ align:start position:0%
+Insurance imagine a world where random
+events going to happen to you you get
+
+ align:start position:0%
+events going to happen to you you get
+ 
+
+ align:start position:0%
+events going to happen to you you get
+hit by a car we talked about why we want
+
+ align:start position:0%
+hit by a car we talked about why we want
+ 
+
+ align:start position:0%
+hit by a car we talked about why we want
+insurance right want Insurance to make
+
+ align:start position:0%
+insurance right want Insurance to make
+ 
+
+ align:start position:0%
+insurance right want Insurance to make
+sure if we get hit by the car don't get
+
+ align:start position:0%
+sure if we get hit by the car don't get
+ 
+
+ align:start position:0%
+sure if we get hit by the car don't get
+hit by the car we're in the same off
+
+ align:start position:0%
+hit by the car we're in the same off
+ 
+
+ align:start position:0%
+hit by the car we're in the same off
+well same thing RS talked about behind
+
+ align:start position:0%
+well same thing RS talked about behind
+ 
+
+ align:start position:0%
+well same thing RS talked about behind
+the veil of ignorance imagine before
+
+ align:start position:0%
+the veil of ignorance imagine before
+ 
+
+ align:start position:0%
+the veil of ignorance imagine before
+you're born you don't know if you're be
+
+ align:start position:0%
+you're born you don't know if you're be
+ 
+
+ align:start position:0%
+you're born you don't know if you're be
+rich or poor you would choose a system
+
+ align:start position:0%
+rich or poor you would choose a system
+ 
+
+ align:start position:0%
+rich or poor you would choose a system
+which would ensure you against being
+
+ align:start position:0%
+which would ensure you against being
+ 
+
+ align:start position:0%
+which would ensure you against being
+poor and that system which would involve
+
+ align:start position:0%
+poor and that system which would involve
+ 
+
+ align:start position:0%
+poor and that system which would involve
+transfers so if much of success is due
+
+ align:start position:0%
+transfers so if much of success is due
+ 
+
+ align:start position:0%
+transfers so if much of success is due
+to luck we're going to want a system
+
+ align:start position:0%
+to luck we're going to want a system
+ 
+
+ align:start position:0%
+to luck we're going to want a system
+that shoots the rich to the poor because
+
+ align:start position:0%
+that shoots the rich to the poor because
+ 
+
+ align:start position:0%
+that shoots the rich to the poor because
+the rich got lucky the poor didn't
+
+ align:start position:0%
+the rich got lucky the poor didn't
+ 
+
+ align:start position:0%
+the rich got lucky the poor didn't
+that's uncertain we want to ensure
+
+ align:start position:0%
+that's uncertain we want to ensure
+ 
+
+ align:start position:0%
+that's uncertain we want to ensure
+against okay fascinating fact if you if
+
+ align:start position:0%
+against okay fascinating fact if you if
+ 
+
+ align:start position:0%
+against okay fascinating fact if you if
+you interview people around the world
+
+ align:start position:0%
+you interview people around the world
+ 
+
+ align:start position:0%
+you interview people around the world
+and ask
+
+ align:start position:0%
+and ask
+ 
+
+ align:start position:0%
+and ask
+them is Success mostly due to hard work
+
+ align:start position:0%
+them is Success mostly due to hard work
+ 
+
+ align:start position:0%
+them is Success mostly due to hard work
+or to luck in the US people say hard
+
+ align:start position:0%
+or to luck in the US people say hard
+ 
+
+ align:start position:0%
+or to luck in the US people say hard
+work in Europe people say luck in Europe
+
+ align:start position:0%
+work in Europe people say luck in Europe
+ 
+
+ align:start position:0%
+work in Europe people say luck in Europe
+they have much higher redistribution
+
+ align:start position:0%
+they have much higher redistribution
+ 
+
+ align:start position:0%
+they have much higher redistribution
+than we do in the US because they have a
+
+ align:start position:0%
+than we do in the US because they have a
+ 
+
+ align:start position:0%
+than we do in the US because they have a
+view that much more success comes from
+
+ align:start position:0%
+view that much more success comes from
+ 
+
+ align:start position:0%
+view that much more success comes from
+luck now the answer is it's both in
+
+ align:start position:0%
+luck now the answer is it's both in
+ 
+
+ align:start position:0%
+luck now the answer is it's both in
+every case but sort of an interesting
+
+ align:start position:0%
+every case but sort of an interesting
+ 
+
+ align:start position:0%
+every case but sort of an interesting
+way to two ways think about the world
+
+ align:start position:0%
+way to two ways think about the world
+ 
+
+ align:start position:0%
+way to two ways think about the world
+and then finally there's a totally
+
+ align:start position:0%
+and then finally there's a totally
+ 
+
+ align:start position:0%
+and then finally there's a totally
+different alternative which has a lot of
+
+ align:start position:0%
+different alternative which has a lot of
+ 
+
+ align:start position:0%
+different alternative which has a lot of
+appeal which is called commodity
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+egalitarianism commodity egalitarianism
+
+ align:start position:0%
+egalitarianism commodity egalitarianism
+ 
+
+ align:start position:0%
+egalitarianism commodity egalitarianism
+this view has a lot of appeal as well
+
+ align:start position:0%
+this view has a lot of appeal as well
+ 
+
+ align:start position:0%
+this view has a lot of appeal as well
+it's simply says
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+look let's get rid of this Focus on me
+
+ align:start position:0%
+look let's get rid of this Focus on me
+ 
+
+ align:start position:0%
+look let's get rid of this Focus on me
+versus you that's just
+
+ align:start position:0%
+versus you that's just
+ 
+
+ align:start position:0%
+versus you that's just
+destructive let's take a page from R's
+
+ align:start position:0%
+destructive let's take a page from R's
+ 
+
+ align:start position:0%
+destructive let's take a page from R's
+book and say look let's just make sure
+
+ align:start position:0%
+book and say look let's just make sure
+ 
+
+ align:start position:0%
+book and say look let's just make sure
+that the poor have enough to live and
+
+ align:start position:0%
+that the poor have enough to live and
+ 
+
+ align:start position:0%
+that the poor have enough to live and
+beyond that let it
+
+ align:start position:0%
+beyond that let it
+ 
+
+ align:start position:0%
+beyond that let it
+rip so Kam the view is much like RS who
+
+ align:start position:0%
+rip so Kam the view is much like RS who
+ 
+
+ align:start position:0%
+rip so Kam the view is much like RS who
+want to make sure the poor are a decent
+
+ align:start position:0%
+want to make sure the poor are a decent
+ 
+
+ align:start position:0%
+want to make sure the poor are a decent
+level but we don't care then how much
+
+ align:start position:0%
+level but we don't care then how much
+ 
+
+ align:start position:0%
+level but we don't care then how much
+more the rich have as long as the poor
+
+ align:start position:0%
+more the rich have as long as the poor
+ 
+
+ align:start position:0%
+more the rich have as long as the poor
+have achieved a standard of living where
+
+ align:start position:0%
+have achieved a standard of living where
+ 
+
+ align:start position:0%
+have achieved a standard of living where
+they can survive then let it rip I don't
+
+ align:start position:0%
+they can survive then let it rip I don't
+ 
+
+ align:start position:0%
+they can survive then let it rip I don't
+care how rich Bill Gates is as long as
+
+ align:start position:0%
+care how rich Bill Gates is as long as
+ 
+
+ align:start position:0%
+care how rich Bill Gates is as long as
+each of you can have shelter and food
+
+ align:start position:0%
+each of you can have shelter and food
+ 
+
+ align:start position:0%
+each of you can have shelter and food
+and basic health care and other basic
+
+ align:start position:0%
+and basic health care and other basic
+ 
+
+ align:start position:0%
+and basic health care and other basic
+needs
+
+ align:start position:0%
+needs
+ 
+
+ align:start position:0%
+needs
+met it's kind of a compelling it's kind
+
+ align:start position:0%
+met it's kind of a compelling it's kind
+ 
+
+ align:start position:0%
+met it's kind of a compelling it's kind
+of a compelling um argument right that
+
+ align:start position:0%
+of a compelling um argument right that
+ 
+
+ align:start position:0%
+of a compelling um argument right that
+basically why should I care about guy
+
+ align:start position:0%
+basically why should I care about guy
+ 
+
+ align:start position:0%
+basically why should I care about guy
+who was a billion versus the guy who was
+
+ align:start position:0%
+who was a billion versus the guy who was
+ 
+
+ align:start position:0%
+who was a billion versus the guy who was
+a million all I care was making sure
+
+ align:start position:0%
+a million all I care was making sure
+ 
+
+ align:start position:0%
+a million all I care was making sure
+everybody can lead a decent
+
+ align:start position:0%
+everybody can lead a decent
+ 
+
+ align:start position:0%
+everybody can lead a decent
+life it's in some sense a nice
+
+ align:start position:0%
+life it's in some sense a nice
+ 
+
+ align:start position:0%
+life it's in some sense a nice
+compromise between a lot of these
+
+ align:start position:0%
+compromise between a lot of these
+ 
+
+ align:start position:0%
+compromise between a lot of these
+different views in many ways and it
+
+ align:start position:0%
+different views in many ways and it
+ 
+
+ align:start position:0%
+different views in many ways and it
+speaks to a key issue we'll talk about
+
+ align:start position:0%
+speaks to a key issue we'll talk about
+ 
+
+ align:start position:0%
+speaks to a key issue we'll talk about
+later which is should we really be
+
+ align:start position:0%
+later which is should we really be
+ 
+
+ align:start position:0%
+later which is should we really be
+giving people money or should we be
+
+ align:start position:0%
+giving people money or should we be
+ 
+
+ align:start position:0%
+giving people money or should we be
+giving people the goods like housing and
+
+ align:start position:0%
+giving people the goods like housing and
+ 
+
+ align:start position:0%
+giving people the goods like housing and
+health care that make up a decent
+
+ align:start position:0%
+health care that make up a decent
+ 
+
+ align:start position:0%
+health care that make up a decent
+standard of
+
+ align:start position:0%
+standard of
+ 
+
+ align:start position:0%
+standard of
+living so these are four different views
+
+ align:start position:0%
+living so these are four different views
+ 
+
+ align:start position:0%
+living so these are four different views
+only two of them can been easily
+
+ align:start position:0%
+only two of them can been easily
+ 
+
+ align:start position:0%
+only two of them can been easily
+expressed mathematically these obviously
+
+ align:start position:0%
+expressed mathematically these obviously
+ 
+
+ align:start position:0%
+expressed mathematically these obviously
+can write down models but they're more
+
+ align:start position:0%
+can write down models but they're more
+ 
+
+ align:start position:0%
+can write down models but they're more
+complicated but the bottom line
+
+ align:start position:0%
+complicated but the bottom line
+ 
+
+ align:start position:0%
+complicated but the bottom line
+is with all these
+
+ align:start position:0%
+is with all these
+ 
+
+ align:start position:0%
+is with all these
+views given those views you can figure
+
+ align:start position:0%
+views given those views you can figure
+ 
+
+ align:start position:0%
+views given those views you can figure
+out whether a given policy that
+
+ align:start position:0%
+out whether a given policy that
+ 
+
+ align:start position:0%
+out whether a given policy that
+transfers a person a to person B makes
+
+ align:start position:0%
+transfers a person a to person B makes
+ 
+
+ align:start position:0%
+transfers a person a to person B makes
+sense
+
+ align:start position:0%
+sense
+ 
+
+ align:start position:0%
+sense
+these are different ways of providing a
+
+ align:start position:0%
+these are different ways of providing a
+ 
+
+ align:start position:0%
+these are different ways of providing a
+social welfare
+
+ align:start position:0%
+social welfare
+ 
+
+ align:start position:0%
+social welfare
+framework okay questions about that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah sure yeah they're related so here's
+
+ align:start position:0%
+yeah sure yeah they're related so here's
+ 
+
+ align:start position:0%
+yeah sure yeah they're related so here's
+the difference let's say we all decide
+
+ align:start position:0%
+the difference let's say we all decide
+ 
+
+ align:start position:0%
+the difference let's say we all decide
+that everyone needs $50,000 to lead a
+
+ align:start position:0%
+that everyone needs $50,000 to lead a
+ 
+
+ align:start position:0%
+that everyone needs $50,000 to lead a
+decent life in
+
+ align:start position:0%
+decent life in
+ 
+
+ align:start position:0%
+decent life in
+America what commodity Garian say is
+
+ align:start position:0%
+America what commodity Garian say is
+ 
+
+ align:start position:0%
+America what commodity Garian say is
+once everyone has $50,000
+
+ align:start position:0%
+once everyone has $50,000
+ 
+
+ align:start position:0%
+once everyone has $50,000
+I don't care how rich people are above
+
+ align:start position:0%
+I don't care how rich people are above
+ 
+
+ align:start position:0%
+I don't care how rich people are above
+that RS would say I do I don't want I
+
+ align:start position:0%
+that RS would say I do I don't want I
+ 
+
+ align:start position:0%
+that RS would say I do I don't want I
+only if everyone is
+
+ align:start position:0%
+only if everyone is
+ 
+
+ align:start position:0%
+only if everyone is
+$50,000 but one guy's 40 but but but if
+
+ align:start position:0%
+$50,000 but one guy's 40 but but but if
+ 
+
+ align:start position:0%
+$50,000 but one guy's 40 but but but if
+I was $50,000 and someone else is a
+
+ align:start position:0%
+I was $50,000 and someone else is a
+ 
+
+ align:start position:0%
+I was $50,000 and someone else is a
+billion dollars we we' rather make
+
+ align:start position:0%
+billion dollars we we' rather make
+ 
+
+ align:start position:0%
+billion dollars we we' rather make
+everyone else that $50,000 and3 and that
+
+ align:start position:0%
+everyone else that $50,000 and3 and that
+ 
+
+ align:start position:0%
+everyone else that $50,000 and3 and that
+guy back come down to 50,000 and3 we
+
+ align:start position:0%
+guy back come down to 50,000 and3 we
+ 
+
+ align:start position:0%
+guy back come down to 50,000 and3 we
+don't want anybody above the minimum we
+
+ align:start position:0%
+don't want anybody above the minimum we
+ 
+
+ align:start position:0%
+don't want anybody above the minimum we
+want to make sure the minimum is high as
+
+ align:start position:0%
+want to make sure the minimum is high as
+ 
+
+ align:start position:0%
+want to make sure the minimum is high as
+it possibly can be where T says as long
+
+ align:start position:0%
+it possibly can be where T says as long
+ 
+
+ align:start position:0%
+it possibly can be where T says as long
+as the minimum is the decent state of
+
+ align:start position:0%
+as the minimum is the decent state of
+ 
+
+ align:start position:0%
+as the minimum is the decent state of
+living let the rich guy have as much as
+
+ align:start position:0%
+living let the rich guy have as much as
+ 
+
+ align:start position:0%
+living let the rich guy have as much as
+he
+
+ align:start position:0%
+he
+ 
+
+ align:start position:0%
+he
+want RS cares about inequality is a
+
+ align:start position:0%
+want RS cares about inequality is a
+ 
+
+ align:start position:0%
+want RS cares about inequality is a
+concept commodity G terrorism
+
+ align:start position:0%
+concept commodity G terrorism
+ 
+
+ align:start position:0%
+concept commodity G terrorism
+doesn't good question other
+
+ align:start position:0%
+doesn't good question other
+ 
+
+ align:start position:0%
+doesn't good question other
+questions okay so armed with these views
+
+ align:start position:0%
+questions okay so armed with these views
+ 
+
+ align:start position:0%
+questions okay so armed with these views
+let's talk about the facts what do we
+
+ align:start position:0%
+let's talk about the facts what do we
+ 
+
+ align:start position:0%
+let's talk about the facts what do we
+know about
+
+ align:start position:0%
+know about
+ 
+
+ align:start position:0%
+know about
+inequality and here I'm just going to
+
+ align:start position:0%
+inequality and here I'm just going to
+ 
+
+ align:start position:0%
+inequality and here I'm just going to
+run through some facts from my textbook
+
+ align:start position:0%
+run through some facts from my textbook
+ 
+
+ align:start position:0%
+run through some facts from my textbook
+that I used from
+
+ align:start position:0%
+that I used from
+ 
+
+ align:start position:0%
+that I used from
+1441 so let's start with figure
+
+ align:start position:0%
+1441 so let's start with figure
+ 
+
+ align:start position:0%
+1441 so let's start with figure
+23-2 this shows relative income
+
+ align:start position:0%
+23-2 this shows relative income
+ 
+
+ align:start position:0%
+23-2 this shows relative income
+inequality in the United States how do
+
+ align:start position:0%
+inequality in the United States how do
+ 
+
+ align:start position:0%
+inequality in the United States how do
+we do that we divide the population to
+
+ align:start position:0%
+we do that we divide the population to
+ 
+
+ align:start position:0%
+we do that we divide the population to
+quintiles that is fifths of the people
+
+ align:start position:0%
+quintiles that is fifths of the people
+ 
+
+ align:start position:0%
+quintiles that is fifths of the people
+so each of these rows is 20% of the
+
+ align:start position:0%
+so each of these rows is 20% of the
+ 
+
+ align:start position:0%
+so each of these rows is 20% of the
+people each number shows the percent of
+
+ align:start position:0%
+people each number shows the percent of
+ 
+
+ align:start position:0%
+people each number shows the percent of
+income earned by that share of people in
+
+ align:start position:0%
+income earned by that share of people in
+ 
+
+ align:start position:0%
+income earned by that share of people in
+other words in a perfectly equal Society
+
+ align:start position:0%
+other words in a perfectly equal Society
+ 
+
+ align:start position:0%
+other words in a perfectly equal Society
+every number in this table would be 20
+
+ align:start position:0%
+every number in this table would be 20
+ 
+
+ align:start position:0%
+every number in this table would be 20
+in a perfectly equal Society every fifth
+
+ align:start position:0%
+in a perfectly equal Society every fifth
+ 
+
+ align:start position:0%
+in a perfectly equal Society every fifth
+of people would get a fifth of the money
+
+ align:start position:0%
+of people would get a fifth of the money
+ 
+
+ align:start position:0%
+of people would get a fifth of the money
+but in fact that's never true anywhere
+
+ align:start position:0%
+but in fact that's never true anywhere
+ 
+
+ align:start position:0%
+but in fact that's never true anywhere
+you see always the higher
+
+ align:start position:0%
+you see always the higher
+ 
+
+ align:start position:0%
+you see always the higher
+quintiles control a larger share of
+
+ align:start position:0%
+quintiles control a larger share of
+ 
+
+ align:start position:0%
+quintiles control a larger share of
+income that's always true what's more
+
+ align:start position:0%
+income that's always true what's more
+ 
+
+ align:start position:0%
+income that's always true what's more
+notable is how it's changed over time
+
+ align:start position:0%
+notable is how it's changed over time
+ 
+
+ align:start position:0%
+notable is how it's changed over time
+from 1967 to 1980 it stayed relatively
+
+ align:start position:0%
+from 1967 to 1980 it stayed relatively
+ 
+
+ align:start position:0%
+from 1967 to 1980 it stayed relatively
+flat but look from 1980 to
+
+ align:start position:0%
+flat but look from 1980 to
+ 
+
+ align:start position:0%
+flat but look from 1980 to
+2019 the share held by the poorest has
+
+ align:start position:0%
+2019 the share held by the poorest has
+ 
+
+ align:start position:0%
+2019 the share held by the poorest has
+fallen by about
+
+ align:start position:0%
+fallen by about
+ 
+
+ align:start position:0%
+fallen by about
+25% the poorest 20% of people used to
+
+ align:start position:0%
+25% the poorest 20% of people used to
+ 
+
+ align:start position:0%
+25% the poorest 20% of people used to
+earn 4.2% of the income now they get
+
+ align:start position:0%
+earn 4.2% of the income now they get
+ 
+
+ align:start position:0%
+earn 4.2% of the income now they get
+3.1% of the income the richest 20% of
+
+ align:start position:0%
+3.1% of the income the richest 20% of
+ 
+
+ align:start position:0%
+3.1% of the income the richest 20% of
+people in 1980 had 44% of the income now
+
+ align:start position:0%
+people in 1980 had 44% of the income now
+ 
+
+ align:start position:0%
+people in 1980 had 44% of the income now
+they have 52% of the
+
+ align:start position:0%
+they have 52% of the
+ 
+
+ align:start position:0%
+they have 52% of the
+income Society has gotten much more
+
+ align:start position:0%
+income Society has gotten much more
+ 
+
+ align:start position:0%
+income Society has gotten much more
+unequal this has been driven not just by
+
+ align:start position:0%
+unequal this has been driven not just by
+ 
+
+ align:start position:0%
+unequal this has been driven not just by
+the richest 20% to be clear the richest
+
+ align:start position:0%
+the richest 20% to be clear the richest
+ 
+
+ align:start position:0%
+the richest 20% to be clear the richest
+just to fix ideas here the richest 20%
+
+ align:start position:0%
+just to fix ideas here the richest 20%
+ 
+
+ align:start position:0%
+just to fix ideas here the richest 20%
+of people would be people with incomes
+
+ align:start position:0%
+of people would be people with incomes
+ 
+
+ align:start position:0%
+of people would be people with incomes
+above say nationally PE with incomes
+
+ align:start position:0%
+above say nationally PE with incomes
+ 
+
+ align:start position:0%
+above say nationally PE with incomes
+above say
+
+ align:start position:0%
+above say
+ 
+
+ align:start position:0%
+above say
+$85,000 so it's not Mega Rich okay or
+
+ align:start position:0%
+$85,000 so it's not Mega Rich okay or
+ 
+
+ align:start position:0%
+$85,000 so it's not Mega Rich okay or
+maybe $100,000 not Mega Rich it's well
+
+ align:start position:0%
+maybe $100,000 not Mega Rich it's well
+ 
+
+ align:start position:0%
+maybe $100,000 not Mega Rich it's well
+off but not Mega rich but this trend has
+
+ align:start position:0%
+off but not Mega rich but this trend has
+ 
+
+ align:start position:0%
+off but not Mega rich but this trend has
+been driven by the very
+
+ align:start position:0%
+been driven by the very
+ 
+
+ align:start position:0%
+been driven by the very
+wealthy figure 233 shows the share of
+
+ align:start position:0%
+wealthy figure 233 shows the share of
+ 
+
+ align:start position:0%
+wealthy figure 233 shows the share of
+income going to the top 1% of income PE
+
+ align:start position:0%
+income going to the top 1% of income PE
+ 
+
+ align:start position:0%
+income going to the top 1% of income PE
+holders this people income above about
+
+ align:start position:0%
+holders this people income above about
+ 
+
+ align:start position:0%
+holders this people income above about
+$500,000 these are the
+
+ align:start position:0%
+$500,000 these are the
+ 
+
+ align:start position:0%
+$500,000 these are the
+rich
+
+ align:start position:0%
+rich
+ 
+
+ align:start position:0%
+rich
+okay at the turn of the C 20 Century
+
+ align:start position:0%
+okay at the turn of the C 20 Century
+ 
+
+ align:start position:0%
+okay at the turn of the C 20 Century
+1913 and peing right before the Great
+
+ align:start position:0%
+1913 and peing right before the Great
+ 
+
+ align:start position:0%
+1913 and peing right before the Great
+Depression the rich held about 25% of
+
+ align:start position:0%
+Depression the rich held about 25% of
+ 
+
+ align:start position:0%
+Depression the rich held about 25% of
+all in income that is 1% of people got
+
+ align:start position:0%
+all in income that is 1% of people got
+ 
+
+ align:start position:0%
+all in income that is 1% of people got
+25% of the income that fell then fell
+
+ align:start position:0%
+25% of the income that fell then fell
+ 
+
+ align:start position:0%
+25% of the income that fell then fell
+precipitously till in the early 1970s 1%
+
+ align:start position:0%
+precipitously till in the early 1970s 1%
+ 
+
+ align:start position:0%
+precipitously till in the early 1970s 1%
+of people only about 10% of income and
+
+ align:start position:0%
+of people only about 10% of income and
+ 
+
+ align:start position:0%
+of people only about 10% of income and
+it's risen dramatically since so we're
+
+ align:start position:0%
+it's risen dramatically since so we're
+ 
+
+ align:start position:0%
+it's risen dramatically since so we're
+back at the level actually above where
+
+ align:start position:0%
+back at the level actually above where
+ 
+
+ align:start position:0%
+back at the level actually above where
+we were at the peak of the 20th century
+
+ align:start position:0%
+we were at the peak of the 20th century
+ 
+
+ align:start position:0%
+we were at the peak of the 20th century
+with one with the top 1% earning more
+
+ align:start position:0%
+with one with the top 1% earning more
+ 
+
+ align:start position:0%
+with one with the top 1% earning more
+than a quarter of all the resources in
+
+ align:start position:0%
+than a quarter of all the resources in
+ 
+
+ align:start position:0%
+than a quarter of all the resources in
+society so it's a very unequal
+
+ align:start position:0%
+society so it's a very unequal
+ 
+
+ align:start position:0%
+society so it's a very unequal
+Society now you might say well how do I
+
+ align:start position:0%
+Society now you might say well how do I
+ 
+
+ align:start position:0%
+Society now you might say well how do I
+know it's an equal what's what's the
+
+ align:start position:0%
+know it's an equal what's what's the
+ 
+
+ align:start position:0%
+know it's an equal what's what's the
+natural state what I want to do is
+
+ align:start position:0%
+natural state what I want to do is
+ 
+
+ align:start position:0%
+natural state what I want to do is
+compare countries figure 234 Compares
+
+ align:start position:0%
+compare countries figure 234 Compares
+ 
+
+ align:start position:0%
+compare countries figure 234 Compares
+countries this is just a small
+
+ align:start position:0%
+countries this is just a small
+ 
+
+ align:start position:0%
+countries this is just a small
+comparison of some countries that are in
+
+ align:start position:0%
+comparison of some countries that are in
+ 
+
+ align:start position:0%
+comparison of some countries that are in
+the um o just a subset alphabetically of
+
+ align:start position:0%
+the um o just a subset alphabetically of
+ 
+
+ align:start position:0%
+the um o just a subset alphabetically of
+countries that are what we call
+
+ align:start position:0%
+countries that are what we call
+ 
+
+ align:start position:0%
+countries that are what we call
+developed countries from countries that
+
+ align:start position:0%
+developed countries from countries that
+ 
+
+ align:start position:0%
+developed countries from countries that
+we consider our peers like the UK or
+
+ align:start position:0%
+we consider our peers like the UK or
+ 
+
+ align:start position:0%
+we consider our peers like the UK or
+Sweden the countries that are poor like
+
+ align:start position:0%
+Sweden the countries that are poor like
+ 
+
+ align:start position:0%
+Sweden the countries that are poor like
+Czechoslovakia or turkey what you show
+
+ align:start position:0%
+Czechoslovakia or turkey what you show
+ 
+
+ align:start position:0%
+Czechoslovakia or turkey what you show
+here is the share of income held by the
+
+ align:start position:0%
+here is the share of income held by the
+ 
+
+ align:start position:0%
+here is the share of income held by the
+bottom
+
+ align:start position:0%
+bottom
+ 
+
+ align:start position:0%
+bottom
+10% the bottom 20% and the bottom 40% as
+
+ align:start position:0%
+10% the bottom 20% and the bottom 40% as
+ 
+
+ align:start position:0%
+10% the bottom 20% and the bottom 40% as
+well as the top 40% the top 20% the top
+
+ align:start position:0%
+well as the top 40% the top 20% the top
+ 
+
+ align:start position:0%
+well as the top 40% the top 20% the top
+10% just compare the bottom two rows the
+
+ align:start position:0%
+10% just compare the bottom two rows the
+ 
+
+ align:start position:0%
+10% just compare the bottom two rows the
+bottom row is the average for all
+
+ align:start position:0%
+bottom row is the average for all
+ 
+
+ align:start position:0%
+bottom row is the average for all
+developed countries so on average on
+
+ align:start position:0%
+developed countries so on average on
+ 
+
+ align:start position:0%
+developed countries so on average on
+average across all developed countries
+
+ align:start position:0%
+average across all developed countries
+ 
+
+ align:start position:0%
+average across all developed countries
+the bottom 10% of people have 3% of the
+
+ align:start position:0%
+the bottom 10% of people have 3% of the
+ 
+
+ align:start position:0%
+the bottom 10% of people have 3% of the
+income and the top 10% of people have
+
+ align:start position:0%
+income and the top 10% of people have
+ 
+
+ align:start position:0%
+income and the top 10% of people have
+25% of the income in the US the bottom
+
+ align:start position:0%
+25% of the income in the US the bottom
+ 
+
+ align:start position:0%
+25% of the income in the US the bottom
+10 perent of only 1.6% of the the income
+
+ align:start position:0%
+10 perent of only 1.6% of the the income
+ 
+
+ align:start position:0%
+10 perent of only 1.6% of the the income
+and the top 10% have almost 30% of the
+
+ align:start position:0%
+and the top 10% have almost 30% of the
+ 
+
+ align:start position:0%
+and the top 10% have almost 30% of the
+income so the US is unequal it's much
+
+ align:start position:0%
+income so the US is unequal it's much
+ 
+
+ align:start position:0%
+income so the US is unequal it's much
+more unequal indeed we are the most
+
+ align:start position:0%
+more unequal indeed we are the most
+ 
+
+ align:start position:0%
+more unequal indeed we are the most
+unequal what's considered developed
+
+ align:start position:0%
+unequal what's considered developed
+ 
+
+ align:start position:0%
+unequal what's considered developed
+country except for
+
+ align:start position:0%
+country except for
+ 
+
+ align:start position:0%
+country except for
+Mexico we're unequal that any other
+
+ align:start position:0%
+Mexico we're unequal that any other
+ 
+
+ align:start position:0%
+Mexico we're unequal that any other
+country consider a developed country we
+
+ align:start position:0%
+country consider a developed country we
+ 
+
+ align:start position:0%
+country consider a developed country we
+the most unequal except for Mexico and
+
+ align:start position:0%
+the most unequal except for Mexico and
+ 
+
+ align:start position:0%
+the most unequal except for Mexico and
+maybe turkey there's some debate
+
+ align:start position:0%
+maybe turkey there's some debate
+ 
+
+ align:start position:0%
+maybe turkey there's some debate
+there okay so we're very
+
+ align:start position:0%
+there okay so we're very
+ 
+
+ align:start position:0%
+there okay so we're very
+unequal
+
+ align:start position:0%
+unequal
+ 
+
+ align:start position:0%
+unequal
+now many people particularly people in
+
+ align:start position:0%
+now many people particularly people in
+ 
+
+ align:start position:0%
+now many people particularly people in
+these camps three and four would say
+
+ align:start position:0%
+these camps three and four would say
+ 
+
+ align:start position:0%
+these camps three and four would say
+well look that's all well and good but
+
+ align:start position:0%
+well look that's all well and good but
+ 
+
+ align:start position:0%
+well look that's all well and good but
+why you so worried about inequality sure
+
+ align:start position:0%
+why you so worried about inequality sure
+ 
+
+ align:start position:0%
+why you so worried about inequality sure
+we got some rich
+
+ align:start position:0%
+we got some rich
+ 
+
+ align:start position:0%
+we got some rich
+guys but we don't care about that we
+
+ align:start position:0%
+guys but we don't care about that we
+ 
+
+ align:start position:0%
+guys but we don't care about that we
+just care that poor people have enough
+
+ align:start position:0%
+just care that poor people have enough
+ 
+
+ align:start position:0%
+just care that poor people have enough
+to live that's what matters we want to
+
+ align:start position:0%
+to live that's what matters we want to
+ 
+
+ align:start position:0%
+to live that's what matters we want to
+focus on what is the standard of living
+
+ align:start position:0%
+focus on what is the standard of living
+ 
+
+ align:start position:0%
+focus on what is the standard of living
+of the
+
+ align:start position:0%
+of the
+ 
+
+ align:start position:0%
+of the
+poor well in other words they want to
+
+ align:start position:0%
+poor well in other words they want to
+ 
+
+ align:start position:0%
+poor well in other words they want to
+shift their focus
+
+ align:start position:0%
+shift their focus
+ 
+
+ align:start position:0%
+shift their focus
+from
+
+ align:start position:0%
+from
+ 
+
+ align:start position:0%
+from
+relative inequality
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+versus
+
+ align:start position:0%
+versus
+ 
+
+ align:start position:0%
+versus
+absolute
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+deprivation that is how what are people
+
+ align:start position:0%
+deprivation that is how what are people
+ 
+
+ align:start position:0%
+deprivation that is how what are people
+actually living on well to do that
+
+ align:start position:0%
+actually living on well to do that
+ 
+
+ align:start position:0%
+actually living on well to do that
+relative the problem with that is
+
+ align:start position:0%
+relative the problem with that is
+ 
+
+ align:start position:0%
+relative the problem with that is
+relative income inequality is easy to
+
+ align:start position:0%
+relative income inequality is easy to
+ 
+
+ align:start position:0%
+relative income inequality is easy to
+measure just look at what group has Rel
+
+ align:start position:0%
+measure just look at what group has Rel
+ 
+
+ align:start position:0%
+measure just look at what group has Rel
+to another it's unit
+
+ align:start position:0%
+to another it's unit
+ 
+
+ align:start position:0%
+to another it's unit
+free once you want to measure absolute
+
+ align:start position:0%
+free once you want to measure absolute
+ 
+
+ align:start position:0%
+free once you want to measure absolute
+deprivation you have to make a stand on
+
+ align:start position:0%
+deprivation you have to make a stand on
+ 
+
+ align:start position:0%
+deprivation you have to make a stand on
+what it means to be
+
+ align:start position:0%
+what it means to be
+ 
+
+ align:start position:0%
+what it means to be
+deprived the the US has taken such a
+
+ align:start position:0%
+deprived the the US has taken such a
+ 
+
+ align:start position:0%
+deprived the the US has taken such a
+stand and we've created something called
+
+ align:start position:0%
+stand and we've created something called
+ 
+
+ align:start position:0%
+stand and we've created something called
+the poverty
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+line the poverty line is the US
+
+ align:start position:0%
+line the poverty line is the US
+ 
+
+ align:start position:0%
+line the poverty line is the US
+measure of what you need to lead a
+
+ align:start position:0%
+measure of what you need to lead a
+ 
+
+ align:start position:0%
+measure of what you need to lead a
+minimally acceptable life in the
+
+ align:start position:0%
+minimally acceptable life in the
+ 
+
+ align:start position:0%
+minimally acceptable life in the
+US okay below which what does it mean to
+
+ align:start position:0%
+US okay below which what does it mean to
+ 
+
+ align:start position:0%
+US okay below which what does it mean to
+be in poverty now this is a pretty
+
+ align:start position:0%
+be in poverty now this is a pretty
+ 
+
+ align:start position:0%
+be in poverty now this is a pretty
+foundational
+
+ align:start position:0%
+foundational
+ 
+
+ align:start position:0%
+foundational
+concept yet its Origins are very modest
+
+ align:start position:0%
+concept yet its Origins are very modest
+ 
+
+ align:start position:0%
+concept yet its Origins are very modest
+for those of you who think that working
+
+ align:start position:0%
+for those of you who think that working
+ 
+
+ align:start position:0%
+for those of you who think that working
+the government doesn't involve pH being
+
+ align:start position:0%
+the government doesn't involve pH being
+ 
+
+ align:start position:0%
+the government doesn't involve pH being
+government bureaucrat doesn't that much
+
+ align:start position:0%
+government bureaucrat doesn't that much
+ 
+
+ align:start position:0%
+government bureaucrat doesn't that much
+power in the mid 1960s a mid-level
+
+ align:start position:0%
+power in the mid 1960s a mid-level
+ 
+
+ align:start position:0%
+power in the mid 1960s a mid-level
+government bureaucrat made this number
+
+ align:start position:0%
+government bureaucrat made this number
+ 
+
+ align:start position:0%
+government bureaucrat made this number
+up she said well look her name was Molly
+
+ align:start position:0%
+up she said well look her name was Molly
+ 
+
+ align:start position:0%
+up she said well look her name was Molly
+oransky she said look poor people spent
+
+ align:start position:0%
+oransky she said look poor people spent
+ 
+
+ align:start position:0%
+oransky she said look poor people spent
+about a third of their budget on food
+
+ align:start position:0%
+about a third of their budget on food
+ 
+
+ align:start position:0%
+about a third of their budget on food
+let me just price out what a n
+
+ align:start position:0%
+let me just price out what a n
+ 
+
+ align:start position:0%
+let me just price out what a n
+nutritionally adequate diet costs
+
+ align:start position:0%
+nutritionally adequate diet costs
+ 
+
+ align:start position:0%
+nutritionally adequate diet costs
+multiply by three and we'll call that
+
+ align:start position:0%
+multiply by three and we'll call that
+ 
+
+ align:start position:0%
+multiply by three and we'll call that
+the poverty line that exercise updated
+
+ align:start position:0%
+the poverty line that exercise updated
+ 
+
+ align:start position:0%
+the poverty line that exercise updated
+by inflation is literally the way today
+
+ align:start position:0%
+by inflation is literally the way today
+ 
+
+ align:start position:0%
+by inflation is literally the way today
+we transfer trillions of dollars in the
+
+ align:start position:0%
+we transfer trillions of dollars in the
+ 
+
+ align:start position:0%
+we transfer trillions of dollars in the
+United
+
+ align:start position:0%
+United
+ 
+
+ align:start position:0%
+United
+States okay so that has remained our
+
+ align:start position:0%
+States okay so that has remained our
+ 
+
+ align:start position:0%
+States okay so that has remained our
+standard for what is
+
+ align:start position:0%
+standard for what is
+ 
+
+ align:start position:0%
+standard for what is
+poor the poverty line itself is shown in
+
+ align:start position:0%
+poor the poverty line itself is shown in
+ 
+
+ align:start position:0%
+poor the poverty line itself is shown in
+figure
+
+ align:start position:0%
+figure
+ 
+
+ align:start position:0%
+figure
+23-5 so the poverty line for a family of
+
+ align:start position:0%
+23-5 so the poverty line for a family of
+ 
+
+ align:start position:0%
+23-5 so the poverty line for a family of
+one is considered to be about
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+$133,000 it then doesn't double per
+
+ align:start position:0%
+$133,000 it then doesn't double per
+ 
+
+ align:start position:0%
+$133,000 it then doesn't double per
+person because we view that living
+
+ align:start position:0%
+person because we view that living
+ 
+
+ align:start position:0%
+person because we view that living
+together has economies of scale we don't
+
+ align:start position:0%
+together has economies of scale we don't
+ 
+
+ align:start position:0%
+together has economies of scale we don't
+think you need twice as much money for
+
+ align:start position:0%
+think you need twice as much money for
+ 
+
+ align:start position:0%
+think you need twice as much money for
+two people to live together
+
+ align:start position:0%
+two people to live together
+ 
+
+ align:start position:0%
+two people to live together
+as you do for one person to live
+
+ align:start position:0%
+as you do for one person to live
+ 
+
+ align:start position:0%
+as you do for one person to live
+together because for instance a
+
+ align:start position:0%
+together because for instance a
+ 
+
+ align:start position:0%
+together because for instance a
+two-bedroom apartment is typically not
+
+ align:start position:0%
+two-bedroom apartment is typically not
+ 
+
+ align:start position:0%
+two-bedroom apartment is typically not
+twice a one-bedroom apartment certainly
+
+ align:start position:0%
+twice a one-bedroom apartment certainly
+ 
+
+ align:start position:0%
+twice a one-bedroom apartment certainly
+a so basically there's economies of
+
+ align:start position:0%
+a so basically there's economies of
+ 
+
+ align:start position:0%
+a so basically there's economies of
+scale so it doesn't double but it goes
+
+ align:start position:0%
+scale so it doesn't double but it goes
+ 
+
+ align:start position:0%
+scale so it doesn't double but it goes
+up thereafter So a family of four we
+
+ align:start position:0%
+up thereafter So a family of four we
+ 
+
+ align:start position:0%
+up thereafter So a family of four we
+think as a poverty line of about twice
+
+ align:start position:0%
+think as a poverty line of about twice
+ 
+
+ align:start position:0%
+think as a poverty line of about twice
+the poverty line for an
+
+ align:start position:0%
+the poverty line for an
+ 
+
+ align:start position:0%
+the poverty line for an
+individual now is that a fair number is
+
+ align:start position:0%
+individual now is that a fair number is
+ 
+
+ align:start position:0%
+individual now is that a fair number is
+that correct well that's a debate for
+
+ align:start position:0%
+that correct well that's a debate for
+ 
+
+ align:start position:0%
+that correct well that's a debate for
+another day we can come to 1441 we spent
+
+ align:start position:0%
+another day we can come to 1441 we spent
+ 
+
+ align:start position:0%
+another day we can come to 1441 we spent
+a lot of time talking about it it's a
+
+ align:start position:0%
+a lot of time talking about it it's a
+ 
+
+ align:start position:0%
+a lot of time talking about it it's a
+very controversial number for many
+
+ align:start position:0%
+very controversial number for many
+ 
+
+ align:start position:0%
+very controversial number for many
+reasons let's take that as given for now
+
+ align:start position:0%
+reasons let's take that as given for now
+ 
+
+ align:start position:0%
+reasons let's take that as given for now
+what does it implies happen over time
+
+ align:start position:0%
+what does it implies happen over time
+ 
+
+ align:start position:0%
+what does it implies happen over time
+well look at figure
+
+ align:start position:0%
+well look at figure
+ 
+
+ align:start position:0%
+well look at figure
+23-6 which shows poverty rates over time
+
+ align:start position:0%
+23-6 which shows poverty rates over time
+ 
+
+ align:start position:0%
+23-6 which shows poverty rates over time
+what you see if you look at the blue
+
+ align:start position:0%
+what you see if you look at the blue
+ 
+
+ align:start position:0%
+what you see if you look at the blue
+line that's all people you see for all
+
+ align:start position:0%
+line that's all people you see for all
+ 
+
+ align:start position:0%
+line that's all people you see for all
+people poverty rates fell dramatically
+
+ align:start position:0%
+people poverty rates fell dramatically
+ 
+
+ align:start position:0%
+people poverty rates fell dramatically
+until about
+
+ align:start position:0%
+until about
+ 
+
+ align:start position:0%
+until about
+1979 and then have been pretty flat
+
+ align:start position:0%
+1979 and then have been pretty flat
+ 
+
+ align:start position:0%
+1979 and then have been pretty flat
+since that's been that's a combination
+
+ align:start position:0%
+since that's been that's a combination
+ 
+
+ align:start position:0%
+since that's been that's a combination
+of a dramatic fall in poverty for those
+
+ align:start position:0%
+of a dramatic fall in poverty for those
+ 
+
+ align:start position:0%
+of a dramatic fall in poverty for those
+I'm sorry that's not the Blue Line uh
+
+ align:start position:0%
+I'm sorry that's not the Blue Line uh
+ 
+
+ align:start position:0%
+I'm sorry that's not the Blue Line uh
+yeah let's see no the I'm sorry the blue
+
+ align:start position:0%
+yeah let's see no the I'm sorry the blue
+ 
+
+ align:start position:0%
+yeah let's see no the I'm sorry the blue
+line is I'm sorry the red line is all
+
+ align:start position:0%
+line is I'm sorry the red line is all
+ 
+
+ align:start position:0%
+line is I'm sorry the red line is all
+people my bad it fell for dramatically
+
+ align:start position:0%
+people my bad it fell for dramatically
+ 
+
+ align:start position:0%
+people my bad it fell for dramatically
+until about 1970 and then it's been flat
+
+ align:start position:0%
+until about 1970 and then it's been flat
+ 
+
+ align:start position:0%
+until about 1970 and then it's been flat
+since that's a combination of a dramatic
+
+ align:start position:0%
+since that's a combination of a dramatic
+ 
+
+ align:start position:0%
+since that's a combination of a dramatic
+Fallen poverty for the elderly which is
+
+ align:start position:0%
+Fallen poverty for the elderly which is
+ 
+
+ align:start position:0%
+Fallen poverty for the elderly which is
+the blue line and actually poverty kind
+
+ align:start position:0%
+the blue line and actually poverty kind
+ 
+
+ align:start position:0%
+the blue line and actually poverty kind
+of has been risen a bit for the for the
+
+ align:start position:0%
+of has been risen a bit for the for the
+ 
+
+ align:start position:0%
+of has been risen a bit for the for the
+for youth that's under 18 but the bottom
+
+ align:start position:0%
+for youth that's under 18 but the bottom
+ 
+
+ align:start position:0%
+for youth that's under 18 but the bottom
+line is you look at this line for about
+
+ align:start position:0%
+line is you look at this line for about
+ 
+
+ align:start position:0%
+line is you look at this line for about
+1980 onward and it all looks pretty flat
+
+ align:start position:0%
+1980 onward and it all looks pretty flat
+ 
+
+ align:start position:0%
+1980 onward and it all looks pretty flat
+right contrast that
+
+ align:start position:0%
+right contrast that
+ 
+
+ align:start position:0%
+right contrast that
+to I'll go all the way back to table
+
+ align:start position:0%
+to I'll go all the way back to table
+ 
+
+ align:start position:0%
+to I'll go all the way back to table
+232 table 2 32 seem to show that
+
+ align:start position:0%
+232 table 2 32 seem to show that
+ 
+
+ align:start position:0%
+232 table 2 32 seem to show that
+inequality's gotten a ton worse since
+
+ align:start position:0%
+inequality's gotten a ton worse since
+ 
+
+ align:start position:0%
+inequality's gotten a ton worse since
+1980 so how you feel about what's
+
+ align:start position:0%
+1980 so how you feel about what's
+ 
+
+ align:start position:0%
+1980 so how you feel about what's
+happened to American society depends
+
+ align:start position:0%
+happened to American society depends
+ 
+
+ align:start position:0%
+happened to American society depends
+very much on how you feel about fig
+
+ align:start position:0%
+very much on how you feel about fig
+ 
+
+ align:start position:0%
+very much on how you feel about fig
+table 232 figure 232 versus figure
+
+ align:start position:0%
+table 232 figure 232 versus figure
+ 
+
+ align:start position:0%
+table 232 figure 232 versus figure
+236 do we care about what's happened
+
+ align:start position:0%
+236 do we care about what's happened
+ 
+
+ align:start position:0%
+236 do we care about what's happened
+relatively which is the rich Rel to the
+
+ align:start position:0%
+relatively which is the rich Rel to the
+ 
+
+ align:start position:0%
+relatively which is the rich Rel to the
+poor which approach one and two would
+
+ align:start position:0%
+poor which approach one and two would
+ 
+
+ align:start position:0%
+poor which approach one and two would
+say we should care
+
+ align:start position:0%
+say we should care
+ 
+
+ align:start position:0%
+say we should care
+about or do we care which happen
+
+ align:start position:0%
+about or do we care which happen
+ 
+
+ align:start position:0%
+about or do we care which happen
+absolutely which is what the poor have
+
+ align:start position:0%
+absolutely which is what the poor have
+ 
+
+ align:start position:0%
+absolutely which is what the poor have
+which is what approach for we should
+
+ align:start position:0%
+which is what approach for we should
+ 
+
+ align:start position:0%
+which is what approach for we should
+worry
+
+ align:start position:0%
+worry
+ 
+
+ align:start position:0%
+worry
+about and there's no right answer but
+
+ align:start position:0%
+about and there's no right answer but
+ 
+
+ align:start position:0%
+about and there's no right answer but
+how you think about it determines how
+
+ align:start position:0%
+how you think about it determines how
+ 
+
+ align:start position:0%
+how you think about it determines how
+you're going to um end up uh end up
+
+ align:start position:0%
+you're going to um end up uh end up
+ 
+
+ align:start position:0%
+you're going to um end up uh end up
+thinking about the
+
+ align:start position:0%
+thinking about the
+ 
+
+ align:start position:0%
+thinking about the
+problem to my mind I think you want some
+
+ align:start position:0%
+problem to my mind I think you want some
+ 
+
+ align:start position:0%
+problem to my mind I think you want some
+of both but to my mind the simplest and
+
+ align:start position:0%
+of both but to my mind the simplest and
+ 
+
+ align:start position:0%
+of both but to my mind the simplest and
+most striking way to think about this is
+
+ align:start position:0%
+most striking way to think about this is
+ 
+
+ align:start position:0%
+most striking way to think about this is
+the following example which is just
+
+ align:start position:0%
+the following example which is just
+ 
+
+ align:start position:0%
+the following example which is just
+stunning many of you may remember about
+
+ align:start position:0%
+stunning many of you may remember about
+ 
+
+ align:start position:0%
+stunning many of you may remember about
+10 years ago there were the maybe less
+
+ align:start position:0%
+10 years ago there were the maybe less
+ 
+
+ align:start position:0%
+10 years ago there were the maybe less
+there was the Freddy gray riots Freddy
+
+ align:start position:0%
+there was the Freddy gray riots Freddy
+ 
+
+ align:start position:0%
+there was the Freddy gray riots Freddy
+gray was a prisoner arrested in a poor
+
+ align:start position:0%
+gray was a prisoner arrested in a poor
+ 
+
+ align:start position:0%
+gray was a prisoner arrested in a poor
+neighborhood of Baltimore he was killed
+
+ align:start position:0%
+neighborhood of Baltimore he was killed
+ 
+
+ align:start position:0%
+neighborhood of Baltimore he was killed
+in the police car on the way to the
+
+ align:start position:0%
+in the police car on the way to the
+ 
+
+ align:start position:0%
+in the police car on the way to the
+police station it led to uh as part of
+
+ align:start position:0%
+police station it led to uh as part of
+ 
+
+ align:start position:0%
+police station it led to uh as part of
+the black you know one of the founding
+
+ align:start position:0%
+the black you know one of the founding
+ 
+
+ align:start position:0%
+the black you know one of the founding
+events of black lives matter movement
+
+ align:start position:0%
+events of black lives matter movement
+ 
+
+ align:start position:0%
+events of black lives matter movement
+led to a lot of riots and things like
+
+ align:start position:0%
+led to a lot of riots and things like
+ 
+
+ align:start position:0%
+led to a lot of riots and things like
+that in
+
+ align:start position:0%
+that in
+ 
+
+ align:start position:0%
+that in
+Baltimore those riots highlighted how
+
+ align:start position:0%
+Baltimore those riots highlighted how
+ 
+
+ align:start position:0%
+Baltimore those riots highlighted how
+much inequality there is in
+
+ align:start position:0%
+much inequality there is in
+ 
+
+ align:start position:0%
+much inequality there is in
+Baltimore go to figure one of my I think
+
+ align:start position:0%
+Baltimore go to figure one of my I think
+ 
+
+ align:start position:0%
+Baltimore go to figure one of my I think
+one of the most stunning figures I've
+
+ align:start position:0%
+one of the most stunning figures I've
+ 
+
+ align:start position:0%
+one of the most stunning figures I've
+ever seen figure 237
+
+ align:start position:0%
+ever seen figure 237
+ 
+
+ align:start position:0%
+ever seen figure 237
+this figure this is just a graph of
+
+ align:start position:0%
+this figure this is just a graph of
+ 
+
+ align:start position:0%
+this figure this is just a graph of
+Baltimore this shows neighborhoods in
+
+ align:start position:0%
+Baltimore this shows neighborhoods in
+ 
+
+ align:start position:0%
+Baltimore this shows neighborhoods in
+Baltimore and the life expectancy in
+
+ align:start position:0%
+Baltimore and the life expectancy in
+ 
+
+ align:start position:0%
+Baltimore and the life expectancy in
+each neighborhood how long you expect to
+
+ align:start position:0%
+each neighborhood how long you expect to
+ 
+
+ align:start position:0%
+each neighborhood how long you expect to
+live and I'm going to highlight two
+
+ align:start position:0%
+live and I'm going to highlight two
+ 
+
+ align:start position:0%
+live and I'm going to highlight two
+neighborhoods Sandtown
+
+ align:start position:0%
+neighborhoods Sandtown
+ 
+
+ align:start position:0%
+neighborhoods Sandtown
+Winchester which is where Freddy gray
+
+ align:start position:0%
+Winchester which is where Freddy gray
+ 
+
+ align:start position:0%
+Winchester which is where Freddy gray
+was from and Roland Park which is three
+
+ align:start position:0%
+was from and Roland Park which is three
+ 
+
+ align:start position:0%
+was from and Roland Park which is three
+miles
+
+ align:start position:0%
+miles
+ 
+
+ align:start position:0%
+miles
+away where Freddy gray was from the
+
+ align:start position:0%
+away where Freddy gray was from the
+ 
+
+ align:start position:0%
+away where Freddy gray was from the
+average life expectancy unless Roland
+
+ align:start position:0%
+average life expectancy unless Roland
+ 
+
+ align:start position:0%
+average life expectancy unless Roland
+Park Roland Park is a wealthy
+
+ align:start position:0%
+Park Roland Park is a wealthy
+ 
+
+ align:start position:0%
+Park Roland Park is a wealthy
+neighborhood typical sort of wealthy
+
+ align:start position:0%
+neighborhood typical sort of wealthy
+ 
+
+ align:start position:0%
+neighborhood typical sort of wealthy
+suburb the average life there is 84
+
+ align:start position:0%
+suburb the average life there is 84
+ 
+
+ align:start position:0%
+suburb the average life there is 84
+that's above the US average three miles
+
+ align:start position:0%
+that's above the US average three miles
+ 
+
+ align:start position:0%
+that's above the US average three miles
+away where Freddy gray is from the
+
+ align:start position:0%
+away where Freddy gray is from the
+ 
+
+ align:start position:0%
+away where Freddy gray is from the
+average Lifey was
+
+ align:start position:0%
+average Lifey was
+ 
+
+ align:start position:0%
+average Lifey was
+67 that is below the life expectancy of
+
+ align:start position:0%
+67 that is below the life expectancy of
+ 
+
+ align:start position:0%
+67 that is below the life expectancy of
+North
+
+ align:start position:0%
+North
+ 
+
+ align:start position:0%
+North
+Korea three miles and a 17year
+
+ align:start position:0%
+Korea three miles and a 17year
+ 
+
+ align:start position:0%
+Korea three miles and a 17year
+difference and how long you can expect
+
+ align:start position:0%
+difference and how long you can expect
+ 
+
+ align:start position:0%
+difference and how long you can expect
+to
+
+ align:start position:0%
+to
+ 
+
+ align:start position:0%
+to
+live I don't see how anyone can look at
+
+ align:start position:0%
+live I don't see how anyone can look at
+ 
+
+ align:start position:0%
+live I don't see how anyone can look at
+that and not care about inequality
+
+ align:start position:0%
+that and not care about inequality
+ 
+
+ align:start position:0%
+that and not care about inequality
+how can you not care about a world where
+
+ align:start position:0%
+how can you not care about a world where
+ 
+
+ align:start position:0%
+how can you not care about a world where
+people living three miles apart have a
+
+ align:start position:0%
+people living three miles apart have a
+ 
+
+ align:start position:0%
+people living three miles apart have a
+17-year difference and how long they
+
+ align:start position:0%
+17-year difference and how long they
+ 
+
+ align:start position:0%
+17-year difference and how long they
+expect to live what's going on three
+
+ align:start position:0%
+expect to live what's going on three
+ 
+
+ align:start position:0%
+expect to live what's going on three
+miles away the average income in Sant
+
+ align:start position:0%
+miles away the average income in Sant
+ 
+
+ align:start position:0%
+miles away the average income in Sant
+toown is four times the average in the
+
+ align:start position:0%
+toown is four times the average in the
+ 
+
+ align:start position:0%
+toown is four times the average in the
+average in sorry Roland Park is four
+
+ align:start position:0%
+average in sorry Roland Park is four
+ 
+
+ align:start position:0%
+average in sorry Roland Park is four
+times the average income in Sandown in
+
+ align:start position:0%
+times the average income in Sandown in
+ 
+
+ align:start position:0%
+times the average income in Sandown in
+Roland Park 2.5% of kids live in poverty
+
+ align:start position:0%
+Roland Park 2.5% of kids live in poverty
+ 
+
+ align:start position:0%
+Roland Park 2.5% of kids live in poverty
+in Sant toown 55% of kids live in
+
+ align:start position:0%
+in Sant toown 55% of kids live in
+ 
+
+ align:start position:0%
+in Sant toown 55% of kids live in
+poverty okay three
+
+ align:start position:0%
+poverty okay three
+ 
+
+ align:start position:0%
+poverty okay three
+miles and and the odds a kid lives in
+
+ align:start position:0%
+miles and and the odds a kid lives in
+ 
+
+ align:start position:0%
+miles and and the odds a kid lives in
+party is 20 times
+
+ align:start position:0%
+party is 20 times
+ 
+
+ align:start position:0%
+party is 20 times
+different these are the reasons why many
+
+ align:start position:0%
+different these are the reasons why many
+ 
+
+ align:start position:0%
+different these are the reasons why many
+of us feel very strong that we need to
+
+ align:start position:0%
+of us feel very strong that we need to
+ 
+
+ align:start position:0%
+of us feel very strong that we need to
+address inequality as well as simply
+
+ align:start position:0%
+address inequality as well as simply
+ 
+
+ align:start position:0%
+address inequality as well as simply
+absolute
+
+ align:start position:0%
+absolute
+ 
+
+ align:start position:0%
+absolute
+deprivation okay questions about
+
+ align:start position:0%
+deprivation okay questions about
+ 
+
+ align:start position:0%
+deprivation okay questions about
+that now with that in mind let's talk
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+about what do we do about it so let's
+
+ align:start position:0%
+about what do we do about it so let's
+ 
+
+ align:start position:0%
+about what do we do about it so let's
+say I've got you at least
+
+ align:start position:0%
+say I've got you at least
+ 
+
+ align:start position:0%
+say I've got you at least
+motivated let's say you came in this not
+
+ align:start position:0%
+motivated let's say you came in this not
+ 
+
+ align:start position:0%
+motivated let's say you came in this not
+really thinking about rich versus poor I
+
+ align:start position:0%
+really thinking about rich versus poor I
+ 
+
+ align:start position:0%
+really thinking about rich versus poor I
+hope at least motivated you think it's
+
+ align:start position:0%
+hope at least motivated you think it's
+ 
+
+ align:start position:0%
+hope at least motivated you think it's
+interesting problem and think about
+
+ align:start position:0%
+interesting problem and think about
+ 
+
+ align:start position:0%
+interesting problem and think about
+maybe it's something we might want to do
+
+ align:start position:0%
+maybe it's something we might want to do
+ 
+
+ align:start position:0%
+maybe it's something we might want to do
+something
+
+ align:start position:0%
+something
+ 
+
+ align:start position:0%
+something
+about well to do so we run
+
+ align:start position:0%
+about well to do so we run
+ 
+
+ align:start position:0%
+about well to do so we run
+into an important problem because
+
+ align:start position:0%
+into an important problem because
+ 
+
+ align:start position:0%
+into an important problem because
+remember with the Dismal science right
+
+ align:start position:0%
+remember with the Dismal science right
+ 
+
+ align:start position:0%
+remember with the Dismal science right
+nothing's
+
+ align:start position:0%
+nothing's
+ 
+
+ align:start position:0%
+nothing's
+easy okay the problem is the efficiency
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+costs of redistribution remember I said
+
+ align:start position:0%
+costs of redistribution remember I said
+ 
+
+ align:start position:0%
+costs of redistribution remember I said
+life isn't typically like our example of
+
+ align:start position:0%
+life isn't typically like our example of
+ 
+
+ align:start position:0%
+life isn't typically like our example of
+perfect competition versus perfectly
+
+ align:start position:0%
+perfect competition versus perfectly
+ 
+
+ align:start position:0%
+perfect competition versus perfectly
+pric monopolist typically in life if we
+
+ align:start position:0%
+pric monopolist typically in life if we
+ 
+
+ align:start position:0%
+pric monopolist typically in life if we
+want to take money from one group we
+
+ align:start position:0%
+want to take money from one group we
+ 
+
+ align:start position:0%
+want to take money from one group we
+give it to another there's a leak in the
+
+ align:start position:0%
+give it to another there's a leak in the
+ 
+
+ align:start position:0%
+give it to another there's a leak in the
+bucket what is that leak in the
+
+ align:start position:0%
+bucket what is that leak in the
+ 
+
+ align:start position:0%
+bucket what is that leak in the
+bucket okay well there's fundamentally
+
+ align:start position:0%
+bucket okay well there's fundamentally
+ 
+
+ align:start position:0%
+bucket okay well there's fundamentally
+two leaks so let's say the way we do
+
+ align:start position:0%
+two leaks so let's say the way we do
+ 
+
+ align:start position:0%
+two leaks so let's say the way we do
+redistribution in reality is we tax the
+
+ align:start position:0%
+redistribution in reality is we tax the
+ 
+
+ align:start position:0%
+redistribution in reality is we tax the
+rich and give money to the
+
+ align:start position:0%
+rich and give money to the
+ 
+
+ align:start position:0%
+rich and give money to the
+poor okay well that leads to S two
+
+ align:start position:0%
+poor okay well that leads to S two
+ 
+
+ align:start position:0%
+poor okay well that leads to S two
+sources of
+
+ align:start position:0%
+sources of
+ 
+
+ align:start position:0%
+sources of
+leakage the first source of leakage is
+
+ align:start position:0%
+leakage the first source of leakage is
+ 
+
+ align:start position:0%
+leakage the first source of leakage is
+when you is the dead weight
+
+ align:start position:0%
+when you is the dead weight
+ 
+
+ align:start position:0%
+when you is the dead weight
+loss of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Taxation when you tax an
+
+ align:start position:0%
+Taxation when you tax an
+ 
+
+ align:start position:0%
+Taxation when you tax an
+activity you create less of it and that
+
+ align:start position:0%
+activity you create less of it and that
+ 
+
+ align:start position:0%
+activity you create less of it and that
+has a dead weight loss because there's
+
+ align:start position:0%
+has a dead weight loss because there's
+ 
+
+ align:start position:0%
+has a dead weight loss because there's
+social optimal trades that no longer get
+
+ align:start position:0%
+social optimal trades that no longer get
+ 
+
+ align:start position:0%
+social optimal trades that no longer get
+made that's the first source of
+
+ align:start position:0%
+made that's the first source of
+ 
+
+ align:start position:0%
+made that's the first source of
+leakage the second source of leeches
+
+ align:start position:0%
+leakage the second source of leeches
+ 
+
+ align:start position:0%
+leakage the second source of leeches
+leakage is the is the dead weight loss
+
+ align:start position:0%
+leakage is the is the dead weight loss
+ 
+
+ align:start position:0%
+leakage is the is the dead weight loss
+of transfers which is a little more
+
+ align:start position:0%
+of transfers which is a little more
+ 
+
+ align:start position:0%
+of transfers which is a little more
+subtle but actually works the same way
+
+ align:start position:0%
+subtle but actually works the same way
+ 
+
+ align:start position:0%
+subtle but actually works the same way
+when you
+
+ align:start position:0%
+when you
+ 
+
+ align:start position:0%
+when you
+subsidize a lack of economic activity
+
+ align:start position:0%
+subsidize a lack of economic activity
+ 
+
+ align:start position:0%
+subsidize a lack of economic activity
+you create more of it that's the moral
+
+ align:start position:0%
+you create more of it that's the moral
+ 
+
+ align:start position:0%
+you create more of it that's the moral
+hazard problem we talked about last
+
+ align:start position:0%
+hazard problem we talked about last
+ 
+
+ align:start position:0%
+hazard problem we talked about last
+time so you tax something activity you
+
+ align:start position:0%
+time so you tax something activity you
+ 
+
+ align:start position:0%
+time so you tax something activity you
+create less of it when you subze a lack
+
+ align:start position:0%
+create less of it when you subze a lack
+ 
+
+ align:start position:0%
+create less of it when you subze a lack
+of activity you create more of it
+
+ align:start position:0%
+of activity you create more of it
+ 
+
+ align:start position:0%
+of activity you create more of it
+transferring from Rich to poor involves
+
+ align:start position:0%
+transferring from Rich to poor involves
+ 
+
+ align:start position:0%
+transferring from Rich to poor involves
+both ends of that so it's double weight
+
+ align:start position:0%
+both ends of that so it's double weight
+ 
+
+ align:start position:0%
+both ends of that so it's double weight
+loss you
+
+ align:start position:0%
+loss you
+ 
+
+ align:start position:0%
+loss you
+create okay so to see that we're going
+
+ align:start position:0%
+create okay so to see that we're going
+ 
+
+ align:start position:0%
+create okay so to see that we're going
+to go through a fairly large example
+
+ align:start position:0%
+to go through a fairly large example
+ 
+
+ align:start position:0%
+to go through a fairly large example
+here we're going to end the lecture with
+
+ align:start position:0%
+here we're going to end the lecture with
+ 
+
+ align:start position:0%
+here we're going to end the lecture with
+sort of a strong example which
+
+ align:start position:0%
+sort of a strong example which
+ 
+
+ align:start position:0%
+sort of a strong example which
+illustrates this point okay in this
+
+ align:start position:0%
+illustrates this point okay in this
+ 
+
+ align:start position:0%
+illustrates this point okay in this
+example we're g to say everyone earns
+
+ align:start position:0%
+example we're g to say everyone earns
+ 
+
+ align:start position:0%
+example we're g to say everyone earns
+$20 an hour so our example the wage for
+
+ align:start position:0%
+$20 an hour so our example the wage for
+ 
+
+ align:start position:0%
+$20 an hour so our example the wage for
+everyone's Society is be $20 an hour so
+
+ align:start position:0%
+everyone's Society is be $20 an hour so
+ 
+
+ align:start position:0%
+everyone's Society is be $20 an hour so
+everyone has the same
+
+ align:start position:0%
+everyone has the same
+ 
+
+ align:start position:0%
+everyone has the same
+underlying marginal product of labor
+
+ align:start position:0%
+underlying marginal product of labor
+ 
+
+ align:start position:0%
+underlying marginal product of labor
+every side he ears $20 an hour marginal
+
+ align:start position:0%
+every side he ears $20 an hour marginal
+ 
+
+ align:start position:0%
+every side he ears $20 an hour marginal
+revenue product of labor
+
+ align:start position:0%
+revenue product of labor
+ 
+
+ align:start position:0%
+revenue product of labor
+but different people earn different
+
+ align:start position:0%
+but different people earn different
+ 
+
+ align:start position:0%
+but different people earn different
+amounts of income and society's
+
+ align:start position:0%
+amounts of income and society's
+ 
+
+ align:start position:0%
+amounts of income and society's
+utilitarian the government utilitarian
+
+ align:start position:0%
+utilitarian the government utilitarian
+ 
+
+ align:start position:0%
+utilitarian the government utilitarian
+so it cares about that different
+
+ align:start position:0%
+so it cares about that different
+ 
+
+ align:start position:0%
+so it cares about that different
+different amounts of income so let's say
+
+ align:start position:0%
+different amounts of income so let's say
+ 
+
+ align:start position:0%
+different amounts of income so let's say
+that the government wants to make sure
+
+ align:start position:0%
+that the government wants to make sure
+ 
+
+ align:start position:0%
+that the government wants to make sure
+that there's a minimum guarantee the
+
+ align:start position:0%
+that there's a minimum guarantee the
+ 
+
+ align:start position:0%
+that there's a minimum guarantee the
+government's a commodity
+
+ align:start position:0%
+government's a commodity
+ 
+
+ align:start position:0%
+government's a commodity
+galarian the government says you know
+
+ align:start position:0%
+galarian the government says you know
+ 
+
+ align:start position:0%
+galarian the government says you know
+what I want to make sure there's a
+
+ align:start position:0%
+what I want to make sure there's a
+ 
+
+ align:start position:0%
+what I want to make sure there's a
+minimum guarantee of
+
+ align:start position:0%
+minimum guarantee of
+ 
+
+ align:start position:0%
+minimum guarantee of
+$5,000 I want to make sure that everyone
+
+ align:start position:0%
+$5,000 I want to make sure that everyone
+ 
+
+ align:start position:0%
+$5,000 I want to make sure that everyone
+in society has at least
+
+ align:start position:0%
+in society has at least
+ 
+
+ align:start position:0%
+in society has at least
+$5,000 because I feel like you can't
+
+ align:start position:0%
+$5,000 because I feel like you can't
+ 
+
+ align:start position:0%
+$5,000 because I feel like you can't
+survive with less than
+
+ align:start position:0%
+survive with less than
+ 
+
+ align:start position:0%
+survive with less than
+$5,000 but I have to pay for that so the
+
+ align:start position:0%
+$5,000 but I have to pay for that so the
+ 
+
+ align:start position:0%
+$5,000 but I have to pay for that so the
+way I'm going to pay for that I'm have
+
+ align:start position:0%
+way I'm going to pay for that I'm have
+ 
+
+ align:start position:0%
+way I'm going to pay for that I'm have
+I'm gonna have a
+
+ align:start position:0%
+I'm gonna have a
+ 
+
+ align:start position:0%
+I'm gonna have a
+tax and the tax is going to
+
+ align:start position:0%
+tax and the tax is going to
+ 
+
+ align:start position:0%
+tax and the tax is going to
+be that anyone with
+
+ align:start position:0%
+be that anyone with
+ 
+
+ align:start position:0%
+be that anyone with
+income
+
+ align:start position:0%
+income
+ 
+
+ align:start position:0%
+income
+um oh I'm sorry let me go back so let me
+
+ align:start position:0%
+um oh I'm sorry let me go back so let me
+ 
+
+ align:start position:0%
+um oh I'm sorry let me go back so let me
+go back let me finish this first there's
+
+ align:start position:0%
+go back let me finish this first there's
+ 
+
+ align:start position:0%
+go back let me finish this first there's
+a guarantee of $5,000 but here's the
+
+ align:start position:0%
+a guarantee of $5,000 but here's the
+ 
+
+ align:start position:0%
+a guarantee of $5,000 but here's the
+thing I'm not going to give everyone
+
+ align:start position:0%
+thing I'm not going to give everyone
+ 
+
+ align:start position:0%
+thing I'm not going to give everyone
+$5,000 I want make sure everybody has
+
+ align:start position:0%
+$5,000 I want make sure everybody has
+ 
+
+ align:start position:0%
+$5,000 I want make sure everybody has
+$5,000 but if you have some money
+
+ align:start position:0%
+$5,000 but if you have some money
+ 
+
+ align:start position:0%
+$5,000 but if you have some money
+already I don't want I don't want to
+
+ align:start position:0%
+already I don't want I don't want to
+ 
+
+ align:start position:0%
+already I don't want I don't want to
+guarantee you have $7,000 I'm make sure
+
+ align:start position:0%
+guarantee you have $7,000 I'm make sure
+ 
+
+ align:start position:0%
+guarantee you have $7,000 I'm make sure
+have $5,000 so what I'm going to do is
+
+ align:start position:0%
+have $5,000 so what I'm going to do is
+ 
+
+ align:start position:0%
+have $5,000 so what I'm going to do is
+I'm set up a transfer program that's
+
+ align:start position:0%
+I'm set up a transfer program that's
+ 
+
+ align:start position:0%
+I'm set up a transfer program that's
+what we call a negative income tax the
+
+ align:start position:0%
+what we call a negative income tax the
+ 
+
+ align:start position:0%
+what we call a negative income tax the
+way it works is if you have zero I give
+
+ align:start position:0%
+way it works is if you have zero I give
+ 
+
+ align:start position:0%
+way it works is if you have zero I give
+you 5,000 you have 100 I give you
+
+ align:start position:0%
+you 5,000 you have 100 I give you
+ 
+
+ align:start position:0%
+you 5,000 you have 100 I give you
+4,900 if you a th000 I give you 4,000
+
+ align:start position:0%
+4,900 if you a th000 I give you 4,000
+ 
+
+ align:start position:0%
+4,900 if you a th000 I give you 4,000
+that is I top up your income to get you
+
+ align:start position:0%
+that is I top up your income to get you
+ 
+
+ align:start position:0%
+that is I top up your income to get you
+to 5,000 in particular I give you a
+
+ align:start position:0%
+to 5,000 in particular I give you a
+ 
+
+ align:start position:0%
+to 5,000 in particular I give you a
+transfer I give you a transfer which is
+
+ align:start position:0%
+transfer I give you a transfer which is
+ 
+
+ align:start position:0%
+transfer I give you a transfer which is
+equal to
+
+ align:start position:0%
+equal to
+ 
+
+ align:start position:0%
+equal to
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+max of 0 comma
+
+ align:start position:0%
+max of 0 comma
+ 
+
+ align:start position:0%
+max of 0 comma
+5000 minus y That's the transfer I give
+
+ align:start position:0%
+5000 minus y That's the transfer I give
+ 
+
+ align:start position:0%
+5000 minus y That's the transfer I give
+you I give you if your income's above
+
+ align:start position:0%
+you I give you if your income's above
+ 
+
+ align:start position:0%
+you I give you if your income's above
+5,000 I give you nothing if your
+
+ align:start position:0%
+5,000 I give you nothing if your
+ 
+
+ align:start position:0%
+5,000 I give you nothing if your
+income's below 5,000 give you enough to
+
+ align:start position:0%
+income's below 5,000 give you enough to
+ 
+
+ align:start position:0%
+income's below 5,000 give you enough to
+get up to 5,000 that's how I Implement
+
+ align:start position:0%
+get up to 5,000 that's how I Implement
+ 
+
+ align:start position:0%
+get up to 5,000 that's how I Implement
+my commodi egalitarianism solution I get
+
+ align:start position:0%
+my commodi egalitarianism solution I get
+ 
+
+ align:start position:0%
+my commodi egalitarianism solution I get
+everyone up to 5,000 people clear on
+
+ align:start position:0%
+everyone up to 5,000 people clear on
+ 
+
+ align:start position:0%
+everyone up to 5,000 people clear on
+that I get them up to
+
+ align:start position:0%
+that I get them up to
+ 
+
+ align:start position:0%
+that I get them up to
+5,000 okay and to assment of a
+
+ align:start position:0%
+5,000 okay and to assment of a
+ 
+
+ align:start position:0%
+5,000 okay and to assment of a
+tax the tax is going to be only on the
+
+ align:start position:0%
+tax the tax is going to be only on the
+ 
+
+ align:start position:0%
+tax the tax is going to be only on the
+rich so what I'm going to do is I'm
+
+ align:start position:0%
+rich so what I'm going to do is I'm
+ 
+
+ align:start position:0%
+rich so what I'm going to do is I'm
+going to say anyone whose earnings is
+
+ align:start position:0%
+going to say anyone whose earnings is
+ 
+
+ align:start position:0%
+going to say anyone whose earnings is
+above
+
+ align:start position:0%
+above
+ 
+
+ align:start position:0%
+above
+$20,000 is going to be is going to pay a
+
+ align:start position:0%
+$20,000 is going to be is going to pay a
+ 
+
+ align:start position:0%
+$20,000 is going to be is going to pay a
+50% tax
+
+ align:start position:0%
+50% tax
+ 
+
+ align:start position:0%
+50% tax
+rate
+
+ align:start position:0%
+rate
+ 
+
+ align:start position:0%
+rate
+above 20K just on your earnings above
+
+ align:start position:0%
+above 20K just on your earnings above
+ 
+
+ align:start position:0%
+above 20K just on your earnings above
+20K so all earnings below 20K I don't
+
+ align:start position:0%
+20K so all earnings below 20K I don't
+ 
+
+ align:start position:0%
+20K so all earnings below 20K I don't
+touch but on any earnings above 20K I'm
+
+ align:start position:0%
+touch but on any earnings above 20K I'm
+ 
+
+ align:start position:0%
+touch but on any earnings above 20K I'm
+going to take back half of it to finance
+
+ align:start position:0%
+going to take back half of it to finance
+ 
+
+ align:start position:0%
+going to take back half of it to finance
+this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+program okay that's the way the program
+
+ align:start position:0%
+program okay that's the way the program
+ 
+
+ align:start position:0%
+program okay that's the way the program
+is going to
+
+ align:start position:0%
+is going to
+ 
+
+ align:start position:0%
+is going to
+work well let's see how that affects
+
+ align:start position:0%
+work well let's see how that affects
+ 
+
+ align:start position:0%
+work well let's see how that affects
+people's budget
+
+ align:start position:0%
+people's budget
+ 
+
+ align:start position:0%
+people's budget
+constraint let's go to figure
+
+ align:start position:0%
+constraint let's go to figure
+ 
+
+ align:start position:0%
+constraint let's go to figure
+23-8 this is a standard Leisure
+
+ align:start position:0%
+23-8 this is a standard Leisure
+ 
+
+ align:start position:0%
+23-8 this is a standard Leisure
+consumption
+
+ align:start position:0%
+consumption
+ 
+
+ align:start position:0%
+consumption
+tradeoff okay we people remember I said
+
+ align:start position:0%
+tradeoff okay we people remember I said
+ 
+
+ align:start position:0%
+tradeoff okay we people remember I said
+earn 20 bucks an hour so without the
+
+ align:start position:0%
+earn 20 bucks an hour so without the
+ 
+
+ align:start position:0%
+earn 20 bucks an hour so without the
+government the budget constraint is the
+
+ align:start position:0%
+government the budget constraint is the
+ 
+
+ align:start position:0%
+government the budget constraint is the
+black line they can work up to 2,000
+
+ align:start position:0%
+black line they can work up to 2,000
+ 
+
+ align:start position:0%
+black line they can work up to 2,000
+hours a
+
+ align:start position:0%
+hours a
+ 
+
+ align:start position:0%
+hours a
+year and have no no
+
+ align:start position:0%
+year and have no no
+ 
+
+ align:start position:0%
+year and have no no
+consumption I'm sorry they can take
+
+ align:start position:0%
+consumption I'm sorry they can take
+ 
+
+ align:start position:0%
+consumption I'm sorry they can take
+2,000 hours a year Leisure my bad
+
+ align:start position:0%
+2,000 hours a year Leisure my bad
+ 
+
+ align:start position:0%
+2,000 hours a year Leisure my bad
+leisures on the exsis they 2,000 hours
+
+ align:start position:0%
+leisures on the exsis they 2,000 hours
+ 
+
+ align:start position:0%
+leisures on the exsis they 2,000 hours
+year Leisure and have no consumption or
+
+ align:start position:0%
+year Leisure and have no consumption or
+ 
+
+ align:start position:0%
+year Leisure and have no consumption or
+take zero Leisure and have 40,000 in
+
+ align:start position:0%
+take zero Leisure and have 40,000 in
+ 
+
+ align:start position:0%
+take zero Leisure and have 40,000 in
+consumption and let's assume we're going
+
+ align:start position:0%
+consumption and let's assume we're going
+ 
+
+ align:start position:0%
+consumption and let's assume we're going
+to measure price of goods is all one so
+
+ align:start position:0%
+to measure price of goods is all one so
+ 
+
+ align:start position:0%
+to measure price of goods is all one so
+consumption is just like this
+
+ align:start position:0%
+consumption is just like this
+ 
+
+ align:start position:0%
+consumption is just like this
+consumption bundle like we talked about
+
+ align:start position:0%
+consumption bundle like we talked about
+ 
+
+ align:start position:0%
+consumption bundle like we talked about
+this numer good idea that basically we
+
+ align:start position:0%
+this numer good idea that basically we
+ 
+
+ align:start position:0%
+this numer good idea that basically we
+think of dollars and units of
+
+ align:start position:0%
+think of dollars and units of
+ 
+
+ align:start position:0%
+think of dollars and units of
+consumption
+
+ align:start position:0%
+consumption
+ 
+
+ align:start position:0%
+consumption
+interchangeably so basically consumption
+
+ align:start position:0%
+interchangeably so basically consumption
+ 
+
+ align:start position:0%
+interchangeably so basically consumption
+costs a dollar the price consumption is
+
+ align:start position:0%
+costs a dollar the price consumption is
+ 
+
+ align:start position:0%
+costs a dollar the price consumption is
+a dollar so basically the trade-off is
+
+ align:start position:0%
+a dollar so basically the trade-off is
+ 
+
+ align:start position:0%
+a dollar so basically the trade-off is
+simply for every hour I take of leisure
+
+ align:start position:0%
+simply for every hour I take of leisure
+ 
+
+ align:start position:0%
+simply for every hour I take of leisure
+I give up $20 of
+
+ align:start position:0%
+I give up $20 of
+ 
+
+ align:start position:0%
+I give up $20 of
+consumption and that leads that black
+
+ align:start position:0%
+consumption and that leads that black
+ 
+
+ align:start position:0%
+consumption and that leads that black
+line the program I just described
+
+ align:start position:0%
+line the program I just described
+ 
+
+ align:start position:0%
+line the program I just described
+changes that line as follows first of
+
+ align:start position:0%
+changes that line as follows first of
+ 
+
+ align:start position:0%
+changes that line as follows first of
+all on the leftand side if you
+
+ align:start position:0%
+all on the leftand side if you
+ 
+
+ align:start position:0%
+all on the leftand side if you
+take if you take uh first of all I'm
+
+ align:start position:0%
+take if you take uh first of all I'm
+ 
+
+ align:start position:0%
+take if you take uh first of all I'm
+sorry on the right hand side my bad on
+
+ align:start position:0%
+sorry on the right hand side my bad on
+ 
+
+ align:start position:0%
+sorry on the right hand side my bad on
+the right hand side if you take more
+
+ align:start position:0%
+the right hand side if you take more
+ 
+
+ align:start position:0%
+the right hand side if you take more
+than 17700 50 hours of
+
+ align:start position:0%
+than 17700 50 hours of
+ 
+
+ align:start position:0%
+than 17700 50 hours of
+leisure we're going to give you money
+
+ align:start position:0%
+leisure we're going to give you money
+ 
+
+ align:start position:0%
+leisure we're going to give you money
+why because if you take less than $750
+
+ align:start position:0%
+why because if you take less than $750
+ 
+
+ align:start position:0%
+why because if you take less than $750
+of leisure you're going to have more
+
+ align:start position:0%
+of leisure you're going to have more
+ 
+
+ align:start position:0%
+of leisure you're going to have more
+than $5,000 already look at the X look
+
+ align:start position:0%
+than $5,000 already look at the X look
+ 
+
+ align:start position:0%
+than $5,000 already look at the X look
+at the y- AIS 750 hours of leisure at
+
+ align:start position:0%
+at the y- AIS 750 hours of leisure at
+ 
+
+ align:start position:0%
+at the y- AIS 750 hours of leisure at
+a$2 wage means you're working 250 hours
+
+ align:start position:0%
+a$2 wage means you're working 250 hours
+ 
+
+ align:start position:0%
+a$2 wage means you're working 250 hours
+mean you got 5,000 in income so your
+
+ align:start position:0%
+mean you got 5,000 in income so your
+ 
+
+ align:start position:0%
+mean you got 5,000 in income so your
+income's below
+
+ align:start position:0%
+income's below
+ 
+
+ align:start position:0%
+income's below
+$5,000 that means you must be taking
+
+ align:start position:0%
+$5,000 that means you must be taking
+ 
+
+ align:start position:0%
+$5,000 that means you must be taking
+more than 1,750 hours of Leisure for
+
+ align:start position:0%
+more than 1,750 hours of Leisure for
+ 
+
+ align:start position:0%
+more than 1,750 hours of Leisure for
+those people who are simply going to say
+
+ align:start position:0%
+those people who are simply going to say
+ 
+
+ align:start position:0%
+those people who are simply going to say
+look we're going to make sure you have
+
+ align:start position:0%
+look we're going to make sure you have
+ 
+
+ align:start position:0%
+look we're going to make sure you have
+at least
+
+ align:start position:0%
+at least
+ 
+
+ align:start position:0%
+at least
+$5,000 what does it do the budget con
+
+ align:start position:0%
+$5,000 what does it do the budget con
+ 
+
+ align:start position:0%
+$5,000 what does it do the budget con
+Str that says it becomes flat from the
+
+ align:start position:0%
+Str that says it becomes flat from the
+ 
+
+ align:start position:0%
+Str that says it becomes flat from the
+point of 1750 all the way to the point
+
+ align:start position:0%
+point of 1750 all the way to the point
+ 
+
+ align:start position:0%
+point of 1750 all the way to the point
+of 2,000 and then drops back down the
+
+ align:start position:0%
+of 2,000 and then drops back down the
+ 
+
+ align:start position:0%
+of 2,000 and then drops back down the
+new budget constraint on the right is
+
+ align:start position:0%
+new budget constraint on the right is
+ 
+
+ align:start position:0%
+new budget constraint on the right is
+the red segment it's a flat segment
+
+ align:start position:0%
+the red segment it's a flat segment
+ 
+
+ align:start position:0%
+the red segment it's a flat segment
+because we're saying no matter how much
+
+ align:start position:0%
+because we're saying no matter how much
+ 
+
+ align:start position:0%
+because we're saying no matter how much
+leure you take above 1750 you always get
+
+ align:start position:0%
+leure you take above 1750 you always get
+ 
+
+ align:start position:0%
+leure you take above 1750 you always get
+$5,000 in income we just send you a
+
+ align:start position:0%
+$5,000 in income we just send you a
+ 
+
+ align:start position:0%
+$5,000 in income we just send you a
+check for the
+
+ align:start position:0%
+check for the
+ 
+
+ align:start position:0%
+check for the
+rest like likewise we're going to pay
+
+ align:start position:0%
+rest like likewise we're going to pay
+ 
+
+ align:start position:0%
+rest like likewise we're going to pay
+for that by a tax on those who earn
+
+ align:start position:0%
+for that by a tax on those who earn
+ 
+
+ align:start position:0%
+for that by a tax on those who earn
+above
+
+ align:start position:0%
+above
+ 
+
+ align:start position:0%
+above
+$20,000 well at $20 an hour that means
+
+ align:start position:0%
+$20,000 well at $20 an hour that means
+ 
+
+ align:start position:0%
+$20,000 well at $20 an hour that means
+people who take less than a thousand
+
+ align:start position:0%
+people who take less than a thousand
+ 
+
+ align:start position:0%
+people who take less than a thousand
+hours of leisure are the ones who earn
+
+ align:start position:0%
+hours of leisure are the ones who earn
+ 
+
+ align:start position:0%
+hours of leisure are the ones who earn
+more than $20,000 so on those people
+
+ align:start position:0%
+more than $20,000 so on those people
+ 
+
+ align:start position:0%
+more than $20,000 so on those people
+were're taxing them 50% so that lowers
+
+ align:start position:0%
+were're taxing them 50% so that lowers
+ 
+
+ align:start position:0%
+were're taxing them 50% so that lowers
+the slope of the budget constraint now
+
+ align:start position:0%
+the slope of the budget constraint now
+ 
+
+ align:start position:0%
+the slope of the budget constraint now
+for every hour you work above a
+
+ align:start position:0%
+for every hour you work above a
+ 
+
+ align:start position:0%
+for every hour you work above a
+thousand you take home only $10 an
+
+ align:start position:0%
+thousand you take home only $10 an
+ 
+
+ align:start position:0%
+thousand you take home only $10 an
+hour so that lowers the opportunity cost
+
+ align:start position:0%
+hour so that lowers the opportunity cost
+ 
+
+ align:start position:0%
+hour so that lowers the opportunity cost
+of work lowers the budget constraint to
+
+ align:start position:0%
+of work lowers the budget constraint to
+ 
+
+ align:start position:0%
+of work lowers the budget constraint to
+the upper left right
+
+ align:start position:0%
+the upper left right
+ 
+
+ align:start position:0%
+the upper left right
+side okay questions about
+
+ align:start position:0%
+side okay questions about
+ 
+
+ align:start position:0%
+side okay questions about
+that okay now let's
+
+ align:start position:0%
+that okay now let's
+ 
+
+ align:start position:0%
+that okay now let's
+assume that there's three people in this
+
+ align:start position:0%
+assume that there's three people in this
+ 
+
+ align:start position:0%
+assume that there's three people in this
+world okay person
+
+ align:start position:0%
+world okay person
+ 
+
+ align:start position:0%
+world okay person
+A and B have the same utility function
+
+ align:start position:0%
+A and B have the same utility function
+ 
+
+ align:start position:0%
+A and B have the same utility function
+their utility function is U equals c to
+
+ align:start position:0%
+their utility function is U equals c to
+ 
+
+ align:start position:0%
+their utility function is U equals c to
+the 34
+
+ align:start position:0%
+the 34
+ 
+
+ align:start position:0%
+the 34
+time L to the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+one4 person C has a different function
+
+ align:start position:0%
+one4 person C has a different function
+ 
+
+ align:start position:0%
+one4 person C has a different function
+they have
+
+ align:start position:0%
+they have
+ 
+
+ align:start position:0%
+they have
+C to the 1
+
+ align:start position:0%
+C to the 1
+ 
+
+ align:start position:0%
+C to the 1
+nth L to the 8
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+9th okay so person C really likes
+
+ align:start position:0%
+9th okay so person C really likes
+ 
+
+ align:start position:0%
+9th okay so person C really likes
+Leisure rela to person A and B right
+
+ align:start position:0%
+Leisure rela to person A and B right
+ 
+
+ align:start position:0%
+Leisure rela to person A and B right
+person A and B have a 3/4 weight on
+
+ align:start position:0%
+person A and B have a 3/4 weight on
+ 
+
+ align:start position:0%
+person A and B have a 3/4 weight on
+consumption versus one quarter on
+
+ align:start position:0%
+consumption versus one quarter on
+ 
+
+ align:start position:0%
+consumption versus one quarter on
+Leisure person C is a one nth way to
+
+ align:start position:0%
+Leisure person C is a one nth way to
+ 
+
+ align:start position:0%
+Leisure person C is a one nth way to
+consumption Rel to eight nths on Leisure
+
+ align:start position:0%
+consumption Rel to eight nths on Leisure
+ 
+
+ align:start position:0%
+consumption Rel to eight nths on Leisure
+person C likes
+
+ align:start position:0%
+person C likes
+ 
+
+ align:start position:0%
+person C likes
+Leisure okay that's the utility
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+function
+
+ align:start position:0%
+function
+ 
+
+ align:start position:0%
+function
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+now in the optimal Choice
+
+ align:start position:0%
+now in the optimal Choice
+ 
+
+ align:start position:0%
+now in the optimal Choice
+set people are going to set their
+
+ align:start position:0%
+set people are going to set their
+ 
+
+ align:start position:0%
+set people are going to set their
+mrss equal to their
+
+ align:start position:0%
+mrss equal to their
+ 
+
+ align:start position:0%
+mrss equal to their
+MRT okay that's going to be the choice
+
+ align:start position:0%
+MRT okay that's going to be the choice
+ 
+
+ align:start position:0%
+MRT okay that's going to be the choice
+people are going to make in the optimal
+
+ align:start position:0%
+people are going to make in the optimal
+ 
+
+ align:start position:0%
+people are going to make in the optimal
+Choice set
+
+ align:start position:0%
+Choice set
+ 
+
+ align:start position:0%
+Choice set
+okay so basically what they're going to
+
+ align:start position:0%
+okay so basically what they're going to
+ 
+
+ align:start position:0%
+okay so basically what they're going to
+do is they're going to find given this
+
+ align:start position:0%
+do is they're going to find given this
+ 
+
+ align:start position:0%
+do is they're going to find given this
+budget constraint the one I depicted in
+
+ align:start position:0%
+budget constraint the one I depicted in
+ 
+
+ align:start position:0%
+budget constraint the one I depicted in
+figure
+
+ align:start position:0%
+figure
+ 
+
+ align:start position:0%
+figure
+238 what is their optimal
+
+ align:start position:0%
+238 what is their optimal
+ 
+
+ align:start position:0%
+238 what is their optimal
+choice and what we're going to
+
+ align:start position:0%
+choice and what we're going to
+ 
+
+ align:start position:0%
+choice and what we're going to
+see is
+
+ align:start position:0%
+see is
+ 
+
+ align:start position:0%
+see is
+that um without the government scheme
+
+ align:start position:0%
+that um without the government scheme
+ 
+
+ align:start position:0%
+that um without the government scheme
+we'll see that in figure 239 and we'll
+
+ align:start position:0%
+we'll see that in figure 239 and we'll
+ 
+
+ align:start position:0%
+we'll see that in figure 239 and we'll
+we'll you we'll solve the math and
+
+ align:start position:0%
+we'll you we'll solve the math and
+ 
+
+ align:start position:0%
+we'll you we'll solve the math and
+section of this example we'll solve the
+
+ align:start position:0%
+section of this example we'll solve the
+ 
+
+ align:start position:0%
+section of this example we'll solve the
+math in section so you can go through it
+
+ align:start position:0%
+math in section so you can go through it
+ 
+
+ align:start position:0%
+math in section so you can go through it
+but I'm showing you what the answer
+
+ align:start position:0%
+but I'm showing you what the answer
+ 
+
+ align:start position:0%
+but I'm showing you what the answer
+answer is we'll go through the math in
+
+ align:start position:0%
+answer is we'll go through the math in
+ 
+
+ align:start position:0%
+answer is we'll go through the math in
+the section you'll see person A and B
+
+ align:start position:0%
+the section you'll see person A and B
+ 
+
+ align:start position:0%
+the section you'll see person A and B
+will choose to be at that intersection
+
+ align:start position:0%
+will choose to be at that intersection
+ 
+
+ align:start position:0%
+will choose to be at that intersection
+on the left on the black line A1 B1 that
+
+ align:start position:0%
+on the left on the black line A1 B1 that
+ 
+
+ align:start position:0%
+on the left on the black line A1 B1 that
+is the choice they'll make given this
+
+ align:start position:0%
+is the choice they'll make given this
+ 
+
+ align:start position:0%
+is the choice they'll make given this
+budget constraint and given these
+
+ align:start position:0%
+budget constraint and given these
+ 
+
+ align:start position:0%
+budget constraint and given these
+preferences they will choose in figure
+
+ align:start position:0%
+preferences they will choose in figure
+ 
+
+ align:start position:0%
+preferences they will choose in figure
+239 be the A1 B1
+
+ align:start position:0%
+239 be the A1 B1
+ 
+
+ align:start position:0%
+239 be the A1 B1
+intersection unsurprisingly person c
+
+ align:start position:0%
+intersection unsurprisingly person c
+ 
+
+ align:start position:0%
+intersection unsurprisingly person c
+will be choose to be way down on the
+
+ align:start position:0%
+will be choose to be way down on the
+ 
+
+ align:start position:0%
+will be choose to be way down on the
+right at the C1 intersection why because
+
+ align:start position:0%
+right at the C1 intersection why because
+ 
+
+ align:start position:0%
+right at the C1 intersection why because
+they love Leisure person C cares way
+
+ align:start position:0%
+they love Leisure person C cares way
+ 
+
+ align:start position:0%
+they love Leisure person C cares way
+about Leisure consumption it's the way
+
+ align:start position:0%
+about Leisure consumption it's the way
+ 
+
+ align:start position:0%
+about Leisure consumption it's the way
+down the right okay we'll work out the
+
+ align:start position:0%
+down the right okay we'll work out the
+ 
+
+ align:start position:0%
+down the right okay we'll work out the
+math just take it to me take take my
+
+ align:start position:0%
+math just take it to me take take my
+ 
+
+ align:start position:0%
+math just take it to me take take my
+word that's what the math
+
+ align:start position:0%
+word that's what the math
+ 
+
+ align:start position:0%
+word that's what the math
+delivers now we put in the tax and
+
+ align:start position:0%
+delivers now we put in the tax and
+ 
+
+ align:start position:0%
+delivers now we put in the tax and
+transfer scheme what happens to person C
+
+ align:start position:0%
+transfer scheme what happens to person C
+ 
+
+ align:start position:0%
+transfer scheme what happens to person C
+why do they move to
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+C2 why do they move to
+
+ align:start position:0%
+C2 why do they move to
+ 
+
+ align:start position:0%
+C2 why do they move to
+C2 well if you think about it think
+
+ align:start position:0%
+C2 well if you think about it think
+ 
+
+ align:start position:0%
+C2 well if you think about it think
+about income and substitution effects
+
+ align:start position:0%
+about income and substitution effects
+ 
+
+ align:start position:0%
+about income and substitution effects
+for person C the substitution effect is
+
+ align:start position:0%
+for person C the substitution effect is
+ 
+
+ align:start position:0%
+for person C the substitution effect is
+when you're at like person C there is a
+
+ align:start position:0%
+when you're at like person C there is a
+ 
+
+ align:start position:0%
+when you're at like person C there is a
+100% tax
+
+ align:start position:0%
+100% tax
+ 
+
+ align:start position:0%
+100% tax
+on your
+
+ align:start position:0%
+on your
+ 
+
+ align:start position:0%
+on your
+earnings look at this 100% tax because
+
+ align:start position:0%
+earnings look at this 100% tax because
+ 
+
+ align:start position:0%
+earnings look at this 100% tax because
+every dollar you earn you get less in
+
+ align:start position:0%
+every dollar you earn you get less in
+ 
+
+ align:start position:0%
+every dollar you earn you get less in
+transfer substitution effect says don't
+
+ align:start position:0%
+transfer substitution effect says don't
+ 
+
+ align:start position:0%
+transfer substitution effect says don't
+work right because if you work you get
+
+ align:start position:0%
+work right because if you work you get
+ 
+
+ align:start position:0%
+work right because if you work you get
+nothing the income effect is your richer
+
+ align:start position:0%
+nothing the income effect is your richer
+ 
+
+ align:start position:0%
+nothing the income effect is your richer
+you're getting a transfer income effect
+
+ align:start position:0%
+you're getting a transfer income effect
+ 
+
+ align:start position:0%
+you're getting a transfer income effect
+also says don't work so they don't work
+
+ align:start position:0%
+also says don't work so they don't work
+ 
+
+ align:start position:0%
+also says don't work so they don't work
+turn that if you pay people not to work
+
+ align:start position:0%
+turn that if you pay people not to work
+ 
+
+ align:start position:0%
+turn that if you pay people not to work
+they won't we learned that in the
+
+ align:start position:0%
+they won't we learned that in the
+ 
+
+ align:start position:0%
+they won't we learned that in the
+Netherlands last time so all the people
+
+ align:start position:0%
+Netherlands last time so all the people
+ 
+
+ align:start position:0%
+Netherlands last time so all the people
+who were C1 go to C2 they stop
+
+ align:start position:0%
+who were C1 go to C2 they stop
+ 
+
+ align:start position:0%
+who were C1 go to C2 they stop
+working what about A1 and B1 well here
+
+ align:start position:0%
+working what about A1 and B1 well here
+ 
+
+ align:start position:0%
+working what about A1 and B1 well here
+it's
+
+ align:start position:0%
+it's
+ 
+
+ align:start position:0%
+it's
+unclear they now face a lower wage
+
+ align:start position:0%
+unclear they now face a lower wage
+ 
+
+ align:start position:0%
+unclear they now face a lower wage
+effective wage of $10 of $20 whether
+
+ align:start position:0%
+effective wage of $10 of $20 whether
+ 
+
+ align:start position:0%
+effective wage of $10 of $20 whether
+they work more or less depends on income
+
+ align:start position:0%
+they work more or less depends on income
+ 
+
+ align:start position:0%
+they work more or less depends on income
+versus substitution
+
+ align:start position:0%
+versus substitution
+ 
+
+ align:start position:0%
+versus substitution
+effects here I'm going to assume
+
+ align:start position:0%
+effects here I'm going to assume
+ 
+
+ align:start position:0%
+effects here I'm going to assume
+substitution effects
+
+ align:start position:0%
+substitution effects
+ 
+
+ align:start position:0%
+substitution effects
+dominate so they work
+
+ align:start position:0%
+dominate so they work
+ 
+
+ align:start position:0%
+dominate so they work
+less so the new equilibrium is the
+
+ align:start position:0%
+less so the new equilibrium is the
+ 
+
+ align:start position:0%
+less so the new equilibrium is the
+person C works less
+
+ align:start position:0%
+person C works less
+ 
+
+ align:start position:0%
+person C works less
+and person A and B work
+
+ align:start position:0%
+and person A and B work
+ 
+
+ align:start position:0%
+and person A and B work
+less what have we found leaks in the
+
+ align:start position:0%
+less what have we found leaks in the
+ 
+
+ align:start position:0%
+less what have we found leaks in the
+bucket we thought we could raise a bunch
+
+ align:start position:0%
+bucket we thought we could raise a bunch
+ 
+
+ align:start position:0%
+bucket we thought we could raise a bunch
+of money from taxiing and being given to
+
+ align:start position:0%
+of money from taxiing and being given to
+ 
+
+ align:start position:0%
+of money from taxiing and being given to
+C but we missed two things first of all
+
+ align:start position:0%
+C but we missed two things first of all
+ 
+
+ align:start position:0%
+C but we missed two things first of all
+A and B don't work as hard so we can't
+
+ align:start position:0%
+A and B don't work as hard so we can't
+ 
+
+ align:start position:0%
+A and B don't work as hard so we can't
+raise as much money from
+
+ align:start position:0%
+raise as much money from
+ 
+
+ align:start position:0%
+raise as much money from
+them second of all C doesn't work so
+
+ align:start position:0%
+them second of all C doesn't work so
+ 
+
+ align:start position:0%
+them second of all C doesn't work so
+hard so we need to get more money to see
+
+ align:start position:0%
+hard so we need to get more money to see
+ 
+
+ align:start position:0%
+hard so we need to get more money to see
+so if you started with 0.1 A1 B1 and C1
+
+ align:start position:0%
+so if you started with 0.1 A1 B1 and C1
+ 
+
+ align:start position:0%
+so if you started with 0.1 A1 B1 and C1
+you would have a certain estimate of how
+
+ align:start position:0%
+you would have a certain estimate of how
+ 
+
+ align:start position:0%
+you would have a certain estimate of how
+much money you have to take to get
+
+ align:start position:0%
+much money you have to take to get
+ 
+
+ align:start position:0%
+much money you have to take to get
+person C1 the transfer your estimate
+
+ align:start position:0%
+person C1 the transfer your estimate
+ 
+
+ align:start position:0%
+person C1 the transfer your estimate
+would be too low why would your estimate
+
+ align:start position:0%
+would be too low why would your estimate
+ 
+
+ align:start position:0%
+would be too low why would your estimate
+be to too low because you'd miss the
+
+ align:start position:0%
+be to too low because you'd miss the
+ 
+
+ align:start position:0%
+be to too low because you'd miss the
+leakage you miss the fact that A1 and B1
+
+ align:start position:0%
+leakage you miss the fact that A1 and B1
+ 
+
+ align:start position:0%
+leakage you miss the fact that A1 and B1
+going to work less so you raise less
+
+ align:start position:0%
+going to work less so you raise less
+ 
+
+ align:start position:0%
+going to work less so you raise less
+money from them and C1 is going to work
+
+ align:start position:0%
+money from them and C1 is going to work
+ 
+
+ align:start position:0%
+money from them and C1 is going to work
+less so you give more money to C1 those
+
+ align:start position:0%
+less so you give more money to C1 those
+ 
+
+ align:start position:0%
+less so you give more money to C1 those
+are the leaks that's a graphical
+
+ align:start position:0%
+are the leaks that's a graphical
+ 
+
+ align:start position:0%
+are the leaks that's a graphical
+illustration of the leaks in the bucket
+
+ align:start position:0%
+illustration of the leaks in the bucket
+ 
+
+ align:start position:0%
+illustration of the leaks in the bucket
+that is how the Leaky bucket works it
+
+ align:start position:0%
+that is how the Leaky bucket works it
+ 
+
+ align:start position:0%
+that is how the Leaky bucket works it
+causes
+
+ align:start position:0%
+causes
+ 
+
+ align:start position:0%
+causes
+taxation causes assuming substitution
+
+ align:start position:0%
+taxation causes assuming substitution
+ 
+
+ align:start position:0%
+taxation causes assuming substitution
+effects dominate taxation causes the
+
+ align:start position:0%
+effects dominate taxation causes the
+ 
+
+ align:start position:0%
+effects dominate taxation causes the
+rich to work less hard which means you
+
+ align:start position:0%
+rich to work less hard which means you
+ 
+
+ align:start position:0%
+rich to work less hard which means you
+raise less money and it causes the poor
+
+ align:start position:0%
+raise less money and it causes the poor
+ 
+
+ align:start position:0%
+raise less money and it causes the poor
+to work less hard which means you have
+
+ align:start position:0%
+to work less hard which means you have
+ 
+
+ align:start position:0%
+to work less hard which means you have
+to spend more money and those the tour
+
+ align:start position:0%
+to spend more money and those the tour
+ 
+
+ align:start position:0%
+to spend more money and those the tour
+so leaked that was very fast and
+
+ align:start position:0%
+so leaked that was very fast and
+ 
+
+ align:start position:0%
+so leaked that was very fast and
+graphical in section you go through the
+
+ align:start position:0%
+graphical in section you go through the
+ 
+
+ align:start position:0%
+graphical in section you go through the
+math but that just gives you a sense of
+
+ align:start position:0%
+math but that just gives you a sense of
+ 
+
+ align:start position:0%
+math but that just gives you a sense of
+how the leakages work we'll follow up on
+
+ align:start position:0%
+how the leakages work we'll follow up on
+ 
+
+ align:start position:0%
+how the leakages work we'll follow up on
+Monday
\ No newline at end of file
diff --git a/8ssjKR7nNck.txt b/8ssjKR7nNck.txt
new file mode 100644
index 0000000000000000000000000000000000000000..7f334dceac8561fc04694aebad2621b7aa62be4a
--- /dev/null
+++ b/8ssjKR7nNck.txt
@@ -0,0 +1,8267 @@
+align:start position:0%
+ 
+um let's get started this is uh
+
+ align:start position:0%
+um let's get started this is uh
+ 
+
+ align:start position:0%
+um let's get started this is uh
+1401 uh microeconomics uh the uh and um
+
+ align:start position:0%
+1401 uh microeconomics uh the uh and um
+ 
+
+ align:start position:0%
+1401 uh microeconomics uh the uh and um
+I'm professor John
+
+ align:start position:0%
+I'm professor John
+ 
+
+ align:start position:0%
+I'm professor John
+Gruber now couple notes about the course
+
+ align:start position:0%
+Gruber now couple notes about the course
+ 
+
+ align:start position:0%
+Gruber now couple notes about the course
+uh there's a distinct policy angle to
+
+ align:start position:0%
+uh there's a distinct policy angle to
+ 
+
+ align:start position:0%
+uh there's a distinct policy angle to
+this course um I think personally what
+
+ align:start position:0%
+this course um I think personally what
+ 
+
+ align:start position:0%
+this course um I think personally what
+makes economics most exciting is it can
+
+ align:start position:0%
+makes economics most exciting is it can
+ 
+
+ align:start position:0%
+makes economics most exciting is it can
+you you can use it to think
+
+ align:start position:0%
+you you can use it to think
+ 
+
+ align:start position:0%
+you you can use it to think
+intelligently about the problems that
+
+ align:start position:0%
+intelligently about the problems that
+ 
+
+ align:start position:0%
+intelligently about the problems that
+policy makers face every day as they try
+
+ align:start position:0%
+policy makers face every day as they try
+ 
+
+ align:start position:0%
+policy makers face every day as they try
+to decide how to make the economy work
+
+ align:start position:0%
+to decide how to make the economy work
+ 
+
+ align:start position:0%
+to decide how to make the economy work
+the best for its citizens um in fact I
+
+ align:start position:0%
+the best for its citizens um in fact I
+ 
+
+ align:start position:0%
+the best for its citizens um in fact I
+teach a whole course about this called
+
+ align:start position:0%
+teach a whole course about this called
+ 
+
+ align:start position:0%
+teach a whole course about this called
+1441 uh but I'm going to bring some of
+
+ align:start position:0%
+1441 uh but I'm going to bring some of
+ 
+
+ align:start position:0%
+1441 uh but I'm going to bring some of
+those insights into this class and use
+
+ align:start position:0%
+those insights into this class and use
+ 
+
+ align:start position:0%
+those insights into this class and use
+policy based examples and things like
+
+ align:start position:0%
+policy based examples and things like
+ 
+
+ align:start position:0%
+policy based examples and things like
+that to try to motivate uh and organize
+
+ align:start position:0%
+that to try to motivate uh and organize
+ 
+
+ align:start position:0%
+that to try to motivate uh and organize
+our thinking about
+
+ align:start position:0%
+our thinking about
+ 
+
+ align:start position:0%
+our thinking about
+economics um lastly uh three points
+
+ align:start position:0%
+economics um lastly uh three points
+ 
+
+ align:start position:0%
+economics um lastly uh three points
+about my teaching style first of all I
+
+ align:start position:0%
+about my teaching style first of all I
+ 
+
+ align:start position:0%
+about my teaching style first of all I
+don't write everything on the board uh
+
+ align:start position:0%
+don't write everything on the board uh
+ 
+
+ align:start position:0%
+don't write everything on the board uh
+for the Freshman here we're not in high
+
+ align:start position:0%
+for the Freshman here we're not in high
+ 
+
+ align:start position:0%
+for the Freshman here we're not in high
+schoool anymore you need to pay
+
+ align:start position:0%
+schoool anymore you need to pay
+ 
+
+ align:start position:0%
+schoool anymore you need to pay
+attention and listen to what I say not
+
+ align:start position:0%
+attention and listen to what I say not
+ 
+
+ align:start position:0%
+attention and listen to what I say not
+just what I write um so it's important
+
+ align:start position:0%
+just what I write um so it's important
+ 
+
+ align:start position:0%
+just what I write um so it's important
+to remember that um uh uh the second
+
+ align:start position:0%
+to remember that um uh uh the second
+ 
+
+ align:start position:0%
+to remember that um uh uh the second
+point is as you can tell I talk really
+
+ align:start position:0%
+point is as you can tell I talk really
+ 
+
+ align:start position:0%
+point is as you can tell I talk really
+fast and my handwriting is really bad
+
+ align:start position:0%
+fast and my handwriting is really bad
+ 
+
+ align:start position:0%
+fast and my handwriting is really bad
+okay so please please don't be afraid to
+
+ align:start position:0%
+okay so please please don't be afraid to
+ 
+
+ align:start position:0%
+okay so please please don't be afraid to
+ask what the hell I just said or wrote
+
+ align:start position:0%
+ask what the hell I just said or wrote
+ 
+
+ align:start position:0%
+ask what the hell I just said or wrote
+okay there is if you don't know chances
+
+ align:start position:0%
+okay there is if you don't know chances
+ 
+
+ align:start position:0%
+okay there is if you don't know chances
+are at least 40% of the class doesn't
+
+ align:start position:0%
+are at least 40% of the class doesn't
+ 
+
+ align:start position:0%
+are at least 40% of the class doesn't
+know either we'll learn later this
+
+ align:start position:0%
+know either we'll learn later this
+ 
+
+ align:start position:0%
+know either we'll learn later this
+semester about the con a public good a
+
+ align:start position:0%
+semester about the con a public good a
+ 
+
+ align:start position:0%
+semester about the con a public good a
+public good is something you do which
+
+ align:start position:0%
+public good is something you do which
+ 
+
+ align:start position:0%
+public good is something you do which
+has a personal cost and a social benefit
+
+ align:start position:0%
+has a personal cost and a social benefit
+ 
+
+ align:start position:0%
+has a personal cost and a social benefit
+I understand raising your raising your
+
+ align:start position:0%
+I understand raising your raising your
+ 
+
+ align:start position:0%
+I understand raising your raising your
+hand in a class as large as this can be
+
+ align:start position:0%
+hand in a class as large as this can be
+ 
+
+ align:start position:0%
+hand in a class as large as this can be
+intimidating but remember in doing so
+
+ align:start position:0%
+intimidating but remember in doing so
+ 
+
+ align:start position:0%
+intimidating but remember in doing so
+you're not just helping yourself you're
+
+ align:start position:0%
+you're not just helping yourself you're
+ 
+
+ align:start position:0%
+you're not just helping yourself you're
+helping your fellow classmates so please
+
+ align:start position:0%
+helping your fellow classmates so please
+ 
+
+ align:start position:0%
+helping your fellow classmates so please
+don't lean and Whisper loudly what the
+
+ align:start position:0%
+don't lean and Whisper loudly what the
+ 
+
+ align:start position:0%
+don't lean and Whisper loudly what the
+hell did you just say to the person next
+
+ align:start position:0%
+hell did you just say to the person next
+ 
+
+ align:start position:0%
+hell did you just say to the person next
+to you raise your hand and ask me
+
+ align:start position:0%
+to you raise your hand and ask me
+ 
+
+ align:start position:0%
+to you raise your hand and ask me
+because if you didn't understand many
+
+ align:start position:0%
+because if you didn't understand many
+ 
+
+ align:start position:0%
+because if you didn't understand many
+other people didn't as well more
+
+ align:start position:0%
+other people didn't as well more
+ 
+
+ align:start position:0%
+other people didn't as well more
+generally it's hard to get class
+
+ align:start position:0%
+generally it's hard to get class
+ 
+
+ align:start position:0%
+generally it's hard to get class
+participation in a class this large but
+
+ align:start position:0%
+participation in a class this large but
+ 
+
+ align:start position:0%
+participation in a class this large but
+I really encourage people to participate
+
+ align:start position:0%
+I really encourage people to participate
+ 
+
+ align:start position:0%
+I really encourage people to participate
+as much as
+
+ align:start position:0%
+as much as
+ 
+
+ align:start position:0%
+as much as
+possible I've never had a year in this
+
+ align:start position:0%
+possible I've never had a year in this
+ 
+
+ align:start position:0%
+possible I've never had a year in this
+class where there's been too much
+
+ align:start position:0%
+class where there's been too much
+ 
+
+ align:start position:0%
+class where there's been too much
+participation I've had every single year
+
+ align:start position:0%
+participation I've had every single year
+ 
+
+ align:start position:0%
+participation I've had every single year
+too little participation so please
+
+ align:start position:0%
+too little participation so please
+ 
+
+ align:start position:0%
+too little participation so please
+follow up with questions uh things like
+
+ align:start position:0%
+follow up with questions uh things like
+ 
+
+ align:start position:0%
+follow up with questions uh things like
+that and then finally the third point
+
+ align:start position:0%
+that and then finally the third point
+ 
+
+ align:start position:0%
+that and then finally the third point
+about my teaching style is I have a bad
+
+ align:start position:0%
+about my teaching style is I have a bad
+ 
+
+ align:start position:0%
+about my teaching style is I have a bad
+tendency to use the term guys in a
+
+ align:start position:0%
+tendency to use the term guys in a
+ 
+
+ align:start position:0%
+tendency to use the term guys in a
+gender neutral sense so when I say guys
+
+ align:start position:0%
+gender neutral sense so when I say guys
+ 
+
+ align:start position:0%
+gender neutral sense so when I say guys
+I don't mean men I mean economic agents
+
+ align:start position:0%
+I don't mean men I mean economic agents
+ 
+
+ align:start position:0%
+I don't mean men I mean economic agents
+people everyone and I'm sorry guys has a
+
+ align:start position:0%
+people everyone and I'm sorry guys has a
+ 
+
+ align:start position:0%
+people everyone and I'm sorry guys has a
+gendered word often I don't mean it that
+
+ align:start position:0%
+gendered word often I don't mean it that
+ 
+
+ align:start position:0%
+gendered word often I don't mean it that
+way it's just kind of a economist talk
+
+ align:start position:0%
+way it's just kind of a economist talk
+ 
+
+ align:start position:0%
+way it's just kind of a economist talk
+for for economic agents we call them
+
+ align:start position:0%
+for for economic agents we call them
+ 
+
+ align:start position:0%
+for for economic agents we call them
+guys what we're going to do today is
+
+ align:start position:0%
+guys what we're going to do today is
+ 
+
+ align:start position:0%
+guys what we're going to do today is
+talk about what is microeconomics what
+
+ align:start position:0%
+talk about what is microeconomics what
+ 
+
+ align:start position:0%
+talk about what is microeconomics what
+are you going to learn in this course
+
+ align:start position:0%
+are you going to learn in this course
+ 
+
+ align:start position:0%
+are you going to learn in this course
+what is the basic field about and then
+
+ align:start position:0%
+what is the basic field about and then
+ 
+
+ align:start position:0%
+what is the basic field about and then
+we'll dive in next time into actually
+
+ align:start position:0%
+we'll dive in next time into actually
+ 
+
+ align:start position:0%
+we'll dive in next time into actually
+starting to learn about the models that
+
+ align:start position:0%
+starting to learn about the models that
+ 
+
+ align:start position:0%
+starting to learn about the models that
+make up basic
+
+ align:start position:0%
+make up basic
+ 
+
+ align:start position:0%
+make up basic
+microeconomics um
+
+ align:start position:0%
+microeconomics um
+ 
+
+ align:start position:0%
+microeconomics um
+microeconomics is fundamentally in a
+
+ align:start position:0%
+microeconomics is fundamentally in a
+ 
+
+ align:start position:0%
+microeconomics is fundamentally in a
+sentence the study of how individuals
+
+ align:start position:0%
+sentence the study of how individuals
+ 
+
+ align:start position:0%
+sentence the study of how individuals
+and firms make themselves as well off as
+
+ align:start position:0%
+and firms make themselves as well off as
+ 
+
+ align:start position:0%
+and firms make themselves as well off as
+possible in a world of scarcity it's how
+
+ align:start position:0%
+possible in a world of scarcity it's how
+ 
+
+ align:start position:0%
+possible in a world of scarcity it's how
+individuals and firms make themselves as
+
+ align:start position:0%
+individuals and firms make themselves as
+ 
+
+ align:start position:0%
+individuals and firms make themselves as
+well off as possible in a world of
+
+ align:start position:0%
+well off as possible in a world of
+ 
+
+ align:start position:0%
+well off as possible in a world of
+scarcity scarcity is key the core of
+
+ align:start position:0%
+scarcity scarcity is key the core of
+ 
+
+ align:start position:0%
+scarcity scarcity is key the core of
+microeconomics is constrained
+
+ align:start position:0%
+microeconomics is constrained
+ 
+
+ align:start position:0%
+microeconomics is constrained
+optimization basically individuals or
+
+ align:start position:0%
+optimization basically individuals or
+ 
+
+ align:start position:0%
+optimization basically individuals or
+firms assessing the tradeoffs they face
+
+ align:start position:0%
+firms assessing the tradeoffs they face
+ 
+
+ align:start position:0%
+firms assessing the tradeoffs they face
+every day in the decisions they make and
+
+ align:start position:0%
+every day in the decisions they make and
+ 
+
+ align:start position:0%
+every day in the decisions they make and
+then trying to decide the best decision
+
+ align:start position:0%
+then trying to decide the best decision
+ 
+
+ align:start position:0%
+then trying to decide the best decision
+given those
+
+ align:start position:0%
+given those
+ 
+
+ align:start position:0%
+given those
+tradeoffs so that is microeconomics is
+
+ align:start position:0%
+tradeoffs so that is microeconomics is
+ 
+
+ align:start position:0%
+tradeoffs so that is microeconomics is
+really about trade-offs mic economics is
+
+ align:start position:0%
+really about trade-offs mic economics is
+ 
+
+ align:start position:0%
+really about trade-offs mic economics is
+really about you can't have it all so
+
+ align:start position:0%
+really about you can't have it all so
+ 
+
+ align:start position:0%
+really about you can't have it all so
+what are you going to do with what you
+
+ align:start position:0%
+what are you going to do with what you
+ 
+
+ align:start position:0%
+what are you going to do with what you
+can have how are you best going to use
+
+ align:start position:0%
+can have how are you best going to use
+ 
+
+ align:start position:0%
+can have how are you best going to use
+your limited
+
+ align:start position:0%
+your limited
+ 
+
+ align:start position:0%
+your limited
+resources and the key concept behind all
+
+ align:start position:0%
+resources and the key concept behind all
+ 
+
+ align:start position:0%
+resources and the key concept behind all
+this the sort of probably the I'm going
+
+ align:start position:0%
+this the sort of probably the I'm going
+ 
+
+ align:start position:0%
+this the sort of probably the I'm going
+to say about 100 times this is one of
+
+ align:start position:0%
+to say about 100 times this is one of
+ 
+
+ align:start position:0%
+to say about 100 times this is one of
+the most important Concepts in economics
+
+ align:start position:0%
+the most important Concepts in economics
+ 
+
+ align:start position:0%
+the most important Concepts in economics
+I'm sorry about that but this is really
+
+ align:start position:0%
+I'm sorry about that but this is really
+ 
+
+ align:start position:0%
+I'm sorry about that but this is really
+one of the most important Concepts in
+
+ align:start position:0%
+one of the most important Concepts in
+ 
+
+ align:start position:0%
+one of the most important Concepts in
+economics is the concept of opportunity
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+cost opportunity cost
+
+ align:start position:0%
+cost opportunity cost
+ 
+
+ align:start position:0%
+cost opportunity cost
+okay and opportunity cost is the notion
+
+ align:start position:0%
+okay and opportunity cost is the notion
+ 
+
+ align:start position:0%
+okay and opportunity cost is the notion
+that every
+
+ align:start position:0%
+that every
+ 
+
+ align:start position:0%
+that every
+action or in action has cost in terms of
+
+ align:start position:0%
+action or in action has cost in terms of
+ 
+
+ align:start position:0%
+action or in action has cost in terms of
+what you could have done instead in
+
+ align:start position:0%
+what you could have done instead in
+ 
+
+ align:start position:0%
+what you could have done instead in
+terms of the next best
+
+ align:start position:0%
+terms of the next best
+ 
+
+ align:start position:0%
+terms of the next best
+opportunity if you buy a shirt you are
+
+ align:start position:0%
+opportunity if you buy a shirt you are
+ 
+
+ align:start position:0%
+opportunity if you buy a shirt you are
+forgoing spending that money on buying
+
+ align:start position:0%
+forgoing spending that money on buying
+ 
+
+ align:start position:0%
+forgoing spending that money on buying
+something else so if you're deciding
+
+ align:start position:0%
+something else so if you're deciding
+ 
+
+ align:start position:0%
+something else so if you're deciding
+between shirts and pants you buy the
+
+ align:start position:0%
+between shirts and pants you buy the
+ 
+
+ align:start position:0%
+between shirts and pants you buy the
+shirt you're for going buying the pair
+
+ align:start position:0%
+shirt you're for going buying the pair
+ 
+
+ align:start position:0%
+shirt you're for going buying the pair
+of
+
+ align:start position:0%
+of
+ 
+
+ align:start position:0%
+of
+pants if you
+
+ align:start position:0%
+pants if you
+ 
+
+ align:start position:0%
+pants if you
+study if you spend all night studying
+
+ align:start position:0%
+study if you spend all night studying
+ 
+
+ align:start position:0%
+study if you spend all night studying
+you're forg going the opportunity to go
+
+ align:start position:0%
+you're forg going the opportunity to go
+ 
+
+ align:start position:0%
+you're forg going the opportunity to go
+see a band you like in concert and vice
+
+ align:start position:0%
+see a band you like in concert and vice
+ 
+
+ align:start position:0%
+see a band you like in concert and vice
+versa every action you take is a
+
+ align:start position:0%
+versa every action you take is a
+ 
+
+ align:start position:0%
+versa every action you take is a
+trade-off every decision you make
+
+ align:start position:0%
+trade-off every decision you make
+ 
+
+ align:start position:0%
+trade-off every decision you make
+involves a trade-off because there's
+
+ align:start position:0%
+involves a trade-off because there's
+ 
+
+ align:start position:0%
+involves a trade-off because there's
+always an opportunity cost there's
+
+ align:start position:0%
+always an opportunity cost there's
+ 
+
+ align:start position:0%
+always an opportunity cost there's
+always something you could have done
+
+ align:start position:0%
+always something you could have done
+ 
+
+ align:start position:0%
+always something you could have done
+instead
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah great question um actually let me
+
+ align:start position:0%
+yeah great question um actually let me
+ 
+
+ align:start position:0%
+yeah great question um actually let me
+come back to that in one minute I want
+
+ align:start position:0%
+come back to that in one minute I want
+ 
+
+ align:start position:0%
+come back to that in one minute I want
+to come back to that or five minutes um
+
+ align:start position:0%
+to come back to that or five minutes um
+ 
+
+ align:start position:0%
+to come back to that or five minutes um
+okay so this is why economics is called
+
+ align:start position:0%
+okay so this is why economics is called
+ 
+
+ align:start position:0%
+okay so this is why economics is called
+the Dismal science we're called the
+
+ align:start position:0%
+the Dismal science we're called the
+ 
+
+ align:start position:0%
+the Dismal science we're called the
+Dismal science because the role of the
+
+ align:start position:0%
+Dismal science because the role of the
+ 
+
+ align:start position:0%
+Dismal science because the role of the
+economist is to basically say well you
+
+ align:start position:0%
+economist is to basically say well you
+ 
+
+ align:start position:0%
+economist is to basically say well you
+think that's free but it's not you think
+
+ align:start position:0%
+think that's free but it's not you think
+ 
+
+ align:start position:0%
+think that's free but it's not you think
+you can just relax and watch TV but you
+
+ align:start position:0%
+you can just relax and watch TV but you
+ 
+
+ align:start position:0%
+you can just relax and watch TV but you
+know by watching TV you're giving up the
+
+ align:start position:0%
+know by watching TV you're giving up the
+ 
+
+ align:start position:0%
+know by watching TV you're giving up the
+opportunity to study the opportunity to
+
+ align:start position:0%
+opportunity to study the opportunity to
+ 
+
+ align:start position:0%
+opportunity to study the opportunity to
+go out see a concert or the opportunity
+
+ align:start position:0%
+go out see a concert or the opportunity
+ 
+
+ align:start position:0%
+go out see a concert or the opportunity
+to do something else okay so that's why
+
+ align:start position:0%
+to do something else okay so that's why
+ 
+
+ align:start position:0%
+to do something else okay so that's why
+they call disal science now some people
+
+ align:start position:0%
+they call disal science now some people
+ 
+
+ align:start position:0%
+they call disal science now some people
+may call dismal I call it fun and maybe
+
+ align:start position:0%
+may call dismal I call it fun and maybe
+ 
+
+ align:start position:0%
+may call dismal I call it fun and maybe
+that's because I was an MIT
+
+ align:start position:0%
+that's because I was an MIT
+ 
+
+ align:start position:0%
+that's because I was an MIT
+undergraduate and what is an engineering
+
+ align:start position:0%
+undergraduate and what is an engineering
+ 
+
+ align:start position:0%
+undergraduate and what is an engineering
+school but the land of constrainted
+
+ align:start position:0%
+school but the land of constrainted
+ 
+
+ align:start position:0%
+school but the land of constrainted
+optimization that's what engineering and
+
+ align:start position:0%
+optimization that's what engineering and
+ 
+
+ align:start position:0%
+optimization that's what engineering and
+science is it's all about what
+
+ align:start position:0%
+science is it's all about what
+ 
+
+ align:start position:0%
+science is it's all about what
+engineering is tra and optimization what
+
+ align:start position:0%
+engineering is tra and optimization what
+ 
+
+ align:start position:0%
+engineering is tra and optimization what
+better example could there be in the
+
+ align:start position:0%
+better example could there be in the
+ 
+
+ align:start position:0%
+better example could there be in the
+two7 contests you're given a set of
+
+ align:start position:0%
+two7 contests you're given a set of
+ 
+
+ align:start position:0%
+two7 contests you're given a set of
+materials and asked to build something
+
+ align:start position:0%
+materials and asked to build something
+ 
+
+ align:start position:0%
+materials and asked to build something
+that's a constrained optimization
+
+ align:start position:0%
+that's a constrained optimization
+ 
+
+ align:start position:0%
+that's a constrained optimization
+exercise indeed economics was invented
+
+ align:start position:0%
+exercise indeed economics was invented
+ 
+
+ align:start position:0%
+exercise indeed economics was invented
+modern economics invented at MIT by The
+
+ align:start position:0%
+modern economics invented at MIT by The
+ 
+
+ align:start position:0%
+modern economics invented at MIT by The
+Economist Paul Samuelson who essentially
+
+ align:start position:0%
+Economist Paul Samuelson who essentially
+ 
+
+ align:start position:0%
+Economist Paul Samuelson who essentially
+said the mathematics that science
+
+ align:start position:0%
+said the mathematics that science
+ 
+
+ align:start position:0%
+said the mathematics that science
+Engineers use can be applied to analyze
+
+ align:start position:0%
+Engineers use can be applied to analyze
+ 
+
+ align:start position:0%
+Engineers use can be applied to analyze
+really the sort of essay likee approach
+
+ align:start position:0%
+really the sort of essay likee approach
+ 
+
+ align:start position:0%
+really the sort of essay likee approach
+that people had taken economics before
+
+ align:start position:0%
+that people had taken economics before
+ 
+
+ align:start position:0%
+that people had taken economics before
+him so he basically brought the tools of
+
+ align:start position:0%
+him so he basically brought the tools of
+ 
+
+ align:start position:0%
+him so he basically brought the tools of
+science to economics and basically
+
+ align:start position:0%
+science to economics and basically
+ 
+
+ align:start position:0%
+science to economics and basically
+developed the course I'll teach today
+
+ align:start position:0%
+developed the course I'll teach today
+ 
+
+ align:start position:0%
+developed the course I'll teach today
+and the course that's taught all over
+
+ align:start position:0%
+and the course that's taught all over
+ 
+
+ align:start position:0%
+and the course that's taught all over
+the world was developed right here at
+
+ align:start position:0%
+the world was developed right here at
+ 
+
+ align:start position:0%
+the world was developed right here at
+MIT modern economics was born here
+
+ align:start position:0%
+MIT modern economics was born here
+ 
+
+ align:start position:0%
+MIT modern economics was born here
+because we introduced the tools of
+
+ align:start position:0%
+because we introduced the tools of
+ 
+
+ align:start position:0%
+because we introduced the tools of
+constraint
+
+ align:start position:0%
+constraint
+ 
+
+ align:start position:0%
+constraint
+optimization now oh over here I'm
+
+ align:start position:0%
+optimization now oh over here I'm
+ 
+
+ align:start position:0%
+optimization now oh over here I'm
+usually going to try to do like an
+
+ align:start position:0%
+usually going to try to do like an
+ 
+
+ align:start position:0%
+usually going to try to do like an
+outline of what we're covering so we
+
+ align:start position:0%
+outline of what we're covering so we
+ 
+
+ align:start position:0%
+outline of what we're covering so we
+talked about course details what is
+
+ align:start position:0%
+talked about course details what is
+ 
+
+ align:start position:0%
+talked about course details what is
+micro just did now let's talk about how
+
+ align:start position:0%
+micro just did now let's talk about how
+ 
+
+ align:start position:0%
+micro just did now let's talk about how
+we do that what economics does which is
+
+ align:start position:0%
+we do that what economics does which is
+ 
+
+ align:start position:0%
+we do that what economics does which is
+we use models and I'm talk about a model
+
+ align:start position:0%
+we use models and I'm talk about a model
+ 
+
+ align:start position:0%
+we use models and I'm talk about a model
+of supply and
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+demand how do we actually teach you all
+
+ align:start position:0%
+demand how do we actually teach you all
+ 
+
+ align:start position:0%
+demand how do we actually teach you all
+about these tradeoffs
+
+ align:start position:0%
+about these tradeoffs
+ 
+
+ align:start position:0%
+about these tradeoffs
+okay the way we do it is by building
+
+ align:start position:0%
+okay the way we do it is by building
+ 
+
+ align:start position:0%
+okay the way we do it is by building
+simplified models okay what is a Model A
+
+ align:start position:0%
+simplified models okay what is a Model A
+ 
+
+ align:start position:0%
+simplified models okay what is a Model A
+model is technically the description of
+
+ align:start position:0%
+model is technically the description of
+ 
+
+ align:start position:0%
+model is technically the description of
+any relationship between two or more
+
+ align:start position:0%
+any relationship between two or more
+ 
+
+ align:start position:0%
+any relationship between two or more
+variables is a
+
+ align:start position:0%
+variables is a
+ 
+
+ align:start position:0%
+variables is a
+model um now but unlike explaining
+
+ align:start position:0%
+model um now but unlike explaining
+ 
+
+ align:start position:0%
+model um now but unlike explaining
+relationship between energy and mass we
+
+ align:start position:0%
+relationship between energy and mass we
+ 
+
+ align:start position:0%
+relationship between energy and mass we
+do not have scientific laws and
+
+ align:start position:0%
+do not have scientific laws and
+ 
+
+ align:start position:0%
+do not have scientific laws and
+constants in our universe okay economics
+
+ align:start position:0%
+constants in our universe okay economics
+ 
+
+ align:start position:0%
+constants in our universe okay economics
+is as much as we hate to say it not a
+
+ align:start position:0%
+is as much as we hate to say it not a
+ 
+
+ align:start position:0%
+is as much as we hate to say it not a
+real science it is a social science
+
+ align:start position:0%
+real science it is a social science
+ 
+
+ align:start position:0%
+real science it is a social science
+which means that basically we don't have
+
+ align:start position:0%
+which means that basically we don't have
+ 
+
+ align:start position:0%
+which means that basically we don't have
+rigid laws that we can write down say
+
+ align:start position:0%
+rigid laws that we can write down say
+ 
+
+ align:start position:0%
+rigid laws that we can write down say
+they're all they're everywhere
+
+ align:start position:0%
+they're all they're everywhere
+ 
+
+ align:start position:0%
+they're all they're everywhere
+applicable okay we we have to use models
+
+ align:start position:0%
+applicable okay we we have to use models
+ 
+
+ align:start position:0%
+applicable okay we we have to use models
+to basically try to explain the world as
+
+ align:start position:0%
+to basically try to explain the world as
+ 
+
+ align:start position:0%
+to basically try to explain the world as
+much as we can and so in doing so we
+
+ align:start position:0%
+much as we can and so in doing so we
+ 
+
+ align:start position:0%
+much as we can and so in doing so we
+have to make a set of simplifying
+
+ align:start position:0%
+have to make a set of simplifying
+ 
+
+ align:start position:0%
+have to make a set of simplifying
+assumptions a set of simplifying
+
+ align:start position:0%
+assumptions a set of simplifying
+ 
+
+ align:start position:0%
+assumptions a set of simplifying
+assumptions to try to essentially trade
+
+ align:start position:0%
+assumptions to try to essentially trade
+ 
+
+ align:start position:0%
+assumptions to try to essentially trade
+off two
+
+ align:start position:0%
+off two
+ 
+
+ align:start position:0%
+off two
+goals one goal is to explain as much as
+
+ align:start position:0%
+goals one goal is to explain as much as
+ 
+
+ align:start position:0%
+goals one goal is to explain as much as
+we can the other goal is to have
+
+ align:start position:0%
+we can the other goal is to have
+ 
+
+ align:start position:0%
+we can the other goal is to have
+parsimonious models that I can teach
+
+ align:start position:0%
+parsimonious models that I can teach
+ 
+
+ align:start position:0%
+parsimonious models that I can teach
+you okay the more complicated the model
+
+ align:start position:0%
+you okay the more complicated the model
+ 
+
+ align:start position:0%
+you okay the more complicated the model
+gets the harder it is to teach the
+
+ align:start position:0%
+gets the harder it is to teach the
+ 
+
+ align:start position:0%
+gets the harder it is to teach the
+harder it is to solve this comes to the
+
+ align:start position:0%
+harder it is to solve this comes to the
+ 
+
+ align:start position:0%
+harder it is to solve this comes to the
+earlier question about are you really
+
+ align:start position:0%
+earlier question about are you really
+ 
+
+ align:start position:0%
+earlier question about are you really
+just trading off two goods well of
+
+ align:start position:0%
+just trading off two goods well of
+ 
+
+ align:start position:0%
+just trading off two goods well of
+course you're never just trading off two
+
+ align:start position:0%
+course you're never just trading off two
+ 
+
+ align:start position:0%
+course you're never just trading off two
+goods but we're going to write our
+
+ align:start position:0%
+goods but we're going to write our
+ 
+
+ align:start position:0%
+goods but we're going to write our
+models like you are and it's going to
+
+ align:start position:0%
+models like you are and it's going to
+ 
+
+ align:start position:0%
+models like you are and it's going to
+turn out that gives you all the
+
+ align:start position:0%
+turn out that gives you all the
+ 
+
+ align:start position:0%
+turn out that gives you all the
+intuition you need for a model with this
+
+ align:start position:0%
+intuition you need for a model with this
+ 
+
+ align:start position:0%
+intuition you need for a model with this
+three or four Goods it's just a lot
+
+ align:start position:0%
+three or four Goods it's just a lot
+ 
+
+ align:start position:0%
+three or four Goods it's just a lot
+easier math so it turns out everything
+
+ align:start position:0%
+easier math so it turns out everything
+ 
+
+ align:start position:0%
+easier math so it turns out everything
+you learn in the model with two goods
+
+ align:start position:0%
+you learn in the model with two goods
+ 
+
+ align:start position:0%
+you learn in the model with two goods
+tells you everything you need to know
+
+ align:start position:0%
+tells you everything you need to know
+ 
+
+ align:start position:0%
+tells you everything you need to know
+for a model with n Goods just with
+
+ align:start position:0%
+for a model with n Goods just with
+ 
+
+ align:start position:0%
+for a model with n Goods just with
+easier math so that's the kind of
+
+ align:start position:0%
+easier math so that's the kind of
+ 
+
+ align:start position:0%
+easier math so that's the kind of
+simplifying assumption that's a
+
+ align:start position:0%
+simplifying assumption that's a
+ 
+
+ align:start position:0%
+simplifying assumption that's a
+fairly um uh that's a fairly uh
+
+ align:start position:0%
+fairly um uh that's a fairly uh
+ 
+
+ align:start position:0%
+fairly um uh that's a fairly uh
+non-offensive simplifying assumption
+
+ align:start position:0%
+non-offensive simplifying assumption
+ 
+
+ align:start position:0%
+non-offensive simplifying assumption
+think it doesn't really change anything
+
+ align:start position:0%
+think it doesn't really change anything
+ 
+
+ align:start position:0%
+think it doesn't really change anything
+we'll make other simplifying assumptions
+
+ align:start position:0%
+we'll make other simplifying assumptions
+ 
+
+ align:start position:0%
+we'll make other simplifying assumptions
+which are noxious and offensive and
+
+ align:start position:0%
+which are noxious and offensive and
+ 
+
+ align:start position:0%
+which are noxious and offensive and
+we'll talk about those and if you are
+
+ align:start position:0%
+we'll talk about those and if you are
+ 
+
+ align:start position:0%
+we'll talk about those and if you are
+offended by them and bothered and want
+
+ align:start position:0%
+offended by them and bothered and want
+ 
+
+ align:start position:0%
+offended by them and bothered and want
+to see what happens without those
+
+ align:start position:0%
+to see what happens without those
+ 
+
+ align:start position:0%
+to see what happens without those
+assumptions then that's exactly why you
+
+ align:start position:0%
+assumptions then that's exactly why you
+ 
+
+ align:start position:0%
+assumptions then that's exactly why you
+should be economics major because that's
+
+ align:start position:0%
+should be economics major because that's
+ 
+
+ align:start position:0%
+should be economics major because that's
+we go on and do in the rest of the
+
+ align:start position:0%
+we go on and do in the rest of the
+ 
+
+ align:start position:0%
+we go on and do in the rest of the
+classes say okay now let's move on from
+
+ align:start position:0%
+classes say okay now let's move on from
+ 
+
+ align:start position:0%
+classes say okay now let's move on from
+these simplified models add some
+
+ align:start position:0%
+these simplified models add some
+ 
+
+ align:start position:0%
+these simplified models add some
+richness and see what it does to the
+
+ align:start position:0%
+richness and see what it does to the
+ 
+
+ align:start position:0%
+richness and see what it does to the
+world okay uh the statistician George
+
+ align:start position:0%
+world okay uh the statistician George
+ 
+
+ align:start position:0%
+world okay uh the statistician George
+box uh once wrote that all models are
+
+ align:start position:0%
+box uh once wrote that all models are
+ 
+
+ align:start position:0%
+box uh once wrote that all models are
+wrong but some are useful okay okay and
+
+ align:start position:0%
+wrong but some are useful okay okay and
+ 
+
+ align:start position:0%
+wrong but some are useful okay okay and
+that's exactly what we're going to try
+
+ align:start position:0%
+that's exactly what we're going to try
+ 
+
+ align:start position:0%
+that's exactly what we're going to try
+to work with today okay when I teach you
+
+ align:start position:0%
+to work with today okay when I teach you
+ 
+
+ align:start position:0%
+to work with today okay when I teach you
+economics I'm going to try to teach it
+
+ align:start position:0%
+economics I'm going to try to teach it
+ 
+
+ align:start position:0%
+economics I'm going to try to teach it
+to you on three levels okay the first is
+
+ align:start position:0%
+to you on three levels okay the first is
+ 
+
+ align:start position:0%
+to you on three levels okay the first is
+word MIT is
+
+ align:start position:0%
+word MIT is
+ 
+
+ align:start position:0%
+word MIT is
+mathematical the second is graphical and
+
+ align:start position:0%
+mathematical the second is graphical and
+ 
+
+ align:start position:0%
+mathematical the second is graphical and
+the third is
+
+ align:start position:0%
+the third is
+ 
+
+ align:start position:0%
+the third is
+intuitive really if you want to succeed
+
+ align:start position:0%
+intuitive really if you want to succeed
+ 
+
+ align:start position:0%
+intuitive really if you want to succeed
+in this class you need to understand all
+
+ align:start position:0%
+in this class you need to understand all
+ 
+
+ align:start position:0%
+in this class you need to understand all
+three now not every model will I use all
+
+ align:start position:0%
+three now not every model will I use all
+ 
+
+ align:start position:0%
+three now not every model will I use all
+three but you want to understand all
+
+ align:start position:0%
+three but you want to understand all
+ 
+
+ align:start position:0%
+three but you want to understand all
+three of those Concepts to really
+
+ align:start position:0%
+three of those Concepts to really
+ 
+
+ align:start position:0%
+three of those Concepts to really
+understand the material we're learning
+
+ align:start position:0%
+understand the material we're learning
+ 
+
+ align:start position:0%
+understand the material we're learning
+here and and we'll start with the model
+
+ align:start position:0%
+here and and we'll start with the model
+ 
+
+ align:start position:0%
+here and and we'll start with the model
+of supply and demand the very first
+
+ align:start position:0%
+of supply and demand the very first
+ 
+
+ align:start position:0%
+of supply and demand the very first
+economic model developed by Adam Smith
+
+ align:start position:0%
+economic model developed by Adam Smith
+ 
+
+ align:start position:0%
+economic model developed by Adam Smith
+in 1776 in the book that was sort of the
+
+ align:start position:0%
+in 1776 in the book that was sort of the
+ 
+
+ align:start position:0%
+in 1776 in the book that was sort of the
+founding of Economics The Wealth of
+
+ align:start position:0%
+founding of Economics The Wealth of
+ 
+
+ align:start position:0%
+founding of Economics The Wealth of
+Nations Adam Smith asked the question um
+
+ align:start position:0%
+Nations Adam Smith asked the question um
+ 
+
+ align:start position:0%
+Nations Adam Smith asked the question um
+think about two goods think about water
+
+ align:start position:0%
+think about two goods think about water
+ 
+
+ align:start position:0%
+think about two goods think about water
+and think about
+
+ align:start position:0%
+and think about
+ 
+
+ align:start position:0%
+and think about
+diamonds okay nothing is more essential
+
+ align:start position:0%
+diamonds okay nothing is more essential
+ 
+
+ align:start position:0%
+diamonds okay nothing is more essential
+for life than water we cannot function
+
+ align:start position:0%
+for life than water we cannot function
+ 
+
+ align:start position:0%
+for life than water we cannot function
+without it nothing is probably less
+
+ align:start position:0%
+without it nothing is probably less
+ 
+
+ align:start position:0%
+without it nothing is probably less
+essential for life than diamonds
+
+ align:start position:0%
+essential for life than diamonds
+ 
+
+ align:start position:0%
+essential for life than diamonds
+especially back then when diamonds
+
+ align:start position:0%
+especially back then when diamonds
+ 
+
+ align:start position:0%
+especially back then when diamonds
+didn't have industrial uses they were
+
+ align:start position:0%
+didn't have industrial uses they were
+ 
+
+ align:start position:0%
+didn't have industrial uses they were
+just
+
+ align:start position:0%
+just
+ 
+
+ align:start position:0%
+just
+bobbles okay water is clearly just
+
+ align:start position:0%
+bobbles okay water is clearly just
+ 
+
+ align:start position:0%
+bobbles okay water is clearly just
+essential diamonds aren't yet the price
+
+ align:start position:0%
+essential diamonds aren't yet the price
+ 
+
+ align:start position:0%
+essential diamonds aren't yet the price
+of diamonds is very high and water is
+
+ align:start position:0%
+of diamonds is very high and water is
+ 
+
+ align:start position:0%
+of diamonds is very high and water is
+essentially free he asked how could this
+
+ align:start position:0%
+essentially free he asked how could this
+ 
+
+ align:start position:0%
+essentially free he asked how could this
+be and the answer is because what I've
+
+ align:start position:0%
+be and the answer is because what I've
+ 
+
+ align:start position:0%
+be and the answer is because what I've
+just described is only one half of the
+
+ align:start position:0%
+just described is only one half of the
+ 
+
+ align:start position:0%
+just described is only one half of the
+model of where we get the price of water
+
+ align:start position:0%
+model of where we get the price of water
+ 
+
+ align:start position:0%
+model of where we get the price of water
+or diamonds I've described the
+
+ align:start position:0%
+or diamonds I've described the
+ 
+
+ align:start position:0%
+or diamonds I've described the
+demand I've describe the demand for
+
+ align:start position:0%
+demand I've describe the demand for
+ 
+
+ align:start position:0%
+demand I've describe the demand for
+water and diamonds I've said the demand
+
+ align:start position:0%
+water and diamonds I've said the demand
+ 
+
+ align:start position:0%
+water and diamonds I've said the demand
+for water is much much larger than the
+
+ align:start position:0%
+for water is much much larger than the
+ 
+
+ align:start position:0%
+for water is much much larger than the
+demand for diamonds
+
+ align:start position:0%
+demand for diamonds
+ 
+
+ align:start position:0%
+demand for diamonds
+what I haven't talked about is the
+
+ align:start position:0%
+what I haven't talked about is the
+ 
+
+ align:start position:0%
+what I haven't talked about is the
+supply which is the supply of water is
+
+ align:start position:0%
+supply which is the supply of water is
+ 
+
+ align:start position:0%
+supply which is the supply of water is
+even more Rel the supply of diamonds
+
+ align:start position:0%
+even more Rel the supply of diamonds
+ 
+
+ align:start position:0%
+even more Rel the supply of diamonds
+water is everywhere diamonds are rare to
+
+ align:start position:0%
+water is everywhere diamonds are rare to
+ 
+
+ align:start position:0%
+water is everywhere diamonds are rare to
+find and what Adam Smith said is that
+
+ align:start position:0%
+find and what Adam Smith said is that
+ 
+
+ align:start position:0%
+find and what Adam Smith said is that
+while the demand for diamonds may not be
+
+ align:start position:0%
+while the demand for diamonds may not be
+ 
+
+ align:start position:0%
+while the demand for diamonds may not be
+as high as the demand for water the
+
+ align:start position:0%
+as high as the demand for water the
+ 
+
+ align:start position:0%
+as high as the demand for water the
+supply of diamonds is much much smaller
+
+ align:start position:0%
+supply of diamonds is much much smaller
+ 
+
+ align:start position:0%
+supply of diamonds is much much smaller
+than the supply of water and that is why
+
+ align:start position:0%
+than the supply of water and that is why
+ 
+
+ align:start position:0%
+than the supply of water and that is why
+you could end up with a good that's
+
+ align:start position:0%
+you could end up with a good that's
+ 
+
+ align:start position:0%
+you could end up with a good that's
+inherently less valuable to life having
+
+ align:start position:0%
+inherently less valuable to life having
+ 
+
+ align:start position:0%
+inherently less valuable to life having
+a higher price
+
+ align:start position:0%
+a higher price
+ 
+
+ align:start position:0%
+a higher price
+okay and Smith's point is you can't just
+
+ align:start position:0%
+okay and Smith's point is you can't just
+ 
+
+ align:start position:0%
+okay and Smith's point is you can't just
+think of supply and demand and isolation
+
+ align:start position:0%
+think of supply and demand and isolation
+ 
+
+ align:start position:0%
+think of supply and demand and isolation
+you need to think of them uh together um
+
+ align:start position:0%
+you need to think of them uh together um
+ 
+
+ align:start position:0%
+you need to think of them uh together um
+is uh oh Pedro could you grab me a copy
+
+ align:start position:0%
+is uh oh Pedro could you grab me a copy
+ 
+
+ align:start position:0%
+is uh oh Pedro could you grab me a copy
+of the handout fix um okay so that's
+
+ align:start position:0%
+of the handout fix um okay so that's
+ 
+
+ align:start position:0%
+of the handout fix um okay so that's
+sort of the
+
+ align:start position:0%
+sort of the
+ 
+
+ align:start position:0%
+sort of the
+intuition that's the intuition Spider
+
+ align:start position:0%
+intuition that's the intuition Spider
+ 
+
+ align:start position:0%
+intuition that's the intuition Spider
+Man model now let's talk about the
+
+ align:start position:0%
+Man model now let's talk about the
+ 
+
+ align:start position:0%
+Man model now let's talk about the
+graphics and the math okay so now let's
+
+ align:start position:0%
+graphics and the math okay so now let's
+ 
+
+ align:start position:0%
+graphics and the math okay so now let's
+talk about an example of a supply demand
+
+ align:start position:0%
+talk about an example of a supply demand
+ 
+
+ align:start position:0%
+talk about an example of a supply demand
+model and let's focus on the market for
+
+ align:start position:0%
+model and let's focus on the market for
+ 
+
+ align:start position:0%
+model and let's focus on the market for
+roses
+
+ align:start position:0%
+roses
+ 
+
+ align:start position:0%
+roses
+what is a market a Market's what it
+
+ align:start position:0%
+what is a market a Market's what it
+ 
+
+ align:start position:0%
+what is a market a Market's what it
+sounds like it's buyers and sellers
+
+ align:start position:0%
+sounds like it's buyers and sellers
+ 
+
+ align:start position:0%
+sounds like it's buyers and sellers
+coming together are there any more any
+
+ align:start position:0%
+coming together are there any more any
+ 
+
+ align:start position:0%
+coming together are there any more any
+extra handouts around is everyone have
+
+ align:start position:0%
+extra handouts around is everyone have
+ 
+
+ align:start position:0%
+extra handouts around is everyone have
+one everyone have a
+
+ align:start position:0%
+one everyone have a
+ 
+
+ align:start position:0%
+one everyone have a
+handout okay good that's fine then okay
+
+ align:start position:0%
+handout okay good that's fine then okay
+ 
+
+ align:start position:0%
+handout okay good that's fine then okay
+let's talk about the the markets for D
+
+ align:start position:0%
+let's talk about the the markets for D
+ 
+
+ align:start position:0%
+let's talk about the the markets for D
+let's talk about the market for Roses
+
+ align:start position:0%
+let's talk about the market for Roses
+ 
+
+ align:start position:0%
+let's talk about the market for Roses
+okay first of all what is a market a
+
+ align:start position:0%
+okay first of all what is a market a
+ 
+
+ align:start position:0%
+okay first of all what is a market a
+market is think of a market to start
+
+ align:start position:0%
+market is think of a market to start
+ 
+
+ align:start position:0%
+market is think of a market to start
+yeah like another page right the hand
+
+ align:start position:0%
+yeah like another page right the hand
+ 
+
+ align:start position:0%
+yeah like another page right the hand
+has graphs on it does anyone have hand
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+out did how me you
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+print what's that is there any is there
+
+ align:start position:0%
+print what's that is there any is there
+ 
+
+ align:start position:0%
+print what's that is there any is there
+an extra pile sitting around there of
+
+ align:start position:0%
+an extra pile sitting around there of
+ 
+
+ align:start position:0%
+an extra pile sitting around there of
+handouts we got some extras there okay
+
+ align:start position:0%
+handouts we got some extras there okay
+ 
+
+ align:start position:0%
+handouts we got some extras there okay
+pass those around make sure you know
+
+ align:start position:0%
+pass those around make sure you know
+ 
+
+ align:start position:0%
+pass those around make sure you know
+pass those around and
+
+ align:start position:0%
+pass those around and
+ 
+
+ align:start position:0%
+pass those around and
+uh yeah next time they'll be in the back
+
+ align:start position:0%
+uh yeah next time they'll be in the back
+ 
+
+ align:start position:0%
+uh yeah next time they'll be in the back
+so please you know raise your hand if
+
+ align:start position:0%
+so please you know raise your hand if
+ 
+
+ align:start position:0%
+so please you know raise your hand if
+you don't have a hand out and let's try
+
+ align:start position:0%
+you don't have a hand out and let's try
+ 
+
+ align:start position:0%
+you don't have a hand out and let's try
+to pass those around okay pedri can you
+
+ align:start position:0%
+to pass those around okay pedri can you
+ 
+
+ align:start position:0%
+to pass those around okay pedri can you
+grab one for me
+
+ align:start position:0%
+grab one for me
+ 
+
+ align:start position:0%
+grab one for me
+um okay so basically let's think about
+
+ align:start position:0%
+um okay so basically let's think about
+ 
+
+ align:start position:0%
+um okay so basically let's think about
+the market for Roses what is a market a
+
+ align:start position:0%
+the market for Roses what is a market a
+ 
+
+ align:start position:0%
+the market for Roses what is a market a
+market is a place where buyers and
+
+ align:start position:0%
+market is a place where buyers and
+ 
+
+ align:start position:0%
+market is a place where buyers and
+sellers come together to make
+
+ align:start position:0%
+sellers come together to make
+ 
+
+ align:start position:0%
+sellers come together to make
+transactions okay think of it like the
+
+ align:start position:0%
+transactions okay think of it like the
+ 
+
+ align:start position:0%
+transactions okay think of it like the
+old timey markets of ancient England
+
+ align:start position:0%
+old timey markets of ancient England
+ 
+
+ align:start position:0%
+old timey markets of ancient England
+were literally the only way to transact
+
+ align:start position:0%
+were literally the only way to transact
+ 
+
+ align:start position:0%
+were literally the only way to transact
+was physically being in the same
+
+ align:start position:0%
+was physically being in the same
+ 
+
+ align:start position:0%
+was physically being in the same
+place where the buyers and sellers would
+
+ align:start position:0%
+place where the buyers and sellers would
+ 
+
+ align:start position:0%
+place where the buyers and sellers would
+come to Market once a week and the
+
+ align:start position:0%
+come to Market once a week and the
+ 
+
+ align:start position:0%
+come to Market once a week and the
+people bring their cows and people who
+
+ align:start position:0%
+people bring their cows and people who
+ 
+
+ align:start position:0%
+people bring their cows and people who
+wanted milk would come in or meat would
+
+ align:start position:0%
+wanted milk would come in or meat would
+ 
+
+ align:start position:0%
+wanted milk would come in or meat would
+come in and they would transact think of
+
+ align:start position:0%
+come in and they would transact think of
+ 
+
+ align:start position:0%
+come in and they would transact think of
+the market that way now of course that's
+
+ align:start position:0%
+the market that way now of course that's
+ 
+
+ align:start position:0%
+the market that way now of course that's
+not how the modern Market works but
+
+ align:start position:0%
+not how the modern Market works but
+ 
+
+ align:start position:0%
+not how the modern Market works but
+that's the way we want you to
+
+ align:start position:0%
+that's the way we want you to
+ 
+
+ align:start position:0%
+that's the way we want you to
+intuitively think of a market it's
+
+ align:start position:0%
+intuitively think of a market it's
+ 
+
+ align:start position:0%
+intuitively think of a market it's
+literally a place where buyers and sells
+
+ align:start position:0%
+literally a place where buyers and sells
+ 
+
+ align:start position:0%
+literally a place where buyers and sells
+are
+
+ align:start position:0%
+are
+ 
+
+ align:start position:0%
+are
+interacting and it turns out that
+
+ align:start position:0%
+interacting and it turns out that
+ 
+
+ align:start position:0%
+interacting and it turns out that
+intuition will work even even given the
+
+ align:start position:0%
+intuition will work even even given the
+ 
+
+ align:start position:0%
+intuition will work even even given the
+modern
+
+ align:start position:0%
+modern
+ 
+
+ align:start position:0%
+modern
+economy okay so now who else doesn't
+
+ align:start position:0%
+economy okay so now who else doesn't
+ 
+
+ align:start position:0%
+economy okay so now who else doesn't
+have handouts everyone got the
+
+ align:start position:0%
+have handouts everyone got the
+ 
+
+ align:start position:0%
+have handouts everyone got the
+graphs okay all right so um now let's
+
+ align:start position:0%
+graphs okay all right so um now let's
+ 
+
+ align:start position:0%
+graphs okay all right so um now let's
+talk about the market for roses in
+
+ align:start position:0%
+talk about the market for roses in
+ 
+
+ align:start position:0%
+talk about the market for roses in
+figure 11 one we have the market for
+
+ align:start position:0%
+figure 11 one we have the market for
+ 
+
+ align:start position:0%
+figure 11 one we have the market for
+Roses okay on the xaxis the horizontal
+
+ align:start position:0%
+Roses okay on the xaxis the horizontal
+ 
+
+ align:start position:0%
+Roses okay on the xaxis the horizontal
+we have the quantity of roses I'm going
+
+ align:start position:0%
+we have the quantity of roses I'm going
+ 
+
+ align:start position:0%
+we have the quantity of roses I'm going
+to by the way try to have handouts for
+
+ align:start position:0%
+to by the way try to have handouts for
+ 
+
+ align:start position:0%
+to by the way try to have handouts for
+all the graphs because my handwriting is
+
+ align:start position:0%
+all the graphs because my handwriting is
+ 
+
+ align:start position:0%
+all the graphs because my handwriting is
+so brutal so uh uh you shouldn't have to
+
+ align:start position:0%
+so brutal so uh uh you shouldn't have to
+ 
+
+ align:start position:0%
+so brutal so uh uh you shouldn't have to
+see hopefully if all goes well the sem
+
+ align:start position:0%
+see hopefully if all goes well the sem
+ 
+
+ align:start position:0%
+see hopefully if all goes well the sem
+you should never see me draw a graph on
+
+ align:start position:0%
+you should never see me draw a graph on
+ 
+
+ align:start position:0%
+you should never see me draw a graph on
+the board um so uh on the x-axis with
+
+ align:start position:0%
+the board um so uh on the x-axis with
+ 
+
+ align:start position:0%
+the board um so uh on the x-axis with
+the quantity of roses on the y axis we
+
+ align:start position:0%
+the quantity of roses on the y axis we
+ 
+
+ align:start position:0%
+the quantity of roses on the y axis we
+have the price of
+
+ align:start position:0%
+have the price of
+ 
+
+ align:start position:0%
+have the price of
+roses okay um the demand curve
+
+ align:start position:0%
+roses okay um the demand curve
+ 
+
+ align:start position:0%
+roses okay um the demand curve
+represents the relationship between
+
+ align:start position:0%
+represents the relationship between
+ 
+
+ align:start position:0%
+represents the relationship between
+price and quantity from the consumer's
+
+ align:start position:0%
+price and quantity from the consumer's
+ 
+
+ align:start position:0%
+price and quantity from the consumer's
+perspective so the domain curve in this
+
+ align:start position:0%
+perspective so the domain curve in this
+ 
+
+ align:start position:0%
+perspective so the domain curve in this
+this case is represented by the
+
+ align:start position:0%
+this case is represented by the
+ 
+
+ align:start position:0%
+this case is represented by the
+equation Q equals
+
+ align:start position:0%
+equation Q equals
+ 
+
+ align:start position:0%
+equation Q equals
+1,800 minus 400
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+P okay now you're immediately say well
+
+ align:start position:0%
+P okay now you're immediately say well
+ 
+
+ align:start position:0%
+P okay now you're immediately say well
+what where's 1800 400 come from it
+
+ align:start position:0%
+what where's 1800 400 come from it
+ 
+
+ align:start position:0%
+what where's 1800 400 come from it
+doesn't matter right now that's what
+
+ align:start position:0%
+doesn't matter right now that's what
+ 
+
+ align:start position:0%
+doesn't matter right now that's what
+we're going to teach you in the next few
+
+ align:start position:0%
+we're going to teach you in the next few
+ 
+
+ align:start position:0%
+we're going to teach you in the next few
+lectures right now that's just that's an
+
+ align:start position:0%
+lectures right now that's just that's an
+ 
+
+ align:start position:0%
+lectures right now that's just that's an
+equation that represents a line and it's
+
+ align:start position:0%
+equation that represents a line and it's
+ 
+
+ align:start position:0%
+equation that represents a line and it's
+the critical aspect of that equation is
+
+ align:start position:0%
+the critical aspect of that equation is
+ 
+
+ align:start position:0%
+the critical aspect of that equation is
+that there's a negative
+
+ align:start position:0%
+that there's a negative
+ 
+
+ align:start position:0%
+that there's a negative
+relationship between
+
+ align:start position:0%
+relationship between
+ 
+
+ align:start position:0%
+relationship between
+price and quantity as price goes up
+
+ align:start position:0%
+price and quantity as price goes up
+ 
+
+ align:start position:0%
+price and quantity as price goes up
+consumers want fewer
+
+ align:start position:0%
+consumers want fewer
+ 
+
+ align:start position:0%
+consumers want fewer
+roses why is that well it's just because
+
+ align:start position:0%
+roses why is that well it's just because
+ 
+
+ align:start position:0%
+roses why is that well it's just because
+of opportunity cost the more expensive
+
+ align:start position:0%
+of opportunity cost the more expensive
+ 
+
+ align:start position:0%
+of opportunity cost the more expensive
+is a rose the more you have to give up
+
+ align:start position:0%
+is a rose the more you have to give up
+ 
+
+ align:start position:0%
+is a rose the more you have to give up
+to buy it so its opportunity cost is
+
+ align:start position:0%
+to buy it so its opportunity cost is
+ 
+
+ align:start position:0%
+to buy it so its opportunity cost is
+higher so you want it
+
+ align:start position:0%
+higher so you want it
+ 
+
+ align:start position:0%
+higher so you want it
+less okay so the higher is the price the
+
+ align:start position:0%
+less okay so the higher is the price the
+ 
+
+ align:start position:0%
+less okay so the higher is the price the
+fewer roses you want so we get a
+
+ align:start position:0%
+fewer roses you want so we get a
+ 
+
+ align:start position:0%
+fewer roses you want so we get a
+downward sloping demand curve the blue
+
+ align:start position:0%
+downward sloping demand curve the blue
+ 
+
+ align:start position:0%
+downward sloping demand curve the blue
+line
+
+ align:start position:0%
+line
+ 
+
+ align:start position:0%
+line
+now the supply curve represents the same
+
+ align:start position:0%
+now the supply curve represents the same
+ 
+
+ align:start position:0%
+now the supply curve represents the same
+relationship between price and quantity
+
+ align:start position:0%
+relationship between price and quantity
+ 
+
+ align:start position:0%
+relationship between price and quantity
+but from the supplier's
+
+ align:start position:0%
+but from the supplier's
+ 
+
+ align:start position:0%
+but from the supplier's
+perspective a supply curve in this case
+
+ align:start position:0%
+perspective a supply curve in this case
+ 
+
+ align:start position:0%
+perspective a supply curve in this case
+that we've drawn here has the equation
+
+ align:start position:0%
+that we've drawn here has the equation
+ 
+
+ align:start position:0%
+that we've drawn here has the equation
+Q equals
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+200p 200p you'll see here there is a
+
+ align:start position:0%
+200p 200p you'll see here there is a
+ 
+
+ align:start position:0%
+200p 200p you'll see here there is a
+positive relationship between price and
+
+ align:start position:0%
+positive relationship between price and
+ 
+
+ align:start position:0%
+positive relationship between price and
+quantity that is supply curve is upward
+
+ align:start position:0%
+quantity that is supply curve is upward
+ 
+
+ align:start position:0%
+quantity that is supply curve is upward
+sloping as price goes up firms will prod
+
+ align:start position:0%
+sloping as price goes up firms will prod
+ 
+
+ align:start position:0%
+sloping as price goes up firms will prod
+firms will produce more roses why once
+
+ align:start position:0%
+firms will produce more roses why once
+ 
+
+ align:start position:0%
+firms will produce more roses why once
+again opportunity
+
+ align:start position:0%
+again opportunity
+ 
+
+ align:start position:0%
+again opportunity
+cost with a low price producing a rose
+
+ align:start position:0%
+cost with a low price producing a rose
+ 
+
+ align:start position:0%
+cost with a low price producing a rose
+means you can't use that farm to produce
+
+ align:start position:0%
+means you can't use that farm to produce
+ 
+
+ align:start position:0%
+means you can't use that farm to produce
+something
+
+ align:start position:0%
+something
+ 
+
+ align:start position:0%
+something
+else if the price of Rose is low you're
+
+ align:start position:0%
+else if the price of Rose is low you're
+ 
+
+ align:start position:0%
+else if the price of Rose is low you're
+going to use the farm for something else
+
+ align:start position:0%
+going to use the farm for something else
+ 
+
+ align:start position:0%
+going to use the farm for something else
+the price of roses is high you will then
+
+ align:start position:0%
+the price of roses is high you will then
+ 
+
+ align:start position:0%
+the price of roses is high you will then
+use that far to produce roses because
+
+ align:start position:0%
+use that far to produce roses because
+ 
+
+ align:start position:0%
+use that far to produce roses because
+that is a better choice than the next
+
+ align:start position:0%
+that is a better choice than the next
+ 
+
+ align:start position:0%
+that is a better choice than the next
+best
+
+ align:start position:0%
+best
+ 
+
+ align:start position:0%
+best
+alternative so once again this concept
+
+ align:start position:0%
+alternative so once again this concept
+ 
+
+ align:start position:0%
+alternative so once again this concept
+of opportunity has already helped
+
+ align:start position:0%
+of opportunity has already helped
+ 
+
+ align:start position:0%
+of opportunity has already helped
+explain the basic model of Economics the
+
+ align:start position:0%
+explain the basic model of Economics the
+ 
+
+ align:start position:0%
+explain the basic model of Economics the
+single most important model of Economics
+
+ align:start position:0%
+single most important model of Economics
+ 
+
+ align:start position:0%
+single most important model of Economics
+is represented in this graph and you can
+
+ align:start position:0%
+is represented in this graph and you can
+ 
+
+ align:start position:0%
+is represented in this graph and you can
+understand it just by the concept of
+
+ align:start position:0%
+understand it just by the concept of
+ 
+
+ align:start position:0%
+understand it just by the concept of
+opportunity cost that is why we are such
+
+ align:start position:0%
+opportunity cost that is why we are such
+ 
+
+ align:start position:0%
+opportunity cost that is why we are such
+a powerful social science that's why all
+
+ align:start position:0%
+a powerful social science that's why all
+ 
+
+ align:start position:0%
+a powerful social science that's why all
+the other social sciences are [ __ ]
+
+ align:start position:0%
+the other social sciences are [ __ ]
+ 
+
+ align:start position:0%
+the other social sciences are [ __ ]
+jealous of us okay because we can use
+
+ align:start position:0%
+jealous of us okay because we can use
+ 
+
+ align:start position:0%
+jealous of us okay because we can use
+Simple tools to explain much to explain
+
+ align:start position:0%
+Simple tools to explain much to explain
+ 
+
+ align:start position:0%
+Simple tools to explain much to explain
+much of the world and here's a perfect
+
+ align:start position:0%
+much of the world and here's a perfect
+ 
+
+ align:start position:0%
+much of the world and here's a perfect
+example okay now we call the point where
+
+ align:start position:0%
+example okay now we call the point where
+ 
+
+ align:start position:0%
+example okay now we call the point where
+those two curves meet the
+
+ align:start position:0%
+those two curves meet the
+ 
+
+ align:start position:0%
+those two curves meet the
+equilibrium the point where supply and
+
+ align:start position:0%
+equilibrium the point where supply and
+ 
+
+ align:start position:0%
+equilibrium the point where supply and
+demand are in agreement is the
+
+ align:start position:0%
+demand are in agreement is the
+ 
+
+ align:start position:0%
+demand are in agreement is the
+equilibrium that is the point at which
+
+ align:start position:0%
+equilibrium that is the point at which
+ 
+
+ align:start position:0%
+equilibrium that is the point at which
+suppliers are willing to sell roses at
+
+ align:start position:0%
+suppliers are willing to sell roses at
+ 
+
+ align:start position:0%
+suppliers are willing to sell roses at
+the same price consumers are willing to
+
+ align:start position:0%
+the same price consumers are willing to
+ 
+
+ align:start position:0%
+the same price consumers are willing to
+pay for them so with 600 roses 600 box
+
+ align:start position:0%
+pay for them so with 600 roses 600 box
+ 
+
+ align:start position:0%
+pay for them so with 600 roses 600 box
+of roses or whatever it is the the
+
+ align:start position:0%
+of roses or whatever it is the the
+ 
+
+ align:start position:0%
+of roses or whatever it is the the
+equilibrium price is $3 well it's a row
+
+ align:start position:0%
+equilibrium price is $3 well it's a row
+ 
+
+ align:start position:0%
+equilibrium price is $3 well it's a row
+so with 600 rows the equili price is $3
+
+ align:start position:0%
+so with 600 rows the equili price is $3
+ 
+
+ align:start position:0%
+so with 600 rows the equili price is $3
+that is both parties are happy in
+
+ align:start position:0%
+that is both parties are happy in
+ 
+
+ align:start position:0%
+that is both parties are happy in
+equilibrium the key point about
+
+ align:start position:0%
+equilibrium the key point about
+ 
+
+ align:start position:0%
+equilibrium the key point about
+equilibrium as the name
+
+ align:start position:0%
+equilibrium as the name
+ 
+
+ align:start position:0%
+equilibrium as the name
+implies as the term equilibrium implies
+
+ align:start position:0%
+implies as the term equilibrium implies
+ 
+
+ align:start position:0%
+implies as the term equilibrium implies
+it's the point where the system has come
+
+ align:start position:0%
+it's the point where the system has come
+ 
+
+ align:start position:0%
+it's the point where the system has come
+to rest where both parties are happy
+
+ align:start position:0%
+to rest where both parties are happy
+ 
+
+ align:start position:0%
+to rest where both parties are happy
+with the outcome both parties are happy
+
+ align:start position:0%
+with the outcome both parties are happy
+ 
+
+ align:start position:0%
+with the outcome both parties are happy
+because it's on the demand and supply
+
+ align:start position:0%
+because it's on the demand and supply
+ 
+
+ align:start position:0%
+because it's on the demand and supply
+curve since it's on the demand curve
+
+ align:start position:0%
+curve since it's on the demand curve
+ 
+
+ align:start position:0%
+curve since it's on the demand curve
+consumers are willing to pay $3 for 600
+
+ align:start position:0%
+consumers are willing to pay $3 for 600
+ 
+
+ align:start position:0%
+consumers are willing to pay $3 for 600
+roses they wouldn't pay $4 600 roses but
+
+ align:start position:0%
+roses they wouldn't pay $4 600 roses but
+ 
+
+ align:start position:0%
+roses they wouldn't pay $4 600 roses but
+they pay three since it's on the supply
+
+ align:start position:0%
+they pay three since it's on the supply
+ 
+
+ align:start position:0%
+they pay three since it's on the supply
+curve suppliers are willing to accept
+
+ align:start position:0%
+curve suppliers are willing to accept
+ 
+
+ align:start position:0%
+curve suppliers are willing to accept
+$3600 roses they wouldn't accept $2600
+
+ align:start position:0%
+$3600 roses they wouldn't accept $2600
+ 
+
+ align:start position:0%
+$3600 roses they wouldn't accept $2600
+roses but they'll accept $3 because it's
+
+ align:start position:0%
+roses but they'll accept $3 because it's
+ 
+
+ align:start position:0%
+roses but they'll accept $3 because it's
+on the Curve
+
+ align:start position:0%
+on the Curve
+ 
+
+ align:start position:0%
+on the Curve
+so basically it's just two equations and
+
+ align:start position:0%
+so basically it's just two equations and
+ 
+
+ align:start position:0%
+so basically it's just two equations and
+two unknowns you set these two things
+
+ align:start position:0%
+two unknowns you set these two things
+ 
+
+ align:start position:0%
+two unknowns you set these two things
+equal to each other and you solve and
+
+ align:start position:0%
+equal to each other and you solve and
+ 
+
+ align:start position:0%
+equal to each other and you solve and
+you get
+
+ align:start position:0%
+you get
+ 
+
+ align:start position:0%
+you get
+qar equals uh qar equals
+
+ align:start position:0%
+qar equals uh qar equals
+ 
+
+ align:start position:0%
+qar equals uh qar equals
+600 and P star equals three just by two
+
+ align:start position:0%
+600 and P star equals three just by two
+ 
+
+ align:start position:0%
+600 and P star equals three just by two
+equations and two unknowns once again
+
+ align:start position:0%
+equations and two unknowns once again
+ 
+
+ align:start position:0%
+equations and two unknowns once again
+why we only have two goods I could have
+
+ align:start position:0%
+why we only have two goods I could have
+ 
+
+ align:start position:0%
+why we only have two goods I could have
+done this in three dimensions the graph
+
+ align:start position:0%
+done this in three dimensions the graph
+ 
+
+ align:start position:0%
+done this in three dimensions the graph
+would have been uglier the math would
+
+ align:start position:0%
+would have been uglier the math would
+ 
+
+ align:start position:0%
+would have been uglier the math would
+have been harder but nothing would have
+
+ align:start position:0%
+have been harder but nothing would have
+ 
+
+ align:start position:0%
+have been harder but nothing would have
+changed yeah
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+oh that's a great question basically
+
+ align:start position:0%
+oh that's a great question basically
+ 
+
+ align:start position:0%
+oh that's a great question basically
+they
+
+ align:start position:0%
+they
+ 
+
+ align:start position:0%
+they
+are it's a good question we write down
+
+ align:start position:0%
+are it's a good question we write down
+ 
+
+ align:start position:0%
+are it's a good question we write down
+the function are basically invertible
+
+ align:start position:0%
+the function are basically invertible
+ 
+
+ align:start position:0%
+the function are basically invertible
+and we use them both ways is the bottom
+
+ align:start position:0%
+and we use them both ways is the bottom
+ 
+
+ align:start position:0%
+and we use them both ways is the bottom
+line it doesn't we're really writing
+
+ align:start position:0%
+line it doesn't we're really writing
+ 
+
+ align:start position:0%
+line it doesn't we're really writing
+down equili relation between q and P it
+
+ align:start position:0%
+down equili relation between q and P it
+ 
+
+ align:start position:0%
+down equili relation between q and P it
+doesn't really matter what X and Y is
+
+ align:start position:0%
+doesn't really matter what X and Y is
+ 
+
+ align:start position:0%
+doesn't really matter what X and Y is
+we're really just writing down an equili
+
+ align:start position:0%
+we're really just writing down an equili
+ 
+
+ align:start position:0%
+we're really just writing down an equili
+relationship it's just the convention is
+
+ align:start position:0%
+relationship it's just the convention is
+ 
+
+ align:start position:0%
+relationship it's just the convention is
+to put Q on the xaxis even though the
+
+ align:start position:0%
+to put Q on the xaxis even though the
+ 
+
+ align:start position:0%
+to put Q on the xaxis even though the
+con even though the convention will
+
+ align:start position:0%
+con even though the convention will
+ 
+
+ align:start position:0%
+con even though the convention will
+sometimes right toand curs was p on the
+
+ align:start position:0%
+sometimes right toand curs was p on the
+ 
+
+ align:start position:0%
+sometimes right toand curs was p on the
+left hand side the graphic convention
+
+ align:start position:0%
+left hand side the graphic convention
+ 
+
+ align:start position:0%
+left hand side the graphic convention
+will never change but how you write the
+
+ align:start position:0%
+will never change but how you write the
+ 
+
+ align:start position:0%
+will never change but how you write the
+curves might change how we write the
+
+ align:start position:0%
+curves might change how we write the
+ 
+
+ align:start position:0%
+curves might change how we write the
+equations might change
+
+ align:start position:0%
+equations might change
+ 
+
+ align:start position:0%
+equations might change
+yeah use opportunity cost to justify why
+
+ align:start position:0%
+yeah use opportunity cost to justify why
+ 
+
+ align:start position:0%
+yeah use opportunity cost to justify why
+demand down sloping great question okay
+
+ align:start position:0%
+demand down sloping great question okay
+ 
+
+ align:start position:0%
+demand down sloping great question okay
+let's go through it that's exactly kind
+
+ align:start position:0%
+let's go through it that's exactly kind
+ 
+
+ align:start position:0%
+let's go through it that's exactly kind
+of question I want to hear the semester
+
+ align:start position:0%
+of question I want to hear the semester
+ 
+
+ align:start position:0%
+of question I want to hear the semester
+the reason demand is to someone take a
+
+ align:start position:0%
+the reason demand is to someone take a
+ 
+
+ align:start position:0%
+the reason demand is to someone take a
+crack at
+
+ align:start position:0%
+crack at
+ 
+
+ align:start position:0%
+crack at
+it any anyone to explain yeah and speak
+
+ align:start position:0%
+it any anyone to explain yeah and speak
+ 
+
+ align:start position:0%
+it any anyone to explain yeah and speak
+up if the price is higher in order to
+
+ align:start position:0%
+up if the price is higher in order to
+ 
+
+ align:start position:0%
+up if the price is higher in order to
+get that Rose you had to give up more
+
+ align:start position:0%
+get that Rose you had to give up more
+ 
+
+ align:start position:0%
+get that Rose you had to give up more
+because the price represents like your
+
+ align:start position:0%
+because the price represents like your
+ 
+
+ align:start position:0%
+because the price represents like your
+opportunity right PR the opportunity
+
+ align:start position:0%
+opportunity right PR the opportunity
+ 
+
+ align:start position:0%
+opportunity right PR the opportunity
+cost of any good in the free market is
+
+ align:start position:0%
+cost of any good in the free market is
+ 
+
+ align:start position:0%
+cost of any good in the free market is
+its
+
+ align:start position:0%
+its
+ 
+
+ align:start position:0%
+its
+price so as the as the price goes up the
+
+ align:start position:0%
+price so as the as the price goes up the
+ 
+
+ align:start position:0%
+price so as the as the price goes up the
+opportunity cost goes up why because
+
+ align:start position:0%
+opportunity cost goes up why because
+ 
+
+ align:start position:0%
+opportunity cost goes up why because
+there's more other stuff you could have
+
+ align:start position:0%
+there's more other stuff you could have
+ 
+
+ align:start position:0%
+there's more other stuff you could have
+bought so if it's three bucks a row you
+
+ align:start position:0%
+bought so if it's three bucks a row you
+ 
+
+ align:start position:0%
+bought so if it's three bucks a row you
+could have bought you know a slice of
+
+ align:start position:0%
+could have bought you know a slice of
+ 
+
+ align:start position:0%
+could have bought you know a slice of
+pizza and a Coke but if four Buck if
+
+ align:start position:0%
+pizza and a Coke but if four Buck if
+ 
+
+ align:start position:0%
+pizza and a Coke but if four Buck if
+it's if it's four bucks a rose you uh
+
+ align:start position:0%
+it's if it's four bucks a rose you uh
+ 
+
+ align:start position:0%
+it's if it's four bucks a rose you uh
+four bucks a rose you don't have enough
+
+ align:start position:0%
+four bucks a rose you don't have enough
+ 
+
+ align:start position:0%
+four bucks a rose you don't have enough
+money left to buy both the Coke and the
+
+ align:start position:0%
+money left to buy both the Coke and the
+ 
+
+ align:start position:0%
+money left to buy both the Coke and the
+and the slice of pizza so and but that's
+
+ align:start position:0%
+and the slice of pizza so and but that's
+ 
+
+ align:start position:0%
+and the slice of pizza so and but that's
+a great question because that's exactly
+
+ align:start position:0%
+a great question because that's exactly
+ 
+
+ align:start position:0%
+a great question because that's exactly
+where we're going to go next is the next
+
+ align:start position:0%
+where we're going to go next is the next
+ 
+
+ align:start position:0%
+where we're going to go next is the next
+three lectures are going to tell you
+
+ align:start position:0%
+three lectures are going to tell you
+ 
+
+ align:start position:0%
+three lectures are going to tell you
+where this equation comes from we're
+
+ align:start position:0%
+where this equation comes from we're
+ 
+
+ align:start position:0%
+where this equation comes from we're
+going to start with the basic principles
+
+ align:start position:0%
+going to start with the basic principles
+ 
+
+ align:start position:0%
+going to start with the basic principles
+of people's preferences really almost
+
+ align:start position:0%
+of people's preferences really almost
+ 
+
+ align:start position:0%
+of people's preferences really almost
+philosophical and we're going to derive
+
+ align:start position:0%
+philosophical and we're going to derive
+ 
+
+ align:start position:0%
+philosophical and we're going to derive
+this
+
+ align:start position:0%
+this
+ 
+
+ align:start position:0%
+this
+curve then after that the next five
+
+ align:start position:0%
+curve then after that the next five
+ 
+
+ align:start position:0%
+curve then after that the next five
+lectures will be deriving this curve
+
+ align:start position:0%
+lectures will be deriving this curve
+ 
+
+ align:start position:0%
+lectures will be deriving this curve
+we'll start with the basic principles of
+
+ align:start position:0%
+we'll start with the basic principles of
+ 
+
+ align:start position:0%
+we'll start with the basic principles of
+how firms make decisions and we'll
+
+ align:start position:0%
+how firms make decisions and we'll
+ 
+
+ align:start position:0%
+how firms make decisions and we'll
+derive the supply curve
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah that that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+well it depends on on what I've written
+
+ align:start position:0%
+well it depends on on what I've written
+ 
+
+ align:start position:0%
+well it depends on on what I've written
+on the axis you're right this is this is
+
+ align:start position:0%
+on the axis you're right this is this is
+ 
+
+ align:start position:0%
+on the axis you're right this is this is
+confusing pedri should make a note we
+
+ align:start position:0%
+confusing pedri should make a note we
+ 
+
+ align:start position:0%
+confusing pedri should make a note we
+should probably make this clearer next
+
+ align:start position:0%
+should probably make this clearer next
+ 
+
+ align:start position:0%
+should probably make this clearer next
+time we should have called this number
+
+ align:start position:0%
+time we should have called this number
+ 
+
+ align:start position:0%
+time we should have called this number
+of roses or shouldn't have been called
+
+ align:start position:0%
+of roses or shouldn't have been called
+ 
+
+ align:start position:0%
+of roses or shouldn't have been called
+quantity of roses that's a great point
+
+ align:start position:0%
+quantity of roses that's a great point
+ 
+
+ align:start position:0%
+quantity of roses that's a great point
+we should call this number of roses or
+
+ align:start position:0%
+we should call this number of roses or
+ 
+
+ align:start position:0%
+we should call this number of roses or
+boxes of roses but it's per a quantity
+
+ align:start position:0%
+boxes of roses but it's per a quantity
+ 
+
+ align:start position:0%
+boxes of roses but it's per a quantity
+that's specified in the model great
+
+ align:start position:0%
+that's specified in the model great
+ 
+
+ align:start position:0%
+that's specified in the model great
+question thinking with MIT you cannot
+
+ align:start position:0%
+question thinking with MIT you cannot
+ 
+
+ align:start position:0%
+question thinking with MIT you cannot
+get away with with sloppiness here I
+
+ align:start position:0%
+get away with with sloppiness here I
+ 
+
+ align:start position:0%
+get away with with sloppiness here I
+love it Harvard what the hell you write
+
+ align:start position:0%
+love it Harvard what the hell you write
+ 
+
+ align:start position:0%
+love it Harvard what the hell you write
+whatever you want
+
+ align:start position:0%
+whatever you want
+ 
+
+ align:start position:0%
+whatever you want
+yeah
+
+ align:start position:0%
+yeah
+ 
+
+ align:start position:0%
+yeah
+usually great question in indeed uh this
+
+ align:start position:0%
+usually great question in indeed uh this
+ 
+
+ align:start position:0%
+usually great question in indeed uh this
+is another cheat we'll do which we'll
+
+ align:start position:0%
+is another cheat we'll do which we'll
+ 
+
+ align:start position:0%
+is another cheat we'll do which we'll
+often write down nonlinear
+
+ align:start position:0%
+often write down nonlinear
+ 
+
+ align:start position:0%
+often write down nonlinear
+representations but draw them
+
+ align:start position:0%
+representations but draw them
+ 
+
+ align:start position:0%
+representations but draw them
+linearly um this is a linear
+
+ align:start position:0%
+linearly um this is a linear
+ 
+
+ align:start position:0%
+linearly um this is a linear
+representation but sometimes we'll have
+
+ align:start position:0%
+representation but sometimes we'll have
+ 
+
+ align:start position:0%
+representation but sometimes we'll have
+nonlinear curves and draw them linearly
+
+ align:start position:0%
+nonlinear curves and draw them linearly
+ 
+
+ align:start position:0%
+nonlinear curves and draw them linearly
+when we do think of it as a local
+
+ align:start position:0%
+when we do think of it as a local
+ 
+
+ align:start position:0%
+when we do think of it as a local
+approximation think of the linear piece
+
+ align:start position:0%
+approximation think of the linear piece
+ 
+
+ align:start position:0%
+approximation think of the linear piece
+as the local approximation to the larger
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+function okay great questions I love it
+
+ align:start position:0%
+function okay great questions I love it
+ 
+
+ align:start position:0%
+function okay great questions I love it
+okay now this raises this model raises a
+
+ align:start position:0%
+okay now this raises this model raises a
+ 
+
+ align:start position:0%
+okay now this raises this model raises a
+very important distinction that we're
+
+ align:start position:0%
+very important distinction that we're
+ 
+
+ align:start position:0%
+very important distinction that we're
+going to focus on the semester it's
+
+ align:start position:0%
+going to focus on the semester it's
+ 
+
+ align:start position:0%
+going to focus on the semester it's
+going to trip you up I guarantee a
+
+ align:start position:0%
+going to trip you up I guarantee a
+ 
+
+ align:start position:0%
+going to trip you up I guarantee a
+number of times so I want you to very
+
+ align:start position:0%
+number of times so I want you to very
+ 
+
+ align:start position:0%
+number of times so I want you to very
+careful thinking about this which is the
+
+ align:start position:0%
+careful thinking about this which is the
+ 
+
+ align:start position:0%
+careful thinking about this which is the
+distinction between
+
+ align:start position:0%
+distinction between
+ 
+
+ align:start position:0%
+distinction between
+positive
+
+ align:start position:0%
+positive
+ 
+
+ align:start position:0%
+positive
+economics and normative
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+economics positive economics is the
+
+ align:start position:0%
+economics positive economics is the
+ 
+
+ align:start position:0%
+economics positive economics is the
+study of the way things
+
+ align:start position:0%
+study of the way things
+ 
+
+ align:start position:0%
+study of the way things
+are while normative economics is the
+
+ align:start position:0%
+are while normative economics is the
+ 
+
+ align:start position:0%
+are while normative economics is the
+study of the way things should be okay
+
+ align:start position:0%
+study of the way things should be okay
+ 
+
+ align:start position:0%
+study of the way things should be okay
+positive economics study the way things
+
+ align:start position:0%
+positive economics study the way things
+ 
+
+ align:start position:0%
+positive economics study the way things
+are normative economics to study the way
+
+ align:start position:0%
+are normative economics to study the way
+ 
+
+ align:start position:0%
+are normative economics to study the way
+things should be
+
+ align:start position:0%
+things should be
+ 
+
+ align:start position:0%
+things should be
+okay now to consider to understand this
+
+ align:start position:0%
+okay now to consider to understand this
+ 
+
+ align:start position:0%
+okay now to consider to understand this
+let's consider a great example of
+
+ align:start position:0%
+let's consider a great example of
+ 
+
+ align:start position:0%
+let's consider a great example of
+Economics at work which is eBay okay
+
+ align:start position:0%
+Economics at work which is eBay okay
+ 
+
+ align:start position:0%
+Economics at work which is eBay okay
+when eBay came along okay I know it is
+
+ align:start position:0%
+when eBay came along okay I know it is
+ 
+
+ align:start position:0%
+when eBay came along okay I know it is
+older than all of you but it's younger
+
+ align:start position:0%
+older than all of you but it's younger
+ 
+
+ align:start position:0%
+older than all of you but it's younger
+than me when eBay came along economists
+
+ align:start position:0%
+than me when eBay came along economists
+ 
+
+ align:start position:0%
+than me when eBay came along economists
+are very excited because economists love
+
+ align:start position:0%
+are very excited because economists love
+ 
+
+ align:start position:0%
+are very excited because economists love
+auctions auctions are if you will The
+
+ align:start position:0%
+auctions auctions are if you will The
+ 
+
+ align:start position:0%
+auctions auctions are if you will The
+Standard Market that used to exist in
+
+ align:start position:0%
+Standard Market that used to exist in
+ 
+
+ align:start position:0%
+Standard Market that used to exist in
+you know 15th century England okay it's
+
+ align:start position:0%
+you know 15th century England okay it's
+ 
+
+ align:start position:0%
+you know 15th century England okay it's
+literally people beating against each
+
+ align:start position:0%
+literally people beating against each
+ 
+
+ align:start position:0%
+literally people beating against each
+other in a way that reveals who wants
+
+ align:start position:0%
+other in a way that reveals who wants
+ 
+
+ align:start position:0%
+other in a way that reveals who wants
+the good the most and what's wonderful
+
+ align:start position:0%
+the good the most and what's wonderful
+ 
+
+ align:start position:0%
+the good the most and what's wonderful
+about that and we'll come back to this
+
+ align:start position:0%
+about that and we'll come back to this
+ 
+
+ align:start position:0%
+about that and we'll come back to this
+throughout the semester is it has two
+
+ align:start position:0%
+throughout the semester is it has two
+ 
+
+ align:start position:0%
+throughout the semester is it has two
+great features one is it makes sure the
+
+ align:start position:0%
+great features one is it makes sure the
+ 
+
+ align:start position:0%
+great features one is it makes sure the
+right amount gets produced and two is it
+
+ align:start position:0%
+right amount gets produced and two is it
+ 
+
+ align:start position:0%
+right amount gets produced and two is it
+makes sure the people who want it the
+
+ align:start position:0%
+makes sure the people who want it the
+ 
+
+ align:start position:0%
+makes sure the people who want it the
+most get it one beautiful feature of
+
+ align:start position:0%
+most get it one beautiful feature of
+ 
+
+ align:start position:0%
+most get it one beautiful feature of
+free markets is that they don't just get
+
+ align:start position:0%
+free markets is that they don't just get
+ 
+
+ align:start position:0%
+free markets is that they don't just get
+you to the right aggregate quantity they
+
+ align:start position:0%
+you to the right aggregate quantity they
+ 
+
+ align:start position:0%
+you to the right aggregate quantity they
+also get the get the goods in the hands
+
+ align:start position:0%
+also get the get the goods in the hands
+ 
+
+ align:start position:0%
+also get the get the goods in the hands
+of people who are willing to pay the
+
+ align:start position:0%
+of people who are willing to pay the
+ 
+
+ align:start position:0%
+of people who are willing to pay the
+most for them and that's what what eBay
+
+ align:start position:0%
+most for them and that's what what eBay
+ 
+
+ align:start position:0%
+most for them and that's what what eBay
+did now one auction eBay got a lot of
+
+ align:start position:0%
+did now one auction eBay got a lot of
+ 
+
+ align:start position:0%
+did now one auction eBay got a lot of
+example got a lot of attention I'm sorry
+
+ align:start position:0%
+example got a lot of attention I'm sorry
+ 
+
+ align:start position:0%
+example got a lot of attention I'm sorry
+got a lot of attention which is that
+
+ align:start position:0%
+got a lot of attention which is that
+ 
+
+ align:start position:0%
+got a lot of attention which is that
+somebody put their kidney for auction on
+
+ align:start position:0%
+somebody put their kidney for auction on
+ 
+
+ align:start position:0%
+somebody put their kidney for auction on
+eBay they auctioned their kidney they
+
+ align:start position:0%
+eBay they auctioned their kidney they
+ 
+
+ align:start position:0%
+eBay they auctioned their kidney they
+said I'll give you my kidney for let the
+
+ align:start position:0%
+said I'll give you my kidney for let the
+ 
+
+ align:start position:0%
+said I'll give you my kidney for let the
+bidding started
+
+ align:start position:0%
+bidding started
+ 
+
+ align:start position:0%
+bidding started
+$225,000 the bidding got up to $5
+
+ align:start position:0%
+$225,000 the bidding got up to $5
+ 
+
+ align:start position:0%
+$225,000 the bidding got up to $5
+million before eBay shut it down and
+
+ align:start position:0%
+million before eBay shut it down and
+ 
+
+ align:start position:0%
+million before eBay shut it down and
+said no auctioning human body parts on
+
+ align:start position:0%
+said no auctioning human body parts on
+ 
+
+ align:start position:0%
+said no auctioning human body parts on
+eBay
+
+ align:start position:0%
+eBay
+ 
+
+ align:start position:0%
+eBay
+okay now I don't know why they stopped
+
+ align:start position:0%
+okay now I don't know why they stopped
+ 
+
+ align:start position:0%
+okay now I don't know why they stopped
+at five million out earlier but whatever
+
+ align:start position:0%
+at five million out earlier but whatever
+ 
+
+ align:start position:0%
+at five million out earlier but whatever
+okay so we can with this example we can
+
+ align:start position:0%
+okay so we can with this example we can
+ 
+
+ align:start position:0%
+okay so we can with this example we can
+ask both a positive and a normative
+
+ align:start position:0%
+ask both a positive and a normative
+ 
+
+ align:start position:0%
+ask both a positive and a normative
+question the positive question is why
+
+ align:start position:0%
+question the positive question is why
+ 
+
+ align:start position:0%
+question the positive question is why
+did the price get so high
+
+ align:start position:0%
+did the price get so high
+ 
+
+ align:start position:0%
+did the price get so high
+and here we only need AAL to supply
+
+ align:start position:0%
+and here we only need AAL to supply
+ 
+
+ align:start position:0%
+and here we only need AAL to supply
+demand
+
+ align:start position:0%
+demand
+ 
+
+ align:start position:0%
+demand
+model the demand for a kidney is going
+
+ align:start position:0%
+model the demand for a kidney is going
+ 
+
+ align:start position:0%
+model the demand for a kidney is going
+to be pretty high if you need a kidney
+
+ align:start position:0%
+to be pretty high if you need a kidney
+ 
+
+ align:start position:0%
+to be pretty high if you need a kidney
+to live you're going to pay
+
+ align:start position:0%
+to live you're going to pay
+ 
+
+ align:start position:0%
+to live you're going to pay
+approximately everything you have to get
+
+ align:start position:0%
+approximately everything you have to get
+ 
+
+ align:start position:0%
+approximately everything you have to get
+it the supply of kidneys on the free
+
+ align:start position:0%
+it the supply of kidneys on the free
+ 
+
+ align:start position:0%
+it the supply of kidneys on the free
+market is pretty low like that was the
+
+ align:start position:0%
+market is pretty low like that was the
+ 
+
+ align:start position:0%
+market is pretty low like that was the
+only one I know of okay so it's a
+
+ align:start position:0%
+only one I know of okay so it's a
+ 
+
+ align:start position:0%
+only one I know of okay so it's a
+classic case with a very high demand and
+
+ align:start position:0%
+classic case with a very high demand and
+ 
+
+ align:start position:0%
+classic case with a very high demand and
+a very low Supply you're going to get a
+
+ align:start position:0%
+a very low Supply you're going to get a
+ 
+
+ align:start position:0%
+a very low Supply you're going to get a
+very high price and so it's not
+
+ align:start position:0%
+very high price and so it's not
+ 
+
+ align:start position:0%
+very high price and so it's not
+surprising the price went up and
+
+ align:start position:0%
+surprising the price went up and
+ 
+
+ align:start position:0%
+surprising the price went up and
+probably would have gone up further if
+
+ align:start position:0%
+probably would have gone up further if
+ 
+
+ align:start position:0%
+probably would have gone up further if
+eBay hadn't shut it
+
+ align:start position:0%
+eBay hadn't shut it
+ 
+
+ align:start position:0%
+eBay hadn't shut it
+down but but now we come to the
+
+ align:start position:0%
+down but but now we come to the
+ 
+
+ align:start position:0%
+down but but now we come to the
+normative question which is more
+
+ align:start position:0%
+normative question which is more
+ 
+
+ align:start position:0%
+normative question which is more
+interesting and
+
+ align:start position:0%
+interesting and
+ 
+
+ align:start position:0%
+interesting and
+harder which is um should we be allowed
+
+ align:start position:0%
+harder which is um should we be allowed
+ 
+
+ align:start position:0%
+harder which is um should we be allowed
+to sell our bodily organs on eBay okay
+
+ align:start position:0%
+to sell our bodily organs on eBay okay
+ 
+
+ align:start position:0%
+to sell our bodily organs on eBay okay
+you might think that this is a question
+
+ align:start position:0%
+you might think that this is a question
+ 
+
+ align:start position:0%
+you might think that this is a question
+here in philosophy class but
+
+ align:start position:0%
+here in philosophy class but
+ 
+
+ align:start position:0%
+here in philosophy class but
+fundamentally it's an economics
+
+ align:start position:0%
+fundamentally it's an economics
+ 
+
+ align:start position:0%
+fundamentally it's an economics
+question okay many folks die in America
+
+ align:start position:0%
+question okay many folks die in America
+ 
+
+ align:start position:0%
+question okay many folks die in America
+because though because we do not have
+
+ align:start position:0%
+because though because we do not have
+ 
+
+ align:start position:0%
+because though because we do not have
+enough organs to help those with organ
+
+ align:start position:0%
+enough organs to help those with organ
+ 
+
+ align:start position:0%
+enough organs to help those with organ
+failure we we have a limited supply of
+
+ align:start position:0%
+failure we we have a limited supply of
+ 
+
+ align:start position:0%
+failure we we have a limited supply of
+organs I hope you all are organ donors
+
+ align:start position:0%
+organs I hope you all are organ donors
+ 
+
+ align:start position:0%
+organs I hope you all are organ donors
+on your driver to licenses doesn't cost
+
+ align:start position:0%
+on your driver to licenses doesn't cost
+ 
+
+ align:start position:0%
+on your driver to licenses doesn't cost
+you anything you're gone in anyway and
+
+ align:start position:0%
+you anything you're gone in anyway and
+ 
+
+ align:start position:0%
+you anything you're gone in anyway and
+it can save a
+
+ align:start position:0%
+it can save a
+ 
+
+ align:start position:0%
+it can save a
+life um but um many people don't do that
+
+ align:start position:0%
+life um but um many people don't do that
+ 
+
+ align:start position:0%
+life um but um many people don't do that
+and uh even if they did we're just we
+
+ align:start position:0%
+and uh even if they did we're just we
+ 
+
+ align:start position:0%
+and uh even if they did we're just we
+have a higher demand for organs than we
+
+ align:start position:0%
+have a higher demand for organs than we
+ 
+
+ align:start position:0%
+have a higher demand for organs than we
+can fit now if someone who wants an
+
+ align:start position:0%
+can fit now if someone who wants an
+ 
+
+ align:start position:0%
+can fit now if someone who wants an
+organ is wealthy and willing to pay a
+
+ align:start position:0%
+organ is wealthy and willing to pay a
+ 
+
+ align:start position:0%
+organ is wealthy and willing to pay a
+lot of money for
+
+ align:start position:0%
+lot of money for
+ 
+
+ align:start position:0%
+lot of money for
+it and there's someone else who says
+
+ align:start position:0%
+it and there's someone else who says
+ 
+
+ align:start position:0%
+it and there's someone else who says
+look I got two kidneys you can function
+
+ align:start position:0%
+look I got two kidneys you can function
+ 
+
+ align:start position:0%
+look I got two kidneys you can function
+just fine with one the oddy of kidney
+
+ align:start position:0%
+just fine with one the oddy of kidney
+ 
+
+ align:start position:0%
+just fine with one the oddy of kidney
+failure is really low someone says look
+
+ align:start position:0%
+failure is really low someone says look
+ 
+
+ align:start position:0%
+failure is really low someone says look
+I am desperate Straits I can't feed my
+
+ align:start position:0%
+I am desperate Straits I can't feed my
+ 
+
+ align:start position:0%
+I am desperate Straits I can't feed my
+family I can't house my
+
+ align:start position:0%
+family I can't house my
+ 
+
+ align:start position:0%
+family I can't house my
+family I could sell one kidney still
+
+ align:start position:0%
+family I could sell one kidney still
+ 
+
+ align:start position:0%
+family I could sell one kidney still
+function fine and change my life forever
+
+ align:start position:0%
+function fine and change my life forever
+ 
+
+ align:start position:0%
+function fine and change my life forever
+educate my children build a house do the
+
+ align:start position:0%
+educate my children build a house do the
+ 
+
+ align:start position:0%
+educate my children build a house do the
+things I need to do why shouldn't we let
+
+ align:start position:0%
+things I need to do why shouldn't we let
+ 
+
+ align:start position:0%
+things I need to do why shouldn't we let
+that happen so standard economics would
+
+ align:start position:0%
+that happen so standard economics would
+ 
+
+ align:start position:0%
+that happen so standard economics would
+say great let them auction their body
+
+ align:start position:0%
+say great let them auction their body
+ 
+
+ align:start position:0%
+say great let them auction their body
+parts but in fact there's reasons why we
+
+ align:start position:0%
+parts but in fact there's reasons why we
+ 
+
+ align:start position:0%
+parts but in fact there's reasons why we
+don't think many there's many reasons
+
+ align:start position:0%
+don't think many there's many reasons
+ 
+
+ align:start position:0%
+don't think many there's many reasons
+why that may not a good outcome what are
+
+ align:start position:0%
+why that may not a good outcome what are
+ 
+
+ align:start position:0%
+why that may not a good outcome what are
+those what are reasons we might not want
+
+ align:start position:0%
+those what are reasons we might not want
+ 
+
+ align:start position:0%
+those what are reasons we might not want
+to just say sure let a
+
+ align:start position:0%
+to just say sure let a
+ 
+
+ align:start position:0%
+to just say sure let a
+rip what are some reasons yeah go
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+ahead yeah so there's fundamentally two
+
+ align:start position:0%
+ahead yeah so there's fundamentally two
+ 
+
+ align:start position:0%
+ahead yeah so there's fundamentally two
+kinds of reasons the first kind is what
+
+ align:start position:0%
+kinds of reasons the first kind is what
+ 
+
+ align:start position:0%
+kinds of reasons the first kind is what
+we'll call market
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+failures market failures are something
+
+ align:start position:0%
+failures market failures are something
+ 
+
+ align:start position:0%
+failures market failures are something
+we're not going to cover for about the
+
+ align:start position:0%
+we're not going to cover for about the
+ 
+
+ align:start position:0%
+we're not going to cover for about the
+first 11 lectures for the first 11
+
+ align:start position:0%
+first 11 lectures for the first 11
+ 
+
+ align:start position:0%
+first 11 lectures for the first 11
+lectures the free market is going to be
+
+ align:start position:0%
+lectures the free market is going to be
+ 
+
+ align:start position:0%
+lectures the free market is going to be
+king let me be very clear with you
+
+ align:start position:0%
+king let me be very clear with you
+ 
+
+ align:start position:0%
+king let me be very clear with you
+economics is fundamentally a right-wing
+
+ align:start position:0%
+economics is fundamentally a right-wing
+ 
+
+ align:start position:0%
+economics is fundamentally a right-wing
+science okay as we'll come clear through
+
+ align:start position:0%
+science okay as we'll come clear through
+ 
+
+ align:start position:0%
+science okay as we'll come clear through
+the semester I'm kind of a leftwing guy
+
+ align:start position:0%
+the semester I'm kind of a leftwing guy
+ 
+
+ align:start position:0%
+the semester I'm kind of a leftwing guy
+but economics is pretty much a
+
+ align:start position:0%
+but economics is pretty much a
+ 
+
+ align:start position:0%
+but economics is pretty much a
+right-wing science in basic economics
+
+ align:start position:0%
+right-wing science in basic economics
+ 
+
+ align:start position:0%
+right-wing science in basic economics
+says the market knows
+
+ align:start position:0%
+says the market knows
+ 
+
+ align:start position:0%
+says the market knows
+best and the and there's only two
+
+ align:start position:0%
+best and the and there's only two
+ 
+
+ align:start position:0%
+best and the and there's only two
+reasons why you should ever interfere
+
+ align:start position:0%
+reasons why you should ever interfere
+ 
+
+ align:start position:0%
+reasons why you should ever interfere
+with with the market and the first is
+
+ align:start position:0%
+with with the market and the first is
+ 
+
+ align:start position:0%
+with with the market and the first is
+because for some reason the Market's not
+
+ align:start position:0%
+because for some reason the Market's not
+ 
+
+ align:start position:0%
+because for some reason the Market's not
+working properly this is an example we
+
+ align:start position:0%
+working properly this is an example we
+ 
+
+ align:start position:0%
+working properly this is an example we
+it would be fine if everyone
+
+ align:start position:0%
+it would be fine if everyone
+ 
+
+ align:start position:0%
+it would be fine if everyone
+knowledgeably went into this
+
+ align:start position:0%
+knowledgeably went into this
+ 
+
+ align:start position:0%
+knowledgeably went into this
+transaction but what if this turns out
+
+ align:start position:0%
+transaction but what if this turns out
+ 
+
+ align:start position:0%
+transaction but what if this turns out
+this can cause people to like force
+
+ align:start position:0%
+this can cause people to like force
+ 
+
+ align:start position:0%
+this can cause people to like force
+force their children to give up their
+
+ align:start position:0%
+force their children to give up their
+ 
+
+ align:start position:0%
+force their children to give up their
+kidney or do things against their will
+
+ align:start position:0%
+kidney or do things against their will
+ 
+
+ align:start position:0%
+kidney or do things against their will
+other criminal activities um what if
+
+ align:start position:0%
+other criminal activities um what if
+ 
+
+ align:start position:0%
+other criminal activities um what if
+people don't really understand how
+
+ align:start position:0%
+people don't really understand how
+ 
+
+ align:start position:0%
+people don't really understand how
+dangerous it is to give your kidney
+
+ align:start position:0%
+dangerous it is to give your kidney
+ 
+
+ align:start position:0%
+dangerous it is to give your kidney
+there's 50,000 Americans every year
+
+ align:start position:0%
+there's 50,000 Americans every year
+ 
+
+ align:start position:0%
+there's 50,000 Americans every year
+there's now currently about 100,000
+
+ align:start position:0%
+there's now currently about 100,000
+ 
+
+ align:start position:0%
+there's now currently about 100,000
+Americans living with hepatitis C which
+
+ align:start position:0%
+Americans living with hepatitis C which
+ 
+
+ align:start position:0%
+Americans living with hepatitis C which
+causes kidney failure he C can live
+
+ align:start position:0%
+causes kidney failure he C can live
+ 
+
+ align:start position:0%
+causes kidney failure he C can live
+dormant for years before you know you
+
+ align:start position:0%
+dormant for years before you know you
+ 
+
+ align:start position:0%
+dormant for years before you know you
+have it what if you give up your kidney
+
+ align:start position:0%
+have it what if you give up your kidney
+ 
+
+ align:start position:0%
+have it what if you give up your kidney
+find hepatitis C then you're dead so
+
+ align:start position:0%
+find hepatitis C then you're dead so
+ 
+
+ align:start position:0%
+find hepatitis C then you're dead so
+there's lots of reasons why I think well
+
+ align:start position:0%
+there's lots of reasons why I think well
+ 
+
+ align:start position:0%
+there's lots of reasons why I think well
+maybe this Market doesn't work quite as
+
+ align:start position:0%
+maybe this Market doesn't work quite as
+ 
+
+ align:start position:0%
+maybe this Market doesn't work quite as
+well as economists say it does people
+
+ align:start position:0%
+well as economists say it does people
+ 
+
+ align:start position:0%
+well as economists say it does people
+might be misinformed people might be F
+
+ align:start position:0%
+might be misinformed people might be F
+ 
+
+ align:start position:0%
+might be misinformed people might be F
+people might be forced to do it what's
+
+ align:start position:0%
+people might be forced to do it what's
+ 
+
+ align:start position:0%
+people might be forced to do it what's
+interesting is the black market is not
+
+ align:start position:0%
+interesting is the black market is not
+ 
+
+ align:start position:0%
+interesting is the black market is not
+necessarily one of those reasons and
+
+ align:start position:0%
+necessarily one of those reasons and
+ 
+
+ align:start position:0%
+necessarily one of those reasons and
+here's why because the black market
+
+ align:start position:0%
+here's why because the black market
+ 
+
+ align:start position:0%
+here's why because the black market
+economists just say is a market let's
+
+ align:start position:0%
+economists just say is a market let's
+ 
+
+ align:start position:0%
+economists just say is a market let's
+say eBay doesn't allow you to sell your
+
+ align:start position:0%
+say eBay doesn't allow you to sell your
+ 
+
+ align:start position:0%
+say eBay doesn't allow you to sell your
+kidneys so you have to sell it on the
+
+ align:start position:0%
+kidneys so you have to sell it on the
+ 
+
+ align:start position:0%
+kidneys so you have to sell it on the
+black market well if there's no other
+
+ align:start position:0%
+black market well if there's no other
+ 
+
+ align:start position:0%
+black market well if there's no other
+market failures that's okay for the same
+
+ align:start position:0%
+market failures that's okay for the same
+ 
+
+ align:start position:0%
+market failures that's okay for the same
+reason economists think it'd be okay to
+
+ align:start position:0%
+reason economists think it'd be okay to
+ 
+
+ align:start position:0%
+reason economists think it'd be okay to
+sell your body parts there's no reason
+
+ align:start position:0%
+sell your body parts there's no reason
+ 
+
+ align:start position:0%
+sell your body parts there's no reason
+why I tell your body parts on a form
+
+ align:start position:0%
+why I tell your body parts on a form
+ 
+
+ align:start position:0%
+why I tell your body parts on a form
+Market informal Market the only reason
+
+ align:start position:0%
+Market informal Market the only reason
+ 
+
+ align:start position:0%
+Market informal Market the only reason
+why it would be bad would that informal
+
+ align:start position:0%
+why it would be bad would that informal
+ 
+
+ align:start position:0%
+why it would be bad would that informal
+Market comes with other unsavory
+
+ align:start position:0%
+Market comes with other unsavory
+ 
+
+ align:start position:0%
+Market comes with other unsavory
+features like forcing people to sell
+
+ align:start position:0%
+features like forcing people to sell
+ 
+
+ align:start position:0%
+features like forcing people to sell
+their body parts or not being informed
+
+ align:start position:0%
+their body parts or not being informed
+ 
+
+ align:start position:0%
+their body parts or not being informed
+that's what it be bad okay what other
+
+ align:start position:0%
+that's what it be bad okay what other
+ 
+
+ align:start position:0%
+that's what it be bad okay what other
+reasons might we care might be worried
+
+ align:start position:0%
+reasons might we care might be worried
+ 
+
+ align:start position:0%
+reasons might we care might be worried
+about people selling the kidneys yeah
+
+ align:start position:0%
+about people selling the kidneys yeah
+ 
+
+ align:start position:0%
+about people selling the kidneys yeah
+why T shouldn't the
+
+ align:start position:0%
+why T shouldn't the
+ 
+
+ align:start position:0%
+why T shouldn't the
+back it would mean that only like really
+
+ align:start position:0%
+back it would mean that only like really
+ 
+
+ align:start position:0%
+back it would mean that only like really
+rich people
+
+ align:start position:0%
+rich people
+ 
+
+ align:start position:0%
+rich people
+great great answers guys the second
+
+ align:start position:0%
+great great answers guys the second
+ 
+
+ align:start position:0%
+great great answers guys the second
+reason we care is what we call Equity or
+
+ align:start position:0%
+reason we care is what we call Equity or
+ 
+
+ align:start position:0%
+reason we care is what we call Equity or
+fairness which is we might not think
+
+ align:start position:0%
+fairness which is we might not think
+ 
+
+ align:start position:0%
+fairness which is we might not think
+it's fair that rich people get to live
+
+ align:start position:0%
+it's fair that rich people get to live
+ 
+
+ align:start position:0%
+it's fair that rich people get to live
+and poor get to live longer and buy the
+
+ align:start position:0%
+and poor get to live longer and buy the
+ 
+
+ align:start position:0%
+and poor get to live longer and buy the
+organs and poor people
+
+ align:start position:0%
+organs and poor people
+ 
+
+ align:start position:0%
+organs and poor people
+don't okay we might think this is that
+
+ align:start position:0%
+don't okay we might think this is that
+ 
+
+ align:start position:0%
+don't okay we might think this is that
+that this is an unfair
+
+ align:start position:0%
+that this is an unfair
+ 
+
+ align:start position:0%
+that this is an unfair
+outcome now this is what's fascinating
+
+ align:start position:0%
+outcome now this is what's fascinating
+ 
+
+ align:start position:0%
+outcome now this is what's fascinating
+about America which is even though we
+
+ align:start position:0%
+about America which is even though we
+ 
+
+ align:start position:0%
+about America which is even though we
+pride ourselves on being the land of the
+
+ align:start position:0%
+pride ourselves on being the land of the
+ 
+
+ align:start position:0%
+pride ourselves on being the land of the
+market economy we also care a lot about
+
+ align:start position:0%
+market economy we also care a lot about
+ 
+
+ align:start position:0%
+market economy we also care a lot about
+fairness as a nation and this is viewed
+
+ align:start position:0%
+fairness as a nation and this is viewed
+ 
+
+ align:start position:0%
+fairness as a nation and this is viewed
+by many as being complately unfair that
+
+ align:start position:0%
+by many as being complately unfair that
+ 
+
+ align:start position:0%
+by many as being complately unfair that
+the Richer you are the more you can just
+
+ align:start position:0%
+the Richer you are the more you can just
+ 
+
+ align:start position:0%
+the Richer you are the more you can just
+buy part body parts off poor
+
+ align:start position:0%
+buy part body parts off poor
+ 
+
+ align:start position:0%
+buy part body parts off poor
+people now here's what's a little bit
+
+ align:start position:0%
+people now here's what's a little bit
+ 
+
+ align:start position:0%
+people now here's what's a little bit
+sad about this class and the sad about
+
+ align:start position:0%
+sad about this class and the sad about
+ 
+
+ align:start position:0%
+sad about this class and the sad about
+the limitation of only having you know
+
+ align:start position:0%
+the limitation of only having you know
+ 
+
+ align:start position:0%
+the limitation of only having you know
+the number of weeks we have which is I'm
+
+ align:start position:0%
+the number of weeks we have which is I'm
+ 
+
+ align:start position:0%
+the number of weeks we have which is I'm
+not going to talk nearly as much about
+
+ align:start position:0%
+not going to talk nearly as much about
+ 
+
+ align:start position:0%
+not going to talk nearly as much about
+Equity as I'd like to 90% of this course
+
+ align:start position:0%
+Equity as I'd like to 90% of this course
+ 
+
+ align:start position:0%
+Equity as I'd like to 90% of this course
+is going to be about efficiency it's
+
+ align:start position:0%
+is going to be about efficiency it's
+ 
+
+ align:start position:0%
+is going to be about efficiency it's
+going to be about does the market work
+
+ align:start position:0%
+going to be about does the market work
+ 
+
+ align:start position:0%
+going to be about does the market work
+does the market deliver the right
+
+ align:start position:0%
+does the market deliver the right
+ 
+
+ align:start position:0%
+does the market deliver the right
+quantity of goods it's not about equity
+
+ align:start position:0%
+quantity of goods it's not about equity
+ 
+
+ align:start position:0%
+quantity of goods it's not about equity
+which is well does that right quantity
+
+ align:start position:0%
+which is well does that right quantity
+ 
+
+ align:start position:0%
+which is well does that right quantity
+end up going end up causing huge
+
+ align:start position:0%
+end up going end up causing huge
+ 
+
+ align:start position:0%
+end up going end up causing huge
+inequality in
+
+ align:start position:0%
+inequality in
+ 
+
+ align:start position:0%
+inequality in
+Society so that is kind of another
+
+ align:start position:0%
+Society so that is kind of another
+ 
+
+ align:start position:0%
+Society so that is kind of another
+reason why we might care okay and we
+
+ align:start position:0%
+reason why we might care okay and we
+ 
+
+ align:start position:0%
+reason why we might care okay and we
+will discuss Equity leing the semester
+
+ align:start position:0%
+will discuss Equity leing the semester
+ 
+
+ align:start position:0%
+will discuss Equity leing the semester
+but unfortunately not to much later all
+
+ align:start position:0%
+but unfortunately not to much later all
+ 
+
+ align:start position:0%
+but unfortunately not to much later all
+right other questions or thoughts about
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that okay let me finally talk about one
+
+ align:start position:0%
+that okay let me finally talk about one
+ 
+
+ align:start position:0%
+that okay let me finally talk about one
+last thing which sort of seems like you
+
+ align:start position:0%
+last thing which sort of seems like you
+ 
+
+ align:start position:0%
+last thing which sort of seems like you
+got to talk about in the first lecture
+
+ align:start position:0%
+got to talk about in the first lecture
+ 
+
+ align:start position:0%
+got to talk about in the first lecture
+of of an economics class which is what
+
+ align:start position:0%
+of of an economics class which is what
+ 
+
+ align:start position:0%
+of of an economics class which is what
+about the underlying structure of the
+
+ align:start position:0%
+about the underlying structure of the
+ 
+
+ align:start position:0%
+about the underlying structure of the
+economy how do we think about different
+
+ align:start position:0%
+economy how do we think about different
+ 
+
+ align:start position:0%
+economy how do we think about different
+models of how economies function and the
+
+ align:start position:0%
+models of how economies function and the
+ 
+
+ align:start position:0%
+models of how economies function and the
+fundamental conflict is between a
+
+ align:start position:0%
+fundamental conflict is between a
+ 
+
+ align:start position:0%
+fundamental conflict is between a
+capitalist
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+model and a command
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+model the capitalist model in its purest
+
+ align:start position:0%
+model the capitalist model in its purest
+ 
+
+ align:start position:0%
+model the capitalist model in its purest
+form What's called the LA fair or let it
+
+ align:start position:0%
+form What's called the LA fair or let it
+ 
+
+ align:start position:0%
+form What's called the LA fair or let it
+be uh model is one where individuals
+
+ align:start position:0%
+be uh model is one where individuals
+ 
+
+ align:start position:0%
+be uh model is one where individuals
+decide what to produce and consume with
+
+ align:start position:0%
+decide what to produce and consume with
+ 
+
+ align:start position:0%
+decide what to produce and consume with
+no interference it's a purely free
+
+ align:start position:0%
+no interference it's a purely free
+ 
+
+ align:start position:0%
+no interference it's a purely free
+market okay it's the market that sort of
+
+ align:start position:0%
+market okay it's the market that sort of
+ 
+
+ align:start position:0%
+market okay it's the market that sort of
+existed 500 years ago before we had sort
+
+ align:start position:0%
+existed 500 years ago before we had sort
+ 
+
+ align:start position:0%
+existed 500 years ago before we had sort
+of the truth is it never existed there's
+
+ align:start position:0%
+of the truth is it never existed there's
+ 
+
+ align:start position:0%
+of the truth is it never existed there's
+no such thing we will do a lot of
+
+ align:start position:0%
+no such thing we will do a lot of
+ 
+
+ align:start position:0%
+no such thing we will do a lot of
+teaching by Extremes in this course
+
+ align:start position:0%
+teaching by Extremes in this course
+ 
+
+ align:start position:0%
+teaching by Extremes in this course
+we'll talk about extremes it's a great
+
+ align:start position:0%
+we'll talk about extremes it's a great
+ 
+
+ align:start position:0%
+we'll talk about extremes it's a great
+learning device but there's no never
+
+ align:start position:0%
+learning device but there's no never
+ 
+
+ align:start position:0%
+learning device but there's no never
+been such as a purely capitalistic
+
+ align:start position:0%
+been such as a purely capitalistic
+ 
+
+ align:start position:0%
+been such as a purely capitalistic
+economy most economies like the US are
+
+ align:start position:0%
+economy most economies like the US are
+ 
+
+ align:start position:0%
+economy most economies like the US are
+Market driven but government and
+
+ align:start position:0%
+Market driven but government and
+ 
+
+ align:start position:0%
+Market driven but government and
+socially constrained what does that mean
+
+ align:start position:0%
+socially constrained what does that mean
+ 
+
+ align:start position:0%
+socially constrained what does that mean
+that means yes we let GM decide how many
+
+ align:start position:0%
+that means yes we let GM decide how many
+ 
+
+ align:start position:0%
+that means yes we let GM decide how many
+cars to produce but we have standards on
+
+ align:start position:0%
+cars to produce but we have standards on
+ 
+
+ align:start position:0%
+cars to produce but we have standards on
+what emissions those cars can have and
+
+ align:start position:0%
+what emissions those cars can have and
+ 
+
+ align:start position:0%
+what emissions those cars can have and
+how safe they have to be in a purely
+
+ align:start position:0%
+how safe they have to be in a purely
+ 
+
+ align:start position:0%
+how safe they have to be in a purely
+capitalist economy GM could produce the
+
+ align:start position:0%
+capitalist economy GM could produce the
+ 
+
+ align:start position:0%
+capitalist economy GM could produce the
+most dangerous cars they wanted no one
+
+ align:start position:0%
+most dangerous cars they wanted no one
+ 
+
+ align:start position:0%
+most dangerous cars they wanted no one
+would care and they could be smog Laden
+
+ align:start position:0%
+would care and they could be smog Laden
+ 
+
+ align:start position:0%
+would care and they could be smog Laden
+and no one would care obviously we don't
+
+ align:start position:0%
+and no one would care obviously we don't
+ 
+
+ align:start position:0%
+and no one would care obviously we don't
+have that in America we have regulations
+
+ align:start position:0%
+have that in America we have regulations
+ 
+
+ align:start position:0%
+have that in America we have regulations
+we have taxes on gas we have rules on
+
+ align:start position:0%
+we have taxes on gas we have rules on
+ 
+
+ align:start position:0%
+we have taxes on gas we have rules on
+what you can learn and where you can
+
+ align:start position:0%
+what you can learn and where you can
+ 
+
+ align:start position:0%
+what you can learn and where you can
+learn it Etc so we have what we call a
+
+ align:start position:0%
+learn it Etc so we have what we call a
+ 
+
+ align:start position:0%
+learn it Etc so we have what we call a
+sort of constrained capitalist economy
+
+ align:start position:0%
+sort of constrained capitalist economy
+ 
+
+ align:start position:0%
+sort of constrained capitalist economy
+where fundamentally the decisions on
+
+ align:start position:0%
+where fundamentally the decisions on
+ 
+
+ align:start position:0%
+where fundamentally the decisions on
+what to produce and what to consume are
+
+ align:start position:0%
+what to produce and what to consume are
+ 
+
+ align:start position:0%
+what to produce and what to consume are
+made by individuals within a set of
+
+ align:start position:0%
+made by individuals within a set of
+ 
+
+ align:start position:0%
+made by individuals within a set of
+rules set up by the government and some
+
+ align:start position:0%
+rules set up by the government and some
+ 
+
+ align:start position:0%
+rules set up by the government and some
+also set up by social
+
+ align:start position:0%
+also set up by social
+ 
+
+ align:start position:0%
+also set up by social
+norms okay now the opposite extreme is
+
+ align:start position:0%
+norms okay now the opposite extreme is
+ 
+
+ align:start position:0%
+norms okay now the opposite extreme is
+what we call a command economy and we
+
+ align:start position:0%
+what we call a command economy and we
+ 
+
+ align:start position:0%
+what we call a command economy and we
+actually had almost the closest model
+
+ align:start position:0%
+actually had almost the closest model
+ 
+
+ align:start position:0%
+actually had almost the closest model
+that could exist to this which was the
+
+ align:start position:0%
+that could exist to this which was the
+ 
+
+ align:start position:0%
+that could exist to this which was the
+Soviet Union of my youth the Soviet
+
+ align:start position:0%
+Soviet Union of my youth the Soviet
+ 
+
+ align:start position:0%
+Soviet Union of my youth the Soviet
+Union of my youth it's typically
+
+ align:start position:0%
+Union of my youth it's typically
+ 
+
+ align:start position:0%
+Union of my youth it's typically
+associated with Communism although it
+
+ align:start position:0%
+associated with Communism although it
+ 
+
+ align:start position:0%
+associated with Communism although it
+doesn't have to be command economies
+
+ align:start position:0%
+doesn't have to be command economies
+ 
+
+ align:start position:0%
+doesn't have to be command economies
+don't have to be associated with
+
+ align:start position:0%
+don't have to be associated with
+ 
+
+ align:start position:0%
+don't have to be associated with
+Communism Germany in World War II was a
+
+ align:start position:0%
+Communism Germany in World War II was a
+ 
+
+ align:start position:0%
+Communism Germany in World War II was a
+command economy in the service of
+
+ align:start position:0%
+command economy in the service of
+ 
+
+ align:start position:0%
+command economy in the service of
+fascism it's typically associated with
+
+ align:start position:0%
+fascism it's typically associated with
+ 
+
+ align:start position:0%
+fascism it's typically associated with
+Communism is what we call a command
+
+ align:start position:0%
+Communism is what we call a command
+ 
+
+ align:start position:0%
+Communism is what we call a command
+economy in in that extreme the
+
+ align:start position:0%
+economy in in that extreme the
+ 
+
+ align:start position:0%
+economy in in that extreme the
+government makes all production
+
+ align:start position:0%
+government makes all production
+ 
+
+ align:start position:0%
+government makes all production
+allocation decisions people don't decide
+
+ align:start position:0%
+allocation decisions people don't decide
+ 
+
+ align:start position:0%
+allocation decisions people don't decide
+what they get the government decides
+
+ align:start position:0%
+what they get the government decides
+ 
+
+ align:start position:0%
+what they get the government decides
+what they get so it's the other extreme
+
+ align:start position:0%
+what they get so it's the other extreme
+ 
+
+ align:start position:0%
+what they get so it's the other extreme
+there's no free
+
+ align:start position:0%
+there's no free
+ 
+
+ align:start position:0%
+there's no free
+transactions it's the government making
+
+ align:start position:0%
+transactions it's the government making
+ 
+
+ align:start position:0%
+transactions it's the government making
+all the rules not just about how much
+
+ align:start position:0%
+all the rules not just about how much
+ 
+
+ align:start position:0%
+all the rules not just about how much
+should be produced but who gets what's
+
+ align:start position:0%
+should be produced but who gets what's
+ 
+
+ align:start position:0%
+should be produced but who gets what's
+produced okay so in the free market the
+
+ align:start position:0%
+produced okay so in the free market the
+ 
+
+ align:start position:0%
+produced okay so in the free market the
+market subject set of government sort of
+
+ align:start position:0%
+market subject set of government sort of
+ 
+
+ align:start position:0%
+market subject set of government sort of
+you guys have bowled there's like the
+
+ align:start position:0%
+you guys have bowled there's like the
+ 
+
+ align:start position:0%
+you guys have bowled there's like the
+bumpers you can up when you're little
+
+ align:start position:0%
+bumpers you can up when you're little
+ 
+
+ align:start position:0%
+bumpers you can up when you're little
+kid and you bowl and they keep the ball
+
+ align:start position:0%
+kid and you bowl and they keep the ball
+ 
+
+ align:start position:0%
+kid and you bowl and they keep the ball
+on that bowling lane so think of the
+
+ align:start position:0%
+on that bowling lane so think of the
+ 
+
+ align:start position:0%
+on that bowling lane so think of the
+government you know in a capital economy
+
+ align:start position:0%
+government you know in a capital economy
+ 
+
+ align:start position:0%
+government you know in a capital economy
+is those sort of those those those uh
+
+ align:start position:0%
+is those sort of those those those uh
+ 
+
+ align:start position:0%
+is those sort of those those those uh
+guides on the side that help keep the
+
+ align:start position:0%
+guides on the side that help keep the
+ 
+
+ align:start position:0%
+guides on the side that help keep the
+ball in the lane but but you get to
+
+ align:start position:0%
+ball in the lane but but you get to
+ 
+
+ align:start position:0%
+ball in the lane but but you get to
+throw the ball on decide what if you're
+
+ align:start position:0%
+throw the ball on decide what if you're
+ 
+
+ align:start position:0%
+throw the ball on decide what if you're
+going to which pin you're going to go
+
+ align:start position:0%
+going to which pin you're going to go
+ 
+
+ align:start position:0%
+going to which pin you're going to go
+for in in command economy they literally
+
+ align:start position:0%
+for in in command economy they literally
+ 
+
+ align:start position:0%
+for in in command economy they literally
+they tell you go to the end of Lane and
+
+ align:start position:0%
+they tell you go to the end of Lane and
+ 
+
+ align:start position:0%
+they tell you go to the end of Lane and
+knock down pin seven okay uh it's a very
+
+ align:start position:0%
+knock down pin seven okay uh it's a very
+ 
+
+ align:start position:0%
+knock down pin seven okay uh it's a very
+it's a very different
+
+ align:start position:0%
+it's a very different
+ 
+
+ align:start position:0%
+it's a very different
+model now in
+
+ align:start position:0%
+model now in
+ 
+
+ align:start position:0%
+model now in
+theory the argument for the command
+
+ align:start position:0%
+theory the argument for the command
+ 
+
+ align:start position:0%
+theory the argument for the command
+model is that it can ensure that the
+
+ align:start position:0%
+model is that it can ensure that the
+ 
+
+ align:start position:0%
+model is that it can ensure that the
+right Goods get produced and distributed
+
+ align:start position:0%
+right Goods get produced and distributed
+ 
+
+ align:start position:0%
+right Goods get produced and distributed
+as fairly as possible the idea this the
+
+ align:start position:0%
+as fairly as possible the idea this the
+ 
+
+ align:start position:0%
+as fairly as possible the idea this the
+theory is quite simple it goes back to
+
+ align:start position:0%
+theory is quite simple it goes back to
+ 
+
+ align:start position:0%
+theory is quite simple it goes back to
+KL marks the theory makes a lot of sense
+
+ align:start position:0%
+KL marks the theory makes a lot of sense
+ 
+
+ align:start position:0%
+KL marks the theory makes a lot of sense
+which is look the government's job is to
+
+ align:start position:0%
+which is look the government's job is to
+ 
+
+ align:start position:0%
+which is look the government's job is to
+make sure society's as well off as
+
+ align:start position:0%
+make sure society's as well off as
+ 
+
+ align:start position:0%
+make sure society's as well off as
+possible it does that by making sure the
+
+ align:start position:0%
+possible it does that by making sure the
+ 
+
+ align:start position:0%
+possible it does that by making sure the
+right things get produced and get to the
+
+ align:start position:0%
+right things get produced and get to the
+ 
+
+ align:start position:0%
+right things get produced and get to the
+right people and we can't trust the
+
+ align:start position:0%
+right people and we can't trust the
+ 
+
+ align:start position:0%
+right people and we can't trust the
+market to do that only the government
+
+ align:start position:0%
+market to do that only the government
+ 
+
+ align:start position:0%
+market to do that only the government
+can do that okay this is a great
+
+ align:start position:0%
+can do that okay this is a great
+ 
+
+ align:start position:0%
+can do that okay this is a great
+argument in theory in practice it
+
+ align:start position:0%
+argument in theory in practice it
+ 
+
+ align:start position:0%
+argument in theory in practice it
+doesn't work and it doesn't work for two
+
+ align:start position:0%
+doesn't work and it doesn't work for two
+ 
+
+ align:start position:0%
+doesn't work and it doesn't work for two
+reasons it first of all it's just too
+
+ align:start position:0%
+reasons it first of all it's just too
+ 
+
+ align:start position:0%
+reasons it first of all it's just too
+damn hard to make all those
+
+ align:start position:0%
+damn hard to make all those
+ 
+
+ align:start position:0%
+damn hard to make all those
+decisions any government no matter how
+
+ align:start position:0%
+decisions any government no matter how
+ 
+
+ align:start position:0%
+decisions any government no matter how
+large and how benevolent cannot make the
+
+ align:start position:0%
+large and how benevolent cannot make the
+ 
+
+ align:start position:0%
+large and how benevolent cannot make the
+enormous massive quantity of billions
+
+ align:start position:0%
+enormous massive quantity of billions
+ 
+
+ align:start position:0%
+enormous massive quantity of billions
+and billions of decisions that need to
+
+ align:start position:0%
+and billions of decisions that need to
+ 
+
+ align:start position:0%
+and billions of decisions that need to
+be made think about every good we
+
+ align:start position:0%
+be made think about every good we
+ 
+
+ align:start position:0%
+be made think about every good we
+consume in America a government deciding
+
+ align:start position:0%
+consume in America a government deciding
+ 
+
+ align:start position:0%
+consume in America a government deciding
+how much of it to make and literally who
+
+ align:start position:0%
+how much of it to make and literally who
+ 
+
+ align:start position:0%
+how much of it to make and literally who
+gets it okay it's overwhelming
+
+ align:start position:0%
+gets it okay it's overwhelming
+ 
+
+ align:start position:0%
+gets it okay it's overwhelming
+governments can't do it so that led to
+
+ align:start position:0%
+governments can't do it so that led to
+ 
+
+ align:start position:0%
+governments can't do it so that led to
+things like in East Germany I was in
+
+ align:start position:0%
+things like in East Germany I was in
+ 
+
+ align:start position:0%
+things like in East Germany I was in
+East Germany a year ago and I went to
+
+ align:start position:0%
+East Germany a year ago and I went to
+ 
+
+ align:start position:0%
+East Germany a year ago and I went to
+went to the Museum of East Germany and
+
+ align:start position:0%
+went to the Museum of East Germany and
+ 
+
+ align:start position:0%
+went to the Museum of East Germany and
+uh they talk about how in in back in
+
+ align:start position:0%
+uh they talk about how in in back in
+ 
+
+ align:start position:0%
+uh they talk about how in in back in
+communist days in East Germany uh no one
+
+ align:start position:0%
+communist days in East Germany uh no one
+ 
+
+ align:start position:0%
+communist days in East Germany uh no one
+had cars but they had so much bread they
+
+ align:start position:0%
+had cars but they had so much bread they
+ 
+
+ align:start position:0%
+had cars but they had so much bread they
+would feed bread to their pigs for food
+
+ align:start position:0%
+would feed bread to their pigs for food
+ 
+
+ align:start position:0%
+would feed bread to their pigs for food
+okay because the government sort of
+
+ align:start position:0%
+okay because the government sort of
+ 
+
+ align:start position:0%
+okay because the government sort of
+screwed up and decided you know
+
+ align:start position:0%
+screwed up and decided you know
+ 
+
+ align:start position:0%
+screwed up and decided you know
+commanded too many too much bread and
+
+ align:start position:0%
+commanded too many too much bread and
+ 
+
+ align:start position:0%
+commanded too many too much bread and
+too few cars okay that's natural it's
+
+ align:start position:0%
+too few cars okay that's natural it's
+ 
+
+ align:start position:0%
+too few cars okay that's natural it's
+going to happen it's just too hard okay
+
+ align:start position:0%
+going to happen it's just too hard okay
+ 
+
+ align:start position:0%
+going to happen it's just too hard okay
+the second problem is that human nature
+
+ align:start position:0%
+the second problem is that human nature
+ 
+
+ align:start position:0%
+the second problem is that human nature
+being what it is a command economy
+
+ align:start position:0%
+being what it is a command economy
+ 
+
+ align:start position:0%
+being what it is a command economy
+inevita leads to massive corruption
+
+ align:start position:0%
+inevita leads to massive corruption
+ 
+
+ align:start position:0%
+inevita leads to massive corruption
+because when a handful of people are in
+
+ align:start position:0%
+because when a handful of people are in
+ 
+
+ align:start position:0%
+because when a handful of people are in
+charge of deciding everything of course
+
+ align:start position:0%
+charge of deciding everything of course
+ 
+
+ align:start position:0%
+charge of deciding everything of course
+they're going to make their lives the
+
+ align:start position:0%
+they're going to make their lives the
+ 
+
+ align:start position:0%
+they're going to make their lives the
+best
+
+ align:start position:0%
+best
+ 
+
+ align:start position:0%
+best
+first so I'm not saying there's not
+
+ align:start position:0%
+first so I'm not saying there's not
+ 
+
+ align:start position:0%
+first so I'm not saying there's not
+corruption in capitalist economies but
+
+ align:start position:0%
+corruption in capitalist economies but
+ 
+
+ align:start position:0%
+corruption in capitalist economies but
+it's sort of inherent in a command
+
+ align:start position:0%
+it's sort of inherent in a command
+ 
+
+ align:start position:0%
+it's sort of inherent in a command
+economy it's inherent because you're
+
+ align:start position:0%
+economy it's inherent because you're
+ 
+
+ align:start position:0%
+economy it's inherent because you're
+giving a set of people the power to
+
+ align:start position:0%
+giving a set of people the power to
+ 
+
+ align:start position:0%
+giving a set of people the power to
+decide who gets what and it's inevitably
+
+ align:start position:0%
+decide who gets what and it's inevitably
+ 
+
+ align:start position:0%
+decide who gets what and it's inevitably
+in human nature they'll decide to give
+
+ align:start position:0%
+in human nature they'll decide to give
+ 
+
+ align:start position:0%
+in human nature they'll decide to give
+themselves the most and
+
+ align:start position:0%
+themselves the most and
+ 
+
+ align:start position:0%
+themselves the most and
+first so that is why really why the
+
+ align:start position:0%
+first so that is why really why the
+ 
+
+ align:start position:0%
+first so that is why really why the
+Soviet Union collapsed because the
+
+ align:start position:0%
+Soviet Union collapsed because the
+ 
+
+ align:start position:0%
+Soviet Union collapsed because the
+command economy simply couldn't get it
+
+ align:start position:0%
+command economy simply couldn't get it
+ 
+
+ align:start position:0%
+command economy simply couldn't get it
+done and let's be clear it did not
+
+ align:start position:0%
+done and let's be clear it did not
+ 
+
+ align:start position:0%
+done and let's be clear it did not
+appear inevitable in the
+
+ align:start position:0%
+appear inevitable in the
+ 
+
+ align:start position:0%
+appear inevitable in the
+1950s there was huge Envy in the US of
+
+ align:start position:0%
+1950s there was huge Envy in the US of
+ 
+
+ align:start position:0%
+1950s there was huge Envy in the US of
+what the Soviet Union was accomplishing
+
+ align:start position:0%
+what the Soviet Union was accomplishing
+ 
+
+ align:start position:0%
+what the Soviet Union was accomplishing
+they came out of a devastating war and
+
+ align:start position:0%
+they came out of a devastating war and
+ 
+
+ align:start position:0%
+they came out of a devastating war and
+built a manufacturing base that was the
+
+ align:start position:0%
+built a manufacturing base that was the
+ 
+
+ align:start position:0%
+built a manufacturing base that was the
+Envy of the entire world even the US
+
+ align:start position:0%
+Envy of the entire world even the US
+ 
+
+ align:start position:0%
+Envy of the entire world even the US
+almost overnight it was incredible
+
+ align:start position:0%
+almost overnight it was incredible
+ 
+
+ align:start position:0%
+almost overnight it was incredible
+and a lot of people questioned whether
+
+ align:start position:0%
+and a lot of people questioned whether
+ 
+
+ align:start position:0%
+and a lot of people questioned whether
+that might after all not be the right
+
+ align:start position:0%
+that might after all not be the right
+ 
+
+ align:start position:0%
+that might after all not be the right
+model it just it turns out over about 30
+
+ align:start position:0%
+model it just it turns out over about 30
+ 
+
+ align:start position:0%
+model it just it turns out over about 30
+years it fell apart because it just
+
+ align:start position:0%
+years it fell apart because it just
+ 
+
+ align:start position:0%
+years it fell apart because it just
+wasn't
+
+ align:start position:0%
+wasn't
+ 
+
+ align:start position:0%
+wasn't
+sustainable now the alternative of
+
+ align:start position:0%
+sustainable now the alternative of
+ 
+
+ align:start position:0%
+sustainable now the alternative of
+course is the uh US economy the capital
+
+ align:start position:0%
+course is the uh US economy the capital
+ 
+
+ align:start position:0%
+course is the uh US economy the capital
+economy which operates by what the
+
+ align:start position:0%
+economy which operates by what the
+ 
+
+ align:start position:0%
+economy which operates by what the
+famous the father of economics Adam
+
+ align:start position:0%
+famous the father of economics Adam
+ 
+
+ align:start position:0%
+famous the father of economics Adam
+Smith calls the Invisible Hand the
+
+ align:start position:0%
+Smith calls the Invisible Hand the
+ 
+
+ align:start position:0%
+Smith calls the Invisible Hand the
+notion invisible hand is you don't need
+
+ align:start position:0%
+notion invisible hand is you don't need
+ 
+
+ align:start position:0%
+notion invisible hand is you don't need
+a government to make all these decisions
+
+ align:start position:0%
+a government to make all these decisions
+ 
+
+ align:start position:0%
+a government to make all these decisions
+because the market makes it for you the
+
+ align:start position:0%
+because the market makes it for you the
+ 
+
+ align:start position:0%
+because the market makes it for you the
+Invisible Hand of the market decides how
+
+ align:start position:0%
+Invisible Hand of the market decides how
+ 
+
+ align:start position:0%
+Invisible Hand of the market decides how
+much you get produced and who should get
+
+ align:start position:0%
+much you get produced and who should get
+ 
+
+ align:start position:0%
+much you get produced and who should get
+it not through any one person making
+
+ align:start position:0%
+it not through any one person making
+ 
+
+ align:start position:0%
+it not through any one person making
+decisions but just through people coming
+
+ align:start position:0%
+decisions but just through people coming
+ 
+
+ align:start position:0%
+decisions but just through people coming
+together in a market and working
+
+ align:start position:0%
+together in a market and working
+ 
+
+ align:start position:0%
+together in a market and working
+together to make those decisions and
+
+ align:start position:0%
+together to make those decisions and
+ 
+
+ align:start position:0%
+together to make those decisions and
+that's what we'll teach you this
+
+ align:start position:0%
+that's what we'll teach you this
+ 
+
+ align:start position:0%
+that's what we'll teach you this
+semester how the market works and how
+
+ align:start position:0%
+semester how the market works and how
+ 
+
+ align:start position:0%
+semester how the market works and how
+those that invisible hand can lead
+
+ align:start position:0%
+those that invisible hand can lead
+ 
+
+ align:start position:0%
+those that invisible hand can lead
+through the magic of the market to the
+
+ align:start position:0%
+through the magic of the market to the
+ 
+
+ align:start position:0%
+through the magic of the market to the
+right Goods being produced and getting
+
+ align:start position:0%
+right Goods being produced and getting
+ 
+
+ align:start position:0%
+right Goods being produced and getting
+in the hands of the right people okay so
+
+ align:start position:0%
+in the hands of the right people okay so
+ 
+
+ align:start position:0%
+in the hands of the right people okay so
+that's a huge advantage and it's worked
+
+ align:start position:0%
+that's a huge advantage and it's worked
+ 
+
+ align:start position:0%
+that's a huge advantage and it's worked
+America is the richest nation in the
+
+ align:start position:0%
+America is the richest nation in the
+ 
+
+ align:start position:0%
+America is the richest nation in the
+world we've grown rapidly for centuries
+
+ align:start position:0%
+world we've grown rapidly for centuries
+ 
+
+ align:start position:0%
+world we've grown rapidly for centuries
+now um and we are um and and we're very
+
+ align:start position:0%
+now um and we are um and and we're very
+ 
+
+ align:start position:0%
+now um and we are um and and we're very
+successful on the other hand it leads to
+
+ align:start position:0%
+successful on the other hand it leads to
+ 
+
+ align:start position:0%
+successful on the other hand it leads to
+tremendous
+
+ align:start position:0%
+tremendous
+ 
+
+ align:start position:0%
+tremendous
+inequality because the way the right
+
+ align:start position:0%
+inequality because the way the right
+ 
+
+ align:start position:0%
+inequality because the way the right
+person to have the good is the person
+
+ align:start position:0%
+person to have the good is the person
+ 
+
+ align:start position:0%
+person to have the good is the person
+who can pay the most for it right in the
+
+ align:start position:0%
+who can pay the most for it right in the
+ 
+
+ align:start position:0%
+who can pay the most for it right in the
+command economy the right person have
+
+ align:start position:0%
+command economy the right person have
+ 
+
+ align:start position:0%
+command economy the right person have
+the good corruption aside is who needs
+
+ align:start position:0%
+the good corruption aside is who needs
+ 
+
+ align:start position:0%
+the good corruption aside is who needs
+it the
+
+ align:start position:0%
+it the
+ 
+
+ align:start position:0%
+it the
+most we take our kidney example the
+
+ align:start position:0%
+most we take our kidney example the
+ 
+
+ align:start position:0%
+most we take our kidney example the
+command economy would say well let's
+
+ align:start position:0%
+command economy would say well let's
+ 
+
+ align:start position:0%
+command economy would say well let's
+find the person close to death and give
+
+ align:start position:0%
+find the person close to death and give
+ 
+
+ align:start position:0%
+find the person close to death and give
+them the kidney the capital econ say
+
+ align:start position:0%
+them the kidney the capital econ say
+ 
+
+ align:start position:0%
+them the kidney the capital econ say
+let's find the person willing to pay the
+
+ align:start position:0%
+let's find the person willing to pay the
+ 
+
+ align:start position:0%
+let's find the person willing to pay the
+most to give them the kidney well that's
+
+ align:start position:0%
+most to give them the kidney well that's
+ 
+
+ align:start position:0%
+most to give them the kidney well that's
+unfair and that is an inevitable outcome
+
+ align:start position:0%
+unfair and that is an inevitable outcome
+ 
+
+ align:start position:0%
+unfair and that is an inevitable outcome
+of a capitalist economy America is the
+
+ align:start position:0%
+of a capitalist economy America is the
+ 
+
+ align:start position:0%
+of a capitalist economy America is the
+most unequal major nation in the world
+
+ align:start position:0%
+most unequal major nation in the world
+ 
+
+ align:start position:0%
+most unequal major nation in the world
+World our inequality dwarfs what we see
+
+ align:start position:0%
+World our inequality dwarfs what we see
+ 
+
+ align:start position:0%
+World our inequality dwarfs what we see
+in other countries around the world the
+
+ align:start position:0%
+in other countries around the world the
+ 
+
+ align:start position:0%
+in other countries around the world the
+top 1% of Americans control 25% of all
+
+ align:start position:0%
+top 1% of Americans control 25% of all
+ 
+
+ align:start position:0%
+top 1% of Americans control 25% of all
+the income in the US which is which is
+
+ align:start position:0%
+the income in the US which is which is
+ 
+
+ align:start position:0%
+the income in the US which is which is
+at least 5% higher than any other major
+
+ align:start position:0%
+at least 5% higher than any other major
+ 
+
+ align:start position:0%
+at least 5% higher than any other major
+nation in the world okay so we have
+
+ align:start position:0%
+nation in the world okay so we have
+ 
+
+ align:start position:0%
+nation in the world okay so we have
+large inequality because basically the
+
+ align:start position:0%
+large inequality because basically the
+ 
+
+ align:start position:0%
+large inequality because basically the
+Mark it's inevitable in a market that'll
+
+ align:start position:0%
+Mark it's inevitable in a market that'll
+ 
+
+ align:start position:0%
+Mark it's inevitable in a market that'll
+happen because people who want to pay
+
+ align:start position:0%
+happen because people who want to pay
+ 
+
+ align:start position:0%
+happen because people who want to pay
+the most get the
+
+ align:start position:0%
+the most get the
+ 
+
+ align:start position:0%
+the most get the
+stuff okay so that gives you the
+
+ align:start position:0%
+stuff okay so that gives you the
+ 
+
+ align:start position:0%
+stuff okay so that gives you the
+tradeoff the consensus I would say among
+
+ align:start position:0%
+tradeoff the consensus I would say among
+ 
+
+ align:start position:0%
+tradeoff the consensus I would say among
+virtually every Economist is that a
+
+ align:start position:0%
+virtually every Economist is that a
+ 
+
+ align:start position:0%
+virtually every Economist is that a
+command economy is not the way to go the
+
+ align:start position:0%
+command economy is not the way to go the
+ 
+
+ align:start position:0%
+command economy is not the way to go the
+debate is within the capitalist
+
+ align:start position:0%
+debate is within the capitalist
+ 
+
+ align:start position:0%
+debate is within the capitalist
+model how far the government should
+
+ align:start position:0%
+model how far the government should
+ 
+
+ align:start position:0%
+model how far the government should
+intervene if you look at countries like
+
+ align:start position:0%
+intervene if you look at countries like
+ 
+
+ align:start position:0%
+intervene if you look at countries like
+Europe they have a much more intervenous
+
+ align:start position:0%
+Europe they have a much more intervenous
+ 
+
+ align:start position:0%
+Europe they have a much more intervenous
+Economist you'll Europe countries being
+
+ align:start position:0%
+Economist you'll Europe countries being
+ 
+
+ align:start position:0%
+Economist you'll Europe countries being
+called socialist they're not socialist
+
+ align:start position:0%
+called socialist they're not socialist
+ 
+
+ align:start position:0%
+called socialist they're not socialist
+socialist means the government controls
+
+ align:start position:0%
+socialist means the government controls
+ 
+
+ align:start position:0%
+socialist means the government controls
+the industry socialist would be there
+
+ align:start position:0%
+the industry socialist would be there
+ 
+
+ align:start position:0%
+the industry socialist would be there
+still consumers don't going decide what
+
+ align:start position:0%
+still consumers don't going decide what
+ 
+
+ align:start position:0%
+still consumers don't going decide what
+to buy but the government produces
+
+ align:start position:0%
+to buy but the government produces
+ 
+
+ align:start position:0%
+to buy but the government produces
+everything the government runs the banks
+
+ align:start position:0%
+everything the government runs the banks
+ 
+
+ align:start position:0%
+everything the government runs the banks
+the government runs the airplanes the
+
+ align:start position:0%
+the government runs the airplanes the
+ 
+
+ align:start position:0%
+the government runs the airplanes the
+government decides how much steel to
+
+ align:start position:0%
+government decides how much steel to
+ 
+
+ align:start position:0%
+government decides how much steel to
+produce the government so in substance a
+
+ align:start position:0%
+produce the government so in substance a
+ 
+
+ align:start position:0%
+produce the government so in substance a
+socialist is sort of halfway between
+
+ align:start position:0%
+socialist is sort of halfway between
+ 
+
+ align:start position:0%
+socialist is sort of halfway between
+capitalist and command economy where the
+
+ align:start position:0%
+capitalist and command economy where the
+ 
+
+ align:start position:0%
+capitalist and command economy where the
+government does the production but
+
+ align:start position:0%
+government does the production but
+ 
+
+ align:start position:0%
+government does the production but
+Market forces decide the
+
+ align:start position:0%
+Market forces decide the
+ 
+
+ align:start position:0%
+Market forces decide the
+allocation that's not true in any other
+
+ align:start position:0%
+allocation that's not true in any other
+ 
+
+ align:start position:0%
+allocation that's not true in any other
+major country in the world okay these
+
+ align:start position:0%
+major country in the world okay these
+ 
+
+ align:start position:0%
+major country in the world okay these
+countries are all different levels of
+
+ align:start position:0%
+countries are all different levels of
+ 
+
+ align:start position:0%
+countries are all different levels of
+constrained capitalist economies they're
+
+ align:start position:0%
+constrained capitalist economies they're
+ 
+
+ align:start position:0%
+constrained capitalist economies they're
+all different width of those bowling
+
+ align:start position:0%
+all different width of those bowling
+ 
+
+ align:start position:0%
+all different width of those bowling
+alleys okay in Europe and many European
+
+ align:start position:0%
+alleys okay in Europe and many European
+ 
+
+ align:start position:0%
+alleys okay in Europe and many European
+nations they have much more constrained
+
+ align:start position:0%
+nations they have much more constrained
+ 
+
+ align:start position:0%
+nations they have much more constrained
+capitalist economies much higher taxes
+
+ align:start position:0%
+capitalist economies much higher taxes
+ 
+
+ align:start position:0%
+capitalist economies much higher taxes
+much more government prevention also
+
+ align:start position:0%
+much more government prevention also
+ 
+
+ align:start position:0%
+much more government prevention also
+much more equal and we'll be talking
+
+ align:start position:0%
+much more equal and we'll be talking
+ 
+
+ align:start position:0%
+much more equal and we'll be talking
+about this semester and what I focus on
+
+ align:start position:0%
+about this semester and what I focus on
+ 
+
+ align:start position:0%
+about this semester and what I focus on
+much more in my course 1441 is how do we
+
+ align:start position:0%
+much more in my course 1441 is how do we
+ 
+
+ align:start position:0%
+much more in my course 1441 is how do we
+think about those
+
+ align:start position:0%
+think about those
+ 
+
+ align:start position:0%
+think about those
+trade-offs between a Freer economy which
+
+ align:start position:0%
+trade-offs between a Freer economy which
+ 
+
+ align:start position:0%
+trade-offs between a Freer economy which
+is larger but leads to more inequality
+
+ align:start position:0%
+is larger but leads to more inequality
+ 
+
+ align:start position:0%
+is larger but leads to more inequality
+than the US and a less free economy with
+
+ align:start position:0%
+than the US and a less free economy with
+ 
+
+ align:start position:0%
+than the US and a less free economy with
+less
+
+ align:start position:0%
+less
+ 
+
+ align:start position:0%
+less
+inequality okay so to guide you to where
+
+ align:start position:0%
+inequality okay so to guide you to where
+ 
+
+ align:start position:0%
+inequality okay so to guide you to where
+we're going to go I'm really big on sort
+
+ align:start position:0%
+we're going to go I'm really big on sort
+ 
+
+ align:start position:0%
+we're going to go I'm really big on sort
+of making sure you have a big picture of
+
+ align:start position:0%
+of making sure you have a big picture of
+ 
+
+ align:start position:0%
+of making sure you have a big picture of
+where we are in this class and once
+
+ align:start position:0%
+where we are in this class and once
+ 
+
+ align:start position:0%
+where we are in this class and once
+again if you're confused not just about
+
+ align:start position:0%
+again if you're confused not just about
+ 
+
+ align:start position:0%
+again if you're confused not just about
+the little picture but the big picture
+
+ align:start position:0%
+the little picture but the big picture
+ 
+
+ align:start position:0%
+the little picture but the big picture
+let's talk I do urge people come talk to
+
+ align:start position:0%
+let's talk I do urge people come talk to
+ 
+
+ align:start position:0%
+let's talk I do urge people come talk to
+me I generally my rule is if it's like a
+
+ align:start position:0%
+me I generally my rule is if it's like a
+ 
+
+ align:start position:0%
+me I generally my rule is if it's like a
+question about a problem set go see the
+
+ align:start position:0%
+question about a problem set go see the
+ 
+
+ align:start position:0%
+question about a problem set go see the
+Tas if it's a question about like I
+
+ align:start position:0%
+Tas if it's a question about like I
+ 
+
+ align:start position:0%
+Tas if it's a question about like I
+don't understand a concept or I want to
+
+ align:start position:0%
+don't understand a concept or I want to
+ 
+
+ align:start position:0%
+don't understand a concept or I want to
+talk about economics in general or life
+
+ align:start position:0%
+talk about economics in general or life
+ 
+
+ align:start position:0%
+talk about economics in general or life
+in general or music or whatever then
+
+ align:start position:0%
+in general or music or whatever then
+ 
+
+ align:start position:0%
+in general or music or whatever then
+come see me okay and I really do urge
+
+ align:start position:0%
+come see me okay and I really do urge
+ 
+
+ align:start position:0%
+come see me okay and I really do urge
+you folks to come come see me uh now
+
+ align:start position:0%
+you folks to come come see me uh now
+ 
+
+ align:start position:0%
+you folks to come come see me uh now
+that I'm chair going I have to be around
+
+ align:start position:0%
+that I'm chair going I have to be around
+ 
+
+ align:start position:0%
+that I'm chair going I have to be around
+all the time so I'm around plenty of
+
+ align:start position:0%
+all the time so I'm around plenty of
+ 
+
+ align:start position:0%
+all the time so I'm around plenty of
+time please just make an appointment and
+
+ align:start position:0%
+time please just make an appointment and
+ 
+
+ align:start position:0%
+time please just make an appointment and
+come see me so where we're going to go
+
+ align:start position:0%
+come see me so where we're going to go
+ 
+
+ align:start position:0%
+come see me so where we're going to go
+from here what we're going to do like I
+
+ align:start position:0%
+from here what we're going to do like I
+ 
+
+ align:start position:0%
+from here what we're going to do like I
+said is the next few lectures we're
+
+ align:start position:0%
+said is the next few lectures we're
+ 
+
+ align:start position:0%
+said is the next few lectures we're
+going to map out what makes a demand
+
+ align:start position:0%
+going to map out what makes a demand
+ 
+
+ align:start position:0%
+going to map out what makes a demand
+curve then we're going to map out what
+
+ align:start position:0%
+curve then we're going to map out what
+ 
+
+ align:start position:0%
+curve then we're going to map out what
+makes a supply curve then we're going to
+
+ align:start position:0%
+makes a supply curve then we're going to
+ 
+
+ align:start position:0%
+makes a supply curve then we're going to
+put them together and talk about
+
+ align:start position:0%
+put them together and talk about
+ 
+
+ align:start position:0%
+put them together and talk about
+basically in some sense come back to
+
+ align:start position:0%
+basically in some sense come back to
+ 
+
+ align:start position:0%
+basically in some sense come back to
+where we started but now with an
+
+ align:start position:0%
+where we started but now with an
+ 
+
+ align:start position:0%
+where we started but now with an
+understanding of what demand and Supply
+
+ align:start position:0%
+understanding of what demand and Supply
+ 
+
+ align:start position:0%
+understanding of what demand and Supply
+mean and why the equilibrium makes sense
+
+ align:start position:0%
+mean and why the equilibrium makes sense
+ 
+
+ align:start position:0%
+mean and why the equilibrium makes sense
+we'll then talk about we'll then turn to
+
+ align:start position:0%
+we'll then talk about we'll then turn to
+ 
+
+ align:start position:0%
+we'll then talk about we'll then turn to
+normative economics and talk about why
+
+ align:start position:0%
+normative economics and talk about why
+ 
+
+ align:start position:0%
+normative economics and talk about why
+the market equilibrium is really the
+
+ align:start position:0%
+the market equilibrium is really the
+ 
+
+ align:start position:0%
+the market equilibrium is really the
+best
+
+ align:start position:0%
+best
+ 
+
+ align:start position:0%
+best
+outcome we're then going to start to
+
+ align:start position:0%
+outcome we're then going to start to
+ 
+
+ align:start position:0%
+outcome we're then going to start to
+talk about where the standard so it's
+
+ align:start position:0%
+talk about where the standard so it's
+ 
+
+ align:start position:0%
+talk about where the standard so it's
+been about the first I would say half of
+
+ align:start position:0%
+been about the first I would say half of
+ 
+
+ align:start position:0%
+been about the first I would say half of
+the class on the standard economic model
+
+ align:start position:0%
+the class on the standard economic model
+ 
+
+ align:start position:0%
+the class on the standard economic model
+the second half of the class will be
+
+ align:start position:0%
+the second half of the class will be
+ 
+
+ align:start position:0%
+the second half of the class will be
+focused on where the standard model
+
+ align:start position:0%
+focused on where the standard model
+ 
+
+ align:start position:0%
+focused on where the standard model
+breaks down
+
+ align:start position:0%
+breaks down
+ 
+
+ align:start position:0%
+breaks down
+what happens when there's monopolies
+
+ align:start position:0%
+what happens when there's monopolies
+ 
+
+ align:start position:0%
+what happens when there's monopolies
+like Google effectively a monopoly on
+
+ align:start position:0%
+like Google effectively a monopoly on
+ 
+
+ align:start position:0%
+like Google effectively a monopoly on
+search engines what happens when we want
+
+ align:start position:0%
+search engines what happens when we want
+ 
+
+ align:start position:0%
+search engines what happens when we want
+to trade with other countries what
+
+ align:start position:0%
+to trade with other countries what
+ 
+
+ align:start position:0%
+to trade with other countries what
+happens when we have to decide how much
+
+ align:start position:0%
+happens when we have to decide how much
+ 
+
+ align:start position:0%
+happens when we have to decide how much
+to save and how hard to work what
+
+ align:start position:0%
+to save and how hard to work what
+ 
+
+ align:start position:0%
+to save and how hard to work what
+happens when we have to decide um where
+
+ align:start position:0%
+happens when we have to decide um where
+ 
+
+ align:start position:0%
+happens when we have to decide um where
+to invest and what to do about global
+
+ align:start position:0%
+to invest and what to do about global
+ 
+
+ align:start position:0%
+to invest and what to do about global
+warming these are all the questions
+
+ align:start position:0%
+warming these are all the questions
+ 
+
+ align:start position:0%
+warming these are all the questions
+we'll tackle in the second half of the
+
+ align:start position:0%
+we'll tackle in the second half of the
+ 
+
+ align:start position:0%
+we'll tackle in the second half of the
+class okay so let me stop there and I
+
+ align:start position:0%
+class okay so let me stop there and I
+ 
+
+ align:start position:0%
+class okay so let me stop there and I
+hope I'll be seeing you all uh every
+
+ align:start position:0%
+hope I'll be seeing you all uh every
+ 
+
+ align:start position:0%
+hope I'll be seeing you all uh every
+Monday and Wednesday thank you
\ No newline at end of file
diff --git a/9SaekDRtGFw.txt b/9SaekDRtGFw.txt
new file mode 100644
index 0000000000000000000000000000000000000000..ade18b2856452645dbd2e7de7196a853168e3c42
--- /dev/null
+++ b/9SaekDRtGFw.txt
@@ -0,0 +1,1083 @@
+align:start position:0%
+ 
+Video
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+five, prototype problems, not products.
+
+ align:start position:0%
+five, prototype problems, not products.
+ 
+
+ align:start position:0%
+five, prototype problems, not products.
+No one likes uncertainty. If you're
+
+ align:start position:0%
+No one likes uncertainty. If you're
+ 
+
+ align:start position:0%
+No one likes uncertainty. If you're
+innovating, that's all you have. Think
+
+ align:start position:0%
+innovating, that's all you have. Think
+ 
+
+ align:start position:0%
+innovating, that's all you have. Think
+about it. You're tackling a problem no
+
+ align:start position:0%
+about it. You're tackling a problem no
+ 
+
+ align:start position:0%
+about it. You're tackling a problem no
+one has before. without a ready-made
+
+ align:start position:0%
+one has before. without a ready-made
+ 
+
+ align:start position:0%
+one has before. without a ready-made
+problem statement, with a technology no
+
+ align:start position:0%
+problem statement, with a technology no
+ 
+
+ align:start position:0%
+problem statement, with a technology no
+one has used quite that way before and
+
+ align:start position:0%
+one has used quite that way before and
+ 
+
+ align:start position:0%
+one has used quite that way before and
+you're working off a hunch. Really, all
+
+ align:start position:0%
+you're working off a hunch. Really, all
+ 
+
+ align:start position:0%
+you're working off a hunch. Really, all
+you have is uncertainty. I am using the
+
+ align:start position:0%
+you have is uncertainty. I am using the
+ 
+
+ align:start position:0%
+you have is uncertainty. I am using the
+word hunch because it's the best word in
+
+ align:start position:0%
+word hunch because it's the best word in
+ 
+
+ align:start position:0%
+word hunch because it's the best word in
+the English language to describe the
+
+ align:start position:0%
+the English language to describe the
+ 
+
+ align:start position:0%
+the English language to describe the
+state of your idea at the very start.
+
+ align:start position:0%
+state of your idea at the very start.
+ 
+
+ align:start position:0%
+state of your idea at the very start.
+When you start, that idea isn't really
+
+ align:start position:0%
+When you start, that idea isn't really
+ 
+
+ align:start position:0%
+When you start, that idea isn't really
+fleshed out. At best, it's something
+
+ align:start position:0%
+fleshed out. At best, it's something
+ 
+
+ align:start position:0%
+fleshed out. At best, it's something
+exciting you want to work on, but you
+
+ align:start position:0%
+exciting you want to work on, but you
+ 
+
+ align:start position:0%
+exciting you want to work on, but you
+know you need to flesh it out before you
+
+ align:start position:0%
+know you need to flesh it out before you
+ 
+
+ align:start position:0%
+know you need to flesh it out before you
+can even work on it. And so instead of
+
+ align:start position:0%
+can even work on it. And so instead of
+ 
+
+ align:start position:0%
+can even work on it. And so instead of
+talking about ideas and putting all
+
+ align:start position:0%
+talking about ideas and putting all
+ 
+
+ align:start position:0%
+talking about ideas and putting all
+those attributes and ideas as scalable,
+
+ align:start position:0%
+those attributes and ideas as scalable,
+ 
+
+ align:start position:0%
+those attributes and ideas as scalable,
+disruptive, and what not, I invite you
+
+ align:start position:0%
+disruptive, and what not, I invite you
+ 
+
+ align:start position:0%
+disruptive, and what not, I invite you
+to think of everything you're thinking
+
+ align:start position:0%
+to think of everything you're thinking
+ 
+
+ align:start position:0%
+to think of everything you're thinking
+about at the start as a hunch, something
+
+ align:start position:0%
+about at the start as a hunch, something
+ 
+
+ align:start position:0%
+about at the start as a hunch, something
+that should get you excited for what
+
+ align:start position:0%
+that should get you excited for what
+ 
+
+ align:start position:0%
+that should get you excited for what
+comes next, as opposed to stressed out
+
+ align:start position:0%
+comes next, as opposed to stressed out
+ 
+
+ align:start position:0%
+comes next, as opposed to stressed out
+for how big or disruptive it needs to
+
+ align:start position:0%
+for how big or disruptive it needs to
+ 
+
+ align:start position:0%
+for how big or disruptive it needs to
+be. The only way to move forward is to
+
+ align:start position:0%
+be. The only way to move forward is to
+ 
+
+ align:start position:0%
+be. The only way to move forward is to
+get real. The sooner the better, so you
+
+ align:start position:0%
+get real. The sooner the better, so you
+ 
+
+ align:start position:0%
+get real. The sooner the better, so you
+can get on with the job, which I told
+
+ align:start position:0%
+can get on with the job, which I told
+ 
+
+ align:start position:0%
+can get on with the job, which I told
+you already, is fixing what's wrong
+
+ align:start position:0%
+you already, is fixing what's wrong
+ 
+
+ align:start position:0%
+you already, is fixing what's wrong
+about your idea. You start by
+
+ align:start position:0%
+about your idea. You start by
+ 
+
+ align:start position:0%
+about your idea. You start by
+prototyping the problem. Yes, the
+
+ align:start position:0%
+prototyping the problem. Yes, the
+ 
+
+ align:start position:0%
+prototyping the problem. Yes, the
+problem. You may be tempted to start
+
+ align:start position:0%
+problem. You may be tempted to start
+ 
+
+ align:start position:0%
+problem. You may be tempted to start
+prototyping some product or the pitch.
+
+ align:start position:0%
+prototyping some product or the pitch.
+ 
+
+ align:start position:0%
+prototyping some product or the pitch.
+But if a user, the product and the
+
+ align:start position:0%
+But if a user, the product and the
+ 
+
+ align:start position:0%
+But if a user, the product and the
+solution are known, then someone else
+
+ align:start position:0%
+solution are known, then someone else
+ 
+
+ align:start position:0%
+solution are known, then someone else
+must have worked out the problem for you
+
+ align:start position:0%
+must have worked out the problem for you
+ 
+
+ align:start position:0%
+must have worked out the problem for you
+like in math class. That's how much we
+
+ align:start position:0%
+like in math class. That's how much we
+ 
+
+ align:start position:0%
+like in math class. That's how much we
+dislike uncertainty. This is how it
+
+ align:start position:0%
+dislike uncertainty. This is how it
+ 
+
+ align:start position:0%
+dislike uncertainty. This is how it
+typically goes. You end up taking a
+
+ align:start position:0%
+typically goes. You end up taking a
+ 
+
+ align:start position:0%
+typically goes. You end up taking a
+gamble on the solution you imagined and
+
+ align:start position:0%
+gamble on the solution you imagined and
+ 
+
+ align:start position:0%
+gamble on the solution you imagined and
+stop paying attention to the problem.
+
+ align:start position:0%
+stop paying attention to the problem.
+ 
+
+ align:start position:0%
+stop paying attention to the problem.
+You leave no room for being wrong. And
+
+ align:start position:0%
+You leave no room for being wrong. And
+ 
+
+ align:start position:0%
+You leave no room for being wrong. And
+by the time you discover how you were
+
+ align:start position:0%
+by the time you discover how you were
+ 
+
+ align:start position:0%
+by the time you discover how you were
+wrong, failing is the only viable option
+
+ align:start position:0%
+wrong, failing is the only viable option
+ 
+
+ align:start position:0%
+wrong, failing is the only viable option
+you have left. In 2013, in an interview
+
+ align:start position:0%
+you have left. In 2013, in an interview
+ 
+
+ align:start position:0%
+you have left. In 2013, in an interview
+with National Public Radio, Chris
+
+ align:start position:0%
+with National Public Radio, Chris
+ 
+
+ align:start position:0%
+with National Public Radio, Chris
+Hatfield, the Canadian astronaut,
+
+ align:start position:0%
+Hatfield, the Canadian astronaut,
+ 
+
+ align:start position:0%
+Hatfield, the Canadian astronaut,
+described how astronauts prepare for a
+
+ align:start position:0%
+described how astronauts prepare for a
+ 
+
+ align:start position:0%
+described how astronauts prepare for a
+mission to the space station in a way
+
+ align:start position:0%
+mission to the space station in a way
+ 
+
+ align:start position:0%
+mission to the space station in a way
+that I believe captures the difference
+
+ align:start position:0%
+that I believe captures the difference
+ 
+
+ align:start position:0%
+that I believe captures the difference
+between prototyping a problem and
+
+ align:start position:0%
+between prototyping a problem and
+ 
+
+ align:start position:0%
+between prototyping a problem and
+focusing on the solution.
+
+ align:start position:0%
+focusing on the solution.
+ 
+
+ align:start position:0%
+focusing on the solution.
+Half of the risk of a six-month flight
+
+ align:start position:0%
+Half of the risk of a six-month flight
+ 
+
+ align:start position:0%
+Half of the risk of a six-month flight
+is in the first 9 minutes. So, as a
+
+ align:start position:0%
+is in the first 9 minutes. So, as a
+ 
+
+ align:start position:0%
+is in the first 9 minutes. So, as a
+crew, how do you stay focused and how do
+
+ align:start position:0%
+crew, how do you stay focused and how do
+ 
+
+ align:start position:0%
+crew, how do you stay focused and how do
+you not get u paralyzed by the fear of
+
+ align:start position:0%
+you not get u paralyzed by the fear of
+ 
+
+ align:start position:0%
+you not get u paralyzed by the fear of
+it? And the way we do it is to break
+
+ align:start position:0%
+it? And the way we do it is to break
+ 
+
+ align:start position:0%
+it? And the way we do it is to break
+down what are the risks. And a nice way
+
+ align:start position:0%
+down what are the risks. And a nice way
+ 
+
+ align:start position:0%
+down what are the risks. And a nice way
+to keep reminding yourself is what's the
+
+ align:start position:0%
+to keep reminding yourself is what's the
+ 
+
+ align:start position:0%
+to keep reminding yourself is what's the
+next thing that's going to kill me? And
+
+ align:start position:0%
+next thing that's going to kill me? And
+ 
+
+ align:start position:0%
+next thing that's going to kill me? And
+it might be 5 seconds away. It might be
+
+ align:start position:0%
+it might be 5 seconds away. It might be
+ 
+
+ align:start position:0%
+it might be 5 seconds away. It might be
+an inadvertent engine shutdown or it
+
+ align:start position:0%
+an inadvertent engine shutdown or it
+ 
+
+ align:start position:0%
+an inadvertent engine shutdown or it
+might be uh staging of the solid rockets
+
+ align:start position:0%
+might be uh staging of the solid rockets
+ 
+
+ align:start position:0%
+might be uh staging of the solid rockets
+coming off or it might be you know some
+
+ align:start position:0%
+coming off or it might be you know some
+ 
+
+ align:start position:0%
+coming off or it might be you know some
+transition or or or some some key next
+
+ align:start position:0%
+transition or or or some some key next
+ 
+
+ align:start position:0%
+transition or or or some some key next
+thing. We've already say had one
+
+ align:start position:0%
+thing. We've already say had one
+ 
+
+ align:start position:0%
+thing. We've already say had one
+computer fail and we've had one
+
+ align:start position:0%
+computer fail and we've had one
+ 
+
+ align:start position:0%
+computer fail and we've had one
+hydraulic system fail. So if these three
+
+ align:start position:0%
+hydraulic system fail. So if these three
+ 
+
+ align:start position:0%
+hydraulic system fail. So if these three
+things fail now we're you know we need
+
+ align:start position:0%
+things fail now we're you know we need
+ 
+
+ align:start position:0%
+things fail now we're you know we need
+to react right away or we're done. So we
+
+ align:start position:0%
+to react right away or we're done. So we
+ 
+
+ align:start position:0%
+to react right away or we're done. So we
+don't just live with that though. And
+
+ align:start position:0%
+don't just live with that though. And
+ 
+
+ align:start position:0%
+don't just live with that though. And
+and the thing that is really useful I
+
+ align:start position:0%
+and the thing that is really useful I
+ 
+
+ align:start position:0%
+and the thing that is really useful I
+think out of all this is we dig into it
+
+ align:start position:0%
+think out of all this is we dig into it
+ 
+
+ align:start position:0%
+think out of all this is we dig into it
+so deeply and we look at okay so this
+
+ align:start position:0%
+so deeply and we look at okay so this
+ 
+
+ align:start position:0%
+so deeply and we look at okay so this
+might kill us. This is something that
+
+ align:start position:0%
+might kill us. This is something that
+ 
+
+ align:start position:0%
+might kill us. This is something that
+would normally panic us. Let's get
+
+ align:start position:0%
+would normally panic us. Let's get
+ 
+
+ align:start position:0%
+would normally panic us. Let's get
+ready. Let's think about it and we go
+
+ align:start position:0%
+ready. Let's think about it and we go
+ 
+
+ align:start position:0%
+ready. Let's think about it and we go
+into every excruciating detail of why
+
+ align:start position:0%
+into every excruciating detail of why
+ 
+
+ align:start position:0%
+into every excruciating detail of why
+that might affect what we're doing and
+
+ align:start position:0%
+that might affect what we're doing and
+ 
+
+ align:start position:0%
+that might affect what we're doing and
+what we can do to resolve it and have a
+
+ align:start position:0%
+what we can do to resolve it and have a
+ 
+
+ align:start position:0%
+what we can do to resolve it and have a
+plan and be comfortable with it and
+
+ align:start position:0%
+plan and be comfortable with it and
+ 
+
+ align:start position:0%
+plan and be comfortable with it and
+practice it. In this interview,
+
+ align:start position:0%
+practice it. In this interview,
+ 
+
+ align:start position:0%
+practice it. In this interview,
+astronaut Chris Hatfield is talking
+
+ align:start position:0%
+astronaut Chris Hatfield is talking
+ 
+
+ align:start position:0%
+astronaut Chris Hatfield is talking
+about focusing on the problem. To them,
+
+ align:start position:0%
+about focusing on the problem. To them,
+ 
+
+ align:start position:0%
+about focusing on the problem. To them,
+that's going to the space station and
+
+ align:start position:0%
+that's going to the space station and
+ 
+
+ align:start position:0%
+that's going to the space station and
+making it back to Earth. And the way
+
+ align:start position:0%
+making it back to Earth. And the way
+ 
+
+ align:start position:0%
+making it back to Earth. And the way
+they do it is by discovering what might
+
+ align:start position:0%
+they do it is by discovering what might
+ 
+
+ align:start position:0%
+they do it is by discovering what might
+go wrong and finding ways to fix it in
+
+ align:start position:0%
+go wrong and finding ways to fix it in
+ 
+
+ align:start position:0%
+go wrong and finding ways to fix it in
+the rocket, through practice, or
+
+ align:start position:0%
+the rocket, through practice, or
+ 
+
+ align:start position:0%
+the rocket, through practice, or
+whatever. When the mission starts, they
+
+ align:start position:0%
+whatever. When the mission starts, they
+ 
+
+ align:start position:0%
+whatever. When the mission starts, they
+are prepared for everything they
+
+ align:start position:0%
+are prepared for everything they
+ 
+
+ align:start position:0%
+are prepared for everything they
+foresaw, and they're ready to handle
+
+ align:start position:0%
+foresaw, and they're ready to handle
+ 
+
+ align:start position:0%
+foresaw, and they're ready to handle
+many things they could not have
+
+ align:start position:0%
+many things they could not have
+ 
+
+ align:start position:0%
+many things they could not have
+predicted.
+
+ align:start position:0%
+predicted.
+ 
+
+ align:start position:0%
+predicted.
+That is what I mean by prototyping the
+
+ align:start position:0%
+That is what I mean by prototyping the
+ 
+
+ align:start position:0%
+That is what I mean by prototyping the
+problem.
+
+ align:start position:0%
+problem.
+ 
+
+ align:start position:0%
+problem.
+When you prototype the problem, your
+
+ align:start position:0%
+When you prototype the problem, your
+ 
+
+ align:start position:0%
+When you prototype the problem, your
+goal is to make the problem tangible
+
+ align:start position:0%
+goal is to make the problem tangible
+ 
+
+ align:start position:0%
+goal is to make the problem tangible
+enough for you and others. The more
+
+ align:start position:0%
+enough for you and others. The more
+ 
+
+ align:start position:0%
+enough for you and others. The more
+tangible your description of the
+
+ align:start position:0%
+tangible your description of the
+ 
+
+ align:start position:0%
+tangible your description of the
+problem, the easier it will be for you
+
+ align:start position:0%
+problem, the easier it will be for you
+ 
+
+ align:start position:0%
+problem, the easier it will be for you
+and them to see ways to solve the
+
+ align:start position:0%
+and them to see ways to solve the
+ 
+
+ align:start position:0%
+and them to see ways to solve the
+problem. In contrast, prototyping a
+
+ align:start position:0%
+problem. In contrast, prototyping a
+ 
+
+ align:start position:0%
+problem. In contrast, prototyping a
+madeup solution for a problem you do not
+
+ align:start position:0%
+madeup solution for a problem you do not
+ 
+
+ align:start position:0%
+madeup solution for a problem you do not
+understand is like putting the carriage
+
+ align:start position:0%
+understand is like putting the carriage
+ 
+
+ align:start position:0%
+understand is like putting the carriage
+before the horse. You do not want to
+
+ align:start position:0%
+before the horse. You do not want to
+ 
+
+ align:start position:0%
+before the horse. You do not want to
+wait until launch day to see if you're
+
+ align:start position:0%
+wait until launch day to see if you're
+ 
+
+ align:start position:0%
+wait until launch day to see if you're
+working on the problem. If you do,
+
+ align:start position:0%
+working on the problem. If you do,
+ 
+
+ align:start position:0%
+working on the problem. If you do,
+you'll miss out on everything that's not
+
+ align:start position:0%
+you'll miss out on everything that's not
+ 
+
+ align:start position:0%
+you'll miss out on everything that's not
+captured by what you imagined to be the
+
+ align:start position:0%
+captured by what you imagined to be the
+ 
+
+ align:start position:0%
+captured by what you imagined to be the
+solution. It would be as if the
+
+ align:start position:0%
+solution. It would be as if the
+ 
+
+ align:start position:0%
+solution. It would be as if the
+astronauts had picked ahead of time the
+
+ align:start position:0%
+astronauts had picked ahead of time the
+ 
+
+ align:start position:0%
+astronauts had picked ahead of time the
+one thing that might go wrong and
+
+ align:start position:0%
+one thing that might go wrong and
+ 
+
+ align:start position:0%
+one thing that might go wrong and
+prepared only for that. There's more I
+
+ align:start position:0%
+prepared only for that. There's more I
+ 
+
+ align:start position:0%
+prepared only for that. There's more I
+would like to tell you about how to
+
+ align:start position:0%
+would like to tell you about how to
+ 
+
+ align:start position:0%
+would like to tell you about how to
+prototype the problem. I am also aware
+
+ align:start position:0%
+prototype the problem. I am also aware
+ 
+
+ align:start position:0%
+prototype the problem. I am also aware
+old habits die hard. You can find out
+
+ align:start position:0%
+old habits die hard. You can find out
+ 
+
+ align:start position:0%
+old habits die hard. You can find out
+about more strategies in my book,
+
+ align:start position:0%
+about more strategies in my book,
+ 
+
+ align:start position:0%
+about more strategies in my book,
+Innovating Adors Manifesto or in the
+
+ align:start position:0%
+Innovating Adors Manifesto or in the
+ 
+
+ align:start position:0%
+Innovating Adors Manifesto or in the
+many materials I've shared online. For
+
+ align:start position:0%
+many materials I've shared online. For
+ 
+
+ align:start position:0%
+many materials I've shared online. For
+now, let me just give you a tip for how
+
+ align:start position:0%
+now, let me just give you a tip for how
+ 
+
+ align:start position:0%
+now, let me just give you a tip for how
+to get started. This is how you can
+
+ align:start position:0%
+to get started. This is how you can
+ 
+
+ align:start position:0%
+to get started. This is how you can
+start practicing.
+
+ align:start position:0%
+start practicing.
+ 
+
+ align:start position:0%
+start practicing.
+Come up with three solutions to the
+
+ align:start position:0%
+Come up with three solutions to the
+ 
+
+ align:start position:0%
+Come up with three solutions to the
+problem.
+
+ align:start position:0%
+problem.
+ 
+
+ align:start position:0%
+problem.
+Prototype all three. Then ask yourself
+
+ align:start position:0%
+Prototype all three. Then ask yourself
+ 
+
+ align:start position:0%
+Prototype all three. Then ask yourself
+or someone else the following two
+
+ align:start position:0%
+or someone else the following two
+ 
+
+ align:start position:0%
+or someone else the following two
+questions. Are these three solutions
+
+ align:start position:0%
+questions. Are these three solutions
+ 
+
+ align:start position:0%
+questions. Are these three solutions
+sufficiently different? And how would
+
+ align:start position:0%
+sufficiently different? And how would
+ 
+
+ align:start position:0%
+sufficiently different? And how would
+you know either of them actually solves
+
+ align:start position:0%
+you know either of them actually solves
+ 
+
+ align:start position:0%
+you know either of them actually solves
+the problem?
+
+ align:start position:0%
+the problem?
+ 
+
+ align:start position:0%
+the problem?
+Once you start getting real, you realize
+
+ align:start position:0%
+Once you start getting real, you realize
+ 
+
+ align:start position:0%
+Once you start getting real, you realize
+there's multiple ways to chip at the
+
+ align:start position:0%
+there's multiple ways to chip at the
+ 
+
+ align:start position:0%
+there's multiple ways to chip at the
+problem and have an impact.
+
+ align:start position:0%
+problem and have an impact.
+ 
+
+ align:start position:0%
+problem and have an impact.
+[Music]
\ No newline at end of file
diff --git a/9hdNPVEQLFE.txt b/9hdNPVEQLFE.txt
new file mode 100644
index 0000000000000000000000000000000000000000..38b6425824cbffd0dc264a7d9b4e7a43da36e9ea
--- /dev/null
+++ b/9hdNPVEQLFE.txt
@@ -0,0 +1,2659 @@
+align:start position:0%
+ 
+so now let me make
+
+ align:start position:0%
+so now let me make
+ 
+
+ align:start position:0%
+so now let me make
+the first of our technical assigns which
+
+ align:start position:0%
+the first of our technical assigns which
+ 
+
+ align:start position:0%
+the first of our technical assigns which
+you can skip over
+
+ align:start position:0%
+you can skip over
+ 
+
+ align:start position:0%
+you can skip over
+if you're not interested in the
+
+ align:start position:0%
+if you're not interested in the
+ 
+
+ align:start position:0%
+if you're not interested in the
+mathematical details but for those of
+
+ align:start position:0%
+mathematical details but for those of
+ 
+
+ align:start position:0%
+mathematical details but for those of
+you that have
+
+ align:start position:0%
+you that have
+ 
+
+ align:start position:0%
+you that have
+a higher level say upper level
+
+ align:start position:0%
+a higher level say upper level
+ 
+
+ align:start position:0%
+a higher level say upper level
+undergraduate
+
+ align:start position:0%
+undergraduate
+ 
+
+ align:start position:0%
+undergraduate
+or even graduate level understanding of
+
+ align:start position:0%
+or even graduate level understanding of
+ 
+
+ align:start position:0%
+or even graduate level understanding of
+transport phenomena fluid mechanics
+
+ align:start position:0%
+transport phenomena fluid mechanics
+ 
+
+ align:start position:0%
+transport phenomena fluid mechanics
+i'd like to show you some of the
+
+ align:start position:0%
+i'd like to show you some of the
+ 
+
+ align:start position:0%
+i'd like to show you some of the
+equations that are behind
+
+ align:start position:0%
+equations that are behind
+ 
+
+ align:start position:0%
+equations that are behind
+the results that i've been quoting in in
+
+ align:start position:0%
+the results that i've been quoting in in
+ 
+
+ align:start position:0%
+the results that i've been quoting in in
+all of the lectures
+
+ align:start position:0%
+all of the lectures
+ 
+
+ align:start position:0%
+all of the lectures
+so in particular let's derive the wells
+
+ align:start position:0%
+so in particular let's derive the wells
+ 
+
+ align:start position:0%
+so in particular let's derive the wells
+curve
+
+ align:start position:0%
+curve
+ 
+
+ align:start position:0%
+curve
+so part of that was
+
+ align:start position:0%
+so part of that was
+ 
+
+ align:start position:0%
+so part of that was
+a theory of drop settling
+
+ align:start position:0%
+a theory of drop settling
+ 
+
+ align:start position:0%
+a theory of drop settling
+here i will quote a certain result
+
+ align:start position:0%
+here i will quote a certain result
+ 
+
+ align:start position:0%
+here i will quote a certain result
+because the derivation would be
+
+ align:start position:0%
+because the derivation would be
+ 
+
+ align:start position:0%
+because the derivation would be
+a lot longer actually for that you could
+
+ align:start position:0%
+a lot longer actually for that you could
+ 
+
+ align:start position:0%
+a lot longer actually for that you could
+refer to my online class 1050x
+
+ align:start position:0%
+refer to my online class 1050x
+ 
+
+ align:start position:0%
+refer to my online class 1050x
+which is that if you have a drop blood
+
+ align:start position:0%
+which is that if you have a drop blood
+ 
+
+ align:start position:0%
+which is that if you have a drop blood
+or a particle
+
+ align:start position:0%
+or a particle
+ 
+
+ align:start position:0%
+or a particle
+of a radius r and it
+
+ align:start position:0%
+of a radius r and it
+ 
+
+ align:start position:0%
+of a radius r and it
+is settling under gravity
+
+ align:start position:0%
+is settling under gravity
+ 
+
+ align:start position:0%
+is settling under gravity
+so it has a mass m and the gravitational
+
+ align:start position:0%
+so it has a mass m and the gravitational
+ 
+
+ align:start position:0%
+so it has a mass m and the gravitational
+force is mg where g is the gravitational
+
+ align:start position:0%
+force is mg where g is the gravitational
+ 
+
+ align:start position:0%
+force is mg where g is the gravitational
+acceleration
+
+ align:start position:0%
+acceleration
+ 
+
+ align:start position:0%
+acceleration
+then there is a flow
+
+ align:start position:0%
+then there is a flow
+ 
+
+ align:start position:0%
+then there is a flow
+of fluid around this object and relative
+
+ align:start position:0%
+of fluid around this object and relative
+ 
+
+ align:start position:0%
+of fluid around this object and relative
+to the moving object the flow is going
+
+ align:start position:0%
+to the moving object the flow is going
+ 
+
+ align:start position:0%
+to the moving object the flow is going
+the other way
+
+ align:start position:0%
+the other way
+ 
+
+ align:start position:0%
+the other way
+and if you solve for the viscous flow
+
+ align:start position:0%
+and if you solve for the viscous flow
+ 
+
+ align:start position:0%
+and if you solve for the viscous flow
+around an object being dragged through a
+
+ align:start position:0%
+around an object being dragged through a
+ 
+
+ align:start position:0%
+around an object being dragged through a
+fluid
+
+ align:start position:0%
+fluid
+ 
+
+ align:start position:0%
+fluid
+then you arrive at the result of stokes
+
+ align:start position:0%
+then you arrive at the result of stokes
+ 
+
+ align:start position:0%
+then you arrive at the result of stokes
+which is the drag on that fluid so if
+
+ align:start position:0%
+which is the drag on that fluid so if
+ 
+
+ align:start position:0%
+which is the drag on that fluid so if
+you're falling at a velocity v
+
+ align:start position:0%
+you're falling at a velocity v
+ 
+
+ align:start position:0%
+you're falling at a velocity v
+then the drag force
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+is fd
+
+ align:start position:0%
+is fd
+ 
+
+ align:start position:0%
+is fd
+is 6 pi times the radius of the drop
+
+ align:start position:0%
+is 6 pi times the radius of the drop
+ 
+
+ align:start position:0%
+is 6 pi times the radius of the drop
+times the viscosity of the fluid
+
+ align:start position:0%
+times the viscosity of the fluid
+ 
+
+ align:start position:0%
+times the viscosity of the fluid
+times the velocity of the drop so we're
+
+ align:start position:0%
+times the velocity of the drop so we're
+ 
+
+ align:start position:0%
+times the velocity of the drop so we're
+falling at a velocity v
+
+ align:start position:0%
+falling at a velocity v
+ 
+
+ align:start position:0%
+falling at a velocity v
+which is the settling velocity and this
+
+ align:start position:0%
+which is the settling velocity and this
+ 
+
+ align:start position:0%
+which is the settling velocity and this
+here is the stokes drag coefficient
+
+ align:start position:0%
+here is the stokes drag coefficient
+ 
+
+ align:start position:0%
+here is the stokes drag coefficient
+which comes from
+
+ align:start position:0%
+which comes from
+ 
+
+ align:start position:0%
+which comes from
+solving the fluid mechanics of viscous
+
+ align:start position:0%
+solving the fluid mechanics of viscous
+ 
+
+ align:start position:0%
+solving the fluid mechanics of viscous
+flow around a sphere
+
+ align:start position:0%
+flow around a sphere
+ 
+
+ align:start position:0%
+flow around a sphere
+translating at a constant speed we can
+
+ align:start position:0%
+translating at a constant speed we can
+ 
+
+ align:start position:0%
+translating at a constant speed we can
+furthermore
+
+ align:start position:0%
+furthermore
+ 
+
+ align:start position:0%
+furthermore
+say that the the
+
+ align:start position:0%
+say that the the
+ 
+
+ align:start position:0%
+say that the the
+mass of the droplet of course
+
+ align:start position:0%
+mass of the droplet of course
+ 
+
+ align:start position:0%
+mass of the droplet of course
+is 4 pi over 3
+
+ align:start position:0%
+is 4 pi over 3
+ 
+
+ align:start position:0%
+is 4 pi over 3
+times the density of the droplet liquid
+
+ align:start position:0%
+times the density of the droplet liquid
+ 
+
+ align:start position:0%
+times the density of the droplet liquid
+times the radius cubed and so given the
+
+ align:start position:0%
+times the radius cubed and so given the
+ 
+
+ align:start position:0%
+times the radius cubed and so given the
+mass of the droplet
+
+ align:start position:0%
+mass of the droplet
+ 
+
+ align:start position:0%
+mass of the droplet
+there's a force balance between the
+
+ align:start position:0%
+there's a force balance between the
+ 
+
+ align:start position:0%
+there's a force balance between the
+gravitational force
+
+ align:start position:0%
+gravitational force
+ 
+
+ align:start position:0%
+gravitational force
+mg and the drag force when the particle
+
+ align:start position:0%
+mg and the drag force when the particle
+ 
+
+ align:start position:0%
+mg and the drag force when the particle
+reaches a terminal velocity so if we
+
+ align:start position:0%
+reaches a terminal velocity so if we
+ 
+
+ align:start position:0%
+reaches a terminal velocity so if we
+think of this vs as the terminal
+
+ align:start position:0%
+think of this vs as the terminal
+ 
+
+ align:start position:0%
+think of this vs as the terminal
+velocity where it's accelerated until
+
+ align:start position:0%
+velocity where it's accelerated until
+ 
+
+ align:start position:0%
+velocity where it's accelerated until
+there's a balance between the forces and
+
+ align:start position:0%
+there's a balance between the forces and
+ 
+
+ align:start position:0%
+there's a balance between the forces and
+is moving at a constant speed
+
+ align:start position:0%
+is moving at a constant speed
+ 
+
+ align:start position:0%
+is moving at a constant speed
+it's given by this force balance and
+
+ align:start position:0%
+it's given by this force balance and
+ 
+
+ align:start position:0%
+it's given by this force balance and
+from that equation we can solve for the
+
+ align:start position:0%
+from that equation we can solve for the
+ 
+
+ align:start position:0%
+from that equation we can solve for the
+settling velocity which
+
+ align:start position:0%
+settling velocity which
+ 
+
+ align:start position:0%
+settling velocity which
+is mg divided by 6 pi
+
+ align:start position:0%
+is mg divided by 6 pi
+ 
+
+ align:start position:0%
+is mg divided by 6 pi
+r and i'll out to use the same notation
+
+ align:start position:0%
+r and i'll out to use the same notation
+ 
+
+ align:start position:0%
+r and i'll out to use the same notation
+before i'll call this mu a of the air
+
+ align:start position:0%
+before i'll call this mu a of the air
+ 
+
+ align:start position:0%
+before i'll call this mu a of the air
+but generally it's the viscosity of the
+
+ align:start position:0%
+but generally it's the viscosity of the
+ 
+
+ align:start position:0%
+but generally it's the viscosity of the
+ambient fluid around the particle as
+
+ align:start position:0%
+ambient fluid around the particle as
+ 
+
+ align:start position:0%
+ambient fluid around the particle as
+it's settling
+
+ align:start position:0%
+it's settling
+ 
+
+ align:start position:0%
+it's settling
+and if we plug in uh the value for mg so
+
+ align:start position:0%
+and if we plug in uh the value for mg so
+ 
+
+ align:start position:0%
+and if we plug in uh the value for mg so
+that's
+
+ align:start position:0%
+that's
+ 
+
+ align:start position:0%
+that's
+four thirds pi
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+rho g r cubed over six
+
+ align:start position:0%
+rho g r cubed over six
+ 
+
+ align:start position:0%
+rho g r cubed over six
+pi r rho a and so if we simplify that
+
+ align:start position:0%
+pi r rho a and so if we simplify that
+ 
+
+ align:start position:0%
+pi r rho a and so if we simplify that
+we end up with 2 9
+
+ align:start position:0%
+we end up with 2 9
+ 
+
+ align:start position:0%
+we end up with 2 9
+rho g r squared
+
+ align:start position:0%
+rho g r squared
+ 
+
+ align:start position:0%
+rho g r squared
+divided by mu a so that's the settling
+
+ align:start position:0%
+divided by mu a so that's the settling
+ 
+
+ align:start position:0%
+divided by mu a so that's the settling
+speed
+
+ align:start position:0%
+speed
+ 
+
+ align:start position:0%
+speed
+and this is a pretty important concept
+
+ align:start position:0%
+and this is a pretty important concept
+ 
+
+ align:start position:0%
+and this is a pretty important concept
+so i'll just sketch it
+
+ align:start position:0%
+so i'll just sketch it
+ 
+
+ align:start position:0%
+so i'll just sketch it
+here so if we want to know what's the
+
+ align:start position:0%
+here so if we want to know what's the
+ 
+
+ align:start position:0%
+here so if we want to know what's the
+settling speed as a function of the
+
+ align:start position:0%
+settling speed as a function of the
+ 
+
+ align:start position:0%
+settling speed as a function of the
+radius of the
+
+ align:start position:0%
+radius of the
+ 
+
+ align:start position:0%
+radius of the
+of the drop then you see it grows like r
+
+ align:start position:0%
+of the drop then you see it grows like r
+ 
+
+ align:start position:0%
+of the drop then you see it grows like r
+squared so it's like this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and then to put a scale on that um if we
+
+ align:start position:0%
+and then to put a scale on that um if we
+ 
+
+ align:start position:0%
+and then to put a scale on that um if we
+have a particle that is three microns
+
+ align:start position:0%
+have a particle that is three microns
+ 
+
+ align:start position:0%
+have a particle that is three microns
+so that's really an aerosol particle
+
+ align:start position:0%
+so that's really an aerosol particle
+ 
+
+ align:start position:0%
+so that's really an aerosol particle
+then the settling speed is around one
+
+ align:start position:0%
+then the settling speed is around one
+ 
+
+ align:start position:0%
+then the settling speed is around one
+millimeter a second if we use
+
+ align:start position:0%
+millimeter a second if we use
+ 
+
+ align:start position:0%
+millimeter a second if we use
+the density of water and the viscosity
+
+ align:start position:0%
+the density of water and the viscosity
+ 
+
+ align:start position:0%
+the density of water and the viscosity
+of air
+
+ align:start position:0%
+of air
+ 
+
+ align:start position:0%
+of air
+for this formula and so that's already a
+
+ align:start position:0%
+for this formula and so that's already a
+ 
+
+ align:start position:0%
+for this formula and so that's already a
+fairly slow settling speed millimeter
+
+ align:start position:0%
+fairly slow settling speed millimeter
+ 
+
+ align:start position:0%
+fairly slow settling speed millimeter
+per second so you can already see the
+
+ align:start position:0%
+per second so you can already see the
+ 
+
+ align:start position:0%
+per second so you can already see the
+particles that are in the micro range
+
+ align:start position:0%
+particles that are in the micro range
+ 
+
+ align:start position:0%
+particles that are in the micro range
+will be suspended in the air for a long
+
+ align:start position:0%
+will be suspended in the air for a long
+ 
+
+ align:start position:0%
+will be suspended in the air for a long
+period of time as long as they don't
+
+ align:start position:0%
+period of time as long as they don't
+ 
+
+ align:start position:0%
+period of time as long as they don't
+evaporate away
+
+ align:start position:0%
+evaporate away
+ 
+
+ align:start position:0%
+evaporate away
+and so that is now the second part of
+
+ align:start position:0%
+and so that is now the second part of
+ 
+
+ align:start position:0%
+and so that is now the second part of
+the calculation
+
+ align:start position:0%
+the calculation
+ 
+
+ align:start position:0%
+the calculation
+oh and actually to finish the first part
+
+ align:start position:0%
+oh and actually to finish the first part
+ 
+
+ align:start position:0%
+oh and actually to finish the first part
+here what we're left with
+
+ align:start position:0%
+here what we're left with
+ 
+
+ align:start position:0%
+here what we're left with
+is that the settling time is
+
+ align:start position:0%
+is that the settling time is
+ 
+
+ align:start position:0%
+is that the settling time is
+l over v s and that's the formula that
+
+ align:start position:0%
+l over v s and that's the formula that
+ 
+
+ align:start position:0%
+l over v s and that's the formula that
+we had
+
+ align:start position:0%
+we had
+ 
+
+ align:start position:0%
+we had
+before which is 9 mu
+
+ align:start position:0%
+before which is 9 mu
+ 
+
+ align:start position:0%
+before which is 9 mu
+a l divided by 2 rho g
+
+ align:start position:0%
+a l divided by 2 rho g
+ 
+
+ align:start position:0%
+a l divided by 2 rho g
+r squared okay so this is our
+
+ align:start position:0%
+r squared okay so this is our
+ 
+
+ align:start position:0%
+r squared okay so this is our
+first part of the wells curve so if i
+
+ align:start position:0%
+first part of the wells curve so if i
+ 
+
+ align:start position:0%
+first part of the wells curve so if i
+draw
+
+ align:start position:0%
+draw
+ 
+
+ align:start position:0%
+draw
+the wells curve over here in the
+
+ align:start position:0%
+the wells curve over here in the
+ 
+
+ align:start position:0%
+the wells curve over here in the
+traditional way
+
+ align:start position:0%
+traditional way
+ 
+
+ align:start position:0%
+traditional way
+where i plot on the horizontal axis the
+
+ align:start position:0%
+where i plot on the horizontal axis the
+ 
+
+ align:start position:0%
+where i plot on the horizontal axis the
+size of the particle and in a downward
+
+ align:start position:0%
+size of the particle and in a downward
+ 
+
+ align:start position:0%
+size of the particle and in a downward
+axis
+
+ align:start position:0%
+axis
+ 
+
+ align:start position:0%
+axis
+we draw the time then we have a curve
+
+ align:start position:0%
+we draw the time then we have a curve
+ 
+
+ align:start position:0%
+we draw the time then we have a curve
+like this
+
+ align:start position:0%
+like this
+ 
+
+ align:start position:0%
+like this
+for settling which and the reason it's
+
+ align:start position:0%
+for settling which and the reason it's
+ 
+
+ align:start position:0%
+for settling which and the reason it's
+drawn down i guess maybe the feeling
+
+ align:start position:0%
+drawn down i guess maybe the feeling
+ 
+
+ align:start position:0%
+drawn down i guess maybe the feeling
+that as you're sort of falling down a
+
+ align:start position:0%
+that as you're sort of falling down a
+ 
+
+ align:start position:0%
+that as you're sort of falling down a
+particle a certain size you hit this
+
+ align:start position:0%
+particle a certain size you hit this
+ 
+
+ align:start position:0%
+particle a certain size you hit this
+curve and that's when you've settled
+
+ align:start position:0%
+curve and that's when you've settled
+ 
+
+ align:start position:0%
+curve and that's when you've settled
+a distance l and fallen out of the air
+
+ align:start position:0%
+a distance l and fallen out of the air
+ 
+
+ align:start position:0%
+a distance l and fallen out of the air
+so now let's look at evaporation
+
+ align:start position:0%
+so now let's look at evaporation
+ 
+
+ align:start position:0%
+so now let's look at evaporation
+which is our second topic um i've lost
+
+ align:start position:0%
+which is our second topic um i've lost
+ 
+
+ align:start position:0%
+which is our second topic um i've lost
+my blue here it is okay
+
+ align:start position:0%
+my blue here it is okay
+ 
+
+ align:start position:0%
+my blue here it is okay
+so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so these droplets are getting very small
+
+ align:start position:0%
+so these droplets are getting very small
+ 
+
+ align:start position:0%
+so these droplets are getting very small
+as they're evaporating and it's
+
+ align:start position:0%
+as they're evaporating and it's
+ 
+
+ align:start position:0%
+as they're evaporating and it's
+happening very quickly
+
+ align:start position:0%
+happening very quickly
+ 
+
+ align:start position:0%
+happening very quickly
+as we shall show in a moment and so a
+
+ align:start position:0%
+as we shall show in a moment and so a
+ 
+
+ align:start position:0%
+as we shall show in a moment and so a
+natural assumption
+
+ align:start position:0%
+natural assumption
+ 
+
+ align:start position:0%
+natural assumption
+is that the uh process is
+
+ align:start position:0%
+is that the uh process is
+ 
+
+ align:start position:0%
+is that the uh process is
+is limited by the diffusion of water
+
+ align:start position:0%
+is limited by the diffusion of water
+ 
+
+ align:start position:0%
+is limited by the diffusion of water
+vapor
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+away from the droplet
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+because essentially we have this little
+
+ align:start position:0%
+because essentially we have this little
+ 
+
+ align:start position:0%
+because essentially we have this little
+drop we have a little droplet here with
+
+ align:start position:0%
+drop we have a little droplet here with
+ 
+
+ align:start position:0%
+drop we have a little droplet here with
+a certain
+
+ align:start position:0%
+a certain
+ 
+
+ align:start position:0%
+a certain
+size r which is now going to be varying
+
+ align:start position:0%
+size r which is now going to be varying
+ 
+
+ align:start position:0%
+size r which is now going to be varying
+with time
+
+ align:start position:0%
+with time
+ 
+
+ align:start position:0%
+with time
+so it has a radius r of t and
+
+ align:start position:0%
+so it has a radius r of t and
+ 
+
+ align:start position:0%
+so it has a radius r of t and
+it's really close to the surface there's
+
+ align:start position:0%
+it's really close to the surface there's
+ 
+
+ align:start position:0%
+it's really close to the surface there's
+an equilibrium concentration
+
+ align:start position:0%
+an equilibrium concentration
+ 
+
+ align:start position:0%
+an equilibrium concentration
+we'll call it cw of water which depends
+
+ align:start position:0%
+we'll call it cw of water which depends
+ 
+
+ align:start position:0%
+we'll call it cw of water which depends
+on the temperature so that's kind of
+
+ align:start position:0%
+on the temperature so that's kind of
+ 
+
+ align:start position:0%
+on the temperature so that's kind of
+that's the saturation concentration of
+
+ align:start position:0%
+that's the saturation concentration of
+ 
+
+ align:start position:0%
+that's the saturation concentration of
+water vapor
+
+ align:start position:0%
+water vapor
+ 
+
+ align:start position:0%
+water vapor
+in the air but then if the water is
+
+ align:start position:0%
+in the air but then if the water is
+ 
+
+ align:start position:0%
+in the air but then if the water is
+going to evaporate more it would create
+
+ align:start position:0%
+going to evaporate more it would create
+ 
+
+ align:start position:0%
+going to evaporate more it would create
+more concentration which would then
+
+ align:start position:0%
+more concentration which would then
+ 
+
+ align:start position:0%
+more concentration which would then
+recondense on the particles so for order
+
+ align:start position:0%
+recondense on the particles so for order
+ 
+
+ align:start position:0%
+recondense on the particles so for order
+for it to continue condensing or
+
+ align:start position:0%
+for it to continue condensing or
+ 
+
+ align:start position:0%
+for it to continue condensing or
+continue evaporating that water vapor
+
+ align:start position:0%
+continue evaporating that water vapor
+ 
+
+ align:start position:0%
+continue evaporating that water vapor
+that is produced has to diffuse away
+
+ align:start position:0%
+that is produced has to diffuse away
+ 
+
+ align:start position:0%
+that is produced has to diffuse away
+so there's going to be a gradient of
+
+ align:start position:0%
+so there's going to be a gradient of
+ 
+
+ align:start position:0%
+so there's going to be a gradient of
+water vapor
+
+ align:start position:0%
+water vapor
+ 
+
+ align:start position:0%
+water vapor
+going outwards from cw
+
+ align:start position:0%
+going outwards from cw
+ 
+
+ align:start position:0%
+going outwards from cw
+is the concentration you know at
+
+ align:start position:0%
+is the concentration you know at
+ 
+
+ align:start position:0%
+is the concentration you know at
+position r
+
+ align:start position:0%
+position r
+ 
+
+ align:start position:0%
+position r
+and then far away there is
+
+ align:start position:0%
+and then far away there is
+ 
+
+ align:start position:0%
+and then far away there is
+a sort of diffusion layer thickness
+
+ align:start position:0%
+a sort of diffusion layer thickness
+ 
+
+ align:start position:0%
+a sort of diffusion layer thickness
+delta and far beyond the diffusion layer
+
+ align:start position:0%
+delta and far beyond the diffusion layer
+ 
+
+ align:start position:0%
+delta and far beyond the diffusion layer
+thickness the concentration is going to
+
+ align:start position:0%
+thickness the concentration is going to
+ 
+
+ align:start position:0%
+thickness the concentration is going to
+approach the equilibrium concentration
+
+ align:start position:0%
+approach the equilibrium concentration
+ 
+
+ align:start position:0%
+approach the equilibrium concentration
+in the ambient air
+
+ align:start position:0%
+in the ambient air
+ 
+
+ align:start position:0%
+in the ambient air
+c at infinity is going to be cw
+
+ align:start position:0%
+c at infinity is going to be cw
+ 
+
+ align:start position:0%
+c at infinity is going to be cw
+times the relative humidity so that's
+
+ align:start position:0%
+times the relative humidity so that's
+ 
+
+ align:start position:0%
+times the relative humidity so that's
+the ratio of the concentration of water
+
+ align:start position:0%
+the ratio of the concentration of water
+ 
+
+ align:start position:0%
+the ratio of the concentration of water
+vapor in the air
+
+ align:start position:0%
+vapor in the air
+ 
+
+ align:start position:0%
+vapor in the air
+to the saturation concentration cw by
+
+ align:start position:0%
+to the saturation concentration cw by
+ 
+
+ align:start position:0%
+to the saturation concentration cw by
+definition
+
+ align:start position:0%
+definition
+ 
+
+ align:start position:0%
+definition
+okay now the math problem that we have
+
+ align:start position:0%
+okay now the math problem that we have
+ 
+
+ align:start position:0%
+okay now the math problem that we have
+to solve
+
+ align:start position:0%
+to solve
+ 
+
+ align:start position:0%
+to solve
+for this diffusion problem with a moving
+
+ align:start position:0%
+for this diffusion problem with a moving
+ 
+
+ align:start position:0%
+for this diffusion problem with a moving
+boundary in this case
+
+ align:start position:0%
+boundary in this case
+ 
+
+ align:start position:0%
+boundary in this case
+but we'll assume it's pseudo steady is
+
+ align:start position:0%
+but we'll assume it's pseudo steady is
+ 
+
+ align:start position:0%
+but we'll assume it's pseudo steady is
+dc dt
+
+ align:start position:0%
+dc dt
+ 
+
+ align:start position:0%
+dc dt
+is the diffusion coefficient of water
+
+ align:start position:0%
+is the diffusion coefficient of water
+ 
+
+ align:start position:0%
+is the diffusion coefficient of water
+times the laplacian of c so just the
+
+ align:start position:0%
+times the laplacian of c so just the
+ 
+
+ align:start position:0%
+times the laplacian of c so just the
+diffusion equation
+
+ align:start position:0%
+diffusion equation
+ 
+
+ align:start position:0%
+diffusion equation
+with these two boundary conditions now
+
+ align:start position:0%
+with these two boundary conditions now
+ 
+
+ align:start position:0%
+with these two boundary conditions now
+an interesting aspect of
+
+ align:start position:0%
+an interesting aspect of
+ 
+
+ align:start position:0%
+an interesting aspect of
+three-dimensional spherical diffusion is
+
+ align:start position:0%
+three-dimensional spherical diffusion is
+ 
+
+ align:start position:0%
+three-dimensional spherical diffusion is
+that at first the diffusion layer grows
+
+ align:start position:0%
+that at first the diffusion layer grows
+ 
+
+ align:start position:0%
+that at first the diffusion layer grows
+but it very quickly reaches a steady
+
+ align:start position:0%
+but it very quickly reaches a steady
+ 
+
+ align:start position:0%
+but it very quickly reaches a steady
+state and if we assume that that
+
+ align:start position:0%
+state and if we assume that that
+ 
+
+ align:start position:0%
+state and if we assume that that
+diffusion time to reach this distance
+
+ align:start position:0%
+diffusion time to reach this distance
+ 
+
+ align:start position:0%
+diffusion time to reach this distance
+delta
+
+ align:start position:0%
+delta
+ 
+
+ align:start position:0%
+delta
+is uh fast so they reach the steady
+
+ align:start position:0%
+is uh fast so they reach the steady
+ 
+
+ align:start position:0%
+is uh fast so they reach the steady
+state it's so it's a kind of
+
+ align:start position:0%
+state it's so it's a kind of
+ 
+
+ align:start position:0%
+state it's so it's a kind of
+quasi-steady or studio steady shrinking
+
+ align:start position:0%
+quasi-steady or studio steady shrinking
+ 
+
+ align:start position:0%
+quasi-steady or studio steady shrinking
+of the droplet with sort of a diffusion
+
+ align:start position:0%
+of the droplet with sort of a diffusion
+ 
+
+ align:start position:0%
+of the droplet with sort of a diffusion
+layer around it that's always
+
+ align:start position:0%
+layer around it that's always
+ 
+
+ align:start position:0%
+layer around it that's always
+kind of at the steady value then it
+
+ align:start position:0%
+kind of at the steady value then it
+ 
+
+ align:start position:0%
+kind of at the steady value then it
+turns out that this diffusion layer
+
+ align:start position:0%
+turns out that this diffusion layer
+ 
+
+ align:start position:0%
+turns out that this diffusion layer
+is avoided the particle size so as the
+
+ align:start position:0%
+is avoided the particle size so as the
+ 
+
+ align:start position:0%
+is avoided the particle size so as the
+particle shrinks the diffusion layer
+
+ align:start position:0%
+particle shrinks the diffusion layer
+ 
+
+ align:start position:0%
+particle shrinks the diffusion layer
+also shrinks
+
+ align:start position:0%
+also shrinks
+ 
+
+ align:start position:0%
+also shrinks
+but it has a well-defined thickness as
+
+ align:start position:0%
+but it has a well-defined thickness as
+ 
+
+ align:start position:0%
+but it has a well-defined thickness as
+opposed to diffusion in one or two
+
+ align:start position:0%
+opposed to diffusion in one or two
+ 
+
+ align:start position:0%
+opposed to diffusion in one or two
+dimensions where the diffusion layer
+
+ align:start position:0%
+dimensions where the diffusion layer
+ 
+
+ align:start position:0%
+dimensions where the diffusion layer
+just keeps growing out to infinity for
+
+ align:start position:0%
+just keeps growing out to infinity for
+ 
+
+ align:start position:0%
+just keeps growing out to infinity for
+example like square root of time
+
+ align:start position:0%
+example like square root of time
+ 
+
+ align:start position:0%
+example like square root of time
+you don't reach a steady state in an
+
+ align:start position:0%
+you don't reach a steady state in an
+ 
+
+ align:start position:0%
+you don't reach a steady state in an
+infinite domain
+
+ align:start position:0%
+infinite domain
+ 
+
+ align:start position:0%
+infinite domain
+so the bottom line of this calculation
+
+ align:start position:0%
+so the bottom line of this calculation
+ 
+
+ align:start position:0%
+so the bottom line of this calculation
+which i will not go through right now
+
+ align:start position:0%
+which i will not go through right now
+ 
+
+ align:start position:0%
+which i will not go through right now
+is that the flux of water on the surface
+
+ align:start position:0%
+is that the flux of water on the surface
+ 
+
+ align:start position:0%
+is that the flux of water on the surface
+is the area of the surface at a given
+
+ align:start position:0%
+is the area of the surface at a given
+ 
+
+ align:start position:0%
+is the area of the surface at a given
+moment where
+
+ align:start position:0%
+moment where
+ 
+
+ align:start position:0%
+moment where
+the sizes are times
+
+ align:start position:0%
+the sizes are times
+ 
+
+ align:start position:0%
+the sizes are times
+the essentially fixed law
+
+ align:start position:0%
+the essentially fixed law
+ 
+
+ align:start position:0%
+the essentially fixed law
+where the driving force the change in
+
+ align:start position:0%
+where the driving force the change in
+ 
+
+ align:start position:0%
+where the driving force the change in
+concentration from the surface to the
+
+ align:start position:0%
+concentration from the surface to the
+ 
+
+ align:start position:0%
+concentration from the surface to the
+bulk
+
+ align:start position:0%
+bulk
+ 
+
+ align:start position:0%
+bulk
+is cw times one minus relative humidity
+
+ align:start position:0%
+is cw times one minus relative humidity
+ 
+
+ align:start position:0%
+is cw times one minus relative humidity
+the diffusivity of water and then
+
+ align:start position:0%
+the diffusivity of water and then
+ 
+
+ align:start position:0%
+the diffusivity of water and then
+divided by delta the diffusion layer
+
+ align:start position:0%
+divided by delta the diffusion layer
+ 
+
+ align:start position:0%
+divided by delta the diffusion layer
+thickness and it turns out that with
+
+ align:start position:0%
+thickness and it turns out that with
+ 
+
+ align:start position:0%
+thickness and it turns out that with
+these coefficients here that's it turns
+
+ align:start position:0%
+these coefficients here that's it turns
+ 
+
+ align:start position:0%
+these coefficients here that's it turns
+out to be exactly r so this is not a
+
+ align:start position:0%
+out to be exactly r so this is not a
+ 
+
+ align:start position:0%
+out to be exactly r so this is not a
+scaling result but actually an exact
+
+ align:start position:0%
+scaling result but actually an exact
+ 
+
+ align:start position:0%
+scaling result but actually an exact
+result
+
+ align:start position:0%
+result
+ 
+
+ align:start position:0%
+result
+for pseudosteady spherical diffusion of
+
+ align:start position:0%
+for pseudosteady spherical diffusion of
+ 
+
+ align:start position:0%
+for pseudosteady spherical diffusion of
+water vapor
+
+ align:start position:0%
+water vapor
+ 
+
+ align:start position:0%
+water vapor
+so now we have the flux on the surface
+
+ align:start position:0%
+so now we have the flux on the surface
+ 
+
+ align:start position:0%
+so now we have the flux on the surface
+it's uniform on the surface
+
+ align:start position:0%
+it's uniform on the surface
+ 
+
+ align:start position:0%
+it's uniform on the surface
+and it's consumed to be pseudo steady
+
+ align:start position:0%
+and it's consumed to be pseudo steady
+ 
+
+ align:start position:0%
+and it's consumed to be pseudo steady
+and so then i can write down
+
+ align:start position:0%
+and so then i can write down
+ 
+
+ align:start position:0%
+and so then i can write down
+that the change in the size of the water
+
+ align:start position:0%
+that the change in the size of the water
+ 
+
+ align:start position:0%
+that the change in the size of the water
+droplet
+
+ align:start position:0%
+droplet
+ 
+
+ align:start position:0%
+droplet
+volume which is 4 pi over cube 3
+
+ align:start position:0%
+volume which is 4 pi over cube 3
+ 
+
+ align:start position:0%
+volume which is 4 pi over cube 3
+4 pi over 3 r cubed is equal to minus
+
+ align:start position:0%
+4 pi over 3 r cubed is equal to minus
+ 
+
+ align:start position:0%
+4 pi over 3 r cubed is equal to minus
+the volume of a water molecule
+
+ align:start position:0%
+the volume of a water molecule
+ 
+
+ align:start position:0%
+the volume of a water molecule
+times the flux of water so that's
+
+ align:start position:0%
+times the flux of water so that's
+ 
+
+ align:start position:0%
+times the flux of water so that's
+basically
+
+ align:start position:0%
+basically
+ 
+
+ align:start position:0%
+basically
+my volume or mass balance of water
+
+ align:start position:0%
+my volume or mass balance of water
+ 
+
+ align:start position:0%
+my volume or mass balance of water
+so if i plug this in here then i get dr
+
+ align:start position:0%
+so if i plug this in here then i get dr
+ 
+
+ align:start position:0%
+so if i plug this in here then i get dr
+dt is equal to uh
+
+ align:start position:0%
+dt is equal to uh
+ 
+
+ align:start position:0%
+dt is equal to uh
+let's see collecting all the terms here
+
+ align:start position:0%
+let's see collecting all the terms here
+ 
+
+ align:start position:0%
+let's see collecting all the terms here
+so derivative r cubed
+
+ align:start position:0%
+so derivative r cubed
+ 
+
+ align:start position:0%
+so derivative r cubed
+is uh 2 r is 3r squared so the 3's
+
+ align:start position:0%
+is uh 2 r is 3r squared so the 3's
+ 
+
+ align:start position:0%
+is uh 2 r is 3r squared so the 3's
+cancel
+
+ align:start position:0%
+cancel
+ 
+
+ align:start position:0%
+cancel
+and then i have a 4 pi r squared which
+
+ align:start position:0%
+and then i have a 4 pi r squared which
+ 
+
+ align:start position:0%
+and then i have a 4 pi r squared which
+cancels this 4 pi
+
+ align:start position:0%
+cancels this 4 pi
+ 
+
+ align:start position:0%
+cancels this 4 pi
+squared so i just have dr dt is minus
+
+ align:start position:0%
+squared so i just have dr dt is minus
+ 
+
+ align:start position:0%
+squared so i just have dr dt is minus
+vw dw cw 1 minus
+
+ align:start position:0%
+vw dw cw 1 minus
+ 
+
+ align:start position:0%
+vw dw cw 1 minus
+rh divided by r
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+if i put this r on the other side here
+
+ align:start position:0%
+if i put this r on the other side here
+ 
+
+ align:start position:0%
+if i put this r on the other side here
+then i have let's continue the
+
+ align:start position:0%
+then i have let's continue the
+ 
+
+ align:start position:0%
+then i have let's continue the
+derivation here
+
+ align:start position:0%
+derivation here
+ 
+
+ align:start position:0%
+derivation here
+i have r dr
+
+ align:start position:0%
+i have r dr
+ 
+
+ align:start position:0%
+i have r dr
+dt is equal to all this stuff
+
+ align:start position:0%
+dt is equal to all this stuff
+ 
+
+ align:start position:0%
+dt is equal to all this stuff
+so minus dw
+
+ align:start position:0%
+so minus dw
+ 
+
+ align:start position:0%
+so minus dw
+dwcw1 minus rh
+
+ align:start position:0%
+dwcw1 minus rh
+ 
+
+ align:start position:0%
+dwcw1 minus rh
+and then this expression here can be
+
+ align:start position:0%
+and then this expression here can be
+ 
+
+ align:start position:0%
+and then this expression here can be
+written as
+
+ align:start position:0%
+written as
+ 
+
+ align:start position:0%
+written as
+one-half the derivative
+
+ align:start position:0%
+one-half the derivative
+ 
+
+ align:start position:0%
+one-half the derivative
+of r squared so we find is that r
+
+ align:start position:0%
+of r squared so we find is that r
+ 
+
+ align:start position:0%
+of r squared so we find is that r
+squared is linear in time
+
+ align:start position:0%
+squared is linear in time
+ 
+
+ align:start position:0%
+squared is linear in time
+and then using the boundary condition
+
+ align:start position:0%
+and then using the boundary condition
+ 
+
+ align:start position:0%
+and then using the boundary condition
+that we
+
+ align:start position:0%
+that we
+ 
+
+ align:start position:0%
+that we
+start out at a certain initial value r
+
+ align:start position:0%
+start out at a certain initial value r
+ 
+
+ align:start position:0%
+start out at a certain initial value r
+naught
+
+ align:start position:0%
+naught
+ 
+
+ align:start position:0%
+naught
+then i'm going to get that the r of t
+
+ align:start position:0%
+then i'm going to get that the r of t
+ 
+
+ align:start position:0%
+then i'm going to get that the r of t
+is the initial value r naught
+
+ align:start position:0%
+is the initial value r naught
+ 
+
+ align:start position:0%
+is the initial value r naught
+times the square root of one minus t
+
+ align:start position:0%
+times the square root of one minus t
+ 
+
+ align:start position:0%
+times the square root of one minus t
+over a certain evaporation time
+
+ align:start position:0%
+over a certain evaporation time
+ 
+
+ align:start position:0%
+over a certain evaporation time
+and that evaporation time
+
+ align:start position:0%
+and that evaporation time
+ 
+
+ align:start position:0%
+and that evaporation time
+is given here by
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+r0 squared uh
+
+ align:start position:0%
+r0 squared uh
+ 
+
+ align:start position:0%
+r0 squared uh
+times basically all these coefficients
+
+ align:start position:0%
+times basically all these coefficients
+ 
+
+ align:start position:0%
+times basically all these coefficients
+here
+
+ align:start position:0%
+here
+ 
+
+ align:start position:0%
+here
+uh where i'll separate out the effective
+
+ align:start position:0%
+uh where i'll separate out the effective
+ 
+
+ align:start position:0%
+uh where i'll separate out the effective
+humidity
+
+ align:start position:0%
+humidity
+ 
+
+ align:start position:0%
+humidity
+and then a bunch of other coefficients
+
+ align:start position:0%
+and then a bunch of other coefficients
+ 
+
+ align:start position:0%
+and then a bunch of other coefficients
+which you can see have units of length
+
+ align:start position:0%
+which you can see have units of length
+ 
+
+ align:start position:0%
+which you can see have units of length
+squared
+
+ align:start position:0%
+squared
+ 
+
+ align:start position:0%
+squared
+over time because our zero is a length
+
+ align:start position:0%
+over time because our zero is a length
+ 
+
+ align:start position:0%
+over time because our zero is a length
+squared so it's effectively some kind of
+
+ align:start position:0%
+squared so it's effectively some kind of
+ 
+
+ align:start position:0%
+squared so it's effectively some kind of
+diffusivity
+
+ align:start position:0%
+diffusivity
+ 
+
+ align:start position:0%
+diffusivity
+and what we get from this calculation is
+
+ align:start position:0%
+and what we get from this calculation is
+ 
+
+ align:start position:0%
+and what we get from this calculation is
+that this effective diffusivity that
+
+ align:start position:0%
+that this effective diffusivity that
+ 
+
+ align:start position:0%
+that this effective diffusivity that
+goes into this
+
+ align:start position:0%
+goes into this
+ 
+
+ align:start position:0%
+goes into this
+expression is there's a factor two from
+
+ align:start position:0%
+expression is there's a factor two from
+ 
+
+ align:start position:0%
+expression is there's a factor two from
+this guy there's a two
+
+ align:start position:0%
+this guy there's a two
+ 
+
+ align:start position:0%
+this guy there's a two
+v w d w c w
+
+ align:start position:0%
+v w d w c w
+ 
+
+ align:start position:0%
+v w d w c w
+and if you plug in values for water
+
+ align:start position:0%
+and if you plug in values for water
+ 
+
+ align:start position:0%
+and if you plug in values for water
+vapor for the saturation pressure and
+
+ align:start position:0%
+vapor for the saturation pressure and
+ 
+
+ align:start position:0%
+vapor for the saturation pressure and
+the diffusivity
+
+ align:start position:0%
+the diffusivity
+ 
+
+ align:start position:0%
+the diffusivity
+and the volume of water in air then this
+
+ align:start position:0%
+and the volume of water in air then this
+ 
+
+ align:start position:0%
+and the volume of water in air then this
+coefficient turns out to be 1.2
+
+ align:start position:0%
+coefficient turns out to be 1.2
+ 
+
+ align:start position:0%
+coefficient turns out to be 1.2
+times 10 to the minus 9 meters squared
+
+ align:start position:0%
+times 10 to the minus 9 meters squared
+ 
+
+ align:start position:0%
+times 10 to the minus 9 meters squared
+per second
+
+ align:start position:0%
+per second
+ 
+
+ align:start position:0%
+per second
+for pure water
+
+ align:start position:0%
+for pure water
+ 
+
+ align:start position:0%
+for pure water
+and that's where you get now the second
+
+ align:start position:0%
+and that's where you get now the second
+ 
+
+ align:start position:0%
+and that's where you get now the second
+part of the wells theory which is the
+
+ align:start position:0%
+part of the wells theory which is the
+ 
+
+ align:start position:0%
+part of the wells theory which is the
+evaporation
+
+ align:start position:0%
+evaporation
+ 
+
+ align:start position:0%
+evaporation
+which gives you a curve looking like
+
+ align:start position:0%
+which gives you a curve looking like
+ 
+
+ align:start position:0%
+which gives you a curve looking like
+this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so that there's this sort of in this
+
+ align:start position:0%
+so that there's this sort of in this
+ 
+
+ align:start position:0%
+so that there's this sort of in this
+theory a natural
+
+ align:start position:0%
+theory a natural
+ 
+
+ align:start position:0%
+theory a natural
+crossover between
+
+ align:start position:0%
+crossover between
+ 
+
+ align:start position:0%
+crossover between
+large drops which in this case here are
+
+ align:start position:0%
+large drops which in this case here are
+ 
+
+ align:start position:0%
+large drops which in this case here are
+ones that are large enough to settle
+
+ align:start position:0%
+ones that are large enough to settle
+ 
+
+ align:start position:0%
+ones that are large enough to settle
+out of the fluid before they evaporate
+
+ align:start position:0%
+out of the fluid before they evaporate
+ 
+
+ align:start position:0%
+out of the fluid before they evaporate
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+small drops which
+
+ align:start position:0%
+small drops which
+ 
+
+ align:start position:0%
+small drops which
+evaporate
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+on the other hand for true biological
+
+ align:start position:0%
+on the other hand for true biological
+ 
+
+ align:start position:0%
+on the other hand for true biological
+fluids that
+
+ align:start position:0%
+fluids that
+ 
+
+ align:start position:0%
+fluids that
+appear in respiratory droplets
+
+ align:start position:0%
+appear in respiratory droplets
+ 
+
+ align:start position:0%
+appear in respiratory droplets
+the evaporation is limited by solutes
+
+ align:start position:0%
+the evaporation is limited by solutes
+ 
+
+ align:start position:0%
+the evaporation is limited by solutes
+and salts
+
+ align:start position:0%
+and salts
+ 
+
+ align:start position:0%
+and salts
+which stop the evaporation and in fact
+
+ align:start position:0%
+which stop the evaporation and in fact
+ 
+
+ align:start position:0%
+which stop the evaporation and in fact
+can attract even more water in some
+
+ align:start position:0%
+can attract even more water in some
+ 
+
+ align:start position:0%
+can attract even more water in some
+cases
+
+ align:start position:0%
+cases
+ 
+
+ align:start position:0%
+cases
+so that the evaporation part of it is
+
+ align:start position:0%
+so that the evaporation part of it is
+ 
+
+ align:start position:0%
+so that the evaporation part of it is
+not as accurate
+
+ align:start position:0%
+not as accurate
+ 
+
+ align:start position:0%
+not as accurate
+and we tend to see that the settling
+
+ align:start position:0%
+and we tend to see that the settling
+ 
+
+ align:start position:0%
+and we tend to see that the settling
+part is more important to consider
+
+ align:start position:0%
+part is more important to consider
+ 
+
+ align:start position:0%
+part is more important to consider
+uh given an equilibrium distribution of
+
+ align:start position:0%
+uh given an equilibrium distribution of
+ 
+
+ align:start position:0%
+uh given an equilibrium distribution of
+droplets that has been measured and
+
+ align:start position:0%
+droplets that has been measured and
+ 
+
+ align:start position:0%
+droplets that has been measured and
+is understood to come from different
+
+ align:start position:0%
+is understood to come from different
+ 
+
+ align:start position:0%
+is understood to come from different
+types of respiration
\ No newline at end of file
diff --git a/AIucNcAQE3A.txt b/AIucNcAQE3A.txt
new file mode 100644
index 0000000000000000000000000000000000000000..59d597e7582b197d2a5ed13ce24c7fcf7e4ad1ae
--- /dev/null
+++ b/AIucNcAQE3A.txt
@@ -0,0 +1,387 @@
+align:start position:0%
+ 
+can you tell me uh your your team name
+
+ align:start position:0%
+can you tell me uh your your team name
+ 
+
+ align:start position:0%
+can you tell me uh your your team name
+and introduce the members of your team
+
+ align:start position:0%
+and introduce the members of your team
+ 
+
+ align:start position:0%
+and introduce the members of your team
+please uh we're Team Firebolt and I'm
+
+ align:start position:0%
+please uh we're Team Firebolt and I'm
+ 
+
+ align:start position:0%
+please uh we're Team Firebolt and I'm
+Chris Pinos I'm Mariel John and I'm
+
+ align:start position:0%
+Chris Pinos I'm Mariel John and I'm
+ 
+
+ align:start position:0%
+Chris Pinos I'm Mariel John and I'm
+Elvia
+
+ align:start position:0%
+Elvia
+ 
+
+ align:start position:0%
+Elvia
+sedun well you made it this far uh how
+
+ align:start position:0%
+sedun well you made it this far uh how
+ 
+
+ align:start position:0%
+sedun well you made it this far uh how
+are you
+
+ align:start position:0%
+are you
+ 
+
+ align:start position:0%
+are you
+feeling pretty good we're proud of the
+
+ align:start position:0%
+feeling pretty good we're proud of the
+ 
+
+ align:start position:0%
+feeling pretty good we're proud of the
+work we've
+
+ align:start position:0%
+work we've
+ 
+
+ align:start position:0%
+work we've
+done uh we we're pretty good we have a
+
+ align:start position:0%
+done uh we we're pretty good we have a
+ 
+
+ align:start position:0%
+done uh we we're pretty good we have a
+uh second place right now but we're
+
+ align:start position:0%
+uh second place right now but we're
+ 
+
+ align:start position:0%
+uh second place right now but we're
+hoping to get first today the next
+
+ align:start position:0%
+hoping to get first today the next
+ 
+
+ align:start position:0%
+hoping to get first today the next
+flight second place huh so so you
+
+ align:start position:0%
+flight second place huh so so you
+ 
+
+ align:start position:0%
+flight second place huh so so you
+competed yesterday yes so what's
+
+ align:start position:0%
+competed yesterday yes so what's
+ 
+
+ align:start position:0%
+competed yesterday yes so what's
+different today what what changes did
+
+ align:start position:0%
+different today what what changes did
+ 
+
+ align:start position:0%
+different today what what changes did
+you make uh we made uh egg canisters
+
+ align:start position:0%
+you make uh we made uh egg canisters
+ 
+
+ align:start position:0%
+you make uh we made uh egg canisters
+that have a lot less drag than the ones
+
+ align:start position:0%
+that have a lot less drag than the ones
+ 
+
+ align:start position:0%
+that have a lot less drag than the ones
+we did yesterday and you think that's
+
+ align:start position:0%
+we did yesterday and you think that's
+ 
+
+ align:start position:0%
+we did yesterday and you think that's
+going to give you the edge
+
+ align:start position:0%
+going to give you the edge
+ 
+
+ align:start position:0%
+going to give you the edge
+yeah what's the most notable design
+
+ align:start position:0%
+yeah what's the most notable design
+ 
+
+ align:start position:0%
+yeah what's the most notable design
+feature of your aircraft what advantage
+
+ align:start position:0%
+feature of your aircraft what advantage
+ 
+
+ align:start position:0%
+feature of your aircraft what advantage
+do you think it gives you uh well we
+
+ align:start position:0%
+do you think it gives you uh well we
+ 
+
+ align:start position:0%
+do you think it gives you uh well we
+have an a really large wingspan which
+
+ align:start position:0%
+have an a really large wingspan which
+ 
+
+ align:start position:0%
+have an a really large wingspan which
+gives us probably the most lift of any
+
+ align:start position:0%
+gives us probably the most lift of any
+ 
+
+ align:start position:0%
+gives us probably the most lift of any
+team here um that gives us lots of drag
+
+ align:start position:0%
+team here um that gives us lots of drag
+ 
+
+ align:start position:0%
+team here um that gives us lots of drag
+but uh I think the lift is the best
+
+ align:start position:0%
+but uh I think the lift is the best
+ 
+
+ align:start position:0%
+but uh I think the lift is the best
+feature
+
+ align:start position:0%
+feature
+ 
+
+ align:start position:0%
+feature
+you've been working on this project as a
+
+ align:start position:0%
+you've been working on this project as a
+ 
+
+ align:start position:0%
+you've been working on this project as a
+team for most of the semester what's
+
+ align:start position:0%
+team for most of the semester what's
+ 
+
+ align:start position:0%
+team for most of the semester what's
+been the most enjoyable part of the
+
+ align:start position:0%
+been the most enjoyable part of the
+ 
+
+ align:start position:0%
+been the most enjoyable part of the
+process I think maybe just spending time
+
+ align:start position:0%
+process I think maybe just spending time
+ 
+
+ align:start position:0%
+process I think maybe just spending time
+in the lab together when we're just kind
+
+ align:start position:0%
+in the lab together when we're just kind
+ 
+
+ align:start position:0%
+in the lab together when we're just kind
+of working on the plane and building or
+
+ align:start position:0%
+of working on the plane and building or
+ 
+
+ align:start position:0%
+of working on the plane and building or
+thinking of ideas of how we can make it
+
+ align:start position:0%
+thinking of ideas of how we can make it
+ 
+
+ align:start position:0%
+thinking of ideas of how we can make it
+better yeah I mean it's nice to uh get a
+
+ align:start position:0%
+better yeah I mean it's nice to uh get a
+ 
+
+ align:start position:0%
+better yeah I mean it's nice to uh get a
+chance to do something Hands-On as
+
+ align:start position:0%
+chance to do something Hands-On as
+ 
+
+ align:start position:0%
+chance to do something Hands-On as
+opposed to you know just problem sets
+
+ align:start position:0%
+opposed to you know just problem sets
+ 
+
+ align:start position:0%
+opposed to you know just problem sets
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+stuff so what was toughest about
+
+ align:start position:0%
+stuff so what was toughest about
+ 
+
+ align:start position:0%
+stuff so what was toughest about
+engineering this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+system I'd like to it doesn't have
+
+ align:start position:0%
+system I'd like to it doesn't have
+ 
+
+ align:start position:0%
+system I'd like to it doesn't have
+things uh things break a lot and uh
+
+ align:start position:0%
+things uh things break a lot and uh
+ 
+
+ align:start position:0%
+things uh things break a lot and uh
+nothing ever goes the way you want so
+
+ align:start position:0%
+nothing ever goes the way you want so
+ 
+
+ align:start position:0%
+nothing ever goes the way you want so
+you have to you know redesign on the Fly
+
+ align:start position:0%
+you have to you know redesign on the Fly
+ 
+
+ align:start position:0%
+you have to you know redesign on the Fly
+and like half of the designing is taking
+
+ align:start position:0%
+and like half of the designing is taking
+ 
+
+ align:start position:0%
+and like half of the designing is taking
+place just in these last few days really
+
+ align:start position:0%
+place just in these last few days really
+ 
+
+ align:start position:0%
+place just in these last few days really
+feels
+
+ align:start position:0%
+feels
+ 
+
+ align:start position:0%
+feels
+like all right well thanks very much you
+
+ align:start position:0%
+like all right well thanks very much you
+ 
+
+ align:start position:0%
+like all right well thanks very much you
+guys good luck with your flight
\ No newline at end of file
diff --git a/AKqq9-c6uMo.txt b/AKqq9-c6uMo.txt
new file mode 100644
index 0000000000000000000000000000000000000000..ed2f5ba77efd6cdbb67124aaa54bfa8e7f383c22
--- /dev/null
+++ b/AKqq9-c6uMo.txt
@@ -0,0 +1,9979 @@
+align:start position:0%
+ 
+all right good morning everybody today
+
+ align:start position:0%
+all right good morning everybody today
+ 
+
+ align:start position:0%
+all right good morning everybody today
+is not a thermodynamics lecture by me we
+
+ align:start position:0%
+is not a thermodynamics lecture by me we
+ 
+
+ align:start position:0%
+is not a thermodynamics lecture by me we
+have a guest lecture by professing Greg
+
+ align:start position:0%
+have a guest lecture by professing Greg
+ 
+
+ align:start position:0%
+have a guest lecture by professing Greg
+Olsen and we just finished a lot of work
+
+ align:start position:0%
+Olsen and we just finished a lot of work
+ 
+
+ align:start position:0%
+Olsen and we just finished a lot of work
+with thermocalc and calfat in general
+
+ align:start position:0%
+with thermocalc and calfat in general
+ 
+
+ align:start position:0%
+with thermocalc and calfat in general
+and solution model in binary phase
+
+ align:start position:0%
+and solution model in binary phase
+ 
+
+ align:start position:0%
+and solution model in binary phase
+diagrams and I've told you throughout
+
+ align:start position:0%
+diagrams and I've told you throughout
+ 
+
+ align:start position:0%
+diagrams and I've told you throughout
+the entire semester that thermodynamic
+
+ align:start position:0%
+the entire semester that thermodynamic
+ 
+
+ align:start position:0%
+the entire semester that thermodynamic
+data is valuable and allows you to make
+
+ align:start position:0%
+data is valuable and allows you to make
+ 
+
+ align:start position:0%
+data is valuable and allows you to make
+make predictions that's why it's
+
+ align:start position:0%
+make predictions that's why it's
+ 
+
+ align:start position:0%
+make predictions that's why it's
+valuable and those predictions allow you
+
+ align:start position:0%
+valuable and those predictions allow you
+ 
+
+ align:start position:0%
+valuable and those predictions allow you
+to make real things in the real world
+
+ align:start position:0%
+to make real things in the real world
+ 
+
+ align:start position:0%
+to make real things in the real world
+possible and um so far you've just had
+
+ align:start position:0%
+possible and um so far you've just had
+ 
+
+ align:start position:0%
+possible and um so far you've just had
+to take my word for it right so so the
+
+ align:start position:0%
+to take my word for it right so so the
+ 
+
+ align:start position:0%
+to take my word for it right so so the
+point of today's guest lecture is that
+
+ align:start position:0%
+point of today's guest lecture is that
+ 
+
+ align:start position:0%
+point of today's guest lecture is that
+um so you can don't have to take my word
+
+ align:start position:0%
+um so you can don't have to take my word
+ 
+
+ align:start position:0%
+um so you can don't have to take my word
+for it anymore so I won't I'll just say
+
+ align:start position:0%
+for it anymore so I won't I'll just say
+ 
+
+ align:start position:0%
+for it anymore so I won't I'll just say
+that Professor olssen is world famous
+
+ align:start position:0%
+that Professor olssen is world famous
+ 
+
+ align:start position:0%
+that Professor olssen is world famous
+for using thermodynamic data um to for
+
+ align:start position:0%
+for using thermodynamic data um to for
+ 
+
+ align:start position:0%
+for using thermodynamic data um to for
+real world impact and I leave it at that
+
+ align:start position:0%
+real world impact and I leave it at that
+ 
+
+ align:start position:0%
+real world impact and I leave it at that
+is that okay Greg that's sufficient I
+
+ align:start position:0%
+is that okay Greg that's sufficient I
+ 
+
+ align:start position:0%
+is that okay Greg that's sufficient I
+think yes yes all right let's hope it's
+
+ align:start position:0%
+think yes yes all right let's hope it's
+ 
+
+ align:start position:0%
+think yes yes all right let's hope it's
+positive impact yes okay very good
+
+ align:start position:0%
+positive impact yes okay very good
+ 
+
+ align:start position:0%
+positive impact yes okay very good
+indeed uh so I'll hand it I'll hand it
+
+ align:start position:0%
+indeed uh so I'll hand it I'll hand it
+ 
+
+ align:start position:0%
+indeed uh so I'll hand it I'll hand it
+over to you all right let me attempt my
+
+ align:start position:0%
+over to you all right let me attempt my
+ 
+
+ align:start position:0%
+over to you all right let me attempt my
+screen
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+share all right my presentation will be
+
+ align:start position:0%
+share all right my presentation will be
+ 
+
+ align:start position:0%
+share all right my presentation will be
+from the perspective of my University
+
+ align:start position:0%
+from the perspective of my University
+ 
+
+ align:start position:0%
+from the perspective of my University
+day job as well as the activities of our
+
+ align:start position:0%
+day job as well as the activities of our
+ 
+
+ align:start position:0%
+day job as well as the activities of our
+computational materials design company
+
+ align:start position:0%
+computational materials design company
+ 
+
+ align:start position:0%
+computational materials design company
+questech and they ongoing collaborations
+
+ align:start position:0%
+questech and they ongoing collaborations
+ 
+
+ align:start position:0%
+questech and they ongoing collaborations
+through the uh Chicago based chimed
+
+ align:start position:0%
+through the uh Chicago based chimed
+ 
+
+ align:start position:0%
+through the uh Chicago based chimed
+materials Design
+
+ align:start position:0%
+materials Design
+ 
+
+ align:start position:0%
+materials Design
+Center uh as thermocalc professor of the
+
+ align:start position:0%
+Center uh as thermocalc professor of the
+ 
+
+ align:start position:0%
+Center uh as thermocalc professor of the
+practice uh my job description is to
+
+ align:start position:0%
+practice uh my job description is to
+ 
+
+ align:start position:0%
+practice uh my job description is to
+make MIT a global Beacon of calad
+
+ align:start position:0%
+make MIT a global Beacon of calad
+ 
+
+ align:start position:0%
+make MIT a global Beacon of calad
+Technology into which we are recruiting
+
+ align:start position:0%
+Technology into which we are recruiting
+ 
+
+ align:start position:0%
+Technology into which we are recruiting
+you and in in uh in the uh in support of
+
+ align:start position:0%
+you and in in uh in the uh in support of
+ 
+
+ align:start position:0%
+you and in in uh in the uh in support of
+that uh we've actually had a range that
+
+ align:start position:0%
+that uh we've actually had a range that
+ 
+
+ align:start position:0%
+that uh we've actually had a range that
+uh MIT would host uh this year's
+
+ align:start position:0%
+uh MIT would host uh this year's
+ 
+
+ align:start position:0%
+uh MIT would host uh this year's
+International calad Conference but
+
+ align:start position:0%
+International calad Conference but
+ 
+
+ align:start position:0%
+International calad Conference but
+unfortunately due to the pandemic we've
+
+ align:start position:0%
+unfortunately due to the pandemic we've
+ 
+
+ align:start position:0%
+unfortunately due to the pandemic we've
+had to post ponent a couple years but I
+
+ align:start position:0%
+had to post ponent a couple years but I
+ 
+
+ align:start position:0%
+had to post ponent a couple years but I
+hope uh you'll still be around to to to
+
+ align:start position:0%
+hope uh you'll still be around to to to
+ 
+
+ align:start position:0%
+hope uh you'll still be around to to to
+join us when that
+
+ align:start position:0%
+join us when that
+ 
+
+ align:start position:0%
+join us when that
+happens uh and I would like you uh
+
+ align:start position:0%
+happens uh and I would like you uh
+ 
+
+ align:start position:0%
+happens uh and I would like you uh
+throughout uh don't hesitate to
+
+ align:start position:0%
+throughout uh don't hesitate to
+ 
+
+ align:start position:0%
+throughout uh don't hesitate to
+interrupt uh just unmute yourself and
+
+ align:start position:0%
+interrupt uh just unmute yourself and
+ 
+
+ align:start position:0%
+interrupt uh just unmute yourself and
+and yell at me if you'd like to discuss
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+anything uh the context of this
+
+ align:start position:0%
+anything uh the context of this
+ 
+
+ align:start position:0%
+anything uh the context of this
+technology is the national materials
+
+ align:start position:0%
+technology is the national materials
+ 
+
+ align:start position:0%
+technology is the national materials
+genome initiative that's a presidential
+
+ align:start position:0%
+genome initiative that's a presidential
+ 
+
+ align:start position:0%
+genome initiative that's a presidential
+initiative announced by President Obama
+
+ align:start position:0%
+initiative announced by President Obama
+ 
+
+ align:start position:0%
+initiative announced by President Obama
+a decade ago uh intended as a decadal
+
+ align:start position:0%
+a decade ago uh intended as a decadal
+ 
+
+ align:start position:0%
+a decade ago uh intended as a decadal
+initiative but in fact a recent National
+
+ align:start position:0%
+initiative but in fact a recent National
+ 
+
+ align:start position:0%
+initiative but in fact a recent National
+Academy study has recommended that it
+
+ align:start position:0%
+Academy study has recommended that it
+ 
+
+ align:start position:0%
+Academy study has recommended that it
+continue for another
+
+ align:start position:0%
+continue for another
+ 
+
+ align:start position:0%
+continue for another
+decade and the uh overarching goal of
+
+ align:start position:0%
+decade and the uh overarching goal of
+ 
+
+ align:start position:0%
+decade and the uh overarching goal of
+this initiative is to build out the
+
+ align:start position:0%
+this initiative is to build out the
+ 
+
+ align:start position:0%
+this initiative is to build out the
+databases and tools that would allow us
+
+ align:start position:0%
+databases and tools that would allow us
+ 
+
+ align:start position:0%
+databases and tools that would allow us
+to take what has been historically a 10
+
+ align:start position:0%
+to take what has been historically a 10
+ 
+
+ align:start position:0%
+to take what has been historically a 10
+to 20 year materials development cycle
+
+ align:start position:0%
+to 20 year materials development cycle
+ 
+
+ align:start position:0%
+to 20 year materials development cycle
+and compress that by at least uh
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+50% the metaphor of the genome uh is
+
+ align:start position:0%
+50% the metaphor of the genome uh is
+ 
+
+ align:start position:0%
+50% the metaphor of the genome uh is
+discussed in the National Academy study
+
+ align:start position:0%
+discussed in the National Academy study
+ 
+
+ align:start position:0%
+discussed in the National Academy study
+going back to
+
+ align:start position:0%
+going back to
+ 
+
+ align:start position:0%
+going back to
+2004 uh on this very subject of
+
+ align:start position:0%
+2004 uh on this very subject of
+ 
+
+ align:start position:0%
+2004 uh on this very subject of
+accelerating the technology transition
+
+ align:start position:0%
+accelerating the technology transition
+ 
+
+ align:start position:0%
+accelerating the technology transition
+of materials and
+
+ align:start position:0%
+of materials and
+ 
+
+ align:start position:0%
+of materials and
+processes uh so it reviewed uh the best
+
+ align:start position:0%
+processes uh so it reviewed uh the best
+ 
+
+ align:start position:0%
+processes uh so it reviewed uh the best
+that had been achieved at that time and
+
+ align:start position:0%
+that had been achieved at that time and
+ 
+
+ align:start position:0%
+that had been achieved at that time and
+then looking forward looked at the
+
+ align:start position:0%
+then looking forward looked at the
+ 
+
+ align:start position:0%
+then looking forward looked at the
+analogy of the human genome initiative
+
+ align:start position:0%
+analogy of the human genome initiative
+ 
+
+ align:start position:0%
+analogy of the human genome initiative
+as possibly the greatest engineering
+
+ align:start position:0%
+as possibly the greatest engineering
+ 
+
+ align:start position:0%
+as possibly the greatest engineering
+database in history that was created not
+
+ align:start position:0%
+database in history that was created not
+ 
+
+ align:start position:0%
+database in history that was created not
+just to support the life sciences but
+
+ align:start position:0%
+just to support the life sciences but
+ 
+
+ align:start position:0%
+just to support the life sciences but
+really to support science-based medicine
+
+ align:start position:0%
+really to support science-based medicine
+ 
+
+ align:start position:0%
+really to support science-based medicine
+an example of which is that mRNA vaccine
+
+ align:start position:0%
+an example of which is that mRNA vaccine
+ 
+
+ align:start position:0%
+an example of which is that mRNA vaccine
+we're all getting these days uh so it's
+
+ align:start position:0%
+we're all getting these days uh so it's
+ 
+
+ align:start position:0%
+we're all getting these days uh so it's
+had a tremendous impact in allowing a
+
+ align:start position:0%
+had a tremendous impact in allowing a
+ 
+
+ align:start position:0%
+had a tremendous impact in allowing a
+more science-based approach to medicine
+
+ align:start position:0%
+more science-based approach to medicine
+ 
+
+ align:start position:0%
+more science-based approach to medicine
+so the concept of the materials genome
+
+ align:start position:0%
+so the concept of the materials genome
+ 
+
+ align:start position:0%
+so the concept of the materials genome
+from the start as uh called for in this
+
+ align:start position:0%
+from the start as uh called for in this
+ 
+
+ align:start position:0%
+from the start as uh called for in this
+2004 study uh was to build out an
+
+ align:start position:0%
+2004 study uh was to build out an
+ 
+
+ align:start position:0%
+2004 study uh was to build out an
+equally fundamental uh
+
+ align:start position:0%
+equally fundamental uh
+ 
+
+ align:start position:0%
+equally fundamental uh
+database uh with the idea that the human
+
+ align:start position:0%
+database uh with the idea that the human
+ 
+
+ align:start position:0%
+database uh with the idea that the human
+genome physically functions as a
+
+ align:start position:0%
+genome physically functions as a
+ 
+
+ align:start position:0%
+genome physically functions as a
+database that directs the Assembly of
+
+ align:start position:0%
+database that directs the Assembly of
+ 
+
+ align:start position:0%
+database that directs the Assembly of
+the structures of Life uh what are the
+
+ align:start position:0%
+the structures of Life uh what are the
+ 
+
+ align:start position:0%
+the structures of Life uh what are the
+equally fundamental parameters that
+
+ align:start position:0%
+equally fundamental parameters that
+ 
+
+ align:start position:0%
+equally fundamental parameters that
+direct the Assembly of the micr
+
+ align:start position:0%
+direct the Assembly of the micr
+ 
+
+ align:start position:0%
+direct the Assembly of the micr
+structure of materials and could we use
+
+ align:start position:0%
+structure of materials and could we use
+ 
+
+ align:start position:0%
+structure of materials and could we use
+such a system to not just support
+
+ align:start position:0%
+such a system to not just support
+ 
+
+ align:start position:0%
+such a system to not just support
+Material Science but to enable a new
+
+ align:start position:0%
+Material Science but to enable a new
+ 
+
+ align:start position:0%
+Material Science but to enable a new
+form of science-based materials
+
+ align:start position:0%
+form of science-based materials
+ 
+
+ align:start position:0%
+form of science-based materials
+engineering so it really was the
+
+ align:start position:0%
+engineering so it really was the
+ 
+
+ align:start position:0%
+engineering so it really was the
+ultimate engineering application and the
+
+ align:start position:0%
+ultimate engineering application and the
+ 
+
+ align:start position:0%
+ultimate engineering application and the
+ability to put our scientific
+
+ align:start position:0%
+ability to put our scientific
+ 
+
+ align:start position:0%
+ability to put our scientific
+understanding uh in a useful predictive
+
+ align:start position:0%
+understanding uh in a useful predictive
+ 
+
+ align:start position:0%
+understanding uh in a useful predictive
+form uh that really was the whole
+
+ align:start position:0%
+form uh that really was the whole
+ 
+
+ align:start position:0%
+form uh that really was the whole
+Central concept of this materialist
+
+ align:start position:0%
+Central concept of this materialist
+ 
+
+ align:start position:0%
+Central concept of this materialist
+genome initiative uh and the
+
+ align:start position:0%
+genome initiative uh and the
+ 
+
+ align:start position:0%
+genome initiative uh and the
+recommendation in 2004 uh is exactly the
+
+ align:start position:0%
+recommendation in 2004 uh is exactly the
+ 
+
+ align:start position:0%
+recommendation in 2004 uh is exactly the
+structure that was formed and then is
+
+ align:start position:0%
+structure that was formed and then is
+ 
+
+ align:start position:0%
+structure that was formed and then is
+continuing today now there have been
+
+ align:start position:0%
+continuing today now there have been
+ 
+
+ align:start position:0%
+continuing today now there have been
+many Academy studies uh acknowledging
+
+ align:start position:0%
+many Academy studies uh acknowledging
+ 
+
+ align:start position:0%
+many Academy studies uh acknowledging
+the new opportunity of computational
+
+ align:start position:0%
+the new opportunity of computational
+ 
+
+ align:start position:0%
+the new opportunity of computational
+materials engineering but one thing that
+
+ align:start position:0%
+materials engineering but one thing that
+ 
+
+ align:start position:0%
+materials engineering but one thing that
+was unique about the 2004 study was the
+
+ align:start position:0%
+was unique about the 2004 study was the
+ 
+
+ align:start position:0%
+was unique about the 2004 study was the
+leading role
+
+ align:start position:0%
+leading role
+ 
+
+ align:start position:0%
+leading role
+of a Global Network of small businesses
+
+ align:start position:0%
+of a Global Network of small businesses
+ 
+
+ align:start position:0%
+of a Global Network of small businesses
+that created and maintained this
+
+ align:start position:0%
+that created and maintained this
+ 
+
+ align:start position:0%
+that created and maintained this
+technology and made this possible uh and
+
+ align:start position:0%
+technology and made this possible uh and
+ 
+
+ align:start position:0%
+technology and made this possible uh and
+so this was a list that was constructed
+
+ align:start position:0%
+so this was a list that was constructed
+ 
+
+ align:start position:0%
+so this was a list that was constructed
+at in that report of what had already
+
+ align:start position:0%
+at in that report of what had already
+ 
+
+ align:start position:0%
+at in that report of what had already
+been made available at that time and
+
+ align:start position:0%
+been made available at that time and
+ 
+
+ align:start position:0%
+been made available at that time and
+demonstrated successes of the
+
+ align:start position:0%
+demonstrated successes of the
+ 
+
+ align:start position:0%
+demonstrated successes of the
+technology uh the principal mechanism by
+
+ align:start position:0%
+technology uh the principal mechanism by
+ 
+
+ align:start position:0%
+technology uh the principal mechanism by
+this the way that uh this technology has
+
+ align:start position:0%
+this the way that uh this technology has
+ 
+
+ align:start position:0%
+this the way that uh this technology has
+moved into major corporations has been
+
+ align:start position:0%
+moved into major corporations has been
+ 
+
+ align:start position:0%
+moved into major corporations has been
+by Acquisitions of various forms that
+
+ align:start position:0%
+by Acquisitions of various forms that
+ 
+
+ align:start position:0%
+by Acquisitions of various forms that
+have affected about a third of the
+
+ align:start position:0%
+have affected about a third of the
+ 
+
+ align:start position:0%
+have affected about a third of the
+companies on this chart so small
+
+ align:start position:0%
+companies on this chart so small
+ 
+
+ align:start position:0%
+companies on this chart so small
+business really did create this
+
+ align:start position:0%
+business really did create this
+ 
+
+ align:start position:0%
+business really did create this
+technology and and Lead the
+
+ align:start position:0%
+technology and and Lead the
+ 
+
+ align:start position:0%
+technology and and Lead the
+Way historic Milestone was a decade ago
+
+ align:start position:0%
+Way historic Milestone was a decade ago
+ 
+
+ align:start position:0%
+Way historic Milestone was a decade ago
+with the first flight of quc ferium s53
+
+ align:start position:0%
+with the first flight of quc ferium s53
+ 
+
+ align:start position:0%
+with the first flight of quc ferium s53
+stainless landing gear steel and this
+
+ align:start position:0%
+stainless landing gear steel and this
+ 
+
+ align:start position:0%
+stainless landing gear steel and this
+was the first stainless steel uh to meet
+
+ align:start position:0%
+was the first stainless steel uh to meet
+ 
+
+ align:start position:0%
+was the first stainless steel uh to meet
+the mechanical performance requirements
+
+ align:start position:0%
+the mechanical performance requirements
+ 
+
+ align:start position:0%
+the mechanical performance requirements
+of aircraft landing gear uh which was
+
+ align:start position:0%
+of aircraft landing gear uh which was
+ 
+
+ align:start position:0%
+of aircraft landing gear uh which was
+driven uh by by the need to eliminate uh
+
+ align:start position:0%
+driven uh by by the need to eliminate uh
+ 
+
+ align:start position:0%
+driven uh by by the need to eliminate uh
+toxic cadmium plating so this was a
+
+ align:start position:0%
+toxic cadmium plating so this was a
+ 
+
+ align:start position:0%
+toxic cadmium plating so this was a
+green steel solving an environmental
+
+ align:start position:0%
+green steel solving an environmental
+ 
+
+ align:start position:0%
+green steel solving an environmental
+issue uh but more significant it
+
+ align:start position:0%
+issue uh but more significant it
+ 
+
+ align:start position:0%
+issue uh but more significant it
+represented the first fully
+
+ align:start position:0%
+represented the first fully
+ 
+
+ align:start position:0%
+represented the first fully
+computationally designed and flight
+
+ align:start position:0%
+computationally designed and flight
+ 
+
+ align:start position:0%
+computationally designed and flight
+qualified material to go all the way to
+
+ align:start position:0%
+qualified material to go all the way to
+ 
+
+ align:start position:0%
+qualified material to go all the way to
+flight and that was just in December of
+
+ align:start position:0%
+flight and that was just in December of
+ 
+
+ align:start position:0%
+flight and that was just in December of
+uh 2010 so that really uh measures a
+
+ align:start position:0%
+uh 2010 so that really uh measures a
+ 
+
+ align:start position:0%
+uh 2010 so that really uh measures a
+high level of maturity of this
+
+ align:start position:0%
+high level of maturity of this
+ 
+
+ align:start position:0%
+high level of maturity of this
+technology even before the national MGI
+
+ align:start position:0%
+technology even before the national MGI
+ 
+
+ align:start position:0%
+technology even before the national MGI
+was
+
+ align:start position:0%
+was
+ 
+
+ align:start position:0%
+was
+created and that is reinforced by this
+
+ align:start position:0%
+created and that is reinforced by this
+ 
+
+ align:start position:0%
+created and that is reinforced by this
+timeline so there had been debate as to
+
+ align:start position:0%
+timeline so there had been debate as to
+ 
+
+ align:start position:0%
+timeline so there had been debate as to
+what a material's genome could be it's
+
+ align:start position:0%
+what a material's genome could be it's
+ 
+
+ align:start position:0%
+what a material's genome could be it's
+very clear the genome we have is in fact
+
+ align:start position:0%
+very clear the genome we have is in fact
+ 
+
+ align:start position:0%
+very clear the genome we have is in fact
+the calad database system uh whose
+
+ align:start position:0%
+the calad database system uh whose
+ 
+
+ align:start position:0%
+the calad database system uh whose
+Origins go back to Kaufman and Cohen at
+
+ align:start position:0%
+Origins go back to Kaufman and Cohen at
+ 
+
+ align:start position:0%
+Origins go back to Kaufman and Cohen at
+MIT in the
+
+ align:start position:0%
+MIT in the
+ 
+
+ align:start position:0%
+MIT in the
+1950s uh with a calculation of the iron
+
+ align:start position:0%
+1950s uh with a calculation of the iron
+ 
+
+ align:start position:0%
+1950s uh with a calculation of the iron
+nickel phase
+
+ align:start position:0%
+nickel phase
+ 
+
+ align:start position:0%
+nickel phase
+diagram um like to emphasize though the
+
+ align:start position:0%
+diagram um like to emphasize though the
+ 
+
+ align:start position:0%
+diagram um like to emphasize though the
+the calad
+
+ align:start position:0%
+the calad
+ 
+
+ align:start position:0%
+the calad
+acronym uh is based on calculation of
+
+ align:start position:0%
+acronym uh is based on calculation of
+ 
+
+ align:start position:0%
+acronym uh is based on calculation of
+phase diagrams but uh the reason for
+
+ align:start position:0%
+phase diagrams but uh the reason for
+ 
+
+ align:start position:0%
+phase diagrams but uh the reason for
+that acronym was to distinguish it from
+
+ align:start position:0%
+that acronym was to distinguish it from
+ 
+
+ align:start position:0%
+that acronym was to distinguish it from
+something called f comp at the time uh
+
+ align:start position:0%
+something called f comp at the time uh
+ 
+
+ align:start position:0%
+something called f comp at the time uh
+that was a technique that was trying to
+
+ align:start position:0%
+that was a technique that was trying to
+ 
+
+ align:start position:0%
+that was a technique that was trying to
+estimate uh solubility limits in Alloys
+
+ align:start position:0%
+estimate uh solubility limits in Alloys
+ 
+
+ align:start position:0%
+estimate uh solubility limits in Alloys
+from the attributes of a single phase
+
+ align:start position:0%
+from the attributes of a single phase
+ 
+
+ align:start position:0%
+from the attributes of a single phase
+and calfat acknowledges that solubility
+
+ align:start position:0%
+and calfat acknowledges that solubility
+ 
+
+ align:start position:0%
+and calfat acknowledges that solubility
+is really uh based on phase competition
+
+ align:start position:0%
+is really uh based on phase competition
+ 
+
+ align:start position:0%
+is really uh based on phase competition
+that is uh represented by phase diagrams
+
+ align:start position:0%
+that is uh represented by phase diagrams
+ 
+
+ align:start position:0%
+that is uh represented by phase diagrams
+uh in the equilibrium uh limit uh but in
+
+ align:start position:0%
+uh in the equilibrium uh limit uh but in
+ 
+
+ align:start position:0%
+uh in the equilibrium uh limit uh but in
+fact I think yes can if you don't mind
+
+ align:start position:0%
+fact I think yes can if you don't mind
+ 
+
+ align:start position:0%
+fact I think yes can if you don't mind
+um can you just
+
+ align:start position:0%
+um can you just
+ 
+
+ align:start position:0%
+um can you just
+briefly uh tell us about landing gear
+
+ align:start position:0%
+briefly uh tell us about landing gear
+ 
+
+ align:start position:0%
+briefly uh tell us about landing gear
+and why that's such an accomplishment
+
+ align:start position:0%
+and why that's such an accomplishment
+ 
+
+ align:start position:0%
+and why that's such an accomplishment
+you know I think we take a lot of these
+
+ align:start position:0%
+you know I think we take a lot of these
+ 
+
+ align:start position:0%
+you know I think we take a lot of these
+things for granted you know what what is
+
+ align:start position:0%
+things for granted you know what what is
+ 
+
+ align:start position:0%
+things for granted you know what what is
+it like if there's one one of many
+
+ align:start position:0%
+it like if there's one one of many
+ 
+
+ align:start position:0%
+it like if there's one one of many
+material criteria for instance that that
+
+ align:start position:0%
+material criteria for instance that that
+ 
+
+ align:start position:0%
+material criteria for instance that that
+makes that such a demanding application
+
+ align:start position:0%
+makes that such a demanding application
+ 
+
+ align:start position:0%
+makes that such a demanding application
+so we can understand why that's a big
+
+ align:start position:0%
+so we can understand why that's a big
+ 
+
+ align:start position:0%
+so we can understand why that's a big
+deal yeah I think I'll come back to it a
+
+ align:start position:0%
+deal yeah I think I'll come back to it a
+ 
+
+ align:start position:0%
+deal yeah I think I'll come back to it a
+bit later but but it is the the big
+
+ align:start position:0%
+bit later but but it is the the big
+ 
+
+ align:start position:0%
+bit later but but it is the the big
+challenge is that the high chromium
+
+ align:start position:0%
+challenge is that the high chromium
+ 
+
+ align:start position:0%
+challenge is that the high chromium
+levels that you need uh to get the
+
+ align:start position:0%
+levels that you need uh to get the
+ 
+
+ align:start position:0%
+levels that you need uh to get the
+corrosion resistance are in conflict
+
+ align:start position:0%
+corrosion resistance are in conflict
+ 
+
+ align:start position:0%
+corrosion resistance are in conflict
+with the things you need for the
+
+ align:start position:0%
+with the things you need for the
+ 
+
+ align:start position:0%
+with the things you need for the
+mechanical performance of strength and
+
+ align:start position:0%
+mechanical performance of strength and
+ 
+
+ align:start position:0%
+mechanical performance of strength and
+Fracture toughness and it was a matter
+
+ align:start position:0%
+Fracture toughness and it was a matter
+ 
+
+ align:start position:0%
+Fracture toughness and it was a matter
+of uh using a predictive science
+
+ align:start position:0%
+of uh using a predictive science
+ 
+
+ align:start position:0%
+of uh using a predictive science
+approach uh to take it to a higher level
+
+ align:start position:0%
+approach uh to take it to a higher level
+ 
+
+ align:start position:0%
+approach uh to take it to a higher level
+of optimization that could uh resolve
+
+ align:start position:0%
+of optimization that could uh resolve
+ 
+
+ align:start position:0%
+of optimization that could uh resolve
+that conflict that wasn't going to
+
+ align:start position:0%
+that conflict that wasn't going to
+ 
+
+ align:start position:0%
+that conflict that wasn't going to
+happen by empirical development yeah and
+
+ align:start position:0%
+happen by empirical development yeah and
+ 
+
+ align:start position:0%
+happen by empirical development yeah and
+I'll I'll illustrate what was key to
+
+ align:start position:0%
+I'll I'll illustrate what was key to
+ 
+
+ align:start position:0%
+I'll I'll illustrate what was key to
+that later
+
+ align:start position:0%
+that later
+ 
+
+ align:start position:0%
+that later
+on but I want to emphasize that uh uh
+
+ align:start position:0%
+on but I want to emphasize that uh uh
+ 
+
+ align:start position:0%
+on but I want to emphasize that uh uh
+actually is the name of your class uh
+
+ align:start position:0%
+actually is the name of your class uh
+ 
+
+ align:start position:0%
+actually is the name of your class uh
+materials at equilibrium still is that
+
+ align:start position:0%
+materials at equilibrium still is that
+ 
+
+ align:start position:0%
+materials at equilibrium still is that
+the name that's used no it's
+
+ align:start position:0%
+the name that's used no it's
+ 
+
+ align:start position:0%
+the name that's used no it's
+thermodynamics but it might as well be
+
+ align:start position:0%
+thermodynamics but it might as well be
+ 
+
+ align:start position:0%
+thermodynamics but it might as well be
+material equilibrium okay all right
+
+ align:start position:0%
+material equilibrium okay all right
+ 
+
+ align:start position:0%
+material equilibrium okay all right
+because uh you know we tend to think of
+
+ align:start position:0%
+because uh you know we tend to think of
+ 
+
+ align:start position:0%
+because uh you know we tend to think of
+uh I think the way thermodynamics is
+
+ align:start position:0%
+uh I think the way thermodynamics is
+ 
+
+ align:start position:0%
+uh I think the way thermodynamics is
+thought often we tend to think of it as
+
+ align:start position:0%
+thought often we tend to think of it as
+ 
+
+ align:start position:0%
+thought often we tend to think of it as
+something that applies only to
+
+ align:start position:0%
+something that applies only to
+ 
+
+ align:start position:0%
+something that applies only to
+equilibrium but but the truth is
+
+ align:start position:0%
+equilibrium but but the truth is
+ 
+
+ align:start position:0%
+equilibrium but but the truth is
+wouldn't be called thermodynamics if it
+
+ align:start position:0%
+wouldn't be called thermodynamics if it
+ 
+
+ align:start position:0%
+wouldn't be called thermodynamics if it
+was only about equilibrium it was
+
+ align:start position:0%
+was only about equilibrium it was
+ 
+
+ align:start position:0%
+was only about equilibrium it was
+created to describe heat engines that
+
+ align:start position:0%
+created to describe heat engines that
+ 
+
+ align:start position:0%
+created to describe heat engines that
+are highly Dynamic systems where in
+
+ align:start position:0%
+are highly Dynamic systems where in
+ 
+
+ align:start position:0%
+are highly Dynamic systems where in
+modeling them it was useful to look at
+
+ align:start position:0%
+modeling them it was useful to look at
+ 
+
+ align:start position:0%
+modeling them it was useful to look at
+equilibrium limits it's also very useful
+
+ align:start position:0%
+equilibrium limits it's also very useful
+ 
+
+ align:start position:0%
+equilibrium limits it's also very useful
+if you want to measure thermodynamics we
+
+ align:start position:0%
+if you want to measure thermodynamics we
+ 
+
+ align:start position:0%
+if you want to measure thermodynamics we
+should take systems to equilibrium so we
+
+ align:start position:0%
+should take systems to equilibrium so we
+ 
+
+ align:start position:0%
+should take systems to equilibrium so we
+know what we're measuring but really the
+
+ align:start position:0%
+know what we're measuring but really the
+ 
+
+ align:start position:0%
+know what we're measuring but really the
+power of of thermodynamics is it
+
+ align:start position:0%
+power of of thermodynamics is it
+ 
+
+ align:start position:0%
+power of of thermodynamics is it
+describes the driving force of dynamic
+
+ align:start position:0%
+describes the driving force of dynamic
+ 
+
+ align:start position:0%
+describes the driving force of dynamic
+systems and it really drives the
+
+ align:start position:0%
+systems and it really drives the
+ 
+
+ align:start position:0%
+systems and it really drives the
+evolution of microstructures and
+
+ align:start position:0%
+evolution of microstructures and
+ 
+
+ align:start position:0%
+evolution of microstructures and
+processing and and service so uh it
+
+ align:start position:0%
+processing and and service so uh it
+ 
+
+ align:start position:0%
+processing and and service so uh it
+really is in that sense the genomic data
+
+ align:start position:0%
+really is in that sense the genomic data
+ 
+
+ align:start position:0%
+really is in that sense the genomic data
+that drives the
+
+ align:start position:0%
+that drives the
+ 
+
+ align:start position:0%
+that drives the
+systems so in fact uh I prefer to uh
+
+ align:start position:0%
+systems so in fact uh I prefer to uh
+ 
+
+ align:start position:0%
+systems so in fact uh I prefer to uh
+describe calad as calculated phase
+
+ align:start position:0%
+describe calad as calculated phase
+ 
+
+ align:start position:0%
+describe calad as calculated phase
+Dynamics and so it starts with
+
+ align:start position:0%
+Dynamics and so it starts with
+ 
+
+ align:start position:0%
+Dynamics and so it starts with
+thermodynamics uh but its real Power
+
+ align:start position:0%
+thermodynamics uh but its real Power
+ 
+
+ align:start position:0%
+thermodynamics uh but its real Power
+Systems far from equilibrium and in fact
+
+ align:start position:0%
+Systems far from equilibrium and in fact
+ 
+
+ align:start position:0%
+Systems far from equilibrium and in fact
+uh when it was invented by Kaufman and
+
+ align:start position:0%
+uh when it was invented by Kaufman and
+ 
+
+ align:start position:0%
+uh when it was invented by Kaufman and
+Cohen uh what they were really trying to
+
+ align:start position:0%
+Cohen uh what they were really trying to
+ 
+
+ align:start position:0%
+Cohen uh what they were really trying to
+do was not uh to calculate a phase
+
+ align:start position:0%
+do was not uh to calculate a phase
+ 
+
+ align:start position:0%
+do was not uh to calculate a phase
+diagram they were trying to take the
+
+ align:start position:0%
+diagram they were trying to take the
+ 
+
+ align:start position:0%
+diagram they were trying to take the
+information that's there in an
+
+ align:start position:0%
+information that's there in an
+ 
+
+ align:start position:0%
+information that's there in an
+equilibrium diagram and reduce it to its
+
+ align:start position:0%
+equilibrium diagram and reduce it to its
+ 
+
+ align:start position:0%
+equilibrium diagram and reduce it to its
+underlying Thermon namics so they could
+
+ align:start position:0%
+underlying Thermon namics so they could
+ 
+
+ align:start position:0%
+underlying Thermon namics so they could
+apply that theramic to Martin cidic
+
+ align:start position:0%
+apply that theramic to Martin cidic
+ 
+
+ align:start position:0%
+apply that theramic to Martin cidic
+Transformations that are far from
+
+ align:start position:0%
+Transformations that are far from
+ 
+
+ align:start position:0%
+Transformations that are far from
+equilibrium so it was really to create
+
+ align:start position:0%
+equilibrium so it was really to create
+ 
+
+ align:start position:0%
+equilibrium so it was really to create
+the get the underlying Thermon namics uh
+
+ align:start position:0%
+the get the underlying Thermon namics uh
+ 
+
+ align:start position:0%
+the get the underlying Thermon namics uh
+to understand the driving forces for the
+
+ align:start position:0%
+to understand the driving forces for the
+ 
+
+ align:start position:0%
+to understand the driving forces for the
+Dynamics of Martin City Transformations
+
+ align:start position:0%
+Dynamics of Martin City Transformations
+ 
+
+ align:start position:0%
+Dynamics of Martin City Transformations
+so it really is the non-equilibrium
+
+ align:start position:0%
+so it really is the non-equilibrium
+ 
+
+ align:start position:0%
+so it really is the non-equilibrium
+applications that drove the creation of
+
+ align:start position:0%
+applications that drove the creation of
+ 
+
+ align:start position:0%
+applications that drove the creation of
+the technology in the first place so it
+
+ align:start position:0%
+the technology in the first place so it
+ 
+
+ align:start position:0%
+the technology in the first place so it
+began uh as solution Thermon namics
+
+ align:start position:0%
+began uh as solution Thermon namics
+ 
+
+ align:start position:0%
+began uh as solution Thermon namics
+uh and uh became an international
+
+ align:start position:0%
+uh and uh became an international
+ 
+
+ align:start position:0%
+uh and uh became an international
+organization in the
+
+ align:start position:0%
+organization in the
+ 
+
+ align:start position:0%
+organization in the
+1970s uh and the first commercial
+
+ align:start position:0%
+1970s uh and the first commercial
+ 
+
+ align:start position:0%
+1970s uh and the first commercial
+software showed up around the
+
+ align:start position:0%
+software showed up around the
+ 
+
+ align:start position:0%
+software showed up around the
+1980s uh but then it expanded from
+
+ align:start position:0%
+1980s uh but then it expanded from
+ 
+
+ align:start position:0%
+1980s uh but then it expanded from
+solution Thermon namics to adding
+
+ align:start position:0%
+solution Thermon namics to adding
+ 
+
+ align:start position:0%
+solution Thermon namics to adding
+Mobility databases and solving
+
+ align:start position:0%
+Mobility databases and solving
+ 
+
+ align:start position:0%
+Mobility databases and solving
+multicomponent diffusion problems moving
+
+ align:start position:0%
+multicomponent diffusion problems moving
+ 
+
+ align:start position:0%
+multicomponent diffusion problems moving
+on to other phase level attributes such
+
+ align:start position:0%
+on to other phase level attributes such
+ 
+
+ align:start position:0%
+on to other phase level attributes such
+as elastic uh constants uh so an
+
+ align:start position:0%
+as elastic uh constants uh so an
+ 
+
+ align:start position:0%
+as elastic uh constants uh so an
+increasing array of phase level uh
+
+ align:start position:0%
+increasing array of phase level uh
+ 
+
+ align:start position:0%
+increasing array of phase level uh
+theramic and kinetic attributes uh over
+
+ align:start position:0%
+theramic and kinetic attributes uh over
+ 
+
+ align:start position:0%
+theramic and kinetic attributes uh over
+an expanding scope of materials from
+
+ align:start position:0%
+an expanding scope of materials from
+ 
+
+ align:start position:0%
+an expanding scope of materials from
+metals to Ceramics and very recently
+
+ align:start position:0%
+metals to Ceramics and very recently
+ 
+
+ align:start position:0%
+metals to Ceramics and very recently
+organic systems as well uh all of which
+
+ align:start position:0%
+organic systems as well uh all of which
+ 
+
+ align:start position:0%
+organic systems as well uh all of which
+was largely based on empirical
+
+ align:start position:0%
+was largely based on empirical
+ 
+
+ align:start position:0%
+was largely based on empirical
+measurement uh but today uh DFT physics
+
+ align:start position:0%
+measurement uh but today uh DFT physics
+ 
+
+ align:start position:0%
+measurement uh but today uh DFT physics
+calculations uh received enough uh
+
+ align:start position:0%
+calculations uh received enough uh
+ 
+
+ align:start position:0%
+calculations uh received enough uh
+accuracy and efficiency that they now
+
+ align:start position:0%
+accuracy and efficiency that they now
+ 
+
+ align:start position:0%
+accuracy and efficiency that they now
+actually actively participate and we
+
+ align:start position:0%
+actually actively participate and we
+ 
+
+ align:start position:0%
+actually actively participate and we
+integrate into the assessment of these
+
+ align:start position:0%
+integrate into the assessment of these
+ 
+
+ align:start position:0%
+integrate into the assessment of these
+databases uh the predictions from uh
+
+ align:start position:0%
+databases uh the predictions from uh
+ 
+
+ align:start position:0%
+databases uh the predictions from uh
+physics calculations at least for zero
+
+ align:start position:0%
+physics calculations at least for zero
+ 
+
+ align:start position:0%
+physics calculations at least for zero
+Kelvin enthalpy
+
+ align:start position:0%
+Kelvin enthalpy
+ 
+
+ align:start position:0%
+Kelvin enthalpy
+predictions uh so it was the uh arrival
+
+ align:start position:0%
+predictions uh so it was the uh arrival
+ 
+
+ align:start position:0%
+predictions uh so it was the uh arrival
+of the thermocalc system as a commercial
+
+ align:start position:0%
+of the thermocalc system as a commercial
+ 
+
+ align:start position:0%
+of the thermocalc system as a commercial
+code uh and a supporting uh software uh
+
+ align:start position:0%
+code uh and a supporting uh software uh
+ 
+
+ align:start position:0%
+code uh and a supporting uh software uh
+database structure uh set by the
+
+ align:start position:0%
+database structure uh set by the
+ 
+
+ align:start position:0%
+database structure uh set by the
+European sgte Consortium that set some
+
+ align:start position:0%
+European sgte Consortium that set some
+ 
+
+ align:start position:0%
+European sgte Consortium that set some
+level of
+
+ align:start position:0%
+level of
+ 
+
+ align:start position:0%
+level of
+standardization uh that really inspired
+
+ align:start position:0%
+standardization uh that really inspired
+ 
+
+ align:start position:0%
+standardization uh that really inspired
+our founding in
+
+ align:start position:0%
+our founding in
+ 
+
+ align:start position:0%
+our founding in
+1985 of our srg uh design Consortium and
+
+ align:start position:0%
+1985 of our srg uh design Consortium and
+ 
+
+ align:start position:0%
+1985 of our srg uh design Consortium and
+this was founded at MIT
+
+ align:start position:0%
+this was founded at MIT
+ 
+
+ align:start position:0%
+this was founded at MIT
+uh and the idea was uh to create a
+
+ align:start position:0%
+uh and the idea was uh to create a
+ 
+
+ align:start position:0%
+uh and the idea was uh to create a
+general methodology of computational
+
+ align:start position:0%
+general methodology of computational
+ 
+
+ align:start position:0%
+general methodology of computational
+materials design that would be enabled
+
+ align:start position:0%
+materials design that would be enabled
+ 
+
+ align:start position:0%
+materials design that would be enabled
+by these underlying calad
+
+ align:start position:0%
+by these underlying calad
+ 
+
+ align:start position:0%
+by these underlying calad
+databases uh with the idea that we would
+
+ align:start position:0%
+databases uh with the idea that we would
+ 
+
+ align:start position:0%
+databases uh with the idea that we would
+use high performance Steels as the first
+
+ align:start position:0%
+use high performance Steels as the first
+ 
+
+ align:start position:0%
+use high performance Steels as the first
+example acknowledging that we studied
+
+ align:start position:0%
+example acknowledging that we studied
+ 
+
+ align:start position:0%
+example acknowledging that we studied
+Steels the longest have the deepest
+
+ align:start position:0%
+Steels the longest have the deepest
+ 
+
+ align:start position:0%
+Steels the longest have the deepest
+predictive Science Foundation in steel
+
+ align:start position:0%
+predictive Science Foundation in steel
+ 
+
+ align:start position:0%
+predictive Science Foundation in steel
+and also at that point the highest
+
+ align:start position:0%
+and also at that point the highest
+ 
+
+ align:start position:0%
+and also at that point the highest
+quality of theramic data was available
+
+ align:start position:0%
+quality of theramic data was available
+ 
+
+ align:start position:0%
+quality of theramic data was available
+for Steels to use that as the
+
+ align:start position:0%
+for Steels to use that as the
+ 
+
+ align:start position:0%
+for Steels to use that as the
+demonstrator so our first projects were
+
+ align:start position:0%
+demonstrator so our first projects were
+ 
+
+ align:start position:0%
+demonstrator so our first projects were
+designs of Steels but throughout the
+
+ align:start position:0%
+designs of Steels but throughout the
+ 
+
+ align:start position:0%
+designs of Steels but throughout the
+1990s uh we did uh a number of demo
+
+ align:start position:0%
+1990s uh we did uh a number of demo
+ 
+
+ align:start position:0%
+1990s uh we did uh a number of demo
+projects that applied the same
+
+ align:start position:0%
+projects that applied the same
+ 
+
+ align:start position:0%
+projects that applied the same
+methodology to other alloy systems
+
+ align:start position:0%
+methodology to other alloy systems
+ 
+
+ align:start position:0%
+methodology to other alloy systems
+polymer Ceramics and even some composits
+
+ align:start position:0%
+polymer Ceramics and even some composits
+ 
+
+ align:start position:0%
+polymer Ceramics and even some composits
+to show its generality and it was the
+
+ align:start position:0%
+to show its generality and it was the
+ 
+
+ align:start position:0%
+to show its generality and it was the
+first steel designs that ultimately led
+
+ align:start position:0%
+first steel designs that ultimately led
+ 
+
+ align:start position:0%
+first steel designs that ultimately led
+to the founding in the late
+
+ align:start position:0%
+to the founding in the late
+ 
+
+ align:start position:0%
+to the founding in the late
+1990s of questec as a company that could
+
+ align:start position:0%
+1990s of questec as a company that could
+ 
+
+ align:start position:0%
+1990s of questec as a company that could
+offer uh computational Design Services
+
+ align:start position:0%
+offer uh computational Design Services
+ 
+
+ align:start position:0%
+offer uh computational Design Services
+based on this technology but what the
+
+ align:start position:0%
+based on this technology but what the
+ 
+
+ align:start position:0%
+based on this technology but what the
+calat is really allowing us to do is is
+
+ align:start position:0%
+calat is really allowing us to do is is
+ 
+
+ align:start position:0%
+calat is really allowing us to do is is
+use this mechanistic understanding we
+
+ align:start position:0%
+use this mechanistic understanding we
+ 
+
+ align:start position:0%
+use this mechanistic understanding we
+already possess but use it in a
+
+ align:start position:0%
+already possess but use it in a
+ 
+
+ align:start position:0%
+already possess but use it in a
+quantitative system specific
+
+ align:start position:0%
+quantitative system specific
+ 
+
+ align:start position:0%
+quantitative system specific
+way and that's what enabled the the
+
+ align:start position:0%
+way and that's what enabled the the
+ 
+
+ align:start position:0%
+way and that's what enabled the the
+successful demonstrations of design of
+
+ align:start position:0%
+successful demonstrations of design of
+ 
+
+ align:start position:0%
+successful demonstrations of design of
+new materials throughout the
+
+ align:start position:0%
+new materials throughout the
+ 
+
+ align:start position:0%
+new materials throughout the
+1990s uh and it was largely that
+
+ align:start position:0%
+1990s uh and it was largely that
+ 
+
+ align:start position:0%
+1990s uh and it was largely that
+demonstrated success that made the case
+
+ align:start position:0%
+demonstrated success that made the case
+ 
+
+ align:start position:0%
+demonstrated success that made the case
+uh for the DARPA aim in initiative which
+
+ align:start position:0%
+uh for the DARPA aim in initiative which
+ 
+
+ align:start position:0%
+uh for the DARPA aim in initiative which
+began at the start of the the New
+
+ align:start position:0%
+began at the start of the the New
+ 
+
+ align:start position:0%
+began at the start of the the New
+Millennium uh and this was really
+
+ align:start position:0%
+Millennium uh and this was really
+ 
+
+ align:start position:0%
+Millennium uh and this was really
+addressing uh the central focus of what
+
+ align:start position:0%
+addressing uh the central focus of what
+ 
+
+ align:start position:0%
+addressing uh the central focus of what
+is now the MGI and what we now call
+
+ align:start position:0%
+is now the MGI and what we now call
+ 
+
+ align:start position:0%
+is now the MGI and what we now call
+Integrated computational materials
+
+ align:start position:0%
+Integrated computational materials
+ 
+
+ align:start position:0%
+Integrated computational materials
+engineering or mcme and this was to go
+
+ align:start position:0%
+engineering or mcme and this was to go
+ 
+
+ align:start position:0%
+engineering or mcme and this was to go
+beyond the design of an alloy and SP set
+
+ align:start position:0%
+beyond the design of an alloy and SP set
+ 
+
+ align:start position:0%
+beyond the design of an alloy and SP set
+a
+
+ align:start position:0%
+a
+ 
+
+ align:start position:0%
+a
+specification of composition and process
+
+ align:start position:0%
+specification of composition and process
+ 
+
+ align:start position:0%
+specification of composition and process
+temperatures uh to really address the
+
+ align:start position:0%
+temperatures uh to really address the
+ 
+
+ align:start position:0%
+temperatures uh to really address the
+full materials development cycle uh and
+
+ align:start position:0%
+full materials development cycle uh and
+ 
+
+ align:start position:0%
+full materials development cycle uh and
+this meant uh connecting materials
+
+ align:start position:0%
+this meant uh connecting materials
+ 
+
+ align:start position:0%
+this meant uh connecting materials
+models to macroscopic process models uh
+
+ align:start position:0%
+models to macroscopic process models uh
+ 
+
+ align:start position:0%
+models to macroscopic process models uh
+to handle uh material production scaleup
+
+ align:start position:0%
+to handle uh material production scaleup
+ 
+
+ align:start position:0%
+to handle uh material production scaleup
+uh uh process optimization at the
+
+ align:start position:0%
+uh uh process optimization at the
+ 
+
+ align:start position:0%
+uh uh process optimization at the
+component level of things like landing
+
+ align:start position:0%
+component level of things like landing
+ 
+
+ align:start position:0%
+component level of things like landing
+gear uh and then most important uh the
+
+ align:start position:0%
+gear uh and then most important uh the
+ 
+
+ align:start position:0%
+gear uh and then most important uh the
+forecast of manufacturing variation so
+
+ align:start position:0%
+forecast of manufacturing variation so
+ 
+
+ align:start position:0%
+forecast of manufacturing variation so
+that you could predict the minimum
+
+ align:start position:0%
+that you could predict the minimum
+ 
+
+ align:start position:0%
+that you could predict the minimum
+properties of a material that uh are
+
+ align:start position:0%
+properties of a material that uh are
+ 
+
+ align:start position:0%
+properties of a material that uh are
+user could count on at a 1% probability
+
+ align:start position:0%
+user could count on at a 1% probability
+ 
+
+ align:start position:0%
+user could count on at a 1% probability
+basis and that's what it takes uh to get
+
+ align:start position:0%
+basis and that's what it takes uh to get
+ 
+
+ align:start position:0%
+basis and that's what it takes uh to get
+a material actually flight qualified for
+
+ align:start position:0%
+a material actually flight qualified for
+ 
+
+ align:start position:0%
+a material actually flight qualified for
+critical applications so at this point
+
+ align:start position:0%
+critical applications so at this point
+ 
+
+ align:start position:0%
+critical applications so at this point
+we've had over six Decades of building
+
+ align:start position:0%
+we've had over six Decades of building
+ 
+
+ align:start position:0%
+we've had over six Decades of building
+out a material's genome with calad
+
+ align:start position:0%
+out a material's genome with calad
+ 
+
+ align:start position:0%
+out a material's genome with calad
+structure uh about 30 years now of uh uh
+
+ align:start position:0%
+structure uh about 30 years now of uh uh
+ 
+
+ align:start position:0%
+structure uh about 30 years now of uh uh
+a full design technology and we've now
+
+ align:start position:0%
+a full design technology and we've now
+ 
+
+ align:start position:0%
+a full design technology and we've now
+been at 20 years of a fully integrated
+
+ align:start position:0%
+been at 20 years of a fully integrated
+ 
+
+ align:start position:0%
+been at 20 years of a fully integrated
+uh process so it's quite uh uh developed
+
+ align:start position:0%
+uh process so it's quite uh uh developed
+ 
+
+ align:start position:0%
+uh process so it's quite uh uh developed
+and as I'll touch on later on uh what
+
+ align:start position:0%
+and as I'll touch on later on uh what
+ 
+
+ align:start position:0%
+and as I'll touch on later on uh what
+this has allowed the compression of the
+
+ align:start position:0%
+this has allowed the compression of the
+ 
+
+ align:start position:0%
+this has allowed the compression of the
+materials developed vment cycle uh
+
+ align:start position:0%
+materials developed vment cycle uh
+ 
+
+ align:start position:0%
+materials developed vment cycle uh
+getting it down to the cycle of product
+
+ align:start position:0%
+getting it down to the cycle of product
+ 
+
+ align:start position:0%
+getting it down to the cycle of product
+development has allowed for the first
+
+ align:start position:0%
+development has allowed for the first
+ 
+
+ align:start position:0%
+development has allowed for the first
+time uh to include materials in
+
+ align:start position:0%
+time uh to include materials in
+ 
+
+ align:start position:0%
+time uh to include materials in
+concurrent engineering historically
+
+ align:start position:0%
+concurrent engineering historically
+ 
+
+ align:start position:0%
+concurrent engineering historically
+concurrent engineering meant everything
+
+ align:start position:0%
+concurrent engineering meant everything
+ 
+
+ align:start position:0%
+concurrent engineering meant everything
+but materials you had to use whatever
+
+ align:start position:0%
+but materials you had to use whatever
+ 
+
+ align:start position:0%
+but materials you had to use whatever
+materials were available uh and now
+
+ align:start position:0%
+materials were available uh and now
+ 
+
+ align:start position:0%
+materials were available uh and now
+there are a number of success stories
+
+ align:start position:0%
+there are a number of success stories
+ 
+
+ align:start position:0%
+there are a number of success stories
+I'll touch on later where materials have
+
+ align:start position:0%
+I'll touch on later where materials have
+ 
+
+ align:start position:0%
+I'll touch on later where materials have
+been fully integrated in concurrency and
+
+ align:start position:0%
+been fully integrated in concurrency and
+ 
+
+ align:start position:0%
+been fully integrated in concurrency and
+and uh allowing a very strong Synergy
+
+ align:start position:0%
+and uh allowing a very strong Synergy
+ 
+
+ align:start position:0%
+and uh allowing a very strong Synergy
+between materials development and
+
+ align:start position:0%
+between materials development and
+ 
+
+ align:start position:0%
+between materials development and
+product
+
+ align:start position:0%
+product
+ 
+
+ align:start position:0%
+product
+development so that's the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+landscape core of our approach uh is the
+
+ align:start position:0%
+landscape core of our approach uh is the
+ 
+
+ align:start position:0%
+landscape core of our approach uh is the
+philosophy of the late great serial
+
+ align:start position:0%
+philosophy of the late great serial
+ 
+
+ align:start position:0%
+philosophy of the late great serial
+Stanley Smith of
+
+ align:start position:0%
+Stanley Smith of
+ 
+
+ align:start position:0%
+Stanley Smith of
+MIT uh who uh looked at the general
+
+ align:start position:0%
+MIT uh who uh looked at the general
+ 
+
+ align:start position:0%
+MIT uh who uh looked at the general
+principles of dynamic interactive
+
+ align:start position:0%
+principles of dynamic interactive
+ 
+
+ align:start position:0%
+principles of dynamic interactive
+multi-level structure or structure
+
+ align:start position:0%
+multi-level structure or structure
+ 
+
+ align:start position:0%
+multi-level structure or structure
+hierarchy uh and acknowledge an
+
+ align:start position:0%
+hierarchy uh and acknowledge an
+ 
+
+ align:start position:0%
+hierarchy uh and acknowledge an
+intrinsic complexity of material
+
+ align:start position:0%
+intrinsic complexity of material
+ 
+
+ align:start position:0%
+intrinsic complexity of material
+structure uh for which he advocated that
+
+ align:start position:0%
+structure uh for which he advocated that
+ 
+
+ align:start position:0%
+structure uh for which he advocated that
+we should be taking a systems approach
+
+ align:start position:0%
+we should be taking a systems approach
+ 
+
+ align:start position:0%
+we should be taking a systems approach
+and essentially using the same framework
+
+ align:start position:0%
+and essentially using the same framework
+ 
+
+ align:start position:0%
+and essentially using the same framework
+of systems engineering uh that the rest
+
+ align:start position:0%
+of systems engineering uh that the rest
+ 
+
+ align:start position:0%
+of systems engineering uh that the rest
+of engineering is already using uh so
+
+ align:start position:0%
+of engineering is already using uh so
+ 
+
+ align:start position:0%
+of engineering is already using uh so
+we've taken that to heart uh and to
+
+ align:start position:0%
+we've taken that to heart uh and to
+ 
+
+ align:start position:0%
+we've taken that to heart uh and to
+implement it another important
+
+ align:start position:0%
+implement it another important
+ 
+
+ align:start position:0%
+implement it another important
+contribution from the late great Morris
+
+ align:start position:0%
+contribution from the late great Morris
+ 
+
+ align:start position:0%
+contribution from the late great Morris
+Cohen of MIT is what he described as a
+
+ align:start position:0%
+Cohen of MIT is what he described as a
+ 
+
+ align:start position:0%
+Cohen of MIT is what he described as a
+reciprocity between the opposite
+
+ align:start position:0%
+reciprocity between the opposite
+ 
+
+ align:start position:0%
+reciprocity between the opposite
+philosophies of Science and Engineering
+
+ align:start position:0%
+philosophies of Science and Engineering
+ 
+
+ align:start position:0%
+philosophies of Science and Engineering
+that are represented by this unique
+
+ align:start position:0%
+that are represented by this unique
+ 
+
+ align:start position:0%
+that are represented by this unique
+linear structure in which the predictive
+
+ align:start position:0%
+linear structure in which the predictive
+ 
+
+ align:start position:0%
+linear structure in which the predictive
+cause and effect logic of science flows
+
+ align:start position:0%
+cause and effect logic of science flows
+ 
+
+ align:start position:0%
+cause and effect logic of science flows
+from left to right
+
+ align:start position:0%
+from left to right
+ 
+
+ align:start position:0%
+from left to right
+and the inductive goals means uh logic
+
+ align:start position:0%
+and the inductive goals means uh logic
+ 
+
+ align:start position:0%
+and the inductive goals means uh logic
+of engineering flows from right to left
+
+ align:start position:0%
+of engineering flows from right to left
+ 
+
+ align:start position:0%
+of engineering flows from right to left
+so it actually allows us to bring these
+
+ align:start position:0%
+so it actually allows us to bring these
+ 
+
+ align:start position:0%
+so it actually allows us to bring these
+two philosophies together in a
+
+ align:start position:0%
+two philosophies together in a
+ 
+
+ align:start position:0%
+two philosophies together in a
+streamlined non-turbulent way so the uh
+
+ align:start position:0%
+streamlined non-turbulent way so the uh
+ 
+
+ align:start position:0%
+streamlined non-turbulent way so the uh
+scientific prediction is that uh however
+
+ align:start position:0%
+scientific prediction is that uh however
+ 
+
+ align:start position:0%
+scientific prediction is that uh however
+we process a material we determine its
+
+ align:start position:0%
+we process a material we determine its
+ 
+
+ align:start position:0%
+we process a material we determine its
+structure the structure will determine
+
+ align:start position:0%
+structure the structure will determine
+ 
+
+ align:start position:0%
+structure the structure will determine
+the properties and the combination of
+
+ align:start position:0%
+the properties and the combination of
+ 
+
+ align:start position:0%
+the properties and the combination of
+properties will determine its
+
+ align:start position:0%
+properties will determine its
+ 
+
+ align:start position:0%
+properties will determine its
+performance uh and this then enables a
+
+ align:start position:0%
+performance uh and this then enables a
+ 
+
+ align:start position:0%
+performance uh and this then enables a
+design system where we can set
+
+ align:start position:0%
+design system where we can set
+ 
+
+ align:start position:0%
+design system where we can set
+performance goals for a new material
+
+ align:start position:0%
+performance goals for a new material
+ 
+
+ align:start position:0%
+performance goals for a new material
+that we map to a set of property
+
+ align:start position:0%
+that we map to a set of property
+ 
+
+ align:start position:0%
+that we map to a set of property
+objectives uh use our knowledge of
+
+ align:start position:0%
+objectives uh use our knowledge of
+ 
+
+ align:start position:0%
+objectives uh use our knowledge of
+structure property relations to devise
+
+ align:start position:0%
+structure property relations to devise
+ 
+
+ align:start position:0%
+structure property relations to devise
+possible micr structures that are
+
+ align:start position:0%
+possible micr structures that are
+ 
+
+ align:start position:0%
+possible micr structures that are
+accessible through prescribed uh
+
+ align:start position:0%
+accessible through prescribed uh
+ 
+
+ align:start position:0%
+accessible through prescribed uh
+processing it's important to know that
+
+ align:start position:0%
+processing it's important to know that
+ 
+
+ align:start position:0%
+processing it's important to know that
+the the flow from left to right is
+
+ align:start position:0%
+the the flow from left to right is
+ 
+
+ align:start position:0%
+the the flow from left to right is
+unique that exactly how we process will
+
+ align:start position:0%
+unique that exactly how we process will
+ 
+
+ align:start position:0%
+unique that exactly how we process will
+determine that structure and a unique
+
+ align:start position:0%
+determine that structure and a unique
+ 
+
+ align:start position:0%
+determine that structure and a unique
+set of properties and performance uh
+
+ align:start position:0%
+set of properties and performance uh
+ 
+
+ align:start position:0%
+set of properties and performance uh
+it's always the nature of this inverse
+
+ align:start position:0%
+it's always the nature of this inverse
+ 
+
+ align:start position:0%
+it's always the nature of this inverse
+problem that we do not have uniqueness
+
+ align:start position:0%
+problem that we do not have uniqueness
+ 
+
+ align:start position:0%
+problem that we do not have uniqueness
+that once we have a set of property
+
+ align:start position:0%
+that once we have a set of property
+ 
+
+ align:start position:0%
+that once we have a set of property
+objectives there are multiple structures
+
+ align:start position:0%
+objectives there are multiple structures
+ 
+
+ align:start position:0%
+objectives there are multiple structures
+and multiple processed Pathways uh that
+
+ align:start position:0%
+and multiple processed Pathways uh that
+ 
+
+ align:start position:0%
+and multiple processed Pathways uh that
+we could use to to achieve that uh so
+
+ align:start position:0%
+we could use to to achieve that uh so
+ 
+
+ align:start position:0%
+we could use to to achieve that uh so
+the approach uh in in adopting a system
+
+ align:start position:0%
+the approach uh in in adopting a system
+ 
+
+ align:start position:0%
+the approach uh in in adopting a system
+framework is to use this as the backbone
+
+ align:start position:0%
+framework is to use this as the backbone
+ 
+
+ align:start position:0%
+framework is to use this as the backbone
+of a system structure and add Smith
+
+ align:start position:0%
+of a system structure and add Smith
+ 
+
+ align:start position:0%
+of a system structure and add Smith
+structural hierarchy to it so the each
+
+ align:start position:0%
+structural hierarchy to it so the each
+ 
+
+ align:start position:0%
+structural hierarchy to it so the each
+design project starts with a system
+
+ align:start position:0%
+design project starts with a system
+ 
+
+ align:start position:0%
+design project starts with a system
+chart uh and the idea here uh is to get
+
+ align:start position:0%
+chart uh and the idea here uh is to get
+ 
+
+ align:start position:0%
+chart uh and the idea here uh is to get
+the entire material down on a page uh so
+
+ align:start position:0%
+the entire material down on a page uh so
+ 
+
+ align:start position:0%
+the entire material down on a page uh so
+the left to right flow of this is the
+
+ align:start position:0%
+the left to right flow of this is the
+ 
+
+ align:start position:0%
+the left to right flow of this is the
+cause and effect logic but the process
+
+ align:start position:0%
+cause and effect logic but the process
+ 
+
+ align:start position:0%
+cause and effect logic but the process
+of design uh Works uh from from right to
+
+ align:start position:0%
+of design uh Works uh from from right to
+ 
+
+ align:start position:0%
+of design uh Works uh from from right to
+left uh where performance uh goals
+
+ align:start position:0%
+left uh where performance uh goals
+ 
+
+ align:start position:0%
+left uh where performance uh goals
+overall will be mapped to a quantitative
+
+ align:start position:0%
+overall will be mapped to a quantitative
+ 
+
+ align:start position:0%
+overall will be mapped to a quantitative
+set of properties such as strength
+
+ align:start position:0%
+set of properties such as strength
+ 
+
+ align:start position:0%
+set of properties such as strength
+toughness for a high performance steel
+
+ align:start position:0%
+toughness for a high performance steel
+ 
+
+ align:start position:0%
+toughness for a high performance steel
+uh and resistance to environmental
+
+ align:start position:0%
+uh and resistance to environmental
+ 
+
+ align:start position:0%
+uh and resistance to environmental
+hydrogen
+
+ align:start position:0%
+hydrogen
+ 
+
+ align:start position:0%
+hydrogen
+embrittlement and from our mechanistic
+
+ align:start position:0%
+embrittlement and from our mechanistic
+ 
+
+ align:start position:0%
+embrittlement and from our mechanistic
+knowledge we know that those properties
+
+ align:start position:0%
+knowledge we know that those properties
+ 
+
+ align:start position:0%
+knowledge we know that those properties
+map back to different subsystems in the
+
+ align:start position:0%
+map back to different subsystems in the
+ 
+
+ align:start position:0%
+map back to different subsystems in the
+hierarchy of microstructural subsystems
+
+ align:start position:0%
+hierarchy of microstructural subsystems
+ 
+
+ align:start position:0%
+hierarchy of microstructural subsystems
+which we know dynamically evolve
+
+ align:start position:0%
+which we know dynamically evolve
+ 
+
+ align:start position:0%
+which we know dynamically evolve
+throughout the stages of materials uh
+
+ align:start position:0%
+throughout the stages of materials uh
+ 
+
+ align:start position:0%
+throughout the stages of materials uh
+processing and that allows us to then
+
+ align:start position:0%
+processing and that allows us to then
+ 
+
+ align:start position:0%
+processing and that allows us to then
+identify and prioritize the key
+
+ align:start position:0%
+identify and prioritize the key
+ 
+
+ align:start position:0%
+identify and prioritize the key
+structure property links and process
+
+ align:start position:0%
+structure property links and process
+ 
+
+ align:start position:0%
+structure property links and process
+structure links for which we want to
+
+ align:start position:0%
+structure links for which we want to
+ 
+
+ align:start position:0%
+structure links for which we want to
+build out our uh design
+
+ align:start position:0%
+build out our uh design
+ 
+
+ align:start position:0%
+build out our uh design
+models uh now that can be done by uh
+
+ align:start position:0%
+models uh now that can be done by uh
+ 
+
+ align:start position:0%
+models uh now that can be done by uh
+empirical correlations that are useful
+
+ align:start position:0%
+empirical correlations that are useful
+ 
+
+ align:start position:0%
+empirical correlations that are useful
+for
+
+ align:start position:0%
+for
+ 
+
+ align:start position:0%
+for
+interpolation uh but we really uh from
+
+ align:start position:0%
+interpolation uh but we really uh from
+ 
+
+ align:start position:0%
+interpolation uh but we really uh from
+from the start we're committed to uh by
+
+ align:start position:0%
+from the start we're committed to uh by
+ 
+
+ align:start position:0%
+from the start we're committed to uh by
+getting the most value out of the calad
+
+ align:start position:0%
+getting the most value out of the calad
+ 
+
+ align:start position:0%
+getting the most value out of the calad
+fundamental data is to use uh predictive
+
+ align:start position:0%
+fundamental data is to use uh predictive
+ 
+
+ align:start position:0%
+fundamental data is to use uh predictive
+science based on mechanistic
+
+ align:start position:0%
+science based on mechanistic
+ 
+
+ align:start position:0%
+science based on mechanistic
+understanding and to express that
+
+ align:start position:0%
+understanding and to express that
+ 
+
+ align:start position:0%
+understanding and to express that
+mechanistic under form that we could
+
+ align:start position:0%
+mechanistic under form that we could
+ 
+
+ align:start position:0%
+mechanistic under form that we could
+parameterize to make uh devise
+
+ align:start position:0%
+parameterize to make uh devise
+ 
+
+ align:start position:0%
+parameterize to make uh devise
+parameters accessible uh to those
+
+ align:start position:0%
+parameters accessible uh to those
+ 
+
+ align:start position:0%
+parameters accessible uh to those
+fundamental
+
+ align:start position:0%
+fundamental
+ 
+
+ align:start position:0%
+fundamental
+databases uh to make uh a quantitative
+
+ align:start position:0%
+databases uh to make uh a quantitative
+ 
+
+ align:start position:0%
+databases uh to make uh a quantitative
+approach to the full design of the
+
+ align:start position:0%
+approach to the full design of the
+ 
+
+ align:start position:0%
+approach to the full design of the
+material that produces different levels
+
+ align:start position:0%
+material that produces different levels
+ 
+
+ align:start position:0%
+material that produces different levels
+of of microstructure throughout
+
+ align:start position:0%
+of of microstructure throughout
+ 
+
+ align:start position:0%
+of of microstructure throughout
+different stages of processing uh and
+
+ align:start position:0%
+different stages of processing uh and
+ 
+
+ align:start position:0%
+different stages of processing uh and
+meets all those uh uh property
+
+ align:start position:0%
+meets all those uh uh property
+ 
+
+ align:start position:0%
+meets all those uh uh property
+requirements for useful
+
+ align:start position:0%
+requirements for useful
+ 
+
+ align:start position:0%
+requirements for useful
+material and what that
+
+ align:start position:0%
+material and what that
+ 
+
+ align:start position:0%
+material and what that
+motivated uh was the models summarized
+
+ align:start position:0%
+motivated uh was the models summarized
+ 
+
+ align:start position:0%
+motivated uh was the models summarized
+here which really is a a subset of
+
+ align:start position:0%
+here which really is a a subset of
+ 
+
+ align:start position:0%
+here which really is a a subset of
+what's available in computational
+
+ align:start position:0%
+what's available in computational
+ 
+
+ align:start position:0%
+what's available in computational
+Material Science that that allowed us to
+
+ align:start position:0%
+Material Science that that allowed us to
+ 
+
+ align:start position:0%
+Material Science that that allowed us to
+do uh quantitative engineering uh so at
+
+ align:start position:0%
+do uh quantitative engineering uh so at
+ 
+
+ align:start position:0%
+do uh quantitative engineering uh so at
+the bottom uh level uh the three fields
+
+ align:start position:0%
+the bottom uh level uh the three fields
+ 
+
+ align:start position:0%
+the bottom uh level uh the three fields
+we uh integrated where the DFT physics
+
+ align:start position:0%
+we uh integrated where the DFT physics
+ 
+
+ align:start position:0%
+we uh integrated where the DFT physics
+that was particularly useful for surface
+
+ align:start position:0%
+that was particularly useful for surface
+ 
+
+ align:start position:0%
+that was particularly useful for surface
+Thermon namics which is more difficult
+
+ align:start position:0%
+Thermon namics which is more difficult
+ 
+
+ align:start position:0%
+Thermon namics which is more difficult
+to measure than bulk Thermon namics and
+
+ align:start position:0%
+to measure than bulk Thermon namics and
+ 
+
+ align:start position:0%
+to measure than bulk Thermon namics and
+of course uh the material science is is
+
+ align:start position:0%
+of course uh the material science is is
+ 
+
+ align:start position:0%
+of course uh the material science is is
+uh particularly advanced in the theory
+
+ align:start position:0%
+uh particularly advanced in the theory
+ 
+
+ align:start position:0%
+uh particularly advanced in the theory
+of uh solid state precipitation and
+
+ align:start position:0%
+of uh solid state precipitation and
+ 
+
+ align:start position:0%
+of uh solid state precipitation and
+precipitation
+
+ align:start position:0%
+precipitation
+ 
+
+ align:start position:0%
+precipitation
+strengthening uh and for structure
+
+ align:start position:0%
+strengthening uh and for structure
+ 
+
+ align:start position:0%
+strengthening uh and for structure
+property relations uh we applied uh
+
+ align:start position:0%
+property relations uh we applied uh
+ 
+
+ align:start position:0%
+property relations uh we applied uh
+brought in the micromechanical
+
+ align:start position:0%
+brought in the micromechanical
+ 
+
+ align:start position:0%
+brought in the micromechanical
+applications of Continuum mechanics uh
+
+ align:start position:0%
+applications of Continuum mechanics uh
+ 
+
+ align:start position:0%
+applications of Continuum mechanics uh
+to simulate unit process of fracture and
+
+ align:start position:0%
+to simulate unit process of fracture and
+ 
+
+ align:start position:0%
+to simulate unit process of fracture and
+fatigue to set the structure property
+
+ align:start position:0%
+fatigue to set the structure property
+ 
+
+ align:start position:0%
+fatigue to set the structure property
+relations so these are really uh the
+
+ align:start position:0%
+relations so these are really uh the
+ 
+
+ align:start position:0%
+relations so these are really uh the
+three disciplines that were integrated
+
+ align:start position:0%
+three disciplines that were integrated
+ 
+
+ align:start position:0%
+three disciplines that were integrated
+in this approach uh for to meet
+
+ align:start position:0%
+in this approach uh for to meet
+ 
+
+ align:start position:0%
+in this approach uh for to meet
+performance goals but equally important
+
+ align:start position:0%
+performance goals but equally important
+ 
+
+ align:start position:0%
+performance goals but equally important
+is to constrain the processibility of a
+
+ align:start position:0%
+is to constrain the processibility of a
+ 
+
+ align:start position:0%
+is to constrain the processibility of a
+material and that's a role for the M
+
+ align:start position:0%
+material and that's a role for the M
+ 
+
+ align:start position:0%
+material and that's a role for the M
+calad based Material Science models of
+
+ align:start position:0%
+calad based Material Science models of
+ 
+
+ align:start position:0%
+calad based Material Science models of
+the solid solid phase Transformations
+
+ align:start position:0%
+the solid solid phase Transformations
+ 
+
+ align:start position:0%
+the solid solid phase Transformations
+and the liquid solid phase
+
+ align:start position:0%
+and the liquid solid phase
+ 
+
+ align:start position:0%
+and the liquid solid phase
+Transformations uh both of we which are
+
+ align:start position:0%
+Transformations uh both of we which are
+ 
+
+ align:start position:0%
+Transformations uh both of we which are
+uh scaled dependent in terms of the size
+
+ align:start position:0%
+uh scaled dependent in terms of the size
+ 
+
+ align:start position:0%
+uh scaled dependent in terms of the size
+of heat treated components uh through
+
+ align:start position:0%
+of heat treated components uh through
+ 
+
+ align:start position:0%
+of heat treated components uh through
+the size dependence of heat transfer uh
+
+ align:start position:0%
+the size dependence of heat transfer uh
+ 
+
+ align:start position:0%
+the size dependence of heat transfer uh
+so ultimately it's the linking of of
+
+ align:start position:0%
+so ultimately it's the linking of of
+ 
+
+ align:start position:0%
+so ultimately it's the linking of of
+these micr structural models to the
+
+ align:start position:0%
+these micr structural models to the
+ 
+
+ align:start position:0%
+these micr structural models to the
+macroscopic process simulations uh that
+
+ align:start position:0%
+macroscopic process simulations uh that
+ 
+
+ align:start position:0%
+macroscopic process simulations uh that
+allow us to constrain materials up front
+
+ align:start position:0%
+allow us to constrain materials up front
+ 
+
+ align:start position:0%
+allow us to constrain materials up front
+theoretically to be processable on a
+
+ align:start position:0%
+theoretically to be processable on a
+ 
+
+ align:start position:0%
+theoretically to be processable on a
+design on a desired scale uh and that
+
+ align:start position:0%
+design on a desired scale uh and that
+ 
+
+ align:start position:0%
+design on a desired scale uh and that
+really uh helps to accelerate the full
+
+ align:start position:0%
+really uh helps to accelerate the full
+ 
+
+ align:start position:0%
+really uh helps to accelerate the full
+cycle uh instead of experimental scaleup
+
+ align:start position:0%
+cycle uh instead of experimental scaleup
+ 
+
+ align:start position:0%
+cycle uh instead of experimental scaleup
+uh so what's represented here on the
+
+ align:start position:0%
+uh so what's represented here on the
+ 
+
+ align:start position:0%
+uh so what's represented here on the
+right are the software models and their
+
+ align:start position:0%
+right are the software models and their
+ 
+
+ align:start position:0%
+right are the software models and their
+uh their their platforms uh and the
+
+ align:start position:0%
+uh their their platforms uh and the
+ 
+
+ align:start position:0%
+uh their their platforms uh and the
+advanced instrumentation is equally
+
+ align:start position:0%
+advanced instrumentation is equally
+ 
+
+ align:start position:0%
+advanced instrumentation is equally
+important the ability to use techniques
+
+ align:start position:0%
+important the ability to use techniques
+ 
+
+ align:start position:0%
+important the ability to use techniques
+such as the atom probe to actually
+
+ align:start position:0%
+such as the atom probe to actually
+ 
+
+ align:start position:0%
+such as the atom probe to actually
+measure the complex compositions of
+
+ align:start position:0%
+measure the complex compositions of
+ 
+
+ align:start position:0%
+measure the complex compositions of
+nanoscale strengthening precipitates in
+
+ align:start position:0%
+nanoscale strengthening precipitates in
+ 
+
+ align:start position:0%
+nanoscale strengthening precipitates in
+our ultra high strength materials so
+
+ align:start position:0%
+our ultra high strength materials so
+ 
+
+ align:start position:0%
+our ultra high strength materials so
+from the start uh uh calibration and
+
+ align:start position:0%
+from the start uh uh calibration and
+ 
+
+ align:start position:0%
+from the start uh uh calibration and
+validation to understand the associated
+
+ align:start position:0%
+validation to understand the associated
+ 
+
+ align:start position:0%
+validation to understand the associated
+uncertainty of our predictions was was
+
+ align:start position:0%
+uncertainty of our predictions was was
+ 
+
+ align:start position:0%
+uncertainty of our predictions was was
+really important uh and that's what the
+
+ align:start position:0%
+really important uh and that's what the
+ 
+
+ align:start position:0%
+really important uh and that's what the
+instrumentation was
+
+ align:start position:0%
+instrumentation was
+ 
+
+ align:start position:0%
+instrumentation was
+enabling so our first example uh
+
+ align:start position:0%
+enabling so our first example uh
+ 
+
+ align:start position:0%
+enabling so our first example uh
+starting out in the 1980s to design
+
+ align:start position:0%
+starting out in the 1980s to design
+ 
+
+ align:start position:0%
+starting out in the 1980s to design
+ultra high strength Steels uh we first
+
+ align:start position:0%
+ultra high strength Steels uh we first
+ 
+
+ align:start position:0%
+ultra high strength Steels uh we first
+took apart the highest performance steel
+
+ align:start position:0%
+took apart the highest performance steel
+ 
+
+ align:start position:0%
+took apart the highest performance steel
+of the time which was the af-1 1410
+
+ align:start position:0%
+of the time which was the af-1 1410
+ 
+
+ align:start position:0%
+of the time which was the af-1 1410
+steel uh which is tempered at 510c to
+
+ align:start position:0%
+steel uh which is tempered at 510c to
+ 
+
+ align:start position:0%
+steel uh which is tempered at 510c to
+precipitate uh alloy m2c carbide so
+
+ align:start position:0%
+precipitate uh alloy m2c carbide so
+ 
+
+ align:start position:0%
+precipitate uh alloy m2c carbide so
+these are hcp carbides where the m is a
+
+ align:start position:0%
+these are hcp carbides where the m is a
+ 
+
+ align:start position:0%
+these are hcp carbides where the m is a
+combination of chromium album and vadium
+
+ align:start position:0%
+combination of chromium album and vadium
+ 
+
+ align:start position:0%
+combination of chromium album and vadium
+and sometimes
+
+ align:start position:0%
+and sometimes
+ 
+
+ align:start position:0%
+and sometimes
+tungsten uh so we brought together a
+
+ align:start position:0%
+tungsten uh so we brought together a
+ 
+
+ align:start position:0%
+tungsten uh so we brought together a
+wide array of uh techniques to map the
+
+ align:start position:0%
+wide array of uh techniques to map the
+ 
+
+ align:start position:0%
+wide array of uh techniques to map the
+time evolution of the precipitate uh
+
+ align:start position:0%
+time evolution of the precipitate uh
+ 
+
+ align:start position:0%
+time evolution of the precipitate uh
+particle size uh the aspect ratio of the
+
+ align:start position:0%
+particle size uh the aspect ratio of the
+ 
+
+ align:start position:0%
+particle size uh the aspect ratio of the
+carbides their number density total
+
+ align:start position:0%
+carbides their number density total
+ 
+
+ align:start position:0%
+carbides their number density total
+volume fraction uh and their uh uh the
+
+ align:start position:0%
+volume fraction uh and their uh uh the
+ 
+
+ align:start position:0%
+volume fraction uh and their uh uh the
+evolution of the carbide lce parameters
+
+ align:start position:0%
+evolution of the carbide lce parameters
+ 
+
+ align:start position:0%
+evolution of the carbide lce parameters
+and Associated composition trajectory
+
+ align:start position:0%
+and Associated composition trajectory
+ 
+
+ align:start position:0%
+and Associated composition trajectory
+and then this summarizes the evolution
+
+ align:start position:0%
+and then this summarizes the evolution
+ 
+
+ align:start position:0%
+and then this summarizes the evolution
+of the precipitation
+
+ align:start position:0%
+of the precipitation
+ 
+
+ align:start position:0%
+of the precipitation
+strengthening uh the evolution of the
+
+ align:start position:0%
+strengthening uh the evolution of the
+ 
+
+ align:start position:0%
+strengthening uh the evolution of the
+size uh was consistent with the theory
+
+ align:start position:0%
+size uh was consistent with the theory
+ 
+
+ align:start position:0%
+size uh was consistent with the theory
+of precipitation at high superp
+
+ align:start position:0%
+of precipitation at high superp
+ 
+
+ align:start position:0%
+of precipitation at high superp
+saturations and in that regime uh we can
+
+ align:start position:0%
+saturations and in that regime uh we can
+ 
+
+ align:start position:0%
+saturations and in that regime uh we can
+treat the initial critical nucleus size
+
+ align:start position:0%
+treat the initial critical nucleus size
+ 
+
+ align:start position:0%
+treat the initial critical nucleus size
+as the fundamental scaling factor for
+
+ align:start position:0%
+as the fundamental scaling factor for
+ 
+
+ align:start position:0%
+as the fundamental scaling factor for
+particle size that's so important to
+
+ align:start position:0%
+particle size that's so important to
+ 
+
+ align:start position:0%
+particle size that's so important to
+strengthening uh and that of course
+
+ align:start position:0%
+strengthening uh and that of course
+ 
+
+ align:start position:0%
+strengthening uh and that of course
+scales inversely with precipitation
+
+ align:start position:0%
+scales inversely with precipitation
+ 
+
+ align:start position:0%
+scales inversely with precipitation
+driving force so this is a way we could
+
+ align:start position:0%
+driving force so this is a way we could
+ 
+
+ align:start position:0%
+driving force so this is a way we could
+uh get a thermodynamic handle on the
+
+ align:start position:0%
+uh get a thermodynamic handle on the
+ 
+
+ align:start position:0%
+uh get a thermodynamic handle on the
+particle size that governs strengthening
+
+ align:start position:0%
+particle size that governs strengthening
+ 
+
+ align:start position:0%
+particle size that governs strengthening
+efficiency in these systems but it was
+
+ align:start position:0%
+efficiency in these systems but it was
+ 
+
+ align:start position:0%
+efficiency in these systems but it was
+important to recognize that the
+
+ align:start position:0%
+important to recognize that the
+ 
+
+ align:start position:0%
+important to recognize that the
+trajectory of the lattice parameters uh
+
+ align:start position:0%
+trajectory of the lattice parameters uh
+ 
+
+ align:start position:0%
+trajectory of the lattice parameters uh
+driven by the composition trajectory of
+
+ align:start position:0%
+driven by the composition trajectory of
+ 
+
+ align:start position:0%
+driven by the composition trajectory of
+the carbides is consistent with the
+
+ align:start position:0%
+the carbides is consistent with the
+ 
+
+ align:start position:0%
+the carbides is consistent with the
+initial nucleation being in a fully
+
+ align:start position:0%
+initial nucleation being in a fully
+ 
+
+ align:start position:0%
+initial nucleation being in a fully
+coherent state so it was necessary to
+
+ align:start position:0%
+coherent state so it was necessary to
+ 
+
+ align:start position:0%
+coherent state so it was necessary to
+add to the calad chemical Thermon namics
+
+ align:start position:0%
+add to the calad chemical Thermon namics
+ 
+
+ align:start position:0%
+add to the calad chemical Thermon namics
+and elastic energy term uh that's
+
+ align:start position:0%
+and elastic energy term uh that's
+ 
+
+ align:start position:0%
+and elastic energy term uh that's
+composition dependent through the
+
+ align:start position:0%
+composition dependent through the
+ 
+
+ align:start position:0%
+composition dependent through the
+composition dependence of the lattice
+
+ align:start position:0%
+composition dependence of the lattice
+ 
+
+ align:start position:0%
+composition dependence of the lattice
+parameter setting the misfit strains so
+
+ align:start position:0%
+parameter setting the misfit strains so
+ 
+
+ align:start position:0%
+parameter setting the misfit strains so
+all that was put together uh to get uh
+
+ align:start position:0%
+all that was put together uh to get uh
+ 
+
+ align:start position:0%
+all that was put together uh to get uh
+precise driving forces for the
+
+ align:start position:0%
+precise driving forces for the
+ 
+
+ align:start position:0%
+precise driving forces for the
+precipitation of these carbides so we
+
+ align:start position:0%
+precipitation of these carbides so we
+ 
+
+ align:start position:0%
+precipitation of these carbides so we
+could efficiently control the particle
+
+ align:start position:0%
+could efficiently control the particle
+ 
+
+ align:start position:0%
+could efficiently control the particle
+size and uh what that leads to then uh
+
+ align:start position:0%
+size and uh what that leads to then uh
+ 
+
+ align:start position:0%
+size and uh what that leads to then uh
+is this simplified parametric approach
+
+ align:start position:0%
+is this simplified parametric approach
+ 
+
+ align:start position:0%
+is this simplified parametric approach
+to strengthening where from the aoan uh
+
+ align:start position:0%
+to strengthening where from the aoan uh
+ 
+
+ align:start position:0%
+to strengthening where from the aoan uh
+strengthening Theory uh the
+
+ align:start position:0%
+strengthening Theory uh the
+ 
+
+ align:start position:0%
+strengthening Theory uh the
+precipitation strengthening scales
+
+ align:start position:0%
+precipitation strengthening scales
+ 
+
+ align:start position:0%
+precipitation strengthening scales
+inversely with the spacing of the
+
+ align:start position:0%
+inversely with the spacing of the
+ 
+
+ align:start position:0%
+inversely with the spacing of the
+obstacles uh and that spacing scales
+
+ align:start position:0%
+obstacles uh and that spacing scales
+ 
+
+ align:start position:0%
+obstacles uh and that spacing scales
+with particle size over phase fraction
+
+ align:start position:0%
+with particle size over phase fraction
+ 
+
+ align:start position:0%
+with particle size over phase fraction
+to the one half uh for the uh spacing uh
+
+ align:start position:0%
+to the one half uh for the uh spacing uh
+ 
+
+ align:start position:0%
+to the one half uh for the uh spacing uh
+in a slip plane uh and that means then
+
+ align:start position:0%
+in a slip plane uh and that means then
+ 
+
+ align:start position:0%
+in a slip plane uh and that means then
+uh the precipitation strengthening goes
+
+ align:start position:0%
+uh the precipitation strengthening goes
+ 
+
+ align:start position:0%
+uh the precipitation strengthening goes
+is f to the 1/2 over particle size and
+
+ align:start position:0%
+is f to the 1/2 over particle size and
+ 
+
+ align:start position:0%
+is f to the 1/2 over particle size and
+if we accept this scaling to the initial
+
+ align:start position:0%
+if we accept this scaling to the initial
+ 
+
+ align:start position:0%
+if we accept this scaling to the initial
+critical nucleus size that scales
+
+ align:start position:0%
+critical nucleus size that scales
+ 
+
+ align:start position:0%
+critical nucleus size that scales
+inversely to the driving force uh then
+
+ align:start position:0%
+inversely to the driving force uh then
+ 
+
+ align:start position:0%
+inversely to the driving force uh then
+we can write that the precipitation
+
+ align:start position:0%
+we can write that the precipitation
+ 
+
+ align:start position:0%
+we can write that the precipitation
+strengthening will will scale directly
+
+ align:start position:0%
+strengthening will will scale directly
+ 
+
+ align:start position:0%
+strengthening will will scale directly
+with that theramic driving force times
+
+ align:start position:0%
+with that theramic driving force times
+ 
+
+ align:start position:0%
+with that theramic driving force times
+phase fraction to the 1/2 uh so this
+
+ align:start position:0%
+phase fraction to the 1/2 uh so this
+ 
+
+ align:start position:0%
+phase fraction to the 1/2 uh so this
+predicted that uh we ought to be able to
+
+ align:start position:0%
+predicted that uh we ought to be able to
+ 
+
+ align:start position:0%
+predicted that uh we ought to be able to
+design Steels uh with higher driving
+
+ align:start position:0%
+design Steels uh with higher driving
+ 
+
+ align:start position:0%
+design Steels uh with higher driving
+forces to get more efficient uh
+
+ align:start position:0%
+forces to get more efficient uh
+ 
+
+ align:start position:0%
+forces to get more efficient uh
+strengthening and That Was Then tested
+
+ align:start position:0%
+strengthening and That Was Then tested
+ 
+
+ align:start position:0%
+strengthening and That Was Then tested
+by making a series of Steels that had a
+
+ align:start position:0%
+by making a series of Steels that had a
+ 
+
+ align:start position:0%
+by making a series of Steels that had a
+fixed carbon content setting uh the
+
+ align:start position:0%
+fixed carbon content setting uh the
+ 
+
+ align:start position:0%
+fixed carbon content setting uh the
+ultimate phase fraction of the
+
+ align:start position:0%
+ultimate phase fraction of the
+ 
+
+ align:start position:0%
+ultimate phase fraction of the
+precipitates uh and then we used our
+
+ align:start position:0%
+precipitates uh and then we used our
+ 
+
+ align:start position:0%
+precipitates uh and then we used our
+herent Thermon namics to predict the
+
+ align:start position:0%
+herent Thermon namics to predict the
+ 
+
+ align:start position:0%
+herent Thermon namics to predict the
+driving force uh but as well uh uh by
+
+ align:start position:0%
+driving force uh but as well uh uh by
+ 
+
+ align:start position:0%
+driving force uh but as well uh uh by
+the time we get to the temperatures
+
+ align:start position:0%
+the time we get to the temperatures
+ 
+
+ align:start position:0%
+the time we get to the temperatures
+where we can have sub substitutional
+
+ align:start position:0%
+where we can have sub substitutional
+ 
+
+ align:start position:0%
+where we can have sub substitutional
+diffusion uh the uh carbon diffusion
+
+ align:start position:0%
+diffusion uh the uh carbon diffusion
+ 
+
+ align:start position:0%
+diffusion uh the uh carbon diffusion
+controlled formation of iron carbides
+
+ align:start position:0%
+controlled formation of iron carbides
+ 
+
+ align:start position:0%
+controlled formation of iron carbides
+like fe3c will already have occurred and
+
+ align:start position:0%
+like fe3c will already have occurred and
+ 
+
+ align:start position:0%
+like fe3c will already have occurred and
+that lowers the chemical potential of
+
+ align:start position:0%
+that lowers the chemical potential of
+ 
+
+ align:start position:0%
+that lowers the chemical potential of
+the carbon so it was necessary to get
+
+ align:start position:0%
+the carbon so it was necessary to get
+ 
+
+ align:start position:0%
+the carbon so it was necessary to get
+these driving forces right uh we had to
+
+ align:start position:0%
+these driving forces right uh we had to
+ 
+
+ align:start position:0%
+these driving forces right uh we had to
+First consider a constrained equilibrium
+
+ align:start position:0%
+First consider a constrained equilibrium
+ 
+
+ align:start position:0%
+First consider a constrained equilibrium
+with
+
+ align:start position:0%
+with
+ 
+
+ align:start position:0%
+with
+fe3c uh to set the Carbon potential
+
+ align:start position:0%
+fe3c uh to set the Carbon potential
+ 
+
+ align:start position:0%
+fe3c uh to set the Carbon potential
+uh and then we were able to validate
+
+ align:start position:0%
+uh and then we were able to validate
+ 
+
+ align:start position:0%
+uh and then we were able to validate
+that with the within the scatter of
+
+ align:start position:0%
+that with the within the scatter of
+ 
+
+ align:start position:0%
+that with the within the scatter of
+these measurements uh the at at a fixed
+
+ align:start position:0%
+these measurements uh the at at a fixed
+ 
+
+ align:start position:0%
+these measurements uh the at at a fixed
+carbon level we could vary uh the the
+
+ align:start position:0%
+carbon level we could vary uh the the
+ 
+
+ align:start position:0%
+carbon level we could vary uh the the
+hardness the peak hardness of this
+
+ align:start position:0%
+hardness the peak hardness of this
+ 
+
+ align:start position:0%
+hardness the peak hardness of this
+strengthen steel over about 20 uh points
+
+ align:start position:0%
+strengthen steel over about 20 uh points
+ 
+
+ align:start position:0%
+strengthen steel over about 20 uh points
+on a rockable C scale so very dramatic
+
+ align:start position:0%
+on a rockable C scale so very dramatic
+ 
+
+ align:start position:0%
+on a rockable C scale so very dramatic
+uh direct uh proportionality predicted
+
+ align:start position:0%
+uh direct uh proportionality predicted
+ 
+
+ align:start position:0%
+uh direct uh proportionality predicted
+by the model and so that calibration
+
+ align:start position:0%
+by the model and so that calibration
+ 
+
+ align:start position:0%
+by the model and so that calibration
+became the the principal tool that we
+
+ align:start position:0%
+became the the principal tool that we
+ 
+
+ align:start position:0%
+became the the principal tool that we
+used to design Steels with much more
+
+ align:start position:0%
+used to design Steels with much more
+ 
+
+ align:start position:0%
+used to design Steels with much more
+efficient strength
+
+ align:start position:0%
+efficient strength
+ 
+
+ align:start position:0%
+efficient strength
+uh demonstrating Alloys that for a given
+
+ align:start position:0%
+uh demonstrating Alloys that for a given
+ 
+
+ align:start position:0%
+uh demonstrating Alloys that for a given
+carbon content could have 50% more
+
+ align:start position:0%
+carbon content could have 50% more
+ 
+
+ align:start position:0%
+carbon content could have 50% more
+strength than than the previous
+
+ align:start position:0%
+strength than than the previous
+ 
+
+ align:start position:0%
+strength than than the previous
+technology so it's an area that's been
+
+ align:start position:0%
+technology so it's an area that's been
+ 
+
+ align:start position:0%
+technology so it's an area that's been
+uh highly developed
+
+ align:start position:0%
+uh highly developed
+ 
+
+ align:start position:0%
+uh highly developed
+empirically uh but in fact uh there was
+
+ align:start position:0%
+empirically uh but in fact uh there was
+ 
+
+ align:start position:0%
+empirically uh but in fact uh there was
+a lot more to be achieved by being more
+
+ align:start position:0%
+a lot more to be achieved by being more
+ 
+
+ align:start position:0%
+a lot more to be achieved by being more
+predictive and taking systems to a high
+
+ align:start position:0%
+predictive and taking systems to a high
+ 
+
+ align:start position:0%
+predictive and taking systems to a high
+level uh of optimization using these
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+tools now what I wanted to uh just touch
+
+ align:start position:0%
+tools now what I wanted to uh just touch
+ 
+
+ align:start position:0%
+tools now what I wanted to uh just touch
+on is uh there's also an important role
+
+ align:start position:0%
+on is uh there's also an important role
+ 
+
+ align:start position:0%
+on is uh there's also an important role
+of the surface thermodynamics and uh
+
+ align:start position:0%
+of the surface thermodynamics and uh
+ 
+
+ align:start position:0%
+of the surface thermodynamics and uh
+this is a case where we made very good
+
+ align:start position:0%
+this is a case where we made very good
+ 
+
+ align:start position:0%
+this is a case where we made very good
+use of the DFT predictions uh but what
+
+ align:start position:0%
+use of the DFT predictions uh but what
+ 
+
+ align:start position:0%
+use of the DFT predictions uh but what
+this chart is about is a correlation of
+
+ align:start position:0%
+this chart is about is a correlation of
+ 
+
+ align:start position:0%
+this chart is about is a correlation of
+the embrittlement potency of interfacial
+
+ align:start position:0%
+the embrittlement potency of interfacial
+ 
+
+ align:start position:0%
+the embrittlement potency of interfacial
+segregants uh against the uh segregation
+
+ align:start position:0%
+segregants uh against the uh segregation
+ 
+
+ align:start position:0%
+segregants uh against the uh segregation
+energy difference between free surfaces
+
+ align:start position:0%
+energy difference between free surfaces
+ 
+
+ align:start position:0%
+energy difference between free surfaces
+and grain boundaries uh and in this case
+
+ align:start position:0%
+and grain boundaries uh and in this case
+ 
+
+ align:start position:0%
+and grain boundaries uh and in this case
+uh there is experimental data to to
+
+ align:start position:0%
+uh there is experimental data to to
+ 
+
+ align:start position:0%
+uh there is experimental data to to
+validate this but this is actually the
+
+ align:start position:0%
+validate this but this is actually the
+ 
+
+ align:start position:0%
+validate this but this is actually the
+case of uh predicting it with our DFT
+
+ align:start position:0%
+case of uh predicting it with our DFT
+ 
+
+ align:start position:0%
+case of uh predicting it with our DFT
+mechanics with pretty good accuracy uh
+
+ align:start position:0%
+mechanics with pretty good accuracy uh
+ 
+
+ align:start position:0%
+mechanics with pretty good accuracy uh
+so these are the well-known interstitial
+
+ align:start position:0%
+so these are the well-known interstitial
+ 
+
+ align:start position:0%
+so these are the well-known interstitial
+components that have been well studied
+
+ align:start position:0%
+components that have been well studied
+ 
+
+ align:start position:0%
+components that have been well studied
+substitutional elements were less well
+
+ align:start position:0%
+substitutional elements were less well
+ 
+
+ align:start position:0%
+substitutional elements were less well
+studied uh so after demonstrating the
+
+ align:start position:0%
+studied uh so after demonstrating the
+ 
+
+ align:start position:0%
+studied uh so after demonstrating the
+ability to compute these numbers we
+
+ align:start position:0%
+ability to compute these numbers we
+ 
+
+ align:start position:0%
+ability to compute these numbers we
+actually built out this database of the
+
+ align:start position:0%
+actually built out this database of the
+ 
+
+ align:start position:0%
+actually built out this database of the
+embrittlement potency from surface
+
+ align:start position:0%
+embrittlement potency from surface
+ 
+
+ align:start position:0%
+embrittlement potency from surface
+thermodynamics uh which was calibrated
+
+ align:start position:0%
+thermodynamics uh which was calibrated
+ 
+
+ align:start position:0%
+thermodynamics uh which was calibrated
+and validated by some large scale uh DFT
+
+ align:start position:0%
+and validated by some large scale uh DFT
+ 
+
+ align:start position:0%
+and validated by some large scale uh DFT
+calculations uh giving us these
+
+ align:start position:0%
+calculations uh giving us these
+ 
+
+ align:start position:0%
+calculations uh giving us these
+predictions from which were able to
+
+ align:start position:0%
+predictions from which were able to
+ 
+
+ align:start position:0%
+predictions from which were able to
+identify these strong cohesion
+
+ align:start position:0%
+identify these strong cohesion
+ 
+
+ align:start position:0%
+identify these strong cohesion
+enhancers uh that could sufficiently
+
+ align:start position:0%
+enhancers uh that could sufficiently
+ 
+
+ align:start position:0%
+enhancers uh that could sufficiently
+enhance grain boundary cohesion to
+
+ align:start position:0%
+enhance grain boundary cohesion to
+ 
+
+ align:start position:0%
+enhance grain boundary cohesion to
+offset the embrittling effect of
+
+ align:start position:0%
+offset the embrittling effect of
+ 
+
+ align:start position:0%
+offset the embrittling effect of
+hydrogen and this allowed us to design
+
+ align:start position:0%
+hydrogen and this allowed us to design
+ 
+
+ align:start position:0%
+hydrogen and this allowed us to design
+these very high performance Steels to to
+
+ align:start position:0%
+these very high performance Steels to to
+ 
+
+ align:start position:0%
+these very high performance Steels to to
+no longer uh be prone to the
+
+ align:start position:0%
+no longer uh be prone to the
+ 
+
+ align:start position:0%
+no longer uh be prone to the
+intergranular form of stress corrosion
+
+ align:start position:0%
+intergranular form of stress corrosion
+ 
+
+ align:start position:0%
+intergranular form of stress corrosion
+cracking so it was a big advance in the
+
+ align:start position:0%
+cracking so it was a big advance in the
+ 
+
+ align:start position:0%
+cracking so it was a big advance in the
+resistance to hydrogen embrittlement in
+
+ align:start position:0%
+resistance to hydrogen embrittlement in
+ 
+
+ align:start position:0%
+resistance to hydrogen embrittlement in
+these class of Steels so it's one
+
+ align:start position:0%
+these class of Steels so it's one
+ 
+
+ align:start position:0%
+these class of Steels so it's one
+example yeah one second can can you um
+
+ align:start position:0%
+example yeah one second can can you um
+ 
+
+ align:start position:0%
+example yeah one second can can you um
+fill in what is DFT
+
+ align:start position:0%
+fill in what is DFT
+ 
+
+ align:start position:0%
+fill in what is DFT
+cou times at this point we talk about
+
+ align:start position:0%
+cou times at this point we talk about
+ 
+
+ align:start position:0%
+cou times at this point we talk about
+data a lot so where does that data come
+
+ align:start position:0%
+data a lot so where does that data come
+ 
+
+ align:start position:0%
+data a lot so where does that data come
+from yeah so that density functional
+
+ align:start position:0%
+from yeah so that density functional
+ 
+
+ align:start position:0%
+from yeah so that density functional
+Theory so so this is uh something that
+
+ align:start position:0%
+Theory so so this is uh something that
+ 
+
+ align:start position:0%
+Theory so so this is uh something that
+we basically have ways to solve the
+
+ align:start position:0%
+we basically have ways to solve the
+ 
+
+ align:start position:0%
+we basically have ways to solve the
+Schrodinger equation uh but there is a
+
+ align:start position:0%
+Schrodinger equation uh but there is a
+ 
+
+ align:start position:0%
+Schrodinger equation uh but there is a
+menu of approximations that you do take
+
+ align:start position:0%
+menu of approximations that you do take
+ 
+
+ align:start position:0%
+menu of approximations that you do take
+along the way uh but it really is
+
+ align:start position:0%
+along the way uh but it really is
+ 
+
+ align:start position:0%
+along the way uh but it really is
+essentially first principal prediction
+
+ align:start position:0%
+essentially first principal prediction
+ 
+
+ align:start position:0%
+essentially first principal prediction
+of energy at zero Kelvin right thank so
+
+ align:start position:0%
+of energy at zero Kelvin right thank so
+ 
+
+ align:start position:0%
+of energy at zero Kelvin right thank so
+we we we use a lot of empirical data in
+
+ align:start position:0%
+we we we use a lot of empirical data in
+ 
+
+ align:start position:0%
+we we we use a lot of empirical data in
+o2o
+
+ align:start position:0%
+o2o
+ 
+
+ align:start position:0%
+o2o
+but you've also probably used um DFT
+
+ align:start position:0%
+but you've also probably used um DFT
+ 
+
+ align:start position:0%
+but you've also probably used um DFT
+derived data even without knowing it so
+
+ align:start position:0%
+derived data even without knowing it so
+ 
+
+ align:start position:0%
+derived data even without knowing it so
+when you have some materials Property
+
+ align:start position:0%
+when you have some materials Property
+ 
+
+ align:start position:0%
+when you have some materials Property
+Data it comes from somewhere and
+
+ align:start position:0%
+Data it comes from somewhere and
+ 
+
+ align:start position:0%
+Data it comes from somewhere and
+sometimes it comes from Theory and
+
+ align:start position:0%
+sometimes it comes from Theory and
+ 
+
+ align:start position:0%
+sometimes it comes from Theory and
+sometimes it comes from measurement and
+
+ align:start position:0%
+sometimes it comes from measurement and
+ 
+
+ align:start position:0%
+sometimes it comes from measurement and
+um oftentimes if it comes from Theory
+
+ align:start position:0%
+um oftentimes if it comes from Theory
+ 
+
+ align:start position:0%
+um oftentimes if it comes from Theory
+comes from DFD
+
+ align:start position:0%
+comes from DFD
+ 
+
+ align:start position:0%
+comes from DFD
+calculations yeah it it is and and uh in
+
+ align:start position:0%
+calculations yeah it it is and and uh in
+ 
+
+ align:start position:0%
+calculations yeah it it is and and uh in
+this there are different approximations
+
+ align:start position:0%
+this there are different approximations
+ 
+
+ align:start position:0%
+this there are different approximations
+and this was an all electron method very
+
+ align:start position:0%
+and this was an all electron method very
+ 
+
+ align:start position:0%
+and this was an all electron method very
+rigorous but it was typically something
+
+ align:start position:0%
+rigorous but it was typically something
+ 
+
+ align:start position:0%
+rigorous but it was typically something
+like 400 hours of super computer time
+
+ align:start position:0%
+like 400 hours of super computer time
+ 
+
+ align:start position:0%
+like 400 hours of super computer time
+for each data point back in the 1980s
+
+ align:start position:0%
+for each data point back in the 1980s
+ 
+
+ align:start position:0%
+for each data point back in the 1980s
+when
+
+ align:start position:0%
+when
+ 
+
+ align:start position:0%
+when
+we asked a question which do you prefer
+
+ align:start position:0%
+we asked a question which do you prefer
+ 
+
+ align:start position:0%
+we asked a question which do you prefer
+I think you mean which I prefer
+
+ align:start position:0%
+I think you mean which I prefer
+ 
+
+ align:start position:0%
+I think you mean which I prefer
+experiment of theory um is that what you
+
+ align:start position:0%
+experiment of theory um is that what you
+ 
+
+ align:start position:0%
+experiment of theory um is that what you
+meant here speak of if you unmute
+
+ align:start position:0%
+meant here speak of if you unmute
+ 
+
+ align:start position:0%
+meant here speak of if you unmute
+yourself it's it's more fun yeah uh I
+
+ align:start position:0%
+yourself it's it's more fun yeah uh I
+ 
+
+ align:start position:0%
+yourself it's it's more fun yeah uh I
+mean like for the applications like of
+
+ align:start position:0%
+mean like for the applications like of
+ 
+
+ align:start position:0%
+mean like for the applications like of
+prediction which is better to
+
+ align:start position:0%
+prediction which is better to
+ 
+
+ align:start position:0%
+prediction which is better to
+extrapolate
+
+ align:start position:0%
+extrapolate
+ 
+
+ align:start position:0%
+extrapolate
+uh so Greg if you had your choice be I
+
+ align:start position:0%
+uh so Greg if you had your choice be I
+ 
+
+ align:start position:0%
+uh so Greg if you had your choice be I
+mean uh I'll just say first of all it's
+
+ align:start position:0%
+mean uh I'll just say first of all it's
+ 
+
+ align:start position:0%
+mean uh I'll just say first of all it's
+often not it's often an apples to
+
+ align:start position:0%
+often not it's often an apples to
+ 
+
+ align:start position:0%
+often not it's often an apples to
+oranges comparison because we use DFT
+
+ align:start position:0%
+oranges comparison because we use DFT
+ 
+
+ align:start position:0%
+oranges comparison because we use DFT
+most often to get data for processes or
+
+ align:start position:0%
+most often to get data for processes or
+ 
+
+ align:start position:0%
+most often to get data for processes or
+situations that we just can't measure
+
+ align:start position:0%
+situations that we just can't measure
+ 
+
+ align:start position:0%
+situations that we just can't measure
+yeah which I think gives you your answer
+
+ align:start position:0%
+yeah which I think gives you your answer
+ 
+
+ align:start position:0%
+yeah which I think gives you your answer
+if you have Apples to Apples if you have
+
+ align:start position:0%
+if you have Apples to Apples if you have
+ 
+
+ align:start position:0%
+if you have Apples to Apples if you have
+a measurement and a calculation of the
+
+ align:start position:0%
+a measurement and a calculation of the
+ 
+
+ align:start position:0%
+a measurement and a calculation of the
+same thing in the same circumstance I
+
+ align:start position:0%
+same thing in the same circumstance I
+ 
+
+ align:start position:0%
+same thing in the same circumstance I
+think Greg and I would would agree we we
+
+ align:start position:0%
+think Greg and I would would agree we we
+ 
+
+ align:start position:0%
+think Greg and I would would agree we we
+if the measurement's a good one um we go
+
+ align:start position:0%
+if the measurement's a good one um we go
+ 
+
+ align:start position:0%
+if the measurement's a good one um we go
+with that yeah if you look at the
+
+ align:start position:0%
+with that yeah if you look at the
+ 
+
+ align:start position:0%
+with that yeah if you look at the
+magnitude of this uh you know we're
+
+ align:start position:0%
+magnitude of this uh you know we're
+ 
+
+ align:start position:0%
+magnitude of this uh you know we're
+we're using this method to find uh the
+
+ align:start position:0%
+we're using this method to find uh the
+ 
+
+ align:start position:0%
+we're using this method to find uh the
+one that have this cohesion enhancing
+
+ align:start position:0%
+one that have this cohesion enhancing
+ 
+
+ align:start position:0%
+one that have this cohesion enhancing
+potency of greater than one
+
+ align:start position:0%
+potency of greater than one
+ 
+
+ align:start position:0%
+potency of greater than one
+EV and the intrinsic uncertainty of even
+
+ align:start position:0%
+EV and the intrinsic uncertainty of even
+ 
+
+ align:start position:0%
+EV and the intrinsic uncertainty of even
+these calculations is about 0.1 EV and
+
+ align:start position:0%
+these calculations is about 0.1 EV and
+ 
+
+ align:start position:0%
+these calculations is about 0.1 EV and
+this other model got it within 0. 2 EV
+
+ align:start position:0%
+this other model got it within 0. 2 EV
+ 
+
+ align:start position:0%
+this other model got it within 0. 2 EV
+so uh it is important to understand the
+
+ align:start position:0%
+so uh it is important to understand the
+ 
+
+ align:start position:0%
+so uh it is important to understand the
+uncertainty of those predictions so if
+
+ align:start position:0%
+uncertainty of those predictions so if
+ 
+
+ align:start position:0%
+uncertainty of those predictions so if
+it's plus or minus 0.1 AV that's fine
+
+ align:start position:0%
+it's plus or minus 0.1 AV that's fine
+ 
+
+ align:start position:0%
+it's plus or minus 0.1 AV that's fine
+for helping you find the 1 EV candidates
+
+ align:start position:0%
+for helping you find the 1 EV candidates
+ 
+
+ align:start position:0%
+for helping you find the 1 EV candidates
+but most often in Metallurgy the number
+
+ align:start position:0%
+but most often in Metallurgy the number
+ 
+
+ align:start position:0%
+but most often in Metallurgy the number
+we want to know is only of the magnitude
+
+ align:start position:0%
+we want to know is only of the magnitude
+ 
+
+ align:start position:0%
+we want to know is only of the magnitude
+0.1 and 0.1 Plus or minus .1 is not very
+
+ align:start position:0%
+0.1 and 0.1 Plus or minus .1 is not very
+ 
+
+ align:start position:0%
+0.1 and 0.1 Plus or minus .1 is not very
+useful uh so it's a good way to to find
+
+ align:start position:0%
+useful uh so it's a good way to to find
+ 
+
+ align:start position:0%
+useful uh so it's a good way to to find
+out where to go for the big numbers but
+
+ align:start position:0%
+out where to go for the big numbers but
+ 
+
+ align:start position:0%
+out where to go for the big numbers but
+most of the time uh we really need the
+
+ align:start position:0%
+most of the time uh we really need the
+ 
+
+ align:start position:0%
+most of the time uh we really need the
+experimental data that gives us higher
+
+ align:start position:0%
+experimental data that gives us higher
+ 
+
+ align:start position:0%
+experimental data that gives us higher
+accuracy than we can get currently from
+
+ align:start position:0%
+accuracy than we can get currently from
+ 
+
+ align:start position:0%
+accuracy than we can get currently from
+the DFT
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+methods y so that's why I was saying
+
+ align:start position:0%
+methods y so that's why I was saying
+ 
+
+ align:start position:0%
+methods y so that's why I was saying
+that upfront uncertainty quantification
+
+ align:start position:0%
+that upfront uncertainty quantification
+ 
+
+ align:start position:0%
+that upfront uncertainty quantification
+was a very important part of the whole
+
+ align:start position:0%
+was a very important part of the whole
+ 
+
+ align:start position:0%
+was a very important part of the whole
+strategy of putting these tools
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+together okay but this is a good example
+
+ align:start position:0%
+together okay but this is a good example
+ 
+
+ align:start position:0%
+together okay but this is a good example
+of maximum use of DFT we had a small set
+
+ align:start position:0%
+of maximum use of DFT we had a small set
+ 
+
+ align:start position:0%
+of maximum use of DFT we had a small set
+of experimental surface thermodynamics
+
+ align:start position:0%
+of experimental surface thermodynamics
+ 
+
+ align:start position:0%
+of experimental surface thermodynamics
+to test against uh and then we could
+
+ align:start position:0%
+to test against uh and then we could
+ 
+
+ align:start position:0%
+to test against uh and then we could
+calibrate against the ability of DFT to
+
+ align:start position:0%
+calibrate against the ability of DFT to
+ 
+
+ align:start position:0%
+calibrate against the ability of DFT to
+predict it uh and then make this
+
+ align:start position:0%
+predict it uh and then make this
+ 
+
+ align:start position:0%
+predict it uh and then make this
+projection across the periodic table so
+
+ align:start position:0%
+projection across the periodic table so
+ 
+
+ align:start position:0%
+projection across the periodic table so
+it's a a surface theramic genome almost
+
+ align:start position:0%
+it's a a surface theramic genome almost
+ 
+
+ align:start position:0%
+it's a a surface theramic genome almost
+entirely from DFT
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+calculations and the way we put it all
+
+ align:start position:0%
+calculations and the way we put it all
+ 
+
+ align:start position:0%
+calculations and the way we put it all
+together is graphical parametric design
+
+ align:start position:0%
+together is graphical parametric design
+ 
+
+ align:start position:0%
+together is graphical parametric design
+so we map the behaviors of Interest back
+
+ align:start position:0%
+so we map the behaviors of Interest back
+ 
+
+ align:start position:0%
+so we map the behaviors of Interest back
+to these parameters like driving force
+
+ align:start position:0%
+to these parameters like driving force
+ 
+
+ align:start position:0%
+to these parameters like driving force
+and phas fraction for strengthening and
+
+ align:start position:0%
+and phas fraction for strengthening and
+ 
+
+ align:start position:0%
+and phas fraction for strengthening and
+so for the actual stainless landing gear
+
+ align:start position:0%
+so for the actual stainless landing gear
+ 
+
+ align:start position:0%
+so for the actual stainless landing gear
+steel uh here's a crossplot versus malum
+
+ align:start position:0%
+steel uh here's a crossplot versus malum
+ 
+
+ align:start position:0%
+steel uh here's a crossplot versus malum
+content affecting the driving force and
+
+ align:start position:0%
+content affecting the driving force and
+ 
+
+ align:start position:0%
+content affecting the driving force and
+the carbon affecting the phase fraction
+
+ align:start position:0%
+the carbon affecting the phase fraction
+ 
+
+ align:start position:0%
+the carbon affecting the phase fraction
+and there are a couple invisible yellow
+
+ align:start position:0%
+and there are a couple invisible yellow
+ 
+
+ align:start position:0%
+and there are a couple invisible yellow
+cont Contour showing how the driving
+
+ align:start position:0%
+cont Contour showing how the driving
+ 
+
+ align:start position:0%
+cont Contour showing how the driving
+force increases with meibum and of
+
+ align:start position:0%
+force increases with meibum and of
+ 
+
+ align:start position:0%
+force increases with meibum and of
+course the carbon sets the phase
+
+ align:start position:0%
+course the carbon sets the phase
+ 
+
+ align:start position:0%
+course the carbon sets the phase
+fraction so it's this region in here uh
+
+ align:start position:0%
+fraction so it's this region in here uh
+ 
+
+ align:start position:0%
+fraction so it's this region in here uh
+that gave us the strength level uh that
+
+ align:start position:0%
+that gave us the strength level uh that
+ 
+
+ align:start position:0%
+that gave us the strength level uh that
+is our goal for the design and super
+
+ align:start position:0%
+is our goal for the design and super
+ 
+
+ align:start position:0%
+is our goal for the design and super
+proposed on that are processability
+
+ align:start position:0%
+proposed on that are processability
+ 
+
+ align:start position:0%
+proposed on that are processability
+constraints such as the Martin site
+
+ align:start position:0%
+constraints such as the Martin site
+ 
+
+ align:start position:0%
+constraints such as the Martin site
+start temperature to have a fully Martin
+
+ align:start position:0%
+start temperature to have a fully Martin
+ 
+
+ align:start position:0%
+start temperature to have a fully Martin
+sutic steel and the solution temperature
+
+ align:start position:0%
+sutic steel and the solution temperature
+ 
+
+ align:start position:0%
+sutic steel and the solution temperature
+to put the reactive components in
+
+ align:start position:0%
+to put the reactive components in
+ 
+
+ align:start position:0%
+to put the reactive components in
+solution so we can precipitate them uh
+
+ align:start position:0%
+solution so we can precipitate them uh
+ 
+
+ align:start position:0%
+solution so we can precipitate them uh
+at at high temperatures uh and the
+
+ align:start position:0%
+at at high temperatures uh and the
+ 
+
+ align:start position:0%
+at at high temperatures uh and the
+relative slopes that we can see from
+
+ align:start position:0%
+relative slopes that we can see from
+ 
+
+ align:start position:0%
+relative slopes that we can see from
+these types of plots also allow us to
+
+ align:start position:0%
+these types of plots also allow us to
+ 
+
+ align:start position:0%
+these types of plots also allow us to
+assess relative sensitivities so we can
+
+ align:start position:0%
+assess relative sensitivities so we can
+ 
+
+ align:start position:0%
+assess relative sensitivities so we can
+develop robust uh design strategies that
+
+ align:start position:0%
+develop robust uh design strategies that
+ 
+
+ align:start position:0%
+develop robust uh design strategies that
+that are that don't require too tight of
+
+ align:start position:0%
+that are that don't require too tight of
+ 
+
+ align:start position:0%
+that are that don't require too tight of
+Tolerance uh so quite typically we we
+
+ align:start position:0%
+Tolerance uh so quite typically we we
+ 
+
+ align:start position:0%
+Tolerance uh so quite typically we we
+start from the last stage of processing
+
+ align:start position:0%
+start from the last stage of processing
+ 
+
+ align:start position:0%
+start from the last stage of processing
+the the nanoscale precipitation that
+
+ align:start position:0%
+the the nanoscale precipitation that
+ 
+
+ align:start position:0%
+the the nanoscale precipitation that
+meets the strength goals and then back
+
+ align:start position:0%
+meets the strength goals and then back
+ 
+
+ align:start position:0%
+meets the strength goals and then back
+up to earlier stages of processing we
+
+ align:start position:0%
+up to earlier stages of processing we
+ 
+
+ align:start position:0%
+up to earlier stages of processing we
+were also using uh these FCC MC type
+
+ align:start position:0%
+were also using uh these FCC MC type
+ 
+
+ align:start position:0%
+were also using uh these FCC MC type
+carbides in this case we've got a a
+
+ align:start position:0%
+carbides in this case we've got a a
+ 
+
+ align:start position:0%
+carbides in this case we've got a a
+composition variable in the processed
+
+ align:start position:0%
+composition variable in the processed
+ 
+
+ align:start position:0%
+composition variable in the processed
+temperature so we're constraining these
+
+ align:start position:0%
+temperature so we're constraining these
+ 
+
+ align:start position:0%
+temperature so we're constraining these
+grain refining particles to be soluble
+
+ align:start position:0%
+grain refining particles to be soluble
+ 
+
+ align:start position:0%
+grain refining particles to be soluble
+at homogeneization temperatures able to
+
+ align:start position:0%
+at homogeneization temperatures able to
+ 
+
+ align:start position:0%
+at homogeneization temperatures able to
+precipitate out at forging temperatures
+
+ align:start position:0%
+precipitate out at forging temperatures
+ 
+
+ align:start position:0%
+precipitate out at forging temperatures
+and then maintain a certain phase
+
+ align:start position:0%
+and then maintain a certain phase
+ 
+
+ align:start position:0%
+and then maintain a certain phase
+fraction in size at the final
+
+ align:start position:0%
+fraction in size at the final
+ 
+
+ align:start position:0%
+fraction in size at the final
+austenitizing temperature of the steel
+
+ align:start position:0%
+austenitizing temperature of the steel
+ 
+
+ align:start position:0%
+austenitizing temperature of the steel
+uh that sets the grain size of the steel
+
+ align:start position:0%
+uh that sets the grain size of the steel
+ 
+
+ align:start position:0%
+uh that sets the grain size of the steel
+so similarly we can back up to even
+
+ align:start position:0%
+so similarly we can back up to even
+ 
+
+ align:start position:0%
+so similarly we can back up to even
+earlier stages of processing specify the
+
+ align:start position:0%
+earlier stages of processing specify the
+ 
+
+ align:start position:0%
+earlier stages of processing specify the
+deoxidation processes that set the
+
+ align:start position:0%
+deoxidation processes that set the
+ 
+
+ align:start position:0%
+deoxidation processes that set the
+primary inclusions at the multi Micron
+
+ align:start position:0%
+primary inclusions at the multi Micron
+ 
+
+ align:start position:0%
+primary inclusions at the multi Micron
+level that are important to toughness
+
+ align:start position:0%
+level that are important to toughness
+ 
+
+ align:start position:0%
+level that are important to toughness
+and fatigue resistance uh but that
+
+ align:start position:0%
+and fatigue resistance uh but that
+ 
+
+ align:start position:0%
+and fatigue resistance uh but that
+graphical strategy uh is uh very
+
+ align:start position:0%
+graphical strategy uh is uh very
+ 
+
+ align:start position:0%
+graphical strategy uh is uh very
+efficient uh and it is the practice that
+
+ align:start position:0%
+efficient uh and it is the practice that
+ 
+
+ align:start position:0%
+efficient uh and it is the practice that
+we use at questec and the practice that
+
+ align:start position:0%
+we use at questec and the practice that
+ 
+
+ align:start position:0%
+we use at questec and the practice that
+I teach in my design
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+class so the first four products uh to
+
+ align:start position:0%
+class so the first four products uh to
+ 
+
+ align:start position:0%
+class so the first four products uh to
+come out of that are are these high
+
+ align:start position:0%
+come out of that are are these high
+ 
+
+ align:start position:0%
+come out of that are are these high
+performance secondary hardening Steels
+
+ align:start position:0%
+performance secondary hardening Steels
+ 
+
+ align:start position:0%
+performance secondary hardening Steels
+uh we have now two uh flight qualified
+
+ align:start position:0%
+uh we have now two uh flight qualified
+ 
+
+ align:start position:0%
+uh we have now two uh flight qualified
+Steels as as well as the stainless
+
+ align:start position:0%
+Steels as as well as the stainless
+ 
+
+ align:start position:0%
+Steels as as well as the stainless
+that's used by the air force uh we have
+
+ align:start position:0%
+that's used by the air force uh we have
+ 
+
+ align:start position:0%
+that's used by the air force uh we have
+a high toughness steel uh that's first
+
+ align:start position:0%
+a high toughness steel uh that's first
+ 
+
+ align:start position:0%
+a high toughness steel uh that's first
+gone into the hook shank application for
+
+ align:start position:0%
+gone into the hook shank application for
+ 
+
+ align:start position:0%
+gone into the hook shank application for
+the carrier-based uh planes uh so both
+
+ align:start position:0%
+the carrier-based uh planes uh so both
+ 
+
+ align:start position:0%
+the carrier-based uh planes uh so both
+of those Steels are flying uh we also
+
+ align:start position:0%
+of those Steels are flying uh we also
+ 
+
+ align:start position:0%
+of those Steels are flying uh we also
+have very high performance carbonizing
+
+ align:start position:0%
+have very high performance carbonizing
+ 
+
+ align:start position:0%
+have very high performance carbonizing
+steals for gear Gear steals for fatigue
+
+ align:start position:0%
+steals for gear Gear steals for fatigue
+ 
+
+ align:start position:0%
+steals for gear Gear steals for fatigue
+resistance and that's doing well uh on
+
+ align:start position:0%
+resistance and that's doing well uh on
+ 
+
+ align:start position:0%
+resistance and that's doing well uh on
+off-road and on track racing uh and in
+
+ align:start position:0%
+off-road and on track racing uh and in
+ 
+
+ align:start position:0%
+off-road and on track racing uh and in
+fact uh the Red Bull Formula 1 team
+
+ align:start position:0%
+fact uh the Red Bull Formula 1 team
+ 
+
+ align:start position:0%
+fact uh the Red Bull Formula 1 team
+that's very competitive this year is
+
+ align:start position:0%
+that's very competitive this year is
+ 
+
+ align:start position:0%
+that's very competitive this year is
+actually using our gear steals for uh
+
+ align:start position:0%
+actually using our gear steals for uh
+ 
+
+ align:start position:0%
+actually using our gear steals for uh
+for their
+
+ align:start position:0%
+for their
+ 
+
+ align:start position:0%
+for their
+reliability uh and those gear steals now
+
+ align:start position:0%
+reliability uh and those gear steals now
+ 
+
+ align:start position:0%
+reliability uh and those gear steals now
+are being qualified for helicopter
+
+ align:start position:0%
+are being qualified for helicopter
+ 
+
+ align:start position:0%
+are being qualified for helicopter
+applications uh but all of these benefit
+
+ align:start position:0%
+applications uh but all of these benefit
+ 
+
+ align:start position:0%
+applications uh but all of these benefit
+uh from that extra uh strengthening
+
+ align:start position:0%
+uh from that extra uh strengthening
+ 
+
+ align:start position:0%
+uh from that extra uh strengthening
+efficiency that we get by refining those
+
+ align:start position:0%
+efficiency that we get by refining those
+ 
+
+ align:start position:0%
+efficiency that we get by refining those
+m2c carbides down to a 3 nanometer size
+
+ align:start position:0%
+m2c carbides down to a 3 nanometer size
+ 
+
+ align:start position:0%
+m2c carbides down to a 3 nanometer size
+scale through that maximization of
+
+ align:start position:0%
+scale through that maximization of
+ 
+
+ align:start position:0%
+scale through that maximization of
+driving force as validated here by an
+
+ align:start position:0%
+driving force as validated here by an
+ 
+
+ align:start position:0%
+driving force as validated here by an
+early 3D atom probe reconstruction so
+
+ align:start position:0%
+early 3D atom probe reconstruction so
+ 
+
+ align:start position:0%
+early 3D atom probe reconstruction so
+all four of those Steels are using
+
+ align:start position:0%
+all four of those Steels are using
+ 
+
+ align:start position:0%
+all four of those Steels are using
+greater strengthening efficiency to
+
+ align:start position:0%
+greater strengthening efficiency to
+ 
+
+ align:start position:0%
+greater strengthening efficiency to
+resolve the conflict between with other
+
+ align:start position:0%
+resolve the conflict between with other
+ 
+
+ align:start position:0%
+resolve the conflict between with other
+properties GRE uh this is the maybe the
+
+ align:start position:0%
+properties GRE uh this is the maybe the
+ 
+
+ align:start position:0%
+properties GRE uh this is the maybe the
+second or more time you've mentioned
+
+ align:start position:0%
+second or more time you've mentioned
+ 
+
+ align:start position:0%
+second or more time you've mentioned
+Adam probe and there's data set right in
+
+ align:start position:0%
+Adam probe and there's data set right in
+ 
+
+ align:start position:0%
+Adam probe and there's data set right in
+the middle here so it seems like a good
+
+ align:start position:0%
+the middle here so it seems like a good
+ 
+
+ align:start position:0%
+the middle here so it seems like a good
+opportunity to talk about what that is
+
+ align:start position:0%
+opportunity to talk about what that is
+ 
+
+ align:start position:0%
+opportunity to talk about what that is
+yes the uh atom probe is a a version of
+
+ align:start position:0%
+yes the uh atom probe is a a version of
+ 
+
+ align:start position:0%
+yes the uh atom probe is a a version of
+the field ion microscope uh that that
+
+ align:start position:0%
+the field ion microscope uh that that
+ 
+
+ align:start position:0%
+the field ion microscope uh that that
+looks at the point of a very sharp pin
+
+ align:start position:0%
+looks at the point of a very sharp pin
+ 
+
+ align:start position:0%
+looks at the point of a very sharp pin
+to get very high electric
+
+ align:start position:0%
+to get very high electric
+ 
+
+ align:start position:0%
+to get very high electric
+Fields uh and uh it can actually cause
+
+ align:start position:0%
+Fields uh and uh it can actually cause
+ 
+
+ align:start position:0%
+Fields uh and uh it can actually cause
+evaporation from the high Fields uh and
+
+ align:start position:0%
+evaporation from the high Fields uh and
+ 
+
+ align:start position:0%
+evaporation from the high Fields uh and
+so we can evaporate atoms off of the tip
+
+ align:start position:0%
+so we can evaporate atoms off of the tip
+ 
+
+ align:start position:0%
+so we can evaporate atoms off of the tip
+and project them to a position sensitive
+
+ align:start position:0%
+and project them to a position sensitive
+ 
+
+ align:start position:0%
+and project them to a position sensitive
+detector and actually reconstruct the
+
+ align:start position:0%
+detector and actually reconstruct the
+ 
+
+ align:start position:0%
+detector and actually reconstruct the
+position all the atoms in the tip so it
+
+ align:start position:0%
+position all the atoms in the tip so it
+ 
+
+ align:start position:0%
+position all the atoms in the tip so it
+really is uh taking us down to nanoscale
+
+ align:start position:0%
+really is uh taking us down to nanoscale
+ 
+
+ align:start position:0%
+really is uh taking us down to nanoscale
+uh spatial
+
+ align:start position:0%
+uh spatial
+ 
+
+ align:start position:0%
+uh spatial
+resolution uh with detectability of all
+
+ align:start position:0%
+resolution uh with detectability of all
+ 
+
+ align:start position:0%
+resolution uh with detectability of all
+atoms in in the periodic table so a very
+
+ align:start position:0%
+atoms in in the periodic table so a very
+ 
+
+ align:start position:0%
+atoms in in the periodic table so a very
+powerful technique I may it pulls a part
+
+ align:start position:0%
+powerful technique I may it pulls a part
+ 
+
+ align:start position:0%
+powerful technique I may it pulls a part
+of material at of by atom and tells you
+
+ align:start position:0%
+of material at of by atom and tells you
+ 
+
+ align:start position:0%
+of material at of by atom and tells you
+where all the atoms were
+
+ align:start position:0%
+where all the atoms were
+ 
+
+ align:start position:0%
+where all the atoms were
+yep that's what it does
+
+ align:start position:0%
+yep that's what it does
+ 
+
+ align:start position:0%
+yep that's what it does
+yes and we have very good facility at
+
+ align:start position:0%
+yes and we have very good facility at
+ 
+
+ align:start position:0%
+yes and we have very good facility at
+Northwestern but there's also a very
+
+ align:start position:0%
+Northwestern but there's also a very
+ 
+
+ align:start position:0%
+Northwestern but there's also a very
+good one uh at at Harvard that we're
+
+ align:start position:0%
+good one uh at at Harvard that we're
+ 
+
+ align:start position:0%
+good one uh at at Harvard that we're
+we're using now
+
+ align:start position:0%
+we're using now
+ 
+
+ align:start position:0%
+we're using now
+oh can you use the material after that
+
+ align:start position:0%
+oh can you use the material after that
+ 
+
+ align:start position:0%
+oh can you use the material after that
+like does it change the
+
+ align:start position:0%
+like does it change the
+ 
+
+ align:start position:0%
+like does it change the
+surface uh yeah this is uh this is true
+
+ align:start position:0%
+surface uh yeah this is uh this is true
+ 
+
+ align:start position:0%
+surface uh yeah this is uh this is true
+tomography so we're fully we are really
+
+ align:start position:0%
+tomography so we're fully we are really
+ 
+
+ align:start position:0%
+tomography so we're fully we are really
+toing the material and taking it apart
+
+ align:start position:0%
+toing the material and taking it apart
+ 
+
+ align:start position:0%
+toing the material and taking it apart
+uh but one thing we can do uh is before
+
+ align:start position:0%
+uh but one thing we can do uh is before
+ 
+
+ align:start position:0%
+uh but one thing we can do uh is before
+we do the tomography we can look at the
+
+ align:start position:0%
+we do the tomography we can look at the
+ 
+
+ align:start position:0%
+we do the tomography we can look at the
+tip uh in the electron microscope so we
+
+ align:start position:0%
+tip uh in the electron microscope so we
+ 
+
+ align:start position:0%
+tip uh in the electron microscope so we
+can get defraction information
+
+ align:start position:0%
+can get defraction information
+ 
+
+ align:start position:0%
+can get defraction information
+crystalographic data fully characterize
+
+ align:start position:0%
+crystalographic data fully characterize
+ 
+
+ align:start position:0%
+crystalographic data fully characterize
+the tip inm before we then take it apart
+
+ align:start position:0%
+the tip inm before we then take it apart
+ 
+
+ align:start position:0%
+the tip inm before we then take it apart
+in the anap but it does it's like
+
+ align:start position:0%
+in the anap but it does it's like
+ 
+
+ align:start position:0%
+in the anap but it does it's like
+getting beamed up but you're never
+
+ align:start position:0%
+getting beamed up but you're never
+ 
+
+ align:start position:0%
+getting beamed up but you're never
+getting beam back down that's right
+
+ align:start position:0%
+getting beam back down that's right
+ 
+
+ align:start position:0%
+getting beam back down that's right
+tears the material of heart Adam by Adam
+
+ align:start position:0%
+tears the material of heart Adam by Adam
+ 
+
+ align:start position:0%
+tears the material of heart Adam by Adam
+and does not put it back together again
+
+ align:start position:0%
+and does not put it back together again
+ 
+
+ align:start position:0%
+and does not put it back together again
+right it well it puts it back together
+
+ align:start position:0%
+right it well it puts it back together
+ 
+
+ align:start position:0%
+right it well it puts it back together
+theoretically
+
+ align:start position:0%
+theoretically
+ 
+
+ align:start position:0%
+theoretically
+right yeah so we reassemble it as
+
+ align:start position:0%
+right yeah so we reassemble it as
+ 
+
+ align:start position:0%
+right yeah so we reassemble it as
+tomography
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yep all
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+right yeah I would uh just touch on the
+
+ align:start position:0%
+right yeah I would uh just touch on the
+ 
+
+ align:start position:0%
+right yeah I would uh just touch on the
+the DARPA aim initiative again this this
+
+ align:start position:0%
+the DARPA aim initiative again this this
+ 
+
+ align:start position:0%
+the DARPA aim initiative again this this
+uh full compression of the cycle is this
+
+ align:start position:0%
+uh full compression of the cycle is this
+ 
+
+ align:start position:0%
+uh full compression of the cycle is this
+linking uh to macroscopic process models
+
+ align:start position:0%
+linking uh to macroscopic process models
+ 
+
+ align:start position:0%
+linking uh to macroscopic process models
+and so we were able to work with GE and
+
+ align:start position:0%
+and so we were able to work with GE and
+ 
+
+ align:start position:0%
+and so we were able to work with GE and
+pratton Whitney and and learn about the
+
+ align:start position:0%
+pratton Whitney and and learn about the
+ 
+
+ align:start position:0%
+pratton Whitney and and learn about the
+technology of multidisiplinary
+
+ align:start position:0%
+technology of multidisiplinary
+ 
+
+ align:start position:0%
+technology of multidisiplinary
+computational engineering so this
+
+ align:start position:0%
+computational engineering so this
+ 
+
+ align:start position:0%
+computational engineering so this
+integrator was linked to all to the
+
+ align:start position:0%
+integrator was linked to all to the
+ 
+
+ align:start position:0%
+integrator was linked to all to the
+tools of macroscopic aerot turbine
+
+ align:start position:0%
+tools of macroscopic aerot turbine
+ 
+
+ align:start position:0%
+tools of macroscopic aerot turbine
+engine design uh including heat transfer
+
+ align:start position:0%
+engine design uh including heat transfer
+ 
+
+ align:start position:0%
+engine design uh including heat transfer
+for heat treatment so we built this
+
+ align:start position:0%
+for heat treatment so we built this
+ 
+
+ align:start position:0%
+for heat treatment so we built this
+prpic simulator so this puts together
+
+ align:start position:0%
+prpic simulator so this puts together
+ 
+
+ align:start position:0%
+prpic simulator so this puts together
+the calad thermo and Mobility databases
+
+ align:start position:0%
+the calad thermo and Mobility databases
+ 
+
+ align:start position:0%
+the calad thermo and Mobility databases
+and adds some surface theramic
+
+ align:start position:0%
+and adds some surface theramic
+ 
+
+ align:start position:0%
+and adds some surface theramic
+quantities uh to actually simulate uh
+
+ align:start position:0%
+quantities uh to actually simulate uh
+ 
+
+ align:start position:0%
+quantities uh to actually simulate uh
+complex nucleation and growth uh in
+
+ align:start position:0%
+complex nucleation and growth uh in
+ 
+
+ align:start position:0%
+complex nucleation and growth uh in
+complex Alloys uh so that we could
+
+ align:start position:0%
+complex Alloys uh so that we could
+ 
+
+ align:start position:0%
+complex Alloys uh so that we could
+actually predict the uh effects of very
+
+ align:start position:0%
+actually predict the uh effects of very
+ 
+
+ align:start position:0%
+actually predict the uh effects of very
+complex heat treatments of turban discs
+
+ align:start position:0%
+complex heat treatments of turban discs
+ 
+
+ align:start position:0%
+complex heat treatments of turban discs
+that had multimodal distributions of
+
+ align:start position:0%
+that had multimodal distributions of
+ 
+
+ align:start position:0%
+that had multimodal distributions of
+gamma Prime precipitates uh and very
+
+ align:start position:0%
+gamma Prime precipitates uh and very
+ 
+
+ align:start position:0%
+gamma Prime precipitates uh and very
+accurately control it and use it to
+
+ align:start position:0%
+accurately control it and use it to
+ 
+
+ align:start position:0%
+accurately control it and use it to
+demonstrate it in process
+
+ align:start position:0%
+demonstrate it in process
+ 
+
+ align:start position:0%
+demonstrate it in process
+optimization uh validating a predicted
+
+ align:start position:0%
+optimization uh validating a predicted
+ 
+
+ align:start position:0%
+optimization uh validating a predicted
+overspin burst speed of a of a turbine
+
+ align:start position:0%
+overspin burst speed of a of a turbine
+ 
+
+ align:start position:0%
+overspin burst speed of a of a turbine
+disc and then ultimately we did develop
+
+ align:start position:0%
+disc and then ultimately we did develop
+ 
+
+ align:start position:0%
+disc and then ultimately we did develop
+strategies to predict the cumulative
+
+ align:start position:0%
+strategies to predict the cumulative
+ 
+
+ align:start position:0%
+strategies to predict the cumulative
+probability distribution of properties
+
+ align:start position:0%
+probability distribution of properties
+ 
+
+ align:start position:0%
+probability distribution of properties
+uh from the variation that can occur uh
+
+ align:start position:0%
+uh from the variation that can occur uh
+ 
+
+ align:start position:0%
+uh from the variation that can occur uh
+from during manufacturing from the
+
+ align:start position:0%
+from during manufacturing from the
+ 
+
+ align:start position:0%
+from during manufacturing from the
+allowed tolerances of the specifications
+
+ align:start position:0%
+allowed tolerances of the specifications
+ 
+
+ align:start position:0%
+allowed tolerances of the specifications
+of material composition and processing
+
+ align:start position:0%
+of material composition and processing
+ 
+
+ align:start position:0%
+of material composition and processing
+and we were able to get information that
+
+ align:start position:0%
+and we were able to get information that
+ 
+
+ align:start position:0%
+and we were able to get information that
+normally would uh take a lot of time and
+
+ align:start position:0%
+normally would uh take a lot of time and
+ 
+
+ align:start position:0%
+normally would uh take a lot of time and
+money uh and a lot of testing like a 300
+
+ align:start position:0%
+money uh and a lot of testing like a 300
+ 
+
+ align:start position:0%
+money uh and a lot of testing like a 300
+turbine disc before you'd have enough
+
+ align:start position:0%
+turbine disc before you'd have enough
+ 
+
+ align:start position:0%
+turbine disc before you'd have enough
+data and we could with only 15 data
+
+ align:start position:0%
+data and we could with only 15 data
+ 
+
+ align:start position:0%
+data and we could with only 15 data
+points and mechanistic models actually
+
+ align:start position:0%
+points and mechanistic models actually
+ 
+
+ align:start position:0%
+points and mechanistic models actually
+predict this uh 1% minimum property at
+
+ align:start position:0%
+predict this uh 1% minimum property at
+ 
+
+ align:start position:0%
+predict this uh 1% minimum property at
+room temperature and elevated
+
+ align:start position:0%
+room temperature and elevated
+ 
+
+ align:start position:0%
+room temperature and elevated
+temperature so we demonstrated the
+
+ align:start position:0%
+temperature so we demonstrated the
+ 
+
+ align:start position:0%
+temperature so we demonstrated the
+strategy to to get the qualification
+
+ align:start position:0%
+strategy to to get the qualification
+ 
+
+ align:start position:0%
+strategy to to get the qualification
+data of necessary minimum properties
+
+ align:start position:0%
+data of necessary minimum properties
+ 
+
+ align:start position:0%
+data of necessary minimum properties
+very efficiently by predictive modeling
+
+ align:start position:0%
+very efficiently by predictive modeling
+ 
+
+ align:start position:0%
+very efficiently by predictive modeling
+based on these calat
+
+ align:start position:0%
+based on these calat
+ 
+
+ align:start position:0%
+based on these calat
+tools uh and so here's the time uh chart
+
+ align:start position:0%
+tools uh and so here's the time uh chart
+ 
+
+ align:start position:0%
+tools uh and so here's the time uh chart
+on the t two uh landing gear Steels so
+
+ align:start position:0%
+on the t two uh landing gear Steels so
+ 
+
+ align:start position:0%
+on the t two uh landing gear Steels so
+this is the technology Readiness levels
+
+ align:start position:0%
+this is the technology Readiness levels
+ 
+
+ align:start position:0%
+this is the technology Readiness levels
+uh at the level of the landing gear
+
+ align:start position:0%
+uh at the level of the landing gear
+ 
+
+ align:start position:0%
+uh at the level of the landing gear
+here's the corresponding materials uh uh
+
+ align:start position:0%
+here's the corresponding materials uh uh
+ 
+
+ align:start position:0%
+here's the corresponding materials uh uh
+milestones and so both of these steals
+
+ align:start position:0%
+milestones and so both of these steals
+ 
+
+ align:start position:0%
+milestones and so both of these steals
+went from a clean sheet of paper to
+
+ align:start position:0%
+went from a clean sheet of paper to
+ 
+
+ align:start position:0%
+went from a clean sheet of paper to
+flight in less than a decade meeting the
+
+ align:start position:0%
+flight in less than a decade meeting the
+ 
+
+ align:start position:0%
+flight in less than a decade meeting the
+MGI goals uh but particularly doing it
+
+ align:start position:0%
+MGI goals uh but particularly doing it
+ 
+
+ align:start position:0%
+MGI goals uh but particularly doing it
+the second time we were able to move
+
+ align:start position:0%
+the second time we were able to move
+ 
+
+ align:start position:0%
+the second time we were able to move
+more quickly uh into the Navy trusting
+
+ align:start position:0%
+more quickly uh into the Navy trusting
+ 
+
+ align:start position:0%
+more quickly uh into the Navy trusting
+our predictions well enough to to give
+
+ align:start position:0%
+our predictions well enough to to give
+ 
+
+ align:start position:0%
+our predictions well enough to to give
+us the technology for the hook shank
+
+ align:start position:0%
+us the technology for the hook shank
+ 
+
+ align:start position:0%
+us the technology for the hook shank
+application so we actually had component
+
+ align:start position:0%
+application so we actually had component
+ 
+
+ align:start position:0%
+application so we actually had component
+qualification within a month of material
+
+ align:start position:0%
+qualification within a month of material
+ 
+
+ align:start position:0%
+qualification within a month of material
+qualification in that case and this has
+
+ align:start position:0%
+qualification in that case and this has
+ 
+
+ align:start position:0%
+qualification in that case and this has
+been a case study uh for the MGI
+
+ align:start position:0%
+been a case study uh for the MGI
+ 
+
+ align:start position:0%
+been a case study uh for the MGI
+program where uh it was reviewed in the
+
+ align:start position:0%
+program where uh it was reviewed in the
+ 
+
+ align:start position:0%
+program where uh it was reviewed in the
+second landing gear steel what were the
+
+ align:start position:0%
+second landing gear steel what were the
+ 
+
+ align:start position:0%
+second landing gear steel what were the
+technology accelerators using this
+
+ align:start position:0%
+technology accelerators using this
+ 
+
+ align:start position:0%
+technology accelerators using this
+technology and what were the Inhibitors
+
+ align:start position:0%
+technology and what were the Inhibitors
+ 
+
+ align:start position:0%
+technology and what were the Inhibitors
+uh doing it in a small business where we
+
+ align:start position:0%
+uh doing it in a small business where we
+ 
+
+ align:start position:0%
+uh doing it in a small business where we
+were uh there were lapses in the federal
+
+ align:start position:0%
+were uh there were lapses in the federal
+ 
+
+ align:start position:0%
+were uh there were lapses in the federal
+funding of the projects and there was a
+
+ align:start position:0%
+funding of the projects and there was a
+ 
+
+ align:start position:0%
+funding of the projects and there was a
+Reliance on toll manufacturing by others
+
+ align:start position:0%
+Reliance on toll manufacturing by others
+ 
+
+ align:start position:0%
+Reliance on toll manufacturing by others
+it was estimated that we had really
+
+ align:start position:0%
+it was estimated that we had really
+ 
+
+ align:start position:0%
+it was estimated that we had really
+developed uh demonstrated technology
+
+ align:start position:0%
+developed uh demonstrated technology
+ 
+
+ align:start position:0%
+developed uh demonstrated technology
+capable of a three-year cycle and that
+
+ align:start position:0%
+capable of a three-year cycle and that
+ 
+
+ align:start position:0%
+capable of a three-year cycle and that
+that's really the important key of
+
+ align:start position:0%
+that's really the important key of
+ 
+
+ align:start position:0%
+that's really the important key of
+that's what enables
+
+ align:start position:0%
+that's what enables
+ 
+
+ align:start position:0%
+that's what enables
+concurrency uh and really the uh most
+
+ align:start position:0%
+concurrency uh and really the uh most
+ 
+
+ align:start position:0%
+concurrency uh and really the uh most
+historic example of that so far uh was
+
+ align:start position:0%
+historic example of that so far uh was
+ 
+
+ align:start position:0%
+historic example of that so far uh was
+the Apple watch announced in
+
+ align:start position:0%
+the Apple watch announced in
+ 
+
+ align:start position:0%
+the Apple watch announced in
+2014 uh so these are all new Alloys
+
+ align:start position:0%
+2014 uh so these are all new Alloys
+ 
+
+ align:start position:0%
+2014 uh so these are all new Alloys
+developed by Apple uh that were uh
+
+ align:start position:0%
+developed by Apple uh that were uh
+ 
+
+ align:start position:0%
+developed by Apple uh that were uh
+designed and developed concurrently uh
+
+ align:start position:0%
+designed and developed concurrently uh
+ 
+
+ align:start position:0%
+designed and developed concurrently uh
+with the development of this device and
+
+ align:start position:0%
+with the development of this device and
+ 
+
+ align:start position:0%
+with the development of this device and
+and actually uh uh deliver in less than
+
+ align:start position:0%
+and actually uh uh deliver in less than
+ 
+
+ align:start position:0%
+and actually uh uh deliver in less than
+two years from their acquiring the
+
+ align:start position:0%
+two years from their acquiring the
+ 
+
+ align:start position:0%
+two years from their acquiring the
+technology from questech to actually do
+
+ align:start position:0%
+technology from questech to actually do
+ 
+
+ align:start position:0%
+technology from questech to actually do
+this and that included the high strength
+
+ align:start position:0%
+this and that included the high strength
+ 
+
+ align:start position:0%
+this and that included the high strength
+anodized aluminum alloy that ultimately
+
+ align:start position:0%
+anodized aluminum alloy that ultimately
+ 
+
+ align:start position:0%
+anodized aluminum alloy that ultimately
+uh went into the 6s iPhone so uh uh it's
+
+ align:start position:0%
+uh went into the 6s iPhone so uh uh it's
+ 
+
+ align:start position:0%
+uh went into the 6s iPhone so uh uh it's
+been estimated there's now a 50% chance
+
+ align:start position:0%
+been estimated there's now a 50% chance
+ 
+
+ align:start position:0%
+been estimated there's now a 50% chance
+that you've got a computationally
+
+ align:start position:0%
+that you've got a computationally
+ 
+
+ align:start position:0%
+that you've got a computationally
+designed material in your pocket uh and
+
+ align:start position:0%
+designed material in your pocket uh and
+ 
+
+ align:start position:0%
+designed material in your pocket uh and
+it came from this calipat based
+
+ align:start position:0%
+it came from this calipat based
+ 
+
+ align:start position:0%
+it came from this calipat based
+technology uh from there uh news travels
+
+ align:start position:0%
+technology uh from there uh news travels
+ 
+
+ align:start position:0%
+technology uh from there uh news travels
+fast in the valley and it the attention
+
+ align:start position:0%
+fast in the valley and it the attention
+ 
+
+ align:start position:0%
+fast in the valley and it the attention
+of this guy uh I actually had the
+
+ align:start position:0%
+of this guy uh I actually had the
+ 
+
+ align:start position:0%
+of this guy uh I actually had the
+opportunity he invited me out to give
+
+ align:start position:0%
+opportunity he invited me out to give
+ 
+
+ align:start position:0%
+opportunity he invited me out to give
+him a half hour elevator pitch uh I
+
+ align:start position:0%
+him a half hour elevator pitch uh I
+ 
+
+ align:start position:0%
+him a half hour elevator pitch uh I
+thought I was selling him our technology
+
+ align:start position:0%
+thought I was selling him our technology
+ 
+
+ align:start position:0%
+thought I was selling him our technology
+turns out I was selling him Charlie
+
+ align:start position:0%
+turns out I was selling him Charlie
+ 
+
+ align:start position:0%
+turns out I was selling him Charlie
+cumin my uh former student who was the
+
+ align:start position:0%
+cumin my uh former student who was the
+ 
+
+ align:start position:0%
+cumin my uh former student who was the
+founding uh president of CEO uh who had
+
+ align:start position:0%
+founding uh president of CEO uh who had
+ 
+
+ align:start position:0%
+founding uh president of CEO uh who had
+gone to Apple and so after three years
+
+ align:start position:0%
+gone to Apple and so after three years
+ 
+
+ align:start position:0%
+gone to Apple and so after three years
+at Apple he he moved uh uh to be vice
+
+ align:start position:0%
+at Apple he he moved uh uh to be vice
+ 
+
+ align:start position:0%
+at Apple he he moved uh uh to be vice
+president of materials technology at
+
+ align:start position:0%
+president of materials technology at
+ 
+
+ align:start position:0%
+president of materials technology at
+both SpaceX and Tesla so this Tech
+
+ align:start position:0%
+both SpaceX and Tesla so this Tech
+ 
+
+ align:start position:0%
+both SpaceX and Tesla so this Tech
+technology has been taken uh even
+
+ align:start position:0%
+technology has been taken uh even
+ 
+
+ align:start position:0%
+technology has been taken uh even
+further in that in that environment uh
+
+ align:start position:0%
+further in that in that environment uh
+ 
+
+ align:start position:0%
+further in that in that environment uh
+and uh notably
+
+ align:start position:0%
+and uh notably
+ 
+
+ align:start position:0%
+and uh notably
+included a burn resistant nickel super
+
+ align:start position:0%
+included a burn resistant nickel super
+ 
+
+ align:start position:0%
+included a burn resistant nickel super
+alloy uh that allows the high oxygen
+
+ align:start position:0%
+alloy uh that allows the high oxygen
+ 
+
+ align:start position:0%
+alloy uh that allows the high oxygen
+pressures that uh really enables the
+
+ align:start position:0%
+pressures that uh really enables the
+ 
+
+ align:start position:0%
+pressures that uh really enables the
+Raptor engine of the Mars Starship so so
+
+ align:start position:0%
+Raptor engine of the Mars Starship so so
+ 
+
+ align:start position:0%
+Raptor engine of the Mars Starship so so
+it gives you a rare example of a
+
+ align:start position:0%
+it gives you a rare example of a
+ 
+
+ align:start position:0%
+it gives you a rare example of a
+corporate CEO bragging about his
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+metallurgist uh I think what I'll do is
+
+ align:start position:0%
+metallurgist uh I think what I'll do is
+ 
+
+ align:start position:0%
+metallurgist uh I think what I'll do is
+I just want to
+
+ align:start position:0%
+I just want to
+ 
+
+ align:start position:0%
+I just want to
+mention uh the back here on planet Earth
+
+ align:start position:0%
+mention uh the back here on planet Earth
+ 
+
+ align:start position:0%
+mention uh the back here on planet Earth
+we've got uh this Chad Center as a
+
+ align:start position:0%
+we've got uh this Chad Center as a
+ 
+
+ align:start position:0%
+we've got uh this Chad Center as a
+decadal center supporting the
+
+ align:start position:0%
+decadal center supporting the
+ 
+
+ align:start position:0%
+decadal center supporting the
+MGI uh it's in its second five years of
+
+ align:start position:0%
+MGI uh it's in its second five years of
+ 
+
+ align:start position:0%
+MGI uh it's in its second five years of
+of its 10 years it's a largely based in
+
+ align:start position:0%
+of its 10 years it's a largely based in
+ 
+
+ align:start position:0%
+of its 10 years it's a largely based in
+Chicago but MIT is a partner to it uh
+
+ align:start position:0%
+Chicago but MIT is a partner to it uh
+ 
+
+ align:start position:0%
+Chicago but MIT is a partner to it uh
+and it's looking at not only uh
+
+ align:start position:0%
+and it's looking at not only uh
+ 
+
+ align:start position:0%
+and it's looking at not only uh
+improving these methodologies but
+
+ align:start position:0%
+improving these methodologies but
+ 
+
+ align:start position:0%
+improving these methodologies but
+greatly expanding their scope notably
+
+ align:start position:0%
+greatly expanding their scope notably
+ 
+
+ align:start position:0%
+greatly expanding their scope notably
+incl including taking this to organic
+
+ align:start position:0%
+incl including taking this to organic
+ 
+
+ align:start position:0%
+incl including taking this to organic
+systems and polymers as as well and
+
+ align:start position:0%
+systems and polymers as as well and
+ 
+
+ align:start position:0%
+systems and polymers as as well and
+they're building out essentially a
+
+ align:start position:0%
+they're building out essentially a
+ 
+
+ align:start position:0%
+they're building out essentially a
+polymer calad uh to design all materials
+
+ align:start position:0%
+polymer calad uh to design all materials
+ 
+
+ align:start position:0%
+polymer calad uh to design all materials
+by the same
+
+ align:start position:0%
+by the same
+ 
+
+ align:start position:0%
+by the same
+methodology uh and I'll just mention
+
+ align:start position:0%
+methodology uh and I'll just mention
+ 
+
+ align:start position:0%
+methodology uh and I'll just mention
+that uh a lot of the current projects
+
+ align:start position:0%
+that uh a lot of the current projects
+ 
+
+ align:start position:0%
+that uh a lot of the current projects
+are looking specifically at the design
+
+ align:start position:0%
+are looking specifically at the design
+ 
+
+ align:start position:0%
+are looking specifically at the design
+of materials uh for the new technology
+
+ align:start position:0%
+of materials uh for the new technology
+ 
+
+ align:start position:0%
+of materials uh for the new technology
+of additive
+
+ align:start position:0%
+of additive
+ 
+
+ align:start position:0%
+of additive
+manufacturing uh and here's a some of
+
+ align:start position:0%
+manufacturing uh and here's a some of
+ 
+
+ align:start position:0%
+manufacturing uh and here's a some of
+the early projects at quc in that field
+
+ align:start position:0%
+the early projects at quc in that field
+ 
+
+ align:start position:0%
+the early projects at quc in that field
+and one of our more important designs
+
+ align:start position:0%
+and one of our more important designs
+ 
+
+ align:start position:0%
+and one of our more important designs
+was a high temperature aluminum that
+
+ align:start position:0%
+was a high temperature aluminum that
+ 
+
+ align:start position:0%
+was a high temperature aluminum that
+uses unique features of additive
+
+ align:start position:0%
+uses unique features of additive
+ 
+
+ align:start position:0%
+uses unique features of additive
+manufacturing that compared to this
+
+ align:start position:0%
+manufacturing that compared to this
+ 
+
+ align:start position:0%
+manufacturing that compared to this
+Scandium bearing alloy we have Scandium
+
+ align:start position:0%
+Scandium bearing alloy we have Scandium
+ 
+
+ align:start position:0%
+Scandium bearing alloy we have Scandium
+free Alloys using some Rare Earth
+
+ align:start position:0%
+free Alloys using some Rare Earth
+ 
+
+ align:start position:0%
+free Alloys using some Rare Earth
+elements uh that are able to sustain
+
+ align:start position:0%
+elements uh that are able to sustain
+ 
+
+ align:start position:0%
+elements uh that are able to sustain
+high strength in aluminum alloy out to
+
+ align:start position:0%
+high strength in aluminum alloy out to
+ 
+
+ align:start position:0%
+high strength in aluminum alloy out to
+very high temperatures very promising
+
+ align:start position:0%
+very high temperatures very promising
+ 
+
+ align:start position:0%
+very high temperatures very promising
+and it's a unique microstructure that
+
+ align:start position:0%
+and it's a unique microstructure that
+ 
+
+ align:start position:0%
+and it's a unique microstructure that
+can only be achieved by additive
+
+ align:start position:0%
+can only be achieved by additive
+ 
+
+ align:start position:0%
+can only be achieved by additive
+manufacturing um did want to mention uh
+
+ align:start position:0%
+manufacturing um did want to mention uh
+ 
+
+ align:start position:0%
+manufacturing um did want to mention uh
+electroceramic we had the opportunity
+
+ align:start position:0%
+electroceramic we had the opportunity
+ 
+
+ align:start position:0%
+electroceramic we had the opportunity
+under this DARPA Simplex program we were
+
+ align:start position:0%
+under this DARPA Simplex program we were
+ 
+
+ align:start position:0%
+under this DARPA Simplex program we were
+asked by DARPA to look at integrating
+
+ align:start position:0%
+asked by DARPA to look at integrating
+ 
+
+ align:start position:0%
+asked by DARPA to look at integrating
+new uh data mining techniques with our
+
+ align:start position:0%
+new uh data mining techniques with our
+ 
+
+ align:start position:0%
+new uh data mining techniques with our
+calad based design strategy and apply it
+
+ align:start position:0%
+calad based design strategy and apply it
+ 
+
+ align:start position:0%
+calad based design strategy and apply it
+specifically to thermoelectric systems
+
+ align:start position:0%
+specifically to thermoelectric systems
+ 
+
+ align:start position:0%
+specifically to thermoelectric systems
+uh so here uh this is the system chart
+
+ align:start position:0%
+uh so here uh this is the system chart
+ 
+
+ align:start position:0%
+uh so here uh this is the system chart
+uh for a thermoelectric material where
+
+ align:start position:0%
+uh for a thermoelectric material where
+ 
+
+ align:start position:0%
+uh for a thermoelectric material where
+the basic conflict is we want electrical
+
+ align:start position:0%
+the basic conflict is we want electrical
+ 
+
+ align:start position:0%
+the basic conflict is we want electrical
+conductivity but not thermal
+
+ align:start position:0%
+conductivity but not thermal
+ 
+
+ align:start position:0%
+conductivity but not thermal
+conductivity and the way to break that
+
+ align:start position:0%
+conductivity and the way to break that
+ 
+
+ align:start position:0%
+conductivity and the way to break that
+uh is to use micr structure for phonon
+
+ align:start position:0%
+uh is to use micr structure for phonon
+ 
+
+ align:start position:0%
+uh is to use micr structure for phonon
+scattering uh to get the
+
+ align:start position:0%
+scattering uh to get the
+ 
+
+ align:start position:0%
+scattering uh to get the
+thermoconductivity down so it was a
+
+ align:start position:0%
+thermoconductivity down so it was a
+ 
+
+ align:start position:0%
+thermoconductivity down so it was a
+chance to use the same kind of
+
+ align:start position:0%
+chance to use the same kind of
+ 
+
+ align:start position:0%
+chance to use the same kind of
+hierarchical uh micr structures that we
+
+ align:start position:0%
+hierarchical uh micr structures that we
+ 
+
+ align:start position:0%
+hierarchical uh micr structures that we
+use in structural Alloys of
+
+ align:start position:0%
+use in structural Alloys of
+ 
+
+ align:start position:0%
+use in structural Alloys of
+precipitation and grain refinement uh to
+
+ align:start position:0%
+precipitation and grain refinement uh to
+ 
+
+ align:start position:0%
+precipitation and grain refinement uh to
+manage the thermoconductivity and one
+
+ align:start position:0%
+manage the thermoconductivity and one
+ 
+
+ align:start position:0%
+manage the thermoconductivity and one
+early example of that was to build out
+
+ align:start position:0%
+early example of that was to build out
+ 
+
+ align:start position:0%
+early example of that was to build out
+the calad Thermon namics of this lead
+
+ align:start position:0%
+the calad Thermon namics of this lead
+ 
+
+ align:start position:0%
+the calad Thermon namics of this lead
+toride lead sulfide system uh taking the
+
+ align:start position:0%
+toride lead sulfide system uh taking the
+ 
+
+ align:start position:0%
+toride lead sulfide system uh taking the
+same framework uh and then actually
+
+ align:start position:0%
+same framework uh and then actually
+ 
+
+ align:start position:0%
+same framework uh and then actually
+predict from a phonon scattering model
+
+ align:start position:0%
+predict from a phonon scattering model
+ 
+
+ align:start position:0%
+predict from a phonon scattering model
+uh if we optimize the particle size
+
+ align:start position:0%
+uh if we optimize the particle size
+ 
+
+ align:start position:0%
+uh if we optimize the particle size
+uh what level of performance we could
+
+ align:start position:0%
+uh what level of performance we could
+ 
+
+ align:start position:0%
+uh what level of performance we could
+achieve as we vary the phase fraction of
+
+ align:start position:0%
+achieve as we vary the phase fraction of
+ 
+
+ align:start position:0%
+achieve as we vary the phase fraction of
+the lead sulfide particles and it showed
+
+ align:start position:0%
+the lead sulfide particles and it showed
+ 
+
+ align:start position:0%
+the lead sulfide particles and it showed
+that it agreed with the data from
+
+ align:start position:0%
+that it agreed with the data from
+ 
+
+ align:start position:0%
+that it agreed with the data from
+empirical development literature at low
+
+ align:start position:0%
+empirical development literature at low
+ 
+
+ align:start position:0%
+empirical development literature at low
+phase fractions but actually said at
+
+ align:start position:0%
+phase fractions but actually said at
+ 
+
+ align:start position:0%
+phase fractions but actually said at
+these higher phase fractions uh if we
+
+ align:start position:0%
+these higher phase fractions uh if we
+ 
+
+ align:start position:0%
+these higher phase fractions uh if we
+were to refine the particles to their
+
+ align:start position:0%
+were to refine the particles to their
+ 
+
+ align:start position:0%
+were to refine the particles to their
+Optimum size there is more performance
+
+ align:start position:0%
+Optimum size there is more performance
+ 
+
+ align:start position:0%
+Optimum size there is more performance
+that you could achieve from that system
+
+ align:start position:0%
+that you could achieve from that system
+ 
+
+ align:start position:0%
+that you could achieve from that system
+so this is a very early uh demo of
+
+ align:start position:0%
+so this is a very early uh demo of
+ 
+
+ align:start position:0%
+so this is a very early uh demo of
+applying calad to these systems as well
+
+ align:start position:0%
+applying calad to these systems as well
+ 
+
+ align:start position:0%
+applying calad to these systems as well
+uh and this is underway now uh in as
+
+ align:start position:0%
+uh and this is underway now uh in as
+ 
+
+ align:start position:0%
+uh and this is underway now uh in as
+part of the Chad Jeff Snider at
+
+ align:start position:0%
+part of the Chad Jeff Snider at
+ 
+
+ align:start position:0%
+part of the Chad Jeff Snider at
+Northwestern is actively developing uh
+
+ align:start position:0%
+Northwestern is actively developing uh
+ 
+
+ align:start position:0%
+Northwestern is actively developing uh
+the use of the calad tools uh to control
+
+ align:start position:0%
+the use of the calad tools uh to control
+ 
+
+ align:start position:0%
+the use of the calad tools uh to control
+predictively control microstructure
+
+ align:start position:0%
+predictively control microstructure
+ 
+
+ align:start position:0%
+predictively control microstructure
+optimization in these same systems but
+
+ align:start position:0%
+optimization in these same systems but
+ 
+
+ align:start position:0%
+optimization in these same systems but
+of course what you really want to know
+
+ align:start position:0%
+of course what you really want to know
+ 
+
+ align:start position:0%
+of course what you really want to know
+is what about bubble gum and so uh we
+
+ align:start position:0%
+is what about bubble gum and so uh we
+ 
+
+ align:start position:0%
+is what about bubble gum and so uh we
+did get support uh from Wrigley uh did
+
+ align:start position:0%
+did get support uh from Wrigley uh did
+ 
+
+ align:start position:0%
+did get support uh from Wrigley uh did
+have four years of support for a doctor
+
+ align:start position:0%
+have four years of support for a doctor
+ 
+
+ align:start position:0%
+have four years of support for a doctor
+of bubble gum uh and we were asked to uh
+
+ align:start position:0%
+of bubble gum uh and we were asked to uh
+ 
+
+ align:start position:0%
+of bubble gum uh and we were asked to uh
+uh make a four component uh easy to
+
+ align:start position:0%
+uh make a four component uh easy to
+ 
+
+ align:start position:0%
+uh make a four component uh easy to
+manufacture uh gum similar to uh Hubba
+
+ align:start position:0%
+manufacture uh gum similar to uh Hubba
+ 
+
+ align:start position:0%
+manufacture uh gum similar to uh Hubba
+Bubba seriously strawberry uh could we
+
+ align:start position:0%
+Bubba seriously strawberry uh could we
+ 
+
+ align:start position:0%
+Bubba seriously strawberry uh could we
+with that simple a formula get the
+
+ align:start position:0%
+with that simple a formula get the
+ 
+
+ align:start position:0%
+with that simple a formula get the
+performance level of uh Hubba Bubba Max
+
+ align:start position:0%
+performance level of uh Hubba Bubba Max
+ 
+
+ align:start position:0%
+performance level of uh Hubba Bubba Max
+which is the highest performance
+
+ align:start position:0%
+which is the highest performance
+ 
+
+ align:start position:0%
+which is the highest performance
+commercial bubble gum but very difficult
+
+ align:start position:0%
+commercial bubble gum but very difficult
+ 
+
+ align:start position:0%
+commercial bubble gum but very difficult
+to manufacture and we did succeed uh
+
+ align:start position:0%
+to manufacture and we did succeed uh
+ 
+
+ align:start position:0%
+to manufacture and we did succeed uh
+with our modeling to uh even outperform
+
+ align:start position:0%
+with our modeling to uh even outperform
+ 
+
+ align:start position:0%
+with our modeling to uh even outperform
+uh the highest performance gum out there
+
+ align:start position:0%
+uh the highest performance gum out there
+ 
+
+ align:start position:0%
+uh the highest performance gum out there
+so we had finally had produced material
+
+ align:start position:0%
+so we had finally had produced material
+ 
+
+ align:start position:0%
+so we had finally had produced material
+that Society could appreciate it was
+
+ align:start position:0%
+that Society could appreciate it was
+ 
+
+ align:start position:0%
+that Society could appreciate it was
+very rewarding and this was aided by a
+
+ align:start position:0%
+very rewarding and this was aided by a
+ 
+
+ align:start position:0%
+very rewarding and this was aided by a
+student team that actually won the ASM
+
+ align:start position:0%
+student team that actually won the ASM
+ 
+
+ align:start position:0%
+student team that actually won the ASM
+design competition back in
+
+ align:start position:0%
+design competition back in
+ 
+
+ align:start position:0%
+design competition back in
+2008 and if you'd like to learn more
+
+ align:start position:0%
+2008 and if you'd like to learn more
+ 
+
+ align:start position:0%
+2008 and if you'd like to learn more
+about that I suggest you sign up uh next
+
+ align:start position:0%
+about that I suggest you sign up uh next
+ 
+
+ align:start position:0%
+about that I suggest you sign up uh next
+year for uh 3041 and learn how to be a
+
+ align:start position:0%
+year for uh 3041 and learn how to be a
+ 
+
+ align:start position:0%
+year for uh 3041 and learn how to be a
+materials designer here's an example of
+
+ align:start position:0%
+materials designer here's an example of
+ 
+
+ align:start position:0%
+materials designer here's an example of
+the five projects currently underway uh
+
+ align:start position:0%
+the five projects currently underway uh
+ 
+
+ align:start position:0%
+the five projects currently underway uh
+all of these connect back to the chime
+
+ align:start position:0%
+all of these connect back to the chime
+ 
+
+ align:start position:0%
+all of these connect back to the chime
+ad research so uh the teams identified
+
+ align:start position:0%
+ad research so uh the teams identified
+ 
+
+ align:start position:0%
+ad research so uh the teams identified
+in R here are all being coached by uh
+
+ align:start position:0%
+in R here are all being coached by uh
+ 
+
+ align:start position:0%
+in R here are all being coached by uh
+doctoral students and postdocs uh whose
+
+ align:start position:0%
+doctoral students and postdocs uh whose
+ 
+
+ align:start position:0%
+doctoral students and postdocs uh whose
+thesis is on that particular design
+
+ align:start position:0%
+thesis is on that particular design
+ 
+
+ align:start position:0%
+thesis is on that particular design
+project to help student teams uh get to
+
+ align:start position:0%
+project to help student teams uh get to
+ 
+
+ align:start position:0%
+project to help student teams uh get to
+the high technical level it uh takes to
+
+ align:start position:0%
+the high technical level it uh takes to
+ 
+
+ align:start position:0%
+the high technical level it uh takes to
+actually do the computational design of
+
+ align:start position:0%
+actually do the computational design of
+ 
+
+ align:start position:0%
+actually do the computational design of
+a complete material with some
+
+ align:start position:0%
+a complete material with some
+ 
+
+ align:start position:0%
+a complete material with some
+challenging objectives uh notably
+
+ align:start position:0%
+challenging objectives uh notably
+ 
+
+ align:start position:0%
+challenging objectives uh notably
+including a project this year that uh
+
+ align:start position:0%
+including a project this year that uh
+ 
+
+ align:start position:0%
+including a project this year that uh
+where apple is the uh client uh and
+
+ align:start position:0%
+where apple is the uh client uh and
+ 
+
+ align:start position:0%
+where apple is the uh client uh and
+we've had a number of students uh coming
+
+ align:start position:0%
+we've had a number of students uh coming
+ 
+
+ align:start position:0%
+we've had a number of students uh coming
+out of the class who have gone to take
+
+ align:start position:0%
+out of the class who have gone to take
+ 
+
+ align:start position:0%
+out of the class who have gone to take
+internships over the summer at Apple
+
+ align:start position:0%
+internships over the summer at Apple
+ 
+
+ align:start position:0%
+internships over the summer at Apple
+they're very pleased with the
+
+ align:start position:0%
+they're very pleased with the
+ 
+
+ align:start position:0%
+they're very pleased with the
+students so I highly recommend you sign
+
+ align:start position:0%
+students so I highly recommend you sign
+ 
+
+ align:start position:0%
+students so I highly recommend you sign
+up and join us next
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+year all right well that was fantastic
+
+ align:start position:0%
+year all right well that was fantastic
+ 
+
+ align:start position:0%
+year all right well that was fantastic
+that covered a lot of ground Greg and
+
+ align:start position:0%
+that covered a lot of ground Greg and
+ 
+
+ align:start position:0%
+that covered a lot of ground Greg and
+and we're right on time so I hope it
+
+ align:start position:0%
+and we're right on time so I hope it
+ 
+
+ align:start position:0%
+and we're right on time so I hope it
+wasn't too dizzying but of course you
+
+ align:start position:0%
+wasn't too dizzying but of course you
+ 
+
+ align:start position:0%
+wasn't too dizzying but of course you
+have the opportunity to go back and play
+
+ align:start position:0%
+have the opportunity to go back and play
+ 
+
+ align:start position:0%
+have the opportunity to go back and play
+it over and slow me
+
+ align:start position:0%
+it over and slow me
+ 
+
+ align:start position:0%
+it over and slow me
+down it was dizzying but it was a really
+
+ align:start position:0%
+down it was dizzying but it was a really
+ 
+
+ align:start position:0%
+down it was dizzying but it was a really
+impressive show of impact so thank you
+
+ align:start position:0%
+impressive show of impact so thank you
+ 
+
+ align:start position:0%
+impressive show of impact so thank you
+we have um so as usual I'm going
+
+ align:start position:0%
+we have um so as usual I'm going
+ 
+
+ align:start position:0%
+we have um so as usual I'm going
+to uh stop recording in a minute but I'm
+
+ align:start position:0%
+to uh stop recording in a minute but I'm
+ 
+
+ align:start position:0%
+to uh stop recording in a minute but I'm
+very happy to take questions or I'm sure
+
+ align:start position:0%
+very happy to take questions or I'm sure
+ 
+
+ align:start position:0%
+very happy to take questions or I'm sure
+Greg is happy to take questions for a
+
+ align:start position:0%
+Greg is happy to take questions for a
+ 
+
+ align:start position:0%
+Greg is happy to take questions for a
+couple minutes indeed till the bottom of
+
+ align:start position:0%
+couple minutes indeed till the bottom of
+ 
+
+ align:start position:0%
+couple minutes indeed till the bottom of
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+hour
+
+ align:start position:0%
+hour
+ 
+
+ align:start position:0%
+hour
+um know questions about calad the
+
+ align:start position:0%
+um know questions about calad the
+ 
+
+ align:start position:0%
+um know questions about calad the
+mechanism the history the the science
+
+ align:start position:0%
+mechanism the history the the science
+ 
+
+ align:start position:0%
+mechanism the history the the science
+landing gear Elon
+
+ align:start position:0%
+landing gear Elon
+ 
+
+ align:start position:0%
+landing gear Elon
+Musk I'm
+
+ align:start position:0%
+Musk I'm
+ 
+
+ align:start position:0%
+Musk I'm
+sure did did you know how important this
+
+ align:start position:0%
+sure did did you know how important this
+ 
+
+ align:start position:0%
+sure did did you know how important this
+was did to your well to your your modern
+
+ align:start position:0%
+was did to your well to your your modern
+ 
+
+ align:start position:0%
+was did to your well to your your modern
+lives even in your
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+iPhone and it will help reduce it will
+
+ align:start position:0%
+iPhone and it will help reduce it will
+ 
+
+ align:start position:0%
+iPhone and it will help reduce it will
+help reduce the price of your Mars
+
+ align:start position:0%
+help reduce the price of your Mars
+ 
+
+ align:start position:0%
+help reduce the price of your Mars
+ticket too the efficiency of the engine
+
+ align:start position:0%
+ticket too the efficiency of the engine
+ 
+
+ align:start position:0%
+ticket too the efficiency of the engine
+yeah the models uh that worked with like
+
+ align:start position:0%
+yeah the models uh that worked with like
+ 
+
+ align:start position:0%
+yeah the models uh that worked with like
+the heat that worked with the heat
+
+ align:start position:0%
+the heat that worked with the heat
+ 
+
+ align:start position:0%
+the heat that worked with the heat
+transfer from other uh companies I think
+
+ align:start position:0%
+transfer from other uh companies I think
+ 
+
+ align:start position:0%
+transfer from other uh companies I think
+you said were working with U I just know
+
+ align:start position:0%
+you said were working with U I just know
+ 
+
+ align:start position:0%
+you said were working with U I just know
+Air Force or ster that uh you
+
+ align:start position:0%
+Air Force or ster that uh you
+ 
+
+ align:start position:0%
+Air Force or ster that uh you
+collaborated with uh other engineering
+
+ align:start position:0%
+collaborated with uh other engineering
+ 
+
+ align:start position:0%
+collaborated with uh other engineering
+yeah so companies right so the idea of
+
+ align:start position:0%
+yeah so companies right so the idea of
+ 
+
+ align:start position:0%
+yeah so companies right so the idea of
+ICM is to link the materials models to
+
+ align:start position:0%
+ICM is to link the materials models to
+ 
+
+ align:start position:0%
+ICM is to link the materials models to
+the macroscopic processing tools where
+
+ align:start position:0%
+the macroscopic processing tools where
+ 
+
+ align:start position:0%
+the macroscopic processing tools where
+very often it's all about the heat
+
+ align:start position:0%
+very often it's all about the heat
+ 
+
+ align:start position:0%
+very often it's all about the heat
+transfer so we were uh in the aim
+
+ align:start position:0%
+transfer so we were uh in the aim
+ 
+
+ align:start position:0%
+transfer so we were uh in the aim
+project we were able to then uh simulate
+
+ align:start position:0%
+project we were able to then uh simulate
+ 
+
+ align:start position:0%
+project we were able to then uh simulate
+the heat transfer the the the actual
+
+ align:start position:0%
+the heat transfer the the the actual
+ 
+
+ align:start position:0%
+the heat transfer the the the actual
+thermal processing of a turban disc uh
+
+ align:start position:0%
+thermal processing of a turban disc uh
+ 
+
+ align:start position:0%
+thermal processing of a turban disc uh
+and then take the thermal history at
+
+ align:start position:0%
+and then take the thermal history at
+ 
+
+ align:start position:0%
+and then take the thermal history at
+different nodes in that simulation uh
+
+ align:start position:0%
+different nodes in that simulation uh
+ 
+
+ align:start position:0%
+different nodes in that simulation uh
+and simulate its full evolution of its
+
+ align:start position:0%
+and simulate its full evolution of its
+ 
+
+ align:start position:0%
+and simulate its full evolution of its
+complex micr structure uh through uh
+
+ align:start position:0%
+complex micr structure uh through uh
+ 
+
+ align:start position:0%
+complex micr structure uh through uh
+that complex uh processing uh and
+
+ align:start position:0%
+that complex uh processing uh and
+ 
+
+ align:start position:0%
+that complex uh processing uh and
+actually predict the spatial variation
+
+ align:start position:0%
+actually predict the spatial variation
+ 
+
+ align:start position:0%
+actually predict the spatial variation
+in the turban dis of uh structure and
+
+ align:start position:0%
+in the turban dis of uh structure and
+ 
+
+ align:start position:0%
+in the turban dis of uh structure and
+properties uh with an accuracy within
+
+ align:start position:0%
+properties uh with an accuracy within
+ 
+
+ align:start position:0%
+properties uh with an accuracy within
+one KSI in the yield
+
+ align:start position:0%
+one KSI in the yield
+ 
+
+ align:start position:0%
+one KSI in the yield
+string what's the models employed by
+
+ align:start position:0%
+string what's the models employed by
+ 
+
+ align:start position:0%
+string what's the models employed by
+inle uh mechan like this mechanical
+
+ align:start position:0%
+inle uh mechan like this mechanical
+ 
+
+ align:start position:0%
+inle uh mechan like this mechanical
+engineering uh uh like like compatible
+
+ align:start position:0%
+engineering uh uh like like compatible
+ 
+
+ align:start position:0%
+engineering uh uh like like compatible
+with the material
+
+ align:start position:0%
+with the material
+ 
+
+ align:start position:0%
+with the material
+models in terms of like the math or
+
+ align:start position:0%
+models in terms of like the math or
+ 
+
+ align:start position:0%
+models in terms of like the math or
+continuity of that stuff yeah well
+
+ align:start position:0%
+continuity of that stuff yeah well
+ 
+
+ align:start position:0%
+continuity of that stuff yeah well
+that's the role of that eyesight uh
+
+ align:start position:0%
+that's the role of that eyesight uh
+ 
+
+ align:start position:0%
+that's the role of that eyesight uh
+process integration and design
+
+ align:start position:0%
+process integration and design
+ 
+
+ align:start position:0%
+process integration and design
+optimization software so there are
+
+ align:start position:0%
+optimization software so there are
+ 
+
+ align:start position:0%
+optimization software so there are
+integration tools like that that are
+
+ align:start position:0%
+integration tools like that that are
+ 
+
+ align:start position:0%
+integration tools like that that are
+intended to connect models from any
+
+ align:start position:0%
+intended to connect models from any
+ 
+
+ align:start position:0%
+intended to connect models from any
+software on any platform and be able to
+
+ align:start position:0%
+software on any platform and be able to
+ 
+
+ align:start position:0%
+software on any platform and be able to
+transfer the output of one as the input
+
+ align:start position:0%
+transfer the output of one as the input
+ 
+
+ align:start position:0%
+transfer the output of one as the input
+to
+
+ align:start position:0%
+to
+ 
+
+ align:start position:0%
+to
+another and I'll say this is um this
+
+ align:start position:0%
+another and I'll say this is um this
+ 
+
+ align:start position:0%
+another and I'll say this is um this
+sort of integration is
+
+ align:start position:0%
+sort of integration is
+ 
+
+ align:start position:0%
+sort of integration is
+um it's part of what you're doing on
+
+ align:start position:0%
+um it's part of what you're doing on
+ 
+
+ align:start position:0%
+um it's part of what you're doing on
+this on not not P at um seven but um P
+
+ align:start position:0%
+this on not not P at um seven but um P
+ 
+
+ align:start position:0%
+this on not not P at um seven but um P
+at 8 which is you know you have software
+
+ align:start position:0%
+at 8 which is you know you have software
+ 
+
+ align:start position:0%
+at 8 which is you know you have software
+and it has data and it outputs some form
+
+ align:start position:0%
+and it has data and it outputs some form
+ 
+
+ align:start position:0%
+and it has data and it outputs some form
+of data and you want to model that so
+
+ align:start position:0%
+of data and you want to model that so
+ 
+
+ align:start position:0%
+of data and you want to model that so
+that you could perhaps use it in a
+
+ align:start position:0%
+that you could perhaps use it in a
+ 
+
+ align:start position:0%
+that you could perhaps use it in a
+different piece of software you know and
+
+ align:start position:0%
+different piece of software you know and
+ 
+
+ align:start position:0%
+different piece of software you know and
+um you know you're doing this uh today
+
+ align:start position:0%
+um you know you're doing this uh today
+ 
+
+ align:start position:0%
+um you know you're doing this uh today
+you know you you're doing this I would
+
+ align:start position:0%
+you know you you're doing this I would
+ 
+
+ align:start position:0%
+you know you you're doing this I would
+in a sense a very low level down in the
+
+ align:start position:0%
+in a sense a very low level down in the
+ 
+
+ align:start position:0%
+in a sense a very low level down in the
+weeds looking at you know a couple
+
+ align:start position:0%
+weeds looking at you know a couple
+ 
+
+ align:start position:0%
+weeds looking at you know a couple
+traces of data but you know once you
+
+ align:start position:0%
+traces of data but you know once you
+ 
+
+ align:start position:0%
+traces of data but you know once you
+understand the sort of things that
+
+ align:start position:0%
+understand the sort of things that
+ 
+
+ align:start position:0%
+understand the sort of things that
+happened down in the weeds you can start
+
+ align:start position:0%
+happened down in the weeds you can start
+ 
+
+ align:start position:0%
+happened down in the weeds you can start
+to step back and look at a bigger
+
+ align:start position:0%
+to step back and look at a bigger
+ 
+
+ align:start position:0%
+to step back and look at a bigger
+picture and imagine more sophisticated
+
+ align:start position:0%
+picture and imagine more sophisticated
+ 
+
+ align:start position:0%
+picture and imagine more sophisticated
+integration so it's it's it's great that
+
+ align:start position:0%
+integration so it's it's it's great that
+ 
+
+ align:start position:0%
+integration so it's it's it's great that
+you brought that
+
+ align:start position:0%
+you brought that
+ 
+
+ align:start position:0%
+you brought that
+up yeah and of course that that is all a
+
+ align:start position:0%
+up yeah and of course that that is all a
+ 
+
+ align:start position:0%
+up yeah and of course that that is all a
+very important part of this concurrent
+
+ align:start position:0%
+very important part of this concurrent
+ 
+
+ align:start position:0%
+very important part of this concurrent
+engineering approach that we can
+
+ align:start position:0%
+engineering approach that we can
+ 
+
+ align:start position:0%
+engineering approach that we can
+actually link the computational tools
+
+ align:start position:0%
+actually link the computational tools
+ 
+
+ align:start position:0%
+actually link the computational tools
+across disciplines and uh simulate the
+
+ align:start position:0%
+across disciplines and uh simulate the
+ 
+
+ align:start position:0%
+across disciplines and uh simulate the
+system level so I guess going going off
+
+ align:start position:0%
+system level so I guess going going off
+ 
+
+ align:start position:0%
+system level so I guess going going off
+of that you mentioned a few times how
+
+ align:start position:0%
+of that you mentioned a few times how
+ 
+
+ align:start position:0%
+of that you mentioned a few times how
+now with all the new technologies and
+
+ align:start position:0%
+now with all the new technologies and
+ 
+
+ align:start position:0%
+now with all the new technologies and
+methods of sort of understanding
+
+ align:start position:0%
+methods of sort of understanding
+ 
+
+ align:start position:0%
+methods of sort of understanding
+materials work how now there's a lot
+
+ align:start position:0%
+materials work how now there's a lot
+ 
+
+ align:start position:0%
+materials work how now there's a lot
+more concurrent engineering taking place
+
+ align:start position:0%
+more concurrent engineering taking place
+ 
+
+ align:start position:0%
+more concurrent engineering taking place
+sort of how the materials are being
+
+ align:start position:0%
+sort of how the materials are being
+ 
+
+ align:start position:0%
+sort of how the materials are being
+developed alongside the the products
+
+ align:start position:0%
+developed alongside the the products
+ 
+
+ align:start position:0%
+developed alongside the the products
+that are going out to Market or for
+
+ align:start position:0%
+that are going out to Market or for
+ 
+
+ align:start position:0%
+that are going out to Market or for
+consumers to use and I was wondering how
+
+ align:start position:0%
+consumers to use and I was wondering how
+ 
+
+ align:start position:0%
+consumers to use and I was wondering how
+tied those two things are like if if you
+
+ align:start position:0%
+tied those two things are like if if you
+ 
+
+ align:start position:0%
+tied those two things are like if if you
+know if there are like different teams
+
+ align:start position:0%
+know if there are like different teams
+ 
+
+ align:start position:0%
+know if there are like different teams
+working on different aspects of it or if
+
+ align:start position:0%
+working on different aspects of it or if
+ 
+
+ align:start position:0%
+working on different aspects of it or if
+it's really becoming more and more
+
+ align:start position:0%
+it's really becoming more and more
+ 
+
+ align:start position:0%
+it's really becoming more and more
+integrated in terms of like the
+
+ align:start position:0%
+integrated in terms of like the
+ 
+
+ align:start position:0%
+integrated in terms of like the
+production
+
+ align:start position:0%
+production
+ 
+
+ align:start position:0%
+production
+teams yeah uh I I would say there there
+
+ align:start position:0%
+teams yeah uh I I would say there there
+ 
+
+ align:start position:0%
+teams yeah uh I I would say there there
+is ever increasing integration
+
+ align:start position:0%
+is ever increasing integration
+ 
+
+ align:start position:0%
+is ever increasing integration
+uh and of course in the case of Apple
+
+ align:start position:0%
+uh and of course in the case of Apple
+ 
+
+ align:start position:0%
+uh and of course in the case of Apple
+these really are consumer products that
+
+ align:start position:0%
+these really are consumer products that
+ 
+
+ align:start position:0%
+these really are consumer products that
+they're uh and very novel products that
+
+ align:start position:0%
+they're uh and very novel products that
+ 
+
+ align:start position:0%
+they're uh and very novel products that
+they are developing on a very
+
+ align:start position:0%
+they are developing on a very
+ 
+
+ align:start position:0%
+they are developing on a very
+accelerated schedule but uh what they're
+
+ align:start position:0%
+accelerated schedule but uh what they're
+ 
+
+ align:start position:0%
+accelerated schedule but uh what they're
+very good at is the manufacturing
+
+ align:start position:0%
+very good at is the manufacturing
+ 
+
+ align:start position:0%
+very good at is the manufacturing
+engineer because they make stuff on such
+
+ align:start position:0%
+engineer because they make stuff on such
+ 
+
+ align:start position:0%
+engineer because they make stuff on such
+a huge scale uh so they're very good at
+
+ align:start position:0%
+a huge scale uh so they're very good at
+ 
+
+ align:start position:0%
+a huge scale uh so they're very good at
+that I think at SpaceX you're seeing uh
+
+ align:start position:0%
+that I think at SpaceX you're seeing uh
+ 
+
+ align:start position:0%
+that I think at SpaceX you're seeing uh
+very Innovative technology uh so the
+
+ align:start position:0%
+very Innovative technology uh so the
+ 
+
+ align:start position:0%
+very Innovative technology uh so the
+early ideation of taking extremely
+
+ align:start position:0%
+early ideation of taking extremely
+ 
+
+ align:start position:0%
+early ideation of taking extremely
+challenging problems like how we get
+
+ align:start position:0%
+challenging problems like how we get
+ 
+
+ align:start position:0%
+challenging problems like how we get
+humans to Mars efficiently
+
+ align:start position:0%
+humans to Mars efficiently
+ 
+
+ align:start position:0%
+humans to Mars efficiently
+uh is making maximum use of this and and
+
+ align:start position:0%
+uh is making maximum use of this and and
+ 
+
+ align:start position:0%
+uh is making maximum use of this and and
+uh there it's it's a very thorough
+
+ align:start position:0%
+uh there it's it's a very thorough
+ 
+
+ align:start position:0%
+uh there it's it's a very thorough
+integration at all levels uh so they use
+
+ align:start position:0%
+integration at all levels uh so they use
+ 
+
+ align:start position:0%
+integration at all levels uh so they use
+this the so-called 80% solution that uh
+
+ align:start position:0%
+this the so-called 80% solution that uh
+ 
+
+ align:start position:0%
+this the so-called 80% solution that uh
+uh it's often said that uh with h with
+
+ align:start position:0%
+uh it's often said that uh with h with
+ 
+
+ align:start position:0%
+uh it's often said that uh with h with
+20 in computation with 20% of the
+
+ align:start position:0%
+20 in computation with 20% of the
+ 
+
+ align:start position:0%
+20 in computation with 20% of the
+resources you can get 80% of the way
+
+ align:start position:0%
+resources you can get 80% of the way
+ 
+
+ align:start position:0%
+resources you can get 80% of the way
+where you're trying to go and then the
+
+ align:start position:0%
+where you're trying to go and then the
+ 
+
+ align:start position:0%
+where you're trying to go and then the
+question is do you really want to spend
+
+ align:start position:0%
+question is do you really want to spend
+ 
+
+ align:start position:0%
+question is do you really want to spend
+the next 80% to only get another 20% uh
+
+ align:start position:0%
+the next 80% to only get another 20% uh
+ 
+
+ align:start position:0%
+the next 80% to only get another 20% uh
+so pretty much at all levels of
+
+ align:start position:0%
+so pretty much at all levels of
+ 
+
+ align:start position:0%
+so pretty much at all levels of
+structure they'll take the computation
+
+ align:start position:0%
+structure they'll take the computation
+ 
+
+ align:start position:0%
+structure they'll take the computation
+to 80% for everything including
+
+ align:start position:0%
+to 80% for everything including
+ 
+
+ align:start position:0%
+to 80% for everything including
+materials now uh and then of course they
+
+ align:start position:0%
+materials now uh and then of course they
+ 
+
+ align:start position:0%
+materials now uh and then of course they
+blow up rockets at SpaceX and those are
+
+ align:start position:0%
+blow up rockets at SpaceX and those are
+ 
+
+ align:start position:0%
+blow up rockets at SpaceX and those are
+highly instrumented blowing up rockets
+
+ align:start position:0%
+highly instrumented blowing up rockets
+ 
+
+ align:start position:0%
+highly instrumented blowing up rockets
+and that the idea is to test it the full
+
+ align:start position:0%
+and that the idea is to test it the full
+ 
+
+ align:start position:0%
+and that the idea is to test it the full
+system level and approach full system
+
+ align:start position:0%
+system level and approach full system
+ 
+
+ align:start position:0%
+system level and approach full system
+level
+
+ align:start position:0%
+level
+ 
+
+ align:start position:0%
+level
+optimization uh taking everything to its
+
+ align:start position:0%
+optimization uh taking everything to its
+ 
+
+ align:start position:0%
+optimization uh taking everything to its
+limits instrumented so they can dial it
+
+ align:start position:0%
+limits instrumented so they can dial it
+ 
+
+ align:start position:0%
+limits instrumented so they can dial it
+back on on the next one uh but the pace
+
+ align:start position:0%
+back on on the next one uh but the pace
+ 
+
+ align:start position:0%
+back on on the next one uh but the pace
+at which they're able to do this is
+
+ align:start position:0%
+at which they're able to do this is
+ 
+
+ align:start position:0%
+at which they're able to do this is
+really incredible by integrating across
+
+ align:start position:0%
+really incredible by integrating across
+ 
+
+ align:start position:0%
+really incredible by integrating across
+all those disciplines
\ No newline at end of file
diff --git a/APv1uyLL6ok.txt b/APv1uyLL6ok.txt
new file mode 100644
index 0000000000000000000000000000000000000000..2e7c667615b86ccdef91a1a19a7a26c61d68953f
--- /dev/null
+++ b/APv1uyLL6ok.txt
@@ -0,0 +1,2492 @@
+PROFESSOR: All right, my trusty
+$5 Timex watch says
+
+it's five after the hour.
+
+So I guess we might
+as well begin.
+
+I have corrected all the
+problems that were turned in--
+
+the puzzles, not problems,
+puzzles.
+
+And I just yesterday
+got hold of the
+
+photographs of you few people.
+
+And I'd like to hand out the
+papers individually so I can
+
+start to put names together
+with faces.
+
+So I'll turn them back
+individually next time.
+
+I have one additional problem
+set that for you.
+
+And again, this is in the
+form of a puzzle.
+
+Be assured that this is the last
+entertaining problem set.
+
+From here on, we move
+into drudgery--
+
+tedious, drawn out things
+that hopefully
+
+will teach you something.
+
+But this is the last one that's
+done with a little bit
+
+of tongue in cheek humor.
+
+This one is a little more subtle
+than the other two.
+
+And for this one, I will hand
+out a solution because I would
+
+like to use these problems to
+make a couple of basic points
+
+about the nature of symmetry
+theory in crystals.
+
+So see how you do on this one.
+
+OK, also before we begin, he
+gets a little bit uneasy
+
+before a crowd.
+
+But I brought a little friend
+in with me today.
+
+And could someone hold
+the box, please, so I
+
+could take him out?
+
+Sorry.
+
+He gets a little bit nervous
+before a crowd.
+
+Come on, take it easy.
+
+Take it easy.
+
+This is Rodney.
+
+He's an old friend of mine.
+
+Rodney is a crystallographic
+abomination.
+
+Rodney has five-fold
+symmetry--
+
+impossible in crystallography,
+an abomination.
+
+Why did Rodney decide
+to do this?
+
+Anybody have any idea?
+
+Why not six fold symmetry?
+
+He's got five-fold symmetry.
+
+Yuck!
+
+But why?
+
+There's always a reason for
+things if you look carefully
+
+enough and know what
+questions to ask.
+
+Yeah?
+
+AUDIENCE: He had narrow
+symmetry.
+
+PROFESSOR: Yeah, he had
+narrow symmetry.
+
+But he could do that-- what
+if you were square?
+
+Why not a square starfish?
+
+Why five?
+
+He did this for a reason.
+
+He's been doing this for
+probably a couple of million
+
+years, he and his ancestors.
+
+There has to be a reason.
+
+OK, let me turn him over.
+
+And maybe that will
+give you a clue.
+
+The backside is not nearly as
+nice as the front side.
+
+And in fact, if you look at
+Rodney carefully, Rodney has
+
+sutures between these
+five arms.
+
+OK, this is what he looks
+like from the top.
+
+But if you look at him from the
+bottom, there are sutures
+
+between these arms
+that do this.
+
+And these sutures are weak
+points in his structure.
+
+And by having five-fold
+symmetry, he puts the suture
+
+between this pair of arms
+opposite the midpoint of the
+
+opposite rib.
+
+And that gives him a great deal
+
+more structural integrity.
+
+So when a large fish comes along
+and gloms onto one of
+
+his arms and shakes, he doesn't
+split in half and end
+
+his career prematurely.
+
+What happens instead, at very
+worst, the tip of the arm
+
+breaks off.
+
+And then, Rodney gets to scamper
+away and make more
+
+starfish or do whatever his
+purpose in our environment is.
+
+If he had an even-fold
+symmetry,
+
+that wouldn't happen.
+
+He would really be
+done in by a fish
+
+grabbing hold and shaking.
+
+AUDIENCE: What if [INAUDIBLE]?
+
+PROFESSOR: That's a very
+good question.
+
+If he had only three arms and
+a fish glomed on and one arm
+
+broke off, his mobility would
+be greatly impaired.
+
+In a way, he would go
+hip, hop, flop.
+
+Hip, hip, flop.
+
+Hip, hip, flop.
+
+Hip, hip, flop.
+
+It'd be a pathetic thing.
+
+So five is much more
+advantageous than three.
+
+AUDIENCE: Why not seven?
+
+PROFESSOR: Why not seven?
+
+That's a good question, too.
+
+Would you believe that on the
+Australian Barrier Reef, there
+
+are starfish with nine-fold
+symmetry?
+
+Quite odd.
+
+That's really a creepy
+thing with all those
+
+arms flopping around.
+
+But as many things in our
+environment in our natural
+
+world, there's a reason for
+things if you can only think
+
+what it might be.
+
+So we gave you another example
+of a non-crystallographic
+
+symmetry, the large cacti of the
+Southwest, the saguaros.
+
+And there are lots of
+other ribbed casts.
+
+They have symmetries that range
+between 19 and 23 fold.
+
+Why do you think they have
+this rib structure?
+
+Why can't they have a
+nice, smooth trunk
+
+like a birch tree?
+
+Any idea there?
+
+I'll give you a hint.
+
+They live out in the desert.
+
+There's not much water.
+
+AUDIENCE: [INAUDIBLE].
+
+PROFESSOR: Hm?
+
+AUDIENCE: More surface area
+for the [INAUDIBLE].
+
+PROFESSOR: Yeah,
+but that's bad.
+
+That means they would
+lose their water.
+
+So things that don't
+want to lose water
+
+through their surface--
+
+you're right-- try to minimize
+their surface.
+
+But you're onto something.
+
+And it is exactly the
+reverse of that.
+
+Water is scarce.
+
+So when it rains, this cactus
+wants to soak up the moisture
+
+and store it.
+
+If he has this pleated
+structure,
+
+he's able to expand.
+
+If he had a smooth surface
+with minimal area,
+
+he would just pop.
+
+And that would be the end of
+him or her, as the case may
+
+be. "It" is probably the
+appropriate term.
+
+But anyway, there's the reason
+for these many, many ribs.
+
+It gives them the ability to
+expand, store water, and then
+
+contract when the water
+evaporates.
+
+So again, it's always
+interesting to look at the
+
+world around us and see examples
+of things that are
+
+strange because it's the strange
+things that very often
+
+can lead to penetrating
+conclusions.
+
+All right, last time we had
+talked about chirality in
+
+finite atomic structures,
+molecules.
+
+And I had pointed out-- but
+did not make the obvious
+
+observation--
+
+I cannot think of a more
+dramatic connection between
+
+structure and properties, which
+is what material science
+
+is all about, than the very,
+very different properties of
+
+molecules that are of
+opposite handedness.
+
+We pointed out, for example,
+that many pharmaceuticals are
+
+of chiral molecules that exist
+in right handed and left
+
+handed forms.
+
+And very often, one form of
+one handedness has a very
+
+different set of properties,
+and in particular
+
+pharmacological action, then
+it it's enan enantiomorph.
+
+So in the case of thalidomide,
+one handedness of the molecule
+
+acts as a tranquilizer.
+
+The other handedness acts as
+a source of birth defects.
+
+One of the other ones less
+familiar to me, but this is
+
+[? ethambutol. ?]
+
+It's used as a drug to
+treat tuberculosis.
+
+The molecule of opposite
+handedness creates blindness.
+
+The drug Ritalin that is used
+to treat hyperactivity, one
+
+handedness of the molecule
+is absolutely useless.
+
+So you only use half of
+what you pay for.
+
+So it's of great interest to
+pharmaceutical companies to be
+
+able to synthesize a molecule
+of one particular handedness
+
+with little if none
+of the other one.
+
+And I looked up a number
+since we met last time.
+
+It turns out that in 1997,
+enantiomorph pure drugs were a
+
+$400 billion dollar industry.
+
+So again, this is structure
+property relations in action.
+
+So let me ask you another
+question.
+
+It turns out that products that
+are derived from nature--
+
+a good example being sugar,
+which is produced by sugar
+
+beets or sugar cane--
+
+produces a molecule only
+of one handedness.
+
+They are [? enantiomer ?]
+
+pure.
+
+But every synthetic compound
+that can exist in right handed
+
+and left handed forms occurs
+with equal probability.
+
+So how do you make a
+pharmaceutical of one
+
+particular handedness?
+
+And this is an interesting
+question because I think it
+
+was two years ago the Nobel
+Prize in chemistry was given
+
+to three people for their work
+in being able to synthesize
+
+molecules of a given
+handedness.
+
+Anybody an idea how you do it?
+
+AUDIENCE: I don't have an idea
+how you do it, but what do you
+
+mean by one handedness
+versus--?
+
+PROFESSOR: OK, left handed
+or right handed.
+
+So my left hand is exactly the
+same as my right hand, but I
+
+cannot match them into
+congruence with one another.
+
+And we don't know how to
+describe this other than we
+
+used the term derived
+from our physiology.
+
+We say left handed
+and right handed.
+
+So when I was referring to a
+molecule of one handedness--
+
+and I'll bring in a Xerox copy
+of a couple of examples.
+
+There are many examples of
+fairly common molecules which
+
+can exist in one form in which
+the hydroxyl group points out
+
+this way, then another form
+where the hydroxyl groups
+
+points out this way.
+
+Sorry, you should have
+asked that earlier.
+
+AUDIENCE: So if it's not the
+same molecule, it would be
+
+that molecule but--?
+
+PROFESSOR: Chemically, it is
+exactly the same concept.
+
+But the way in which those
+component models are
+
+configured has the same number
+of side groups, the same
+
+number of appendages.
+
+But they, don't have
+a better word.
+
+One is left handed.
+
+One is right handed.
+
+I'll give you some examples
+next time.
+
+Somebody else, you
+had a question?
+
+AUDIENCE: I was just going to
+see if I could venture a guess
+
+how they do it.
+
+I was going to guess they use an
+electric field that has its
+
+bearings to set the right handed
+course [INAUDIBLE] that
+
+would make [? enantiomorphs ?]
+
+or more advantageous
+than [INAUDIBLE].
+
+PROFESSOR: That's
+not a bad idea.
+
+Anything that could bias the
+energy of one configuration
+
+over the other would do it.
+
+But actually, no reason why you
+should know how to do it.
+
+If you knew how to do it, maybe
+you could have gotten
+
+the Nobel Prize instead
+of these other guys.
+
+But actually, you do it
+through catalysis.
+
+And you use a catalyst which
+itself has chirality.
+
+And that chirality favors the
+formation of one molecule over
+
+the other almost exclusively.
+
+And that's why living
+plants make--
+
+or animals-- make chiral
+molecules in just one
+
+handedness as well.
+
+So it's using a catalyst that
+also has some chirality.
+
+AUDIENCE: How do you get the
+one hundred catalysts
+
+[INAUDIBLE]?
+
+PROFESSOR: How do
+you have it--?
+
+OK, there are lots
+of materials.
+
+Any crystalline material that
+does not have a mirror plane
+
+in it can exist in
+chiral forms.
+
+And one of the classic examples
+of this is quartz.
+
+Quartz is SiO2.
+
+And quartz has actually only
+a threefold symmetry.
+
+But it forms crystals that look
+prismatic, as though they
+
+were hexagonal prisms.
+
+And if I draw two of these
+prisms side by side, you could
+
+not tell which prism
+was left handed and
+
+which was right handed.
+
+But quartz ends up growing with
+a couple of little facets
+
+on it that look like this.
+
+They spiral up this way in a
+crystal of one handedness and
+
+they spiral up in the opposite
+direction for a crystal of
+
+opposite handedness.
+
+So the external faces on the
+crystal show you that this
+
+crystal shape cannot be mapped
+one into another.
+
+They are of opposite
+handedness.
+
+And they have very different
+properties.
+
+And so here's an example.
+
+I'm not answer your question.
+
+I'm talking around it very
+adroitly in the hope that if I
+
+talk enough you will forget
+what you asked.
+
+But how do you make
+a chiral catalyst?
+
+Well, there are some materials
+if you prepare them in a
+
+single crystal form, once you
+nucleate one enantiomorph,
+
+that will continue to grow.
+
+So I would presume one
+could do exactly
+
+the same with a catalyst.
+
+Actually, the properties of
+quartz are strikingly
+
+different for these two
+different forms.
+
+If you would subject the crystal
+to compression, this
+
+crystal would develop
+a positive
+
+charge on the surface.
+
+This crystal would develop
+a negative
+
+charge on the surface.
+
+That's a property that we'll
+discuss in detail later on.
+
+That's something called
+piezoelectricity, literally
+
+pressure electricity.
+
+So the nature of the charge
+induced on the crystal is
+
+different for the crystals
+of the two chiralities.
+
+OK, any other comment
+or question?
+
+OK, last time we had taken the
+first small steps in what will
+
+turn out to be a long and
+
+protracted process of synthesis.
+
+We've covered by now some of
+the general notions of
+
+operations that can exist in
+a pattern, two dimensional
+
+pattern of wallpaper or fabric
+or a three dimensional pattern
+
+that constitutes a crystal.
+
+And we said that in three
+dimensions, there are four
+
+basic different operations that
+can exist that tell you
+
+how one part of the system
+is related to another.
+
+There is an operation
+of translation.
+
+And this has all the
+characteristics of a vector,
+
+magnitude and direction.
+
+We summarize that translational
+periodicity by a
+
+set of fiducial markers that
+are called lattice points.
+
+And analytically, the
+transformation takes the
+
+coordinate x, y, z.
+
+And if you do the operation
+once, maps this to x plus a, y
+
+plus b, z plus c where the
+translation has components a,
+
+b, and c in x, y, and
+z directions.
+
+Another operation is the
+operation of reflection.
+
+And what this operation does is
+to take the coordinates of
+
+an initial part of the space
+atom or location and maps it
+
+into some location where one
+direction is reversed in sign.
+
+Which direction that is or
+whether it's a pair of
+
+directions will depend on how
+the reflection locus is
+
+located relative to the
+coordinate system.
+
+Next, there was an operation
+of rotation.
+
+And this involves repeating
+things at angular intervals.
+
+Take the space or the location
+of the atom and rotate it
+
+through some angle, alpha,
+about some rotation, a.
+
+And in a sense, this is
+a periodicity which is
+
+reminiscent of translation
+except translation strings
+
+things out in a line.
+
+Rotation wraps up the
+directions about
+
+some central axis.
+
+But it's also periodic.
+
+Then finally, in three
+dimensions, there is another
+
+operation called inversion.
+
+And what this does is--
+
+to could describe it as such
+in literal terms--
+
+take something and turns it
+inside out to a point.
+
+So if the inversion point were
+at the origin, it would take
+
+x, y, z, and map it into minus
+x, minus y, minus z.
+
+And then, we concluded last time
+with a definition of a
+
+vocabulary for indicating
+analytically a single
+
+operation, the set of operations
+that constitutes
+
+the symmetry element, and then
+a geometric symbol for the
+
+locus of that operation.
+
+And for translation, we could
+represent a single
+
+operation by t.
+
+The set of operations
+could be--
+
+and I'll use this customary
+set of braces to
+
+indicate the set--
+
+this would be a one dimensional
+lattice, a set of
+
+operations, p, where p is
+an integer times t.
+
+The geometric symbol, it's
+convenient to use an arrow
+
+extending from one lattice
+point to another.
+
+But I emphasize that there's
+no unique origin to the
+
+translation.
+
+We cannot be entitled to say
+it sits here as opposed to
+
+down here or down here.
+
+There are an infinite number
+of parallel directions that
+
+could specify a given interval
+between lattice points.
+
+For rotation operations, the
+notation for a single
+
+operation in as much as we must
+specify two things, the
+
+point about which we rotate and
+then the angular interval
+
+about which we perform
+the rotation.
+
+And so we need to specify two
+things, the location of the
+
+axis, a point a, and
+the angle, alpha,
+
+through which we rotate.
+
+The set of operations, the
+rotation axis, is indicated by
+
+an integer, n, where the
+rotation part of the operation
+
+is 2 pi divided by
+the integer, n.
+
+So we would use, for example, 2
+to represent a rotation axis
+
+where things were moved through
+180 degrees, 3 for a
+
+symmetry where things were
+mapped through intervals of
+
+120 degrees, and 22 for my
+good friend, the Saguaro
+
+cactus, which is left invariant
+perhaps by a
+
+rotation through 1/22 of 2 pi.
+
+For the geometric symbol for a
+rotation axis, we will use a
+
+little polyhedron.
+
+Triangle for a threefold axis.
+
+Square for a fourfold axis.
+
+For a twofold axis, the
+polyhedron that had that
+
+symmetry would be
+a line segment.
+
+So we'll take a little artistic
+license and let the
+
+middle of the line segment
+bulge out a little bit.
+
+Finally for inversion, for
+reasons that will not become
+
+clear for another meeting or
+two, the single operation is
+
+denoted one bar.
+
+The set of operations of which
+there are only two, inverting
+
+and coming back again,
+also indicated by
+
+the symbol one bar.
+
+And the geometric symbol for
+the locus is a little, tiny
+
+circle that's open large enough
+to be noticed, but not
+
+so large that it looks like an
+atom in an atomic arrangement.
+
+So there's our basic
+bag of tricks.
+
+And last time, we had already
+used some simple geometry to
+
+come to a rather astonishing
+conclusion.
+
+Yes, sir?
+
+AUDIENCE: Reflection?
+
+PROFESSOR: Reflection, that's
+this middle one.
+
+Whoops, not going to help.
+
+Thank you very much.
+
+I get excited and
+carried away.
+
+OK, reflection, the
+second operation.
+
+Single operation, although
+crystallographers don't often
+
+use it in condensed matter
+physics, a single operation is
+
+represented by the
+symbol sigma.
+
+Symbol for a mirror plane is
+m, easily appreciated.
+
+And the geometric locus across
+which things are reflected
+
+left to right and vice versa
+is done with a bold, solid
+
+line when you're looking down
+parallel to the surface of the
+
+reflection locus.
+
+Then, I will now be caught up.
+
+And I can set off on
+something new.
+
+We had said that in a pattern,
+very often more than one of
+
+these operations are combined
+in a single space.
+
+And one of the things that
+must be present--
+
+if the symmetry of
+the entity we are
+
+discussing is a crystal--
+
+one of the things that must be
+present is a translation.
+
+And so I asked last time the
+question, what if we want to
+
+say that our space has a
+translational periodicity
+
+described by t.
+
+And then, I add to one lattice
+point a rotation operation, A
+
+alpha, that has to get
+translated to another location
+
+where that operation,
+A alpha, exists.
+
+And if A alpha exists and I
+repeat that translation by a
+
+rotation alpha, I'm going to
+have a sheath of translations
+
+all separated by a
+distance alpha.
+
+If I single out the one that is
+removed from the first by
+
+an operation of rotation A alpha
+in a counterclockwise
+
+direction and single out from
+that sheath another one that
+
+is alpha away in the clockwise
+direction.
+
+Then, I have lattice points
+at the end of all of these
+
+translations.
+
+But these two guys up here
+are also lattice points.
+
+And therefore, I have mucked up
+to the entire construction
+
+unless I can claim that this
+distance between these two
+
+lattice points is either T or
+some multiple P times T, where
+
+P is an integer.
+
+And then lickety split, before
+you could catch your breath in
+
+wonder, I dropped a
+perpendicular down to the
+
+original translation.
+
+This distance in here was PT.
+
+This distance on either
+side was T times
+
+the cosine of alpha.
+
+And that led me to a constraint
+that alpha, that
+
+rotation operation A alpha, if
+it were to be combined with
+
+translation, would be restricted
+to values such that
+
+the cosine of alpha was equal
+to 1 minus an integer P
+
+divided by 2.
+
+Wow, simple, but so incredibly
+profound.
+
+What came out of this
+was that alpha could
+
+either be 0 or 360 degrees.
+
+That was a one-fold axis.
+
+Alpha could be 180 degrees.
+
+That was a two-fold axis.
+
+120, which would be the
+angular rotation of a
+
+three-fold axis.
+
+90, that would be the operation
+of a four-fold axis.
+
+Or 60, that would be the
+operation of a six-fold axis.
+
+It's incredible.
+
+Anything, any pattern, any
+crystal that is based on a
+
+lattice can contain only these
+five rotational symmetries
+
+including no symmetry at all.
+
+So this says a lot about what
+the morphology of crystalline
+
+materials are permitted to be.
+
+Then, we looked at the nature
+of the lattices that were
+
+described by these angular
+rotations.
+
+And we found that there were
+only three types of lattices
+
+that were required
+by rotation.
+
+These were two dimensional
+lattice nets.
+
+One was a general oblique net
+which had two different
+
+translations, some arbitrary
+angle between them, two
+
+translations, T1 and T2, which
+were not equal to one another.
+
+We would call this
+the oblique net.
+
+Then, there was another net that
+was square in the sense
+
+that two translations,
+T1 and T2, were
+
+identical to one another--
+
+not close, but identical.
+
+And the angle between them was
+identically 90 degrees.
+
+This oblique net could accept
+either a one-fold axis or a
+
+two-fold axis.
+
+This was the specialized shape
+that was required by a
+
+four-fold axis.
+
+And then finally, there was
+another net that looked
+
+oblique except it was a
+specialized oblique net.
+
+It had two translations, T1 and
+T2, which were identical
+
+just as in the square net and
+an angle between them, which
+
+was exactly 120 degrees.
+
+And this same sort of net
+could be compatible with
+
+either a three-fold axis
+or a six-fold axis.
+
+Then, we took the only other
+operation that could be
+
+present in a two dimensional
+pattern, and this was the
+
+operation of reflection,
+a mirror point, m.
+
+And we saw that this by itself
+could require two different
+
+sorts of specializations in a
+lattice, a lattice in which
+
+two directions were exactly
+orthogonal but the lengths of
+
+the translations were unequal.
+
+And then, a diamond
+shaped net--
+
+and this was a new wrinkle.
+
+This was a net that had two
+translations that were
+
+Identical in length and an
+arbitrary angle between them.
+
+Or alternatively, if we chose
+to pick a redundant lattice,
+
+one that had two translations,
+T1 and T2 prime which were
+
+different but an angle between
+them that was exactly 90
+
+degrees, so this one we would
+refer to as a rectangular
+
+lattice, a rectangular net,
+and this one as a centered
+
+rectangular net--
+
+same shape, but an extra lattice
+point in the middle.
+
+Why pick a double cell, which
+is redundant, takes up more,
+
+and doesn't convey any
+more information?
+
+And the advantage comes when
+you want to analytically
+
+describe the relation between
+different directions or the
+
+positions of atoms
+within the cell.
+
+In that case, an orthogonal
+coordinate system, even if
+
+it's not Cartesian, is of
+immense advantage as opposed
+
+to an oblique system.
+
+OK, slightly out of breath, but
+that is everything we've
+
+covered to this point.
+
+And you can find this material
+discussed in the first
+
+chapter, in the introduction,
+and then half of the second
+
+chapter of Berger's book if
+you want to read over it.
+
+OK, any questions or comments?
+
+All right, I wanted to say a
+little bit more about lattices
+
+and something with which you
+are no doubt familiar, but
+
+perhaps have some questions
+about why one does it in such
+
+an obscure, difficult way.
+
+And let me introduce what's done
+by an analogy which we
+
+have around us in
+everyday life.
+
+Let me draw a system of streets
+and avenues for a city
+
+that might be one like Boston
+where the streets were laid
+
+out by cows wandering around
+in search of forage.
+
+And suppose somebody met you on
+the street and said, may I
+
+stop you here at point A
+and ask you a question?
+
+How do I get from point
+A to point B?
+
+That's not a vector.
+
+That's a point.
+
+How do I do that?
+
+You would not say, go 342 meters
+to the east and 26.4
+
+meters to the south.
+
+That's perfectly logical that is
+admirably Cartesian but you
+
+wouldn't do it that way what we
+just said you would say go
+
+one block straight ahead, and
+then turn one block to your
+
+left, and then go down the
+street to your right and turn
+
+to your right again, and
+you'll be right there.
+
+You can't miss it.
+
+Of course, the person in Boston
+would miss it and would
+
+have to stop a second time and
+ask again and by a method of
+
+successive approximations
+eventually get to where he or
+
+she would like to be.
+
+I submit if a system gives you
+a grid, it makes sense to use
+
+that grid as the basis vectors
+of coordinate system even if
+
+the intervals are different, in
+two different directions,
+
+and even though the intervals
+might be not vectors that are
+
+orthogonal to one another.
+
+If the system is periodic and
+has this grid work to it, it
+
+makes sense to use that as the
+basis of a coordinate system.
+
+So if we have a lattice that
+is oblique and there are
+
+lattice points defined by these
+two translations, T1 and
+
+T2, it makes great sense if you
+want to specify the vector
+
+that runs from this lattice
+point to this lattice point to
+
+do that by saying that this is a
+lattice point that is at the
+
+end of the vector
+1 T1 plus 2 T2.
+
+And that, just as a system of
+streets and avenues, is a lot
+
+more efficient than saying go
+12.2 angstroms in the x
+
+direction and go 15.3 angstroms
+in the y direction.
+
+What we have defined here is
+something that is called a
+
+rational direction.
+
+And a rational direction is
+something that is going to be
+
+a direction that extends
+between lattice points.
+
+And what's rational about it
+is that the coefficients in
+
+front of T1 and T2 that would
+appear would be integers.
+
+And an integers is sometimes
+referred to
+
+as a rational number.
+
+That would be quite different
+from a vector that extended
+
+from a lattice point to, let's
+say, some atom that is within
+
+the boundaries of this cell.
+
+And this might be a radial
+vector from the
+
+origin to one lattice.
+
+And that could be used
+to specify the atomic
+
+coordinates.
+
+This is going to complete the
+dichotomy, a feature that is
+
+referred to as irrational.
+
+Why?
+
+Because the components of the
+steps along T1, x, and along
+
+T2, y, are going to be
+fractional numbers.
+
+So you'll hit irrational
+notation for directions that
+
+go to different locations
+with a unit cell.
+
+You'll use rational vectors in
+directions that extend between
+
+integral numbers of
+lattice points.
+
+These directions occur all the
+time when one discusses the
+
+physical properties
+of crystals.
+
+I'm sure in any class that
+you've had that's discussed
+
+mechanical properties, one of
+the favorite topics is to
+
+discuss the ways in which close
+
+packed metals can deform.
+
+And this can be discussed easily
+in terms of one layer
+
+of close packed spheres
+sliding over another.
+
+And one of the ways that the
+layer can slide to go from one
+
+set of close packed hollows
+to another is in a
+
+direction like this.
+
+And that turns out to be
+a rational direction.
+
+And these are directions in
+which a close packed metal
+
+will easily deform.
+
+So directions of easy plastic
+deformations almost always
+
+involve rational directions.
+
+So there is a unique application
+of these sorts of
+
+features in the discussion
+of mechanical properties.
+
+Another thing that can happen
+is that a particular
+
+structure, if it is weakly
+bonded or relatively weakly
+
+bonded in one direction, if you
+come down with a chisel on
+
+that plane and give it a little
+tunk with a hammer, the
+
+crystal will fall exactly in
+half and give you two very
+
+smooth surfaces on either
+side of some plane.
+
+And the reason is if you look
+down into the guts of the
+
+crystal and look at the atoms
+and how they're bonded
+
+together, there may be some
+direction of weak bonding
+
+between atoms that is very
+easily separated by some sort
+
+of mechanical force.
+
+This is true even for crystals
+that are very strongly bonded.
+
+The way in which people begin
+to facet diamonds, for
+
+example, is to sit for a month
+and study the diamond and then
+
+decide how you're going to put a
+straight edge to it and give
+
+it a little tunk so that it
+falls neatly into two pieces
+
+at the sides that you
+want to facet.
+
+Doesn't always work, so you sit
+for a long time to figure
+
+out just what you're
+going to do.
+
+I think diamond cutters burn
+out early and have a useful
+
+career that last perhaps
+3 and 1/2 years.
+
+And then, they're burned out.
+
+I don't know that for sure.
+
+But it must be a nerve
+wracking way
+
+of making an existence.
+
+Not a far-fetched story.
+
+At one time, I was doing a
+diffraction study on a
+
+material which was a low
+temperature face, very
+
+interesting, but formed stable
+only at such low temperatures
+
+that you could not make it by
+cooking the components.
+
+But it had been found as a
+mineral in the Swiss Alps, all
+
+sorts of exotica attached to
+this particular material.
+
+There was a particular place
+up in the Alps which had a
+
+very unusual chemistry involving
+lead and arsenic and
+
+thallium and sulfur--
+
+not what you find in your usual
+backyard rock pile.
+
+And there was something like 37
+unique minerals that were
+
+found in this little spot that
+were known nowhere else on the
+
+face of the Earth.
+
+And I was very interested
+in the atomic
+
+arrangements in one of them.
+
+So I wrote to the British Museum
+that had found the sole
+
+supplier of this
+material that--
+
+back in about 1901 or so--
+
+I wrote and I said,
+do you have any
+
+crystals of this stuff?
+
+Yes.
+
+Would you like to study it?
+
+And I said yes, I would.
+
+Well, we'd be happy
+to send it.
+
+But please be careful not to
+damage the morphology because
+
+it is a very rare material.
+
+So I said fine.
+
+I'm as careful as the
+next meticulous guy.
+
+They sent two crystals.
+
+The crystals measured--
+
+one of them was 2/10 of a
+millimeter in diameter.
+
+One of them was about 0.15
+millimeters in diameter.
+
+And I was supposed to take off
+a piece for study without
+
+damaging the morphology.
+
+Man, I felt just like one of
+these Dutch diamond cutters.
+
+I sat and I looked at those two
+little suckers under the
+
+microscope for, I
+think, a week.
+
+And then finally, the moment of
+truth, and I took a needle
+
+and popped off a corner.
+
+And it went into two pieces.
+
+One went for a microprobe
+analysis to determine the
+
+composition.
+
+One of them went to a single
+crystal x-ray diffraction
+
+study to determine the
+atomic arrangement.
+
+Both analyses can be done on a
+very small piece of material.
+
+So my story about the diamond
+cutter agonizing before
+
+looking for a cleavage or a
+fracture surface is not just
+
+made up fiction.
+
+It is something that, when you
+work with crystals very often,
+
+is encountered.
+
+OK, cleavage planes are also
+rational directions.
+
+The cleavage plane of rock
+salt is legendary.
+
+And it's nice, really, to spend
+an afternoon splitting
+
+it up just to see how
+neat it falls apart.
+
+OK, how are we going to denote
+rational planes?
+
+Talked about rational and
+irrational directions, and
+
+that's easy.
+
+How are we going to describe
+rational planes in crystals?
+
+And this is rather bizarre.
+
+So let me tell you what you do,
+which is something you've
+
+probably heard before, and
+then explain why one
+
+does it this way.
+
+Let's suppose we have three
+vectors that are the vectors
+
+we will use to define
+the lattice.
+
+And if there is a plane hanging
+on one of these
+
+lattice points, everything is
+translationally periodic, so
+
+there must be a similar plane
+in the same orientation that
+
+passes through all the
+lattice points.
+
+So let me look at a very special
+plane, namely one that
+
+cuts a lattice point at
+an integral number of
+
+translations, T3, and an
+integral number of
+
+translations, T2, and an
+integral number of
+
+translations, T1.
+
+And I don't want any common
+factor here, so let's look at
+
+this point here.
+
+And now, let's connect these
+lattice points together.
+
+And that will define
+a plane uniquely.
+
+And what is special about this
+point is that it hits a
+
+lattice point on each
+of these three axes.
+
+And this is a plane that I'll
+call the intercept plane.
+
+There will be a similar plane
+hanging on all of these other
+
+lattice points.
+
+But those planes will not hit
+a lattice point on the
+
+directions of T1, T2, and T3.
+
+This is the first one out from
+the origin that does that.
+
+Now, we will use this oblique
+set of vectors, T1, T2, and
+
+T3, as the coordinate system
+for specifying
+
+direction and angles.
+
+So let me ask a question now
+that's going to blow you away.
+
+What is the equation for the
+locus of this plane If I use
+
+this oblique coordinate system
+based on T1, T2, and T3 as my
+
+coordinate system?
+
+Holy mackerel.
+
+What a way to wrap
+up a Tuesday.
+
+Actually, it's very,
+very easy.
+
+First of all, it has to
+be a linear equation.
+
+So it's going to be linear
+in x, y, and z.
+
+So something times x, something
+times y, something
+
+times z equals a constant.
+
+That's going to define, if I use
+the proper coefficients,
+
+the equation for this plane.
+
+And let me determine quite
+easily what those
+
+coefficients are.
+
+What is the coordinate of this
+point, which sits on the plane
+
+and therefore must satisfy
+this equation?
+
+Well, y is 0. z is zero.
+
+So this is the point--
+
+if I am a translations out from
+the origin, this is the
+
+point x equals A.
+
+So if I'm three translations
+out from the origin, that
+
+integer is the coefficient in
+front of x because when y and
+
+z are 0, if I make the constants
+on the right hand
+
+side equal to 1, this is
+the point x equals a.
+
+And it's nice to have one
+on the right hand side.
+
+That's about as nice and neat
+and tidy a constant as you
+
+could have.
+
+We do the same thing for this
+point at the end of two
+
+translations, T2.
+
+let's say in general that for
+this intercept plane, we are
+
+two translations out along T2.
+
+So for the point 0--
+
+this point, 0--
+
+if I put the number of
+translations, b, in front of
+
+y, This is the point y equals
+b when x and z are 0.
+
+And in the same way, if we are C
+translations out along T3, C
+
+times z-- that integer--
+is equal to 1.
+
+AUDIENCE: Can you explain
+it again?
+
+[INAUDIBLE]
+
+PROFESSOR: I'm sorry.
+
+What?
+
+AUDIENCE: [INAUDIBLE].
+
+PROFESSOR: Yeah, I'm saying I'm
+going to [INAUDIBLE] my
+
+definition at a plane which
+cuts the direction of T1,
+
+which is what I called
+the variable x, at a
+
+translations out.
+
+In this case, this is 3.
+
+This is 2.
+
+And this is 1.
+
+So for this particular example,
+I would have 3x plus
+
+2y plus 1z equals 1 because when
+y is 0 and z is 0, the
+
+point on the surface is--
+
+1/3.
+
+Sorry.
+
+Good question.
+
+OK, that's a lot better.
+
+I would've gotten in much deeper
+trouble if you had let
+
+me persist in that.
+
+So thank you for
+the correction.
+
+But now, I would like to have
+integers out in front here.
+
+So let me multiply both sides
+through by A times B times C.
+
+And now, I do get something with
+integers in front of x
+
+and integers in front of y.
+
+And this would be A times C,
+and integers in front of z.
+
+And that's A times B equals--
+
+and now on the right side, I
+would have a times B times C.
+
+So everything, every coefficient
+and the term on
+
+the right hand side are
+products of integers.
+
+So they are all integers
+themselves.
+
+OK, let me next ask the question
+these planes passing
+
+through all of the other
+lattice points that are
+
+contained within this little
+tetrahedron of volume are
+
+going to be equally spaced.
+
+How will I claim that these
+planes are all equally spaced?
+
+Well, that's easy just
+in general terms.
+
+Here is a lattice point.
+
+There's a plane passing
+through it.
+
+There's some lattice point
+neighboring it that's out at
+
+distance, D. Here is another
+lattice point.
+
+It has a plane passing
+through it.
+
+There must be a plane out here
+on D. And I'm not going to be
+
+able to have the same
+environment for every lattice
+
+point unless all of these planes
+have the same spacing
+
+from one another.
+
+So to say that they pass in
+lattice points in the
+
+environment of everybody lattice
+point is by definition
+
+identical is possible only if
+the planes are equally spaced.
+
+Next question--
+
+and I'm not going to be gutsy
+enough to try to demonstrate
+
+this in three dimensions,
+so let me do it in two.
+
+Let us ask the question, how
+many planes are there hanging
+
+on all the lattice points
+between the origin and the
+
+intercept plane?
+
+And let me demonstrate that for
+a two dimensional case.
+
+And I will refer you to a
+drawing in Berger's book
+
+because this is not convincing
+unless you do
+
+it absolutely exactly.
+
+And to do that in front of a
+live audience with chalk is
+
+not always the easiest
+thing in the world.
+
+So here is T1.
+
+Here is T2.
+
+And let me look at this plane.
+
+This is the intercept plane.
+
+A is equal to 3 and
+B is equal to 2.
+
+Now, what I'm going to do is
+to use plus and minus the
+
+translation T1 to repeat
+this intercept plane.
+
+OK, I go minus T1.
+
+And that's going to give
+me a plane in here.
+
+I'm going to go minus
+T1 again.
+
+And that's going to give
+me a plane in here.
+
+So I have split the interval
+between the origin and the
+
+intercept plane into A parts.
+
+OK so far?
+
+Let me now use the
+translation T2.
+
+And I will use the plus and
+minus the translation T2 to
+
+take this stack of A planes
+and repeat it B times.
+
+And that's going to take the
+plane at the origin and move
+
+it up to here.
+
+It's going to move the planes
+into stacks like this.
+
+I will map the stack of
+A planes B times.
+
+And that is going to give me A
+times B intervals except if a
+
+special condition applies.
+
+And then, I will go back
+to it in a moment.
+
+This is the equation of
+the intercept plane.
+
+I will argue that the three
+dimensional analogy of what
+
+I've done is that there will be,
+if I let the translations
+
+T1, T2, and T3 go to work, there
+will be A times B times
+
+C intervals between the origin
+and the intercept plane.
+
+So if this is the intercept
+plane and this is A times B
+
+times C times the spacing
+between the planes out from
+
+the origin, then the first plane
+from the origin is going
+
+to happen to intercept which
+is 1ABC to the first.
+
+And ABC divided by ABC turns out
+to be 1 for any value of
+
+A, B, and C.
+
+So the first plane from the
+origin is going to have the
+
+simple equation be BC times x
+plus AC times y plus AB times
+
+z equals 1.
+
+And the second plane out from
+the origin will have the same
+
+coefficients except the term
+on the left will be 2.
+
+Third plane will have 3 on the
+right and finally the integer
+
+ABC when we get to the
+intercept plane.
+
+OK, now I'm ready to make a
+momentous definition just as
+
+we get five of the hour.
+
+B times C is an integer.
+
+Let me define that integer
+by a single integer.
+
+And just for the heck of it,
+I'll call it H. A times C is
+
+an integer.
+
+Let me call that integer K.
+And AB is an integer.
+
+Let me call that integer L.
+
+So using T1 and T2 and T3 as
+the basis vectors of my
+
+coordinate system, the first
+plane from the origin has the
+
+equation Hx plus Ky
+plus Lz equals 1.
+
+And these three integers, H, K,
+and L, are said to be the
+
+Miller indices of this plane.
+
+PROFESSOR: Yes, sir?
+
+AUDIENCE: Just on that figure,
+[INAUDIBLE] connect to the
+
+lattice points.
+
+I'm trying to make sense of why
+did you put the planes in
+
+between them?
+
+PROFESSOR: OK, what I did was
+I started with just these
+
+three hanging on the lattice
+point separated by T1.
+
+And then, I move this by T2.
+
+OK, so T2 has a plane
+in the middle of it.
+
+And it's going to move
+that up to here and
+
+give me another plane.
+
+If you just draw this out--
+and you're going to get a
+
+problem that asks
+you to do this--
+
+since these integers are
+mutually prime, the second
+
+translation is going to
+interleave planes
+
+between the first set.
+
+And it gets even worse in three
+dimensions because the
+
+third translation, which is the
+axis C translations out,
+
+is going to interleave that
+set of AB planes C times.
+
+And they have to be at
+equal distances.
+
+Otherwise, the definition of
+the lattice point having
+
+identical environment
+is violated.
+
+OK, these are the infamous
+Miller indices that are the
+
+downfall of all freshman
+who take 309.1.
+
+It is not necessarily a very
+straightforward definition.
+
+But the advantage of it is that
+it lets you analytically
+
+describe the locus of the
+lattice planes in a very, very
+
+convenient way.
+
+Actually, let me tell you
+something maybe you have not
+
+heard before.
+
+These indices were not invented
+by a fellow named
+
+Miller who was an Englishman
+who wrote a book, an early
+
+book on crystallography that
+incorporated this notation.
+
+The guy who invented them and
+first proposed them was
+
+Auguste Bravais, a very famous
+French crystallographer--
+
+mathematician, actually--
+
+who gave his name to the three
+dimensional space lattices.
+
+These are universally
+known as the Bravais
+
+lattices, 14 of them.
+
+It's a great name.
+
+It's music. it rolls
+of the tongue--
+
+Bravis, Bravais.
+
+Actually, Bravias wasn't
+the first guy to
+
+try to derive them.
+
+The first guy who tried to
+drive the lattices was
+
+somebody named Frankenheim.
+
+He blew it.
+
+He didn't get 14.
+
+He only found 13.
+
+So there's a moral here.
+
+If immortality is your game,
+get it right the first time
+
+because everybody has heard
+of Bravais, Bravais.
+
+Nobody has heard
+of Frankenheim.
+
+And for that, I say thank god.
+
+What a name!
+
+It makes you think of somebody
+who's got plugs in his neck
+
+and walks around like this
+and has a green face.
+
+Frankenheim--
+
+bah!
+
+Bravais, Bravais, it really
+sings to you.
+
+OK, I'm getting silly so it's
+time to quit and take a break.
+
+Come up and say hello
+to Rodney.
\ No newline at end of file
diff --git a/AyCLokHV774.txt b/AyCLokHV774.txt
new file mode 100644
index 0000000000000000000000000000000000000000..bbeef60fde867de2af2fe790aea3c0ec93d2bdca
--- /dev/null
+++ b/AyCLokHV774.txt
@@ -0,0 +1,1203 @@
+align:start position:0%
+ 
+we often think of a Bernoulli process as
+
+ align:start position:0%
+we often think of a Bernoulli process as
+ 
+
+ align:start position:0%
+we often think of a Bernoulli process as
+a stream of arriving traffic what
+
+ align:start position:0%
+a stream of arriving traffic what
+ 
+
+ align:start position:0%
+a stream of arriving traffic what
+happens if we merge two streams for
+
+ align:start position:0%
+happens if we merge two streams for
+ 
+
+ align:start position:0%
+happens if we merge two streams for
+example consider a server that receives
+
+ align:start position:0%
+example consider a server that receives
+ 
+
+ align:start position:0%
+example consider a server that receives
+traffic from two independent sources how
+
+ align:start position:0%
+traffic from two independent sources how
+ 
+
+ align:start position:0%
+traffic from two independent sources how
+do we describe the total traffic that
+
+ align:start position:0%
+do we describe the total traffic that
+ 
+
+ align:start position:0%
+do we describe the total traffic that
+arrives to this server here's a precise
+
+ align:start position:0%
+arrives to this server here's a precise
+ 
+
+ align:start position:0%
+arrives to this server here's a precise
+model we have two streams that
+
+ align:start position:0%
+model we have two streams that
+ 
+
+ align:start position:0%
+model we have two streams that
+correspond to Bernoulli processes with
+
+ align:start position:0%
+correspond to Bernoulli processes with
+ 
+
+ align:start position:0%
+correspond to Bernoulli processes with
+some parameters each P and Q
+
+ align:start position:0%
+some parameters each P and Q
+ 
+
+ align:start position:0%
+some parameters each P and Q
+respectively
+
+ align:start position:0%
+respectively
+ 
+
+ align:start position:0%
+respectively
+and each one of these processes receives
+
+ align:start position:0%
+and each one of these processes receives
+ 
+
+ align:start position:0%
+and each one of these processes receives
+arrivals at certain times that we
+
+ align:start position:0%
+arrivals at certain times that we
+ 
+
+ align:start position:0%
+arrivals at certain times that we
+indicate by crosses and similarly for
+
+ align:start position:0%
+indicate by crosses and similarly for
+ 
+
+ align:start position:0%
+indicate by crosses and similarly for
+the second process we assume that these
+
+ align:start position:0%
+the second process we assume that these
+ 
+
+ align:start position:0%
+the second process we assume that these
+two processes are independent and what
+
+ align:start position:0%
+two processes are independent and what
+ 
+
+ align:start position:0%
+two processes are independent and what
+we mean by this is that any collection
+
+ align:start position:0%
+we mean by this is that any collection
+ 
+
+ align:start position:0%
+we mean by this is that any collection
+of random variables associated with the
+
+ align:start position:0%
+of random variables associated with the
+ 
+
+ align:start position:0%
+of random variables associated with the
+first process will be independent from
+
+ align:start position:0%
+first process will be independent from
+ 
+
+ align:start position:0%
+first process will be independent from
+any collection of random variables
+
+ align:start position:0%
+any collection of random variables
+ 
+
+ align:start position:0%
+any collection of random variables
+associated with the second process we
+
+ align:start position:0%
+associated with the second process we
+ 
+
+ align:start position:0%
+associated with the second process we
+now merge the two processes as follows
+
+ align:start position:0%
+now merge the two processes as follows
+ 
+
+ align:start position:0%
+now merge the two processes as follows
+whenever there is an arrival in any of
+
+ align:start position:0%
+whenever there is an arrival in any of
+ 
+
+ align:start position:0%
+whenever there is an arrival in any of
+the original processes we record an
+
+ align:start position:0%
+the original processes we record an
+ 
+
+ align:start position:0%
+the original processes we record an
+arrival in the merged process as in this
+
+ align:start position:0%
+arrival in the merged process as in this
+ 
+
+ align:start position:0%
+arrival in the merged process as in this
+picture notice that we do not make a
+
+ align:start position:0%
+picture notice that we do not make a
+ 
+
+ align:start position:0%
+picture notice that we do not make a
+distinction between those slots at which
+
+ align:start position:0%
+distinction between those slots at which
+ 
+
+ align:start position:0%
+distinction between those slots at which
+there was an arrival in only one of the
+
+ align:start position:0%
+there was an arrival in only one of the
+ 
+
+ align:start position:0%
+there was an arrival in only one of the
+original process versus those slots in
+
+ align:start position:0%
+original process versus those slots in
+ 
+
+ align:start position:0%
+original process versus those slots in
+which there was an arrival in both of
+
+ align:start position:0%
+which there was an arrival in both of
+ 
+
+ align:start position:0%
+which there was an arrival in both of
+the original processes in both cases we
+
+ align:start position:0%
+the original processes in both cases we
+ 
+
+ align:start position:0%
+the original processes in both cases we
+just say that there was an arrival in
+
+ align:start position:0%
+just say that there was an arrival in
+ 
+
+ align:start position:0%
+just say that there was an arrival in
+the merged process and so collisions
+
+ align:start position:0%
+the merged process and so collisions
+ 
+
+ align:start position:0%
+the merged process and so collisions
+arrivals in both of the original
+
+ align:start position:0%
+arrivals in both of the original
+ 
+
+ align:start position:0%
+arrivals in both of the original
+processes are counted as only one
+
+ align:start position:0%
+processes are counted as only one
+ 
+
+ align:start position:0%
+processes are counted as only one
+arrival in the merged process now what
+
+ align:start position:0%
+arrival in the merged process now what
+ 
+
+ align:start position:0%
+arrival in the merged process now what
+can we say about the merged process we
+
+ align:start position:0%
+can we say about the merged process we
+ 
+
+ align:start position:0%
+can we say about the merged process we
+will argue that it is a Bernoulli
+
+ align:start position:0%
+will argue that it is a Bernoulli
+ 
+
+ align:start position:0%
+will argue that it is a Bernoulli
+process with a certain parameter that we
+
+ align:start position:0%
+process with a certain parameter that we
+ 
+
+ align:start position:0%
+process with a certain parameter that we
+will compute to check the Bernoulli
+
+ align:start position:0%
+will compute to check the Bernoulli
+ 
+
+ align:start position:0%
+will compute to check the Bernoulli
+property for the merged process the
+
+ align:start position:0%
+property for the merged process the
+ 
+
+ align:start position:0%
+property for the merged process the
+first thing we need to ensure is the
+
+ align:start position:0%
+first thing we need to ensure is the
+ 
+
+ align:start position:0%
+first thing we need to ensure is the
+independence assumption independence
+
+ align:start position:0%
+independence assumption independence
+ 
+
+ align:start position:0%
+independence assumption independence
+across slots let us look at two typical
+
+ align:start position:0%
+across slots let us look at two typical
+ 
+
+ align:start position:0%
+across slots let us look at two typical
+slots and to do this it helps to define
+
+ align:start position:0%
+slots and to do this it helps to define
+ 
+
+ align:start position:0%
+slots and to do this it helps to define
+some notation that XT and YT
+
+ align:start position:0%
+some notation that XT and YT
+ 
+
+ align:start position:0%
+some notation that XT and YT
+the original processes and let ZT be the
+
+ align:start position:0%
+the original processes and let ZT be the
+ 
+
+ align:start position:0%
+the original processes and let ZT be the
+merged process the random variable Z T
+
+ align:start position:0%
+merged process the random variable Z T
+ 
+
+ align:start position:0%
+merged process the random variable Z T
+is determined in some way by the random
+
+ align:start position:0%
+is determined in some way by the random
+ 
+
+ align:start position:0%
+is determined in some way by the random
+variables XT and YT if I told you if
+
+ align:start position:0%
+variables XT and YT if I told you if
+ 
+
+ align:start position:0%
+variables XT and YT if I told you if
+there was an arrival in the first and
+
+ align:start position:0%
+there was an arrival in the first and
+ 
+
+ align:start position:0%
+there was an arrival in the first and
+the second process you can tell whether
+
+ align:start position:0%
+the second process you can tell whether
+ 
+
+ align:start position:0%
+the second process you can tell whether
+there was an arrival in the merged
+
+ align:start position:0%
+there was an arrival in the merged
+ 
+
+ align:start position:0%
+there was an arrival in the merged
+process and similarly the random
+
+ align:start position:0%
+process and similarly the random
+ 
+
+ align:start position:0%
+process and similarly the random
+variable Z T plus one is determined in
+
+ align:start position:0%
+variable Z T plus one is determined in
+ 
+
+ align:start position:0%
+variable Z T plus one is determined in
+some way from XT plus one and YT plus
+
+ align:start position:0%
+some way from XT plus one and YT plus
+ 
+
+ align:start position:0%
+some way from XT plus one and YT plus
+one what this is saying is that whether
+
+ align:start position:0%
+one what this is saying is that whether
+ 
+
+ align:start position:0%
+one what this is saying is that whether
+we have an arrival at this slot is
+
+ align:start position:0%
+we have an arrival at this slot is
+ 
+
+ align:start position:0%
+we have an arrival at this slot is
+determined by what happens in these two
+
+ align:start position:0%
+determined by what happens in these two
+ 
+
+ align:start position:0%
+determined by what happens in these two
+slots and whether we have an arrival in
+
+ align:start position:0%
+slots and whether we have an arrival in
+ 
+
+ align:start position:0%
+slots and whether we have an arrival in
+this slot is determined by whatever
+
+ align:start position:0%
+this slot is determined by whatever
+ 
+
+ align:start position:0%
+this slot is determined by whatever
+happens in these two slots now we have
+
+ align:start position:0%
+happens in these two slots now we have
+ 
+
+ align:start position:0%
+happens in these two slots now we have
+assumed that the two processes are
+
+ align:start position:0%
+assumed that the two processes are
+ 
+
+ align:start position:0%
+assumed that the two processes are
+independent so these two random
+
+ align:start position:0%
+independent so these two random
+ 
+
+ align:start position:0%
+independent so these two random
+variables are independent from those two
+
+ align:start position:0%
+variables are independent from those two
+ 
+
+ align:start position:0%
+variables are independent from those two
+random variables and furthermore across
+
+ align:start position:0%
+random variables and furthermore across
+ 
+
+ align:start position:0%
+random variables and furthermore across
+time this random variable will be
+
+ align:start position:0%
+time this random variable will be
+ 
+
+ align:start position:0%
+time this random variable will be
+independent from that random variable
+
+ align:start position:0%
+independent from that random variable
+ 
+
+ align:start position:0%
+independent from that random variable
+and this random variable will be
+
+ align:start position:0%
+and this random variable will be
+ 
+
+ align:start position:0%
+and this random variable will be
+independent from that random variable so
+
+ align:start position:0%
+independent from that random variable so
+ 
+
+ align:start position:0%
+independent from that random variable so
+these four random variables are
+
+ align:start position:0%
+these four random variables are
+ 
+
+ align:start position:0%
+these four random variables are
+independent of each other because of
+
+ align:start position:0%
+independent of each other because of
+ 
+
+ align:start position:0%
+independent of each other because of
+this we have ZT a function of two random
+
+ align:start position:0%
+this we have ZT a function of two random
+ 
+
+ align:start position:0%
+this we have ZT a function of two random
+variables that are independent from the
+
+ align:start position:0%
+variables that are independent from the
+ 
+
+ align:start position:0%
+variables that are independent from the
+two random variables that determine ZT
+
+ align:start position:0%
+two random variables that determine ZT
+ 
+
+ align:start position:0%
+two random variables that determine ZT
+plus one and for this reason ZT and ZT
+
+ align:start position:0%
+plus one and for this reason ZT and ZT
+ 
+
+ align:start position:0%
+plus one and for this reason ZT and ZT
+plus one will be independent
+
+ align:start position:0%
+plus one will be independent
+ 
+
+ align:start position:0%
+plus one will be independent
+this proves a pairwise independence
+
+ align:start position:0%
+this proves a pairwise independence
+ 
+
+ align:start position:0%
+this proves a pairwise independence
+property for the merged process but we
+
+ align:start position:0%
+property for the merged process but we
+ 
+
+ align:start position:0%
+property for the merged process but we
+can extend this argument to argue that
+
+ align:start position:0%
+can extend this argument to argue that
+ 
+
+ align:start position:0%
+can extend this argument to argue that
+the collection of random variables Z 1
+
+ align:start position:0%
+the collection of random variables Z 1
+ 
+
+ align:start position:0%
+the collection of random variables Z 1
+up to ZT is a collection of independent
+
+ align:start position:0%
+up to ZT is a collection of independent
+ 
+
+ align:start position:0%
+up to ZT is a collection of independent
+random variables so we have the
+
+ align:start position:0%
+random variables so we have the
+ 
+
+ align:start position:0%
+random variables so we have the
+independence property now let us
+
+ align:start position:0%
+independence property now let us
+ 
+
+ align:start position:0%
+independence property now let us
+calculate the probability of an arrival
+
+ align:start position:0%
+calculate the probability of an arrival
+ 
+
+ align:start position:0%
+calculate the probability of an arrival
+during a typical slot during a typical
+
+ align:start position:0%
+during a typical slot during a typical
+ 
+
+ align:start position:0%
+during a typical slot during a typical
+time slot there are four possibilities
+
+ align:start position:0%
+time slot there are four possibilities
+ 
+
+ align:start position:0%
+time slot there are four possibilities
+for what may occur and these
+
+ align:start position:0%
+for what may occur and these
+ 
+
+ align:start position:0%
+for what may occur and these
+possibilities have to do with whether in
+
+ align:start position:0%
+possibilities have to do with whether in
+ 
+
+ align:start position:0%
+possibilities have to do with whether in
+the X process we have an arrival or not
+
+ align:start position:0%
+the X process we have an arrival or not
+ 
+
+ align:start position:0%
+the X process we have an arrival or not
+and in the
+
+ align:start position:0%
+and in the
+ 
+
+ align:start position:0%
+and in the
+I process whether we have an arrival or
+
+ align:start position:0%
+I process whether we have an arrival or
+ 
+
+ align:start position:0%
+I process whether we have an arrival or
+not the probability that we have an
+
+ align:start position:0%
+not the probability that we have an
+ 
+
+ align:start position:0%
+not the probability that we have an
+arrival in both processes because of
+
+ align:start position:0%
+arrival in both processes because of
+ 
+
+ align:start position:0%
+arrival in both processes because of
+Independence is the product of the
+
+ align:start position:0%
+Independence is the product of the
+ 
+
+ align:start position:0%
+Independence is the product of the
+probability that we have an arrival in
+
+ align:start position:0%
+probability that we have an arrival in
+ 
+
+ align:start position:0%
+probability that we have an arrival in
+the first process with the probability
+
+ align:start position:0%
+the first process with the probability
+ 
+
+ align:start position:0%
+the first process with the probability
+that we have an arrival in the second
+
+ align:start position:0%
+that we have an arrival in the second
+ 
+
+ align:start position:0%
+that we have an arrival in the second
+process similarly there is a probability
+
+ align:start position:0%
+process similarly there is a probability
+ 
+
+ align:start position:0%
+process similarly there is a probability
+P of an arrival in the first process and
+
+ align:start position:0%
+P of an arrival in the first process and
+ 
+
+ align:start position:0%
+P of an arrival in the first process and
+no arrival in the second there is a
+
+ align:start position:0%
+no arrival in the second there is a
+ 
+
+ align:start position:0%
+no arrival in the second there is a
+probability 1 minus P of no arrival in
+
+ align:start position:0%
+probability 1 minus P of no arrival in
+ 
+
+ align:start position:0%
+probability 1 minus P of no arrival in
+the first process and an arrival in the
+
+ align:start position:0%
+the first process and an arrival in the
+ 
+
+ align:start position:0%
+the first process and an arrival in the
+second process and finally there is
+
+ align:start position:0%
+second process and finally there is
+ 
+
+ align:start position:0%
+second process and finally there is
+probability 1 minus P times one minus Q
+
+ align:start position:0%
+probability 1 minus P times one minus Q
+ 
+
+ align:start position:0%
+probability 1 minus P times one minus Q
+of no arrival in either of the two
+
+ align:start position:0%
+of no arrival in either of the two
+ 
+
+ align:start position:0%
+of no arrival in either of the two
+processes the probability that we have
+
+ align:start position:0%
+processes the probability that we have
+ 
+
+ align:start position:0%
+processes the probability that we have
+an arrival in the merged process is the
+
+ align:start position:0%
+an arrival in the merged process is the
+ 
+
+ align:start position:0%
+an arrival in the merged process is the
+probability of this green event these
+
+ align:start position:0%
+probability of this green event these
+ 
+
+ align:start position:0%
+probability of this green event these
+are the cases in which an arrival gets
+
+ align:start position:0%
+are the cases in which an arrival gets
+ 
+
+ align:start position:0%
+are the cases in which an arrival gets
+recorded in the merged process so the
+
+ align:start position:0%
+recorded in the merged process so the
+ 
+
+ align:start position:0%
+recorded in the merged process so the
+probability of an arrival in the merged
+
+ align:start position:0%
+probability of an arrival in the merged
+ 
+
+ align:start position:0%
+probability of an arrival in the merged
+process is the sum of those three
+
+ align:start position:0%
+process is the sum of those three
+ 
+
+ align:start position:0%
+process is the sum of those three
+probabilities or another way to
+
+ align:start position:0%
+probabilities or another way to
+ 
+
+ align:start position:0%
+probabilities or another way to
+calculate it is 1 minus this probability
+
+ align:start position:0%
+calculate it is 1 minus this probability
+ 
+
+ align:start position:0%
+calculate it is 1 minus this probability
+here namely 1 minus 1 minus P times 1
+
+ align:start position:0%
+here namely 1 minus 1 minus P times 1
+ 
+
+ align:start position:0%
+here namely 1 minus 1 minus P times 1
+minus Q and after you expand this
+
+ align:start position:0%
+minus Q and after you expand this
+ 
+
+ align:start position:0%
+minus Q and after you expand this
+product and do some cancellations you
+
+ align:start position:0%
+product and do some cancellations you
+ 
+
+ align:start position:0%
+product and do some cancellations you
+end up with this expression which is the
+
+ align:start position:0%
+end up with this expression which is the
+ 
+
+ align:start position:0%
+end up with this expression which is the
+probability of an arrival during a slot
+
+ align:start position:0%
+probability of an arrival during a slot
+ 
+
+ align:start position:0%
+probability of an arrival during a slot
+in the merged process of course this
+
+ align:start position:0%
+in the merged process of course this
+ 
+
+ align:start position:0%
+in the merged process of course this
+probability is constant across time and
+
+ align:start position:0%
+probability is constant across time and
+ 
+
+ align:start position:0%
+probability is constant across time and
+this together with the independence
+
+ align:start position:0%
+this together with the independence
+ 
+
+ align:start position:0%
+this together with the independence
+property establishes that the merged
+
+ align:start position:0%
+property establishes that the merged
+ 
+
+ align:start position:0%
+property establishes that the merged
+process is actually a Bernoulli process
+
+ align:start position:0%
+process is actually a Bernoulli process
+ 
+
+ align:start position:0%
+process is actually a Bernoulli process
+now let us end by answering one more
+
+ align:start position:0%
+now let us end by answering one more
+ 
+
+ align:start position:0%
+now let us end by answering one more
+question if I told you that at a certain
+
+ align:start position:0%
+question if I told you that at a certain
+ 
+
+ align:start position:0%
+question if I told you that at a certain
+time slot there was at least one arrival
+
+ align:start position:0%
+time slot there was at least one arrival
+ 
+
+ align:start position:0%
+time slot there was at least one arrival
+in the two processes which means that
+
+ align:start position:0%
+in the two processes which means that
+ 
+
+ align:start position:0%
+in the two processes which means that
+there was an arrival in the merged
+
+ align:start position:0%
+there was an arrival in the merged
+ 
+
+ align:start position:0%
+there was an arrival in the merged
+process what is the probability that
+
+ align:start position:0%
+process what is the probability that
+ 
+
+ align:start position:0%
+process what is the probability that
+there was an arrival in the first
+
+ align:start position:0%
+there was an arrival in the first
+ 
+
+ align:start position:0%
+there was an arrival in the first
+process now the event that there was an
+
+ align:start position:0%
+process now the event that there was an
+ 
+
+ align:start position:0%
+process now the event that there was an
+arrival in the first process is this
+
+ align:start position:0%
+arrival in the first process is this
+ 
+
+ align:start position:0%
+arrival in the first process is this
+event here so we're trying to calculate
+
+ align:start position:0%
+event here so we're trying to calculate
+ 
+
+ align:start position:0%
+event here so we're trying to calculate
+the conditional probability of the blue
+
+ align:start position:0%
+the conditional probability of the blue
+ 
+
+ align:start position:0%
+the conditional probability of the blue
+event given that the green event has
+
+ align:start position:0%
+event given that the green event has
+ 
+
+ align:start position:0%
+event given that the green event has
+occurred we use the definition of
+
+ align:start position:0%
+occurred we use the definition of
+ 
+
+ align:start position:0%
+occurred we use the definition of
+conditional probabilities the
+
+ align:start position:0%
+conditional probabilities the
+ 
+
+ align:start position:0%
+conditional probabilities the
+conditional probability is
+
+ align:start position:0%
+conditional probability is
+ 
+
+ align:start position:0%
+conditional probability is
+equal to the probability that both
+
+ align:start position:0%
+equal to the probability that both
+ 
+
+ align:start position:0%
+equal to the probability that both
+events happen which in this case is the
+
+ align:start position:0%
+events happen which in this case is the
+ 
+
+ align:start position:0%
+events happen which in this case is the
+intersection of the blue and the green
+
+ align:start position:0%
+intersection of the blue and the green
+ 
+
+ align:start position:0%
+intersection of the blue and the green
+event which coincides with the blue
+
+ align:start position:0%
+event which coincides with the blue
+ 
+
+ align:start position:0%
+event which coincides with the blue
+event and the probability of the blue
+
+ align:start position:0%
+event and the probability of the blue
+ 
+
+ align:start position:0%
+event and the probability of the blue
+event is the sum of these two numbers is
+
+ align:start position:0%
+event is the sum of these two numbers is
+ 
+
+ align:start position:0%
+event is the sum of these two numbers is
+equal to P and then we divide by the
+
+ align:start position:0%
+equal to P and then we divide by the
+ 
+
+ align:start position:0%
+equal to P and then we divide by the
+probability of the conditioning event
+
+ align:start position:0%
+probability of the conditioning event
+ 
+
+ align:start position:0%
+probability of the conditioning event
+this is the probability of an arrival
+
+ align:start position:0%
+this is the probability of an arrival
+ 
+
+ align:start position:0%
+this is the probability of an arrival
+but this is what we have just calculated
+
+ align:start position:0%
+but this is what we have just calculated
+ 
+
+ align:start position:0%
+but this is what we have just calculated
+which is P plus Q minus P times Q
\ No newline at end of file
diff --git a/B7F6vh_plHw.txt b/B7F6vh_plHw.txt
new file mode 100644
index 0000000000000000000000000000000000000000..08f7ab58a63504f11b02df5be81c064bf5c64a00
--- /dev/null
+++ b/B7F6vh_plHw.txt
@@ -0,0 +1,255 @@
+Network technologies were developed to connect
+components (in this case individual computer
+
+systems) separated by larger distances, i.e.,
+distances measured in meters instead of centimeters.
+
+Communicating over these larger distances
+led to different design tradeoffs.
+
+In early networks, information was sent as
+a sequence of bits over the shared communication
+
+medium.
+
+The bits were organized into packets, each
+containing the address of the destination.
+
+Packets also included a checksum used to detect
+errors in transmission and the protocol supported
+
+the ability to request the retransmission
+of corrupted packets.
+
+The software controlling the network is divided
+into a "stack" of modules, each implementing
+
+a different communication abstraction.
+
+The lowest-level physical layer is responsible
+for transmitting and receiving an individual
+
+packet of bits.
+
+Bit errors are detected and corrected, and
+packets with uncorrectable errors are discarded.
+
+There are different physical-layer modules
+available for the different types of physical
+
+networks.
+
+The network layer deals with the addressing
+and routing of packets.
+
+Clever routing algorithms find the shortest
+communication path through the multi-hop network
+
+and deal with momentary or long-term outages
+on particular network links.
+
+The transport layer is responsible for providing
+the reliable communication of a stream of
+
+data, dealing with the issues of discarded
+or out-of-order packets.
+
+In an effort to optimize network usage and
+limit packet loses due to network congestion,
+
+the transport layer deals with flow control,
+i.e., the rate at which packets are sent.
+
+A key idea in the networking community is
+the notion of building a reliable communication
+
+channel on top of a "best efforts" packet
+network.
+
+Higher layers of the protocol are designed
+so that its possible to recover from errors
+
+in the lower layers.
+
+This has proven to be much more cost-effective
+and robust than trying to achieve 100% reliability
+
+at each layer.
+
+As we saw in the previous section, there are
+a lot of electrical issues when trying to
+
+communicate over a shared wire with multiple
+drivers and receivers.
+
+Slowing down the rate of communication helps
+to solve the problems, but "slow" isn't in
+
+the cards for today's high-performance systems.
+
+Experience in the network world has shown
+that the fastest and least problematic communication
+
+channels have a single driver communicating
+with a single receiver, what's called a point-to-point
+
+link.
+
+Using differential signaling is particularly
+robust.
+
+With differential signaling, the receiver
+measures the voltage difference across the
+
+two signaling wires.
+
+Electrical effects that might induce voltage
+noise on one signaling wire will affect the
+
+other in equal measure, so the voltage difference
+will be largely unaffected by most noise.
+
+Almost all high-performance communication
+links use differential signaling.
+
+If we're sending digital data, does that mean
+we also have to send a separate clock signal
+
+so the receiver knows when to sample the signal
+to determine the next bit?
+
+With some cleverness, it turns out that we
+can recover the timing information from the
+
+received signal assuming we know the nominal
+clock period at the transmitter.
+
+If the transmitter changes the bit its sending
+at the rising edge of the transmitter's clock,
+
+then the receiver can use the transitions
+in the received waveform to infer the timing
+
+for some of the clock edges.
+
+Then the receiver can use its knowledge of
+the transmitter's nominal clock period to
+
+infer the location of the remaining clock
+edges.
+
+It does this by using a phase-locked loop
+to generate a local facsimile of the transmitter's
+
+clock, using any received transitions to correct
+the phase and period of the local clock.
+
+The transmitter adds a training sequence of
+bits at the front of packet to ensure that
+
+the receiver's phased-lock loop is properly
+synchronized before the packet data itself
+
+is transmitted.
+
+A unique bit sequence is used to separate
+the training signal from the packet data so
+
+the receiver can tell exactly where the packet
+starts
+
+even if it missed a few training bits while
+the clocks were being properly synchronized.
+
+Once the receiver knows the timing of the
+clock edges, it can then sample the incoming
+
+waveform towards the end of each clock period
+to determine the transmitted bit.
+
+To keep the local clock in sync with the transmitter's
+clock, the incoming waveform needs to have
+
+reasonably frequent transitions.
+
+But if the transmitter is sending say, all
+zeroes, how can we guarantee frequent-enough
+
+clock edges?
+
+The trick, invented by IBM, is for the transmitter
+to take the stream of message bits and re-encode
+
+them into a bit stream that is guaranteed
+to have transitions no matter what the message
+
+bits are.
+
+The most commonly used encoding is 8b10b,
+where 8 message bits are encoded into 10 transmitted
+
+bits, where the encoding guarantees a transition
+at least every 6 bit times.
+
+Of course, the receiver has to reverse the
+8b10b encoding to recover the actual message
+
+bits.
+
+Pretty neat!
+
+The benefit of this trick is that we truly
+only need to send a single stream of bits.
+
+The receiver will be able to recover both
+the timing information and the data without
+
+also needing to transmit a separate clock
+signal.
+
+Using these lessons, networks have evolved
+from using shared communication channels to
+
+using point-to-point links.
+
+Today local-area networks use 10, 100, or
+1000 BaseT wiring which includes separate
+
+differential pairs for sending and receiving,
+i.e., each sending or receiving channel is
+
+unidirectional with a single driver and single
+receiver.
+
+The network uses separate switches and routers
+to receive packets from a sender and then
+
+forward the packets over a point-to-point
+link to the next switch,
+
+and so on, across multiple point-to-point
+links until the packet arrives at its destination.
+
+System-level connections have evolved to use
+the same communication strategy: point-to-point
+
+links with switches for routing packets to
+their intended destination.
+
+Note that communication along each link is
+independent, so a network with many links
+
+can actually support a lot of communication
+bandwidth.
+
+With a small amount of packet buffering in
+the switches to deal with momentary contention
+
+for a particular link,
+this is a very effective strategy for moving
+
+massive amounts of information from one component
+to the next.
+
+In the next section, we'll look at some of
+the more interesting details.
\ No newline at end of file
diff --git a/Bb-bgJdOqig.txt b/Bb-bgJdOqig.txt
new file mode 100644
index 0000000000000000000000000000000000000000..0fd4bbcf998965e968992413c7930c8619244046
--- /dev/null
+++ b/Bb-bgJdOqig.txt
@@ -0,0 +1,1288 @@
+align:start position:0%
+ 
+hi welcome back to recitation uh in last
+
+ align:start position:0%
+hi welcome back to recitation uh in last
+ 
+
+ align:start position:0%
+hi welcome back to recitation uh in last
+lecture we talked about finding the
+
+ align:start position:0%
+lecture we talked about finding the
+ 
+
+ align:start position:0%
+lecture we talked about finding the
+derivatives of trigonometric functions
+
+ align:start position:0%
+derivatives of trigonometric functions
+ 
+
+ align:start position:0%
+derivatives of trigonometric functions
+in particular the sign function and the
+
+ align:start position:0%
+in particular the sign function and the
+ 
+
+ align:start position:0%
+in particular the sign function and the
+cosine function so today let's do a an
+
+ align:start position:0%
+cosine function so today let's do a an
+ 
+
+ align:start position:0%
+cosine function so today let's do a an
+example of putting that into practice so
+
+ align:start position:0%
+example of putting that into practice so
+ 
+
+ align:start position:0%
+example of putting that into practice so
+here's a function H ofx = to sin of x +
+
+ align:start position:0%
+here's a function H ofx = to sin of x +
+ 
+
+ align:start position:0%
+here's a function H ofx = to sin of x +
+< TK 3 * cosine of x and I'm asking you
+
+ align:start position:0%
+< TK 3 * cosine of x and I'm asking you
+ 
+
+ align:start position:0%
+< TK 3 * cosine of x and I'm asking you
+to find which values of X have the
+
+ align:start position:0%
+to find which values of X have the
+ 
+
+ align:start position:0%
+to find which values of X have the
+property that the derivative of H ofx is
+
+ align:start position:0%
+property that the derivative of H ofx is
+ 
+
+ align:start position:0%
+property that the derivative of H ofx is
+equal to zero so why don't you take a
+
+ align:start position:0%
+equal to zero so why don't you take a
+ 
+
+ align:start position:0%
+equal to zero so why don't you take a
+minute to think about that work it out
+
+ align:start position:0%
+minute to think about that work it out
+ 
+
+ align:start position:0%
+minute to think about that work it out
+on your own pause the video and we'll
+
+ align:start position:0%
+on your own pause the video and we'll
+ 
+
+ align:start position:0%
+on your own pause the video and we'll
+come back and we'll work it out
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+together all right so you've hopefully
+
+ align:start position:0%
+together all right so you've hopefully
+ 
+
+ align:start position:0%
+together all right so you've hopefully
+had a chance to look over this problem
+
+ align:start position:0%
+had a chance to look over this problem
+ 
+
+ align:start position:0%
+had a chance to look over this problem
+try it out for yourself now let's see
+
+ align:start position:0%
+try it out for yourself now let's see
+ 
+
+ align:start position:0%
+try it out for yourself now let's see
+how to go about it so we have the
+
+ align:start position:0%
+how to go about it so we have the
+ 
+
+ align:start position:0%
+how to go about it so we have the
+function H ofx it's Al to sin plusk 3
+
+ align:start position:0%
+function H ofx it's Al to sin plusk 3
+ 
+
+ align:start position:0%
+function H ofx it's Al to sin plusk 3
+cosin x and we want to know when its
+
+ align:start position:0%
+cosin x and we want to know when its
+ 
+
+ align:start position:0%
+cosin x and we want to know when its
+derivative is equal to zero so in order
+
+ align:start position:0%
+derivative is equal to zero so in order
+ 
+
+ align:start position:0%
+derivative is equal to zero so in order
+to answer that question we should figure
+
+ align:start position:0%
+to answer that question we should figure
+ 
+
+ align:start position:0%
+to answer that question we should figure
+out what its derivative actually is and
+
+ align:start position:0%
+out what its derivative actually is and
+ 
+
+ align:start position:0%
+out what its derivative actually is and
+try and write down a formula for its
+
+ align:start position:0%
+try and write down a formula for its
+ 
+
+ align:start position:0%
+try and write down a formula for its
+derivative so in this case that's not
+
+ align:start position:0%
+derivative so in this case that's not
+ 
+
+ align:start position:0%
+derivative so in this case that's not
+that bad U if we take a derivative of H
+
+ align:start position:0%
+that bad U if we take a derivative of H
+ 
+
+ align:start position:0%
+that bad U if we take a derivative of H
+well H is a sum of two functions sinx
+
+ align:start position:0%
+well H is a sum of two functions sinx
+ 
+
+ align:start position:0%
+well H is a sum of two functions sinx
+and < TK of 3 cine X and we know that
+
+ align:start position:0%
+and < TK of 3 cine X and we know that
+ 
+
+ align:start position:0%
+and < TK of 3 cine X and we know that
+the derivative a s of a sum is just the
+
+ align:start position:0%
+the derivative a s of a sum is just the
+ 
+
+ align:start position:0%
+the derivative a s of a sum is just the
+sum of the derivatives um so we have
+
+ align:start position:0%
+sum of the derivatives um so we have
+ 
+
+ align:start position:0%
+sum of the derivatives um so we have
+that H Prime of x
+
+ align:start position:0%
+that H Prime of x
+ 
+
+ align:start position:0%
+that H Prime of x
+is equal to D over
+
+ align:start position:0%
+is equal to D over
+ 
+
+ align:start position:0%
+is equal to D over
+DX of
+
+ align:start position:0%
+DX of
+ 
+
+ align:start position:0%
+DX of
+sinx
+
+ align:start position:0%
+sinx
+ 
+
+ align:start position:0%
+sinx
+plus d over DX of < TK 3
+
+ align:start position:0%
+plus d over DX of < TK 3
+ 
+
+ align:start position:0%
+plus d over DX of < TK 3
+* cosine X now uh we learned last time
+
+ align:start position:0%
+* cosine X now uh we learned last time
+ 
+
+ align:start position:0%
+* cosine X now uh we learned last time
+in in lecture that that the derivative
+
+ align:start position:0%
+in in lecture that that the derivative
+ 
+
+ align:start position:0%
+in in lecture that that the derivative
+of sinx is cosine of x and we learned
+
+ align:start position:0%
+of sinx is cosine of x and we learned
+ 
+
+ align:start position:0%
+of sinx is cosine of x and we learned
+the derivative of cosine of x is minus
+
+ align:start position:0%
+the derivative of cosine of x is minus
+ 
+
+ align:start position:0%
+the derivative of cosine of x is minus
+sin x so here we have a constant
+
+ align:start position:0%
+sin x so here we have a constant
+ 
+
+ align:start position:0%
+sin x so here we have a constant
+multiple but by the constant multiple
+
+ align:start position:0%
+multiple but by the constant multiple
+ 
+
+ align:start position:0%
+multiple but by the constant multiple
+rule that just gets pulled out so this
+
+ align:start position:0%
+rule that just gets pulled out so this
+ 
+
+ align:start position:0%
+rule that just gets pulled out so this
+is equal
+
+ align:start position:0%
+is equal
+ 
+
+ align:start position:0%
+is equal
+to cosine
+
+ align:start position:0%
+to cosine
+ 
+
+ align:start position:0%
+to cosine
+xus < TK 3
+
+ align:start position:0%
+xus < TK 3
+ 
+
+ align:start position:0%
+xus < TK 3
+time sinx so this is H Prime of X and
+
+ align:start position:0%
+time sinx so this is H Prime of X and
+ 
+
+ align:start position:0%
+time sinx so this is H Prime of X and
+now we want to solve the equation H
+
+ align:start position:0%
+now we want to solve the equation H
+ 
+
+ align:start position:0%
+now we want to solve the equation H
+Prime of x equals z
+
+ align:start position:0%
+Prime of x equals z
+ 
+
+ align:start position:0%
+Prime of x equals z
+so so we
+
+ align:start position:0%
+so so we
+ 
+
+ align:start position:0%
+so so we
+want to find those values of X such that
+
+ align:start position:0%
+want to find those values of X such that
+ 
+
+ align:start position:0%
+want to find those values of X such that
+cosine x minus < TK 3
+
+ align:start position:0%
+cosine x minus < TK 3
+ 
+
+ align:start position:0%
+cosine x minus < TK 3
+sinx is equal to zero now there are a
+
+ align:start position:0%
+sinx is equal to zero now there are a
+ 
+
+ align:start position:0%
+sinx is equal to zero now there are a
+couple different ways to go about this I
+
+ align:start position:0%
+couple different ways to go about this I
+ 
+
+ align:start position:0%
+couple different ways to go about this I
+think my preferred way is I would add
+
+ align:start position:0%
+think my preferred way is I would add
+ 
+
+ align:start position:0%
+think my preferred way is I would add
+the sare < TK of 3 sinx to one side and
+
+ align:start position:0%
+the sare < TK of 3 sinx to one side and
+ 
+
+ align:start position:0%
+the sare < TK of 3 sinx to one side and
+then I want to get my x's together so I
+
+ align:start position:0%
+then I want to get my x's together so I
+ 
+
+ align:start position:0%
+then I want to get my x's together so I
+would divide by cosine X so that gives
+
+ align:start position:0%
+would divide by cosine X so that gives
+ 
+
+ align:start position:0%
+would divide by cosine X so that gives
+me so on the left side I'll be left with
+
+ align:start position:0%
+me so on the left side I'll be left with
+ 
+
+ align:start position:0%
+me so on the left side I'll be left with
+cosine x ided cosine X so that's just
+
+ align:start position:0%
+cosine x ided cosine X so that's just
+ 
+
+ align:start position:0%
+cosine x ided cosine X so that's just
+one and on the right side I'll have < TK
+
+ align:start position:0%
+one and on the right side I'll have < TK
+ 
+
+ align:start position:0%
+one and on the right side I'll have < TK
+
+ align:start position:0%
+ 
+
+ align:start position:0%
+* sin
+
+ align:start position:0%
+* sin
+ 
+
+ align:start position:0%
+* sin
+x over cine X so that's just < TK
+
+ align:start position:0%
+x over cine X so that's just < TK
+ 
+
+ align:start position:0%
+x over cine X so that's just < TK
+3 * Tan x um or and I can rewrite this
+
+ align:start position:0%
+3 * Tan x um or and I can rewrite this
+ 
+
+ align:start position:0%
+3 * Tan x um or and I can rewrite this
+as tan of X is equal to 1
+
+ align:start position:0%
+as tan of X is equal to 1
+ 
+
+ align:start position:0%
+as tan of X is equal to 1
+/ < TK 3 now to find X here either you
+
+ align:start position:0%
+/ < TK 3 now to find X here either you
+ 
+
+ align:start position:0%
+/ < TK 3 now to find X here either you
+can remember your your special trig
+
+ align:start position:0%
+can remember your your special trig
+ 
+
+ align:start position:0%
+can remember your your special trig
+angles and and know which which values
+
+ align:start position:0%
+angles and and know which which values
+ 
+
+ align:start position:0%
+angles and and know which which values
+of X make this work or you could apply
+
+ align:start position:0%
+of X make this work or you could apply
+ 
+
+ align:start position:0%
+of X make this work or you could apply
+the arct tangent function here so in
+
+ align:start position:0%
+the arct tangent function here so in
+ 
+
+ align:start position:0%
+the arct tangent function here so in
+either case the the
+
+ align:start position:0%
+either case the the
+ 
+
+ align:start position:0%
+either case the the
+simplest solution here is
+
+ align:start position:0%
+simplest solution here is
+ 
+
+ align:start position:0%
+simplest solution here is
+xal pi over 6 so if you like you can
+
+ align:start position:0%
+xal pi over 6 so if you like you can
+ 
+
+ align:start position:0%
+xal pi over 6 so if you like you can
+draw a little right
+
+ align:start position:0%
+draw a little right
+ 
+
+ align:start position:0%
+draw a little right
+triangle you know if this is X if Tan x
+
+ align:start position:0%
+triangle you know if this is X if Tan x
+ 
+
+ align:start position:0%
+triangle you know if this is X if Tan x
+is 1 over < TK of 3 we should have this
+
+ align:start position:0%
+is 1 over < TK of 3 we should have this
+ 
+
+ align:start position:0%
+is 1 over < TK of 3 we should have this
+side being one and this side
+
+ align:start position:0%
+side being one and this side
+ 
+
+ align:start position:0%
+side being one and this side
+being squ < TK of 3 and in and okay in
+
+ align:start position:0%
+being squ < TK of 3 and in and okay in
+ 
+
+ align:start position:0%
+being squ < TK of 3 and in and okay in
+that case in this right triangle the
+
+ align:start position:0%
+that case in this right triangle the
+ 
+
+ align:start position:0%
+that case in this right triangle the
+hypotenuse would be two
+
+ align:start position:0%
+hypotenuse would be two
+ 
+
+ align:start position:0%
+hypotenuse would be two
+and so then you you know would recognize
+
+ align:start position:0%
+and so then you you know would recognize
+ 
+
+ align:start position:0%
+and so then you you know would recognize
+this is a a 30° angle or pi/ 6 radian
+
+ align:start position:0%
+this is a a 30° angle or pi/ 6 radian
+ 
+
+ align:start position:0%
+this is a a 30° angle or pi/ 6 radian
+angle um but one thing to remember is
+
+ align:start position:0%
+angle um but one thing to remember is
+ 
+
+ align:start position:0%
+angle um but one thing to remember is
+that tangent of X is a periodic function
+
+ align:start position:0%
+that tangent of X is a periodic function
+ 
+
+ align:start position:0%
+that tangent of X is a periodic function
+with period Pi so not only is pi over 6
+
+ align:start position:0%
+with period Pi so not only is pi over 6
+ 
+
+ align:start position:0%
+with period Pi so not only is pi over 6
+a solution but pi over 6 plus pi is a
+
+ align:start position:0%
+a solution but pi over 6 plus pi is a
+ 
+
+ align:start position:0%
+a solution but pi over 6 plus pi is a
+solution um so that's 7 pi/ 6 or pi over
+
+ align:start position:0%
+solution um so that's 7 pi/ 6 or pi over
+ 
+
+ align:start position:0%
+solution um so that's 7 pi/ 6 or pi over
+6 + 2 pi which is 13 pi over 6 or pi
+
+ align:start position:0%
+6 + 2 pi which is 13 pi over 6 or pi
+ 
+
+ align:start position:0%
+6 + 2 pi which is 13 pi over 6 or pi
+over 6 minus Pi which is min -5
+
+ align:start position:0%
+over 6 minus Pi which is min -5
+ 
+
+ align:start position:0%
+over 6 minus Pi which is min -5
+pi over 6 Etc so there're actually
+
+ align:start position:0%
+pi over 6 Etc so there're actually
+ 
+
+ align:start position:0%
+pi over 6 Etc so there're actually
+infinitely many solutions they're
+
+ align:start position:0%
+infinitely many solutions they're
+ 
+
+ align:start position:0%
+infinitely many solutions they're
+they're given by pi over 6 plus an
+
+ align:start position:0%
+they're given by pi over 6 plus an
+ 
+
+ align:start position:0%
+they're given by pi over 6 plus an
+arbitrary multiple of Pi uh so then
+
+ align:start position:0%
+arbitrary multiple of Pi uh so then
+ 
+
+ align:start position:0%
+arbitrary multiple of Pi uh so then
+we're done um so I do want to mention
+
+ align:start position:0%
+we're done um so I do want to mention
+ 
+
+ align:start position:0%
+we're done um so I do want to mention
+though that there's a there's another
+
+ align:start position:0%
+though that there's a there's another
+ 
+
+ align:start position:0%
+though that there's a there's another
+approach to this question which is we
+
+ align:start position:0%
+approach to this question which is we
+ 
+
+ align:start position:0%
+approach to this question which is we
+can start by multiplying this expression
+
+ align:start position:0%
+can start by multiplying this expression
+ 
+
+ align:start position:0%
+can start by multiplying this expression
+for H of X so if you look at h of X It's
+
+ align:start position:0%
+for H of X so if you look at h of X It's
+ 
+
+ align:start position:0%
+for H of X so if you look at h of X It's
+s of X Plus s of 3 * cosine X um it
+
+ align:start position:0%
+s of X Plus s of 3 * cosine X um it
+ 
+
+ align:start position:0%
+s of X Plus s of 3 * cosine X um it
+resembles closely one of your uh
+
+ align:start position:0%
+resembles closely one of your uh
+ 
+
+ align:start position:0%
+resembles closely one of your uh
+trigonometric identities that that you
+
+ align:start position:0%
+trigonometric identities that that you
+ 
+
+ align:start position:0%
+trigonometric identities that that you
+know about um so in particular to make
+
+ align:start position:0%
+know about um so in particular to make
+ 
+
+ align:start position:0%
+know about um so in particular to make
+it resemble it even more I can multiply
+
+ align:start position:0%
+it resemble it even more I can multiply
+ 
+
+ align:start position:0%
+it resemble it even more I can multiply
+and divide by two so I can rewrite h ofx
+
+ align:start position:0%
+and divide by two so I can rewrite h ofx
+ 
+
+ align:start position:0%
+and divide by two so I can rewrite h ofx
+= 2
+
+ align:start position:0%
+= 2
+ 
+
+ align:start position:0%
+= 2
+* 12
+
+ align:start position:0%
+* 12
+ 
+
+ align:start position:0%
+* 12
+sinx + < TK 3 /
+
+ align:start position:0%
+sinx + < TK 3 /
+ 
+
+ align:start position:0%
+sinx + < TK 3 /
+2 * cosine X and now 12 is equal to cine
+
+ align:start position:0%
+2 * cosine X and now 12 is equal to cine
+ 
+
+ align:start position:0%
+2 * cosine X and now 12 is equal to cine
+of pi/ 3 and square 32 is equal to S of
+
+ align:start position:0%
+of pi/ 3 and square 32 is equal to S of
+ 
+
+ align:start position:0%
+of pi/ 3 and square 32 is equal to S of
+pi over 3 so I can rewrite this as 2
+
+ align:start position:0%
+pi over 3 so I can rewrite this as 2
+ 
+
+ align:start position:0%
+pi over 3 so I can rewrite this as 2
+* what did I say I said cosine pi over
+
+ align:start position:0%
+* what did I say I said cosine pi over
+ 
+
+ align:start position:0%
+* what did I say I said cosine pi over
+3 sin x plus sin pi over 3 cosine X and
+
+ align:start position:0%
+3 sin x plus sin pi over 3 cosine X and
+ 
+
+ align:start position:0%
+3 sin x plus sin pi over 3 cosine X and
+this is exactly what you get when you do
+
+ align:start position:0%
+this is exactly what you get when you do
+ 
+
+ align:start position:0%
+this is exactly what you get when you do
+the angle addition formula for S um this
+
+ align:start position:0%
+the angle addition formula for S um this
+ 
+
+ align:start position:0%
+the angle addition formula for S um this
+is the expanded out form and so we can
+
+ align:start position:0%
+is the expanded out form and so we can
+ 
+
+ align:start position:0%
+is the expanded out form and so we can
+apply it in reverse and get that this is
+
+ align:start position:0%
+apply it in reverse and get that this is
+ 
+
+ align:start position:0%
+apply it in reverse and get that this is
+equal to 2 * s
+
+ align:start position:0%
+equal to 2 * s
+ 
+
+ align:start position:0%
+equal to 2 * s
+of x
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
++ pi over 3 so so far we haven't done
+
+ align:start position:0%
++ pi over 3 so so far we haven't done
+ 
+
+ align:start position:0%
++ pi over 3 so so far we haven't done
+any calculus we've just done so so in
+
+ align:start position:0%
+any calculus we've just done so so in
+ 
+
+ align:start position:0%
+any calculus we've just done so so in
+this solution our first solution we did
+
+ align:start position:0%
+this solution our first solution we did
+ 
+
+ align:start position:0%
+this solution our first solution we did
+some calculus first and then some
+
+ align:start position:0%
+some calculus first and then some
+ 
+
+ align:start position:0%
+some calculus first and then some
+algebra and trigonometry so so far we've
+
+ align:start position:0%
+algebra and trigonometry so so far we've
+ 
+
+ align:start position:0%
+algebra and trigonometry so so far we've
+just done some algebra and trigonometry
+
+ align:start position:0%
+just done some algebra and trigonometry
+ 
+
+ align:start position:0%
+just done some algebra and trigonometry
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+now the points where H Prime of X is
+
+ align:start position:0%
+now the points where H Prime of X is
+ 
+
+ align:start position:0%
+now the points where H Prime of X is
+equal to zero are the points where the
+
+ align:start position:0%
+equal to zero are the points where the
+ 
+
+ align:start position:0%
+equal to zero are the points where the
+graph of this function has a horizontal
+
+ align:start position:0%
+graph of this function has a horizontal
+ 
+
+ align:start position:0%
+graph of this function has a horizontal
+tangent line so either you can compute
+
+ align:start position:0%
+tangent line so either you can compute
+ 
+
+ align:start position:0%
+tangent line so either you can compute
+its derivative using your your rules or
+
+ align:start position:0%
+its derivative using your your rules or
+ 
+
+ align:start position:0%
+its derivative using your your rules or
+by the definition or you can just say oh
+
+ align:start position:0%
+by the definition or you can just say oh
+ 
+
+ align:start position:0%
+by the definition or you can just say oh
+we know what this graph looks like so
+
+ align:start position:0%
+we know what this graph looks like so
+ 
+
+ align:start position:0%
+we know what this graph looks like so
+I've I've sort of drawn a schematic up
+
+ align:start position:0%
+I've I've sort of drawn a schematic up
+ 
+
+ align:start position:0%
+I've I've sort of drawn a schematic up
+here so this is a graph this is this
+
+ align:start position:0%
+here so this is a graph this is this
+ 
+
+ align:start position:0%
+here so this is a graph this is this
+graph is okay so this is the graph y =
+
+ align:start position:0%
+graph is okay so this is the graph y =
+ 
+
+ align:start position:0%
+graph is okay so this is the graph y =
+2 sin of x + pi over 3 it's what you get
+
+ align:start position:0%
+2 sin of x + pi over 3 it's what you get
+ 
+
+ align:start position:0%
+2 sin of x + pi over 3 it's what you get
+if you take the graph yal sinx and you
+
+ align:start position:0%
+if you take the graph yal sinx and you
+ 
+
+ align:start position:0%
+if you take the graph yal sinx and you
+shift it left by pi over 3 and you you
+
+ align:start position:0%
+shift it left by pi over 3 and you you
+ 
+
+ align:start position:0%
+shift it left by pi over 3 and you you
+scale it up by a factor of two so this
+
+ align:start position:0%
+scale it up by a factor of two so this
+ 
+
+ align:start position:0%
+scale it up by a factor of two so this
+this here is at x = minus pi over 3 this
+
+ align:start position:0%
+this here is at x = minus pi over 3 this
+ 
+
+ align:start position:0%
+this here is at x = minus pi over 3 this
+root is x = 2 pi over 3 um and the
+
+ align:start position:0%
+root is x = 2 pi over 3 um and the
+ 
+
+ align:start position:0%
+root is x = 2 pi over 3 um and the
+points we're interested in are the
+
+ align:start position:0%
+points we're interested in are the
+ 
+
+ align:start position:0%
+points we're interested in are the
+points where there's a horizontal
+
+ align:start position:0%
+points where there's a horizontal
+ 
+
+ align:start position:0%
+points where there's a horizontal
+tangent line where the derivative is
+
+ align:start position:0%
+tangent line where the derivative is
+ 
+
+ align:start position:0%
+tangent line where the derivative is
+zero and so there's one of these right
+
+ align:start position:0%
+zero and so there's one of these right
+ 
+
+ align:start position:0%
+zero and so there's one of these right
+at this value which is pi over 6 and
+
+ align:start position:0%
+at this value which is pi over 6 and
+ 
+
+ align:start position:0%
+at this value which is pi over 6 and
+then the second one is this is that
+
+ align:start position:0%
+then the second one is this is that
+ 
+
+ align:start position:0%
+then the second one is this is that
+minimum there so that happens at x = 7
+
+ align:start position:0%
+minimum there so that happens at x = 7
+ 
+
+ align:start position:0%
+minimum there so that happens at x = 7
+piun 6 Pi 6 because for the usual sign
+
+ align:start position:0%
+piun 6 Pi 6 because for the usual sign
+ 
+
+ align:start position:0%
+piun 6 Pi 6 because for the usual sign
+function it happens at pi over 2 but we
+
+ align:start position:0%
+function it happens at pi over 2 but we
+ 
+
+ align:start position:0%
+function it happens at pi over 2 but we
+shifted everything left by pi over 3 and
+
+ align:start position:0%
+shifted everything left by pi over 3 and
+ 
+
+ align:start position:0%
+shifted everything left by pi over 3 and
+so pi over 2 minus pi over 3 is pi over
+
+ align:start position:0%
+so pi over 2 minus pi over 3 is pi over
+ 
+
+ align:start position:0%
+so pi over 2 minus pi over 3 is pi over
+6 and here for for this for just yals
+
+ align:start position:0%
+6 and here for for this for just yals
+ 
+
+ align:start position:0%
+6 and here for for this for just yals
+sinx this minimum would happen at 3 pi
+
+ align:start position:0%
+sinx this minimum would happen at 3 pi
+ 
+
+ align:start position:0%
+sinx this minimum would happen at 3 pi
+over 2 but we've shifted it left by pi
+
+ align:start position:0%
+over 2 but we've shifted it left by pi
+ 
+
+ align:start position:0%
+over 2 but we've shifted it left by pi
+over 3 um and so on you know every every
+
+ align:start position:0%
+over 3 um and so on you know every every
+ 
+
+ align:start position:0%
+over 3 um and so on you know every every
+there's a there's another trough over
+
+ align:start position:0%
+there's a there's another trough over
+ 
+
+ align:start position:0%
+there's a there's another trough over
+here and another Peak over there and and
+
+ align:start position:0%
+here and another Peak over there and and
+ 
+
+ align:start position:0%
+here and another Peak over there and and
+so on um so that's the the second way
+
+ align:start position:0%
+so on um so that's the the second way
+ 
+
+ align:start position:0%
+so on um so that's the the second way
+you can do this question um using this
+
+ align:start position:0%
+you can do this question um using this
+ 
+
+ align:start position:0%
+you can do this question um using this
+this cute trig identity here and that's
+
+ align:start position:0%
+this cute trig identity here and that's
+ 
+
+ align:start position:0%
+this cute trig identity here and that's
+that
\ No newline at end of file
diff --git a/CCoTAyZ14XM.txt b/CCoTAyZ14XM.txt
new file mode 100644
index 0000000000000000000000000000000000000000..9df3487ea1f0ac06e8b251f426344ab50d412ee9
--- /dev/null
+++ b/CCoTAyZ14XM.txt
@@ -0,0 +1,2152 @@
+align:start position:0%
+ 
+hi welcome back to recitation in lecture
+
+ align:start position:0%
+hi welcome back to recitation in lecture
+ 
+
+ align:start position:0%
+hi welcome back to recitation in lecture
+you've been learning about flux and
+
+ align:start position:0%
+you've been learning about flux and
+ 
+
+ align:start position:0%
+you've been learning about flux and
+surface integrals in the Divergence
+
+ align:start position:0%
+surface integrals in the Divergence
+ 
+
+ align:start position:0%
+surface integrals in the Divergence
+Theorem and I have a nice problem about
+
+ align:start position:0%
+Theorem and I have a nice problem about
+ 
+
+ align:start position:0%
+Theorem and I have a nice problem about
+that for you here so I've got this field
+
+ align:start position:0%
+that for you here so I've got this field
+ 
+
+ align:start position:0%
+that for you here so I've got this field
+F it's a little bit ugly right all right
+
+ align:start position:0%
+F it's a little bit ugly right all right
+ 
+
+ align:start position:0%
+F it's a little bit ugly right all right
+so it's its coordinates are X to 4 y -
+
+ align:start position:0%
+so it's its coordinates are X to 4 y -
+ 
+
+ align:start position:0%
+so it's its coordinates are X to 4 y -
+2x Cub y^ 2 and z^ squ and it's passing
+
+ align:start position:0%
+2x Cub y^ 2 and z^ squ and it's passing
+ 
+
+ align:start position:0%
+2x Cub y^ 2 and z^ squ and it's passing
+through the surface of a solid that's
+
+ align:start position:0%
+through the surface of a solid that's
+ 
+
+ align:start position:0%
+through the surface of a solid that's
+bounded by the plane Z equals z by the
+
+ align:start position:0%
+bounded by the plane Z equals z by the
+ 
+
+ align:start position:0%
+bounded by the plane Z equals z by the
+plane zal H and by the by the surface
+
+ align:start position:0%
+plane zal H and by the by the surface
+ 
+
+ align:start position:0%
+plane zal H and by the by the surface
+x^2 + y^2 = R2 so often we call this
+
+ align:start position:0%
+x^2 + y^2 = R2 so often we call this
+ 
+
+ align:start position:0%
+x^2 + y^2 = R2 so often we call this
+solid a cylinder um so it's got its
+
+ align:start position:0%
+solid a cylinder um so it's got its
+ 
+
+ align:start position:0%
+solid a cylinder um so it's got its
+bottom surface in the plane Z equals z
+
+ align:start position:0%
+bottom surface in the plane Z equals z
+ 
+
+ align:start position:0%
+bottom surface in the plane Z equals z
+and its top surface in the plane Z
+
+ align:start position:0%
+and its top surface in the plane Z
+ 
+
+ align:start position:0%
+and its top surface in the plane Z
+equals H and it's got a circular base
+
+ align:start position:0%
+equals H and it's got a circular base
+ 
+
+ align:start position:0%
+equals H and it's got a circular base
+with radius R there um so what I'd like
+
+ align:start position:0%
+with radius R there um so what I'd like
+ 
+
+ align:start position:0%
+with radius R there um so what I'd like
+you to do is to compute the flux of this
+
+ align:start position:0%
+you to do is to compute the flux of this
+ 
+
+ align:start position:0%
+you to do is to compute the flux of this
+field F through this through this
+
+ align:start position:0%
+field F through this through this
+ 
+
+ align:start position:0%
+field F through this through this
+cylinder um so I'll I'll point out
+
+ align:start position:0%
+cylinder um so I'll I'll point out
+ 
+
+ align:start position:0%
+cylinder um so I'll I'll point out
+before I before I let you at it that
+
+ align:start position:0%
+before I before I let you at it that
+ 
+
+ align:start position:0%
+before I before I let you at it that
+that this is you know to compute this as
+
+ align:start position:0%
+that this is you know to compute this as
+ 
+
+ align:start position:0%
+that this is you know to compute this as
+a surface integral you could do it you
+
+ align:start position:0%
+a surface integral you could do it you
+ 
+
+ align:start position:0%
+a surface integral you could do it you
+could do it if you really want an
+
+ align:start position:0%
+could do it if you really want an
+ 
+
+ align:start position:0%
+could do it if you really want an
+exercise in nasty arithmetic I invite
+
+ align:start position:0%
+exercise in nasty arithmetic I invite
+ 
+
+ align:start position:0%
+exercise in nasty arithmetic I invite
+you to do it but you might be able to
+
+ align:start position:0%
+you to do it but you might be able to
+ 
+
+ align:start position:0%
+you to do it but you might be able to
+think of a of a way to do this that
+
+ align:start position:0%
+think of a of a way to do this that
+ 
+
+ align:start position:0%
+think of a of a way to do this that
+requires less effort than than
+
+ align:start position:0%
+requires less effort than than
+ 
+
+ align:start position:0%
+requires less effort than than
+parameterizing the three surfaces and
+
+ align:start position:0%
+parameterizing the three surfaces and
+ 
+
+ align:start position:0%
+parameterizing the three surfaces and
+integrating and so on so I'll leave with
+
+ align:start position:0%
+integrating and so on so I'll leave with
+ 
+
+ align:start position:0%
+integrating and so on so I'll leave with
+that why don't you pause the video um
+
+ align:start position:0%
+that why don't you pause the video um
+ 
+
+ align:start position:0%
+that why don't you pause the video um
+work this one out come back and we can
+
+ align:start position:0%
+work this one out come back and we can
+ 
+
+ align:start position:0%
+work this one out come back and we can
+work on it
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+together hopefully you had some luck
+
+ align:start position:0%
+together hopefully you had some luck
+ 
+
+ align:start position:0%
+together hopefully you had some luck
+working on this problem right before I
+
+ align:start position:0%
+working on this problem right before I
+ 
+
+ align:start position:0%
+working on this problem right before I
+left I mentioned that you were Computing
+
+ align:start position:0%
+left I mentioned that you were Computing
+ 
+
+ align:start position:0%
+left I mentioned that you were Computing
+a flux uh through a through a surface
+
+ align:start position:0%
+a flux uh through a through a surface
+ 
+
+ align:start position:0%
+a flux uh through a through a surface
+here but that doing it as a surface
+
+ align:start position:0%
+here but that doing it as a surface
+ 
+
+ align:start position:0%
+here but that doing it as a surface
+integral was maybe not the best way to
+
+ align:start position:0%
+integral was maybe not the best way to
+ 
+
+ align:start position:0%
+integral was maybe not the best way to
+go and so you know even without that
+
+ align:start position:0%
+go and so you know even without that
+ 
+
+ align:start position:0%
+go and so you know even without that
+hint probably many of you realize that
+
+ align:start position:0%
+hint probably many of you realize that
+ 
+
+ align:start position:0%
+hint probably many of you realize that
+really the way that we want to go about
+
+ align:start position:0%
+really the way that we want to go about
+ 
+
+ align:start position:0%
+really the way that we want to go about
+this problem is with the Divergence
+
+ align:start position:0%
+this problem is with the Divergence
+ 
+
+ align:start position:0%
+this problem is with the Divergence
+Theorem okay so the Divergence Theorem
+
+ align:start position:0%
+Theorem okay so the Divergence Theorem
+ 
+
+ align:start position:0%
+Theorem okay so the Divergence Theorem
+says
+
+ align:start position:0%
+says
+ 
+
+ align:start position:0%
+says
+that in our case the Divergence Theorem
+
+ align:start position:0%
+that in our case the Divergence Theorem
+ 
+
+ align:start position:0%
+that in our case the Divergence Theorem
+I'm just abbreviating it div THM here
+
+ align:start position:0%
+I'm just abbreviating it div THM here
+ 
+
+ align:start position:0%
+I'm just abbreviating it div THM here
+says that the that the double integral
+
+ align:start position:0%
+says that the that the double integral
+ 
+
+ align:start position:0%
+says that the that the double integral
+over the surface of f Dot
+
+ align:start position:0%
+over the surface of f Dot
+ 
+
+ align:start position:0%
+over the surface of f Dot
+N D surface area so that's the so s here
+
+ align:start position:0%
+N D surface area so that's the so s here
+ 
+
+ align:start position:0%
+N D surface area so that's the so s here
+is the surface of this solid um so the
+
+ align:start position:0%
+is the surface of this solid um so the
+ 
+
+ align:start position:0%
+is the surface of this solid um so the
+Divergence Theorem says that this that
+
+ align:start position:0%
+Divergence Theorem says that this that
+ 
+
+ align:start position:0%
+Divergence Theorem says that this that
+this double integral which is or this
+
+ align:start position:0%
+this double integral which is or this
+ 
+
+ align:start position:0%
+this double integral which is or this
+surface integral rather which is the
+
+ align:start position:0%
+surface integral rather which is the
+ 
+
+ align:start position:0%
+surface integral rather which is the
+flux that we're interested in is equal
+
+ align:start position:0%
+flux that we're interested in is equal
+ 
+
+ align:start position:0%
+flux that we're interested in is equal
+to the triple integral over the solid
+
+ align:start position:0%
+to the triple integral over the solid
+ 
+
+ align:start position:0%
+to the triple integral over the solid
+region D so that's bounded by the
+
+ align:start position:0%
+region D so that's bounded by the
+ 
+
+ align:start position:0%
+region D so that's bounded by the
+surface so that's the solid cylinder
+
+ align:start position:0%
+surface so that's the solid cylinder
+ 
+
+ align:start position:0%
+surface so that's the solid cylinder
+here is equal to the triple integral
+
+ align:start position:0%
+here is equal to the triple integral
+ 
+
+ align:start position:0%
+here is equal to the triple integral
+over D
+
+ align:start position:0%
+over D
+ 
+
+ align:start position:0%
+over D
+of div F
+
+ align:start position:0%
+of div F
+ 
+
+ align:start position:0%
+of div F
+DV okay
+
+ align:start position:0%
+DV okay
+ 
+
+ align:start position:0%
+DV okay
+so in our case this is nice because in
+
+ align:start position:0%
+so in our case this is nice because in
+ 
+
+ align:start position:0%
+so in our case this is nice because in
+fact this solid region D is an easier to
+
+ align:start position:0%
+fact this solid region D is an easier to
+ 
+
+ align:start position:0%
+fact this solid region D is an easier to
+understand or easy to easier to Grapple
+
+ align:start position:0%
+understand or easy to easier to Grapple
+ 
+
+ align:start position:0%
+understand or easy to easier to Grapple
+with region than than the surface that
+
+ align:start position:0%
+with region than than the surface that
+ 
+
+ align:start position:0%
+with region than than the surface that
+we started with right it's it's just one
+
+ align:start position:0%
+we started with right it's it's just one
+ 
+
+ align:start position:0%
+we started with right it's it's just one
+solid piece whereas that's easy to
+
+ align:start position:0%
+solid piece whereas that's easy to
+ 
+
+ align:start position:0%
+solid piece whereas that's easy to
+parameterize in fact you know that's
+
+ align:start position:0%
+parameterize in fact you know that's
+ 
+
+ align:start position:0%
+parameterize in fact you know that's
+easy to describe in in especially in
+
+ align:start position:0%
+easy to describe in in especially in
+ 
+
+ align:start position:0%
+easy to describe in in especially in
+cylindrical coordinates but also in
+
+ align:start position:0%
+cylindrical coordinates but also in
+ 
+
+ align:start position:0%
+cylindrical coordinates but also in
+rectangular coordinates um whereas the
+
+ align:start position:0%
+rectangular coordinates um whereas the
+ 
+
+ align:start position:0%
+rectangular coordinates um whereas the
+surface s if we wanted to talk about it
+
+ align:start position:0%
+surface s if we wanted to talk about it
+ 
+
+ align:start position:0%
+surface s if we wanted to talk about it
+we need to split it up into three pieces
+
+ align:start position:0%
+we need to split it up into three pieces
+ 
+
+ align:start position:0%
+we need to split it up into three pieces
+and we'd need to parameterize it and
+
+ align:start position:0%
+and we'd need to parameterize it and
+ 
+
+ align:start position:0%
+and we'd need to parameterize it and
+that's kind of a hassle relatively
+
+ align:start position:0%
+that's kind of a hassle relatively
+ 
+
+ align:start position:0%
+that's kind of a hassle relatively
+speaking um also the Divergence of this
+
+ align:start position:0%
+speaking um also the Divergence of this
+ 
+
+ align:start position:0%
+speaking um also the Divergence of this
+field f is is a lot simpler than the
+
+ align:start position:0%
+field f is is a lot simpler than the
+ 
+
+ align:start position:0%
+field f is is a lot simpler than the
+field itself if you if we go and look at
+
+ align:start position:0%
+field itself if you if we go and look at
+ 
+
+ align:start position:0%
+field itself if you if we go and look at
+this field right this is a field all all
+
+ align:start position:0%
+this field right this is a field all all
+ 
+
+ align:start position:0%
+this field right this is a field all all
+of its components are pols um to compute
+
+ align:start position:0%
+of its components are pols um to compute
+ 
+
+ align:start position:0%
+of its components are pols um to compute
+its Divergence we take derivatives of
+
+ align:start position:0%
+its Divergence we take derivatives of
+ 
+
+ align:start position:0%
+its Divergence we take derivatives of
+all of them um and so that makes their
+
+ align:start position:0%
+all of them um and so that makes their
+ 
+
+ align:start position:0%
+all of them um and so that makes their
+degrees lower and and then we just add
+
+ align:start position:0%
+degrees lower and and then we just add
+ 
+
+ align:start position:0%
+degrees lower and and then we just add
+them it's it's a little bit life is a
+
+ align:start position:0%
+them it's it's a little bit life is a
+ 
+
+ align:start position:0%
+them it's it's a little bit life is a
+little bit simpler um so okay so so so
+
+ align:start position:0%
+little bit simpler um so okay so so so
+ 
+
+ align:start position:0%
+little bit simpler um so okay so so so
+so this process using the Divergence
+
+ align:start position:0%
+so this process using the Divergence
+ 
+
+ align:start position:0%
+so this process using the Divergence
+Theorem is going to make this this Our
+
+ align:start position:0%
+Theorem is going to make this this Our
+ 
+
+ align:start position:0%
+Theorem is going to make this this Our
+Lives easier it's going to make this
+
+ align:start position:0%
+Lives easier it's going to make this
+ 
+
+ align:start position:0%
+Lives easier it's going to make this
+kind of nasty surface integral into an
+
+ align:start position:0%
+kind of nasty surface integral into an
+ 
+
+ align:start position:0%
+kind of nasty surface integral into an
+easy to compute uh triple integral so
+
+ align:start position:0%
+easy to compute uh triple integral so
+ 
+
+ align:start position:0%
+easy to compute uh triple integral so
+let's let's see actually how it does so
+
+ align:start position:0%
+let's let's see actually how it does so
+ 
+
+ align:start position:0%
+let's let's see actually how it does so
+let's let's compute div F first um so we
+
+ align:start position:0%
+let's let's compute div F first um so we
+ 
+
+ align:start position:0%
+let's let's compute div F first um so we
+know what the integrand is so div F all
+
+ align:start position:0%
+know what the integrand is so div F all
+ 
+
+ align:start position:0%
+know what the integrand is so div F all
+right so it's so we look we need to look
+
+ align:start position:0%
+right so it's so we look we need to look
+ 
+
+ align:start position:0%
+right so it's so we look we need to look
+at the components of F and so we need to
+
+ align:start position:0%
+at the components of F and so we need to
+ 
+
+ align:start position:0%
+at the components of F and so we need to
+take the partial of the first one with
+
+ align:start position:0%
+take the partial of the first one with
+ 
+
+ align:start position:0%
+take the partial of the first one with
+respect to X so that's X to 4th y with
+
+ align:start position:0%
+respect to X so that's X to 4th y with
+ 
+
+ align:start position:0%
+respect to X so that's X to 4th y with
+respect to X so put that down over here
+
+ align:start position:0%
+respect to X so put that down over here
+ 
+
+ align:start position:0%
+respect to X so put that down over here
+that's 4 x cubed y we just treat y as a
+
+ align:start position:0%
+that's 4 x cubed y we just treat y as a
+ 
+
+ align:start position:0%
+that's 4 x cubed y we just treat y as a
+constant okay so now we come back and we
+
+ align:start position:0%
+constant okay so now we come back and we
+ 
+
+ align:start position:0%
+constant okay so now we come back and we
+need to look at the second one so it's -
+
+ align:start position:0%
+need to look at the second one so it's -
+ 
+
+ align:start position:0%
+need to look at the second one so it's -
+2x Cub y^ 2 and it's the second one we
+
+ align:start position:0%
+2x Cub y^ 2 and it's the second one we
+ 
+
+ align:start position:0%
+2x Cub y^ 2 and it's the second one we
+take it's partial with respect to Y so
+
+ align:start position:0%
+take it's partial with respect to Y so
+ 
+
+ align:start position:0%
+take it's partial with respect to Y so
+okay so that's going to be - 2x Cub * 2
+
+ align:start position:0%
+okay so that's going to be - 2x Cub * 2
+ 
+
+ align:start position:0%
+okay so that's going to be - 2x Cub * 2
+y so that's going to be Min
+
+ align:start position:0%
+y so that's going to be Min
+ 
+
+ align:start position:0%
+y so that's going to be Min
+-4 x cubed Y and then the last okay so
+
+ align:start position:0%
+-4 x cubed Y and then the last okay so
+ 
+
+ align:start position:0%
+-4 x cubed Y and then the last okay so
+then we come back and we look at the
+
+ align:start position:0%
+then we come back and we look at the
+ 
+
+ align:start position:0%
+then we come back and we look at the
+last component and that's z^ 2 and so we
+
+ align:start position:0%
+last component and that's z^ 2 and so we
+ 
+
+ align:start position:0%
+last component and that's z^ 2 and so we
+need to take its partial with respect to
+
+ align:start position:0%
+need to take its partial with respect to
+ 
+
+ align:start position:0%
+need to take its partial with respect to
+Z so in this case that's just 2 Z and so
+
+ align:start position:0%
+Z so in this case that's just 2 Z and so
+ 
+
+ align:start position:0%
+Z so in this case that's just 2 Z and so
+we add that on as well plus 2 Z and in
+
+ align:start position:0%
+we add that on as well plus 2 Z and in
+ 
+
+ align:start position:0%
+we add that on as well plus 2 Z and in
+this case not only are these polinomial
+
+ align:start position:0%
+this case not only are these polinomial
+ 
+
+ align:start position:0%
+this case not only are these polinomial
+simpler than the than the coordinates of
+
+ align:start position:0%
+simpler than the than the coordinates of
+ 
+
+ align:start position:0%
+simpler than the than the coordinates of
+F that we had but in fact two of them
+
+ align:start position:0%
+F that we had but in fact two of them
+ 
+
+ align:start position:0%
+F that we had but in fact two of them
+you know there's we've got some
+
+ align:start position:0%
+you know there's we've got some
+ 
+
+ align:start position:0%
+you know there's we've got some
+simplification here life it it gets
+
+ align:start position:0%
+simplification here life it it gets
+ 
+
+ align:start position:0%
+simplification here life it it gets
+really really simple so so in fact this
+
+ align:start position:0%
+really really simple so so in fact this
+ 
+
+ align:start position:0%
+really really simple so so in fact this
+is just going to work out to 2 Z so the
+
+ align:start position:0%
+is just going to work out to 2 Z so the
+ 
+
+ align:start position:0%
+is just going to work out to 2 Z so the
+Divergence here is is very simple
+
+ align:start position:0%
+Divergence here is is very simple
+ 
+
+ align:start position:0%
+Divergence here is is very simple
+compared with the function f more simple
+
+ align:start position:0%
+compared with the function f more simple
+ 
+
+ align:start position:0%
+compared with the function f more simple
+than we sort of have a right to expect
+
+ align:start position:0%
+than we sort of have a right to expect
+ 
+
+ align:start position:0%
+than we sort of have a right to expect
+but but in any case good it's nice to
+
+ align:start position:0%
+but but in any case good it's nice to
+ 
+
+ align:start position:0%
+but but in any case good it's nice to
+work with um okay so that's the
+
+ align:start position:0%
+work with um okay so that's the
+ 
+
+ align:start position:0%
+work with um okay so that's the
+Divergence uh so now so the thing that I
+
+ align:start position:0%
+Divergence uh so now so the thing that I
+ 
+
+ align:start position:0%
+Divergence uh so now so the thing that I
+want so I'm going to I'm going to write
+
+ align:start position:0%
+want so I'm going to I'm going to write
+ 
+
+ align:start position:0%
+want so I'm going to I'm going to write
+this is the flux these integrals that
+
+ align:start position:0%
+this is the flux these integrals that
+ 
+
+ align:start position:0%
+this is the flux these integrals that
+we're interested in this this surface
+
+ align:start position:0%
+we're interested in this this surface
+ 
+
+ align:start position:0%
+we're interested in this this surface
+integral and then by the Divergence
+
+ align:start position:0%
+integral and then by the Divergence
+ 
+
+ align:start position:0%
+integral and then by the Divergence
+Theorem that's the same as this triple
+
+ align:start position:0%
+Theorem that's the same as this triple
+ 
+
+ align:start position:0%
+Theorem that's the same as this triple
+integral okay so the Divergence is this
+
+ align:start position:0%
+integral okay so the Divergence is this
+ 
+
+ align:start position:0%
+integral okay so the Divergence is this
+2 Z so the flux is what I get when I
+
+ align:start position:0%
+2 Z so the flux is what I get when I
+ 
+
+ align:start position:0%
+2 Z so the flux is what I get when I
+just put that in here so
+
+ align:start position:0%
+just put that in here so
+ 
+
+ align:start position:0%
+just put that in here so
+flux is equal to so it's equal to the
+
+ align:start position:0%
+flux is equal to so it's equal to the
+ 
+
+ align:start position:0%
+flux is equal to so it's equal to the
+triple
+
+ align:start position:0%
+triple
+ 
+
+ align:start position:0%
+triple
+integral over our solid of of 2 Z DV
+
+ align:start position:0%
+integral over our solid of of 2 Z DV
+ 
+
+ align:start position:0%
+integral over our solid of of 2 Z DV
+okay so I've I've left some stuff out of
+
+ align:start position:0%
+okay so I've I've left some stuff out of
+ 
+
+ align:start position:0%
+okay so I've I've left some stuff out of
+this and so because I'm going to start
+
+ align:start position:0%
+this and so because I'm going to start
+ 
+
+ align:start position:0%
+this and so because I'm going to start
+I'm going to start
+
+ align:start position:0%
+I'm going to start
+ 
+
+ align:start position:0%
+I'm going to start
+writing down the bounds and writing this
+
+ align:start position:0%
+writing down the bounds and writing this
+ 
+
+ align:start position:0%
+writing down the bounds and writing this
+down as an iterated integral now um okay
+
+ align:start position:0%
+down as an iterated integral now um okay
+ 
+
+ align:start position:0%
+down as an iterated integral now um okay
+so we so we have to choose some some
+
+ align:start position:0%
+so we so we have to choose some some
+ 
+
+ align:start position:0%
+so we so we have to choose some some
+coordinate system in which to to
+
+ align:start position:0%
+coordinate system in which to to
+ 
+
+ align:start position:0%
+coordinate system in which to to
+integrate over this solid and so there
+
+ align:start position:0%
+integrate over this solid and so there
+ 
+
+ align:start position:0%
+integrate over this solid and so there
+are you know we have we have three kind
+
+ align:start position:0%
+are you know we have we have three kind
+ 
+
+ align:start position:0%
+are you know we have we have three kind
+of natural choices that we always look
+
+ align:start position:0%
+of natural choices that we always look
+ 
+
+ align:start position:0%
+of natural choices that we always look
+back to there's rectangular coordinates
+
+ align:start position:0%
+back to there's rectangular coordinates
+ 
+
+ align:start position:0%
+back to there's rectangular coordinates
+and cylindrical coordinates and
+
+ align:start position:0%
+and cylindrical coordinates and
+ 
+
+ align:start position:0%
+and cylindrical coordinates and
+spherical coordinates so spherical
+
+ align:start position:0%
+spherical coordinates so spherical
+ 
+
+ align:start position:0%
+spherical coordinates so spherical
+coordinates seems pretty clearly
+
+ align:start position:0%
+coordinates seems pretty clearly
+ 
+
+ align:start position:0%
+coordinates seems pretty clearly
+inappropriate rectangular and
+
+ align:start position:0%
+inappropriate rectangular and
+ 
+
+ align:start position:0%
+inappropriate rectangular and
+cylindrical you know you could try and
+
+ align:start position:0%
+cylindrical you know you could try and
+ 
+
+ align:start position:0%
+cylindrical you know you could try and
+do it in rectangular
+
+ align:start position:0%
+do it in rectangular
+ 
+
+ align:start position:0%
+do it in rectangular
+that's not it's not horrible but this is
+
+ align:start position:0%
+that's not it's not horrible but this is
+ 
+
+ align:start position:0%
+that's not it's not horrible but this is
+a cylinder right I mean it it's crying
+
+ align:start position:0%
+a cylinder right I mean it it's crying
+ 
+
+ align:start position:0%
+a cylinder right I mean it it's crying
+out for us to use cylindrical
+
+ align:start position:0%
+out for us to use cylindrical
+ 
+
+ align:start position:0%
+out for us to use cylindrical
+coordinates so so let's use cylindrical
+
+ align:start position:0%
+coordinates so so let's use cylindrical
+ 
+
+ align:start position:0%
+coordinates so so let's use cylindrical
+coordinates so if we're going to use
+
+ align:start position:0%
+coordinates so if we're going to use
+ 
+
+ align:start position:0%
+coordinates so if we're going to use
+cylindrical coordinates what we get here
+
+ align:start position:0%
+cylindrical coordinates what we get here
+ 
+
+ align:start position:0%
+cylindrical coordinates what we get here
+for DV so we we need a z an r and a
+
+ align:start position:0%
+for DV so we we need a z an r and a
+ 
+
+ align:start position:0%
+for DV so we we need a z an r and a
+Theta but but remember there's this
+
+ align:start position:0%
+Theta but but remember there's this
+ 
+
+ align:start position:0%
+Theta but but remember there's this
+extra factor of R so it's going to be 2z
+
+ align:start position:0%
+extra factor of R so it's going to be 2z
+ 
+
+ align:start position:0%
+extra factor of R so it's going to be 2z
+times okay so it's R DZ Dr D Theta right
+
+ align:start position:0%
+times okay so it's R DZ Dr D Theta right
+ 
+
+ align:start position:0%
+times okay so it's R DZ Dr D Theta right
+this is DV this R DZ d d Theta
+
+ align:start position:0%
+this is DV this R DZ d d Theta
+ 
+
+ align:start position:0%
+this is DV this R DZ d d Theta
+part so that's what DV is when we use
+
+ align:start position:0%
+part so that's what DV is when we use
+ 
+
+ align:start position:0%
+part so that's what DV is when we use
+cylindrical coordinates okay so now
+
+ align:start position:0%
+cylindrical coordinates okay so now
+ 
+
+ align:start position:0%
+cylindrical coordinates okay so now
+let's uh let's figure out what the
+
+ align:start position:0%
+let's uh let's figure out what the
+ 
+
+ align:start position:0%
+let's uh let's figure out what the
+bounds are so let's go look at this
+
+ align:start position:0%
+bounds are so let's go look at this
+ 
+
+ align:start position:0%
+bounds are so let's go look at this
+cylinder that we had over here um so
+
+ align:start position:0%
+cylinder that we had over here um so
+ 
+
+ align:start position:0%
+cylinder that we had over here um so
+let's see so it's got so it's bounded
+
+ align:start position:0%
+let's see so it's got so it's bounded
+ 
+
+ align:start position:0%
+let's see so it's got so it's bounded
+between Z equals z the bottom surface
+
+ align:start position:0%
+between Z equals z the bottom surface
+ 
+
+ align:start position:0%
+between Z equals z the bottom surface
+and Z equals H the top surface okay well
+
+ align:start position:0%
+and Z equals H the top surface okay well
+ 
+
+ align:start position:0%
+and Z equals H the top surface okay well
+that's so that's easy enough that's
+
+ align:start position:0%
+that's so that's easy enough that's
+ 
+
+ align:start position:0%
+that's so that's easy enough that's
+that's what the bounds on ZR so okay so
+
+ align:start position:0%
+that's what the bounds on ZR so okay so
+ 
+
+ align:start position:0%
+that's what the bounds on ZR so okay so
+let's put those in so Z that's the
+
+ align:start position:0%
+let's put those in so Z that's the
+ 
+
+ align:start position:0%
+let's put those in so Z that's the
+innermost one so that's going from 0 to
+
+ align:start position:0%
+innermost one so that's going from 0 to
+ 
+
+ align:start position:0%
+innermost one so that's going from 0 to
+H okay how about the next one so the
+
+ align:start position:0%
+H okay how about the next one so the
+ 
+
+ align:start position:0%
+H okay how about the next one so the
+next one is R so let's go back over here
+
+ align:start position:0%
+next one is R so let's go back over here
+ 
+
+ align:start position:0%
+next one is R so let's go back over here
+so R um is the is the radius here after
+
+ align:start position:0%
+so R um is the is the radius here after
+ 
+
+ align:start position:0%
+so R um is the is the radius here after
+we you know we we project it down um we
+
+ align:start position:0%
+we you know we we project it down um we
+ 
+
+ align:start position:0%
+we you know we we project it down um we
+just get this circle of radius Big R
+
+ align:start position:0%
+just get this circle of radius Big R
+ 
+
+ align:start position:0%
+just get this circle of radius Big R
+centered at the origin so little r is
+
+ align:start position:0%
+centered at the origin so little r is
+ 
+
+ align:start position:0%
+centered at the origin so little r is
+going from zero to Big R and Theta is
+
+ align:start position:0%
+going from zero to Big R and Theta is
+ 
+
+ align:start position:0%
+going from zero to Big R and Theta is
+going you know it's the circle it's the
+
+ align:start position:0%
+going you know it's the circle it's the
+ 
+
+ align:start position:0%
+going you know it's the circle it's the
+whole circle so Theta is going from 0 to
+
+ align:start position:0%
+whole circle so Theta is going from 0 to
+ 
+
+ align:start position:0%
+whole circle so Theta is going from 0 to
+2 pi so okay so cylinders really easy to
+
+ align:start position:0%
+2 pi so okay so cylinders really easy to
+ 
+
+ align:start position:0%
+2 pi so okay so cylinders really easy to
+describe what they look like in
+
+ align:start position:0%
+describe what they look like in
+ 
+
+ align:start position:0%
+describe what they look like in
+cylindrical coordinates so let's put
+
+ align:start position:0%
+cylindrical coordinates so let's put
+ 
+
+ align:start position:0%
+cylindrical coordinates so let's put
+those in so little r is going from0 to
+
+ align:start position:0%
+those in so little r is going from0 to
+ 
+
+ align:start position:0%
+those in so little r is going from0 to
+Big R and Theta is going from zero to 2
+
+ align:start position:0%
+Big R and Theta is going from zero to 2
+ 
+
+ align:start position:0%
+Big R and Theta is going from zero to 2
+pi 2
+
+ align:start position:0%
+pi 2
+ 
+
+ align:start position:0%
+pi 2
+pi okay wonderful now we just have to
+
+ align:start position:0%
+pi okay wonderful now we just have to
+ 
+
+ align:start position:0%
+pi okay wonderful now we just have to
+compute this right I mean we've got it
+
+ align:start position:0%
+compute this right I mean we've got it
+ 
+
+ align:start position:0%
+compute this right I mean we've got it
+we've got our flux is this triple
+
+ align:start position:0%
+we've got our flux is this triple
+ 
+
+ align:start position:0%
+we've got our flux is this triple
+integral so let's compute it let's let's
+
+ align:start position:0%
+integral so let's compute it let's let's
+ 
+
+ align:start position:0%
+integral so let's compute it let's let's
+walk over to this little bit of empty
+
+ align:start position:0%
+walk over to this little bit of empty
+ 
+
+ align:start position:0%
+walk over to this little bit of empty
+board space so okay so we have an
+
+ align:start position:0%
+board space so okay so we have an
+ 
+
+ align:start position:0%
+board space so okay so we have an
+iterated integral so we do it let's do
+
+ align:start position:0%
+iterated integral so we do it let's do
+ 
+
+ align:start position:0%
+iterated integral so we do it let's do
+it so the inner
+
+ align:start position:0%
+it so the inner
+ 
+
+ align:start position:0%
+it so the inner
+integral is the integral from0 to H of 2
+
+ align:start position:0%
+integral is the integral from0 to H of 2
+ 
+
+ align:start position:0%
+integral is the integral from0 to H of 2
+ZR DZ well that's not that bad that's
+
+ align:start position:0%
+ZR DZ well that's not that bad that's
+ 
+
+ align:start position:0%
+ZR DZ well that's not that bad that's
+equal to R is a constant so it's equal
+
+ align:start position:0%
+equal to R is a constant so it's equal
+ 
+
+ align:start position:0%
+equal to R is a constant so it's equal
+to RZ squared as Z goes between zero and
+
+ align:start position:0%
+to RZ squared as Z goes between zero and
+ 
+
+ align:start position:0%
+to RZ squared as Z goes between zero and
+H so this is a z go you know was DZ so Z
+
+ align:start position:0%
+H so this is a z go you know was DZ so Z
+ 
+
+ align:start position:0%
+H so this is a z go you know was DZ so Z
+is going from Zer to H so this is okay
+
+ align:start position:0%
+is going from Zer to H so this is okay
+ 
+
+ align:start position:0%
+is going from Zer to H so this is okay
+we plug in and we just get h^2 R minus 0
+
+ align:start position:0%
+we plug in and we just get h^2 R minus 0
+ 
+
+ align:start position:0%
+we plug in and we just get h^2 R minus 0
+so just h^2 R okay so now let's do the
+
+ align:start position:0%
+so just h^2 R okay so now let's do the
+ 
+
+ align:start position:0%
+so just h^2 R okay so now let's do the
+middle
+
+ align:start position:0%
+middle
+ 
+
+ align:start position:0%
+middle
+integral so the middle integral is the
+
+ align:start position:0%
+integral so the middle integral is the
+ 
+
+ align:start position:0%
+integral so the middle integral is the
+integral from zero to Big R D little r
+
+ align:start position:0%
+integral from zero to Big R D little r
+ 
+
+ align:start position:0%
+integral from zero to Big R D little r
+of the inner integral so this is the
+
+ align:start position:0%
+of the inner integral so this is the
+ 
+
+ align:start position:0%
+of the inner integral so this is the
+integral from zero to Big R of the inner
+
+ align:start position:0%
+integral from zero to Big R of the inner
+ 
+
+ align:start position:0%
+integral from zero to Big R of the inner
+integral which was h^2 little r d little
+
+ align:start position:0%
+integral which was h^2 little r d little
+ 
+
+ align:start position:0%
+integral which was h^2 little r d little
+r okay and that's not that bad either so
+
+ align:start position:0%
+r okay and that's not that bad either so
+ 
+
+ align:start position:0%
+r okay and that's not that bad either so
+H is just a constant so this is equal to
+
+ align:start position:0%
+H is just a constant so this is equal to
+ 
+
+ align:start position:0%
+H is just a constant so this is equal to
+
+ align:start position:0%
+ 
+
+ align:start position:0%
+H2 R
+
+ align:start position:0%
+H2 R
+ 
+
+ align:start position:0%
+H2 R
+2 from R = 0 to Big R and so that's 12
+
+ align:start position:0%
+2 from R = 0 to Big R and so that's 12
+ 
+
+ align:start position:0%
+2 from R = 0 to Big R and so that's 12
+h^2 Big R 2 that's the middle integral
+
+ align:start position:0%
+h^2 Big R 2 that's the middle integral
+ 
+
+ align:start position:0%
+h^2 Big R 2 that's the middle integral
+so the outer
+
+ align:start position:0%
+so the outer
+ 
+
+ align:start position:0%
+so the outer
+one now okay so let's go back and look
+
+ align:start position:0%
+one now okay so let's go back and look
+ 
+
+ align:start position:0%
+one now okay so let's go back and look
+so we're doing D Theta as Theta goes
+
+ align:start position:0%
+so we're doing D Theta as Theta goes
+ 
+
+ align:start position:0%
+so we're doing D Theta as Theta goes
+from 0 to 2 pi of whatever the middle
+
+ align:start position:0%
+from 0 to 2 pi of whatever the middle
+ 
+
+ align:start position:0%
+from 0 to 2 pi of whatever the middle
+integral was so it's the integral from
+
+ align:start position:0%
+integral was so it's the integral from
+ 
+
+ align:start position:0%
+integral was so it's the integral from
+from 0 to 2 pi of whatever the value of
+
+ align:start position:0%
+from 0 to 2 pi of whatever the value of
+ 
+
+ align:start position:0%
+from 0 to 2 pi of whatever the value of
+the middle integral was so this is 12 h²
+
+ align:start position:0%
+the middle integral was so this is 12 h²
+ 
+
+ align:start position:0%
+the middle integral was so this is 12 h²
+Big R 2 D Theta and this is all just
+
+ align:start position:0%
+Big R 2 D Theta and this is all just
+ 
+
+ align:start position:0%
+Big R 2 D Theta and this is all just
+constant with respect to Theta so that's
+
+ align:start position:0%
+constant with respect to Theta so that's
+ 
+
+ align:start position:0%
+constant with respect to Theta so that's
+going to be just pi h^2 r 2 you you know
+
+ align:start position:0%
+going to be just pi h^2 r 2 you you know
+ 
+
+ align:start position:0%
+going to be just pi h^2 r 2 you you know
+just multiplying it by 2 pi all right so
+
+ align:start position:0%
+just multiplying it by 2 pi all right so
+ 
+
+ align:start position:0%
+just multiplying it by 2 pi all right so
+pi h^2 r 2 so those our final answer
+
+ align:start position:0%
+pi h^2 r 2 so those our final answer
+ 
+
+ align:start position:0%
+pi h^2 r 2 so those our final answer
+let's just quickly recap what we did we
+
+ align:start position:0%
+let's just quickly recap what we did we
+ 
+
+ align:start position:0%
+let's just quickly recap what we did we
+had to compute the flux
+
+ align:start position:0%
+had to compute the flux
+ 
+
+ align:start position:0%
+had to compute the flux
+of this field F through the surface of a
+
+ align:start position:0%
+of this field F through the surface of a
+ 
+
+ align:start position:0%
+of this field F through the surface of a
+solid um with of a of a
+
+ align:start position:0%
+solid um with of a of a
+ 
+
+ align:start position:0%
+solid um with of a of a
+cylinder and so we had options we could
+
+ align:start position:0%
+cylinder and so we had options we could
+ 
+
+ align:start position:0%
+cylinder and so we had options we could
+do it directly by trying to compute the
+
+ align:start position:0%
+do it directly by trying to compute the
+ 
+
+ align:start position:0%
+do it directly by trying to compute the
+surface integrals but in this case life
+
+ align:start position:0%
+surface integrals but in this case life
+ 
+
+ align:start position:0%
+surface integrals but in this case life
+was a lot easier if we applied the
+
+ align:start position:0%
+was a lot easier if we applied the
+ 
+
+ align:start position:0%
+was a lot easier if we applied the
+Divergence Theorem so the Divergence
+
+ align:start position:0%
+Divergence Theorem so the Divergence
+ 
+
+ align:start position:0%
+Divergence Theorem so the Divergence
+Theorem says that that flux which is
+
+ align:start position:0%
+Theorem says that that flux which is
+ 
+
+ align:start position:0%
+Theorem says that that flux which is
+equal to this surface integral can also
+
+ align:start position:0%
+equal to this surface integral can also
+ 
+
+ align:start position:0%
+equal to this surface integral can also
+be written as the triple integral over
+
+ align:start position:0%
+be written as the triple integral over
+ 
+
+ align:start position:0%
+be written as the triple integral over
+the solid region bounded by the surface
+
+ align:start position:0%
+the solid region bounded by the surface
+ 
+
+ align:start position:0%
+the solid region bounded by the surface
+of of the Divergence of the field all
+
+ align:start position:0%
+of of the Divergence of the field all
+ 
+
+ align:start position:0%
+of of the Divergence of the field all
+right and so in our case the Divergence
+
+ align:start position:0%
+right and so in our case the Divergence
+ 
+
+ align:start position:0%
+right and so in our case the Divergence
+was very nice and simple and the region
+
+ align:start position:0%
+was very nice and simple and the region
+ 
+
+ align:start position:0%
+was very nice and simple and the region
+the solid region D was relatively
+
+ align:start position:0%
+the solid region D was relatively
+ 
+
+ align:start position:0%
+the solid region D was relatively
+simpler to describe than its surface uh
+
+ align:start position:0%
+simpler to describe than its surface uh
+ 
+
+ align:start position:0%
+simpler to describe than its surface uh
+that Bounds at s um so this is why we
+
+ align:start position:0%
+that Bounds at s um so this is why we
+ 
+
+ align:start position:0%
+that Bounds at s um so this is why we
+think of the Divergence Theorem because
+
+ align:start position:0%
+think of the Divergence Theorem because
+ 
+
+ align:start position:0%
+think of the Divergence Theorem because
+the Divergence of the field is easy to
+
+ align:start position:0%
+the Divergence of the field is easy to
+ 
+
+ align:start position:0%
+the Divergence of the field is easy to
+understand and the and the and the solid
+
+ align:start position:0%
+understand and the and the and the solid
+ 
+
+ align:start position:0%
+understand and the and the and the solid
+is easier to describe than its surface
+
+ align:start position:0%
+is easier to describe than its surface
+ 
+
+ align:start position:0%
+is easier to describe than its surface
+so those are both things that make us
+
+ align:start position:0%
+so those are both things that make us
+ 
+
+ align:start position:0%
+so those are both things that make us
+think to use the Divergence Theorem for
+
+ align:start position:0%
+think to use the Divergence Theorem for
+ 
+
+ align:start position:0%
+think to use the Divergence Theorem for
+a problem like this and so okay so so
+
+ align:start position:0%
+a problem like this and so okay so so
+ 
+
+ align:start position:0%
+a problem like this and so okay so so
+then by the Divergence Theorem the flux
+
+ align:start position:0%
+then by the Divergence Theorem the flux
+ 
+
+ align:start position:0%
+then by the Divergence Theorem the flux
+is just that integral that triple
+
+ align:start position:0%
+is just that integral that triple
+ 
+
+ align:start position:0%
+is just that integral that triple
+integral and so we wrote it out here we
+
+ align:start position:0%
+integral and so we wrote it out here we
+ 
+
+ align:start position:0%
+integral and so we wrote it out here we
+were integrating over a cylinder so a
+
+ align:start position:0%
+were integrating over a cylinder so a
+ 
+
+ align:start position:0%
+were integrating over a cylinder so a
+natural thing to do is use cylindrical
+
+ align:start position:0%
+natural thing to do is use cylindrical
+ 
+
+ align:start position:0%
+natural thing to do is use cylindrical
+coordinates and then we computed the
+
+ align:start position:0%
+coordinates and then we computed the
+ 
+
+ align:start position:0%
+coordinates and then we computed the
+triple integral just like we always do
+
+ align:start position:0%
+triple integral just like we always do
+ 
+
+ align:start position:0%
+triple integral just like we always do
+you know I did it in three steps inner
+
+ align:start position:0%
+you know I did it in three steps inner
+ 
+
+ align:start position:0%
+you know I did it in three steps inner
+middle and outer you don't have to do it
+
+ align:start position:0%
+middle and outer you don't have to do it
+ 
+
+ align:start position:0%
+middle and outer you don't have to do it
+exactly this way if you don't want to
+
+ align:start position:0%
+exactly this way if you don't want to
+ 
+
+ align:start position:0%
+exactly this way if you don't want to
+but it works for me um okay and we got
+
+ align:start position:0%
+but it works for me um okay and we got
+ 
+
+ align:start position:0%
+but it works for me um okay and we got
+our final answer pi h^2 r 2 I'll stop
+
+ align:start position:0%
+our final answer pi h^2 r 2 I'll stop
+ 
+
+ align:start position:0%
+our final answer pi h^2 r 2 I'll stop
+there
\ No newline at end of file
diff --git a/CMbvq16z0gA.txt b/CMbvq16z0gA.txt
new file mode 100644
index 0000000000000000000000000000000000000000..db20c9b99b7c5d5bbf382bb44d6604042d698ac2
--- /dev/null
+++ b/CMbvq16z0gA.txt
@@ -0,0 +1,2651 @@
+align:start position:0%
+ 
+welcome back to recitation in this video
+
+ align:start position:0%
+welcome back to recitation in this video
+ 
+
+ align:start position:0%
+welcome back to recitation in this video
+I'd like us to find an anti-derivative
+
+ align:start position:0%
+I'd like us to find an anti-derivative
+ 
+
+ align:start position:0%
+I'd like us to find an anti-derivative
+of the function 1 over x^2 - 8x + 1 so
+
+ align:start position:0%
+of the function 1 over x^2 - 8x + 1 so
+ 
+
+ align:start position:0%
+of the function 1 over x^2 - 8x + 1 so
+I'll give you a while to work on it and
+
+ align:start position:0%
+I'll give you a while to work on it and
+ 
+
+ align:start position:0%
+I'll give you a while to work on it and
+then I'll come back and I'll show you
+
+ align:start position:0%
+then I'll come back and I'll show you
+ 
+
+ align:start position:0%
+then I'll come back and I'll show you
+how I
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+started so welcome back well what we'd
+
+ align:start position:0%
+started so welcome back well what we'd
+ 
+
+ align:start position:0%
+started so welcome back well what we'd
+like to do is find an anti-derivative to
+
+ align:start position:0%
+like to do is find an anti-derivative to
+ 
+
+ align:start position:0%
+like to do is find an anti-derivative to
+1x^2 - 8x + 1 and how we're going to do
+
+ align:start position:0%
+1x^2 - 8x + 1 and how we're going to do
+ 
+
+ align:start position:0%
+1x^2 - 8x + 1 and how we're going to do
+that is we're going to use the technique
+
+ align:start position:0%
+that is we're going to use the technique
+ 
+
+ align:start position:0%
+that is we're going to use the technique
+completing the square and I'm going to
+
+ align:start position:0%
+completing the square and I'm going to
+ 
+
+ align:start position:0%
+completing the square and I'm going to
+set up the problem I'm going to get it
+
+ align:start position:0%
+set up the problem I'm going to get it
+ 
+
+ align:start position:0%
+set up the problem I'm going to get it
+to a certain place and then I'm going to
+
+ align:start position:0%
+to a certain place and then I'm going to
+ 
+
+ align:start position:0%
+to a certain place and then I'm going to
+let you finish it and how do you know if
+
+ align:start position:0%
+let you finish it and how do you know if
+ 
+
+ align:start position:0%
+let you finish it and how do you know if
+you got the right answer well you
+
+ align:start position:0%
+you got the right answer well you
+ 
+
+ align:start position:0%
+you got the right answer well you
+actually take a derivative of your
+
+ align:start position:0%
+actually take a derivative of your
+ 
+
+ align:start position:0%
+actually take a derivative of your
+answer and see if it gives you back 1x^2
+
+ align:start position:0%
+answer and see if it gives you back 1x^2
+ 
+
+ align:start position:0%
+answer and see if it gives you back 1x^2
+- 8x + 1 that's how you can check so
+
+ align:start position:0%
+- 8x + 1 that's how you can check so
+ 
+
+ align:start position:0%
+- 8x + 1 that's how you can check so
+let's start off if I want to complete
+
+ align:start position:0%
+let's start off if I want to complete
+ 
+
+ align:start position:0%
+let's start off if I want to complete
+the square let's just remind ourselves
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+how to complete the square on this uh on
+
+ align:start position:0%
+how to complete the square on this uh on
+ 
+
+ align:start position:0%
+how to complete the square on this uh on
+on this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+quadratic so I'd like
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+something right here that makes this a
+
+ align:start position:0%
+something right here that makes this a
+ 
+
+ align:start position:0%
+something right here that makes this a
+perfect square right well the eight here
+
+ align:start position:0%
+perfect square right well the eight here
+ 
+
+ align:start position:0%
+perfect square right well the eight here
+in the middle if I want a perfect square
+
+ align:start position:0%
+in the middle if I want a perfect square
+ 
+
+ align:start position:0%
+in the middle if I want a perfect square
+if you think about this I'm going to
+
+ align:start position:0%
+if you think about this I'm going to
+ 
+
+ align:start position:0%
+if you think about this I'm going to
+have an x minus I need a number here
+
+ align:start position:0%
+have an x minus I need a number here
+ 
+
+ align:start position:0%
+have an x minus I need a number here
+that when I multiply it by two that's
+
+ align:start position:0%
+that when I multiply it by two that's
+ 
+
+ align:start position:0%
+that when I multiply it by two that's
+where this eight comes from gives me
+
+ align:start position:0%
+where this eight comes from gives me
+ 
+
+ align:start position:0%
+where this eight comes from gives me
+eight so obviously I need this number to
+
+ align:start position:0%
+eight so obviously I need this number to
+ 
+
+ align:start position:0%
+eight so obviously I need this number to
+be a four right which puts what here
+
+ align:start position:0%
+be a four right which puts what here
+ 
+
+ align:start position:0%
+be a four right which puts what here
+puts a 16 here
+
+ align:start position:0%
+puts a 16 here
+ 
+
+ align:start position:0%
+puts a 16 here
+right so it just to double check what
+
+ align:start position:0%
+right so it just to double check what
+ 
+
+ align:start position:0%
+right so it just to double check what
+I'm looking for is a number here I I
+
+ align:start position:0%
+I'm looking for is a number here I I
+ 
+
+ align:start position:0%
+I'm looking for is a number here I I
+need a number right here that when I
+
+ align:start position:0%
+need a number right here that when I
+ 
+
+ align:start position:0%
+need a number right here that when I
+multiply by two gives me8 and then I
+
+ align:start position:0%
+multiply by two gives me8 and then I
+ 
+
+ align:start position:0%
+multiply by two gives me8 and then I
+need it to to figure out what it squares
+
+ align:start position:0%
+need it to to figure out what it squares
+ 
+
+ align:start position:0%
+need it to to figure out what it squares
+to so that number is ne4 and it squares
+
+ align:start position:0%
+to so that number is ne4 and it squares
+ 
+
+ align:start position:0%
+to so that number is ne4 and it squares
+to 16 but obviously this isn't what I
+
+ align:start position:0%
+to 16 but obviously this isn't what I
+ 
+
+ align:start position:0%
+to 16 but obviously this isn't what I
+have right I have plus one so what have
+
+ align:start position:0%
+have right I have plus one so what have
+ 
+
+ align:start position:0%
+have right I have plus one so what have
+I had to do to get from here to here
+
+ align:start position:0%
+I had to do to get from here to here
+ 
+
+ align:start position:0%
+I had to do to get from here to here
+well I had plus one and now I have plus
+
+ align:start position:0%
+well I had plus one and now I have plus
+ 
+
+ align:start position:0%
+well I had plus one and now I have plus
+16 so obviously I've added 15 so I have
+
+ align:start position:0%
+16 so obviously I've added 15 so I have
+ 
+
+ align:start position:0%
+16 so obviously I've added 15 so I have
+to subtract 15
+
+ align:start position:0%
+to subtract 15
+ 
+
+ align:start position:0%
+to subtract 15
+to keep this to keep these three lines
+
+ align:start position:0%
+to keep this to keep these three lines
+ 
+
+ align:start position:0%
+to keep this to keep these three lines
+all equal to each other so to understand
+
+ align:start position:0%
+all equal to each other so to understand
+ 
+
+ align:start position:0%
+all equal to each other so to understand
+where that comes from let's just let me
+
+ align:start position:0%
+where that comes from let's just let me
+ 
+
+ align:start position:0%
+where that comes from let's just let me
+just remind you my denominator was
+
+ align:start position:0%
+just remind you my denominator was
+ 
+
+ align:start position:0%
+just remind you my denominator was
+looking like this I'd like it to have a
+
+ align:start position:0%
+looking like this I'd like it to have a
+ 
+
+ align:start position:0%
+looking like this I'd like it to have a
+perfect square and then and then
+
+ align:start position:0%
+perfect square and then and then
+ 
+
+ align:start position:0%
+perfect square and then and then
+subtract a constant or add a constant
+
+ align:start position:0%
+subtract a constant or add a constant
+ 
+
+ align:start position:0%
+subtract a constant or add a constant
+right now I have something that I I
+
+ align:start position:0%
+right now I have something that I I
+ 
+
+ align:start position:0%
+right now I have something that I I
+don't have a perfect square in here I
+
+ align:start position:0%
+don't have a perfect square in here I
+ 
+
+ align:start position:0%
+don't have a perfect square in here I
+can't I can't make this into a perfect
+
+ align:start position:0%
+can't I can't make this into a perfect
+ 
+
+ align:start position:0%
+can't I can't make this into a perfect
+square unless I add a certain amount to
+
+ align:start position:0%
+square unless I add a certain amount to
+ 
+
+ align:start position:0%
+square unless I add a certain amount to
+the constant right here so I had to add
+
+ align:start position:0%
+the constant right here so I had to add
+ 
+
+ align:start position:0%
+the constant right here so I had to add
+15 to the constant here notice 16us 15
+
+ align:start position:0%
+15 to the constant here notice 16us 15
+ 
+
+ align:start position:0%
+15 to the constant here notice 16us 15
+is one that's my check also that the
+
+ align:start position:0%
+is one that's my check also that the
+ 
+
+ align:start position:0%
+is one that's my check also that the
+lines are equal and so what I've done is
+
+ align:start position:0%
+lines are equal and so what I've done is
+ 
+
+ align:start position:0%
+lines are equal and so what I've done is
+I've added 15 and subtracted 15 and then
+
+ align:start position:0%
+I've added 15 and subtracted 15 and then
+ 
+
+ align:start position:0%
+I've added 15 and subtracted 15 and then
+I put this plus 16 into here x - 4^ s is
+
+ align:start position:0%
+I put this plus 16 into here x - 4^ s is
+ 
+
+ align:start position:0%
+I put this plus 16 into here x - 4^ s is
+exactly these first three terms and then
+
+ align:start position:0%
+exactly these first three terms and then
+ 
+
+ align:start position:0%
+exactly these first three terms and then
+I keep the minus5 now you might say why
+
+ align:start position:0%
+I keep the minus5 now you might say why
+ 
+
+ align:start position:0%
+I keep the minus5 now you might say why
+and why did you do this so let's make
+
+ align:start position:0%
+and why did you do this so let's make
+ 
+
+ align:start position:0%
+and why did you do this so let's make
+sure we understand why we're completing
+
+ align:start position:0%
+sure we understand why we're completing
+ 
+
+ align:start position:0%
+sure we understand why we're completing
+the square on this if we come back I'm
+
+ align:start position:0%
+the square on this if we come back I'm
+ 
+
+ align:start position:0%
+the square on this if we come back I'm
+going to put this line in place of
+
+ align:start position:0%
+going to put this line in place of
+ 
+
+ align:start position:0%
+going to put this line in place of
+what's in the denominator there because
+
+ align:start position:0%
+what's in the denominator there because
+ 
+
+ align:start position:0%
+what's in the denominator there because
+these three things are all equal so this
+
+ align:start position:0%
+these three things are all equal so this
+ 
+
+ align:start position:0%
+these three things are all equal so this
+is actually the integral of
+
+ align:start position:0%
+is actually the integral of
+ 
+
+ align:start position:0%
+is actually the integral of
+DX over x - 4 quantity Square quantity
+
+ align:start position:0%
+DX over x - 4 quantity Square quantity
+ 
+
+ align:start position:0%
+DX over x - 4 quantity Square quantity
+squared minus
+
+ align:start position:0%
+squared minus
+ 
+
+ align:start position:0%
+squared minus
+15 now you might say Christine this
+
+ align:start position:0%
+15 now you might say Christine this
+ 
+
+ align:start position:0%
+15 now you might say Christine this
+looks no easier I don't know why you did
+
+ align:start position:0%
+looks no easier I don't know why you did
+ 
+
+ align:start position:0%
+looks no easier I don't know why you did
+this but it actually is one of our
+
+ align:start position:0%
+this but it actually is one of our
+ 
+
+ align:start position:0%
+this but it actually is one of our
+favorite or least favorite depending on
+
+ align:start position:0%
+favorite or least favorite depending on
+ 
+
+ align:start position:0%
+favorite or least favorite depending on
+how you feel about it uh types of types
+
+ align:start position:0%
+how you feel about it uh types of types
+ 
+
+ align:start position:0%
+how you feel about it uh types of types
+of Tricks we use now which is the trig
+
+ align:start position:0%
+of Tricks we use now which is the trig
+ 
+
+ align:start position:0%
+of Tricks we use now which is the trig
+substitution so some people love this
+
+ align:start position:0%
+substitution so some people love this
+ 
+
+ align:start position:0%
+substitution so some people love this
+because they just have to memorize a
+
+ align:start position:0%
+because they just have to memorize a
+ 
+
+ align:start position:0%
+because they just have to memorize a
+little formula and some people love it
+
+ align:start position:0%
+little formula and some people love it
+ 
+
+ align:start position:0%
+little formula and some people love it
+because they can draw a triangle and
+
+ align:start position:0%
+because they can draw a triangle and
+ 
+
+ align:start position:0%
+because they can draw a triangle and
+understand what they choose um I'm going
+
+ align:start position:0%
+understand what they choose um I'm going
+ 
+
+ align:start position:0%
+understand what they choose um I'm going
+to show you remind you what the formula
+
+ align:start position:0%
+to show you remind you what the formula
+ 
+
+ align:start position:0%
+to show you remind you what the formula
+was you saw in class uh I believe
+
+ align:start position:0%
+was you saw in class uh I believe
+ 
+
+ align:start position:0%
+was you saw in class uh I believe
+Professor Jaron said something like this
+
+ align:start position:0%
+Professor Jaron said something like this
+ 
+
+ align:start position:0%
+Professor Jaron said something like this
+if the denominator is in the form U
+
+ align:start position:0%
+if the denominator is in the form U
+ 
+
+ align:start position:0%
+if the denominator is in the form U
+minus a^ 2 this implies that you make U
+
+ align:start position:0%
+minus a^ 2 this implies that you make U
+ 
+
+ align:start position:0%
+minus a^ 2 this implies that you make U
+equal to a secant
+
+ align:start position:0%
+equal to a secant
+ 
+
+ align:start position:0%
+equal to a secant
+Theta now he probably wrote it as X but
+
+ align:start position:0%
+Theta now he probably wrote it as X but
+ 
+
+ align:start position:0%
+Theta now he probably wrote it as X but
+I wrote it as U for a very specific
+
+ align:start position:0%
+I wrote it as U for a very specific
+ 
+
+ align:start position:0%
+I wrote it as U for a very specific
+reason
+
+ align:start position:0%
+reason
+ 
+
+ align:start position:0%
+reason
+because here I have x - 4 I have x - 4
+
+ align:start position:0%
+because here I have x - 4 I have x - 4
+ 
+
+ align:start position:0%
+because here I have x - 4 I have x - 4
+Quan squared now this is where it gets a
+
+ align:start position:0%
+Quan squared now this is where it gets a
+ 
+
+ align:start position:0%
+Quan squared now this is where it gets a
+little rough right this is not a perfect
+
+ align:start position:0%
+little rough right this is not a perfect
+ 
+
+ align:start position:0%
+little rough right this is not a perfect
+square but it is the perfect square it
+
+ align:start position:0%
+square but it is the perfect square it
+ 
+
+ align:start position:0%
+square but it is the perfect square it
+is the square of the square root of 15
+
+ align:start position:0%
+is the square of the square root of 15
+ 
+
+ align:start position:0%
+is the square of the square root of 15
+so I can write the denominator in the
+
+ align:start position:0%
+so I can write the denominator in the
+ 
+
+ align:start position:0%
+so I can write the denominator in the
+form something squared minus something
+
+ align:start position:0%
+form something squared minus something
+ 
+
+ align:start position:0%
+form something squared minus something
+else squared and again you might say why
+
+ align:start position:0%
+else squared and again you might say why
+ 
+
+ align:start position:0%
+else squared and again you might say why
+is this good well what we're going to be
+
+ align:start position:0%
+is this good well what we're going to be
+ 
+
+ align:start position:0%
+is this good well what we're going to be
+able to do is we're going to be able to
+
+ align:start position:0%
+able to do is we're going to be able to
+ 
+
+ align:start position:0%
+able to do is we're going to be able to
+rewrite this in terms of trigonometric
+
+ align:start position:0%
+rewrite this in terms of trigonometric
+ 
+
+ align:start position:0%
+rewrite this in terms of trigonometric
+function functions which will make it
+
+ align:start position:0%
+function functions which will make it
+ 
+
+ align:start position:0%
+function functions which will make it
+much simpler to solve so let's use what
+
+ align:start position:0%
+much simpler to solve so let's use what
+ 
+
+ align:start position:0%
+much simpler to solve so let's use what
+what Professor Jaron gave us and so what
+
+ align:start position:0%
+what Professor Jaron gave us and so what
+ 
+
+ align:start position:0%
+what Professor Jaron gave us and so what
+we see is that this is U and this is
+
+ align:start position:0%
+we see is that this is U and this is
+ 
+
+ align:start position:0%
+we see is that this is U and this is
+a right so I get uh x - 4 is equal to
+
+ align:start position:0%
+a right so I get uh x - 4 is equal to
+ 
+
+ align:start position:0%
+a right so I get uh x - 4 is equal to
+square < TK of
+
+ align:start position:0%
+square < TK of
+ 
+
+ align:start position:0%
+square < TK of
+15 secant Theta now you might not like
+
+ align:start position:0%
+15 secant Theta now you might not like
+ 
+
+ align:start position:0%
+15 secant Theta now you might not like
+the square root of 15 but it's just
+
+ align:start position:0%
+the square root of 15 but it's just
+ 
+
+ align:start position:0%
+the square root of 15 but it's just
+hanging out is not causing any problems
+
+ align:start position:0%
+hanging out is not causing any problems
+ 
+
+ align:start position:0%
+hanging out is not causing any problems
+it's just a number there so we'll keep
+
+ align:start position:0%
+it's just a number there so we'll keep
+ 
+
+ align:start position:0%
+it's just a number there so we'll keep
+it a square root of 15 so you don't have
+
+ align:start position:0%
+it a square root of 15 so you don't have
+ 
+
+ align:start position:0%
+it a square root of 15 so you don't have
+to worry about it now what's the point
+
+ align:start position:0%
+to worry about it now what's the point
+ 
+
+ align:start position:0%
+to worry about it now what's the point
+again let me just remind you the object
+
+ align:start position:0%
+again let me just remind you the object
+ 
+
+ align:start position:0%
+again let me just remind you the object
+is to get this in terms of the trig
+
+ align:start position:0%
+is to get this in terms of the trig
+ 
+
+ align:start position:0%
+is to get this in terms of the trig
+functions so we should anticipate that
+
+ align:start position:0%
+functions so we should anticipate that
+ 
+
+ align:start position:0%
+functions so we should anticipate that
+probably we'll have some some tangent
+
+ align:start position:0%
+probably we'll have some some tangent
+ 
+
+ align:start position:0%
+probably we'll have some some tangent
+functions to go with this and there are
+
+ align:start position:0%
+functions to go with this and there are
+ 
+
+ align:start position:0%
+functions to go with this and there are
+two reasons to to think that the first
+
+ align:start position:0%
+two reasons to to think that the first
+ 
+
+ align:start position:0%
+two reasons to to think that the first
+reason to think that is at some point I
+
+ align:start position:0%
+reason to think that is at some point I
+ 
+
+ align:start position:0%
+reason to think that is at some point I
+have to find DX well the derivative of
+
+ align:start position:0%
+have to find DX well the derivative of
+ 
+
+ align:start position:0%
+have to find DX well the derivative of
+secant involves secant and tangent right
+
+ align:start position:0%
+secant involves secant and tangent right
+ 
+
+ align:start position:0%
+secant involves secant and tangent right
+so that's going to pull in a tangent
+
+ align:start position:0%
+so that's going to pull in a tangent
+ 
+
+ align:start position:0%
+so that's going to pull in a tangent
+function somewhere I'm also going to
+
+ align:start position:0%
+function somewhere I'm also going to
+ 
+
+ align:start position:0%
+function somewhere I'm also going to
+have a tangent function show up
+
+ align:start position:0%
+have a tangent function show up
+ 
+
+ align:start position:0%
+have a tangent function show up
+somewhere else and where that's going to
+
+ align:start position:0%
+somewhere else and where that's going to
+ 
+
+ align:start position:0%
+somewhere else and where that's going to
+be is coming from this denominator this
+
+ align:start position:0%
+be is coming from this denominator this
+ 
+
+ align:start position:0%
+be is coming from this denominator this
+expression in the denominator because
+
+ align:start position:0%
+expression in the denominator because
+ 
+
+ align:start position:0%
+expression in the denominator because
+there's a certain trig identity that we
+
+ align:start position:0%
+there's a certain trig identity that we
+ 
+
+ align:start position:0%
+there's a certain trig identity that we
+we should have memorized but I'll just
+
+ align:start position:0%
+we should have memorized but I'll just
+ 
+
+ align:start position:0%
+we should have memorized but I'll just
+remind you I'll write it here and put a
+
+ align:start position:0%
+remind you I'll write it here and put a
+ 
+
+ align:start position:0%
+remind you I'll write it here and put a
+star next to it it's 1 + tangent s thet
+
+ align:start position:0%
+star next to it it's 1 + tangent s thet
+ 
+
+ align:start position:0%
+star next to it it's 1 + tangent s thet
+is equal to secant squ
+
+ align:start position:0%
+is equal to secant squ
+ 
+
+ align:start position:0%
+is equal to secant squ
+thet so this is a I'll even put a star
+
+ align:start position:0%
+thet so this is a I'll even put a star
+ 
+
+ align:start position:0%
+thet so this is a I'll even put a star
+on the other side so we should really
+
+ align:start position:0%
+on the other side so we should really
+ 
+
+ align:start position:0%
+on the other side so we should really
+remember this now where does it come
+
+ align:start position:0%
+remember this now where does it come
+ 
+
+ align:start position:0%
+remember this now where does it come
+from comes from the cosine squ theta
+
+ align:start position:0%
+from comes from the cosine squ theta
+ 
+
+ align:start position:0%
+from comes from the cosine squ theta
+plus sin squ theta equals one identity
+
+ align:start position:0%
+plus sin squ theta equals one identity
+ 
+
+ align:start position:0%
+plus sin squ theta equals one identity
+you can divide everything by cosine squ
+
+ align:start position:0%
+you can divide everything by cosine squ
+ 
+
+ align:start position:0%
+you can divide everything by cosine squ
+thet and get this one so we have this
+
+ align:start position:0%
+thet and get this one so we have this
+ 
+
+ align:start position:0%
+thet and get this one so we have this
+identity and so if you notice we're
+
+ align:start position:0%
+identity and so if you notice we're
+ 
+
+ align:start position:0%
+identity and so if you notice we're
+going to be able to manipulate we're
+
+ align:start position:0%
+going to be able to manipulate we're
+ 
+
+ align:start position:0%
+going to be able to manipulate we're
+going to be able to manipulate this the
+
+ align:start position:0%
+going to be able to manipulate this the
+ 
+
+ align:start position:0%
+going to be able to manipulate this the
+expression right here and get the
+
+ align:start position:0%
+expression right here and get the
+ 
+
+ align:start position:0%
+expression right here and get the
+denominator to look like tangent squ
+
+ align:start position:0%
+denominator to look like tangent squ
+ 
+
+ align:start position:0%
+denominator to look like tangent squ
+Theta so let's do some of that work off
+
+ align:start position:0%
+Theta so let's do some of that work off
+ 
+
+ align:start position:0%
+Theta so let's do some of that work off
+to the right
+
+ align:start position:0%
+to the right
+ 
+
+ align:start position:0%
+to the right
+here so what did I say we needed we have
+
+ align:start position:0%
+here so what did I say we needed we have
+ 
+
+ align:start position:0%
+here so what did I say we needed we have
+this expression we need DX so let's find
+
+ align:start position:0%
+this expression we need DX so let's find
+ 
+
+ align:start position:0%
+this expression we need DX so let's find
+actually no let's find the denominator
+
+ align:start position:0%
+actually no let's find the denominator
+ 
+
+ align:start position:0%
+actually no let's find the denominator
+first because I was just talking about
+
+ align:start position:0%
+first because I was just talking about
+ 
+
+ align:start position:0%
+first because I was just talking about
+it so if I look at what x - 4^ squar is
+
+ align:start position:0%
+it so if I look at what x - 4^ squar is
+ 
+
+ align:start position:0%
+it so if I look at what x - 4^ squar is
+I'm going to substitute in this
+
+ align:start position:0%
+I'm going to substitute in this
+ 
+
+ align:start position:0%
+I'm going to substitute in this
+expression
+
+ align:start position:0%
+expression
+ 
+
+ align:start position:0%
+expression
+so x -
+
+ align:start position:0%
+so x -
+ 
+
+ align:start position:0%
+so x -
+4^ 2ar - 15 is the same as based on this
+
+ align:start position:0%
+4^ 2ar - 15 is the same as based on this
+ 
+
+ align:start position:0%
+4^ 2ar - 15 is the same as based on this
+substitution < TK 15 secant
+
+ align:start position:0%
+substitution < TK 15 secant
+ 
+
+ align:start position:0%
+substitution < TK 15 secant
+Theta squarus 15 which is 15 secant 2
+
+ align:start position:0%
+Theta squarus 15 which is 15 secant 2
+ 
+
+ align:start position:0%
+Theta squarus 15 which is 15 secant 2
+Theta minus 15 which just to hammer home
+
+ align:start position:0%
+Theta minus 15 which just to hammer home
+ 
+
+ align:start position:0%
+Theta minus 15 which just to hammer home
+the point is 15 * the quantity SEC 2
+
+ align:start position:0%
+the point is 15 * the quantity SEC 2
+ 
+
+ align:start position:0%
+the point is 15 * the quantity SEC 2
+thetus 1
+
+ align:start position:0%
+thetus 1
+ 
+
+ align:start position:0%
+thetus 1
+okay everybody follows hopefully all
+
+ align:start position:0%
+okay everybody follows hopefully all
+ 
+
+ align:start position:0%
+okay everybody follows hopefully all
+I've done is the substitution I made and
+
+ align:start position:0%
+I've done is the substitution I made and
+ 
+
+ align:start position:0%
+I've done is the substitution I made and
+then I started expanding or I squared
+
+ align:start position:0%
+then I started expanding or I squared
+ 
+
+ align:start position:0%
+then I started expanding or I squared
+this term and I factored out the 15 and
+
+ align:start position:0%
+this term and I factored out the 15 and
+ 
+
+ align:start position:0%
+this term and I factored out the 15 and
+now let's go back to my St expression
+
+ align:start position:0%
+now let's go back to my St expression
+ 
+
+ align:start position:0%
+now let's go back to my St expression
+what is secant squ Theta minus 1 it's
+
+ align:start position:0%
+what is secant squ Theta minus 1 it's
+ 
+
+ align:start position:0%
+what is secant squ Theta minus 1 it's
+tangent Square thet so we get 15 tangent
+
+ align:start position:0%
+tangent Square thet so we get 15 tangent
+ 
+
+ align:start position:0%
+tangent Square thet so we get 15 tangent
+squ thet so that is actually what the
+
+ align:start position:0%
+squ thet so that is actually what the
+ 
+
+ align:start position:0%
+squ thet so that is actually what the
+denominator of our of our integral is
+
+ align:start position:0%
+denominator of our of our integral is
+ 
+
+ align:start position:0%
+denominator of our of our integral is
+going to be over there so I'm going to
+
+ align:start position:0%
+going to be over there so I'm going to
+ 
+
+ align:start position:0%
+going to be over there so I'm going to
+come in and and put that part actually
+
+ align:start position:0%
+come in and and put that part actually
+ 
+
+ align:start position:0%
+come in and and put that part actually
+let me even put this here too so right
+
+ align:start position:0%
+let me even put this here too so right
+ 
+
+ align:start position:0%
+let me even put this here too so right
+now our
+
+ align:start position:0%
+now our
+ 
+
+ align:start position:0%
+now our
+denominator is tangent 15 tangent SAR
+
+ align:start position:0%
+denominator is tangent 15 tangent SAR
+ 
+
+ align:start position:0%
+denominator is tangent 15 tangent SAR
+Theta so far so good but of course if I
+
+ align:start position:0%
+Theta so far so good but of course if I
+ 
+
+ align:start position:0%
+Theta so far so good but of course if I
+put a DX up here I'm in trouble because
+
+ align:start position:0%
+put a DX up here I'm in trouble because
+ 
+
+ align:start position:0%
+put a DX up here I'm in trouble because
+I have it's a function of theta now so I
+
+ align:start position:0%
+I have it's a function of theta now so I
+ 
+
+ align:start position:0%
+I have it's a function of theta now so I
+need to write this I shouldn't write in
+
+ align:start position:0%
+need to write this I shouldn't write in
+ 
+
+ align:start position:0%
+need to write this I shouldn't write in
+terms of X I need to figure out what it
+
+ align:start position:0%
+terms of X I need to figure out what it
+ 
+
+ align:start position:0%
+terms of X I need to figure out what it
+is in terms of theta and to do that we
+
+ align:start position:0%
+is in terms of theta and to do that we
+ 
+
+ align:start position:0%
+is in terms of theta and to do that we
+again use the the substitution that we
+
+ align:start position:0%
+again use the the substitution that we
+ 
+
+ align:start position:0%
+again use the the substitution that we
+made which is just above the St
+
+ align:start position:0%
+made which is just above the St
+ 
+
+ align:start position:0%
+made which is just above the St
+expression it was that x - 4al Square <
+
+ align:start position:0%
+expression it was that x - 4al Square <
+ 
+
+ align:start position:0%
+expression it was that x - 4al Square <
+TK 15 secant Theta this is going to
+
+ align:start position:0%
+TK 15 secant Theta this is going to
+ 
+
+ align:start position:0%
+TK 15 secant Theta this is going to
+allow us to find what D Theta is in
+
+ align:start position:0%
+allow us to find what D Theta is in
+ 
+
+ align:start position:0%
+allow us to find what D Theta is in
+terms of
+
+ align:start position:0%
+terms of
+ 
+
+ align:start position:0%
+terms of
+DX okay so let's do
+
+ align:start position:0%
+DX okay so let's do
+ 
+
+ align:start position:0%
+DX okay so let's do
+that so I'm not done by the way over
+
+ align:start position:0%
+that so I'm not done by the way over
+ 
+
+ align:start position:0%
+that so I'm not done by the way over
+here I'm not done I've got a little Gap
+
+ align:start position:0%
+here I'm not done I've got a little Gap
+ 
+
+ align:start position:0%
+here I'm not done I've got a little Gap
+I've got to fill in in the numerator so
+
+ align:start position:0%
+I've got to fill in in the numerator so
+ 
+
+ align:start position:0%
+I've got to fill in in the numerator so
+let's come back over here so now we have
+
+ align:start position:0%
+let's come back over here so now we have
+ 
+
+ align:start position:0%
+let's come back over here so now we have
+X x - 4 let me just write that one more
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+time so we get DX is equal to square <
+
+ align:start position:0%
+time so we get DX is equal to square <
+ 
+
+ align:start position:0%
+time so we get DX is equal to square <
+TK of 15 well what's the derivative of
+
+ align:start position:0%
+TK of 15 well what's the derivative of
+ 
+
+ align:start position:0%
+TK of 15 well what's the derivative of
+secant Theta it's secant
+
+ align:start position:0%
+secant Theta it's secant
+ 
+
+ align:start position:0%
+secant Theta it's secant
+Theta tangent
+
+ align:start position:0%
+Theta tangent
+ 
+
+ align:start position:0%
+Theta tangent
+Theta D Theta so now I have all the
+
+ align:start position:0%
+Theta D Theta so now I have all the
+ 
+
+ align:start position:0%
+Theta D Theta so now I have all the
+pieces I need and I'm actually going to
+
+ align:start position:0%
+pieces I need and I'm actually going to
+ 
+
+ align:start position:0%
+pieces I need and I'm actually going to
+rewrite the whole thing over over here
+
+ align:start position:0%
+rewrite the whole thing over over here
+ 
+
+ align:start position:0%
+rewrite the whole thing over over here
+underneath so that I can work with it a
+
+ align:start position:0%
+underneath so that I can work with it a
+ 
+
+ align:start position:0%
+underneath so that I can work with it a
+little bit more so the DX is in the
+
+ align:start position:0%
+little bit more so the DX is in the
+ 
+
+ align:start position:0%
+little bit more so the DX is in the
+numerator
+
+ align:start position:0%
+numerator
+ 
+
+ align:start position:0%
+numerator
+Ator < TK
+
+ align:start position:0%
+Ator < TK
+ 
+
+ align:start position:0%
+Ator < TK
+15 secant Theta tan Theta D
+
+ align:start position:0%
+15 secant Theta tan Theta D
+ 
+
+ align:start position:0%
+15 secant Theta tan Theta D
+Theta all over
+
+ align:start position:0%
+Theta all over
+ 
+
+ align:start position:0%
+Theta all over
+15 tan^ 2
+
+ align:start position:0%
+15 tan^ 2
+ 
+
+ align:start position:0%
+15 tan^ 2
+thet now this might still look a little
+
+ align:start position:0%
+thet now this might still look a little
+ 
+
+ align:start position:0%
+thet now this might still look a little
+messy but we can simplify it some
+
+ align:start position:0%
+messy but we can simplify it some
+ 
+
+ align:start position:0%
+messy but we can simplify it some
+more we divide out by one tangent we'll
+
+ align:start position:0%
+more we divide out by one tangent we'll
+ 
+
+ align:start position:0%
+more we divide out by one tangent we'll
+pull this out in front and notice what's
+
+ align:start position:0%
+pull this out in front and notice what's
+ 
+
+ align:start position:0%
+pull this out in front and notice what's
+secant secant Theta is 1/ cosine Theta
+
+ align:start position:0%
+secant secant Theta is 1/ cosine Theta
+ 
+
+ align:start position:0%
+secant secant Theta is 1/ cosine Theta
+and tangent Theta is s th cosine Theta
+
+ align:start position:0%
+and tangent Theta is s th cosine Theta
+ 
+
+ align:start position:0%
+and tangent Theta is s th cosine Theta
+so let's write that down so this
+
+ align:start position:0%
+so let's write that down so this
+ 
+
+ align:start position:0%
+so let's write that down so this
+becomes < TK 15 15 we'll just leave it
+
+ align:start position:0%
+becomes < TK 15 15 we'll just leave it
+ 
+
+ align:start position:0%
+becomes < TK 15 15 we'll just leave it
+out there it's not hurting
+
+ align:start position:0%
+out there it's not hurting
+ 
+
+ align:start position:0%
+out there it's not hurting
+anyone so we get a one over cosine
+
+ align:start position:0%
+anyone so we get a one over cosine
+ 
+
+ align:start position:0%
+anyone so we get a one over cosine
+Theta times Well tangent Theta one over
+
+ align:start position:0%
+Theta times Well tangent Theta one over
+ 
+
+ align:start position:0%
+Theta times Well tangent Theta one over
+tangent Theta is coent Theta also
+
+ align:start position:0%
+tangent Theta is coent Theta also
+ 
+
+ align:start position:0%
+tangent Theta is coent Theta also
+there's another way to think about it so
+
+ align:start position:0%
+there's another way to think about it so
+ 
+
+ align:start position:0%
+there's another way to think about it so
+it's cosine Theta over sin
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Theta D
+
+ align:start position:0%
+Theta D
+ 
+
+ align:start position:0%
+Theta D
+Theta so these divide out and I'm left
+
+ align:start position:0%
+Theta so these divide out and I'm left
+ 
+
+ align:start position:0%
+Theta so these divide out and I'm left
+with I'm taking now an anti-derivative
+
+ align:start position:0%
+with I'm taking now an anti-derivative
+ 
+
+ align:start position:0%
+with I'm taking now an anti-derivative
+of 1/ sin Theta which is cose Theta so I
+
+ align:start position:0%
+of 1/ sin Theta which is cose Theta so I
+ 
+
+ align:start position:0%
+of 1/ sin Theta which is cose Theta so I
+have to find an anti-derivative of
+
+ align:start position:0%
+have to find an anti-derivative of
+ 
+
+ align:start position:0%
+have to find an anti-derivative of
+cosecant Theta well you can find that
+
+ align:start position:0%
+cosecant Theta well you can find that
+ 
+
+ align:start position:0%
+cosecant Theta well you can find that
+with the exact same strategy you found
+
+ align:start position:0%
+with the exact same strategy you found
+ 
+
+ align:start position:0%
+with the exact same strategy you found
+or I should say that Professor jarrison
+
+ align:start position:0%
+or I should say that Professor jarrison
+ 
+
+ align:start position:0%
+or I should say that Professor jarrison
+used in class or maybe it was actually
+
+ align:start position:0%
+used in class or maybe it was actually
+ 
+
+ align:start position:0%
+used in class or maybe it was actually
+Professor Miller in in that lecture to
+
+ align:start position:0%
+Professor Miller in in that lecture to
+ 
+
+ align:start position:0%
+Professor Miller in in that lecture to
+find uh an anti-derivative of secant
+
+ align:start position:0%
+find uh an anti-derivative of secant
+ 
+
+ align:start position:0%
+find uh an anti-derivative of secant
+Theta so you can do the same kind of
+
+ align:start position:0%
+Theta so you can do the same kind of
+ 
+
+ align:start position:0%
+Theta so you can do the same kind of
+thing with cosecant Theta because they
+
+ align:start position:0%
+thing with cosecant Theta because they
+ 
+
+ align:start position:0%
+thing with cosecant Theta because they
+have the same kind of derivatives
+
+ align:start position:0%
+have the same kind of derivatives
+ 
+
+ align:start position:0%
+have the same kind of derivatives
+cosecant and cotangent have very similar
+
+ align:start position:0%
+cosecant and cotangent have very similar
+ 
+
+ align:start position:0%
+cosecant and cotangent have very similar
+looking derivatives to tangent and
+
+ align:start position:0%
+looking derivatives to tangent and
+ 
+
+ align:start position:0%
+looking derivatives to tangent and
+secant same kinds of relationships so
+
+ align:start position:0%
+secant same kinds of relationships so
+ 
+
+ align:start position:0%
+secant same kinds of relationships so
+you can actually find that
+
+ align:start position:0%
+you can actually find that
+ 
+
+ align:start position:0%
+you can actually find that
+anti-derivative so this is some constant
+
+ align:start position:0%
+anti-derivative so this is some constant
+ 
+
+ align:start position:0%
+anti-derivative so this is some constant
+we don't care
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+about
+
+ align:start position:0%
+about
+ 
+
+ align:start position:0%
+about
+uh and once you find that this will be
+
+ align:start position:0%
+uh and once you find that this will be
+ 
+
+ align:start position:0%
+uh and once you find that this will be
+in terms of theta your final answer
+
+ align:start position:0%
+in terms of theta your final answer
+ 
+
+ align:start position:0%
+in terms of theta your final answer
+needs to be in terms of X but you saw
+
+ align:start position:0%
+needs to be in terms of X but you saw
+ 
+
+ align:start position:0%
+needs to be in terms of X but you saw
+how to do that actually you just need to
+
+ align:start position:0%
+how to do that actually you just need to
+ 
+
+ align:start position:0%
+how to do that actually you just need to
+make a triangle that represents the
+
+ align:start position:0%
+make a triangle that represents the
+ 
+
+ align:start position:0%
+make a triangle that represents the
+relationship between uh between X and
+
+ align:start position:0%
+relationship between uh between X and
+ 
+
+ align:start position:0%
+relationship between uh between X and
+Theta so I'll draw picture of that
+
+ align:start position:0%
+Theta so I'll draw picture of that
+ 
+
+ align:start position:0%
+Theta so I'll draw picture of that
+triangle then I'll give a little summary
+
+ align:start position:0%
+triangle then I'll give a little summary
+ 
+
+ align:start position:0%
+triangle then I'll give a little summary
+of what we did and then we'll stop so
+
+ align:start position:0%
+of what we did and then we'll stop so
+ 
+
+ align:start position:0%
+of what we did and then we'll stop so
+let me draw a picture of that triangle
+
+ align:start position:0%
+let me draw a picture of that triangle
+ 
+
+ align:start position:0%
+let me draw a picture of that triangle
+so from here all you would do is
+
+ align:start position:0%
+so from here all you would do is
+ 
+
+ align:start position:0%
+so from here all you would do is
+actually find this
+
+ align:start position:0%
+actually find this
+ 
+
+ align:start position:0%
+actually find this
+anti-derivative and then you would have
+
+ align:start position:0%
+anti-derivative and then you would have
+ 
+
+ align:start position:0%
+anti-derivative and then you would have
+to make the right kind of substitution
+
+ align:start position:0%
+to make the right kind of substitution
+ 
+
+ align:start position:0%
+to make the right kind of substitution
+in terms of theta we want to know how do
+
+ align:start position:0%
+in terms of theta we want to know how do
+ 
+
+ align:start position:0%
+in terms of theta we want to know how do
+we find that do that
+
+ align:start position:0%
+we find that do that
+ 
+
+ align:start position:0%
+we find that do that
+substitution so the triangle is going to
+
+ align:start position:0%
+substitution so the triangle is going to
+ 
+
+ align:start position:0%
+substitution so the triangle is going to
+come from the following thing we know x
+
+ align:start position:0%
+come from the following thing we know x
+ 
+
+ align:start position:0%
+come from the following thing we know x
+- 4 again is square < TK of 15 secant
+
+ align:start position:0%
+- 4 again is square < TK of 15 secant
+ 
+
+ align:start position:0%
+- 4 again is square < TK of 15 secant
+Theta so I'm going to make this Theta
+
+ align:start position:0%
+Theta so I'm going to make this Theta
+ 
+
+ align:start position:0%
+Theta so I'm going to make this Theta
+secant
+
+ align:start position:0%
+secant
+ 
+
+ align:start position:0%
+secant
+what's one cosine thet cosine is
+
+ align:start position:0%
+what's one cosine thet cosine is
+ 
+
+ align:start position:0%
+what's one cosine thet cosine is
+adjacent over hypotenuse so secant is
+
+ align:start position:0%
+adjacent over hypotenuse so secant is
+ 
+
+ align:start position:0%
+adjacent over hypotenuse so secant is
+hypotenuse over
+
+ align:start position:0%
+hypotenuse over
+ 
+
+ align:start position:0%
+hypotenuse over
+adjacent right that's the relationship
+
+ align:start position:0%
+adjacent right that's the relationship
+ 
+
+ align:start position:0%
+adjacent right that's the relationship
+so x - 4 over 15 is equal to the
+
+ align:start position:0%
+so x - 4 over 15 is equal to the
+ 
+
+ align:start position:0%
+so x - 4 over 15 is equal to the
+hypotenuse over the
+
+ align:start position:0%
+hypotenuse over the
+ 
+
+ align:start position:0%
+hypotenuse over the
+adjacent did I square root sorry square
+
+ align:start position:0%
+adjacent did I square root sorry square
+ 
+
+ align:start position:0%
+adjacent did I square root sorry square
+root so the hypotenuse is x -
+
+ align:start position:0%
+root so the hypotenuse is x -
+ 
+
+ align:start position:0%
+root so the hypotenuse is x -
+4 the adjac is square < TK of 15 and
+
+ align:start position:0%
+4 the adjac is square < TK of 15 and
+ 
+
+ align:start position:0%
+4 the adjac is square < TK of 15 and
+then now I can fill in the opposite by
+
+ align:start position:0%
+then now I can fill in the opposite by
+ 
+
+ align:start position:0%
+then now I can fill in the opposite by
+Pythagorean theorem right I just take
+
+ align:start position:0%
+Pythagorean theorem right I just take
+ 
+
+ align:start position:0%
+Pythagorean theorem right I just take
+this squared and I subtract this squared
+
+ align:start position:0%
+this squared and I subtract this squared
+ 
+
+ align:start position:0%
+this squared and I subtract this squared
+and then I take the square root so I get
+
+ align:start position:0%
+and then I take the square root so I get
+ 
+
+ align:start position:0%
+and then I take the square root so I get
+the square root of x - 4^ 2ar minus
+
+ align:start position:0%
+the square root of x - 4^ 2ar minus
+ 
+
+ align:start position:0%
+the square root of x - 4^ 2ar minus
+15 so whatever I have in terms of theta
+
+ align:start position:0%
+15 so whatever I have in terms of theta
+ 
+
+ align:start position:0%
+15 so whatever I have in terms of theta
+I just look at this triangle if I had in
+
+ align:start position:0%
+I just look at this triangle if I had in
+ 
+
+ align:start position:0%
+I just look at this triangle if I had in
+my answer sin Theta I would replace sin
+
+ align:start position:0%
+my answer sin Theta I would replace sin
+ 
+
+ align:start position:0%
+my answer sin Theta I would replace sin
+Theta by this square root divided by xus
+
+ align:start position:0%
+Theta by this square root divided by xus
+ 
+
+ align:start position:0%
+Theta by this square root divided by xus
+4 because that's what sin Theta is and
+
+ align:start position:0%
+4 because that's what sin Theta is and
+ 
+
+ align:start position:0%
+4 because that's what sin Theta is and
+so from that's how I finish this type of
+
+ align:start position:0%
+so from that's how I finish this type of
+ 
+
+ align:start position:0%
+so from that's how I finish this type of
+problem always I want to have a picture
+
+ align:start position:0%
+problem always I want to have a picture
+ 
+
+ align:start position:0%
+problem always I want to have a picture
+this triangle label a Theta use my
+
+ align:start position:0%
+this triangle label a Theta use my
+ 
+
+ align:start position:0%
+this triangle label a Theta use my
+substitution to give me what the two of
+
+ align:start position:0%
+substitution to give me what the two of
+ 
+
+ align:start position:0%
+substitution to give me what the two of
+the sides are use the Pythagorean
+
+ align:start position:0%
+the sides are use the Pythagorean
+ 
+
+ align:start position:0%
+the sides are use the Pythagorean
+theorem to get the third side so that's
+
+ align:start position:0%
+theorem to get the third side so that's
+ 
+
+ align:start position:0%
+theorem to get the third side so that's
+the strategy so let's go back and just
+
+ align:start position:0%
+the strategy so let's go back and just
+ 
+
+ align:start position:0%
+the strategy so let's go back and just
+remind ourselves where we came from
+
+ align:start position:0%
+remind ourselves where we came from
+ 
+
+ align:start position:0%
+remind ourselves where we came from
+we're going to go all the way to the
+
+ align:start position:0%
+we're going to go all the way to the
+ 
+
+ align:start position:0%
+we're going to go all the way to the
+other side this was a long long
+
+ align:start position:0%
+other side this was a long long
+ 
+
+ align:start position:0%
+other side this was a long long
+problem so what did we do in this
+
+ align:start position:0%
+problem so what did we do in this
+ 
+
+ align:start position:0%
+problem so what did we do in this
+problem I wanted us to find an
+
+ align:start position:0%
+problem I wanted us to find an
+ 
+
+ align:start position:0%
+problem I wanted us to find an
+anti-derivative of something and right
+
+ align:start position:0%
+anti-derivative of something and right
+ 
+
+ align:start position:0%
+anti-derivative of something and right
+away we can't use uh we can't use
+
+ align:start position:0%
+away we can't use uh we can't use
+ 
+
+ align:start position:0%
+away we can't use uh we can't use
+partial fractions because we can't
+
+ align:start position:0%
+partial fractions because we can't
+ 
+
+ align:start position:0%
+partial fractions because we can't
+factor out an X here so I'm forced to
+
+ align:start position:0%
+factor out an X here so I'm forced to
+ 
+
+ align:start position:0%
+factor out an X here so I'm forced to
+use completing the square so I completed
+
+ align:start position:0%
+use completing the square so I completed
+ 
+
+ align:start position:0%
+use completing the square so I completed
+the square first that was a little
+
+ align:start position:0%
+the square first that was a little
+ 
+
+ align:start position:0%
+the square first that was a little
+algebra that I had to do first then once
+
+ align:start position:0%
+algebra that I had to do first then once
+ 
+
+ align:start position:0%
+algebra that I had to do first then once
+I have that little bit of Algebra I get
+
+ align:start position:0%
+I have that little bit of Algebra I get
+ 
+
+ align:start position:0%
+I have that little bit of Algebra I get
+into a situation where I'm set up for a
+
+ align:start position:0%
+into a situation where I'm set up for a
+ 
+
+ align:start position:0%
+into a situation where I'm set up for a
+trig
+
+ align:start position:0%
+trig
+ 
+
+ align:start position:0%
+trig
+substitution so then I had to start off
+
+ align:start position:0%
+substitution so then I had to start off
+ 
+
+ align:start position:0%
+substitution so then I had to start off
+and do some trig substituting and the
+
+ align:start position:0%
+and do some trig substituting and the
+ 
+
+ align:start position:0%
+and do some trig substituting and the
+things you have to do to make a trig
+
+ align:start position:0%
+things you have to do to make a trig
+ 
+
+ align:start position:0%
+things you have to do to make a trig
+substitution work are pick the pick the
+
+ align:start position:0%
+substitution work are pick the pick the
+ 
+
+ align:start position:0%
+substitution work are pick the pick the
+right substitution that makes sense
+
+ align:start position:0%
+right substitution that makes sense
+ 
+
+ align:start position:0%
+right substitution that makes sense
+which you were given that in class you
+
+ align:start position:0%
+which you were given that in class you
+ 
+
+ align:start position:0%
+which you were given that in class you
+can also figure it out from a a triangle
+
+ align:start position:0%
+can also figure it out from a a triangle
+ 
+
+ align:start position:0%
+can also figure it out from a a triangle
+picture if you wanted to and then you
+
+ align:start position:0%
+picture if you wanted to and then you
+ 
+
+ align:start position:0%
+picture if you wanted to and then you
+have to make sure you substitute not
+
+ align:start position:0%
+have to make sure you substitute not
+ 
+
+ align:start position:0%
+have to make sure you substitute not
+just for the the expression the function
+
+ align:start position:0%
+just for the the expression the function
+ 
+
+ align:start position:0%
+just for the the expression the function
+of X but also the DX so we did all that
+
+ align:start position:0%
+of X but also the DX so we did all that
+ 
+
+ align:start position:0%
+of X but also the DX so we did all that
+and then we came over further further
+
+ align:start position:0%
+and then we came over further further
+ 
+
+ align:start position:0%
+and then we came over further further
+further further further here and we had
+
+ align:start position:0%
+further further further here and we had
+ 
+
+ align:start position:0%
+further further further here and we had
+everything in terms of theta so then we
+
+ align:start position:0%
+everything in terms of theta so then we
+ 
+
+ align:start position:0%
+everything in terms of theta so then we
+had to look at the we had all these
+
+ align:start position:0%
+had to look at the we had all these
+ 
+
+ align:start position:0%
+had to look at the we had all these
+trigonometric functions of theta we
+
+ align:start position:0%
+trigonometric functions of theta we
+ 
+
+ align:start position:0%
+trigonometric functions of theta we
+simplified that as far as we could we
+
+ align:start position:0%
+simplified that as far as we could we
+ 
+
+ align:start position:0%
+simplified that as far as we could we
+got one we could find then we finally we
+
+ align:start position:0%
+got one we could find then we finally we
+ 
+
+ align:start position:0%
+got one we could find then we finally we
+take the anti-derivative there and then
+
+ align:start position:0%
+take the anti-derivative there and then
+ 
+
+ align:start position:0%
+take the anti-derivative there and then
+in the very end we're going to
+
+ align:start position:0%
+in the very end we're going to
+ 
+
+ align:start position:0%
+in the very end we're going to
+substitute in fora using the triangle
+
+ align:start position:0%
+substitute in fora using the triangle
+ 
+
+ align:start position:0%
+substitute in fora using the triangle
+we've drawn up
+
+ align:start position:0%
+we've drawn up
+ 
+
+ align:start position:0%
+we've drawn up
+here so I think that's where I'm going
+
+ align:start position:0%
+here so I think that's where I'm going
+ 
+
+ align:start position:0%
+here so I think that's where I'm going
+to stop this one also I ran out of board
+
+ align:start position:0%
+to stop this one also I ran out of board
+ 
+
+ align:start position:0%
+to stop this one also I ran out of board
+space so I have to stop
\ No newline at end of file
diff --git a/CR-eOhdxbes.txt b/CR-eOhdxbes.txt
new file mode 100644
index 0000000000000000000000000000000000000000..b9751cabf504b2991459de48b7879d26c33ec96d
--- /dev/null
+++ b/CR-eOhdxbes.txt
@@ -0,0 +1,2219 @@
+align:start position:0%
+ 
+superposition is uh
+
+ align:start position:0%
+superposition is uh
+ 
+
+ align:start position:0%
+superposition is uh
+very unusual and very interesting now
+
+ align:start position:0%
+very unusual and very interesting now
+ 
+
+ align:start position:0%
+very unusual and very interesting now
+we've said about
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+superposition that In classical physics
+
+ align:start position:0%
+superposition that In classical physics
+ 
+
+ align:start position:0%
+superposition that In classical physics
+when we talk about superposition we have
+
+ align:start position:0%
+when we talk about superposition we have
+ 
+
+ align:start position:0%
+when we talk about superposition we have
+electric fields and you add the electric
+
+ align:start position:0%
+electric fields and you add the electric
+ 
+
+ align:start position:0%
+electric fields and you add the electric
+fields and the total electric field is
+
+ align:start position:0%
+fields and the total electric field is
+ 
+
+ align:start position:0%
+fields and the total electric field is
+the sum of electric fields and it's an
+
+ align:start position:0%
+the sum of electric fields and it's an
+ 
+
+ align:start position:0%
+the sum of electric fields and it's an
+electric field and there's nothing
+
+ align:start position:0%
+electric field and there's nothing
+ 
+
+ align:start position:0%
+electric field and there's nothing
+strange about it the nature of
+
+ align:start position:0%
+strange about it the nature of
+ 
+
+ align:start position:0%
+strange about it the nature of
+superposition in quantum mechanics is
+
+ align:start position:0%
+superposition in quantum mechanics is
+ 
+
+ align:start position:0%
+superposition in quantum mechanics is
+very strange
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+superposition I will illustrate it in a
+
+ align:start position:0%
+superposition I will illustrate it in a
+ 
+
+ align:start position:0%
+superposition I will illustrate it in a
+couple of different ways one way is with
+
+ align:start position:0%
+couple of different ways one way is with
+ 
+
+ align:start position:0%
+couple of different ways one way is with
+a device that we will get accustomed to
+
+ align:start position:0%
+a device that we will get accustomed to
+ 
+
+ align:start position:0%
+a device that we will get accustomed to
+it it's called The M
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Zender Zender
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+interferometer which is a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+device with a beam
+
+ align:start position:0%
+device with a beam
+ 
+
+ align:start position:0%
+device with a beam
+splitter in here you send in a beam of
+
+ align:start position:0%
+splitter in here you send in a beam of
+ 
+
+ align:start position:0%
+splitter in here you send in a beam of
+light
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+input beam
+
+ align:start position:0%
+input beam
+ 
+
+ align:start position:0%
+input beam
+splitter and then the light inde half of
+
+ align:start position:0%
+splitter and then the light inde half of
+ 
+
+ align:start position:0%
+splitter and then the light inde half of
+it gets reflected half of it gets
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+transmitted then you put a mirror
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+here mirror one you put a mirror two
+
+ align:start position:0%
+here mirror one you put a mirror two
+ 
+
+ align:start position:0%
+here mirror one you put a mirror two
+here and this gets
+
+ align:start position:0%
+here and this gets
+ 
+
+ align:start position:0%
+here and this gets
+recombined into another beam
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+splitter and then you know if there
+
+ align:start position:0%
+splitter and then you know if there
+ 
+
+ align:start position:0%
+splitter and then you know if there
+would be just a light going in here
+
+ align:start position:0%
+would be just a light going in here
+ 
+
+ align:start position:0%
+would be just a light going in here
+there would be two things going out
+
+ align:start position:0%
+there would be two things going out
+ 
+
+ align:start position:0%
+there would be two things going out
+there's another one coming from the bot
+
+ align:start position:0%
+there's another one coming from the bot
+ 
+
+ align:start position:0%
+there's another one coming from the bot
+botom there will be two there will be
+
+ align:start position:0%
+botom there will be two there will be
+ 
+
+ align:start position:0%
+botom there will be two there will be
+interference so you put a detector d0
+
+ align:start position:0%
+interference so you put a detector d0
+ 
+
+ align:start position:0%
+interference so you put a detector d0
+here and a detector D1
+
+ align:start position:0%
+here and a detector D1
+ 
+
+ align:start position:0%
+here and a detector D1
+here to detect the light so that's um
+
+ align:start position:0%
+here to detect the light so that's um
+ 
+
+ align:start position:0%
+here to detect the light so that's um
+the sketch of the max Zender
+
+ align:start position:0%
+the sketch of the max Zender
+ 
+
+ align:start position:0%
+the sketch of the max Zender
+interferometer beam
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Splitters and mirrors take a beam split
+
+ align:start position:0%
+Splitters and mirrors take a beam split
+ 
+
+ align:start position:0%
+Splitters and mirrors take a beam split
+the light
+
+ align:start position:0%
+the light
+ 
+
+ align:start position:0%
+the light
+go down up and then recombine it and go
+
+ align:start position:0%
+go down up and then recombine it and go
+ 
+
+ align:start position:0%
+go down up and then recombine it and go
+into
+
+ align:start position:0%
+into
+ 
+
+ align:start position:0%
+into
+detectors you can get on this is 18 uh
+
+ align:start position:0%
+detectors you can get on this is 18 uh
+ 
+
+ align:start position:0%
+detectors you can get on this is 18 uh
+was invented by these two people
+
+ align:start position:0%
+was invented by these two people
+ 
+
+ align:start position:0%
+was invented by these two people
+independently
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+1890s
+
+ align:start position:0%
+1890s
+ 
+
+ align:start position:0%
+1890s
+91 to 92
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+apparently and people did this with with
+
+ align:start position:0%
+apparently and people did this with with
+ 
+
+ align:start position:0%
+apparently and people did this with with
+the light beams of light
+
+ align:start position:0%
+the light beams of light
+ 
+
+ align:start position:0%
+the light beams of light
+before they realize their
+
+ align:start position:0%
+before they realize their
+ 
+
+ align:start position:0%
+before they realize their
+photons and what happens with a beam of
+
+ align:start position:0%
+photons and what happens with a beam of
+ 
+
+ align:start position:0%
+photons and what happens with a beam of
+light it's h interesting you know comes
+
+ align:start position:0%
+light it's h interesting you know comes
+ 
+
+ align:start position:0%
+light it's h interesting you know comes
+a beam of light the beam
+
+ align:start position:0%
+a beam of light the beam
+ 
+
+ align:start position:0%
+a beam of light the beam
+splitter sends half of the light one way
+
+ align:start position:0%
+splitter sends half of the light one way
+ 
+
+ align:start position:0%
+splitter sends half of the light one way
+half of the light the other way you
+
+ align:start position:0%
+half of the light the other way you
+ 
+
+ align:start position:0%
+half of the light the other way you
+already know with quantum mechanics
+
+ align:start position:0%
+already know with quantum mechanics
+ 
+
+ align:start position:0%
+already know with quantum mechanics
+that's going to be probabilistic some
+
+ align:start position:0%
+that's going to be probabilistic some
+ 
+
+ align:start position:0%
+that's going to be probabilistic some
+photons will go up maybe some photons
+
+ align:start position:0%
+photons will go up maybe some photons
+ 
+
+ align:start position:0%
+photons will go up maybe some photons
+will go down
+
+ align:start position:0%
+will go down
+ 
+
+ align:start position:0%
+will go down
+or something more strange can
+
+ align:start position:0%
+or something more strange can
+ 
+
+ align:start position:0%
+or something more strange can
+happen if you have a
+
+ align:start position:0%
+happen if you have a
+ 
+
+ align:start position:0%
+happen if you have a
+superposition some photons may go both
+
+ align:start position:0%
+superposition some photons may go both
+ 
+
+ align:start position:0%
+superposition some photons may go both
+up and
+
+ align:start position:0%
+up and
+ 
+
+ align:start position:0%
+up and
+down so that's what can happen in
+
+ align:start position:0%
+down so that's what can happen in
+ 
+
+ align:start position:0%
+down so that's what can happen in
+quantum mechanics we can get if you send
+
+ align:start position:0%
+quantum mechanics we can get if you send
+ 
+
+ align:start position:0%
+quantum mechanics we can get if you send
+the beam classical physics it divides
+
+ align:start position:0%
+the beam classical physics it divides
+ 
+
+ align:start position:0%
+the beam classical physics it divides
+half and half and then combines and
+
+ align:start position:0%
+half and half and then combines and
+ 
+
+ align:start position:0%
+half and half and then combines and
+there's an interference effect here and
+
+ align:start position:0%
+there's an interference effect here and
+ 
+
+ align:start position:0%
+there's an interference effect here and
+we will Design This interferometer in
+
+ align:start position:0%
+we will Design This interferometer in
+ 
+
+ align:start position:0%
+we will Design This interferometer in
+such a way that sometimes we can produce
+
+ align:start position:0%
+such a way that sometimes we can produce
+ 
+
+ align:start position:0%
+such a way that sometimes we can produce
+an interference that everything goes to
+
+ align:start position:0%
+an interference that everything goes to
+ 
+
+ align:start position:0%
+an interference that everything goes to
+D or everything goes to D1 or we can
+
+ align:start position:0%
+D or everything goes to D1 or we can
+ 
+
+ align:start position:0%
+D or everything goes to D1 or we can
+produce suitable interferences that we
+
+ align:start position:0%
+produce suitable interferences that we
+ 
+
+ align:start position:0%
+produce suitable interferences that we
+can get fractions of the power going
+
+ align:start position:0%
+can get fractions of the power going
+ 
+
+ align:start position:0%
+can get fractions of the power going
+into D1 and
+
+ align:start position:0%
+into D1 and
+ 
+
+ align:start position:0%
+into D1 and
+D2 d0 and D1 so uh we can do it in
+
+ align:start position:0%
+D2 d0 and D1 so uh we can do it in
+ 
+
+ align:start position:0%
+D2 d0 and D1 so uh we can do it in
+different ways but uh we should think of
+
+ align:start position:0%
+different ways but uh we should think of
+ 
+
+ align:start position:0%
+different ways but uh we should think of
+this as a single photons single photons
+
+ align:start position:0%
+this as a single photons single photons
+ 
+
+ align:start position:0%
+this as a single photons single photons
+going one at a time you see whatever
+
+ align:start position:0%
+going one at a time you see whatever
+ 
+
+ align:start position:0%
+going one at a time you see whatever
+light you put in here experimentally the
+
+ align:start position:0%
+light you put in here experimentally the
+ 
+
+ align:start position:0%
+light you put in here experimentally the
+same frequency goes out here so what is
+
+ align:start position:0%
+same frequency goes out here so what is
+ 
+
+ align:start position:0%
+same frequency goes out here so what is
+interference you might think intuitively
+
+ align:start position:0%
+interference you might think intuitively
+ 
+
+ align:start position:0%
+interference you might think intuitively
+that
+
+ align:start position:0%
+that
+ 
+
+ align:start position:0%
+that
+interference is one Photon interfering
+
+ align:start position:0%
+interference is one Photon interfering
+ 
+
+ align:start position:0%
+interference is one Photon interfering
+with another one but it can't
+
+ align:start position:0%
+with another one but it can't
+ 
+
+ align:start position:0%
+with another one but it can't
+be if two photons would interfere in a
+
+ align:start position:0%
+be if two photons would interfere in a
+ 
+
+ align:start position:0%
+be if two photons would interfere in a
+cancelling destructive interference you
+
+ align:start position:0%
+cancelling destructive interference you
+ 
+
+ align:start position:0%
+cancelling destructive interference you
+would have a bunch of energy it goes
+
+ align:start position:0%
+would have a bunch of energy it goes
+ 
+
+ align:start position:0%
+would have a bunch of energy it goes
+into nothing it's
+
+ align:start position:0%
+into nothing it's
+ 
+
+ align:start position:0%
+into nothing it's
+impossible if they would interfere
+
+ align:start position:0%
+impossible if they would interfere
+ 
+
+ align:start position:0%
+impossible if they would interfere
+constructively you would add the
+
+ align:start position:0%
+constructively you would add the
+ 
+
+ align:start position:0%
+constructively you would add the
+electric fields and the amplitude would
+
+ align:start position:0%
+electric fields and the amplitude would
+ 
+
+ align:start position:0%
+electric fields and the amplitude would
+be four times as big because it's
+
+ align:start position:0%
+be four times as big because it's
+ 
+
+ align:start position:0%
+be four times as big because it's
+proportional to the square so but two
+
+ align:start position:0%
+proportional to the square so but two
+ 
+
+ align:start position:0%
+proportional to the square so but two
+photons are not going to go to four
+
+ align:start position:0%
+photons are not going to go to four
+ 
+
+ align:start position:0%
+photons are not going to go to four
+photons cannot conserve energy so first
+
+ align:start position:0%
+photons cannot conserve energy so first
+ 
+
+ align:start position:0%
+photons cannot conserve energy so first
+of all when you get light
+
+ align:start position:0%
+of all when you get light
+ 
+
+ align:start position:0%
+of all when you get light
+interference each photon is interfering
+
+ align:start position:0%
+interference each photon is interfering
+ 
+
+ align:start position:0%
+interference each photon is interfering
+with itself
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+it's uh sounds crazy but it's the only
+
+ align:start position:0%
+it's uh sounds crazy but it's the only
+ 
+
+ align:start position:0%
+it's uh sounds crazy but it's the only
+possibility they cannot interfere with
+
+ align:start position:0%
+possibility they cannot interfere with
+ 
+
+ align:start position:0%
+possibility they cannot interfere with
+each other you can send the photons one
+
+ align:start position:0%
+each other you can send the photons one
+ 
+
+ align:start position:0%
+each other you can send the photons one
+at a
+
+ align:start position:0%
+at a
+ 
+
+ align:start position:0%
+at a
+time and therefore each
+
+ align:start position:0%
+time and therefore each
+ 
+
+ align:start position:0%
+time and therefore each
+Photon will have to be in both beams at
+
+ align:start position:0%
+Photon will have to be in both beams at
+ 
+
+ align:start position:0%
+Photon will have to be in both beams at
+the same time and then each Photon as it
+
+ align:start position:0%
+the same time and then each Photon as it
+ 
+
+ align:start position:0%
+the same time and then each Photon as it
+goes along there will be an interference
+
+ align:start position:0%
+goes along there will be an interference
+ 
+
+ align:start position:0%
+goes along there will be an interference
+effect and the photon may end up here or
+
+ align:start position:0%
+effect and the photon may end up here or
+ 
+
+ align:start position:0%
+effect and the photon may end up here or
+end up there in in a probabilistic way
+
+ align:start position:0%
+end up there in in a probabilistic way
+ 
+
+ align:start position:0%
+end up there in in a probabilistic way
+so you have an example of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+superposition per position a single
+
+ align:start position:0%
+superposition per position a single
+ 
+
+ align:start position:0%
+superposition per position a single
+Photon
+
+ align:start position:0%
+Photon
+ 
+
+ align:start position:0%
+Photon
+State a single
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+photon is a super is equal to
+
+ align:start position:0%
+photon is a super is equal to
+ 
+
+ align:start position:0%
+photon is a super is equal to
+superposition of a
+
+ align:start position:0%
+superposition of a
+ 
+
+ align:start position:0%
+superposition of a
+photon in the upper beam
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and a
+
+ align:start position:0%
+and a
+ 
+
+ align:start position:0%
+and a
+photon in the lower
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+beam it's like two different states a
+
+ align:start position:0%
+beam it's like two different states a
+ 
+
+ align:start position:0%
+beam it's like two different states a
+little different from here you had
+
+ align:start position:0%
+little different from here you had
+ 
+
+ align:start position:0%
+little different from here you had
+photons in two different polarization
+
+ align:start position:0%
+photons in two different polarization
+ 
+
+ align:start position:0%
+photons in two different polarization
+States superposed here you have photons
+
+ align:start position:0%
+States superposed here you have photons
+ 
+
+ align:start position:0%
+States superposed here you have photons
+in two different beams a single photon
+
+ align:start position:0%
+in two different beams a single photon
+ 
+
+ align:start position:0%
+in two different beams a single photon
+is in both beams at the same time and
+
+ align:start position:0%
+is in both beams at the same time and
+ 
+
+ align:start position:0%
+is in both beams at the same time and
+unless you have that you cannot get a
+
+ align:start position:0%
+unless you have that you cannot get a
+ 
+
+ align:start position:0%
+unless you have that you cannot get a
+superposition and an interference that
+
+ align:start position:0%
+superposition and an interference that
+ 
+
+ align:start position:0%
+superposition and an interference that
+is consistent with the experiment so
+
+ align:start position:0%
+is consistent with the experiment so
+ 
+
+ align:start position:0%
+is consistent with the experiment so
+what does that mean um for
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+superpositions well it means something U
+
+ align:start position:0%
+superpositions well it means something U
+ 
+
+ align:start position:0%
+superpositions well it means something U
+that we
+
+ align:start position:0%
+that we
+ 
+
+ align:start position:0%
+that we
+can discuss and uh I can say things that
+
+ align:start position:0%
+can discuss and uh I can say things that
+ 
+
+ align:start position:0%
+can discuss and uh I can say things that
+at this moment may not make too
+
+ align:start position:0%
+at this moment may not make too
+ 
+
+ align:start position:0%
+at this moment may not make too
+much sense but uh would be a good idea
+
+ align:start position:0%
+much sense but uh would be a good idea
+ 
+
+ align:start position:0%
+much sense but uh would be a good idea
+that you think about them a little bit
+
+ align:start position:0%
+that you think about them a little bit
+ 
+
+ align:start position:0%
+that you think about them a little bit
+we Associated states with
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+vectors States and vectors are the same
+
+ align:start position:0%
+vectors States and vectors are the same
+ 
+
+ align:start position:0%
+vectors States and vectors are the same
+thing and it so happens that when you
+
+ align:start position:0%
+thing and it so happens that when you
+ 
+
+ align:start position:0%
+thing and it so happens that when you
+have vectors you can write them as the
+
+ align:start position:0%
+have vectors you can write them as the
+ 
+
+ align:start position:0%
+have vectors you can write them as the
+sum of other
+
+ align:start position:0%
+sum of other
+ 
+
+ align:start position:0%
+sum of other
+vectors so the sum of these two vectors
+
+ align:start position:0%
+vectors so the sum of these two vectors
+ 
+
+ align:start position:0%
+vectors so the sum of these two vectors
+may be this Vector but you can also
+
+ align:start position:0%
+may be this Vector but you can also
+ 
+
+ align:start position:0%
+may be this Vector but you can also
+write it as the sum of these two vectors
+
+ align:start position:0%
+write it as the sum of these two vectors
+ 
+
+ align:start position:0%
+write it as the sum of these two vectors
+these two vectors add to this thing and
+
+ align:start position:0%
+these two vectors add to this thing and
+ 
+
+ align:start position:0%
+these two vectors add to this thing and
+you can write any Vector as a sum of
+
+ align:start position:0%
+you can write any Vector as a sum of
+ 
+
+ align:start position:0%
+you can write any Vector as a sum of
+different
+
+ align:start position:0%
+different
+ 
+
+ align:start position:0%
+different
+vectors and that's actually quite
+
+ align:start position:0%
+vectors and that's actually quite
+ 
+
+ align:start position:0%
+vectors and that's actually quite
+relevant you will be doing that in
+
+ align:start position:0%
+relevant you will be doing that in
+ 
+
+ align:start position:0%
+relevant you will be doing that in
+during the semester writing a state a
+
+ align:start position:0%
+during the semester writing a state a
+ 
+
+ align:start position:0%
+during the semester writing a state a
+superposition of different things and in
+
+ align:start position:0%
+superposition of different things and in
+ 
+
+ align:start position:0%
+superposition of different things and in
+that way you will understand the physics
+
+ align:start position:0%
+that way you will understand the physics
+ 
+
+ align:start position:0%
+that way you will understand the physics
+of those States so for example we can
+
+ align:start position:0%
+of those States so for example we can
+ 
+
+ align:start position:0%
+of those States so for example we can
+think of two states
+
+ align:start position:0%
+think of two states
+ 
+
+ align:start position:0%
+think of two states
+A and B and you see as I said States
+
+ align:start position:0%
+A and B and you see as I said States
+ 
+
+ align:start position:0%
+A and B and you see as I said States
+wave functions vectors we're all calling
+
+ align:start position:0%
+wave functions vectors we're all calling
+ 
+
+ align:start position:0%
+wave functions vectors we're all calling
+them the same thing if you have a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+superposition
+
+ align:start position:0%
+superposition
+ 
+
+ align:start position:0%
+superposition
+position of the states
+
+ align:start position:0%
+position of the states
+ 
+
+ align:start position:0%
+position of the states
+A and
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+B what can
+
+ align:start position:0%
+B what can
+ 
+
+ align:start position:0%
+B what can
+happen all right we we'll do it the
+
+ align:start position:0%
+happen all right we we'll do it the
+ 
+
+ align:start position:0%
+happen all right we we'll do it the
+following way let's
+
+ align:start position:0%
+following way let's
+ 
+
+ align:start position:0%
+following way let's
+assume
+
+ align:start position:0%
+assume
+ 
+
+ align:start position:0%
+assume
+assume if you
+
+ align:start position:0%
+assume if you
+ 
+
+ align:start position:0%
+assume if you
+measure some property
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+on
+
+ align:start position:0%
+on
+ 
+
+ align:start position:0%
+on
+a you always
+
+ align:start position:0%
+a you always
+ 
+
+ align:start position:0%
+a you always
+get value
+
+ align:start position:0%
+get value
+ 
+
+ align:start position:0%
+get value
+a so you measure something position
+
+ align:start position:0%
+a so you measure something position
+ 
+
+ align:start position:0%
+a so you measure something position
+momentum angular momentum
+
+ align:start position:0%
+momentum angular momentum
+ 
+
+ align:start position:0%
+momentum angular momentum
+spin energy
+
+ align:start position:0%
+spin energy
+ 
+
+ align:start position:0%
+spin energy
+something on
+
+ align:start position:0%
+something on
+ 
+
+ align:start position:0%
+something on
+a is a state that you always get a
+
+ align:start position:0%
+a is a state that you always get a
+ 
+
+ align:start position:0%
+a is a state that you always get a
+suppose you measure the
+
+ align:start position:0%
+suppose you measure the
+ 
+
+ align:start position:0%
+suppose you measure the
+same property on B
+
+ align:start position:0%
+same property on B
+ 
+
+ align:start position:0%
+same property on B
+you always
+
+ align:start position:0%
+you always
+ 
+
+ align:start position:0%
+you always
+get b as the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+value and
+
+ align:start position:0%
+value and
+ 
+
+ align:start position:0%
+value and
+now suppose you have a quantum
+
+ align:start position:0%
+now suppose you have a quantum
+ 
+
+ align:start position:0%
+now suppose you have a quantum
+mechanical
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+State and the state is Alpha
+
+ align:start position:0%
+State and the state is Alpha
+ 
+
+ align:start position:0%
+State and the state is Alpha
+a plus beta B is a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+superos this is your
+
+ align:start position:0%
+superos this is your
+ 
+
+ align:start position:0%
+superos this is your
+state you superimpose A and B and now
+
+ align:start position:0%
+state you superimpose A and B and now
+ 
+
+ align:start position:0%
+state you superimpose A and B and now
+you
+
+ align:start position:0%
+you
+ 
+
+ align:start position:0%
+you
+measure that
+
+ align:start position:0%
+measure that
+ 
+
+ align:start position:0%
+measure that
+property that same property you could
+
+ align:start position:0%
+property that same property you could
+ 
+
+ align:start position:0%
+property that same property you could
+measure here you measure it in your
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+state the the question is what will you
+
+ align:start position:0%
+state the the question is what will you
+ 
+
+ align:start position:0%
+state the the question is what will you
+get you've now superposed those states
+
+ align:start position:0%
+get you've now superposed those states
+ 
+
+ align:start position:0%
+get you've now superposed those states
+on the first state you always get a on
+
+ align:start position:0%
+on the first state you always get a on
+ 
+
+ align:start position:0%
+on the first state you always get a on
+the second state you always get B what
+
+ align:start position:0%
+the second state you always get B what
+ 
+
+ align:start position:0%
+the second state you always get B what
+do you get on the super Post State where
+
+ align:start position:0%
+do you get on the super Post State where
+ 
+
+ align:start position:0%
+do you get on the super Post State where
+Alpha and beta are
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+numbers complex numbers in
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+general well the most uh perhaps
+
+ align:start position:0%
+general well the most uh perhaps
+ 
+
+ align:start position:0%
+general well the most uh perhaps
+immediate guess is that you would get
+
+ align:start position:0%
+immediate guess is that you would get
+ 
+
+ align:start position:0%
+immediate guess is that you would get
+something in between maybe Alpha a plus
+
+ align:start position:0%
+something in between maybe Alpha a plus
+ 
+
+ align:start position:0%
+something in between maybe Alpha a plus
+beta b or an average or
+
+ align:start position:0%
+beta b or an average or
+ 
+
+ align:start position:0%
+beta b or an average or
+something but no that's not what happens
+
+ align:start position:0%
+something but no that's not what happens
+ 
+
+ align:start position:0%
+something but no that's not what happens
+in quantum mechanics in quantum
+
+ align:start position:0%
+in quantum mechanics in quantum
+ 
+
+ align:start position:0%
+in quantum mechanics in quantum
+mechanics it you always get a
+
+ align:start position:0%
+mechanics it you always get a
+ 
+
+ align:start position:0%
+mechanics it you always get a
+or you always get
+
+ align:start position:0%
+or you always get
+ 
+
+ align:start position:0%
+or you always get
+B so you can do the experiment many
+
+ align:start position:0%
+B so you can do the experiment many
+ 
+
+ align:start position:0%
+B so you can do the experiment many
+times and you will get a many times and
+
+ align:start position:0%
+times and you will get a many times and
+ 
+
+ align:start position:0%
+times and you will get a many times and
+you may get B many times but you never
+
+ align:start position:0%
+you may get B many times but you never
+ 
+
+ align:start position:0%
+you may get B many times but you never
+get something
+
+ align:start position:0%
+get something
+ 
+
+ align:start position:0%
+get something
+intermediate so this is very different
+
+ align:start position:0%
+intermediate so this is very different
+ 
+
+ align:start position:0%
+intermediate so this is very different
+than In classical physics if a wave has
+
+ align:start position:0%
+than In classical physics if a wave has
+ 
+
+ align:start position:0%
+than In classical physics if a wave has
+some amplitude and you add another wave
+
+ align:start position:0%
+some amplitude and you add another wave
+ 
+
+ align:start position:0%
+some amplitude and you add another wave
+of different amplitude you measure the
+
+ align:start position:0%
+of different amplitude you measure the
+ 
+
+ align:start position:0%
+of different amplitude you measure the
+energy you get something intermediate
+
+ align:start position:0%
+energy you get something intermediate
+ 
+
+ align:start position:0%
+energy you get something intermediate
+here not you make the superposition and
+
+ align:start position:0%
+here not you make the superposition and
+ 
+
+ align:start position:0%
+here not you make the superposition and
+as you measure you will either get the
+
+ align:start position:0%
+as you measure you will either get the
+ 
+
+ align:start position:0%
+as you measure you will either get the
+little a or the little B but with
+
+ align:start position:0%
+little a or the little B but with
+ 
+
+ align:start position:0%
+little a or the little B but with
+different probabilities so roughly
+
+ align:start position:0%
+different probabilities so roughly
+ 
+
+ align:start position:0%
+different probabilities so roughly
+speaking the
+
+ align:start position:0%
+speaking the
+ 
+
+ align:start position:0%
+speaking the
+probability to get little a is
+
+ align:start position:0%
+probability to get little a is
+ 
+
+ align:start position:0%
+probability to get little a is
+proportional to the number in front of
+
+ align:start position:0%
+proportional to the number in front of
+ 
+
+ align:start position:0%
+proportional to the number in front of
+here is Alpha
+
+ align:start position:0%
+here is Alpha
+ 
+
+ align:start position:0%
+here is Alpha
+squared and the
+
+ align:start position:0%
+squared and the
+ 
+
+ align:start position:0%
+squared and the
+probability to measure little B is
+
+ align:start position:0%
+probability to measure little B is
+ 
+
+ align:start position:0%
+probability to measure little B is
+proportional to Beta
+
+ align:start position:0%
+proportional to Beta
+ 
+
+ align:start position:0%
+proportional to Beta
+squar so
+
+ align:start position:0%
+squar so
+ 
+
+ align:start position:0%
+squar so
+in a Quantum
+
+ align:start position:0%
+in a Quantum
+ 
+
+ align:start position:0%
+in a Quantum
+superposition a single measurement
+
+ align:start position:0%
+superposition a single measurement
+ 
+
+ align:start position:0%
+superposition a single measurement
+doesn't yield an average result or an
+
+ align:start position:0%
+doesn't yield an average result or an
+ 
+
+ align:start position:0%
+doesn't yield an average result or an
+intermediate result it leads one or the
+
+ align:start position:0%
+intermediate result it leads one or the
+ 
+
+ align:start position:0%
+intermediate result it leads one or the
+other and this should connect with this
+
+ align:start position:0%
+other and this should connect with this
+ 
+
+ align:start position:0%
+other and this should connect with this
+um think of the photon we were talking
+
+ align:start position:0%
+um think of the photon we were talking
+ 
+
+ align:start position:0%
+um think of the photon we were talking
+before if you think of the photon that
+
+ align:start position:0%
+before if you think of the photon that
+ 
+
+ align:start position:0%
+before if you think of the photon that
+was at an angle Alpha in this way you
+
+ align:start position:0%
+was at an angle Alpha in this way you
+ 
+
+ align:start position:0%
+was at an angle Alpha in this way you
+could say that the part polarizer is
+
+ align:start position:0%
+could say that the part polarizer is
+ 
+
+ align:start position:0%
+could say that the part polarizer is
+measuring the polarization of the object
+
+ align:start position:0%
+measuring the polarization of the object
+ 
+
+ align:start position:0%
+measuring the polarization of the object
+and therefore what is the possible
+
+ align:start position:0%
+and therefore what is the possible
+ 
+
+ align:start position:0%
+and therefore what is the possible
+result it may
+
+ align:start position:0%
+result it may
+ 
+
+ align:start position:0%
+result it may
+measure the polarization and say oh if
+
+ align:start position:0%
+measure the polarization and say oh if
+ 
+
+ align:start position:0%
+measure the polarization and say oh if
+it's in the X
+
+ align:start position:0%
+it's in the X
+ 
+
+ align:start position:0%
+it's in the X
+Direction you get it right and what is
+
+ align:start position:0%
+Direction you get it right and what is
+ 
+
+ align:start position:0%
+Direction you get it right and what is
+the probability that you get it to be in
+
+ align:start position:0%
+the probability that you get it to be in
+ 
+
+ align:start position:0%
+the probability that you get it to be in
+the X direction is proportional to
+
+ align:start position:0%
+the X direction is proportional to
+ 
+
+ align:start position:0%
+the X direction is proportional to
+cosine squar Alpha the coefficient here
+
+ align:start position:0%
+cosine squar Alpha the coefficient here
+ 
+
+ align:start position:0%
+cosine squar Alpha the coefficient here
+squared so the probability that you find
+
+ align:start position:0%
+squared so the probability that you find
+ 
+
+ align:start position:0%
+squared so the probability that you find
+the photon after measuring in the X
+
+ align:start position:0%
+the photon after measuring in the X
+ 
+
+ align:start position:0%
+the photon after measuring in the X
+direction is cosine squ Alpha and the
+
+ align:start position:0%
+direction is cosine squ Alpha and the
+ 
+
+ align:start position:0%
+direction is cosine squ Alpha and the
+probability that you'll find it here is
+
+ align:start position:0%
+probability that you'll find it here is
+ 
+
+ align:start position:0%
+probability that you'll find it here is
+sin squ Alpha and after you measure you
+
+ align:start position:0%
+sin squ Alpha and after you measure you
+ 
+
+ align:start position:0%
+sin squ Alpha and after you measure you
+get this state which is to say the
+
+ align:start position:0%
+get this state which is to say the
+ 
+
+ align:start position:0%
+get this state which is to say the
+following thing the
+
+ align:start position:0%
+following thing the
+ 
+
+ align:start position:0%
+following thing the
+probability to get the value a is Alpha
+
+ align:start position:0%
+probability to get the value a is Alpha
+ 
+
+ align:start position:0%
+probability to get the value a is Alpha
+squar but if you get
+
+ align:start position:0%
+squar but if you get
+ 
+
+ align:start position:0%
+squar but if you get
+a if you get
+
+ align:start position:0%
+a if you get
+ 
+
+ align:start position:0%
+a if you get
+a the
+
+ align:start position:0%
+a the
+ 
+
+ align:start position:0%
+a the
+state be
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+becomes
+
+ align:start position:0%
+becomes
+ 
+
+ align:start position:0%
+becomes
+a because this whole state of the system
+
+ align:start position:0%
+a because this whole state of the system
+ 
+
+ align:start position:0%
+a because this whole state of the system
+becomes that because successive
+
+ align:start position:0%
+becomes that because successive
+ 
+
+ align:start position:0%
+becomes that because successive
+measurements will keep giving you the
+
+ align:start position:0%
+measurements will keep giving you the
+ 
+
+ align:start position:0%
+measurements will keep giving you the
+value
+
+ align:start position:0%
+value
+ 
+
+ align:start position:0%
+value
+a if you
+
+ align:start position:0%
+a if you
+ 
+
+ align:start position:0%
+a if you
+get
+
+ align:start position:0%
+get
+ 
+
+ align:start position:0%
+get
+B the state
+
+ align:start position:0%
+B the state
+ 
+
+ align:start position:0%
+B the state
+becomes B so this is a what is called
+
+ align:start position:0%
+becomes B so this is a what is called
+ 
+
+ align:start position:0%
+becomes B so this is a what is called
+the postulate of measurement and the
+
+ align:start position:0%
+the postulate of measurement and the
+ 
+
+ align:start position:0%
+the postulate of measurement and the
+nature of superposition this is perhaps
+
+ align:start position:0%
+nature of superposition this is perhaps
+ 
+
+ align:start position:0%
+nature of superposition this is perhaps
+the most sophisticated idea we've
+
+ align:start position:0%
+the most sophisticated idea we've
+ 
+
+ align:start position:0%
+the most sophisticated idea we've
+discussed
+
+ align:start position:0%
+discussed
+ 
+
+ align:start position:0%
+discussed
+today in which in our Quantum
+
+ align:start position:0%
+today in which in our Quantum
+ 
+
+ align:start position:0%
+today in which in our Quantum
+superposition the results are not
+
+ align:start position:0%
+superposition the results are not
+ 
+
+ align:start position:0%
+superposition the results are not
+intermediate so when you want to figure
+
+ align:start position:0%
+intermediate so when you want to figure
+ 
+
+ align:start position:0%
+intermediate so when you want to figure
+out what state you have you have to
+
+ align:start position:0%
+out what state you have you have to
+ 
+
+ align:start position:0%
+out what state you have you have to
+prepare many copies of your state in
+
+ align:start position:0%
+prepare many copies of your state in
+ 
+
+ align:start position:0%
+prepare many copies of your state in
+this Quantum system and do the
+
+ align:start position:0%
+this Quantum system and do the
+ 
+
+ align:start position:0%
+this Quantum system and do the
+experiment many times because sometimes
+
+ align:start position:0%
+experiment many times because sometimes
+ 
+
+ align:start position:0%
+experiment many times because sometimes
+you'll get a sometimes you'll get B
+
+ align:start position:0%
+you'll get a sometimes you'll get B
+ 
+
+ align:start position:0%
+you'll get a sometimes you'll get B
+after you've measured many times you can
+
+ align:start position:0%
+after you've measured many times you can
+ 
+
+ align:start position:0%
+after you've measured many times you can
+assess the probabilities and reconstruct
+
+ align:start position:0%
+assess the probabilities and reconstruct
+ 
+
+ align:start position:0%
+assess the probabilities and reconstruct
+the state
\ No newline at end of file
diff --git a/CWlJLpAE4BI.txt b/CWlJLpAE4BI.txt
new file mode 100644
index 0000000000000000000000000000000000000000..52e05e405e90b45e93d3dfe711cb777956b85dd3
--- /dev/null
+++ b/CWlJLpAE4BI.txt
@@ -0,0 +1,8035 @@
+align:start position:0%
+ 
+[Music]
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+oh
+
+ align:start position:0%
+oh
+ 
+
+ align:start position:0%
+oh
+[Applause]
+
+ align:start position:0%
+[Applause]
+ 
+
+ align:start position:0%
+[Applause]
+[Music]
+
+ align:start position:0%
+[Music]
+ 
+
+ align:start position:0%
+[Music]
+[Applause]
+
+ align:start position:0%
+[Applause]
+ 
+
+ align:start position:0%
+[Applause]
+[Music]
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+hi last time we had looked at an
+
+ align:start position:0%
+hi last time we had looked at an
+ 
+
+ align:start position:0%
+hi last time we had looked at an
+introduction to compensation of feedback
+
+ align:start position:0%
+introduction to compensation of feedback
+ 
+
+ align:start position:0%
+introduction to compensation of feedback
+systems in other words how do we modify
+
+ align:start position:0%
+systems in other words how do we modify
+ 
+
+ align:start position:0%
+systems in other words how do we modify
+Loop transmission of a feedback system
+
+ align:start position:0%
+Loop transmission of a feedback system
+ 
+
+ align:start position:0%
+Loop transmission of a feedback system
+in order to improve its performance
+
+ align:start position:0%
+in order to improve its performance
+ 
+
+ align:start position:0%
+in order to improve its performance
+possibly increase its speed of response
+
+ align:start position:0%
+possibly increase its speed of response
+ 
+
+ align:start position:0%
+possibly increase its speed of response
+or increase
+
+ align:start position:0%
+or increase
+ 
+
+ align:start position:0%
+or increase
+sensitivity improve the stability of the
+
+ align:start position:0%
+sensitivity improve the stability of the
+ 
+
+ align:start position:0%
+sensitivity improve the stability of the
+system those sorts of modifications that
+
+ align:start position:0%
+system those sorts of modifications that
+ 
+
+ align:start position:0%
+system those sorts of modifications that
+we very frequently want to make to to
+
+ align:start position:0%
+we very frequently want to make to to
+ 
+
+ align:start position:0%
+we very frequently want to make to to
+feedback
+
+ align:start position:0%
+feedback
+ 
+
+ align:start position:0%
+feedback
+systems the simplest kind of
+
+ align:start position:0%
+systems the simplest kind of
+ 
+
+ align:start position:0%
+systems the simplest kind of
+modification we can make is to change
+
+ align:start position:0%
+modification we can make is to change
+ 
+
+ align:start position:0%
+modification we can make is to change
+the low frequency magnitude of the loop
+
+ align:start position:0%
+the low frequency magnitude of the loop
+ 
+
+ align:start position:0%
+the low frequency magnitude of the loop
+Transmission in the notation we've been
+
+ align:start position:0%
+Transmission in the notation we've been
+ 
+
+ align:start position:0%
+Transmission in the notation we've been
+using the a fnot product and we've
+
+ align:start position:0%
+using the a fnot product and we've
+ 
+
+ align:start position:0%
+using the a fnot product and we've
+looked at how that influences the root
+
+ align:start position:0%
+looked at how that influences the root
+ 
+
+ align:start position:0%
+looked at how that influences the root
+Locust diagram for example and and last
+
+ align:start position:0%
+Locust diagram for example and and last
+ 
+
+ align:start position:0%
+Locust diagram for example and and last
+time looked at how that might improve
+
+ align:start position:0%
+time looked at how that might improve
+ 
+
+ align:start position:0%
+time looked at how that might improve
+the stability of the system today I'd
+
+ align:start position:0%
+the stability of the system today I'd
+ 
+
+ align:start position:0%
+the stability of the system today I'd
+like to look at somewhat more
+
+ align:start position:0%
+like to look at somewhat more
+ 
+
+ align:start position:0%
+like to look at somewhat more
+complicated modifications of the loop
+
+ align:start position:0%
+complicated modifications of the loop
+ 
+
+ align:start position:0%
+complicated modifications of the loop
+Transmission in particular ones that
+
+ align:start position:0%
+Transmission in particular ones that
+ 
+
+ align:start position:0%
+Transmission in particular ones that
+change the Dynamics associated with the
+
+ align:start position:0%
+change the Dynamics associated with the
+ 
+
+ align:start position:0%
+change the Dynamics associated with the
+loop
+
+ align:start position:0%
+loop
+ 
+
+ align:start position:0%
+loop
+transmission the simplest thing that we
+
+ align:start position:0%
+transmission the simplest thing that we
+ 
+
+ align:start position:0%
+transmission the simplest thing that we
+can do is to add a dominant Pole to the
+
+ align:start position:0%
+can do is to add a dominant Pole to the
+ 
+
+ align:start position:0%
+can do is to add a dominant Pole to the
+system suppose we start with A system
+
+ align:start position:0%
+system suppose we start with A system
+ 
+
+ align:start position:0%
+system suppose we start with A system
+that has a bod plot as shown here's the
+
+ align:start position:0%
+that has a bod plot as shown here's the
+ 
+
+ align:start position:0%
+that has a bod plot as shown here's the
+AF product as a function of
+
+ align:start position:0%
+AF product as a function of
+ 
+
+ align:start position:0%
+AF product as a function of
+frequency the magnitude and the angle in
+
+ align:start position:0%
+frequency the magnitude and the angle in
+ 
+
+ align:start position:0%
+frequency the magnitude and the angle in
+our usual body plot
+
+ align:start position:0%
+our usual body plot
+ 
+
+ align:start position:0%
+our usual body plot
+coordinates and as I've drawn things the
+
+ align:start position:0%
+coordinates and as I've drawn things the
+ 
+
+ align:start position:0%
+coordinates and as I've drawn things the
+system is actually
+
+ align:start position:0%
+system is actually
+ 
+
+ align:start position:0%
+system is actually
+unstable uh this is the unity magnitude
+
+ align:start position:0%
+unstable uh this is the unity magnitude
+ 
+
+ align:start position:0%
+unstable uh this is the unity magnitude
+point so this would be the crossover
+
+ align:start position:0%
+point so this would be the crossover
+ 
+
+ align:start position:0%
+point so this would be the crossover
+frequency for the system the frequency
+
+ align:start position:0%
+frequency for the system the frequency
+ 
+
+ align:start position:0%
+frequency for the system the frequency
+at which the magnitude of the AF product
+
+ align:start position:0%
+at which the magnitude of the AF product
+ 
+
+ align:start position:0%
+at which the magnitude of the AF product
+goes through unity and we notice that by
+
+ align:start position:0%
+goes through unity and we notice that by
+ 
+
+ align:start position:0%
+goes through unity and we notice that by
+that frequency the angle associated with
+
+ align:start position:0%
+that frequency the angle associated with
+ 
+
+ align:start position:0%
+that frequency the angle associated with
+the AF product has gone through minus
+
+ align:start position:0%
+the AF product has gone through minus
+ 
+
+ align:start position:0%
+the AF product has gone through minus
+180° consequently this is a system
+
+ align:start position:0%
+180° consequently this is a system
+ 
+
+ align:start position:0%
+180° consequently this is a system
+that's unstable as shown
+
+ align:start position:0%
+that's unstable as shown
+ 
+
+ align:start position:0%
+that's unstable as shown
+now suppose I'd like to modify that
+
+ align:start position:0%
+now suppose I'd like to modify that
+ 
+
+ align:start position:0%
+now suppose I'd like to modify that
+system and in fact try to increase its
+
+ align:start position:0%
+system and in fact try to increase its
+ 
+
+ align:start position:0%
+system and in fact try to increase its
+phase margin possibly to
+
+ align:start position:0%
+phase margin possibly to
+ 
+
+ align:start position:0%
+phase margin possibly to
+45° if I added one more Pole to the
+
+ align:start position:0%
+45° if I added one more Pole to the
+ 
+
+ align:start position:0%
+45° if I added one more Pole to the
+system at a sufficiently low frequency
+
+ align:start position:0%
+system at a sufficiently low frequency
+ 
+
+ align:start position:0%
+system at a sufficiently low frequency
+what I could do is get the magnitude to
+
+ align:start position:0%
+what I could do is get the magnitude to
+ 
+
+ align:start position:0%
+what I could do is get the magnitude to
+roll off and in fact get down to Unity
+
+ align:start position:0%
+roll off and in fact get down to Unity
+ 
+
+ align:start position:0%
+roll off and in fact get down to Unity
+before I
+
+ align:start position:0%
+before I
+ 
+
+ align:start position:0%
+before I
+acquired enough phase shift to cause
+
+ align:start position:0%
+acquired enough phase shift to cause
+ 
+
+ align:start position:0%
+acquired enough phase shift to cause
+instability let's see how we might do
+
+ align:start position:0%
+instability let's see how we might do
+ 
+
+ align:start position:0%
+instability let's see how we might do
+that I know that if I add a single pole
+
+ align:start position:0%
+that I know that if I add a single pole
+ 
+
+ align:start position:0%
+that I know that if I add a single pole
+well below crossover by the time I get
+
+ align:start position:0%
+well below crossover by the time I get
+ 
+
+ align:start position:0%
+well below crossover by the time I get
+out to the crossover frequency the phase
+
+ align:start position:0%
+out to the crossover frequency the phase
+ 
+
+ align:start position:0%
+out to the crossover frequency the phase
+shift associated with that pole will be
+
+ align:start position:0%
+shift associated with that pole will be
+ 
+
+ align:start position:0%
+shift associated with that pole will be
+very nearly minus
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+90° suppose I look at the original uncom
+
+ align:start position:0%
+90° suppose I look at the original uncom
+ 
+
+ align:start position:0%
+90° suppose I look at the original uncom
+uncompensated bod plot and find the
+
+ align:start position:0%
+uncompensated bod plot and find the
+ 
+
+ align:start position:0%
+uncompensated bod plot and find the
+frequency where the phase shift of the
+
+ align:start position:0%
+frequency where the phase shift of the
+ 
+
+ align:start position:0%
+frequency where the phase shift of the
+original uncompensated system is minus
+
+ align:start position:0%
+original uncompensated system is minus
+ 
+
+ align:start position:0%
+original uncompensated system is minus
+45 degrees I recognize that if I added
+
+ align:start position:0%
+45 degrees I recognize that if I added
+ 
+
+ align:start position:0%
+45 degrees I recognize that if I added
+an additional 90 degrees of negative
+
+ align:start position:0%
+an additional 90 degrees of negative
+ 
+
+ align:start position:0%
+an additional 90 degrees of negative
+phase shift I'd end up with the angle at
+
+ align:start position:0%
+phase shift I'd end up with the angle at
+ 
+
+ align:start position:0%
+phase shift I'd end up with the angle at
+this frequency being minus 135° in other
+
+ align:start position:0%
+this frequency being minus 135° in other
+ 
+
+ align:start position:0%
+this frequency being minus 135° in other
+words if I could force crossover to
+
+ align:start position:0%
+words if I could force crossover to
+ 
+
+ align:start position:0%
+words if I could force crossover to
+occur at this frequency by adding a
+
+ align:start position:0%
+occur at this frequency by adding a
+ 
+
+ align:start position:0%
+occur at this frequency by adding a
+single pole to the loop transmission at
+
+ align:start position:0%
+single pole to the loop transmission at
+ 
+
+ align:start position:0%
+single pole to the loop transmission at
+a sufficiently low frequency I would end
+
+ align:start position:0%
+a sufficiently low frequency I would end
+ 
+
+ align:start position:0%
+a sufficiently low frequency I would end
+up with a system that has 45 degrees of
+
+ align:start position:0%
+up with a system that has 45 degrees of
+ 
+
+ align:start position:0%
+up with a system that has 45 degrees of
+phase margin so let's see if we can do
+
+ align:start position:0%
+phase margin so let's see if we can do
+ 
+
+ align:start position:0%
+phase margin so let's see if we can do
+that all we do assuming the physical
+
+ align:start position:0%
+that all we do assuming the physical
+ 
+
+ align:start position:0%
+that all we do assuming the physical
+constraints of the system allow that is
+
+ align:start position:0%
+constraints of the system allow that is
+ 
+
+ align:start position:0%
+constraints of the system allow that is
+to somehow add energy storage to the
+
+ align:start position:0%
+to somehow add energy storage to the
+ 
+
+ align:start position:0%
+to somehow add energy storage to the
+system
+
+ align:start position:0%
+system
+ 
+
+ align:start position:0%
+system
+and let's suppose as we indicated we'd
+
+ align:start position:0%
+and let's suppose as we indicated we'd
+ 
+
+ align:start position:0%
+and let's suppose as we indicated we'd
+like to cross over at this
+
+ align:start position:0%
+like to cross over at this
+ 
+
+ align:start position:0%
+like to cross over at this
+frequency and that tells us that we'd
+
+ align:start position:0%
+frequency and that tells us that we'd
+ 
+
+ align:start position:0%
+frequency and that tells us that we'd
+like to have a single pole roll
+
+ align:start position:0%
+like to have a single pole roll
+ 
+
+ align:start position:0%
+like to have a single pole roll
+off like so in the vicinity of crossover
+
+ align:start position:0%
+off like so in the vicinity of crossover
+ 
+
+ align:start position:0%
+off like so in the vicinity of crossover
+if I've accomplished that by adding a
+
+ align:start position:0%
+if I've accomplished that by adding a
+ 
+
+ align:start position:0%
+if I've accomplished that by adding a
+single pole at a sufficiently low
+
+ align:start position:0%
+single pole at a sufficiently low
+ 
+
+ align:start position:0%
+single pole at a sufficiently low
+frequency why we'd end up with a loop
+
+ align:start position:0%
+frequency why we'd end up with a loop
+ 
+
+ align:start position:0%
+frequency why we'd end up with a loop
+transmission magnitude that looks
+
+ align:start position:0%
+transmission magnitude that looks
+ 
+
+ align:start position:0%
+transmission magnitude that looks
+something like this after compensation
+
+ align:start position:0%
+something like this after compensation
+ 
+
+ align:start position:0%
+something like this after compensation
+out in this region we actually have to
+
+ align:start position:0%
+out in this region we actually have to
+ 
+
+ align:start position:0%
+out in this region we actually have to
+follow the original curve uh on top of
+
+ align:start position:0%
+follow the original curve uh on top of
+ 
+
+ align:start position:0%
+follow the original curve uh on top of
+the single pole roll off so possibly
+
+ align:start position:0%
+the single pole roll off so possibly
+ 
+
+ align:start position:0%
+the single pole roll off so possibly
+we'd get a a magnitude that looks
+
+ align:start position:0%
+we'd get a a magnitude that looks
+ 
+
+ align:start position:0%
+we'd get a a magnitude that looks
+something like that the influence on the
+
+ align:start position:0%
+something like that the influence on the
+ 
+
+ align:start position:0%
+something like that the influence on the
+angle associated with the AF product is
+
+ align:start position:0%
+angle associated with the AF product is
+ 
+
+ align:start position:0%
+angle associated with the AF product is
+simply to add an additional 90 de of
+
+ align:start position:0%
+simply to add an additional 90 de of
+ 
+
+ align:start position:0%
+simply to add an additional 90 de of
+phase shift 45 of it occurs at the
+
+ align:start position:0%
+phase shift 45 of it occurs at the
+ 
+
+ align:start position:0%
+phase shift 45 of it occurs at the
+location of the pole and then we ASM
+
+ align:start position:0%
+location of the pole and then we ASM
+ 
+
+ align:start position:0%
+location of the pole and then we ASM
+totically Trail off to an additional 90°
+
+ align:start position:0%
+totically Trail off to an additional 90°
+ 
+
+ align:start position:0%
+totically Trail off to an additional 90°
+of negative phase shift so the
+
+ align:start position:0%
+of negative phase shift so the
+ 
+
+ align:start position:0%
+of negative phase shift so the
+compensated angle might look something
+
+ align:start position:0%
+compensated angle might look something
+ 
+
+ align:start position:0%
+compensated angle might look something
+like
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so here we've acquired our additional 90
+
+ align:start position:0%
+so here we've acquired our additional 90
+ 
+
+ align:start position:0%
+so here we've acquired our additional 90
+de of phase shift and we now go and
+
+ align:start position:0%
+de of phase shift and we now go and
+ 
+
+ align:start position:0%
+de of phase shift and we now go and
+continue parallel to the original angle
+
+ align:start position:0%
+continue parallel to the original angle
+ 
+
+ align:start position:0%
+continue parallel to the original angle
+curve but displaced by minus
+
+ align:start position:0%
+curve but displaced by minus
+ 
+
+ align:start position:0%
+curve but displaced by minus
+90° so our new angle curve might look
+
+ align:start position:0%
+90° so our new angle curve might look
+ 
+
+ align:start position:0%
+90° so our new angle curve might look
+something like that and now we've in
+
+ align:start position:0%
+something like that and now we've in
+ 
+
+ align:start position:0%
+something like that and now we've in
+fact accomplished our objective of
+
+ align:start position:0%
+fact accomplished our objective of
+ 
+
+ align:start position:0%
+fact accomplished our objective of
+achieving 45° of phase margin for the
+
+ align:start position:0%
+achieving 45° of phase margin for the
+ 
+
+ align:start position:0%
+achieving 45° of phase margin for the
+compensated
+
+ align:start position:0%
+compensated
+ 
+
+ align:start position:0%
+compensated
+system the price we've paid however is a
+
+ align:start position:0%
+system the price we've paid however is a
+ 
+
+ align:start position:0%
+system the price we've paid however is a
+very significant one in terms of the
+
+ align:start position:0%
+very significant one in terms of the
+ 
+
+ align:start position:0%
+very significant one in terms of the
+bandwidth of the resultant system
+
+ align:start position:0%
+bandwidth of the resultant system
+ 
+
+ align:start position:0%
+bandwidth of the resultant system
+originally our crossover frequency was
+
+ align:start position:0%
+originally our crossover frequency was
+ 
+
+ align:start position:0%
+originally our crossover frequency was
+out here we've made a very very major
+
+ align:start position:0%
+out here we've made a very very major
+ 
+
+ align:start position:0%
+out here we've made a very very major
+change in crossover frequency we've
+
+ align:start position:0%
+change in crossover frequency we've
+ 
+
+ align:start position:0%
+change in crossover frequency we've
+lowered crossover frequency considerably
+
+ align:start position:0%
+lowered crossover frequency considerably
+ 
+
+ align:start position:0%
+lowered crossover frequency considerably
+by putting in our dominant pole starting
+
+ align:start position:0%
+by putting in our dominant pole starting
+ 
+
+ align:start position:0%
+by putting in our dominant pole starting
+the roll off at a much lower frequency
+
+ align:start position:0%
+the roll off at a much lower frequency
+ 
+
+ align:start position:0%
+the roll off at a much lower frequency
+uh than we originally did we've also
+
+ align:start position:0%
+uh than we originally did we've also
+ 
+
+ align:start position:0%
+uh than we originally did we've also
+lost desensitivity over a very wide
+
+ align:start position:0%
+lost desensitivity over a very wide
+ 
+
+ align:start position:0%
+lost desensitivity over a very wide
+range of frequencies we notice of course
+
+ align:start position:0%
+range of frequencies we notice of course
+ 
+
+ align:start position:0%
+range of frequencies we notice of course
+here's the original magnitude curve
+
+ align:start position:0%
+here's the original magnitude curve
+ 
+
+ align:start position:0%
+here's the original magnitude curve
+we've lowered the AF product at all
+
+ align:start position:0%
+we've lowered the AF product at all
+ 
+
+ align:start position:0%
+we've lowered the AF product at all
+frequencies Beyond this frequency and so
+
+ align:start position:0%
+frequencies Beyond this frequency and so
+ 
+
+ align:start position:0%
+frequencies Beyond this frequency and so
+again compared to the original
+
+ align:start position:0%
+again compared to the original
+ 
+
+ align:start position:0%
+again compared to the original
+uncompensated system we've lost
+
+ align:start position:0%
+uncompensated system we've lost
+ 
+
+ align:start position:0%
+uncompensated system we've lost
+desensitivity and and the Shaded area is
+
+ align:start position:0%
+desensitivity and and the Shaded area is
+ 
+
+ align:start position:0%
+desensitivity and and the Shaded area is
+a measure of the amount of desensitivity
+
+ align:start position:0%
+a measure of the amount of desensitivity
+ 
+
+ align:start position:0%
+a measure of the amount of desensitivity
+we've lost as a function of
+
+ align:start position:0%
+we've lost as a function of
+ 
+
+ align:start position:0%
+we've lost as a function of
+frequency say the disadvantage of that
+
+ align:start position:0%
+frequency say the disadvantage of that
+ 
+
+ align:start position:0%
+frequency say the disadvantage of that
+sort of compensation is simply the
+
+ align:start position:0%
+sort of compensation is simply the
+ 
+
+ align:start position:0%
+sort of compensation is simply the
+greatly narrowing effect that it has on
+
+ align:start position:0%
+greatly narrowing effect that it has on
+ 
+
+ align:start position:0%
+greatly narrowing effect that it has on
+the bandwidth of the system but there's
+
+ align:start position:0%
+the bandwidth of the system but there's
+ 
+
+ align:start position:0%
+the bandwidth of the system but there's
+one important class of of systems where
+
+ align:start position:0%
+one important class of of systems where
+ 
+
+ align:start position:0%
+one important class of of systems where
+that sort of of approach is a very very
+
+ align:start position:0%
+that sort of of approach is a very very
+ 
+
+ align:start position:0%
+that sort of of approach is a very very
+good one to to
+
+ align:start position:0%
+good one to to
+ 
+
+ align:start position:0%
+good one to to
+compensation in particular suppose our
+
+ align:start position:0%
+compensation in particular suppose our
+ 
+
+ align:start position:0%
+compensation in particular suppose our
+objective is to build a regulator that
+
+ align:start position:0%
+objective is to build a regulator that
+ 
+
+ align:start position:0%
+objective is to build a regulator that
+is a system where the intent is to keep
+
+ align:start position:0%
+is a system where the intent is to keep
+ 
+
+ align:start position:0%
+is a system where the intent is to keep
+an output variable fixed this is in
+
+ align:start position:0%
+an output variable fixed this is in
+ 
+
+ align:start position:0%
+an output variable fixed this is in
+contrast to the usual following kind of
+
+ align:start position:0%
+contrast to the usual following kind of
+ 
+
+ align:start position:0%
+contrast to the usual following kind of
+feedback system where we try to command
+
+ align:start position:0%
+feedback system where we try to command
+ 
+
+ align:start position:0%
+feedback system where we try to command
+an output to follow a Time varying input
+
+ align:start position:0%
+an output to follow a Time varying input
+ 
+
+ align:start position:0%
+an output to follow a Time varying input
+and under those conditions when we're
+
+ align:start position:0%
+and under those conditions when we're
+ 
+
+ align:start position:0%
+and under those conditions when we're
+trying to track a Time varying input the
+
+ align:start position:0%
+trying to track a Time varying input the
+ 
+
+ align:start position:0%
+trying to track a Time varying input the
+bandwidth of the system is of course
+
+ align:start position:0%
+bandwidth of the system is of course
+ 
+
+ align:start position:0%
+bandwidth of the system is of course
+very important the closed loop bandwidth
+
+ align:start position:0%
+very important the closed loop bandwidth
+ 
+
+ align:start position:0%
+very important the closed loop bandwidth
+however when we're trying to get the
+
+ align:start position:0%
+however when we're trying to get the
+ 
+
+ align:start position:0%
+however when we're trying to get the
+output of a system to be time invariant
+
+ align:start position:0%
+output of a system to be time invariant
+ 
+
+ align:start position:0%
+output of a system to be time invariant
+a regulator where we want the output to
+
+ align:start position:0%
+a regulator where we want the output to
+ 
+
+ align:start position:0%
+a regulator where we want the output to
+to remain fixed in for all time adding
+
+ align:start position:0%
+to remain fixed in for all time adding
+ 
+
+ align:start position:0%
+to remain fixed in for all time adding
+energy storage to the output creating a
+
+ align:start position:0%
+energy storage to the output creating a
+ 
+
+ align:start position:0%
+energy storage to the output creating a
+dominant pole by basically adding energy
+
+ align:start position:0%
+dominant pole by basically adding energy
+ 
+
+ align:start position:0%
+dominant pole by basically adding energy
+storage to the output really improves
+
+ align:start position:0%
+storage to the output really improves
+ 
+
+ align:start position:0%
+storage to the output really improves
+the stiffness of the output if you will
+
+ align:start position:0%
+the stiffness of the output if you will
+ 
+
+ align:start position:0%
+the stiffness of the output if you will
+it improves the ability of the output to
+
+ align:start position:0%
+it improves the ability of the output to
+ 
+
+ align:start position:0%
+it improves the ability of the output to
+resist
+
+ align:start position:0%
+resist
+ 
+
+ align:start position:0%
+resist
+disturbances as an example of that
+
+ align:start position:0%
+disturbances as an example of that
+ 
+
+ align:start position:0%
+disturbances as an example of that
+consider what happens if we take an
+
+ align:start position:0%
+consider what happens if we take an
+ 
+
+ align:start position:0%
+consider what happens if we take an
+ordinary laboratory power supply and we
+
+ align:start position:0%
+ordinary laboratory power supply and we
+ 
+
+ align:start position:0%
+ordinary laboratory power supply and we
+go searching around and find the largest
+
+ align:start position:0%
+go searching around and find the largest
+ 
+
+ align:start position:0%
+go searching around and find the largest
+capacitor we can find and roll that up
+
+ align:start position:0%
+capacitor we can find and roll that up
+ 
+
+ align:start position:0%
+capacitor we can find and roll that up
+to the power supply and just clamp it
+
+ align:start position:0%
+to the power supply and just clamp it
+ 
+
+ align:start position:0%
+to the power supply and just clamp it
+onto the output terminals we may have
+
+ align:start position:0%
+onto the output terminals we may have
+ 
+
+ align:start position:0%
+onto the output terminals we may have
+some trouble starting the supply when we
+
+ align:start position:0%
+some trouble starting the supply when we
+ 
+
+ align:start position:0%
+some trouble starting the supply when we
+first turn it on it may take a while to
+
+ align:start position:0%
+first turn it on it may take a while to
+ 
+
+ align:start position:0%
+first turn it on it may take a while to
+charge up the large capacitor that we've
+
+ align:start position:0%
+charge up the large capacitor that we've
+ 
+
+ align:start position:0%
+charge up the large capacitor that we've
+added to the output of the system but
+
+ align:start position:0%
+added to the output of the system but
+ 
+
+ align:start position:0%
+added to the output of the system but
+once we finally get the capacitor
+
+ align:start position:0%
+once we finally get the capacitor
+ 
+
+ align:start position:0%
+once we finally get the capacitor
+charged we're in very good shape the
+
+ align:start position:0%
+charged we're in very good shape the
+ 
+
+ align:start position:0%
+charged we're in very good shape the
+capacitor at the output of the feedback
+
+ align:start position:0%
+capacitor at the output of the feedback
+ 
+
+ align:start position:0%
+capacitor at the output of the feedback
+system or the regulator in this case
+
+ align:start position:0%
+system or the regulator in this case
+ 
+
+ align:start position:0%
+system or the regulator in this case
+resists disturbances that come for
+
+ align:start position:0%
+resists disturbances that come for
+ 
+
+ align:start position:0%
+resists disturbances that come for
+example from changes in load current
+
+ align:start position:0%
+example from changes in load current
+ 
+
+ align:start position:0%
+example from changes in load current
+from changes in primary unregulated
+
+ align:start position:0%
+from changes in primary unregulated
+ 
+
+ align:start position:0%
+from changes in primary unregulated
+voltage and so forth and really helps
+
+ align:start position:0%
+voltage and so forth and really helps
+ 
+
+ align:start position:0%
+voltage and so forth and really helps
+improve the resistance of the system to
+
+ align:start position:0%
+improve the resistance of the system to
+ 
+
+ align:start position:0%
+improve the resistance of the system to
+those kinds of of disturbances so if our
+
+ align:start position:0%
+those kinds of of disturbances so if our
+ 
+
+ align:start position:0%
+those kinds of of disturbances so if our
+intent is to build a regulator where
+
+ align:start position:0%
+intent is to build a regulator where
+ 
+
+ align:start position:0%
+intent is to build a regulator where
+what we want to do is keep the output of
+
+ align:start position:0%
+what we want to do is keep the output of
+ 
+
+ align:start position:0%
+what we want to do is keep the output of
+the system time in variant then adding a
+
+ align:start position:0%
+the system time in variant then adding a
+ 
+
+ align:start position:0%
+the system time in variant then adding a
+dominant pole providing we put the
+
+ align:start position:0%
+dominant pole providing we put the
+ 
+
+ align:start position:0%
+dominant pole providing we put the
+energy storage associated with the pole
+
+ align:start position:0%
+energy storage associated with the pole
+ 
+
+ align:start position:0%
+energy storage associated with the pole
+at the output of the system at the
+
+ align:start position:0%
+at the output of the system at the
+ 
+
+ align:start position:0%
+at the output of the system at the
+variable where we're trying that we're
+
+ align:start position:0%
+variable where we're trying that we're
+ 
+
+ align:start position:0%
+variable where we're trying that we're
+trying to keep constant why we get an
+
+ align:start position:0%
+trying to keep constant why we get an
+ 
+
+ align:start position:0%
+trying to keep constant why we get an
+improvement in
+
+ align:start position:0%
+improvement in
+ 
+
+ align:start position:0%
+improvement in
+performance I do an example in the book
+
+ align:start position:0%
+performance I do an example in the book
+ 
+
+ align:start position:0%
+performance I do an example in the book
+of an electronic regulator and show how
+
+ align:start position:0%
+of an electronic regulator and show how
+ 
+
+ align:start position:0%
+of an electronic regulator and show how
+that works what I'd like to talk about
+
+ align:start position:0%
+that works what I'd like to talk about
+ 
+
+ align:start position:0%
+that works what I'd like to talk about
+here as an alternative is a speed
+
+ align:start position:0%
+here as an alternative is a speed
+ 
+
+ align:start position:0%
+here as an alternative is a speed
+control system so let's look at that a
+
+ align:start position:0%
+control system so let's look at that a
+ 
+
+ align:start position:0%
+control system so let's look at that a
+little
+
+ align:start position:0%
+little
+ 
+
+ align:start position:0%
+little
+bit here we have a system where we
+
+ align:start position:0%
+bit here we have a system where we
+ 
+
+ align:start position:0%
+bit here we have a system where we
+assume that what we're trying to do is
+
+ align:start position:0%
+assume that what we're trying to do is
+ 
+
+ align:start position:0%
+assume that what we're trying to do is
+keep an output velocity which I indicate
+
+ align:start position:0%
+keep an output velocity which I indicate
+ 
+
+ align:start position:0%
+keep an output velocity which I indicate
+as aega response fixed we might command
+
+ align:start position:0%
+as aega response fixed we might command
+ 
+
+ align:start position:0%
+as aega response fixed we might command
+some
+
+ align:start position:0%
+some
+ 
+
+ align:start position:0%
+some
+speed but we assume that this command is
+
+ align:start position:0%
+speed but we assume that this command is
+ 
+
+ align:start position:0%
+speed but we assume that this command is
+is really a fixed quantity or at most
+
+ align:start position:0%
+is really a fixed quantity or at most
+ 
+
+ align:start position:0%
+is really a fixed quantity or at most
+incred incredibly slowly time varying so
+
+ align:start position:0%
+incred incredibly slowly time varying so
+ 
+
+ align:start position:0%
+incred incredibly slowly time varying so
+we put in a command and our hope is that
+
+ align:start position:0%
+we put in a command and our hope is that
+ 
+
+ align:start position:0%
+we put in a command and our hope is that
+eventually the system reaches a speed
+
+ align:start position:0%
+eventually the system reaches a speed
+ 
+
+ align:start position:0%
+eventually the system reaches a speed
+that's about equal to that command in
+
+ align:start position:0%
+that's about equal to that command in
+ 
+
+ align:start position:0%
+that's about equal to that command in
+the system I've shown notice that we
+
+ align:start position:0%
+the system I've shown notice that we
+ 
+
+ align:start position:0%
+the system I've shown notice that we
+have Unity feedback in this system and
+
+ align:start position:0%
+have Unity feedback in this system and
+ 
+
+ align:start position:0%
+have Unity feedback in this system and
+from then on we're supposed to keep or
+
+ align:start position:0%
+from then on we're supposed to keep or
+ 
+
+ align:start position:0%
+from then on we're supposed to keep or
+the intent of the feedback system is to
+
+ align:start position:0%
+the intent of the feedback system is to
+ 
+
+ align:start position:0%
+the intent of the feedback system is to
+keep the output velocity fixed and the
+
+ align:start position:0%
+keep the output velocity fixed and the
+ 
+
+ align:start position:0%
+keep the output velocity fixed and the
+disturbances that we'll consider are
+
+ align:start position:0%
+disturbances that we'll consider are
+ 
+
+ align:start position:0%
+disturbances that we'll consider are
+torque disturbances that are applied to
+
+ align:start position:0%
+torque disturbances that are applied to
+ 
+
+ align:start position:0%
+torque disturbances that are applied to
+the mechanical system our system
+
+ align:start position:0%
+the mechanical system our system
+ 
+
+ align:start position:0%
+the mechanical system our system
+consists of an amplifier driving a motor
+
+ align:start position:0%
+consists of an amplifier driving a motor
+ 
+
+ align:start position:0%
+consists of an amplifier driving a motor
+we measure the velocity of the motor
+
+ align:start position:0%
+we measure the velocity of the motor
+ 
+
+ align:start position:0%
+we measure the velocity of the motor
+with some sort of a device they're
+
+ align:start position:0%
+with some sort of a device they're
+ 
+
+ align:start position:0%
+with some sort of a device they're
+called tachometers which allows us to
+
+ align:start position:0%
+called tachometers which allows us to
+ 
+
+ align:start position:0%
+called tachometers which allows us to
+feed back information concerning the
+
+ align:start position:0%
+feed back information concerning the
+ 
+
+ align:start position:0%
+feed back information concerning the
+output velocity We compare that with a
+
+ align:start position:0%
+output velocity We compare that with a
+ 
+
+ align:start position:0%
+output velocity We compare that with a
+set point or commanded velocity amplify
+
+ align:start position:0%
+set point or commanded velocity amplify
+ 
+
+ align:start position:0%
+set point or commanded velocity amplify
+the difference and of course apply that
+
+ align:start position:0%
+the difference and of course apply that
+ 
+
+ align:start position:0%
+the difference and of course apply that
+voltage to the motor we assume that the
+
+ align:start position:0%
+voltage to the motor we assume that the
+ 
+
+ align:start position:0%
+voltage to the motor we assume that the
+total inertia of the load this includes
+
+ align:start position:0%
+total inertia of the load this includes
+ 
+
+ align:start position:0%
+total inertia of the load this includes
+the Armature inertia of the motor uh any
+
+ align:start position:0%
+the Armature inertia of the motor uh any
+ 
+
+ align:start position:0%
+the Armature inertia of the motor uh any
+rotating load that we have we assume
+
+ align:start position:0%
+rotating load that we have we assume
+ 
+
+ align:start position:0%
+rotating load that we have we assume
+that the that total inertia is J and as
+
+ align:start position:0%
+that the that total inertia is J and as
+ 
+
+ align:start position:0%
+that the that total inertia is J and as
+I say the objective of the system is to
+
+ align:start position:0%
+I say the objective of the system is to
+ 
+
+ align:start position:0%
+I say the objective of the system is to
+keep this velocity fixed as we apply
+
+ align:start position:0%
+keep this velocity fixed as we apply
+ 
+
+ align:start position:0%
+keep this velocity fixed as we apply
+torque disturbances to the
+
+ align:start position:0%
+torque disturbances to the
+ 
+
+ align:start position:0%
+torque disturbances to the
+system we have to start out modeling the
+
+ align:start position:0%
+system we have to start out modeling the
+ 
+
+ align:start position:0%
+system we have to start out modeling the
+motor and there's a large and important
+
+ align:start position:0%
+motor and there's a large and important
+ 
+
+ align:start position:0%
+motor and there's a large and important
+class of Motors that are very well
+
+ align:start position:0%
+class of Motors that are very well
+ 
+
+ align:start position:0%
+class of Motors that are very well
+modeled by this simple a model if we
+
+ align:start position:0%
+modeled by this simple a model if we
+ 
+
+ align:start position:0%
+modeled by this simple a model if we
+have a motor that has a fixed magnetic
+
+ align:start position:0%
+have a motor that has a fixed magnetic
+ 
+
+ align:start position:0%
+have a motor that has a fixed magnetic
+field either as a consequence of a
+
+ align:start position:0%
+field either as a consequence of a
+ 
+
+ align:start position:0%
+field either as a consequence of a
+winding excited by fixed current
+
+ align:start position:0%
+winding excited by fixed current
+ 
+
+ align:start position:0%
+winding excited by fixed current
+or as a consequence of a permanent
+
+ align:start position:0%
+or as a consequence of a permanent
+ 
+
+ align:start position:0%
+or as a consequence of a permanent
+magnet why we're very often able to
+
+ align:start position:0%
+magnet why we're very often able to
+ 
+
+ align:start position:0%
+magnet why we're very often able to
+model that kind of a motor in this way
+
+ align:start position:0%
+model that kind of a motor in this way
+ 
+
+ align:start position:0%
+model that kind of a motor in this way
+here we have a resistance which is the
+
+ align:start position:0%
+here we have a resistance which is the
+ 
+
+ align:start position:0%
+here we have a resistance which is the
+Armature resistance of the motor and
+
+ align:start position:0%
+Armature resistance of the motor and
+ 
+
+ align:start position:0%
+Armature resistance of the motor and
+there's a back voltage generator whose
+
+ align:start position:0%
+there's a back voltage generator whose
+ 
+
+ align:start position:0%
+there's a back voltage generator whose
+voltage is some constant that has to do
+
+ align:start position:0%
+voltage is some constant that has to do
+ 
+
+ align:start position:0%
+voltage is some constant that has to do
+with the way the motor is constructed
+
+ align:start position:0%
+with the way the motor is constructed
+ 
+
+ align:start position:0%
+with the way the motor is constructed
+times the mechanical shaft velocity of
+
+ align:start position:0%
+times the mechanical shaft velocity of
+ 
+
+ align:start position:0%
+times the mechanical shaft velocity of
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+motor at the same time the torque that
+
+ align:start position:0%
+motor at the same time the torque that
+ 
+
+ align:start position:0%
+motor at the same time the torque that
+the motor supplies is simply equal to
+
+ align:start position:0%
+the motor supplies is simply equal to
+ 
+
+ align:start position:0%
+the motor supplies is simply equal to
+the Armature current multiplied by a
+
+ align:start position:0%
+the Armature current multiplied by a
+ 
+
+ align:start position:0%
+the Armature current multiplied by a
+constant and in fact if we're working in
+
+ align:start position:0%
+constant and in fact if we're working in
+ 
+
+ align:start position:0%
+constant and in fact if we're working in
+a set of units such as MKS units where
+
+ align:start position:0%
+a set of units such as MKS units where
+ 
+
+ align:start position:0%
+a set of units such as MKS units where
+the product of velocity times torque
+
+ align:start position:0%
+the product of velocity times torque
+ 
+
+ align:start position:0%
+the product of velocity times torque
+gives us power in the same units as the
+
+ align:start position:0%
+gives us power in the same units as the
+ 
+
+ align:start position:0%
+gives us power in the same units as the
+product of current times voltage these
+
+ align:start position:0%
+product of current times voltage these
+ 
+
+ align:start position:0%
+product of current times voltage these
+two KS have to be the same so uh this is
+
+ align:start position:0%
+two KS have to be the same so uh this is
+ 
+
+ align:start position:0%
+two KS have to be the same so uh this is
+this K and this K are in fact identical
+
+ align:start position:0%
+this K and this K are in fact identical
+ 
+
+ align:start position:0%
+this K and this K are in fact identical
+providing uh we're working in in MKS
+
+ align:start position:0%
+providing uh we're working in in MKS
+ 
+
+ align:start position:0%
+providing uh we're working in in MKS
+units well with that model for the motor
+
+ align:start position:0%
+units well with that model for the motor
+ 
+
+ align:start position:0%
+units well with that model for the motor
+let's go ahead and construct a block
+
+ align:start position:0%
+let's go ahead and construct a block
+ 
+
+ align:start position:0%
+let's go ahead and construct a block
+diagram for our speed control system we
+
+ align:start position:0%
+diagram for our speed control system we
+ 
+
+ align:start position:0%
+diagram for our speed control system we
+have our commanded value for Speed or
+
+ align:start position:0%
+have our commanded value for Speed or
+ 
+
+ align:start position:0%
+have our commanded value for Speed or
+shaft
+
+ align:start position:0%
+shaft
+ 
+
+ align:start position:0%
+shaft
+velocity and we have the response of the
+
+ align:start position:0%
+velocity and we have the response of the
+ 
+
+ align:start position:0%
+velocity and we have the response of the
+system out here and we subtract the two
+
+ align:start position:0%
+system out here and we subtract the two
+ 
+
+ align:start position:0%
+system out here and we subtract the two
+of them to develop an error signal we
+
+ align:start position:0%
+of them to develop an error signal we
+ 
+
+ align:start position:0%
+of them to develop an error signal we
+amplify that error signal and the
+
+ align:start position:0%
+amplify that error signal and the
+ 
+
+ align:start position:0%
+amplify that error signal and the
+resultant voltage is that that we apply
+
+ align:start position:0%
+resultant voltage is that that we apply
+ 
+
+ align:start position:0%
+resultant voltage is that that we apply
+to the motor but in order to complete
+
+ align:start position:0%
+to the motor but in order to complete
+ 
+
+ align:start position:0%
+to the motor but in order to complete
+our block diagram we have to find out
+
+ align:start position:0%
+our block diagram we have to find out
+ 
+
+ align:start position:0%
+our block diagram we have to find out
+what torque the motor
+
+ align:start position:0%
+what torque the motor
+ 
+
+ align:start position:0%
+what torque the motor
+supplies and we notice from our motor
+
+ align:start position:0%
+supplies and we notice from our motor
+ 
+
+ align:start position:0%
+supplies and we notice from our motor
+model that the torque is proportional to
+
+ align:start position:0%
+model that the torque is proportional to
+ 
+
+ align:start position:0%
+model that the torque is proportional to
+the Armature current well how do we find
+
+ align:start position:0%
+the Armature current well how do we find
+ 
+
+ align:start position:0%
+the Armature current well how do we find
+the Armature current the Armature
+
+ align:start position:0%
+the Armature current the Armature
+ 
+
+ align:start position:0%
+the Armature current the Armature
+current is equal to the voltage that we
+
+ align:start position:0%
+current is equal to the voltage that we
+ 
+
+ align:start position:0%
+current is equal to the voltage that we
+apply to the motor terminals minus the
+
+ align:start position:0%
+apply to the motor terminals minus the
+ 
+
+ align:start position:0%
+apply to the motor terminals minus the
+voltage of the back voltage generator
+
+ align:start position:0%
+voltage of the back voltage generator
+ 
+
+ align:start position:0%
+voltage of the back voltage generator
+that difference is the voltage across
+
+ align:start position:0%
+that difference is the voltage across
+ 
+
+ align:start position:0%
+that difference is the voltage across
+this resistor and if we divide that
+
+ align:start position:0%
+this resistor and if we divide that
+ 
+
+ align:start position:0%
+this resistor and if we divide that
+voltage by the value of the resistance
+
+ align:start position:0%
+voltage by the value of the resistance
+ 
+
+ align:start position:0%
+voltage by the value of the resistance
+we get the Armature current and we can
+
+ align:start position:0%
+we get the Armature current and we can
+ 
+
+ align:start position:0%
+we get the Armature current and we can
+do that on a block diagram basis by
+
+ align:start position:0%
+do that on a block diagram basis by
+ 
+
+ align:start position:0%
+do that on a block diagram basis by
+taking the voltage out of the amplifier
+
+ align:start position:0%
+taking the voltage out of the amplifier
+ 
+
+ align:start position:0%
+taking the voltage out of the amplifier
+subtracting the back voltage of the
+
+ align:start position:0%
+subtracting the back voltage of the
+ 
+
+ align:start position:0%
+subtracting the back voltage of the
+motor which we get by multiplying the
+
+ align:start position:0%
+motor which we get by multiplying the
+ 
+
+ align:start position:0%
+motor which we get by multiplying the
+motor
+
+ align:start position:0%
+motor
+ 
+
+ align:start position:0%
+motor
+velocity by K so we subtract that back
+
+ align:start position:0%
+velocity by K so we subtract that back
+ 
+
+ align:start position:0%
+velocity by K so we subtract that back
+voltage from the voltage supplied by the
+
+ align:start position:0%
+voltage from the voltage supplied by the
+ 
+
+ align:start position:0%
+voltage from the voltage supplied by the
+amplifier we D divide the resultant
+
+ align:start position:0%
+amplifier we D divide the resultant
+ 
+
+ align:start position:0%
+amplifier we D divide the resultant
+Difference by R and we get the Armature
+
+ align:start position:0%
+Difference by R and we get the Armature
+ 
+
+ align:start position:0%
+Difference by R and we get the Armature
+current once we have the Armature
+
+ align:start position:0%
+current once we have the Armature
+ 
+
+ align:start position:0%
+current once we have the Armature
+current we can get the the torque that
+
+ align:start position:0%
+current we can get the the torque that
+ 
+
+ align:start position:0%
+current we can get the the torque that
+the motor supplying
+
+ align:start position:0%
+the motor supplying
+ 
+
+ align:start position:0%
+the motor supplying
+electrically simply by multiplying that
+
+ align:start position:0%
+electrically simply by multiplying that
+ 
+
+ align:start position:0%
+electrically simply by multiplying that
+Armature current by the constant
+
+ align:start position:0%
+Armature current by the constant
+ 
+
+ align:start position:0%
+Armature current by the constant
+K so at this point in the block diagram
+
+ align:start position:0%
+K so at this point in the block diagram
+ 
+
+ align:start position:0%
+K so at this point in the block diagram
+we have the electrical torque being
+
+ align:start position:0%
+we have the electrical torque being
+ 
+
+ align:start position:0%
+we have the electrical torque being
+supplied by the motor or the torque
+
+ align:start position:0%
+supplied by the motor or the torque
+ 
+
+ align:start position:0%
+supplied by the motor or the torque
+that's a consequence of the energy
+
+ align:start position:0%
+that's a consequence of the energy
+ 
+
+ align:start position:0%
+that's a consequence of the energy
+conversion process associated with the
+
+ align:start position:0%
+conversion process associated with the
+ 
+
+ align:start position:0%
+conversion process associated with the
+motor we add to that the disturbance
+
+ align:start position:0%
+motor we add to that the disturbance
+ 
+
+ align:start position:0%
+motor we add to that the disturbance
+torque that's applied externally to the
+
+ align:start position:0%
+torque that's applied externally to the
+ 
+
+ align:start position:0%
+torque that's applied externally to the
+system and the sum of these two is the
+
+ align:start position:0%
+system and the sum of these two is the
+ 
+
+ align:start position:0%
+system and the sum of these two is the
+net torque applied to the inertia of
+
+ align:start position:0%
+net torque applied to the inertia of
+ 
+
+ align:start position:0%
+net torque applied to the inertia of
+associated with both the motor
+
+ align:start position:0%
+associated with both the motor
+ 
+
+ align:start position:0%
+associated with both the motor
+Armature and additional rotating inertia
+
+ align:start position:0%
+Armature and additional rotating inertia
+ 
+
+ align:start position:0%
+Armature and additional rotating inertia
+in the system the inertia J as we
+
+ align:start position:0%
+in the system the inertia J as we
+ 
+
+ align:start position:0%
+in the system the inertia J as we
+defined it earlier if we divide that net
+
+ align:start position:0%
+defined it earlier if we divide that net
+ 
+
+ align:start position:0%
+defined it earlier if we divide that net
+torque by J we get acceleration of the
+
+ align:start position:0%
+torque by J we get acceleration of the
+ 
+
+ align:start position:0%
+torque by J we get acceleration of the
+motor and load combination if we then
+
+ align:start position:0%
+motor and load combination if we then
+ 
+
+ align:start position:0%
+motor and load combination if we then
+integrate multiply by 1 / s we get the
+
+ align:start position:0%
+integrate multiply by 1 / s we get the
+ 
+
+ align:start position:0%
+integrate multiply by 1 / s we get the
+velocity of the motor load
+
+ align:start position:0%
+velocity of the motor load
+ 
+
+ align:start position:0%
+velocity of the motor load
+combination once we've gotten to that
+
+ align:start position:0%
+combination once we've gotten to that
+ 
+
+ align:start position:0%
+combination once we've gotten to that
+point in the block diagram of course we
+
+ align:start position:0%
+point in the block diagram of course we
+ 
+
+ align:start position:0%
+point in the block diagram of course we
+have the variable necessary to complete
+
+ align:start position:0%
+have the variable necessary to complete
+ 
+
+ align:start position:0%
+have the variable necessary to complete
+the various feedback paths we multiply
+
+ align:start position:0%
+the various feedback paths we multiply
+ 
+
+ align:start position:0%
+the various feedback paths we multiply
+by motor velocity by our constant K to
+
+ align:start position:0%
+by motor velocity by our constant K to
+ 
+
+ align:start position:0%
+by motor velocity by our constant K to
+get the back voltage associated with the
+
+ align:start position:0%
+get the back voltage associated with the
+ 
+
+ align:start position:0%
+get the back voltage associated with the
+motor similarly we bring back velocity
+
+ align:start position:0%
+motor similarly we bring back velocity
+ 
+
+ align:start position:0%
+motor similarly we bring back velocity
+information probably via some sort of a
+
+ align:start position:0%
+information probably via some sort of a
+ 
+
+ align:start position:0%
+information probably via some sort of a
+transducer as I mentioned earlier a
+
+ align:start position:0%
+transducer as I mentioned earlier a
+ 
+
+ align:start position:0%
+transducer as I mentioned earlier a
+tachometer to the input of the
+
+ align:start position:0%
+tachometer to the input of the
+ 
+
+ align:start position:0%
+tachometer to the input of the
+system well we can now look at the
+
+ align:start position:0%
+system well we can now look at the
+ 
+
+ align:start position:0%
+system well we can now look at the
+properties of this sort of a feedback
+
+ align:start position:0%
+properties of this sort of a feedback
+ 
+
+ align:start position:0%
+properties of this sort of a feedback
+system if I have a sufficiently large
+
+ align:start position:0%
+system if I have a sufficiently large
+ 
+
+ align:start position:0%
+system if I have a sufficiently large
+value for a we have a system that has
+
+ align:start position:0%
+value for a we have a system that has
+ 
+
+ align:start position:0%
+value for a we have a system that has
+unity feedback between the out put
+
+ align:start position:0%
+unity feedback between the out put
+ 
+
+ align:start position:0%
+unity feedback between the out put
+variable and our input summing point so
+
+ align:start position:0%
+variable and our input summing point so
+ 
+
+ align:start position:0%
+variable and our input summing point so
+we have a system uh which has a
+
+ align:start position:0%
+we have a system uh which has a
+ 
+
+ align:start position:0%
+we have a system uh which has a
+so-called major Loop that has an F or a
+
+ align:start position:0%
+so-called major Loop that has an F or a
+ 
+
+ align:start position:0%
+so-called major Loop that has an F or a
+feedback transfer function of one and in
+
+ align:start position:0%
+feedback transfer function of one and in
+ 
+
+ align:start position:0%
+feedback transfer function of one and in
+fact providing a is sufficiently large
+
+ align:start position:0%
+fact providing a is sufficiently large
+ 
+
+ align:start position:0%
+fact providing a is sufficiently large
+the gain from the input of the system to
+
+ align:start position:0%
+the gain from the input of the system to
+ 
+
+ align:start position:0%
+the gain from the input of the system to
+the output of the system is about equal
+
+ align:start position:0%
+the output of the system is about equal
+ 
+
+ align:start position:0%
+the output of the system is about equal
+to Unity the reciprocal of the feedback
+
+ align:start position:0%
+to Unity the reciprocal of the feedback
+ 
+
+ align:start position:0%
+to Unity the reciprocal of the feedback
+path and this tells us that for a large
+
+ align:start position:0%
+path and this tells us that for a large
+ 
+
+ align:start position:0%
+path and this tells us that for a large
+a the response speed should be just
+
+ align:start position:0%
+a the response speed should be just
+ 
+
+ align:start position:0%
+a the response speed should be just
+about equal to the commanded speed our
+
+ align:start position:0%
+about equal to the commanded speed our
+ 
+
+ align:start position:0%
+about equal to the commanded speed our
+real interest in this particular example
+
+ align:start position:0%
+real interest in this particular example
+ 
+
+ align:start position:0%
+real interest in this particular example
+however is how well the system rejects
+
+ align:start position:0%
+however is how well the system rejects
+ 
+
+ align:start position:0%
+however is how well the system rejects
+torque disturbances that are applied to
+
+ align:start position:0%
+torque disturbances that are applied to
+ 
+
+ align:start position:0%
+torque disturbances that are applied to
+the motor load combination so what we
+
+ align:start position:0%
+the motor load combination so what we
+ 
+
+ align:start position:0%
+the motor load combination so what we
+really want to do is look at the
+
+ align:start position:0%
+really want to do is look at the
+ 
+
+ align:start position:0%
+really want to do is look at the
+response the change in speed that occurs
+
+ align:start position:0%
+response the change in speed that occurs
+ 
+
+ align:start position:0%
+response the change in speed that occurs
+for a given torque disturbance we so we
+
+ align:start position:0%
+for a given torque disturbance we so we
+ 
+
+ align:start position:0%
+for a given torque disturbance we so we
+want to write the closed loop transfer
+
+ align:start position:0%
+want to write the closed loop transfer
+ 
+
+ align:start position:0%
+want to write the closed loop transfer
+function aega R over
+
+ align:start position:0%
+function aega R over
+ 
+
+ align:start position:0%
+function aega R over
+TD if we do that this expression results
+
+ align:start position:0%
+TD if we do that this expression results
+ 
+
+ align:start position:0%
+TD if we do that this expression results
+we find out that the dependence of
+
+ align:start position:0%
+we find out that the dependence of
+ 
+
+ align:start position:0%
+we find out that the dependence of
+output velocity on disturbing torque
+
+ align:start position:0%
+output velocity on disturbing torque
+ 
+
+ align:start position:0%
+output velocity on disturbing torque
+depends of course on various system
+
+ align:start position:0%
+depends of course on various system
+ 
+
+ align:start position:0%
+depends of course on various system
+parameters the multiplying factor out in
+
+ align:start position:0%
+parameters the multiplying factor out in
+ 
+
+ align:start position:0%
+parameters the multiplying factor out in
+front R over K * k + a we we can sort of
+
+ align:start position:0%
+front R over K * k + a we we can sort of
+ 
+
+ align:start position:0%
+front R over K * k + a we we can sort of
+rationalize why that ought to ought to
+
+ align:start position:0%
+rationalize why that ought to ought to
+ 
+
+ align:start position:0%
+rationalize why that ought to ought to
+be if we had a larger amplifier gain of
+
+ align:start position:0%
+be if we had a larger amplifier gain of
+ 
+
+ align:start position:0%
+be if we had a larger amplifier gain of
+course we'd get greater attenuation the
+
+ align:start position:0%
+course we'd get greater attenuation the
+ 
+
+ align:start position:0%
+course we'd get greater attenuation the
+system would be less sensitive to
+
+ align:start position:0%
+system would be less sensitive to
+ 
+
+ align:start position:0%
+system would be less sensitive to
+applied torque
+
+ align:start position:0%
+applied torque
+ 
+
+ align:start position:0%
+applied torque
+disturbances similarly if R is smaller
+
+ align:start position:0%
+disturbances similarly if R is smaller
+ 
+
+ align:start position:0%
+disturbances similarly if R is smaller
+the motor itself giv is greater current
+
+ align:start position:0%
+the motor itself giv is greater current
+ 
+
+ align:start position:0%
+the motor itself giv is greater current
+and hence greater or experiences greater
+
+ align:start position:0%
+and hence greater or experiences greater
+ 
+
+ align:start position:0%
+and hence greater or experiences greater
+Armature current and hence provides
+
+ align:start position:0%
+Armature current and hence provides
+ 
+
+ align:start position:0%
+Armature current and hence provides
+greater torque for a given voltage
+
+ align:start position:0%
+greater torque for a given voltage
+ 
+
+ align:start position:0%
+greater torque for a given voltage
+applied to the motor and so that's the
+
+ align:start position:0%
+applied to the motor and so that's the
+ 
+
+ align:start position:0%
+applied to the motor and so that's the
+reason that R appears as it does a
+
+ align:start position:0%
+reason that R appears as it does a
+ 
+
+ align:start position:0%
+reason that R appears as it does a
+smaller R leading to smaller
+
+ align:start position:0%
+smaller R leading to smaller
+ 
+
+ align:start position:0%
+smaller R leading to smaller
+disturbances similarly if the back
+
+ align:start position:0%
+disturbances similarly if the back
+ 
+
+ align:start position:0%
+disturbances similarly if the back
+voltage coefficient uh is larger the
+
+ align:start position:0%
+voltage coefficient uh is larger the
+ 
+
+ align:start position:0%
+voltage coefficient uh is larger the
+motor sort of intrinsically U tends to
+
+ align:start position:0%
+motor sort of intrinsically U tends to
+ 
+
+ align:start position:0%
+motor sort of intrinsically U tends to
+minimize disturbances applied to it
+
+ align:start position:0%
+minimize disturbances applied to it
+ 
+
+ align:start position:0%
+minimize disturbances applied to it
+velocity disturbances so this collection
+
+ align:start position:0%
+velocity disturbances so this collection
+ 
+
+ align:start position:0%
+velocity disturbances so this collection
+of constants out in front gives us the
+
+ align:start position:0%
+of constants out in front gives us the
+ 
+
+ align:start position:0%
+of constants out in front gives us the
+rejection if you will at at low
+
+ align:start position:0%
+rejection if you will at at low
+ 
+
+ align:start position:0%
+rejection if you will at at low
+frequencies this is hopefully a small
+
+ align:start position:0%
+frequencies this is hopefully a small
+ 
+
+ align:start position:0%
+frequencies this is hopefully a small
+number and then at some higher frequency
+
+ align:start position:0%
+number and then at some higher frequency
+ 
+
+ align:start position:0%
+number and then at some higher frequency
+we get a single pole associated with
+
+ align:start position:0%
+we get a single pole associated with
+ 
+
+ align:start position:0%
+we get a single pole associated with
+this transfer function rep reflecting
+
+ align:start position:0%
+this transfer function rep reflecting
+ 
+
+ align:start position:0%
+this transfer function rep reflecting
+the energy storage associated with the
+
+ align:start position:0%
+the energy storage associated with the
+ 
+
+ align:start position:0%
+the energy storage associated with the
+rotating inertia so
+
+ align:start position:0%
+rotating inertia so
+ 
+
+ align:start position:0%
+rotating inertia so
+our disturbance to controlled variable
+
+ align:start position:0%
+our disturbance to controlled variable
+ 
+
+ align:start position:0%
+our disturbance to controlled variable
+transfer function has some low frequency
+
+ align:start position:0%
+transfer function has some low frequency
+ 
+
+ align:start position:0%
+transfer function has some low frequency
+magnitude given by this expression and
+
+ align:start position:0%
+magnitude given by this expression and
+ 
+
+ align:start position:0%
+magnitude given by this expression and
+then a single pole the important point
+
+ align:start position:0%
+then a single pole the important point
+ 
+
+ align:start position:0%
+then a single pole the important point
+to note is that if we increase the
+
+ align:start position:0%
+to note is that if we increase the
+ 
+
+ align:start position:0%
+to note is that if we increase the
+inertia in this expression it doesn't
+
+ align:start position:0%
+inertia in this expression it doesn't
+ 
+
+ align:start position:0%
+inertia in this expression it doesn't
+change the low frequency rejection at
+
+ align:start position:0%
+change the low frequency rejection at
+ 
+
+ align:start position:0%
+change the low frequency rejection at
+all but what it does is lower the
+
+ align:start position:0%
+all but what it does is lower the
+ 
+
+ align:start position:0%
+all but what it does is lower the
+frequency at which the pole comes in and
+
+ align:start position:0%
+frequency at which the pole comes in and
+ 
+
+ align:start position:0%
+frequency at which the pole comes in and
+we can look at the effect on this
+
+ align:start position:0%
+we can look at the effect on this
+ 
+
+ align:start position:0%
+we can look at the effect on this
+transfer function of changing inertia in
+
+ align:start position:0%
+transfer function of changing inertia in
+ 
+
+ align:start position:0%
+transfer function of changing inertia in
+bod plot
+
+ align:start position:0%
+bod plot
+ 
+
+ align:start position:0%
+bod plot
+form and I show that over here here we
+
+ align:start position:0%
+form and I show that over here here we
+ 
+
+ align:start position:0%
+form and I show that over here here we
+plot the magnitude of the speed over the
+
+ align:start position:0%
+plot the magnitude of the speed over the
+ 
+
+ align:start position:0%
+plot the magnitude of the speed over the
+disturbance in
+
+ align:start position:0%
+disturbance in
+ 
+
+ align:start position:0%
+disturbance in
+bod plot coordinates as a function of
+
+ align:start position:0%
+bod plot coordinates as a function of
+ 
+
+ align:start position:0%
+bod plot coordinates as a function of
+frequency so what we're doing is
+
+ align:start position:0%
+frequency so what we're doing is
+ 
+
+ align:start position:0%
+frequency so what we're doing is
+measuring the sosal steady state
+
+ align:start position:0%
+measuring the sosal steady state
+ 
+
+ align:start position:0%
+measuring the sosal steady state
+rejection of disturbing torqus we're
+
+ align:start position:0%
+rejection of disturbing torqus we're
+ 
+
+ align:start position:0%
+rejection of disturbing torqus we're
+proposing an experiment where we go in
+
+ align:start position:0%
+proposing an experiment where we go in
+ 
+
+ align:start position:0%
+proposing an experiment where we go in
+and apply a sinusoidally varying torque
+
+ align:start position:0%
+and apply a sinusoidally varying torque
+ 
+
+ align:start position:0%
+and apply a sinusoidally varying torque
+to the Armature load combination and we
+
+ align:start position:0%
+to the Armature load combination and we
+ 
+
+ align:start position:0%
+to the Armature load combination and we
+look at how well the motor rejects
+
+ align:start position:0%
+look at how well the motor rejects
+ 
+
+ align:start position:0%
+look at how well the motor rejects
+that uh there's a DC value which was
+
+ align:start position:0%
+that uh there's a DC value which was
+ 
+
+ align:start position:0%
+that uh there's a DC value which was
+given in our earlier expression that's R
+
+ align:start position:0%
+given in our earlier expression that's R
+ 
+
+ align:start position:0%
+given in our earlier expression that's R
+over K * k + a so that's the low
+
+ align:start position:0%
+over K * k + a so that's the low
+ 
+
+ align:start position:0%
+over K * k + a so that's the low
+frequency value
+
+ align:start position:0%
+frequency value
+ 
+
+ align:start position:0%
+frequency value
+and then there's a corner frequency
+
+ align:start position:0%
+and then there's a corner frequency
+ 
+
+ align:start position:0%
+and then there's a corner frequency
+associated with the system and it
+
+ align:start position:0%
+associated with the system and it
+ 
+
+ align:start position:0%
+associated with the system and it
+involves a collection of constants but
+
+ align:start position:0%
+involves a collection of constants but
+ 
+
+ align:start position:0%
+involves a collection of constants but
+the important point is that that corner
+
+ align:start position:0%
+the important point is that that corner
+ 
+
+ align:start position:0%
+the important point is that that corner
+frequency is inversely proportional to
+
+ align:start position:0%
+frequency is inversely proportional to
+ 
+
+ align:start position:0%
+frequency is inversely proportional to
+the total inertia it's inversely
+
+ align:start position:0%
+the total inertia it's inversely
+ 
+
+ align:start position:0%
+the total inertia it's inversely
+proportional to
+
+ align:start position:0%
+proportional to
+ 
+
+ align:start position:0%
+proportional to
+J and so if we add an additional J we
+
+ align:start position:0%
+J and so if we add an additional J we
+ 
+
+ align:start position:0%
+J and so if we add an additional J we
+build up our system uh we adjust k for
+
+ align:start position:0%
+build up our system uh we adjust k for
+ 
+
+ align:start position:0%
+build up our system uh we adjust k for
+example uh in order to control our our
+
+ align:start position:0%
+example uh in order to control our our
+ 
+
+ align:start position:0%
+example uh in order to control our our
+DC sensitivity to the level that we'd
+
+ align:start position:0%
+DC sensitivity to the level that we'd
+ 
+
+ align:start position:0%
+DC sensitivity to the level that we'd
+like to have it um we then can by
+
+ align:start position:0%
+like to have it um we then can by
+ 
+
+ align:start position:0%
+like to have it um we then can by
+appropriate choice of J ensure that the
+
+ align:start position:0%
+appropriate choice of J ensure that the
+ 
+
+ align:start position:0%
+appropriate choice of J ensure that the
+system crosses over before higher order
+
+ align:start position:0%
+system crosses over before higher order
+ 
+
+ align:start position:0%
+system crosses over before higher order
+poles in the system transfer function
+
+ align:start position:0%
+poles in the system transfer function
+ 
+
+ align:start position:0%
+poles in the system transfer function
+become important so we can ensure that
+
+ align:start position:0%
+become important so we can ensure that
+ 
+
+ align:start position:0%
+become important so we can ensure that
+we have stability uh possibly as much as
+
+ align:start position:0%
+we have stability uh possibly as much as
+ 
+
+ align:start position:0%
+we have stability uh possibly as much as
+90 degrees of phase margin by forcing
+
+ align:start position:0%
+90 degrees of phase margin by forcing
+ 
+
+ align:start position:0%
+90 degrees of phase margin by forcing
+Crossover at a sufficiently low
+
+ align:start position:0%
+Crossover at a sufficiently low
+ 
+
+ align:start position:0%
+Crossover at a sufficiently low
+frequency through appropriate choice of
+
+ align:start position:0%
+frequency through appropriate choice of
+ 
+
+ align:start position:0%
+frequency through appropriate choice of
+J and as we make J larger the system
+
+ align:start position:0%
+J and as we make J larger the system
+ 
+
+ align:start position:0%
+J and as we make J larger the system
+performance improves the rejection of
+
+ align:start position:0%
+performance improves the rejection of
+ 
+
+ align:start position:0%
+performance improves the rejection of
+the system gets better because an
+
+ align:start position:0%
+the system gets better because an
+ 
+
+ align:start position:0%
+the system gets better because an
+increasing J lowers the frequency of
+
+ align:start position:0%
+increasing J lowers the frequency of
+ 
+
+ align:start position:0%
+increasing J lowers the frequency of
+this
+
+ align:start position:0%
+this
+ 
+
+ align:start position:0%
+this
+pole for example we might get this sort
+
+ align:start position:0%
+pole for example we might get this sort
+ 
+
+ align:start position:0%
+pole for example we might get this sort
+of a transfer function when we increase
+
+ align:start position:0%
+of a transfer function when we increase
+ 
+
+ align:start position:0%
+of a transfer function when we increase
+J and so this then in our body plot is
+
+ align:start position:0%
+J and so this then in our body plot is
+ 
+
+ align:start position:0%
+J and so this then in our body plot is
+the direction of increasing
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+inertia and we see that the rejection of
+
+ align:start position:0%
+inertia and we see that the rejection of
+ 
+
+ align:start position:0%
+inertia and we see that the rejection of
+the system remember we'd ideally like to
+
+ align:start position:0%
+the system remember we'd ideally like to
+ 
+
+ align:start position:0%
+the system remember we'd ideally like to
+have this transfer function zero we'd
+
+ align:start position:0%
+have this transfer function zero we'd
+ 
+
+ align:start position:0%
+have this transfer function zero we'd
+ideally like to have no change in speed
+
+ align:start position:0%
+ideally like to have no change in speed
+ 
+
+ align:start position:0%
+ideally like to have no change in speed
+for a given torque disturbance but we
+
+ align:start position:0%
+for a given torque disturbance but we
+ 
+
+ align:start position:0%
+for a given torque disturbance but we
+push the first pole down as we increase
+
+ align:start position:0%
+push the first pole down as we increase
+ 
+
+ align:start position:0%
+push the first pole down as we increase
+J and in fact in the limit uh we could
+
+ align:start position:0%
+J and in fact in the limit uh we could
+ 
+
+ align:start position:0%
+J and in fact in the limit uh we could
+increase the band of frequencies over
+
+ align:start position:0%
+increase the band of frequencies over
+ 
+
+ align:start position:0%
+increase the band of frequencies over
+which we got very high attenuation by
+
+ align:start position:0%
+which we got very high attenuation by
+ 
+
+ align:start position:0%
+which we got very high attenuation by
+using a sufficiently large rotating
+
+ align:start position:0%
+using a sufficiently large rotating
+ 
+
+ align:start position:0%
+using a sufficiently large rotating
+inertia so in this is one important
+
+ align:start position:0%
+inertia so in this is one important
+ 
+
+ align:start position:0%
+inertia so in this is one important
+class of
+
+ align:start position:0%
+class of
+ 
+
+ align:start position:0%
+class of
+systems Regulators where the objective
+
+ align:start position:0%
+systems Regulators where the objective
+ 
+
+ align:start position:0%
+systems Regulators where the objective
+is
+
+ align:start position:0%
+is
+ 
+
+ align:start position:0%
+is
+to reduce or ideally eliminate a
+
+ align:start position:0%
+to reduce or ideally eliminate a
+ 
+
+ align:start position:0%
+to reduce or ideally eliminate a
+disturbance why creating a dominant pole
+
+ align:start position:0%
+disturbance why creating a dominant pole
+ 
+
+ align:start position:0%
+disturbance why creating a dominant pole
+is probably the compensation Form of
+
+ align:start position:0%
+is probably the compensation Form of
+ 
+
+ align:start position:0%
+is probably the compensation Form of
+choice
+
+ align:start position:0%
+choice
+ 
+
+ align:start position:0%
+choice
+particularly if we can locate the
+
+ align:start position:0%
+particularly if we can locate the
+ 
+
+ align:start position:0%
+particularly if we can locate the
+dominant pole at the output if we can
+
+ align:start position:0%
+dominant pole at the output if we can
+ 
+
+ align:start position:0%
+dominant pole at the output if we can
+put our energy storage that creates the
+
+ align:start position:0%
+put our energy storage that creates the
+ 
+
+ align:start position:0%
+put our energy storage that creates the
+dominant pole at the output of the
+
+ align:start position:0%
+dominant pole at the output of the
+ 
+
+ align:start position:0%
+dominant pole at the output of the
+system our attempts to reduce
+
+ align:start position:0%
+system our attempts to reduce
+ 
+
+ align:start position:0%
+system our attempts to reduce
+disturbances are greatly aided by the
+
+ align:start position:0%
+disturbances are greatly aided by the
+ 
+
+ align:start position:0%
+disturbances are greatly aided by the
+inertia or in the case of the power
+
+ align:start position:0%
+inertia or in the case of the power
+ 
+
+ align:start position:0%
+inertia or in the case of the power
+supply the electrical power supply the
+
+ align:start position:0%
+supply the electrical power supply the
+ 
+
+ align:start position:0%
+supply the electrical power supply the
+energy storage and the capacitor that we
+
+ align:start position:0%
+energy storage and the capacitor that we
+ 
+
+ align:start position:0%
+energy storage and the capacitor that we
+attach to the
+
+ align:start position:0%
+attach to the
+ 
+
+ align:start position:0%
+attach to the
+output well suppose we have a system
+
+ align:start position:0%
+output well suppose we have a system
+ 
+
+ align:start position:0%
+output well suppose we have a system
+where we can't
+
+ align:start position:0%
+where we can't
+ 
+
+ align:start position:0%
+where we can't
+tolerate the bandwidth decrease that
+
+ align:start position:0%
+tolerate the bandwidth decrease that
+ 
+
+ align:start position:0%
+tolerate the bandwidth decrease that
+comes via cre a dominant Pole or that
+
+ align:start position:0%
+comes via cre a dominant Pole or that
+ 
+
+ align:start position:0%
+comes via cre a dominant Pole or that
+comes along with creating a dominant
+
+ align:start position:0%
+comes along with creating a dominant
+ 
+
+ align:start position:0%
+comes along with creating a dominant
+pole there are other modifications that
+
+ align:start position:0%
+pole there are other modifications that
+ 
+
+ align:start position:0%
+pole there are other modifications that
+we can make to the loop Transmission in
+
+ align:start position:0%
+we can make to the loop Transmission in
+ 
+
+ align:start position:0%
+we can make to the loop Transmission in
+order to improve the stability of the
+
+ align:start position:0%
+order to improve the stability of the
+ 
+
+ align:start position:0%
+order to improve the stability of the
+system and typically uh they retain more
+
+ align:start position:0%
+system and typically uh they retain more
+ 
+
+ align:start position:0%
+system and typically uh they retain more
+more desensitivity than does the option
+
+ align:start position:0%
+more desensitivity than does the option
+ 
+
+ align:start position:0%
+more desensitivity than does the option
+of creating a dominant pole and possibly
+
+ align:start position:0%
+of creating a dominant pole and possibly
+ 
+
+ align:start position:0%
+of creating a dominant pole and possibly
+retain more of the system bandwidth than
+
+ align:start position:0%
+retain more of the system bandwidth than
+ 
+
+ align:start position:0%
+retain more of the system bandwidth than
+would occur if we forced a dominant pole
+
+ align:start position:0%
+would occur if we forced a dominant pole
+ 
+
+ align:start position:0%
+would occur if we forced a dominant pole
+and let's look at the kinds of things we
+
+ align:start position:0%
+and let's look at the kinds of things we
+ 
+
+ align:start position:0%
+and let's look at the kinds of things we
+might like to
+
+ align:start position:0%
+might like to
+ 
+
+ align:start position:0%
+might like to
+do here again I've shown a bod plot for
+
+ align:start position:0%
+do here again I've shown a bod plot for
+ 
+
+ align:start position:0%
+do here again I've shown a bod plot for
+the AF product for some hypothetical
+
+ align:start position:0%
+the AF product for some hypothetical
+ 
+
+ align:start position:0%
+the AF product for some hypothetical
+feedback system this time I've show
+
+ align:start position:0%
+feedback system this time I've show
+ 
+
+ align:start position:0%
+feedback system this time I've show
+showed a stable one uh the
+
+ align:start position:0%
+showed a stable one uh the
+ 
+
+ align:start position:0%
+showed a stable one uh the
+magnitude is flat at DC uh possibly a
+
+ align:start position:0%
+magnitude is flat at DC uh possibly a
+ 
+
+ align:start position:0%
+magnitude is flat at DC uh possibly a
+single pole roll off in this region and
+
+ align:start position:0%
+single pole roll off in this region and
+ 
+
+ align:start position:0%
+single pole roll off in this region and
+then some higher order poles or
+
+ align:start position:0%
+then some higher order poles or
+ 
+
+ align:start position:0%
+then some higher order poles or
+additional Dynamics at higher
+
+ align:start position:0%
+additional Dynamics at higher
+ 
+
+ align:start position:0%
+additional Dynamics at higher
+frequencies an Associated angle might be
+
+ align:start position:0%
+frequencies an Associated angle might be
+ 
+
+ align:start position:0%
+frequencies an Associated angle might be
+one that was near 0 degrees at at low
+
+ align:start position:0%
+one that was near 0 degrees at at low
+ 
+
+ align:start position:0%
+one that was near 0 degrees at at low
+frequencies uh here's the 180° point or
+
+ align:start position:0%
+frequencies uh here's the 180° point or
+ 
+
+ align:start position:0%
+frequencies uh here's the 180° point or
+minus 180° point start out close to zero
+
+ align:start position:0%
+minus 180° point start out close to zero
+ 
+
+ align:start position:0%
+minus 180° point start out close to zero
+we get about 90° of phase shift
+
+ align:start position:0%
+we get about 90° of phase shift
+ 
+
+ align:start position:0%
+we get about 90° of phase shift
+reflecting this first pole and then at
+
+ align:start position:0%
+reflecting this first pole and then at
+ 
+
+ align:start position:0%
+reflecting this first pole and then at
+higher frequencies again reflecting the
+
+ align:start position:0%
+higher frequencies again reflecting the
+ 
+
+ align:start position:0%
+higher frequencies again reflecting the
+energy storage or the other modes of
+
+ align:start position:0%
+energy storage or the other modes of
+ 
+
+ align:start position:0%
+energy storage or the other modes of
+energy storage in the system the angle
+
+ align:start position:0%
+energy storage in the system the angle
+ 
+
+ align:start position:0%
+energy storage in the system the angle
+associated with the AF product begins to
+
+ align:start position:0%
+associated with the AF product begins to
+ 
+
+ align:start position:0%
+associated with the AF product begins to
+drop off eventually goes through minus
+
+ align:start position:0%
+drop off eventually goes through minus
+ 
+
+ align:start position:0%
+drop off eventually goes through minus
+180° in this case uh I've assumed that
+
+ align:start position:0%
+180° in this case uh I've assumed that
+ 
+
+ align:start position:0%
+180° in this case uh I've assumed that
+the system is stable in other words the
+
+ align:start position:0%
+the system is stable in other words the
+ 
+
+ align:start position:0%
+the system is stable in other words the
+way I've drawn things we go through
+
+ align:start position:0%
+way I've drawn things we go through
+ 
+
+ align:start position:0%
+way I've drawn things we go through
+Unity
+
+ align:start position:0%
+Unity
+ 
+
+ align:start position:0%
+Unity
+magnitude before the angle gets to- 180°
+
+ align:start position:0%
+magnitude before the angle gets to- 180°
+ 
+
+ align:start position:0%
+magnitude before the angle gets to- 180°
+but I've also tried to show in the
+
+ align:start position:0%
+but I've also tried to show in the
+ 
+
+ align:start position:0%
+but I've also tried to show in the
+drawing that we have a very small amount
+
+ align:start position:0%
+drawing that we have a very small amount
+ 
+
+ align:start position:0%
+drawing that we have a very small amount
+of phase margin in this case we might
+
+ align:start position:0%
+of phase margin in this case we might
+ 
+
+ align:start position:0%
+of phase margin in this case we might
+not feel that the system has adequate
+
+ align:start position:0%
+not feel that the system has adequate
+ 
+
+ align:start position:0%
+not feel that the system has adequate
+stability let's see what we're able to
+
+ align:start position:0%
+stability let's see what we're able to
+ 
+
+ align:start position:0%
+stability let's see what we're able to
+do to improve that
+
+ align:start position:0%
+do to improve that
+ 
+
+ align:start position:0%
+do to improve that
+situation the U kinds of modifications
+
+ align:start position:0%
+situation the U kinds of modifications
+ 
+
+ align:start position:0%
+situation the U kinds of modifications
+we might like to make are the following
+
+ align:start position:0%
+we might like to make are the following
+ 
+
+ align:start position:0%
+we might like to make are the following
+suppose we could do something to
+
+ align:start position:0%
+suppose we could do something to
+ 
+
+ align:start position:0%
+suppose we could do something to
+increase the angle associated with a
+
+ align:start position:0%
+increase the angle associated with a
+ 
+
+ align:start position:0%
+increase the angle associated with a
+transfer function or with Loop
+
+ align:start position:0%
+transfer function or with Loop
+ 
+
+ align:start position:0%
+transfer function or with Loop
+transmission out in this region if we
+
+ align:start position:0%
+transmission out in this region if we
+ 
+
+ align:start position:0%
+transmission out in this region if we
+could somehow push up the angle and do
+
+ align:start position:0%
+could somehow push up the angle and do
+ 
+
+ align:start position:0%
+could somehow push up the angle and do
+that in a way that didn't increase
+
+ align:start position:0%
+that in a way that didn't increase
+ 
+
+ align:start position:0%
+that in a way that didn't increase
+crossover frequency here we've shown the
+
+ align:start position:0%
+crossover frequency here we've shown the
+ 
+
+ align:start position:0%
+crossover frequency here we've shown the
+crossover frequency of the system uh if
+
+ align:start position:0%
+crossover frequency of the system uh if
+ 
+
+ align:start position:0%
+crossover frequency of the system uh if
+we could do that in a way that didn't
+
+ align:start position:0%
+we could do that in a way that didn't
+ 
+
+ align:start position:0%
+we could do that in a way that didn't
+increase the crossover frequency so that
+
+ align:start position:0%
+increase the crossover frequency so that
+ 
+
+ align:start position:0%
+increase the crossover frequency so that
+we didn't get additional negative phase
+
+ align:start position:0%
+we didn't get additional negative phase
+ 
+
+ align:start position:0%
+we didn't get additional negative phase
+shift associated with the uncompensated
+
+ align:start position:0%
+shift associated with the uncompensated
+ 
+
+ align:start position:0%
+shift associated with the uncompensated
+system hurting is we could just push up
+
+ align:start position:0%
+system hurting is we could just push up
+ 
+
+ align:start position:0%
+system hurting is we could just push up
+this magnitude this angle but keep the
+
+ align:start position:0%
+this magnitude this angle but keep the
+ 
+
+ align:start position:0%
+this magnitude this angle but keep the
+magnitude the same out here that would
+
+ align:start position:0%
+magnitude the same out here that would
+ 
+
+ align:start position:0%
+magnitude the same out here that would
+certainly help if we could make this
+
+ align:start position:0%
+certainly help if we could make this
+ 
+
+ align:start position:0%
+certainly help if we could make this
+angle more positive of course we'd
+
+ align:start position:0%
+angle more positive of course we'd
+ 
+
+ align:start position:0%
+angle more positive of course we'd
+increase the phase margin of the system
+
+ align:start position:0%
+increase the phase margin of the system
+ 
+
+ align:start position:0%
+increase the phase margin of the system
+and thereby improve the stability so
+
+ align:start position:0%
+and thereby improve the stability so
+ 
+
+ align:start position:0%
+and thereby improve the stability so
+that's one thing that that we might like
+
+ align:start position:0%
+that's one thing that that we might like
+ 
+
+ align:start position:0%
+that's one thing that that we might like
+to
+
+ align:start position:0%
+to
+ 
+
+ align:start position:0%
+to
+do another thing that we might like to
+
+ align:start position:0%
+do another thing that we might like to
+ 
+
+ align:start position:0%
+do another thing that we might like to
+do is somehow push down the magnitude
+
+ align:start position:0%
+do is somehow push down the magnitude
+ 
+
+ align:start position:0%
+do is somehow push down the magnitude
+but not at all frequencies we spoke last
+
+ align:start position:0%
+but not at all frequencies we spoke last
+ 
+
+ align:start position:0%
+but not at all frequencies we spoke last
+time about simply lowering the a fnot
+
+ align:start position:0%
+time about simply lowering the a fnot
+ 
+
+ align:start position:0%
+time about simply lowering the a fnot
+product which of course pushes down the
+
+ align:start position:0%
+product which of course pushes down the
+ 
+
+ align:start position:0%
+product which of course pushes down the
+magnitude at all frequencies the
+
+ align:start position:0%
+magnitude at all frequencies the
+ 
+
+ align:start position:0%
+magnitude at all frequencies the
+disadvantage to that approach is that it
+
+ align:start position:0%
+disadvantage to that approach is that it
+ 
+
+ align:start position:0%
+disadvantage to that approach is that it
+lowers desensitivity at all frequencies
+
+ align:start position:0%
+lowers desensitivity at all frequencies
+ 
+
+ align:start position:0%
+lowers desensitivity at all frequencies
+suppose we could find a way of modifying
+
+ align:start position:0%
+suppose we could find a way of modifying
+ 
+
+ align:start position:0%
+suppose we could find a way of modifying
+the loop transmission so that we push
+
+ align:start position:0%
+the loop transmission so that we push
+ 
+
+ align:start position:0%
+the loop transmission so that we push
+down the magnitude in this vicinity so
+
+ align:start position:0%
+down the magnitude in this vicinity so
+ 
+
+ align:start position:0%
+down the magnitude in this vicinity so
+that we crossed over at a lower
+
+ align:start position:0%
+that we crossed over at a lower
+ 
+
+ align:start position:0%
+that we crossed over at a lower
+frequency without making a significant
+
+ align:start position:0%
+frequency without making a significant
+ 
+
+ align:start position:0%
+frequency without making a significant
+change in the angle if that were the
+
+ align:start position:0%
+change in the angle if that were the
+ 
+
+ align:start position:0%
+change in the angle if that were the
+case crossover frequency would lower
+
+ align:start position:0%
+case crossover frequency would lower
+ 
+
+ align:start position:0%
+case crossover frequency would lower
+we'd still have our original
+
+ align:start position:0%
+we'd still have our original
+ 
+
+ align:start position:0%
+we'd still have our original
+desensitivity at lower frequencies
+
+ align:start position:0%
+desensitivity at lower frequencies
+ 
+
+ align:start position:0%
+desensitivity at lower frequencies
+because the crossover frequency lowers
+
+ align:start position:0%
+because the crossover frequency lowers
+ 
+
+ align:start position:0%
+because the crossover frequency lowers
+we'd end up with a greater amount of
+
+ align:start position:0%
+we'd end up with a greater amount of
+ 
+
+ align:start position:0%
+we'd end up with a greater amount of
+phase margin so those those are the two
+
+ align:start position:0%
+phase margin so those those are the two
+ 
+
+ align:start position:0%
+phase margin so those those are the two
+things we might like to do either push
+
+ align:start position:0%
+things we might like to do either push
+ 
+
+ align:start position:0%
+things we might like to do either push
+up the angle portion of the bod plot in
+
+ align:start position:0%
+up the angle portion of the bod plot in
+ 
+
+ align:start position:0%
+up the angle portion of the bod plot in
+the vicinity of the crossover frequency
+
+ align:start position:0%
+the vicinity of the crossover frequency
+ 
+
+ align:start position:0%
+the vicinity of the crossover frequency
+without making a corresponding change in
+
+ align:start position:0%
+without making a corresponding change in
+ 
+
+ align:start position:0%
+without making a corresponding change in
+the crossover frequency or a
+
+ align:start position:0%
+the crossover frequency or a
+ 
+
+ align:start position:0%
+the crossover frequency or a
+corresponding change in the magnitude
+
+ align:start position:0%
+corresponding change in the magnitude
+ 
+
+ align:start position:0%
+corresponding change in the magnitude
+or push down the magnitude curve in the
+
+ align:start position:0%
+or push down the magnitude curve in the
+ 
+
+ align:start position:0%
+or push down the magnitude curve in the
+vicinity of crossover to lower crossover
+
+ align:start position:0%
+vicinity of crossover to lower crossover
+ 
+
+ align:start position:0%
+vicinity of crossover to lower crossover
+without making changes or significant
+
+ align:start position:0%
+without making changes or significant
+ 
+
+ align:start position:0%
+without making changes or significant
+changes at much lower frequencies and
+
+ align:start position:0%
+changes at much lower frequencies and
+ 
+
+ align:start position:0%
+changes at much lower frequencies and
+without modifying the angle associated
+
+ align:start position:0%
+without modifying the angle associated
+ 
+
+ align:start position:0%
+without modifying the angle associated
+with the transfer function well
+
+ align:start position:0%
+with the transfer function well
+ 
+
+ align:start position:0%
+with the transfer function well
+unfortunately our ability to do that
+
+ align:start position:0%
+unfortunately our ability to do that
+ 
+
+ align:start position:0%
+unfortunately our ability to do that
+limited the implications of physical
+
+ align:start position:0%
+limited the implications of physical
+ 
+
+ align:start position:0%
+limited the implications of physical
+realizability uh tell us that there's a
+
+ align:start position:0%
+realizability uh tell us that there's a
+ 
+
+ align:start position:0%
+realizability uh tell us that there's a
+relationship between the magnitude and
+
+ align:start position:0%
+relationship between the magnitude and
+ 
+
+ align:start position:0%
+relationship between the magnitude and
+the angle of a transfer function and in
+
+ align:start position:0%
+the angle of a transfer function and in
+ 
+
+ align:start position:0%
+the angle of a transfer function and in
+fact the kinds of things we like to do
+
+ align:start position:0%
+fact the kinds of things we like to do
+ 
+
+ align:start position:0%
+fact the kinds of things we like to do
+we really can't do with finite with
+
+ align:start position:0%
+we really can't do with finite with
+ 
+
+ align:start position:0%
+we really can't do with finite with
+elements that contain a finite number of
+
+ align:start position:0%
+elements that contain a finite number of
+ 
+
+ align:start position:0%
+elements that contain a finite number of
+of of
+
+ align:start position:0%
+of of
+ 
+
+ align:start position:0%
+of of
+elements uh consider for example a a
+
+ align:start position:0%
+elements uh consider for example a a
+ 
+
+ align:start position:0%
+elements uh consider for example a a
+transfer function that does uh the first
+
+ align:start position:0%
+transfer function that does uh the first
+ 
+
+ align:start position:0%
+transfer function that does uh the first
+operation one that gives us positive
+
+ align:start position:0%
+operation one that gives us positive
+ 
+
+ align:start position:0%
+operation one that gives us positive
+phase shift without corresponding
+
+ align:start position:0%
+phase shift without corresponding
+ 
+
+ align:start position:0%
+phase shift without corresponding
+magnitude changes such a transfer
+
+ align:start position:0%
+magnitude changes such a transfer
+ 
+
+ align:start position:0%
+magnitude changes such a transfer
+function is e to the Plus St but
+
+ align:start position:0%
+function is e to the Plus St but
+ 
+
+ align:start position:0%
+function is e to the Plus St but
+unfortunately e to the plus s to is the
+
+ align:start position:0%
+unfortunately e to the plus s to is the
+ 
+
+ align:start position:0%
+unfortunately e to the plus s to is the
+transfer function of an element that
+
+ align:start position:0%
+transfer function of an element that
+ 
+
+ align:start position:0%
+transfer function of an element that
+predicts in other words the impulse
+
+ align:start position:0%
+predicts in other words the impulse
+ 
+
+ align:start position:0%
+predicts in other words the impulse
+response of an an element whose transfer
+
+ align:start position:0%
+response of an an element whose transfer
+ 
+
+ align:start position:0%
+response of an an element whose transfer
+function is e to the Plus St is an
+
+ align:start position:0%
+function is e to the Plus St is an
+ 
+
+ align:start position:0%
+function is e to the Plus St is an
+Impulse that occurs exactly to seconds
+
+ align:start position:0%
+Impulse that occurs exactly to seconds
+ 
+
+ align:start position:0%
+Impulse that occurs exactly to seconds
+before we put in the original impulse
+
+ align:start position:0%
+before we put in the original impulse
+ 
+
+ align:start position:0%
+before we put in the original impulse
+and consequently obviously a physically
+
+ align:start position:0%
+and consequently obviously a physically
+ 
+
+ align:start position:0%
+and consequently obviously a physically
+unrealizable Network in fact if we had
+
+ align:start position:0%
+unrealizable Network in fact if we had
+ 
+
+ align:start position:0%
+unrealizable Network in fact if we had
+such a network there's far probably far
+
+ align:start position:0%
+such a network there's far probably far
+ 
+
+ align:start position:0%
+such a network there's far probably far
+better things to do with it than waste
+
+ align:start position:0%
+better things to do with it than waste
+ 
+
+ align:start position:0%
+better things to do with it than waste
+it on feedback systems we can get
+
+ align:start position:0%
+it on feedback systems we can get
+ 
+
+ align:start position:0%
+it on feedback systems we can get
+tomorrow stock market reports and that
+
+ align:start position:0%
+tomorrow stock market reports and that
+ 
+
+ align:start position:0%
+tomorrow stock market reports and that
+sort of thing and not waste it on
+
+ align:start position:0%
+sort of thing and not waste it on
+ 
+
+ align:start position:0%
+sort of thing and not waste it on
+building feedback systems so those kinds
+
+ align:start position:0%
+building feedback systems so those kinds
+ 
+
+ align:start position:0%
+building feedback systems so those kinds
+of things we we we're not really
+
+ align:start position:0%
+of things we we we're not really
+ 
+
+ align:start position:0%
+of things we we we're not really
+completely able to do we don't have the
+
+ align:start position:0%
+completely able to do we don't have the
+ 
+
+ align:start position:0%
+completely able to do we don't have the
+complete Freedom we'd like to have to
+
+ align:start position:0%
+complete Freedom we'd like to have to
+ 
+
+ align:start position:0%
+complete Freedom we'd like to have to
+make the kinds of changes that would
+
+ align:start position:0%
+make the kinds of changes that would
+ 
+
+ align:start position:0%
+make the kinds of changes that would
+give us the greatest Improvement in the
+
+ align:start position:0%
+give us the greatest Improvement in the
+ 
+
+ align:start position:0%
+give us the greatest Improvement in the
+stability of our feedback system but we
+
+ align:start position:0%
+stability of our feedback system but we
+ 
+
+ align:start position:0%
+stability of our feedback system but we
+do have some degrees of freedom and in
+
+ align:start position:0%
+do have some degrees of freedom and in
+ 
+
+ align:start position:0%
+do have some degrees of freedom and in
+fact the simple transfer functions that
+
+ align:start position:0%
+fact the simple transfer functions that
+ 
+
+ align:start position:0%
+fact the simple transfer functions that
+work in this direction are th those that
+
+ align:start position:0%
+work in this direction are th those that
+ 
+
+ align:start position:0%
+work in this direction are th those that
+include pole zero doublets a single pole
+
+ align:start position:0%
+include pole zero doublets a single pole
+ 
+
+ align:start position:0%
+include pole zero doublets a single pole
+and a single zero are the simplest forms
+
+ align:start position:0%
+and a single zero are the simplest forms
+ 
+
+ align:start position:0%
+and a single zero are the simplest forms
+of networks that go in this direction or
+
+ align:start position:0%
+of networks that go in this direction or
+ 
+
+ align:start position:0%
+of networks that go in this direction or
+the simplest forms of transfer functions
+
+ align:start position:0%
+the simplest forms of transfer functions
+ 
+
+ align:start position:0%
+the simplest forms of transfer functions
+that go in this
+
+ align:start position:0%
+that go in this
+ 
+
+ align:start position:0%
+that go in this
+Direction one of the transfer functions
+
+ align:start position:0%
+Direction one of the transfer functions
+ 
+
+ align:start position:0%
+Direction one of the transfer functions
+that we're interested in and that we can
+
+ align:start position:0%
+that we're interested in and that we can
+ 
+
+ align:start position:0%
+that we're interested in and that we can
+use to improve the performance of
+
+ align:start position:0%
+use to improve the performance of
+ 
+
+ align:start position:0%
+use to improve the performance of
+feedback systems is is called a lead
+
+ align:start position:0%
+feedback systems is is called a lead
+ 
+
+ align:start position:0%
+feedback systems is is called a lead
+transfer function and the output over
+
+ align:start position:0%
+transfer function and the output over
+ 
+
+ align:start position:0%
+transfer function and the output over
+the input for that sort of system as a
+
+ align:start position:0%
+the input for that sort of system as a
+ 
+
+ align:start position:0%
+the input for that sort of system as a
+function of s uh is one that combines a
+
+ align:start position:0%
+function of s uh is one that combines a
+ 
+
+ align:start position:0%
+function of s uh is one that combines a
+low frequency zero with a Pole located
+
+ align:start position:0%
+low frequency zero with a Pole located
+ 
+
+ align:start position:0%
+low frequency zero with a Pole located
+at a higher frequency in this
+
+ align:start position:0%
+at a higher frequency in this
+ 
+
+ align:start position:0%
+at a higher frequency in this
+representation we assume that Alpha is a
+
+ align:start position:0%
+representation we assume that Alpha is a
+ 
+
+ align:start position:0%
+representation we assume that Alpha is a
+number larger than one consequently we
+
+ align:start position:0%
+number larger than one consequently we
+ 
+
+ align:start position:0%
+number larger than one consequently we
+get a zero in the lead transfer function
+
+ align:start position:0%
+get a zero in the lead transfer function
+ 
+
+ align:start position:0%
+get a zero in the lead transfer function
+at a relatively lower frequency than the
+
+ align:start position:0%
+at a relatively lower frequency than the
+ 
+
+ align:start position:0%
+at a relatively lower frequency than the
+pole if I normalize the expression by
+
+ align:start position:0%
+pole if I normalize the expression by
+ 
+
+ align:start position:0%
+pole if I normalize the expression by
+bringing a one over Alpha out in front I
+
+ align:start position:0%
+bringing a one over Alpha out in front I
+ 
+
+ align:start position:0%
+bringing a one over Alpha out in front I
+get a an expression that can be realized
+
+ align:start position:0%
+get a an expression that can be realized
+ 
+
+ align:start position:0%
+get a an expression that can be realized
+with a simple passive Network and so
+
+ align:start position:0%
+with a simple passive Network and so
+ 
+
+ align:start position:0%
+with a simple passive Network and so
+very frequently a lead type transfer
+
+ align:start position:0%
+very frequently a lead type transfer
+ 
+
+ align:start position:0%
+very frequently a lead type transfer
+function is written as 1 over alpha
+
+ align:start position:0%
+function is written as 1 over alpha
+ 
+
+ align:start position:0%
+function is written as 1 over alpha
+alpha to S +1 over to S + one the lead
+
+ align:start position:0%
+alpha to S +1 over to S + one the lead
+ 
+
+ align:start position:0%
+alpha to S +1 over to S + one the lead
+type transfer function as the name name
+
+ align:start position:0%
+type transfer function as the name name
+ 
+
+ align:start position:0%
+type transfer function as the name name
+implies gives us positive or leading
+
+ align:start position:0%
+implies gives us positive or leading
+ 
+
+ align:start position:0%
+implies gives us positive or leading
+phase shift actually at all frequencies
+
+ align:start position:0%
+phase shift actually at all frequencies
+ 
+
+ align:start position:0%
+phase shift actually at all frequencies
+but with the greatest positive phase
+
+ align:start position:0%
+but with the greatest positive phase
+ 
+
+ align:start position:0%
+but with the greatest positive phase
+shift occur uring between the zero and
+
+ align:start position:0%
+shift occur uring between the zero and
+ 
+
+ align:start position:0%
+shift occur uring between the zero and
+the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+pole if we'd like to have something to
+
+ align:start position:0%
+pole if we'd like to have something to
+ 
+
+ align:start position:0%
+pole if we'd like to have something to
+look at we can mechanize a lead type
+
+ align:start position:0%
+look at we can mechanize a lead type
+ 
+
+ align:start position:0%
+look at we can mechanize a lead type
+transfer function with a simple Network
+
+ align:start position:0%
+transfer function with a simple Network
+ 
+
+ align:start position:0%
+transfer function with a simple Network
+shown here two resistors and a single
+
+ align:start position:0%
+shown here two resistors and a single
+ 
+
+ align:start position:0%
+shown here two resistors and a single
+capacitor if we Define 1/ Alpha as being
+
+ align:start position:0%
+capacitor if we Define 1/ Alpha as being
+ 
+
+ align:start position:0%
+capacitor if we Define 1/ Alpha as being
+equal to the attenuation ratio R2 over
+
+ align:start position:0%
+equal to the attenuation ratio R2 over
+ 
+
+ align:start position:0%
+equal to the attenuation ratio R2 over
+r1+
+
+ align:start position:0%
+r1+
+ 
+
+ align:start position:0%
+r1+
+R2 why the low frequency gain of this
+
+ align:start position:0%
+R2 why the low frequency gain of this
+ 
+
+ align:start position:0%
+R2 why the low frequency gain of this
+network is of course uh simply one over
+
+ align:start position:0%
+network is of course uh simply one over
+ 
+
+ align:start position:0%
+network is of course uh simply one over
+Alpha at low frequencies the capacitor
+
+ align:start position:0%
+Alpha at low frequencies the capacitor
+ 
+
+ align:start position:0%
+Alpha at low frequencies the capacitor
+has no influence on the performance of
+
+ align:start position:0%
+has no influence on the performance of
+ 
+
+ align:start position:0%
+has no influence on the performance of
+the network at high frequencies the gain
+
+ align:start position:0%
+the network at high frequencies the gain
+ 
+
+ align:start position:0%
+the network at high frequencies the gain
+becomes one and so we have a transfer
+
+ align:start position:0%
+becomes one and so we have a transfer
+ 
+
+ align:start position:0%
+becomes one and so we have a transfer
+function that must have a zero uh that
+
+ align:start position:0%
+function that must have a zero uh that
+ 
+
+ align:start position:0%
+function that must have a zero uh that
+causes the gain to increase from its low
+
+ align:start position:0%
+causes the gain to increase from its low
+ 
+
+ align:start position:0%
+causes the gain to increase from its low
+frequency value we have a single pole
+
+ align:start position:0%
+frequency value we have a single pole
+ 
+
+ align:start position:0%
+frequency value we have a single pole
+that eventually causes the gain to
+
+ align:start position:0%
+that eventually causes the gain to
+ 
+
+ align:start position:0%
+that eventually causes the gain to
+flatten out out if you simply write the
+
+ align:start position:0%
+flatten out out if you simply write the
+ 
+
+ align:start position:0%
+flatten out out if you simply write the
+network Expressions you find out that
+
+ align:start position:0%
+network Expressions you find out that
+ 
+
+ align:start position:0%
+network Expressions you find out that
+you get this form uh the zero at a
+
+ align:start position:0%
+you get this form uh the zero at a
+ 
+
+ align:start position:0%
+you get this form uh the zero at a
+relatively lower frequency than the pole
+
+ align:start position:0%
+relatively lower frequency than the pole
+ 
+
+ align:start position:0%
+relatively lower frequency than the pole
+for the V out over Vin transfer function
+
+ align:start position:0%
+for the V out over Vin transfer function
+ 
+
+ align:start position:0%
+for the V out over Vin transfer function
+where Alpha and the time constant are as
+
+ align:start position:0%
+where Alpha and the time constant are as
+ 
+
+ align:start position:0%
+where Alpha and the time constant are as
+defined here so here's a a simple
+
+ align:start position:0%
+defined here so here's a a simple
+ 
+
+ align:start position:0%
+defined here so here's a a simple
+electrical Network that provides an
+
+ align:start position:0%
+electrical Network that provides an
+ 
+
+ align:start position:0%
+electrical Network that provides an
+output over input transfer function
+
+ align:start position:0%
+output over input transfer function
+ 
+
+ align:start position:0%
+output over input transfer function
+which has lead type characteristics
+
+ align:start position:0%
+which has lead type characteristics
+ 
+
+ align:start position:0%
+which has lead type characteristics
+we can look at both the magnitude and
+
+ align:start position:0%
+we can look at both the magnitude and
+ 
+
+ align:start position:0%
+we can look at both the magnitude and
+the angle associated with that sort of
+
+ align:start position:0%
+the angle associated with that sort of
+ 
+
+ align:start position:0%
+the angle associated with that sort of
+lead transfer function here's the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+magnitude uh for several different
+
+ align:start position:0%
+magnitude uh for several different
+ 
+
+ align:start position:0%
+magnitude uh for several different
+values of alpha here we have an alpha
+
+ align:start position:0%
+values of alpha here we have an alpha
+ 
+
+ align:start position:0%
+values of alpha here we have an alpha
+equals 20 so we start out at low
+
+ align:start position:0%
+equals 20 so we start out at low
+ 
+
+ align:start position:0%
+equals 20 so we start out at low
+frequencies with a magnitude of 12th
+
+ align:start position:0%
+frequencies with a magnitude of 12th
+ 
+
+ align:start position:0%
+frequencies with a magnitude of 12th
+05 in this case we're normaliz to a
+
+ align:start position:0%
+05 in this case we're normaliz to a
+ 
+
+ align:start position:0%
+05 in this case we're normaliz to a
+common pole location for all of the
+
+ align:start position:0%
+common pole location for all of the
+ 
+
+ align:start position:0%
+common pole location for all of the
+networks the pole location being one
+
+ align:start position:0%
+networks the pole location being one
+ 
+
+ align:start position:0%
+networks the pole location being one
+unit on the frequency axis uh in the
+
+ align:start position:0%
+unit on the frequency axis uh in the
+ 
+
+ align:start position:0%
+unit on the frequency axis uh in the
+case of alpha equals 20 our zero would
+
+ align:start position:0%
+case of alpha equals 20 our zero would
+ 
+
+ align:start position:0%
+case of alpha equals 20 our zero would
+occur a factor of 20 below that at
+
+ align:start position:0%
+occur a factor of 20 below that at
+ 
+
+ align:start position:0%
+occur a factor of 20 below that at
+0.005 units and we then get basically a
+
+ align:start position:0%
+0.005 units and we then get basically a
+ 
+
+ align:start position:0%
+0.005 units and we then get basically a
+single zero rise in this region then we
+
+ align:start position:0%
+single zero rise in this region then we
+ 
+
+ align:start position:0%
+single zero rise in this region then we
+get the pole associated with the lead
+
+ align:start position:0%
+get the pole associated with the lead
+ 
+
+ align:start position:0%
+get the pole associated with the lead
+type Network similarly if we look at the
+
+ align:start position:0%
+type Network similarly if we look at the
+ 
+
+ align:start position:0%
+type Network similarly if we look at the
+lead characteristics for Alpha equals 10
+
+ align:start position:0%
+lead characteristics for Alpha equals 10
+ 
+
+ align:start position:0%
+lead characteristics for Alpha equals 10
+why we get this characteristic a tenth
+
+ align:start position:0%
+why we get this characteristic a tenth
+ 
+
+ align:start position:0%
+why we get this characteristic a tenth
+at low frequencies a zero location at a
+
+ align:start position:0%
+at low frequencies a zero location at a
+ 
+
+ align:start position:0%
+at low frequencies a zero location at a
+tenth of unit on the frequency axis and
+
+ align:start position:0%
+tenth of unit on the frequency axis and
+ 
+
+ align:start position:0%
+tenth of unit on the frequency axis and
+similarly for Alpha equals 5 so this
+
+ align:start position:0%
+similarly for Alpha equals 5 so this
+ 
+
+ align:start position:0%
+similarly for Alpha equals 5 so this
+then is the magnitude associated with a
+
+ align:start position:0%
+then is the magnitude associated with a
+ 
+
+ align:start position:0%
+then is the magnitude associated with a
+lead Network and we show parametrically
+
+ align:start position:0%
+lead Network and we show parametrically
+ 
+
+ align:start position:0%
+lead Network and we show parametrically
+the behavior for various values of
+
+ align:start position:0%
+the behavior for various values of
+ 
+
+ align:start position:0%
+the behavior for various values of
+alpha we can look at the angle at the
+
+ align:start position:0%
+alpha we can look at the angle at the
+ 
+
+ align:start position:0%
+alpha we can look at the angle at the
+same time or for the same kind of
+
+ align:start position:0%
+same time or for the same kind of
+ 
+
+ align:start position:0%
+same time or for the same kind of
+transfer
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+function and here is the angle
+
+ align:start position:0%
+function and here is the angle
+ 
+
+ align:start position:0%
+function and here is the angle
+associated with the lead type trans ER
+
+ align:start position:0%
+associated with the lead type trans ER
+ 
+
+ align:start position:0%
+associated with the lead type trans ER
+function we notice that even for a
+
+ align:start position:0%
+function we notice that even for a
+ 
+
+ align:start position:0%
+function we notice that even for a
+relatively small value of alpha we get a
+
+ align:start position:0%
+relatively small value of alpha we get a
+ 
+
+ align:start position:0%
+relatively small value of alpha we get a
+positive phase shift whose maximum value
+
+ align:start position:0%
+positive phase shift whose maximum value
+ 
+
+ align:start position:0%
+positive phase shift whose maximum value
+actually occurs at the geometric mean
+
+ align:start position:0%
+actually occurs at the geometric mean
+ 
+
+ align:start position:0%
+actually occurs at the geometric mean
+between the zero and the pole location
+
+ align:start position:0%
+between the zero and the pole location
+ 
+
+ align:start position:0%
+between the zero and the pole location
+remember that all of our networks were
+
+ align:start position:0%
+remember that all of our networks were
+ 
+
+ align:start position:0%
+remember that all of our networks were
+normalized to Unity for the location of
+
+ align:start position:0%
+normalized to Unity for the location of
+ 
+
+ align:start position:0%
+normalized to Unity for the location of
+the pole so all of our networks have the
+
+ align:start position:0%
+the pole so all of our networks have the
+ 
+
+ align:start position:0%
+the pole so all of our networks have the
+pole at this frequency at in the case of
+
+ align:start position:0%
+pole at this frequency at in the case of
+ 
+
+ align:start position:0%
+pole at this frequency at in the case of
+an alpha equals 5 the zero occurs a
+
+ align:start position:0%
+an alpha equals 5 the zero occurs a
+ 
+
+ align:start position:0%
+an alpha equals 5 the zero occurs a
+factor of Five Below that at this
+
+ align:start position:0%
+factor of Five Below that at this
+ 
+
+ align:start position:0%
+factor of Five Below that at this
+frequency we notice the maximum positive
+
+ align:start position:0%
+frequency we notice the maximum positive
+ 
+
+ align:start position:0%
+frequency we notice the maximum positive
+phase shift out of our Network at the
+
+ align:start position:0%
+phase shift out of our Network at the
+ 
+
+ align:start position:0%
+phase shift out of our Network at the
+geometric mean of those two frequencies
+
+ align:start position:0%
+geometric mean of those two frequencies
+ 
+
+ align:start position:0%
+geometric mean of those two frequencies
+and we get somewhere something over 40°
+
+ align:start position:0%
+and we get somewhere something over 40°
+ 
+
+ align:start position:0%
+and we get somewhere something over 40°
+of phase shift at the maximum a maximum
+
+ align:start position:0%
+of phase shift at the maximum a maximum
+ 
+
+ align:start position:0%
+of phase shift at the maximum a maximum
+when Alpha equals 5 uh similarly for
+
+ align:start position:0%
+when Alpha equals 5 uh similarly for
+ 
+
+ align:start position:0%
+when Alpha equals 5 uh similarly for
+Alpha equal 10 Alpha equals 20 we get up
+
+ align:start position:0%
+Alpha equal 10 Alpha equals 20 we get up
+ 
+
+ align:start position:0%
+Alpha equal 10 Alpha equals 20 we get up
+to something like 65 degrees of Maximum
+
+ align:start position:0%
+to something like 65 degrees of Maximum
+ 
+
+ align:start position:0%
+to something like 65 degrees of Maximum
+phase shift again occurring at the
+
+ align:start position:0%
+phase shift again occurring at the
+ 
+
+ align:start position:0%
+phase shift again occurring at the
+geometric mean of
+
+ align:start position:0%
+geometric mean of
+ 
+
+ align:start position:0%
+geometric mean of
+the zero and the pole in the case of of
+
+ align:start position:0%
+the zero and the pole in the case of of
+ 
+
+ align:start position:0%
+the zero and the pole in the case of of
+an alpha equals 20 here's the Z location
+
+ align:start position:0%
+an alpha equals 20 here's the Z location
+ 
+
+ align:start position:0%
+an alpha equals 20 here's the Z location
+for Alpha equals 20 at 05 on our
+
+ align:start position:0%
+for Alpha equals 20 at 05 on our
+ 
+
+ align:start position:0%
+for Alpha equals 20 at 05 on our
+frequency scale again here's the pole
+
+ align:start position:0%
+frequency scale again here's the pole
+ 
+
+ align:start position:0%
+frequency scale again here's the pole
+location the maximum positive phase
+
+ align:start position:0%
+location the maximum positive phase
+ 
+
+ align:start position:0%
+location the maximum positive phase
+shift from our lead Network occurs at
+
+ align:start position:0%
+shift from our lead Network occurs at
+ 
+
+ align:start position:0%
+shift from our lead Network occurs at
+the geometric mean of those two
+
+ align:start position:0%
+the geometric mean of those two
+ 
+
+ align:start position:0%
+the geometric mean of those two
+frequencies the important thing to that
+
+ align:start position:0%
+frequencies the important thing to that
+ 
+
+ align:start position:0%
+frequencies the important thing to that
+that we exploit in this sort of a
+
+ align:start position:0%
+that we exploit in this sort of a
+ 
+
+ align:start position:0%
+that we exploit in this sort of a
+transfer function or at least one of the
+
+ align:start position:0%
+transfer function or at least one of the
+ 
+
+ align:start position:0%
+transfer function or at least one of the
+things that we frequently exploit with
+
+ align:start position:0%
+things that we frequently exploit with
+ 
+
+ align:start position:0%
+things that we frequently exploit with
+this sort of a transfer function to
+
+ align:start position:0%
+this sort of a transfer function to
+ 
+
+ align:start position:0%
+this sort of a transfer function to
+improve the performance of a feedback
+
+ align:start position:0%
+improve the performance of a feedback
+ 
+
+ align:start position:0%
+improve the performance of a feedback
+system is that we begin to get positive
+
+ align:start position:0%
+system is that we begin to get positive
+ 
+
+ align:start position:0%
+system is that we begin to get positive
+phase shift
+
+ align:start position:0%
+phase shift
+ 
+
+ align:start position:0%
+phase shift
+before we have make an appreciable
+
+ align:start position:0%
+before we have make an appreciable
+ 
+
+ align:start position:0%
+before we have make an appreciable
+change in the magnitude characteristics
+
+ align:start position:0%
+change in the magnitude characteristics
+ 
+
+ align:start position:0%
+change in the magnitude characteristics
+if we look at our angle curve we notice
+
+ align:start position:0%
+if we look at our angle curve we notice
+ 
+
+ align:start position:0%
+if we look at our angle curve we notice
+that there's appreciable positive phase
+
+ align:start position:0%
+that there's appreciable positive phase
+ 
+
+ align:start position:0%
+that there's appreciable positive phase
+shift out of all three of the
+
+ align:start position:0%
+shift out of all three of the
+ 
+
+ align:start position:0%
+shift out of all three of the
+characteristics shown at the location of
+
+ align:start position:0%
+characteristics shown at the location of
+ 
+
+ align:start position:0%
+characteristics shown at the location of
+the zero here's the zero location for
+
+ align:start position:0%
+the zero here's the zero location for
+ 
+
+ align:start position:0%
+the zero here's the zero location for
+Alpha equals 20 and we actually have
+
+ align:start position:0%
+Alpha equals 20 and we actually have
+ 
+
+ align:start position:0%
+Alpha equals 20 and we actually have
+more than 40 degrees of positive phase
+
+ align:start position:0%
+more than 40 degrees of positive phase
+ 
+
+ align:start position:0%
+more than 40 degrees of positive phase
+shift at that frequency here's the zero
+
+ align:start position:0%
+shift at that frequency here's the zero
+ 
+
+ align:start position:0%
+shift at that frequency here's the zero
+location for Alpha equals 10 once again
+
+ align:start position:0%
+location for Alpha equals 10 once again
+ 
+
+ align:start position:0%
+location for Alpha equals 10 once again
+we have just about 40° of positive phase
+
+ align:start position:0%
+we have just about 40° of positive phase
+ 
+
+ align:start position:0%
+we have just about 40° of positive phase
+shift at that frequency here's the zero
+
+ align:start position:0%
+shift at that frequency here's the zero
+ 
+
+ align:start position:0%
+shift at that frequency here's the zero
+location for Alpha equals 5 and we have
+
+ align:start position:0%
+location for Alpha equals 5 and we have
+ 
+
+ align:start position:0%
+location for Alpha equals 5 and we have
+somewhere on the order of 35° of
+
+ align:start position:0%
+somewhere on the order of 35° of
+ 
+
+ align:start position:0%
+somewhere on the order of 35° of
+positive phase shift in that case so we
+
+ align:start position:0%
+positive phase shift in that case so we
+ 
+
+ align:start position:0%
+positive phase shift in that case so we
+begin to get a a very significant
+
+ align:start position:0%
+begin to get a a very significant
+ 
+
+ align:start position:0%
+begin to get a a very significant
+angular contrib contribution remember
+
+ align:start position:0%
+angular contrib contribution remember
+ 
+
+ align:start position:0%
+angular contrib contribution remember
+that we are interested in of times and
+
+ align:start position:0%
+that we are interested in of times and
+ 
+
+ align:start position:0%
+that we are interested in of times and
+getting phase margins and systems on the
+
+ align:start position:0%
+getting phase margins and systems on the
+ 
+
+ align:start position:0%
+getting phase margins and systems on the
+order of 45 degrees and so 45 degrees of
+
+ align:start position:0%
+order of 45 degrees and so 45 degrees of
+ 
+
+ align:start position:0%
+order of 45 degrees and so 45 degrees of
+positive phase shift can make a very
+
+ align:start position:0%
+positive phase shift can make a very
+ 
+
+ align:start position:0%
+positive phase shift can make a very
+important Improvement in the performance
+
+ align:start position:0%
+important Improvement in the performance
+ 
+
+ align:start position:0%
+important Improvement in the performance
+of a system here we have transfer
+
+ align:start position:0%
+of a system here we have transfer
+ 
+
+ align:start position:0%
+of a system here we have transfer
+characteristics that give us that sort
+
+ align:start position:0%
+characteristics that give us that sort
+ 
+
+ align:start position:0%
+characteristics that give us that sort
+of phase shift at the location of the
+
+ align:start position:0%
+of phase shift at the location of the
+ 
+
+ align:start position:0%
+of phase shift at the location of the
+zero well let's look back at the
+
+ align:start position:0%
+zero well let's look back at the
+ 
+
+ align:start position:0%
+zero well let's look back at the
+magnitude characteristics for a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+moment and again let's examine the
+
+ align:start position:0%
+moment and again let's examine the
+ 
+
+ align:start position:0%
+moment and again let's examine the
+magnitude characteristics at the
+
+ align:start position:0%
+magnitude characteristics at the
+ 
+
+ align:start position:0%
+magnitude characteristics at the
+location of the zero we notice that at
+
+ align:start position:0%
+location of the zero we notice that at
+ 
+
+ align:start position:0%
+location of the zero we notice that at
+the location of the zero there's only
+
+ align:start position:0%
+the location of the zero there's only
+ 
+
+ align:start position:0%
+the location of the zero there's only
+about a factor of
+
+ align:start position:0%
+about a factor of
+ 
+
+ align:start position:0%
+about a factor of
+1.4 increase in the magnitude here again
+
+ align:start position:0%
+1.4 increase in the magnitude here again
+ 
+
+ align:start position:0%
+1.4 increase in the magnitude here again
+is the zero location for Alpha equals 20
+
+ align:start position:0%
+is the zero location for Alpha equals 20
+ 
+
+ align:start position:0%
+is the zero location for Alpha equals 20
+the magnitude is increased from its low
+
+ align:start position:0%
+the magnitude is increased from its low
+ 
+
+ align:start position:0%
+the magnitude is increased from its low
+frequency value by about a factor of 1.4
+
+ align:start position:0%
+frequency value by about a factor of 1.4
+ 
+
+ align:start position:0%
+frequency value by about a factor of 1.4
+at the zero location similarly here
+
+ align:start position:0%
+at the zero location similarly here
+ 
+
+ align:start position:0%
+at the zero location similarly here
+here so the important part about the
+
+ align:start position:0%
+here so the important part about the
+ 
+
+ align:start position:0%
+here so the important part about the
+lead transfer function or at least one
+
+ align:start position:0%
+lead transfer function or at least one
+ 
+
+ align:start position:0%
+lead transfer function or at least one
+of the properties of the lead type
+
+ align:start position:0%
+of the properties of the lead type
+ 
+
+ align:start position:0%
+of the properties of the lead type
+transfer function that we're able to
+
+ align:start position:0%
+transfer function that we're able to
+ 
+
+ align:start position:0%
+transfer function that we're able to
+exploit is the fact that the phase shift
+
+ align:start position:0%
+exploit is the fact that the phase shift
+ 
+
+ align:start position:0%
+exploit is the fact that the phase shift
+becomes positive by a very significant
+
+ align:start position:0%
+becomes positive by a very significant
+ 
+
+ align:start position:0%
+becomes positive by a very significant
+amount at least in terms of improving
+
+ align:start position:0%
+amount at least in terms of improving
+ 
+
+ align:start position:0%
+amount at least in terms of improving
+the performance of a feedback system
+
+ align:start position:0%
+the performance of a feedback system
+ 
+
+ align:start position:0%
+the performance of a feedback system
+before there's much change in the
+
+ align:start position:0%
+before there's much change in the
+ 
+
+ align:start position:0%
+before there's much change in the
+magnitude characteristics and we can use
+
+ align:start position:0%
+magnitude characteristics and we can use
+ 
+
+ align:start position:0%
+magnitude characteristics and we can use
+that and the way we use it is as
+
+ align:start position:0%
+that and the way we use it is as
+ 
+
+ align:start position:0%
+that and the way we use it is as
+follows here's our magnitude
+
+ align:start position:0%
+follows here's our magnitude
+ 
+
+ align:start position:0%
+follows here's our magnitude
+characteristics for our uncompensated
+
+ align:start position:0%
+characteristics for our uncompensated
+ 
+
+ align:start position:0%
+characteristics for our uncompensated
+system let's locate the zero at least
+
+ align:start position:0%
+system let's locate the zero at least
+ 
+
+ align:start position:0%
+system let's locate the zero at least
+one of the things we can do and of
+
+ align:start position:0%
+one of the things we can do and of
+ 
+
+ align:start position:0%
+one of the things we can do and of
+course there are many ways of using
+
+ align:start position:0%
+course there are many ways of using
+ 
+
+ align:start position:0%
+course there are many ways of using
+these kinds of transfer functions to
+
+ align:start position:0%
+these kinds of transfer functions to
+ 
+
+ align:start position:0%
+these kinds of transfer functions to
+improve performance but one of the
+
+ align:start position:0%
+improve performance but one of the
+ 
+
+ align:start position:0%
+improve performance but one of the
+things we might do is locate the zero of
+
+ align:start position:0%
+things we might do is locate the zero of
+ 
+
+ align:start position:0%
+things we might do is locate the zero of
+the lead Network somewhere in the
+
+ align:start position:0%
+the lead Network somewhere in the
+ 
+
+ align:start position:0%
+the lead Network somewhere in the
+vicinity of crossover for the
+
+ align:start position:0%
+vicinity of crossover for the
+ 
+
+ align:start position:0%
+vicinity of crossover for the
+uncompensated system we might locate it
+
+ align:start position:0%
+uncompensated system we might locate it
+ 
+
+ align:start position:0%
+uncompensated system we might locate it
+somewhere out in here
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+maybe like so so our magnitude
+
+ align:start position:0%
+maybe like so so our magnitude
+ 
+
+ align:start position:0%
+maybe like so so our magnitude
+characteristics would begin to go up in
+
+ align:start position:0%
+characteristics would begin to go up in
+ 
+
+ align:start position:0%
+characteristics would begin to go up in
+this
+
+ align:start position:0%
+this
+ 
+
+ align:start position:0%
+this
+region what we depend on is the fact
+
+ align:start position:0%
+region what we depend on is the fact
+ 
+
+ align:start position:0%
+region what we depend on is the fact
+that in this region before the magnitude
+
+ align:start position:0%
+that in this region before the magnitude
+ 
+
+ align:start position:0%
+that in this region before the magnitude
+has increased appreciably that would
+
+ align:start position:0%
+has increased appreciably that would
+ 
+
+ align:start position:0%
+has increased appreciably that would
+lead us to much higher crossover
+
+ align:start position:0%
+lead us to much higher crossover
+ 
+
+ align:start position:0%
+lead us to much higher crossover
+frequencies in in this vicinity we get
+
+ align:start position:0%
+frequencies in in this vicinity we get
+ 
+
+ align:start position:0%
+frequencies in in this vicinity we get
+appreciable positive phase shift out of
+
+ align:start position:0%
+appreciable positive phase shift out of
+ 
+
+ align:start position:0%
+appreciable positive phase shift out of
+our lead type transfer function and so
+
+ align:start position:0%
+our lead type transfer function and so
+ 
+
+ align:start position:0%
+our lead type transfer function and so
+the hope would be that the modification
+
+ align:start position:0%
+the hope would be that the modification
+ 
+
+ align:start position:0%
+the hope would be that the modification
+made to the angle is something like so
+
+ align:start position:0%
+made to the angle is something like so
+ 
+
+ align:start position:0%
+made to the angle is something like so
+eventually it drops off again but our
+
+ align:start position:0%
+eventually it drops off again but our
+ 
+
+ align:start position:0%
+eventually it drops off again but our
+hope is that we can get enough positive
+
+ align:start position:0%
+hope is that we can get enough positive
+ 
+
+ align:start position:0%
+hope is that we can get enough positive
+phase shift in the vicinity of crossover
+
+ align:start position:0%
+phase shift in the vicinity of crossover
+ 
+
+ align:start position:0%
+phase shift in the vicinity of crossover
+notice here crossovers increase just a
+
+ align:start position:0%
+notice here crossovers increase just a
+ 
+
+ align:start position:0%
+notice here crossovers increase just a
+little
+
+ align:start position:0%
+little
+ 
+
+ align:start position:0%
+little
+bit but the hope is that we've gotten
+
+ align:start position:0%
+bit but the hope is that we've gotten
+ 
+
+ align:start position:0%
+bit but the hope is that we've gotten
+appreciable positive phase shift in the
+
+ align:start position:0%
+appreciable positive phase shift in the
+ 
+
+ align:start position:0%
+appreciable positive phase shift in the
+vicinity of crossover so that we improve
+
+ align:start position:0%
+vicinity of crossover so that we improve
+ 
+
+ align:start position:0%
+vicinity of crossover so that we improve
+the phase margin of our system
+
+ align:start position:0%
+the phase margin of our system
+ 
+
+ align:start position:0%
+the phase margin of our system
+consequently its relative
+
+ align:start position:0%
+consequently its relative
+ 
+
+ align:start position:0%
+consequently its relative
+stability so that's one kind of
+
+ align:start position:0%
+stability so that's one kind of
+ 
+
+ align:start position:0%
+stability so that's one kind of
+modification we might like to make to
+
+ align:start position:0%
+modification we might like to make to
+ 
+
+ align:start position:0%
+modification we might like to make to
+the loop transmission of our feedback
+
+ align:start position:0%
+the loop transmission of our feedback
+ 
+
+ align:start position:0%
+the loop transmission of our feedback
+system
+
+ align:start position:0%
+system
+ 
+
+ align:start position:0%
+system
+a second possibility is to add a
+
+ align:start position:0%
+a second possibility is to add a
+ 
+
+ align:start position:0%
+a second possibility is to add a
+transfer function to the loop
+
+ align:start position:0%
+transfer function to the loop
+ 
+
+ align:start position:0%
+transfer function to the loop
+transmission that's called a lag type
+
+ align:start position:0%
+transmission that's called a lag type
+ 
+
+ align:start position:0%
+transmission that's called a lag type
+transfer
+
+ align:start position:0%
+transfer
+ 
+
+ align:start position:0%
+transfer
+function and here's the expression for a
+
+ align:start position:0%
+function and here's the expression for a
+ 
+
+ align:start position:0%
+function and here's the expression for a
+a lag transfer function again the output
+
+ align:start position:0%
+a lag transfer function again the output
+ 
+
+ align:start position:0%
+a lag transfer function again the output
+over the input is a combination this
+
+ align:start position:0%
+over the input is a combination this
+ 
+
+ align:start position:0%
+over the input is a combination this
+time of a pole at a relatively lower
+
+ align:start position:0%
+time of a pole at a relatively lower
+ 
+
+ align:start position:0%
+time of a pole at a relatively lower
+frequency than the zero we have this
+
+ align:start position:0%
+frequency than the zero we have this
+ 
+
+ align:start position:0%
+frequency than the zero we have this
+sort of a pole zero diagram for a lag
+
+ align:start position:0%
+sort of a pole zero diagram for a lag
+ 
+
+ align:start position:0%
+sort of a pole zero diagram for a lag
+kind of transfer function the pole
+
+ align:start position:0%
+kind of transfer function the pole
+ 
+
+ align:start position:0%
+kind of transfer function the pole
+occurs at a frequency one over Alpha to
+
+ align:start position:0%
+occurs at a frequency one over Alpha to
+ 
+
+ align:start position:0%
+occurs at a frequency one over Alpha to
+the zero at a frequency one over to
+
+ align:start position:0%
+the zero at a frequency one over to
+ 
+
+ align:start position:0%
+the zero at a frequency one over to
+again assuming Alpha is a number larger
+
+ align:start position:0%
+again assuming Alpha is a number larger
+ 
+
+ align:start position:0%
+again assuming Alpha is a number larger
+than one we get a Pole located at a
+
+ align:start position:0%
+than one we get a Pole located at a
+ 
+
+ align:start position:0%
+than one we get a Pole located at a
+lower frequency than the
+
+ align:start position:0%
+lower frequency than the
+ 
+
+ align:start position:0%
+lower frequency than the
+zero let's look at the characteristics
+
+ align:start position:0%
+zero let's look at the characteristics
+ 
+
+ align:start position:0%
+zero let's look at the characteristics
+of that sort of a network or first let's
+
+ align:start position:0%
+of that sort of a network or first let's
+ 
+
+ align:start position:0%
+of that sort of a network or first let's
+look at at how we might Implement that
+
+ align:start position:0%
+look at at how we might Implement that
+ 
+
+ align:start position:0%
+look at at how we might Implement that
+kind of a network and then let's look at
+
+ align:start position:0%
+kind of a network and then let's look at
+ 
+
+ align:start position:0%
+kind of a network and then let's look at
+its
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+characteristics
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um here's the kind of a network that
+
+ align:start position:0%
+um here's the kind of a network that
+ 
+
+ align:start position:0%
+um here's the kind of a network that
+will give us a lag type transfer
+
+ align:start position:0%
+will give us a lag type transfer
+ 
+
+ align:start position:0%
+will give us a lag type transfer
+function uh we have again two resistors
+
+ align:start position:0%
+function uh we have again two resistors
+ 
+
+ align:start position:0%
+function uh we have again two resistors
+a single capacitor at sufficiently low
+
+ align:start position:0%
+a single capacitor at sufficiently low
+ 
+
+ align:start position:0%
+a single capacitor at sufficiently low
+frequencies where the capacitor is an
+
+ align:start position:0%
+frequencies where the capacitor is an
+ 
+
+ align:start position:0%
+frequencies where the capacitor is an
+open circuit uh the output over the
+
+ align:start position:0%
+open circuit uh the output over the
+ 
+
+ align:start position:0%
+open circuit uh the output over the
+input is simply one whereas at higher
+
+ align:start position:0%
+input is simply one whereas at higher
+ 
+
+ align:start position:0%
+input is simply one whereas at higher
+frequencies we get an attenuation R2
+
+ align:start position:0%
+frequencies we get an attenuation R2
+ 
+
+ align:start position:0%
+frequencies we get an attenuation R2
+over R1 + R2 the net result is that we
+
+ align:start position:0%
+over R1 + R2 the net result is that we
+ 
+
+ align:start position:0%
+over R1 + R2 the net result is that we
+get an input to Output transfer function
+
+ align:start position:0%
+get an input to Output transfer function
+ 
+
+ align:start position:0%
+get an input to Output transfer function
+of the form I I showed on the Blackboard
+
+ align:start position:0%
+of the form I I showed on the Blackboard
+ 
+
+ align:start position:0%
+of the form I I showed on the Blackboard
+to s+1 over Alpha to s+ one Again by
+
+ align:start position:0%
+to s+1 over Alpha to s+ one Again by
+ 
+
+ align:start position:0%
+to s+1 over Alpha to s+ one Again by
+doing a little bit of arithmetic we're
+
+ align:start position:0%
+doing a little bit of arithmetic we're
+ 
+
+ align:start position:0%
+doing a little bit of arithmetic we're
+able to identify Alpha as being the
+
+ align:start position:0%
+able to identify Alpha as being the
+ 
+
+ align:start position:0%
+able to identify Alpha as being the
+reciprocal of the attenuation ratio uh
+
+ align:start position:0%
+reciprocal of the attenuation ratio uh
+ 
+
+ align:start position:0%
+reciprocal of the attenuation ratio uh
+Alpha is r1+ R2 over over R2 and to is
+
+ align:start position:0%
+Alpha is r1+ R2 over over R2 and to is
+ 
+
+ align:start position:0%
+Alpha is r1+ R2 over over R2 and to is
+simply R2 C for this particular Network
+
+ align:start position:0%
+simply R2 C for this particular Network
+ 
+
+ align:start position:0%
+simply R2 C for this particular Network
+topology as the name implies a lag
+
+ align:start position:0%
+topology as the name implies a lag
+ 
+
+ align:start position:0%
+topology as the name implies a lag
+Network gives us lagging or negative
+
+ align:start position:0%
+Network gives us lagging or negative
+ 
+
+ align:start position:0%
+Network gives us lagging or negative
+phase shift at all frequencies and let's
+
+ align:start position:0%
+phase shift at all frequencies and let's
+ 
+
+ align:start position:0%
+phase shift at all frequencies and let's
+look at the phase shift characteristics
+
+ align:start position:0%
+look at the phase shift characteristics
+ 
+
+ align:start position:0%
+look at the phase shift characteristics
+of a lag Network um for a lead Network
+
+ align:start position:0%
+of a lag Network um for a lead Network
+ 
+
+ align:start position:0%
+of a lag Network um for a lead Network
+we said that we have this sort of
+
+ align:start position:0%
+we said that we have this sort of
+ 
+
+ align:start position:0%
+we said that we have this sort of
+characteristic positive phase shift at
+
+ align:start position:0%
+characteristic positive phase shift at
+ 
+
+ align:start position:0%
+characteristic positive phase shift at
+all frequencies well the lag Network
+
+ align:start position:0%
+all frequencies well the lag Network
+ 
+
+ align:start position:0%
+all frequencies well the lag Network
+basically gives us characteristics like
+
+ align:start position:0%
+basically gives us characteristics like
+ 
+
+ align:start position:0%
+basically gives us characteristics like
+that it's a little bit confusing in this
+
+ align:start position:0%
+that it's a little bit confusing in this
+ 
+
+ align:start position:0%
+that it's a little bit confusing in this
+form we have a little problem with the
+
+ align:start position:0%
+form we have a little problem with the
+ 
+
+ align:start position:0%
+form we have a little problem with the
+axes but it emphasizes the Symmetry uh
+
+ align:start position:0%
+axes but it emphasizes the Symmetry uh
+ 
+
+ align:start position:0%
+axes but it emphasizes the Symmetry uh
+between a lead and a lag Network and is
+
+ align:start position:0%
+between a lead and a lag Network and is
+ 
+
+ align:start position:0%
+between a lead and a lag Network and is
+actually the correct form if we simply
+
+ align:start position:0%
+actually the correct form if we simply
+ 
+
+ align:start position:0%
+actually the correct form if we simply
+modify the the
+
+ align:start position:0%
+modify the the
+ 
+
+ align:start position:0%
+modify the the
+axes
+
+ align:start position:0%
+axes
+ 
+
+ align:start position:0%
+axes
+here is the actual
+
+ align:start position:0%
+here is the actual
+ 
+
+ align:start position:0%
+here is the actual
+angle characteristic for a lag
+
+ align:start position:0%
+angle characteristic for a lag
+ 
+
+ align:start position:0%
+angle characteristic for a lag
+Network again for several different
+
+ align:start position:0%
+Network again for several different
+ 
+
+ align:start position:0%
+Network again for several different
+values of of Alpha we have negative
+
+ align:start position:0%
+values of of Alpha we have negative
+ 
+
+ align:start position:0%
+values of of Alpha we have negative
+phase shift at at all frequencies of
+
+ align:start position:0%
+phase shift at at all frequencies of
+ 
+
+ align:start position:0%
+phase shift at at all frequencies of
+course running from 0 degrees down and
+
+ align:start position:0%
+course running from 0 degrees down and
+ 
+
+ align:start position:0%
+course running from 0 degrees down and
+so forth uh we have an for Alpha equals
+
+ align:start position:0%
+so forth uh we have an for Alpha equals
+ 
+
+ align:start position:0%
+so forth uh we have an for Alpha equals
+5 we hit a maximum negative phase shift
+
+ align:start position:0%
+5 we hit a maximum negative phase shift
+ 
+
+ align:start position:0%
+5 we hit a maximum negative phase shift
+of of again about minus 42 or 43 degrees
+
+ align:start position:0%
+of of again about minus 42 or 43 degrees
+ 
+
+ align:start position:0%
+of of again about minus 42 or 43 degrees
+the same amount as we got in the lead
+
+ align:start position:0%
+the same amount as we got in the lead
+ 
+
+ align:start position:0%
+the same amount as we got in the lead
+Network only the opposite sign and so
+
+ align:start position:0%
+Network only the opposite sign and so
+ 
+
+ align:start position:0%
+Network only the opposite sign and so
+forth so this is a completely identic
+
+ align:start position:0%
+forth so this is a completely identic
+ 
+
+ align:start position:0%
+forth so this is a completely identic
+curve except flipped over to that that
+
+ align:start position:0%
+curve except flipped over to that that
+ 
+
+ align:start position:0%
+curve except flipped over to that that
+we got for the lead network uh these are
+
+ align:start position:0%
+we got for the lead network uh these are
+ 
+
+ align:start position:0%
+we got for the lead network uh these are
+all normalized uh to a common pole
+
+ align:start position:0%
+all normalized uh to a common pole
+ 
+
+ align:start position:0%
+all normalized uh to a common pole
+location and uh we get
+
+ align:start position:0%
+location and uh we get
+ 
+
+ align:start position:0%
+location and uh we get
+the characteristics as we've we've shown
+
+ align:start position:0%
+the characteristics as we've we've shown
+ 
+
+ align:start position:0%
+the characteristics as we've we've shown
+them let's look at the corresponding
+
+ align:start position:0%
+them let's look at the corresponding
+ 
+
+ align:start position:0%
+them let's look at the corresponding
+magnitude
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+characteristics and here are the
+
+ align:start position:0%
+characteristics and here are the
+ 
+
+ align:start position:0%
+characteristics and here are the
+magnitude characteristics uh for the lag
+
+ align:start position:0%
+magnitude characteristics uh for the lag
+ 
+
+ align:start position:0%
+magnitude characteristics uh for the lag
+net nwor again all normalized in this
+
+ align:start position:0%
+net nwor again all normalized in this
+ 
+
+ align:start position:0%
+net nwor again all normalized in this
+case to a pole location of one the zero
+
+ align:start position:0%
+case to a pole location of one the zero
+ 
+
+ align:start position:0%
+case to a pole location of one the zero
+comes out at progressively higher
+
+ align:start position:0%
+comes out at progressively higher
+ 
+
+ align:start position:0%
+comes out at progressively higher
+frequencies for increasing
+
+ align:start position:0%
+frequencies for increasing
+ 
+
+ align:start position:0%
+frequencies for increasing
+Alpha the way
+
+ align:start position:0%
+Alpha the way
+ 
+
+ align:start position:0%
+Alpha the way
+we exploit this network or at least one
+
+ align:start position:0%
+we exploit this network or at least one
+ 
+
+ align:start position:0%
+we exploit this network or at least one
+way that we can do it is as
+
+ align:start position:0%
+way that we can do it is as
+ 
+
+ align:start position:0%
+way that we can do it is as
+follows we try to use the lag Network to
+
+ align:start position:0%
+follows we try to use the lag Network to
+ 
+
+ align:start position:0%
+follows we try to use the lag Network to
+push down the magnitude over a range of
+
+ align:start position:0%
+push down the magnitude over a range of
+ 
+
+ align:start position:0%
+push down the magnitude over a range of
+frequencies in other words we locate the
+
+ align:start position:0%
+frequencies in other words we locate the
+ 
+
+ align:start position:0%
+frequencies in other words we locate the
+mag the lag type transfer function
+
+ align:start position:0%
+mag the lag type transfer function
+ 
+
+ align:start position:0%
+mag the lag type transfer function
+locate the pole and the zero somewhere
+
+ align:start position:0%
+locate the pole and the zero somewhere
+ 
+
+ align:start position:0%
+locate the pole and the zero somewhere
+below crossover and we recognize because
+
+ align:start position:0%
+below crossover and we recognize because
+ 
+
+ align:start position:0%
+below crossover and we recognize because
+of the attenuation characteristics
+
+ align:start position:0%
+of the attenuation characteristics
+ 
+
+ align:start position:0%
+of the attenuation characteristics
+associated with the lag type transfer
+
+ align:start position:0%
+associated with the lag type transfer
+ 
+
+ align:start position:0%
+associated with the lag type transfer
+function that will push the magnitude
+
+ align:start position:0%
+function that will push the magnitude
+ 
+
+ align:start position:0%
+function that will push the magnitude
+curve
+
+ align:start position:0%
+curve
+ 
+
+ align:start position:0%
+curve
+down but not at DC it doesn't have the
+
+ align:start position:0%
+down but not at DC it doesn't have the
+ 
+
+ align:start position:0%
+down but not at DC it doesn't have the
+same effect as as simply lowering the a
+
+ align:start position:0%
+same effect as as simply lowering the a
+ 
+
+ align:start position:0%
+same effect as as simply lowering the a
+fnot product it pushes the magnitude
+
+ align:start position:0%
+fnot product it pushes the magnitude
+ 
+
+ align:start position:0%
+fnot product it pushes the magnitude
+down at frequencies beyond the pole
+
+ align:start position:0%
+down at frequencies beyond the pole
+ 
+
+ align:start position:0%
+down at frequencies beyond the pole
+associated with the lag type transfer
+
+ align:start position:0%
+associated with the lag type transfer
+ 
+
+ align:start position:0%
+associated with the lag type transfer
+function so the modification that we
+
+ align:start position:0%
+function so the modification that we
+ 
+
+ align:start position:0%
+function so the modification that we
+might make in the case of lag is to
+
+ align:start position:0%
+might make in the case of lag is to
+ 
+
+ align:start position:0%
+might make in the case of lag is to
+possibly put the pole in here the curve
+
+ align:start position:0%
+possibly put the pole in here the curve
+ 
+
+ align:start position:0%
+possibly put the pole in here the curve
+would drop down we then add the zero and
+
+ align:start position:0%
+would drop down we then add the zero and
+ 
+
+ align:start position:0%
+would drop down we then add the zero and
+we
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+eventually end up with our compensated
+
+ align:start position:0%
+eventually end up with our compensated
+ 
+
+ align:start position:0%
+eventually end up with our compensated
+curve going parallel to the original
+
+ align:start position:0%
+curve going parallel to the original
+ 
+
+ align:start position:0%
+curve going parallel to the original
+curve what happens to the angle under
+
+ align:start position:0%
+curve what happens to the angle under
+ 
+
+ align:start position:0%
+curve what happens to the angle under
+those conditions well here's the pole
+
+ align:start position:0%
+those conditions well here's the pole
+ 
+
+ align:start position:0%
+those conditions well here's the pole
+and here's the zero associated with our
+
+ align:start position:0%
+and here's the zero associated with our
+ 
+
+ align:start position:0%
+and here's the zero associated with our
+lag transfer function and we recall from
+
+ align:start position:0%
+lag transfer function and we recall from
+ 
+
+ align:start position:0%
+lag transfer function and we recall from
+the plot of the angle characteristics of
+
+ align:start position:0%
+the plot of the angle characteristics of
+ 
+
+ align:start position:0%
+the plot of the angle characteristics of
+the lag function and the lead function
+
+ align:start position:0%
+the lag function and the lead function
+ 
+
+ align:start position:0%
+the lag function and the lead function
+for that matter that the most profound
+
+ align:start position:0%
+for that matter that the most profound
+ 
+
+ align:start position:0%
+for that matter that the most profound
+effect on the angle occurs over a
+
+ align:start position:0%
+effect on the angle occurs over a
+ 
+
+ align:start position:0%
+effect on the angle occurs over a
+frequency range between the two
+
+ align:start position:0%
+frequency range between the two
+ 
+
+ align:start position:0%
+frequency range between the two
+singularities between the pole and the
+
+ align:start position:0%
+singularities between the pole and the
+ 
+
+ align:start position:0%
+singularities between the pole and the
+zero associated with the transfer
+
+ align:start position:0%
+zero associated with the transfer
+ 
+
+ align:start position:0%
+zero associated with the transfer
+function so here in the case of of a lag
+
+ align:start position:0%
+function so here in the case of of a lag
+ 
+
+ align:start position:0%
+function so here in the case of of a lag
+Network put in possibly in this range
+
+ align:start position:0%
+Network put in possibly in this range
+ 
+
+ align:start position:0%
+Network put in possibly in this range
+we'd anticipate that we'd put a negative
+
+ align:start position:0%
+we'd anticipate that we'd put a negative
+ 
+
+ align:start position:0%
+we'd anticipate that we'd put a negative
+lump in
+
+ align:start position:0%
+lump in
+ 
+
+ align:start position:0%
+lump in
+the phase characteristics we do
+
+ align:start position:0%
+the phase characteristics we do
+ 
+
+ align:start position:0%
+the phase characteristics we do
+something like
+
+ align:start position:0%
+something like
+ 
+
+ align:start position:0%
+something like
+this but but the hope is that we locate
+
+ align:start position:0%
+this but but the hope is that we locate
+ 
+
+ align:start position:0%
+this but but the hope is that we locate
+the lag Network so that the angle has
+
+ align:start position:0%
+the lag Network so that the angle has
+ 
+
+ align:start position:0%
+the lag Network so that the angle has
+very nearly returned to its
+
+ align:start position:0%
+very nearly returned to its
+ 
+
+ align:start position:0%
+very nearly returned to its
+uncompensated value before crossover
+
+ align:start position:0%
+uncompensated value before crossover
+ 
+
+ align:start position:0%
+uncompensated value before crossover
+notice that with the lag Network we've
+
+ align:start position:0%
+notice that with the lag Network we've
+ 
+
+ align:start position:0%
+notice that with the lag Network we've
+lowered
+
+ align:start position:0%
+lowered
+ 
+
+ align:start position:0%
+lowered
+crossover back to this frequency and if
+
+ align:start position:0%
+crossover back to this frequency and if
+ 
+
+ align:start position:0%
+crossover back to this frequency and if
+we can locate the lag Network at a low
+
+ align:start position:0%
+we can locate the lag Network at a low
+ 
+
+ align:start position:0%
+we can locate the lag Network at a low
+enough frequency we can ensure that the
+
+ align:start position:0%
+enough frequency we can ensure that the
+ 
+
+ align:start position:0%
+enough frequency we can ensure that the
+residual negative phase shift associated
+
+ align:start position:0%
+residual negative phase shift associated
+ 
+
+ align:start position:0%
+residual negative phase shift associated
+with the lag network has become very
+
+ align:start position:0%
+with the lag network has become very
+ 
+
+ align:start position:0%
+with the lag network has become very
+small and as I've shown in this
+
+ align:start position:0%
+small and as I've shown in this
+ 
+
+ align:start position:0%
+small and as I've shown in this
+Construction we end up improving the
+
+ align:start position:0%
+Construction we end up improving the
+ 
+
+ align:start position:0%
+Construction we end up improving the
+phase margin of the system from its
+
+ align:start position:0%
+phase margin of the system from its
+ 
+
+ align:start position:0%
+phase margin of the system from its
+original uncompensated value to this
+
+ align:start position:0%
+original uncompensated value to this
+ 
+
+ align:start position:0%
+original uncompensated value to this
+value by simply pushing down the
+
+ align:start position:0%
+value by simply pushing down the
+ 
+
+ align:start position:0%
+value by simply pushing down the
+magnitude curve causing the crossover
+
+ align:start position:0%
+magnitude curve causing the crossover
+ 
+
+ align:start position:0%
+magnitude curve causing the crossover
+frequency to lower
+
+ align:start position:0%
+frequency to lower
+ 
+
+ align:start position:0%
+frequency to lower
+and without having if we've located
+
+ align:start position:0%
+and without having if we've located
+ 
+
+ align:start position:0%
+and without having if we've located
+things properly so we don't have a great
+
+ align:start position:0%
+things properly so we don't have a great
+ 
+
+ align:start position:0%
+things properly so we don't have a great
+deal of residual negative phase shift
+
+ align:start position:0%
+deal of residual negative phase shift
+ 
+
+ align:start position:0%
+deal of residual negative phase shift
+from the lag Network we improve the
+
+ align:start position:0%
+from the lag Network we improve the
+ 
+
+ align:start position:0%
+from the lag Network we improve the
+phase margin of the system in that way
+
+ align:start position:0%
+phase margin of the system in that way
+ 
+
+ align:start position:0%
+phase margin of the system in that way
+while we've lowered desensitivity over a
+
+ align:start position:0%
+while we've lowered desensitivity over a
+ 
+
+ align:start position:0%
+while we've lowered desensitivity over a
+range of frequencies here we haven't
+
+ align:start position:0%
+range of frequencies here we haven't
+ 
+
+ align:start position:0%
+range of frequencies here we haven't
+located lower desensitivity back in this
+
+ align:start position:0%
+located lower desensitivity back in this
+ 
+
+ align:start position:0%
+located lower desensitivity back in this
+region so we're able to use the lag
+
+ align:start position:0%
+region so we're able to use the lag
+ 
+
+ align:start position:0%
+region so we're able to use the lag
+Network to improve our desensi or
+
+ align:start position:0%
+Network to improve our desensi or
+ 
+
+ align:start position:0%
+Network to improve our desensi or
+maintain our desensitivity at lower
+
+ align:start position:0%
+maintain our desensitivity at lower
+ 
+
+ align:start position:0%
+maintain our desensitivity at lower
+frequencies and yet improve the
+
+ align:start position:0%
+frequencies and yet improve the
+ 
+
+ align:start position:0%
+frequencies and yet improve the
+stability of the system and so that's
+
+ align:start position:0%
+stability of the system and so that's
+ 
+
+ align:start position:0%
+stability of the system and so that's
+the way we typically use a lag type
+
+ align:start position:0%
+the way we typically use a lag type
+ 
+
+ align:start position:0%
+the way we typically use a lag type
+transfer function to improve the
+
+ align:start position:0%
+transfer function to improve the
+ 
+
+ align:start position:0%
+transfer function to improve the
+performance of a feedback system one
+
+ align:start position:0%
+performance of a feedback system one
+ 
+
+ align:start position:0%
+performance of a feedback system one
+final thing that's useful for design
+
+ align:start position:0%
+final thing that's useful for design
+ 
+
+ align:start position:0%
+final thing that's useful for design
+purposes in in these when we use these
+
+ align:start position:0%
+purposes in in these when we use these
+ 
+
+ align:start position:0%
+purposes in in these when we use these
+kinds of networks is the maximum phase
+
+ align:start position:0%
+kinds of networks is the maximum phase
+ 
+
+ align:start position:0%
+kinds of networks is the maximum phase
+shift that we get out of a network or a
+
+ align:start position:0%
+shift that we get out of a network or a
+ 
+
+ align:start position:0%
+shift that we get out of a network or a
+trans transfer function uh the maximum
+
+ align:start position:0%
+trans transfer function uh the maximum
+ 
+
+ align:start position:0%
+trans transfer function uh the maximum
+angle associated with either a lead or a
+
+ align:start position:0%
+angle associated with either a lead or a
+ 
+
+ align:start position:0%
+angle associated with either a lead or a
+lag transfer function the only
+
+ align:start position:0%
+lag transfer function the only
+ 
+
+ align:start position:0%
+lag transfer function the only
+difference is the sign of course we
+
+ align:start position:0%
+difference is the sign of course we
+ 
+
+ align:start position:0%
+difference is the sign of course we
+notice that for a lead type transfer
+
+ align:start position:0%
+notice that for a lead type transfer
+ 
+
+ align:start position:0%
+notice that for a lead type transfer
+function we get positive phase shift for
+
+ align:start position:0%
+function we get positive phase shift for
+ 
+
+ align:start position:0%
+function we get positive phase shift for
+a lag type we get Negative phase shift
+
+ align:start position:0%
+a lag type we get Negative phase shift
+ 
+
+ align:start position:0%
+a lag type we get Negative phase shift
+the maximum angle is simply the arc sign
+
+ align:start position:0%
+the maximum angle is simply the arc sign
+ 
+
+ align:start position:0%
+the maximum angle is simply the arc sign
+of alpha minus one over Alpha + one for
+
+ align:start position:0%
+of alpha minus one over Alpha + one for
+ 
+
+ align:start position:0%
+of alpha minus one over Alpha + one for
+either the lead or the lag type transfer
+
+ align:start position:0%
+either the lead or the lag type transfer
+ 
+
+ align:start position:0%
+either the lead or the lag type transfer
+function we also recognize that we have
+
+ align:start position:0%
+function we also recognize that we have
+ 
+
+ align:start position:0%
+function we also recognize that we have
+to have more degrees of freedom than
+
+ align:start position:0%
+to have more degrees of freedom than
+ 
+
+ align:start position:0%
+to have more degrees of freedom than
+simply adding these transfer fun
+
+ align:start position:0%
+simply adding these transfer fun
+ 
+
+ align:start position:0%
+simply adding these transfer fun
+functions very frequently we combine a
+
+ align:start position:0%
+functions very frequently we combine a
+ 
+
+ align:start position:0%
+functions very frequently we combine a
+lead or a lag type transfer function
+
+ align:start position:0%
+lead or a lag type transfer function
+ 
+
+ align:start position:0%
+lead or a lag type transfer function
+with a modification to the a fnot
+
+ align:start position:0%
+with a modification to the a fnot
+ 
+
+ align:start position:0%
+with a modification to the a fnot
+product and that combination is a very
+
+ align:start position:0%
+product and that combination is a very
+ 
+
+ align:start position:0%
+product and that combination is a very
+very powerful way to improve or to
+
+ align:start position:0%
+very powerful way to improve or to
+ 
+
+ align:start position:0%
+very powerful way to improve or to
+modify the performance of a feedback
+
+ align:start position:0%
+modify the performance of a feedback
+ 
+
+ align:start position:0%
+modify the performance of a feedback
+system next time I'd like to look at how
+
+ align:start position:0%
+system next time I'd like to look at how
+ 
+
+ align:start position:0%
+system next time I'd like to look at how
+we use these ideas to compensate an
+
+ align:start position:0%
+we use these ideas to compensate an
+ 
+
+ align:start position:0%
+we use these ideas to compensate an
+actual feedback system we'll do a
+
+ align:start position:0%
+actual feedback system we'll do a
+ 
+
+ align:start position:0%
+actual feedback system we'll do a
+demonstration where we take an amplifier
+
+ align:start position:0%
+demonstration where we take an amplifier
+ 
+
+ align:start position:0%
+demonstration where we take an amplifier
+and with given characteristics and see
+
+ align:start position:0%
+and with given characteristics and see
+ 
+
+ align:start position:0%
+and with given characteristics and see
+how we use these kinds of Concepts to
+
+ align:start position:0%
+how we use these kinds of Concepts to
+ 
+
+ align:start position:0%
+how we use these kinds of Concepts to
+improve the performance of the of the
+
+ align:start position:0%
+improve the performance of the of the
+ 
+
+ align:start position:0%
+improve the performance of the of the
+feedback system that includes that
+
+ align:start position:0%
+feedback system that includes that
+ 
+
+ align:start position:0%
+feedback system that includes that
+amplifier thank you
\ No newline at end of file
diff --git a/C_pgH5QhIZ8.txt b/C_pgH5QhIZ8.txt
new file mode 100644
index 0000000000000000000000000000000000000000..fa84f85144de1f28b3a4e9c2eccfef4f09d113b8
--- /dev/null
+++ b/C_pgH5QhIZ8.txt
@@ -0,0 +1,331 @@
+align:start position:0%
+ 
+the following content is provided under
+
+ align:start position:0%
+the following content is provided under
+ 
+
+ align:start position:0%
+the following content is provided under
+a Creative Commons license your support
+
+ align:start position:0%
+a Creative Commons license your support
+ 
+
+ align:start position:0%
+a Creative Commons license your support
+will help MIT open courseware continue
+
+ align:start position:0%
+will help MIT open courseware continue
+ 
+
+ align:start position:0%
+will help MIT open courseware continue
+to offer highquality educational
+
+ align:start position:0%
+to offer highquality educational
+ 
+
+ align:start position:0%
+to offer highquality educational
+resources for free to make a donation or
+
+ align:start position:0%
+resources for free to make a donation or
+ 
+
+ align:start position:0%
+resources for free to make a donation or
+view additional materials from hundreds
+
+ align:start position:0%
+view additional materials from hundreds
+ 
+
+ align:start position:0%
+view additional materials from hundreds
+of MIT courses visit MIT opencourseware
+
+ align:start position:0%
+of MIT courses visit MIT opencourseware
+ 
+
+ align:start position:0%
+of MIT courses visit MIT opencourseware
+at
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+ocw.mit.edu so we have a class car
+
+ align:start position:0%
+ocw.mit.edu so we have a class car
+ 
+
+ align:start position:0%
+ocw.mit.edu so we have a class car
+here object as as usual the init method
+
+ align:start position:0%
+here object as as usual the init method
+ 
+
+ align:start position:0%
+here object as as usual the init method
+here takes in self as usual a w and a d
+
+ align:start position:0%
+here takes in self as usual a w and a d
+ 
+
+ align:start position:0%
+here takes in self as usual a w and a d
+so uh so a car gets initialized with two
+
+ align:start position:0%
+so uh so a car gets initialized with two
+ 
+
+ align:start position:0%
+so uh so a car gets initialized with two
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+parameters and we assign the wheels data
+
+ align:start position:0%
+parameters and we assign the wheels data
+ 
+
+ align:start position:0%
+parameters and we assign the wheels data
+attribute to the first one and the do's
+
+ align:start position:0%
+attribute to the first one and the do's
+ 
+
+ align:start position:0%
+attribute to the first one and the do's
+data attribute to the second one and
+
+ align:start position:0%
+data attribute to the second one and
+ 
+
+ align:start position:0%
+data attribute to the second one and
+then we're going to also assign a color
+
+ align:start position:0%
+then we're going to also assign a color
+ 
+
+ align:start position:0%
+then we're going to also assign a color
+data attribute um to be the empty string
+
+ align:start position:0%
+data attribute um to be the empty string
+ 
+
+ align:start position:0%
+data attribute um to be the empty string
+so I'm giving you four choices here and
+
+ align:start position:0%
+so I'm giving you four choices here and
+ 
+
+ align:start position:0%
+so I'm giving you four choices here and
+the question says which of the above is
+
+ align:start position:0%
+the question says which of the above is
+ 
+
+ align:start position:0%
+the question says which of the above is
+a getter method for the number of Wheels
+
+ align:start position:0%
+a getter method for the number of Wheels
+ 
+
+ align:start position:0%
+a getter method for the number of Wheels
+okay so getter
+
+ align:start position:0%
+okay so getter
+ 
+
+ align:start position:0%
+okay so getter
+method is something that's going to get
+
+ align:start position:0%
+method is something that's going to get
+ 
+
+ align:start position:0%
+method is something that's going to get
+a data
+
+ align:start position:0%
+a data
+ 
+
+ align:start position:0%
+a data
+attribute a method is really just a
+
+ align:start position:0%
+attribute a method is really just a
+ 
+
+ align:start position:0%
+attribute a method is really just a
+function so of course we're going to
+
+ align:start position:0%
+function so of course we're going to
+ 
+
+ align:start position:0%
+function so of course we're going to
+have DF get wheels is a good name for it
+
+ align:start position:0%
+have DF get wheels is a good name for it
+ 
+
+ align:start position:0%
+have DF get wheels is a good name for it
+since it's a method for this class we
+
+ align:start position:0%
+since it's a method for this class we
+ 
+
+ align:start position:0%
+since it's a method for this class we
+have to have self in the par parameters
+
+ align:start position:0%
+have to have self in the par parameters
+ 
+
+ align:start position:0%
+have to have self in the par parameters
+so we know it's going to be between c
+
+ align:start position:0%
+so we know it's going to be between c
+ 
+
+ align:start position:0%
+so we know it's going to be between c
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+d and so then what are we going to
+
+ align:start position:0%
+d and so then what are we going to
+ 
+
+ align:start position:0%
+d and so then what are we going to
+return the first one is going to return
+
+ align:start position:0%
+return the first one is going to return
+ 
+
+ align:start position:0%
+return the first one is going to return
+Wheels which in this particular case is
+
+ align:start position:0%
+Wheels which in this particular case is
+ 
+
+ align:start position:0%
+Wheels which in this particular case is
+just going to be a variable that we
+
+ align:start position:0%
+just going to be a variable that we
+ 
+
+ align:start position:0%
+just going to be a variable that we
+haven't defined but it's a variable a
+
+ align:start position:0%
+haven't defined but it's a variable a
+ 
+
+ align:start position:0%
+haven't defined but it's a variable a
+getter return returns a data attribute
+
+ align:start position:0%
+getter return returns a data attribute
+ 
+
+ align:start position:0%
+getter return returns a data attribute
+of a particular instance so we actually
+
+ align:start position:0%
+of a particular instance so we actually
+ 
+
+ align:start position:0%
+of a particular instance so we actually
+have to say self dot if we want to
+
+ align:start position:0%
+have to say self dot if we want to
+ 
+
+ align:start position:0%
+have to say self dot if we want to
+return a data attribute of an instance
+
+ align:start position:0%
+return a data attribute of an instance
+ 
+
+ align:start position:0%
+return a data attribute of an instance
+as opposed to just a a regular variable
+
+ align:start position:0%
+as opposed to just a a regular variable
+ 
+
+ align:start position:0%
+as opposed to just a a regular variable
+so the correct answer is D great job
\ No newline at end of file
diff --git a/DkOgvZywshI.txt b/DkOgvZywshI.txt
new file mode 100644
index 0000000000000000000000000000000000000000..ea316e98a285527625b236bc838b89ee14fec8a2
--- /dev/null
+++ b/DkOgvZywshI.txt
@@ -0,0 +1,803 @@
+align:start position:0%
+ 
+most frequently-used Odie's solver
+
+ align:start position:0%
+most frequently-used Odie's solver
+ 
+
+ align:start position:0%
+most frequently-used Odie's solver
+MATLAB and Simulink is OD 4/5 it's based
+
+ align:start position:0%
+MATLAB and Simulink is OD 4/5 it's based
+ 
+
+ align:start position:0%
+MATLAB and Simulink is OD 4/5 it's based
+on method published by British
+
+ align:start position:0%
+on method published by British
+ 
+
+ align:start position:0%
+on method published by British
+mathematicians junior Normand and PJ
+
+ align:start position:0%
+mathematicians junior Normand and PJ
+ 
+
+ align:start position:0%
+mathematicians junior Normand and PJ
+Prince in 1980 the basic method is order
+
+ align:start position:0%
+Prince in 1980 the basic method is order
+ 
+
+ align:start position:0%
+Prince in 1980 the basic method is order
+5 the error correction uses a companion
+
+ align:start position:0%
+5 the error correction uses a companion
+ 
+
+ align:start position:0%
+5 the error correction uses a companion
+order for method the first slope of TN
+
+ align:start position:0%
+order for method the first slope of TN
+ 
+
+ align:start position:0%
+order for method the first slope of TN
+is first same as last left over from the
+
+ align:start position:0%
+is first same as last left over from the
+ 
+
+ align:start position:0%
+is first same as last left over from the
+previous successful step then there are
+
+ align:start position:0%
+previous successful step then there are
+ 
+
+ align:start position:0%
+previous successful step then there are
+five more slopes from function values at
+
+ align:start position:0%
+five more slopes from function values at
+ 
+
+ align:start position:0%
+five more slopes from function values at
+50 H 3/10 H 4/5 h89 H and then at TN
+
+ align:start position:0%
+50 H 3/10 H 4/5 h89 H and then at TN
+ 
+
+ align:start position:0%
+50 H 3/10 H 4/5 h89 H and then at TN
+plus 1 these six slopes linear
+
+ align:start position:0%
+plus 1 these six slopes linear
+ 
+
+ align:start position:0%
+plus 1 these six slopes linear
+combinations of them are used to produce
+
+ align:start position:0%
+combinations of them are used to produce
+ 
+
+ align:start position:0%
+combinations of them are used to produce
+yn plus 1 the function value the
+
+ align:start position:0%
+yn plus 1 the function value the
+ 
+
+ align:start position:0%
+yn plus 1 the function value the
+function is evaluated at TN plus 1 and
+
+ align:start position:0%
+function is evaluated at TN plus 1 and
+ 
+
+ align:start position:0%
+function is evaluated at TN plus 1 and
+yn plus 1 to get a seventh slope and
+
+ align:start position:0%
+yn plus 1 to get a seventh slope and
+ 
+
+ align:start position:0%
+yn plus 1 to get a seventh slope and
+then linear combinations of these are
+
+ align:start position:0%
+then linear combinations of these are
+ 
+
+ align:start position:0%
+then linear combinations of these are
+used to produce the error estimate again
+
+ align:start position:0%
+used to produce the error estimate again
+ 
+
+ align:start position:0%
+used to produce the error estimate again
+if the error estimate is less than the
+
+ align:start position:0%
+if the error estimate is less than the
+ 
+
+ align:start position:0%
+if the error estimate is less than the
+specified accuracy requirement the step
+
+ align:start position:0%
+specified accuracy requirement the step
+ 
+
+ align:start position:0%
+specified accuracy requirement the step
+is successful and then that that error
+
+ align:start position:0%
+is successful and then that that error
+ 
+
+ align:start position:0%
+is successful and then that that error
+estimate is used to get the next step
+
+ align:start position:0%
+estimate is used to get the next step
+ 
+
+ align:start position:0%
+estimate is used to get the next step
+size if the air is too big the step is
+
+ align:start position:0%
+size if the air is too big the step is
+ 
+
+ align:start position:0%
+size if the air is too big the step is
+unsuccessful and that their estimate is
+
+ align:start position:0%
+unsuccessful and that their estimate is
+ 
+
+ align:start position:0%
+unsuccessful and that their estimate is
+used to get the used to get the step
+
+ align:start position:0%
+used to get the used to get the step
+ 
+
+ align:start position:0%
+used to get the used to get the step
+size to do the step over again we want
+
+ align:start position:0%
+size to do the step over again we want
+ 
+
+ align:start position:0%
+size to do the step over again we want
+to see the actual coefficients they're
+
+ align:start position:0%
+to see the actual coefficients they're
+ 
+
+ align:start position:0%
+to see the actual coefficients they're
+used you can go into the code for OD 4/5
+
+ align:start position:0%
+used you can go into the code for OD 4/5
+ 
+
+ align:start position:0%
+used you can go into the code for OD 4/5
+there's a table with the coefficients or
+
+ align:start position:0%
+there's a table with the coefficients or
+ 
+
+ align:start position:0%
+there's a table with the coefficients or
+you can go to the Wikipedia page for the
+
+ align:start position:0%
+you can go to the Wikipedia page for the
+ 
+
+ align:start position:0%
+you can go to the Wikipedia page for the
+dormant Prince method and there's the
+
+ align:start position:0%
+dormant Prince method and there's the
+ 
+
+ align:start position:0%
+dormant Prince method and there's the
+same coefficients as an aside here is an
+
+ align:start position:0%
+same coefficients as an aside here is an
+ 
+
+ align:start position:0%
+same coefficients as an aside here is an
+interesting fact about higher order
+
+ align:start position:0%
+interesting fact about higher order
+ 
+
+ align:start position:0%
+interesting fact about higher order
+runge-kutta methods classical
+
+ align:start position:0%
+runge-kutta methods classical
+ 
+
+ align:start position:0%
+runge-kutta methods classical
+runge-kutta required for function
+
+ align:start position:0%
+runge-kutta required for function
+ 
+
+ align:start position:0%
+runge-kutta required for function
+evaluation
+
+ align:start position:0%
+evaluation
+ 
+
+ align:start position:0%
+evaluation
+per step to get order for doorman Prince
+
+ align:start position:0%
+per step to get order for doorman Prince
+ 
+
+ align:start position:0%
+per step to get order for doorman Prince
+requires six function evaluations per
+
+ align:start position:0%
+requires six function evaluations per
+ 
+
+ align:start position:0%
+requires six function evaluations per
+step to get order five you can't get
+
+ align:start position:0%
+step to get order five you can't get
+ 
+
+ align:start position:0%
+step to get order five you can't get
+order five with just five function
+
+ align:start position:0%
+order five with just five function
+ 
+
+ align:start position:0%
+order five with just five function
+evaluations and then as we try it if we
+
+ align:start position:0%
+evaluations and then as we try it if we
+ 
+
+ align:start position:0%
+evaluations and then as we try it if we
+were to try and achieve higher order it
+
+ align:start position:0%
+were to try and achieve higher order it
+ 
+
+ align:start position:0%
+were to try and achieve higher order it
+would take even more function
+
+ align:start position:0%
+would take even more function
+ 
+
+ align:start position:0%
+would take even more function
+evaluations per step let's use OD 45 to
+
+ align:start position:0%
+evaluations per step let's use OD 45 to
+ 
+
+ align:start position:0%
+evaluations per step let's use OD 45 to
+compute thee to the T Y prime is equal
+
+ align:start position:0%
+compute thee to the T Y prime is equal
+ 
+
+ align:start position:0%
+compute thee to the T Y prime is equal
+to Y we can ask for output by supplying
+
+ align:start position:0%
+to Y we can ask for output by supplying
+ 
+
+ align:start position:0%
+to Y we can ask for output by supplying
+an argument called T span zero and steps
+
+ align:start position:0%
+an argument called T span zero and steps
+ 
+
+ align:start position:0%
+an argument called T span zero and steps
+of 0.1 to 1 if we supply that as the
+
+ align:start position:0%
+of 0.1 to 1 if we supply that as the
+ 
+
+ align:start position:0%
+of 0.1 to 1 if we supply that as the
+input argument to solve this
+
+ align:start position:0%
+input argument to solve this
+ 
+
+ align:start position:0%
+input argument to solve this
+differential equation and get the output
+
+ align:start position:0%
+differential equation and get the output
+ 
+
+ align:start position:0%
+differential equation and get the output
+at those points that we get that back as
+
+ align:start position:0%
+at those points that we get that back as
+ 
+
+ align:start position:0%
+at those points that we get that back as
+the output and now here's the
+
+ align:start position:0%
+the output and now here's the
+ 
+
+ align:start position:0%
+the output and now here's the
+approximation of a solution to that
+
+ align:start position:0%
+approximation of a solution to that
+ 
+
+ align:start position:0%
+approximation of a solution to that
+differential equation at that of those
+
+ align:start position:0%
+differential equation at that of those
+ 
+
+ align:start position:0%
+differential equation at that of those
+points if we plot it here's the solution
+
+ align:start position:0%
+points if we plot it here's the solution
+ 
+
+ align:start position:0%
+points if we plot it here's the solution
+at those points and to see how accurate
+
+ align:start position:0%
+at those points and to see how accurate
+ 
+
+ align:start position:0%
+at those points and to see how accurate
+it is we see that we're actually getting
+
+ align:start position:0%
+it is we see that we're actually getting
+ 
+
+ align:start position:0%
+it is we see that we're actually getting
+this result to nine in digits OD e 45 is
+
+ align:start position:0%
+this result to nine in digits OD e 45 is
+ 
+
+ align:start position:0%
+this result to nine in digits OD e 45 is
+very accurate let's look at step size
+
+ align:start position:0%
+very accurate let's look at step size
+ 
+
+ align:start position:0%
+very accurate let's look at step size
+choice on our problem with near
+
+ align:start position:0%
+choice on our problem with near
+ 
+
+ align:start position:0%
+choice on our problem with near
+singularity is a quarter y naught is
+
+ align:start position:0%
+singularity is a quarter y naught is
+ 
+
+ align:start position:0%
+singularity is a quarter y naught is
+close to 16 the differential equation is
+
+ align:start position:0%
+close to 16 the differential equation is
+ 
+
+ align:start position:0%
+close to 16 the differential equation is
+y prime is 2 a minus T y squared we let
+
+ align:start position:0%
+y prime is 2 a minus T y squared we let
+ 
+
+ align:start position:0%
+y prime is 2 a minus T y squared we let
+OD 45 choose its own step size by
+
+ align:start position:0%
+OD 45 choose its own step size by
+ 
+
+ align:start position:0%
+OD 45 choose its own step size by
+indicating we just want to indicate from
+
+ align:start position:0%
+indicating we just want to indicate from
+ 
+
+ align:start position:0%
+indicating we just want to indicate from
+integrate from 0 to 1 we capture the
+
+ align:start position:0%
+integrate from 0 to 1 we capture the
+ 
+
+ align:start position:0%
+integrate from 0 to 1 we capture the
+output in T and Y and plot it
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+now here there's a lot of points here
+
+ align:start position:0%
+now here there's a lot of points here
+ 
+
+ align:start position:0%
+now here there's a lot of points here
+but this is misleading because OD e 45
+
+ align:start position:0%
+but this is misleading because OD e 45
+ 
+
+ align:start position:0%
+but this is misleading because OD e 45
+is using by default is using the refine
+
+ align:start position:0%
+is using by default is using the refine
+ 
+
+ align:start position:0%
+is using by default is using the refine
+option it's only evaluated actually
+
+ align:start position:0%
+option it's only evaluated actually
+ 
+
+ align:start position:0%
+option it's only evaluated actually
+evaluating the function at every 4th one
+
+ align:start position:0%
+evaluating the function at every 4th one
+ 
+
+ align:start position:0%
+evaluating the function at every 4th one
+of these points and then using the
+
+ align:start position:0%
+of these points and then using the
+ 
+
+ align:start position:0%
+of these points and then using the
+interpolant to fill in in between so we
+
+ align:start position:0%
+interpolant to fill in in between so we
+ 
+
+ align:start position:0%
+interpolant to fill in in between so we
+actually need a little different plot
+
+ align:start position:0%
+actually need a little different plot
+ 
+
+ align:start position:0%
+actually need a little different plot
+here this plot shows a little better
+
+ align:start position:0%
+here this plot shows a little better
+ 
+
+ align:start position:0%
+here this plot shows a little better
+what's going on the big dots are the
+
+ align:start position:0%
+what's going on the big dots are the
+ 
+
+ align:start position:0%
+what's going on the big dots are the
+points that OD 45 chose to evaluate the
+
+ align:start position:0%
+points that OD 45 chose to evaluate the
+ 
+
+ align:start position:0%
+points that OD 45 chose to evaluate the
+the differential equation and the little
+
+ align:start position:0%
+the differential equation and the little
+ 
+
+ align:start position:0%
+the differential equation and the little
+dots are filled in with interpolant so
+
+ align:start position:0%
+dots are filled in with interpolant so
+ 
+
+ align:start position:0%
+dots are filled in with interpolant so
+the big dots are every fourth point and
+
+ align:start position:0%
+the big dots are every fourth point and
+ 
+
+ align:start position:0%
+the big dots are every fourth point and
+the refine option says that the big dots
+
+ align:start position:0%
+the refine option says that the big dots
+ 
+
+ align:start position:0%
+the refine option says that the big dots
+are too far apart and we need to fill it
+
+ align:start position:0%
+are too far apart and we need to fill it
+ 
+
+ align:start position:0%
+are too far apart and we need to fill it
+in with the interpolant so this is the
+
+ align:start position:0%
+in with the interpolant so this is the
+ 
+
+ align:start position:0%
+in with the interpolant so this is the
+continuous interpolate in action the big
+
+ align:start position:0%
+continuous interpolate in action the big
+ 
+
+ align:start position:0%
+continuous interpolate in action the big
+dots are concentrated are more closely
+
+ align:start position:0%
+dots are concentrated are more closely
+ 
+
+ align:start position:0%
+dots are concentrated are more closely
+concentrated as we have to go around the
+
+ align:start position:0%
+concentrated as we have to go around the
+ 
+
+ align:start position:0%
+concentrated as we have to go around the
+curve and then as we get farther away
+
+ align:start position:0%
+curve and then as we get farther away
+ 
+
+ align:start position:0%
+curve and then as we get farther away
+from the singularity the step size
+
+ align:start position:0%
+from the singularity the step size
+ 
+
+ align:start position:0%
+from the singularity the step size
+increases so this shows the high
+
+ align:start position:0%
+increases so this shows the high
+ 
+
+ align:start position:0%
+increases so this shows the high
+accuracy of ode45 and the automatic step
+
+ align:start position:0%
+accuracy of ode45 and the automatic step
+ 
+
+ align:start position:0%
+accuracy of ode45 and the automatic step
+size choice in action here's an exercise
+
+ align:start position:0%
+size choice in action here's an exercise
+ 
+
+ align:start position:0%
+size choice in action here's an exercise
+compare OD e23 and OD 45 by using each
+
+ align:start position:0%
+compare OD e23 and OD 45 by using each
+ 
+
+ align:start position:0%
+compare OD e23 and OD 45 by using each
+of them to keep you PI the integral four
+
+ align:start position:0%
+of them to keep you PI the integral four
+ 
+
+ align:start position:0%
+of them to keep you PI the integral four
+over one plus t-squared from zero to one
+
+ align:start position:0%
+over one plus t-squared from zero to one
+ 
+
+ align:start position:0%
+over one plus t-squared from zero to one
+is pi you can express that as a
+
+ align:start position:0%
+is pi you can express that as a
+ 
+
+ align:start position:0%
+is pi you can express that as a
+differential equation use each of the
+
+ align:start position:0%
+differential equation use each of the
+ 
+
+ align:start position:0%
+differential equation use each of the
+routines to integrate that differential
+
+ align:start position:0%
+routines to integrate that differential
+ 
+
+ align:start position:0%
+routines to integrate that differential
+equation and see how close they get to
+
+ align:start position:0%
+equation and see how close they get to
+ 
+
+ align:start position:0%
+equation and see how close they get to
+compute
+
+ align:start position:0%
+compute
+ 
+
+ align:start position:0%
+compute
+in PI
\ No newline at end of file
diff --git a/EMyRV3H4Vf4.txt b/EMyRV3H4Vf4.txt
new file mode 100644
index 0000000000000000000000000000000000000000..a1e82945ae218d9fc2e514588596f95e6b6e07ad
--- /dev/null
+++ b/EMyRV3H4Vf4.txt
@@ -0,0 +1,203 @@
+align:start position:0%
+ 
+if a student comes to me and uh they're
+
+ align:start position:0%
+if a student comes to me and uh they're
+ 
+
+ align:start position:0%
+if a student comes to me and uh they're
+getting really stuck and solving their
+
+ align:start position:0%
+getting really stuck and solving their
+ 
+
+ align:start position:0%
+getting really stuck and solving their
+problem then I would suggest to them uh
+
+ align:start position:0%
+problem then I would suggest to them uh
+ 
+
+ align:start position:0%
+problem then I would suggest to them uh
+collaborate more uh but I find
+
+ align:start position:0%
+collaborate more uh but I find
+ 
+
+ align:start position:0%
+collaborate more uh but I find
+collaboration is really the best way
+
+ align:start position:0%
+collaboration is really the best way
+ 
+
+ align:start position:0%
+collaboration is really the best way
+both to do brainstorming because you get
+
+ align:start position:0%
+both to do brainstorming because you get
+ 
+
+ align:start position:0%
+both to do brainstorming because you get
+very quick feedback uh in ideas but also
+
+ align:start position:0%
+very quick feedback uh in ideas but also
+ 
+
+ align:start position:0%
+very quick feedback uh in ideas but also
+you get this kind of compounding effect
+
+ align:start position:0%
+you get this kind of compounding effect
+ 
+
+ align:start position:0%
+you get this kind of compounding effect
+where your ideas Inspire the maybe more
+
+ align:start position:0%
+where your ideas Inspire the maybe more
+ 
+
+ align:start position:0%
+where your ideas Inspire the maybe more
+experienced person to have some other
+
+ align:start position:0%
+experienced person to have some other
+ 
+
+ align:start position:0%
+experienced person to have some other
+idea and oh that reminds me of this
+
+ align:start position:0%
+idea and oh that reminds me of this
+ 
+
+ align:start position:0%
+idea and oh that reminds me of this
+other paper maybe you should go look at
+
+ align:start position:0%
+other paper maybe you should go look at
+ 
+
+ align:start position:0%
+other paper maybe you should go look at
+this um and so just talking with people
+
+ align:start position:0%
+this um and so just talking with people
+ 
+
+ align:start position:0%
+this um and so just talking with people
+about your problem makes a huge impact
+
+ align:start position:0%
+about your problem makes a huge impact
+ 
+
+ align:start position:0%
+about your problem makes a huge impact
+and maybe they join in and help solve it
+
+ align:start position:0%
+and maybe they join in and help solve it
+ 
+
+ align:start position:0%
+and maybe they join in and help solve it
+or maybe they just give one idea that
+
+ align:start position:0%
+or maybe they just give one idea that
+ 
+
+ align:start position:0%
+or maybe they just give one idea that
+leads you down the right path but I
+
+ align:start position:0%
+leads you down the right path but I
+ 
+
+ align:start position:0%
+leads you down the right path but I
+think if you work by yourself uh all for
+
+ align:start position:0%
+think if you work by yourself uh all for
+ 
+
+ align:start position:0%
+think if you work by yourself uh all for
+a long period eventually you're just
+
+ align:start position:0%
+a long period eventually you're just
+ 
+
+ align:start position:0%
+a long period eventually you're just
+going to get stuck because it's hard to
+
+ align:start position:0%
+going to get stuck because it's hard to
+ 
+
+ align:start position:0%
+going to get stuck because it's hard to
+maintain that kind of momentum all by
+
+ align:start position:0%
+maintain that kind of momentum all by
+ 
+
+ align:start position:0%
+maintain that kind of momentum all by
+yourself but when you feed off the
+
+ align:start position:0%
+yourself but when you feed off the
+ 
+
+ align:start position:0%
+yourself but when you feed off the
+energy of other people you can really go
+
+ align:start position:0%
+energy of other people you can really go
+ 
+
+ align:start position:0%
+energy of other people you can really go
+much much farther it's also more fun
+
+ align:start position:0%
+much much farther it's also more fun
+ 
+
+ align:start position:0%
+much much farther it's also more fun
+because you get to be hanging out while
+
+ align:start position:0%
+because you get to be hanging out while
+ 
+
+ align:start position:0%
+because you get to be hanging out while
+you're doing it so
\ No newline at end of file
diff --git a/F5-87RM_zHA.txt b/F5-87RM_zHA.txt
new file mode 100644
index 0000000000000000000000000000000000000000..cd76ae290a904e526ea949cbf60a6f2aca250d7e
--- /dev/null
+++ b/F5-87RM_zHA.txt
@@ -0,0 +1,347 @@
+Today we're going to talk about how to translate
+high-level languages into code that computers
+
+can execute.
+
+So far we've seen the Beta ISA, which includes
+instructions that control the datapath operations
+
+performed on 32-bit data stored in the registers.
+
+There are also instructions for accessing
+main memory and changing the program counter.
+
+The instructions are formatted as opcode,
+source, and destination fields that form 32-bit
+
+values in main memory.
+
+To make our lives easier, we developed assembly
+language as a way of specifying sequences
+
+of instructions.
+
+Each assembly language statement corresponds
+to a single instruction.
+
+As assembly language programmers, we're responsible
+for managing which values are in registers
+
+and which are in main memory, and we need
+to figure out how to break down complicated
+
+operations,
+e.g., accessing an element of an array, into
+
+the right sequence of Beta operations.
+
+We can go one step further and use high-level
+languages to describe the computations we
+
+want to perform.
+
+These languages use variables and other data
+structures to abstract away the details of
+
+storage allocation and the movement of data
+to and from main memory.
+
+We can just refer to a data object by name
+and let the language processor handle the
+
+details.
+
+Similarly, we'll write expressions and other
+operators such as assignment (=) to efficiently
+
+describe what would require many statements
+in assembly language.
+
+Today we're going to dive into how to translate
+high-level language programs into code that
+
+will run on the Beta.
+
+Here we see Euclid's algorithm for determining
+the greatest common divisor of two numbers,
+
+in this case the algorithm is written in the
+C programming language.
+
+We'll be using a simple subset of C as our
+example high-level language.
+
+Please see the brief overview of C in the
+Handouts section if you'd like an introduction
+
+to C syntax and semantics.
+
+C was developed by Dennis Ritchie at AT&T
+Bell Labs in the late 60's and early 70's
+
+to use when implementing the Unix operating
+system.
+
+Since that time many new high-level languages
+have been introduced providing modern abstractions
+
+like object-oriented programming along with
+useful new data and control structures.
+
+Using C allows us describe a computation without
+referring to any of the details of the Beta
+
+ISA like registers, specific Beta instructions,
+and so on.
+
+The absence of such details means there is
+less work required to create the program and
+
+makes it easier for others to read and understand
+the algorithm implemented by the program.
+
+There are many advantages to using a high-level
+language.
+
+They enable programmers to be very productive
+since the programs are concise and readable.
+
+These attributes also make it easy to maintain
+the code.
+
+Often it is harder to make certain types of
+mistakes since the language allows us to check
+
+for silly errors like storing a string value
+into a numeric variable.
+
+And more complicated tasks like dynamically
+allocating and deallocating storage can be
+
+completely automated.
+
+The result is that it can take much less time
+to create a correct program in a high-level
+
+language than it would it when writing in
+assembly language.
+
+Since the high-level language has abstracted
+away the details of a particular ISA, the
+
+programs are portable in the sense that we
+can expect to run the same code on different
+
+ISAs without having to rewrite the code.
+
+What do we lose by using a high-level language?
+
+Should we worry that we'll pay a price in
+terms of the efficiency and performance we
+
+might get by crafting each instruction by
+hand?
+
+The answer depends on how we choose to run
+high-level language programs.
+
+The two basic execution strategies are "interpretation"
+and "compilation".
+
+To interpret a high-level language program,
+we'll write a special program called an "interpreter"
+
+that runs on the actual computer, M1.
+
+The interpreter mimics the behavior of some
+abstract easy-to-program machine M2 and for
+
+each M2 operation executes sequences of M1
+instructions to achieve the desired result.
+
+We can think of the interpreter along with
+M1 as an implementation of M2, i.e., given
+
+a program written for M2, the interpreter
+will, step-by-step, emulate the effect of
+
+M2 instructions.
+
+We often use several layers of interpretation
+when tackling computation tasks.
+
+For example, an engineer may use her laptop
+with an Intel CPU to run the Python interpreter.
+
+In Python, she loads the SciPy toolkit, which
+provides a calculator-like interface for numerical
+
+analysis for matrices and data.
+
+For each SciPy command, e.g., "find the maximum
+value of a dataset", the SciPy tool kit executes
+
+many Python statements, e.g., to loop over
+each element of the array, remembering the
+
+largest value.
+
+For each Python statement, the Python interpreter
+executes many x86 instructions, e.g., to increment
+
+the loop index and check for loop termination.
+
+Executing a single SciPy command may require
+executing of tens of Python statements, which
+
+in turn each may require executing hundreds
+of x86 instructions.
+
+The engineer is very happy she didn't have
+to write each of those instructions herself!
+
+Interpretation is an effective implementation
+strategy when performing a computation once,
+
+or when exploring which computational approach
+is most effective before making a more substantial
+
+investment in creating a more efficient implementation.
+
+We'll use a compilation implementation strategy
+when we have computational tasks that we need
+
+to execute repeatedly and hence we are willing
+to invest more time up-front for more efficiency
+
+in the long-term.
+
+In compilation, we also start with our actual
+computer M1.
+
+Then we'll take our high-level language program
+P2 and translate it statement-by-statement
+
+into a program for M1.
+
+Note that we're not actually running the P2
+program.
+
+Instead we're using it as a template to create
+an equivalent P1 program that can execute
+
+directly on M1.
+
+The translation process is called "compilation"
+and the program that does the translation
+
+is called a "compiler".
+
+We compile the P2 program once to get the
+translation P1, and then we'll run P1 on M1
+
+whenever we want to execute P2.
+
+Running P1 avoids the overhead of having to
+process the P2 source and the costs of executing
+
+any intervening layers of interpretation.
+
+Instead of dynamically figuring out the necessary
+machine instructions for each P2 statement
+
+as it's encountered,
+in effect we've arranged to capture that stream
+
+of machine instructions and save them as a
+P1 program for later execution.
+
+If we're willing to pay the up-front costs
+of compilation, we'll get more efficient execution.
+
+And, with different compilers, we can arrange
+to run P2 on many different machines - M2,
+
+M3, etc. - without having rewrite P2.
+
+So we now have two ways to execute a high-level
+language program: interpretation and compilation.
+
+Both allow us to change the original source
+program.
+
+Both allow us to abstract away the details
+of the actual computer we'll use to run the
+
+program.
+
+And both strategies are widely used in modern
+computer systems!
+
+Let's summarize the differences between interpretation
+and compilation.
+
+Suppose the statement "x+2" appears in the
+high-level program.
+
+When the interpreter processes this statement
+it immediately fetches the value of the variable
+
+x and adds 2 to it.
+
+On the other hand, the compiler would generate
+Beta instructions that would LD the variable
+
+x into a register and then ADD 2 to that value.
+
+The interpreter is executing each statement
+as it's processed and, in fact, may process
+
+and execute the same statement many times
+if, e.g., it was in a loop.
+
+The compiler is just generating instructions
+to be executed at some later time.
+
+Interpreters have the overhead of processing
+the high-level source code during execution
+
+and that overhead may be incurred many times
+in loops.
+
+Compilers incur the processing overhead once,
+making the eventual execution more efficient.
+
+But during development, the programmer may
+have to compile and run the program many times,
+
+often incurring the cost of compilation for
+only a single execution of the program.
+
+So the compile-run-debug loop can take more
+time.
+
+The interpreter is making decisions about
+the data type of x and the type of operations
+
+necessary at run time, i.e., while the program
+is running.
+
+The compiler is making those decisions during
+the compilation process.
+
+Which is the better approach?
+
+In general, executing compiled code is much
+faster than running the code interpretively.
+
+But since the interpreter is making decisions
+at run time, it can change its behavior depending,
+
+say, on the type of the data in the variable
+X, offering considerable flexibility in handling
+
+different types of data with the same algorithm.
+
+Compilers take away that flexibility in exchange
+for fast execution.
\ No newline at end of file
diff --git a/FaLqAip6A0Q.txt b/FaLqAip6A0Q.txt
new file mode 100644
index 0000000000000000000000000000000000000000..c8906b0df07f3c50e086960d99f4ec8af7349922
--- /dev/null
+++ b/FaLqAip6A0Q.txt
@@ -0,0 +1,14395 @@
+align:start position:0%
+ 
+the following content is provided under
+
+ align:start position:0%
+the following content is provided under
+ 
+
+ align:start position:0%
+the following content is provided under
+a Creative Commons license your support
+
+ align:start position:0%
+a Creative Commons license your support
+ 
+
+ align:start position:0%
+a Creative Commons license your support
+will help MIT open courseware continue
+
+ align:start position:0%
+will help MIT open courseware continue
+ 
+
+ align:start position:0%
+will help MIT open courseware continue
+to offer highquality educational
+
+ align:start position:0%
+to offer highquality educational
+ 
+
+ align:start position:0%
+to offer highquality educational
+resources for free to make a donation or
+
+ align:start position:0%
+resources for free to make a donation or
+ 
+
+ align:start position:0%
+resources for free to make a donation or
+view additional materials from hundreds
+
+ align:start position:0%
+view additional materials from hundreds
+ 
+
+ align:start position:0%
+view additional materials from hundreds
+of MIT courses visit MIT opencourseware
+
+ align:start position:0%
+of MIT courses visit MIT opencourseware
+ 
+
+ align:start position:0%
+of MIT courses visit MIT opencourseware
+at
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+ocw.mit.edu
+
+ align:start position:0%
+ocw.mit.edu
+ 
+
+ align:start position:0%
+ocw.mit.edu
+so today what we're going to talk about
+
+ align:start position:0%
+so today what we're going to talk about
+ 
+
+ align:start position:0%
+so today what we're going to talk about
+we're going to move
+
+ align:start position:0%
+we're going to move
+ 
+
+ align:start position:0%
+we're going to move
+from sort of the descriptive discussions
+
+ align:start position:0%
+from sort of the descriptive discussions
+ 
+
+ align:start position:0%
+from sort of the descriptive discussions
+of organizational decisionmaking to a
+
+ align:start position:0%
+of organizational decisionmaking to a
+ 
+
+ align:start position:0%
+of organizational decisionmaking to a
+couple of prescriptive sessions which is
+
+ align:start position:0%
+couple of prescriptive sessions which is
+ 
+
+ align:start position:0%
+couple of prescriptive sessions which is
+if you're running an energy business how
+
+ align:start position:0%
+if you're running an energy business how
+ 
+
+ align:start position:0%
+if you're running an energy business how
+do you do it one of the things as this
+
+ align:start position:0%
+do you do it one of the things as this
+ 
+
+ align:start position:0%
+do you do it one of the things as this
+indicates that we talked about you
+
+ align:start position:0%
+indicates that we talked about you
+ 
+
+ align:start position:0%
+indicates that we talked about you
+should do you should be doing present
+
+ align:start position:0%
+should do you should be doing present
+ 
+
+ align:start position:0%
+should do you should be doing present
+value analysis Net Present Value
+
+ align:start position:0%
+value analysis Net Present Value
+ 
+
+ align:start position:0%
+value analysis Net Present Value
+analysis of investment
+
+ align:start position:0%
+analysis of investment
+ 
+
+ align:start position:0%
+analysis of investment
+opportunities but that's not strategy so
+
+ align:start position:0%
+opportunities but that's not strategy so
+ 
+
+ align:start position:0%
+opportunities but that's not strategy so
+today and next time we're going to be
+
+ align:start position:0%
+today and next time we're going to be
+ 
+
+ align:start position:0%
+today and next time we're going to be
+talking about strategy we'll talk about
+
+ align:start position:0%
+talking about strategy we'll talk about
+ 
+
+ align:start position:0%
+talking about strategy we'll talk about
+industry attractiveness
+
+ align:start position:0%
+industry attractiveness
+ 
+
+ align:start position:0%
+industry attractiveness
+briefly kinds of strategies and niches
+
+ align:start position:0%
+briefly kinds of strategies and niches
+ 
+
+ align:start position:0%
+briefly kinds of strategies and niches
+within Industries and then the Husky
+
+ align:start position:0%
+within Industries and then the Husky
+ 
+
+ align:start position:0%
+within Industries and then the Husky
+case Wednesday Don lassard's going to be
+
+ align:start position:0%
+case Wednesday Don lassard's going to be
+ 
+
+ align:start position:0%
+case Wednesday Don lassard's going to be
+here and explore with you uh business
+
+ align:start position:0%
+here and explore with you uh business
+ 
+
+ align:start position:0%
+here and explore with you uh business
+models particularly in Innovative
+
+ align:start position:0%
+models particularly in Innovative
+ 
+
+ align:start position:0%
+models particularly in Innovative
+segments so it isn't project by project
+
+ align:start position:0%
+segments so it isn't project by project
+ 
+
+ align:start position:0%
+segments so it isn't project by project
+Net Present Value isn't strategy if if a
+
+ align:start position:0%
+Net Present Value isn't strategy if if a
+ 
+
+ align:start position:0%
+Net Present Value isn't strategy if if a
+firm accepts every Proposal with a net
+
+ align:start position:0%
+firm accepts every Proposal with a net
+ 
+
+ align:start position:0%
+firm accepts every Proposal with a net
+present
+
+ align:start position:0%
+present
+ 
+
+ align:start position:0%
+present
+value a positive Net Present Value the
+
+ align:start position:0%
+value a positive Net Present Value the
+ 
+
+ align:start position:0%
+value a positive Net Present Value the
+result is likely to be very incoherent
+
+ align:start position:0%
+result is likely to be very incoherent
+ 
+
+ align:start position:0%
+result is likely to be very incoherent
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+unmanageable the Brey piece is a is sort
+
+ align:start position:0%
+unmanageable the Brey piece is a is sort
+ 
+
+ align:start position:0%
+unmanageable the Brey piece is a is sort
+of a finance person's
+
+ align:start position:0%
+of a finance person's
+ 
+
+ align:start position:0%
+of a finance person's
+skepticism the first thing you note is
+
+ align:start position:0%
+skepticism the first thing you note is
+ 
+
+ align:start position:0%
+skepticism the first thing you note is
+you only see proposals with positive Net
+
+ align:start position:0%
+you only see proposals with positive Net
+ 
+
+ align:start position:0%
+you only see proposals with positive Net
+Present
+
+ align:start position:0%
+Present
+ 
+
+ align:start position:0%
+Present
+Value uh if someone likes a project it
+
+ align:start position:0%
+Value uh if someone likes a project it
+ 
+
+ align:start position:0%
+Value uh if someone likes a project it
+turns out it has a positive Net Present
+
+ align:start position:0%
+turns out it has a positive Net Present
+ 
+
+ align:start position:0%
+turns out it has a positive Net Present
+Value
+
+ align:start position:0%
+Value
+ 
+
+ align:start position:0%
+Value
+so the what they propose and we'll
+
+ align:start position:0%
+so the what they propose and we'll
+ 
+
+ align:start position:0%
+so the what they propose and we'll
+explore a little bit is thinking about
+
+ align:start position:0%
+explore a little bit is thinking about
+ 
+
+ align:start position:0%
+explore a little bit is thinking about
+dise equilibrium thinking about will it
+
+ align:start position:0%
+dise equilibrium thinking about will it
+ 
+
+ align:start position:0%
+dise equilibrium thinking about will it
+last it has a Net Present Value because
+
+ align:start position:0%
+last it has a Net Present Value because
+ 
+
+ align:start position:0%
+last it has a Net Present Value because
+we're cheaper than they are okay why are
+
+ align:start position:0%
+we're cheaper than they are okay why are
+ 
+
+ align:start position:0%
+we're cheaper than they are okay why are
+we cheaper than they are we can buy
+
+ align:start position:0%
+we cheaper than they are we can buy
+ 
+
+ align:start position:0%
+we cheaper than they are we can buy
+materials more cheaply than they why
+
+ align:start position:0%
+materials more cheaply than they why
+ 
+
+ align:start position:0%
+materials more cheaply than they why
+will it last will it last anuka and I
+
+ align:start position:0%
+will it last will it last anuka and I
+ 
+
+ align:start position:0%
+will it last will it last anuka and I
+saw before vacation uh a very detailed
+
+ align:start position:0%
+saw before vacation uh a very detailed
+ 
+
+ align:start position:0%
+saw before vacation uh a very detailed
+analysis of US versus Chinese
+
+ align:start position:0%
+analysis of US versus Chinese
+ 
+
+ align:start position:0%
+analysis of US versus Chinese
+photovoltaic manufacturing costs that
+
+ align:start position:0%
+photovoltaic manufacturing costs that
+ 
+
+ align:start position:0%
+photovoltaic manufacturing costs that
+concluded that the big Chinese Advantage
+
+ align:start position:0%
+concluded that the big Chinese Advantage
+ 
+
+ align:start position:0%
+concluded that the big Chinese Advantage
+was they could materials and supplies
+
+ align:start position:0%
+was they could materials and supplies
+ 
+
+ align:start position:0%
+was they could materials and supplies
+25% cheaper and the first question is
+
+ align:start position:0%
+25% cheaper and the first question is
+ 
+
+ align:start position:0%
+25% cheaper and the first question is
+why is that going to last the people
+
+ align:start position:0%
+why is that going to last the people
+ 
+
+ align:start position:0%
+why is that going to last the people
+who' done the study hadn't quite
+
+ align:start position:0%
+who' done the study hadn't quite
+ 
+
+ align:start position:0%
+who' done the study hadn't quite
+inquired into that and said it was
+
+ align:start position:0%
+inquired into that and said it was
+ 
+
+ align:start position:0%
+inquired into that and said it was
+Superior bargaining
+
+ align:start position:0%
+Superior bargaining
+ 
+
+ align:start position:0%
+Superior bargaining
+power Superior bargaining power doesn't
+
+ align:start position:0%
+power Superior bargaining power doesn't
+ 
+
+ align:start position:0%
+power Superior bargaining power doesn't
+last so first first point in the bre at
+
+ align:start position:0%
+last so first first point in the bre at
+ 
+
+ align:start position:0%
+last so first first point in the bre at
+all piece is skepticism about present
+
+ align:start position:0%
+all piece is skepticism about present
+ 
+
+ align:start position:0%
+all piece is skepticism about present
+value Porter's paper is in a way more
+
+ align:start position:0%
+value Porter's paper is in a way more
+ 
+
+ align:start position:0%
+value Porter's paper is in a way more
+profound and really does deserve a
+
+ align:start position:0%
+profound and really does deserve a
+ 
+
+ align:start position:0%
+profound and really does deserve a
+serious read
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+strategy Is What You Won't Do what is it
+
+ align:start position:0%
+strategy Is What You Won't Do what is it
+ 
+
+ align:start position:0%
+strategy Is What You Won't Do what is it
+you won't do as a company someone walks
+
+ align:start position:0%
+you won't do as a company someone walks
+ 
+
+ align:start position:0%
+you won't do as a company someone walks
+in the door with a project with a
+
+ align:start position:0%
+in the door with a project with a
+ 
+
+ align:start position:0%
+in the door with a project with a
+positive Net Present Value which when do
+
+ align:start position:0%
+positive Net Present Value which when do
+ 
+
+ align:start position:0%
+positive Net Present Value which when do
+you just say no you're right that's a
+
+ align:start position:0%
+you just say no you're right that's a
+ 
+
+ align:start position:0%
+you just say no you're right that's a
+positive Net Present Value we're not
+
+ align:start position:0%
+positive Net Present Value we're not
+ 
+
+ align:start position:0%
+positive Net Present Value we're not
+going to do
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+it the argument is
+
+ align:start position:0%
+it the argument is
+ 
+
+ align:start position:0%
+it the argument is
+this if you're doing the same thing your
+
+ align:start position:0%
+this if you're doing the same thing your
+ 
+
+ align:start position:0%
+this if you're doing the same thing your
+competitors are you're in a wonderful
+
+ align:start position:0%
+competitors are you're in a wonderful
+ 
+
+ align:start position:0%
+competitors are you're in a wonderful
+world and there are a bunch of them
+
+ align:start position:0%
+world and there are a bunch of them
+ 
+
+ align:start position:0%
+world and there are a bunch of them
+you're in a wonderful world of perfect
+
+ align:start position:0%
+you're in a wonderful world of perfect
+ 
+
+ align:start position:0%
+you're in a wonderful world of perfect
+competition we all enjoy that it's in
+
+ align:start position:0%
+competition we all enjoy that it's in
+ 
+
+ align:start position:0%
+competition we all enjoy that it's in
+the textbooks it's easy to analyze and
+
+ align:start position:0%
+the textbooks it's easy to analyze and
+ 
+
+ align:start position:0%
+the textbooks it's easy to analyze and
+it's no
+
+ align:start position:0%
+it's no
+ 
+
+ align:start position:0%
+it's no
+fun you don't make any money
+
+ align:start position:0%
+fun you don't make any money
+ 
+
+ align:start position:0%
+fun you don't make any money
+particularly if there are opportunities
+
+ align:start position:0%
+particularly if there are opportunities
+ 
+
+ align:start position:0%
+particularly if there are opportunities
+to innovate you have to innovate just to
+
+ align:start position:0%
+to innovate you have to innovate just to
+ 
+
+ align:start position:0%
+to innovate you have to innovate just to
+cover your cost of
+
+ align:start position:0%
+cover your cost of
+ 
+
+ align:start position:0%
+cover your cost of
+capital there's a piece there's a little
+
+ align:start position:0%
+capital there's a piece there's a little
+ 
+
+ align:start position:0%
+capital there's a piece there's a little
+quote from Warren Buffett which I think
+
+ align:start position:0%
+quote from Warren Buffett which I think
+ 
+
+ align:start position:0%
+quote from Warren Buffett which I think
+still holds true that since the dawn of
+
+ align:start position:0%
+still holds true that since the dawn of
+ 
+
+ align:start position:0%
+still holds true that since the dawn of
+Aviation the total profits earned by
+
+ align:start position:0%
+Aviation the total profits earned by
+ 
+
+ align:start position:0%
+Aviation the total profits earned by
+Airlines adds up to
+
+ align:start position:0%
+Airlines adds up to
+ 
+
+ align:start position:0%
+Airlines adds up to
+zero Airlines have gotten enormously
+
+ align:start position:0%
+zero Airlines have gotten enormously
+ 
+
+ align:start position:0%
+zero Airlines have gotten enormously
+more efficient they've done enormous
+
+ align:start position:0%
+more efficient they've done enormous
+ 
+
+ align:start position:0%
+more efficient they've done enormous
+things for transportation for the
+
+ align:start position:0%
+things for transportation for the
+ 
+
+ align:start position:0%
+things for transportation for the
+country as a whole but they haven't made
+
+ align:start position:0%
+country as a whole but they haven't made
+ 
+
+ align:start position:0%
+country as a whole but they haven't made
+any money because mostly they're all
+
+ align:start position:0%
+any money because mostly they're all
+ 
+
+ align:start position:0%
+any money because mostly they're all
+doing the same thing and there are a
+
+ align:start position:0%
+doing the same thing and there are a
+ 
+
+ align:start position:0%
+doing the same thing and there are a
+bunch of them and there's no
+
+ align:start position:0%
+bunch of them and there's no
+ 
+
+ align:start position:0%
+bunch of them and there's no
+differentiation or stickiness
+
+ align:start position:0%
+differentiation or stickiness
+ 
+
+ align:start position:0%
+differentiation or stickiness
+so the first lesson is if you're running
+
+ align:start position:0%
+so the first lesson is if you're running
+ 
+
+ align:start position:0%
+so the first lesson is if you're running
+a company you don't want to be
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+there as Porter points out if you're in
+
+ align:start position:0%
+there as Porter points out if you're in
+ 
+
+ align:start position:0%
+there as Porter points out if you're in
+that situation I mean Airlines have
+
+ align:start position:0%
+that situation I mean Airlines have
+ 
+
+ align:start position:0%
+that situation I mean Airlines have
+improved efficiency enormously over the
+
+ align:start position:0%
+improved efficiency enormously over the
+ 
+
+ align:start position:0%
+improved efficiency enormously over the
+years fuel costs are down electronic
+
+ align:start position:0%
+years fuel costs are down electronic
+ 
+
+ align:start position:0%
+years fuel costs are down electronic
+reservation systems baggage handling
+
+ align:start position:0%
+reservation systems baggage handling
+ 
+
+ align:start position:0%
+reservation systems baggage handling
+much more efficient than they used to be
+
+ align:start position:0%
+much more efficient than they used to be
+ 
+
+ align:start position:0%
+much more efficient than they used to be
+and they're still not making any money
+
+ align:start position:0%
+and they're still not making any money
+ 
+
+ align:start position:0%
+and they're still not making any money
+because they're all doing it and if you
+
+ align:start position:0%
+because they're all doing it and if you
+ 
+
+ align:start position:0%
+because they're all doing it and if you
+don't innovate and improve you lose
+
+ align:start position:0%
+don't innovate and improve you lose
+ 
+
+ align:start position:0%
+don't innovate and improve you lose
+Andrew just drying your nail polish okay
+
+ align:start position:0%
+Andrew just drying your nail polish okay
+ 
+
+ align:start position:0%
+Andrew just drying your nail polish okay
+good
+
+ align:start position:0%
+good
+ 
+
+ align:start position:0%
+good
+good it's important to important to have
+
+ align:start position:0%
+good it's important to important to have
+ 
+
+ align:start position:0%
+good it's important to important to have
+it dry um so lesson one is you don't
+
+ align:start position:0%
+it dry um so lesson one is you don't
+ 
+
+ align:start position:0%
+it dry um so lesson one is you don't
+want to do that
+
+ align:start position:0%
+want to do that
+ 
+
+ align:start position:0%
+want to do that
+lesson two is sort of the obvious
+
+ align:start position:0%
+lesson two is sort of the obvious
+ 
+
+ align:start position:0%
+lesson two is sort of the obvious
+Counterpoint which is well when you set
+
+ align:start position:0%
+Counterpoint which is well when you set
+ 
+
+ align:start position:0%
+Counterpoint which is well when you set
+up a business you'd like to be doing
+
+ align:start position:0%
+up a business you'd like to be doing
+ 
+
+ align:start position:0%
+up a business you'd like to be doing
+something get a value to somebody that
+
+ align:start position:0%
+something get a value to somebody that
+ 
+
+ align:start position:0%
+something get a value to somebody that
+can't be easily imitated the buzzword is
+
+ align:start position:0%
+can't be easily imitated the buzzword is
+ 
+
+ align:start position:0%
+can't be easily imitated the buzzword is
+sustainable
+
+ align:start position:0%
+sustainable
+ 
+
+ align:start position:0%
+sustainable
+Advantage so the notion that Chinese
+
+ align:start position:0%
+Advantage so the notion that Chinese
+ 
+
+ align:start position:0%
+Advantage so the notion that Chinese
+photovoltaics will always be cheaper
+
+ align:start position:0%
+photovoltaics will always be cheaper
+ 
+
+ align:start position:0%
+photovoltaics will always be cheaper
+because Chinese bargaining power enables
+
+ align:start position:0%
+because Chinese bargaining power enables
+ 
+
+ align:start position:0%
+because Chinese bargaining power enables
+them to get silicon 25% cheaper than us
+
+ align:start position:0%
+them to get silicon 25% cheaper than us
+ 
+
+ align:start position:0%
+them to get silicon 25% cheaper than us
+firms that doesn't wash if that's what's
+
+ align:start position:0%
+firms that doesn't wash if that's what's
+ 
+
+ align:start position:0%
+firms that doesn't wash if that's what's
+going on that's not
+
+ align:start position:0%
+going on that's not
+ 
+
+ align:start position:0%
+going on that's not
+sustainable if there's some cost
+
+ align:start position:0%
+sustainable if there's some cost
+ 
+
+ align:start position:0%
+sustainable if there's some cost
+advantage in Silicon production that's
+
+ align:start position:0%
+advantage in Silicon production that's
+ 
+
+ align:start position:0%
+advantage in Silicon production that's
+more interesting but if all you know is
+
+ align:start position:0%
+more interesting but if all you know is
+ 
+
+ align:start position:0%
+more interesting but if all you know is
+it's cheaper and all you hear is
+
+ align:start position:0%
+it's cheaper and all you hear is
+ 
+
+ align:start position:0%
+it's cheaper and all you hear is
+bargaining power that's not
+
+ align:start position:0%
+bargaining power that's not
+ 
+
+ align:start position:0%
+bargaining power that's not
+sustainable so if strategy is what you
+
+ align:start position:0%
+sustainable so if strategy is what you
+ 
+
+ align:start position:0%
+sustainable so if strategy is what you
+don't do and it needs to be something
+
+ align:start position:0%
+don't do and it needs to be something
+ 
+
+ align:start position:0%
+don't do and it needs to be something
+that can't easily be imitated how about
+
+ align:start position:0%
+that can't easily be imitated how about
+ 
+
+ align:start position:0%
+that can't easily be imitated how about
+the question I posed there does MIT have
+
+ align:start position:0%
+the question I posed there does MIT have
+ 
+
+ align:start position:0%
+the question I posed there does MIT have
+a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+strategy if so what is it or what are
+
+ align:start position:0%
+strategy if so what is it or what are
+ 
+
+ align:start position:0%
+strategy if so what is it or what are
+what are elements of
+
+ align:start position:0%
+what are elements of
+ 
+
+ align:start position:0%
+what are elements of
+it yeah Hands On Learning Hands-On
+
+ align:start position:0%
+it yeah Hands On Learning Hands-On
+ 
+
+ align:start position:0%
+it yeah Hands On Learning Hands-On
+learning okay what is that rule
+
+ align:start position:0%
+learning okay what is that rule
+ 
+
+ align:start position:0%
+learning okay what is that rule
+out I it's an element of what MIT is
+
+ align:start position:0%
+out I it's an element of what MIT is
+ 
+
+ align:start position:0%
+out I it's an element of what MIT is
+about
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+absolutely Lim
+
+ align:start position:0%
+absolutely Lim
+ 
+
+ align:start position:0%
+absolutely Lim
+people have ,000
+
+ align:start position:0%
+people have ,000
+ 
+
+ align:start position:0%
+people have ,000
+people okay so it's a it's a high cost
+
+ align:start position:0%
+people okay so it's a it's a high cost
+ 
+
+ align:start position:0%
+people okay so it's a it's a high cost
+strategy um what's it say about
+
+ align:start position:0%
+strategy um what's it say about
+ 
+
+ align:start position:0%
+strategy um what's it say about
+the kinds of things you teach medical
+
+ align:start position:0%
+the kinds of things you teach medical
+ 
+
+ align:start position:0%
+the kinds of things you teach medical
+school has has Hands-On learning MIT
+
+ align:start position:0%
+school has has Hands-On learning MIT
+ 
+
+ align:start position:0%
+school has has Hands-On learning MIT
+doesn't have a medical
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+school simpler question Caroline what's
+
+ align:start position:0%
+school simpler question Caroline what's
+ 
+
+ align:start position:0%
+school simpler question Caroline what's
+Welsley strategy does Welsley have a
+
+ align:start position:0%
+Welsley strategy does Welsley have a
+ 
+
+ align:start position:0%
+Welsley strategy does Welsley have a
+strategy um yes to educate women educate
+
+ align:start position:0%
+strategy um yes to educate women educate
+ 
+
+ align:start position:0%
+strategy um yes to educate women educate
+women in everything as well as they have
+
+ align:start position:0%
+women in everything as well as they have
+ 
+
+ align:start position:0%
+women in everything as well as they have
+a big engineering
+
+ align:start position:0%
+a big engineering
+ 
+
+ align:start position:0%
+a big engineering
+school liberal arts focuses on women
+
+ align:start position:0%
+school liberal arts focuses on women
+ 
+
+ align:start position:0%
+school liberal arts focuses on women
+focuses on liberal arts doesn't offer
+
+ align:start position:0%
+focuses on liberal arts doesn't offer
+ 
+
+ align:start position:0%
+focuses on liberal arts doesn't offer
+graduate
+
+ align:start position:0%
+graduate
+ 
+
+ align:start position:0%
+graduate
+degrees stays small that's pretty easy
+
+ align:start position:0%
+degrees stays small that's pretty easy
+ 
+
+ align:start position:0%
+degrees stays small that's pretty easy
+what about MIT it's more than just
+
+ align:start position:0%
+what about MIT it's more than just
+ 
+
+ align:start position:0%
+what about MIT it's more than just
+Hands-On learning MIT doesn't have a law
+
+ align:start position:0%
+Hands-On learning MIT doesn't have a law
+ 
+
+ align:start position:0%
+Hands-On learning MIT doesn't have a law
+school Harvard has a law school
+
+ align:start position:0%
+school Harvard has a law school
+ 
+
+ align:start position:0%
+school Harvard has a law school
+Harvard's had a law school for a long
+
+ align:start position:0%
+Harvard's had a law school for a long
+ 
+
+ align:start position:0%
+Harvard's had a law school for a long
+time presumably those are strategic
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+differences yes somebody actually sat
+
+ align:start position:0%
+differences yes somebody actually sat
+ 
+
+ align:start position:0%
+differences yes somebody actually sat
+down and said why should MIT have a law
+
+ align:start position:0%
+down and said why should MIT have a law
+ 
+
+ align:start position:0%
+down and said why should MIT have a law
+school no MIT shouldn't I mean that
+
+ align:start position:0%
+school no MIT shouldn't I mean that
+ 
+
+ align:start position:0%
+school no MIT shouldn't I mean that
+decision's been looked at several times
+
+ align:start position:0%
+decision's been looked at several times
+ 
+
+ align:start position:0%
+decision's been looked at several times
+in history why do you
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+think so they can focus on being the
+
+ align:start position:0%
+think so they can focus on being the
+ 
+
+ align:start position:0%
+think so they can focus on being the
+best in science and engineering it
+
+ align:start position:0%
+best in science and engineering it
+ 
+
+ align:start position:0%
+best in science and engineering it
+focuses on science and engineering and
+
+ align:start position:0%
+focuses on science and engineering and
+ 
+
+ align:start position:0%
+focuses on science and engineering and
+things that compl and work with
+
+ align:start position:0%
+things that compl and work with
+ 
+
+ align:start position:0%
+things that compl and work with
+it so does economics make sense yeah it
+
+ align:start position:0%
+it so does economics make sense yeah it
+ 
+
+ align:start position:0%
+it so does economics make sense yeah it
+does historically it does one of the
+
+ align:start position:0%
+does historically it does one of the
+ 
+
+ align:start position:0%
+does historically it does one of the
+early presidents of MIT was the founder
+
+ align:start position:0%
+early presidents of MIT was the founder
+ 
+
+ align:start position:0%
+early presidents of MIT was the founder
+of the American economic Association so
+
+ align:start position:0%
+of the American economic Association so
+ 
+
+ align:start position:0%
+of the American economic Association so
+somebody thought it made sense um we've
+
+ align:start position:0%
+somebody thought it made sense um we've
+ 
+
+ align:start position:0%
+somebody thought it made sense um we've
+done business for a long time since
+
+ align:start position:0%
+done business for a long time since
+ 
+
+ align:start position:0%
+done business for a long time since
+almost since the start of the
+
+ align:start position:0%
+almost since the start of the
+ 
+
+ align:start position:0%
+almost since the start of the
+Institute how about
+
+ align:start position:0%
+Institute how about
+ 
+
+ align:start position:0%
+Institute how about
+Linguistics why do we do
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Linguistics H well I've heard it's lar
+
+ align:start position:0%
+Linguistics H well I've heard it's lar
+ 
+
+ align:start position:0%
+Linguistics H well I've heard it's lar
+because can't
+
+ align:start position:0%
+because can't
+ 
+
+ align:start position:0%
+because can't
+develop yeah I think that's the right
+
+ align:start position:0%
+develop yeah I think that's the right
+ 
+
+ align:start position:0%
+develop yeah I think that's the right
+answer I mean my sense is a whole bunch
+
+ align:start position:0%
+answer I mean my sense is a whole bunch
+ 
+
+ align:start position:0%
+answer I mean my sense is a whole bunch
+of decisions have been made that a whole
+
+ align:start position:0%
+of decisions have been made that a whole
+ 
+
+ align:start position:0%
+of decisions have been made that a whole
+bunch of areas will be basically service
+
+ align:start position:0%
+bunch of areas will be basically service
+ 
+
+ align:start position:0%
+bunch of areas will be basically service
+departments so that we can actually give
+
+ align:start position:0%
+departments so that we can actually give
+ 
+
+ align:start position:0%
+departments so that we can actually give
+a rounded
+
+ align:start position:0%
+a rounded
+ 
+
+ align:start position:0%
+a rounded
+education and into that history we don't
+
+ align:start position:0%
+education and into that history we don't
+ 
+
+ align:start position:0%
+education and into that history we don't
+do Advanced degrees in history uh and
+
+ align:start position:0%
+do Advanced degrees in history uh and
+ 
+
+ align:start position:0%
+do Advanced degrees in history uh and
+sociology we don't have psychology is
+
+ align:start position:0%
+sociology we don't have psychology is
+ 
+
+ align:start position:0%
+sociology we don't have psychology is
+very focused but but into languages and
+
+ align:start position:0%
+very focused but but into languages and
+ 
+
+ align:start position:0%
+very focused but but into languages and
+Linguistics stumbles gome Chomsky and
+
+ align:start position:0%
+Linguistics stumbles gome Chomsky and
+ 
+
+ align:start position:0%
+Linguistics stumbles gome Chomsky and
+you say oh my God what an opportunity
+
+ align:start position:0%
+you say oh my God what an opportunity
+ 
+
+ align:start position:0%
+you say oh my God what an opportunity
+this is and so you build on him but it's
+
+ align:start position:0%
+this is and so you build on him but it's
+ 
+
+ align:start position:0%
+this is and so you build on him but it's
+not a big department and it's pretty
+
+ align:start position:0%
+not a big department and it's pretty
+ 
+
+ align:start position:0%
+not a big department and it's pretty
+focused and we don't have a lot of
+
+ align:start position:0%
+focused and we don't have a lot of
+ 
+
+ align:start position:0%
+focused and we don't have a lot of
+modern languages we don't have a French
+
+ align:start position:0%
+modern languages we don't have a French
+ 
+
+ align:start position:0%
+modern languages we don't have a French
+Department we don't have a Spanish
+
+ align:start position:0%
+Department we don't have a Spanish
+ 
+
+ align:start position:0%
+Department we don't have a Spanish
+Department there's probably a French
+
+ align:start position:0%
+Department there's probably a French
+ 
+
+ align:start position:0%
+Department there's probably a French
+department at Welsley yes yeah we don't
+
+ align:start position:0%
+department at Welsley yes yeah we don't
+ 
+
+ align:start position:0%
+department at Welsley yes yeah we don't
+have one so MIT does have a strategy
+
+ align:start position:0%
+have one so MIT does have a strategy
+ 
+
+ align:start position:0%
+have one so MIT does have a strategy
+it's not
+
+ align:start position:0%
+it's not
+ 
+
+ align:start position:0%
+it's not
+perfectly not easily written down but I
+
+ align:start position:0%
+perfectly not easily written down but I
+ 
+
+ align:start position:0%
+perfectly not easily written down but I
+mean the the Strategic descriptions have
+
+ align:start position:0%
+mean the the Strategic descriptions have
+ 
+
+ align:start position:0%
+mean the the Strategic descriptions have
+to do with science engineering and
+
+ align:start position:0%
+to do with science engineering and
+ 
+
+ align:start position:0%
+to do with science engineering and
+related fields and complimentary Fields
+
+ align:start position:0%
+related fields and complimentary Fields
+ 
+
+ align:start position:0%
+related fields and complimentary Fields
+Welsley is pretty clear Harvard's
+
+ align:start position:0%
+Welsley is pretty clear Harvard's
+ 
+
+ align:start position:0%
+Welsley is pretty clear Harvard's
+is we do almost everything we're a full
+
+ align:start position:0%
+is we do almost everything we're a full
+ 
+
+ align:start position:0%
+is we do almost everything we're a full
+service
+
+ align:start position:0%
+service
+ 
+
+ align:start position:0%
+service
+supplier it is interesting Harvard
+
+ align:start position:0%
+supplier it is interesting Harvard
+ 
+
+ align:start position:0%
+supplier it is interesting Harvard
+doesn't have a veterinary school I'm
+
+ align:start position:0%
+doesn't have a veterinary school I'm
+ 
+
+ align:start position:0%
+doesn't have a veterinary school I'm
+quite sure why but but they have just
+
+ align:start position:0%
+quite sure why but but they have just
+ 
+
+ align:start position:0%
+quite sure why but but they have just
+about everything else you could think
+
+ align:start position:0%
+about everything else you could think
+ 
+
+ align:start position:0%
+about everything else you could think
+about just I don't I don't think they
+
+ align:start position:0%
+about just I don't I don't think they
+ 
+
+ align:start position:0%
+about just I don't I don't think they
+have Library science but just about
+
+ align:start position:0%
+have Library science but just about
+ 
+
+ align:start position:0%
+have Library science but just about
+everything else so those are very those
+
+ align:start position:0%
+everything else so those are very those
+ 
+
+ align:start position:0%
+everything else so those are very those
+are strategies MIT has faced the
+
+ align:start position:0%
+are strategies MIT has faced the
+ 
+
+ align:start position:0%
+are strategies MIT has faced the
+possibility of a law school MIT could
+
+ align:start position:0%
+possibility of a law school MIT could
+ 
+
+ align:start position:0%
+possibility of a law school MIT could
+make money with a law school has decided
+
+ align:start position:0%
+make money with a law school has decided
+ 
+
+ align:start position:0%
+make money with a law school has decided
+not to do it has decided not to have a
+
+ align:start position:0%
+not to do it has decided not to have a
+ 
+
+ align:start position:0%
+not to do it has decided not to have a
+medical
+
+ align:start position:0%
+medical
+ 
+
+ align:start position:0%
+medical
+school that's a harder call that's a
+
+ align:start position:0%
+school that's a harder call that's a
+ 
+
+ align:start position:0%
+school that's a harder call that's a
+more interesting call but has decided
+
+ align:start position:0%
+more interesting call but has decided
+ 
+
+ align:start position:0%
+more interesting call but has decided
+not to do a medical school
+
+ align:start position:0%
+not to do a medical school
+ 
+
+ align:start position:0%
+not to do a medical school
+strategy is to an important extent What
+
+ align:start position:0%
+strategy is to an important extent What
+ 
+
+ align:start position:0%
+strategy is to an important extent What
+You Won't Do and you could certainly do
+
+ align:start position:0%
+You Won't Do and you could certainly do
+ 
+
+ align:start position:0%
+You Won't Do and you could certainly do
+a net presentes value calculation for
+
+ align:start position:0%
+a net presentes value calculation for
+ 
+
+ align:start position:0%
+a net presentes value calculation for
+the MIT medical
+
+ align:start position:0%
+the MIT medical
+ 
+
+ align:start position:0%
+the MIT medical
+school and come out with a positive and
+
+ align:start position:0%
+school and come out with a positive and
+ 
+
+ align:start position:0%
+school and come out with a positive and
+also social impact you could also talk
+
+ align:start position:0%
+also social impact you could also talk
+ 
+
+ align:start position:0%
+also social impact you could also talk
+about a law school with heavy focus on
+
+ align:start position:0%
+about a law school with heavy focus on
+ 
+
+ align:start position:0%
+about a law school with heavy focus on
+patent law and intellectual and related
+
+ align:start position:0%
+patent law and intellectual and related
+ 
+
+ align:start position:0%
+patent law and intellectual and related
+intellectual property fields which does
+
+ align:start position:0%
+intellectual property fields which does
+ 
+
+ align:start position:0%
+intellectual property fields which does
+to a certain extent
+
+ align:start position:0%
+to a certain extent
+ 
+
+ align:start position:0%
+to a certain extent
+compliment but also distracts and that's
+
+ align:start position:0%
+compliment but also distracts and that's
+ 
+
+ align:start position:0%
+compliment but also distracts and that's
+a strategic choice so univ I ities like
+
+ align:start position:0%
+a strategic choice so univ I ities like
+ 
+
+ align:start position:0%
+a strategic choice so univ I ities like
+all kinds of other organizations need to
+
+ align:start position:0%
+all kinds of other organizations need to
+ 
+
+ align:start position:0%
+all kinds of other organizations need to
+have strategic need to make strategic
+
+ align:start position:0%
+have strategic need to make strategic
+ 
+
+ align:start position:0%
+have strategic need to make strategic
+choices another another strategy might
+
+ align:start position:0%
+choices another another strategy might
+ 
+
+ align:start position:0%
+choices another another strategy might
+be we'll do we'll do almost anything
+
+ align:start position:0%
+be we'll do we'll do almost anything
+ 
+
+ align:start position:0%
+be we'll do we'll do almost anything
+that will turn a profit and you see some
+
+ align:start position:0%
+that will turn a profit and you see some
+ 
+
+ align:start position:0%
+that will turn a profit and you see some
+places look like that MIT very much
+
+ align:start position:0%
+places look like that MIT very much
+ 
+
+ align:start position:0%
+places look like that MIT very much
+doesn't so if you're really thinking
+
+ align:start position:0%
+doesn't so if you're really thinking
+ 
+
+ align:start position:0%
+doesn't so if you're really thinking
+about a sustainable advantage of some
+
+ align:start position:0%
+about a sustainable advantage of some
+ 
+
+ align:start position:0%
+about a sustainable advantage of some
+sort a coherent strategy you have to
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+consider you have to consider the next
+
+ align:start position:0%
+consider you have to consider the next
+ 
+
+ align:start position:0%
+consider you have to consider the next
+bullet or
+
+ align:start position:0%
+bullet or
+ 
+
+ align:start position:0%
+bullet or
+not okay what the next bullet says is
+
+ align:start position:0%
+not okay what the next bullet says is
+ 
+
+ align:start position:0%
+not okay what the next bullet says is
+when the slide works you have to think
+
+ align:start position:0%
+when the slide works you have to think
+ 
+
+ align:start position:0%
+when the slide works you have to think
+about
+
+ align:start position:0%
+about
+ 
+
+ align:start position:0%
+about
+complementarities or fit among
+
+ align:start position:0%
+complementarities or fit among
+ 
+
+ align:start position:0%
+complementarities or fit among
+investment
+
+ align:start position:0%
+investment
+ 
+
+ align:start position:0%
+investment
+projects meantime I'm going to figure
+
+ align:start position:0%
+projects meantime I'm going to figure
+ 
+
+ align:start position:0%
+projects meantime I'm going to figure
+out why this works the why this doesn't
+
+ align:start position:0%
+out why this works the why this doesn't
+ 
+
+ align:start position:0%
+out why this works the why this doesn't
+work the nice piece that we
+
+ align:start position:0%
+work the nice piece that we
+ 
+
+ align:start position:0%
+work the nice piece that we
+had okay tech support please I have a
+
+ align:start position:0%
+had okay tech support please I have a
+ 
+
+ align:start position:0%
+had okay tech support please I have a
+frozen machine at the moment there are
+
+ align:start position:0%
+frozen machine at the moment there are
+ 
+
+ align:start position:0%
+frozen machine at the moment there are
+nice examples in Porter about Ikea and
+
+ align:start position:0%
+nice examples in Porter about Ikea and
+ 
+
+ align:start position:0%
+nice examples in Porter about Ikea and
+about Southwest
+
+ align:start position:0%
+about Southwest
+ 
+
+ align:start position:0%
+about Southwest
+Airlines and they're great examples of
+
+ align:start position:0%
+Airlines and they're great examples of
+ 
+
+ align:start position:0%
+Airlines and they're great examples of
+taking on things that fit together right
+
+ align:start position:0%
+taking on things that fit together right
+ 
+
+ align:start position:0%
+taking on things that fit together right
+Southwest Airlines doesn't offer food
+
+ align:start position:0%
+Southwest Airlines doesn't offer food
+ 
+
+ align:start position:0%
+Southwest Airlines doesn't offer food
+Southwest Airlines flies out of small
+
+ align:start position:0%
+Southwest Airlines flies out of small
+ 
+
+ align:start position:0%
+Southwest Airlines flies out of small
+airports Southwest Airlines flies one
+
+ align:start position:0%
+airports Southwest Airlines flies one
+ 
+
+ align:start position:0%
+airports Southwest Airlines flies one
+kind of
+
+ align:start position:0%
+kind of
+ 
+
+ align:start position:0%
+kind of
+airplane all those things fit together
+
+ align:start position:0%
+airplane all those things fit together
+ 
+
+ align:start position:0%
+airplane all those things fit together
+lowcost
+
+ align:start position:0%
+lowcost
+ 
+
+ align:start position:0%
+lowcost
+convenient lowcost convenient you could
+
+ align:start position:0%
+convenient lowcost convenient you could
+ 
+
+ align:start position:0%
+convenient lowcost convenient you could
+make a case that g if we had more if we
+
+ align:start position:0%
+make a case that g if we had more if we
+ 
+
+ align:start position:0%
+make a case that g if we had more if we
+had uh oh and you don't book through
+
+ align:start position:0%
+had uh oh and you don't book through
+ 
+
+ align:start position:0%
+had uh oh and you don't book through
+online
+
+ align:start position:0%
+online
+ 
+
+ align:start position:0%
+online
+services You Had A Hammer no I have ah
+
+ align:start position:0%
+services You Had A Hammer no I have ah
+ 
+
+ align:start position:0%
+services You Had A Hammer no I have ah
+okay thank
+
+ align:start position:0%
+okay thank
+ 
+
+ align:start position:0%
+okay thank
+you all right we're going to try to do
+
+ align:start position:0%
+you all right we're going to try to do
+ 
+
+ align:start position:0%
+you all right we're going to try to do
+this without slides it's going to be
+
+ align:start position:0%
+this without slides it's going to be
+ 
+
+ align:start position:0%
+this without slides it's going to be
+good uh the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um the examples there are things that
+
+ align:start position:0%
+um the examples there are things that
+ 
+
+ align:start position:0%
+um the examples there are things that
+fit together you could imagine Southwest
+
+ align:start position:0%
+fit together you could imagine Southwest
+ 
+
+ align:start position:0%
+fit together you could imagine Southwest
+doing a calculation and saying well if
+
+ align:start position:0%
+doing a calculation and saying well if
+ 
+
+ align:start position:0%
+doing a calculation and saying well if
+we used online booking Services we'd get
+
+ align:start position:0%
+we used online booking Services we'd get
+ 
+
+ align:start position:0%
+we used online booking Services we'd get
+more volume and that'll cost us x% and
+
+ align:start position:0%
+more volume and that'll cost us x% and
+ 
+
+ align:start position:0%
+more volume and that'll cost us x% and
+you could imagine saying well it'll
+
+ align:start position:0%
+you could imagine saying well it'll
+ 
+
+ align:start position:0%
+you could imagine saying well it'll
+increase our costs a little bit but
+
+ align:start position:0%
+increase our costs a little bit but
+ 
+
+ align:start position:0%
+increase our costs a little bit but
+it'll pay off they have a Relentless
+
+ align:start position:0%
+it'll pay off they have a Relentless
+ 
+
+ align:start position:0%
+it'll pay off they have a Relentless
+focus on costs we're not going to do it
+
+ align:start position:0%
+focus on costs we're not going to do it
+ 
+
+ align:start position:0%
+focus on costs we're not going to do it
+we're not going to have assigned seats
+
+ align:start position:0%
+we're not going to have assigned seats
+ 
+
+ align:start position:0%
+we're not going to have assigned seats
+that takes time and extra gate Personnel
+
+ align:start position:0%
+that takes time and extra gate Personnel
+ 
+
+ align:start position:0%
+that takes time and extra gate Personnel
+we're not going to f we're not going to
+
+ align:start position:0%
+we're not going to f we're not going to
+ 
+
+ align:start position:0%
+we're not going to f we're not going to
+do online reservations because that
+
+ align:start position:0%
+do online reservations because that
+ 
+
+ align:start position:0%
+do online reservations because that
+limits that that'll increase our costs
+
+ align:start position:0%
+limits that that'll increase our costs
+ 
+
+ align:start position:0%
+limits that that'll increase our costs
+we're going to be lowcost convenient
+
+ align:start position:0%
+we're going to be lowcost convenient
+ 
+
+ align:start position:0%
+we're going to be lowcost convenient
+we're not going to have different kinds
+
+ align:start position:0%
+we're not going to have different kinds
+ 
+
+ align:start position:0%
+we're not going to have different kinds
+of planes even though on some routes we
+
+ align:start position:0%
+of planes even though on some routes we
+ 
+
+ align:start position:0%
+of planes even though on some routes we
+might want to fly larger planes because
+
+ align:start position:0%
+might want to fly larger planes because
+ 
+
+ align:start position:0%
+might want to fly larger planes because
+that'll increase our costs so Southwest
+
+ align:start position:0%
+that'll increase our costs so Southwest
+ 
+
+ align:start position:0%
+that'll increase our costs so Southwest
+thinks about how its decisions fit
+
+ align:start position:0%
+thinks about how its decisions fit
+ 
+
+ align:start position:0%
+thinks about how its decisions fit
+together similarly the example of
+
+ align:start position:0%
+together similarly the example of
+ 
+
+ align:start position:0%
+together similarly the example of
+Ikea which you all probably know better
+
+ align:start position:0%
+Ikea which you all probably know better
+ 
+
+ align:start position:0%
+Ikea which you all probably know better
+than I do but but you go into a
+
+ align:start position:0%
+than I do but but you go into a
+ 
+
+ align:start position:0%
+than I do but but you go into a
+traditional furniture store you can get
+
+ align:start position:0%
+traditional furniture store you can get
+ 
+
+ align:start position:0%
+traditional furniture store you can get
+all kinds of different things you order
+
+ align:start position:0%
+all kinds of different things you order
+ 
+
+ align:start position:0%
+all kinds of different things you order
+them many Fabrics many styles it takes
+
+ align:start position:0%
+them many Fabrics many styles it takes
+ 
+
+ align:start position:0%
+them many Fabrics many styles it takes
+six to 8 weeks some some slave in North
+
+ align:start position:0%
+six to 8 weeks some some slave in North
+ 
+
+ align:start position:0%
+six to 8 weeks some some slave in North
+Carolina makes it and it's shipped
+
+ align:start position:0%
+Carolina makes it and it's shipped
+ 
+
+ align:start position:0%
+Carolina makes it and it's shipped
+up I K doesn't offer that doesn't offer
+
+ align:start position:0%
+up I K doesn't offer that doesn't offer
+ 
+
+ align:start position:0%
+up I K doesn't offer that doesn't offer
+the customization it offers cost
+
+ align:start position:0%
+the customization it offers cost
+ 
+
+ align:start position:0%
+the customization it offers cost
+convenience and a certain
+
+ align:start position:0%
+convenience and a certain
+ 
+
+ align:start position:0%
+convenience and a certain
+look that's what it focuses on all of
+
+ align:start position:0%
+look that's what it focuses on all of
+ 
+
+ align:start position:0%
+look that's what it focuses on all of
+its decisions aim for that so that's a
+
+ align:start position:0%
+its decisions aim for that so that's a
+ 
+
+ align:start position:0%
+its decisions aim for that so that's a
+coherent strategy you you don't just
+
+ align:start position:0%
+coherent strategy you you don't just
+ 
+
+ align:start position:0%
+coherent strategy you you don't just
+take anything with a positive Net
+
+ align:start position:0%
+take anything with a positive Net
+ 
+
+ align:start position:0%
+take anything with a positive Net
+Present Value you ask how does it fit
+
+ align:start position:0%
+Present Value you ask how does it fit
+ 
+
+ align:start position:0%
+Present Value you ask how does it fit
+with what we're trying to do how does it
+
+ align:start position:0%
+with what we're trying to do how does it
+ 
+
+ align:start position:0%
+with what we're trying to do how does it
+fit with what we're trying to do an MIT
+
+ align:start position:0%
+fit with what we're trying to do an MIT
+ 
+
+ align:start position:0%
+fit with what we're trying to do an MIT
+law
+
+ align:start position:0%
+law
+ 
+
+ align:start position:0%
+law
+school might have positive might have
+
+ align:start position:0%
+school might have positive might have
+ 
+
+ align:start position:0%
+school might have positive might have
+positive benefits how does it fit with
+
+ align:start position:0%
+positive benefits how does it fit with
+ 
+
+ align:start position:0%
+positive benefits how does it fit with
+the main focus how would the Law School
+
+ align:start position:0%
+the main focus how would the Law School
+ 
+
+ align:start position:0%
+the main focus how would the Law School
+faculty interact with other faculty
+
+ align:start position:0%
+faculty interact with other faculty
+ 
+
+ align:start position:0%
+faculty interact with other faculty
+would it be the kinds of people who will
+
+ align:start position:0%
+would it be the kinds of people who will
+ 
+
+ align:start position:0%
+would it be the kinds of people who will
+fit well on the campus how would law
+
+ align:start position:0%
+fit well on the campus how would law
+ 
+
+ align:start position:0%
+fit well on the campus how would law
+students relate da da da da da that's
+
+ align:start position:0%
+students relate da da da da da that's
+ 
+
+ align:start position:0%
+students relate da da da da da that's
+that's not to say that that's an obvious
+
+ align:start position:0%
+that's not to say that that's an obvious
+ 
+
+ align:start position:0%
+that's not to say that that's an obvious
+question I always think a a more
+
+ align:start position:0%
+question I always think a a more
+ 
+
+ align:start position:0%
+question I always think a a more
+interesting strategic choice is should
+
+ align:start position:0%
+interesting strategic choice is should
+ 
+
+ align:start position:0%
+interesting strategic choice is should
+MIT invest more in public policy we have
+
+ align:start position:0%
+MIT invest more in public policy we have
+ 
+
+ align:start position:0%
+MIT invest more in public policy we have
+uh STS and so forth we don't have the
+
+ align:start position:0%
+uh STS and so forth we don't have the
+ 
+
+ align:start position:0%
+uh STS and so forth we don't have the
+Kennedy School you could imagine a case
+
+ align:start position:0%
+Kennedy School you could imagine a case
+ 
+
+ align:start position:0%
+Kennedy School you could imagine a case
+being made for a serious public public
+
+ align:start position:0%
+being made for a serious public public
+ 
+
+ align:start position:0%
+being made for a serious public public
+policy School focused on science and
+
+ align:start position:0%
+policy School focused on science and
+ 
+
+ align:start position:0%
+policy School focused on science and
+technology that case hasn't been made
+
+ align:start position:0%
+technology that case hasn't been made
+ 
+
+ align:start position:0%
+technology that case hasn't been made
+and that's a money Loser by the way but
+
+ align:start position:0%
+and that's a money Loser by the way but
+ 
+
+ align:start position:0%
+and that's a money Loser by the way but
+it might be it might have other
+
+ align:start position:0%
+it might be it might have other
+ 
+
+ align:start position:0%
+it might be it might have other
+strategic value any hope they have to
+
+ align:start position:0%
+strategic value any hope they have to
+ 
+
+ align:start position:0%
+strategic value any hope they have to
+REO the machine they have to reboot the
+
+ align:start position:0%
+REO the machine they have to reboot the
+ 
+
+ align:start position:0%
+REO the machine they have to reboot the
+machine
+
+ align:start position:0%
+machine
+ 
+
+ align:start position:0%
+machine
+okay we now go to Blackboard for the
+
+ align:start position:0%
+okay we now go to Blackboard for the
+ 
+
+ align:start position:0%
+okay we now go to Blackboard for the
+next
+
+ align:start position:0%
+next
+ 
+
+ align:start position:0%
+next
+Slide the next slide has to do
+
+ align:start position:0%
+Slide the next slide has to do
+ 
+
+ align:start position:0%
+Slide the next slide has to do
+with and I can't do Blackboard with a
+
+ align:start position:0%
+with and I can't do Blackboard with a
+ 
+
+ align:start position:0%
+with and I can't do Blackboard with a
+jacket on so so the next slide has to do
+
+ align:start position:0%
+jacket on so so the next slide has to do
+ 
+
+ align:start position:0%
+jacket on so so the next slide has to do
+with industry
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+attractiveness so as I said this is
+
+ align:start position:0%
+attractiveness so as I said this is
+ 
+
+ align:start position:0%
+attractiveness so as I said this is
+about thinking
+
+ align:start position:0%
+about thinking
+ 
+
+ align:start position:0%
+about thinking
+about what activities you are doing what
+
+ align:start position:0%
+about what activities you are doing what
+ 
+
+ align:start position:0%
+about what activities you are doing what
+are you offering customers if you're
+
+ align:start position:0%
+are you offering customers if you're
+ 
+
+ align:start position:0%
+are you offering customers if you're
+offering customers the same things as a
+
+ align:start position:0%
+offering customers the same things as a
+ 
+
+ align:start position:0%
+offering customers the same things as a
+lot of competitors then you can be
+
+ align:start position:0%
+lot of competitors then you can be
+ 
+
+ align:start position:0%
+lot of competitors then you can be
+really good but unless there's some way
+
+ align:start position:0%
+really good but unless there's some way
+ 
+
+ align:start position:0%
+really good but unless there's some way
+you're better that can't be imitated
+
+ align:start position:0%
+you're better that can't be imitated
+ 
+
+ align:start position:0%
+you're better that can't be imitated
+you've got a problem so so if you look
+
+ align:start position:0%
+you've got a problem so so if you look
+ 
+
+ align:start position:0%
+you've got a problem so so if you look
+at an
+
+ align:start position:0%
+at an
+ 
+
+ align:start position:0%
+at an
+industry and you
+
+ align:start position:0%
+industry and you
+ 
+
+ align:start position:0%
+industry and you
+ask what things affect
+
+ align:start position:0%
+ask what things affect
+ 
+
+ align:start position:0%
+ask what things affect
+profits one thing is the intensity of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+competition another thing is pressure
+
+ align:start position:0%
+competition another thing is pressure
+ 
+
+ align:start position:0%
+competition another thing is pressure
+from suppliers I'll give you examples in
+
+ align:start position:0%
+from suppliers I'll give you examples in
+ 
+
+ align:start position:0%
+from suppliers I'll give you examples in
+a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+minute another thing is pressure from
+
+ align:start position:0%
+minute another thing is pressure from
+ 
+
+ align:start position:0%
+minute another thing is pressure from
+buyers
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+substitutes and
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+entry this is the famous uh this is an
+
+ align:start position:0%
+entry this is the famous uh this is an
+ 
+
+ align:start position:0%
+entry this is the famous uh this is an
+ugly version of the famous Mike
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Porter five forces
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+if you understand this fully you're a
+
+ align:start position:0%
+if you understand this fully you're a
+ 
+
+ align:start position:0%
+if you understand this fully you're a
+third of the way through the MBA course
+
+ align:start position:0%
+third of the way through the MBA course
+ 
+
+ align:start position:0%
+third of the way through the MBA course
+in strategy so let me let me try to do
+
+ align:start position:0%
+in strategy so let me let me try to do
+ 
+
+ align:start position:0%
+in strategy so let me let me try to do
+it quickly it's not very
+
+ align:start position:0%
+it quickly it's not very
+ 
+
+ align:start position:0%
+it quickly it's not very
+hard
+
+ align:start position:0%
+hard
+ 
+
+ align:start position:0%
+hard
+uh maybe maybe only a quarter of the way
+
+ align:start position:0%
+uh maybe maybe only a quarter of the way
+ 
+
+ align:start position:0%
+uh maybe maybe only a quarter of the way
+through look I mean regardless
+
+ align:start position:0%
+through look I mean regardless
+ 
+
+ align:start position:0%
+through look I mean regardless
+regardless of what the what the supply
+
+ align:start position:0%
+regardless of what the what the supply
+ 
+
+ align:start position:0%
+regardless of what the what the supply
+conditions are and whether they're
+
+ align:start position:0%
+conditions are and whether they're
+ 
+
+ align:start position:0%
+conditions are and whether they're
+entrance or not if if the industry is
+
+ align:start position:0%
+entrance or not if if the industry is
+ 
+
+ align:start position:0%
+entrance or not if if the industry is
+perfectly competitive nobody makes any
+
+ align:start position:0%
+perfectly competitive nobody makes any
+ 
+
+ align:start position:0%
+perfectly competitive nobody makes any
+money that's sort of the definition and
+
+ align:start position:0%
+money that's sort of the definition and
+ 
+
+ align:start position:0%
+money that's sort of the definition and
+obviously competition runs along some
+
+ align:start position:0%
+obviously competition runs along some
+ 
+
+ align:start position:0%
+obviously competition runs along some
+sort of spectrum between a lot of small
+
+ align:start position:0%
+sort of spectrum between a lot of small
+ 
+
+ align:start position:0%
+sort of spectrum between a lot of small
+firms beating each other's brains out
+
+ align:start position:0%
+firms beating each other's brains out
+ 
+
+ align:start position:0%
+firms beating each other's brains out
+and one Monopoly taking everything there
+
+ align:start position:0%
+and one Monopoly taking everything there
+ 
+
+ align:start position:0%
+and one Monopoly taking everything there
+is to be had so this is one force that
+
+ align:start position:0%
+is to be had so this is one force that
+ 
+
+ align:start position:0%
+is to be had so this is one force that
+can affect competition can affect
+
+ align:start position:0%
+can affect competition can affect
+ 
+
+ align:start position:0%
+can affect competition can affect
+profits is the intensity of competition
+
+ align:start position:0%
+profits is the intensity of competition
+ 
+
+ align:start position:0%
+profits is the intensity of competition
+within the
+
+ align:start position:0%
+within the
+ 
+
+ align:start position:0%
+within the
+industry another
+
+ align:start position:0%
+industry another
+ 
+
+ align:start position:0%
+industry another
+force is the existence of close
+
+ align:start position:0%
+force is the existence of close
+ 
+
+ align:start position:0%
+force is the existence of close
+substitutes we all make wax paper and
+
+ align:start position:0%
+substitutes we all make wax paper and
+ 
+
+ align:start position:0%
+substitutes we all make wax paper and
+we're great wax paper manufacturers but
+
+ align:start position:0%
+we're great wax paper manufacturers but
+ 
+
+ align:start position:0%
+we're great wax paper manufacturers but
+you know plastic wrap is eating our
+
+ align:start position:0%
+you know plastic wrap is eating our
+ 
+
+ align:start position:0%
+you know plastic wrap is eating our
+lunch and so there may be only two or
+
+ align:start position:0%
+lunch and so there may be only two or
+ 
+
+ align:start position:0%
+lunch and so there may be only two or
+three of us making making wax paper but
+
+ align:start position:0%
+three of us making making wax paper but
+ 
+
+ align:start position:0%
+three of us making making wax paper but
+with the availability of cheap plastic
+
+ align:start position:0%
+with the availability of cheap plastic
+ 
+
+ align:start position:0%
+with the availability of cheap plastic
+wrap it means we have probably declining
+
+ align:start position:0%
+wrap it means we have probably declining
+ 
+
+ align:start position:0%
+wrap it means we have probably declining
+demand it means we probably have a
+
+ align:start position:0%
+demand it means we probably have a
+ 
+
+ align:start position:0%
+demand it means we probably have a
+highly elastic demand curve and even
+
+ align:start position:0%
+highly elastic demand curve and even
+ 
+
+ align:start position:0%
+highly elastic demand curve and even
+with a monopoly we can't make any money
+
+ align:start position:0%
+with a monopoly we can't make any money
+ 
+
+ align:start position:0%
+with a monopoly we can't make any money
+so close good substitutes erode
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+profits I'm a w please have at it I'm a
+
+ align:start position:0%
+profits I'm a w please have at it I'm a
+ 
+
+ align:start position:0%
+profits I'm a w please have at it I'm a
+wax paper manufacturer there's only one
+
+ align:start position:0%
+wax paper manufacturer there's only one
+ 
+
+ align:start position:0%
+wax paper manufacturer there's only one
+of me but anybody in his kid sister can
+
+ align:start position:0%
+of me but anybody in his kid sister can
+ 
+
+ align:start position:0%
+of me but anybody in his kid sister can
+make wax paper that's not quite right
+
+ align:start position:0%
+make wax paper that's not quite right
+ 
+
+ align:start position:0%
+make wax paper that's not quite right
+and it could be his kid brother too
+
+ align:start position:0%
+and it could be his kid brother too
+ 
+
+ align:start position:0%
+and it could be his kid brother too
+don't mean to be sexist but but if it's
+
+ align:start position:0%
+don't mean to be sexist but but if it's
+ 
+
+ align:start position:0%
+don't mean to be sexist but but if it's
+really easy for competitors to come in
+
+ align:start position:0%
+really easy for competitors to come in
+ 
+
+ align:start position:0%
+really easy for competitors to come in
+if anybody's making any money nobody's
+
+ align:start position:0%
+if anybody's making any money nobody's
+ 
+
+ align:start position:0%
+if anybody's making any money nobody's
+going to can sustain it can sustain High
+
+ align:start position:0%
+going to can sustain it can sustain High
+ 
+
+ align:start position:0%
+going to can sustain it can sustain High
+profits so you look at entry when you do
+
+ align:start position:0%
+profits so you look at entry when you do
+ 
+
+ align:start position:0%
+profits so you look at entry when you do
+an industry analysis is it easy for
+
+ align:start position:0%
+an industry analysis is it easy for
+ 
+
+ align:start position:0%
+an industry analysis is it easy for
+Outsiders to come in what are the
+
+ align:start position:0%
+Outsiders to come in what are the
+ 
+
+ align:start position:0%
+Outsiders to come in what are the
+obstacles do you need specialized n know
+
+ align:start position:0%
+obstacles do you need specialized n know
+ 
+
+ align:start position:0%
+obstacles do you need specialized n know
+do you need huge capital what's what are
+
+ align:start position:0%
+do you need huge capital what's what are
+ 
+
+ align:start position:0%
+do you need huge capital what's what are
+the problems if there aren't any obvious
+
+ align:start position:0%
+the problems if there aren't any obvious
+ 
+
+ align:start position:0%
+the problems if there aren't any obvious
+barriers we're making Furniture in North
+
+ align:start position:0%
+barriers we're making Furniture in North
+ 
+
+ align:start position:0%
+barriers we're making Furniture in North
+Carolina what do you need to make
+
+ align:start position:0%
+Carolina what do you need to make
+ 
+
+ align:start position:0%
+Carolina what do you need to make
+furniture in North Carolina you need to
+
+ align:start position:0%
+furniture in North Carolina you need to
+ 
+
+ align:start position:0%
+furniture in North Carolina you need to
+hire good carpenters and get a supply of
+
+ align:start position:0%
+hire good carpenters and get a supply of
+ 
+
+ align:start position:0%
+hire good carpenters and get a supply of
+wood and have some design skill are
+
+ align:start position:0%
+wood and have some design skill are
+ 
+
+ align:start position:0%
+wood and have some design skill are
+those High barriers to entry probably
+
+ align:start position:0%
+those High barriers to entry probably
+ 
+
+ align:start position:0%
+those High barriers to entry probably
+not so would you expect even if they're
+
+ align:start position:0%
+not so would you expect even if they're
+ 
+
+ align:start position:0%
+not so would you expect even if they're
+only a small number of furniture
+
+ align:start position:0%
+only a small number of furniture
+ 
+
+ align:start position:0%
+only a small number of furniture
+manufacturers would you expect them to
+
+ align:start position:0%
+manufacturers would you expect them to
+ 
+
+ align:start position:0%
+manufacturers would you expect them to
+make a lot of money probably not
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+suppliers um my favorite example here
+
+ align:start position:0%
+suppliers um my favorite example here
+ 
+
+ align:start position:0%
+suppliers um my favorite example here
+really is
+
+ align:start position:0%
+really is
+ 
+
+ align:start position:0%
+really is
+Airlines um because one of the things
+
+ align:start position:0%
+Airlines um because one of the things
+ 
+
+ align:start position:0%
+Airlines um because one of the things
+that characterized Airlines particularly
+
+ align:start position:0%
+that characterized Airlines particularly
+ 
+
+ align:start position:0%
+that characterized Airlines particularly
+under regulation is very strong
+
+ align:start position:0%
+under regulation is very strong
+ 
+
+ align:start position:0%
+under regulation is very strong
+unions so while the airlines didn't make
+
+ align:start position:0%
+unions so while the airlines didn't make
+ 
+
+ align:start position:0%
+unions so while the airlines didn't make
+any
+
+ align:start position:0%
+any
+ 
+
+ align:start position:0%
+any
+money Airline employees
+
+ align:start position:0%
+money Airline employees
+ 
+
+ align:start position:0%
+money Airline employees
+did Pilots earn very high salaries for
+
+ align:start position:0%
+did Pilots earn very high salaries for
+ 
+
+ align:start position:0%
+did Pilots earn very high salaries for
+relatively little work flight attendant
+
+ align:start position:0%
+relatively little work flight attendant
+ 
+
+ align:start position:0%
+relatively little work flight attendant
+is this is again in the days of
+
+ align:start position:0%
+is this is again in the days of
+ 
+
+ align:start position:0%
+is this is again in the days of
+Regulation flight attendants earned very
+
+ align:start position:0%
+Regulation flight attendants earned very
+ 
+
+ align:start position:0%
+Regulation flight attendants earned very
+high salaries The Regulators pushed
+
+ align:start position:0%
+high salaries The Regulators pushed
+ 
+
+ align:start position:0%
+high salaries The Regulators pushed
+prices up and most of the rent most of
+
+ align:start position:0%
+prices up and most of the rent most of
+ 
+
+ align:start position:0%
+prices up and most of the rent most of
+the profit went down here to the
+
+ align:start position:0%
+the profit went down here to the
+ 
+
+ align:start position:0%
+the profit went down here to the
+unionized suppliers because there was
+
+ align:start position:0%
+unionized suppliers because there was
+ 
+
+ align:start position:0%
+unionized suppliers because there was
+pretty heavy competition up here so you
+
+ align:start position:0%
+pretty heavy competition up here so you
+ 
+
+ align:start position:0%
+pretty heavy competition up here so you
+had competition here the ability here to
+
+ align:start position:0%
+had competition here the ability here to
+ 
+
+ align:start position:0%
+had competition here the ability here to
+earn rent you see this in a lot of
+
+ align:start position:0%
+earn rent you see this in a lot of
+ 
+
+ align:start position:0%
+earn rent you see this in a lot of
+Industries where there's relatively
+
+ align:start position:0%
+Industries where there's relatively
+ 
+
+ align:start position:0%
+Industries where there's relatively
+little competition in the industry
+
+ align:start position:0%
+little competition in the industry
+ 
+
+ align:start position:0%
+little competition in the industry
+competition within the industry Subs
+
+ align:start position:0%
+competition within the industry Subs
+ 
+
+ align:start position:0%
+competition within the industry Subs
+inutes buyers entrance
+
+ align:start position:0%
+inutes buyers entrance
+ 
+
+ align:start position:0%
+inutes buyers entrance
+suppliers is injection molding a good
+
+ align:start position:0%
+suppliers is injection molding a good
+ 
+
+ align:start position:0%
+suppliers is injection molding a good
+business to be in in 1995 Julian why
+
+ align:start position:0%
+business to be in in 1995 Julian why
+ 
+
+ align:start position:0%
+business to be in in 1995 Julian why
+not because China does it cheaper well
+
+ align:start position:0%
+not because China does it cheaper well
+ 
+
+ align:start position:0%
+not because China does it cheaper well
+not in 1995 they didn't uh we're talking
+
+ align:start position:0%
+not in 1995 they didn't uh we're talking
+ 
+
+ align:start position:0%
+not in 1995 they didn't uh we're talking
+let's stay within the let's stay within
+
+ align:start position:0%
+let's stay within the let's stay within
+ 
+
+ align:start position:0%
+let's stay within the let's stay within
+the bounds of the case if we can um
+
+ align:start position:0%
+the bounds of the case if we can um
+ 
+
+ align:start position:0%
+the bounds of the case if we can um
+anybody else Charlotte um no because at
+
+ align:start position:0%
+anybody else Charlotte um no because at
+ 
+
+ align:start position:0%
+anybody else Charlotte um no because at
+that point competitors are figuring out
+
+ align:start position:0%
+that point competitors are figuring out
+ 
+
+ align:start position:0%
+that point competitors are figuring out
+ways to do things cheaper and to charge
+
+ align:start position:0%
+ways to do things cheaper and to charge
+ 
+
+ align:start position:0%
+ways to do things cheaper and to charge
+less money and then also because the
+
+ align:start position:0%
+less money and then also because the
+ 
+
+ align:start position:0%
+less money and then also because the
+buyers were these people using the
+
+ align:start position:0%
+buyers were these people using the
+ 
+
+ align:start position:0%
+buyers were these people using the
+machines that they were making and the
+
+ align:start position:0%
+machines that they were making and the
+ 
+
+ align:start position:0%
+machines that they were making and the
+the uh materials they needed were in
+
+ align:start position:0%
+the uh materials they needed were in
+ 
+
+ align:start position:0%
+the uh materials they needed were in
+high demand so the prices were going up
+
+ align:start position:0%
+high demand so the prices were going up
+ 
+
+ align:start position:0%
+high demand so the prices were going up
+that's the that's the resin we we'll
+
+ align:start position:0%
+that's the that's the resin we we'll
+ 
+
+ align:start position:0%
+that's the that's the resin we we'll
+come to that but this thing you're
+
+ align:start position:0%
+come to that but this thing you're
+ 
+
+ align:start position:0%
+come to that but this thing you're
+you're saying there just a lot going on
+
+ align:start position:0%
+you're saying there just a lot going on
+ 
+
+ align:start position:0%
+you're saying there just a lot going on
+here within the industry very intense
+
+ align:start position:0%
+here within the industry very intense
+ 
+
+ align:start position:0%
+here within the industry very intense
+competition uh what's interesting about
+
+ align:start position:0%
+competition uh what's interesting about
+ 
+
+ align:start position:0%
+competition uh what's interesting about
+this is that's right
+
+ align:start position:0%
+this is that's right
+ 
+
+ align:start position:0%
+this is that's right
+uh it doesn't look like most of that
+
+ align:start position:0%
+uh it doesn't look like most of that
+ 
+
+ align:start position:0%
+uh it doesn't look like most of that
+industry is very attractive even though
+
+ align:start position:0%
+industry is very attractive even though
+ 
+
+ align:start position:0%
+industry is very attractive even though
+it's growing like
+
+ align:start position:0%
+it's growing like
+ 
+
+ align:start position:0%
+it's growing like
+crazy the industry is growing like crazy
+
+ align:start position:0%
+crazy the industry is growing like crazy
+ 
+
+ align:start position:0%
+crazy the industry is growing like crazy
+it's a great example of everybody having
+
+ align:start position:0%
+it's a great example of everybody having
+ 
+
+ align:start position:0%
+it's a great example of everybody having
+to run fast to stay in the same place
+
+ align:start position:0%
+to run fast to stay in the same place
+ 
+
+ align:start position:0%
+to run fast to stay in the same place
+right because there's a lot of
+
+ align:start position:0%
+right because there's a lot of
+ 
+
+ align:start position:0%
+right because there's a lot of
+innovation as Charlotte says and if
+
+ align:start position:0%
+innovation as Charlotte says and if
+ 
+
+ align:start position:0%
+innovation as Charlotte says and if
+you're not doing it you
+
+ align:start position:0%
+you're not doing it you
+ 
+
+ align:start position:0%
+you're not doing it you
+lose so industries that look like that
+
+ align:start position:0%
+lose so industries that look like that
+ 
+
+ align:start position:0%
+lose so industries that look like that
+are not uncommon you think about the
+
+ align:start position:0%
+are not uncommon you think about the
+ 
+
+ align:start position:0%
+are not uncommon you think about the
+early day again Warren Buffett the early
+
+ align:start position:0%
+early day again Warren Buffett the early
+ 
+
+ align:start position:0%
+early day again Warren Buffett the early
+days of
+
+ align:start position:0%
+days of
+ 
+
+ align:start position:0%
+days of
+automobiles there were hundreds of
+
+ align:start position:0%
+automobiles there were hundreds of
+ 
+
+ align:start position:0%
+automobiles there were hundreds of
+people
+
+ align:start position:0%
+people
+ 
+
+ align:start position:0%
+people
+Automobiles and they were all making
+
+ align:start position:0%
+Automobiles and they were all making
+ 
+
+ align:start position:0%
+Automobiles and they were all making
+great progress and innovating like crazy
+
+ align:start position:0%
+great progress and innovating like crazy
+ 
+
+ align:start position:0%
+great progress and innovating like crazy
+and automobile sales were taking off
+
+ align:start position:0%
+and automobile sales were taking off
+ 
+
+ align:start position:0%
+and automobile sales were taking off
+like a rocket and most of them
+
+ align:start position:0%
+like a rocket and most of them
+ 
+
+ align:start position:0%
+like a rocket and most of them
+died because they were offering more or
+
+ align:start position:0%
+died because they were offering more or
+ 
+
+ align:start position:0%
+died because they were offering more or
+less the same kind of product doing more
+
+ align:start position:0%
+less the same kind of product doing more
+ 
+
+ align:start position:0%
+less the same kind of product doing more
+or less the same things as everybody
+
+ align:start position:0%
+or less the same things as everybody
+ 
+
+ align:start position:0%
+or less the same things as everybody
+else and had to run to keep in place
+
+ align:start position:0%
+else and had to run to keep in place
+ 
+
+ align:start position:0%
+else and had to run to keep in place
+so I think in terms of we worry a little
+
+ align:start position:0%
+so I think in terms of we worry a little
+ 
+
+ align:start position:0%
+so I think in terms of we worry a little
+bit about we hear a little bit about
+
+ align:start position:0%
+bit about we hear a little bit about
+ 
+
+ align:start position:0%
+bit about we hear a little bit about
+buyers only a little bit one of the big
+
+ align:start position:0%
+buyers only a little bit one of the big
+ 
+
+ align:start position:0%
+buyers only a little bit one of the big
+uh bottl makers is mentioned as a as a
+
+ align:start position:0%
+uh bottl makers is mentioned as a as a
+ 
+
+ align:start position:0%
+uh bottl makers is mentioned as a as a
+powerful buyer we don't know much about
+
+ align:start position:0%
+powerful buyer we don't know much about
+ 
+
+ align:start position:0%
+powerful buyer we don't know much about
+that substitutes we seem to be pretty
+
+ align:start position:0%
+that substitutes we seem to be pretty
+ 
+
+ align:start position:0%
+that substitutes we seem to be pretty
+good this looks like an industry people
+
+ align:start position:0%
+good this looks like an industry people
+ 
+
+ align:start position:0%
+good this looks like an industry people
+can enter this does not look like a high
+
+ align:start position:0%
+can enter this does not look like a high
+ 
+
+ align:start position:0%
+can enter this does not look like a high
+barrier industry we're not told much
+
+ align:start position:0%
+barrier industry we're not told much
+ 
+
+ align:start position:0%
+barrier industry we're not told much
+about that but we don't see much of a
+
+ align:start position:0%
+about that but we don't see much of a
+ 
+
+ align:start position:0%
+about that but we don't see much of a
+problem there there seem to be lots of
+
+ align:start position:0%
+problem there there seem to be lots of
+ 
+
+ align:start position:0%
+problem there there seem to be lots of
+mold makers and lots of suppliers of
+
+ align:start position:0%
+mold makers and lots of suppliers of
+ 
+
+ align:start position:0%
+mold makers and lots of suppliers of
+components so we don't seem to have a
+
+ align:start position:0%
+components so we don't seem to have a
+ 
+
+ align:start position:0%
+components so we don't seem to have a
+problem here the real problem in this
+
+ align:start position:0%
+problem here the real problem in this
+ 
+
+ align:start position:0%
+problem here the real problem in this
+industry is here where there's just very
+
+ align:start position:0%
+industry is here where there's just very
+ 
+
+ align:start position:0%
+industry is here where there's just very
+intense competition
+
+ align:start position:0%
+intense competition
+ 
+
+ align:start position:0%
+intense competition
+I even though there's high growth even
+
+ align:start position:0%
+I even though there's high growth even
+ 
+
+ align:start position:0%
+I even though there's high growth even
+though there's Innovation everybody's
+
+ align:start position:0%
+though there's Innovation everybody's
+ 
+
+ align:start position:0%
+though there's Innovation everybody's
+innovating everybody's moving and
+
+ align:start position:0%
+innovating everybody's moving and
+ 
+
+ align:start position:0%
+innovating everybody's moving and
+everybody's running very fast to stay in
+
+ align:start position:0%
+everybody's running very fast to stay in
+ 
+
+ align:start position:0%
+everybody's running very fast to stay in
+the same
+
+ align:start position:0%
+the same
+ 
+
+ align:start position:0%
+the same
+place so how do you beat this well let
+
+ align:start position:0%
+place so how do you beat this well let
+ 
+
+ align:start position:0%
+place so how do you beat this well let
+me talk generically and then we'll then
+
+ align:start position:0%
+me talk generically and then we'll then
+ 
+
+ align:start position:0%
+me talk generically and then we'll then
+we'll go to
+
+ align:start position:0%
+we'll go to
+ 
+
+ align:start position:0%
+we'll go to
+husky so
+
+ align:start position:0%
+husky so
+ 
+
+ align:start position:0%
+husky so
+generically
+
+ align:start position:0%
+generically
+ 
+
+ align:start position:0%
+generically
+um stepping way back you've got to both
+
+ align:start position:0%
+um stepping way back you've got to both
+ 
+
+ align:start position:0%
+um stepping way back you've got to both
+create value and and capture it so the
+
+ align:start position:0%
+create value and and capture it so the
+ 
+
+ align:start position:0%
+create value and and capture it so the
+if you think
+
+ align:start position:0%
+if you think
+ 
+
+ align:start position:0%
+if you think
+about oh
+
+ align:start position:0%
+about oh
+ 
+
+ align:start position:0%
+about oh
+suppliers what would you get for
+
+ align:start position:0%
+suppliers what would you get for
+ 
+
+ align:start position:0%
+suppliers what would you get for
+airplanes and aircraft Personnel uh uh
+
+ align:start position:0%
+airplanes and aircraft Personnel uh uh
+ 
+
+ align:start position:0%
+airplanes and aircraft Personnel uh uh
+sorry Airline
+
+ align:start position:0%
+sorry Airline
+ 
+
+ align:start position:0%
+sorry Airline
+Personnel how what would you have to pay
+
+ align:start position:0%
+Personnel how what would you have to pay
+ 
+
+ align:start position:0%
+Personnel how what would you have to pay
+to get a pilot to fly as opposed to what
+
+ align:start position:0%
+to get a pilot to fly as opposed to what
+ 
+
+ align:start position:0%
+to get a pilot to fly as opposed to what
+you do pay to get a pilot to fly again
+
+ align:start position:0%
+you do pay to get a pilot to fly again
+ 
+
+ align:start position:0%
+you do pay to get a pilot to fly again
+in the in the great old days of of
+
+ align:start position:0%
+in the in the great old days of of
+ 
+
+ align:start position:0%
+in the in the great old days of of
+limited competition there's there may be
+
+ align:start position:0%
+limited competition there's there may be
+ 
+
+ align:start position:0%
+limited competition there's there may be
+there may well be a gap between the
+
+ align:start position:0%
+there may well be a gap between the
+ 
+
+ align:start position:0%
+there may well be a gap between the
+suppliers opportunity cost what else
+
+ align:start position:0%
+suppliers opportunity cost what else
+ 
+
+ align:start position:0%
+suppliers opportunity cost what else
+could they do with their capital labor
+
+ align:start position:0%
+could they do with their capital labor
+ 
+
+ align:start position:0%
+could they do with their capital labor
+and what they sell for that's captured
+
+ align:start position:0%
+and what they sell for that's captured
+ 
+
+ align:start position:0%
+and what they sell for that's captured
+by the
+
+ align:start position:0%
+by the
+ 
+
+ align:start position:0%
+by the
+supplier there better be some gap
+
+ align:start position:0%
+supplier there better be some gap
+ 
+
+ align:start position:0%
+supplier there better be some gap
+between what buyers are willingness to
+
+ align:start position:0%
+between what buyers are willingness to
+ 
+
+ align:start position:0%
+between what buyers are willingness to
+pay and buyers are willing to
+
+ align:start position:0%
+pay and buyers are willing to
+ 
+
+ align:start position:0%
+pay and buyers are willing to
+pay uh and what they actually
+
+ align:start position:0%
+pay uh and what they actually
+ 
+
+ align:start position:0%
+pay uh and what they actually
+pay and the difference is what you get
+
+ align:start position:0%
+pay and the difference is what you get
+ 
+
+ align:start position:0%
+pay and the difference is what you get
+to take home the difference between what
+
+ align:start position:0%
+to take home the difference between what
+ 
+
+ align:start position:0%
+to take home the difference between what
+it actually costs you and what you can
+
+ align:start position:0%
+it actually costs you and what you can
+ 
+
+ align:start position:0%
+it actually costs you and what you can
+sell that this is like yeah this is
+
+ align:start position:0%
+sell that this is like yeah this is
+ 
+
+ align:start position:0%
+sell that this is like yeah this is
+pretty straightforward and pretty
+
+ align:start position:0%
+pretty straightforward and pretty
+ 
+
+ align:start position:0%
+pretty straightforward and pretty
+obvious but you really do need to think
+
+ align:start position:0%
+obvious but you really do need to think
+ 
+
+ align:start position:0%
+obvious but you really do need to think
+through and I love the animation you do
+
+ align:start position:0%
+through and I love the animation you do
+ 
+
+ align:start position:0%
+through and I love the animation you do
+need to think
+
+ align:start position:0%
+need to think
+ 
+
+ align:start position:0%
+need to think
+through who captures it if you go to the
+
+ align:start position:0%
+through who captures it if you go to the
+ 
+
+ align:start position:0%
+through who captures it if you go to the
+airlines there's
+
+ align:start position:0%
+airlines there's
+ 
+
+ align:start position:0%
+airlines there's
+enormous value created by the airline
+
+ align:start position:0%
+enormous value created by the airline
+ 
+
+ align:start position:0%
+enormous value created by the airline
+industry historically imagine it going
+
+ align:start position:0%
+industry historically imagine it going
+ 
+
+ align:start position:0%
+industry historically imagine it going
+away it's not captured by and large by
+
+ align:start position:0%
+away it's not captured by and large by
+ 
+
+ align:start position:0%
+away it's not captured by and large by
+the airline
+
+ align:start position:0%
+the airline
+ 
+
+ align:start position:0%
+the airline
+companies where does it go well with the
+
+ align:start position:0%
+companies where does it go well with the
+ 
+
+ align:start position:0%
+companies where does it go well with the
+decline of Airline unions less of it
+
+ align:start position:0%
+decline of Airline unions less of it
+ 
+
+ align:start position:0%
+decline of Airline unions less of it
+gets captured by
+
+ align:start position:0%
+gets captured by
+ 
+
+ align:start position:0%
+gets captured by
+suppliers and more of it's captured by
+
+ align:start position:0%
+suppliers and more of it's captured by
+ 
+
+ align:start position:0%
+suppliers and more of it's captured by
+us right if you think about the
+
+ align:start position:0%
+us right if you think about the
+ 
+
+ align:start position:0%
+us right if you think about the
+alternative way
+
+ align:start position:0%
+alternative way
+ 
+
+ align:start position:0%
+alternative way
+of I was in Florida last week and
+
+ align:start position:0%
+of I was in Florida last week and
+ 
+
+ align:start position:0%
+of I was in Florida last week and
+driving to Florida which I have done is
+
+ align:start position:0%
+driving to Florida which I have done is
+ 
+
+ align:start position:0%
+driving to Florida which I have done is
+not much fun so I'd be willing I would
+
+ align:start position:0%
+not much fun so I'd be willing I would
+ 
+
+ align:start position:0%
+not much fun so I'd be willing I would
+have been willing to spend a lot more
+
+ align:start position:0%
+have been willing to spend a lot more
+ 
+
+ align:start position:0%
+have been willing to spend a lot more
+than it cost me uh to fly I I got a huge
+
+ align:start position:0%
+than it cost me uh to fly I I got a huge
+ 
+
+ align:start position:0%
+than it cost me uh to fly I I got a huge
+Surplus um I don't have the impression
+
+ align:start position:0%
+Surplus um I don't have the impression
+ 
+
+ align:start position:0%
+Surplus um I don't have the impression
+that the folks supplying the airline
+
+ align:start position:0%
+that the folks supplying the airline
+ 
+
+ align:start position:0%
+that the folks supplying the airline
+were getting a lot of money and I know
+
+ align:start position:0%
+were getting a lot of money and I know
+ 
+
+ align:start position:0%
+were getting a lot of money and I know
+the airline wasn't getting much in terms
+
+ align:start position:0%
+the airline wasn't getting much in terms
+ 
+
+ align:start position:0%
+the airline wasn't getting much in terms
+of captured Surplus so the basic
+
+ align:start position:0%
+of captured Surplus so the basic
+ 
+
+ align:start position:0%
+of captured Surplus so the basic
+strategic question is in any kind of
+
+ align:start position:0%
+strategic question is in any kind of
+ 
+
+ align:start position:0%
+strategic question is in any kind of
+industry attractive or
+
+ align:start position:0%
+industry attractive or
+ 
+
+ align:start position:0%
+industry attractive or
+unattractive can you do
+
+ align:start position:0%
+unattractive can you do
+ 
+
+ align:start position:0%
+unattractive can you do
+this so where Porter is pointing and
+
+ align:start position:0%
+this so where Porter is pointing and
+ 
+
+ align:start position:0%
+this so where Porter is pointing and
+where this case points
+
+ align:start position:0%
+where this case points
+ 
+
+ align:start position:0%
+where this case points
+us is to ways to not do the same thing
+
+ align:start position:0%
+us is to ways to not do the same thing
+ 
+
+ align:start position:0%
+us is to ways to not do the same thing
+your competitors are
+
+ align:start position:0%
+your competitors are
+ 
+
+ align:start position:0%
+your competitors are
+doing what can we do
+
+ align:start position:0%
+doing what can we do
+ 
+
+ align:start position:0%
+doing what can we do
+differently well the first basic this is
+
+ align:start position:0%
+differently well the first basic this is
+ 
+
+ align:start position:0%
+differently well the first basic this is
+sort of the Southwest
+
+ align:start position:0%
+sort of the Southwest
+ 
+
+ align:start position:0%
+sort of the Southwest
+strategy this says we are going to drive
+
+ align:start position:0%
+strategy this says we are going to drive
+ 
+
+ align:start position:0%
+strategy this says we are going to drive
+down costs
+
+ align:start position:0%
+down costs
+ 
+
+ align:start position:0%
+down costs
+and in a way that's hard to imitate
+
+ align:start position:0%
+and in a way that's hard to imitate
+ 
+
+ align:start position:0%
+and in a way that's hard to imitate
+we'll talk about what makes it hard to
+
+ align:start position:0%
+we'll talk about what makes it hard to
+ 
+
+ align:start position:0%
+we'll talk about what makes it hard to
+imitate we're going to drive down costs
+
+ align:start position:0%
+imitate we're going to drive down costs
+ 
+
+ align:start position:0%
+imitate we're going to drive down costs
+and maybe we Supply a somewhat different
+
+ align:start position:0%
+and maybe we Supply a somewhat different
+ 
+
+ align:start position:0%
+and maybe we Supply a somewhat different
+product southwest's product is not very
+
+ align:start position:0%
+product southwest's product is not very
+ 
+
+ align:start position:0%
+product southwest's product is not very
+useful for somebody who not very
+
+ align:start position:0%
+useful for somebody who not very
+ 
+
+ align:start position:0%
+useful for somebody who not very
+interesting to somebody who always flies
+
+ align:start position:0%
+interesting to somebody who always flies
+ 
+
+ align:start position:0%
+interesting to somebody who always flies
+first class and cares about it they
+
+ align:start position:0%
+first class and cares about it they
+ 
+
+ align:start position:0%
+first class and cares about it they
+don't do first class they've written
+
+ align:start position:0%
+don't do first class they've written
+ 
+
+ align:start position:0%
+don't do first class they've written
+that off they've written off they don't
+
+ align:start position:0%
+that off they've written off they don't
+ 
+
+ align:start position:0%
+that off they've written off they don't
+do frequent flyer I don't think maybe
+
+ align:start position:0%
+do frequent flyer I don't think maybe
+ 
+
+ align:start position:0%
+do frequent flyer I don't think maybe
+they do but but for a whole set of
+
+ align:start position:0%
+they do but but for a whole set of
+ 
+
+ align:start position:0%
+they do but but for a whole set of
+business Travelers they're not that
+
+ align:start position:0%
+business Travelers they're not that
+ 
+
+ align:start position:0%
+business Travelers they're not that
+attractive
+
+ align:start position:0%
+attractive
+ 
+
+ align:start position:0%
+attractive
+they're cheap yeah but if somebody else
+
+ align:start position:0%
+they're cheap yeah but if somebody else
+ 
+
+ align:start position:0%
+they're cheap yeah but if somebody else
+is paying my airfare that's not too
+
+ align:start position:0%
+is paying my airfare that's not too
+ 
+
+ align:start position:0%
+is paying my airfare that's not too
+attractive they're not convenient
+
+ align:start position:0%
+attractive they're not convenient
+ 
+
+ align:start position:0%
+attractive they're not convenient
+because I can't book online think about
+
+ align:start position:0%
+because I can't book online think about
+ 
+
+ align:start position:0%
+because I can't book online think about
+my own travel usually somebody else is
+
+ align:start position:0%
+my own travel usually somebody else is
+ 
+
+ align:start position:0%
+my own travel usually somebody else is
+paying and I book online for Simplicity
+
+ align:start position:0%
+paying and I book online for Simplicity
+ 
+
+ align:start position:0%
+paying and I book online for Simplicity
+I never fly
+
+ align:start position:0%
+I never fly
+ 
+
+ align:start position:0%
+I never fly
+Southwest because the fair difference
+
+ align:start position:0%
+Southwest because the fair difference
+ 
+
+ align:start position:0%
+Southwest because the fair difference
+doesn't bother the people who are paying
+
+ align:start position:0%
+doesn't bother the people who are paying
+ 
+
+ align:start position:0%
+doesn't bother the people who are paying
+my airfare and online booking is so
+
+ align:start position:0%
+my airfare and online booking is so
+ 
+
+ align:start position:0%
+my airfare and online booking is so
+enormously convenient that I just do it
+
+ align:start position:0%
+enormously convenient that I just do it
+ 
+
+ align:start position:0%
+enormously convenient that I just do it
+so I'm not in their I'm not in the set
+
+ align:start position:0%
+so I'm not in their I'm not in the set
+ 
+
+ align:start position:0%
+so I'm not in their I'm not in the set
+of consumers they're aiming at so what
+
+ align:start position:0%
+of consumers they're aiming at so what
+ 
+
+ align:start position:0%
+of consumers they're aiming at so what
+there are enough of them there are
+
+ align:start position:0%
+there are enough of them there are
+ 
+
+ align:start position:0%
+there are enough of them there are
+enough people and enough travel
+
+ align:start position:0%
+enough people and enough travel
+ 
+
+ align:start position:0%
+enough people and enough travel
+occasions and I could imagine occasions
+
+ align:start position:0%
+occasions and I could imagine occasions
+ 
+
+ align:start position:0%
+occasions and I could imagine occasions
+when I would I would check Southwest
+
+ align:start position:0%
+when I would I would check Southwest
+ 
+
+ align:start position:0%
+when I would I would check Southwest
+just to see if they're
+
+ align:start position:0%
+just to see if they're
+ 
+
+ align:start position:0%
+just to see if they're
+cheaper that's a that's a strategy the
+
+ align:start position:0%
+cheaper that's a that's a strategy the
+ 
+
+ align:start position:0%
+cheaper that's a that's a strategy the
+the issue
+
+ align:start position:0%
+the issue
+ 
+
+ align:start position:0%
+the issue
+there is what makes it hard to
+
+ align:start position:0%
+there is what makes it hard to
+ 
+
+ align:start position:0%
+there is what makes it hard to
+imitate what makes it hard to imitate as
+
+ align:start position:0%
+imitate what makes it hard to imitate as
+ 
+
+ align:start position:0%
+imitate what makes it hard to imitate as
+Charlotte pointed out in the injection
+
+ align:start position:0%
+Charlotte pointed out in the injection
+ 
+
+ align:start position:0%
+Charlotte pointed out in the injection
+molding business everybody's everybody's
+
+ align:start position:0%
+molding business everybody's everybody's
+ 
+
+ align:start position:0%
+molding business everybody's everybody's
+innovating so and in the airline
+
+ align:start position:0%
+innovating so and in the airline
+ 
+
+ align:start position:0%
+innovating so and in the airline
+business business everybody does
+
+ align:start position:0%
+business business everybody does
+ 
+
+ align:start position:0%
+business business everybody does
+electronic reservations and everybody
+
+ align:start position:0%
+electronic reservations and everybody
+ 
+
+ align:start position:0%
+electronic reservations and everybody
+does this and everybody does that lots
+
+ align:start position:0%
+does this and everybody does that lots
+ 
+
+ align:start position:0%
+does this and everybody does that lots
+of
+
+ align:start position:0%
+of
+ 
+
+ align:start position:0%
+of
+innovation everybody driving down costs
+
+ align:start position:0%
+innovation everybody driving down costs
+ 
+
+ align:start position:0%
+innovation everybody driving down costs
+more fuel efficient engines no barriers
+
+ align:start position:0%
+more fuel efficient engines no barriers
+ 
+
+ align:start position:0%
+more fuel efficient engines no barriers
+to
+
+ align:start position:0%
+to
+ 
+
+ align:start position:0%
+to
+imitation United can copy what American
+
+ align:start position:0%
+imitation United can copy what American
+ 
+
+ align:start position:0%
+imitation United can copy what American
+does American can copy what United
+
+ align:start position:0%
+does American can copy what United
+ 
+
+ align:start position:0%
+does American can copy what United
+does there are seminars on industry best
+
+ align:start position:0%
+does there are seminars on industry best
+ 
+
+ align:start position:0%
+does there are seminars on industry best
+practice everybody does industry best
+
+ align:start position:0%
+practice everybody does industry best
+ 
+
+ align:start position:0%
+practice everybody does industry best
+practice you don't make any money doing
+
+ align:start position:0%
+practice you don't make any money doing
+ 
+
+ align:start position:0%
+practice you don't make any money doing
+industry best practice you may avoid
+
+ align:start position:0%
+industry best practice you may avoid
+ 
+
+ align:start position:0%
+industry best practice you may avoid
+losing money so that's Strate
+
+ align:start position:0%
+losing money so that's Strate
+ 
+
+ align:start position:0%
+losing money so that's Strate
+one can I somehow get low costs and I
+
+ align:start position:0%
+one can I somehow get low costs and I
+ 
+
+ align:start position:0%
+one can I somehow get low costs and I
+highlight this some
+
+ align:start position:0%
+highlight this some
+ 
+
+ align:start position:0%
+highlight this some
+consumers because Southwest and Ikea are
+
+ align:start position:0%
+consumers because Southwest and Ikea are
+ 
+
+ align:start position:0%
+consumers because Southwest and Ikea are
+nice examples of picking a piece of the
+
+ align:start position:0%
+nice examples of picking a piece of the
+ 
+
+ align:start position:0%
+nice examples of picking a piece of the
+market which a lowcost strategy makes
+
+ align:start position:0%
+market which a lowcost strategy makes
+ 
+
+ align:start position:0%
+market which a lowcost strategy makes
+sense not everybody goes to
+
+ align:start position:0%
+sense not everybody goes to
+ 
+
+ align:start position:0%
+sense not everybody goes to
+Ikea I've never been in an Ikea as it
+
+ align:start position:0%
+Ikea I've never been in an Ikea as it
+ 
+
+ align:start position:0%
+Ikea I've never been in an Ikea as it
+happens um but but uh lots of people do
+
+ align:start position:0%
+happens um but but uh lots of people do
+ 
+
+ align:start position:0%
+happens um but but uh lots of people do
+and that's enough to make them a lot of
+
+ align:start position:0%
+and that's enough to make them a lot of
+ 
+
+ align:start position:0%
+and that's enough to make them a lot of
+money the other strategy not too
+
+ align:start position:0%
+money the other strategy not too
+ 
+
+ align:start position:0%
+money the other strategy not too
+surprisingly is to go the other
+
+ align:start position:0%
+surprisingly is to go the other
+ 
+
+ align:start position:0%
+surprisingly is to go the other
+direction is to find a way to increase
+
+ align:start position:0%
+direction is to find a way to increase
+ 
+
+ align:start position:0%
+direction is to find a way to increase
+perceived quality willingness to pay for
+
+ align:start position:0%
+perceived quality willingness to pay for
+ 
+
+ align:start position:0%
+perceived quality willingness to pay for
+some
+
+ align:start position:0%
+some
+ 
+
+ align:start position:0%
+some
+buyers to justify higher
+
+ align:start position:0%
+buyers to justify higher
+ 
+
+ align:start position:0%
+buyers to justify higher
+prices what can we do to justify higher
+
+ align:start position:0%
+prices what can we do to justify higher
+ 
+
+ align:start position:0%
+prices what can we do to justify higher
+prices and
+
+ align:start position:0%
+prices and
+ 
+
+ align:start position:0%
+prices and
+again they're examples right
+
+ align:start position:0%
+again they're examples right
+ 
+
+ align:start position:0%
+again they're examples right
+Mercedes-Benz is a high quality they
+
+ align:start position:0%
+Mercedes-Benz is a high quality they
+ 
+
+ align:start position:0%
+Mercedes-Benz is a high quality they
+don't do the same thing that everybody
+
+ align:start position:0%
+don't do the same thing that everybody
+ 
+
+ align:start position:0%
+don't do the same thing that everybody
+else does not the same kind of car it
+
+ align:start position:0%
+else does not the same kind of car it
+ 
+
+ align:start position:0%
+else does not the same kind of car it
+costs more it absolutely costs more this
+
+ align:start position:0%
+costs more it absolutely costs more this
+ 
+
+ align:start position:0%
+costs more it absolutely costs more this
+in this example the costs are the same
+
+ align:start position:0%
+in this example the costs are the same
+ 
+
+ align:start position:0%
+in this example the costs are the same
+but you know you could still make a lot
+
+ align:start position:0%
+but you know you could still make a lot
+ 
+
+ align:start position:0%
+but you know you could still make a lot
+of money if those costs are a little
+
+ align:start position:0%
+of money if those costs are a little
+ 
+
+ align:start position:0%
+of money if those costs are a little
+higher as long
+
+ align:start position:0%
+higher as long
+ 
+
+ align:start position:0%
+higher as long
+as the differentiation is
+
+ align:start position:0%
+as the differentiation is
+ 
+
+ align:start position:0%
+as the differentiation is
+effective so this kind of strategy you
+
+ align:start position:0%
+effective so this kind of strategy you
+ 
+
+ align:start position:0%
+effective so this kind of strategy you
+pick
+
+ align:start position:0%
+pick
+ 
+
+ align:start position:0%
+pick
+something that somebody
+
+ align:start position:0%
+something that somebody
+ 
+
+ align:start position:0%
+something that somebody
+values um actually the online booking
+
+ align:start position:0%
+values um actually the online booking
+ 
+
+ align:start position:0%
+values um actually the online booking
+system well not not quite that's an
+
+ align:start position:0%
+system well not not quite that's an
+ 
+
+ align:start position:0%
+system well not not quite that's an
+interesting story um you meet the needs
+
+ align:start position:0%
+interesting story um you meet the needs
+ 
+
+ align:start position:0%
+interesting story um you meet the needs
+you add costs you get premium prices
+
+ align:start position:0%
+you add costs you get premium prices
+ 
+
+ align:start position:0%
+you add costs you get premium prices
+terrific
+
+ align:start position:0%
+terrific
+ 
+
+ align:start position:0%
+terrific
+story
+
+ align:start position:0%
+story
+ 
+
+ align:start position:0%
+story
+but it has to be cost effective that is
+
+ align:start position:0%
+but it has to be cost effective that is
+ 
+
+ align:start position:0%
+but it has to be cost effective that is
+to say you can raise the price but if
+
+ align:start position:0%
+to say you can raise the price but if
+ 
+
+ align:start position:0%
+to say you can raise the price but if
+your costs go up by more than the price
+
+ align:start position:0%
+your costs go up by more than the price
+ 
+
+ align:start position:0%
+your costs go up by more than the price
+you lose and you come down to the
+
+ align:start position:0%
+you lose and you come down to the
+ 
+
+ align:start position:0%
+you lose and you come down to the
+same issue is imitation difficult is
+
+ align:start position:0%
+same issue is imitation difficult is
+ 
+
+ align:start position:0%
+same issue is imitation difficult is
+imitation difficult again we see we're
+
+ align:start position:0%
+imitation difficult again we see we're
+ 
+
+ align:start position:0%
+imitation difficult again we see we're
+going to see this in husky is imitation
+
+ align:start position:0%
+going to see this in husky is imitation
+ 
+
+ align:start position:0%
+going to see this in husky is imitation
+difficult there's sort
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+of nice diagram there's sort of three
+
+ align:start position:0%
+of nice diagram there's sort of three
+ 
+
+ align:start position:0%
+of nice diagram there's sort of three
+kinds of
+
+ align:start position:0%
+kinds of
+ 
+
+ align:start position:0%
+kinds of
+stories about ways that that imitation
+
+ align:start position:0%
+stories about ways that that imitation
+ 
+
+ align:start position:0%
+stories about ways that that imitation
+can be
+
+ align:start position:0%
+can be
+ 
+
+ align:start position:0%
+can be
+difficult the first is sort of the Ikea
+
+ align:start position:0%
+difficult the first is sort of the Ikea
+ 
+
+ align:start position:0%
+difficult the first is sort of the Ikea
+Southwest up on top the
+
+ align:start position:0%
+Southwest up on top the
+ 
+
+ align:start position:0%
+Southwest up on top the
+integration that if you have to build
+
+ align:start position:0%
+integration that if you have to build
+ 
+
+ align:start position:0%
+integration that if you have to build
+the company to deliver on a strategy
+
+ align:start position:0%
+the company to deliver on a strategy
+ 
+
+ align:start position:0%
+the company to deliver on a strategy
+effectively
+
+ align:start position:0%
+effectively
+ 
+
+ align:start position:0%
+effectively
+that's again in Porter the Southwest
+
+ align:start position:0%
+that's again in Porter the Southwest
+ 
+
+ align:start position:0%
+that's again in Porter the Southwest
+Airlines versus what was it Continental
+
+ align:start position:0%
+Airlines versus what was it Continental
+ 
+
+ align:start position:0%
+Airlines versus what was it Continental
+light so Continental decides they can
+
+ align:start position:0%
+light so Continental decides they can
+ 
+
+ align:start position:0%
+light so Continental decides they can
+compete with these lowcost carriers
+
+ align:start position:0%
+compete with these lowcost carriers
+ 
+
+ align:start position:0%
+compete with these lowcost carriers
+they'll offer a lowcost carrier they
+
+ align:start position:0%
+they'll offer a lowcost carrier they
+ 
+
+ align:start position:0%
+they'll offer a lowcost carrier they
+won't serve meals and they won't do
+
+ align:start position:0%
+won't serve meals and they won't do
+ 
+
+ align:start position:0%
+won't serve meals and they won't do
+assigned
+
+ align:start position:0%
+assigned
+ 
+
+ align:start position:0%
+assigned
+seats but they do baggage interchange
+
+ align:start position:0%
+seats but they do baggage interchange
+ 
+
+ align:start position:0%
+seats but they do baggage interchange
+with other airlines because they're
+
+ align:start position:0%
+with other airlines because they're
+ 
+
+ align:start position:0%
+with other airlines because they're
+Continental they do online booking
+
+ align:start position:0%
+Continental they do online booking
+ 
+
+ align:start position:0%
+Continental they do online booking
+because they're
+
+ align:start position:0%
+because they're
+ 
+
+ align:start position:0%
+because they're
+Continental they do a variety of other
+
+ align:start position:0%
+Continental they do a variety of other
+ 
+
+ align:start position:0%
+Continental they do a variety of other
+things because they're continental and
+
+ align:start position:0%
+things because they're continental and
+ 
+
+ align:start position:0%
+things because they're continental and
+they can't get the cost down that
+
+ align:start position:0%
+they can't get the cost down that
+ 
+
+ align:start position:0%
+they can't get the cost down that
+low to get the cost down that low you've
+
+ align:start position:0%
+low to get the cost down that low you've
+ 
+
+ align:start position:0%
+low to get the cost down that low you've
+got to integrate the whole thing you've
+
+ align:start position:0%
+got to integrate the whole thing you've
+ 
+
+ align:start position:0%
+got to integrate the whole thing you've
+got to build the you got to build an
+
+ align:start position:0%
+got to build the you got to build an
+ 
+
+ align:start position:0%
+got to build the you got to build an
+Ikea to deliver
+
+ align:start position:0%
+Ikea to deliver
+ 
+
+ align:start position:0%
+Ikea to deliver
+Ikea you can't have an Ikea tacked on to
+
+ align:start position:0%
+Ikea you can't have an Ikea tacked on to
+ 
+
+ align:start position:0%
+Ikea you can't have an Ikea tacked on to
+something
+
+ align:start position:0%
+something
+ 
+
+ align:start position:0%
+something
+else which means it's hard for an
+
+ align:start position:0%
+else which means it's hard for an
+ 
+
+ align:start position:0%
+else which means it's hard for an
+existing firm to copy the notion that
+
+ align:start position:0%
+existing firm to copy the notion that
+ 
+
+ align:start position:0%
+existing firm to copy the notion that
+you have to integrate the whole
+
+ align:start position:0%
+you have to integrate the whole
+ 
+
+ align:start position:0%
+you have to integrate the whole
+system
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um I guess another sort of example like
+
+ align:start position:0%
+um I guess another sort of example like
+ 
+
+ align:start position:0%
+um I guess another sort of example like
+that would be Jiffy Lube or one of the
+
+ align:start position:0%
+that would be Jiffy Lube or one of the
+ 
+
+ align:start position:0%
+that would be Jiffy Lube or one of the
+one of the uh quick lube places that
+
+ align:start position:0%
+one of the uh quick lube places that
+ 
+
+ align:start position:0%
+one of the uh quick lube places that
+used to you don't see them as much as
+
+ align:start position:0%
+used to you don't see them as much as
+ 
+
+ align:start position:0%
+used to you don't see them as much as
+you used to that offers cheap oil change
+
+ align:start position:0%
+you used to that offers cheap oil change
+ 
+
+ align:start position:0%
+you used to that offers cheap oil change
+that's all they do or all they did and
+
+ align:start position:0%
+that's all they do or all they did and
+ 
+
+ align:start position:0%
+that's all they do or all they did and
+could you imitate that yeah you could
+
+ align:start position:0%
+could you imitate that yeah you could
+ 
+
+ align:start position:0%
+could you imitate that yeah you could
+but you'd really have to have the
+
+ align:start position:0%
+but you'd really have to have the
+ 
+
+ align:start position:0%
+but you'd really have to have the
+company focused on doing just that you
+
+ align:start position:0%
+company focused on doing just that you
+ 
+
+ align:start position:0%
+company focused on doing just that you
+can't do cheap oil change as part of a a
+
+ align:start position:0%
+can't do cheap oil change as part of a a
+ 
+
+ align:start position:0%
+can't do cheap oil change as part of a a
+full service repair shop that does other
+
+ align:start position:0%
+full service repair shop that does other
+ 
+
+ align:start position:0%
+full service repair shop that does other
+things CU you got all that overhead and
+
+ align:start position:0%
+things CU you got all that overhead and
+ 
+
+ align:start position:0%
+things CU you got all that overhead and
+all of the systems that to handle
+
+ align:start position:0%
+all of the systems that to handle
+ 
+
+ align:start position:0%
+all of the systems that to handle
+everything if you just do oil change
+
+ align:start position:0%
+everything if you just do oil change
+ 
+
+ align:start position:0%
+everything if you just do oil change
+it's a simple business you could do it
+
+ align:start position:0%
+it's a simple business you could do it
+ 
+
+ align:start position:0%
+it's a simple business you could do it
+very cheaply if you do more you got to
+
+ align:start position:0%
+very cheaply if you do more you got to
+ 
+
+ align:start position:0%
+very cheaply if you do more you got to
+hire different people you got to have
+
+ align:start position:0%
+hire different people you got to have
+ 
+
+ align:start position:0%
+hire different people you got to have
+different systems you got to have
+
+ align:start position:0%
+different systems you got to have
+ 
+
+ align:start position:0%
+different systems you got to have
+different inventory so one reason it can
+
+ align:start position:0%
+different inventory so one reason it can
+ 
+
+ align:start position:0%
+different inventory so one reason it can
+be hard is that everything is integrated
+
+ align:start position:0%
+be hard is that everything is integrated
+ 
+
+ align:start position:0%
+be hard is that everything is integrated
+everything is integrated it would be
+
+ align:start position:0%
+everything is integrated it would be
+ 
+
+ align:start position:0%
+everything is integrated it would be
+hard well I interestingly enough if you
+
+ align:start position:0%
+hard well I interestingly enough if you
+ 
+
+ align:start position:0%
+hard well I interestingly enough if you
+think about General
+
+ align:start position:0%
+think about General
+ 
+
+ align:start position:0%
+think about General
+Motors uh
+
+ align:start position:0%
+Motors uh
+ 
+
+ align:start position:0%
+Motors uh
+historically Cadillac was focused on
+
+ align:start position:0%
+historically Cadillac was focused on
+ 
+
+ align:start position:0%
+historically Cadillac was focused on
+luxury cars and was sort of kept
+
+ align:start position:0%
+luxury cars and was sort of kept
+ 
+
+ align:start position:0%
+luxury cars and was sort of kept
+separate
+
+ align:start position:0%
+separate
+ 
+
+ align:start position:0%
+separate
+from the rest of GM in the glory years
+
+ align:start position:0%
+from the rest of GM in the glory years
+ 
+
+ align:start position:0%
+from the rest of GM in the glory years
+Cadillac delivered luxury cars you
+
+ align:start position:0%
+Cadillac delivered luxury cars you
+ 
+
+ align:start position:0%
+Cadillac delivered luxury cars you
+couldn't have the Cadillac operation
+
+ align:start position:0%
+couldn't have the Cadillac operation
+ 
+
+ align:start position:0%
+couldn't have the Cadillac operation
+closely integrated with the Chevrolet
+
+ align:start position:0%
+closely integrated with the Chevrolet
+ 
+
+ align:start position:0%
+closely integrated with the Chevrolet
+operation right you just you have
+
+ align:start position:0%
+operation right you just you have
+ 
+
+ align:start position:0%
+operation right you just you have
+different philosophies you have
+
+ align:start position:0%
+different philosophies you have
+ 
+
+ align:start position:0%
+different philosophies you have
+different purchasing you have different
+
+ align:start position:0%
+different purchasing you have different
+ 
+
+ align:start position:0%
+different purchasing you have different
+design approaches Cadillac everything
+
+ align:start position:0%
+design approaches Cadillac everything
+ 
+
+ align:start position:0%
+design approaches Cadillac everything
+was focused on a certain kind of
+
+ align:start position:0%
+was focused on a certain kind of
+ 
+
+ align:start position:0%
+was focused on a certain kind of
+car integrated built to
+
+ align:start position:0%
+car integrated built to
+ 
+
+ align:start position:0%
+car integrated built to
+deliver you'd have to build a system as
+
+ align:start position:0%
+deliver you'd have to build a system as
+ 
+
+ align:start position:0%
+deliver you'd have to build a system as
+many people did it turns out uh to
+
+ align:start position:0%
+many people did it turns out uh to
+ 
+
+ align:start position:0%
+many people did it turns out uh to
+compete the
+
+ align:start position:0%
+compete the
+ 
+
+ align:start position:0%
+compete the
+second there on the right a capture
+
+ align:start position:0%
+second there on the right a capture
+ 
+
+ align:start position:0%
+second there on the right a capture
+model is cost if you have a cost
+
+ align:start position:0%
+model is cost if you have a cost
+ 
+
+ align:start position:0%
+model is cost if you have a cost
+Advantage how can you have a cost
+
+ align:start position:0%
+Advantage how can you have a cost
+ 
+
+ align:start position:0%
+Advantage how can you have a cost
+Advantage well there might be economies
+
+ align:start position:0%
+Advantage well there might be economies
+ 
+
+ align:start position:0%
+Advantage well there might be economies
+of
+
+ align:start position:0%
+of
+ 
+
+ align:start position:0%
+of
+scale you might have learning advantages
+
+ align:start position:0%
+scale you might have learning advantages
+ 
+
+ align:start position:0%
+scale you might have learning advantages
+you might have other kinds of advantages
+
+ align:start position:0%
+you might have other kinds of advantages
+ 
+
+ align:start position:0%
+you might have other kinds of advantages
+there are lots of ways you can have an
+
+ align:start position:0%
+there are lots of ways you can have an
+ 
+
+ align:start position:0%
+there are lots of ways you can have an
+advantage in cost yeah
+
+ align:start position:0%
+advantage in cost yeah
+ 
+
+ align:start position:0%
+advantage in cost yeah
+Andrew I said a question regarding
+
+ align:start position:0%
+Andrew I said a question regarding
+ 
+
+ align:start position:0%
+Andrew I said a question regarding
+integration and these might be really
+
+ align:start position:0%
+integration and these might be really
+ 
+
+ align:start position:0%
+integration and these might be really
+examples I'm just curious where they fit
+
+ align:start position:0%
+examples I'm just curious where they fit
+ 
+
+ align:start position:0%
+examples I'm just curious where they fit
+in like uh company like Walmart or like
+
+ align:start position:0%
+in like uh company like Walmart or like
+ 
+
+ align:start position:0%
+in like uh company like Walmart or like
+Toyota that are like quite large scale
+
+ align:start position:0%
+Toyota that are like quite large scale
+ 
+
+ align:start position:0%
+Toyota that are like quite large scale
+but then again I've heard like many
+
+ align:start position:0%
+but then again I've heard like many
+ 
+
+ align:start position:0%
+but then again I've heard like many
+things about the way they for example
+
+ align:start position:0%
+things about the way they for example
+ 
+
+ align:start position:0%
+things about the way they for example
+for to Yota how they have like a uh like
+
+ align:start position:0%
+for to Yota how they have like a uh like
+ 
+
+ align:start position:0%
+for to Yota how they have like a uh like
+really integrated system from the
+
+ align:start position:0%
+really integrated system from the
+ 
+
+ align:start position:0%
+really integrated system from the
+supplier to like the end product and all
+
+ align:start position:0%
+supplier to like the end product and all
+ 
+
+ align:start position:0%
+supplier to like the end product and all
+the thing I was just curious are they
+
+ align:start position:0%
+the thing I was just curious are they
+ 
+
+ align:start position:0%
+the thing I was just curious are they
+like simply um uh like um exceptions or
+
+ align:start position:0%
+like simply um uh like um exceptions or
+ 
+
+ align:start position:0%
+like simply um uh like um exceptions or
+are they doing some other things also
+
+ align:start position:0%
+are they doing some other things also
+ 
+
+ align:start position:0%
+are they doing some other things also
+that I'm not seen well Toyota Toyota is
+
+ align:start position:0%
+that I'm not seen well Toyota Toyota is
+ 
+
+ align:start position:0%
+that I'm not seen well Toyota Toyota is
+a great case and others may know that
+
+ align:start position:0%
+a great case and others may know that
+ 
+
+ align:start position:0%
+a great case and others may know that
+system better than I do they combine a
+
+ align:start position:0%
+system better than I do they combine a
+ 
+
+ align:start position:0%
+system better than I do they combine a
+number of things but it is it is an
+
+ align:start position:0%
+number of things but it is it is an
+ 
+
+ align:start position:0%
+number of things but it is it is an
+example of a system built to do a couple
+
+ align:start position:0%
+example of a system built to do a couple
+ 
+
+ align:start position:0%
+example of a system built to do a couple
+of things well
+
+ align:start position:0%
+of things well
+ 
+
+ align:start position:0%
+of things well
+first
+
+ align:start position:0%
+first
+ 
+
+ align:start position:0%
+first
+um they built a product development
+
+ align:start position:0%
+um they built a product development
+ 
+
+ align:start position:0%
+um they built a product development
+system that was much quicker than
+
+ align:start position:0%
+system that was much quicker than
+ 
+
+ align:start position:0%
+system that was much quicker than
+American manufacturers and indeed much
+
+ align:start position:0%
+American manufacturers and indeed much
+ 
+
+ align:start position:0%
+American manufacturers and indeed much
+quicker than European manufacturers so
+
+ align:start position:0%
+quicker than European manufacturers so
+ 
+
+ align:start position:0%
+quicker than European manufacturers so
+they could go from concept to model on
+
+ align:start position:0%
+they could go from concept to model on
+ 
+
+ align:start position:0%
+they could go from concept to model on
+the street quicker so that's the
+
+ align:start position:0%
+the street quicker so that's the
+ 
+
+ align:start position:0%
+the street quicker so that's the
+Innovation speed down there in the
+
+ align:start position:0%
+Innovation speed down there in the
+ 
+
+ align:start position:0%
+Innovation speed down there in the
+left um could you imitate it a lot of
+
+ align:start position:0%
+left um could you imitate it a lot of
+ 
+
+ align:start position:0%
+left um could you imitate it a lot of
+people tried um there were no obvious
+
+ align:start position:0%
+people tried um there were no obvious
+ 
+
+ align:start position:0%
+people tried um there were no obvious
+barriers to imitating that they also had
+
+ align:start position:0%
+barriers to imitating that they also had
+ 
+
+ align:start position:0%
+barriers to imitating that they also had
+some some clever ways they did
+
+ align:start position:0%
+some some clever ways they did
+ 
+
+ align:start position:0%
+some some clever ways they did
+manufacturing just in time and the whole
+
+ align:start position:0%
+manufacturing just in time and the whole
+ 
+
+ align:start position:0%
+manufacturing just in time and the whole
+caman and quality circles there was a
+
+ align:start position:0%
+caman and quality circles there was a
+ 
+
+ align:start position:0%
+caman and quality circles there was a
+whole manufacturing
+
+ align:start position:0%
+whole manufacturing
+ 
+
+ align:start position:0%
+whole manufacturing
+system could you copy it well a lot of
+
+ align:start position:0%
+system could you copy it well a lot of
+ 
+
+ align:start position:0%
+system could you copy it well a lot of
+people
+
+ align:start position:0%
+people
+ 
+
+ align:start position:0%
+people
+tried and that's what's interesting
+
+ align:start position:0%
+tried and that's what's interesting
+ 
+
+ align:start position:0%
+tried and that's what's interesting
+right there was the there was the to
+
+ align:start position:0%
+right there was the there was the to
+ 
+
+ align:start position:0%
+right there was the there was the to
+Toyota General Motors joint venture that
+
+ align:start position:0%
+Toyota General Motors joint venture that
+ 
+
+ align:start position:0%
+Toyota General Motors joint venture that
+produced what was it that they produced
+
+ align:start position:0%
+produced what was it that they produced
+ 
+
+ align:start position:0%
+produced what was it that they produced
+in California new me yes and General
+
+ align:start position:0%
+in California new me yes and General
+ 
+
+ align:start position:0%
+in California new me yes and General
+Motors was going to learn the Toyota
+
+ align:start position:0%
+Motors was going to learn the Toyota
+ 
+
+ align:start position:0%
+Motors was going to learn the Toyota
+system and copy
+
+ align:start position:0%
+system and copy
+ 
+
+ align:start position:0%
+system and copy
+it well the cultures were different and
+
+ align:start position:0%
+it well the cultures were different and
+ 
+
+ align:start position:0%
+it well the cultures were different and
+the GM
+
+ align:start position:0%
+the GM
+ 
+
+ align:start position:0%
+the GM
+Workforce you know you've been doing
+
+ align:start position:0%
+Workforce you know you've been doing
+ 
+
+ align:start position:0%
+Workforce you know you've been doing
+something some way for 30 years and
+
+ align:start position:0%
+something some way for 30 years and
+ 
+
+ align:start position:0%
+something some way for 30 years and
+somebody says now we're going to do it
+
+ align:start position:0%
+somebody says now we're going to do it
+ 
+
+ align:start position:0%
+somebody says now we're going to do it
+this other
+
+ align:start position:0%
+this other
+ 
+
+ align:start position:0%
+this other
+way that's
+
+ align:start position:0%
+way that's
+ 
+
+ align:start position:0%
+way that's
+hard and you have to change the
+
+ align:start position:0%
+hard and you have to change the
+ 
+
+ align:start position:0%
+hard and you have to change the
+inventory control system and your
+
+ align:start position:0%
+inventory control system and your
+ 
+
+ align:start position:0%
+inventory control system and your
+purchasing system then you go to your
+
+ align:start position:0%
+purchasing system then you go to your
+ 
+
+ align:start position:0%
+purchasing system then you go to your
+designers and you got to change the
+
+ align:start position:0%
+designers and you got to change the
+ 
+
+ align:start position:0%
+designers and you got to change the
+speed at which you produce new products
+
+ align:start position:0%
+speed at which you produce new products
+ 
+
+ align:start position:0%
+speed at which you produce new products
+by changing that system I mean I'd say
+
+ align:start position:0%
+by changing that system I mean I'd say
+ 
+
+ align:start position:0%
+by changing that system I mean I'd say
+Toyota was successfully
+
+ align:start position:0%
+Toyota was successfully
+ 
+
+ align:start position:0%
+Toyota was successfully
+copied over a long time I wouldn't say
+
+ align:start position:0%
+copied over a long time I wouldn't say
+ 
+
+ align:start position:0%
+copied over a long time I wouldn't say
+GM has successfully copied them it
+
+ align:start position:0%
+GM has successfully copied them it
+ 
+
+ align:start position:0%
+GM has successfully copied them it
+wasn't that Toyota was bigger than
+
+ align:start position:0%
+wasn't that Toyota was bigger than
+ 
+
+ align:start position:0%
+wasn't that Toyota was bigger than
+anybody
+
+ align:start position:0%
+anybody
+ 
+
+ align:start position:0%
+anybody
+else they were doing a better job when
+
+ align:start position:0%
+else they were doing a better job when
+ 
+
+ align:start position:0%
+else they were doing a better job when
+they were smaller certainly smaller than
+
+ align:start position:0%
+they were smaller certainly smaller than
+ 
+
+ align:start position:0%
+they were smaller certainly smaller than
+the American companies so there
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+there's an they got cost by developing a
+
+ align:start position:0%
+there's an they got cost by developing a
+ 
+
+ align:start position:0%
+there's an they got cost by developing a
+manufacturing and design system that was
+
+ align:start position:0%
+manufacturing and design system that was
+ 
+
+ align:start position:0%
+manufacturing and design system that was
+simply better and the advantage
+
+ align:start position:0%
+simply better and the advantage
+ 
+
+ align:start position:0%
+simply better and the advantage
+held because even though it looked like
+
+ align:start position:0%
+held because even though it looked like
+ 
+
+ align:start position:0%
+held because even though it looked like
+you could copy it and there were
+
+ align:start position:0%
+you could copy it and there were
+ 
+
+ align:start position:0%
+you could copy it and there were
+articles and books written on how you do
+
+ align:start position:0%
+articles and books written on how you do
+ 
+
+ align:start position:0%
+articles and books written on how you do
+the Toyota the Japanese system it turned
+
+ align:start position:0%
+the Toyota the Japanese system it turned
+ 
+
+ align:start position:0%
+the Toyota the Japanese system it turned
+out to be harder to put it in place
+
+ align:start position:0%
+out to be harder to put it in place
+ 
+
+ align:start position:0%
+out to be harder to put it in place
+because you had to do it all and again
+
+ align:start position:0%
+because you had to do it all and again
+ 
+
+ align:start position:0%
+because you had to do it all and again
+over time over time there are lots of
+
+ align:start position:0%
+over time over time there are lots of
+ 
+
+ align:start position:0%
+over time over time there are lots of
+studies where you see companies now that
+
+ align:start position:0%
+studies where you see companies now that
+ 
+
+ align:start position:0%
+studies where you see companies now that
+have that approach but it was
+
+ align:start position:0%
+have that approach but it was
+ 
+
+ align:start position:0%
+have that approach but it was
+sustainable and Toyota is in not in
+
+ align:start position:0%
+sustainable and Toyota is in not in
+ 
+
+ align:start position:0%
+sustainable and Toyota is in not in
+great shape uh it was it was um
+
+ align:start position:0%
+great shape uh it was it was um
+ 
+
+ align:start position:0%
+great shape uh it was it was um
+sustainable in part because of the fact
+
+ align:start position:0%
+sustainable in part because of the fact
+ 
+
+ align:start position:0%
+sustainable in part because of the fact
+that it was a system you had to do the
+
+ align:start position:0%
+that it was a system you had to do the
+ 
+
+ align:start position:0%
+that it was a system you had to do the
+whole thing you couldn't just Change
+
+ align:start position:0%
+whole thing you couldn't just Change
+ 
+
+ align:start position:0%
+whole thing you couldn't just Change
+inventory you couldn't just change
+
+ align:start position:0%
+inventory you couldn't just change
+ 
+
+ align:start position:0%
+inventory you couldn't just change
+design you had to take the whole thing
+
+ align:start position:0%
+design you had to take the whole thing
+ 
+
+ align:start position:0%
+design you had to take the whole thing
+and that meant bringing people along
+
+ align:start position:0%
+and that meant bringing people along
+ 
+
+ align:start position:0%
+and that meant bringing people along
+could you do a startup that way yeah
+
+ align:start position:0%
+could you do a startup that way yeah
+ 
+
+ align:start position:0%
+could you do a startup that way yeah
+much easier to do a startup much easier
+
+ align:start position:0%
+much easier to do a startup much easier
+ 
+
+ align:start position:0%
+much easier to do a startup much easier
+to take people who've never built or
+
+ align:start position:0%
+to take people who've never built or
+ 
+
+ align:start position:0%
+to take people who've never built or
+designed Automobiles and say here's how
+
+ align:start position:0%
+designed Automobiles and say here's how
+ 
+
+ align:start position:0%
+designed Automobiles and say here's how
+we're going to do it but then you've got
+
+ align:start position:0%
+we're going to do it but then you've got
+ 
+
+ align:start position:0%
+we're going to do it but then you've got
+a whole bunch of people who've never
+
+ align:start position:0%
+a whole bunch of people who've never
+ 
+
+ align:start position:0%
+a whole bunch of people who've never
+built or designed automobiles so so you
+
+ align:start position:0%
+built or designed automobiles so so you
+ 
+
+ align:start position:0%
+built or designed automobiles so so you
+know it's U it's a nice example thank
+
+ align:start position:0%
+know it's U it's a nice example thank
+ 
+
+ align:start position:0%
+know it's U it's a nice example thank
+you anything
+
+ align:start position:0%
+you anything
+ 
+
+ align:start position:0%
+you anything
+else any other
+
+ align:start position:0%
+else any other
+ 
+
+ align:start position:0%
+else any other
+comments
+
+ align:start position:0%
+comments
+ 
+
+ align:start position:0%
+comments
+okay let's do
+
+ align:start position:0%
+okay let's do
+ 
+
+ align:start position:0%
+okay let's do
+husky what's Husky's
+
+ align:start position:0%
+husky what's Husky's
+ 
+
+ align:start position:0%
+husky what's Husky's
+strategy what is it that we're 95 what
+
+ align:start position:0%
+strategy what is it that we're 95 what
+ 
+
+ align:start position:0%
+strategy what is it that we're 95 what
+is it historically husky wouldn't do
+
+ align:start position:0%
+is it historically husky wouldn't do
+ 
+
+ align:start position:0%
+is it historically husky wouldn't do
+Mary um so they Stu to several core
+
+ align:start position:0%
+Mary um so they Stu to several core
+ 
+
+ align:start position:0%
+Mary um so they Stu to several core
+values like perfectionism and dedicating
+
+ align:start position:0%
+values like perfectionism and dedicating
+ 
+
+ align:start position:0%
+values like perfectionism and dedicating
+to hard work and they also um devoted a
+
+ align:start position:0%
+to hard work and they also um devoted a
+ 
+
+ align:start position:0%
+to hard work and they also um devoted a
+lot of stuff to health and so that's a
+
+ align:start position:0%
+lot of stuff to health and so that's a
+ 
+
+ align:start position:0%
+lot of stuff to health and so that's a
+good description of the
+
+ align:start position:0%
+good description of the
+ 
+
+ align:start position:0%
+good description of the
+culture of how they went about doing
+
+ align:start position:0%
+culture of how they went about doing
+ 
+
+ align:start position:0%
+culture of how they went about doing
+what they did how did they what did they
+
+ align:start position:0%
+what they did how did they what did they
+ 
+
+ align:start position:0%
+what they did how did they what did they
+do what were their activities did they
+
+ align:start position:0%
+do what were their activities did they
+ 
+
+ align:start position:0%
+do what were their activities did they
+focus were they trying to do all kinds
+
+ align:start position:0%
+focus were they trying to do all kinds
+ 
+
+ align:start position:0%
+focus were they trying to do all kinds
+of injection molding some kinds of
+
+ align:start position:0%
+of injection molding some kinds of
+ 
+
+ align:start position:0%
+of injection molding some kinds of
+injection molding lowend end highend
+
+ align:start position:0%
+injection molding lowend end highend
+ 
+
+ align:start position:0%
+injection molding lowend end highend
+middle of the market they focused on the
+
+ align:start position:0%
+middle of the market they focused on the
+ 
+
+ align:start position:0%
+middle of the market they focused on the
+P pet and the thin wall business so they
+
+ align:start position:0%
+P pet and the thin wall business so they
+ 
+
+ align:start position:0%
+P pet and the thin wall business so they
+focused on two segments okay they didn't
+
+ align:start position:0%
+focused on two segments okay they didn't
+ 
+
+ align:start position:0%
+focused on two segments okay they didn't
+do everything and as you say they had
+
+ align:start position:0%
+do everything and as you say they had
+ 
+
+ align:start position:0%
+do everything and as you say they had
+this very interesting culture
+
+ align:start position:0%
+this very interesting culture
+ 
+
+ align:start position:0%
+this very interesting culture
+um so we got that one don't freeze
+
+ align:start position:0%
+um so we got that one don't freeze
+ 
+
+ align:start position:0%
+um so we got that one don't freeze
+again what distinguished those segments
+
+ align:start position:0%
+again what distinguished those segments
+ 
+
+ align:start position:0%
+again what distinguished those segments
+from other
+
+ align:start position:0%
+from other
+ 
+
+ align:start position:0%
+from other
+segments how were the
+
+ align:start position:0%
+segments how were the
+ 
+
+ align:start position:0%
+segments how were the
+pet and the thin wall segment different
+
+ align:start position:0%
+pet and the thin wall segment different
+ 
+
+ align:start position:0%
+pet and the thin wall segment different
+from other parts of the business other
+
+ align:start position:0%
+from other parts of the business other
+ 
+
+ align:start position:0%
+from other parts of the business other
+segments any obvious way yeah they were
+
+ align:start position:0%
+segments any obvious way yeah they were
+ 
+
+ align:start position:0%
+segments any obvious way yeah they were
+trying to sorry I forgot my name t but
+
+ align:start position:0%
+trying to sorry I forgot my name t but
+ 
+
+ align:start position:0%
+trying to sorry I forgot my name t but
+you do remember who you are though we're
+
+ align:start position:0%
+you do remember who you are though we're
+ 
+
+ align:start position:0%
+you do remember who you are though we're
+good there okay yes I think they were
+
+ align:start position:0%
+good there okay yes I think they were
+ 
+
+ align:start position:0%
+good there okay yes I think they were
+trying to find segments where like a
+
+ align:start position:0%
+trying to find segments where like a
+ 
+
+ align:start position:0%
+trying to find segments where like a
+technological advantage is like
+
+ align:start position:0%
+technological advantage is like
+ 
+
+ align:start position:0%
+technological advantage is like
+sustainable actually makes a difference
+
+ align:start position:0%
+sustainable actually makes a difference
+ 
+
+ align:start position:0%
+sustainable actually makes a difference
+like within wall business they it's like
+
+ align:start position:0%
+like within wall business they it's like
+ 
+
+ align:start position:0%
+like within wall business they it's like
+I guess this requires more like
+
+ align:start position:0%
+I guess this requires more like
+ 
+
+ align:start position:0%
+I guess this requires more like
+technological know how to make it and it
+
+ align:start position:0%
+technological know how to make it and it
+ 
+
+ align:start position:0%
+technological know how to make it and it
+allows you to make the walls thinner you
+
+ align:start position:0%
+allows you to make the walls thinner you
+ 
+
+ align:start position:0%
+allows you to make the walls thinner you
+can make it machine go faster and
+
+ align:start position:0%
+can make it machine go faster and
+ 
+
+ align:start position:0%
+can make it machine go faster and
+something stuff like that where it
+
+ align:start position:0%
+something stuff like that where it
+ 
+
+ align:start position:0%
+something stuff like that where it
+hasn't been totally demonetized yet so
+
+ align:start position:0%
+hasn't been totally demonetized yet so
+ 
+
+ align:start position:0%
+hasn't been totally demonetized yet so
+that allows to stay higher what about
+
+ align:start position:0%
+that allows to stay higher what about
+ 
+
+ align:start position:0%
+that allows to stay higher what about
+the pet bottle business what's what's
+
+ align:start position:0%
+the pet bottle business what's what's
+ 
+
+ align:start position:0%
+the pet bottle business what's what's
+how how is that different um it seemed
+
+ align:start position:0%
+how how is that different um it seemed
+ 
+
+ align:start position:0%
+how how is that different um it seemed
+like I wasn't really sure it's some they
+
+ align:start position:0%
+like I wasn't really sure it's some they
+ 
+
+ align:start position:0%
+like I wasn't really sure it's some they
+kind of wind up in that like kind of by
+
+ align:start position:0%
+kind of wind up in that like kind of by
+ 
+
+ align:start position:0%
+kind of wind up in that like kind of by
+accident sort of like well think about I
+
+ align:start position:0%
+accident sort of like well think about I
+ 
+
+ align:start position:0%
+accident sort of like well think about I
+mean there's some nice description of
+
+ align:start position:0%
+mean there's some nice description of
+ 
+
+ align:start position:0%
+mean there's some nice description of
+suppose you're you're doing coke bottles
+
+ align:start position:0%
+suppose you're you're doing coke bottles
+ 
+
+ align:start position:0%
+suppose you're you're doing coke bottles
+and you're running this in incredibly
+
+ align:start position:0%
+and you're running this in incredibly
+ 
+
+ align:start position:0%
+and you're running this in incredibly
+rapid bottling apparatus and you produce
+
+ align:start position:0%
+rapid bottling apparatus and you produce
+ 
+
+ align:start position:0%
+rapid bottling apparatus and you produce
+the bottles and you fill the bottles
+
+ align:start position:0%
+the bottles and you fill the bottles
+ 
+
+ align:start position:0%
+the bottles and you fill the bottles
+under pressure what matters a
+
+ align:start position:0%
+under pressure what matters a
+ 
+
+ align:start position:0%
+under pressure what matters a
+lot quality maybe defects maybe cuz when
+
+ align:start position:0%
+lot quality maybe defects maybe cuz when
+ 
+
+ align:start position:0%
+lot quality maybe defects maybe cuz when
+a when a bottle explodes and you've got
+
+ align:start position:0%
+a when a bottle explodes and you've got
+ 
+
+ align:start position:0%
+a when a bottle explodes and you've got
+to stop the line that's
+
+ align:start position:0%
+to stop the line that's
+ 
+
+ align:start position:0%
+to stop the line that's
+terrible so performance and Technology
+
+ align:start position:0%
+terrible so performance and Technology
+ 
+
+ align:start position:0%
+terrible so performance and Technology
+matter in those segments they're not
+
+ align:start position:0%
+matter in those segments they're not
+ 
+
+ align:start position:0%
+matter in those segments they're not
+making the blow ma only
+
+ align:start position:0%
+making the blow ma only
+ 
+
+ align:start position:0%
+making the blow ma only
+the yeah but you want to make those free
+
+ align:start position:0%
+the yeah but you want to make those free
+ 
+
+ align:start position:0%
+the yeah but you want to make those free
+of defects is when you blow them up when
+
+ align:start position:0%
+of defects is when you blow them up when
+ 
+
+ align:start position:0%
+of defects is when you blow them up when
+you blow them up yeah if you've got
+
+ align:start position:0%
+you blow them up yeah if you've got
+ 
+
+ align:start position:0%
+you blow them up yeah if you've got
+there was there's I think there's a
+
+ align:start position:0%
+there was there's I think there's a
+ 
+
+ align:start position:0%
+there was there's I think there's a
+number in the case about it sort of
+
+ align:start position:0%
+number in the case about it sort of
+ 
+
+ align:start position:0%
+number in the case about it sort of
+typical defects in one of theirs versus
+
+ align:start position:0%
+typical defects in one of theirs versus
+ 
+
+ align:start position:0%
+typical defects in one of theirs versus
+typical defects in competitors and it's
+
+ align:start position:0%
+typical defects in competitors and it's
+ 
+
+ align:start position:0%
+typical defects in competitors and it's
+a big difference and the story is when
+
+ align:start position:0%
+a big difference and the story is when
+ 
+
+ align:start position:0%
+a big difference and the story is when
+you blow them up and then you fill them
+
+ align:start position:0%
+you blow them up and then you fill them
+ 
+
+ align:start position:0%
+you blow them up and then you fill them
+under
+
+ align:start position:0%
+under
+ 
+
+ align:start position:0%
+under
+pressure and they explode and stop a
+
+ align:start position:0%
+pressure and they explode and stop a
+ 
+
+ align:start position:0%
+pressure and they explode and stop a
+bottling line that's terrible so if you
+
+ align:start position:0%
+bottling line that's terrible so if you
+ 
+
+ align:start position:0%
+bottling line that's terrible so if you
+can deliver product that won't do that
+
+ align:start position:0%
+can deliver product that won't do that
+ 
+
+ align:start position:0%
+can deliver product that won't do that
+you've got an advantage okay so it just
+
+ align:start position:0%
+you've got an advantage okay so it just
+ 
+
+ align:start position:0%
+you've got an advantage okay so it just
+it's segments where performance matters
+
+ align:start position:0%
+it's segments where performance matters
+ 
+
+ align:start position:0%
+it's segments where performance matters
+where technology is useful um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+one of the things that comes out in the
+
+ align:start position:0%
+one of the things that comes out in the
+ 
+
+ align:start position:0%
+one of the things that comes out in the
+case you have to read it kind of closely
+
+ align:start position:0%
+case you have to read it kind of closely
+ 
+
+ align:start position:0%
+case you have to read it kind of closely
+to get this
+
+ align:start position:0%
+to get this
+ 
+
+ align:start position:0%
+to get this
+but it it buys a lot of stuff it makes
+
+ align:start position:0%
+but it it buys a lot of stuff it makes
+ 
+
+ align:start position:0%
+but it it buys a lot of stuff it makes
+some molds but it buys a lot of
+
+ align:start position:0%
+some molds but it buys a lot of
+ 
+
+ align:start position:0%
+some molds but it buys a lot of
+inputs uh more than its competitors any
+
+ align:start position:0%
+inputs uh more than its competitors any
+ 
+
+ align:start position:0%
+inputs uh more than its competitors any
+obvious
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+reason Catherine uh well it doesn't the
+
+ align:start position:0%
+reason Catherine uh well it doesn't the
+ 
+
+ align:start position:0%
+reason Catherine uh well it doesn't the
+case that like their campuses are very
+
+ align:start position:0%
+case that like their campuses are very
+ 
+
+ align:start position:0%
+case that like their campuses are very
+centralized and like part goes back to
+
+ align:start position:0%
+centralized and like part goes back to
+ 
+
+ align:start position:0%
+centralized and like part goes back to
+the culture like their employees like
+
+ align:start position:0%
+the culture like their employees like
+ 
+
+ align:start position:0%
+the culture like their employees like
+are generally very happy there and so it
+
+ align:start position:0%
+are generally very happy there and so it
+ 
+
+ align:start position:0%
+are generally very happy there and so it
+say that they buy a lot of their molds
+
+ align:start position:0%
+say that they buy a lot of their molds
+ 
+
+ align:start position:0%
+say that they buy a lot of their molds
+from people who like generally former
+
+ align:start position:0%
+from people who like generally former
+ 
+
+ align:start position:0%
+from people who like generally former
+employees so they buy a lot from former
+
+ align:start position:0%
+employees so they buy a lot from former
+ 
+
+ align:start position:0%
+employees so they buy a lot from former
+employees y so that's part of the
+
+ align:start position:0%
+employees y so that's part of the
+ 
+
+ align:start position:0%
+employees y so that's part of the
+ecosystem as the phrase goes
+
+ align:start position:0%
+ecosystem as the phrase goes
+ 
+
+ align:start position:0%
+ecosystem as the phrase goes
+um but as focused as they are on
+
+ align:start position:0%
+um but as focused as they are on
+ 
+
+ align:start position:0%
+um but as focused as they are on
+technical Excellence of their
+
+ align:start position:0%
+technical Excellence of their
+ 
+
+ align:start position:0%
+technical Excellence of their
+machines could they do that for
+
+ align:start position:0%
+machines could they do that for
+ 
+
+ align:start position:0%
+machines could they do that for
+everything all the
+
+ align:start position:0%
+everything all the
+ 
+
+ align:start position:0%
+everything all the
+puts well they're
+
+ align:start position:0%
+puts well they're
+ 
+
+ align:start position:0%
+puts well they're
+like in instead of trying to just like
+
+ align:start position:0%
+like in instead of trying to just like
+ 
+
+ align:start position:0%
+like in instead of trying to just like
+manufacture like products they they like
+
+ align:start position:0%
+manufacture like products they they like
+ 
+
+ align:start position:0%
+manufacture like products they they like
+have a focus on like service and focus
+
+ align:start position:0%
+have a focus on like service and focus
+ 
+
+ align:start position:0%
+have a focus on like service and focus
+package basically so they they try to
+
+ align:start position:0%
+package basically so they they try to
+ 
+
+ align:start position:0%
+package basically so they they try to
+specialize more because then they can
+
+ align:start position:0%
+specialize more because then they can
+ 
+
+ align:start position:0%
+specialize more because then they can
+provide more services the equipment so
+
+ align:start position:0%
+provide more services the equipment so
+ 
+
+ align:start position:0%
+provide more services the equipment so
+they have technical people out in the
+
+ align:start position:0%
+they have technical people out in the
+ 
+
+ align:start position:0%
+they have technical people out in the
+field so they can provide a great deal
+
+ align:start position:0%
+field so they can provide a great deal
+ 
+
+ align:start position:0%
+field so they can provide a great deal
+of service and sort of co-engineering
+
+ align:start position:0%
+of service and sort of co-engineering
+ 
+
+ align:start position:0%
+of service and sort of co-engineering
+with their with their clients and
+
+ align:start position:0%
+with their with their clients and
+ 
+
+ align:start position:0%
+with their with their clients and
+they're in segments where that
+
+ align:start position:0%
+they're in segments where that
+ 
+
+ align:start position:0%
+they're in segments where that
+matters and trying to do that for all of
+
+ align:start position:0%
+matters and trying to do that for all of
+ 
+
+ align:start position:0%
+matters and trying to do that for all of
+the components and trying to be to hyper
+
+ align:start position:0%
+the components and trying to be to hyper
+ 
+
+ align:start position:0%
+the components and trying to be to hyper
+engineer all of their components would
+
+ align:start position:0%
+engineer all of their components would
+ 
+
+ align:start position:0%
+engineer all of their components would
+spread them a little thin I think and I
+
+ align:start position:0%
+spread them a little thin I think and I
+ 
+
+ align:start position:0%
+spread them a little thin I think and I
+think that's one reason
+
+ align:start position:0%
+think that's one reason
+ 
+
+ align:start position:0%
+think that's one reason
+why um that they they make fewer inputs
+
+ align:start position:0%
+why um that they they make fewer inputs
+ 
+
+ align:start position:0%
+why um that they they make fewer inputs
+than their competitors because they've
+
+ align:start position:0%
+than their competitors because they've
+ 
+
+ align:start position:0%
+than their competitors because they've
+decided to focus on the parts of the
+
+ align:start position:0%
+decided to focus on the parts of the
+ 
+
+ align:start position:0%
+decided to focus on the parts of the
+business where performance and quality
+
+ align:start position:0%
+business where performance and quality
+ 
+
+ align:start position:0%
+business where performance and quality
+and Technology matter um
+
+ align:start position:0%
+and Technology matter um
+ 
+
+ align:start position:0%
+and Technology matter um
+what's the answer to that they
+
+ align:start position:0%
+what's the answer to that they
+ 
+
+ align:start position:0%
+what's the answer to that they
+offer they make some molds particularly
+
+ align:start position:0%
+offer they make some molds particularly
+ 
+
+ align:start position:0%
+offer they make some molds particularly
+for for pet they offer um what hot
+
+ align:start position:0%
+for for pet they offer um what hot
+ 
+
+ align:start position:0%
+for for pet they offer um what hot
+Runners and a variety of other things
+
+ align:start position:0%
+Runners and a variety of other things
+ 
+
+ align:start position:0%
+Runners and a variety of other things
+that competitors don't any reasons
+
+ align:start position:0%
+that competitors don't any reasons
+ 
+
+ align:start position:0%
+that competitors don't any reasons
+why what reading with a hot Runners was
+
+ align:start position:0%
+why what reading with a hot Runners was
+ 
+
+ align:start position:0%
+why what reading with a hot Runners was
+they were selling a hot Runners to
+
+ align:start position:0%
+they were selling a hot Runners to
+ 
+
+ align:start position:0%
+they were selling a hot Runners to
+Gillette or whatever um but Gillette
+
+ align:start position:0%
+Gillette or whatever um but Gillette
+ 
+
+ align:start position:0%
+Gillette or whatever um but Gillette
+wasn't using their um actual mold
+
+ align:start position:0%
+wasn't using their um actual mold
+ 
+
+ align:start position:0%
+wasn't using their um actual mold
+machines but they were using hot Runners
+
+ align:start position:0%
+machines but they were using hot Runners
+ 
+
+ align:start position:0%
+machines but they were using hot Runners
+and then later on they were able to grab
+
+ align:start position:0%
+and then later on they were able to grab
+ 
+
+ align:start position:0%
+and then later on they were able to grab
+cont that you for the actual so it's
+
+ align:start position:0%
+cont that you for the actual so it's
+ 
+
+ align:start position:0%
+cont that you for the actual so it's
+it's part of the system being good at
+
+ align:start position:0%
+it's part of the system being good at
+ 
+
+ align:start position:0%
+it's part of the system being good at
+that adds to Performance and gives you a
+
+ align:start position:0%
+that adds to Performance and gives you a
+ 
+
+ align:start position:0%
+that adds to Performance and gives you a
+business Edge and they're very tightly
+
+ align:start position:0%
+business Edge and they're very tightly
+ 
+
+ align:start position:0%
+business Edge and they're very tightly
+focused on these two segments so you
+
+ align:start position:0%
+focused on these two segments so you
+ 
+
+ align:start position:0%
+focused on these two segments so you
+want to make everything you can for
+
+ align:start position:0%
+want to make everything you can for
+ 
+
+ align:start position:0%
+want to make everything you can for
+those segments you want to not worry
+
+ align:start position:0%
+those segments you want to not worry
+ 
+
+ align:start position:0%
+those segments you want to not worry
+about not worry about the
+
+ align:start position:0%
+about not worry about the
+ 
+
+ align:start position:0%
+about not worry about the
+inputs
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so why hasn't and it's made a lot of
+
+ align:start position:0%
+so why hasn't and it's made a lot of
+ 
+
+ align:start position:0%
+so why hasn't and it's made a lot of
+money right the the case makes it clear
+
+ align:start position:0%
+money right the the case makes it clear
+ 
+
+ align:start position:0%
+money right the the case makes it clear
+it's grown like Gang Busters it's got a
+
+ align:start position:0%
+it's grown like Gang Busters it's got a
+ 
+
+ align:start position:0%
+it's grown like Gang Busters it's got a
+return on Equity of something like
+
+ align:start position:0%
+return on Equity of something like
+ 
+
+ align:start position:0%
+return on Equity of something like
+40% why at least until recently hasn't
+
+ align:start position:0%
+40% why at least until recently hasn't
+ 
+
+ align:start position:0%
+40% why at least until recently hasn't
+anybody copied
+
+ align:start position:0%
+anybody copied
+ 
+
+ align:start position:0%
+anybody copied
+them what are the barriers to imitation
+
+ align:start position:0%
+them what are the barriers to imitation
+ 
+
+ align:start position:0%
+them what are the barriers to imitation
+what has made this strategy sustainable
+
+ align:start position:0%
+what has made this strategy sustainable
+ 
+
+ align:start position:0%
+what has made this strategy sustainable
+at least for a while nothing's forever
+
+ align:start position:0%
+at least for a while nothing's forever
+ 
+
+ align:start position:0%
+at least for a while nothing's forever
+Brendan uh they have very you know they
+
+ align:start position:0%
+Brendan uh they have very you know they
+ 
+
+ align:start position:0%
+Brendan uh they have very you know they
+have a huge technological advantage like
+
+ align:start position:0%
+have a huge technological advantage like
+ 
+
+ align:start position:0%
+have a huge technological advantage like
+that machines are a lot more expensive
+
+ align:start position:0%
+that machines are a lot more expensive
+ 
+
+ align:start position:0%
+that machines are a lot more expensive
+there's a deep knowledge Bas there so
+
+ align:start position:0%
+there's a deep knowledge Bas there so
+ 
+
+ align:start position:0%
+there's a deep knowledge Bas there so
+it's like hard to copy the kind of
+
+ align:start position:0%
+it's like hard to copy the kind of
+ 
+
+ align:start position:0%
+it's like hard to copy the kind of
+quality machine that they produce but
+
+ align:start position:0%
+quality machine that they produce but
+ 
+
+ align:start position:0%
+quality machine that they produce but
+you could imagine they don't have nobody
+
+ align:start position:0%
+you could imagine they don't have nobody
+ 
+
+ align:start position:0%
+you could imagine they don't have nobody
+talks about patents though we don't hear
+
+ align:start position:0%
+talks about patents though we don't hear
+ 
+
+ align:start position:0%
+talks about patents though we don't hear
+patent barriers so you could imagine
+
+ align:start position:0%
+patent barriers so you could imagine
+ 
+
+ align:start position:0%
+patent barriers so you could imagine
+they have the only Advanced
+
+ align:start position:0%
+they have the only Advanced
+ 
+
+ align:start position:0%
+they have the only Advanced
+manufacturing center right they've set
+
+ align:start position:0%
+manufacturing center right they've set
+ 
+
+ align:start position:0%
+manufacturing center right they've set
+up a little Think Tank I don't know how
+
+ align:start position:0%
+up a little Think Tank I don't know how
+ 
+
+ align:start position:0%
+up a little Think Tank I don't know how
+little it is they set up a think tank to
+
+ align:start position:0%
+little it is they set up a think tank to
+ 
+
+ align:start position:0%
+little it is they set up a think tank to
+do
+
+ align:start position:0%
+do
+ 
+
+ align:start position:0%
+do
+R&D why don't other people do that they
+
+ align:start position:0%
+R&D why don't other people do that they
+ 
+
+ align:start position:0%
+R&D why don't other people do that they
+don't wantest their money they rather
+
+ align:start position:0%
+don't wantest their money they rather
+ 
+
+ align:start position:0%
+don't wantest their money they rather
+say spend the money elsewhere not have
+
+ align:start position:0%
+say spend the money elsewhere not have
+ 
+
+ align:start position:0%
+say spend the money elsewhere not have
+that cost so they have this is a this is
+
+ align:start position:0%
+that cost so they have this is a this is
+ 
+
+ align:start position:0%
+that cost so they have this is a this is
+part
+
+ align:start position:0%
+part
+ 
+
+ align:start position:0%
+part
+of you could well let me let me push you
+
+ align:start position:0%
+of you could well let me let me push you
+ 
+
+ align:start position:0%
+of you could well let me let me push you
+on that a little bit because they're
+
+ align:start position:0%
+on that a little bit because they're
+ 
+
+ align:start position:0%
+on that a little bit because they're
+making so much much money right they're
+
+ align:start position:0%
+making so much much money right they're
+ 
+
+ align:start position:0%
+making so much much money right they're
+growing gang like Gang Busters they're
+
+ align:start position:0%
+growing gang like Gang Busters they're
+ 
+
+ align:start position:0%
+growing gang like Gang Busters they're
+making so much money wouldn't you
+
+ align:start position:0%
+making so much money wouldn't you
+ 
+
+ align:start position:0%
+making so much money wouldn't you
+imitate them if you could I mean so yeah
+
+ align:start position:0%
+imitate them if you could I mean so yeah
+ 
+
+ align:start position:0%
+imitate them if you could I mean so yeah
+you got to buy a you got to set up a
+
+ align:start position:0%
+you got to buy a you got to set up a
+ 
+
+ align:start position:0%
+you got to buy a you got to set up a
+manufacturing center these are big
+
+ align:start position:0%
+manufacturing center these are big
+ 
+
+ align:start position:0%
+manufacturing center these are big
+companies Manis man is a big company
+
+ align:start position:0%
+companies Manis man is a big company
+ 
+
+ align:start position:0%
+companies Manis man is a big company
+that's why companies eventually did kind
+
+ align:start position:0%
+that's why companies eventually did kind
+ 
+
+ align:start position:0%
+that's why companies eventually did kind
+of get into those the markets that they
+
+ align:start position:0%
+of get into those the markets that they
+ 
+
+ align:start position:0%
+of get into those the markets that they
+s they saw it yeah you they sold cheaper
+
+ align:start position:0%
+s they saw it yeah you they sold cheaper
+ 
+
+ align:start position:0%
+s they saw it yeah you they sold cheaper
+machines that could do the same job
+
+ align:start position:0%
+machines that could do the same job
+ 
+
+ align:start position:0%
+machines that could do the same job
+maybe not the same quality close and try
+
+ align:start position:0%
+maybe not the same quality close and try
+ 
+
+ align:start position:0%
+maybe not the same quality close and try
+to come in on price yeah the kind of
+
+ align:start position:0%
+to come in on price yeah the kind of
+ 
+
+ align:start position:0%
+to come in on price yeah the kind of
+customer though that's like concerned
+
+ align:start position:0%
+customer though that's like concerned
+ 
+
+ align:start position:0%
+customer though that's like concerned
+about quality and is willing to pay more
+
+ align:start position:0%
+about quality and is willing to pay more
+ 
+
+ align:start position:0%
+about quality and is willing to pay more
+for it like it would make more sense it
+
+ align:start position:0%
+for it like it would make more sense it
+ 
+
+ align:start position:0%
+for it like it would make more sense it
+would go with the company that has been
+
+ align:start position:0%
+would go with the company that has been
+ 
+
+ align:start position:0%
+would go with the company that has been
+doing it for longer and kind of has the
+
+ align:start position:0%
+doing it for longer and kind of has the
+ 
+
+ align:start position:0%
+doing it for longer and kind of has the
+history and reputation rather than you
+
+ align:start position:0%
+history and reputation rather than you
+ 
+
+ align:start position:0%
+history and reputation rather than you
+know a company that is just like copy
+
+ align:start position:0%
+know a company that is just like copy
+ 
+
+ align:start position:0%
+know a company that is just like copy
+their technology and is doing that n of
+
+ align:start position:0%
+their technology and is doing that n of
+ 
+
+ align:start position:0%
+their technology and is doing that n of
+the market and doesn't have reputation
+
+ align:start position:0%
+the market and doesn't have reputation
+ 
+
+ align:start position:0%
+the market and doesn't have reputation
+and they've really sort of built the
+
+ align:start position:0%
+and they've really sort of built the
+ 
+
+ align:start position:0%
+and they've really sort of built the
+company to do this haven't they Mario
+
+ align:start position:0%
+company to do this haven't they Mario
+ 
+
+ align:start position:0%
+company to do this haven't they Mario
+well my guess would be um if you if you
+
+ align:start position:0%
+well my guess would be um if you if you
+ 
+
+ align:start position:0%
+well my guess would be um if you if you
+try to imitate you're effectively
+
+ align:start position:0%
+try to imitate you're effectively
+ 
+
+ align:start position:0%
+try to imitate you're effectively
+increaseing competition that you know
+
+ align:start position:0%
+increaseing competition that you know
+ 
+
+ align:start position:0%
+increaseing competition that you know
+does make into bits not as profitable as
+
+ align:start position:0%
+does make into bits not as profitable as
+ 
+
+ align:start position:0%
+does make into bits not as profitable as
+it would be otherwise so the segment may
+
+ align:start position:0%
+it would be otherwise so the segment may
+ 
+
+ align:start position:0%
+it would be otherwise so the segment may
+not be may not be that big you're saying
+
+ align:start position:0%
+not be may not be that big you're saying
+ 
+
+ align:start position:0%
+not be may not be that big you're saying
+and so you'd have to do the numbers to
+
+ align:start position:0%
+and so you'd have to do the numbers to
+ 
+
+ align:start position:0%
+and so you'd have to do the numbers to
+say is there room for two of us to play
+
+ align:start position:0%
+say is there room for two of us to play
+ 
+
+ align:start position:0%
+say is there room for two of us to play
+this game Maxwell also a lot to do with
+
+ align:start position:0%
+this game Maxwell also a lot to do with
+ 
+
+ align:start position:0%
+this game Maxwell also a lot to do with
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+culture that
+
+ align:start position:0%
+culture that
+ 
+
+ align:start position:0%
+culture that
+cure it's hard to swi entire culture
+
+ align:start position:0%
+cure it's hard to swi entire culture
+ 
+
+ align:start position:0%
+cure it's hard to swi entire culture
+yeah the culture is sort of part of it
+
+ align:start position:0%
+yeah the culture is sort of part of it
+ 
+
+ align:start position:0%
+yeah the culture is sort of part of it
+is an intriguing part of it isn't it
+
+ align:start position:0%
+is an intriguing part of it isn't it
+ 
+
+ align:start position:0%
+is an intriguing part of it isn't it
+they've got a peculiar culture and I
+
+ align:start position:0%
+they've got a peculiar culture and I
+ 
+
+ align:start position:0%
+they've got a peculiar culture and I
+want to come back to that Charlotte also
+
+ align:start position:0%
+want to come back to that Charlotte also
+ 
+
+ align:start position:0%
+want to come back to that Charlotte also
+the fact that like we said they were
+
+ align:start position:0%
+the fact that like we said they were
+ 
+
+ align:start position:0%
+the fact that like we said they were
+they're only focusing on this one thing
+
+ align:start position:0%
+they're only focusing on this one thing
+ 
+
+ align:start position:0%
+they're only focusing on this one thing
+whereas other companies that were also
+
+ align:start position:0%
+whereas other companies that were also
+ 
+
+ align:start position:0%
+whereas other companies that were also
+in this mold making business focus more
+
+ align:start position:0%
+in this mold making business focus more
+ 
+
+ align:start position:0%
+in this mold making business focus more
+widely like even when they started to
+
+ align:start position:0%
+widely like even when they started to
+ 
+
+ align:start position:0%
+widely like even when they started to
+come into this area they sort of added
+
+ align:start position:0%
+come into this area they sort of added
+ 
+
+ align:start position:0%
+come into this area they sort of added
+it on to the machines they already had
+
+ align:start position:0%
+it on to the machines they already had
+ 
+
+ align:start position:0%
+it on to the machines they already had
+instead of like actually changing into
+
+ align:start position:0%
+instead of like actually changing into
+ 
+
+ align:start position:0%
+instead of like actually changing into
+the same company as H like nobody like
+
+ align:start position:0%
+the same company as H like nobody like
+ 
+
+ align:start position:0%
+the same company as H like nobody like
+shut down all their other manufacturing
+
+ align:start position:0%
+shut down all their other manufacturing
+ 
+
+ align:start position:0%
+shut down all their other manufacturing
+and focused specifically on these two
+
+ align:start position:0%
+and focused specifically on these two
+ 
+
+ align:start position:0%
+and focused specifically on these two
+things they kind of just like
+
+ align:start position:0%
+things they kind of just like
+ 
+
+ align:start position:0%
+things they kind of just like
+Incorporated it into what they were
+
+ align:start position:0%
+Incorporated it into what they were
+ 
+
+ align:start position:0%
+Incorporated it into what they were
+already doing so maybe companies like
+
+ align:start position:0%
+already doing so maybe companies like
+ 
+
+ align:start position:0%
+already doing so maybe companies like
+whenever they calculated what it would
+
+ align:start position:0%
+whenever they calculated what it would
+ 
+
+ align:start position:0%
+whenever they calculated what it would
+take for them to get to the point where
+
+ align:start position:0%
+take for them to get to the point where
+ 
+
+ align:start position:0%
+take for them to get to the point where
+husky was would just have like change
+
+ align:start position:0%
+husky was would just have like change
+ 
+
+ align:start position:0%
+husky was would just have like change
+their compy so this is It's would sort
+
+ align:start position:0%
+their compy so this is It's would sort
+ 
+
+ align:start position:0%
+their compy so this is It's would sort
+of be a little bit of the reverse of
+
+ align:start position:0%
+of be a little bit of the reverse of
+ 
+
+ align:start position:0%
+of be a little bit of the reverse of
+Continental versus Continental light
+
+ align:start position:0%
+Continental versus Continental light
+ 
+
+ align:start position:0%
+Continental versus Continental light
+this would be like um well they tried it
+
+ align:start position:0%
+this would be like um well they tried it
+ 
+
+ align:start position:0%
+this would be like um well they tried it
+this would be like grafting a luxury car
+
+ align:start position:0%
+this would be like grafting a luxury car
+ 
+
+ align:start position:0%
+this would be like grafting a luxury car
+business onto Volkswagen or as Toyota
+
+ align:start position:0%
+business onto Volkswagen or as Toyota
+ 
+
+ align:start position:0%
+business onto Volkswagen or as Toyota
+did doing Lexus which they set off to
+
+ align:start position:0%
+did doing Lexus which they set off to
+ 
+
+ align:start position:0%
+did doing Lexus which they set off to
+one side because you really couldn't do
+
+ align:start position:0%
+one side because you really couldn't do
+ 
+
+ align:start position:0%
+one side because you really couldn't do
+the mainstream Toyota business and the
+
+ align:start position:0%
+the mainstream Toyota business and the
+ 
+
+ align:start position:0%
+the mainstream Toyota business and the
+Lexus business under the same management
+
+ align:start position:0%
+Lexus business under the same management
+ 
+
+ align:start position:0%
+Lexus business under the same management
+so part of it is they really built it
+
+ align:start position:0%
+so part of it is they really built it
+ 
+
+ align:start position:0%
+so part of it is they really built it
+for this uh do you think it has higher
+
+ align:start position:0%
+for this uh do you think it has higher
+ 
+
+ align:start position:0%
+for this uh do you think it has higher
+or lower than average costs that's
+
+ align:start position:0%
+or lower than average costs that's
+ 
+
+ align:start position:0%
+or lower than average costs that's
+pretty clear I
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+think Matthew what do you think you
+
+ align:start position:0%
+think Matthew what do you think you
+ 
+
+ align:start position:0%
+think Matthew what do you think you
+think Husky's a high cost operation or a
+
+ align:start position:0%
+think Husky's a high cost operation or a
+ 
+
+ align:start position:0%
+think Husky's a high cost operation or a
+lowcost
+
+ align:start position:0%
+lowcost
+ 
+
+ align:start position:0%
+lowcost
+operation uh well I mean they're they're
+
+ align:start position:0%
+operation uh well I mean they're they're
+ 
+
+ align:start position:0%
+operation uh well I mean they're they're
+high in the sense of like charging no
+
+ align:start position:0%
+high in the sense of like charging no
+ 
+
+ align:start position:0%
+high in the sense of like charging no
+not in terms of high price but in terms
+
+ align:start position:0%
+not in terms of high price but in terms
+ 
+
+ align:start position:0%
+not in terms of high price but in terms
+of their cost
+
+ align:start position:0%
+of their cost
+ 
+
+ align:start position:0%
+of their cost
+oh even though they've got this lab on
+
+ align:start position:0%
+oh even though they've got this lab on
+ 
+
+ align:start position:0%
+oh even though they've got this lab on
+the side they've got this Advanced
+
+ align:start position:0%
+the side they've got this Advanced
+ 
+
+ align:start position:0%
+the side they've got this Advanced
+manufacturing center they've got daycare
+
+ align:start position:0%
+manufacturing center they've got daycare
+ 
+
+ align:start position:0%
+manufacturing center they've got daycare
+they very ecologically
+
+ align:start position:0%
+they very ecologically
+ 
+
+ align:start position:0%
+they very ecologically
+good charging high for is that nobody
+
+ align:start position:0%
+good charging high for is that nobody
+ 
+
+ align:start position:0%
+good charging high for is that nobody
+can
+
+ align:start position:0%
+can
+ 
+
+ align:start position:0%
+can
+produce nice as they are and so like I'm
+
+ align:start position:0%
+produce nice as they are and so like I'm
+ 
+
+ align:start position:0%
+produce nice as they are and so like I'm
+I'm saying low in comparison to what
+
+ align:start position:0%
+I'm saying low in comparison to what
+ 
+
+ align:start position:0%
+I'm saying low in comparison to what
+they're charging that may be but but in
+
+ align:start position:0%
+they're charging that may be but but in
+ 
+
+ align:start position:0%
+they're charging that may be but but in
+comparison to their competitors uh
+
+ align:start position:0%
+comparison to their competitors uh
+ 
+
+ align:start position:0%
+comparison to their competitors uh
+they're higher because they're producing
+
+ align:start position:0%
+they're higher because they're producing
+ 
+
+ align:start position:0%
+they're higher because they're producing
+higher quality they're producing higher
+
+ align:start position:0%
+higher quality they're producing higher
+ 
+
+ align:start position:0%
+higher quality they're producing higher
+quality and if you think about the
+
+ align:start position:0%
+quality and if you think about the
+ 
+
+ align:start position:0%
+quality and if you think about the
+culture and everything else this is not
+
+ align:start position:0%
+culture and everything else this is not
+ 
+
+ align:start position:0%
+culture and everything else this is not
+a company that
+
+ align:start position:0%
+a company that
+ 
+
+ align:start position:0%
+a company that
+skimps this is not a company that skimps
+
+ align:start position:0%
+skimps this is not a company that skimps
+ 
+
+ align:start position:0%
+skimps this is not a company that skimps
+they invest in R&D they invest in
+
+ align:start position:0%
+they invest in R&D they invest in
+ 
+
+ align:start position:0%
+they invest in R&D they invest in
+technology they invest in their people
+
+ align:start position:0%
+technology they invest in their people
+ 
+
+ align:start position:0%
+technology they invest in their people
+um do you think that's important the
+
+ align:start position:0%
+um do you think that's important the
+ 
+
+ align:start position:0%
+um do you think that's important the
+culture is that is that a key part of
+
+ align:start position:0%
+culture is that is that a key part of
+ 
+
+ align:start position:0%
+culture is that is that a key part of
+the story you
+
+ align:start position:0%
+the story you
+ 
+
+ align:start position:0%
+the story you
+think not sure I know the answer to this
+
+ align:start position:0%
+think not sure I know the answer to this
+ 
+
+ align:start position:0%
+think not sure I know the answer to this
+but um just we've mentioned before it's
+
+ align:start position:0%
+but um just we've mentioned before it's
+ 
+
+ align:start position:0%
+but um just we've mentioned before it's
+something you can get up in the morning
+
+ align:start position:0%
+something you can get up in the morning
+ 
+
+ align:start position:0%
+something you can get up in the morning
+go and work for Keeps people motivated
+
+ align:start position:0%
+go and work for Keeps people motivated
+ 
+
+ align:start position:0%
+go and work for Keeps people motivated
+keeps your
+
+ align:start position:0%
+keeps your
+ 
+
+ align:start position:0%
+keeps your
+work even getting your tsquare imagine T
+
+ align:start position:0%
+work even getting your tsquare imagine T
+ 
+
+ align:start position:0%
+work even getting your tsquare imagine T
+squares even getting your tsquare
+
+ align:start position:0%
+squares even getting your tsquare
+ 
+
+ align:start position:0%
+squares even getting your tsquare
+straightened on your desk you think
+
+ align:start position:0%
+straightened on your desk you think
+ 
+
+ align:start position:0%
+straightened on your desk you think
+I mean it's it's it's a it's
+
+ align:start position:0%
+I mean it's it's it's a it's
+ 
+
+ align:start position:0%
+I mean it's it's it's a it's
+an yeah it's an neatening your code when
+
+ align:start position:0%
+an yeah it's an neatening your code when
+ 
+
+ align:start position:0%
+an yeah it's an neatening your code when
+you're gone it's an interesting culture
+
+ align:start position:0%
+you're gone it's an interesting culture
+ 
+
+ align:start position:0%
+you're gone it's an interesting culture
+I have to say Matthew you raising your
+
+ align:start position:0%
+I have to say Matthew you raising your
+ 
+
+ align:start position:0%
+I have to say Matthew you raising your
+hand yeah uh I mean they said in there
+
+ align:start position:0%
+hand yeah uh I mean they said in there
+ 
+
+ align:start position:0%
+hand yeah uh I mean they said in there
+that whenever they extended had like
+
+ align:start position:0%
+that whenever they extended had like
+ 
+
+ align:start position:0%
+that whenever they extended had like
+extended daycare hours it was uh kind of
+
+ align:start position:0%
+extended daycare hours it was uh kind of
+ 
+
+ align:start position:0%
+extended daycare hours it was uh kind of
+a things like make them work harder not
+
+ align:start position:0%
+a things like make them work harder not
+ 
+
+ align:start position:0%
+a things like make them work harder not
+just for extended dayare hours for the
+
+ align:start position:0%
+just for extended dayare hours for the
+ 
+
+ align:start position:0%
+just for extended dayare hours for the
+kids well they're not they're not doing
+
+ align:start position:0%
+kids well they're not they're not doing
+ 
+
+ align:start position:0%
+kids well they're not they're not doing
+charity are they but they have a
+
+ align:start position:0%
+charity are they but they have a
+ 
+
+ align:start position:0%
+charity are they but they have a
+particular culture of we value our
+
+ align:start position:0%
+particular culture of we value our
+ 
+
+ align:start position:0%
+particular culture of we value our
+people we value the environment we value
+
+ align:start position:0%
+people we value the environment we value
+ 
+
+ align:start position:0%
+people we value the environment we value
+Excellence which would be a tough
+
+ align:start position:0%
+Excellence which would be a tough
+ 
+
+ align:start position:0%
+Excellence which would be a tough
+culture to sustain if they were ending
+
+ align:start position:0%
+culture to sustain if they were ending
+ 
+
+ align:start position:0%
+culture to sustain if they were ending
+for the aiming for the low end of the
+
+ align:start position:0%
+for the aiming for the low end of the
+ 
+
+ align:start position:0%
+for the aiming for the low end of the
+market right if you're aiming for the
+
+ align:start position:0%
+market right if you're aiming for the
+ 
+
+ align:start position:0%
+market right if you're aiming for the
+lowend that's tough if you're aiming for
+
+ align:start position:0%
+lowend that's tough if you're aiming for
+ 
+
+ align:start position:0%
+lowend that's tough if you're aiming for
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+highend it's like Ritz Carlton aim
+
+ align:start position:0%
+highend it's like Ritz Carlton aim
+ 
+
+ align:start position:0%
+highend it's like Ritz Carlton aim
+hotels aim for a particular kind of
+
+ align:start position:0%
+hotels aim for a particular kind of
+ 
+
+ align:start position:0%
+hotels aim for a particular kind of
+service and their code is ladies and
+
+ align:start position:0%
+service and their code is ladies and
+ 
+
+ align:start position:0%
+service and their code is ladies and
+gentlemen served by ladies and gentlemen
+
+ align:start position:0%
+gentlemen served by ladies and gentlemen
+ 
+
+ align:start position:0%
+gentlemen served by ladies and gentlemen
+if you're going to treat your people
+
+ align:start position:0%
+if you're going to treat your people
+ 
+
+ align:start position:0%
+if you're going to treat your people
+like ladies and
+
+ align:start position:0%
+like ladies and
+ 
+
+ align:start position:0%
+like ladies and
+gentlemen you're going to have higher
+
+ align:start position:0%
+gentlemen you're going to have higher
+ 
+
+ align:start position:0%
+gentlemen you're going to have higher
+costs than if you treat them like Pon
+
+ align:start position:0%
+costs than if you treat them like Pon
+ 
+
+ align:start position:0%
+costs than if you treat them like Pon
+scum you will also with some luck get
+
+ align:start position:0%
+scum you will also with some luck get
+ 
+
+ align:start position:0%
+scum you will also with some luck get
+better get better service so this is a
+
+ align:start position:0%
+better get better service so this is a
+ 
+
+ align:start position:0%
+better get better service so this is a
+culture that really does aim high would
+
+ align:start position:0%
+culture that really does aim high would
+ 
+
+ align:start position:0%
+culture that really does aim high would
+you like to work
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+there show of hands who'd like to work
+
+ align:start position:0%
+there show of hands who'd like to work
+ 
+
+ align:start position:0%
+there show of hands who'd like to work
+for this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+company okay who would find it really
+
+ align:start position:0%
+company okay who would find it really
+ 
+
+ align:start position:0%
+company okay who would find it really
+awful Charlotte would not like her T
+
+ align:start position:0%
+awful Charlotte would not like her T
+ 
+
+ align:start position:0%
+awful Charlotte would not like her T
+Square straightened NE neither would
+
+ align:start position:0%
+Square straightened NE neither would
+ 
+
+ align:start position:0%
+Square straightened NE neither would
+Maxwell okay I mean it's a it's it's for
+
+ align:start position:0%
+Maxwell okay I mean it's a it's it's for
+ 
+
+ align:start position:0%
+Maxwell okay I mean it's a it's it's for
+some people and not for others right
+
+ align:start position:0%
+some people and not for others right
+ 
+
+ align:start position:0%
+some people and not for others right
+it's it's
+
+ align:start position:0%
+it's it's
+ 
+
+ align:start position:0%
+it's it's
+autocratic the boss runs it one of the
+
+ align:start position:0%
+autocratic the boss runs it one of the
+ 
+
+ align:start position:0%
+autocratic the boss runs it one of the
+questions it's suggested for discussion
+
+ align:start position:0%
+questions it's suggested for discussion
+ 
+
+ align:start position:0%
+questions it's suggested for discussion
+is could you do this company without um
+
+ align:start position:0%
+is could you do this company without um
+ 
+
+ align:start position:0%
+is could you do this company without um
+uh what's his face shap in charge uh
+
+ align:start position:0%
+uh what's his face shap in charge uh
+ 
+
+ align:start position:0%
+uh what's his face shap in charge uh
+could you Shad rather could you do this
+
+ align:start position:0%
+could you Shad rather could you do this
+ 
+
+ align:start position:0%
+could you Shad rather could you do this
+without an autocrat in charge such a
+
+ align:start position:0%
+without an autocrat in charge such a
+ 
+
+ align:start position:0%
+without an autocrat in charge such a
+strong culture such a tight Focus
+
+ align:start position:0%
+strong culture such a tight Focus
+ 
+
+ align:start position:0%
+strong culture such a tight Focus
+not obvious not
+
+ align:start position:0%
+not obvious not
+ 
+
+ align:start position:0%
+not obvious not
+obvious
+
+ align:start position:0%
+obvious
+ 
+
+ align:start position:0%
+obvious
+okay uh what else do I want to do this
+
+ align:start position:0%
+okay uh what else do I want to do this
+ 
+
+ align:start position:0%
+okay uh what else do I want to do this
+is some numbers which I I don't expect
+
+ align:start position:0%
+is some numbers which I I don't expect
+ 
+
+ align:start position:0%
+is some numbers which I I don't expect
+you to have done and I should have made
+
+ align:start position:0%
+you to have done and I should have made
+ 
+
+ align:start position:0%
+you to have done and I should have made
+this clear because you can do a fair
+
+ align:start position:0%
+this clear because you can do a fair
+ 
+
+ align:start position:0%
+this clear because you can do a fair
+amount of work on the numbers but and
+
+ align:start position:0%
+amount of work on the numbers but and
+ 
+
+ align:start position:0%
+amount of work on the numbers but and
+I'll illustrate this kind of analysis
+
+ align:start position:0%
+I'll illustrate this kind of analysis
+ 
+
+ align:start position:0%
+I'll illustrate this kind of analysis
+for products like
+
+ align:start position:0%
+for products like
+ 
+
+ align:start position:0%
+for products like
+this you can it is often
+
+ align:start position:0%
+this you can it is often
+ 
+
+ align:start position:0%
+this you can it is often
+useful and Energy Products a lot of them
+
+ align:start position:0%
+useful and Energy Products a lot of them
+ 
+
+ align:start position:0%
+useful and Energy Products a lot of them
+come into this category like light bulbs
+
+ align:start position:0%
+come into this category like light bulbs
+ 
+
+ align:start position:0%
+come into this category like light bulbs
+you can you can do the demand analysis
+
+ align:start position:0%
+you can you can do the demand analysis
+ 
+
+ align:start position:0%
+you can you can do the demand analysis
+by simply turning yourself around and
+
+ align:start position:0%
+by simply turning yourself around and
+ 
+
+ align:start position:0%
+by simply turning yourself around and
+thinking about this as a
+
+ align:start position:0%
+thinking about this as a
+ 
+
+ align:start position:0%
+thinking about this as a
+buyer if you were a buyer producing
+
+ align:start position:0%
+buyer if you were a buyer producing
+ 
+
+ align:start position:0%
+buyer if you were a buyer producing
+bottles what would you be willing to pay
+
+ align:start position:0%
+bottles what would you be willing to pay
+ 
+
+ align:start position:0%
+bottles what would you be willing to pay
+for a husky system versus some other
+
+ align:start position:0%
+for a husky system versus some other
+ 
+
+ align:start position:0%
+for a husky system versus some other
+system given the parameters and that
+
+ align:start position:0%
+system given the parameters and that
+ 
+
+ align:start position:0%
+system given the parameters and that
+gives you a sense of what husky can
+
+ align:start position:0%
+gives you a sense of what husky can
+ 
+
+ align:start position:0%
+gives you a sense of what husky can
+charge given other people's it's it's a
+
+ align:start position:0%
+charge given other people's it's it's a
+ 
+
+ align:start position:0%
+charge given other people's it's it's a
+um it's easier when it's something like
+
+ align:start position:0%
+um it's easier when it's something like
+ 
+
+ align:start position:0%
+um it's easier when it's something like
+we're making bottles it's a little
+
+ align:start position:0%
+we're making bottles it's a little
+ 
+
+ align:start position:0%
+we're making bottles it's a little
+harder when we're making Priuses is cuz
+
+ align:start position:0%
+harder when we're making Priuses is cuz
+ 
+
+ align:start position:0%
+harder when we're making Priuses is cuz
+you don't know what the willingness to
+
+ align:start position:0%
+you don't know what the willingness to
+ 
+
+ align:start position:0%
+you don't know what the willingness to
+pay for intangibles
+
+ align:start position:0%
+pay for intangibles
+ 
+
+ align:start position:0%
+pay for intangibles
+is or hardwood Interiors in a car that
+
+ align:start position:0%
+is or hardwood Interiors in a car that
+ 
+
+ align:start position:0%
+is or hardwood Interiors in a car that
+you can't sort of read off the process
+
+ align:start position:0%
+you can't sort of read off the process
+ 
+
+ align:start position:0%
+you can't sort of read off the process
+figures but but for something like light
+
+ align:start position:0%
+figures but but for something like light
+ 
+
+ align:start position:0%
+figures but but for something like light
+bulbs for something like injection
+
+ align:start position:0%
+bulbs for something like injection
+ 
+
+ align:start position:0%
+bulbs for something like injection
+molding machines you can say okay I'm
+
+ align:start position:0%
+molding machines you can say okay I'm
+ 
+
+ align:start position:0%
+molding machines you can say okay I'm
+running a factory what would I buy at
+
+ align:start position:0%
+running a factory what would I buy at
+ 
+
+ align:start position:0%
+running a factory what would I buy at
+different prices and turn the analysis
+
+ align:start position:0%
+different prices and turn the analysis
+ 
+
+ align:start position:0%
+different prices and turn the analysis
+around and I'll just show you the
+
+ align:start position:0%
+around and I'll just show you the
+ 
+
+ align:start position:0%
+around and I'll just show you the
+results these aren't my numbers these
+
+ align:start position:0%
+results these aren't my numbers these
+ 
+
+ align:start position:0%
+results these aren't my numbers these
+are somebody else's numbers but it's
+
+ align:start position:0%
+are somebody else's numbers but it's
+ 
+
+ align:start position:0%
+are somebody else's numbers but it's
+it's useful for this kind of analysis
+
+ align:start position:0%
+it's useful for this kind of analysis
+ 
+
+ align:start position:0%
+it's useful for this kind of analysis
+you basically want to say start with
+
+ align:start position:0%
+you basically want to say start with
+ 
+
+ align:start position:0%
+you basically want to say start with
+arriv
+
+ align:start position:0%
+arriv
+ 
+
+ align:start position:0%
+arriv
+Ral what would it cost in terms of the
+
+ align:start position:0%
+Ral what would it cost in terms of the
+ 
+
+ align:start position:0%
+Ral what would it cost in terms of the
+machine maybe the fact that you've got
+
+ align:start position:0%
+machine maybe the fact that you've got
+ 
+
+ align:start position:0%
+machine maybe the fact that you've got
+to get more machines because it's not as
+
+ align:start position:0%
+to get more machines because it's not as
+ 
+
+ align:start position:0%
+to get more machines because it's not as
+productive the fact that maybe it takes
+
+ align:start position:0%
+productive the fact that maybe it takes
+ 
+
+ align:start position:0%
+productive the fact that maybe it takes
+more energy the fact that it takes more
+
+ align:start position:0%
+more energy the fact that it takes more
+ 
+
+ align:start position:0%
+more energy the fact that it takes more
+raw materials what would it cost you
+
+ align:start position:0%
+raw materials what would it cost you
+ 
+
+ align:start position:0%
+raw materials what would it cost you
+this is called P star to do what you get
+
+ align:start position:0%
+this is called P star to do what you get
+ 
+
+ align:start position:0%
+this is called P star to do what you get
+out of a Husky system for price P you
+
+ align:start position:0%
+out of a Husky system for price P you
+ 
+
+ align:start position:0%
+out of a Husky system for price P you
+there's enough in the case you can do
+
+ align:start position:0%
+there's enough in the case you can do
+ 
+
+ align:start position:0%
+there's enough in the case you can do
+this if you're very
+
+ align:start position:0%
+this if you're very
+ 
+
+ align:start position:0%
+this if you're very
+ambitious for thin walls and for pet
+
+ align:start position:0%
+ambitious for thin walls and for pet
+ 
+
+ align:start position:0%
+ambitious for thin walls and for pet
+systems this is the calculation a
+
+ align:start position:0%
+systems this is the calculation a
+ 
+
+ align:start position:0%
+systems this is the calculation a
+calculation for thin
+
+ align:start position:0%
+calculation for thin
+ 
+
+ align:start position:0%
+calculation for thin
+wall the
+
+ align:start position:0%
+wall the
+ 
+
+ align:start position:0%
+wall the
+competitors for Mar used marger and
+
+ align:start position:0%
+competitors for Mar used marger and
+ 
+
+ align:start position:0%
+competitors for Mar used marger and
+containers the competitor's system takes
+
+ align:start position:0%
+containers the competitor's system takes
+ 
+
+ align:start position:0%
+containers the competitor's system takes
+has a longer cycle time it produces uh a
+
+ align:start position:0%
+has a longer cycle time it produces uh a
+ 
+
+ align:start position:0%
+has a longer cycle time it produces uh a
+heavier components a heavier weight
+
+ align:start position:0%
+heavier components a heavier weight
+ 
+
+ align:start position:0%
+heavier components a heavier weight
+container it costs less
+
+ align:start position:0%
+container it costs less
+ 
+
+ align:start position:0%
+container it costs less
+so to get the same
+
+ align:start position:0%
+so to get the same
+ 
+
+ align:start position:0%
+so to get the same
+output again this assumes you have a
+
+ align:start position:0%
+output again this assumes you have a
+ 
+
+ align:start position:0%
+output again this assumes you have a
+large Factory you'd need one and 2/3
+
+ align:start position:0%
+large Factory you'd need one and 2/3
+ 
+
+ align:start position:0%
+large Factory you'd need one and 2/3
+competitor machines uh for uh to get as
+
+ align:start position:0%
+competitor machines uh for uh to get as
+ 
+
+ align:start position:0%
+competitor machines uh for uh to get as
+much as out of a Husky
+
+ align:start position:0%
+much as out of a Husky
+ 
+
+ align:start position:0%
+much as out of a Husky
+machine that means one and 2/3 time 350
+
+ align:start position:0%
+machine that means one and 2/3 time 350
+ 
+
+ align:start position:0%
+machine that means one and 2/3 time 350
+is
+
+ align:start position:0%
+is
+ 
+
+ align:start position:0%
+is
+408 there's also a resin saving because
+
+ align:start position:0%
+408 there's also a resin saving because
+ 
+
+ align:start position:0%
+408 there's also a resin saving because
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+Husky container is
+
+ align:start position:0%
+Husky container is
+ 
+
+ align:start position:0%
+Husky container is
+lighter so to replace a $400,000 husky
+
+ align:start position:0%
+lighter so to replace a $400,000 husky
+ 
+
+ align:start position:0%
+lighter so to replace a $400,000 husky
+machine
+
+ align:start position:0%
+machine
+ 
+
+ align:start position:0%
+machine
+machine you'd have to do uh
+
+ align:start position:0%
+machine you'd have to do uh
+ 
+
+ align:start position:0%
+machine you'd have to do uh
+$448,000 versus worth of competitor
+
+ align:start position:0%
+$448,000 versus worth of competitor
+ 
+
+ align:start position:0%
+$448,000 versus worth of competitor
+Equipment Plus extra resin per year all
+
+ align:start position:0%
+Equipment Plus extra resin per year all
+ 
+
+ align:start position:0%
+Equipment Plus extra resin per year all
+right that's a willingness to pay
+
+ align:start position:0%
+right that's a willingness to pay
+ 
+
+ align:start position:0%
+right that's a willingness to pay
+analysis so that says husky could
+
+ align:start position:0%
+analysis so that says husky could
+ 
+
+ align:start position:0%
+analysis so that says husky could
+depending on how the competitor
+
+ align:start position:0%
+depending on how the competitor
+ 
+
+ align:start position:0%
+depending on how the competitor
+discounted and depending on how much the
+
+ align:start position:0%
+discounted and depending on how much the
+ 
+
+ align:start position:0%
+discounted and depending on how much the
+competitor produced husky could charge
+
+ align:start position:0%
+competitor produced husky could charge
+ 
+
+ align:start position:0%
+competitor produced husky could charge
+even more than
+
+ align:start position:0%
+even more than
+ 
+
+ align:start position:0%
+even more than
+$400,000 and would still be the machine
+
+ align:start position:0%
+$400,000 and would still be the machine
+ 
+
+ align:start position:0%
+$400,000 and would still be the machine
+of
+
+ align:start position:0%
+of
+ 
+
+ align:start position:0%
+of
+choice right this is the kind of
+
+ align:start position:0%
+choice right this is the kind of
+ 
+
+ align:start position:0%
+choice right this is the kind of
+analysis you would expect a buyer to do
+
+ align:start position:0%
+analysis you would expect a buyer to do
+ 
+
+ align:start position:0%
+analysis you would expect a buyer to do
+deciding what kind of machine to buy and
+
+ align:start position:0%
+deciding what kind of machine to buy and
+ 
+
+ align:start position:0%
+deciding what kind of machine to buy and
+it's the kind of analysis you'd expect
+
+ align:start position:0%
+it's the kind of analysis you'd expect
+ 
+
+ align:start position:0%
+it's the kind of analysis you'd expect
+husky to do in thinking about
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+price in the past I've taught a a
+
+ align:start position:0%
+price in the past I've taught a a
+ 
+
+ align:start position:0%
+price in the past I've taught a a
+pricing course here at Sloan and my my
+
+ align:start position:0%
+pricing course here at Sloan and my my
+ 
+
+ align:start position:0%
+pricing course here at Sloan and my my
+favorite my favorite case is a case
+
+ align:start position:0%
+favorite my favorite case is a case
+ 
+
+ align:start position:0%
+favorite my favorite case is a case
+about contact lenses for
+
+ align:start position:0%
+about contact lenses for
+ 
+
+ align:start position:0%
+about contact lenses for
+chickens and it's a great it's a great
+
+ align:start position:0%
+chickens and it's a great it's a great
+ 
+
+ align:start position:0%
+chickens and it's a great it's a great
+pricing case because the contact lenses
+
+ align:start position:0%
+pricing case because the contact lenses
+ 
+
+ align:start position:0%
+pricing case because the contact lenses
+for chickens cost
+
+ align:start position:0%
+for chickens cost
+ 
+
+ align:start position:0%
+for chickens cost
+nothing you you put them in the chicken
+
+ align:start position:0%
+nothing you you put them in the chicken
+ 
+
+ align:start position:0%
+nothing you you put them in the chicken
+for about 25 cents a chicken they cost
+
+ align:start position:0%
+for about 25 cents a chicken they cost
+ 
+
+ align:start position:0%
+for about 25 cents a chicken they cost
+about a penny and they keep the chickens
+
+ align:start position:0%
+about a penny and they keep the chickens
+ 
+
+ align:start position:0%
+about a penny and they keep the chickens
+if they work from pecking each other to
+
+ align:start position:0%
+if they work from pecking each other to
+ 
+
+ align:start position:0%
+if they work from pecking each other to
+death and if you do the calculation you
+
+ align:start position:0%
+death and if you do the calculation you
+ 
+
+ align:start position:0%
+death and if you do the calculation you
+find those lenses are worth about four
+
+ align:start position:0%
+find those lenses are worth about four
+ 
+
+ align:start position:0%
+find those lenses are worth about four
+bucks a piece madeup number but very
+
+ align:start position:0%
+bucks a piece madeup number but very
+ 
+
+ align:start position:0%
+bucks a piece madeup number but very
+very
+
+ align:start position:0%
+very
+ 
+
+ align:start position:0%
+very
+high and most people in the class
+
+ align:start position:0%
+high and most people in the class
+ 
+
+ align:start position:0%
+high and most people in the class
+immediately say well you know it cost 25
+
+ align:start position:0%
+immediately say well you know it cost 25
+ 
+
+ align:start position:0%
+immediately say well you know it cost 25
+cents so what we'll do is we'll mark it
+
+ align:start position:0%
+cents so what we'll do is we'll mark it
+ 
+
+ align:start position:0%
+cents so what we'll do is we'll mark it
+up to 30
+
+ align:start position:0%
+up to 30
+ 
+
+ align:start position:0%
+up to 30
+and the answer is no if you do the
+
+ align:start position:0%
+and the answer is no if you do the
+ 
+
+ align:start position:0%
+and the answer is no if you do the
+willingness to pay answer you can mark
+
+ align:start position:0%
+willingness to pay answer you can mark
+ 
+
+ align:start position:0%
+willingness to pay answer you can mark
+it up to three
+
+ align:start position:0%
+it up to three
+ 
+
+ align:start position:0%
+it up to three
+bucks as long as you've got the patent
+
+ align:start position:0%
+bucks as long as you've got the patent
+ 
+
+ align:start position:0%
+bucks as long as you've got the patent
+Monopoly on it the buyer would be
+
+ align:start position:0%
+Monopoly on it the buyer would be
+ 
+
+ align:start position:0%
+Monopoly on it the buyer would be
+willing to pay three bucks rather than
+
+ align:start position:0%
+willing to pay three bucks rather than
+ 
+
+ align:start position:0%
+willing to pay three bucks rather than
+do without it in fact if you if it's
+
+ align:start position:0%
+do without it in fact if you if it's
+ 
+
+ align:start position:0%
+do without it in fact if you if it's
+worth $4 on this kind of analysis you
+
+ align:start position:0%
+worth $4 on this kind of analysis you
+ 
+
+ align:start position:0%
+worth $4 on this kind of analysis you
+charge $3 and they're
+
+ align:start position:0%
+charge $3 and they're
+ 
+
+ align:start position:0%
+charge $3 and they're
+happy uh so this is a kind of analysis
+
+ align:start position:0%
+happy uh so this is a kind of analysis
+ 
+
+ align:start position:0%
+happy uh so this is a kind of analysis
+you can do for Industrial
+
+ align:start position:0%
+you can do for Industrial
+ 
+
+ align:start position:0%
+you can do for Industrial
+Products that's a great case except as
+
+ align:start position:0%
+Products that's a great case except as
+ 
+
+ align:start position:0%
+Products that's a great case except as
+it turns out the contact lenses fell out
+
+ align:start position:0%
+it turns out the contact lenses fell out
+ 
+
+ align:start position:0%
+it turns out the contact lenses fell out
+of the chickens the chickens plucked
+
+ align:start position:0%
+of the chickens the chickens plucked
+ 
+
+ align:start position:0%
+of the chickens the chickens plucked
+each other to death and the firm went
+
+ align:start position:0%
+each other to death and the firm went
+ 
+
+ align:start position:0%
+each other to death and the firm went
+broke but
+
+ align:start position:0%
+broke but
+ 
+
+ align:start position:0%
+broke but
+still still it's a great case to teach
+
+ align:start position:0%
+still still it's a great case to teach
+ 
+
+ align:start position:0%
+still still it's a great case to teach
+uh it it it it fails only the realistic
+
+ align:start position:0%
+uh it it it it fails only the realistic
+ 
+
+ align:start position:0%
+uh it it it it fails only the realistic
+test this says the more containers the
+
+ align:start position:0%
+test this says the more containers the
+ 
+
+ align:start position:0%
+test this says the more containers the
+uh somebody wants to produce and the
+
+ align:start position:0%
+uh somebody wants to produce and the
+ 
+
+ align:start position:0%
+uh somebody wants to produce and the
+lower their discount rate uh the better
+
+ align:start position:0%
+lower their discount rate uh the better
+ 
+
+ align:start position:0%
+lower their discount rate uh the better
+the Husky system is this is a similar
+
+ align:start position:0%
+the Husky system is this is a similar
+ 
+
+ align:start position:0%
+the Husky system is this is a similar
+analysis of willingness to pay analysis
+
+ align:start position:0%
+analysis of willingness to pay analysis
+ 
+
+ align:start position:0%
+analysis of willingness to pay analysis
+for a pet preform system and
+
+ align:start position:0%
+for a pet preform system and
+ 
+
+ align:start position:0%
+for a pet preform system and
+again the
+
+ align:start position:0%
+again the
+ 
+
+ align:start position:0%
+again the
+husky husky container weight is lower um
+
+ align:start position:0%
+husky husky container weight is lower um
+ 
+
+ align:start position:0%
+husky husky container weight is lower um
+the cost
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+is lower takes up well I'm going to have
+
+ align:start position:0%
+is lower takes up well I'm going to have
+ 
+
+ align:start position:0%
+is lower takes up well I'm going to have
+to go back the the key things you see
+
+ align:start position:0%
+to go back the the key things you see
+ 
+
+ align:start position:0%
+to go back the the key things you see
+will turn out to be the Energy
+
+ align:start position:0%
+will turn out to be the Energy
+ 
+
+ align:start position:0%
+will turn out to be the Energy
+savings and the resin
+
+ align:start position:0%
+savings and the resin
+ 
+
+ align:start position:0%
+savings and the resin
+savings so what you get here is it
+
+ align:start position:0%
+savings so what you get here is it
+ 
+
+ align:start position:0%
+savings so what you get here is it
+produces a lighter container so there's
+
+ align:start position:0%
+produces a lighter container so there's
+ 
+
+ align:start position:0%
+produces a lighter container so there's
+a residence saving it's more efficient
+
+ align:start position:0%
+a residence saving it's more efficient
+ 
+
+ align:start position:0%
+a residence saving it's more efficient
+so there's an energy saving there's also
+
+ align:start position:0%
+so there's an energy saving there's also
+ 
+
+ align:start position:0%
+so there's an energy saving there's also
+a little floor space saving so it's the
+
+ align:start position:0%
+a little floor space saving so it's the
+ 
+
+ align:start position:0%
+a little floor space saving so it's the
+same thing to replace a husky system
+
+ align:start position:0%
+same thing to replace a husky system
+ 
+
+ align:start position:0%
+same thing to replace a husky system
+costing a million
+
+ align:start position:0%
+costing a million
+ 
+
+ align:start position:0%
+costing a million
+to you'd need to spend more
+
+ align:start position:0%
+to you'd need to spend more
+ 
+
+ align:start position:0%
+to you'd need to spend more
+capacity and more yearly cost so again
+
+ align:start position:0%
+capacity and more yearly cost so again
+ 
+
+ align:start position:0%
+capacity and more yearly cost so again
+when you think
+
+ align:start position:0%
+when you think
+ 
+
+ align:start position:0%
+when you think
+about an industrial
+
+ align:start position:0%
+about an industrial
+ 
+
+ align:start position:0%
+about an industrial
+product this is the sort of analysis you
+
+ align:start position:0%
+product this is the sort of analysis you
+ 
+
+ align:start position:0%
+product this is the sort of analysis you
+go
+
+ align:start position:0%
+go
+ 
+
+ align:start position:0%
+go
+through when you're a buyer you do it
+
+ align:start position:0%
+through when you're a buyer you do it
+ 
+
+ align:start position:0%
+through when you're a buyer you do it
+and when you're seller you do it now
+
+ align:start position:0%
+and when you're seller you do it now
+ 
+
+ align:start position:0%
+and when you're seller you do it now
+again the analysis may be different for
+
+ align:start position:0%
+again the analysis may be different for
+ 
+
+ align:start position:0%
+again the analysis may be different for
+different customers this is a case where
+
+ align:start position:0%
+different customers this is a case where
+ 
+
+ align:start position:0%
+different customers this is a case where
+you're assuming that
+
+ align:start position:0%
+you're assuming that
+ 
+
+ align:start position:0%
+you're assuming that
+again uh I
+
+ align:start position:0%
+again uh I
+ 
+
+ align:start position:0%
+again uh I
+can where have I got it yeah I need 1.34
+
+ align:start position:0%
+can where have I got it yeah I need 1.34
+ 
+
+ align:start position:0%
+can where have I got it yeah I need 1.34
+rival systems to to uh replace a husky
+
+ align:start position:0%
+rival systems to to uh replace a husky
+ 
+
+ align:start position:0%
+rival systems to to uh replace a husky
+system because the Husky system is more
+
+ align:start position:0%
+system because the Husky system is more
+ 
+
+ align:start position:0%
+system because the Husky system is more
+productive well depending on how big the
+
+ align:start position:0%
+productive well depending on how big the
+ 
+
+ align:start position:0%
+productive well depending on how big the
+factory is that may or may not make any
+
+ align:start position:0%
+factory is that may or may not make any
+ 
+
+ align:start position:0%
+factory is that may or may not make any
+sense because they don't come in
+
+ align:start position:0%
+sense because they don't come in
+ 
+
+ align:start position:0%
+sense because they don't come in
+fractions if it's a large thing yeah if
+
+ align:start position:0%
+fractions if it's a large thing yeah if
+ 
+
+ align:start position:0%
+fractions if it's a large thing yeah if
+a typical customer has one
+
+ align:start position:0%
+a typical customer has one
+ 
+
+ align:start position:0%
+a typical customer has one
+system then the analysis is going to be
+
+ align:start position:0%
+system then the analysis is going to be
+ 
+
+ align:start position:0%
+system then the analysis is going to be
+different okay any questions about this
+
+ align:start position:0%
+different okay any questions about this
+ 
+
+ align:start position:0%
+different okay any questions about this
+kind of analysis this sort of you know
+
+ align:start position:0%
+kind of analysis this sort of you know
+ 
+
+ align:start position:0%
+kind of analysis this sort of you know
+folks with an engineering background
+
+ align:start position:0%
+folks with an engineering background
+ 
+
+ align:start position:0%
+folks with an engineering background
+this sort of ought to come pretty
+
+ align:start position:0%
+this sort of ought to come pretty
+ 
+
+ align:start position:0%
+this sort of ought to come pretty
+naturally just working out on a
+
+ align:start position:0%
+naturally just working out on a
+ 
+
+ align:start position:0%
+naturally just working out on a
+spreadsheet how would you what would you
+
+ align:start position:0%
+spreadsheet how would you what would you
+ 
+
+ align:start position:0%
+spreadsheet how would you what would you
+do if you didn't buy
+
+ align:start position:0%
+do if you didn't buy
+ 
+
+ align:start position:0%
+do if you didn't buy
+ours uh how would you do it what would
+
+ align:start position:0%
+ours uh how would you do it what would
+ 
+
+ align:start position:0%
+ours uh how would you do it what would
+it cost if is there a Gap is there a Gap
+
+ align:start position:0%
+it cost if is there a Gap is there a Gap
+ 
+
+ align:start position:0%
+it cost if is there a Gap is there a Gap
+so the answer to this is at least as of
+
+ align:start position:0%
+so the answer to this is at least as of
+ 
+
+ align:start position:0%
+so the answer to this is at least as of
+1995 before troubles begin husky
+
+ align:start position:0%
+1995 before troubles begin husky
+ 
+
+ align:start position:0%
+1995 before troubles begin husky
+systems are worth I mean we're charging
+
+ align:start position:0%
+systems are worth I mean we're charging
+ 
+
+ align:start position:0%
+systems are worth I mean we're charging
+a million to for the system but to
+
+ align:start position:0%
+a million to for the system but to
+ 
+
+ align:start position:0%
+a million to for the system but to
+replace it you'd have to spend a
+
+ align:start position:0%
+replace it you'd have to spend a
+ 
+
+ align:start position:0%
+replace it you'd have to spend a
+million3 plus 500,000 a year so in one
+
+ align:start position:0%
+million3 plus 500,000 a year so in one
+ 
+
+ align:start position:0%
+million3 plus 500,000 a year so in one
+sense we are leaving a little money on
+
+ align:start position:0%
+sense we are leaving a little money on
+ 
+
+ align:start position:0%
+sense we are leaving a little money on
+the table in another sense you have to
+
+ align:start position:0%
+the table in another sense you have to
+ 
+
+ align:start position:0%
+the table in another sense you have to
+leave a little money on the table
+
+ align:start position:0%
+leave a little money on the table
+ 
+
+ align:start position:0%
+leave a little money on the table
+because these are approximate
+
+ align:start position:0%
+because these are approximate
+ 
+
+ align:start position:0%
+because these are approximate
+calculations but the answer is Husky
+
+ align:start position:0%
+calculations but the answer is Husky
+ 
+
+ align:start position:0%
+calculations but the answer is Husky
+premiums husky systems Justified their
+
+ align:start position:0%
+premiums husky systems Justified their
+ 
+
+ align:start position:0%
+premiums husky systems Justified their
+premium price going into
+
+ align:start position:0%
+premium price going into
+ 
+
+ align:start position:0%
+premium price going into
+1995 the electricity savings were not an
+
+ align:start position:0%
+1995 the electricity savings were not an
+ 
+
+ align:start position:0%
+1995 the electricity savings were not an
+a trivial part of the reason at least
+
+ align:start position:0%
+a trivial part of the reason at least
+ 
+
+ align:start position:0%
+a trivial part of the reason at least
+for pet preform is this reasonably
+
+ align:start position:0%
+for pet preform is this reasonably
+ 
+
+ align:start position:0%
+for pet preform is this reasonably
+straightforward how you would think
+
+ align:start position:0%
+straightforward how you would think
+ 
+
+ align:start position:0%
+straightforward how you would think
+about doing it just engineer it one way
+
+ align:start position:0%
+about doing it just engineer it one way
+ 
+
+ align:start position:0%
+about doing it just engineer it one way
+engineer it the other way and and check
+
+ align:start position:0%
+engineer it the other way and and check
+ 
+
+ align:start position:0%
+engineer it the other way and and check
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+costs uh all the costs
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay we're now in
+
+ align:start position:0%
+okay we're now in
+ 
+
+ align:start position:0%
+okay we're now in
+1995 what's gone
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+wrong it's a summer of 95 they had a
+
+ align:start position:0%
+wrong it's a summer of 95 they had a
+ 
+
+ align:start position:0%
+wrong it's a summer of 95 they had a
+great year they're depressed yes res
+
+ align:start position:0%
+great year they're depressed yes res
+ 
+
+ align:start position:0%
+great year they're depressed yes res
+costs are increasing okay resin costs
+
+ align:start position:0%
+costs are increasing okay resin costs
+ 
+
+ align:start position:0%
+costs are increasing okay resin costs
+are increasing that's leading to a
+
+ align:start position:0%
+are increasing that's leading to a
+ 
+
+ align:start position:0%
+are increasing that's leading to a
+decrease in
+
+ align:start position:0%
+decrease in
+ 
+
+ align:start position:0%
+decrease in
+demand is that likely to be a temporary
+
+ align:start position:0%
+demand is that likely to be a temporary
+ 
+
+ align:start position:0%
+demand is that likely to be a temporary
+or a permanent situation do you think
+
+ align:start position:0%
+or a permanent situation do you think
+ 
+
+ align:start position:0%
+or a permanent situation do you think
+temporary yeah it's going to be disequil
+
+ align:start position:0%
+temporary yeah it's going to be disequil
+ 
+
+ align:start position:0%
+temporary yeah it's going to be disequil
+we've seen it before it's a commodity
+
+ align:start position:0%
+we've seen it before it's a commodity
+ 
+
+ align:start position:0%
+we've seen it before it's a commodity
+chemical they just have a capacity
+
+ align:start position:0%
+chemical they just have a capacity
+ 
+
+ align:start position:0%
+chemical they just have a capacity
+shortage so we wouldn't get too Twitchy
+
+ align:start position:0%
+shortage so we wouldn't get too Twitchy
+ 
+
+ align:start position:0%
+shortage so we wouldn't get too Twitchy
+about that anything else Matthew a lot
+
+ align:start position:0%
+about that anything else Matthew a lot
+ 
+
+ align:start position:0%
+about that anything else Matthew a lot
+of competing companies have noticed
+
+ align:start position:0%
+of competing companies have noticed
+ 
+
+ align:start position:0%
+of competing companies have noticed
+their success starting step try to take
+
+ align:start position:0%
+their success starting step try to take
+ 
+
+ align:start position:0%
+their success starting step try to take
+some now we got a problem that's more
+
+ align:start position:0%
+some now we got a problem that's more
+ 
+
+ align:start position:0%
+some now we got a problem that's more
+serious that's more
+
+ align:start position:0%
+serious that's more
+ 
+
+ align:start position:0%
+serious that's more
+serious so um and you know these guys
+
+ align:start position:0%
+serious so um and you know these guys
+ 
+
+ align:start position:0%
+serious so um and you know these guys
+have been through resin shortages and
+
+ align:start position:0%
+have been through resin shortages and
+ 
+
+ align:start position:0%
+have been through resin shortages and
+they don't have a lot of debt and
+
+ align:start position:0%
+they don't have a lot of debt and
+ 
+
+ align:start position:0%
+they don't have a lot of debt and
+they'll probably get through this one
+
+ align:start position:0%
+they'll probably get through this one
+ 
+
+ align:start position:0%
+they'll probably get through this one
+in fact I think it fixed itself within a
+
+ align:start position:0%
+in fact I think it fixed itself within a
+ 
+
+ align:start position:0%
+in fact I think it fixed itself within a
+a year maybe two but the lower cost
+
+ align:start position:0%
+a year maybe two but the lower cost
+ 
+
+ align:start position:0%
+a year maybe two but the lower cost
+competitors going after your Prime
+
+ align:start position:0%
+competitors going after your Prime
+ 
+
+ align:start position:0%
+competitors going after your Prime
+customers with lower
+
+ align:start position:0%
+customers with lower
+ 
+
+ align:start position:0%
+customers with lower
+costs that's
+
+ align:start position:0%
+costs that's
+ 
+
+ align:start position:0%
+costs that's
+Troublesome
+
+ align:start position:0%
+Troublesome
+ 
+
+ align:start position:0%
+Troublesome
+so let's look at this two ways let's
+
+ align:start position:0%
+so let's look at this two ways let's
+ 
+
+ align:start position:0%
+so let's look at this two ways let's
+look at it from the point of view first
+
+ align:start position:0%
+look at it from the point of view first
+ 
+
+ align:start position:0%
+look at it from the point of view first
+of a
+
+ align:start position:0%
+of a
+ 
+
+ align:start position:0%
+of a
+competitor suppose you're one of those
+
+ align:start position:0%
+competitor suppose you're one of those
+ 
+
+ align:start position:0%
+competitor suppose you're one of those
+lowcost
+
+ align:start position:0%
+lowcost
+ 
+
+ align:start position:0%
+lowcost
+competitors you know Husky's going to do
+
+ align:start position:0%
+competitors you know Husky's going to do
+ 
+
+ align:start position:0%
+competitors you know Husky's going to do
+something what do you think Husky's
+
+ align:start position:0%
+something what do you think Husky's
+ 
+
+ align:start position:0%
+something what do you think Husky's
+going to do
+
+ align:start position:0%
+going to do
+ 
+
+ align:start position:0%
+going to do
+one question is what will they do and
+
+ align:start position:0%
+one question is what will they do and
+ 
+
+ align:start position:0%
+one question is what will they do and
+what would you think they would do as a
+
+ align:start position:0%
+what would you think they would do as a
+ 
+
+ align:start position:0%
+what would you think they would do as a
+as a competitor and the other is what
+
+ align:start position:0%
+as a competitor and the other is what
+ 
+
+ align:start position:0%
+as a competitor and the other is what
+would you recommend they do those may be
+
+ align:start position:0%
+would you recommend they do those may be
+ 
+
+ align:start position:0%
+would you recommend they do those may be
+the same if they're as smart as you are
+
+ align:start position:0%
+the same if they're as smart as you are
+ 
+
+ align:start position:0%
+the same if they're as smart as you are
+but they may not be they may not be any
+
+ align:start position:0%
+but they may not be they may not be any
+ 
+
+ align:start position:0%
+but they may not be they may not be any
+thoughts about you're a competitor what
+
+ align:start position:0%
+thoughts about you're a competitor what
+ 
+
+ align:start position:0%
+thoughts about you're a competitor what
+do you think husky
+
+ align:start position:0%
+do you think husky
+ 
+
+ align:start position:0%
+do you think husky
+does Sam their customers and stress like
+
+ align:start position:0%
+does Sam their customers and stress like
+ 
+
+ align:start position:0%
+does Sam their customers and stress like
+the quality of their product like these
+
+ align:start position:0%
+the quality of their product like these
+ 
+
+ align:start position:0%
+the quality of their product like these
+guys are new and they're doing low cost
+
+ align:start position:0%
+guys are new and they're doing low cost
+ 
+
+ align:start position:0%
+guys are new and they're doing low cost
+but the only way they do that is they're
+
+ align:start position:0%
+but the only way they do that is they're
+ 
+
+ align:start position:0%
+but the only way they do that is they're
+cut and corn is like our product for but
+
+ align:start position:0%
+cut and corn is like our product for but
+ 
+
+ align:start position:0%
+cut and corn is like our product for but
+you've worked with us for years you know
+
+ align:start position:0%
+you've worked with us for years you know
+ 
+
+ align:start position:0%
+you've worked with us for years you know
+it's trustworthy and just kind of so you
+
+ align:start position:0%
+it's trustworthy and just kind of so you
+ 
+
+ align:start position:0%
+it's trustworthy and just kind of so you
+think so you think what they would do
+
+ align:start position:0%
+think so you think what they would do
+ 
+
+ align:start position:0%
+think so you think what they would do
+would be to because they've always been
+
+ align:start position:0%
+would be to because they've always been
+ 
+
+ align:start position:0%
+would be to because they've always been
+about technology and technological
+
+ align:start position:0%
+about technology and technological
+ 
+
+ align:start position:0%
+about technology and technological
+leadership and quality they're just
+
+ align:start position:0%
+leadership and quality they're just
+ 
+
+ align:start position:0%
+leadership and quality they're just
+going to double down on that they're
+
+ align:start position:0%
+going to double down on that they're
+ 
+
+ align:start position:0%
+going to double down on that they're
+going to do more communication they're
+
+ align:start position:0%
+going to do more communication they're
+ 
+
+ align:start position:0%
+going to do more communication they're
+going to do more
+
+ align:start position:0%
+going to do more
+ 
+
+ align:start position:0%
+going to do more
+Innovation they're going to ride the
+
+ align:start position:0%
+Innovation they're going to ride the
+ 
+
+ align:start position:0%
+Innovation they're going to ride the
+same horse that's more what I think they
+
+ align:start position:0%
+same horse that's more what I think they
+ 
+
+ align:start position:0%
+same horse that's more what I think they
+should do what do you think they will
+
+ align:start position:0%
+should do what do you think they will
+ 
+
+ align:start position:0%
+should do what do you think they will
+do probably I feel like the first thing
+
+ align:start position:0%
+do probably I feel like the first thing
+ 
+
+ align:start position:0%
+do probably I feel like the first thing
+they might try and do lower their costs
+
+ align:start position:0%
+they might try and do lower their costs
+ 
+
+ align:start position:0%
+they might try and do lower their costs
+drop their prices a little bit I I
+
+ align:start position:0%
+drop their prices a little bit I I
+ 
+
+ align:start position:0%
+drop their prices a little bit I I
+that's they would why do you think they
+
+ align:start position:0%
+that's they would why do you think they
+ 
+
+ align:start position:0%
+that's they would why do you think they
+will do
+
+ align:start position:0%
+will do
+ 
+
+ align:start position:0%
+will do
+it you had me sold you had me sold that
+
+ align:start position:0%
+it you had me sold you had me sold that
+ 
+
+ align:start position:0%
+it you had me sold you had me sold that
+that given their whole culture and given
+
+ align:start position:0%
+that given their whole culture and given
+ 
+
+ align:start position:0%
+that given their whole culture and given
+the way the company's been built that
+
+ align:start position:0%
+the way the company's been built that
+ 
+
+ align:start position:0%
+the way the company's been built that
+they would double down on
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Innovation I it's easier to lower it's
+
+ align:start position:0%
+Innovation I it's easier to lower it's
+ 
+
+ align:start position:0%
+Innovation I it's easier to lower it's
+easier to lower easier to lower price in
+
+ align:start position:0%
+easier to lower easier to lower price in
+ 
+
+ align:start position:0%
+easier to lower easier to lower price in
+response I Philip what do you think they
+
+ align:start position:0%
+response I Philip what do you think they
+ 
+
+ align:start position:0%
+response I Philip what do you think they
+will do yeah probably lower the price um
+
+ align:start position:0%
+will do yeah probably lower the price um
+ 
+
+ align:start position:0%
+will do yeah probably lower the price um
+because uh part uh willingness to pay of
+
+ align:start position:0%
+because uh part uh willingness to pay of
+ 
+
+ align:start position:0%
+because uh part uh willingness to pay of
+the buyers is probably going to decrease
+
+ align:start position:0%
+the buyers is probably going to decrease
+ 
+
+ align:start position:0%
+the buyers is probably going to decrease
+because these low competitors because
+
+ align:start position:0%
+because these low competitors because
+ 
+
+ align:start position:0%
+because these low competitors because
+what because the low cost competitors
+
+ align:start position:0%
+what because the low cost competitors
+ 
+
+ align:start position:0%
+what because the low cost competitors
+are rising so the cost of replacing
+
+ align:start position:0%
+are rising so the cost of replacing
+ 
+
+ align:start position:0%
+are rising so the cost of replacing
+their um product is less so they
+
+ align:start position:0%
+their um product is less so they
+ 
+
+ align:start position:0%
+their um product is less so they
+should so you so you think if you you're
+
+ align:start position:0%
+should so you so you think if you you're
+ 
+
+ align:start position:0%
+should so you so you think if you you're
+a competitor the first thing you expect
+
+ align:start position:0%
+a competitor the first thing you expect
+ 
+
+ align:start position:0%
+a competitor the first thing you expect
+them to do is is a price
+
+ align:start position:0%
+them to do is is a price
+ 
+
+ align:start position:0%
+them to do is is a price
+cut okay okay anybody else have any
+
+ align:start position:0%
+cut okay okay anybody else have any
+ 
+
+ align:start position:0%
+cut okay okay anybody else have any
+expect because that's the natural
+
+ align:start position:0%
+expect because that's the natural
+ 
+
+ align:start position:0%
+expect because that's the natural
+response to a lowcost entrant is to come
+
+ align:start position:0%
+response to a lowcost entrant is to come
+ 
+
+ align:start position:0%
+response to a lowcost entrant is to come
+down a bit anybody
+
+ align:start position:0%
+down a bit anybody
+ 
+
+ align:start position:0%
+down a bit anybody
+else David I would not expect them to
+
+ align:start position:0%
+else David I would not expect them to
+ 
+
+ align:start position:0%
+else David I would not expect them to
+cut their prices just because that kills
+
+ align:start position:0%
+cut their prices just because that kills
+ 
+
+ align:start position:0%
+cut their prices just because that kills
+them that's like slip very slow thing
+
+ align:start position:0%
+them that's like slip very slow thing
+ 
+
+ align:start position:0%
+them that's like slip very slow thing
+where then their customers will not be
+
+ align:start position:0%
+where then their customers will not be
+ 
+
+ align:start position:0%
+where then their customers will not be
+willing to pay the higher prices and
+
+ align:start position:0%
+willing to pay the higher prices and
+ 
+
+ align:start position:0%
+willing to pay the higher prices and
+they can't afford to sustain their
+
+ align:start position:0%
+they can't afford to sustain their
+ 
+
+ align:start position:0%
+they can't afford to sustain their
+competitive Advantage you know well are
+
+ align:start position:0%
+competitive Advantage you know well are
+ 
+
+ align:start position:0%
+competitive Advantage you know well are
+you saying what they should do or what
+
+ align:start position:0%
+you saying what they should do or what
+ 
+
+ align:start position:0%
+you saying what they should do or what
+they will do as as someone as a
+
+ align:start position:0%
+they will do as as someone as a
+ 
+
+ align:start position:0%
+they will do as as someone as a
+competitor especially if I'm part of a
+
+ align:start position:0%
+competitor especially if I'm part of a
+ 
+
+ align:start position:0%
+competitor especially if I'm part of a
+larger corporation like the Man Group uh
+
+ align:start position:0%
+larger corporation like the Man Group uh
+ 
+
+ align:start position:0%
+larger corporation like the Man Group uh
+I would not expect them to come down to
+
+ align:start position:0%
+I would not expect them to come down to
+ 
+
+ align:start position:0%
+I would not expect them to come down to
+my price rather they try to stay high
+
+ align:start position:0%
+my price rather they try to stay high
+ 
+
+ align:start position:0%
+my price rather they try to stay high
+and maybe I diversify a little into like
+
+ align:start position:0%
+and maybe I diversify a little into like
+ 
+
+ align:start position:0%
+and maybe I diversify a little into like
+so you you you think they would that
+
+ align:start position:0%
+so you you you think they would that
+ 
+
+ align:start position:0%
+so you you you think they would that
+that Chad would say I can't play a price
+
+ align:start position:0%
+that Chad would say I can't play a price
+ 
+
+ align:start position:0%
+that Chad would say I can't play a price
+game with these
+
+ align:start position:0%
+game with these
+ 
+
+ align:start position:0%
+game with these
+guys I'm going to I'm going to play my
+
+ align:start position:0%
+guys I'm going to I'm going to play my
+ 
+
+ align:start position:0%
+guys I'm going to I'm going to play my
+long suit I'm going to stick with
+
+ align:start position:0%
+long suit I'm going to stick with
+ 
+
+ align:start position:0%
+long suit I'm going to stick with
+technology and high price and
+
+ align:start position:0%
+technology and high price and
+ 
+
+ align:start position:0%
+technology and high price and
+communication and all of those good
+
+ align:start position:0%
+communication and all of those good
+ 
+
+ align:start position:0%
+communication and all of those good
+things okay let's we we're going to get
+
+ align:start position:0%
+things okay let's we we're going to get
+ 
+
+ align:start position:0%
+things okay let's we we're going to get
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+the at least the analysis in the
+
+ align:start position:0%
+the at least the analysis in the
+ 
+
+ align:start position:0%
+the at least the analysis in the
+teaching note on this case says given
+
+ align:start position:0%
+teaching note on this case says given
+ 
+
+ align:start position:0%
+teaching note on this case says given
+what Shad did to get through the 70s you
+
+ align:start position:0%
+what Shad did to get through the 70s you
+ 
+
+ align:start position:0%
+what Shad did to get through the 70s you
+might expect him to double down on
+
+ align:start position:0%
+might expect him to double down on
+ 
+
+ align:start position:0%
+might expect him to double down on
+technology to keep innovating but what
+
+ align:start position:0%
+technology to keep innovating but what
+ 
+
+ align:start position:0%
+technology to keep innovating but what
+should he do I mean there are a whole
+
+ align:start position:0%
+should he do I mean there are a whole
+ 
+
+ align:start position:0%
+should he do I mean there are a whole
+set of things he could
+
+ align:start position:0%
+set of things he could
+ 
+
+ align:start position:0%
+set of things he could
+do right he could cut prices he could
+
+ align:start position:0%
+do right he could cut prices he could
+ 
+
+ align:start position:0%
+do right he could cut prices he could
+cut them generally he could cut them
+
+ align:start position:0%
+cut them generally he could cut them
+ 
+
+ align:start position:0%
+cut them generally he could cut them
+selectively he could cut them in
+
+ align:start position:0%
+selectively he could cut them in
+ 
+
+ align:start position:0%
+selectively he could cut them in
+different markets he could cut them in
+
+ align:start position:0%
+different markets he could cut them in
+ 
+
+ align:start position:0%
+different markets he could cut them in
+different segments he could enter their
+
+ align:start position:0%
+different segments he could enter their
+ 
+
+ align:start position:0%
+different segments he could enter their
+segments Husky's a little small in terms
+
+ align:start position:0%
+segments Husky's a little small in terms
+ 
+
+ align:start position:0%
+segments Husky's a little small in terms
+of production capacity they might try to
+
+ align:start position:0%
+of production capacity they might try to
+ 
+
+ align:start position:0%
+of production capacity they might try to
+get scale by
+
+ align:start position:0%
+get scale by
+ 
+
+ align:start position:0%
+get scale by
+counterattacking they could cut
+
+ align:start position:0%
+counterattacking they could cut
+ 
+
+ align:start position:0%
+counterattacking they could cut
+costs given they're facing low price
+
+ align:start position:0%
+costs given they're facing low price
+ 
+
+ align:start position:0%
+costs given they're facing low price
+competition but they've got this
+
+ align:start position:0%
+competition but they've got this
+ 
+
+ align:start position:0%
+competition but they've got this
+culture that's not a cost focused
+
+ align:start position:0%
+culture that's not a cost focused
+ 
+
+ align:start position:0%
+culture that's not a cost focused
+culture it's a quality focused people
+
+ align:start position:0%
+culture it's a quality focused people
+ 
+
+ align:start position:0%
+culture it's a quality focused people
+focused culture so if you if you do
+
+ align:start position:0%
+focused culture so if you if you do
+ 
+
+ align:start position:0%
+focused culture so if you if you do
+that um
+
+ align:start position:0%
+that um
+ 
+
+ align:start position:0%
+that um
+you know then then for sure Charlotte
+
+ align:start position:0%
+you know then then for sure Charlotte
+ 
+
+ align:start position:0%
+you know then then for sure Charlotte
+won't want to work there because not
+
+ align:start position:0%
+won't want to work there because not
+ 
+
+ align:start position:0%
+won't want to work there because not
+only do they straighten your tea they
+
+ align:start position:0%
+only do they straighten your tea they
+ 
+
+ align:start position:0%
+only do they straighten your tea they
+cut out child care they do all kinds of
+
+ align:start position:0%
+cut out child care they do all kinds of
+ 
+
+ align:start position:0%
+cut out child care they do all kinds of
+other things to cut
+
+ align:start position:0%
+other things to cut
+ 
+
+ align:start position:0%
+other things to cut
+costs you could either raise or lower
+
+ align:start position:0%
+costs you could either raise or lower
+ 
+
+ align:start position:0%
+costs you could either raise or lower
+all this stuff the service the technical
+
+ align:start position:0%
+all this stuff the service the technical
+ 
+
+ align:start position:0%
+all this stuff the service the technical
+people in the field they've got a
+
+ align:start position:0%
+people in the field they've got a
+ 
+
+ align:start position:0%
+people in the field they've got a
+probably a high- price Salesforce
+
+ align:start position:0%
+probably a high- price Salesforce
+ 
+
+ align:start position:0%
+probably a high- price Salesforce
+because they're all technical people you
+
+ align:start position:0%
+because they're all technical people you
+ 
+
+ align:start position:0%
+because they're all technical people you
+could go back to plain old salespeople
+
+ align:start position:0%
+could go back to plain old salespeople
+ 
+
+ align:start position:0%
+could go back to plain old salespeople
+you could cut out this manufacturer
+
+ align:start position:0%
+you could cut out this manufacturer
+ 
+
+ align:start position:0%
+you could cut out this manufacturer
+Advanced manufacturing center which
+
+ align:start position:0%
+Advanced manufacturing center which
+ 
+
+ align:start position:0%
+Advanced manufacturing center which
+nobody else has got you could stop
+
+ align:start position:0%
+nobody else has got you could stop
+ 
+
+ align:start position:0%
+nobody else has got you could stop
+working on Research or you could do more
+
+ align:start position:0%
+working on Research or you could do more
+ 
+
+ align:start position:0%
+working on Research or you could do more
+of all of
+
+ align:start position:0%
+of all of
+ 
+
+ align:start position:0%
+of all of
+those you could whoa that was
+
+ align:start position:0%
+those you could whoa that was
+ 
+
+ align:start position:0%
+those you could whoa that was
+cute uh bad button you could um uh
+
+ align:start position:0%
+cute uh bad button you could um uh
+ 
+
+ align:start position:0%
+cute uh bad button you could um uh
+decide that there really are scale
+
+ align:start position:0%
+decide that there really are scale
+ 
+
+ align:start position:0%
+decide that there really are scale
+economies in building your own inputs
+
+ align:start position:0%
+economies in building your own inputs
+ 
+
+ align:start position:0%
+economies in building your own inputs
+instead of buying them you could try to
+
+ align:start position:0%
+instead of buying them you could try to
+ 
+
+ align:start position:0%
+instead of buying them you could try to
+integrate upstream or you could do
+
+ align:start position:0%
+integrate upstream or you could do
+ 
+
+ align:start position:0%
+integrate upstream or you could do
+things I haven't thought
+
+ align:start position:0%
+things I haven't thought
+ 
+
+ align:start position:0%
+things I haven't thought
+of so instead of what would they do what
+
+ align:start position:0%
+of so instead of what would they do what
+ 
+
+ align:start position:0%
+of so instead of what would they do what
+should they do Sam you had a you were
+
+ align:start position:0%
+should they do Sam you had a you were
+ 
+
+ align:start position:0%
+should they do Sam you had a you were
+doing a should right you were you were
+
+ align:start position:0%
+doing a should right you were you were
+ 
+
+ align:start position:0%
+doing a should right you were you were
+saying they should focus on
+
+ align:start position:0%
+saying they should focus on
+ 
+
+ align:start position:0%
+saying they should focus on
+communicating the advantage to customers
+
+ align:start position:0%
+communicating the advantage to customers
+ 
+
+ align:start position:0%
+communicating the advantage to customers
+and I also think they
+
+ align:start position:0%
+and I also think they
+ 
+
+ align:start position:0%
+and I also think they
+probably should raise spending on like
+
+ align:start position:0%
+probably should raise spending on like
+ 
+
+ align:start position:0%
+probably should raise spending on like
+technology and quality and all that
+
+ align:start position:0%
+technology and quality and all that
+ 
+
+ align:start position:0%
+technology and quality and all that
+because that's what they're good at okay
+
+ align:start position:0%
+because that's what they're good at okay
+ 
+
+ align:start position:0%
+because that's what they're good at okay
+Max where are you going I think they
+
+ align:start position:0%
+Max where are you going I think they
+ 
+
+ align:start position:0%
+Max where are you going I think they
+should do an analysis of who their main
+
+ align:start position:0%
+should do an analysis of who their main
+ 
+
+ align:start position:0%
+should do an analysis of who their main
+customers are and they only make a
+
+ align:start position:0%
+customers are and they only make a
+ 
+
+ align:start position:0%
+customers are and they only make a
+couple hundred machines a year so if all
+
+ align:start position:0%
+couple hundred machines a year so if all
+ 
+
+ align:start position:0%
+couple hundred machines a year so if all
+those machines are going to the same
+
+ align:start position:0%
+those machines are going to the same
+ 
+
+ align:start position:0%
+those machines are going to the same
+customers or similar customers and they
+
+ align:start position:0%
+customers or similar customers and they
+ 
+
+ align:start position:0%
+customers or similar customers and they
+can probably Bank on loyalty and should
+
+ align:start position:0%
+can probably Bank on loyalty and should
+ 
+
+ align:start position:0%
+can probably Bank on loyalty and should
+focus on communicating the advantages
+
+ align:start position:0%
+focus on communicating the advantages
+ 
+
+ align:start position:0%
+focus on communicating the advantages
+because they can sell that but if a lot
+
+ align:start position:0%
+because they can sell that but if a lot
+ 
+
+ align:start position:0%
+because they can sell that but if a lot
+of those machines are going into new
+
+ align:start position:0%
+of those machines are going into new
+ 
+
+ align:start position:0%
+of those machines are going into new
+companies that are trying to look to
+
+ align:start position:0%
+companies that are trying to look to
+ 
+
+ align:start position:0%
+companies that are trying to look to
+reduce costs initially then they might
+
+ align:start position:0%
+reduce costs initially then they might
+ 
+
+ align:start position:0%
+reduce costs initially then they might
+want to think about cutting cost to stay
+
+ align:start position:0%
+want to think about cutting cost to stay
+ 
+
+ align:start position:0%
+want to think about cutting cost to stay
+competitive in that market so that's
+
+ align:start position:0%
+competitive in that market so that's
+ 
+
+ align:start position:0%
+competitive in that market so that's
+interesting so if it's the same
+
+ align:start position:0%
+interesting so if it's the same
+ 
+
+ align:start position:0%
+interesting so if it's the same
+customers then it's it's an advantage to
+
+ align:start position:0%
+customers then it's it's an advantage to
+ 
+
+ align:start position:0%
+customers then it's it's an advantage to
+the customer to have only one supplier
+
+ align:start position:0%
+the customer to have only one supplier
+ 
+
+ align:start position:0%
+the customer to have only one supplier
+to have husky machines throughout so if
+
+ align:start position:0%
+to have husky machines throughout so if
+ 
+
+ align:start position:0%
+to have husky machines throughout so if
+if the growth is coming from sales to
+
+ align:start position:0%
+if the growth is coming from sales to
+ 
+
+ align:start position:0%
+if the growth is coming from sales to
+customers that already have husky
+
+ align:start position:0%
+customers that already have husky
+ 
+
+ align:start position:0%
+customers that already have husky
+machines you could stress the fact that
+
+ align:start position:0%
+machines you could stress the fact that
+ 
+
+ align:start position:0%
+machines you could stress the fact that
+look I mean you got one supplier you've
+
+ align:start position:0%
+look I mean you got one supplier you've
+ 
+
+ align:start position:0%
+look I mean you got one supplier you've
+only got to have one set of spare ports
+
+ align:start position:0%
+only got to have one set of spare ports
+ 
+
+ align:start position:0%
+only got to have one set of spare ports
+you've only got to call one person when
+
+ align:start position:0%
+you've only got to call one person when
+ 
+
+ align:start position:0%
+you've only got to call one person when
+it breaks down be a Husky Shop but
+
+ align:start position:0%
+it breaks down be a Husky Shop but
+ 
+
+ align:start position:0%
+it breaks down be a Husky Shop but
+you're right it might be different if
+
+ align:start position:0%
+you're right it might be different if
+ 
+
+ align:start position:0%
+you're right it might be different if
+they're new people and they worry more
+
+ align:start position:0%
+they're new people and they worry more
+ 
+
+ align:start position:0%
+they're new people and they worry more
+about about upfront cost okay anybody
+
+ align:start position:0%
+about about upfront cost okay anybody
+ 
+
+ align:start position:0%
+about about upfront cost okay anybody
+else any other approaches
+
+ align:start position:0%
+else any other approaches
+ 
+
+ align:start position:0%
+else any other approaches
+Erica would it be unreasonable to like
+
+ align:start position:0%
+Erica would it be unreasonable to like
+ 
+
+ align:start position:0%
+Erica would it be unreasonable to like
+look into cutting costs while
+
+ align:start position:0%
+look into cutting costs while
+ 
+
+ align:start position:0%
+look into cutting costs while
+maintaining like quality so I guess like
+
+ align:start position:0%
+maintaining like quality so I guess like
+ 
+
+ align:start position:0%
+maintaining like quality so I guess like
+investing Research into like cutting
+
+ align:start position:0%
+investing Research into like cutting
+ 
+
+ align:start position:0%
+investing Research into like cutting
+cost but maining p
+
+ align:start position:0%
+cost but maining p
+ 
+
+ align:start position:0%
+cost but maining p
+well you what cut you'd cut
+
+ align:start position:0%
+well you what cut you'd cut
+ 
+
+ align:start position:0%
+well you what cut you'd cut
+manufacturing costs or you'd cut out the
+
+ align:start position:0%
+manufacturing costs or you'd cut out the
+ 
+
+ align:start position:0%
+manufacturing costs or you'd cut out the
+daycare center you wouldn't cut out the
+
+ align:start position:0%
+daycare center you wouldn't cut out the
+ 
+
+ align:start position:0%
+daycare center you wouldn't cut out the
+daycare okay like manufacturing costs
+
+ align:start position:0%
+daycare okay like manufacturing costs
+ 
+
+ align:start position:0%
+daycare okay like manufacturing costs
+like how to make how to produce things
+
+ align:start position:0%
+like how to make how to produce things
+ 
+
+ align:start position:0%
+like how to make how to produce things
+more efficiently so you'd Focus you'd
+
+ align:start position:0%
+more efficiently so you'd Focus you'd
+ 
+
+ align:start position:0%
+more efficiently so you'd Focus you'd
+focus on manufacturing costs would you
+
+ align:start position:0%
+focus on manufacturing costs would you
+ 
+
+ align:start position:0%
+focus on manufacturing costs would you
+also uh raise or this is a fair amount
+
+ align:start position:0%
+also uh raise or this is a fair amount
+ 
+
+ align:start position:0%
+also uh raise or this is a fair amount
+of cost in here uh having this
+
+ align:start position:0%
+of cost in here uh having this
+ 
+
+ align:start position:0%
+of cost in here uh having this
+high-priced field Force this Advanced
+
+ align:start position:0%
+high-priced field Force this Advanced
+ 
+
+ align:start position:0%
+high-priced field Force this Advanced
+manufacturing center the spending on
+
+ align:start position:0%
+manufacturing center the spending on
+ 
+
+ align:start position:0%
+manufacturing center the spending on
+Innovation that's a cost would you cut
+
+ align:start position:0%
+Innovation that's a cost would you cut
+ 
+
+ align:start position:0%
+Innovation that's a cost would you cut
+cost there or would you cut cost in
+
+ align:start position:0%
+cost there or would you cut cost in
+ 
+
+ align:start position:0%
+cost there or would you cut cost in
+focus on manufacturing cost well I mean
+
+ align:start position:0%
+focus on manufacturing cost well I mean
+ 
+
+ align:start position:0%
+focus on manufacturing cost well I mean
+I guess it I guess like from I was
+
+ align:start position:0%
+I guess it I guess like from I was
+ 
+
+ align:start position:0%
+I guess it I guess like from I was
+focusing on manufacturing cost okay I
+
+ align:start position:0%
+focusing on manufacturing cost okay I
+ 
+
+ align:start position:0%
+focusing on manufacturing cost okay I
+mean those daycare center stays but
+
+ align:start position:0%
+mean those daycare center stays but
+ 
+
+ align:start position:0%
+mean those daycare center stays but
+we're going to we're going to really try
+
+ align:start position:0%
+we're going to we're going to really try
+ 
+
+ align:start position:0%
+we're going to we're going to really try
+to get these things built more cheaply
+
+ align:start position:0%
+to get these things built more cheaply
+ 
+
+ align:start position:0%
+to get these things built more cheaply
+yeah okay and then would you use that to
+
+ align:start position:0%
+yeah okay and then would you use that to
+ 
+
+ align:start position:0%
+yeah okay and then would you use that to
+cut
+
+ align:start position:0%
+cut
+ 
+
+ align:start position:0%
+cut
+prices I mean you could and like I mean
+
+ align:start position:0%
+prices I mean you could and like I mean
+ 
+
+ align:start position:0%
+prices I mean you could and like I mean
+if you if like cutting prices reflects
+
+ align:start position:0%
+if you if like cutting prices reflects
+ 
+
+ align:start position:0%
+if you if like cutting prices reflects
+like lower quality like that would be
+
+ align:start position:0%
+like lower quality like that would be
+ 
+
+ align:start position:0%
+like lower quality like that would be
+bad yeah but like you could also stress
+
+ align:start position:0%
+bad yeah but like you could also stress
+ 
+
+ align:start position:0%
+bad yeah but like you could also stress
+that like it's you could like have like
+
+ align:start position:0%
+that like it's you could like have like
+ 
+
+ align:start position:0%
+that like it's you could like have like
+better quality machines or okay
+
+ align:start position:0%
+better quality machines or okay
+ 
+
+ align:start position:0%
+better quality machines or okay
+Jacqueline I was going to say agree with
+
+ align:start position:0%
+Jacqueline I was going to say agree with
+ 
+
+ align:start position:0%
+Jacqueline I was going to say agree with
+that that you could use that to cut
+
+ align:start position:0%
+that that you could use that to cut
+ 
+
+ align:start position:0%
+that that you could use that to cut
+prices but at the same time still
+
+ align:start position:0%
+prices but at the same time still
+ 
+
+ align:start position:0%
+prices but at the same time still
+highlight the quality of your product
+
+ align:start position:0%
+highlight the quality of your product
+ 
+
+ align:start position:0%
+highlight the quality of your product
+and that advantage to can do multiple
+
+ align:start position:0%
+and that advantage to can do multiple
+ 
+
+ align:start position:0%
+and that advantage to can do multiple
+strategy okay okay anybody who hasn't
+
+ align:start position:0%
+strategy okay okay anybody who hasn't
+ 
+
+ align:start position:0%
+strategy okay okay anybody who hasn't
+yeah um I'd say like increased services
+
+ align:start position:0%
+yeah um I'd say like increased services
+ 
+
+ align:start position:0%
+yeah um I'd say like increased services
+at the point of purchase so like they
+
+ align:start position:0%
+at the point of purchase so like they
+ 
+
+ align:start position:0%
+at the point of purchase so like they
+offer you know free installation or
+
+ align:start position:0%
+offer you know free installation or
+ 
+
+ align:start position:0%
+offer you know free installation or
+servicing of old husky machines for
+
+ align:start position:0%
+servicing of old husky machines for
+ 
+
+ align:start position:0%
+servicing of old husky machines for
+whenever you buy new ones or something
+
+ align:start position:0%
+whenever you buy new ones or something
+ 
+
+ align:start position:0%
+whenever you buy new ones or something
+like that to focus when they're going to
+
+ align:start position:0%
+like that to focus when they're going to
+ 
+
+ align:start position:0%
+like that to focus when they're going to
+buy a machine they're going to have it
+
+ align:start position:0%
+buy a machine they're going to have it
+ 
+
+ align:start position:0%
+buy a machine they're going to have it
+for a while so focusing like right on
+
+ align:start position:0%
+for a while so focusing like right on
+ 
+
+ align:start position:0%
+for a while so focusing like right on
+that point so I'm rais that's costing me
+
+ align:start position:0%
+that point so I'm rais that's costing me
+ 
+
+ align:start position:0%
+that point so I'm rais that's costing me
+money so how am I going to get it back
+
+ align:start position:0%
+money so how am I going to get it back
+ 
+
+ align:start position:0%
+money so how am I going to get it back
+or am I not Customer Loyalty just
+
+ align:start position:0%
+or am I not Customer Loyalty just
+ 
+
+ align:start position:0%
+or am I not Customer Loyalty just
+selling you're going to sell those
+
+ align:start position:0%
+selling you're going to sell those
+ 
+
+ align:start position:0%
+selling you're going to sell those
+machines I guess you have to lay that
+
+ align:start position:0%
+machines I guess you have to lay that
+ 
+
+ align:start position:0%
+machines I guess you have to lay that
+kind of back and forth but hopefully
+
+ align:start position:0%
+kind of back and forth but hopefully
+ 
+
+ align:start position:0%
+kind of back and forth but hopefully
+ends positive yeah I mean one approach
+
+ align:start position:0%
+ends positive yeah I mean one approach
+ 
+
+ align:start position:0%
+ends positive yeah I mean one approach
+here is to say game over uh I made a lot
+
+ align:start position:0%
+here is to say game over uh I made a lot
+ 
+
+ align:start position:0%
+here is to say game over uh I made a lot
+of money before people came into my
+
+ align:start position:0%
+of money before people came into my
+ 
+
+ align:start position:0%
+of money before people came into my
+segment and I'm not going to make that
+
+ align:start position:0%
+segment and I'm not going to make that
+ 
+
+ align:start position:0%
+segment and I'm not going to make that
+kind of money again so what I want to
+
+ align:start position:0%
+kind of money again so what I want to
+ 
+
+ align:start position:0%
+kind of money again so what I want to
+make sure is that I maintain a position
+
+ align:start position:0%
+make sure is that I maintain a position
+ 
+
+ align:start position:0%
+make sure is that I maintain a position
+through high service and whatever uh and
+
+ align:start position:0%
+through high service and whatever uh and
+ 
+
+ align:start position:0%
+through high service and whatever uh and
+don't get swamped I kind of Niche myself
+
+ align:start position:0%
+don't get swamped I kind of Niche myself
+ 
+
+ align:start position:0%
+don't get swamped I kind of Niche myself
+even a little more Charlotte well I
+
+ align:start position:0%
+even a little more Charlotte well I
+ 
+
+ align:start position:0%
+even a little more Charlotte well I
+think that like they are a very
+
+ align:start position:0%
+think that like they are a very
+ 
+
+ align:start position:0%
+think that like they are a very
+different company than their competitors
+
+ align:start position:0%
+different company than their competitors
+ 
+
+ align:start position:0%
+different company than their competitors
+right like they're focusing on this kind
+
+ align:start position:0%
+right like they're focusing on this kind
+ 
+
+ align:start position:0%
+right like they're focusing on this kind
+of assembly line manufacturer that
+
+ align:start position:0%
+of assembly line manufacturer that
+ 
+
+ align:start position:0%
+of assembly line manufacturer that
+allows them to specialize products for
+
+ align:start position:0%
+allows them to specialize products for
+ 
+
+ align:start position:0%
+allows them to specialize products for
+what their consumer wants so they could
+
+ align:start position:0%
+what their consumer wants so they could
+ 
+
+ align:start position:0%
+what their consumer wants so they could
+focus on that and even take that a
+
+ align:start position:0%
+focus on that and even take that a
+ 
+
+ align:start position:0%
+focus on that and even take that a
+little bit further and maybe like if
+
+ align:start position:0%
+little bit further and maybe like if
+ 
+
+ align:start position:0%
+little bit further and maybe like if
+there's a huge price difference in what
+
+ align:start position:0%
+there's a huge price difference in what
+ 
+
+ align:start position:0%
+there's a huge price difference in what
+their competitors are now charging to
+
+ align:start position:0%
+their competitors are now charging to
+ 
+
+ align:start position:0%
+their competitors are now charging to
+kind of like modify the machines and
+
+ align:start position:0%
+kind of like modify the machines and
+ 
+
+ align:start position:0%
+kind of like modify the machines and
+what they have been charging they could
+
+ align:start position:0%
+what they have been charging they could
+ 
+
+ align:start position:0%
+what they have been charging they could
+cut price a little so there's still a
+
+ align:start position:0%
+cut price a little so there's still a
+ 
+
+ align:start position:0%
+cut price a little so there's still a
+high
+
+ align:start position:0%
+high
+ 
+
+ align:start position:0%
+high
+quality uh company like like higher more
+
+ align:start position:0%
+quality uh company like like higher more
+ 
+
+ align:start position:0%
+quality uh company like like higher more
+luxury but not as much they would for
+
+ align:start position:0%
+luxury but not as much they would for
+ 
+
+ align:start position:0%
+luxury but not as much they would for
+because they were charging like really
+
+ align:start position:0%
+because they were charging like really
+ 
+
+ align:start position:0%
+because they were charging like really
+really high premiums too like they could
+
+ align:start position:0%
+really high premiums too like they could
+ 
+
+ align:start position:0%
+really high premiums too like they could
+just change that they could come down a
+
+ align:start position:0%
+just change that they could come down a
+ 
+
+ align:start position:0%
+just change that they could come down a
+bit I mean although the premium seem to
+
+ align:start position:0%
+bit I mean although the premium seem to
+ 
+
+ align:start position:0%
+bit I mean although the premium seem to
+be justified based on that analysis
+
+ align:start position:0%
+be justified based on that analysis
+ 
+
+ align:start position:0%
+be justified based on that analysis
+anybody over here Pedro I tend look left
+
+ align:start position:0%
+anybody over here Pedro I tend look left
+ 
+
+ align:start position:0%
+anybody over here Pedro I tend look left
+so you need to you need to wave your
+
+ align:start position:0%
+so you need to you need to wave your
+ 
+
+ align:start position:0%
+so you need to you need to wave your
+hand I also I was at the beginning I was
+
+ align:start position:0%
+hand I also I was at the beginning I was
+ 
+
+ align:start position:0%
+hand I also I was at the beginning I was
+also thinking of um the manufacturing
+
+ align:start position:0%
+also thinking of um the manufacturing
+ 
+
+ align:start position:0%
+also thinking of um the manufacturing
+cost of the machines like produce um
+
+ align:start position:0%
+cost of the machines like produce um
+ 
+
+ align:start position:0%
+cost of the machines like produce um
+that are more energy efficient um so
+
+ align:start position:0%
+that are more energy efficient um so
+ 
+
+ align:start position:0%
+that are more energy efficient um so
+that's um heat production cost so I was
+
+ align:start position:0%
+that's um heat production cost so I was
+ 
+
+ align:start position:0%
+that's um heat production cost so I was
+thinking at the beginning but then I was
+
+ align:start position:0%
+thinking at the beginning but then I was
+ 
+
+ align:start position:0%
+thinking at the beginning but then I was
+also thinking um just thought of um
+
+ align:start position:0%
+also thinking um just thought of um
+ 
+
+ align:start position:0%
+also thinking um just thought of um
+maybe expanding the market a little bit
+
+ align:start position:0%
+maybe expanding the market a little bit
+ 
+
+ align:start position:0%
+maybe expanding the market a little bit
+um like how about um because so the
+
+ align:start position:0%
+um like how about um because so the
+ 
+
+ align:start position:0%
+um like how about um because so the
+other c um the other companies produce
+
+ align:start position:0%
+other c um the other companies produce
+ 
+
+ align:start position:0%
+other c um the other companies produce
+more types of be blessing so I of so
+
+ align:start position:0%
+more types of be blessing so I of so
+ 
+
+ align:start position:0%
+more types of be blessing so I of so
+maybe go into some other segments okay
+
+ align:start position:0%
+maybe go into some other segments okay
+ 
+
+ align:start position:0%
+maybe go into some other segments okay
+let me let me give you a few thoughts
+
+ align:start position:0%
+let me let me give you a few thoughts
+ 
+
+ align:start position:0%
+let me let me give you a few thoughts
+they have a lot of choices here um and
+
+ align:start position:0%
+they have a lot of choices here um and
+ 
+
+ align:start position:0%
+they have a lot of choices here um and
+it's it's
+
+ align:start position:0%
+it's it's
+ 
+
+ align:start position:0%
+it's it's
+interesting looking at this whole menu
+
+ align:start position:0%
+interesting looking at this whole menu
+ 
+
+ align:start position:0%
+interesting looking at this whole menu
+one of the things I must say that struck
+
+ align:start position:0%
+one of the things I must say that struck
+ 
+
+ align:start position:0%
+one of the things I must say that struck
+me is before 1995 this is a great
+
+ align:start position:0%
+me is before 1995 this is a great
+ 
+
+ align:start position:0%
+me is before 1995 this is a great
+example of how all the pieces fit
+
+ align:start position:0%
+example of how all the pieces fit
+ 
+
+ align:start position:0%
+example of how all the pieces fit
+together they focused on a segment they
+
+ align:start position:0%
+together they focused on a segment they
+ 
+
+ align:start position:0%
+together they focused on a segment they
+figured out what that that that segment
+
+ align:start position:0%
+figured out what that that that segment
+ 
+
+ align:start position:0%
+figured out what that that that segment
+cares about performance they're all
+
+ align:start position:0%
+cares about performance they're all
+ 
+
+ align:start position:0%
+cares about performance they're all
+about performance and Technical
+
+ align:start position:0%
+about performance and Technical
+ 
+
+ align:start position:0%
+about performance and Technical
+Excellence they got a culture that fits
+
+ align:start position:0%
+Excellence they got a culture that fits
+ 
+
+ align:start position:0%
+Excellence they got a culture that fits
+with that all the pieces fit together
+
+ align:start position:0%
+with that all the pieces fit together
+ 
+
+ align:start position:0%
+with that all the pieces fit together
+it's Ikea it's um Southwest
+
+ align:start position:0%
+it's Ikea it's um Southwest
+ 
+
+ align:start position:0%
+it's Ikea it's um Southwest
+Airlines and comes now this this
+
+ align:start position:0%
+Airlines and comes now this this
+ 
+
+ align:start position:0%
+Airlines and comes now this this
+difficult time can you make the things
+
+ align:start position:0%
+difficult time can you make the things
+ 
+
+ align:start position:0%
+difficult time can you make the things
+fit together so a couple of
+
+ align:start position:0%
+fit together so a couple of
+ 
+
+ align:start position:0%
+fit together so a couple of
+choices their basic options I mean you
+
+ align:start position:0%
+choices their basic options I mean you
+ 
+
+ align:start position:0%
+choices their basic options I mean you
+can try to you can try to increase
+
+ align:start position:0%
+can try to you can try to increase
+ 
+
+ align:start position:0%
+can try to you can try to increase
+that's all is one of the entrance you
+
+ align:start position:0%
+that's all is one of the entrance you
+ 
+
+ align:start position:0%
+that's all is one of the entrance you
+will recall you can try to increase uh
+
+ align:start position:0%
+will recall you can try to increase uh
+ 
+
+ align:start position:0%
+will recall you can try to increase uh
+willingness to pay you can think about
+
+ align:start position:0%
+willingness to pay you can think about
+ 
+
+ align:start position:0%
+willingness to pay you can think about
+um uh more service more
+
+ align:start position:0%
+um uh more service more
+ 
+
+ align:start position:0%
+um uh more service more
+R&D the question Shad has to ask himself
+
+ align:start position:0%
+R&D the question Shad has to ask himself
+ 
+
+ align:start position:0%
+R&D the question Shad has to ask himself
+one of the questions is is there room
+
+ align:start position:0%
+one of the questions is is there room
+ 
+
+ align:start position:0%
+one of the questions is is there room
+for
+
+ align:start position:0%
+for
+ 
+
+ align:start position:0%
+for
+that right differentiation makes you
+
+ align:start position:0%
+that right differentiation makes you
+ 
+
+ align:start position:0%
+that right differentiation makes you
+money if it's cost effective so the
+
+ align:start position:0%
+money if it's cost effective so the
+ 
+
+ align:start position:0%
+money if it's cost effective so the
+question is how much more service what
+
+ align:start position:0%
+question is how much more service what
+ 
+
+ align:start position:0%
+question is how much more service what
+would you get from increased service the
+
+ align:start position:0%
+would you get from increased service the
+ 
+
+ align:start position:0%
+would you get from increased service the
+question of thinking about who your
+
+ align:start position:0%
+question of thinking about who your
+ 
+
+ align:start position:0%
+question of thinking about who your
+customers are are they are they repeat
+
+ align:start position:0%
+customers are are they are they repeat
+ 
+
+ align:start position:0%
+customers are are they are they repeat
+is this the same people expanding is it
+
+ align:start position:0%
+is this the same people expanding is it
+ 
+
+ align:start position:0%
+is this the same people expanding is it
+new people what's the return to that you
+
+ align:start position:0%
+new people what's the return to that you
+ 
+
+ align:start position:0%
+new people what's the return to that you
+could improve the cost position remember
+
+ align:start position:0%
+could improve the cost position remember
+ 
+
+ align:start position:0%
+could improve the cost position remember
+these two basic approaches you can
+
+ align:start position:0%
+these two basic approaches you can
+ 
+
+ align:start position:0%
+these two basic approaches you can
+differentiate you can lower
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+cost can you cut cost and still
+
+ align:start position:0%
+cost can you cut cost and still
+ 
+
+ align:start position:0%
+cost can you cut cost and still
+deliver if you cut the perks cut the
+
+ align:start position:0%
+deliver if you cut the perks cut the
+ 
+
+ align:start position:0%
+deliver if you cut the perks cut the
+Salesforce will you affect the culture
+
+ align:start position:0%
+Salesforce will you affect the culture
+ 
+
+ align:start position:0%
+Salesforce will you affect the culture
+can you continue to deliver if you do an
+
+ align:start position:0%
+can you continue to deliver if you do an
+ 
+
+ align:start position:0%
+can you continue to deliver if you do an
+aggressive cost cut and you can cut
+
+ align:start position:0%
+aggressive cost cut and you can cut
+ 
+
+ align:start position:0%
+aggressive cost cut and you can cut
+margins they've got pretty good margins
+
+ align:start position:0%
+margins they've got pretty good margins
+ 
+
+ align:start position:0%
+margins they've got pretty good margins
+they've got room to cut
+
+ align:start position:0%
+they've got room to cut
+ 
+
+ align:start position:0%
+they've got room to cut
+margins
+
+ align:start position:0%
+margins
+ 
+
+ align:start position:0%
+margins
+um but to become the lowcost producer
+
+ align:start position:0%
+um but to become the lowcost producer
+ 
+
+ align:start position:0%
+um but to become the lowcost producer
+probably not the they could go after
+
+ align:start position:0%
+probably not the they could go after
+ 
+
+ align:start position:0%
+probably not the they could go after
+other segments they only serve part of
+
+ align:start position:0%
+other segments they only serve part of
+ 
+
+ align:start position:0%
+other segments they only serve part of
+the business they could grow by going to
+
+ align:start position:0%
+the business they could grow by going to
+ 
+
+ align:start position:0%
+the business they could grow by going to
+other segments but given that they're a
+
+ align:start position:0%
+other segments but given that they're a
+ 
+
+ align:start position:0%
+other segments but given that they're a
+high-cost company and have a particular
+
+ align:start position:0%
+high-cost company and have a particular
+ 
+
+ align:start position:0%
+high-cost company and have a particular
+culture the question you'd have to ask
+
+ align:start position:0%
+culture the question you'd have to ask
+ 
+
+ align:start position:0%
+culture the question you'd have to ask
+is does that fit can we do
+
+ align:start position:0%
+is does that fit can we do
+ 
+
+ align:start position:0%
+is does that fit can we do
+that and
+
+ align:start position:0%
+that and
+ 
+
+ align:start position:0%
+that and
+then you you would like the whole
+
+ align:start position:0%
+then you you would like the whole
+ 
+
+ align:start position:0%
+then you you would like the whole
+package to
+
+ align:start position:0%
+package to
+ 
+
+ align:start position:0%
+package to
+fit and at this
+
+ align:start position:0%
+fit and at this
+ 
+
+ align:start position:0%
+fit and at this
+point how old was Shad Shad was 67 in
+
+ align:start position:0%
+point how old was Shad Shad was 67 in
+ 
+
+ align:start position:0%
+point how old was Shad Shad was 67 in
+19995 so as someone in that age bracket
+
+ align:start position:0%
+19995 so as someone in that age bracket
+ 
+
+ align:start position:0%
+19995 so as someone in that age bracket
+let me just say uh he obviously has to
+
+ align:start position:0%
+let me just say uh he obviously has to
+ 
+
+ align:start position:0%
+let me just say uh he obviously has to
+think about what am I handing off am I
+
+ align:start position:0%
+think about what am I handing off am I
+ 
+
+ align:start position:0%
+think about what am I handing off am I
+going to create something that's going
+
+ align:start position:0%
+going to create something that's going
+ 
+
+ align:start position:0%
+going to create something that's going
+to go on because he's not going to be
+
+ align:start position:0%
+to go on because he's not going to be
+ 
+
+ align:start position:0%
+to go on because he's not going to be
+leading that well one assumes he's not
+
+ align:start position:0%
+leading that well one assumes he's not
+ 
+
+ align:start position:0%
+leading that well one assumes he's not
+going to be an active participant for
+
+ align:start position:0%
+going to be an active participant for
+ 
+
+ align:start position:0%
+going to be an active participant for
+another 20
+
+ align:start position:0%
+another 20
+ 
+
+ align:start position:0%
+another 20
+years
+
+ align:start position:0%
+years
+ 
+
+ align:start position:0%
+years
+so what he
+
+ align:start position:0%
+so what he
+ 
+
+ align:start position:0%
+so what he
+did was actually quite
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+drastic I don't know whether this was
+
+ align:start position:0%
+drastic I don't know whether this was
+ 
+
+ align:start position:0%
+drastic I don't know whether this was
+right or wrong but this is what he did
+
+ align:start position:0%
+right or wrong but this is what he did
+ 
+
+ align:start position:0%
+right or wrong but this is what he did
+they went into other other uh niches
+
+ align:start position:0%
+they went into other other uh niches
+ 
+
+ align:start position:0%
+they went into other other uh niches
+they moved out they increased their
+
+ align:start position:0%
+they moved out they increased their
+ 
+
+ align:start position:0%
+they moved out they increased their
+manufacturing capacity substantially
+
+ align:start position:0%
+manufacturing capacity substantially
+ 
+
+ align:start position:0%
+manufacturing capacity substantially
+they thought they were too small for
+
+ align:start position:0%
+they thought they were too small for
+ 
+
+ align:start position:0%
+they thought they were too small for
+scale so they added capacity they cut
+
+ align:start position:0%
+scale so they added capacity they cut
+ 
+
+ align:start position:0%
+scale so they added capacity they cut
+prices
+
+ align:start position:0%
+prices
+ 
+
+ align:start position:0%
+prices
+dramatically in response to low price
+
+ align:start position:0%
+dramatically in response to low price
+ 
+
+ align:start position:0%
+dramatically in response to low price
+entrance probably isn't going to keep
+
+ align:start position:0%
+entrance probably isn't going to keep
+ 
+
+ align:start position:0%
+entrance probably isn't going to keep
+them out they work to cut
+
+ align:start position:0%
+them out they work to cut
+ 
+
+ align:start position:0%
+them out they work to cut
+costs cutting prices it was argued was a
+
+ align:start position:0%
+costs cutting prices it was argued was a
+ 
+
+ align:start position:0%
+costs cutting prices it was argued was a
+way to put pressure on
+
+ align:start position:0%
+way to put pressure on
+ 
+
+ align:start position:0%
+way to put pressure on
+costs and a hope you can keep the
+
+ align:start position:0%
+costs and a hope you can keep the
+ 
+
+ align:start position:0%
+costs and a hope you can keep the
+culture you basically say to your people
+
+ align:start position:0%
+culture you basically say to your people
+ 
+
+ align:start position:0%
+culture you basically say to your people
+look we're getting killed on price we've
+
+ align:start position:0%
+look we're getting killed on price we've
+ 
+
+ align:start position:0%
+look we're getting killed on price we've
+got a match and the only way we're going
+
+ align:start position:0%
+got a match and the only way we're going
+ 
+
+ align:start position:0%
+got a match and the only way we're going
+to make any money as if we can find a
+
+ align:start position:0%
+to make any money as if we can find a
+ 
+
+ align:start position:0%
+to make any money as if we can find a
+way to get the cost down but they didn't
+
+ align:start position:0%
+way to get the cost down but they didn't
+ 
+
+ align:start position:0%
+way to get the cost down but they didn't
+decrease R&D they didn't decrease the
+
+ align:start position:0%
+decrease R&D they didn't decrease the
+ 
+
+ align:start position:0%
+decrease R&D they didn't decrease the
+manufacturing center they didn't
+
+ align:start position:0%
+manufacturing center they didn't
+ 
+
+ align:start position:0%
+manufacturing center they didn't
+decrease the sales force they began to
+
+ align:start position:0%
+decrease the sales force they began to
+ 
+
+ align:start position:0%
+decrease the sales force they began to
+build more in
+
+ align:start position:0%
+build more in
+ 
+
+ align:start position:0%
+build more in
+house and they had an
+
+ align:start position:0%
+house and they had an
+ 
+
+ align:start position:0%
+house and they had an
+IPO sold off the company in 1968 how
+
+ align:start position:0%
+IPO sold off the company in 1968 how
+ 
+
+ align:start position:0%
+IPO sold off the company in 1968 how
+well do you think this package
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+worked saying words not so well yeah I
+
+ align:start position:0%
+worked saying words not so well yeah I
+ 
+
+ align:start position:0%
+worked saying words not so well yeah I
+mean also with hindsight I would argue
+
+ align:start position:0%
+mean also with hindsight I would argue
+ 
+
+ align:start position:0%
+mean also with hindsight I would argue
+that you'd have globalization in the
+
+ align:start position:0%
+that you'd have globalization in the
+ 
+
+ align:start position:0%
+that you'd have globalization in the
+early 21st century as well so I would
+
+ align:start position:0%
+early 21st century as well so I would
+ 
+
+ align:start position:0%
+early 21st century as well so I would
+argue that the R cost manufacturers in
+
+ align:start position:0%
+argue that the R cost manufacturers in
+ 
+
+ align:start position:0%
+argue that the R cost manufacturers in
+the US would get undercut by Chinese
+
+ align:start position:0%
+the US would get undercut by Chinese
+ 
+
+ align:start position:0%
+the US would get undercut by Chinese
+manufacturers and the best way to stay
+
+ align:start position:0%
+manufacturers and the best way to stay
+ 
+
+ align:start position:0%
+manufacturers and the best way to stay
+competitive was to stay high cost high
+
+ align:start position:0%
+competitive was to stay high cost high
+ 
+
+ align:start position:0%
+competitive was to stay high cost high
+high quality yeah I mean it's a curious
+
+ align:start position:0%
+high quality yeah I mean it's a curious
+ 
+
+ align:start position:0%
+high quality yeah I mean it's a curious
+It's a curious mixture isn't it because
+
+ align:start position:0%
+It's a curious mixture isn't it because
+ 
+
+ align:start position:0%
+It's a curious mixture isn't it because
+the company was built for high cost high
+
+ align:start position:0%
+the company was built for high cost high
+ 
+
+ align:start position:0%
+the company was built for high cost high
+quality
+
+ align:start position:0%
+quality
+ 
+
+ align:start position:0%
+quality
+and they tried to position themselves as
+
+ align:start position:0%
+and they tried to position themselves as
+ 
+
+ align:start position:0%
+and they tried to position themselves as
+the high cost high quality firm across
+
+ align:start position:0%
+the high cost high quality firm across
+ 
+
+ align:start position:0%
+the high cost high quality firm across
+the market in all of these
+
+ align:start position:0%
+the market in all of these
+ 
+
+ align:start position:0%
+the market in all of these
+niches even though in a bunch of the
+
+ align:start position:0%
+niches even though in a bunch of the
+ 
+
+ align:start position:0%
+niches even though in a bunch of the
+niches quality wasn't that
+
+ align:start position:0%
+niches quality wasn't that
+ 
+
+ align:start position:0%
+niches quality wasn't that
+important
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so I've seen numbers through 1999 and
+
+ align:start position:0%
+so I've seen numbers through 1999 and
+ 
+
+ align:start position:0%
+so I've seen numbers through 1999 and
+they continued to grow because the
+
+ align:start position:0%
+they continued to grow because the
+ 
+
+ align:start position:0%
+they continued to grow because the
+business grew their profitability was
+
+ align:start position:0%
+business grew their profitability was
+ 
+
+ align:start position:0%
+business grew their profitability was
+not
+
+ align:start position:0%
+not
+ 
+
+ align:start position:0%
+not
+terrific it was pretty erratic because
+
+ align:start position:0%
+terrific it was pretty erratic because
+ 
+
+ align:start position:0%
+terrific it was pretty erratic because
+they're changing the company rather
+
+ align:start position:0%
+they're changing the company rather
+ 
+
+ align:start position:0%
+they're changing the company rather
+dramatically and you can't get any more
+
+ align:start position:0%
+dramatically and you can't get any more
+ 
+
+ align:start position:0%
+dramatically and you can't get any more
+numbers because they went private last
+
+ align:start position:0%
+numbers because they went private last
+ 
+
+ align:start position:0%
+numbers because they went private last
+year so their website now is just an
+
+ align:start position:0%
+year so their website now is just an
+ 
+
+ align:start position:0%
+year so their website now is just an
+advertisement for their technology they
+
+ align:start position:0%
+advertisement for their technology they
+ 
+
+ align:start position:0%
+advertisement for their technology they
+no numbers available because they're a
+
+ align:start position:0%
+no numbers available because they're a
+ 
+
+ align:start position:0%
+no numbers available because they're a
+privately held
+
+ align:start position:0%
+privately held
+ 
+
+ align:start position:0%
+privately held
+company they're still in Bolton
+
+ align:start position:0%
+company they're still in Bolton
+ 
+
+ align:start position:0%
+company they're still in Bolton
+Ontario um questions comments reactions
+
+ align:start position:0%
+Ontario um questions comments reactions
+ 
+
+ align:start position:0%
+Ontario um questions comments reactions
+thoughts yeah they go private by some
+
+ align:start position:0%
+thoughts yeah they go private by some
+ 
+
+ align:start position:0%
+thoughts yeah they go private by some
+sort of buyout because of Po performance
+
+ align:start position:0%
+sort of buyout because of Po performance
+ 
+
+ align:start position:0%
+sort of buyout because of Po performance
+uh you know the website doesn't say we
+
+ align:start position:0%
+uh you know the website doesn't say we
+ 
+
+ align:start position:0%
+uh you know the website doesn't say we
+went private because we were performing
+
+ align:start position:0%
+went private because we were performing
+ 
+
+ align:start position:0%
+went private because we were performing
+poorly the website just says such and
+
+ align:start position:0%
+poorly the website just says such and
+ 
+
+ align:start position:0%
+poorly the website just says such and
+such a private Equity Firm bought them
+
+ align:start position:0%
+such a private Equity Firm bought them
+ 
+
+ align:start position:0%
+such a private Equity Firm bought them
+uh I I don't think that's implausible
+
+ align:start position:0%
+uh I I don't think that's implausible
+ 
+
+ align:start position:0%
+uh I I don't think that's implausible
+but I don't know it's not implausible
+
+ align:start position:0%
+but I don't know it's not implausible
+ 
+
+ align:start position:0%
+but I don't know it's not implausible
+that this strategy that a private that a
+
+ align:start position:0%
+that this strategy that a private that a
+ 
+
+ align:start position:0%
+that this strategy that a private that a
+private Equity Firm said this strategy
+
+ align:start position:0%
+private Equity Firm said this strategy
+ 
+
+ align:start position:0%
+private Equity Firm said this strategy
+is a loser and we can make this firm
+
+ align:start position:0%
+is a loser and we can make this firm
+ 
+
+ align:start position:0%
+is a loser and we can make this firm
+more profitable by changing strategy but
+
+ align:start position:0%
+more profitable by changing strategy but
+ 
+
+ align:start position:0%
+more profitable by changing strategy but
+I don't know that okay see you all next
+
+ align:start position:0%
+I don't know that okay see you all next
+ 
+
+ align:start position:0%
+I don't know that okay see you all next
+time
\ No newline at end of file
diff --git a/Fnsu19QD1D8.txt b/Fnsu19QD1D8.txt
new file mode 100644
index 0000000000000000000000000000000000000000..b049ba7d5393632cef07bf395c7c461643d885ee
--- /dev/null
+++ b/Fnsu19QD1D8.txt
@@ -0,0 +1,3300 @@
+The following
+content is provided
+
+under a Creative
+Commons license.
+
+Your support will help MIT
+OpenCourseWare continue
+
+to offer high-quality
+educational resources for free.
+
+To make a donation or
+view additional materials
+
+from hundreds of MIT courses,
+visit MIT OpenCourseWare
+
+at ocw.mit.edu.
+
+PROFESSOR: OK.
+
+Here is the menu for today.
+
+We're discussing line
+shifts and line broadening.
+
+And I want to finish
+up today this chapter
+
+by describing collisional
+narrowing, also called
+
+Dicke narrowing.
+
+Then I want to have
+two more shorter topics
+
+on two other aspects which
+lead to important line shapes
+
+and line broadening.
+
+So I want to quickly discuss
+the spectrum of emitted light
+
+by an atom.
+
+And I want to discuss
+collisional broadening.
+
+None of that will
+be done in-depth.
+
+The spectrum of emitted
+light is really open-ended,
+
+and we will have a more
+advanced treatment in 8.422.
+
+But I do feel if I show you
+all are kinds of line shifts
+
+and line broadening,
+I should at least
+
+mention here the basic things.
+
+And collisional
+broadening, I'm not
+
+sure how many atomic
+physics courses
+
+you will find which teach
+about collision broadening,
+
+because this is the physics
+from gas discharge lamps,
+
+the old-fashioned physics.
+
+However, I've realized
+that a lot of people
+
+know now about clock shifts,
+and mean field broadening,
+
+and mean field, and
+the ultra-cold gases.
+
+And they have no idea that
+similar physics actually
+
+happens in ordinary gas.
+
+So at least in terms of
+broadening your understanding,
+
+I want to talk just 10 minutes
+about collisional broadening.
+
+I've completely eliminated
+from this course
+
+the quantitative description
+about collisional broadening,
+
+but I want to show
+you a few cartoons
+
+and put some pictures
+into your mind.
+
+And probably, we have time to
+start the next chapter, which
+
+is actually a pretty short
+one, on two-photon transitions.
+
+For me, actually,
+Dicke narrowing
+
+is really the highlight
+of the course,
+
+because it provides
+conceptual insight
+
+into what really
+line broadening is,
+
+and to realize that collisions
+can narrow lines and not
+
+just broaden them.
+
+This is sort of
+subtle and insightful.
+
+And similar to photon
+transitions, it's short,
+
+but I hope it's also a
+highlight, because there's
+
+so many people-- you and other
+people-- who are sometimes
+
+struggling-- a photon is
+absorbed and is emitted.
+
+Usually, the photon
+is not absorbed,
+
+the photon is scattered.
+
+And whenever you think
+about photon in, photon out,
+
+you really should think
+about two-photon transitions.
+
+So the framework of
+two-photon transitions
+
+allows me now to give you the
+tools how you should really
+
+think about whenever you have
+atoms interacting with light.
+
+The light is not absorbed,
+the light is just scattered.
+
+And so you need that.
+
+On the other hand, based
+on all the descriptions
+
+I've given you about
+light-atom interaction,
+
+two-photon
+transitions would just
+
+mean we need one more order
+of perturbation theory,
+
+and then it's the same thing
+you have already learned.
+
+So it's a highlight, and it's
+to some extent also a review.
+
+You will actually recognize, in
+some situations, the difference
+
+between two-photon processes
+and one-photon processes.
+
+It's not so big, it's just
+you have to-- you'll see.
+
+You have to use a
+different Rabi frequency
+
+and some different concepts.
+
+OK.
+
+So that's, I think, really
+an agenda of highlights.
+
+Let's go back to the physical
+picture we drew up on Wednesday
+
+about Dicke narrowing.
+
+I just explained
+to you that when
+
+we have an atom which is
+trapped and tightly confined,
+
+that the spectrum consists of
+a sharp light and sidebands.
+
+And now I was addressing
+the situation--
+
+what happens if you
+have an atom which
+
+is surrounded by buffer gas?
+
+I would say, well, that's a
+cheap trap created by nature,
+
+because when the particle
+wants to fly away,
+
+it collides with
+a buffer gas atom.
+
+So it stays put.
+
+So it's a cheap trap, but
+it's also a lousy trap,
+
+because there is some randomness
+in the number of collisions.
+
+But I'm waving my
+arm, so that maybe you
+
+can go along with the picture
+that it is an ensemble of traps
+
+which have very different
+trap frequencies.
+
+And then we would expect,
+based on our understanding
+
+of the spectrum of
+confined particles,
+
+that we have a carrier,
+which is always the same,
+
+at the electronic
+excitation frequency.
+
+But then we have sidebands
+at the trap frequency.
+
+But those sidebands
+are now smeared out,
+
+because we do not have a
+defined harmonic oscillator
+
+potential here.
+
+So therefore, I sort of
+tried to lead you in the way
+
+that that may be one way how you
+can think about the situation.
+
+And well, now I want to give you
+a different way to look at it.
+
+And let's see how those
+things come together.
+
+So if I would ask you, give
+me a quantitative estimate
+
+how wide this line
+is, do you have
+
+any idea how we can do that?
+
+Or let me even put it this way.
+
+It's again one of
+those kind of things--
+
+you have the knowledge, but
+to put it together is hard.
+
+But I would guarantee
+everybody in this room
+
+has the knowledge to write
+down in one line what
+
+is the width of this line.
+
+What is the width of this line?
+
+It's an inverse time.
+
+What time?
+
+Coherence time.
+
+Yeah.
+
+But now, if you have an
+atom which is now starting
+
+and it hits buffer
+gas, how would you
+
+estimate the coherence time?
+
+AUDIENCE: Mean free pass.
+
+PROFESSOR: Mean free
+pass will be important.
+
+But the coherence
+time-- how long
+
+will the atom talk to the laser
+beam in a phase-coherent way?
+
+So what do we have to
+compare to the wavelengths?
+
+AUDIENCE: Mean free pass.
+
+PROFESSOR: The mean free pass.
+
+This will be the
+important parameter.
+
+But if the mean free
+pass is much shorter
+
+than the wavelengths?
+
+Well, the atom has just
+moved a tiny bit, one mean.
+
+Is it still coherent
+at this time?
+
+AUDIENCE: It's
+shorter than the wave.
+
+PROFESSOR: If the mean free
+path is shorter than the wave.
+
+So it will do many collisions.
+
+But since it stays localized, it
+will still coherently interact.
+
+When will it stop
+coherently interacting?
+
+AUDIENCE: Mean free path.
+
+PROFESSOR: No, the mean
+free path is always smaller.
+
+Let's just assume that.
+
+I hear "diffusion."
+
+AUDIENCE: [INAUDIBLE].
+
+PROFESSOR: Yes.
+
+The atom has a short
+mean free path,
+
+but it will do a random walk.
+
+And the movement it diffuses
+by more than a wavelength,
+
+it has randomly changed its
+position by a wavelength.
+
+And that would
+mean it experiences
+
+the phase of the drive
+field in a random way.
+
+End of coherence.
+
+1 over this time
+is its line width.
+
+OK.
+
+So let me write that down.
+
+So based on the
+concepts we have learned
+
+by looking at Doppler
+broadening and all that,
+
+we realize the
+important aspect is,
+
+when do atoms in an ensemble
+randomly move by a wavelength?
+
+So therefore, our
+estimate is now--
+
+estimate the widths
+of the sharp peak.
+
+We use a model
+which is diffusion.
+
+We know that in diffusion,
+the random walk, the RMS
+
+position in atom has moved away.
+
+Ballistic motion
+is linear in time.
+
+Diffusive motion is the
+square root of time,
+
+or z square is linear in time.
+
+And we have the
+diffusion constant.
+
+Diffusion by, well,
+lambda or lambda
+
+bar after time, which
+is wavelength squared.
+
+So therefore, we would
+expect that the full width
+
+at 1/2 maximum of our peak
+is k squared-- k, the wave
+
+vector of the light, and D
+is the diffusion constant.
+
+Well, since you mentioned
+the mean free path, let me,
+
+already at this point-- I
+wanted to do it earlier,
+
+but it fits in very well here.
+
+In an ideal gas, the
+diffusion constant
+
+is given by some thermal average
+speed times the mean free path.
+
+And if you look
+up some textbooks,
+
+there's a factor of 3.
+
+So our delta omega,
+which is k squared
+
+D. Let me write it
+as k times v bar.
+
+And the other k I write
+as 1 over lambda bar.
+
+So this is k squared,
+and I need l.
+
+So this is nothing
+else than k squared--
+
+I take this expression,
+k squared l.
+
+This is one k, this
+is the other k.
+
+And v bar times l is
+the ideal gas expression
+
+for the diffusion constant.
+
+But now you realize that k, dot,
+v-- since in a gas, the most
+
+probably velocity is
+also the momentum spread,
+
+this is nothing else
+than the Doppler width.
+
+So therefore, we find
+that the line widths
+
+in Dicke narrowing--
+if we have buffer gas
+
+and we have diffusive
+motion-- is much smaller--
+
+and this is why it's
+called Dicke narrowing--
+
+than the Doppler broadening
+if the mean free path is
+
+much smaller than
+the wavelength.
+
+So this is where the
+mean free path comes in.
+
+What happens if
+the mean free path
+
+is much longer than
+the wavelength?
+
+What line widths do we then get?
+
+Do we then have a
+line width which
+
+is larger than the
+Doppler broadening,
+
+or do we get the
+Doppler broadening?
+
+Let's have a clicker question.
+
+So if l is much smaller
+than lambda bar,
+
+is delta omega-- and this
+is your option A-- equal to?
+
+Or option B, larger?
+
+OK.
+
+So what do you think?
+
+It's always a question
+when we derive something,
+
+how seriously you should
+take what we derived.
+
+So this expression
+for delta omega Dicke
+
+shows that the line width
+would get larger and larger
+
+the longer the
+mean free path is.
+
+And the question is,
+is that correct or not?
+
+OK.
+
+Any more takers?
+
+Whoops.
+
+Oops.
+
+Sorry, press again.
+
+I erased it by clicking
+the wrong button.
+
+You've already
+made up your mind.
+
+You know the answer.
+
+So stop, display.
+
+Yes.
+
+The majority answer
+is definitely correct.
+
+What happens until the
+first collision happens,
+
+you just have
+normal Doppler-- you
+
+don't have diffusive motion,
+you have ballistic motion.
+
+And if the line width is already
+determined once the atoms have
+
+spread out by a wavelength,
+that's it already.
+
+And then if then the particles
+collide, it doesn't matter.
+
+So what we have assumed
+is we've assumed
+
+that the relevant model for
+the spread out to a wavelength
+
+is a diffusive model.
+
+And if we are past that--
+because the mean free path is
+
+larger than the
+wavelength-- we have
+
+to go back to normal
+Doppler broadening.
+
+OK.
+
+But now let me calculate
+Dicke narrowing
+
+by using the formalism
+we have developed.
+
+So let's use the correlation
+function for that.
+
+And we know that the line
+width was nothing else
+
+than the Fourier transform
+of the correlation function,
+
+how the atoms
+experience the drive
+
+field at two different times.
+
+So we had here the
+matrix element,
+
+the Rabi frequency squared.
+
+We have between time
+t and t plus tau,
+
+the phase of the drive
+field accumulates
+
+e to the i omega tau.
+
+But now we have the e
+to the minus ikr factor.
+
+And r, or the position--
+in diffusion, you
+
+often call it s-- changes now,
+because the particle undergoes
+
+a random walk.
+
+So what we have to do is to
+describe collisional narrowing,
+
+we have to take this
+factor and average it
+
+over our ensemble of
+diffusing particles.
+
+And well, diffusion means that
+if particles start out at t
+
+equals 0 at the
+origin, the probability
+
+that we find the
+particle at time t,
+
+a distance s away
+from the origin--
+
+so I'm depicting this one here.
+
+The particle does
+sort of a random walk.
+
+And after time t, it
+is out at a position s.
+
+And the probability for
+that is e to the minus
+
+s squared over 4 Dt.
+
+And you see it's s
+is quadratic over t.
+
+This is a random walk. s
+increases s's square root
+
+of time.
+
+And the probability is
+normalized by this expression.
+
+So therefore, this red average
+in the correlation function
+
+is calculated by convoluting
+with this probability
+
+distribution for
+the random walk.
+
+So it is e to the minus
+iks, e to the minus
+
+s squared over 4 D. The
+time is now called tau.
+
+We used to integrate
+over all possibilities.
+
+And e to the i omega
+tau is a common factor.
+
+My notes show that the integral
+is done from minus infinity
+
+to plus infinity.
+
+Either this is right, or
+there's a factor of two
+
+to be accounted, because
+well, it depends.
+
+Now, is s a coordinate,
+or is s in radians?
+
+In one case, it has a sign,
+in the other case, it has not.
+
+I'm not able to
+reconstruct it now,
+
+but it's just a
+numerical factor,
+
+which would be affected by that.
+
+So the result of
+this integral is
+
+that we obtain an
+exponential function.
+
+So what we find out
+is that there is now
+
+an exponentially
+decaying function.
+
+Remember, we had situations
+where the correlation function
+
+for how the atom
+experiences a coherent field
+
+was decaying
+exponentially because
+
+of spontaneous lifetime?
+
+And now we have an
+exponential decay,
+
+because the particle
+is defusing around.
+
+But we also know, of course,
+that exponential decay, when
+
+we Fourier analyze it,
+gives us a Lorentzian.
+
+So when we ask what is the
+rate, Fermi's golden rule's
+
+rate expression, the
+rate for excitation.
+
+We want to do the Fourier
+transform of this correlation
+
+function.
+
+And what we obtain is, well,
+a Lorentzian which looks
+
+like the Lorentzian for
+spontaneous emission,
+
+except for that we have
+a different width now.
+
+It's a Lorentzian with a
+width 2 k squared times D.
+
+So pretty straightforward.
+
+But I hope you've
+seen and you've
+
+enjoyed there's a very
+intuitive picture.
+
+But the correlation
+function-- if you just
+
+look at it from the
+perspective of the atoms,
+
+how do I experience
+a coherent field?
+
+You put in simply
+the diffusive motion.
+
+You can exactly calculate
+what the line shape is.
+
+And that's definitely
+something you would not
+
+have known how to do it
+without this formalism.
+
+OK.
+
+I have a question for you.
+
+And this is, how does the
+spectrum for diffusive motion
+
+look like?
+
+What we have just
+calculated was that it
+
+is a Lorentzian with the line
+widths we've just determined.
+
+But I want to give
+you another choice.
+
+And this is what we discussed
+at the end of the last class.
+
+This picture where we took
+the confined particles
+
+to the ridiculous limit-- where
+there was no trap anymore,
+
+just collisions--
+suggested actually
+
+that we have some sharp line.
+
+But then this envelope
+of those sidebands
+
+give some unresolved pedestal.
+
+So the question is,
+what is correct?
+
+We have just done a
+quantitative calculation
+
+using the model, a
+diffusion propagator.
+
+But we also had this
+intuitive picture,
+
+which had more this kind
+of bimodal distribution.
+
+A broad pedestal
+and a sharp peak.
+
+And I want you to think
+about it for a few seconds.
+
+What would you expect to
+be the correct answer?
+
+Is the line shape
+just a Lorentzian,
+
+or does the line shape have
+two different parts to it?
+
+OK.
+
+Does somebody want to speak out
+in favor of his or her choice?
+
+Well, one argument is,
+when you derive something,
+
+it must be more correct than
+when you wave your hands.
+
+Therefore, we
+derived a Lorentzian,
+
+and the other picture
+was just waving our hands
+
+and using some analogy.
+
+OK.
+
+That would be one
+argument to vote
+
+for A. Somebody
+wants to defend B?
+
+Pardon?
+
+AUDIENCE: More intuitive.
+
+PROFESSOR: More intuitive.
+
+Yes.
+
+You know, something
+must be right about it.
+
+I mean, in some limit,
+this must be like a trap,
+
+and there should
+be some sidebands.
+
+Yes.
+
+OK.
+
+But now I would ask you-- Nancy,
+if you say it's more intuitive,
+
+why don't we get
+those broadening?
+
+Why don't we get
+this extra pedestal
+
+in our quantitative derivation?
+
+AUDIENCE: [INAUDIBLE].
+
+PROFESSOR: But what?
+
+Didn't we lose the exact
+probability distribution
+
+for diffusive process?
+
+AUDIENCE: There's no
+harmonic oscillator.
+
+The sidebands [INAUDIBLE]
+harmonic oscillator.
+
+PROFESSOR: So that's
+an argument also for A.
+
+We don't have a
+harmonic oscillator.
+
+And when I said there is sort
+of this trap-type feature,
+
+I'm really over-extending
+the analogy.
+
+AUDIENCE: The mean
+free path is not--
+
+PROFESSOR: Pardon?
+
+AUDIENCE: The mean free path
+is not infinitesimally small.
+
+PROFESSOR: The mean free path
+is not infinitesimally small.
+
+Now we're getting close.
+
+We assumed diffusive motion.
+
+We put in the exact expression
+for diffusive motion.
+
+And of course, you also know,
+when you describe a line width,
+
+what happens in the
+middle at detuning
+
+0 is more what happens in
+the limit of long times.
+
+What happens further and further
+out happens at shorter times.
+
+What is the motion of
+atoms at short times?
+
+Before the first collision
+happens, it moves straight.
+
+So the diffusive
+propagator which we put in
+
+is only valid after
+the first collision.
+
+Until the first collision
+happens, we have free motion.
+
+And free motion should give rise
+to simple Doppler broadening.
+
+So until the first
+collision happens,
+
+we should get a little
+bit of Doppler broadening.
+
+But once the
+collisions happened,
+
+we should be very well
+within the description
+
+of the diffusion operator.
+
+And to address your
+concern, actually,
+
+in the limit of many
+sideband, often,
+
+the envelope of
+all those sidebands
+
+is actually determined
+by the Doppler profile.
+
+There is a limit, if you have
+a large modulation index,
+
+that you have many sidebands.
+
+And in some
+semi-classical limit,
+
+the sidebands have an envelope
+which is the Doppler profile.
+
+So now I think the
+two pictures agree.
+
+If we had used a propagator
+which would interpolate
+
+between the first moment where
+the particle moves straight,
+
+and then diffusion, we would
+have gotten little pedestals
+
+here.
+
+And so that sort of tells us
+that the smeared outside bands,
+
+yes, strictly speaking, they
+are linked to harmonic motion.
+
+But they are sort
+of the leftover
+
+of the motional effect,
+which is the Doppler effect.
+
+OK.
+
+Good.
+
+So we have the
+correct answer here.
+
+And here, it is the model
+neglects ballistic motion
+
+until the first collision.
+
+Questions?
+
+OK.
+
+Let's now spend 10
+minutes discussing
+
+the fluorescent
+spectrum of an atom.
+
+As I pointed out in my overview,
+we teach much more about it
+
+in 8.422.
+
+We use a dressed atom picture.
+
+But something would be missing
+if I wouldn't do it also
+
+in this course, because
+we have discussed
+
+to quite some extent what
+happens when we excite atoms
+
+with light.
+
+And what we have
+discussed so far
+
+is that we excite atom and scan
+the laser, or the excitation
+
+frequency.
+
+And when we are plotting the
+intensity of the fluorescence,
+
+we are looking at the
+number of scattered photon.
+
+And what we are scanning is
+the detuning of the laser.
+
+We would expect, in the case
+of a motionless atom, simply
+
+a Lorentzian, or in
+the general limit,
+
+a power-broadened Lorentzian.
+
+Just to be clear, what I'm
+discussing in those 10 minutes
+
+is I'm completely ignoring
+that the atom can move.
+
+So you should think
+that it's either
+
+an atom with infinite mass,
+or it's an atom tightly
+
+localized in the
+Lamb-Dicke limit,
+
+and all we are looking at is the
+structure of the central peak.
+
+So no motional effects.
+
+We just look at the pure
+kind of intrinsic line
+
+widths of the
+electronic transition.
+
+OK.
+
+So we have discussed that.
+
+But now I want to look at
+another aspect of spectroscopy.
+
+And this is another
+scan we can do.
+
+We want to have
+a fixed detuning.
+
+And we look at the spectrum
+of the emitted light.
+
+So let's assume that
+we have a laser which
+
+is at a detuning delta.
+
+The laser is fixed.
+
+The light is emitting.
+
+But we are now dispersing
+with a spectrograph.
+
+We are analyzing what is the
+frequency of the emitted light.
+
+And we determine the spectrum.
+
+And yes, the question is,
+how does it look like?
+
+And I want to give
+you four options.
+
+So this is 0 detuning
+at resonance.
+
+Oops, I need one more.
+
+Let me relabel it
+to make it clear.
+
+So our option one
+is our spectrum
+
+is a delta function at
+the resonance of the atom.
+
+Option two is it is a Lorentzian
+centered around the resonance.
+
+Option three is it is a
+delta function at the laser
+
+frequency.
+
+And option four is it is a
+Lorentzian with line width
+
+gamma.
+
+So we have two options.
+
+Is it a delta function
+at omega 0 or omega l?
+
+Or is it a Lorentzian-broadened
+function at either omega 0
+
+or omega l.
+
+And since we want to
+keep things simple,
+
+we want to first discuss the
+case of the perturbative case
+
+that the laser which excites
+the atom has very low power.
+
+So what would you expect?
+
+An atom is excited, it's
+a little light bulb.
+
+You analyze the spectrum
+of the light bulb.
+
+Which of the four
+spectrum will you measure?
+
+OK.
+
+Let's try again.
+
+[LAUGHTER]
+
+And maybe I should, like
+our online learning system,
+
+try to give you one hint.
+
+I want you to really think hard
+what energy conservation means
+
+in this problem.
+
+OK.
+
+OK, we're getting closer.
+
+Now, the way how I want
+you to think about it
+
+is if you take the
+limit of low power,
+
+you should really think
+about it that there
+
+is only one photon in
+your whole laboratory.
+
+This photon is
+scattered of an atom,
+
+and then you measure the
+frequency of the photon.
+
+And energy conservation clearly
+tells us that the frequency
+
+of the scattered photon cannot
+be at the resonance frequency.
+
+It has to be at the
+laser frequency.
+
+Otherwise, we would
+violate energy.
+
+But it seems-- still,
+the more subtle thing
+
+is, is it a delta function?
+
+Of course, a delta
+function will be broadened.
+
+If you do the experiment
+for one second,
+
+you will have a Fourier
+line width which is 1 hertz.
+
+But that's, for
+practical reasons, almost
+
+like a delta function, because
+the spectral line widths,
+
+or the natural line widths
+of your favorite atom
+
+is 10 megahertz.
+
+So there will be some
+temporal broadening,
+
+which is in case in any
+realistic experiment.
+
+But we are talking about, are
+you limited by the experiment
+
+and by technical
+noise, or are you
+
+limited by the
+natural line widths?
+
+Now, I would argue, just
+with energy conservation--
+
+but I'll give you another
+argument in a second--
+
+that if I have a
+monochromatic laser,
+
+the photon which
+has to come out has
+
+to be exactly the
+same frequency.
+
+Because we talked about
+energy conservation.
+
+And if I would start with a
+photon at the laser frequency
+
+and I would measure a photon
+which has 10 megahertz away,
+
+I would violate energy
+conservation by 10 megahertz.
+
+So the argument is
+actually correct.
+
+It's a delta function
+at the drive frequency.
+
+But I want to give
+you another argument.
+
+It's, again, something you
+have heard in the course.
+
+But you should really
+take it seriously,
+
+and apply to that situation.
+
+And that's the following.
+
+Remember when we talked
+about the AC stark effect.
+
+I told you that
+you should really
+
+think about the atom as
+a harmonic oscillator.
+
+We even introduced for you
+the oscillator strengths
+
+that we could even
+quantitatively describe
+
+the response of the atom
+to the scattering of light
+
+by pretty much a model where we
+have a mechanical model where
+
+an electron is attached
+with a spring to an origin.
+
+OK.
+
+Let me now paraphrase
+the question.
+
+Well, I've given you the answer.
+
+Before giving you
+the answer, I should
+
+have asked you the
+following-- if you now
+
+make the assumption that you
+have a harmonic oscillator,
+
+the harmonic oscillator has a
+resonance frequency of omega 0.
+
+And it has a damping
+rate of gamma.
+
+But we are driving the harmonic
+oscillator not at omega 0;
+
+we were driving it at
+a frequency omega l.
+
+At what frequency does the
+harmonic oscillator respond?
+
+At the drive frequency
+or at its own frequency?
+
+AUDIENCE: Drive.
+
+PROFESSOR: Of course.
+
+It's a drive frequency.
+
+And if you have a CW experiment,
+I said let's wait a second,
+
+let's really do a
+long experiment,
+
+if you have a driven
+harmonic oscillator,
+
+and you drive it
+for a long time,
+
+and you analyze the
+spectrum of the motion,
+
+is the frequency spectrum of
+the driven harmonic oscillator
+
+absolutely sharp at
+the drive frequency?
+
+Or is it broadened by
+gamma, the damping constant
+
+of the harmonic oscillator?
+
+AUDIENCE: Sharp.
+
+PROFESSOR: Who
+thinks it's sharp?
+
+Who thinks it's broad?
+
+Hands up for sharp.
+
+Hands up for broad.
+
+OK.
+
+AUDIENCE: [INAUDIBLE].
+
+PROFESSOR: Look, what you are
+overlooking is the following.
+
+There is the difference
+between a transient, which
+
+is damped out at a rate gamma.
+
+But then there is
+the CW response.
+
+If you have an ultra-weak drive,
+you leave it on for an hour,
+
+the harmonic oscillator
+will reach steady state.
+
+And it will just oscillate
+driven by your drive.
+
+And it's actually monochromatic.
+
+And if you analyze
+the motion, it's
+
+a harmonic oscillator in
+steady state with a drive,
+
+and it just moves with a fixed
+amplitude and fixed frequency.
+
+I mean, the way how
+I shake my hands,
+
+this is a delta function
+at the drive frequency.
+
+So in this simple
+harmonic oscillator model,
+
+gamma and damping
+comes in when you
+
+do what I discussed
+earlier, when
+
+you change the drive frequency.
+
+But this is a completely
+different experiment.
+
+We are not changing
+the drive frequency
+
+and looking for the response.
+
+We are a fixed drive
+frequency, and we
+
+are analyzing what the
+motion is which comes out.
+
+And then, as you know from
+differential equation,
+
+you may have a grade transient.
+
+You may have a transient
+at the resonance frequency
+
+which dies out
+with a rate gamma.
+
+This is when you suddenly
+switch on your drive,
+
+and you're not adiabatically
+switching on your drive.
+
+But this is just a transient.
+
+But what we are asking here
+when you do a CW experiment,
+
+you drive it for a long
+time, you look what happens.
+
+And the motion of the
+driven harmonic oscillator
+
+is a delta function
+at the drive.
+
+And what is valid for
+a harmonic oscillator
+
+is also valid for
+the atom, pretty much
+
+for the same reasons.
+
+Any questions?
+
+Yes.
+
+AUDIENCE: Regarding the
+energy conservation in D,
+
+wouldn't the photon processes
+explain energy conservation?
+
+PROFESSOR: OK.
+
+You are now really
+asking-- Nancy
+
+is asking about
+two-photon processes.
+
+Well, we don't
+want to stop here.
+
+We want to see something
+more interesting.
+
+This is just sort of the
+trivial, simple harmonic
+
+oscillator.
+
+The question is now, if you
+want to see something richer,
+
+if we want to see a
+little bit of broadening,
+
+or we want to see something
+which is not as boring as just
+
+a classical harmonic oscillator,
+what do we have to do?
+
+AUDIENCE: Increase the strength.
+
+PROFESSOR: Increase the
+strengths of the field.
+
+And I heard somebody
+saying, two photons.
+
+And that may be--
+
+AUDIENCE: Next-order
+perturbation theory.
+
+PROFESSOR: Pardon?
+
+AUDIENCE: It's like next
+order perturbation theory.
+
+PROFESSOR: Next-order
+perturbation theory.
+
+But just in the sort
+of intuitive picture,
+
+if you have two photons
+which come quickly enough--
+
+and how quickly the two
+photons come will be debated.
+
+Of course, it's parametrized
+by the Rabi frequency,
+
+the strengths of the drive.
+
+But if two photons come
+quickly, each photon
+
+has to be scattered with
+a delta function because
+
+of energy conservation.
+
+But if we have two
+photons, suddenly, it's
+
+possible that one is scattered
+here and one is scattered here.
+
+And we still conserve energy.
+
+So if you want to see some form
+of line broadening, if you want
+
+to see all the things
+you have mentioned,
+
+we have to go away from
+the low power limit.
+
+And this is what we do next.
+
+So we assume that we
+have higher power.
+
+We are on resonance.
+
+And let me assume that the Rabi
+frequency is larger than gamma.
+
+So what is the physics now
+of the atom if the Rabi
+
+frequency is larger than gamma?
+
+It can do Rabi oscillation
+before it's damped.
+
+So now we have a
+system which has
+
+an internal dynamics
+at the Rabi frequency.
+
+And you know if you
+have an emitter,
+
+if you have an antenna
+which emits light,
+
+and you move the antenna
+around at a frequency--
+
+we had the example of a trapped
+particle which has a trapped
+
+frequency of omega
+trap-- the spectrum,
+
+if you Fourier transform, it
+leads to the basal function,
+
+it leads to the sideband.
+
+So therefore, we know now,
+based on all the analogies,
+
+if you have a modulated
+emitter, we obtain sidebands.
+
+That's what we would
+expect classically.
+
+So let me now ask you the
+three following possibilities.
+
+Maybe we still get
+a delta function.
+
+Maybe we get three peaks where
+the splitting is the Rabi
+
+frequency.
+
+So the two outer
+peaks have a-- and the
+
+third option is that yes, we
+observe the Rabi frequency,
+
+but the Rabi frequency
+is the splitting
+
+between the outer peaks.
+
+So the first and second
+answer differ by a factor of 2
+
+in the sideband spacing.
+
+So we have three choices.
+
+Do we expect sidebands?
+
+That's A and B. Or would
+you expect that we still
+
+have a delta function,
+because, well, maybe energy has
+
+to be conserved at the
+single photon level?
+
+And then is the splitting
+Rabi frequency on each side,
+
+or Rabi frequency between
+the two sidebands?
+
+All right.
+
+Yes.
+
+It's indeed the situation.
+
+For those who picked
+A, it's pretty much
+
+the definition of what
+the Rabi frequency is.
+
+After one cycle of
+the Rabi frequency,
+
+the atom has gone
+from the ground state
+
+to the excited state and
+back to the ground state.
+
+So the model you should have is
+that you have an object which
+
+is emitting light,
+but the object
+
+has some internal modulation
+at the Rabi frequency.
+
+Whatever factor of 2
+you had in the amplitude
+
+versus probability or
+something, all this
+
+has been factored into
+the definition of the Rabi
+
+frequency in such a way
+the atom is really blinking
+
+between ground and excited
+state with a frequency
+
+which is the Rabi frequency.
+
+And this frequency
+leads-- and the spectrum
+
+is now the sum and difference
+of the relevant frequencies.
+
+And the relevant frequency
+is the resonance frequency
+
+and the Rabi frequency.
+
+So the answer is B.
+
+But this was sort of more
+in form of a stick diagram.
+
+Now I want to bring in
+in the next question
+
+the line broadening.
+
+So the question is-- and
+there are again four choices.
+
+The question is, we have
+now our three sticks.
+
+One is a carrier, and these
+are the two sidebands split off
+
+by a Rabi frequency.
+
+Are all three sticks now
+sharp delta functions?
+
+Are all three sticks broadened
+by the natural line widths?
+
+Is the central part
+sharp, and only the
+
+sidebands are broadened?
+
+Or do we have a sharp
+stick with a pedestal,
+
+and then two sidebands?
+
+I'm not actually expecting
+all of you to know the answer,
+
+because this is
+really now getting
+
+into more subtle things.
+
+But just in terms
+of show-and-tell,
+
+and attract your curiosity
+to the second part
+
+of the course, what
+would you expect?
+
+OK.
+
+Yes.
+
+Good.
+
+A is definitely eliminated.
+
+I mean, if we scatter two
+photons simultaneously, there
+
+will be sort of
+broadening of gamma,
+
+because the atom has
+a natural broadening.
+
+So we can't expect that the
+two photon processes are sharp.
+
+There's no reason
+to expect that.
+
+The answer between B,
+C, and D depends now.
+
+If we have very, very little
+power, what we observe
+
+is, of course, the
+low-power delta function.
+
+And then we observe very,
+very small sidebands
+
+which are broadened.
+
+So answer C is correct.
+
+If you just think
+about it-- what
+
+is the structure of
+infinitesimal peaks?
+
+But when you crank up the
+power, and what you have is
+
+you have an elastic
+scattering peak,
+
+which has a delta function,
+energy conservation
+
+at the single photon level.
+
+And then you have those-- they
+are called inelastic peaks.
+
+But when you crank up the
+power, then the central feature
+
+has also an inelastic component.
+
+You can sort of argue
+that in Rabi oscillation,
+
+you are in the ground state,
+excited state, ground state,
+
+excited state.
+
+But if you do now light
+scattering in the excited
+
+state, you
+automatically broaden it
+
+by the lifetime of
+the excited state.
+
+And if you crank up the
+power higher and higher,
+
+the elastic peak will be
+more and more suppressed.
+
+And you find actually
+a spectrum which
+
+has only three broadened
+peaks, and the delta function
+
+has disappeared.
+
+It will actually be something
+where we need more knowledge.
+
+The broadening of those
+peaks is not gamma anymore.
+
+One of them will be 3/2
+gamma, the other one
+
+will be 1/2 gamma.
+
+But this now really requires
+a deeper understanding
+
+in terms of the atom picture.
+
+But the scale of
+all the broadening
+
+is a factor on the order
+of unity times gamma.
+
+Any questions?
+
+So the general answer, sorry,
+would be-- the generic picture
+
+which you should keep
+in your mind is that.
+
+You have inelastic scattering
+on all three peaks.
+
+But the limit of D at
+very low power is that.
+
+And at very high power, is that.
+
+The elastic component
+of the central peak
+
+is either 100% or 0%.
+
+OK.
+
+So our last topic for line
+shapes and line broadening
+
+is pressure broadening.
+
+And as I mentioned
+in the introduction,
+
+pressure broadening has
+made modern appearances
+
+in the form of clock shift,
+and mean field shifts,
+
+and mean field broadenings
+in Bose-Einstein condensates.
+
+But let me sort of
+tell you how you
+
+should understand
+pressure broadening.
+
+I'm using here the
+semi-classical picture
+
+that an excited atom
+acts as an oscillator.
+
+And what happened is the atom--
+you can say the oscillation
+
+is superposition of
+ground and excited state.
+
+It oscillates.
+
+But after some time tau, there
+may be a quenching collision,
+
+a de-excitation collision.
+
+Then the atom is sort
+of in the ground state.
+
+And then it waits until it's
+excited again by the laser,
+
+and the atomic dipole
+is oscillating again.
+
+In a situation like
+this, you would
+
+expect that the total
+line widths is actually
+
+the sum of two rates.
+
+One is the spontaneous
+emission rate,
+
+and the other one would be the
+collision rate, which is this.
+
+And in general, this is sort
+of how people looked at it.
+
+You vary the pressure
+in your buffer gas cell,
+
+and you find that the line
+width has a component which
+
+increases linearly
+with pressure.
+
+So this is one model
+how you can imagine
+
+what happens in a collision.
+
+These are like
+knock-out collisions.
+
+When an atom collides,
+the excitation, the energy
+
+disappears.
+
+The atom is quenched
+to the ground state.
+
+Well, we can draw
+up another model,
+
+where we have an oscillation
+of our atomic oscillator.
+
+But then after
+the same time tau,
+
+there is now a
+hiccup in the phase.
+
+It collides with another atom.
+
+The other atom is
+not de-exciting.
+
+It's not removing the energy.
+
+But after the
+collision, the atom
+
+continues to oscillate, but with
+a very, very different phase.
+
+And sort of what I assumed
+here is this time where
+
+the collision happens
+is very short.
+
+It's a very short
+collision time.
+
+That I can approximate
+the collisions
+
+as simply imparting random
+phase jumps to the atom.
+
+Well, if you ask,
+what is the widths
+
+of the spectroscopic line,
+it's exactly the same result.
+
+It just means we have
+a different rate.
+
+It's now a de-phasing
+rate, which is 1 over tau.
+
+And this is added to the
+spectroscopic widths.
+
+OK.
+
+This is sort of just creating
+some phenomenological picture.
+
+Let's now ask a little
+bit more microscopically.
+
+How can it happen?
+
+How can it happen that there
+is a phase change, that there's
+
+a change in the phase of
+the atomic oscillator?
+
+And this leads us now to
+consider the interaction
+
+potential as a function
+of r between two atoms.
+
+We have one atom which is
+sort of our active atom, which
+
+has an excited and ground state.
+
+And this atom is now
+getting closer to,
+
+let's say, an argon atom,
+which acts as buffer gas.
+
+And what I'm plotting
+in this graph now
+
+is the interaction potential
+between our light-emitting,
+
+or light-absorbing, atoms
+and the buffer gas atom.
+
+And let's just
+genetically assume there
+
+is sort of something like
+a molecular potential.
+
+But in general, the
+molecular potentials
+
+will be different in the
+ground and excited state.
+
+And of course, if you
+do hyperfine transitions
+
+between atoms in a
+Bose-Einstein condensate,
+
+you may have a
+scattering length,
+
+which is different
+in the two states.
+
+And I think you
+see the connection.
+
+So in general, if the
+interaction environment
+
+is different between
+ground and excited state,
+
+we expect that the
+interaction potential
+
+causes certain shifts.
+
+So we could use the picture
+that we have a phase evolution.
+
+And the phase evolution
+is a frequency difference
+
+which is simply given by
+the difference of the two
+
+potentials.
+
+So the picture is a little
+bit-- which is actually
+
+very valid for cold
+collisions, which-- well,
+
+really a new chapter
+in atomic physics
+
+opened up by laser cooling
+and magneto-optic traps.
+
+An atom, when it emits a
+photon, would emit here
+
+at the resonance frequency.
+
+But if the collision
+is very, very slow,
+
+it will actually emit,
+with a certain probability,
+
+a photon which is shifted
+by exactly this expression.
+
+And in that limit, that
+could be very interesting,
+
+because by analyzing
+the spectrum
+
+of the immediate light,
+you learn something
+
+about the interaction
+potential of two atoms.
+
+But of course, this argument
+has a little bit of a flaw,
+
+because you can observe a
+frequency not instantaneously.
+
+You can observe-- if a
+collision happens very fast,
+
+you would actually go through
+those frequency changes so fast
+
+that you cannot resolve them.
+
+The question is,
+which one is larger?
+
+So if the frequency
+shift is larger
+
+than the inverse time for the
+duration of the collision,
+
+then you can observe it.
+
+Otherwise, you can't.
+
+So the picture we should
+draw is now the following.
+
+And this is sort of
+a microscopic picture
+
+on those phase jumps,
+which I mentioned earlier.
+
+That you have your
+atomic oscillator.
+
+The atom is oscillating.
+
+But now it comes
+close to another atom.
+
+And let's assume there
+is an energy increase
+
+between ground and excited
+state due to the presence
+
+of the buffer gas atom.
+
+Then you would say you
+get a quick oscillation.
+
+Depending on the
+impact parameter,
+
+it can last various
+amount of time.
+
+And then later, the
+oscillation starts.
+
+But essentially, this
+causes a random phase jump.
+
+So this time here is the
+collision time tau c.
+
+What we expect now is we
+have to now interpolate
+
+between two models.
+
+I'm not taking it any
+further than that.
+
+We have an interesting
+line shape.
+
+There may be a central part
+which is simply collisionally
+
+broadened by the
+interruptions of the phase,
+
+by the number of collisions
+with the collision time tau.
+
+But if when the atoms collide,
+there is a huge frequency shift
+
+momentarily, that this will
+actually affect the wings.
+
+So for frequency shifts which
+come from the interaction
+
+potential which are much
+larger than the collision time,
+
+than the time
+between collisions,
+
+we will observe
+something which goes
+
+by the name "far
+wing broadening."
+
+And also, the central part
+of the potential is simply,
+
+you can say, it's a
+Lorentzian which is simply
+
+broadened by the collision rate.
+
+There is no microscopic
+information--
+
+what is the nature,
+what is going on
+
+during the phase jumps.
+
+The wings will have
+actually information
+
+about the molecular potential.
+
+And I just wanted to present
+it to you in this way
+
+to sort of show how you
+actually have, in a line shape,
+
+often two effects.
+
+One is pretty much
+just the interruption
+
+of the coherence which
+gives the central line.
+
+But you still have, at
+least in some limit,
+
+information about what
+causes those phase jumps.
+
+And this appears in the wings.
+
+20 years ago in the
+atomic physics course,
+
+we taught you a theory
+how to describe that.
+
+It could be probably
+taught in one hour.
+
+There are some
+links on the Wiki,
+
+but I don't want to
+carry that further.
+
+Any questions about that?
+
+AUDIENCE: So why has the
+importance decreased?
+
+PROFESSOR: The
+importance has decreased
+
+of that, because
+I mean, who of you
+
+is studying atoms and gas cells?
+
+Nobody.
+
+The frontier has moved on.
+
+We are much more in a
+regime where we are not
+
+observing atoms in
+certain environment.
+
+We are creating an interesting
+system out of atoms
+
+by putting the atoms in a
+well-defined environment where
+
+those things are absent.
+
+Or in the ultra-cold
+domain, and de Broglie
+
+wavelengths is so long that this
+kind of model for collisions
+
+is no longer applicable.
+
+We are in the extreme case of
+a single partial wave, where
+
+a single parameter,
+the scattering lengths,
+
+describes all of it.
+
+OK.
+
+Cory?
+
+AUDIENCE: Yeah.
+
+Could you talk for a
+little bit about how
+
+this model of collisions
+breaks down and allows
+
+for Dicke narrowing?
+
+PROFESSOR: Yes.
+
+Thank you.
+
+That was one comment I forgot.
+
+What happens is you have Dicke--
+thanks for this question.
+
+You have Dicke-- I drew up
+the two potential curves.
+
+If the two potential curves
+are absolutely identical,
+
+the atoms can approach
+each other and can collide.
+
+But there is never
+any perturbation
+
+to the atomic oscillator,
+because the frequency
+
+between ground and
+excited state is omega 0,
+
+no matter whether the atom
+undergoes a collision or not.
+
+In this limit, which is
+often realized in collisions
+
+with rare gases,
+in this limit, you
+
+do not have any phase
+interruption by the collision.
+
+And this is the prerequisite
+for Dicke narrowing.
+
+OK.
+
+I think we have the
+full picture now.
+
+And that means we can move
+on to two-photon excitations.
+
+So whenever you
+start a new chapter,
+
+you should motivate it.
+
+And the question is, why
+should you be interested?
+
+Well, I can also turn it
+around and said, why not?
+
+Because those things happen.
+
+And if those things happen,
+we want to learn about them.
+
+And they actually
+happen very naturally.
+
+The moment you go to
+higher laser power
+
+and you go beyond the lowest
+order of perturbation theory,
+
+you may actually excite two
+photons at the same time.
+
+And actually, what we just
+discussed about the emission
+
+spectrum of an atom, with the
+sidebands, with the broadening,
+
+these are actually
+examples where we really
+
+have to think about it in
+a two-photon picture, not
+
+a single-photon picture.
+
+The second motivation
+is very practical.
+
+We may want to excite an
+atom from a low-lying level
+
+to a high-lying level.
+
+But the only laser we can
+buy, or the only laser we have
+
+in the laboratory
+has lower frequency.
+
+That doesn't mean
+that the case is
+
+lost by just stacking two
+photons on top of each other.
+
+We can bridge the
+gap and still excite
+
+the atom, which has
+transitions only far in the UV.
+
+And all we have is
+these visible lasers.
+
+There's another
+thing which changes.
+
+Maybe we want to excite hydrogen
+from the 1s to the 2s level.
+
+1s and 2s have the same parity.
+
+And if we try to excite
+it with one photon,
+
+because of the dipole
+operator which has odd parity,
+
+this is not allowed.
+
+So there are maybe
+selection rules
+
+where we can go to
+desirable final state
+
+only with two photons
+and not with one photon.
+
+Finally, I will show you
+on Wednesday-- remember,
+
+there is no class on Monday,
+because the whole CUA
+
+will go crazy with the NSF
+site visit on Monday, Tuesday.
+
+So the next class on Wednesday.
+
+And on Wednesday,
+I will actually
+
+show you if the two photons come
+from counter-propagating beams,
+
+the net momentum transfer
+to the atom is 0.
+
+And net momentum transfer of
+0 means zero Doppler shift.
+
+So two photons give
+us an opportunity,
+
+which doesn't exist
+with the single photon.
+
+We can excite the atom
+without transferring momentum.
+
+And this is the basis of a
+Doppler free spectroscopy
+
+technique.
+
+And finally, for purely
+conceptional reasons,
+
+we've talked so much about
+excitation of an atom,
+
+and then ask, what is the
+rate of light scattering?
+
+So we have actually used
+two-photon processes
+
+in the course many, many
+times without actually
+
+adequately addressing them.
+
+I didn't tell you
+anything wrong.
+
+I was sort of choosing
+my words carefully,
+
+that everything I told you about
+light emission and absorption
+
+is comparable with
+the correct picture.
+
+And the correct picture
+is if a photon goes in
+
+and a photon goes out,
+you have to describe it
+
+as one process
+involving two photons.
+
+So I think we have
+enough reasons why
+
+we should be interested.
+
+And if I take this picture,
+that I start in one state
+
+and have a two-photon
+absorption process,
+
+I actually want to
+redraw it, because
+
+in the dipole approximation,
+which I want to use here,
+
+we have the dipole operator,
+and second quantization
+
+is a plus a dagger.
+
+The electric field
+is a plus a dagger.
+
+So each application
+of the operator
+
+takes us from one state to
+the next with a single photon.
+
+So therefore, if you
+talk about two photons,
+
+we can only absorb
+them if we have
+
+an intermediate state,
+which I will call f.
+
+So we should really think
+about two-photon absorption
+
+as a two-step process which
+involves an intermediate state.
+
+And it has to be
+like that if we want
+
+to use, as the
+operator for atom light
+
+interaction, the
+dipole operator,
+
+because a dipole
+operator is creating
+
+and-- the dipole operator
+involves electric field.
+
+And that creates or annihilates
+one photon at a time.
+
+Let me just make a
+side remark, but this
+
+will be addressed in 8.422.
+
+If you use the description
+of the interaction
+
+with the electromagnetic
+field, which
+
+is the p minus e Hamiltonian,
+and you square it,
+
+if you square that, you
+get an A squared term.
+
+The A squared term is
+actually the product
+
+of a plus a dagger squared.
+
+So you can actually,
+with the A squared term,
+
+scatter two photons by going
+from one state to another one.
+
+But I'm not discussing it here.
+
+And I leave a detailed
+comparison and discussion
+
+of that to 8.422.
+
+Now we are strictly adhering
+to the dipole approximation.
+
+Oh, actually, let me
+make a comment about it,
+
+because I just realized if I
+say something and don't say it
+
+fully, I may confuse people.
+
+So what I want to say is,
+we will show, in 8.422
+
+that the two pictures, the
+pap minus a Hamiltonian
+
+and the dipole Hamiltonian
+are equivalent.
+
+They're connected by
+canonical transformation.
+
+So therefore, it is not a
+fundamental aspect of nature,
+
+whether you can scatter
+only one photon when
+
+you go from one
+state to the other.
+
+There are two
+equivalent descriptions.
+
+In one description, you
+sometimes scatter two photons.
+
+In the other description,
+you scatter only one photon.
+
+And you will all
+get a PSET in 8.422
+
+where you show for one
+example that the results are
+
+the same when you sum up
+over all possibilities.
+
+So therefore, I can
+maybe here should rather
+
+take the position, the generic
+description of light scattering
+
+uses the dipole approximation.
+
+And in the dipole
+approximation, we
+
+are describing the
+atoms, that they only
+
+exchange one photon when they
+go from one state to the next.
+
+And this is a full description
+but not the only description.
+
+So therefore, we need
+an intermediate state.
+
+But assuming that the
+first laser is not
+
+resonant with the transition
+to the intermediate state,
+
+we need this dashed line.
+
+This dashed line is sometimes
+called a virtual state.
+
+And in the following
+discussion, we
+
+will really learn what is the
+nature of the virtual state
+
+and what does it mean.
+
+But we need a stepping stone
+for a two-photon process
+
+in the form of
+intermediate states.
+
+So maybe I should
+just use three minutes
+
+and show you how you
+would calculate it.
+
+I use pre-written
+slides here, because I'm
+
+getting a little bit
+bored of just writing down
+
+the same or similar
+perturbative expressions.
+
+And I just step you through.
+
+So I said we use
+the dipole operator.
+
+But now-- and this
+is a new thing--
+
+the electric field
+has not only one
+
+component and one frequency.
+
+We want to look at two
+photons, so therefore, it
+
+has two frequencies.
+
+So therefore, our
+perturbation Hamiltonian
+
+is what we had so far
+for monochromatic field.
+
+But then we have
+an additional term
+
+where we just change the
+index from one to two
+
+to have the second
+laser field described.
+
+So let me now introduce
+matrix elements.
+
+We have to go from state a
+to some intermediate state.
+
+And then we go to state b.
+
+So therefore, we
+need matrix elements
+
+which take us from
+state a to state f.
+
+And again, we have two
+such possibilities--
+
+one at omega 1,
+one at omega 2, one
+
+driven by field 1, the
+other one driven by field 2.
+
+And yeah, we all have
+the counter-rotating and
+
+co-rotating terms.
+
+What happens is we have, of
+course, a complex conjugate.
+
+But I told you
+already several times
+
+that there is an e
+to the minus i omega
+
+1, which is responsible
+for absorption.
+
+The plus i omega
+1 does emission.
+
+And let me just-- I want
+to do the rotating wave
+
+approximation, only
+keep the relevant term.
+
+So I look at
+two-photon absorption.
+
+And that means I only keep
+forward the minus terms.
+
+You could, if you
+want, duplicate
+
+the lengths of each
+formula and carry forward
+
+the counter-rotating term.
+
+You're not learning
+anything new.
+
+You get additional
+Bloch-Siegerts
+
+and AC stark shifts.
+
+This is not the new feature
+I want to implement.
+
+So let's focus on
+the new aspect.
+
+And this is the following.
+
+We do first-order
+perturbation theory,
+
+which takes us in the first
+step to the intermediate state.
+
+And you have seen this
+expression many, many times.
+
+The only thing is in addition to
+what we had for one laser beam,
+
+we have to add a second
+possibility, which
+
+comes from the second field.
+
+And now we are at the
+intermediate step.
+
+And we want to take the second
+step to the final state.
+
+So what we are now doing is we
+are writing down Schrodinger's
+
+equation, derivative
+of the wave function
+
+is Hamiltonian times
+the wave function.
+
+And we are especially
+interested in how
+
+do we accumulate probability or
+amplitude in the final state.
+
+But what we are doing is
+on the right-hand side,
+
+because we can't start
+in the ground state,
+
+we've gone to the
+intermediate state,
+
+we are now plugging in
+the previous result,
+
+the first-order result for
+the intermediate state.
+
+So therefore, by using
+second-order perturbation
+
+theory, we want the second-order
+perturbation theory,
+
+so we integrate this equation
+with respect to time.
+
+But on the right side, we
+use our first-order result,
+
+which we had derived earlier.
+
+And then we just write
+down the integral.
+
+Everything is just
+exponential function.
+
+And we get the result here.
+
+So now with two steps, we
+have obtained an expression
+
+for-- I know time
+is over, but let
+
+me just finish the argument.
+
+So we have now an expression
+in second-order perturbation
+
+theory.
+
+What is the amplitude
+in the final state?
+
+And things look a
+little bit messy,
+
+because we have four terms.
+
+And we should get
+four terms, because we
+
+have two interactions.
+
+We can take one
+photon of one laser
+
+beam-- first step, omega
+1; second step, omega two.
+
+We can switch the
+order of photons.
+
+And of course, if you write
+down everything correctly,
+
+nothing is forbidding the atom
+of taking both photons out
+
+of the same laser beam.
+
+Yeah, let me stop here.
\ No newline at end of file
diff --git a/FvwDJ3Op2Js.txt b/FvwDJ3Op2Js.txt
new file mode 100644
index 0000000000000000000000000000000000000000..5e55094acdd7d1470b2b734a89398f5385e3ada0
--- /dev/null
+++ b/FvwDJ3Op2Js.txt
@@ -0,0 +1,14459 @@
+align:start position:0%
+ 
+the following content is provided under
+
+ align:start position:0%
+the following content is provided under
+ 
+
+ align:start position:0%
+the following content is provided under
+a Creative Commons license your support
+
+ align:start position:0%
+a Creative Commons license your support
+ 
+
+ align:start position:0%
+a Creative Commons license your support
+will help MIT open courseware continue
+
+ align:start position:0%
+will help MIT open courseware continue
+ 
+
+ align:start position:0%
+will help MIT open courseware continue
+to offer highquality educational
+
+ align:start position:0%
+to offer highquality educational
+ 
+
+ align:start position:0%
+to offer highquality educational
+resources for free to make a donation or
+
+ align:start position:0%
+resources for free to make a donation or
+ 
+
+ align:start position:0%
+resources for free to make a donation or
+view additional materials from hundreds
+
+ align:start position:0%
+view additional materials from hundreds
+ 
+
+ align:start position:0%
+view additional materials from hundreds
+of MIT courses visit mitop courseware at
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+ocw.mit.edu how's everybody
+
+ align:start position:0%
+ocw.mit.edu how's everybody
+ 
+
+ align:start position:0%
+ocw.mit.edu how's everybody
+doing good yeah
+
+ align:start position:0%
+doing good yeah
+ 
+
+ align:start position:0%
+doing good yeah
+I wanted to start with some
+
+ align:start position:0%
+I wanted to start with some
+ 
+
+ align:start position:0%
+I wanted to start with some
+inspiration um and uh so because I love
+
+ align:start position:0%
+inspiration um and uh so because I love
+ 
+
+ align:start position:0%
+inspiration um and uh so because I love
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+videos and I think that's a way of
+
+ align:start position:0%
+videos and I think that's a way of
+ 
+
+ align:start position:0%
+videos and I think that's a way of
+inspiring and sometimes I think if you
+
+ align:start position:0%
+inspiring and sometimes I think if you
+ 
+
+ align:start position:0%
+inspiring and sometimes I think if you
+feel really passionate about something
+
+ align:start position:0%
+feel really passionate about something
+ 
+
+ align:start position:0%
+feel really passionate about something
+you can use uh song and video as a way
+
+ align:start position:0%
+you can use uh song and video as a way
+ 
+
+ align:start position:0%
+you can use uh song and video as a way
+of conveying your ideas I have a good
+
+ align:start position:0%
+of conveying your ideas I have a good
+ 
+
+ align:start position:0%
+of conveying your ideas I have a good
+friend actually who's been doing that um
+
+ align:start position:0%
+friend actually who's been doing that um
+ 
+
+ align:start position:0%
+friend actually who's been doing that um
+so I want to show you anybody heard to
+
+ align:start position:0%
+so I want to show you anybody heard to
+ 
+
+ align:start position:0%
+so I want to show you anybody heard to
+fog and
+
+ align:start position:0%
+fog and
+ 
+
+ align:start position:0%
+fog and
+smog okay I'm going to show you this
+
+ align:start position:0%
+smog okay I'm going to show you this
+ 
+
+ align:start position:0%
+smog okay I'm going to show you this
+little
+
+ align:start position:0%
+little
+ 
+
+ align:start position:0%
+little
+video
+
+ align:start position:0%
+video
+ 
+
+ align:start position:0%
+video
+um just a minute or just a minute of
+
+ align:start position:0%
+um just a minute or just a minute of
+ 
+
+ align:start position:0%
+um just a minute or just a minute of
+it I mean you know what's crazy to me is
+
+ align:start position:0%
+it I mean you know what's crazy to me is
+ 
+
+ align:start position:0%
+it I mean you know what's crazy to me is
+like nobody ever talks in person anymore
+
+ align:start position:0%
+like nobody ever talks in person anymore
+ 
+
+ align:start position:0%
+like nobody ever talks in person anymore
+you know like you got Twitter Facebook
+
+ align:start position:0%
+you know like you got Twitter Facebook
+ 
+
+ align:start position:0%
+you know like you got Twitter Facebook
+and everybody's sending text messages
+
+ align:start position:0%
+and everybody's sending text messages
+ 
+
+ align:start position:0%
+and everybody's sending text messages
+but like nobody's ever sitting down like
+
+ align:start position:0%
+but like nobody's ever sitting down like
+ 
+
+ align:start position:0%
+but like nobody's ever sitting down like
+this and just talking you know I mean
+
+ align:start position:0%
+this and just talking you know I mean
+ 
+
+ align:start position:0%
+this and just talking you know I mean
+for all these Technologies we're
+
+ align:start position:0%
+for all these Technologies we're
+ 
+
+ align:start position:0%
+for all these Technologies we're
+actually further apart you know what I'm
+
+ align:start position:0%
+actually further apart you know what I'm
+ 
+
+ align:start position:0%
+actually further apart you know what I'm
+saying hello
+
+ align:start position:0%
+saying hello
+ 
+
+ align:start position:0%
+saying hello
+it's my good friend DJ
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+[Music]
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Dave my favorite Cafe trying to get my
+
+ align:start position:0%
+Dave my favorite Cafe trying to get my
+ 
+
+ align:start position:0%
+Dave my favorite Cafe trying to get my
+coffee like I do every single day this
+
+ align:start position:0%
+coffee like I do every single day this
+ 
+
+ align:start position:0%
+coffee like I do every single day this
+dude of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+aamn
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+of L he to the counter like um I'm like
+
+ align:start position:0%
+of L he to the counter like um I'm like
+ 
+
+ align:start position:0%
+of L he to the counter like um I'm like
+man you're hell
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+dumb all right so I won show the whole
+
+ align:start position:0%
+dumb all right so I won show the whole
+ 
+
+ align:start position:0%
+dumb all right so I won show the whole
+thing that's actually a good family
+
+ align:start position:0%
+thing that's actually a good family
+ 
+
+ align:start position:0%
+thing that's actually a good family
+friend DJ Dave he I I lived in his room
+
+ align:start position:0%
+friend DJ Dave he I I lived in his room
+ 
+
+ align:start position:0%
+friend DJ Dave he I I lived in his room
+for a year awesome guy um uh and uh uh
+
+ align:start position:0%
+for a year awesome guy um uh and uh uh
+ 
+
+ align:start position:0%
+for a year awesome guy um uh and uh uh
+he's made some some really nice videos
+
+ align:start position:0%
+he's made some some really nice videos
+ 
+
+ align:start position:0%
+he's made some some really nice videos
+the point is this is not quantum
+
+ align:start position:0%
+the point is this is not quantum
+ 
+
+ align:start position:0%
+the point is this is not quantum
+mechanics related um it is a topic near
+
+ align:start position:0%
+mechanics related um it is a topic near
+ 
+
+ align:start position:0%
+mechanics related um it is a topic near
+and dear to my heart as some of you know
+
+ align:start position:0%
+and dear to my heart as some of you know
+ 
+
+ align:start position:0%
+and dear to my heart as some of you know
+um and I'm sure you're all closing your
+
+ align:start position:0%
+um and I'm sure you're all closing your
+ 
+
+ align:start position:0%
+um and I'm sure you're all closing your
+laptops and putting your phones down um
+
+ align:start position:0%
+laptops and putting your phones down um
+ 
+
+ align:start position:0%
+laptops and putting your phones down um
+especially after seeing that um but the
+
+ align:start position:0%
+especially after seeing that um but the
+ 
+
+ align:start position:0%
+especially after seeing that um but the
+point is he's passionate so what does he
+
+ align:start position:0%
+point is he's passionate so what does he
+ 
+
+ align:start position:0%
+point is he's passionate so what does he
+do he conveys his passion in song now if
+
+ align:start position:0%
+do he conveys his passion in song now if
+ 
+
+ align:start position:0%
+do he conveys his passion in song now if
+any of you some of you so this is
+
+ align:start position:0%
+any of you some of you so this is
+ 
+
+ align:start position:0%
+any of you some of you so this is
+related to the class if any of you have
+
+ align:start position:0%
+related to the class if any of you have
+ 
+
+ align:start position:0%
+related to the class if any of you have
+an idea that you're passionate about
+
+ align:start position:0%
+an idea that you're passionate about
+ 
+
+ align:start position:0%
+an idea that you're passionate about
+like say for your final project and you
+
+ align:start position:0%
+like say for your final project and you
+ 
+
+ align:start position:0%
+like say for your final project and you
+You' like to do something like that I
+
+ align:start position:0%
+You' like to do something like that I
+ 
+
+ align:start position:0%
+You' like to do something like that I
+would really um be fully supportive I
+
+ align:start position:0%
+would really um be fully supportive I
+ 
+
+ align:start position:0%
+would really um be fully supportive I
+tried to um some of you may remember my
+
+ align:start position:0%
+tried to um some of you may remember my
+ 
+
+ align:start position:0%
+tried to um some of you may remember my
+attempts to get you to do that in uh
+
+ align:start position:0%
+attempts to get you to do that in uh
+ 
+
+ align:start position:0%
+attempts to get you to do that in uh
+3012 and now guess how many people
+
+ align:start position:0%
+3012 and now guess how many people
+ 
+
+ align:start position:0%
+3012 and now guess how many people
+actually did that in
+
+ align:start position:0%
+actually did that in
+ 
+
+ align:start position:0%
+actually did that in
+3012 right not so many but if somebody
+
+ align:start position:0%
+3012 right not so many but if somebody
+ 
+
+ align:start position:0%
+3012 right not so many but if somebody
+wants to somebody wants to take a crack
+
+ align:start position:0%
+wants to somebody wants to take a crack
+ 
+
+ align:start position:0%
+wants to somebody wants to take a crack
+at you know conveying their project in
+
+ align:start position:0%
+at you know conveying their project in
+ 
+
+ align:start position:0%
+at you know conveying their project in
+uh you know in this format
+
+ align:start position:0%
+uh you know in this format
+ 
+
+ align:start position:0%
+uh you know in this format
+um is there's got to be a bonus point or
+
+ align:start position:0%
+um is there's got to be a bonus point or
+ 
+
+ align:start position:0%
+um is there's got to be a bonus point or
+two in that just alone right um and how
+
+ align:start position:0%
+two in that just alone right um and how
+ 
+
+ align:start position:0%
+two in that just alone right um and how
+many of you are any of you Juniors
+
+ align:start position:0%
+many of you are any of you Juniors
+ 
+
+ align:start position:0%
+many of you are any of you Juniors
+Junior lab are you doing that in vanet's
+
+ align:start position:0%
+Junior lab are you doing that in vanet's
+ 
+
+ align:start position:0%
+Junior lab are you doing that in vanet's
+class yeah so I saw some of those and
+
+ align:start position:0%
+class yeah so I saw some of those and
+ 
+
+ align:start position:0%
+class yeah so I saw some of those and
+I'm like man I I you know it made me I
+
+ align:start position:0%
+I'm like man I I you know it made me I
+ 
+
+ align:start position:0%
+I'm like man I I you know it made me I
+want that you know I think that's I
+
+ align:start position:0%
+want that you know I think that's I
+ 
+
+ align:start position:0%
+want that you know I think that's I
+think that's really creative and cool so
+
+ align:start position:0%
+think that's really creative and cool so
+ 
+
+ align:start position:0%
+think that's really creative and cool so
+I I see a lot of really cool stuff I saw
+
+ align:start position:0%
+I I see a lot of really cool stuff I saw
+ 
+
+ align:start position:0%
+I I see a lot of really cool stuff I saw
+a couple of those they were really great
+
+ align:start position:0%
+a couple of those they were really great
+ 
+
+ align:start position:0%
+a couple of those they were really great
+so if anybody wants um um uh to do that
+
+ align:start position:0%
+so if anybody wants um um uh to do that
+ 
+
+ align:start position:0%
+so if anybody wants um um uh to do that
+let me know and i' I'd be happy to
+
+ align:start position:0%
+let me know and i' I'd be happy to
+ 
+
+ align:start position:0%
+let me know and i' I'd be happy to
+support however I can put you in touch
+
+ align:start position:0%
+support however I can put you in touch
+ 
+
+ align:start position:0%
+support however I can put you in touch
+with CJ Dave if you want um or whatever
+
+ align:start position:0%
+with CJ Dave if you want um or whatever
+ 
+
+ align:start position:0%
+with CJ Dave if you want um or whatever
+okay all right any questions about uh
+
+ align:start position:0%
+okay all right any questions about uh
+ 
+
+ align:start position:0%
+okay all right any questions about uh
+class project so so you know I've been
+
+ align:start position:0%
+class project so so you know I've been
+ 
+
+ align:start position:0%
+class project so so you know I've been
+talking to some of you about the
+
+ align:start position:0%
+talking to some of you about the
+ 
+
+ align:start position:0%
+talking to some of you about the
+projects um and uh um if anyone is still
+
+ align:start position:0%
+projects um and uh um if anyone is still
+ 
+
+ align:start position:0%
+projects um and uh um if anyone is still
+interested it's not too late um but
+
+ align:start position:0%
+interested it's not too late um but
+ 
+
+ align:start position:0%
+interested it's not too late um but
+we're getting close to being too late so
+
+ align:start position:0%
+we're getting close to being too late so
+ 
+
+ align:start position:0%
+we're getting close to being too late so
+please come talk to me if you still want
+
+ align:start position:0%
+please come talk to me if you still want
+ 
+
+ align:start position:0%
+please come talk to me if you still want
+to do a project this would be like the
+
+ align:start position:0%
+to do a project this would be like the
+ 
+
+ align:start position:0%
+to do a project this would be like the
+last week I think to um get something
+
+ align:start position:0%
+last week I think to um get something
+ 
+
+ align:start position:0%
+last week I think to um get something
+going
+
+ align:start position:0%
+going
+ 
+
+ align:start position:0%
+going
+um what I want to do today is well
+
+ align:start position:0%
+um what I want to do today is well
+ 
+
+ align:start position:0%
+um what I want to do today is well
+before I start um here's where we are
+
+ align:start position:0%
+before I start um here's where we are
+ 
+
+ align:start position:0%
+before I start um here's where we are
+okay so what I want to do is is continue
+
+ align:start position:0%
+okay so what I want to do is is continue
+ 
+
+ align:start position:0%
+okay so what I want to do is is continue
+on our March we talked about atoms to
+
+ align:start position:0%
+on our March we talked about atoms to
+ 
+
+ align:start position:0%
+on our March we talked about atoms to
+solids laid a little the groundwork
+
+ align:start position:0%
+solids laid a little the groundwork
+ 
+
+ align:start position:0%
+solids laid a little the groundwork
+we'll review some of that and then go on
+
+ align:start position:0%
+we'll review some of that and then go on
+ 
+
+ align:start position:0%
+we'll review some of that and then go on
+to um um you know sort of some of the
+
+ align:start position:0%
+to um um you know sort of some of the
+ 
+
+ align:start position:0%
+to um um you know sort of some of the
+things you can do uh once you model
+
+ align:start position:0%
+things you can do uh once you model
+ 
+
+ align:start position:0%
+things you can do uh once you model
+solids and I want to do some
+
+ align:start position:0%
+solids and I want to do some
+ 
+
+ align:start position:0%
+solids and I want to do some
+calculations assuming that it works um
+
+ align:start position:0%
+calculations assuming that it works um
+ 
+
+ align:start position:0%
+calculations assuming that it works um
+uh using the nanohub interactively
+
+ align:start position:0%
+uh using the nanohub interactively
+ 
+
+ align:start position:0%
+uh using the nanohub interactively
+together because again there is nothing
+
+ align:start position:0%
+together because again there is nothing
+ 
+
+ align:start position:0%
+together because again there is nothing
+like calculating um the behavior of
+
+ align:start position:0%
+like calculating um the behavior of
+ 
+
+ align:start position:0%
+like calculating um the behavior of
+electrons with friends there's no better
+
+ align:start position:0%
+electrons with friends there's no better
+ 
+
+ align:start position:0%
+electrons with friends there's no better
+way to you know create good group
+
+ align:start position:0%
+way to you know create good group
+ 
+
+ align:start position:0%
+way to you know create good group
+dynamics and
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+interactions there's some I mean
+
+ align:start position:0%
+interactions there's some I mean
+ 
+
+ align:start position:0%
+interactions there's some I mean
+Computing uh has kind of the the the
+
+ align:start position:0%
+Computing uh has kind of the the the
+ 
+
+ align:start position:0%
+Computing uh has kind of the the the
+nuts and bolts uh a lot of which we're
+
+ align:start position:0%
+nuts and bolts uh a lot of which we're
+ 
+
+ align:start position:0%
+nuts and bolts uh a lot of which we're
+talking about some of which were not um
+
+ align:start position:0%
+talking about some of which were not um
+ 
+
+ align:start position:0%
+talking about some of which were not um
+and and then it has sort of the
+
+ align:start position:0%
+and and then it has sort of the
+ 
+
+ align:start position:0%
+and and then it has sort of the
+philosophy right and you know I I really
+
+ align:start position:0%
+philosophy right and you know I I really
+ 
+
+ align:start position:0%
+philosophy right and you know I I really
+tend to agree with some of the things
+
+ align:start position:0%
+tend to agree with some of the things
+ 
+
+ align:start position:0%
+tend to agree with some of the things
+that um people have said
+
+ align:start position:0%
+that um people have said
+ 
+
+ align:start position:0%
+that um people have said
+over the years on on how to use
+
+ align:start position:0%
+over the years on on how to use
+ 
+
+ align:start position:0%
+over the years on on how to use
+Computing um and so I just want to bring
+
+ align:start position:0%
+Computing um and so I just want to bring
+ 
+
+ align:start position:0%
+Computing um and so I just want to bring
+this in and I'll come back to this sort
+
+ align:start position:0%
+this in and I'll come back to this sort
+ 
+
+ align:start position:0%
+this in and I'll come back to this sort
+of at the end of of the term a little
+
+ align:start position:0%
+of at the end of of the term a little
+ 
+
+ align:start position:0%
+of at the end of of the term a little
+bit more but you know Richard Hamming
+
+ align:start position:0%
+bit more but you know Richard Hamming
+ 
+
+ align:start position:0%
+bit more but you know Richard Hamming
+had a number of very interesting things
+
+ align:start position:0%
+had a number of very interesting things
+ 
+
+ align:start position:0%
+had a number of very interesting things
+to say about research and and about
+
+ align:start position:0%
+to say about research and and about
+ 
+
+ align:start position:0%
+to say about research and and about
+Computing the P purpose of computing is
+
+ align:start position:0%
+Computing the P purpose of computing is
+ 
+
+ align:start position:0%
+Computing the P purpose of computing is
+Insight not numbers right so you know
+
+ align:start position:0%
+Insight not numbers right so you know
+ 
+
+ align:start position:0%
+Insight not numbers right so you know
+the computation is only as good as your
+
+ align:start position:0%
+the computation is only as good as your
+ 
+
+ align:start position:0%
+the computation is only as good as your
+creativity and your thinking on both
+
+ align:start position:0%
+creativity and your thinking on both
+ 
+
+ align:start position:0%
+creativity and your thinking on both
+sides what you put into the computer and
+
+ align:start position:0%
+sides what you put into the computer and
+ 
+
+ align:start position:0%
+sides what you put into the computer and
+what you get out um he also said um what
+
+ align:start position:0%
+what you get out um he also said um what
+ 
+
+ align:start position:0%
+what you get out um he also said um what
+are the most important problems in your
+
+ align:start position:0%
+are the most important problems in your
+ 
+
+ align:start position:0%
+are the most important problems in your
+field are you working on one of them why
+
+ align:start position:0%
+field are you working on one of them why
+ 
+
+ align:start position:0%
+field are you working on one of them why
+not I love that and that's that's very
+
+ align:start position:0%
+not I love that and that's that's very
+ 
+
+ align:start position:0%
+not I love that and that's that's very
+much you know that's kind of an MIT
+
+ align:start position:0%
+much you know that's kind of an MIT
+ 
+
+ align:start position:0%
+much you know that's kind of an MIT
+ecosystem way right but it's not true
+
+ align:start position:0%
+ecosystem way right but it's not true
+ 
+
+ align:start position:0%
+ecosystem way right but it's not true
+everywhere but we should always remind
+
+ align:start position:0%
+everywhere but we should always remind
+ 
+
+ align:start position:0%
+everywhere but we should always remind
+ourselves even if I solve this problem
+
+ align:start position:0%
+ourselves even if I solve this problem
+ 
+
+ align:start position:0%
+ourselves even if I solve this problem
+so i' say my problem is I want to change
+
+ align:start position:0%
+so i' say my problem is I want to change
+ 
+
+ align:start position:0%
+so i' say my problem is I want to change
+the bandap of silicon from indirect to
+
+ align:start position:0%
+the bandap of silicon from indirect to
+ 
+
+ align:start position:0%
+the bandap of silicon from indirect to
+direct okay I can do that now because
+
+ align:start position:0%
+direct okay I can do that now because
+ 
+
+ align:start position:0%
+direct okay I can do that now because
+we've learned how to do that using
+
+ align:start position:0%
+we've learned how to do that using
+ 
+
+ align:start position:0%
+we've learned how to do that using
+simulation so I can probe materials
+
+ align:start position:0%
+simulation so I can probe materials
+ 
+
+ align:start position:0%
+simulation so I can probe materials
+using a computer you should still say
+
+ align:start position:0%
+using a computer you should still say
+ 
+
+ align:start position:0%
+using a computer you should still say
+why right and that's not the the point
+
+ align:start position:0%
+why right and that's not the the point
+ 
+
+ align:start position:0%
+why right and that's not the the point
+isn't you can't just say why well
+
+ align:start position:0%
+isn't you can't just say why well
+ 
+
+ align:start position:0%
+isn't you can't just say why well
+because it would be useful or why well
+
+ align:start position:0%
+because it would be useful or why well
+ 
+
+ align:start position:0%
+because it would be useful or why well
+because I can make a better solar cell
+
+ align:start position:0%
+because I can make a better solar cell
+ 
+
+ align:start position:0%
+because I can make a better solar cell
+that's not enough right it's really how
+
+ align:start position:0%
+that's not enough right it's really how
+ 
+
+ align:start position:0%
+that's not enough right it's really how
+much impact can you have right what is
+
+ align:start position:0%
+much impact can you have right what is
+ 
+
+ align:start position:0%
+much impact can you have right what is
+this going to do to the technology
+
+ align:start position:0%
+this going to do to the technology
+ 
+
+ align:start position:0%
+this going to do to the technology
+you're working on or the science problem
+
+ align:start position:0%
+you're working on or the science problem
+ 
+
+ align:start position:0%
+you're working on or the science problem
+you're trying to uh answer and taking it
+
+ align:start position:0%
+you're trying to uh answer and taking it
+ 
+
+ align:start position:0%
+you're trying to uh answer and taking it
+those extra steps goes a long way and
+
+ align:start position:0%
+those extra steps goes a long way and
+ 
+
+ align:start position:0%
+those extra steps goes a long way and
+that applies to Computing just like any
+
+ align:start position:0%
+that applies to Computing just like any
+ 
+
+ align:start position:0%
+that applies to Computing just like any
+other area of of research better to
+
+ align:start position:0%
+other area of of research better to
+ 
+
+ align:start position:0%
+other area of of research better to
+solve the right problem the wrong way
+
+ align:start position:0%
+solve the right problem the wrong way
+ 
+
+ align:start position:0%
+solve the right problem the wrong way
+than the wrong problem the right way
+
+ align:start position:0%
+than the wrong problem the right way
+ 
+
+ align:start position:0%
+than the wrong problem the right way
+right so CH choosing the problem that's
+
+ align:start position:0%
+right so CH choosing the problem that's
+ 
+
+ align:start position:0%
+right so CH choosing the problem that's
+a related statement in research if you
+
+ align:start position:0%
+a related statement in research if you
+ 
+
+ align:start position:0%
+a related statement in research if you
+know what you're doing then you
+
+ align:start position:0%
+know what you're doing then you
+ 
+
+ align:start position:0%
+know what you're doing then you
+shouldn't be doing it I like that a lot
+
+ align:start position:0%
+shouldn't be doing it I like that a lot
+ 
+
+ align:start position:0%
+shouldn't be doing it I like that a lot
+right so we you know and and that's
+
+ align:start position:0%
+right so we you know and and that's
+ 
+
+ align:start position:0%
+right so we you know and and that's
+where um computation is is a real
+
+ align:start position:0%
+where um computation is is a real
+ 
+
+ align:start position:0%
+where um computation is is a real
+enabler right I I love I'm mean
+
+ align:start position:0%
+enabler right I I love I'm mean
+ 
+
+ align:start position:0%
+enabler right I I love I'm mean
+experiments too but I love the the the
+
+ align:start position:0%
+experiments too but I love the the the
+ 
+
+ align:start position:0%
+experiments too but I love the the the
+world of computation um especially at
+
+ align:start position:0%
+world of computation um especially at
+ 
+
+ align:start position:0%
+world of computation um especially at
+this scale where you can you can Design
+
+ align:start position:0%
+this scale where you can you can Design
+ 
+
+ align:start position:0%
+this scale where you can you can Design
+Within you know a limited number of
+
+ align:start position:0%
+Within you know a limited number of
+ 
+
+ align:start position:0%
+Within you know a limited number of
+atoms you can design anything you can
+
+ align:start position:0%
+atoms you can design anything you can
+ 
+
+ align:start position:0%
+atoms you can design anything you can
+think up anything and try it right so
+
+ align:start position:0%
+think up anything and try it right so
+ 
+
+ align:start position:0%
+think up anything and try it right so
+there's really um you know the face
+
+ align:start position:0%
+there's really um you know the face
+ 
+
+ align:start position:0%
+there's really um you know the face
+space is just enormous and you can
+
+ align:start position:0%
+space is just enormous and you can
+ 
+
+ align:start position:0%
+space is just enormous and you can
+really play around um and try crazy
+
+ align:start position:0%
+really play around um and try crazy
+ 
+
+ align:start position:0%
+really play around um and try crazy
+ideas um random thoughts and tangents
+
+ align:start position:0%
+ideas um random thoughts and tangents
+ 
+
+ align:start position:0%
+ideas um random thoughts and tangents
+out as you go those are often where the
+
+ align:start position:0%
+out as you go those are often where the
+ 
+
+ align:start position:0%
+out as you go those are often where the
+best uh creativity happens and then this
+
+ align:start position:0%
+best uh creativity happens and then this
+ 
+
+ align:start position:0%
+best uh creativity happens and then this
+is it right machines should work people
+
+ align:start position:0%
+is it right machines should work people
+ 
+
+ align:start position:0%
+is it right machines should work people
+should think
+
+ align:start position:0%
+should think
+ 
+
+ align:start position:0%
+should think
+so you know as you go after this class
+
+ align:start position:0%
+so you know as you go after this class
+ 
+
+ align:start position:0%
+so you know as you go after this class
+you come out you know one of the most
+
+ align:start position:0%
+you come out you know one of the most
+ 
+
+ align:start position:0%
+you come out you know one of the most
+important things to come out of this is
+
+ align:start position:0%
+important things to come out of this is
+ 
+
+ align:start position:0%
+important things to come out of this is
+it's it's always a balance when you do
+
+ align:start position:0%
+it's it's always a balance when you do
+ 
+
+ align:start position:0%
+it's it's always a balance when you do
+computation it's a balance between your
+
+ align:start position:0%
+computation it's a balance between your
+ 
+
+ align:start position:0%
+computation it's a balance between your
+time and the computer's time and what
+
+ align:start position:0%
+time and the computer's time and what
+ 
+
+ align:start position:0%
+time and the computer's time and what
+you'd like to do is create a balance
+
+ align:start position:0%
+you'd like to do is create a balance
+ 
+
+ align:start position:0%
+you'd like to do is create a balance
+such that the computer is solving things
+
+ align:start position:0%
+such that the computer is solving things
+ 
+
+ align:start position:0%
+such that the computer is solving things
+for you um and you're spending most of
+
+ align:start position:0%
+for you um and you're spending most of
+ 
+
+ align:start position:0%
+for you um and you're spending most of
+your time not solving those things not
+
+ align:start position:0%
+your time not solving those things not
+ 
+
+ align:start position:0%
+your time not solving those things not
+wasting your time on things that the
+
+ align:start position:0%
+wasting your time on things that the
+ 
+
+ align:start position:0%
+wasting your time on things that the
+computer could do um but rather on
+
+ align:start position:0%
+computer could do um but rather on
+ 
+
+ align:start position:0%
+computer could do um but rather on
+thinking about the kind of problem that
+
+ align:start position:0%
+thinking about the kind of problem that
+ 
+
+ align:start position:0%
+thinking about the kind of problem that
+you're going to make it do and and you'd
+
+ align:start position:0%
+you're going to make it do and and you'd
+ 
+
+ align:start position:0%
+you're going to make it do and and you'd
+be surprised how often in computation
+
+ align:start position:0%
+be surprised how often in computation
+ 
+
+ align:start position:0%
+be surprised how often in computation
+this balance is not well-kept okay
+
+ align:start position:0%
+this balance is not well-kept okay
+ 
+
+ align:start position:0%
+this balance is not well-kept okay
+and and how often you might spend a lot
+
+ align:start position:0%
+and and how often you might spend a lot
+ 
+
+ align:start position:0%
+and and how often you might spend a lot
+of your time actually um spinning your
+
+ align:start position:0%
+of your time actually um spinning your
+ 
+
+ align:start position:0%
+of your time actually um spinning your
+wheels on something that the machine
+
+ align:start position:0%
+wheels on something that the machine
+ 
+
+ align:start position:0%
+wheels on something that the machine
+could actually handle right um and how
+
+ align:start position:0%
+could actually handle right um and how
+ 
+
+ align:start position:0%
+could actually handle right um and how
+much you might think the machine is
+
+ align:start position:0%
+much you might think the machine is
+ 
+
+ align:start position:0%
+much you might think the machine is
+actually going to somehow solve a
+
+ align:start position:0%
+actually going to somehow solve a
+ 
+
+ align:start position:0%
+actually going to somehow solve a
+problem um that actually you need to
+
+ align:start position:0%
+problem um that actually you need to
+ 
+
+ align:start position:0%
+problem um that actually you need to
+think about to solve or how much more
+
+ align:start position:0%
+think about to solve or how much more
+ 
+
+ align:start position:0%
+think about to solve or how much more
+quickly you could solve it if you just
+
+ align:start position:0%
+quickly you could solve it if you just
+ 
+
+ align:start position:0%
+quickly you could solve it if you just
+thought for an hour you might have saved
+
+ align:start position:0%
+thought for an hour you might have saved
+ 
+
+ align:start position:0%
+thought for an hour you might have saved
+a million hours of computer time right
+
+ align:start position:0%
+a million hours of computer time right
+ 
+
+ align:start position:0%
+a million hours of computer time right
+seriously so those that balance always
+
+ align:start position:0%
+seriously so those that balance always
+ 
+
+ align:start position:0%
+seriously so those that balance always
+has has to be kept in mind and then the
+
+ align:start position:0%
+has has to be kept in mind and then the
+ 
+
+ align:start position:0%
+has has to be kept in mind and then the
+one i' like to add is Spider-Man's Uncle
+
+ align:start position:0%
+one i' like to add is Spider-Man's Uncle
+ 
+
+ align:start position:0%
+one i' like to add is Spider-Man's Uncle
+with great power comes great
+
+ align:start position:0%
+with great power comes great
+ 
+
+ align:start position:0%
+with great power comes great
+responsibility because you have now
+
+ align:start position:0%
+responsibility because you have now
+ 
+
+ align:start position:0%
+responsibility because you have now
+power you're gaining power that's what
+
+ align:start position:0%
+power you're gaining power that's what
+ 
+
+ align:start position:0%
+power you're gaining power that's what
+this class is doing to you you're
+
+ align:start position:0%
+this class is doing to you you're
+ 
+
+ align:start position:0%
+this class is doing to you you're
+gaining the power to calculate things
+
+ align:start position:0%
+gaining the power to calculate things
+ 
+
+ align:start position:0%
+gaining the power to calculate things
+like band structures right and the
+
+ align:start position:0%
+like band structures right and the
+ 
+
+ align:start position:0%
+like band structures right and the
+responsibility is that you I want you to
+
+ align:start position:0%
+responsibility is that you I want you to
+ 
+
+ align:start position:0%
+responsibility is that you I want you to
+know what you're doing in the sense that
+
+ align:start position:0%
+know what you're doing in the sense that
+ 
+
+ align:start position:0%
+know what you're doing in the sense that
+you know you don't just say I'm going to
+
+ align:start position:0%
+you know you don't just say I'm going to
+ 
+
+ align:start position:0%
+you know you don't just say I'm going to
+do a band structure oh here it is that
+
+ align:start position:0%
+do a band structure oh here it is that
+ 
+
+ align:start position:0%
+do a band structure oh here it is that
+you check and you you you're you're
+
+ align:start position:0%
+you check and you you you're you're
+ 
+
+ align:start position:0%
+you check and you you you're you're
+careful about it right and you
+
+ align:start position:0%
+careful about it right and you
+ 
+
+ align:start position:0%
+careful about it right and you
+understand how to validate the
+
+ align:start position:0%
+understand how to validate the
+ 
+
+ align:start position:0%
+understand how to validate the
+calculations that you're doing against
+
+ align:start position:0%
+calculations that you're doing against
+ 
+
+ align:start position:0%
+calculations that you're doing against
+uh experiment right you understand how
+
+ align:start position:0%
+uh experiment right you understand how
+ 
+
+ align:start position:0%
+uh experiment right you understand how
+to converge the
+
+ align:start position:0%
+to converge the
+ 
+
+ align:start position:0%
+to converge the
+calculations right you understand how to
+
+ align:start position:0%
+calculations right you understand how to
+ 
+
+ align:start position:0%
+calculations right you understand how to
+make sure you understand what they mean
+
+ align:start position:0%
+make sure you understand what they mean
+ 
+
+ align:start position:0%
+make sure you understand what they mean
+that's the responsibility okay so um a
+
+ align:start position:0%
+that's the responsibility okay so um a
+ 
+
+ align:start position:0%
+that's the responsibility okay so um a
+little bit of philosophy there anyway
+
+ align:start position:0%
+little bit of philosophy there anyway
+ 
+
+ align:start position:0%
+little bit of philosophy there anyway
+okay we're going to review a little bit
+
+ align:start position:0%
+okay we're going to review a little bit
+ 
+
+ align:start position:0%
+okay we're going to review a little bit
+and we'll talk about some properties
+
+ align:start position:0%
+and we'll talk about some properties
+ 
+
+ align:start position:0%
+and we'll talk about some properties
+we'll come back to this band structure
+
+ align:start position:0%
+we'll come back to this band structure
+ 
+
+ align:start position:0%
+we'll come back to this band structure
+which is is so critical to um this part
+
+ align:start position:0%
+which is is so critical to um this part
+ 
+
+ align:start position:0%
+which is is so critical to um this part
+of of the class um and if I have time
+
+ align:start position:0%
+of of the class um and if I have time
+ 
+
+ align:start position:0%
+of of the class um and if I have time
+I'll talk about magnetization but
+
+ align:start position:0%
+I'll talk about magnetization but
+ 
+
+ align:start position:0%
+I'll talk about magnetization but
+probably I'll I'll talk about
+
+ align:start position:0%
+probably I'll I'll talk about
+ 
+
+ align:start position:0%
+probably I'll I'll talk about
+magnetization on on Thursday a little
+
+ align:start position:0%
+magnetization on on Thursday a little
+ 
+
+ align:start position:0%
+magnetization on on Thursday a little
+all
+
+ align:start position:0%
+all
+ 
+
+ align:start position:0%
+all
+right any questions so we've had a a
+
+ align:start position:0%
+right any questions so we've had a a
+ 
+
+ align:start position:0%
+right any questions so we've had a a
+wrap video some
+
+ align:start position:0%
+wrap video some
+ 
+
+ align:start position:0%
+wrap video some
+philosophy a little bit of an outline
+
+ align:start position:0%
+philosophy a little bit of an outline
+ 
+
+ align:start position:0%
+philosophy a little bit of an outline
+where else could we go right things are
+
+ align:start position:0%
+where else could we go right things are
+ 
+
+ align:start position:0%
+where else could we go right things are
+good Rondo did what's up with that was
+
+ align:start position:0%
+good Rondo did what's up with that was
+ 
+
+ align:start position:0%
+good Rondo did what's up with that was
+that a good decision no how many people
+
+ align:start position:0%
+that a good decision no how many people
+ 
+
+ align:start position:0%
+that a good decision no how many people
+saw that I just want to know okay so a
+
+ align:start position:0%
+saw that I just want to know okay so a
+ 
+
+ align:start position:0%
+saw that I just want to know okay so a
+little more people are wa but you only
+
+ align:start position:0%
+little more people are wa but you only
+ 
+
+ align:start position:0%
+little more people are wa but you only
+saw it on a highlight oh you watched the
+
+ align:start position:0%
+saw it on a highlight oh you watched the
+ 
+
+ align:start position:0%
+saw it on a highlight oh you watched the
+game all right
+
+ align:start position:0%
+game all right
+ 
+
+ align:start position:0%
+game all right
+good yeah but they're going to win
+
+ align:start position:0%
+good yeah but they're going to win
+ 
+
+ align:start position:0%
+good yeah but they're going to win
+without Rondo tonight anyway okay yeah
+
+ align:start position:0%
+without Rondo tonight anyway okay yeah
+ 
+
+ align:start position:0%
+without Rondo tonight anyway okay yeah
+you bump a ref on purpose come on come
+
+ align:start position:0%
+you bump a ref on purpose come on come
+ 
+
+ align:start position:0%
+you bump a ref on purpose come on come
+on man anyway I can't I can't spend more
+
+ align:start position:0%
+on man anyway I can't I can't spend more
+ 
+
+ align:start position:0%
+on man anyway I can't I can't spend more
+time on it I don't want to do that um
+
+ align:start position:0%
+time on it I don't want to do that um
+ 
+
+ align:start position:0%
+time on it I don't want to do that um
+let's take a walk through memory lane
+
+ align:start position:0%
+let's take a walk through memory lane
+ 
+
+ align:start position:0%
+let's take a walk through memory lane
+for just a moment because I want to make
+
+ align:start position:0%
+for just a moment because I want to make
+ 
+
+ align:start position:0%
+for just a moment because I want to make
+sure we all know where we are
+
+ align:start position:0%
+sure we all know where we are
+ 
+
+ align:start position:0%
+sure we all know where we are
+right we started with this there were
+
+ align:start position:0%
+right we started with this there were
+ 
+
+ align:start position:0%
+right we started with this there were
+some strange observations by some very
+
+ align:start position:0%
+some strange observations by some very
+ 
+
+ align:start position:0%
+some strange observations by some very
+smart people tell me what those are you
+
+ align:start position:0%
+smart people tell me what those are you
+ 
+
+ align:start position:0%
+smart people tell me what those are you
+know we could ask questions like about
+
+ align:start position:0%
+know we could ask questions like about
+ 
+
+ align:start position:0%
+know we could ask questions like about
+these on the quiz those are electrons
+
+ align:start position:0%
+these on the quiz those are electrons
+ 
+
+ align:start position:0%
+these on the quiz those are electrons
+yeah that's an electron those are
+
+ align:start position:0%
+yeah that's an electron those are
+ 
+
+ align:start position:0%
+yeah that's an electron those are
+electrons what's this
+
+ align:start position:0%
+electrons what's this
+ 
+
+ align:start position:0%
+electrons what's this
+experiment this one is what's this
+
+ align:start position:0%
+experiment this one is what's this
+ 
+
+ align:start position:0%
+experiment this one is what's this
+one why does it
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+collapse classical then it's got to
+
+ align:start position:0%
+collapse classical then it's got to
+ 
+
+ align:start position:0%
+collapse classical then it's got to
+be what
+
+ align:start position:0%
+be what
+ 
+
+ align:start position:0%
+be what
+energy yeah it's giving off energy and
+
+ align:start position:0%
+energy yeah it's giving off energy and
+ 
+
+ align:start position:0%
+energy yeah it's giving off energy and
+it's not going to hang in to its orbit
+
+ align:start position:0%
+it's not going to hang in to its orbit
+ 
+
+ align:start position:0%
+it's not going to hang in to its orbit
+but then quantum mechanics came along
+
+ align:start position:0%
+but then quantum mechanics came along
+ 
+
+ align:start position:0%
+but then quantum mechanics came along
+and said no that's not true right
+
+ align:start position:0%
+and said no that's not true right
+ 
+
+ align:start position:0%
+and said no that's not true right
+because
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+what it just it just is it's the it just
+
+ align:start position:0%
+what it just it just is it's the it just
+ 
+
+ align:start position:0%
+what it just it just is it's the it just
+is answer no because what it said is
+
+ align:start position:0%
+is answer no because what it said is
+ 
+
+ align:start position:0%
+is answer no because what it said is
+that the levels of a quantum mechanical
+
+ align:start position:0%
+that the levels of a quantum mechanical
+ 
+
+ align:start position:0%
+that the levels of a quantum mechanical
+object are quantized and they have to be
+
+ align:start position:0%
+object are quantized and they have to be
+ 
+
+ align:start position:0%
+object are quantized and they have to be
+in those places and there's no in
+
+ align:start position:0%
+in those places and there's no in
+ 
+
+ align:start position:0%
+in those places and there's no in
+between and that's what this is
+
+ align:start position:0%
+between and that's what this is
+ 
+
+ align:start position:0%
+between and that's what this is
+what's
+
+ align:start position:0%
+what's
+ 
+
+ align:start position:0%
+what's
+this which comes from that same
+
+ align:start position:0%
+this which comes from that same
+ 
+
+ align:start position:0%
+this which comes from that same
+observation you'd think that the the
+
+ align:start position:0%
+observation you'd think that the the
+ 
+
+ align:start position:0%
+observation you'd think that the the
+universe the hydrogen might emit colors
+
+ align:start position:0%
+universe the hydrogen might emit colors
+ 
+
+ align:start position:0%
+universe the hydrogen might emit colors
+in any frequency but instead only
+
+ align:start position:0%
+in any frequency but instead only
+ 
+
+ align:start position:0%
+in any frequency but instead only
+certain frequencies and it comes from
+
+ align:start position:0%
+certain frequencies and it comes from
+ 
+
+ align:start position:0%
+certain frequencies and it comes from
+that quantization of those electron
+
+ align:start position:0%
+that quantization of those electron
+ 
+
+ align:start position:0%
+that quantization of those electron
+levels and this somebody already said
+
+ align:start position:0%
+levels and this somebody already said
+ 
+
+ align:start position:0%
+levels and this somebody already said
+this right photoelectric effect okay now
+
+ align:start position:0%
+this right photoelectric effect okay now
+ 
+
+ align:start position:0%
+this right photoelectric effect okay now
+those are very smart people so and the
+
+ align:start position:0%
+those are very smart people so and the
+ 
+
+ align:start position:0%
+those are very smart people so and the
+weirdness kept going now is that guy
+
+ align:start position:0%
+weirdness kept going now is that guy
+ 
+
+ align:start position:0%
+weirdness kept going now is that guy
+ordering two drinks at the bar why does
+
+ align:start position:0%
+ordering two drinks at the bar why does
+ 
+
+ align:start position:0%
+ordering two drinks at the bar why does
+he have two
+
+ align:start position:0%
+he have two
+ 
+
+ align:start position:0%
+he have two
+double sled experiment that was a cool
+
+ align:start position:0%
+double sled experiment that was a cool
+ 
+
+ align:start position:0%
+double sled experiment that was a cool
+one um and the weirdness just kept going
+
+ align:start position:0%
+one um and the weirdness just kept going
+ 
+
+ align:start position:0%
+one um and the weirdness just kept going
+right now it became very clear that
+
+ align:start position:0%
+right now it became very clear that
+ 
+
+ align:start position:0%
+right now it became very clear that
+matter behaved like
+
+ align:start position:0%
+matter behaved like
+ 
+
+ align:start position:0%
+matter behaved like
+waves you know if we took this little 10
+
+ align:start position:0%
+waves you know if we took this little 10
+ 
+
+ align:start position:0%
+waves you know if we took this little 10
+slide um kind of where we are quick you
+
+ align:start position:0%
+slide um kind of where we are quick you
+ 
+
+ align:start position:0%
+slide um kind of where we are quick you
+know what road have we come on and we
+
+ align:start position:0%
+know what road have we come on and we
+ 
+
+ align:start position:0%
+know what road have we come on and we
+turned it into a music video
+
+ align:start position:0%
+turned it into a music video
+ 
+
+ align:start position:0%
+turned it into a music video
+right anybody want to do that that's uh
+
+ align:start position:0%
+right anybody want to do that that's uh
+ 
+
+ align:start position:0%
+right anybody want to do that that's uh
+that's exciting okay
+
+ align:start position:0%
+that's exciting okay
+ 
+
+ align:start position:0%
+that's exciting okay
+um became clear that matter behaved like
+
+ align:start position:0%
+um became clear that matter behaved like
+ 
+
+ align:start position:0%
+um became clear that matter behaved like
+waves and vice versa okay um and that we
+
+ align:start position:0%
+waves and vice versa okay um and that we
+ 
+
+ align:start position:0%
+waves and vice versa okay um and that we
+had to lose our sort of classical
+
+ align:start position:0%
+had to lose our sort of classical
+ 
+
+ align:start position:0%
+had to lose our sort of classical
+concepts of absolute position and
+
+ align:start position:0%
+concepts of absolute position and
+ 
+
+ align:start position:0%
+concepts of absolute position and
+momentum and instead consider a particle
+
+ align:start position:0%
+momentum and instead consider a particle
+ 
+
+ align:start position:0%
+momentum and instead consider a particle
+as a wave whose square is the
+
+ align:start position:0%
+as a wave whose square is the
+ 
+
+ align:start position:0%
+as a wave whose square is the
+probability of finding it and there it
+
+ align:start position:0%
+probability of finding it and there it
+ 
+
+ align:start position:0%
+probability of finding it and there it
+is and this became our goal our task of
+
+ align:start position:0%
+is and this became our goal our task of
+ 
+
+ align:start position:0%
+is and this became our goal our task of
+finding that right that's what we needed
+
+ align:start position:0%
+finding that right that's what we needed
+ 
+
+ align:start position:0%
+finding that right that's what we needed
+to do on a computer um oh and there's a
+
+ align:start position:0%
+to do on a computer um oh and there's a
+ 
+
+ align:start position:0%
+to do on a computer um oh and there's a
+picture of a wave right how do we do do
+
+ align:start position:0%
+picture of a wave right how do we do do
+ 
+
+ align:start position:0%
+picture of a wave right how do we do do
+this how do we describe this well um we
+
+ align:start position:0%
+this how do we describe this well um we
+ 
+
+ align:start position:0%
+this how do we describe this well um we
+needed our f equals ma right right so
+
+ align:start position:0%
+needed our f equals ma right right so
+ 
+
+ align:start position:0%
+needed our f equals ma right right so
+when when when matter is just a particle
+
+ align:start position:0%
+when when when matter is just a particle
+ 
+
+ align:start position:0%
+when when when matter is just a particle
+we have fals ma but now that it's a wave
+
+ align:start position:0%
+we have fals ma but now that it's a wave
+ 
+
+ align:start position:0%
+we have fals ma but now that it's a wave
+um we needed something different and and
+
+ align:start position:0%
+um we needed something different and and
+ 
+
+ align:start position:0%
+um we needed something different and and
+from the elements and the bits of pieces
+
+ align:start position:0%
+from the elements and the bits of pieces
+ 
+
+ align:start position:0%
+from the elements and the bits of pieces
+of quantum mechanics which people were
+
+ align:start position:0%
+of quantum mechanics which people were
+ 
+
+ align:start position:0%
+of quantum mechanics which people were
+putting together right um outomes the
+
+ align:start position:0%
+putting together right um outomes the
+ 
+
+ align:start position:0%
+putting together right um outomes the
+shinger equation right and that's our
+
+ align:start position:0%
+shinger equation right and that's our
+ 
+
+ align:start position:0%
+shinger equation right and that's our
+fals ma which tells us how to um how to
+
+ align:start position:0%
+fals ma which tells us how to um how to
+ 
+
+ align:start position:0%
+fals ma which tells us how to um how to
+describ the behavior of waves if they're
+
+ align:start position:0%
+describ the behavior of waves if they're
+ 
+
+ align:start position:0%
+describ the behavior of waves if they're
+quantum mechanical and it was
+
+ align:start position:0%
+quantum mechanical and it was
+ 
+
+ align:start position:0%
+quantum mechanical and it was
+wonderful it explained many things it
+
+ align:start position:0%
+wonderful it explained many things it
+ 
+
+ align:start position:0%
+wonderful it explained many things it
+gave us Atomic orbitals it predicted the
+
+ align:start position:0%
+gave us Atomic orbitals it predicted the
+ 
+
+ align:start position:0%
+gave us Atomic orbitals it predicted the
+energy levels of hydrogen remember how
+
+ align:start position:0%
+energy levels of hydrogen remember how
+ 
+
+ align:start position:0%
+energy levels of hydrogen remember how
+how wonderful that was um it gave us
+
+ align:start position:0%
+how wonderful that was um it gave us
+ 
+
+ align:start position:0%
+how wonderful that was um it gave us
+basically the means to understand a
+
+ align:start position:0%
+basically the means to understand a
+ 
+
+ align:start position:0%
+basically the means to understand a
+whole lot of this right
+
+ align:start position:0%
+whole lot of this right
+ 
+
+ align:start position:0%
+whole lot of this right
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+but right but um it nature does more
+
+ align:start position:0%
+but right but um it nature does more
+ 
+
+ align:start position:0%
+but right but um it nature does more
+than one
+
+ align:start position:0%
+than one
+ 
+
+ align:start position:0%
+than one
+electron and it was impossible to solve
+
+ align:start position:0%
+electron and it was impossible to solve
+ 
+
+ align:start position:0%
+electron and it was impossible to solve
+for more than a single electron so
+
+ align:start position:0%
+for more than a single electron so
+ 
+
+ align:start position:0%
+for more than a single electron so
+here's where computational quantum
+
+ align:start position:0%
+here's where computational quantum
+ 
+
+ align:start position:0%
+here's where computational quantum
+mechanics comes in
+
+ align:start position:0%
+mechanics comes in
+ 
+
+ align:start position:0%
+mechanics comes in
+okay um but there was still a problem
+
+ align:start position:0%
+okay um but there was still a problem
+ 
+
+ align:start position:0%
+okay um but there was still a problem
+and the problem is that we don't have
+
+ align:start position:0%
+and the problem is that we don't have
+ 
+
+ align:start position:0%
+and the problem is that we don't have
+the age of the universe to do our
+
+ align:start position:0%
+the age of the universe to do our
+ 
+
+ align:start position:0%
+the age of the universe to do our
+calculations and so that that's how long
+
+ align:start position:0%
+calculations and so that that's how long
+ 
+
+ align:start position:0%
+calculations and so that that's how long
+it would take to currently solve the
+
+ align:start position:0%
+it would take to currently solve the
+ 
+
+ align:start position:0%
+it would take to currently solve the
+shary equation exactly on a computer for
+
+ align:start position:0%
+shary equation exactly on a computer for
+ 
+
+ align:start position:0%
+shary equation exactly on a computer for
+like only a handful of of particles
+
+ align:start position:0%
+like only a handful of of particles
+ 
+
+ align:start position:0%
+like only a handful of of particles
+right so you know obviously you could
+
+ align:start position:0%
+right so you know obviously you could
+ 
+
+ align:start position:0%
+right so you know obviously you could
+solve it for one or two particles
+
+ align:start position:0%
+solve it for one or two particles
+ 
+
+ align:start position:0%
+solve it for one or two particles
+exactly you know a lot less time than
+
+ align:start position:0%
+exactly you know a lot less time than
+ 
+
+ align:start position:0%
+exactly you know a lot less time than
+that but once you get up to 10 you're
+
+ align:start position:0%
+that but once you get up to 10 you're
+ 
+
+ align:start position:0%
+that but once you get up to 10 you're
+done um and so we we started to try to
+
+ align:start position:0%
+done um and so we we started to try to
+ 
+
+ align:start position:0%
+done um and so we we started to try to
+take some inspiration and we looked at
+
+ align:start position:0%
+take some inspiration and we looked at
+ 
+
+ align:start position:0%
+take some inspiration and we looked at
+this guy's
+
+ align:start position:0%
+this guy's
+ 
+
+ align:start position:0%
+this guy's
+back and we said okay well maybe that's
+
+ align:start position:0%
+back and we said okay well maybe that's
+ 
+
+ align:start position:0%
+back and we said okay well maybe that's
+telling us something it's telling us a
+
+ align:start position:0%
+telling us something it's telling us a
+ 
+
+ align:start position:0%
+telling us something it's telling us a
+lot uh but it's telling us some
+
+ align:start position:0%
+lot uh but it's telling us some
+ 
+
+ align:start position:0%
+lot uh but it's telling us some
+interesting physics it's telling us that
+
+ align:start position:0%
+interesting physics it's telling us that
+ 
+
+ align:start position:0%
+interesting physics it's telling us that
+the ions are a whole lot heavier and
+
+ align:start position:0%
+the ions are a whole lot heavier and
+ 
+
+ align:start position:0%
+the ions are a whole lot heavier and
+slower than the electrons so we can
+
+ align:start position:0%
+slower than the electrons so we can
+ 
+
+ align:start position:0%
+slower than the electrons so we can
+freeze them out right so we started to
+
+ align:start position:0%
+freeze them out right so we started to
+ 
+
+ align:start position:0%
+freeze them out right so we started to
+peel away at the sh your equation and we
+
+ align:start position:0%
+peel away at the sh your equation and we
+ 
+
+ align:start position:0%
+peel away at the sh your equation and we
+made it simpler okay we made some
+
+ align:start position:0%
+made it simpler okay we made some
+ 
+
+ align:start position:0%
+made it simpler okay we made some
+approximations
+
+ align:start position:0%
+approximations
+ 
+
+ align:start position:0%
+approximations
+um and there were basically the two
+
+ align:start position:0%
+um and there were basically the two
+ 
+
+ align:start position:0%
+um and there were basically the two
+paths that I talked about in those
+
+ align:start position:0%
+paths that I talked about in those
+ 
+
+ align:start position:0%
+paths that I talked about in those
+approximations um at the time it's about
+
+ align:start position:0%
+approximations um at the time it's about
+ 
+
+ align:start position:0%
+approximations um at the time it's about
+50 years ago uh maybe 60 um you know
+
+ align:start position:0%
+50 years ago uh maybe 60 um you know
+ 
+
+ align:start position:0%
+50 years ago uh maybe 60 um you know
+these two paths were fairly distinct and
+
+ align:start position:0%
+these two paths were fairly distinct and
+ 
+
+ align:start position:0%
+these two paths were fairly distinct and
+the chemists mostly worked on saying
+
+ align:start position:0%
+the chemists mostly worked on saying
+ 
+
+ align:start position:0%
+the chemists mostly worked on saying
+well here's the equation we have to
+
+ align:start position:0%
+well here's the equation we have to
+ 
+
+ align:start position:0%
+well here's the equation we have to
+solve we can't solve it let's make Sai
+
+ align:start position:0%
+solve we can't solve it let's make Sai
+ 
+
+ align:start position:0%
+solve we can't solve it let's make Sai
+something simpler let's simplify Sai and
+
+ align:start position:0%
+something simpler let's simplify Sai and
+ 
+
+ align:start position:0%
+something simpler let's simplify Sai and
+the physicist sort of most
+
+ align:start position:0%
+the physicist sort of most
+ 
+
+ align:start position:0%
+the physicist sort of most
+said well let's not think about s let's
+
+ align:start position:0%
+said well let's not think about s let's
+ 
+
+ align:start position:0%
+said well let's not think about s let's
+just change the hamiltonian that's H
+
+ align:start position:0%
+just change the hamiltonian that's H
+ 
+
+ align:start position:0%
+just change the hamiltonian that's H
+there right um and those are sort of two
+
+ align:start position:0%
+there right um and those are sort of two
+ 
+
+ align:start position:0%
+there right um and those are sort of two
+um two approaches that led to many
+
+ align:start position:0%
+um two approaches that led to many
+ 
+
+ align:start position:0%
+um two approaches that led to many
+different models many different theories
+
+ align:start position:0%
+different models many different theories
+ 
+
+ align:start position:0%
+different models many different theories
+okay many different theories um in in
+
+ align:start position:0%
+okay many different theories um in in
+ 
+
+ align:start position:0%
+okay many different theories um in in
+the theories in both sides the effect of
+
+ align:start position:0%
+the theories in both sides the effect of
+ 
+
+ align:start position:0%
+the theories in both sides the effect of
+these simplifications led to the um the
+
+ align:start position:0%
+these simplifications led to the um the
+ 
+
+ align:start position:0%
+these simplifications led to the um the
+picture that we call a mean fill picture
+
+ align:start position:0%
+picture that we call a mean fill picture
+ 
+
+ align:start position:0%
+picture that we call a mean fill picture
+which is that instead of having to worry
+
+ align:start position:0%
+which is that instead of having to worry
+ 
+
+ align:start position:0%
+which is that instead of having to worry
+about all these quantum mechanical
+
+ align:start position:0%
+about all these quantum mechanical
+ 
+
+ align:start position:0%
+about all these quantum mechanical
+electrons interacting with each other we
+
+ align:start position:0%
+electrons interacting with each other we
+ 
+
+ align:start position:0%
+electrons interacting with each other we
+just worry about them as if it's each
+
+ align:start position:0%
+just worry about them as if it's each
+ 
+
+ align:start position:0%
+just worry about them as if it's each
+one is in the field of the others an
+
+ align:start position:0%
+one is in the field of the others an
+ 
+
+ align:start position:0%
+one is in the field of the others an
+average field of the others and that's
+
+ align:start position:0%
+average field of the others and that's
+ 
+
+ align:start position:0%
+average field of the others and that's
+called a mean fill method okay those are
+
+ align:start position:0%
+called a mean fill method okay those are
+ 
+
+ align:start position:0%
+called a mean fill method okay those are
+the methods we're using in this class
+
+ align:start position:0%
+the methods we're using in this class
+ 
+
+ align:start position:0%
+the methods we're using in this class
+that's the method we're
+
+ align:start position:0%
+that's the method we're
+ 
+
+ align:start position:0%
+that's the method we're
+using and then we talked about density
+
+ align:start position:0%
+using and then we talked about density
+ 
+
+ align:start position:0%
+using and then we talked about density
+functional
+
+ align:start position:0%
+functional
+ 
+
+ align:start position:0%
+functional
+Theory and um and there the the
+
+ align:start position:0%
+Theory and um and there the the
+ 
+
+ align:start position:0%
+Theory and um and there the the
+Breakthrough there is that you know
+
+ align:start position:0%
+Breakthrough there is that you know
+ 
+
+ align:start position:0%
+Breakthrough there is that you know
+trying to keep track of a wave function
+
+ align:start position:0%
+trying to keep track of a wave function
+ 
+
+ align:start position:0%
+trying to keep track of a wave function
+let's say on a grid of a you know 2x two
+
+ align:start position:0%
+let's say on a grid of a you know 2x two
+ 
+
+ align:start position:0%
+let's say on a grid of a you know 2x two
+Grid or 3x3 or whatever um if you had uh
+
+ align:start position:0%
+Grid or 3x3 or whatever um if you had uh
+ 
+
+ align:start position:0%
+Grid or 3x3 or whatever um if you had uh
+well this is for actually a 2X 2 X2 grid
+
+ align:start position:0%
+well this is for actually a 2X 2 X2 grid
+ 
+
+ align:start position:0%
+well this is for actually a 2X 2 X2 grid
+and you have n partic n
+
+ align:start position:0%
+and you have n partic n
+ 
+
+ align:start position:0%
+and you have n partic n
+electrons well if you just have one if
+
+ align:start position:0%
+electrons well if you just have one if
+ 
+
+ align:start position:0%
+electrons well if you just have one if
+you have n is one so one
+
+ align:start position:0%
+you have n is one so one
+ 
+
+ align:start position:0%
+you have n is one so one
+electron okay you have um eight points
+
+ align:start position:0%
+electron okay you have um eight points
+ 
+
+ align:start position:0%
+electron okay you have um eight points
+you need to keep track of but if you had
+
+ align:start position:0%
+you need to keep track of but if you had
+ 
+
+ align:start position:0%
+you need to keep track of but if you had
+just 10 electrons then um you see that
+
+ align:start position:0%
+just 10 electrons then um you see that
+ 
+
+ align:start position:0%
+just 10 electrons then um you see that
+you go to 10 to the 9th points okay this
+
+ align:start position:0%
+you go to 10 to the 9th points okay this
+ 
+
+ align:start position:0%
+you go to 10 to the 9th points okay this
+is the problem of grids of using grids
+
+ align:start position:0%
+is the problem of grids of using grids
+ 
+
+ align:start position:0%
+is the problem of grids of using grids
+to represent things and so if you use
+
+ align:start position:0%
+to represent things and so if you use
+ 
+
+ align:start position:0%
+to represent things and so if you use
+the density instead it's just a constant
+
+ align:start position:0%
+the density instead it's just a constant
+ 
+
+ align:start position:0%
+the density instead it's just a constant
+right the tracking the density is is
+
+ align:start position:0%
+right the tracking the density is is
+ 
+
+ align:start position:0%
+right the tracking the density is is
+much um easier and and the the Crux of
+
+ align:start position:0%
+much um easier and and the the Crux of
+ 
+
+ align:start position:0%
+much um easier and and the the Crux of
+density functional Theory which was
+
+ align:start position:0%
+density functional Theory which was
+ 
+
+ align:start position:0%
+density functional Theory which was
+worked out in the 60s is that there is a
+
+ align:start position:0%
+worked out in the 60s is that there is a
+ 
+
+ align:start position:0%
+worked out in the 60s is that there is a
+onetoone correspondence between the
+
+ align:start position:0%
+onetoone correspondence between the
+ 
+
+ align:start position:0%
+onetoone correspondence between the
+exact density of the system and the wave
+
+ align:start position:0%
+exact density of the system and the wave
+ 
+
+ align:start position:0%
+exact density of the system and the wave
+function
+
+ align:start position:0%
+function
+ 
+
+ align:start position:0%
+function
+okay um and we talked about this last
+
+ align:start position:0%
+okay um and we talked about this last
+ 
+
+ align:start position:0%
+okay um and we talked about this last
+time about how we sit here because it's
+
+ align:start position:0%
+time about how we sit here because it's
+ 
+
+ align:start position:0%
+time about how we sit here because it's
+a nice compromise between uh accuracy
+
+ align:start position:0%
+a nice compromise between uh accuracy
+ 
+
+ align:start position:0%
+a nice compromise between uh accuracy
+and applicability but I want to come
+
+ align:start position:0%
+and applicability but I want to come
+ 
+
+ align:start position:0%
+and applicability but I want to come
+back to this because this is not you you
+
+ align:start position:0%
+back to this because this is not you you
+ 
+
+ align:start position:0%
+back to this because this is not you you
+know part of the reason I wanted to
+
+ align:start position:0%
+know part of the reason I wanted to
+ 
+
+ align:start position:0%
+know part of the reason I wanted to
+remind you of this is is is it it's just
+
+ align:start position:0%
+remind you of this is is is it it's just
+ 
+
+ align:start position:0%
+remind you of this is is is it it's just
+always fun to take these walks through
+
+ align:start position:0%
+always fun to take these walks through
+ 
+
+ align:start position:0%
+always fun to take these walks through
+memory lane and it only took us 5
+
+ align:start position:0%
+memory lane and it only took us 5
+ 
+
+ align:start position:0%
+memory lane and it only took us 5
+minutes but another reason is that um I
+
+ align:start position:0%
+minutes but another reason is that um I
+ 
+
+ align:start position:0%
+minutes but another reason is that um I
+want to remind you that we are not
+
+ align:start position:0%
+want to remind you that we are not
+ 
+
+ align:start position:0%
+want to remind you that we are not
+solving for quantum mechanics exactly
+
+ align:start position:0%
+solving for quantum mechanics exactly
+ 
+
+ align:start position:0%
+solving for quantum mechanics exactly
+we're not we cannot okay and so um and
+
+ align:start position:0%
+we're not we cannot okay and so um and
+ 
+
+ align:start position:0%
+we're not we cannot okay and so um and
+so this is not you you this is what I
+
+ align:start position:0%
+so this is not you you this is what I
+ 
+
+ align:start position:0%
+so this is not you you this is what I
+mean by the
+
+ align:start position:0%
+mean by the
+ 
+
+ align:start position:0%
+mean by the
+responsibility part okay there are some
+
+ align:start position:0%
+responsibility part okay there are some
+ 
+
+ align:start position:0%
+responsibility part okay there are some
+things that DFT um can can give you can
+
+ align:start position:0%
+things that DFT um can can give you can
+ 
+
+ align:start position:0%
+things that DFT um can can give you can
+calculate about those electrons that
+
+ align:start position:0%
+calculate about those electrons that
+ 
+
+ align:start position:0%
+calculate about those electrons that
+that are typically very accurate but
+
+ align:start position:0%
+that are typically very accurate but
+ 
+
+ align:start position:0%
+that are typically very accurate but
+there are some things where it's
+
+ align:start position:0%
+there are some things where it's
+ 
+
+ align:start position:0%
+there are some things where it's
+actually quite off okay it's an
+
+ align:start position:0%
+actually quite off okay it's an
+ 
+
+ align:start position:0%
+actually quite off okay it's an
+approximation does anybody remember what
+
+ align:start position:0%
+approximation does anybody remember what
+ 
+
+ align:start position:0%
+approximation does anybody remember what
+where it it tends to do well I I did
+
+ align:start position:0%
+where it it tends to do well I I did
+ 
+
+ align:start position:0%
+where it it tends to do well I I did
+talk about this in the third or fourth
+
+ align:start position:0%
+talk about this in the third or fourth
+ 
+
+ align:start position:0%
+talk about this in the third or fourth
+lecture and where it tends to do badly
+
+ align:start position:0%
+lecture and where it tends to do badly
+ 
+
+ align:start position:0%
+lecture and where it tends to do badly
+you know or one of those
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+two structur okay what about the solids
+
+ align:start position:0%
+two structur okay what about the solids
+ 
+
+ align:start position:0%
+two structur okay what about the solids
+what properties
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah that would be a case where it falls
+
+ align:start position:0%
+yeah that would be a case where it falls
+ 
+
+ align:start position:0%
+yeah that would be a case where it falls
+into the not so well
+
+ align:start position:0%
+into the not so well
+ 
+
+ align:start position:0%
+into the not so well
+category
+
+ align:start position:0%
+category
+ 
+
+ align:start position:0%
+category
+okay so this is pretty important so
+
+ align:start position:0%
+okay so this is pretty important so
+ 
+
+ align:start position:0%
+okay so this is pretty important so
+um lce parameters yes it tends to do
+
+ align:start position:0%
+um lce parameters yes it tends to do
+ 
+
+ align:start position:0%
+um lce parameters yes it tends to do
+very well for Lattis parameters so the
+
+ align:start position:0%
+very well for Lattis parameters so the
+ 
+
+ align:start position:0%
+very well for Lattis parameters so the
+you know how far apart should atoms be
+
+ align:start position:0%
+you know how far apart should atoms be
+ 
+
+ align:start position:0%
+you know how far apart should atoms be
+if they come together in a molecule or
+
+ align:start position:0%
+if they come together in a molecule or
+ 
+
+ align:start position:0%
+if they come together in a molecule or
+solid or liquid DFT can do very well um
+
+ align:start position:0%
+solid or liquid DFT can do very well um
+ 
+
+ align:start position:0%
+solid or liquid DFT can do very well um
+it does very well for vibrational
+
+ align:start position:0%
+it does very well for vibrational
+ 
+
+ align:start position:0%
+it does very well for vibrational
+properties vibrational Spectrum right
+
+ align:start position:0%
+properties vibrational Spectrum right
+ 
+
+ align:start position:0%
+properties vibrational Spectrum right
+the bons in a
+
+ align:start position:0%
+the bons in a
+ 
+
+ align:start position:0%
+the bons in a
+material it tends to do worse for
+
+ align:start position:0%
+material it tends to do worse for
+ 
+
+ align:start position:0%
+material it tends to do worse for
+excited States like you know looking at
+
+ align:start position:0%
+excited States like you know looking at
+ 
+
+ align:start position:0%
+excited States like you know looking at
+say the optical Gap or the electronic
+
+ align:start position:0%
+say the optical Gap or the electronic
+ 
+
+ align:start position:0%
+say the optical Gap or the electronic
+gap of material is um it it tends to to
+
+ align:start position:0%
+gap of material is um it it tends to to
+ 
+
+ align:start position:0%
+gap of material is um it it tends to to
+uh you know the approximations that we
+
+ align:start position:0%
+uh you know the approximations that we
+ 
+
+ align:start position:0%
+uh you know the approximations that we
+had to use to get a method that's
+
+ align:start position:0%
+had to use to get a method that's
+ 
+
+ align:start position:0%
+had to use to get a method that's
+workable all of these have
+
+ align:start position:0%
+workable all of these have
+ 
+
+ align:start position:0%
+workable all of these have
+approximations except this see we're up
+
+ align:start position:0%
+approximations except this see we're up
+ 
+
+ align:start position:0%
+approximations except this see we're up
+to two electrons here um uh those
+
+ align:start position:0%
+to two electrons here um uh those
+ 
+
+ align:start position:0%
+to two electrons here um uh those
+approximations um lead to DFT uh not
+
+ align:start position:0%
+approximations um lead to DFT uh not
+ 
+
+ align:start position:0%
+approximations um lead to DFT uh not
+doing so well for the back for the Gap
+
+ align:start position:0%
+doing so well for the back for the Gap
+ 
+
+ align:start position:0%
+doing so well for the back for the Gap
+however um as you may have noticed in
+
+ align:start position:0%
+however um as you may have noticed in
+ 
+
+ align:start position:0%
+however um as you may have noticed in
+your homeworks that's one of the things
+
+ align:start position:0%
+your homeworks that's one of the things
+ 
+
+ align:start position:0%
+your homeworks that's one of the things
+you have to calculate in your second
+
+ align:start position:0%
+you have to calculate in your second
+ 
+
+ align:start position:0%
+you have to calculate in your second
+homework right so here's the point I
+
+ align:start position:0%
+homework right so here's the point I
+ 
+
+ align:start position:0%
+homework right so here's the point I
+want to make um these methods have
+
+ align:start position:0%
+want to make um these methods have
+ 
+
+ align:start position:0%
+want to make um these methods have
+advantages and disadvantages they all
+
+ align:start position:0%
+advantages and disadvantages they all
+ 
+
+ align:start position:0%
+advantages and disadvantages they all
+are approximate some quantum mechanical
+
+ align:start position:0%
+are approximate some quantum mechanical
+ 
+
+ align:start position:0%
+are approximate some quantum mechanical
+methods can describe some things very
+
+ align:start position:0%
+methods can describe some things very
+ 
+
+ align:start position:0%
+methods can describe some things very
+accurately and some things um not as
+
+ align:start position:0%
+accurately and some things um not as
+ 
+
+ align:start position:0%
+accurately and some things um not as
+accurately and others may have different
+
+ align:start position:0%
+accurately and others may have different
+ 
+
+ align:start position:0%
+accurately and others may have different
+balances and as you go down to more
+
+ align:start position:0%
+balances and as you go down to more
+ 
+
+ align:start position:0%
+balances and as you go down to more
+accurate methods that can describe more
+
+ align:start position:0%
+accurate methods that can describe more
+ 
+
+ align:start position:0%
+accurate methods that can describe more
+things very accurately you tend to be
+
+ align:start position:0%
+things very accurately you tend to be
+ 
+
+ align:start position:0%
+things very accurately you tend to be
+able to do less and less numbers of
+
+ align:start position:0%
+able to do less and less numbers of
+ 
+
+ align:start position:0%
+able to do less and less numbers of
+electrons right limit your phase space
+
+ align:start position:0%
+electrons right limit your phase space
+ 
+
+ align:start position:0%
+electrons right limit your phase space
+to you know 12 20 electrons and you're
+
+ align:start position:0%
+to you know 12 20 electrons and you're
+ 
+
+ align:start position:0%
+to you know 12 20 electrons and you're
+pretty Limited in in how many materials
+
+ align:start position:0%
+pretty Limited in in how many materials
+ 
+
+ align:start position:0%
+pretty Limited in in how many materials
+you can explore right so um uh uh now
+
+ align:start position:0%
+you can explore right so um uh uh now
+ 
+
+ align:start position:0%
+you can explore right so um uh uh now
+why can we still calculate the Gap well
+
+ align:start position:0%
+why can we still calculate the Gap well
+ 
+
+ align:start position:0%
+why can we still calculate the Gap well
+and this is actually there's going to be
+
+ align:start position:0%
+and this is actually there's going to be
+ 
+
+ align:start position:0%
+and this is actually there's going to be
+an addendum to your homework okay which
+
+ align:start position:0%
+an addendum to your homework okay which
+ 
+
+ align:start position:0%
+an addendum to your homework okay which
+um I'm gonna have to um I forgot to put
+
+ align:start position:0%
+um I'm gonna have to um I forgot to put
+ 
+
+ align:start position:0%
+um I'm gonna have to um I forgot to put
+this in there but um you know if this is
+
+ align:start position:0%
+this in there but um you know if this is
+ 
+
+ align:start position:0%
+this in there but um you know if this is
+the density of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+States okay let's say that's the den of
+
+ align:start position:0%
+States okay let's say that's the den of
+ 
+
+ align:start position:0%
+States okay let's say that's the den of
+States um by the way if I asked you
+
+ align:start position:0%
+States um by the way if I asked you
+ 
+
+ align:start position:0%
+States um by the way if I asked you
+what's the gap of this material um what
+
+ align:start position:0%
+what's the gap of this material um what
+ 
+
+ align:start position:0%
+what's the gap of this material um what
+would you
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+say yeah is between the first
+
+ align:start position:0%
+say yeah is between the first
+ 
+
+ align:start position:0%
+say yeah is between the first
+well that would be true but I need to
+
+ align:start position:0%
+well that would be true but I need to
+ 
+
+ align:start position:0%
+well that would be true but I need to
+know one thing very importantly or I
+
+ align:start position:0%
+know one thing very importantly or I
+ 
+
+ align:start position:0%
+know one thing very importantly or I
+cannot answer whether that's the case
+
+ align:start position:0%
+cannot answer whether that's the case
+ 
+
+ align:start position:0%
+cannot answer whether that's the case
+what do I need to
+
+ align:start position:0%
+what do I need to
+ 
+
+ align:start position:0%
+what do I need to
+know I need to know the position of
+
+ align:start position:0%
+know I need to know the position of
+ 
+
+ align:start position:0%
+know I need to know the position of
+something
+
+ align:start position:0%
+something
+ 
+
+ align:start position:0%
+something
+here the firmy energy who said that very
+
+ align:start position:0%
+here the firmy energy who said that very
+ 
+
+ align:start position:0%
+here the firmy energy who said that very
+good FM energy came from over there okay
+
+ align:start position:0%
+good FM energy came from over there okay
+ 
+
+ align:start position:0%
+good FM energy came from over there okay
+now if I tell you that the FM energy in
+
+ align:start position:0%
+now if I tell you that the FM energy in
+ 
+
+ align:start position:0%
+now if I tell you that the FM energy in
+is here then you're absolutely right
+
+ align:start position:0%
+is here then you're absolutely right
+ 
+
+ align:start position:0%
+is here then you're absolutely right
+it's the it's the difference and and in
+
+ align:start position:0%
+it's the it's the difference and and in
+ 
+
+ align:start position:0%
+it's the it's the difference and and in
+the in the Dos plots you get on the Nano
+
+ align:start position:0%
+the in the Dos plots you get on the Nano
+ 
+
+ align:start position:0%
+the in the Dos plots you get on the Nano
+Hub it's it's these are enally levels
+
+ align:start position:0%
+Hub it's it's these are enally levels
+ 
+
+ align:start position:0%
+Hub it's it's these are enally levels
+that come out um you know if it's a
+
+ align:start position:0%
+that come out um you know if it's a
+ 
+
+ align:start position:0%
+that come out um you know if it's a
+molecule they're levels that come out
+
+ align:start position:0%
+molecule they're levels that come out
+ 
+
+ align:start position:0%
+molecule they're levels that come out
+and then they're spread out a little bit
+
+ align:start position:0%
+and then they're spread out a little bit
+ 
+
+ align:start position:0%
+and then they're spread out a little bit
+so it's very likely this peak height
+
+ align:start position:0%
+so it's very likely this peak height
+ 
+
+ align:start position:0%
+so it's very likely this peak height
+versus that is going to give you the
+
+ align:start position:0%
+versus that is going to give you the
+ 
+
+ align:start position:0%
+versus that is going to give you the
+Gap okay and in in the nanohub tool the
+
+ align:start position:0%
+Gap okay and in in the nanohub tool the
+ 
+
+ align:start position:0%
+Gap okay and in in the nanohub tool the
+the firmy energy is always set to zero
+
+ align:start position:0%
+the firmy energy is always set to zero
+ 
+
+ align:start position:0%
+the firmy energy is always set to zero
+for you okay but if I don't specify it
+
+ align:start position:0%
+for you okay but if I don't specify it
+ 
+
+ align:start position:0%
+for you okay but if I don't specify it
+you may not
+
+ align:start position:0%
+you may not
+ 
+
+ align:start position:0%
+you may not
+know now is that a semiconductor or an
+
+ align:start position:0%
+know now is that a semiconductor or an
+ 
+
+ align:start position:0%
+know now is that a semiconductor or an
+insulator is it a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+metal semiconductor how do you know you
+
+ align:start position:0%
+metal semiconductor how do you know you
+ 
+
+ align:start position:0%
+metal semiconductor how do you know you
+have a feeling okay well let's say I put
+
+ align:start position:0%
+have a feeling okay well let's say I put
+ 
+
+ align:start position:0%
+have a feeling okay well let's say I put
+it
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+here semiconductor
+
+ align:start position:0%
+here semiconductor
+ 
+
+ align:start position:0%
+here semiconductor
+insulator wait why why can I not answer
+
+ align:start position:0%
+insulator wait why why can I not answer
+ 
+
+ align:start position:0%
+insulator wait why why can I not answer
+that question what don't you
+
+ align:start position:0%
+that question what don't you
+ 
+
+ align:start position:0%
+that question what don't you
+know how how big of what what if I told
+
+ align:start position:0%
+know how how big of what what if I told
+ 
+
+ align:start position:0%
+know how how big of what what if I told
+you that this was
+
+ align:start position:0%
+you that this was
+ 
+
+ align:start position:0%
+you that this was
+0.1 and this was 0.2 and the scale is an
+
+ align:start position:0%
+0.1 and this was 0.2 and the scale is an
+ 
+
+ align:start position:0%
+0.1 and this was 0.2 and the scale is an
+EV then what is it
+
+ align:start position:0%
+EV then what is it
+ 
+
+ align:start position:0%
+EV then what is it
+it's a 0.1 EV Gap semiconductor right
+
+ align:start position:0%
+it's a 0.1 EV Gap semiconductor right
+ 
+
+ align:start position:0%
+it's a 0.1 EV Gap semiconductor right
+okay so well that's sort of like almost
+
+ align:start position:0%
+okay so well that's sort of like almost
+ 
+
+ align:start position:0%
+okay so well that's sort of like almost
+the metal but it's still a semiconductor
+
+ align:start position:0%
+the metal but it's still a semiconductor
+ 
+
+ align:start position:0%
+the metal but it's still a semiconductor
+it's a very low band Gap semiconductor
+
+ align:start position:0%
+it's a very low band Gap semiconductor
+ 
+
+ align:start position:0%
+it's a very low band Gap semiconductor
+that where actually electrons will
+
+ align:start position:0%
+that where actually electrons will
+ 
+
+ align:start position:0%
+that where actually electrons will
+probably populate um the conduction band
+
+ align:start position:0%
+probably populate um the conduction band
+ 
+
+ align:start position:0%
+probably populate um the conduction band
+just thermally to to you know an
+
+ align:start position:0%
+just thermally to to you know an
+ 
+
+ align:start position:0%
+just thermally to to you know an
+interesting probability um now uh if I
+
+ align:start position:0%
+interesting probability um now uh if I
+ 
+
+ align:start position:0%
+interesting probability um now uh if I
+told you this was 10 EV what would it
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+be insulator okay now um and and and I
+
+ align:start position:0%
+be insulator okay now um and and and I
+ 
+
+ align:start position:0%
+be insulator okay now um and and and I
+I'm going to go on Don't worry um but
+
+ align:start position:0%
+I'm going to go on Don't worry um but
+ 
+
+ align:start position:0%
+I'm going to go on Don't worry um but
+the last point is dftt I'm I'm I'm not
+
+ align:start position:0%
+the last point is dftt I'm I'm I'm not
+ 
+
+ align:start position:0%
+the last point is dftt I'm I'm I'm not
+going to go into the the details of why
+
+ align:start position:0%
+going to go into the the details of why
+ 
+
+ align:start position:0%
+going to go into the the details of why
+but DFT tends to underestimate the band
+
+ align:start position:0%
+but DFT tends to underestimate the band
+ 
+
+ align:start position:0%
+but DFT tends to underestimate the band
+Gap okay and
+
+ align:start position:0%
+Gap okay and
+ 
+
+ align:start position:0%
+Gap okay and
+so there are now sophisticated ways of
+
+ align:start position:0%
+so there are now sophisticated ways of
+ 
+
+ align:start position:0%
+so there are now sophisticated ways of
+correcting that and going Beyond DFT
+
+ align:start position:0%
+correcting that and going Beyond DFT
+ 
+
+ align:start position:0%
+correcting that and going Beyond DFT
+that we're not going to talk about in
+
+ align:start position:0%
+that we're not going to talk about in
+ 
+
+ align:start position:0%
+that we're not going to talk about in
+this class but what we are going to do
+
+ align:start position:0%
+this class but what we are going to do
+ 
+
+ align:start position:0%
+this class but what we are going to do
+is we're going to use an approximation
+
+ align:start position:0%
+is we're going to use an approximation
+ 
+
+ align:start position:0%
+is we're going to use an approximation
+that was used for 20 years in the
+
+ align:start position:0%
+that was used for 20 years in the
+ 
+
+ align:start position:0%
+that was used for 20 years in the
+scientific literature and Community um
+
+ align:start position:0%
+scientific literature and Community um
+ 
+
+ align:start position:0%
+scientific literature and Community um
+to correct for this problem and that is
+
+ align:start position:0%
+to correct for this problem and that is
+ 
+
+ align:start position:0%
+to correct for this problem and that is
+simply called a scissor shift where
+
+ align:start position:0%
+simply called a scissor shift where
+ 
+
+ align:start position:0%
+simply called a scissor shift where
+basically you see DFT gets the band Gap
+
+ align:start position:0%
+basically you see DFT gets the band Gap
+ 
+
+ align:start position:0%
+basically you see DFT gets the band Gap
+wrong but it gets qualitatively very
+
+ align:start position:0%
+wrong but it gets qualitatively very
+ 
+
+ align:start position:0%
+wrong but it gets qualitatively very
+often the picture right it just gets the
+
+ align:start position:0%
+often the picture right it just gets the
+ 
+
+ align:start position:0%
+often the picture right it just gets the
+bang Gap too small so very often we just
+
+ align:start position:0%
+bang Gap too small so very often we just
+ 
+
+ align:start position:0%
+bang Gap too small so very often we just
+shift the conduction band
+
+ align:start position:0%
+shift the conduction band
+ 
+
+ align:start position:0%
+shift the conduction band
+states by some some correction
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay I will give you that correction
+
+ align:start position:0%
+okay I will give you that correction
+ 
+
+ align:start position:0%
+okay I will give you that correction
+that'll be the addendum in in the
+
+ align:start position:0%
+that'll be the addendum in in the
+ 
+
+ align:start position:0%
+that'll be the addendum in in the
+homework because you you'll need that so
+
+ align:start position:0%
+homework because you you'll need that so
+ 
+
+ align:start position:0%
+homework because you you'll need that so
+that the Dos plots that you calculate
+
+ align:start position:0%
+that the Dos plots that you calculate
+ 
+
+ align:start position:0%
+that the Dos plots that you calculate
+for these solar
+
+ align:start position:0%
+for these solar
+ 
+
+ align:start position:0%
+for these solar
+fuels think of them as as pretty good
+
+ align:start position:0%
+fuels think of them as as pretty good
+ 
+
+ align:start position:0%
+fuels think of them as as pretty good
+except you have to shift these states up
+
+ align:start position:0%
+except you have to shift these states up
+ 
+
+ align:start position:0%
+except you have to shift these states up
+so qualitatively these states are not
+
+ align:start position:0%
+so qualitatively these states are not
+ 
+
+ align:start position:0%
+so qualitatively these states are not
+are are not bad but they're just too low
+
+ align:start position:0%
+are are not bad but they're just too low
+ 
+
+ align:start position:0%
+are are not bad but they're just too low
+in energy compared to the to the
+
+ align:start position:0%
+in energy compared to the to the
+ 
+
+ align:start position:0%
+in energy compared to the to the
+occupied States okay so that's um that's
+
+ align:start position:0%
+occupied States okay so that's um that's
+ 
+
+ align:start position:0%
+occupied States okay so that's um that's
+a method that um is not really used very
+
+ align:start position:0%
+a method that um is not really used very
+ 
+
+ align:start position:0%
+a method that um is not really used very
+often anymore but it was used heavily in
+
+ align:start position:0%
+often anymore but it was used heavily in
+ 
+
+ align:start position:0%
+often anymore but it was used heavily in
+the 70s and 80s to use DFT um to look at
+
+ align:start position:0%
+the 70s and 80s to use DFT um to look at
+ 
+
+ align:start position:0%
+the 70s and 80s to use DFT um to look at
+at Doss and band structures
+
+ align:start position:0%
+at Doss and band structures
+ 
+
+ align:start position:0%
+at Doss and band structures
+um nowadays we do have methods that go
+
+ align:start position:0%
+um nowadays we do have methods that go
+ 
+
+ align:start position:0%
+um nowadays we do have methods that go
+further that allow us to to actually
+
+ align:start position:0%
+further that allow us to to actually
+ 
+
+ align:start position:0%
+further that allow us to to actually
+calculate these things without some sort
+
+ align:start position:0%
+calculate these things without some sort
+ 
+
+ align:start position:0%
+calculate these things without some sort
+of rigid shift approximation but
+
+ align:start position:0%
+of rigid shift approximation but
+ 
+
+ align:start position:0%
+of rigid shift approximation but
+calculate them more from first
+
+ align:start position:0%
+calculate them more from first
+ 
+
+ align:start position:0%
+calculate them more from first
+principles but I won't go into those in
+
+ align:start position:0%
+principles but I won't go into those in
+ 
+
+ align:start position:0%
+principles but I won't go into those in
+this class okay any questions so you'll
+
+ align:start position:0%
+this class okay any questions so you'll
+ 
+
+ align:start position:0%
+this class okay any questions so you'll
+have to download your dos plot and do
+
+ align:start position:0%
+have to download your dos plot and do
+ 
+
+ align:start position:0%
+have to download your dos plot and do
+the shift that I give you to the data
+
+ align:start position:0%
+the shift that I give you to the data
+ 
+
+ align:start position:0%
+the shift that I give you to the data
+all
+
+ align:start position:0%
+all
+ 
+
+ align:start position:0%
+all
+right seems kind of like a
+
+ align:start position:0%
+right seems kind of like a
+ 
+
+ align:start position:0%
+right seems kind of like a
+cheat you know and it actually is a
+
+ align:start position:0%
+cheat you know and it actually is a
+ 
+
+ align:start position:0%
+cheat you know and it actually is a
+cheat but um like I said the qualitative
+
+ align:start position:0%
+cheat but um like I said the qualitative
+ 
+
+ align:start position:0%
+cheat but um like I said the qualitative
+nature of these states is still very
+
+ align:start position:0%
+nature of these states is still very
+ 
+
+ align:start position:0%
+nature of these states is still very
+good often okay so that's a property DFT
+
+ align:start position:0%
+good often okay so that's a property DFT
+ 
+
+ align:start position:0%
+good often okay so that's a property DFT
+does not do so well
+
+ align:start position:0%
+does not do so well
+ 
+
+ align:start position:0%
+does not do so well
+on okay I won't go through the the
+
+ align:start position:0%
+on okay I won't go through the the
+ 
+
+ align:start position:0%
+on okay I won't go through the the
+self-consistence cycle what what we did
+
+ align:start position:0%
+self-consistence cycle what what we did
+ 
+
+ align:start position:0%
+self-consistence cycle what what we did
+on
+
+ align:start position:0%
+on
+ 
+
+ align:start position:0%
+on
+Tuesday is we talked about solids okay
+
+ align:start position:0%
+Tuesday is we talked about solids okay
+ 
+
+ align:start position:0%
+Tuesday is we talked about solids okay
+so we talked about the periodic cell and
+
+ align:start position:0%
+so we talked about the periodic cell and
+ 
+
+ align:start position:0%
+so we talked about the periodic cell and
+we talked about Crystal symmetries and
+
+ align:start position:0%
+we talked about Crystal symmetries and
+ 
+
+ align:start position:0%
+we talked about Crystal symmetries and
+this was all review I think for most of
+
+ align:start position:0%
+this was all review I think for most of
+ 
+
+ align:start position:0%
+this was all review I think for most of
+you and most symmetries are um most
+
+ align:start position:0%
+you and most symmetries are um most
+ 
+
+ align:start position:0%
+you and most symmetries are um most
+common lates are cubic or hexagonal Clos
+
+ align:start position:0%
+common lates are cubic or hexagonal Clos
+ 
+
+ align:start position:0%
+common lates are cubic or hexagonal Clos
+pack anybody know
+
+ align:start position:0%
+pack anybody know
+ 
+
+ align:start position:0%
+pack anybody know
+why
+
+ align:start position:0%
+why
+ 
+
+ align:start position:0%
+why
+yeah yeah get to because of
+
+ align:start position:0%
+yeah yeah get to because of
+ 
+
+ align:start position:0%
+yeah yeah get to because of
+what yeah kind of pack them in right
+
+ align:start position:0%
+what yeah kind of pack them in right
+ 
+
+ align:start position:0%
+what yeah kind of pack them in right
+makes sense okay um and then and this is
+
+ align:start position:0%
+makes sense okay um and then and this is
+ 
+
+ align:start position:0%
+makes sense okay um and then and this is
+sort of where we spent some time Tuesday
+
+ align:start position:0%
+sort of where we spent some time Tuesday
+ 
+
+ align:start position:0%
+sort of where we spent some time Tuesday
+and I want to make sure we we feel our
+
+ align:start position:0%
+and I want to make sure we we feel our
+ 
+
+ align:start position:0%
+and I want to make sure we we feel our
+Oneness with this Cas Spas thing so
+
+ align:start position:0%
+Oneness with this Cas Spas thing so
+ 
+
+ align:start position:0%
+Oneness with this Cas Spas thing so
+associated with real space latus there
+
+ align:start position:0%
+associated with real space latus there
+ 
+
+ align:start position:0%
+associated with real space latus there
+exists something we call reciprocal lce
+
+ align:start position:0%
+exists something we call reciprocal lce
+ 
+
+ align:start position:0%
+exists something we call reciprocal lce
+it's a set of wave vectors which are
+
+ align:start position:0%
+it's a set of wave vectors which are
+ 
+
+ align:start position:0%
+it's a set of wave vectors which are
+commensurate with the real space lattice
+
+ align:start position:0%
+commensurate with the real space lattice
+ 
+
+ align:start position:0%
+commensurate with the real space lattice
+sometimes we call it
+
+ align:start position:0%
+sometimes we call it
+ 
+
+ align:start position:0%
+sometimes we call it
+g yeah why not those are the lce vectors
+
+ align:start position:0%
+g yeah why not those are the lce vectors
+ 
+
+ align:start position:0%
+g yeah why not those are the lce vectors
+in reciprocal space and we Define them
+
+ align:start position:0%
+in reciprocal space and we Define them
+ 
+
+ align:start position:0%
+in reciprocal space and we Define them
+as you know a star B Star C star um
+
+ align:start position:0%
+as you know a star B Star C star um
+ 
+
+ align:start position:0%
+as you know a star B Star C star um
+that's a lce in real space FC uh BCC BCC
+
+ align:start position:0%
+that's a lce in real space FC uh BCC BCC
+ 
+
+ align:start position:0%
+that's a lce in real space FC uh BCC BCC
+lattice and there's the reciprocal space
+
+ align:start position:0%
+lattice and there's the reciprocal space
+ 
+
+ align:start position:0%
+lattice and there's the reciprocal space
+lattice it's a real lce it has like
+
+ align:start position:0%
+lattice it's a real lce it has like
+ 
+
+ align:start position:0%
+lattice it's a real lce it has like
+distances in lattice World in reciprocal
+
+ align:start position:0%
+distances in lattice World in reciprocal
+ 
+
+ align:start position:0%
+distances in lattice World in reciprocal
+lattice world right it just looks looks
+
+ align:start position:0%
+lattice world right it just looks looks
+ 
+
+ align:start position:0%
+lattice world right it just looks looks
+different and actually the inverse of
+
+ align:start position:0%
+different and actually the inverse of
+ 
+
+ align:start position:0%
+different and actually the inverse of
+BCC is FCC okay so we talked about all
+
+ align:start position:0%
+BCC is FCC okay so we talked about all
+ 
+
+ align:start position:0%
+BCC is FCC okay so we talked about all
+this and then we talked about how you
+
+ align:start position:0%
+this and then we talked about how you
+ 
+
+ align:start position:0%
+this and then we talked about how you
+can define a Zone within reciprocal
+
+ align:start position:0%
+can define a Zone within reciprocal
+ 
+
+ align:start position:0%
+can define a Zone within reciprocal
+space and the first um if you take you
+
+ align:start position:0%
+space and the first um if you take you
+ 
+
+ align:start position:0%
+space and the first um if you take you
+know if you if you draw lines between
+
+ align:start position:0%
+know if you if you draw lines between
+ 
+
+ align:start position:0%
+know if you if you draw lines between
+neighbors and nearest neighbors and you
+
+ align:start position:0%
+neighbors and nearest neighbors and you
+ 
+
+ align:start position:0%
+neighbors and nearest neighbors and you
+draw bisections then you define that
+
+ align:start position:0%
+draw bisections then you define that
+ 
+
+ align:start position:0%
+draw bisections then you define that
+zone right and that's called The brillin
+
+ align:start position:0%
+zone right and that's called The brillin
+ 
+
+ align:start position:0%
+zone right and that's called The brillin
+Zone and so you see here in this Square
+
+ align:start position:0%
+Zone and so you see here in this Square
+ 
+
+ align:start position:0%
+Zone and so you see here in this Square
+lattice it's a square um in here it's
+
+ align:start position:0%
+lattice it's a square um in here it's
+ 
+
+ align:start position:0%
+lattice it's a square um in here it's
+going to be a hexagon and if we Define
+
+ align:start position:0%
+going to be a hexagon and if we Define
+ 
+
+ align:start position:0%
+going to be a hexagon and if we Define
+that zone in three dimensions um well
+
+ align:start position:0%
+that zone in three dimensions um well
+ 
+
+ align:start position:0%
+that zone in three dimensions um well
+here it's squares and hexagons right um
+
+ align:start position:0%
+here it's squares and hexagons right um
+ 
+
+ align:start position:0%
+here it's squares and hexagons right um
+on the on the edges but it's a
+
+ align:start position:0%
+on the on the edges but it's a
+ 
+
+ align:start position:0%
+on the on the edges but it's a
+volume okay does everybody so we're just
+
+ align:start position:0%
+volume okay does everybody so we're just
+ 
+
+ align:start position:0%
+volume okay does everybody so we're just
+defining space still and then came the
+
+ align:start position:0%
+defining space still and then came the
+ 
+
+ align:start position:0%
+defining space still and then came the
+blocks
+
+ align:start position:0%
+blocks
+ 
+
+ align:start position:0%
+blocks
+theorem and in blocks
+
+ align:start position:0%
+theorem and in blocks
+ 
+
+ align:start position:0%
+theorem and in blocks
+theorem you know what we said is that
+
+ align:start position:0%
+theorem you know what we said is that
+ 
+
+ align:start position:0%
+theorem you know what we said is that
+you know values of a function like the
+
+ align:start position:0%
+you know values of a function like the
+ 
+
+ align:start position:0%
+you know values of a function like the
+density should be the same because it's
+
+ align:start position:0%
+density should be the same because it's
+ 
+
+ align:start position:0%
+density should be the same because it's
+a crystal um but the wave function is
+
+ align:start position:0%
+a crystal um but the wave function is
+ 
+
+ align:start position:0%
+a crystal um but the wave function is
+periodic only when multiplied by a phase
+
+ align:start position:0%
+periodic only when multiplied by a phase
+ 
+
+ align:start position:0%
+periodic only when multiplied by a phase
+factor and that's you know I didn't go
+
+ align:start position:0%
+factor and that's you know I didn't go
+ 
+
+ align:start position:0%
+factor and that's you know I didn't go
+into a lot of detail but that's block
+
+ align:start position:0%
+into a lot of detail but that's block
+ 
+
+ align:start position:0%
+into a lot of detail but that's block
+theerum so it says that the wave
+
+ align:start position:0%
+theerum so it says that the wave
+ 
+
+ align:start position:0%
+theerum so it says that the wave
+function picks up a phase factor which
+
+ align:start position:0%
+function picks up a phase factor which
+ 
+
+ align:start position:0%
+function picks up a phase factor which
+depends on this new quantum
+
+ align:start position:0%
+depends on this new quantum
+ 
+
+ align:start position:0%
+depends on this new quantum
+number okay that's all review from
+
+ align:start position:0%
+number okay that's all review from
+ 
+
+ align:start position:0%
+number okay that's all review from
+Tuesday from last week and um and and
+
+ align:start position:0%
+Tuesday from last week and um and and
+ 
+
+ align:start position:0%
+Tuesday from last week and um and and
+you can see that if the wave function
+
+ align:start position:0%
+you can see that if the wave function
+ 
+
+ align:start position:0%
+you can see that if the wave function
+looks like that so if you add um the
+
+ align:start position:0%
+looks like that so if you add um the
+ 
+
+ align:start position:0%
+looks like that so if you add um the
+periodicity of the lattice as Big R R is
+
+ align:start position:0%
+periodicity of the lattice as Big R R is
+ 
+
+ align:start position:0%
+periodicity of the lattice as Big R R is
+just anywhere in real space then you're
+
+ align:start position:0%
+just anywhere in real space then you're
+ 
+
+ align:start position:0%
+just anywhere in real space then you're
+going to get the space factor and if you
+
+ align:start position:0%
+going to get the space factor and if you
+ 
+
+ align:start position:0%
+going to get the space factor and if you
+square them say to get the density then
+
+ align:start position:0%
+square them say to get the density then
+ 
+
+ align:start position:0%
+square them say to get the density then
+you can show that the dens densities are
+
+ align:start position:0%
+you can show that the dens densities are
+ 
+
+ align:start position:0%
+you can show that the dens densities are
+are the same okay um also in and this is
+
+ align:start position:0%
+are the same okay um also in and this is
+ 
+
+ align:start position:0%
+are the same okay um also in and this is
+important the wave function picks up a
+
+ align:start position:0%
+important the wave function picks up a
+ 
+
+ align:start position:0%
+important the wave function picks up a
+phase if you go by by the periodicity of
+
+ align:start position:0%
+phase if you go by by the periodicity of
+ 
+
+ align:start position:0%
+phase if you go by by the periodicity of
+the real space lce but if I increase K
+
+ align:start position:0%
+the real space lce but if I increase K
+ 
+
+ align:start position:0%
+the real space lce but if I increase K
+if I add a an inverse lattice Vector to
+
+ align:start position:0%
+if I add a an inverse lattice Vector to
+ 
+
+ align:start position:0%
+if I add a an inverse lattice Vector to
+k then they're they they're exactly the
+
+ align:start position:0%
+k then they're they they're exactly the
+ 
+
+ align:start position:0%
+k then they're they they're exactly the
+same so in k space I can also translate
+
+ align:start position:0%
+same so in k space I can also translate
+ 
+
+ align:start position:0%
+same so in k space I can also translate
+around okay and the energies are the
+
+ align:start position:0%
+around okay and the energies are the
+ 
+
+ align:start position:0%
+around okay and the energies are the
+same we're going somewhere here
+
+ align:start position:0%
+same we're going somewhere here
+ 
+
+ align:start position:0%
+same we're going somewhere here
+okay we're going somewhere give me a
+
+ align:start position:0%
+okay we're going somewhere give me a
+ 
+
+ align:start position:0%
+okay we're going somewhere give me a
+minute and then I showed you this and
+
+ align:start position:0%
+minute and then I showed you this and
+ 
+
+ align:start position:0%
+minute and then I showed you this and
+does anybody have questions about this
+
+ align:start position:0%
+does anybody have questions about this
+ 
+
+ align:start position:0%
+does anybody have questions about this
+the parallel here I think is pretty
+
+ align:start position:0%
+the parallel here I think is pretty
+ 
+
+ align:start position:0%
+the parallel here I think is pretty
+self-explanatory
+
+ align:start position:0%
+self-explanatory
+ 
+
+ align:start position:0%
+self-explanatory
+right in the hydrogen
+
+ align:start position:0%
+right in the hydrogen
+ 
+
+ align:start position:0%
+right in the hydrogen
+atom we impose this spherical Symmetry
+
+ align:start position:0%
+atom we impose this spherical Symmetry
+ 
+
+ align:start position:0%
+atom we impose this spherical Symmetry
+gunti and we got out of that
+
+ align:start position:0%
+gunti and we got out of that
+ 
+
+ align:start position:0%
+gunti and we got out of that
+quantization we solved and here we
+
+ align:start position:0%
+quantization we solved and here we
+ 
+
+ align:start position:0%
+quantization we solved and here we
+impose the translational Symmetry and we
+
+ align:start position:0%
+impose the translational Symmetry and we
+ 
+
+ align:start position:0%
+impose the translational Symmetry and we
+get out of that K
+
+ align:start position:0%
+get out of that K
+ 
+
+ align:start position:0%
+get out of that K
+vectorization we but K is not a Quant k
+
+ align:start position:0%
+vectorization we but K is not a Quant k
+ 
+
+ align:start position:0%
+vectorization we but K is not a Quant k
+is a quantum number but it can be
+
+ align:start position:0%
+is a quantum number but it can be
+ 
+
+ align:start position:0%
+is a quantum number but it can be
+continuous it can be continuous okay and
+
+ align:start position:0%
+continuous it can be continuous okay and
+ 
+
+ align:start position:0%
+continuous it can be continuous okay and
+and you look at it in the first bran
+
+ align:start position:0%
+and you look at it in the first bran
+ 
+
+ align:start position:0%
+and you look at it in the first bran
+zone now somebody tell me given
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this why would I worry about K
+
+ align:start position:0%
+this why would I worry about K
+ 
+
+ align:start position:0%
+this why would I worry about K
+only no
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+problem
+
+ align:start position:0%
+problem
+ 
+
+ align:start position:0%
+problem
+oh okay so I should stop like kind
+
+ align:start position:0%
+oh okay so I should stop like kind
+ 
+
+ align:start position:0%
+oh okay so I should stop like kind
+of all right uh that wrap kind of got me
+
+ align:start position:0%
+of all right uh that wrap kind of got me
+ 
+
+ align:start position:0%
+of all right uh that wrap kind of got me
+a little bit excited so uh let's go back
+
+ align:start position:0%
+a little bit excited so uh let's go back
+ 
+
+ align:start position:0%
+a little bit excited so uh let's go back
+to slide one
+
+ align:start position:0%
+to slide one
+ 
+
+ align:start position:0%
+to slide one
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+um so I'm adding a an inverse lattice
+
+ align:start position:0%
+um so I'm adding a an inverse lattice
+ 
+
+ align:start position:0%
+um so I'm adding a an inverse lattice
+Vector a full Vector that gets me to
+
+ align:start position:0%
+Vector a full Vector that gets me to
+ 
+
+ align:start position:0%
+Vector a full Vector that gets me to
+another lce point in inverse space and I
+
+ align:start position:0%
+another lce point in inverse space and I
+ 
+
+ align:start position:0%
+another lce point in inverse space and I
+say my wave function is the same okay
+
+ align:start position:0%
+say my wave function is the same okay
+ 
+
+ align:start position:0%
+say my wave function is the same okay
+now why is it I also defin a bran
+
+ align:start position:0%
+now why is it I also defin a bran
+ 
+
+ align:start position:0%
+now why is it I also defin a bran
+zone right um and you can see my
+
+ align:start position:0%
+zone right um and you can see my
+ 
+
+ align:start position:0%
+zone right um and you can see my
+definition of the one zone is in fact
+
+ align:start position:0%
+definition of the one zone is in fact
+ 
+
+ align:start position:0%
+definition of the one zone is in fact
+that it's a zone that you know it's a
+
+ align:start position:0%
+that it's a zone that you know it's a
+ 
+
+ align:start position:0%
+that it's a zone that you know it's a
+lattice Vector you see those are lce
+
+ align:start position:0%
+lattice Vector you see those are lce
+ 
+
+ align:start position:0%
+lattice Vector you see those are lce
+vectors why is it that I only now care
+
+ align:start position:0%
+vectors why is it that I only now care
+ 
+
+ align:start position:0%
+vectors why is it that I only now care
+about the variation of K within that
+
+ align:start position:0%
+about the variation of K within that
+ 
+
+ align:start position:0%
+about the variation of K within that
+first bran Zone yeah
+
+ align:start position:0%
+first bran Zone yeah
+ 
+
+ align:start position:0%
+first bran Zone yeah
+same the same right that's why we care
+
+ align:start position:0%
+same the same right that's why we care
+ 
+
+ align:start position:0%
+same the same right that's why we care
+so much about that bruan zone what is it
+
+ align:start position:0%
+so much about that bruan zone what is it
+ 
+
+ align:start position:0%
+so much about that bruan zone what is it
+well it's the boundaries of the
+
+ align:start position:0%
+well it's the boundaries of the
+ 
+
+ align:start position:0%
+well it's the boundaries of the
+variability of the wave
+
+ align:start position:0%
+variability of the wave
+ 
+
+ align:start position:0%
+variability of the wave
+function in so in in in terms of how it
+
+ align:start position:0%
+function in so in in in terms of how it
+ 
+
+ align:start position:0%
+function in so in in in terms of how it
+depends on K so I only need to vary K in
+
+ align:start position:0%
+depends on K so I only need to vary K in
+ 
+
+ align:start position:0%
+depends on K so I only need to vary K in
+this first Zone but I do need to vary it
+
+ align:start position:0%
+this first Zone but I do need to vary it
+ 
+
+ align:start position:0%
+this first Zone but I do need to vary it
+in that zone I have to vary it in that
+
+ align:start position:0%
+in that zone I have to vary it in that
+ 
+
+ align:start position:0%
+in that zone I have to vary it in that
+zone because there will be variation if
+
+ align:start position:0%
+zone because there will be variation if
+ 
+
+ align:start position:0%
+zone because there will be variation if
+it's a
+
+ align:start position:0%
+it's a
+ 
+
+ align:start position:0%
+it's a
+solid okay but if I vary it and I go out
+
+ align:start position:0%
+solid okay but if I vary it and I go out
+ 
+
+ align:start position:0%
+solid okay but if I vary it and I go out
+here well you know it's just I can
+
+ align:start position:0%
+here well you know it's just I can
+ 
+
+ align:start position:0%
+here well you know it's just I can
+translate it back and it's the same
+
+ align:start position:0%
+translate it back and it's the same
+ 
+
+ align:start position:0%
+translate it back and it's the same
+thing you see so I need to I need to
+
+ align:start position:0%
+thing you see so I need to I need to
+ 
+
+ align:start position:0%
+thing you see so I need to I need to
+move K around in this first
+
+ align:start position:0%
+move K around in this first
+ 
+
+ align:start position:0%
+move K around in this first
+Zone and when I do and this is a slide
+
+ align:start position:0%
+Zone and when I do and this is a slide
+ 
+
+ align:start position:0%
+Zone and when I do and this is a slide
+I've showed before when I do what you
+
+ align:start position:0%
+I've showed before when I do what you
+ 
+
+ align:start position:0%
+I've showed before when I do what you
+get is as you go as you think about a
+
+ align:start position:0%
+get is as you go as you think about a
+ 
+
+ align:start position:0%
+get is as you go as you think about a
+system going from atoms to molecules to
+
+ align:start position:0%
+system going from atoms to molecules to
+ 
+
+ align:start position:0%
+system going from atoms to molecules to
+bands in your solid you see this is the
+
+ align:start position:0%
+bands in your solid you see this is the
+ 
+
+ align:start position:0%
+bands in your solid you see this is the
+energy of that band it Wiggles that's
+
+ align:start position:0%
+energy of that band it Wiggles that's
+ 
+
+ align:start position:0%
+energy of that band it Wiggles that's
+what happens in that first Zone you have
+
+ align:start position:0%
+what happens in that first Zone you have
+ 
+
+ align:start position:0%
+what happens in that first Zone you have
+a new quantum number you change it and
+
+ align:start position:0%
+a new quantum number you change it and
+ 
+
+ align:start position:0%
+a new quantum number you change it and
+you vary the energy right it Wiggles so
+
+ align:start position:0%
+you vary the energy right it Wiggles so
+ 
+
+ align:start position:0%
+you vary the energy right it Wiggles so
+now these orbitals are Wiggly okay
+
+ align:start position:0%
+now these orbitals are Wiggly okay
+ 
+
+ align:start position:0%
+now these orbitals are Wiggly okay
+that's the the big the most important
+
+ align:start position:0%
+that's the the big the most important
+ 
+
+ align:start position:0%
+that's the the big the most important
+thing and you can see here so here's my
+
+ align:start position:0%
+thing and you can see here so here's my
+ 
+
+ align:start position:0%
+thing and you can see here so here's my
+k space right and I can vary KX KY KZ if
+
+ align:start position:0%
+k space right and I can vary KX KY KZ if
+ 
+
+ align:start position:0%
+k space right and I can vary KX KY KZ if
+it's threedimensional
+
+ align:start position:0%
+it's threedimensional
+ 
+
+ align:start position:0%
+it's threedimensional
+solid and at each point in k space
+
+ align:start position:0%
+solid and at each point in k space
+ 
+
+ align:start position:0%
+solid and at each point in k space
+you're going to get a set of
+
+ align:start position:0%
+you're going to get a set of
+ 
+
+ align:start position:0%
+you're going to get a set of
+levels right just like you did for that
+
+ align:start position:0%
+levels right just like you did for that
+ 
+
+ align:start position:0%
+levels right just like you did for that
+atom or molecule you're going to get a
+
+ align:start position:0%
+atom or molecule you're going to get a
+ 
+
+ align:start position:0%
+atom or molecule you're going to get a
+set of levels and they they will vary
+
+ align:start position:0%
+set of levels and they they will vary
+ 
+
+ align:start position:0%
+set of levels and they they will vary
+but they will be the
+
+ align:start position:0%
+but they will be the
+ 
+
+ align:start position:0%
+but they will be the
+same if I translate by the um inverse
+
+ align:start position:0%
+same if I translate by the um inverse
+ 
+
+ align:start position:0%
+same if I translate by the um inverse
+lce Vector so if I go from here out some
+
+ align:start position:0%
+lce Vector so if I go from here out some
+ 
+
+ align:start position:0%
+lce Vector so if I go from here out some
+G Vector then I get exactly the same
+
+ align:start position:0%
+G Vector then I get exactly the same
+ 
+
+ align:start position:0%
+G Vector then I get exactly the same
+levels but if I'm inside this BR one
+
+ align:start position:0%
+levels but if I'm inside this BR one
+ 
+
+ align:start position:0%
+levels but if I'm inside this BR one
+zone they're going to vary
+
+ align:start position:0%
+zone they're going to vary
+ 
+
+ align:start position:0%
+zone they're going to vary
+okay right any questions kpace is really
+
+ align:start position:0%
+okay right any questions kpace is really
+ 
+
+ align:start position:0%
+okay right any questions kpace is really
+important for
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+solids okay and so what do we do well so
+
+ align:start position:0%
+solids okay and so what do we do well so
+ 
+
+ align:start position:0%
+solids okay and so what do we do well so
+the inverse lattice you know it's
+
+ align:start position:0%
+the inverse lattice you know it's
+ 
+
+ align:start position:0%
+the inverse lattice you know it's
+related to the real space lattice if I
+
+ align:start position:0%
+related to the real space lattice if I
+ 
+
+ align:start position:0%
+related to the real space lattice if I
+double the real space
+
+ align:start position:0%
+double the real space
+ 
+
+ align:start position:0%
+double the real space
+lattice so it's periodic but with more
+
+ align:start position:0%
+lattice so it's periodic but with more
+ 
+
+ align:start position:0%
+lattice so it's periodic but with more
+atoms in the cell right so it's periodic
+
+ align:start position:0%
+atoms in the cell right so it's periodic
+ 
+
+ align:start position:0%
+atoms in the cell right so it's periodic
+over a larger domain then basically I'm
+
+ align:start position:0%
+over a larger domain then basically I'm
+ 
+
+ align:start position:0%
+over a larger domain then basically I'm
+change you know it's it's like a forier
+
+ align:start position:0%
+change you know it's it's like a forier
+ 
+
+ align:start position:0%
+change you know it's it's like a forier
+series right so if I go to larger real
+
+ align:start position:0%
+series right so if I go to larger real
+ 
+
+ align:start position:0%
+series right so if I go to larger real
+space lattice then I have finer and
+
+ align:start position:0%
+space lattice then I have finer and
+ 
+
+ align:start position:0%
+space lattice then I have finer and
+finer k
+
+ align:start position:0%
+finer k
+ 
+
+ align:start position:0%
+finer k
+space right and so what that means is
+
+ align:start position:0%
+space right and so what that means is
+ 
+
+ align:start position:0%
+space right and so what that means is
+that you know you you can choose a
+
+ align:start position:0%
+that you know you you can choose a
+ 
+
+ align:start position:0%
+that you know you you can choose a
+certain K mesh this is a variable in the
+
+ align:start position:0%
+certain K mesh this is a variable in the
+ 
+
+ align:start position:0%
+certain K mesh this is a variable in the
+input now for solids for solids this is
+
+ align:start position:0%
+input now for solids for solids this is
+ 
+
+ align:start position:0%
+input now for solids for solids this is
+a new critical variable in your
+
+ align:start position:0%
+a new critical variable in your
+ 
+
+ align:start position:0%
+a new critical variable in your
+calculations okay of solids you need a k
+
+ align:start position:0%
+calculations okay of solids you need a k
+ 
+
+ align:start position:0%
+calculations okay of solids you need a k
+mesh and this is just a number you'll
+
+ align:start position:0%
+mesh and this is just a number you'll
+ 
+
+ align:start position:0%
+mesh and this is just a number you'll
+enter eight or two or four and it'll
+
+ align:start position:0%
+enter eight or two or four and it'll
+ 
+
+ align:start position:0%
+enter eight or two or four and it'll
+just do a cube because it's simple but
+
+ align:start position:0%
+just do a cube because it's simple but
+ 
+
+ align:start position:0%
+just do a cube because it's simple but
+you don't have to do a cube but the code
+
+ align:start position:0%
+you don't have to do a cube but the code
+ 
+
+ align:start position:0%
+you don't have to do a cube but the code
+does a cube on the nanohub so if I enter
+
+ align:start position:0%
+does a cube on the nanohub so if I enter
+ 
+
+ align:start position:0%
+does a cube on the nanohub so if I enter
+8 by 8 by 8 I get 512k points on the
+
+ align:start position:0%
+8 by 8 by 8 I get 512k points on the
+ 
+
+ align:start position:0%
+8 by 8 by 8 I get 512k points on the
+mesh and what that does is it allows me
+
+ align:start position:0%
+mesh and what that does is it allows me
+ 
+
+ align:start position:0%
+mesh and what that does is it allows me
+to um it it is it
+
+ align:start position:0%
+to um it it is it
+ 
+
+ align:start position:0%
+to um it it is it
+effectively is like increasing how much
+
+ align:start position:0%
+effectively is like increasing how much
+ 
+
+ align:start position:0%
+effectively is like increasing how much
+real space I had right because they're
+
+ align:start position:0%
+real space I had right because they're
+ 
+
+ align:start position:0%
+real space I had right because they're
+they're related if I had a larger unit
+
+ align:start position:0%
+they're related if I had a larger unit
+ 
+
+ align:start position:0%
+they're related if I had a larger unit
+cell with more real space I'd have finer
+
+ align:start position:0%
+cell with more real space I'd have finer
+ 
+
+ align:start position:0%
+cell with more real space I'd have finer
+finer uh um Cas space and and so you can
+
+ align:start position:0%
+finer uh um Cas space and and so you can
+ 
+
+ align:start position:0%
+finer uh um Cas space and and so you can
+think about these things as being able
+
+ align:start position:0%
+think about these things as being able
+ 
+
+ align:start position:0%
+think about these things as being able
+to go back and
+
+ align:start position:0%
+to go back and
+ 
+
+ align:start position:0%
+to go back and
+forth
+
+ align:start position:0%
+forth
+ 
+
+ align:start position:0%
+forth
+right okay now the reason that you don't
+
+ align:start position:0%
+right okay now the reason that you don't
+ 
+
+ align:start position:0%
+right okay now the reason that you don't
+go to and now oh well how many k points
+
+ align:start position:0%
+go to and now oh well how many k points
+ 
+
+ align:start position:0%
+go to and now oh well how many k points
+do you need well you need to have enough
+
+ align:start position:0%
+do you need well you need to have enough
+ 
+
+ align:start position:0%
+do you need well you need to have enough
+K points you need to distribute K points
+
+ align:start position:0%
+K points you need to distribute K points
+ 
+
+ align:start position:0%
+K points you need to distribute K points
+in your bran Zone such that what what's
+
+ align:start position:0%
+in your bran Zone such that what what's
+ 
+
+ align:start position:0%
+in your bran Zone such that what what's
+the answer how many k points do I need
+
+ align:start position:0%
+the answer how many k points do I need
+ 
+
+ align:start position:0%
+the answer how many k points do I need
+it's my favorite answer
+
+ align:start position:0%
+it's my favorite answer
+ 
+
+ align:start position:0%
+it's my favorite answer
+depends it
+
+ align:start position:0%
+depends it
+ 
+
+ align:start position:0%
+depends it
+depends what does it depend on did that
+
+ align:start position:0%
+depends what does it depend on did that
+ 
+
+ align:start position:0%
+depends what does it depend on did that
+come from the back I love it what does
+
+ align:start position:0%
+come from the back I love it what does
+ 
+
+ align:start position:0%
+come from the back I love it what does
+it depend
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+on okay it might depend on the
+
+ align:start position:0%
+on okay it might depend on the
+ 
+
+ align:start position:0%
+on okay it might depend on the
+electrons what else might it depend on
+
+ align:start position:0%
+electrons what else might it depend on
+ 
+
+ align:start position:0%
+electrons what else might it depend on
+how many k points do I
+
+ align:start position:0%
+how many k points do I
+ 
+
+ align:start position:0%
+how many k points do I
+need okay yes yes look at this picture
+
+ align:start position:0%
+need okay yes yes look at this picture
+ 
+
+ align:start position:0%
+need okay yes yes look at this picture
+let's look back at this picture think
+
+ align:start position:0%
+let's look back at this picture think
+ 
+
+ align:start position:0%
+let's look back at this picture think
+about this and now try to think about
+
+ align:start position:0%
+about this and now try to think about
+ 
+
+ align:start position:0%
+about this and now try to think about
+how many k points do I
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+needu exactly I need enough right now
+
+ align:start position:0%
+needu exactly I need enough right now
+ 
+
+ align:start position:0%
+needu exactly I need enough right now
+what's enough well enough so that you
+
+ align:start position:0%
+what's enough well enough so that you
+ 
+
+ align:start position:0%
+what's enough well enough so that you
+can
+
+ align:start position:0%
+can
+ 
+
+ align:start position:0%
+can
+resolve how the energy is going to
+
+ align:start position:0%
+resolve how the energy is going to
+ 
+
+ align:start position:0%
+resolve how the energy is going to
+change
+
+ align:start position:0%
+change
+ 
+
+ align:start position:0%
+change
+okay so now tell me if the Wiggles
+
+ align:start position:0%
+okay so now tell me if the Wiggles
+ 
+
+ align:start position:0%
+okay so now tell me if the Wiggles
+are are slow and not so much right
+
+ align:start position:0%
+are are slow and not so much right
+ 
+
+ align:start position:0%
+are are slow and not so much right
+if the Wiggles are like this or maybe
+
+ align:start position:0%
+if the Wiggles are like this or maybe
+ 
+
+ align:start position:0%
+if the Wiggles are like this or maybe
+even they're really flat do I need a lot
+
+ align:start position:0%
+even they're really flat do I need a lot
+ 
+
+ align:start position:0%
+even they're really flat do I need a lot
+of K points or a little bit of K
+
+ align:start position:0%
+of K points or a little bit of K
+ 
+
+ align:start position:0%
+of K points or a little bit of K
+points how many a
+
+ align:start position:0%
+points how many a
+ 
+
+ align:start position:0%
+points how many a
+lot just a little bit because there's
+
+ align:start position:0%
+lot just a little bit because there's
+ 
+
+ align:start position:0%
+lot just a little bit because there's
+just not that much variation but if the
+
+ align:start position:0%
+just not that much variation but if the
+ 
+
+ align:start position:0%
+just not that much variation but if the
+Wiggles look like
+
+ align:start position:0%
+Wiggles look like
+ 
+
+ align:start position:0%
+Wiggles look like
+this would I need a lot or a little
+
+ align:start position:0%
+this would I need a lot or a little
+ 
+
+ align:start position:0%
+this would I need a lot or a little
+right and and so this is the behavior of
+
+ align:start position:0%
+right and and so this is the behavior of
+ 
+
+ align:start position:0%
+right and and so this is the behavior of
+of bands that look like this are more
+
+ align:start position:0%
+of bands that look like this are more
+ 
+
+ align:start position:0%
+of bands that look like this are more
+sort of
+
+ align:start position:0%
+sort of
+ 
+
+ align:start position:0%
+sort of
+metallicy okay and the behavior of bands
+
+ align:start position:0%
+metallicy okay and the behavior of bands
+ 
+
+ align:start position:0%
+metallicy okay and the behavior of bands
+that look like this the the flat ones
+
+ align:start position:0%
+that look like this the the flat ones
+ 
+
+ align:start position:0%
+that look like this the the flat ones
+are more kind of like insulator
+
+ align:start position:0%
+are more kind of like insulator
+ 
+
+ align:start position:0%
+are more kind of like insulator
+e okay and in between and we'll see on
+
+ align:start position:0%
+e okay and in between and we'll see on
+ 
+
+ align:start position:0%
+e okay and in between and we'll see on
+Thursday we'll talk about how you can
+
+ align:start position:0%
+Thursday we'll talk about how you can
+ 
+
+ align:start position:0%
+Thursday we'll talk about how you can
+actually calculate the mobility from
+
+ align:start position:0%
+actually calculate the mobility from
+ 
+
+ align:start position:0%
+actually calculate the mobility from
+these bands from this wiggle okay um and
+
+ align:start position:0%
+these bands from this wiggle okay um and
+ 
+
+ align:start position:0%
+these bands from this wiggle okay um and
+but you can um how many do you need well
+
+ align:start position:0%
+but you can um how many do you need well
+ 
+
+ align:start position:0%
+but you can um how many do you need well
+it depends it depends on the nature of
+
+ align:start position:0%
+it depends it depends on the nature of
+ 
+
+ align:start position:0%
+it depends it depends on the nature of
+the material but you have to converge
+
+ align:start position:0%
+the material but you have to converge
+ 
+
+ align:start position:0%
+the material but you have to converge
+that that's part of that responsibility
+
+ align:start position:0%
+that that's part of that responsibility
+ 
+
+ align:start position:0%
+that that's part of that responsibility
+Spider-Man's Uncle knew all about it
+
+ align:start position:0%
+Spider-Man's Uncle knew all about it
+ 
+
+ align:start position:0%
+Spider-Man's Uncle knew all about it
+okay and so this is sort of where we
+
+ align:start position:0%
+okay and so this is sort of where we
+ 
+
+ align:start position:0%
+okay and so this is sort of where we
+ended
+
+ align:start position:0%
+ended
+ 
+
+ align:start position:0%
+ended
+oh man come on there we go this is where
+
+ align:start position:0%
+oh man come on there we go this is where
+ 
+
+ align:start position:0%
+oh man come on there we go this is where
+we ended and you know so you have energy
+
+ align:start position:0%
+we ended and you know so you have energy
+ 
+
+ align:start position:0%
+we ended and you know so you have energy
+levels in the bran Zone um K is a
+
+ align:start position:0%
+levels in the bran Zone um K is a
+ 
+
+ align:start position:0%
+levels in the bran Zone um K is a
+continuous variable but you don't
+
+ align:start position:0%
+continuous variable but you don't
+ 
+
+ align:start position:0%
+continuous variable but you don't
+actually continue it everywhere because
+
+ align:start position:0%
+actually continue it everywhere because
+ 
+
+ align:start position:0%
+actually continue it everywhere because
+it's too hard so you just do what the
+
+ align:start position:0%
+it's too hard so you just do what the
+ 
+
+ align:start position:0%
+it's too hard so you just do what the
+computer does is a bunch of calculations
+
+ align:start position:0%
+computer does is a bunch of calculations
+ 
+
+ align:start position:0%
+computer does is a bunch of calculations
+at different K points on the grid you
+
+ align:start position:0%
+at different K points on the grid you
+ 
+
+ align:start position:0%
+at different K points on the grid you
+give it okay um and what you're doing
+
+ align:start position:0%
+give it okay um and what you're doing
+ 
+
+ align:start position:0%
+give it okay um and what you're doing
+then is you're moving through when you
+
+ align:start position:0%
+then is you're moving through when you
+ 
+
+ align:start position:0%
+then is you're moving through when you
+give it different cas points literally
+
+ align:start position:0%
+give it different cas points literally
+ 
+
+ align:start position:0%
+give it different cas points literally
+this is what you do you say compute the
+
+ align:start position:0%
+this is what you do you say compute the
+ 
+
+ align:start position:0%
+this is what you do you say compute the
+the what what the computer is doing is
+
+ align:start position:0%
+the what what the computer is doing is
+ 
+
+ align:start position:0%
+the what what the computer is doing is
+it's saying compute the energy levels at
+
+ align:start position:0%
+it's saying compute the energy levels at
+ 
+
+ align:start position:0%
+it's saying compute the energy levels at
+k. now compute the energy levels at K
+
+ align:start position:0%
+k. now compute the energy levels at K
+ 
+
+ align:start position:0%
+k. now compute the energy levels at K
+point you know uh.
+
+ align:start position:0%
+point you know uh.
+ 
+
+ align:start position:0%
+point you know uh.
+1.1.1 right and you literally just give
+
+ align:start position:0%
+1.1.1 right and you literally just give
+ 
+
+ align:start position:0%
+1.1.1 right and you literally just give
+it coordinates of K points within the
+
+ align:start position:0%
+it coordinates of K points within the
+ 
+
+ align:start position:0%
+it coordinates of K points within the
+Broan Zone and for each of those K
+
+ align:start position:0%
+Broan Zone and for each of those K
+ 
+
+ align:start position:0%
+Broan Zone and for each of those K
+points it does the calculations and it
+
+ align:start position:0%
+points it does the calculations and it
+ 
+
+ align:start position:0%
+points it does the calculations and it
+finds a set of energy levels which are
+
+ align:start position:0%
+finds a set of energy levels which are
+ 
+
+ align:start position:0%
+finds a set of energy levels which are
+different and those and then you fill
+
+ align:start position:0%
+different and those and then you fill
+ 
+
+ align:start position:0%
+different and those and then you fill
+that in and you get your curvy bands
+
+ align:start position:0%
+that in and you get your curvy bands
+ 
+
+ align:start position:0%
+that in and you get your curvy bands
+okay who's with me who's who's got
+
+ align:start position:0%
+okay who's with me who's who's got
+ 
+
+ align:start position:0%
+okay who's with me who's who's got
+questions anyone have
+
+ align:start position:0%
+questions anyone have
+ 
+
+ align:start position:0%
+questions anyone have
+questions that's the new yeah so each is
+
+ align:start position:0%
+questions that's the new yeah so each is
+ 
+
+ align:start position:0%
+questions that's the new yeah so each is
+a distinct number of energy
+
+ align:start position:0%
+a distinct number of energy
+ 
+
+ align:start position:0%
+a distinct number of energy
+states yeah well each K point is the
+
+ align:start position:0%
+states yeah well each K point is the
+ 
+
+ align:start position:0%
+states yeah well each K point is the
+same number of of energy states but they
+
+ align:start position:0%
+same number of of energy states but they
+ 
+
+ align:start position:0%
+same number of of energy states but they
+can move
+
+ align:start position:0%
+can move
+ 
+
+ align:start position:0%
+can move
+around depending on where you are in
+
+ align:start position:0%
+around depending on where you are in
+ 
+
+ align:start position:0%
+around depending on where you are in
+that BR one zone okay and their moving
+
+ align:start position:0%
+that BR one zone okay and their moving
+ 
+
+ align:start position:0%
+that BR one zone okay and their moving
+around this is what gives you the band
+
+ align:start position:0%
+around this is what gives you the band
+ 
+
+ align:start position:0%
+around this is what gives you the band
+structure
+
+ align:start position:0%
+structure
+ 
+
+ align:start position:0%
+structure
+um so you know in the code and and this
+
+ align:start position:0%
+um so you know in the code and and this
+ 
+
+ align:start position:0%
+um so you know in the code and and this
+on the previous slide I didn't talk
+
+ align:start position:0%
+on the previous slide I didn't talk
+ 
+
+ align:start position:0%
+on the previous slide I didn't talk
+about it was the second point but on the
+
+ align:start position:0%
+about it was the second point but on the
+ 
+
+ align:start position:0%
+about it was the second point but on the
+code you you know each one of these you
+
+ align:start position:0%
+code you you know each one of these you
+ 
+
+ align:start position:0%
+code you you know each one of these you
+can think of as sort of occupied by
+
+ align:start position:0%
+can think of as sort of occupied by
+ 
+
+ align:start position:0%
+can think of as sort of occupied by
+electrons okay because it's it's sort of
+
+ align:start position:0%
+electrons okay because it's it's sort of
+ 
+
+ align:start position:0%
+electrons okay because it's it's sort of
+looking at this K point right and then
+
+ align:start position:0%
+looking at this K point right and then
+ 
+
+ align:start position:0%
+looking at this K point right and then
+this K Point um but when you think about
+
+ align:start position:0%
+this K Point um but when you think about
+ 
+
+ align:start position:0%
+this K Point um but when you think about
+the full band structure of a material
+
+ align:start position:0%
+the full band structure of a material
+ 
+
+ align:start position:0%
+the full band structure of a material
+that is not how you look at it right do
+
+ align:start position:0%
+that is not how you look at it right do
+ 
+
+ align:start position:0%
+that is not how you look at it right do
+you don't have you know you would to
+
+ align:start position:0%
+you don't have you know you would to
+ 
+
+ align:start position:0%
+you don't have you know you would to
+keep increasing your cap mes you would
+
+ align:start position:0%
+keep increasing your cap mes you would
+ 
+
+ align:start position:0%
+keep increasing your cap mes you would
+have infinite number of electrons in a
+
+ align:start position:0%
+have infinite number of electrons in a
+ 
+
+ align:start position:0%
+have infinite number of electrons in a
+band um that is not the case what you
+
+ align:start position:0%
+band um that is not the case what you
+ 
+
+ align:start position:0%
+band um that is not the case what you
+have is the same as before the same
+
+ align:start position:0%
+have is the same as before the same
+ 
+
+ align:start position:0%
+have is the same as before the same
+exact thing as you know molecular states
+
+ align:start position:0%
+exact thing as you know molecular states
+ 
+
+ align:start position:0%
+exact thing as you know molecular states
+which is that you can have one band can
+
+ align:start position:0%
+which is that you can have one band can
+ 
+
+ align:start position:0%
+which is that you can have one band can
+hold two electrons one up one down
+
+ align:start position:0%
+hold two electrons one up one down
+ 
+
+ align:start position:0%
+hold two electrons one up one down
+that's exactly the same as as in you
+
+ align:start position:0%
+that's exactly the same as as in you
+ 
+
+ align:start position:0%
+that's exactly the same as as in you
+know a molecular
+
+ align:start position:0%
+know a molecular
+ 
+
+ align:start position:0%
+know a molecular
+State
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay but depending on where you are in
+
+ align:start position:0%
+okay but depending on where you are in
+ 
+
+ align:start position:0%
+okay but depending on where you are in
+the bruan zone the energy of that that
+
+ align:start position:0%
+the bruan zone the energy of that that
+ 
+
+ align:start position:0%
+the bruan zone the energy of that that
+band now can change dramatically and
+
+ align:start position:0%
+band now can change dramatically and
+ 
+
+ align:start position:0%
+band now can change dramatically and
+that changes everything in terms of
+
+ align:start position:0%
+that changes everything in terms of
+ 
+
+ align:start position:0%
+that changes everything in terms of
+properties of material in particular
+
+ align:start position:0%
+properties of material in particular
+ 
+
+ align:start position:0%
+properties of material in particular
+what we're focusing on here is Optical
+
+ align:start position:0%
+what we're focusing on here is Optical
+ 
+
+ align:start position:0%
+what we're focusing on here is Optical
+properties in electronic properties
+
+ align:start position:0%
+properties in electronic properties
+ 
+
+ align:start position:0%
+properties in electronic properties
+because those are very Quantum
+
+ align:start position:0%
+because those are very Quantum
+ 
+
+ align:start position:0%
+because those are very Quantum
+mechanically which we like okay now and
+
+ align:start position:0%
+mechanically which we like okay now and
+ 
+
+ align:start position:0%
+mechanically which we like okay now and
+the firmy energy is um in in the code
+
+ align:start position:0%
+the firmy energy is um in in the code
+ 
+
+ align:start position:0%
+the firmy energy is um in in the code
+the we talked about the firmy energy a
+
+ align:start position:0%
+the we talked about the firmy energy a
+ 
+
+ align:start position:0%
+the we talked about the firmy energy a
+little bit for molecules um it's sort of
+
+ align:start position:0%
+little bit for molecules um it's sort of
+ 
+
+ align:start position:0%
+little bit for molecules um it's sort of
+the energy at which you stop filling
+
+ align:start position:0%
+the energy at which you stop filling
+ 
+
+ align:start position:0%
+the energy at which you stop filling
+right it's it's the energy so you you
+
+ align:start position:0%
+right it's it's the energy so you you
+ 
+
+ align:start position:0%
+right it's it's the energy so you you
+fill your bands up to the fir you can
+
+ align:start position:0%
+fill your bands up to the fir you can
+ 
+
+ align:start position:0%
+fill your bands up to the fir you can
+just think about it that way okay don't
+
+ align:start position:0%
+just think about it that way okay don't
+ 
+
+ align:start position:0%
+just think about it that way okay don't
+worry about so much about whether it's
+
+ align:start position:0%
+worry about so much about whether it's
+ 
+
+ align:start position:0%
+worry about so much about whether it's
+in the gap or where it is in the Gap we
+
+ align:start position:0%
+in the gap or where it is in the Gap we
+ 
+
+ align:start position:0%
+in the gap or where it is in the Gap we
+don't need to worry about that in this
+
+ align:start position:0%
+don't need to worry about that in this
+ 
+
+ align:start position:0%
+don't need to worry about that in this
+class okay but it is the energy at where
+
+ align:start position:0%
+class okay but it is the energy at where
+ 
+
+ align:start position:0%
+class okay but it is the energy at where
+at which you stop filling and so you can
+
+ align:start position:0%
+at which you stop filling and so you can
+ 
+
+ align:start position:0%
+at which you stop filling and so you can
+see that um if you oh I have some
+
+ align:start position:0%
+see that um if you oh I have some
+ 
+
+ align:start position:0%
+see that um if you oh I have some
+properties I thought I had something
+
+ align:start position:0%
+properties I thought I had something
+ 
+
+ align:start position:0%
+properties I thought I had something
+else but if
+
+ align:start position:0%
+else but if
+ 
+
+ align:start position:0%
+else but if
+you if you were to um fill
+
+ align:start position:0%
+you if you were to um fill
+ 
+
+ align:start position:0%
+you if you were to um fill
+these and the bands and and these bands
+
+ align:start position:0%
+these and the bands and and these bands
+ 
+
+ align:start position:0%
+these and the bands and and these bands
+didn't stop nicely like this but they
+
+ align:start position:0%
+didn't stop nicely like this but they
+ 
+
+ align:start position:0%
+didn't stop nicely like this but they
+just kind of crossed over it what would
+
+ align:start position:0%
+just kind of crossed over it what would
+ 
+
+ align:start position:0%
+just kind of crossed over it what would
+you have what kind of material would you
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+have
+
+ align:start position:0%
+have
+ 
+
+ align:start position:0%
+have
+yeah it's a
+
+ align:start position:0%
+yeah it's a
+ 
+
+ align:start position:0%
+yeah it's a
+metal it's a metal right and if you if
+
+ align:start position:0%
+metal it's a metal right and if you if
+ 
+
+ align:start position:0%
+metal it's a metal right and if you if
+you have the bands stop where you stop
+
+ align:start position:0%
+you have the bands stop where you stop
+ 
+
+ align:start position:0%
+you have the bands stop where you stop
+filling and then there's a gap it's a
+
+ align:start position:0%
+filling and then there's a gap it's a
+ 
+
+ align:start position:0%
+filling and then there's a gap it's a
+semiconductor or an insulator okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um let's do a few
+
+ align:start position:0%
+um let's do a few
+ 
+
+ align:start position:0%
+um let's do a few
+calculations um and then I'll come back
+
+ align:start position:0%
+calculations um and then I'll come back
+ 
+
+ align:start position:0%
+calculations um and then I'll come back
+to structural properties okay we are on
+
+ align:start position:0%
+to structural properties okay we are on
+ 
+
+ align:start position:0%
+to structural properties okay we are on
+our favorite
+
+ align:start position:0%
+our favorite
+ 
+
+ align:start position:0%
+our favorite
+place the Hub of
+
+ align:start position:0%
+place the Hub of
+ 
+
+ align:start position:0%
+place the Hub of
+Nano right yeah okay come
+
+ align:start position:0%
+Nano right yeah okay come
+ 
+
+ align:start position:0%
+Nano right yeah okay come
+on yes okay we got to that
+
+ align:start position:0%
+on yes okay we got to that
+ 
+
+ align:start position:0%
+on yes okay we got to that
+stage launch Tool sounds like a good
+
+ align:start position:0%
+stage launch Tool sounds like a good
+ 
+
+ align:start position:0%
+stage launch Tool sounds like a good
+idea and
+
+ align:start position:0%
+idea and
+ 
+
+ align:start position:0%
+idea and
+this is where we we had some issues last
+
+ align:start position:0%
+this is where we we had some issues last
+ 
+
+ align:start position:0%
+this is where we we had some issues last
+time not going to kid you there it is
+
+ align:start position:0%
+time not going to kid you there it is
+ 
+
+ align:start position:0%
+time not going to kid you there it is
+okay and we go to here now let's do a
+
+ align:start position:0%
+okay and we go to here now let's do a
+ 
+
+ align:start position:0%
+okay and we go to here now let's do a
+few things
+
+ align:start position:0%
+few things
+ 
+
+ align:start position:0%
+few things
+okay um
+
+ align:start position:0%
+okay um
+ 
+
+ align:start position:0%
+okay um
+and okay so this is the same as okay so
+
+ align:start position:0%
+and okay so this is the same as okay so
+ 
+
+ align:start position:0%
+and okay so this is the same as okay so
+it's not letting me scroll again that's
+
+ align:start position:0%
+it's not letting me scroll again that's
+ 
+
+ align:start position:0%
+it's not letting me scroll again that's
+wonderful
+
+ align:start position:0%
+wonderful
+ 
+
+ align:start position:0%
+wonderful
+right
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um there it is okay now um this is the
+
+ align:start position:0%
+um there it is okay now um this is the
+ 
+
+ align:start position:0%
+um there it is okay now um this is the
+same as um as the tool that you're using
+
+ align:start position:0%
+same as um as the tool that you're using
+ 
+
+ align:start position:0%
+same as um as the tool that you're using
+for um for the homework number two okay
+
+ align:start position:0%
+for um for the homework number two okay
+ 
+
+ align:start position:0%
+for um for the homework number two okay
+to look at molecules and in looking at
+
+ align:start position:0%
+to look at molecules and in looking at
+ 
+
+ align:start position:0%
+to look at molecules and in looking at
+molecules you just select
+
+ align:start position:0%
+molecules you just select
+ 
+
+ align:start position:0%
+molecules you just select
+molecule but all the code is doing when
+
+ align:start position:0%
+molecule but all the code is doing when
+ 
+
+ align:start position:0%
+molecule but all the code is doing when
+you look at molecules you know all the
+
+ align:start position:0%
+you look at molecules you know all the
+ 
+
+ align:start position:0%
+you look at molecules you know all the
+code is doing is it's saying well
+
+ align:start position:0%
+code is doing is it's saying well
+ 
+
+ align:start position:0%
+code is doing is it's saying well
+whatever you give me you know whatever
+
+ align:start position:0%
+whatever you give me you know whatever
+ 
+
+ align:start position:0%
+whatever you give me you know whatever
+sort of thing you give me I'm G to put
+
+ align:start position:0%
+sort of thing you give me I'm G to put
+ 
+
+ align:start position:0%
+sort of thing you give me I'm G to put
+space in my you know in my periodic
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+cell I'm G to put enough space so that
+
+ align:start position:0%
+cell I'm G to put enough space so that
+ 
+
+ align:start position:0%
+cell I'm G to put enough space so that
+it doesn't see its own
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+image okay that's all it's doing it's
+
+ align:start position:0%
+image okay that's all it's doing it's
+ 
+
+ align:start position:0%
+image okay that's all it's doing it's
+still a periodic calculation it's just
+
+ align:start position:0%
+still a periodic calculation it's just
+ 
+
+ align:start position:0%
+still a periodic calculation it's just
+putting a whole bunch of space in there
+
+ align:start position:0%
+putting a whole bunch of space in there
+ 
+
+ align:start position:0%
+putting a whole bunch of space in there
+um you could choose solid and do
+
+ align:start position:0%
+um you could choose solid and do
+ 
+
+ align:start position:0%
+um you could choose solid and do
+molecule calculations and just make sure
+
+ align:start position:0%
+molecule calculations and just make sure
+ 
+
+ align:start position:0%
+molecule calculations and just make sure
+that that there's space between um what
+
+ align:start position:0%
+that that there's space between um what
+ 
+
+ align:start position:0%
+that that there's space between um what
+you put in
+
+ align:start position:0%
+you put in
+ 
+
+ align:start position:0%
+you put in
+okay however when you choose solid then
+
+ align:start position:0%
+okay however when you choose solid then
+ 
+
+ align:start position:0%
+okay however when you choose solid then
+um you can see that it's actually
+
+ align:start position:0%
+um you can see that it's actually
+ 
+
+ align:start position:0%
+um you can see that it's actually
+entering the coordinates in a different
+
+ align:start position:0%
+entering the coordinates in a different
+ 
+
+ align:start position:0%
+entering the coordinates in a different
+way it's using a slightly different
+
+ align:start position:0%
+way it's using a slightly different
+ 
+
+ align:start position:0%
+way it's using a slightly different
+language um has anybody seen n this
+
+ align:start position:0%
+language um has anybody seen n this
+ 
+
+ align:start position:0%
+language um has anybody seen n this
+beautiful non-scrolling
+
+ align:start position:0%
+beautiful non-scrolling
+ 
+
+ align:start position:0%
+beautiful non-scrolling
+thing
+
+ align:start position:0%
+thing
+ 
+
+ align:start position:0%
+thing
+man oh yeah well it's good to be
+
+ align:start position:0%
+man oh yeah well it's good to be
+ 
+
+ align:start position:0%
+man oh yeah well it's good to be
+challenged that's
+
+ align:start position:0%
+challenged that's
+ 
+
+ align:start position:0%
+challenged that's
+fun okay so uh
+
+ align:start position:0%
+fun okay so uh
+ 
+
+ align:start position:0%
+fun okay so uh
+you gota be kidding
+
+ align:start position:0%
+you gota be kidding
+ 
+
+ align:start position:0%
+you gota be kidding
+me did you see that coming did somebody
+
+ align:start position:0%
+me did you see that coming did somebody
+ 
+
+ align:start position:0%
+me did you see that coming did somebody
+see that
+
+ align:start position:0%
+see that
+ 
+
+ align:start position:0%
+see that
+coming all right should we go back to
+
+ align:start position:0%
+coming all right should we go back to
+ 
+
+ align:start position:0%
+coming all right should we go back to
+the uh to DJ Dave wait
+
+ align:start position:0%
+the uh to DJ Dave wait
+ 
+
+ align:start position:0%
+the uh to DJ Dave wait
+um what if I did um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Firefox is that
+
+ align:start position:0%
+Firefox is that
+ 
+
+ align:start position:0%
+Firefox is that
+better it's the same that's beautiful
+
+ align:start position:0%
+better it's the same that's beautiful
+ 
+
+ align:start position:0%
+better it's the same that's beautiful
+you get the same thing
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay it did remember me okay now let's
+
+ align:start position:0%
+okay it did remember me okay now let's
+ 
+
+ align:start position:0%
+okay it did remember me okay now let's
+close
+
+ align:start position:0%
+close
+ 
+
+ align:start position:0%
+close
+that how often does that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+happen but like what percentage would
+
+ align:start position:0%
+happen but like what percentage would
+ 
+
+ align:start position:0%
+happen but like what percentage would
+you
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+say 60% of the
+
+ align:start position:0%
+say 60% of the
+ 
+
+ align:start position:0%
+say 60% of the
+time
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+60 oh no no no you can't be this on a
+
+ align:start position:0%
+60 oh no no no you can't be this on a
+ 
+
+ align:start position:0%
+60 oh no no no you can't be this on a
+Mac this is because it's not a Mac okay
+
+ align:start position:0%
+Mac this is because it's not a Mac okay
+ 
+
+ align:start position:0%
+Mac this is because it's not a Mac okay
+thank you it must
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+be
+
+ align:start position:0%
+be
+ 
+
+ align:start position:0%
+be
+Windows well that's a big
+
+ align:start position:0%
+Windows well that's a big
+ 
+
+ align:start position:0%
+Windows well that's a big
+problem um okay so here we are this
+
+ align:start position:0%
+problem um okay so here we are this
+ 
+
+ align:start position:0%
+problem um okay so here we are this
+looks a little bit better now when you
+
+ align:start position:0%
+looks a little bit better now when you
+ 
+
+ align:start position:0%
+looks a little bit better now when you
+choose solid okay so now we have look at
+
+ align:start position:0%
+choose solid okay so now we have look at
+ 
+
+ align:start position:0%
+choose solid okay so now we have look at
+this you can choose your Crystal
+
+ align:start position:0%
+this you can choose your Crystal
+ 
+
+ align:start position:0%
+this you can choose your Crystal
+symmetry because it's a solid and
+
+ align:start position:0%
+symmetry because it's a solid and
+ 
+
+ align:start position:0%
+symmetry because it's a solid and
+remember those symmetries that you saw
+
+ align:start position:0%
+remember those symmetries that you saw
+ 
+
+ align:start position:0%
+remember those symmetries that you saw
+well these are those symmetries except
+
+ align:start position:0%
+well these are those symmetries except
+ 
+
+ align:start position:0%
+well these are those symmetries except
+now you have to choose a lattice
+
+ align:start position:0%
+now you have to choose a lattice
+ 
+
+ align:start position:0%
+now you have to choose a lattice
+constant see when you did the molecule
+
+ align:start position:0%
+constant see when you did the molecule
+ 
+
+ align:start position:0%
+constant see when you did the molecule
+the lattice constant was simply um big
+
+ align:start position:0%
+the lattice constant was simply um big
+ 
+
+ align:start position:0%
+the lattice constant was simply um big
+it was just big so that the molecule
+
+ align:start position:0%
+it was just big so that the molecule
+ 
+
+ align:start position:0%
+it was just big so that the molecule
+didn't feel its periodic image but now
+
+ align:start position:0%
+didn't feel its periodic image but now
+ 
+
+ align:start position:0%
+didn't feel its periodic image but now
+that we're doing a solid the lattice
+
+ align:start position:0%
+that we're doing a solid the lattice
+ 
+
+ align:start position:0%
+that we're doing a solid the lattice
+constant has to be well like the lattice
+
+ align:start position:0%
+constant has to be well like the lattice
+ 
+
+ align:start position:0%
+constant has to be well like the lattice
+constant right of the material and
+
+ align:start position:0%
+constant right of the material and
+ 
+
+ align:start position:0%
+constant right of the material and
+depending on the symmetry of the
+
+ align:start position:0%
+depending on the symmetry of the
+ 
+
+ align:start position:0%
+depending on the symmetry of the
+material you know you're going to get
+
+ align:start position:0%
+material you know you're going to get
+ 
+
+ align:start position:0%
+material you know you're going to get
+different lce constants so if I um now
+
+ align:start position:0%
+different lce constants so if I um now
+ 
+
+ align:start position:0%
+different lce constants so if I um now
+and have any of you seen fractional
+
+ align:start position:0%
+and have any of you seen fractional
+ 
+
+ align:start position:0%
+and have any of you seen fractional
+coordinates before do anybody know what
+
+ align:start position:0%
+coordinates before do anybody know what
+ 
+
+ align:start position:0%
+coordinates before do anybody know what
+this is
+
+ align:start position:0%
+this is
+ 
+
+ align:start position:0%
+this is
+so so this is actually an important
+
+ align:start position:0%
+so so this is actually an important
+ 
+
+ align:start position:0%
+so so this is actually an important
+language of solids um where you know
+
+ align:start position:0%
+language of solids um where you know
+ 
+
+ align:start position:0%
+language of solids um where you know
+often times so with a solid you have a
+
+ align:start position:0%
+often times so with a solid you have a
+ 
+
+ align:start position:0%
+often times so with a solid you have a
+periodically repeating space that is set
+
+ align:start position:0%
+periodically repeating space that is set
+ 
+
+ align:start position:0%
+periodically repeating space that is set
+by a lattice constant and so often it's
+
+ align:start position:0%
+by a lattice constant and so often it's
+ 
+
+ align:start position:0%
+by a lattice constant and so often it's
+um it's sort of simpler to think about
+
+ align:start position:0%
+um it's sort of simpler to think about
+ 
+
+ align:start position:0%
+um it's sort of simpler to think about
+the coordinates that go inside that
+
+ align:start position:0%
+the coordinates that go inside that
+ 
+
+ align:start position:0%
+the coordinates that go inside that
+space the basis if you want as fractions
+
+ align:start position:0%
+space the basis if you want as fractions
+ 
+
+ align:start position:0%
+space the basis if you want as fractions
+of the
+
+ align:start position:0%
+of the
+ 
+
+ align:start position:0%
+of the
+lattice right so for silicon actually
+
+ align:start position:0%
+lattice right so for silicon actually
+ 
+
+ align:start position:0%
+lattice right so for silicon actually
+for silicon it's an FCC cryst
+
+ align:start position:0%
+for silicon it's an FCC cryst
+ 
+
+ align:start position:0%
+for silicon it's an FCC cryst
+C with a basis at one corner of the FCC
+
+ align:start position:0%
+C with a basis at one corner of the FCC
+ 
+
+ align:start position:0%
+C with a basis at one corner of the FCC
+and another atom at a quarter quarter
+
+ align:start position:0%
+and another atom at a quarter quarter
+ 
+
+ align:start position:0%
+and another atom at a quarter quarter
+quarter out in terms of the lattice this
+
+ align:start position:0%
+quarter out in terms of the lattice this
+ 
+
+ align:start position:0%
+quarter out in terms of the lattice this
+is not at a quarter quarter quarter
+
+ align:start position:0%
+is not at a quarter quarter quarter
+ 
+
+ align:start position:0%
+is not at a quarter quarter quarter
+ingstrom right this is a quarter quarter
+
+ align:start position:0%
+ingstrom right this is a quarter quarter
+ 
+
+ align:start position:0%
+ingstrom right this is a quarter quarter
+quarter scaled by that
+
+ align:start position:0%
+quarter scaled by that
+ 
+
+ align:start position:0%
+quarter scaled by that
+lattice okay does everybody see that
+
+ align:start position:0%
+lattice okay does everybody see that
+ 
+
+ align:start position:0%
+lattice okay does everybody see that
+which is a cubic face centered
+
+ align:start position:0%
+which is a cubic face centered
+ 
+
+ align:start position:0%
+which is a cubic face centered
+lattice okay so that's fractional
+
+ align:start position:0%
+lattice okay so that's fractional
+ 
+
+ align:start position:0%
+lattice okay so that's fractional
+coordinates you can go back and forth I
+
+ align:start position:0%
+coordinates you can go back and forth I
+ 
+
+ align:start position:0%
+coordinates you can go back and forth I
+mean you can you know you can write a
+
+ align:start position:0%
+mean you can you know you can write a
+ 
+
+ align:start position:0%
+mean you can you know you can write a
+10line you know python script to go back
+
+ align:start position:0%
+10line you know python script to go back
+ 
+
+ align:start position:0%
+10line you know python script to go back
+and forth between the two but in solids
+
+ align:start position:0%
+and forth between the two but in solids
+ 
+
+ align:start position:0%
+and forth between the two but in solids
+often we like to think about positions
+
+ align:start position:0%
+often we like to think about positions
+ 
+
+ align:start position:0%
+often we like to think about positions
+in terms of the symmetry of the lattice
+
+ align:start position:0%
+in terms of the symmetry of the lattice
+ 
+
+ align:start position:0%
+in terms of the symmetry of the lattice
+and so that's how we write them okay now
+
+ align:start position:0%
+and so that's how we write them okay now
+ 
+
+ align:start position:0%
+and so that's how we write them okay now
+in this case I have two silicon
+
+ align:start position:0%
+in this case I have two silicon
+ 
+
+ align:start position:0%
+in this case I have two silicon
+atoms
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and um we're going to ignore everything
+
+ align:start position:0%
+and um we're going to ignore everything
+ 
+
+ align:start position:0%
+and um we're going to ignore everything
+and just run
+
+ align:start position:0%
+and just run
+ 
+
+ align:start position:0%
+and just run
+it is that how you guys do it anyway you
+
+ align:start position:0%
+it is that how you guys do it anyway you
+ 
+
+ align:start position:0%
+it is that how you guys do it anyway you
+just like
+
+ align:start position:0%
+just like
+ 
+
+ align:start position:0%
+just like
+simulate it's fun to do that just
+
+ align:start position:0%
+simulate it's fun to do that just
+ 
+
+ align:start position:0%
+simulate it's fun to do that just
+simulate um
+
+ align:start position:0%
+simulate um
+ 
+
+ align:start position:0%
+simulate um
+except that you need to kind of know
+
+ align:start position:0%
+except that you need to kind of know
+ 
+
+ align:start position:0%
+except that you need to kind of know
+what you did um now that's what I I want
+
+ align:start position:0%
+what you did um now that's what I I want
+ 
+
+ align:start position:0%
+what you did um now that's what I I want
+to ask you about is what did I do okay
+
+ align:start position:0%
+to ask you about is what did I do okay
+ 
+
+ align:start position:0%
+to ask you about is what did I do okay
+oh look at that this is solid I only
+
+ align:start position:0%
+oh look at that this is solid I only
+ 
+
+ align:start position:0%
+oh look at that this is solid I only
+gave it two atoms and yet because it has
+
+ align:start position:0%
+gave it two atoms and yet because it has
+ 
+
+ align:start position:0%
+gave it two atoms and yet because it has
+the Symmetry and the lattice and all
+
+ align:start position:0%
+the Symmetry and the lattice and all
+ 
+
+ align:start position:0%
+the Symmetry and the lattice and all
+that it knows how to construct a solid
+
+ align:start position:0%
+that it knows how to construct a solid
+ 
+
+ align:start position:0%
+that it knows how to construct a solid
+right that's what it looks like when the
+
+ align:start position:0%
+right that's what it looks like when the
+ 
+
+ align:start position:0%
+right that's what it looks like when the
+computer thinks about it it thinks about
+
+ align:start position:0%
+computer thinks about it it thinks about
+ 
+
+ align:start position:0%
+computer thinks about it it thinks about
+it like that um uh
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+oh where's the
+
+ align:start position:0%
+oh where's the
+ 
+
+ align:start position:0%
+oh where's the
+oh here we
+
+ align:start position:0%
+oh here we
+ 
+
+ align:start position:0%
+oh here we
+go now key outputs
+
+ align:start position:0%
+go now key outputs
+ 
+
+ align:start position:0%
+go now key outputs
+okay it's telling you that um it has
+
+ align:start position:0%
+okay it's telling you that um it has
+ 
+
+ align:start position:0%
+okay it's telling you that um it has
+well these should really be four um it
+
+ align:start position:0%
+well these should really be four um it
+ 
+
+ align:start position:0%
+well these should really be four um it
+has four up electrons and four down
+
+ align:start position:0%
+has four up electrons and four down
+ 
+
+ align:start position:0%
+has four up electrons and four down
+electrons okay that doesn't sound like
+
+ align:start position:0%
+electrons okay that doesn't sound like
+ 
+
+ align:start position:0%
+electrons okay that doesn't sound like
+that many electrons how come I only have
+
+ align:start position:0%
+that many electrons how come I only have
+ 
+
+ align:start position:0%
+that many electrons how come I only have
+eight electrons in my simulation and I'm
+
+ align:start position:0%
+eight electrons in my simulation and I'm
+ 
+
+ align:start position:0%
+eight electrons in my simulation and I'm
+simulating like an infinite
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Crystal yeah okay so very good but how
+
+ align:start position:0%
+Crystal yeah okay so very good but how
+ 
+
+ align:start position:0%
+Crystal yeah okay so very good but how
+come okay so it's only the veence
+
+ align:start position:0%
+come okay so it's only the veence
+ 
+
+ align:start position:0%
+come okay so it's only the veence
+because that's where all the chemistry
+
+ align:start position:0%
+because that's where all the chemistry
+ 
+
+ align:start position:0%
+because that's where all the chemistry
+happens we talked about that but um why
+
+ align:start position:0%
+happens we talked about that but um why
+ 
+
+ align:start position:0%
+happens we talked about that but um why
+are there only two atoms how can I
+
+ align:start position:0%
+are there only two atoms how can I
+ 
+
+ align:start position:0%
+are there only two atoms how can I
+simulate a solid with only two
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+atoms because it's
+
+ align:start position:0%
+atoms because it's
+ 
+
+ align:start position:0%
+atoms because it's
+symmetric
+
+ align:start position:0%
+symmetric
+ 
+
+ align:start position:0%
+symmetric
+however because I only have two atoms
+
+ align:start position:0%
+however because I only have two atoms
+ 
+
+ align:start position:0%
+however because I only have two atoms
+especially and it's symmetric and it
+
+ align:start position:0%
+especially and it's symmetric and it
+ 
+
+ align:start position:0%
+especially and it's symmetric and it
+repeats I need to worry about the
+
+ align:start position:0%
+repeats I need to worry about the
+ 
+
+ align:start position:0%
+repeats I need to worry about the
+convergence of what which we just talked
+
+ align:start position:0%
+convergence of what which we just talked
+ 
+
+ align:start position:0%
+convergence of what which we just talked
+about
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and so you saw the density States we've
+
+ align:start position:0%
+and so you saw the density States we've
+ 
+
+ align:start position:0%
+and so you saw the density States we've
+talked about oh this beautiful look at
+
+ align:start position:0%
+talked about oh this beautiful look at
+ 
+
+ align:start position:0%
+talked about oh this beautiful look at
+this it's beautiful right those are the
+
+ align:start position:0%
+this it's beautiful right those are the
+ 
+
+ align:start position:0%
+this it's beautiful right those are the
+peaks of the solid of of Crystal and
+
+ align:start position:0%
+peaks of the solid of of Crystal and
+ 
+
+ align:start position:0%
+peaks of the solid of of Crystal and
+silicon it's just like in the molecules
+
+ align:start position:0%
+silicon it's just like in the molecules
+ 
+
+ align:start position:0%
+silicon it's just like in the molecules
+in the molecules we had the levels and
+
+ align:start position:0%
+in the molecules we had the levels and
+ 
+
+ align:start position:0%
+in the molecules we had the levels and
+we turn them on their
+
+ align:start position:0%
+we turn them on their
+ 
+
+ align:start position:0%
+we turn them on their
+side we turned the levels on their side
+
+ align:start position:0%
+side we turned the levels on their side
+ 
+
+ align:start position:0%
+side we turned the levels on their side
+and we said that's the same as the Doss
+
+ align:start position:0%
+and we said that's the same as the Doss
+ 
+
+ align:start position:0%
+and we said that's the same as the Doss
+but in the solid it's the band structure
+
+ align:start position:0%
+but in the solid it's the band structure
+ 
+
+ align:start position:0%
+but in the solid it's the band structure
+we turn on its side here's the band
+
+ align:start position:0%
+we turn on its side here's the band
+ 
+
+ align:start position:0%
+we turn on its side here's the band
+structure
+
+ align:start position:0%
+structure
+ 
+
+ align:start position:0%
+structure
+okay so those are my levels now those
+
+ align:start position:0%
+okay so those are my levels now those
+ 
+
+ align:start position:0%
+okay so those are my levels now those
+are my levels they're Wiggly in
+
+ align:start position:0%
+are my levels they're Wiggly in
+ 
+
+ align:start position:0%
+are my levels they're Wiggly in
+reciprocal space but if I turn I can
+
+ align:start position:0%
+reciprocal space but if I turn I can
+ 
+
+ align:start position:0%
+reciprocal space but if I turn I can
+still turn them on their side and when I
+
+ align:start position:0%
+still turn them on their side and when I
+ 
+
+ align:start position:0%
+still turn them on their side and when I
+do that I get the density of states
+
+ align:start position:0%
+do that I get the density of states
+ 
+
+ align:start position:0%
+do that I get the density of states
+right directly comparable to the
+
+ align:start position:0%
+right directly comparable to the
+ 
+
+ align:start position:0%
+right directly comparable to the
+situation of of the molecules but in the
+
+ align:start position:0%
+situation of of the molecules but in the
+ 
+
+ align:start position:0%
+situation of of the molecules but in the
+molecules what I turned on the side
+
+ align:start position:0%
+molecules what I turned on the side
+ 
+
+ align:start position:0%
+molecules what I turned on the side
+didn't wiggle okay does everybody see
+
+ align:start position:0%
+didn't wiggle okay does everybody see
+ 
+
+ align:start position:0%
+didn't wiggle okay does everybody see
+that okay so there's the band structure
+
+ align:start position:0%
+that okay so there's the band structure
+ 
+
+ align:start position:0%
+that okay so there's the band structure
+now this is um the Nano Hub has issues
+
+ align:start position:0%
+now this is um the Nano Hub has issues
+ 
+
+ align:start position:0%
+now this is um the Nano Hub has issues
+with putting um Greek letters on plots
+
+ align:start position:0%
+with putting um Greek letters on plots
+ 
+
+ align:start position:0%
+with putting um Greek letters on plots
+so this is the band structure with the
+
+ align:start position:0%
+so this is the band structure with the
+ 
+
+ align:start position:0%
+so this is the band structure with the
+Greek letters and I'll talk about well
+
+ align:start position:0%
+Greek letters and I'll talk about well
+ 
+
+ align:start position:0%
+Greek letters and I'll talk about well
+actually I don't need to wait these just
+
+ align:start position:0%
+actually I don't need to wait these just
+ 
+
+ align:start position:0%
+actually I don't need to wait these just
+correspond to different points in that
+
+ align:start position:0%
+correspond to different points in that
+ 
+
+ align:start position:0%
+correspond to different points in that
+bran zone right you you cruise through
+
+ align:start position:0%
+bran zone right you you cruise through
+ 
+
+ align:start position:0%
+bran zone right you you cruise through
+phase space in the bran Zone and you
+
+ align:start position:0%
+phase space in the bran Zone and you
+ 
+
+ align:start position:0%
+phase space in the bran Zone and you
+plot the energies the code is plotting
+
+ align:start position:0%
+plot the energies the code is plotting
+ 
+
+ align:start position:0%
+plot the energies the code is plotting
+the energies along that that path so you
+
+ align:start position:0%
+the energies along that that path so you
+ 
+
+ align:start position:0%
+the energies along that that path so you
+get a sense of the
+
+ align:start position:0%
+get a sense of the
+ 
+
+ align:start position:0%
+get a sense of the
+variation could these
+
+ align:start position:0%
+variation could these
+ 
+
+ align:start position:0%
+variation could these
+energies vary differently than I've
+
+ align:start position:0%
+energies vary differently than I've
+ 
+
+ align:start position:0%
+energies vary differently than I've
+plotted
+
+ align:start position:0%
+plotted
+ 
+
+ align:start position:0%
+plotted
+here could they vary
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+differently how could they vary
+
+ align:start position:0%
+differently how could they vary
+ 
+
+ align:start position:0%
+differently how could they vary
+differently the answer is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yes this is a cruise through face Bas
+
+ align:start position:0%
+yes this is a cruise through face Bas
+ 
+
+ align:start position:0%
+yes this is a cruise through face Bas
+gamma is always the origin gamma is at
+
+ align:start position:0%
+gamma is always the origin gamma is at
+ 
+
+ align:start position:0%
+gamma is always the origin gamma is at
+k. and then I went to some other K point
+
+ align:start position:0%
+k. and then I went to some other K point
+ 
+
+ align:start position:0%
+k. and then I went to some other K point
+and we called it X we like to give High
+
+ align:start position:0%
+and we called it X we like to give High
+ 
+
+ align:start position:0%
+and we called it X we like to give High
+symmetry um points in the bran Zone a
+
+ align:start position:0%
+symmetry um points in the bran Zone a
+ 
+
+ align:start position:0%
+symmetry um points in the bran Zone a
+letter right a Greek letter um or not um
+
+ align:start position:0%
+letter right a Greek letter um or not um
+ 
+
+ align:start position:0%
+letter right a Greek letter um or not um
+and then I went back to gamma here I
+
+ align:start position:0%
+and then I went back to gamma here I
+ 
+
+ align:start position:0%
+and then I went back to gamma here I
+went to a point we called
+
+ align:start position:0%
+went to a point we called
+ 
+
+ align:start position:0%
+went to a point we called
+L and I the way you do this is you just
+
+ align:start position:0%
+L and I the way you do this is you just
+ 
+
+ align:start position:0%
+L and I the way you do this is you just
+basically go in a line from this point
+
+ align:start position:0%
+basically go in a line from this point
+ 
+
+ align:start position:0%
+basically go in a line from this point
+to that point and you plot the change in
+
+ align:start position:0%
+to that point and you plot the change in
+ 
+
+ align:start position:0%
+to that point and you plot the change in
+the energy of each band as you go from
+
+ align:start position:0%
+the energy of each band as you go from
+ 
+
+ align:start position:0%
+the energy of each band as you go from
+point to point in the BR one zone so now
+
+ align:start position:0%
+point to point in the BR one zone so now
+ 
+
+ align:start position:0%
+point to point in the BR one zone so now
+tell me are those the only variations
+
+ align:start position:0%
+tell me are those the only variations
+ 
+
+ align:start position:0%
+tell me are those the only variations
+that you could have why not
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+tell me why
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+not if you choose a different path this
+
+ align:start position:0%
+not if you choose a different path this
+ 
+
+ align:start position:0%
+not if you choose a different path this
+is just one path going from L to gamma
+
+ align:start position:0%
+is just one path going from L to gamma
+ 
+
+ align:start position:0%
+is just one path going from L to gamma
+to X you see here we are I went you see
+
+ align:start position:0%
+to X you see here we are I went you see
+ 
+
+ align:start position:0%
+to X you see here we are I went you see
+here they are for FCC okay I think or
+
+ align:start position:0%
+here they are for FCC okay I think or
+ 
+
+ align:start position:0%
+here they are for FCC okay I think or
+maybe it's BCC I went from gamma to L to
+
+ align:start position:0%
+maybe it's BCC I went from gamma to L to
+ 
+
+ align:start position:0%
+maybe it's BCC I went from gamma to L to
+X I went just along a line in this bran
+
+ align:start position:0%
+X I went just along a line in this bran
+ 
+
+ align:start position:0%
+X I went just along a line in this bran
+Zone but what if I had gone G like this
+
+ align:start position:0%
+Zone but what if I had gone G like this
+ 
+
+ align:start position:0%
+Zone but what if I had gone G like this
+or what if I had done like
+
+ align:start position:0%
+or what if I had done like
+ 
+
+ align:start position:0%
+or what if I had done like
+this would I get different
+
+ align:start position:0%
+this would I get different
+ 
+
+ align:start position:0%
+this would I get different
+curvatures you better believe
+
+ align:start position:0%
+curvatures you better believe
+ 
+
+ align:start position:0%
+curvatures you better believe
+it right you are taking paths through
+
+ align:start position:0%
+it right you are taking paths through
+ 
+
+ align:start position:0%
+it right you are taking paths through
+the bruan zone to get the band structure
+
+ align:start position:0%
+the bruan zone to get the band structure
+ 
+
+ align:start position:0%
+the bruan zone to get the band structure
+that's how you got the band
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+structure
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+now what ends up
+
+ align:start position:0%
+now what ends up
+ 
+
+ align:start position:0%
+now what ends up
+happening is that the interesting
+
+ align:start position:0%
+happening is that the interesting
+ 
+
+ align:start position:0%
+happening is that the interesting
+variations in these energy bands the
+
+ align:start position:0%
+variations in these energy bands the
+ 
+
+ align:start position:0%
+variations in these energy bands the
+interesting ones the ones that are
+
+ align:start position:0%
+interesting ones the ones that are
+ 
+
+ align:start position:0%
+interesting ones the ones that are
+important for optical and electronic
+
+ align:start position:0%
+important for optical and electronic
+ 
+
+ align:start position:0%
+important for optical and electronic
+properties tend to happen between the
+
+ align:start position:0%
+properties tend to happen between the
+ 
+
+ align:start position:0%
+properties tend to happen between the
+high symmetry points in the Broan Zone
+
+ align:start position:0%
+high symmetry points in the Broan Zone
+ 
+
+ align:start position:0%
+high symmetry points in the Broan Zone
+they tend to happen between the origin
+
+ align:start position:0%
+they tend to happen between the origin
+ 
+
+ align:start position:0%
+they tend to happen between the origin
+and the center of this face and the
+
+ align:start position:0%
+and the center of this face and the
+ 
+
+ align:start position:0%
+and the center of this face and the
+center of this Edge and going back to An
+
+ align:start position:0%
+center of this Edge and going back to An
+ 
+
+ align:start position:0%
+center of this Edge and going back to An
+Origin they tend to happen between the
+
+ align:start position:0%
+Origin they tend to happen between the
+ 
+
+ align:start position:0%
+Origin they tend to happen between the
+the path of one high symmetry point to
+
+ align:start position:0%
+the path of one high symmetry point to
+ 
+
+ align:start position:0%
+the path of one high symmetry point to
+another and so you know sort of de facto
+
+ align:start position:0%
+another and so you know sort of de facto
+ 
+
+ align:start position:0%
+another and so you know sort of de facto
+we we we just don't care much about
+
+ align:start position:0%
+we we we just don't care much about
+ 
+
+ align:start position:0%
+we we we just don't care much about
+everything else in the B one Z because
+
+ align:start position:0%
+everything else in the B one Z because
+ 
+
+ align:start position:0%
+everything else in the B one Z because
+it doesn't really give us extra
+
+ align:start position:0%
+it doesn't really give us extra
+ 
+
+ align:start position:0%
+it doesn't really give us extra
+information it would give us a different
+
+ align:start position:0%
+information it would give us a different
+ 
+
+ align:start position:0%
+information it would give us a different
+band structure but it's not that um it's
+
+ align:start position:0%
+band structure but it's not that um it's
+ 
+
+ align:start position:0%
+band structure but it's not that um it's
+not giving us something that's um uh
+
+ align:start position:0%
+not giving us something that's um uh
+ 
+
+ align:start position:0%
+not giving us something that's um uh
+that's as relevant to the key
+
+ align:start position:0%
+that's as relevant to the key
+ 
+
+ align:start position:0%
+that's as relevant to the key
+fundamental properties we care about
+
+ align:start position:0%
+fundamental properties we care about
+ 
+
+ align:start position:0%
+fundamental properties we care about
+okay um so that's one thing now so
+
+ align:start position:0%
+okay um so that's one thing now so
+ 
+
+ align:start position:0%
+okay um so that's one thing now so
+that's where those now um the code just
+
+ align:start position:0%
+that's where those now um the code just
+ 
+
+ align:start position:0%
+that's where those now um the code just
+picks the paths but in all these codes
+
+ align:start position:0%
+picks the paths but in all these codes
+ 
+
+ align:start position:0%
+picks the paths but in all these codes
+you can enter whatever path you want so
+
+ align:start position:0%
+you can enter whatever path you want so
+ 
+
+ align:start position:0%
+you can enter whatever path you want so
+if you want to cruise around in caspace
+
+ align:start position:0%
+if you want to cruise around in caspace
+ 
+
+ align:start position:0%
+if you want to cruise around in caspace
+and get energy variations you can do it
+
+ align:start position:0%
+and get energy variations you can do it
+ 
+
+ align:start position:0%
+and get energy variations you can do it
+you are not
+
+ align:start position:0%
+you are not
+ 
+
+ align:start position:0%
+you are not
+limited um now uh is this the right band
+
+ align:start position:0%
+limited um now uh is this the right band
+ 
+
+ align:start position:0%
+limited um now uh is this the right band
+structure for
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+silicon let's go back to our not bad
+
+ align:start position:0%
+silicon let's go back to our not bad
+ 
+
+ align:start position:0%
+silicon let's go back to our not bad
+look pretty good I like that that's what
+
+ align:start position:0%
+look pretty good I like that that's what
+ 
+
+ align:start position:0%
+look pretty good I like that that's what
+I want now if we go back to the
+
+ align:start position:0%
+I want now if we go back to the
+ 
+
+ align:start position:0%
+I want now if we go back to the
+input what is it that that um of these
+
+ align:start position:0%
+input what is it that that um of these
+ 
+
+ align:start position:0%
+input what is it that that um of these
+parameters what is it that I might need
+
+ align:start position:0%
+parameters what is it that I might need
+ 
+
+ align:start position:0%
+parameters what is it that I might need
+to
+
+ align:start position:0%
+to
+ 
+
+ align:start position:0%
+to
+check what is that say that
+
+ align:start position:0%
+check what is that say that
+ 
+
+ align:start position:0%
+check what is that say that
+again okay so I might I have a 4x4 grid
+
+ align:start position:0%
+again okay so I might I have a 4x4 grid
+ 
+
+ align:start position:0%
+again okay so I might I have a 4x4 grid
+would I get a B would I get curvy band
+
+ align:start position:0%
+would I get a B would I get curvy band
+ 
+
+ align:start position:0%
+would I get a B would I get curvy band
+structures if I do a one by one by
+
+ align:start position:0%
+structures if I do a one by one by
+ 
+
+ align:start position:0%
+structures if I do a one by one by
+one ah let's see let's try
+
+ align:start position:0%
+one ah let's see let's try
+ 
+
+ align:start position:0%
+one ah let's see let's try
+it don't do
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+14 okay um this seems to be stable for
+
+ align:start position:0%
+14 okay um this seems to be stable for
+ 
+
+ align:start position:0%
+14 okay um this seems to be stable for
+now uh
+
+ align:start position:0%
+now uh
+ 
+
+ align:start position:0%
+now uh
+oh where's my simulate
+
+ align:start position:0%
+oh where's my simulate
+ 
+
+ align:start position:0%
+oh where's my simulate
+button
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+ah
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay uh there it is okay so I'm doing a
+
+ align:start position:0%
+okay uh there it is okay so I'm doing a
+ 
+
+ align:start position:0%
+okay uh there it is okay so I'm doing a
+one by
+
+ align:start position:0%
+one by
+ 
+
+ align:start position:0%
+one by
+one
+
+ align:start position:0%
+one
+ 
+
+ align:start position:0%
+one
+um one by one by one k point this is
+
+ align:start position:0%
+um one by one by one k point this is
+ 
+
+ align:start position:0%
+um one by one by one k point this is
+kind of another key concept I want to
+
+ align:start position:0%
+kind of another key concept I want to
+ 
+
+ align:start position:0%
+kind of another key concept I want to
+make make sure we understand okay there
+
+ align:start position:0%
+make make sure we understand okay there
+ 
+
+ align:start position:0%
+make make sure we understand okay there
+it is there's silicon I didn't change
+
+ align:start position:0%
+it is there's silicon I didn't change
+ 
+
+ align:start position:0%
+it is there's silicon I didn't change
+anything about the real space I didn't
+
+ align:start position:0%
+anything about the real space I didn't
+ 
+
+ align:start position:0%
+anything about the real space I didn't
+change anything about the k space I just
+
+ align:start position:0%
+change anything about the k space I just
+ 
+
+ align:start position:0%
+change anything about the k space I just
+only evaluated the density at one point
+
+ align:start position:0%
+only evaluated the density at one point
+ 
+
+ align:start position:0%
+only evaluated the density at one point
+now here's what's going to perhaps
+
+ align:start position:0%
+now here's what's going to perhaps
+ 
+
+ align:start position:0%
+now here's what's going to perhaps
+surprise you which is that the band
+
+ align:start position:0%
+surprise you which is that the band
+ 
+
+ align:start position:0%
+surprise you which is that the band
+structure still
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+curves now um and it curves differently
+
+ align:start position:0%
+curves now um and it curves differently
+ 
+
+ align:start position:0%
+curves now um and it curves differently
+actually um than it did when I had 4x4x4
+
+ align:start position:0%
+actually um than it did when I had 4x4x4
+ 
+
+ align:start position:0%
+actually um than it did when I had 4x4x4
+um why would it still
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+curve this is actually uh something I
+
+ align:start position:0%
+curve this is actually uh something I
+ 
+
+ align:start position:0%
+curve this is actually uh something I
+didn't talk about yet but it is in a
+
+ align:start position:0%
+didn't talk about yet but it is in a
+ 
+
+ align:start position:0%
+didn't talk about yet but it is in a
+slide that I was going to talk about but
+
+ align:start position:0%
+slide that I was going to talk about but
+ 
+
+ align:start position:0%
+slide that I was going to talk about but
+since I have it here I'll just talk
+
+ align:start position:0%
+since I have it here I'll just talk
+ 
+
+ align:start position:0%
+since I have it here I'll just talk
+about it now
+
+ align:start position:0%
+about it now
+ 
+
+ align:start position:0%
+about it now
+yeah I probably could have done all that
+
+ align:start position:0%
+yeah I probably could have done all that
+ 
+
+ align:start position:0%
+yeah I probably could have done all that
+internally without voicing it but here
+
+ align:start position:0%
+internally without voicing it but here
+ 
+
+ align:start position:0%
+internally without voicing it but here
+we are um so uh you see when you
+
+ align:start position:0%
+we are um so uh you see when you
+ 
+
+ align:start position:0%
+we are um so uh you see when you
+calculate the band structure
+
+ align:start position:0%
+calculate the band structure
+ 
+
+ align:start position:0%
+calculate the band structure
+what you do is you do two things first
+
+ align:start position:0%
+what you do is you do two things first
+ 
+
+ align:start position:0%
+what you do is you do two things first
+you converge the wave function in
+
+ align:start position:0%
+you converge the wave function in
+ 
+
+ align:start position:0%
+you converge the wave function in
+density first you converge the density
+
+ align:start position:0%
+density first you converge the density
+ 
+
+ align:start position:0%
+density first you converge the density
+at the K points I input into the
+
+ align:start position:0%
+at the K points I input into the
+ 
+
+ align:start position:0%
+at the K points I input into the
+input right so I have a 1 by one by one
+
+ align:start position:0%
+input right so I have a 1 by one by one
+ 
+
+ align:start position:0%
+input right so I have a 1 by one by one
+kpoint density well that gives me some
+
+ align:start position:0%
+kpoint density well that gives me some
+ 
+
+ align:start position:0%
+kpoint density well that gives me some
+uh uh grid that gives me some density
+
+ align:start position:0%
+uh uh grid that gives me some density
+ 
+
+ align:start position:0%
+uh uh grid that gives me some density
+and some wave function
+
+ align:start position:0%
+and some wave function
+ 
+
+ align:start position:0%
+and some wave function
+okay now then to calculate the band
+
+ align:start position:0%
+okay now then to calculate the band
+ 
+
+ align:start position:0%
+okay now then to calculate the band
+structure what the code does is it does
+
+ align:start position:0%
+structure what the code does is it does
+ 
+
+ align:start position:0%
+structure what the code does is it does
+a second step it takes that converge
+
+ align:start position:0%
+a second step it takes that converge
+ 
+
+ align:start position:0%
+a second step it takes that converge
+density and it cruises around in kpace
+
+ align:start position:0%
+density and it cruises around in kpace
+ 
+
+ align:start position:0%
+density and it cruises around in kpace
+and that's how it plots this out but it
+
+ align:start position:0%
+and that's how it plots this out but it
+ 
+
+ align:start position:0%
+and that's how it plots this out but it
+doesn't change the density anymore it
+
+ align:start position:0%
+doesn't change the density anymore it
+ 
+
+ align:start position:0%
+doesn't change the density anymore it
+doesn't change the converg wave function
+
+ align:start position:0%
+doesn't change the converg wave function
+ 
+
+ align:start position:0%
+doesn't change the converg wave function
+it just evaluates it at all kinds of
+
+ align:start position:0%
+it just evaluates it at all kinds of
+ 
+
+ align:start position:0%
+it just evaluates it at all kinds of
+different points in kpace so there's two
+
+ align:start position:0%
+different points in kpace so there's two
+ 
+
+ align:start position:0%
+different points in kpace so there's two
+steps first you converge the density at
+
+ align:start position:0%
+steps first you converge the density at
+ 
+
+ align:start position:0%
+steps first you converge the density at
+some number of K
+
+ align:start position:0%
+some number of K
+ 
+
+ align:start position:0%
+some number of K
+points then you cruise around in the
+
+ align:start position:0%
+points then you cruise around in the
+ 
+
+ align:start position:0%
+points then you cruise around in the
+bribon zone with that density and you
+
+ align:start position:0%
+bribon zone with that density and you
+ 
+
+ align:start position:0%
+bribon zone with that density and you
+evaluate your functions and sure the D
+
+ align:start position:0%
+evaluate your functions and sure the D
+ 
+
+ align:start position:0%
+evaluate your functions and sure the D
+you know the wrong density will still
+
+ align:start position:0%
+you know the wrong density will still
+ 
+
+ align:start position:0%
+you know the wrong density will still
+wiggle as you move around in kpace it'll
+
+ align:start position:0%
+wiggle as you move around in kpace it'll
+ 
+
+ align:start position:0%
+wiggle as you move around in kpace it'll
+still wiggle but it's the wrong density
+
+ align:start position:0%
+still wiggle but it's the wrong density
+ 
+
+ align:start position:0%
+still wiggle but it's the wrong density
+because I didn't have enough K points in
+
+ align:start position:0%
+because I didn't have enough K points in
+ 
+
+ align:start position:0%
+because I didn't have enough K points in
+the first place to converge it does
+
+ align:start position:0%
+the first place to converge it does
+ 
+
+ align:start position:0%
+the first place to converge it does
+everybody see
+
+ align:start position:0%
+everybody see
+ 
+
+ align:start position:0%
+everybody see
+that okay so now how many k points do I
+
+ align:start position:0%
+that okay so now how many k points do I
+ 
+
+ align:start position:0%
+that okay so now how many k points do I
+need well the number of K points I need
+
+ align:start position:0%
+need well the number of K points I need
+ 
+
+ align:start position:0%
+need well the number of K points I need
+is when this converges and doesn't
+
+ align:start position:0%
+is when this converges and doesn't
+ 
+
+ align:start position:0%
+is when this converges and doesn't
+change anymore right if the band
+
+ align:start position:0%
+change anymore right if the band
+ 
+
+ align:start position:0%
+change anymore right if the band
+structure if properties of the band
+
+ align:start position:0%
+structure if properties of the band
+ 
+
+ align:start position:0%
+structure if properties of the band
+structure are what I want that's how
+
+ align:start position:0%
+structure are what I want that's how
+ 
+
+ align:start position:0%
+structure are what I want that's how
+many k points I need right
+
+ align:start position:0%
+many k points I need right
+ 
+
+ align:start position:0%
+many k points I need right
+does everybody see that that's the
+
+ align:start position:0%
+does everybody see that that's the
+ 
+
+ align:start position:0%
+does everybody see that that's the
+difference now
+
+ align:start position:0%
+difference now
+ 
+
+ align:start position:0%
+difference now
+uh okay ah no that wasn't good here we
+
+ align:start position:0%
+uh okay ah no that wasn't good here we
+ 
+
+ align:start position:0%
+uh okay ah no that wasn't good here we
+go oh yeah these so-called web browsers
+
+ align:start position:0%
+go oh yeah these so-called web browsers
+ 
+
+ align:start position:0%
+go oh yeah these so-called web browsers
+Mark andreon was my student by the way
+
+ align:start position:0%
+Mark andreon was my student by the way
+ 
+
+ align:start position:0%
+Mark andreon was my student by the way
+at uh does anybody know who he is nobody
+
+ align:start position:0%
+at uh does anybody know who he is nobody
+ 
+
+ align:start position:0%
+at uh does anybody know who he is nobody
+knows who he is I'm dated no um he was
+
+ align:start position:0%
+knows who he is I'm dated no um he was
+ 
+
+ align:start position:0%
+knows who he is I'm dated no um he was
+at Illinois where I did my PhD and I was
+
+ align:start position:0%
+at Illinois where I did my PhD and I was
+ 
+
+ align:start position:0%
+at Illinois where I did my PhD and I was
+his ta and um he he went and founded
+
+ align:start position:0%
+his ta and um he he went and founded
+ 
+
+ align:start position:0%
+his ta and um he he went and founded
+Netscape right um good guy okay uh
+
+ align:start position:0%
+Netscape right um good guy okay uh
+ 
+
+ align:start position:0%
+Netscape right um good guy okay uh
+except that's not one of my browser
+
+ align:start position:0%
+except that's not one of my browser
+ 
+
+ align:start position:0%
+except that's not one of my browser
+options anymore so what what's up with
+
+ align:start position:0%
+options anymore so what what's up with
+ 
+
+ align:start position:0%
+options anymore so what what's up with
+that um now okay what I want to do now
+
+ align:start position:0%
+that um now okay what I want to do now
+ 
+
+ align:start position:0%
+that um now okay what I want to do now
+is the following I'm going to go to one
+
+ align:start position:0%
+is the following I'm going to go to one
+ 
+
+ align:start position:0%
+is the following I'm going to go to one
+atom
+
+ align:start position:0%
+atom
+ 
+
+ align:start position:0%
+atom
+okay and what I want to know is um and
+
+ align:start position:0%
+okay and what I want to know is um and
+ 
+
+ align:start position:0%
+okay and what I want to know is um and
+you can do that just like before you can
+
+ align:start position:0%
+you can do that just like before you can
+ 
+
+ align:start position:0%
+you can do that just like before you can
+kind of mess around
+
+ align:start position:0%
+kind of mess around
+ 
+
+ align:start position:0%
+kind of mess around
+okay one
+
+ align:start position:0%
+okay one
+ 
+
+ align:start position:0%
+okay one
+atom we'll just leave it at one k point
+
+ align:start position:0%
+atom we'll just leave it at one k point
+ 
+
+ align:start position:0%
+atom we'll just leave it at one k point
+and what I want to know is am I going to
+
+ align:start position:0%
+and what I want to know is am I going to
+ 
+
+ align:start position:0%
+and what I want to know is am I going to
+get a band structure with one atom in
+
+ align:start position:0%
+get a band structure with one atom in
+ 
+
+ align:start position:0%
+get a band structure with one atom in
+the unit
+
+ align:start position:0%
+the unit
+ 
+
+ align:start position:0%
+the unit
+cell oh there it is they're kind of far
+
+ align:start position:0%
+cell oh there it is they're kind of far
+ 
+
+ align:start position:0%
+cell oh there it is they're kind of far
+apart right what do you guys
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+think that's one atom in the corner of
+
+ align:start position:0%
+think that's one atom in the corner of
+ 
+
+ align:start position:0%
+think that's one atom in the corner of
+an FCC
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+cell will I get a band structure
+
+ align:start position:0%
+cell will I get a band structure
+ 
+
+ align:start position:0%
+cell will I get a band structure
+just say yes or
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+no there it is now why is it
+
+ align:start position:0%
+no there it is now why is it
+ 
+
+ align:start position:0%
+no there it is now why is it
+curving let let me ask a different way
+
+ align:start position:0%
+curving let let me ask a different way
+ 
+
+ align:start position:0%
+curving let let me ask a different way
+how could I get these bands to stop
+
+ align:start position:0%
+how could I get these bands to stop
+ 
+
+ align:start position:0%
+how could I get these bands to stop
+curving just stop curving
+
+ align:start position:0%
+curving just stop curving
+ 
+
+ align:start position:0%
+curving just stop curving
+already what is that
+
+ align:start position:0%
+already what is that
+ 
+
+ align:start position:0%
+already what is that
+larger larger k space or other
+
+ align:start position:0%
+larger larger k space or other
+ 
+
+ align:start position:0%
+larger larger k space or other
+space why are they curving
+
+ align:start position:0%
+space why are they curving
+ 
+
+ align:start position:0%
+space why are they curving
+again why are these things curving
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah it has to do with
+
+ align:start position:0%
+yeah it has to do with
+ 
+
+ align:start position:0%
+yeah it has to do with
+that but why do you get we we talked you
+
+ align:start position:0%
+that but why do you get we we talked you
+ 
+
+ align:start position:0%
+that but why do you get we we talked you
+know a lot in the last half hour about
+
+ align:start position:0%
+know a lot in the last half hour about
+ 
+
+ align:start position:0%
+know a lot in the last half hour about
+how you get this variation in c space of
+
+ align:start position:0%
+how you get this variation in c space of
+ 
+
+ align:start position:0%
+how you get this variation in c space of
+the band why do you get that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+again why do you get that I mean you get
+
+ align:start position:0%
+again why do you get that I mean you get
+ 
+
+ align:start position:0%
+again why do you get that I mean you get
+it because of blocks theorem I'll tell
+
+ align:start position:0%
+it because of blocks theorem I'll tell
+ 
+
+ align:start position:0%
+it because of blocks theorem I'll tell
+you that but why does that matter
+
+ align:start position:0%
+you that but why does that matter
+ 
+
+ align:start position:0%
+you that but why does that matter
+it's
+
+ align:start position:0%
+it's
+ 
+
+ align:start position:0%
+it's
+periodic you got a periodic potential
+
+ align:start position:0%
+periodic you got a periodic potential
+ 
+
+ align:start position:0%
+periodic you got a periodic potential
+and so if it's so so when would you
+
+ align:start position:0%
+and so if it's so so when would you
+ 
+
+ align:start position:0%
+and so if it's so so when would you
+expect the curviness to stop
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+curving well or if you don't really have
+
+ align:start position:0%
+curving well or if you don't really have
+ 
+
+ align:start position:0%
+curving well or if you don't really have
+a crystal anymore right I mean this
+
+ align:start position:0%
+a crystal anymore right I mean this
+ 
+
+ align:start position:0%
+a crystal anymore right I mean this
+looks a little less curvy what if I
+
+ align:start position:0%
+looks a little less curvy what if I
+ 
+
+ align:start position:0%
+looks a little less curvy what if I
+actually made the spacing if I change
+
+ align:start position:0%
+actually made the spacing if I change
+ 
+
+ align:start position:0%
+actually made the spacing if I change
+the lattice constant to
+
+ align:start position:0%
+the lattice constant to
+ 
+
+ align:start position:0%
+the lattice constant to
+10 and then simulated what's going to
+
+ align:start position:0%
+10 and then simulated what's going to
+ 
+
+ align:start position:0%
+10 and then simulated what's going to
+happen
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+then okay that was pretty fast and look
+
+ align:start position:0%
+then okay that was pretty fast and look
+ 
+
+ align:start position:0%
+then okay that was pretty fast and look
+at that now they're far apart they sort
+
+ align:start position:0%
+at that now they're far apart they sort
+ 
+
+ align:start position:0%
+at that now they're far apart they sort
+of look
+
+ align:start position:0%
+of look
+ 
+
+ align:start position:0%
+of look
+like
+
+ align:start position:0%
+like
+ 
+
+ align:start position:0%
+like
+where let's see there's the band
+
+ align:start position:0%
+where let's see there's the band
+ 
+
+ align:start position:0%
+where let's see there's the band
+structure
+
+ align:start position:0%
+structure
+ 
+
+ align:start position:0%
+structure
+oh I love that reaction there that was
+
+ align:start position:0%
+oh I love that reaction there that was
+ 
+
+ align:start position:0%
+oh I love that reaction there that was
+that that had some meaning in it right
+
+ align:start position:0%
+that that had some meaning in it right
+ 
+
+ align:start position:0%
+that that had some meaning in it right
+whoever that was thank you cuz I felt
+
+ align:start position:0%
+whoever that was thank you cuz I felt
+ 
+
+ align:start position:0%
+whoever that was thank you cuz I felt
+the connection I what just just happened
+
+ align:start position:0%
+the connection I what just just happened
+ 
+
+ align:start position:0%
+the connection I what just just happened
+what is this what are
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+these energy bands they are still energy
+
+ align:start position:0%
+these energy bands they are still energy
+ 
+
+ align:start position:0%
+these energy bands they are still energy
+bands varying in k space but they don't
+
+ align:start position:0%
+bands varying in k space but they don't
+ 
+
+ align:start position:0%
+bands varying in k space but they don't
+vary in k space but you doesn't mean you
+
+ align:start position:0%
+vary in k space but you doesn't mean you
+ 
+
+ align:start position:0%
+vary in k space but you doesn't mean you
+can't compute them at different K points
+
+ align:start position:0%
+can't compute them at different K points
+ 
+
+ align:start position:0%
+can't compute them at different K points
+which the code did but they're flat
+
+ align:start position:0%
+which the code did but they're flat
+ 
+
+ align:start position:0%
+which the code did but they're flat
+which means they're not
+
+ align:start position:0%
+which means they're not
+ 
+
+ align:start position:0%
+which means they're not
+really interacting in any sort of
+
+ align:start position:0%
+really interacting in any sort of
+ 
+
+ align:start position:0%
+really interacting in any sort of
+periodic way anymore they're so far
+
+ align:start position:0%
+periodic way anymore they're so far
+ 
+
+ align:start position:0%
+periodic way anymore they're so far
+apart that the periodic potentials don't
+
+ align:start position:0%
+apart that the periodic potentials don't
+ 
+
+ align:start position:0%
+apart that the periodic potentials don't
+really overlap they don't feel each
+
+ align:start position:0%
+really overlap they don't feel each
+ 
+
+ align:start position:0%
+really overlap they don't feel each
+other so what do I have left then what
+
+ align:start position:0%
+other so what do I have left then what
+ 
+
+ align:start position:0%
+other so what do I have left then what
+is it what am I staring
+
+ align:start position:0%
+is it what am I staring
+ 
+
+ align:start position:0%
+is it what am I staring
+at silicon atom that's all that those
+
+ align:start position:0%
+at silicon atom that's all that those
+ 
+
+ align:start position:0%
+at silicon atom that's all that those
+are the states that's what state is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that yeah but which which state is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that it would be if we had all the
+
+ align:start position:0%
+that it would be if we had all the
+ 
+
+ align:start position:0%
+that it would be if we had all the
+electrons so that's a little tough but
+
+ align:start position:0%
+electrons so that's a little tough but
+ 
+
+ align:start position:0%
+electrons so that's a little tough but
+we only have the outer four so it's it's
+
+ align:start position:0%
+we only have the outer four so it's it's
+ 
+
+ align:start position:0%
+we only have the outer four so it's it's
+actually the 3s right 3s 3p our friend
+
+ align:start position:0%
+actually the 3s right 3s 3p our friend
+ 
+
+ align:start position:0%
+actually the 3s right 3s 3p our friend
+silicon atom is back we went from atoms
+
+ align:start position:0%
+silicon atom is back we went from atoms
+ 
+
+ align:start position:0%
+silicon atom is back we went from atoms
+to molecules to solids and now we just
+
+ align:start position:0%
+to molecules to solids and now we just
+ 
+
+ align:start position:0%
+to molecules to solids and now we just
+did an atom right um and you see as I
+
+ align:start position:0%
+did an atom right um and you see as I
+ 
+
+ align:start position:0%
+did an atom right um and you see as I
+bring those atoms as I so those are the
+
+ align:start position:0%
+bring those atoms as I so those are the
+ 
+
+ align:start position:0%
+bring those atoms as I so those are the
+atomic levels of
+
+ align:start position:0%
+atomic levels of
+ 
+
+ align:start position:0%
+atomic levels of
+silicon um they don't vary in case Spas
+
+ align:start position:0%
+silicon um they don't vary in case Spas
+ 
+
+ align:start position:0%
+silicon um they don't vary in case Spas
+a molecule of silicon wouldn't vary in
+
+ align:start position:0%
+a molecule of silicon wouldn't vary in
+ 
+
+ align:start position:0%
+a molecule of silicon wouldn't vary in
+case space but as I start to make this
+
+ align:start position:0%
+case space but as I start to make this
+ 
+
+ align:start position:0%
+case space but as I start to make this
+thing feel a
+
+ align:start position:0%
+thing feel a
+ 
+
+ align:start position:0%
+thing feel a
+repeat
+
+ align:start position:0%
+repeat
+ 
+
+ align:start position:0%
+repeat
+eness then block stum kicks in
+
+ align:start position:0%
+eness then block stum kicks in
+ 
+
+ align:start position:0%
+eness then block stum kicks in
+and energies depend on K and that
+
+ align:start position:0%
+and energies depend on K and that
+ 
+
+ align:start position:0%
+and energies depend on K and that
+changes the properties of the material
+
+ align:start position:0%
+changes the properties of the material
+ 
+
+ align:start position:0%
+changes the properties of the material
+okay so that's um that's all really
+
+ align:start position:0%
+okay so that's um that's all really
+ 
+
+ align:start position:0%
+okay so that's um that's all really
+important
+
+ align:start position:0%
+important
+ 
+
+ align:start position:0%
+important
+now one more thing while we have the
+
+ align:start position:0%
+now one more thing while we have the
+ 
+
+ align:start position:0%
+now one more thing while we have the
+tool
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+up well so now we're actually we're
+
+ align:start position:0%
+up well so now we're actually we're
+ 
+
+ align:start position:0%
+up well so now we're actually we're
+pretty well equipped to try a whole
+
+ align:start position:0%
+pretty well equipped to try a whole
+ 
+
+ align:start position:0%
+pretty well equipped to try a whole
+bunch of stuff right and we're going to
+
+ align:start position:0%
+bunch of stuff right and we're going to
+ 
+
+ align:start position:0%
+bunch of stuff right and we're going to
+understand what we're doing let me just
+
+ align:start position:0%
+understand what we're doing let me just
+ 
+
+ align:start position:0%
+understand what we're doing let me just
+um ask you one more thing if I look at
+
+ align:start position:0%
+um ask you one more thing if I look at
+ 
+
+ align:start position:0%
+um ask you one more thing if I look at
+these inputs let's pull up uh Alpha
+
+ align:start position:0%
+these inputs let's pull up uh Alpha
+ 
+
+ align:start position:0%
+these inputs let's pull up uh Alpha
+quartz let's say there's Alpha
+
+ align:start position:0%
+quartz let's say there's Alpha
+ 
+
+ align:start position:0%
+quartz let's say there's Alpha
+quartz um now if I look at these inputs
+
+ align:start position:0%
+quartz um now if I look at these inputs
+ 
+
+ align:start position:0%
+quartz um now if I look at these inputs
+um what else might you want to think
+
+ align:start position:0%
+um what else might you want to think
+ 
+
+ align:start position:0%
+um what else might you want to think
+about converging we talked about the
+
+ align:start position:0%
+about converging we talked about the
+ 
+
+ align:start position:0%
+about converging we talked about the
+kpoint
+
+ align:start position:0%
+kpoint
+ 
+
+ align:start position:0%
+kpoint
+mesh uh something not as bad as Alpha
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+quartz
+
+ align:start position:0%
+quartz
+ 
+
+ align:start position:0%
+quartz
+aluminum oh that's nice one
+
+ align:start position:0%
+aluminum oh that's nice one
+ 
+
+ align:start position:0%
+aluminum oh that's nice one
+atom what else besides the kpo mesh and
+
+ align:start position:0%
+atom what else besides the kpo mesh and
+ 
+
+ align:start position:0%
+atom what else besides the kpo mesh and
+you better use more K points than one
+
+ align:start position:0%
+you better use more K points than one
+ 
+
+ align:start position:0%
+you better use more K points than one
+for
+
+ align:start position:0%
+for
+ 
+
+ align:start position:0%
+for
+aluminum besides that what else might I
+
+ align:start position:0%
+aluminum besides that what else might I
+ 
+
+ align:start position:0%
+aluminum besides that what else might I
+just pointed to it might I want to
+
+ align:start position:0%
+just pointed to it might I want to
+ 
+
+ align:start position:0%
+just pointed to it might I want to
+converge or make sure is right the lce
+
+ align:start position:0%
+converge or make sure is right the lce
+ 
+
+ align:start position:0%
+converge or make sure is right the lce
+constant you see I'm just giv this to
+
+ align:start position:0%
+constant you see I'm just giv this to
+ 
+
+ align:start position:0%
+constant you see I'm just giv this to
+you because you know it's there um where
+
+ align:start position:0%
+you because you know it's there um where
+ 
+
+ align:start position:0%
+you because you know it's there um where
+did it come from is it the right lattice
+
+ align:start position:0%
+did it come from is it the right lattice
+ 
+
+ align:start position:0%
+did it come from is it the right lattice
+constant for this choice of theory and
+
+ align:start position:0%
+constant for this choice of theory and
+ 
+
+ align:start position:0%
+constant for this choice of theory and
+basis
+
+ align:start position:0%
+basis
+ 
+
+ align:start position:0%
+basis
+set right is it the right one well you
+
+ align:start position:0%
+set right is it the right one well you
+ 
+
+ align:start position:0%
+set right is it the right one well you
+should you should make sure there are no
+
+ align:start position:0%
+should you should make sure there are no
+ 
+
+ align:start position:0%
+should you should make sure there are no
+forces in the system you should relax
+
+ align:start position:0%
+forces in the system you should relax
+ 
+
+ align:start position:0%
+forces in the system you should relax
+your system and that gets to the point I
+
+ align:start position:0%
+your system and that gets to the point I
+ 
+
+ align:start position:0%
+your system and that gets to the point I
+want to make how do you relax a solid
+
+ align:start position:0%
+want to make how do you relax a solid
+ 
+
+ align:start position:0%
+want to make how do you relax a solid
+because there's now two things not one
+
+ align:start position:0%
+because there's now two things not one
+ 
+
+ align:start position:0%
+because there's now two things not one
+that you need to care about tell me what
+
+ align:start position:0%
+that you need to care about tell me what
+ 
+
+ align:start position:0%
+that you need to care about tell me what
+the two things
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+are well how do you relax a molecule
+
+ align:start position:0%
+are well how do you relax a molecule
+ 
+
+ align:start position:0%
+are well how do you relax a molecule
+when you say optimize structure what's
+
+ align:start position:0%
+when you say optimize structure what's
+ 
+
+ align:start position:0%
+when you say optimize structure what's
+it
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+doing okay by doing
+
+ align:start position:0%
+doing okay by doing
+ 
+
+ align:start position:0%
+doing okay by doing
+what what's it
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+calculate which is also called what
+
+ align:start position:0%
+calculate which is also called what
+ 
+
+ align:start position:0%
+calculate which is also called what
+force the force on each at and it pushes
+
+ align:start position:0%
+force the force on each at and it pushes
+ 
+
+ align:start position:0%
+force the force on each at and it pushes
+them along the force until they get to
+
+ align:start position:0%
+them along the force until they get to
+ 
+
+ align:start position:0%
+them along the force until they get to
+some minimum right now when I have a
+
+ align:start position:0%
+some minimum right now when I have a
+ 
+
+ align:start position:0%
+some minimum right now when I have a
+solid I have two things I have the force
+
+ align:start position:0%
+solid I have two things I have the force
+ 
+
+ align:start position:0%
+solid I have two things I have the force
+on each atom same as in the molecule the
+
+ align:start position:0%
+on each atom same as in the molecule the
+ 
+
+ align:start position:0%
+on each atom same as in the molecule the
+force on each atom in the basis as well
+
+ align:start position:0%
+force on each atom in the basis as well
+ 
+
+ align:start position:0%
+force on each atom in the basis as well
+as
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+what the volume which is set by the what
+
+ align:start position:0%
+what the volume which is set by the what
+ 
+
+ align:start position:0%
+what the volume which is set by the what
+by the lattice constant okay so you need
+
+ align:start position:0%
+by the lattice constant okay so you need
+ 
+
+ align:start position:0%
+by the lattice constant okay so you need
+to converge both of
+
+ align:start position:0%
+to converge both of
+ 
+
+ align:start position:0%
+to converge both of
+those okay and well in aluminum there's
+
+ align:start position:0%
+those okay and well in aluminum there's
+ 
+
+ align:start position:0%
+those okay and well in aluminum there's
+only one atom in the basis because you
+
+ align:start position:0%
+only one atom in the basis because you
+ 
+
+ align:start position:0%
+only one atom in the basis because you
+see aluminum is is an FCC
+
+ align:start position:0%
+see aluminum is is an FCC
+ 
+
+ align:start position:0%
+see aluminum is is an FCC
+metal so all I need is one atom in the
+
+ align:start position:0%
+metal so all I need is one atom in the
+ 
+
+ align:start position:0%
+metal so all I need is one atom in the
+corner of an FCC unit cell and I can
+
+ align:start position:0%
+corner of an FCC unit cell and I can
+ 
+
+ align:start position:0%
+corner of an FCC unit cell and I can
+simulate it but there is the lattice
+
+ align:start position:0%
+simulate it but there is the lattice
+ 
+
+ align:start position:0%
+simulate it but there is the lattice
+constant that I need to play with now if
+
+ align:start position:0%
+constant that I need to play with now if
+ 
+
+ align:start position:0%
+constant that I need to play with now if
+I had a more complex solid like Alpha
+
+ align:start position:0%
+I had a more complex solid like Alpha
+ 
+
+ align:start position:0%
+I had a more complex solid like Alpha
+quartz which has a number of atoms in
+
+ align:start position:0%
+quartz which has a number of atoms in
+ 
+
+ align:start position:0%
+quartz which has a number of atoms in
+the basis then the relative positions of
+
+ align:start position:0%
+the basis then the relative positions of
+ 
+
+ align:start position:0%
+the basis then the relative positions of
+those atoms may be
+
+ align:start position:0%
+those atoms may be
+ 
+
+ align:start position:0%
+those atoms may be
+important
+
+ align:start position:0%
+important
+ 
+
+ align:start position:0%
+important
+right um and you may need to relax that
+
+ align:start position:0%
+right um and you may need to relax that
+ 
+
+ align:start position:0%
+right um and you may need to relax that
+you may may not but it's something you
+
+ align:start position:0%
+you may may not but it's something you
+ 
+
+ align:start position:0%
+you may may not but it's something you
+need to be aware of and you can go in
+
+ align:start position:0%
+need to be aware of and you can go in
+ 
+
+ align:start position:0%
+need to be aware of and you can go in
+and you can look at the forces on these
+
+ align:start position:0%
+and you can look at the forces on these
+ 
+
+ align:start position:0%
+and you can look at the forces on these
+materials and you definitely have to
+
+ align:start position:0%
+materials and you definitely have to
+ 
+
+ align:start position:0%
+materials and you definitely have to
+know um whether you're at the minimum in
+
+ align:start position:0%
+know um whether you're at the minimum in
+ 
+
+ align:start position:0%
+know um whether you're at the minimum in
+terms of the lattice constant okay so
+
+ align:start position:0%
+terms of the lattice constant okay so
+ 
+
+ align:start position:0%
+terms of the lattice constant okay so
+let's do aluminum just because it's here
+
+ align:start position:0%
+let's do aluminum just because it's here
+ 
+
+ align:start position:0%
+let's do aluminum just because it's here
+we'll do 4K points which is not enough
+
+ align:start position:0%
+we'll do 4K points which is not enough
+ 
+
+ align:start position:0%
+we'll do 4K points which is not enough
+to look at a metal but we'll do it
+
+ align:start position:0%
+to look at a metal but we'll do it
+ 
+
+ align:start position:0%
+to look at a metal but we'll do it
+because it should be fairly
+
+ align:start position:0%
+because it should be fairly
+ 
+
+ align:start position:0%
+because it should be fairly
+fast
+
+ align:start position:0%
+fast
+ 
+
+ align:start position:0%
+fast
+um okay there's the energy
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and oh look at that isn't that beautiful
+
+ align:start position:0%
+and oh look at that isn't that beautiful
+ 
+
+ align:start position:0%
+and oh look at that isn't that beautiful
+it new to change the color and
+
+ align:start position:0%
+it new to change the color and
+ 
+
+ align:start position:0%
+it new to change the color and
+everything very smart smart tool and
+
+ align:start position:0%
+everything very smart smart tool and
+ 
+
+ align:start position:0%
+everything very smart smart tool and
+here we go back and tell me somebody
+
+ align:start position:0%
+here we go back and tell me somebody
+ 
+
+ align:start position:0%
+here we go back and tell me somebody
+tell me what they think the band
+
+ align:start position:0%
+tell me what they think the band
+ 
+
+ align:start position:0%
+tell me what they think the band
+structure is going to look like for
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+aluminum is it going to be what
+
+ align:start position:0%
+aluminum is it going to be what
+ 
+
+ align:start position:0%
+aluminum is it going to be what
+flatv curved how many you say curved how
+
+ align:start position:0%
+flatv curved how many you say curved how
+ 
+
+ align:start position:0%
+flatv curved how many you say curved how
+many say
+
+ align:start position:0%
+many say
+ 
+
+ align:start position:0%
+many say
+flat okay
+
+ align:start position:0%
+flat okay
+ 
+
+ align:start position:0%
+flat okay
+good look at that that's curved that's
+
+ align:start position:0%
+good look at that that's curved that's
+ 
+
+ align:start position:0%
+good look at that that's curved that's
+seriously curved right um and if we
+
+ align:start position:0%
+seriously curved right um and if we
+ 
+
+ align:start position:0%
+seriously curved right um and if we
+include you know if we looked at
+
+ align:start position:0%
+include you know if we looked at
+ 
+
+ align:start position:0%
+include you know if we looked at
+different energies we'd see even more
+
+ align:start position:0%
+different energies we'd see even more
+ 
+
+ align:start position:0%
+different energies we'd see even more
+spaghetti right um lots of curvy oh and
+
+ align:start position:0%
+spaghetti right um lots of curvy oh and
+ 
+
+ align:start position:0%
+spaghetti right um lots of curvy oh and
+look at this oh let's get the Doss this
+
+ align:start position:0%
+look at this oh let's get the Doss this
+ 
+
+ align:start position:0%
+look at this oh let's get the Doss this
+is so exciting I forgot about the
+
+ align:start position:0%
+is so exciting I forgot about the
+ 
+
+ align:start position:0%
+is so exciting I forgot about the
+Doss there's the Doss near the firmy
+
+ align:start position:0%
+Doss there's the Doss near the firmy
+ 
+
+ align:start position:0%
+Doss there's the Doss near the firmy
+energy
+
+ align:start position:0%
+energy
+ 
+
+ align:start position:0%
+energy
+okay firy energy is right here is there
+
+ align:start position:0%
+okay firy energy is right here is there
+ 
+
+ align:start position:0%
+okay firy energy is right here is there
+a Gap in this material no Should there
+
+ align:start position:0%
+a Gap in this material no Should there
+ 
+
+ align:start position:0%
+a Gap in this material no Should there
+have been no because remember in a metal
+
+ align:start position:0%
+have been no because remember in a metal
+ 
+
+ align:start position:0%
+have been no because remember in a metal
+you've got States coming coming in all
+
+ align:start position:0%
+you've got States coming coming in all
+ 
+
+ align:start position:0%
+you've got States coming coming in all
+over the place from below the firy
+
+ align:start position:0%
+over the place from below the firy
+ 
+
+ align:start position:0%
+over the place from below the firy
+energy and above continues across it
+
+ align:start position:0%
+energy and above continues across it
+ 
+
+ align:start position:0%
+energy and above continues across it
+right that's what tells you it's a
+
+ align:start position:0%
+right that's what tells you it's a
+ 
+
+ align:start position:0%
+right that's what tells you it's a
+metal okay now is Alpha quartz let's
+
+ align:start position:0%
+metal okay now is Alpha quartz let's
+ 
+
+ align:start position:0%
+metal okay now is Alpha quartz let's
+that's a nice material mostly um I want
+
+ align:start position:0%
+that's a nice material mostly um I want
+ 
+
+ align:start position:0%
+that's a nice material mostly um I want
+to simulate it CU I think it'll be
+
+ align:start position:0%
+to simulate it CU I think it'll be
+ 
+
+ align:start position:0%
+to simulate it CU I think it'll be
+pretty
+
+ align:start position:0%
+pretty
+ 
+
+ align:start position:0%
+pretty
+looking and there it is now is Alpha
+
+ align:start position:0%
+looking and there it is now is Alpha
+ 
+
+ align:start position:0%
+looking and there it is now is Alpha
+quartz I'm going to go down
+
+ align:start position:0%
+quartz I'm going to go down
+ 
+
+ align:start position:0%
+quartz I'm going to go down
+to
+
+ align:start position:0%
+to
+ 
+
+ align:start position:0%
+to
+two by
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+two is Alpha quartz a metal or a
+
+ align:start position:0%
+two is Alpha quartz a metal or a
+ 
+
+ align:start position:0%
+two is Alpha quartz a metal or a
+semiconductor or what is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+it
+
+ align:start position:0%
+it
+ 
+
+ align:start position:0%
+it
+insulator yeah what's one clue to the
+
+ align:start position:0%
+insulator yeah what's one clue to the
+ 
+
+ align:start position:0%
+insulator yeah what's one clue to the
+fact that it's an insulator
+
+ align:start position:0%
+fact that it's an insulator
+ 
+
+ align:start position:0%
+fact that it's an insulator
+what is that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+in I'm that easy to read man I got to
+
+ align:start position:0%
+in I'm that easy to read man I got to
+ 
+
+ align:start position:0%
+in I'm that easy to read man I got to
+work on that is it an insulator or a
+
+ align:start position:0%
+work on that is it an insulator or a
+ 
+
+ align:start position:0%
+work on that is it an insulator or a
+metal um I I'll try well besides the
+
+ align:start position:0%
+metal um I I'll try well besides the
+ 
+
+ align:start position:0%
+metal um I I'll try well besides the
+inflection in my voice what else could
+
+ align:start position:0%
+inflection in my voice what else could
+ 
+
+ align:start position:0%
+inflection in my voice what else could
+give you a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+clue well look at it right like is it is
+
+ align:start position:0%
+clue well look at it right like is it is
+ 
+
+ align:start position:0%
+clue well look at it right like is it is
+it a transparent material well you can't
+
+ align:start position:0%
+it a transparent material well you can't
+ 
+
+ align:start position:0%
+it a transparent material well you can't
+tell there oh it is pretty look at this
+
+ align:start position:0%
+tell there oh it is pretty look at this
+ 
+
+ align:start position:0%
+tell there oh it is pretty look at this
+Isn't that cool see this is a this is a
+
+ align:start position:0%
+Isn't that cool see this is a this is a
+ 
+
+ align:start position:0%
+Isn't that cool see this is a this is a
+a periodically repeating structure but
+
+ align:start position:0%
+a periodically repeating structure but
+ 
+
+ align:start position:0%
+a periodically repeating structure but
+the basis has nine atoms in it right
+
+ align:start position:0%
+the basis has nine atoms in it right
+ 
+
+ align:start position:0%
+the basis has nine atoms in it right
+it's a more complex
+
+ align:start position:0%
+it's a more complex
+ 
+
+ align:start position:0%
+it's a more complex
+structure okay and
+
+ align:start position:0%
+structure okay and
+ 
+
+ align:start position:0%
+structure okay and
+um and let's look now it's an insulator
+
+ align:start position:0%
+um and let's look now it's an insulator
+ 
+
+ align:start position:0%
+um and let's look now it's an insulator
+I'm going to I'm going to totally uh
+
+ align:start position:0%
+I'm going to I'm going to totally uh
+ 
+
+ align:start position:0%
+I'm going to I'm going to totally uh
+agree with that you see right through it
+
+ align:start position:0%
+agree with that you see right through it
+ 
+
+ align:start position:0%
+agree with that you see right through it
+right so you know it's not
+
+ align:start position:0%
+right so you know it's not
+ 
+
+ align:start position:0%
+right so you know it's not
+what absorbing in the visible at least
+
+ align:start position:0%
+what absorbing in the visible at least
+ 
+
+ align:start position:0%
+what absorbing in the visible at least
+right um but since it's an insulator
+
+ align:start position:0%
+right um but since it's an insulator
+ 
+
+ align:start position:0%
+right um but since it's an insulator
+um and it has a large band Gap even
+
+ align:start position:0%
+um and it has a large band Gap even
+ 
+
+ align:start position:0%
+um and it has a large band Gap even
+though it's a solid what do you think
+
+ align:start position:0%
+though it's a solid what do you think
+ 
+
+ align:start position:0%
+though it's a solid what do you think
+the bands are going to look like curvy
+
+ align:start position:0%
+the bands are going to look like curvy
+ 
+
+ align:start position:0%
+the bands are going to look like curvy
+or not so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+curvy that is curvy right they're not
+
+ align:start position:0%
+curvy that is curvy right they're not
+ 
+
+ align:start position:0%
+curvy that is curvy right they're not
+usually as curvy okay so here's the Doss
+
+ align:start position:0%
+usually as curvy okay so here's the Doss
+ 
+
+ align:start position:0%
+usually as curvy okay so here's the Doss
+look at that beautiful bang
+
+ align:start position:0%
+look at that beautiful bang
+ 
+
+ align:start position:0%
+look at that beautiful bang
+Gap this is a bang Gap
+
+ align:start position:0%
+Gap this is a bang Gap
+ 
+
+ align:start position:0%
+Gap this is a bang Gap
+only a mother could what father or
+
+ align:start position:0%
+only a mother could what father or
+ 
+
+ align:start position:0%
+only a mother could what father or
+mother I mean that's a beautiful and um
+
+ align:start position:0%
+mother I mean that's a beautiful and um
+ 
+
+ align:start position:0%
+mother I mean that's a beautiful and um
+look at this
+
+ align:start position:0%
+look at this
+ 
+
+ align:start position:0%
+look at this
+um there's the band structure okay and
+
+ align:start position:0%
+um there's the band structure okay and
+ 
+
+ align:start position:0%
+um there's the band structure okay and
+uh you can see that look at all those
+
+ align:start position:0%
+uh you can see that look at all those
+ 
+
+ align:start position:0%
+uh you can see that look at all those
+bands okay look at all those levels and
+
+ align:start position:0%
+bands okay look at all those levels and
+ 
+
+ align:start position:0%
+bands okay look at all those levels and
+they do curve they do curve but they're
+
+ align:start position:0%
+they do curve they do curve but they're
+ 
+
+ align:start position:0%
+they do curve they do curve but they're
+not as like crazy well they are kind of
+
+ align:start position:0%
+not as like crazy well they are kind of
+ 
+
+ align:start position:0%
+not as like crazy well they are kind of
+spaghetti like but they're not spaghetti
+
+ align:start position:0%
+spaghetti like but they're not spaghetti
+ 
+
+ align:start position:0%
+spaghetti like but they're not spaghetti
+like near the firmy energy or near the
+
+ align:start position:0%
+like near the firmy energy or near the
+ 
+
+ align:start position:0%
+like near the firmy energy or near the
+Gap so you look at that and you're like
+
+ align:start position:0%
+Gap so you look at that and you're like
+ 
+
+ align:start position:0%
+Gap so you look at that and you're like
+insulator first of all just because of
+
+ align:start position:0%
+insulator first of all just because of
+ 
+
+ align:start position:0%
+insulator first of all just because of
+how big the Gap is and then what we're
+
+ align:start position:0%
+how big the Gap is and then what we're
+ 
+
+ align:start position:0%
+how big the Gap is and then what we're
+going to do and I still have just 10
+
+ align:start position:0%
+going to do and I still have just 10
+ 
+
+ align:start position:0%
+going to do and I still have just 10
+minutes more today but on on Thursday
+
+ align:start position:0%
+minutes more today but on on Thursday
+ 
+
+ align:start position:0%
+minutes more today but on on Thursday
+what we're going to do is we're going to
+
+ align:start position:0%
+what we're going to do is we're going to
+ 
+
+ align:start position:0%
+what we're going to do is we're going to
+show how when you look at this you can
+
+ align:start position:0%
+show how when you look at this you can
+ 
+
+ align:start position:0%
+show how when you look at this you can
+say not a very good conductor certainly
+
+ align:start position:0%
+say not a very good conductor certainly
+ 
+
+ align:start position:0%
+say not a very good conductor certainly
+not a good whole
+
+ align:start position:0%
+not a good whole
+ 
+
+ align:start position:0%
+not a good whole
+conductor this is where the holes would
+
+ align:start position:0%
+conductor this is where the holes would
+ 
+
+ align:start position:0%
+conductor this is where the holes would
+move this is where the electrons would
+
+ align:start position:0%
+move this is where the electrons would
+ 
+
+ align:start position:0%
+move this is where the electrons would
+move because we're going to get to that
+
+ align:start position:0%
+move because we're going to get to that
+ 
+
+ align:start position:0%
+move because we're going to get to that
+a little bit on Thursday band structure
+
+ align:start position:0%
+a little bit on Thursday band structure
+ 
+
+ align:start position:0%
+a little bit on Thursday band structure
+is so rich with information it's a
+
+ align:start position:0%
+is so rich with information it's a
+ 
+
+ align:start position:0%
+is so rich with information it's a
+beautiful thing it's
+
+ align:start position:0%
+beautiful thing it's
+ 
+
+ align:start position:0%
+beautiful thing it's
+emotional and if any of you are feeling
+
+ align:start position:0%
+emotional and if any of you are feeling
+ 
+
+ align:start position:0%
+emotional and if any of you are feeling
+that it's okay I'm touching the mic
+
+ align:start position:0%
+that it's okay I'm touching the mic
+ 
+
+ align:start position:0%
+that it's okay I'm touching the mic
+again sorry it's okay we're
+
+ align:start position:0%
+again sorry it's okay we're
+ 
+
+ align:start position:0%
+again sorry it's okay we're
+good check that Roger
+
+ align:start position:0%
+good check that Roger
+ 
+
+ align:start position:0%
+good check that Roger
+okay so
+
+ align:start position:0%
+okay so
+ 
+
+ align:start position:0%
+okay so
+okay we're we're simulating solids you
+
+ align:start position:0%
+okay we're we're simulating solids you
+ 
+
+ align:start position:0%
+okay we're we're simulating solids you
+understand about band structures we've
+
+ align:start position:0%
+understand about band structures we've
+ 
+
+ align:start position:0%
+understand about band structures we've
+talked about silicon
+
+ align:start position:0%
+talked about silicon
+ 
+
+ align:start position:0%
+talked about silicon
+um and occupied
+
+ align:start position:0%
+um and occupied
+ 
+
+ align:start position:0%
+um and occupied
+unoccupied okay you can get the
+
+ align:start position:0%
+unoccupied okay you can get the
+ 
+
+ align:start position:0%
+unoccupied okay you can get the
+densities just like you can in molecules
+
+ align:start position:0%
+densities just like you can in molecules
+ 
+
+ align:start position:0%
+densities just like you can in molecules
+um and as I said you can calculate um
+
+ align:start position:0%
+um and as I said you can calculate um
+ 
+
+ align:start position:0%
+um and as I said you can calculate um
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+uh uh well you need to find the
+
+ align:start position:0%
+uh uh well you need to find the
+ 
+
+ align:start position:0%
+uh uh well you need to find the
+equilibrium lattice constant okay and so
+
+ align:start position:0%
+equilibrium lattice constant okay and so
+ 
+
+ align:start position:0%
+equilibrium lattice constant okay and so
+if you if you if you just do the
+
+ align:start position:0%
+if you if you if you just do the
+ 
+
+ align:start position:0%
+if you if you if you just do the
+calculation at different lattice
+
+ align:start position:0%
+calculation at different lattice
+ 
+
+ align:start position:0%
+calculation at different lattice
+constants you'll get a variation in
+
+ align:start position:0%
+constants you'll get a variation in
+ 
+
+ align:start position:0%
+constants you'll get a variation in
+energy right that's what'll happen and
+
+ align:start position:0%
+energy right that's what'll happen and
+ 
+
+ align:start position:0%
+energy right that's what'll happen and
+you'll get a minimum and that'll be the
+
+ align:start position:0%
+you'll get a minimum and that'll be the
+ 
+
+ align:start position:0%
+you'll get a minimum and that'll be the
+lattice constant that you should run at
+
+ align:start position:0%
+lattice constant that you should run at
+ 
+
+ align:start position:0%
+lattice constant that you should run at
+for your simulations that's pretty
+
+ align:start position:0%
+for your simulations that's pretty
+ 
+
+ align:start position:0%
+for your simulations that's pretty
+important okay um but if you had that
+
+ align:start position:0%
+important okay um but if you had that
+ 
+
+ align:start position:0%
+important okay um but if you had that
+curve already well then you've also got
+
+ align:start position:0%
+curve already well then you've also got
+ 
+
+ align:start position:0%
+curve already well then you've also got
+the bulk modulus which is pretty cool
+
+ align:start position:0%
+the bulk modulus which is pretty cool
+ 
+
+ align:start position:0%
+the bulk modulus which is pretty cool
+now I think that you probably did this
+
+ align:start position:0%
+now I think that you probably did this
+ 
+
+ align:start position:0%
+now I think that you probably did this
+calculation using classical um
+
+ align:start position:0%
+calculation using classical um
+ 
+
+ align:start position:0%
+calculation using classical um
+potentials is that right
+
+ align:start position:0%
+potentials is that right
+ 
+
+ align:start position:0%
+potentials is that right
+you you calculated the bulk modulus so
+
+ align:start position:0%
+you you calculated the bulk modulus so
+ 
+
+ align:start position:0%
+you you calculated the bulk modulus so
+this isn't any different I mean it's
+
+ align:start position:0%
+this isn't any different I mean it's
+ 
+
+ align:start position:0%
+this isn't any different I mean it's
+just the did you do um you did
+
+ align:start position:0%
+just the did you do um you did
+ 
+
+ align:start position:0%
+just the did you do um you did
+periodically repeating structures
+
+ align:start position:0%
+periodically repeating structures
+ 
+
+ align:start position:0%
+periodically repeating structures
+right using classical force
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+fields I'm seeing a whole lot of I'm not
+
+ align:start position:0%
+fields I'm seeing a whole lot of I'm not
+ 
+
+ align:start position:0%
+fields I'm seeing a whole lot of I'm not
+sure
+
+ align:start position:0%
+sure
+ 
+
+ align:start position:0%
+sure
+yeah it's a very I'm not sure kind of
+
+ align:start position:0%
+yeah it's a very I'm not sure kind of
+ 
+
+ align:start position:0%
+yeah it's a very I'm not sure kind of
+Bowman it's okay it's okay is it did did
+
+ align:start position:0%
+Bowman it's okay it's okay is it did did
+ 
+
+ align:start position:0%
+Bowman it's okay it's okay is it did did
+you look at solid materials in your
+
+ align:start position:0%
+you look at solid materials in your
+ 
+
+ align:start position:0%
+you look at solid materials in your
+homeworks it's still no not so sure
+
+ align:start position:0%
+homeworks it's still no not so sure
+ 
+
+ align:start position:0%
+homeworks it's still no not so sure
+silicon carbon not so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+much proteins okay so proteins are are
+
+ align:start position:0%
+much proteins okay so proteins are are
+ 
+
+ align:start position:0%
+much proteins okay so proteins are are
+um are a bit more complex of a beast by
+
+ align:start position:0%
+um are a bit more complex of a beast by
+ 
+
+ align:start position:0%
+um are a bit more complex of a beast by
+the way which you can't really do using
+
+ align:start position:0%
+the way which you can't really do using
+ 
+
+ align:start position:0%
+the way which you can't really do using
+I mean you can do parts of proteins
+
+ align:start position:0%
+I mean you can do parts of proteins
+ 
+
+ align:start position:0%
+I mean you can do parts of proteins
+using quantum mechanics but it's just
+
+ align:start position:0%
+using quantum mechanics but it's just
+ 
+
+ align:start position:0%
+using quantum mechanics but it's just
+too hard it's too big you know you can't
+
+ align:start position:0%
+too hard it's too big you know you can't
+ 
+
+ align:start position:0%
+too hard it's too big you know you can't
+do that many ATS right to do most uh
+
+ align:start position:0%
+do that many ATS right to do most uh
+ 
+
+ align:start position:0%
+do that many ATS right to do most uh
+full size
+
+ align:start position:0%
+full size
+ 
+
+ align:start position:0%
+full size
+proteins um so that's a great problem um
+
+ align:start position:0%
+proteins um so that's a great problem um
+ 
+
+ align:start position:0%
+proteins um so that's a great problem um
+to study with classical models um for
+
+ align:start position:0%
+to study with classical models um for
+ 
+
+ align:start position:0%
+to study with classical models um for
+crystals like the two atom silicon eight
+
+ align:start position:0%
+crystals like the two atom silicon eight
+ 
+
+ align:start position:0%
+crystals like the two atom silicon eight
+electrons or all those crystals in there
+
+ align:start position:0%
+electrons or all those crystals in there
+ 
+
+ align:start position:0%
+electrons or all those crystals in there
+and up to say a thousand electrons um
+
+ align:start position:0%
+and up to say a thousand electrons um
+ 
+
+ align:start position:0%
+and up to say a thousand electrons um
+you can do things like calculate the
+
+ align:start position:0%
+you can do things like calculate the
+ 
+
+ align:start position:0%
+you can do things like calculate the
+change in the lattice with uh change in
+
+ align:start position:0%
+change in the lattice with uh change in
+ 
+
+ align:start position:0%
+change in the lattice with uh change in
+energy with lattice and from that um
+
+ align:start position:0%
+energy with lattice and from that um
+ 
+
+ align:start position:0%
+energy with lattice and from that um
+well this is the volume right but that's
+
+ align:start position:0%
+well this is the volume right but that's
+ 
+
+ align:start position:0%
+well this is the volume right but that's
+just the same as the change in the
+
+ align:start position:0%
+just the same as the change in the
+ 
+
+ align:start position:0%
+just the same as the change in the
+lattice and um and from from that second
+
+ align:start position:0%
+lattice and um and from from that second
+ 
+
+ align:start position:0%
+lattice and um and from from that second
+derivative you can get the bulk modulus
+
+ align:start position:0%
+derivative you can get the bulk modulus
+ 
+
+ align:start position:0%
+derivative you can get the bulk modulus
+which is a very important property
+
+ align:start position:0%
+which is a very important property
+ 
+
+ align:start position:0%
+which is a very important property
+um okay and this is something I just
+
+ align:start position:0%
+um okay and this is something I just
+ 
+
+ align:start position:0%
+um okay and this is something I just
+went through this was that slide that I
+
+ align:start position:0%
+went through this was that slide that I
+ 
+
+ align:start position:0%
+went through this was that slide that I
+talked about but it was really should
+
+ align:start position:0%
+talked about but it was really should
+ 
+
+ align:start position:0%
+talked about but it was really should
+have been an internal discussion um and
+
+ align:start position:0%
+have been an internal discussion um and
+ 
+
+ align:start position:0%
+have been an internal discussion um and
+and where you you know you find the
+
+ align:start position:0%
+and where you you know you find the
+ 
+
+ align:start position:0%
+and where you you know you find the
+converg ground state density and
+
+ align:start position:0%
+converg ground state density and
+ 
+
+ align:start position:0%
+converg ground state density and
+potential with some kpoint mesh that you
+
+ align:start position:0%
+potential with some kpoint mesh that you
+ 
+
+ align:start position:0%
+potential with some kpoint mesh that you
+gave it that's what you input is the K
+
+ align:start position:0%
+gave it that's what you input is the K
+ 
+
+ align:start position:0%
+gave it that's what you input is the K
+points that go into that calculation and
+
+ align:start position:0%
+points that go into that calculation and
+ 
+
+ align:start position:0%
+points that go into that calculation and
+then for that you calculate the energies
+
+ align:start position:0%
+then for that you calculate the energies
+ 
+
+ align:start position:0%
+then for that you calculate the energies
+that K points along all the lines and
+
+ align:start position:0%
+that K points along all the lines and
+ 
+
+ align:start position:0%
+that K points along all the lines and
+some software well step three is not
+
+ align:start position:0%
+some software well step three is not
+ 
+
+ align:start position:0%
+some software well step three is not
+really a step right but use some
+
+ align:start position:0%
+really a step right but use some
+ 
+
+ align:start position:0%
+really a step right but use some
+software to plot it okay and you can
+
+ align:start position:0%
+software to plot it okay and you can
+ 
+
+ align:start position:0%
+software to plot it okay and you can
+download the data for this from the
+
+ align:start position:0%
+download the data for this from the
+ 
+
+ align:start position:0%
+download the data for this from the
+nanohub there's a I've been showing you
+
+ align:start position:0%
+nanohub there's a I've been showing you
+ 
+
+ align:start position:0%
+nanohub there's a I've been showing you
+the version of the plot that gives you
+
+ align:start position:0%
+the version of the plot that gives you
+ 
+
+ align:start position:0%
+the version of the plot that gives you
+the Greek characters which is an image
+
+ align:start position:0%
+the Greek characters which is an image
+ 
+
+ align:start position:0%
+the Greek characters which is an image
+but there's another version that gives
+
+ align:start position:0%
+but there's another version that gives
+ 
+
+ align:start position:0%
+but there's another version that gives
+you the raw data it just doesn't put the
+
+ align:start position:0%
+you the raw data it just doesn't put the
+ 
+
+ align:start position:0%
+you the raw data it just doesn't put the
+characters on it but that will allow you
+
+ align:start position:0%
+characters on it but that will allow you
+ 
+
+ align:start position:0%
+characters on it but that will allow you
+to compare one run to another and
+
+ align:start position:0%
+to compare one run to another and
+ 
+
+ align:start position:0%
+to compare one run to another and
+download the raw
+
+ align:start position:0%
+download the raw
+ 
+
+ align:start position:0%
+download the raw
+data and then um calculating the Doss is
+
+ align:start position:0%
+data and then um calculating the Doss is
+ 
+
+ align:start position:0%
+data and then um calculating the Doss is
+um um is also a two-step process you
+
+ align:start position:0%
+um um is also a two-step process you
+ 
+
+ align:start position:0%
+um um is also a two-step process you
+converge the ground state density and
+
+ align:start position:0%
+converge the ground state density and
+ 
+
+ align:start position:0%
+converge the ground state density and
+potential and then you use that
+
+ align:start position:0%
+potential and then you use that
+ 
+
+ align:start position:0%
+potential and then you use that
+potential to calculate the energies and
+
+ align:start position:0%
+potential to calculate the energies and
+ 
+
+ align:start position:0%
+potential to calculate the energies and
+usually you want to do this at a dense K
+
+ align:start position:0%
+usually you want to do this at a dense K
+ 
+
+ align:start position:0%
+usually you want to do this at a dense K
+mesh because the subtle variations see
+
+ align:start position:0%
+mesh because the subtle variations see
+ 
+
+ align:start position:0%
+mesh because the subtle variations see
+in a in a
+
+ align:start position:0%
+in a in a
+ 
+
+ align:start position:0%
+in a in a
+molecule often times the Dos is is
+
+ align:start position:0%
+molecule often times the Dos is is
+ 
+
+ align:start position:0%
+molecule often times the Dos is is
+pretty clear you know I mean if I turn
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um oh I guess I could have just done
+
+ align:start position:0%
+um oh I guess I could have just done
+ 
+
+ align:start position:0%
+um oh I guess I could have just done
+this look at that if I turn um if I turn
+
+ align:start position:0%
+this look at that if I turn um if I turn
+ 
+
+ align:start position:0%
+this look at that if I turn um if I turn
+say an atom or a molecule on its side
+
+ align:start position:0%
+say an atom or a molecule on its side
+ 
+
+ align:start position:0%
+say an atom or a molecule on its side
+then I have this and you use some kind
+
+ align:start position:0%
+then I have this and you use some kind
+ 
+
+ align:start position:0%
+then I have this and you use some kind
+of you know smearing function and so
+
+ align:start position:0%
+of you know smearing function and so
+ 
+
+ align:start position:0%
+of you know smearing function and so
+your well that was a bad centering and
+
+ align:start position:0%
+your well that was a bad centering and
+ 
+
+ align:start position:0%
+your well that was a bad centering and
+so your Doss would look like that right
+
+ align:start position:0%
+so your Doss would look like that right
+ 
+
+ align:start position:0%
+so your Doss would look like that right
+but there'd be bigger Peaks where you
+
+ align:start position:0%
+but there'd be bigger Peaks where you
+ 
+
+ align:start position:0%
+but there'd be bigger Peaks where you
+have like lots of states and smaller
+
+ align:start position:0%
+have like lots of states and smaller
+ 
+
+ align:start position:0%
+have like lots of states and smaller
+Peaks where you don't have many but you
+
+ align:start position:0%
+Peaks where you don't have many but you
+ 
+
+ align:start position:0%
+Peaks where you don't have many but you
+see now I'm turning a band structure and
+
+ align:start position:0%
+see now I'm turning a band structure and
+ 
+
+ align:start position:0%
+see now I'm turning a band structure and
+you saw Alpha quartz right so now I'm
+
+ align:start position:0%
+you saw Alpha quartz right so now I'm
+ 
+
+ align:start position:0%
+you saw Alpha quartz right so now I'm
+turning um see if I I can just show it
+
+ align:start position:0%
+turning um see if I I can just show it
+ 
+
+ align:start position:0%
+turning um see if I I can just show it
+one more
+
+ align:start position:0%
+one more
+ 
+
+ align:start position:0%
+one more
+time oh man seriously oh it was in
+
+ align:start position:0%
+time oh man seriously oh it was in
+ 
+
+ align:start position:0%
+time oh man seriously oh it was in
+another right I'm turning this on its
+
+ align:start position:0%
+another right I'm turning this on its
+ 
+
+ align:start position:0%
+another right I'm turning this on its
+side now and that's uh not as easy right
+
+ align:start position:0%
+side now and that's uh not as easy right
+ 
+
+ align:start position:0%
+side now and that's uh not as easy right
+that's trickier so there's different
+
+ align:start position:0%
+that's trickier so there's different
+ 
+
+ align:start position:0%
+that's trickier so there's different
+weights of a band at different parts in
+
+ align:start position:0%
+weights of a band at different parts in
+ 
+
+ align:start position:0%
+weights of a band at different parts in
+energy and when I turn this on the side
+
+ align:start position:0%
+energy and when I turn this on the side
+ 
+
+ align:start position:0%
+energy and when I turn this on the side
+you can get um Doss uh shapes density of
+
+ align:start position:0%
+you can get um Doss uh shapes density of
+ 
+
+ align:start position:0%
+you can get um Doss uh shapes density of
+states that are um that have a you know
+
+ align:start position:0%
+states that are um that have a you know
+ 
+
+ align:start position:0%
+states that are um that have a you know
+more sort of features in them and to get
+
+ align:start position:0%
+more sort of features in them and to get
+ 
+
+ align:start position:0%
+more sort of features in them and to get
+all those features just right um You
+
+ align:start position:0%
+all those features just right um You
+ 
+
+ align:start position:0%
+all those features just right um You
+need to use the dense kpoint mesh which
+
+ align:start position:0%
+need to use the dense kpoint mesh which
+ 
+
+ align:start position:0%
+need to use the dense kpoint mesh which
+is what the code does okay um this can
+
+ align:start position:0%
+is what the code does okay um this can
+ 
+
+ align:start position:0%
+is what the code does okay um this can
+be measured the Doss can be measured
+
+ align:start position:0%
+be measured the Doss can be measured
+ 
+
+ align:start position:0%
+be measured the Doss can be measured
+right
+
+ align:start position:0%
+right
+ 
+
+ align:start position:0%
+right
+experimentally right you can use STM to
+
+ align:start position:0%
+experimentally right you can use STM to
+ 
+
+ align:start position:0%
+experimentally right you can use STM to
+actually directly measure the
+
+ align:start position:0%
+actually directly measure the
+ 
+
+ align:start position:0%
+actually directly measure the
+Doss
+
+ align:start position:0%
+Doss
+ 
+
+ align:start position:0%
+Doss
+okay and we talked about this already
+
+ align:start position:0%
+okay and we talked about this already
+ 
+
+ align:start position:0%
+okay and we talked about this already
+you fill up your electrons to the
+
+ align:start position:0%
+you fill up your electrons to the
+ 
+
+ align:start position:0%
+you fill up your electrons to the
+firming level um if there's any bands
+
+ align:start position:0%
+firming level um if there's any bands
+ 
+
+ align:start position:0%
+firming level um if there's any bands
+Crossing it's a metal if not it's an
+
+ align:start position:0%
+Crossing it's a metal if not it's an
+ 
+
+ align:start position:0%
+Crossing it's a metal if not it's an
+insulator or a semiconductor if you have
+
+ align:start position:0%
+insulator or a semiconductor if you have
+ 
+
+ align:start position:0%
+insulator or a semiconductor if you have
+an odd number of electrons in the unit
+
+ align:start position:0%
+an odd number of electrons in the unit
+ 
+
+ align:start position:0%
+an odd number of electrons in the unit
+cell it it um it has to be a metal
+
+ align:start position:0%
+cell it it um it has to be a metal
+ 
+
+ align:start position:0%
+cell it it um it has to be a metal
+because the firming level is going to
+
+ align:start position:0%
+because the firming level is going to
+ 
+
+ align:start position:0%
+because the firming level is going to
+come in you know in the middle each band
+
+ align:start position:0%
+come in you know in the middle each band
+ 
+
+ align:start position:0%
+come in you know in the middle each band
+takes two electrons so if you fill up to
+
+ align:start position:0%
+takes two electrons so if you fill up to
+ 
+
+ align:start position:0%
+takes two electrons so if you fill up to
+the firmy level and the firmy level is
+
+ align:start position:0%
+the firmy level and the firmy level is
+ 
+
+ align:start position:0%
+the firmy level and the firmy level is
+in the middle of a band by definition
+
+ align:start position:0%
+in the middle of a band by definition
+ 
+
+ align:start position:0%
+in the middle of a band by definition
+it's a metal right
+
+ align:start position:0%
+it's a metal right
+ 
+
+ align:start position:0%
+it's a metal right
+okay okay
+
+ align:start position:0%
+okay okay
+ 
+
+ align:start position:0%
+okay okay
+sodium um and then here's a picture of
+
+ align:start position:0%
+sodium um and then here's a picture of
+ 
+
+ align:start position:0%
+sodium um and then here's a picture of
+diamond and the thing that I want to um
+
+ align:start position:0%
+diamond and the thing that I want to um
+ 
+
+ align:start position:0%
+diamond and the thing that I want to um
+again emphasize is that from
+
+ align:start position:0%
+again emphasize is that from
+ 
+
+ align:start position:0%
+again emphasize is that from
+DFT uh
+
+ align:start position:0%
+DFT uh
+ 
+
+ align:start position:0%
+DFT uh
+these characters of these Wiggles and of
+
+ align:start position:0%
+these characters of these Wiggles and of
+ 
+
+ align:start position:0%
+these characters of these Wiggles and of
+these features are pretty darn good but
+
+ align:start position:0%
+these features are pretty darn good but
+ 
+
+ align:start position:0%
+these features are pretty darn good but
+this distance is not and so we what
+
+ align:start position:0%
+this distance is not and so we what
+ 
+
+ align:start position:0%
+this distance is not and so we what
+we're going to do in this
+
+ align:start position:0%
+we're going to do in this
+ 
+
+ align:start position:0%
+we're going to do in this
+class and we're going to be proud about
+
+ align:start position:0%
+class and we're going to be proud about
+ 
+
+ align:start position:0%
+class and we're going to be proud about
+it is we're going to just shift these
+
+ align:start position:0%
+it is we're going to just shift these
+ 
+
+ align:start position:0%
+it is we're going to just shift these
+bands up by a rigid amount to fix the
+
+ align:start position:0%
+bands up by a rigid amount to fix the
+ 
+
+ align:start position:0%
+bands up by a rigid amount to fix the
+Gap that was probably electron volts
+
+ align:start position:0%
+Gap that was probably electron volts
+ 
+
+ align:start position:0%
+Gap that was probably electron volts
+yeah it says it here e electron volts
+
+ align:start position:0%
+yeah it says it here e electron volts
+ 
+
+ align:start position:0%
+yeah it says it here e electron volts
+and here
+
+ align:start position:0%
+and here
+ 
+
+ align:start position:0%
+and here
+um it looks like what do we have like a
+
+ align:start position:0%
+um it looks like what do we have like a
+ 
+
+ align:start position:0%
+um it looks like what do we have like a
+3 EV 3 EV Gap from DFT and so that's
+
+ align:start position:0%
+3 EV 3 EV Gap from DFT and so that's
+ 
+
+ align:start position:0%
+3 EV 3 EV Gap from DFT and so that's
+about half very often DFT gives you a
+
+ align:start position:0%
+about half very often DFT gives you a
+ 
+
+ align:start position:0%
+about half very often DFT gives you a
+gap that's about half of the
+
+ align:start position:0%
+gap that's about half of the
+ 
+
+ align:start position:0%
+gap that's about half of the
+experimental Gap very often not at all
+
+ align:start position:0%
+experimental Gap very often not at all
+ 
+
+ align:start position:0%
+experimental Gap very often not at all
+always but very
+
+ align:start position:0%
+always but very
+ 
+
+ align:start position:0%
+always but very
+often for germanium it makes it a semi
+
+ align:start position:0%
+often for germanium it makes it a semi
+ 
+
+ align:start position:0%
+often for germanium it makes it a semi
+metal which it's not does anybody know
+
+ align:start position:0%
+metal which it's not does anybody know
+ 
+
+ align:start position:0%
+metal which it's not does anybody know
+what a semi metal is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+not
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+quite here's a here's an indirect band
+
+ align:start position:0%
+quite here's a here's an indirect band
+ 
+
+ align:start position:0%
+quite here's a here's an indirect band
+Gap a semi metal is a cool material
+
+ align:start position:0%
+Gap a semi metal is a cool material
+ 
+
+ align:start position:0%
+Gap a semi metal is a cool material
+geranium is not a semimetal but DFT will
+
+ align:start position:0%
+geranium is not a semimetal but DFT will
+ 
+
+ align:start position:0%
+geranium is not a semimetal but DFT will
+tell you it is because of the Gap
+
+ align:start position:0%
+tell you it is because of the Gap
+ 
+
+ align:start position:0%
+tell you it is because of the Gap
+problem um here's an indirect bandap
+
+ align:start position:0%
+problem um here's an indirect bandap
+ 
+
+ align:start position:0%
+problem um here's an indirect bandap
+material which one is
+
+ align:start position:0%
+material which one is
+ 
+
+ align:start position:0%
+material which one is
+it yeah sure why
+
+ align:start position:0%
+it yeah sure why
+ 
+
+ align:start position:0%
+it yeah sure why
+not okay and if it's silicon this will
+
+ align:start position:0%
+not okay and if it's silicon this will
+ 
+
+ align:start position:0%
+not okay and if it's silicon this will
+be 1.1 EV in
+
+ align:start position:0%
+be 1.1 EV in
+ 
+
+ align:start position:0%
+be 1.1 EV in
+experiment and about 0.6 EV
+
+ align:start position:0%
+experiment and about 0.6 EV
+ 
+
+ align:start position:0%
+experiment and about 0.6 EV
+in
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+DFT okay and that's the band Gap error
+
+ align:start position:0%
+DFT okay and that's the band Gap error
+ 
+
+ align:start position:0%
+DFT okay and that's the band Gap error
+but again you can shift it and that's
+
+ align:start position:0%
+but again you can shift it and that's
+ 
+
+ align:start position:0%
+but again you can shift it and that's
+what we're going to do we're going to be
+
+ align:start position:0%
+what we're going to do we're going to be
+ 
+
+ align:start position:0%
+what we're going to do we're going to be
+okay with that um in uh if you switch to
+
+ align:start position:0%
+okay with that um in uh if you switch to
+ 
+
+ align:start position:0%
+okay with that um in uh if you switch to
+geranium experiment says it's about A6
+
+ align:start position:0%
+geranium experiment says it's about A6
+ 
+
+ align:start position:0%
+geranium experiment says it's about A6
+or 7 EV Gap something around there but
+
+ align:start position:0%
+or 7 EV Gap something around there but
+ 
+
+ align:start position:0%
+or 7 EV Gap something around there but
+DFT um that's silicon okay but DFT will
+
+ align:start position:0%
+DFT um that's silicon okay but DFT will
+ 
+
+ align:start position:0%
+DFT um that's silicon okay but DFT will
+put it here it'll put this conduction
+
+ align:start position:0%
+put it here it'll put this conduction
+ 
+
+ align:start position:0%
+put it here it'll put this conduction
+band below
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+right it has to actually it's why didn't
+
+ align:start position:0%
+right it has to actually it's why didn't
+ 
+
+ align:start position:0%
+right it has to actually it's why didn't
+I draw that right it's actually um comes
+
+ align:start position:0%
+I draw that right it's actually um comes
+ 
+
+ align:start position:0%
+I draw that right it's actually um comes
+below
+
+ align:start position:0%
+below
+ 
+
+ align:start position:0%
+below
+so that is a semi
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+metal when you have uh basically it's
+
+ align:start position:0%
+metal when you have uh basically it's
+ 
+
+ align:start position:0%
+metal when you have uh basically it's
+Crossings okay across the firmy level
+
+ align:start position:0%
+Crossings okay across the firmy level
+ 
+
+ align:start position:0%
+Crossings okay across the firmy level
+but in an indirect from indirect States
+
+ align:start position:0%
+but in an indirect from indirect States
+ 
+
+ align:start position:0%
+but in an indirect from indirect States
+right that's called the semi metal and
+
+ align:start position:0%
+right that's called the semi metal and
+ 
+
+ align:start position:0%
+right that's called the semi metal and
+DFT will tell you geranium is that which
+
+ align:start position:0%
+DFT will tell you geranium is that which
+ 
+
+ align:start position:0%
+DFT will tell you geranium is that which
+is not but you you can still shift all
+
+ align:start position:0%
+is not but you you can still shift all
+ 
+
+ align:start position:0%
+is not but you you can still shift all
+those States up which we do okay oh
+
+ align:start position:0%
+those States up which we do okay oh
+ 
+
+ align:start position:0%
+those States up which we do okay oh
+there's a metal oh look at that
+
+ align:start position:0%
+there's a metal oh look at that
+ 
+
+ align:start position:0%
+there's a metal oh look at that
+spaghetti you now know oh and there it
+
+ align:start position:0%
+spaghetti you now know oh and there it
+ 
+
+ align:start position:0%
+spaghetti you now know oh and there it
+is see often in papers you'll see in the
+
+ align:start position:0%
+is see often in papers you'll see in the
+ 
+
+ align:start position:0%
+is see often in papers you'll see in the
+literature so you now becoming sort of
+
+ align:start position:0%
+literature so you now becoming sort of
+ 
+
+ align:start position:0%
+literature so you now becoming sort of
+experts at seeing a band structure and
+
+ align:start position:0%
+experts at seeing a band structure and
+ 
+
+ align:start position:0%
+experts at seeing a band structure and
+seeing it really seeing it you know and
+
+ align:start position:0%
+seeing it really seeing it you know and
+ 
+
+ align:start position:0%
+seeing it really seeing it you know and
+it's a powerful thing and there it is
+
+ align:start position:0%
+it's a powerful thing and there it is
+ 
+
+ align:start position:0%
+it's a powerful thing and there it is
+with the Doss next to it you see because
+
+ align:start position:0%
+with the Doss next to it you see because
+ 
+
+ align:start position:0%
+with the Doss next to it you see because
+that's just this on the side which is
+
+ align:start position:0%
+that's just this on the side which is
+ 
+
+ align:start position:0%
+that's just this on the side which is
+why you then plot the Doss sideways
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+often um except that doesn't quite look
+
+ align:start position:0%
+often um except that doesn't quite look
+ 
+
+ align:start position:0%
+often um except that doesn't quite look
+right but anyway
+
+ align:start position:0%
+right but anyway
+ 
+
+ align:start position:0%
+right but anyway
+um oh maybe this
+
+ align:start position:0%
+um oh maybe this
+ 
+
+ align:start position:0%
+um oh maybe this
+yeah that's what it should
+
+ align:start position:0%
+yeah that's what it should
+ 
+
+ align:start position:0%
+yeah that's what it should
+be
+
+ align:start position:0%
+be
+ 
+
+ align:start position:0%
+be
+okay um and then you know we've we've
+
+ align:start position:0%
+okay um and then you know we've we've
+ 
+
+ align:start position:0%
+okay um and then you know we've we've
+talked about this and we're going to
+
+ align:start position:0%
+talked about this and we're going to
+ 
+
+ align:start position:0%
+talked about this and we're going to
+talk about this um we're going to come
+
+ align:start position:0%
+talk about this um we're going to come
+ 
+
+ align:start position:0%
+talk about this um we're going to come
+back to this a little bit when we talk
+
+ align:start position:0%
+back to this a little bit when we talk
+ 
+
+ align:start position:0%
+back to this a little bit when we talk
+about solar cells um but I have
+
+ align:start position:0%
+about solar cells um but I have
+ 
+
+ align:start position:0%
+about solar cells um but I have
+mentioned this a bunch certainly this
+
+ align:start position:0%
+mentioned this a bunch certainly this
+ 
+
+ align:start position:0%
+mentioned this a bunch certainly this
+would be a a good third homework set um
+
+ align:start position:0%
+would be a a good third homework set um
+ 
+
+ align:start position:0%
+would be a a good third homework set um
+is to think about this you know indirect
+
+ align:start position:0%
+is to think about this you know indirect
+ 
+
+ align:start position:0%
+is to think about this you know indirect
+versus direct bandap problem somebody
+
+ align:start position:0%
+versus direct bandap problem somebody
+ 
+
+ align:start position:0%
+versus direct bandap problem somebody
+tell me again why silicon solar cells
+
+ align:start position:0%
+tell me again why silicon solar cells
+ 
+
+ align:start position:0%
+tell me again why silicon solar cells
+are expensive just so I can go home
+
+ align:start position:0%
+are expensive just so I can go home
+ 
+
+ align:start position:0%
+are expensive just so I can go home
+today and feel really
+
+ align:start position:0%
+today and feel really
+ 
+
+ align:start position:0%
+today and feel really
+good or really bad because it's bad
+
+ align:start position:0%
+good or really bad because it's bad
+ 
+
+ align:start position:0%
+good or really bad because it's bad
+news yeah but why is that why does that
+
+ align:start position:0%
+news yeah but why is that why does that
+ 
+
+ align:start position:0%
+news yeah but why is that why does that
+make silicon solar cells
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+expensive why do you have to make them
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+thick yeah because you got to get you
+
+ align:start position:0%
+thick yeah because you got to get you
+ 
+
+ align:start position:0%
+thick yeah because you got to get you
+see you got to get I think I had it
+
+ align:start position:0%
+see you got to get I think I had it
+ 
+
+ align:start position:0%
+see you got to get I think I had it
+shown here yeah yeah see that's easy for
+
+ align:start position:0%
+shown here yeah yeah see that's easy for
+ 
+
+ align:start position:0%
+shown here yeah yeah see that's easy for
+a photon to do right I've talked about
+
+ align:start position:0%
+a photon to do right I've talked about
+ 
+
+ align:start position:0%
+a photon to do right I've talked about
+this now here is in the cartoon that's
+
+ align:start position:0%
+this now here is in the cartoon that's
+ 
+
+ align:start position:0%
+this now here is in the cartoon that's
+easy for a photon to do okay um that's
+
+ align:start position:0%
+easy for a photon to do okay um that's
+ 
+
+ align:start position:0%
+easy for a photon to do okay um that's
+easy for a photon to do at different
+
+ align:start position:0%
+easy for a photon to do at different
+ 
+
+ align:start position:0%
+easy for a photon to do at different
+places in energy and this would be
+
+ align:start position:0%
+places in energy and this would be
+ 
+
+ align:start position:0%
+places in energy and this would be
+absorbing light these blue arrows would
+
+ align:start position:0%
+absorbing light these blue arrows would
+ 
+
+ align:start position:0%
+absorbing light these blue arrows would
+be the light that come from the solar
+
+ align:start position:0%
+be the light that come from the solar
+ 
+
+ align:start position:0%
+be the light that come from the solar
+flux that you're downloading in your
+
+ align:start position:0%
+flux that you're downloading in your
+ 
+
+ align:start position:0%
+flux that you're downloading in your
+homework right that's where these blue
+
+ align:start position:0%
+homework right that's where these blue
+ 
+
+ align:start position:0%
+homework right that's where these blue
+arrows come um and it's easy for those
+
+ align:start position:0%
+arrows come um and it's easy for those
+ 
+
+ align:start position:0%
+arrows come um and it's easy for those
+blue arrows to do this but to see the
+
+ align:start position:0%
+blue arrows to do this but to see the
+ 
+
+ align:start position:0%
+blue arrows to do this but to see the
+thing that matters is this minimum
+
+ align:start position:0%
+thing that matters is this minimum
+ 
+
+ align:start position:0%
+thing that matters is this minimum
+amount of energy the band gap of the
+
+ align:start position:0%
+amount of energy the band gap of the
+ 
+
+ align:start position:0%
+amount of energy the band gap of the
+material uh that is the lowest amount of
+
+ align:start position:0%
+material uh that is the lowest amount of
+ 
+
+ align:start position:0%
+material uh that is the lowest amount of
+energy that it would take to get an
+
+ align:start position:0%
+energy that it would take to get an
+ 
+
+ align:start position:0%
+energy that it would take to get an
+electron up from the valance into the
+
+ align:start position:0%
+electron up from the valance into the
+ 
+
+ align:start position:0%
+electron up from the valance into the
+conduction bands and that in this case
+
+ align:start position:0%
+conduction bands and that in this case
+ 
+
+ align:start position:0%
+conduction bands and that in this case
+is not vertical it's not vertical it's
+
+ align:start position:0%
+is not vertical it's not vertical it's
+ 
+
+ align:start position:0%
+is not vertical it's not vertical it's
+an indirect Gap did I have it there um
+
+ align:start position:0%
+an indirect Gap did I have it there um
+ 
+
+ align:start position:0%
+an indirect Gap did I have it there um
+and because of that it's not very good
+
+ align:start position:0%
+and because of that it's not very good
+ 
+
+ align:start position:0%
+and because of that it's not very good
+at absorbing light those photons those
+
+ align:start position:0%
+at absorbing light those photons those
+ 
+
+ align:start position:0%
+at absorbing light those photons those
+blue
+
+ align:start position:0%
+blue
+ 
+
+ align:start position:0%
+blue
+lines um let just get them back here
+
+ align:start position:0%
+lines um let just get them back here
+ 
+
+ align:start position:0%
+lines um let just get them back here
+those blue lines they need help
+
+ align:start position:0%
+those blue lines they need help
+ 
+
+ align:start position:0%
+those blue lines they need help
+help they can do this but they can't do
+
+ align:start position:0%
+help they can do this but they can't do
+ 
+
+ align:start position:0%
+help they can do this but they can't do
+this and to do this you need help okay
+
+ align:start position:0%
+this and to do this you need help okay
+ 
+
+ align:start position:0%
+this and to do this you need help okay
+so you need some kind of uh kick and
+
+ align:start position:0%
+so you need some kind of uh kick and
+ 
+
+ align:start position:0%
+so you need some kind of uh kick and
+that means it's a much less efficient
+
+ align:start position:0%
+that means it's a much less efficient
+ 
+
+ align:start position:0%
+that means it's a much less efficient
+process and absorbing light in that
+
+ align:start position:0%
+process and absorbing light in that
+ 
+
+ align:start position:0%
+process and absorbing light in that
+whole region of the spectrum where a
+
+ align:start position:0%
+whole region of the spectrum where a
+ 
+
+ align:start position:0%
+whole region of the spectrum where a
+photon would need to do this that whole
+
+ align:start position:0%
+photon would need to do this that whole
+ 
+
+ align:start position:0%
+photon would need to do this that whole
+region is very inefficient and yet
+
+ align:start position:0%
+region is very inefficient and yet
+ 
+
+ align:start position:0%
+region is very inefficient and yet
+that's where the sun is that's where the
+
+ align:start position:0%
+that's where the sun is that's where the
+ 
+
+ align:start position:0%
+that's where the sun is that's where the
+sun is and so you got to make them
+
+ align:start position:0%
+sun is and so you got to make them
+ 
+
+ align:start position:0%
+sun is and so you got to make them
+really thick it's inefficient but not
+
+ align:start position:0%
+really thick it's inefficient but not
+ 
+
+ align:start position:0%
+really thick it's inefficient but not
+zero so you make them really thick so
+
+ align:start position:0%
+zero so you make them really thick so
+ 
+
+ align:start position:0%
+zero so you make them really thick so
+you get that region of the Sun but to
+
+ align:start position:0%
+you get that region of the Sun but to
+ 
+
+ align:start position:0%
+you get that region of the Sun but to
+make them really thick um you see you're
+
+ align:start position:0%
+make them really thick um you see you're
+ 
+
+ align:start position:0%
+make them really thick um you see you're
+generating electrons in
+
+ align:start position:0%
+generating electrons in
+ 
+
+ align:start position:0%
+generating electrons in
+holes and those that generation of
+
+ align:start position:0%
+holes and those that generation of
+ 
+
+ align:start position:0%
+holes and those that generation of
+electrons and holes well that then you
+
+ align:start position:0%
+electrons and holes well that then you
+ 
+
+ align:start position:0%
+electrons and holes well that then you
+got to get them
+
+ align:start position:0%
+got to get them
+ 
+
+ align:start position:0%
+got to get them
+out right you can't just let them stay
+
+ align:start position:0%
+out right you can't just let them stay
+ 
+
+ align:start position:0%
+out right you can't just let them stay
+there and to get them out well you need
+
+ align:start position:0%
+there and to get them out well you need
+ 
+
+ align:start position:0%
+there and to get them out well you need
+a good
+
+ align:start position:0%
+a good
+ 
+
+ align:start position:0%
+a good
+material and if they have to go a long
+
+ align:start position:0%
+material and if they have to go a long
+ 
+
+ align:start position:0%
+material and if they have to go a long
+ways to get out which they do because
+
+ align:start position:0%
+ways to get out which they do because
+ 
+
+ align:start position:0%
+ways to get out which they do because
+they have to make it so thick because it
+
+ align:start position:0%
+they have to make it so thick because it
+ 
+
+ align:start position:0%
+they have to make it so thick because it
+doesn't absorb light well because of the
+
+ align:start position:0%
+doesn't absorb light well because of the
+ 
+
+ align:start position:0%
+doesn't absorb light well because of the
+band structure
+
+ align:start position:0%
+band structure
+ 
+
+ align:start position:0%
+band structure
+then um where was I again no then you uh
+
+ align:start position:0%
+then um where was I again no then you uh
+ 
+
+ align:start position:0%
+then um where was I again no then you uh
+you need it to be a really pure material
+
+ align:start position:0%
+you need it to be a really pure material
+ 
+
+ align:start position:0%
+you need it to be a really pure material
+that costs money okay otherwise they'll
+
+ align:start position:0%
+that costs money okay otherwise they'll
+ 
+
+ align:start position:0%
+that costs money okay otherwise they'll
+run into traps and and other things so
+
+ align:start position:0%
+run into traps and and other things so
+ 
+
+ align:start position:0%
+run into traps and and other things so
+what we're going to do is on Thursday
+
+ align:start position:0%
+what we're going to do is on Thursday
+ 
+
+ align:start position:0%
+what we're going to do is on Thursday
+we'll talk a little bit more about um
+
+ align:start position:0%
+we'll talk a little bit more about um
+ 
+
+ align:start position:0%
+we'll talk a little bit more about um
+some other properties we'll talk about
+
+ align:start position:0%
+some other properties we'll talk about
+ 
+
+ align:start position:0%
+some other properties we'll talk about
+magnetism very briefly show you that you
+
+ align:start position:0%
+magnetism very briefly show you that you
+ 
+
+ align:start position:0%
+magnetism very briefly show you that you
+can do molecular Dynamics um couple
+
+ align:start position:0%
+can do molecular Dynamics um couple
+ 
+
+ align:start position:0%
+can do molecular Dynamics um couple
+other things and then we'll start
+
+ align:start position:0%
+other things and then we'll start
+ 
+
+ align:start position:0%
+other things and then we'll start
+turning our attention to solar cells
+
+ align:start position:0%
+turning our attention to solar cells
+ 
+
+ align:start position:0%
+turning our attention to solar cells
+okay for
\ No newline at end of file
diff --git a/GLVrOlHLJ1U.txt b/GLVrOlHLJ1U.txt
new file mode 100644
index 0000000000000000000000000000000000000000..5beb2e215ca50f2a9e2af98636191be358ff42e0
--- /dev/null
+++ b/GLVrOlHLJ1U.txt
@@ -0,0 +1,13035 @@
+align:start position:0%
+ 
+the following content is provided under
+
+ align:start position:0%
+the following content is provided under
+ 
+
+ align:start position:0%
+the following content is provided under
+a Creative Commons license your support
+
+ align:start position:0%
+a Creative Commons license your support
+ 
+
+ align:start position:0%
+a Creative Commons license your support
+will help MIT OpenCourseWare continue to
+
+ align:start position:0%
+will help MIT OpenCourseWare continue to
+ 
+
+ align:start position:0%
+will help MIT OpenCourseWare continue to
+offer high quality educational resources
+
+ align:start position:0%
+offer high quality educational resources
+ 
+
+ align:start position:0%
+offer high quality educational resources
+for free
+
+ align:start position:0%
+for free
+ 
+
+ align:start position:0%
+for free
+to make a donation or to view additional
+
+ align:start position:0%
+to make a donation or to view additional
+ 
+
+ align:start position:0%
+to make a donation or to view additional
+materials from hundreds of MIT courses
+
+ align:start position:0%
+materials from hundreds of MIT courses
+ 
+
+ align:start position:0%
+materials from hundreds of MIT courses
+visit MIT opencourseware at ocw.mit.edu
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+thank you again for all being here we
+
+ align:start position:0%
+thank you again for all being here we
+ 
+
+ align:start position:0%
+thank you again for all being here we
+were gonna talk a little bit about the
+
+ align:start position:0%
+were gonna talk a little bit about the
+ 
+
+ align:start position:0%
+were gonna talk a little bit about the
+challenges of blockchain technology
+
+ align:start position:0%
+challenges of blockchain technology
+ 
+
+ align:start position:0%
+challenges of blockchain technology
+I'm apologizing in advance I'm supposed
+
+ align:start position:0%
+I'm apologizing in advance I'm supposed
+ 
+
+ align:start position:0%
+I'm apologizing in advance I'm supposed
+to be like across campus for a 4:00
+
+ align:start position:0%
+to be like across campus for a 4:00
+ 
+
+ align:start position:0%
+to be like across campus for a 4:00
+o'clock meeting so I won't have much
+
+ align:start position:0%
+o'clock meeting so I won't have much
+ 
+
+ align:start position:0%
+o'clock meeting so I won't have much
+time right at the end to do the little
+
+ align:start position:0%
+time right at the end to do the little
+ 
+
+ align:start position:0%
+time right at the end to do the little
+rap with students coming up I will note
+
+ align:start position:0%
+rap with students coming up I will note
+ 
+
+ align:start position:0%
+rap with students coming up I will note
+also that if you want to come see me I'm
+
+ align:start position:0%
+also that if you want to come see me I'm
+ 
+
+ align:start position:0%
+also that if you want to come see me I'm
+open to it next week's a great week by
+
+ align:start position:0%
+open to it next week's a great week by
+ 
+
+ align:start position:0%
+open to it next week's a great week by
+the way cuz I'm here all four or five
+
+ align:start position:0%
+the way cuz I'm here all four or five
+ 
+
+ align:start position:0%
+the way cuz I'm here all four or five
+days but I don't have set office hours
+
+ align:start position:0%
+days but I don't have set office hours
+ 
+
+ align:start position:0%
+days but I don't have set office hours
+just email me copy Dylan who's the new
+
+ align:start position:0%
+just email me copy Dylan who's the new
+ 
+
+ align:start position:0%
+just email me copy Dylan who's the new
+course administrator there was a swap
+
+ align:start position:0%
+course administrator there was a swap
+ 
+
+ align:start position:0%
+course administrator there was a swap
+out from Ryan or copy Toledo or Sabrina
+
+ align:start position:0%
+out from Ryan or copy Toledo or Sabrina
+ 
+
+ align:start position:0%
+out from Ryan or copy Toledo or Sabrina
+or something but just shoot me an email
+
+ align:start position:0%
+or something but just shoot me an email
+ 
+
+ align:start position:0%
+or something but just shoot me an email
+and then I'll set something up with you
+
+ align:start position:0%
+and then I'll set something up with you
+ 
+
+ align:start position:0%
+and then I'll set something up with you
+if you want to follow up either on your
+
+ align:start position:0%
+if you want to follow up either on your
+ 
+
+ align:start position:0%
+if you want to follow up either on your
+projects or it's a question about
+
+ align:start position:0%
+projects or it's a question about
+ 
+
+ align:start position:0%
+projects or it's a question about
+anything around blockchain I also want
+
+ align:start position:0%
+anything around blockchain I also want
+ 
+
+ align:start position:0%
+anything around blockchain I also want
+to thank we don't usually have people
+
+ align:start position:0%
+to thank we don't usually have people
+ 
+
+ align:start position:0%
+to thank we don't usually have people
+here with jackets on but we have six or
+
+ align:start position:0%
+here with jackets on but we have six or
+ 
+
+ align:start position:0%
+here with jackets on but we have six or
+eight veterans who have served our
+
+ align:start position:0%
+eight veterans who have served our
+ 
+
+ align:start position:0%
+eight veterans who have served our
+country and I thank you for your service
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+they're here to observe us I I don't
+
+ align:start position:0%
+they're here to observe us I I don't
+ 
+
+ align:start position:0%
+they're here to observe us I I don't
+know whether we'll scare them away or
+
+ align:start position:0%
+know whether we'll scare them away or
+ 
+
+ align:start position:0%
+know whether we'll scare them away or
+not but thank you for for joining us
+
+ align:start position:0%
+not but thank you for for joining us
+ 
+
+ align:start position:0%
+not but thank you for for joining us
+so today's topics are gonna be around of
+
+ align:start position:0%
+so today's topics are gonna be around of
+ 
+
+ align:start position:0%
+so today's topics are gonna be around of
+course we're gonna go through the
+
+ align:start position:0%
+course we're gonna go through the
+ 
+
+ align:start position:0%
+course we're gonna go through the
+readings a little bit we don't have
+
+ align:start position:0%
+readings a little bit we don't have
+ 
+
+ align:start position:0%
+readings a little bit we don't have
+Larry lesyk and it's a little bit more
+
+ align:start position:0%
+Larry lesyk and it's a little bit more
+ 
+
+ align:start position:0%
+Larry lesyk and it's a little bit more
+relaxed so I might be doing some cold
+
+ align:start position:0%
+relaxed so I might be doing some cold
+ 
+
+ align:start position:0%
+relaxed so I might be doing some cold
+calling if that's alright I'm gonna go
+
+ align:start position:0%
+calling if that's alright I'm gonna go
+ 
+
+ align:start position:0%
+calling if that's alright I'm gonna go
+back a little bit to the technical
+
+ align:start position:0%
+back a little bit to the technical
+ 
+
+ align:start position:0%
+back a little bit to the technical
+features in a quick wrap in two slides
+
+ align:start position:0%
+features in a quick wrap in two slides
+ 
+
+ align:start position:0%
+features in a quick wrap in two slides
+or three slides but I just want to do
+
+ align:start position:0%
+or three slides but I just want to do
+ 
+
+ align:start position:0%
+or three slides but I just want to do
+that is the set up again and of course
+
+ align:start position:0%
+that is the set up again and of course
+ 
+
+ align:start position:0%
+that is the set up again and of course
+because you all love hash functions so
+
+ align:start position:0%
+because you all love hash functions so
+ 
+
+ align:start position:0%
+because you all love hash functions so
+much it's just a way to bring it back to
+
+ align:start position:0%
+much it's just a way to bring it back to
+ 
+
+ align:start position:0%
+much it's just a way to bring it back to
+some of the technical features to set up
+
+ align:start position:0%
+some of the technical features to set up
+ 
+
+ align:start position:0%
+some of the technical features to set up
+really what are some of the issues we
+
+ align:start position:0%
+really what are some of the issues we
+ 
+
+ align:start position:0%
+really what are some of the issues we
+have
+
+ align:start position:0%
+have
+ 
+
+ align:start position:0%
+have
+I think it's lecture eleven and twelve
+
+ align:start position:0%
+I think it's lecture eleven and twelve
+ 
+
+ align:start position:0%
+I think it's lecture eleven and twelve
+where it's just what I call Act two is
+
+ align:start position:0%
+where it's just what I call Act two is
+ 
+
+ align:start position:0%
+where it's just what I call Act two is
+the economics but I want to set up a
+
+ align:start position:0%
+the economics but I want to set up a
+ 
+
+ align:start position:0%
+the economics but I want to set up a
+little bit about the economics you saw
+
+ align:start position:0%
+little bit about the economics you saw
+ 
+
+ align:start position:0%
+little bit about the economics you saw
+that in the reading
+
+ align:start position:0%
+that in the reading
+ 
+
+ align:start position:0%
+that in the reading
+the xxi Geneva report that Simon Johnson
+
+ align:start position:0%
+the xxi Geneva report that Simon Johnson
+ 
+
+ align:start position:0%
+the xxi Geneva report that Simon Johnson
+and Nahan Narula and my Casey and Joan
+
+ align:start position:0%
+and Nahan Narula and my Casey and Joan
+ 
+
+ align:start position:0%
+and Nahan Narula and my Casey and Joan
+and I wrote so now you all
+
+ align:start position:0%
+and I wrote so now you all
+ 
+
+ align:start position:0%
+and I wrote so now you all
+I only assigned just seven pages out of
+
+ align:start position:0%
+I only assigned just seven pages out of
+ 
+
+ align:start position:0%
+I only assigned just seven pages out of
+it so I hope that your raid read the
+
+ align:start position:0%
+it so I hope that your raid read the
+ 
+
+ align:start position:0%
+it so I hope that your raid read the
+seven pages but some of the costs and
+
+ align:start position:0%
+seven pages but some of the costs and
+ 
+
+ align:start position:0%
+seven pages but some of the costs and
+trade-offs the challenges of blockchain
+
+ align:start position:0%
+trade-offs the challenges of blockchain
+ 
+
+ align:start position:0%
+trade-offs the challenges of blockchain
+technology that are very real I'll give
+
+ align:start position:0%
+technology that are very real I'll give
+ 
+
+ align:start position:0%
+technology that are very real I'll give
+you my own perspective on where I think
+
+ align:start position:0%
+you my own perspective on where I think
+ 
+
+ align:start position:0%
+you my own perspective on where I think
+this will sort out over the next three
+
+ align:start position:0%
+this will sort out over the next three
+ 
+
+ align:start position:0%
+this will sort out over the next three
+to ten years so I'll do some predictions
+
+ align:start position:0%
+to ten years so I'll do some predictions
+ 
+
+ align:start position:0%
+to ten years so I'll do some predictions
+Vitalik Bou Durant has also talked about
+
+ align:start position:0%
+Vitalik Bou Durant has also talked about
+ 
+
+ align:start position:0%
+Vitalik Bou Durant has also talked about
+a trilemma and I want to chat about that
+
+ align:start position:0%
+a trilemma and I want to chat about that
+ 
+
+ align:start position:0%
+a trilemma and I want to chat about that
+and that was one of the readings if I
+
+ align:start position:0%
+and that was one of the readings if I
+ 
+
+ align:start position:0%
+and that was one of the readings if I
+recall he's such a leader in this
+
+ align:start position:0%
+recall he's such a leader in this
+ 
+
+ align:start position:0%
+recall he's such a leader in this
+community that when he writes and says
+
+ align:start position:0%
+community that when he writes and says
+ 
+
+ align:start position:0%
+community that when he writes and says
+something like this it was relevant I
+
+ align:start position:0%
+something like this it was relevant I
+ 
+
+ align:start position:0%
+something like this it was relevant I
+think that everybody's understand what
+
+ align:start position:0%
+think that everybody's understand what
+ 
+
+ align:start position:0%
+think that everybody's understand what
+Vitalik bitter ends kind of trilemma as
+
+ align:start position:0%
+Vitalik bitter ends kind of trilemma as
+ 
+
+ align:start position:0%
+Vitalik bitter ends kind of trilemma as
+even though that some people think he's
+
+ align:start position:0%
+even though that some people think he's
+ 
+
+ align:start position:0%
+even though that some people think he's
+mistaken some possible solutions to this
+
+ align:start position:0%
+mistaken some possible solutions to this
+ 
+
+ align:start position:0%
+mistaken some possible solutions to this
+we have who's attending today
+
+ align:start position:0%
+we have who's attending today
+ 
+
+ align:start position:0%
+we have who's attending today
+Amador's who was actually one of the
+
+ align:start position:0%
+Amador's who was actually one of the
+ 
+
+ align:start position:0%
+Amador's who was actually one of the
+developers on some of the solutions
+
+ align:start position:0%
+developers on some of the solutions
+ 
+
+ align:start position:0%
+developers on some of the solutions
+around zero knowledge proof sand he
+
+ align:start position:0%
+around zero knowledge proof sand he
+ 
+
+ align:start position:0%
+around zero knowledge proof sand he
+might get caught on he works over the
+
+ align:start position:0%
+might get caught on he works over the
+ 
+
+ align:start position:0%
+might get caught on he works over the
+digital currency initiative I'm hope
+
+ align:start position:0%
+digital currency initiative I'm hope
+ 
+
+ align:start position:0%
+digital currency initiative I'm hope
+you're ready and and why I think
+
+ align:start position:0%
+you're ready and and why I think
+ 
+
+ align:start position:0%
+you're ready and and why I think
+governance is the most challenging piece
+
+ align:start position:0%
+governance is the most challenging piece
+ 
+
+ align:start position:0%
+governance is the most challenging piece
+so with that the readings I have a list
+
+ align:start position:0%
+so with that the readings I have a list
+ 
+
+ align:start position:0%
+so with that the readings I have a list
+of everybody that hasn't spoken yet so
+
+ align:start position:0%
+of everybody that hasn't spoken yet so
+ 
+
+ align:start position:0%
+of everybody that hasn't spoken yet so
+the goal is to speak that's what class
+
+ align:start position:0%
+the goal is to speak that's what class
+ 
+
+ align:start position:0%
+the goal is to speak that's what class
+participation is like I'm gonna be
+
+ align:start position:0%
+participation is like I'm gonna be
+ 
+
+ align:start position:0%
+participation is like I'm gonna be
+light-hearted about it I it's not that
+
+ align:start position:0%
+light-hearted about it I it's not that
+ 
+
+ align:start position:0%
+light-hearted about it I it's not that
+long ago I was a student really I
+
+ align:start position:0%
+long ago I was a student really I
+ 
+
+ align:start position:0%
+long ago I was a student really I
+remember all this you know you want to
+
+ align:start position:0%
+remember all this you know you want to
+ 
+
+ align:start position:0%
+remember all this you know you want to
+get your name off this list just just
+
+ align:start position:0%
+get your name off this list just just
+ 
+
+ align:start position:0%
+get your name off this list just just
+what I say that kind of encouraging so
+
+ align:start position:0%
+what I say that kind of encouraging so
+ 
+
+ align:start position:0%
+what I say that kind of encouraging so
+should I do it alphabetical from the
+
+ align:start position:0%
+should I do it alphabetical from the
+ 
+
+ align:start position:0%
+should I do it alphabetical from the
+list as to who wants to tell me no no or
+
+ align:start position:0%
+list as to who wants to tell me no no or
+ 
+
+ align:start position:0%
+list as to who wants to tell me no no or
+you look like you're ducking your head
+
+ align:start position:0%
+you look like you're ducking your head
+ 
+
+ align:start position:0%
+you look like you're ducking your head
+what's your name Wendy what did you take
+
+ align:start position:0%
+what's your name Wendy what did you take
+ 
+
+ align:start position:0%
+what's your name Wendy what did you take
+from the seven pages of the Geneva
+
+ align:start position:0%
+from the seven pages of the Geneva
+ 
+
+ align:start position:0%
+from the seven pages of the Geneva
+report
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+did you read did you do the readings
+
+ align:start position:0%
+did you read did you do the readings
+ 
+
+ align:start position:0%
+did you read did you do the readings
+lady take from the great work of Simon
+
+ align:start position:0%
+lady take from the great work of Simon
+ 
+
+ align:start position:0%
+lady take from the great work of Simon
+Johnson and I helped him out you know
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+anything about the business challenges
+
+ align:start position:0%
+anything about the business challenges
+ 
+
+ align:start position:0%
+anything about the business challenges
+of blockchain from the readings so one
+
+ align:start position:0%
+of blockchain from the readings so one
+ 
+
+ align:start position:0%
+of blockchain from the readings so one
+one challenge is time latency it takes a
+
+ align:start position:0%
+one challenge is time latency it takes a
+ 
+
+ align:start position:0%
+one challenge is time latency it takes a
+long time to do a Wendy raise raises yes
+
+ align:start position:0%
+long time to do a Wendy raise raises yes
+ 
+
+ align:start position:0%
+long time to do a Wendy raise raises yes
+if you can say your first name help
+
+ align:start position:0%
+if you can say your first name help
+ 
+
+ align:start position:0%
+if you can say your first name help
+Sabrina out get you off the list
+
+ align:start position:0%
+Sabrina out get you off the list
+ 
+
+ align:start position:0%
+Sabrina out get you off the list
+so you it's self-motivation to say your
+
+ align:start position:0%
+so you it's self-motivation to say your
+ 
+
+ align:start position:0%
+so you it's self-motivation to say your
+name so catalina sort of related they're
+
+ align:start position:0%
+name so catalina sort of related they're
+ 
+
+ align:start position:0%
+name so catalina sort of related they're
+there they're not alone but performance
+
+ align:start position:0%
+there they're not alone but performance
+ 
+
+ align:start position:0%
+there they're not alone but performance
+scalability the time it takes to do a
+
+ align:start position:0%
+scalability the time it takes to do a
+ 
+
+ align:start position:0%
+scalability the time it takes to do a
+transaction other challenges yes how to
+
+ align:start position:0%
+transaction other challenges yes how to
+ 
+
+ align:start position:0%
+transaction other challenges yes how to
+do micro payments you want to tease that
+
+ align:start position:0%
+do micro payments you want to tease that
+ 
+
+ align:start position:0%
+do micro payments you want to tease that
+out why why is there a problem with
+
+ align:start position:0%
+out why why is there a problem with
+ 
+
+ align:start position:0%
+out why why is there a problem with
+micro payments do micro payments in the
+
+ align:start position:0%
+micro payments do micro payments in the
+ 
+
+ align:start position:0%
+micro payments do micro payments in the
+small micro payments partly because
+
+ align:start position:0%
+small micro payments partly because
+ 
+
+ align:start position:0%
+small micro payments partly because
+they're so small maybe relative to the
+
+ align:start position:0%
+they're so small maybe relative to the
+ 
+
+ align:start position:0%
+they're so small maybe relative to the
+fees and the cost of the network Alexis
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+may try to change the transaction
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+there's economic incentives that are
+
+ align:start position:0%
+there's economic incentives that are
+ 
+
+ align:start position:0%
+there's economic incentives that are
+involved here we're now moving a little
+
+ align:start position:0%
+involved here we're now moving a little
+ 
+
+ align:start position:0%
+involved here we're now moving a little
+bit away from all that you know that
+
+ align:start position:0%
+bit away from all that you know that
+ 
+
+ align:start position:0%
+bit away from all that you know that
+stuff the the broccoli that I said that
+
+ align:start position:0%
+stuff the the broccoli that I said that
+ 
+
+ align:start position:0%
+stuff the the broccoli that I said that
+we were all going to be eating about
+
+ align:start position:0%
+we were all going to be eating about
+ 
+
+ align:start position:0%
+we were all going to be eating about
+hash functions and so forth
+
+ align:start position:0%
+hash functions and so forth
+ 
+
+ align:start position:0%
+hash functions and so forth
+akira yeah privacy regulators concerns
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+here just raise a bunch of points about
+
+ align:start position:0%
+here just raise a bunch of points about
+ 
+
+ align:start position:0%
+here just raise a bunch of points about
+privacy and security about the
+
+ align:start position:0%
+privacy and security about the
+ 
+
+ align:start position:0%
+privacy and security about the
+individuals and the regulators is
+
+ align:start position:0%
+individuals and the regulators is
+ 
+
+ align:start position:0%
+individuals and the regulators is
+anybody want to tease that out a little
+
+ align:start position:0%
+anybody want to tease that out a little
+ 
+
+ align:start position:0%
+anybody want to tease that out a little
+bit more incentive to keep that natural
+
+ align:start position:0%
+bit more incentive to keep that natural
+ 
+
+ align:start position:0%
+bit more incentive to keep that natural
+public policy tension that doesn't only
+
+ align:start position:0%
+public policy tension that doesn't only
+ 
+
+ align:start position:0%
+public policy tension that doesn't only
+exist around one side there's a
+
+ align:start position:0%
+exist around one side there's a
+ 
+
+ align:start position:0%
+exist around one side there's a
+commercial interest to keep and
+
+ align:start position:0%
+commercial interest to keep and
+ 
+
+ align:start position:0%
+commercial interest to keep and
+interestingly on top of it the official
+
+ align:start position:0%
+interestingly on top of it the official
+ 
+
+ align:start position:0%
+interestingly on top of it the official
+sector also wants privacy for everybody
+
+ align:start position:0%
+sector also wants privacy for everybody
+ 
+
+ align:start position:0%
+sector also wants privacy for everybody
+other than the official sector so like
+
+ align:start position:0%
+other than the official sector so like
+ 
+
+ align:start position:0%
+other than the official sector so like
+in Europe there's a new requirement that
+
+ align:start position:0%
+in Europe there's a new requirement that
+ 
+
+ align:start position:0%
+in Europe there's a new requirement that
+wasn't in the breeze don't worry but is
+
+ align:start position:0%
+wasn't in the breeze don't worry but is
+ 
+
+ align:start position:0%
+wasn't in the breeze don't worry but is
+anybody familiar with the directive the
+
+ align:start position:0%
+anybody familiar with the directive the
+ 
+
+ align:start position:0%
+anybody familiar with the directive the
+privacy directive called GDP or Aaron
+
+ align:start position:0%
+privacy directive called GDP or Aaron
+ 
+
+ align:start position:0%
+privacy directive called GDP or Aaron
+Aaron doesn't tell the class a little
+
+ align:start position:0%
+Aaron doesn't tell the class a little
+ 
+
+ align:start position:0%
+Aaron doesn't tell the class a little
+bit about GDP or or if you there I just
+
+ align:start position:0%
+bit about GDP or or if you there I just
+ 
+
+ align:start position:0%
+bit about GDP or or if you there I just
+know that it's like a big deal right now
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+especially when it comes like
+
+ align:start position:0%
+especially when it comes like
+ 
+
+ align:start position:0%
+especially when it comes like
+advertising to consumers they have
+
+ align:start position:0%
+advertising to consumers they have
+ 
+
+ align:start position:0%
+advertising to consumers they have
+consumers in like the EU have to like
+
+ align:start position:0%
+consumers in like the EU have to like
+ 
+
+ align:start position:0%
+consumers in like the EU have to like
+really like type certain boxes to
+
+ align:start position:0%
+really like type certain boxes to
+ 
+
+ align:start position:0%
+really like type certain boxes to
+we need to be advertised to as apposed
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and Joe Quinn you have the right to out
+
+ align:start position:0%
+and Joe Quinn you have the right to out
+ 
+
+ align:start position:0%
+and Joe Quinn you have the right to out
+of being everything you do work on
+
+ align:start position:0%
+of being everything you do work on
+ 
+
+ align:start position:0%
+of being everything you do work on
+summer we had to put purging mechanisms
+
+ align:start position:0%
+summer we had to put purging mechanisms
+ 
+
+ align:start position:0%
+summer we had to put purging mechanisms
+into our database right so it's a
+
+ align:start position:0%
+into our database right so it's a
+ 
+
+ align:start position:0%
+into our database right so it's a
+remarkable new law Europe is in a sense
+
+ align:start position:0%
+remarkable new law Europe is in a sense
+ 
+
+ align:start position:0%
+remarkable new law Europe is in a sense
+if you wish to say either more privacy
+
+ align:start position:0%
+if you wish to say either more privacy
+ 
+
+ align:start position:0%
+if you wish to say either more privacy
+protection or ahead of the u.s. or you
+
+ align:start position:0%
+protection or ahead of the u.s. or you
+ 
+
+ align:start position:0%
+protection or ahead of the u.s. or you
+know and each jurisdiction has their own
+
+ align:start position:0%
+know and each jurisdiction has their own
+ 
+
+ align:start position:0%
+know and each jurisdiction has their own
+cultural and political norms but Europe
+
+ align:start position:0%
+cultural and political norms but Europe
+ 
+
+ align:start position:0%
+cultural and political norms but Europe
+as a whole is moved further in a sense
+
+ align:start position:0%
+as a whole is moved further in a sense
+ 
+
+ align:start position:0%
+as a whole is moved further in a sense
+you have a right to be forgotten you
+
+ align:start position:0%
+you have a right to be forgotten you
+ 
+
+ align:start position:0%
+you have a right to be forgotten you
+have a right to access the information
+
+ align:start position:0%
+have a right to access the information
+ 
+
+ align:start position:0%
+have a right to access the information
+as well and so how to be forgotten in
+
+ align:start position:0%
+as well and so how to be forgotten in
+ 
+
+ align:start position:0%
+as well and so how to be forgotten in
+the context of an immutable blockchain
+
+ align:start position:0%
+the context of an immutable blockchain
+ 
+
+ align:start position:0%
+the context of an immutable blockchain
+isn't interesting just technical set of
+
+ align:start position:0%
+isn't interesting just technical set of
+ 
+
+ align:start position:0%
+isn't interesting just technical set of
+issues yes I work for a company this
+
+ align:start position:0%
+issues yes I work for a company this
+ 
+
+ align:start position:0%
+issues yes I work for a company this
+summer the processes transactions and it
+
+ align:start position:0%
+summer the processes transactions and it
+ 
+
+ align:start position:0%
+summer the processes transactions and it
+was our understanding speaking with
+
+ align:start position:0%
+was our understanding speaking with
+ 
+
+ align:start position:0%
+was our understanding speaking with
+lawyers in Europe that under gdpr you're
+
+ align:start position:0%
+lawyers in Europe that under gdpr you're
+ 
+
+ align:start position:0%
+lawyers in Europe that under gdpr you're
+allowed to request your transactions
+
+ align:start position:0%
+allowed to request your transactions
+ 
+
+ align:start position:0%
+allowed to request your transactions
+because the transactions counters
+
+ align:start position:0%
+because the transactions counters
+ 
+
+ align:start position:0%
+because the transactions counters
+personal information you're allowed to
+
+ align:start position:0%
+personal information you're allowed to
+ 
+
+ align:start position:0%
+personal information you're allowed to
+request your transactions to be erased
+
+ align:start position:0%
+request your transactions to be erased
+ 
+
+ align:start position:0%
+request your transactions to be erased
+from the ledger which obviously opens
+
+ align:start position:0%
+from the ledger which obviously opens
+ 
+
+ align:start position:0%
+from the ledger which obviously opens
+the door to all kinds of fraudulent
+
+ align:start position:0%
+the door to all kinds of fraudulent
+ 
+
+ align:start position:0%
+the door to all kinds of fraudulent
+behavior I'm just curious to know you've
+
+ align:start position:0%
+behavior I'm just curious to know you've
+ 
+
+ align:start position:0%
+behavior I'm just curious to know you've
+heard of any sort of resolution to that
+
+ align:start position:0%
+heard of any sort of resolution to that
+ 
+
+ align:start position:0%
+heard of any sort of resolution to that
+I haven't I was speaking at a conference
+
+ align:start position:0%
+I haven't I was speaking at a conference
+ 
+
+ align:start position:0%
+I haven't I was speaking at a conference
+earlier today here at MIT with a bunch
+
+ align:start position:0%
+earlier today here at MIT with a bunch
+ 
+
+ align:start position:0%
+earlier today here at MIT with a bunch
+of member companies to the computer
+
+ align:start position:0%
+of member companies to the computer
+ 
+
+ align:start position:0%
+of member companies to the computer
+science and AI lab and one of the
+
+ align:start position:0%
+science and AI lab and one of the
+ 
+
+ align:start position:0%
+science and AI lab and one of the
+participants said they thought they had
+
+ align:start position:0%
+participants said they thought they had
+ 
+
+ align:start position:0%
+participants said they thought they had
+a technical set of solutions to it so
+
+ align:start position:0%
+a technical set of solutions to it so
+ 
+
+ align:start position:0%
+a technical set of solutions to it so
+we're gonna talk more about the privacy
+
+ align:start position:0%
+we're gonna talk more about the privacy
+ 
+
+ align:start position:0%
+we're gonna talk more about the privacy
+issues and GDP or in the public policy
+
+ align:start position:0%
+issues and GDP or in the public policy
+ 
+
+ align:start position:0%
+issues and GDP or in the public policy
+session next week so I'll try to I'll
+
+ align:start position:0%
+session next week so I'll try to I'll
+ 
+
+ align:start position:0%
+session next week so I'll try to I'll
+try to Kyle remind me and I will try to
+
+ align:start position:0%
+try to Kyle remind me and I will try to
+ 
+
+ align:start position:0%
+try to Kyle remind me and I will try to
+get more up to speed on that Kelly
+
+ align:start position:0%
+get more up to speed on that Kelly
+ 
+
+ align:start position:0%
+get more up to speed on that Kelly
+it's specifically for chapter there was
+
+ align:start position:0%
+it's specifically for chapter there was
+ 
+
+ align:start position:0%
+it's specifically for chapter there was
+something mentioned about what makes
+
+ align:start position:0%
+something mentioned about what makes
+ 
+
+ align:start position:0%
+something mentioned about what makes
+watching uniquely qualified to solve a
+
+ align:start position:0%
+watching uniquely qualified to solve a
+ 
+
+ align:start position:0%
+watching uniquely qualified to solve a
+lot of these solutions and I found the
+
+ align:start position:0%
+lot of these solutions and I found the
+ 
+
+ align:start position:0%
+lot of these solutions and I found the
+date had coincided with what special
+
+ align:start position:0%
+date had coincided with what special
+ 
+
+ align:start position:0%
+date had coincided with what special
+Essex said last class about there are
+
+ align:start position:0%
+Essex said last class about there are
+ 
+
+ align:start position:0%
+Essex said last class about there are
+significant trade-offs that often come
+
+ align:start position:0%
+significant trade-offs that often come
+ 
+
+ align:start position:0%
+significant trade-offs that often come
+down to the cost of trust but it's so
+
+ align:start position:0%
+down to the cost of trust but it's so
+ 
+
+ align:start position:0%
+down to the cost of trust but it's so
+thanks affection with so many technical
+
+ align:start position:0%
+thanks affection with so many technical
+ 
+
+ align:start position:0%
+thanks affection with so many technical
+challenges why other thoughts or
+
+ align:start position:0%
+challenges why other thoughts or
+ 
+
+ align:start position:0%
+challenges why other thoughts or
+questions from the readings it's okay
+
+ align:start position:0%
+questions from the readings it's okay
+ 
+
+ align:start position:0%
+questions from the readings it's okay
+about having a second layer to provide
+
+ align:start position:0%
+about having a second layer to provide
+ 
+
+ align:start position:0%
+about having a second layer to provide
+the efficiency and the high performance
+
+ align:start position:0%
+the efficiency and the high performance
+ 
+
+ align:start position:0%
+the efficiency and the high performance
+but it's ready offline yeah so we are
+
+ align:start position:0%
+but it's ready offline yeah so we are
+ 
+
+ align:start position:0%
+but it's ready offline yeah so we are
+expecting to trust in second base
+
+ align:start position:0%
+expecting to trust in second base
+ 
+
+ align:start position:0%
+expecting to trust in second base
+offline and then goes and put inside the
+
+ align:start position:0%
+offline and then goes and put inside the
+ 
+
+ align:start position:0%
+offline and then goes and put inside the
+box chain how feasible how can we twist
+
+ align:start position:0%
+box chain how feasible how can we twist
+ 
+
+ align:start position:0%
+box chain how feasible how can we twist
+the question is about possible solutions
+
+ align:start position:0%
+the question is about possible solutions
+ 
+
+ align:start position:0%
+the question is about possible solutions
+to address performance and scalability
+
+ align:start position:0%
+to address performance and scalability
+ 
+
+ align:start position:0%
+to address performance and scalability
+and I have a few slides on that but in
+
+ align:start position:0%
+and I have a few slides on that but in
+ 
+
+ align:start position:0%
+and I have a few slides on that but in
+essence if the if the principal protocol
+
+ align:start position:0%
+essence if the if the principal protocol
+ 
+
+ align:start position:0%
+essence if the if the principal protocol
+the Bitcoin protocol or the etherium
+
+ align:start position:0%
+the Bitcoin protocol or the etherium
+ 
+
+ align:start position:0%
+the Bitcoin protocol or the etherium
+protocol or maybe tomorrow be EOS or
+
+ align:start position:0%
+protocol or maybe tomorrow be EOS or
+ 
+
+ align:start position:0%
+protocol or maybe tomorrow be EOS or
+some other protocol has some performance
+
+ align:start position:0%
+some other protocol has some performance
+ 
+
+ align:start position:0%
+some other protocol has some performance
+issues could some activity be moved to
+
+ align:start position:0%
+issues could some activity be moved to
+ 
+
+ align:start position:0%
+issues could some activity be moved to
+another channel that channel could be
+
+ align:start position:0%
+another channel that channel could be
+ 
+
+ align:start position:0%
+another channel that channel could be
+caught a layer two and the Lightning
+
+ align:start position:0%
+caught a layer two and the Lightning
+ 
+
+ align:start position:0%
+caught a layer two and the Lightning
+Network which was there was a reading
+
+ align:start position:0%
+Network which was there was a reading
+ 
+
+ align:start position:0%
+Network which was there was a reading
+about that that could be with a little
+
+ align:start position:0%
+about that that could be with a little
+ 
+
+ align:start position:0%
+about that that could be with a little
+bit different technology called side
+
+ align:start position:0%
+bit different technology called side
+ 
+
+ align:start position:0%
+bit different technology called side
+chains or shorting which I think was an
+
+ align:start position:0%
+chains or shorting which I think was an
+ 
+
+ align:start position:0%
+chains or shorting which I think was an
+optional yeah I did that optionally I
+
+ align:start position:0%
+optional yeah I did that optionally I
+ 
+
+ align:start position:0%
+optional yeah I did that optionally I
+didn't force you all so there's a number
+
+ align:start position:0%
+didn't force you all so there's a number
+ 
+
+ align:start position:0%
+didn't force you all so there's a number
+of alternative channels and though the
+
+ align:start position:0%
+of alternative channels and though the
+ 
+
+ align:start position:0%
+of alternative channels and though the
+technologies are - technologists
+
+ align:start position:0%
+technologies are - technologists
+ 
+
+ align:start position:0%
+technologies are - technologists
+importantly different sharding and side
+
+ align:start position:0%
+importantly different sharding and side
+ 
+
+ align:start position:0%
+importantly different sharding and side
+chains and layer two for this purpose
+
+ align:start position:0%
+chains and layer two for this purpose
+ 
+
+ align:start position:0%
+chains and layer two for this purpose
+for a moment let me
+
+ align:start position:0%
+for a moment let me
+ 
+
+ align:start position:0%
+for a moment let me
+blur over the differences the question
+
+ align:start position:0%
+blur over the differences the question
+ 
+
+ align:start position:0%
+blur over the differences the question
+that Lea Lea our dros ask is well is
+
+ align:start position:0%
+that Lea Lea our dros ask is well is
+ 
+
+ align:start position:0%
+that Lea Lea our dros ask is well is
+that meaning that we have to trust I
+
+ align:start position:0%
+that meaning that we have to trust I
+ 
+
+ align:start position:0%
+that meaning that we have to trust I
+would contend we already have to trust
+
+ align:start position:0%
+would contend we already have to trust
+ 
+
+ align:start position:0%
+would contend we already have to trust
+the protocol that the Bitcoin core
+
+ align:start position:0%
+the protocol that the Bitcoin core
+ 
+
+ align:start position:0%
+the protocol that the Bitcoin core
+developers have written it's open github
+
+ align:start position:0%
+developers have written it's open github
+ 
+
+ align:start position:0%
+developers have written it's open github
+it's open code but very few people are
+
+ align:start position:0%
+it's open code but very few people are
+ 
+
+ align:start position:0%
+it's open code but very few people are
+actually gonna investigate it enough to
+
+ align:start position:0%
+actually gonna investigate it enough to
+ 
+
+ align:start position:0%
+actually gonna investigate it enough to
+be assured there's not a bug or an error
+
+ align:start position:0%
+be assured there's not a bug or an error
+ 
+
+ align:start position:0%
+be assured there's not a bug or an error
+but I agree with you that the the core
+
+ align:start position:0%
+but I agree with you that the the core
+ 
+
+ align:start position:0%
+but I agree with you that the the core
+the Bitcoin core or the etherium core
+
+ align:start position:0%
+the Bitcoin core or the etherium core
+ 
+
+ align:start position:0%
+the Bitcoin core or the etherium core
+has been living in if I could call it
+
+ align:start position:0%
+has been living in if I could call it
+ 
+
+ align:start position:0%
+has been living in if I could call it
+the technological and commercial swamp
+
+ align:start position:0%
+the technological and commercial swamp
+ 
+
+ align:start position:0%
+the technological and commercial swamp
+it's been attacked by so many viruses
+
+ align:start position:0%
+it's been attacked by so many viruses
+ 
+
+ align:start position:0%
+it's been attacked by so many viruses
+and bugs you have some reason to trust
+
+ align:start position:0%
+and bugs you have some reason to trust
+ 
+
+ align:start position:0%
+and bugs you have some reason to trust
+it but you should never be a hundred
+
+ align:start position:0%
+it but you should never be a hundred
+ 
+
+ align:start position:0%
+it but you should never be a hundred
+percent sure the side the side chains
+
+ align:start position:0%
+percent sure the side the side chains
+ 
+
+ align:start position:0%
+percent sure the side the side chains
+are less tested but I do agree with you
+
+ align:start position:0%
+are less tested but I do agree with you
+ 
+
+ align:start position:0%
+are less tested but I do agree with you
+you have some trust and unless I
+
+ align:start position:0%
+you have some trust and unless I
+ 
+
+ align:start position:0%
+you have some trust and unless I
+misunderstand the question I thought it
+
+ align:start position:0%
+misunderstand the question I thought it
+ 
+
+ align:start position:0%
+misunderstand the question I thought it
+was a trust in the in the underlying
+
+ align:start position:0%
+was a trust in the in the underlying
+ 
+
+ align:start position:0%
+was a trust in the in the underlying
+code working with me that's if you're
+
+ align:start position:0%
+code working with me that's if you're
+ 
+
+ align:start position:0%
+code working with me that's if you're
+off chain should you be more worried I
+
+ align:start position:0%
+off chain should you be more worried I
+ 
+
+ align:start position:0%
+off chain should you be more worried I
+was addressing just a narrow part about
+
+ align:start position:0%
+was addressing just a narrow part about
+ 
+
+ align:start position:0%
+was addressing just a narrow part about
+the code you're saying should you be
+
+ align:start position:0%
+the code you're saying should you be
+ 
+
+ align:start position:0%
+the code you're saying should you be
+worried because it doesn't have the same
+
+ align:start position:0%
+worried because it doesn't have the same
+ 
+
+ align:start position:0%
+worried because it doesn't have the same
+validation models so can I hold that
+
+ align:start position:0%
+validation models so can I hold that
+ 
+
+ align:start position:0%
+validation models so can I hold that
+question until we get to the slides
+
+ align:start position:0%
+question until we get to the slides
+ 
+
+ align:start position:0%
+question until we get to the slides
+because I think that I think you do
+
+ align:start position:0%
+because I think that I think you do
+ 
+
+ align:start position:0%
+because I think that I think you do
+actually have some pretty good
+
+ align:start position:0%
+actually have some pretty good
+ 
+
+ align:start position:0%
+actually have some pretty good
+validation but I think you're right that
+
+ align:start position:0%
+validation but I think you're right that
+ 
+
+ align:start position:0%
+validation but I think you're right that
+it's a it's a valid question is the
+
+ align:start position:0%
+it's a it's a valid question is the
+ 
+
+ align:start position:0%
+it's a it's a valid question is the
+validation and these off chains still
+
+ align:start position:0%
+validation and these off chains still
+ 
+
+ align:start position:0%
+validation and these off chains still
+work there was a question back here I
+
+ align:start position:0%
+work there was a question back here I
+ 
+
+ align:start position:0%
+work there was a question back here I
+was just sort of gonna respond to the
+
+ align:start position:0%
+was just sort of gonna respond to the
+ 
+
+ align:start position:0%
+was just sort of gonna respond to the
+issue like sort of trusting these
+
+ align:start position:0%
+issue like sort of trusting these
+ 
+
+ align:start position:0%
+issue like sort of trusting these
+offline mechanisms it's not in the same
+
+ align:start position:0%
+offline mechanisms it's not in the same
+ 
+
+ align:start position:0%
+offline mechanisms it's not in the same
+thing but like 90% of according to this
+
+ align:start position:0%
+thing but like 90% of according to this
+ 
+
+ align:start position:0%
+thing but like 90% of according to this
+of like daily trading volume occurs in
+
+ align:start position:0%
+of like daily trading volume occurs in
+ 
+
+ align:start position:0%
+of like daily trading volume occurs in
+these crypto exchanges so that's also
+
+ align:start position:0%
+these crypto exchanges so that's also
+ 
+
+ align:start position:0%
+these crypto exchanges so that's also
+like sort of happening off the chain so
+
+ align:start position:0%
+like sort of happening off the chain so
+ 
+
+ align:start position:0%
+like sort of happening off the chain so
+I think that like in this community of
+
+ align:start position:0%
+I think that like in this community of
+ 
+
+ align:start position:0%
+I think that like in this community of
+people who are like currently
+
+ align:start position:0%
+people who are like currently
+ 
+
+ align:start position:0%
+people who are like currently
+participating there's no reason that
+
+ align:start position:0%
+participating there's no reason that
+ 
+
+ align:start position:0%
+participating there's no reason that
+like we're not going to
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so you're raising the point and it's a
+
+ align:start position:0%
+so you're raising the point and it's a
+ 
+
+ align:start position:0%
+so you're raising the point and it's a
+sort of an irony of the whole ecosystem
+
+ align:start position:0%
+sort of an irony of the whole ecosystem
+ 
+
+ align:start position:0%
+sort of an irony of the whole ecosystem
+that the majority and in some crypto
+
+ align:start position:0%
+that the majority and in some crypto
+ 
+
+ align:start position:0%
+that the majority and in some crypto
+currencies over 90% of the actual daily
+
+ align:start position:0%
+currencies over 90% of the actual daily
+ 
+
+ align:start position:0%
+currencies over 90% of the actual daily
+transactions are happening in in very
+
+ align:start position:0%
+transactions are happening in in very
+ 
+
+ align:start position:0%
+transactions are happening in in very
+centralized ways on exchanges
+
+ align:start position:0%
+centralized ways on exchanges
+ 
+
+ align:start position:0%
+centralized ways on exchanges
+particularly the centralized crypto
+
+ align:start position:0%
+particularly the centralized crypto
+ 
+
+ align:start position:0%
+particularly the centralized crypto
+exchanges where I can't remember what it
+
+ align:start position:0%
+exchanges where I can't remember what it
+ 
+
+ align:start position:0%
+exchanges where I can't remember what it
+was about half of you have owned Bitcoin
+
+ align:start position:0%
+was about half of you have owned Bitcoin
+ 
+
+ align:start position:0%
+was about half of you have owned Bitcoin
+at some point in time but can I ask how
+
+ align:start position:0%
+at some point in time but can I ask how
+ 
+
+ align:start position:0%
+at some point in time but can I ask how
+many of you have actually operated a
+
+ align:start position:0%
+many of you have actually operated a
+ 
+
+ align:start position:0%
+many of you have actually operated a
+full node so there's the two
+
+ align:start position:0%
+full node so there's the two
+ 
+
+ align:start position:0%
+full node so there's the two
+technologists at the middle table and
+
+ align:start position:0%
+technologists at the middle table and
+ 
+
+ align:start position:0%
+technologists at the middle table and
+Hugo who's also if I remember
+
+ align:start position:0%
+Hugo who's also if I remember
+ 
+
+ align:start position:0%
+Hugo who's also if I remember
+engineering PhD student okay
+
+ align:start position:0%
+engineering PhD student okay
+ 
+
+ align:start position:0%
+engineering PhD student okay
+so we have our three PhD students who
+
+ align:start position:0%
+so we have our three PhD students who
+ 
+
+ align:start position:0%
+so we have our three PhD students who
+have operated full notes honors to you
+
+ align:start position:0%
+have operated full notes honors to you
+ 
+
+ align:start position:0%
+have operated full notes honors to you
+but for most of you and it was half the
+
+ align:start position:0%
+but for most of you and it was half the
+ 
+
+ align:start position:0%
+but for most of you and it was half the
+class of own some Bitcoin you've trusted
+
+ align:start position:0%
+class of own some Bitcoin you've trusted
+ 
+
+ align:start position:0%
+class of own some Bitcoin you've trusted
+some other authority to hold your
+
+ align:start position:0%
+some other authority to hold your
+ 
+
+ align:start position:0%
+some other authority to hold your
+private keys I'm not saying you're wrong
+
+ align:start position:0%
+private keys I'm not saying you're wrong
+ 
+
+ align:start position:0%
+private keys I'm not saying you're wrong
+or right but it's an interesting and an
+
+ align:start position:0%
+or right but it's an interesting and an
+ 
+
+ align:start position:0%
+or right but it's an interesting and an
+important point about this ecosystem so
+
+ align:start position:0%
+important point about this ecosystem so
+ 
+
+ align:start position:0%
+important point about this ecosystem so
+let me let me unless there's other
+
+ align:start position:0%
+let me let me unless there's other
+ 
+
+ align:start position:0%
+let me let me unless there's other
+points just go through some of how I
+
+ align:start position:0%
+points just go through some of how I
+ 
+
+ align:start position:0%
+points just go through some of how I
+thought about these things and laid it
+
+ align:start position:0%
+thought about these things and laid it
+ 
+
+ align:start position:0%
+thought about these things and laid it
+out and I I of course the study
+
+ align:start position:0%
+out and I I of course the study
+ 
+
+ align:start position:0%
+out and I I of course the study
+questions we've been talking about so
+
+ align:start position:0%
+questions we've been talking about so
+ 
+
+ align:start position:0%
+questions we've been talking about so
+I'll come come back but we will talk a
+
+ align:start position:0%
+I'll come come back but we will talk a
+ 
+
+ align:start position:0%
+I'll come come back but we will talk a
+little bit about hard forks and and we
+
+ align:start position:0%
+little bit about hard forks and and we
+ 
+
+ align:start position:0%
+little bit about hard forks and and we
+we I didn't hear anybody talk about
+
+ align:start position:0%
+we I didn't hear anybody talk about
+ 
+
+ align:start position:0%
+we I didn't hear anybody talk about
+interoperability so we'll come back to
+
+ align:start position:0%
+interoperability so we'll come back to
+ 
+
+ align:start position:0%
+interoperability so we'll come back to
+that as well we've talked more about
+
+ align:start position:0%
+that as well we've talked more about
+ 
+
+ align:start position:0%
+that as well we've talked more about
+performance and privacy issues just back
+
+ align:start position:0%
+performance and privacy issues just back
+ 
+
+ align:start position:0%
+performance and privacy issues just back
+to the technical features it's just
+
+ align:start position:0%
+to the technical features it's just
+ 
+
+ align:start position:0%
+to the technical features it's just
+repetition sorry but I do think it's
+
+ align:start position:0%
+repetition sorry but I do think it's
+ 
+
+ align:start position:0%
+repetition sorry but I do think it's
+worthwhile there's of course the
+
+ align:start position:0%
+worthwhile there's of course the
+ 
+
+ align:start position:0%
+worthwhile there's of course the
+cryptography and timestamp logs so the
+
+ align:start position:0%
+cryptography and timestamp logs so the
+ 
+
+ align:start position:0%
+cryptography and timestamp logs so the
+the bedrock of of this technology that
+
+ align:start position:0%
+the bedrock of of this technology that
+ 
+
+ align:start position:0%
+the bedrock of of this technology that
+we did three or four lectures ago you
+
+ align:start position:0%
+we did three or four lectures ago you
+ 
+
+ align:start position:0%
+we did three or four lectures ago you
+will find that in permission systems
+
+ align:start position:0%
+will find that in permission systems
+ 
+
+ align:start position:0%
+will find that in permission systems
+you'll find it in permissionless systems
+
+ align:start position:0%
+you'll find it in permissionless systems
+ 
+
+ align:start position:0%
+you'll find it in permissionless systems
+that is a bedrock you will find it in a
+
+ align:start position:0%
+that is a bedrock you will find it in a
+ 
+
+ align:start position:0%
+that is a bedrock you will find it in a
+theory of Bitcoin and sixteen hundred
+
+ align:start position:0%
+theory of Bitcoin and sixteen hundred
+ 
+
+ align:start position:0%
+theory of Bitcoin and sixteen hundred
+others there there will be some shifts
+
+ align:start position:0%
+others there there will be some shifts
+ 
+
+ align:start position:0%
+others there there will be some shifts
+around the hash functions might be a
+
+ align:start position:0%
+around the hash functions might be a
+ 
+
+ align:start position:0%
+around the hash functions might be a
+little different but that's kind of a
+
+ align:start position:0%
+little different but that's kind of a
+ 
+
+ align:start position:0%
+little different but that's kind of a
+bedrock
+
+ align:start position:0%
+bedrock
+ 
+
+ align:start position:0%
+bedrock
+of this technology the network consensus
+
+ align:start position:0%
+of this technology the network consensus
+ 
+
+ align:start position:0%
+of this technology the network consensus
+is not necessarily always the same as we
+
+ align:start position:0%
+is not necessarily always the same as we
+ 
+
+ align:start position:0%
+is not necessarily always the same as we
+talked about sometimes it's proof of
+
+ align:start position:0%
+talked about sometimes it's proof of
+ 
+
+ align:start position:0%
+talked about sometimes it's proof of
+work sometimes it's proof of stake or in
+
+ align:start position:0%
+work sometimes it's proof of stake or in
+ 
+
+ align:start position:0%
+work sometimes it's proof of stake or in
+the permission systems the consensus is
+
+ align:start position:0%
+the permission systems the consensus is
+ 
+
+ align:start position:0%
+the permission systems the consensus is
+really are you amongst the club and then
+
+ align:start position:0%
+really are you amongst the club and then
+ 
+
+ align:start position:0%
+really are you amongst the club and then
+there's kind of some form of a club deal
+
+ align:start position:0%
+there's kind of some form of a club deal
+ 
+
+ align:start position:0%
+there's kind of some form of a club deal
+if you're the Australian Stock Exchange
+
+ align:start position:0%
+if you're the Australian Stock Exchange
+ 
+
+ align:start position:0%
+if you're the Australian Stock Exchange
+the only member of the club is the
+
+ align:start position:0%
+the only member of the club is the
+ 
+
+ align:start position:0%
+the only member of the club is the
+Australian Stock Exchange but in other
+
+ align:start position:0%
+Australian Stock Exchange but in other
+ 
+
+ align:start position:0%
+Australian Stock Exchange but in other
+permission systems it's 20 banks or 15
+
+ align:start position:0%
+permission systems it's 20 banks or 15
+ 
+
+ align:start position:0%
+permission systems it's 20 banks or 15
+banks that are sharing that some
+
+ align:start position:0%
+banks that are sharing that some
+ 
+
+ align:start position:0%
+banks that are sharing that some
+delegated randomized Authority to say
+
+ align:start position:0%
+delegated randomized Authority to say
+ 
+
+ align:start position:0%
+delegated randomized Authority to say
+what's the next amendment to thee and
+
+ align:start position:0%
+what's the next amendment to thee and
+ 
+
+ align:start position:0%
+what's the next amendment to thee and
+then the transactions code and Ledger's
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+shifts largely dependent upon whether
+
+ align:start position:0%
+shifts largely dependent upon whether
+ 
+
+ align:start position:0%
+shifts largely dependent upon whether
+it's a transaction ledger or an account
+
+ align:start position:0%
+it's a transaction ledger or an account
+ 
+
+ align:start position:0%
+it's a transaction ledger or an account
+ledger so transaction Ledger's have to
+
+ align:start position:0%
+ledger so transaction Ledger's have to
+ 
+
+ align:start position:0%
+ledger so transaction Ledger's have to
+have some way to record transactions
+
+ align:start position:0%
+have some way to record transactions
+ 
+
+ align:start position:0%
+have some way to record transactions
+account ledgers have to have some way to
+
+ align:start position:0%
+account ledgers have to have some way to
+ 
+
+ align:start position:0%
+account ledgers have to have some way to
+record the change in accounts which eat
+
+ align:start position:0%
+record the change in accounts which eat
+ 
+
+ align:start position:0%
+record the change in accounts which eat
+their cause state transitions but either
+
+ align:start position:0%
+their cause state transitions but either
+ 
+
+ align:start position:0%
+their cause state transitions but either
+you have to record a transaction or you
+
+ align:start position:0%
+you have to record a transaction or you
+ 
+
+ align:start position:0%
+you have to record a transaction or you
+have to record a change in the state or
+
+ align:start position:0%
+have to record a change in the state or
+ 
+
+ align:start position:0%
+have to record a change in the state or
+a change in the account an account would
+
+ align:start position:0%
+a change in the account an account would
+ 
+
+ align:start position:0%
+a change in the account an account would
+say that would be like the income
+
+ align:start position:0%
+say that would be like the income
+ 
+
+ align:start position:0%
+say that would be like the income
+statement versus the balance sheet but
+
+ align:start position:0%
+statement versus the balance sheet but
+ 
+
+ align:start position:0%
+statement versus the balance sheet but
+you kind of need to record that and
+
+ align:start position:0%
+you kind of need to record that and
+ 
+
+ align:start position:0%
+you kind of need to record that and
+basically all of these technologies as I
+
+ align:start position:0%
+basically all of these technologies as I
+ 
+
+ align:start position:0%
+basically all of these technologies as I
+understand it have some way to keep
+
+ align:start position:0%
+understand it have some way to keep
+ 
+
+ align:start position:0%
+understand it have some way to keep
+those Ledger's though there's multiple
+
+ align:start position:0%
+those Ledger's though there's multiple
+ 
+
+ align:start position:0%
+those Ledger's though there's multiple
+ways to do it and as we talked about
+
+ align:start position:0%
+ways to do it and as we talked about
+ 
+
+ align:start position:0%
+ways to do it and as we talked about
+last week some have one Merkle tree and
+
+ align:start position:0%
+last week some have one Merkle tree and
+ 
+
+ align:start position:0%
+last week some have one Merkle tree and
+some have four or five Merkle trees and
+
+ align:start position:0%
+some have four or five Merkle trees and
+ 
+
+ align:start position:0%
+some have four or five Merkle trees and
+so forth but it's it's embedded in this
+
+ align:start position:0%
+so forth but it's it's embedded in this
+ 
+
+ align:start position:0%
+so forth but it's it's embedded in this
+and they could have different scripting
+
+ align:start position:0%
+and they could have different scripting
+ 
+
+ align:start position:0%
+and they could have different scripting
+questions just that's like the thumbnail
+
+ align:start position:0%
+questions just that's like the thumbnail
+ 
+
+ align:start position:0%
+questions just that's like the thumbnail
+just to remind you about the technology
+
+ align:start position:0%
+just to remind you about the technology
+ 
+
+ align:start position:0%
+just to remind you about the technology
+it's the T and MIT so for a transaction
+
+ align:start position:0%
+it's the T and MIT so for a transaction
+ 
+
+ align:start position:0%
+it's the T and MIT so for a transaction
+versus account in an account based
+
+ align:start position:0%
+versus account in an account based
+ 
+
+ align:start position:0%
+versus account in an account based
+ledger does it say like if you spend
+
+ align:start position:0%
+ledger does it say like if you spend
+ 
+
+ align:start position:0%
+ledger does it say like if you spend
+five dollars to say who you're spending
+
+ align:start position:0%
+five dollars to say who you're spending
+ 
+
+ align:start position:0%
+five dollars to say who you're spending
+that five dollars to just say your
+
+ align:start position:0%
+that five dollars to just say your
+ 
+
+ align:start position:0%
+that five dollars to just say your
+account went down five dollars and
+
+ align:start position:0%
+account went down five dollars and
+ 
+
+ align:start position:0%
+account went down five dollars and
+somebody else went out five dollars it
+
+ align:start position:0%
+somebody else went out five dollars it
+ 
+
+ align:start position:0%
+somebody else went out five dollars it
+doesn't matter
+
+ align:start position:0%
+doesn't matter
+ 
+
+ align:start position:0%
+doesn't matter
+so I'm gonna take as I understand ether
+
+ align:start position:0%
+so I'm gonna take as I understand ether
+ 
+
+ align:start position:0%
+so I'm gonna take as I understand ether
+and medoras you'll bail me out but you
+
+ align:start position:0%
+and medoras you'll bail me out but you
+ 
+
+ align:start position:0%
+and medoras you'll bail me out but you
+you put a state-transition instead of a
+
+ align:start position:0%
+you put a state-transition instead of a
+ 
+
+ align:start position:0%
+you put a state-transition instead of a
+transaction input it's a
+
+ align:start position:0%
+transaction input it's a
+ 
+
+ align:start position:0%
+transaction input it's a
+state-transition input and that state
+
+ align:start position:0%
+state-transition input and that state
+ 
+
+ align:start position:0%
+state-transition input and that state
+transition input does have one account
+
+ align:start position:0%
+transition input does have one account
+ 
+
+ align:start position:0%
+transition input does have one account
+going down another count going up you
+
+ align:start position:0%
+going down another count going up you
+ 
+
+ align:start position:0%
+going down another count going up you
+can see both sides of it as I understand
+
+ align:start position:0%
+can see both sides of it as I understand
+ 
+
+ align:start position:0%
+can see both sides of it as I understand
+and there's a receipt ledger there's
+
+ align:start position:0%
+and there's a receipt ledger there's
+ 
+
+ align:start position:0%
+and there's a receipt ledger there's
+actually a receipt Merkle tree that then
+
+ align:start position:0%
+actually a receipt Merkle tree that then
+ 
+
+ align:start position:0%
+actually a receipt Merkle tree that then
+keeps this state transition happened did
+
+ align:start position:0%
+keeps this state transition happened did
+ 
+
+ align:start position:0%
+keeps this state transition happened did
+I did I roughly get that right Medora
+
+ align:start position:0%
+I did I roughly get that right Medora
+ 
+
+ align:start position:0%
+I did I roughly get that right Medora
+Wow all right medoras actually does this
+
+ align:start position:0%
+Wow all right medoras actually does this
+ 
+
+ align:start position:0%
+Wow all right medoras actually does this
+for a living I mean he's he's the one of
+
+ align:start position:0%
+for a living I mean he's he's the one of
+ 
+
+ align:start position:0%
+for a living I mean he's he's the one of
+the founding people of Z cash so and a
+
+ align:start position:0%
+the founding people of Z cash so and a
+ 
+
+ align:start position:0%
+the founding people of Z cash so and a
+bunch of other wonderful things I'm not
+
+ align:start position:0%
+bunch of other wonderful things I'm not
+ 
+
+ align:start position:0%
+bunch of other wonderful things I'm not
+going to go through each of the details
+
+ align:start position:0%
+going to go through each of the details
+ 
+
+ align:start position:0%
+going to go through each of the details
+but there was about 15 or 20 details in
+
+ align:start position:0%
+but there was about 15 or 20 details in
+ 
+
+ align:start position:0%
+but there was about 15 or 20 details in
+these slides about the differences
+
+ align:start position:0%
+these slides about the differences
+ 
+
+ align:start position:0%
+these slides about the differences
+between Bitcoin and ether and I just use
+
+ align:start position:0%
+between Bitcoin and ether and I just use
+ 
+
+ align:start position:0%
+between Bitcoin and ether and I just use
+it to remind because it's saying okay
+
+ align:start position:0%
+it to remind because it's saying okay
+ 
+
+ align:start position:0%
+it to remind because it's saying okay
+why why why did the professor why did
+
+ align:start position:0%
+why why why did the professor why did
+ 
+
+ align:start position:0%
+why why why did the professor why did
+the why did Gary put it up there this
+
+ align:start position:0%
+the why did Gary put it up there this
+ 
+
+ align:start position:0%
+the why did Gary put it up there this
+professor lesyk that was nice for Larry
+
+ align:start position:0%
+professor lesyk that was nice for Larry
+ 
+
+ align:start position:0%
+professor lesyk that was nice for Larry
+but for me but in essence the big
+
+ align:start position:0%
+but for me but in essence the big
+ 
+
+ align:start position:0%
+but for me but in essence the big
+difference is account based versus
+
+ align:start position:0%
+difference is account based versus
+ 
+
+ align:start position:0%
+difference is account based versus
+transaction base the kind of big
+
+ align:start position:0%
+transaction base the kind of big
+ 
+
+ align:start position:0%
+transaction base the kind of big
+difference is ether does seem to go
+
+ align:start position:0%
+difference is ether does seem to go
+ 
+
+ align:start position:0%
+difference is ether does seem to go
+faster but it doesn't have a lot of
+
+ align:start position:0%
+faster but it doesn't have a lot of
+ 
+
+ align:start position:0%
+faster but it doesn't have a lot of
+throughput they still both use proof of
+
+ align:start position:0%
+throughput they still both use proof of
+ 
+
+ align:start position:0%
+throughput they still both use proof of
+work even though ether says they're
+
+ align:start position:0%
+work even though ether says they're
+ 
+
+ align:start position:0%
+work even though ether says they're
+going to move to proof of state they're
+
+ align:start position:0%
+going to move to proof of state they're
+ 
+
+ align:start position:0%
+going to move to proof of state they're
+not there yet when they get there we'll
+
+ align:start position:0%
+not there yet when they get there we'll
+ 
+
+ align:start position:0%
+not there yet when they get there we'll
+all know together the economics are a
+
+ align:start position:0%
+all know together the economics are a
+ 
+
+ align:start position:0%
+all know together the economics are a
+bit difference of course as well and but
+
+ align:start position:0%
+bit difference of course as well and but
+ 
+
+ align:start position:0%
+bit difference of course as well and but
+all of these details are part of the
+
+ align:start position:0%
+all of these details are part of the
+ 
+
+ align:start position:0%
+all of these details are part of the
+reason why there's problems and so you
+
+ align:start position:0%
+reason why there's problems and so you
+ 
+
+ align:start position:0%
+reason why there's problems and so you
+read in the Geneva report a little bit
+
+ align:start position:0%
+read in the Geneva report a little bit
+ 
+
+ align:start position:0%
+read in the Geneva report a little bit
+about a professor an economist from the
+
+ align:start position:0%
+about a professor an economist from the
+ 
+
+ align:start position:0%
+about a professor an economist from the
+1930s does anybody want to take a crack
+
+ align:start position:0%
+1930s does anybody want to take a crack
+ 
+
+ align:start position:0%
+1930s does anybody want to take a crack
+at it or should I just do my slides here
+
+ align:start position:0%
+at it or should I just do my slides here
+ 
+
+ align:start position:0%
+at it or should I just do my slides here
+we go
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+like cost-benefit analysis so that like
+
+ align:start position:0%
+like cost-benefit analysis so that like
+ 
+
+ align:start position:0%
+like cost-benefit analysis so that like
+if one wants to use tool of changes in
+
+ align:start position:0%
+if one wants to use tool of changes in
+ 
+
+ align:start position:0%
+if one wants to use tool of changes in
+tries Network you should take into
+
+ align:start position:0%
+tries Network you should take into
+ 
+
+ align:start position:0%
+tries Network you should take into
+account like all the benefits in terms
+
+ align:start position:0%
+account like all the benefits in terms
+ 
+
+ align:start position:0%
+account like all the benefits in terms
+of reducing cost of petrology enhancing
+
+ align:start position:0%
+of reducing cost of petrology enhancing
+ 
+
+ align:start position:0%
+of reducing cost of petrology enhancing
+security but also like the cost of like
+
+ align:start position:0%
+security but also like the cost of like
+ 
+
+ align:start position:0%
+security but also like the cost of like
+switching to it isn't release
+
+ align:start position:0%
+switching to it isn't release
+ 
+
+ align:start position:0%
+switching to it isn't release
+Koko's is a is an economist from the
+
+ align:start position:0%
+Koko's is a is an economist from the
+ 
+
+ align:start position:0%
+Koko's is a is an economist from the
+1930s who wrote extensively about the
+
+ align:start position:0%
+1930s who wrote extensively about the
+ 
+
+ align:start position:0%
+1930s who wrote extensively about the
+costs and appearing about the
+
+ align:start position:0%
+costs and appearing about the
+ 
+
+ align:start position:0%
+costs and appearing about the
+corporation kelly much earlier time way
+
+ align:start position:0%
+corporation kelly much earlier time way
+ 
+
+ align:start position:0%
+corporation kelly much earlier time way
+pre bitcoin but a different why does
+
+ align:start position:0%
+pre bitcoin but a different why does
+ 
+
+ align:start position:0%
+pre bitcoin but a different why does
+economic activity cluster into a firm
+
+ align:start position:0%
+economic activity cluster into a firm
+ 
+
+ align:start position:0%
+economic activity cluster into a firm
+rather than if it was truly market base
+
+ align:start position:0%
+rather than if it was truly market base
+ 
+
+ align:start position:0%
+rather than if it was truly market base
+i might just be selling my services in
+
+ align:start position:0%
+i might just be selling my services in
+ 
+
+ align:start position:0%
+i might just be selling my services in
+essence he was asking the question why
+
+ align:start position:0%
+essence he was asking the question why
+ 
+
+ align:start position:0%
+essence he was asking the question why
+don't we have a fully gig economy in the
+
+ align:start position:0%
+don't we have a fully gig economy in the
+ 
+
+ align:start position:0%
+don't we have a fully gig economy in the
+1930s where everybody's free labor and
+
+ align:start position:0%
+1930s where everybody's free labor and
+ 
+
+ align:start position:0%
+1930s where everybody's free labor and
+and and and even capital and labor meets
+
+ align:start position:0%
+and and and even capital and labor meets
+ 
+
+ align:start position:0%
+and and and even capital and labor meets
+individually and we collect up together
+
+ align:start position:0%
+individually and we collect up together
+ 
+
+ align:start position:0%
+individually and we collect up together
+that was kind of the body of his
+
+ align:start position:0%
+that was kind of the body of his
+ 
+
+ align:start position:0%
+that was kind of the body of his
+question that he was so centralization
+
+ align:start position:0%
+question that he was so centralization
+ 
+
+ align:start position:0%
+question that he was so centralization
+versus decentralization eighty years ago
+
+ align:start position:0%
+versus decentralization eighty years ago
+ 
+
+ align:start position:0%
+versus decentralization eighty years ago
+studied by a great economist so just
+
+ align:start position:0%
+studied by a great economist so just
+ 
+
+ align:start position:0%
+studied by a great economist so just
+thinking about it here a little bit
+
+ align:start position:0%
+thinking about it here a little bit
+ 
+
+ align:start position:0%
+thinking about it here a little bit
+i think that when you go from
+
+ align:start position:0%
+i think that when you go from
+ 
+
+ align:start position:0%
+i think that when you go from
+decentralization to centralization you
+
+ align:start position:0%
+decentralization to centralization you
+ 
+
+ align:start position:0%
+decentralization to centralization you
+tend on the centralized side you get
+
+ align:start position:0%
+tend on the centralized side you get
+ 
+
+ align:start position:0%
+tend on the centralized side you get
+capture you get economic rents and you
+
+ align:start position:0%
+capture you get economic rents and you
+ 
+
+ align:start position:0%
+capture you get economic rents and you
+do have a single point of failure in
+
+ align:start position:0%
+do have a single point of failure in
+ 
+
+ align:start position:0%
+do have a single point of failure in
+some sense the resiliency of the system
+
+ align:start position:0%
+some sense the resiliency of the system
+ 
+
+ align:start position:0%
+some sense the resiliency of the system
+whether it's in finance where you worry
+
+ align:start position:0%
+whether it's in finance where you worry
+ 
+
+ align:start position:0%
+whether it's in finance where you worry
+about systemic risk that one Clearing
+
+ align:start position:0%
+about systemic risk that one Clearing
+ 
+
+ align:start position:0%
+about systemic risk that one Clearing
+House one central bank one government if
+
+ align:start position:0%
+House one central bank one government if
+ 
+
+ align:start position:0%
+House one central bank one government if
+it's knocked out it's so relevant to the
+
+ align:start position:0%
+it's knocked out it's so relevant to the
+ 
+
+ align:start position:0%
+it's knocked out it's so relevant to the
+economy writ large it brings it down or
+
+ align:start position:0%
+economy writ large it brings it down or
+ 
+
+ align:start position:0%
+economy writ large it brings it down or
+if it's one database you have a single
+
+ align:start position:0%
+if it's one database you have a single
+ 
+
+ align:start position:0%
+if it's one database you have a single
+point in essence of failure economic
+
+ align:start position:0%
+point in essence of failure economic
+ 
+
+ align:start position:0%
+point in essence of failure economic
+rents is an ability to collect excess
+
+ align:start position:0%
+rents is an ability to collect excess
+ 
+
+ align:start position:0%
+rents is an ability to collect excess
+profits I assure you everybody in this
+
+ align:start position:0%
+profits I assure you everybody in this
+ 
+
+ align:start position:0%
+profits I assure you everybody in this
+class wants to collect economic
+
+ align:start position:0%
+class wants to collect economic
+ 
+
+ align:start position:0%
+class wants to collect economic
+rats we store it out as venture
+
+ align:start position:0%
+rats we store it out as venture
+ 
+
+ align:start position:0%
+rats we store it out as venture
+capitalists and entrepreneurs but we
+
+ align:start position:0%
+capitalists and entrepreneurs but we
+ 
+
+ align:start position:0%
+capitalists and entrepreneurs but we
+have a motivation and an incentive to be
+
+ align:start position:0%
+have a motivation and an incentive to be
+ 
+
+ align:start position:0%
+have a motivation and an incentive to be
+monopolist but we don't want to do it
+
+ align:start position:0%
+monopolist but we don't want to do it
+ 
+
+ align:start position:0%
+monopolist but we don't want to do it
+illegal of course I mean we just want to
+
+ align:start position:0%
+illegal of course I mean we just want to
+ 
+
+ align:start position:0%
+illegal of course I mean we just want to
+get there you know by dominating the
+
+ align:start position:0%
+get there you know by dominating the
+ 
+
+ align:start position:0%
+get there you know by dominating the
+market I'm sorry was there a question
+
+ align:start position:0%
+market I'm sorry was there a question
+ 
+
+ align:start position:0%
+market I'm sorry was there a question
+here you just read you're shaking your
+
+ align:start position:0%
+here you just read you're shaking your
+ 
+
+ align:start position:0%
+here you just read you're shaking your
+head and I didn't know but on the other
+
+ align:start position:0%
+head and I didn't know but on the other
+ 
+
+ align:start position:0%
+head and I didn't know but on the other
+side there's there's the benefits the
+
+ align:start position:0%
+side there's there's the benefits the
+ 
+
+ align:start position:0%
+side there's there's the benefits the
+the y scale is not written on here the Y
+
+ align:start position:0%
+the y scale is not written on here the Y
+ 
+
+ align:start position:0%
+the y scale is not written on here the Y
+scale is however you want to think of it
+
+ align:start position:0%
+scale is however you want to think of it
+ 
+
+ align:start position:0%
+scale is however you want to think of it
+but I think of it as kind of costs so
+
+ align:start position:0%
+but I think of it as kind of costs so
+ 
+
+ align:start position:0%
+but I think of it as kind of costs so
+the Y scale up the Y scale is like
+
+ align:start position:0%
+the Y scale up the Y scale is like
+ 
+
+ align:start position:0%
+the Y scale up the Y scale is like
+greater cost decentralization the big
+
+ align:start position:0%
+greater cost decentralization the big
+ 
+
+ align:start position:0%
+greater cost decentralization the big
+costs that come there is coordination
+
+ align:start position:0%
+costs that come there is coordination
+ 
+
+ align:start position:0%
+costs that come there is coordination
+you have a lot of collective action
+
+ align:start position:0%
+you have a lot of collective action
+ 
+
+ align:start position:0%
+you have a lot of collective action
+issues if the hundred or so people in
+
+ align:start position:0%
+issues if the hundred or so people in
+ 
+
+ align:start position:0%
+issues if the hundred or so people in
+this room we're trying to do something
+
+ align:start position:0%
+this room we're trying to do something
+ 
+
+ align:start position:0%
+this room we're trying to do something
+together you have to figure out how to
+
+ align:start position:0%
+together you have to figure out how to
+ 
+
+ align:start position:0%
+together you have to figure out how to
+do it collectively and coordination and
+
+ align:start position:0%
+do it collectively and coordination and
+ 
+
+ align:start position:0%
+do it collectively and coordination and
+that's true of every blockchain that you
+
+ align:start position:0%
+that's true of every blockchain that you
+ 
+
+ align:start position:0%
+that's true of every blockchain that you
+can think about governance relates to
+
+ align:start position:0%
+can think about governance relates to
+ 
+
+ align:start position:0%
+can think about governance relates to
+coordination and collective action
+
+ align:start position:0%
+coordination and collective action
+ 
+
+ align:start position:0%
+coordination and collective action
+issues and then security and scalability
+
+ align:start position:0%
+issues and then security and scalability
+ 
+
+ align:start position:0%
+issues and then security and scalability
+these two lines are not in any of the
+
+ align:start position:0%
+these two lines are not in any of the
+ 
+
+ align:start position:0%
+these two lines are not in any of the
+readings but they try to capture what
+
+ align:start position:0%
+readings but they try to capture what
+ 
+
+ align:start position:0%
+readings but they try to capture what
+and depending them on the slope of the
+
+ align:start position:0%
+and depending them on the slope of the
+ 
+
+ align:start position:0%
+and depending them on the slope of the
+two lines you might say that a market
+
+ align:start position:0%
+two lines you might say that a market
+ 
+
+ align:start position:0%
+two lines you might say that a market
+might tend towards more centralization
+
+ align:start position:0%
+might tend towards more centralization
+ 
+
+ align:start position:0%
+might tend towards more centralization
+in theory if I change the slope it would
+
+ align:start position:0%
+in theory if I change the slope it would
+ 
+
+ align:start position:0%
+in theory if I change the slope it would
+be further to the decentralized side
+
+ align:start position:0%
+be further to the decentralized side
+ 
+
+ align:start position:0%
+be further to the decentralized side
+right if the cost of decentralization is
+
+ align:start position:0%
+right if the cost of decentralization is
+ 
+
+ align:start position:0%
+right if the cost of decentralization is
+a lower slope and the cost of
+
+ align:start position:0%
+a lower slope and the cost of
+ 
+
+ align:start position:0%
+a lower slope and the cost of
+centralization is higher we will tend
+
+ align:start position:0%
+centralization is higher we will tend
+ 
+
+ align:start position:0%
+centralization is higher we will tend
+more towards decentralization so it's
+
+ align:start position:0%
+more towards decentralization so it's
+ 
+
+ align:start position:0%
+more towards decentralization so it's
+just a way that to visualize here are
+
+ align:start position:0%
+just a way that to visualize here are
+ 
+
+ align:start position:0%
+just a way that to visualize here are
+the costs of centralization which are
+
+ align:start position:0%
+the costs of centralization which are
+ 
+
+ align:start position:0%
+the costs of centralization which are
+basically capture rents and single point
+
+ align:start position:0%
+basically capture rents and single point
+ 
+
+ align:start position:0%
+basically capture rents and single point
+of failure not that there aren't other
+
+ align:start position:0%
+of failure not that there aren't other
+ 
+
+ align:start position:0%
+of failure not that there aren't other
+costs of centralization here are the
+
+ align:start position:0%
+costs of centralization here are the
+ 
+
+ align:start position:0%
+costs of centralization here are the
+costs of decentralization I think in
+
+ align:start position:0%
+costs of decentralization I think in
+ 
+
+ align:start position:0%
+costs of decentralization I think in
+each one of the applications when you're
+
+ align:start position:0%
+each one of the applications when you're
+ 
+
+ align:start position:0%
+each one of the applications when you're
+thinking of use cases it's worthy this
+
+ align:start position:0%
+thinking of use cases it's worthy this
+ 
+
+ align:start position:0%
+thinking of use cases it's worthy this
+is kind of a core thing well this
+
+ align:start position:0%
+is kind of a core thing well this
+ 
+
+ align:start position:0%
+is kind of a core thing well this
+application lend itself to a low slope
+
+ align:start position:0%
+application lend itself to a low slope
+ 
+
+ align:start position:0%
+application lend itself to a low slope
+decentralization curve and a high slope
+
+ align:start position:0%
+decentralization curve and a high slope
+ 
+
+ align:start position:0%
+decentralization curve and a high slope
+centralization curve
+
+ align:start position:0%
+centralization curve
+ 
+
+ align:start position:0%
+centralization curve
+are there a lot of economic rents so
+
+ align:start position:0%
+are there a lot of economic rents so
+ 
+
+ align:start position:0%
+are there a lot of economic rents so
+their real problems with single points
+
+ align:start position:0%
+their real problems with single points
+ 
+
+ align:start position:0%
+their real problems with single points
+of failure and capture and if it's a
+
+ align:start position:0%
+of failure and capture and if it's a
+ 
+
+ align:start position:0%
+of failure and capture and if it's a
+slow slope decentralization curve
+
+ align:start position:0%
+slow slope decentralization curve
+ 
+
+ align:start position:0%
+slow slope decentralization curve
+meaning there's not much cost to the
+
+ align:start position:0%
+meaning there's not much cost to the
+ 
+
+ align:start position:0%
+meaning there's not much cost to the
+governance coordination and scalability
+
+ align:start position:0%
+governance coordination and scalability
+ 
+
+ align:start position:0%
+governance coordination and scalability
+issues and you're going to be more
+
+ align:start position:0%
+issues and you're going to be more
+ 
+
+ align:start position:0%
+issues and you're going to be more
+towards decentralization that this isn't
+
+ align:start position:0%
+towards decentralization that this isn't
+ 
+
+ align:start position:0%
+towards decentralization that this isn't
+any reading or book it's just you know a
+
+ align:start position:0%
+any reading or book it's just you know a
+ 
+
+ align:start position:0%
+any reading or book it's just you know a
+shot at trying to visualize it Shawn
+
+ align:start position:0%
+shot at trying to visualize it Shawn
+ 
+
+ align:start position:0%
+shot at trying to visualize it Shawn
+any question
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+John's question is why are the privacy
+
+ align:start position:0%
+John's question is why are the privacy
+ 
+
+ align:start position:0%
+John's question is why are the privacy
+coins forked
+
+ align:start position:0%
+coins forked
+ 
+
+ align:start position:0%
+coins forked
+not all of them but many of them are
+
+ align:start position:0%
+not all of them but many of them are
+ 
+
+ align:start position:0%
+not all of them but many of them are
+forked off of Bitcoin or one of the
+
+ align:start position:0%
+forked off of Bitcoin or one of the
+ 
+
+ align:start position:0%
+forked off of Bitcoin or one of the
+major coins medoras you want to say did
+
+ align:start position:0%
+major coins medoras you want to say did
+ 
+
+ align:start position:0%
+major coins medoras you want to say did
+you you have one privacy coin high
+
+ align:start position:0%
+you you have one privacy coin high
+ 
+
+ align:start position:0%
+you you have one privacy coin high
+quality code so you can build up on it
+
+ align:start position:0%
+quality code so you can build up on it
+ 
+
+ align:start position:0%
+quality code so you can build up on it
+so it's natural to like add privacy on
+
+ align:start position:0%
+so it's natural to like add privacy on
+ 
+
+ align:start position:0%
+so it's natural to like add privacy on
+top of Bitcoin in your fork rather than
+
+ align:start position:0%
+top of Bitcoin in your fork rather than
+ 
+
+ align:start position:0%
+top of Bitcoin in your fork rather than
+write it from scratch medoras is the
+
+ align:start position:0%
+write it from scratch medoras is the
+ 
+
+ align:start position:0%
+write it from scratch medoras is the
+answering is there's something that's
+
+ align:start position:0%
+answering is there's something that's
+ 
+
+ align:start position:0%
+answering is there's something that's
+freely available the Bitcoin core code
+
+ align:start position:0%
+freely available the Bitcoin core code
+ 
+
+ align:start position:0%
+freely available the Bitcoin core code
+it's actually under a copyright license
+
+ align:start position:0%
+it's actually under a copyright license
+ 
+
+ align:start position:0%
+it's actually under a copyright license
+here at MIT which makes it free that was
+
+ align:start position:0%
+here at MIT which makes it free that was
+ 
+
+ align:start position:0%
+here at MIT which makes it free that was
+Satoshi nakamoto's decision it wasn't
+
+ align:start position:0%
+Satoshi nakamoto's decision it wasn't
+ 
+
+ align:start position:0%
+Satoshi nakamoto's decision it wasn't
+that well maybe Nakamoto does work here
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the clue but it's it's it's been
+
+ align:start position:0%
+the clue but it's it's it's been
+ 
+
+ align:start position:0%
+the clue but it's it's it's been
+developed and it's knocked around as I
+
+ align:start position:0%
+developed and it's knocked around as I
+ 
+
+ align:start position:0%
+developed and it's knocked around as I
+call it in the proverbial swamp I mean
+
+ align:start position:0%
+call it in the proverbial swamp I mean
+ 
+
+ align:start position:0%
+call it in the proverbial swamp I mean
+with all these attack viruses and so
+
+ align:start position:0%
+with all these attack viruses and so
+ 
+
+ align:start position:0%
+with all these attack viruses and so
+forth and Soma doors are saying build
+
+ align:start position:0%
+forth and Soma doors are saying build
+ 
+
+ align:start position:0%
+forth and Soma doors are saying build
+off of that and basically get that code
+
+ align:start position:0%
+off of that and basically get that code
+ 
+
+ align:start position:0%
+off of that and basically get that code
+for free and then fork that so the
+
+ align:start position:0%
+for free and then fork that so the
+ 
+
+ align:start position:0%
+for free and then fork that so the
+challenge is we talked about it a
+
+ align:start position:0%
+challenge is we talked about it a
+ 
+
+ align:start position:0%
+challenge is we talked about it a
+performance scalability efficiency
+
+ align:start position:0%
+performance scalability efficiency
+ 
+
+ align:start position:0%
+performance scalability efficiency
+privacy security what there was less
+
+ align:start position:0%
+privacy security what there was less
+ 
+
+ align:start position:0%
+privacy security what there was less
+talk about was interoperability
+
+ align:start position:0%
+talk about was interoperability
+ 
+
+ align:start position:0%
+talk about was interoperability
+governance and collective action and I'm
+
+ align:start position:0%
+governance and collective action and I'm
+ 
+
+ align:start position:0%
+governance and collective action and I'm
+going to dig into those two more because
+
+ align:start position:0%
+going to dig into those two more because
+ 
+
+ align:start position:0%
+going to dig into those two more because
+it feels like that's worthwhile I also
+
+ align:start position:0%
+it feels like that's worthwhile I also
+ 
+
+ align:start position:0%
+it feels like that's worthwhile I also
+believe that the first bucket
+
+ align:start position:0%
+believe that the first bucket
+ 
+
+ align:start position:0%
+believe that the first bucket
+performance and privacy buckets are more
+
+ align:start position:0%
+performance and privacy buckets are more
+ 
+
+ align:start position:0%
+performance and privacy buckets are more
+susceptible to fixes though that might
+
+ align:start position:0%
+susceptible to fixes though that might
+ 
+
+ align:start position:0%
+susceptible to fixes though that might
+take three or five or even eight or ten
+
+ align:start position:0%
+take three or five or even eight or ten
+ 
+
+ align:start position:0%
+take three or five or even eight or ten
+years to happen I think they're more
+
+ align:start position:0%
+years to happen I think they're more
+ 
+
+ align:start position:0%
+years to happen I think they're more
+susceptible to the sort of bright men
+
+ align:start position:0%
+susceptible to the sort of bright men
+ 
+
+ align:start position:0%
+susceptible to the sort of bright men
+and women that are in these fields
+
+ align:start position:0%
+and women that are in these fields
+ 
+
+ align:start position:0%
+and women that are in these fields
+addressing themselves to the computer
+
+ align:start position:0%
+addressing themselves to the computer
+ 
+
+ align:start position:0%
+addressing themselves to the computer
+science and cryptography of the space
+
+ align:start position:0%
+science and cryptography of the space
+ 
+
+ align:start position:0%
+science and cryptography of the space
+whereas governance and collective action
+
+ align:start position:0%
+whereas governance and collective action
+ 
+
+ align:start position:0%
+whereas governance and collective action
+might be solvable but I think it's it's
+
+ align:start position:0%
+might be solvable but I think it's it's
+ 
+
+ align:start position:0%
+might be solvable but I think it's it's
+sort of inherent in the human element
+
+ align:start position:0%
+sort of inherent in the human element
+ 
+
+ align:start position:0%
+sort of inherent in the human element
+and the commercial arrangements that
+
+ align:start position:0%
+and the commercial arrangements that
+ 
+
+ align:start position:0%
+and the commercial arrangements that
+governance and collective action or the
+
+ align:start position:0%
+governance and collective action or the
+ 
+
+ align:start position:0%
+governance and collective action or the
+harder of these four buckets that's just
+
+ align:start position:0%
+harder of these four buckets that's just
+ 
+
+ align:start position:0%
+harder of these four buckets that's just
+one person's read of it but we'll go
+
+ align:start position:0%
+one person's read of it but we'll go
+ 
+
+ align:start position:0%
+one person's read of it but we'll go
+through some of the reasons as well why
+
+ align:start position:0%
+through some of the reasons as well why
+ 
+
+ align:start position:0%
+through some of the reasons as well why
+I kind of I get it to that view
+
+ align:start position:0%
+I kind of I get it to that view
+ 
+
+ align:start position:0%
+I kind of I get it to that view
+there's also commercial use case
+
+ align:start position:0%
+there's also commercial use case
+ 
+
+ align:start position:0%
+there's also commercial use case
+challenges we're not going to dig into
+
+ align:start position:0%
+challenges we're not going to dig into
+ 
+
+ align:start position:0%
+challenges we're not going to dig into
+that much here that's mostly the second
+
+ align:start position:0%
+that much here that's mostly the second
+ 
+
+ align:start position:0%
+that much here that's mostly the second
+half of the semester but I just wanted
+
+ align:start position:0%
+half of the semester but I just wanted
+ 
+
+ align:start position:0%
+half of the semester but I just wanted
+to mention that's a real thing that a
+
+ align:start position:0%
+to mention that's a real thing that a
+ 
+
+ align:start position:0%
+to mention that's a real thing that a
+lot of folks are saying well I have to
+
+ align:start position:0%
+lot of folks are saying well I have to
+ 
+
+ align:start position:0%
+lot of folks are saying well I have to
+make sure that this is the best
+
+ align:start position:0%
+make sure that this is the best
+ 
+
+ align:start position:0%
+make sure that this is the best
+commercial application and so forth and
+
+ align:start position:0%
+commercial application and so forth and
+ 
+
+ align:start position:0%
+commercial application and so forth and
+can I make money I mean ultimately on it
+
+ align:start position:0%
+can I make money I mean ultimately on it
+ 
+
+ align:start position:0%
+can I make money I mean ultimately on it
+and then we are next week going to talk
+
+ align:start position:0%
+and then we are next week going to talk
+ 
+
+ align:start position:0%
+and then we are next week going to talk
+about the public policy issues and
+
+ align:start position:0%
+about the public policy issues and
+ 
+
+ align:start position:0%
+about the public policy issues and
+challenges and they all kind of
+
+ align:start position:0%
+challenges and they all kind of
+ 
+
+ align:start position:0%
+challenges and they all kind of
+intersect in a way as well
+
+ align:start position:0%
+intersect in a way as well
+ 
+
+ align:start position:0%
+intersect in a way as well
+so Vitalik buddha ran I think there was
+
+ align:start position:0%
+so Vitalik buddha ran I think there was
+ 
+
+ align:start position:0%
+so Vitalik buddha ran I think there was
+a medium post I had you all read bow do
+
+ align:start position:0%
+a medium post I had you all read bow do
+ 
+
+ align:start position:0%
+a medium post I had you all read bow do
+you want me to tell you tell us a little
+
+ align:start position:0%
+you want me to tell you tell us a little
+ 
+
+ align:start position:0%
+you want me to tell you tell us a little
+bit about what you think is metallic not
+
+ align:start position:0%
+bit about what you think is metallic not
+ 
+
+ align:start position:0%
+bit about what you think is metallic not
+only a brilliant computer scientist but
+
+ align:start position:0%
+only a brilliant computer scientist but
+ 
+
+ align:start position:0%
+only a brilliant computer scientist but
+does he get the economics of this right
+
+ align:start position:0%
+does he get the economics of this right
+ 
+
+ align:start position:0%
+does he get the economics of this right
+or you think he's off you're gonna be on
+
+ align:start position:0%
+or you think he's off you're gonna be on
+ 
+
+ align:start position:0%
+or you think he's off you're gonna be on
+there's no right answer I know people
+
+ align:start position:0%
+there's no right answer I know people
+ 
+
+ align:start position:0%
+there's no right answer I know people
+that feel both ends of the spectrum
+
+ align:start position:0%
+that feel both ends of the spectrum
+ 
+
+ align:start position:0%
+that feel both ends of the spectrum
+about his trilemma so I'm setting you up
+
+ align:start position:0%
+about his trilemma so I'm setting you up
+ 
+
+ align:start position:0%
+about his trilemma so I'm setting you up
+that old saying about what how many of
+
+ align:start position:0%
+that old saying about what how many of
+ 
+
+ align:start position:0%
+that old saying about what how many of
+you have ever hired a contractor to fix
+
+ align:start position:0%
+you have ever hired a contractor to fix
+ 
+
+ align:start position:0%
+you have ever hired a contractor to fix
+something in your kitchen or renovate
+
+ align:start position:0%
+something in your kitchen or renovate
+ 
+
+ align:start position:0%
+something in your kitchen or renovate
+renovate something I mean I have them a
+
+ align:start position:0%
+renovate something I mean I have them a
+ 
+
+ align:start position:0%
+renovate something I mean I have them a
+little older right you know the old saw
+
+ align:start position:0%
+little older right you know the old saw
+ 
+
+ align:start position:0%
+little older right you know the old saw
+that it's good quick cheap but you can't
+
+ align:start position:0%
+that it's good quick cheap but you can't
+ 
+
+ align:start position:0%
+that it's good quick cheap but you can't
+you can't get all three you can only get
+
+ align:start position:0%
+you can't get all three you can only get
+ 
+
+ align:start position:0%
+you can't get all three you can only get
+two out of three that's sort of the
+
+ align:start position:0%
+two out of three that's sort of the
+ 
+
+ align:start position:0%
+two out of three that's sort of the
+contractor dilemma but but what do you
+
+ align:start position:0%
+contractor dilemma but but what do you
+ 
+
+ align:start position:0%
+contractor dilemma but but what do you
+think do you think he's right or do you
+
+ align:start position:0%
+think do you think he's right or do you
+ 
+
+ align:start position:0%
+think do you think he's right or do you
+think you could maybe overtime get all
+
+ align:start position:0%
+think you could maybe overtime get all
+ 
+
+ align:start position:0%
+think you could maybe overtime get all
+three good cheap quick scalable
+
+ align:start position:0%
+three good cheap quick scalable
+ 
+
+ align:start position:0%
+three good cheap quick scalable
+decentralized and secure my very
+
+ align:start position:0%
+decentralized and secure my very
+ 
+
+ align:start position:0%
+decentralized and secure my very
+unsophisticated the other side just to
+
+ align:start position:0%
+unsophisticated the other side just to
+ 
+
+ align:start position:0%
+unsophisticated the other side just to
+have some fun in some debate sure yeah
+
+ align:start position:0%
+have some fun in some debate sure yeah
+ 
+
+ align:start position:0%
+have some fun in some debate sure yeah
+go out at Leonardo that systems have had
+
+ align:start position:0%
+go out at Leonardo that systems have had
+ 
+
+ align:start position:0%
+go out at Leonardo that systems have had
+to develop so they mention for example
+
+ align:start position:0%
+to develop so they mention for example
+ 
+
+ align:start position:0%
+to develop so they mention for example
+visa has at sixty years
+
+ align:start position:0%
+visa has at sixty years
+ 
+
+ align:start position:0%
+visa has at sixty years
+develop a system that works some of
+
+ align:start position:0%
+develop a system that works some of
+ 
+
+ align:start position:0%
+develop a system that works some of
+those currencies and at three four or
+
+ align:start position:0%
+those currencies and at three four or
+ 
+
+ align:start position:0%
+those currencies and at three four or
+five years number his personal opinion
+
+ align:start position:0%
+five years number his personal opinion
+ 
+
+ align:start position:0%
+five years number his personal opinion
+the tax was like less than five percent
+
+ align:start position:0%
+the tax was like less than five percent
+ 
+
+ align:start position:0%
+the tax was like less than five percent
+they would not overcome I don't know if
+
+ align:start position:0%
+they would not overcome I don't know if
+ 
+
+ align:start position:0%
+they would not overcome I don't know if
+that is like a wrong but I think the
+
+ align:start position:0%
+that is like a wrong but I think the
+ 
+
+ align:start position:0%
+that is like a wrong but I think the
+fact that this is a new technology yes
+
+ align:start position:0%
+fact that this is a new technology yes
+ 
+
+ align:start position:0%
+fact that this is a new technology yes
+maybe Vitalik is right that only 5%
+
+ align:start position:0%
+maybe Vitalik is right that only 5%
+ 
+
+ align:start position:0%
+maybe Vitalik is right that only 5%
+maybe only one person
+
+ align:start position:0%
+maybe only one person
+ 
+
+ align:start position:0%
+maybe only one person
+that will succeed but to say that no one
+
+ align:start position:0%
+that will succeed but to say that no one
+ 
+
+ align:start position:0%
+that will succeed but to say that no one
+will deal with these three points in in
+
+ align:start position:0%
+will deal with these three points in in
+ 
+
+ align:start position:0%
+will deal with these three points in in
+a simultaneous satisfactory way and
+
+ align:start position:0%
+a simultaneous satisfactory way and
+ 
+
+ align:start position:0%
+a simultaneous satisfactory way and
+ultimately it has to be satisfactory in
+
+ align:start position:0%
+ultimately it has to be satisfactory in
+ 
+
+ align:start position:0%
+ultimately it has to be satisfactory in
+a commercial way you know taking the
+
+ align:start position:0%
+a commercial way you know taking the
+ 
+
+ align:start position:0%
+a commercial way you know taking the
+risk and trade-offs so Leonardo takes
+
+ align:start position:0%
+risk and trade-offs so Leonardo takes
+ 
+
+ align:start position:0%
+risk and trade-offs so Leonardo takes
+the other side anybody want to say why
+
+ align:start position:0%
+the other side anybody want to say why
+ 
+
+ align:start position:0%
+the other side anybody want to say why
+Leonardo Hugo were you which side are
+
+ align:start position:0%
+Leonardo Hugo were you which side are
+ 
+
+ align:start position:0%
+Leonardo Hugo were you which side are
+you taking Leonardo's side or Vitalik
+
+ align:start position:0%
+you taking Leonardo's side or Vitalik
+ 
+
+ align:start position:0%
+you taking Leonardo's side or Vitalik
+side suffering the middle okay so I
+
+ align:start position:0%
+side suffering the middle okay so I
+ 
+
+ align:start position:0%
+side suffering the middle okay so I
+think that there is a trade-off but I
+
+ align:start position:0%
+think that there is a trade-off but I
+ 
+
+ align:start position:0%
+think that there is a trade-off but I
+agree that it might take time to improve
+
+ align:start position:0%
+agree that it might take time to improve
+ 
+
+ align:start position:0%
+agree that it might take time to improve
+all three simultaneously I mean one
+
+ align:start position:0%
+all three simultaneously I mean one
+ 
+
+ align:start position:0%
+all three simultaneously I mean one
+thing that happened just this last week
+
+ align:start position:0%
+thing that happened just this last week
+ 
+
+ align:start position:0%
+thing that happened just this last week
+in Bitcoin was there was a vulnerability
+
+ align:start position:0%
+in Bitcoin was there was a vulnerability
+ 
+
+ align:start position:0%
+in Bitcoin was there was a vulnerability
+discovered and like as somebody who
+
+ align:start position:0%
+discovered and like as somebody who
+ 
+
+ align:start position:0%
+discovered and like as somebody who
+doesn't know how to check the codebase
+
+ align:start position:0%
+doesn't know how to check the codebase
+ 
+
+ align:start position:0%
+doesn't know how to check the codebase
+really like I'm not a computer science
+
+ align:start position:0%
+really like I'm not a computer science
+ 
+
+ align:start position:0%
+really like I'm not a computer science
+person so I'm never like checked for
+
+ align:start position:0%
+person so I'm never like checked for
+ 
+
+ align:start position:0%
+person so I'm never like checked for
+bugs or anything that I want to do that
+
+ align:start position:0%
+bugs or anything that I want to do that
+ 
+
+ align:start position:0%
+bugs or anything that I want to do that
+I kind of just take the software as it
+
+ align:start position:0%
+I kind of just take the software as it
+ 
+
+ align:start position:0%
+I kind of just take the software as it
+stands and unload it and install it and
+
+ align:start position:0%
+stands and unload it and install it and
+ 
+
+ align:start position:0%
+stands and unload it and install it and
+when they say I need to update my
+
+ align:start position:0%
+when they say I need to update my
+ 
+
+ align:start position:0%
+when they say I need to update my
+software because there's a bug I'll
+
+ align:start position:0%
+software because there's a bug I'll
+ 
+
+ align:start position:0%
+software because there's a bug I'll
+update the software there's a bug and
+
+ align:start position:0%
+update the software there's a bug and
+ 
+
+ align:start position:0%
+update the software there's a bug and
+that kind of feels like more of a
+
+ align:start position:0%
+that kind of feels like more of a
+ 
+
+ align:start position:0%
+that kind of feels like more of a
+centralized system but you're getting
+
+ align:start position:0%
+centralized system but you're getting
+ 
+
+ align:start position:0%
+centralized system but you're getting
+that security but then the
+
+ align:start position:0%
+that security but then the
+ 
+
+ align:start position:0%
+that security but then the
+decentralization comes something from
+
+ align:start position:0%
+decentralization comes something from
+ 
+
+ align:start position:0%
+decentralization comes something from
+the fact that the network is still
+
+ align:start position:0%
+the fact that the network is still
+ 
+
+ align:start position:0%
+the fact that the network is still
+spread out over something you know it's
+
+ align:start position:0%
+spread out over something you know it's
+ 
+
+ align:start position:0%
+spread out over something you know it's
+so like there are trade-offs that I
+
+ align:start position:0%
+so like there are trade-offs that I
+ 
+
+ align:start position:0%
+so like there are trade-offs that I
+think you can kind of build on one and
+
+ align:start position:0%
+think you can kind of build on one and
+ 
+
+ align:start position:0%
+think you can kind of build on one and
+then climb another cliff like kind of
+
+ align:start position:0%
+then climb another cliff like kind of
+ 
+
+ align:start position:0%
+then climb another cliff like kind of
+build on each but not at the same time
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+I'm probably an optimist enough on the
+
+ align:start position:0%
+I'm probably an optimist enough on the
+ 
+
+ align:start position:0%
+I'm probably an optimist enough on the
+human condition and that the
+
+ align:start position:0%
+human condition and that the
+ 
+
+ align:start position:0%
+human condition and that the
+technologist will solve more than
+
+ align:start position:0%
+technologist will solve more than
+ 
+
+ align:start position:0%
+technologist will solve more than
+metallics so I'm not saying I'm all the
+
+ align:start position:0%
+metallics so I'm not saying I'm all the
+ 
+
+ align:start position:0%
+metallics so I'm not saying I'm all the
+way we're Leonardo or wherever yeah
+
+ align:start position:0%
+way we're Leonardo or wherever yeah
+ 
+
+ align:start position:0%
+way we're Leonardo or wherever yeah
+there would be but I'm probably closer
+
+ align:start position:0%
+there would be but I'm probably closer
+ 
+
+ align:start position:0%
+there would be but I'm probably closer
+to Leonardo than to vitalik but that's
+
+ align:start position:0%
+to Leonardo than to vitalik but that's
+ 
+
+ align:start position:0%
+to Leonardo than to vitalik but that's
+just my points of view I also find an
+
+ align:start position:0%
+just my points of view I also find an
+ 
+
+ align:start position:0%
+just my points of view I also find an
+interesting of it's all right if I say
+
+ align:start position:0%
+interesting of it's all right if I say
+ 
+
+ align:start position:0%
+interesting of it's all right if I say
+Hugo's an engineering doctoral student
+
+ align:start position:0%
+Hugo's an engineering doctoral student
+ 
+
+ align:start position:0%
+Hugo's an engineering doctoral student
+here and yet he's not checking the code
+
+ align:start position:0%
+here and yet he's not checking the code
+ 
+
+ align:start position:0%
+here and yet he's not checking the code
+not any right because right so there's a
+
+ align:start position:0%
+not any right because right so there's a
+ 
+
+ align:start position:0%
+not any right because right so there's a
+trust issue that in the marketplace the
+
+ align:start position:0%
+trust issue that in the marketplace the
+ 
+
+ align:start position:0%
+trust issue that in the marketplace the
+trust of the code we also trust Facebook
+
+ align:start position:0%
+trust of the code we also trust Facebook
+ 
+
+ align:start position:0%
+trust of the code we also trust Facebook
+and Dropbox and and and broadly speaking
+
+ align:start position:0%
+and Dropbox and and and broadly speaking
+ 
+
+ align:start position:0%
+and Dropbox and and and broadly speaking
+the Internet as well Priya
+
+ align:start position:0%
+the Internet as well Priya
+ 
+
+ align:start position:0%
+the Internet as well Priya
+there are several examples throughout
+
+ align:start position:0%
+there are several examples throughout
+ 
+
+ align:start position:0%
+there are several examples throughout
+the evolution of human interaction where
+
+ align:start position:0%
+the evolution of human interaction where
+ 
+
+ align:start position:0%
+the evolution of human interaction where
+these three things have been sorted so
+
+ align:start position:0%
+these three things have been sorted so
+ 
+
+ align:start position:0%
+these three things have been sorted so
+it might not be that and in some systems
+
+ align:start position:0%
+it might not be that and in some systems
+ 
+
+ align:start position:0%
+it might not be that and in some systems
+at any one time all these three nodes
+
+ align:start position:0%
+at any one time all these three nodes
+ 
+
+ align:start position:0%
+at any one time all these three nodes
+are working right like four are
+
+ align:start position:0%
+are working right like four are
+ 
+
+ align:start position:0%
+are working right like four are
+currently in existence there are moments
+
+ align:start position:0%
+currently in existence there are moments
+ 
+
+ align:start position:0%
+currently in existence there are moments
+of vulnerability yes but then you catch
+
+ align:start position:0%
+of vulnerability yes but then you catch
+ 
+
+ align:start position:0%
+of vulnerability yes but then you catch
+it sooner or later so I feel like it's
+
+ align:start position:0%
+it sooner or later so I feel like it's
+ 
+
+ align:start position:0%
+it sooner or later so I feel like it's
+maybe not it's about having it all
+
+ align:start position:0%
+maybe not it's about having it all
+ 
+
+ align:start position:0%
+maybe not it's about having it all
+perfect right now versus will you get to
+
+ align:start position:0%
+perfect right now versus will you get to
+ 
+
+ align:start position:0%
+perfect right now versus will you get to
+a point where all three are mostly in
+
+ align:start position:0%
+a point where all three are mostly in
+ 
+
+ align:start position:0%
+a point where all three are mostly in
+place and working like how Priya said
+
+ align:start position:0%
+place and working like how Priya said
+ 
+
+ align:start position:0%
+place and working like how Priya said
+working enough right it doesn't have to
+
+ align:start position:0%
+working enough right it doesn't have to
+ 
+
+ align:start position:0%
+working enough right it doesn't have to
+be scalable to the place where it's
+
+ align:start position:0%
+be scalable to the place where it's
+ 
+
+ align:start position:0%
+be scalable to the place where it's
+millions of transactions a second but
+
+ align:start position:0%
+millions of transactions a second but
+ 
+
+ align:start position:0%
+millions of transactions a second but
+maybe it needs to be faster than seven
+
+ align:start position:0%
+maybe it needs to be faster than seven
+ 
+
+ align:start position:0%
+maybe it needs to be faster than seven
+or ten transactions a second or a theory
+
+ align:start position:0%
+or ten transactions a second or a theory
+ 
+
+ align:start position:0%
+or ten transactions a second or a theory
+I'm 20 transactions a second we had I
+
+ align:start position:0%
+I'm 20 transactions a second we had I
+ 
+
+ align:start position:0%
+I'm 20 transactions a second we had I
+should also remind everybody Tuesday
+
+ align:start position:0%
+should also remind everybody Tuesday
+ 
+
+ align:start position:0%
+should also remind everybody Tuesday
+nights we have dinner Simon Johnson
+
+ align:start position:0%
+nights we have dinner Simon Johnson
+ 
+
+ align:start position:0%
+nights we have dinner Simon Johnson
+treats every Tuesday night it's not
+
+ align:start position:0%
+treats every Tuesday night it's not
+ 
+
+ align:start position:0%
+treats every Tuesday night it's not
+required to come but it's 5:30 to 7:00
+
+ align:start position:0%
+required to come but it's 5:30 to 7:00
+ 
+
+ align:start position:0%
+required to come but it's 5:30 to 7:00
+that we have an outside speaker around
+
+ align:start position:0%
+that we have an outside speaker around
+ 
+
+ align:start position:0%
+that we have an outside speaker around
+the block chain space and you're welcome
+
+ align:start position:0%
+the block chain space and you're welcome
+ 
+
+ align:start position:0%
+the block chain space and you're welcome
+to come Michelle is here who Michelle
+
+ align:start position:0%
+to come Michelle is here who Michelle
+ 
+
+ align:start position:0%
+to come Michelle is here who Michelle
+Fiorenza anybody that wants to come but
+
+ align:start position:0%
+Fiorenza anybody that wants to come but
+ 
+
+ align:start position:0%
+Fiorenza anybody that wants to come but
+this past week we had somebody speaking
+
+ align:start position:0%
+this past week we had somebody speaking
+ 
+
+ align:start position:0%
+this past week we had somebody speaking
+about the scalability issues and when
+
+ align:start position:0%
+about the scalability issues and when
+ 
+
+ align:start position:0%
+about the scalability issues and when
+his company did a twenty five million
+
+ align:start position:0%
+his company did a twenty five million
+ 
+
+ align:start position:0%
+his company did a twenty five million
+dollar initial coin offering the day of
+
+ align:start position:0%
+dollar initial coin offering the day of
+ 
+
+ align:start position:0%
+dollar initial coin offering the day of
+the offering which only had 40 to 50
+
+ align:start position:0%
+the offering which only had 40 to 50
+ 
+
+ align:start position:0%
+the offering which only had 40 to 50
+thousand purchasers so forty or fifty
+
+ align:start position:0%
+thousand purchasers so forty or fifty
+ 
+
+ align:start position:0%
+thousand purchasers so forty or fifty
+thousand purchasers on that day that
+
+ align:start position:0%
+thousand purchasers on that day that
+ 
+
+ align:start position:0%
+thousand purchasers on that day that
+means the smart contract had to be
+
+ align:start position:0%
+means the smart contract had to be
+ 
+
+ align:start position:0%
+means the smart contract had to be
+triggered numerous times that day took
+
+ align:start position:0%
+triggered numerous times that day took
+ 
+
+ align:start position:0%
+triggered numerous times that day took
+over a third of the entire aetherium
+
+ align:start position:0%
+over a third of the entire aetherium
+ 
+
+ align:start position:0%
+over a third of the entire aetherium
+network on that day and it's sluggish
+
+ align:start position:0%
+network on that day and it's sluggish
+ 
+
+ align:start position:0%
+network on that day and it's sluggish
+and just to close and settle on his
+
+ align:start position:0%
+and just to close and settle on his
+ 
+
+ align:start position:0%
+and just to close and settle on his
+initial coin offering I was saying jeez
+
+ align:start position:0%
+initial coin offering I was saying jeez
+ 
+
+ align:start position:0%
+initial coin offering I was saying jeez
+that that's not the scalability you know
+
+ align:start position:0%
+that that's not the scalability you know
+ 
+
+ align:start position:0%
+that that's not the scalability you know
+we want so we know that's where we are
+
+ align:start position:0%
+we want so we know that's where we are
+ 
+
+ align:start position:0%
+we want so we know that's where we are
+today
+
+ align:start position:0%
+today
+ 
+
+ align:start position:0%
+today
+visa runs around 20 to 30,000
+
+ align:start position:0%
+visa runs around 20 to 30,000
+ 
+
+ align:start position:0%
+visa runs around 20 to 30,000
+transactions a second DTCC which settles
+
+ align:start position:0%
+transactions a second DTCC which settles
+ 
+
+ align:start position:0%
+transactions a second DTCC which settles
+all the stock and equity trades here in
+
+ align:start position:0%
+all the stock and equity trades here in
+ 
+
+ align:start position:0%
+all the stock and equity trades here in
+the US has to be available to transact
+
+ align:start position:0%
+the US has to be available to transact
+ 
+
+ align:start position:0%
+the US has to be available to transact
+at least a hundred thousand a second
+
+ align:start position:0%
+at least a hundred thousand a second
+ 
+
+ align:start position:0%
+at least a hundred thousand a second
+most seconds it's five or ten or some
+
+ align:start position:0%
+most seconds it's five or ten or some
+ 
+
+ align:start position:0%
+most seconds it's five or ten or some
+seconds it's thirty thousand but the
+
+ align:start position:0%
+seconds it's thirty thousand but the
+ 
+
+ align:start position:0%
+seconds it's thirty thousand but the
+Securities and Exchange Commission says
+
+ align:start position:0%
+Securities and Exchange Commission says
+ 
+
+ align:start position:0%
+Securities and Exchange Commission says
+no you have to be rated for four times
+
+ align:start position:0%
+no you have to be rated for four times
+ 
+
+ align:start position:0%
+no you have to be rated for four times
+your average roughly so this gives you a
+
+ align:start position:0%
+your average roughly so this gives you a
+ 
+
+ align:start position:0%
+your average roughly so this gives you a
+sense of the scalability issues just in
+
+ align:start position:0%
+sense of the scalability issues just in
+ 
+
+ align:start position:0%
+sense of the scalability issues just in
+the current environment if one layer is
+
+ align:start position:0%
+the current environment if one layer is
+ 
+
+ align:start position:0%
+the current environment if one layer is
+the Internet of Things on top of it
+
+ align:start position:0%
+the Internet of Things on top of it
+ 
+
+ align:start position:0%
+the Internet of Things on top of it
+there's somewhere and I've heard
+
+ align:start position:0%
+there's somewhere and I've heard
+ 
+
+ align:start position:0%
+there's somewhere and I've heard
+different estimates of eight to ten
+
+ align:start position:0%
+different estimates of eight to ten
+ 
+
+ align:start position:0%
+different estimates of eight to ten
+billion devices currently connected to
+
+ align:start position:0%
+billion devices currently connected to
+ 
+
+ align:start position:0%
+billion devices currently connected to
+the Internet and that's likely to grow
+
+ align:start position:0%
+the Internet and that's likely to grow
+ 
+
+ align:start position:0%
+the Internet and that's likely to grow
+as more refrigerators and street lights
+
+ align:start position:0%
+as more refrigerators and street lights
+ 
+
+ align:start position:0%
+as more refrigerators and street lights
+and traffic lights are tied into the
+
+ align:start position:0%
+and traffic lights are tied into the
+ 
+
+ align:start position:0%
+and traffic lights are tied into the
+Internet in the next five or ten years
+
+ align:start position:0%
+Internet in the next five or ten years
+ 
+
+ align:start position:0%
+Internet in the next five or ten years
+to fifty to a hundred billion devices
+
+ align:start position:0%
+to fifty to a hundred billion devices
+ 
+
+ align:start position:0%
+to fifty to a hundred billion devices
+tied to the Internet
+
+ align:start position:0%
+tied to the Internet
+ 
+
+ align:start position:0%
+tied to the Internet
+if they start communicating to each
+
+ align:start position:0%
+if they start communicating to each
+ 
+
+ align:start position:0%
+if they start communicating to each
+other will it be a blockchain for
+
+ align:start position:0%
+other will it be a blockchain for
+ 
+
+ align:start position:0%
+other will it be a blockchain for
+Internet of Things can't do it at these
+
+ align:start position:0%
+Internet of Things can't do it at these
+ 
+
+ align:start position:0%
+Internet of Things can't do it at these
+types of scaling numbers or can you do
+
+ align:start position:0%
+types of scaling numbers or can you do
+ 
+
+ align:start position:0%
+types of scaling numbers or can you do
+it in some alternative method proof of
+
+ align:start position:0%
+it in some alternative method proof of
+ 
+
+ align:start position:0%
+it in some alternative method proof of
+work is also has a bunch of energy
+
+ align:start position:0%
+work is also has a bunch of energy
+ 
+
+ align:start position:0%
+work is also has a bunch of energy
+consumption we didn't have that a lot in
+
+ align:start position:0%
+consumption we didn't have that a lot in
+ 
+
+ align:start position:0%
+consumption we didn't have that a lot in
+the writing we chose not to put a bunch
+
+ align:start position:0%
+the writing we chose not to put a bunch
+ 
+
+ align:start position:0%
+the writing we chose not to put a bunch
+of that in the Geneva report one
+
+ align:start position:0%
+of that in the Geneva report one
+ 
+
+ align:start position:0%
+of that in the Geneva report one
+estimate is that it's 200 million
+
+ align:start position:0%
+estimate is that it's 200 million
+ 
+
+ align:start position:0%
+estimate is that it's 200 million
+kilowatt hours per day that's equivalent
+
+ align:start position:0%
+kilowatt hours per day that's equivalent
+ 
+
+ align:start position:0%
+kilowatt hours per day that's equivalent
+about seven million US homes on average
+
+ align:start position:0%
+about seven million US homes on average
+ 
+
+ align:start position:0%
+about seven million US homes on average
+just give you a rough didge economists
+
+ align:start position:0%
+just give you a rough didge economists
+ 
+
+ align:start position:0%
+just give you a rough didge economists
+estimate that's one third of 1% of all
+
+ align:start position:0%
+estimate that's one third of 1% of all
+ 
+
+ align:start position:0%
+estimate that's one third of 1% of all
+the world's electricity just a scale
+
+ align:start position:0%
+the world's electricity just a scale
+ 
+
+ align:start position:0%
+the world's electricity just a scale
+scale it if you now you can have a nice
+
+ align:start position:0%
+scale it if you now you can have a nice
+ 
+
+ align:start position:0%
+scale it if you now you can have a nice
+dinner you know dinner party
+
+ align:start position:0%
+dinner you know dinner party
+ 
+
+ align:start position:0%
+dinner you know dinner party
+conversation point it's the it's the
+
+ align:start position:0%
+conversation point it's the it's the
+ 
+
+ align:start position:0%
+conversation point it's the it's the
+electricity of the country of Austria is
+
+ align:start position:0%
+electricity of the country of Austria is
+ 
+
+ align:start position:0%
+electricity of the country of Austria is
+anybody Austrian no I just was you know
+
+ align:start position:0%
+anybody Austrian no I just was you know
+ 
+
+ align:start position:0%
+anybody Austrian no I just was you know
+so it's that's one set of trade-offs of
+
+ align:start position:0%
+so it's that's one set of trade-offs of
+ 
+
+ align:start position:0%
+so it's that's one set of trade-offs of
+proof-of-work as well but it also costs
+
+ align:start position:0%
+proof-of-work as well but it also costs
+ 
+
+ align:start position:0%
+proof-of-work as well but it also costs
+a lot of
+
+ align:start position:0%
+a lot of
+ 
+
+ align:start position:0%
+a lot of
+to run the banking system so I think
+
+ align:start position:0%
+to run the banking system so I think
+ 
+
+ align:start position:0%
+to run the banking system so I think
+that when somebody says well it's
+
+ align:start position:0%
+that when somebody says well it's
+ 
+
+ align:start position:0%
+that when somebody says well it's
+terrible it's challenging all this
+
+ align:start position:0%
+terrible it's challenging all this
+ 
+
+ align:start position:0%
+terrible it's challenging all this
+electric costs yes we always want to
+
+ align:start position:0%
+electric costs yes we always want to
+ 
+
+ align:start position:0%
+electric costs yes we always want to
+lower costs but the US financial system
+
+ align:start position:0%
+lower costs but the US financial system
+ 
+
+ align:start position:0%
+lower costs but the US financial system
+is seven and a half percent of our
+
+ align:start position:0%
+is seven and a half percent of our
+ 
+
+ align:start position:0%
+is seven and a half percent of our
+economy and cost one and a half trillion
+
+ align:start position:0%
+economy and cost one and a half trillion
+ 
+
+ align:start position:0%
+economy and cost one and a half trillion
+dollars so the payment system around the
+
+ align:start position:0%
+dollars so the payment system around the
+ 
+
+ align:start position:0%
+dollars so the payment system around the
+globe cost a half a percent to a percent
+
+ align:start position:0%
+globe cost a half a percent to a percent
+ 
+
+ align:start position:0%
+globe cost a half a percent to a percent
+of the global economy which is more than
+
+ align:start position:0%
+of the global economy which is more than
+ 
+
+ align:start position:0%
+of the global economy which is more than
+one-third of 1% of the world electricity
+
+ align:start position:0%
+one-third of 1% of the world electricity
+ 
+
+ align:start position:0%
+one-third of 1% of the world electricity
+cost so I'm just putting it in its back
+
+ align:start position:0%
+cost so I'm just putting it in its back
+ 
+
+ align:start position:0%
+cost so I'm just putting it in its back
+to this question of which cost of trust
+
+ align:start position:0%
+to this question of which cost of trust
+ 
+
+ align:start position:0%
+to this question of which cost of trust
+which costs neither a maximalist or a
+
+ align:start position:0%
+which costs neither a maximalist or a
+ 
+
+ align:start position:0%
+which costs neither a maximalist or a
+minimalist as you recall so what are
+
+ align:start position:0%
+minimalist as you recall so what are
+ 
+
+ align:start position:0%
+minimalist as you recall so what are
+some of the alternatives and we're not
+
+ align:start position:0%
+some of the alternatives and we're not
+ 
+
+ align:start position:0%
+some of the alternatives and we're not
+going to dig into each of these side
+
+ align:start position:0%
+going to dig into each of these side
+ 
+
+ align:start position:0%
+going to dig into each of these side
+chains shorting layer 2 payment channels
+
+ align:start position:0%
+chains shorting layer 2 payment channels
+ 
+
+ align:start position:0%
+chains shorting layer 2 payment channels
+anybody want to take a crack they're not
+
+ align:start position:0%
+anybody want to take a crack they're not
+ 
+
+ align:start position:0%
+anybody want to take a crack they're not
+all the identical
+
+ align:start position:0%
+all the identical
+ 
+
+ align:start position:0%
+all the identical
+it's a medoras and I had a conversation
+
+ align:start position:0%
+it's a medoras and I had a conversation
+ 
+
+ align:start position:0%
+it's a medoras and I had a conversation
+earlier today said I could even get my
+
+ align:start position:0%
+earlier today said I could even get my
+ 
+
+ align:start position:0%
+earlier today said I could even get my
+head around because I get confused but
+
+ align:start position:0%
+head around because I get confused but
+ 
+
+ align:start position:0%
+head around because I get confused but
+does anybody want to give the basic we
+
+ align:start position:0%
+does anybody want to give the basic we
+ 
+
+ align:start position:0%
+does anybody want to give the basic we
+were talking about it earlier the basic
+
+ align:start position:0%
+were talking about it earlier the basic
+ 
+
+ align:start position:0%
+were talking about it earlier the basic
+tenets cuz you had a reading about the
+
+ align:start position:0%
+tenets cuz you had a reading about the
+ 
+
+ align:start position:0%
+tenets cuz you had a reading about the
+Lightning Network as to what's what's
+
+ align:start position:0%
+Lightning Network as to what's what's
+ 
+
+ align:start position:0%
+Lightning Network as to what's what's
+the economic thing and technical thing
+
+ align:start position:0%
+the economic thing and technical thing
+ 
+
+ align:start position:0%
+the economic thing and technical thing
+that's being attempted in all four of
+
+ align:start position:0%
+that's being attempted in all four of
+ 
+
+ align:start position:0%
+that's being attempted in all four of
+these types of things with James was
+
+ align:start position:0%
+these types of things with James was
+ 
+
+ align:start position:0%
+these types of things with James was
+that a hand up you're gonna give it a
+
+ align:start position:0%
+that a hand up you're gonna give it a
+ 
+
+ align:start position:0%
+that a hand up you're gonna give it a
+shot give it a shot most of these are on
+
+ align:start position:0%
+shot give it a shot most of these are on
+ 
+
+ align:start position:0%
+shot give it a shot most of these are on
+the chain so most of these are off the
+
+ align:start position:0%
+the chain so most of these are off the
+ 
+
+ align:start position:0%
+the chain so most of these are off the
+chain but some is on the chain the idea
+
+ align:start position:0%
+chain but some is on the chain the idea
+ 
+
+ align:start position:0%
+chain but some is on the chain the idea
+is you transact off the chain
+
+ align:start position:0%
+is you transact off the chain
+ 
+
+ align:start position:0%
+is you transact off the chain
+balances are traded in the net results
+
+ align:start position:0%
+balances are traded in the net results
+ 
+
+ align:start position:0%
+balances are traded in the net results
+onto the chain so you try and speed up
+
+ align:start position:0%
+onto the chain so you try and speed up
+ 
+
+ align:start position:0%
+onto the chain so you try and speed up
+by processing off the chain it's like
+
+ align:start position:0%
+by processing off the chain it's like
+ 
+
+ align:start position:0%
+by processing off the chain it's like
+saying there's this chain this this this
+
+ align:start position:0%
+saying there's this chain this this this
+ 
+
+ align:start position:0%
+saying there's this chain this this this
+this this this channel if you wish that
+
+ align:start position:0%
+this this this channel if you wish that
+ 
+
+ align:start position:0%
+this this this channel if you wish that
+the water is running in or the digital
+
+ align:start position:0%
+the water is running in or the digital
+ 
+
+ align:start position:0%
+the water is running in or the digital
+money is running in that only has a
+
+ align:start position:0%
+money is running in that only has a
+ 
+
+ align:start position:0%
+money is running in that only has a
+certain speed it can only take a certain
+
+ align:start position:0%
+certain speed it can only take a certain
+ 
+
+ align:start position:0%
+certain speed it can only take a certain
+amount of performance why not take a lot
+
+ align:start position:0%
+amount of performance why not take a lot
+ 
+
+ align:start position:0%
+amount of performance why not take a lot
+of activity and put it in a side channel
+
+ align:start position:0%
+of activity and put it in a side channel
+ 
+
+ align:start position:0%
+of activity and put it in a side channel
+which is called a payment channel
+
+ align:start position:0%
+which is called a payment channel
+ 
+
+ align:start position:0%
+which is called a payment channel
+actually but a side chain or a payment
+
+ align:start position:0%
+actually but a side chain or a payment
+ 
+
+ align:start position:0%
+actually but a side chain or a payment
+channel or a layer to all with slightly
+
+ align:start position:0%
+channel or a layer to all with slightly
+ 
+
+ align:start position:0%
+channel or a layer to all with slightly
+different technical features and maybe
+
+ align:start position:0%
+different technical features and maybe
+ 
+
+ align:start position:0%
+different technical features and maybe
+do millions of things off here and only
+
+ align:start position:0%
+do millions of things off here and only
+ 
+
+ align:start position:0%
+do millions of things off here and only
+but some here it is not new to
+
+ align:start position:0%
+but some here it is not new to
+ 
+
+ align:start position:0%
+but some here it is not new to
+blockchain and Bitcoin we already have
+
+ align:start position:0%
+blockchain and Bitcoin we already have
+ 
+
+ align:start position:0%
+blockchain and Bitcoin we already have
+that in the world of finance for decades
+
+ align:start position:0%
+that in the world of finance for decades
+ 
+
+ align:start position:0%
+that in the world of finance for decades
+in some way or another where some
+
+ align:start position:0%
+in some way or another where some
+ 
+
+ align:start position:0%
+in some way or another where some
+activity can't go to a central
+
+ align:start position:0%
+activity can't go to a central
+ 
+
+ align:start position:0%
+activity can't go to a central
+settlement system and recalling Ledger's
+
+ align:start position:0%
+settlement system and recalling Ledger's
+ 
+
+ align:start position:0%
+settlement system and recalling Ledger's
+the central bank whether it's the US
+
+ align:start position:0%
+the central bank whether it's the US
+ 
+
+ align:start position:0%
+the central bank whether it's the US
+central bank or any central bank could
+
+ align:start position:0%
+central bank or any central bank could
+ 
+
+ align:start position:0%
+central bank or any central bank could
+have been set up that all of our deposit
+
+ align:start position:0%
+have been set up that all of our deposit
+ 
+
+ align:start position:0%
+have been set up that all of our deposit
+accounts were directly with the central
+
+ align:start position:0%
+accounts were directly with the central
+ 
+
+ align:start position:0%
+accounts were directly with the central
+bank and in a sense the side chains in
+
+ align:start position:0%
+bank and in a sense the side chains in
+ 
+
+ align:start position:0%
+bank and in a sense the side chains in
+finance right now are 9,000 commercial
+
+ align:start position:0%
+finance right now are 9,000 commercial
+ 
+
+ align:start position:0%
+finance right now are 9,000 commercial
+banks 9,000 commercial banks are dealing
+
+ align:start position:0%
+banks 9,000 commercial banks are dealing
+ 
+
+ align:start position:0%
+banks 9,000 commercial banks are dealing
+with our money flows and then sort of
+
+ align:start position:0%
+with our money flows and then sort of
+ 
+
+ align:start position:0%
+with our money flows and then sort of
+net settling to the central bank's
+
+ align:start position:0%
+net settling to the central bank's
+ 
+
+ align:start position:0%
+net settling to the central bank's
+ledger in what's called digital reserves
+
+ align:start position:0%
+ledger in what's called digital reserves
+ 
+
+ align:start position:0%
+ledger in what's called digital reserves
+and in fact even the banking system the
+
+ align:start position:0%
+and in fact even the banking system the
+ 
+
+ align:start position:0%
+and in fact even the banking system the
+9000 banks in the US have their side
+
+ align:start position:0%
+9000 banks in the US have their side
+ 
+
+ align:start position:0%
+9000 banks in the US have their side
+chains Visa MasterCard first data that
+
+ align:start position:0%
+chains Visa MasterCard first data that
+ 
+
+ align:start position:0%
+chains Visa MasterCard first data that
+all the money processing so there's
+
+ align:start position:0%
+all the money processing so there's
+ 
+
+ align:start position:0%
+all the money processing so there's
+already a layering I look at layer two
+
+ align:start position:0%
+already a layering I look at layer two
+ 
+
+ align:start position:0%
+already a layering I look at layer two
+and sidechains
+
+ align:start position:0%
+and sidechains
+ 
+
+ align:start position:0%
+and sidechains
+is kind of taking a similar economic
+
+ align:start position:0%
+is kind of taking a similar economic
+ 
+
+ align:start position:0%
+is kind of taking a similar economic
+approach and technical approach that's
+
+ align:start position:0%
+approach and technical approach that's
+ 
+
+ align:start position:0%
+approach and technical approach that's
+already been around but in a new way I
+
+ align:start position:0%
+already been around but in a new way I
+ 
+
+ align:start position:0%
+already been around but in a new way I
+grabbed a chart from 2015 it the details
+
+ align:start position:0%
+grabbed a chart from 2015 it the details
+ 
+
+ align:start position:0%
+grabbed a chart from 2015 it the details
+don't matter but this was I did it
+
+ align:start position:0%
+don't matter but this was I did it
+ 
+
+ align:start position:0%
+don't matter but this was I did it
+because it was three years old this was
+
+ align:start position:0%
+because it was three years old this was
+ 
+
+ align:start position:0%
+because it was three years old this was
+one you know person's truth coin one
+
+ align:start position:0%
+one you know person's truth coin one
+ 
+
+ align:start position:0%
+one you know person's truth coin one
+person's view is what sidechains
+
+ align:start position:0%
+person's view is what sidechains
+ 
+
+ align:start position:0%
+person's view is what sidechains
+basically what James says lots of
+
+ align:start position:0%
+basically what James says lots of
+ 
+
+ align:start position:0%
+basically what James says lots of
+activity over here and only a few things
+
+ align:start position:0%
+activity over here and only a few things
+ 
+
+ align:start position:0%
+activity over here and only a few things
+go over to the main chain the visual is
+
+ align:start position:0%
+go over to the main chain the visual is
+ 
+
+ align:start position:0%
+go over to the main chain the visual is
+what I wanted to get across it was just
+
+ align:start position:0%
+what I wanted to get across it was just
+ 
+
+ align:start position:0%
+what I wanted to get across it was just
+that it's kind of think of it as loads
+
+ align:start position:0%
+that it's kind of think of it as loads
+ 
+
+ align:start position:0%
+that it's kind of think of it as loads
+of activity over here and then we only
+
+ align:start position:0%
+of activity over here and then we only
+ 
+
+ align:start position:0%
+of activity over here and then we only
+settle at sometimes to the main chain
+
+ align:start position:0%
+settle at sometimes to the main chain
+ 
+
+ align:start position:0%
+settle at sometimes to the main chain
+another visualization of a different is
+
+ align:start position:0%
+another visualization of a different is
+ 
+
+ align:start position:0%
+another visualization of a different is
+the Lightning Network again a lot of
+
+ align:start position:0%
+the Lightning Network again a lot of
+ 
+
+ align:start position:0%
+the Lightning Network again a lot of
+activity then settle to the main chain
+
+ align:start position:0%
+activity then settle to the main chain
+ 
+
+ align:start position:0%
+activity then settle to the main chain
+questions trade off a lot of people are
+
+ align:start position:0%
+questions trade off a lot of people are
+ 
+
+ align:start position:0%
+questions trade off a lot of people are
+proponents of making the block size
+
+ align:start position:0%
+proponents of making the block size
+ 
+
+ align:start position:0%
+proponents of making the block size
+bigger a lot of people say the side
+
+ align:start position:0%
+bigger a lot of people say the side
+ 
+
+ align:start position:0%
+bigger a lot of people say the side
+chains I have trouble understanding
+
+ align:start position:0%
+chains I have trouble understanding
+ 
+
+ align:start position:0%
+chains I have trouble understanding
+trade offs between those two so what
+
+ align:start position:0%
+trade offs between those two so what
+ 
+
+ align:start position:0%
+trade offs between those two so what
+what it like why not just a bigger block
+
+ align:start position:0%
+what it like why not just a bigger block
+ 
+
+ align:start position:0%
+what it like why not just a bigger block
+what's the problem there's a there's a
+
+ align:start position:0%
+what's the problem there's a there's a
+ 
+
+ align:start position:0%
+what's the problem there's a there's a
+series of trade offs of economics and
+
+ align:start position:0%
+series of trade offs of economics and
+ 
+
+ align:start position:0%
+series of trade offs of economics and
+technology the more you put inside the
+
+ align:start position:0%
+technology the more you put inside the
+ 
+
+ align:start position:0%
+technology the more you put inside the
+let's call it the main chain that that
+
+ align:start position:0%
+let's call it the main chain that that
+ 
+
+ align:start position:0%
+let's call it the main chain that that
+blue the blue boxes at the bottom so so
+
+ align:start position:0%
+blue the blue boxes at the bottom so so
+ 
+
+ align:start position:0%
+blue the blue boxes at the bottom so so
+to speak the more you're putting in
+
+ align:start position:0%
+to speak the more you're putting in
+ 
+
+ align:start position:0%
+to speak the more you're putting in
+there you weighed it down there's
+
+ align:start position:0%
+there you weighed it down there's
+ 
+
+ align:start position:0%
+there you weighed it down there's
+there's there's more processing of
+
+ align:start position:0%
+there's there's more processing of
+ 
+
+ align:start position:0%
+there's there's more processing of
+course and more storage and so forth but
+
+ align:start position:0%
+course and more storage and so forth but
+ 
+
+ align:start position:0%
+course and more storage and so forth but
+also there's some there's too much
+
+ align:start position:0%
+also there's some there's too much
+ 
+
+ align:start position:0%
+also there's some there's too much
+latency in Bitcoin it's every 10 minutes
+
+ align:start position:0%
+latency in Bitcoin it's every 10 minutes
+ 
+
+ align:start position:0%
+latency in Bitcoin it's every 10 minutes
+and you're not really sure until three
+
+ align:start position:0%
+and you're not really sure until three
+ 
+
+ align:start position:0%
+and you're not really sure until three
+four or five some would say six blocks
+
+ align:start position:0%
+four or five some would say six blocks
+ 
+
+ align:start position:0%
+four or five some would say six blocks
+to an hour go by so economically if you
+
+ align:start position:0%
+to an hour go by so economically if you
+ 
+
+ align:start position:0%
+to an hour go by so economically if you
+want high frequency low latency short
+
+ align:start position:0%
+want high frequency low latency short
+ 
+
+ align:start position:0%
+want high frequency low latency short
+time periods you might say I can't get
+
+ align:start position:0%
+time periods you might say I can't get
+ 
+
+ align:start position:0%
+time periods you might say I can't get
+that on the main chain because the main
+
+ align:start position:0%
+that on the main chain because the main
+ 
+
+ align:start position:0%
+that on the main chain because the main
+chain wants to have low latency every
+
+ align:start position:0%
+chain wants to have low latency every
+ 
+
+ align:start position:0%
+chain wants to have low latency every
+ten minutes is lower latency now low
+
+ align:start position:0%
+ten minutes is lower latency now low
+ 
+
+ align:start position:0%
+ten minutes is lower latency now low
+latency to be more secure to keep the
+
+ align:start position:0%
+latency to be more secure to keep the
+ 
+
+ align:start position:0%
+latency to be more secure to keep the
+mining cost and the proof-of-work up so
+
+ align:start position:0%
+mining cost and the proof-of-work up so
+ 
+
+ align:start position:0%
+mining cost and the proof-of-work up so
+there's some economic and technological
+
+ align:start position:0%
+there's some economic and technological
+ 
+
+ align:start position:0%
+there's some economic and technological
+both crosscurrents with that unrelated
+
+ align:start position:0%
+both crosscurrents with that unrelated
+ 
+
+ align:start position:0%
+both crosscurrents with that unrelated
+to what I just said but overlapping
+
+ align:start position:0%
+to what I just said but overlapping
+ 
+
+ align:start position:0%
+to what I just said but overlapping
+there's also a bunch of miner and mining
+
+ align:start position:0%
+there's also a bunch of miner and mining
+ 
+
+ align:start position:0%
+there's also a bunch of miner and mining
+pool operator economics as to whether
+
+ align:start position:0%
+pool operator economics as to whether
+ 
+
+ align:start position:0%
+pool operator economics as to whether
+they want big blocks or small blocks and
+
+ align:start position:0%
+they want big blocks or small blocks and
+ 
+
+ align:start position:0%
+they want big blocks or small blocks and
+part of the split last year was but uh
+
+ align:start position:0%
+part of the split last year was but uh
+ 
+
+ align:start position:0%
+part of the split last year was but uh
+it was sort of more motivated around
+
+ align:start position:0%
+it was sort of more motivated around
+ 
+
+ align:start position:0%
+it was sort of more motivated around
+local politics rather than global
+
+ align:start position:0%
+local politics rather than global
+ 
+
+ align:start position:0%
+local politics rather than global
+politics as the former Speaker of the
+
+ align:start position:0%
+politics as the former Speaker of the
+ 
+
+ align:start position:0%
+politics as the former Speaker of the
+House Tip O'Neill said all politics is
+
+ align:start position:0%
+House Tip O'Neill said all politics is
+ 
+
+ align:start position:0%
+House Tip O'Neill said all politics is
+local
+
+ align:start position:0%
+local
+ 
+
+ align:start position:0%
+local
+I think some of the debates last year
+
+ align:start position:0%
+I think some of the debates last year
+ 
+
+ align:start position:0%
+I think some of the debates last year
+was about local economics and the
+
+ align:start position:0%
+was about local economics and the
+ 
+
+ align:start position:0%
+was about local economics and the
+economics of miners but I don't know
+
+ align:start position:0%
+economics of miners but I don't know
+ 
+
+ align:start position:0%
+economics of miners but I don't know
+medoras do you Medora was in probably in
+
+ align:start position:0%
+medoras do you Medora was in probably in
+ 
+
+ align:start position:0%
+medoras do you Medora was in probably in
+the middle of some of those debates but
+
+ align:start position:0%
+the middle of some of those debates but
+ 
+
+ align:start position:0%
+the middle of some of those debates but
+would you have a different view is there
+
+ align:start position:0%
+would you have a different view is there
+ 
+
+ align:start position:0%
+would you have a different view is there
+was a big debate last year as to whether
+
+ align:start position:0%
+was a big debate last year as to whether
+ 
+
+ align:start position:0%
+was a big debate last year as to whether
+the Bitcoin block should go bigger or
+
+ align:start position:0%
+the Bitcoin block should go bigger or
+ 
+
+ align:start position:0%
+the Bitcoin block should go bigger or
+stay the size it was not the only reason
+
+ align:start position:0%
+stay the size it was not the only reason
+ 
+
+ align:start position:0%
+stay the size it was not the only reason
+but it was part of the reason we have
+
+ align:start position:0%
+but it was part of the reason we have
+ 
+
+ align:start position:0%
+but it was part of the reason we have
+now Bitcoin cash and Bitcoin we
+
+ align:start position:0%
+now Bitcoin cash and Bitcoin we
+ 
+
+ align:start position:0%
+now Bitcoin cash and Bitcoin we
+because Bitcoin cash has a bigger block
+
+ align:start position:0%
+because Bitcoin cash has a bigger block
+ 
+
+ align:start position:0%
+because Bitcoin cash has a bigger block
+size and a shorter two and a half minute
+
+ align:start position:0%
+size and a shorter two and a half minute
+ 
+
+ align:start position:0%
+size and a shorter two and a half minute
+processing time mining centralization
+
+ align:start position:0%
+processing time mining centralization
+ 
+
+ align:start position:0%
+processing time mining centralization
+the bigger block Co problem leads of
+
+ align:start position:0%
+the bigger block Co problem leads of
+ 
+
+ align:start position:0%
+the bigger block Co problem leads of
+miners and handles enormous blocks will
+
+ align:start position:0%
+miners and handles enormous blocks will
+ 
+
+ align:start position:0%
+miners and handles enormous blocks will
+be able to stay in business and what
+
+ align:start position:0%
+be able to stay in business and what
+ 
+
+ align:start position:0%
+be able to stay in business and what
+decentralization means was security
+
+ align:start position:0%
+decentralization means was security
+ 
+
+ align:start position:0%
+decentralization means was security
+there's in something for some
+
+ align:start position:0%
+there's in something for some
+ 
+
+ align:start position:0%
+there's in something for some
+decentralization and security to keep
+
+ align:start position:0%
+decentralization and security to keep
+ 
+
+ align:start position:0%
+decentralization and security to keep
+the Box looks smaller
+
+ align:start position:0%
+the Box looks smaller
+ 
+
+ align:start position:0%
+the Box looks smaller
+so what medoras is saying is there's
+
+ align:start position:0%
+so what medoras is saying is there's
+ 
+
+ align:start position:0%
+so what medoras is saying is there's
+also a bit of economics around
+
+ align:start position:0%
+also a bit of economics around
+ 
+
+ align:start position:0%
+also a bit of economics around
+centralization the bigger the blocks the
+
+ align:start position:0%
+centralization the bigger the blocks the
+ 
+
+ align:start position:0%
+centralization the bigger the blocks the
+fewer miners can handle it the fewer
+
+ align:start position:0%
+fewer miners can handle it the fewer
+ 
+
+ align:start position:0%
+fewer miners can handle it the fewer
+miners the more centralization and thus
+
+ align:start position:0%
+miners the more centralization and thus
+ 
+
+ align:start position:0%
+miners the more centralization and thus
+less secure and maybe even economic
+
+ align:start position:0%
+less secure and maybe even economic
+ 
+
+ align:start position:0%
+less secure and maybe even economic
+rents because every centralized system
+
+ align:start position:0%
+rents because every centralized system
+ 
+
+ align:start position:0%
+rents because every centralized system
+can collect economic rents alene that if
+
+ align:start position:0%
+can collect economic rents alene that if
+ 
+
+ align:start position:0%
+can collect economic rents alene that if
+you have bigger blocks they take longer
+
+ align:start position:0%
+you have bigger blocks they take longer
+ 
+
+ align:start position:0%
+you have bigger blocks they take longer
+to propagate to the network and in sort
+
+ align:start position:0%
+to propagate to the network and in sort
+ 
+
+ align:start position:0%
+to propagate to the network and in sort
+of non-intuitive ways if that happens to
+
+ align:start position:0%
+of non-intuitive ways if that happens to
+ 
+
+ align:start position:0%
+of non-intuitive ways if that happens to
+give more accidental Forks in the
+
+ align:start position:0%
+give more accidental Forks in the
+ 
+
+ align:start position:0%
+give more accidental Forks in the
+blockchain and people can accident
+
+ align:start position:0%
+blockchain and people can accident
+ 
+
+ align:start position:0%
+blockchain and people can accident
+before especially Minot State
+
+ align:start position:0%
+before especially Minot State
+ 
+
+ align:start position:0%
+before especially Minot State
+accidentally loose coins when there's a
+
+ align:start position:0%
+accidentally loose coins when there's a
+ 
+
+ align:start position:0%
+accidentally loose coins when there's a
+technical feature as bigger blocks are
+
+ align:start position:0%
+technical feature as bigger blocks are
+ 
+
+ align:start position:0%
+technical feature as bigger blocks are
+more likely to take time to propagate
+
+ align:start position:0%
+more likely to take time to propagate
+ 
+
+ align:start position:0%
+more likely to take time to propagate
+through the network and thus you might
+
+ align:start position:0%
+through the network and thus you might
+ 
+
+ align:start position:0%
+through the network and thus you might
+end up inadvertently having more chains
+
+ align:start position:0%
+end up inadvertently having more chains
+ 
+
+ align:start position:0%
+end up inadvertently having more chains
+that are discredited in a sense because
+
+ align:start position:0%
+that are discredited in a sense because
+ 
+
+ align:start position:0%
+that are discredited in a sense because
+they there there was work being done
+
+ align:start position:0%
+they there there was work being done
+ 
+
+ align:start position:0%
+they there there was work being done
+until the first one gets propagated so
+
+ align:start position:0%
+until the first one gets propagated so
+ 
+
+ align:start position:0%
+until the first one gets propagated so
+Leonar leandro no debt no
+
+ align:start position:0%
+Leonar leandro no debt no
+ 
+
+ align:start position:0%
+Leonar leandro no debt no
+Leandra okay was he asking how do we
+
+ align:start position:0%
+Leandra okay was he asking how do we
+ 
+
+ align:start position:0%
+Leandra okay was he asking how do we
+validate the Lightning Network and how
+
+ align:start position:0%
+validate the Lightning Network and how
+ 
+
+ align:start position:0%
+validate the Lightning Network and how
+do we assure that that is though working
+
+ align:start position:0%
+do we assure that that is though working
+ 
+
+ align:start position:0%
+do we assure that that is though working
+with net to important in the chain how
+
+ align:start position:0%
+with net to important in the chain how
+ 
+
+ align:start position:0%
+with net to important in the chain how
+do we record everything that's ok so the
+
+ align:start position:0%
+do we record everything that's ok so the
+ 
+
+ align:start position:0%
+do we record everything that's ok so the
+side chains are not recorded gross on
+
+ align:start position:0%
+side chains are not recorded gross on
+ 
+
+ align:start position:0%
+side chains are not recorded gross on
+the main chain they're in essence
+
+ align:start position:0%
+the main chain they're in essence
+ 
+
+ align:start position:0%
+the main chain they're in essence
+recorded
+
+ align:start position:0%
+recorded
+ 
+
+ align:start position:0%
+recorded
+and in lightning Network I said I wasn't
+
+ align:start position:0%
+and in lightning Network I said I wasn't
+ 
+
+ align:start position:0%
+and in lightning Network I said I wasn't
+and get into the differences but here I
+
+ align:start position:0%
+and get into the differences but here I
+ 
+
+ align:start position:0%
+and get into the differences but here I
+go the Lightning Network is more a
+
+ align:start position:0%
+go the Lightning Network is more a
+ 
+
+ align:start position:0%
+go the Lightning Network is more a
+bilateral network it can be it can take
+
+ align:start position:0%
+bilateral network it can be it can take
+ 
+
+ align:start position:0%
+bilateral network it can be it can take
+on the the feeling of multilateral
+
+ align:start position:0%
+on the the feeling of multilateral
+ 
+
+ align:start position:0%
+on the the feeling of multilateral
+because I could have a transaction with
+
+ align:start position:0%
+because I could have a transaction with
+ 
+
+ align:start position:0%
+because I could have a transaction with
+James James could have a transaction
+
+ align:start position:0%
+James James could have a transaction
+ 
+
+ align:start position:0%
+James James could have a transaction
+with Kelly and it feels like it's three
+
+ align:start position:0%
+with Kelly and it feels like it's three
+ 
+
+ align:start position:0%
+with Kelly and it feels like it's three
+of us but it's bilateral James and Gary
+
+ align:start position:0%
+of us but it's bilateral James and Gary
+ 
+
+ align:start position:0%
+of us but it's bilateral James and Gary
+bilateral James and Kelly as I
+
+ align:start position:0%
+bilateral James and Kelly as I
+ 
+
+ align:start position:0%
+bilateral James and Kelly as I
+understand it and so those individual
+
+ align:start position:0%
+understand it and so those individual
+ 
+
+ align:start position:0%
+understand it and so those individual
+transactions while they're recorded if
+
+ align:start position:0%
+transactions while they're recorded if
+ 
+
+ align:start position:0%
+transactions while they're recorded if
+keep it going here
+
+ align:start position:0%
+keep it going here
+ 
+
+ align:start position:0%
+keep it going here
+recorded in the Lightning Network
+
+ align:start position:0%
+recorded in the Lightning Network
+ 
+
+ align:start position:0%
+recorded in the Lightning Network
+they're not on the main chain we
+
+ align:start position:0%
+they're not on the main chain we
+ 
+
+ align:start position:0%
+they're not on the main chain we
+ultimately then net settle to the main
+
+ align:start position:0%
+ultimately then net settle to the main
+ 
+
+ align:start position:0%
+ultimately then net settle to the main
+chain and we actually in a sense
+
+ align:start position:0%
+chain and we actually in a sense
+ 
+
+ align:start position:0%
+chain and we actually in a sense
+pre-fund or pre it's a it's a form
+
+ align:start position:0%
+pre-fund or pre it's a it's a form
+ 
+
+ align:start position:0%
+pre-fund or pre it's a it's a form
+loosely of escrowing
+
+ align:start position:0%
+loosely of escrowing
+ 
+
+ align:start position:0%
+loosely of escrowing
+at the beginning so James and I might be
+
+ align:start position:0%
+at the beginning so James and I might be
+ 
+
+ align:start position:0%
+at the beginning so James and I might be
+messing with each other but we're
+
+ align:start position:0%
+messing with each other but we're
+ 
+
+ align:start position:0%
+messing with each other but we're
+bilateral and so we've have another
+
+ align:start position:0%
+bilateral and so we've have another
+ 
+
+ align:start position:0%
+bilateral and so we've have another
+approach to the trust in addition to the
+
+ align:start position:0%
+approach to the trust in addition to the
+ 
+
+ align:start position:0%
+approach to the trust in addition to the
+computer code its James and I might have
+
+ align:start position:0%
+computer code its James and I might have
+ 
+
+ align:start position:0%
+computer code its James and I might have
+other reasons to trust Joe Quinn so and
+
+ align:start position:0%
+other reasons to trust Joe Quinn so and
+ 
+
+ align:start position:0%
+other reasons to trust Joe Quinn so and
+and what keeps me out of double spending
+
+ align:start position:0%
+and what keeps me out of double spending
+ 
+
+ align:start position:0%
+and what keeps me out of double spending
+once on the lady network and another one
+
+ align:start position:0%
+once on the lady network and another one
+ 
+
+ align:start position:0%
+once on the lady network and another one
+on the blockchain main network at the
+
+ align:start position:0%
+on the blockchain main network at the
+ 
+
+ align:start position:0%
+on the blockchain main network at the
+same time because there's a yourself I
+
+ align:start position:0%
+same time because there's a yourself I
+ 
+
+ align:start position:0%
+same time because there's a yourself I
+want to be careful because I'm using the
+
+ align:start position:0%
+want to be careful because I'm using the
+ 
+
+ align:start position:0%
+want to be careful because I'm using the
+terms loosely there's a form of
+
+ align:start position:0%
+terms loosely there's a form of
+ 
+
+ align:start position:0%
+terms loosely there's a form of
+pre-funding it's not that you actually
+
+ align:start position:0%
+pre-funding it's not that you actually
+ 
+
+ align:start position:0%
+pre-funding it's not that you actually
+fund on to the main chain but there's a
+
+ align:start position:0%
+fund on to the main chain but there's a
+ 
+
+ align:start position:0%
+fund on to the main chain but there's a
+little bit of partitioning that Medora
+
+ align:start position:0%
+little bit of partitioning that Medora
+ 
+
+ align:start position:0%
+little bit of partitioning that Medora
+alright I keep looking at Matt doors
+
+ align:start position:0%
+alright I keep looking at Matt doors
+ 
+
+ align:start position:0%
+alright I keep looking at Matt doors
+because he's actually coded this so
+
+ align:start position:0%
+because he's actually coded this so
+ 
+
+ align:start position:0%
+because he's actually coded this so
+that's what protects you in essence that
+
+ align:start position:0%
+that's what protects you in essence that
+ 
+
+ align:start position:0%
+that's what protects you in essence that
+James and I if I'm saying well I'll send
+
+ align:start position:0%
+James and I if I'm saying well I'll send
+ 
+
+ align:start position:0%
+James and I if I'm saying well I'll send
+you a one Bitcoin and tomorrow if the
+
+ align:start position:0%
+you a one Bitcoin and tomorrow if the
+ 
+
+ align:start position:0%
+you a one Bitcoin and tomorrow if the
+Sun does come up tomorrow you'll send me
+
+ align:start position:0%
+Sun does come up tomorrow you'll send me
+ 
+
+ align:start position:0%
+Sun does come up tomorrow you'll send me
+a half we were partitioning that one
+
+ align:start position:0%
+a half we were partitioning that one
+ 
+
+ align:start position:0%
+a half we were partitioning that one
+Bitcoin or his half Bitcoin until we
+
+ align:start position:0%
+Bitcoin or his half Bitcoin until we
+ 
+
+ align:start position:0%
+Bitcoin or his half Bitcoin until we
+then close out that it's written into
+
+ align:start position:0%
+then close out that it's written into
+ 
+
+ align:start position:0%
+then close out that it's written into
+the scripting code and it's written
+
+ align:start position:0%
+the scripting code and it's written
+ 
+
+ align:start position:0%
+the scripting code and it's written
+almost like a smart contract but it's
+
+ align:start position:0%
+almost like a smart contract but it's
+ 
+
+ align:start position:0%
+almost like a smart contract but it's
+not called smart contracts
+
+ align:start position:0%
+not called smart contracts
+ 
+
+ align:start position:0%
+not called smart contracts
+to sort of partition or you might
+
+ align:start position:0%
+to sort of partition or you might
+ 
+
+ align:start position:0%
+to sort of partition or you might
+loosely think of it as escrow it even
+
+ align:start position:0%
+loosely think of it as escrow it even
+ 
+
+ align:start position:0%
+loosely think of it as escrow it even
+though technically it might be different
+
+ align:start position:0%
+though technically it might be different
+ 
+
+ align:start position:0%
+though technically it might be different
+but stop by and we can and if not some
+
+ align:start position:0%
+but stop by and we can and if not some
+ 
+
+ align:start position:0%
+but stop by and we can and if not some
+of our colleagues at the digital
+
+ align:start position:0%
+of our colleagues at the digital
+ 
+
+ align:start position:0%
+of our colleagues at the digital
+currency initiative like Tosh draaga who
+
+ align:start position:0%
+currency initiative like Tosh draaga who
+ 
+
+ align:start position:0%
+currency initiative like Tosh draaga who
+program the Lightning Network I mean
+
+ align:start position:0%
+program the Lightning Network I mean
+ 
+
+ align:start position:0%
+program the Lightning Network I mean
+that's an MIT collaboration with others
+
+ align:start position:0%
+that's an MIT collaboration with others
+ 
+
+ align:start position:0%
+that's an MIT collaboration with others
+and we don't we don't promote it just
+
+ align:start position:0%
+and we don't we don't promote it just
+ 
+
+ align:start position:0%
+and we don't we don't promote it just
+because it's MIT it's like one of the
+
+ align:start position:0%
+because it's MIT it's like one of the
+ 
+
+ align:start position:0%
+because it's MIT it's like one of the
+leading ways to do performance it
+
+ align:start position:0%
+leading ways to do performance it
+ 
+
+ align:start position:0%
+leading ways to do performance it
+happens to be MIT so let me talk about
+
+ align:start position:0%
+happens to be MIT so let me talk about
+ 
+
+ align:start position:0%
+happens to be MIT so let me talk about
+other ways to do performance and kind of
+
+ align:start position:0%
+other ways to do performance and kind of
+ 
+
+ align:start position:0%
+other ways to do performance and kind of
+move on we already talked about
+
+ align:start position:0%
+move on we already talked about
+ 
+
+ align:start position:0%
+move on we already talked about
+alternative consensus protocols
+
+ align:start position:0%
+alternative consensus protocols
+ 
+
+ align:start position:0%
+alternative consensus protocols
+you've seen this slide I'm just bringing
+
+ align:start position:0%
+you've seen this slide I'm just bringing
+ 
+
+ align:start position:0%
+you've seen this slide I'm just bringing
+it back because it is a way to deal with
+
+ align:start position:0%
+it back because it is a way to deal with
+ 
+
+ align:start position:0%
+it back because it is a way to deal with
+scalability it's a really critical
+
+ align:start position:0%
+scalability it's a really critical
+ 
+
+ align:start position:0%
+scalability it's a really critical
+important ways proof-of-work course what
+
+ align:start position:0%
+important ways proof-of-work course what
+ 
+
+ align:start position:0%
+important ways proof-of-work course what
+are the issues about scalability and
+
+ align:start position:0%
+are the issues about scalability and
+ 
+
+ align:start position:0%
+are the issues about scalability and
+generally I'm summarizing I'm
+
+ align:start position:0%
+generally I'm summarizing I'm
+ 
+
+ align:start position:0%
+generally I'm summarizing I'm
+simplifying in a sense but generally all
+
+ align:start position:0%
+simplifying in a sense but generally all
+ 
+
+ align:start position:0%
+simplifying in a sense but generally all
+the alternatives have some way to
+
+ align:start position:0%
+the alternatives have some way to
+ 
+
+ align:start position:0%
+the alternatives have some way to
+randomize or delegate the node that will
+
+ align:start position:0%
+randomize or delegate the node that will
+ 
+
+ align:start position:0%
+randomize or delegate the node that will
+do the next block it kind of all comes
+
+ align:start position:0%
+do the next block it kind of all comes
+ 
+
+ align:start position:0%
+do the next block it kind of all comes
+back how do you add another block and
+
+ align:start position:0%
+back how do you add another block and
+ 
+
+ align:start position:0%
+back how do you add another block and
+Stewart Hebert in the 1990s when he
+
+ align:start position:0%
+Stewart Hebert in the 1990s when he
+ 
+
+ align:start position:0%
+Stewart Hebert in the 1990s when he
+started with all this blockchain stuff
+
+ align:start position:0%
+started with all this blockchain stuff
+ 
+
+ align:start position:0%
+started with all this blockchain stuff
+and put it in the New York Times had a
+
+ align:start position:0%
+and put it in the New York Times had a
+ 
+
+ align:start position:0%
+and put it in the New York Times had a
+central authority and he set up that
+
+ align:start position:0%
+central authority and he set up that
+ 
+
+ align:start position:0%
+central authority and he set up that
+company surety and he put it in the New
+
+ align:start position:0%
+company surety and he put it in the New
+ 
+
+ align:start position:0%
+company surety and he put it in the New
+York Times and what Nakamoto consensus
+
+ align:start position:0%
+York Times and what Nakamoto consensus
+ 
+
+ align:start position:0%
+York Times and what Nakamoto consensus
+is as he said well no we're not going to
+
+ align:start position:0%
+is as he said well no we're not going to
+ 
+
+ align:start position:0%
+is as he said well no we're not going to
+have Hebert and and an essential
+
+ align:start position:0%
+have Hebert and and an essential
+ 
+
+ align:start position:0%
+have Hebert and and an essential
+Authority it's going to be decentralized
+
+ align:start position:0%
+Authority it's going to be decentralized
+ 
+
+ align:start position:0%
+Authority it's going to be decentralized
+so these other consensus protocols
+
+ align:start position:0%
+so these other consensus protocols
+ 
+
+ align:start position:0%
+so these other consensus protocols
+generally have some randomized approach
+
+ align:start position:0%
+generally have some randomized approach
+ 
+
+ align:start position:0%
+generally have some randomized approach
+to delegate the selection of the next
+
+ align:start position:0%
+to delegate the selection of the next
+ 
+
+ align:start position:0%
+to delegate the selection of the next
+block it's not always that way but they
+
+ align:start position:0%
+block it's not always that way but they
+ 
+
+ align:start position:0%
+block it's not always that way but they
+may also have a mechanism to do a second
+
+ align:start position:0%
+may also have a mechanism to do a second
+ 
+
+ align:start position:0%
+may also have a mechanism to do a second
+thing a second touch silvio Macaulay's
+
+ align:start position:0%
+thing a second touch silvio Macaulay's
+ 
+
+ align:start position:0%
+thing a second touch silvio Macaulay's
+Algar and he's a professor over the
+
+ align:start position:0%
+Algar and he's a professor over the
+ 
+
+ align:start position:0%
+Algar and he's a professor over the
+computer science and AI lab and touring
+
+ align:start position:0%
+computer science and AI lab and touring
+ 
+
+ align:start position:0%
+computer science and AI lab and touring
+award-winner he's got a company that has
+
+ align:start position:0%
+award-winner he's got a company that has
+ 
+
+ align:start position:0%
+award-winner he's got a company that has
+an interesting thing it's like a jury
+
+ align:start position:0%
+an interesting thing it's like a jury
+ 
+
+ align:start position:0%
+an interesting thing it's like a jury
+selection it's like picking somebody for
+
+ align:start position:0%
+selection it's like picking somebody for
+ 
+
+ align:start position:0%
+selection it's like picking somebody for
+the jury that's that's picking this
+
+ align:start position:0%
+the jury that's that's picking this
+ 
+
+ align:start position:0%
+the jury that's that's picking this
+short group of 12 nodes that might do
+
+ align:start position:0%
+short group of 12 nodes that might do
+ 
+
+ align:start position:0%
+short group of 12 nodes that might do
+something and every block has that
+
+ align:start position:0%
+something and every block has that
+ 
+
+ align:start position:0%
+something and every block has that
+selection process but then there's an
+
+ align:start position:0%
+selection process but then there's an
+ 
+
+ align:start position:0%
+selection process but then there's an
+another broader group that then can
+
+ align:start position:0%
+another broader group that then can
+ 
+
+ align:start position:0%
+another broader group that then can
+check the work of the jury so often
+
+ align:start position:0%
+check the work of the jury so often
+ 
+
+ align:start position:0%
+check the work of the jury so often
+there's kind of a second automated way
+
+ align:start position:0%
+there's kind of a second automated way
+ 
+
+ align:start position:0%
+there's kind of a second automated way
+because Trust isn't there ensuring that
+
+ align:start position:0%
+because Trust isn't there ensuring that
+ 
+
+ align:start position:0%
+because Trust isn't there ensuring that
+there's a quick second check did they
+
+ align:start position:0%
+there's a quick second check did they
+ 
+
+ align:start position:0%
+there's a quick second check did they
+decide guilty err or innocent correctly
+
+ align:start position:0%
+decide guilty err or innocent correctly
+ 
+
+ align:start position:0%
+decide guilty err or innocent correctly
+so to speak again I apologize if I'm a
+
+ align:start position:0%
+so to speak again I apologize if I'm a
+ 
+
+ align:start position:0%
+so to speak again I apologize if I'm a
+little oversimplifying so vo is
+
+ align:start position:0%
+little oversimplifying so vo is
+ 
+
+ align:start position:0%
+little oversimplifying so vo is
+brilliant work but it's so it could be
+
+ align:start position:0%
+brilliant work but it's so it could be
+ 
+
+ align:start position:0%
+brilliant work but it's so it could be
+proof of stake proof activity proof of
+
+ align:start position:0%
+proof of stake proof activity proof of
+ 
+
+ align:start position:0%
+proof of stake proof activity proof of
+burn as we talked about proof of
+
+ align:start position:0%
+burn as we talked about proof of
+ 
+
+ align:start position:0%
+burn as we talked about proof of
+capacity and as I mentioned last week
+
+ align:start position:0%
+capacity and as I mentioned last week
+ 
+
+ align:start position:0%
+capacity and as I mentioned last week
+there's not large-scale uses but - and
+
+ align:start position:0%
+there's not large-scale uses but - and
+ 
+
+ align:start position:0%
+there's not large-scale uses but - and
+neo both have some form of this going
+
+ align:start position:0%
+neo both have some form of this going
+ 
+
+ align:start position:0%
+neo both have some form of this going
+one right now and aetherium has a big
+
+ align:start position:0%
+one right now and aetherium has a big
+ 
+
+ align:start position:0%
+one right now and aetherium has a big
+project I'm confusing their two projects
+
+ align:start position:0%
+project I'm confusing their two projects
+ 
+
+ align:start position:0%
+project I'm confusing their two projects
+there's plasma and there's Casper Casper
+
+ align:start position:0%
+there's plasma and there's Casper Casper
+ 
+
+ align:start position:0%
+there's plasma and there's Casper Casper
+is their project to get to proof a stake
+
+ align:start position:0%
+is their project to get to proof a stake
+ 
+
+ align:start position:0%
+is their project to get to proof a stake
+but they're not they're privacy and
+
+ align:start position:0%
+but they're not they're privacy and
+ 
+
+ align:start position:0%
+but they're not they're privacy and
+security so try to remember who raised
+
+ align:start position:0%
+security so try to remember who raised
+ 
+
+ align:start position:0%
+security so try to remember who raised
+the contradictory tensions the
+
+ align:start position:0%
+the contradictory tensions the
+ 
+
+ align:start position:0%
+the contradictory tensions the
+contradictory tensions is law
+
+ align:start position:0%
+contradictory tensions is law
+ 
+
+ align:start position:0%
+contradictory tensions is law
+enforcement and regulators want more
+
+ align:start position:0%
+enforcement and regulators want more
+ 
+
+ align:start position:0%
+enforcement and regulators want more
+transparency even though the FBI did you
+
+ align:start position:0%
+transparency even though the FBI did you
+ 
+
+ align:start position:0%
+transparency even though the FBI did you
+know sort of figure out some Russians
+
+ align:start position:0%
+know sort of figure out some Russians
+ 
+
+ align:start position:0%
+know sort of figure out some Russians
+we're using Bitcoin to mess in our
+
+ align:start position:0%
+we're using Bitcoin to mess in our
+ 
+
+ align:start position:0%
+we're using Bitcoin to mess in our
+elections they want some more
+
+ align:start position:0%
+elections they want some more
+ 
+
+ align:start position:0%
+elections they want some more
+transparency and financial institutions
+
+ align:start position:0%
+transparency and financial institutions
+ 
+
+ align:start position:0%
+transparency and financial institutions
+users and even some regulators want less
+
+ align:start position:0%
+users and even some regulators want less
+ 
+
+ align:start position:0%
+users and even some regulators want less
+transparency so it's it's not kind of
+
+ align:start position:0%
+transparency so it's it's not kind of
+ 
+
+ align:start position:0%
+transparency so it's it's not kind of
+goes both ways but these I think are
+
+ align:start position:0%
+goes both ways but these I think are
+ 
+
+ align:start position:0%
+goes both ways but these I think are
+also truly solvable well for for
+
+ align:start position:0%
+also truly solvable well for for
+ 
+
+ align:start position:0%
+also truly solvable well for for
+consumers there's - and Manero and zee
+
+ align:start position:0%
+consumers there's - and Manero and zee
+ 
+
+ align:start position:0%
+consumers there's - and Manero and zee
+cash and there's even mechanisms called
+
+ align:start position:0%
+cash and there's even mechanisms called
+ 
+
+ align:start position:0%
+cash and there's even mechanisms called
+mixing and tumbling which I truthfully
+
+ align:start position:0%
+mixing and tumbling which I truthfully
+ 
+
+ align:start position:0%
+mixing and tumbling which I truthfully
+can't tell you the difference but I can
+
+ align:start position:0%
+can't tell you the difference but I can
+ 
+
+ align:start position:0%
+can't tell you the difference but I can
+tell you regulators talk about mixers
+
+ align:start position:0%
+tell you regulators talk about mixers
+ 
+
+ align:start position:0%
+tell you regulators talk about mixers
+and tumblers and privacy coins when when
+
+ align:start position:0%
+and tumblers and privacy coins when when
+ 
+
+ align:start position:0%
+and tumblers and privacy coins when when
+I go to some regulatory conferences
+
+ align:start position:0%
+I go to some regulatory conferences
+ 
+
+ align:start position:0%
+I go to some regulatory conferences
+because they sometimes invite me as a
+
+ align:start position:0%
+because they sometimes invite me as a
+ 
+
+ align:start position:0%
+because they sometimes invite me as a
+former that middle slide the the privacy
+
+ align:start position:0%
+former that middle slide the the privacy
+ 
+
+ align:start position:0%
+former that middle slide the the privacy
+coins and the mixers and tumblers
+
+ align:start position:0%
+coins and the mixers and tumblers
+ 
+
+ align:start position:0%
+coins and the mixers and tumblers
+the the finance ministries and the
+
+ align:start position:0%
+the the finance ministries and the
+ 
+
+ align:start position:0%
+the the finance ministries and the
+law-enforcement stuff that's where they
+
+ align:start position:0%
+law-enforcement stuff that's where they
+ 
+
+ align:start position:0%
+law-enforcement stuff that's where they
+kind of get worried medoras you want to
+
+ align:start position:0%
+kind of get worried medoras you want to
+ 
+
+ align:start position:0%
+kind of get worried medoras you want to
+come up here and tell us anything about
+
+ align:start position:0%
+come up here and tell us anything about
+ 
+
+ align:start position:0%
+come up here and tell us anything about
+Z cash or you want to do it from there
+
+ align:start position:0%
+Z cash or you want to do it from there
+ 
+
+ align:start position:0%
+Z cash or you want to do it from there
+as to what inspired you to do a privacy
+
+ align:start position:0%
+as to what inspired you to do a privacy
+ 
+
+ align:start position:0%
+as to what inspired you to do a privacy
+coin that a bunch of law enforcement
+
+ align:start position:0%
+coin that a bunch of law enforcement
+ 
+
+ align:start position:0%
+coin that a bunch of law enforcement
+folks don't like it's legal I mean it's
+
+ align:start position:0%
+folks don't like it's legal I mean it's
+ 
+
+ align:start position:0%
+folks don't like it's legal I mean it's
+a coin it's real just like cash can be
+
+ align:start position:0%
+a coin it's real just like cash can be
+ 
+
+ align:start position:0%
+a coin it's real just like cash can be
+used for religious purposes also systems
+
+ align:start position:0%
+used for religious purposes also systems
+ 
+
+ align:start position:0%
+used for religious purposes also systems
+that provide strong privacy like tor can
+
+ align:start position:0%
+that provide strong privacy like tor can
+ 
+
+ align:start position:0%
+that provide strong privacy like tor can
+be used for so it said privacy is a
+
+ align:start position:0%
+be used for so it said privacy is a
+ 
+
+ align:start position:0%
+be used for so it said privacy is a
+human right and we shouldn't be giving
+
+ align:start position:0%
+human right and we shouldn't be giving
+ 
+
+ align:start position:0%
+human right and we shouldn't be giving
+up our fun intro independence too
+
+ align:start position:0%
+up our fun intro independence too
+ 
+
+ align:start position:0%
+up our fun intro independence too
+because I want to buy a coffee I don't
+
+ align:start position:0%
+because I want to buy a coffee I don't
+ 
+
+ align:start position:0%
+because I want to buy a coffee I don't
+want to reveal all my other transactions
+
+ align:start position:0%
+want to reveal all my other transactions
+ 
+
+ align:start position:0%
+want to reveal all my other transactions
+I think there are mechanisms called
+
+ align:start position:0%
+I think there are mechanisms called
+ 
+
+ align:start position:0%
+I think there are mechanisms called
+law enforcement can it gets our
+
+ align:start position:0%
+law enforcement can it gets our
+ 
+
+ align:start position:0%
+law enforcement can it gets our
+regulatory objectives but privacy I
+
+ align:start position:0%
+regulatory objectives but privacy I
+ 
+
+ align:start position:0%
+regulatory objectives but privacy I
+think is fundamental right so we should
+
+ align:start position:0%
+think is fundamental right so we should
+ 
+
+ align:start position:0%
+think is fundamental right so we should
+fight for it and so when did you start
+
+ align:start position:0%
+fight for it and so when did you start
+ 
+
+ align:start position:0%
+fight for it and so when did you start
+working on the project so you started
+
+ align:start position:0%
+working on the project so you started
+ 
+
+ align:start position:0%
+working on the project so you started
+with the paper these kind of like
+
+ align:start position:0%
+with the paper these kind of like
+ 
+
+ align:start position:0%
+with the paper these kind of like
+prototype code base we put it open
+
+ align:start position:0%
+prototype code base we put it open
+ 
+
+ align:start position:0%
+prototype code base we put it open
+source and or with the companies that go
+
+ align:start position:0%
+source and or with the companies that go
+ 
+
+ align:start position:0%
+source and or with the companies that go
+for Monza and I think C cash now is
+
+ align:start position:0%
+for Monza and I think C cash now is
+ 
+
+ align:start position:0%
+for Monza and I think C cash now is
+somewhere around a billion dollar market
+
+ align:start position:0%
+somewhere around a billion dollar market
+ 
+
+ align:start position:0%
+somewhere around a billion dollar market
+cap if so so that's why you're here it
+
+ align:start position:0%
+cap if so so that's why you're here it
+ 
+
+ align:start position:0%
+cap if so so that's why you're here it
+went down no no you don't need to answer
+
+ align:start position:0%
+went down no no you don't need to answer
+ 
+
+ align:start position:0%
+went down no no you don't need to answer
+that that's sorry privacy but but in
+
+ align:start position:0%
+that that's sorry privacy but but in
+ 
+
+ align:start position:0%
+that that's sorry privacy but but in
+essence what medoras is saying that he
+
+ align:start position:0%
+essence what medoras is saying that he
+ 
+
+ align:start position:0%
+essence what medoras is saying that he
+came to this what were you doing in 2014
+
+ align:start position:0%
+came to this what were you doing in 2014
+ 
+
+ align:start position:0%
+came to this what were you doing in 2014
+were you I was mostly working on zero
+
+ align:start position:0%
+were you I was mostly working on zero
+ 
+
+ align:start position:0%
+were you I was mostly working on zero
+knowledge groups seem to be like a
+
+ align:start position:0%
+knowledge groups seem to be like a
+ 
+
+ align:start position:0%
+knowledge groups seem to be like a
+natural application like Bitcoin plus I
+
+ align:start position:0%
+natural application like Bitcoin plus I
+ 
+
+ align:start position:0%
+natural application like Bitcoin plus I
+think I think techniques maybe there's
+
+ align:start position:0%
+think I think techniques maybe there's
+ 
+
+ align:start position:0%
+think I think techniques maybe there's
+something there so here a talented
+
+ align:start position:0%
+something there so here a talented
+ 
+
+ align:start position:0%
+something there so here a talented
+graduate student at MIT with it with the
+
+ align:start position:0%
+graduate student at MIT with it with the
+ 
+
+ align:start position:0%
+graduate student at MIT with it with the
+collaboration of other said here's this
+
+ align:start position:0%
+collaboration of other said here's this
+ 
+
+ align:start position:0%
+collaboration of other said here's this
+cryptographic mechanism called zero
+
+ align:start position:0%
+cryptographic mechanism called zero
+ 
+
+ align:start position:0%
+cryptographic mechanism called zero
+knowledge proof switch we'll chat about
+
+ align:start position:0%
+knowledge proof switch we'll chat about
+ 
+
+ align:start position:0%
+knowledge proof switch we'll chat about
+in 30 seconds and here's something
+
+ align:start position:0%
+in 30 seconds and here's something
+ 
+
+ align:start position:0%
+in 30 seconds and here's something
+called Bitcoin why don't we bring
+
+ align:start position:0%
+called Bitcoin why don't we bring
+ 
+
+ align:start position:0%
+called Bitcoin why don't we bring
+together and we could promote in his own
+
+ align:start position:0%
+together and we could promote in his own
+ 
+
+ align:start position:0%
+together and we could promote in his own
+words some human rights just did you buy
+
+ align:start position:0%
+words some human rights just did you buy
+ 
+
+ align:start position:0%
+words some human rights just did you buy
+a cup of coffee and you don't have to
+
+ align:start position:0%
+a cup of coffee and you don't have to
+ 
+
+ align:start position:0%
+a cup of coffee and you don't have to
+say who you are you could use this new
+
+ align:start position:0%
+say who you are you could use this new
+ 
+
+ align:start position:0%
+say who you are you could use this new
+Bitcoin and enhanced zero knowledge
+
+ align:start position:0%
+Bitcoin and enhanced zero knowledge
+ 
+
+ align:start position:0%
+Bitcoin and enhanced zero knowledge
+proof Z cash shot if I useful to one
+
+ align:start position:0%
+proof Z cash shot if I useful to one
+ 
+
+ align:start position:0%
+proof Z cash shot if I useful to one
+arrow or three cash as a way to get the
+
+ align:start position:0%
+arrow or three cash as a way to get the
+ 
+
+ align:start position:0%
+arrow or three cash as a way to get the
+money out of that I don't I don't
+
+ align:start position:0%
+money out of that I don't I don't
+ 
+
+ align:start position:0%
+money out of that I don't I don't
+fortunately I don't have to define
+
+ align:start position:0%
+fortunately I don't have to define
+ 
+
+ align:start position:0%
+fortunately I don't have to define
+illicit activity but generally societies
+
+ align:start position:0%
+illicit activity but generally societies
+ 
+
+ align:start position:0%
+illicit activity but generally societies
+come together through their reasonable
+
+ align:start position:0%
+come together through their reasonable
+ 
+
+ align:start position:0%
+come together through their reasonable
+mechanisms whether they're democratic
+
+ align:start position:0%
+mechanisms whether they're democratic
+ 
+
+ align:start position:0%
+mechanisms whether they're democratic
+societies or not but they come together
+
+ align:start position:0%
+societies or not but they come together
+ 
+
+ align:start position:0%
+societies or not but they come together
+through their legislative branches and
+
+ align:start position:0%
+through their legislative branches and
+ 
+
+ align:start position:0%
+through their legislative branches and
+their executive branches and their
+
+ align:start position:0%
+their executive branches and their
+ 
+
+ align:start position:0%
+their executive branches and their
+courts and define some things that are
+
+ align:start position:0%
+courts and define some things that are
+ 
+
+ align:start position:0%
+courts and define some things that are
+not allowed but generally speaking when
+
+ align:start position:0%
+not allowed but generally speaking when
+ 
+
+ align:start position:0%
+not allowed but generally speaking when
+I'm using the term in this class I'm
+
+ align:start position:0%
+I'm using the term in this class I'm
+ 
+
+ align:start position:0%
+I'm using the term in this class I'm
+thinking about four or five buckets most
+
+ align:start position:0%
+thinking about four or five buckets most
+ 
+
+ align:start position:0%
+thinking about four or five buckets most
+societies do not want to shrink their
+
+ align:start position:0%
+societies do not want to shrink their
+ 
+
+ align:start position:0%
+societies do not want to shrink their
+tax base so they want economic activity
+
+ align:start position:0%
+tax base so they want economic activity
+ 
+
+ align:start position:0%
+tax base so they want economic activity
+be inside the tax envelope rather than
+
+ align:start position:0%
+be inside the tax envelope rather than
+ 
+
+ align:start position:0%
+be inside the tax envelope rather than
+outside the tax envelope and that's
+
+ align:start position:0%
+outside the tax envelope and that's
+ 
+
+ align:start position:0%
+outside the tax envelope and that's
+usually the words that finance ministers
+
+ align:start position:0%
+usually the words that finance ministers
+ 
+
+ align:start position:0%
+usually the words that finance ministers
+call that as a tax base how much is
+
+ align:start position:0%
+call that as a tax base how much is
+ 
+
+ align:start position:0%
+call that as a tax base how much is
+outside versus inside secondly most law
+
+ align:start position:0%
+outside versus inside secondly most law
+ 
+
+ align:start position:0%
+outside versus inside secondly most law
+enforcement and most societies do not
+
+ align:start position:0%
+enforcement and most societies do not
+ 
+
+ align:start position:0%
+enforcement and most societies do not
+want to have the the money rails the
+
+ align:start position:0%
+want to have the the money rails the
+ 
+
+ align:start position:0%
+want to have the the money rails the
+banking and other ways you can move
+
+ align:start position:0%
+banking and other ways you can move
+ 
+
+ align:start position:0%
+banking and other ways you can move
+value to facilitate otherwise illegal
+
+ align:start position:0%
+value to facilitate otherwise illegal
+ 
+
+ align:start position:0%
+value to facilitate otherwise illegal
+activity so it's using money to
+
+ align:start position:0%
+activity so it's using money to
+ 
+
+ align:start position:0%
+activity so it's using money to
+facilitate otherwise illegal activity so
+
+ align:start position:0%
+facilitate otherwise illegal activity so
+ 
+
+ align:start position:0%
+facilitate otherwise illegal activity so
+the otherwise illegal activity might be
+
+ align:start position:0%
+the otherwise illegal activity might be
+ 
+
+ align:start position:0%
+the otherwise illegal activity might be
+drug running the otherwise illegal
+
+ align:start position:0%
+drug running the otherwise illegal
+ 
+
+ align:start position:0%
+drug running the otherwise illegal
+activity might be terrorism it might be
+
+ align:start position:0%
+activity might be terrorism it might be
+ 
+
+ align:start position:0%
+activity might be terrorism it might be
+child slavery literally so it's whatever
+
+ align:start position:0%
+child slavery literally so it's whatever
+ 
+
+ align:start position:0%
+child slavery literally so it's whatever
+the otherwise illegal activity you know
+
+ align:start position:0%
+the otherwise illegal activity you know
+ 
+
+ align:start position:0%
+the otherwise illegal activity you know
+is to use money and that's generally
+
+ align:start position:0%
+is to use money and that's generally
+ 
+
+ align:start position:0%
+is to use money and that's generally
+called money laundering or other things
+
+ align:start position:0%
+called money laundering or other things
+ 
+
+ align:start position:0%
+called money laundering or other things
+so you're absolutely right another thing
+
+ align:start position:0%
+so you're absolutely right another thing
+ 
+
+ align:start position:0%
+so you're absolutely right another thing
+is for
+
+ align:start position:0%
+is for
+ 
+
+ align:start position:0%
+is for
+some countries less than a majority but
+
+ align:start position:0%
+some countries less than a majority but
+ 
+
+ align:start position:0%
+some countries less than a majority but
+some countries have capital controls
+
+ align:start position:0%
+some countries have capital controls
+ 
+
+ align:start position:0%
+some countries have capital controls
+they're trying to maintain the value of
+
+ align:start position:0%
+they're trying to maintain the value of
+ 
+
+ align:start position:0%
+they're trying to maintain the value of
+their fiat currency relative to other
+
+ align:start position:0%
+their fiat currency relative to other
+ 
+
+ align:start position:0%
+their fiat currency relative to other
+fiat currencies and in an effort to
+
+ align:start position:0%
+fiat currencies and in an effort to
+ 
+
+ align:start position:0%
+fiat currencies and in an effort to
+maintain some either fixed or
+
+ align:start position:0%
+maintain some either fixed or
+ 
+
+ align:start position:0%
+maintain some either fixed or
+relationship they have capital controls
+
+ align:start position:0%
+relationship they have capital controls
+ 
+
+ align:start position:0%
+relationship they have capital controls
+and and thus in those countries they
+
+ align:start position:0%
+and and thus in those countries they
+ 
+
+ align:start position:0%
+and and thus in those countries they
+might say illicit activity also is
+
+ align:start position:0%
+might say illicit activity also is
+ 
+
+ align:start position:0%
+might say illicit activity also is
+running around the the capital controls
+
+ align:start position:0%
+running around the the capital controls
+ 
+
+ align:start position:0%
+running around the the capital controls
+but it's it's each country each society
+
+ align:start position:0%
+but it's it's each country each society
+ 
+
+ align:start position:0%
+but it's it's each country each society
+and Shawn you raise a good point as to
+
+ align:start position:0%
+and Shawn you raise a good point as to
+ 
+
+ align:start position:0%
+and Shawn you raise a good point as to
+what does it mean I I I mean it not to
+
+ align:start position:0%
+what does it mean I I I mean it not to
+ 
+
+ align:start position:0%
+what does it mean I I I mean it not to
+show any value I'm saying there's a
+
+ align:start position:0%
+show any value I'm saying there's a
+ 
+
+ align:start position:0%
+show any value I'm saying there's a
+there's a series of these things that
+
+ align:start position:0%
+there's a series of these things that
+ 
+
+ align:start position:0%
+there's a series of these things that
+each society comes together and says
+
+ align:start position:0%
+each society comes together and says
+ 
+
+ align:start position:0%
+each society comes together and says
+usually around the tax base usually
+
+ align:start position:0%
+usually around the tax base usually
+ 
+
+ align:start position:0%
+usually around the tax base usually
+around trying to not use money to
+
+ align:start position:0%
+around trying to not use money to
+ 
+
+ align:start position:0%
+around trying to not use money to
+facilitate otherwise bad stuff and in
+
+ align:start position:0%
+facilitate otherwise bad stuff and in
+ 
+
+ align:start position:0%
+facilitate otherwise bad stuff and in
+some countries the capital controls I
+
+ align:start position:0%
+some countries the capital controls I
+ 
+
+ align:start position:0%
+some countries the capital controls I
+saw a hand here Daniel no wizard and
+
+ align:start position:0%
+saw a hand here Daniel no wizard and
+ 
+
+ align:start position:0%
+saw a hand here Daniel no wizard and
+we're gonna do more about illicit
+
+ align:start position:0%
+we're gonna do more about illicit
+ 
+
+ align:start position:0%
+we're gonna do more about illicit
+activity next week or about guarding
+
+ align:start position:0%
+activity next week or about guarding
+ 
+
+ align:start position:0%
+activity next week or about guarding
+against illicit activity I hope the
+
+ align:start position:0%
+against illicit activity I hope the
+ 
+
+ align:start position:0%
+against illicit activity I hope the
+correction got film too so there's
+
+ align:start position:0%
+correction got film too so there's
+ 
+
+ align:start position:0%
+correction got film too so there's
+another set of security issues around
+
+ align:start position:0%
+another set of security issues around
+ 
+
+ align:start position:0%
+another set of security issues around
+private keys and to most of us that have
+
+ align:start position:0%
+private keys and to most of us that have
+ 
+
+ align:start position:0%
+private keys and to most of us that have
+passwords you know if you lose your
+
+ align:start position:0%
+passwords you know if you lose your
+ 
+
+ align:start position:0%
+passwords you know if you lose your
+password they're usually in essence a
+
+ align:start position:0%
+password they're usually in essence a
+ 
+
+ align:start position:0%
+password they're usually in essence a
+backdoor that somehow the the platform
+
+ align:start position:0%
+backdoor that somehow the the platform
+ 
+
+ align:start position:0%
+backdoor that somehow the the platform
+whether it's Facebook or even at Bank of
+
+ align:start position:0%
+whether it's Facebook or even at Bank of
+ 
+
+ align:start position:0%
+whether it's Facebook or even at Bank of
+America if you lose your password
+
+ align:start position:0%
+America if you lose your password
+ 
+
+ align:start position:0%
+America if you lose your password
+there's a backdoor and they can say
+
+ align:start position:0%
+there's a backdoor and they can say
+ 
+
+ align:start position:0%
+there's a backdoor and they can say
+there's a way to validate with enough
+
+ align:start position:0%
+there's a way to validate with enough
+ 
+
+ align:start position:0%
+there's a way to validate with enough
+probability waiting that I'm Gary
+
+ align:start position:0%
+probability waiting that I'm Gary
+ 
+
+ align:start position:0%
+probability waiting that I'm Gary
+Gensler and they'll give me a new
+
+ align:start position:0%
+Gensler and they'll give me a new
+ 
+
+ align:start position:0%
+Gensler and they'll give me a new
+password I mean in some circumstances
+
+ align:start position:0%
+password I mean in some circumstances
+ 
+
+ align:start position:0%
+password I mean in some circumstances
+it's a high bar and there's some
+
+ align:start position:0%
+it's a high bar and there's some
+ 
+
+ align:start position:0%
+it's a high bar and there's some
+biometrics involved but in most cases
+
+ align:start position:0%
+biometrics involved but in most cases
+ 
+
+ align:start position:0%
+biometrics involved but in most cases
+it's a pretty low bar and they'll give
+
+ align:start position:0%
+it's a pretty low bar and they'll give
+ 
+
+ align:start position:0%
+it's a pretty low bar and they'll give
+you sort of another password if you can
+
+ align:start position:0%
+you sort of another password if you can
+ 
+
+ align:start position:0%
+you sort of another password if you can
+like me remember the answer to who my
+
+ align:start position:0%
+like me remember the answer to who my
+ 
+
+ align:start position:0%
+like me remember the answer to who my
+high school girlfriend was or something
+
+ align:start position:0%
+high school girlfriend was or something
+ 
+
+ align:start position:0%
+high school girlfriend was or something
+you know these questions like I remember
+
+ align:start position:0%
+you know these questions like I remember
+ 
+
+ align:start position:0%
+you know these questions like I remember
+it's Irene but then I've just given up
+
+ align:start position:0%
+it's Irene but then I've just given up
+ 
+
+ align:start position:0%
+it's Irene but then I've just given up
+I'm just giving it up that's terrible
+
+ align:start position:0%
+I'm just giving it up that's terrible
+ 
+
+ align:start position:0%
+I'm just giving it up that's terrible
+I have to change it so but custodial of
+
+ align:start position:0%
+I have to change it so but custodial of
+ 
+
+ align:start position:0%
+I have to change it so but custodial of
+private keys is a very real thing and
+
+ align:start position:0%
+private keys is a very real thing and
+ 
+
+ align:start position:0%
+private keys is a very real thing and
+you've read about the hacking and will
+
+ align:start position:0%
+you've read about the hacking and will
+ 
+
+ align:start position:0%
+you've read about the hacking and will
+read more about it when we get to crypto
+
+ align:start position:0%
+read more about it when we get to crypto
+ 
+
+ align:start position:0%
+read more about it when we get to crypto
+exchanges it's it's a very dominant
+
+ align:start position:0%
+exchanges it's it's a very dominant
+ 
+
+ align:start position:0%
+exchanges it's it's a very dominant
+issue not just for individuals but for
+
+ align:start position:0%
+issue not just for individuals but for
+ 
+
+ align:start position:0%
+issue not just for individuals but for
+institutional actors how does a hedge
+
+ align:start position:0%
+institutional actors how does a hedge
+ 
+
+ align:start position:0%
+institutional actors how does a hedge
+fund or more likely how does Blackrock
+
+ align:start position:0%
+fund or more likely how does Blackrock
+ 
+
+ align:start position:0%
+fund or more likely how does Blackrock
+or fidelity as an asset manager secure
+
+ align:start position:0%
+or fidelity as an asset manager secure
+ 
+
+ align:start position:0%
+or fidelity as an asset manager secure
+custody in a way that works and it's an
+
+ align:start position:0%
+custody in a way that works and it's an
+ 
+
+ align:start position:0%
+custody in a way that works and it's an
+asymmetric risk it's a tricky risk for
+
+ align:start position:0%
+asymmetric risk it's a tricky risk for
+ 
+
+ align:start position:0%
+asymmetric risk it's a tricky risk for
+most of finance they don't have custody
+
+ align:start position:0%
+most of finance they don't have custody
+ 
+
+ align:start position:0%
+most of finance they don't have custody
+any longer of the securities when I
+
+ align:start position:0%
+any longer of the securities when I
+ 
+
+ align:start position:0%
+any longer of the securities when I
+started a wall street they were still
+
+ align:start position:0%
+started a wall street they were still
+ 
+
+ align:start position:0%
+started a wall street they were still
+the cage CAG II there was a physical
+
+ align:start position:0%
+the cage CAG II there was a physical
+ 
+
+ align:start position:0%
+the cage CAG II there was a physical
+cage where the the remnants of paper
+
+ align:start position:0%
+cage where the the remnants of paper
+ 
+
+ align:start position:0%
+cage where the the remnants of paper
+stock certificates were still in the
+
+ align:start position:0%
+stock certificates were still in the
+ 
+
+ align:start position:0%
+stock certificates were still in the
+cage
+
+ align:start position:0%
+cage
+ 
+
+ align:start position:0%
+cage
+I didn't start so long ago that it was
+
+ align:start position:0%
+I didn't start so long ago that it was
+ 
+
+ align:start position:0%
+I didn't start so long ago that it was
+before DTCC was already things were
+
+ align:start position:0%
+before DTCC was already things were
+ 
+
+ align:start position:0%
+before DTCC was already things were
+getting electric you know digital but
+
+ align:start position:0%
+getting electric you know digital but
+ 
+
+ align:start position:0%
+getting electric you know digital but
+there was still a physical cage for some
+
+ align:start position:0%
+there was still a physical cage for some
+ 
+
+ align:start position:0%
+there was still a physical cage for some
+physical paper certificates if you lost
+
+ align:start position:0%
+physical paper certificates if you lost
+ 
+
+ align:start position:0%
+physical paper certificates if you lost
+the paper certificate you could still go
+
+ align:start position:0%
+the paper certificate you could still go
+ 
+
+ align:start position:0%
+the paper certificate you could still go
+to the government or the company that
+
+ align:start position:0%
+to the government or the company that
+ 
+
+ align:start position:0%
+to the government or the company that
+issued it and back door and get a new
+
+ align:start position:0%
+issued it and back door and get a new
+ 
+
+ align:start position:0%
+issued it and back door and get a new
+paper certificate
+
+ align:start position:0%
+paper certificate
+ 
+
+ align:start position:0%
+paper certificate
+it took time it was hard it was to
+
+ align:start position:0%
+it took time it was hard it was to
+ 
+
+ align:start position:0%
+it took time it was hard it was to
+authenticated but in this circumstance
+
+ align:start position:0%
+authenticated but in this circumstance
+ 
+
+ align:start position:0%
+authenticated but in this circumstance
+if you lose the private key there's not
+
+ align:start position:0%
+if you lose the private key there's not
+ 
+
+ align:start position:0%
+if you lose the private key there's not
+the back door issue or to get the next
+
+ align:start position:0%
+the back door issue or to get the next
+ 
+
+ align:start position:0%
+the back door issue or to get the next
+one so it's a very interesting issue not
+
+ align:start position:0%
+one so it's a very interesting issue not
+ 
+
+ align:start position:0%
+one so it's a very interesting issue not
+just a technological issue but in a
+
+ align:start position:0%
+just a technological issue but in a
+ 
+
+ align:start position:0%
+just a technological issue but in a
+cyber security issue but it's a whole
+
+ align:start position:0%
+cyber security issue but it's a whole
+ 
+
+ align:start position:0%
+cyber security issue but it's a whole
+set of financial custody issues an
+
+ align:start position:0%
+set of financial custody issues an
+ 
+
+ align:start position:0%
+set of financial custody issues an
+asymmetric risk if you're Goldman Sachs
+
+ align:start position:0%
+asymmetric risk if you're Goldman Sachs
+ 
+
+ align:start position:0%
+asymmetric risk if you're Goldman Sachs
+or fidelity and you lost a key or it got
+
+ align:start position:0%
+or fidelity and you lost a key or it got
+ 
+
+ align:start position:0%
+or fidelity and you lost a key or it got
+hacked and it was billions of dollars so
+
+ align:start position:0%
+hacked and it was billions of dollars so
+ 
+
+ align:start position:0%
+hacked and it was billions of dollars so
+it's just a interesting I don't think
+
+ align:start position:0%
+it's just a interesting I don't think
+ 
+
+ align:start position:0%
+it's just a interesting I don't think
+it's unique to blockchain but it's
+
+ align:start position:0%
+it's unique to blockchain but it's
+ 
+
+ align:start position:0%
+it's unique to blockchain but it's
+rather specific to blockchain and
+
+ align:start position:0%
+rather specific to blockchain and
+ 
+
+ align:start position:0%
+rather specific to blockchain and
+finance and how it overlaps it so some
+
+ align:start position:0%
+finance and how it overlaps it so some
+ 
+
+ align:start position:0%
+finance and how it overlaps it so some
+of the solutions that I do think there
+
+ align:start position:0%
+of the solutions that I do think there
+ 
+
+ align:start position:0%
+of the solutions that I do think there
+are solutions here are some of the
+
+ align:start position:0%
+are solutions here are some of the
+ 
+
+ align:start position:0%
+are solutions here are some of the
+things that that medoras and Nahan
+
+ align:start position:0%
+things that that medoras and Nahan
+ 
+
+ align:start position:0%
+things that that medoras and Nahan
+Narula who runs the digital currency
+
+ align:start position:0%
+Narula who runs the digital currency
+ 
+
+ align:start position:0%
+Narula who runs the digital currency
+initiative or work
+
+ align:start position:0%
+initiative or work
+ 
+
+ align:start position:0%
+initiative or work
+and they're working on using two
+
+ align:start position:0%
+and they're working on using two
+ 
+
+ align:start position:0%
+and they're working on using two
+cryptographic primitives we're not going
+
+ align:start position:0%
+cryptographic primitives we're not going
+ 
+
+ align:start position:0%
+cryptographic primitives we're not going
+to deeply go into we did hash functions
+
+ align:start position:0%
+to deeply go into we did hash functions
+ 
+
+ align:start position:0%
+to deeply go into we did hash functions
+and we did digital signatures those are
+
+ align:start position:0%
+and we did digital signatures those are
+ 
+
+ align:start position:0%
+and we did digital signatures those are
+algorithms or they're called
+
+ align:start position:0%
+algorithms or they're called
+ 
+
+ align:start position:0%
+algorithms or they're called
+cryptographic primitives
+
+ align:start position:0%
+cryptographic primitives
+ 
+
+ align:start position:0%
+cryptographic primitives
+well there's dozens cryptographic
+
+ align:start position:0%
+well there's dozens cryptographic
+ 
+
+ align:start position:0%
+well there's dozens cryptographic
+primitives math algorithms well the
+
+ align:start position:0%
+primitives math algorithms well the
+ 
+
+ align:start position:0%
+primitives math algorithms well the
+other two that are used a lot in this
+
+ align:start position:0%
+other two that are used a lot in this
+ 
+
+ align:start position:0%
+other two that are used a lot in this
+field or zero knowledge proof and less
+
+ align:start position:0%
+field or zero knowledge proof and less
+ 
+
+ align:start position:0%
+field or zero knowledge proof and less
+often probably as Peterson commitments
+
+ align:start position:0%
+often probably as Peterson commitments
+ 
+
+ align:start position:0%
+often probably as Peterson commitments
+and I put up there my words
+
+ align:start position:0%
+and I put up there my words
+ 
+
+ align:start position:0%
+and I put up there my words
+I got medoras to help me write this one
+
+ align:start position:0%
+I got medoras to help me write this one
+ 
+
+ align:start position:0%
+I got medoras to help me write this one
+but my words is zero knowledge proof
+
+ align:start position:0%
+but my words is zero knowledge proof
+ 
+
+ align:start position:0%
+but my words is zero knowledge proof
+let's someone prove a statement is true
+
+ align:start position:0%
+let's someone prove a statement is true
+ 
+
+ align:start position:0%
+let's someone prove a statement is true
+without revealing the details of exactly
+
+ align:start position:0%
+without revealing the details of exactly
+ 
+
+ align:start position:0%
+without revealing the details of exactly
+why that statement is true you might say
+
+ align:start position:0%
+why that statement is true you might say
+ 
+
+ align:start position:0%
+why that statement is true you might say
+wait a minute you can prove something's
+
+ align:start position:0%
+wait a minute you can prove something's
+ 
+
+ align:start position:0%
+wait a minute you can prove something's
+true it's sort of like if you walk into
+
+ align:start position:0%
+true it's sort of like if you walk into
+ 
+
+ align:start position:0%
+true it's sort of like if you walk into
+a bar and they need to know you're 21 to
+
+ align:start position:0%
+a bar and they need to know you're 21 to
+ 
+
+ align:start position:0%
+a bar and they need to know you're 21 to
+get a drink let's make this tangible
+
+ align:start position:0%
+get a drink let's make this tangible
+ 
+
+ align:start position:0%
+get a drink let's make this tangible
+what do you need to prove that you're 21
+
+ align:start position:0%
+what do you need to prove that you're 21
+ 
+
+ align:start position:0%
+what do you need to prove that you're 21
+you need to prove that you were born
+
+ align:start position:0%
+you need to prove that you were born
+ 
+
+ align:start position:0%
+you need to prove that you were born
+before 1997 September 27th but you don't
+
+ align:start position:0%
+before 1997 September 27th but you don't
+ 
+
+ align:start position:0%
+before 1997 September 27th but you don't
+need a lot more details and so there's
+
+ align:start position:0%
+need a lot more details and so there's
+ 
+
+ align:start position:0%
+need a lot more details and so there's
+some computer scientists here at MIT
+
+ align:start position:0%
+some computer scientists here at MIT
+ 
+
+ align:start position:0%
+some computer scientists here at MIT
+that actually did the foundational work
+
+ align:start position:0%
+that actually did the foundational work
+ 
+
+ align:start position:0%
+that actually did the foundational work
+when zero knowledge proves 20 to 30
+
+ align:start position:0%
+when zero knowledge proves 20 to 30
+ 
+
+ align:start position:0%
+when zero knowledge proves 20 to 30
+years ago Silvio McCauley and others for
+
+ align:start position:0%
+years ago Silvio McCauley and others for
+ 
+
+ align:start position:0%
+years ago Silvio McCauley and others for
+which I think was part of why they won
+
+ align:start position:0%
+which I think was part of why they won
+ 
+
+ align:start position:0%
+which I think was part of why they won
+the Turing award and amongst other work
+
+ align:start position:0%
+the Turing award and amongst other work
+ 
+
+ align:start position:0%
+the Turing award and amongst other work
+so zero knowledge proof sir very
+
+ align:start position:0%
+so zero knowledge proof sir very
+ 
+
+ align:start position:0%
+so zero knowledge proof sir very
+interesting cryptographic mathematical
+
+ align:start position:0%
+interesting cryptographic mathematical
+ 
+
+ align:start position:0%
+interesting cryptographic mathematical
+puzzle solving that medoras used for z
+
+ align:start position:0%
+puzzle solving that medoras used for z
+ 
+
+ align:start position:0%
+puzzle solving that medoras used for z
+cache nahama doris is using for
+
+ align:start position:0%
+cache nahama doris is using for
+ 
+
+ align:start position:0%
+cache nahama doris is using for
+something called ZK ledger which was an
+
+ align:start position:0%
+something called ZK ledger which was an
+ 
+
+ align:start position:0%
+something called ZK ledger which was an
+optional reading my gut tells me there
+
+ align:start position:0%
+optional reading my gut tells me there
+ 
+
+ align:start position:0%
+optional reading my gut tells me there
+are ways that we can go forward that
+
+ align:start position:0%
+are ways that we can go forward that
+ 
+
+ align:start position:0%
+are ways that we can go forward that
+regulators and the official sector can
+
+ align:start position:0%
+regulators and the official sector can
+ 
+
+ align:start position:0%
+regulators and the official sector can
+get there transparency they want and the
+
+ align:start position:0%
+get there transparency they want and the
+ 
+
+ align:start position:0%
+get there transparency they want and the
+financial sector at the same time can
+
+ align:start position:0%
+financial sector at the same time can
+ 
+
+ align:start position:0%
+financial sector at the same time can
+get the privacy they want that the two
+
+ align:start position:0%
+get the privacy they want that the two
+ 
+
+ align:start position:0%
+get the privacy they want that the two
+can actually coexist through the modern
+
+ align:start position:0%
+can actually coexist through the modern
+ 
+
+ align:start position:0%
+can actually coexist through the modern
+methods of technology Alexi is that a
+
+ align:start position:0%
+methods of technology Alexi is that a
+ 
+
+ align:start position:0%
+methods of technology Alexi is that a
+hand up or just waving no all right you
+
+ align:start position:0%
+hand up or just waving no all right you
+ 
+
+ align:start position:0%
+hand up or just waving no all right you
+want to add anything Medora since your
+
+ align:start position:0%
+want to add anything Medora since your
+ 
+
+ align:start position:0%
+want to add anything Medora since your
+the co-author of this ZK ledger paper
+
+ align:start position:0%
+the co-author of this ZK ledger paper
+ 
+
+ align:start position:0%
+the co-author of this ZK ledger paper
+that was optional
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+coin zero coy using Peterson clearance
+
+ align:start position:0%
+coin zero coy using Peterson clearance
+ 
+
+ align:start position:0%
+coin zero coy using Peterson clearance
+on Z cash
+
+ align:start position:0%
+on Z cash
+ 
+
+ align:start position:0%
+on Z cash
+bidding tears Peters and commitments
+
+ align:start position:0%
+bidding tears Peters and commitments
+ 
+
+ align:start position:0%
+bidding tears Peters and commitments
+like small talk very interesting history
+
+ align:start position:0%
+like small talk very interesting history
+ 
+
+ align:start position:0%
+like small talk very interesting history
+behind and Peterson commitments are yet
+
+ align:start position:0%
+behind and Peterson commitments are yet
+ 
+
+ align:start position:0%
+behind and Peterson commitments are yet
+another cryptographic primitive or
+
+ align:start position:0%
+another cryptographic primitive or
+ 
+
+ align:start position:0%
+another cryptographic primitive or
+algorithm which interestingly they're
+
+ align:start position:0%
+algorithm which interestingly they're
+ 
+
+ align:start position:0%
+algorithm which interestingly they're
+similar to hash functions where you take
+
+ align:start position:0%
+similar to hash functions where you take
+ 
+
+ align:start position:0%
+similar to hash functions where you take
+a bunch of data and you squish it
+
+ align:start position:0%
+a bunch of data and you squish it
+ 
+
+ align:start position:0%
+a bunch of data and you squish it
+together in a sense you compress it and
+
+ align:start position:0%
+together in a sense you compress it and
+ 
+
+ align:start position:0%
+together in a sense you compress it and
+get a commitment but you can actually
+
+ align:start position:0%
+get a commitment but you can actually
+ 
+
+ align:start position:0%
+get a commitment but you can actually
+add and subtract them it's it's an
+
+ align:start position:0%
+add and subtract them it's it's an
+ 
+
+ align:start position:0%
+add and subtract them it's it's an
+interesting thing where you can commit
+
+ align:start position:0%
+interesting thing where you can commit
+ 
+
+ align:start position:0%
+interesting thing where you can commit
+today to like a hash but you can also
+
+ align:start position:0%
+today to like a hash but you can also
+ 
+
+ align:start position:0%
+today to like a hash but you can also
+add and and and sort of subtract
+
+ align:start position:0%
+add and and and sort of subtract
+ 
+
+ align:start position:0%
+add and and and sort of subtract
+commitments so it has some interesting
+
+ align:start position:0%
+commitments so it has some interesting
+ 
+
+ align:start position:0%
+commitments so it has some interesting
+features if you're deeply interested I
+
+ align:start position:0%
+features if you're deeply interested I
+ 
+
+ align:start position:0%
+features if you're deeply interested I
+will probably line up Sabrina to help
+
+ align:start position:0%
+will probably line up Sabrina to help
+ 
+
+ align:start position:0%
+will probably line up Sabrina to help
+you or medoras might help because I'm at
+
+ align:start position:0%
+you or medoras might help because I'm at
+ 
+
+ align:start position:0%
+you or medoras might help because I'm at
+the edge but what I'm saying from a
+
+ align:start position:0%
+the edge but what I'm saying from a
+ 
+
+ align:start position:0%
+the edge but what I'm saying from a
+business side is my hunch and this is
+
+ align:start position:0%
+business side is my hunch and this is
+ 
+
+ align:start position:0%
+business side is my hunch and this is
+that we're at the we're at the cutting
+
+ align:start position:0%
+that we're at the we're at the cutting
+ 
+
+ align:start position:0%
+that we're at the we're at the cutting
+edge here at MIT of some of the folks
+
+ align:start position:0%
+edge here at MIT of some of the folks
+ 
+
+ align:start position:0%
+edge here at MIT of some of the folks
+try to figure out how to do privacy and
+
+ align:start position:0%
+try to figure out how to do privacy and
+ 
+
+ align:start position:0%
+try to figure out how to do privacy and
+security at the same time questions on
+
+ align:start position:0%
+security at the same time questions on
+ 
+
+ align:start position:0%
+security at the same time questions on
+that because we're gonna get to the
+
+ align:start position:0%
+that because we're gonna get to the
+ 
+
+ align:start position:0%
+that because we're gonna get to the
+tougher things interoperability linking
+
+ align:start position:0%
+tougher things interoperability linking
+ 
+
+ align:start position:0%
+tougher things interoperability linking
+blockchain applications to legacy
+
+ align:start position:0%
+blockchain applications to legacy
+ 
+
+ align:start position:0%
+blockchain applications to legacy
+databases or linking them to each other
+
+ align:start position:0%
+databases or linking them to each other
+ 
+
+ align:start position:0%
+databases or linking them to each other
+so you might want to link a blockchain
+
+ align:start position:0%
+so you might want to link a blockchain
+ 
+
+ align:start position:0%
+so you might want to link a blockchain
+application if you're if you're thinking
+
+ align:start position:0%
+application if you're if you're thinking
+ 
+
+ align:start position:0%
+application if you're if you're thinking
+about a payments protocol how does that
+
+ align:start position:0%
+about a payments protocol how does that
+ 
+
+ align:start position:0%
+about a payments protocol how does that
+payments protocol and blockchain world
+
+ align:start position:0%
+payments protocol and blockchain world
+ 
+
+ align:start position:0%
+payments protocol and blockchain world
+link to the Fiat because ultimately if
+
+ align:start position:0%
+link to the Fiat because ultimately if
+ 
+
+ align:start position:0%
+link to the Fiat because ultimately if
+you're doing let's say remittances and
+
+ align:start position:0%
+you're doing let's say remittances and
+ 
+
+ align:start position:0%
+you're doing let's say remittances and
+you want to move money from here to
+
+ align:start position:0%
+you want to move money from here to
+ 
+
+ align:start position:0%
+you want to move money from here to
+Mexico
+
+ align:start position:0%
+Mexico
+ 
+
+ align:start position:0%
+Mexico
+somebody wants Mexican peso they might
+
+ align:start position:0%
+somebody wants Mexican peso they might
+ 
+
+ align:start position:0%
+somebody wants Mexican peso they might
+be starting in US dollars how do you how
+
+ align:start position:0%
+be starting in US dollars how do you how
+ 
+
+ align:start position:0%
+be starting in US dollars how do you how
+do you operate basically with three
+
+ align:start position:0%
+do you operate basically with three
+ 
+
+ align:start position:0%
+do you operate basically with three
+different systems in that case you know
+
+ align:start position:0%
+different systems in that case you know
+ 
+
+ align:start position:0%
+different systems in that case you know
+you're ingenious innovative startup but
+
+ align:start position:0%
+you're ingenious innovative startup but
+ 
+
+ align:start position:0%
+you're ingenious innovative startup but
+the US dollar Fiats system and the
+
+ align:start position:0%
+the US dollar Fiats system and the
+ 
+
+ align:start position:0%
+the US dollar Fiats system and the
+Mexican peso system so that's a form of
+
+ align:start position:0%
+Mexican peso system so that's a form of
+ 
+
+ align:start position:0%
+Mexican peso system so that's a form of
+interoperability and and the challenge
+
+ align:start position:0%
+interoperability and and the challenge
+ 
+
+ align:start position:0%
+interoperability and and the challenge
+around it or blockchain to blockchain if
+
+ align:start position:0%
+around it or blockchain to blockchain if
+ 
+
+ align:start position:0%
+around it or blockchain to blockchain if
+we've got sixteen hundred of them or
+
+ align:start position:0%
+we've got sixteen hundred of them or
+ 
+
+ align:start position:0%
+we've got sixteen hundred of them or
+even interoperability of the main chain
+
+ align:start position:0%
+even interoperability of the main chain
+ 
+
+ align:start position:0%
+even interoperability of the main chain
+and some of these layer to inside shades
+
+ align:start position:0%
+and some of these layer to inside shades
+ 
+
+ align:start position:0%
+and some of these layer to inside shades
+that's an easier
+
+ align:start position:0%
+that's an easier
+ 
+
+ align:start position:0%
+that's an easier
+interoperability because it's kind of
+
+ align:start position:0%
+interoperability because it's kind of
+ 
+
+ align:start position:0%
+interoperability because it's kind of
+coded right in but it's always it and
+
+ align:start position:0%
+coded right in but it's always it and
+ 
+
+ align:start position:0%
+coded right in but it's always it and
+this is not a new thing banking has had
+
+ align:start position:0%
+this is not a new thing banking has had
+ 
+
+ align:start position:0%
+this is not a new thing banking has had
+interoperability all the time take my
+
+ align:start position:0%
+interoperability all the time take my
+ 
+
+ align:start position:0%
+interoperability all the time take my
+example of the u.s. to Mexico to move US
+
+ align:start position:0%
+example of the u.s. to Mexico to move US
+ 
+
+ align:start position:0%
+example of the u.s. to Mexico to move US
+Dollars and convert it to Mexican peso
+
+ align:start position:0%
+Dollars and convert it to Mexican peso
+ 
+
+ align:start position:0%
+Dollars and convert it to Mexican peso
+is in two entirely different banking
+
+ align:start position:0%
+is in two entirely different banking
+ 
+
+ align:start position:0%
+is in two entirely different banking
+systems in two entirely different ledger
+
+ align:start position:0%
+systems in two entirely different ledger
+ 
+
+ align:start position:0%
+systems in two entirely different ledger
+systems so we have to have this question
+
+ align:start position:0%
+systems so we have to have this question
+ 
+
+ align:start position:0%
+systems so we have to have this question
+of interoperability even pre blockchain
+
+ align:start position:0%
+of interoperability even pre blockchain
+ 
+
+ align:start position:0%
+of interoperability even pre blockchain
+but it's just bringing it to this new
+
+ align:start position:0%
+but it's just bringing it to this new
+ 
+
+ align:start position:0%
+but it's just bringing it to this new
+technology
+
+ align:start position:0%
+technology
+ 
+
+ align:start position:0%
+technology
+it raises cost of trust in coordinating
+
+ align:start position:0%
+it raises cost of trust in coordinating
+ 
+
+ align:start position:0%
+it raises cost of trust in coordinating
+the transfer assets and information
+
+ align:start position:0%
+the transfer assets and information
+ 
+
+ align:start position:0%
+the transfer assets and information
+across chains in essence or as we talked
+
+ align:start position:0%
+across chains in essence or as we talked
+ 
+
+ align:start position:0%
+across chains in essence or as we talked
+about across Ledger's so it's a it's an
+
+ align:start position:0%
+about across Ledger's so it's a it's an
+ 
+
+ align:start position:0%
+about across Ledger's so it's a it's an
+issue that's it's been around we just
+
+ align:start position:0%
+issue that's it's been around we just
+ 
+
+ align:start position:0%
+issue that's it's been around we just
+got to sort of see how we solve it here
+
+ align:start position:0%
+got to sort of see how we solve it here
+ 
+
+ align:start position:0%
+got to sort of see how we solve it here
+one solution it doesn't mean it's the
+
+ align:start position:0%
+one solution it doesn't mean it's the
+ 
+
+ align:start position:0%
+one solution it doesn't mean it's the
+right solution is the only solution well
+
+ align:start position:0%
+right solution is the only solution well
+ 
+
+ align:start position:0%
+right solution is the only solution well
+one solution is to do through some
+
+ align:start position:0%
+one solution is to do through some
+ 
+
+ align:start position:0%
+one solution is to do through some
+decentralized mechanisms including side
+
+ align:start position:0%
+decentralized mechanisms including side
+ 
+
+ align:start position:0%
+decentralized mechanisms including side
+chains or one of the favorites of the
+
+ align:start position:0%
+chains or one of the favorites of the
+ 
+
+ align:start position:0%
+chains or one of the favorites of the
+director of the Media Lab Joey Ito
+
+ align:start position:0%
+director of the Media Lab Joey Ito
+ 
+
+ align:start position:0%
+director of the Media Lab Joey Ito
+thinks maybe if we have layer two we
+
+ align:start position:0%
+thinks maybe if we have layer two we
+ 
+
+ align:start position:0%
+thinks maybe if we have layer two we
+should also have layer zero underneath
+
+ align:start position:0%
+should also have layer zero underneath
+ 
+
+ align:start position:0%
+should also have layer zero underneath
+all of these these coins underneath
+
+ align:start position:0%
+all of these these coins underneath
+ 
+
+ align:start position:0%
+all of these these coins underneath
+aetherium and bitcoin maybe there's a
+
+ align:start position:0%
+aetherium and bitcoin maybe there's a
+ 
+
+ align:start position:0%
+aetherium and bitcoin maybe there's a
+layer that we can technologically create
+
+ align:start position:0%
+layer that we can technologically create
+ 
+
+ align:start position:0%
+layer that we can technologically create
+nobody's done this yet but Joey's a
+
+ align:start position:0%
+nobody's done this yet but Joey's a
+ 
+
+ align:start position:0%
+nobody's done this yet but Joey's a
+visionary Joey we've had the first
+
+ align:start position:0%
+visionary Joey we've had the first
+ 
+
+ align:start position:0%
+visionary Joey we've had the first
+Internet service provider in Japan at
+
+ align:start position:0%
+Internet service provider in Japan at
+ 
+
+ align:start position:0%
+Internet service provider in Japan at
+the age of 23 when he got fifteen
+
+ align:start position:0%
+the age of 23 when he got fifteen
+ 
+
+ align:start position:0%
+the age of 23 when he got fifteen
+hundred dollars of computer equipment
+
+ align:start position:0%
+hundred dollars of computer equipment
+ 
+
+ align:start position:0%
+hundred dollars of computer equipment
+and put it in his bathroom and that's
+
+ align:start position:0%
+and put it in his bathroom and that's
+ 
+
+ align:start position:0%
+and put it in his bathroom and that's
+how he started yes yes his bathroom it
+
+ align:start position:0%
+how he started yes yes his bathroom it
+ 
+
+ align:start position:0%
+how he started yes yes his bathroom it
+was the only real estate he had so you
+
+ align:start position:0%
+was the only real estate he had so you
+ 
+
+ align:start position:0%
+was the only real estate he had so you
+know which way does this go you hadn't
+
+ align:start position:0%
+know which way does this go you hadn't
+ 
+
+ align:start position:0%
+know which way does this go you hadn't
+heard that about Joey yeah so it's a way
+
+ align:start position:0%
+heard that about Joey yeah so it's a way
+ 
+
+ align:start position:0%
+heard that about Joey yeah so it's a way
+to start a company and and I think far
+
+ align:start position:0%
+to start a company and and I think far
+ 
+
+ align:start position:0%
+to start a company and and I think far
+more work needs to be done so it may be
+
+ align:start position:0%
+more work needs to be done so it may be
+ 
+
+ align:start position:0%
+more work needs to be done so it may be
+solvable I'm not I'm I'm not sure and
+
+ align:start position:0%
+solvable I'm not I'm I'm not sure and
+ 
+
+ align:start position:0%
+solvable I'm not I'm I'm not sure and
+then consensus required for software
+
+ align:start position:0%
+then consensus required for software
+ 
+
+ align:start position:0%
+then consensus required for software
+updates it's a tough one
+
+ align:start position:0%
+updates it's a tough one
+ 
+
+ align:start position:0%
+updates it's a tough one
+open-source software updates which are
+
+ align:start position:0%
+open-source software updates which are
+ 
+
+ align:start position:0%
+open-source software updates which are
+not backward-compatible like can I
+
+ align:start position:0%
+not backward-compatible like can I
+ 
+
+ align:start position:0%
+not backward-compatible like can I
+update the
+
+ align:start position:0%
+update the
+ 
+
+ align:start position:0%
+update the
+software but then you can't use it for
+
+ align:start position:0%
+software but then you can't use it for
+ 
+
+ align:start position:0%
+software but then you can't use it for
+the 500000 blocks that are already out
+
+ align:start position:0%
+the 500000 blocks that are already out
+ 
+
+ align:start position:0%
+the 500000 blocks that are already out
+there in Bitcoin or in some or the
+
+ align:start position:0%
+there in Bitcoin or in some or the
+ 
+
+ align:start position:0%
+there in Bitcoin or in some or the
+millions of blocks and ether so the
+
+ align:start position:0%
+millions of blocks and ether so the
+ 
+
+ align:start position:0%
+millions of blocks and ether so the
+problem often happens that the older
+
+ align:start position:0%
+problem often happens that the older
+ 
+
+ align:start position:0%
+problem often happens that the older
+versions won't validate all the new
+
+ align:start position:0%
+versions won't validate all the new
+ 
+
+ align:start position:0%
+versions won't validate all the new
+blocks and if they won't validate all
+
+ align:start position:0%
+blocks and if they won't validate all
+ 
+
+ align:start position:0%
+blocks and if they won't validate all
+the new blocks I'm simplifying again
+
+ align:start position:0%
+the new blocks I'm simplifying again
+ 
+
+ align:start position:0%
+the new blocks I'm simplifying again
+think of like Excel and you get that
+
+ align:start position:0%
+think of like Excel and you get that
+ 
+
+ align:start position:0%
+think of like Excel and you get that
+update on Excel or word for window and
+
+ align:start position:0%
+update on Excel or word for window and
+ 
+
+ align:start position:0%
+update on Excel or word for window and
+you can't open your old files I mean
+
+ align:start position:0%
+you can't open your old files I mean
+ 
+
+ align:start position:0%
+you can't open your old files I mean
+it's a you know it's a rough lay
+
+ align:start position:0%
+it's a you know it's a rough lay
+ 
+
+ align:start position:0%
+it's a you know it's a rough lay
+definition of what what this issue is
+
+ align:start position:0%
+definition of what what this issue is
+ 
+
+ align:start position:0%
+definition of what what this issue is
+and so it leads to something called hard
+
+ align:start position:0%
+and so it leads to something called hard
+ 
+
+ align:start position:0%
+and so it leads to something called hard
+Forks and this little visual on the
+
+ align:start position:0%
+Forks and this little visual on the
+ 
+
+ align:start position:0%
+Forks and this little visual on the
+right hand side is basically what
+
+ align:start position:0%
+right hand side is basically what
+ 
+
+ align:start position:0%
+right hand side is basically what
+happens is you can't validate all the
+
+ align:start position:0%
+happens is you can't validate all the
+ 
+
+ align:start position:0%
+happens is you can't validate all the
+old blocks because the new software is
+
+ align:start position:0%
+old blocks because the new software is
+ 
+
+ align:start position:0%
+old blocks because the new software is
+kind of going beyond it a hard fork
+
+ align:start position:0%
+kind of going beyond it a hard fork
+ 
+
+ align:start position:0%
+kind of going beyond it a hard fork
+would happen is if you took two megabyte
+
+ align:start position:0%
+would happen is if you took two megabyte
+ 
+
+ align:start position:0%
+would happen is if you took two megabyte
+blocks if you made the block size bigger
+
+ align:start position:0%
+blocks if you made the block size bigger
+ 
+
+ align:start position:0%
+blocks if you made the block size bigger
+the old the old software would not take
+
+ align:start position:0%
+the old the old software would not take
+ 
+
+ align:start position:0%
+the old the old software would not take
+that I've got this right that would be a
+
+ align:start position:0%
+that I've got this right that would be a
+ 
+
+ align:start position:0%
+that I've got this right that would be a
+hard fork and so that's a that's an
+
+ align:start position:0%
+hard fork and so that's a that's an
+ 
+
+ align:start position:0%
+hard fork and so that's a that's an
+issue and it's happened the theory of
+
+ align:start position:0%
+issue and it's happened the theory of
+ 
+
+ align:start position:0%
+issue and it's happened the theory of
+network has E theorem classic and a Z
+
+ align:start position:0%
+network has E theorem classic and a Z
+ 
+
+ align:start position:0%
+network has E theorem classic and a Z
+theorem because of a hard fork that was
+
+ align:start position:0%
+theorem because of a hard fork that was
+ 
+
+ align:start position:0%
+theorem because of a hard fork that was
+encouraged by Vitalik Butera and the
+
+ align:start position:0%
+encouraged by Vitalik Butera and the
+ 
+
+ align:start position:0%
+encouraged by Vitalik Butera and the
+Bitcoin network has won from last year
+
+ align:start position:0%
+Bitcoin network has won from last year
+ 
+
+ align:start position:0%
+Bitcoin network has won from last year
+where it was this debate about block
+
+ align:start position:0%
+where it was this debate about block
+ 
+
+ align:start position:0%
+where it was this debate about block
+sizes so it's most software for decades
+
+ align:start position:0%
+sizes so it's most software for decades
+ 
+
+ align:start position:0%
+sizes so it's most software for decades
+is dealt with how do we update software
+
+ align:start position:0%
+is dealt with how do we update software
+ 
+
+ align:start position:0%
+is dealt with how do we update software
+but they can push it to us and we get it
+
+ align:start position:0%
+but they can push it to us and we get it
+ 
+
+ align:start position:0%
+but they can push it to us and we get it
+and we hit a button and we get it and
+
+ align:start position:0%
+and we hit a button and we get it and
+ 
+
+ align:start position:0%
+and we hit a button and we get it and
+after a while we get annoyed and we
+
+ align:start position:0%
+after a while we get annoyed and we
+ 
+
+ align:start position:0%
+after a while we get annoyed and we
+don't update if you're like me but the
+
+ align:start position:0%
+don't update if you're like me but the
+ 
+
+ align:start position:0%
+don't update if you're like me but the
+consensus remember this was a graph that
+
+ align:start position:0%
+consensus remember this was a graph that
+ 
+
+ align:start position:0%
+consensus remember this was a graph that
+we had the consensus always supports the
+
+ align:start position:0%
+we had the consensus always supports the
+ 
+
+ align:start position:0%
+we had the consensus always supports the
+longest chain
+
+ align:start position:0%
+longest chain
+ 
+
+ align:start position:0%
+longest chain
+if the consensus is to adopt this new
+
+ align:start position:0%
+if the consensus is to adopt this new
+ 
+
+ align:start position:0%
+if the consensus is to adopt this new
+technology and only 80 or 90% adopt it
+
+ align:start position:0%
+technology and only 80 or 90% adopt it
+ 
+
+ align:start position:0%
+technology and only 80 or 90% adopt it
+it's a question of whether the other 10
+
+ align:start position:0%
+it's a question of whether the other 10
+ 
+
+ align:start position:0%
+it's a question of whether the other 10
+or 15% will keep maintaining the shorter
+
+ align:start position:0%
+or 15% will keep maintaining the shorter
+ 
+
+ align:start position:0%
+or 15% will keep maintaining the shorter
+chain and in Bitcoin cache they have and
+
+ align:start position:0%
+chain and in Bitcoin cache they have and
+ 
+
+ align:start position:0%
+chain and in Bitcoin cache they have and
+so in essence now you have two
+
+ align:start position:0%
+so in essence now you have two
+ 
+
+ align:start position:0%
+so in essence now you have two
+currencies if for some reason it
+
+ align:start position:0%
+currencies if for some reason it
+ 
+
+ align:start position:0%
+currencies if for some reason it
+atrophied and they
+
+ align:start position:0%
+atrophied and they
+ 
+
+ align:start position:0%
+atrophied and they
+stopped maintaining it then the value in
+
+ align:start position:0%
+stopped maintaining it then the value in
+ 
+
+ align:start position:0%
+stopped maintaining it then the value in
+a sense in a commercial setting might go
+
+ align:start position:0%
+a sense in a commercial setting might go
+ 
+
+ align:start position:0%
+a sense in a commercial setting might go
+to zero is your question so broadly
+
+ align:start position:0%
+to zero is your question so broadly
+ 
+
+ align:start position:0%
+to zero is your question so broadly
+speaking I think the toughest issue is
+
+ align:start position:0%
+speaking I think the toughest issue is
+ 
+
+ align:start position:0%
+speaking I think the toughest issue is
+about collective action and governance
+
+ align:start position:0%
+about collective action and governance
+ 
+
+ align:start position:0%
+about collective action and governance
+how do you get a whole group of people
+
+ align:start position:0%
+how do you get a whole group of people
+ 
+
+ align:start position:0%
+how do you get a whole group of people
+to be moving in a similar direction
+
+ align:start position:0%
+to be moving in a similar direction
+ 
+
+ align:start position:0%
+to be moving in a similar direction
+blockchain applications derived part of
+
+ align:start position:0%
+blockchain applications derived part of
+ 
+
+ align:start position:0%
+blockchain applications derived part of
+their value from participation of
+
+ align:start position:0%
+their value from participation of
+ 
+
+ align:start position:0%
+their value from participation of
+multiple parties on the network as well
+
+ align:start position:0%
+multiple parties on the network as well
+ 
+
+ align:start position:0%
+multiple parties on the network as well
+that multiple people are involved it's
+
+ align:start position:0%
+that multiple people are involved it's
+ 
+
+ align:start position:0%
+that multiple people are involved it's
+remarkable in hindsight this Satoshi
+
+ align:start position:0%
+remarkable in hindsight this Satoshi
+ 
+
+ align:start position:0%
+remarkable in hindsight this Satoshi
+Nakamoto whomever he or she was got this
+
+ align:start position:0%
+Nakamoto whomever he or she was got this
+ 
+
+ align:start position:0%
+Nakamoto whomever he or she was got this
+many people there's nearly a hundred
+
+ align:start position:0%
+many people there's nearly a hundred
+ 
+
+ align:start position:0%
+many people there's nearly a hundred
+people in this room studying this ten
+
+ align:start position:0%
+people in this room studying this ten
+ 
+
+ align:start position:0%
+people in this room studying this ten
+years later but somehow he solved a
+
+ align:start position:0%
+years later but somehow he solved a
+ 
+
+ align:start position:0%
+years later but somehow he solved a
+collective action issue because it was
+
+ align:start position:0%
+collective action issue because it was
+ 
+
+ align:start position:0%
+collective action issue because it was
+just software code back in 2009 but it's
+
+ align:start position:0%
+just software code back in 2009 but it's
+ 
+
+ align:start position:0%
+just software code back in 2009 but it's
+still the example how does Silvio
+
+ align:start position:0%
+still the example how does Silvio
+ 
+
+ align:start position:0%
+still the example how does Silvio
+McCauley with a very clever blockchain
+
+ align:start position:0%
+McCauley with a very clever blockchain
+ 
+
+ align:start position:0%
+McCauley with a very clever blockchain
+adaptation and Algar and how does he get
+
+ align:start position:0%
+adaptation and Algar and how does he get
+ 
+
+ align:start position:0%
+adaptation and Algar and how does he get
+people to start using it and until he
+
+ align:start position:0%
+people to start using it and until he
+ 
+
+ align:start position:0%
+people to start using it and until he
+starts to get people to use it
+
+ align:start position:0%
+starts to get people to use it
+ 
+
+ align:start position:0%
+starts to get people to use it
+where's the value or if you have an
+
+ align:start position:0%
+where's the value or if you have an
+ 
+
+ align:start position:0%
+where's the value or if you have an
+application that's to be file-sharing or
+
+ align:start position:0%
+application that's to be file-sharing or
+ 
+
+ align:start position:0%
+application that's to be file-sharing or
+for medical records there's a medical
+
+ align:start position:0%
+for medical records there's a medical
+ 
+
+ align:start position:0%
+for medical records there's a medical
+records project here at MIT but how do
+
+ align:start position:0%
+records project here at MIT but how do
+ 
+
+ align:start position:0%
+records project here at MIT but how do
+you start to get people to use it and
+
+ align:start position:0%
+you start to get people to use it and
+ 
+
+ align:start position:0%
+you start to get people to use it and
+you know these are solved every day in
+
+ align:start position:0%
+you know these are solved every day in
+ 
+
+ align:start position:0%
+you know these are solved every day in
+the internet space but blockchain has a
+
+ align:start position:0%
+the internet space but blockchain has a
+ 
+
+ align:start position:0%
+the internet space but blockchain has a
+little bit greater Rik wrinkles so
+
+ align:start position:0%
+little bit greater Rik wrinkles so
+ 
+
+ align:start position:0%
+little bit greater Rik wrinkles so
+there's a chicken and egg issue Priya
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+question is is there some perception
+
+ align:start position:0%
+question is is there some perception
+ 
+
+ align:start position:0%
+question is is there some perception
+look can I use that word there's some
+
+ align:start position:0%
+look can I use that word there's some
+ 
+
+ align:start position:0%
+look can I use that word there's some
+perception it's not a real thing so it
+
+ align:start position:0%
+perception it's not a real thing so it
+ 
+
+ align:start position:0%
+perception it's not a real thing so it
+might not propagate and there might not
+
+ align:start position:0%
+might not propagate and there might not
+ 
+
+ align:start position:0%
+might not propagate and there might not
+be as much consumer adoption that I that
+
+ align:start position:0%
+be as much consumer adoption that I that
+ 
+
+ align:start position:0%
+be as much consumer adoption that I that
+may well be one of the commercial
+
+ align:start position:0%
+may well be one of the commercial
+ 
+
+ align:start position:0%
+may well be one of the commercial
+challenges Elon did you have someone
+
+ align:start position:0%
+challenges Elon did you have someone
+ 
+
+ align:start position:0%
+challenges Elon did you have someone
+ended up in Bitcoin was because people
+
+ align:start position:0%
+ended up in Bitcoin was because people
+ 
+
+ align:start position:0%
+ended up in Bitcoin was because people
+were interested in the innovation so in
+
+ align:start position:0%
+were interested in the innovation so in
+ 
+
+ align:start position:0%
+were interested in the innovation so in
+a very solution and then hiriam and
+
+ align:start position:0%
+a very solution and then hiriam and
+ 
+
+ align:start position:0%
+a very solution and then hiriam and
+other chains or
+
+ align:start position:0%
+other chains or
+ 
+
+ align:start position:0%
+other chains or
+basically pouring money into the
+
+ align:start position:0%
+basically pouring money into the
+ 
+
+ align:start position:0%
+basically pouring money into the
+ecosystem giving money to developers to
+
+ align:start position:0%
+ecosystem giving money to developers to
+ 
+
+ align:start position:0%
+ecosystem giving money to developers to
+develop solutions because they they are
+
+ align:start position:0%
+develop solutions because they they are
+ 
+
+ align:start position:0%
+develop solutions because they they are
+betting on every one of you as you're
+
+ align:start position:0%
+betting on every one of you as you're
+ 
+
+ align:start position:0%
+betting on every one of you as you're
+thinking about your final projects this
+
+ align:start position:0%
+thinking about your final projects this
+ 
+
+ align:start position:0%
+thinking about your final projects this
+collective action issue has multiple
+
+ align:start position:0%
+collective action issue has multiple
+ 
+
+ align:start position:0%
+collective action issue has multiple
+features one to me is the governance of
+
+ align:start position:0%
+features one to me is the governance of
+ 
+
+ align:start position:0%
+features one to me is the governance of
+the blockchain software updates which we
+
+ align:start position:0%
+the blockchain software updates which we
+ 
+
+ align:start position:0%
+the blockchain software updates which we
+said is a little bit about hard Forks
+
+ align:start position:0%
+said is a little bit about hard Forks
+ 
+
+ align:start position:0%
+said is a little bit about hard Forks
+and so forth and how do you have
+
+ align:start position:0%
+and so forth and how do you have
+ 
+
+ align:start position:0%
+and so forth and how do you have
+consensus and how centralized to the
+
+ align:start position:0%
+consensus and how centralized to the
+ 
+
+ align:start position:0%
+consensus and how centralized to the
+governance stay which we'll come back to
+
+ align:start position:0%
+governance stay which we'll come back to
+ 
+
+ align:start position:0%
+governance stay which we'll come back to
+when we talk about the Securities and
+
+ align:start position:0%
+when we talk about the Securities and
+ 
+
+ align:start position:0%
+when we talk about the Securities and
+Exchange Commission and whether it's a
+
+ align:start position:0%
+Exchange Commission and whether it's a
+ 
+
+ align:start position:0%
+Exchange Commission and whether it's a
+token that's regulated as a security so
+
+ align:start position:0%
+token that's regulated as a security so
+ 
+
+ align:start position:0%
+token that's regulated as a security so
+there's that part of governance but then
+
+ align:start position:0%
+there's that part of governance but then
+ 
+
+ align:start position:0%
+there's that part of governance but then
+there's the collective action issue that
+
+ align:start position:0%
+there's the collective action issue that
+ 
+
+ align:start position:0%
+there's the collective action issue that
+if you have a payments or medical
+
+ align:start position:0%
+if you have a payments or medical
+ 
+
+ align:start position:0%
+if you have a payments or medical
+records or or trade finance how do you
+
+ align:start position:0%
+records or or trade finance how do you
+ 
+
+ align:start position:0%
+records or or trade finance how do you
+get folks to adopt and in the banking
+
+ align:start position:0%
+get folks to adopt and in the banking
+ 
+
+ align:start position:0%
+get folks to adopt and in the banking
+sector the banks are the big the big
+
+ align:start position:0%
+sector the banks are the big the big
+ 
+
+ align:start position:0%
+sector the banks are the big the big
+sort of elephants in the room the big
+
+ align:start position:0%
+sort of elephants in the room the big
+ 
+
+ align:start position:0%
+sort of elephants in the room the big
+dominant incumbents how do you get them
+
+ align:start position:0%
+dominant incumbents how do you get them
+ 
+
+ align:start position:0%
+dominant incumbents how do you get them
+to adopt or you somehow competing away
+
+ align:start position:0%
+to adopt or you somehow competing away
+ 
+
+ align:start position:0%
+to adopt or you somehow competing away
+their profits and not having them adopt
+
+ align:start position:0%
+their profits and not having them adopt
+ 
+
+ align:start position:0%
+their profits and not having them adopt
+which is more a commercial business
+
+ align:start position:0%
+which is more a commercial business
+ 
+
+ align:start position:0%
+which is more a commercial business
+issue about collective action so the
+
+ align:start position:0%
+issue about collective action so the
+ 
+
+ align:start position:0%
+issue about collective action so the
+financial sector as we've talked about
+
+ align:start position:0%
+financial sector as we've talked about
+ 
+
+ align:start position:0%
+financial sector as we've talked about
+favors permission block chains that
+
+ align:start position:0%
+favors permission block chains that
+ 
+
+ align:start position:0%
+favors permission block chains that
+don't have as many they have some
+
+ align:start position:0%
+don't have as many they have some
+ 
+
+ align:start position:0%
+don't have as many they have some
+collective action issues but they don't
+
+ align:start position:0%
+collective action issues but they don't
+ 
+
+ align:start position:0%
+collective action issues but they don't
+have as many collective action issues
+
+ align:start position:0%
+have as many collective action issues
+ 
+
+ align:start position:0%
+have as many collective action issues
+they have four fewer scalability and
+
+ align:start position:0%
+they have four fewer scalability and
+ 
+
+ align:start position:0%
+they have four fewer scalability and
+performance issues because they say I'm
+
+ align:start position:0%
+performance issues because they say I'm
+ 
+
+ align:start position:0%
+performance issues because they say I'm
+not using proof-of-work there might be
+
+ align:start position:0%
+not using proof-of-work there might be
+ 
+
+ align:start position:0%
+not using proof-of-work there might be
+15 20 or even 75 or a hundred nodes but
+
+ align:start position:0%
+15 20 or even 75 or a hundred nodes but
+ 
+
+ align:start position:0%
+15 20 or even 75 or a hundred nodes but
+they think that way they can secure
+
+ align:start position:0%
+they think that way they can secure
+ 
+
+ align:start position:0%
+they think that way they can secure
+their privacy and security
+
+ align:start position:0%
+their privacy and security
+ 
+
+ align:start position:0%
+their privacy and security
+now medoras and Nahas paper on zk ledger
+
+ align:start position:0%
+now medoras and Nahas paper on zk ledger
+ 
+
+ align:start position:0%
+now medoras and Nahas paper on zk ledger
+might be a solution and some of those
+
+ align:start position:0%
+might be a solution and some of those
+ 
+
+ align:start position:0%
+might be a solution and some of those
+banks might start using that but I'm
+
+ align:start position:0%
+banks might start using that but I'm
+ 
+
+ align:start position:0%
+banks might start using that but I'm
+talking about 2018 I'm not talking about
+
+ align:start position:0%
+talking about 2018 I'm not talking about
+ 
+
+ align:start position:0%
+talking about 2018 I'm not talking about
+2020 or 2025 right now they're favoring
+
+ align:start position:0%
+2020 or 2025 right now they're favoring
+ 
+
+ align:start position:0%
+2020 or 2025 right now they're favoring
+permissioned closed-loop systems rather
+
+ align:start position:0%
+permissioned closed-loop systems rather
+ 
+
+ align:start position:0%
+permissioned closed-loop systems rather
+than permissionless open loose systems
+
+ align:start position:0%
+than permissionless open loose systems
+ 
+
+ align:start position:0%
+than permissionless open loose systems
+so next week we're going to be moving to
+
+ align:start position:0%
+so next week we're going to be moving to
+ 
+
+ align:start position:0%
+so next week we're going to be moving to
+public policy oh my god you're gonna get
+
+ align:start position:0%
+public policy oh my god you're gonna get
+ 
+
+ align:start position:0%
+public policy oh my god you're gonna get
+to read my testimony
+
+ align:start position:0%
+to read my testimony
+ 
+
+ align:start position:0%
+ 
+all 28 pages of it yeah can I get it but
+
+ align:start position:0%
+all 28 pages of it yeah can I get it but
+ 
+
+ align:start position:0%
+all 28 pages of it yeah can I get it but
+I was asked to testify in the House
+
+ align:start position:0%
+I was asked to testify in the House
+ 
+
+ align:start position:0%
+I was asked to testify in the House
+Agriculture Committee in July it's a
+
+ align:start position:0%
+Agriculture Committee in July it's a
+ 
+
+ align:start position:0%
+Agriculture Committee in July it's a
+venue I'd been at a whole bunch of times
+
+ align:start position:0%
+venue I'd been at a whole bunch of times
+ 
+
+ align:start position:0%
+venue I'd been at a whole bunch of times
+it was fun to be back in front of the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+chairman Conaway from Texas and Colin
+
+ align:start position:0%
+chairman Conaway from Texas and Colin
+ 
+
+ align:start position:0%
+chairman Conaway from Texas and Colin
+Petersen for Minnesota but yes you'll
+
+ align:start position:0%
+Petersen for Minnesota but yes you'll
+ 
+
+ align:start position:0%
+Petersen for Minnesota but yes you'll
+get to read mine it was I I knew that
+
+ align:start position:0%
+get to read mine it was I I knew that
+ 
+
+ align:start position:0%
+get to read mine it was I I knew that
+there was no legislation that was going
+
+ align:start position:0%
+there was no legislation that was going
+ 
+
+ align:start position:0%
+there was no legislation that was going
+to happen this year I want to just give
+
+ align:start position:0%
+to happen this year I want to just give
+ 
+
+ align:start position:0%
+to happen this year I want to just give
+you the feedback but some the
+
+ align:start position:0%
+you the feedback but some the
+ 
+
+ align:start position:0%
+you the feedback but some the
+Republicans run the committee they get
+
+ align:start position:0%
+Republicans run the committee they get
+ 
+
+ align:start position:0%
+Republicans run the committee they get
+to invite as many witnesses they want
+
+ align:start position:0%
+to invite as many witnesses they want
+ 
+
+ align:start position:0%
+to invite as many witnesses they want
+and then they let the minority invite
+
+ align:start position:0%
+and then they let the minority invite
+ 
+
+ align:start position:0%
+and then they let the minority invite
+one sometimes two witnesses so I got the
+
+ align:start position:0%
+one sometimes two witnesses so I got the
+ 
+
+ align:start position:0%
+one sometimes two witnesses so I got the
+call to testify because I'm like the old
+
+ align:start position:0%
+call to testify because I'm like the old
+ 
+
+ align:start position:0%
+call to testify because I'm like the old
+you know sea dog and they're bringing me
+
+ align:start position:0%
+you know sea dog and they're bringing me
+ 
+
+ align:start position:0%
+you know sea dog and they're bringing me
+in or something but it was flood but I
+
+ align:start position:0%
+in or something but it was flood but I
+ 
+
+ align:start position:0%
+in or something but it was flood but I
+it sort of I was preparing for this
+
+ align:start position:0%
+it sort of I was preparing for this
+ 
+
+ align:start position:0%
+it sort of I was preparing for this
+class anyway so I kind of wrote the
+
+ align:start position:0%
+class anyway so I kind of wrote the
+ 
+
+ align:start position:0%
+class anyway so I kind of wrote the
+testimony for you all Congress thought
+
+ align:start position:0%
+testimony for you all Congress thought
+ 
+
+ align:start position:0%
+testimony for you all Congress thought
+it was for them and it was it was but
+
+ align:start position:0%
+it was for them and it was it was but
+ 
+
+ align:start position:0%
+it was for them and it was it was but
+that's the main thing Mark Carney who
+
+ align:start position:0%
+that's the main thing Mark Carney who
+ 
+
+ align:start position:0%
+that's the main thing Mark Carney who
+runs the Bank of England wrote this
+
+ align:start position:0%
+runs the Bank of England wrote this
+ 
+
+ align:start position:0%
+runs the Bank of England wrote this
+really beautifully written piece that he
+
+ align:start position:0%
+really beautifully written piece that he
+ 
+
+ align:start position:0%
+really beautifully written piece that he
+gave in the spring about a little bit
+
+ align:start position:0%
+gave in the spring about a little bit
+ 
+
+ align:start position:0%
+gave in the spring about a little bit
+the history currency and so forth but
+
+ align:start position:0%
+the history currency and so forth but
+ 
+
+ align:start position:0%
+the history currency and so forth but
+mark also runs the financial stability
+
+ align:start position:0%
+mark also runs the financial stability
+ 
+
+ align:start position:0%
+mark also runs the financial stability
+the it so the the the Financial
+
+ align:start position:0%
+the it so the the the Financial
+ 
+
+ align:start position:0%
+the it so the the the Financial
+Stability Board which has the finance
+
+ align:start position:0%
+Stability Board which has the finance
+ 
+
+ align:start position:0%
+Stability Board which has the finance
+ministers and central bank governors and
+
+ align:start position:0%
+ministers and central bank governors and
+ 
+
+ align:start position:0%
+ministers and central bank governors and
+securities regulators from 20 countries
+
+ align:start position:0%
+securities regulators from 20 countries
+ 
+
+ align:start position:0%
+securities regulators from 20 countries
+so it's the g20 s finance heavies I used
+
+ align:start position:0%
+so it's the g20 s finance heavies I used
+ 
+
+ align:start position:0%
+so it's the g20 s finance heavies I used
+to go to that not as a finance heavy but
+
+ align:start position:0%
+to go to that not as a finance heavy but
+ 
+
+ align:start position:0%
+to go to that not as a finance heavy but
+I used to go because they wanted me
+
+ align:start position:0%
+I used to go because they wanted me
+ 
+
+ align:start position:0%
+I used to go because they wanted me
+inside the tent rather than outside the
+
+ align:start position:0%
+inside the tent rather than outside the
+ 
+
+ align:start position:0%
+inside the tent rather than outside the
+tent because we were doing derivatives
+
+ align:start position:0%
+tent because we were doing derivatives
+ 
+
+ align:start position:0%
+tent because we were doing derivatives
+reform here in the US and some of the
+
+ align:start position:0%
+reform here in the US and some of the
+ 
+
+ align:start position:0%
+reform here in the US and some of the
+foreign finance ministers had a
+
+ align:start position:0%
+foreign finance ministers had a
+ 
+
+ align:start position:0%
+foreign finance ministers had a
+different point of view and when it got
+
+ align:start position:0%
+different point of view and when it got
+ 
+
+ align:start position:0%
+different point of view and when it got
+to the place when seven finance
+
+ align:start position:0%
+to the place when seven finance
+ 
+
+ align:start position:0%
+to the place when seven finance
+ministers and it was an interesting
+
+ align:start position:0%
+ministers and it was an interesting
+ 
+
+ align:start position:0%
+ministers and it was an interesting
+group the Russian finance minister in
+
+ align:start position:0%
+group the Russian finance minister in
+ 
+
+ align:start position:0%
+group the Russian finance minister in
+the UK and the South African and four
+
+ align:start position:0%
+the UK and the South African and four
+ 
+
+ align:start position:0%
+the UK and the South African and four
+others wrote a joint letter to secretary
+
+ align:start position:0%
+others wrote a joint letter to secretary
+ 
+
+ align:start position:0%
+others wrote a joint letter to secretary
+Geithner pointing out some shall we say
+
+ align:start position:0%
+Geithner pointing out some shall we say
+ 
+
+ align:start position:0%
+Geithner pointing out some shall we say
+observations and what we were doing
+
+ align:start position:0%
+observations and what we were doing
+ 
+
+ align:start position:0%
+observations and what we were doing
+they had differences I got invited so I
+
+ align:start position:0%
+they had differences I got invited so I
+ 
+
+ align:start position:0%
+they had differences I got invited so I
+used to go I got to know mark very well
+
+ align:start position:0%
+used to go I got to know mark very well
+ 
+
+ align:start position:0%
+used to go I got to know mark very well
+but it's it's a good paper and and
+
+ align:start position:0%
+but it's it's a good paper and and
+ 
+
+ align:start position:0%
+but it's it's a good paper and and
+you'll get a sense really from I would
+
+ align:start position:0%
+you'll get a sense really from I would
+ 
+
+ align:start position:0%
+you'll get a sense really from I would
+say mark is neither a Bitcoin maximalist
+
+ align:start position:0%
+say mark is neither a Bitcoin maximalist
+ 
+
+ align:start position:0%
+say mark is neither a Bitcoin maximalist
+or minimalist but he does say don't use
+
+ align:start position:0%
+or minimalist but he does say don't use
+ 
+
+ align:start position:0%
+or minimalist but he does say don't use
+the word cryptocurrency use the term
+
+ align:start position:0%
+the word cryptocurrency use the term
+ 
+
+ align:start position:0%
+the word cryptocurrency use the term
+crypto asset so it's kind of an
+
+ align:start position:0%
+crypto asset so it's kind of an
+ 
+
+ align:start position:0%
+crypto asset so it's kind of an
+interesting piece and then I don't know
+
+ align:start position:0%
+interesting piece and then I don't know
+ 
+
+ align:start position:0%
+interesting piece and then I don't know
+how many of you are Sloan fellows that
+
+ align:start position:0%
+how many of you are Sloan fellows that
+ 
+
+ align:start position:0%
+how many of you are Sloan fellows that
+are here I recognize some of the Sloan
+
+ align:start position:0%
+are here I recognize some of the Sloan
+ 
+
+ align:start position:0%
+are here I recognize some of the Sloan
+fellows I think about 20 or 25 percent
+
+ align:start position:0%
+fellows I think about 20 or 25 percent
+ 
+
+ align:start position:0%
+fellows I think about 20 or 25 percent
+of the class or so fellas you're gonna
+
+ align:start position:0%
+of the class or so fellas you're gonna
+ 
+
+ align:start position:0%
+of the class or so fellas you're gonna
+get to see Joe Stiglitz in New York in a
+
+ align:start position:0%
+get to see Joe Stiglitz in New York in a
+ 
+
+ align:start position:0%
+get to see Joe Stiglitz in New York in a
+few weeks and I think yeah this is the
+
+ align:start position:0%
+few weeks and I think yeah this is the
+ 
+
+ align:start position:0%
+few weeks and I think yeah this is the
+CNBC piece where Joe who's Nobel
+
+ align:start position:0%
+CNBC piece where Joe who's Nobel
+ 
+
+ align:start position:0%
+CNBC piece where Joe who's Nobel
+laureate at Columbia University has a
+
+ align:start position:0%
+laureate at Columbia University has a
+ 
+
+ align:start position:0%
+laureate at Columbia University has a
+stork and distinct point of view about
+
+ align:start position:0%
+stork and distinct point of view about
+ 
+
+ align:start position:0%
+stork and distinct point of view about
+Bitcoin I've had two or three lively
+
+ align:start position:0%
+Bitcoin I've had two or three lively
+ 
+
+ align:start position:0%
+Bitcoin I've had two or three lively
+conversations with Joe about this later
+
+ align:start position:0%
+conversations with Joe about this later
+ 
+
+ align:start position:0%
+conversations with Joe about this later
+in the semester you'll read Paul Krugman
+
+ align:start position:0%
+in the semester you'll read Paul Krugman
+ 
+
+ align:start position:0%
+in the semester you'll read Paul Krugman
+in Nouriel Roubini and and and there's a
+
+ align:start position:0%
+in Nouriel Roubini and and and there's a
+ 
+
+ align:start position:0%
+in Nouriel Roubini and and and there's a
+little video of Bill Gates talking about
+
+ align:start position:0%
+little video of Bill Gates talking about
+ 
+
+ align:start position:0%
+little video of Bill Gates talking about
+Bitcoin
+
+ align:start position:0%
+Bitcoin
+ 
+
+ align:start position:0%
+Bitcoin
+I want you ought to be aware of the
+
+ align:start position:0%
+I want you ought to be aware of the
+ 
+
+ align:start position:0%
+I want you ought to be aware of the
+Bitcoin minimalist and understand what
+
+ align:start position:0%
+Bitcoin minimalist and understand what
+ 
+
+ align:start position:0%
+Bitcoin minimalist and understand what
+they're saying and I would put Joe on a
+
+ align:start position:0%
+they're saying and I would put Joe on a
+ 
+
+ align:start position:0%
+they're saying and I would put Joe on a
+one to ten scale at maybe one and a half
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+or maybe two Paul you'll read Paul
+
+ align:start position:0%
+or maybe two Paul you'll read Paul
+ 
+
+ align:start position:0%
+or maybe two Paul you'll read Paul
+Krugman's piece a little later he's kind
+
+ align:start position:0%
+Krugman's piece a little later he's kind
+ 
+
+ align:start position:0%
+Krugman's piece a little later he's kind
+of down there too I can't just they
+
+ align:start position:0%
+of down there too I can't just they
+ 
+
+ align:start position:0%
+of down there too I can't just they
+can't modulate between them but I think
+
+ align:start position:0%
+can't modulate between them but I think
+ 
+
+ align:start position:0%
+can't modulate between them but I think
+it's really important to understand what
+
+ align:start position:0%
+it's really important to understand what
+ 
+
+ align:start position:0%
+it's really important to understand what
+some really great minds are thinking
+
+ align:start position:0%
+some really great minds are thinking
+ 
+
+ align:start position:0%
+some really great minds are thinking
+about this from that side as well so
+
+ align:start position:0%
+about this from that side as well so
+ 
+
+ align:start position:0%
+about this from that side as well so
+that's what the three things are for
+
+ align:start position:0%
+that's what the three things are for
+ 
+
+ align:start position:0%
+that's what the three things are for
+next week and then the conclusion I
+
+ align:start position:0%
+next week and then the conclusion I
+ 
+
+ align:start position:0%
+next week and then the conclusion I
+think that it does provide the
+
+ align:start position:0%
+think that it does provide the
+ 
+
+ align:start position:0%
+think that it does provide the
+networking but it comes with cost as we
+
+ align:start position:0%
+networking but it comes with cost as we
+ 
+
+ align:start position:0%
+networking but it comes with cost as we
+said they're a bunch of trade offs
+
+ align:start position:0%
+said they're a bunch of trade offs
+ 
+
+ align:start position:0%
+said they're a bunch of trade offs
+I think the scalability the efficiency
+
+ align:start position:0%
+I think the scalability the efficiency
+ 
+
+ align:start position:0%
+I think the scalability the efficiency
+the privacy the ones are solvable I
+
+ align:start position:0%
+the privacy the ones are solvable I
+ 
+
+ align:start position:0%
+the privacy the ones are solvable I
+can't prove it but I think in a matter
+
+ align:start position:0%
+can't prove it but I think in a matter
+ 
+
+ align:start position:0%
+can't prove it but I think in a matter
+of years and it might be three or ten
+
+ align:start position:0%
+of years and it might be three or ten
+ 
+
+ align:start position:0%
+of years and it might be three or ten
+years it won't be three to ten months
+
+ align:start position:0%
+years it won't be three to ten months
+ 
+
+ align:start position:0%
+years it won't be three to ten months
+though I think a lot of that is
+
+ align:start position:0%
+though I think a lot of that is
+ 
+
+ align:start position:0%
+though I think a lot of that is
+susceptible to the bright minds of MIT
+
+ align:start position:0%
+susceptible to the bright minds of MIT
+ 
+
+ align:start position:0%
+susceptible to the bright minds of MIT
+and elsewhere as computer scientists I
+
+ align:start position:0%
+and elsewhere as computer scientists I
+ 
+
+ align:start position:0%
+and elsewhere as computer scientists I
+think the challenges that are tougher
+
+ align:start position:0%
+think the challenges that are tougher
+ 
+
+ align:start position:0%
+think the challenges that are tougher
+it really relates to governance
+
+ align:start position:0%
+it really relates to governance
+ 
+
+ align:start position:0%
+it really relates to governance
+I think governance and collective action
+
+ align:start position:0%
+I think governance and collective action
+ 
+
+ align:start position:0%
+I think governance and collective action
+and back to those two graphs there
+
+ align:start position:0%
+and back to those two graphs there
+ 
+
+ align:start position:0%
+and back to those two graphs there
+really are places that are better to
+
+ align:start position:0%
+really are places that are better to
+ 
+
+ align:start position:0%
+really are places that are better to
+centralize then decentralize and we're
+
+ align:start position:0%
+centralize then decentralize and we're
+ 
+
+ align:start position:0%
+centralize then decentralize and we're
+gonna be exploring that for the rest of
+
+ align:start position:0%
+gonna be exploring that for the rest of
+ 
+
+ align:start position:0%
+gonna be exploring that for the rest of
+the semester together so thank you thank
+
+ align:start position:0%
+the semester together so thank you thank
+ 
+
+ align:start position:0%
+the semester together so thank you thank
+you for the veterans who do sat through
+
+ align:start position:0%
+you for the veterans who do sat through
+ 
+
+ align:start position:0%
+you for the veterans who do sat through
+all that
+
+ align:start position:0%
+all that
+ 
+
+ align:start position:0%
+all that
+[Applause]
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+you
\ No newline at end of file
diff --git a/GQKFkoy4VOw.txt b/GQKFkoy4VOw.txt
new file mode 100644
index 0000000000000000000000000000000000000000..4e3ace87eae2f308d52a80259c6d8054c7ff5b74
--- /dev/null
+++ b/GQKFkoy4VOw.txt
@@ -0,0 +1,6091 @@
+align:start position:0%
+ 
+the following content is provided under
+
+ align:start position:0%
+the following content is provided under
+ 
+
+ align:start position:0%
+the following content is provided under
+a Creative Commons license your support
+
+ align:start position:0%
+a Creative Commons license your support
+ 
+
+ align:start position:0%
+a Creative Commons license your support
+will help MIT open courseware continue
+
+ align:start position:0%
+will help MIT open courseware continue
+ 
+
+ align:start position:0%
+will help MIT open courseware continue
+to offer highquality educational
+
+ align:start position:0%
+to offer highquality educational
+ 
+
+ align:start position:0%
+to offer highquality educational
+resources for free to make a donation or
+
+ align:start position:0%
+resources for free to make a donation or
+ 
+
+ align:start position:0%
+resources for free to make a donation or
+view additional materials from hundreds
+
+ align:start position:0%
+view additional materials from hundreds
+ 
+
+ align:start position:0%
+view additional materials from hundreds
+of MIT courses visit MIT opencourseware
+
+ align:start position:0%
+of MIT courses visit MIT opencourseware
+ 
+
+ align:start position:0%
+of MIT courses visit MIT opencourseware
+at ocw.mit.edu
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+hi today we begin our discussion of
+
+ align:start position:0%
+hi today we begin our discussion of
+ 
+
+ align:start position:0%
+hi today we begin our discussion of
+differential equations it has been said
+
+ align:start position:0%
+differential equations it has been said
+ 
+
+ align:start position:0%
+differential equations it has been said
+that the language of the universe is
+
+ align:start position:0%
+that the language of the universe is
+ 
+
+ align:start position:0%
+that the language of the universe is
+differential equations and for this
+
+ align:start position:0%
+differential equations and for this
+ 
+
+ align:start position:0%
+differential equations and for this
+reason I would suspect from a practical
+
+ align:start position:0%
+reason I would suspect from a practical
+ 
+
+ align:start position:0%
+reason I would suspect from a practical
+point of view differential equations is
+
+ align:start position:0%
+point of view differential equations is
+ 
+
+ align:start position:0%
+point of view differential equations is
+most important for example one is use to
+
+ align:start position:0%
+most important for example one is use to
+ 
+
+ align:start position:0%
+most important for example one is use to
+stating physical principles in terms of
+
+ align:start position:0%
+stating physical principles in terms of
+ 
+
+ align:start position:0%
+stating physical principles in terms of
+rates of change to say for example that
+
+ align:start position:0%
+rates of change to say for example that
+ 
+
+ align:start position:0%
+rates of change to say for example that
+the rate of change is proportional to
+
+ align:start position:0%
+the rate of change is proportional to
+ 
+
+ align:start position:0%
+the rate of change is proportional to
+the amount present is a rather simple
+
+ align:start position:0%
+the amount present is a rather simple
+ 
+
+ align:start position:0%
+the amount present is a rather simple
+sounding physical principle the idea is
+
+ align:start position:0%
+sounding physical principle the idea is
+ 
+
+ align:start position:0%
+sounding physical principle the idea is
+knowing that the rate of change is
+
+ align:start position:0%
+knowing that the rate of change is
+ 
+
+ align:start position:0%
+knowing that the rate of change is
+proportional to the amount present we
+
+ align:start position:0%
+proportional to the amount present we
+ 
+
+ align:start position:0%
+proportional to the amount present we
+sometimes like to find out explicitly
+
+ align:start position:0%
+sometimes like to find out explicitly
+ 
+
+ align:start position:0%
+sometimes like to find out explicitly
+what the what the amount looks like as a
+
+ align:start position:0%
+what the what the amount looks like as a
+ 
+
+ align:start position:0%
+what the what the amount looks like as a
+function of time and that's what we mean
+
+ align:start position:0%
+function of time and that's what we mean
+ 
+
+ align:start position:0%
+function of time and that's what we mean
+by a solution or a general solution to
+
+ align:start position:0%
+by a solution or a general solution to
+ 
+
+ align:start position:0%
+by a solution or a general solution to
+differential equations and that will be
+
+ align:start position:0%
+differential equations and that will be
+ 
+
+ align:start position:0%
+differential equations and that will be
+our subject for our first lesson in our
+
+ align:start position:0%
+our subject for our first lesson in our
+ 
+
+ align:start position:0%
+our subject for our first lesson in our
+study of differential equations the
+
+ align:start position:0%
+study of differential equations the
+ 
+
+ align:start position:0%
+study of differential equations the
+concept of a general solution the first
+
+ align:start position:0%
+concept of a general solution the first
+ 
+
+ align:start position:0%
+concept of a general solution the first
+and simplest type of equation that we're
+
+ align:start position:0%
+and simplest type of equation that we're
+ 
+
+ align:start position:0%
+and simplest type of equation that we're
+going to talk talk about is the
+
+ align:start position:0%
+going to talk talk about is the
+ 
+
+ align:start position:0%
+going to talk talk about is the
+differential equation which we say has
+
+ align:start position:0%
+differential equation which we say has
+ 
+
+ align:start position:0%
+differential equation which we say has
+order one in other words the greatest
+
+ align:start position:0%
+order one in other words the greatest
+ 
+
+ align:start position:0%
+order one in other words the greatest
+derivative that appears is the first
+
+ align:start position:0%
+derivative that appears is the first
+ 
+
+ align:start position:0%
+derivative that appears is the first
+derivative there are no second
+
+ align:start position:0%
+derivative there are no second
+ 
+
+ align:start position:0%
+derivative there are no second
+derivatives involved in other words a
+
+ align:start position:0%
+derivatives involved in other words a
+ 
+
+ align:start position:0%
+derivatives involved in other words a
+problem where in terms of kinematics you
+
+ align:start position:0%
+problem where in terms of kinematics you
+ 
+
+ align:start position:0%
+problem where in terms of kinematics you
+are told what the velocity looks like in
+
+ align:start position:0%
+are told what the velocity looks like in
+ 
+
+ align:start position:0%
+are told what the velocity looks like in
+terms of the time uh in other words and
+
+ align:start position:0%
+terms of the time uh in other words and
+ 
+
+ align:start position:0%
+terms of the time uh in other words and
+you want to find the answer in terms of
+
+ align:start position:0%
+you want to find the answer in terms of
+ 
+
+ align:start position:0%
+you want to find the answer in terms of
+displacement dvdt equals uh DX DT equals
+
+ align:start position:0%
+displacement dvdt equals uh DX DT equals
+ 
+
+ align:start position:0%
+displacement dvdt equals uh DX DT equals
+something find what x looks like
+
+ align:start position:0%
+something find what x looks like
+ 
+
+ align:start position:0%
+something find what x looks like
+explicitly in terms of T now in general
+
+ align:start position:0%
+explicitly in terms of T now in general
+ 
+
+ align:start position:0%
+explicitly in terms of T now in general
+what we're saying is all we know about a
+
+ align:start position:0%
+what we're saying is all we know about a
+ 
+
+ align:start position:0%
+what we're saying is all we know about a
+first order differential equation is
+
+ align:start position:0%
+first order differential equation is
+ 
+
+ align:start position:0%
+first order differential equation is
+that there is some relationship between
+
+ align:start position:0%
+that there is some relationship between
+ 
+
+ align:start position:0%
+that there is some relationship between
+the independent variable X the dependent
+
+ align:start position:0%
+the independent variable X the dependent
+ 
+
+ align:start position:0%
+the independent variable X the dependent
+variable Y and dydx and the symbolic way
+
+ align:start position:0%
+variable Y and dydx and the symbolic way
+ 
+
+ align:start position:0%
+variable Y and dydx and the symbolic way
+of writing that is to say that some
+
+ align:start position:0%
+of writing that is to say that some
+ 
+
+ align:start position:0%
+of writing that is to say that some
+functions say capital f of x y and Dy DX
+
+ align:start position:0%
+functions say capital f of x y and Dy DX
+ 
+
+ align:start position:0%
+functions say capital f of x y and Dy DX
+is zero that's just a mathematical
+
+ align:start position:0%
+is zero that's just a mathematical
+ 
+
+ align:start position:0%
+is zero that's just a mathematical
+symbolism for writing down the most
+
+ align:start position:0%
+symbolism for writing down the most
+ 
+
+ align:start position:0%
+symbolism for writing down the most
+General first order differential
+
+ align:start position:0%
+General first order differential
+ 
+
+ align:start position:0%
+General first order differential
+equation now the question that comes up
+
+ align:start position:0%
+equation now the question that comes up
+ 
+
+ align:start position:0%
+equation now the question that comes up
+is twofold one is first of all does
+
+ align:start position:0%
+is twofold one is first of all does
+ 
+
+ align:start position:0%
+is twofold one is first of all does
+equation one even have a solution how do
+
+ align:start position:0%
+equation one even have a solution how do
+ 
+
+ align:start position:0%
+equation one even have a solution how do
+we know that just because we can State
+
+ align:start position:0%
+we know that just because we can State
+ 
+
+ align:start position:0%
+we know that just because we can State
+the differential equation that there is
+
+ align:start position:0%
+the differential equation that there is
+ 
+
+ align:start position:0%
+the differential equation that there is
+a specific function say Y is a function
+
+ align:start position:0%
+a specific function say Y is a function
+ 
+
+ align:start position:0%
+a specific function say Y is a function
+of X that satisfies the equation and the
+
+ align:start position:0%
+of X that satisfies the equation and the
+ 
+
+ align:start position:0%
+of X that satisfies the equation and the
+second is assuming that there is a
+
+ align:start position:0%
+second is assuming that there is a
+ 
+
+ align:start position:0%
+second is assuming that there is a
+function y as a function of X in other
+
+ align:start position:0%
+function y as a function of X in other
+ 
+
+ align:start position:0%
+function y as a function of X in other
+words that y as a function of X does
+
+ align:start position:0%
+words that y as a function of X does
+ 
+
+ align:start position:0%
+words that y as a function of X does
+satisfy this equation how do we know
+
+ align:start position:0%
+satisfy this equation how do we know
+ 
+
+ align:start position:0%
+satisfy this equation how do we know
+that that solution is unique two
+
+ align:start position:0%
+that that solution is unique two
+ 
+
+ align:start position:0%
+that that solution is unique two
+questions does the equation have a
+
+ align:start position:0%
+questions does the equation have a
+ 
+
+ align:start position:0%
+questions does the equation have a
+solution is the solution unique and I
+
+ align:start position:0%
+solution is the solution unique and I
+ 
+
+ align:start position:0%
+solution is the solution unique and I
+think that the easiest way way to
+
+ align:start position:0%
+think that the easiest way way to
+ 
+
+ align:start position:0%
+think that the easiest way way to
+illustrate this is in terms of part one
+
+ align:start position:0%
+illustrate this is in terms of part one
+ 
+
+ align:start position:0%
+illustrate this is in terms of part one
+of our course where we already solved a
+
+ align:start position:0%
+of our course where we already solved a
+ 
+
+ align:start position:0%
+of our course where we already solved a
+rather simple type of differential
+
+ align:start position:0%
+rather simple type of differential
+ 
+
+ align:start position:0%
+rather simple type of differential
+equation namely that differential
+
+ align:start position:0%
+equation namely that differential
+ 
+
+ align:start position:0%
+equation namely that differential
+equation that had the specific form dydx
+
+ align:start position:0%
+equation that had the specific form dydx
+ 
+
+ align:start position:0%
+equation that had the specific form dydx
+is some function of X in particular
+
+ align:start position:0%
+is some function of X in particular
+ 
+
+ align:start position:0%
+is some function of X in particular
+suppose I were to say find all solutions
+
+ align:start position:0%
+suppose I were to say find all solutions
+ 
+
+ align:start position:0%
+suppose I were to say find all solutions
+of dydx = 2x uh and I'll just add on
+
+ align:start position:0%
+of dydx = 2x uh and I'll just add on
+ 
+
+ align:start position:0%
+of dydx = 2x uh and I'll just add on
+here which pass through a particular
+
+ align:start position:0%
+here which pass through a particular
+ 
+
+ align:start position:0%
+here which pass through a particular
+Point x0 y z I'll come back to that in a
+
+ align:start position:0%
+Point x0 y z I'll come back to that in a
+ 
+
+ align:start position:0%
+Point x0 y z I'll come back to that in a
+moment by the way notice what I mean by
+
+ align:start position:0%
+moment by the way notice what I mean by
+ 
+
+ align:start position:0%
+moment by the way notice what I mean by
+an explicit solution if somebody says to
+
+ align:start position:0%
+an explicit solution if somebody says to
+ 
+
+ align:start position:0%
+an explicit solution if somebody says to
+me find all functions y such that Dy DX
+
+ align:start position:0%
+me find all functions y such that Dy DX
+ 
+
+ align:start position:0%
+me find all functions y such that Dy DX
+equal 2x in the language of sets notice
+
+ align:start position:0%
+equal 2x in the language of sets notice
+ 
+
+ align:start position:0%
+equal 2x in the language of sets notice
+that somebody could get kind of cute
+
+ align:start position:0%
+that somebody could get kind of cute
+ 
+
+ align:start position:0%
+that somebody could get kind of cute
+with us and say G isn't that just a set
+
+ align:start position:0%
+with us and say G isn't that just a set
+ 
+
+ align:start position:0%
+with us and say G isn't that just a set
+of all functions y such that dydx equal
+
+ align:start position:0%
+of all functions y such that dydx equal
+ 
+
+ align:start position:0%
+of all functions y such that dydx equal
+2X and the answer is that is correct of
+
+ align:start position:0%
+2X and the answer is that is correct of
+ 
+
+ align:start position:0%
+2X and the answer is that is correct of
+course that's the answer but what we
+
+ align:start position:0%
+course that's the answer but what we
+ 
+
+ align:start position:0%
+course that's the answer but what we
+mean is we would like to know what y
+
+ align:start position:0%
+mean is we would like to know what y
+ 
+
+ align:start position:0%
+mean is we would like to know what y
+looks like explicitly in terms of X in
+
+ align:start position:0%
+looks like explicitly in terms of X in
+ 
+
+ align:start position:0%
+looks like explicitly in terms of X in
+other words given x what is y this only
+
+ align:start position:0%
+other words given x what is y this only
+ 
+
+ align:start position:0%
+other words given x what is y this only
+tells me what dyd looks like explicitly
+
+ align:start position:0%
+tells me what dyd looks like explicitly
+ 
+
+ align:start position:0%
+tells me what dyd looks like explicitly
+in terms of X so what I am really
+
+ align:start position:0%
+in terms of X so what I am really
+ 
+
+ align:start position:0%
+in terms of X so what I am really
+interested in problems of this type is
+
+ align:start position:0%
+interested in problems of this type is
+ 
+
+ align:start position:0%
+interested in problems of this type is
+to convert from the set builder this
+
+ align:start position:0%
+to convert from the set builder this
+ 
+
+ align:start position:0%
+to convert from the set builder this
+implicit solution set to an explicit
+
+ align:start position:0%
+implicit solution set to an explicit
+ 
+
+ align:start position:0%
+implicit solution set to an explicit
+solution set and as a trivial review
+
+ align:start position:0%
+solution set and as a trivial review
+ 
+
+ align:start position:0%
+solution set and as a trivial review
+recall that in this case we knew that if
+
+ align:start position:0%
+recall that in this case we knew that if
+ 
+
+ align:start position:0%
+recall that in this case we knew that if
+Dy DX was 2x then y had to be x^2 + C in
+
+ align:start position:0%
+Dy DX was 2x then y had to be x^2 + C in
+ 
+
+ align:start position:0%
+Dy DX was 2x then y had to be x^2 + C in
+other words the solution set s written
+
+ align:start position:0%
+other words the solution set s written
+ 
+
+ align:start position:0%
+other words the solution set s written
+in explicit form is the set of all y
+
+ align:start position:0%
+in explicit form is the set of all y
+ 
+
+ align:start position:0%
+in explicit form is the set of all y
+such that y = x^2 + C and I suppose if
+
+ align:start position:0%
+such that y = x^2 + C and I suppose if
+ 
+
+ align:start position:0%
+such that y = x^2 + C and I suppose if
+you wanted another definition of what it
+
+ align:start position:0%
+you wanted another definition of what it
+ 
+
+ align:start position:0%
+you wanted another definition of what it
+means to solve a differential equation
+
+ align:start position:0%
+means to solve a differential equation
+ 
+
+ align:start position:0%
+means to solve a differential equation
+why couldn't we just say just like we do
+
+ align:start position:0%
+why couldn't we just say just like we do
+ 
+
+ align:start position:0%
+why couldn't we just say just like we do
+in algebra in a sense that solving a
+
+ align:start position:0%
+in algebra in a sense that solving a
+ 
+
+ align:start position:0%
+in algebra in a sense that solving a
+differential equation essentially means
+
+ align:start position:0%
+differential equation essentially means
+ 
+
+ align:start position:0%
+differential equation essentially means
+to convert from the set builder the
+
+ align:start position:0%
+to convert from the set builder the
+ 
+
+ align:start position:0%
+to convert from the set builder the
+implicit form to the explicit form so in
+
+ align:start position:0%
+implicit form to the explicit form so in
+ 
+
+ align:start position:0%
+implicit form to the explicit form so in
+other words explicitly to Express Y in
+
+ align:start position:0%
+other words explicitly to Express Y in
+ 
+
+ align:start position:0%
+other words explicitly to Express Y in
+terms of X the set of all y such that y
+
+ align:start position:0%
+terms of X the set of all y such that y
+ 
+
+ align:start position:0%
+terms of X the set of all y such that y
+= x^2 + C see now I know what y looks
+
+ align:start position:0%
+= x^2 + C see now I know what y looks
+ 
+
+ align:start position:0%
+= x^2 + C see now I know what y looks
+like in terms of X up to an arbitrary
+
+ align:start position:0%
+like in terms of X up to an arbitrary
+ 
+
+ align:start position:0%
+like in terms of X up to an arbitrary
+constant is the solution set of the
+
+ align:start position:0%
+constant is the solution set of the
+ 
+
+ align:start position:0%
+constant is the solution set of the
+differential equation dydx = 2x now you
+
+ align:start position:0%
+differential equation dydx = 2x now you
+ 
+
+ align:start position:0%
+differential equation dydx = 2x now you
+may have noticed I said as part of the
+
+ align:start position:0%
+may have noticed I said as part of the
+ 
+
+ align:start position:0%
+may have noticed I said as part of the
+problem let's see if there is a solution
+
+ align:start position:0%
+problem let's see if there is a solution
+ 
+
+ align:start position:0%
+problem let's see if there is a solution
+which passes through a particular Point
+
+ align:start position:0%
+which passes through a particular Point
+ 
+
+ align:start position:0%
+which passes through a particular Point
+x0 y0 what I do is is I look at this
+
+ align:start position:0%
+x0 y0 what I do is is I look at this
+ 
+
+ align:start position:0%
+x0 y0 what I do is is I look at this
+particular equation and I replace X by
+
+ align:start position:0%
+particular equation and I replace X by
+ 
+
+ align:start position:0%
+particular equation and I replace X by
+x0 and Y by y0 and solve for C and by
+
+ align:start position:0%
+x0 and Y by y0 and solve for C and by
+ 
+
+ align:start position:0%
+x0 and Y by y0 and solve for C and by
+the way I would intuitively expect to be
+
+ align:start position:0%
+the way I would intuitively expect to be
+ 
+
+ align:start position:0%
+the way I would intuitively expect to be
+able to find that value of C because
+
+ align:start position:0%
+able to find that value of C because
+ 
+
+ align:start position:0%
+able to find that value of C because
+after all I have an arbitrary constant
+
+ align:start position:0%
+after all I have an arbitrary constant
+ 
+
+ align:start position:0%
+after all I have an arbitrary constant
+in here which means I have a degree of
+
+ align:start position:0%
+in here which means I have a degree of
+ 
+
+ align:start position:0%
+in here which means I have a degree of
+freedom and therefore I would suspect
+
+ align:start position:0%
+freedom and therefore I would suspect
+ 
+
+ align:start position:0%
+freedom and therefore I would suspect
+that by replacing X by x0 and Y by y z I
+
+ align:start position:0%
+that by replacing X by x0 and Y by y z I
+ 
+
+ align:start position:0%
+that by replacing X by x0 and Y by y z I
+should be able to find a specific value
+
+ align:start position:0%
+should be able to find a specific value
+ 
+
+ align:start position:0%
+should be able to find a specific value
+of C now notice what this leads to if I
+
+ align:start position:0%
+of C now notice what this leads to if I
+ 
+
+ align:start position:0%
+of C now notice what this leads to if I
+replace X by x0 y by y0 I get y0 = x02 +
+
+ align:start position:0%
+replace X by x0 y by y0 I get y0 = x02 +
+ 
+
+ align:start position:0%
+replace X by x0 y by y0 I get y0 = x02 +
+C consequently C is y0 - x 0^ 2 x0 and
+
+ align:start position:0%
+C consequently C is y0 - x 0^ 2 x0 and
+ 
+
+ align:start position:0%
+C consequently C is y0 - x 0^ 2 x0 and
+y0 were specific numbers real numbers
+
+ align:start position:0%
+y0 were specific numbers real numbers
+ 
+
+ align:start position:0%
+y0 were specific numbers real numbers
+consequently y0 - x0 2 is a specific
+
+ align:start position:0%
+consequently y0 - x0 2 is a specific
+ 
+
+ align:start position:0%
+consequently y0 - x0 2 is a specific
+number and consequently the specific
+
+ align:start position:0%
+number and consequently the specific
+ 
+
+ align:start position:0%
+number and consequently the specific
+choice of C such that the equation
+
+ align:start position:0%
+choice of C such that the equation
+ 
+
+ align:start position:0%
+choice of C such that the equation
+becomes what y = x^2 plus the constant
+
+ align:start position:0%
+becomes what y = x^2 plus the constant
+ 
+
+ align:start position:0%
+becomes what y = x^2 plus the constant
+y0 - x 0^ 2 is the only
+
+ align:start position:0%
+y0 - x 0^ 2 is the only
+ 
+
+ align:start position:0%
+y0 - x 0^ 2 is the only
+solution of what the equation dydx = 2x
+
+ align:start position:0%
+solution of what the equation dydx = 2x
+ 
+
+ align:start position:0%
+solution of what the equation dydx = 2x
+that passes through the point x0 y0 this
+
+ align:start position:0%
+that passes through the point x0 y0 this
+ 
+
+ align:start position:0%
+that passes through the point x0 y0 this
+is kind of baby stuff in terms of the
+
+ align:start position:0%
+is kind of baby stuff in terms of the
+ 
+
+ align:start position:0%
+is kind of baby stuff in terms of the
+fact that it was Elementary in part one
+
+ align:start position:0%
+fact that it was Elementary in part one
+ 
+
+ align:start position:0%
+fact that it was Elementary in part one
+of our course but remember this solution
+
+ align:start position:0%
+of our course but remember this solution
+ 
+
+ align:start position:0%
+of our course but remember this solution
+set is what it's a set of parabas which
+
+ align:start position:0%
+set is what it's a set of parabas which
+ 
+
+ align:start position:0%
+set is what it's a set of parabas which
+are essentially a a parallel family of
+
+ align:start position:0%
+are essentially a a parallel family of
+ 
+
+ align:start position:0%
+are essentially a a parallel family of
+parabas and which is sort of saying is
+
+ align:start position:0%
+parabas and which is sort of saying is
+ 
+
+ align:start position:0%
+parabas and which is sort of saying is
+Gee it seems obvious geometrically that
+
+ align:start position:0%
+Gee it seems obvious geometrically that
+ 
+
+ align:start position:0%
+Gee it seems obvious geometrically that
+since I have this infinite family of
+
+ align:start position:0%
+since I have this infinite family of
+ 
+
+ align:start position:0%
+since I have this infinite family of
+parallel parabas that specifying a point
+
+ align:start position:0%
+parallel parabas that specifying a point
+ 
+
+ align:start position:0%
+parallel parabas that specifying a point
+that has to beond the parabola uniquely
+
+ align:start position:0%
+that has to beond the parabola uniquely
+ 
+
+ align:start position:0%
+that has to beond the parabola uniquely
+determines a member of that family at
+
+ align:start position:0%
+determines a member of that family at
+ 
+
+ align:start position:0%
+determines a member of that family at
+any rate I don't want to be labor this
+
+ align:start position:0%
+any rate I don't want to be labor this
+ 
+
+ align:start position:0%
+any rate I don't want to be labor this
+point I want to get to the greater
+
+ align:start position:0%
+point I want to get to the greater
+ 
+
+ align:start position:0%
+point I want to get to the greater
+subtleties that come up in handling
+
+ align:start position:0%
+subtleties that come up in handling
+ 
+
+ align:start position:0%
+subtleties that come up in handling
+first order differential equations so
+
+ align:start position:0%
+first order differential equations so
+ 
+
+ align:start position:0%
+first order differential equations so
+I've picked a slightly tougher problem
+
+ align:start position:0%
+I've picked a slightly tougher problem
+ 
+
+ align:start position:0%
+I've picked a slightly tougher problem
+for example two example two and by the
+
+ align:start position:0%
+for example two example two and by the
+ 
+
+ align:start position:0%
+for example two example two and by the
+way this is a special equation I've
+
+ align:start position:0%
+way this is a special equation I've
+ 
+
+ align:start position:0%
+way this is a special equation I've
+picked it's known as Claro's equation
+
+ align:start position:0%
+picked it's known as Claro's equation
+ 
+
+ align:start position:0%
+picked it's known as Claro's equation
+and the equation is this it's y = x dydx
+
+ align:start position:0%
+and the equation is this it's y = x dydx
+ 
+
+ align:start position:0%
+and the equation is this it's y = x dydx
+minus Dy dx^ 2 Claro's equation is any
+
+ align:start position:0%
+minus Dy dx^ 2 Claro's equation is any
+ 
+
+ align:start position:0%
+minus Dy dx^ 2 Claro's equation is any
+equation which has the form y = x * Dy
+
+ align:start position:0%
+equation which has the form y = x * Dy
+ 
+
+ align:start position:0%
+equation which has the form y = x * Dy
+DX plus something which depends only on
+
+ align:start position:0%
+DX plus something which depends only on
+ 
+
+ align:start position:0%
+DX plus something which depends only on
+Dy DX in other words rather than write
+
+ align:start position:0%
+Dy DX in other words rather than write
+ 
+
+ align:start position:0%
+Dy DX in other words rather than write
+this uh in an abstract form I decided to
+
+ align:start position:0%
+this uh in an abstract form I decided to
+ 
+
+ align:start position:0%
+this uh in an abstract form I decided to
+pick a particular application of this
+
+ align:start position:0%
+pick a particular application of this
+ 
+
+ align:start position:0%
+pick a particular application of this
+and that is let's just pick this
+
+ align:start position:0%
+and that is let's just pick this
+ 
+
+ align:start position:0%
+and that is let's just pick this
+particular example that's one special
+
+ align:start position:0%
+particular example that's one special
+ 
+
+ align:start position:0%
+particular example that's one special
+form of claro equation that's what y = x
+
+ align:start position:0%
+form of claro equation that's what y = x
+ 
+
+ align:start position:0%
+form of claro equation that's what y = x
+dydx minus Dy dx^ 2 x * Dy DX and what's
+
+ align:start position:0%
+dydx minus Dy dx^ 2 x * Dy DX and what's
+ 
+
+ align:start position:0%
+dydx minus Dy dx^ 2 x * Dy DX and what's
+left is a function of dydx alone at any
+
+ align:start position:0%
+left is a function of dydx alone at any
+ 
+
+ align:start position:0%
+left is a function of dydx alone at any
+rate it turns out that that one explicit
+
+ align:start position:0%
+rate it turns out that that one explicit
+ 
+
+ align:start position:0%
+rate it turns out that that one explicit
+solution of claro equation is very
+
+ align:start position:0%
+solution of claro equation is very
+ 
+
+ align:start position:0%
+solution of claro equation is very
+interesting thing is you simply replace
+
+ align:start position:0%
+interesting thing is you simply replace
+ 
+
+ align:start position:0%
+interesting thing is you simply replace
+dydx by C very amazing thing in other
+
+ align:start position:0%
+dydx by C very amazing thing in other
+ 
+
+ align:start position:0%
+dydx by C very amazing thing in other
+words if you have a claro equation and
+
+ align:start position:0%
+words if you have a claro equation and
+ 
+
+ align:start position:0%
+words if you have a claro equation and
+you want a solution every place you see
+
+ align:start position:0%
+you want a solution every place you see
+ 
+
+ align:start position:0%
+you want a solution every place you see
+dydx replace it by C for example in this
+
+ align:start position:0%
+dydx replace it by C for example in this
+ 
+
+ align:start position:0%
+dydx replace it by C for example in this
+case I would get what Y is equal to XC
+
+ align:start position:0%
+case I would get what Y is equal to XC
+ 
+
+ align:start position:0%
+case I would get what Y is equal to XC
+or CX I guess you like to write the
+
+ align:start position:0%
+or CX I guess you like to write the
+ 
+
+ align:start position:0%
+or CX I guess you like to write the
+constant first CX - c^ 2 which by the
+
+ align:start position:0%
+constant first CX - c^ 2 which by the
+ 
+
+ align:start position:0%
+constant first CX - c^ 2 which by the
+way is what a straight line whose slope
+
+ align:start position:0%
+way is what a straight line whose slope
+ 
+
+ align:start position:0%
+way is what a straight line whose slope
+is C and whose intercept is minus c^2 by
+
+ align:start position:0%
+is C and whose intercept is minus c^2 by
+ 
+
+ align:start position:0%
+is C and whose intercept is minus c^2 by
+the way the proof that this is is a
+
+ align:start position:0%
+the way the proof that this is is a
+ 
+
+ align:start position:0%
+the way the proof that this is is a
+solution is simply differentiate this
+
+ align:start position:0%
+solution is simply differentiate this
+ 
+
+ align:start position:0%
+solution is simply differentiate this
+you get that Dy DX equal C since C is
+
+ align:start position:0%
+you get that Dy DX equal C since C is
+ 
+
+ align:start position:0%
+you get that Dy DX equal C since C is
+dydx every place you see a c replace it
+
+ align:start position:0%
+dydx every place you see a c replace it
+ 
+
+ align:start position:0%
+dydx every place you see a c replace it
+by Dy DX and that will give you what y =
+
+ align:start position:0%
+by Dy DX and that will give you what y =
+ 
+
+ align:start position:0%
+by Dy DX and that will give you what y =
+x dydx minus Dy dx^ 2 I'll give you more
+
+ align:start position:0%
+x dydx minus Dy dx^ 2 I'll give you more
+ 
+
+ align:start position:0%
+x dydx minus Dy dx^ 2 I'll give you more
+on that in the exercises on how one
+
+ align:start position:0%
+on that in the exercises on how one
+ 
+
+ align:start position:0%
+on that in the exercises on how one
+solves claro equations I want it for
+
+ align:start position:0%
+solves claro equations I want it for
+ 
+
+ align:start position:0%
+solves claro equations I want it for
+illustrative purposes here so anyway
+
+ align:start position:0%
+illustrative purposes here so anyway
+ 
+
+ align:start position:0%
+illustrative purposes here so anyway
+this is a solution of this particular
+
+ align:start position:0%
+this is a solution of this particular
+ 
+
+ align:start position:0%
+this is a solution of this particular
+equation and it's only one solution I I
+
+ align:start position:0%
+equation and it's only one solution I I
+ 
+
+ align:start position:0%
+equation and it's only one solution I I
+don't know if there are other Solutions
+
+ align:start position:0%
+don't know if there are other Solutions
+ 
+
+ align:start position:0%
+don't know if there are other Solutions
+or what have you the next question that
+
+ align:start position:0%
+or what have you the next question that
+ 
+
+ align:start position:0%
+or what have you the next question that
+I would investigate here just as in the
+
+ align:start position:0%
+I would investigate here just as in the
+ 
+
+ align:start position:0%
+I would investigate here just as in the
+previous case I would say G I wonder
+
+ align:start position:0%
+previous case I would say G I wonder
+ 
+
+ align:start position:0%
+previous case I would say G I wonder
+what C must be if I want a solution
+
+ align:start position:0%
+what C must be if I want a solution
+ 
+
+ align:start position:0%
+what C must be if I want a solution
+curve to pass through the point x0 y0 in
+
+ align:start position:0%
+curve to pass through the point x0 y0 in
+ 
+
+ align:start position:0%
+curve to pass through the point x0 y0 in
+the XY
+
+ align:start position:0%
+the XY
+ 
+
+ align:start position:0%
+the XY
+plane so what I do purely algebraically
+
+ align:start position:0%
+plane so what I do purely algebraically
+ 
+
+ align:start position:0%
+plane so what I do purely algebraically
+is I replace X by x0 y by y0 and solve
+
+ align:start position:0%
+is I replace X by x0 y by y0 and solve
+ 
+
+ align:start position:0%
+is I replace X by x0 y by y0 and solve
+the resulting equation for C namely y0 =
+
+ align:start position:0%
+the resulting equation for C namely y0 =
+ 
+
+ align:start position:0%
+the resulting equation for C namely y0 =
+x0 cus c^ 2 and I now observe remember X
+
+ align:start position:0%
+x0 cus c^ 2 and I now observe remember X
+ 
+
+ align:start position:0%
+x0 cus c^ 2 and I now observe remember X
+and Y look like variables with the
+
+ align:start position:0%
+and Y look like variables with the
+ 
+
+ align:start position:0%
+and Y look like variables with the
+subscript zero they represent fixed X
+
+ align:start position:0%
+subscript zero they represent fixed X
+ 
+
+ align:start position:0%
+subscript zero they represent fixed X
+and Y coordinates of a point C is the
+
+ align:start position:0%
+and Y coordinates of a point C is the
+ 
+
+ align:start position:0%
+and Y coordinates of a point C is the
+only variable in here in other words
+
+ align:start position:0%
+only variable in here in other words
+ 
+
+ align:start position:0%
+only variable in here in other words
+this is a quadratic equation in C and
+
+ align:start position:0%
+this is a quadratic equation in C and
+ 
+
+ align:start position:0%
+this is a quadratic equation in C and
+solving this quadratic equation by the
+
+ align:start position:0%
+solving this quadratic equation by the
+ 
+
+ align:start position:0%
+solving this quadratic equation by the
+quadratic formula I find that c is equal
+
+ align:start position:0%
+quadratic formula I find that c is equal
+ 
+
+ align:start position:0%
+quadratic formula I find that c is equal
+to this expression here remembering that
+
+ align:start position:0%
+to this expression here remembering that
+ 
+
+ align:start position:0%
+to this expression here remembering that
+we're dealing with real variables
+
+ align:start position:0%
+we're dealing with real variables
+ 
+
+ align:start position:0%
+we're dealing with real variables
+I now know that I'm in trouble if this
+
+ align:start position:0%
+I now know that I'm in trouble if this
+ 
+
+ align:start position:0%
+I now know that I'm in trouble if this
+thing here happens to be negative in
+
+ align:start position:0%
+thing here happens to be negative in
+ 
+
+ align:start position:0%
+thing here happens to be negative in
+other words if this is negative I have
+
+ align:start position:0%
+other words if this is negative I have
+ 
+
+ align:start position:0%
+other words if this is negative I have
+an imaginary number when I take the
+
+ align:start position:0%
+an imaginary number when I take the
+ 
+
+ align:start position:0%
+an imaginary number when I take the
+square root in other words there will be
+
+ align:start position:0%
+square root in other words there will be
+ 
+
+ align:start position:0%
+square root in other words there will be
+no solution at least of this particular
+
+ align:start position:0%
+no solution at least of this particular
+ 
+
+ align:start position:0%
+no solution at least of this particular
+type there'll be no solution to this
+
+ align:start position:0%
+type there'll be no solution to this
+ 
+
+ align:start position:0%
+type there'll be no solution to this
+equation if y happens to be if y0 is
+
+ align:start position:0%
+equation if y happens to be if y0 is
+ 
+
+ align:start position:0%
+equation if y happens to be if y0 is
+greater than 1/4 x 0^ 2 and that means
+
+ align:start position:0%
+greater than 1/4 x 0^ 2 and that means
+ 
+
+ align:start position:0%
+greater than 1/4 x 0^ 2 and that means
+there will be no solution if you're
+
+ align:start position:0%
+there will be no solution if you're
+ 
+
+ align:start position:0%
+there will be no solution if you're
+above the parabola y = 1/4 X2
+
+ align:start position:0%
+above the parabola y = 1/4 X2
+ 
+
+ align:start position:0%
+above the parabola y = 1/4 X2
+remember the set of all points X comma y
+
+ align:start position:0%
+remember the set of all points X comma y
+ 
+
+ align:start position:0%
+remember the set of all points X comma y
+for which Y is greater than 1/4 x^2
+
+ align:start position:0%
+for which Y is greater than 1/4 x^2
+ 
+
+ align:start position:0%
+for which Y is greater than 1/4 x^2
+means you're above the parabola y = 1/4
+
+ align:start position:0%
+means you're above the parabola y = 1/4
+ 
+
+ align:start position:0%
+means you're above the parabola y = 1/4
+x^2 because on that Parabola since Y is
+
+ align:start position:0%
+x^2 because on that Parabola since Y is
+ 
+
+ align:start position:0%
+x^2 because on that Parabola since Y is
+equal to 1/4 x^2 you would have to go
+
+ align:start position:0%
+equal to 1/4 x^2 you would have to go
+ 
+
+ align:start position:0%
+equal to 1/4 x^2 you would have to go
+above that to make y greater than 1/4
+
+ align:start position:0%
+above that to make y greater than 1/4
+ 
+
+ align:start position:0%
+above that to make y greater than 1/4
+x^2 by the way you see all this proves
+
+ align:start position:0%
+x^2 by the way you see all this proves
+ 
+
+ align:start position:0%
+x^2 by the way you see all this proves
+is that there is no solution of this
+
+ align:start position:0%
+is that there is no solution of this
+ 
+
+ align:start position:0%
+is that there is no solution of this
+type to this particular equation if
+
+ align:start position:0%
+type to this particular equation if
+ 
+
+ align:start position:0%
+type to this particular equation if
+you're above the parabola y = 1/4x squ
+
+ align:start position:0%
+you're above the parabola y = 1/4x squ
+ 
+
+ align:start position:0%
+you're above the parabola y = 1/4x squ
+the question is what if I didn't give
+
+ align:start position:0%
+the question is what if I didn't give
+ 
+
+ align:start position:0%
+the question is what if I didn't give
+you this as a hint suppose I just gave
+
+ align:start position:0%
+you this as a hint suppose I just gave
+ 
+
+ align:start position:0%
+you this as a hint suppose I just gave
+you this equation didn't even give you a
+
+ align:start position:0%
+you this equation didn't even give you a
+ 
+
+ align:start position:0%
+you this equation didn't even give you a
+hint as to what the solution should be
+
+ align:start position:0%
+hint as to what the solution should be
+ 
+
+ align:start position:0%
+hint as to what the solution should be
+and just said tell me where there will
+
+ align:start position:0%
+and just said tell me where there will
+ 
+
+ align:start position:0%
+and just said tell me where there will
+be Solutions notice that you did not
+
+ align:start position:0%
+be Solutions notice that you did not
+ 
+
+ align:start position:0%
+be Solutions notice that you did not
+need this piece of information to get
+
+ align:start position:0%
+need this piece of information to get
+ 
+
+ align:start position:0%
+need this piece of information to get
+started on this problem namely all you
+
+ align:start position:0%
+started on this problem namely all you
+ 
+
+ align:start position:0%
+started on this problem namely all you
+had to say was G this is a quadratic
+
+ align:start position:0%
+had to say was G this is a quadratic
+ 
+
+ align:start position:0%
+had to say was G this is a quadratic
+equation in dydx let me solve this
+
+ align:start position:0%
+equation in dydx let me solve this
+ 
+
+ align:start position:0%
+equation in dydx let me solve this
+quadratic equation see what I could have
+
+ align:start position:0%
+quadratic equation see what I could have
+ 
+
+ align:start position:0%
+quadratic equation see what I could have
+done was what I could have said Dy dx^ 2
+
+ align:start position:0%
+done was what I could have said Dy dx^ 2
+ 
+
+ align:start position:0%
+done was what I could have said Dy dx^ 2
+- x Dy DX + y = 0 and then solve that
+
+ align:start position:0%
+- x Dy DX + y = 0 and then solve that
+ 
+
+ align:start position:0%
+- x Dy DX + y = 0 and then solve that
+equation for dydx without boring you
+
+ align:start position:0%
+equation for dydx without boring you
+ 
+
+ align:start position:0%
+equation for dydx without boring you
+with the details of the quadratic
+
+ align:start position:0%
+with the details of the quadratic
+ 
+
+ align:start position:0%
+with the details of the quadratic
+formula all over again it would have
+
+ align:start position:0%
+formula all over again it would have
+ 
+
+ align:start position:0%
+formula all over again it would have
+turned out more generally that Dy DX is
+
+ align:start position:0%
+turned out more generally that Dy DX is
+ 
+
+ align:start position:0%
+turned out more generally that Dy DX is
+equal to X plus or minus the < TK of x^2
+
+ align:start position:0%
+equal to X plus or minus the < TK of x^2
+ 
+
+ align:start position:0%
+equal to X plus or minus the < TK of x^2
+- 4 y / 2 and then I would have seen
+
+ align:start position:0%
+- 4 y / 2 and then I would have seen
+ 
+
+ align:start position:0%
+- 4 y / 2 and then I would have seen
+right from
+
+ align:start position:0%
+right from
+ 
+
+ align:start position:0%
+right from
+this without even knowing where the
+
+ align:start position:0%
+this without even knowing where the
+ 
+
+ align:start position:0%
+this without even knowing where the
+solution was that Dy DX isn't even a
+
+ align:start position:0%
+solution was that Dy DX isn't even a
+ 
+
+ align:start position:0%
+solution was that Dy DX isn't even a
+real number remember Dy DX geometrically
+
+ align:start position:0%
+real number remember Dy DX geometrically
+ 
+
+ align:start position:0%
+real number remember Dy DX geometrically
+is slope and slope is real so this
+
+ align:start position:0%
+is slope and slope is real so this
+ 
+
+ align:start position:0%
+is slope and slope is real so this
+wouldn't even be a real number if y was
+
+ align:start position:0%
+wouldn't even be a real number if y was
+ 
+
+ align:start position:0%
+wouldn't even be a real number if y was
+greater than 1/4 x^2 so no matter what
+
+ align:start position:0%
+greater than 1/4 x^2 so no matter what
+ 
+
+ align:start position:0%
+greater than 1/4 x^2 so no matter what
+the solution is the geometry of this
+
+ align:start position:0%
+the solution is the geometry of this
+ 
+
+ align:start position:0%
+the solution is the geometry of this
+problem tells me there can be no
+
+ align:start position:0%
+problem tells me there can be no
+ 
+
+ align:start position:0%
+problem tells me there can be no
+solution if Y is greater than 1/4 x^2
+
+ align:start position:0%
+solution if Y is greater than 1/4 x^2
+ 
+
+ align:start position:0%
+solution if Y is greater than 1/4 x^2
+and what that means is if I draw the
+
+ align:start position:0%
+and what that means is if I draw the
+ 
+
+ align:start position:0%
+and what that means is if I draw the
+graph now see in other words this is the
+
+ align:start position:0%
+graph now see in other words this is the
+ 
+
+ align:start position:0%
+graph now see in other words this is the
+x axis the Y AIS this is the the
+
+ align:start position:0%
+x axis the Y AIS this is the the
+ 
+
+ align:start position:0%
+x axis the Y AIS this is the the
+parabola yal 4x^2 there are no solutions
+
+ align:start position:0%
+parabola yal 4x^2 there are no solutions
+ 
+
+ align:start position:0%
+parabola yal 4x^2 there are no solutions
+that pass through any points in here no
+
+ align:start position:0%
+that pass through any points in here no
+ 
+
+ align:start position:0%
+that pass through any points in here no
+Solutions in here by the way the plus or
+
+ align:start position:0%
+Solutions in here by the way the plus or
+ 
+
+ align:start position:0%
+Solutions in here by the way the plus or
+minus sign here is relatively
+
+ align:start position:0%
+minus sign here is relatively
+ 
+
+ align:start position:0%
+minus sign here is relatively
+unimportant what it means is dydx is a
+
+ align:start position:0%
+unimportant what it means is dydx is a
+ 
+
+ align:start position:0%
+unimportant what it means is dydx is a
+double valued function we we would solve
+
+ align:start position:0%
+double valued function we we would solve
+ 
+
+ align:start position:0%
+double valued function we we would solve
+this in real life as two separate
+
+ align:start position:0%
+this in real life as two separate
+ 
+
+ align:start position:0%
+this in real life as two separate
+problems namely dydx = X plus the squ <
+
+ align:start position:0%
+problems namely dydx = X plus the squ <
+ 
+
+ align:start position:0%
+problems namely dydx = X plus the squ <
+TK x^2 - 4 Y /2 and dydx is x - the < TK
+
+ align:start position:0%
+TK x^2 - 4 Y /2 and dydx is x - the < TK
+ 
+
+ align:start position:0%
+TK x^2 - 4 Y /2 and dydx is x - the < TK
+of x^2 - 4 y/2 notice that that the plus
+
+ align:start position:0%
+of x^2 - 4 y/2 notice that that the plus
+ 
+
+ align:start position:0%
+of x^2 - 4 y/2 notice that that the plus
+of minus sign has no bearing on the fact
+
+ align:start position:0%
+of minus sign has no bearing on the fact
+ 
+
+ align:start position:0%
+of minus sign has no bearing on the fact
+that the crucial point is that y must be
+
+ align:start position:0%
+that the crucial point is that y must be
+ 
+
+ align:start position:0%
+that the crucial point is that y must be
+no greater than 1 4
+
+ align:start position:0%
+no greater than 1 4
+ 
+
+ align:start position:0%
+no greater than 1 4
+x^2 all right by way if you want to see
+
+ align:start position:0%
+x^2 all right by way if you want to see
+ 
+
+ align:start position:0%
+x^2 all right by way if you want to see
+this geometrically notice that y = CX -
+
+ align:start position:0%
+this geometrically notice that y = CX -
+ 
+
+ align:start position:0%
+this geometrically notice that y = CX -
+c s is what kind of a line it's the
+
+ align:start position:0%
+c s is what kind of a line it's the
+ 
+
+ align:start position:0%
+c s is what kind of a line it's the
+straight line whose Y intercept is minus
+
+ align:start position:0%
+straight line whose Y intercept is minus
+ 
+
+ align:start position:0%
+straight line whose Y intercept is minus
+c^ 2 notice that minus c s is negative
+
+ align:start position:0%
+c^ 2 notice that minus c s is negative
+ 
+
+ align:start position:0%
+c^ 2 notice that minus c s is negative
+whether C is positive or negative
+
+ align:start position:0%
+whether C is positive or negative
+ 
+
+ align:start position:0%
+whether C is positive or negative
+because the square c^ s can't be
+
+ align:start position:0%
+because the square c^ s can't be
+ 
+
+ align:start position:0%
+because the square c^ s can't be
+negative so minus c^ s can't be positive
+
+ align:start position:0%
+negative so minus c^ s can't be positive
+ 
+
+ align:start position:0%
+negative so minus c^ s can't be positive
+notice however if C is positive C is the
+
+ align:start position:0%
+notice however if C is positive C is the
+ 
+
+ align:start position:0%
+notice however if C is positive C is the
+slope of this line if C is positive the
+
+ align:start position:0%
+slope of this line if C is positive the
+ 
+
+ align:start position:0%
+slope of this line if C is positive the
+straight line goes through this point
+
+ align:start position:0%
+straight line goes through this point
+ 
+
+ align:start position:0%
+straight line goes through this point
+all right and has this slope if C is
+
+ align:start position:0%
+all right and has this slope if C is
+ 
+
+ align:start position:0%
+all right and has this slope if C is
+negative it goes through this point with
+
+ align:start position:0%
+negative it goes through this point with
+ 
+
+ align:start position:0%
+negative it goes through this point with
+this slope there's a very amazing
+
+ align:start position:0%
+this slope there's a very amazing
+ 
+
+ align:start position:0%
+this slope there's a very amazing
+property that the parabola 1/4 x^2 has
+
+ align:start position:0%
+property that the parabola 1/4 x^2 has
+ 
+
+ align:start position:0%
+property that the parabola 1/4 x^2 has
+with respect to this family of straight
+
+ align:start position:0%
+with respect to this family of straight
+ 
+
+ align:start position:0%
+with respect to this family of straight
+lines and I'll also talk about that more
+
+ align:start position:0%
+lines and I'll also talk about that more
+ 
+
+ align:start position:0%
+lines and I'll also talk about that more
+in the exercises the parabola y = 1/4
+
+ align:start position:0%
+in the exercises the parabola y = 1/4
+ 
+
+ align:start position:0%
+in the exercises the parabola y = 1/4
+x^2 is called the envelope of this
+
+ align:start position:0%
+x^2 is called the envelope of this
+ 
+
+ align:start position:0%
+x^2 is called the envelope of this
+family of straight lines the amazing
+
+ align:start position:0%
+family of straight lines the amazing
+ 
+
+ align:start position:0%
+family of straight lines the amazing
+thing is that every straight line in
+
+ align:start position:0%
+thing is that every straight line in
+ 
+
+ align:start position:0%
+thing is that every straight line in
+this family is tangent to this Parabola
+
+ align:start position:0%
+this family is tangent to this Parabola
+ 
+
+ align:start position:0%
+this family is tangent to this Parabola
+and conversely the tangent line at any
+
+ align:start position:0%
+and conversely the tangent line at any
+ 
+
+ align:start position:0%
+and conversely the tangent line at any
+point of this Parabola is a line that
+
+ align:start position:0%
+point of this Parabola is a line that
+ 
+
+ align:start position:0%
+point of this Parabola is a line that
+belongs to this family and that leads to
+
+ align:start position:0%
+belongs to this family and that leads to
+ 
+
+ align:start position:0%
+belongs to this family and that leads to
+a very remarkable thing which is not
+
+ align:start position:0%
+a very remarkable thing which is not
+ 
+
+ align:start position:0%
+a very remarkable thing which is not
+immediately intuitively obvious and that
+
+ align:start position:0%
+immediately intuitively obvious and that
+ 
+
+ align:start position:0%
+immediately intuitively obvious and that
+is in particular it must mean that the
+
+ align:start position:0%
+is in particular it must mean that the
+ 
+
+ align:start position:0%
+is in particular it must mean that the
+parabola itself must be a solution of my
+
+ align:start position:0%
+parabola itself must be a solution of my
+ 
+
+ align:start position:0%
+parabola itself must be a solution of my
+differential equation you see after all
+
+ align:start position:0%
+differential equation you see after all
+ 
+
+ align:start position:0%
+differential equation you see after all
+if I pick a point now that's on the
+
+ align:start position:0%
+if I pick a point now that's on the
+ 
+
+ align:start position:0%
+if I pick a point now that's on the
+parabola and draw the tangent line in
+
+ align:start position:0%
+parabola and draw the tangent line in
+ 
+
+ align:start position:0%
+parabola and draw the tangent line in
+here that tangent line belongs to this
+
+ align:start position:0%
+here that tangent line belongs to this
+ 
+
+ align:start position:0%
+here that tangent line belongs to this
+family because this point is on this
+
+ align:start position:0%
+family because this point is on this
+ 
+
+ align:start position:0%
+family because this point is on this
+tangent line it must be a solution to
+
+ align:start position:0%
+tangent line it must be a solution to
+ 
+
+ align:start position:0%
+tangent line it must be a solution to
+the original differential equation but
+
+ align:start position:0%
+the original differential equation but
+ 
+
+ align:start position:0%
+the original differential equation but
+that point is also on the parabola the
+
+ align:start position:0%
+that point is also on the parabola the
+ 
+
+ align:start position:0%
+that point is also on the parabola the
+point doesn't know whether I'm
+
+ align:start position:0%
+point doesn't know whether I'm
+ 
+
+ align:start position:0%
+point doesn't know whether I'm
+considering it as being part of the
+
+ align:start position:0%
+considering it as being part of the
+ 
+
+ align:start position:0%
+considering it as being part of the
+parabola or part of the uh family of
+
+ align:start position:0%
+parabola or part of the uh family of
+ 
+
+ align:start position:0%
+parabola or part of the uh family of
+straight lines consequently what it
+
+ align:start position:0%
+straight lines consequently what it
+ 
+
+ align:start position:0%
+straight lines consequently what it
+means is that this Parabola must also
+
+ align:start position:0%
+means is that this Parabola must also
+ 
+
+ align:start position:0%
+means is that this Parabola must also
+satisfy the differential equation and
+
+ align:start position:0%
+satisfy the differential equation and
+ 
+
+ align:start position:0%
+satisfy the differential equation and
+the best way of proving that is to show
+
+ align:start position:0%
+the best way of proving that is to show
+ 
+
+ align:start position:0%
+the best way of proving that is to show
+you that it does satisfy the equation
+
+ align:start position:0%
+you that it does satisfy the equation
+ 
+
+ align:start position:0%
+you that it does satisfy the equation
+namely if y = 1/4 x^2 notice that d y DX
+
+ align:start position:0%
+namely if y = 1/4 x^2 notice that d y DX
+ 
+
+ align:start position:0%
+namely if y = 1/4 x^2 notice that d y DX
+is x/ 2 consequently Dy dx^ 2 is x^2 4
+
+ align:start position:0%
+is x/ 2 consequently Dy dx^ 2 is x^2 4
+ 
+
+ align:start position:0%
+is x/ 2 consequently Dy dx^ 2 is x^2 4
+the differential equation I'm trying to
+
+ align:start position:0%
+the differential equation I'm trying to
+ 
+
+ align:start position:0%
+the differential equation I'm trying to
+satisfy is this one if I replace y by
+
+ align:start position:0%
+satisfy is this one if I replace y by
+ 
+
+ align:start position:0%
+satisfy is this one if I replace y by
+1/4 x^2 dydx by
+
+ align:start position:0%
+1/4 x^2 dydx by
+ 
+
+ align:start position:0%
+1/4 x^2 dydx by
+x/2 and look at what this says it says
+
+ align:start position:0%
+x/2 and look at what this says it says
+ 
+
+ align:start position:0%
+x/2 and look at what this says it says
+x^2 / 4 is equal to x^2 / 2 - x^2 over 4
+
+ align:start position:0%
+x^2 / 4 is equal to x^2 / 2 - x^2 over 4
+ 
+
+ align:start position:0%
+x^2 / 4 is equal to x^2 / 2 - x^2 over 4
+which of course is x^2 over 4 and indeed
+
+ align:start position:0%
+which of course is x^2 over 4 and indeed
+ 
+
+ align:start position:0%
+which of course is x^2 over 4 and indeed
+the parabola does satisfy this equation
+
+ align:start position:0%
+the parabola does satisfy this equation
+ 
+
+ align:start position:0%
+the parabola does satisfy this equation
+and now you see we've run into a very
+
+ align:start position:0%
+and now you see we've run into a very
+ 
+
+ align:start position:0%
+and now you see we've run into a very
+interesting uh situation here namely on
+
+ align:start position:0%
+interesting uh situation here namely on
+ 
+
+ align:start position:0%
+interesting uh situation here namely on
+the parabola y = 1/4 x^2 y = x Dy dxus
+
+ align:start position:0%
+the parabola y = 1/4 x^2 y = x Dy dxus
+ 
+
+ align:start position:0%
+the parabola y = 1/4 x^2 y = x Dy dxus
+Dy dx^ 2 has at least two solutions
+
+ align:start position:0%
+Dy dx^ 2 has at least two solutions
+ 
+
+ align:start position:0%
+Dy dx^ 2 has at least two solutions
+namely a member of the family of
+
+ align:start position:0%
+namely a member of the family of
+ 
+
+ align:start position:0%
+namely a member of the family of
+straight lines y = cxus c^2 and also the
+
+ align:start position:0%
+straight lines y = cxus c^2 and also the
+ 
+
+ align:start position:0%
+straight lines y = cxus c^2 and also the
+parabola y = 1/4
+
+ align:start position:0%
+parabola y = 1/4
+ 
+
+ align:start position:0%
+parabola y = 1/4
+x^2 remember at the beginning of our
+
+ align:start position:0%
+x^2 remember at the beginning of our
+ 
+
+ align:start position:0%
+x^2 remember at the beginning of our
+lecture today we mentioned two questions
+
+ align:start position:0%
+lecture today we mentioned two questions
+ 
+
+ align:start position:0%
+lecture today we mentioned two questions
+first of all does the differential
+
+ align:start position:0%
+first of all does the differential
+ 
+
+ align:start position:0%
+first of all does the differential
+equation have a solution and if it does
+
+ align:start position:0%
+equation have a solution and if it does
+ 
+
+ align:start position:0%
+equation have a solution and if it does
+have a solution is the solution unique
+
+ align:start position:0%
+have a solution is the solution unique
+ 
+
+ align:start position:0%
+have a solution is the solution unique
+what we've shown so far is that on the
+
+ align:start position:0%
+what we've shown so far is that on the
+ 
+
+ align:start position:0%
+what we've shown so far is that on the
+parabola the solution is not unique
+
+ align:start position:0%
+parabola the solution is not unique
+ 
+
+ align:start position:0%
+parabola the solution is not unique
+namely there are two solutions on the
+
+ align:start position:0%
+namely there are two solutions on the
+ 
+
+ align:start position:0%
+namely there are two solutions on the
+parabola and we've shown that above the
+
+ align:start position:0%
+parabola and we've shown that above the
+ 
+
+ align:start position:0%
+parabola and we've shown that above the
+parabola the equation has no Solutions
+
+ align:start position:0%
+parabola the equation has no Solutions
+ 
+
+ align:start position:0%
+parabola the equation has no Solutions
+consequently the answers to both
+
+ align:start position:0%
+consequently the answers to both
+ 
+
+ align:start position:0%
+consequently the answers to both
+questions one and two can be in the
+
+ align:start position:0%
+questions one and two can be in the
+ 
+
+ align:start position:0%
+questions one and two can be in the
+negative and this is what makes
+
+ align:start position:0%
+negative and this is what makes
+ 
+
+ align:start position:0%
+negative and this is what makes
+differential equations a very tough
+
+ align:start position:0%
+differential equations a very tough
+ 
+
+ align:start position:0%
+differential equations a very tough
+subject and why it's difficult to talk
+
+ align:start position:0%
+subject and why it's difficult to talk
+ 
+
+ align:start position:0%
+subject and why it's difficult to talk
+about the solution or a solution or what
+
+ align:start position:0%
+about the solution or a solution or what
+ 
+
+ align:start position:0%
+about the solution or a solution or what
+have you but fortunately there is a key
+
+ align:start position:0%
+have you but fortunately there is a key
+ 
+
+ align:start position:0%
+have you but fortunately there is a key
+theorem which we have at our disposal a
+
+ align:start position:0%
+theorem which we have at our disposal a
+ 
+
+ align:start position:0%
+theorem which we have at our disposal a
+theorem Which is far more difficult to
+
+ align:start position:0%
+theorem Which is far more difficult to
+ 
+
+ align:start position:0%
+theorem Which is far more difficult to
+prove than it is to State and memorize
+
+ align:start position:0%
+prove than it is to State and memorize
+ 
+
+ align:start position:0%
+prove than it is to State and memorize
+and I will settle right now for just
+
+ align:start position:0%
+and I will settle right now for just
+ 
+
+ align:start position:0%
+and I will settle right now for just
+stating the theorem and having you see
+
+ align:start position:0%
+stating the theorem and having you see
+ 
+
+ align:start position:0%
+stating the theorem and having you see
+what it means the key theorem is this
+
+ align:start position:0%
+what it means the key theorem is this
+ 
+
+ align:start position:0%
+what it means the key theorem is this
+let's assume for the sake of argument
+
+ align:start position:0%
+let's assume for the sake of argument
+ 
+
+ align:start position:0%
+let's assume for the sake of argument
+that we can write our differential
+
+ align:start position:0%
+that we can write our differential
+ 
+
+ align:start position:0%
+that we can write our differential
+equation explicitly in terms of dydx in
+
+ align:start position:0%
+equation explicitly in terms of dydx in
+ 
+
+ align:start position:0%
+equation explicitly in terms of dydx in
+other words that dydx is explicitly some
+
+ align:start position:0%
+other words that dydx is explicitly some
+ 
+
+ align:start position:0%
+other words that dydx is explicitly some
+function of X and Y if it turns out that
+
+ align:start position:0%
+function of X and Y if it turns out that
+ 
+
+ align:start position:0%
+function of X and Y if it turns out that
+that F and its partial with respect to Y
+
+ align:start position:0%
+that F and its partial with respect to Y
+ 
+
+ align:start position:0%
+that F and its partial with respect to Y
+are continuous in some region R then at
+
+ align:start position:0%
+are continuous in some region R then at
+ 
+
+ align:start position:0%
+are continuous in some region R then at
+each point in R there is a unique
+
+ align:start position:0%
+each point in R there is a unique
+ 
+
+ align:start position:0%
+each point in R there is a unique
+solution of dydx equal f ofx y which
+
+ align:start position:0%
+solution of dydx equal f ofx y which
+ 
+
+ align:start position:0%
+solution of dydx equal f ofx y which
+passes through x0 y0 you see notice that
+
+ align:start position:0%
+passes through x0 y0 you see notice that
+ 
+
+ align:start position:0%
+passes through x0 y0 you see notice that
+in the particular problem that we were
+
+ align:start position:0%
+in the particular problem that we were
+ 
+
+ align:start position:0%
+in the particular problem that we were
+just dealing with what was f ofx y f ofx
+
+ align:start position:0%
+just dealing with what was f ofx y f ofx
+ 
+
+ align:start position:0%
+just dealing with what was f ofx y f ofx
+y was this function here notice that f
+
+ align:start position:0%
+y was this function here notice that f
+ 
+
+ align:start position:0%
+y was this function here notice that f
+ofx y will be continuous as long as this
+
+ align:start position:0%
+ofx y will be continuous as long as this
+ 
+
+ align:start position:0%
+ofx y will be continuous as long as this
+expression exists in other words F of XY
+
+ align:start position:0%
+expression exists in other words F of XY
+ 
+
+ align:start position:0%
+expression exists in other words F of XY
+will be continuous as long as Y is less
+
+ align:start position:0%
+will be continuous as long as Y is less
+ 
+
+ align:start position:0%
+will be continuous as long as Y is less
+than or equal to 1/4 x^2 what about the
+
+ align:start position:0%
+than or equal to 1/4 x^2 what about the
+ 
+
+ align:start position:0%
+than or equal to 1/4 x^2 what about the
+partial of f respect to Y to find the
+
+ align:start position:0%
+partial of f respect to Y to find the
+ 
+
+ align:start position:0%
+partial of f respect to Y to find the
+partial of f respect to Y I have to
+
+ align:start position:0%
+partial of f respect to Y I have to
+ 
+
+ align:start position:0%
+partial of f respect to Y I have to
+differentiate this thing notice that Y
+
+ align:start position:0%
+differentiate this thing notice that Y
+ 
+
+ align:start position:0%
+differentiate this thing notice that Y
+is under the integral under the square
+
+ align:start position:0%
+is under the integral under the square
+ 
+
+ align:start position:0%
+is under the integral under the square
+root sign when I differentiate the
+
+ align:start position:0%
+root sign when I differentiate the
+ 
+
+ align:start position:0%
+root sign when I differentiate the
+square root the square root comes down
+
+ align:start position:0%
+square root the square root comes down
+ 
+
+ align:start position:0%
+square root the square root comes down
+into the denominator I can't allow a
+
+ align:start position:0%
+into the denominator I can't allow a
+ 
+
+ align:start position:0%
+into the denominator I can't allow a
+zero denominator so that tells tells me
+
+ align:start position:0%
+zero denominator so that tells tells me
+ 
+
+ align:start position:0%
+zero denominator so that tells tells me
+that not only must must y be less than
+
+ align:start position:0%
+that not only must must y be less than
+ 
+
+ align:start position:0%
+that not only must must y be less than
+or equal to 1/4 x^2 but rather y must
+
+ align:start position:0%
+or equal to 1/4 x^2 but rather y must
+ 
+
+ align:start position:0%
+or equal to 1/4 x^2 but rather y must
+be less than 1/4 x^2 because if y equal
+
+ align:start position:0%
+be less than 1/4 x^2 because if y equal
+ 
+
+ align:start position:0%
+be less than 1/4 x^2 because if y equal
+1/4 x^2 when this Factor comes down into
+
+ align:start position:0%
+1/4 x^2 when this Factor comes down into
+ 
+
+ align:start position:0%
+1/4 x^2 when this Factor comes down into
+the denominator I'm in trouble I have a
+
+ align:start position:0%
+the denominator I'm in trouble I have a
+ 
+
+ align:start position:0%
+the denominator I'm in trouble I have a
+zero denominator notice by the way the
+
+ align:start position:0%
+zero denominator notice by the way the
+ 
+
+ align:start position:0%
+zero denominator notice by the way the
+bad solution that we got in other words
+
+ align:start position:0%
+bad solution that we got in other words
+ 
+
+ align:start position:0%
+bad solution that we got in other words
+notice that where we got the two
+
+ align:start position:0%
+notice that where we got the two
+ 
+
+ align:start position:0%
+notice that where we got the two
+solutions occurred where y was equal to
+
+ align:start position:0%
+solutions occurred where y was equal to
+ 
+
+ align:start position:0%
+solutions occurred where y was equal to
+1/4 x squ and our key theorem doesn't
+
+ align:start position:0%
+1/4 x squ and our key theorem doesn't
+ 
+
+ align:start position:0%
+1/4 x squ and our key theorem doesn't
+apply in that case because notice that
+
+ align:start position:0%
+apply in that case because notice that
+ 
+
+ align:start position:0%
+apply in that case because notice that
+our key theorem says that the solution
+
+ align:start position:0%
+our key theorem says that the solution
+ 
+
+ align:start position:0%
+our key theorem says that the solution
+will be unique only in that region R
+
+ align:start position:0%
+will be unique only in that region R
+ 
+
+ align:start position:0%
+will be unique only in that region R
+where F and F suby are
+
+ align:start position:0%
+where F and F suby are
+ 
+
+ align:start position:0%
+where F and F suby are
+continuous you see notice that below the
+
+ align:start position:0%
+continuous you see notice that below the
+ 
+
+ align:start position:0%
+continuous you see notice that below the
+parabola F and F suby were continuous
+
+ align:start position:0%
+parabola F and F suby were continuous
+ 
+
+ align:start position:0%
+parabola F and F suby were continuous
+now these functions couldn't go bad in
+
+ align:start position:0%
+now these functions couldn't go bad in
+ 
+
+ align:start position:0%
+now these functions couldn't go bad in
+our problem consequently since we had
+
+ align:start position:0%
+our problem consequently since we had
+ 
+
+ align:start position:0%
+our problem consequently since we had
+one solution of the form y = CX - c^2
+
+ align:start position:0%
+one solution of the form y = CX - c^2
+ 
+
+ align:start position:0%
+one solution of the form y = CX - c^2
+that passed through every point that
+
+ align:start position:0%
+that passed through every point that
+ 
+
+ align:start position:0%
+that passed through every point that
+below the parabola the fact that this
+
+ align:start position:0%
+below the parabola the fact that this
+ 
+
+ align:start position:0%
+below the parabola the fact that this
+theorem applies says there can't be any
+
+ align:start position:0%
+theorem applies says there can't be any
+ 
+
+ align:start position:0%
+theorem applies says there can't be any
+other solution because once you found
+
+ align:start position:0%
+other solution because once you found
+ 
+
+ align:start position:0%
+other solution because once you found
+one solution that's all there are that's
+
+ align:start position:0%
+one solution that's all there are that's
+ 
+
+ align:start position:0%
+one solution that's all there are that's
+exactly what you mean by unique see in
+
+ align:start position:0%
+exactly what you mean by unique see in
+ 
+
+ align:start position:0%
+exactly what you mean by unique see in
+other words if the solution is unique
+
+ align:start position:0%
+other words if the solution is unique
+ 
+
+ align:start position:0%
+other words if the solution is unique
+then we can talk about a general
+
+ align:start position:0%
+then we can talk about a general
+ 
+
+ align:start position:0%
+then we can talk about a general
+solution namely that solution that has
+
+ align:start position:0%
+solution namely that solution that has
+ 
+
+ align:start position:0%
+solution namely that solution that has
+one arbitrary consonant we can find what
+
+ align:start position:0%
+one arbitrary consonant we can find what
+ 
+
+ align:start position:0%
+one arbitrary consonant we can find what
+point it passes through by solving for
+
+ align:start position:0%
+point it passes through by solving for
+ 
+
+ align:start position:0%
+point it passes through by solving for
+the arbitrary constant and that's what
+
+ align:start position:0%
+the arbitrary constant and that's what
+ 
+
+ align:start position:0%
+the arbitrary constant and that's what
+we mean by a particular solution in fact
+
+ align:start position:0%
+we mean by a particular solution in fact
+ 
+
+ align:start position:0%
+we mean by a particular solution in fact
+let me just summarize that for you in
+
+ align:start position:0%
+let me just summarize that for you in
+ 
+
+ align:start position:0%
+let me just summarize that for you in
+terms of our two examples by a general
+
+ align:start position:0%
+terms of our two examples by a general
+ 
+
+ align:start position:0%
+terms of our two examples by a general
+solution you mean what you mean a
+
+ align:start position:0%
+solution you mean what you mean a
+ 
+
+ align:start position:0%
+solution you mean what you mean a
+solution that has one arbitrary constant
+
+ align:start position:0%
+solution that has one arbitrary constant
+ 
+
+ align:start position:0%
+solution that has one arbitrary constant
+such that through any point in your
+
+ align:start position:0%
+such that through any point in your
+ 
+
+ align:start position:0%
+such that through any point in your
+region you can get one and only one
+
+ align:start position:0%
+region you can get one and only one
+ 
+
+ align:start position:0%
+region you can get one and only one
+solution notice that the differential
+
+ align:start position:0%
+solution notice that the differential
+ 
+
+ align:start position:0%
+solution notice that the differential
+equation Dy DX = 2x has one solution y =
+
+ align:start position:0%
+equation Dy DX = 2x has one solution y =
+ 
+
+ align:start position:0%
+equation Dy DX = 2x has one solution y =
+x^2 + C one family of solutions all
+
+ align:start position:0%
+x^2 + C one family of solutions all
+ 
+
+ align:start position:0%
+x^2 + C one family of solutions all
+right that's the general solution notice
+
+ align:start position:0%
+right that's the general solution notice
+ 
+
+ align:start position:0%
+right that's the general solution notice
+that 2x you see if f ofx X Y is 2x f is
+
+ align:start position:0%
+that 2x you see if f ofx X Y is 2x f is
+ 
+
+ align:start position:0%
+that 2x you see if f ofx X Y is 2x f is
+certainly continuous the partial of f
+
+ align:start position:0%
+certainly continuous the partial of f
+ 
+
+ align:start position:0%
+certainly continuous the partial of f
+with respect to Y since f of x y is just
+
+ align:start position:0%
+with respect to Y since f of x y is just
+ 
+
+ align:start position:0%
+with respect to Y since f of x y is just
+2x is a function of X alone the partial
+
+ align:start position:0%
+2x is a function of X alone the partial
+ 
+
+ align:start position:0%
+2x is a function of X alone the partial
+respect to Y is zero which is certainly
+
+ align:start position:0%
+respect to Y is zero which is certainly
+ 
+
+ align:start position:0%
+respect to Y is zero which is certainly
+a continuous function in other words
+
+ align:start position:0%
+a continuous function in other words
+ 
+
+ align:start position:0%
+a continuous function in other words
+that's another way of seeing what we had
+
+ align:start position:0%
+that's another way of seeing what we had
+ 
+
+ align:start position:0%
+that's another way of seeing what we had
+in part one another way of looking at it
+
+ align:start position:0%
+in part one another way of looking at it
+ 
+
+ align:start position:0%
+in part one another way of looking at it
+that's in terms of our key theorem here
+
+ align:start position:0%
+that's in terms of our key theorem here
+ 
+
+ align:start position:0%
+that's in terms of our key theorem here
+why we have a unique family of solutions
+
+ align:start position:0%
+why we have a unique family of solutions
+ 
+
+ align:start position:0%
+why we have a unique family of solutions
+that in the whole XY plane 2X and its
+
+ align:start position:0%
+that in the whole XY plane 2X and its
+ 
+
+ align:start position:0%
+that in the whole XY plane 2X and its
+partial with respect to Y happen to be
+
+ align:start position:0%
+partial with respect to Y happen to be
+ 
+
+ align:start position:0%
+partial with respect to Y happen to be
+continuous on the other hand in example
+
+ align:start position:0%
+continuous on the other hand in example
+ 
+
+ align:start position:0%
+continuous on the other hand in example
+two the general solution was y = CX -
+
+ align:start position:0%
+two the general solution was y = CX -
+ 
+
+ align:start position:0%
+two the general solution was y = CX -
+c^2 provided that our region R was
+
+ align:start position:0%
+c^2 provided that our region R was
+ 
+
+ align:start position:0%
+c^2 provided that our region R was
+restricted to being what that we were
+
+ align:start position:0%
+restricted to being what that we were
+ 
+
+ align:start position:0%
+restricted to being what that we were
+below the parabola y = 1/4 x^2 by a
+
+ align:start position:0%
+below the parabola y = 1/4 x^2 by a
+ 
+
+ align:start position:0%
+below the parabola y = 1/4 x^2 by a
+particular solution we mean a solution
+
+ align:start position:0%
+particular solution we mean a solution
+ 
+
+ align:start position:0%
+particular solution we mean a solution
+that you can get to pass through a
+
+ align:start position:0%
+that you can get to pass through a
+ 
+
+ align:start position:0%
+that you can get to pass through a
+particular point in other words by
+
+ align:start position:0%
+particular point in other words by
+ 
+
+ align:start position:0%
+particular point in other words by
+arbitrarily specifying a value of the
+
+ align:start position:0%
+arbitrarily specifying a value of the
+ 
+
+ align:start position:0%
+arbitrarily specifying a value of the
+constant for example referring to
+
+ align:start position:0%
+constant for example referring to
+ 
+
+ align:start position:0%
+constant for example referring to
+example one again if I pick C to be 7
+
+ align:start position:0%
+example one again if I pick C to be 7
+ 
+
+ align:start position:0%
+example one again if I pick C to be 7
+or- see y = x^2 + 7 y = x^2 - these are
+
+ align:start position:0%
+or- see y = x^2 + 7 y = x^2 - these are
+ 
+
+ align:start position:0%
+or- see y = x^2 + 7 y = x^2 - these are
+particular Solutions of the equation
+
+ align:start position:0%
+particular Solutions of the equation
+ 
+
+ align:start position:0%
+particular Solutions of the equation
+that we're talking about in particular
+
+ align:start position:0%
+that we're talking about in particular
+ 
+
+ align:start position:0%
+that we're talking about in particular
+what we're saying is if you want the
+
+ align:start position:0%
+what we're saying is if you want the
+ 
+
+ align:start position:0%
+what we're saying is if you want the
+particular solution see maybe I should
+
+ align:start position:0%
+particular solution see maybe I should
+ 
+
+ align:start position:0%
+particular solution see maybe I should
+emphasize that the particular solution
+
+ align:start position:0%
+emphasize that the particular solution
+ 
+
+ align:start position:0%
+emphasize that the particular solution
+that passes through the point x0 y0 your
+
+ align:start position:0%
+that passes through the point x0 y0 your
+ 
+
+ align:start position:0%
+that passes through the point x0 y0 your
+constant must be chosen to be y 0 - x 0^
+
+ align:start position:0%
+constant must be chosen to be y 0 - x 0^
+ 
+
+ align:start position:0%
+constant must be chosen to be y 0 - x 0^
+2 in example two the general solution if
+
+ align:start position:0%
+2 in example two the general solution if
+ 
+
+ align:start position:0%
+2 in example two the general solution if
+we were the right if we were below the
+
+ align:start position:0%
+we were the right if we were below the
+ 
+
+ align:start position:0%
+we were the right if we were below the
+parabola was y = CX - c^ 2 in particular
+
+ align:start position:0%
+parabola was y = CX - c^ 2 in particular
+ 
+
+ align:start position:0%
+parabola was y = CX - c^ 2 in particular
+if I were to pick C to be 3 a particular
+
+ align:start position:0%
+if I were to pick C to be 3 a particular
+ 
+
+ align:start position:0%
+if I were to pick C to be 3 a particular
+solution would be what y = 3x - 9 or to
+
+ align:start position:0%
+solution would be what y = 3x - 9 or to
+ 
+
+ align:start position:0%
+solution would be what y = 3x - 9 or to
+do this more generally given the point
+
+ align:start position:0%
+do this more generally given the point
+ 
+
+ align:start position:0%
+do this more generally given the point
+x0 y0 the particular solution of Y = CX
+
+ align:start position:0%
+x0 y0 the particular solution of Y = CX
+ 
+
+ align:start position:0%
+x0 y0 the particular solution of Y = CX
+- c^ 2 which passes through this point
+
+ align:start position:0%
+- c^ 2 which passes through this point
+ 
+
+ align:start position:0%
+- c^ 2 which passes through this point
+is determined by C being this expression
+
+ align:start position:0%
+is determined by C being this expression
+ 
+
+ align:start position:0%
+is determined by C being this expression
+where the plus or minus sign is not
+
+ align:start position:0%
+where the plus or minus sign is not
+ 
+
+ align:start position:0%
+where the plus or minus sign is not
+really ambiguous here what we me meant
+
+ align:start position:0%
+really ambiguous here what we me meant
+ 
+
+ align:start position:0%
+really ambiguous here what we me meant
+was is that when we have the plus or
+
+ align:start position:0%
+was is that when we have the plus or
+ 
+
+ align:start position:0%
+was is that when we have the plus or
+minus sign we look at this as two
+
+ align:start position:0%
+minus sign we look at this as two
+ 
+
+ align:start position:0%
+minus sign we look at this as two
+separate problems finally we come to a
+
+ align:start position:0%
+separate problems finally we come to a
+ 
+
+ align:start position:0%
+separate problems finally we come to a
+third concept that's called a singular
+
+ align:start position:0%
+third concept that's called a singular
+ 
+
+ align:start position:0%
+third concept that's called a singular
+solution a singular solution occurs only
+
+ align:start position:0%
+solution a singular solution occurs only
+ 
+
+ align:start position:0%
+solution a singular solution occurs only
+when you're in a region where F or it's
+
+ align:start position:0%
+when you're in a region where F or it's
+ 
+
+ align:start position:0%
+when you're in a region where F or it's
+partial with respect to Y are not
+
+ align:start position:0%
+partial with respect to Y are not
+ 
+
+ align:start position:0%
+partial with respect to Y are not
+continuous for example there are no
+
+ align:start position:0%
+continuous for example there are no
+ 
+
+ align:start position:0%
+continuous for example there are no
+singular solutions to example one on the
+
+ align:start position:0%
+singular solutions to example one on the
+ 
+
+ align:start position:0%
+singular solutions to example one on the
+other hand a singular solution to
+
+ align:start position:0%
+other hand a singular solution to
+ 
+
+ align:start position:0%
+other hand a singular solution to
+example 2 was y = 1/4 x^2 why do I call
+
+ align:start position:0%
+example 2 was y = 1/4 x^2 why do I call
+ 
+
+ align:start position:0%
+example 2 was y = 1/4 x^2 why do I call
+it a singular a solution let me point
+
+ align:start position:0%
+it a singular a solution let me point
+ 
+
+ align:start position:0%
+it a singular a solution let me point
+out that you there is no way of getting
+
+ align:start position:0%
+out that you there is no way of getting
+ 
+
+ align:start position:0%
+out that you there is no way of getting
+y = 1/4
+
+ align:start position:0%
+y = 1/4
+ 
+
+ align:start position:0%
+y = 1/4
+x^2 by judiciously choosing the constant
+
+ align:start position:0%
+x^2 by judiciously choosing the constant
+ 
+
+ align:start position:0%
+x^2 by judiciously choosing the constant
+c as long as C is a constant observe
+
+ align:start position:0%
+c as long as C is a constant observe
+ 
+
+ align:start position:0%
+c as long as C is a constant observe
+that for every choice of c y = CX - c^2
+
+ align:start position:0%
+that for every choice of c y = CX - c^2
+ 
+
+ align:start position:0%
+that for every choice of c y = CX - c^2
+is a straight line in particular the
+
+ align:start position:0%
+is a straight line in particular the
+ 
+
+ align:start position:0%
+is a straight line in particular the
+straight line whose slope is C and Whose
+
+ align:start position:0%
+straight line whose slope is C and Whose
+ 
+
+ align:start position:0%
+straight line whose slope is C and Whose
+y intercept is - c^ 2 in other words I
+
+ align:start position:0%
+y intercept is - c^ 2 in other words I
+ 
+
+ align:start position:0%
+y intercept is - c^ 2 in other words I
+cannot get the curve y = 1/4 x^2 by
+
+ align:start position:0%
+cannot get the curve y = 1/4 x^2 by
+ 
+
+ align:start position:0%
+cannot get the curve y = 1/4 x^2 by
+specifying a constant here that's why
+
+ align:start position:0%
+specifying a constant here that's why
+ 
+
+ align:start position:0%
+specifying a constant here that's why
+it's called a singular solution it it
+
+ align:start position:0%
+it's called a singular solution it it
+ 
+
+ align:start position:0%
+it's called a singular solution it it
+cannot be obtained from the general
+
+ align:start position:0%
+cannot be obtained from the general
+ 
+
+ align:start position:0%
+cannot be obtained from the general
+solution but notice that that singular
+
+ align:start position:0%
+solution but notice that that singular
+ 
+
+ align:start position:0%
+solution but notice that that singular
+solution only existed because we
+
+ align:start position:0%
+solution only existed because we
+ 
+
+ align:start position:0%
+solution only existed because we
+violated the condition that our region B
+
+ align:start position:0%
+violated the condition that our region B
+ 
+
+ align:start position:0%
+violated the condition that our region B
+below the parabola in other words once
+
+ align:start position:0%
+below the parabola in other words once
+ 
+
+ align:start position:0%
+below the parabola in other words once
+we get outside of the region where F and
+
+ align:start position:0%
+we get outside of the region where F and
+ 
+
+ align:start position:0%
+we get outside of the region where F and
+F suby were continuous then mongral type
+
+ align:start position:0%
+F suby were continuous then mongral type
+ 
+
+ align:start position:0%
+F suby were continuous then mongral type
+solutions could have snuck in and those
+
+ align:start position:0%
+solutions could have snuck in and those
+ 
+
+ align:start position:0%
+solutions could have snuck in and those
+are what are called singular Solutions
+
+ align:start position:0%
+are what are called singular Solutions
+ 
+
+ align:start position:0%
+are what are called singular Solutions
+but I'll talk about those more uh in the
+
+ align:start position:0%
+but I'll talk about those more uh in the
+ 
+
+ align:start position:0%
+but I'll talk about those more uh in the
+exercise
+
+ align:start position:0%
+exercise
+ 
+
+ align:start position:0%
+exercise
+what I thought I would like to do for
+
+ align:start position:0%
+what I thought I would like to do for
+ 
+
+ align:start position:0%
+what I thought I would like to do for
+the remainder of this
+
+ align:start position:0%
+the remainder of this
+ 
+
+ align:start position:0%
+the remainder of this
+lecture is to talk specifically about
+
+ align:start position:0%
+lecture is to talk specifically about
+ 
+
+ align:start position:0%
+lecture is to talk specifically about
+what the textbook is all about and uh
+
+ align:start position:0%
+what the textbook is all about and uh
+ 
+
+ align:start position:0%
+what the textbook is all about and uh
+what we'll be dealing with for the next
+
+ align:start position:0%
+what we'll be dealing with for the next
+ 
+
+ align:start position:0%
+what we'll be dealing with for the next
+few lessons you see the next few units
+
+ align:start position:0%
+few lessons you see the next few units
+ 
+
+ align:start position:0%
+few lessons you see the next few units
+will not have any lectures this is the
+
+ align:start position:0%
+will not have any lectures this is the
+ 
+
+ align:start position:0%
+will not have any lectures this is the
+lecture that will launch you into
+
+ align:start position:0%
+lecture that will launch you into
+ 
+
+ align:start position:0%
+lecture that will launch you into
+solving first order first deegree
+
+ align:start position:0%
+solving first order first deegree
+ 
+
+ align:start position:0%
+solving first order first deegree
+equations from this point on until we
+
+ align:start position:0%
+equations from this point on until we
+ 
+
+ align:start position:0%
+equations from this point on until we
+get to uh second order equations there
+
+ align:start position:0%
+get to uh second order equations there
+ 
+
+ align:start position:0%
+get to uh second order equations there
+will be no lectures simply reading a
+
+ align:start position:0%
+will be no lectures simply reading a
+ 
+
+ align:start position:0%
+will be no lectures simply reading a
+assignments in the text and learning
+
+ align:start position:0%
+assignments in the text and learning
+ 
+
+ align:start position:0%
+assignments in the text and learning
+exercises where I'll try to give you the
+
+ align:start position:0%
+exercises where I'll try to give you the
+ 
+
+ align:start position:0%
+exercises where I'll try to give you the
+so-called cookbook part of differential
+
+ align:start position:0%
+so-called cookbook part of differential
+ 
+
+ align:start position:0%
+so-called cookbook part of differential
+equations but I thought that to lead
+
+ align:start position:0%
+equations but I thought that to lead
+ 
+
+ align:start position:0%
+equations but I thought that to lead
+into that what I thought I wanted to
+
+ align:start position:0%
+into that what I thought I wanted to
+ 
+
+ align:start position:0%
+into that what I thought I wanted to
+bring out was this let's suppose that we
+
+ align:start position:0%
+bring out was this let's suppose that we
+ 
+
+ align:start position:0%
+bring out was this let's suppose that we
+restrict our attention to not only first
+
+ align:start position:0%
+restrict our attention to not only first
+ 
+
+ align:start position:0%
+restrict our attention to not only first
+order equations but first deegree
+
+ align:start position:0%
+order equations but first deegree
+ 
+
+ align:start position:0%
+order equations but first deegree
+equations in other words not only does
+
+ align:start position:0%
+equations in other words not only does
+ 
+
+ align:start position:0%
+equations in other words not only does
+the only derivative that appears is the
+
+ align:start position:0%
+the only derivative that appears is the
+ 
+
+ align:start position:0%
+the only derivative that appears is the
+be the first derivative but it also
+
+ align:start position:0%
+be the first derivative but it also
+ 
+
+ align:start position:0%
+be the first derivative but it also
+happens to appear only to the first
+
+ align:start position:0%
+happens to appear only to the first
+ 
+
+ align:start position:0%
+happens to appear only to the first
+Power all right notice that in that
+
+ align:start position:0%
+Power all right notice that in that
+ 
+
+ align:start position:0%
+Power all right notice that in that
+situation as I look at every term in my
+
+ align:start position:0%
+situation as I look at every term in my
+ 
+
+ align:start position:0%
+situation as I look at every term in my
+differential equation they fall into two
+
+ align:start position:0%
+differential equation they fall into two
+ 
+
+ align:start position:0%
+differential equation they fall into two
+types there'll be a term in which dydx
+
+ align:start position:0%
+types there'll be a term in which dydx
+ 
+
+ align:start position:0%
+types there'll be a term in which dydx
+is a factor or a term where dydx is not
+
+ align:start position:0%
+is a factor or a term where dydx is not
+ 
+
+ align:start position:0%
+is a factor or a term where dydx is not
+a factor what I can therefore do is
+
+ align:start position:0%
+a factor what I can therefore do is
+ 
+
+ align:start position:0%
+a factor what I can therefore do is
+collect all the terms which have Dy DX
+
+ align:start position:0%
+collect all the terms which have Dy DX
+ 
+
+ align:start position:0%
+collect all the terms which have Dy DX
+as a factor and factor out Dy DX so I
+
+ align:start position:0%
+as a factor and factor out Dy DX so I
+ 
+
+ align:start position:0%
+as a factor and factor out Dy DX so I
+have a term of the form what some
+
+ align:start position:0%
+have a term of the form what some
+ 
+
+ align:start position:0%
+have a term of the form what some
+function n of X and Y * Dy DX
+
+ align:start position:0%
+function n of X and Y * Dy DX
+ 
+
+ align:start position:0%
+function n of X and Y * Dy DX
+plus what a bunch of terms involving
+
+ align:start position:0%
+plus what a bunch of terms involving
+ 
+
+ align:start position:0%
+plus what a bunch of terms involving
+only X and Y which have no dydx in them
+
+ align:start position:0%
+only X and Y which have no dydx in them
+ 
+
+ align:start position:0%
+only X and Y which have no dydx in them
+equals zero I know words this is the
+
+ align:start position:0%
+equals zero I know words this is the
+ 
+
+ align:start position:0%
+equals zero I know words this is the
+most general form of my first order
+
+ align:start position:0%
+most general form of my first order
+ 
+
+ align:start position:0%
+most general form of my first order
+first degree equation if I now treat
+
+ align:start position:0%
+first degree equation if I now treat
+ 
+
+ align:start position:0%
+first degree equation if I now treat
+these as differentials and multiply
+
+ align:start position:0%
+these as differentials and multiply
+ 
+
+ align:start position:0%
+these as differentials and multiply
+through by DX notice that I'm back to
+
+ align:start position:0%
+through by DX notice that I'm back to
+ 
+
+ align:start position:0%
+through by DX notice that I'm back to
+the standard differential equation form
+
+ align:start position:0%
+the standard differential equation form
+ 
+
+ align:start position:0%
+the standard differential equation form
+that we talked about in fact I'll bring
+
+ align:start position:0%
+that we talked about in fact I'll bring
+ 
+
+ align:start position:0%
+that we talked about in fact I'll bring
+this up again in a moment in block three
+
+ align:start position:0%
+this up again in a moment in block three
+ 
+
+ align:start position:0%
+this up again in a moment in block three
+when we introduced exact differentials
+
+ align:start position:0%
+when we introduced exact differentials
+ 
+
+ align:start position:0%
+when we introduced exact differentials
+namely I have an equation of what form M
+
+ align:start position:0%
+namely I have an equation of what form M
+ 
+
+ align:start position:0%
+namely I have an equation of what form M
+DX plus n Dy y equal 0 by the way to
+
+ align:start position:0%
+DX plus n Dy y equal 0 by the way to
+ 
+
+ align:start position:0%
+DX plus n Dy y equal 0 by the way to
+correlate this with our key theorem
+
+ align:start position:0%
+correlate this with our key theorem
+ 
+
+ align:start position:0%
+correlate this with our key theorem
+notice that from here I could have
+
+ align:start position:0%
+notice that from here I could have
+ 
+
+ align:start position:0%
+notice that from here I could have
+written that Dy DX was minus M of XY
+
+ align:start position:0%
+written that Dy DX was minus M of XY
+ 
+
+ align:start position:0%
+written that Dy DX was minus M of XY
+Over N of XY and that's the f ofx y that
+
+ align:start position:0%
+Over N of XY and that's the f ofx y that
+ 
+
+ align:start position:0%
+Over N of XY and that's the f ofx y that
+I'm talking about in our key theorem
+
+ align:start position:0%
+I'm talking about in our key theorem
+ 
+
+ align:start position:0%
+I'm talking about in our key theorem
+that we talked about earlier see in
+
+ align:start position:0%
+that we talked about earlier see in
+ 
+
+ align:start position:0%
+that we talked about earlier see in
+other words f ofx y is the right hand
+
+ align:start position:0%
+other words f ofx y is the right hand
+ 
+
+ align:start position:0%
+other words f ofx y is the right hand
+side of the equation when the left hand
+
+ align:start position:0%
+side of the equation when the left hand
+ 
+
+ align:start position:0%
+side of the equation when the left hand
+side is specifically dydx so in other
+
+ align:start position:0%
+side is specifically dydx so in other
+ 
+
+ align:start position:0%
+side is specifically dydx so in other
+words what I'm guaranteed of is this as
+
+ align:start position:0%
+words what I'm guaranteed of is this as
+ 
+
+ align:start position:0%
+words what I'm guaranteed of is this as
+long as this function on the right hand
+
+ align:start position:0%
+long as this function on the right hand
+ 
+
+ align:start position:0%
+long as this function on the right hand
+side is continuous and it's partial with
+
+ align:start position:0%
+side is continuous and it's partial with
+ 
+
+ align:start position:0%
+side is continuous and it's partial with
+respect to Y is continuous I'm
+
+ align:start position:0%
+respect to Y is continuous I'm
+ 
+
+ align:start position:0%
+respect to Y is continuous I'm
+guaranteed that this equation has a
+
+ align:start position:0%
+guaranteed that this equation has a
+ 
+
+ align:start position:0%
+guaranteed that this equation has a
+general solution in particular if m&n
+
+ align:start position:0%
+general solution in particular if m&n
+ 
+
+ align:start position:0%
+general solution in particular if m&n
+happen to be continuously differentiable
+
+ align:start position:0%
+happen to be continuously differentiable
+ 
+
+ align:start position:0%
+happen to be continuously differentiable
+functions the general solution will
+
+ align:start position:0%
+functions the general solution will
+ 
+
+ align:start position:0%
+functions the general solution will
+exist provided only that n and its
+
+ align:start position:0%
+exist provided only that n and its
+ 
+
+ align:start position:0%
+exist provided only that n and its
+partial with respect to Y are not zero
+
+ align:start position:0%
+partial with respect to Y are not zero
+ 
+
+ align:start position:0%
+partial with respect to Y are not zero
+because after all to differentiate this
+
+ align:start position:0%
+because after all to differentiate this
+ 
+
+ align:start position:0%
+because after all to differentiate this
+with respect to Y this is a
+
+ align:start position:0%
+with respect to Y this is a
+ 
+
+ align:start position:0%
+with respect to Y this is a
+quotient and the only place that I'm
+
+ align:start position:0%
+quotient and the only place that I'm
+ 
+
+ align:start position:0%
+quotient and the only place that I'm
+going to be in trouble is that the
+
+ align:start position:0%
+going to be in trouble is that the
+ 
+
+ align:start position:0%
+going to be in trouble is that the
+square of the denominator appears when I
+
+ align:start position:0%
+square of the denominator appears when I
+ 
+
+ align:start position:0%
+square of the denominator appears when I
+use the quotient rule so I have to be
+
+ align:start position:0%
+use the quotient rule so I have to be
+ 
+
+ align:start position:0%
+use the quotient rule so I have to be
+careful where where
+
+ align:start position:0%
+careful where where
+ 
+
+ align:start position:0%
+careful where where
+either the partial event respect to y or
+
+ align:start position:0%
+either the partial event respect to y or
+ 
+
+ align:start position:0%
+either the partial event respect to y or
+n itself happen to be zero but if that
+
+ align:start position:0%
+n itself happen to be zero but if that
+ 
+
+ align:start position:0%
+n itself happen to be zero but if that
+doesn't happen it means there is a
+
+ align:start position:0%
+doesn't happen it means there is a
+ 
+
+ align:start position:0%
+doesn't happen it means there is a
+general solution now you may remember I
+
+ align:start position:0%
+general solution now you may remember I
+ 
+
+ align:start position:0%
+general solution now you may remember I
+back in block three we said you know if
+
+ align:start position:0%
+back in block three we said you know if
+ 
+
+ align:start position:0%
+back in block three we said you know if
+this differential happens to be exact in
+
+ align:start position:0%
+this differential happens to be exact in
+ 
+
+ align:start position:0%
+this differential happens to be exact in
+other words if there happens to be a fun
+
+ align:start position:0%
+other words if there happens to be a fun
+ 
+
+ align:start position:0%
+other words if there happens to be a fun
+function W such that DW is MDX plus ndy
+
+ align:start position:0%
+function W such that DW is MDX plus ndy
+ 
+
+ align:start position:0%
+function W such that DW is MDX plus ndy
+then it's trivial to solve this equation
+
+ align:start position:0%
+then it's trivial to solve this equation
+ 
+
+ align:start position:0%
+then it's trivial to solve this equation
+in particular for what we mean by an
+
+ align:start position:0%
+in particular for what we mean by an
+ 
+
+ align:start position:0%
+in particular for what we mean by an
+exact differential equation is simply
+
+ align:start position:0%
+exact differential equation is simply
+ 
+
+ align:start position:0%
+exact differential equation is simply
+this if MDX plus mdy is exact then we
+
+ align:start position:0%
+this if MDX plus mdy is exact then we
+ 
+
+ align:start position:0%
+this if MDX plus mdy is exact then we
+call the equation MDX plus ndy equal 0
+
+ align:start position:0%
+call the equation MDX plus ndy equal 0
+ 
+
+ align:start position:0%
+call the equation MDX plus ndy equal 0
+an exact differential equation and the
+
+ align:start position:0%
+an exact differential equation and the
+ 
+
+ align:start position:0%
+an exact differential equation and the
+solution of that equation is simply f
+
+ align:start position:0%
+solution of that equation is simply f
+ 
+
+ align:start position:0%
+solution of that equation is simply f
+ofx yal c where f is any fun function
+
+ align:start position:0%
+ofx yal c where f is any fun function
+ 
+
+ align:start position:0%
+ofx yal c where f is any fun function
+such that DF is MDX plus ndy and we're
+
+ align:start position:0%
+such that DF is MDX plus ndy and we're
+ 
+
+ align:start position:0%
+such that DF is MDX plus ndy and we're
+sure that such a function f exists by
+
+ align:start position:0%
+sure that such a function f exists by
+ 
+
+ align:start position:0%
+sure that such a function f exists by
+definition of MDX plus n Dy being exact
+
+ align:start position:0%
+definition of MDX plus n Dy being exact
+ 
+
+ align:start position:0%
+definition of MDX plus n Dy being exact
+see by way of example suppose I were
+
+ align:start position:0%
+see by way of example suppose I were
+ 
+
+ align:start position:0%
+see by way of example suppose I were
+given the equation ydx plus XD y equal 0
+
+ align:start position:0%
+given the equation ydx plus XD y equal 0
+ 
+
+ align:start position:0%
+given the equation ydx plus XD y equal 0
+forget about the fact that I could have
+
+ align:start position:0%
+forget about the fact that I could have
+ 
+
+ align:start position:0%
+forget about the fact that I could have
+solved this easier by just separating
+
+ align:start position:0%
+solved this easier by just separating
+ 
+
+ align:start position:0%
+solved this easier by just separating
+the variables notice by way of
+
+ align:start position:0%
+the variables notice by way of
+ 
+
+ align:start position:0%
+the variables notice by way of
+illustration that the left hand side
+
+ align:start position:0%
+illustration that the left hand side
+ 
+
+ align:start position:0%
+illustration that the left hand side
+here is just the differential of X X Y
+
+ align:start position:0%
+here is just the differential of X X Y
+ 
+
+ align:start position:0%
+here is just the differential of X X Y
+in other words y DX plus x d y equal 0
+
+ align:start position:0%
+in other words y DX plus x d y equal 0
+ 
+
+ align:start position:0%
+in other words y DX plus x d y equal 0
+says that the differential of XY is zero
+
+ align:start position:0%
+says that the differential of XY is zero
+ 
+
+ align:start position:0%
+says that the differential of XY is zero
+where Y is implicitly now some function
+
+ align:start position:0%
+where Y is implicitly now some function
+ 
+
+ align:start position:0%
+where Y is implicitly now some function
+of X now if the differential of some
+
+ align:start position:0%
+of X now if the differential of some
+ 
+
+ align:start position:0%
+of X now if the differential of some
+function of X is zero then that function
+
+ align:start position:0%
+function of X is zero then that function
+ 
+
+ align:start position:0%
+function of X is zero then that function
+itself must be a constant consequently
+
+ align:start position:0%
+itself must be a constant consequently
+ 
+
+ align:start position:0%
+itself must be a constant consequently
+XY equals a constant is a solution of
+
+ align:start position:0%
+XY equals a constant is a solution of
+ 
+
+ align:start position:0%
+XY equals a constant is a solution of
+this differential
+
+ align:start position:0%
+this differential
+ 
+
+ align:start position:0%
+this differential
+equation the problem that comes up is
+
+ align:start position:0%
+equation the problem that comes up is
+ 
+
+ align:start position:0%
+equation the problem that comes up is
+wouldn't it be nice that's not the
+
+ align:start position:0%
+wouldn't it be nice that's not the
+ 
+
+ align:start position:0%
+wouldn't it be nice that's not the
+problem the question is wouldn't it be
+
+ align:start position:0%
+problem the question is wouldn't it be
+ 
+
+ align:start position:0%
+problem the question is wouldn't it be
+nice if every first order first deegree
+
+ align:start position:0%
+nice if every first order first deegree
+ 
+
+ align:start position:0%
+nice if every first order first deegree
+differential equation happened to be
+
+ align:start position:0%
+differential equation happened to be
+ 
+
+ align:start position:0%
+differential equation happened to be
+exact see if if it were we'd be all done
+
+ align:start position:0%
+exact see if if it were we'd be all done
+ 
+
+ align:start position:0%
+exact see if if it were we'd be all done
+we talked about that as I say back in
+
+ align:start position:0%
+we talked about that as I say back in
+ 
+
+ align:start position:0%
+we talked about that as I say back in
+block three If This Were exact this is
+
+ align:start position:0%
+block three If This Were exact this is
+ 
+
+ align:start position:0%
+block three If This Were exact this is
+how we solve it but we also saw in block
+
+ align:start position:0%
+how we solve it but we also saw in block
+ 
+
+ align:start position:0%
+how we solve it but we also saw in block
+three that it's very uh very unique if
+
+ align:start position:0%
+three that it's very uh very unique if
+ 
+
+ align:start position:0%
+three that it's very uh very unique if
+the thing happens to be exact see in
+
+ align:start position:0%
+the thing happens to be exact see in
+ 
+
+ align:start position:0%
+the thing happens to be exact see in
+general the differential won't be exact
+
+ align:start position:0%
+general the differential won't be exact
+ 
+
+ align:start position:0%
+general the differential won't be exact
+and that's why I look now at non-exact
+
+ align:start position:0%
+and that's why I look now at non-exact
+ 
+
+ align:start position:0%
+and that's why I look now at non-exact
+equations see non-exact means what not
+
+ align:start position:0%
+equations see non-exact means what not
+ 
+
+ align:start position:0%
+equations see non-exact means what not
+that the equation is isn't exact but the
+
+ align:start position:0%
+that the equation is isn't exact but the
+ 
+
+ align:start position:0%
+that the equation is isn't exact but the
+differential isn't an exact differential
+
+ align:start position:0%
+differential isn't an exact differential
+ 
+
+ align:start position:0%
+differential isn't an exact differential
+look at ydx - xdy the partial of Y with
+
+ align:start position:0%
+look at ydx - xdy the partial of Y with
+ 
+
+ align:start position:0%
+look at ydx - xdy the partial of Y with
+respect to Y is 1 the partial of Min - x
+
+ align:start position:0%
+respect to Y is 1 the partial of Min - x
+ 
+
+ align:start position:0%
+respect to Y is 1 the partial of Min - x
+with respect to X is minus one this
+
+ align:start position:0%
+with respect to X is minus one this
+ 
+
+ align:start position:0%
+with respect to X is minus one this
+thing is not exact consequently this is
+
+ align:start position:0%
+thing is not exact consequently this is
+ 
+
+ align:start position:0%
+thing is not exact consequently this is
+not the differential of any particular
+
+ align:start position:0%
+not the differential of any particular
+ 
+
+ align:start position:0%
+not the differential of any particular
+function let me show you a little trick
+
+ align:start position:0%
+function let me show you a little trick
+ 
+
+ align:start position:0%
+function let me show you a little trick
+over here though this sort of suggests
+
+ align:start position:0%
+over here though this sort of suggests
+ 
+
+ align:start position:0%
+over here though this sort of suggests
+the quotient rule see the denominator
+
+ align:start position:0%
+the quotient rule see the denominator
+ 
+
+ align:start position:0%
+the quotient rule see the denominator
+times the differential of the numerator
+
+ align:start position:0%
+times the differential of the numerator
+ 
+
+ align:start position:0%
+times the differential of the numerator
+minus the numerator times the
+
+ align:start position:0%
+minus the numerator times the
+ 
+
+ align:start position:0%
+minus the numerator times the
+differential of the denominator except
+
+ align:start position:0%
+differential of the denominator except
+ 
+
+ align:start position:0%
+differential of the denominator except
+there should be a denominator here
+
+ align:start position:0%
+there should be a denominator here
+ 
+
+ align:start position:0%
+there should be a denominator here
+appearing as y squ you see and what I do
+
+ align:start position:0%
+appearing as y squ you see and what I do
+ 
+
+ align:start position:0%
+appearing as y squ you see and what I do
+is I say okay why don't I just divide
+
+ align:start position:0%
+is I say okay why don't I just divide
+ 
+
+ align:start position:0%
+is I say okay why don't I just divide
+both sides of this equation by
+
+ align:start position:0%
+both sides of this equation by
+ 
+
+ align:start position:0%
+both sides of this equation by
+y^2 if I do that and invoke the rule
+
+ align:start position:0%
+y^2 if I do that and invoke the rule
+ 
+
+ align:start position:0%
+y^2 if I do that and invoke the rule
+that equals / equals are equal being
+
+ align:start position:0%
+that equals / equals are equal being
+ 
+
+ align:start position:0%
+that equals / equals are equal being
+careful to remember that I'm in trouble
+
+ align:start position:0%
+careful to remember that I'm in trouble
+ 
+
+ align:start position:0%
+careful to remember that I'm in trouble
+when y equals z i got to keep that in
+
+ align:start position:0%
+when y equals z i got to keep that in
+ 
+
+ align:start position:0%
+when y equals z i got to keep that in
+the back of my mind remembering that Y
+
+ align:start position:0%
+the back of my mind remembering that Y
+ 
+
+ align:start position:0%
+the back of my mind remembering that Y
+is zero at any rate this equation
+
+ align:start position:0%
+is zero at any rate this equation
+ 
+
+ align:start position:0%
+is zero at any rate this equation
+transforms into y DX - xdy over y^2 = 0
+
+ align:start position:0%
+transforms into y DX - xdy over y^2 = 0
+ 
+
+ align:start position:0%
+transforms into y DX - xdy over y^2 = 0
+the left hand side this this
+
+ align:start position:0%
+the left hand side this this
+ 
+
+ align:start position:0%
+the left hand side this this
+differential is now exact believe it or
+
+ align:start position:0%
+differential is now exact believe it or
+ 
+
+ align:start position:0%
+differential is now exact believe it or
+not it wasn't exact to begin with but by
+
+ align:start position:0%
+not it wasn't exact to begin with but by
+ 
+
+ align:start position:0%
+not it wasn't exact to begin with but by
+dividing it by y^2 it became exact in
+
+ align:start position:0%
+dividing it by y^2 it became exact in
+ 
+
+ align:start position:0%
+dividing it by y^2 it became exact in
+fact the left hand side is not the
+
+ align:start position:0%
+fact the left hand side is not the
+ 
+
+ align:start position:0%
+fact the left hand side is not the
+differential of X over Y in other words
+
+ align:start position:0%
+differential of X over Y in other words
+ 
+
+ align:start position:0%
+differential of X over Y in other words
+the differential of X over Y is zero
+
+ align:start position:0%
+the differential of X over Y is zero
+ 
+
+ align:start position:0%
+the differential of X over Y is zero
+therefore X over Y is a constant or in
+
+ align:start position:0%
+therefore X over Y is a constant or in
+ 
+
+ align:start position:0%
+therefore X over Y is a constant or in
+particular Y is some constant time x by
+
+ align:start position:0%
+particular Y is some constant time x by
+ 
+
+ align:start position:0%
+particular Y is some constant time x by
+the way remembering that y had to be
+
+ align:start position:0%
+the way remembering that y had to be
+ 
+
+ align:start position:0%
+the way remembering that y had to be
+unequal to zero for this to be true
+
+ align:start position:0%
+unequal to zero for this to be true
+ 
+
+ align:start position:0%
+unequal to zero for this to be true
+notice that we have to check y equals 0
+
+ align:start position:0%
+notice that we have to check y equals 0
+ 
+
+ align:start position:0%
+notice that we have to check y equals 0
+separately notice by the way that y
+
+ align:start position:0%
+separately notice by the way that y
+ 
+
+ align:start position:0%
+separately notice by the way that y
+equals 0 is a particular solution of
+
+ align:start position:0%
+equals 0 is a particular solution of
+ 
+
+ align:start position:0%
+equals 0 is a particular solution of
+this equation obtained by choosing c
+
+ align:start position:0%
+this equation obtained by choosing c
+ 
+
+ align:start position:0%
+this equation obtained by choosing c
+equal to 0 so y equals 0 gives us no
+
+ align:start position:0%
+equal to 0 so y equals 0 gives us no
+ 
+
+ align:start position:0%
+equal to 0 so y equals 0 gives us no
+great hot here but the thing I'm leading
+
+ align:start position:0%
+great hot here but the thing I'm leading
+ 
+
+ align:start position:0%
+great hot here but the thing I'm leading
+up to and I'm sorry for all these asides
+
+ align:start position:0%
+up to and I'm sorry for all these asides
+ 
+
+ align:start position:0%
+up to and I'm sorry for all these asides
+but what I'm leading up to is something
+
+ align:start position:0%
+but what I'm leading up to is something
+ 
+
+ align:start position:0%
+but what I'm leading up to is something
+called an integrating factor and that's
+
+ align:start position:0%
+called an integrating factor and that's
+ 
+
+ align:start position:0%
+called an integrating factor and that's
+what we just used over here what we say
+
+ align:start position:0%
+what we just used over here what we say
+ 
+
+ align:start position:0%
+what we just used over here what we say
+is if MDX plus mdy is not zero equals
+
+ align:start position:0%
+is if MDX plus mdy is not zero equals
+ 
+
+ align:start position:0%
+is if MDX plus mdy is not zero equals
+zero is not exact make it exact what
+
+ align:start position:0%
+zero is not exact make it exact what
+ 
+
+ align:start position:0%
+zero is not exact make it exact what
+does that mean find a function U of X
+
+ align:start position:0%
+does that mean find a function U of X
+ 
+
+ align:start position:0%
+does that mean find a function U of X
+and Y such that when I multiply or
+
+ align:start position:0%
+and Y such that when I multiply or
+ 
+
+ align:start position:0%
+and Y such that when I multiply or
+divide makes no difference both sides of
+
+ align:start position:0%
+divide makes no difference both sides of
+ 
+
+ align:start position:0%
+divide makes no difference both sides of
+this equation byy it the new equation
+
+ align:start position:0%
+this equation byy it the new equation
+ 
+
+ align:start position:0%
+this equation byy it the new equation
+which you
+
+ align:start position:0%
+which you
+ 
+
+ align:start position:0%
+which you
+has the same solution set as this one
+
+ align:start position:0%
+has the same solution set as this one
+ 
+
+ align:start position:0%
+has the same solution set as this one
+see in other
+
+ align:start position:0%
+see in other
+ 
+
+ align:start position:0%
+see in other
+words a solution something is a solution
+
+ align:start position:0%
+words a solution something is a solution
+ 
+
+ align:start position:0%
+words a solution something is a solution
+of this equation if and only if it's a
+
+ align:start position:0%
+of this equation if and only if it's a
+ 
+
+ align:start position:0%
+of this equation if and only if it's a
+solution of this equation see it's
+
+ align:start position:0%
+solution of this equation see it's
+ 
+
+ align:start position:0%
+solution of this equation see it's
+equals multiplied by equals or equal
+
+ align:start position:0%
+equals multiplied by equals or equal
+ 
+
+ align:start position:0%
+equals multiplied by equals or equal
+what if this is exact see that's
+
+ align:start position:0%
+what if this is exact see that's
+ 
+
+ align:start position:0%
+what if this is exact see that's
+precisely what we did up here y DX - xdy
+
+ align:start position:0%
+precisely what we did up here y DX - xdy
+ 
+
+ align:start position:0%
+precisely what we did up here y DX - xdy
+was not exact the U of XY in that case
+
+ align:start position:0%
+was not exact the U of XY in that case
+ 
+
+ align:start position:0%
+was not exact the U of XY in that case
+was just 1 over y^2 we multiplied both
+
+ align:start position:0%
+was just 1 over y^2 we multiplied both
+ 
+
+ align:start position:0%
+was just 1 over y^2 we multiplied both
+sides of the equation by 1 over y^2 and
+
+ align:start position:0%
+sides of the equation by 1 over y^2 and
+ 
+
+ align:start position:0%
+sides of the equation by 1 over y^2 and
+made this exact the problem is this
+
+ align:start position:0%
+made this exact the problem is this
+ 
+
+ align:start position:0%
+made this exact the problem is this
+though
+
+ align:start position:0%
+though
+ 
+
+ align:start position:0%
+though
+it turns out theoretically that if an
+
+ align:start position:0%
+it turns out theoretically that if an
+ 
+
+ align:start position:0%
+it turns out theoretically that if an
+equation of first order first degree is
+
+ align:start position:0%
+equation of first order first degree is
+ 
+
+ align:start position:0%
+equation of first order first degree is
+not exact there is an integrating Factor
+
+ align:start position:0%
+not exact there is an integrating Factor
+ 
+
+ align:start position:0%
+not exact there is an integrating Factor
+another words something that you can
+
+ align:start position:0%
+another words something that you can
+ 
+
+ align:start position:0%
+another words something that you can
+multiply it by to make it exact the
+
+ align:start position:0%
+multiply it by to make it exact the
+ 
+
+ align:start position:0%
+multiply it by to make it exact the
+problem is that in real life that factor
+
+ align:start position:0%
+problem is that in real life that factor
+ 
+
+ align:start position:0%
+problem is that in real life that factor
+is harder to find than the solution of
+
+ align:start position:0%
+is harder to find than the solution of
+ 
+
+ align:start position:0%
+is harder to find than the solution of
+the original equation in most cases
+
+ align:start position:0%
+the original equation in most cases
+ 
+
+ align:start position:0%
+the original equation in most cases
+namely how would I find a u such that
+
+ align:start position:0%
+namely how would I find a u such that
+ 
+
+ align:start position:0%
+namely how would I find a u such that
+this was exact remember the condition
+
+ align:start position:0%
+this was exact remember the condition
+ 
+
+ align:start position:0%
+this was exact remember the condition
+for exactness is that the partial of
+
+ align:start position:0%
+for exactness is that the partial of
+ 
+
+ align:start position:0%
+for exactness is that the partial of
+this with respect to Y has to equal the
+
+ align:start position:0%
+this with respect to Y has to equal the
+ 
+
+ align:start position:0%
+this with respect to Y has to equal the
+partial of this with respect to X
+
+ align:start position:0%
+partial of this with respect to X
+ 
+
+ align:start position:0%
+partial of this with respect to X
+remembering that U is a function of X
+
+ align:start position:0%
+remembering that U is a function of X
+ 
+
+ align:start position:0%
+remembering that U is a function of X
+and Y I have to use the product rule
+
+ align:start position:0%
+and Y I have to use the product rule
+ 
+
+ align:start position:0%
+and Y I have to use the product rule
+over here I get U * the partial of n
+
+ align:start position:0%
+over here I get U * the partial of n
+ 
+
+ align:start position:0%
+over here I get U * the partial of n
+respect to Y plus the partial of U
+
+ align:start position:0%
+respect to Y plus the partial of U
+ 
+
+ align:start position:0%
+respect to Y plus the partial of U
+respect to y * n equals U * the partial
+
+ align:start position:0%
+respect to y * n equals U * the partial
+ 
+
+ align:start position:0%
+respect to y * n equals U * the partial
+of n respect to X plus the parti respect
+
+ align:start position:0%
+of n respect to X plus the parti respect
+ 
+
+ align:start position:0%
+of n respect to X plus the parti respect
+to x * n and look at this equation I'm
+
+ align:start position:0%
+to x * n and look at this equation I'm
+ 
+
+ align:start position:0%
+to x * n and look at this equation I'm
+trying to solve this for you and notice
+
+ align:start position:0%
+trying to solve this for you and notice
+ 
+
+ align:start position:0%
+trying to solve this for you and notice
+that this is still a differential
+
+ align:start position:0%
+that this is still a differential
+ 
+
+ align:start position:0%
+that this is still a differential
+equation but it involves even partial
+
+ align:start position:0%
+equation but it involves even partial
+ 
+
+ align:start position:0%
+equation but it involves even partial
+derivatives in other words to solve this
+
+ align:start position:0%
+derivatives in other words to solve this
+ 
+
+ align:start position:0%
+derivatives in other words to solve this
+equation involves having to solve a
+
+ align:start position:0%
+equation involves having to solve a
+ 
+
+ align:start position:0%
+equation involves having to solve a
+partial differential equation which is
+
+ align:start position:0%
+partial differential equation which is
+ 
+
+ align:start position:0%
+partial differential equation which is
+even harder to do than the equation that
+
+ align:start position:0%
+even harder to do than the equation that
+ 
+
+ align:start position:0%
+even harder to do than the equation that
+we're trying to solve now well at any
+
+ align:start position:0%
+we're trying to solve now well at any
+ 
+
+ align:start position:0%
+we're trying to solve now well at any
+rate let me show you now in summary why
+
+ align:start position:0%
+rate let me show you now in summary why
+ 
+
+ align:start position:0%
+rate let me show you now in summary why
+people refer to differential equations
+
+ align:start position:0%
+people refer to differential equations
+ 
+
+ align:start position:0%
+people refer to differential equations
+as a cookbook course philosophically
+
+ align:start position:0%
+as a cookbook course philosophically
+ 
+
+ align:start position:0%
+as a cookbook course philosophically
+there's nothing to solving first order
+
+ align:start position:0%
+there's nothing to solving first order
+ 
+
+ align:start position:0%
+there's nothing to solving first order
+first-degree differential equations
+
+ align:start position:0%
+first-degree differential equations
+ 
+
+ align:start position:0%
+first-degree differential equations
+namely look at the differential if it's
+
+ align:start position:0%
+namely look at the differential if it's
+ 
+
+ align:start position:0%
+namely look at the differential if it's
+exact bang you just integrate it
+
+ align:start position:0%
+exact bang you just integrate it
+ 
+
+ align:start position:0%
+exact bang you just integrate it
+directly find the W such that DW is MDX
+
+ align:start position:0%
+directly find the W such that DW is MDX
+ 
+
+ align:start position:0%
+directly find the W such that DW is MDX
+Plus mdy y then W equals a constant as a
+
+ align:start position:0%
+Plus mdy y then W equals a constant as a
+ 
+
+ align:start position:0%
+Plus mdy y then W equals a constant as a
+solution if it's not exact find an
+
+ align:start position:0%
+solution if it's not exact find an
+ 
+
+ align:start position:0%
+solution if it's not exact find an
+integrating Factor Make It exact the
+
+ align:start position:0%
+integrating Factor Make It exact the
+ 
+
+ align:start position:0%
+integrating Factor Make It exact the
+trouble is that in real life given a
+
+ align:start position:0%
+trouble is that in real life given a
+ 
+
+ align:start position:0%
+trouble is that in real life given a
+particular equation it's very very
+
+ align:start position:0%
+particular equation it's very very
+ 
+
+ align:start position:0%
+particular equation it's very very
+difficult to find the integrating Factor
+
+ align:start position:0%
+difficult to find the integrating Factor
+ 
+
+ align:start position:0%
+difficult to find the integrating Factor
+consequently what one does is one
+
+ align:start position:0%
+consequently what one does is one
+ 
+
+ align:start position:0%
+consequently what one does is one
+categorizes various types of first order
+
+ align:start position:0%
+categorizes various types of first order
+ 
+
+ align:start position:0%
+categorizes various types of first order
+first-degree differential equations
+
+ align:start position:0%
+first-degree differential equations
+ 
+
+ align:start position:0%
+first-degree differential equations
+according to their structure and shows
+
+ align:start position:0%
+according to their structure and shows
+ 
+
+ align:start position:0%
+according to their structure and shows
+little tricks for solving special kinds
+
+ align:start position:0%
+little tricks for solving special kinds
+ 
+
+ align:start position:0%
+little tricks for solving special kinds
+of equations speci types where we can
+
+ align:start position:0%
+of equations speci types where we can
+ 
+
+ align:start position:0%
+of equations speci types where we can
+cut through the red tape and either find
+
+ align:start position:0%
+cut through the red tape and either find
+ 
+
+ align:start position:0%
+cut through the red tape and either find
+our integrating factor or a direct
+
+ align:start position:0%
+our integrating factor or a direct
+ 
+
+ align:start position:0%
+our integrating factor or a direct
+solution rather uh easily at any rate
+
+ align:start position:0%
+solution rather uh easily at any rate
+ 
+
+ align:start position:0%
+solution rather uh easily at any rate
+that part is taken care of magnificently
+
+ align:start position:0%
+that part is taken care of magnificently
+ 
+
+ align:start position:0%
+that part is taken care of magnificently
+in the textbook and coupled with my
+
+ align:start position:0%
+in the textbook and coupled with my
+ 
+
+ align:start position:0%
+in the textbook and coupled with my
+unique learning exercises you will get
+
+ align:start position:0%
+unique learning exercises you will get
+ 
+
+ align:start position:0%
+unique learning exercises you will get
+an excellent amount of drill in how to
+
+ align:start position:0%
+an excellent amount of drill in how to
+ 
+
+ align:start position:0%
+an excellent amount of drill in how to
+do the mechanics but what I wanted this
+
+ align:start position:0%
+do the mechanics but what I wanted this
+ 
+
+ align:start position:0%
+do the mechanics but what I wanted this
+lecture to do was to have you at least
+
+ align:start position:0%
+lecture to do was to have you at least
+ 
+
+ align:start position:0%
+lecture to do was to have you at least
+understand for sure what you meant by a
+
+ align:start position:0%
+understand for sure what you meant by a
+ 
+
+ align:start position:0%
+understand for sure what you meant by a
+solution to an equation what you meant
+
+ align:start position:0%
+solution to an equation what you meant
+ 
+
+ align:start position:0%
+solution to an equation what you meant
+by a en solution a particular solution a
+
+ align:start position:0%
+by a en solution a particular solution a
+ 
+
+ align:start position:0%
+by a en solution a particular solution a
+singular solution Etc at any rate then
+
+ align:start position:0%
+singular solution Etc at any rate then
+ 
+
+ align:start position:0%
+singular solution Etc at any rate then
+until we meet again for second and
+
+ align:start position:0%
+until we meet again for second and
+ 
+
+ align:start position:0%
+until we meet again for second and
+higher order differential equations
+
+ align:start position:0%
+higher order differential equations
+ 
+
+ align:start position:0%
+higher order differential equations
+let's just say soong for
+
+ align:start position:0%
+let's just say soong for
+ 
+
+ align:start position:0%
+let's just say soong for
+now funding for the publication of this
+
+ align:start position:0%
+now funding for the publication of this
+ 
+
+ align:start position:0%
+now funding for the publication of this
+video was provided by the Gabriella and
+
+ align:start position:0%
+video was provided by the Gabriella and
+ 
+
+ align:start position:0%
+video was provided by the Gabriella and
+Paul rosenbom
+
+ align:start position:0%
+Paul rosenbom
+ 
+
+ align:start position:0%
+Paul rosenbom
+foundation help ocw continue to provide
+
+ align:start position:0%
+foundation help ocw continue to provide
+ 
+
+ align:start position:0%
+foundation help ocw continue to provide
+free and open access to MIT courses by
+
+ align:start position:0%
+free and open access to MIT courses by
+ 
+
+ align:start position:0%
+free and open access to MIT courses by
+making a donation at ocw mit.edu donate
\ No newline at end of file
diff --git a/I_w8ruM-mmY.txt b/I_w8ruM-mmY.txt
new file mode 100644
index 0000000000000000000000000000000000000000..ce89eb22e1f7fe760baf09b65e65ab53266eaa9a
--- /dev/null
+++ b/I_w8ruM-mmY.txt
@@ -0,0 +1,779 @@
+align:start position:0%
+ 
+the inductive attenuator demonstrates
+
+ align:start position:0%
+the inductive attenuator demonstrates
+ 
+
+ align:start position:0%
+the inductive attenuator demonstrates
+the laplacian nature of magnetic fields
+
+ align:start position:0%
+the laplacian nature of magnetic fields
+ 
+
+ align:start position:0%
+the laplacian nature of magnetic fields
+in free space
+
+ align:start position:0%
+in free space
+ 
+
+ align:start position:0%
+in free space
+the way that currents distribute
+
+ align:start position:0%
+the way that currents distribute
+ 
+
+ align:start position:0%
+the way that currents distribute
+themselves on the surfaces of perfect
+
+ align:start position:0%
+themselves on the surfaces of perfect
+ 
+
+ align:start position:0%
+themselves on the surfaces of perfect
+conductors
+
+ align:start position:0%
+conductors
+ 
+
+ align:start position:0%
+conductors
+and the use of the vector potential in
+
+ align:start position:0%
+and the use of the vector potential in
+ 
+
+ align:start position:0%
+and the use of the vector potential in
+describing magnetic fields in
+
+ align:start position:0%
+describing magnetic fields in
+ 
+
+ align:start position:0%
+describing magnetic fields in
+two-dimensional systems
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+in this model
+
+ align:start position:0%
+in this model
+ 
+
+ align:start position:0%
+in this model
+the floor is the x-y plane
+
+ align:start position:0%
+the floor is the x-y plane
+ 
+
+ align:start position:0%
+the floor is the x-y plane
+the altitude of the surface is the
+
+ align:start position:0%
+the altitude of the surface is the
+ 
+
+ align:start position:0%
+the altitude of the surface is the
+vector potential
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+here's the direction of periodicity
+
+ align:start position:0%
+here's the direction of periodicity
+ 
+
+ align:start position:0%
+here's the direction of periodicity
+here's the direction of decay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+because it represents a solution to
+
+ align:start position:0%
+because it represents a solution to
+ 
+
+ align:start position:0%
+because it represents a solution to
+laplace's equation every point on the
+
+ align:start position:0%
+laplace's equation every point on the
+ 
+
+ align:start position:0%
+laplace's equation every point on the
+surface having a positive curvature
+
+ align:start position:0%
+surface having a positive curvature
+ 
+
+ align:start position:0%
+surface having a positive curvature
+in the y direction
+
+ align:start position:0%
+in the y direction
+ 
+
+ align:start position:0%
+in the y direction
+must have a negative curvature in the x
+
+ align:start position:0%
+must have a negative curvature in the x
+ 
+
+ align:start position:0%
+must have a negative curvature in the x
+direction
+
+ align:start position:0%
+direction
+ 
+
+ align:start position:0%
+direction
+this is why periodicity in one direction
+
+ align:start position:0%
+this is why periodicity in one direction
+ 
+
+ align:start position:0%
+this is why periodicity in one direction
+implies decay in the other
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+for this solution to laplace's equation
+
+ align:start position:0%
+for this solution to laplace's equation
+ 
+
+ align:start position:0%
+for this solution to laplace's equation
+three of the rectangular boundaries have
+
+ align:start position:0%
+three of the rectangular boundaries have
+ 
+
+ align:start position:0%
+three of the rectangular boundaries have
+a constant vector potential
+
+ align:start position:0%
+a constant vector potential
+ 
+
+ align:start position:0%
+a constant vector potential
+the fourth is a sinusoid
+
+ align:start position:0%
+the fourth is a sinusoid
+ 
+
+ align:start position:0%
+the fourth is a sinusoid
+in our physical situation this fourth
+
+ align:start position:0%
+in our physical situation this fourth
+ 
+
+ align:start position:0%
+in our physical situation this fourth
+boundary is elevated to a uniform vector
+
+ align:start position:0%
+boundary is elevated to a uniform vector
+ 
+
+ align:start position:0%
+boundary is elevated to a uniform vector
+potential
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this can be represented by a
+
+ align:start position:0%
+this can be represented by a
+ 
+
+ align:start position:0%
+this can be represented by a
+superposition of these solutions
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+in our model
+
+ align:start position:0%
+in our model
+ 
+
+ align:start position:0%
+in our model
+lines of constant altitude are lines of
+
+ align:start position:0%
+lines of constant altitude are lines of
+ 
+
+ align:start position:0%
+lines of constant altitude are lines of
+constant vector potential
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+in two dimensions lines of constant a
+
+ align:start position:0%
+in two dimensions lines of constant a
+ 
+
+ align:start position:0%
+in two dimensions lines of constant a
+sub z
+
+ align:start position:0%
+sub z
+ 
+
+ align:start position:0%
+sub z
+are lines of magnetic flux density
+
+ align:start position:0%
+are lines of magnetic flux density
+ 
+
+ align:start position:0%
+are lines of magnetic flux density
+so the wires are the lines of magnetic
+
+ align:start position:0%
+so the wires are the lines of magnetic
+ 
+
+ align:start position:0%
+so the wires are the lines of magnetic
+flux density
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this is the actual apparatus
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+here are the side walls
+
+ align:start position:0%
+here are the side walls
+ 
+
+ align:start position:0%
+here are the side walls
+insulated from each other
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+here's the top plate
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+current from this source passes forward
+
+ align:start position:0%
+current from this source passes forward
+ 
+
+ align:start position:0%
+current from this source passes forward
+through the upper plate
+
+ align:start position:0%
+through the upper plate
+ 
+
+ align:start position:0%
+through the upper plate
+and is returned by the shorts through
+
+ align:start position:0%
+and is returned by the shorts through
+ 
+
+ align:start position:0%
+and is returned by the shorts through
+the side walls
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+here are the connections at the back end
+
+ align:start position:0%
+here are the connections at the back end
+ 
+
+ align:start position:0%
+here are the connections at the back end
+the source is connected by the center
+
+ align:start position:0%
+the source is connected by the center
+ 
+
+ align:start position:0%
+the source is connected by the center
+conductor of a coaxial cable
+
+ align:start position:0%
+conductor of a coaxial cable
+ 
+
+ align:start position:0%
+conductor of a coaxial cable
+to the upper electrode here
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the driving current is returned to the
+
+ align:start position:0%
+the driving current is returned to the
+ 
+
+ align:start position:0%
+the driving current is returned to the
+source by these wires
+
+ align:start position:0%
+source by these wires
+ 
+
+ align:start position:0%
+source by these wires
+and the coax shield conductor
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+these leads are connected to the top
+
+ align:start position:0%
+these leads are connected to the top
+ 
+
+ align:start position:0%
+these leads are connected to the top
+trace of our scope
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the top trace
+
+ align:start position:0%
+the top trace
+ 
+
+ align:start position:0%
+the top trace
+is the driving voltage
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+here at the back the bottom plate is
+
+ align:start position:0%
+here at the back the bottom plate is
+ 
+
+ align:start position:0%
+here at the back the bottom plate is
+shorted to the side walls
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+it is also shorted at the front
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+through these wires
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+we measure the current induced in this
+
+ align:start position:0%
+we measure the current induced in this
+ 
+
+ align:start position:0%
+we measure the current induced in this
+electrode by means of this current probe
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the lower trace on the scope represents
+
+ align:start position:0%
+the lower trace on the scope represents
+ 
+
+ align:start position:0%
+the lower trace on the scope represents
+the output current from the probe
+
+ align:start position:0%
+the output current from the probe
+ 
+
+ align:start position:0%
+the output current from the probe
+it represents the net current induced in
+
+ align:start position:0%
+it represents the net current induced in
+ 
+
+ align:start position:0%
+it represents the net current induced in
+the lower electrode
+
+ align:start position:0%
+the lower electrode
+ 
+
+ align:start position:0%
+the lower electrode
+here's how the current induced in the
+
+ align:start position:0%
+here's how the current induced in the
+ 
+
+ align:start position:0%
+here's how the current induced in the
+lower electrode varies as the driving
+
+ align:start position:0%
+lower electrode varies as the driving
+ 
+
+ align:start position:0%
+lower electrode varies as the driving
+electrode is lowered
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+as the spacing is increased
+
+ align:start position:0%
+as the spacing is increased
+ 
+
+ align:start position:0%
+as the spacing is increased
+again with the driving voltage
+
+ align:start position:0%
+again with the driving voltage
+ 
+
+ align:start position:0%
+again with the driving voltage
+essentially held fixed
+
+ align:start position:0%
+essentially held fixed
+ 
+
+ align:start position:0%
+essentially held fixed
+the induced current decreases
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+as the driving electrode approaches the
+
+ align:start position:0%
+as the driving electrode approaches the
+ 
+
+ align:start position:0%
+as the driving electrode approaches the
+lower electrode it increases again
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+with the electrodes this close almost
+
+ align:start position:0%
+with the electrodes this close almost
+ 
+
+ align:start position:0%
+with the electrodes this close almost
+all of the current in the upper
+
+ align:start position:0%
+all of the current in the upper
+ 
+
+ align:start position:0%
+all of the current in the upper
+electrode is imaged in the lower
+
+ align:start position:0%
+electrode is imaged in the lower
+ 
+
+ align:start position:0%
+electrode is imaged in the lower
+electrode
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+as the distance between electrodes
+
+ align:start position:0%
+as the distance between electrodes
+ 
+
+ align:start position:0%
+as the distance between electrodes
+increases
+
+ align:start position:0%
+increases
+ 
+
+ align:start position:0%
+increases
+the fraction of the current that returns
+
+ align:start position:0%
+the fraction of the current that returns
+ 
+
+ align:start position:0%
+the fraction of the current that returns
+in the lower electrode
+
+ align:start position:0%
+in the lower electrode
+ 
+
+ align:start position:0%
+in the lower electrode
+is reduced
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the inductive attenuator has illustrated
+
+ align:start position:0%
+the inductive attenuator has illustrated
+ 
+
+ align:start position:0%
+the inductive attenuator has illustrated
+the laplacian nature of free space
+
+ align:start position:0%
+the laplacian nature of free space
+ 
+
+ align:start position:0%
+the laplacian nature of free space
+magneto-quasi-static fields
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the magnetic field induced by applying a
+
+ align:start position:0%
+the magnetic field induced by applying a
+ 
+
+ align:start position:0%
+the magnetic field induced by applying a
+voltage to the upper electrode
+
+ align:start position:0%
+voltage to the upper electrode
+ 
+
+ align:start position:0%
+voltage to the upper electrode
+decays essentially exponentially into
+
+ align:start position:0%
+decays essentially exponentially into
+ 
+
+ align:start position:0%
+decays essentially exponentially into
+the rectangular region
+
+ align:start position:0%
+the rectangular region
+ 
+
+ align:start position:0%
+the rectangular region
+bounded by the essentially perfectly
+
+ align:start position:0%
+bounded by the essentially perfectly
+ 
+
+ align:start position:0%
+bounded by the essentially perfectly
+conducting side walls
+
+ align:start position:0%
+conducting side walls
+ 
+
+ align:start position:0%
+conducting side walls
+and the bottom electrode
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+you
\ No newline at end of file
diff --git a/IfwfCe-JZaI.txt b/IfwfCe-JZaI.txt
new file mode 100644
index 0000000000000000000000000000000000000000..e0b8533d89f5f92c94883b831bf81d7bd5f70ff6
--- /dev/null
+++ b/IfwfCe-JZaI.txt
@@ -0,0 +1,9835 @@
+align:start position:0%
+ 
+okay I want to begin by giving some
+
+ align:start position:0%
+okay I want to begin by giving some
+ 
+
+ align:start position:0%
+okay I want to begin by giving some
+comments regarding their Wikipedia
+
+ align:start position:0%
+comments regarding their Wikipedia
+ 
+
+ align:start position:0%
+comments regarding their Wikipedia
+assignment so I sent out an email about
+
+ align:start position:0%
+assignment so I sent out an email about
+ 
+
+ align:start position:0%
+assignment so I sent out an email about
+this last night and so first of all you
+
+ align:start position:0%
+this last night and so first of all you
+ 
+
+ align:start position:0%
+this last night and so first of all you
+know thank you for your contributions to
+
+ align:start position:0%
+know thank you for your contributions to
+ 
+
+ align:start position:0%
+know thank you for your contributions to
+to this assignment to Wikipedia it plays
+
+ align:start position:0%
+to this assignment to Wikipedia it plays
+ 
+
+ align:start position:0%
+to this assignment to Wikipedia it plays
+a really important role in educating a
+
+ align:start position:0%
+a really important role in educating a
+ 
+
+ align:start position:0%
+a really important role in educating a
+wider audience
+
+ align:start position:0%
+wider audience
+ 
+
+ align:start position:0%
+wider audience
+what this subject is about because as
+
+ align:start position:0%
+what this subject is about because as
+ 
+
+ align:start position:0%
+what this subject is about because as
+many of you have experienced the first
+
+ align:start position:0%
+many of you have experienced the first
+ 
+
+ align:start position:0%
+many of you have experienced the first
+time if you heard of some term you have
+
+ align:start position:0%
+time if you heard of some term you have
+ 
+
+ align:start position:0%
+time if you heard of some term you have
+no idea what it is you put it into
+
+ align:start position:0%
+no idea what it is you put it into
+ 
+
+ align:start position:0%
+no idea what it is you put it into
+Google and often Wikipedia entry is one
+
+ align:start position:0%
+Google and often Wikipedia entry is one
+ 
+
+ align:start position:0%
+Google and often Wikipedia entry is one
+of the top results that come up and what
+
+ align:start position:0%
+of the top results that come up and what
+ 
+
+ align:start position:0%
+of the top results that come up and what
+gets written there actually plays a
+
+ align:start position:0%
+gets written there actually plays a
+ 
+
+ align:start position:0%
+gets written there actually plays a
+fairly influential role in educating a
+
+ align:start position:0%
+fairly influential role in educating a
+ 
+
+ align:start position:0%
+fairly influential role in educating a
+broader audience about what this topic
+
+ align:start position:0%
+broader audience about what this topic
+ 
+
+ align:start position:0%
+broader audience about what this topic
+is about and so I won't you emphasize
+
+ align:start position:0%
+is about and so I won't you emphasize
+ 
+
+ align:start position:0%
+is about and so I won't you emphasize
+that you know this is not simply some
+
+ align:start position:0%
+that you know this is not simply some
+ 
+
+ align:start position:0%
+that you know this is not simply some
+homework assignment it's something that
+
+ align:start position:0%
+homework assignment it's something that
+ 
+
+ align:start position:0%
+homework assignment it's something that
+it's a real contribution and it's
+
+ align:start position:0%
+it's a real contribution and it's
+ 
+
+ align:start position:0%
+it's a real contribution and it's
+something that contributes to the
+
+ align:start position:0%
+something that contributes to the
+ 
+
+ align:start position:0%
+something that contributes to the
+dissemination of knowledge and for that
+
+ align:start position:0%
+dissemination of knowledge and for that
+ 
+
+ align:start position:0%
+dissemination of knowledge and for that
+it is really important to do a good job
+
+ align:start position:0%
+it is really important to do a good job
+ 
+
+ align:start position:0%
+it is really important to do a good job
+to do a write to do a well so that next
+
+ align:start position:0%
+to do a write to do a well so that next
+ 
+
+ align:start position:0%
+to do a write to do a well so that next
+time someone maybe even yourselves you
+
+ align:start position:0%
+time someone maybe even yourselves you
+ 
+
+ align:start position:0%
+time someone maybe even yourselves you
+know have you forgotten what the subject
+
+ align:start position:0%
+know have you forgotten what the subject
+ 
+
+ align:start position:0%
+know have you forgotten what the subject
+is about and go back and you want to
+
+ align:start position:0%
+is about and go back and you want to
+ 
+
+ align:start position:0%
+is about and go back and you want to
+look it up again and remind yourself you
+
+ align:start position:0%
+look it up again and remind yourself you
+ 
+
+ align:start position:0%
+look it up again and remind yourself you
+will have a useful resource to look into
+
+ align:start position:0%
+will have a useful resource to look into
+ 
+
+ align:start position:0%
+will have a useful resource to look into
+but also let's say someone wants to find
+
+ align:start position:0%
+but also let's say someone wants to find
+ 
+
+ align:start position:0%
+but also let's say someone wants to find
+out you know what is extrema graph
+
+ align:start position:0%
+out you know what is extrema graph
+ 
+
+ align:start position:0%
+out you know what is extrema graph
+theory about what is additive
+
+ align:start position:0%
+theory about what is additive
+ 
+
+ align:start position:0%
+theory about what is additive
+combinatorics about you want them to
+
+ align:start position:0%
+combinatorics about you want them to
+ 
+
+ align:start position:0%
+combinatorics about you want them to
+land on a page that points you to the
+
+ align:start position:0%
+land on a page that points you to the
+ 
+
+ align:start position:0%
+land on a page that points you to the
+right type of places right that points
+
+ align:start position:0%
+right type of places right that points
+ 
+
+ align:start position:0%
+right type of places right that points
+you to use for resources that opens
+
+ align:start position:0%
+you to use for resources that opens
+ 
+
+ align:start position:0%
+you to use for resources that opens
+doors so that you can explore further
+
+ align:start position:0%
+doors so that you can explore further
+ 
+
+ align:start position:0%
+doors so that you can explore further
+and and some of the contributions indeed
+
+ align:start position:0%
+and and some of the contributions indeed
+ 
+
+ align:start position:0%
+and and some of the contributions indeed
+server well in that purpose it opens
+
+ align:start position:0%
+server well in that purpose it opens
+ 
+
+ align:start position:0%
+server well in that purpose it opens
+doors to many things and part of the
+
+ align:start position:0%
+doors to many things and part of the
+ 
+
+ align:start position:0%
+doors to many things and part of the
+spirit of this assignment is for you to
+
+ align:start position:0%
+spirit of this assignment is for you to
+ 
+
+ align:start position:0%
+spirit of this assignment is for you to
+do your own research do your own
+
+ align:start position:0%
+do your own research do your own
+ 
+
+ align:start position:0%
+do your own research do your own
+literature search to learn more about
+
+ align:start position:0%
+literature search to learn more about
+ 
+
+ align:start position:0%
+literature search to learn more about
+the subject you know more than what has
+
+ align:start position:0%
+the subject you know more than what has
+ 
+
+ align:start position:0%
+the subject you know more than what has
+been taught in this in these lectures so
+
+ align:start position:0%
+been taught in this in these lectures so
+ 
+
+ align:start position:0%
+been taught in this in these lectures so
+that you can write about it on Wikipedia
+
+ align:start position:0%
+that you can write about it on Wikipedia
+ 
+
+ align:start position:0%
+that you can write about it on Wikipedia
+you can link to more references you know
+
+ align:start position:0%
+you can link to more references you know
+ 
+
+ align:start position:0%
+you can link to more references you know
+show the world what this subject is
+
+ align:start position:0%
+show the world what this subject is
+ 
+
+ align:start position:0%
+show the world what this subject is
+about okay can you do with our program
+
+ align:start position:0%
+about okay can you do with our program
+ 
+
+ align:start position:0%
+about okay can you do with our program
+so we spent the past few lectures
+
+ align:start position:0%
+so we spent the past few lectures
+ 
+
+ align:start position:0%
+so we spent the past few lectures
+developing tools regarding the structure
+
+ align:start position:0%
+developing tools regarding the structure
+ 
+
+ align:start position:0%
+developing tools regarding the structure
+of set Edition so that we can
+
+ align:start position:0%
+of set Edition so that we can
+ 
+
+ align:start position:0%
+of set Edition so that we can
+proof Fryman theorem so that's been our
+
+ align:start position:0%
+proof Fryman theorem so that's been our
+ 
+
+ align:start position:0%
+proof Fryman theorem so that's been our
+goal for the past few lectures and today
+
+ align:start position:0%
+goal for the past few lectures and today
+ 
+
+ align:start position:0%
+goal for the past few lectures and today
+will finally prove Freeman's theorem but
+
+ align:start position:0%
+will finally prove Freeman's theorem but
+ 
+
+ align:start position:0%
+will finally prove Freeman's theorem but
+let me first remind you the statement so
+
+ align:start position:0%
+let me first remind you the statement so
+ 
+
+ align:start position:0%
+let me first remind you the statement so
+in fragments theorem we would like to
+
+ align:start position:0%
+in fragments theorem we would like to
+ 
+
+ align:start position:0%
+in fragments theorem we would like to
+show that if you are in a substance if
+
+ align:start position:0%
+show that if you are in a substance if
+ 
+
+ align:start position:0%
+show that if you are in a substance if
+you're in the integers you have a set a
+
+ align:start position:0%
+you're in the integers you have a set a
+ 
+
+ align:start position:0%
+you're in the integers you have a set a
+path bang the doubling doubling constant
+
+ align:start position:0%
+path bang the doubling doubling constant
+ 
+
+ align:start position:0%
+path bang the doubling doubling constant
+constant K then the set must be
+
+ align:start position:0%
+constant K then the set must be
+ 
+
+ align:start position:0%
+constant K then the set must be
+contained in a small generalized
+
+ align:start position:0%
+contained in a small generalized
+ 
+
+ align:start position:0%
+contained in a small generalized
+arithmetic progression down the
+
+ align:start position:0%
+arithmetic progression down the
+ 
+
+ align:start position:0%
+arithmetic progression down the
+dimension and size only a constant
+
+ align:start position:0%
+dimension and size only a constant
+ 
+
+ align:start position:0%
+dimension and size only a constant
+factor larger than a we developed
+
+ align:start position:0%
+factor larger than a we developed
+ 
+
+ align:start position:0%
+factor larger than a we developed
+various tools the past three lectures
+
+ align:start position:0%
+various tools the past three lectures
+ 
+
+ align:start position:0%
+various tools the past three lectures
+building up to various intermediate
+
+ align:start position:0%
+building up to various intermediate
+ 
+
+ align:start position:0%
+building up to various intermediate
+results but we also collected this very
+
+ align:start position:0%
+results but we also collected this very
+ 
+
+ align:start position:0%
+results but we also collected this very
+nice set of tools for proving Freeman's
+
+ align:start position:0%
+nice set of tools for proving Freeman's
+ 
+
+ align:start position:0%
+nice set of tools for proving Freeman's
+theorem so let me review some of them
+
+ align:start position:0%
+theorem so let me review some of them
+ 
+
+ align:start position:0%
+theorem so let me review some of them
+which we'll encounter again today learn
+
+ align:start position:0%
+which we'll encounter again today learn
+ 
+
+ align:start position:0%
+which we'll encounter again today learn
+the karuta inequality tells you that if
+
+ align:start position:0%
+the karuta inequality tells you that if
+ 
+
+ align:start position:0%
+the karuta inequality tells you that if
+you have a set where small toppling then
+
+ align:start position:0%
+you have a set where small toppling then
+ 
+
+ align:start position:0%
+you have a set where small toppling then
+the further inter weighted sums are also
+
+ align:start position:0%
+the further inter weighted sums are also
+ 
+
+ align:start position:0%
+the further inter weighted sums are also
+controlled so I want you to think of
+
+ align:start position:0%
+controlled so I want you to think of
+ 
+
+ align:start position:0%
+controlled so I want you to think of
+these parameters as you know K is a
+
+ align:start position:0%
+these parameters as you know K is a
+ 
+
+ align:start position:0%
+these parameters as you know K is a
+constant so okay some powers to a
+
+ align:start position:0%
+constant so okay some powers to a
+ 
+
+ align:start position:0%
+constant so okay some powers to a
+constant but also I don't really care
+
+ align:start position:0%
+constant but also I don't really care
+ 
+
+ align:start position:0%
+constant but also I don't really care
+about polynomial changes in case so I
+
+ align:start position:0%
+about polynomial changes in case so I
+ 
+
+ align:start position:0%
+about polynomial changes in case so I
+changes in K and view this constant more
+
+ align:start position:0%
+changes in K and view this constant more
+ 
+
+ align:start position:0%
+changes in K and view this constant more
+or less as the origin okay itself so if
+
+ align:start position:0%
+or less as the origin okay itself so if
+ 
+
+ align:start position:0%
+or less as the origin okay itself so if
+some if the a plus a is around the same
+
+ align:start position:0%
+some if the a plus a is around the same
+ 
+
+ align:start position:0%
+some if the a plus a is around the same
+side st. and further iterations also do
+
+ align:start position:0%
+side st. and further iterations also do
+ 
+
+ align:start position:0%
+side st. and further iterations also do
+not change the sizes very much rules are
+
+ align:start position:0%
+not change the sizes very much rules are
+ 
+
+ align:start position:0%
+not change the sizes very much rules are
+covering lemma right so this was some
+
+ align:start position:0%
+covering lemma right so this was some
+ 
+
+ align:start position:0%
+covering lemma right so this was some
+statement that if X plus B looks like it
+
+ align:start position:0%
+statement that if X plus B looks like it
+ 
+
+ align:start position:0%
+statement that if X plus B looks like it
+could be covered by copies of B just in
+
+ align:start position:0%
+could be covered by copies of B just in
+ 
+
+ align:start position:0%
+could be covered by copies of B just in
+terms of their sizes alone then
+
+ align:start position:0%
+terms of their sizes alone then
+ 
+
+ align:start position:0%
+terms of their sizes alone then
+in fact X could be covered by a small
+
+ align:start position:0%
+in fact X could be covered by a small
+ 
+
+ align:start position:0%
+in fact X could be covered by a small
+number translates of a slightly larger
+
+ align:start position:0%
+number translates of a slightly larger
+ 
+
+ align:start position:0%
+number translates of a slightly larger
+ball but here can be any set we have
+
+ align:start position:0%
+ball but here can be any set we have
+ 
+
+ align:start position:0%
+ball but here can be any set we have
+this thing called remodeling lemma in
+
+ align:start position:0%
+this thing called remodeling lemma in
+ 
+
+ align:start position:0%
+this thing called remodeling lemma in
+particular consequence of it is that if
+
+ align:start position:0%
+particular consequence of it is that if
+ 
+
+ align:start position:0%
+particular consequence of it is that if
+a has small doubling then there exists a
+
+ align:start position:0%
+a has small doubling then there exists a
+ 
+
+ align:start position:0%
+a has small doubling then there exists a
+prime and that's not too much bigger
+
+ align:start position:0%
+prime and that's not too much bigger
+ 
+
+ align:start position:0%
+prime and that's not too much bigger
+than the size of a and a very large
+
+ align:start position:0%
+than the size of a and a very large
+ 
+
+ align:start position:0%
+than the size of a and a very large
+proportion an eighth of a subset of
+
+ align:start position:0%
+proportion an eighth of a subset of
+ 
+
+ align:start position:0%
+proportion an eighth of a subset of
+eighth such that the subset a prime is
+
+ align:start position:0%
+eighth such that the subset a prime is
+ 
+
+ align:start position:0%
+eighth such that the subset a prime is
+prime 1/8 isomorphic to a subset of Z
+
+ align:start position:0%
+prime 1/8 isomorphic to a subset of Z
+ 
+
+ align:start position:0%
+prime 1/8 isomorphic to a subset of Z
+mod n so even though you start with a
+
+ align:start position:0%
+mod n so even though you start with a
+ 
+
+ align:start position:0%
+mod n so even though you start with a
+set as potentially very spread out
+
+ align:start position:0%
+set as potentially very spread out
+ 
+
+ align:start position:0%
+set as potentially very spread out
+provided I have small doubling I can
+
+ align:start position:0%
+provided I have small doubling I can
+ 
+
+ align:start position:0%
+provided I have small doubling I can
+pick out a pretty large piece of it and
+
+ align:start position:0%
+pick out a pretty large piece of it and
+ 
+
+ align:start position:0%
+pick out a pretty large piece of it and
+model it by something in a fairly
+
+ align:start position:0%
+model it by something in a fairly
+ 
+
+ align:start position:0%
+model it by something in a fairly
+small cyclic group and here the modeling
+
+ align:start position:0%
+small cyclic group and here the modeling
+ 
+
+ align:start position:0%
+small cyclic group and here the modeling
+is eight isomorphic so it preserves sums
+
+ align:start position:0%
+is eight isomorphic so it preserves sums
+ 
+
+ align:start position:0%
+is eight isomorphic so it preserves sums
+up to eight term songs we had boggling
+
+ align:start position:0%
+up to eight term songs we had boggling
+ 
+
+ align:start position:0%
+up to eight term songs we had boggling
+buffs lemma so now we're inside a small
+
+ align:start position:0%
+buffs lemma so now we're inside a small
+ 
+
+ align:start position:0%
+buffs lemma so now we're inside a small
+cyclic group of a large subset of a
+
+ align:start position:0%
+cyclic group of a large subset of a
+ 
+
+ align:start position:0%
+cyclic group of a large subset of a
+small cyclic group then pokéballs lemma
+
+ align:start position:0%
+small cyclic group then pokéballs lemma
+ 
+
+ align:start position:0%
+small cyclic group then pokéballs lemma
+says that - a - - a contains a
+
+ align:start position:0%
+says that - a - - a contains a
+ 
+
+ align:start position:0%
+says that - a - - a contains a
+large-bore set a large structure within
+
+ align:start position:0%
+large-bore set a large structure within
+ 
+
+ align:start position:0%
+large-bore set a large structure within
+this iterated some set and last time we
+
+ align:start position:0%
+this iterated some set and last time we
+ 
+
+ align:start position:0%
+this iterated some set and last time we
+showed that via geometry of numbers via
+
+ align:start position:0%
+showed that via geometry of numbers via
+ 
+
+ align:start position:0%
+showed that via geometry of numbers via
+minkovski second theorem one can deduce
+
+ align:start position:0%
+minkovski second theorem one can deduce
+ 
+
+ align:start position:0%
+minkovski second theorem one can deduce
+that every bore set of small dimension
+
+ align:start position:0%
+that every bore set of small dimension
+ 
+
+ align:start position:0%
+that every bore set of small dimension
+and and small with contains of large
+
+ align:start position:0%
+and and small with contains of large
+ 
+
+ align:start position:0%
+and and small with contains of large
+with contains a proper gaap that's
+
+ align:start position:0%
+with contains a proper gaap that's
+ 
+
+ align:start position:0%
+with contains a proper gaap that's
+pretty large so putting these two
+
+ align:start position:0%
+pretty large so putting these two
+ 
+
+ align:start position:0%
+pretty large so putting these two
+together putting the last two things
+
+ align:start position:0%
+together putting the last two things
+ 
+
+ align:start position:0%
+together putting the last two things
+together we obtain that if you have a
+
+ align:start position:0%
+together we obtain that if you have a
+ 
+
+ align:start position:0%
+together we obtain that if you have a
+subset of the cyclic group and and prime
+
+ align:start position:0%
+subset of the cyclic group and and prime
+ 
+
+ align:start position:0%
+subset of the cyclic group and and prime
+okay so here previous statements so n is
+
+ align:start position:0%
+okay so here previous statements so n is
+ 
+
+ align:start position:0%
+okay so here previous statements so n is
+prime then and a is pretty large then -
+
+ align:start position:0%
+prime then and a is pretty large then -
+ 
+
+ align:start position:0%
+prime then and a is pretty large then -
+a - - a contains a proper generalized
+
+ align:start position:0%
+a - - a contains a proper generalized
+ 
+
+ align:start position:0%
+a - - a contains a proper generalized
+arithmetic progression of dimension at
+
+ align:start position:0%
+arithmetic progression of dimension at
+ 
+
+ align:start position:0%
+arithmetic progression of dimension at
+most alpha to the minus 2 and size at
+
+ align:start position:0%
+most alpha to the minus 2 and size at
+ 
+
+ align:start position:0%
+most alpha to the minus 2 and size at
+least 1 over 42 d times ok so just
+
+ align:start position:0%
+least 1 over 42 d times ok so just
+ 
+
+ align:start position:0%
+least 1 over 42 d times ok so just
+starting from the size of a - a - - a
+
+ align:start position:0%
+starting from the size of a - a - - a
+ 
+
+ align:start position:0%
+starting from the size of a - a - - a
+contains a pretty large gaap so we're
+
+ align:start position:0%
+contains a pretty large gaap so we're
+ 
+
+ align:start position:0%
+contains a pretty large gaap so we're
+gonna put all of these ingredients
+
+ align:start position:0%
+gonna put all of these ingredients
+ 
+
+ align:start position:0%
+gonna put all of these ingredients
+together and show that you can now
+
+ align:start position:0%
+together and show that you can now
+ 
+
+ align:start position:0%
+together and show that you can now
+contain the original set a in a small JP
+
+ align:start position:0%
+contain the original set a in a small JP
+ 
+
+ align:start position:0%
+contain the original set a in a small JP
+alright so just from knowing that some
+
+ align:start position:0%
+alright so just from knowing that some
+ 
+
+ align:start position:0%
+alright so just from knowing that some
+subset of it - a - 2 m so two things - a
+
+ align:start position:0%
+subset of it - a - 2 m so two things - a
+ 
+
+ align:start position:0%
+subset of it - a - 2 m so two things - a
+prime minus 2 a prime contains this
+
+ align:start position:0%
+prime minus 2 a prime contains this
+ 
+
+ align:start position:0%
+prime minus 2 a prime contains this
+large JP we're going to use it to boost
+
+ align:start position:0%
+large JP we're going to use it to boost
+ 
+
+ align:start position:0%
+large JP we're going to use it to boost
+it up to a cover
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so now let's proof friends they're
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+using the modeling memo using the modern
+
+ align:start position:0%
+using the modeling memo using the modern
+ 
+
+ align:start position:0%
+using the modeling memo using the modern
+dilemma the corollary of the modeling
+
+ align:start position:0%
+dilemma the corollary of the modeling
+ 
+
+ align:start position:0%
+dilemma the corollary of the modeling
+memo we find that since a plus a this
+
+ align:start position:0%
+memo we find that since a plus a this
+ 
+
+ align:start position:0%
+memo we find that since a plus a this
+size at most K times the size of a there
+
+ align:start position:0%
+size at most K times the size of a there
+ 
+
+ align:start position:0%
+size at most K times the size of a there
+exists sound Prime and at most 2k to the
+
+ align:start position:0%
+exists sound Prime and at most 2k to the
+ 
+
+ align:start position:0%
+exists sound Prime and at most 2k to the
+16 I'm saying and so I'm just copying
+
+ align:start position:0%
+16 I'm saying and so I'm just copying
+ 
+
+ align:start position:0%
+16 I'm saying and so I'm just copying
+the consequence of this modeling memo so
+
+ align:start position:0%
+the consequence of this modeling memo so
+ 
+
+ align:start position:0%
+the consequence of this modeling memo so
+I find a pretty large subset of a such
+
+ align:start position:0%
+I find a pretty large subset of a such
+ 
+
+ align:start position:0%
+I find a pretty large subset of a such
+that a prime is Fryman 8 isomorphic to a
+
+ align:start position:0%
+that a prime is Fryman 8 isomorphic to a
+ 
+
+ align:start position:0%
+that a prime is Fryman 8 isomorphic to a
+subset of Zima in now applying the final
+
+ align:start position:0%
+subset of Zima in now applying the final
+ 
+
+ align:start position:0%
+subset of Zima in now applying the final
+corollary with alpha being the size of
+
+ align:start position:0%
+corollary with alpha being the size of
+ 
+
+ align:start position:0%
+corollary with alpha being the size of
+this a prime which is at least the size
+
+ align:start position:0%
+this a prime which is at least the size
+ 
+
+ align:start position:0%
+this a prime which is at least the size
+of a over N which is at least 1 over 16
+
+ align:start position:0%
+of a over N which is at least 1 over 16
+ 
+
+ align:start position:0%
+of a over N which is at least 1 over 16
+to the times K to the power 16 so olbes
+
+ align:start position:0%
+to the times K to the power 16 so olbes
+ 
+
+ align:start position:0%
+to the times K to the power 16 so olbes
+constants we see that to a prime - okay
+
+ align:start position:0%
+constants we see that to a prime - okay
+ 
+
+ align:start position:0%
+constants we see that to a prime - okay
+so let me actually let me change the
+
+ align:start position:0%
+so let me actually let me change the
+ 
+
+ align:start position:0%
+so let me actually let me change the
+letters and call a prime B Prime
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+subset of a is coffee okay so to be - to
+
+ align:start position:0%
+subset of a is coffee okay so to be - to
+ 
+
+ align:start position:0%
+subset of a is coffee okay so to be - to
+be now contains a large GA p and the g
+
+ align:start position:0%
+be now contains a large GA p and the g
+ 
+
+ align:start position:0%
+be now contains a large GA p and the g
+AP has dimension D bounded right so the
+
+ align:start position:0%
+AP has dimension D bounded right so the
+ 
+
+ align:start position:0%
+AP has dimension D bounded right so the
+dimension is bounded by alpha to the
+
+ align:start position:0%
+dimension is bounded by alpha to the
+ 
+
+ align:start position:0%
+dimension is bounded by alpha to the
+minus two so so it's some constant and
+
+ align:start position:0%
+minus two so so it's some constant and
+ 
+
+ align:start position:0%
+minus two so so it's some constant and
+the size is pretty large size is at
+
+ align:start position:0%
+the size is pretty large size is at
+ 
+
+ align:start position:0%
+the size is pretty large size is at
+least one over 40 if you only care about
+
+ align:start position:0%
+least one over 40 if you only care about
+ 
+
+ align:start position:0%
+least one over 40 if you only care about
+constants just remember that everything
+
+ align:start position:0%
+constants just remember that everything
+ 
+
+ align:start position:0%
+constants just remember that everything
+that depends on K or D is a constant
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay because b is Fryman eight
+
+ align:start position:0%
+okay because b is Fryman eight
+ 
+
+ align:start position:0%
+okay because b is Fryman eight
+isomorphic eight isomorphic to be is a
+
+ align:start position:0%
+isomorphic eight isomorphic to be is a
+ 
+
+ align:start position:0%
+isomorphic eight isomorphic to be is a
+prime is a subset of a and b is the
+
+ align:start position:0%
+prime is a subset of a and b is the
+ 
+
+ align:start position:0%
+prime is a subset of a and b is the
+subset of Z mod b is a subset of Z mod n
+
+ align:start position:0%
+subset of Z mod b is a subset of Z mod n
+ 
+
+ align:start position:0%
+subset of Z mod b is a subset of Z mod n
+that a Prime's a isomorphic to so since
+
+ align:start position:0%
+that a Prime's a isomorphic to so since
+ 
+
+ align:start position:0%
+that a Prime's a isomorphic to so since
+P is eight isomorphic to a prime every
+
+ align:start position:0%
+P is eight isomorphic to a prime every
+ 
+
+ align:start position:0%
+P is eight isomorphic to a prime every
+GA p in B also so if you think about
+
+ align:start position:0%
+GA p in B also so if you think about
+ 
+
+ align:start position:0%
+GA p in B also so if you think about
+what eight isomorphism preserves you
+
+ align:start position:0%
+what eight isomorphism preserves you
+ 
+
+ align:start position:0%
+what eight isomorphism preserves you
+find that if you look at to be - to be
+
+ align:start position:0%
+find that if you look at to be - to be
+ 
+
+ align:start position:0%
+find that if you look at to be - to be
+it must be too friendly to isomorphic to
+
+ align:start position:0%
+it must be too friendly to isomorphic to
+ 
+
+ align:start position:0%
+it must be too friendly to isomorphic to
+to a prime minus Q eight right so the
+
+ align:start position:0%
+to a prime minus Q eight right so the
+ 
+
+ align:start position:0%
+to a prime minus Q eight right so the
+point of Fryman isomorphism is that we
+
+ align:start position:0%
+point of Fryman isomorphism is that we
+ 
+
+ align:start position:0%
+point of Fryman isomorphism is that we
+just want in to preserve enough additive
+
+ align:start position:0%
+just want in to preserve enough additive
+ 
+
+ align:start position:0%
+just want in to preserve enough additive
+structure while we're doing to preserve
+
+ align:start position:0%
+structure while we're doing to preserve
+ 
+
+ align:start position:0%
+structure while we're doing to preserve
+all the additive structure
+
+ align:start position:0%
+all the additive structure
+ 
+
+ align:start position:0%
+all the additive structure
+but just enough additive structure to do
+
+ align:start position:0%
+but just enough additive structure to do
+ 
+
+ align:start position:0%
+but just enough additive structure to do
+what we need to do and being able to
+
+ align:start position:0%
+what we need to do and being able to
+ 
+
+ align:start position:0%
+what we need to do and being able to
+preserve an arithmetic progression or in
+
+ align:start position:0%
+preserve an arithmetic progression or in
+ 
+
+ align:start position:0%
+preserve an arithmetic progression or in
+general or generalized arithmetic
+
+ align:start position:0%
+general or generalized arithmetic
+ 
+
+ align:start position:0%
+general or generalized arithmetic
+progression requires you to preserve
+
+ align:start position:0%
+progression requires you to preserve
+ 
+
+ align:start position:0%
+progression requires you to preserve
+Fryman to isomorphism and that's where
+
+ align:start position:0%
+Fryman to isomorphism and that's where
+ 
+
+ align:start position:0%
+Fryman to isomorphism and that's where
+the ink comes in I want to analyze to be
+
+ align:start position:0%
+the ink comes in I want to analyze to be
+ 
+
+ align:start position:0%
+the ink comes in I want to analyze to be
+- to be and I want that preserve to
+
+ align:start position:0%
+- to be and I want that preserve to
+ 
+
+ align:start position:0%
+- to be and I want that preserve to
+isomorphisms so initially I want B to
+
+ align:start position:0%
+isomorphisms so initially I want B to
+ 
+
+ align:start position:0%
+isomorphisms so initially I want B to
+preserve eight isomorphism so - P - 2
+
+ align:start position:0%
+preserve eight isomorphism so - P - 2
+ 
+
+ align:start position:0%
+preserve eight isomorphism so - P - 2
+B's find an isomorphic to - a prime
+
+ align:start position:0%
+B's find an isomorphic to - a prime
+ 
+
+ align:start position:0%
+B's find an isomorphic to - a prime
+minus 2 a prime so the g AP which we
+
+ align:start position:0%
+minus 2 a prime so the g AP which we
+ 
+
+ align:start position:0%
+minus 2 a prime so the g AP which we
+found earlier in 2b minus 2b is mapped
+
+ align:start position:0%
+found earlier in 2b minus 2b is mapped
+ 
+
+ align:start position:0%
+found earlier in 2b minus 2b is mapped
+via this friendly isomorphism to a
+
+ align:start position:0%
+via this friendly isomorphism to a
+ 
+
+ align:start position:0%
+via this friendly isomorphism to a
+proper g AP which we'll call q now
+
+ align:start position:0%
+proper g AP which we'll call q now
+ 
+
+ align:start position:0%
+proper g AP which we'll call q now
+sitting side to a - to it and preserving
+
+ align:start position:0%
+sitting side to a - to it and preserving
+ 
+
+ align:start position:0%
+sitting side to a - to it and preserving
+the same dimension and sighs so Fryman
+
+ align:start position:0%
+the same dimension and sighs so Fryman
+ 
+
+ align:start position:0%
+the same dimension and sighs so Fryman
+isomorphisms are good for preserving
+
+ align:start position:0%
+isomorphisms are good for preserving
+ 
+
+ align:start position:0%
+isomorphisms are good for preserving
+these partial additive structures like
+
+ align:start position:0%
+these partial additive structures like
+ 
+
+ align:start position:0%
+these partial additive structures like
+JPS
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+correct so questions were you saying so
+
+ align:start position:0%
+correct so questions were you saying so
+ 
+
+ align:start position:0%
+correct so questions were you saying so
+because we have to pass the to be - to
+
+ align:start position:0%
+because we have to pass the to be - to
+ 
+
+ align:start position:0%
+because we have to pass the to be - to
+be we want to be - to be to be friendly
+
+ align:start position:0%
+be we want to be - to be to be friendly
+ 
+
+ align:start position:0%
+be we want to be - to be to be friendly
+isomorphic to - a prime minus 2 a prime
+
+ align:start position:0%
+isomorphic to - a prime minus 2 a prime
+ 
+
+ align:start position:0%
+isomorphic to - a prime minus 2 a prime
+so that's why in the proof I won't be to
+
+ align:start position:0%
+so that's why in the proof I won't be to
+ 
+
+ align:start position:0%
+so that's why in the proof I won't be to
+be 8 isomorphic to a prime so you see so
+
+ align:start position:0%
+be 8 isomorphic to a prime so you see so
+ 
+
+ align:start position:0%
+be 8 isomorphic to a prime so you see so
+I'm skipping details of this step but if
+
+ align:start position:0%
+I'm skipping details of this step but if
+ 
+
+ align:start position:0%
+I'm skipping details of this step but if
+you read the definition of Fryman s
+
+ align:start position:0%
+you read the definition of Fryman s
+ 
+
+ align:start position:0%
+you read the definition of Fryman s
+isomorphism you see that this
+
+ align:start position:0%
+isomorphism you see that this
+ 
+
+ align:start position:0%
+isomorphism you see that this
+implication holds no - isomorphism is a
+
+ align:start position:0%
+implication holds no - isomorphism is a
+ 
+
+ align:start position:0%
+implication holds no - isomorphism is a
+weaker condition to isomorphism just
+
+ align:start position:0%
+weaker condition to isomorphism just
+ 
+
+ align:start position:0%
+weaker condition to isomorphism just
+means that you're preserving two wise
+
+ align:start position:0%
+means that you're preserving two wise
+ 
+
+ align:start position:0%
+means that you're preserving two wise
+sons think about the definition you're
+
+ align:start position:0%
+sons think about the definition you're
+ 
+
+ align:start position:0%
+sons think about the definition you're
+framing to isomorphism in particular if
+
+ align:start position:0%
+framing to isomorphism in particular if
+ 
+
+ align:start position:0%
+framing to isomorphism in particular if
+two sets are Fryman - isomorphic and you
+
+ align:start position:0%
+two sets are Fryman - isomorphic and you
+ 
+
+ align:start position:0%
+two sets are Fryman - isomorphic and you
+have a arithmetic progression in one
+
+ align:start position:0%
+have a arithmetic progression in one
+ 
+
+ align:start position:0%
+have a arithmetic progression in one
+then that arithmetic progression is also
+
+ align:start position:0%
+then that arithmetic progression is also
+ 
+
+ align:start position:0%
+then that arithmetic progression is also
+an arithmetic progression in the other
+
+ align:start position:0%
+an arithmetic progression in the other
+ 
+
+ align:start position:0%
+an arithmetic progression in the other
+okay so it's just enough a data
+
+ align:start position:0%
+okay so it's just enough a data
+ 
+
+ align:start position:0%
+okay so it's just enough a data
+structure to preserve things like
+
+ align:start position:0%
+structure to preserve things like
+ 
+
+ align:start position:0%
+structure to preserve things like
+arithmetic progressions and generalized
+
+ align:start position:0%
+arithmetic progressions and generalized
+ 
+
+ align:start position:0%
+arithmetic progressions and generalized
+arithmetic progressions okay so we found
+
+ align:start position:0%
+arithmetic progressions okay so we found
+ 
+
+ align:start position:0%
+arithmetic progressions okay so we found
+this large GAAP in - a - to it so this
+
+ align:start position:0%
+this large GAAP in - a - to it so this
+ 
+
+ align:start position:0%
+this large GAAP in - a - to it so this
+is this is America so we wanted to
+
+ align:start position:0%
+is this is America so we wanted to
+ 
+
+ align:start position:0%
+is this is America so we wanted to
+contain a in the GAAP seems that playing
+
+ align:start position:0%
+contain a in the GAAP seems that playing
+ 
+
+ align:start position:0%
+contain a in the GAAP seems that playing
+out with doing something sliding the
+
+ align:start position:0%
+out with doing something sliding the
+ 
+
+ align:start position:0%
+out with doing something sliding the
+opposite direction we find a large GA P
+
+ align:start position:0%
+opposite direction we find a large GA P
+ 
+
+ align:start position:0%
+opposite direction we find a large GA P
+within - a - to it but something we've
+
+ align:start position:0%
+within - a - to it but something we've
+ 
+
+ align:start position:0%
+within - a - to it but something we've
+seen before we're going to use this to
+
+ align:start position:0%
+seen before we're going to use this to
+ 
+
+ align:start position:0%
+seen before we're going to use this to
+boost ourselves to a covering of a via
+
+ align:start position:0%
+boost ourselves to a covering of a via
+ 
+
+ align:start position:0%
+boost ourselves to a covering of a via
+the Rouge are covering lemma right so
+
+ align:start position:0%
+the Rouge are covering lemma right so
+ 
+
+ align:start position:0%
+the Rouge are covering lemma right so
+once you find this large structure you
+
+ align:start position:0%
+once you find this large structure you
+ 
+
+ align:start position:0%
+once you find this large structure you
+can now try to take translates of it to
+
+ align:start position:0%
+can now try to take translates of it to
+ 
+
+ align:start position:0%
+can now try to take translates of it to
+cover and this is if there's any take
+
+ align:start position:0%
+cover and this is if there's any take
+ 
+
+ align:start position:0%
+cover and this is if there's any take
+away from the spirit of this proof is
+
+ align:start position:0%
+away from the spirit of this proof is
+ 
+
+ align:start position:0%
+away from the spirit of this proof is
+this idea even though I want to cover
+
+ align:start position:0%
+this idea even though I want to cover
+ 
+
+ align:start position:0%
+this idea even though I want to cover
+the whole set it's okay I just find a
+
+ align:start position:0%
+the whole set it's okay I just find a
+ 
+
+ align:start position:0%
+the whole set it's okay I just find a
+large structure within it and then I use
+
+ align:start position:0%
+large structure within it and then I use
+ 
+
+ align:start position:0%
+large structure within it and then I use
+translates to cover how do we do this
+
+ align:start position:0%
+translates to cover how do we do this
+ 
+
+ align:start position:0%
+translates to cover how do we do this
+so since Q is containing 2a minus 2a we
+
+ align:start position:0%
+so since Q is containing 2a minus 2a we
+ 
+
+ align:start position:0%
+so since Q is containing 2a minus 2a we
+find that Q plus a is containing 3a
+
+ align:start position:0%
+find that Q plus a is containing 3a
+ 
+
+ align:start position:0%
+find that Q plus a is containing 3a
+minus 2a therefore by Clinique Arusha
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+clinical Russa inequality the size of Q
+
+ align:start position:0%
+clinical Russa inequality the size of Q
+ 
+
+ align:start position:0%
+clinical Russa inequality the size of Q
+plus a is at most the size of 3a minus
+
+ align:start position:0%
+plus a is at most the size of 3a minus
+ 
+
+ align:start position:0%
+plus a is at most the size of 3a minus
+2a which is at most K to the fifth power
+
+ align:start position:0%
+2a which is at most K to the fifth power
+ 
+
+ align:start position:0%
+2a which is at most K to the fifth power
+times the size of a and I claim that
+
+ align:start position:0%
+times the size of a and I claim that
+ 
+
+ align:start position:0%
+times the size of a and I claim that
+this final quantity is also not so
+
+ align:start position:0%
+this final quantity is also not so
+ 
+
+ align:start position:0%
+this final quantity is also not so
+different from the size of Q right
+
+ align:start position:0%
+different from the size of Q right
+ 
+
+ align:start position:0%
+different from the size of Q right
+because okay so all of these I mean the
+
+ align:start position:0%
+because okay so all of these I mean the
+ 
+
+ align:start position:0%
+because okay so all of these I mean the
+point here is we are doing all of these
+
+ align:start position:0%
+point here is we are doing all of these
+ 
+
+ align:start position:0%
+point here is we are doing all of these
+transformations passing down to subsets
+
+ align:start position:0%
+transformations passing down to subsets
+ 
+
+ align:start position:0%
+transformations passing down to subsets
+putting something bigger putting getting
+
+ align:start position:0%
+putting something bigger putting getting
+ 
+
+ align:start position:0%
+putting something bigger putting getting
+to something smaller but each time we
+
+ align:start position:0%
+to something smaller but each time we
+ 
+
+ align:start position:0%
+to something smaller but each time we
+only lose something that is polynomial
+
+ align:start position:0%
+only lose something that is polynomial
+ 
+
+ align:start position:0%
+only lose something that is polynomial
+in K we're not losing much more
+
+ align:start position:0%
+in K we're not losing much more
+ 
+
+ align:start position:0%
+in K we're not losing much more
+I'm also only losing a constant factor
+
+ align:start position:0%
+I'm also only losing a constant factor
+ 
+
+ align:start position:0%
+I'm also only losing a constant factor
+there's sometimes a bit more than more
+
+ align:start position:0%
+there's sometimes a bit more than more
+ 
+
+ align:start position:0%
+there's sometimes a bit more than more
+than polynomial but in any case we're
+
+ align:start position:0%
+than polynomial but in any case we're
+ 
+
+ align:start position:0%
+than polynomial but in any case we're
+losing only a constant factor at each
+
+ align:start position:0%
+losing only a constant factor at each
+ 
+
+ align:start position:0%
+losing only a constant factor at each
+step so in particular since and upper
+
+ align:start position:0%
+step so in particular since and upper
+ 
+
+ align:start position:0%
+step so in particular since and upper
+bounds size a prime and it's larger than
+
+ align:start position:0%
+bounds size a prime and it's larger than
+ 
+
+ align:start position:0%
+bounds size a prime and it's larger than
+a prime which is at least a constant
+
+ align:start position:0%
+a prime which is at least a constant
+ 
+
+ align:start position:0%
+a prime which is at least a constant
+fraction of a and the size of Q is at
+
+ align:start position:0%
+fraction of a and the size of Q is at
+ 
+
+ align:start position:0%
+fraction of a and the size of Q is at
+least one over 40 raised to D times and
+
+ align:start position:0%
+least one over 40 raised to D times and
+ 
+
+ align:start position:0%
+least one over 40 raised to D times and
+so we find that this
+
+ align:start position:0%
+so we find that this
+ 
+
+ align:start position:0%
+so we find that this
+bound upper bound earlier on q+ a we can
+
+ align:start position:0%
+bound upper bound earlier on q+ a we can
+ 
+
+ align:start position:0%
+bound upper bound earlier on q+ a we can
+write it in terms of size of cube where
+
+ align:start position:0%
+write it in terms of size of cube where
+ 
+
+ align:start position:0%
+write it in terms of size of cube where
+K prime is put all of these numbers
+
+ align:start position:0%
+K prime is put all of these numbers
+ 
+
+ align:start position:0%
+K prime is put all of these numbers
+together what it specifically doesn't
+
+ align:start position:0%
+together what it specifically doesn't
+ 
+
+ align:start position:0%
+together what it specifically doesn't
+matter so much other than that it is a
+
+ align:start position:0%
+matter so much other than that it is a
+ 
+
+ align:start position:0%
+matter so much other than that it is a
+constant D is polynomial in K so what we
+
+ align:start position:0%
+constant D is polynomial in K so what we
+ 
+
+ align:start position:0%
+constant D is polynomial in K so what we
+have here is something that's
+
+ align:start position:0%
+have here is something that's
+ 
+
+ align:start position:0%
+have here is something that's
+exponential in the polynomial of K okay
+
+ align:start position:0%
+exponential in the polynomial of K okay
+ 
+
+ align:start position:0%
+exponential in the polynomial of K okay
+so now we're in a position to apply the
+
+ align:start position:0%
+so now we're in a position to apply the
+ 
+
+ align:start position:0%
+so now we're in a position to apply the
+Rouge are covering lemma so look at that
+
+ align:start position:0%
+Rouge are covering lemma so look at that
+ 
+
+ align:start position:0%
+Rouge are covering lemma so look at that
+statement up there so what is it saying
+
+ align:start position:0%
+statement up there so what is it saying
+ 
+
+ align:start position:0%
+statement up there so what is it saying
+that a plus Q looks like it could be
+
+ align:start position:0%
+that a plus Q looks like it could be
+ 
+
+ align:start position:0%
+that a plus Q looks like it could be
+covered by Q just in terms of size so I
+
+ align:start position:0%
+covered by Q just in terms of size so I
+ 
+
+ align:start position:0%
+covered by Q just in terms of size so I
+should expect to cover a by a small
+
+ align:start position:0%
+should expect to cover a by a small
+ 
+
+ align:start position:0%
+should expect to cover a by a small
+number of translates of Q minus Q so by
+
+ align:start position:0%
+number of translates of Q minus Q so by
+ 
+
+ align:start position:0%
+number of translates of Q minus Q so by
+covering lemma a it's contained in some
+
+ align:start position:0%
+covering lemma a it's contained in some
+ 
+
+ align:start position:0%
+covering lemma a it's contained in some
+X plus Q minus Q for some X where the
+
+ align:start position:0%
+X plus Q minus Q for some X where the
+ 
+
+ align:start position:0%
+X plus Q minus Q for some X where the
+size of X is at most K Prime I claim so
+
+ align:start position:0%
+size of X is at most K Prime I claim so
+ 
+
+ align:start position:0%
+size of X is at most K Prime I claim so
+we've covered it by something Q is a ga
+
+ align:start position:0%
+we've covered it by something Q is a ga
+ 
+
+ align:start position:0%
+we've covered it by something Q is a ga
+P X is a bounded size set and I claim
+
+ align:start position:0%
+P X is a bounded size set and I claim
+ 
+
+ align:start position:0%
+P X is a bounded size set and I claim
+that this is the type of object that
+
+ align:start position:0%
+that this is the type of object that
+ 
+
+ align:start position:0%
+that this is the type of object that
+we're happy to have just to spell out
+
+ align:start position:0%
+we're happy to have just to spell out
+ 
+
+ align:start position:0%
+we're happy to have just to spell out
+some details first note that X is
+
+ align:start position:0%
+some details first note that X is
+ 
+
+ align:start position:0%
+some details first note that X is
+contained in a JP dimension x so X minus
+
+ align:start position:0%
+contained in a JP dimension x so X minus
+ 
+
+ align:start position:0%
+contained in a JP dimension x so X minus
+1 with length 2 in each direction
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+to add a new direction for every element
+
+ align:start position:0%
+to add a new direction for every element
+ 
+
+ align:start position:0%
+to add a new direction for every element
+of X it's wasteful but everything is
+
+ align:start position:0%
+of X it's wasteful but everything is
+ 
+
+ align:start position:0%
+of X it's wasteful but everything is
+constant and recall that the dimension
+
+ align:start position:0%
+constant and recall that the dimension
+ 
+
+ align:start position:0%
+constant and recall that the dimension
+of Q as a G a PSD so X plus Q minus Q is
+
+ align:start position:0%
+of Q as a G a PSD so X plus Q minus Q is
+ 
+
+ align:start position:0%
+of Q as a G a PSD so X plus Q minus Q is
+contained in Ag AP of dimension okay so
+
+ align:start position:0%
+contained in Ag AP of dimension okay so
+ 
+
+ align:start position:0%
+contained in Ag AP of dimension okay so
+what's the dimension also when I do Q
+
+ align:start position:0%
+what's the dimension also when I do Q
+ 
+
+ align:start position:0%
+what's the dimension also when I do Q
+minus Q is like taking a box and
+
+ align:start position:0%
+minus Q is like taking a box and
+ 
+
+ align:start position:0%
+minus Q is like taking a box and
+toppling its dimension doubling its
+
+ align:start position:0%
+toppling its dimension doubling its
+ 
+
+ align:start position:0%
+toppling its dimension doubling its
+length I'm not changing the number of
+
+ align:start position:0%
+length I'm not changing the number of
+ 
+
+ align:start position:0%
+length I'm not changing the number of
+dimensions so the dimension of Q minus Q
+
+ align:start position:0%
+dimensions so the dimension of Q minus Q
+ 
+
+ align:start position:0%
+dimensions so the dimension of Q minus Q
+is still deep a dimension of X is at
+
+ align:start position:0%
+is still deep a dimension of X is at
+ 
+
+ align:start position:0%
+is still deep a dimension of X is at
+most size of X all of these things are
+
+ align:start position:0%
+most size of X all of these things are
+ 
+
+ align:start position:0%
+most size of X all of these things are
+constants so so we're happy but just
+
+ align:start position:0%
+constants so so we're happy but just
+ 
+
+ align:start position:0%
+constants so so we're happy but just
+spell it out the constant here is K
+
+ align:start position:0%
+spell it out the constant here is K
+ 
+
+ align:start position:0%
+spell it out the constant here is K
+prime is what we wrote up there this is
+
+ align:start position:0%
+prime is what we wrote up there this is
+ 
+
+ align:start position:0%
+prime is what we wrote up there this is
+a constant and the size right so what is
+
+ align:start position:0%
+a constant and the size right so what is
+ 
+
+ align:start position:0%
+a constant and the size right so what is
+the size of the gaap that contains this
+
+ align:start position:0%
+the size of the gaap that contains this
+ 
+
+ align:start position:0%
+the size of the gaap that contains this
+guy here so I'm expanding X to a GAAP by
+
+ align:start position:0%
+guy here so I'm expanding X to a GAAP by
+ 
+
+ align:start position:0%
+guy here so I'm expanding X to a GAAP by
+adding a new direction for every element
+
+ align:start position:0%
+adding a new direction for every element
+ 
+
+ align:start position:0%
+adding a new direction for every element
+of X and I might expand that size a
+
+ align:start position:0%
+of X and I might expand that size a
+ 
+
+ align:start position:0%
+of X and I might expand that size a
+little bit but the size of this GAAP
+
+ align:start position:0%
+little bit but the size of this GAAP
+ 
+
+ align:start position:0%
+little bit but the size of this GAAP
+that contains X it's no more than 2 to
+
+ align:start position:0%
+that contains X it's no more than 2 to
+ 
+
+ align:start position:0%
+that contains X it's no more than 2 to
+the power X - 2 raised to the size of X
+
+ align:start position:0%
+the power X - 2 raised to the size of X
+ 
+
+ align:start position:0%
+the power X - 2 raised to the size of X
+when there's the size of the gaap Q - Q
+
+ align:start position:0%
+when there's the size of the gaap Q - Q
+ 
+
+ align:start position:0%
+when there's the size of the gaap Q - Q
+so Q is a JP of dimension D and we know
+
+ align:start position:0%
+so Q is a JP of dimension D and we know
+ 
+
+ align:start position:0%
+so Q is a JP of dimension D and we know
+that a ga P of dimension D has doubling
+
+ align:start position:0%
+that a ga P of dimension D has doubling
+ 
+
+ align:start position:0%
+that a ga P of dimension D has doubling
+constant and those two to the D
+
+ align:start position:0%
+constant and those two to the D
+ 
+
+ align:start position:0%
+constant and those two to the D
+to to the D times the size of you okay
+
+ align:start position:0%
+to to the D times the size of you okay
+ 
+
+ align:start position:0%
+to to the D times the size of you okay
+and because Q is contained in QA - to a
+
+ align:start position:0%
+and because Q is contained in QA - to a
+ 
+
+ align:start position:0%
+and because Q is contained in QA - to a
+we find that Q is contained in to a - 2
+
+ align:start position:0%
+we find that Q is contained in to a - 2
+ 
+
+ align:start position:0%
+we find that Q is contained in to a - 2
+a and 2 to the X well I know what the
+
+ align:start position:0%
+a and 2 to the X well I know what the
+ 
+
+ align:start position:0%
+a and 2 to the X well I know what the
+size of X is bounded by a prime plus the
+
+ align:start position:0%
+size of X is bounded by a prime plus the
+ 
+
+ align:start position:0%
+size of X is bounded by a prime plus the
+size of X is size of X's are most K
+
+ align:start position:0%
+size of X is size of X's are most K
+ 
+
+ align:start position:0%
+size of X is size of X's are most K
+prime and then I have 2 to the D over
+
+ align:start position:0%
+prime and then I have 2 to the D over
+ 
+
+ align:start position:0%
+prime and then I have 2 to the D over
+here - a - to a by Polonia kirusha is
+
+ align:start position:0%
+here - a - to a by Polonia kirusha is
+ 
+
+ align:start position:0%
+here - a - to a by Polonia kirusha is
+our most K to the for the size of a ok
+
+ align:start position:0%
+our most K to the for the size of a ok
+ 
+
+ align:start position:0%
+our most K to the for the size of a ok
+you put everything together we find that
+
+ align:start position:0%
+you put everything together we find that
+ 
+
+ align:start position:0%
+you put everything together we find that
+this bound here is doubly exponential in
+
+ align:start position:0%
+this bound here is doubly exponential in
+ 
+
+ align:start position:0%
+this bound here is doubly exponential in
+the polynomial okay and that's it this
+
+ align:start position:0%
+the polynomial okay and that's it this
+ 
+
+ align:start position:0%
+the polynomial okay and that's it this
+proofs from it's due to recap
+
+ align:start position:0%
+proofs from it's due to recap
+ 
+
+ align:start position:0%
+proofs from it's due to recap
+we went through several steps so first
+
+ align:start position:0%
+we went through several steps so first
+ 
+
+ align:start position:0%
+we went through several steps so first
+using the modeling lemma we know that if
+
+ align:start position:0%
+using the modeling lemma we know that if
+ 
+
+ align:start position:0%
+using the modeling lemma we know that if
+a set a has small doubling then we can
+
+ align:start position:0%
+a set a has small doubling then we can
+ 
+
+ align:start position:0%
+a set a has small doubling then we can
+pass a large part of a to a relatively
+
+ align:start position:0%
+pass a large part of a to a relatively
+ 
+
+ align:start position:0%
+pass a large part of a to a relatively
+small cyclic group I'm going to work
+
+ align:start position:0%
+small cyclic group I'm going to work
+ 
+
+ align:start position:0%
+small cyclic group I'm going to work
+inside a cyclic group using bug Labov
+
+ align:start position:0%
+inside a cyclic group using bug Labov
+ 
+
+ align:start position:0%
+inside a cyclic group using bug Labov
+lemma and and it's geometry of numbers
+
+ align:start position:0%
+lemma and and it's geometry of numbers
+ 
+
+ align:start position:0%
+lemma and and it's geometry of numbers
+corollary which I find that inside the
+
+ align:start position:0%
+corollary which I find that inside the
+ 
+
+ align:start position:0%
+corollary which I find that inside the
+cyclic group the corresponding set which
+
+ align:start position:0%
+cyclic group the corresponding set which
+ 
+
+ align:start position:0%
+cyclic group the corresponding set which
+we call B it's such that 2 B minus 2 B
+
+ align:start position:0%
+we call B it's such that 2 B minus 2 B
+ 
+
+ align:start position:0%
+we call B it's such that 2 B minus 2 B
+contains a large GA P we passed that
+
+ align:start position:0%
+contains a large GA P we passed that
+ 
+
+ align:start position:0%
+contains a large GA P we passed that
+gaap back to the original set a because
+
+ align:start position:0%
+gaap back to the original set a because
+ 
+
+ align:start position:0%
+gaap back to the original set a because
+we are preserving 8 isomorphisms Fryman
+
+ align:start position:0%
+we are preserving 8 isomorphisms Fryman
+ 
+
+ align:start position:0%
+we are preserving 8 isomorphisms Fryman
+8 isomorphisms in Ruza modeling lemma so
+
+ align:start position:0%
+8 isomorphisms in Ruza modeling lemma so
+ 
+
+ align:start position:0%
+8 isomorphisms in Ruza modeling lemma so
+we can pass through the origin of set a
+
+ align:start position:0%
+we can pass through the origin of set a
+ 
+
+ align:start position:0%
+we can pass through the origin of set a
+and find a large GA P in to a minus 2 a
+
+ align:start position:0%
+and find a large GA P in to a minus 2 a
+ 
+
+ align:start position:0%
+and find a large GA P in to a minus 2 a
+once we find as large GA p 2a minus 2 a
+
+ align:start position:0%
+once we find as large GA p 2a minus 2 a
+ 
+
+ align:start position:0%
+once we find as large GA p 2a minus 2 a
+then we're going to use the Ruza
+
+ align:start position:0%
+then we're going to use the Ruza
+ 
+
+ align:start position:0%
+then we're going to use the Ruza
+covering lemma to contain a inside a
+
+ align:start position:0%
+covering lemma to contain a inside a
+ 
+
+ align:start position:0%
+covering lemma to contain a inside a
+small number of translates of this GA p
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay you put all of these things
+
+ align:start position:0%
+okay you put all of these things
+ 
+
+ align:start position:0%
+okay you put all of these things
+together and the appropriate bounds
+
+ align:start position:0%
+together and the appropriate bounds
+ 
+
+ align:start position:0%
+together and the appropriate bounds
+coming from putting the kirusha
+
+ align:start position:0%
+coming from putting the kirusha
+ 
+
+ align:start position:0%
+coming from putting the kirusha
+inequalities and you get and this is a
+
+ align:start position:0%
+inequalities and you get and this is a
+ 
+
+ align:start position:0%
+inequalities and you get and this is a
+proof of Ryman's theorem
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay question how do you make it proper
+
+ align:start position:0%
+okay question how do you make it proper
+ 
+
+ align:start position:0%
+okay question how do you make it proper
+up and tell the step with Q it is still
+
+ align:start position:0%
+up and tell the step with Q it is still
+ 
+
+ align:start position:0%
+up and tell the step with Q it is still
+proper so the very last step over here
+
+ align:start position:0%
+proper so the very last step over here
+ 
+
+ align:start position:0%
+proper so the very last step over here
+it is you might have destroyed
+
+ align:start position:0%
+it is you might have destroyed
+ 
+
+ align:start position:0%
+it is you might have destroyed
+properties so this proof here doesn't
+
+ align:start position:0%
+properties so this proof here doesn't
+ 
+
+ align:start position:0%
+properties so this proof here doesn't
+give you properties so I mention in the
+
+ align:start position:0%
+give you properties so I mention in the
+ 
+
+ align:start position:0%
+give you properties so I mention in the
+beginning that in Fryman serum you can
+
+ align:start position:0%
+beginning that in Fryman serum you can
+ 
+
+ align:start position:0%
+beginning that in Fryman serum you can
+obtain properties of the an additional
+
+ align:start position:0%
+obtain properties of the an additional
+ 
+
+ align:start position:0%
+obtain properties of the an additional
+argument so that I'm not going to show
+
+ align:start position:0%
+argument so that I'm not going to show
+ 
+
+ align:start position:0%
+argument so that I'm not going to show
+this some more work which is related to
+
+ align:start position:0%
+this some more work which is related to
+ 
+
+ align:start position:0%
+this some more work which is related to
+geometry of numbers so from so for
+
+ align:start position:0%
+geometry of numbers so from so for
+ 
+
+ align:start position:0%
+geometry of numbers so from so for
+example you can look up in the textbook
+
+ align:start position:0%
+example you can look up in the textbook
+ 
+
+ align:start position:0%
+example you can look up in the textbook
+by Tao and you see how to get from a
+
+ align:start position:0%
+by Tao and you see how to get from a
+ 
+
+ align:start position:0%
+by Tao and you see how to get from a
+GAAP to contain it in a proper GAAP
+
+ align:start position:0%
+GAAP to contain it in a proper GAAP
+ 
+
+ align:start position:0%
+GAAP to contain it in a proper GAAP
+without losing too much in terms of size
+
+ align:start position:0%
+without losing too much in terms of size
+ 
+
+ align:start position:0%
+without losing too much in terms of size
+so in terms of the man you think about
+
+ align:start position:0%
+so in terms of the man you think about
+ 
+
+ align:start position:0%
+so in terms of the man you think about
+it this way so how when is an one do you
+
+ align:start position:0%
+it this way so how when is an one do you
+ 
+
+ align:start position:0%
+it this way so how when is an one do you
+have something which is not properly
+
+ align:start position:0%
+have something which is not properly
+ 
+
+ align:start position:0%
+have something which is not properly
+when you have and if some linear
+
+ align:start position:0%
+when you have and if some linear
+ 
+
+ align:start position:0%
+when you have and if some linear
+dependence when you have some integer
+
+ align:start position:0%
+dependence when you have some integer
+ 
+
+ align:start position:0%
+dependence when you have some integer
+linear dependence and in that case you
+
+ align:start position:0%
+linear dependence and in that case you
+ 
+
+ align:start position:0%
+linear dependence and in that case you
+kind of lost the dimension we have
+
+ align:start position:0%
+kind of lost the dimension we have
+ 
+
+ align:start position:0%
+kind of lost the dimension we have
+improper news you actually go down the
+
+ align:start position:0%
+improper news you actually go down the
+ 
+
+ align:start position:0%
+improper news you actually go down the
+dimension but then you need to salvage
+
+ align:start position:0%
+dimension but then you need to salvage
+ 
+
+ align:start position:0%
+dimension but then you need to salvage
+to the sides to make sure that the size
+
+ align:start position:0%
+to the sides to make sure that the size
+ 
+
+ align:start position:0%
+to the sides to make sure that the size
+doesn't blow up too much and so there
+
+ align:start position:0%
+doesn't blow up too much and so there
+ 
+
+ align:start position:0%
+doesn't blow up too much and so there
+are some arguments to be done there and
+
+ align:start position:0%
+are some arguments to be done there and
+ 
+
+ align:start position:0%
+are some arguments to be done there and
+we're not gonna do so the question is to
+
+ align:start position:0%
+we're not gonna do so the question is to
+ 
+
+ align:start position:0%
+we're not gonna do so the question is to
+get proper nice do I have to modify the
+
+ align:start position:0%
+get proper nice do I have to modify the
+ 
+
+ align:start position:0%
+get proper nice do I have to modify the
+proof oh can I use Freeman's theorem as
+
+ align:start position:0%
+proof oh can I use Freeman's theorem as
+ 
+
+ align:start position:0%
+proof oh can I use Freeman's theorem as
+witness a black box so my understanding
+
+ align:start position:0%
+witness a black box so my understanding
+ 
+
+ align:start position:0%
+witness a black box so my understanding
+is that you can use the statements a
+
+ align:start position:0%
+is that you can use the statements a
+ 
+
+ align:start position:0%
+is that you can use the statements a
+black box and obtain properties but if
+
+ align:start position:0%
+black box and obtain properties but if
+ 
+
+ align:start position:0%
+black box and obtain properties but if
+you want to get good balance maybe you
+
+ align:start position:0%
+you want to get good balance maybe you
+ 
+
+ align:start position:0%
+you want to get good balance maybe you
+have to go into the proof I'm not sure
+
+ align:start position:0%
+have to go into the proof I'm not sure
+ 
+
+ align:start position:0%
+have to go into the proof I'm not sure
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+any more questions all right so
+
+ align:start position:0%
+any more questions all right so
+ 
+
+ align:start position:0%
+any more questions all right so
+so this took a while so this was the
+
+ align:start position:0%
+so this took a while so this was the
+ 
+
+ align:start position:0%
+so this took a while so this was the
+most involved proof we've done in this
+
+ align:start position:0%
+most involved proof we've done in this
+ 
+
+ align:start position:0%
+most involved proof we've done in this
+course so far
+
+ align:start position:0%
+course so far
+ 
+
+ align:start position:0%
+course so far
+improving Freeman's theorems we had to
+
+ align:start position:0%
+improving Freeman's theorems we had to
+ 
+
+ align:start position:0%
+improving Freeman's theorems we had to
+develop a large number of tools and we
+
+ align:start position:0%
+develop a large number of tools and we
+ 
+
+ align:start position:0%
+develop a large number of tools and we
+came up so and we eventually arrived at
+
+ align:start position:0%
+came up so and we eventually arrived at
+ 
+
+ align:start position:0%
+came up so and we eventually arrived at
+you know it's a beautiful theory so this
+
+ align:start position:0%
+you know it's a beautiful theory so this
+ 
+
+ align:start position:0%
+you know it's a beautiful theory so this
+is a fantastic result
+
+ align:start position:0%
+is a fantastic result
+ 
+
+ align:start position:0%
+is a fantastic result
+that gives you an inverse structure
+
+ align:start position:0%
+that gives you an inverse structure
+ 
+
+ align:start position:0%
+that gives you an inverse structure
+something we know that GP s-- have small
+
+ align:start position:0%
+something we know that GP s-- have small
+ 
+
+ align:start position:0%
+something we know that GP s-- have small
+doubling and converts s if something has
+
+ align:start position:0%
+doubling and converts s if something has
+ 
+
+ align:start position:0%
+doubling and converts s if something has
+small doubling it has to in some sense
+
+ align:start position:0%
+small doubling it has to in some sense
+ 
+
+ align:start position:0%
+small doubling it has to in some sense
+look like a GP you see that the proof is
+
+ align:start position:0%
+look like a GP you see that the proof is
+ 
+
+ align:start position:0%
+look like a GP you see that the proof is
+quite involved in has a lot of beautiful
+
+ align:start position:0%
+quite involved in has a lot of beautiful
+ 
+
+ align:start position:0%
+quite involved in has a lot of beautiful
+ideas in the remainder of today's
+
+ align:start position:0%
+ideas in the remainder of today's
+ 
+
+ align:start position:0%
+ideas in the remainder of today's
+lecture I want to present some remarks
+
+ align:start position:0%
+lecture I want to present some remarks
+ 
+
+ align:start position:0%
+lecture I want to present some remarks
+on additional extensions and
+
+ align:start position:0%
+on additional extensions and
+ 
+
+ align:start position:0%
+on additional extensions and
+generalizations of Freeman's theorem and
+
+ align:start position:0%
+generalizations of Freeman's theorem and
+ 
+
+ align:start position:0%
+generalizations of Freeman's theorem and
+what we're not going to do any proofs
+
+ align:start position:0%
+what we're not going to do any proofs
+ 
+
+ align:start position:0%
+what we're not going to do any proofs
+there's a lot of deep and beautiful
+
+ align:start position:0%
+there's a lot of deep and beautiful
+ 
+
+ align:start position:0%
+there's a lot of deep and beautiful
+mathematics that are involved in in the
+
+ align:start position:0%
+mathematics that are involved in in the
+ 
+
+ align:start position:0%
+mathematics that are involved in in the
+subject so this is I want to take you to
+
+ align:start position:0%
+subject so this is I want to take you to
+ 
+
+ align:start position:0%
+subject so this is I want to take you to
+a tour through some of them more things
+
+ align:start position:0%
+a tour through some of them more things
+ 
+
+ align:start position:0%
+a tour through some of them more things
+that we can talk about when it comes to
+
+ align:start position:0%
+that we can talk about when it comes to
+ 
+
+ align:start position:0%
+that we can talk about when it comes to
+fragments theorem but first let me
+
+ align:start position:0%
+fragments theorem but first let me
+ 
+
+ align:start position:0%
+fragments theorem but first let me
+mention a few things that I mentioned
+
+ align:start position:0%
+mention a few things that I mentioned
+ 
+
+ align:start position:0%
+mention a few things that I mentioned
+very quickly when we first introduced
+
+ align:start position:0%
+very quickly when we first introduced
+ 
+
+ align:start position:0%
+very quickly when we first introduced
+Freeman's theorem namely some remarks on
+
+ align:start position:0%
+Freeman's theorem namely some remarks on
+ 
+
+ align:start position:0%
+Freeman's theorem namely some remarks on
+the balance so the proof that we just
+
+ align:start position:0%
+the balance so the proof that we just
+ 
+
+ align:start position:0%
+the balance so the proof that we just
+saw gives you a pound which is basically
+
+ align:start position:0%
+saw gives you a pound which is basically
+ 
+
+ align:start position:0%
+saw gives you a pound which is basically
+exponential in the dimension and doubly
+
+ align:start position:0%
+exponential in the dimension and doubly
+ 
+
+ align:start position:0%
+exponential in the dimension and doubly
+exponential for the size blow up all
+
+ align:start position:0%
+exponential for the size blow up all
+ 
+
+ align:start position:0%
+exponential for the size blow up all
+constants so if that's you only care
+
+ align:start position:0%
+constants so if that's you only care
+ 
+
+ align:start position:0%
+constants so if that's you only care
+about constants then then this is just
+
+ align:start position:0%
+about constants then then this is just
+ 
+
+ align:start position:0%
+about constants then then this is just
+fine but you might ask are we losing too
+
+ align:start position:0%
+fine but you might ask are we losing too
+ 
+
+ align:start position:0%
+fine but you might ask are we losing too
+much what is the the right type of
+
+ align:start position:0%
+much what is the the right type of
+ 
+
+ align:start position:0%
+much what is the the right type of
+dependence so what is the right type of
+
+ align:start position:0%
+dependence so what is the right type of
+ 
+
+ align:start position:0%
+dependence so what is the right type of
+dependence so we saw in an example so we
+
+ align:start position:0%
+dependence so we saw in an example so we
+ 
+
+ align:start position:0%
+dependence so we saw in an example so we
+saw an example where if you start with a
+
+ align:start position:0%
+saw an example where if you start with a
+ 
+
+ align:start position:0%
+saw an example where if you start with a
+being a highly dissociated set where
+
+ align:start position:0%
+being a highly dissociated set where
+ 
+
+ align:start position:0%
+being a highly dissociated set where
+there is basically no additive structure
+
+ align:start position:0%
+there is basically no additive structure
+ 
+
+ align:start position:0%
+there is basically no additive structure
+within a then you do need so this
+
+ align:start position:0%
+within a then you do need so this
+ 
+
+ align:start position:0%
+within a then you do need so this
+example shows that you cannot do better
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+then polynomial well actually that
+
+ align:start position:0%
+then polynomial well actually that
+ 
+
+ align:start position:0%
+then polynomial well actually that
+linear in K in dimension and exponential
+
+ align:start position:0%
+linear in K in dimension and exponential
+ 
+
+ align:start position:0%
+linear in K in dimension and exponential
+in the size blow-up so in particular you
+
+ align:start position:0%
+in the size blow-up so in particular you
+ 
+
+ align:start position:0%
+in the size blow-up so in particular you
+do need to blow up the size to by by
+
+ align:start position:0%
+do need to blow up the size to by by
+ 
+
+ align:start position:0%
+do need to blow up the size to by by
+some exponential quantity in K so here K
+
+ align:start position:0%
+some exponential quantity in K so here K
+ 
+
+ align:start position:0%
+some exponential quantity in K so here K
+is in this example and you can you can
+
+ align:start position:0%
+is in this example and you can you can
+ 
+
+ align:start position:0%
+is in this example and you can you can
+create modifications of the example to
+
+ align:start position:0%
+create modifications of the example to
+ 
+
+ align:start position:0%
+create modifications of the example to
+keep K constant and a getting larger but
+
+ align:start position:0%
+keep K constant and a getting larger but
+ 
+
+ align:start position:0%
+keep K constant and a getting larger but
+the point is that you cannot do better
+
+ align:start position:0%
+the point is that you cannot do better
+ 
+
+ align:start position:0%
+the point is that you cannot do better
+than this type of dependence simply from
+
+ align:start position:0%
+than this type of dependence simply from
+ 
+
+ align:start position:0%
+than this type of dependence simply from
+that example and it's conjecture that
+
+ align:start position:0%
+that example and it's conjecture that
+ 
+
+ align:start position:0%
+that example and it's conjecture that
+that is the truth we're almost there
+
+ align:start position:0%
+that is the truth we're almost there
+ 
+
+ align:start position:0%
+that is the truth we're almost there
+improving this conjecture but not quite
+
+ align:start position:0%
+improving this conjecture but not quite
+ 
+
+ align:start position:0%
+improving this conjecture but not quite
+although the proof that we just gave is
+
+ align:start position:0%
+although the proof that we just gave is
+ 
+
+ align:start position:0%
+although the proof that we just gave is
+somewhat far because you lose an
+
+ align:start position:0%
+somewhat far because you lose an
+ 
+
+ align:start position:0%
+somewhat far because you lose an
+exponent in each bound there is a
+
+ align:start position:0%
+exponent in each bound there is a
+ 
+
+ align:start position:0%
+exponent in each bound there is a
+refinement of the final step in the
+
+ align:start position:0%
+refinement of the final step in the
+ 
+
+ align:start position:0%
+refinement of the final step in the
+argument so let me comment on that so we
+
+ align:start position:0%
+argument so let me comment on that so we
+ 
+
+ align:start position:0%
+argument so let me comment on that so we
+can refine the final step the final
+
+ align:start position:0%
+can refine the final step the final
+ 
+
+ align:start position:0%
+can refine the final step the final
+steps and proof to get polynomial pounds
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+to get polynomial pounds which is much
+
+ align:start position:0%
+to get polynomial pounds which is much
+ 
+
+ align:start position:0%
+to get polynomial pounds which is much
+more in the right ballpark compared to
+
+ align:start position:0%
+more in the right ballpark compared to
+ 
+
+ align:start position:0%
+more in the right ballpark compared to
+what we got and the idea is basically
+
+ align:start position:0%
+what we got and the idea is basically
+ 
+
+ align:start position:0%
+what we got and the idea is basically
+over here we used recovering lemma so we
+
+ align:start position:0%
+over here we used recovering lemma so we
+ 
+
+ align:start position:0%
+over here we used recovering lemma so we
+started with that q up there
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+up until this point you should think of
+
+ align:start position:0%
+up until this point you should think of
+ 
+
+ align:start position:0%
+up until this point you should think of
+this stuff as everything coming from
+
+ align:start position:0%
+this stuff as everything coming from
+ 
+
+ align:start position:0%
+this stuff as everything coming from
+baklava and its corollary so that stays
+
+ align:start position:0%
+baklava and its corollary so that stays
+ 
+
+ align:start position:0%
+baklava and its corollary so that stays
+the same
+
+ align:start position:0%
+the same
+ 
+
+ align:start position:0%
+the same
+another question starting without Q what
+
+ align:start position:0%
+another question starting without Q what
+ 
+
+ align:start position:0%
+another question starting without Q what
+would you use how would you use this Q
+
+ align:start position:0%
+would you use how would you use this Q
+ 
+
+ align:start position:0%
+would you use how would you use this Q
+to try to cover a wholly this a applied
+
+ align:start position:0%
+to try to cover a wholly this a applied
+ 
+
+ align:start position:0%
+to try to cover a wholly this a applied
+which are covering lemma remember how
+
+ align:start position:0%
+which are covering lemma remember how
+ 
+
+ align:start position:0%
+which are covering lemma remember how
+the proof which are covering lemma goes
+
+ align:start position:0%
+the proof which are covering lemma goes
+ 
+
+ align:start position:0%
+the proof which are covering lemma goes
+you take a maximal set of translates
+
+ align:start position:0%
+you take a maximal set of translates
+ 
+
+ align:start position:0%
+you take a maximal set of translates
+destroying translates and if you blow
+
+ align:start position:0%
+destroying translates and if you blow
+ 
+
+ align:start position:0%
+destroying translates and if you blow
+everything up by a factor to that you
+
+ align:start position:0%
+everything up by a factor to that you
+ 
+
+ align:start position:0%
+everything up by a factor to that you
+get a cover but it turns out to be
+
+ align:start position:0%
+get a cover but it turns out to be
+ 
+
+ align:start position:0%
+get a cover but it turns out to be
+somewhat wasteful you see there's a lot
+
+ align:start position:0%
+somewhat wasteful you see there's a lot
+ 
+
+ align:start position:0%
+somewhat wasteful you see there's a lot
+of wasting going from X to 2 to the X so
+
+ align:start position:0%
+of wasting going from X to 2 to the X so
+ 
+
+ align:start position:0%
+of wasting going from X to 2 to the X so
+you could do that step more slowly so so
+
+ align:start position:0%
+you could do that step more slowly so so
+ 
+
+ align:start position:0%
+you could do that step more slowly so so
+starting with Q cover now some not all
+
+ align:start position:0%
+starting with Q cover now some not all
+ 
+
+ align:start position:0%
+starting with Q cover now some not all
+of a so cover parts of it by translates
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+to minus Q so we do reach are covering
+
+ align:start position:0%
+to minus Q so we do reach are covering
+ 
+
+ align:start position:0%
+to minus Q so we do reach are covering
+them out you don't cover the whole thing
+
+ align:start position:0%
+them out you don't cover the whole thing
+ 
+
+ align:start position:0%
+them out you don't cover the whole thing
+but nibble away cover a little bit and
+
+ align:start position:0%
+but nibble away cover a little bit and
+ 
+
+ align:start position:0%
+but nibble away cover a little bit and
+then look at the thing that you get
+
+ align:start position:0%
+then look at the thing that you get
+ 
+
+ align:start position:0%
+then look at the thing that you get
+which is Q becomes some new thing let's
+
+ align:start position:0%
+which is Q becomes some new thing let's
+ 
+
+ align:start position:0%
+which is Q becomes some new thing let's
+say Q 1 I now cover more by Q 1 minus Q
+
+ align:start position:0%
+say Q 1 I now cover more by Q 1 minus Q
+ 
+
+ align:start position:0%
+say Q 1 I now cover more by Q 1 minus Q
+1 so apparently if you do the covering
+
+ align:start position:0%
+1 so apparently if you do the covering
+ 
+
+ align:start position:0%
+1 so apparently if you do the covering
+step more slowly you can obtain better
+
+ align:start position:0%
+step more slowly you can obtain better
+ 
+
+ align:start position:0%
+step more slowly you can obtain better
+bounce and that's enough to save you
+
+ align:start position:0%
+bounce and that's enough to save you
+ 
+
+ align:start position:0%
+bounce and that's enough to save you
+this exponent that go down to
+
+ align:start position:0%
+this exponent that go down to
+ 
+
+ align:start position:0%
+this exponent that go down to
+exponential battle to go down to
+
+ align:start position:0%
+exponential battle to go down to
+ 
+
+ align:start position:0%
+exponential battle to go down to
+polynomial type bounds for fragments
+
+ align:start position:0%
+polynomial type bounds for fragments
+ 
+
+ align:start position:0%
+polynomial type bounds for fragments
+theorem this is roughly the idea so you
+
+ align:start position:0%
+theorem this is roughly the idea so you
+ 
+
+ align:start position:0%
+theorem this is roughly the idea so you
+can modify the final step to obtain this
+
+ align:start position:0%
+can modify the final step to obtain this
+ 
+
+ align:start position:0%
+can modify the final step to obtain this
+bound the best bound so far is due to
+
+ align:start position:0%
+bound the best bound so far is due to
+ 
+
+ align:start position:0%
+bound the best bound so far is due to
+Tom Sanders who proved Freeman's theorem
+
+ align:start position:0%
+Tom Sanders who proved Freeman's theorem
+ 
+
+ align:start position:0%
+Tom Sanders who proved Freeman's theorem
+for
+
+ align:start position:0%
+for
+ 
+
+ align:start position:0%
+for
+pounds dimension that's like K times
+
+ align:start position:0%
+pounds dimension that's like K times
+ 
+
+ align:start position:0%
+pounds dimension that's like K times
+polynomial of then this poly logarithmic
+
+ align:start position:0%
+polynomial of then this poly logarithmic
+ 
+
+ align:start position:0%
+polynomial of then this poly logarithmic
+factor it's basically the right answer
+
+ align:start position:0%
+factor it's basically the right answer
+ 
+
+ align:start position:0%
+factor it's basically the right answer
+so this proof is much more sophisticated
+
+ align:start position:0%
+so this proof is much more sophisticated
+ 
+
+ align:start position:0%
+so this proof is much more sophisticated
+so it goes goes much more in-depth into
+
+ align:start position:0%
+so it goes goes much more in-depth into
+ 
+
+ align:start position:0%
+so it goes goes much more in-depth into
+analyzing the structure of set addition
+
+ align:start position:0%
+analyzing the structure of set addition
+ 
+
+ align:start position:0%
+analyzing the structure of set addition
+so senders is a very nice survey article
+
+ align:start position:0%
+so senders is a very nice survey article
+ 
+
+ align:start position:0%
+so senders is a very nice survey article
+called the structure of said addition
+
+ align:start position:0%
+called the structure of said addition
+ 
+
+ align:start position:0%
+called the structure of said addition
+that analyzes some of the modern
+
+ align:start position:0%
+that analyzes some of the modern
+ 
+
+ align:start position:0%
+that analyzes some of the modern
+techniques that are used to prove these
+
+ align:start position:0%
+techniques that are used to prove these
+ 
+
+ align:start position:0%
+techniques that are used to prove these
+types of results there is one more issue
+
+ align:start position:0%
+types of results there is one more issue
+ 
+
+ align:start position:0%
+types of results there is one more issue
+which I want to discuss at length in the
+
+ align:start position:0%
+which I want to discuss at length in the
+ 
+
+ align:start position:0%
+which I want to discuss at length in the
+second half of this lecture which is
+
+ align:start position:0%
+second half of this lecture which is
+ 
+
+ align:start position:0%
+second half of this lecture which is
+that you might be very unhappy with this
+
+ align:start position:0%
+that you might be very unhappy with this
+ 
+
+ align:start position:0%
+that you might be very unhappy with this
+exponential blow-up because if you think
+
+ align:start position:0%
+exponential blow-up because if you think
+ 
+
+ align:start position:0%
+exponential blow-up because if you think
+about what happens in these examples or
+
+ align:start position:0%
+about what happens in these examples or
+ 
+
+ align:start position:0%
+about what happens in these examples or
+not the examples but if you think about
+
+ align:start position:0%
+not the examples but if you think about
+ 
+
+ align:start position:0%
+not the examples but if you think about
+what happens like the spirit what we're
+
+ align:start position:0%
+what happens like the spirit what we're
+ 
+
+ align:start position:0%
+what happens like the spirit what we're
+trying to say
+
+ align:start position:0%
+trying to say
+ 
+
+ align:start position:0%
+trying to say
+Fryman Sturm is some kind of an inverse
+
+ align:start position:0%
+Fryman Sturm is some kind of an inverse
+ 
+
+ align:start position:0%
+Fryman Sturm is some kind of an inverse
+theorem and to go forward you're trying
+
+ align:start position:0%
+theorem and to go forward you're trying
+ 
+
+ align:start position:0%
+theorem and to go forward you're trying
+to say that if you have a ga P of
+
+ align:start position:0%
+to say that if you have a ga P of
+ 
+
+ align:start position:0%
+to say that if you have a ga P of
+dimension D then the size blow up is
+
+ align:start position:0%
+dimension D then the size blow up is
+ 
+
+ align:start position:0%
+dimension D then the size blow up is
+like 2 to the D right so we want to say
+
+ align:start position:0%
+like 2 to the D right so we want to say
+ 
+
+ align:start position:0%
+like 2 to the D right so we want to say
+some structure
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+price small topic and finance theorem
+
+ align:start position:0%
+price small topic and finance theorem
+ 
+
+ align:start position:0%
+price small topic and finance theorem
+tells the reverse that you have small
+
+ align:start position:0%
+tells the reverse that you have small
+ 
+
+ align:start position:0%
+tells the reverse that you have small
+doubling then you obtain this structure
+
+ align:start position:0%
+doubling then you obtain this structure
+ 
+
+ align:start position:0%
+doubling then you obtain this structure
+and seems like you are losing I mean
+
+ align:start position:0%
+and seems like you are losing I mean
+ 
+
+ align:start position:0%
+and seems like you are losing I mean
+getting from here to here there is a
+
+ align:start position:0%
+getting from here to here there is a
+ 
+
+ align:start position:0%
+getting from here to here there is a
+polynomial type of loss whereas going
+
+ align:start position:0%
+polynomial type of loss whereas going
+ 
+
+ align:start position:0%
+polynomial type of loss whereas going
+from here to here it seems that we're
+
+ align:start position:0%
+from here to here it seems that we're
+ 
+
+ align:start position:0%
+from here to here it seems that we're
+incurring some exponential type of loss
+
+ align:start position:0%
+incurring some exponential type of loss
+ 
+
+ align:start position:0%
+incurring some exponential type of loss
+and you'll be nice to have some kind of
+
+ align:start position:0%
+and you'll be nice to have some kind of
+ 
+
+ align:start position:0%
+and you'll be nice to have some kind of
+inverse theorem that also preserves
+
+ align:start position:0%
+inverse theorem that also preserves
+ 
+
+ align:start position:0%
+inverse theorem that also preserves
+these relationships qualitatively so
+
+ align:start position:0%
+these relationships qualitatively so
+ 
+
+ align:start position:0%
+these relationships qualitatively so
+that may not make sense in this moment
+
+ align:start position:0%
+that may not make sense in this moment
+ 
+
+ align:start position:0%
+that may not make sense in this moment
+but we'll get back to it later the
+
+ align:start position:0%
+but we'll get back to it later the
+ 
+
+ align:start position:0%
+but we'll get back to it later the
+structure point is there's more than
+
+ align:start position:0%
+structure point is there's more than
+ 
+
+ align:start position:0%
+structure point is there's more than
+this much more to be said about the
+
+ align:start position:0%
+this much more to be said about the
+ 
+
+ align:start position:0%
+this much more to be said about the
+bounds here even though right now it
+
+ align:start position:0%
+bounds here even though right now it
+ 
+
+ align:start position:0%
+bounds here even though right now it
+looks as if they're very close to each
+
+ align:start position:0%
+looks as if they're very close to each
+ 
+
+ align:start position:0%
+looks as if they're very close to each
+other one more thing that I want to
+
+ align:start position:0%
+other one more thing that I want to
+ 
+
+ align:start position:0%
+other one more thing that I want to
+expand on is we've stated and proved
+
+ align:start position:0%
+expand on is we've stated and proved
+ 
+
+ align:start position:0%
+expand on is we've stated and proved
+Freeman's theorem in the integers and
+
+ align:start position:0%
+Freeman's theorem in the integers and
+ 
+
+ align:start position:0%
+Freeman's theorem in the integers and
+you might ask what about in other groups
+
+ align:start position:0%
+you might ask what about in other groups
+ 
+
+ align:start position:0%
+you might ask what about in other groups
+we also proved Freeman's theorem in f2
+
+ align:start position:0%
+we also proved Freeman's theorem in f2
+ 
+
+ align:start position:0%
+we also proved Freeman's theorem in f2
+to the M or more generally groups of
+
+ align:start position:0%
+to the M or more generally groups of
+ 
+
+ align:start position:0%
+to the M or more generally groups of
+bounded exponent of bounded portion so
+
+ align:start position:0%
+bounded exponent of bounded portion so
+ 
+
+ align:start position:0%
+bounded exponent of bounded portion so
+billion groups have bounded exponent for
+
+ align:start position:0%
+billion groups have bounded exponent for
+ 
+
+ align:start position:0%
+billion groups have bounded exponent for
+general abelian groups so general groups
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+you might ask what happens here and in
+
+ align:start position:0%
+you might ask what happens here and in
+ 
+
+ align:start position:0%
+you might ask what happens here and in
+some sense what is even the statement of
+
+ align:start position:0%
+some sense what is even the statement of
+ 
+
+ align:start position:0%
+some sense what is even the statement of
+the theorem we want something which
+
+ align:start position:0%
+the theorem we want something which
+ 
+
+ align:start position:0%
+the theorem we want something which
+combines somehow two different types of
+
+ align:start position:0%
+combines somehow two different types of
+ 
+
+ align:start position:0%
+combines somehow two different types of
+behavior on one hand you have Z which is
+
+ align:start position:0%
+behavior on one hand you have Z which is
+ 
+
+ align:start position:0%
+behavior on one hand you have Z which is
+what we just did and here the model
+
+ align:start position:0%
+what we just did and here the model
+ 
+
+ align:start position:0%
+what we just did and here the model
+structures are G APs and on the other
+
+ align:start position:0%
+structures are G APs and on the other
+ 
+
+ align:start position:0%
+structures are G APs and on the other
+hand we have which we also proved things
+
+ align:start position:0%
+hand we have which we also proved things
+ 
+
+ align:start position:0%
+hand we have which we also proved things
+like f2 to the M where the model
+
+ align:start position:0%
+like f2 to the M where the model
+ 
+
+ align:start position:0%
+like f2 to the M where the model
+structures are subgroups and there's a
+
+ align:start position:0%
+structures are subgroups and there's a
+ 
+
+ align:start position:0%
+structures are subgroups and there's a
+sense in which these are not the G ApS
+
+ align:start position:0%
+sense in which these are not the G ApS
+ 
+
+ align:start position:0%
+sense in which these are not the G ApS
+or subgroups they have some similar
+
+ align:start position:0%
+or subgroups they have some similar
+ 
+
+ align:start position:0%
+or subgroups they have some similar
+properties but they're now really like
+
+ align:start position:0%
+properties but they're now really like
+ 
+
+ align:start position:0%
+properties but they're now really like
+each other
+
+ align:start position:0%
+each other
+ 
+
+ align:start position:0%
+each other
+so now if I give you a general group
+
+ align:start position:0%
+so now if I give you a general group
+ 
+
+ align:start position:0%
+so now if I give you a general group
+which might be some combination of
+
+ align:start position:0%
+which might be some combination of
+ 
+
+ align:start position:0%
+which might be some combination of
+infinite portion or very large torsion
+
+ align:start position:0%
+infinite portion or very large torsion
+ 
+
+ align:start position:0%
+infinite portion or very large torsion
+elements versus very small portion
+
+ align:start position:0%
+elements versus very small portion
+ 
+
+ align:start position:0%
+elements versus very small portion
+elements so for example take a Cartesian
+
+ align:start position:0%
+elements so for example take a Cartesian
+ 
+
+ align:start position:0%
+elements so for example take a Cartesian
+product of these groups is there a
+
+ align:start position:0%
+product of these groups is there a
+ 
+
+ align:start position:0%
+product of these groups is there a
+freeman's theorem and what as such a
+
+ align:start position:0%
+freeman's theorem and what as such a
+ 
+
+ align:start position:0%
+freeman's theorem and what as such a
+theorem looked like what are the
+
+ align:start position:0%
+theorem looked like what are the
+ 
+
+ align:start position:0%
+theorem looked like what are the
+structures what are the subsets of
+
+ align:start position:0%
+structures what are the subsets of
+ 
+
+ align:start position:0%
+structures what are the subsets of
+bounded doubly so that's kind of thing
+
+ align:start position:0%
+bounded doubly so that's kind of thing
+ 
+
+ align:start position:0%
+bounded doubly so that's kind of thing
+we want to think about so it turns out
+
+ align:start position:0%
+we want to think about so it turns out
+ 
+
+ align:start position:0%
+we want to think about so it turns out
+for Prime Minster mean fine in general
+
+ align:start position:0%
+for Prime Minster mean fine in general
+ 
+
+ align:start position:0%
+for Prime Minster mean fine in general
+abelian groups okay so there is a
+
+ align:start position:0%
+abelian groups okay so there is a
+ 
+
+ align:start position:0%
+abelian groups okay so there is a
+theorem so this theorem was proved by
+
+ align:start position:0%
+theorem so this theorem was proved by
+ 
+
+ align:start position:0%
+theorem so this theorem was proved by
+Green and Russia
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so following a very similar type of
+
+ align:start position:0%
+so following a very similar type of
+ 
+
+ align:start position:0%
+so following a very similar type of
+proof framework although it be
+
+ align:start position:0%
+proof framework although it be
+ 
+
+ align:start position:0%
+proof framework although it be
+individual steps in particular the
+
+ align:start position:0%
+individual steps in particular the
+ 
+
+ align:start position:0%
+individual steps in particular the
+modeling lemma needs to be modified and
+
+ align:start position:0%
+modeling lemma needs to be modified and
+ 
+
+ align:start position:0%
+modeling lemma needs to be modified and
+let me tell you about the statement is
+
+ align:start position:0%
+let me tell you about the statement is
+ 
+
+ align:start position:0%
+let me tell you about the statement is
+so the common generalization of GA piece
+
+ align:start position:0%
+so the common generalization of GA piece
+ 
+
+ align:start position:0%
+so the common generalization of GA piece
+and subgroups is something called a
+
+ align:start position:0%
+and subgroups is something called a
+ 
+
+ align:start position:0%
+and subgroups is something called a
+coset progression so a coset progression
+
+ align:start position:0%
+coset progression so a coset progression
+ 
+
+ align:start position:0%
+coset progression so a coset progression
+is a subset which is a direct sum of the
+
+ align:start position:0%
+is a subset which is a direct sum of the
+ 
+
+ align:start position:0%
+is a subset which is a direct sum of the
+form p plus h where p is a proper gaap
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+definition of GA p works just fine in
+
+ align:start position:0%
+definition of GA p works just fine in
+ 
+
+ align:start position:0%
+definition of GA p works just fine in
+every abelian group where you start with
+
+ align:start position:0%
+every abelian group where you start with
+ 
+
+ align:start position:0%
+every abelian group where you start with
+an initial point a few directions and
+
+ align:start position:0%
+an initial point a few directions and
+ 
+
+ align:start position:0%
+an initial point a few directions and
+you look at a great expansion of those
+
+ align:start position:0%
+you look at a great expansion of those
+ 
+
+ align:start position:0%
+you look at a great expansion of those
+directions piece of property a P and H
+
+ align:start position:0%
+directions piece of property a P and H
+ 
+
+ align:start position:0%
+directions piece of property a P and H
+is a subgroup and here the direct sum
+
+ align:start position:0%
+is a subgroup and here the direct sum
+ 
+
+ align:start position:0%
+is a subgroup and here the direct sum
+refers to fact that every so if P plus h
+
+ align:start position:0%
+refers to fact that every so if P plus h
+ 
+
+ align:start position:0%
+refers to fact that every so if P plus h
+equals to P prime plus h prime for some
+
+ align:start position:0%
+equals to P prime plus h prime for some
+ 
+
+ align:start position:0%
+equals to P prime plus h prime for some
+P and P Prime Minister set P and H H
+
+ align:start position:0%
+P and P Prime Minister set P and H H
+ 
+
+ align:start position:0%
+P and P Prime Minister set P and H H
+prime is a set H then P equals to P
+
+ align:start position:0%
+prime is a set H then P equals to P
+ 
+
+ align:start position:0%
+prime is a set H then P equals to P
+Prime and H
+
+ align:start position:0%
+Prime and H
+ 
+
+ align:start position:0%
+Prime and H
+so every element in here is written in a
+
+ align:start position:0%
+so every element in here is written in a
+ 
+
+ align:start position:0%
+so every element in here is written in a
+unique way as some people some age so
+
+ align:start position:0%
+unique way as some people some age so
+ 
+
+ align:start position:0%
+unique way as some people some age so
+that's what I mean by director song for
+
+ align:start position:0%
+that's what I mean by director song for
+ 
+
+ align:start position:0%
+that's what I mean by director song for
+such an object so such a concept
+
+ align:start position:0%
+such an object so such a concept
+ 
+
+ align:start position:0%
+such an object so such a concept
+progression I call it's dimension to be
+
+ align:start position:0%
+progression I call it's dimension to be
+ 
+
+ align:start position:0%
+progression I call it's dimension to be
+the dimension of the GA P P and its size
+
+ align:start position:0%
+the dimension of the GA P P and its size
+ 
+
+ align:start position:0%
+the dimension of the GA P P and its size
+in this case actually it's just the size
+
+ align:start position:0%
+in this case actually it's just the size
+ 
+
+ align:start position:0%
+in this case actually it's just the size
+of the set which is also the size P
+
+ align:start position:0%
+of the set which is also the size P
+ 
+
+ align:start position:0%
+of the set which is also the size P
+times the size of H so the theorem is
+
+ align:start position:0%
+times the size of H so the theorem is
+ 
+
+ align:start position:0%
+times the size of H so the theorem is
+that if a is a subset of an arbitrary
+
+ align:start position:0%
+that if a is a subset of an arbitrary
+ 
+
+ align:start position:0%
+that if a is a subset of an arbitrary
+abelian group and it has founded
+
+ align:start position:0%
+abelian group and it has founded
+ 
+
+ align:start position:0%
+abelian group and it has founded
+toppling then a is contained in a coset
+
+ align:start position:0%
+toppling then a is contained in a coset
+ 
+
+ align:start position:0%
+toppling then a is contained in a coset
+progression founded dimension and size
+
+ align:start position:0%
+progression founded dimension and size
+ 
+
+ align:start position:0%
+progression founded dimension and size
+founded blow-up of the size of a and
+
+ align:start position:0%
+founded blow-up of the size of a and
+ 
+
+ align:start position:0%
+founded blow-up of the size of a and
+here these constants P and K they are
+
+ align:start position:0%
+here these constants P and K they are
+ 
+
+ align:start position:0%
+here these constants P and K they are
+universal they do not depend on the
+
+ align:start position:0%
+universal they do not depend on the
+ 
+
+ align:start position:0%
+universal they do not depend on the
+group so there are some specific numbers
+
+ align:start position:0%
+group so there are some specific numbers
+ 
+
+ align:start position:0%
+group so there are some specific numbers
+functions you can write down they do not
+
+ align:start position:0%
+functions you can write down they do not
+ 
+
+ align:start position:0%
+functions you can write down they do not
+depend on the group so so this theorem
+
+ align:start position:0%
+depend on the group so so this theorem
+ 
+
+ align:start position:0%
+depend on the group so so this theorem
+gives you the characterization of
+
+ align:start position:0%
+gives you the characterization of
+ 
+
+ align:start position:0%
+gives you the characterization of
+subsets in general abelian groups that
+
+ align:start position:0%
+subsets in general abelian groups that
+ 
+
+ align:start position:0%
+subsets in general abelian groups that
+have small toppling any questions
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that's a good question so I think you
+
+ align:start position:0%
+that's a good question so I think you
+ 
+
+ align:start position:0%
+that's a good question so I think you
+could go into their paper and see that
+
+ align:start position:0%
+could go into their paper and see that
+ 
+
+ align:start position:0%
+could go into their paper and see that
+you can get polynomial type bounds and I
+
+ align:start position:0%
+you can get polynomial type bounds and I
+ 
+
+ align:start position:0%
+you can get polynomial type bounds and I
+think Sanders results also work for this
+
+ align:start position:0%
+think Sanders results also work for this
+ 
+
+ align:start position:0%
+think Sanders results also work for this
+type of setting to give you these type
+
+ align:start position:0%
+type of setting to give you these type
+ 
+
+ align:start position:0%
+type of setting to give you these type
+of bounds but I yeah so she's looking to
+
+ align:start position:0%
+of bounds but I yeah so she's looking to
+ 
+
+ align:start position:0%
+of bounds but I yeah so she's looking to
+Sanders paper and you are explaining I
+
+ align:start position:0%
+Sanders paper and you are explaining I
+ 
+
+ align:start position:0%
+Sanders paper and you are explaining I
+think incentives paper
+
+ align:start position:0%
+think incentives paper
+ 
+
+ align:start position:0%
+think incentives paper
+he works in general billion groups the
+
+ align:start position:0%
+he works in general billion groups the
+ 
+
+ align:start position:0%
+he works in general billion groups the
+next question I want to address is okay
+
+ align:start position:0%
+next question I want to address is okay
+ 
+
+ align:start position:0%
+next question I want to address is okay
+what do you think is the next question
+
+ align:start position:0%
+what do you think is the next question
+ 
+
+ align:start position:0%
+what do you think is the next question
+another billion groups so fragments
+
+ align:start position:0%
+another billion groups so fragments
+ 
+
+ align:start position:0%
+another billion groups so fragments
+theorem in non abelian groups or rather
+
+ align:start position:0%
+theorem in non abelian groups or rather
+ 
+
+ align:start position:0%
+theorem in non abelian groups or rather
+the Fryman problem now here's a basic
+
+ align:start position:0%
+the Fryman problem now here's a basic
+ 
+
+ align:start position:0%
+the Fryman problem now here's a basic
+question if I guess there's non abelian
+
+ align:start position:0%
+question if I guess there's non abelian
+ 
+
+ align:start position:0%
+question if I guess there's non abelian
+group what subsets I've found the table
+
+ align:start position:0%
+group what subsets I've found the table
+ 
+
+ align:start position:0%
+group what subsets I've found the table
+of course the examples from abelian
+
+ align:start position:0%
+of course the examples from abelian
+ 
+
+ align:start position:0%
+of course the examples from abelian
+groups also working non abelian groups
+
+ align:start position:0%
+groups also working non abelian groups
+ 
+
+ align:start position:0%
+groups also working non abelian groups
+well you have subgroups you have
+
+ align:start position:0%
+well you have subgroups you have
+ 
+
+ align:start position:0%
+well you have subgroups you have
+generalized arithmetic progressions but
+
+ align:start position:0%
+generalized arithmetic progressions but
+ 
+
+ align:start position:0%
+generalized arithmetic progressions but
+are they're genuinely new examples of
+
+ align:start position:0%
+are they're genuinely new examples of
+ 
+
+ align:start position:0%
+are they're genuinely new examples of
+sets in non abelian groups that have
+
+ align:start position:0%
+sets in non abelian groups that have
+ 
+
+ align:start position:0%
+sets in non abelian groups that have
+bounded doubly so think about that and
+
+ align:start position:0%
+bounded doubly so think about that and
+ 
+
+ align:start position:0%
+bounded doubly so think about that and
+let's take a quick break
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay can you think of examples seeing
+
+ align:start position:0%
+okay can you think of examples seeing
+ 
+
+ align:start position:0%
+okay can you think of examples seeing
+non abelian groups that have small
+
+ align:start position:0%
+non abelian groups that have small
+ 
+
+ align:start position:0%
+non abelian groups that have small
+doubling that do not come from the
+
+ align:start position:0%
+doubling that do not come from the
+ 
+
+ align:start position:0%
+doubling that do not come from the
+examples that we have seen before so let
+
+ align:start position:0%
+examples that we have seen before so let
+ 
+
+ align:start position:0%
+examples that we have seen before so let
+me show you one construction and this is
+
+ align:start position:0%
+me show you one construction and this is
+ 
+
+ align:start position:0%
+me show you one construction and this is
+an important construction in for non
+
+ align:start position:0%
+an important construction in for non
+ 
+
+ align:start position:0%
+an important construction in for non
+abelian groups so it has a name it's
+
+ align:start position:0%
+abelian groups so it has a name it's
+ 
+
+ align:start position:0%
+abelian groups so it has a name it's
+called a discrete Heisenberg which is
+
+ align:start position:0%
+called a discrete Heisenberg which is
+ 
+
+ align:start position:0%
+called a discrete Heisenberg which is
+the matrix consisting of matrices that
+
+ align:start position:0%
+the matrix consisting of matrices that
+ 
+
+ align:start position:0%
+the matrix consisting of matrices that
+look like what I've written so yeah
+
+ align:start position:0%
+look like what I've written so yeah
+ 
+
+ align:start position:0%
+look like what I've written so yeah
+integer entries above the diagonal one
+
+ align:start position:0%
+integer entries above the diagonal one
+ 
+
+ align:start position:0%
+integer entries above the diagonal one
+on the diagonal and zero below the back
+
+ align:start position:0%
+on the diagonal and zero below the back
+ 
+
+ align:start position:0%
+on the diagonal and zero below the back
+so let's do some elementary matrix
+
+ align:start position:0%
+so let's do some elementary matrix
+ 
+
+ align:start position:0%
+so let's do some elementary matrix
+multiplication to see how good
+
+ align:start position:0%
+multiplication to see how good
+ 
+
+ align:start position:0%
+multiplication to see how good
+multiplication in this group works so if
+
+ align:start position:0%
+multiplication in this group works so if
+ 
+
+ align:start position:0%
+multiplication in this group works so if
+I have two such matrices I multiply them
+
+ align:start position:0%
+I have two such matrices I multiply them
+ 
+
+ align:start position:0%
+I have two such matrices I multiply them
+together and then you see that the
+
+ align:start position:0%
+together and then you see that the
+ 
+
+ align:start position:0%
+together and then you see that the
+diagnosed preserved of course but the
+
+ align:start position:0%
+diagnosed preserved of course but the
+ 
+
+ align:start position:0%
+diagnosed preserved of course but the
+this entry over here is simply addition
+
+ align:start position:0%
+this entry over here is simply addition
+ 
+
+ align:start position:0%
+this entry over here is simply addition
+so this entry here is just addition this
+
+ align:start position:0%
+so this entry here is just addition this
+ 
+
+ align:start position:0%
+so this entry here is just addition this
+entry over here it's also addition and
+
+ align:start position:0%
+entry over here it's also addition and
+ 
+
+ align:start position:0%
+entry over here it's also addition and
+the top right entry is a bit more
+
+ align:start position:0%
+the top right entry is a bit more
+ 
+
+ align:start position:0%
+the top right entry is a bit more
+complicated it's some addition but
+
+ align:start position:0%
+complicated it's some addition but
+ 
+
+ align:start position:0%
+complicated it's some addition but
+there's an additional twist
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so this is how matrix multiplication
+
+ align:start position:0%
+so this is how matrix multiplication
+ 
+
+ align:start position:0%
+so this is how matrix multiplication
+works in this group I mean this whole
+
+ align:start position:0%
+works in this group I mean this whole
+ 
+
+ align:start position:0%
+works in this group I mean this whole
+matrix multiplication works but in terms
+
+ align:start position:0%
+matrix multiplication works but in terms
+ 
+
+ align:start position:0%
+matrix multiplication works but in terms
+of so you see it's kind of like an
+
+ align:start position:0%
+of so you see it's kind of like an
+ 
+
+ align:start position:0%
+of so you see it's kind of like an
+abelian group but there's an extra twist
+
+ align:start position:0%
+abelian group but there's an extra twist
+ 
+
+ align:start position:0%
+abelian group but there's an extra twist
+so it's almost a billion first step you
+
+ align:start position:0%
+so it's almost a billion first step you
+ 
+
+ align:start position:0%
+so it's almost a billion first step you
+can take away from the billion and and
+
+ align:start position:0%
+can take away from the billion and and
+ 
+
+ align:start position:0%
+can take away from the billion and and
+there's a way to quantify this notions
+
+ align:start position:0%
+there's a way to quantify this notions
+ 
+
+ align:start position:0%
+there's a way to quantify this notions
+called neo potency so we'll get to that
+
+ align:start position:0%
+called neo potency so we'll get to that
+ 
+
+ align:start position:0%
+called neo potency so we'll get to that
+in a second but in particular if you set
+
+ align:start position:0%
+in a second but in particular if you set
+ 
+
+ align:start position:0%
+in a second but in particular if you set
+s to be the following generators so if
+
+ align:start position:0%
+s to be the following generators so if
+ 
+
+ align:start position:0%
+s to be the following generators so if
+you take s the babies four elements and
+
+ align:start position:0%
+you take s the babies four elements and
+ 
+
+ align:start position:0%
+you take s the babies four elements and
+you ask what does the RF power of s
+
+ align:start position:0%
+you ask what does the RF power of s
+ 
+
+ align:start position:0%
+you ask what does the RF power of s
+looked like so I look at all the
+
+ align:start position:0%
+looked like so I look at all the
+ 
+
+ align:start position:0%
+looked like so I look at all the
+elements which can be written by our or
+
+ align:start position:0%
+elements which can be written by our or
+ 
+
+ align:start position:0%
+elements which can be written by our or
+and most are elements from s or do these
+
+ align:start position:0%
+and most are elements from s or do these
+ 
+
+ align:start position:0%
+and most are elements from s or do these
+elements look like what do you think
+
+ align:start position:0%
+elements look like what do you think
+ 
+
+ align:start position:0%
+elements look like what do you think
+right so if you look at elements in here
+
+ align:start position:0%
+right so if you look at elements in here
+ 
+
+ align:start position:0%
+right so if you look at elements in here
+how large can this entry the 1 comma 2
+
+ align:start position:0%
+how large can this entry the 1 comma 2
+ 
+
+ align:start position:0%
+how large can this entry the 1 comma 2
+entry be each time you do addition so
+
+ align:start position:0%
+entry be each time you do addition so
+ 
+
+ align:start position:0%
+entry be each time you do addition so
+it's a most art ok so let me be a bit
+
+ align:start position:0%
+it's a most art ok so let me be a bit
+ 
+
+ align:start position:0%
+it's a most art ok so let me be a bit
+rough here and say it's Big O of are and
+
+ align:start position:0%
+rough here and say it's Big O of are and
+ 
+
+ align:start position:0%
+rough here and say it's Big O of are and
+likewise the 2 1 2 3 entries also Big O
+
+ align:start position:0%
+likewise the 2 1 2 3 entries also Big O
+ 
+
+ align:start position:0%
+likewise the 2 1 2 3 entries also Big O
+of our what about the top right entry
+
+ align:start position:0%
+of our what about the top right entry
+ 
+
+ align:start position:0%
+of our what about the top right entry
+over here yeah so it grows like R
+
+ align:start position:0%
+over here yeah so it grows like R
+ 
+
+ align:start position:0%
+over here yeah so it grows like R
+squared because there's an extra
+
+ align:start position:0%
+squared because there's an extra
+ 
+
+ align:start position:0%
+squared because there's an extra
+multiplication term ok so you can be
+
+ align:start position:0%
+multiplication term ok so you can be
+ 
+
+ align:start position:0%
+multiplication term ok so you can be
+much more precise about the growth rate
+
+ align:start position:0%
+much more precise about the growth rate
+ 
+
+ align:start position:0%
+much more precise about the growth rate
+of these individual entries but very
+
+ align:start position:0%
+of these individual entries but very
+ 
+
+ align:start position:0%
+of these individual entries but very
+roughly it looks like this over here so
+
+ align:start position:0%
+roughly it looks like this over here so
+ 
+
+ align:start position:0%
+roughly it looks like this over here so
+the size of s are all of s is roughly on
+
+ align:start position:0%
+the size of s are all of s is roughly on
+ 
+
+ align:start position:0%
+the size of s are all of s is roughly on
+the order of fourth power of our
+
+ align:start position:0%
+the order of fourth power of our
+ 
+
+ align:start position:0%
+the order of fourth power of our
+so in particular the doubling constant
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+ours will be large is what happens we go
+
+ align:start position:0%
+ours will be large is what happens we go
+ 
+
+ align:start position:0%
+ours will be large is what happens we go
+from r2 to r2 the size increases by a
+
+ align:start position:0%
+from r2 to r2 the size increases by a
+ 
+
+ align:start position:0%
+from r2 to r2 the size increases by a
+factor of around 16 okay so that's an
+
+ align:start position:0%
+factor of around 16 okay so that's an
+ 
+
+ align:start position:0%
+factor of around 16 okay so that's an
+example of a set in a non abelian group
+
+ align:start position:0%
+example of a set in a non abelian group
+ 
+
+ align:start position:0%
+example of a set in a non abelian group
+with founded doubly which is genuinely
+
+ align:start position:0%
+with founded doubly which is genuinely
+ 
+
+ align:start position:0%
+with founded doubly which is genuinely
+different from the examples we have seen
+
+ align:start position:0%
+different from the examples we have seen
+ 
+
+ align:start position:0%
+different from the examples we have seen
+so far right so that's non abelian
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+questions oh it's a size we've shown the
+
+ align:start position:0%
+questions oh it's a size we've shown the
+ 
+
+ align:start position:0%
+questions oh it's a size we've shown the
+sizes I'm not being very precise here
+
+ align:start position:0%
+sizes I'm not being very precise here
+ 
+
+ align:start position:0%
+sizes I'm not being very precise here
+but you can do upper bound and lower
+
+ align:start position:0%
+but you can do upper bound and lower
+ 
+
+ align:start position:0%
+but you can do upper bound and lower
+bound so it sighs turns out to be the
+
+ align:start position:0%
+bound so it sighs turns out to be the
+ 
+
+ align:start position:0%
+bound so it sighs turns out to be the
+water of our to the form so you want to
+
+ align:start position:0%
+water of our to the form so you want to
+ 
+
+ align:start position:0%
+water of our to the form so you want to
+show that there are actually enough
+
+ align:start position:0%
+show that there are actually enough
+ 
+
+ align:start position:0%
+show that there are actually enough
+elements over here that you can fill in
+
+ align:start position:0%
+elements over here that you can fill in
+ 
+
+ align:start position:0%
+elements over here that you can fill in
+but I'll be okay can you build other
+
+ align:start position:0%
+but I'll be okay can you build other
+ 
+
+ align:start position:0%
+but I'll be okay can you build other
+examples like this one
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay questions how do we know this isn't
+
+ align:start position:0%
+okay questions how do we know this isn't
+ 
+
+ align:start position:0%
+okay questions how do we know this isn't
+like a cassette some a cassette
+
+ align:start position:0%
+like a cassette some a cassette
+ 
+
+ align:start position:0%
+like a cassette some a cassette
+progression of one thing this is not a
+
+ align:start position:0%
+progression of one thing this is not a
+ 
+
+ align:start position:0%
+progression of one thing this is not a
+billion s if you multiply entries of s
+
+ align:start position:0%
+billion s if you multiply entries of s
+ 
+
+ align:start position:0%
+billion s if you multiply entries of s
+in different waters you get different
+
+ align:start position:0%
+in different waters you get different
+ 
+
+ align:start position:0%
+in different waters you get different
+elements so in already in that way it's
+
+ align:start position:0%
+elements so in already in that way it's
+ 
+
+ align:start position:0%
+elements so in already in that way it's
+different from the examples that we have
+
+ align:start position:0%
+different from the examples that we have
+ 
+
+ align:start position:0%
+different from the examples that we have
+seen before
+
+ align:start position:0%
+seen before
+ 
+
+ align:start position:0%
+seen before
+but no you're right so maybe we can
+
+ align:start position:0%
+but no you're right so maybe we can
+ 
+
+ align:start position:0%
+but no you're right so maybe we can
+write this a semi direct product in
+
+ align:start position:0%
+write this a semi direct product in
+ 
+
+ align:start position:0%
+write this a semi direct product in
+terms of things we have seen before and
+
+ align:start position:0%
+terms of things we have seen before and
+ 
+
+ align:start position:0%
+terms of things we have seen before and
+it is in some sense a semi direct
+
+ align:start position:0%
+it is in some sense a semi direct
+ 
+
+ align:start position:0%
+it is in some sense a semi direct
+product but it's a very special kind of
+
+ align:start position:0%
+product but it's a very special kind of
+ 
+
+ align:start position:0%
+product but it's a very special kind of
+semi direct product okay from that
+
+ align:start position:0%
+semi direct product okay from that
+ 
+
+ align:start position:0%
+semi direct product okay from that
+example you can build bigger examples of
+
+ align:start position:0%
+example you can build bigger examples of
+ 
+
+ align:start position:0%
+example you can build bigger examples of
+course with more entries in the matrix
+
+ align:start position:0%
+course with more entries in the matrix
+ 
+
+ align:start position:0%
+course with more entries in the matrix
+but more generally these things are what
+
+ align:start position:0%
+but more generally these things are what
+ 
+
+ align:start position:0%
+but more generally these things are what
+are known as neo potent groups right so
+
+ align:start position:0%
+are known as neo potent groups right so
+ 
+
+ align:start position:0%
+are known as neo potent groups right so
+there's an example important group and
+
+ align:start position:0%
+there's an example important group and
+ 
+
+ align:start position:0%
+there's an example important group and
+remind you the definition of a new Putin
+
+ align:start position:0%
+remind you the definition of a new Putin
+ 
+
+ align:start position:0%
+remind you the definition of a new Putin
+group is a group where the lower central
+
+ align:start position:0%
+group is a group where the lower central
+ 
+
+ align:start position:0%
+group is a group where the lower central
+series eventually terminates if you look
+
+ align:start position:0%
+series eventually terminates if you look
+ 
+
+ align:start position:0%
+series eventually terminates if you look
+hard so this is the commutator of G look
+
+ align:start position:0%
+hard so this is the commutator of G look
+ 
+
+ align:start position:0%
+hard so this is the commutator of G look
+at all the elements within s XY X
+
+ align:start position:0%
+at all the elements within s XY X
+ 
+
+ align:start position:0%
+at all the elements within s XY X
+inverse Y inverse set of elements that
+
+ align:start position:0%
+inverse Y inverse set of elements that
+ 
+
+ align:start position:0%
+inverse Y inverse set of elements that
+can be written this way so that's a
+
+ align:start position:0%
+can be written this way so that's a
+ 
+
+ align:start position:0%
+can be written this way so that's a
+subgroup and if I repeat this operation
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+enough times I eventually would get just
+
+ align:start position:0%
+enough times I eventually would get just
+ 
+
+ align:start position:0%
+enough times I eventually would get just
+the identity and you could try it on
+
+ align:start position:0%
+the identity and you could try it on
+ 
+
+ align:start position:0%
+the identity and you could try it on
+that group if you do the commutator okay
+
+ align:start position:0%
+that group if you do the commutator okay
+ 
+
+ align:start position:0%
+that group if you do the commutator okay
+so you essentially you get rid of a
+
+ align:start position:0%
+so you essentially you get rid of a
+ 
+
+ align:start position:0%
+so you essentially you get rid of a
+billion Asst and you move up the Hodag
+
+ align:start position:0%
+billion Asst and you move up the Hodag
+ 
+
+ align:start position:0%
+billion Asst and you move up the Hodag
+you know
+
+ align:start position:0%
+you know
+ 
+
+ align:start position:0%
+you know
+take a commentator you get rid of this
+
+ align:start position:0%
+take a commentator you get rid of this
+ 
+
+ align:start position:0%
+take a commentator you get rid of this
+you zero out these two entries together
+
+ align:start position:0%
+you zero out these two entries together
+ 
+
+ align:start position:0%
+you zero out these two entries together
+Z alone if you do it one more time you
+
+ align:start position:0%
+Z alone if you do it one more time you
+ 
+
+ align:start position:0%
+Z alone if you do it one more time you
+zero out that entry and so more
+
+ align:start position:0%
+zero out that entry and so more
+ 
+
+ align:start position:0%
+zero out that entry and so more
+generally all of these new potent groups
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so if you take set of generators and
+
+ align:start position:0%
+so if you take set of generators and
+ 
+
+ align:start position:0%
+so if you take set of generators and
+look at all
+
+ align:start position:0%
+look at all
+ 
+
+ align:start position:0%
+look at all
+and look at the volume of all ha there's
+
+ align:start position:0%
+and look at the volume of all ha there's
+ 
+
+ align:start position:0%
+and look at the volume of all ha there's
+a volume of the bulk grow with the
+
+ align:start position:0%
+a volume of the bulk grow with the
+ 
+
+ align:start position:0%
+a volume of the bulk grow with the
+radius it grows like a polynomial and so
+
+ align:start position:0%
+radius it grows like a polynomial and so
+ 
+
+ align:start position:0%
+radius it grows like a polynomial and so
+let me define that
+
+ align:start position:0%
+let me define that
+ 
+
+ align:start position:0%
+let me define that
+so given G a finitely generated coop so
+
+ align:start position:0%
+so given G a finitely generated coop so
+ 
+
+ align:start position:0%
+so given G a finitely generated coop so
+generated by s we say that G has
+
+ align:start position:0%
+generated by s we say that G has
+ 
+
+ align:start position:0%
+generated by s we say that G has
+polynomial growth if the size has to be
+
+ align:start position:0%
+polynomial growth if the size has to be
+ 
+
+ align:start position:0%
+polynomial growth if the size has to be
+our growth like at most a polynomial in
+
+ align:start position:0%
+our growth like at most a polynomial in
+ 
+
+ align:start position:0%
+our growth like at most a polynomial in
+R it's worth noting that this definition
+
+ align:start position:0%
+R it's worth noting that this definition
+ 
+
+ align:start position:0%
+R it's worth noting that this definition
+is really a definition about G it does
+
+ align:start position:0%
+is really a definition about G it does
+ 
+
+ align:start position:0%
+is really a definition about G it does
+not depend on the choice of generators
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+you have different choices generators
+
+ align:start position:0%
+you have different choices generators
+ 
+
+ align:start position:0%
+you have different choices generators
+for the group but polynomial growth with
+
+ align:start position:0%
+for the group but polynomial growth with
+ 
+
+ align:start position:0%
+for the group but polynomial growth with
+respect to one set of generators then
+
+ align:start position:0%
+respect to one set of generators then
+ 
+
+ align:start position:0%
+respect to one set of generators then
+it's the same it's also has polynomial
+
+ align:start position:0%
+it's the same it's also has polynomial
+ 
+
+ align:start position:0%
+it's the same it's also has polynomial
+growth with regards to every other set
+
+ align:start position:0%
+growth with regards to every other set
+ 
+
+ align:start position:0%
+growth with regards to every other set
+so we've seen an example of groups with
+
+ align:start position:0%
+so we've seen an example of groups with
+ 
+
+ align:start position:0%
+so we've seen an example of groups with
+polynomial growth abelian groups have
+
+ align:start position:0%
+polynomial growth abelian groups have
+ 
+
+ align:start position:0%
+polynomial growth abelian groups have
+polynomial growth okay so if you think a
+
+ align:start position:0%
+polynomial growth okay so if you think a
+ 
+
+ align:start position:0%
+polynomial growth okay so if you think a
+polynomial thing you know lattice Z to
+
+ align:start position:0%
+polynomial thing you know lattice Z to
+ 
+
+ align:start position:0%
+polynomial thing you know lattice Z to
+the N take a ball growing so it has size
+
+ align:start position:0%
+the N take a ball growing so it has size
+ 
+
+ align:start position:0%
+the N take a ball growing so it has size
+growing like
+
+ align:start position:0%
+growing like
+ 
+
+ align:start position:0%
+growing like
+are to the dimension but no potent group
+
+ align:start position:0%
+are to the dimension but no potent group
+ 
+
+ align:start position:0%
+are to the dimension but no potent group
+is another example of groups with
+
+ align:start position:0%
+is another example of groups with
+ 
+
+ align:start position:0%
+is another example of groups with
+polynomial growth you may want to and
+
+ align:start position:0%
+polynomial growth you may want to and
+ 
+
+ align:start position:0%
+polynomial growth you may want to and
+these are intuitive theories for now
+
+ align:start position:0%
+these are intuitive theories for now
+ 
+
+ align:start position:0%
+these are intuitive theories for now
+related you found the table the
+
+ align:start position:0%
+related you found the table the
+ 
+
+ align:start position:0%
+related you found the table the
+polynomial Coughlin has found a doubling
+
+ align:start position:0%
+polynomial Coughlin has found a doubling
+ 
+
+ align:start position:0%
+polynomial Coughlin has found a doubling
+so is there a classification of groups
+
+ align:start position:0%
+so is there a classification of groups
+ 
+
+ align:start position:0%
+so is there a classification of groups
+with bound with polynomial growth so if
+
+ align:start position:0%
+with bound with polynomial growth so if
+ 
+
+ align:start position:0%
+with bound with polynomial growth so if
+I tell you a group so infinite group
+
+ align:start position:0%
+I tell you a group so infinite group
+ 
+
+ align:start position:0%
+I tell you a group so infinite group
+always because other ways finite then
+
+ align:start position:0%
+always because other ways finite then
+ 
+
+ align:start position:0%
+always because other ways finite then
+maxes out already at some point so I
+
+ align:start position:0%
+maxes out already at some point so I
+ 
+
+ align:start position:0%
+maxes out already at some point so I
+give you an infinite group I tell you
+
+ align:start position:0%
+give you an infinite group I tell you
+ 
+
+ align:start position:0%
+give you an infinite group I tell you
+has polynomial growth what can you tell
+
+ align:start position:0%
+has polynomial growth what can you tell
+ 
+
+ align:start position:0%
+has polynomial growth what can you tell
+me about this group is there some
+
+ align:start position:0%
+me about this group is there some
+ 
+
+ align:start position:0%
+me about this group is there some
+characterization that's an inverse of
+
+ align:start position:0%
+characterization that's an inverse of
+ 
+
+ align:start position:0%
+characterization that's an inverse of
+what we've seen so far and the answer is
+
+ align:start position:0%
+what we've seen so far and the answer is
+ 
+
+ align:start position:0%
+what we've seen so far and the answer is
+yes and this is a famous and deep result
+
+ align:start position:0%
+yes and this is a famous and deep result
+ 
+
+ align:start position:0%
+yes and this is a famous and deep result
+of robot so chromis theorem polynomial
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+from the 80s romoff showed that a finely
+
+ align:start position:0%
+from the 80s romoff showed that a finely
+ 
+
+ align:start position:0%
+from the 80s romoff showed that a finely
+generated virtually new poll where
+
+ align:start position:0%
+generated virtually new poll where
+ 
+
+ align:start position:0%
+generated virtually new poll where
+virtually is an adverb in group theory
+
+ align:start position:0%
+virtually is an adverb in group theory
+ 
+
+ align:start position:0%
+virtually is an adverb in group theory
+when you have some property like a
+
+ align:start position:0%
+when you have some property like a
+ 
+
+ align:start position:0%
+when you have some property like a
+billion or solvable or whatever so new
+
+ align:start position:0%
+billion or solvable or whatever so new
+ 
+
+ align:start position:0%
+billion or solvable or whatever so new
+virtually P means that there exists a
+
+ align:start position:0%
+virtually P means that there exists a
+ 
+
+ align:start position:0%
+virtually P means that there exists a
+finite index subject with property P so
+
+ align:start position:0%
+finite index subject with property P so
+ 
+
+ align:start position:0%
+finite index subject with property P so
+virtually no Putin is that there's a
+
+ align:start position:0%
+virtually no Putin is that there's a
+ 
+
+ align:start position:0%
+virtually no Putin is that there's a
+finite index subgroup that is no potent
+
+ align:start position:0%
+finite index subgroup that is no potent
+ 
+
+ align:start position:0%
+finite index subgroup that is no potent
+so it completely characterizes groups of
+
+ align:start position:0%
+so it completely characterizes groups of
+ 
+
+ align:start position:0%
+so it completely characterizes groups of
+polynomial growth so basically all the
+
+ align:start position:0%
+polynomial growth so basically all the
+ 
+
+ align:start position:0%
+polynomial growth so basically all the
+examples we've seen so far are
+
+ align:start position:0%
+examples we've seen so far are
+ 
+
+ align:start position:0%
+examples we've seen so far are
+representatives so up to changing by a
+
+ align:start position:0%
+representatives so up to changing by a
+ 
+
+ align:start position:0%
+representatives so up to changing by a
+finite index subgroup
+
+ align:start position:0%
+finite index subgroup
+ 
+
+ align:start position:0%
+finite index subgroup
+expect shouldn't change the growth
+
+ align:start position:0%
+expect shouldn't change the growth
+ 
+
+ align:start position:0%
+expect shouldn't change the growth
+nature by so much there are some
+
+ align:start position:0%
+nature by so much there are some
+ 
+
+ align:start position:0%
+nature by so much there are some
+analogies to be made here with for
+
+ align:start position:0%
+analogies to be made here with for
+ 
+
+ align:start position:0%
+analogies to be made here with for
+example in geometry you ask in Euclidean
+
+ align:start position:0%
+example in geometry you ask in Euclidean
+ 
+
+ align:start position:0%
+example in geometry you ask in Euclidean
+space how fast is the ball of radius R
+
+ align:start position:0%
+space how fast is the ball of radius R
+ 
+
+ align:start position:0%
+space how fast is the ball of radius R
+grown in dimension T it grows like R to
+
+ align:start position:0%
+grown in dimension T it grows like R to
+ 
+
+ align:start position:0%
+grown in dimension T it grows like R to
+the D what about in the hyperbolic space
+
+ align:start position:0%
+the D what about in the hyperbolic space
+ 
+
+ align:start position:0%
+the D what about in the hyperbolic space
+does anyone know how fast in hyperbolic
+
+ align:start position:0%
+does anyone know how fast in hyperbolic
+ 
+
+ align:start position:0%
+does anyone know how fast in hyperbolic
+space ball of radius R grows it's
+
+ align:start position:0%
+space ball of radius R grows it's
+ 
+
+ align:start position:0%
+space ball of radius R grows it's
+exponential in the radius so for now
+
+ align:start position:0%
+exponential in the radius so for now
+ 
+
+ align:start position:0%
+exponential in the radius so for now
+negatively curved spaces the boss grow
+
+ align:start position:0%
+negatively curved spaces the boss grow
+ 
+
+ align:start position:0%
+negatively curved spaces the boss grow
+polynomially but for something that's
+
+ align:start position:0%
+polynomially but for something that's
+ 
+
+ align:start position:0%
+polynomially but for something that's
+negatively curvature in particular the
+
+ align:start position:0%
+negatively curvature in particular the
+ 
+
+ align:start position:0%
+negatively curvature in particular the
+hyperbolic space the ball growth might
+
+ align:start position:0%
+hyperbolic space the ball growth might
+ 
+
+ align:start position:0%
+hyperbolic space the ball growth might
+be exponential you have a similar
+
+ align:start position:0%
+be exponential you have a similar
+ 
+
+ align:start position:0%
+be exponential you have a similar
+phenomenon happening here the opposite
+
+ align:start position:0%
+phenomenon happening here the opposite
+ 
+
+ align:start position:0%
+phenomenon happening here the opposite
+of polynomial growth is super polynomial
+
+ align:start position:0%
+of polynomial growth is super polynomial
+ 
+
+ align:start position:0%
+of polynomial growth is super polynomial
+growth but one specific example is that
+
+ align:start position:0%
+growth but one specific example is that
+ 
+
+ align:start position:0%
+growth but one specific example is that
+of a free group where there are no
+
+ align:start position:0%
+of a free group where there are no
+ 
+
+ align:start position:0%
+of a free group where there are no
+relations between the generators in that
+
+ align:start position:0%
+relations between the generators in that
+ 
+
+ align:start position:0%
+relations between the generators in that
+case the balls they grow like
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+exponentially the all-school
+
+ align:start position:0%
+exponentially the all-school
+ 
+
+ align:start position:0%
+exponentially the all-school
+exponentially in the radius groom offs
+
+ align:start position:0%
+exponentially in the radius groom offs
+ 
+
+ align:start position:0%
+exponentially in the radius groom offs
+there is a deep theorem and it's
+
+ align:start position:0%
+there is a deep theorem and it's
+ 
+
+ align:start position:0%
+there is a deep theorem and it's
+original proof used some very hard tools
+
+ align:start position:0%
+original proof used some very hard tools
+ 
+
+ align:start position:0%
+original proof used some very hard tools
+coming from geometry and Gromov
+
+ align:start position:0%
+coming from geometry and Gromov
+ 
+
+ align:start position:0%
+coming from geometry and Gromov
+developed a notion of convergence of
+
+ align:start position:0%
+developed a notion of convergence of
+ 
+
+ align:start position:0%
+developed a notion of convergence of
+metric spaces somewhat akin to our
+
+ align:start position:0%
+metric spaces somewhat akin to our
+ 
+
+ align:start position:0%
+metric spaces somewhat akin to our
+discussion of graph limits so starting
+
+ align:start position:0%
+discussion of graph limits so starting
+ 
+
+ align:start position:0%
+discussion of graph limits so starting
+with discrete objects you looked at some
+
+ align:start position:0%
+with discrete objects you looked at some
+ 
+
+ align:start position:0%
+with discrete objects you looked at some
+convergence to some continuous objects
+
+ align:start position:0%
+convergence to some continuous objects
+ 
+
+ align:start position:0%
+convergence to some continuous objects
+and then used some very deep results
+
+ align:start position:0%
+and then used some very deep results
+ 
+
+ align:start position:0%
+and then used some very deep results
+from the classification of locally
+
+ align:start position:0%
+from the classification of locally
+ 
+
+ align:start position:0%
+from the classification of locally
+compact groups to derive this result
+
+ align:start position:0%
+compact groups to derive this result
+ 
+
+ align:start position:0%
+compact groups to derive this result
+over here
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so this proof has been quite influential
+
+ align:start position:0%
+so this proof has been quite influential
+ 
+
+ align:start position:0%
+so this proof has been quite influential
+and it's related to something called
+
+ align:start position:0%
+and it's related to something called
+ 
+
+ align:start position:0%
+and it's related to something called
+Hilbert's fifth problem which concern
+
+ align:start position:0%
+Hilbert's fifth problem which concern
+ 
+
+ align:start position:0%
+Hilbert's fifth problem which concern
+characterizations of B groups inverse
+
+ align:start position:0%
+characterizations of B groups inverse
+ 
+
+ align:start position:0%
+characterizations of B groups inverse
+high problems and tell you some
+
+ align:start position:0%
+high problems and tell you some
+ 
+
+ align:start position:0%
+high problems and tell you some
+structure has some property describe
+
+ align:start position:0%
+structure has some property describe
+ 
+
+ align:start position:0%
+structure has some property describe
+that structure okay what does this all
+
+ align:start position:0%
+that structure okay what does this all
+ 
+
+ align:start position:0%
+that structure okay what does this all
+have to do with fragments theorem
+
+ align:start position:0%
+have to do with fragments theorem
+ 
+
+ align:start position:0%
+have to do with fragments theorem
+well already you see some relation right
+
+ align:start position:0%
+well already you see some relation right
+ 
+
+ align:start position:0%
+well already you see some relation right
+so there seemed at least intuitively
+
+ align:start position:0%
+so there seemed at least intuitively
+ 
+
+ align:start position:0%
+so there seemed at least intuitively
+some relationship between groups of
+
+ align:start position:0%
+some relationship between groups of
+ 
+
+ align:start position:0%
+some relationship between groups of
+polynomial growth versus subsets have
+
+ align:start position:0%
+polynomial growth versus subsets have
+ 
+
+ align:start position:0%
+polynomial growth versus subsets have
+found the doubling a one implies the
+
+ align:start position:0%
+found the doubling a one implies the
+ 
+
+ align:start position:0%
+found the doubling a one implies the
+other although not in the converse and
+
+ align:start position:0%
+other although not in the converse and
+ 
+
+ align:start position:0%
+other although not in the converse and
+they are indeed we dated and this comes
+
+ align:start position:0%
+they are indeed we dated and this comes
+ 
+
+ align:start position:0%
+they are indeed we dated and this comes
+out of some very recent work oh I should
+
+ align:start position:0%
+out of some very recent work oh I should
+ 
+
+ align:start position:0%
+out of some very recent work oh I should
+also mention that Cuomo's theorem has
+
+ align:start position:0%
+also mention that Cuomo's theorem has
+ 
+
+ align:start position:0%
+also mention that Cuomo's theorem has
+been major simplified by kleiner who
+
+ align:start position:0%
+been major simplified by kleiner who
+ 
+
+ align:start position:0%
+been major simplified by kleiner who
+gave an important simplification more
+
+ align:start position:0%
+gave an important simplification more
+ 
+
+ align:start position:0%
+gave an important simplification more
+elementary proof of grow MOFs
+
+ align:start position:0%
+elementary proof of grow MOFs
+ 
+
+ align:start position:0%
+elementary proof of grow MOFs
+theorem okay so let's talk about a non
+
+ align:start position:0%
+theorem okay so let's talk about a non
+ 
+
+ align:start position:0%
+theorem okay so let's talk about a non
+abelian version of Fryman still we would
+
+ align:start position:0%
+abelian version of Fryman still we would
+ 
+
+ align:start position:0%
+abelian version of Fryman still we would
+like some result that says that it's a
+
+ align:start position:0%
+like some result that says that it's a
+ 
+
+ align:start position:0%
+like some result that says that it's a
+true that every set must every set so
+
+ align:start position:0%
+true that every set must every set so
+ 
+
+ align:start position:0%
+true that every set must every set so
+previously we had a small table you want
+
+ align:start position:0%
+previously we had a small table you want
+ 
+
+ align:start position:0%
+previously we had a small table you want
+to have some similar notion although it
+
+ align:start position:0%
+to have some similar notion although it
+ 
+
+ align:start position:0%
+to have some similar notion although it
+might not be exactly small doubling but
+
+ align:start position:0%
+might not be exactly small doubling but
+ 
+
+ align:start position:0%
+might not be exactly small doubling but
+let me not be very precise and to say
+
+ align:start position:0%
+let me not be very precise and to say
+ 
+
+ align:start position:0%
+let me not be very precise and to say
+hold small doubling in literature these
+
+ align:start position:0%
+hold small doubling in literature these
+ 
+
+ align:start position:0%
+hold small doubling in literature these
+things are sometimes also known as
+
+ align:start position:0%
+things are sometimes also known as
+ 
+
+ align:start position:0%
+things are sometimes also known as
+approximate groups you catch the
+
+ align:start position:0%
+approximate groups you catch the
+ 
+
+ align:start position:0%
+approximate groups you catch the
+relevant literature on this subject most
+
+ align:start position:0%
+relevant literature on this subject most
+ 
+
+ align:start position:0%
+relevant literature on this subject most
+every set of small doubling in some non
+
+ align:start position:0%
+every set of small doubling in some non
+ 
+
+ align:start position:0%
+every set of small doubling in some non
+abelian group behave like one of these
+
+ align:start position:0%
+abelian group behave like one of these
+ 
+
+ align:start position:0%
+abelian group behave like one of these
+known examples something which is some
+
+ align:start position:0%
+known examples something which is some
+ 
+
+ align:start position:0%
+known examples something which is some
+combination
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+of subgroups and no potent balls so
+
+ align:start position:0%
+of subgroups and no potent balls so
+ 
+
+ align:start position:0%
+of subgroups and no potent balls so
+these combinations are sometimes known
+
+ align:start position:0%
+these combinations are sometimes known
+ 
+
+ align:start position:0%
+these combinations are sometimes known
+as Cosette Neal progressions so this was
+
+ align:start position:0%
+as Cosette Neal progressions so this was
+ 
+
+ align:start position:0%
+as Cosette Neal progressions so this was
+very this was something that was only
+
+ align:start position:0%
+very this was something that was only
+ 
+
+ align:start position:0%
+very this was something that was only
+explore in the past ten years or so and
+
+ align:start position:0%
+explore in the past ten years or so and
+ 
+
+ align:start position:0%
+explore in the past ten years or so and
+a series of very difficult works
+
+ align:start position:0%
+a series of very difficult works
+ 
+
+ align:start position:0%
+a series of very difficult works
+previously have been known and still
+
+ align:start position:0%
+previously have been known and still
+ 
+
+ align:start position:0%
+previously have been known and still
+it's being investigated for various
+
+ align:start position:0%
+it's being investigated for various
+ 
+
+ align:start position:0%
+it's being investigated for various
+special classes of matrix groups or
+
+ align:start position:0%
+special classes of matrix groups or
+ 
+
+ align:start position:0%
+special classes of matrix groups or
+special classes of groups like solve a
+
+ align:start position:0%
+special classes of groups like solve a
+ 
+
+ align:start position:0%
+special classes of groups like solve a
+group solvable groups and whatnot that
+
+ align:start position:0%
+group solvable groups and whatnot that
+ 
+
+ align:start position:0%
+group solvable groups and whatnot that
+are more explicit or easier to handle or
+
+ align:start position:0%
+are more explicit or easier to handle or
+ 
+
+ align:start position:0%
+are more explicit or easier to handle or
+closer to the abelian analog there was
+
+ align:start position:0%
+closer to the abelian analog there was
+ 
+
+ align:start position:0%
+closer to the abelian analog there was
+important work of push off scheme which
+
+ align:start position:0%
+important work of push off scheme which
+ 
+
+ align:start position:0%
+important work of push off scheme which
+was published about ten years ago who
+
+ align:start position:0%
+was published about ten years ago who
+ 
+
+ align:start position:0%
+was published about ten years ago who
+showed using model theory techniques so
+
+ align:start position:0%
+showed using model theory techniques so
+ 
+
+ align:start position:0%
+showed using model theory techniques so
+using methods from logic that a weak
+
+ align:start position:0%
+using methods from logic that a weak
+ 
+
+ align:start position:0%
+using methods from logic that a weak
+version of Freeman's theorem is true and
+
+ align:start position:0%
+version of Freeman's theorem is true and
+ 
+
+ align:start position:0%
+version of Freeman's theorem is true and
+later on
+
+ align:start position:0%
+later on
+ 
+
+ align:start position:0%
+later on
+Priya green and hell building on
+
+ align:start position:0%
+Priya green and hell building on
+ 
+
+ align:start position:0%
+Priya green and hell building on
+Kirchhoff's kiss work so this actually
+
+ align:start position:0%
+Kirchhoff's kiss work so this actually
+ 
+
+ align:start position:0%
+Kirchhoff's kiss work so this actually
+came quite a bit later even though the
+
+ align:start position:0%
+came quite a bit later even though the
+ 
+
+ align:start position:0%
+came quite a bit later even though the
+journal publication dates are the same
+
+ align:start position:0%
+journal publication dates are the same
+ 
+
+ align:start position:0%
+journal publication dates are the same
+year so they were able to build on
+
+ align:start position:0%
+year so they were able to build on
+ 
+
+ align:start position:0%
+year so they were able to build on
+Kirchhoff's keys work and but greatly
+
+ align:start position:0%
+Kirchhoff's keys work and but greatly
+ 
+
+ align:start position:0%
+Kirchhoff's keys work and but greatly
+expanding on it and going back to some
+
+ align:start position:0%
+expanding on it and going back to some
+ 
+
+ align:start position:0%
+expanding on it and going back to some
+of the older techniques coming from
+
+ align:start position:0%
+of the older techniques coming from
+ 
+
+ align:start position:0%
+of the older techniques coming from
+Gilbert's fifth problem and as a result
+
+ align:start position:0%
+Gilbert's fifth problem and as a result
+ 
+
+ align:start position:0%
+Gilbert's fifth problem and as a result
+proved an inverse structure theorem that
+
+ align:start position:0%
+proved an inverse structure theorem that
+ 
+
+ align:start position:0%
+proved an inverse structure theorem that
+gave some kind of answer to this
+
+ align:start position:0%
+gave some kind of answer to this
+ 
+
+ align:start position:0%
+gave some kind of answer to this
+question of non abelian Fryman so we now
+
+ align:start position:0%
+question of non abelian Fryman so we now
+ 
+
+ align:start position:0%
+question of non abelian Fryman so we now
+do have some theorem which is like
+
+ align:start position:0%
+do have some theorem which is like
+ 
+
+ align:start position:0%
+do have some theorem which is like
+Fryman Sturm for abelian groups that
+
+ align:start position:0%
+Fryman Sturm for abelian groups that
+ 
+
+ align:start position:0%
+Fryman Sturm for abelian groups that
+says in a bit non abelian group if you
+
+ align:start position:0%
+says in a bit non abelian group if you
+ 
+
+ align:start position:0%
+says in a bit non abelian group if you
+have something that resembles small
+
+ align:start position:0%
+have something that resembles small
+ 
+
+ align:start position:0%
+have something that resembles small
+doubling then the set must in some sense
+
+ align:start position:0%
+doubling then the set must in some sense
+ 
+
+ align:start position:0%
+doubling then the set must in some sense
+look like a combination
+
+ align:start position:0%
+look like a combination
+ 
+
+ align:start position:0%
+look like a combination
+of subgroups and neo potent boss but let
+
+ align:start position:0%
+of subgroups and neo potent boss but let
+ 
+
+ align:start position:0%
+of subgroups and neo potent boss but let
+me not be precise at all the methods
+
+ align:start position:0%
+me not be precise at all the methods
+ 
+
+ align:start position:0%
+me not be precise at all the methods
+here build on Kirchhoff's key and which
+
+ align:start position:0%
+here build on Kirchhoff's key and which
+ 
+
+ align:start position:0%
+here build on Kirchhoff's key and which
+also used model theory which is kind of
+
+ align:start position:0%
+also used model theory which is kind of
+ 
+
+ align:start position:0%
+also used model theory which is kind of
+I mean it's something we're okay in
+
+ align:start position:0%
+I mean it's something we're okay in
+ 
+
+ align:start position:0%
+I mean it's something we're okay in
+particular one feature of all of these
+
+ align:start position:0%
+particular one feature of all of these
+ 
+
+ align:start position:0%
+particular one feature of all of these
+proofs is that they give no bounds
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+similar to what we seen earlier in the
+
+ align:start position:0%
+similar to what we seen earlier in the
+ 
+
+ align:start position:0%
+similar to what we seen earlier in the
+course improves our involved compactness
+
+ align:start position:0%
+course improves our involved compactness
+ 
+
+ align:start position:0%
+course improves our involved compactness
+what happens here is that the arguments
+
+ align:start position:0%
+what happens here is that the arguments
+ 
+
+ align:start position:0%
+what happens here is that the arguments
+use ultra filters so there are these
+
+ align:start position:0%
+use ultra filters so there are these
+ 
+
+ align:start position:0%
+use ultra filters so there are these
+constructions from mathematical logic
+
+ align:start position:0%
+constructions from mathematical logic
+ 
+
+ align:start position:0%
+constructions from mathematical logic
+and like compactness they give no bats
+
+ align:start position:0%
+and like compactness they give no bats
+ 
+
+ align:start position:0%
+and like compactness they give no bats
+so it remains an open problem to proof
+
+ align:start position:0%
+so it remains an open problem to proof
+ 
+
+ align:start position:0%
+so it remains an open problem to proof
+Fryman stands for non abelian groups
+
+ align:start position:0%
+Fryman stands for non abelian groups
+ 
+
+ align:start position:0%
+Fryman stands for non abelian groups
+with some concrete bands question so
+
+ align:start position:0%
+with some concrete bands question so
+ 
+
+ align:start position:0%
+with some concrete bands question so
+what is new potent bomb I wouldn't want
+
+ align:start position:0%
+what is new potent bomb I wouldn't want
+ 
+
+ align:start position:0%
+what is new potent bomb I wouldn't want
+to give a precise definition but roughly
+
+ align:start position:0%
+to give a precise definition but roughly
+ 
+
+ align:start position:0%
+to give a precise definition but roughly
+speaking it's balls that come out of
+
+ align:start position:0%
+speaking it's balls that come out of
+ 
+
+ align:start position:0%
+speaking it's balls that come out of
+those types of constructions right so
+
+ align:start position:0%
+those types of constructions right so
+ 
+
+ align:start position:0%
+those types of constructions right so
+you take a new potent subgroup you take
+
+ align:start position:0%
+you take a new potent subgroup you take
+ 
+
+ align:start position:0%
+you take a new potent subgroup you take
+an important group you look at the image
+
+ align:start position:0%
+an important group you look at the image
+ 
+
+ align:start position:0%
+an important group you look at the image
+when you're potent group into your group
+
+ align:start position:0%
+when you're potent group into your group
+ 
+
+ align:start position:0%
+when you're potent group into your group
+and then look at the image of that ball
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so something that looks like one of the
+
+ align:start position:0%
+so something that looks like one of the
+ 
+
+ align:start position:0%
+so something that looks like one of the
+previous constructions okay so that's
+
+ align:start position:0%
+previous constructions okay so that's
+ 
+
+ align:start position:0%
+previous constructions okay so that's
+all I want to say about non abelian
+
+ align:start position:0%
+all I want to say about non abelian
+ 
+
+ align:start position:0%
+all I want to say about non abelian
+extensions are fragments theorem any
+
+ align:start position:0%
+extensions are fragments theorem any
+ 
+
+ align:start position:0%
+extensions are fragments theorem any
+questions okay so what I mean by so you
+
+ align:start position:0%
+questions okay so what I mean by so you
+ 
+
+ align:start position:0%
+questions okay so what I mean by so you
+can look in the papers to see the
+
+ align:start position:0%
+can look in the papers to see the
+ 
+
+ align:start position:0%
+can look in the papers to see the
+precise definitions but roughly speaking
+
+ align:start position:0%
+precise definitions but roughly speaking
+ 
+
+ align:start position:0%
+precise definitions but roughly speaking
+it's that if you have therefore one
+
+ align:start position:0%
+it's that if you have therefore one
+ 
+
+ align:start position:0%
+it's that if you have therefore one
+there are different kinds of definitions
+
+ align:start position:0%
+there are different kinds of definitions
+ 
+
+ align:start position:0%
+there are different kinds of definitions
+and most of them are equivalent but one
+
+ align:start position:0%
+and most of them are equivalent but one
+ 
+
+ align:start position:0%
+and most of them are equivalent but one
+versions that you have a set a such that
+
+ align:start position:0%
+versions that you have a set a such that
+ 
+
+ align:start position:0%
+versions that you have a set a such that
+a a is coverable by hey
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so to bid more than just the size
+
+ align:start position:0%
+so to bid more than just the size
+ 
+
+ align:start position:0%
+so to bid more than just the size
+information but it's actually related to
+
+ align:start position:0%
+information but it's actually related to
+ 
+
+ align:start position:0%
+information but it's actually related to
+size information so we've already seen
+
+ align:start position:0%
+size information so we've already seen
+ 
+
+ align:start position:0%
+size information so we've already seen
+its course how many of these different
+
+ align:start position:0%
+its course how many of these different
+ 
+
+ align:start position:0%
+its course how many of these different
+notions you can go back and forth from
+
+ align:start position:0%
+notions you can go back and forth from
+ 
+
+ align:start position:0%
+notions you can go back and forth from
+one to the other I'm covering two to
+
+ align:start position:0%
+one to the other I'm covering two to
+ 
+
+ align:start position:0%
+one to the other I'm covering two to
+size and whatnot okay
+
+ align:start position:0%
+size and whatnot okay
+ 
+
+ align:start position:0%
+size and whatnot okay
+the final thing I want to discuss today
+
+ align:start position:0%
+the final thing I want to discuss today
+ 
+
+ align:start position:0%
+the final thing I want to discuss today
+is one of the most central open problems
+
+ align:start position:0%
+is one of the most central open problems
+ 
+
+ align:start position:0%
+is one of the most central open problems
+in additive combinatorics going back to
+
+ align:start position:0%
+in additive combinatorics going back to
+ 
+
+ align:start position:0%
+in additive combinatorics going back to
+the abelian version so this is known as
+
+ align:start position:0%
+the abelian version so this is known as
+ 
+
+ align:start position:0%
+the abelian version so this is known as
+the polynomial Fryman Rouge our
+
+ align:start position:0%
+the polynomial Fryman Rouge our
+ 
+
+ align:start position:0%
+the polynomial Fryman Rouge our
+conjecture
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so we would like some kind of a Fryman
+
+ align:start position:0%
+so we would like some kind of a Fryman
+ 
+
+ align:start position:0%
+so we would like some kind of a Fryman
+theorem that preserves the constants up
+
+ align:start position:0%
+theorem that preserves the constants up
+ 
+
+ align:start position:0%
+theorem that preserves the constants up
+to polynomial changes without losing an
+
+ align:start position:0%
+to polynomial changes without losing an
+ 
+
+ align:start position:0%
+to polynomial changes without losing an
+exponent from earlier discussions I
+
+ align:start position:0%
+exponent from earlier discussions I
+ 
+
+ align:start position:0%
+exponent from earlier discussions I
+showed you that the bounds that we
+
+ align:start position:0%
+showed you that the bounds that we
+ 
+
+ align:start position:0%
+showed you that the bounds that we
+almost proved is close to the truth you
+
+ align:start position:0%
+almost proved is close to the truth you
+ 
+
+ align:start position:0%
+almost proved is close to the truth you
+do need some kind of exponential loss in
+
+ align:start position:0%
+do need some kind of exponential loss in
+ 
+
+ align:start position:0%
+do need some kind of exponential loss in
+the blow-up size of the GA p but it
+
+ align:start position:0%
+the blow-up size of the GA p but it
+ 
+
+ align:start position:0%
+the blow-up size of the GA p but it
+turns out those kind of examples are
+
+ align:start position:0%
+turns out those kind of examples are
+ 
+
+ align:start position:0%
+turns out those kind of examples are
+slightly misleading all right so let's
+
+ align:start position:0%
+slightly misleading all right so let's
+ 
+
+ align:start position:0%
+slightly misleading all right so let's
+look at the examples the constructions
+
+ align:start position:0%
+look at the examples the constructions
+ 
+
+ align:start position:0%
+look at the examples the constructions
+again so if a so just for simplicity
+
+ align:start position:0%
+again so if a so just for simplicity
+ 
+
+ align:start position:0%
+again so if a so just for simplicity
+exposition I'm going to stick with f2 to
+
+ align:start position:0%
+exposition I'm going to stick with f2 to
+ 
+
+ align:start position:0%
+exposition I'm going to stick with f2 to
+the N at least initially so if a is an
+
+ align:start position:0%
+the N at least initially so if a is an
+ 
+
+ align:start position:0%
+the N at least initially so if a is an
+independent set of size and then okay
+
+ align:start position:0%
+independent set of size and then okay
+ 
+
+ align:start position:0%
+independent set of size and then okay
+being the doubling constant of a trophy
+
+ align:start position:0%
+being the doubling constant of a trophy
+ 
+
+ align:start position:0%
+being the doubling constant of a trophy
+like n over 2 and yet the subgroup that
+
+ align:start position:0%
+like n over 2 and yet the subgroup that
+ 
+
+ align:start position:0%
+like n over 2 and yet the subgroup that
+contains a size true to be something on
+
+ align:start position:0%
+contains a size true to be something on
+ 
+
+ align:start position:0%
+contains a size true to be something on
+the water okay times hey so you
+
+ align:start position:0%
+the water okay times hey so you
+ 
+
+ align:start position:0%
+the water okay times hey so you
+necessarily incur an exponential loss
+
+ align:start position:0%
+necessarily incur an exponential loss
+ 
+
+ align:start position:0%
+necessarily incur an exponential loss
+over here now you might complain what
+
+ align:start position:0%
+over here now you might complain what
+ 
+
+ align:start position:0%
+over here now you might complain what
+the size of a here is basically K but of
+
+ align:start position:0%
+the size of a here is basically K but of
+ 
+
+ align:start position:0%
+the size of a here is basically K but of
+course I can blow up this example by
+
+ align:start position:0%
+course I can blow up this example by
+ 
+
+ align:start position:0%
+course I can blow up this example by
+considering what happens if you take
+
+ align:start position:0%
+considering what happens if you take
+ 
+
+ align:start position:0%
+considering what happens if you take
+each element here
+
+ align:start position:0%
+each element here
+ 
+
+ align:start position:0%
+each element here
+into entire subspace so these are the
+
+ align:start position:0%
+into entire subspace so these are the
+ 
+
+ align:start position:0%
+into entire subspace so these are the
+coordinate vectors so now I'm sitting
+
+ align:start position:0%
+coordinate vectors so now I'm sitting
+ 
+
+ align:start position:0%
+coordinate vectors so now I'm sitting
+inside F 2 to the M plus N and that
+
+ align:start position:0%
+inside F 2 to the M plus N and that
+ 
+
+ align:start position:0%
+inside F 2 to the M plus N and that
+gives you this set the toppling constant
+
+ align:start position:0%
+gives you this set the toppling constant
+ 
+
+ align:start position:0%
+gives you this set the toppling constant
+is still the same as before and yet we
+
+ align:start position:0%
+is still the same as before and yet we
+ 
+
+ align:start position:0%
+is still the same as before and yet we
+see that the generated by a still has
+
+ align:start position:0%
+see that the generated by a still has
+ 
+
+ align:start position:0%
+see that the generated by a still has
+this exponential blow-up in this
+
+ align:start position:0%
+this exponential blow-up in this
+ 
+
+ align:start position:0%
+this exponential blow-up in this
+constant exponential in the doubling
+
+ align:start position:0%
+constant exponential in the doubling
+ 
+
+ align:start position:0%
+constant exponential in the doubling
+constant but now you see in this example
+
+ align:start position:0%
+constant but now you see in this example
+ 
+
+ align:start position:0%
+constant but now you see in this example
+here even though the subgroup generated
+
+ align:start position:0%
+here even though the subgroup generated
+ 
+
+ align:start position:0%
+here even though the subgroup generated
+by a can be much larger than a by so
+
+ align:start position:0%
+by a can be much larger than a by so
+ 
+
+ align:start position:0%
+by a can be much larger than a by so
+everything's still constant so much
+
+ align:start position:0%
+everything's still constant so much
+ 
+
+ align:start position:0%
+everything's still constant so much
+largest in terms of them as a function
+
+ align:start position:0%
+largest in terms of them as a function
+ 
+
+ align:start position:0%
+largest in terms of them as a function
+of the toppling constant a has a very
+
+ align:start position:0%
+of the toppling constant a has a very
+ 
+
+ align:start position:0%
+of the toppling constant a has a very
+large structure so a has contains a very
+
+ align:start position:0%
+large structure so a has contains a very
+ 
+
+ align:start position:0%
+large structure so a has contains a very
+large subspace subspace I mean a fine
+
+ align:start position:0%
+large subspace subspace I mean a fine
+ 
+
+ align:start position:0%
+large subspace subspace I mean a fine
+subspace and this subspace here is
+
+ align:start position:0%
+subspace and this subspace here is
+ 
+
+ align:start position:0%
+subspace and this subspace here is
+comparable to the size of a itself so
+
+ align:start position:0%
+comparable to the size of a itself so
+ 
+
+ align:start position:0%
+comparable to the size of a itself so
+you might wonder if you don't care about
+
+ align:start position:0%
+you might wonder if you don't care about
+ 
+
+ align:start position:0%
+you might wonder if you don't care about
+containing a inside a single subspace
+
+ align:start position:0%
+containing a inside a single subspace
+ 
+
+ align:start position:0%
+containing a inside a single subspace
+can you do much better in terms of
+
+ align:start position:0%
+can you do much better in terms of
+ 
+
+ align:start position:0%
+can you do much better in terms of
+bounds and that's the content of the
+
+ align:start position:0%
+bounds and that's the content of the
+ 
+
+ align:start position:0%
+bounds and that's the content of the
+polynomial frame intruder conjecture or
+
+ align:start position:0%
+polynomial frame intruder conjecture or
+ 
+
+ align:start position:0%
+polynomial frame intruder conjecture or
+conjecture for f2 to the M says that if
+
+ align:start position:0%
+conjecture for f2 to the M says that if
+ 
+
+ align:start position:0%
+conjecture for f2 to the M says that if
+you have a subset of f2 to the M and a
+
+ align:start position:0%
+you have a subset of f2 to the M and a
+ 
+
+ align:start position:0%
+you have a subset of f2 to the M and a
+plus a is size and most K times the size
+
+ align:start position:0%
+plus a is size and most K times the size
+ 
+
+ align:start position:0%
+plus a is size and most K times the size
+of a then there exists a subspace V of
+
+ align:start position:0%
+of a then there exists a subspace V of
+ 
+
+ align:start position:0%
+of a then there exists a subspace V of
+size at most
+
+ align:start position:0%
+size at most
+ 
+
+ align:start position:0%
+size at most
+such that the contains a large
+
+ align:start position:0%
+such that the contains a large
+ 
+
+ align:start position:0%
+such that the contains a large
+proportion and the large year we only
+
+ align:start position:0%
+proportion and the large year we only
+ 
+
+ align:start position:0%
+proportion and the large year we only
+lose something that is polynomial in
+
+ align:start position:0%
+lose something that is polynomial in
+ 
+
+ align:start position:0%
+lose something that is polynomial in
+these doubling constants so that's the
+
+ align:start position:0%
+these doubling constants so that's the
+ 
+
+ align:start position:0%
+these doubling constants so that's the
+case over here so instead of containing
+
+ align:start position:0%
+case over here so instead of containing
+ 
+
+ align:start position:0%
+case over here so instead of containing
+a in the inside an entire subspace
+
+ align:start position:0%
+a in the inside an entire subspace
+ 
+
+ align:start position:0%
+a in the inside an entire subspace
+I just want to contain a large fraction
+
+ align:start position:0%
+I just want to contain a large fraction
+ 
+
+ align:start position:0%
+I just want to contain a large fraction
+of a in a subspace and the conjecture is
+
+ align:start position:0%
+of a in a subspace and the conjecture is
+ 
+
+ align:start position:0%
+of a in a subspace and the conjecture is
+that I do not need to incur exponential
+
+ align:start position:0%
+that I do not need to incur exponential
+ 
+
+ align:start position:0%
+that I do not need to incur exponential
+losses in the constants question is V an
+
+ align:start position:0%
+losses in the constants question is V an
+ 
+
+ align:start position:0%
+losses in the constants question is V an
+affine subspace you can think of V s
+
+ align:start position:0%
+affine subspace you can think of V s
+ 
+
+ align:start position:0%
+affine subspace you can think of V s
+mattifying south chase you can think of
+
+ align:start position:0%
+mattifying south chase you can think of
+ 
+
+ align:start position:0%
+mattifying south chase you can think of
+V is a subspace it doesn't actually
+
+ align:start position:0%
+V is a subspace it doesn't actually
+ 
+
+ align:start position:0%
+V is a subspace it doesn't actually
+matter in this formulation okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+there's an equivalent formulation which
+
+ align:start position:0%
+there's an equivalent formulation which
+ 
+
+ align:start position:0%
+there's an equivalent formulation which
+you might like better where initially my
+
+ align:start position:0%
+you might like better where initially my
+ 
+
+ align:start position:0%
+you might like better where initially my
+complaint well initially PFR is
+
+ align:start position:0%
+complaint well initially PFR is
+ 
+
+ align:start position:0%
+complaint well initially PFR is
+initially Fryman terms about covering it
+
+ align:start position:0%
+initially Fryman terms about covering it
+ 
+
+ align:start position:0%
+initially Fryman terms about covering it
+and now we've only covered a part of it
+
+ align:start position:0%
+and now we've only covered a part of it
+ 
+
+ align:start position:0%
+and now we've only covered a part of it
+of course we saw from earlier arguments
+
+ align:start position:0%
+of course we saw from earlier arguments
+ 
+
+ align:start position:0%
+of course we saw from earlier arguments
+you can use recovering lam article from
+
+ align:start position:0%
+you can use recovering lam article from
+ 
+
+ align:start position:0%
+you can use recovering lam article from
+covering a part of a to covering all of
+
+ align:start position:0%
+covering a part of a to covering all of
+ 
+
+ align:start position:0%
+covering a part of a to covering all of
+it
+
+ align:start position:0%
+it
+ 
+
+ align:start position:0%
+it
+indeed is this the case that this
+
+ align:start position:0%
+indeed is this the case that this
+ 
+
+ align:start position:0%
+indeed is this the case that this
+formulation is equivalent to the
+
+ align:start position:0%
+formulation is equivalent to the
+ 
+
+ align:start position:0%
+formulation is equivalent to the
+formulation that if a the same after the
+
+ align:start position:0%
+formulation that if a the same after the
+ 
+
+ align:start position:0%
+formulation that if a the same after the
+N and a plus a sighs the most K times a
+
+ align:start position:0%
+N and a plus a sighs the most K times a
+ 
+
+ align:start position:0%
+N and a plus a sighs the most K times a
+then there exists some subspace V with
+
+ align:start position:0%
+then there exists some subspace V with
+ 
+
+ align:start position:0%
+then there exists some subspace V with
+the size of e no larger than the size of
+
+ align:start position:0%
+the size of e no larger than the size of
+ 
+
+ align:start position:0%
+the size of e no larger than the size of
+a such that a can be covered by
+
+ align:start position:0%
+a such that a can be covered by
+ 
+
+ align:start position:0%
+a such that a can be covered by
+polynomial in K many Co sets we see that
+
+ align:start position:0%
+polynomial in K many Co sets we see that
+ 
+
+ align:start position:0%
+polynomial in K many Co sets we see that
+here here a has doubling constant K
+
+ align:start position:0%
+here here a has doubling constant K
+ 
+
+ align:start position:0%
+here here a has doubling constant K
+which is around the same as and and even
+
+ align:start position:0%
+which is around the same as and and even
+ 
+
+ align:start position:0%
+which is around the same as and and even
+though I cannot contain a by a single
+
+ align:start position:0%
+though I cannot contain a by a single
+ 
+
+ align:start position:0%
+though I cannot contain a by a single
+subspace of well fee the same size I can
+
+ align:start position:0%
+subspace of well fee the same size I can
+ 
+
+ align:start position:0%
+subspace of well fee the same size I can
+use K different translates to cover a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+any questions so I want to leave it to
+
+ align:start position:0%
+any questions so I want to leave it to
+ 
+
+ align:start position:0%
+any questions so I want to leave it to
+you as an exercise to prove that these
+
+ align:start position:0%
+you as an exercise to prove that these
+ 
+
+ align:start position:0%
+you as an exercise to prove that these
+two versions are equivalent to each
+
+ align:start position:0%
+two versions are equivalent to each
+ 
+
+ align:start position:0%
+two versions are equivalent to each
+other
+
+ align:start position:0%
+other
+ 
+
+ align:start position:0%
+other
+okay so it's not too hard so it's on
+
+ align:start position:0%
+okay so it's not too hard so it's on
+ 
+
+ align:start position:0%
+okay so it's not too hard so it's on
+something I have more time I would show
+
+ align:start position:0%
+something I have more time I would show
+ 
+
+ align:start position:0%
+something I have more time I would show
+you it's useless
+
+ align:start position:0%
+you it's useless
+ 
+
+ align:start position:0%
+you it's useless
+roots are covering lemma to prove this
+
+ align:start position:0%
+roots are covering lemma to prove this
+ 
+
+ align:start position:0%
+roots are covering lemma to prove this
+equivalence the nice thing about the
+
+ align:start position:0%
+equivalence the nice thing about the
+ 
+
+ align:start position:0%
+equivalence the nice thing about the
+poly no polynomial frame illusion
+
+ align:start position:0%
+poly no polynomial frame illusion
+ 
+
+ align:start position:0%
+poly no polynomial frame illusion
+conjecture pfr conjecture is considered
+
+ align:start position:0%
+conjecture pfr conjecture is considered
+ 
+
+ align:start position:0%
+conjecture pfr conjecture is considered
+a central conjecture in additive
+
+ align:start position:0%
+a central conjecture in additive
+ 
+
+ align:start position:0%
+a central conjecture in additive
+combinatorics because it has many
+
+ align:start position:0%
+combinatorics because it has many
+ 
+
+ align:start position:0%
+combinatorics because it has many
+equivalent formulation and relate to
+
+ align:start position:0%
+equivalent formulation and relate to
+ 
+
+ align:start position:0%
+equivalent formulation and relate to
+many problems that are central to the
+
+ align:start position:0%
+many problems that are central to the
+ 
+
+ align:start position:0%
+many problems that are central to the
+subject so we would like some kind of an
+
+ align:start position:0%
+subject so we would like some kind of an
+ 
+
+ align:start position:0%
+subject so we would like some kind of an
+inverse theorem that gives you these
+
+ align:start position:0%
+inverse theorem that gives you these
+ 
+
+ align:start position:0%
+inverse theorem that gives you these
+polynomial bounds and I'll mention a
+
+ align:start position:0%
+polynomial bounds and I'll mention a
+ 
+
+ align:start position:0%
+polynomial bounds and I'll mention a
+couple of these equivalent formulations
+
+ align:start position:0%
+couple of these equivalent formulations
+ 
+
+ align:start position:0%
+couple of these equivalent formulations
+here's an important formulation which is
+
+ align:start position:0%
+here's an important formulation which is
+ 
+
+ align:start position:0%
+here's an important formulation which is
+rather attractive where instead of
+
+ align:start position:0%
+rather attractive where instead of
+ 
+
+ align:start position:0%
+rather attractive where instead of
+considering subsets we're going to
+
+ align:start position:0%
+considering subsets we're going to
+ 
+
+ align:start position:0%
+considering subsets we're going to
+formulate something that has to do with
+
+ align:start position:0%
+formulate something that has to do with
+ 
+
+ align:start position:0%
+formulate something that has to do with
+approximate homomorphisms so the
+
+ align:start position:0%
+approximate homomorphisms so the
+ 
+
+ align:start position:0%
+approximate homomorphisms so the
+statements are still conjecture is that
+
+ align:start position:0%
+statements are still conjecture is that
+ 
+
+ align:start position:0%
+statements are still conjecture is that
+if it's a function from moving in space
+
+ align:start position:0%
+if it's a function from moving in space
+ 
+
+ align:start position:0%
+if it's a function from moving in space
+to another podium space is such that F
+
+ align:start position:0%
+to another podium space is such that F
+ 
+
+ align:start position:0%
+to another podium space is such that F
+is approximately a homomorphism in a
+
+ align:start position:0%
+is approximately a homomorphism in a
+ 
+
+ align:start position:0%
+is approximately a homomorphism in a
+sense that the set of possible errors if
+
+ align:start position:0%
+sense that the set of possible errors if
+ 
+
+ align:start position:0%
+sense that the set of possible errors if
+it's actually a homomorphism and this
+
+ align:start position:0%
+it's actually a homomorphism and this
+ 
+
+ align:start position:0%
+it's actually a homomorphism and this
+quantity is always equal to zero but
+
+ align:start position:0%
+quantity is always equal to zero but
+ 
+
+ align:start position:0%
+quantity is always equal to zero but
+it's approximately a whole more physical
+
+ align:start position:0%
+it's approximately a whole more physical
+ 
+
+ align:start position:0%
+it's approximately a whole more physical
+in the sense that the set of such errors
+
+ align:start position:0%
+in the sense that the set of such errors
+ 
+
+ align:start position:0%
+in the sense that the set of such errors
+is bounded by K in size the conclusion
+
+ align:start position:0%
+is bounded by K in size the conclusion
+ 
+
+ align:start position:0%
+is bounded by K in size the conclusion
+so the conjecture claims that then there
+
+ align:start position:0%
+so the conjecture claims that then there
+ 
+
+ align:start position:0%
+so the conjecture claims that then there
+exists an actual homomorphism an actual
+
+ align:start position:0%
+exists an actual homomorphism an actual
+ 
+
+ align:start position:0%
+exists an actual homomorphism an actual
+linear map
+
+ align:start position:0%
+linear map
+ 
+
+ align:start position:0%
+linear map
+G
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+such that F is very close to G as in
+
+ align:start position:0%
+such that F is very close to G as in
+ 
+
+ align:start position:0%
+such that F is very close to G as in
+that the set of possible discrepancies
+
+ align:start position:0%
+that the set of possible discrepancies
+ 
+
+ align:start position:0%
+that the set of possible discrepancies
+between F and G yes Bank where you only
+
+ align:start position:0%
+between F and G yes Bank where you only
+ 
+
+ align:start position:0%
+between F and G yes Bank where you only
+lose a most polynomial in K so if you
+
+ align:start position:0%
+lose a most polynomial in K so if you
+ 
+
+ align:start position:0%
+lose a most polynomial in K so if you
+are an approximate homomorphism in this
+
+ align:start position:0%
+are an approximate homomorphism in this
+ 
+
+ align:start position:0%
+are an approximate homomorphism in this
+sense then you're actually very close to
+
+ align:start position:0%
+sense then you're actually very close to
+ 
+
+ align:start position:0%
+sense then you're actually very close to
+an actual linear map now it is not too
+
+ align:start position:0%
+an actual linear map now it is not too
+ 
+
+ align:start position:0%
+an actual linear map now it is not too
+hard to prove a much weaker
+
+ align:start position:0%
+hard to prove a much weaker
+ 
+
+ align:start position:0%
+hard to prove a much weaker
+quantitatively weaker version of the
+
+ align:start position:0%
+quantitatively weaker version of the
+ 
+
+ align:start position:0%
+quantitatively weaker version of the
+statement so I claim that it is trivial
+
+ align:start position:0%
+statement so I claim that it is trivial
+ 
+
+ align:start position:0%
+statement so I claim that it is trivial
+to show upper bound of at most two to
+
+ align:start position:0%
+to show upper bound of at most two to
+ 
+
+ align:start position:0%
+to show upper bound of at most two to
+the K over here so think about why so if
+
+ align:start position:0%
+the K over here so think about why so if
+ 
+
+ align:start position:0%
+the K over here so think about why so if
+I give you an F I can just think about
+
+ align:start position:0%
+I give you an F I can just think about
+ 
+
+ align:start position:0%
+I give you an F I can just think about
+what the values of F are on the basis
+
+ align:start position:0%
+what the values of F are on the basis
+ 
+
+ align:start position:0%
+what the values of F are on the basis
+and extend it to a linear map this set
+
+ align:start position:0%
+and extend it to a linear map this set
+ 
+
+ align:start position:0%
+and extend it to a linear map this set
+it's necessarily a span of that set so
+
+ align:start position:0%
+it's necessarily a span of that set so
+ 
+
+ align:start position:0%
+it's necessarily a span of that set so
+has size at most 2 to the K but it's
+
+ align:start position:0%
+has size at most 2 to the K but it's
+ 
+
+ align:start position:0%
+has size at most 2 to the K but it's
+open to show you only have to lose a
+
+ align:start position:0%
+open to show you only have to lose a
+ 
+
+ align:start position:0%
+open to show you only have to lose a
+polynomial in
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+[Applause]
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+there's also a version of the polynomial
+
+ align:start position:0%
+there's also a version of the polynomial
+ 
+
+ align:start position:0%
+there's also a version of the polynomial
+frame illusion conjecture which is
+
+ align:start position:0%
+frame illusion conjecture which is
+ 
+
+ align:start position:0%
+frame illusion conjecture which is
+related to things we've discussed
+
+ align:start position:0%
+related to things we've discussed
+ 
+
+ align:start position:0%
+related to things we've discussed
+earlier regarding some Reddy's theorem
+
+ align:start position:0%
+earlier regarding some Reddy's theorem
+ 
+
+ align:start position:0%
+earlier regarding some Reddy's theorem
+and in fact the the polynomial Fryman
+
+ align:start position:0%
+and in fact the the polynomial Fryman
+ 
+
+ align:start position:0%
+and in fact the the polynomial Fryman
+Ruza conjecture kind of came back into
+
+ align:start position:0%
+Ruza conjecture kind of came back into
+ 
+
+ align:start position:0%
+Ruza conjecture kind of came back into
+popularity partly because of cowers
+
+ align:start position:0%
+popularity partly because of cowers
+ 
+
+ align:start position:0%
+popularity partly because of cowers
+proof of some rarities theorem that used
+
+ align:start position:0%
+proof of some rarities theorem that used
+ 
+
+ align:start position:0%
+proof of some rarities theorem that used
+many of these tools so let me state it
+
+ align:start position:0%
+many of these tools so let me state it
+ 
+
+ align:start position:0%
+many of these tools so let me state it
+here okay so we've seen some statement
+
+ align:start position:0%
+here okay so we've seen some statement
+ 
+
+ align:start position:0%
+here okay so we've seen some statement
+like this in an earlier lecture but but
+
+ align:start position:0%
+like this in an earlier lecture but but
+ 
+
+ align:start position:0%
+like this in an earlier lecture but but
+not very precisely not precisely in this
+
+ align:start position:0%
+not very precisely not precisely in this
+ 
+
+ align:start position:0%
+not very precisely not precisely in this
+form i won't define you all the notation
+
+ align:start position:0%
+form i won't define you all the notation
+ 
+
+ align:start position:0%
+form i won't define you all the notation
+here but hopefully you get a rough sense
+
+ align:start position:0%
+here but hopefully you get a rough sense
+ 
+
+ align:start position:0%
+here but hopefully you get a rough sense
+of what what it's about so we want some
+
+ align:start position:0%
+of what what it's about so we want some
+ 
+
+ align:start position:0%
+of what what it's about so we want some
+kind of an inverse statement for
+
+ align:start position:0%
+kind of an inverse statement for
+ 
+
+ align:start position:0%
+kind of an inverse statement for
+quadratic uniformity more
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so recall back to our discussion of
+
+ align:start position:0%
+so recall back to our discussion of
+ 
+
+ align:start position:0%
+so recall back to our discussion of
+proof of Roth's theorem a Fourier
+
+ align:start position:0%
+proof of Roth's theorem a Fourier
+ 
+
+ align:start position:0%
+proof of Roth's theorem a Fourier
+analytic proof of roster we want to say
+
+ align:start position:0%
+analytic proof of roster we want to say
+ 
+
+ align:start position:0%
+analytic proof of roster we want to say
+that but now think about not three a ps4
+
+ align:start position:0%
+that but now think about not three a ps4
+ 
+
+ align:start position:0%
+that but now think about not three a ps4
+four ATP's so we want to know if you
+
+ align:start position:0%
+four ATP's so we want to know if you
+ 
+
+ align:start position:0%
+four ATP's so we want to know if you
+have a function the pudding cube and
+
+ align:start position:0%
+have a function the pudding cube and
+ 
+
+ align:start position:0%
+have a function the pudding cube and
+this function is unbounded and I'm going
+
+ align:start position:0%
+this function is unbounded and I'm going
+ 
+
+ align:start position:0%
+this function is unbounded and I'm going
+to write down some notation which we are
+
+ align:start position:0%
+to write down some notation which we are
+ 
+
+ align:start position:0%
+to write down some notation which we are
+not going to define but the cowers u3
+
+ align:start position:0%
+not going to define but the cowers u3
+ 
+
+ align:start position:0%
+not going to define but the cowers u3
+norm is at least some Delta so this is
+
+ align:start position:0%
+norm is at least some Delta so this is
+ 
+
+ align:start position:0%
+norm is at least some Delta so this is
+something which is related to for AP
+
+ align:start position:0%
+something which is related to for AP
+ 
+
+ align:start position:0%
+something which is related to for AP
+counts so in particular if this number
+
+ align:start position:0%
+counts so in particular if this number
+ 
+
+ align:start position:0%
+counts so in particular if this number
+is small then you have a counting number
+
+ align:start position:0%
+is small then you have a counting number
+ 
+
+ align:start position:0%
+is small then you have a counting number
+for for term arithmetic progressions
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+if this is true then there exists a
+
+ align:start position:0%
+if this is true then there exists a
+ 
+
+ align:start position:0%
+if this is true then there exists a
+quadratic polynomial Q n variables over
+
+ align:start position:0%
+quadratic polynomial Q n variables over
+ 
+
+ align:start position:0%
+quadratic polynomial Q n variables over
+f2 such that your function f correlates
+
+ align:start position:0%
+f2 such that your function f correlates
+ 
+
+ align:start position:0%
+f2 such that your function f correlates
+with this quadratic exponential in Q and
+
+ align:start position:0%
+with this quadratic exponential in Q and
+ 
+
+ align:start position:0%
+with this quadratic exponential in Q and
+the correlation here is something where
+
+ align:start position:0%
+the correlation here is something where
+ 
+
+ align:start position:0%
+the correlation here is something where
+you have you only lose a polynomial in
+
+ align:start position:0%
+you have you only lose a polynomial in
+ 
+
+ align:start position:0%
+you have you only lose a polynomial in
+the parameters so previously I quoted
+
+ align:start position:0%
+the parameters so previously I quoted
+ 
+
+ align:start position:0%
+the parameters so previously I quoted
+something where you lose something
+
+ align:start position:0%
+something where you lose something
+ 
+
+ align:start position:0%
+something where you lose something
+that's only a constant in Delta and that
+
+ align:start position:0%
+that's only a constant in Delta and that
+ 
+
+ align:start position:0%
+that's only a constant in Delta and that
+is true that is no we believe so it's a
+
+ align:start position:0%
+is true that is no we believe so it's a
+ 
+
+ align:start position:0%
+is true that is no we believe so it's a
+conjecture that you only do so
+
+ align:start position:0%
+conjecture that you only do so
+ 
+
+ align:start position:0%
+conjecture that you only do so
+polynomial in these parameters so this
+
+ align:start position:0%
+polynomial in these parameters so this
+ 
+
+ align:start position:0%
+polynomial in these parameters so this
+type of statement remember now prove a
+
+ align:start position:0%
+type of statement remember now prove a
+ 
+
+ align:start position:0%
+type of statement remember now prove a
+roster something like this came up so
+
+ align:start position:0%
+roster something like this came up so
+ 
+
+ align:start position:0%
+roster something like this came up so
+something like this came up as a crucial
+
+ align:start position:0%
+something like this came up as a crucial
+ 
+
+ align:start position:0%
+something like this came up as a crucial
+step in the proof of roster if you have
+
+ align:start position:0%
+step in the proof of roster if you have
+ 
+
+ align:start position:0%
+step in the proof of roster if you have
+something where you look at counting
+
+ align:start position:0%
+something where you look at counting
+ 
+
+ align:start position:0%
+something where you look at counting
+lemma you exhibit something like this
+
+ align:start position:0%
+lemma you exhibit something like this
+ 
+
+ align:start position:0%
+lemma you exhibit something like this
+then you can exhibit a large Fourier
+
+ align:start position:0%
+then you can exhibit a large Fourier
+ 
+
+ align:start position:0%
+then you can exhibit a large Fourier
+character and in higher worded Fourier
+
+ align:start position:0%
+character and in higher worded Fourier
+ 
+
+ align:start position:0%
+character and in higher worded Fourier
+analysis something like this corresponds
+
+ align:start position:0%
+analysis something like this corresponds
+ 
+
+ align:start position:0%
+analysis something like this corresponds
+to a large four-year care having a large
+
+ align:start position:0%
+to a large four-year care having a large
+ 
+
+ align:start position:0%
+to a large four-year care having a large
+Fourier transform it turns out that all
+
+ align:start position:0%
+Fourier transform it turns out that all
+ 
+
+ align:start position:0%
+Fourier transform it turns out that all
+of these formulations of polynomial
+
+ align:start position:0%
+of these formulations of polynomial
+ 
+
+ align:start position:0%
+of these formulations of polynomial
+Fryman lucha conjectures are equivalent
+
+ align:start position:0%
+Fryman lucha conjectures are equivalent
+ 
+
+ align:start position:0%
+Fryman lucha conjectures are equivalent
+to each other and they're all equivalent
+
+ align:start position:0%
+to each other and they're all equivalent
+ 
+
+ align:start position:0%
+to each other and they're all equivalent
+in a very quantitative sense so upto
+
+ align:start position:0%
+in a very quantitative sense so upto
+ 
+
+ align:start position:0%
+in a very quantitative sense so upto
+polynomial changes depends so
+
+ align:start position:0%
+polynomial changes depends so
+ 
+
+ align:start position:0%
+polynomial changes depends so
+particularly if you can prove some
+
+ align:start position:0%
+particularly if you can prove some
+ 
+
+ align:start position:0%
+particularly if you can prove some
+bounds for some version then that
+
+ align:start position:0%
+bounds for some version then that
+ 
+
+ align:start position:0%
+bounds for some version then that
+automatically leads to balance for the
+
+ align:start position:0%
+automatically leads to balance for the
+ 
+
+ align:start position:0%
+automatically leads to balance for the
+other versions it was proof of
+
+ align:start position:0%
+other versions it was proof of
+ 
+
+ align:start position:0%
+other versions it was proof of
+equivalence is just not trivial but it's
+
+ align:start position:0%
+equivalence is just not trivial but it's
+ 
+
+ align:start position:0%
+equivalence is just not trivial but it's
+also it's not too complicated take some
+
+ align:start position:0%
+also it's not too complicated take some
+ 
+
+ align:start position:0%
+also it's not too complicated take some
+work but it's not too complicated the
+
+ align:start position:0%
+work but it's not too complicated the
+ 
+
+ align:start position:0%
+work but it's not too complicated the
+best bounds for the polynomial Fryman
+
+ align:start position:0%
+best bounds for the polynomial Fryman
+ 
+
+ align:start position:0%
+best bounds for the polynomial Fryman
+ruzic
+
+ align:start position:0%
+ruzic
+ 
+
+ align:start position:0%
+ruzic
+injector and thanks for all of these
+
+ align:start position:0%
+injector and thanks for all of these
+ 
+
+ align:start position:0%
+injector and thanks for all of these
+versions is again due to Tom Sanders and
+
+ align:start position:0%
+versions is again due to Tom Sanders and
+ 
+
+ align:start position:0%
+versions is again due to Tom Sanders and
+he proved a version of PFR with
+
+ align:start position:0%
+he proved a version of PFR with
+ 
+
+ align:start position:0%
+he proved a version of PFR with
+quasi-polynomial balanced with high
+
+ align:start position:0%
+quasi-polynomial balanced with high
+ 
+
+ align:start position:0%
+quasi-polynomial balanced with high
+quality polynomial bounds I mean for
+
+ align:start position:0%
+quality polynomial bounds I mean for
+ 
+
+ align:start position:0%
+quality polynomial bounds I mean for
+instance over here instead of K he
+
+ align:start position:0%
+instance over here instead of K he
+ 
+
+ align:start position:0%
+instance over here instead of K he
+proved it for something which is like e
+
+ align:start position:0%
+proved it for something which is like e
+ 
+
+ align:start position:0%
+proved it for something which is like e
+to the poly log K so like K to the log K
+
+ align:start position:0%
+to the poly log K so like K to the log K
+ 
+
+ align:start position:0%
+to the poly log K so like K to the log K
+but K to the poly knocking so it's
+
+ align:start position:0%
+but K to the poly knocking so it's
+ 
+
+ align:start position:0%
+but K to the poly knocking so it's
+almost polynomial but not quite there
+
+ align:start position:0%
+almost polynomial but not quite there
+ 
+
+ align:start position:0%
+almost polynomial but not quite there
+and it's considered a central open
+
+ align:start position:0%
+and it's considered a central open
+ 
+
+ align:start position:0%
+and it's considered a central open
+problem to better understand the
+
+ align:start position:0%
+problem to better understand the
+ 
+
+ align:start position:0%
+problem to better understand the
+polynomial Fryman Ruza conjecture and we
+
+ align:start position:0%
+polynomial Fryman Ruza conjecture and we
+ 
+
+ align:start position:0%
+polynomial Fryman Ruza conjecture and we
+believe that this is something that
+
+ align:start position:0%
+believe that this is something that
+ 
+
+ align:start position:0%
+believe that this is something that
+could be to a lot of important new tools
+
+ align:start position:0%
+could be to a lot of important new tools
+ 
+
+ align:start position:0%
+could be to a lot of important new tools
+and techniques that are relevant to the
+
+ align:start position:0%
+and techniques that are relevant to the
+ 
+
+ align:start position:0%
+and techniques that are relevant to the
+rest of additive combinatorics
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so question is so we know that that
+
+ align:start position:0%
+okay so question is so we know that that
+ 
+
+ align:start position:0%
+okay so question is so we know that that
+up there has 2 to the K okay so you're
+
+ align:start position:0%
+up there has 2 to the K okay so you're
+ 
+
+ align:start position:0%
+up there has 2 to the K okay so you're
+asking can you use this 2 to the K to
+
+ align:start position:0%
+asking can you use this 2 to the K to
+ 
+
+ align:start position:0%
+asking can you use this 2 to the K to
+get some bound for polynomial before for
+
+ align:start position:0%
+get some bound for polynomial before for
+ 
+
+ align:start position:0%
+get some bound for polynomial before for
+something like this and and the answer
+
+ align:start position:0%
+something like this and and the answer
+ 
+
+ align:start position:0%
+something like this and and the answer
+is yes so you can use that proof to go
+
+ align:start position:0%
+is yes so you can use that proof to go
+ 
+
+ align:start position:0%
+is yes so you can use that proof to go
+through some proofs and get here I don't
+
+ align:start position:0%
+through some proofs and get here I don't
+ 
+
+ align:start position:0%
+through some proofs and get here I don't
+remember how this equivalence goes but
+
+ align:start position:0%
+remember how this equivalence goes but
+ 
+
+ align:start position:0%
+remember how this equivalence goes but
+now remember that the proof of Freeman's
+
+ align:start position:0%
+now remember that the proof of Freeman's
+ 
+
+ align:start position:0%
+now remember that the proof of Freeman's
+theorem for f2 to the N wasn't so hard
+
+ align:start position:0%
+theorem for f2 to the N wasn't so hard
+ 
+
+ align:start position:0%
+theorem for f2 to the N wasn't so hard
+right so we didn't use very many tools
+
+ align:start position:0%
+right so we didn't use very many tools
+ 
+
+ align:start position:0%
+right so we didn't use very many tools
+unfortunately I don't have time to tell
+
+ align:start position:0%
+unfortunately I don't have time to tell
+ 
+
+ align:start position:0%
+unfortunately I don't have time to tell
+you the formulations of polynomial
+
+ align:start position:0%
+you the formulations of polynomial
+ 
+
+ align:start position:0%
+you the formulations of polynomial
+Fryman which a congestion over the
+
+ align:start position:0%
+Fryman which a congestion over the
+ 
+
+ align:start position:0%
+Fryman which a congestion over the
+integers and also over are billion
+
+ align:start position:0%
+integers and also over are billion
+ 
+
+ align:start position:0%
+integers and also over are billion
+arbitrary abelian groups but there are
+
+ align:start position:0%
+arbitrary abelian groups but there are
+ 
+
+ align:start position:0%
+arbitrary abelian groups but there are
+formulations over the integers and and
+
+ align:start position:0%
+formulations over the integers and and
+ 
+
+ align:start position:0%
+formulations over the integers and and
+that's one that people care just as much
+
+ align:start position:0%
+that's one that people care just as much
+ 
+
+ align:start position:0%
+that's one that people care just as much
+about and and there are also different
+
+ align:start position:0%
+about and and there are also different
+ 
+
+ align:start position:0%
+about and and there are also different
+equivalent versions but things are a bit
+
+ align:start position:0%
+equivalent versions but things are a bit
+ 
+
+ align:start position:0%
+equivalent versions but things are a bit
+nicer in the boolean case I'm sorry can
+
+ align:start position:0%
+nicer in the boolean case I'm sorry can
+ 
+
+ align:start position:0%
+nicer in the boolean case I'm sorry can
+you repeat the question
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+well this is me ah so this is what's
+
+ align:start position:0%
+well this is me ah so this is what's
+ 
+
+ align:start position:0%
+well this is me ah so this is what's
+called a coward uniformity norm okay so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+something I encourage the male cop in
+
+ align:start position:0%
+something I encourage the male cop in
+ 
+
+ align:start position:0%
+something I encourage the male cop in
+fact there's an unassigned problem in
+
+ align:start position:0%
+fact there's an unassigned problem in
+ 
+
+ align:start position:0%
+fact there's an unassigned problem in
+problem set that's related to the couch
+
+ align:start position:0%
+problem set that's related to the couch
+ 
+
+ align:start position:0%
+problem set that's related to the couch
+uniformity no one before you - which is
+
+ align:start position:0%
+uniformity no one before you - which is
+ 
+
+ align:start position:0%
+uniformity no one before you - which is
+related for analysis but you three years
+
+ align:start position:0%
+related for analysis but you three years
+ 
+
+ align:start position:0%
+related for analysis but you three years
+we did it - for EPS and quadratic for
+
+ align:start position:0%
+we did it - for EPS and quadratic for
+ 
+
+ align:start position:0%
+we did it - for EPS and quadratic for
+urinalysis
\ No newline at end of file
diff --git a/IggngxY3riU.txt b/IggngxY3riU.txt
new file mode 100644
index 0000000000000000000000000000000000000000..1ace6fe7dd8d6cab3ab021fa06a984ceebd8c52c
--- /dev/null
+++ b/IggngxY3riU.txt
@@ -0,0 +1,483 @@
+align:start position:0%
+ 
+[Music]
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+hi I'm Jessica and today I'm going to be
+
+ align:start position:0%
+hi I'm Jessica and today I'm going to be
+ 
+
+ align:start position:0%
+hi I'm Jessica and today I'm going to be
+talking about a chemical demonstration
+
+ align:start position:0%
+talking about a chemical demonstration
+ 
+
+ align:start position:0%
+talking about a chemical demonstration
+called the Briggs rasher
+
+ align:start position:0%
+called the Briggs rasher
+ 
+
+ align:start position:0%
+called the Briggs rasher
+reaction this reaction was discovered by
+
+ align:start position:0%
+reaction this reaction was discovered by
+ 
+
+ align:start position:0%
+reaction this reaction was discovered by
+two San Francisco area high school
+
+ align:start position:0%
+two San Francisco area high school
+ 
+
+ align:start position:0%
+two San Francisco area high school
+chemistry teachers Briggs and rasher who
+
+ align:start position:0%
+chemistry teachers Briggs and rasher who
+ 
+
+ align:start position:0%
+chemistry teachers Briggs and rasher who
+were working in a lab to come up with a
+
+ align:start position:0%
+were working in a lab to come up with a
+ 
+
+ align:start position:0%
+were working in a lab to come up with a
+visually striking way to demonstrate an
+
+ align:start position:0%
+visually striking way to demonstrate an
+ 
+
+ align:start position:0%
+visually striking way to demonstrate an
+oscillating clock reaction
+
+ align:start position:0%
+oscillating clock reaction
+ 
+
+ align:start position:0%
+oscillating clock reaction
+let's watch mit's Dr John Dolan show us
+
+ align:start position:0%
+let's watch mit's Dr John Dolan show us
+ 
+
+ align:start position:0%
+let's watch mit's Dr John Dolan show us
+the reaction here he is at the Cambridge
+
+ align:start position:0%
+the reaction here he is at the Cambridge
+ 
+
+ align:start position:0%
+the reaction here he is at the Cambridge
+Science Festival okay so what I'm going
+
+ align:start position:0%
+Science Festival okay so what I'm going
+ 
+
+ align:start position:0%
+Science Festival okay so what I'm going
+to do is I'm going to pour three
+
+ align:start position:0%
+to do is I'm going to pour three
+ 
+
+ align:start position:0%
+to do is I'm going to pour three
+colorless Solutions into this
+
+ align:start position:0%
+colorless Solutions into this
+ 
+
+ align:start position:0%
+colorless Solutions into this
+speaker solution number one and I'm
+
+ align:start position:0%
+speaker solution number one and I'm
+ 
+
+ align:start position:0%
+speaker solution number one and I'm
+going to use kitchen chemistry so I'm
+
+ align:start position:0%
+going to use kitchen chemistry so I'm
+ 
+
+ align:start position:0%
+going to use kitchen chemistry so I'm
+using my eye here let me just see okay
+
+ align:start position:0%
+using my eye here let me just see okay
+ 
+
+ align:start position:0%
+using my eye here let me just see okay
+there we are
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+second
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+solution and the third solution
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so what happened Dr Dolan mixed three
+
+ align:start position:0%
+so what happened Dr Dolan mixed three
+ 
+
+ align:start position:0%
+so what happened Dr Dolan mixed three
+clear colorless Solutions together the
+
+ align:start position:0%
+clear colorless Solutions together the
+ 
+
+ align:start position:0%
+clear colorless Solutions together the
+first solution contains potassium iodate
+
+ align:start position:0%
+first solution contains potassium iodate
+ 
+
+ align:start position:0%
+first solution contains potassium iodate
+and sulfuric acid dissolved in water
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the second solution is malonic acid and
+
+ align:start position:0%
+the second solution is malonic acid and
+ 
+
+ align:start position:0%
+the second solution is malonic acid and
+manganese sulfate monohydrate in
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+water and the third is hydrogen peroxide
+
+ align:start position:0%
+water and the third is hydrogen peroxide
+ 
+
+ align:start position:0%
+water and the third is hydrogen peroxide
+in water and when mixed together things
+
+ align:start position:0%
+in water and when mixed together things
+ 
+
+ align:start position:0%
+in water and when mixed together things
+get complicated the overall reaction is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this so iodate hydrogen peroxide malonic
+
+ align:start position:0%
+this so iodate hydrogen peroxide malonic
+ 
+
+ align:start position:0%
+this so iodate hydrogen peroxide malonic
+acid in the presence of sulfuric acid
+
+ align:start position:0%
+acid in the presence of sulfuric acid
+ 
+
+ align:start position:0%
+acid in the presence of sulfuric acid
+reacts to produce this compound oxygen
+
+ align:start position:0%
+reacts to produce this compound oxygen
+ 
+
+ align:start position:0%
+reacts to produce this compound oxygen
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+water but think about the reaction this
+
+ align:start position:0%
+water but think about the reaction this
+ 
+
+ align:start position:0%
+water but think about the reaction this
+way it's equivalent to saying that metal
+
+ align:start position:0%
+way it's equivalent to saying that metal
+ 
+
+ align:start position:0%
+way it's equivalent to saying that metal
+and plastic react to produce a bicycle
+
+ align:start position:0%
+and plastic react to produce a bicycle
+ 
+
+ align:start position:0%
+and plastic react to produce a bicycle
+in reality there are many steps that
+
+ align:start position:0%
+in reality there are many steps that
+ 
+
+ align:start position:0%
+in reality there are many steps that
+occur between those raw materials and
+
+ align:start position:0%
+occur between those raw materials and
+ 
+
+ align:start position:0%
+occur between those raw materials and
+the finished result and the Brigs rasher
+
+ align:start position:0%
+the finished result and the Brigs rasher
+ 
+
+ align:start position:0%
+the finished result and the Brigs rasher
+reaction is similar here are the many
+
+ align:start position:0%
+reaction is similar here are the many
+ 
+
+ align:start position:0%
+reaction is similar here are the many
+subreactions that occur to get from the
+
+ align:start position:0%
+subreactions that occur to get from the
+ 
+
+ align:start position:0%
+subreactions that occur to get from the
+reactants to the products what we see is
+
+ align:start position:0%
+reactants to the products what we see is
+ 
+
+ align:start position:0%
+reactants to the products what we see is
+a cycle from colorless to
+
+ align:start position:0%
+a cycle from colorless to
+ 
+
+ align:start position:0%
+a cycle from colorless to
+Amber to dark
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+blue and as these reactions run the
+
+ align:start position:0%
+blue and as these reactions run the
+ 
+
+ align:start position:0%
+blue and as these reactions run the
+relative amounts of the reactants and
+
+ align:start position:0%
+relative amounts of the reactants and
+ 
+
+ align:start position:0%
+relative amounts of the reactants and
+the products dictate the color of the
+
+ align:start position:0%
+the products dictate the color of the
+ 
+
+ align:start position:0%
+the products dictate the color of the
+solution I2 is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Amber I minus is
+
+ align:start position:0%
+Amber I minus is
+ 
+
+ align:start position:0%
+Amber I minus is
+colorless and I3 minus is Deep Blue when
+
+ align:start position:0%
+colorless and I3 minus is Deep Blue when
+ 
+
+ align:start position:0%
+colorless and I3 minus is Deep Blue when
+it interacts with starch in the
+
+ align:start position:0%
+it interacts with starch in the
+ 
+
+ align:start position:0%
+it interacts with starch in the
+solution triiodide is formed when iodine
+
+ align:start position:0%
+solution triiodide is formed when iodine
+ 
+
+ align:start position:0%
+solution triiodide is formed when iodine
+and IOD died
+
+ align:start position:0%
+and IOD died
+ 
+
+ align:start position:0%
+and IOD died
+interact and this cycle continues until
+
+ align:start position:0%
+interact and this cycle continues until
+ 
+
+ align:start position:0%
+interact and this cycle continues until
+all the reactants are used up hope you
+
+ align:start position:0%
+all the reactants are used up hope you
+ 
+
+ align:start position:0%
+all the reactants are used up hope you
+enjoyed the video and I'll see you next
+
+ align:start position:0%
+enjoyed the video and I'll see you next
+ 
+
+ align:start position:0%
+enjoyed the video and I'll see you next
+time
+
+ align:start position:0%
+time
+ 
+
+ align:start position:0%
+time
+[Music]
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+n
+
+ align:start position:0%
+n
+ 
+
+ align:start position:0%
+n
+[Music]
\ No newline at end of file
diff --git a/IrRgAWI6bmw.txt b/IrRgAWI6bmw.txt
new file mode 100644
index 0000000000000000000000000000000000000000..3bc8b14143b46b8e0e05be47d8301f511e6049e6
--- /dev/null
+++ b/IrRgAWI6bmw.txt
@@ -0,0 +1,1707 @@
+align:start position:0%
+ 
+hi everyone so today I'd like to take a
+
+ align:start position:0%
+hi everyone so today I'd like to take a
+ 
+
+ align:start position:0%
+hi everyone so today I'd like to take a
+look at linear equations linear first
+
+ align:start position:0%
+look at linear equations linear first
+ 
+
+ align:start position:0%
+look at linear equations linear first
+order differential equations and
+
+ align:start position:0%
+order differential equations and
+ 
+
+ align:start position:0%
+order differential equations and
+specifically we're going to look at just
+
+ align:start position:0%
+specifically we're going to look at just
+ 
+
+ align:start position:0%
+specifically we're going to look at just
+exactly what is a linear equation so for
+
+ align:start position:0%
+exactly what is a linear equation so for
+ 
+
+ align:start position:0%
+exactly what is a linear equation so for
+example which of these equations are
+
+ align:start position:0%
+example which of these equations are
+ 
+
+ align:start position:0%
+example which of these equations are
+linear and then second of all we're
+
+ align:start position:0%
+linear and then second of all we're
+ 
+
+ align:start position:0%
+linear and then second of all we're
+going to take a look at
+
+ align:start position:0%
+going to take a look at
+ 
+
+ align:start position:0%
+going to take a look at
+superposition and I uh we ask to
+
+ align:start position:0%
+superposition and I uh we ask to
+ 
+
+ align:start position:0%
+superposition and I uh we ask to
+consider the differential equation Y dot
+
+ align:start position:0%
+consider the differential equation Y dot
+ 
+
+ align:start position:0%
+consider the differential equation Y dot
++ y^2 = some function Q of T and just to
+
+ align:start position:0%
++ y^2 = some function Q of T and just to
+ 
+
+ align:start position:0%
++ y^2 = some function Q of T and just to
+demonstrate that this equation does not
+
+ align:start position:0%
+demonstrate that this equation does not
+ 
+
+ align:start position:0%
+demonstrate that this equation does not
+satisfy the superposition principle so
+
+ align:start position:0%
+satisfy the superposition principle so
+ 
+
+ align:start position:0%
+satisfy the superposition principle so
+I'll let you take a look at this problem
+
+ align:start position:0%
+I'll let you take a look at this problem
+ 
+
+ align:start position:0%
+I'll let you take a look at this problem
+and try and work it out for yourself and
+
+ align:start position:0%
+and try and work it out for yourself and
+ 
+
+ align:start position:0%
+and try and work it out for yourself and
+I'll be back in a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+minute hi everyone welcome back all
+
+ align:start position:0%
+minute hi everyone welcome back all
+ 
+
+ align:start position:0%
+minute hi everyone welcome back all
+right so we're asked to figure out which
+
+ align:start position:0%
+right so we're asked to figure out which
+ 
+
+ align:start position:0%
+right so we're asked to figure out which
+of these equations are linear so just a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+recap what does it mean for an equation
+
+ align:start position:0%
+recap what does it mean for an equation
+ 
+
+ align:start position:0%
+recap what does it mean for an equation
+to be linear what does it mean for a
+
+ align:start position:0%
+to be linear what does it mean for a
+ 
+
+ align:start position:0%
+to be linear what does it mean for a
+first order equation to be
+
+ align:start position:0%
+first order equation to be
+ 
+
+ align:start position:0%
+first order equation to be
+linear well it means that we can write
+
+ align:start position:0%
+linear well it means that we can write
+ 
+
+ align:start position:0%
+linear well it means that we can write
+it in the general
+
+ align:start position:0%
+it in the general
+ 
+
+ align:start position:0%
+it in the general
+form so if it if it's a function of X
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+dydx plus some general function of X and
+
+ align:start position:0%
+dydx plus some general function of X and
+ 
+
+ align:start position:0%
+dydx plus some general function of X and
+this could be
+
+ align:start position:0%
+this could be
+ 
+
+ align:start position:0%
+this could be
+anything but the point is that it's
+
+ align:start position:0%
+anything but the point is that it's
+ 
+
+ align:start position:0%
+anything but the point is that it's
+multiplied just by y
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and then it can equal some arbitrary
+
+ align:start position:0%
+and then it can equal some arbitrary
+ 
+
+ align:start position:0%
+and then it can equal some arbitrary
+function Q ofx on the right hand side so
+
+ align:start position:0%
+function Q ofx on the right hand side so
+ 
+
+ align:start position:0%
+function Q ofx on the right hand side so
+every first order linear equation can be
+
+ align:start position:0%
+every first order linear equation can be
+ 
+
+ align:start position:0%
+every first order linear equation can be
+Rewritten in this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+form so let's tackle part A all right y
+
+ align:start position:0%
+form so let's tackle part A all right y
+ 
+
+ align:start position:0%
+form so let's tackle part A all right y
+dot plus KY equals Zer or Y dot equals
+
+ align:start position:0%
+dot plus KY equals Zer or Y dot equals
+ 
+
+ align:start position:0%
+dot plus KY equals Zer or Y dot equals
+KY we can just rewrite it
+
+ align:start position:0%
+KY we can just rewrite it
+ 
+
+ align:start position:0%
+KY we can just rewrite it
+as y do equals negative
+
+ align:start position:0%
+as y do equals negative
+ 
+
+ align:start position:0%
+as y do equals negative
+KY note that just some constant k is a
+
+ align:start position:0%
+KY note that just some constant k is a
+ 
+
+ align:start position:0%
+KY note that just some constant k is a
+function of time it's a constant
+
+ align:start position:0%
+function of time it's a constant
+ 
+
+ align:start position:0%
+function of time it's a constant
+function of time but it can just be
+
+ align:start position:0%
+function of time but it can just be
+ 
+
+ align:start position:0%
+function of time but it can just be
+thought of as a function of Time same
+
+ align:start position:0%
+thought of as a function of Time same
+ 
+
+ align:start position:0%
+thought of as a function of Time same
+with the right hand side it's zero and
+
+ align:start position:0%
+with the right hand side it's zero and
+ 
+
+ align:start position:0%
+with the right hand side it's zero and
+so this equation has the same form as
+
+ align:start position:0%
+so this equation has the same form as
+ 
+
+ align:start position:0%
+so this equation has the same form as
+our general uh first order linear
+
+ align:start position:0%
+our general uh first order linear
+ 
+
+ align:start position:0%
+our general uh first order linear
+equation so this is a linear
+
+ align:start position:0%
+equation so this is a linear
+ 
+
+ align:start position:0%
+equation so this is a linear
+equation let's take a look at question
+
+ align:start position:0%
+equation let's take a look at question
+ 
+
+ align:start position:0%
+equation let's take a look at question
+two part two we have y
+
+ align:start position:0%
+two part two we have y
+ 
+
+ align:start position:0%
+two part two we have y
+dot + y^2 T I'll bring the Y to the
+
+ align:start position:0%
+dot + y^2 T I'll bring the Y to the
+ 
+
+ align:start position:0%
+dot + y^2 T I'll bring the Y to the
+right or the left hand
+
+ align:start position:0%
+right or the left hand
+ 
+
+ align:start position:0%
+right or the left hand
+side if we do that we get this
+
+ align:start position:0%
+side if we do that we get this
+ 
+
+ align:start position:0%
+side if we do that we get this
+and just by comparing this to our
+
+ align:start position:0%
+and just by comparing this to our
+ 
+
+ align:start position:0%
+and just by comparing this to our
+generic first order linear OD we note
+
+ align:start position:0%
+generic first order linear OD we note
+ 
+
+ align:start position:0%
+generic first order linear OD we note
+that it's not of this form so
+
+ align:start position:0%
+that it's not of this form so
+ 
+
+ align:start position:0%
+that it's not of this form so
+specifically this is the term this is
+
+ align:start position:0%
+specifically this is the term this is
+ 
+
+ align:start position:0%
+specifically this is the term this is
+the bad term in question you see that
+
+ align:start position:0%
+the bad term in question you see that
+ 
+
+ align:start position:0%
+the bad term in question you see that
+it's y^2 *
+
+ align:start position:0%
+it's y^2 *
+ 
+
+ align:start position:0%
+it's y^2 *
+T notice how we can't we're not allowed
+
+ align:start position:0%
+T notice how we can't we're not allowed
+ 
+
+ align:start position:0%
+T notice how we can't we're not allowed
+to have any term that's y^
+
+ align:start position:0%
+to have any term that's y^
+ 
+
+ align:start position:0%
+to have any term that's y^
+s uh in our first order linear equation
+
+ align:start position:0%
+s uh in our first order linear equation
+ 
+
+ align:start position:0%
+s uh in our first order linear equation
+now I will say this just as an
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+aside this equation is also known as a
+
+ align:start position:0%
+aside this equation is also known as a
+ 
+
+ align:start position:0%
+aside this equation is also known as a
+beri equation and as an aside if you
+
+ align:start position:0%
+beri equation and as an aside if you
+ 
+
+ align:start position:0%
+beri equation and as an aside if you
+were to make a substitution u = 1 /
+
+ align:start position:0%
+were to make a substitution u = 1 /
+ 
+
+ align:start position:0%
+were to make a substitution u = 1 /
+Y and rewrote this equation in terms of
+
+ align:start position:0%
+Y and rewrote this equation in terms of
+ 
+
+ align:start position:0%
+Y and rewrote this equation in terms of
+U as the independent variable you'd find
+
+ align:start position:0%
+U as the independent variable you'd find
+ 
+
+ align:start position:0%
+U as the independent variable you'd find
+out that this equation would be linear
+
+ align:start position:0%
+out that this equation would be linear
+ 
+
+ align:start position:0%
+out that this equation would be linear
+in terms of U but as it's written now in
+
+ align:start position:0%
+in terms of U but as it's written now in
+ 
+
+ align:start position:0%
+in terms of U but as it's written now in
+terms of Y it's not
+
+ align:start position:0%
+terms of Y it's not
+ 
+
+ align:start position:0%
+terms of Y it's not
+linear so this is kind of an interesting
+
+ align:start position:0%
+linear so this is kind of an interesting
+ 
+
+ align:start position:0%
+linear so this is kind of an interesting
+point that sometimes we can get lucky
+
+ align:start position:0%
+point that sometimes we can get lucky
+ 
+
+ align:start position:0%
+point that sometimes we can get lucky
+and do a nonlinear transformation and
+
+ align:start position:0%
+and do a nonlinear transformation and
+ 
+
+ align:start position:0%
+and do a nonlinear transformation and
+convert a nonlinear equation into a
+
+ align:start position:0%
+convert a nonlinear equation into a
+ 
+
+ align:start position:0%
+convert a nonlinear equation into a
+linear one
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so for part three we
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+have y prime plus cosx
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Y equals X
+
+ align:start position:0%
+Y equals X
+ 
+
+ align:start position:0%
+Y equals X
+cubed so again we see that this is a
+
+ align:start position:0%
+cubed so again we see that this is a
+ 
+
+ align:start position:0%
+cubed so again we see that this is a
+linear equation because we can
+
+ align:start position:0%
+linear equation because we can
+ 
+
+ align:start position:0%
+linear equation because we can
+identify P of X with cosine
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+x q of X with x
+
+ align:start position:0%
+x q of X with x
+ 
+
+ align:start position:0%
+x q of X with x
+cubed so this equation has the general
+
+ align:start position:0%
+cubed so this equation has the general
+ 
+
+ align:start position:0%
+cubed so this equation has the general
+form of a linear
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+OD for part
+
+ align:start position:0%
+OD for part
+ 
+
+ align:start position:0%
+OD for part
+four well if we take a look at it right
+
+ align:start position:0%
+four well if we take a look at it right
+ 
+
+ align:start position:0%
+four well if we take a look at it right
+away y dot ided Y is equal to T
+
+ align:start position:0%
+away y dot ided Y is equal to T
+ 
+
+ align:start position:0%
+away y dot ided Y is equal to T
+^2 it doesn't appear to be linear but of
+
+ align:start position:0%
+^2 it doesn't appear to be linear but of
+ 
+
+ align:start position:0%
+^2 it doesn't appear to be linear but of
+course we can multiply through by Y and
+
+ align:start position:0%
+course we can multiply through by Y and
+ 
+
+ align:start position:0%
+course we can multiply through by Y and
+rewrite
+
+ align:start position:0%
+rewrite
+ 
+
+ align:start position:0%
+rewrite
+things and of course this equation is
+
+ align:start position:0%
+things and of course this equation is
+ 
+
+ align:start position:0%
+things and of course this equation is
+equivalent to y dotus t^2 y y equal
+
+ align:start position:0%
+equivalent to y dotus t^2 y y equal
+ 
+
+ align:start position:0%
+equivalent to y dotus t^2 y y equal
+0 uh which again is linear
+
+ align:start position:0%
+0 uh which again is linear
+ 
+
+ align:start position:0%
+0 uh which again is linear
+because P of
+
+ align:start position:0%
+because P of
+ 
+
+ align:start position:0%
+because P of
+T can be identified with - t ^2 and Q of
+
+ align:start position:0%
+T can be identified with - t ^2 and Q of
+ 
+
+ align:start position:0%
+T can be identified with - t ^2 and Q of
+T can be identified with
+
+ align:start position:0%
+T can be identified with
+ 
+
+ align:start position:0%
+T can be identified with
+zero and then
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+lastly for part five we
+
+ align:start position:0%
+lastly for part five we
+ 
+
+ align:start position:0%
+lastly for part five we
+have x^2 y y
+
+ align:start position:0%
+have x^2 y y
+ 
+
+ align:start position:0%
+have x^2 y y
+Prime + 4x
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+equals X
+
+ align:start position:0%
+equals X
+ 
+
+ align:start position:0%
+equals X
+cubed and again if we were to try to
+
+ align:start position:0%
+cubed and again if we were to try to
+ 
+
+ align:start position:0%
+cubed and again if we were to try to
+write it in the general form of a linear
+
+ align:start position:0%
+write it in the general form of a linear
+ 
+
+ align:start position:0%
+write it in the general form of a linear
+OD which we have
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+here it would look
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+like 4X / x^2
+
+ align:start position:0%
+like 4X / x^2
+ 
+
+ align:start position:0%
+like 4X / x^2
+y minus X Cub / x^2
+
+ align:start position:0%
+y minus X Cub / x^2
+ 
+
+ align:start position:0%
+y minus X Cub / x^2
+y equals z and because there's a y on
+
+ align:start position:0%
+y equals z and because there's a y on
+ 
+
+ align:start position:0%
+y equals z and because there's a y on
+the denominator here this equation
+
+ align:start position:0%
+the denominator here this equation
+ 
+
+ align:start position:0%
+the denominator here this equation
+doesn't have the general form of a first
+
+ align:start position:0%
+doesn't have the general form of a first
+ 
+
+ align:start position:0%
+doesn't have the general form of a first
+order linear
+
+ align:start position:0%
+order linear
+ 
+
+ align:start position:0%
+order linear
+equation now again uh I I note that if
+
+ align:start position:0%
+equation now again uh I I note that if
+ 
+
+ align:start position:0%
+equation now again uh I I note that if
+you were to make a
+
+ align:start position:0%
+you were to make a
+ 
+
+ align:start position:0%
+you were to make a
+substitution U equal
+
+ align:start position:0%
+substitution U equal
+ 
+
+ align:start position:0%
+substitution U equal
+y^2 that substitution would make this
+
+ align:start position:0%
+y^2 that substitution would make this
+ 
+
+ align:start position:0%
+y^2 that substitution would make this
+equation
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+linear okay so this concludes part a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so for Part B we're given a differential
+
+ align:start position:0%
+so for Part B we're given a differential
+ 
+
+ align:start position:0%
+so for Part B we're given a differential
+equation Y
+
+ align:start position:0%
+equation Y
+ 
+
+ align:start position:0%
+equation Y
+dot plus
+
+ align:start position:0%
+dot plus
+ 
+
+ align:start position:0%
+dot plus
+y^2 is equal to Q of
+
+ align:start position:0%
+y^2 is equal to Q of
+ 
+
+ align:start position:0%
+y^2 is equal to Q of
+T and we want to show that this uh this
+
+ align:start position:0%
+T and we want to show that this uh this
+ 
+
+ align:start position:0%
+T and we want to show that this uh this
+equation doesn't satisfy the
+
+ align:start position:0%
+equation doesn't satisfy the
+ 
+
+ align:start position:0%
+equation doesn't satisfy the
+superposition
+
+ align:start position:0%
+superposition
+ 
+
+ align:start position:0%
+superposition
+principle now you might note that this
+
+ align:start position:0%
+principle now you might note that this
+ 
+
+ align:start position:0%
+principle now you might note that this
+equation is not
+
+ align:start position:0%
+equation is not
+ 
+
+ align:start position:0%
+equation is not
+linear so and uh second of all we know
+
+ align:start position:0%
+linear so and uh second of all we know
+ 
+
+ align:start position:0%
+linear so and uh second of all we know
+that linear equations satisfy the
+
+ align:start position:0%
+that linear equations satisfy the
+ 
+
+ align:start position:0%
+that linear equations satisfy the
+superposition
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+principle so we're we need to exploit
+
+ align:start position:0%
+principle so we're we need to exploit
+ 
+
+ align:start position:0%
+principle so we're we need to exploit
+the fact that it's a nonlinear equation
+
+ align:start position:0%
+the fact that it's a nonlinear equation
+ 
+
+ align:start position:0%
+the fact that it's a nonlinear equation
+to make it fail uh the superposition
+
+ align:start position:0%
+to make it fail uh the superposition
+ 
+
+ align:start position:0%
+to make it fail uh the superposition
+principle and just as an example what we
+
+ align:start position:0%
+principle and just as an example what we
+ 
+
+ align:start position:0%
+principle and just as an example what we
+can do is I can just pick a couple right
+
+ align:start position:0%
+can do is I can just pick a couple right
+ 
+
+ align:start position:0%
+can do is I can just pick a couple right
+hand sides Q uh as examples of uh this
+
+ align:start position:0%
+hand sides Q uh as examples of uh this
+ 
+
+ align:start position:0%
+hand sides Q uh as examples of uh this
+OD so we can imagine we have a solution
+
+ align:start position:0%
+OD so we can imagine we have a solution
+ 
+
+ align:start position:0%
+OD so we can imagine we have a solution
+y1 which solves the
+
+ align:start position:0%
+y1 which solves the
+ 
+
+ align:start position:0%
+y1 which solves the
+OD y1 dot +
+
+ align:start position:0%
+OD y1 dot +
+ 
+
+ align:start position:0%
+OD y1 dot +
+y12 equals I'm just going to say one on
+
+ align:start position:0%
+y12 equals I'm just going to say one on
+ 
+
+ align:start position:0%
+y12 equals I'm just going to say one on
+the right hand side
+
+ align:start position:0%
+the right hand side
+ 
+
+ align:start position:0%
+the right hand side
+and I can also take another function
+
+ align:start position:0%
+and I can also take another function
+ 
+
+ align:start position:0%
+and I can also take another function
+Y2 which say satisfies this differential
+
+ align:start position:0%
+Y2 which say satisfies this differential
+ 
+
+ align:start position:0%
+Y2 which say satisfies this differential
+equation say t so all I've done is I've
+
+ align:start position:0%
+equation say t so all I've done is I've
+ 
+
+ align:start position:0%
+equation say t so all I've done is I've
+just picked one q1 on the right hand
+
+ align:start position:0%
+just picked one q1 on the right hand
+ 
+
+ align:start position:0%
+just picked one q1 on the right hand
+side and another function Q2 and I
+
+ align:start position:0%
+side and another function Q2 and I
+ 
+
+ align:start position:0%
+side and another function Q2 and I
+imagine that I have a solution y1 which
+
+ align:start position:0%
+imagine that I have a solution y1 which
+ 
+
+ align:start position:0%
+imagine that I have a solution y1 which
+satisfies this differential equation and
+
+ align:start position:0%
+satisfies this differential equation and
+ 
+
+ align:start position:0%
+satisfies this differential equation and
+Y2 which satisfies this differential
+
+ align:start position:0%
+Y2 which satisfies this differential
+ 
+
+ align:start position:0%
+Y2 which satisfies this differential
+equation so what does the superposition
+
+ align:start position:0%
+equation so what does the superposition
+ 
+
+ align:start position:0%
+equation so what does the superposition
+principle
+
+ align:start position:0%
+principle
+ 
+
+ align:start position:0%
+principle
+say well super
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+position
+
+ align:start position:0%
+position
+ 
+
+ align:start position:0%
+position
+says that if y1 solves this equation and
+
+ align:start position:0%
+says that if y1 solves this equation and
+ 
+
+ align:start position:0%
+says that if y1 solves this equation and
+Y2 solves this equation then the
+
+ align:start position:0%
+Y2 solves this equation then the
+ 
+
+ align:start position:0%
+Y2 solves this equation then the
+function
+
+ align:start position:0%
+function
+ 
+
+ align:start position:0%
+function
+yal
+
+ align:start position:0%
+yal
+ 
+
+ align:start position:0%
+yal
+y1 + Y
+
+ align:start position:0%
+y1 + Y
+ 
+
+ align:start position:0%
+y1 + Y
+2 must solve the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+equation Y dot + y^ 2 equals the sum of
+
+ align:start position:0%
+equation Y dot + y^ 2 equals the sum of
+ 
+
+ align:start position:0%
+equation Y dot + y^ 2 equals the sum of
+the right hand side 1 plus
+
+ align:start position:0%
+the right hand side 1 plus
+ 
+
+ align:start position:0%
+the right hand side 1 plus
+T so if we try and substitute in y1 + Y2
+
+ align:start position:0%
+T so if we try and substitute in y1 + Y2
+ 
+
+ align:start position:0%
+T so if we try and substitute in y1 + Y2
+into this equation we're going to come
+
+ align:start position:0%
+into this equation we're going to come
+ 
+
+ align:start position:0%
+into this equation we're going to come
+to a contradiction so let's do that now
+
+ align:start position:0%
+to a contradiction so let's do that now
+ 
+
+ align:start position:0%
+to a contradiction so let's do that now
+so we take d by
+
+ align:start position:0%
+so we take d by
+ 
+
+ align:start position:0%
+so we take d by
+DT of y1 + Y
+
+ align:start position:0%
+DT of y1 + Y
+ 
+
+ align:start position:0%
+DT of y1 + Y
+2 and I'm going to add it to y1 + Y 2
+
+ align:start position:0%
+2 and I'm going to add it to y1 + Y 2
+ 
+
+ align:start position:0%
+2 and I'm going to add it to y1 + Y 2
+quantity
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+squared
+
+ align:start position:0%
+squared
+ 
+
+ align:start position:0%
+squared
+okay and now what I can do is I can just
+
+ align:start position:0%
+okay and now what I can do is I can just
+ 
+
+ align:start position:0%
+okay and now what I can do is I can just
+simplify this so I get y1 dot plus Y2
+
+ align:start position:0%
+simplify this so I get y1 dot plus Y2
+ 
+
+ align:start position:0%
+simplify this so I get y1 dot plus Y2
+Dot and I can expand out this
+
+ align:start position:0%
+Dot and I can expand out this
+ 
+
+ align:start position:0%
+Dot and I can expand out this
+Square so I get y1 2 + Y 2^
+
+ align:start position:0%
+Square so I get y1 2 + Y 2^
+ 
+
+ align:start position:0%
+Square so I get y1 2 + Y 2^
+2 + 2 y1 y
+
+ align:start position:0%
+2 + 2 y1 y
+ 
+
+ align:start position:0%
+2 + 2 y1 y
+2 and now what I'm going to do is I'm
+
+ align:start position:0%
+2 and now what I'm going to do is I'm
+ 
+
+ align:start position:0%
+2 and now what I'm going to do is I'm
+going to combine the term
+
+ align:start position:0%
+going to combine the term
+ 
+
+ align:start position:0%
+going to combine the term
+y1 with
+
+ align:start position:0%
+y1 with
+ 
+
+ align:start position:0%
+y1 with
+y12 and by
+
+ align:start position:0%
+y12 and by
+ 
+
+ align:start position:0%
+y12 and by
+construction y1 do + y12 is equal to 1
+
+ align:start position:0%
+construction y1 do + y12 is equal to 1
+ 
+
+ align:start position:0%
+construction y1 do + y12 is equal to 1
+because I assume that it s satisfied
+
+ align:start position:0%
+because I assume that it s satisfied
+ 
+
+ align:start position:0%
+because I assume that it s satisfied
+this differential
+
+ align:start position:0%
+this differential
+ 
+
+ align:start position:0%
+this differential
+equation and then in addition by
+
+ align:start position:0%
+equation and then in addition by
+ 
+
+ align:start position:0%
+equation and then in addition by
+construction Y2 dot + Y 2^ 2
+
+ align:start position:0%
+construction Y2 dot + Y 2^ 2
+ 
+
+ align:start position:0%
+construction Y2 dot + Y 2^ 2
+satisfies uh the right hand side of the
+
+ align:start position:0%
+satisfies uh the right hand side of the
+ 
+
+ align:start position:0%
+satisfies uh the right hand side of the
+second equation with
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+T so I get 1+
+
+ align:start position:0%
+T so I get 1+
+ 
+
+ align:start position:0%
+T so I get 1+
+T but I'm left over with this other
+
+ align:start position:0%
+T but I'm left over with this other
+ 
+
+ align:start position:0%
+T but I'm left over with this other
+piece 2 y1 Y
+
+ align:start position:0%
+piece 2 y1 Y
+ 
+
+ align:start position:0%
+piece 2 y1 Y
+2 okay so in general if I take a
+
+ align:start position:0%
+2 okay so in general if I take a
+ 
+
+ align:start position:0%
+2 okay so in general if I take a
+function which solves this differential
+
+ align:start position:0%
+function which solves this differential
+ 
+
+ align:start position:0%
+function which solves this differential
+equation and another function which
+
+ align:start position:0%
+equation and another function which
+ 
+
+ align:start position:0%
+equation and another function which
+solves this differential equation and I
+
+ align:start position:0%
+solves this differential equation and I
+ 
+
+ align:start position:0%
+solves this differential equation and I
+add them together and plug it into the
+
+ align:start position:0%
+add them together and plug it into the
+ 
+
+ align:start position:0%
+add them together and plug it into the
+left hand side of this differential
+
+ align:start position:0%
+left hand side of this differential
+ 
+
+ align:start position:0%
+left hand side of this differential
+equation I get something which is 1+ t
+
+ align:start position:0%
+equation I get something which is 1+ t
+ 
+
+ align:start position:0%
+equation I get something which is 1+ t
+plus some other
+
+ align:start position:0%
+plus some other
+ 
+
+ align:start position:0%
+plus some other
+stuff and if it did satisfy the
+
+ align:start position:0%
+stuff and if it did satisfy the
+ 
+
+ align:start position:0%
+stuff and if it did satisfy the
+principle of
+
+ align:start position:0%
+principle of
+ 
+
+ align:start position:0%
+principle of
+superposition it must
+
+ align:start position:0%
+superposition it must
+ 
+
+ align:start position:0%
+superposition it must
+satisfy it must equal 1 plus
+
+ align:start position:0%
+satisfy it must equal 1 plus
+ 
+
+ align:start position:0%
+satisfy it must equal 1 plus
+T so we arrive at a contradiction
+
+ align:start position:0%
+T so we arrive at a contradiction
+ 
+
+ align:start position:0%
+T so we arrive at a contradiction
+because it doesn't equal 1+ T in fact it
+
+ align:start position:0%
+because it doesn't equal 1+ T in fact it
+ 
+
+ align:start position:0%
+because it doesn't equal 1+ T in fact it
+fails to equal 1 plus T by this term 2
+
+ align:start position:0%
+fails to equal 1 plus T by this term 2
+ 
+
+ align:start position:0%
+fails to equal 1 plus T by this term 2
+y1 Y2 and this term comes directly from
+
+ align:start position:0%
+y1 Y2 and this term comes directly from
+ 
+
+ align:start position:0%
+y1 Y2 and this term comes directly from
+the fact that we had a nonlinearity in
+
+ align:start position:0%
+the fact that we had a nonlinearity in
+ 
+
+ align:start position:0%
+the fact that we had a nonlinearity in
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+equation so this is just one uh
+
+ align:start position:0%
+equation so this is just one uh
+ 
+
+ align:start position:0%
+equation so this is just one uh
+illustration of the fact that a
+
+ align:start position:0%
+illustration of the fact that a
+ 
+
+ align:start position:0%
+illustration of the fact that a
+nonlinear equation doesn't necessarily
+
+ align:start position:0%
+nonlinear equation doesn't necessarily
+ 
+
+ align:start position:0%
+nonlinear equation doesn't necessarily
+satisfy the super superposition
+
+ align:start position:0%
+satisfy the super superposition
+ 
+
+ align:start position:0%
+satisfy the super superposition
+principle whereas every linear equation
+
+ align:start position:0%
+principle whereas every linear equation
+ 
+
+ align:start position:0%
+principle whereas every linear equation
+satisfies a superposition principle this
+
+ align:start position:0%
+satisfies a superposition principle this
+ 
+
+ align:start position:0%
+satisfies a superposition principle this
+is is one reason we love linear
+
+ align:start position:0%
+is is one reason we love linear
+ 
+
+ align:start position:0%
+is is one reason we love linear
+equations and we study them
+
+ align:start position:0%
+equations and we study them
+ 
+
+ align:start position:0%
+equations and we study them
+extensively okay so uh I'd just like to
+
+ align:start position:0%
+extensively okay so uh I'd just like to
+ 
+
+ align:start position:0%
+extensively okay so uh I'd just like to
+conclude here and I'll uh see you next
+
+ align:start position:0%
+conclude here and I'll uh see you next
+ 
+
+ align:start position:0%
+conclude here and I'll uh see you next
+time
\ No newline at end of file
diff --git a/IwF_N2IDB48.txt b/IwF_N2IDB48.txt
new file mode 100644
index 0000000000000000000000000000000000000000..0cfff68ab9c1904b2ef2ef8f064c5949b4bbe77c
--- /dev/null
+++ b/IwF_N2IDB48.txt
@@ -0,0 +1,8235 @@
+align:start position:0%
+ 
+the following content is provided under
+
+ align:start position:0%
+the following content is provided under
+ 
+
+ align:start position:0%
+the following content is provided under
+a Creative Commons license your support
+
+ align:start position:0%
+a Creative Commons license your support
+ 
+
+ align:start position:0%
+a Creative Commons license your support
+will help MIT open courseware continue
+
+ align:start position:0%
+will help MIT open courseware continue
+ 
+
+ align:start position:0%
+will help MIT open courseware continue
+to offer highquality educational
+
+ align:start position:0%
+to offer highquality educational
+ 
+
+ align:start position:0%
+to offer highquality educational
+resources for free to make a donation or
+
+ align:start position:0%
+resources for free to make a donation or
+ 
+
+ align:start position:0%
+resources for free to make a donation or
+to view additional materials from
+
+ align:start position:0%
+to view additional materials from
+ 
+
+ align:start position:0%
+to view additional materials from
+hundreds of MIT courses visit MIT open
+
+ align:start position:0%
+hundreds of MIT courses visit MIT open
+ 
+
+ align:start position:0%
+hundreds of MIT courses visit MIT open
+courseware at
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+ocw.mit.edu uh one announcement there'll
+
+ align:start position:0%
+ocw.mit.edu uh one announcement there'll
+ 
+
+ align:start position:0%
+ocw.mit.edu uh one announcement there'll
+be the uh uh quiz 9 weekly quiz tomorrow
+
+ align:start position:0%
+be the uh uh quiz 9 weekly quiz tomorrow
+ 
+
+ align:start position:0%
+be the uh uh quiz 9 weekly quiz tomorrow
+based on the content of homework 9 which
+
+ align:start position:0%
+based on the content of homework 9 which
+ 
+
+ align:start position:0%
+based on the content of homework 9 which
+is uh um
+
+ align:start position:0%
+is uh um
+ 
+
+ align:start position:0%
+is uh um
+I don't remember what it is but you know
+
+ align:start position:0%
+I don't remember what it is but you know
+ 
+
+ align:start position:0%
+I don't remember what it is but you know
+what it
+
+ align:start position:0%
+what it
+ 
+
+ align:start position:0%
+what it
+is I made it up it's I'm already
+
+ align:start position:0%
+is I made it up it's I'm already
+ 
+
+ align:start position:0%
+is I made it up it's I'm already
+thinking about the next the next
+
+ align:start position:0%
+thinking about the next the next
+ 
+
+ align:start position:0%
+thinking about the next the next
+glorious event
+
+ align:start position:0%
+glorious event
+ 
+
+ align:start position:0%
+glorious event
+so oh there's I now remember there's
+
+ align:start position:0%
+so oh there's I now remember there's
+ 
+
+ align:start position:0%
+so oh there's I now remember there's
+chemical
+
+ align:start position:0%
+chemical
+ 
+
+ align:start position:0%
+chemical
+kinetics and glasses that's right
+
+ align:start position:0%
+kinetics and glasses that's right
+ 
+
+ align:start position:0%
+kinetics and glasses that's right
+chemical kinetics and amorphous solids
+
+ align:start position:0%
+chemical kinetics and amorphous solids
+ 
+
+ align:start position:0%
+chemical kinetics and amorphous solids
+that's right good okay um last day we
+
+ align:start position:0%
+that's right good okay um last day we
+ 
+
+ align:start position:0%
+that's right good okay um last day we
+started talking about diffusion which is
+
+ align:start position:0%
+started talking about diffusion which is
+ 
+
+ align:start position:0%
+started talking about diffusion which is
+a solid state mass transport by random
+
+ align:start position:0%
+a solid state mass transport by random
+ 
+
+ align:start position:0%
+a solid state mass transport by random
+Aton I motion uh and we were drawn to
+
+ align:start position:0%
+Aton I motion uh and we were drawn to
+ 
+
+ align:start position:0%
+Aton I motion uh and we were drawn to
+the paper that's up on the display which
+
+ align:start position:0%
+the paper that's up on the display which
+ 
+
+ align:start position:0%
+the paper that's up on the display which
+was published in 1855 by uh Adolf Fick
+
+ align:start position:0%
+was published in 1855 by uh Adolf Fick
+ 
+
+ align:start position:0%
+was published in 1855 by uh Adolf Fick
+which uh gave us the uh law that bears
+
+ align:start position:0%
+which uh gave us the uh law that bears
+ 
+
+ align:start position:0%
+which uh gave us the uh law that bears
+his name uh describing how matter
+
+ align:start position:0%
+his name uh describing how matter
+ 
+
+ align:start position:0%
+his name uh describing how matter
+diffuses through matter uh but fi was uh
+
+ align:start position:0%
+diffuses through matter uh but fi was uh
+ 
+
+ align:start position:0%
+diffuses through matter uh but fi was uh
+a very talented individual and I want to
+
+ align:start position:0%
+a very talented individual and I want to
+ 
+
+ align:start position:0%
+a very talented individual and I want to
+draw attention to something else um in
+
+ align:start position:0%
+draw attention to something else um in
+ 
+
+ align:start position:0%
+draw attention to something else um in
+1870 he described the way of U remember
+
+ align:start position:0%
+1870 he described the way of U remember
+ 
+
+ align:start position:0%
+1870 he described the way of U remember
+he was a phys physiologist he actually
+
+ align:start position:0%
+he was a phys physiologist he actually
+ 
+
+ align:start position:0%
+he was a phys physiologist he actually
+did some work in medicine as well and uh
+
+ align:start position:0%
+did some work in medicine as well and uh
+ 
+
+ align:start position:0%
+did some work in medicine as well and uh
+he described what uh survives to this
+
+ align:start position:0%
+he described what uh survives to this
+ 
+
+ align:start position:0%
+he described what uh survives to this
+day as the Fick principle for
+
+ align:start position:0%
+day as the Fick principle for
+ 
+
+ align:start position:0%
+day as the Fick principle for
+determining uh cardiac output and
+
+ align:start position:0%
+determining uh cardiac output and
+ 
+
+ align:start position:0%
+determining uh cardiac output and
+basically equates the amount of uptake
+
+ align:start position:0%
+basically equates the amount of uptake
+ 
+
+ align:start position:0%
+basically equates the amount of uptake
+of oxygen by the lungs with the amount
+
+ align:start position:0%
+of oxygen by the lungs with the amount
+ 
+
+ align:start position:0%
+of oxygen by the lungs with the amount
+that should be distributed uh in the
+
+ align:start position:0%
+that should be distributed uh in the
+ 
+
+ align:start position:0%
+that should be distributed uh in the
+blood but you have to take arterial
+
+ align:start position:0%
+blood but you have to take arterial
+ 
+
+ align:start position:0%
+blood but you have to take arterial
+oxygen pressure minus uh venal oxygen
+
+ align:start position:0%
+oxygen pressure minus uh venal oxygen
+ 
+
+ align:start position:0%
+oxygen pressure minus uh venal oxygen
+pressure to get the efficiency of the
+
+ align:start position:0%
+pressure to get the efficiency of the
+ 
+
+ align:start position:0%
+pressure to get the efficiency of the
+heart and so uh found this little uh uh
+
+ align:start position:0%
+heart and so uh found this little uh uh
+ 
+
+ align:start position:0%
+heart and so uh found this little uh uh
+Cartoon off the web that just uh briefly
+
+ align:start position:0%
+Cartoon off the web that just uh briefly
+ 
+
+ align:start position:0%
+Cartoon off the web that just uh briefly
+uh encapsulates the notion of the FI
+
+ align:start position:0%
+uh encapsulates the notion of the FI
+ 
+
+ align:start position:0%
+uh encapsulates the notion of the FI
+principle for uh measuring a cardiac
+
+ align:start position:0%
+principle for uh measuring a cardiac
+ 
+
+ align:start position:0%
+principle for uh measuring a cardiac
+output his nephew by the way uh who was
+
+ align:start position:0%
+output his nephew by the way uh who was
+ 
+
+ align:start position:0%
+output his nephew by the way uh who was
+orphaned as a young child came also has
+
+ align:start position:0%
+orphaned as a young child came also has
+ 
+
+ align:start position:0%
+orphaned as a young child came also has
+the name Adolf Fick and the young Adolf
+
+ align:start position:0%
+the name Adolf Fick and the young Adolf
+ 
+
+ align:start position:0%
+the name Adolf Fick and the young Adolf
+Fick uh the nephew um was strongly
+
+ align:start position:0%
+Fick uh the nephew um was strongly
+ 
+
+ align:start position:0%
+Fick uh the nephew um was strongly
+influenced by um the uncle and he went
+
+ align:start position:0%
+influenced by um the uncle and he went
+ 
+
+ align:start position:0%
+influenced by um the uncle and he went
+on to invent uh the contact lens so this
+
+ align:start position:0%
+on to invent uh the contact lens so this
+ 
+
+ align:start position:0%
+on to invent uh the contact lens so this
+has been quite uh prolific in ways that
+
+ align:start position:0%
+has been quite uh prolific in ways that
+ 
+
+ align:start position:0%
+has been quite uh prolific in ways that
+influence many of us how many in this
+
+ align:start position:0%
+influence many of us how many in this
+ 
+
+ align:start position:0%
+influence many of us how many in this
+room are wearing contact
+
+ align:start position:0%
+room are wearing contact
+ 
+
+ align:start position:0%
+room are wearing contact
+lenses and uh I think we're all thankful
+
+ align:start position:0%
+lenses and uh I think we're all thankful
+ 
+
+ align:start position:0%
+lenses and uh I think we're all thankful
+that there is some cardiac efficiency so
+
+ align:start position:0%
+that there is some cardiac efficiency so
+ 
+
+ align:start position:0%
+that there is some cardiac efficiency so
+I think we're all
+
+ align:start position:0%
+I think we're all
+ 
+
+ align:start position:0%
+I think we're all
+beneficiaries okay so let's take a look
+
+ align:start position:0%
+beneficiaries okay so let's take a look
+ 
+
+ align:start position:0%
+beneficiaries okay so let's take a look
+uh in more detail at what Fick taught us
+
+ align:start position:0%
+uh in more detail at what Fick taught us
+ 
+
+ align:start position:0%
+uh in more detail at what Fick taught us
+he said that if we have Ingress of
+
+ align:start position:0%
+he said that if we have Ingress of
+ 
+
+ align:start position:0%
+he said that if we have Ingress of
+species ey into some solid um the rate
+
+ align:start position:0%
+species ey into some solid um the rate
+ 
+
+ align:start position:0%
+species ey into some solid um the rate
+of Ingress is given by the uh equation
+
+ align:start position:0%
+of Ingress is given by the uh equation
+ 
+
+ align:start position:0%
+of Ingress is given by the uh equation
+shown here which expresses the flux
+
+ align:start position:0%
+shown here which expresses the flux
+ 
+
+ align:start position:0%
+shown here which expresses the flux
+which is mass per unit time uh per unit
+
+ align:start position:0%
+which is mass per unit time uh per unit
+ 
+
+ align:start position:0%
+which is mass per unit time uh per unit
+cross-sectional area as proportional to
+
+ align:start position:0%
+cross-sectional area as proportional to
+ 
+
+ align:start position:0%
+cross-sectional area as proportional to
+the concentration gradient and the
+
+ align:start position:0%
+the concentration gradient and the
+ 
+
+ align:start position:0%
+the concentration gradient and the
+proportionality constant is the
+
+ align:start position:0%
+proportionality constant is the
+ 
+
+ align:start position:0%
+proportionality constant is the
+diffusion coefficient and what we see
+
+ align:start position:0%
+diffusion coefficient and what we see
+ 
+
+ align:start position:0%
+diffusion coefficient and what we see
+here is uh a uh a sketch of what that
+
+ align:start position:0%
+here is uh a uh a sketch of what that
+ 
+
+ align:start position:0%
+here is uh a uh a sketch of what that
+might look like uh some initial surface
+
+ align:start position:0%
+might look like uh some initial surface
+ 
+
+ align:start position:0%
+might look like uh some initial surface
+concentration uh held constant with
+
+ align:start position:0%
+concentration uh held constant with
+ 
+
+ align:start position:0%
+concentration uh held constant with
+Ingress of material and since the uh
+
+ align:start position:0%
+Ingress of material and since the uh
+ 
+
+ align:start position:0%
+Ingress of material and since the uh
+flux is the derivative you can see that
+
+ align:start position:0%
+flux is the derivative you can see that
+ 
+
+ align:start position:0%
+flux is the derivative you can see that
+the the flux but for some multiplication
+
+ align:start position:0%
+the the flux but for some multiplication
+ 
+
+ align:start position:0%
+the the flux but for some multiplication
+Factor tracks with the uh concentration
+
+ align:start position:0%
+Factor tracks with the uh concentration
+ 
+
+ align:start position:0%
+Factor tracks with the uh concentration
+we have the steepest concentration
+
+ align:start position:0%
+we have the steepest concentration
+ 
+
+ align:start position:0%
+we have the steepest concentration
+gradient at the surface and deep inside
+
+ align:start position:0%
+gradient at the surface and deep inside
+ 
+
+ align:start position:0%
+gradient at the surface and deep inside
+the specimen there is uh essentially no
+
+ align:start position:0%
+the specimen there is uh essentially no
+ 
+
+ align:start position:0%
+the specimen there is uh essentially no
+concentration gradient so the flux
+
+ align:start position:0%
+concentration gradient so the flux
+ 
+
+ align:start position:0%
+concentration gradient so the flux
+attenuates so flux shown here in fuchsia
+
+ align:start position:0%
+attenuates so flux shown here in fuchsia
+ 
+
+ align:start position:0%
+attenuates so flux shown here in fuchsia
+and concentration shown here and profile
+
+ align:start position:0%
+and concentration shown here and profile
+ 
+
+ align:start position:0%
+and concentration shown here and profile
+when I say
+
+ align:start position:0%
+when I say
+ 
+
+ align:start position:0%
+when I say
+profile profile means uh something as a
+
+ align:start position:0%
+profile profile means uh something as a
+ 
+
+ align:start position:0%
+profile profile means uh something as a
+function of of distance so profile in
+
+ align:start position:0%
+function of of distance so profile in
+ 
+
+ align:start position:0%
+function of of distance so profile in
+this case it's a concentration profile
+
+ align:start position:0%
+this case it's a concentration profile
+ 
+
+ align:start position:0%
+this case it's a concentration profile
+or a flux profile so you can see those
+
+ align:start position:0%
+or a flux profile so you can see those
+ 
+
+ align:start position:0%
+or a flux profile so you can see those
+two and then we started looking at uh
+
+ align:start position:0%
+two and then we started looking at uh
+ 
+
+ align:start position:0%
+two and then we started looking at uh
+some of the atomistics and we reason
+
+ align:start position:0%
+some of the atomistics and we reason
+ 
+
+ align:start position:0%
+some of the atomistics and we reason
+that there's some uh jumping involved
+
+ align:start position:0%
+that there's some uh jumping involved
+ 
+
+ align:start position:0%
+that there's some uh jumping involved
+and with the jumping comes the notion of
+
+ align:start position:0%
+and with the jumping comes the notion of
+ 
+
+ align:start position:0%
+and with the jumping comes the notion of
+activation yeah we looked at this and we
+
+ align:start position:0%
+activation yeah we looked at this and we
+ 
+
+ align:start position:0%
+activation yeah we looked at this and we
+concluded that there's an activation
+
+ align:start position:0%
+concluded that there's an activation
+ 
+
+ align:start position:0%
+concluded that there's an activation
+energy associated with jumping uh
+
+ align:start position:0%
+energy associated with jumping uh
+ 
+
+ align:start position:0%
+energy associated with jumping uh
+through that saddle point an arous type
+
+ align:start position:0%
+through that saddle point an arous type
+ 
+
+ align:start position:0%
+through that saddle point an arous type
+Behavior natural log of D linear in
+
+ align:start position:0%
+Behavior natural log of D linear in
+ 
+
+ align:start position:0%
+Behavior natural log of D linear in
+reciprocal of the absolute temperature
+
+ align:start position:0%
+reciprocal of the absolute temperature
+ 
+
+ align:start position:0%
+reciprocal of the absolute temperature
+remember this is not the ridberg
+
+ align:start position:0%
+remember this is not the ridberg
+ 
+
+ align:start position:0%
+remember this is not the ridberg
+constant this is the gas constant which
+
+ align:start position:0%
+constant this is the gas constant which
+ 
+
+ align:start position:0%
+constant this is the gas constant which
+is the product of the boltzman
+
+ align:start position:0%
+is the product of the boltzman
+ 
+
+ align:start position:0%
+is the product of the boltzman
+constant the boltzman constant and the
+
+ align:start position:0%
+constant the boltzman constant and the
+ 
+
+ align:start position:0%
+constant the boltzman constant and the
+avagadro number and units will give you
+
+ align:start position:0%
+avagadro number and units will give you
+ 
+
+ align:start position:0%
+avagadro number and units will give you
+a clue as to which to use if the uh
+
+ align:start position:0%
+a clue as to which to use if the uh
+ 
+
+ align:start position:0%
+a clue as to which to use if the uh
+activation energy is in units per mole
+
+ align:start position:0%
+activation energy is in units per mole
+ 
+
+ align:start position:0%
+activation energy is in units per mole
+then obviously use the gas constant
+
+ align:start position:0%
+then obviously use the gas constant
+ 
+
+ align:start position:0%
+then obviously use the gas constant
+otherwise you use the bolman constant
+
+ align:start position:0%
+otherwise you use the bolman constant
+ 
+
+ align:start position:0%
+otherwise you use the bolman constant
+and when we looked at the atomistics
+
+ align:start position:0%
+and when we looked at the atomistics
+ 
+
+ align:start position:0%
+and when we looked at the atomistics
+further we reasoned that when we have
+
+ align:start position:0%
+further we reasoned that when we have
+ 
+
+ align:start position:0%
+further we reasoned that when we have
+diffusion by vacancy jump mechanism this
+
+ align:start position:0%
+diffusion by vacancy jump mechanism this
+ 
+
+ align:start position:0%
+diffusion by vacancy jump mechanism this
+activation energy up here in the
+
+ align:start position:0%
+activation energy up here in the
+ 
+
+ align:start position:0%
+activation energy up here in the
+equation is the sum of two components
+
+ align:start position:0%
+equation is the sum of two components
+ 
+
+ align:start position:0%
+equation is the sum of two components
+one being the enthalpy of vacancy
+
+ align:start position:0%
+one being the enthalpy of vacancy
+ 
+
+ align:start position:0%
+one being the enthalpy of vacancy
+formation which is really the negative
+
+ align:start position:0%
+formation which is really the negative
+ 
+
+ align:start position:0%
+formation which is really the negative
+of the bonding energy and then the
+
+ align:start position:0%
+of the bonding energy and then the
+ 
+
+ align:start position:0%
+of the bonding energy and then the
+energy associated with the atom
+
+ align:start position:0%
+energy associated with the atom
+ 
+
+ align:start position:0%
+energy associated with the atom
+migration which is the energy of
+
+ align:start position:0%
+migration which is the energy of
+ 
+
+ align:start position:0%
+migration which is the energy of
+squeezing through that Saddle Point
+
+ align:start position:0%
+squeezing through that Saddle Point
+ 
+
+ align:start position:0%
+squeezing through that Saddle Point
+shown in the in the figure in the case
+
+ align:start position:0%
+shown in the in the figure in the case
+ 
+
+ align:start position:0%
+shown in the in the figure in the case
+of interstitial diffusion we don't have
+
+ align:start position:0%
+of interstitial diffusion we don't have
+ 
+
+ align:start position:0%
+of interstitial diffusion we don't have
+to uh form vacancies there's enough
+
+ align:start position:0%
+to uh form vacancies there's enough
+ 
+
+ align:start position:0%
+to uh form vacancies there's enough
+vacant sites by virtue of the fact that
+
+ align:start position:0%
+vacant sites by virtue of the fact that
+ 
+
+ align:start position:0%
+vacant sites by virtue of the fact that
+uh we've got so much free volume even in
+
+ align:start position:0%
+uh we've got so much free volume even in
+ 
+
+ align:start position:0%
+uh we've got so much free volume even in
+a close-packed solid so we're really
+
+ align:start position:0%
+a close-packed solid so we're really
+ 
+
+ align:start position:0%
+a close-packed solid so we're really
+just paying for the um uh enthalpy of
+
+ align:start position:0%
+just paying for the um uh enthalpy of
+ 
+
+ align:start position:0%
+just paying for the um uh enthalpy of
+migration and then lastly we looked at
+
+ align:start position:0%
+migration and then lastly we looked at
+ 
+
+ align:start position:0%
+migration and then lastly we looked at
+how these two are related to the degree
+
+ align:start position:0%
+how these two are related to the degree
+ 
+
+ align:start position:0%
+how these two are related to the degree
+of confinement in other words the atom
+
+ align:start position:0%
+of confinement in other words the atom
+ 
+
+ align:start position:0%
+of confinement in other words the atom
+is restricted by the the the ease with
+
+ align:start position:0%
+is restricted by the the the ease with
+ 
+
+ align:start position:0%
+is restricted by the the the ease with
+which it can run down its appropriate
+
+ align:start position:0%
+which it can run down its appropriate
+ 
+
+ align:start position:0%
+which it can run down its appropriate
+Raceway and and we re reason that going
+
+ align:start position:0%
+Raceway and and we re reason that going
+ 
+
+ align:start position:0%
+Raceway and and we re reason that going
+through the bulk lattice is the most uh
+
+ align:start position:0%
+through the bulk lattice is the most uh
+ 
+
+ align:start position:0%
+through the bulk lattice is the most uh
+tortuous path and has the highest
+
+ align:start position:0%
+tortuous path and has the highest
+ 
+
+ align:start position:0%
+tortuous path and has the highest
+activation energy lowest diffusion
+
+ align:start position:0%
+activation energy lowest diffusion
+ 
+
+ align:start position:0%
+activation energy lowest diffusion
+coefficient grain boundaries have atoms
+
+ align:start position:0%
+coefficient grain boundaries have atoms
+ 
+
+ align:start position:0%
+coefficient grain boundaries have atoms
+with fewer uh nearest neighbors the
+
+ align:start position:0%
+with fewer uh nearest neighbors the
+ 
+
+ align:start position:0%
+with fewer uh nearest neighbors the
+lower coordination num so the diffusion
+
+ align:start position:0%
+lower coordination num so the diffusion
+ 
+
+ align:start position:0%
+lower coordination num so the diffusion
+coefficient is higher in the grain
+
+ align:start position:0%
+coefficient is higher in the grain
+ 
+
+ align:start position:0%
+coefficient is higher in the grain
+boundary and it is highest along the
+
+ align:start position:0%
+boundary and it is highest along the
+ 
+
+ align:start position:0%
+boundary and it is highest along the
+free surface and we saw last day that
+
+ align:start position:0%
+free surface and we saw last day that
+ 
+
+ align:start position:0%
+free surface and we saw last day that
+the diffusion coefficient along the free
+
+ align:start position:0%
+the diffusion coefficient along the free
+ 
+
+ align:start position:0%
+the diffusion coefficient along the free
+surface of a solid approaches
+
+ align:start position:0%
+surface of a solid approaches
+ 
+
+ align:start position:0%
+surface of a solid approaches
+values equivalent to that of diffusion
+
+ align:start position:0%
+values equivalent to that of diffusion
+ 
+
+ align:start position:0%
+values equivalent to that of diffusion
+in a liquid state so what I want to do
+
+ align:start position:0%
+in a liquid state so what I want to do
+ 
+
+ align:start position:0%
+in a liquid state so what I want to do
+today is to step back to the Continuum
+
+ align:start position:0%
+today is to step back to the Continuum
+ 
+
+ align:start position:0%
+today is to step back to the Continuum
+and use fix law to uh describe what's
+
+ align:start position:0%
+and use fix law to uh describe what's
+ 
+
+ align:start position:0%
+and use fix law to uh describe what's
+going on mathematically uh in the macro
+
+ align:start position:0%
+going on mathematically uh in the macro
+ 
+
+ align:start position:0%
+going on mathematically uh in the macro
+world so I want to first start start
+
+ align:start position:0%
+world so I want to first start start
+ 
+
+ align:start position:0%
+world so I want to first start start
+with diffusion across a membrane so this
+
+ align:start position:0%
+with diffusion across a membrane so this
+ 
+
+ align:start position:0%
+with diffusion across a membrane so this
+is a membrane of some thickness
+
+ align:start position:0%
+is a membrane of some thickness
+ 
+
+ align:start position:0%
+is a membrane of some thickness
+um of some thickness L membrane of some
+
+ align:start position:0%
+um of some thickness L membrane of some
+ 
+
+ align:start position:0%
+um of some thickness L membrane of some
+thickness L and I'm going to put a gas
+
+ align:start position:0%
+thickness L and I'm going to put a gas
+ 
+
+ align:start position:0%
+thickness L and I'm going to put a gas
+uh to the left P1 and I'm going to hold
+
+ align:start position:0%
+uh to the left P1 and I'm going to hold
+ 
+
+ align:start position:0%
+uh to the left P1 and I'm going to hold
+it constant and to the right I'm going
+
+ align:start position:0%
+it constant and to the right I'm going
+ 
+
+ align:start position:0%
+it constant and to the right I'm going
+to have a gas at P2 also being held
+
+ align:start position:0%
+to have a gas at P2 also being held
+ 
+
+ align:start position:0%
+to have a gas at P2 also being held
+constant and just so that we're all on
+
+ align:start position:0%
+constant and just so that we're all on
+ 
+
+ align:start position:0%
+constant and just so that we're all on
+the same page I'm going to make P1
+
+ align:start position:0%
+the same page I'm going to make P1
+ 
+
+ align:start position:0%
+the same page I'm going to make P1
+greater than P2 so that means that
+
+ align:start position:0%
+greater than P2 so that means that
+ 
+
+ align:start position:0%
+greater than P2 so that means that
+matter will diffuse from high pressure
+
+ align:start position:0%
+matter will diffuse from high pressure
+ 
+
+ align:start position:0%
+matter will diffuse from high pressure
+to low pressure high concentration to
+
+ align:start position:0%
+to low pressure high concentration to
+ 
+
+ align:start position:0%
+to low pressure high concentration to
+low concentration so that means the flux
+
+ align:start position:0%
+low concentration so that means the flux
+ 
+
+ align:start position:0%
+low concentration so that means the flux
+will be uh left to right and we can use
+
+ align:start position:0%
+will be uh left to right and we can use
+ 
+
+ align:start position:0%
+will be uh left to right and we can use
+the universal gas law pressure volume
+
+ align:start position:0%
+the universal gas law pressure volume
+ 
+
+ align:start position:0%
+the universal gas law pressure volume
+equals the product of mole number times
+
+ align:start position:0%
+equals the product of mole number times
+ 
+
+ align:start position:0%
+equals the product of mole number times
+gas constant times temperature in order
+
+ align:start position:0%
+gas constant times temperature in order
+ 
+
+ align:start position:0%
+gas constant times temperature in order
+to convert pressure units into
+
+ align:start position:0%
+to convert pressure units into
+ 
+
+ align:start position:0%
+to convert pressure units into
+concentration units we know that the
+
+ align:start position:0%
+concentration units we know that the
+ 
+
+ align:start position:0%
+concentration units we know that the
+concentration of a species I is simply
+
+ align:start position:0%
+concentration of a species I is simply
+ 
+
+ align:start position:0%
+concentration of a species I is simply
+equal to the mole number I divided by
+
+ align:start position:0%
+equal to the mole number I divided by
+ 
+
+ align:start position:0%
+equal to the mole number I divided by
+the total volume of the system right
+
+ align:start position:0%
+the total volume of the system right
+ 
+
+ align:start position:0%
+the total volume of the system right
+this is moles per unit volume so that's
+
+ align:start position:0%
+this is moles per unit volume so that's
+ 
+
+ align:start position:0%
+this is moles per unit volume so that's
+a concentration and so that means then
+
+ align:start position:0%
+a concentration and so that means then
+ 
+
+ align:start position:0%
+a concentration and so that means then
+that if we go to the universe of gas law
+
+ align:start position:0%
+that if we go to the universe of gas law
+ 
+
+ align:start position:0%
+that if we go to the universe of gas law
+that will give us p over RT so if we
+
+ align:start position:0%
+that will give us p over RT so if we
+ 
+
+ align:start position:0%
+that will give us p over RT so if we
+take a pressure divid it by the product
+
+ align:start position:0%
+take a pressure divid it by the product
+ 
+
+ align:start position:0%
+take a pressure divid it by the product
+of the gas constant temperature we'll
+
+ align:start position:0%
+of the gas constant temperature we'll
+ 
+
+ align:start position:0%
+of the gas constant temperature we'll
+move from pressure units to
+
+ align:start position:0%
+move from pressure units to
+ 
+
+ align:start position:0%
+move from pressure units to
+concentration units and so what I'd like
+
+ align:start position:0%
+concentration units and so what I'd like
+ 
+
+ align:start position:0%
+concentration units and so what I'd like
+to do is show what this this system
+
+ align:start position:0%
+to do is show what this this system
+ 
+
+ align:start position:0%
+to do is show what this this system
+looks like after some period of time so
+
+ align:start position:0%
+looks like after some period of time so
+ 
+
+ align:start position:0%
+looks like after some period of time so
+I'm going to put the convention with
+
+ align:start position:0%
+I'm going to put the convention with
+ 
+
+ align:start position:0%
+I'm going to put the convention with
+zero on the left surface so this is
+
+ align:start position:0%
+zero on the left surface so this is
+ 
+
+ align:start position:0%
+zero on the left surface so this is
+distance moving from left to right so
+
+ align:start position:0%
+distance moving from left to right so
+ 
+
+ align:start position:0%
+distance moving from left to right so
+xal 0 is the left surface of the
+
+ align:start position:0%
+xal 0 is the left surface of the
+ 
+
+ align:start position:0%
+xal 0 is the left surface of the
+membrane xals L is the right surface of
+
+ align:start position:0%
+membrane xals L is the right surface of
+ 
+
+ align:start position:0%
+membrane xals L is the right surface of
+the membrane and now let's put
+
+ align:start position:0%
+the membrane and now let's put
+ 
+
+ align:start position:0%
+the membrane and now let's put
+concentration C1 on the left surface and
+
+ align:start position:0%
+concentration C1 on the left surface and
+ 
+
+ align:start position:0%
+concentration C1 on the left surface and
+C2 on the right surface and what we know
+
+ align:start position:0%
+C2 on the right surface and what we know
+ 
+
+ align:start position:0%
+C2 on the right surface and what we know
+is we expect that after some period of
+
+ align:start position:0%
+is we expect that after some period of
+ 
+
+ align:start position:0%
+is we expect that after some period of
+time if if C1 is held constant if C1 is
+
+ align:start position:0%
+time if if C1 is held constant if C1 is
+ 
+
+ align:start position:0%
+time if if C1 is held constant if C1 is
+held constant and C2 is held constant
+
+ align:start position:0%
+held constant and C2 is held constant
+ 
+
+ align:start position:0%
+held constant and C2 is held constant
+then after some period of time we expect
+
+ align:start position:0%
+then after some period of time we expect
+ 
+
+ align:start position:0%
+then after some period of time we expect
+to have a profile that is linear we
+
+ align:start position:0%
+to have a profile that is linear we
+ 
+
+ align:start position:0%
+to have a profile that is linear we
+expect to have a profile that is linear
+
+ align:start position:0%
+expect to have a profile that is linear
+ 
+
+ align:start position:0%
+expect to have a profile that is linear
+and we should be able to uh infer that
+
+ align:start position:0%
+and we should be able to uh infer that
+ 
+
+ align:start position:0%
+and we should be able to uh infer that
+from fixed first law we know that fixed
+
+ align:start position:0%
+from fixed first law we know that fixed
+ 
+
+ align:start position:0%
+from fixed first law we know that fixed
+first law tells us that J is equal to
+
+ align:start position:0%
+first law tells us that J is equal to
+ 
+
+ align:start position:0%
+first law tells us that J is equal to
+minus D DC by
+
+ align:start position:0%
+minus D DC by
+ 
+
+ align:start position:0%
+minus D DC by
+DX
+
+ align:start position:0%
+DX
+ 
+
+ align:start position:0%
+DX
+so if I'm
+
+ align:start position:0%
+so if I'm
+ 
+
+ align:start position:0%
+so if I'm
+holding the concentrations on both sides
+
+ align:start position:0%
+holding the concentrations on both sides
+ 
+
+ align:start position:0%
+holding the concentrations on both sides
+sides constant then it tells me then
+
+ align:start position:0%
+sides constant then it tells me then
+ 
+
+ align:start position:0%
+sides constant then it tells me then
+that the gradient is going to be
+
+ align:start position:0%
+that the gradient is going to be
+ 
+
+ align:start position:0%
+that the gradient is going to be
+constant otherwise I have some sources
+
+ align:start position:0%
+constant otherwise I have some sources
+ 
+
+ align:start position:0%
+constant otherwise I have some sources
+or syns which uh we don't allow for so
+
+ align:start position:0%
+or syns which uh we don't allow for so
+ 
+
+ align:start position:0%
+or syns which uh we don't allow for so
+after this short time we have this
+
+ align:start position:0%
+after this short time we have this
+ 
+
+ align:start position:0%
+after this short time we have this
+profile which we term steady
+
+ align:start position:0%
+profile which we term steady
+ 
+
+ align:start position:0%
+profile which we term steady
+state steady state and it's term steady
+
+ align:start position:0%
+state steady state and it's term steady
+ 
+
+ align:start position:0%
+state steady state and it's term steady
+state because it's invariant with time
+
+ align:start position:0%
+state because it's invariant with time
+ 
+
+ align:start position:0%
+state because it's invariant with time
+the flux is not a function of time the
+
+ align:start position:0%
+the flux is not a function of time the
+ 
+
+ align:start position:0%
+the flux is not a function of time the
+flux entering the free surface on the
+
+ align:start position:0%
+flux entering the free surface on the
+ 
+
+ align:start position:0%
+flux entering the free surface on the
+left equals the flux exiting on the free
+
+ align:start position:0%
+left equals the flux exiting on the free
+ 
+
+ align:start position:0%
+left equals the flux exiting on the free
+surface on the right and therefore the
+
+ align:start position:0%
+surface on the right and therefore the
+ 
+
+ align:start position:0%
+surface on the right and therefore the
+flux must be constant throughout the
+
+ align:start position:0%
+flux must be constant throughout the
+ 
+
+ align:start position:0%
+flux must be constant throughout the
+membrane because if J is constant and
+
+ align:start position:0%
+membrane because if J is constant and
+ 
+
+ align:start position:0%
+membrane because if J is constant and
+I'm assuming that the diffusion
+
+ align:start position:0%
+I'm assuming that the diffusion
+ 
+
+ align:start position:0%
+I'm assuming that the diffusion
+coefficient doesn't change with time
+
+ align:start position:0%
+coefficient doesn't change with time
+ 
+
+ align:start position:0%
+coefficient doesn't change with time
+then it means that this gradient must be
+
+ align:start position:0%
+then it means that this gradient must be
+ 
+
+ align:start position:0%
+then it means that this gradient must be
+constant so the slope must be the same
+
+ align:start position:0%
+constant so the slope must be the same
+ 
+
+ align:start position:0%
+constant so the slope must be the same
+all the way along reinforcing the notion
+
+ align:start position:0%
+all the way along reinforcing the notion
+ 
+
+ align:start position:0%
+all the way along reinforcing the notion
+that we have a straight line
+
+ align:start position:0%
+that we have a straight line
+ 
+
+ align:start position:0%
+that we have a straight line
+profile now there's one assumption here
+
+ align:start position:0%
+profile now there's one assumption here
+ 
+
+ align:start position:0%
+profile now there's one assumption here
+of course and that is that the diffusion
+
+ align:start position:0%
+of course and that is that the diffusion
+ 
+
+ align:start position:0%
+of course and that is that the diffusion
+coefficient is independent of
+
+ align:start position:0%
+coefficient is independent of
+ 
+
+ align:start position:0%
+coefficient is independent of
+concentration it could be and we'll
+
+ align:start position:0%
+concentration it could be and we'll
+ 
+
+ align:start position:0%
+concentration it could be and we'll
+return to that later and see what
+
+ align:start position:0%
+return to that later and see what
+ 
+
+ align:start position:0%
+return to that later and see what
+happens if we have the uh concentration
+
+ align:start position:0%
+happens if we have the uh concentration
+ 
+
+ align:start position:0%
+happens if we have the uh concentration
+dependent diffusivity we can describe at
+
+ align:start position:0%
+dependent diffusivity we can describe at
+ 
+
+ align:start position:0%
+dependent diffusivity we can describe at
+steady state everything we need to know
+
+ align:start position:0%
+steady state everything we need to know
+ 
+
+ align:start position:0%
+steady state everything we need to know
+about the behavior of this system with
+
+ align:start position:0%
+about the behavior of this system with
+ 
+
+ align:start position:0%
+about the behavior of this system with
+fixed first law alone fixed first law
+
+ align:start position:0%
+fixed first law alone fixed first law
+ 
+
+ align:start position:0%
+fixed first law alone fixed first law
+alone is sufficient so one of the kinds
+
+ align:start position:0%
+alone is sufficient so one of the kinds
+ 
+
+ align:start position:0%
+alone is sufficient so one of the kinds
+of things that we might want to know we
+
+ align:start position:0%
+of things that we might want to know we
+ 
+
+ align:start position:0%
+of things that we might want to know we
+might want to ask is um oh how much
+
+ align:start position:0%
+might want to ask is um oh how much
+ 
+
+ align:start position:0%
+might want to ask is um oh how much
+material uh diffuses over time okay Mass
+
+ align:start position:0%
+material uh diffuses over time okay Mass
+ 
+
+ align:start position:0%
+material uh diffuses over time okay Mass
+per unit
+
+ align:start position:0%
+per unit
+ 
+
+ align:start position:0%
+per unit
+time passing through the
+
+ align:start position:0%
+time passing through the
+ 
+
+ align:start position:0%
+time passing through the
+membrane passing through the membrane
+
+ align:start position:0%
+membrane passing through the membrane
+ 
+
+ align:start position:0%
+membrane passing through the membrane
+all we need is fixed first law because
+
+ align:start position:0%
+all we need is fixed first law because
+ 
+
+ align:start position:0%
+all we need is fixed first law because
+we know that we can say that that um the
+
+ align:start position:0%
+we know that we can say that that um the
+ 
+
+ align:start position:0%
+we know that we can say that that um the
+mass will simply equal the flux which is
+
+ align:start position:0%
+mass will simply equal the flux which is
+ 
+
+ align:start position:0%
+mass will simply equal the flux which is
+mass per unit area per unit time if I
+
+ align:start position:0%
+mass per unit area per unit time if I
+ 
+
+ align:start position:0%
+mass per unit area per unit time if I
+know the total area of the membrane and
+
+ align:start position:0%
+know the total area of the membrane and
+ 
+
+ align:start position:0%
+know the total area of the membrane and
+I know the time then that's all I need
+
+ align:start position:0%
+I know the time then that's all I need
+ 
+
+ align:start position:0%
+I know the time then that's all I need
+so fixed first law is very
+
+ align:start position:0%
+so fixed first law is very
+ 
+
+ align:start position:0%
+so fixed first law is very
+uh thorough in describing system at
+
+ align:start position:0%
+uh thorough in describing system at
+ 
+
+ align:start position:0%
+uh thorough in describing system at
+steady state um last thing about this
+
+ align:start position:0%
+steady state um last thing about this
+ 
+
+ align:start position:0%
+steady state um last thing about this
+concentration
+
+ align:start position:0%
+concentration
+ 
+
+ align:start position:0%
+concentration
+profile the operative definition of
+
+ align:start position:0%
+profile the operative definition of
+ 
+
+ align:start position:0%
+profile the operative definition of
+steady state is that J doesn't change
+
+ align:start position:0%
+steady state is that J doesn't change
+ 
+
+ align:start position:0%
+steady state is that J doesn't change
+with time in other words if I look at
+
+ align:start position:0%
+with time in other words if I look at
+ 
+
+ align:start position:0%
+with time in other words if I look at
+this some later time as long as I
+
+ align:start position:0%
+this some later time as long as I
+ 
+
+ align:start position:0%
+this some later time as long as I
+maintain constant n compositions I'll
+
+ align:start position:0%
+maintain constant n compositions I'll
+ 
+
+ align:start position:0%
+maintain constant n compositions I'll
+have this same profile but suppose I had
+
+ align:start position:0%
+have this same profile but suppose I had
+ 
+
+ align:start position:0%
+have this same profile but suppose I had
+a situation like this where the
+
+ align:start position:0%
+a situation like this where the
+ 
+
+ align:start position:0%
+a situation like this where the
+diffusion coefficient is not independent
+
+ align:start position:0%
+diffusion coefficient is not independent
+ 
+
+ align:start position:0%
+diffusion coefficient is not independent
+of concentration I'll give you an
+
+ align:start position:0%
+of concentration I'll give you an
+ 
+
+ align:start position:0%
+of concentration I'll give you an
+example um uh diffusion coefficient of
+
+ align:start position:0%
+example um uh diffusion coefficient of
+ 
+
+ align:start position:0%
+example um uh diffusion coefficient of
+carbon in Iron this is steel diffusion
+
+ align:start position:0%
+carbon in Iron this is steel diffusion
+ 
+
+ align:start position:0%
+carbon in Iron this is steel diffusion
+coefficient of carbon in Iron as a
+
+ align:start position:0%
+coefficient of carbon in Iron as a
+ 
+
+ align:start position:0%
+coefficient of carbon in Iron as a
+function of the concentration of carbon
+
+ align:start position:0%
+function of the concentration of carbon
+ 
+
+ align:start position:0%
+function of the concentration of carbon
+in
+
+ align:start position:0%
+in
+ 
+
+ align:start position:0%
+in
+iron it turns out that as more and more
+
+ align:start position:0%
+iron it turns out that as more and more
+ 
+
+ align:start position:0%
+iron it turns out that as more and more
+carbon goes into iron the diffusion
+
+ align:start position:0%
+carbon goes into iron the diffusion
+ 
+
+ align:start position:0%
+carbon goes into iron the diffusion
+coefficient changes you'd expect that
+
+ align:start position:0%
+coefficient changes you'd expect that
+ 
+
+ align:start position:0%
+coefficient changes you'd expect that
+because now some of the SES are occupied
+
+ align:start position:0%
+because now some of the SES are occupied
+ 
+
+ align:start position:0%
+because now some of the SES are occupied
+right so which is it do you think that
+
+ align:start position:0%
+right so which is it do you think that
+ 
+
+ align:start position:0%
+right so which is it do you think that
+the diffusion coefficient as you get
+
+ align:start position:0%
+the diffusion coefficient as you get
+ 
+
+ align:start position:0%
+the diffusion coefficient as you get
+more and more carbon into iron start
+
+ align:start position:0%
+more and more carbon into iron start
+ 
+
+ align:start position:0%
+more and more carbon into iron start
+starts to fall like
+
+ align:start position:0%
+starts to fall like
+ 
+
+ align:start position:0%
+starts to fall like
+this or do you think the diffusion
+
+ align:start position:0%
+this or do you think the diffusion
+ 
+
+ align:start position:0%
+this or do you think the diffusion
+coefficient Rises like this so that at
+
+ align:start position:0%
+coefficient Rises like this so that at
+ 
+
+ align:start position:0%
+coefficient Rises like this so that at
+higher concentrations it becomes more
+
+ align:start position:0%
+higher concentrations it becomes more
+ 
+
+ align:start position:0%
+higher concentrations it becomes more
+difficult to diffuse well this might
+
+ align:start position:0%
+difficult to diffuse well this might
+ 
+
+ align:start position:0%
+difficult to diffuse well this might
+sound appealing because the SES are
+
+ align:start position:0%
+sound appealing because the SES are
+ 
+
+ align:start position:0%
+sound appealing because the SES are
+getting blocked makes sense right
+
+ align:start position:0%
+getting blocked makes sense right
+ 
+
+ align:start position:0%
+getting blocked makes sense right
+there's fewer empty SES but in point of
+
+ align:start position:0%
+there's fewer empty SES but in point of
+ 
+
+ align:start position:0%
+there's fewer empty SES but in point of
+fact the diffusion coefficient actually
+
+ align:start position:0%
+fact the diffusion coefficient actually
+ 
+
+ align:start position:0%
+fact the diffusion coefficient actually
+Rises why well I've told you that the
+
+ align:start position:0%
+Rises why well I've told you that the
+ 
+
+ align:start position:0%
+Rises why well I've told you that the
+carbon atom is larger than the
+
+ align:start position:0%
+carbon atom is larger than the
+ 
+
+ align:start position:0%
+carbon atom is larger than the
+interstitial site so when the carbons go
+
+ align:start position:0%
+interstitial site so when the carbons go
+ 
+
+ align:start position:0%
+interstitial site so when the carbons go
+into the interstitial sites they act as
+
+ align:start position:0%
+into the interstitial sites they act as
+ 
+
+ align:start position:0%
+into the interstitial sites they act as
+wedges and they actually wedge open the
+
+ align:start position:0%
+wedges and they actually wedge open the
+ 
+
+ align:start position:0%
+wedges and they actually wedge open the
+system and make it easier for the
+
+ align:start position:0%
+system and make it easier for the
+ 
+
+ align:start position:0%
+system and make it easier for the
+succeeding atoms to diffuse through so
+
+ align:start position:0%
+succeeding atoms to diffuse through so
+ 
+
+ align:start position:0%
+succeeding atoms to diffuse through so
+in point of fact this is what happens
+
+ align:start position:0%
+in point of fact this is what happens
+ 
+
+ align:start position:0%
+in point of fact this is what happens
+but it's could be either so let's
+
+ align:start position:0%
+but it's could be either so let's
+ 
+
+ align:start position:0%
+but it's could be either so let's
+imagine suppose we have case number one
+
+ align:start position:0%
+imagine suppose we have case number one
+ 
+
+ align:start position:0%
+imagine suppose we have case number one
+where the diffusion coefficient uh Falls
+
+ align:start position:0%
+where the diffusion coefficient uh Falls
+ 
+
+ align:start position:0%
+where the diffusion coefficient uh Falls
+as concentration Rises and now I've got
+
+ align:start position:0%
+as concentration Rises and now I've got
+ 
+
+ align:start position:0%
+as concentration Rises and now I've got
+a steady state concentration profile
+
+ align:start position:0%
+a steady state concentration profile
+ 
+
+ align:start position:0%
+a steady state concentration profile
+I've got C1 constant on the left C D2
+
+ align:start position:0%
+I've got C1 constant on the left C D2
+ 
+
+ align:start position:0%
+I've got C1 constant on the left C D2
+constant on the right here's the
+
+ align:start position:0%
+constant on the right here's the
+ 
+
+ align:start position:0%
+constant on the right here's the
+equation we have to look at minus D DC
+
+ align:start position:0%
+equation we have to look at minus D DC
+ 
+
+ align:start position:0%
+equation we have to look at minus D DC
+by DX but this is now a function of
+
+ align:start position:0%
+by DX but this is now a function of
+ 
+
+ align:start position:0%
+by DX but this is now a function of
+concentration so when concentration if I
+
+ align:start position:0%
+concentration so when concentration if I
+ 
+
+ align:start position:0%
+concentration so when concentration if I
+have case number one when I have the
+
+ align:start position:0%
+have case number one when I have the
+ 
+
+ align:start position:0%
+have case number one when I have the
+highest concentration up here if this is
+
+ align:start position:0%
+highest concentration up here if this is
+ 
+
+ align:start position:0%
+highest concentration up here if this is
+going to remain constant if the
+
+ align:start position:0%
+going to remain constant if the
+ 
+
+ align:start position:0%
+going to remain constant if the
+concentration the dependence of the
+
+ align:start position:0%
+concentration the dependence of the
+ 
+
+ align:start position:0%
+concentration the dependence of the
+diffusion coefficient says D is low when
+
+ align:start position:0%
+diffusion coefficient says D is low when
+ 
+
+ align:start position:0%
+diffusion coefficient says D is low when
+C is high then that suggest ask them to
+
+ align:start position:0%
+C is high then that suggest ask them to
+ 
+
+ align:start position:0%
+C is high then that suggest ask them to
+keep a
+
+ align:start position:0%
+keep a
+ 
+
+ align:start position:0%
+keep a
+constant flux DC DX must be high when C
+
+ align:start position:0%
+constant flux DC DX must be high when C
+ 
+
+ align:start position:0%
+constant flux DC DX must be high when C
+is high so that means instead of a
+
+ align:start position:0%
+is high so that means instead of a
+ 
+
+ align:start position:0%
+is high so that means instead of a
+straight line we are going to see
+
+ align:start position:0%
+straight line we are going to see
+ 
+
+ align:start position:0%
+straight line we are going to see
+something that looks like this so this
+
+ align:start position:0%
+something that looks like this so this
+ 
+
+ align:start position:0%
+something that looks like this so this
+is case number one how about case number
+
+ align:start position:0%
+is case number one how about case number
+ 
+
+ align:start position:0%
+is case number one how about case number
+two where the concentration dependence
+
+ align:start position:0%
+two where the concentration dependence
+ 
+
+ align:start position:0%
+two where the concentration dependence
+of the diffusivity is indicated with a
+
+ align:start position:0%
+of the diffusivity is indicated with a
+ 
+
+ align:start position:0%
+of the diffusivity is indicated with a
+rise well that means at high
+
+ align:start position:0%
+rise well that means at high
+ 
+
+ align:start position:0%
+rise well that means at high
+concentration my diffusion coefficient
+
+ align:start position:0%
+concentration my diffusion coefficient
+ 
+
+ align:start position:0%
+concentration my diffusion coefficient
+is going to be higher than it is at low
+
+ align:start position:0%
+is going to be higher than it is at low
+ 
+
+ align:start position:0%
+is going to be higher than it is at low
+concentration so if this number is
+
+ align:start position:0%
+concentration so if this number is
+ 
+
+ align:start position:0%
+concentration so if this number is
+higher
+
+ align:start position:0%
+higher
+ 
+
+ align:start position:0%
+higher
+at high concentration then this number
+
+ align:start position:0%
+at high concentration then this number
+ 
+
+ align:start position:0%
+at high concentration then this number
+has to be lower so that the product will
+
+ align:start position:0%
+has to be lower so that the product will
+ 
+
+ align:start position:0%
+has to be lower so that the product will
+remain constant the product will remain
+
+ align:start position:0%
+remain constant the product will remain
+ 
+
+ align:start position:0%
+remain constant the product will remain
+constant so this is case number
+
+ align:start position:0%
+constant so this is case number
+ 
+
+ align:start position:0%
+constant so this is case number
+two so these are all variants of steady
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+state steady state J is not a function
+
+ align:start position:0%
+state steady state J is not a function
+ 
+
+ align:start position:0%
+state steady state J is not a function
+of time J is not a function of time
+
+ align:start position:0%
+of time J is not a function of time
+ 
+
+ align:start position:0%
+of time J is not a function of time
+independent of time so now I want to ask
+
+ align:start position:0%
+independent of time so now I want to ask
+ 
+
+ align:start position:0%
+independent of time so now I want to ask
+what happens in that initial moment when
+
+ align:start position:0%
+what happens in that initial moment when
+ 
+
+ align:start position:0%
+what happens in that initial moment when
+we first first pressurize the system
+
+ align:start position:0%
+we first first pressurize the system
+ 
+
+ align:start position:0%
+we first first pressurize the system
+let's say we start off and there's
+
+ align:start position:0%
+let's say we start off and there's
+ 
+
+ align:start position:0%
+let's say we start off and there's
+nothing inside
+
+ align:start position:0%
+nothing inside
+ 
+
+ align:start position:0%
+nothing inside
+the membrane and just to keep things
+
+ align:start position:0%
+the membrane and just to keep things
+ 
+
+ align:start position:0%
+the membrane and just to keep things
+simple I'm going to make uh P equals z
+
+ align:start position:0%
+simple I'm going to make uh P equals z
+ 
+
+ align:start position:0%
+simple I'm going to make uh P equals z
+on the right hand side so left side is
+
+ align:start position:0%
+on the right hand side so left side is
+ 
+
+ align:start position:0%
+on the right hand side so left side is
+P1 and at Time Zero we initially
+
+ align:start position:0%
+P1 and at Time Zero we initially
+ 
+
+ align:start position:0%
+P1 and at Time Zero we initially
+pressurize we have a concentration C1
+
+ align:start position:0%
+pressurize we have a concentration C1
+ 
+
+ align:start position:0%
+pressurize we have a concentration C1
+instantly at the surface what's the set
+
+ align:start position:0%
+instantly at the surface what's the set
+ 
+
+ align:start position:0%
+instantly at the surface what's the set
+of events that occurs leading up to the
+
+ align:start position:0%
+of events that occurs leading up to the
+ 
+
+ align:start position:0%
+of events that occurs leading up to the
+establishment of the steady state
+
+ align:start position:0%
+establishment of the steady state
+ 
+
+ align:start position:0%
+establishment of the steady state
+profile we'd expect after a short time
+
+ align:start position:0%
+profile we'd expect after a short time
+ 
+
+ align:start position:0%
+profile we'd expect after a short time
+we'd see concentration profile showing
+
+ align:start position:0%
+we'd see concentration profile showing
+ 
+
+ align:start position:0%
+we'd see concentration profile showing
+like this and then after a longer period
+
+ align:start position:0%
+like this and then after a longer period
+ 
+
+ align:start position:0%
+like this and then after a longer period
+of time like this and then after a
+
+ align:start position:0%
+of time like this and then after a
+ 
+
+ align:start position:0%
+of time like this and then after a
+longer period of time like this and then
+
+ align:start position:0%
+longer period of time like this and then
+ 
+
+ align:start position:0%
+longer period of time like this and then
+finally of
+
+ align:start position:0%
+finally of
+ 
+
+ align:start position:0%
+finally of
+course we establish so this is time is
+
+ align:start position:0%
+course we establish so this is time is
+ 
+
+ align:start position:0%
+course we establish so this is time is
+increasing from low to high so this
+
+ align:start position:0%
+increasing from low to high so this
+ 
+
+ align:start position:0%
+increasing from low to high so this
+could be T1 T2 T3 and so we can then say
+
+ align:start position:0%
+could be T1 T2 T3 and so we can then say
+ 
+
+ align:start position:0%
+could be T1 T2 T3 and so we can then say
+let's park ourselves at some value X1 on
+
+ align:start position:0%
+let's park ourselves at some value X1 on
+ 
+
+ align:start position:0%
+let's park ourselves at some value X1 on
+Zer to L and look at what's happening
+
+ align:start position:0%
+Zer to L and look at what's happening
+ 
+
+ align:start position:0%
+Zer to L and look at what's happening
+initially if I take the slope it's a
+
+ align:start position:0%
+initially if I take the slope it's a
+ 
+
+ align:start position:0%
+initially if I take the slope it's a
+it's a low number if I take the slope at
+
+ align:start position:0%
+it's a low number if I take the slope at
+ 
+
+ align:start position:0%
+it's a low number if I take the slope at
+a later time it's a higher number if I
+
+ align:start position:0%
+a later time it's a higher number if I
+ 
+
+ align:start position:0%
+a later time it's a higher number if I
+take the slope at a later time it's an
+
+ align:start position:0%
+take the slope at a later time it's an
+ 
+
+ align:start position:0%
+take the slope at a later time it's an
+even higher number and ultimately it's
+
+ align:start position:0%
+even higher number and ultimately it's
+ 
+
+ align:start position:0%
+even higher number and ultimately it's
+going to be as high as the steady state
+
+ align:start position:0%
+going to be as high as the steady state
+ 
+
+ align:start position:0%
+going to be as high as the steady state
+value so I could take that data set and
+
+ align:start position:0%
+value so I could take that data set and
+ 
+
+ align:start position:0%
+value so I could take that data set and
+plot the flux
+
+ align:start position:0%
+plot the flux
+ 
+
+ align:start position:0%
+plot the flux
+at xal X1 I'm sitting here and watching
+
+ align:start position:0%
+at xal X1 I'm sitting here and watching
+ 
+
+ align:start position:0%
+at xal X1 I'm sitting here and watching
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+the profile evolve with time initially
+
+ align:start position:0%
+the profile evolve with time initially
+ 
+
+ align:start position:0%
+the profile evolve with time initially
+it's zero because there's nothing in the
+
+ align:start position:0%
+it's zero because there's nothing in the
+ 
+
+ align:start position:0%
+it's zero because there's nothing in the
+in the uh membrane and then it slowly
+
+ align:start position:0%
+in the uh membrane and then it slowly
+ 
+
+ align:start position:0%
+in the uh membrane and then it slowly
+Rises and reaches the steady state value
+
+ align:start position:0%
+Rises and reaches the steady state value
+ 
+
+ align:start position:0%
+Rises and reaches the steady state value
+so this is this is J at steady state
+
+ align:start position:0%
+so this is this is J at steady state
+ 
+
+ align:start position:0%
+so this is this is J at steady state
+here J at steady state and this could be
+
+ align:start position:0%
+here J at steady state and this could be
+ 
+
+ align:start position:0%
+here J at steady state and this could be
+T1 T2 and T3 so you can see that coming
+
+ align:start position:0%
+T1 T2 and T3 so you can see that coming
+ 
+
+ align:start position:0%
+T1 T2 and T3 so you can see that coming
+off the
+
+ align:start position:0%
+off the
+ 
+
+ align:start position:0%
+off the
+slope so clearly when we're moving
+
+ align:start position:0%
+slope so clearly when we're moving
+ 
+
+ align:start position:0%
+slope so clearly when we're moving
+through this time period
+
+ align:start position:0%
+through this time period
+ 
+
+ align:start position:0%
+through this time period
+J is very much a function of time
+
+ align:start position:0%
+J is very much a function of time
+ 
+
+ align:start position:0%
+J is very much a function of time
+because if you close your eyes and wait
+
+ align:start position:0%
+because if you close your eyes and wait
+ 
+
+ align:start position:0%
+because if you close your eyes and wait
+you'll see that the profile has changed
+
+ align:start position:0%
+you'll see that the profile has changed
+ 
+
+ align:start position:0%
+you'll see that the profile has changed
+and if the profile has changed it means
+
+ align:start position:0%
+and if the profile has changed it means
+ 
+
+ align:start position:0%
+and if the profile has changed it means
+that the instant value of flux is
+
+ align:start position:0%
+that the instant value of flux is
+ 
+
+ align:start position:0%
+that the instant value of flux is
+changed so flux is a function of time so
+
+ align:start position:0%
+changed so flux is a function of time so
+ 
+
+ align:start position:0%
+changed so flux is a function of time so
+this is not steady state this is
+
+ align:start position:0%
+this is not steady state this is
+ 
+
+ align:start position:0%
+this is not steady state this is
+not steady state instead it is transient
+
+ align:start position:0%
+not steady state instead it is transient
+ 
+
+ align:start position:0%
+not steady state instead it is transient
+we're in the transient
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+regime transient regime
+
+ align:start position:0%
+regime transient regime
+ 
+
+ align:start position:0%
+regime transient regime
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+so as is always the case we can draw
+
+ align:start position:0%
+so as is always the case we can draw
+ 
+
+ align:start position:0%
+so as is always the case we can draw
+these curves they start at a high value
+
+ align:start position:0%
+these curves they start at a high value
+ 
+
+ align:start position:0%
+these curves they start at a high value
+they attenuate to zero What's the
+
+ align:start position:0%
+they attenuate to zero What's the
+ 
+
+ align:start position:0%
+they attenuate to zero What's the
+magical question what is the shape what
+
+ align:start position:0%
+magical question what is the shape what
+ 
+
+ align:start position:0%
+magical question what is the shape what
+is the shape that's the only reason I
+
+ align:start position:0%
+is the shape that's the only reason I
+ 
+
+ align:start position:0%
+is the shape that's the only reason I
+need math to tell me the shape of those
+
+ align:start position:0%
+need math to tell me the shape of those
+ 
+
+ align:start position:0%
+need math to tell me the shape of those
+curves is is this a an exponential decay
+
+ align:start position:0%
+curves is is this a an exponential decay
+ 
+
+ align:start position:0%
+curves is is this a an exponential decay
+is this half of a sinusoid what is the
+
+ align:start position:0%
+is this half of a sinusoid what is the
+ 
+
+ align:start position:0%
+is this half of a sinusoid what is the
+shape of the curves I want to know C
+
+ align:start position:0%
+shape of the curves I want to know C
+ 
+
+ align:start position:0%
+shape of the curves I want to know C
+versus X at all times at all times
+
+ align:start position:0%
+versus X at all times at all times
+ 
+
+ align:start position:0%
+versus X at all times at all times
+because it's changing as a function of
+
+ align:start position:0%
+because it's changing as a function of
+ 
+
+ align:start position:0%
+because it's changing as a function of
+time that means I need to know c as a
+
+ align:start position:0%
+time that means I need to know c as a
+ 
+
+ align:start position:0%
+time that means I need to know c as a
+function of x and t I've got to solve
+
+ align:start position:0%
+function of x and t I've got to solve
+ 
+
+ align:start position:0%
+function of x and t I've got to solve
+this and fi gave us the solution to this
+
+ align:start position:0%
+this and fi gave us the solution to this
+ 
+
+ align:start position:0%
+this and fi gave us the solution to this
+as
+
+ align:start position:0%
+as
+ 
+
+ align:start position:0%
+as
+well the solution of this is the
+
+ align:start position:0%
+well the solution of this is the
+ 
+
+ align:start position:0%
+well the solution of this is the
+solution to an
+
+ align:start position:0%
+solution to an
+ 
+
+ align:start position:0%
+solution to an
+equation known as fix Second Law so
+
+ align:start position:0%
+equation known as fix Second Law so
+ 
+
+ align:start position:0%
+equation known as fix Second Law so
+let's look at fixed Second
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Law fix second law
+
+ align:start position:0%
+Law fix second law
+ 
+
+ align:start position:0%
+Law fix second law
+and I'm going to write it in the special
+
+ align:start position:0%
+and I'm going to write it in the special
+ 
+
+ align:start position:0%
+and I'm going to write it in the special
+casee when D is independent of
+
+ align:start position:0%
+casee when D is independent of
+ 
+
+ align:start position:0%
+casee when D is independent of
+composition D has to be independent of
+
+ align:start position:0%
+composition D has to be independent of
+ 
+
+ align:start position:0%
+composition D has to be independent of
+composition for me to do what I'm going
+
+ align:start position:0%
+composition for me to do what I'm going
+ 
+
+ align:start position:0%
+composition for me to do what I'm going
+to do next and it's a pretty good
+
+ align:start position:0%
+to do next and it's a pretty good
+ 
+
+ align:start position:0%
+to do next and it's a pretty good
+assumption in many industrial settings
+
+ align:start position:0%
+assumption in many industrial settings
+ 
+
+ align:start position:0%
+assumption in many industrial settings
+and so I'm just going to write it it's a
+
+ align:start position:0%
+and so I'm just going to write it it's a
+ 
+
+ align:start position:0%
+and so I'm just going to write it it's a
+partial differential
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+equation and so what it's telling you is
+
+ align:start position:0%
+equation and so what it's telling you is
+ 
+
+ align:start position:0%
+equation and so what it's telling you is
+that the partial with respect to time is
+
+ align:start position:0%
+that the partial with respect to time is
+ 
+
+ align:start position:0%
+that the partial with respect to time is
+equal to the product of the diffusion
+
+ align:start position:0%
+equal to the product of the diffusion
+ 
+
+ align:start position:0%
+equal to the product of the diffusion
+coefficient times the partial of the
+
+ align:start position:0%
+coefficient times the partial of the
+ 
+
+ align:start position:0%
+coefficient times the partial of the
+gradient in concentration and so clearly
+
+ align:start position:0%
+gradient in concentration and so clearly
+ 
+
+ align:start position:0%
+gradient in concentration and so clearly
+this is a partial differential equation
+
+ align:start position:0%
+this is a partial differential equation
+ 
+
+ align:start position:0%
+this is a partial differential equation
+and that's bad that's bad you can't
+
+ align:start position:0%
+and that's bad that's bad you can't
+ 
+
+ align:start position:0%
+and that's bad that's bad you can't
+solve this one not yet okay but the good
+
+ align:start position:0%
+solve this one not yet okay but the good
+ 
+
+ align:start position:0%
+solve this one not yet okay but the good
+news is it's a linear partial
+
+ align:start position:0%
+news is it's a linear partial
+ 
+
+ align:start position:0%
+news is it's a linear partial
+differential equation and that's good
+
+ align:start position:0%
+differential equation and that's good
+ 
+
+ align:start position:0%
+differential equation and that's good
+because I can show you a solution that
+
+ align:start position:0%
+because I can show you a solution that
+ 
+
+ align:start position:0%
+because I can show you a solution that
+applies for a given setting and then you
+
+ align:start position:0%
+applies for a given setting and then you
+ 
+
+ align:start position:0%
+applies for a given setting and then you
+can play with the boundary conditions
+
+ align:start position:0%
+can play with the boundary conditions
+ 
+
+ align:start position:0%
+can play with the boundary conditions
+and use the same solu solution so that's
+
+ align:start position:0%
+and use the same solu solution so that's
+ 
+
+ align:start position:0%
+and use the same solu solution so that's
+the good news it's linear all right so
+
+ align:start position:0%
+the good news it's linear all right so
+ 
+
+ align:start position:0%
+the good news it's linear all right so
+um but the solution to this is both in x
+
+ align:start position:0%
+um but the solution to this is both in x
+ 
+
+ align:start position:0%
+um but the solution to this is both in x
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+t and the solution looks like this
+
+ align:start position:0%
+t and the solution looks like this
+ 
+
+ align:start position:0%
+t and the solution looks like this
+solution looks like
+
+ align:start position:0%
+solution looks like
+ 
+
+ align:start position:0%
+solution looks like
+this let's say we have an initial
+
+ align:start position:0%
+this let's say we have an initial
+ 
+
+ align:start position:0%
+this let's say we have an initial
+concentration c
+
+ align:start position:0%
+concentration c
+ 
+
+ align:start position:0%
+concentration c
+not C is a function of X so I have an
+
+ align:start position:0%
+not C is a function of X so I have an
+ 
+
+ align:start position:0%
+not C is a function of X so I have an
+initial nonzero concentration c not and
+
+ align:start position:0%
+initial nonzero concentration c not and
+ 
+
+ align:start position:0%
+initial nonzero concentration c not and
+I have a surface concentration fixed at
+
+ align:start position:0%
+I have a surface concentration fixed at
+ 
+
+ align:start position:0%
+I have a surface concentration fixed at
+Cs and this is the system that we're
+
+ align:start position:0%
+Cs and this is the system that we're
+ 
+
+ align:start position:0%
+Cs and this is the system that we're
+trying to model and the general
+
+ align:start position:0%
+trying to model and the general
+ 
+
+ align:start position:0%
+trying to model and the general
+solution the general solution to fixed
+
+ align:start position:0%
+solution the general solution to fixed
+ 
+
+ align:start position:0%
+solution the general solution to fixed
+Second Law is C of x and t is some
+
+ align:start position:0%
+Second Law is C of x and t is some
+ 
+
+ align:start position:0%
+Second Law is C of x and t is some
+constant a plus a constant B times a
+
+ align:start position:0%
+constant a plus a constant B times a
+ 
+
+ align:start position:0%
+constant a plus a constant B times a
+function which I'm going to Define for
+
+ align:start position:0%
+function which I'm going to Define for
+ 
+
+ align:start position:0%
+function which I'm going to Define for
+you in a second the error function
+
+ align:start position:0%
+you in a second the error function
+ 
+
+ align:start position:0%
+you in a second the error function
+gaussian error function of x / square
+
+ align:start position:0%
+gaussian error function of x / square
+ 
+
+ align:start position:0%
+gaussian error function of x / square
+roots of DT so these are both constants
+
+ align:start position:0%
+roots of DT so these are both constants
+ 
+
+ align:start position:0%
+roots of DT so these are both constants
+to be determined this is the gaussian
+
+ align:start position:0%
+to be determined this is the gaussian
+ 
+
+ align:start position:0%
+to be determined this is the gaussian
+error
+
+ align:start position:0%
+error
+ 
+
+ align:start position:0%
+error
+function the error function X's
+
+ align:start position:0%
+function the error function X's
+ 
+
+ align:start position:0%
+function the error function X's
+position T is time and D is the
+
+ align:start position:0%
+position T is time and D is the
+ 
+
+ align:start position:0%
+position T is time and D is the
+diffusion coefficient and this is
+
+ align:start position:0%
+diffusion coefficient and this is
+ 
+
+ align:start position:0%
+diffusion coefficient and this is
+nothing but a transcendental function
+
+ align:start position:0%
+nothing but a transcendental function
+ 
+
+ align:start position:0%
+nothing but a transcendental function
+that varies from 0 to one and you know I
+
+ align:start position:0%
+that varies from 0 to one and you know I
+ 
+
+ align:start position:0%
+that varies from 0 to one and you know I
+could have said s if I said it's sin x
+
+ align:start position:0%
+could have said s if I said it's sin x
+ 
+
+ align:start position:0%
+could have said s if I said it's sin x
+over uh 2 roots of DT you know the the
+
+ align:start position:0%
+over uh 2 roots of DT you know the the
+ 
+
+ align:start position:0%
+over uh 2 roots of DT you know the the
+definition of s it's got some weird
+
+ align:start position:0%
+definition of s it's got some weird
+ 
+
+ align:start position:0%
+definition of s it's got some weird
+integral and blah blah blah nobody pays
+
+ align:start position:0%
+integral and blah blah blah nobody pays
+ 
+
+ align:start position:0%
+integral and blah blah blah nobody pays
+any attention to it you know it goes
+
+ align:start position:0%
+any attention to it you know it goes
+ 
+
+ align:start position:0%
+any attention to it you know it goes
+from 0 to one it's linear low values of
+
+ align:start position:0%
+from 0 to one it's linear low values of
+ 
+
+ align:start position:0%
+from 0 to one it's linear low values of
+theta so what so we're going to learn
+
+ align:start position:0%
+theta so what so we're going to learn
+ 
+
+ align:start position:0%
+theta so what so we're going to learn
+what the properties of this are but I
+
+ align:start position:0%
+what the properties of this are but I
+ 
+
+ align:start position:0%
+what the properties of this are but I
+can tell you something right off the bat
+
+ align:start position:0%
+can tell you something right off the bat
+ 
+
+ align:start position:0%
+can tell you something right off the bat
+what do you think the shape of the error
+
+ align:start position:0%
+what do you think the shape of the error
+ 
+
+ align:start position:0%
+what do you think the shape of the error
+function is what's the shape of the
+
+ align:start position:0%
+function is what's the shape of the
+ 
+
+ align:start position:0%
+function is what's the shape of the
+error function that's the shape that's
+
+ align:start position:0%
+error function that's the shape that's
+ 
+
+ align:start position:0%
+error function that's the shape that's
+the shape okay that's what math is math
+
+ align:start position:0%
+the shape okay that's what math is math
+ 
+
+ align:start position:0%
+the shape okay that's what math is math
+is finding the
+
+ align:start position:0%
+is finding the
+ 
+
+ align:start position:0%
+is finding the
+shape otherwise doesn't make any sense
+
+ align:start position:0%
+shape otherwise doesn't make any sense
+ 
+
+ align:start position:0%
+shape otherwise doesn't make any sense
+and what are these These are scale
+
+ align:start position:0%
+and what are these These are scale
+ 
+
+ align:start position:0%
+and what are these These are scale
+factors you know you've done this on a
+
+ align:start position:0%
+factors you know you've done this on a
+ 
+
+ align:start position:0%
+factors you know you've done this on a
+computer where you take some image and
+
+ align:start position:0%
+computer where you take some image and
+ 
+
+ align:start position:0%
+computer where you take some image and
+you pull it you stretch it and so on and
+
+ align:start position:0%
+you pull it you stretch it and so on and
+ 
+
+ align:start position:0%
+you pull it you stretch it and so on and
+you can lock the aspect ratio right can
+
+ align:start position:0%
+you can lock the aspect ratio right can
+ 
+
+ align:start position:0%
+you can lock the aspect ratio right can
+lock the aspect R well that's all you're
+
+ align:start position:0%
+lock the aspect R well that's all you're
+ 
+
+ align:start position:0%
+lock the aspect R well that's all you're
+doing here mathematically we're going to
+
+ align:start position:0%
+doing here mathematically we're going to
+ 
+
+ align:start position:0%
+doing here mathematically we're going to
+pull this why are we going to pull it
+
+ align:start position:0%
+pull this why are we going to pull it
+ 
+
+ align:start position:0%
+pull this why are we going to pull it
+because at a later time it looks like
+
+ align:start position:0%
+because at a later time it looks like
+ 
+
+ align:start position:0%
+because at a later time it looks like
+this but the relationship between all of
+
+ align:start position:0%
+this but the relationship between all of
+ 
+
+ align:start position:0%
+this but the relationship between all of
+these points is the same so that's what
+
+ align:start position:0%
+these points is the same so that's what
+ 
+
+ align:start position:0%
+these points is the same so that's what
+math does if it doesn't fire it you know
+
+ align:start position:0%
+math does if it doesn't fire it you know
+ 
+
+ align:start position:0%
+math does if it doesn't fire it you know
+math works for you you don't work for
+
+ align:start position:0%
+math works for you you don't work for
+ 
+
+ align:start position:0%
+math works for you you don't work for
+math so let's put this thing to work
+
+ align:start position:0%
+math so let's put this thing to work
+ 
+
+ align:start position:0%
+math so let's put this thing to work
+lazy right so what we're going to do is
+
+ align:start position:0%
+lazy right so what we're going to do is
+ 
+
+ align:start position:0%
+lazy right so what we're going to do is
+we have to solve for A and B now you
+
+ align:start position:0%
+we have to solve for A and B now you
+ 
+
+ align:start position:0%
+we have to solve for A and B now you
+know that when you uh when you
+
+ align:start position:0%
+know that when you uh when you
+ 
+
+ align:start position:0%
+know that when you uh when you
+differentiate you throw away information
+
+ align:start position:0%
+differentiate you throw away information
+ 
+
+ align:start position:0%
+differentiate you throw away information
+all right so every time you throw away
+
+ align:start position:0%
+all right so every time you throw away
+ 
+
+ align:start position:0%
+all right so every time you throw away
+information we need to add some so we
+
+ align:start position:0%
+information we need to add some so we
+ 
+
+ align:start position:0%
+information we need to add some so we
+need to have one time based boundary
+
+ align:start position:0%
+need to have one time based boundary
+ 
+
+ align:start position:0%
+need to have one time based boundary
+condition and we need to have two
+
+ align:start position:0%
+condition and we need to have two
+ 
+
+ align:start position:0%
+condition and we need to have two
+spatially based boundary conditions
+
+ align:start position:0%
+spatially based boundary conditions
+ 
+
+ align:start position:0%
+spatially based boundary conditions
+because we threw away three bits of
+
+ align:start position:0%
+because we threw away three bits of
+ 
+
+ align:start position:0%
+because we threw away three bits of
+information so that's what we're going
+
+ align:start position:0%
+information so that's what we're going
+ 
+
+ align:start position:0%
+information so that's what we're going
+to do and if we go ahead and do that
+
+ align:start position:0%
+to do and if we go ahead and do that
+ 
+
+ align:start position:0%
+to do and if we go ahead and do that
+here's what the uh A and B will solve to
+
+ align:start position:0%
+here's what the uh A and B will solve to
+ 
+
+ align:start position:0%
+here's what the uh A and B will solve to
+and this works for all cases C minus the
+
+ align:start position:0%
+and this works for all cases C minus the
+ 
+
+ align:start position:0%
+and this works for all cases C minus the
+surface concentration divided by the
+
+ align:start position:0%
+surface concentration divided by the
+ 
+
+ align:start position:0%
+surface concentration divided by the
+initial concentration minus the surface
+
+ align:start position:0%
+initial concentration minus the surface
+ 
+
+ align:start position:0%
+initial concentration minus the surface
+Sur concentration equals error function
+
+ align:start position:0%
+Sur concentration equals error function
+ 
+
+ align:start position:0%
+Sur concentration equals error function
+of x/
+
+ align:start position:0%
+of x/
+ 
+
+ align:start position:0%
+of x/
+2 roots of DT so C is the what you're
+
+ align:start position:0%
+2 roots of DT so C is the what you're
+ 
+
+ align:start position:0%
+2 roots of DT so C is the what you're
+looking for this is c as a function of x
+
+ align:start position:0%
+looking for this is c as a function of x
+ 
+
+ align:start position:0%
+looking for this is c as a function of x
+and t CS is surface concentration Co is
+
+ align:start position:0%
+and t CS is surface concentration Co is
+ 
+
+ align:start position:0%
+and t CS is surface concentration Co is
+the uh initial concentration and let's
+
+ align:start position:0%
+the uh initial concentration and let's
+ 
+
+ align:start position:0%
+the uh initial concentration and let's
+take a look at what that
+
+ align:start position:0%
+take a look at what that
+ 
+
+ align:start position:0%
+take a look at what that
+function plots out to be so I'm going to
+
+ align:start position:0%
+function plots out to be so I'm going to
+ 
+
+ align:start position:0%
+function plots out to be so I'm going to
+plot Earth of
+
+ align:start position:0%
+plot Earth of
+ 
+
+ align:start position:0%
+plot Earth of
+Z Earth of Z as a function of Z it
+
+ align:start position:0%
+Z Earth of Z as a function of Z it
+ 
+
+ align:start position:0%
+Z Earth of Z as a function of Z it
+varies from 0 to
+
+ align:start position:0%
+varies from 0 to
+ 
+
+ align:start position:0%
+varies from 0 to
+one and it starts off like so many
+
+ align:start position:0%
+one and it starts off like so many
+ 
+
+ align:start position:0%
+one and it starts off like so many
+functions it's linear for low values of
+
+ align:start position:0%
+functions it's linear for low values of
+ 
+
+ align:start position:0%
+functions it's linear for low values of
+Z Earth of Z equals z and in fact up to
+
+ align:start position:0%
+Z Earth of Z equals z and in fact up to
+ 
+
+ align:start position:0%
+Z Earth of Z equals z and in fact up to
+about
+
+ align:start position:0%
+about
+ 
+
+ align:start position:0%
+about
+0.6 you're good to within 1% Earth of Z
+
+ align:start position:0%
+0.6 you're good to within 1% Earth of Z
+ 
+
+ align:start position:0%
+0.6 you're good to within 1% Earth of Z
+equals z to within 1% and then once it
+
+ align:start position:0%
+equals z to within 1% and then once it
+ 
+
+ align:start position:0%
+equals z to within 1% and then once it
+gets up to0 6 then it starts to Veer off
+
+ align:start position:0%
+gets up to0 6 then it starts to Veer off
+ 
+
+ align:start position:0%
+gets up to0 6 then it starts to Veer off
+and then ASM totically
+
+ align:start position:0%
+and then ASM totically
+ 
+
+ align:start position:0%
+and then ASM totically
+approach uh Earth
+
+ align:start position:0%
+approach uh Earth
+ 
+
+ align:start position:0%
+approach uh Earth
+uh Earth Z equals 1 so in fact we can
+
+ align:start position:0%
+uh Earth Z equals 1 so in fact we can
+ 
+
+ align:start position:0%
+uh Earth Z equals 1 so in fact we can
+write here Earth of Earth of one equals
+
+ align:start position:0%
+write here Earth of Earth of one equals
+ 
+
+ align:start position:0%
+write here Earth of Earth of one equals
+0.84 so you can see now it's not linear
+
+ align:start position:0%
+0.84 so you can see now it's not linear
+ 
+
+ align:start position:0%
+0.84 so you can see now it's not linear
+and Earth of two equals
+
+ align:start position:0%
+and Earth of two equals
+ 
+
+ align:start position:0%
+and Earth of two equals
+0.995 so once you get out here to two
+
+ align:start position:0%
+0.995 so once you get out here to two
+ 
+
+ align:start position:0%
+0.995 so once you get out here to two
+you're practically at the ASM toote and
+
+ align:start position:0%
+you're practically at the ASM toote and
+ 
+
+ align:start position:0%
+you're practically at the ASM toote and
+it's defined here's the integral it's
+
+ align:start position:0%
+it's defined here's the integral it's
+ 
+
+ align:start position:0%
+it's defined here's the integral it's
+defined Earth of Z is the integral from
+
+ align:start position:0%
+defined Earth of Z is the integral from
+ 
+
+ align:start position:0%
+defined Earth of Z is the integral from
+Z
+
+ align:start position:0%
+Z
+ 
+
+ align:start position:0%
+Z
+from zero Pardon Me 0 to Z of e to the
+
+ align:start position:0%
+from zero Pardon Me 0 to Z of e to the
+ 
+
+ align:start position:0%
+from zero Pardon Me 0 to Z of e to the
+minus u^2 du so that's that's this e to
+
+ align:start position:0%
+minus u^2 du so that's that's this e to
+ 
+
+ align:start position:0%
+minus u^2 du so that's that's this e to
+Theus u^ 2 e to Theus u^2 as a function
+
+ align:start position:0%
+Theus u^ 2 e to Theus u^2 as a function
+ 
+
+ align:start position:0%
+Theus u^ 2 e to Theus u^2 as a function
+of U is the gaussian error function
+
+ align:start position:0%
+of U is the gaussian error function
+ 
+
+ align:start position:0%
+of U is the gaussian error function
+right that's the bell curve so this is
+
+ align:start position:0%
+right that's the bell curve so this is
+ 
+
+ align:start position:0%
+right that's the bell curve so this is
+the area under the bell curve if we
+
+ align:start position:0%
+the area under the bell curve if we
+ 
+
+ align:start position:0%
+the area under the bell curve if we
+start at X at U equals z we're going to
+
+ align:start position:0%
+start at X at U equals z we're going to
+ 
+
+ align:start position:0%
+start at X at U equals z we're going to
+integrate as far as we need to out here
+
+ align:start position:0%
+integrate as far as we need to out here
+ 
+
+ align:start position:0%
+integrate as far as we need to out here
+and the integral from 0 to Infinity of
+
+ align:start position:0%
+and the integral from 0 to Infinity of
+ 
+
+ align:start position:0%
+and the integral from 0 to Infinity of
+this thing isun Pi / 2 two and we want
+
+ align:start position:0%
+this thing isun Pi / 2 two and we want
+ 
+
+ align:start position:0%
+this thing isun Pi / 2 two and we want
+this to go from 0 to 1 so we'll put the
+
+ align:start position:0%
+this to go from 0 to 1 so we'll put the
+ 
+
+ align:start position:0%
+this to go from 0 to 1 so we'll put the
+factor 2 overun pi out in front and that
+
+ align:start position:0%
+factor 2 overun pi out in front and that
+ 
+
+ align:start position:0%
+factor 2 overun pi out in front and that
+way when we integrate this from zero to
+
+ align:start position:0%
+way when we integrate this from zero to
+ 
+
+ align:start position:0%
+way when we integrate this from zero to
+Infinity Earth of infinity becomes one
+
+ align:start position:0%
+Infinity Earth of infinity becomes one
+ 
+
+ align:start position:0%
+Infinity Earth of infinity becomes one
+so Earth runs from 0 to one and that's
+
+ align:start position:0%
+so Earth runs from 0 to one and that's
+ 
+
+ align:start position:0%
+so Earth runs from 0 to one and that's
+the area under this curve so that's why
+
+ align:start position:0%
+the area under this curve so that's why
+ 
+
+ align:start position:0%
+the area under this curve so that's why
+some people call this the gaussian error
+
+ align:start position:0%
+some people call this the gaussian error
+ 
+
+ align:start position:0%
+some people call this the gaussian error
+function because the gaussian curve is
+
+ align:start position:0%
+function because the gaussian curve is
+ 
+
+ align:start position:0%
+function because the gaussian curve is
+associated with random statistics in
+
+ align:start position:0%
+associated with random statistics in
+ 
+
+ align:start position:0%
+associated with random statistics in
+terms of of Errors so this now is the
+
+ align:start position:0%
+terms of of Errors so this now is the
+ 
+
+ align:start position:0%
+terms of of Errors so this now is the
+template this is the template if I have
+
+ align:start position:0%
+template this is the template if I have
+ 
+
+ align:start position:0%
+template this is the template if I have
+uh any reaction this is all I have to
+
+ align:start position:0%
+uh any reaction this is all I have to
+ 
+
+ align:start position:0%
+uh any reaction this is all I have to
+fit using these um using
+
+ align:start position:0%
+fit using these um using
+ 
+
+ align:start position:0%
+fit using these um using
+these multiplication factors so let's
+
+ align:start position:0%
+these multiplication factors so let's
+ 
+
+ align:start position:0%
+these multiplication factors so let's
+play Mr dress up here and we're going to
+
+ align:start position:0%
+play Mr dress up here and we're going to
+ 
+
+ align:start position:0%
+play Mr dress up here and we're going to
+just use this function to describe all
+
+ align:start position:0%
+just use this function to describe all
+ 
+
+ align:start position:0%
+just use this function to describe all
+of the typical uh industrial processes
+
+ align:start position:0%
+of the typical uh industrial processes
+ 
+
+ align:start position:0%
+of the typical uh industrial processes
+so there's only two types of processes
+
+ align:start position:0%
+so there's only two types of processes
+ 
+
+ align:start position:0%
+so there's only two types of processes
+those that are diffusing substance in
+
+ align:start position:0%
+those that are diffusing substance in
+ 
+
+ align:start position:0%
+those that are diffusing substance in
+and then those that are pulling
+
+ align:start position:0%
+and then those that are pulling
+ 
+
+ align:start position:0%
+and then those that are pulling
+substance out so let's look at the two
+
+ align:start position:0%
+substance out so let's look at the two
+ 
+
+ align:start position:0%
+substance out so let's look at the two
+cases so let's look first of all at the
+
+ align:start position:0%
+cases so let's look first of all at the
+ 
+
+ align:start position:0%
+cases so let's look first of all at the
+one that's uh showing right up there so
+
+ align:start position:0%
+one that's uh showing right up there so
+ 
+
+ align:start position:0%
+one that's uh showing right up there so
+this would be for something like out
+
+ align:start position:0%
+this would be for something like out
+ 
+
+ align:start position:0%
+this would be for something like out
+gassing out gassing or uh drying many uh
+
+ align:start position:0%
+gassing out gassing or uh drying many uh
+ 
+
+ align:start position:0%
+gassing out gassing or uh drying many uh
+many processes involve drying which is
+
+ align:start position:0%
+many processes involve drying which is
+ 
+
+ align:start position:0%
+many processes involve drying which is
+to get the water out of the um content
+
+ align:start position:0%
+to get the water out of the um content
+ 
+
+ align:start position:0%
+to get the water out of the um content
+of a of a solid piece and so as you can
+
+ align:start position:0%
+of a of a solid piece and so as you can
+ 
+
+ align:start position:0%
+of a of a solid piece and so as you can
+imagine you've got some initial
+
+ align:start position:0%
+imagine you've got some initial
+ 
+
+ align:start position:0%
+imagine you've got some initial
+concentration C notot and you take the
+
+ align:start position:0%
+concentration C notot and you take the
+ 
+
+ align:start position:0%
+concentration C notot and you take the
+surface concentration whatever this is
+
+ align:start position:0%
+surface concentration whatever this is
+ 
+
+ align:start position:0%
+surface concentration whatever this is
+and obviously if you want to draw
+
+ align:start position:0%
+and obviously if you want to draw
+ 
+
+ align:start position:0%
+and obviously if you want to draw
+something out and move matter from right
+
+ align:start position:0%
+something out and move matter from right
+ 
+
+ align:start position:0%
+something out and move matter from right
+to left then the surface concentration
+
+ align:start position:0%
+to left then the surface concentration
+ 
+
+ align:start position:0%
+to left then the surface concentration
+by necessity must be less than the
+
+ align:start position:0%
+by necessity must be less than the
+ 
+
+ align:start position:0%
+by necessity must be less than the
+initial concentration otherwise why is
+
+ align:start position:0%
+initial concentration otherwise why is
+ 
+
+ align:start position:0%
+initial concentration otherwise why is
+something going to move so this means
+
+ align:start position:0%
+something going to move so this means
+ 
+
+ align:start position:0%
+something going to move so this means
+this I'll call
+
+ align:start position:0%
+this I'll call
+ 
+
+ align:start position:0%
+this I'll call
+effusion something is eusing so this is
+
+ align:start position:0%
+effusion something is eusing so this is
+ 
+
+ align:start position:0%
+effusion something is eusing so this is
+a fusion the flux is moving from right
+
+ align:start position:0%
+a fusion the flux is moving from right
+ 
+
+ align:start position:0%
+a fusion the flux is moving from right
+to left and the the determinant here is
+
+ align:start position:0%
+to left and the the determinant here is
+ 
+
+ align:start position:0%
+to left and the the determinant here is
+c not is greater than CS the surface
+
+ align:start position:0%
+c not is greater than CS the surface
+ 
+
+ align:start position:0%
+c not is greater than CS the surface
+concentration is less than the initial
+
+ align:start position:0%
+concentration is less than the initial
+ 
+
+ align:start position:0%
+concentration is less than the initial
+concentration so I'm going to pin the
+
+ align:start position:0%
+concentration so I'm going to pin the
+ 
+
+ align:start position:0%
+concentration so I'm going to pin the
+concentration at CS I've got c0 deep
+
+ align:start position:0%
+concentration at CS I've got c0 deep
+ 
+
+ align:start position:0%
+concentration at CS I've got c0 deep
+inside and this is telling me what the
+
+ align:start position:0%
+inside and this is telling me what the
+ 
+
+ align:start position:0%
+inside and this is telling me what the
+shape of the curve is this is telling me
+
+ align:start position:0%
+shape of the curve is this is telling me
+ 
+
+ align:start position:0%
+shape of the curve is this is telling me
+what the shape of the curve is so I just
+
+ align:start position:0%
+what the shape of the curve is so I just
+ 
+
+ align:start position:0%
+what the shape of the curve is so I just
+write with impunity cus CS over C minus
+
+ align:start position:0%
+write with impunity cus CS over C minus
+ 
+
+ align:start position:0%
+write with impunity cus CS over C minus
+CS equals error function X over two 2
+
+ align:start position:0%
+CS equals error function X over two 2
+ 
+
+ align:start position:0%
+CS equals error function X over two 2
+roots of
+
+ align:start position:0%
+roots of
+ 
+
+ align:start position:0%
+roots of
+DT and that's the answer for all such
+
+ align:start position:0%
+DT and that's the answer for all such
+ 
+
+ align:start position:0%
+DT and that's the answer for all such
+problems and because it's linear it
+
+ align:start position:0%
+problems and because it's linear it
+ 
+
+ align:start position:0%
+problems and because it's linear it
+doesn't matter if I change the initial
+
+ align:start position:0%
+doesn't matter if I change the initial
+ 
+
+ align:start position:0%
+doesn't matter if I change the initial
+concentration to a new value I can just
+
+ align:start position:0%
+concentration to a new value I can just
+ 
+
+ align:start position:0%
+concentration to a new value I can just
+add we can add and multiply because it's
+
+ align:start position:0%
+add we can add and multiply because it's
+ 
+
+ align:start position:0%
+add we can add and multiply because it's
+a linear equation linear functionality
+
+ align:start position:0%
+a linear equation linear functionality
+ 
+
+ align:start position:0%
+a linear equation linear functionality
+and I think here we've got some uh oh
+
+ align:start position:0%
+and I think here we've got some uh oh
+ 
+
+ align:start position:0%
+and I think here we've got some uh oh
+yeah we looked at those this is the
+
+ align:start position:0%
+yeah we looked at those this is the
+ 
+
+ align:start position:0%
+yeah we looked at those this is the
+tabulation this is in the uh
+
+ align:start position:0%
+tabulation this is in the uh
+ 
+
+ align:start position:0%
+tabulation this is in the uh
+supplemental text there's a table of uh
+
+ align:start position:0%
+supplemental text there's a table of uh
+ 
+
+ align:start position:0%
+supplemental text there's a table of uh
+error function values so that if you
+
+ align:start position:0%
+error function values so that if you
+ 
+
+ align:start position:0%
+error function values so that if you
+happen to get into this regime Beyond um
+
+ align:start position:0%
+happen to get into this regime Beyond um
+ 
+
+ align:start position:0%
+happen to get into this regime Beyond um
+Z equals 0.6 you'll you'll have the the
+
+ align:start position:0%
+Z equals 0.6 you'll you'll have the the
+ 
+
+ align:start position:0%
+Z equals 0.6 you'll you'll have the the
+values that you
+
+ align:start position:0%
+values that you
+ 
+
+ align:start position:0%
+values that you
+need so let's look at another case let's
+
+ align:start position:0%
+need so let's look at another case let's
+ 
+
+ align:start position:0%
+need so let's look at another case let's
+look at driving material in so that for
+
+ align:start position:0%
+look at driving material in so that for
+ 
+
+ align:start position:0%
+look at driving material in so that for
+for example is something like um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+doping doping or
+
+ align:start position:0%
+doping doping or
+ 
+
+ align:start position:0%
+doping doping or
+nitriding doping nitriding
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+carburising if we want to case harden a
+
+ align:start position:0%
+carburising if we want to case harden a
+ 
+
+ align:start position:0%
+carburising if we want to case harden a
+material will raise the carbon content
+
+ align:start position:0%
+material will raise the carbon content
+ 
+
+ align:start position:0%
+material will raise the carbon content
+at the free surface have something
+
+ align:start position:0%
+at the free surface have something
+ 
+
+ align:start position:0%
+at the free surface have something
+that's soft and ductile inside all right
+
+ align:start position:0%
+that's soft and ductile inside all right
+ 
+
+ align:start position:0%
+that's soft and ductile inside all right
+so for that here's the here's the scheme
+
+ align:start position:0%
+so for that here's the here's the scheme
+ 
+
+ align:start position:0%
+so for that here's the here's the scheme
+here's the scheme we have a surface
+
+ align:start position:0%
+here's the scheme we have a surface
+ 
+
+ align:start position:0%
+here's the scheme we have a surface
+concentration
+
+ align:start position:0%
+concentration
+ 
+
+ align:start position:0%
+concentration
+CS we have an initial
+
+ align:start position:0%
+CS we have an initial
+ 
+
+ align:start position:0%
+CS we have an initial
+concentration this is getting a little
+
+ align:start position:0%
+concentration this is getting a little
+ 
+
+ align:start position:0%
+concentration this is getting a little
+crowded let me clean this up surface
+
+ align:start position:0%
+crowded let me clean this up surface
+ 
+
+ align:start position:0%
+crowded let me clean this up surface
+concentration CS an initial
+
+ align:start position:0%
+concentration CS an initial
+ 
+
+ align:start position:0%
+concentration CS an initial
+concentration c not and in this case C
+
+ align:start position:0%
+concentration c not and in this case C
+ 
+
+ align:start position:0%
+concentration c not and in this case C
+not is less than CS surface
+
+ align:start position:0%
+not is less than CS surface
+ 
+
+ align:start position:0%
+not is less than CS surface
+concentration is higher so material now
+
+ align:start position:0%
+concentration is higher so material now
+ 
+
+ align:start position:0%
+concentration is higher so material now
+wants to move from left to right and so
+
+ align:start position:0%
+wants to move from left to right and so
+ 
+
+ align:start position:0%
+wants to move from left to right and so
+this is
+
+ align:start position:0%
+this is
+ 
+
+ align:start position:0%
+this is
+infusion
+
+ align:start position:0%
+infusion
+ 
+
+ align:start position:0%
+infusion
+infusion and what's the curve going to
+
+ align:start position:0%
+infusion and what's the curve going to
+ 
+
+ align:start position:0%
+infusion and what's the curve going to
+look like it looks like this looks like
+
+ align:start position:0%
+look like it looks like this looks like
+ 
+
+ align:start position:0%
+look like it looks like this looks like
+this which is simply that
+
+ align:start position:0%
+this which is simply that
+ 
+
+ align:start position:0%
+this which is simply that
+one flipped upside down by subtracting
+
+ align:start position:0%
+one flipped upside down by subtracting
+ 
+
+ align:start position:0%
+one flipped upside down by subtracting
+it from from one which I'll show you in
+
+ align:start position:0%
+it from from one which I'll show you in
+ 
+
+ align:start position:0%
+it from from one which I'll show you in
+a second and again this same general
+
+ align:start position:0%
+a second and again this same general
+ 
+
+ align:start position:0%
+a second and again this same general
+solution applies the same general
+
+ align:start position:0%
+solution applies the same general
+ 
+
+ align:start position:0%
+solution applies the same general
+solution applies whether C the surface
+
+ align:start position:0%
+solution applies whether C the surface
+ 
+
+ align:start position:0%
+solution applies whether C the surface
+concentration is higher or lower than
+
+ align:start position:0%
+concentration is higher or lower than
+ 
+
+ align:start position:0%
+concentration is higher or lower than
+the uh initial bulk concentration it
+
+ align:start position:0%
+the uh initial bulk concentration it
+ 
+
+ align:start position:0%
+the uh initial bulk concentration it
+comes out in the math here so again we
+
+ align:start position:0%
+comes out in the math here so again we
+ 
+
+ align:start position:0%
+comes out in the math here so again we
+write c - CS over c - CS equal Earth X
+
+ align:start position:0%
+write c - CS over c - CS equal Earth X
+ 
+
+ align:start position:0%
+write c - CS over c - CS equal Earth X
+over two roots of
+
+ align:start position:0%
+over two roots of
+ 
+
+ align:start position:0%
+over two roots of
+DT and this one comes up very of this is
+
+ align:start position:0%
+DT and this one comes up very of this is
+ 
+
+ align:start position:0%
+DT and this one comes up very of this is
+the way it works in doping of
+
+ align:start position:0%
+the way it works in doping of
+ 
+
+ align:start position:0%
+the way it works in doping of
+semiconductors and comes up so often
+
+ align:start position:0%
+semiconductors and comes up so often
+ 
+
+ align:start position:0%
+semiconductors and comes up so often
+that uh it it's convenient to Define uh
+
+ align:start position:0%
+that uh it it's convenient to Define uh
+ 
+
+ align:start position:0%
+that uh it it's convenient to Define uh
+another function where in many instances
+
+ align:start position:0%
+another function where in many instances
+ 
+
+ align:start position:0%
+another function where in many instances
+uh c not equals zero right when we're
+
+ align:start position:0%
+uh c not equals zero right when we're
+ 
+
+ align:start position:0%
+uh c not equals zero right when we're
+doping pure silicon the initial
+
+ align:start position:0%
+doping pure silicon the initial
+ 
+
+ align:start position:0%
+doping pure silicon the initial
+concentration of boron or phosphorus and
+
+ align:start position:0%
+concentration of boron or phosphorus and
+ 
+
+ align:start position:0%
+concentration of boron or phosphorus and
+pure silicon is going to be zero so for
+
+ align:start position:0%
+pure silicon is going to be zero so for
+ 
+
+ align:start position:0%
+pure silicon is going to be zero so for
+many of those so for many of those cases
+
+ align:start position:0%
+many of those so for many of those cases
+ 
+
+ align:start position:0%
+many of those so for many of those cases
+you'll end up with something that if you
+
+ align:start position:0%
+you'll end up with something that if you
+ 
+
+ align:start position:0%
+you'll end up with something that if you
+go through the math this is a zero
+
+ align:start position:0%
+go through the math this is a zero
+ 
+
+ align:start position:0%
+go through the math this is a zero
+transpose you'll end up with this as the
+
+ align:start position:0%
+transpose you'll end up with this as the
+ 
+
+ align:start position:0%
+transpose you'll end up with this as the
+solution Cal CS
+
+ align:start position:0%
+solution Cal CS
+ 
+
+ align:start position:0%
+solution Cal CS
+times the complimentary error function
+
+ align:start position:0%
+times the complimentary error function
+ 
+
+ align:start position:0%
+times the complimentary error function
+Earth complement X over two roots of DT
+
+ align:start position:0%
+Earth complement X over two roots of DT
+ 
+
+ align:start position:0%
+Earth complement X over two roots of DT
+where the complimentary error function
+
+ align:start position:0%
+where the complimentary error function
+ 
+
+ align:start position:0%
+where the complimentary error function
+Earth complement of Z is simply 1 minus
+
+ align:start position:0%
+Earth complement of Z is simply 1 minus
+ 
+
+ align:start position:0%
+Earth complement of Z is simply 1 minus
+Earth of Z so if you see that in the
+
+ align:start position:0%
+Earth of Z so if you see that in the
+ 
+
+ align:start position:0%
+Earth of Z so if you see that in the
+literature that's all they're all
+
+ align:start position:0%
+literature that's all they're all
+ 
+
+ align:start position:0%
+literature that's all they're all
+they're doing so now the question is
+
+ align:start position:0%
+they're doing so now the question is
+ 
+
+ align:start position:0%
+they're doing so now the question is
+I've told you that there's special
+
+ align:start position:0%
+I've told you that there's special
+ 
+
+ align:start position:0%
+I've told you that there's special
+conditions that validate the error
+
+ align:start position:0%
+conditions that validate the error
+ 
+
+ align:start position:0%
+conditions that validate the error
+function Solutions what are the
+
+ align:start position:0%
+function Solutions what are the
+ 
+
+ align:start position:0%
+function Solutions what are the
+conditions when when to use
+
+ align:start position:0%
+conditions when when to use
+ 
+
+ align:start position:0%
+conditions when when to use
+earth when to use Earth because that's
+
+ align:start position:0%
+earth when to use Earth because that's
+ 
+
+ align:start position:0%
+earth when to use Earth because that's
+not the only solution to fix second law
+
+ align:start position:0%
+not the only solution to fix second law
+ 
+
+ align:start position:0%
+not the only solution to fix second law
+when these are the conditions C of
+
+ align:start position:0%
+when these are the conditions C of
+ 
+
+ align:start position:0%
+when these are the conditions C of
+X at Time Zero is a constant so this is
+
+ align:start position:0%
+X at Time Zero is a constant so this is
+ 
+
+ align:start position:0%
+X at Time Zero is a constant so this is
+boundary condition number one boundary
+
+ align:start position:0%
+boundary condition number one boundary
+ 
+
+ align:start position:0%
+boundary condition number one boundary
+condition number one
+
+ align:start position:0%
+condition number one
+ 
+
+ align:start position:0%
+condition number one
+we threw away some time data so here's
+
+ align:start position:0%
+we threw away some time data so here's
+ 
+
+ align:start position:0%
+we threw away some time data so here's
+data at time equals zero the initial
+
+ align:start position:0%
+data at time equals zero the initial
+ 
+
+ align:start position:0%
+data at time equals zero the initial
+condition this is called the initial
+
+ align:start position:0%
+condition this is called the initial
+ 
+
+ align:start position:0%
+condition this is called the initial
+condition initial condition must be a
+
+ align:start position:0%
+condition initial condition must be a
+ 
+
+ align:start position:0%
+condition initial condition must be a
+constant and that's okay there are many
+
+ align:start position:0%
+constant and that's okay there are many
+ 
+
+ align:start position:0%
+constant and that's okay there are many
+systems for which the initial value of
+
+ align:start position:0%
+systems for which the initial value of
+ 
+
+ align:start position:0%
+systems for which the initial value of
+the material that's being diffused is
+
+ align:start position:0%
+the material that's being diffused is
+ 
+
+ align:start position:0%
+the material that's being diffused is
+constant throughout the material as
+
+ align:start position:0%
+constant throughout the material as
+ 
+
+ align:start position:0%
+constant throughout the material as
+opposed to bopping all over the place or
+
+ align:start position:0%
+opposed to bopping all over the place or
+ 
+
+ align:start position:0%
+opposed to bopping all over the place or
+maybe already having some kind of a
+
+ align:start position:0%
+maybe already having some kind of a
+ 
+
+ align:start position:0%
+maybe already having some kind of a
+gradient as long as you can make this
+
+ align:start position:0%
+gradient as long as you can make this
+ 
+
+ align:start position:0%
+gradient as long as you can make this
+assumption you're on the road now we
+
+ align:start position:0%
+assumption you're on the road now we
+ 
+
+ align:start position:0%
+assumption you're on the road now we
+need two more boundary conditions we
+
+ align:start position:0%
+need two more boundary conditions we
+ 
+
+ align:start position:0%
+need two more boundary conditions we
+need boundary conditions two and three
+
+ align:start position:0%
+need boundary conditions two and three
+ 
+
+ align:start position:0%
+need boundary conditions two and three
+over here because we got a double
+
+ align:start position:0%
+over here because we got a double
+ 
+
+ align:start position:0%
+over here because we got a double
+derivative right you got a some function
+
+ align:start position:0%
+derivative right you got a some function
+ 
+
+ align:start position:0%
+derivative right you got a some function
+plus constant when you do d by DX
+
+ align:start position:0%
+plus constant when you do d by DX
+ 
+
+ align:start position:0%
+plus constant when you do d by DX
+constant goes into the trash bin we need
+
+ align:start position:0%
+constant goes into the trash bin we need
+ 
+
+ align:start position:0%
+constant goes into the trash bin we need
+to recover that information somehow so
+
+ align:start position:0%
+to recover that information somehow so
+ 
+
+ align:start position:0%
+to recover that information somehow so
+here's what I've got I've got C for x
+
+ align:start position:0%
+here's what I've got I've got C for x
+ 
+
+ align:start position:0%
+here's what I've got I've got C for x
+equals z at all time is a constant the
+
+ align:start position:0%
+equals z at all time is a constant the
+ 
+
+ align:start position:0%
+equals z at all time is a constant the
+surface concentration is fixed as a
+
+ align:start position:0%
+surface concentration is fixed as a
+ 
+
+ align:start position:0%
+surface concentration is fixed as a
+constant okay and you say well well what
+
+ align:start position:0%
+constant okay and you say well well what
+ 
+
+ align:start position:0%
+constant okay and you say well well what
+else could it be well I could have a
+
+ align:start position:0%
+else could it be well I could have a
+ 
+
+ align:start position:0%
+else could it be well I could have a
+slowly Rising surface concentration or I
+
+ align:start position:0%
+slowly Rising surface concentration or I
+ 
+
+ align:start position:0%
+slowly Rising surface concentration or I
+could have a surface concentration that
+
+ align:start position:0%
+could have a surface concentration that
+ 
+
+ align:start position:0%
+could have a surface concentration that
+varies sinusoidally or something those
+
+ align:start position:0%
+varies sinusoidally or something those
+ 
+
+ align:start position:0%
+varies sinusoidally or something those
+won't work it must be fixed at a
+
+ align:start position:0%
+won't work it must be fixed at a
+ 
+
+ align:start position:0%
+won't work it must be fixed at a
+constant value so that's one so this is
+
+ align:start position:0%
+constant value so that's one so this is
+ 
+
+ align:start position:0%
+constant value so that's one so this is
+boundary condition this is boundary
+
+ align:start position:0%
+boundary condition this is boundary
+ 
+
+ align:start position:0%
+boundary condition this is boundary
+condition number one this is boundary
+
+ align:start position:0%
+condition number one this is boundary
+ 
+
+ align:start position:0%
+condition number one this is boundary
+condition boundary condition number two
+
+ align:start position:0%
+condition boundary condition number two
+ 
+
+ align:start position:0%
+condition boundary condition number two
+and then I've got I need a third one and
+
+ align:start position:0%
+and then I've got I need a third one and
+ 
+
+ align:start position:0%
+and then I've got I need a third one and
+the third one I'm going to get is this
+
+ align:start position:0%
+the third one I'm going to get is this
+ 
+
+ align:start position:0%
+the third one I'm going to get is this
+one I'm going to give you it looks funny
+
+ align:start position:0%
+one I'm going to give you it looks funny
+ 
+
+ align:start position:0%
+one I'm going to give you it looks funny
+when I write it mathematically but
+
+ align:start position:0%
+when I write it mathematically but
+ 
+
+ align:start position:0%
+when I write it mathematically but
+you'll you'll understand what I mean in
+
+ align:start position:0%
+you'll you'll understand what I mean in
+ 
+
+ align:start position:0%
+you'll you'll understand what I mean in
+a second uh at Infinity
+
+ align:start position:0%
+a second uh at Infinity
+ 
+
+ align:start position:0%
+a second uh at Infinity
+the concentration doesn't change you say
+
+ align:start position:0%
+the concentration doesn't change you say
+ 
+
+ align:start position:0%
+the concentration doesn't change you say
+well duh but this really has this really
+
+ align:start position:0%
+well duh but this really has this really
+ 
+
+ align:start position:0%
+well duh but this really has this really
+has some meaning we know that our we
+
+ align:start position:0%
+has some meaning we know that our we
+ 
+
+ align:start position:0%
+has some meaning we know that our we
+know that the size of our of our uh
+
+ align:start position:0%
+know that the size of our of our uh
+ 
+
+ align:start position:0%
+know that the size of our of our uh
+piece is not infinite but here's what
+
+ align:start position:0%
+piece is not infinite but here's what
+ 
+
+ align:start position:0%
+piece is not infinite but here's what
+we're assuming we're assuming that over
+
+ align:start position:0%
+we're assuming we're assuming that over
+ 
+
+ align:start position:0%
+we're assuming we're assuming that over
+the time scale of the process that for
+
+ align:start position:0%
+the time scale of the process that for
+ 
+
+ align:start position:0%
+the time scale of the process that for
+all intents and purposes the dimension
+
+ align:start position:0%
+all intents and purposes the dimension
+ 
+
+ align:start position:0%
+all intents and purposes the dimension
+of the Silicon wafer for example is so
+
+ align:start position:0%
+of the Silicon wafer for example is so
+ 
+
+ align:start position:0%
+of the Silicon wafer for example is so
+large in comparison to the depth of the
+
+ align:start position:0%
+large in comparison to the depth of the
+ 
+
+ align:start position:0%
+large in comparison to the depth of the
+diffusion profile file that assuming
+
+ align:start position:0%
+diffusion profile file that assuming
+ 
+
+ align:start position:0%
+diffusion profile file that assuming
+assuming that the wafer is semi infinite
+
+ align:start position:0%
+assuming that the wafer is semi infinite
+ 
+
+ align:start position:0%
+assuming that the wafer is semi infinite
+because we've got to diffusing in from
+
+ align:start position:0%
+because we've got to diffusing in from
+ 
+
+ align:start position:0%
+because we've got to diffusing in from
+both sides all right but let's just
+
+ align:start position:0%
+both sides all right but let's just
+ 
+
+ align:start position:0%
+both sides all right but let's just
+assume from the one side that we can
+
+ align:start position:0%
+assume from the one side that we can
+ 
+
+ align:start position:0%
+assume from the one side that we can
+assume that it's infinite because
+
+ align:start position:0%
+assume that it's infinite because
+ 
+
+ align:start position:0%
+assume that it's infinite because
+ultimately what happens if we wait long
+
+ align:start position:0%
+ultimately what happens if we wait long
+ 
+
+ align:start position:0%
+ultimately what happens if we wait long
+enough we start to have a tail over here
+
+ align:start position:0%
+enough we start to have a tail over here
+ 
+
+ align:start position:0%
+enough we start to have a tail over here
+because the system still thinks that the
+
+ align:start position:0%
+because the system still thinks that the
+ 
+
+ align:start position:0%
+because the system still thinks that the
+wafer exists but we're saying no it it
+
+ align:start position:0%
+wafer exists but we're saying no it it
+ 
+
+ align:start position:0%
+wafer exists but we're saying no it it
+stops here but this value is so small
+
+ align:start position:0%
+stops here but this value is so small
+ 
+
+ align:start position:0%
+stops here but this value is so small
+during the time scale of the uh process
+
+ align:start position:0%
+during the time scale of the uh process
+ 
+
+ align:start position:0%
+during the time scale of the uh process
+that we can neglect it and by allowing
+
+ align:start position:0%
+that we can neglect it and by allowing
+ 
+
+ align:start position:0%
+that we can neglect it and by allowing
+ourselves to assume that the material is
+
+ align:start position:0%
+ourselves to assume that the material is
+ 
+
+ align:start position:0%
+ourselves to assume that the material is
+semi-infinite it simplifies the math if
+
+ align:start position:0%
+semi-infinite it simplifies the math if
+ 
+
+ align:start position:0%
+semi-infinite it simplifies the math if
+we have a finite sized piece a finite
+
+ align:start position:0%
+we have a finite sized piece a finite
+ 
+
+ align:start position:0%
+we have a finite sized piece a finite
+size specimen we can't use this
+
+ align:start position:0%
+size specimen we can't use this
+ 
+
+ align:start position:0%
+size specimen we can't use this
+simplified solution and things get very
+
+ align:start position:0%
+simplified solution and things get very
+ 
+
+ align:start position:0%
+simplified solution and things get very
+very messy but there's another way of
+
+ align:start position:0%
+very messy but there's another way of
+ 
+
+ align:start position:0%
+very messy but there's another way of
+expressing it there's another way of
+
+ align:start position:0%
+expressing it there's another way of
+ 
+
+ align:start position:0%
+expressing it there's another way of
+expressing it you see this relationship
+
+ align:start position:0%
+expressing it you see this relationship
+ 
+
+ align:start position:0%
+expressing it you see this relationship
+it's always Earth X over 2 * the < TK of
+
+ align:start position:0%
+it's always Earth X over 2 * the < TK of
+ 
+
+ align:start position:0%
+it's always Earth X over 2 * the < TK of
+DT look it something would be infinite
+
+ align:start position:0%
+DT look it something would be infinite
+ 
+
+ align:start position:0%
+DT look it something would be infinite
+would mean it was it's very large
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+large Dimension let's say large length
+
+ align:start position:0%
+large Dimension let's say large length
+ 
+
+ align:start position:0%
+large Dimension let's say large length
+scale large length
+
+ align:start position:0%
+scale large length
+ 
+
+ align:start position:0%
+scale large length
+scale that's a large physical Dimension
+
+ align:start position:0%
+scale that's a large physical Dimension
+ 
+
+ align:start position:0%
+scale that's a large physical Dimension
+so that means the argument of this is
+
+ align:start position:0%
+so that means the argument of this is
+ 
+
+ align:start position:0%
+so that means the argument of this is
+very very large but there's another way
+
+ align:start position:0%
+very very large but there's another way
+ 
+
+ align:start position:0%
+very very large but there's another way
+to get the same
+
+ align:start position:0%
+to get the same
+ 
+
+ align:start position:0%
+to get the same
+result short time
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+scale so that means that every diffusion
+
+ align:start position:0%
+scale so that means that every diffusion
+ 
+
+ align:start position:0%
+scale so that means that every diffusion
+experiment
+
+ align:start position:0%
+experiment
+ 
+
+ align:start position:0%
+experiment
+initially is operating in a material
+
+ align:start position:0%
+initially is operating in a material
+ 
+
+ align:start position:0%
+initially is operating in a material
+that for all intents and purposes is
+
+ align:start position:0%
+that for all intents and purposes is
+ 
+
+ align:start position:0%
+that for all intents and purposes is
+infinite because when those first
+
+ align:start position:0%
+infinite because when those first
+ 
+
+ align:start position:0%
+infinite because when those first
+phosphorus atoms start diffusing into
+
+ align:start position:0%
+phosphorus atoms start diffusing into
+ 
+
+ align:start position:0%
+phosphorus atoms start diffusing into
+the Silicon they don't know the Silicon
+
+ align:start position:0%
+the Silicon they don't know the Silicon
+ 
+
+ align:start position:0%
+the Silicon they don't know the Silicon
+is only a millimeter thick as far as
+
+ align:start position:0%
+is only a millimeter thick as far as
+ 
+
+ align:start position:0%
+is only a millimeter thick as far as
+they're concerned it's infinitely thick
+
+ align:start position:0%
+they're concerned it's infinitely thick
+ 
+
+ align:start position:0%
+they're concerned it's infinitely thick
+so this solution is valid everywhere as
+
+ align:start position:0%
+so this solution is valid everywhere as
+ 
+
+ align:start position:0%
+so this solution is valid everywhere as
+long as you've got concentration initial
+
+ align:start position:0%
+long as you've got concentration initial
+ 
+
+ align:start position:0%
+long as you've got concentration initial
+fixed concentration surface fixed at
+
+ align:start position:0%
+fixed concentration surface fixed at
+ 
+
+ align:start position:0%
+fixed concentration surface fixed at
+Short times at Short times this solution
+
+ align:start position:0%
+Short times at Short times this solution
+ 
+
+ align:start position:0%
+Short times at Short times this solution
+is valid valid over at a short time so
+
+ align:start position:0%
+is valid valid over at a short time so
+ 
+
+ align:start position:0%
+is valid valid over at a short time so
+that means it's got great utility
+
+ align:start position:0%
+that means it's got great utility
+ 
+
+ align:start position:0%
+that means it's got great utility
+great utility and now I want to show you
+
+ align:start position:0%
+great utility and now I want to show you
+ 
+
+ align:start position:0%
+great utility and now I want to show you
+something that takes everything we've
+
+ align:start position:0%
+something that takes everything we've
+ 
+
+ align:start position:0%
+something that takes everything we've
+learned and crashes it into a simple
+
+ align:start position:0%
+learned and crashes it into a simple
+ 
+
+ align:start position:0%
+learned and crashes it into a simple
+rule of thumb rule of thumb and these
+
+ align:start position:0%
+rule of thumb rule of thumb and these
+ 
+
+ align:start position:0%
+rule of thumb rule of thumb and these
+are the kinds of of rules that I hope
+
+ align:start position:0%
+are the kinds of of rules that I hope
+ 
+
+ align:start position:0%
+are the kinds of of rules that I hope
+you'll retain long after what was it
+
+ align:start position:0%
+you'll retain long after what was it
+ 
+
+ align:start position:0%
+you'll retain long after what was it
+Franklin said education is what remains
+
+ align:start position:0%
+Franklin said education is what remains
+ 
+
+ align:start position:0%
+Franklin said education is what remains
+when you've forgotten all of your
+
+ align:start position:0%
+when you've forgotten all of your
+ 
+
+ align:start position:0%
+when you've forgotten all of your
+schooling so this is what you'll
+
+ align:start position:0%
+schooling so this is what you'll
+ 
+
+ align:start position:0%
+schooling so this is what you'll
+remember um you see you've got C minus
+
+ align:start position:0%
+remember um you see you've got C minus
+ 
+
+ align:start position:0%
+remember um you see you've got C minus
+CS over C minus Cs and that's equal to
+
+ align:start position:0%
+CS over C minus Cs and that's equal to
+ 
+
+ align:start position:0%
+CS over C minus Cs and that's equal to
+over here Earth X over 2 roots of DT
+
+ align:start position:0%
+over here Earth X over 2 roots of DT
+ 
+
+ align:start position:0%
+over here Earth X over 2 roots of DT
+that's the accurate solution so if I
+
+ align:start position:0%
+that's the accurate solution so if I
+ 
+
+ align:start position:0%
+that's the accurate solution so if I
+wanted to capture the whole defusion
+
+ align:start position:0%
+wanted to capture the whole defusion
+ 
+
+ align:start position:0%
+wanted to capture the whole defusion
+process in one tiny little
+
+ align:start position:0%
+process in one tiny little
+ 
+
+ align:start position:0%
+process in one tiny little
+sentence what would be an average value
+
+ align:start position:0%
+sentence what would be an average value
+ 
+
+ align:start position:0%
+sentence what would be an average value
+this is a normalized ratio isn't it it
+
+ align:start position:0%
+this is a normalized ratio isn't it it
+ 
+
+ align:start position:0%
+this is a normalized ratio isn't it it
+goes from 0 to one so what's an average
+
+ align:start position:0%
+goes from 0 to one so what's an average
+ 
+
+ align:start position:0%
+goes from 0 to one so what's an average
+value between zero and one I don't know
+
+ align:start position:0%
+value between zero and one I don't know
+ 
+
+ align:start position:0%
+value between zero and one I don't know
+how about a half so suppose I just
+
+ align:start position:0%
+how about a half so suppose I just
+ 
+
+ align:start position:0%
+how about a half so suppose I just
+choose this as an average value for the
+
+ align:start position:0%
+choose this as an average value for the
+ 
+
+ align:start position:0%
+choose this as an average value for the
+whole diffusion process everything that
+
+ align:start position:0%
+whole diffusion process everything that
+ 
+
+ align:start position:0%
+whole diffusion process everything that
+can ever happen in
+
+ align:start position:0%
+can ever happen in
+ 
+
+ align:start position:0%
+can ever happen in
+Fusion well a half is less than 6 since
+
+ align:start position:0%
+Fusion well a half is less than 6 since
+ 
+
+ align:start position:0%
+Fusion well a half is less than 6 since
+a half is less than 6 I can approximate
+
+ align:start position:0%
+a half is less than 6 I can approximate
+ 
+
+ align:start position:0%
+a half is less than 6 I can approximate
+Earth X over 2 roots of DT is simply X
+
+ align:start position:0%
+Earth X over 2 roots of DT is simply X
+ 
+
+ align:start position:0%
+Earth X over 2 roots of DT is simply X
+over 2 roots of DT so now I've got this
+
+ align:start position:0%
+over 2 roots of DT so now I've got this
+ 
+
+ align:start position:0%
+over 2 roots of DT so now I've got this
+equals this so I'll cancel out the twos
+
+ align:start position:0%
+equals this so I'll cancel out the twos
+ 
+
+ align:start position:0%
+equals this so I'll cancel out the twos
+and I cross multiply and then that gives
+
+ align:start position:0%
+and I cross multiply and then that gives
+ 
+
+ align:start position:0%
+and I cross multiply and then that gives
+me X goes as two roots of DT as an
+
+ align:start position:0%
+me X goes as two roots of DT as an
+ 
+
+ align:start position:0%
+me X goes as two roots of DT as an
+overarching equation for everything that
+
+ align:start position:0%
+overarching equation for everything that
+ 
+
+ align:start position:0%
+overarching equation for everything that
+happens in short-term
+
+ align:start position:0%
+happens in short-term
+ 
+
+ align:start position:0%
+happens in short-term
+diffusion short-term diffusion I can't
+
+ align:start position:0%
+diffusion short-term diffusion I can't
+ 
+
+ align:start position:0%
+diffusion short-term diffusion I can't
+tell you how many times I've been in
+
+ align:start position:0%
+tell you how many times I've been in
+ 
+
+ align:start position:0%
+tell you how many times I've been in
+situations where I'm in some conference
+
+ align:start position:0%
+situations where I'm in some conference
+ 
+
+ align:start position:0%
+situations where I'm in some conference
+room and a bunch of people are sitting
+
+ align:start position:0%
+room and a bunch of people are sitting
+ 
+
+ align:start position:0%
+room and a bunch of people are sitting
+around trying to figure out what to do
+
+ align:start position:0%
+around trying to figure out what to do
+ 
+
+ align:start position:0%
+around trying to figure out what to do
+and somebody's getting ready to do some
+
+ align:start position:0%
+and somebody's getting ready to do some
+ 
+
+ align:start position:0%
+and somebody's getting ready to do some
+you know finite element calculation to
+
+ align:start position:0%
+you know finite element calculation to
+ 
+
+ align:start position:0%
+you know finite element calculation to
+go mathematically model this whole
+
+ align:start position:0%
+go mathematically model this whole
+ 
+
+ align:start position:0%
+go mathematically model this whole
+process and I sit back and I go gee well
+
+ align:start position:0%
+process and I sit back and I go gee well
+ 
+
+ align:start position:0%
+process and I sit back and I go gee well
+I know the length scales it's on the
+
+ align:start position:0%
+I know the length scales it's on the
+ 
+
+ align:start position:0%
+I know the length scales it's on the
+order of um well why don't we do one why
+
+ align:start position:0%
+order of um well why don't we do one why
+ 
+
+ align:start position:0%
+order of um well why don't we do one why
+don't we do one let's do one let's put
+
+ align:start position:0%
+don't we do one let's do one let's put
+ 
+
+ align:start position:0%
+don't we do one let's do one let's put
+the let's put the rest that myth have
+
+ align:start position:0%
+the let's put the rest that myth have
+ 
+
+ align:start position:0%
+the let's put the rest that myth have
+you ever been told told this thing about
+
+ align:start position:0%
+you ever been told told this thing about
+ 
+
+ align:start position:0%
+you ever been told told this thing about
+Cathedral Windows why the glass at the
+
+ align:start position:0%
+Cathedral Windows why the glass at the
+ 
+
+ align:start position:0%
+Cathedral Windows why the glass at the
+bottom of a cathedral window is is
+
+ align:start position:0%
+bottom of a cathedral window is is
+ 
+
+ align:start position:0%
+bottom of a cathedral window is is
+thicker than it is at the top and it has
+
+ align:start position:0%
+thicker than it is at the top and it has
+ 
+
+ align:start position:0%
+thicker than it is at the top and it has
+to do with the fact that glass is is
+
+ align:start position:0%
+to do with the fact that glass is is
+ 
+
+ align:start position:0%
+to do with the fact that glass is is
+really a viscous liquid and and over 500
+
+ align:start position:0%
+really a viscous liquid and and over 500
+ 
+
+ align:start position:0%
+really a viscous liquid and and over 500
+years it it it trickles and it gets
+
+ align:start position:0%
+years it it it trickles and it gets
+ 
+
+ align:start position:0%
+years it it it trickles and it gets
+wider it's nuts it's nuts and I can show
+
+ align:start position:0%
+wider it's nuts it's nuts and I can show
+ 
+
+ align:start position:0%
+wider it's nuts it's nuts and I can show
+you like this it's very simple you
+
+ align:start position:0%
+you like this it's very simple you
+ 
+
+ align:start position:0%
+you like this it's very simple you
+already know that you know the average
+
+ align:start position:0%
+already know that you know the average
+ 
+
+ align:start position:0%
+already know that you know the average
+what's the average temperature in a
+
+ align:start position:0%
+what's the average temperature in a
+ 
+
+ align:start position:0%
+what's the average temperature in a
+cathedral in northern Europe it's zero
+
+ align:start position:0%
+cathedral in northern Europe it's zero
+ 
+
+ align:start position:0%
+cathedral in northern Europe it's zero
+in the winter it's 20° in the summer
+
+ align:start position:0%
+in the winter it's 20° in the summer
+ 
+
+ align:start position:0%
+in the winter it's 20° in the summer
+let's pick a number 10° C all right so
+
+ align:start position:0%
+let's pick a number 10° C all right so
+ 
+
+ align:start position:0%
+let's pick a number 10° C all right so
+10° C what do you think the diffusion
+
+ align:start position:0%
+10° C what do you think the diffusion
+ 
+
+ align:start position:0%
+10° C what do you think the diffusion
+coefficient of silicate glass at 10° C
+
+ align:start position:0%
+coefficient of silicate glass at 10° C
+ 
+
+ align:start position:0%
+coefficient of silicate glass at 10° C
+would have to be for this thing to go
+
+ align:start position:0%
+would have to be for this thing to go
+ 
+
+ align:start position:0%
+would have to be for this thing to go
+anywhere so here's what I did I said all
+
+ align:start position:0%
+anywhere so here's what I did I said all
+ 
+
+ align:start position:0%
+anywhere so here's what I did I said all
+right well let's use this so here's my
+
+ align:start position:0%
+right well let's use this so here's my
+ 
+
+ align:start position:0%
+right well let's use this so here's my
+simple model of a of the cathedral
+
+ align:start position:0%
+simple model of a of the cathedral
+ 
+
+ align:start position:0%
+simple model of a of the cathedral
+window and this is the crosssection okay
+
+ align:start position:0%
+window and this is the crosssection okay
+ 
+
+ align:start position:0%
+window and this is the crosssection okay
+and and I figure I need a length scale
+
+ align:start position:0%
+and and I figure I need a length scale
+ 
+
+ align:start position:0%
+and and I figure I need a length scale
+so I chose a length scale if something's
+
+ align:start position:0%
+so I chose a length scale if something's
+ 
+
+ align:start position:0%
+so I chose a length scale if something's
+going to diffuse on the order of I don't
+
+ align:start position:0%
+going to diffuse on the order of I don't
+ 
+
+ align:start position:0%
+going to diffuse on the order of I don't
+know 10 cm you can quibble if you want
+
+ align:start position:0%
+know 10 cm you can quibble if you want
+ 
+
+ align:start position:0%
+know 10 cm you can quibble if you want
+to make it 1 cm I don't care I'm going
+
+ align:start position:0%
+to make it 1 cm I don't care I'm going
+ 
+
+ align:start position:0%
+to make it 1 cm I don't care I'm going
+to blow this thing so far out of the
+
+ align:start position:0%
+to blow this thing so far out of the
+ 
+
+ align:start position:0%
+to blow this thing so far out of the
+water it won't matter won't matter all
+
+ align:start position:0%
+water it won't matter won't matter all
+ 
+
+ align:start position:0%
+water it won't matter won't matter all
+right so this is about 10 cm right and
+
+ align:start position:0%
+right so this is about 10 cm right and
+ 
+
+ align:start position:0%
+right so this is about 10 cm right and
+it's going to get thicker on the bottom
+
+ align:start position:0%
+it's going to get thicker on the bottom
+ 
+
+ align:start position:0%
+it's going to get thicker on the bottom
+and and and I figure I'm going to give
+
+ align:start position:0%
+and and and I figure I'm going to give
+ 
+
+ align:start position:0%
+and and and I figure I'm going to give
+this a really long run time so I'm going
+
+ align:start position:0%
+this a really long run time so I'm going
+ 
+
+ align:start position:0%
+this a really long run time so I'm going
+to make it 500 years 500 years and what
+
+ align:start position:0%
+to make it 500 years 500 years and what
+ 
+
+ align:start position:0%
+to make it 500 years 500 years and what
+I'm going to do I want to show you how
+
+ align:start position:0%
+I'm going to do I want to show you how
+ 
+
+ align:start position:0%
+I'm going to do I want to show you how
+to put this problem to the test what I'm
+
+ align:start position:0%
+to put this problem to the test what I'm
+ 
+
+ align:start position:0%
+to put this problem to the test what I'm
+going to do is I'm going to derive a
+
+ align:start position:0%
+going to do is I'm going to derive a
+ 
+
+ align:start position:0%
+going to do is I'm going to derive a
+quantity that I can say yes or no to so
+
+ align:start position:0%
+quantity that I can say yes or no to so
+ 
+
+ align:start position:0%
+quantity that I can say yes or no to so
+what I'm going to try to do is pull out
+
+ align:start position:0%
+what I'm going to try to do is pull out
+ 
+
+ align:start position:0%
+what I'm going to try to do is pull out
+a value of the diffusion coefficient so
+
+ align:start position:0%
+a value of the diffusion coefficient so
+ 
+
+ align:start position:0%
+a value of the diffusion coefficient so
+I know that X x^2 = DT if I just Square
+
+ align:start position:0%
+I know that X x^2 = DT if I just Square
+ 
+
+ align:start position:0%
+I know that X x^2 = DT if I just Square
+both sides of that thing so that means
+
+ align:start position:0%
+both sides of that thing so that means
+ 
+
+ align:start position:0%
+both sides of that thing so that means
+that D the diffusion coefficient should
+
+ align:start position:0%
+that D the diffusion coefficient should
+ 
+
+ align:start position:0%
+that D the diffusion coefficient should
+be x^2 divided
+
+ align:start position:0%
+be x^2 divided
+ 
+
+ align:start position:0%
+be x^2 divided
+T so I'm going to I'm going to do this
+
+ align:start position:0%
+T so I'm going to I'm going to do this
+ 
+
+ align:start position:0%
+T so I'm going to I'm going to do this
+in in C uh centimeters so this is 10 squ
+
+ align:start position:0%
+in in C uh centimeters so this is 10 squ
+ 
+
+ align:start position:0%
+in in C uh centimeters so this is 10 squ
+on the top and time is 500 years so
+
+ align:start position:0%
+on the top and time is 500 years so
+ 
+
+ align:start position:0%
+on the top and time is 500 years so
+that's 500 and how many seconds in a
+
+ align:start position:0%
+that's 500 and how many seconds in a
+ 
+
+ align:start position:0%
+that's 500 and how many seconds in a
+year
+
+ align:start position:0%
+year
+ 
+
+ align:start position:0%
+year
+quick Pi * 10 to the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+7th pi times 10 million is good to
+
+ align:start position:0%
+7th pi times 10 million is good to
+ 
+
+ align:start position:0%
+7th pi times 10 million is good to
+within about a percent
+
+ align:start position:0%
+within about a percent
+ 
+
+ align:start position:0%
+within about a percent
+okay so that's it I mean who cares we're
+
+ align:start position:0%
+okay so that's it I mean who cares we're
+ 
+
+ align:start position:0%
+okay so that's it I mean who cares we're
+this is a diffusion calculation you
+
+ align:start position:0%
+this is a diffusion calculation you
+ 
+
+ align:start position:0%
+this is a diffusion calculation you
+don't need it anymore you're not going
+
+ align:start position:0%
+don't need it anymore you're not going
+ 
+
+ align:start position:0%
+don't need it anymore you're not going
+to go the 365 days how many leap years
+
+ align:start position:0%
+to go the 365 days how many leap years
+ 
+
+ align:start position:0%
+to go the 365 days how many leap years
+were there and there come on get with it
+
+ align:start position:0%
+were there and there come on get with it
+ 
+
+ align:start position:0%
+were there and there come on get with it
+all right so
+
+ align:start position:0%
+all right so
+ 
+
+ align:start position:0%
+all right so
+6.4 time 10 to- 9 cm squar per second
+
+ align:start position:0%
+6.4 time 10 to- 9 cm squar per second
+ 
+
+ align:start position:0%
+6.4 time 10 to- 9 cm squar per second
+I'd need a diffusion coefficient of a
+
+ align:start position:0%
+I'd need a diffusion coefficient of a
+ 
+
+ align:start position:0%
+I'd need a diffusion coefficient of a
+silicate glass of 10 Theus n i mean
+
+ align:start position:0%
+silicate glass of 10 Theus n i mean
+ 
+
+ align:start position:0%
+silicate glass of 10 Theus n i mean
+that's the diffusion coefficient of a
+
+ align:start position:0%
+that's the diffusion coefficient of a
+ 
+
+ align:start position:0%
+that's the diffusion coefficient of a
+close- packed metal at its melting point
+
+ align:start position:0%
+close- packed metal at its melting point
+ 
+
+ align:start position:0%
+close- packed metal at its melting point
+so I went I looked up some data and
+
+ align:start position:0%
+so I went I looked up some data and
+ 
+
+ align:start position:0%
+so I went I looked up some data and
+here's what I found for the diffusion
+
+ align:start position:0%
+here's what I found for the diffusion
+ 
+
+ align:start position:0%
+here's what I found for the diffusion
+coefficient of sodium in a soda lime
+
+ align:start position:0%
+coefficient of sodium in a soda lime
+ 
+
+ align:start position:0%
+coefficient of sodium in a soda lime
+glass such as the type that would be
+
+ align:start position:0%
+glass such as the type that would be
+ 
+
+ align:start position:0%
+glass such as the type that would be
+used in those
+
+ align:start position:0%
+used in those
+ 
+
+ align:start position:0%
+used in those
+windows and using those data at 10° C
+
+ align:start position:0%
+windows and using those data at 10° C
+ 
+
+ align:start position:0%
+windows and using those data at 10° C
+the diffusion coefficient would be
+
+ align:start position:0%
+the diffusion coefficient would be
+ 
+
+ align:start position:0%
+the diffusion coefficient would be
+10-19 cm squar per second it's off by a
+
+ align:start position:0%
+10-19 cm squar per second it's off by a
+ 
+
+ align:start position:0%
+10-19 cm squar per second it's off by a
+mere 10 orders of magnitude so I don't
+
+ align:start position:0%
+mere 10 orders of magnitude so I don't
+ 
+
+ align:start position:0%
+mere 10 orders of magnitude so I don't
+care if you want to make this 1 cmet if
+
+ align:start position:0%
+care if you want to make this 1 cmet if
+ 
+
+ align:start position:0%
+care if you want to make this 1 cmet if
+you want to make it 1 millimeter there's
+
+ align:start position:0%
+you want to make it 1 millimeter there's
+ 
+
+ align:start position:0%
+you want to make it 1 millimeter there's
+no way there's no way that's the X
+
+ align:start position:0%
+no way there's no way that's the X
+ 
+
+ align:start position:0%
+no way there's no way that's the X
+explanation we know what the reason is I
+
+ align:start position:0%
+explanation we know what the reason is I
+ 
+
+ align:start position:0%
+explanation we know what the reason is I
+mean this proves that it can't be I what
+
+ align:start position:0%
+mean this proves that it can't be I what
+ 
+
+ align:start position:0%
+mean this proves that it can't be I what
+I want to show you is that you can come
+
+ align:start position:0%
+I want to show you is that you can come
+ 
+
+ align:start position:0%
+I want to show you is that you can come
+at it from both sides you know the other
+
+ align:start position:0%
+at it from both sides you know the other
+ 
+
+ align:start position:0%
+at it from both sides you know the other
+thing is to figure out how do they make
+
+ align:start position:0%
+thing is to figure out how do they make
+ 
+
+ align:start position:0%
+thing is to figure out how do they make
+the glass you know how they made the
+
+ align:start position:0%
+the glass you know how they made the
+ 
+
+ align:start position:0%
+the glass you know how they made the
+glass they pull it out of a layer and
+
+ align:start position:0%
+glass they pull it out of a layer and
+ 
+
+ align:start position:0%
+glass they pull it out of a layer and
+they put it on a spinning
+
+ align:start position:0%
+they put it on a spinning
+ 
+
+ align:start position:0%
+they put it on a spinning
+table that's how they could flatten it
+
+ align:start position:0%
+table that's how they could flatten it
+ 
+
+ align:start position:0%
+table that's how they could flatten it
+they didn't have the float glass process
+
+ align:start position:0%
+they didn't have the float glass process
+ 
+
+ align:start position:0%
+they didn't have the float glass process
+where you pour silicate on top of liquid
+
+ align:start position:0%
+where you pour silicate on top of liquid
+ 
+
+ align:start position:0%
+where you pour silicate on top of liquid
+tin and liquid tin has a perfectly flat
+
+ align:start position:0%
+tin and liquid tin has a perfectly flat
+ 
+
+ align:start position:0%
+tin and liquid tin has a perfectly flat
+surface and the silicate glass is less
+
+ align:start position:0%
+surface and the silicate glass is less
+ 
+
+ align:start position:0%
+surface and the silicate glass is less
+dense and it's insoluble and so it
+
+ align:start position:0%
+dense and it's insoluble and so it
+ 
+
+ align:start position:0%
+dense and it's insoluble and so it
+floats on the liquid tin surface and is
+
+ align:start position:0%
+floats on the liquid tin surface and is
+ 
+
+ align:start position:0%
+floats on the liquid tin surface and is
+perfectly flat they didn't do that back
+
+ align:start position:0%
+perfectly flat they didn't do that back
+ 
+
+ align:start position:0%
+perfectly flat they didn't do that back
+in medieval times they spun they they
+
+ align:start position:0%
+in medieval times they spun they they
+ 
+
+ align:start position:0%
+in medieval times they spun they they
+they they spun cast it it was like a
+
+ align:start position:0%
+they they spun cast it it was like a
+ 
+
+ align:start position:0%
+they they spun cast it it was like a
+spin coating technique so you got some
+
+ align:start position:0%
+spin coating technique so you got some
+ 
+
+ align:start position:0%
+spin coating technique so you got some
+table spinning this is top view some
+
+ align:start position:0%
+table spinning this is top view some
+ 
+
+ align:start position:0%
+table spinning this is top view some
+table spinning and you plop some glass
+
+ align:start position:0%
+table spinning and you plop some glass
+ 
+
+ align:start position:0%
+table spinning and you plop some glass
+on it goes by centrifugal force right so
+
+ align:start position:0%
+on it goes by centrifugal force right so
+ 
+
+ align:start position:0%
+on it goes by centrifugal force right so
+now the cross-section of the glass
+
+ align:start position:0%
+now the cross-section of the glass
+ 
+
+ align:start position:0%
+now the cross-section of the glass
+what's it look like well let's start
+
+ align:start position:0%
+what's it look like well let's start
+ 
+
+ align:start position:0%
+what's it look like well let's start
+from the center and go out guess what
+
+ align:start position:0%
+from the center and go out guess what
+ 
+
+ align:start position:0%
+from the center and go out guess what
+not to scale it's ever so slightly
+
+ align:start position:0%
+not to scale it's ever so slightly
+ 
+
+ align:start position:0%
+not to scale it's ever so slightly
+thicker on the outside than the inside
+
+ align:start position:0%
+thicker on the outside than the inside
+ 
+
+ align:start position:0%
+thicker on the outside than the inside
+and people would actually be very
+
+ align:start position:0%
+and people would actually be very
+ 
+
+ align:start position:0%
+and people would actually be very
+careful about choosing the pieces and
+
+ align:start position:0%
+careful about choosing the pieces and
+ 
+
+ align:start position:0%
+careful about choosing the pieces and
+then the glazers said when you mount the
+
+ align:start position:0%
+then the glazers said when you mount the
+ 
+
+ align:start position:0%
+then the glazers said when you mount the
+windows let's put all the glass in with
+
+ align:start position:0%
+windows let's put all the glass in with
+ 
+
+ align:start position:0%
+windows let's put all the glass in with
+the thick side down wouldn't that make
+
+ align:start position:0%
+the thick side down wouldn't that make
+ 
+
+ align:start position:0%
+the thick side down wouldn't that make
+sense and that's why the glass is
+
+ align:start position:0%
+sense and that's why the glass is
+ 
+
+ align:start position:0%
+sense and that's why the glass is
+thicker because it was made that
+
+ align:start position:0%
+thicker because it was made that
+ 
+
+ align:start position:0%
+thicker because it was made that
+way simple answer but you can do the
+
+ align:start position:0%
+way simple answer but you can do the
+ 
+
+ align:start position:0%
+way simple answer but you can do the
+calculation I don't know how many times
+
+ align:start position:0%
+calculation I don't know how many times
+ 
+
+ align:start position:0%
+calculation I don't know how many times
+I get I get this asked this at least
+
+ align:start position:0%
+I get I get this asked this at least
+ 
+
+ align:start position:0%
+I get I get this asked this at least
+once a year someone says is it true that
+
+ align:start position:0%
+once a year someone says is it true that
+ 
+
+ align:start position:0%
+once a year someone says is it true that
+the cathedrals and I go okay does this
+
+ align:start position:0%
+the cathedrals and I go okay does this
+ 
+
+ align:start position:0%
+the cathedrals and I go okay does this
+person know fixed law or not don't know
+
+ align:start position:0%
+person know fixed law or not don't know
+ 
+
+ align:start position:0%
+person know fixed law or not don't know
+okay so we have to give a different
+
+ align:start position:0%
+okay so we have to give a different
+ 
+
+ align:start position:0%
+okay so we have to give a different
+explanation all right so um good now I
+
+ align:start position:0%
+explanation all right so um good now I
+ 
+
+ align:start position:0%
+explanation all right so um good now I
+want to finish the story of the uh
+
+ align:start position:0%
+want to finish the story of the uh
+ 
+
+ align:start position:0%
+want to finish the story of the uh
+automobile uh exhaust catalyst and show
+
+ align:start position:0%
+automobile uh exhaust catalyst and show
+ 
+
+ align:start position:0%
+automobile uh exhaust catalyst and show
+how we can bring a lot of what we've
+
+ align:start position:0%
+how we can bring a lot of what we've
+ 
+
+ align:start position:0%
+how we can bring a lot of what we've
+been learning the last several days
+
+ align:start position:0%
+been learning the last several days
+ 
+
+ align:start position:0%
+been learning the last several days
+together so just to review uh this is an
+
+ align:start position:0%
+together so just to review uh this is an
+ 
+
+ align:start position:0%
+together so just to review uh this is an
+old sketch because it was taken from an
+
+ align:start position:0%
+old sketch because it was taken from an
+ 
+
+ align:start position:0%
+old sketch because it was taken from an
+early General Motors publication
+
+ align:start position:0%
+early General Motors publication
+ 
+
+ align:start position:0%
+early General Motors publication
+from the 80s but uh basically what
+
+ align:start position:0%
+from the 80s but uh basically what
+ 
+
+ align:start position:0%
+from the 80s but uh basically what
+you've got is we've seen the catalytic
+
+ align:start position:0%
+you've got is we've seen the catalytic
+ 
+
+ align:start position:0%
+you've got is we've seen the catalytic
+converter and it's taking the the
+
+ align:start position:0%
+converter and it's taking the the
+ 
+
+ align:start position:0%
+converter and it's taking the the
+exhaust gases and trying to convert some
+
+ align:start position:0%
+exhaust gases and trying to convert some
+ 
+
+ align:start position:0%
+exhaust gases and trying to convert some
+of the toxins into something less
+
+ align:start position:0%
+of the toxins into something less
+ 
+
+ align:start position:0%
+of the toxins into something less
+offensive um and and i' reported to you
+
+ align:start position:0%
+offensive um and and i' reported to you
+ 
+
+ align:start position:0%
+offensive um and and i' reported to you
+that we need to control in order to
+
+ align:start position:0%
+that we need to control in order to
+ 
+
+ align:start position:0%
+that we need to control in order to
+achieve both oxidation and reduction and
+
+ align:start position:0%
+achieve both oxidation and reduction and
+ 
+
+ align:start position:0%
+achieve both oxidation and reduction and
+how do we control we control with the
+
+ align:start position:0%
+how do we control we control with the
+ 
+
+ align:start position:0%
+how do we control we control with the
+aid of an oxygen sensor and Matt could
+
+ align:start position:0%
+aid of an oxygen sensor and Matt could
+ 
+
+ align:start position:0%
+aid of an oxygen sensor and Matt could
+we switch to the um document camera
+
+ align:start position:0%
+we switch to the um document camera
+ 
+
+ align:start position:0%
+we switch to the um document camera
+please for a second
+
+ align:start position:0%
+please for a second
+ 
+
+ align:start position:0%
+please for a second
+take that input so what I'm showing you
+
+ align:start position:0%
+take that input so what I'm showing you
+ 
+
+ align:start position:0%
+take that input so what I'm showing you
+is an oxygen sensor uh this is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+a good and
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+autofocus good all right so what you're
+
+ align:start position:0%
+autofocus good all right so what you're
+ 
+
+ align:start position:0%
+autofocus good all right so what you're
+looking at is this is the metal uh
+
+ align:start position:0%
+looking at is this is the metal uh
+ 
+
+ align:start position:0%
+looking at is this is the metal uh
+sleeve on top of the oxygen sensor and
+
+ align:start position:0%
+sleeve on top of the oxygen sensor and
+ 
+
+ align:start position:0%
+sleeve on top of the oxygen sensor and
+you can see veins here and this is
+
+ align:start position:0%
+you can see veins here and this is
+ 
+
+ align:start position:0%
+you can see veins here and this is
+inserted uh just past the engine before
+
+ align:start position:0%
+inserted uh just past the engine before
+ 
+
+ align:start position:0%
+inserted uh just past the engine before
+the catalytic converter and what I want
+
+ align:start position:0%
+the catalytic converter and what I want
+ 
+
+ align:start position:0%
+the catalytic converter and what I want
+want to do is to describe the solid
+
+ align:start position:0%
+want to do is to describe the solid
+ 
+
+ align:start position:0%
+want to do is to describe the solid
+state chemistry that's going on inside
+
+ align:start position:0%
+state chemistry that's going on inside
+ 
+
+ align:start position:0%
+state chemistry that's going on inside
+there so Matt may we go back to the
+
+ align:start position:0%
+there so Matt may we go back to the
+ 
+
+ align:start position:0%
+there so Matt may we go back to the
+computer
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+please thank you okay so that what I
+
+ align:start position:0%
+please thank you okay so that what I
+ 
+
+ align:start position:0%
+please thank you okay so that what I
+just showed you is sitting right here
+
+ align:start position:0%
+just showed you is sitting right here
+ 
+
+ align:start position:0%
+just showed you is sitting right here
+just as the exhaust gases leave the
+
+ align:start position:0%
+just as the exhaust gases leave the
+ 
+
+ align:start position:0%
+just as the exhaust gases leave the
+engine and what they're doing is they're
+
+ align:start position:0%
+engine and what they're doing is they're
+ 
+
+ align:start position:0%
+engine and what they're doing is they're
+measuring the oxygen pressure in the
+
+ align:start position:0%
+measuring the oxygen pressure in the
+ 
+
+ align:start position:0%
+measuring the oxygen pressure in the
+exhaust gases so that we can control the
+
+ align:start position:0%
+exhaust gases so that we can control the
+ 
+
+ align:start position:0%
+exhaust gases so that we can control the
+air to fuel ratio because it turns out
+
+ align:start position:0%
+air to fuel ratio because it turns out
+ 
+
+ align:start position:0%
+air to fuel ratio because it turns out
+that to convert the co and the
+
+ align:start position:0%
+that to convert the co and the
+ 
+
+ align:start position:0%
+that to convert the co and the
+hydrocarbons to the desired products in
+
+ align:start position:0%
+hydrocarbons to the desired products in
+ 
+
+ align:start position:0%
+hydrocarbons to the desired products in
+other words carbon dioxide water vapor
+
+ align:start position:0%
+other words carbon dioxide water vapor
+ 
+
+ align:start position:0%
+other words carbon dioxide water vapor
+and carbon dioxide you need to oxidize
+
+ align:start position:0%
+and carbon dioxide you need to oxidize
+ 
+
+ align:start position:0%
+and carbon dioxide you need to oxidize
+and the catalyst is pretty good at very
+
+ align:start position:0%
+and the catalyst is pretty good at very
+ 
+
+ align:start position:0%
+and the catalyst is pretty good at very
+very high air ratios and to reduce nox
+
+ align:start position:0%
+very high air ratios and to reduce nox
+ 
+
+ align:start position:0%
+very high air ratios and to reduce nox
+to nitrogen you need to have Rich fuel
+
+ align:start position:0%
+to nitrogen you need to have Rich fuel
+ 
+
+ align:start position:0%
+to nitrogen you need to have Rich fuel
+ratios and mercifully nature was kind
+
+ align:start position:0%
+ratios and mercifully nature was kind
+ 
+
+ align:start position:0%
+ratios and mercifully nature was kind
+and there's this tiny window at about
+
+ align:start position:0%
+and there's this tiny window at about
+ 
+
+ align:start position:0%
+and there's this tiny window at about
+14.6 to1 where you get fairly high
+
+ align:start position:0%
+14.6 to1 where you get fairly high
+ 
+
+ align:start position:0%
+14.6 to1 where you get fairly high
+yields on both catalytic reactions so
+
+ align:start position:0%
+yields on both catalytic reactions so
+ 
+
+ align:start position:0%
+yields on both catalytic reactions so
+this is where you want to Park yourself
+
+ align:start position:0%
+this is where you want to Park yourself
+ 
+
+ align:start position:0%
+this is where you want to Park yourself
+but you so now you need to have a sensor
+
+ align:start position:0%
+but you so now you need to have a sensor
+ 
+
+ align:start position:0%
+but you so now you need to have a sensor
+and that sensor looks like this it is
+
+ align:start position:0%
+and that sensor looks like this it is
+ 
+
+ align:start position:0%
+and that sensor looks like this it is
+zironia it's an ionic oxide and it's
+
+ align:start position:0%
+zironia it's an ionic oxide and it's
+ 
+
+ align:start position:0%
+zironia it's an ionic oxide and it's
+doped with calcium oxide to create
+
+ align:start position:0%
+doped with calcium oxide to create
+ 
+
+ align:start position:0%
+doped with calcium oxide to create
+oxygen vacancies so we're going to get
+
+ align:start position:0%
+oxygen vacancies so we're going to get
+ 
+
+ align:start position:0%
+oxygen vacancies so we're going to get
+defects involved and we're going to talk
+
+ align:start position:0%
+defects involved and we're going to talk
+ 
+
+ align:start position:0%
+defects involved and we're going to talk
+about diffusion when we put calcium
+
+ align:start position:0%
+about diffusion when we put calcium
+ 
+
+ align:start position:0%
+about diffusion when we put calcium
+oxide into zironia we have two plus C on
+
+ align:start position:0%
+oxide into zironia we have two plus C on
+ 
+
+ align:start position:0%
+oxide into zironia we have two plus C on
+a four plus site and so we need to make
+
+ align:start position:0%
+a four plus site and so we need to make
+ 
+
+ align:start position:0%
+a four plus site and so we need to make
+an oxygen vacancy to compensate so as we
+
+ align:start position:0%
+an oxygen vacancy to compensate so as we
+ 
+
+ align:start position:0%
+an oxygen vacancy to compensate so as we
+add calcium oxide we make more oxygen
+
+ align:start position:0%
+add calcium oxide we make more oxygen
+ 
+
+ align:start position:0%
+add calcium oxide we make more oxygen
+vacancies which means that the diffusion
+
+ align:start position:0%
+vacancies which means that the diffusion
+ 
+
+ align:start position:0%
+vacancies which means that the diffusion
+coefficient goes up and that shortens
+
+ align:start position:0%
+coefficient goes up and that shortens
+ 
+
+ align:start position:0%
+coefficient goes up and that shortens
+the response time it's no good having a
+
+ align:start position:0%
+the response time it's no good having a
+ 
+
+ align:start position:0%
+the response time it's no good having a
+sensor that responds on a scale time
+
+ align:start position:0%
+sensor that responds on a scale time
+ 
+
+ align:start position:0%
+sensor that responds on a scale time
+scale of minutes when your driving
+
+ align:start position:0%
+scale of minutes when your driving
+ 
+
+ align:start position:0%
+scale of minutes when your driving
+conditions are changing on a time scale
+
+ align:start position:0%
+conditions are changing on a time scale
+ 
+
+ align:start position:0%
+conditions are changing on a time scale
+of seconds and so we dope with a
+
+ align:start position:0%
+of seconds and so we dope with a
+ 
+
+ align:start position:0%
+of seconds and so we dope with a
+subvalent oxide in order to improve the
+
+ align:start position:0%
+subvalent oxide in order to improve the
+ 
+
+ align:start position:0%
+subvalent oxide in order to improve the
+performance and here's a a cartoon that
+
+ align:start position:0%
+performance and here's a a cartoon that
+ 
+
+ align:start position:0%
+performance and here's a a cartoon that
+uh shows this is what's underneath the
+
+ align:start position:0%
+uh shows this is what's underneath the
+ 
+
+ align:start position:0%
+uh shows this is what's underneath the
+vein this blue that I've drawn is a
+
+ align:start position:0%
+vein this blue that I've drawn is a
+ 
+
+ align:start position:0%
+vein this blue that I've drawn is a
+closed one-end zercon your tube there
+
+ align:start position:0%
+closed one-end zercon your tube there
+ 
+
+ align:start position:0%
+closed one-end zercon your tube there
+are electrodes on the inside and the uh
+
+ align:start position:0%
+are electrodes on the inside and the uh
+ 
+
+ align:start position:0%
+are electrodes on the inside and the uh
+on the inside this is the exhaust and on
+
+ align:start position:0%
+on the inside this is the exhaust and on
+ 
+
+ align:start position:0%
+on the inside this is the exhaust and on
+the outside it's open to the air and
+
+ align:start position:0%
+the outside it's open to the air and
+ 
+
+ align:start position:0%
+the outside it's open to the air and
+this measures a voltage across the
+
+ align:start position:0%
+this measures a voltage across the
+ 
+
+ align:start position:0%
+this measures a voltage across the
+zirconia sensor and that voltage goes to
+
+ align:start position:0%
+zirconia sensor and that voltage goes to
+ 
+
+ align:start position:0%
+zirconia sensor and that voltage goes to
+the CPU every car has several computers
+
+ align:start position:0%
+the CPU every car has several computers
+ 
+
+ align:start position:0%
+the CPU every car has several computers
+on it but the first cars to have
+
+ align:start position:0%
+on it but the first cars to have
+ 
+
+ align:start position:0%
+on it but the first cars to have
+computers had them in order to control
+
+ align:start position:0%
+computers had them in order to control
+ 
+
+ align:start position:0%
+computers had them in order to control
+air to fuel ratio to make the catalytic
+
+ align:start position:0%
+air to fuel ratio to make the catalytic
+ 
+
+ align:start position:0%
+air to fuel ratio to make the catalytic
+converter effective and then that goes
+
+ align:start position:0%
+converter effective and then that goes
+ 
+
+ align:start position:0%
+converter effective and then that goes
+to control either the carburetor or
+
+ align:start position:0%
+to control either the carburetor or
+ 
+
+ align:start position:0%
+to control either the carburetor or
+nowadays the uh fuel injectors which
+
+ align:start position:0%
+nowadays the uh fuel injectors which
+ 
+
+ align:start position:0%
+nowadays the uh fuel injectors which
+then keeps the fuel to air ratio so that
+
+ align:start position:0%
+then keeps the fuel to air ratio so that
+ 
+
+ align:start position:0%
+then keeps the fuel to air ratio so that
+this keeps measuring 14.6 to1 and if you
+
+ align:start position:0%
+this keeps measuring 14.6 to1 and if you
+ 
+
+ align:start position:0%
+this keeps measuring 14.6 to1 and if you
+change altitude if the if you get stuck
+
+ align:start position:0%
+change altitude if the if you get stuck
+ 
+
+ align:start position:0%
+change altitude if the if you get stuck
+in the Callahan tunnel and the ambient
+
+ align:start position:0%
+in the Callahan tunnel and the ambient
+ 
+
+ align:start position:0%
+in the Callahan tunnel and the ambient
+conditions are changing this can respond
+
+ align:start position:0%
+conditions are changing this can respond
+ 
+
+ align:start position:0%
+conditions are changing this can respond
+can respond to changes in temperature
+
+ align:start position:0%
+can respond to changes in temperature
+ 
+
+ align:start position:0%
+can respond to changes in temperature
+what do you think the uh partial
+
+ align:start position:0%
+what do you think the uh partial
+ 
+
+ align:start position:0%
+what do you think the uh partial
+pressure of oxygen is about 20% in air
+
+ align:start position:0%
+pressure of oxygen is about 20% in air
+ 
+
+ align:start position:0%
+pressure of oxygen is about 20% in air
+but how much oxygen per unit volume do
+
+ align:start position:0%
+but how much oxygen per unit volume do
+ 
+
+ align:start position:0%
+but how much oxygen per unit volume do
+you have at 100° Fahrenheit versus 0
+
+ align:start position:0%
+you have at 100° Fahrenheit versus 0
+ 
+
+ align:start position:0%
+you have at 100° Fahrenheit versus 0
+degrees Fahrenheit this thing can figure
+
+ align:start position:0%
+degrees Fahrenheit this thing can figure
+ 
+
+ align:start position:0%
+degrees Fahrenheit this thing can figure
+all that out and thereby run the system
+
+ align:start position:0%
+all that out and thereby run the system
+ 
+
+ align:start position:0%
+all that out and thereby run the system
+at the optimum fuel to aair ratio to
+
+ align:start position:0%
+at the optimum fuel to aair ratio to
+ 
+
+ align:start position:0%
+at the optimum fuel to aair ratio to
+maximally get the output from the
+
+ align:start position:0%
+maximally get the output from the
+ 
+
+ align:start position:0%
+maximally get the output from the
+catalytic converter and so in 3091 we've
+
+ align:start position:0%
+catalytic converter and so in 3091 we've
+ 
+
+ align:start position:0%
+catalytic converter and so in 3091 we've
+learned about the doping of silicon to
+
+ align:start position:0%
+learned about the doping of silicon to
+ 
+
+ align:start position:0%
+learned about the doping of silicon to
+make what goes into here we've learned
+
+ align:start position:0%
+make what goes into here we've learned
+ 
+
+ align:start position:0%
+make what goes into here we've learned
+about the ceramics that go into the
+
+ align:start position:0%
+about the ceramics that go into the
+ 
+
+ align:start position:0%
+about the ceramics that go into the
+catalytic converter and the Catalyst
+
+ align:start position:0%
+catalytic converter and the Catalyst
+ 
+
+ align:start position:0%
+catalytic converter and the Catalyst
+that goes on it and now we've learned
+
+ align:start position:0%
+that goes on it and now we've learned
+ 
+
+ align:start position:0%
+that goes on it and now we've learned
+about diffusion and everything that goes
+
+ align:start position:0%
+about diffusion and everything that goes
+ 
+
+ align:start position:0%
+about diffusion and everything that goes
+into the oxygen sensor that's why I tell
+
+ align:start position:0%
+into the oxygen sensor that's why I tell
+ 
+
+ align:start position:0%
+into the oxygen sensor that's why I tell
+you chemistry is the central science to
+
+ align:start position:0%
+you chemistry is the central science to
+ 
+
+ align:start position:0%
+you chemistry is the central science to
+Energy Efficiency
+
+ align:start position:0%
+Energy Efficiency
+ 
+
+ align:start position:0%
+Energy Efficiency
+and environmental Conservancy learn your
+
+ align:start position:0%
+and environmental Conservancy learn your
+ 
+
+ align:start position:0%
+and environmental Conservancy learn your
+Chemistry it's the most important
+
+ align:start position:0%
+Chemistry it's the most important
+ 
+
+ align:start position:0%
+Chemistry it's the most important
+subject and with that I'll say have a
+
+ align:start position:0%
+subject and with that I'll say have a
+ 
+
+ align:start position:0%
+subject and with that I'll say have a
+nice day and we'll see you on Wednesday
\ No newline at end of file
diff --git a/L-Sv1oL43ew.txt b/L-Sv1oL43ew.txt
new file mode 100644
index 0000000000000000000000000000000000000000..e678091b1236d7861dc3327e175f4a291de1741a
--- /dev/null
+++ b/L-Sv1oL43ew.txt
@@ -0,0 +1,651 @@
+align:start position:0%
+ 
+the beach ball strategy is a way to get
+
+ align:start position:0%
+the beach ball strategy is a way to get
+ 
+
+ align:start position:0%
+the beach ball strategy is a way to get
+students who might not want to answer
+
+ align:start position:0%
+students who might not want to answer
+ 
+
+ align:start position:0%
+students who might not want to answer
+questions or be a little less outgoing
+
+ align:start position:0%
+questions or be a little less outgoing
+ 
+
+ align:start position:0%
+questions or be a little less outgoing
+in their answering of questions to
+
+ align:start position:0%
+in their answering of questions to
+ 
+
+ align:start position:0%
+in their answering of questions to
+answer questions so there's a few
+
+ align:start position:0%
+answer questions so there's a few
+ 
+
+ align:start position:0%
+answer questions so there's a few
+different ways to use the beach ball
+
+ align:start position:0%
+different ways to use the beach ball
+ 
+
+ align:start position:0%
+different ways to use the beach ball
+actually and and one is you just uh pose
+
+ align:start position:0%
+actually and and one is you just uh pose
+ 
+
+ align:start position:0%
+actually and and one is you just uh pose
+a question that has enough variation in
+
+ align:start position:0%
+a question that has enough variation in
+ 
+
+ align:start position:0%
+a question that has enough variation in
+the types of responses so you wouldn't
+
+ align:start position:0%
+the types of responses so you wouldn't
+ 
+
+ align:start position:0%
+the types of responses so you wouldn't
+say okay what's 2 plus too as a as an as
+
+ align:start position:0%
+say okay what's 2 plus too as a as an as
+ 
+
+ align:start position:0%
+say okay what's 2 plus too as a as an as
+an example for the beach ball question
+
+ align:start position:0%
+an example for the beach ball question
+ 
+
+ align:start position:0%
+an example for the beach ball question
+you would have to have something that
+
+ align:start position:0%
+you would have to have something that
+ 
+
+ align:start position:0%
+you would have to have something that
+was a little bit more a little bit
+
+ align:start position:0%
+was a little bit more a little bit
+ 
+
+ align:start position:0%
+was a little bit more a little bit
+richer and then you throw the ball at at
+
+ align:start position:0%
+richer and then you throw the ball at at
+ 
+
+ align:start position:0%
+richer and then you throw the ball at at
+one student or up into the up into the
+
+ align:start position:0%
+one student or up into the up into the
+ 
+
+ align:start position:0%
+one student or up into the up into the
+lecture hall if it's a big lecture hall
+
+ align:start position:0%
+lecture hall if it's a big lecture hall
+ 
+
+ align:start position:0%
+lecture hall if it's a big lecture hall
+and whoever catches it has to
+
+ align:start position:0%
+and whoever catches it has to
+ 
+
+ align:start position:0%
+and whoever catches it has to
+respond and that response you share it
+
+ align:start position:0%
+respond and that response you share it
+ 
+
+ align:start position:0%
+respond and that response you share it
+with the group comment on it if you want
+
+ align:start position:0%
+with the group comment on it if you want
+ 
+
+ align:start position:0%
+with the group comment on it if you want
+to comment on it and then that person
+
+ align:start position:0%
+to comment on it and then that person
+ 
+
+ align:start position:0%
+to comment on it and then that person
+who gave the first response throws the
+
+ align:start position:0%
+who gave the first response throws the
+ 
+
+ align:start position:0%
+who gave the first response throws the
+ball to somebody else and then whoever
+
+ align:start position:0%
+ball to somebody else and then whoever
+ 
+
+ align:start position:0%
+ball to somebody else and then whoever
+catches the ball that time responds Etc
+
+ align:start position:0%
+catches the ball that time responds Etc
+ 
+
+ align:start position:0%
+catches the ball that time responds Etc
+um you can use it coupled with a picture
+
+ align:start position:0%
+um you can use it coupled with a picture
+ 
+
+ align:start position:0%
+um you can use it coupled with a picture
+prompt or or a graph so if you show a
+
+ align:start position:0%
+prompt or or a graph so if you show a
+ 
+
+ align:start position:0%
+prompt or or a graph so if you show a
+graph or an image and you say tell me
+
+ align:start position:0%
+graph or an image and you say tell me
+ 
+
+ align:start position:0%
+graph or an image and you say tell me
+one thing tell me something you observe
+
+ align:start position:0%
+one thing tell me something you observe
+ 
+
+ align:start position:0%
+one thing tell me something you observe
+about this image and then you throw the
+
+ align:start position:0%
+about this image and then you throw the
+ 
+
+ align:start position:0%
+about this image and then you throw the
+ball and the person that catches it
+
+ align:start position:0%
+ball and the person that catches it
+ 
+
+ align:start position:0%
+ball and the person that catches it
+first says one thing they observe and
+
+ align:start position:0%
+first says one thing they observe and
+ 
+
+ align:start position:0%
+first says one thing they observe and
+they throw it and the next person says
+
+ align:start position:0%
+they throw it and the next person says
+ 
+
+ align:start position:0%
+they throw it and the next person says
+something that they observed about the
+
+ align:start position:0%
+something that they observed about the
+ 
+
+ align:start position:0%
+something that they observed about the
+picture prompt so that that that gives a
+
+ align:start position:0%
+picture prompt so that that that gives a
+ 
+
+ align:start position:0%
+picture prompt so that that that gives a
+foundation and and it opens up uh space
+
+ align:start position:0%
+foundation and and it opens up uh space
+ 
+
+ align:start position:0%
+foundation and and it opens up uh space
+for lots of
+
+ align:start position:0%
+for lots of
+ 
+
+ align:start position:0%
+for lots of
+responses um it does a the beach ball
+
+ align:start position:0%
+responses um it does a the beach ball
+ 
+
+ align:start position:0%
+responses um it does a the beach ball
+does a few things one is that as the
+
+ align:start position:0%
+does a few things one is that as the
+ 
+
+ align:start position:0%
+does a few things one is that as the
+instructor you don't have to be the one
+
+ align:start position:0%
+instructor you don't have to be the one
+ 
+
+ align:start position:0%
+instructor you don't have to be the one
+that calls on on the students all the
+
+ align:start position:0%
+that calls on on the students all the
+ 
+
+ align:start position:0%
+that calls on on the students all the
+time so the students don't feel like
+
+ align:start position:0%
+time so the students don't feel like
+ 
+
+ align:start position:0%
+time so the students don't feel like
+you're picking on them that you're the
+
+ align:start position:0%
+you're picking on them that you're the
+ 
+
+ align:start position:0%
+you're picking on them that you're the
+one that's cold calling on them and in
+
+ align:start position:0%
+one that's cold calling on them and in
+ 
+
+ align:start position:0%
+one that's cold calling on them and in
+fact you can throw the beach ball
+
+ align:start position:0%
+fact you can throw the beach ball
+ 
+
+ align:start position:0%
+fact you can throw the beach ball
+completely blind the first time close
+
+ align:start position:0%
+completely blind the first time close
+ 
+
+ align:start position:0%
+completely blind the first time close
+your eyes throw the ball and and so
+
+ align:start position:0%
+your eyes throw the ball and and so
+ 
+
+ align:start position:0%
+your eyes throw the ball and and so
+nobody really feels that you've called
+
+ align:start position:0%
+nobody really feels that you've called
+ 
+
+ align:start position:0%
+nobody really feels that you've called
+on them and then subsequently it's other
+
+ align:start position:0%
+on them and then subsequently it's other
+ 
+
+ align:start position:0%
+on them and then subsequently it's other
+students that are throwing the ball so
+
+ align:start position:0%
+students that are throwing the ball so
+ 
+
+ align:start position:0%
+students that are throwing the ball so
+there's no issue about about that you're
+
+ align:start position:0%
+there's no issue about about that you're
+ 
+
+ align:start position:0%
+there's no issue about about that you're
+the one that's picking on the students
+
+ align:start position:0%
+the one that's picking on the students
+ 
+
+ align:start position:0%
+the one that's picking on the students
+um the other thing is it's kind of fun
+
+ align:start position:0%
+um the other thing is it's kind of fun
+ 
+
+ align:start position:0%
+um the other thing is it's kind of fun
+you're throwing the ball around so
+
+ align:start position:0%
+you're throwing the ball around so
+ 
+
+ align:start position:0%
+you're throwing the ball around so
+it uh it's hard to get upset it's hard
+
+ align:start position:0%
+it uh it's hard to get upset it's hard
+ 
+
+ align:start position:0%
+it uh it's hard to get upset it's hard
+to get as a student or nervous that
+
+ align:start position:0%
+to get as a student or nervous that
+ 
+
+ align:start position:0%
+to get as a student or nervous that
+you're going to you're going to have to
+
+ align:start position:0%
+you're going to you're going to have to
+ 
+
+ align:start position:0%
+you're going to you're going to have to
+answer the question and in fact you
+
+ align:start position:0%
+answer the question and in fact you
+ 
+
+ align:start position:0%
+answer the question and in fact you
+could Dodge the ball if you really
+
+ align:start position:0%
+could Dodge the ball if you really
+ 
+
+ align:start position:0%
+could Dodge the ball if you really
+didn't want to answer the question um so
+
+ align:start position:0%
+didn't want to answer the question um so
+ 
+
+ align:start position:0%
+didn't want to answer the question um so
+it's a great way to get students talking
+
+ align:start position:0%
+it's a great way to get students talking
+ 
+
+ align:start position:0%
+it's a great way to get students talking
+and in general it's it's pretty fun and
+
+ align:start position:0%
+and in general it's it's pretty fun and
+ 
+
+ align:start position:0%
+and in general it's it's pretty fun and
+at first I I thought oh I can't really
+
+ align:start position:0%
+at first I I thought oh I can't really
+ 
+
+ align:start position:0%
+at first I I thought oh I can't really
+use this with grad students it's it's
+
+ align:start position:0%
+use this with grad students it's it's
+ 
+
+ align:start position:0%
+use this with grad students it's it's
+too goofy it's too it's too baby or
+
+ align:start position:0%
+too goofy it's too it's too baby or
+ 
+
+ align:start position:0%
+too goofy it's too it's too baby or
+silly but but actually every time I use
+
+ align:start position:0%
+silly but but actually every time I use
+ 
+
+ align:start position:0%
+silly but but actually every time I use
+it with grad students post
+
+ align:start position:0%
+it with grad students post
+ 
+
+ align:start position:0%
+it with grad students post
+everybody seems perfectly fine with it I
+
+ align:start position:0%
+everybody seems perfectly fine with it I
+ 
+
+ align:start position:0%
+everybody seems perfectly fine with it I
+think it's more to do with the nature of
+
+ align:start position:0%
+think it's more to do with the nature of
+ 
+
+ align:start position:0%
+think it's more to do with the nature of
+the question if you just ask stupid
+
+ align:start position:0%
+the question if you just ask stupid
+ 
+
+ align:start position:0%
+the question if you just ask stupid
+questions and throw the ball around
+
+ align:start position:0%
+questions and throw the ball around
+ 
+
+ align:start position:0%
+questions and throw the ball around
+it'll be stupid but if you ask good
+
+ align:start position:0%
+it'll be stupid but if you ask good
+ 
+
+ align:start position:0%
+it'll be stupid but if you ask good
+questions and it's a way for students to
+
+ align:start position:0%
+questions and it's a way for students to
+ 
+
+ align:start position:0%
+questions and it's a way for students to
+get uh to give you their answers then it
+
+ align:start position:0%
+get uh to give you their answers then it
+ 
+
+ align:start position:0%
+get uh to give you their answers then it
+seems to work totally fine that's the
+
+ align:start position:0%
+seems to work totally fine that's the
+ 
+
+ align:start position:0%
+seems to work totally fine that's the
+general way sometimes I'll actually
+
+ align:start position:0%
+general way sometimes I'll actually
+ 
+
+ align:start position:0%
+general way sometimes I'll actually
+write questions on the beach ball and
+
+ align:start position:0%
+write questions on the beach ball and
+ 
+
+ align:start position:0%
+write questions on the beach ball and
+then throw the ball into the into the
+
+ align:start position:0%
+then throw the ball into the into the
+ 
+
+ align:start position:0%
+then throw the ball into the into the
+class and then students are Loosely
+
+ align:start position:0%
+class and then students are Loosely
+ 
+
+ align:start position:0%
+class and then students are Loosely
+supposed to answer the question that's
+
+ align:start position:0%
+supposed to answer the question that's
+ 
+
+ align:start position:0%
+supposed to answer the question that's
+in front of them when they catch the
+
+ align:start position:0%
+in front of them when they catch the
+ 
+
+ align:start position:0%
+in front of them when they catch the
+ball so that's another way to do it um
+
+ align:start position:0%
+ball so that's another way to do it um
+ 
+
+ align:start position:0%
+ball so that's another way to do it um
+but it's a nice inexpensive fairly
+
+ align:start position:0%
+but it's a nice inexpensive fairly
+ 
+
+ align:start position:0%
+but it's a nice inexpensive fairly
+flexible technique
\ No newline at end of file
diff --git a/M6ibQYbbuq8.txt b/M6ibQYbbuq8.txt
new file mode 100644
index 0000000000000000000000000000000000000000..f40128b35aec9bbefc803d609be0bd080126a037
--- /dev/null
+++ b/M6ibQYbbuq8.txt
@@ -0,0 +1,4168 @@
+align:start position:0%
+ 
+the following content is provided under
+
+ align:start position:0%
+the following content is provided under
+ 
+
+ align:start position:0%
+the following content is provided under
+a Creative Commons license your support
+
+ align:start position:0%
+a Creative Commons license your support
+ 
+
+ align:start position:0%
+a Creative Commons license your support
+will help MIT open courseware continue
+
+ align:start position:0%
+will help MIT open courseware continue
+ 
+
+ align:start position:0%
+will help MIT open courseware continue
+to offer highquality educational
+
+ align:start position:0%
+to offer highquality educational
+ 
+
+ align:start position:0%
+to offer highquality educational
+resources for free to make a donation or
+
+ align:start position:0%
+resources for free to make a donation or
+ 
+
+ align:start position:0%
+resources for free to make a donation or
+view additional materials from hundreds
+
+ align:start position:0%
+view additional materials from hundreds
+ 
+
+ align:start position:0%
+view additional materials from hundreds
+of MIT courses visit MIT opencourseware
+
+ align:start position:0%
+of MIT courses visit MIT opencourseware
+ 
+
+ align:start position:0%
+of MIT courses visit MIT opencourseware
+at ocw.mit.edu
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+edgerton's Boomer illustrates the
+
+ align:start position:0%
+edgerton's Boomer illustrates the
+ 
+
+ align:start position:0%
+edgerton's Boomer illustrates the
+induction of a current in a conductor
+
+ align:start position:0%
+induction of a current in a conductor
+ 
+
+ align:start position:0%
+induction of a current in a conductor
+subjected to a Time varying magnetic
+
+ align:start position:0%
+subjected to a Time varying magnetic
+ 
+
+ align:start position:0%
+subjected to a Time varying magnetic
+field and the associated magnetic
+
+ align:start position:0%
+field and the associated magnetic
+ 
+
+ align:start position:0%
+field and the associated magnetic
+forces it illustrates the interplay
+
+ align:start position:0%
+forces it illustrates the interplay
+ 
+
+ align:start position:0%
+forces it illustrates the interplay
+between the laws of feraday ampere and
+
+ align:start position:0%
+between the laws of feraday ampere and
+ 
+
+ align:start position:0%
+between the laws of feraday ampere and
+ohm that determines the distribution
+
+ align:start position:0%
+ohm that determines the distribution
+ 
+
+ align:start position:0%
+ohm that determines the distribution
+duration and magnitude of currents in
+
+ align:start position:0%
+duration and magnitude of currents in
+ 
+
+ align:start position:0%
+duration and magnitude of currents in
+conductors under Magneto quasistatic
+
+ align:start position:0%
+conductors under Magneto quasistatic
+ 
+
+ align:start position:0%
+conductors under Magneto quasistatic
+conditions
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the time varying magnetic field will be
+
+ align:start position:0%
+the time varying magnetic field will be
+ 
+
+ align:start position:0%
+the time varying magnetic field will be
+produced by a current through the
+
+ align:start position:0%
+produced by a current through the
+ 
+
+ align:start position:0%
+produced by a current through the
+windings of this
+
+ align:start position:0%
+windings of this
+ 
+
+ align:start position:0%
+windings of this
+coil to produce this current we'll first
+
+ align:start position:0%
+coil to produce this current we'll first
+ 
+
+ align:start position:0%
+coil to produce this current we'll first
+charge this capacitor to 4
+
+ align:start position:0%
+charge this capacitor to 4
+ 
+
+ align:start position:0%
+charge this capacitor to 4
+Kilts and then discharge the capacitor
+
+ align:start position:0%
+Kilts and then discharge the capacitor
+ 
+
+ align:start position:0%
+Kilts and then discharge the capacitor
+through the coil by closing this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+switch this is the
+
+ align:start position:0%
+switch this is the
+ 
+
+ align:start position:0%
+switch this is the
+coil the winding wire circulates like
+
+ align:start position:0%
+coil the winding wire circulates like
+ 
+
+ align:start position:0%
+coil the winding wire circulates like
+so and is connected Ed to the capacitors
+
+ align:start position:0%
+so and is connected Ed to the capacitors
+ 
+
+ align:start position:0%
+so and is connected Ed to the capacitors
+in this cabinet by these
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+leads when the high voltage power supply
+
+ align:start position:0%
+leads when the high voltage power supply
+ 
+
+ align:start position:0%
+leads when the high voltage power supply
+in the cabinet is turned
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+[Music]
+
+ align:start position:0%
+[Music]
+ 
+
+ align:start position:0%
+[Music]
+on the capacitor is charged to 4
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Kilts the switch then connects the
+
+ align:start position:0%
+Kilts the switch then connects the
+ 
+
+ align:start position:0%
+Kilts the switch then connects the
+capacitor to the coil it's closed when
+
+ align:start position:0%
+capacitor to the coil it's closed when
+ 
+
+ align:start position:0%
+capacitor to the coil it's closed when
+this button is pushed
+
+ align:start position:0%
+this button is pushed
+ 
+
+ align:start position:0%
+this button is pushed
+[Music]
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the switch consists of a spark gap which
+
+ align:start position:0%
+the switch consists of a spark gap which
+ 
+
+ align:start position:0%
+the switch consists of a spark gap which
+we just heard we can see it if we open
+
+ align:start position:0%
+we just heard we can see it if we open
+ 
+
+ align:start position:0%
+we just heard we can see it if we open
+this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+[Music]
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+panel the switch is closed by a spark
+
+ align:start position:0%
+panel the switch is closed by a spark
+ 
+
+ align:start position:0%
+panel the switch is closed by a spark
+cross this
+
+ align:start position:0%
+cross this
+ 
+
+ align:start position:0%
+cross this
+Gap that spark is activated by applying
+
+ align:start position:0%
+Gap that spark is activated by applying
+ 
+
+ align:start position:0%
+Gap that spark is activated by applying
+a voltage to this electrode to make a
+
+ align:start position:0%
+a voltage to this electrode to make a
+ 
+
+ align:start position:0%
+a voltage to this electrode to make a
+smaller electrical breakdown in the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Gap just once we'll bypass the safety
+
+ align:start position:0%
+Gap just once we'll bypass the safety
+ 
+
+ align:start position:0%
+Gap just once we'll bypass the safety
+interlock that ordinarily disconnects
+
+ align:start position:0%
+interlock that ordinarily disconnects
+ 
+
+ align:start position:0%
+interlock that ordinarily disconnects
+the circuit when the panel is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+opened then when we push the button we
+
+ align:start position:0%
+opened then when we push the button we
+ 
+
+ align:start position:0%
+opened then when we push the button we
+can not only hear the spark discharge
+
+ align:start position:0%
+can not only hear the spark discharge
+ 
+
+ align:start position:0%
+can not only hear the spark discharge
+that closes the switch but see the
+
+ align:start position:0%
+that closes the switch but see the
+ 
+
+ align:start position:0%
+that closes the switch but see the
+associated flash as as
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+well maybe we can do it once
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+more given the initial capacitor voltage
+
+ align:start position:0%
+more given the initial capacitor voltage
+ 
+
+ align:start position:0%
+more given the initial capacitor voltage
+of 4 Kilts and that the coil has 50
+
+ align:start position:0%
+of 4 Kilts and that the coil has 50
+ 
+
+ align:start position:0%
+of 4 Kilts and that the coil has 50
+turns we can use basic principles to
+
+ align:start position:0%
+turns we can use basic principles to
+ 
+
+ align:start position:0%
+turns we can use basic principles to
+estimate the winding current and hence
+
+ align:start position:0%
+estimate the winding current and hence
+ 
+
+ align:start position:0%
+estimate the winding current and hence
+the mag itic field intensity produced by
+
+ align:start position:0%
+the mag itic field intensity produced by
+ 
+
+ align:start position:0%
+the mag itic field intensity produced by
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+coil first we use ampere's integral law
+
+ align:start position:0%
+coil first we use ampere's integral law
+ 
+
+ align:start position:0%
+coil first we use ampere's integral law
+to relate the current to the
+
+ align:start position:0%
+to relate the current to the
+ 
+
+ align:start position:0%
+to relate the current to the
+field the line Contour encloses the
+
+ align:start position:0%
+field the line Contour encloses the
+ 
+
+ align:start position:0%
+field the line Contour encloses the
+current in the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+coil ampers integral law applied to this
+
+ align:start position:0%
+coil ampers integral law applied to this
+ 
+
+ align:start position:0%
+coil ampers integral law applied to this
+Contour
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+C given that the Contour has a radius
+
+ align:start position:0%
+C given that the Contour has a radius
+ 
+
+ align:start position:0%
+C given that the Contour has a radius
+equal to the average r radius of the
+
+ align:start position:0%
+equal to the average r radius of the
+ 
+
+ align:start position:0%
+equal to the average r radius of the
+coil winding
+
+ align:start position:0%
+coil winding
+ 
+
+ align:start position:0%
+coil winding
+a the Contour integral is approximated
+
+ align:start position:0%
+a the Contour integral is approximated
+ 
+
+ align:start position:0%
+a the Contour integral is approximated
+by the circumference 2 pi a multiplied
+
+ align:start position:0%
+by the circumference 2 pi a multiplied
+ 
+
+ align:start position:0%
+by the circumference 2 pi a multiplied
+by the average magnetic field
+
+ align:start position:0%
+by the average magnetic field
+ 
+
+ align:start position:0%
+by the average magnetic field
+intensity the current passing through
+
+ align:start position:0%
+intensity the current passing through
+ 
+
+ align:start position:0%
+intensity the current passing through
+the enclosed
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+surface is the number of turns N Sub
+
+ align:start position:0%
+surface is the number of turns N Sub
+ 
+
+ align:start position:0%
+surface is the number of turns N Sub
+one times the
+
+ align:start position:0%
+one times the
+ 
+
+ align:start position:0%
+one times the
+current so we can solve for the average
+
+ align:start position:0%
+current so we can solve for the average
+ 
+
+ align:start position:0%
+current so we can solve for the average
+magnetic field intens
+
+ align:start position:0%
+magnetic field intens
+ 
+
+ align:start position:0%
+magnetic field intens
+density to use this expression we need
+
+ align:start position:0%
+density to use this expression we need
+ 
+
+ align:start position:0%
+density to use this expression we need
+to know the coil current I
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+sub1 if the resistive loss of the
+
+ align:start position:0%
+sub1 if the resistive loss of the
+ 
+
+ align:start position:0%
+sub1 if the resistive loss of the
+circuit is small compared to the
+
+ align:start position:0%
+circuit is small compared to the
+ 
+
+ align:start position:0%
+circuit is small compared to the
+inductive and capacitive energy storage
+
+ align:start position:0%
+inductive and capacitive energy storage
+ 
+
+ align:start position:0%
+inductive and capacitive energy storage
+this current is a damped
+
+ align:start position:0%
+this current is a damped
+ 
+
+ align:start position:0%
+this current is a damped
+oscillation in that case after a quarter
+
+ align:start position:0%
+oscillation in that case after a quarter
+ 
+
+ align:start position:0%
+oscillation in that case after a quarter
+of one oscillation all of the energy
+
+ align:start position:0%
+of one oscillation all of the energy
+ 
+
+ align:start position:0%
+of one oscillation all of the energy
+initially stored in the capacitor
+
+ align:start position:0%
+initially stored in the capacitor
+ 
+
+ align:start position:0%
+initially stored in the capacitor
+essentially ends up stored in the
+
+ align:start position:0%
+essentially ends up stored in the
+ 
+
+ align:start position:0%
+essentially ends up stored in the
+inductor
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the peak energy in the
+
+ align:start position:0%
+the peak energy in the
+ 
+
+ align:start position:0%
+the peak energy in the
+capacitor is 1/2 the capacitance c times
+
+ align:start position:0%
+capacitor is 1/2 the capacitance c times
+ 
+
+ align:start position:0%
+capacitor is 1/2 the capacitance c times
+the square of the initial
+
+ align:start position:0%
+the square of the initial
+ 
+
+ align:start position:0%
+the square of the initial
+voltage the peak energy in the coil a
+
+ align:start position:0%
+voltage the peak energy in the coil a
+ 
+
+ align:start position:0%
+voltage the peak energy in the coil a
+quarter of a cycle later is 1 half its
+
+ align:start position:0%
+quarter of a cycle later is 1 half its
+ 
+
+ align:start position:0%
+quarter of a cycle later is 1 half its
+inductance times the peak current
+
+ align:start position:0%
+inductance times the peak current
+ 
+
+ align:start position:0%
+inductance times the peak current
+squared so the peak coil current is
+
+ align:start position:0%
+squared so the peak coil current is
+ 
+
+ align:start position:0%
+squared so the peak coil current is
+proportional to the initial capacitor
+
+ align:start position:0%
+proportional to the initial capacitor
+ 
+
+ align:start position:0%
+proportional to the initial capacitor
+voltage to use this expression we must
+
+ align:start position:0%
+voltage to use this expression we must
+ 
+
+ align:start position:0%
+voltage to use this expression we must
+estimate the coil indu
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+remember ampers law was used to find
+
+ align:start position:0%
+remember ampers law was used to find
+ 
+
+ align:start position:0%
+remember ampers law was used to find
+this average magnetic field
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+intensity the average flux linked by all
+
+ align:start position:0%
+intensity the average flux linked by all
+ 
+
+ align:start position:0%
+intensity the average flux linked by all
+the turns of the coil is the number of
+
+ align:start position:0%
+the turns of the coil is the number of
+ 
+
+ align:start position:0%
+the turns of the coil is the number of
+turns times the average coil
+
+ align:start position:0%
+turns times the average coil
+ 
+
+ align:start position:0%
+turns times the average coil
+area multiplied by this flux
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+density if we use our approximate field
+
+ align:start position:0%
+density if we use our approximate field
+ 
+
+ align:start position:0%
+density if we use our approximate field
+intensity to evaluate this flux we see
+
+ align:start position:0%
+intensity to evaluate this flux we see
+ 
+
+ align:start position:0%
+intensity to evaluate this flux we see
+that it is proportional to
+
+ align:start position:0%
+that it is proportional to
+ 
+
+ align:start position:0%
+that it is proportional to
+i1 the coefficient is the desired coil
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+inductance for our coil a is on the
+
+ align:start position:0%
+inductance for our coil a is on the
+ 
+
+ align:start position:0%
+inductance for our coil a is on the
+order of 7
+
+ align:start position:0%
+order of 7
+ 
+
+ align:start position:0%
+order of 7
+cm there are about 50
+
+ align:start position:0%
+cm there are about 50
+ 
+
+ align:start position:0%
+cm there are about 50
+turns so the coil inductance is about
+
+ align:start position:0%
+turns so the coil inductance is about
+ 
+
+ align:start position:0%
+turns so the coil inductance is about
+1/10 of a
+
+ align:start position:0%
+1/10 of a
+ 
+
+ align:start position:0%
+1/10 of a
+millihenry in turn we can now
+
+ align:start position:0%
+millihenry in turn we can now
+ 
+
+ align:start position:0%
+millihenry in turn we can now
+approximate the peak coil
+
+ align:start position:0%
+approximate the peak coil
+ 
+
+ align:start position:0%
+approximate the peak coil
+current the capacitance is 16
+
+ align:start position:0%
+current the capacitance is 16
+ 
+
+ align:start position:0%
+current the capacitance is 16
+microfarads so for an initial voltage of
+
+ align:start position:0%
+microfarads so for an initial voltage of
+ 
+
+ align:start position:0%
+microfarads so for an initial voltage of
+
+ align:start position:0%
+ 
+
+ align:start position:0%
+Kilts the peak coil current is about
+
+ align:start position:0%
+Kilts the peak coil current is about
+ 
+
+ align:start position:0%
+Kilts the peak coil current is about
+1,600
+
+ align:start position:0%
+1,600
+ 
+
+ align:start position:0%
+1,600
+amp from this current it follows from
+
+ align:start position:0%
+amp from this current it follows from
+ 
+
+ align:start position:0%
+amp from this current it follows from
+ampers law that the peak magnetic field
+
+ align:start position:0%
+ampers law that the peak magnetic field
+ 
+
+ align:start position:0%
+ampers law that the peak magnetic field
+intensity is 1.8 * 10 5th amps per
+
+ align:start position:0%
+intensity is 1.8 * 10 5th amps per
+ 
+
+ align:start position:0%
+intensity is 1.8 * 10 5th amps per
+meter in free space the peak flux
+
+ align:start position:0%
+meter in free space the peak flux
+ 
+
+ align:start position:0%
+meter in free space the peak flux
+density is therefore 23 T
+
+ align:start position:0%
+density is therefore 23 T
+ 
+
+ align:start position:0%
+density is therefore 23 T
+Tesla about 2300
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Gus the energy oscillates back and forth
+
+ align:start position:0%
+Gus the energy oscillates back and forth
+ 
+
+ align:start position:0%
+Gus the energy oscillates back and forth
+between the capacitor and the
+
+ align:start position:0%
+between the capacitor and the
+ 
+
+ align:start position:0%
+between the capacitor and the
+inductor provided that the circuit
+
+ align:start position:0%
+inductor provided that the circuit
+ 
+
+ align:start position:0%
+inductor provided that the circuit
+resistance is not too large this is the
+
+ align:start position:0%
+resistance is not too large this is the
+ 
+
+ align:start position:0%
+resistance is not too large this is the
+frequency of the
+
+ align:start position:0%
+frequency of the
+ 
+
+ align:start position:0%
+frequency of the
+oscillation once again using the
+
+ align:start position:0%
+oscillation once again using the
+ 
+
+ align:start position:0%
+oscillation once again using the
+inductance of 1/10
+
+ align:start position:0%
+inductance of 1/10
+ 
+
+ align:start position:0%
+inductance of 1/10
+mhenry the capacitance of 16
+
+ align:start position:0%
+mhenry the capacitance of 16
+ 
+
+ align:start position:0%
+mhenry the capacitance of 16
+microfarads we estimate the frequency to
+
+ align:start position:0%
+microfarads we estimate the frequency to
+ 
+
+ align:start position:0%
+microfarads we estimate the frequency to
+be about 4
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+khz before we go on let's see how well
+
+ align:start position:0%
+khz before we go on let's see how well
+ 
+
+ align:start position:0%
+khz before we go on let's see how well
+we've approximated the current and
+
+ align:start position:0%
+we've approximated the current and
+ 
+
+ align:start position:0%
+we've approximated the current and
+field this current probe will link one
+
+ align:start position:0%
+field this current probe will link one
+ 
+
+ align:start position:0%
+field this current probe will link one
+of the wires connected to the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+coil we display the coil current on the
+
+ align:start position:0%
+coil we display the coil current on the
+ 
+
+ align:start position:0%
+coil we display the coil current on the
+lower scope
+
+ align:start position:0%
+lower scope
+ 
+
+ align:start position:0%
+lower scope
+trace the voltage induced at the
+
+ align:start position:0%
+trace the voltage induced at the
+ 
+
+ align:start position:0%
+trace the voltage induced at the
+terminals of this
+
+ align:start position:0%
+terminals of this
+ 
+
+ align:start position:0%
+terminals of this
+coil by the time ing magnetic flux
+
+ align:start position:0%
+coil by the time ing magnetic flux
+ 
+
+ align:start position:0%
+coil by the time ing magnetic flux
+density will be used to deduce
+
+ align:start position:0%
+density will be used to deduce
+ 
+
+ align:start position:0%
+density will be used to deduce
+B this voltage will be displayed as the
+
+ align:start position:0%
+B this voltage will be displayed as the
+ 
+
+ align:start position:0%
+B this voltage will be displayed as the
+upper scope
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Trace here are the responses to the
+
+ align:start position:0%
+Trace here are the responses to the
+ 
+
+ align:start position:0%
+Trace here are the responses to the
+discharge of the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+capacitor the time axis is 2/10 of a
+
+ align:start position:0%
+capacitor the time axis is 2/10 of a
+ 
+
+ align:start position:0%
+capacitor the time axis is 2/10 of a
+millisecond per
+
+ align:start position:0%
+millisecond per
+ 
+
+ align:start position:0%
+millisecond per
+division so the period of the
+
+ align:start position:0%
+division so the period of the
+ 
+
+ align:start position:0%
+division so the period of the
+oscillation is about 1/3 of a
+
+ align:start position:0%
+oscillation is about 1/3 of a
+ 
+
+ align:start position:0%
+oscillation is about 1/3 of a
+millisecond the oscillation frequency is
+
+ align:start position:0%
+millisecond the oscillation frequency is
+ 
+
+ align:start position:0%
+millisecond the oscillation frequency is
+roughly the predicted 4
+
+ align:start position:0%
+roughly the predicted 4
+ 
+
+ align:start position:0%
+roughly the predicted 4
+khz the duration of the lower Trace
+
+ align:start position:0%
+khz the duration of the lower Trace
+ 
+
+ align:start position:0%
+khz the duration of the lower Trace
+current and hence of the field is on the
+
+ align:start position:0%
+current and hence of the field is on the
+ 
+
+ align:start position:0%
+current and hence of the field is on the
+order of 1
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+millisecond the peak in the current on
+
+ align:start position:0%
+millisecond the peak in the current on
+ 
+
+ align:start position:0%
+millisecond the peak in the current on
+the lower Trace is about one
+
+ align:start position:0%
+the lower Trace is about one
+ 
+
+ align:start position:0%
+the lower Trace is about one
+division there are 1,000 amps per
+
+ align:start position:0%
+division there are 1,000 amps per
+ 
+
+ align:start position:0%
+division there are 1,000 amps per
+division so the peak current is about
+
+ align:start position:0%
+division so the peak current is about
+ 
+
+ align:start position:0%
+division so the peak current is about
+1,000 amps
+
+ align:start position:0%
+1,000 amps
+ 
+
+ align:start position:0%
+1,000 amps
+this is in the range of the estimated
+
+ align:start position:0%
+this is in the range of the estimated
+ 
+
+ align:start position:0%
+this is in the range of the estimated
+value of 1600 amps remember we've not
+
+ align:start position:0%
+value of 1600 amps remember we've not
+ 
+
+ align:start position:0%
+value of 1600 amps remember we've not
+accounted for losses in the spark gap in
+
+ align:start position:0%
+accounted for losses in the spark gap in
+ 
+
+ align:start position:0%
+accounted for losses in the spark gap in
+the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+coil finally the voltage of our
+
+ align:start position:0%
+coil finally the voltage of our
+ 
+
+ align:start position:0%
+coil finally the voltage of our
+induction Loop the upper Trace is
+
+ align:start position:0%
+induction Loop the upper Trace is
+ 
+
+ align:start position:0%
+induction Loop the upper Trace is
+related to the coil area and turns by
+
+ align:start position:0%
+related to the coil area and turns by
+ 
+
+ align:start position:0%
+related to the coil area and turns by
+Faraday's
+
+ align:start position:0%
+Faraday's
+ 
+
+ align:start position:0%
+Faraday's
+law the coil voltage is the rate of
+
+ align:start position:0%
+law the coil voltage is the rate of
+ 
+
+ align:start position:0%
+law the coil voltage is the rate of
+change of the flux the product of its
+
+ align:start position:0%
+change of the flux the product of its
+ 
+
+ align:start position:0%
+change of the flux the product of its
+area its turns and the magnetic flux
+
+ align:start position:0%
+area its turns and the magnetic flux
+ 
+
+ align:start position:0%
+area its turns and the magnetic flux
+density we approximate the derivative by
+
+ align:start position:0%
+density we approximate the derivative by
+ 
+
+ align:start position:0%
+density we approximate the derivative by
+Omega so this is
+
+ align:start position:0%
+Omega so this is
+ 
+
+ align:start position:0%
+Omega so this is
+B there are 200 turns the area is 2.4 *
+
+ align:start position:0%
+B there are 200 turns the area is 2.4 *
+ 
+
+ align:start position:0%
+B there are 200 turns the area is 2.4 *
+10-4 M
+
+ align:start position:0%
+10-4 M
+ 
+
+ align:start position:0%
+10-4 M
+squar the estimated frequency is 4
+
+ align:start position:0%
+squar the estimated frequency is 4
+ 
+
+ align:start position:0%
+squar the estimated frequency is 4
+khz and the peak voltage is 500
+
+ align:start position:0%
+khz and the peak voltage is 500
+ 
+
+ align:start position:0%
+khz and the peak voltage is 500
+volt we conclude that near the center of
+
+ align:start position:0%
+volt we conclude that near the center of
+ 
+
+ align:start position:0%
+volt we conclude that near the center of
+the coil the peak magnetic flux density
+
+ align:start position:0%
+the coil the peak magnetic flux density
+ 
+
+ align:start position:0%
+the coil the peak magnetic flux density
+is4 Tesla
+
+ align:start position:0%
+is4 Tesla
+ 
+
+ align:start position:0%
+is4 Tesla
+4,000
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+gaus our estimate of the space average
+
+ align:start position:0%
+gaus our estimate of the space average
+ 
+
+ align:start position:0%
+gaus our estimate of the space average
+for this peak value of the flux density
+
+ align:start position:0%
+for this peak value of the flux density
+ 
+
+ align:start position:0%
+for this peak value of the flux density
+was 2,300 GA somewhat less as it should
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+be now suppose that a conducting disc is
+
+ align:start position:0%
+be now suppose that a conducting disc is
+ 
+
+ align:start position:0%
+be now suppose that a conducting disc is
+placed just above the
+
+ align:start position:0%
+placed just above the
+ 
+
+ align:start position:0%
+placed just above the
+coil what's the current induced in the
+
+ align:start position:0%
+coil what's the current induced in the
+ 
+
+ align:start position:0%
+coil what's the current induced in the
+disc to obtain a rough approximation We
+
+ align:start position:0%
+disc to obtain a rough approximation We
+ 
+
+ align:start position:0%
+disc to obtain a rough approximation We
+Begin by applying Faraday's integral law
+
+ align:start position:0%
+Begin by applying Faraday's integral law
+ 
+
+ align:start position:0%
+Begin by applying Faraday's integral law
+to this this
+
+ align:start position:0%
+to this this
+ 
+
+ align:start position:0%
+to this this
+Contour it encloses the surface s lying
+
+ align:start position:0%
+Contour it encloses the surface s lying
+ 
+
+ align:start position:0%
+Contour it encloses the surface s lying
+in the plane of the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+disc the line integral of the azimuthal
+
+ align:start position:0%
+disc the line integral of the azimuthal
+ 
+
+ align:start position:0%
+disc the line integral of the azimuthal
+electric
+
+ align:start position:0%
+electric
+ 
+
+ align:start position:0%
+electric
+field is the product of the average
+
+ align:start position:0%
+field is the product of the average
+ 
+
+ align:start position:0%
+field is the product of the average
+circumference and that electric field
+
+ align:start position:0%
+circumference and that electric field
+ 
+
+ align:start position:0%
+circumference and that electric field
+intensity it's equal to the time rate of
+
+ align:start position:0%
+intensity it's equal to the time rate of
+ 
+
+ align:start position:0%
+intensity it's equal to the time rate of
+change of the net flux through the
+
+ align:start position:0%
+change of the net flux through the
+ 
+
+ align:start position:0%
+change of the net flux through the
+enclosed area Pi a^ 2
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the current density circulating in the
+
+ align:start position:0%
+the current density circulating in the
+ 
+
+ align:start position:0%
+the current density circulating in the
+disc follows from this field and ohms
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+law the disc could represent a
+
+ align:start position:0%
+law the disc could represent a
+ 
+
+ align:start position:0%
+law the disc could represent a
+hand in that case the experiment can
+
+ align:start position:0%
+hand in that case the experiment can
+ 
+
+ align:start position:0%
+hand in that case the experiment can
+literally give a feel for the
+
+ align:start position:0%
+literally give a feel for the
+ 
+
+ align:start position:0%
+literally give a feel for the
+consequence of subjecting a conductor to
+
+ align:start position:0%
+consequence of subjecting a conductor to
+ 
+
+ align:start position:0%
+consequence of subjecting a conductor to
+a Time varying magnetic
+
+ align:start position:0%
+a Time varying magnetic
+ 
+
+ align:start position:0%
+a Time varying magnetic
+field if the disc represents a hand what
+
+ align:start position:0%
+field if the disc represents a hand what
+ 
+
+ align:start position:0%
+field if the disc represents a hand what
+current density would be
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+felt here's our estimated current
+
+ align:start position:0%
+felt here's our estimated current
+ 
+
+ align:start position:0%
+felt here's our estimated current
+density for flush the conductivity is on
+
+ align:start position:0%
+density for flush the conductivity is on
+ 
+
+ align:start position:0%
+density for flush the conductivity is on
+the order of one semen per
+
+ align:start position:0%
+the order of one semen per
+ 
+
+ align:start position:0%
+the order of one semen per
+meter here's the permeability of free
+
+ align:start position:0%
+meter here's the permeability of free
+ 
+
+ align:start position:0%
+meter here's the permeability of free
+space and the average coil
+
+ align:start position:0%
+space and the average coil
+ 
+
+ align:start position:0%
+space and the average coil
+radius the angular frequency roughly 2
+
+ align:start position:0%
+radius the angular frequency roughly 2
+ 
+
+ align:start position:0%
+radius the angular frequency roughly 2
+pi * 4
+
+ align:start position:0%
+pi * 4
+ 
+
+ align:start position:0%
+pi * 4
+khz this is our calculated average field
+
+ align:start position:0%
+khz this is our calculated average field
+ 
+
+ align:start position:0%
+khz this is our calculated average field
+intensity so so the current density is
+
+ align:start position:0%
+intensity so so the current density is
+ 
+
+ align:start position:0%
+intensity so so the current density is
+approximately 200 amps per square
+
+ align:start position:0%
+approximately 200 amps per square
+ 
+
+ align:start position:0%
+approximately 200 amps per square
+met because a square cm is typical of
+
+ align:start position:0%
+met because a square cm is typical of
+ 
+
+ align:start position:0%
+met because a square cm is typical of
+the cross-sectional area through a
+
+ align:start position:0%
+the cross-sectional area through a
+ 
+
+ align:start position:0%
+the cross-sectional area through a
+hand we have a better feel for this
+
+ align:start position:0%
+hand we have a better feel for this
+ 
+
+ align:start position:0%
+hand we have a better feel for this
+number expressed as 20 milliamps per
+
+ align:start position:0%
+number expressed as 20 milliamps per
+ 
+
+ align:start position:0%
+number expressed as 20 milliamps per
+square
+
+ align:start position:0%
+square
+ 
+
+ align:start position:0%
+square
+cm this is more than enough to give a
+
+ align:start position:0%
+cm this is more than enough to give a
+ 
+
+ align:start position:0%
+cm this is more than enough to give a
+good
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+shock magnetic field created by the coil
+
+ align:start position:0%
+shock magnetic field created by the coil
+ 
+
+ align:start position:0%
+shock magnetic field created by the coil
+is
+
+ align:start position:0%
+is
+ 
+
+ align:start position:0%
+is
+non-uniform far away that of a
+
+ align:start position:0%
+non-uniform far away that of a
+ 
+
+ align:start position:0%
+non-uniform far away that of a
+dipole so we can discern what we're
+
+ align:start position:0%
+dipole so we can discern what we're
+ 
+
+ align:start position:0%
+dipole so we can discern what we're
+getting into by feeling the induced
+
+ align:start position:0%
+getting into by feeling the induced
+ 
+
+ align:start position:0%
+getting into by feeling the induced
+current in
+
+ align:start position:0%
+current in
+ 
+
+ align:start position:0%
+current in
+[Music]
+
+ align:start position:0%
+[Music]
+ 
+
+ align:start position:0%
+[Music]
+stages the sensation is of a short
+
+ align:start position:0%
+stages the sensation is of a short
+ 
+
+ align:start position:0%
+stages the sensation is of a short
+duration
+
+ align:start position:0%
+duration
+ 
+
+ align:start position:0%
+duration
+twinge much as would be expected for a
+
+ align:start position:0%
+twinge much as would be expected for a
+ 
+
+ align:start position:0%
+twinge much as would be expected for a
+pulse that lasts 1 millisecond
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh I've been given to understand that
+
+ align:start position:0%
+uh I've been given to understand that
+ 
+
+ align:start position:0%
+uh I've been given to understand that
+Professor Zan is not going to try it
+
+ align:start position:0%
+Professor Zan is not going to try it
+ 
+
+ align:start position:0%
+Professor Zan is not going to try it
+with his hand lower than
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this so that you can see evidence of the
+
+ align:start position:0%
+this so that you can see evidence of the
+ 
+
+ align:start position:0%
+this so that you can see evidence of the
+field that you can't feel
+
+ align:start position:0%
+field that you can't feel
+ 
+
+ align:start position:0%
+field that you can't feel
+firsthand let's replace his hand by this
+
+ align:start position:0%
+firsthand let's replace his hand by this
+ 
+
+ align:start position:0%
+firsthand let's replace his hand by this
+wire
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Loop the wire is open at this
+
+ align:start position:0%
+Loop the wire is open at this
+ 
+
+ align:start position:0%
+Loop the wire is open at this
+point with the ends barely touching
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so the field induced around the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Contour is concentrated at the
+
+ align:start position:0%
+Contour is concentrated at the
+ 
+
+ align:start position:0%
+Contour is concentrated at the
+Gap we go to a higher f- stop to protect
+
+ align:start position:0%
+Gap we go to a higher f- stop to protect
+ 
+
+ align:start position:0%
+Gap we go to a higher f- stop to protect
+the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+camera the integral of the electric
+
+ align:start position:0%
+camera the integral of the electric
+ 
+
+ align:start position:0%
+camera the integral of the electric
+field intensity is concentrated in a gap
+
+ align:start position:0%
+field intensity is concentrated in a gap
+ 
+
+ align:start position:0%
+field intensity is concentrated in a gap
+region that is initially relatively
+
+ align:start position:0%
+region that is initially relatively
+ 
+
+ align:start position:0%
+region that is initially relatively
+insulating so so the electric field
+
+ align:start position:0%
+insulating so so the electric field
+ 
+
+ align:start position:0%
+insulating so so the electric field
+intensity between the almost touching
+
+ align:start position:0%
+intensity between the almost touching
+ 
+
+ align:start position:0%
+intensity between the almost touching
+wires is enough to produce a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+spark the conductivity of this aluminum
+
+ align:start position:0%
+spark the conductivity of this aluminum
+ 
+
+ align:start position:0%
+spark the conductivity of this aluminum
+disc is more than 10 million times
+
+ align:start position:0%
+disc is more than 10 million times
+ 
+
+ align:start position:0%
+disc is more than 10 million times
+larger than for human flesh and there's
+
+ align:start position:0%
+larger than for human flesh and there's
+ 
+
+ align:start position:0%
+larger than for human flesh and there's
+no Gap to limit the induced current
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+if we presume that the coil links the
+
+ align:start position:0%
+if we presume that the coil links the
+ 
+
+ align:start position:0%
+if we presume that the coil links the
+aluminum disc with the same magnetic
+
+ align:start position:0%
+aluminum disc with the same magnetic
+ 
+
+ align:start position:0%
+aluminum disc with the same magnetic
+flux as it does the hand the laws of
+
+ align:start position:0%
+flux as it does the hand the laws of
+ 
+
+ align:start position:0%
+flux as it does the hand the laws of
+Faraday and ohm would say that the
+
+ align:start position:0%
+Faraday and ohm would say that the
+ 
+
+ align:start position:0%
+Faraday and ohm would say that the
+current density should be more than 10
+
+ align:start position:0%
+current density should be more than 10
+ 
+
+ align:start position:0%
+current density should be more than 10
+million times
+
+ align:start position:0%
+million times
+ 
+
+ align:start position:0%
+million times
+larger the conductivity of the disc is
+
+ align:start position:0%
+larger the conductivity of the disc is
+ 
+
+ align:start position:0%
+larger the conductivity of the disc is
+3.5 * 10 7 seans per
+
+ align:start position:0%
+3.5 * 10 7 seans per
+ 
+
+ align:start position:0%
+3.5 * 10 7 seans per
+meter rather than about one as it was
+
+ align:start position:0%
+meter rather than about one as it was
+ 
+
+ align:start position:0%
+meter rather than about one as it was
+for the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+hand however the current induced in the
+
+ align:start position:0%
+hand however the current induced in the
+ 
+
+ align:start position:0%
+hand however the current induced in the
+dis is so large that it produces a field
+
+ align:start position:0%
+dis is so large that it produces a field
+ 
+
+ align:start position:0%
+dis is so large that it produces a field
+of its own that limits the flux actually
+
+ align:start position:0%
+of its own that limits the flux actually
+ 
+
+ align:start position:0%
+of its own that limits the flux actually
+linked by the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+dis the current induced in the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+disc is so large that it produces a
+
+ align:start position:0%
+disc is so large that it produces a
+ 
+
+ align:start position:0%
+disc is so large that it produces a
+field of its
+
+ align:start position:0%
+field of its
+ 
+
+ align:start position:0%
+field of its
+own that limits the flux actually linked
+
+ align:start position:0%
+own that limits the flux actually linked
+ 
+
+ align:start position:0%
+own that limits the flux actually linked
+by the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+dis this induced magnetic field tends to
+
+ align:start position:0%
+dis this induced magnetic field tends to
+ 
+
+ align:start position:0%
+dis this induced magnetic field tends to
+Buck out the field from the coil
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+to see this let's again use ampers
+
+ align:start position:0%
+to see this let's again use ampers
+ 
+
+ align:start position:0%
+to see this let's again use ampers
+integral law to estimate the magnetic
+
+ align:start position:0%
+integral law to estimate the magnetic
+ 
+
+ align:start position:0%
+integral law to estimate the magnetic
+field
+
+ align:start position:0%
+field
+ 
+
+ align:start position:0%
+field
+intensity this time it's the field
+
+ align:start position:0%
+intensity this time it's the field
+ 
+
+ align:start position:0%
+intensity this time it's the field
+associated with a current that is
+
+ align:start position:0%
+associated with a current that is
+ 
+
+ align:start position:0%
+associated with a current that is
+induced in the
+
+ align:start position:0%
+induced in the
+ 
+
+ align:start position:0%
+induced in the
+dis the result is the same as it was for
+
+ align:start position:0%
+dis the result is the same as it was for
+ 
+
+ align:start position:0%
+dis the result is the same as it was for
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+coil except that now that current is in
+
+ align:start position:0%
+coil except that now that current is in
+ 
+
+ align:start position:0%
+coil except that now that current is in
+the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+dis this current is roughly the current
+
+ align:start position:0%
+dis this current is roughly the current
+ 
+
+ align:start position:0%
+dis this current is roughly the current
+density
+
+ align:start position:0%
+density
+ 
+
+ align:start position:0%
+density
+times the average cross-sectional area
+
+ align:start position:0%
+times the average cross-sectional area
+ 
+
+ align:start position:0%
+times the average cross-sectional area
+of the
+
+ align:start position:0%
+of the
+ 
+
+ align:start position:0%
+of the
+disc the average radius a times the disc
+
+ align:start position:0%
+disc the average radius a times the disc
+ 
+
+ align:start position:0%
+disc the average radius a times the disc
+thickness
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Delta provided this induced field is not
+
+ align:start position:0%
+Delta provided this induced field is not
+ 
+
+ align:start position:0%
+Delta provided this induced field is not
+too large compared to that from the coil
+
+ align:start position:0%
+too large compared to that from the coil
+ 
+
+ align:start position:0%
+too large compared to that from the coil
+we've already approximated this current
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+density so we can now evaluate the ratio
+
+ align:start position:0%
+density so we can now evaluate the ratio
+ 
+
+ align:start position:0%
+density so we can now evaluate the ratio
+of the field associated with the disc
+
+ align:start position:0%
+of the field associated with the disc
+ 
+
+ align:start position:0%
+of the field associated with the disc
+current to that imposed by the coil
+
+ align:start position:0%
+current to that imposed by the coil
+ 
+
+ align:start position:0%
+current to that imposed by the coil
+current with the time rate of change
+
+ align:start position:0%
+current with the time rate of change
+ 
+
+ align:start position:0%
+current with the time rate of change
+taken as being roughly the angular
+
+ align:start position:0%
+taken as being roughly the angular
+ 
+
+ align:start position:0%
+taken as being roughly the angular
+frequency times the peak composed field
+
+ align:start position:0%
+frequency times the peak composed field
+ 
+
+ align:start position:0%
+frequency times the peak composed field
+intensity this ratio is within 4 Pi of
+
+ align:start position:0%
+intensity this ratio is within 4 Pi of
+ 
+
+ align:start position:0%
+intensity this ratio is within 4 Pi of
+the product of the angular frequency and
+
+ align:start position:0%
+the product of the angular frequency and
+ 
+
+ align:start position:0%
+the product of the angular frequency and
+the Magnetic diffusion
+
+ align:start position:0%
+the Magnetic diffusion
+ 
+
+ align:start position:0%
+the Magnetic diffusion
+time this time is based on the geometric
+
+ align:start position:0%
+time this time is based on the geometric
+ 
+
+ align:start position:0%
+time this time is based on the geometric
+mean of the dis
+
+ align:start position:0%
+mean of the dis
+ 
+
+ align:start position:0%
+mean of the dis
+thickness and its average
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+radius if the frequency is high
+
+ align:start position:0%
+radius if the frequency is high
+ 
+
+ align:start position:0%
+radius if the frequency is high
+or this magnetic diffusion time is long
+
+ align:start position:0%
+or this magnetic diffusion time is long
+ 
+
+ align:start position:0%
+or this magnetic diffusion time is long
+the current induced in the dis is large
+
+ align:start position:0%
+the current induced in the dis is large
+ 
+
+ align:start position:0%
+the current induced in the dis is large
+enough to prevent much of the magnetic
+
+ align:start position:0%
+enough to prevent much of the magnetic
+ 
+
+ align:start position:0%
+enough to prevent much of the magnetic
+flux from the coil penetrating through
+
+ align:start position:0%
+flux from the coil penetrating through
+ 
+
+ align:start position:0%
+flux from the coil penetrating through
+its
+
+ align:start position:0%
+its
+ 
+
+ align:start position:0%
+its
+surface in the limit where Omega to m is
+
+ align:start position:0%
+surface in the limit where Omega to m is
+ 
+
+ align:start position:0%
+surface in the limit where Omega to m is
+large the dis acts as a secondary of an
+
+ align:start position:0%
+large the dis acts as a secondary of an
+ 
+
+ align:start position:0%
+large the dis acts as a secondary of an
+ideal
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Transformer if the coil current is like
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this its induced field is upward
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the current in the dis then
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+responds so as to Buck out this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+flux so the disc current is in the
+
+ align:start position:0%
+flux so the disc current is in the
+ 
+
+ align:start position:0%
+flux so the disc current is in the
+opposite direction of the coil
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+current is the product of the frequency
+
+ align:start position:0%
+current is the product of the frequency
+ 
+
+ align:start position:0%
+current is the product of the frequency
+and the Magnetic diffusion time for the
+
+ align:start position:0%
+and the Magnetic diffusion time for the
+ 
+
+ align:start position:0%
+and the Magnetic diffusion time for the
+aluminum
+
+ align:start position:0%
+aluminum
+ 
+
+ align:start position:0%
+aluminum
+disc large enough that it does tend to
+
+ align:start position:0%
+disc large enough that it does tend to
+ 
+
+ align:start position:0%
+disc large enough that it does tend to
+Buck out the imposed field
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+first let's evaluate to
+
+ align:start position:0%
+first let's evaluate to
+ 
+
+ align:start position:0%
+first let's evaluate to
+M the thickness is 2
+
+ align:start position:0%
+M the thickness is 2
+ 
+
+ align:start position:0%
+M the thickness is 2
+mm the average radius is 7
+
+ align:start position:0%
+mm the average radius is 7
+ 
+
+ align:start position:0%
+mm the average radius is 7
+cm and the conductivity of aluminum is
+
+ align:start position:0%
+cm and the conductivity of aluminum is
+ 
+
+ align:start position:0%
+cm and the conductivity of aluminum is
+3.5 * 10 7th Seaman per
+
+ align:start position:0%
+3.5 * 10 7th Seaman per
+ 
+
+ align:start position:0%
+3.5 * 10 7th Seaman per
+meter so TM is 6
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+milliseconds the ratio of H induced to H
+
+ align:start position:0%
+milliseconds the ratio of H induced to H
+ 
+
+ align:start position:0%
+milliseconds the ratio of H induced to H
+imposed Omega to over 4 Pi is about 12
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+12 with the aluminum disc we are indeed
+
+ align:start position:0%
+12 with the aluminum disc we are indeed
+ 
+
+ align:start position:0%
+12 with the aluminum disc we are indeed
+in the range where the disc current
+
+ align:start position:0%
+in the range where the disc current
+ 
+
+ align:start position:0%
+in the range where the disc current
+produces a field that bucks out the coil
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+current according to our approximate
+
+ align:start position:0%
+current according to our approximate
+ 
+
+ align:start position:0%
+current according to our approximate
+analysis the net field should tend to be
+
+ align:start position:0%
+analysis the net field should tend to be
+ 
+
+ align:start position:0%
+analysis the net field should tend to be
+shielded out of the disc by its own
+
+ align:start position:0%
+shielded out of the disc by its own
+ 
+
+ align:start position:0%
+shielded out of the disc by its own
+current the net field tends to be
+
+ align:start position:0%
+current the net field tends to be
+ 
+
+ align:start position:0%
+current the net field tends to be
+tangential to the
+
+ align:start position:0%
+tangential to the
+ 
+
+ align:start position:0%
+tangential to the
+disc one result is a net upward force on
+
+ align:start position:0%
+disc one result is a net upward force on
+ 
+
+ align:start position:0%
+disc one result is a net upward force on
+the disc
+
+ align:start position:0%
+the disc
+ 
+
+ align:start position:0%
+the disc
+this force is the result of a force
+
+ align:start position:0%
+this force is the result of a force
+ 
+
+ align:start position:0%
+this force is the result of a force
+density J crossed with
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+B
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+J crossed with
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+B the force can be used to shape metals
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+here the upward force is evident in the
+
+ align:start position:0%
+here the upward force is evident in the
+ 
+
+ align:start position:0%
+here the upward force is evident in the
+shaping of the outer edge of a foil disc
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+for this experiment we use three times
+
+ align:start position:0%
+for this experiment we use three times
+ 
+
+ align:start position:0%
+for this experiment we use three times
+as much
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+capacitance if the force can be used to
+
+ align:start position:0%
+capacitance if the force can be used to
+ 
+
+ align:start position:0%
+capacitance if the force can be used to
+shape the metal it can also be used to
+
+ align:start position:0%
+shape the metal it can also be used to
+ 
+
+ align:start position:0%
+shape the metal it can also be used to
+launch the
+
+ align:start position:0%
+launch the
+ 
+
+ align:start position:0%
+launch the
+disc if we leave the disc alone will it
+
+ align:start position:0%
+disc if we leave the disc alone will it
+ 
+
+ align:start position:0%
+disc if we leave the disc alone will it
+lift off after the button is
+
+ align:start position:0%
+lift off after the button is
+ 
+
+ align:start position:0%
+lift off after the button is
+pushed it's tempting to take an
+
+ align:start position:0%
+pushed it's tempting to take an
+ 
+
+ align:start position:0%
+pushed it's tempting to take an
+experimental approach but it's more fun
+
+ align:start position:0%
+experimental approach but it's more fun
+ 
+
+ align:start position:0%
+experimental approach but it's more fun
+to first see what we
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+predict the net force on the disc is the
+
+ align:start position:0%
+predict the net force on the disc is the
+ 
+
+ align:start position:0%
+predict the net force on the disc is the
+force density J crossb integrated over
+
+ align:start position:0%
+force density J crossb integrated over
+ 
+
+ align:start position:0%
+force density J crossb integrated over
+the disc
+
+ align:start position:0%
+the disc
+ 
+
+ align:start position:0%
+the disc
+volume essentially this is the surface
+
+ align:start position:0%
+volume essentially this is the surface
+ 
+
+ align:start position:0%
+volume essentially this is the surface
+current density in the
+
+ align:start position:0%
+current density in the
+ 
+
+ align:start position:0%
+current density in the
+dis times the magnetic flux density in
+
+ align:start position:0%
+dis times the magnetic flux density in
+ 
+
+ align:start position:0%
+dis times the magnetic flux density in
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+gap multiplied by the dis
+
+ align:start position:0%
+gap multiplied by the dis
+ 
+
+ align:start position:0%
+gap multiplied by the dis
+area the 1/2 accounts for the variation
+
+ align:start position:0%
+area the 1/2 accounts for the variation
+ 
+
+ align:start position:0%
+area the 1/2 accounts for the variation
+of B through the
+
+ align:start position:0%
+of B through the
+ 
+
+ align:start position:0%
+of B through the
+dis because Omega tow m is large the
+
+ align:start position:0%
+dis because Omega tow m is large the
+ 
+
+ align:start position:0%
+dis because Omega tow m is large the
+disc tends to act as a nearly perfect
+
+ align:start position:0%
+disc tends to act as a nearly perfect
+ 
+
+ align:start position:0%
+disc tends to act as a nearly perfect
+conductor current in the disc is then
+
+ align:start position:0%
+conductor current in the disc is then
+ 
+
+ align:start position:0%
+conductor current in the disc is then
+essentially equal to the field intensity
+
+ align:start position:0%
+essentially equal to the field intensity
+ 
+
+ align:start position:0%
+essentially equal to the field intensity
+in the
+
+ align:start position:0%
+in the
+ 
+
+ align:start position:0%
+in the
+Gap so this force is proportional to the
+
+ align:start position:0%
+Gap so this force is proportional to the
+ 
+
+ align:start position:0%
+Gap so this force is proportional to the
+force per unit area 12 mu
+
+ align:start position:0%
+force per unit area 12 mu
+ 
+
+ align:start position:0%
+force per unit area 12 mu
+h^2 times the area of the disc
+
+ align:start position:0%
+h^2 times the area of the disc
+ 
+
+ align:start position:0%
+h^2 times the area of the disc
+the additional 1/2 is because it is the
+
+ align:start position:0%
+the additional 1/2 is because it is the
+ 
+
+ align:start position:0%
+the additional 1/2 is because it is the
+time average of the square that is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+affected to evaluate this Force we guess
+
+ align:start position:0%
+affected to evaluate this Force we guess
+ 
+
+ align:start position:0%
+affected to evaluate this Force we guess
+that the field intensity in the Gap is
+
+ align:start position:0%
+that the field intensity in the Gap is
+ 
+
+ align:start position:0%
+that the field intensity in the Gap is
+perhaps two times that caused by the
+
+ align:start position:0%
+perhaps two times that caused by the
+ 
+
+ align:start position:0%
+perhaps two times that caused by the
+coil
+
+ align:start position:0%
+coil
+ 
+
+ align:start position:0%
+coil
+alone then the force Peaks at about 625
+
+ align:start position:0%
+alone then the force Peaks at about 625
+ 
+
+ align:start position:0%
+alone then the force Peaks at about 625
+Newtons the dis weighs about 80 gr so
+
+ align:start position:0%
+Newtons the dis weighs about 80 gr so
+ 
+
+ align:start position:0%
+Newtons the dis weighs about 80 gr so
+that the force of gravity is a little
+
+ align:start position:0%
+that the force of gravity is a little
+ 
+
+ align:start position:0%
+that the force of gravity is a little
+less than 1
+
+ align:start position:0%
+less than 1
+ 
+
+ align:start position:0%
+less than 1
+nton the magnetic force is about 800
+
+ align:start position:0%
+nton the magnetic force is about 800
+ 
+
+ align:start position:0%
+nton the magnetic force is about 800
+times greater than that due to
+
+ align:start position:0%
+times greater than that due to
+ 
+
+ align:start position:0%
+times greater than that due to
+gravity so we expect
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+liftoff but the force only acts for
+
+ align:start position:0%
+liftoff but the force only acts for
+ 
+
+ align:start position:0%
+liftoff but the force only acts for
+about a
+
+ align:start position:0%
+about a
+ 
+
+ align:start position:0%
+about a
+millisecond with what velocity will it
+
+ align:start position:0%
+millisecond with what velocity will it
+ 
+
+ align:start position:0%
+millisecond with what velocity will it
+leave the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+coil with aerodynamic drag ignored
+
+ align:start position:0%
+coil with aerodynamic drag ignored
+ 
+
+ align:start position:0%
+coil with aerodynamic drag ignored
+Newton's law states that this force is
+
+ align:start position:0%
+Newton's law states that this force is
+ 
+
+ align:start position:0%
+Newton's law states that this force is
+equal to the mass m of the dis times its
+
+ align:start position:0%
+equal to the mass m of the dis times its
+ 
+
+ align:start position:0%
+equal to the mass m of the dis times its
+acceleration ation the rate of change of
+
+ align:start position:0%
+acceleration ation the rate of change of
+ 
+
+ align:start position:0%
+acceleration ation the rate of change of
+its
+
+ align:start position:0%
+its
+ 
+
+ align:start position:0%
+its
+velocity here the force is represented
+
+ align:start position:0%
+velocity here the force is represented
+ 
+
+ align:start position:0%
+velocity here the force is represented
+by an
+
+ align:start position:0%
+by an
+ 
+
+ align:start position:0%
+by an
+Impulse having a duration T and A
+
+ align:start position:0%
+Impulse having a duration T and A
+ 
+
+ align:start position:0%
+Impulse having a duration T and A
+magnitude F Sub 0 equal to that just
+
+ align:start position:0%
+magnitude F Sub 0 equal to that just
+ 
+
+ align:start position:0%
+magnitude F Sub 0 equal to that just
+calculated integration of this
+
+ align:start position:0%
+calculated integration of this
+ 
+
+ align:start position:0%
+calculated integration of this
+expression from just before the button
+
+ align:start position:0%
+expression from just before the button
+ 
+
+ align:start position:0%
+expression from just before the button
+is pushed when the dis is at rest to
+
+ align:start position:0%
+is pushed when the dis is at rest to
+ 
+
+ align:start position:0%
+is pushed when the dis is at rest to
+just after shows that the initial
+
+ align:start position:0%
+just after shows that the initial
+ 
+
+ align:start position:0%
+just after shows that the initial
+velocity is this Force impulse divided
+
+ align:start position:0%
+velocity is this Force impulse divided
+ 
+
+ align:start position:0%
+velocity is this Force impulse divided
+by the mass of the dis
+
+ align:start position:0%
+by the mass of the dis
+ 
+
+ align:start position:0%
+by the mass of the dis
+for our numbers this velocity is 8
+
+ align:start position:0%
+for our numbers this velocity is 8
+ 
+
+ align:start position:0%
+for our numbers this velocity is 8
+m/s or about 18
+
+ align:start position:0%
+m/s or about 18
+ 
+
+ align:start position:0%
+m/s or about 18
+mph a good velocity for a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+bicycle uh perhaps we should estimate
+
+ align:start position:0%
+bicycle uh perhaps we should estimate
+ 
+
+ align:start position:0%
+bicycle uh perhaps we should estimate
+how high the disc will go before we push
+
+ align:start position:0%
+how high the disc will go before we push
+ 
+
+ align:start position:0%
+how high the disc will go before we push
+the button if the disc hurts the ceiling
+
+ align:start position:0%
+the button if the disc hurts the ceiling
+ 
+
+ align:start position:0%
+the button if the disc hurts the ceiling
+one of us might get fired
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the initial kinetic energy of the disc
+
+ align:start position:0%
+the initial kinetic energy of the disc
+ 
+
+ align:start position:0%
+the initial kinetic energy of the disc
+will be converted to potential form when
+
+ align:start position:0%
+will be converted to potential form when
+ 
+
+ align:start position:0%
+will be converted to potential form when
+it reaches its maximum height
+
+ align:start position:0%
+it reaches its maximum height
+ 
+
+ align:start position:0%
+it reaches its maximum height
+h g is the gravitational
+
+ align:start position:0%
+h g is the gravitational
+ 
+
+ align:start position:0%
+h g is the gravitational
+acceleration we predict a height of 3
+
+ align:start position:0%
+acceleration we predict a height of 3
+ 
+
+ align:start position:0%
+acceleration we predict a height of 3
+m which is sufficiently small that we
+
+ align:start position:0%
+m which is sufficiently small that we
+ 
+
+ align:start position:0%
+m which is sufficiently small that we
+can perhaps responsibly push the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+button I'm melter and as you know that's
+
+ align:start position:0%
+button I'm melter and as you know that's
+ 
+
+ align:start position:0%
+button I'm melter and as you know that's
+Zan we brought along an illuminary here
+
+ align:start position:0%
+Zan we brought along an illuminary here
+ 
+
+ align:start position:0%
+Zan we brought along an illuminary here
+to push that button finally this is
+
+ align:start position:0%
+to push that button finally this is
+ 
+
+ align:start position:0%
+to push that button finally this is
+Professor Doc ederton and uh it's his
+
+ align:start position:0%
+Professor Doc ederton and uh it's his
+ 
+
+ align:start position:0%
+Professor Doc ederton and uh it's his
+machine what we've done of course is to
+
+ align:start position:0%
+machine what we've done of course is to
+ 
+
+ align:start position:0%
+machine what we've done of course is to
+show you this disc and now if uh doc you
+
+ align:start position:0%
+show you this disc and now if uh doc you
+ 
+
+ align:start position:0%
+show you this disc and now if uh doc you
+turn on your machine ready here we go
+
+ align:start position:0%
+turn on your machine ready here we go
+ 
+
+ align:start position:0%
+turn on your machine ready here we go
+I'm going to step out of this I'll turn
+
+ align:start position:0%
+I'm going to step out of this I'll turn
+ 
+
+ align:start position:0%
+I'm going to step out of this I'll turn
+on the main power let it come up to
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+charge want do it again do you have a
+
+ align:start position:0%
+charge want do it again do you have a
+ 
+
+ align:start position:0%
+charge want do it again do you have a
+favorite one there well the everyone's a
+
+ align:start position:0%
+favorite one there well the everyone's a
+ 
+
+ align:start position:0%
+favorite one there well the everyone's a
+little different Mr try this one what do
+
+ align:start position:0%
+little different Mr try this one what do
+ 
+
+ align:start position:0%
+little different Mr try this one what do
+you
+
+ align:start position:0%
+you
+ 
+
+ align:start position:0%
+you
+say
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+power little different ring to it little
+
+ align:start position:0%
+power little different ring to it little
+ 
+
+ align:start position:0%
+power little different ring to it little
+different ring now as I understand it
+
+ align:start position:0%
+different ring now as I understand it
+ 
+
+ align:start position:0%
+different ring now as I understand it
+this thing's got uh more capacitors in
+
+ align:start position:0%
+this thing's got uh more capacitors in
+ 
+
+ align:start position:0%
+this thing's got uh more capacitors in
+it maybe we get Zan to uh put a little
+
+ align:start position:0%
+it maybe we get Zan to uh put a little
+ 
+
+ align:start position:0%
+it maybe we get Zan to uh put a little
+more in there yeah you like to have it
+
+ align:start position:0%
+more in there yeah you like to have it
+ 
+
+ align:start position:0%
+more in there yeah you like to have it
+go a little the one of the reasons I
+
+ align:start position:0%
+go a little the one of the reasons I
+ 
+
+ align:start position:0%
+go a little the one of the reasons I
+brought this man along is that uh in
+
+ align:start position:0%
+brought this man along is that uh in
+ 
+
+ align:start position:0%
+brought this man along is that uh in
+fact he mainly paid for this building so
+
+ align:start position:0%
+fact he mainly paid for this building so
+ 
+
+ align:start position:0%
+fact he mainly paid for this building so
+you see we don't care too much if we
+
+ align:start position:0%
+you see we don't care too much if we
+ 
+
+ align:start position:0%
+you see we don't care too much if we
+hurt that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+ceiling it'd be nice to have an imprint
+
+ align:start position:0%
+ceiling it'd be nice to have an imprint
+ 
+
+ align:start position:0%
+ceiling it'd be nice to have an imprint
+up there wouldn't it right with you here
+
+ align:start position:0%
+up there wouldn't it right with you here
+ 
+
+ align:start position:0%
+up there wouldn't it right with you here
+I can say that okay let's see what
+
+ align:start position:0%
+I can say that okay let's see what
+ 
+
+ align:start position:0%
+I can say that okay let's see what
+happens this time well you got three
+
+ align:start position:0%
+happens this time well you got three
+ 
+
+ align:start position:0%
+happens this time well you got three
+capacitors on instead of one it should
+
+ align:start position:0%
+capacitors on instead of one it should
+ 
+
+ align:start position:0%
+capacitors on instead of one it should
+go a little
+
+ align:start position:0%
+go a little
+ 
+
+ align:start position:0%
+go a little
+higher one two three
+
+ align:start position:0%
+higher one two three
+ 
+
+ align:start position:0%
+higher one two three
+go missed me want to try our favorite
+
+ align:start position:0%
+go missed me want to try our favorite
+ 
+
+ align:start position:0%
+go missed me want to try our favorite
+let's try that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+one hey knocked a hole in the ceiling I
+
+ align:start position:0%
+one hey knocked a hole in the ceiling I
+ 
+
+ align:start position:0%
+one hey knocked a hole in the ceiling I
+can see you enjoy that huh all right
+
+ align:start position:0%
+can see you enjoy that huh all right
+ 
+
+ align:start position:0%
+can see you enjoy that huh all right
+thank you very much sir now actually
+
+ align:start position:0%
+thank you very much sir now actually
+ 
+
+ align:start position:0%
+thank you very much sir now actually
+you're getting the impression this is
+
+ align:start position:0%
+you're getting the impression this is
+ 
+
+ align:start position:0%
+you're getting the impression this is
+all just fun in games if you look in
+
+ align:start position:0%
+all just fun in games if you look in
+ 
+
+ align:start position:0%
+all just fun in games if you look in
+inside this box you'll find a number on
+
+ align:start position:0%
+inside this box you'll find a number on
+ 
+
+ align:start position:0%
+inside this box you'll find a number on
+it
+
+ align:start position:0%
+it
+ 
+
+ align:start position:0%
+it
+1960 and uh Circa sometime like that
+
+ align:start position:0%
+1960 and uh Circa sometime like that
+ 
+
+ align:start position:0%
+1960 and uh Circa sometime like that
+this man was busy sounding the bottom of
+
+ align:start position:0%
+this man was busy sounding the bottom of
+ 
+
+ align:start position:0%
+this man was busy sounding the bottom of
+the ocean with this device in fact a few
+
+ align:start position:0%
+the ocean with this device in fact a few
+ 
+
+ align:start position:0%
+the ocean with this device in fact a few
+minutes ago he showed me a book that's
+
+ align:start position:0%
+minutes ago he showed me a book that's
+ 
+
+ align:start position:0%
+minutes ago he showed me a book that's
+out it's uh what sonar images by Harold
+
+ align:start position:0%
+out it's uh what sonar images by Harold
+ 
+
+ align:start position:0%
+out it's uh what sonar images by Harold
+e ederton and uh we were just picking
+
+ align:start position:0%
+e ederton and uh we were just picking
+ 
+
+ align:start position:0%
+e ederton and uh we were just picking
+out something in here that might give
+
+ align:start position:0%
+out something in here that might give
+ 
+
+ align:start position:0%
+out something in here that might give
+you an idea of the kind of um of serious
+
+ align:start position:0%
+you an idea of the kind of um of serious
+ 
+
+ align:start position:0%
+you an idea of the kind of um of serious
+business that a boomer like this or
+
+ align:start position:0%
+business that a boomer like this or
+ 
+
+ align:start position:0%
+business that a boomer like this or
+other sonar devices uh can carry out
+
+ align:start position:0%
+other sonar devices uh can carry out
+ 
+
+ align:start position:0%
+other sonar devices uh can carry out
+maybe doc you could try and explain this
+
+ align:start position:0%
+maybe doc you could try and explain this
+ 
+
+ align:start position:0%
+maybe doc you could try and explain this
+to us this this is the surface of the
+
+ align:start position:0%
+to us this this is the surface of the
+ 
+
+ align:start position:0%
+to us this this is the surface of the
+ocean and then the sound goes down and
+
+ align:start position:0%
+ocean and then the sound goes down and
+ 
+
+ align:start position:0%
+ocean and then the sound goes down and
+reflects off the bottom this the bottom
+
+ align:start position:0%
+reflects off the bottom this the bottom
+ 
+
+ align:start position:0%
+reflects off the bottom this the bottom
+of the ocean and with these powerful
+
+ align:start position:0%
+of the ocean and with these powerful
+ 
+
+ align:start position:0%
+of the ocean and with these powerful
+sources where you get enough energy
+
+ align:start position:0%
+sources where you get enough energy
+ 
+
+ align:start position:0%
+sources where you get enough energy
+it'll go through and gives you sub
+
+ align:start position:0%
+it'll go through and gives you sub
+ 
+
+ align:start position:0%
+it'll go through and gives you sub
+bottoms that are down below that are
+
+ align:start position:0%
+bottoms that are down below that are
+ 
+
+ align:start position:0%
+bottoms that are down below that are
+tremendous interest of the geologists
+
+ align:start position:0%
+tremendous interest of the geologists
+ 
+
+ align:start position:0%
+tremendous interest of the geologists
+they all want to know where these sub
+
+ align:start position:0%
+they all want to know where these sub
+ 
+
+ align:start position:0%
+they all want to know where these sub
+bottoms are and as I understand it if we
+
+ align:start position:0%
+bottoms are and as I understand it if we
+ 
+
+ align:start position:0%
+bottoms are and as I understand it if we
+have a big enough disc we make a a low
+
+ align:start position:0%
+have a big enough disc we make a a low
+ 
+
+ align:start position:0%
+have a big enough disc we make a a low
+enough frequency energy that it does
+
+ align:start position:0%
+enough frequency energy that it does
+ 
+
+ align:start position:0%
+enough frequency energy that it does
+penetrate that substrate yep so you gave
+
+ align:start position:0%
+penetrate that substrate yep so you gave
+ 
+
+ align:start position:0%
+penetrate that substrate yep so you gave
+me a little bigger disc here huh yeah
+
+ align:start position:0%
+me a little bigger disc here huh yeah
+ 
+
+ align:start position:0%
+me a little bigger disc here huh yeah
+let me get it out for
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+us and I think you realize Jim this now
+
+ align:start position:0%
+us and I think you realize Jim this now
+ 
+
+ align:start position:0%
+us and I think you realize Jim this now
+there's a disc huh yeah this coil isn't
+
+ align:start position:0%
+there's a disc huh yeah this coil isn't
+ 
+
+ align:start position:0%
+there's a disc huh yeah this coil isn't
+as big as the coil would be as big as
+
+ align:start position:0%
+as big as the coil would be as big as
+ 
+
+ align:start position:0%
+as big as the coil would be as big as
+this and we'd have maybe 10 times as
+
+ align:start position:0%
+this and we'd have maybe 10 times as
+ 
+
+ align:start position:0%
+this and we'd have maybe 10 times as
+many capacitors on it
+
+ align:start position:0%
+many capacitors on it
+ 
+
+ align:start position:0%
+many capacitors on it
+so yes what we got a small one on there
+
+ align:start position:0%
+so yes what we got a small one on there
+ 
+
+ align:start position:0%
+so yes what we got a small one on there
+now I was trying to get him to bring us
+
+ align:start position:0%
+now I was trying to get him to bring us
+ 
+
+ align:start position:0%
+now I was trying to get him to bring us
+over a disc that has pits in it from the
+
+ align:start position:0%
+over a disc that has pits in it from the
+ 
+
+ align:start position:0%
+over a disc that has pits in it from the
+cavitation unfortunately he's thrown it
+
+ align:start position:0%
+cavitation unfortunately he's thrown it
+ 
+
+ align:start position:0%
+cavitation unfortunately he's thrown it
+out are we going to hit it with that
+
+ align:start position:0%
+out are we going to hit it with that
+ 
+
+ align:start position:0%
+out are we going to hit it with that
+maximum capacity yeah well he's got them
+
+ align:start position:0%
+maximum capacity yeah well he's got them
+ 
+
+ align:start position:0%
+maximum capacity yeah well he's got them
+all in right back off little I don't
+
+ align:start position:0%
+all in right back off little I don't
+ 
+
+ align:start position:0%
+all in right back off little I don't
+think it'll go very high but I'll back
+
+ align:start position:0%
+think it'll go very high but I'll back
+ 
+
+ align:start position:0%
+think it'll go very high but I'll back
+off it'll make a noise I think it'll
+
+ align:start position:0%
+off it'll make a noise I think it'll
+ 
+
+ align:start position:0%
+off it'll make a noise I think it'll
+make a noise that's the point you ready
+
+ align:start position:0%
+make a noise that's the point you ready
+ 
+
+ align:start position:0%
+make a noise that's the point you ready
+go that's worth trying again
+
+ align:start position:0%
+go that's worth trying again
+ 
+
+ align:start position:0%
+go that's worth trying again
+yeah it jumps up about a/ inch if you
+
+ align:start position:0%
+yeah it jumps up about a/ inch if you
+ 
+
+ align:start position:0%
+yeah it jumps up about a/ inch if you
+put enough energy you can throw the
+
+ align:start position:0%
+put enough energy you can throw the
+ 
+
+ align:start position:0%
+put enough energy you can throw the
+thing clear clear over doc thank you
+
+ align:start position:0%
+thing clear clear over doc thank you
+ 
+
+ align:start position:0%
+thing clear clear over doc thank you
+very much for being here thank
+
+ align:start position:0%
+very much for being here thank
+ 
+
+ align:start position:0%
+very much for being here thank
+you still ringing h
\ No newline at end of file
diff --git a/MT3LjjdODHA.txt b/MT3LjjdODHA.txt
new file mode 100644
index 0000000000000000000000000000000000000000..3d410a1c6d7106892d7ab6b61c3ec27283f04191
--- /dev/null
+++ b/MT3LjjdODHA.txt
@@ -0,0 +1,3099 @@
+align:start position:0%
+ 
+me I would say that most of even
+
+ align:start position:0%
+me I would say that most of even
+ 
+
+ align:start position:0%
+me I would say that most of even
+contemporary views about cre are still
+
+ align:start position:0%
+contemporary views about cre are still
+ 
+
+ align:start position:0%
+contemporary views about cre are still
+driven by the same racism that
+
+ align:start position:0%
+driven by the same racism that
+ 
+
+ align:start position:0%
+driven by the same racism that
+characterize slavery and then they they
+
+ align:start position:0%
+characterize slavery and then they they
+ 
+
+ align:start position:0%
+characterize slavery and then they they
+they conclude and I want to take that
+
+ align:start position:0%
+they conclude and I want to take that
+ 
+
+ align:start position:0%
+they conclude and I want to take that
+conclusion very seriously that that
+
+ align:start position:0%
+conclusion very seriously that that
+ 
+
+ align:start position:0%
+conclusion very seriously that that
+although we might use a label Creole but
+
+ align:start position:0%
+although we might use a label Creole but
+ 
+
+ align:start position:0%
+although we might use a label Creole but
+that label doesn't mean that it's that
+
+ align:start position:0%
+that label doesn't mean that it's that
+ 
+
+ align:start position:0%
+that label doesn't mean that it's that
+have a linguistic structural class class
+
+ align:start position:0%
+have a linguistic structural class class
+ 
+
+ align:start position:0%
+have a linguistic structural class class
+of cre languages the term creal is just
+
+ align:start position:0%
+of cre languages the term creal is just
+ 
+
+ align:start position:0%
+of cre languages the term creal is just
+a historical term that applies to this
+
+ align:start position:0%
+a historical term that applies to this
+ 
+
+ align:start position:0%
+a historical term that applies to this
+particular group of languages um but not
+
+ align:start position:0%
+particular group of languages um but not
+ 
+
+ align:start position:0%
+particular group of languages um but not
+isn't isn't refer to special
+
+ align:start position:0%
+isn't isn't refer to special
+ 
+
+ align:start position:0%
+isn't isn't refer to special
+developmental or special structural
+
+ align:start position:0%
+developmental or special structural
+ 
+
+ align:start position:0%
+developmental or special structural
+patterns you know they're just they're
+
+ align:start position:0%
+patterns you know they're just they're
+ 
+
+ align:start position:0%
+patterns you know they're just they're
+just just a language that's what the cre
+
+ align:start position:0%
+just just a language that's what the cre
+ 
+
+ align:start position:0%
+just just a language that's what the cre
+is okay um so but then you know what we
+
+ align:start position:0%
+is okay um so but then you know what we
+ 
+
+ align:start position:0%
+is okay um so but then you know what we
+have to ask is you know where do we go
+
+ align:start position:0%
+have to ask is you know where do we go
+ 
+
+ align:start position:0%
+have to ask is you know where do we go
+from here so we know of that but then
+
+ align:start position:0%
+from here so we know of that but then
+ 
+
+ align:start position:0%
+from here so we know of that but then
+what was the issue there um and in fact
+
+ align:start position:0%
+what was the issue there um and in fact
+ 
+
+ align:start position:0%
+what was the issue there um and in fact
+we can do one thing that and this is
+
+ align:start position:0%
+we can do one thing that and this is
+ 
+
+ align:start position:0%
+we can do one thing that and this is
+from mu work so this is this I like this
+
+ align:start position:0%
+from mu work so this is this I like this
+ 
+
+ align:start position:0%
+from mu work so this is this I like this
+map because what it shows is what we
+
+ align:start position:0%
+map because what it shows is what we
+ 
+
+ align:start position:0%
+map because what it shows is what we
+discussed earlier right the fact that if
+
+ align:start position:0%
+discussed earlier right the fact that if
+ 
+
+ align:start position:0%
+discussed earlier right the fact that if
+you really look at CRS without biases
+
+ align:start position:0%
+you really look at CRS without biases
+ 
+
+ align:start position:0%
+you really look at CRS without biases
+and you think of the development and you
+
+ align:start position:0%
+and you think of the development and you
+ 
+
+ align:start position:0%
+and you think of the development and you
+go back in time and you think of the
+
+ align:start position:0%
+go back in time and you think of the
+ 
+
+ align:start position:0%
+go back in time and you think of the
+development of of romance languages
+
+ align:start position:0%
+development of of romance languages
+ 
+
+ align:start position:0%
+development of of romance languages
+right so this is the way romance evolve
+
+ align:start position:0%
+right so this is the way romance evolve
+ 
+
+ align:start position:0%
+right so this is the way romance evolve
+so you had Latin conquerors going from
+
+ align:start position:0%
+so you had Latin conquerors going from
+ 
+
+ align:start position:0%
+so you had Latin conquerors going from
+Rome into go Iberia Etc and that's how
+
+ align:start position:0%
+Rome into go Iberia Etc and that's how
+ 
+
+ align:start position:0%
+Rome into go Iberia Etc and that's how
+the romance languages were created by
+
+ align:start position:0%
+the romance languages were created by
+ 
+
+ align:start position:0%
+the romance languages were created by
+through conquest and and contact of
+
+ align:start position:0%
+through conquest and and contact of
+ 
+
+ align:start position:0%
+through conquest and and contact of
+populations and in the same way if you
+
+ align:start position:0%
+populations and in the same way if you
+ 
+
+ align:start position:0%
+populations and in the same way if you
+look at you know what happened to French
+
+ align:start position:0%
+look at you know what happened to French
+ 
+
+ align:start position:0%
+look at you know what happened to French
+when French went to North America the
+
+ align:start position:0%
+when French went to North America the
+ 
+
+ align:start position:0%
+when French went to North America the
+Caribbean Africa all the way to Asia
+
+ align:start position:0%
+Caribbean Africa all the way to Asia
+ 
+
+ align:start position:0%
+Caribbean Africa all the way to Asia
+that's also how Crees were created you
+
+ align:start position:0%
+that's also how Crees were created you
+ 
+
+ align:start position:0%
+that's also how Crees were created you
+know you got hisan cre M Creole macius
+
+ align:start position:0%
+know you got hisan cre M Creole macius
+ 
+
+ align:start position:0%
+know you got hisan cre M Creole macius
+Creole Cel Creole and and this is where
+
+ align:start position:0%
+Creole Cel Creole and and this is where
+ 
+
+ align:start position:0%
+Creole Cel Creole and and this is where
+you get the kopon right um alongside Fon
+
+ align:start position:0%
+you get the kopon right um alongside Fon
+ 
+
+ align:start position:0%
+you get the kopon right um alongside Fon
+of course but the claim I've made so far
+
+ align:start position:0%
+of course but the claim I've made so far
+ 
+
+ align:start position:0%
+of course but the claim I've made so far
+is that you have similar patterns not
+
+ align:start position:0%
+is that you have similar patterns not
+ 
+
+ align:start position:0%
+is that you have similar patterns not
+only in terms of language contact but
+
+ align:start position:0%
+only in terms of language contact but
+ 
+
+ align:start position:0%
+only in terms of language contact but
+also in terms of structural development
+
+ align:start position:0%
+also in terms of structural development
+ 
+
+ align:start position:0%
+also in terms of structural development
+um so from that perspective again there
+
+ align:start position:0%
+um so from that perspective again there
+ 
+
+ align:start position:0%
+um so from that perspective again there
+cannot be there need not be this this
+
+ align:start position:0%
+cannot be there need not be this this
+ 
+
+ align:start position:0%
+cannot be there need not be this this
+divide this fundamental divide that
+
+ align:start position:0%
+divide this fundamental divide that
+ 
+
+ align:start position:0%
+divide this fundamental divide that
+language often draw between language
+
+ align:start position:0%
+language often draw between language
+ 
+
+ align:start position:0%
+language often draw between language
+change as in the history of French and
+
+ align:start position:0%
+change as in the history of French and
+ 
+
+ align:start position:0%
+change as in the history of French and
+then cre formation as in the hist paent
+
+ align:start position:0%
+then cre formation as in the hist paent
+ 
+
+ align:start position:0%
+then cre formation as in the hist paent
+Creole you see um so earlier we talked
+
+ align:start position:0%
+Creole you see um so earlier we talked
+ 
+
+ align:start position:0%
+Creole you see um so earlier we talked
+about these um
+
+ align:start position:0%
+about these um
+ 
+
+ align:start position:0%
+about these um
+these myths uh uh about V cre so now
+
+ align:start position:0%
+these myths uh uh about V cre so now
+ 
+
+ align:start position:0%
+these myths uh uh about V cre so now
+what we could ask is um and so now this
+
+ align:start position:0%
+what we could ask is um and so now this
+ 
+
+ align:start position:0%
+what we could ask is um and so now this
+is just in case you want to you want to
+
+ align:start position:0%
+is just in case you want to you want to
+ 
+
+ align:start position:0%
+is just in case you want to you want to
+read more about it so you can go to my
+
+ align:start position:0%
+read more about it so you can go to my
+ 
+
+ align:start position:0%
+read more about it so you can go to my
+website and you you'll find lots and
+
+ align:start position:0%
+website and you you'll find lots and
+ 
+
+ align:start position:0%
+website and you you'll find lots and
+lots of arguments against this um this
+
+ align:start position:0%
+lots of arguments against this um this
+ 
+
+ align:start position:0%
+lots of arguments against this um this
+idea that you have this this cycle and
+
+ align:start position:0%
+idea that you have this this cycle and
+ 
+
+ align:start position:0%
+idea that you have this this cycle and
+then but what we have to now and here
+
+ align:start position:0%
+then but what we have to now and here
+ 
+
+ align:start position:0%
+then but what we have to now and here
+I'm going to be using some of the SL
+
+ align:start position:0%
+I'm going to be using some of the SL
+ 
+
+ align:start position:0%
+I'm going to be using some of the SL
+that I showed at the at the UN last week
+
+ align:start position:0%
+that I showed at the at the UN last week
+ 
+
+ align:start position:0%
+that I showed at the at the UN last week
+so because what we want to ask
+
+ align:start position:0%
+so because what we want to ask
+ 
+
+ align:start position:0%
+so because what we want to ask
+connecting to the issues of identity and
+
+ align:start position:0%
+connecting to the issues of identity and
+ 
+
+ align:start position:0%
+connecting to the issues of identity and
+education that were touched on uh by
+
+ align:start position:0%
+education that were touched on uh by
+ 
+
+ align:start position:0%
+education that were touched on uh by
+Karen and and Rachel is you know why why
+
+ align:start position:0%
+Karen and and Rachel is you know why why
+ 
+
+ align:start position:0%
+Karen and and Rachel is you know why why
+do these meats endure and then actually
+
+ align:start position:0%
+do these meats endure and then actually
+ 
+
+ align:start position:0%
+do these meats endure and then actually
+now this I can go quickly actually
+
+ align:start position:0%
+now this I can go quickly actually
+ 
+
+ align:start position:0%
+now this I can go quickly actually
+because you've You' you've seen all of
+
+ align:start position:0%
+because you've You' you've seen all of
+ 
+
+ align:start position:0%
+because you've You' you've seen all of
+these before right but I just wanted to
+
+ align:start position:0%
+these before right but I just wanted to
+ 
+
+ align:start position:0%
+these before right but I just wanted to
+to to bring them back very quickly you
+
+ align:start position:0%
+to to bring them back very quickly you
+ 
+
+ align:start position:0%
+to to bring them back very quickly you
+know so now this is again this is you
+
+ align:start position:0%
+know so now this is again this is you
+ 
+
+ align:start position:0%
+know so now this is again this is you
+find this meth in you know very well
+
+ align:start position:0%
+find this meth in you know very well
+ 
+
+ align:start position:0%
+find this meth in you know very well
+read popular newspapers magazines like
+
+ align:start position:0%
+read popular newspapers magazines like
+ 
+
+ align:start position:0%
+read popular newspapers magazines like
+Newsweek the New York Times um riters
+
+ align:start position:0%
+Newsweek the New York Times um riters
+ 
+
+ align:start position:0%
+Newsweek the New York Times um riters
+even the New Yorker you know and all of
+
+ align:start position:0%
+even the New Yorker you know and all of
+ 
+
+ align:start position:0%
+even the New Yorker you know and all of
+these that something in common that we
+
+ align:start position:0%
+these that something in common that we
+ 
+
+ align:start position:0%
+these that something in common that we
+saw earlier right that now should be too
+
+ align:start position:0%
+saw earlier right that now should be too
+ 
+
+ align:start position:0%
+saw earlier right that now should be too
+familiar which is you know cre or French
+
+ align:start position:0%
+familiar which is you know cre or French
+ 
+
+ align:start position:0%
+familiar which is you know cre or French
+pwa broken French you know they're like
+
+ align:start position:0%
+pwa broken French you know they're like
+ 
+
+ align:start position:0%
+pwa broken French you know they're like
+primitive languages this is uh or this
+
+ align:start position:0%
+primitive languages this is uh or this
+ 
+
+ align:start position:0%
+primitive languages this is uh or this
+one is the most poetic and I like this
+
+ align:start position:0%
+one is the most poetic and I like this
+ 
+
+ align:start position:0%
+one is the most poetic and I like this
+one because it makes me into a special
+
+ align:start position:0%
+one because it makes me into a special
+ 
+
+ align:start position:0%
+one because it makes me into a special
+specimen of of humanity right because
+
+ align:start position:0%
+specimen of of humanity right because
+ 
+
+ align:start position:0%
+specimen of of humanity right because
+really that's what it means right that
+
+ align:start position:0%
+really that's what it means right that
+ 
+
+ align:start position:0%
+really that's what it means right that
+means that you know as I like to say
+
+ align:start position:0%
+means that you know as I like to say
+ 
+
+ align:start position:0%
+means that you know as I like to say
+when I give this talk in public when I
+
+ align:start position:0%
+when I give this talk in public when I
+ 
+
+ align:start position:0%
+when I give this talk in public when I
+when I switch from speaking English to
+
+ align:start position:0%
+when I switch from speaking English to
+ 
+
+ align:start position:0%
+when I switch from speaking English to
+speaking cre oh I go from being a modern
+
+ align:start position:0%
+speaking cre oh I go from being a modern
+ 
+
+ align:start position:0%
+speaking cre oh I go from being a modern
+human to being a primitive human because
+
+ align:start position:0%
+human to being a primitive human because
+ 
+
+ align:start position:0%
+human to being a primitive human because
+I can all of a sudden on my tongue you
+
+ align:start position:0%
+I can all of a sudden on my tongue you
+ 
+
+ align:start position:0%
+I can all of a sudden on my tongue you
+know I get to pronounce this linguistic
+
+ align:start position:0%
+know I get to pronounce this linguistic
+ 
+
+ align:start position:0%
+know I get to pronounce this linguistic
+fossils which are the equivalent of the
+
+ align:start position:0%
+fossils which are the equivalent of the
+ 
+
+ align:start position:0%
+fossils which are the equivalent of the
+calabos towin I this is this is
+
+ align:start position:0%
+calabos towin I this is this is
+ 
+
+ align:start position:0%
+calabos towin I this is this is
+spectacular this is a spectacular claim
+
+ align:start position:0%
+spectacular this is a spectacular claim
+ 
+
+ align:start position:0%
+spectacular this is a spectacular claim
+right I mean and this is Newsweek you
+
+ align:start position:0%
+right I mean and this is Newsweek you
+ 
+
+ align:start position:0%
+right I mean and this is Newsweek you
+know this is the New York Times but is
+
+ align:start position:0%
+know this is the New York Times but is
+ 
+
+ align:start position:0%
+know this is the New York Times but is
+to show you how acceptable these claims
+
+ align:start position:0%
+to show you how acceptable these claims
+ 
+
+ align:start position:0%
+to show you how acceptable these claims
+are right but then you know again to
+
+ align:start position:0%
+are right but then you know again to
+ 
+
+ align:start position:0%
+are right but then you know again to
+wrap up from what we discussed earlier
+
+ align:start position:0%
+wrap up from what we discussed earlier
+ 
+
+ align:start position:0%
+wrap up from what we discussed earlier
+uh this is in very much in Sy with uh
+
+ align:start position:0%
+uh this is in very much in Sy with uh
+ 
+
+ align:start position:0%
+uh this is in very much in Sy with uh
+with Michelle Hof too right uh now this
+
+ align:start position:0%
+with Michelle Hof too right uh now this
+ 
+
+ align:start position:0%
+with Michelle Hof too right uh now this
+is going back to the early part of this
+
+ align:start position:0%
+is going back to the early part of this
+ 
+
+ align:start position:0%
+is going back to the early part of this
+of this class which where we you know
+
+ align:start position:0%
+of this class which where we you know
+ 
+
+ align:start position:0%
+of this class which where we you know
+looking at history so what we see is
+
+ align:start position:0%
+looking at history so what we see is
+ 
+
+ align:start position:0%
+looking at history so what we see is
+that the same way that Creos have been
+
+ align:start position:0%
+that the same way that Creos have been
+ 
+
+ align:start position:0%
+that the same way that Creos have been
+silenced the fact that cre are normal
+
+ align:start position:0%
+silenced the fact that cre are normal
+ 
+
+ align:start position:0%
+silenced the fact that cre are normal
+languages that has been silenced is also
+
+ align:start position:0%
+languages that has been silenced is also
+ 
+
+ align:start position:0%
+languages that has been silenced is also
+the same way that um Asian history has
+
+ align:start position:0%
+the same way that um Asian history has
+ 
+
+ align:start position:0%
+the same way that um Asian history has
+been silenced for the same reason
+
+ align:start position:0%
+been silenced for the same reason
+ 
+
+ align:start position:0%
+been silenced for the same reason
+because how many of you before this
+
+ align:start position:0%
+because how many of you before this
+ 
+
+ align:start position:0%
+because how many of you before this
+class knew about Asian
+
+ align:start position:0%
+class knew about Asian
+ 
+
+ align:start position:0%
+class knew about Asian
+history right you because you have a
+
+ align:start position:0%
+history right you because you have a
+ 
+
+ align:start position:0%
+history right you because you have a
+Asian boyfriend right
+
+ align:start position:0%
+Asian boyfriend right
+ 
+
+ align:start position:0%
+Asian boyfriend right
+yeah but but most of us you know and
+
+ align:start position:0%
+yeah but but most of us you know and
+ 
+
+ align:start position:0%
+yeah but but most of us you know and
+when I asked that question you know even
+
+ align:start position:0%
+when I asked that question you know even
+ 
+
+ align:start position:0%
+when I asked that question you know even
+in my in big classes like you know 24900
+
+ align:start position:0%
+in my in big classes like you know 24900
+ 
+
+ align:start position:0%
+in my in big classes like you know 24900
+with hundred of students I get maybe one
+
+ align:start position:0%
+with hundred of students I get maybe one
+ 
+
+ align:start position:0%
+with hundred of students I get maybe one
+or two people to know that thean
+
+ align:start position:0%
+or two people to know that thean
+ 
+
+ align:start position:0%
+or two people to know that thean
+Revolution was even more dramatic in
+
+ align:start position:0%
+Revolution was even more dramatic in
+ 
+
+ align:start position:0%
+Revolution was even more dramatic in
+terms of its claims than both the French
+
+ align:start position:0%
+terms of its claims than both the French
+ 
+
+ align:start position:0%
+terms of its claims than both the French
+and the American Revolutions know it was
+
+ align:start position:0%
+and the American Revolutions know it was
+ 
+
+ align:start position:0%
+and the American Revolutions know it was
+the only one in the in the 18th century
+
+ align:start position:0%
+the only one in the in the 18th century
+ 
+
+ align:start position:0%
+the only one in the in the 18th century
+to Proclaim Liberty and equality for all
+
+ align:start position:0%
+to Proclaim Liberty and equality for all
+ 
+
+ align:start position:0%
+to Proclaim Liberty and equality for all
+the only one the French one the friend
+
+ align:start position:0%
+the only one the French one the friend
+ 
+
+ align:start position:0%
+the only one the French one the friend
+still had slaves the American one
+
+ align:start position:0%
+still had slaves the American one
+ 
+
+ align:start position:0%
+still had slaves the American one
+Jefferson Med all these guys they still
+
+ align:start position:0%
+Jefferson Med all these guys they still
+ 
+
+ align:start position:0%
+Jefferson Med all these guys they still
+had slaves know Haiti was the only
+
+ align:start position:0%
+had slaves know Haiti was the only
+ 
+
+ align:start position:0%
+had slaves know Haiti was the only
+Revolution where there was this claim
+
+ align:start position:0%
+Revolution where there was this claim
+ 
+
+ align:start position:0%
+Revolution where there was this claim
+for uh Liberty for all but you know this
+
+ align:start position:0%
+for uh Liberty for all but you know this
+ 
+
+ align:start position:0%
+for uh Liberty for all but you know this
+is from Toyo that you know as Haiti was
+
+ align:start position:0%
+is from Toyo that you know as Haiti was
+ 
+
+ align:start position:0%
+is from Toyo that you know as Haiti was
+entering history you know it was being
+
+ align:start position:0%
+entering history you know it was being
+ 
+
+ align:start position:0%
+entering history you know it was being
+written about by people who could not
+
+ align:start position:0%
+written about by people who could not
+ 
+
+ align:start position:0%
+written about by people who could not
+conceive of the Africans as equals to
+
+ align:start position:0%
+conceive of the Africans as equals to
+ 
+
+ align:start position:0%
+conceive of the Africans as equals to
+the Europeans right so so according to
+
+ align:start position:0%
+the Europeans right so so according to
+ 
+
+ align:start position:0%
+the Europeans right so so according to
+Toyo those 18th century Scholars uh they
+
+ align:start position:0%
+Toyo those 18th century Scholars uh they
+ 
+
+ align:start position:0%
+Toyo those 18th century Scholars uh they
+could only read the news news only with
+
+ align:start position:0%
+could only read the news news only with
+ 
+
+ align:start position:0%
+could only read the news news only with
+the ready made lenses and it meant that
+
+ align:start position:0%
+the ready made lenses and it meant that
+ 
+
+ align:start position:0%
+the ready made lenses and it meant that
+African Liberation the fact that an
+
+ align:start position:0%
+African Liberation the fact that an
+ 
+
+ align:start position:0%
+African Liberation the fact that an
+African Army could win over Napoleon
+
+ align:start position:0%
+African Army could win over Napoleon
+ 
+
+ align:start position:0%
+African Army could win over Napoleon
+they couldn't process that you know it
+
+ align:start position:0%
+they couldn't process that you know it
+ 
+
+ align:start position:0%
+they couldn't process that you know it
+was incompatible with the idea of a
+
+ align:start position:0%
+was incompatible with the idea of a
+ 
+
+ align:start position:0%
+was incompatible with the idea of a
+slave revolution and the same way for
+
+ align:start position:0%
+slave revolution and the same way for
+ 
+
+ align:start position:0%
+slave revolution and the same way for
+language so the same Scholars looking at
+
+ align:start position:0%
+language so the same Scholars looking at
+ 
+
+ align:start position:0%
+language so the same Scholars looking at
+hies Revolution they also looking at at
+
+ align:start position:0%
+hies Revolution they also looking at at
+ 
+
+ align:start position:0%
+hies Revolution they also looking at at
+cre language and they couldn't imagine
+
+ align:start position:0%
+cre language and they couldn't imagine
+ 
+
+ align:start position:0%
+cre language and they couldn't imagine
+for them it was impossible that cre
+
+ align:start position:0%
+for them it was impossible that cre
+ 
+
+ align:start position:0%
+for them it was impossible that cre
+would be normal languages right so so
+
+ align:start position:0%
+would be normal languages right so so
+ 
+
+ align:start position:0%
+would be normal languages right so so
+you can just pass on that um so so the
+
+ align:start position:0%
+you can just pass on that um so so the
+ 
+
+ align:start position:0%
+you can just pass on that um so so the
+so this is very familiar uh so this is
+
+ align:start position:0%
+so this is very familiar uh so this is
+ 
+
+ align:start position:0%
+so this is very familiar uh so this is
+the root of all these myth so the root
+
+ align:start position:0%
+the root of all these myth so the root
+ 
+
+ align:start position:0%
+the root of all these myth so the root
+of these myth is basically in the idea
+
+ align:start position:0%
+of these myth is basically in the idea
+ 
+
+ align:start position:0%
+of these myth is basically in the idea
+that um the Africans were lesser and
+
+ align:start position:0%
+that um the Africans were lesser and
+ 
+
+ align:start position:0%
+that um the Africans were lesser and
+whatever this they could produce as
+
+ align:start position:0%
+whatever this they could produce as
+ 
+
+ align:start position:0%
+whatever this they could produce as
+language had to be lesser therefore they
+
+ align:start position:0%
+language had to be lesser therefore they
+ 
+
+ align:start position:0%
+language had to be lesser therefore they
+could not be part of the same kind of um
+
+ align:start position:0%
+could not be part of the same kind of um
+ 
+
+ align:start position:0%
+could not be part of the same kind of um
+Theory as um normal language change as
+
+ align:start position:0%
+Theory as um normal language change as
+ 
+
+ align:start position:0%
+Theory as um normal language change as
+the of French so but again I can say you
+
+ align:start position:0%
+the of French so but again I can say you
+ 
+
+ align:start position:0%
+the of French so but again I can say you
+know it's the economist to meaning that
+
+ align:start position:0%
+know it's the economist to meaning that
+ 
+
+ align:start position:0%
+know it's the economist to meaning that
+you know the driving in fact this is not
+
+ align:start position:0%
+you know the driving in fact this is not
+ 
+
+ align:start position:0%
+you know the driving in fact this is not
+clear you know so yesterday actually so
+
+ align:start position:0%
+clear you know so yesterday actually so
+ 
+
+ align:start position:0%
+clear you know so yesterday actually so
+n chumsky was in Black matters and I
+
+ align:start position:0%
+n chumsky was in Black matters and I
+ 
+
+ align:start position:0%
+n chumsky was in Black matters and I
+asked that question about um you know
+
+ align:start position:0%
+asked that question about um you know
+ 
+
+ align:start position:0%
+asked that question about um you know
+what what came first the economy you
+
+ align:start position:0%
+what what came first the economy you
+ 
+
+ align:start position:0%
+what what came first the economy you
+know Empire or or racism right because
+
+ align:start position:0%
+know Empire or or racism right because
+ 
+
+ align:start position:0%
+know Empire or or racism right because
+one could say that racism is a result of
+
+ align:start position:0%
+one could say that racism is a result of
+ 
+
+ align:start position:0%
+one could say that racism is a result of
+Empire you know if you want to create if
+
+ align:start position:0%
+Empire you know if you want to create if
+ 
+
+ align:start position:0%
+Empire you know if you want to create if
+you want to make the Africans as B of
+
+ align:start position:0%
+you want to make the Africans as B of
+ 
+
+ align:start position:0%
+you want to make the Africans as B of
+Labor in order to produce wealth then
+
+ align:start position:0%
+Labor in order to produce wealth then
+ 
+
+ align:start position:0%
+Labor in order to produce wealth then
+you're going to deman know the color the
+
+ align:start position:0%
+you're going to deman know the color the
+ 
+
+ align:start position:0%
+you're going to deman know the color the
+culture the language or is it was Rec in
+
+ align:start position:0%
+culture the language or is it was Rec in
+ 
+
+ align:start position:0%
+culture the language or is it was Rec in
+there before and therefore made it okay
+
+ align:start position:0%
+there before and therefore made it okay
+ 
+
+ align:start position:0%
+there before and therefore made it okay
+to make them into space that's that's a
+
+ align:start position:0%
+to make them into space that's that's a
+ 
+
+ align:start position:0%
+to make them into space that's that's a
+hard question to
+
+ align:start position:0%
+hard question to
+ 
+
+ align:start position:0%
+hard question to
+answer that's that's it's hard to know
+
+ align:start position:0%
+answer that's that's it's hard to know
+ 
+
+ align:start position:0%
+answer that's that's it's hard to know
+maybe maybe the two as chumsky puts it
+
+ align:start position:0%
+maybe maybe the two as chumsky puts it
+ 
+
+ align:start position:0%
+maybe maybe the two as chumsky puts it
+the two kind of reinforce each other you
+
+ align:start position:0%
+the two kind of reinforce each other you
+ 
+
+ align:start position:0%
+the two kind of reinforce each other you
+see in the case of hati though I mean we
+
+ align:start position:0%
+see in the case of hati though I mean we
+ 
+
+ align:start position:0%
+see in the case of hati though I mean we
+have all these documents that show that
+
+ align:start position:0%
+have all these documents that show that
+ 
+
+ align:start position:0%
+have all these documents that show that
+um that uh that clearly there was this
+
+ align:start position:0%
+um that uh that clearly there was this
+ 
+
+ align:start position:0%
+um that uh that clearly there was this
+one of the driving force behind the
+
+ align:start position:0%
+one of the driving force behind the
+ 
+
+ align:start position:0%
+one of the driving force behind the
+black code which was a code that would
+
+ align:start position:0%
+black code which was a code that would
+ 
+
+ align:start position:0%
+black code which was a code that would
+you know to regulate the the the the
+
+ align:start position:0%
+you know to regulate the the the the
+ 
+
+ align:start position:0%
+you know to regulate the the the the
+slaves in in the Caribbean you
+
+ align:start position:0%
+slaves in in the Caribbean you
+ 
+
+ align:start position:0%
+slaves in in the Caribbean you
+know the driving force behind it was
+
+ align:start position:0%
+know the driving force behind it was
+ 
+
+ align:start position:0%
+know the driving force behind it was
+economics right um you know something
+
+ align:start position:0%
+economics right um you know something
+ 
+
+ align:start position:0%
+economics right um you know something
+like that right
+
+ align:start position:0%
+like that right
+ 
+
+ align:start position:0%
+like that right
+so uh so theya that you know the cre
+
+ align:start position:0%
+so uh so theya that you know the cre
+ 
+
+ align:start position:0%
+so uh so theya that you know the cre
+blacks are superior because they are in
+
+ align:start position:0%
+blacks are superior because they are in
+ 
+
+ align:start position:0%
+blacks are superior because they are in
+the company of whites you know something
+
+ align:start position:0%
+the company of whites you know something
+ 
+
+ align:start position:0%
+the company of whites you know something
+like that you know so for all the task
+
+ align:start position:0%
+like that you know so for all the task
+ 
+
+ align:start position:0%
+like that you know so for all the task
+is the cre slaves that are preferred and
+
+ align:start position:0%
+is the cre slaves that are preferred and
+ 
+
+ align:start position:0%
+is the cre slaves that are preferred and
+here the that know the cre slaves are
+
+ align:start position:0%
+here the that know the cre slaves are
+ 
+
+ align:start position:0%
+here the that know the cre slaves are
+those who are born in the Caribbean uh
+
+ align:start position:0%
+those who are born in the Caribbean uh
+ 
+
+ align:start position:0%
+those who are born in the Caribbean uh
+they they have African ancestry but they
+
+ align:start position:0%
+they they have African ancestry but they
+ 
+
+ align:start position:0%
+they they have African ancestry but they
+BN in the Caribbean and and and they
+
+ align:start position:0%
+BN in the Caribbean and and and they
+ 
+
+ align:start position:0%
+BN in the Caribbean and and and they
+have more worth why because um they are
+
+ align:start position:0%
+have more worth why because um they are
+ 
+
+ align:start position:0%
+have more worth why because um they are
+being uh assimilated into European
+
+ align:start position:0%
+being uh assimilated into European
+ 
+
+ align:start position:0%
+being uh assimilated into European
+culture talking about assimilation so
+
+ align:start position:0%
+culture talking about assimilation so
+ 
+
+ align:start position:0%
+culture talking about assimilation so
+here assimilation comes with a benefit
+
+ align:start position:0%
+here assimilation comes with a benefit
+ 
+
+ align:start position:0%
+here assimilation comes with a benefit
+as you being assimilated you acquire and
+
+ align:start position:0%
+as you being assimilated you acquire and
+ 
+
+ align:start position:0%
+as you being assimilated you acquire and
+actually this guy this is the same guy
+
+ align:start position:0%
+actually this guy this is the same guy
+ 
+
+ align:start position:0%
+actually this guy this is the same guy
+actually who came up with this 128 P of
+
+ align:start position:0%
+actually who came up with this 128 P of
+ 
+
+ align:start position:0%
+actually who came up with this 128 P of
+blood right you could compute qualities
+
+ align:start position:0%
+blood right you could compute qualities
+ 
+
+ align:start position:0%
+blood right you could compute qualities
+of of different mixes based on the
+
+ align:start position:0%
+of of different mixes based on the
+ 
+
+ align:start position:0%
+of of different mixes based on the
+quanta of blood white blood versus black
+
+ align:start position:0%
+quanta of blood white blood versus black
+ 
+
+ align:start position:0%
+quanta of blood white blood versus black
+blood he also had quanta in terms of
+
+ align:start position:0%
+blood he also had quanta in terms of
+ 
+
+ align:start position:0%
+blood he also had quanta in terms of
+uh the worth of cre slaves versus those
+
+ align:start position:0%
+uh the worth of cre slaves versus those
+ 
+
+ align:start position:0%
+uh the worth of cre slaves versus those
+of African slaves a quarter more um to
+
+ align:start position:0%
+of African slaves a quarter more um to
+ 
+
+ align:start position:0%
+of African slaves a quarter more um to
+imagine um and of course you know the
+
+ align:start position:0%
+imagine um and of course you know the
+ 
+
+ align:start position:0%
+imagine um and of course you know the
+idea that you know what made them better
+
+ align:start position:0%
+idea that you know what made them better
+ 
+
+ align:start position:0%
+idea that you know what made them better
+is because they had been assimilated or
+
+ align:start position:0%
+is because they had been assimilated or
+ 
+
+ align:start position:0%
+is because they had been assimilated or
+in this case he use the poetic term
+
+ align:start position:0%
+in this case he use the poetic term
+ 
+
+ align:start position:0%
+in this case he use the poetic term
+embellished that the Domesticity meaning
+
+ align:start position:0%
+embellished that the Domesticity meaning
+ 
+
+ align:start position:0%
+embellished that the Domesticity meaning
+slavery by whites would embellish the
+
+ align:start position:0%
+slavery by whites would embellish the
+ 
+
+ align:start position:0%
+slavery by whites would embellish the
+black species right um
+
+ align:start position:0%
+black species right um
+ 
+
+ align:start position:0%
+black species right um
+so this is some of the background behind
+
+ align:start position:0%
+so this is some of the background behind
+ 
+
+ align:start position:0%
+so this is some of the background behind
+all these claims about cre languages um
+
+ align:start position:0%
+all these claims about cre languages um
+ 
+
+ align:start position:0%
+all these claims about cre languages um
+but of course the other part of the
+
+ align:start position:0%
+but of course the other part of the
+ 
+
+ align:start position:0%
+but of course the other part of the
+background that you know is the fact
+
+ align:start position:0%
+background that you know is the fact
+ 
+
+ align:start position:0%
+background that you know is the fact
+that um there was this revolution that
+
+ align:start position:0%
+that um there was this revolution that
+ 
+
+ align:start position:0%
+that um there was this revolution that
+had to be silenced this is the book that
+
+ align:start position:0%
+had to be silenced this is the book that
+ 
+
+ align:start position:0%
+had to be silenced this is the book that
+you read uh as you put of it that you
+
+ align:start position:0%
+you read uh as you put of it that you
+ 
+
+ align:start position:0%
+you read uh as you put of it that you
+read uh about silencing the past and and
+
+ align:start position:0%
+read uh about silencing the past and and
+ 
+
+ align:start position:0%
+read uh about silencing the past and and
+so what I'm driving at here is that um
+
+ align:start position:0%
+so what I'm driving at here is that um
+ 
+
+ align:start position:0%
+so what I'm driving at here is that um
+all this together you
+
+ align:start position:0%
+all this together you
+ 
+
+ align:start position:0%
+all this together you
+know created the roots of um this View
+
+ align:start position:0%
+know created the roots of um this View
+ 
+
+ align:start position:0%
+know created the roots of um this View
+use that cre are special and and again
+
+ align:start position:0%
+use that cre are special and and again
+ 
+
+ align:start position:0%
+use that cre are special and and again
+just for good measure I want to stress
+
+ align:start position:0%
+just for good measure I want to stress
+ 
+
+ align:start position:0%
+just for good measure I want to stress
+again um espcially as as we wrap up this
+
+ align:start position:0%
+again um espcially as as we wrap up this
+ 
+
+ align:start position:0%
+again um espcially as as we wrap up this
+course that you know this these Notions
+
+ align:start position:0%
+course that you know this these Notions
+ 
+
+ align:start position:0%
+course that you know this these Notions
+of Crees being lesser and to be
+
+ align:start position:0%
+of Crees being lesser and to be
+ 
+
+ align:start position:0%
+of Crees being lesser and to be
+excluded actually they've been fought
+
+ align:start position:0%
+excluded actually they've been fought
+ 
+
+ align:start position:0%
+excluded actually they've been fought
+against even in the 19th century so this
+
+ align:start position:0%
+against even in the 19th century so this
+ 
+
+ align:start position:0%
+against even in the 19th century so this
+is the Salin our first president and now
+
+ align:start position:0%
+is the Salin our first president and now
+ 
+
+ align:start position:0%
+is the Salin our first president and now
+this is the that famous quote in French
+
+ align:start position:0%
+this is the that famous quote in French
+ 
+
+ align:start position:0%
+this is the that famous quote in French
+because it's written by a French
+
+ align:start position:0%
+because it's written by a French
+ 
+
+ align:start position:0%
+because it's written by a French
+Observer and but the key Point here here
+
+ align:start position:0%
+Observer and but the key Point here here
+ 
+
+ align:start position:0%
+Observer and but the key Point here here
+is the fact that the saline would get
+
+ align:start position:0%
+is the fact that the saline would get
+ 
+
+ align:start position:0%
+is the fact that the saline would get
+very upset when someone was was back
+
+ align:start position:0%
+very upset when someone was was back
+ 
+
+ align:start position:0%
+very upset when someone was was back
+then well back they were they weren't
+
+ align:start position:0%
+then well back they were they weren't
+ 
+
+ align:start position:0%
+then well back they were they weren't
+haian yet because he was still under the
+
+ align:start position:0%
+haian yet because he was still under the
+ 
+
+ align:start position:0%
+haian yet because he was still under the
+The Colony but he would tell uh anyone
+
+ align:start position:0%
+The Colony but he would tell uh anyone
+ 
+
+ align:start position:0%
+The Colony but he would tell uh anyone
+who spoke French to him that you know
+
+ align:start position:0%
+who spoke French to him that you know
+ 
+
+ align:start position:0%
+who spoke French to him that you know
+why do you speak French you have your
+
+ align:start position:0%
+why do you speak French you have your
+ 
+
+ align:start position:0%
+why do you speak French you have your
+own language you know so this is cre
+
+ align:start position:0%
+own language you know so this is cre
+ 
+
+ align:start position:0%
+own language you know so this is cre
+actually you have your language and as
+
+ align:start position:0%
+actually you have your language and as
+ 
+
+ align:start position:0%
+actually you have your language and as
+he was um looking at them with disdain
+
+ align:start position:0%
+he was um looking at them with disdain
+ 
+
+ align:start position:0%
+he was um looking at them with disdain
+why look for
+
+ align:start position:0%
+why look for
+ 
+
+ align:start position:0%
+why look for
+another language why look for someone
+
+ align:start position:0%
+another language why look for someone
+ 
+
+ align:start position:0%
+another language why look for someone
+else's language so so the point is that
+
+ align:start position:0%
+else's language so so the point is that
+ 
+
+ align:start position:0%
+else's language so so the point is that
+thein even as he was technically a FR
+
+ align:start position:0%
+thein even as he was technically a FR
+ 
+
+ align:start position:0%
+thein even as he was technically a FR
+citizen as he was fighting for
+
+ align:start position:0%
+citizen as he was fighting for
+ 
+
+ align:start position:0%
+citizen as he was fighting for
+Independence he understood the power of
+
+ align:start position:0%
+Independence he understood the power of
+ 
+
+ align:start position:0%
+Independence he understood the power of
+the cre language okay and then now that
+
+ align:start position:0%
+the cre language okay and then now that
+ 
+
+ align:start position:0%
+the cre language okay and then now that
+same decid now this is um to remind you
+
+ align:start position:0%
+same decid now this is um to remind you
+ 
+
+ align:start position:0%
+same decid now this is um to remind you
+this length between you know politics
+
+ align:start position:0%
+this length between you know politics
+ 
+
+ align:start position:0%
+this length between you know politics
+and identity uh you know as he was so
+
+ align:start position:0%
+and identity uh you know as he was so
+ 
+
+ align:start position:0%
+and identity uh you know as he was so
+this is one of the first
+
+ align:start position:0%
+this is one of the first
+ 
+
+ align:start position:0%
+this is one of the first
+1805 uh um law in Haiti creating Haiti
+
+ align:start position:0%
+1805 uh um law in Haiti creating Haiti
+ 
+
+ align:start position:0%
+1805 uh um law in Haiti creating Haiti
+right so this is article one the people
+
+ align:start position:0%
+right so this is article one the people
+ 
+
+ align:start position:0%
+right so this is article one the people
+inhabiting the island from domain agree
+
+ align:start position:0%
+inhabiting the island from domain agree
+ 
+
+ align:start position:0%
+inhabiting the island from domain agree
+to form themselves into a free state
+
+ align:start position:0%
+to form themselves into a free state
+ 
+
+ align:start position:0%
+to form themselves into a free state
+Sovereign and independent of any other
+
+ align:start position:0%
+Sovereign and independent of any other
+ 
+
+ align:start position:0%
+Sovereign and independent of any other
+power right so this was the the most
+
+ align:start position:0%
+power right so this was the the most
+ 
+
+ align:start position:0%
+power right so this was the the most
+disturbing part about Haiti um slavery
+
+ align:start position:0%
+disturbing part about Haiti um slavery
+ 
+
+ align:start position:0%
+disturbing part about Haiti um slavery
+is abolished this was 1805 at the time
+
+ align:start position:0%
+is abolished this was 1805 at the time
+ 
+
+ align:start position:0%
+is abolished this was 1805 at the time
+when both Europe and the Americas both
+
+ align:start position:0%
+when both Europe and the Americas both
+ 
+
+ align:start position:0%
+when both Europe and the Americas both
+North and South America including
+
+ align:start position:0%
+North and South America including
+ 
+
+ align:start position:0%
+North and South America including
+countries like Colombia Venezuela
+
+ align:start position:0%
+countries like Colombia Venezuela
+ 
+
+ align:start position:0%
+countries like Colombia Venezuela
+Bolivia who actually been benefited from
+
+ align:start position:0%
+Bolivia who actually been benefited from
+ 
+
+ align:start position:0%
+Bolivia who actually been benefited from
+Haiti in terms of their own independence
+
+ align:start position:0%
+Haiti in terms of their own independence
+ 
+
+ align:start position:0%
+Haiti in terms of their own independence
+they still had slaves um so slavery is
+
+ align:start position:0%
+they still had slaves um so slavery is
+ 
+
+ align:start position:0%
+they still had slaves um so slavery is
+forever abolished um but the part that
+
+ align:start position:0%
+forever abolished um but the part that
+ 
+
+ align:start position:0%
+forever abolished um but the part that
+remember is also important is that
+
+ align:start position:0%
+remember is also important is that
+ 
+
+ align:start position:0%
+remember is also important is that
+excluding whites from owning any piece
+
+ align:start position:0%
+excluding whites from owning any piece
+ 
+
+ align:start position:0%
+excluding whites from owning any piece
+of Haiti which has now been changed um
+
+ align:start position:0%
+of Haiti which has now been changed um
+ 
+
+ align:start position:0%
+of Haiti which has now been changed um
+but that part that I want to stress is
+
+ align:start position:0%
+but that part that I want to stress is
+ 
+
+ align:start position:0%
+but that part that I want to stress is
+the fact that they understood also the
+
+ align:start position:0%
+the fact that they understood also the
+ 
+
+ align:start position:0%
+the fact that they understood also the
+power of identity now this is 1805 and
+
+ align:start position:0%
+power of identity now this is 1805 and
+ 
+
+ align:start position:0%
+power of identity now this is 1805 and
+he says that you know all uh exception
+
+ align:start position:0%
+he says that you know all uh exception
+ 
+
+ align:start position:0%
+he says that you know all uh exception
+means difference of color um
+
+ align:start position:0%
+means difference of color um
+ 
+
+ align:start position:0%
+means difference of color um
+will seize the Haitians shall henceforth
+
+ align:start position:0%
+will seize the Haitians shall henceforth
+ 
+
+ align:start position:0%
+will seize the Haitians shall henceforth
+be known only by dep of blacks okay
+
+ align:start position:0%
+be known only by dep of blacks okay
+ 
+
+ align:start position:0%
+be known only by dep of blacks okay
+that's 1805 okay was this written in
+
+ align:start position:0%
+that's 1805 okay was this written in
+ 
+
+ align:start position:0%
+that's 1805 okay was this written in
+English well well remember so this was
+
+ align:start position:0%
+English well well remember so this was
+ 
+
+ align:start position:0%
+English well well remember so this was
+at the time when this was both in
+
+ align:start position:0%
+at the time when this was both in
+ 
+
+ align:start position:0%
+at the time when this was both in
+English and French because thisin
+
+ align:start position:0%
+English and French because thisin
+ 
+
+ align:start position:0%
+English and French because thisin
+understood that he had to let the world
+
+ align:start position:0%
+understood that he had to let the world
+ 
+
+ align:start position:0%
+understood that he had to let the world
+know that this is my position in fact
+
+ align:start position:0%
+know that this is my position in fact
+ 
+
+ align:start position:0%
+know that this is my position in fact
+someone so this book
+
+ align:start position:0%
+someone so this book
+ 
+
+ align:start position:0%
+someone so this book
+here addresses this question so why why
+
+ align:start position:0%
+here addresses this question so why why
+ 
+
+ align:start position:0%
+here addresses this question so why why
+were why was the Salen since he was so
+
+ align:start position:0%
+were why was the Salen since he was so
+ 
+
+ align:start position:0%
+were why was the Salen since he was so
+procore why was he writing in French and
+
+ align:start position:0%
+procore why was he writing in French and
+ 
+
+ align:start position:0%
+procore why was he writing in French and
+English right and the point is that when
+
+ align:start position:0%
+English right and the point is that when
+ 
+
+ align:start position:0%
+English right and the point is that when
+he was speaking like here he was being
+
+ align:start position:0%
+he was speaking like here he was being
+ 
+
+ align:start position:0%
+he was speaking like here he was being
+cre but he when he had people right for
+
+ align:start position:0%
+cre but he when he had people right for
+ 
+
+ align:start position:0%
+cre but he when he had people right for
+him because he most most of the time he
+
+ align:start position:0%
+him because he most most of the time he
+ 
+
+ align:start position:0%
+him because he most most of the time he
+he had people right for him he wanted
+
+ align:start position:0%
+he had people right for him he wanted
+ 
+
+ align:start position:0%
+he had people right for him he wanted
+the world to understand what was his
+
+ align:start position:0%
+the world to understand what was his
+ 
+
+ align:start position:0%
+the world to understand what was his
+position about this issue right so he
+
+ align:start position:0%
+position about this issue right so he
+ 
+
+ align:start position:0%
+position about this issue right so he
+had to write in French and English
+
+ align:start position:0%
+had to write in French and English
+ 
+
+ align:start position:0%
+had to write in French and English
+because he was speaking to not to
+
+ align:start position:0%
+because he was speaking to not to
+ 
+
+ align:start position:0%
+because he was speaking to not to
+Haitians and he was speaking to they was
+
+ align:start position:0%
+Haitians and he was speaking to they was
+ 
+
+ align:start position:0%
+Haitians and he was speaking to they was
+say this is this is opposition so beware
+
+ align:start position:0%
+say this is this is opposition so beware
+ 
+
+ align:start position:0%
+say this is this is opposition so beware
+um but then of course you know
+
+ align:start position:0%
+um but then of course you know
+ 
+
+ align:start position:0%
+um but then of course you know
+um is what this this is a book from a
+
+ align:start position:0%
+um is what this this is a book from a
+ 
+
+ align:start position:0%
+um is what this this is a book from a
+book by Paul
+
+ align:start position:0%
+book by Paul
+ 
+
+ align:start position:0%
+book by Paul
+former so this part
+
+ align:start position:0%
+former so this part
+ 
+
+ align:start position:0%
+former so this part
+is moving from 1805 to the present and
+
+ align:start position:0%
+is moving from 1805 to the present and
+ 
+
+ align:start position:0%
+is moving from 1805 to the present and
+to understand why up to today they still
+
+ align:start position:0%
+to understand why up to today they still
+ 
+
+ align:start position:0%
+to understand why up to today they still
+the struggle around language and
+
+ align:start position:0%
+the struggle around language and
+ 
+
+ align:start position:0%
+the struggle around language and
+identity in the Caribbean you know
+
+ align:start position:0%
+identity in the Caribbean you know
+ 
+
+ align:start position:0%
+identity in the Caribbean you know
+especially Haiti is is you have to that
+
+ align:start position:0%
+especially Haiti is is you have to that
+ 
+
+ align:start position:0%
+especially Haiti is is you have to that
+from the very beginning uh after
+
+ align:start position:0%
+from the very beginning uh after
+ 
+
+ align:start position:0%
+from the very beginning uh after
+Independence there were all this
+
+ align:start position:0%
+Independence there were all this
+ 
+
+ align:start position:0%
+Independence there were all this
+pressure you know for hat to remain and
+
+ align:start position:0%
+pressure you know for hat to remain and
+ 
+
+ align:start position:0%
+pressure you know for hat to remain and
+the French dominion and under then
+
+ align:start position:0%
+the French dominion and under then
+ 
+
+ align:start position:0%
+the French dominion and under then
+American Dominion as you know you know
+
+ align:start position:0%
+American Dominion as you know you know
+ 
+
+ align:start position:0%
+American Dominion as you know you know
+America the US occupied Haiti for 15
+
+ align:start position:0%
+America the US occupied Haiti for 15
+ 
+
+ align:start position:0%
+America the US occupied Haiti for 15
+years in the early part of the 20th
+
+ align:start position:0%
+years in the early part of the 20th
+ 
+
+ align:start position:0%
+years in the early part of the 20th
+century but even in 1825 the French
+
+ align:start position:0%
+century but even in 1825 the French
+ 
+
+ align:start position:0%
+century but even in 1825 the French
+managed to
+
+ align:start position:0%
+managed to
+ 
+
+ align:start position:0%
+managed to
+extract this
+
+ align:start position:0%
+extract this
+ 
+
+ align:start position:0%
+extract this
+Indemnity from Haiti for you know this
+
+ align:start position:0%
+Indemnity from Haiti for you know this
+ 
+
+ align:start position:0%
+Indemnity from Haiti for you know this
+is this was huge back then I think this
+
+ align:start position:0%
+is this was huge back then I think this
+ 
+
+ align:start position:0%
+is this was huge back then I think this
+is not worth you know billions of
+
+ align:start position:0%
+is not worth you know billions of
+ 
+
+ align:start position:0%
+is not worth you know billions of
+dollars can anyone can anyone read this
+
+ align:start position:0%
+dollars can anyone can anyone read this
+ 
+
+ align:start position:0%
+dollars can anyone can anyone read this
+uh from
+
+ align:start position:0%
+uh from
+ 
+
+ align:start position:0%
+uh from
+here who wants to read
+
+ align:start position:0%
+here who wants to read
+ 
+
+ align:start position:0%
+here who wants to read
+this okay K president V for 150 million
+
+ align:start position:0%
+this okay K president V for 150 million
+ 
+
+ align:start position:0%
+this okay K president V for 150 million
+Franks and the having of Customs charges
+
+ align:start position:0%
+Franks and the having of Customs charges
+ 
+
+ align:start position:0%
+Franks and the having of Customs charges
+for the French trade all as Indemnity
+
+ align:start position:0%
+for the French trade all as Indemnity
+ 
+
+ align:start position:0%
+for the French trade all as Indemnity
+for the losses of the plantation owners
+
+ align:start position:0%
+for the losses of the plantation owners
+ 
+
+ align:start position:0%
+for the losses of the plantation owners
+these conditions accepted in 1825 led to
+
+ align:start position:0%
+these conditions accepted in 1825 led to
+ 
+
+ align:start position:0%
+these conditions accepted in 1825 led to
+Decades of French domination of Haitian
+
+ align:start position:0%
+Decades of French domination of Haitian
+ 
+
+ align:start position:0%
+Decades of French domination of Haitian
+finance and had a catastrophic effect on
+
+ align:start position:0%
+finance and had a catastrophic effect on
+ 
+
+ align:start position:0%
+finance and had a catastrophic effect on
+the new nation's delicate economy
+
+ align:start position:0%
+the new nation's delicate economy
+ 
+
+ align:start position:0%
+the new nation's delicate economy
+despite its nominal Independence Haiti
+
+ align:start position:0%
+despite its nominal Independence Haiti
+ 
+
+ align:start position:0%
+despite its nominal Independence Haiti
+could not escape the shackles of foreign
+
+ align:start position:0%
+could not escape the shackles of foreign
+ 
+
+ align:start position:0%
+could not escape the shackles of foreign
+domination the very fact of a debt to
+
+ align:start position:0%
+domination the very fact of a debt to
+ 
+
+ align:start position:0%
+domination the very fact of a debt to
+France strikes the modern Observer as
+
+ align:start position:0%
+France strikes the modern Observer as
+ 
+
+ align:start position:0%
+France strikes the modern Observer as
+odd why might a country of former slaves
+
+ align:start position:0%
+odd why might a country of former slaves
+ 
+
+ align:start position:0%
+odd why might a country of former slaves
+feel compelled to enumerate the
+
+ align:start position:0%
+feel compelled to enumerate the
+ 
+
+ align:start position:0%
+feel compelled to enumerate the
+plantocracy for losses incurred in a war
+
+ align:start position:0%
+plantocracy for losses incurred in a war
+ 
+
+ align:start position:0%
+plantocracy for losses incurred in a war
+of Liberation yeah so so basically so
+
+ align:start position:0%
+of Liberation yeah so so basically so
+ 
+
+ align:start position:0%
+of Liberation yeah so so basically so
+the answer says that you know the elite
+
+ align:start position:0%
+the answer says that you know the elite
+ 
+
+ align:start position:0%
+the answer says that you know the elite
+had to make this compromise the elite
+
+ align:start position:0%
+had to make this compromise the elite
+ 
+
+ align:start position:0%
+had to make this compromise the elite
+wanted to be recognized by Europe and by
+
+ align:start position:0%
+wanted to be recognized by Europe and by
+ 
+
+ align:start position:0%
+wanted to be recognized by Europe and by
+and by America okay so and and so this
+
+ align:start position:0%
+and by America okay so and and so this
+ 
+
+ align:start position:0%
+and by America okay so and and so this
+struggle so that question here points to
+
+ align:start position:0%
+struggle so that question here points to
+ 
+
+ align:start position:0%
+struggle so that question here points to
+this basic ination history that from the
+
+ align:start position:0%
+this basic ination history that from the
+ 
+
+ align:start position:0%
+this basic ination history that from the
+very beginning uh the new Elite that
+
+ align:start position:0%
+very beginning uh the new Elite that
+ 
+
+ align:start position:0%
+very beginning uh the new Elite that
+became the the leader of the leaders of
+
+ align:start position:0%
+became the the leader of the leaders of
+ 
+
+ align:start position:0%
+became the the leader of the leaders of
+the country they in many ways replicated
+
+ align:start position:0%
+the country they in many ways replicated
+ 
+
+ align:start position:0%
+the country they in many ways replicated
+what the french had done you see um so
+
+ align:start position:0%
+what the french had done you see um so
+ 
+
+ align:start position:0%
+what the french had done you see um so
+that's why me so this is now after the
+
+ align:start position:0%
+that's why me so this is now after the
+ 
+
+ align:start position:0%
+that's why me so this is now after the
+earthquake this is from the Boston Globe
+
+ align:start position:0%
+earthquake this is from the Boston Globe
+ 
+
+ align:start position:0%
+earthquake this is from the Boston Globe
+right um and this is a straight
+
+ align:start position:0%
+right um and this is a straight
+ 
+
+ align:start position:0%
+right um and this is a straight
+continuation of what Paul Farmer
+
+ align:start position:0%
+continuation of what Paul Farmer
+ 
+
+ align:start position:0%
+continuation of what Paul Farmer
+discussed in that previous quote so
+
+ align:start position:0%
+discussed in that previous quote so
+ 
+
+ align:start position:0%
+discussed in that previous quote so
+wants to read this this part
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+here
+
+ align:start position:0%
+here
+ 
+
+ align:start position:0%
+here
+good the question now is whether the
+
+ align:start position:0%
+good the question now is whether the
+ 
+
+ align:start position:0%
+good the question now is whether the
+wealthy Elite that controls the B the
+
+ align:start position:0%
+wealthy Elite that controls the B the
+ 
+
+ align:start position:0%
+wealthy Elite that controls the B the
+economy will help rebuild Haiti and
+
+ align:start position:0%
+economy will help rebuild Haiti and
+ 
+
+ align:start position:0%
+economy will help rebuild Haiti and
+create a thriving middle class 80% of
+
+ align:start position:0%
+create a thriving middle class 80% of
+ 
+
+ align:start position:0%
+create a thriving middle class 80% of
+patients live in poverty while a handful
+
+ align:start position:0%
+patients live in poverty while a handful
+ 
+
+ align:start position:0%
+patients live in poverty while a handful
+of often light-skinned descendants of
+
+ align:start position:0%
+of often light-skinned descendants of
+ 
+
+ align:start position:0%
+of often light-skinned descendants of
+the French who ruled the country's
+
+ align:start position:0%
+the French who ruled the country's
+ 
+
+ align:start position:0%
+the French who ruled the country's
+coffee and sugar slave plantations until
+
+ align:start position:0%
+coffee and sugar slave plantations until
+ 
+
+ align:start position:0%
+coffee and sugar slave plantations until
+Haiti declared independence in 1804 and
+
+ align:start position:0%
+Haiti declared independence in 1804 and
+ 
+
+ align:start position:0%
+Haiti declared independence in 1804 and
+other groups control most of the right
+
+ align:start position:0%
+other groups control most of the right
+ 
+
+ align:start position:0%
+other groups control most of the right
+so so basically you see the cleavage is
+
+ align:start position:0%
+so so basically you see the cleavage is
+ 
+
+ align:start position:0%
+so so basically you see the cleavage is
+still there right and this is so this
+
+ align:start position:0%
+still there right and this is so this
+ 
+
+ align:start position:0%
+still there right and this is so this
+cleavage and I think here know we can
+
+ align:start position:0%
+cleavage and I think here know we can
+ 
+
+ align:start position:0%
+cleavage and I think here know we can
+refer back to Karen and Rachel's
+
+ align:start position:0%
+refer back to Karen and Rachel's
+ 
+
+ align:start position:0%
+refer back to Karen and Rachel's
+presentation this cleavage between the
+
+ align:start position:0%
+presentation this cleavage between the
+ 
+
+ align:start position:0%
+presentation this cleavage between the
+elite and the masses also has this um
+
+ align:start position:0%
+elite and the masses also has this um
+ 
+
+ align:start position:0%
+elite and the masses also has this um
+this reflex this linguistic reflex where
+
+ align:start position:0%
+this reflex this linguistic reflex where
+ 
+
+ align:start position:0%
+this reflex this linguistic reflex where
+French is a language of power versus um
+
+ align:start position:0%
+French is a language of power versus um
+ 
+
+ align:start position:0%
+French is a language of power versus um
+Creole being the language that's still
+
+ align:start position:0%
+Creole being the language that's still
+ 
+
+ align:start position:0%
+Creole being the language that's still
+struggling uh to become a tool for for
+
+ align:start position:0%
+struggling uh to become a tool for for
+ 
+
+ align:start position:0%
+struggling uh to become a tool for for
+Liberation right so so here I think we
+
+ align:start position:0%
+Liberation right so so here I think we
+ 
+
+ align:start position:0%
+Liberation right so so here I think we
+have this um tight connection this tight
+
+ align:start position:0%
+have this um tight connection this tight
+ 
+
+ align:start position:0%
+have this um tight connection this tight
+Nexus between language power and an
+
+ align:start position:0%
+Nexus between language power and an
+ 
+
+ align:start position:0%
+Nexus between language power and an
+identity
\ No newline at end of file
diff --git a/MuRVOQY8KoY.txt b/MuRVOQY8KoY.txt
new file mode 100644
index 0000000000000000000000000000000000000000..132cc48048ca118038a48deb31283258e73b7bb9
--- /dev/null
+++ b/MuRVOQY8KoY.txt
@@ -0,0 +1,19555 @@
+align:start position:0%
+ 
+here's the agenda for today as usual a
+
+ align:start position:0%
+here's the agenda for today as usual a
+ 
+
+ align:start position:0%
+here's the agenda for today as usual a
+bunch of announcements in
+
+ align:start position:0%
+bunch of announcements in
+ 
+
+ align:start position:0%
+bunch of announcements in
+red assignment 4 was graded there will
+
+ align:start position:0%
+red assignment 4 was graded there will
+ 
+
+ align:start position:0%
+red assignment 4 was graded there will
+be
+
+ align:start position:0%
+be
+ 
+
+ align:start position:0%
+be
+comments showing up online on stellar
+
+ align:start position:0%
+comments showing up online on stellar
+ 
+
+ align:start position:0%
+comments showing up online on stellar
+soon on any of you didn't get a near
+
+ align:start position:0%
+soon on any of you didn't get a near
+ 
+
+ align:start position:0%
+soon on any of you didn't get a near
+perfect score
+
+ align:start position:0%
+perfect score
+ 
+
+ align:start position:0%
+perfect score
+on it and i'll also be going over a
+
+ align:start position:0%
+on it and i'll also be going over a
+ 
+
+ align:start position:0%
+on it and i'll also be going over a
+little bit of it in
+
+ align:start position:0%
+little bit of it in
+ 
+
+ align:start position:0%
+little bit of it in
+in a moment
+
+ align:start position:0%
+in a moment
+ 
+
+ align:start position:0%
+in a moment
+and then once we do that we're going to
+
+ align:start position:0%
+and then once we do that we're going to
+ 
+
+ align:start position:0%
+and then once we do that we're going to
+talk about navigation how we know where
+
+ align:start position:0%
+talk about navigation how we know where
+ 
+
+ align:start position:0%
+talk about navigation how we know where
+we are and how to get from here to
+
+ align:start position:0%
+we are and how to get from here to
+ 
+
+ align:start position:0%
+we are and how to get from here to
+someplace else which is much more
+
+ align:start position:0%
+someplace else which is much more
+ 
+
+ align:start position:0%
+someplace else which is much more
+awesome than it sounds at first as you
+
+ align:start position:0%
+awesome than it sounds at first as you
+ 
+
+ align:start position:0%
+awesome than it sounds at first as you
+will see
+
+ align:start position:0%
+will see
+ 
+
+ align:start position:0%
+will see
+okay so quick uh review
+
+ align:start position:0%
+okay so quick uh review
+ 
+
+ align:start position:0%
+okay so quick uh review
+um okay so what was the key point why
+
+ align:start position:0%
+um okay so what was the key point why
+ 
+
+ align:start position:0%
+um okay so what was the key point why
+did i assign the hackspeed 2001 article
+
+ align:start position:0%
+did i assign the hackspeed 2001 article
+ 
+
+ align:start position:0%
+did i assign the hackspeed 2001 article
+for you guys to read it it presents this
+
+ align:start position:0%
+for you guys to read it it presents this
+ 
+
+ align:start position:0%
+for you guys to read it it presents this
+important challenge to the functional
+
+ align:start position:0%
+important challenge to the functional
+ 
+
+ align:start position:0%
+important challenge to the functional
+specificity of the face area and the
+
+ align:start position:0%
+specificity of the face area and the
+ 
+
+ align:start position:0%
+specificity of the face area and the
+place area what was that challenge
+
+ align:start position:0%
+place area what was that challenge
+ 
+
+ align:start position:0%
+place area what was that challenge
+what was hacksby's key point
+
+ align:start position:0%
+what was hacksby's key point
+ 
+
+ align:start position:0%
+what was hacksby's key point
+yes isabelle whether the um
+
+ align:start position:0%
+yes isabelle whether the um
+ 
+
+ align:start position:0%
+yes isabelle whether the um
+va is just
+
+ align:start position:0%
+va is just
+ 
+
+ align:start position:0%
+va is just
+attracts like it's just uh
+
+ align:start position:0%
+attracts like it's just uh
+ 
+
+ align:start position:0%
+attracts like it's just uh
+has a preference for rick linear
+
+ align:start position:0%
+has a preference for rick linear
+ 
+
+ align:start position:0%
+has a preference for rick linear
+that's what central standard for it's
+
+ align:start position:0%
+that's what central standard for it's
+ 
+
+ align:start position:0%
+that's what central standard for it's
+not truly detecting whether something
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah he wasn't worrying about
+
+ align:start position:0%
+yeah he wasn't worrying about
+ 
+
+ align:start position:0%
+yeah he wasn't worrying about
+rectilinearity so much back then but his
+
+ align:start position:0%
+rectilinearity so much back then but his
+ 
+
+ align:start position:0%
+rectilinearity so much back then but his
+point was that if you that we shouldn't
+
+ align:start position:0%
+point was that if you that we shouldn't
+ 
+
+ align:start position:0%
+point was that if you that we shouldn't
+care just about the overall magnitude of
+
+ align:start position:0%
+care just about the overall magnitude of
+ 
+
+ align:start position:0%
+care just about the overall magnitude of
+response of a region like okay it's nice
+
+ align:start position:0%
+response of a region like okay it's nice
+ 
+
+ align:start position:0%
+response of a region like okay it's nice
+if the face area responds like this to
+
+ align:start position:0%
+if the face area responds like this to
+ 
+
+ align:start position:0%
+if the face area responds like this to
+face isn't like that to objects
+
+ align:start position:0%
+face isn't like that to objects
+ 
+
+ align:start position:0%
+face isn't like that to objects
+but even if it responds low and the same
+
+ align:start position:0%
+but even if it responds low and the same
+ 
+
+ align:start position:0%
+but even if it responds low and the same
+to cars and chairs
+
+ align:start position:0%
+to cars and chairs
+ 
+
+ align:start position:0%
+to cars and chairs
+it might still have information to
+
+ align:start position:0%
+it might still have information to
+ 
+
+ align:start position:0%
+it might still have information to
+enable you to distinguish cars from
+
+ align:start position:0%
+enable you to distinguish cars from
+ 
+
+ align:start position:0%
+enable you to distinguish cars from
+chairs if the pattern of response across
+
+ align:start position:0%
+chairs if the pattern of response across
+ 
+
+ align:start position:0%
+chairs if the pattern of response across
+voxels in that region was stably
+
+ align:start position:0%
+voxels in that region was stably
+ 
+
+ align:start position:0%
+voxels in that region was stably
+different for cars and chairs
+
+ align:start position:0%
+different for cars and chairs
+ 
+
+ align:start position:0%
+different for cars and chairs
+okay that's really key we'll go over it
+
+ align:start position:0%
+okay that's really key we'll go over it
+ 
+
+ align:start position:0%
+okay that's really key we'll go over it
+a few more points but that's that's
+
+ align:start position:0%
+a few more points but that's that's
+ 
+
+ align:start position:0%
+a few more points but that's that's
+essential right a lot of the details
+
+ align:start position:0%
+essential right a lot of the details
+ 
+
+ align:start position:0%
+essential right a lot of the details
+that i'm going to teach you that that go
+
+ align:start position:0%
+that i'm going to teach you that that go
+ 
+
+ align:start position:0%
+that i'm going to teach you that that go
+by in class don't matter but i really
+
+ align:start position:0%
+by in class don't matter but i really
+ 
+
+ align:start position:0%
+by in class don't matter but i really
+want you guys to understand in vpa and
+
+ align:start position:0%
+want you guys to understand in vpa and
+ 
+
+ align:start position:0%
+want you guys to understand in vpa and
+that's the nub of it okay so the idea is
+
+ align:start position:0%
+that's the nub of it okay so the idea is
+ 
+
+ align:start position:0%
+that's the nub of it okay so the idea is
+that selective his
+
+ align:start position:0%
+that selective his
+ 
+
+ align:start position:0%
+that selective his
+his kind of um
+
+ align:start position:0%
+his kind of um
+ 
+
+ align:start position:0%
+his kind of um
+claim is that selective regions like the
+
+ align:start position:0%
+claim is that selective regions like the
+ 
+
+ align:start position:0%
+claim is that selective regions like the
+face area contain information about
+
+ align:start position:0%
+face area contain information about
+ 
+
+ align:start position:0%
+face area contain information about
+non-preferred stimuli that is like
+
+ align:start position:0%
+non-preferred stimuli that is like
+ 
+
+ align:start position:0%
+non-preferred stimuli that is like
+non-faces for the face area or
+
+ align:start position:0%
+non-faces for the face area or
+ 
+
+ align:start position:0%
+non-faces for the face area or
+non-places for the place area
+
+ align:start position:0%
+non-places for the place area
+ 
+
+ align:start position:0%
+non-places for the place area
+and because they contain information
+
+ align:start position:0%
+and because they contain information
+ 
+
+ align:start position:0%
+and because they contain information
+those regions don't care only about
+
+ align:start position:0%
+those regions don't care only about
+ 
+
+ align:start position:0%
+those regions don't care only about
+their preferred category so
+
+ align:start position:0%
+their preferred category so
+ 
+
+ align:start position:0%
+their preferred category so
+why does can washer get off saying the
+
+ align:start position:0%
+why does can washer get off saying the
+ 
+
+ align:start position:0%
+why does can washer get off saying the
+ffa is only about faces and the ppa is
+
+ align:start position:0%
+ffa is only about faces and the ppa is
+ 
+
+ align:start position:0%
+ffa is only about faces and the ppa is
+only about places if we can see
+
+ align:start position:0%
+only about places if we can see
+ 
+
+ align:start position:0%
+only about places if we can see
+information about other things in those
+
+ align:start position:0%
+information about other things in those
+ 
+
+ align:start position:0%
+information about other things in those
+regions okay that's a really important
+
+ align:start position:0%
+regions okay that's a really important
+ 
+
+ align:start position:0%
+regions okay that's a really important
+critique that's why we're spending time
+
+ align:start position:0%
+critique that's why we're spending time
+ 
+
+ align:start position:0%
+critique that's why we're spending time
+on it okay okay
+
+ align:start position:0%
+on it okay okay
+ 
+
+ align:start position:0%
+on it okay okay
+next what kind of empirical data
+
+ align:start position:0%
+next what kind of empirical data
+ 
+
+ align:start position:0%
+next what kind of empirical data
+might
+
+ align:start position:0%
+might
+ 
+
+ align:start position:0%
+might
+be an answer
+
+ align:start position:0%
+be an answer
+ 
+
+ align:start position:0%
+be an answer
+to haxby's charge
+
+ align:start position:0%
+to haxby's charge
+ 
+
+ align:start position:0%
+to haxby's charge
+i've presented at least three different
+
+ align:start position:0%
+i've presented at least three different
+ 
+
+ align:start position:0%
+i've presented at least three different
+kinds of data that can address this and
+
+ align:start position:0%
+kinds of data that can address this and
+ 
+
+ align:start position:0%
+kinds of data that can address this and
+say hey wait a minute you know you have
+
+ align:start position:0%
+say hey wait a minute you know you have
+ 
+
+ align:start position:0%
+say hey wait a minute you know you have
+a point but
+
+ align:start position:0%
+a point but
+ 
+
+ align:start position:0%
+a point but
+what kind of data could speak to that
+
+ align:start position:0%
+what kind of data could speak to that
+ 
+
+ align:start position:0%
+what kind of data could speak to that
+and respond to to hacksby
+
+ align:start position:0%
+and respond to to hacksby
+ 
+
+ align:start position:0%
+and respond to to hacksby
+we didn't actually talk about this
+
+ align:start position:0%
+we didn't actually talk about this
+ 
+
+ align:start position:0%
+we didn't actually talk about this
+explicitly in class but think about it
+
+ align:start position:0%
+explicitly in class but think about it
+ 
+
+ align:start position:0%
+explicitly in class but think about it
+here's the here's the claim he makes
+
+ align:start position:0%
+here's the here's the claim he makes
+ 
+
+ align:start position:0%
+here's the here's the claim he makes
+what might we say right so that's that's
+
+ align:start position:0%
+what might we say right so that's that's
+ 
+
+ align:start position:0%
+what might we say right so that's that's
+empirically true like you look in the
+
+ align:start position:0%
+empirically true like you look in the
+ 
+
+ align:start position:0%
+empirically true like you look in the
+ffa even in my own data i can
+
+ align:start position:0%
+ffa even in my own data i can
+ 
+
+ align:start position:0%
+ffa even in my own data i can
+distinguish
+
+ align:start position:0%
+distinguish
+ 
+
+ align:start position:0%
+distinguish
+uh chairs from shoes a little teeny bit
+
+ align:start position:0%
+uh chairs from shoes a little teeny bit
+ 
+
+ align:start position:0%
+uh chairs from shoes a little teeny bit
+in the ffa okay so that empirical claim
+
+ align:start position:0%
+in the ffa okay so that empirical claim
+ 
+
+ align:start position:0%
+in the ffa okay so that empirical claim
+is true
+
+ align:start position:0%
+is true
+ 
+
+ align:start position:0%
+is true
+why might it nonetheless
+
+ align:start position:0%
+why might it nonetheless
+ 
+
+ align:start position:0%
+why might it nonetheless
+be the case
+
+ align:start position:0%
+be the case
+ 
+
+ align:start position:0%
+be the case
+that the face area is really only about
+
+ align:start position:0%
+that the face area is really only about
+ 
+
+ align:start position:0%
+that the face area is really only about
+face recognition what other data have
+
+ align:start position:0%
+face recognition what other data have
+ 
+
+ align:start position:0%
+face recognition what other data have
+you heard
+
+ align:start position:0%
+you heard
+ 
+
+ align:start position:0%
+you heard
+in here that might
+
+ align:start position:0%
+in here that might
+ 
+
+ align:start position:0%
+in here that might
+make you think that yes ben
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yes
+
+ align:start position:0%
+yes
+ 
+
+ align:start position:0%
+yes
+sorry the
+
+ align:start position:0%
+sorry the
+ 
+
+ align:start position:0%
+sorry the
+presence of low-level stimuli that are
+
+ align:start position:0%
+presence of low-level stimuli that are
+ 
+
+ align:start position:0%
+presence of low-level stimuli that are
+generally in bases but can also
+
+ align:start position:0%
+generally in bases but can also
+ 
+
+ align:start position:0%
+generally in bases but can also
+um sparsely adopt chairs and cars
+
+ align:start position:0%
+um sparsely adopt chairs and cars
+ 
+
+ align:start position:0%
+um sparsely adopt chairs and cars
+[Music]
+
+ align:start position:0%
+[Music]
+ 
+
+ align:start position:0%
+[Music]
+absolutely so yes so put another way
+
+ align:start position:0%
+absolutely so yes so put another way
+ 
+
+ align:start position:0%
+absolutely so yes so put another way
+even if you had a perfect
+
+ align:start position:0%
+even if you had a perfect
+ 
+
+ align:start position:0%
+even if you had a perfect
+coder for faces you know like take your
+
+ align:start position:0%
+coder for faces you know like take your
+ 
+
+ align:start position:0%
+coder for faces you know like take your
+best deep net for face recognition vgg
+
+ align:start position:0%
+best deep net for face recognition vgg
+ 
+
+ align:start position:0%
+best deep net for face recognition vgg
+face
+
+ align:start position:0%
+face
+ 
+
+ align:start position:0%
+face
+it can distinguish chairs and shoes too
+
+ align:start position:0%
+it can distinguish chairs and shoes too
+ 
+
+ align:start position:0%
+it can distinguish chairs and shoes too
+right the features that you use to
+
+ align:start position:0%
+right the features that you use to
+ 
+
+ align:start position:0%
+right the features that you use to
+represent faces will slightly
+
+ align:start position:0%
+represent faces will slightly
+ 
+
+ align:start position:0%
+represent faces will slightly
+discriminate between other non-face
+
+ align:start position:0%
+discriminate between other non-face
+ 
+
+ align:start position:0%
+discriminate between other non-face
+objects so the fact that we can see that
+
+ align:start position:0%
+objects so the fact that we can see that
+ 
+
+ align:start position:0%
+objects so the fact that we can see that
+information in itself isn't strong
+
+ align:start position:0%
+information in itself isn't strong
+ 
+
+ align:start position:0%
+information in itself isn't strong
+evidence that that region isn't doing
+
+ align:start position:0%
+evidence that that region isn't doing
+ 
+
+ align:start position:0%
+evidence that that region isn't doing
+selectively isn't selective for face
+
+ align:start position:0%
+selectively isn't selective for face
+ 
+
+ align:start position:0%
+selectively isn't selective for face
+perception absolutely what else
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah okay with the like transcranial
+
+ align:start position:0%
+yeah okay with the like transcranial
+ 
+
+ align:start position:0%
+yeah okay with the like transcranial
+magnetic stimulation that when you
+
+ align:start position:0%
+magnetic stimulation that when you
+ 
+
+ align:start position:0%
+magnetic stimulation that when you
+stimulate like the ffa you look at a
+
+ align:start position:0%
+stimulate like the ffa you look at a
+ 
+
+ align:start position:0%
+stimulate like the ffa you look at a
+face that affects it but when you are
+
+ align:start position:0%
+face that affects it but when you are
+ 
+
+ align:start position:0%
+face that affects it but when you are
+looking at other objects
+
+ align:start position:0%
+looking at other objects
+ 
+
+ align:start position:0%
+looking at other objects
+exactly and so what does that tell you
+
+ align:start position:0%
+exactly and so what does that tell you
+ 
+
+ align:start position:0%
+exactly and so what does that tell you
+about okay so there's pattern
+
+ align:start position:0%
+about okay so there's pattern
+ 
+
+ align:start position:0%
+about okay so there's pattern
+information in there
+
+ align:start position:0%
+information in there
+ 
+
+ align:start position:0%
+information in there
+about other things beyond faces
+
+ align:start position:0%
+about other things beyond faces
+ 
+
+ align:start position:0%
+about other things beyond faces
+but
+
+ align:start position:0%
+but
+ 
+
+ align:start position:0%
+but
+apparently it's not used right
+
+ align:start position:0%
+apparently it's not used right
+ 
+
+ align:start position:0%
+apparently it's not used right
+now with every bit of evidence you can
+
+ align:start position:0%
+now with every bit of evidence you can
+ 
+
+ align:start position:0%
+now with every bit of evidence you can
+always argue back people say well tms
+
+ align:start position:0%
+always argue back people say well tms
+ 
+
+ align:start position:0%
+always argue back people say well tms
+those effects are tiny maybe there isn't
+
+ align:start position:0%
+those effects are tiny maybe there isn't
+ 
+
+ align:start position:0%
+those effects are tiny maybe there isn't
+we didn't have power detected blah blah
+
+ align:start position:0%
+we didn't have power detected blah blah
+ 
+
+ align:start position:0%
+we didn't have power detected blah blah
+blah blah but at least absolutely you're
+
+ align:start position:0%
+blah blah but at least absolutely you're
+ 
+
+ align:start position:0%
+blah blah but at least absolutely you're
+right tms argues against that what else
+
+ align:start position:0%
+right tms argues against that what else
+ 
+
+ align:start position:0%
+right tms argues against that what else
+or at least is a way to argue against it
+
+ align:start position:0%
+or at least is a way to argue against it
+ 
+
+ align:start position:0%
+or at least is a way to argue against it
+and the picture paper that i assigned
+
+ align:start position:0%
+and the picture paper that i assigned
+ 
+
+ align:start position:0%
+and the picture paper that i assigned
+and other papers that we've talked about
+
+ align:start position:0%
+and other papers that we've talked about
+ 
+
+ align:start position:0%
+and other papers that we've talked about
+in here provide some evidence that
+
+ align:start position:0%
+in here provide some evidence that
+ 
+
+ align:start position:0%
+in here provide some evidence that
+actually at least the occipital face
+
+ align:start position:0%
+actually at least the occipital face
+ 
+
+ align:start position:0%
+actually at least the occipital face
+area really is only causally involved in
+
+ align:start position:0%
+area really is only causally involved in
+ 
+
+ align:start position:0%
+area really is only causally involved in
+face perception even if there's
+
+ align:start position:0%
+face perception even if there's
+ 
+
+ align:start position:0%
+face perception even if there's
+information in there about other things
+
+ align:start position:0%
+information in there about other things
+ 
+
+ align:start position:0%
+information in there about other things
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+what else what other methods can address
+
+ align:start position:0%
+what else what other methods can address
+ 
+
+ align:start position:0%
+what else what other methods can address
+this
+
+ align:start position:0%
+this
+ 
+
+ align:start position:0%
+this
+yeah
+
+ align:start position:0%
+yeah
+ 
+
+ align:start position:0%
+yeah
+simulation
+
+ align:start position:0%
+simulation
+ 
+
+ align:start position:0%
+simulation
+even when you president
+
+ align:start position:0%
+even when you president
+ 
+
+ align:start position:0%
+even when you president
+takes uh
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+exactly exactly so these are both causal
+
+ align:start position:0%
+exactly exactly so these are both causal
+ 
+
+ align:start position:0%
+exactly exactly so these are both causal
+tests right okay there's information in
+
+ align:start position:0%
+tests right okay there's information in
+ 
+
+ align:start position:0%
+tests right okay there's information in
+there but is it causally used in
+
+ align:start position:0%
+there but is it causally used in
+ 
+
+ align:start position:0%
+there but is it causally used in
+behavior right tms suggests not the
+
+ align:start position:0%
+behavior right tms suggests not the
+ 
+
+ align:start position:0%
+behavior right tms suggests not the
+little bit of
+
+ align:start position:0%
+little bit of
+ 
+
+ align:start position:0%
+little bit of
+a direct
+
+ align:start position:0%
+a direct
+ 
+
+ align:start position:0%
+a direct
+intracranial stimulation data that i
+
+ align:start position:0%
+intracranial stimulation data that i
+ 
+
+ align:start position:0%
+intracranial stimulation data that i
+showed you also suggests the causal
+
+ align:start position:0%
+showed you also suggests the causal
+ 
+
+ align:start position:0%
+showed you also suggests the causal
+effects when you stimulate that region
+
+ align:start position:0%
+effects when you stimulate that region
+ 
+
+ align:start position:0%
+effects when you stimulate that region
+are specific to face perception again
+
+ align:start position:0%
+are specific to face perception again
+ 
+
+ align:start position:0%
+are specific to face perception again
+suggesting that even if there's pattern
+
+ align:start position:0%
+suggesting that even if there's pattern
+ 
+
+ align:start position:0%
+suggesting that even if there's pattern
+information in there it's not doing
+
+ align:start position:0%
+information in there it's not doing
+ 
+
+ align:start position:0%
+information in there it's not doing
+anything important because we can mess
+
+ align:start position:0%
+anything important because we can mess
+ 
+
+ align:start position:0%
+anything important because we can mess
+it up and nothing happens to the
+
+ align:start position:0%
+it up and nothing happens to the
+ 
+
+ align:start position:0%
+it up and nothing happens to the
+perception of things that aren't faces
+
+ align:start position:0%
+perception of things that aren't faces
+ 
+
+ align:start position:0%
+perception of things that aren't faces
+absolutely what else
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+we talked about it very briefly a few
+
+ align:start position:0%
+we talked about it very briefly a few
+ 
+
+ align:start position:0%
+we talked about it very briefly a few
+weeks ago
+
+ align:start position:0%
+weeks ago
+ 
+
+ align:start position:0%
+weeks ago
+yeah
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+it just completely makes a person
+
+ align:start position:0%
+it just completely makes a person
+ 
+
+ align:start position:0%
+it just completely makes a person
+incapable of perceiving this that that
+
+ align:start position:0%
+incapable of perceiving this that that
+ 
+
+ align:start position:0%
+incapable of perceiving this that that
+is like
+
+ align:start position:0%
+is like
+ 
+
+ align:start position:0%
+is like
+yes but yes but the crucial way yes but
+
+ align:start position:0%
+yes but yes but the crucial way yes but
+ 
+
+ align:start position:0%
+yes but yes but the crucial way yes but
+the crucial way
+
+ align:start position:0%
+the crucial way
+ 
+
+ align:start position:0%
+the crucial way
+to address hacks be be would be what
+
+ align:start position:0%
+to address hacks be be would be what
+ 
+
+ align:start position:0%
+to address hacks be be would be what
+further aspect of that yes
+
+ align:start position:0%
+further aspect of that yes
+ 
+
+ align:start position:0%
+further aspect of that yes
+apparently and by the way we don't
+
+ align:start position:0%
+apparently and by the way we don't
+ 
+
+ align:start position:0%
+apparently and by the way we don't
+remove the area in humans
+
+ align:start position:0%
+remove the area in humans
+ 
+
+ align:start position:0%
+remove the area in humans
+but occasionally we find a human who had
+
+ align:start position:0%
+but occasionally we find a human who had
+ 
+
+ align:start position:0%
+but occasionally we find a human who had
+a lesion there due to a stroke and then
+
+ align:start position:0%
+a lesion there due to a stroke and then
+ 
+
+ align:start position:0%
+a lesion there due to a stroke and then
+we studied them so they're still able to
+
+ align:start position:0%
+we studied them so they're still able to
+ 
+
+ align:start position:0%
+we studied them so they're still able to
+do other categories exactly
+
+ align:start position:0%
+do other categories exactly
+ 
+
+ align:start position:0%
+do other categories exactly
+exactly so all three lines of evidence
+
+ align:start position:0%
+exactly so all three lines of evidence
+ 
+
+ align:start position:0%
+exactly so all three lines of evidence
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+suggest from studies of prosopagnosia
+
+ align:start position:0%
+suggest from studies of prosopagnosia
+ 
+
+ align:start position:0%
+suggest from studies of prosopagnosia
+electrical stimulation directly on the
+
+ align:start position:0%
+electrical stimulation directly on the
+ 
+
+ align:start position:0%
+electrical stimulation directly on the
+brain and tms all can provide evidence
+
+ align:start position:0%
+brain and tms all can provide evidence
+ 
+
+ align:start position:0%
+brain and tms all can provide evidence
+to various degrees again one can quibble
+
+ align:start position:0%
+to various degrees again one can quibble
+ 
+
+ align:start position:0%
+to various degrees again one can quibble
+about each of these particular studies
+
+ align:start position:0%
+about each of these particular studies
+ 
+
+ align:start position:0%
+about each of these particular studies
+but all of those suggest that even
+
+ align:start position:0%
+but all of those suggest that even
+ 
+
+ align:start position:0%
+but all of those suggest that even
+though there's information in the
+
+ align:start position:0%
+though there's information in the
+ 
+
+ align:start position:0%
+though there's information in the
+pattern haxby's right there's
+
+ align:start position:0%
+pattern haxby's right there's
+ 
+
+ align:start position:0%
+pattern haxby's right there's
+information in there about other things
+
+ align:start position:0%
+information in there about other things
+ 
+
+ align:start position:0%
+information in there about other things
+that aren't faces the only causal
+
+ align:start position:0%
+that aren't faces the only causal
+ 
+
+ align:start position:0%
+that aren't faces the only causal
+effects when you mess up with that
+
+ align:start position:0%
+effects when you mess up with that
+ 
+
+ align:start position:0%
+effects when you mess up with that
+region are on faces not on other things
+
+ align:start position:0%
+region are on faces not on other things
+ 
+
+ align:start position:0%
+region are on faces not on other things
+that suggests that pattern information
+
+ align:start position:0%
+that suggests that pattern information
+ 
+
+ align:start position:0%
+that suggests that pattern information
+is what they sometimes say in
+
+ align:start position:0%
+is what they sometimes say in
+ 
+
+ align:start position:0%
+is what they sometimes say in
+philosophical circles as epi phenomenal
+
+ align:start position:0%
+philosophical circles as epi phenomenal
+ 
+
+ align:start position:0%
+philosophical circles as epi phenomenal
+that is it's just not related to
+
+ align:start position:0%
+that is it's just not related to
+ 
+
+ align:start position:0%
+that is it's just not related to
+um to
+
+ align:start position:0%
+um to
+ 
+
+ align:start position:0%
+um to
+behavior and and
+
+ align:start position:0%
+behavior and and
+ 
+
+ align:start position:0%
+behavior and and
+perception makes sense okay
+
+ align:start position:0%
+perception makes sense okay
+ 
+
+ align:start position:0%
+perception makes sense okay
+moving along
+
+ align:start position:0%
+moving along
+ 
+
+ align:start position:0%
+moving along
+how can we then use haxby's method to
+
+ align:start position:0%
+how can we then use haxby's method to
+ 
+
+ align:start position:0%
+how can we then use haxby's method to
+not just engage in this little fight
+
+ align:start position:0%
+not just engage in this little fight
+ 
+
+ align:start position:0%
+not just engage in this little fight
+about the ffa and how specific it is
+
+ align:start position:0%
+about the ffa and how specific it is
+ 
+
+ align:start position:0%
+about the ffa and how specific it is
+um but to ask whether to harness this
+
+ align:start position:0%
+um but to ask whether to harness this
+ 
+
+ align:start position:0%
+um but to ask whether to harness this
+method and ask other interesting
+
+ align:start position:0%
+method and ask other interesting
+ 
+
+ align:start position:0%
+method and ask other interesting
+questions
+
+ align:start position:0%
+questions
+ 
+
+ align:start position:0%
+questions
+from functional mri data how can we use
+
+ align:start position:0%
+from functional mri data how can we use
+ 
+
+ align:start position:0%
+from functional mri data how can we use
+it to find out for example does the
+
+ align:start position:0%
+it to find out for example does the
+ 
+
+ align:start position:0%
+it to find out for example does the
+place area discriminate say beach scenes
+
+ align:start position:0%
+place area discriminate say beach scenes
+ 
+
+ align:start position:0%
+place area discriminate say beach scenes
+from city scenes we want to know what's
+
+ align:start position:0%
+from city scenes we want to know what's
+ 
+
+ align:start position:0%
+from city scenes we want to know what's
+represented in there how could we use
+
+ align:start position:0%
+represented in there how could we use
+ 
+
+ align:start position:0%
+represented in there how could we use
+this method to find out
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yes
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+because i did and like trying to decode
+
+ align:start position:0%
+because i did and like trying to decode
+ 
+
+ align:start position:0%
+because i did and like trying to decode
+her and see if it could
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+[Music]
+
+ align:start position:0%
+[Music]
+ 
+
+ align:start position:0%
+[Music]
+exactly
+
+ align:start position:0%
+exactly
+ 
+
+ align:start position:0%
+exactly
+exactly so we talked about decoding
+
+ align:start position:0%
+exactly so we talked about decoding
+ 
+
+ align:start position:0%
+exactly so we talked about decoding
+methods last time as a way to use
+
+ align:start position:0%
+methods last time as a way to use
+ 
+
+ align:start position:0%
+methods last time as a way to use
+machine learning to look at the pattern
+
+ align:start position:0%
+machine learning to look at the pattern
+ 
+
+ align:start position:0%
+machine learning to look at the pattern
+of response in a region of the brain
+
+ align:start position:0%
+of response in a region of the brain
+ 
+
+ align:start position:0%
+of response in a region of the brain
+and train the decoder so it knows what
+
+ align:start position:0%
+and train the decoder so it knows what
+ 
+
+ align:start position:0%
+and train the decoder so it knows what
+bc what the response looks like
+
+ align:start position:0%
+bc what the response looks like
+ 
+
+ align:start position:0%
+bc what the response looks like
+during viewing of beach scenes train it
+
+ align:start position:0%
+during viewing of beach scenes train it
+ 
+
+ align:start position:0%
+during viewing of beach scenes train it
+so it knows what the response in that
+
+ align:start position:0%
+so it knows what the response in that
+ 
+
+ align:start position:0%
+so it knows what the response in that
+region looks like when you're looking at
+
+ align:start position:0%
+region looks like when you're looking at
+ 
+
+ align:start position:0%
+region looks like when you're looking at
+city schemes and then take a new pattern
+
+ align:start position:0%
+city schemes and then take a new pattern
+ 
+
+ align:start position:0%
+city schemes and then take a new pattern
+and say okay is this more like the beach
+
+ align:start position:0%
+and say okay is this more like the beach
+ 
+
+ align:start position:0%
+and say okay is this more like the beach
+pattern or is it more like the city
+
+ align:start position:0%
+pattern or is it more like the city
+ 
+
+ align:start position:0%
+pattern or is it more like the city
+pattern and that's how you could decode
+
+ align:start position:0%
+pattern and that's how you could decode
+ 
+
+ align:start position:0%
+pattern and that's how you could decode
+from that region yes that doesn't tell
+
+ align:start position:0%
+from that region yes that doesn't tell
+ 
+
+ align:start position:0%
+from that region yes that doesn't tell
+us right in the sense that it's
+
+ align:start position:0%
+us right in the sense that it's
+ 
+
+ align:start position:0%
+us right in the sense that it's
+it's not telling the i mean we know that
+
+ align:start position:0%
+it's not telling the i mean we know that
+ 
+
+ align:start position:0%
+it's not telling the i mean we know that
+the this residue of information
+
+ align:start position:0%
+the this residue of information
+ 
+
+ align:start position:0%
+the this residue of information
+nevertheless and a discriminator can be
+
+ align:start position:0%
+nevertheless and a discriminator can be
+ 
+
+ align:start position:0%
+nevertheless and a discriminator can be
+built on any region to figure out
+
+ align:start position:0%
+built on any region to figure out
+ 
+
+ align:start position:0%
+built on any region to figure out
+anything
+
+ align:start position:0%
+anything
+ 
+
+ align:start position:0%
+anything
+almost
+
+ align:start position:0%
+almost
+ 
+
+ align:start position:0%
+almost
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+we have a true nile list here
+
+ align:start position:0%
+we have a true nile list here
+ 
+
+ align:start position:0%
+we have a true nile list here
+um no it's a good question
+
+ align:start position:0%
+um no it's a good question
+ 
+
+ align:start position:0%
+um no it's a good question
+it's not the case
+
+ align:start position:0%
+it's not the case
+ 
+
+ align:start position:0%
+it's not the case
+that you can discriminate anything based
+
+ align:start position:0%
+that you can discriminate anything based
+ 
+
+ align:start position:0%
+that you can discriminate anything based
+on any region of the brain
+
+ align:start position:0%
+on any region of the brain
+ 
+
+ align:start position:0%
+on any region of the brain
+so there are some constraints there's
+
+ align:start position:0%
+so there are some constraints there's
+ 
+
+ align:start position:0%
+so there are some constraints there's
+some things you can find in some places
+
+ align:start position:0%
+some things you can find in some places
+ 
+
+ align:start position:0%
+some things you can find in some places
+and other things you can find
+
+ align:start position:0%
+and other things you can find
+ 
+
+ align:start position:0%
+and other things you can find
+in other places and they're not
+
+ align:start position:0%
+in other places and they're not
+ 
+
+ align:start position:0%
+in other places and they're not
+uniformly distributed over the brain
+
+ align:start position:0%
+uniformly distributed over the brain
+ 
+
+ align:start position:0%
+uniformly distributed over the brain
+however the fact we just the point i
+
+ align:start position:0%
+however the fact we just the point i
+ 
+
+ align:start position:0%
+however the fact we just the point i
+just made about yes there's
+
+ align:start position:0%
+just made about yes there's
+ 
+
+ align:start position:0%
+just made about yes there's
+discriminative information in the face
+
+ align:start position:0%
+discriminative information in the face
+ 
+
+ align:start position:0%
+discriminative information in the face
+area about non-faces but maybe it's not
+
+ align:start position:0%
+area about non-faces but maybe it's not
+ 
+
+ align:start position:0%
+area about non-faces but maybe it's not
+used
+
+ align:start position:0%
+used
+ 
+
+ align:start position:0%
+used
+should raise a huge caveat about this
+
+ align:start position:0%
+should raise a huge caveat about this
+ 
+
+ align:start position:0%
+should raise a huge caveat about this
+whole method how do we ever know we see
+
+ align:start position:0%
+whole method how do we ever know we see
+ 
+
+ align:start position:0%
+whole method how do we ever know we see
+some discriminative information how do
+
+ align:start position:0%
+some discriminative information how do
+ 
+
+ align:start position:0%
+some discriminative information how do
+we know whether it's actually used by
+
+ align:start position:0%
+we know whether it's actually used by
+ 
+
+ align:start position:0%
+we know whether it's actually used by
+the brain part of the brain's own code
+
+ align:start position:0%
+the brain part of the brain's own code
+ 
+
+ align:start position:0%
+the brain part of the brain's own code
+for information or just epiphenomenal
+
+ align:start position:0%
+for information or just epiphenomenal
+ 
+
+ align:start position:0%
+for information or just epiphenomenal
+garbage that's a byproduct of something
+
+ align:start position:0%
+garbage that's a byproduct of something
+ 
+
+ align:start position:0%
+garbage that's a byproduct of something
+else
+
+ align:start position:0%
+else
+ 
+
+ align:start position:0%
+else
+it's a really important question about
+
+ align:start position:0%
+it's a really important question about
+ 
+
+ align:start position:0%
+it's a really important question about
+all of pattern analysis
+
+ align:start position:0%
+all of pattern analysis
+ 
+
+ align:start position:0%
+all of pattern analysis
+okay we do it anyway because we're
+
+ align:start position:0%
+okay we do it anyway because we're
+ 
+
+ align:start position:0%
+okay we do it anyway because we're
+beggars we can't be choosers in terms of
+
+ align:start position:0%
+beggars we can't be choosers in terms of
+ 
+
+ align:start position:0%
+beggars we can't be choosers in terms of
+methods with human cognitive
+
+ align:start position:0%
+methods with human cognitive
+ 
+
+ align:start position:0%
+methods with human cognitive
+neuroscience and we want to know
+
+ align:start position:0%
+neuroscience and we want to know
+ 
+
+ align:start position:0%
+neuroscience and we want to know
+desperately what's represented in each
+
+ align:start position:0%
+desperately what's represented in each
+ 
+
+ align:start position:0%
+desperately what's represented in each
+region so we do this but whenever you
+
+ align:start position:0%
+region so we do this but whenever you
+ 
+
+ align:start position:0%
+region so we do this but whenever you
+see these lovely i can decode x from y
+
+ align:start position:0%
+see these lovely i can decode x from y
+ 
+
+ align:start position:0%
+see these lovely i can decode x from y
+things you should always be wondering
+
+ align:start position:0%
+things you should always be wondering
+ 
+
+ align:start position:0%
+things you should always be wondering
+who knows if that fact that you the
+
+ align:start position:0%
+who knows if that fact that you the
+ 
+
+ align:start position:0%
+who knows if that fact that you the
+scientist can decode it from that region
+
+ align:start position:0%
+scientist can decode it from that region
+ 
+
+ align:start position:0%
+scientist can decode it from that region
+means the brain itself is reading that
+
+ align:start position:0%
+means the brain itself is reading that
+ 
+
+ align:start position:0%
+means the brain itself is reading that
+information out of that region
+
+ align:start position:0%
+information out of that region
+ 
+
+ align:start position:0%
+information out of that region
+big important question
+
+ align:start position:0%
+big important question
+ 
+
+ align:start position:0%
+big important question
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+all right put another way um so jimmy
+
+ align:start position:0%
+all right put another way um so jimmy
+ 
+
+ align:start position:0%
+all right put another way um so jimmy
+mentioned just decoding in general
+
+ align:start position:0%
+mentioned just decoding in general
+ 
+
+ align:start position:0%
+mentioned just decoding in general
+that's absolutely right but to directly
+
+ align:start position:0%
+that's absolutely right but to directly
+ 
+
+ align:start position:0%
+that's absolutely right but to directly
+harness the haxby version of this what
+
+ align:start position:0%
+harness the haxby version of this what
+ 
+
+ align:start position:0%
+harness the haxby version of this what
+would we do first we would functionally
+
+ align:start position:0%
+would we do first we would functionally
+ 
+
+ align:start position:0%
+would we do first we would functionally
+localize the ppa
+
+ align:start position:0%
+localize the ppa
+ 
+
+ align:start position:0%
+localize the ppa
+but by scanning them looking at scenes
+
+ align:start position:0%
+but by scanning them looking at scenes
+ 
+
+ align:start position:0%
+but by scanning them looking at scenes
+and objects find that region in each
+
+ align:start position:0%
+and objects find that region in each
+ 
+
+ align:start position:0%
+and objects find that region in each
+subject
+
+ align:start position:0%
+subject
+ 
+
+ align:start position:0%
+subject
+then we would collect the pattern of
+
+ align:start position:0%
+then we would collect the pattern of
+ 
+
+ align:start position:0%
+then we would collect the pattern of
+response across voxels in the ppa
+
+ align:start position:0%
+response across voxels in the ppa
+ 
+
+ align:start position:0%
+response across voxels in the ppa
+while subjects were looking at say beach
+
+ align:start position:0%
+while subjects were looking at say beach
+ 
+
+ align:start position:0%
+while subjects were looking at say beach
+scenes and so if this is the ppa this is
+
+ align:start position:0%
+scenes and so if this is the ppa this is
+ 
+
+ align:start position:0%
+scenes and so if this is the ppa this is
+the pattern of response across voxels in
+
+ align:start position:0%
+the pattern of response across voxels in
+ 
+
+ align:start position:0%
+the pattern of response across voxels in
+that region when they're looking at
+
+ align:start position:0%
+that region when they're looking at
+ 
+
+ align:start position:0%
+that region when they're looking at
+beach scenes fake data obviously just to
+
+ align:start position:0%
+beach scenes fake data obviously just to
+ 
+
+ align:start position:0%
+beach scenes fake data obviously just to
+give you the idea
+
+ align:start position:0%
+give you the idea
+ 
+
+ align:start position:0%
+give you the idea
+right so we would split the data in half
+
+ align:start position:0%
+right so we would split the data in half
+ 
+
+ align:start position:0%
+right so we would split the data in half
+even runs odd runs that would be like
+
+ align:start position:0%
+even runs odd runs that would be like
+ 
+
+ align:start position:0%
+even runs odd runs that would be like
+even runs then we get another pattern
+
+ align:start position:0%
+even runs then we get another pattern
+ 
+
+ align:start position:0%
+even runs then we get another pattern
+for odd runs and then we get another
+
+ align:start position:0%
+for odd runs and then we get another
+ 
+
+ align:start position:0%
+for odd runs and then we get another
+pattern for when they're looking at city
+
+ align:start position:0%
+pattern for when they're looking at city
+ 
+
+ align:start position:0%
+pattern for when they're looking at city
+scenes with even runs and another
+
+ align:start position:0%
+scenes with even runs and another
+ 
+
+ align:start position:0%
+scenes with even runs and another
+pattern when they're looking at city
+
+ align:start position:0%
+pattern when they're looking at city
+ 
+
+ align:start position:0%
+pattern when they're looking at city
+scenes and odd runs okay
+
+ align:start position:0%
+scenes and odd runs okay
+ 
+
+ align:start position:0%
+scenes and odd runs okay
+so then
+
+ align:start position:0%
+so then
+ 
+
+ align:start position:0%
+so then
+once we have those four patterns what is
+
+ align:start position:0%
+once we have those four patterns what is
+ 
+
+ align:start position:0%
+once we have those four patterns what is
+the key prediction
+
+ align:start position:0%
+the key prediction
+ 
+
+ align:start position:0%
+the key prediction
+if uh using haxby's correlation method
+
+ align:start position:0%
+if uh using haxby's correlation method
+ 
+
+ align:start position:0%
+if uh using haxby's correlation method
+what is the key prediction if the ppa
+
+ align:start position:0%
+what is the key prediction if the ppa
+ 
+
+ align:start position:0%
+what is the key prediction if the ppa
+if pattern of response in the ppa can
+
+ align:start position:0%
+if pattern of response in the ppa can
+ 
+
+ align:start position:0%
+if pattern of response in the ppa can
+discriminate beach scenes from city
+
+ align:start position:0%
+discriminate beach scenes from city
+ 
+
+ align:start position:0%
+discriminate beach scenes from city
+scenes what should we see from these
+
+ align:start position:0%
+scenes what should we see from these
+ 
+
+ align:start position:0%
+scenes what should we see from these
+patterns what's the key prediction
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+claire
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+key prediction you have these four
+
+ align:start position:0%
+key prediction you have these four
+ 
+
+ align:start position:0%
+key prediction you have these four
+patterns
+
+ align:start position:0%
+patterns
+ 
+
+ align:start position:0%
+patterns
+in the ppa and now you want to know is
+
+ align:start position:0%
+in the ppa and now you want to know is
+ 
+
+ align:start position:0%
+in the ppa and now you want to know is
+there information in there
+
+ align:start position:0%
+there information in there
+ 
+
+ align:start position:0%
+there information in there
+that enables you to discriminate beach
+
+ align:start position:0%
+that enables you to discriminate beach
+ 
+
+ align:start position:0%
+that enables you to discriminate beach
+scenes from city scenes is that like
+
+ align:start position:0%
+scenes from city scenes is that like
+ 
+
+ align:start position:0%
+scenes from city scenes is that like
+beach even in the beach odd or less than
+
+ align:start position:0%
+beach even in the beach odd or less than
+ 
+
+ align:start position:0%
+beach even in the beach odd or less than
+the achievement city
+
+ align:start position:0%
+the achievement city
+ 
+
+ align:start position:0%
+the achievement city
+exactly exactly right it's actually you
+
+ align:start position:0%
+exactly exactly right it's actually you
+ 
+
+ align:start position:0%
+exactly exactly right it's actually you
+know it sounds all like complicated it's
+
+ align:start position:0%
+know it sounds all like complicated it's
+ 
+
+ align:start position:0%
+know it sounds all like complicated it's
+easy to get confused but the nub of the
+
+ align:start position:0%
+easy to get confused but the nub of the
+ 
+
+ align:start position:0%
+easy to get confused but the nub of the
+idea is really simple it just says look
+
+ align:start position:0%
+idea is really simple it just says look
+ 
+
+ align:start position:0%
+idea is really simple it just says look
+the beach patterns are stable we do
+
+ align:start position:0%
+the beach patterns are stable we do
+ 
+
+ align:start position:0%
+the beach patterns are stable we do
+beach a few times we get the same
+
+ align:start position:0%
+beach a few times we get the same
+ 
+
+ align:start position:0%
+beach a few times we get the same
+pattern more or less
+
+ align:start position:0%
+pattern more or less
+ 
+
+ align:start position:0%
+pattern more or less
+we do city we get a different pattern
+
+ align:start position:0%
+we do city we get a different pattern
+ 
+
+ align:start position:0%
+we do city we get a different pattern
+and we keep doing city we get the same
+
+ align:start position:0%
+and we keep doing city we get the same
+ 
+
+ align:start position:0%
+and we keep doing city we get the same
+pattern more or less and the beach
+
+ align:start position:0%
+pattern more or less and the beach
+ 
+
+ align:start position:0%
+pattern more or less and the beach
+pattern and the city pattern are
+
+ align:start position:0%
+pattern and the city pattern are
+ 
+
+ align:start position:0%
+pattern and the city pattern are
+different
+
+ align:start position:0%
+different
+ 
+
+ align:start position:0%
+different
+so that's the nova the idea and so you
+
+ align:start position:0%
+so that's the nova the idea and so you
+ 
+
+ align:start position:0%
+so that's the nova the idea and so you
+can implement it with decoding methods
+
+ align:start position:0%
+can implement it with decoding methods
+ 
+
+ align:start position:0%
+can implement it with decoding methods
+or the hacks b versions just to ask
+
+ align:start position:0%
+or the hacks b versions just to ask
+ 
+
+ align:start position:0%
+or the hacks b versions just to ask
+whether the correlation between
+
+ align:start position:0%
+whether the correlation between
+ 
+
+ align:start position:0%
+whether the correlation between
+two beach patterns beach even beach odd
+
+ align:start position:0%
+two beach patterns beach even beach odd
+ 
+
+ align:start position:0%
+two beach patterns beach even beach odd
+is more similar than the pattern between
+
+ align:start position:0%
+is more similar than the pattern between
+ 
+
+ align:start position:0%
+is more similar than the pattern between
+one of the beaches and one of the cities
+
+ align:start position:0%
+one of the beaches and one of the cities
+ 
+
+ align:start position:0%
+one of the beaches and one of the cities
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+just asking are they more are they
+
+ align:start position:0%
+just asking are they more are they
+ 
+
+ align:start position:0%
+just asking are they more are they
+stably similar within a category and
+
+ align:start position:0%
+stably similar within a category and
+ 
+
+ align:start position:0%
+stably similar within a category and
+stably different from another category
+
+ align:start position:0%
+stably different from another category
+ 
+
+ align:start position:0%
+stably different from another category
+does that make sense okay
+
+ align:start position:0%
+does that make sense okay
+ 
+
+ align:start position:0%
+does that make sense okay
+um boom this is just so it's just a
+
+ align:start position:0%
+um boom this is just so it's just a
+ 
+
+ align:start position:0%
+um boom this is just so it's just a
+variant of this thing i showed you guys
+
+ align:start position:0%
+variant of this thing i showed you guys
+ 
+
+ align:start position:0%
+variant of this thing i showed you guys
+before we just harness this to
+
+ align:start position:0%
+before we just harness this to
+ 
+
+ align:start position:0%
+before we just harness this to
+to ask whether that region can
+
+ align:start position:0%
+to ask whether that region can
+ 
+
+ align:start position:0%
+to ask whether that region can
+discriminate okay and i just said all of
+
+ align:start position:0%
+discriminate okay and i just said all of
+ 
+
+ align:start position:0%
+discriminate okay and i just said all of
+this
+
+ align:start position:0%
+this
+ 
+
+ align:start position:0%
+this
+okay if you still feel shaky on this
+
+ align:start position:0%
+okay if you still feel shaky on this
+ 
+
+ align:start position:0%
+okay if you still feel shaky on this
+there's a few things you can do um a
+
+ align:start position:0%
+there's a few things you can do um a
+ 
+
+ align:start position:0%
+there's a few things you can do um a
+version of my little lecture on on this
+
+ align:start position:0%
+version of my little lecture on on this
+ 
+
+ align:start position:0%
+version of my little lecture on on this
+method is here at the on my website you
+
+ align:start position:0%
+method is here at the on my website you
+ 
+
+ align:start position:0%
+method is here at the on my website you
+can look at that it's just like six
+
+ align:start position:0%
+can look at that it's just like six
+ 
+
+ align:start position:0%
+can look at that it's just like six
+minutes and it's basically what i did
+
+ align:start position:0%
+minutes and it's basically what i did
+ 
+
+ align:start position:0%
+minutes and it's basically what i did
+before but if you want to go over it
+
+ align:start position:0%
+before but if you want to go over it
+ 
+
+ align:start position:0%
+before but if you want to go over it
+again there it is
+
+ align:start position:0%
+again there it is
+ 
+
+ align:start position:0%
+again there it is
+you can reread the hacksby paper which i
+
+ align:start position:0%
+you can reread the hacksby paper which i
+ 
+
+ align:start position:0%
+you can reread the hacksby paper which i
+know is not super easy but it's actually
+
+ align:start position:0%
+know is not super easy but it's actually
+ 
+
+ align:start position:0%
+know is not super easy but it's actually
+nicely written and if you read it
+
+ align:start position:0%
+nicely written and if you read it
+ 
+
+ align:start position:0%
+nicely written and if you read it
+carefully it explains the method pretty
+
+ align:start position:0%
+carefully it explains the method pretty
+ 
+
+ align:start position:0%
+carefully it explains the method pretty
+clearly you can talk to me or a ta
+
+ align:start position:0%
+clearly you can talk to me or a ta
+ 
+
+ align:start position:0%
+clearly you can talk to me or a ta
+and we'll get back to this question of
+
+ align:start position:0%
+and we'll get back to this question of
+ 
+
+ align:start position:0%
+and we'll get back to this question of
+whether we should do a whole matlab
+
+ align:start position:0%
+whether we should do a whole matlab
+ 
+
+ align:start position:0%
+whether we should do a whole matlab
+based problem set on this
+
+ align:start position:0%
+based problem set on this
+ 
+
+ align:start position:0%
+based problem set on this
+all right
+
+ align:start position:0%
+all right
+ 
+
+ align:start position:0%
+all right
+okay let's move on and talk about
+
+ align:start position:0%
+okay let's move on and talk about
+ 
+
+ align:start position:0%
+okay let's move on and talk about
+navigation
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay this is a monarch butterfly
+
+ align:start position:0%
+okay this is a monarch butterfly
+ 
+
+ align:start position:0%
+okay this is a monarch butterfly
+it weighs about half a gram
+
+ align:start position:0%
+it weighs about half a gram
+ 
+
+ align:start position:0%
+it weighs about half a gram
+and yet
+
+ align:start position:0%
+and yet
+ 
+
+ align:start position:0%
+and yet
+each fall
+
+ align:start position:0%
+each fall
+ 
+
+ align:start position:0%
+each fall
+the monarch migrates over 2000 miles
+
+ align:start position:0%
+the monarch migrates over 2000 miles
+ 
+
+ align:start position:0%
+the monarch migrates over 2000 miles
+from the usa in canada down to mexico
+
+ align:start position:0%
+from the usa in canada down to mexico
+ 
+
+ align:start position:0%
+from the usa in canada down to mexico
+in fact it migrates
+
+ align:start position:0%
+in fact it migrates
+ 
+
+ align:start position:0%
+in fact it migrates
+it fly a single monarch flies 50 miles
+
+ align:start position:0%
+it fly a single monarch flies 50 miles
+ 
+
+ align:start position:0%
+it fly a single monarch flies 50 miles
+in a single day it's pretty amazing for
+
+ align:start position:0%
+in a single day it's pretty amazing for
+ 
+
+ align:start position:0%
+in a single day it's pretty amazing for
+this tiny little beautiful delicate
+
+ align:start position:0%
+this tiny little beautiful delicate
+ 
+
+ align:start position:0%
+this tiny little beautiful delicate
+thing
+
+ align:start position:0%
+thing
+ 
+
+ align:start position:0%
+thing
+even more amazing it flies to a very
+
+ align:start position:0%
+even more amazing it flies to a very
+ 
+
+ align:start position:0%
+even more amazing it flies to a very
+specific forest in mexico that's just a
+
+ align:start position:0%
+specific forest in mexico that's just a
+ 
+
+ align:start position:0%
+specific forest in mexico that's just a
+few acres in size and it arrives at that
+
+ align:start position:0%
+few acres in size and it arrives at that
+ 
+
+ align:start position:0%
+few acres in size and it arrives at that
+particular forest
+
+ align:start position:0%
+particular forest
+ 
+
+ align:start position:0%
+particular forest
+now that's already amazing but here's
+
+ align:start position:0%
+now that's already amazing but here's
+ 
+
+ align:start position:0%
+now that's already amazing but here's
+the part that is just totally
+
+ align:start position:0%
+the part that is just totally
+ 
+
+ align:start position:0%
+the part that is just totally
+mind-blowing
+
+ align:start position:0%
+mind-blowing
+ 
+
+ align:start position:0%
+mind-blowing
+and that is
+
+ align:start position:0%
+and that is
+ 
+
+ align:start position:0%
+and that is
+and it flies back north in the spring
+
+ align:start position:0%
+and it flies back north in the spring
+ 
+
+ align:start position:0%
+and it flies back north in the spring
+and that is that this whole cycle
+
+ align:start position:0%
+and that is that this whole cycle
+ 
+
+ align:start position:0%
+and that is that this whole cycle
+takes four generations to complete
+
+ align:start position:0%
+takes four generations to complete
+ 
+
+ align:start position:0%
+takes four generations to complete
+and that means that the monarch that
+
+ align:start position:0%
+and that means that the monarch that
+ 
+
+ align:start position:0%
+and that means that the monarch that
+starts up in canada and flies down to
+
+ align:start position:0%
+starts up in canada and flies down to
+ 
+
+ align:start position:0%
+starts up in canada and flies down to
+that forest in mexico one monarch does
+
+ align:start position:0%
+that forest in mexico one monarch does
+ 
+
+ align:start position:0%
+that forest in mexico one monarch does
+that
+
+ align:start position:0%
+that
+ 
+
+ align:start position:0%
+that
+is the great great grandkid
+
+ align:start position:0%
+is the great great grandkid
+ 
+
+ align:start position:0%
+is the great great grandkid
+of his ancestor that last went on that
+
+ align:start position:0%
+of his ancestor that last went on that
+ 
+
+ align:start position:0%
+of his ancestor that last went on that
+route
+
+ align:start position:0%
+route
+ 
+
+ align:start position:0%
+route
+put that in your head and smoke it
+
+ align:start position:0%
+put that in your head and smoke it
+ 
+
+ align:start position:0%
+put that in your head and smoke it
+that's pretty amazing
+
+ align:start position:0%
+that's pretty amazing
+ 
+
+ align:start position:0%
+that's pretty amazing
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+all right
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+consider the female loggerhead turtle
+
+ align:start position:0%
+consider the female loggerhead turtle
+ 
+
+ align:start position:0%
+consider the female loggerhead turtle
+she um hatches at a beach and goes out
+
+ align:start position:0%
+she um hatches at a beach and goes out
+ 
+
+ align:start position:0%
+she um hatches at a beach and goes out
+in the sea
+
+ align:start position:0%
+in the sea
+ 
+
+ align:start position:0%
+in the sea
+and swims around in the sea for 20 years
+
+ align:start position:0%
+and swims around in the sea for 20 years
+ 
+
+ align:start position:0%
+and swims around in the sea for 20 years
+before she comes back 20 years later for
+
+ align:start position:0%
+before she comes back 20 years later for
+ 
+
+ align:start position:0%
+before she comes back 20 years later for
+the first time to the beach that she
+
+ align:start position:0%
+the first time to the beach that she
+ 
+
+ align:start position:0%
+the first time to the beach that she
+hatched at
+
+ align:start position:0%
+hatched at
+ 
+
+ align:start position:0%
+hatched at
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+now it's pretty amazing but some mothers
+
+ align:start position:0%
+now it's pretty amazing but some mothers
+ 
+
+ align:start position:0%
+now it's pretty amazing but some mothers
+miss by 20 miles they go to the wrong
+
+ align:start position:0%
+miss by 20 miles they go to the wrong
+ 
+
+ align:start position:0%
+miss by 20 miles they go to the wrong
+island or the wrong beach on the same
+
+ align:start position:0%
+island or the wrong beach on the same
+ 
+
+ align:start position:0%
+island or the wrong beach on the same
+island okay
+
+ align:start position:0%
+island okay
+ 
+
+ align:start position:0%
+island okay
+and so
+
+ align:start position:0%
+and so
+ 
+
+ align:start position:0%
+and so
+you might think okay it's pretty good
+
+ align:start position:0%
+you might think okay it's pretty good
+ 
+
+ align:start position:0%
+you might think okay it's pretty good
+it's not amazing
+
+ align:start position:0%
+it's not amazing
+ 
+
+ align:start position:0%
+it's not amazing
+but here's the thing
+
+ align:start position:0%
+but here's the thing
+ 
+
+ align:start position:0%
+but here's the thing
+the wrong beach that those mothers go to
+
+ align:start position:0%
+the wrong beach that those mothers go to
+ 
+
+ align:start position:0%
+the wrong beach that those mothers go to
+is the exactly right beach had the
+
+ align:start position:0%
+is the exactly right beach had the
+ 
+
+ align:start position:0%
+is the exactly right beach had the
+earth's magnetic field not shifted
+
+ align:start position:0%
+earth's magnetic field not shifted
+ 
+
+ align:start position:0%
+earth's magnetic field not shifted
+slightly over those 20 years
+
+ align:start position:0%
+slightly over those 20 years
+ 
+
+ align:start position:0%
+slightly over those 20 years
+they're exactly precise
+
+ align:start position:0%
+they're exactly precise
+ 
+
+ align:start position:0%
+they're exactly precise
+but they just don't compensate for the
+
+ align:start position:0%
+but they just don't compensate for the
+ 
+
+ align:start position:0%
+but they just don't compensate for the
+shift in the earth's magnetic field
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+here's a bat
+
+ align:start position:0%
+here's a bat
+ 
+
+ align:start position:0%
+here's a bat
+this bat
+
+ align:start position:0%
+this bat
+ 
+
+ align:start position:0%
+this bat
+maintains its sense of direction
+
+ align:start position:0%
+maintains its sense of direction
+ 
+
+ align:start position:0%
+maintains its sense of direction
+even while it flies 30 to 50 miles in a
+
+ align:start position:0%
+even while it flies 30 to 50 miles in a
+ 
+
+ align:start position:0%
+even while it flies 30 to 50 miles in a
+single night in the dark
+
+ align:start position:0%
+single night in the dark
+ 
+
+ align:start position:0%
+single night in the dark
+catching food
+
+ align:start position:0%
+catching food
+ 
+
+ align:start position:0%
+catching food
+okay and it maintains its sense of
+
+ align:start position:0%
+okay and it maintains its sense of
+ 
+
+ align:start position:0%
+okay and it maintains its sense of
+direction even though it's flying around
+
+ align:start position:0%
+direction even though it's flying around
+ 
+
+ align:start position:0%
+direction even though it's flying around
+in all different orientations in three
+
+ align:start position:0%
+in all different orientations in three
+ 
+
+ align:start position:0%
+in all different orientations in three
+dimensions
+
+ align:start position:0%
+dimensions
+ 
+
+ align:start position:0%
+dimensions
+and even as it flips over and lands
+
+ align:start position:0%
+and even as it flips over and lands
+ 
+
+ align:start position:0%
+and even as it flips over and lands
+to
+
+ align:start position:0%
+to
+ 
+
+ align:start position:0%
+to
+perch on the surface of a cave
+
+ align:start position:0%
+perch on the surface of a cave
+ 
+
+ align:start position:0%
+perch on the surface of a cave
+doesn't get confused by being upside
+
+ align:start position:0%
+doesn't get confused by being upside
+ 
+
+ align:start position:0%
+doesn't get confused by being upside
+down
+
+ align:start position:0%
+down
+ 
+
+ align:start position:0%
+down
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this is cataglyphus the tunisian desert
+
+ align:start position:0%
+this is cataglyphus the tunisian desert
+ 
+
+ align:start position:0%
+this is cataglyphus the tunisian desert
+ant these guys are amazing they crawl
+
+ align:start position:0%
+ant these guys are amazing they crawl
+ 
+
+ align:start position:0%
+ant these guys are amazing they crawl
+around on the surface of the tunisian
+
+ align:start position:0%
+around on the surface of the tunisian
+ 
+
+ align:start position:0%
+around on the surface of the tunisian
+desert where it's 140 degrees in the
+
+ align:start position:0%
+desert where it's 140 degrees in the
+ 
+
+ align:start position:0%
+desert where it's 140 degrees in the
+daytime
+
+ align:start position:0%
+daytime
+ 
+
+ align:start position:0%
+daytime
+they have to crawl around up there to
+
+ align:start position:0%
+they have to crawl around up there to
+ 
+
+ align:start position:0%
+they have to crawl around up there to
+forage for food
+
+ align:start position:0%
+forage for food
+ 
+
+ align:start position:0%
+forage for food
+and then because it's so damn hot as
+
+ align:start position:0%
+and then because it's so damn hot as
+ 
+
+ align:start position:0%
+and then because it's so damn hot as
+soon as they find food they zoom back to
+
+ align:start position:0%
+soon as they find food they zoom back to
+ 
+
+ align:start position:0%
+soon as they find food they zoom back to
+their nest and go down in the nest where
+
+ align:start position:0%
+their nest and go down in the nest where
+ 
+
+ align:start position:0%
+their nest and go down in the nest where
+it's cooler
+
+ align:start position:0%
+it's cooler
+ 
+
+ align:start position:0%
+it's cooler
+so here is a track of cataglyphus
+
+ align:start position:0%
+so here is a track of cataglyphus
+ 
+
+ align:start position:0%
+so here is a track of cataglyphus
+starting at point a
+
+ align:start position:0%
+starting at point a
+ 
+
+ align:start position:0%
+starting at point a
+and foraging he's meandering around
+
+ align:start position:0%
+and foraging he's meandering around
+ 
+
+ align:start position:0%
+and foraging he's meandering around
+looking for food going along this whole
+
+ align:start position:0%
+looking for food going along this whole
+ 
+
+ align:start position:0%
+looking for food going along this whole
+crazy path to point b
+
+ align:start position:0%
+crazy path to point b
+ 
+
+ align:start position:0%
+crazy path to point b
+and then if he finds food at point b
+
+ align:start position:0%
+and then if he finds food at point b
+ 
+
+ align:start position:0%
+and then if he finds food at point b
+boom
+
+ align:start position:0%
+boom
+ 
+
+ align:start position:0%
+boom
+straight line back exactly to the nest
+
+ align:start position:0%
+straight line back exactly to the nest
+ 
+
+ align:start position:0%
+straight line back exactly to the nest
+now we might ask how does cataglyphus
+
+ align:start position:0%
+now we might ask how does cataglyphus
+ 
+
+ align:start position:0%
+now we might ask how does cataglyphus
+keep track because he's doing all this
+
+ align:start position:0%
+keep track because he's doing all this
+ 
+
+ align:start position:0%
+keep track because he's doing all this
+stuff
+
+ align:start position:0%
+stuff
+ 
+
+ align:start position:0%
+stuff
+of where his heading is back to his nest
+
+ align:start position:0%
+of where his heading is back to his nest
+ 
+
+ align:start position:0%
+of where his heading is back to his nest
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+the first thing you might think of is
+
+ align:start position:0%
+the first thing you might think of is
+ 
+
+ align:start position:0%
+the first thing you might think of is
+things like what it looks like maybe
+
+ align:start position:0%
+things like what it looks like maybe
+ 
+
+ align:start position:0%
+things like what it looks like maybe
+their landmarks maybe their odors maybe
+
+ align:start position:0%
+their landmarks maybe their odors maybe
+ 
+
+ align:start position:0%
+their landmarks maybe their odors maybe
+their odors
+
+ align:start position:0%
+their odors
+ 
+
+ align:start position:0%
+their odors
+but no
+
+ align:start position:0%
+but no
+ 
+
+ align:start position:0%
+but no
+he doesn't use any of those things and
+
+ align:start position:0%
+he doesn't use any of those things and
+ 
+
+ align:start position:0%
+he doesn't use any of those things and
+we know that
+
+ align:start position:0%
+we know that
+ 
+
+ align:start position:0%
+we know that
+because when scientists who have set up
+
+ align:start position:0%
+because when scientists who have set up
+ 
+
+ align:start position:0%
+because when scientists who have set up
+this measurement device
+
+ align:start position:0%
+this measurement device
+ 
+
+ align:start position:0%
+this measurement device
+capture cataglyphus after he goes out on
+
+ align:start position:0%
+capture cataglyphus after he goes out on
+ 
+
+ align:start position:0%
+capture cataglyphus after he goes out on
+this tortuous path and finds the feeding
+
+ align:start position:0%
+this tortuous path and finds the feeding
+ 
+
+ align:start position:0%
+this tortuous path and finds the feeding
+station they capture him and move them
+
+ align:start position:0%
+station they capture him and move them
+ 
+
+ align:start position:0%
+station they capture him and move them
+across the desert on which they've drawn
+
+ align:start position:0%
+across the desert on which they've drawn
+ 
+
+ align:start position:0%
+across the desert on which they've drawn
+all these grid lines for the convenience
+
+ align:start position:0%
+all these grid lines for the convenience
+ 
+
+ align:start position:0%
+all these grid lines for the convenience
+of their experiment and they release him
+
+ align:start position:0%
+of their experiment and they release him
+ 
+
+ align:start position:0%
+of their experiment and they release him
+here and what does cataglyphus do
+
+ align:start position:0%
+here and what does cataglyphus do
+ 
+
+ align:start position:0%
+here and what does cataglyphus do
+he goes on the exactly correct vector
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+no landmarks no relevant odors
+
+ align:start position:0%
+no landmarks no relevant odors
+ 
+
+ align:start position:0%
+no landmarks no relevant odors
+and yet he's obviously encoded the exact
+
+ align:start position:0%
+and yet he's obviously encoded the exact
+ 
+
+ align:start position:0%
+and yet he's obviously encoded the exact
+vector of how to get home
+
+ align:start position:0%
+vector of how to get home
+ 
+
+ align:start position:0%
+vector of how to get home
+think about what that entails and what's
+
+ align:start position:0%
+think about what that entails and what's
+ 
+
+ align:start position:0%
+think about what that entails and what's
+involved
+
+ align:start position:0%
+involved
+ 
+
+ align:start position:0%
+involved
+okay the same vector with respect to
+
+ align:start position:0%
+okay the same vector with respect to
+ 
+
+ align:start position:0%
+okay the same vector with respect to
+north with respect to this yes yes well
+
+ align:start position:0%
+north with respect to this yes yes well
+ 
+
+ align:start position:0%
+north with respect to this yes yes well
+with respect to like absolute
+
+ align:start position:0%
+with respect to like absolute
+ 
+
+ align:start position:0%
+with respect to like absolute
+um external direction absolutely
+
+ align:start position:0%
+um external direction absolutely
+ 
+
+ align:start position:0%
+um external direction absolutely
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+so that's what i just said
+
+ align:start position:0%
+so that's what i just said
+ 
+
+ align:start position:0%
+so that's what i just said
+so these feats of animal navigation
+
+ align:start position:0%
+so these feats of animal navigation
+ 
+
+ align:start position:0%
+so these feats of animal navigation
+uh are amazing
+
+ align:start position:0%
+uh are amazing
+ 
+
+ align:start position:0%
+uh are amazing
+um and animals have evolved ways to
+
+ align:start position:0%
+um and animals have evolved ways to
+ 
+
+ align:start position:0%
+um and animals have evolved ways to
+solve all these problems unique to their
+
+ align:start position:0%
+solve all these problems unique to their
+ 
+
+ align:start position:0%
+solve all these problems unique to their
+environment
+
+ align:start position:0%
+environment
+ 
+
+ align:start position:0%
+environment
+they've evolved these
+
+ align:start position:0%
+they've evolved these
+ 
+
+ align:start position:0%
+they've evolved these
+abilities because they really have to be
+
+ align:start position:0%
+abilities because they really have to be
+ 
+
+ align:start position:0%
+abilities because they really have to be
+able to find food
+
+ align:start position:0%
+able to find food
+ 
+
+ align:start position:0%
+able to find food
+and mates
+
+ align:start position:0%
+and mates
+ 
+
+ align:start position:0%
+and mates
+and shelter
+
+ align:start position:0%
+and shelter
+ 
+
+ align:start position:0%
+and shelter
+and this is not just esoterica in the
+
+ align:start position:0%
+and this is not just esoterica in the
+ 
+
+ align:start position:0%
+and this is not just esoterica in the
+natural world
+
+ align:start position:0%
+natural world
+ 
+
+ align:start position:0%
+natural world
+mit students too need to be able to find
+
+ align:start position:0%
+mit students too need to be able to find
+ 
+
+ align:start position:0%
+mit students too need to be able to find
+food
+
+ align:start position:0%
+food
+ 
+
+ align:start position:0%
+food
+and mates
+
+ align:start position:0%
+and mates
+ 
+
+ align:start position:0%
+and mates
+and shelter
+
+ align:start position:0%
+and shelter
+ 
+
+ align:start position:0%
+and shelter
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+what is navigation anyway uh and what
+
+ align:start position:0%
+what is navigation anyway uh and what
+ 
+
+ align:start position:0%
+what is navigation anyway uh and what
+does it entail
+
+ align:start position:0%
+does it entail
+ 
+
+ align:start position:0%
+does it entail
+uh well i'll argue over the next two
+
+ align:start position:0%
+uh well i'll argue over the next two
+ 
+
+ align:start position:0%
+uh well i'll argue over the next two
+lectures that there are two fundamental
+
+ align:start position:0%
+lectures that there are two fundamental
+ 
+
+ align:start position:0%
+lectures that there are two fundamental
+questions that organisms need to solve
+
+ align:start position:0%
+questions that organisms need to solve
+ 
+
+ align:start position:0%
+questions that organisms need to solve
+to be able to navigate first one is
+
+ align:start position:0%
+to be able to navigate first one is
+ 
+
+ align:start position:0%
+to be able to navigate first one is
+where am i
+
+ align:start position:0%
+where am i
+ 
+
+ align:start position:0%
+where am i
+and the second one is how do i get from
+
+ align:start position:0%
+and the second one is how do i get from
+ 
+
+ align:start position:0%
+and the second one is how do i get from
+here to there a to b wherever there is
+
+ align:start position:0%
+here to there a to b wherever there is
+ 
+
+ align:start position:0%
+here to there a to b wherever there is
+that you need to get
+
+ align:start position:0%
+that you need to get
+ 
+
+ align:start position:0%
+that you need to get
+okay so we'll unpack this or many
+
+ align:start position:0%
+okay so we'll unpack this or many
+ 
+
+ align:start position:0%
+okay so we'll unpack this or many
+different facets of each
+
+ align:start position:0%
+different facets of each
+ 
+
+ align:start position:0%
+different facets of each
+but so for example
+
+ align:start position:0%
+but so for example
+ 
+
+ align:start position:0%
+but so for example
+if you see this image
+
+ align:start position:0%
+if you see this image
+ 
+
+ align:start position:0%
+if you see this image
+you immediately know
+
+ align:start position:0%
+you immediately know
+ 
+
+ align:start position:0%
+you immediately know
+where you are
+
+ align:start position:0%
+where you are
+ 
+
+ align:start position:0%
+where you are
+and you also know
+
+ align:start position:0%
+and you also know
+ 
+
+ align:start position:0%
+and you also know
+where to go if for example it starts
+
+ align:start position:0%
+where to go if for example it starts
+ 
+
+ align:start position:0%
+where to go if for example it starts
+raining
+
+ align:start position:0%
+raining
+ 
+
+ align:start position:0%
+raining
+you might rush into lobby 7.
+
+ align:start position:0%
+you might rush into lobby 7.
+ 
+
+ align:start position:0%
+you might rush into lobby 7.
+or if you're hungry you might turn
+
+ align:start position:0%
+or if you're hungry you might turn
+ 
+
+ align:start position:0%
+or if you're hungry you might turn
+around and go back to the student center
+
+ align:start position:0%
+around and go back to the student center
+ 
+
+ align:start position:0%
+around and go back to the student center
+right
+
+ align:start position:0%
+right
+ 
+
+ align:start position:0%
+right
+same deal here if you see this
+
+ align:start position:0%
+same deal here if you see this
+ 
+
+ align:start position:0%
+same deal here if you see this
+then you know where you are and where
+
+ align:start position:0%
+then you know where you are and where
+ 
+
+ align:start position:0%
+then you know where you are and where
+you would go to get to various things
+
+ align:start position:0%
+you would go to get to various things
+ 
+
+ align:start position:0%
+you would go to get to various things
+okay now these judgments rely on the
+
+ align:start position:0%
+okay now these judgments rely on the
+ 
+
+ align:start position:0%
+okay now these judgments rely on the
+specific knowledge you you guys have of
+
+ align:start position:0%
+specific knowledge you you guys have of
+ 
+
+ align:start position:0%
+specific knowledge you you guys have of
+those particular places you recognize
+
+ align:start position:0%
+those particular places you recognize
+ 
+
+ align:start position:0%
+those particular places you recognize
+that exact place and you know
+
+ align:start position:0%
+that exact place and you know
+ 
+
+ align:start position:0%
+that exact place and you know
+you have some kind of map in your head
+
+ align:start position:0%
+you have some kind of map in your head
+ 
+
+ align:start position:0%
+you have some kind of map in your head
+that we'll talk more about in a moment
+
+ align:start position:0%
+that we'll talk more about in a moment
+ 
+
+ align:start position:0%
+that we'll talk more about in a moment
+that tells you where everything else is
+
+ align:start position:0%
+that tells you where everything else is
+ 
+
+ align:start position:0%
+that tells you where everything else is
+with respect to it
+
+ align:start position:0%
+with respect to it
+ 
+
+ align:start position:0%
+with respect to it
+but even if you're in a place you don't
+
+ align:start position:0%
+but even if you're in a place you don't
+ 
+
+ align:start position:0%
+but even if you're in a place you don't
+know at all
+
+ align:start position:0%
+know at all
+ 
+
+ align:start position:0%
+know at all
+you can still extract some information
+
+ align:start position:0%
+you can still extract some information
+ 
+
+ align:start position:0%
+you can still extract some information
+so suppose you miraculously found
+
+ align:start position:0%
+so suppose you miraculously found
+ 
+
+ align:start position:0%
+so suppose you miraculously found
+yourself boom here
+
+ align:start position:0%
+yourself boom here
+ 
+
+ align:start position:0%
+yourself boom here
+i wouldn't mind actually but that's not
+
+ align:start position:0%
+i wouldn't mind actually but that's not
+ 
+
+ align:start position:0%
+i wouldn't mind actually but that's not
+in the cards for a while
+
+ align:start position:0%
+in the cards for a while
+ 
+
+ align:start position:0%
+in the cards for a while
+um so you're here
+
+ align:start position:0%
+um so you're here
+ 
+
+ align:start position:0%
+um so you're here
+even if you've just hiked around the
+
+ align:start position:0%
+even if you've just hiked around the
+ 
+
+ align:start position:0%
+even if you've just hiked around the
+corner if you've never seen this place
+
+ align:start position:0%
+corner if you've never seen this place
+ 
+
+ align:start position:0%
+corner if you've never seen this place
+before
+
+ align:start position:0%
+before
+ 
+
+ align:start position:0%
+before
+you have some kind of idea what sort of
+
+ align:start position:0%
+you have some kind of idea what sort of
+ 
+
+ align:start position:0%
+you have some kind of idea what sort of
+place this is where would you pitch your
+
+ align:start position:0%
+place this is where would you pitch your
+ 
+
+ align:start position:0%
+place this is where would you pitch your
+tent
+
+ align:start position:0%
+tent
+ 
+
+ align:start position:0%
+tent
+you know where might you try to go to
+
+ align:start position:0%
+you know where might you try to go to
+ 
+
+ align:start position:0%
+you know where might you try to go to
+get out of this valley if it was me i
+
+ align:start position:0%
+get out of this valley if it was me i
+ 
+
+ align:start position:0%
+get out of this valley if it was me i
+wouldn't i have friends who would go
+
+ align:start position:0%
+wouldn't i have friends who would go
+ 
+
+ align:start position:0%
+wouldn't i have friends who would go
+straight up there and try to drag me
+
+ align:start position:0%
+straight up there and try to drag me
+ 
+
+ align:start position:0%
+straight up there and try to drag me
+along complaining if it was me i'd
+
+ align:start position:0%
+along complaining if it was me i'd
+ 
+
+ align:start position:0%
+along complaining if it was me i'd
+rather look for some other route
+
+ align:start position:0%
+rather look for some other route
+ 
+
+ align:start position:0%
+rather look for some other route
+but you can tell all of that just by
+
+ align:start position:0%
+but you can tell all of that just by
+ 
+
+ align:start position:0%
+but you can tell all of that just by
+looking at this image
+
+ align:start position:0%
+looking at this image
+ 
+
+ align:start position:0%
+looking at this image
+okay okay where you can go from there
+
+ align:start position:0%
+okay okay where you can go from there
+ 
+
+ align:start position:0%
+okay okay where you can go from there
+not just what kind of a place it is but
+
+ align:start position:0%
+not just what kind of a place it is but
+ 
+
+ align:start position:0%
+not just what kind of a place it is but
+what are the possible routes you might
+
+ align:start position:0%
+what are the possible routes you might
+ 
+
+ align:start position:0%
+what are the possible routes you might
+take
+
+ align:start position:0%
+take
+ 
+
+ align:start position:0%
+take
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+so these fundamental problems that we
+
+ align:start position:0%
+so these fundamental problems that we
+ 
+
+ align:start position:0%
+so these fundamental problems that we
+solve in navigation of knowing where am
+
+ align:start position:0%
+solve in navigation of knowing where am
+ 
+
+ align:start position:0%
+solve in navigation of knowing where am
+i and how do i get from here to there
+
+ align:start position:0%
+i and how do i get from here to there
+ 
+
+ align:start position:0%
+i and how do i get from here to there
+include multiple components in terms of
+
+ align:start position:0%
+include multiple components in terms of
+ 
+
+ align:start position:0%
+include multiple components in terms of
+where am i the first the first piece is
+
+ align:start position:0%
+where am i the first the first piece is
+ 
+
+ align:start position:0%
+where am i the first the first piece is
+recognizing a specific place you know
+
+ align:start position:0%
+recognizing a specific place you know
+ 
+
+ align:start position:0%
+recognizing a specific place you know
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+so you might open your eyes and say okay
+
+ align:start position:0%
+so you might open your eyes and say okay
+ 
+
+ align:start position:0%
+so you might open your eyes and say okay
+this is my living room i know this
+
+ align:start position:0%
+this is my living room i know this
+ 
+
+ align:start position:0%
+this is my living room i know this
+particular place
+
+ align:start position:0%
+particular place
+ 
+
+ align:start position:0%
+particular place
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+but as i just pointed out even if the
+
+ align:start position:0%
+but as i just pointed out even if the
+ 
+
+ align:start position:0%
+but as i just pointed out even if the
+place is unfamiliar
+
+ align:start position:0%
+place is unfamiliar
+ 
+
+ align:start position:0%
+place is unfamiliar
+we can get a sense of what kind of place
+
+ align:start position:0%
+we can get a sense of what kind of place
+ 
+
+ align:start position:0%
+we can get a sense of what kind of place
+this is right am i in an urban
+
+ align:start position:0%
+this is right am i in an urban
+ 
+
+ align:start position:0%
+this is right am i in an urban
+environment a natural environment a
+
+ align:start position:0%
+environment a natural environment a
+ 
+
+ align:start position:0%
+environment a natural environment a
+living room a bathroom where am
+
+ align:start position:0%
+living room a bathroom where am
+ 
+
+ align:start position:0%
+living room a bathroom where am
+i a third aspect of where am i a third
+
+ align:start position:0%
+i a third aspect of where am i a third
+ 
+
+ align:start position:0%
+i a third aspect of where am i a third
+way that we might answer that question
+
+ align:start position:0%
+way that we might answer that question
+ 
+
+ align:start position:0%
+way that we might answer that question
+is something about the geometry of the
+
+ align:start position:0%
+is something about the geometry of the
+ 
+
+ align:start position:0%
+is something about the geometry of the
+environment we're in
+
+ align:start position:0%
+environment we're in
+ 
+
+ align:start position:0%
+environment we're in
+so try this right now close your eyes
+
+ align:start position:0%
+so try this right now close your eyes
+ 
+
+ align:start position:0%
+so try this right now close your eyes
+okay now think about how far the wall is
+
+ align:start position:0%
+okay now think about how far the wall is
+ 
+
+ align:start position:0%
+okay now think about how far the wall is
+in front of you don't open your eyes
+
+ align:start position:0%
+in front of you don't open your eyes
+ 
+
+ align:start position:0%
+in front of you don't open your eyes
+just think about how far away it is how
+
+ align:start position:0%
+just think about how far away it is how
+ 
+
+ align:start position:0%
+just think about how far away it is how
+far away the left wall is and the right
+
+ align:start position:0%
+far away the left wall is and the right
+ 
+
+ align:start position:0%
+far away the left wall is and the right
+wall is and how about the wall behind
+
+ align:start position:0%
+wall is and how about the wall behind
+ 
+
+ align:start position:0%
+wall is and how about the wall behind
+you don't open your eyes how far back is
+
+ align:start position:0%
+you don't open your eyes how far back is
+ 
+
+ align:start position:0%
+you don't open your eyes how far back is
+the wall behind you from where you are
+
+ align:start position:0%
+the wall behind you from where you are
+ 
+
+ align:start position:0%
+the wall behind you from where you are
+right now
+
+ align:start position:0%
+right now
+ 
+
+ align:start position:0%
+right now
+okay you can open your eyes it's not
+
+ align:start position:0%
+okay you can open your eyes it's not
+ 
+
+ align:start position:0%
+okay you can open your eyes it's not
+rocket science i just wanted you to
+
+ align:start position:0%
+rocket science i just wanted you to
+ 
+
+ align:start position:0%
+rocket science i just wanted you to
+intuit that even though you're
+
+ align:start position:0%
+intuit that even though you're
+ 
+
+ align:start position:0%
+intuit that even though you're
+presumably riveted by this lecture and
+
+ align:start position:0%
+presumably riveted by this lecture and
+ 
+
+ align:start position:0%
+presumably riveted by this lecture and
+thinking only about navigation you sort
+
+ align:start position:0%
+thinking only about navigation you sort
+ 
+
+ align:start position:0%
+thinking only about navigation you sort
+of have a kind of situational awareness
+
+ align:start position:0%
+of have a kind of situational awareness
+ 
+
+ align:start position:0%
+of have a kind of situational awareness
+of the spatial layout of the space
+
+ align:start position:0%
+of the spatial layout of the space
+ 
+
+ align:start position:0%
+of the spatial layout of the space
+you're in
+
+ align:start position:0%
+you're in
+ 
+
+ align:start position:0%
+you're in
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+you might have a sense of okay i'm in a
+
+ align:start position:0%
+you might have a sense of okay i'm in a
+ 
+
+ align:start position:0%
+you might have a sense of okay i'm in a
+space like this and i'm over here in it
+
+ align:start position:0%
+space like this and i'm over here in it
+ 
+
+ align:start position:0%
+space like this and i'm over here in it
+right
+
+ align:start position:0%
+right
+ 
+
+ align:start position:0%
+right
+and we'll talk more about that exact
+
+ align:start position:0%
+and we'll talk more about that exact
+ 
+
+ align:start position:0%
+and we'll talk more about that exact
+kind of awareness of your position
+
+ align:start position:0%
+kind of awareness of your position
+ 
+
+ align:start position:0%
+kind of awareness of your position
+relative to the spatial layout of your
+
+ align:start position:0%
+relative to the spatial layout of your
+ 
+
+ align:start position:0%
+relative to the spatial layout of your
+immediate environment it's something
+
+ align:start position:0%
+immediate environment it's something
+ 
+
+ align:start position:0%
+immediate environment it's something
+that's very important in navigation
+
+ align:start position:0%
+that's very important in navigation
+ 
+
+ align:start position:0%
+that's very important in navigation
+and another part of that is you might
+
+ align:start position:0%
+and another part of that is you might
+ 
+
+ align:start position:0%
+and another part of that is you might
+think how would i get out of here if i'm
+
+ align:start position:0%
+think how would i get out of here if i'm
+ 
+
+ align:start position:0%
+think how would i get out of here if i'm
+seriously bored by the lecture or for
+
+ align:start position:0%
+seriously bored by the lecture or for
+ 
+
+ align:start position:0%
+seriously bored by the lecture or for
+any other reason i urgently need to get
+
+ align:start position:0%
+any other reason i urgently need to get
+ 
+
+ align:start position:0%
+any other reason i urgently need to get
+out of here you probably know exactly
+
+ align:start position:0%
+out of here you probably know exactly
+ 
+
+ align:start position:0%
+out of here you probably know exactly
+where the doors are in this space it's
+
+ align:start position:0%
+where the doors are in this space it's
+ 
+
+ align:start position:0%
+where the doors are in this space it's
+just part of those one of those things
+
+ align:start position:0%
+just part of those one of those things
+ 
+
+ align:start position:0%
+just part of those one of those things
+that we
+
+ align:start position:0%
+that we
+ 
+
+ align:start position:0%
+that we
+keep track of okay
+
+ align:start position:0%
+keep track of okay
+ 
+
+ align:start position:0%
+keep track of okay
+okay so those are aspects of where am i
+
+ align:start position:0%
+okay so those are aspects of where am i
+ 
+
+ align:start position:0%
+okay so those are aspects of where am i
+in this place
+
+ align:start position:0%
+in this place
+ 
+
+ align:start position:0%
+in this place
+what are the things we need to know to
+
+ align:start position:0%
+what are the things we need to know to
+ 
+
+ align:start position:0%
+what are the things we need to know to
+know how we would get from here to
+
+ align:start position:0%
+know how we would get from here to
+ 
+
+ align:start position:0%
+know how we would get from here to
+someplace else
+
+ align:start position:0%
+someplace else
+ 
+
+ align:start position:0%
+someplace else
+okay well the simplest way to navigate
+
+ align:start position:0%
+okay well the simplest way to navigate
+ 
+
+ align:start position:0%
+okay well the simplest way to navigate
+to another location another goal is
+
+ align:start position:0%
+to another location another goal is
+ 
+
+ align:start position:0%
+to another location another goal is
+called beaconing and this is the case
+
+ align:start position:0%
+called beaconing and this is the case
+ 
+
+ align:start position:0%
+called beaconing and this is the case
+where you can directly see or hear your
+
+ align:start position:0%
+where you can directly see or hear your
+ 
+
+ align:start position:0%
+where you can directly see or hear your
+target location so you're sailing in the
+
+ align:start position:0%
+target location so you're sailing in the
+ 
+
+ align:start position:0%
+target location so you're sailing in the
+fog you can't see a damn thing but you
+
+ align:start position:0%
+fog you can't see a damn thing but you
+ 
+
+ align:start position:0%
+fog you can't see a damn thing but you
+hear the fog horn over there and you
+
+ align:start position:0%
+hear the fog horn over there and you
+ 
+
+ align:start position:0%
+hear the fog horn over there and you
+know you're sailing to that point so you
+
+ align:start position:0%
+know you're sailing to that point so you
+ 
+
+ align:start position:0%
+know you're sailing to that point so you
+just go toward the sound
+
+ align:start position:0%
+just go toward the sound
+ 
+
+ align:start position:0%
+just go toward the sound
+nice and simple you don't need any
+
+ align:start position:0%
+nice and simple you don't need any
+ 
+
+ align:start position:0%
+nice and simple you don't need any
+broader map of anything else you just
+
+ align:start position:0%
+broader map of anything else you just
+ 
+
+ align:start position:0%
+broader map of anything else you just
+hear it and head toward it
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+or
+
+ align:start position:0%
+or
+ 
+
+ align:start position:0%
+or
+if you see this
+
+ align:start position:0%
+if you see this
+ 
+
+ align:start position:0%
+if you see this
+and your goal is to get to the green
+
+ align:start position:0%
+and your goal is to get to the green
+ 
+
+ align:start position:0%
+and your goal is to get to the green
+building
+
+ align:start position:0%
+building
+ 
+
+ align:start position:0%
+building
+well you know there's a green building
+
+ align:start position:0%
+well you know there's a green building
+ 
+
+ align:start position:0%
+well you know there's a green building
+and you just head that way now you're
+
+ align:start position:0%
+and you just head that way now you're
+ 
+
+ align:start position:0%
+and you just head that way now you're
+gonna have to like go around a little
+
+ align:start position:0%
+gonna have to like go around a little
+ 
+
+ align:start position:0%
+gonna have to like go around a little
+bit to get around those obstacles but
+
+ align:start position:0%
+bit to get around those obstacles but
+ 
+
+ align:start position:0%
+bit to get around those obstacles but
+you know where to head because you can
+
+ align:start position:0%
+you know where to head because you can
+ 
+
+ align:start position:0%
+you know where to head because you can
+see your target directly okay these are
+
+ align:start position:0%
+see your target directly okay these are
+ 
+
+ align:start position:0%
+see your target directly okay these are
+cases where you don't need a broader
+
+ align:start position:0%
+cases where you don't need a broader
+ 
+
+ align:start position:0%
+cases where you don't need a broader
+long-term knowledge of the whole
+
+ align:start position:0%
+long-term knowledge of the whole
+ 
+
+ align:start position:0%
+long-term knowledge of the whole
+environment if you can see your target
+
+ align:start position:0%
+environment if you can see your target
+ 
+
+ align:start position:0%
+environment if you can see your target
+you just go straight for it okay so
+
+ align:start position:0%
+you just go straight for it okay so
+ 
+
+ align:start position:0%
+you just go straight for it okay so
+that's beaconing
+
+ align:start position:0%
+that's beaconing
+ 
+
+ align:start position:0%
+that's beaconing
+simplest kind of a to b
+
+ align:start position:0%
+simplest kind of a to b
+ 
+
+ align:start position:0%
+simplest kind of a to b
+um and it requires no mental map no kind
+
+ align:start position:0%
+um and it requires no mental map no kind
+ 
+
+ align:start position:0%
+um and it requires no mental map no kind
+of internal model of the whole world
+
+ align:start position:0%
+of internal model of the whole world
+ 
+
+ align:start position:0%
+of internal model of the whole world
+you're navigating in
+
+ align:start position:0%
+you're navigating in
+ 
+
+ align:start position:0%
+you're navigating in
+but if you can't see the place you want
+
+ align:start position:0%
+but if you can't see the place you want
+ 
+
+ align:start position:0%
+but if you can't see the place you want
+to go
+
+ align:start position:0%
+to go
+ 
+
+ align:start position:0%
+to go
+then you need some kind of mental map of
+
+ align:start position:0%
+then you need some kind of mental map of
+ 
+
+ align:start position:0%
+then you need some kind of mental map of
+the world so what do we mean by a mental
+
+ align:start position:0%
+the world so what do we mean by a mental
+ 
+
+ align:start position:0%
+the world so what do we mean by a mental
+map of the world
+
+ align:start position:0%
+map of the world
+ 
+
+ align:start position:0%
+map of the world
+well this idea was first articulated in
+
+ align:start position:0%
+well this idea was first articulated in
+ 
+
+ align:start position:0%
+well this idea was first articulated in
+a classic experiment way back in the
+
+ align:start position:0%
+a classic experiment way back in the
+ 
+
+ align:start position:0%
+a classic experiment way back in the
+1940s
+
+ align:start position:0%
+1940s
+ 
+
+ align:start position:0%
+1940s
+so this was actually one of the original
+
+ align:start position:0%
+so this was actually one of the original
+ 
+
+ align:start position:0%
+so this was actually one of the original
+experiments that launched the cognitive
+
+ align:start position:0%
+experiments that launched the cognitive
+ 
+
+ align:start position:0%
+experiments that launched the cognitive
+revolution when we emerged from the the
+
+ align:start position:0%
+revolution when we emerged from the the
+ 
+
+ align:start position:0%
+revolution when we emerged from the the
+scourge of behaviorism uh to realize it
+
+ align:start position:0%
+scourge of behaviorism uh to realize it
+ 
+
+ align:start position:0%
+scourge of behaviorism uh to realize it
+was actually okay and indeed of the
+
+ align:start position:0%
+was actually okay and indeed of the
+ 
+
+ align:start position:0%
+was actually okay and indeed of the
+essence to talk about what's going on in
+
+ align:start position:0%
+essence to talk about what's going on in
+ 
+
+ align:start position:0%
+essence to talk about what's going on in
+the mind
+
+ align:start position:0%
+the mind
+ 
+
+ align:start position:0%
+the mind
+and a really influential study that
+
+ align:start position:0%
+and a really influential study that
+ 
+
+ align:start position:0%
+and a really influential study that
+launched the cognitive revolution
+
+ align:start position:0%
+launched the cognitive revolution
+ 
+
+ align:start position:0%
+launched the cognitive revolution
+by tolman
+
+ align:start position:0%
+by tolman
+ 
+
+ align:start position:0%
+by tolman
+was done on rats and it went like this
+
+ align:start position:0%
+was done on rats and it went like this
+ 
+
+ align:start position:0%
+was done on rats and it went like this
+he trained rats he put them down in this
+
+ align:start position:0%
+he trained rats he put them down in this
+ 
+
+ align:start position:0%
+he trained rats he put them down in this
+area and they had to learn that there
+
+ align:start position:0%
+area and they had to learn that there
+ 
+
+ align:start position:0%
+area and they had to learn that there
+would be full
+
+ align:start position:0%
+would be full
+ 
+
+ align:start position:0%
+would be full
+food out there at the goal and so they
+
+ align:start position:0%
+food out there at the goal and so they
+ 
+
+ align:start position:0%
+food out there at the goal and so they
+just have to make the series of left and
+
+ align:start position:0%
+just have to make the series of left and
+ 
+
+ align:start position:0%
+just have to make the series of left and
+right turns to find the food okay so you
+
+ align:start position:0%
+right turns to find the food okay so you
+ 
+
+ align:start position:0%
+right turns to find the food okay so you
+train them on that for a while until
+
+ align:start position:0%
+train them on that for a while until
+ 
+
+ align:start position:0%
+train them on that for a while until
+they're really good at it
+
+ align:start position:0%
+they're really good at it
+ 
+
+ align:start position:0%
+they're really good at it
+and then you put the rats in this
+
+ align:start position:0%
+and then you put the rats in this
+ 
+
+ align:start position:0%
+and then you put the rats in this
+environment
+
+ align:start position:0%
+environment
+ 
+
+ align:start position:0%
+environment
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+now
+
+ align:start position:0%
+now
+ 
+
+ align:start position:0%
+now
+the environment is similar except
+
+ align:start position:0%
+the environment is similar except
+ 
+
+ align:start position:0%
+the environment is similar except
+there's multiple paths
+
+ align:start position:0%
+there's multiple paths
+ 
+
+ align:start position:0%
+there's multiple paths
+one that seems analogous to the old
+
+ align:start position:0%
+one that seems analogous to the old
+ 
+
+ align:start position:0%
+one that seems analogous to the old
+route
+
+ align:start position:0%
+route
+ 
+
+ align:start position:0%
+route
+so what do the rats do in this situation
+
+ align:start position:0%
+so what do the rats do in this situation
+ 
+
+ align:start position:0%
+so what do the rats do in this situation
+they run down here
+
+ align:start position:0%
+they run down here
+ 
+
+ align:start position:0%
+they run down here
+they run into a wall and they realize
+
+ align:start position:0%
+they run into a wall and they realize
+ 
+
+ align:start position:0%
+they run into a wall and they realize
+okay that's not going to work okay
+
+ align:start position:0%
+okay that's not going to work okay
+ 
+
+ align:start position:0%
+okay that's not going to work okay
+nothing no surprises yet
+
+ align:start position:0%
+nothing no surprises yet
+ 
+
+ align:start position:0%
+nothing no surprises yet
+but then the rats immediately come back
+
+ align:start position:0%
+but then the rats immediately come back
+ 
+
+ align:start position:0%
+but then the rats immediately come back
+out and they go straight out that way
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+what does that tell you
+
+ align:start position:0%
+what does that tell you
+ 
+
+ align:start position:0%
+what does that tell you
+what do they learn
+
+ align:start position:0%
+what do they learn
+ 
+
+ align:start position:0%
+what do they learn
+did they learn a series of like go
+
+ align:start position:0%
+did they learn a series of like go
+ 
+
+ align:start position:0%
+did they learn a series of like go
+straight and then left and then right
+
+ align:start position:0%
+straight and then left and then right
+ 
+
+ align:start position:0%
+straight and then left and then right
+and then right and then go for a long
+
+ align:start position:0%
+and then right and then go for a long
+ 
+
+ align:start position:0%
+and then right and then go for a long
+ways
+
+ align:start position:0%
+ways
+ 
+
+ align:start position:0%
+ways
+no that wouldn't work over here
+
+ align:start position:0%
+no that wouldn't work over here
+ 
+
+ align:start position:0%
+no that wouldn't work over here
+they learned something much more
+
+ align:start position:0%
+they learned something much more
+ 
+
+ align:start position:0%
+they learned something much more
+interesting even though they were only
+
+ align:start position:0%
+interesting even though they were only
+ 
+
+ align:start position:0%
+interesting even though they were only
+being trained on this task here they
+
+ align:start position:0%
+being trained on this task here they
+ 
+
+ align:start position:0%
+being trained on this task here they
+learned some much more interesting thing
+
+ align:start position:0%
+learned some much more interesting thing
+ 
+
+ align:start position:0%
+learned some much more interesting thing
+about the kind of vector average of all
+
+ align:start position:0%
+about the kind of vector average of all
+ 
+
+ align:start position:0%
+about the kind of vector average of all
+of those turns
+
+ align:start position:0%
+of those turns
+ 
+
+ align:start position:0%
+of those turns
+everybody get this it's really simple
+
+ align:start position:0%
+everybody get this it's really simple
+ 
+
+ align:start position:0%
+everybody get this it's really simple
+but really deep
+
+ align:start position:0%
+but really deep
+ 
+
+ align:start position:0%
+but really deep
+okay so from this tolman and others
+
+ align:start position:0%
+okay so from this tolman and others
+ 
+
+ align:start position:0%
+okay so from this tolman and others
+started talking about cognitive maps
+
+ align:start position:0%
+started talking about cognitive maps
+ 
+
+ align:start position:0%
+started talking about cognitive maps
+whatever it is you have to have learned
+
+ align:start position:0%
+whatever it is you have to have learned
+ 
+
+ align:start position:0%
+whatever it is you have to have learned
+in a situation like this so you can
+
+ align:start position:0%
+in a situation like this so you can
+ 
+
+ align:start position:0%
+in a situation like this so you can
+abstract the general direction
+
+ align:start position:0%
+abstract the general direction
+ 
+
+ align:start position:0%
+abstract the general direction
+okay we don't just learn specific roots
+
+ align:start position:0%
+okay we don't just learn specific roots
+ 
+
+ align:start position:0%
+okay we don't just learn specific roots
+as a series of
+
+ align:start position:0%
+as a series of
+ 
+
+ align:start position:0%
+as a series of
+stimulus and responses okay so there
+
+ align:start position:0%
+stimulus and responses okay so there
+ 
+
+ align:start position:0%
+stimulus and responses okay so there
+must be some kind of map in your head to
+
+ align:start position:0%
+must be some kind of map in your head to
+ 
+
+ align:start position:0%
+must be some kind of map in your head to
+be able to do this
+
+ align:start position:0%
+be able to do this
+ 
+
+ align:start position:0%
+be able to do this
+and rats have that
+
+ align:start position:0%
+and rats have that
+ 
+
+ align:start position:0%
+and rats have that
+and so do you
+
+ align:start position:0%
+and so do you
+ 
+
+ align:start position:0%
+and so do you
+so let's consider this question right
+
+ align:start position:0%
+so let's consider this question right
+ 
+
+ align:start position:0%
+so let's consider this question right
+now where am i where are
+
+ align:start position:0%
+now where am i where are
+ 
+
+ align:start position:0%
+now where am i where are
+you to answer that question to yourself
+
+ align:start position:0%
+you to answer that question to yourself
+ 
+
+ align:start position:0%
+you to answer that question to yourself
+there's something like this in your head
+
+ align:start position:0%
+there's something like this in your head
+ 
+
+ align:start position:0%
+there's something like this in your head
+and it probably doesn't look exactly
+
+ align:start position:0%
+and it probably doesn't look exactly
+ 
+
+ align:start position:0%
+and it probably doesn't look exactly
+like that in your head but there's some
+
+ align:start position:0%
+like that in your head but there's some
+ 
+
+ align:start position:0%
+like that in your head but there's some
+version of this information
+
+ align:start position:0%
+version of this information
+ 
+
+ align:start position:0%
+version of this information
+that's in your head
+
+ align:start position:0%
+that's in your head
+ 
+
+ align:start position:0%
+that's in your head
+that you're using when you answer the
+
+ align:start position:0%
+that you're using when you answer the
+ 
+
+ align:start position:0%
+that you're using when you answer the
+question of where you are
+
+ align:start position:0%
+question of where you are
+ 
+
+ align:start position:0%
+question of where you are
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+um and you have some way to say in that
+
+ align:start position:0%
+um and you have some way to say in that
+ 
+
+ align:start position:0%
+um and you have some way to say in that
+map of the world i know not just what
+
+ align:start position:0%
+map of the world i know not just what
+ 
+
+ align:start position:0%
+map of the world i know not just what
+the mit campus looks like and how it's
+
+ align:start position:0%
+the mit campus looks like and how it's
+ 
+
+ align:start position:0%
+the mit campus looks like and how it's
+arranged but i know where i am in it
+
+ align:start position:0%
+arranged but i know where i am in it
+ 
+
+ align:start position:0%
+arranged but i know where i am in it
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+now if you want to know how to get
+
+ align:start position:0%
+now if you want to know how to get
+ 
+
+ align:start position:0%
+now if you want to know how to get
+somewhere else like suppose you're
+
+ align:start position:0%
+somewhere else like suppose you're
+ 
+
+ align:start position:0%
+somewhere else like suppose you're
+hungry and you want to go over to the
+
+ align:start position:0%
+hungry and you want to go over to the
+ 
+
+ align:start position:0%
+hungry and you want to go over to the
+stata cafeteria over there
+
+ align:start position:0%
+stata cafeteria over there
+ 
+
+ align:start position:0%
+stata cafeteria over there
+what else do you need to know besides
+
+ align:start position:0%
+what else do you need to know besides
+ 
+
+ align:start position:0%
+what else do you need to know besides
+knowledge of the map of your environment
+
+ align:start position:0%
+knowledge of the map of your environment
+ 
+
+ align:start position:0%
+knowledge of the map of your environment
+and where you are in it what else do you
+
+ align:start position:0%
+and where you are in it what else do you
+ 
+
+ align:start position:0%
+and where you are in it what else do you
+need to know
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+you know
+
+ align:start position:0%
+you know
+ 
+
+ align:start position:0%
+you know
+you have this map you know where you are
+
+ align:start position:0%
+you have this map you know where you are
+ 
+
+ align:start position:0%
+you have this map you know where you are
+and you know where your goal is now you
+
+ align:start position:0%
+and you know where your goal is now you
+ 
+
+ align:start position:0%
+and you know where your goal is now you
+have to plan how to get over there what
+
+ align:start position:0%
+have to plan how to get over there what
+ 
+
+ align:start position:0%
+have to plan how to get over there what
+else do you need to know
+
+ align:start position:0%
+else do you need to know
+ 
+
+ align:start position:0%
+else do you need to know
+yeah you have to know which parts are
+
+ align:start position:0%
+yeah you have to know which parts are
+ 
+
+ align:start position:0%
+yeah you have to know which parts are
+like paths and which parts are buildings
+
+ align:start position:0%
+like paths and which parts are buildings
+ 
+
+ align:start position:0%
+like paths and which parts are buildings
+yes exactly where can you go in there
+
+ align:start position:0%
+yes exactly where can you go in there
+ 
+
+ align:start position:0%
+yes exactly where can you go in there
+actually where can you physically get
+
+ align:start position:0%
+actually where can you physically get
+ 
+
+ align:start position:0%
+actually where can you physically get
+through like actually our vector is
+
+ align:start position:0%
+through like actually our vector is
+ 
+
+ align:start position:0%
+through like actually our vector is
+right over there but you can't go that
+
+ align:start position:0%
+right over there but you can't go that
+ 
+
+ align:start position:0%
+right over there but you can't go that
+way because you can't go through that
+
+ align:start position:0%
+way because you can't go through that
+ 
+
+ align:start position:0%
+way because you can't go through that
+glass even though you can see through it
+
+ align:start position:0%
+glass even though you can see through it
+ 
+
+ align:start position:0%
+glass even though you can see through it
+right so knowledge of physical barriers
+
+ align:start position:0%
+right so knowledge of physical barriers
+ 
+
+ align:start position:0%
+right so knowledge of physical barriers
+and what what's an actual path and what
+
+ align:start position:0%
+and what what's an actual path and what
+ 
+
+ align:start position:0%
+and what what's an actual path and what
+isn't is crucial what else do you need
+
+ align:start position:0%
+isn't is crucial what else do you need
+ 
+
+ align:start position:0%
+isn't is crucial what else do you need
+to know
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+suppose we had a robot in this room
+
+ align:start position:0%
+suppose we had a robot in this room
+ 
+
+ align:start position:0%
+suppose we had a robot in this room
+sitting
+
+ align:start position:0%
+sitting
+ 
+
+ align:start position:0%
+sitting
+right here facing the front of room like
+
+ align:start position:0%
+right here facing the front of room like
+ 
+
+ align:start position:0%
+right here facing the front of room like
+you guys and we're programming the robot
+
+ align:start position:0%
+you guys and we're programming the robot
+ 
+
+ align:start position:0%
+you guys and we're programming the robot
+on how to get over there what are other
+
+ align:start position:0%
+on how to get over there what are other
+ 
+
+ align:start position:0%
+on how to get over there what are other
+things we'd have to tell that robot to
+
+ align:start position:0%
+things we'd have to tell that robot to
+ 
+
+ align:start position:0%
+things we'd have to tell that robot to
+get it to plan
+
+ align:start position:0%
+get it to plan
+ 
+
+ align:start position:0%
+get it to plan
+how to get over to the stata cafeteria
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah things to watch out for like cars
+
+ align:start position:0%
+yeah things to watch out for like cars
+ 
+
+ align:start position:0%
+yeah things to watch out for like cars
+and traffic absolutely we'd have to know
+
+ align:start position:0%
+and traffic absolutely we'd have to know
+ 
+
+ align:start position:0%
+and traffic absolutely we'd have to know
+about obstacles like moving obstacles
+
+ align:start position:0%
+about obstacles like moving obstacles
+ 
+
+ align:start position:0%
+about obstacles like moving obstacles
+not just fixed ones absolutely what else
+
+ align:start position:0%
+not just fixed ones absolutely what else
+ 
+
+ align:start position:0%
+not just fixed ones absolutely what else
+yeah an issue or your addition yes he
+
+ align:start position:0%
+yeah an issue or your addition yes he
+ 
+
+ align:start position:0%
+yeah an issue or your addition yes he
+has to know which way he's headed
+
+ align:start position:0%
+has to know which way he's headed
+ 
+
+ align:start position:0%
+has to know which way he's headed
+right you're going to give this robot
+
+ align:start position:0%
+right you're going to give this robot
+ 
+
+ align:start position:0%
+right you're going to give this robot
+instructions on which way to go it
+
+ align:start position:0%
+instructions on which way to go it
+ 
+
+ align:start position:0%
+instructions on which way to go it
+matters a whole lot if the robot is
+
+ align:start position:0%
+matters a whole lot if the robot is
+ 
+
+ align:start position:0%
+matters a whole lot if the robot is
+starting like this
+
+ align:start position:0%
+starting like this
+ 
+
+ align:start position:0%
+starting like this
+or starting like that the instructions
+
+ align:start position:0%
+or starting like that the instructions
+ 
+
+ align:start position:0%
+or starting like that the instructions
+are different in the two cases and
+
+ align:start position:0%
+are different in the two cases and
+ 
+
+ align:start position:0%
+are different in the two cases and
+likewise for you guys to plan a route
+
+ align:start position:0%
+likewise for you guys to plan a route
+ 
+
+ align:start position:0%
+likewise for you guys to plan a route
+you need to know which way you're
+
+ align:start position:0%
+you need to know which way you're
+ 
+
+ align:start position:0%
+you need to know which way you're
+heading
+
+ align:start position:0%
+heading
+ 
+
+ align:start position:0%
+heading
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+if you guys ever been in in manhattan
+
+ align:start position:0%
+if you guys ever been in in manhattan
+ 
+
+ align:start position:0%
+if you guys ever been in in manhattan
+and you come up from the subway and you
+
+ align:start position:0%
+and you come up from the subway and you
+ 
+
+ align:start position:0%
+and you come up from the subway and you
+see the streets going like this and you
+
+ align:start position:0%
+see the streets going like this and you
+ 
+
+ align:start position:0%
+see the streets going like this and you
+know it's north south and you don't know
+
+ align:start position:0%
+know it's north south and you don't know
+ 
+
+ align:start position:0%
+know it's north south and you don't know
+if you're heading south or north right
+
+ align:start position:0%
+if you're heading south or north right
+ 
+
+ align:start position:0%
+if you're heading south or north right
+really common thing okay you need to
+
+ align:start position:0%
+really common thing okay you need to
+ 
+
+ align:start position:0%
+really common thing okay you need to
+it's not enough to know i'm at the
+
+ align:start position:0%
+it's not enough to know i'm at the
+ 
+
+ align:start position:0%
+it's not enough to know i'm at the
+junction of 5th and 22nd you need to
+
+ align:start position:0%
+junction of 5th and 22nd you need to
+ 
+
+ align:start position:0%
+junction of 5th and 22nd you need to
+know am i facing south or north
+
+ align:start position:0%
+know am i facing south or north
+ 
+
+ align:start position:0%
+know am i facing south or north
+otherwise you can't figure out which way
+
+ align:start position:0%
+otherwise you can't figure out which way
+ 
+
+ align:start position:0%
+otherwise you can't figure out which way
+to go
+
+ align:start position:0%
+to go
+ 
+
+ align:start position:0%
+to go
+that's called heading direction okay
+
+ align:start position:0%
+that's called heading direction okay
+ 
+
+ align:start position:0%
+that's called heading direction okay
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+okay we just did all that okay you need
+
+ align:start position:0%
+okay we just did all that okay you need
+ 
+
+ align:start position:0%
+okay we just did all that okay you need
+to know your current heading
+
+ align:start position:0%
+to know your current heading
+ 
+
+ align:start position:0%
+to know your current heading
+okay you also need to know the direction
+
+ align:start position:0%
+okay you also need to know the direction
+ 
+
+ align:start position:0%
+okay you also need to know the direction
+of your goal in order to plan a route to
+
+ align:start position:0%
+of your goal in order to plan a route to
+ 
+
+ align:start position:0%
+of your goal in order to plan a route to
+it
+
+ align:start position:0%
+it
+ 
+
+ align:start position:0%
+it
+okay so in this kind of taxonomy of all
+
+ align:start position:0%
+okay so in this kind of taxonomy of all
+ 
+
+ align:start position:0%
+okay so in this kind of taxonomy of all
+the things you need to know to navigate
+
+ align:start position:0%
+the things you need to know to navigate
+ 
+
+ align:start position:0%
+the things you need to know to navigate
+uh we've just added that if you're gonna
+
+ align:start position:0%
+uh we've just added that if you're gonna
+ 
+
+ align:start position:0%
+uh we've just added that if you're gonna
+navigate in your known environment you
+
+ align:start position:0%
+navigate in your known environment you
+ 
+
+ align:start position:0%
+navigate in your known environment you
+need to know where not just where you
+
+ align:start position:0%
+need to know where not just where you
+ 
+
+ align:start position:0%
+need to know where not just where you
+are in it
+
+ align:start position:0%
+are in it
+ 
+
+ align:start position:0%
+are in it
+but which way you are facing in that
+
+ align:start position:0%
+but which way you are facing in that
+ 
+
+ align:start position:0%
+but which way you are facing in that
+mental map
+
+ align:start position:0%
+mental map
+ 
+
+ align:start position:0%
+mental map
+okay and we also talked about this
+
+ align:start position:0%
+okay and we also talked about this
+ 
+
+ align:start position:0%
+okay and we also talked about this
+business of what routes are possible
+
+ align:start position:0%
+business of what routes are possible
+ 
+
+ align:start position:0%
+business of what routes are possible
+from here how do we move around
+
+ align:start position:0%
+from here how do we move around
+ 
+
+ align:start position:0%
+from here how do we move around
+obstacles
+
+ align:start position:0%
+obstacles
+ 
+
+ align:start position:0%
+obstacles
+uh where are the doors uh where the
+
+ align:start position:0%
+uh where are the doors uh where the
+ 
+
+ align:start position:0%
+uh where are the doors uh where the
+hazards like cars
+
+ align:start position:0%
+hazards like cars
+ 
+
+ align:start position:0%
+hazards like cars
+etc a final thing you need to know
+
+ align:start position:0%
+etc a final thing you need to know
+ 
+
+ align:start position:0%
+etc a final thing you need to know
+is that even if you have a good system
+
+ align:start position:0%
+is that even if you have a good system
+ 
+
+ align:start position:0%
+is that even if you have a good system
+for all of these other bits it's still
+
+ align:start position:0%
+for all of these other bits it's still
+ 
+
+ align:start position:0%
+for all of these other bits it's still
+possible to get lost in all kinds of
+
+ align:start position:0%
+possible to get lost in all kinds of
+ 
+
+ align:start position:0%
+possible to get lost in all kinds of
+ways you lose track you get confused you
+
+ align:start position:0%
+ways you lose track you get confused you
+ 
+
+ align:start position:0%
+ways you lose track you get confused you
+get lost
+
+ align:start position:0%
+get lost
+ 
+
+ align:start position:0%
+get lost
+so we also need a way to reorient
+
+ align:start position:0%
+so we also need a way to reorient
+ 
+
+ align:start position:0%
+so we also need a way to reorient
+ourselves when we're lost and we'll talk
+
+ align:start position:0%
+ourselves when we're lost and we'll talk
+ 
+
+ align:start position:0%
+ourselves when we're lost and we'll talk
+a lot about that in the next lecture
+
+ align:start position:0%
+a lot about that in the next lecture
+ 
+
+ align:start position:0%
+a lot about that in the next lecture
+okay so this is just common sense we're
+
+ align:start position:0%
+okay so this is just common sense we're
+ 
+
+ align:start position:0%
+okay so this is just common sense we're
+doing a kind of low-tech version of mar
+
+ align:start position:0%
+doing a kind of low-tech version of mar
+ 
+
+ align:start position:0%
+doing a kind of low-tech version of mar
+computational theory for navigation like
+
+ align:start position:0%
+computational theory for navigation like
+ 
+
+ align:start position:0%
+computational theory for navigation like
+what are the things that we would need
+
+ align:start position:0%
+what are the things that we would need
+ 
+
+ align:start position:0%
+what are the things that we would need
+to know or that a robot would need to
+
+ align:start position:0%
+to know or that a robot would need to
+ 
+
+ align:start position:0%
+to know or that a robot would need to
+know to be able to navigate
+
+ align:start position:0%
+know to be able to navigate
+ 
+
+ align:start position:0%
+know to be able to navigate
+okay just thinking about the nature of
+
+ align:start position:0%
+okay just thinking about the nature of
+ 
+
+ align:start position:0%
+okay just thinking about the nature of
+the problem
+
+ align:start position:0%
+the problem
+ 
+
+ align:start position:0%
+the problem
+all right
+
+ align:start position:0%
+all right
+ 
+
+ align:start position:0%
+all right
+so that's what we need uh what's the
+
+ align:start position:0%
+so that's what we need uh what's the
+ 
+
+ align:start position:0%
+so that's what we need uh what's the
+neural basis of all of this
+
+ align:start position:0%
+neural basis of all of this
+ 
+
+ align:start position:0%
+neural basis of all of this
+all right
+
+ align:start position:0%
+all right
+ 
+
+ align:start position:0%
+all right
+so i'm going to start right in with the
+
+ align:start position:0%
+so i'm going to start right in with the
+ 
+
+ align:start position:0%
+so i'm going to start right in with the
+parahippocampal place area not to imply
+
+ align:start position:0%
+parahippocampal place area not to imply
+ 
+
+ align:start position:0%
+parahippocampal place area not to imply
+it is the total neural neural basis of
+
+ align:start position:0%
+it is the total neural neural basis of
+ 
+
+ align:start position:0%
+it is the total neural neural basis of
+this whole thing it's just one little
+
+ align:start position:0%
+this whole thing it's just one little
+ 
+
+ align:start position:0%
+this whole thing it's just one little
+piece of a much bigger puzzle but we'll
+
+ align:start position:0%
+piece of a much bigger puzzle but we'll
+ 
+
+ align:start position:0%
+piece of a much bigger puzzle but we'll
+start in there because it's nice and
+
+ align:start position:0%
+start in there because it's nice and
+ 
+
+ align:start position:0%
+start in there because it's nice and
+concrete okay
+
+ align:start position:0%
+concrete okay
+ 
+
+ align:start position:0%
+concrete okay
+all right so this story starts oh god
+
+ align:start position:0%
+all right so this story starts oh god
+ 
+
+ align:start position:0%
+all right so this story starts oh god
+about 20 years ago uh i think i
+
+ align:start position:0%
+about 20 years ago uh i think i
+ 
+
+ align:start position:0%
+about 20 years ago uh i think i
+mentioned some of this in the first
+
+ align:start position:0%
+mentioned some of this in the first
+ 
+
+ align:start position:0%
+mentioned some of this in the first
+class when i talked about the story of
+
+ align:start position:0%
+class when i talked about the story of
+ 
+
+ align:start position:0%
+class when i talked about the story of
+bob and i talked about russell epstein
+
+ align:start position:0%
+bob and i talked about russell epstein
+ 
+
+ align:start position:0%
+bob and i talked about russell epstein
+who was in my postdoc
+
+ align:start position:0%
+who was in my postdoc
+ 
+
+ align:start position:0%
+who was in my postdoc
+and it was doing nice behavioral
+
+ align:start position:0%
+and it was doing nice behavioral
+ 
+
+ align:start position:0%
+and it was doing nice behavioral
+experiments and thought it was trashy
+
+ align:start position:0%
+experiments and thought it was trashy
+ 
+
+ align:start position:0%
+experiments and thought it was trashy
+and cheap to mess around with brain
+
+ align:start position:0%
+and cheap to mess around with brain
+ 
+
+ align:start position:0%
+and cheap to mess around with brain
+imaging and he was going to have none of
+
+ align:start position:0%
+imaging and he was going to have none of
+ 
+
+ align:start position:0%
+imaging and he was going to have none of
+it until i said russell just do one
+
+ align:start position:0%
+it until i said russell just do one
+ 
+
+ align:start position:0%
+it until i said russell just do one
+experiment scan subject looking at
+
+ align:start position:0%
+experiment scan subject looking at
+ 
+
+ align:start position:0%
+experiment scan subject looking at
+scenes i know it's kind of stupid but
+
+ align:start position:0%
+scenes i know it's kind of stupid but
+ 
+
+ align:start position:0%
+scenes i know it's kind of stupid but
+just do it then you'll have a slide for
+
+ align:start position:0%
+just do it then you'll have a slide for
+ 
+
+ align:start position:0%
+just do it then you'll have a slide for
+your job talk
+
+ align:start position:0%
+your job talk
+ 
+
+ align:start position:0%
+your job talk
+and he scans subjects looking at scenes
+
+ align:start position:0%
+and he scans subjects looking at scenes
+ 
+
+ align:start position:0%
+and he scans subjects looking at scenes
+and looking at objects and here is one
+
+ align:start position:0%
+and looking at objects and here is one
+ 
+
+ align:start position:0%
+and looking at objects and here is one
+of those early subjects probably me i
+
+ align:start position:0%
+of those early subjects probably me i
+ 
+
+ align:start position:0%
+of those early subjects probably me i
+don't remember
+
+ align:start position:0%
+don't remember
+ 
+
+ align:start position:0%
+don't remember
+with a bunch of vertical slices through
+
+ align:start position:0%
+with a bunch of vertical slices through
+ 
+
+ align:start position:0%
+with a bunch of vertical slices through
+the brain near the back of the brain
+
+ align:start position:0%
+the brain near the back of the brain
+ 
+
+ align:start position:0%
+the brain near the back of the brain
+down there moving forward as we go up to
+
+ align:start position:0%
+down there moving forward as we go up to
+ 
+
+ align:start position:0%
+down there moving forward as we go up to
+here everybody oriented
+
+ align:start position:0%
+here everybody oriented
+ 
+
+ align:start position:0%
+here everybody oriented
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+so sorry it's not showing up very well
+
+ align:start position:0%
+so sorry it's not showing up very well
+ 
+
+ align:start position:0%
+so sorry it's not showing up very well
+in this lighting but there's a little
+
+ align:start position:0%
+in this lighting but there's a little
+ 
+
+ align:start position:0%
+in this lighting but there's a little
+bilateral region right in the middle
+
+ align:start position:0%
+bilateral region right in the middle
+ 
+
+ align:start position:0%
+bilateral region right in the middle
+there that shows a stronger response
+
+ align:start position:0%
+there that shows a stronger response
+ 
+
+ align:start position:0%
+there that shows a stronger response
+when people look at pictures of scenes
+
+ align:start position:0%
+when people look at pictures of scenes
+ 
+
+ align:start position:0%
+when people look at pictures of scenes
+than when they look at pictures of
+
+ align:start position:0%
+than when they look at pictures of
+ 
+
+ align:start position:0%
+than when they look at pictures of
+objects
+
+ align:start position:0%
+objects
+ 
+
+ align:start position:0%
+objects
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+we didn't we hadn't predicted this yeah
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah yeah pink yeah pink is yeah all the
+
+ align:start position:0%
+yeah yeah pink yeah pink is yeah all the
+ 
+
+ align:start position:0%
+yeah yeah pink yeah pink is yeah all the
+colors are um there's significance maps
+
+ align:start position:0%
+colors are um there's significance maps
+ 
+
+ align:start position:0%
+colors are um there's significance maps
+or p levels right so pink is higher than
+
+ align:start position:0%
+or p levels right so pink is higher than
+ 
+
+ align:start position:0%
+or p levels right so pink is higher than
+blue but you know blue is borderline
+
+ align:start position:0%
+blue but you know blue is borderline
+ 
+
+ align:start position:0%
+blue but you know blue is borderline
+significant
+
+ align:start position:0%
+significant
+ 
+
+ align:start position:0%
+significant
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+so this was kind of dopey we didn't
+
+ align:start position:0%
+so this was kind of dopey we didn't
+ 
+
+ align:start position:0%
+so this was kind of dopey we didn't
+actually predict it for any deep reason
+
+ align:start position:0%
+actually predict it for any deep reason
+ 
+
+ align:start position:0%
+actually predict it for any deep reason
+we hadn't been thinking about theories
+
+ align:start position:0%
+we hadn't been thinking about theories
+ 
+
+ align:start position:0%
+we hadn't been thinking about theories
+of navigation or anything like that it
+
+ align:start position:0%
+of navigation or anything like that it
+ 
+
+ align:start position:0%
+of navigation or anything like that it
+was just one of those dumb experiments
+
+ align:start position:0%
+was just one of those dumb experiments
+ 
+
+ align:start position:0%
+was just one of those dumb experiments
+where we found something and we followed
+
+ align:start position:0%
+where we found something and we followed
+ 
+
+ align:start position:0%
+where we found something and we followed
+the data so we found this and it's like
+
+ align:start position:0%
+the data so we found this and it's like
+ 
+
+ align:start position:0%
+the data so we found this and it's like
+okay let's try some other subjects
+
+ align:start position:0%
+okay let's try some other subjects
+ 
+
+ align:start position:0%
+okay let's try some other subjects
+so here are the first nine subjects we
+
+ align:start position:0%
+so here are the first nine subjects we
+ 
+
+ align:start position:0%
+so here are the first nine subjects we
+scanned every single subject had that
+
+ align:start position:0%
+scanned every single subject had that
+ 
+
+ align:start position:0%
+scanned every single subject had that
+kind of signature response in exactly
+
+ align:start position:0%
+kind of signature response in exactly
+ 
+
+ align:start position:0%
+kind of signature response in exactly
+the same place
+
+ align:start position:0%
+the same place
+ 
+
+ align:start position:0%
+the same place
+okay in a part of the brain called
+
+ align:start position:0%
+okay in a part of the brain called
+ 
+
+ align:start position:0%
+okay in a part of the brain called
+parahippocampal cortex
+
+ align:start position:0%
+parahippocampal cortex
+ 
+
+ align:start position:0%
+parahippocampal cortex
+okay so this is very systematic and
+
+ align:start position:0%
+okay so this is very systematic and
+ 
+
+ align:start position:0%
+okay so this is very systematic and
+there's lots of ways to make progress in
+
+ align:start position:0%
+there's lots of ways to make progress in
+ 
+
+ align:start position:0%
+there's lots of ways to make progress in
+science one way is to have a big theory
+
+ align:start position:0%
+science one way is to have a big theory
+ 
+
+ align:start position:0%
+science one way is to have a big theory
+and use it to motivate
+
+ align:start position:0%
+and use it to motivate
+ 
+
+ align:start position:0%
+and use it to motivate
+brilliant elegantly designed experiments
+
+ align:start position:0%
+brilliant elegantly designed experiments
+ 
+
+ align:start position:0%
+brilliant elegantly designed experiments
+and another is you just see something
+
+ align:start position:0%
+and another is you just see something
+ 
+
+ align:start position:0%
+and another is you just see something
+salient and robust that you didn't
+
+ align:start position:0%
+salient and robust that you didn't
+ 
+
+ align:start position:0%
+salient and robust that you didn't
+predict and you follow your nose and try
+
+ align:start position:0%
+predict and you follow your nose and try
+ 
+
+ align:start position:0%
+predict and you follow your nose and try
+to figure it out so that's what we did
+
+ align:start position:0%
+to figure it out so that's what we did
+ 
+
+ align:start position:0%
+to figure it out so that's what we did
+in this case it's like okay what the
+
+ align:start position:0%
+in this case it's like okay what the
+ 
+
+ align:start position:0%
+in this case it's like okay what the
+hell is that
+
+ align:start position:0%
+hell is that
+ 
+
+ align:start position:0%
+hell is that
+all right
+
+ align:start position:0%
+all right
+ 
+
+ align:start position:0%
+all right
+so um
+
+ align:start position:0%
+so um
+ 
+
+ align:start position:0%
+so um
+if you think about we eventually called
+
+ align:start position:0%
+if you think about we eventually called
+ 
+
+ align:start position:0%
+if you think about we eventually called
+it the para campbell place area after a
+
+ align:start position:0%
+it the para campbell place area after a
+ 
+
+ align:start position:0%
+it the para campbell place area after a
+little more work
+
+ align:start position:0%
+little more work
+ 
+
+ align:start position:0%
+little more work
+if you think about what we have so far
+
+ align:start position:0%
+if you think about what we have so far
+ 
+
+ align:start position:0%
+if you think about what we have so far
+we've scanned people looking at pictures
+
+ align:start position:0%
+we've scanned people looking at pictures
+ 
+
+ align:start position:0%
+we've scanned people looking at pictures
+like this and pictures like that and
+
+ align:start position:0%
+like this and pictures like that and
+ 
+
+ align:start position:0%
+like this and pictures like that and
+what we've shown is that little patch of
+
+ align:start position:0%
+what we've shown is that little patch of
+ 
+
+ align:start position:0%
+what we've shown is that little patch of
+brain responds a bunch more to these
+
+ align:start position:0%
+brain responds a bunch more to these
+ 
+
+ align:start position:0%
+brain responds a bunch more to these
+than those
+
+ align:start position:0%
+than those
+ 
+
+ align:start position:0%
+than those
+so my first question is is that a
+
+ align:start position:0%
+so my first question is is that a
+ 
+
+ align:start position:0%
+so my first question is is that a
+minimal pair
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+talia's had a minimal pair sorry i'm
+
+ align:start position:0%
+talia's had a minimal pair sorry i'm
+ 
+
+ align:start position:0%
+talia's had a minimal pair sorry i'm
+like
+
+ align:start position:0%
+like
+ 
+
+ align:start position:0%
+like
+boys
+
+ align:start position:0%
+boys
+ 
+
+ align:start position:0%
+boys
+sorry simple simple simple we're
+
+ align:start position:0%
+sorry simple simple simple we're
+ 
+
+ align:start position:0%
+sorry simple simple simple we're
+contrasting this with that
+
+ align:start position:0%
+contrasting this with that
+ 
+
+ align:start position:0%
+contrasting this with that
+um can you remind me what i'm going to
+
+ align:start position:0%
+um can you remind me what i'm going to
+ 
+
+ align:start position:0%
+um can you remind me what i'm going to
+do okay minimal pair is this thing we
+
+ align:start position:0%
+do okay minimal pair is this thing we
+ 
+
+ align:start position:0%
+do okay minimal pair is this thing we
+aspire towards in experimental design
+
+ align:start position:0%
+aspire towards in experimental design
+ 
+
+ align:start position:0%
+aspire towards in experimental design
+where we have two conditions that are
+
+ align:start position:0%
+where we have two conditions that are
+ 
+
+ align:start position:0%
+where we have two conditions that are
+identical except for one little thing
+
+ align:start position:0%
+identical except for one little thing
+ 
+
+ align:start position:0%
+identical except for one little thing
+we're manipulating
+
+ align:start position:0%
+we're manipulating
+ 
+
+ align:start position:0%
+we're manipulating
+i
+
+ align:start position:0%
+i
+ 
+
+ align:start position:0%
+i
+don't i don't really think it's a
+
+ align:start position:0%
+don't i don't really think it's a
+ 
+
+ align:start position:0%
+don't i don't really think it's a
+minimal pair but i'm not really sure
+
+ align:start position:0%
+minimal pair but i'm not really sure
+ 
+
+ align:start position:0%
+minimal pair but i'm not really sure
+like
+
+ align:start position:0%
+like
+ 
+
+ align:start position:0%
+like
+well i even told you what we were
+
+ align:start position:0%
+well i even told you what we were
+ 
+
+ align:start position:0%
+well i even told you what we were
+designing to manipulate but
+
+ align:start position:0%
+designing to manipulate but
+ 
+
+ align:start position:0%
+designing to manipulate but
+there seems to be like too many
+
+ align:start position:0%
+there seems to be like too many
+ 
+
+ align:start position:0%
+there seems to be like too many
+differences between the living room and
+
+ align:start position:0%
+differences between the living room and
+ 
+
+ align:start position:0%
+differences between the living room and
+like
+
+ align:start position:0%
+like
+ 
+
+ align:start position:0%
+like
+it's ludicrous right i mean it's a
+
+ align:start position:0%
+it's ludicrous right i mean it's a
+ 
+
+ align:start position:0%
+it's ludicrous right i mean it's a
+million differences here right so we
+
+ align:start position:0%
+million differences here right so we
+ 
+
+ align:start position:0%
+million differences here right so we
+don't know that we have anything yet
+
+ align:start position:0%
+don't know that we have anything yet
+ 
+
+ align:start position:0%
+don't know that we have anything yet
+there's all kinds of uninteresting
+
+ align:start position:0%
+there's all kinds of uninteresting
+ 
+
+ align:start position:0%
+there's all kinds of uninteresting
+accounts of the systematic activation in
+
+ align:start position:0%
+accounts of the systematic activation in
+ 
+
+ align:start position:0%
+accounts of the systematic activation in
+that part of the brain right so just to
+
+ align:start position:0%
+that part of the brain right so just to
+ 
+
+ align:start position:0%
+that part of the brain right so just to
+list a few that you've probably already
+
+ align:start position:0%
+list a few that you've probably already
+ 
+
+ align:start position:0%
+list a few that you've probably already
+noticed
+
+ align:start position:0%
+noticed
+ 
+
+ align:start position:0%
+noticed
+these things have rich high level
+
+ align:start position:0%
+these things have rich high level
+ 
+
+ align:start position:0%
+these things have rich high level
+meaning and complexity right so you
+
+ align:start position:0%
+meaning and complexity right so you
+ 
+
+ align:start position:0%
+meaning and complexity right so you
+could think about living rooms or where
+
+ align:start position:0%
+could think about living rooms or where
+ 
+
+ align:start position:0%
+could think about living rooms or where
+you might sit or you know somebody's
+
+ align:start position:0%
+you might sit or you know somebody's
+ 
+
+ align:start position:0%
+you might sit or you know somebody's
+aesthetic
+
+ align:start position:0%
+aesthetic
+ 
+
+ align:start position:0%
+aesthetic
+you know home design or you know god
+
+ align:start position:0%
+you know home design or you know god
+ 
+
+ align:start position:0%
+you know home design or you know god
+there's all kinds of stuff to think
+
+ align:start position:0%
+there's all kinds of stuff to think
+ 
+
+ align:start position:0%
+there's all kinds of stuff to think
+about there
+
+ align:start position:0%
+about there
+ 
+
+ align:start position:0%
+about there
+much more than just okay it's a blender
+
+ align:start position:0%
+much more than just okay it's a blender
+ 
+
+ align:start position:0%
+much more than just okay it's a blender
+right so there's just just complexity in
+
+ align:start position:0%
+right so there's just just complexity in
+ 
+
+ align:start position:0%
+right so there's just just complexity in
+every possible way
+
+ align:start position:0%
+every possible way
+ 
+
+ align:start position:0%
+every possible way
+there are also
+
+ align:start position:0%
+there are also
+ 
+
+ align:start position:0%
+there are also
+lots of objects present here
+
+ align:start position:0%
+lots of objects present here
+ 
+
+ align:start position:0%
+lots of objects present here
+and only a single object over there so
+
+ align:start position:0%
+and only a single object over there so
+ 
+
+ align:start position:0%
+and only a single object over there so
+maybe that region it just represents
+
+ align:start position:0%
+maybe that region it just represents
+ 
+
+ align:start position:0%
+maybe that region it just represents
+objects and if you have more objects you
+
+ align:start position:0%
+objects and if you have more objects you
+ 
+
+ align:start position:0%
+objects and if you have more objects you
+get a higher signal right
+
+ align:start position:0%
+get a higher signal right
+ 
+
+ align:start position:0%
+get a higher signal right
+there's another possibility
+
+ align:start position:0%
+there's another possibility
+ 
+
+ align:start position:0%
+there's another possibility
+and that is that these images depict
+
+ align:start position:0%
+and that is that these images depict
+ 
+
+ align:start position:0%
+and that is that these images depict
+spatial layout and that one does not
+
+ align:start position:0%
+spatial layout and that one does not
+ 
+
+ align:start position:0%
+spatial layout and that one does not
+okay so you have some sense of the walls
+
+ align:start position:0%
+okay so you have some sense of the walls
+ 
+
+ align:start position:0%
+okay so you have some sense of the walls
+and the floor and like the layout of the
+
+ align:start position:0%
+and the floor and like the layout of the
+ 
+
+ align:start position:0%
+and the floor and like the layout of the
+local environment here that you don't
+
+ align:start position:0%
+local environment here that you don't
+ 
+
+ align:start position:0%
+local environment here that you don't
+have over there
+
+ align:start position:0%
+have over there
+ 
+
+ align:start position:0%
+have over there
+all right and we could probably list a
+
+ align:start position:0%
+all right and we could probably list a
+ 
+
+ align:start position:0%
+all right and we could probably list a
+million other things okay that's a very
+
+ align:start position:0%
+million other things okay that's a very
+ 
+
+ align:start position:0%
+million other things okay that's a very
+very sloppy contrast
+
+ align:start position:0%
+very sloppy contrast
+ 
+
+ align:start position:0%
+very sloppy contrast
+okay so how are we going to ask which of
+
+ align:start position:0%
+okay so how are we going to ask which of
+ 
+
+ align:start position:0%
+okay so how are we going to ask which of
+these things might be driving the
+
+ align:start position:0%
+these things might be driving the
+ 
+
+ align:start position:0%
+these things might be driving the
+response of that region
+
+ align:start position:0%
+response of that region
+ 
+
+ align:start position:0%
+response of that region
+well
+
+ align:start position:0%
+well
+ 
+
+ align:start position:0%
+well
+a natural thing to do is just
+
+ align:start position:0%
+a natural thing to do is just
+ 
+
+ align:start position:0%
+a natural thing to do is just
+deconstruct the stimuli
+
+ align:start position:0%
+deconstruct the stimuli
+ 
+
+ align:start position:0%
+deconstruct the stimuli
+so here's what we did uh this is
+
+ align:start position:0%
+so here's what we did uh this is
+ 
+
+ align:start position:0%
+so here's what we did uh this is
+actually way back 20 years ago there
+
+ align:start position:0%
+actually way back 20 years ago there
+ 
+
+ align:start position:0%
+actually way back 20 years ago there
+were better methods at the time but i
+
+ align:start position:0%
+were better methods at the time but i
+ 
+
+ align:start position:0%
+were better methods at the time but i
+didn't know them so i actually drove
+
+ align:start position:0%
+didn't know them so i actually drove
+ 
+
+ align:start position:0%
+didn't know them so i actually drove
+around cambridge photographs my friends
+
+ align:start position:0%
+around cambridge photographs my friends
+ 
+
+ align:start position:0%
+around cambridge photographs my friends
+apartments left the camera on the same
+
+ align:start position:0%
+apartments left the camera on the same
+ 
+
+ align:start position:0%
+apartments left the camera on the same
+tripod moved all the furniture out of
+
+ align:start position:0%
+tripod moved all the furniture out of
+ 
+
+ align:start position:0%
+tripod moved all the furniture out of
+the way and photographed the space again
+
+ align:start position:0%
+the way and photographed the space again
+ 
+
+ align:start position:0%
+the way and photographed the space again
+i know
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and then these we probably cut out with
+
+ align:start position:0%
+and then these we probably cut out with
+ 
+
+ align:start position:0%
+and then these we probably cut out with
+some
+
+ align:start position:0%
+some
+ 
+
+ align:start position:0%
+some
+horrific version of adobe photoshop that
+
+ align:start position:0%
+horrific version of adobe photoshop that
+ 
+
+ align:start position:0%
+horrific version of adobe photoshop that
+existed 20 years ago
+
+ align:start position:0%
+existed 20 years ago
+ 
+
+ align:start position:0%
+existed 20 years ago
+anyway we deconstructed the scenes into
+
+ align:start position:0%
+anyway we deconstructed the scenes into
+ 
+
+ align:start position:0%
+anyway we deconstructed the scenes into
+their component objects and the bare
+
+ align:start position:0%
+their component objects and the bare
+ 
+
+ align:start position:0%
+their component objects and the bare
+spatial layout
+
+ align:start position:0%
+spatial layout
+ 
+
+ align:start position:0%
+spatial layout
+okay everybody get the logic here just
+
+ align:start position:0%
+okay everybody get the logic here just
+ 
+
+ align:start position:0%
+okay everybody get the logic here just
+to try to make a big cut in this
+
+ align:start position:0%
+to try to make a big cut in this
+ 
+
+ align:start position:0%
+to try to make a big cut in this
+hypothesis space of what might be
+
+ align:start position:0%
+hypothesis space of what might be
+ 
+
+ align:start position:0%
+hypothesis space of what might be
+driving that region
+
+ align:start position:0%
+driving that region
+ 
+
+ align:start position:0%
+driving that region
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+so what do we predict that the ppa will
+
+ align:start position:0%
+so what do we predict that the ppa will
+ 
+
+ align:start position:0%
+so what do we predict that the ppa will
+resp how how strongly will it respond
+
+ align:start position:0%
+resp how how strongly will it respond
+ 
+
+ align:start position:0%
+resp how how strongly will it respond
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+oops
+
+ align:start position:0%
+oops
+ 
+
+ align:start position:0%
+oops
+how strongly will it respond if these
+
+ align:start position:0%
+how strongly will it respond if these
+ 
+
+ align:start position:0%
+how strongly will it respond if these
+two things are true if it's a complexity
+
+ align:start position:0%
+two things are true if it's a complexity
+ 
+
+ align:start position:0%
+two things are true if it's a complexity
+or multiplicity of objects that's
+
+ align:start position:0%
+or multiplicity of objects that's
+ 
+
+ align:start position:0%
+or multiplicity of objects that's
+driving it what do you predict we will
+
+ align:start position:0%
+driving it what do you predict we will
+ 
+
+ align:start position:0%
+driving it what do you predict we will
+see over there we already know you get a
+
+ align:start position:0%
+see over there we already know you get a
+ 
+
+ align:start position:0%
+see over there we already know you get a
+high response here what do we get over
+
+ align:start position:0%
+high response here what do we get over
+ 
+
+ align:start position:0%
+high response here what do we get over
+there
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah probably
+
+ align:start position:0%
+yeah probably
+ 
+
+ align:start position:0%
+yeah probably
+yeah we'll respond more to this than
+
+ align:start position:0%
+yeah we'll respond more to this than
+ 
+
+ align:start position:0%
+yeah we'll respond more to this than
+that
+
+ align:start position:0%
+that
+ 
+
+ align:start position:0%
+that
+right it's really simple-minded right
+
+ align:start position:0%
+right it's really simple-minded right
+ 
+
+ align:start position:0%
+right it's really simple-minded right
+if ins if instead it responds more to
+
+ align:start position:0%
+if ins if instead it responds more to
+ 
+
+ align:start position:0%
+if ins if instead it responds more to
+the spatial layout
+
+ align:start position:0%
+the spatial layout
+ 
+
+ align:start position:0%
+the spatial layout
+what do we predict
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the is
+
+ align:start position:0%
+the is
+ 
+
+ align:start position:0%
+the is
+yeah
+
+ align:start position:0%
+yeah
+ 
+
+ align:start position:0%
+yeah
+and that seems like a weird hypothesis
+
+ align:start position:0%
+and that seems like a weird hypothesis
+ 
+
+ align:start position:0%
+and that seems like a weird hypothesis
+because these are really boring there's
+
+ align:start position:0%
+because these are really boring there's
+ 
+
+ align:start position:0%
+because these are really boring there's
+kind of nothing going on here and
+
+ align:start position:0%
+kind of nothing going on here and
+ 
+
+ align:start position:0%
+kind of nothing going on here and
+there's just lots of stuff going on here
+
+ align:start position:0%
+there's just lots of stuff going on here
+ 
+
+ align:start position:0%
+there's just lots of stuff going on here
+i mean it's not riveting but it's a
+
+ align:start position:0%
+i mean it's not riveting but it's a
+ 
+
+ align:start position:0%
+i mean it's not riveting but it's a
+whole much
+
+ align:start position:0%
+whole much
+ 
+
+ align:start position:0%
+whole much
+whole lot more interesting to look at
+
+ align:start position:0%
+whole lot more interesting to look at
+ 
+
+ align:start position:0%
+whole lot more interesting to look at
+these than those believe me i got
+
+ align:start position:0%
+these than those believe me i got
+ 
+
+ align:start position:0%
+these than those believe me i got
+scanned for hours and hours looking at
+
+ align:start position:0%
+scanned for hours and hours looking at
+ 
+
+ align:start position:0%
+scanned for hours and hours looking at
+these things and whenever the empty
+
+ align:start position:0%
+these things and whenever the empty
+ 
+
+ align:start position:0%
+these things and whenever the empty
+rooms came on i was like oh my god i'm
+
+ align:start position:0%
+rooms came on i was like oh my god i'm
+ 
+
+ align:start position:0%
+rooms came on i was like oh my god i'm
+just so bored right there's just nothing
+
+ align:start position:0%
+just so bored right there's just nothing
+ 
+
+ align:start position:0%
+just so bored right there's just nothing
+here whereas here at least there's stuff
+
+ align:start position:0%
+here whereas here at least there's stuff
+ 
+
+ align:start position:0%
+here whereas here at least there's stuff
+right
+
+ align:start position:0%
+right
+ 
+
+ align:start position:0%
+right
+but that's not what the ppa thinks
+
+ align:start position:0%
+but that's not what the ppa thinks
+ 
+
+ align:start position:0%
+but that's not what the ppa thinks
+what the pva does oops
+
+ align:start position:0%
+what the pva does oops
+ 
+
+ align:start position:0%
+what the pva does oops
+oops we just did the localizer okay
+
+ align:start position:0%
+oops we just did the localizer okay
+ 
+
+ align:start position:0%
+oops we just did the localizer okay
+it responds like this this is percent
+
+ align:start position:0%
+it responds like this this is percent
+ 
+
+ align:start position:0%
+it responds like this this is percent
+signal change a measure of magnitude of
+
+ align:start position:0%
+signal change a measure of magnitude of
+ 
+
+ align:start position:0%
+signal change a measure of magnitude of
+response to the full scenes
+
+ align:start position:0%
+response to the full scenes
+ 
+
+ align:start position:0%
+response to the full scenes
+way down less than half the response to
+
+ align:start position:0%
+way down less than half the response to
+ 
+
+ align:start position:0%
+way down less than half the response to
+all those objects and almost the same
+
+ align:start position:0%
+all those objects and almost the same
+ 
+
+ align:start position:0%
+all those objects and almost the same
+response as the original scene
+
+ align:start position:0%
+response as the original scene
+ 
+
+ align:start position:0%
+response as the original scene
+when all you have is a bare spatial
+
+ align:start position:0%
+when all you have is a bare spatial
+ 
+
+ align:start position:0%
+when all you have is a bare spatial
+layout
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+pretty surprising isn't it
+
+ align:start position:0%
+pretty surprising isn't it
+ 
+
+ align:start position:0%
+pretty surprising isn't it
+we were blown away we're like what what
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+but can you see how even this really
+
+ align:start position:0%
+but can you see how even this really
+ 
+
+ align:start position:0%
+but can you see how even this really
+simple-minded experiment enables us to
+
+ align:start position:0%
+simple-minded experiment enables us to
+ 
+
+ align:start position:0%
+simple-minded experiment enables us to
+just pretty much rule out that whole
+
+ align:start position:0%
+just pretty much rule out that whole
+ 
+
+ align:start position:0%
+just pretty much rule out that whole
+space of hypotheses it's not about the
+
+ align:start position:0%
+space of hypotheses it's not about the
+ 
+
+ align:start position:0%
+space of hypotheses it's not about the
+richness or interest or multiplicity of
+
+ align:start position:0%
+richness or interest or multiplicity of
+ 
+
+ align:start position:0%
+richness or interest or multiplicity of
+objects
+
+ align:start position:0%
+objects
+ 
+
+ align:start position:0%
+objects
+it's something much more like spatial
+
+ align:start position:0%
+it's something much more like spatial
+ 
+
+ align:start position:0%
+it's something much more like spatial
+layout because that's kind of all there
+
+ align:start position:0%
+layout because that's kind of all there
+ 
+
+ align:start position:0%
+layout because that's kind of all there
+is in those empty rooms
+
+ align:start position:0%
+is in those empty rooms
+ 
+
+ align:start position:0%
+is in those empty rooms
+i mean it could be something like you
+
+ align:start position:0%
+i mean it could be something like you
+ 
+
+ align:start position:0%
+i mean it could be something like you
+know the texture of wood floors or
+
+ align:start position:0%
+know the texture of wood floors or
+ 
+
+ align:start position:0%
+know the texture of wood floors or
+something weird like that
+
+ align:start position:0%
+something weird like that
+ 
+
+ align:start position:0%
+something weird like that
+but one's first guess is it's something
+
+ align:start position:0%
+but one's first guess is it's something
+ 
+
+ align:start position:0%
+but one's first guess is it's something
+about spatial layout does this make
+
+ align:start position:0%
+about spatial layout does this make
+ 
+
+ align:start position:0%
+about spatial layout does this make
+sense it's just a way to take a
+
+ align:start position:0%
+sense it's just a way to take a
+ 
+
+ align:start position:0%
+sense it's just a way to take a
+a big sloppy contrast and try to
+
+ align:start position:0%
+a big sloppy contrast and try to
+ 
+
+ align:start position:0%
+a big sloppy contrast and try to
+formulate initial hypotheses and knock
+
+ align:start position:0%
+formulate initial hypotheses and knock
+ 
+
+ align:start position:0%
+formulate initial hypotheses and knock
+out a whole big space of hypotheses yes
+
+ align:start position:0%
+out a whole big space of hypotheses yes
+ 
+
+ align:start position:0%
+out a whole big space of hypotheses yes
+is it alana yeah yeah
+
+ align:start position:0%
+is it alana yeah yeah
+ 
+
+ align:start position:0%
+is it alana yeah yeah
+i'm sorry i might have missed your
+
+ align:start position:0%
+i'm sorry i might have missed your
+ 
+
+ align:start position:0%
+i'm sorry i might have missed your
+original design
+
+ align:start position:0%
+original design
+ 
+
+ align:start position:0%
+original design
+looking at the empty room
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+ah good question i skipped over all of
+
+ align:start position:0%
+ah good question i skipped over all of
+ 
+
+ align:start position:0%
+ah good question i skipped over all of
+that
+
+ align:start position:0%
+that
+ 
+
+ align:start position:0%
+that
+uh we didn't
+
+ align:start position:0%
+uh we didn't
+ 
+
+ align:start position:0%
+uh we didn't
+we did yes that's true we did mush them
+
+ align:start position:0%
+we did yes that's true we did mush them
+ 
+
+ align:start position:0%
+we did yes that's true we did mush them
+all together and one could worry about
+
+ align:start position:0%
+all together and one could worry about
+ 
+
+ align:start position:0%
+all together and one could worry about
+that
+
+ align:start position:0%
+that
+ 
+
+ align:start position:0%
+that
+that when you see this you remember that
+
+ align:start position:0%
+that when you see this you remember that
+ 
+
+ align:start position:0%
+that when you see this you remember that
+that's a version of this
+
+ align:start position:0%
+that's a version of this
+ 
+
+ align:start position:0%
+that's a version of this
+right
+
+ align:start position:0%
+right
+ 
+
+ align:start position:0%
+right
+absolutely
+
+ align:start position:0%
+absolutely
+ 
+
+ align:start position:0%
+absolutely
+absolutely
+
+ align:start position:0%
+absolutely
+ 
+
+ align:start position:0%
+absolutely
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+and so maybe yes
+
+ align:start position:0%
+and so maybe yes
+ 
+
+ align:start position:0%
+and so maybe yes
+um nonetheless if what you were doing
+
+ align:start position:0%
+um nonetheless if what you were doing
+ 
+
+ align:start position:0%
+um nonetheless if what you were doing
+that's absolutely true but if what you
+
+ align:start position:0%
+that's absolutely true but if what you
+ 
+
+ align:start position:0%
+that's absolutely true but if what you
+were doing here
+
+ align:start position:0%
+were doing here
+ 
+
+ align:start position:0%
+were doing here
+is kind of mentally recalling this
+
+ align:start position:0%
+is kind of mentally recalling this
+ 
+
+ align:start position:0%
+is kind of mentally recalling this
+right then why couldn't you also do that
+
+ align:start position:0%
+right then why couldn't you also do that
+ 
+
+ align:start position:0%
+right then why couldn't you also do that
+here
+
+ align:start position:0%
+here
+ 
+
+ align:start position:0%
+here
+maybe you could
+
+ align:start position:0%
+maybe you could
+ 
+
+ align:start position:0%
+maybe you could
+you might argue that this is more
+
+ align:start position:0%
+you might argue that this is more
+ 
+
+ align:start position:0%
+you might argue that this is more
+evocative of that than this is but it's
+
+ align:start position:0%
+evocative of that than this is but it's
+ 
+
+ align:start position:0%
+evocative of that than this is but it's
+also got lots of relevant information
+
+ align:start position:0%
+also got lots of relevant information
+ 
+
+ align:start position:0%
+also got lots of relevant information
+okay yeah jimmy you
+
+ align:start position:0%
+okay yeah jimmy you
+ 
+
+ align:start position:0%
+okay yeah jimmy you
+guys the furniture do you guys try
+
+ align:start position:0%
+guys the furniture do you guys try
+ 
+
+ align:start position:0%
+guys the furniture do you guys try
+placing them in the same exact position
+
+ align:start position:0%
+placing them in the same exact position
+ 
+
+ align:start position:0%
+placing them in the same exact position
+as the scene and seeing if that we did
+
+ align:start position:0%
+as the scene and seeing if that we did
+ 
+
+ align:start position:0%
+as the scene and seeing if that we did
+both versions for exactly the reasons
+
+ align:start position:0%
+both versions for exactly the reasons
+ 
+
+ align:start position:0%
+both versions for exactly the reasons
+you guys are pointing out uh and it
+
+ align:start position:0%
+you guys are pointing out uh and it
+ 
+
+ align:start position:0%
+you guys are pointing out uh and it
+didn't make a difference
+
+ align:start position:0%
+didn't make a difference
+ 
+
+ align:start position:0%
+didn't make a difference
+yeah
+
+ align:start position:0%
+yeah
+ 
+
+ align:start position:0%
+yeah
+yeah uh sorry coolly uh maybe did you
+
+ align:start position:0%
+yeah uh sorry coolly uh maybe did you
+ 
+
+ align:start position:0%
+yeah uh sorry coolly uh maybe did you
+turn for if the if they were just like
+
+ align:start position:0%
+turn for if the if they were just like
+ 
+
+ align:start position:0%
+turn for if the if they were just like
+responding to that there's like
+
+ align:start position:0%
+responding to that there's like
+ 
+
+ align:start position:0%
+responding to that there's like
+more
+
+ align:start position:0%
+more
+ 
+
+ align:start position:0%
+more
+stuff
+
+ align:start position:0%
+stuff
+ 
+
+ align:start position:0%
+stuff
+like in the empty room
+
+ align:start position:0%
+like in the empty room
+ 
+
+ align:start position:0%
+like in the empty room
+there's more background but there's did
+
+ align:start position:0%
+there's more background but there's did
+ 
+
+ align:start position:0%
+there's more background but there's did
+more background totally you're
+
+ align:start position:0%
+more background totally you're
+ 
+
+ align:start position:0%
+more background totally you're
+absolutely right this has taken us
+
+ align:start position:0%
+absolutely right this has taken us
+ 
+
+ align:start position:0%
+absolutely right this has taken us
+pretty far but it's still pretty sloppy
+
+ align:start position:0%
+pretty far but it's still pretty sloppy
+ 
+
+ align:start position:0%
+pretty far but it's still pretty sloppy
+this stuff goes all the way out to the
+
+ align:start position:0%
+this stuff goes all the way out to the
+ 
+
+ align:start position:0%
+this stuff goes all the way out to the
+edge of the frame and here there's lots
+
+ align:start position:0%
+edge of the frame and here there's lots
+ 
+
+ align:start position:0%
+edge of the frame and here there's lots
+of empty space is that what you're
+
+ align:start position:0%
+of empty space is that what you're
+ 
+
+ align:start position:0%
+of empty space is that what you're
+getting at
+
+ align:start position:0%
+getting at
+ 
+
+ align:start position:0%
+getting at
+absolutely i took out those slides
+
+ align:start position:0%
+absolutely i took out those slides
+ 
+
+ align:start position:0%
+absolutely i took out those slides
+because i felt i didn't want to spend
+
+ align:start position:0%
+because i felt i didn't want to spend
+ 
+
+ align:start position:0%
+because i felt i didn't want to spend
+the entire lecture doing millions of
+
+ align:start position:0%
+the entire lecture doing millions of
+ 
+
+ align:start position:0%
+the entire lecture doing millions of
+control conditions on the ppa i thought
+
+ align:start position:0%
+control conditions on the ppa i thought
+ 
+
+ align:start position:0%
+control conditions on the ppa i thought
+you'd get bored but actually another
+
+ align:start position:0%
+you'd get bored but actually another
+ 
+
+ align:start position:0%
+you'd get bored but actually another
+version
+
+ align:start position:0%
+version
+ 
+
+ align:start position:0%
+version
+that we did was we then
+
+ align:start position:0%
+that we did was we then
+ 
+
+ align:start position:0%
+that we did was we then
+took all of these conditions and we
+
+ align:start position:0%
+took all of these conditions and we
+ 
+
+ align:start position:0%
+took all of these conditions and we
+chopped them into little bits and
+
+ align:start position:0%
+chopped them into little bits and
+ 
+
+ align:start position:0%
+chopped them into little bits and
+rearranged the bits
+
+ align:start position:0%
+rearranged the bits
+ 
+
+ align:start position:0%
+rearranged the bits
+so that you have much more coverage of
+
+ align:start position:0%
+so that you have much more coverage of
+ 
+
+ align:start position:0%
+so that you have much more coverage of
+stuff when in the chopped up scenes than
+
+ align:start position:0%
+stuff when in the chopped up scenes than
+ 
+
+ align:start position:0%
+stuff when in the chopped up scenes than
+the chopped up
+
+ align:start position:0%
+the chopped up
+ 
+
+ align:start position:0%
+the chopped up
+uh objects
+
+ align:start position:0%
+uh objects
+ 
+
+ align:start position:0%
+uh objects
+and it in the chopped up versions it
+
+ align:start position:0%
+and it in the chopped up versions it
+ 
+
+ align:start position:0%
+and it in the chopped up versions it
+doesn't respond differently at all so
+
+ align:start position:0%
+doesn't respond differently at all so
+ 
+
+ align:start position:0%
+doesn't respond differently at all so
+it's not the amount of total spatial
+
+ align:start position:0%
+it's not the amount of total spatial
+ 
+
+ align:start position:0%
+it's not the amount of total spatial
+coverage it's the actual something more
+
+ align:start position:0%
+coverage it's the actual something more
+ 
+
+ align:start position:0%
+coverage it's the actual something more
+like the depiction of space
+
+ align:start position:0%
+like the depiction of space
+ 
+
+ align:start position:0%
+like the depiction of space
+was there a question over there yeah i
+
+ align:start position:0%
+was there a question over there yeah i
+ 
+
+ align:start position:0%
+was there a question over there yeah i
+was wondering if there would be any
+
+ align:start position:0%
+was wondering if there would be any
+ 
+
+ align:start position:0%
+was wondering if there would be any
+difference between shooting images as 2d
+
+ align:start position:0%
+difference between shooting images as 2d
+ 
+
+ align:start position:0%
+difference between shooting images as 2d
+for the 3d scene and actually being
+
+ align:start position:0%
+for the 3d scene and actually being
+ 
+
+ align:start position:0%
+for the 3d scene and actually being
+there to see the treatment
+
+ align:start position:0%
+there to see the treatment
+ 
+
+ align:start position:0%
+there to see the treatment
+totally totally it's a real challenge
+
+ align:start position:0%
+totally totally it's a real challenge
+ 
+
+ align:start position:0%
+totally totally it's a real challenge
+with navigation navigation is you know
+
+ align:start position:0%
+with navigation navigation is you know
+ 
+
+ align:start position:0%
+with navigation navigation is you know
+very much about being there and moving
+
+ align:start position:0%
+very much about being there and moving
+ 
+
+ align:start position:0%
+very much about being there and moving
+around in the space
+
+ align:start position:0%
+around in the space
+ 
+
+ align:start position:0%
+around in the space
+and this is just a pretty rudimentary
+
+ align:start position:0%
+and this is just a pretty rudimentary
+ 
+
+ align:start position:0%
+and this is just a pretty rudimentary
+thing where you're lying in the scanner
+
+ align:start position:0%
+thing where you're lying in the scanner
+ 
+
+ align:start position:0%
+thing where you're lying in the scanner
+and these images are just flashing
+
+ align:start position:0%
+and these images are just flashing
+ 
+
+ align:start position:0%
+and these images are just flashing
+flashing on and you're doing some simple
+
+ align:start position:0%
+flashing on and you're doing some simple
+ 
+
+ align:start position:0%
+flashing on and you're doing some simple
+tasks like pressing a button when
+
+ align:start position:0%
+tasks like pressing a button when
+ 
+
+ align:start position:0%
+tasks like pressing a button when
+consecutive images are identical it's
+
+ align:start position:0%
+consecutive images are identical it's
+ 
+
+ align:start position:0%
+consecutive images are identical it's
+not like moving around in the real world
+
+ align:start position:0%
+not like moving around in the real world
+ 
+
+ align:start position:0%
+not like moving around in the real world
+you don't think you're actually there
+
+ align:start position:0%
+you don't think you're actually there
+ 
+
+ align:start position:0%
+you don't think you're actually there
+but here's where video games and vr come
+
+ align:start position:0%
+but here's where video games and vr come
+ 
+
+ align:start position:0%
+but here's where video games and vr come
+in
+
+ align:start position:0%
+in
+ 
+
+ align:start position:0%
+in
+because actually you know they produce a
+
+ align:start position:0%
+because actually you know they produce a
+ 
+
+ align:start position:0%
+because actually you know they produce a
+pretty powerful simulation of knowing
+
+ align:start position:0%
+pretty powerful simulation of knowing
+ 
+
+ align:start position:0%
+pretty powerful simulation of knowing
+your environment feeling you're in a
+
+ align:start position:0%
+your environment feeling you're in a
+ 
+
+ align:start position:0%
+your environment feeling you're in a
+place in it and so lots of studies have
+
+ align:start position:0%
+place in it and so lots of studies have
+ 
+
+ align:start position:0%
+place in it and so lots of studies have
+used those methods to
+
+ align:start position:0%
+used those methods to
+ 
+
+ align:start position:0%
+used those methods to
+give something closer to the actual
+
+ align:start position:0%
+give something closer to the actual
+ 
+
+ align:start position:0%
+give something closer to the actual
+experience of navigation
+
+ align:start position:0%
+experience of navigation
+ 
+
+ align:start position:0%
+experience of navigation
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+so where are we so far we've said the
+
+ align:start position:0%
+so where are we so far we've said the
+ 
+
+ align:start position:0%
+so where are we so far we've said the
+ppa seems to be involved in recognizing
+
+ align:start position:0%
+ppa seems to be involved in recognizing
+ 
+
+ align:start position:0%
+ppa seems to be involved in recognizing
+a particular scene so it so this just
+
+ align:start position:0%
+a particular scene so it so this just
+ 
+
+ align:start position:0%
+a particular scene so it so this just
+says it responds to scenes and something
+
+ align:start position:0%
+says it responds to scenes and something
+ 
+
+ align:start position:0%
+says it responds to scenes and something
+about spatial layout maybe
+
+ align:start position:0%
+about spatial layout maybe
+ 
+
+ align:start position:0%
+about spatial layout maybe
+does it care
+
+ align:start position:0%
+does it care
+ 
+
+ align:start position:0%
+does it care
+about that particular scene
+
+ align:start position:0%
+about that particular scene
+ 
+
+ align:start position:0%
+about that particular scene
+or something do you have to recognize
+
+ align:start position:0%
+or something do you have to recognize
+ 
+
+ align:start position:0%
+or something do you have to recognize
+that particular scene to be able to use
+
+ align:start position:0%
+that particular scene to be able to use
+ 
+
+ align:start position:0%
+that particular scene to be able to use
+the information
+
+ align:start position:0%
+the information
+ 
+
+ align:start position:0%
+the information
+now our subjects mostly didn't know
+
+ align:start position:0%
+now our subjects mostly didn't know
+ 
+
+ align:start position:0%
+now our subjects mostly didn't know
+those particular scenes but we wanted to
+
+ align:start position:0%
+those particular scenes but we wanted to
+ 
+
+ align:start position:0%
+those particular scenes but we wanted to
+do a tighter contrast asking if
+
+ align:start position:0%
+do a tighter contrast asking if
+ 
+
+ align:start position:0%
+do a tighter contrast asking if
+knowledge of the particular scene
+
+ align:start position:0%
+knowledge of the particular scene
+ 
+
+ align:start position:0%
+knowledge of the particular scene
+matters
+
+ align:start position:0%
+matters
+ 
+
+ align:start position:0%
+matters
+so what we did was we took a bunch of
+
+ align:start position:0%
+so what we did was we took a bunch of
+ 
+
+ align:start position:0%
+so what we did was we took a bunch of
+pictures around the mit campus and we
+
+ align:start position:0%
+pictures around the mit campus and we
+ 
+
+ align:start position:0%
+pictures around the mit campus and we
+took a bunch of pictures around the
+
+ align:start position:0%
+took a bunch of pictures around the
+ 
+
+ align:start position:0%
+took a bunch of pictures around the
+tufts campus and we scanned mit students
+
+ align:start position:0%
+tufts campus and we scanned mit students
+ 
+
+ align:start position:0%
+tufts campus and we scanned mit students
+looking at mit pictures versus tufts
+
+ align:start position:0%
+looking at mit pictures versus tufts
+ 
+
+ align:start position:0%
+looking at mit pictures versus tufts
+pictures
+
+ align:start position:0%
+pictures
+ 
+
+ align:start position:0%
+pictures
+and then what else do we do
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah why
+
+ align:start position:0%
+yeah why
+ 
+
+ align:start position:0%
+yeah why
+oh just to make sure that uh it's not
+
+ align:start position:0%
+oh just to make sure that uh it's not
+ 
+
+ align:start position:0%
+oh just to make sure that uh it's not
+all about the weird architecture
+
+ align:start position:0%
+all about the weird architecture
+ 
+
+ align:start position:0%
+all about the weird architecture
+exactly exactly so this is called
+
+ align:start position:0%
+exactly exactly so this is called
+ 
+
+ align:start position:0%
+exactly exactly so this is called
+counter yes who's weird architecture i
+
+ align:start position:0%
+counter yes who's weird architecture i
+ 
+
+ align:start position:0%
+counter yes who's weird architecture i
+think ours is weirder um
+
+ align:start position:0%
+think ours is weirder um
+ 
+
+ align:start position:0%
+think ours is weirder um
+so it's not just about the particular
+
+ align:start position:0%
+so it's not just about the particular
+ 
+
+ align:start position:0%
+so it's not just about the particular
+scenes or the particular subjects so
+
+ align:start position:0%
+scenes or the particular subjects so
+ 
+
+ align:start position:0%
+scenes or the particular subjects so
+everybody get how with that
+
+ align:start position:0%
+everybody get how with that
+ 
+
+ align:start position:0%
+everybody get how with that
+counterbalance design you can really
+
+ align:start position:0%
+counterbalance design you can really
+ 
+
+ align:start position:0%
+counterbalance design you can really
+pull out the essence of familiarity
+
+ align:start position:0%
+pull out the essence of familiarity
+ 
+
+ align:start position:0%
+pull out the essence of familiarity
+itself unconfounded from the particular
+
+ align:start position:0%
+itself unconfounded from the particular
+ 
+
+ align:start position:0%
+itself unconfounded from the particular
+images
+
+ align:start position:0%
+images
+ 
+
+ align:start position:0%
+images
+okay so when we did that
+
+ align:start position:0%
+okay so when we did that
+ 
+
+ align:start position:0%
+okay so when we did that
+we found a very similar response
+
+ align:start position:0%
+we found a very similar response
+ 
+
+ align:start position:0%
+we found a very similar response
+magnitude in the ppa for the
+
+ align:start position:0%
+magnitude in the ppa for the
+ 
+
+ align:start position:0%
+magnitude in the ppa for the
+tough students and for the familiar and
+
+ align:start position:0%
+tough students and for the familiar and
+ 
+
+ align:start position:0%
+tough students and for the familiar and
+unfamiliar scenes okay
+
+ align:start position:0%
+unfamiliar scenes okay
+ 
+
+ align:start position:0%
+unfamiliar scenes okay
+really really didn't make much
+
+ align:start position:0%
+really really didn't make much
+ 
+
+ align:start position:0%
+really really didn't make much
+difference
+
+ align:start position:0%
+difference
+ 
+
+ align:start position:0%
+difference
+yeah
+
+ align:start position:0%
+yeah
+ 
+
+ align:start position:0%
+yeah
+uh taking a step back so we started with
+
+ align:start position:0%
+uh taking a step back so we started with
+ 
+
+ align:start position:0%
+uh taking a step back so we started with
+the wrong question of navigation yeah
+
+ align:start position:0%
+the wrong question of navigation yeah
+ 
+
+ align:start position:0%
+the wrong question of navigation yeah
+and it involving all these different
+
+ align:start position:0%
+and it involving all these different
+ 
+
+ align:start position:0%
+and it involving all these different
+components
+
+ align:start position:0%
+components
+ 
+
+ align:start position:0%
+components
+uh i just want the place where this
+
+ align:start position:0%
+uh i just want the place where this
+ 
+
+ align:start position:0%
+uh i just want the place where this
+we're getting there we're getting there
+
+ align:start position:0%
+we're getting there we're getting there
+ 
+
+ align:start position:0%
+we're getting there we're getting there
+there won't be like a perfect answer
+
+ align:start position:0%
+there won't be like a perfect answer
+ 
+
+ align:start position:0%
+there won't be like a perfect answer
+we're not going to end up with that
+
+ align:start position:0%
+we're not going to end up with that
+ 
+
+ align:start position:0%
+we're not going to end up with that
+slide with the exact brain region of
+
+ align:start position:0%
+slide with the exact brain region of
+ 
+
+ align:start position:0%
+slide with the exact brain region of
+each of those things uh we'll get some
+
+ align:start position:0%
+each of those things uh we'll get some
+ 
+
+ align:start position:0%
+each of those things uh we'll get some
+gisty vague senses of what this is
+
+ align:start position:0%
+gisty vague senses of what this is
+ 
+
+ align:start position:0%
+gisty vague senses of what this is
+yeah
+
+ align:start position:0%
+yeah
+ 
+
+ align:start position:0%
+yeah
+okay so this tells us it's not about
+
+ align:start position:0%
+okay so this tells us it's not about
+ 
+
+ align:start position:0%
+okay so this tells us it's not about
+it
+
+ align:start position:0%
+it
+ 
+
+ align:start position:0%
+it
+it's whatever you do whatever the ppa is
+
+ align:start position:0%
+it's whatever you do whatever the ppa is
+ 
+
+ align:start position:0%
+it's whatever you do whatever the ppa is
+responding to in a scene it's not
+
+ align:start position:0%
+responding to in a scene it's not
+ 
+
+ align:start position:0%
+responding to in a scene it's not
+something that hinges on knowing that
+
+ align:start position:0%
+something that hinges on knowing that
+ 
+
+ align:start position:0%
+something that hinges on knowing that
+exact scene so it can't be something
+
+ align:start position:0%
+exact scene so it can't be something
+ 
+
+ align:start position:0%
+exact scene so it can't be something
+like okay if i was here and i wanted to
+
+ align:start position:0%
+like okay if i was here and i wanted to
+ 
+
+ align:start position:0%
+like okay if i was here and i wanted to
+get coffee what would my route from this
+
+ align:start position:0%
+get coffee what would my route from this
+ 
+
+ align:start position:0%
+get coffee what would my route from this
+location be given my knowledge of the
+
+ align:start position:0%
+location be given my knowledge of the
+ 
+
+ align:start position:0%
+location be given my knowledge of the
+environment because otherwise we
+
+ align:start position:0%
+environment because otherwise we
+ 
+
+ align:start position:0%
+environment because otherwise we
+wouldn't get this result so whatever it
+
+ align:start position:0%
+wouldn't get this result so whatever it
+ 
+
+ align:start position:0%
+wouldn't get this result so whatever it
+is it's something more immediate and
+
+ align:start position:0%
+is it's something more immediate and
+ 
+
+ align:start position:0%
+is it's something more immediate and
+perceptual to do with just seeing this
+
+ align:start position:0%
+perceptual to do with just seeing this
+ 
+
+ align:start position:0%
+perceptual to do with just seeing this
+place
+
+ align:start position:0%
+place
+ 
+
+ align:start position:0%
+place
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+all right
+
+ align:start position:0%
+all right
+ 
+
+ align:start position:0%
+all right
+all right so where are we
+
+ align:start position:0%
+all right so where are we
+ 
+
+ align:start position:0%
+all right so where are we
+we've said that there's this region that
+
+ align:start position:0%
+we've said that there's this region that
+ 
+
+ align:start position:0%
+we've said that there's this region that
+responds more to scenes and objects
+
+ align:start position:0%
+responds more to scenes and objects
+ 
+
+ align:start position:0%
+responds more to scenes and objects
+that when all the objects are removed
+
+ align:start position:0%
+that when all the objects are removed
+ 
+
+ align:start position:0%
+that when all the objects are removed
+from the scenes the response you know
+
+ align:start position:0%
+from the scenes the response you know
+ 
+
+ align:start position:0%
+from the scenes the response you know
+barely drops okay
+
+ align:start position:0%
+barely drops okay
+ 
+
+ align:start position:0%
+barely drops okay
+and its response is pretty much the same
+
+ align:start position:0%
+and its response is pretty much the same
+ 
+
+ align:start position:0%
+and its response is pretty much the same
+for familiar and unfamiliar scenes
+
+ align:start position:0%
+for familiar and unfamiliar scenes
+ 
+
+ align:start position:0%
+for familiar and unfamiliar scenes
+so all of that suggests that it's
+
+ align:start position:0%
+so all of that suggests that it's
+ 
+
+ align:start position:0%
+so all of that suggests that it's
+involved in something like perceiving
+
+ align:start position:0%
+involved in something like perceiving
+ 
+
+ align:start position:0%
+involved in something like perceiving
+the shape of space around you
+
+ align:start position:0%
+the shape of space around you
+ 
+
+ align:start position:0%
+the shape of space around you
+it doesn't nail it yet but it
+
+ align:start position:0%
+it doesn't nail it yet but it
+ 
+
+ align:start position:0%
+it doesn't nail it yet but it
+kind of pushes you towards that
+
+ align:start position:0%
+kind of pushes you towards that
+ 
+
+ align:start position:0%
+kind of pushes you towards that
+hypothesis yeah was there a question
+
+ align:start position:0%
+hypothesis yeah was there a question
+ 
+
+ align:start position:0%
+hypothesis yeah was there a question
+here a second ago oh no okay
+
+ align:start position:0%
+here a second ago oh no okay
+ 
+
+ align:start position:0%
+here a second ago oh no okay
+experiment no
+
+ align:start position:0%
+experiment no
+ 
+
+ align:start position:0%
+experiment no
+is it activating you look at it back
+
+ align:start position:0%
+is it activating you look at it back
+ 
+
+ align:start position:0%
+is it activating you look at it back
+oh great question uh not very much
+
+ align:start position:0%
+oh great question uh not very much
+ 
+
+ align:start position:0%
+oh great question uh not very much
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+yeah if you take pictures of places from
+
+ align:start position:0%
+yeah if you take pictures of places from
+ 
+
+ align:start position:0%
+yeah if you take pictures of places from
+above versus this kind of view you get a
+
+ align:start position:0%
+above versus this kind of view you get a
+ 
+
+ align:start position:0%
+above versus this kind of view you get a
+response in this kind of view but not
+
+ align:start position:0%
+response in this kind of view but not
+ 
+
+ align:start position:0%
+response in this kind of view but not
+above
+
+ align:start position:0%
+above
+ 
+
+ align:start position:0%
+above
+yeah
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+very telling yeah
+
+ align:start position:0%
+very telling yeah
+ 
+
+ align:start position:0%
+very telling yeah
+okay so i'm going to skip we're not
+
+ align:start position:0%
+okay so i'm going to skip we're not
+ 
+
+ align:start position:0%
+okay so i'm going to skip we're not
+going to do like you know the 30 other
+
+ align:start position:0%
+going to do like you know the 30 other
+ 
+
+ align:start position:0%
+going to do like you know the 30 other
+experiments we're going to skip to the
+
+ align:start position:0%
+experiments we're going to skip to the
+ 
+
+ align:start position:0%
+experiments we're going to skip to the
+general picture that here's the ppa and
+
+ align:start position:0%
+general picture that here's the ppa and
+ 
+
+ align:start position:0%
+general picture that here's the ppa and
+four subjects in this very stereotype
+
+ align:start position:0%
+four subjects in this very stereotype
+ 
+
+ align:start position:0%
+four subjects in this very stereotype
+location and here are some of the many
+
+ align:start position:0%
+location and here are some of the many
+ 
+
+ align:start position:0%
+location and here are some of the many
+conditions we've tested it's not just
+
+ align:start position:0%
+conditions we've tested it's not just
+ 
+
+ align:start position:0%
+conditions we've tested it's not just
+you know abstract maps like this they
+
+ align:start position:0%
+you know abstract maps like this they
+ 
+
+ align:start position:0%
+you know abstract maps like this they
+don't produce a strong response oh this
+
+ align:start position:0%
+don't produce a strong response oh this
+ 
+
+ align:start position:0%
+don't produce a strong response oh this
+is an answer to cooley's question way
+
+ align:start position:0%
+is an answer to cooley's question way
+ 
+
+ align:start position:0%
+is an answer to cooley's question way
+back here's the scrambled up scene much
+
+ align:start position:0%
+back here's the scrambled up scene much
+ 
+
+ align:start position:0%
+back here's the scrambled up scene much
+lower response so it's not just coverage
+
+ align:start position:0%
+lower response so it's not just coverage
+ 
+
+ align:start position:0%
+lower response so it's not just coverage
+of visual junk right
+
+ align:start position:0%
+of visual junk right
+ 
+
+ align:start position:0%
+of visual junk right
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+it responds pretty strongly to scenes
+
+ align:start position:0%
+it responds pretty strongly to scenes
+ 
+
+ align:start position:0%
+it responds pretty strongly to scenes
+made out of legos compared to objects
+
+ align:start position:0%
+made out of legos compared to objects
+ 
+
+ align:start position:0%
+made out of legos compared to objects
+made out of legos and various other
+
+ align:start position:0%
+made out of legos and various other
+ 
+
+ align:start position:0%
+made out of legos and various other
+silly things
+
+ align:start position:0%
+silly things
+ 
+
+ align:start position:0%
+silly things
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+so all of that seems to suggest that
+
+ align:start position:0%
+so all of that seems to suggest that
+ 
+
+ align:start position:0%
+so all of that seems to suggest that
+it's processing something like the shape
+
+ align:start position:0%
+it's processing something like the shape
+ 
+
+ align:start position:0%
+it's processing something like the shape
+or geometry of space around you visible
+
+ align:start position:0%
+or geometry of space around you visible
+ 
+
+ align:start position:0%
+or geometry of space around you visible
+space in your immediate environment
+
+ align:start position:0%
+space in your immediate environment
+ 
+
+ align:start position:0%
+space in your immediate environment
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+nonetheless
+
+ align:start position:0%
+nonetheless
+ 
+
+ align:start position:0%
+nonetheless
+there's always push back
+
+ align:start position:0%
+there's always push back
+ 
+
+ align:start position:0%
+there's always push back
+and there's push back on multiple fronts
+
+ align:start position:0%
+and there's push back on multiple fronts
+ 
+
+ align:start position:0%
+and there's push back on multiple fronts
+and there should be that's proper
+
+ align:start position:0%
+and there should be that's proper
+ 
+
+ align:start position:0%
+and there should be that's proper
+science
+
+ align:start position:0%
+science
+ 
+
+ align:start position:0%
+science
+so one of the lines of pushback
+
+ align:start position:0%
+so one of the lines of pushback
+ 
+
+ align:start position:0%
+so one of the lines of pushback
+was this paper by nasser at all
+
+ align:start position:0%
+was this paper by nasser at all
+ 
+
+ align:start position:0%
+was this paper by nasser at all
+that i didn't assign i signed you the
+
+ align:start position:0%
+that i didn't assign i signed you the
+ 
+
+ align:start position:0%
+that i didn't assign i signed you the
+response to it anyway what nostradal did
+
+ align:start position:0%
+response to it anyway what nostradal did
+ 
+
+ align:start position:0%
+response to it anyway what nostradal did
+was scan people looking at
+
+ align:start position:0%
+was scan people looking at
+ 
+
+ align:start position:0%
+was scan people looking at
+rectilinear things like cubes and
+
+ align:start position:0%
+rectilinear things like cubes and
+ 
+
+ align:start position:0%
+rectilinear things like cubes and
+pyramids versus curvilinear roundy
+
+ align:start position:0%
+pyramids versus curvilinear roundy
+ 
+
+ align:start position:0%
+pyramids versus curvilinear roundy
+things like cones and spheres
+
+ align:start position:0%
+things like cones and spheres
+ 
+
+ align:start position:0%
+things like cones and spheres
+and what they showed is that ppa
+
+ align:start position:0%
+and what they showed is that ppa
+ 
+
+ align:start position:0%
+and what they showed is that ppa
+responds more to the rectilinear than
+
+ align:start position:0%
+responds more to the rectilinear than
+ 
+
+ align:start position:0%
+responds more to the rectilinear than
+the curvilinear shapes
+
+ align:start position:0%
+the curvilinear shapes
+ 
+
+ align:start position:0%
+the curvilinear shapes
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+okay that's the first thing
+
+ align:start position:0%
+okay that's the first thing
+ 
+
+ align:start position:0%
+okay that's the first thing
+and so then they argue that
+
+ align:start position:0%
+and so then they argue that
+ 
+
+ align:start position:0%
+and so then they argue that
+in general scenes have more rectilinear
+
+ align:start position:0%
+in general scenes have more rectilinear
+ 
+
+ align:start position:0%
+in general scenes have more rectilinear
+structure than curvilinear structure and
+
+ align:start position:0%
+structure than curvilinear structure and
+ 
+
+ align:start position:0%
+structure than curvilinear structure and
+they did a bunch of math to make that
+
+ align:start position:0%
+they did a bunch of math to make that
+ 
+
+ align:start position:0%
+they did a bunch of math to make that
+case
+
+ align:start position:0%
+case
+ 
+
+ align:start position:0%
+case
+and so
+
+ align:start position:0%
+and so
+ 
+
+ align:start position:0%
+and so
+they they argue
+
+ align:start position:0%
+they they argue
+ 
+
+ align:start position:0%
+they they argue
+that maybe the apparent scene
+
+ align:start position:0%
+that maybe the apparent scene
+ 
+
+ align:start position:0%
+that maybe the apparent scene
+selectivity of the ppa is due to a what
+
+ align:start position:0%
+selectivity of the ppa is due to a what
+ 
+
+ align:start position:0%
+selectivity of the ppa is due to a what
+of scenes with rectilinearity
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah
+
+ align:start position:0%
+yeah
+ 
+
+ align:start position:0%
+yeah
+yes exactly a confound this is exactly
+
+ align:start position:0%
+yes exactly a confound this is exactly
+ 
+
+ align:start position:0%
+yes exactly a confound this is exactly
+what a confound is something else that
+
+ align:start position:0%
+what a confound is something else that
+ 
+
+ align:start position:0%
+what a confound is something else that
+co-varies with the manipulation you care
+
+ align:start position:0%
+co-varies with the manipulation you care
+ 
+
+ align:start position:0%
+co-varies with the manipulation you care
+about that gives you an alternative
+
+ align:start position:0%
+about that gives you an alternative
+ 
+
+ align:start position:0%
+about that gives you an alternative
+account namely okay it's not seeing
+
+ align:start position:0%
+account namely okay it's not seeing
+ 
+
+ align:start position:0%
+account namely okay it's not seeing
+selectivity it's just rectilinearity i
+
+ align:start position:0%
+selectivity it's just rectilinearity i
+ 
+
+ align:start position:0%
+selectivity it's just rectilinearity i
+mean that might be interesting to other
+
+ align:start position:0%
+mean that might be interesting to other
+ 
+
+ align:start position:0%
+mean that might be interesting to other
+people but it would make it not very
+
+ align:start position:0%
+people but it would make it not very
+ 
+
+ align:start position:0%
+people but it would make it not very
+relevant to navigation and much less
+
+ align:start position:0%
+relevant to navigation and much less
+ 
+
+ align:start position:0%
+relevant to navigation and much less
+interesting to me at least right okay
+
+ align:start position:0%
+interesting to me at least right okay
+ 
+
+ align:start position:0%
+interesting to me at least right okay
+so that's an important criticism
+
+ align:start position:0%
+so that's an important criticism
+ 
+
+ align:start position:0%
+so that's an important criticism
+and so then the brian at all paper that
+
+ align:start position:0%
+and so then the brian at all paper that
+ 
+
+ align:start position:0%
+and so then the brian at all paper that
+you guys read starts from there and says
+
+ align:start position:0%
+you guys read starts from there and says
+ 
+
+ align:start position:0%
+you guys read starts from there and says
+okay let's take that seriously let's
+
+ align:start position:0%
+okay let's take that seriously let's
+ 
+
+ align:start position:0%
+okay let's take that seriously let's
+find out
+
+ align:start position:0%
+find out
+ 
+
+ align:start position:0%
+find out
+and so
+
+ align:start position:0%
+and so
+ 
+
+ align:start position:0%
+and so
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+you guys should have read all of this
+
+ align:start position:0%
+you guys should have read all of this
+ 
+
+ align:start position:0%
+you guys should have read all of this
+but just to remind you they have a nice
+
+ align:start position:0%
+but just to remind you they have a nice
+ 
+
+ align:start position:0%
+but just to remind you they have a nice
+little two by two design remember we
+
+ align:start position:0%
+little two by two design remember we
+ 
+
+ align:start position:0%
+little two by two design remember we
+talked about two by two designs where
+
+ align:start position:0%
+talked about two by two designs where
+ 
+
+ align:start position:0%
+talked about two by two designs where
+they manipulate whether the image has a
+
+ align:start position:0%
+they manipulate whether the image has a
+ 
+
+ align:start position:0%
+they manipulate whether the image has a
+lot of rectilinear structure or less
+
+ align:start position:0%
+lot of rectilinear structure or less
+ 
+
+ align:start position:0%
+lot of rectilinear structure or less
+rectilinear structure and whether the
+
+ align:start position:0%
+rectilinear structure and whether the
+ 
+
+ align:start position:0%
+rectilinear structure and whether the
+image is a place or a face
+
+ align:start position:0%
+image is a place or a face
+ 
+
+ align:start position:0%
+image is a place or a face
+okay um
+
+ align:start position:0%
+okay um
+ 
+
+ align:start position:0%
+okay um
+and what they find in the ppa is the
+
+ align:start position:0%
+and what they find in the ppa is the
+ 
+
+ align:start position:0%
+and what they find in the ppa is the
+same response to these
+
+ align:start position:0%
+same response to these
+ 
+
+ align:start position:0%
+same response to these
+and it's higher to the scenes than the
+
+ align:start position:0%
+and it's higher to the scenes than the
+ 
+
+ align:start position:0%
+and it's higher to the scenes than the
+faces
+
+ align:start position:0%
+faces
+ 
+
+ align:start position:0%
+faces
+uh and rectilinearity didn't matter
+
+ align:start position:0%
+uh and rectilinearity didn't matter
+ 
+
+ align:start position:0%
+uh and rectilinearity didn't matter
+for the scenes okay so evidently even
+
+ align:start position:0%
+for the scenes okay so evidently even
+ 
+
+ align:start position:0%
+for the scenes okay so evidently even
+though it does matter with these
+
+ align:start position:0%
+though it does matter with these
+ 
+
+ align:start position:0%
+though it does matter with these
+abstract shapes in actual scenes it
+
+ align:start position:0%
+abstract shapes in actual scenes it
+ 
+
+ align:start position:0%
+abstract shapes in actual scenes it
+doesn't seem and faces it doesn't seem
+
+ align:start position:0%
+doesn't seem and faces it doesn't seem
+ 
+
+ align:start position:0%
+doesn't seem and faces it doesn't seem
+to be doing much it's not accounting for
+
+ align:start position:0%
+to be doing much it's not accounting for
+ 
+
+ align:start position:0%
+to be doing much it's not accounting for
+this difference
+
+ align:start position:0%
+this difference
+ 
+
+ align:start position:0%
+this difference
+okay everybody get that
+
+ align:start position:0%
+okay everybody get that
+ 
+
+ align:start position:0%
+okay everybody get that
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+okay let's talk about this graph
+
+ align:start position:0%
+okay let's talk about this graph
+ 
+
+ align:start position:0%
+okay let's talk about this graph
+are there main effects or interactions
+
+ align:start position:0%
+are there main effects or interactions
+ 
+
+ align:start position:0%
+are there main effects or interactions
+here and what are those main effects or
+
+ align:start position:0%
+here and what are those main effects or
+ 
+
+ align:start position:0%
+here and what are those main effects or
+interactions
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yes fully there's immediate scenes yeah
+
+ align:start position:0%
+yes fully there's immediate scenes yeah
+ 
+
+ align:start position:0%
+yes fully there's immediate scenes yeah
+of category scene versus face yeah
+
+ align:start position:0%
+of category scene versus face yeah
+ 
+
+ align:start position:0%
+of category scene versus face yeah
+anything else
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that was the first thing
+
+ align:start position:0%
+that was the first thing
+ 
+
+ align:start position:0%
+that was the first thing
+in
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+oh
+
+ align:start position:0%
+oh
+ 
+
+ align:start position:0%
+oh
+wait this here these are scenes and
+
+ align:start position:0%
+wait this here these are scenes and
+ 
+
+ align:start position:0%
+wait this here these are scenes and
+those are phases
+
+ align:start position:0%
+those are phases
+ 
+
+ align:start position:0%
+those are phases
+okay and i'm sorry and this is the code
+
+ align:start position:0%
+okay and i'm sorry and this is the code
+ 
+
+ align:start position:0%
+okay and i'm sorry and this is the code
+here these are rectilinear versus
+
+ align:start position:0%
+here these are rectilinear versus
+ 
+
+ align:start position:0%
+here these are rectilinear versus
+curvilinear
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+just one main effect or is there an
+
+ align:start position:0%
+just one main effect or is there an
+ 
+
+ align:start position:0%
+just one main effect or is there an
+interaction or another main effect
+
+ align:start position:0%
+interaction or another main effect
+ 
+
+ align:start position:0%
+interaction or another main effect
+no just one main effect okay
+
+ align:start position:0%
+no just one main effect okay
+ 
+
+ align:start position:0%
+no just one main effect okay
+right these guys are higher than those
+
+ align:start position:0%
+right these guys are higher than those
+ 
+
+ align:start position:0%
+right these guys are higher than those
+guys that's it
+
+ align:start position:0%
+guys that's it
+ 
+
+ align:start position:0%
+guys that's it
+okay so that just tells you there's
+
+ align:start position:0%
+okay so that just tells you there's
+ 
+
+ align:start position:0%
+okay so that just tells you there's
+nothing else going on in these data
+
+ align:start position:0%
+nothing else going on in these data
+ 
+
+ align:start position:0%
+nothing else going on in these data
+other than seeing selectivity
+
+ align:start position:0%
+other than seeing selectivity
+ 
+
+ align:start position:0%
+other than seeing selectivity
+okay rectilinearity doesn't interact
+
+ align:start position:0%
+okay rectilinearity doesn't interact
+ 
+
+ align:start position:0%
+okay rectilinearity doesn't interact
+with or modify scene selectivity and it
+
+ align:start position:0%
+with or modify scene selectivity and it
+ 
+
+ align:start position:0%
+with or modify scene selectivity and it
+doesn't have a separate effect
+
+ align:start position:0%
+doesn't have a separate effect
+ 
+
+ align:start position:0%
+doesn't have a separate effect
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+nonetheless
+
+ align:start position:0%
+nonetheless
+ 
+
+ align:start position:0%
+nonetheless
+as we've been arguing with all the whole
+
+ align:start position:0%
+as we've been arguing with all the whole
+ 
+
+ align:start position:0%
+as we've been arguing with all the whole
+hacks be rigmarole does the fact that
+
+ align:start position:0%
+hacks be rigmarole does the fact that
+ 
+
+ align:start position:0%
+hacks be rigmarole does the fact that
+there's no
+
+ align:start position:0%
+there's no
+ 
+
+ align:start position:0%
+there's no
+main effect of rectilinearity in here
+
+ align:start position:0%
+main effect of rectilinearity in here
+ 
+
+ align:start position:0%
+main effect of rectilinearity in here
+mean that the ppa doesn't have
+
+ align:start position:0%
+mean that the ppa doesn't have
+ 
+
+ align:start position:0%
+mean that the ppa doesn't have
+information about rectilinearity
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+no josh why
+
+ align:start position:0%
+no josh why
+ 
+
+ align:start position:0%
+no josh why
+i mean there's still a tiny amount that
+
+ align:start position:0%
+i mean there's still a tiny amount that
+ 
+
+ align:start position:0%
+i mean there's still a tiny amount that
+could that could be enough
+
+ align:start position:0%
+could that could be enough
+ 
+
+ align:start position:0%
+could that could be enough
+this is not the right experiment that's
+
+ align:start position:0%
+this is not the right experiment that's
+ 
+
+ align:start position:0%
+this is not the right experiment that's
+right this is a big well it's a right
+
+ align:start position:0%
+right this is a big well it's a right
+ 
+
+ align:start position:0%
+right this is a big well it's a right
+experiment but not the right analysis
+
+ align:start position:0%
+experiment but not the right analysis
+ 
+
+ align:start position:0%
+experiment but not the right analysis
+right it's the big average responses are
+
+ align:start position:0%
+right it's the big average responses are
+ 
+
+ align:start position:0%
+right it's the big average responses are
+the same but maybe the patterns are
+
+ align:start position:0%
+the same but maybe the patterns are
+ 
+
+ align:start position:0%
+the same but maybe the patterns are
+different okay that wouldn't directly
+
+ align:start position:0%
+different okay that wouldn't directly
+ 
+
+ align:start position:0%
+different okay that wouldn't directly
+engage with us but we want to know is
+
+ align:start position:0%
+engage with us but we want to know is
+ 
+
+ align:start position:0%
+engage with us but we want to know is
+there information in there about
+
+ align:start position:0%
+there information in there about
+ 
+
+ align:start position:0%
+there information in there about
+rectilinearity
+
+ align:start position:0%
+rectilinearity
+ 
+
+ align:start position:0%
+rectilinearity
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+so how would we find out
+
+ align:start position:0%
+so how would we find out
+ 
+
+ align:start position:0%
+so how would we find out
+so this was your assignment and i think
+
+ align:start position:0%
+so this was your assignment and i think
+ 
+
+ align:start position:0%
+so this was your assignment and i think
+most people got it right but in case
+
+ align:start position:0%
+most people got it right but in case
+ 
+
+ align:start position:0%
+most people got it right but in case
+anybody missed it
+
+ align:start position:0%
+anybody missed it
+ 
+
+ align:start position:0%
+anybody missed it
+we were zooming in on these this figure
+
+ align:start position:0%
+we were zooming in on these this figure
+ 
+
+ align:start position:0%
+we were zooming in on these this figure
+four here so again this is just the same
+
+ align:start position:0%
+four here so again this is just the same
+ 
+
+ align:start position:0%
+four here so again this is just the same
+basic design of experiment two
+
+ align:start position:0%
+basic design of experiment two
+ 
+
+ align:start position:0%
+basic design of experiment two
+and now let's consider what's going on
+
+ align:start position:0%
+and now let's consider what's going on
+ 
+
+ align:start position:0%
+and now let's consider what's going on
+here so you guys read the paper and you
+
+ align:start position:0%
+here so you guys read the paper and you
+ 
+
+ align:start position:0%
+here so you guys read the paper and you
+understood what was going on here what's
+
+ align:start position:0%
+understood what was going on here what's
+ 
+
+ align:start position:0%
+understood what was going on here what's
+represented in that cell right there
+
+ align:start position:0%
+represented in that cell right there
+ 
+
+ align:start position:0%
+represented in that cell right there
+what is the point of this diagram what
+
+ align:start position:0%
+what is the point of this diagram what
+ 
+
+ align:start position:0%
+what is the point of this diagram what
+are they doing here and what does that
+
+ align:start position:0%
+are they doing here and what does that
+ 
+
+ align:start position:0%
+are they doing here and what does that
+cell mean in that matrix
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+you can't understand the paper without
+
+ align:start position:0%
+you can't understand the paper without
+ 
+
+ align:start position:0%
+you can't understand the paper without
+knowing that
+
+ align:start position:0%
+knowing that
+ 
+
+ align:start position:0%
+knowing that
+is it ali
+
+ align:start position:0%
+is it ali
+ 
+
+ align:start position:0%
+is it ali
+no sorry
+
+ align:start position:0%
+no sorry
+ 
+
+ align:start position:0%
+no sorry
+what's your name
+
+ align:start position:0%
+what's your name
+ 
+
+ align:start position:0%
+what's your name
+sharon i've only asked you like six
+
+ align:start position:0%
+sharon i've only asked you like six
+ 
+
+ align:start position:0%
+sharon i've only asked you like six
+times yeah go ahead
+
+ align:start position:0%
+times yeah go ahead
+ 
+
+ align:start position:0%
+times yeah go ahead
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+they want to see whether
+
+ align:start position:0%
+they want to see whether
+ 
+
+ align:start position:0%
+they want to see whether
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+activation patterns can better
+
+ align:start position:0%
+activation patterns can better
+ 
+
+ align:start position:0%
+activation patterns can better
+discriminate between
+
+ align:start position:0%
+discriminate between
+ 
+
+ align:start position:0%
+discriminate between
+rectilinearity of the same category of
+
+ align:start position:0%
+rectilinearity of the same category of
+ 
+
+ align:start position:0%
+rectilinearity of the same category of
+things or between categories of things
+
+ align:start position:0%
+things or between categories of things
+ 
+
+ align:start position:0%
+things or between categories of things
+with the same rectilinearity so they um
+
+ align:start position:0%
+with the same rectilinearity so they um
+ 
+
+ align:start position:0%
+with the same rectilinearity so they um
+the first thing i said is
+
+ align:start position:0%
+the first thing i said is
+ 
+
+ align:start position:0%
+the first thing i said is
+to the
+
+ align:start position:0%
+to the
+ 
+
+ align:start position:0%
+to the
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+left and the second one is the right
+
+ align:start position:0%
+left and the second one is the right
+ 
+
+ align:start position:0%
+left and the second one is the right
+and they
+
+ align:start position:0%
+and they
+ 
+
+ align:start position:0%
+and they
+sorry wait here and here no the right
+
+ align:start position:0%
+sorry wait here and here no the right
+ 
+
+ align:start position:0%
+sorry wait here and here no the right
+side yeah so this part that part is
+
+ align:start position:0%
+side yeah so this part that part is
+ 
+
+ align:start position:0%
+side yeah so this part that part is
+discriminating between um
+
+ align:start position:0%
+discriminating between um
+ 
+
+ align:start position:0%
+discriminating between um
+vertical linearity and that side is
+
+ align:start position:0%
+vertical linearity and that side is
+ 
+
+ align:start position:0%
+vertical linearity and that side is
+distributing between categories
+
+ align:start position:0%
+distributing between categories
+ 
+
+ align:start position:0%
+distributing between categories
+and they take the differences of
+
+ align:start position:0%
+and they take the differences of
+ 
+
+ align:start position:0%
+and they take the differences of
+well not the difference if they take
+
+ align:start position:0%
+well not the difference if they take
+ 
+
+ align:start position:0%
+well not the difference if they take
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+how well it can distinguish between each
+
+ align:start position:0%
+how well it can distinguish between each
+ 
+
+ align:start position:0%
+how well it can distinguish between each
+of those categories and plug them down
+
+ align:start position:0%
+of those categories and plug them down
+ 
+
+ align:start position:0%
+of those categories and plug them down
+there
+
+ align:start position:0%
+there
+ 
+
+ align:start position:0%
+there
+right okay
+
+ align:start position:0%
+right okay
+ 
+
+ align:start position:0%
+right okay
+that's exactly right so this is how well
+
+ align:start position:0%
+that's exactly right so this is how well
+ 
+
+ align:start position:0%
+that's exactly right so this is how well
+it can discriminate plotted down here
+
+ align:start position:0%
+it can discriminate plotted down here
+ 
+
+ align:start position:0%
+it can discriminate plotted down here
+but based on an analysis that follows
+
+ align:start position:0%
+but based on an analysis that follows
+ 
+
+ align:start position:0%
+but based on an analysis that follows
+this scheme
+
+ align:start position:0%
+this scheme
+ 
+
+ align:start position:0%
+this scheme
+so what does that cell in there
+
+ align:start position:0%
+so what does that cell in there
+ 
+
+ align:start position:0%
+so what does that cell in there
+represent
+
+ align:start position:0%
+represent
+ 
+
+ align:start position:0%
+represent
+that dark green cell what do they
+
+ align:start position:0%
+that dark green cell what do they
+ 
+
+ align:start position:0%
+that dark green cell what do they
+what is the number that's going to be
+
+ align:start position:0%
+what is the number that's going to be
+ 
+
+ align:start position:0%
+what is the number that's going to be
+calculated from the data corresponding
+
+ align:start position:0%
+calculated from the data corresponding
+ 
+
+ align:start position:0%
+calculated from the data corresponding
+to that cell
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+similarities of uh saying that
+
+ align:start position:0%
+similarities of uh saying that
+ 
+
+ align:start position:0%
+similarities of uh saying that
+continuity
+
+ align:start position:0%
+continuity
+ 
+
+ align:start position:0%
+continuity
+exactly exactly so just as if you want
+
+ align:start position:0%
+exactly exactly so just as if you want
+ 
+
+ align:start position:0%
+exactly exactly so just as if you want
+to distinguish chairs from cars or
+
+ align:start position:0%
+to distinguish chairs from cars or
+ 
+
+ align:start position:0%
+to distinguish chairs from cars or
+something else if you want to know is
+
+ align:start position:0%
+something else if you want to know is
+ 
+
+ align:start position:0%
+something else if you want to know is
+there information about rectilinearity
+
+ align:start position:0%
+there information about rectilinearity
+ 
+
+ align:start position:0%
+there information about rectilinearity
+in there
+
+ align:start position:0%
+in there
+ 
+
+ align:start position:0%
+in there
+you take these two cases which are the
+
+ align:start position:0%
+you take these two cases which are the
+ 
+
+ align:start position:0%
+you take these two cases which are the
+same in rectilinearity both high
+
+ align:start position:0%
+same in rectilinearity both high
+ 
+
+ align:start position:0%
+same in rectilinearity both high
+rectilinear both low rectilinear
+
+ align:start position:0%
+rectilinear both low rectilinear
+ 
+
+ align:start position:0%
+rectilinear both low rectilinear
+for run one and run two and that's the
+
+ align:start position:0%
+for run one and run two and that's the
+ 
+
+ align:start position:0%
+for run one and run two and that's the
+correlation between run and one 2 for
+
+ align:start position:0%
+correlation between run and one 2 for
+ 
+
+ align:start position:0%
+correlation between run and one 2 for
+those cells
+
+ align:start position:0%
+those cells
+ 
+
+ align:start position:0%
+those cells
+that's the within rectilinearity case
+
+ align:start position:0%
+that's the within rectilinearity case
+ 
+
+ align:start position:0%
+that's the within rectilinearity case
+right and if there's information about
+
+ align:start position:0%
+right and if there's information about
+ 
+
+ align:start position:0%
+right and if there's information about
+rectilinearity the prediction is those
+
+ align:start position:0%
+rectilinearity the prediction is those
+ 
+
+ align:start position:0%
+rectilinearity the prediction is those
+within correlations are higher than the
+
+ align:start position:0%
+within correlations are higher than the
+ 
+
+ align:start position:0%
+within correlations are higher than the
+between correlations
+
+ align:start position:0%
+between correlations
+ 
+
+ align:start position:0%
+between correlations
+just as we argued a bit back with you
+
+ align:start position:0%
+just as we argued a bit back with you
+ 
+
+ align:start position:0%
+just as we argued a bit back with you
+know beaches and cities and everything
+
+ align:start position:0%
+know beaches and cities and everything
+ 
+
+ align:start position:0%
+know beaches and cities and everything
+else okay same argument this is just
+
+ align:start position:0%
+else okay same argument this is just
+ 
+
+ align:start position:0%
+else okay same argument this is just
+presenting the data in terms of run one
+
+ align:start position:0%
+presenting the data in terms of run one
+ 
+
+ align:start position:0%
+presenting the data in terms of run one
+and run two and which cells do we grab
+
+ align:start position:0%
+and run two and which cells do we grab
+ 
+
+ align:start position:0%
+and run two and which cells do we grab
+to do this computation
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+um so each of the cells in there for
+
+ align:start position:0%
+um so each of the cells in there for
+ 
+
+ align:start position:0%
+um so each of the cells in there for
+each of the cells we're going to
+
+ align:start position:0%
+each of the cells we're going to
+ 
+
+ align:start position:0%
+each of the cells we're going to
+calculate an r value of how similar
+
+ align:start position:0%
+calculate an r value of how similar
+ 
+
+ align:start position:0%
+calculate an r value of how similar
+those patterns are
+
+ align:start position:0%
+those patterns are
+ 
+
+ align:start position:0%
+those patterns are
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+pattern and
+
+ align:start position:0%
+pattern and
+ 
+
+ align:start position:0%
+pattern and
+you know a pattern for rectilinear
+
+ align:start position:0%
+you know a pattern for rectilinear
+ 
+
+ align:start position:0%
+you know a pattern for rectilinear
+scenes in run and run two a pattern for
+
+ align:start position:0%
+scenes in run and run two a pattern for
+ 
+
+ align:start position:0%
+scenes in run and run two a pattern for
+rectilinear scenes in run one this cell
+
+ align:start position:0%
+rectilinear scenes in run one this cell
+ 
+
+ align:start position:0%
+rectilinear scenes in run one this cell
+is the correlation between those two
+
+ align:start position:0%
+is the correlation between those two
+ 
+
+ align:start position:0%
+is the correlation between those two
+patterns how stable is that pattern
+
+ align:start position:0%
+patterns how stable is that pattern
+ 
+
+ align:start position:0%
+patterns how stable is that pattern
+across repeated measures
+
+ align:start position:0%
+across repeated measures
+ 
+
+ align:start position:0%
+across repeated measures
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+all right so that's what that r value is
+
+ align:start position:0%
+all right so that's what that r value is
+ 
+
+ align:start position:0%
+all right so that's what that r value is
+the two darker blue scare
+
+ align:start position:0%
+the two darker blue scare
+ 
+
+ align:start position:0%
+the two darker blue scare
+squares here
+
+ align:start position:0%
+squares here
+ 
+
+ align:start position:0%
+squares here
+are the r values
+
+ align:start position:0%
+are the r values
+ 
+
+ align:start position:0%
+are the r values
+for stimuli that differ in
+
+ align:start position:0%
+for stimuli that differ in
+ 
+
+ align:start position:0%
+for stimuli that differ in
+rectilinearity
+
+ align:start position:0%
+rectilinearity
+ 
+
+ align:start position:0%
+rectilinearity
+and remember that the essence of the hex
+
+ align:start position:0%
+and remember that the essence of the hex
+ 
+
+ align:start position:0%
+and remember that the essence of the hex
+b style pattern analysis
+
+ align:start position:0%
+b style pattern analysis
+ 
+
+ align:start position:0%
+b style pattern analysis
+is to
+
+ align:start position:0%
+is to
+ 
+
+ align:start position:0%
+is to
+see if the within correlations are
+
+ align:start position:0%
+see if the within correlations are
+ 
+
+ align:start position:0%
+see if the within correlations are
+higher than the between correlations
+
+ align:start position:0%
+higher than the between correlations
+ 
+
+ align:start position:0%
+higher than the between correlations
+in this case the within correlations are
+
+ align:start position:0%
+in this case the within correlations are
+ 
+
+ align:start position:0%
+in this case the within correlations are
+within rectilinearity versus between
+
+ align:start position:0%
+within rectilinearity versus between
+ 
+
+ align:start position:0%
+within rectilinearity versus between
+rectilinearity
+
+ align:start position:0%
+rectilinearity
+ 
+
+ align:start position:0%
+rectilinearity
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+all right
+
+ align:start position:0%
+all right
+ 
+
+ align:start position:0%
+all right
+and so then they calculate all those
+
+ align:start position:0%
+and so then they calculate all those
+ 
+
+ align:start position:0%
+and so then they calculate all those
+correlation differences and they plot
+
+ align:start position:0%
+correlation differences and they plot
+ 
+
+ align:start position:0%
+correlation differences and they plot
+them as discriminate discrimination
+
+ align:start position:0%
+them as discriminate discrimination
+ 
+
+ align:start position:0%
+them as discriminate discrimination
+abilities
+
+ align:start position:0%
+abilities
+ 
+
+ align:start position:0%
+abilities
+and so
+
+ align:start position:0%
+and so
+ 
+
+ align:start position:0%
+and so
+what this is showing us here is that
+
+ align:start position:0%
+what this is showing us here is that
+ 
+
+ align:start position:0%
+what this is showing us here is that
+actually the ppa doesn't have any
+
+ align:start position:0%
+actually the ppa doesn't have any
+ 
+
+ align:start position:0%
+actually the ppa doesn't have any
+information in its pattern of response
+
+ align:start position:0%
+information in its pattern of response
+ 
+
+ align:start position:0%
+information in its pattern of response
+about the rectilinearity of the scene
+
+ align:start position:0%
+about the rectilinearity of the scene
+ 
+
+ align:start position:0%
+about the rectilinearity of the scene
+however if we take the same data
+
+ align:start position:0%
+however if we take the same data
+ 
+
+ align:start position:0%
+however if we take the same data
+and now choose within category versus
+
+ align:start position:0%
+and now choose within category versus
+ 
+
+ align:start position:0%
+and now choose within category versus
+between category
+
+ align:start position:0%
+between category
+ 
+
+ align:start position:0%
+between category
+ignoring rectilinearity and we get the
+
+ align:start position:0%
+ignoring rectilinearity and we get the
+ 
+
+ align:start position:0%
+ignoring rectilinearity and we get the
+same kind of um
+
+ align:start position:0%
+same kind of um
+ 
+
+ align:start position:0%
+same kind of um
+selectivity
+
+ align:start position:0%
+selectivity
+ 
+
+ align:start position:0%
+selectivity
+correlation difference within versus
+
+ align:start position:0%
+correlation difference within versus
+ 
+
+ align:start position:0%
+correlation difference within versus
+between for category there's heaps of
+
+ align:start position:0%
+between for category there's heaps of
+ 
+
+ align:start position:0%
+between for category there's heaps of
+information about category
+
+ align:start position:0%
+information about category
+ 
+
+ align:start position:0%
+information about category
+does that make sense
+
+ align:start position:0%
+does that make sense
+ 
+
+ align:start position:0%
+does that make sense
+okay again if you're fuzzy about this
+
+ align:start position:0%
+okay again if you're fuzzy about this
+ 
+
+ align:start position:0%
+okay again if you're fuzzy about this
+look back on that slide i have lots of
+
+ align:start position:0%
+look back on that slide i have lots of
+ 
+
+ align:start position:0%
+look back on that slide i have lots of
+suggestions for how to unfuzzy yourself
+
+ align:start position:0%
+suggestions for how to unfuzzy yourself
+ 
+
+ align:start position:0%
+suggestions for how to unfuzzy yourself
+on it okay
+
+ align:start position:0%
+on it okay
+ 
+
+ align:start position:0%
+on it okay
+all right so
+
+ align:start position:0%
+all right so
+ 
+
+ align:start position:0%
+all right so
+into room summary pba responds more to
+
+ align:start position:0%
+into room summary pba responds more to
+ 
+
+ align:start position:0%
+into room summary pba responds more to
+scenes and objects
+
+ align:start position:0%
+scenes and objects
+ 
+
+ align:start position:0%
+scenes and objects
+it seems to like spatial layout in
+
+ align:start position:0%
+it seems to like spatial layout in
+ 
+
+ align:start position:0%
+it seems to like spatial layout in
+particular it does respond more to boxes
+
+ align:start position:0%
+particular it does respond more to boxes
+ 
+
+ align:start position:0%
+particular it does respond more to boxes
+and circles but that rectilinearity bias
+
+ align:start position:0%
+and circles but that rectilinearity bias
+ 
+
+ align:start position:0%
+and circles but that rectilinearity bias
+can't account for scene selectivity
+
+ align:start position:0%
+can't account for scene selectivity
+ 
+
+ align:start position:0%
+can't account for scene selectivity
+that's all very nice
+
+ align:start position:0%
+that's all very nice
+ 
+
+ align:start position:0%
+that's all very nice
+but what is a whole other kind of
+
+ align:start position:0%
+but what is a whole other kind of
+ 
+
+ align:start position:0%
+but what is a whole other kind of
+fundamental question we haven't yet
+
+ align:start position:0%
+fundamental question we haven't yet
+ 
+
+ align:start position:0%
+fundamental question we haven't yet
+asked about the ppa
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so we've been messing around with
+
+ align:start position:0%
+so we've been messing around with
+ 
+
+ align:start position:0%
+so we've been messing around with
+functional mri measuring magnitudes of
+
+ align:start position:0%
+functional mri measuring magnitudes of
+ 
+
+ align:start position:0%
+functional mri measuring magnitudes of
+response trying to test these kind of
+
+ align:start position:0%
+response trying to test these kind of
+ 
+
+ align:start position:0%
+response trying to test these kind of
+vague
+
+ align:start position:0%
+vague
+ 
+
+ align:start position:0%
+vague
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+you know general hypotheses about what
+
+ align:start position:0%
+you know general hypotheses about what
+ 
+
+ align:start position:0%
+you know general hypotheses about what
+it might be responding to yes
+
+ align:start position:0%
+it might be responding to yes
+ 
+
+ align:start position:0%
+it might be responding to yes
+yes what what particular causation
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+i guess like how it's in scenes
+
+ align:start position:0%
+i guess like how it's in scenes
+ 
+
+ align:start position:0%
+i guess like how it's in scenes
+like how
+
+ align:start position:0%
+like how
+ 
+
+ align:start position:0%
+like how
+the pva liquid will work place in person
+
+ align:start position:0%
+the pva liquid will work place in person
+ 
+
+ align:start position:0%
+the pva liquid will work place in person
+exactly exactly again we can test the
+
+ align:start position:0%
+exactly exactly again we can test the
+ 
+
+ align:start position:0%
+exactly exactly again we can test the
+causal role of a stimulus on the ppa all
+
+ align:start position:0%
+causal role of a stimulus on the ppa all
+ 
+
+ align:start position:0%
+causal role of a stimulus on the ppa all
+of the stuff i talked about did that
+
+ align:start position:0%
+of the stuff i talked about did that
+ 
+
+ align:start position:0%
+of the stuff i talked about did that
+manipulate the stimulus find different
+
+ align:start position:0%
+manipulate the stimulus find different
+ 
+
+ align:start position:0%
+manipulate the stimulus find different
+ppa responses but what we haven't done
+
+ align:start position:0%
+ppa responses but what we haven't done
+ 
+
+ align:start position:0%
+ppa responses but what we haven't done
+yet is ask
+
+ align:start position:0%
+yet is ask
+ 
+
+ align:start position:0%
+yet is ask
+what is a relation the causal
+
+ align:start position:0%
+what is a relation the causal
+ 
+
+ align:start position:0%
+what is a relation the causal
+relationship if any between activity in
+
+ align:start position:0%
+relationship if any between activity in
+ 
+
+ align:start position:0%
+relationship if any between activity in
+the ppa and perception of scenes or
+
+ align:start position:0%
+the ppa and perception of scenes or
+ 
+
+ align:start position:0%
+the ppa and perception of scenes or
+navigation okay
+
+ align:start position:0%
+navigation okay
+ 
+
+ align:start position:0%
+navigation okay
+so so far this is all just suggestive we
+
+ align:start position:0%
+so so far this is all just suggestive we
+ 
+
+ align:start position:0%
+so so far this is all just suggestive we
+have no causal evidence for its role in
+
+ align:start position:0%
+have no causal evidence for its role in
+ 
+
+ align:start position:0%
+have no causal evidence for its role in
+navigation
+
+ align:start position:0%
+navigation
+ 
+
+ align:start position:0%
+navigation
+right or perception
+
+ align:start position:0%
+right or perception
+ 
+
+ align:start position:0%
+right or perception
+all right so let's get some
+
+ align:start position:0%
+all right so let's get some
+ 
+
+ align:start position:0%
+all right so let's get some
+i'll show you a few examples
+
+ align:start position:0%
+i'll show you a few examples
+ 
+
+ align:start position:0%
+i'll show you a few examples
+um so one as you guys have learned by
+
+ align:start position:0%
+um so one as you guys have learned by
+ 
+
+ align:start position:0%
+um so one as you guys have learned by
+now is these rare cases where there's
+
+ align:start position:0%
+now is these rare cases where there's
+ 
+
+ align:start position:0%
+now is these rare cases where there's
+direct electrical stimulation of a
+
+ align:start position:0%
+direct electrical stimulation of a
+ 
+
+ align:start position:0%
+direct electrical stimulation of a
+region and there's one patient in whom
+
+ align:start position:0%
+region and there's one patient in whom
+ 
+
+ align:start position:0%
+region and there's one patient in whom
+this is reported this patient again is
+
+ align:start position:0%
+this is reported this patient again is
+ 
+
+ align:start position:0%
+this is reported this patient again is
+being mapped out before neurosurgery
+
+ align:start position:0%
+being mapped out before neurosurgery
+ 
+
+ align:start position:0%
+being mapped out before neurosurgery
+there's
+
+ align:start position:0%
+there's
+ 
+
+ align:start position:0%
+there's
+they did functional mri in the patient
+
+ align:start position:0%
+they did functional mri in the patient
+ 
+
+ align:start position:0%
+they did functional mri in the patient
+first this is his functional mri
+
+ align:start position:0%
+first this is his functional mri
+ 
+
+ align:start position:0%
+first this is his functional mri
+response to i think houses versus
+
+ align:start position:0%
+response to i think houses versus
+ 
+
+ align:start position:0%
+response to i think houses versus
+objects houses are not as strong
+
+ align:start position:0%
+objects houses are not as strong
+ 
+
+ align:start position:0%
+objects houses are not as strong
+an activator as scenes for the ppa but
+
+ align:start position:0%
+an activator as scenes for the ppa but
+ 
+
+ align:start position:0%
+an activator as scenes for the ppa but
+they're pretty good ppa responds much
+
+ align:start position:0%
+they're pretty good ppa responds much
+ 
+
+ align:start position:0%
+they're pretty good ppa responds much
+more to houses than other objects and so
+
+ align:start position:0%
+more to houses than other objects and so
+ 
+
+ align:start position:0%
+more to houses than other objects and so
+that's a nice activation map showing the
+
+ align:start position:0%
+that's a nice activation map showing the
+ 
+
+ align:start position:0%
+that's a nice activation map showing the
+ppa and those little circles are where
+
+ align:start position:0%
+ppa and those little circles are where
+ 
+
+ align:start position:0%
+ppa and those little circles are where
+the electrodes are little black circles
+
+ align:start position:0%
+the electrodes are little black circles
+ 
+
+ align:start position:0%
+the electrodes are little black circles
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+so um so they know they're in the ppa
+
+ align:start position:0%
+so um so they know they're in the ppa
+ 
+
+ align:start position:0%
+so um so they know they're in the ppa
+because they did functional mri first to
+
+ align:start position:0%
+because they did functional mri first to
+ 
+
+ align:start position:0%
+because they did functional mri first to
+localize that region now those
+
+ align:start position:0%
+localize that region now those
+ 
+
+ align:start position:0%
+localize that region now those
+electrodes are sitting there
+
+ align:start position:0%
+electrodes are sitting there
+ 
+
+ align:start position:0%
+electrodes are sitting there
+and so first thing we do is record or
+
+ align:start position:0%
+and so first thing we do is record or
+ 
+
+ align:start position:0%
+and so first thing we do is record or
+the first thing they did is record
+
+ align:start position:0%
+the first thing they did is record
+ 
+
+ align:start position:0%
+the first thing they did is record
+responses they flash up a bunch of
+
+ align:start position:0%
+responses they flash up a bunch of
+ 
+
+ align:start position:0%
+responses they flash up a bunch of
+different kind of images and they
+
+ align:start position:0%
+different kind of images and they
+ 
+
+ align:start position:0%
+different kind of images and they
+measure the response in those electrodes
+
+ align:start position:0%
+measure the response in those electrodes
+ 
+
+ align:start position:0%
+measure the response in those electrodes
+and so what you see is in those
+
+ align:start position:0%
+and so what you see is in those
+ 
+
+ align:start position:0%
+and so what you see is in those
+electrodes right over there one two
+
+ align:start position:0%
+electrodes right over there one two
+ 
+
+ align:start position:0%
+electrodes right over there one two
+three that correspond to the ppa
+
+ align:start position:0%
+three that correspond to the ppa
+ 
+
+ align:start position:0%
+three that correspond to the ppa
+you see a higher response to house
+
+ align:start position:0%
+you see a higher response to house
+ 
+
+ align:start position:0%
+you see a higher response to house
+images than to any of the other images
+
+ align:start position:0%
+images than to any of the other images
+ 
+
+ align:start position:0%
+images than to any of the other images
+and you see the time course here over a
+
+ align:start position:0%
+and you see the time course here over a
+ 
+
+ align:start position:0%
+and you see the time course here over a
+few seconds
+
+ align:start position:0%
+few seconds
+ 
+
+ align:start position:0%
+few seconds
+okay everybody clear this is not causal
+
+ align:start position:0%
+okay everybody clear this is not causal
+ 
+
+ align:start position:0%
+okay everybody clear this is not causal
+evidence yet it's just amazing direct
+
+ align:start position:0%
+evidence yet it's just amazing direct
+ 
+
+ align:start position:0%
+evidence yet it's just amazing direct
+intracranial recordings from the ppa
+
+ align:start position:0%
+intracranial recordings from the ppa
+ 
+
+ align:start position:0%
+intracranial recordings from the ppa
+i think the only time this was ever done
+
+ align:start position:0%
+i think the only time this was ever done
+ 
+
+ align:start position:0%
+i think the only time this was ever done
+because it's pretty rare to have the
+
+ align:start position:0%
+because it's pretty rare to have the
+ 
+
+ align:start position:0%
+because it's pretty rare to have the
+electrodes right there in a patient
+
+ align:start position:0%
+electrodes right there in a patient
+ 
+
+ align:start position:0%
+electrodes right there in a patient
+who's willing to look at your silly
+
+ align:start position:0%
+who's willing to look at your silly
+ 
+
+ align:start position:0%
+who's willing to look at your silly
+pictures and all of that right
+
+ align:start position:0%
+pictures and all of that right
+ 
+
+ align:start position:0%
+pictures and all of that right
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+but now
+
+ align:start position:0%
+but now
+ 
+
+ align:start position:0%
+but now
+what happens when they stimulate there
+
+ align:start position:0%
+what happens when they stimulate there
+ 
+
+ align:start position:0%
+what happens when they stimulate there
+okay so let's look at what happens when
+
+ align:start position:0%
+okay so let's look at what happens when
+ 
+
+ align:start position:0%
+okay so let's look at what happens when
+they stimulate
+
+ align:start position:0%
+they stimulate
+ 
+
+ align:start position:0%
+they stimulate
+um on these sites um
+
+ align:start position:0%
+um on these sites um
+ 
+
+ align:start position:0%
+um on these sites um
+four and three that are off to the side
+
+ align:start position:0%
+four and three that are off to the side
+ 
+
+ align:start position:0%
+four and three that are off to the side
+of the scene selectivity and this is
+
+ align:start position:0%
+of the scene selectivity and this is
+ 
+
+ align:start position:0%
+of the scene selectivity and this is
+just a dialogue we don't have a video
+
+ align:start position:0%
+just a dialogue we don't have a video
+ 
+
+ align:start position:0%
+just a dialogue we don't have a video
+unfortunately the videos are more fun
+
+ align:start position:0%
+unfortunately the videos are more fun
+ 
+
+ align:start position:0%
+unfortunately the videos are more fun
+but it's just a dialogue between the
+
+ align:start position:0%
+but it's just a dialogue between the
+ 
+
+ align:start position:0%
+but it's just a dialogue between the
+neurologist and the patient
+
+ align:start position:0%
+neurologist and the patient
+ 
+
+ align:start position:0%
+neurologist and the patient
+and the neurologist electrically
+
+ align:start position:0%
+and the neurologist electrically
+ 
+
+ align:start position:0%
+and the neurologist electrically
+stimulates that region
+
+ align:start position:0%
+stimulates that region
+ 
+
+ align:start position:0%
+stimulates that region
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+and says did you see anything there
+
+ align:start position:0%
+and says did you see anything there
+ 
+
+ align:start position:0%
+and says did you see anything there
+patient says i don't know i started
+
+ align:start position:0%
+patient says i don't know i started
+ 
+
+ align:start position:0%
+patient says i don't know i started
+feeling something i don't know it's
+
+ align:start position:0%
+feeling something i don't know it's
+ 
+
+ align:start position:0%
+feeling something i don't know it's
+probably just me oh no it's not you
+
+ align:start position:0%
+probably just me oh no it's not you
+ 
+
+ align:start position:0%
+probably just me oh no it's not you
+and then they stimulate again anything
+
+ align:start position:0%
+and then they stimulate again anything
+ 
+
+ align:start position:0%
+and then they stimulate again anything
+there no anything here no okay so that's
+
+ align:start position:0%
+there no anything here no okay so that's
+ 
+
+ align:start position:0%
+there no anything here no okay so that's
+right next to the side of the scene
+
+ align:start position:0%
+right next to the side of the scene
+ 
+
+ align:start position:0%
+right next to the side of the scene
+selective electrodes right next door a
+
+ align:start position:0%
+selective electrodes right next door a
+ 
+
+ align:start position:0%
+selective electrodes right next door a
+few millimeters away
+
+ align:start position:0%
+few millimeters away
+ 
+
+ align:start position:0%
+few millimeters away
+then they move uh their stimulator over
+
+ align:start position:0%
+then they move uh their stimulator over
+ 
+
+ align:start position:0%
+then they move uh their stimulator over
+here they don't move anything they just
+
+ align:start position:0%
+here they don't move anything they just
+ 
+
+ align:start position:0%
+here they don't move anything they just
+control where they're going to stimulate
+
+ align:start position:0%
+control where they're going to stimulate
+ 
+
+ align:start position:0%
+control where they're going to stimulate
+patient of course has no idea
+
+ align:start position:0%
+patient of course has no idea
+ 
+
+ align:start position:0%
+patient of course has no idea
+neurologist says anything here do you
+
+ align:start position:0%
+neurologist says anything here do you
+ 
+
+ align:start position:0%
+neurologist says anything here do you
+see anything
+
+ align:start position:0%
+see anything
+ 
+
+ align:start position:0%
+see anything
+feel anything
+
+ align:start position:0%
+feel anything
+ 
+
+ align:start position:0%
+feel anything
+patient says yeah i feel like he looks
+
+ align:start position:0%
+patient says yeah i feel like he looks
+ 
+
+ align:start position:0%
+patient says yeah i feel like he looks
+perplexed
+
+ align:start position:0%
+perplexed
+ 
+
+ align:start position:0%
+perplexed
+puts hand to forehead
+
+ align:start position:0%
+puts hand to forehead
+ 
+
+ align:start position:0%
+puts hand to forehead
+i feel like i saw like
+
+ align:start position:0%
+i feel like i saw like
+ 
+
+ align:start position:0%
+i feel like i saw like
+some other site we were at the train
+
+ align:start position:0%
+some other site we were at the train
+ 
+
+ align:start position:0%
+some other site we were at the train
+station
+
+ align:start position:0%
+station
+ 
+
+ align:start position:0%
+station
+neurologist cleverly says so it feels
+
+ align:start position:0%
+neurologist cleverly says so it feels
+ 
+
+ align:start position:0%
+neurologist cleverly says so it feels
+like you're at a train station
+
+ align:start position:0%
+like you're at a train station
+ 
+
+ align:start position:0%
+like you're at a train station
+patient says yeah
+
+ align:start position:0%
+patient says yeah
+ 
+
+ align:start position:0%
+patient says yeah
+outside the train station neurologist
+
+ align:start position:0%
+outside the train station neurologist
+ 
+
+ align:start position:0%
+outside the train station neurologist
+let me know if you get any sensation
+
+ align:start position:0%
+let me know if you get any sensation
+ 
+
+ align:start position:0%
+let me know if you get any sensation
+like that again
+
+ align:start position:0%
+like that again
+ 
+
+ align:start position:0%
+like that again
+it stimulates do you feel anything here
+
+ align:start position:0%
+it stimulates do you feel anything here
+ 
+
+ align:start position:0%
+it stimulates do you feel anything here
+no
+
+ align:start position:0%
+no
+ 
+
+ align:start position:0%
+no
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+and he does it again do you see the um
+
+ align:start position:0%
+and he does it again do you see the um
+ 
+
+ align:start position:0%
+and he does it again do you see the um
+do you see the the train station or did
+
+ align:start position:0%
+do you see the the train station or did
+ 
+
+ align:start position:0%
+do you see the the train station or did
+it oh did you see the train station or
+
+ align:start position:0%
+it oh did you see the train station or
+ 
+
+ align:start position:0%
+it oh did you see the train station or
+did it feel like you were at the train
+
+ align:start position:0%
+did it feel like you were at the train
+ 
+
+ align:start position:0%
+did it feel like you were at the train
+station
+
+ align:start position:0%
+station
+ 
+
+ align:start position:0%
+station
+patient i saw it
+
+ align:start position:0%
+patient i saw it
+ 
+
+ align:start position:0%
+patient i saw it
+right these are very sparse precious
+
+ align:start position:0%
+right these are very sparse precious
+ 
+
+ align:start position:0%
+right these are very sparse precious
+data but that's so telling it's not that
+
+ align:start position:0%
+data but that's so telling it's not that
+ 
+
+ align:start position:0%
+data but that's so telling it's not that
+he knew he was at the train station
+
+ align:start position:0%
+he knew he was at the train station
+ 
+
+ align:start position:0%
+he knew he was at the train station
+abstractly he saw it okay
+
+ align:start position:0%
+abstractly he saw it okay
+ 
+
+ align:start position:0%
+abstractly he saw it okay
+so then they stimulate again right on
+
+ align:start position:0%
+so then they stimulate again right on
+ 
+
+ align:start position:0%
+so then they stimulate again right on
+those
+
+ align:start position:0%
+those
+ 
+
+ align:start position:0%
+those
+scene selective regions the patient says
+
+ align:start position:0%
+scene selective regions the patient says
+ 
+
+ align:start position:0%
+scene selective regions the patient says
+again i saw almost like i don't know
+
+ align:start position:0%
+again i saw almost like i don't know
+ 
+
+ align:start position:0%
+again i saw almost like i don't know
+like i saw it was very brief neurologist
+
+ align:start position:0%
+like i saw it was very brief neurologist
+ 
+
+ align:start position:0%
+like i saw it was very brief neurologist
+says i'm going to show it to you one
+
+ align:start position:0%
+says i'm going to show it to you one
+ 
+
+ align:start position:0%
+says i'm going to show it to you one
+more time really what he means is i'm
+
+ align:start position:0%
+more time really what he means is i'm
+ 
+
+ align:start position:0%
+more time really what he means is i'm
+going to stimulate you in the same place
+
+ align:start position:0%
+going to stimulate you in the same place
+ 
+
+ align:start position:0%
+going to stimulate you in the same place
+one more time see if you can describe it
+
+ align:start position:0%
+one more time see if you can describe it
+ 
+
+ align:start position:0%
+one more time see if you can describe it
+any further um
+
+ align:start position:0%
+any further um
+ 
+
+ align:start position:0%
+any further um
+i'm going to give you one last time what
+
+ align:start position:0%
+i'm going to give you one last time what
+ 
+
+ align:start position:0%
+i'm going to give you one last time what
+do you think
+
+ align:start position:0%
+do you think
+ 
+
+ align:start position:0%
+do you think
+i don't really know what to make of it
+
+ align:start position:0%
+i don't really know what to make of it
+ 
+
+ align:start position:0%
+i don't really know what to make of it
+but i saw like another staircase
+
+ align:start position:0%
+but i saw like another staircase
+ 
+
+ align:start position:0%
+but i saw like another staircase
+the rest i couldn't make out
+
+ align:start position:0%
+the rest i couldn't make out
+ 
+
+ align:start position:0%
+the rest i couldn't make out
+but i saw a closet space but not this
+
+ align:start position:0%
+but i saw a closet space but not this
+ 
+
+ align:start position:0%
+but i saw a closet space but not this
+one he points to a closet door in the
+
+ align:start position:0%
+one he points to a closet door in the
+ 
+
+ align:start position:0%
+one he points to a closet door in the
+room
+
+ align:start position:0%
+room
+ 
+
+ align:start position:0%
+room
+that one was stuffed and it was blue
+
+ align:start position:0%
+that one was stuffed and it was blue
+ 
+
+ align:start position:0%
+that one was stuffed and it was blue
+have you seen it before it's a
+
+ align:start position:0%
+have you seen it before it's a
+ 
+
+ align:start position:0%
+have you seen it before it's a
+neurologist have you seen it before at
+
+ align:start position:0%
+neurologist have you seen it before at
+ 
+
+ align:start position:0%
+neurologist have you seen it before at
+some point in your life you think yeah i
+
+ align:start position:0%
+some point in your life you think yeah i
+ 
+
+ align:start position:0%
+some point in your life you think yeah i
+mean when i saw the train station
+
+ align:start position:0%
+mean when i saw the train station
+ 
+
+ align:start position:0%
+mean when i saw the train station
+train station you've been at yeah et
+
+ align:start position:0%
+train station you've been at yeah et
+ 
+
+ align:start position:0%
+train station you've been at yeah et
+cetera et cetera
+
+ align:start position:0%
+cetera et cetera
+ 
+
+ align:start position:0%
+cetera et cetera
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+it's not a lot of data but it's very
+
+ align:start position:0%
+it's not a lot of data but it's very
+ 
+
+ align:start position:0%
+it's not a lot of data but it's very
+compelling right what is the patient
+
+ align:start position:0%
+compelling right what is the patient
+ 
+
+ align:start position:0%
+compelling right what is the patient
+describing
+
+ align:start position:0%
+describing
+ 
+
+ align:start position:0%
+describing
+places that he's in that he sees
+
+ align:start position:0%
+places that he's in that he sees
+ 
+
+ align:start position:0%
+places that he's in that he sees
+and then he describes this closet space
+
+ align:start position:0%
+and then he describes this closet space
+ 
+
+ align:start position:0%
+and then he describes this closet space
+and its colors interestingly color
+
+ align:start position:0%
+and its colors interestingly color
+ 
+
+ align:start position:0%
+and its colors interestingly color
+regions are right next to scene region
+
+ align:start position:0%
+regions are right next to scene region
+ 
+
+ align:start position:0%
+regions are right next to scene region
+so that's kind of cool too
+
+ align:start position:0%
+so that's kind of cool too
+ 
+
+ align:start position:0%
+so that's kind of cool too
+right
+
+ align:start position:0%
+right
+ 
+
+ align:start position:0%
+right
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+it's causal evidence it's sparse ideally
+
+ align:start position:0%
+it's causal evidence it's sparse ideally
+ 
+
+ align:start position:0%
+it's causal evidence it's sparse ideally
+we'd like more in science but
+
+ align:start position:0%
+we'd like more in science but
+ 
+
+ align:start position:0%
+we'd like more in science but
+it's pretty cool
+
+ align:start position:0%
+it's pretty cool
+ 
+
+ align:start position:0%
+it's pretty cool
+yeah and all this far the patient is
+
+ align:start position:0%
+yeah and all this far the patient is
+ 
+
+ align:start position:0%
+yeah and all this far the patient is
+just staring at a bank
+
+ align:start position:0%
+just staring at a bank
+ 
+
+ align:start position:0%
+just staring at a bank
+you know i actually forget in the paper
+
+ align:start position:0%
+you know i actually forget in the paper
+ 
+
+ align:start position:0%
+you know i actually forget in the paper
+i've got to go look that up i forget
+
+ align:start position:0%
+i've got to go look that up i forget
+ 
+
+ align:start position:0%
+i've got to go look that up i forget
+exactly what the patient was doing
+
+ align:start position:0%
+exactly what the patient was doing
+ 
+
+ align:start position:0%
+exactly what the patient was doing
+whether i think he's just in the room
+
+ align:start position:0%
+whether i think he's just in the room
+ 
+
+ align:start position:0%
+whether i think he's just in the room
+looking out
+
+ align:start position:0%
+looking out
+ 
+
+ align:start position:0%
+looking out
+usually they don't control it that much
+
+ align:start position:0%
+usually they don't control it that much
+ 
+
+ align:start position:0%
+usually they don't control it that much
+because it's done kind of for clinical
+
+ align:start position:0%
+because it's done kind of for clinical
+ 
+
+ align:start position:0%
+because it's done kind of for clinical
+reasons and the patient is in their
+
+ align:start position:0%
+reasons and the patient is in their
+ 
+
+ align:start position:0%
+reasons and the patient is in their
+hospital bed and they're just
+
+ align:start position:0%
+hospital bed and they're just
+ 
+
+ align:start position:0%
+hospital bed and they're just
+stimulating so he's probably just
+
+ align:start position:0%
+stimulating so he's probably just
+ 
+
+ align:start position:0%
+stimulating so he's probably just
+looking out at the space he's in in fact
+
+ align:start position:0%
+looking out at the space he's in in fact
+ 
+
+ align:start position:0%
+looking out at the space he's in in fact
+he must have been because at one point
+
+ align:start position:0%
+he must have been because at one point
+ 
+
+ align:start position:0%
+he must have been because at one point
+he says a closet not like that one over
+
+ align:start position:0%
+he says a closet not like that one over
+ 
+
+ align:start position:0%
+he says a closet not like that one over
+there so if he was staring at a blank
+
+ align:start position:0%
+there so if he was staring at a blank
+ 
+
+ align:start position:0%
+there so if he was staring at a blank
+thing he was also
+
+ align:start position:0%
+thing he was also
+ 
+
+ align:start position:0%
+thing he was also
+looking out at his room
+
+ align:start position:0%
+looking out at his room
+ 
+
+ align:start position:0%
+looking out at his room
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+yeah so
+
+ align:start position:0%
+yeah so
+ 
+
+ align:start position:0%
+yeah so
+this may be a little bit off topic you
+
+ align:start position:0%
+this may be a little bit off topic you
+ 
+
+ align:start position:0%
+this may be a little bit off topic you
+said the region of color perception is
+
+ align:start position:0%
+said the region of color perception is
+ 
+
+ align:start position:0%
+said the region of color perception is
+very close to this
+
+ align:start position:0%
+very close to this
+ 
+
+ align:start position:0%
+very close to this
+is there any relationship between like
+
+ align:start position:0%
+is there any relationship between like
+ 
+
+ align:start position:0%
+is there any relationship between like
+functional proximity and
+
+ align:start position:0%
+functional proximity and
+ 
+
+ align:start position:0%
+functional proximity and
+that's a great question nobody in the
+
+ align:start position:0%
+that's a great question nobody in the
+ 
+
+ align:start position:0%
+that's a great question nobody in the
+field has an answer to this people often
+
+ align:start position:0%
+field has an answer to this people often
+ 
+
+ align:start position:0%
+field has an answer to this people often
+make hay about the proximity of two
+
+ align:start position:0%
+make hay about the proximity of two
+ 
+
+ align:start position:0%
+make hay about the proximity of two
+regions like oh there's some deep link
+
+ align:start position:0%
+regions like oh there's some deep link
+ 
+
+ align:start position:0%
+regions like oh there's some deep link
+because this thing is next to that thing
+
+ align:start position:0%
+because this thing is next to that thing
+ 
+
+ align:start position:0%
+because this thing is next to that thing
+uh you know the body selective region is
+
+ align:start position:0%
+uh you know the body selective region is
+ 
+
+ align:start position:0%
+uh you know the body selective region is
+right next to and in fact slightly
+
+ align:start position:0%
+right next to and in fact slightly
+ 
+
+ align:start position:0%
+right next to and in fact slightly
+overlapping with uh area mt that
+
+ align:start position:0%
+overlapping with uh area mt that
+ 
+
+ align:start position:0%
+overlapping with uh area mt that
+responds to motion it's like oh bodies
+
+ align:start position:0%
+responds to motion it's like oh bodies
+ 
+
+ align:start position:0%
+responds to motion it's like oh bodies
+you know faces move and cars move too so
+
+ align:start position:0%
+you know faces move and cars move too so
+ 
+
+ align:start position:0%
+you know faces move and cars move too so
+you know like i don't know it's
+
+ align:start position:0%
+you know like i don't know it's
+ 
+
+ align:start position:0%
+you know like i don't know it's
+tantalizing it feels like it ought to
+
+ align:start position:0%
+tantalizing it feels like it ought to
+ 
+
+ align:start position:0%
+tantalizing it feels like it ought to
+mean something and people often talk
+
+ align:start position:0%
+mean something and people often talk
+ 
+
+ align:start position:0%
+mean something and people often talk
+about you know talk as if it does and
+
+ align:start position:0%
+about you know talk as if it does and
+ 
+
+ align:start position:0%
+about you know talk as if it does and
+maybe it does but nobody's really put
+
+ align:start position:0%
+maybe it does but nobody's really put
+ 
+
+ align:start position:0%
+maybe it does but nobody's really put
+their finger on what exactly it would
+
+ align:start position:0%
+their finger on what exactly it would
+ 
+
+ align:start position:0%
+their finger on what exactly it would
+mean
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+but it's useful right so when when rosa
+
+ align:start position:0%
+but it's useful right so when when rosa
+ 
+
+ align:start position:0%
+but it's useful right so when when rosa
+lay for souza who you met in the color
+
+ align:start position:0%
+lay for souza who you met in the color
+ 
+
+ align:start position:0%
+lay for souza who you met in the color
+demo
+
+ align:start position:0%
+demo
+ 
+
+ align:start position:0%
+demo
+and i showed that in
+
+ align:start position:0%
+and i showed that in
+ 
+
+ align:start position:0%
+and i showed that in
+in humans you get face color and place
+
+ align:start position:0%
+in humans you get face color and place
+ 
+
+ align:start position:0%
+in humans you get face color and place
+regions right next to each other in that
+
+ align:start position:0%
+regions right next to each other in that
+ 
+
+ align:start position:0%
+regions right next to each other in that
+order that was really cool because rosa
+
+ align:start position:0%
+order that was really cool because rosa
+ 
+
+ align:start position:0%
+order that was really cool because rosa
+had previously shown that in monkeys
+
+ align:start position:0%
+had previously shown that in monkeys
+ 
+
+ align:start position:0%
+had previously shown that in monkeys
+in the monkey brain it goes face color
+
+ align:start position:0%
+in the monkey brain it goes face color
+ 
+
+ align:start position:0%
+in the monkey brain it goes face color
+place in exactly the same order
+
+ align:start position:0%
+place in exactly the same order
+ 
+
+ align:start position:0%
+place in exactly the same order
+and so we thought okay that's really
+
+ align:start position:0%
+and so we thought okay that's really
+ 
+
+ align:start position:0%
+and so we thought okay that's really
+interesting that suggests common
+
+ align:start position:0%
+interesting that suggests common
+ 
+
+ align:start position:0%
+interesting that suggests common
+inheritance because that's so weird and
+
+ align:start position:0%
+inheritance because that's so weird and
+ 
+
+ align:start position:0%
+inheritance because that's so weird and
+arbitrary why would it be the same so it
+
+ align:start position:0%
+arbitrary why would it be the same so it
+ 
+
+ align:start position:0%
+arbitrary why would it be the same so it
+can be useful in ways like that
+
+ align:start position:0%
+can be useful in ways like that
+ 
+
+ align:start position:0%
+can be useful in ways like that
+at least
+
+ align:start position:0%
+at least
+ 
+
+ align:start position:0%
+at least
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+so we just went through all of this so
+
+ align:start position:0%
+so we just went through all of this so
+ 
+
+ align:start position:0%
+so we just went through all of this so
+how does this go beyond what we knew
+
+ align:start position:0%
+how does this go beyond what we knew
+ 
+
+ align:start position:0%
+how does this go beyond what we knew
+from functional mri
+
+ align:start position:0%
+from functional mri
+ 
+
+ align:start position:0%
+from functional mri
+i'm insulting your intelligence you know
+
+ align:start position:0%
+i'm insulting your intelligence you know
+ 
+
+ align:start position:0%
+i'm insulting your intelligence you know
+the answer to this it goes beyond it
+
+ align:start position:0%
+the answer to this it goes beyond it
+ 
+
+ align:start position:0%
+the answer to this it goes beyond it
+because it tells you it implies that
+
+ align:start position:0%
+because it tells you it implies that
+ 
+
+ align:start position:0%
+because it tells you it implies that
+there's a causal role of that region in
+
+ align:start position:0%
+there's a causal role of that region in
+ 
+
+ align:start position:0%
+there's a causal role of that region in
+place perception some aspect of
+
+ align:start position:0%
+place perception some aspect of
+ 
+
+ align:start position:0%
+place perception some aspect of
+seeing a place okay
+
+ align:start position:0%
+seeing a place okay
+ 
+
+ align:start position:0%
+seeing a place okay
+now all of this about the ppa i just
+
+ align:start position:0%
+now all of this about the ppa i just
+ 
+
+ align:start position:0%
+now all of this about the ppa i just
+started in there because it's nice and
+
+ align:start position:0%
+started in there because it's nice and
+ 
+
+ align:start position:0%
+started in there because it's nice and
+concrete and easy to think about but no
+
+ align:start position:0%
+concrete and easy to think about but no
+ 
+
+ align:start position:0%
+concrete and easy to think about but no
+complex mental process happens in just
+
+ align:start position:0%
+complex mental process happens in just
+ 
+
+ align:start position:0%
+complex mental process happens in just
+one brain region nothing is ever like
+
+ align:start position:0%
+one brain region nothing is ever like
+ 
+
+ align:start position:0%
+one brain region nothing is ever like
+that
+
+ align:start position:0%
+that
+ 
+
+ align:start position:0%
+that
+uh and likewise scene perception and
+
+ align:start position:0%
+uh and likewise scene perception and
+ 
+
+ align:start position:0%
+uh and likewise scene perception and
+navigation is part of a much broader set
+
+ align:start position:0%
+navigation is part of a much broader set
+ 
+
+ align:start position:0%
+navigation is part of a much broader set
+of regions so if you do a contrast scan
+
+ align:start position:0%
+of regions so if you do a contrast scan
+ 
+
+ align:start position:0%
+of regions so if you do a contrast scan
+people looking at scenes versus objects
+
+ align:start position:0%
+people looking at scenes versus objects
+ 
+
+ align:start position:0%
+people looking at scenes versus objects
+you'll see not just the ppa in here
+
+ align:start position:0%
+you'll see not just the ppa in here
+ 
+
+ align:start position:0%
+you'll see not just the ppa in here
+again this is a folded up brain and this
+
+ align:start position:0%
+again this is a folded up brain and this
+ 
+
+ align:start position:0%
+again this is a folded up brain and this
+is the mathematically unfolded version
+
+ align:start position:0%
+is the mathematically unfolded version
+ 
+
+ align:start position:0%
+is the mathematically unfolded version
+so you can see the whole cortex dark
+
+ align:start position:0%
+so you can see the whole cortex dark
+ 
+
+ align:start position:0%
+so you can see the whole cortex dark
+bits are the bits that were that used to
+
+ align:start position:0%
+bits are the bits that were that used to
+ 
+
+ align:start position:0%
+bits are the bits that were that used to
+be inside a sulcus until it was
+
+ align:start position:0%
+be inside a sulcus until it was
+ 
+
+ align:start position:0%
+be inside a sulcus until it was
+mathematically unfolded
+
+ align:start position:0%
+mathematically unfolded
+ 
+
+ align:start position:0%
+mathematically unfolded
+so there's the ppa kind of hiding up in
+
+ align:start position:0%
+so there's the ppa kind of hiding up in
+ 
+
+ align:start position:0%
+so there's the ppa kind of hiding up in
+that sulcus and when you unfold it you
+
+ align:start position:0%
+that sulcus and when you unfold it you
+ 
+
+ align:start position:0%
+that sulcus and when you unfold it you
+see this nice big huge region okay
+
+ align:start position:0%
+see this nice big huge region okay
+ 
+
+ align:start position:0%
+see this nice big huge region okay
+but you also see all these other regions
+
+ align:start position:0%
+but you also see all these other regions
+ 
+
+ align:start position:0%
+but you also see all these other regions
+okay now there's a bunch of terminology
+
+ align:start position:0%
+okay now there's a bunch of terminology
+ 
+
+ align:start position:0%
+okay now there's a bunch of terminology
+and i don't panic i don't think you
+
+ align:start position:0%
+and i don't panic i don't think you
+ 
+
+ align:start position:0%
+and i don't panic i don't think you
+should memorize everything about each
+
+ align:start position:0%
+should memorize everything about each
+ 
+
+ align:start position:0%
+should memorize everything about each
+region you should know that there's
+
+ align:start position:0%
+region you should know that there's
+ 
+
+ align:start position:0%
+region you should know that there's
+multiple scene regions you should know
+
+ align:start position:0%
+multiple scene regions you should know
+ 
+
+ align:start position:0%
+multiple scene regions you should know
+some of the kinds of ways you tease
+
+ align:start position:0%
+some of the kinds of ways you tease
+ 
+
+ align:start position:0%
+some of the kinds of ways you tease
+apart the functions and some of the
+
+ align:start position:0%
+apart the functions and some of the
+ 
+
+ align:start position:0%
+apart the functions and some of the
+functions that have been
+
+ align:start position:0%
+functions that have been
+ 
+
+ align:start position:0%
+functions that have been
+tested and how they're tested but you
+
+ align:start position:0%
+tested and how they're tested but you
+ 
+
+ align:start position:0%
+tested and how they're tested but you
+don't need to memorize every last detail
+
+ align:start position:0%
+don't need to memorize every last detail
+ 
+
+ align:start position:0%
+don't need to memorize every last detail
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+because it's going to get a little hairy
+
+ align:start position:0%
+because it's going to get a little hairy
+ 
+
+ align:start position:0%
+because it's going to get a little hairy
+okay so here's a second scene region
+
+ align:start position:0%
+okay so here's a second scene region
+ 
+
+ align:start position:0%
+okay so here's a second scene region
+right there
+
+ align:start position:0%
+right there
+ 
+
+ align:start position:0%
+right there
+called retrosplenial cortex or rsc
+
+ align:start position:0%
+called retrosplenial cortex or rsc
+ 
+
+ align:start position:0%
+called retrosplenial cortex or rsc
+and uh actually russell epstein and i
+
+ align:start position:0%
+and uh actually russell epstein and i
+ 
+
+ align:start position:0%
+and uh actually russell epstein and i
+saw that activation in the very very
+
+ align:start position:0%
+saw that activation in the very very
+ 
+
+ align:start position:0%
+saw that activation in the very very
+first experiments we did in the 1990s
+
+ align:start position:0%
+first experiments we did in the 1990s
+ 
+
+ align:start position:0%
+first experiments we did in the 1990s
+but we really didn't know what we were
+
+ align:start position:0%
+but we really didn't know what we were
+ 
+
+ align:start position:0%
+but we really didn't know what we were
+doing back then and we knew that this is
+
+ align:start position:0%
+doing back then and we knew that this is
+ 
+
+ align:start position:0%
+doing back then and we knew that this is
+right near the calcarine sulcus
+
+ align:start position:0%
+right near the calcarine sulcus
+ 
+
+ align:start position:0%
+right near the calcarine sulcus
+remind me what happens in the calculus
+
+ align:start position:0%
+remind me what happens in the calculus
+ 
+
+ align:start position:0%
+remind me what happens in the calculus
+sulcus what functional region lives in
+
+ align:start position:0%
+sulcus what functional region lives in
+ 
+
+ align:start position:0%
+sulcus what functional region lives in
+the calcren sulcus
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+it's just a weird little fact but it's
+
+ align:start position:0%
+it's just a weird little fact but it's
+ 
+
+ align:start position:0%
+it's just a weird little fact but it's
+kind of an important one
+
+ align:start position:0%
+kind of an important one
+ 
+
+ align:start position:0%
+kind of an important one
+that we mentioned weeks ago
+
+ align:start position:0%
+that we mentioned weeks ago
+ 
+
+ align:start position:0%
+that we mentioned weeks ago
+v1 primary visual cortex
+
+ align:start position:0%
+v1 primary visual cortex
+ 
+
+ align:start position:0%
+v1 primary visual cortex
+that's where primary visual cortex lives
+
+ align:start position:0%
+that's where primary visual cortex lives
+ 
+
+ align:start position:0%
+that's where primary visual cortex lives
+and remember primary visual cortex
+
+ align:start position:0%
+and remember primary visual cortex
+ 
+
+ align:start position:0%
+and remember primary visual cortex
+has a map of retinotopic space with
+
+ align:start position:0%
+has a map of retinotopic space with
+ 
+
+ align:start position:0%
+has a map of retinotopic space with
+next-door bits of primary visual cortex
+
+ align:start position:0%
+next-door bits of primary visual cortex
+ 
+
+ align:start position:0%
+next-door bits of primary visual cortex
+responding to next-door bits of space
+
+ align:start position:0%
+responding to next-door bits of space
+ 
+
+ align:start position:0%
+responding to next-door bits of space
+and in fact that map has the center of
+
+ align:start position:0%
+and in fact that map has the center of
+ 
+
+ align:start position:0%
+and in fact that map has the center of
+gaze out here and the periphery out
+
+ align:start position:0%
+gaze out here and the periphery out
+ 
+
+ align:start position:0%
+gaze out here and the periphery out
+there
+
+ align:start position:0%
+there
+ 
+
+ align:start position:0%
+there
+so when russell and i first saw that
+
+ align:start position:0%
+so when russell and i first saw that
+ 
+
+ align:start position:0%
+so when russell and i first saw that
+activation we had the same worry that
+
+ align:start position:0%
+activation we had the same worry that
+ 
+
+ align:start position:0%
+activation we had the same worry that
+quilley mentioned a while back and that
+
+ align:start position:0%
+quilley mentioned a while back and that
+ 
+
+ align:start position:0%
+quilley mentioned a while back and that
+is the scenes are sticking out there's
+
+ align:start position:0%
+is the scenes are sticking out there's
+ 
+
+ align:start position:0%
+is the scenes are sticking out there's
+stuff everywhere the objects there isn't
+
+ align:start position:0%
+stuff everywhere the objects there isn't
+ 
+
+ align:start position:0%
+stuff everywhere the objects there isn't
+that much sticking out and we thought oh
+
+ align:start position:0%
+that much sticking out and we thought oh
+ 
+
+ align:start position:0%
+that much sticking out and we thought oh
+that's just peripheral retina topic
+
+ align:start position:0%
+that's just peripheral retina topic
+ 
+
+ align:start position:0%
+that's just peripheral retina topic
+cortex but it's not it's right next to
+
+ align:start position:0%
+cortex but it's not it's right next to
+ 
+
+ align:start position:0%
+cortex but it's not it's right next to
+there and it's a totally different thing
+
+ align:start position:0%
+there and it's a totally different thing
+ 
+
+ align:start position:0%
+there and it's a totally different thing
+and it turns out to be extremely
+
+ align:start position:0%
+and it turns out to be extremely
+ 
+
+ align:start position:0%
+and it turns out to be extremely
+interesting
+
+ align:start position:0%
+interesting
+ 
+
+ align:start position:0%
+interesting
+you don't need to know all that it's
+
+ align:start position:0%
+you don't need to know all that it's
+ 
+
+ align:start position:0%
+you don't need to know all that it's
+just silly little history
+
+ align:start position:0%
+just silly little history
+ 
+
+ align:start position:0%
+just silly little history
+okay there's a third region up there
+
+ align:start position:0%
+okay there's a third region up there
+ 
+
+ align:start position:0%
+okay there's a third region up there
+that's on the outer surface out there
+
+ align:start position:0%
+that's on the outer surface out there
+ 
+
+ align:start position:0%
+that's on the outer surface out there
+um that used to be called tos and now is
+
+ align:start position:0%
+um that used to be called tos and now is
+ 
+
+ align:start position:0%
+um that used to be called tos and now is
+now called opa i'm sorry about that you
+
+ align:start position:0%
+now called opa i'm sorry about that you
+ 
+
+ align:start position:0%
+now called opa i'm sorry about that you
+don't need to remember this know that
+
+ align:start position:0%
+don't need to remember this know that
+ 
+
+ align:start position:0%
+don't need to remember this know that
+there's not there are at least three
+
+ align:start position:0%
+there's not there are at least three
+ 
+
+ align:start position:0%
+there's not there are at least three
+regions
+
+ align:start position:0%
+regions
+ 
+
+ align:start position:0%
+regions
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+what but t os opa is interesting because
+
+ align:start position:0%
+what but t os opa is interesting because
+ 
+
+ align:start position:0%
+what but t os opa is interesting because
+there's a method we can apply
+
+ align:start position:0%
+there's a method we can apply
+ 
+
+ align:start position:0%
+there's a method we can apply
+to it that we can't apply to the others
+
+ align:start position:0%
+to it that we can't apply to the others
+ 
+
+ align:start position:0%
+to it that we can't apply to the others
+what would that method be
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah tms it's right out on the surface
+
+ align:start position:0%
+yeah tms it's right out on the surface
+ 
+
+ align:start position:0%
+yeah tms it's right out on the surface
+you just stick the coil there and go zap
+
+ align:start position:0%
+you just stick the coil there and go zap
+ 
+
+ align:start position:0%
+you just stick the coil there and go zap
+so of course
+
+ align:start position:0%
+so of course
+ 
+
+ align:start position:0%
+so of course
+we've done a lot of that okay you can't
+
+ align:start position:0%
+we've done a lot of that okay you can't
+ 
+
+ align:start position:0%
+we've done a lot of that okay you can't
+get the coil into the ppa or rsc it's
+
+ align:start position:0%
+get the coil into the ppa or rsc it's
+ 
+
+ align:start position:0%
+get the coil into the ppa or rsc it's
+too medial
+
+ align:start position:0%
+too medial
+ 
+
+ align:start position:0%
+too medial
+all right
+
+ align:start position:0%
+all right
+ 
+
+ align:start position:0%
+all right
+okay and there's another region that
+
+ align:start position:0%
+okay and there's another region that
+ 
+
+ align:start position:0%
+okay and there's another region that
+we'll talk about more next time called
+
+ align:start position:0%
+we'll talk about more next time called
+ 
+
+ align:start position:0%
+we'll talk about more next time called
+the hippocampus you saw the hippocampus
+
+ align:start position:0%
+the hippocampus you saw the hippocampus
+ 
+
+ align:start position:0%
+the hippocampus you saw the hippocampus
+when ann graybill spent all that time
+
+ align:start position:0%
+when ann graybill spent all that time
+ 
+
+ align:start position:0%
+when ann graybill spent all that time
+digging in the temporal lobe to find
+
+ align:start position:0%
+digging in the temporal lobe to find
+ 
+
+ align:start position:0%
+digging in the temporal lobe to find
+that bumpy little dentite gyrus
+
+ align:start position:0%
+that bumpy little dentite gyrus
+ 
+
+ align:start position:0%
+that bumpy little dentite gyrus
+approximately right in there
+
+ align:start position:0%
+approximately right in there
+ 
+
+ align:start position:0%
+approximately right in there
+and so all of these and probably other
+
+ align:start position:0%
+and so all of these and probably other
+ 
+
+ align:start position:0%
+and so all of these and probably other
+regions but these are the core elements
+
+ align:start position:0%
+regions but these are the core elements
+ 
+
+ align:start position:0%
+regions but these are the core elements
+of the
+
+ align:start position:0%
+of the
+ 
+
+ align:start position:0%
+of the
+of the scene selective regions that are
+
+ align:start position:0%
+of the scene selective regions that are
+ 
+
+ align:start position:0%
+of the scene selective regions that are
+implicated in different aspects of
+
+ align:start position:0%
+implicated in different aspects of
+ 
+
+ align:start position:0%
+implicated in different aspects of
+navigation
+
+ align:start position:0%
+navigation
+ 
+
+ align:start position:0%
+navigation
+okay so when you have
+
+ align:start position:0%
+okay so when you have
+ 
+
+ align:start position:0%
+okay so when you have
+multiple regions that seem to be part of
+
+ align:start position:0%
+multiple regions that seem to be part of
+ 
+
+ align:start position:0%
+multiple regions that seem to be part of
+a system that's an opportunity
+
+ align:start position:0%
+a system that's an opportunity
+ 
+
+ align:start position:0%
+a system that's an opportunity
+because now we have the possibility that
+
+ align:start position:0%
+because now we have the possibility that
+ 
+
+ align:start position:0%
+because now we have the possibility that
+maybe we could figure out different
+
+ align:start position:0%
+maybe we could figure out different
+ 
+
+ align:start position:0%
+maybe we could figure out different
+functions for different regions and then
+
+ align:start position:0%
+functions for different regions and then
+ 
+
+ align:start position:0%
+functions for different regions and then
+maybe that would really tell us more
+
+ align:start position:0%
+maybe that would really tell us more
+ 
+
+ align:start position:0%
+maybe that would really tell us more
+than just okay scenes and navigation end
+
+ align:start position:0%
+than just okay scenes and navigation end
+ 
+
+ align:start position:0%
+than just okay scenes and navigation end
+of story it's kind of rude of entry
+
+ align:start position:0%
+of story it's kind of rude of entry
+ 
+
+ align:start position:0%
+of story it's kind of rude of entry
+right it'll be nice if different aspects
+
+ align:start position:0%
+right it'll be nice if different aspects
+ 
+
+ align:start position:0%
+right it'll be nice if different aspects
+of the navigation story
+
+ align:start position:0%
+of the navigation story
+ 
+
+ align:start position:0%
+of the navigation story
+engage different parts of the system
+
+ align:start position:0%
+engage different parts of the system
+ 
+
+ align:start position:0%
+engage different parts of the system
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+so really what we want to know is how
+
+ align:start position:0%
+so really what we want to know is how
+ 
+
+ align:start position:0%
+so really what we want to know is how
+does each of these regions help us
+
+ align:start position:0%
+does each of these regions help us
+ 
+
+ align:start position:0%
+does each of these regions help us
+navigate and see scenes
+
+ align:start position:0%
+navigate and see scenes
+ 
+
+ align:start position:0%
+navigate and see scenes
+and i'm not going to answer that fully
+
+ align:start position:0%
+and i'm not going to answer that fully
+ 
+
+ align:start position:0%
+and i'm not going to answer that fully
+we're still what the the field is still
+
+ align:start position:0%
+we're still what the the field is still
+ 
+
+ align:start position:0%
+we're still what the the field is still
+trying to understand all of this but
+
+ align:start position:0%
+trying to understand all of this but
+ 
+
+ align:start position:0%
+trying to understand all of this but
+i'll give you a few tantalizing little
+
+ align:start position:0%
+i'll give you a few tantalizing little
+ 
+
+ align:start position:0%
+i'll give you a few tantalizing little
+snippets okay
+
+ align:start position:0%
+snippets okay
+ 
+
+ align:start position:0%
+snippets okay
+so let's take retrosplenial cortex right
+
+ align:start position:0%
+so let's take retrosplenial cortex right
+ 
+
+ align:start position:0%
+so let's take retrosplenial cortex right
+here
+
+ align:start position:0%
+here
+ 
+
+ align:start position:0%
+here
+so um richard so this is first the
+
+ align:start position:0%
+so um richard so this is first the
+ 
+
+ align:start position:0%
+so um richard so this is first the
+response of the ppa right there in
+
+ align:start position:0%
+response of the ppa right there in
+ 
+
+ align:start position:0%
+response of the ppa right there in
+retrospective cortex which is just
+
+ align:start position:0%
+retrospective cortex which is just
+ 
+
+ align:start position:0%
+retrospective cortex which is just
+behind it
+
+ align:start position:0%
+behind it
+ 
+
+ align:start position:0%
+behind it
+this is just its mean response to a
+
+ align:start position:0%
+this is just its mean response to a
+ 
+
+ align:start position:0%
+this is just its mean response to a
+bunch of different kinds of stimuli
+
+ align:start position:0%
+bunch of different kinds of stimuli
+ 
+
+ align:start position:0%
+bunch of different kinds of stimuli
+showing the you that it likes landscapes
+
+ align:start position:0%
+showing the you that it likes landscapes
+ 
+
+ align:start position:0%
+showing the you that it likes landscapes
+and cityscapes scenes more than a bunch
+
+ align:start position:0%
+and cityscapes scenes more than a bunch
+ 
+
+ align:start position:0%
+and cityscapes scenes more than a bunch
+of other categories of objects and
+
+ align:start position:0%
+of other categories of objects and
+ 
+
+ align:start position:0%
+of other categories of objects and
+that's true of both the ppa and rsc
+
+ align:start position:0%
+that's true of both the ppa and rsc
+ 
+
+ align:start position:0%
+that's true of both the ppa and rsc
+okay no surprises here they're both
+
+ align:start position:0%
+okay no surprises here they're both
+ 
+
+ align:start position:0%
+okay no surprises here they're both
+somewhat seen selective
+
+ align:start position:0%
+somewhat seen selective
+ 
+
+ align:start position:0%
+somewhat seen selective
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+but then in a whole bunch of other
+
+ align:start position:0%
+but then in a whole bunch of other
+ 
+
+ align:start position:0%
+but then in a whole bunch of other
+studies
+
+ align:start position:0%
+studies
+ 
+
+ align:start position:0%
+studies
+summarized in this graph here
+
+ align:start position:0%
+summarized in this graph here
+ 
+
+ align:start position:0%
+summarized in this graph here
+russell epstein and his colleagues
+
+ align:start position:0%
+russell epstein and his colleagues
+ 
+
+ align:start position:0%
+russell epstein and his colleagues
+had subjects engage in different tasks
+
+ align:start position:0%
+had subjects engage in different tasks
+ 
+
+ align:start position:0%
+had subjects engage in different tasks
+while they were looking at scenes in
+
+ align:start position:0%
+while they were looking at scenes in
+ 
+
+ align:start position:0%
+while they were looking at scenes in
+some tasks they had to say where they
+
+ align:start position:0%
+some tasks they had to say where they
+ 
+
+ align:start position:0%
+some tasks they had to say where they
+were
+
+ align:start position:0%
+were
+ 
+
+ align:start position:0%
+were
+he's at u pen and he showed his subjects
+
+ align:start position:0%
+he's at u pen and he showed his subjects
+ 
+
+ align:start position:0%
+he's at u pen and he showed his subjects
+pictures of the eupan campus and they
+
+ align:start position:0%
+pictures of the eupan campus and they
+ 
+
+ align:start position:0%
+pictures of the eupan campus and they
+had to answer all kinds of questions
+
+ align:start position:0%
+had to answer all kinds of questions
+ 
+
+ align:start position:0%
+had to answer all kinds of questions
+about
+
+ align:start position:0%
+about
+ 
+
+ align:start position:0%
+about
+what part of campus they were where they
+
+ align:start position:0%
+what part of campus they were where they
+ 
+
+ align:start position:0%
+what part of campus they were where they
+were in on campus and also about which
+
+ align:start position:0%
+were in on campus and also about which
+ 
+
+ align:start position:0%
+were in on campus and also about which
+way they were facing given the view of
+
+ align:start position:0%
+way they were facing given the view of
+ 
+
+ align:start position:0%
+way they were facing given the view of
+the campus they were looking at
+
+ align:start position:0%
+the campus they were looking at
+ 
+
+ align:start position:0%
+the campus they were looking at
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+then he also showed people familiar
+
+ align:start position:0%
+then he also showed people familiar
+ 
+
+ align:start position:0%
+then he also showed people familiar
+scenes and unfamiliar scenes much like
+
+ align:start position:0%
+scenes and unfamiliar scenes much like
+ 
+
+ align:start position:0%
+scenes and unfamiliar scenes much like
+we did with our tough study
+
+ align:start position:0%
+we did with our tough study
+ 
+
+ align:start position:0%
+we did with our tough study
+and he had object controls
+
+ align:start position:0%
+and he had object controls
+ 
+
+ align:start position:0%
+and he had object controls
+and you can see the ppa doesn't care
+
+ align:start position:0%
+and you can see the ppa doesn't care
+ 
+
+ align:start position:0%
+and you can see the ppa doesn't care
+about any of that doesn't care really if
+
+ align:start position:0%
+about any of that doesn't care really if
+ 
+
+ align:start position:0%
+about any of that doesn't care really if
+they're familiar or unfamiliar doesn't
+
+ align:start position:0%
+they're familiar or unfamiliar doesn't
+ 
+
+ align:start position:0%
+they're familiar or unfamiliar doesn't
+care what task you're doing on the scene
+
+ align:start position:0%
+care what task you're doing on the scene
+ 
+
+ align:start position:0%
+care what task you're doing on the scene
+you're looking at a scene it's just
+
+ align:start position:0%
+you're looking at a scene it's just
+ 
+
+ align:start position:0%
+you're looking at a scene it's just
+going
+
+ align:start position:0%
+going
+ 
+
+ align:start position:0%
+going
+okay so we we didn't really tease of
+
+ align:start position:0%
+okay so we we didn't really tease of
+ 
+
+ align:start position:0%
+okay so we we didn't really tease of
+heart functions there
+
+ align:start position:0%
+heart functions there
+ 
+
+ align:start position:0%
+heart functions there
+but
+
+ align:start position:0%
+but
+ 
+
+ align:start position:0%
+but
+rsc responds differently in these
+
+ align:start position:0%
+rsc responds differently in these
+ 
+
+ align:start position:0%
+rsc responds differently in these
+conditions
+
+ align:start position:0%
+conditions
+ 
+
+ align:start position:0%
+conditions
+it's more um
+
+ align:start position:0%
+it's more um
+ 
+
+ align:start position:0%
+it's more um
+it's engaged in both the location task
+
+ align:start position:0%
+it's engaged in both the location task
+ 
+
+ align:start position:0%
+it's engaged in both the location task
+and the orientation task
+
+ align:start position:0%
+and the orientation task
+ 
+
+ align:start position:0%
+and the orientation task
+um it's um it doesn't oh it responds
+
+ align:start position:0%
+um it's um it doesn't oh it responds
+ 
+
+ align:start position:0%
+um it's um it doesn't oh it responds
+substantially more
+
+ align:start position:0%
+substantially more
+ 
+
+ align:start position:0%
+substantially more
+when you look at images of a familiar
+
+ align:start position:0%
+when you look at images of a familiar
+ 
+
+ align:start position:0%
+when you look at images of a familiar
+place than an unfamiliar place so this
+
+ align:start position:0%
+place than an unfamiliar place so this
+ 
+
+ align:start position:0%
+place than an unfamiliar place so this
+is the first time we've seen that in the
+
+ align:start position:0%
+is the first time we've seen that in the
+ 
+
+ align:start position:0%
+is the first time we've seen that in the
+scene network and so now think about all
+
+ align:start position:0%
+scene network and so now think about all
+ 
+
+ align:start position:0%
+scene network and so now think about all
+the things you can do when you're
+
+ align:start position:0%
+the things you can do when you're
+ 
+
+ align:start position:0%
+the things you can do when you're
+looking at a picture of a scene and you
+
+ align:start position:0%
+looking at a picture of a scene and you
+ 
+
+ align:start position:0%
+looking at a picture of a scene and you
+know that place
+
+ align:start position:0%
+know that place
+ 
+
+ align:start position:0%
+know that place
+you have memories of having been there
+
+ align:start position:0%
+you have memories of having been there
+ 
+
+ align:start position:0%
+you have memories of having been there
+you can think about you know what you
+
+ align:start position:0%
+you can think about you know what you
+ 
+
+ align:start position:0%
+you can think about you know what you
+might do if you were there how you would
+
+ align:start position:0%
+might do if you were there how you would
+ 
+
+ align:start position:0%
+might do if you were there how you would
+get from there to some place else all of
+
+ align:start position:0%
+get from there to some place else all of
+ 
+
+ align:start position:0%
+get from there to some place else all of
+those things are possible things that
+
+ align:start position:0%
+those things are possible things that
+ 
+
+ align:start position:0%
+those things are possible things that
+might be driving
+
+ align:start position:0%
+might be driving
+ 
+
+ align:start position:0%
+might be driving
+rsc
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+another thing that might be driving rsc
+
+ align:start position:0%
+another thing that might be driving rsc
+ 
+
+ align:start position:0%
+another thing that might be driving rsc
+is that if you're looking at a picture
+
+ align:start position:0%
+is that if you're looking at a picture
+ 
+
+ align:start position:0%
+is that if you're looking at a picture
+of a familiar place
+
+ align:start position:0%
+of a familiar place
+ 
+
+ align:start position:0%
+of a familiar place
+you orient yourself with respect to the
+
+ align:start position:0%
+you orient yourself with respect to the
+ 
+
+ align:start position:0%
+you orient yourself with respect to the
+broader environment that that view is
+
+ align:start position:0%
+broader environment that that view is
+ 
+
+ align:start position:0%
+broader environment that that view is
+part of
+
+ align:start position:0%
+part of
+ 
+
+ align:start position:0%
+part of
+right so when i showed you that picture
+
+ align:start position:0%
+right so when i showed you that picture
+ 
+
+ align:start position:0%
+right so when i showed you that picture
+of the front of stata you immediately
+
+ align:start position:0%
+of the front of stata you immediately
+ 
+
+ align:start position:0%
+of the front of stata you immediately
+imagine oh like i'm out on vassar street
+
+ align:start position:0%
+imagine oh like i'm out on vassar street
+ 
+
+ align:start position:0%
+imagine oh like i'm out on vassar street
+facing that way roughly
+
+ align:start position:0%
+facing that way roughly
+ 
+
+ align:start position:0%
+facing that way roughly
+northwest i think
+
+ align:start position:0%
+northwest i think
+ 
+
+ align:start position:0%
+northwest i think
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+if you look at a picture of a scene you
+
+ align:start position:0%
+if you look at a picture of a scene you
+ 
+
+ align:start position:0%
+if you look at a picture of a scene you
+don't know that scene it doesn't tell
+
+ align:start position:0%
+don't know that scene it doesn't tell
+ 
+
+ align:start position:0%
+don't know that scene it doesn't tell
+you anything about your broader heading
+
+ align:start position:0%
+you anything about your broader heading
+ 
+
+ align:start position:0%
+you anything about your broader heading
+in the in the broader world okay so all
+
+ align:start position:0%
+in the in the broader world okay so all
+ 
+
+ align:start position:0%
+in the in the broader world okay so all
+of those are things that
+
+ align:start position:0%
+of those are things that
+ 
+
+ align:start position:0%
+of those are things that
+the rsc
+
+ align:start position:0%
+the rsc
+ 
+
+ align:start position:0%
+the rsc
+its function seems to depend on knowing
+
+ align:start position:0%
+its function seems to depend on knowing
+ 
+
+ align:start position:0%
+its function seems to depend on knowing
+that place
+
+ align:start position:0%
+that place
+ 
+
+ align:start position:0%
+that place
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+perhaps the most telling case comes from
+
+ align:start position:0%
+perhaps the most telling case comes from
+ 
+
+ align:start position:0%
+perhaps the most telling case comes from
+a patient who had damage in
+
+ align:start position:0%
+a patient who had damage in
+ 
+
+ align:start position:0%
+a patient who had damage in
+retrosplenial cortex
+
+ align:start position:0%
+retrosplenial cortex
+ 
+
+ align:start position:0%
+retrosplenial cortex
+and the description in the paper of this
+
+ align:start position:0%
+and the description in the paper of this
+ 
+
+ align:start position:0%
+and the description in the paper of this
+says that this patient
+
+ align:start position:0%
+says that this patient
+ 
+
+ align:start position:0%
+says that this patient
+could recognize buildings and the and
+
+ align:start position:0%
+could recognize buildings and the and
+ 
+
+ align:start position:0%
+could recognize buildings and the and
+the landmarks and therefore understand
+
+ align:start position:0%
+the landmarks and therefore understand
+ 
+
+ align:start position:0%
+the landmarks and therefore understand
+where he was
+
+ align:start position:0%
+where he was
+ 
+
+ align:start position:0%
+where he was
+okay so lots is intact can recognize
+
+ align:start position:0%
+okay so lots is intact can recognize
+ 
+
+ align:start position:0%
+okay so lots is intact can recognize
+scenes and know where he is
+
+ align:start position:0%
+scenes and know where he is
+ 
+
+ align:start position:0%
+scenes and know where he is
+but the landmarks he recognized did not
+
+ align:start position:0%
+but the landmarks he recognized did not
+ 
+
+ align:start position:0%
+but the landmarks he recognized did not
+provoke directional information about
+
+ align:start position:0%
+provoke directional information about
+ 
+
+ align:start position:0%
+provoke directional information about
+any other places with respect to those
+
+ align:start position:0%
+any other places with respect to those
+ 
+
+ align:start position:0%
+any other places with respect to those
+landmarks
+
+ align:start position:0%
+landmarks
+ 
+
+ align:start position:0%
+landmarks
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+so this person can look at a picture and
+
+ align:start position:0%
+so this person can look at a picture and
+ 
+
+ align:start position:0%
+so this person can look at a picture and
+say yeah i know that place you know
+
+ align:start position:0%
+say yeah i know that place you know
+ 
+
+ align:start position:0%
+say yeah i know that place you know
+that's the front of my house
+
+ align:start position:0%
+that's the front of my house
+ 
+
+ align:start position:0%
+that's the front of my house
+but then if you say you know in which
+
+ align:start position:0%
+but then if you say you know in which
+ 
+
+ align:start position:0%
+but then if you say you know in which
+direction is you know a coffee shop two
+
+ align:start position:0%
+direction is you know a coffee shop two
+ 
+
+ align:start position:0%
+direction is you know a coffee shop two
+blocks away
+
+ align:start position:0%
+blocks away
+ 
+
+ align:start position:0%
+blocks away
+he doesn't know which way it is from
+
+ align:start position:0%
+he doesn't know which way it is from
+ 
+
+ align:start position:0%
+he doesn't know which way it is from
+there
+
+ align:start position:0%
+there
+ 
+
+ align:start position:0%
+there
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+so um this should sound familiar
+
+ align:start position:0%
+so um this should sound familiar
+ 
+
+ align:start position:0%
+so um this should sound familiar
+this is my guess of the bit that my
+
+ align:start position:0%
+this is my guess of the bit that my
+ 
+
+ align:start position:0%
+this is my guess of the bit that my
+friend bob
+
+ align:start position:0%
+friend bob
+ 
+
+ align:start position:0%
+friend bob
+got messed up
+
+ align:start position:0%
+got messed up
+ 
+
+ align:start position:0%
+got messed up
+yeah this is exactly his description he
+
+ align:start position:0%
+yeah this is exactly his description he
+ 
+
+ align:start position:0%
+yeah this is exactly his description he
+could recognize places but it wouldn't
+
+ align:start position:0%
+could recognize places but it wouldn't
+ 
+
+ align:start position:0%
+could recognize places but it wouldn't
+tell him how to get from there to
+
+ align:start position:0%
+tell him how to get from there to
+ 
+
+ align:start position:0%
+tell him how to get from there to
+somewhere else
+
+ align:start position:0%
+somewhere else
+ 
+
+ align:start position:0%
+somewhere else
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+and so the best current guess about
+
+ align:start position:0%
+and so the best current guess about
+ 
+
+ align:start position:0%
+and so the best current guess about
+retrospinal cortex is it is involved in
+
+ align:start position:0%
+retrospinal cortex is it is involved in
+ 
+
+ align:start position:0%
+retrospinal cortex is it is involved in
+you know anchoring where you are you
+
+ align:start position:0%
+you know anchoring where you are you
+ 
+
+ align:start position:0%
+you know anchoring where you are you
+have this mental map of the world
+
+ align:start position:0%
+have this mental map of the world
+ 
+
+ align:start position:0%
+have this mental map of the world
+and you have a scene and you're trying
+
+ align:start position:0%
+and you have a scene and you're trying
+ 
+
+ align:start position:0%
+and you have a scene and you're trying
+to put them together given that i see
+
+ align:start position:0%
+to put them together given that i see
+ 
+
+ align:start position:0%
+to put them together given that i see
+this
+
+ align:start position:0%
+this
+ 
+
+ align:start position:0%
+this
+where am i on the map and which way am i
+
+ align:start position:0%
+where am i on the map and which way am i
+ 
+
+ align:start position:0%
+where am i on the map and which way am i
+heading in that map
+
+ align:start position:0%
+heading in that map
+ 
+
+ align:start position:0%
+heading in that map
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+again think about the problem you face
+
+ align:start position:0%
+again think about the problem you face
+ 
+
+ align:start position:0%
+again think about the problem you face
+when you emerge from the subway in
+
+ align:start position:0%
+when you emerge from the subway in
+ 
+
+ align:start position:0%
+when you emerge from the subway in
+manhattan right like you look around
+
+ align:start position:0%
+manhattan right like you look around
+ 
+
+ align:start position:0%
+manhattan right like you look around
+where am i and which way am i heading
+
+ align:start position:0%
+where am i and which way am i heading
+ 
+
+ align:start position:0%
+where am i and which way am i heading
+that's what you need retrospective
+
+ align:start position:0%
+that's what you need retrospective
+ 
+
+ align:start position:0%
+that's what you need retrospective
+cortex for
+
+ align:start position:0%
+cortex for
+ 
+
+ align:start position:0%
+cortex for
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+all right how about this tos thing i'll
+
+ align:start position:0%
+all right how about this tos thing i'll
+ 
+
+ align:start position:0%
+all right how about this tos thing i'll
+give you there's lots of studies of it
+
+ align:start position:0%
+give you there's lots of studies of it
+ 
+
+ align:start position:0%
+give you there's lots of studies of it
+i'll give you just one little offering
+
+ align:start position:0%
+i'll give you just one little offering
+ 
+
+ align:start position:0%
+i'll give you just one little offering
+okay so
+
+ align:start position:0%
+okay so
+ 
+
+ align:start position:0%
+okay so
+this is a
+
+ align:start position:0%
+this is a
+ 
+
+ align:start position:0%
+this is a
+causal investigation because as we
+
+ align:start position:0%
+causal investigation because as we
+ 
+
+ align:start position:0%
+causal investigation because as we
+discussed tos is out on the lateral
+
+ align:start position:0%
+discussed tos is out on the lateral
+ 
+
+ align:start position:0%
+discussed tos is out on the lateral
+surface so we can zap it and so of
+
+ align:start position:0%
+surface so we can zap it and so of
+ 
+
+ align:start position:0%
+surface so we can zap it and so of
+course we do
+
+ align:start position:0%
+course we do
+ 
+
+ align:start position:0%
+course we do
+and so in this study
+
+ align:start position:0%
+and so in this study
+ 
+
+ align:start position:0%
+and so in this study
+we were asking
+
+ align:start position:0%
+we were asking
+ 
+
+ align:start position:0%
+we were asking
+whether tos is involved in perceiving
+
+ align:start position:0%
+whether tos is involved in perceiving
+ 
+
+ align:start position:0%
+whether tos is involved in perceiving
+the structure of space around you
+
+ align:start position:0%
+the structure of space around you
+ 
+
+ align:start position:0%
+the structure of space around you
+so we took scenes like this from cad
+
+ align:start position:0%
+so we took scenes like this from cad
+ 
+
+ align:start position:0%
+so we took scenes like this from cad
+programs and we just varied them
+
+ align:start position:0%
+programs and we just varied them
+ 
+
+ align:start position:0%
+programs and we just varied them
+slightly so for example the position of
+
+ align:start position:0%
+slightly so for example the position of
+ 
+
+ align:start position:0%
+slightly so for example the position of
+this wall moves around
+
+ align:start position:0%
+this wall moves around
+ 
+
+ align:start position:0%
+this wall moves around
+the aspect ratio the height of the
+
+ align:start position:0%
+the aspect ratio the height of the
+ 
+
+ align:start position:0%
+the aspect ratio the height of the
+ceiling moves around and we make this
+
+ align:start position:0%
+ceiling moves around and we make this
+ 
+
+ align:start position:0%
+ceiling moves around and we make this
+subtle morph space of different versions
+
+ align:start position:0%
+subtle morph space of different versions
+ 
+
+ align:start position:0%
+subtle morph space of different versions
+of this image
+
+ align:start position:0%
+of this image
+ 
+
+ align:start position:0%
+of this image
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+and then for control condition we do the
+
+ align:start position:0%
+and then for control condition we do the
+ 
+
+ align:start position:0%
+and then for control condition we do the
+same with faces we morph between this
+
+ align:start position:0%
+same with faces we morph between this
+ 
+
+ align:start position:0%
+same with faces we morph between this
+guy and that guy who make a whole
+
+ align:start position:0%
+guy and that guy who make a whole
+ 
+
+ align:start position:0%
+guy and that guy who make a whole
+spectrum in between
+
+ align:start position:0%
+spectrum in between
+ 
+
+ align:start position:0%
+spectrum in between
+and then in the task what we do is
+
+ align:start position:0%
+and then in the task what we do is
+ 
+
+ align:start position:0%
+and then in the task what we do is
+here's one trial
+
+ align:start position:0%
+here's one trial
+ 
+
+ align:start position:0%
+here's one trial
+one of the scenes or faces comes on
+
+ align:start position:0%
+one of the scenes or faces comes on
+ 
+
+ align:start position:0%
+one of the scenes or faces comes on
+uh briefly and then shortly thereafter
+
+ align:start position:0%
+uh briefly and then shortly thereafter
+ 
+
+ align:start position:0%
+uh briefly and then shortly thereafter
+you get a choice of two and you have to
+
+ align:start position:0%
+you get a choice of two and you have to
+ 
+
+ align:start position:0%
+you get a choice of two and you have to
+say which of these matches that one
+
+ align:start position:0%
+say which of these matches that one
+ 
+
+ align:start position:0%
+say which of these matches that one
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+and then what we do is we zap people
+
+ align:start position:0%
+and then what we do is we zap people
+ 
+
+ align:start position:0%
+and then what we do is we zap people
+right after we present this stimulus
+
+ align:start position:0%
+right after we present this stimulus
+ 
+
+ align:start position:0%
+right after we present this stimulus
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+and so the idea is this is as close as
+
+ align:start position:0%
+and so the idea is this is as close as
+ 
+
+ align:start position:0%
+and so the idea is this is as close as
+we can get to a pretty pure perceptual
+
+ align:start position:0%
+we can get to a pretty pure perceptual
+ 
+
+ align:start position:0%
+we can get to a pretty pure perceptual
+task how well can you see the shape of
+
+ align:start position:0%
+task how well can you see the shape of
+ 
+
+ align:start position:0%
+task how well can you see the shape of
+that environment or the shape of that
+
+ align:start position:0%
+that environment or the shape of that
+ 
+
+ align:start position:0%
+that environment or the shape of that
+face
+
+ align:start position:0%
+face
+ 
+
+ align:start position:0%
+face
+okay you don't have to remember it for
+
+ align:start position:0%
+okay you don't have to remember it for
+ 
+
+ align:start position:0%
+okay you don't have to remember it for
+more than a few hundred milliseconds so
+
+ align:start position:0%
+more than a few hundred milliseconds so
+ 
+
+ align:start position:0%
+more than a few hundred milliseconds so
+it's really more of a perception task
+
+ align:start position:0%
+it's really more of a perception task
+ 
+
+ align:start position:0%
+it's really more of a perception task
+than a memory task okay and what we
+
+ align:start position:0%
+than a memory task okay and what we
+ 
+
+ align:start position:0%
+than a memory task okay and what we
+measure is we actually
+
+ align:start position:0%
+measure is we actually
+ 
+
+ align:start position:0%
+measure is we actually
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+muck with how different these two images
+
+ align:start position:0%
+muck with how different these two images
+ 
+
+ align:start position:0%
+muck with how different these two images
+are in each trial and measure how far
+
+ align:start position:0%
+are in each trial and measure how far
+ 
+
+ align:start position:0%
+are in each trial and measure how far
+apart they have to be in morph space for
+
+ align:start position:0%
+apart they have to be in morph space for
+ 
+
+ align:start position:0%
+apart they have to be in morph space for
+you to be about 75 percent correct okay
+
+ align:start position:0%
+you to be about 75 percent correct okay
+ 
+
+ align:start position:0%
+you to be about 75 percent correct okay
+that's a kind of
+
+ align:start position:0%
+that's a kind of
+ 
+
+ align:start position:0%
+that's a kind of
+standard psychophysical measure the
+
+ align:start position:0%
+standard psychophysical measure the
+ 
+
+ align:start position:0%
+standard psychophysical measure the
+details don't matter but our dependent
+
+ align:start position:0%
+details don't matter but our dependent
+ 
+
+ align:start position:0%
+details don't matter but our dependent
+measure is how different did the stimuli
+
+ align:start position:0%
+measure is how different did the stimuli
+ 
+
+ align:start position:0%
+measure is how different did the stimuli
+have to be for you to discriminate them
+
+ align:start position:0%
+have to be for you to discriminate them
+ 
+
+ align:start position:0%
+have to be for you to discriminate them
+as a function of what do you get whether
+
+ align:start position:0%
+as a function of what do you get whether
+ 
+
+ align:start position:0%
+as a function of what do you get whether
+you're getting zapped in tos or not
+
+ align:start position:0%
+you're getting zapped in tos or not
+ 
+
+ align:start position:0%
+you're getting zapped in tos or not
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+and so here are the data
+
+ align:start position:0%
+and so here are the data
+ 
+
+ align:start position:0%
+and so here are the data
+so let's take the case where you're
+
+ align:start position:0%
+so let's take the case where you're
+ 
+
+ align:start position:0%
+so let's take the case where you're
+doing the scene task here
+
+ align:start position:0%
+doing the scene task here
+ 
+
+ align:start position:0%
+doing the scene task here
+what this threshold is is again how
+
+ align:start position:0%
+what this threshold is is again how
+ 
+
+ align:start position:0%
+what this threshold is is again how
+different the stimuli need to be for you
+
+ align:start position:0%
+different the stimuli need to be for you
+ 
+
+ align:start position:0%
+different the stimuli need to be for you
+to discriminate them so the higher the
+
+ align:start position:0%
+to discriminate them so the higher the
+ 
+
+ align:start position:0%
+to discriminate them so the higher the
+bar
+
+ align:start position:0%
+bar
+ 
+
+ align:start position:0%
+bar
+the worse performance okay they have to
+
+ align:start position:0%
+the worse performance okay they have to
+ 
+
+ align:start position:0%
+the worse performance okay they have to
+be really different or you can't tell
+
+ align:start position:0%
+be really different or you can't tell
+ 
+
+ align:start position:0%
+be really different or you can't tell
+them apart
+
+ align:start position:0%
+them apart
+ 
+
+ align:start position:0%
+them apart
+and so what you see is
+
+ align:start position:0%
+and so what you see is
+ 
+
+ align:start position:0%
+and so what you see is
+when you zap
+
+ align:start position:0%
+when you zap
+ 
+
+ align:start position:0%
+when you zap
+opa
+
+ align:start position:0%
+opa
+ 
+
+ align:start position:0%
+opa
+that lateral scene selective region
+
+ align:start position:0%
+that lateral scene selective region
+ 
+
+ align:start position:0%
+that lateral scene selective region
+discrimination
+
+ align:start position:0%
+discrimination
+ 
+
+ align:start position:0%
+discrimination
+threshold goes up a bit that means you
+
+ align:start position:0%
+threshold goes up a bit that means you
+ 
+
+ align:start position:0%
+threshold goes up a bit that means you
+get worse at the discrimination the
+
+ align:start position:0%
+get worse at the discrimination the
+ 
+
+ align:start position:0%
+get worse at the discrimination the
+stimuli need to be more different
+
+ align:start position:0%
+stimuli need to be more different
+ 
+
+ align:start position:0%
+stimuli need to be more different
+compared to zapping the top of your head
+
+ align:start position:0%
+compared to zapping the top of your head
+ 
+
+ align:start position:0%
+compared to zapping the top of your head
+okay remember you always want to control
+
+ align:start position:0%
+okay remember you always want to control
+ 
+
+ align:start position:0%
+okay remember you always want to control
+condition and there's no perfect control
+
+ align:start position:0%
+condition and there's no perfect control
+ 
+
+ align:start position:0%
+condition and there's no perfect control
+condition because it feels differently
+
+ align:start position:0%
+condition because it feels differently
+ 
+
+ align:start position:0%
+condition because it feels differently
+to be zapped in different places but
+
+ align:start position:0%
+to be zapped in different places but
+ 
+
+ align:start position:0%
+to be zapped in different places but
+getting zapped up here is a
+
+ align:start position:0%
+getting zapped up here is a
+ 
+
+ align:start position:0%
+getting zapped up here is a
+you know
+
+ align:start position:0%
+you know
+ 
+
+ align:start position:0%
+you know
+better than nothing control
+
+ align:start position:0%
+better than nothing control
+ 
+
+ align:start position:0%
+better than nothing control
+and then here's the occipital face area
+
+ align:start position:0%
+and then here's the occipital face area
+ 
+
+ align:start position:0%
+and then here's the occipital face area
+that's the lateral face region we talked
+
+ align:start position:0%
+that's the lateral face region we talked
+ 
+
+ align:start position:0%
+that's the lateral face region we talked
+about before when i showed you another
+
+ align:start position:0%
+about before when i showed you another
+ 
+
+ align:start position:0%
+about before when i showed you another
+tms study basically whenever there's
+
+ align:start position:0%
+tms study basically whenever there's
+ 
+
+ align:start position:0%
+tms study basically whenever there's
+anything lateral we zap it because we
+
+ align:start position:0%
+anything lateral we zap it because we
+ 
+
+ align:start position:0%
+anything lateral we zap it because we
+can't
+
+ align:start position:0%
+can't
+ 
+
+ align:start position:0%
+can't
+and see it's not affected here
+
+ align:start position:0%
+and see it's not affected here
+ 
+
+ align:start position:0%
+and see it's not affected here
+zapping the occipital face area does not
+
+ align:start position:0%
+zapping the occipital face area does not
+ 
+
+ align:start position:0%
+zapping the occipital face area does not
+mess up your ability to discriminate the
+
+ align:start position:0%
+mess up your ability to discriminate the
+ 
+
+ align:start position:0%
+mess up your ability to discriminate the
+scenes
+
+ align:start position:0%
+scenes
+ 
+
+ align:start position:0%
+scenes
+however
+
+ align:start position:0%
+however
+ 
+
+ align:start position:0%
+however
+in the face task we see the opposite
+
+ align:start position:0%
+in the face task we see the opposite
+ 
+
+ align:start position:0%
+in the face task we see the opposite
+pattern for the face task
+
+ align:start position:0%
+pattern for the face task
+ 
+
+ align:start position:0%
+pattern for the face task
+zapping
+
+ align:start position:0%
+zapping
+ 
+
+ align:start position:0%
+zapping
+the occipital place area doesn't do
+
+ align:start position:0%
+the occipital place area doesn't do
+ 
+
+ align:start position:0%
+the occipital place area doesn't do
+anything compared to zapping the top of
+
+ align:start position:0%
+anything compared to zapping the top of
+ 
+
+ align:start position:0%
+anything compared to zapping the top of
+your head but zapping the face area does
+
+ align:start position:0%
+your head but zapping the face area does
+ 
+
+ align:start position:0%
+your head but zapping the face area does
+this is a double dissociation
+
+ align:start position:0%
+this is a double dissociation
+ 
+
+ align:start position:0%
+this is a double dissociation
+okay if we just had
+
+ align:start position:0%
+okay if we just had
+ 
+
+ align:start position:0%
+okay if we just had
+if we just had the scene task and be
+
+ align:start position:0%
+if we just had the scene task and be
+ 
+
+ align:start position:0%
+if we just had the scene task and be
+like yeah maybe
+
+ align:start position:0%
+like yeah maybe
+ 
+
+ align:start position:0%
+like yeah maybe
+who knows
+
+ align:start position:0%
+who knows
+ 
+
+ align:start position:0%
+who knows
+maybe
+
+ align:start position:0%
+maybe
+ 
+
+ align:start position:0%
+maybe
+maybe who knows why but you know it's
+
+ align:start position:0%
+maybe who knows why but you know it's
+ 
+
+ align:start position:0%
+maybe who knows why but you know it's
+not very strong but when you have these
+
+ align:start position:0%
+not very strong but when you have these
+ 
+
+ align:start position:0%
+not very strong but when you have these
+opposite things then we really have much
+
+ align:start position:0%
+opposite things then we really have much
+ 
+
+ align:start position:0%
+opposite things then we really have much
+more
+
+ align:start position:0%
+more
+ 
+
+ align:start position:0%
+more
+um strong evidence that these two
+
+ align:start position:0%
+um strong evidence that these two
+ 
+
+ align:start position:0%
+um strong evidence that these two
+regions have different functions from
+
+ align:start position:0%
+regions have different functions from
+ 
+
+ align:start position:0%
+regions have different functions from
+each other
+
+ align:start position:0%
+each other
+ 
+
+ align:start position:0%
+each other
+okay everybody get that this is a double
+
+ align:start position:0%
+okay everybody get that this is a double
+ 
+
+ align:start position:0%
+okay everybody get that this is a double
+dissociation in the same sense of when
+
+ align:start position:0%
+dissociation in the same sense of when
+ 
+
+ align:start position:0%
+dissociation in the same sense of when
+you have one patient with damage in one
+
+ align:start position:0%
+you have one patient with damage in one
+ 
+
+ align:start position:0%
+you have one patient with damage in one
+location and another patient with damage
+
+ align:start position:0%
+location and another patient with damage
+ 
+
+ align:start position:0%
+location and another patient with damage
+in another location and they have
+
+ align:start position:0%
+in another location and they have
+ 
+
+ align:start position:0%
+in another location and they have
+opposite patterns of deficit then we're
+
+ align:start position:0%
+opposite patterns of deficit then we're
+ 
+
+ align:start position:0%
+opposite patterns of deficit then we're
+really kind of in business then we can
+
+ align:start position:0%
+really kind of in business then we can
+ 
+
+ align:start position:0%
+really kind of in business then we can
+draw strong inferences
+
+ align:start position:0%
+draw strong inferences
+ 
+
+ align:start position:0%
+draw strong inferences
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+all right so we just said all of that
+
+ align:start position:0%
+all right so we just said all of that
+ 
+
+ align:start position:0%
+all right so we just said all of that
+okay so that's just a little snippet
+
+ align:start position:0%
+okay so that's just a little snippet
+ 
+
+ align:start position:0%
+okay so that's just a little snippet
+these and other data suggest that that
+
+ align:start position:0%
+these and other data suggest that that
+ 
+
+ align:start position:0%
+these and other data suggest that that
+region
+
+ align:start position:0%
+region
+ 
+
+ align:start position:0%
+region
+um is strongly active when you look at
+
+ align:start position:0%
+um is strongly active when you look at
+ 
+
+ align:start position:0%
+um is strongly active when you look at
+scenes uh and it seems to be involved in
+
+ align:start position:0%
+scenes uh and it seems to be involved in
+ 
+
+ align:start position:0%
+scenes uh and it seems to be involved in
+something like perceiving you know
+
+ align:start position:0%
+something like perceiving you know
+ 
+
+ align:start position:0%
+something like perceiving you know
+directly online perceiving the structure
+
+ align:start position:0%
+directly online perceiving the structure
+ 
+
+ align:start position:0%
+directly online perceiving the structure
+of the space in front of you
+
+ align:start position:0%
+of the space in front of you
+ 
+
+ align:start position:0%
+of the space in front of you
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+all right um so
+
+ align:start position:0%
+all right um so
+ 
+
+ align:start position:0%
+all right um so
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+yeah we already did retrosplenial cortex
+
+ align:start position:0%
+yeah we already did retrosplenial cortex
+ 
+
+ align:start position:0%
+yeah we already did retrosplenial cortex
+and next time we'll talk about the
+
+ align:start position:0%
+and next time we'll talk about the
+ 
+
+ align:start position:0%
+and next time we'll talk about the
+hippocampus in there and its role
+
+ align:start position:0%
+hippocampus in there and its role
+ 
+
+ align:start position:0%
+hippocampus in there and its role
+in the whole navigation thing
+
+ align:start position:0%
+in the whole navigation thing
+ 
+
+ align:start position:0%
+in the whole navigation thing
+now since i
+
+ align:start position:0%
+now since i
+ 
+
+ align:start position:0%
+now since i
+have
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+ended early
+
+ align:start position:0%
+ended early
+ 
+
+ align:start position:0%
+ended early
+a rare event i actually put together a
+
+ align:start position:0%
+a rare event i actually put together a
+ 
+
+ align:start position:0%
+a rare event i actually put together a
+whole other piece of this lecture and i
+
+ align:start position:0%
+whole other piece of this lecture and i
+ 
+
+ align:start position:0%
+whole other piece of this lecture and i
+thought no don't always have a part you
+
+ align:start position:0%
+thought no don't always have a part you
+ 
+
+ align:start position:0%
+thought no don't always have a part you
+don't get to
+
+ align:start position:0%
+don't get to
+ 
+
+ align:start position:0%
+don't get to
+but then it turns out
+
+ align:start position:0%
+but then it turns out
+ 
+
+ align:start position:0%
+but then it turns out
+maybe we do get to it
+
+ align:start position:0%
+maybe we do get to it
+ 
+
+ align:start position:0%
+maybe we do get to it
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+okay we're gonna we're gonna go over
+
+ align:start position:0%
+okay we're gonna we're gonna go over
+ 
+
+ align:start position:0%
+okay we're gonna we're gonna go over
+this more later but we're going to start
+
+ align:start position:0%
+this more later but we're going to start
+ 
+
+ align:start position:0%
+this more later but we're going to start
+with this
+
+ align:start position:0%
+with this
+ 
+
+ align:start position:0%
+with this
+business right here so anybody have
+
+ align:start position:0%
+business right here so anybody have
+ 
+
+ align:start position:0%
+business right here so anybody have
+questions about the stuff so far
+
+ align:start position:0%
+questions about the stuff so far
+ 
+
+ align:start position:0%
+questions about the stuff so far
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+so i've spent a lot of time talking
+
+ align:start position:0%
+so i've spent a lot of time talking
+ 
+
+ align:start position:0%
+so i've spent a lot of time talking
+about multiple voxel pattern analysis
+
+ align:start position:0%
+about multiple voxel pattern analysis
+ 
+
+ align:start position:0%
+about multiple voxel pattern analysis
+because it's the only method i've
+
+ align:start position:0%
+because it's the only method i've
+ 
+
+ align:start position:0%
+because it's the only method i've
+mentioned so far that enables us to go
+
+ align:start position:0%
+mentioned so far that enables us to go
+ 
+
+ align:start position:0%
+mentioned so far that enables us to go
+beyond the business of saying
+
+ align:start position:0%
+beyond the business of saying
+ 
+
+ align:start position:0%
+beyond the business of saying
+how strongly do the neurons fire in this
+
+ align:start position:0%
+how strongly do the neurons fire in this
+ 
+
+ align:start position:0%
+how strongly do the neurons fire in this
+region to the more interesting question
+
+ align:start position:0%
+region to the more interesting question
+ 
+
+ align:start position:0%
+region to the more interesting question
+of what information is contained in this
+
+ align:start position:0%
+of what information is contained in this
+ 
+
+ align:start position:0%
+of what information is contained in this
+region okay
+
+ align:start position:0%
+region okay
+ 
+
+ align:start position:0%
+region okay
+but i also ended the last lecture with
+
+ align:start position:0%
+but i also ended the last lecture with
+ 
+
+ align:start position:0%
+but i also ended the last lecture with
+this kind of depressive note
+
+ align:start position:0%
+this kind of depressive note
+ 
+
+ align:start position:0%
+this kind of depressive note
+that you can't see much with mvpa
+
+ align:start position:0%
+that you can't see much with mvpa
+ 
+
+ align:start position:0%
+that you can't see much with mvpa
+applied to face patches
+
+ align:start position:0%
+applied to face patches
+ 
+
+ align:start position:0%
+applied to face patches
+even when we know there's information in
+
+ align:start position:0%
+even when we know there's information in
+ 
+
+ align:start position:0%
+even when we know there's information in
+there with electrophysiology data
+
+ align:start position:0%
+there with electrophysiology data
+ 
+
+ align:start position:0%
+there with electrophysiology data
+remember i showed you that monkey study
+
+ align:start position:0%
+remember i showed you that monkey study
+ 
+
+ align:start position:0%
+remember i showed you that monkey study
+where they tried mvpa in the face
+
+ align:start position:0%
+where they tried mvpa in the face
+ 
+
+ align:start position:0%
+where they tried mvpa in the face
+patches and monkeys and they couldn't
+
+ align:start position:0%
+patches and monkeys and they couldn't
+ 
+
+ align:start position:0%
+patches and monkeys and they couldn't
+kind of read out a damn thing
+
+ align:start position:0%
+kind of read out a damn thing
+ 
+
+ align:start position:0%
+kind of read out a damn thing
+and then they try mvpa on individual
+
+ align:start position:0%
+and then they try mvpa on individual
+ 
+
+ align:start position:0%
+and then they try mvpa on individual
+neural responses of the same region and
+
+ align:start position:0%
+neural responses of the same region and
+ 
+
+ align:start position:0%
+neural responses of the same region and
+they can read out all kinds of
+
+ align:start position:0%
+they can read out all kinds of
+ 
+
+ align:start position:0%
+they can read out all kinds of
+information and that tells you the
+
+ align:start position:0%
+information and that tells you the
+ 
+
+ align:start position:0%
+information and that tells you the
+information is there and we just can't
+
+ align:start position:0%
+information is there and we just can't
+ 
+
+ align:start position:0%
+information is there and we just can't
+always see it with mvpa now today you've
+
+ align:start position:0%
+always see it with mvpa now today you've
+ 
+
+ align:start position:0%
+always see it with mvpa now today you've
+seen cases where you can see stuff with
+
+ align:start position:0%
+seen cases where you can see stuff with
+ 
+
+ align:start position:0%
+seen cases where you can see stuff with
+mvpa in the scene region so sometimes it
+
+ align:start position:0%
+mvpa in the scene region so sometimes it
+ 
+
+ align:start position:0%
+mvpa in the scene region so sometimes it
+works sometimes it doesn't
+
+ align:start position:0%
+works sometimes it doesn't
+ 
+
+ align:start position:0%
+works sometimes it doesn't
+and when it doesn't work we're left in
+
+ align:start position:0%
+and when it doesn't work we're left in
+ 
+
+ align:start position:0%
+and when it doesn't work we're left in
+this unsatisfying situation that we
+
+ align:start position:0%
+this unsatisfying situation that we
+ 
+
+ align:start position:0%
+this unsatisfying situation that we
+don't know if the information isn't
+
+ align:start position:0%
+don't know if the information isn't
+ 
+
+ align:start position:0%
+don't know if the information isn't
+there
+
+ align:start position:0%
+there
+ 
+
+ align:start position:0%
+there
+or if the neurons are just so scrambled
+
+ align:start position:0%
+or if the neurons are just so scrambled
+ 
+
+ align:start position:0%
+or if the neurons are just so scrambled
+together
+
+ align:start position:0%
+together
+ 
+
+ align:start position:0%
+together
+that we just don't we can't see the um
+
+ align:start position:0%
+that we just don't we can't see the um
+ 
+
+ align:start position:0%
+that we just don't we can't see the um
+see the different patterns
+
+ align:start position:0%
+see the different patterns
+ 
+
+ align:start position:0%
+see the different patterns
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+so bottom line we need another method
+
+ align:start position:0%
+so bottom line we need another method
+ 
+
+ align:start position:0%
+so bottom line we need another method
+mvpa is a whole lot better than nothing
+
+ align:start position:0%
+mvpa is a whole lot better than nothing
+ 
+
+ align:start position:0%
+mvpa is a whole lot better than nothing
+but we want to be able to ask is there
+
+ align:start position:0%
+but we want to be able to ask is there
+ 
+
+ align:start position:0%
+but we want to be able to ask is there
+information present in this region
+
+ align:start position:0%
+information present in this region
+ 
+
+ align:start position:0%
+information present in this region
+even when we think the relevant neurons
+
+ align:start position:0%
+even when we think the relevant neurons
+ 
+
+ align:start position:0%
+even when we think the relevant neurons
+are all spatially intermingled
+
+ align:start position:0%
+are all spatially intermingled
+ 
+
+ align:start position:0%
+are all spatially intermingled
+okay so let me just do a little bit of
+
+ align:start position:0%
+okay so let me just do a little bit of
+ 
+
+ align:start position:0%
+okay so let me just do a little bit of
+this and then we'll continue later okay
+
+ align:start position:0%
+this and then we'll continue later okay
+ 
+
+ align:start position:0%
+this and then we'll continue later okay
+so goal we want to this is this new
+
+ align:start position:0%
+so goal we want to this is this new
+ 
+
+ align:start position:0%
+so goal we want to this is this new
+method is called
+
+ align:start position:0%
+method is called
+ 
+
+ align:start position:0%
+method is called
+event related functional mri adaptation
+
+ align:start position:0%
+event related functional mri adaptation
+ 
+
+ align:start position:0%
+event related functional mri adaptation
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+and we use it when we want to know if
+
+ align:start position:0%
+and we use it when we want to know if
+ 
+
+ align:start position:0%
+and we use it when we want to know if
+neural populations in a particular
+
+ align:start position:0%
+neural populations in a particular
+ 
+
+ align:start position:0%
+neural populations in a particular
+region can discriminate between two
+
+ align:start position:0%
+region can discriminate between two
+ 
+
+ align:start position:0%
+region can discriminate between two
+stimuli or two stimulus classes
+
+ align:start position:0%
+stimuli or two stimulus classes
+ 
+
+ align:start position:0%
+stimuli or two stimulus classes
+so for example
+
+ align:start position:0%
+so for example
+ 
+
+ align:start position:0%
+so for example
+do neurons in the ffa distinguish
+
+ align:start position:0%
+do neurons in the ffa distinguish
+ 
+
+ align:start position:0%
+do neurons in the ffa distinguish
+between this image
+
+ align:start position:0%
+between this image
+ 
+
+ align:start position:0%
+between this image
+and that image
+
+ align:start position:0%
+and that image
+ 
+
+ align:start position:0%
+and that image
+okay so if we want to know that
+
+ align:start position:0%
+okay so if we want to know that
+ 
+
+ align:start position:0%
+okay so if we want to know that
+we could measure the functional mri
+
+ align:start position:0%
+we could measure the functional mri
+ 
+
+ align:start position:0%
+we could measure the functional mri
+response in the ffa and find this would
+
+ align:start position:0%
+response in the ffa and find this would
+ 
+
+ align:start position:0%
+response in the ffa and find this would
+be an event related response similar
+
+ align:start position:0%
+be an event related response similar
+ 
+
+ align:start position:0%
+be an event related response similar
+responses to the two
+
+ align:start position:0%
+responses to the two
+ 
+
+ align:start position:0%
+responses to the two
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+and as i just mentioned
+
+ align:start position:0%
+and as i just mentioned
+ 
+
+ align:start position:0%
+and as i just mentioned
+that wouldn't mean that there isn't
+
+ align:start position:0%
+that wouldn't mean that there isn't
+ 
+
+ align:start position:0%
+that wouldn't mean that there isn't
+information
+
+ align:start position:0%
+information
+ 
+
+ align:start position:0%
+information
+in the ffa that discriminates that it
+
+ align:start position:0%
+in the ffa that discriminates that it
+ 
+
+ align:start position:0%
+in the ffa that discriminates that it
+just says they have the same mean
+
+ align:start position:0%
+just says they have the same mean
+ 
+
+ align:start position:0%
+just says they have the same mean
+response everybody get that
+
+ align:start position:0%
+response everybody get that
+ 
+
+ align:start position:0%
+response everybody get that
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+now
+
+ align:start position:0%
+now
+ 
+
+ align:start position:0%
+now
+if we zoom in and think about what might
+
+ align:start position:0%
+if we zoom in and think about what might
+ 
+
+ align:start position:0%
+if we zoom in and think about what might
+neurons be doing
+
+ align:start position:0%
+neurons be doing
+ 
+
+ align:start position:0%
+neurons be doing
+it's still possible even with the same
+
+ align:start position:0%
+it's still possible even with the same
+ 
+
+ align:start position:0%
+it's still possible even with the same
+mean response that neurons could be
+
+ align:start position:0%
+mean response that neurons could be
+ 
+
+ align:start position:0%
+mean response that neurons could be
+organized like this with some of them
+
+ align:start position:0%
+organized like this with some of them
+ 
+
+ align:start position:0%
+organized like this with some of them
+responding only to this image and some
+
+ align:start position:0%
+responding only to this image and some
+ 
+
+ align:start position:0%
+responding only to this image and some
+of them responding only to that image
+
+ align:start position:0%
+of them responding only to that image
+ 
+
+ align:start position:0%
+of them responding only to that image
+but it's also possible that all of the
+
+ align:start position:0%
+but it's also possible that all of the
+ 
+
+ align:start position:0%
+but it's also possible that all of the
+neurons respond equally to both
+
+ align:start position:0%
+neurons respond equally to both
+ 
+
+ align:start position:0%
+neurons respond equally to both
+and we kind of desperately need to know
+
+ align:start position:0%
+and we kind of desperately need to know
+ 
+
+ align:start position:0%
+and we kind of desperately need to know
+i mean not in this case this is a toy
+
+ align:start position:0%
+i mean not in this case this is a toy
+ 
+
+ align:start position:0%
+i mean not in this case this is a toy
+example obviously but we often when
+
+ align:start position:0%
+example obviously but we often when
+ 
+
+ align:start position:0%
+example obviously but we often when
+we're trying to understand a region of
+
+ align:start position:0%
+we're trying to understand a region of
+ 
+
+ align:start position:0%
+we're trying to understand a region of
+the brain we need to know which
+
+ align:start position:0%
+the brain we need to know which
+ 
+
+ align:start position:0%
+the brain we need to know which
+situation we're in
+
+ align:start position:0%
+situation we're in
+ 
+
+ align:start position:0%
+situation we're in
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+that neural population can discriminate
+
+ align:start position:0%
+that neural population can discriminate
+ 
+
+ align:start position:0%
+that neural population can discriminate
+these two and that one can't
+
+ align:start position:0%
+these two and that one can't
+ 
+
+ align:start position:0%
+these two and that one can't
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+how are we going to tell which is true
+
+ align:start position:0%
+how are we going to tell which is true
+ 
+
+ align:start position:0%
+how are we going to tell which is true
+well we talked before about multiple
+
+ align:start position:0%
+well we talked before about multiple
+ 
+
+ align:start position:0%
+well we talked before about multiple
+voxel pattern analysis but as i just
+
+ align:start position:0%
+voxel pattern analysis but as i just
+ 
+
+ align:start position:0%
+voxel pattern analysis but as i just
+said it only works
+
+ align:start position:0%
+said it only works
+ 
+
+ align:start position:0%
+said it only works
+when the neurons are spatially clustered
+
+ align:start position:0%
+when the neurons are spatially clustered
+ 
+
+ align:start position:0%
+when the neurons are spatially clustered
+on the scale of voxels
+
+ align:start position:0%
+on the scale of voxels
+ 
+
+ align:start position:0%
+on the scale of voxels
+okay so
+
+ align:start position:0%
+okay so
+ 
+
+ align:start position:0%
+okay so
+imagine you have these situations here
+
+ align:start position:0%
+imagine you have these situations here
+ 
+
+ align:start position:0%
+imagine you have these situations here
+this is getting more and more of a toy
+
+ align:start position:0%
+this is getting more and more of a toy
+ 
+
+ align:start position:0%
+this is getting more and more of a toy
+example but just to give you the idea
+
+ align:start position:0%
+example but just to give you the idea
+ 
+
+ align:start position:0%
+example but just to give you the idea
+suppose where those neural populations
+
+ align:start position:0%
+suppose where those neural populations
+ 
+
+ align:start position:0%
+suppose where those neural populations
+land with respect to voxels is like this
+
+ align:start position:0%
+land with respect to voxels is like this
+ 
+
+ align:start position:0%
+land with respect to voxels is like this
+so if each of these is a voxel in the
+
+ align:start position:0%
+so if each of these is a voxel in the
+ 
+
+ align:start position:0%
+so if each of these is a voxel in the
+brain a little say two by two by three
+
+ align:start position:0%
+brain a little say two by two by three
+ 
+
+ align:start position:0%
+brain a little say two by two by three
+millimeter chunk of brain that we're
+
+ align:start position:0%
+millimeter chunk of brain that we're
+ 
+
+ align:start position:0%
+millimeter chunk of brain that we're
+getting an mri signal from
+
+ align:start position:0%
+getting an mri signal from
+ 
+
+ align:start position:0%
+getting an mri signal from
+if you have the different neural
+
+ align:start position:0%
+if you have the different neural
+ 
+
+ align:start position:0%
+if you have the different neural
+populations spatially segregated enough
+
+ align:start position:0%
+populations spatially segregated enough
+ 
+
+ align:start position:0%
+populations spatially segregated enough
+that they mostly land in different
+
+ align:start position:0%
+that they mostly land in different
+ 
+
+ align:start position:0%
+that they mostly land in different
+voxels
+
+ align:start position:0%
+voxels
+ 
+
+ align:start position:0%
+voxels
+then mvpa might work here
+
+ align:start position:0%
+then mvpa might work here
+ 
+
+ align:start position:0%
+then mvpa might work here
+is that intuitive do you guys all see
+
+ align:start position:0%
+is that intuitive do you guys all see
+ 
+
+ align:start position:0%
+is that intuitive do you guys all see
+that then we get a different pattern in
+
+ align:start position:0%
+that then we get a different pattern in
+ 
+
+ align:start position:0%
+that then we get a different pattern in
+these voxels
+
+ align:start position:0%
+these voxels
+ 
+
+ align:start position:0%
+these voxels
+for looking at those two different
+
+ align:start position:0%
+for looking at those two different
+ 
+
+ align:start position:0%
+for looking at those two different
+images
+
+ align:start position:0%
+images
+ 
+
+ align:start position:0%
+images
+but even if we have
+
+ align:start position:0%
+but even if we have
+ 
+
+ align:start position:0%
+but even if we have
+the situation here which is kind of
+
+ align:start position:0%
+the situation here which is kind of
+ 
+
+ align:start position:0%
+the situation here which is kind of
+informationally the same if they're
+
+ align:start position:0%
+informationally the same if they're
+ 
+
+ align:start position:0%
+informationally the same if they're
+spatially scrambled
+
+ align:start position:0%
+spatially scrambled
+ 
+
+ align:start position:0%
+spatially scrambled
+so that they're in roughly equal
+
+ align:start position:0%
+so that they're in roughly equal
+ 
+
+ align:start position:0%
+so that they're in roughly equal
+proportion in each voxel mvpa won't work
+
+ align:start position:0%
+proportion in each voxel mvpa won't work
+ 
+
+ align:start position:0%
+proportion in each voxel mvpa won't work
+does that make sense
+
+ align:start position:0%
+does that make sense
+ 
+
+ align:start position:0%
+does that make sense
+and so that's when we need this other
+
+ align:start position:0%
+and so that's when we need this other
+ 
+
+ align:start position:0%
+and so that's when we need this other
+method called functional memory
+
+ align:start position:0%
+method called functional memory
+ 
+
+ align:start position:0%
+method called functional memory
+adaptation
+
+ align:start position:0%
+adaptation
+ 
+
+ align:start position:0%
+adaptation
+makes sense
+
+ align:start position:0%
+makes sense
+ 
+
+ align:start position:0%
+makes sense
+okay i'm going to go one minute over
+
+ align:start position:0%
+okay i'm going to go one minute over
+ 
+
+ align:start position:0%
+okay i'm going to go one minute over
+probably
+
+ align:start position:0%
+probably
+ 
+
+ align:start position:0%
+probably
+okay so the point of functional mri
+
+ align:start position:0%
+okay so the point of functional mri
+ 
+
+ align:start position:0%
+okay so the point of functional mri
+adaptation is it can work even when
+
+ align:start position:0%
+adaptation is it can work even when
+ 
+
+ align:start position:0%
+adaptation is it can work even when
+there's no spatial clustering of the
+
+ align:start position:0%
+there's no spatial clustering of the
+ 
+
+ align:start position:0%
+there's no spatial clustering of the
+relevant neural populations on the scale
+
+ align:start position:0%
+relevant neural populations on the scale
+ 
+
+ align:start position:0%
+relevant neural populations on the scale
+of voxels so let me go through it
+
+ align:start position:0%
+of voxels so let me go through it
+ 
+
+ align:start position:0%
+of voxels so let me go through it
+quickly and we'll come back to it later
+
+ align:start position:0%
+quickly and we'll come back to it later
+ 
+
+ align:start position:0%
+quickly and we'll come back to it later
+so here's how it goes the basic idea is
+
+ align:start position:0%
+so here's how it goes the basic idea is
+ 
+
+ align:start position:0%
+so here's how it goes the basic idea is
+any measure that's sensitive to the
+
+ align:start position:0%
+any measure that's sensitive to the
+ 
+
+ align:start position:0%
+any measure that's sensitive to the
+sameness versus difference between two
+
+ align:start position:0%
+sameness versus difference between two
+ 
+
+ align:start position:0%
+sameness versus difference between two
+stimuli
+
+ align:start position:0%
+stimuli
+ 
+
+ align:start position:0%
+stimuli
+can reveal what that system takes to be
+
+ align:start position:0%
+can reveal what that system takes to be
+ 
+
+ align:start position:0%
+can reveal what that system takes to be
+same or different
+
+ align:start position:0%
+same or different
+ 
+
+ align:start position:0%
+same or different
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+so for example if a brain region
+
+ align:start position:0%
+so for example if a brain region
+ 
+
+ align:start position:0%
+so for example if a brain region
+discriminates between two similar
+
+ align:start position:0%
+discriminates between two similar
+ 
+
+ align:start position:0%
+discriminates between two similar
+stimuli like these
+
+ align:start position:0%
+stimuli like these
+ 
+
+ align:start position:0%
+stimuli like these
+then
+
+ align:start position:0%
+then
+ 
+
+ align:start position:0%
+then
+if we measure the functional mri
+
+ align:start position:0%
+if we measure the functional mri
+ 
+
+ align:start position:0%
+if we measure the functional mri
+response in that region to same versus
+
+ align:start position:0%
+response in that region to same versus
+ 
+
+ align:start position:0%
+response in that region to same versus
+different trials
+
+ align:start position:0%
+different trials
+ 
+
+ align:start position:0%
+different trials
+okay so this would be a different trial
+
+ align:start position:0%
+okay so this would be a different trial
+ 
+
+ align:start position:0%
+okay so this would be a different trial
+you present
+
+ align:start position:0%
+you present
+ 
+
+ align:start position:0%
+you present
+trump and then the chimp back to back
+
+ align:start position:0%
+trump and then the chimp back to back
+ 
+
+ align:start position:0%
+trump and then the chimp back to back
+that's one trial
+
+ align:start position:0%
+that's one trial
+ 
+
+ align:start position:0%
+that's one trial
+compared to a same trial chimp and then
+
+ align:start position:0%
+compared to a same trial chimp and then
+ 
+
+ align:start position:0%
+compared to a same trial chimp and then
+chimp
+
+ align:start position:0%
+chimp
+ 
+
+ align:start position:0%
+chimp
+and of course we counter balance
+
+ align:start position:0%
+and of course we counter balance
+ 
+
+ align:start position:0%
+and of course we counter balance
+everything so we also do chimp and then
+
+ align:start position:0%
+everything so we also do chimp and then
+ 
+
+ align:start position:0%
+everything so we also do chimp and then
+trump in another different case and then
+
+ align:start position:0%
+trump in another different case and then
+ 
+
+ align:start position:0%
+trump in another different case and then
+trump and then trump in another same
+
+ align:start position:0%
+trump and then trump in another same
+ 
+
+ align:start position:0%
+trump and then trump in another same
+case right
+
+ align:start position:0%
+case right
+ 
+
+ align:start position:0%
+case right
+if we find
+
+ align:start position:0%
+if we find
+ 
+
+ align:start position:0%
+if we find
+that the neural response is higher when
+
+ align:start position:0%
+that the neural response is higher when
+ 
+
+ align:start position:0%
+that the neural response is higher when
+the two stimuli are different than when
+
+ align:start position:0%
+the two stimuli are different than when
+ 
+
+ align:start position:0%
+the two stimuli are different than when
+they're the same
+
+ align:start position:0%
+they're the same
+ 
+
+ align:start position:0%
+they're the same
+then
+
+ align:start position:0%
+then
+ 
+
+ align:start position:0%
+then
+we know that that region has neurons
+
+ align:start position:0%
+we know that that region has neurons
+ 
+
+ align:start position:0%
+we know that that region has neurons
+that respond differentially to the two
+
+ align:start position:0%
+that respond differentially to the two
+ 
+
+ align:start position:0%
+that respond differentially to the two
+okay so remember we started with a case
+
+ align:start position:0%
+okay so remember we started with a case
+ 
+
+ align:start position:0%
+okay so remember we started with a case
+where the mean response is the same
+
+ align:start position:0%
+where the mean response is the same
+ 
+
+ align:start position:0%
+where the mean response is the same
+to this image in this image if you just
+
+ align:start position:0%
+to this image in this image if you just
+ 
+
+ align:start position:0%
+to this image in this image if you just
+measure them along
+
+ align:start position:0%
+measure them along
+ 
+
+ align:start position:0%
+measure them along
+but now we want to know are
+
+ align:start position:0%
+but now we want to know are
+ 
+
+ align:start position:0%
+but now we want to know are
+do we really have neurons that respond
+
+ align:start position:0%
+do we really have neurons that respond
+ 
+
+ align:start position:0%
+do we really have neurons that respond
+differentially so we're using the fact
+
+ align:start position:0%
+differentially so we're using the fact
+ 
+
+ align:start position:0%
+differentially so we're using the fact
+that neurons are like people and muscles
+
+ align:start position:0%
+that neurons are like people and muscles
+ 
+
+ align:start position:0%
+that neurons are like people and muscles
+if you keep doing the same thing to them
+
+ align:start position:0%
+if you keep doing the same thing to them
+ 
+
+ align:start position:0%
+if you keep doing the same thing to them
+they get bored
+
+ align:start position:0%
+they get bored
+ 
+
+ align:start position:0%
+they get bored
+been there done that okay
+
+ align:start position:0%
+been there done that okay
+ 
+
+ align:start position:0%
+been there done that okay
+so you present this back to back you get
+
+ align:start position:0%
+so you present this back to back you get
+ 
+
+ align:start position:0%
+so you present this back to back you get
+a lower response than if you present
+
+ align:start position:0%
+a lower response than if you present
+ 
+
+ align:start position:0%
+a lower response than if you present
+this and then this
+
+ align:start position:0%
+this and then this
+ 
+
+ align:start position:0%
+this and then this
+okay that's called functional mri
+
+ align:start position:0%
+okay that's called functional mri
+ 
+
+ align:start position:0%
+okay that's called functional mri
+adaptation it's like that waterfall mta
+
+ align:start position:0%
+adaptation it's like that waterfall mta
+ 
+
+ align:start position:0%
+adaptation it's like that waterfall mta
+adaptation we talked about before but
+
+ align:start position:0%
+adaptation we talked about before but
+ 
+
+ align:start position:0%
+adaptation we talked about before but
+just crammed into a fine time scale
+
+ align:start position:0%
+just crammed into a fine time scale
+ 
+
+ align:start position:0%
+just crammed into a fine time scale
+okay and so then if you do that you can
+
+ align:start position:0%
+okay and so then if you do that you can
+ 
+
+ align:start position:0%
+okay and so then if you do that you can
+ask what a region thinks is the same
+
+ align:start position:0%
+ask what a region thinks is the same
+ 
+
+ align:start position:0%
+ask what a region thinks is the same
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+so then we could ask okay what about
+
+ align:start position:0%
+so then we could ask okay what about
+ 
+
+ align:start position:0%
+so then we could ask okay what about
+these two images
+
+ align:start position:0%
+these two images
+ 
+
+ align:start position:0%
+these two images
+does it think those are the same
+
+ align:start position:0%
+does it think those are the same
+ 
+
+ align:start position:0%
+does it think those are the same
+and if we find a response like that what
+
+ align:start position:0%
+and if we find a response like that what
+ 
+
+ align:start position:0%
+and if we find a response like that what
+have we learned so if these two respond
+
+ align:start position:0%
+have we learned so if these two respond
+ 
+
+ align:start position:0%
+have we learned so if these two respond
+like that what have we learned
+
+ align:start position:0%
+like that what have we learned
+ 
+
+ align:start position:0%
+like that what have we learned
+about a region that shows this is all
+
+ align:start position:0%
+about a region that shows this is all
+ 
+
+ align:start position:0%
+about a region that shows this is all
+fake data obviously but if we saw that
+
+ align:start position:0%
+fake data obviously but if we saw that
+ 
+
+ align:start position:0%
+fake data obviously but if we saw that
+what have we learned
+
+ align:start position:0%
+what have we learned
+ 
+
+ align:start position:0%
+what have we learned
+and then i'll let you go
+
+ align:start position:0%
+and then i'll let you go
+ 
+
+ align:start position:0%
+and then i'll let you go
+as soon as i get a nice answer to this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um so if it's the same between two
+
+ align:start position:0%
+um so if it's the same between two
+ 
+
+ align:start position:0%
+um so if it's the same between two
+pictures of the same stimuli that means
+
+ align:start position:0%
+pictures of the same stimuli that means
+ 
+
+ align:start position:0%
+pictures of the same stimuli that means
+that it's activated like it can
+
+ align:start position:0%
+that it's activated like it can
+ 
+
+ align:start position:0%
+that it's activated like it can
+discriminate but if it were um
+
+ align:start position:0%
+discriminate but if it were um
+ 
+
+ align:start position:0%
+discriminate but if it were um
+if the yellow line had the same degree
+
+ align:start position:0%
+if the yellow line had the same degree
+ 
+
+ align:start position:0%
+if the yellow line had the same degree
+as the red you would just be reacting to
+
+ align:start position:0%
+as the red you would just be reacting to
+ 
+
+ align:start position:0%
+as the red you would just be reacting to
+different pictures
+
+ align:start position:0%
+different pictures
+ 
+
+ align:start position:0%
+different pictures
+i totally get that it's probably right
+
+ align:start position:0%
+i totally get that it's probably right
+ 
+
+ align:start position:0%
+i totally get that it's probably right
+but totally get it
+
+ align:start position:0%
+but totally get it
+ 
+
+ align:start position:0%
+but totally get it
+key point just because i don't want to
+
+ align:start position:0%
+key point just because i don't want to
+ 
+
+ align:start position:0%
+key point just because i don't want to
+torture you guys and go way over but key
+
+ align:start position:0%
+torture you guys and go way over but key
+ 
+
+ align:start position:0%
+torture you guys and go way over but key
+point is
+
+ align:start position:0%
+point is
+ 
+
+ align:start position:0%
+point is
+it's
+
+ align:start position:0%
+it's
+ 
+
+ align:start position:0%
+it's
+the same response is the lower response
+
+ align:start position:0%
+the same response is the lower response
+ 
+
+ align:start position:0%
+the same response is the lower response
+we tell that with this case when we
+
+ align:start position:0%
+we tell that with this case when we
+ 
+
+ align:start position:0%
+we tell that with this case when we
+actually give it a same one so same is
+
+ align:start position:0%
+actually give it a same one so same is
+ 
+
+ align:start position:0%
+actually give it a same one so same is
+lower than different that's just how
+
+ align:start position:0%
+lower than different that's just how
+ 
+
+ align:start position:0%
+lower than different that's just how
+this method works
+
+ align:start position:0%
+this method works
+ 
+
+ align:start position:0%
+this method works
+then we're basically asking does that
+
+ align:start position:0%
+then we're basically asking does that
+ 
+
+ align:start position:0%
+then we're basically asking does that
+count as the same to this brain region
+
+ align:start position:0%
+count as the same to this brain region
+ 
+
+ align:start position:0%
+count as the same to this brain region
+and we're finding yes it does
+
+ align:start position:0%
+and we're finding yes it does
+ 
+
+ align:start position:0%
+and we're finding yes it does
+that tells us that those neurons are
+
+ align:start position:0%
+that tells us that those neurons are
+ 
+
+ align:start position:0%
+that tells us that those neurons are
+invariant to all kinds of things
+
+ align:start position:0%
+invariant to all kinds of things
+ 
+
+ align:start position:0%
+invariant to all kinds of things
+viewpoint facial expression
+
+ align:start position:0%
+viewpoint facial expression
+ 
+
+ align:start position:0%
+viewpoint facial expression
+you know when he last dyed his hair you
+
+ align:start position:0%
+you know when he last dyed his hair you
+ 
+
+ align:start position:0%
+you know when he last dyed his hair you
+know who the hell knows all these other
+
+ align:start position:0%
+know who the hell knows all these other
+ 
+
+ align:start position:0%
+know who the hell knows all these other
+things right
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so we'll talk more about this but the
+
+ align:start position:0%
+so we'll talk more about this but the
+ 
+
+ align:start position:0%
+so we'll talk more about this but the
+idea is now we have another method in
+
+ align:start position:0%
+idea is now we have another method in
+ 
+
+ align:start position:0%
+idea is now we have another method in
+addition to mvpa that can start to tell
+
+ align:start position:0%
+addition to mvpa that can start to tell
+ 
+
+ align:start position:0%
+addition to mvpa that can start to tell
+us what neurons are actually
+
+ align:start position:0%
+us what neurons are actually
+ 
+
+ align:start position:0%
+us what neurons are actually
+discriminating okay sorry to go over
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+you
\ No newline at end of file
diff --git a/MuqLI4otMIQ.txt b/MuqLI4otMIQ.txt
new file mode 100644
index 0000000000000000000000000000000000000000..c056e1a5314b7c131befdc86250213d370265453
--- /dev/null
+++ b/MuqLI4otMIQ.txt
@@ -0,0 +1,1531 @@
+align:start position:0%
+ 
+we will now work with a geometric random
+
+ align:start position:0%
+we will now work with a geometric random
+ 
+
+ align:start position:0%
+we will now work with a geometric random
+variable and put to use our
+
+ align:start position:0%
+variable and put to use our
+ 
+
+ align:start position:0%
+variable and put to use our
+understanding of conditional pmfs and
+
+ align:start position:0%
+understanding of conditional pmfs and
+ 
+
+ align:start position:0%
+understanding of conditional pmfs and
+conditional expectations remember that a
+
+ align:start position:0%
+conditional expectations remember that a
+ 
+
+ align:start position:0%
+conditional expectations remember that a
+geometric random variable corresponds to
+
+ align:start position:0%
+geometric random variable corresponds to
+ 
+
+ align:start position:0%
+geometric random variable corresponds to
+the number of independent coin tosses
+
+ align:start position:0%
+the number of independent coin tosses
+ 
+
+ align:start position:0%
+the number of independent coin tosses
+until the first head occurs and here P
+
+ align:start position:0%
+until the first head occurs and here P
+ 
+
+ align:start position:0%
+until the first head occurs and here P
+is a parameter that describes the coin
+
+ align:start position:0%
+is a parameter that describes the coin
+ 
+
+ align:start position:0%
+is a parameter that describes the coin
+it is the probability of heads at each
+
+ align:start position:0%
+it is the probability of heads at each
+ 
+
+ align:start position:0%
+it is the probability of heads at each
+coin toss we have already seen the
+
+ align:start position:0%
+coin toss we have already seen the
+ 
+
+ align:start position:0%
+coin toss we have already seen the
+formula for the geometric PMF and the
+
+ align:start position:0%
+formula for the geometric PMF and the
+ 
+
+ align:start position:0%
+formula for the geometric PMF and the
+corresponding plot we will now add one
+
+ align:start position:0%
+corresponding plot we will now add one
+ 
+
+ align:start position:0%
+corresponding plot we will now add one
+very important property which is usually
+
+ align:start position:0%
+very important property which is usually
+ 
+
+ align:start position:0%
+very important property which is usually
+called memorylessness ultimately this
+
+ align:start position:0%
+called memorylessness ultimately this
+ 
+
+ align:start position:0%
+called memorylessness ultimately this
+property has to do with the fact that
+
+ align:start position:0%
+property has to do with the fact that
+ 
+
+ align:start position:0%
+property has to do with the fact that
+independent coin tosses do not have any
+
+ align:start position:0%
+independent coin tosses do not have any
+ 
+
+ align:start position:0%
+independent coin tosses do not have any
+memory past coin tosses do not affect
+
+ align:start position:0%
+memory past coin tosses do not affect
+ 
+
+ align:start position:0%
+memory past coin tosses do not affect
+future coin tosses so consider a coin
+
+ align:start position:0%
+future coin tosses so consider a coin
+ 
+
+ align:start position:0%
+future coin tosses so consider a coin
+tossing experiment with independent
+
+ align:start position:0%
+tossing experiment with independent
+ 
+
+ align:start position:0%
+tossing experiment with independent
+tosses and let X be the number of tosses
+
+ align:start position:0%
+tosses and let X be the number of tosses
+ 
+
+ align:start position:0%
+tosses and let X be the number of tosses
+until the first heads and X is geometric
+
+ align:start position:0%
+until the first heads and X is geometric
+ 
+
+ align:start position:0%
+until the first heads and X is geometric
+with parameter P suppose that you show
+
+ align:start position:0%
+with parameter P suppose that you show
+ 
+
+ align:start position:0%
+with parameter P suppose that you show
+up a little after the experiment has
+
+ align:start position:0%
+up a little after the experiment has
+ 
+
+ align:start position:0%
+up a little after the experiment has
+started and you are told that there were
+
+ align:start position:0%
+started and you are told that there were
+ 
+
+ align:start position:0%
+started and you are told that there were
+so far just 1 coin toss and that this
+
+ align:start position:0%
+so far just 1 coin toss and that this
+ 
+
+ align:start position:0%
+so far just 1 coin toss and that this
+coin toss resulted in tails now you have
+
+ align:start position:0%
+coin toss resulted in tails now you have
+ 
+
+ align:start position:0%
+coin toss resulted in tails now you have
+to take over and carry out the remaining
+
+ align:start position:0%
+to take over and carry out the remaining
+ 
+
+ align:start position:0%
+to take over and carry out the remaining
+tosses until heads are observed what
+
+ align:start position:0%
+tosses until heads are observed what
+ 
+
+ align:start position:0%
+tosses until heads are observed what
+should your model be about the future
+
+ align:start position:0%
+should your model be about the future
+ 
+
+ align:start position:0%
+should your model be about the future
+well you will be making independent coin
+
+ align:start position:0%
+well you will be making independent coin
+ 
+
+ align:start position:0%
+well you will be making independent coin
+tosses until the first heads so the
+
+ align:start position:0%
+tosses until the first heads so the
+ 
+
+ align:start position:0%
+tosses until the first heads so the
+number of such tosses will be a random
+
+ align:start position:0%
+number of such tosses will be a random
+ 
+
+ align:start position:0%
+number of such tosses will be a random
+variable which is geometric with
+
+ align:start position:0%
+variable which is geometric with
+ 
+
+ align:start position:0%
+variable which is geometric with
+parameter P so this duration as far as
+
+ align:start position:0%
+parameter P so this duration as far as
+ 
+
+ align:start position:0%
+parameter P so this duration as far as
+you are concerned is geometric with
+
+ align:start position:0%
+you are concerned is geometric with
+ 
+
+ align:start position:0%
+you are concerned is geometric with
+parameter P therefore the number of
+
+ align:start position:0%
+parameter P therefore the number of
+ 
+
+ align:start position:0%
+parameter P therefore the number of
+remaining coin tosses starting from here
+
+ align:start position:0%
+remaining coin tosses starting from here
+ 
+
+ align:start position:0%
+remaining coin tosses starting from here
+given that the first toss was tails has
+
+ align:start position:0%
+given that the first toss was tails has
+ 
+
+ align:start position:0%
+given that the first toss was tails has
+the same geometric distribution as the
+
+ align:start position:0%
+the same geometric distribution as the
+ 
+
+ align:start position:0%
+the same geometric distribution as the
+original random variable X this is the
+
+ align:start position:0%
+original random variable X this is the
+ 
+
+ align:start position:0%
+original random variable X this is the
+memorylessness property
+
+ align:start position:0%
+memorylessness property
+ 
+
+ align:start position:0%
+memorylessness property
+now since X is the total number of coin
+
+ align:start position:0%
+now since X is the total number of coin
+ 
+
+ align:start position:0%
+now since X is the total number of coin
+tosses and since your coin tosses were
+
+ align:start position:0%
+tosses and since your coin tosses were
+ 
+
+ align:start position:0%
+tosses and since your coin tosses were
+all of them except for the first one the
+
+ align:start position:0%
+all of them except for the first one the
+ 
+
+ align:start position:0%
+all of them except for the first one the
+random variable that you are concerned
+
+ align:start position:0%
+random variable that you are concerned
+ 
+
+ align:start position:0%
+random variable that you are concerned
+with is X minus 1 and so the geometric
+
+ align:start position:0%
+with is X minus 1 and so the geometric
+ 
+
+ align:start position:0%
+with is X minus 1 and so the geometric
+distribution that you are seeing here is
+
+ align:start position:0%
+distribution that you are seeing here is
+ 
+
+ align:start position:0%
+distribution that you are seeing here is
+the conditional distribution of X minus
+
+ align:start position:0%
+the conditional distribution of X minus
+ 
+
+ align:start position:0%
+the conditional distribution of X minus
+1 given that the first toss resulted in
+
+ align:start position:0%
+1 given that the first toss resulted in
+ 
+
+ align:start position:0%
+1 given that the first toss resulted in
+tails which is the same as the event
+
+ align:start position:0%
+tails which is the same as the event
+ 
+
+ align:start position:0%
+tails which is the same as the event
+that X is strictly larger than 1 so the
+
+ align:start position:0%
+that X is strictly larger than 1 so the
+ 
+
+ align:start position:0%
+that X is strictly larger than 1 so the
+statement that we have been making is
+
+ align:start position:0%
+statement that we have been making is
+ 
+
+ align:start position:0%
+statement that we have been making is
+the following in more mathematical
+
+ align:start position:0%
+the following in more mathematical
+ 
+
+ align:start position:0%
+the following in more mathematical
+language that conditioned on X being
+
+ align:start position:0%
+language that conditioned on X being
+ 
+
+ align:start position:0%
+language that conditioned on X being
+larger than 1 the random variable X
+
+ align:start position:0%
+larger than 1 the random variable X
+ 
+
+ align:start position:0%
+larger than 1 the random variable X
+minus 1 which is the remaining number of
+
+ align:start position:0%
+minus 1 which is the remaining number of
+ 
+
+ align:start position:0%
+minus 1 which is the remaining number of
+coin tosses has a geometric distribution
+
+ align:start position:0%
+coin tosses has a geometric distribution
+ 
+
+ align:start position:0%
+coin tosses has a geometric distribution
+with parameter P let us now give a more
+
+ align:start position:0%
+with parameter P let us now give a more
+ 
+
+ align:start position:0%
+with parameter P let us now give a more
+precise mathematical arguments but first
+
+ align:start position:0%
+precise mathematical arguments but first
+ 
+
+ align:start position:0%
+precise mathematical arguments but first
+for a special case let us look at the
+
+ align:start position:0%
+for a special case let us look at the
+ 
+
+ align:start position:0%
+for a special case let us look at the
+conditional probabilities for the random
+
+ align:start position:0%
+conditional probabilities for the random
+ 
+
+ align:start position:0%
+conditional probabilities for the random
+variable X minus 1 and calculate for
+
+ align:start position:0%
+variable X minus 1 and calculate for
+ 
+
+ align:start position:0%
+variable X minus 1 and calculate for
+example the conditional probability that
+
+ align:start position:0%
+example the conditional probability that
+ 
+
+ align:start position:0%
+example the conditional probability that
+X minus 1 is equal to 3 given that X is
+
+ align:start position:0%
+X minus 1 is equal to 3 given that X is
+ 
+
+ align:start position:0%
+X minus 1 is equal to 3 given that X is
+larger than 1 which is the same as
+
+ align:start position:0%
+larger than 1 which is the same as
+ 
+
+ align:start position:0%
+larger than 1 which is the same as
+saying that the first toss resulted in
+
+ align:start position:0%
+saying that the first toss resulted in
+ 
+
+ align:start position:0%
+saying that the first toss resulted in
+tails now the first toss resulted in
+
+ align:start position:0%
+tails now the first toss resulted in
+ 
+
+ align:start position:0%
+tails now the first toss resulted in
+tails this is the probability that you
+
+ align:start position:0%
+tails this is the probability that you
+ 
+
+ align:start position:0%
+tails this is the probability that you
+will need 3 more tosses until you
+
+ align:start position:0%
+will need 3 more tosses until you
+ 
+
+ align:start position:0%
+will need 3 more tosses until you
+observe heads needing three more tosses
+
+ align:start position:0%
+observe heads needing three more tosses
+ 
+
+ align:start position:0%
+observe heads needing three more tosses
+until you observe heads is the event
+
+ align:start position:0%
+until you observe heads is the event
+ 
+
+ align:start position:0%
+until you observe heads is the event
+that you had tails in the second toss
+
+ align:start position:0%
+that you had tails in the second toss
+ 
+
+ align:start position:0%
+that you had tails in the second toss
+tails in the third tours and heads in
+
+ align:start position:0%
+tails in the third tours and heads in
+ 
+
+ align:start position:0%
+tails in the third tours and heads in
+the fourth dose and all that is
+
+ align:start position:0%
+the fourth dose and all that is
+ 
+
+ align:start position:0%
+the fourth dose and all that is
+conditioned on the first toss having
+
+ align:start position:0%
+conditioned on the first toss having
+ 
+
+ align:start position:0%
+conditioned on the first toss having
+resulted in tails
+
+ align:start position:0%
+resulted in tails
+ 
+
+ align:start position:0%
+resulted in tails
+however the different coin tosses are
+
+ align:start position:0%
+however the different coin tosses are
+ 
+
+ align:start position:0%
+however the different coin tosses are
+independent so the conditional
+
+ align:start position:0%
+independent so the conditional
+ 
+
+ align:start position:0%
+independent so the conditional
+probabilities given the event that the
+
+ align:start position:0%
+probabilities given the event that the
+ 
+
+ align:start position:0%
+probabilities given the event that the
+first toss was tails should be the same
+
+ align:start position:0%
+first toss was tails should be the same
+ 
+
+ align:start position:0%
+first toss was tails should be the same
+as the unconditional probabilities
+
+ align:start position:0%
+as the unconditional probabilities
+ 
+
+ align:start position:0%
+as the unconditional probabilities
+first toss does not change our beliefs
+
+ align:start position:0%
+first toss does not change our beliefs
+ 
+
+ align:start position:0%
+first toss does not change our beliefs
+about the probabilities associated with
+
+ align:start position:0%
+about the probabilities associated with
+ 
+
+ align:start position:0%
+about the probabilities associated with
+the remaining tosses now this
+
+ align:start position:0%
+the remaining tosses now this
+ 
+
+ align:start position:0%
+the remaining tosses now this
+unconditional probability is easy to
+
+ align:start position:0%
+unconditional probability is easy to
+ 
+
+ align:start position:0%
+unconditional probability is easy to
+calculate it is 1 minus P squared
+
+ align:start position:0%
+calculate it is 1 minus P squared
+ 
+
+ align:start position:0%
+calculate it is 1 minus P squared
+because we have two tails in a row times
+
+ align:start position:0%
+because we have two tails in a row times
+ 
+
+ align:start position:0%
+because we have two tails in a row times
+P now we observe that this quantity here
+
+ align:start position:0%
+P now we observe that this quantity here
+ 
+
+ align:start position:0%
+P now we observe that this quantity here
+is the probability that a geometric
+
+ align:start position:0%
+is the probability that a geometric
+ 
+
+ align:start position:0%
+is the probability that a geometric
+random variable takes the value of 3
+
+ align:start position:0%
+random variable takes the value of 3
+ 
+
+ align:start position:0%
+random variable takes the value of 3
+here what have we calculated we have
+
+ align:start position:0%
+here what have we calculated we have
+ 
+
+ align:start position:0%
+here what have we calculated we have
+calculated the PMF of the random
+
+ align:start position:0%
+calculated the PMF of the random
+ 
+
+ align:start position:0%
+calculated the PMF of the random
+variable X minus 1 in a conditional
+
+ align:start position:0%
+variable X minus 1 in a conditional
+ 
+
+ align:start position:0%
+variable X minus 1 in a conditional
+universe where X is larger than 1 and we
+
+ align:start position:0%
+universe where X is larger than 1 and we
+ 
+
+ align:start position:0%
+universe where X is larger than 1 and we
+evaluated it for a value of 3 the
+
+ align:start position:0%
+evaluated it for a value of 3 the
+ 
+
+ align:start position:0%
+evaluated it for a value of 3 the
+probability that our random variable X
+
+ align:start position:0%
+probability that our random variable X
+ 
+
+ align:start position:0%
+probability that our random variable X
+minus 1 takes the value of 3 so what we
+
+ align:start position:0%
+minus 1 takes the value of 3 so what we
+ 
+
+ align:start position:0%
+minus 1 takes the value of 3 so what we
+have shown is that this conditional PMF
+
+ align:start position:0%
+have shown is that this conditional PMF
+ 
+
+ align:start position:0%
+have shown is that this conditional PMF
+is the same as the unconditional PMF now
+
+ align:start position:0%
+is the same as the unconditional PMF now
+ 
+
+ align:start position:0%
+is the same as the unconditional PMF now
+there is nothing special about the
+
+ align:start position:0%
+there is nothing special about the
+ 
+
+ align:start position:0%
+there is nothing special about the
+number 3 you can generalize this
+
+ align:start position:0%
+number 3 you can generalize this
+ 
+
+ align:start position:0%
+number 3 you can generalize this
+argument and establish that the
+
+ align:start position:0%
+argument and establish that the
+ 
+
+ align:start position:0%
+argument and establish that the
+conditional probability of X minus 1
+
+ align:start position:0%
+conditional probability of X minus 1
+ 
+
+ align:start position:0%
+conditional probability of X minus 1
+given that X is strictly larger than 1
+
+ align:start position:0%
+given that X is strictly larger than 1
+ 
+
+ align:start position:0%
+given that X is strictly larger than 1
+for any particular K is the same as the
+
+ align:start position:0%
+for any particular K is the same as the
+ 
+
+ align:start position:0%
+for any particular K is the same as the
+corresponding probability for the random
+
+ align:start position:0%
+corresponding probability for the random
+ 
+
+ align:start position:0%
+corresponding probability for the random
+variable X which is the t-one given by
+
+ align:start position:0%
+variable X which is the t-one given by
+ 
+
+ align:start position:0%
+variable X which is the t-one given by
+the geometric PMF finally there is
+
+ align:start position:0%
+the geometric PMF finally there is
+ 
+
+ align:start position:0%
+the geometric PMF finally there is
+nothing special about the value of 1
+
+ align:start position:0%
+nothing special about the value of 1
+ 
+
+ align:start position:0%
+nothing special about the value of 1
+that we are using here in fact we can
+
+ align:start position:0%
+that we are using here in fact we can
+ 
+
+ align:start position:0%
+that we are using here in fact we can
+generalize and argue as follows suppose
+
+ align:start position:0%
+generalize and argue as follows suppose
+ 
+
+ align:start position:0%
+generalize and argue as follows suppose
+that I tell you that X is strictly
+
+ align:start position:0%
+that I tell you that X is strictly
+ 
+
+ align:start position:0%
+that I tell you that X is strictly
+larger than n that is the first n tosses
+
+ align:start position:0%
+larger than n that is the first n tosses
+ 
+
+ align:start position:0%
+larger than n that is the first n tosses
+resulted in tails once more
+
+ align:start position:0%
+resulted in tails once more
+ 
+
+ align:start position:0%
+resulted in tails once more
+these past tosses were wasted but have
+
+ align:start position:0%
+these past tosses were wasted but have
+ 
+
+ align:start position:0%
+these past tosses were wasted but have
+no effect on the future so the
+
+ align:start position:0%
+no effect on the future so the
+ 
+
+ align:start position:0%
+no effect on the future so the
+conditional PMF of the remaining number
+
+ align:start position:0%
+conditional PMF of the remaining number
+ 
+
+ align:start position:0%
+conditional PMF of the remaining number
+of tosses should be again the same
+
+ align:start position:0%
+of tosses should be again the same
+ 
+
+ align:start position:0%
+of tosses should be again the same
+therefore the statement were making is
+
+ align:start position:0%
+therefore the statement were making is
+ 
+
+ align:start position:0%
+therefore the statement were making is
+that this geometric PMF will also be the
+
+ align:start position:0%
+that this geometric PMF will also be the
+ 
+
+ align:start position:0%
+that this geometric PMF will also be the
+PMF of X minus n given that X is
+
+ align:start position:0%
+PMF of X minus n given that X is
+ 
+
+ align:start position:0%
+PMF of X minus n given that X is
+strictly larger than n and this will be
+
+ align:start position:0%
+strictly larger than n and this will be
+ 
+
+ align:start position:0%
+strictly larger than n and this will be
+true no matter what argument we plug in
+
+ align:start position:0%
+true no matter what argument we plug in
+ 
+
+ align:start position:0%
+true no matter what argument we plug in
+into the PMF
+
+ align:start position:0%
+into the PMF
+ 
+
+ align:start position:0%
+into the PMF
+we will now exploit the memorylessness
+
+ align:start position:0%
+we will now exploit the memorylessness
+ 
+
+ align:start position:0%
+we will now exploit the memorylessness
+property of the geometric PMF and use it
+
+ align:start position:0%
+property of the geometric PMF and use it
+ 
+
+ align:start position:0%
+property of the geometric PMF and use it
+together with the total expectation
+
+ align:start position:0%
+together with the total expectation
+ 
+
+ align:start position:0%
+together with the total expectation
+theorem to calculate the mean or
+
+ align:start position:0%
+theorem to calculate the mean or
+ 
+
+ align:start position:0%
+theorem to calculate the mean or
+expectation of the geometric PMF if we
+
+ align:start position:0%
+expectation of the geometric PMF if we
+ 
+
+ align:start position:0%
+expectation of the geometric PMF if we
+wanted to calculate the expected value
+
+ align:start position:0%
+wanted to calculate the expected value
+ 
+
+ align:start position:0%
+wanted to calculate the expected value
+of a geometric using the definition of
+
+ align:start position:0%
+of a geometric using the definition of
+ 
+
+ align:start position:0%
+of a geometric using the definition of
+the expectation we would have to
+
+ align:start position:0%
+the expectation we would have to
+ 
+
+ align:start position:0%
+the expectation we would have to
+calculate this infinite sum here which
+
+ align:start position:0%
+calculate this infinite sum here which
+ 
+
+ align:start position:0%
+calculate this infinite sum here which
+is quite difficult instead we're going
+
+ align:start position:0%
+is quite difficult instead we're going
+ 
+
+ align:start position:0%
+is quite difficult instead we're going
+to use a certain trick the trick is the
+
+ align:start position:0%
+to use a certain trick the trick is the
+ 
+
+ align:start position:0%
+to use a certain trick the trick is the
+following to break down the expected
+
+ align:start position:0%
+following to break down the expected
+ 
+
+ align:start position:0%
+following to break down the expected
+value calculation into two different
+
+ align:start position:0%
+value calculation into two different
+ 
+
+ align:start position:0%
+value calculation into two different
+scenarios under one scenario we obtain
+
+ align:start position:0%
+scenarios under one scenario we obtain
+ 
+
+ align:start position:0%
+scenarios under one scenario we obtain
+heads in the first tours and in that
+
+ align:start position:0%
+heads in the first tours and in that
+ 
+
+ align:start position:0%
+heads in the first tours and in that
+case the random variable X the number of
+
+ align:start position:0%
+case the random variable X the number of
+ 
+
+ align:start position:0%
+case the random variable X the number of
+tosses until the first head is equal to
+
+ align:start position:0%
+tosses until the first head is equal to
+ 
+
+ align:start position:0%
+tosses until the first head is equal to
+1 and this scenario occurs with
+
+ align:start position:0%
+1 and this scenario occurs with
+ 
+
+ align:start position:0%
+1 and this scenario occurs with
+probability P and we have another
+
+ align:start position:0%
+probability P and we have another
+ 
+
+ align:start position:0%
+probability P and we have another
+scenario with probability 1 minus P
+
+ align:start position:0%
+scenario with probability 1 minus P
+ 
+
+ align:start position:0%
+scenario with probability 1 minus P
+where we obtain tails in the first toss
+
+ align:start position:0%
+where we obtain tails in the first toss
+ 
+
+ align:start position:0%
+where we obtain tails in the first toss
+and in that case a random variable is
+
+ align:start position:0%
+and in that case a random variable is
+ 
+
+ align:start position:0%
+and in that case a random variable is
+strictly larger than 1 now the expected
+
+ align:start position:0%
+strictly larger than 1 now the expected
+ 
+
+ align:start position:0%
+strictly larger than 1 now the expected
+value of x consists of two pieces we
+
+ align:start position:0%
+value of x consists of two pieces we
+ 
+
+ align:start position:0%
+value of x consists of two pieces we
+have a first toss no matter what and
+
+ align:start position:0%
+have a first toss no matter what and
+ 
+
+ align:start position:0%
+have a first toss no matter what and
+then we have the number of remaining
+
+ align:start position:0%
+then we have the number of remaining
+ 
+
+ align:start position:0%
+then we have the number of remaining
+tosses which is X minus 1 so this is
+
+ align:start position:0%
+tosses which is X minus 1 so this is
+ 
+
+ align:start position:0%
+tosses which is X minus 1 so this is
+true by linearity of expectations now
+
+ align:start position:0%
+true by linearity of expectations now
+ 
+
+ align:start position:0%
+true by linearity of expectations now
+the expected value of X minus 1 consists
+
+ align:start position:0%
+the expected value of X minus 1 consists
+ 
+
+ align:start position:0%
+the expected value of X minus 1 consists
+of two pieces using the total
+
+ align:start position:0%
+of two pieces using the total
+ 
+
+ align:start position:0%
+of two pieces using the total
+expectation theorem the probability of
+
+ align:start position:0%
+expectation theorem the probability of
+ 
+
+ align:start position:0%
+expectation theorem the probability of
+the first scenario times the expected
+
+ align:start position:0%
+the first scenario times the expected
+ 
+
+ align:start position:0%
+the first scenario times the expected
+value of X minus 1 given that X is equal
+
+ align:start position:0%
+value of X minus 1 given that X is equal
+ 
+
+ align:start position:0%
+value of X minus 1 given that X is equal
+to 1 plus 1 minus P the probability of
+
+ align:start position:0%
+to 1 plus 1 minus P the probability of
+ 
+
+ align:start position:0%
+to 1 plus 1 minus P the probability of
+the second scenario times the expected
+
+ align:start position:0%
+the second scenario times the expected
+ 
+
+ align:start position:0%
+the second scenario times the expected
+value of X minus 1 given that X is
+
+ align:start position:0%
+value of X minus 1 given that X is
+ 
+
+ align:start position:0%
+value of X minus 1 given that X is
+bigger than 1
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+now this term here is zero
+
+ align:start position:0%
+now this term here is zero
+ 
+
+ align:start position:0%
+now this term here is zero
+why if I tell you that X is equal to one
+
+ align:start position:0%
+why if I tell you that X is equal to one
+ 
+
+ align:start position:0%
+why if I tell you that X is equal to one
+then you are certain that X minus one is
+
+ align:start position:0%
+then you are certain that X minus one is
+ 
+
+ align:start position:0%
+then you are certain that X minus one is
+equal to 0 so this term gives a zero
+
+ align:start position:0%
+equal to 0 so this term gives a zero
+ 
+
+ align:start position:0%
+equal to 0 so this term gives a zero
+contribution how about the next term we
+
+ align:start position:0%
+contribution how about the next term we
+ 
+
+ align:start position:0%
+contribution how about the next term we
+have a 1 minus P here times this
+
+ align:start position:0%
+have a 1 minus P here times this
+ 
+
+ align:start position:0%
+have a 1 minus P here times this
+expected value now this random variable
+
+ align:start position:0%
+expected value now this random variable
+ 
+
+ align:start position:0%
+expected value now this random variable
+conditioned on this event has the same
+
+ align:start position:0%
+conditioned on this event has the same
+ 
+
+ align:start position:0%
+conditioned on this event has the same
+distribution as an ordinary
+
+ align:start position:0%
+distribution as an ordinary
+ 
+
+ align:start position:0%
+distribution as an ordinary
+unconditioned geometric random variable
+
+ align:start position:0%
+unconditioned geometric random variable
+ 
+
+ align:start position:0%
+unconditioned geometric random variable
+so this expectation here must be the
+
+ align:start position:0%
+so this expectation here must be the
+ 
+
+ align:start position:0%
+so this expectation here must be the
+same as the expectation of an ordinary
+
+ align:start position:0%
+same as the expectation of an ordinary
+ 
+
+ align:start position:0%
+same as the expectation of an ordinary
+unconditioned geometric random variable
+
+ align:start position:0%
+unconditioned geometric random variable
+ 
+
+ align:start position:0%
+unconditioned geometric random variable
+and this gives us an equality both sides
+
+ align:start position:0%
+and this gives us an equality both sides
+ 
+
+ align:start position:0%
+and this gives us an equality both sides
+involve the expected value of x but we
+
+ align:start position:0%
+involve the expected value of x but we
+ 
+
+ align:start position:0%
+involve the expected value of x but we
+can solve this equation for the expected
+
+ align:start position:0%
+can solve this equation for the expected
+ 
+
+ align:start position:0%
+can solve this equation for the expected
+value and we obtain the end result that
+
+ align:start position:0%
+value and we obtain the end result that
+ 
+
+ align:start position:0%
+value and we obtain the end result that
+the expected value is 1 over P by the
+
+ align:start position:0%
+the expected value is 1 over P by the
+ 
+
+ align:start position:0%
+the expected value is 1 over P by the
+way this answer makes intuitive sense if
+
+ align:start position:0%
+way this answer makes intuitive sense if
+ 
+
+ align:start position:0%
+way this answer makes intuitive sense if
+P is small this means that the odds of
+
+ align:start position:0%
+P is small this means that the odds of
+ 
+
+ align:start position:0%
+P is small this means that the odds of
+seeing heads is small then in that case
+
+ align:start position:0%
+seeing heads is small then in that case
+ 
+
+ align:start position:0%
+seeing heads is small then in that case
+we need to wait longer and longer until
+
+ align:start position:0%
+we need to wait longer and longer until
+ 
+
+ align:start position:0%
+we need to wait longer and longer until
+we see heads for the first time setting
+
+ align:start position:0%
+we see heads for the first time setting
+ 
+
+ align:start position:0%
+we see heads for the first time setting
+aside the specific form of the answer
+
+ align:start position:0%
+aside the specific form of the answer
+ 
+
+ align:start position:0%
+aside the specific form of the answer
+that we found what we have just done
+
+ align:start position:0%
+that we found what we have just done
+ 
+
+ align:start position:0%
+that we found what we have just done
+actually illustrates that fairly
+
+ align:start position:0%
+actually illustrates that fairly
+ 
+
+ align:start position:0%
+actually illustrates that fairly
+difficult calculations can become very
+
+ align:start position:0%
+difficult calculations can become very
+ 
+
+ align:start position:0%
+difficult calculations can become very
+simple if one breaks down a model or a
+
+ align:start position:0%
+simple if one breaks down a model or a
+ 
+
+ align:start position:0%
+simple if one breaks down a model or a
+problem in a clever way this is going to
+
+ align:start position:0%
+problem in a clever way this is going to
+ 
+
+ align:start position:0%
+problem in a clever way this is going to
+be a recurrent theme throughout this
+
+ align:start position:0%
+be a recurrent theme throughout this
+ 
+
+ align:start position:0%
+be a recurrent theme throughout this
+class
\ No newline at end of file
diff --git a/N-67gRDE3UQ.txt b/N-67gRDE3UQ.txt
new file mode 100644
index 0000000000000000000000000000000000000000..f30eaf611e52c9b46aaef15f0d6dcd836165201b
--- /dev/null
+++ b/N-67gRDE3UQ.txt
@@ -0,0 +1,14939 @@
+align:start position:0%
+ 
+foreign
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+to examining empirical things
+
+ align:start position:0%
+to examining empirical things
+ 
+
+ align:start position:0%
+to examining empirical things
+you guys have read my paper I'm going to
+
+ align:start position:0%
+you guys have read my paper I'm going to
+ 
+
+ align:start position:0%
+you guys have read my paper I'm going to
+talk a bit about that and I'm going to
+
+ align:start position:0%
+talk a bit about that and I'm going to
+ 
+
+ align:start position:0%
+talk a bit about that and I'm going to
+talk also about it on on Monday so some
+
+ align:start position:0%
+talk also about it on on Monday so some
+ 
+
+ align:start position:0%
+talk also about it on on Monday so some
+of the questions that you had many of
+
+ align:start position:0%
+of the questions that you had many of
+ 
+
+ align:start position:0%
+of the questions that you had many of
+the questions comments you had were on
+
+ align:start position:0%
+the questions comments you had were on
+ 
+
+ align:start position:0%
+the questions comments you had were on
+the returns to education piece and those
+
+ align:start position:0%
+the returns to education piece and those
+ 
+
+ align:start position:0%
+the returns to education piece and those
+we'll discuss we'll discuss on Monday
+
+ align:start position:0%
+we'll discuss we'll discuss on Monday
+ 
+
+ align:start position:0%
+we'll discuss we'll discuss on Monday
+but there are a number of things that
+
+ align:start position:0%
+but there are a number of things that
+ 
+
+ align:start position:0%
+but there are a number of things that
+come up that should uh that should be
+
+ align:start position:0%
+come up that should uh that should be
+ 
+
+ align:start position:0%
+come up that should uh that should be
+able to address today
+
+ align:start position:0%
+able to address today
+ 
+
+ align:start position:0%
+able to address today
+so if you remember we we ended up last
+
+ align:start position:0%
+so if you remember we we ended up last
+ 
+
+ align:start position:0%
+so if you remember we we ended up last
+time by saying oh we at some point uh
+
+ align:start position:0%
+time by saying oh we at some point uh
+ 
+
+ align:start position:0%
+time by saying oh we at some point uh
+alas um on Monday we had this equation
+
+ align:start position:0%
+alas um on Monday we had this equation
+ 
+
+ align:start position:0%
+alas um on Monday we had this equation
+that the level of Education chosen by a
+
+ align:start position:0%
+that the level of Education chosen by a
+ 
+
+ align:start position:0%
+that the level of Education chosen by a
+family for their kids is going to be a
+
+ align:start position:0%
+family for their kids is going to be a
+ 
+
+ align:start position:0%
+family for their kids is going to be a
+function of the costs of Education the
+
+ align:start position:0%
+function of the costs of Education the
+ 
+
+ align:start position:0%
+function of the costs of Education the
+marginal cost for them of acquiring one
+
+ align:start position:0%
+marginal cost for them of acquiring one
+ 
+
+ align:start position:0%
+marginal cost for them of acquiring one
+more unit of human capital and of the
+
+ align:start position:0%
+more unit of human capital and of the
+ 
+
+ align:start position:0%
+more unit of human capital and of the
+returns to education both the immediate
+
+ align:start position:0%
+returns to education both the immediate
+ 
+
+ align:start position:0%
+returns to education both the immediate
+financial return in the form of wages as
+
+ align:start position:0%
+financial return in the form of wages as
+ 
+
+ align:start position:0%
+financial return in the form of wages as
+well as
+
+ align:start position:0%
+well as
+ 
+
+ align:start position:0%
+well as
+the human how is it it's going to
+
+ align:start position:0%
+the human how is it it's going to
+ 
+
+ align:start position:0%
+the human how is it it's going to
+acquire the human capital of the Next
+
+ align:start position:0%
+acquire the human capital of the Next
+ 
+
+ align:start position:0%
+acquire the human capital of the Next
+Generation so this is these are all
+
+ align:start position:0%
+Generation so this is these are all
+ 
+
+ align:start position:0%
+Generation so this is these are all
+things that people have been looked at
+
+ align:start position:0%
+things that people have been looked at
+ 
+
+ align:start position:0%
+things that people have been looked at
+I've looked at
+
+ align:start position:0%
+I've looked at
+ 
+
+ align:start position:0%
+I've looked at
+uh so we should expect people to respond
+
+ align:start position:0%
+uh so we should expect people to respond
+ 
+
+ align:start position:0%
+uh so we should expect people to respond
+both to costs and benefits
+
+ align:start position:0%
+both to costs and benefits
+ 
+
+ align:start position:0%
+both to costs and benefits
+so the cost piece seems relatively
+
+ align:start position:0%
+so the cost piece seems relatively
+ 
+
+ align:start position:0%
+so the cost piece seems relatively
+straightforward uh one would look for a
+
+ align:start position:0%
+straightforward uh one would look for a
+ 
+
+ align:start position:0%
+straightforward uh one would look for a
+setting where cost to education director
+
+ align:start position:0%
+setting where cost to education director
+ 
+
+ align:start position:0%
+setting where cost to education director
+in in direct went down and then look at
+
+ align:start position:0%
+in in direct went down and then look at
+ 
+
+ align:start position:0%
+in in direct went down and then look at
+and look at whether people respond by
+
+ align:start position:0%
+and look at whether people respond by
+ 
+
+ align:start position:0%
+and look at whether people respond by
+educating their kids more
+
+ align:start position:0%
+educating their kids more
+ 
+
+ align:start position:0%
+educating their kids more
+and then the benefits is whether people
+
+ align:start position:0%
+and then the benefits is whether people
+ 
+
+ align:start position:0%
+and then the benefits is whether people
+respond to returns to education that
+
+ align:start position:0%
+respond to returns to education that
+ 
+
+ align:start position:0%
+respond to returns to education that
+might be a little bit more
+
+ align:start position:0%
+might be a little bit more
+ 
+
+ align:start position:0%
+might be a little bit more
+tricky and we are going to do a bit of
+
+ align:start position:0%
+tricky and we are going to do a bit of
+ 
+
+ align:start position:0%
+tricky and we are going to do a bit of
+that
+
+ align:start position:0%
+that
+ 
+
+ align:start position:0%
+that
+both the actual benefits and the
+
+ align:start position:0%
+both the actual benefits and the
+ 
+
+ align:start position:0%
+both the actual benefits and the
+perceived benefits which of course is in
+
+ align:start position:0%
+perceived benefits which of course is in
+ 
+
+ align:start position:0%
+perceived benefits which of course is in
+this equation implicitly something we
+
+ align:start position:0%
+this equation implicitly something we
+ 
+
+ align:start position:0%
+this equation implicitly something we
+hardly discussed but just a little bit
+
+ align:start position:0%
+hardly discussed but just a little bit
+ 
+
+ align:start position:0%
+hardly discussed but just a little bit
+last time is whether the perceived
+
+ align:start position:0%
+last time is whether the perceived
+ 
+
+ align:start position:0%
+last time is whether the perceived
+benefits are the same as the real
+
+ align:start position:0%
+benefits are the same as the real
+ 
+
+ align:start position:0%
+benefits are the same as the real
+benefits
+
+ align:start position:0%
+benefits
+ 
+
+ align:start position:0%
+benefits
+so let's start with the customers that's
+
+ align:start position:0%
+so let's start with the customers that's
+ 
+
+ align:start position:0%
+so let's start with the customers that's
+sort of the straightforward piece
+
+ align:start position:0%
+sort of the straightforward piece
+ 
+
+ align:start position:0%
+sort of the straightforward piece
+so there are a number of papers that
+
+ align:start position:0%
+so there are a number of papers that
+ 
+
+ align:start position:0%
+so there are a number of papers that
+look at the reaction to the direct cost
+
+ align:start position:0%
+look at the reaction to the direct cost
+ 
+
+ align:start position:0%
+look at the reaction to the direct cost
+of education so
+
+ align:start position:0%
+of education so
+ 
+
+ align:start position:0%
+of education so
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+in particular but this is a bit of a
+
+ align:start position:0%
+in particular but this is a bit of a
+ 
+
+ align:start position:0%
+in particular but this is a bit of a
+biased review of the literature because
+
+ align:start position:0%
+biased review of the literature because
+ 
+
+ align:start position:0%
+biased review of the literature because
+it has mostly my papers but I have a
+
+ align:start position:0%
+it has mostly my papers but I have a
+ 
+
+ align:start position:0%
+it has mostly my papers but I have a
+paper with Pascal in Japan Michael
+
+ align:start position:0%
+paper with Pascal in Japan Michael
+ 
+
+ align:start position:0%
+paper with Pascal in Japan Michael
+camera where we provide the school
+
+ align:start position:0%
+camera where we provide the school
+ 
+
+ align:start position:0%
+camera where we provide the school
+uniforms
+
+ align:start position:0%
+uniforms
+ 
+
+ align:start position:0%
+uniforms
+for kids in you know entering grade
+
+ align:start position:0%
+for kids in you know entering grade
+ 
+
+ align:start position:0%
+for kids in you know entering grade
+seven or grade uh grade six or seven or
+
+ align:start position:0%
+seven or grade uh grade six or seven or
+ 
+
+ align:start position:0%
+seven or grade uh grade six or seven or
+eight
+
+ align:start position:0%
+eight
+ 
+
+ align:start position:0%
+eight
+and we found pretty large effect there
+
+ align:start position:0%
+and we found pretty large effect there
+ 
+
+ align:start position:0%
+and we found pretty large effect there
+we then have a literature that we'll
+
+ align:start position:0%
+we then have a literature that we'll
+ 
+
+ align:start position:0%
+we then have a literature that we'll
+discuss in much more detail we have a
+
+ align:start position:0%
+discuss in much more detail we have a
+ 
+
+ align:start position:0%
+discuss in much more detail we have a
+paper on the secondary school to
+
+ align:start position:0%
+paper on the secondary school to
+ 
+
+ align:start position:0%
+paper on the secondary school to
+education which are much larger than the
+
+ align:start position:0%
+education which are much larger than the
+ 
+
+ align:start position:0%
+education which are much larger than the
+school uniform uh which which we'll
+
+ align:start position:0%
+school uniform uh which which we'll
+ 
+
+ align:start position:0%
+school uniform uh which which we'll
+discuss in the detail on Monday and
+
+ align:start position:0%
+discuss in the detail on Monday and
+ 
+
+ align:start position:0%
+discuss in the detail on Monday and
+you're gonna read uh which again show
+
+ align:start position:0%
+you're gonna read uh which again show
+ 
+
+ align:start position:0%
+you're gonna read uh which again show
+pretty large impact
+
+ align:start position:0%
+pretty large impact
+ 
+
+ align:start position:0%
+pretty large impact
+in a sense what is and Michael as other
+
+ align:start position:0%
+in a sense what is and Michael as other
+ 
+
+ align:start position:0%
+in a sense what is and Michael as other
+people with other people on various form
+
+ align:start position:0%
+people with other people on various form
+ 
+
+ align:start position:0%
+people with other people on various form
+of scholarships for schools
+
+ align:start position:0%
+of scholarships for schools
+ 
+
+ align:start position:0%
+of scholarships for schools
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+so this literature is interesting I
+
+ align:start position:0%
+so this literature is interesting I
+ 
+
+ align:start position:0%
+so this literature is interesting I
+don't I in particular the uniform
+
+ align:start position:0%
+don't I in particular the uniform
+ 
+
+ align:start position:0%
+don't I in particular the uniform
+literature because on the one hand you
+
+ align:start position:0%
+literature because on the one hand you
+ 
+
+ align:start position:0%
+literature because on the one hand you
+you think uh effect impact of paying for
+
+ align:start position:0%
+you think uh effect impact of paying for
+ 
+
+ align:start position:0%
+you think uh effect impact of paying for
+uniform on on schooling
+
+ align:start position:0%
+uniform on on schooling
+ 
+
+ align:start position:0%
+uniform on on schooling
+so that would suggest that people are
+
+ align:start position:0%
+so that would suggest that people are
+ 
+
+ align:start position:0%
+so that would suggest that people are
+you know appropriately responding to
+
+ align:start position:0%
+you know appropriately responding to
+ 
+
+ align:start position:0%
+you know appropriately responding to
+cost
+
+ align:start position:0%
+cost
+ 
+
+ align:start position:0%
+cost
+on the other hand these impacts are
+
+ align:start position:0%
+on the other hand these impacts are
+ 
+
+ align:start position:0%
+on the other hand these impacts are
+really large
+
+ align:start position:0%
+really large
+ 
+
+ align:start position:0%
+really large
+uh really really large so you get for
+
+ align:start position:0%
+uh really really large so you get for
+ 
+
+ align:start position:0%
+uh really really large so you get for
+example in our uniform paper you get
+
+ align:start position:0%
+example in our uniform paper you get
+ 
+
+ align:start position:0%
+example in our uniform paper you get
+reduction in in Dropout of a few
+
+ align:start position:0%
+reduction in in Dropout of a few
+ 
+
+ align:start position:0%
+reduction in in Dropout of a few
+percentage points and the cost of a
+
+ align:start position:0%
+percentage points and the cost of a
+ 
+
+ align:start position:0%
+percentage points and the cost of a
+school uniform is is five dollars or so
+
+ align:start position:0%
+school uniform is is five dollars or so
+ 
+
+ align:start position:0%
+school uniform is is five dollars or so
+so with even for a Kenyan family is not
+
+ align:start position:0%
+so with even for a Kenyan family is not
+ 
+
+ align:start position:0%
+so with even for a Kenyan family is not
+that big
+
+ align:start position:0%
+that big
+ 
+
+ align:start position:0%
+that big
+so that is
+
+ align:start position:0%
+so that is
+ 
+
+ align:start position:0%
+so that is
+at this on the one hand you get the
+
+ align:start position:0%
+at this on the one hand you get the
+ 
+
+ align:start position:0%
+at this on the one hand you get the
+magnitude right on the other hand it is
+
+ align:start position:0%
+magnitude right on the other hand it is
+ 
+
+ align:start position:0%
+magnitude right on the other hand it is
+not really I would say a Vindication of
+
+ align:start position:0%
+not really I would say a Vindication of
+ 
+
+ align:start position:0%
+not really I would say a Vindication of
+this model because the impacts are too
+
+ align:start position:0%
+this model because the impacts are too
+ 
+
+ align:start position:0%
+this model because the impacts are too
+large
+
+ align:start position:0%
+large
+ 
+
+ align:start position:0%
+large
+in the sense that it if it if if the
+
+ align:start position:0%
+in the sense that it if it if if the
+ 
+
+ align:start position:0%
+in the sense that it if it if if the
+only reason why the cost to education
+
+ align:start position:0%
+only reason why the cost to education
+ 
+
+ align:start position:0%
+only reason why the cost to education
+enter is you're comparing them to the
+
+ align:start position:0%
+enter is you're comparing them to the
+ 
+
+ align:start position:0%
+enter is you're comparing them to the
+interest rate then clearly uh I know to
+
+ align:start position:0%
+interest rate then clearly uh I know to
+ 
+
+ align:start position:0%
+interest rate then clearly uh I know to
+into the the benefits and appropriately
+
+ align:start position:0%
+into the the benefits and appropriately
+ 
+
+ align:start position:0%
+into the the benefits and appropriately
+discounted by the interest rate then
+
+ align:start position:0%
+discounted by the interest rate then
+ 
+
+ align:start position:0%
+discounted by the interest rate then
+that seems way too large
+
+ align:start position:0%
+that seems way too large
+ 
+
+ align:start position:0%
+that seems way too large
+either indicating huge credit constraint
+
+ align:start position:0%
+either indicating huge credit constraint
+ 
+
+ align:start position:0%
+either indicating huge credit constraint
+that they can't even fight five dollars
+
+ align:start position:0%
+that they can't even fight five dollars
+ 
+
+ align:start position:0%
+that they can't even fight five dollars
+or something else is is going on
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+why did you think about
+
+ align:start position:0%
+why did you think about
+ 
+
+ align:start position:0%
+why did you think about
+[Music]
+
+ align:start position:0%
+[Music]
+ 
+
+ align:start position:0%
+[Music]
+mustard
+
+ align:start position:0%
+mustard
+ 
+
+ align:start position:0%
+mustard
+everybody says it's a big deal like
+
+ align:start position:0%
+everybody says it's a big deal like
+ 
+
+ align:start position:0%
+everybody says it's a big deal like
+everybody says it's a big deal in fact
+
+ align:start position:0%
+everybody says it's a big deal in fact
+ 
+
+ align:start position:0%
+everybody says it's a big deal in fact
+we got to uniform we this is a paper
+
+ align:start position:0%
+we got to uniform we this is a paper
+ 
+
+ align:start position:0%
+we got to uniform we this is a paper
+where we looked at the
+
+ align:start position:0%
+where we looked at the
+ 
+
+ align:start position:0%
+where we looked at the
+HIV uh we looked at we we were very
+
+ align:start position:0%
+HIV uh we looked at we we were very
+ 
+
+ align:start position:0%
+HIV uh we looked at we we were very
+interested in in testing the impact of
+
+ align:start position:0%
+interested in in testing the impact of
+ 
+
+ align:start position:0%
+interested in in testing the impact of
+the government HIV uh school um
+
+ align:start position:0%
+the government HIV uh school um
+ 
+
+ align:start position:0%
+the government HIV uh school um
+intervention so the government in Kenya
+
+ align:start position:0%
+intervention so the government in Kenya
+ 
+
+ align:start position:0%
+intervention so the government in Kenya
+was introducing a new program for HIV
+
+ align:start position:0%
+was introducing a new program for HIV
+ 
+
+ align:start position:0%
+was introducing a new program for HIV
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+which we actually were reasonably
+
+ align:start position:0%
+which we actually were reasonably
+ 
+
+ align:start position:0%
+which we actually were reasonably
+skeptical about this is called the ABCD
+
+ align:start position:0%
+skeptical about this is called the ABCD
+ 
+
+ align:start position:0%
+skeptical about this is called the ABCD
+strategy which was followed at the time
+
+ align:start position:0%
+strategy which was followed at the time
+ 
+
+ align:start position:0%
+strategy which was followed at the time
+by most country in East Africa
+
+ align:start position:0%
+by most country in East Africa
+ 
+
+ align:start position:0%
+by most country in East Africa
+that stands for abstain be careful use a
+
+ align:start position:0%
+that stands for abstain be careful use a
+ 
+
+ align:start position:0%
+that stands for abstain be careful use a
+condom or you die
+
+ align:start position:0%
+condom or you die
+ 
+
+ align:start position:0%
+condom or you die
+um that was relatively uh kind of
+
+ align:start position:0%
+um that was relatively uh kind of
+ 
+
+ align:start position:0%
+um that was relatively uh kind of
+fear-mongering among in this orders who
+
+ align:start position:0%
+fear-mongering among in this orders who
+ 
+
+ align:start position:0%
+fear-mongering among in this orders who
+abstain is the best be faithful user
+
+ align:start position:0%
+abstain is the best be faithful user
+ 
+
+ align:start position:0%
+abstain is the best be faithful user
+condom or you die so this was a an
+
+ align:start position:0%
+condom or you die so this was a an
+ 
+
+ align:start position:0%
+condom or you die so this was a an
+example of what's called a risk of
+
+ align:start position:0%
+example of what's called a risk of
+ 
+
+ align:start position:0%
+example of what's called a risk of
+avoiding all risk risk avoidance
+
+ align:start position:0%
+avoiding all risk risk avoidance
+ 
+
+ align:start position:0%
+avoiding all risk risk avoidance
+strategy as opposed to risk mitigation
+
+ align:start position:0%
+strategy as opposed to risk mitigation
+ 
+
+ align:start position:0%
+strategy as opposed to risk mitigation
+strategy
+
+ align:start position:0%
+strategy
+ 
+
+ align:start position:0%
+strategy
+so this program was introduced among
+
+ align:start position:0%
+so this program was introduced among
+ 
+
+ align:start position:0%
+so this program was introduced among
+upper Primary School students this is
+
+ align:start position:0%
+upper Primary School students this is
+ 
+
+ align:start position:0%
+upper Primary School students this is
+grade six to eight uh in Kenya we were
+
+ align:start position:0%
+grade six to eight uh in Kenya we were
+ 
+
+ align:start position:0%
+grade six to eight uh in Kenya we were
+they were interested in evaluating and
+
+ align:start position:0%
+they were interested in evaluating and
+ 
+
+ align:start position:0%
+they were interested in evaluating and
+we were interested in evaluating it but
+
+ align:start position:0%
+we were interested in evaluating it but
+ 
+
+ align:start position:0%
+we were interested in evaluating it but
+at the same time we were quite skeptical
+
+ align:start position:0%
+at the same time we were quite skeptical
+ 
+
+ align:start position:0%
+at the same time we were quite skeptical
+and we wanted to compare that with the
+
+ align:start position:0%
+and we wanted to compare that with the
+ 
+
+ align:start position:0%
+and we wanted to compare that with the
+strategy that is just keeping girls in
+
+ align:start position:0%
+strategy that is just keeping girls in
+ 
+
+ align:start position:0%
+strategy that is just keeping girls in
+school
+
+ align:start position:0%
+school
+ 
+
+ align:start position:0%
+school
+as a direct protective uh measure as
+
+ align:start position:0%
+as a direct protective uh measure as
+ 
+
+ align:start position:0%
+as a direct protective uh measure as
+opposed to trying to teach them
+
+ align:start position:0%
+opposed to trying to teach them
+ 
+
+ align:start position:0%
+opposed to trying to teach them
+something on HIV when they're in school
+
+ align:start position:0%
+something on HIV when they're in school
+ 
+
+ align:start position:0%
+something on HIV when they're in school
+so we wanted to have that
+
+ align:start position:0%
+so we wanted to have that
+ 
+
+ align:start position:0%
+so we wanted to have that
+and um it was pretty obvious to us that
+
+ align:start position:0%
+and um it was pretty obvious to us that
+ 
+
+ align:start position:0%
+and um it was pretty obvious to us that
+for for kids that age the uniform is a
+
+ align:start position:0%
+for for kids that age the uniform is a
+ 
+
+ align:start position:0%
+for for kids that age the uniform is a
+big constraint they cannot go to school
+
+ align:start position:0%
+big constraint they cannot go to school
+ 
+
+ align:start position:0%
+big constraint they cannot go to school
+without the uniform the school send them
+
+ align:start position:0%
+without the uniform the school send them
+ 
+
+ align:start position:0%
+without the uniform the school send them
+back without the uniform primaries
+
+ align:start position:0%
+back without the uniform primaries
+ 
+
+ align:start position:0%
+back without the uniform primaries
+initially when we started the project
+
+ align:start position:0%
+initially when we started the project
+ 
+
+ align:start position:0%
+initially when we started the project
+conceiving of the project there were
+
+ align:start position:0%
+conceiving of the project there were
+ 
+
+ align:start position:0%
+conceiving of the project there were
+school fees so we were going to pay for
+
+ align:start position:0%
+school fees so we were going to pay for
+ 
+
+ align:start position:0%
+school fees so we were going to pay for
+the school fee and the school fee went
+
+ align:start position:0%
+the school fee and the school fee went
+ 
+
+ align:start position:0%
+the school fee and the school fee went
+to West so we uh but we realized that
+
+ align:start position:0%
+to West so we uh but we realized that
+ 
+
+ align:start position:0%
+to West so we uh but we realized that
+the uniform were still a barrier so
+
+ align:start position:0%
+the uniform were still a barrier so
+ 
+
+ align:start position:0%
+the uniform were still a barrier so
+that's why we did the program even
+
+ align:start position:0%
+that's why we did the program even
+ 
+
+ align:start position:0%
+that's why we did the program even
+though
+
+ align:start position:0%
+though
+ 
+
+ align:start position:0%
+though
+if you think about it from the comfort
+
+ align:start position:0%
+if you think about it from the comfort
+ 
+
+ align:start position:0%
+if you think about it from the comfort
+of your office people shouldn't really
+
+ align:start position:0%
+of your office people shouldn't really
+ 
+
+ align:start position:0%
+of your office people shouldn't really
+be responsive to the cost of to the
+
+ align:start position:0%
+be responsive to the cost of to the
+ 
+
+ align:start position:0%
+be responsive to the cost of to the
+presence of the uniform but as it turns
+
+ align:start position:0%
+presence of the uniform but as it turns
+ 
+
+ align:start position:0%
+presence of the uniform but as it turns
+out they are
+
+ align:start position:0%
+out they are
+ 
+
+ align:start position:0%
+out they are
+so that's kind of how we came to to that
+
+ align:start position:0%
+so that's kind of how we came to to that
+ 
+
+ align:start position:0%
+so that's kind of how we came to to that
+it was less of
+
+ align:start position:0%
+it was less of
+ 
+
+ align:start position:0%
+it was less of
+and the results are pretty interesting
+
+ align:start position:0%
+and the results are pretty interesting
+ 
+
+ align:start position:0%
+and the results are pretty interesting
+in the sense that keeping just
+
+ align:start position:0%
+in the sense that keeping just
+ 
+
+ align:start position:0%
+in the sense that keeping just
+going keeping kids in school keeping
+
+ align:start position:0%
+going keeping kids in school keeping
+ 
+
+ align:start position:0%
+going keeping kids in school keeping
+girls in school does reduce HIV that
+
+ align:start position:0%
+girls in school does reduce HIV that
+ 
+
+ align:start position:0%
+girls in school does reduce HIV that
+program doesn't work
+
+ align:start position:0%
+program doesn't work
+ 
+
+ align:start position:0%
+program doesn't work
+and in fact that program endures the
+
+ align:start position:0%
+and in fact that program endures the
+ 
+
+ align:start position:0%
+and in fact that program endures the
+effect of the of keeping girls in school
+
+ align:start position:0%
+effect of the of keeping girls in school
+ 
+
+ align:start position:0%
+effect of the of keeping girls in school
+um so it is better to just pay for the
+
+ align:start position:0%
+um so it is better to just pay for the
+ 
+
+ align:start position:0%
+um so it is better to just pay for the
+uniform and do nothing else that's worse
+
+ align:start position:0%
+uniform and do nothing else that's worse
+ 
+
+ align:start position:0%
+uniform and do nothing else that's worse
+that it is worse than trying to teach
+
+ align:start position:0%
+that it is worse than trying to teach
+ 
+
+ align:start position:0%
+that it is worse than trying to teach
+them the ABCD program while they're in
+
+ align:start position:0%
+them the ABCD program while they're in
+ 
+
+ align:start position:0%
+them the ABCD program while they're in
+school
+
+ align:start position:0%
+school
+ 
+
+ align:start position:0%
+school
+for instance that we probably will get
+
+ align:start position:0%
+for instance that we probably will get
+ 
+
+ align:start position:0%
+for instance that we probably will get
+into when we talk more about health so
+
+ align:start position:0%
+into when we talk more about health so
+ 
+
+ align:start position:0%
+into when we talk more about health so
+that's that's how this this came about
+
+ align:start position:0%
+that's that's how this this came about
+ 
+
+ align:start position:0%
+that's that's how this this came about
+so this is like something that everybody
+
+ align:start position:0%
+so this is like something that everybody
+ 
+
+ align:start position:0%
+so this is like something that everybody
+talks about the school uniform even
+
+ align:start position:0%
+talks about the school uniform even
+ 
+
+ align:start position:0%
+talks about the school uniform even
+though
+
+ align:start position:0%
+though
+ 
+
+ align:start position:0%
+though
+this is not consistent with this model
+
+ align:start position:0%
+this is not consistent with this model
+ 
+
+ align:start position:0%
+this is not consistent with this model
+uh but that's probably a failure of the
+
+ align:start position:0%
+uh but that's probably a failure of the
+ 
+
+ align:start position:0%
+uh but that's probably a failure of the
+model as opposed to a failure of
+
+ align:start position:0%
+model as opposed to a failure of
+ 
+
+ align:start position:0%
+model as opposed to a failure of
+people's thinking
+
+ align:start position:0%
+people's thinking
+ 
+
+ align:start position:0%
+people's thinking
+so that's the first set of costs so I
+
+ align:start position:0%
+so that's the first set of costs so I
+ 
+
+ align:start position:0%
+so that's the first set of costs so I
+would say just as a Vindication of this
+
+ align:start position:0%
+would say just as a Vindication of this
+ 
+
+ align:start position:0%
+would say just as a Vindication of this
+model
+
+ align:start position:0%
+model
+ 
+
+ align:start position:0%
+model
+it's not very uh it's a bit half up
+
+ align:start position:0%
+it's not very uh it's a bit half up
+ 
+
+ align:start position:0%
+it's not very uh it's a bit half up
+because on the one hand you see people
+
+ align:start position:0%
+because on the one hand you see people
+ 
+
+ align:start position:0%
+because on the one hand you see people
+responded to cost on the other and
+
+ align:start position:0%
+responded to cost on the other and
+ 
+
+ align:start position:0%
+responded to cost on the other and
+they're way too responsive
+
+ align:start position:0%
+they're way too responsive
+ 
+
+ align:start position:0%
+they're way too responsive
+then there are the indirect costs which
+
+ align:start position:0%
+then there are the indirect costs which
+ 
+
+ align:start position:0%
+then there are the indirect costs which
+is the opportunity cost of being in
+
+ align:start position:0%
+is the opportunity cost of being in
+ 
+
+ align:start position:0%
+is the opportunity cost of being in
+schools while you're in school you you
+
+ align:start position:0%
+schools while you're in school you you
+ 
+
+ align:start position:0%
+schools while you're in school you you
+don't make money for the family
+
+ align:start position:0%
+don't make money for the family
+ 
+
+ align:start position:0%
+don't make money for the family
+and it is believed in particular for
+
+ align:start position:0%
+and it is believed in particular for
+ 
+
+ align:start position:0%
+and it is believed in particular for
+slightly older students middle school
+
+ align:start position:0%
+slightly older students middle school
+ 
+
+ align:start position:0%
+slightly older students middle school
+high school that it it's prevents some
+
+ align:start position:0%
+high school that it it's prevents some
+ 
+
+ align:start position:0%
+high school that it it's prevents some
+kids from being in school and this is
+
+ align:start position:0%
+kids from being in school and this is
+ 
+
+ align:start position:0%
+kids from being in school and this is
+one of the motivation of conditional
+
+ align:start position:0%
+one of the motivation of conditional
+ 
+
+ align:start position:0%
+one of the motivation of conditional
+cash transfer programs which were
+
+ align:start position:0%
+cash transfer programs which were
+ 
+
+ align:start position:0%
+cash transfer programs which were
+introduced initially in Latin America
+
+ align:start position:0%
+introduced initially in Latin America
+ 
+
+ align:start position:0%
+introduced initially in Latin America
+which has a comp which has a component
+
+ align:start position:0%
+which has a comp which has a component
+ 
+
+ align:start position:0%
+which has a comp which has a component
+that is a conditional on sending kids to
+
+ align:start position:0%
+that is a conditional on sending kids to
+ 
+
+ align:start position:0%
+that is a conditional on sending kids to
+school and the idea is that that's
+
+ align:start position:0%
+school and the idea is that that's
+ 
+
+ align:start position:0%
+school and the idea is that that's
+actually a fair amount of money that
+
+ align:start position:0%
+actually a fair amount of money that
+ 
+
+ align:start position:0%
+actually a fair amount of money that
+people get from the condition cash
+
+ align:start position:0%
+people get from the condition cash
+ 
+
+ align:start position:0%
+people get from the condition cash
+transfer
+
+ align:start position:0%
+transfer
+ 
+
+ align:start position:0%
+transfer
+and it generates so as long as your kids
+
+ align:start position:0%
+and it generates so as long as your kids
+ 
+
+ align:start position:0%
+and it generates so as long as your kids
+Goes to School regularly and it's not
+
+ align:start position:0%
+Goes to School regularly and it's not
+ 
+
+ align:start position:0%
+Goes to School regularly and it's not
+absent too much it's enroll in an absent
+
+ align:start position:0%
+absent too much it's enroll in an absent
+ 
+
+ align:start position:0%
+absent too much it's enroll in an absent
+too much you get a transfer monthly
+
+ align:start position:0%
+too much you get a transfer monthly
+ 
+
+ align:start position:0%
+too much you get a transfer monthly
+so that sort of compensate for not
+
+ align:start position:0%
+so that sort of compensate for not
+ 
+
+ align:start position:0%
+so that sort of compensate for not
+having
+
+ align:start position:0%
+having
+ 
+
+ align:start position:0%
+having
+for not having the uh their earnings if
+
+ align:start position:0%
+for not having the uh their earnings if
+ 
+
+ align:start position:0%
+for not having the uh their earnings if
+they worked on the market or on a farm
+
+ align:start position:0%
+they worked on the market or on a farm
+ 
+
+ align:start position:0%
+they worked on the market or on a farm
+or something like that so that's sort of
+
+ align:start position:0%
+or something like that so that's sort of
+ 
+
+ align:start position:0%
+or something like that so that's sort of
+that's also a way of manipulating the
+
+ align:start position:0%
+that's also a way of manipulating the
+ 
+
+ align:start position:0%
+that's also a way of manipulating the
+cost to education by creating a benefit
+
+ align:start position:0%
+cost to education by creating a benefit
+ 
+
+ align:start position:0%
+cost to education by creating a benefit
+that of sets an existing cost
+
+ align:start position:0%
+that of sets an existing cost
+ 
+
+ align:start position:0%
+that of sets an existing cost
+so that's a form of uh in in the cash
+
+ align:start position:0%
+so that's a form of uh in in the cash
+ 
+
+ align:start position:0%
+so that's a form of uh in in the cash
+transfer
+
+ align:start position:0%
+transfer
+ 
+
+ align:start position:0%
+transfer
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+there again I would say the results the
+
+ align:start position:0%
+there again I would say the results the
+ 
+
+ align:start position:0%
+there again I would say the results the
+evidence to want you know
+
+ align:start position:0%
+evidence to want you know
+ 
+
+ align:start position:0%
+evidence to want you know
+in favor of this model and relatively is
+
+ align:start position:0%
+in favor of this model and relatively is
+ 
+
+ align:start position:0%
+in favor of this model and relatively is
+is mixed because on the one hand people
+
+ align:start position:0%
+is mixed because on the one hand people
+ 
+
+ align:start position:0%
+is mixed because on the one hand people
+are very responsive to conditional cash
+
+ align:start position:0%
+are very responsive to conditional cash
+ 
+
+ align:start position:0%
+are very responsive to conditional cash
+transfer you do uh they are now been
+
+ align:start position:0%
+transfer you do uh they are now been
+ 
+
+ align:start position:0%
+transfer you do uh they are now been
+evaluating in in dozens of countries
+
+ align:start position:0%
+evaluating in in dozens of countries
+ 
+
+ align:start position:0%
+evaluating in in dozens of countries
+starting with the evaluation in Mexico
+
+ align:start position:0%
+starting with the evaluation in Mexico
+ 
+
+ align:start position:0%
+starting with the evaluation in Mexico
+which was one of the first big prominent
+
+ align:start position:0%
+which was one of the first big prominent
+ 
+
+ align:start position:0%
+which was one of the first big prominent
+City in development
+
+ align:start position:0%
+City in development
+ 
+
+ align:start position:0%
+City in development
+it was kind of replicated in lots of
+
+ align:start position:0%
+it was kind of replicated in lots of
+ 
+
+ align:start position:0%
+it was kind of replicated in lots of
+countries and
+
+ align:start position:0%
+countries and
+ 
+
+ align:start position:0%
+countries and
+maybe bizarrely enough because the first
+
+ align:start position:0%
+maybe bizarrely enough because the first
+ 
+
+ align:start position:0%
+maybe bizarrely enough because the first
+one was done with an experiment
+
+ align:start position:0%
+one was done with an experiment
+ 
+
+ align:start position:0%
+one was done with an experiment
+everybody so they had to have their
+
+ align:start position:0%
+everybody so they had to have their
+ 
+
+ align:start position:0%
+everybody so they had to have their
+experiment too so it was experimented in
+
+ align:start position:0%
+experiment too so it was experimented in
+ 
+
+ align:start position:0%
+experiment too so it was experimented in
+many many many different places
+
+ align:start position:0%
+many many many different places
+ 
+
+ align:start position:0%
+many many many different places
+and in and you tend to always find uh
+
+ align:start position:0%
+and in and you tend to always find uh
+ 
+
+ align:start position:0%
+and in and you tend to always find uh
+impact on education particularly uh for
+
+ align:start position:0%
+impact on education particularly uh for
+ 
+
+ align:start position:0%
+impact on education particularly uh for
+these older kids
+
+ align:start position:0%
+these older kids
+ 
+
+ align:start position:0%
+these older kids
+so that would be good you know that sort
+
+ align:start position:0%
+so that would be good you know that sort
+ 
+
+ align:start position:0%
+so that would be good you know that sort
+of people respond to the cost of
+
+ align:start position:0%
+of people respond to the cost of
+ 
+
+ align:start position:0%
+of people respond to the cost of
+Education
+
+ align:start position:0%
+Education
+ 
+
+ align:start position:0%
+Education
+however
+
+ align:start position:0%
+however
+ 
+
+ align:start position:0%
+however
+they also response when the when the
+
+ align:start position:0%
+they also response when the when the
+ 
+
+ align:start position:0%
+they also response when the when the
+cash transfer are unconditional
+
+ align:start position:0%
+cash transfer are unconditional
+ 
+
+ align:start position:0%
+cash transfer are unconditional
+and there again remember in our model an
+
+ align:start position:0%
+and there again remember in our model an
+ 
+
+ align:start position:0%
+and there again remember in our model an
+easier just a little lump sum transfer
+
+ align:start position:0%
+easier just a little lump sum transfer
+ 
+
+ align:start position:0%
+easier just a little lump sum transfer
+shouldn't have an impact
+
+ align:start position:0%
+shouldn't have an impact
+ 
+
+ align:start position:0%
+shouldn't have an impact
+well you could say maybe it's credit
+
+ align:start position:0%
+well you could say maybe it's credit
+ 
+
+ align:start position:0%
+well you could say maybe it's credit
+constraint or something like that but
+
+ align:start position:0%
+constraint or something like that but
+ 
+
+ align:start position:0%
+constraint or something like that but
+um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+it's certainly not directly uh a
+
+ align:start position:0%
+it's certainly not directly uh a
+ 
+
+ align:start position:0%
+it's certainly not directly uh a
+response to the cost to education so
+
+ align:start position:0%
+response to the cost to education so
+ 
+
+ align:start position:0%
+response to the cost to education so
+people are just about
+
+ align:start position:0%
+people are just about
+ 
+
+ align:start position:0%
+people are just about
+in some studies you find them somewhat
+
+ align:start position:0%
+in some studies you find them somewhat
+ 
+
+ align:start position:0%
+in some studies you find them somewhat
+more responsive to conditional cash
+
+ align:start position:0%
+more responsive to conditional cash
+ 
+
+ align:start position:0%
+more responsive to conditional cash
+transfer in many studies there is no
+
+ align:start position:0%
+transfer in many studies there is no
+ 
+
+ align:start position:0%
+transfer in many studies there is no
+difference so we did one in Morocco for
+
+ align:start position:0%
+difference so we did one in Morocco for
+ 
+
+ align:start position:0%
+difference so we did one in Morocco for
+example where we found
+
+ align:start position:0%
+example where we found
+ 
+
+ align:start position:0%
+example where we found
+that conditional and unconditional
+
+ align:start position:0%
+that conditional and unconditional
+ 
+
+ align:start position:0%
+that conditional and unconditional
+transfer are more or less equivalent
+
+ align:start position:0%
+transfer are more or less equivalent
+ 
+
+ align:start position:0%
+transfer are more or less equivalent
+with unconditional cash transfer
+
+ align:start position:0%
+with unconditional cash transfer
+ 
+
+ align:start position:0%
+with unconditional cash transfer
+possibly a little more effective
+
+ align:start position:0%
+possibly a little more effective
+ 
+
+ align:start position:0%
+possibly a little more effective
+actually that the conditional cash
+
+ align:start position:0%
+actually that the conditional cash
+ 
+
+ align:start position:0%
+actually that the conditional cash
+transfer
+
+ align:start position:0%
+transfer
+ 
+
+ align:start position:0%
+transfer
+so again that's kind of mixed while
+
+ align:start position:0%
+so again that's kind of mixed while
+ 
+
+ align:start position:0%
+so again that's kind of mixed while
+people respond to things that are meant
+
+ align:start position:0%
+people respond to things that are meant
+ 
+
+ align:start position:0%
+people respond to things that are meant
+to send them to school maybe meant to
+
+ align:start position:0%
+to send them to school maybe meant to
+ 
+
+ align:start position:0%
+to send them to school maybe meant to
+reduce the the cost but they seem to do
+
+ align:start position:0%
+reduce the the cost but they seem to do
+ 
+
+ align:start position:0%
+reduce the the cost but they seem to do
+that even though
+
+ align:start position:0%
+that even though
+ 
+
+ align:start position:0%
+that even though
+the transfer is not directly affected to
+
+ align:start position:0%
+the transfer is not directly affected to
+ 
+
+ align:start position:0%
+the transfer is not directly affected to
+the cost
+
+ align:start position:0%
+the cost
+ 
+
+ align:start position:0%
+the cost
+and then of course there is another form
+
+ align:start position:0%
+and then of course there is another form
+ 
+
+ align:start position:0%
+and then of course there is another form
+of indirect indirect reducing the
+
+ align:start position:0%
+of indirect indirect reducing the
+ 
+
+ align:start position:0%
+of indirect indirect reducing the
+indirect cost is is reducing the
+
+ align:start position:0%
+indirect cost is is reducing the
+ 
+
+ align:start position:0%
+indirect cost is is reducing the
+distance to school
+
+ align:start position:0%
+distance to school
+ 
+
+ align:start position:0%
+distance to school
+so someone asked you know how do you
+
+ align:start position:0%
+so someone asked you know how do you
+ 
+
+ align:start position:0%
+so someone asked you know how do you
+think about this intervention the school
+
+ align:start position:0%
+think about this intervention the school
+ 
+
+ align:start position:0%
+think about this intervention the school
+construction intervention and one very
+
+ align:start position:0%
+construction intervention and one very
+ 
+
+ align:start position:0%
+construction intervention and one very
+natural way to think about is you reduce
+
+ align:start position:0%
+natural way to think about is you reduce
+ 
+
+ align:start position:0%
+natural way to think about is you reduce
+the cost of going to school by making
+
+ align:start position:0%
+the cost of going to school by making
+ 
+
+ align:start position:0%
+the cost of going to school by making
+the school very nearby so it's much
+
+ align:start position:0%
+the school very nearby so it's much
+ 
+
+ align:start position:0%
+the school very nearby so it's much
+easier to to go there for the child and
+
+ align:start position:0%
+easier to to go there for the child and
+ 
+
+ align:start position:0%
+easier to to go there for the child and
+for the parents
+
+ align:start position:0%
+for the parents
+ 
+
+ align:start position:0%
+for the parents
+uh so that's that's the that's the idea
+
+ align:start position:0%
+uh so that's that's the that's the idea
+ 
+
+ align:start position:0%
+uh so that's that's the that's the idea
+of of the of my paper on Indonesia so
+
+ align:start position:0%
+of of the of my paper on Indonesia so
+ 
+
+ align:start position:0%
+of of the of my paper on Indonesia so
+someone asked how I came up about uh
+
+ align:start position:0%
+someone asked how I came up about uh
+ 
+
+ align:start position:0%
+someone asked how I came up about uh
+with with this idea
+
+ align:start position:0%
+with with this idea
+ 
+
+ align:start position:0%
+with with this idea
+um so maybe that's relevant second years
+
+ align:start position:0%
+um so maybe that's relevant second years
+ 
+
+ align:start position:0%
+um so maybe that's relevant second years
+I've already had said me that because I
+
+ align:start position:0%
+I've already had said me that because I
+ 
+
+ align:start position:0%
+I've already had said me that because I
+I mentioned it in the in the paper
+
+ align:start position:0%
+I mentioned it in the in the paper
+ 
+
+ align:start position:0%
+I mentioned it in the in the paper
+writing class but that turned out to be
+
+ align:start position:0%
+writing class but that turned out to be
+ 
+
+ align:start position:0%
+writing class but that turned out to be
+my job market paper although I didn't
+
+ align:start position:0%
+my job market paper although I didn't
+ 
+
+ align:start position:0%
+my job market paper although I didn't
+know it was going to be my job market
+
+ align:start position:0%
+know it was going to be my job market
+ 
+
+ align:start position:0%
+know it was going to be my job market
+paper
+
+ align:start position:0%
+paper
+ 
+
+ align:start position:0%
+paper
+uh but I was sitting in development and
+
+ align:start position:0%
+uh but I was sitting in development and
+ 
+
+ align:start position:0%
+uh but I was sitting in development and
+ending in labor and in labor we only
+
+ align:start position:0%
+ending in labor and in labor we only
+ 
+
+ align:start position:0%
+ending in labor and in labor we only
+talked about instrumenting for education
+
+ align:start position:0%
+talked about instrumenting for education
+ 
+
+ align:start position:0%
+talked about instrumenting for education
+and saying it's so important to
+
+ align:start position:0%
+and saying it's so important to
+ 
+
+ align:start position:0%
+and saying it's so important to
+instrument for Education because there
+
+ align:start position:0%
+instrument for Education because there
+ 
+
+ align:start position:0%
+instrument for Education because there
+might be ability by us people who are
+
+ align:start position:0%
+might be ability by us people who are
+ 
+
+ align:start position:0%
+might be ability by us people who are
+more likely to to go to school are also
+
+ align:start position:0%
+more likely to to go to school are also
+ 
+
+ align:start position:0%
+more likely to to go to school are also
+maybe more competent in various ways and
+
+ align:start position:0%
+maybe more competent in various ways and
+ 
+
+ align:start position:0%
+maybe more competent in various ways and
+therefore they'll earn more money anyway
+
+ align:start position:0%
+therefore they'll earn more money anyway
+ 
+
+ align:start position:0%
+therefore they'll earn more money anyway
+even if they don't go to school right so
+
+ align:start position:0%
+even if they don't go to school right so
+ 
+
+ align:start position:0%
+even if they don't go to school right so
+that's the ability bias
+
+ align:start position:0%
+that's the ability bias
+ 
+
+ align:start position:0%
+that's the ability bias
+I thought well in development that seems
+
+ align:start position:0%
+I thought well in development that seems
+ 
+
+ align:start position:0%
+I thought well in development that seems
+worse because it's not just your ability
+
+ align:start position:0%
+worse because it's not just your ability
+ 
+
+ align:start position:0%
+worse because it's not just your ability
+best that in fact we doesn't seem to
+
+ align:start position:0%
+best that in fact we doesn't seem to
+ 
+
+ align:start position:0%
+best that in fact we doesn't seem to
+really be there in rich countries
+
+ align:start position:0%
+really be there in rich countries
+ 
+
+ align:start position:0%
+really be there in rich countries
+you don't seem to have uh
+
+ align:start position:0%
+you don't seem to have uh
+ 
+
+ align:start position:0%
+you don't seem to have uh
+to change the return to education much
+
+ align:start position:0%
+to change the return to education much
+ 
+
+ align:start position:0%
+to change the return to education much
+when you control for this election best
+
+ align:start position:0%
+when you control for this election best
+ 
+
+ align:start position:0%
+when you control for this election best
+but I thought probably in development
+
+ align:start position:0%
+but I thought probably in development
+ 
+
+ align:start position:0%
+but I thought probably in development
+things would be quite different because
+
+ align:start position:0%
+things would be quite different because
+ 
+
+ align:start position:0%
+things would be quite different because
+there are many reasons why kids would go
+
+ align:start position:0%
+there are many reasons why kids would go
+ 
+
+ align:start position:0%
+there are many reasons why kids would go
+to school like in particular the
+
+ align:start position:0%
+to school like in particular the
+ 
+
+ align:start position:0%
+to school like in particular the
+connections of their parents the money
+
+ align:start position:0%
+connections of their parents the money
+ 
+
+ align:start position:0%
+connections of their parents the money
+of their parents that might be related
+
+ align:start position:0%
+of their parents that might be related
+ 
+
+ align:start position:0%
+of their parents that might be related
+with someone's ability to uh to get a
+
+ align:start position:0%
+with someone's ability to uh to get a
+ 
+
+ align:start position:0%
+with someone's ability to uh to get a
+job later
+
+ align:start position:0%
+job later
+ 
+
+ align:start position:0%
+job later
+so I thought the ability bias would have
+
+ align:start position:0%
+so I thought the ability bias would have
+ 
+
+ align:start position:0%
+so I thought the ability bias would have
+to be larger
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and then I was very surprised that there
+
+ align:start position:0%
+and then I was very surprised that there
+ 
+
+ align:start position:0%
+and then I was very surprised that there
+was no study using instrumental viable
+
+ align:start position:0%
+was no study using instrumental viable
+ 
+
+ align:start position:0%
+was no study using instrumental viable
+in development
+
+ align:start position:0%
+in development
+ 
+
+ align:start position:0%
+in development
+so I thought someone should hide to
+
+ align:start position:0%
+so I thought someone should hide to
+ 
+
+ align:start position:0%
+so I thought someone should hide to
+study and I was trying to think about
+
+ align:start position:0%
+study and I was trying to think about
+ 
+
+ align:start position:0%
+study and I was trying to think about
+what would be a good instrument and
+
+ align:start position:0%
+what would be a good instrument and
+ 
+
+ align:start position:0%
+what would be a good instrument and
+thinking about distance to school being
+
+ align:start position:0%
+thinking about distance to school being
+ 
+
+ align:start position:0%
+thinking about distance to school being
+a good instrument
+
+ align:start position:0%
+a good instrument
+ 
+
+ align:start position:0%
+a good instrument
+but then thinking well that's not going
+
+ align:start position:0%
+but then thinking well that's not going
+ 
+
+ align:start position:0%
+but then thinking well that's not going
+to work because if people are closer to
+
+ align:start position:0%
+to work because if people are closer to
+ 
+
+ align:start position:0%
+to work because if people are closer to
+school I probably are in more urban
+
+ align:start position:0%
+school I probably are in more urban
+ 
+
+ align:start position:0%
+school I probably are in more urban
+setting
+
+ align:start position:0%
+setting
+ 
+
+ align:start position:0%
+setting
+to what you really need is a change in
+
+ align:start position:0%
+to what you really need is a change in
+ 
+
+ align:start position:0%
+to what you really need is a change in
+the distance to school
+
+ align:start position:0%
+the distance to school
+ 
+
+ align:start position:0%
+the distance to school
+well where would that come from
+
+ align:start position:0%
+well where would that come from
+ 
+
+ align:start position:0%
+well where would that come from
+well if a country started building a lot
+
+ align:start position:0%
+well if a country started building a lot
+ 
+
+ align:start position:0%
+well if a country started building a lot
+of schools that would reduce the
+
+ align:start position:0%
+of schools that would reduce the
+ 
+
+ align:start position:0%
+of schools that would reduce the
+distance to school
+
+ align:start position:0%
+distance to school
+ 
+
+ align:start position:0%
+distance to school
+is there a country that has built a lot
+
+ align:start position:0%
+is there a country that has built a lot
+ 
+
+ align:start position:0%
+is there a country that has built a lot
+of schools
+
+ align:start position:0%
+of schools
+ 
+
+ align:start position:0%
+of schools
+and so I in the back of my mind I was
+
+ align:start position:0%
+and so I in the back of my mind I was
+ 
+
+ align:start position:0%
+and so I in the back of my mind I was
+looking for that country which had built
+
+ align:start position:0%
+looking for that country which had built
+ 
+
+ align:start position:0%
+looking for that country which had built
+a lot of schools now separately we had
+
+ align:start position:0%
+a lot of schools now separately we had
+ 
+
+ align:start position:0%
+a lot of schools now separately we had
+at the time we didn't have a second year
+
+ align:start position:0%
+at the time we didn't have a second year
+ 
+
+ align:start position:0%
+at the time we didn't have a second year
+people but we had to write an
+
+ align:start position:0%
+people but we had to write an
+ 
+
+ align:start position:0%
+people but we had to write an
+econometrics paper and I had written my
+
+ align:start position:0%
+econometrics paper and I had written my
+ 
+
+ align:start position:0%
+econometrics paper and I had written my
+own Indonesia because there was a good
+
+ align:start position:0%
+own Indonesia because there was a good
+ 
+
+ align:start position:0%
+own Indonesia because there was a good
+data set that a lot of people used to do
+
+ align:start position:0%
+data set that a lot of people used to do
+ 
+
+ align:start position:0%
+data set that a lot of people used to do
+any number of things called the
+
+ align:start position:0%
+any number of things called the
+ 
+
+ align:start position:0%
+any number of things called the
+Indonesia Family Life survey
+
+ align:start position:0%
+Indonesia Family Life survey
+ 
+
+ align:start position:0%
+Indonesia Family Life survey
+so kind of kind of started with
+
+ align:start position:0%
+so kind of kind of started with
+ 
+
+ align:start position:0%
+so kind of kind of started with
+Indonesia and I went to the library and
+
+ align:start position:0%
+Indonesia and I went to the library and
+ 
+
+ align:start position:0%
+Indonesia and I went to the library and
+they have all the World Bank reports one
+
+ align:start position:0%
+they have all the World Bank reports one
+ 
+
+ align:start position:0%
+they have all the World Bank reports one
+of you found this report that I found
+
+ align:start position:0%
+of you found this report that I found
+ 
+
+ align:start position:0%
+of you found this report that I found
+1989 report that but they have a bunch
+
+ align:start position:0%
+1989 report that but they have a bunch
+ 
+
+ align:start position:0%
+1989 report that but they have a bunch
+on all of the countries and what they
+
+ align:start position:0%
+on all of the countries and what they
+ 
+
+ align:start position:0%
+on all of the countries and what they
+are doing every year and I thought let
+
+ align:start position:0%
+are doing every year and I thought let
+ 
+
+ align:start position:0%
+are doing every year and I thought let
+me start with Indonesia since there is
+
+ align:start position:0%
+me start with Indonesia since there is
+ 
+
+ align:start position:0%
+me start with Indonesia since there is
+this data set we already know
+
+ align:start position:0%
+this data set we already know
+ 
+
+ align:start position:0%
+this data set we already know
+and then I uh I found that
+
+ align:start position:0%
+and then I uh I found that
+ 
+
+ align:start position:0%
+and then I uh I found that
+I said that's great that's a lot of
+
+ align:start position:0%
+I said that's great that's a lot of
+ 
+
+ align:start position:0%
+I said that's great that's a lot of
+schools that should reduce the number of
+
+ align:start position:0%
+schools that should reduce the number of
+ 
+
+ align:start position:0%
+schools that should reduce the number of
+of schools a lot so let me uh let me see
+
+ align:start position:0%
+of schools a lot so let me uh let me see
+ 
+
+ align:start position:0%
+of schools a lot so let me uh let me see
+whether I can do something uh with that
+
+ align:start position:0%
+whether I can do something uh with that
+ 
+
+ align:start position:0%
+whether I can do something uh with that
+and then I quickly realized that so
+
+ align:start position:0%
+and then I quickly realized that so
+ 
+
+ align:start position:0%
+and then I quickly realized that so
+first of all I had to fund a number of
+
+ align:start position:0%
+first of all I had to fund a number of
+ 
+
+ align:start position:0%
+first of all I had to fund a number of
+schools
+
+ align:start position:0%
+schools
+ 
+
+ align:start position:0%
+schools
+and I had to find a large data set
+
+ align:start position:0%
+and I had to find a large data set
+ 
+
+ align:start position:0%
+and I had to find a large data set
+I figured that such loves it as it
+
+ align:start position:0%
+I figured that such loves it as it
+ 
+
+ align:start position:0%
+I figured that such loves it as it
+exists
+
+ align:start position:0%
+exists
+ 
+
+ align:start position:0%
+exists
+maybe from that same report that they
+
+ align:start position:0%
+maybe from that same report that they
+ 
+
+ align:start position:0%
+maybe from that same report that they
+were using it this kind of large census
+
+ align:start position:0%
+were using it this kind of large census
+ 
+
+ align:start position:0%
+were using it this kind of large census
+and intercances survey so I knew that
+
+ align:start position:0%
+and intercances survey so I knew that
+ 
+
+ align:start position:0%
+and intercances survey so I knew that
+this data set existed I didn't know
+
+ align:start position:0%
+this data set existed I didn't know
+ 
+
+ align:start position:0%
+this data set existed I didn't know
+that the number the data on the number
+
+ align:start position:0%
+that the number the data on the number
+ 
+
+ align:start position:0%
+that the number the data on the number
+of school existed
+
+ align:start position:0%
+of school existed
+ 
+
+ align:start position:0%
+of school existed
+but I thought probably it somewhere has
+
+ align:start position:0%
+but I thought probably it somewhere has
+ 
+
+ align:start position:0%
+but I thought probably it somewhere has
+to be in some library in Indonesia
+
+ align:start position:0%
+to be in some library in Indonesia
+ 
+
+ align:start position:0%
+to be in some library in Indonesia
+so I went to Indonesia
+
+ align:start position:0%
+so I went to Indonesia
+ 
+
+ align:start position:0%
+so I went to Indonesia
+during the summer
+
+ align:start position:0%
+during the summer
+ 
+
+ align:start position:0%
+during the summer
+and I
+
+ align:start position:0%
+and I
+ 
+
+ align:start position:0%
+and I
+hunted for the data which I knew existed
+
+ align:start position:0%
+hunted for the data which I knew existed
+ 
+
+ align:start position:0%
+hunted for the data which I knew existed
+that's the outcome leader I had to go to
+
+ align:start position:0%
+that's the outcome leader I had to go to
+ 
+
+ align:start position:0%
+that's the outcome leader I had to go to
+the statistical office to find it
+
+ align:start position:0%
+the statistical office to find it
+ 
+
+ align:start position:0%
+the statistical office to find it
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+I think you know I so I I know I paid
+
+ align:start position:0%
+I think you know I so I I know I paid
+ 
+
+ align:start position:0%
+I think you know I so I I know I paid
+some money to someone and they gave me
+
+ align:start position:0%
+some money to someone and they gave me
+ 
+
+ align:start position:0%
+some money to someone and they gave me
+the data and I
+
+ align:start position:0%
+the data and I
+ 
+
+ align:start position:0%
+the data and I
+and I didn't poop too much like
+
+ align:start position:0%
+and I didn't poop too much like
+ 
+
+ align:start position:0%
+and I didn't poop too much like
+but that happened now it's much easier
+
+ align:start position:0%
+but that happened now it's much easier
+ 
+
+ align:start position:0%
+but that happened now it's much easier
+the data since then the data from
+
+ align:start position:0%
+the data since then the data from
+ 
+
+ align:start position:0%
+the data since then the data from
+Indonesia is very very easily available
+
+ align:start position:0%
+Indonesia is very very easily available
+ 
+
+ align:start position:0%
+Indonesia is very very easily available
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+Australian National agency front gave
+
+ align:start position:0%
+Australian National agency front gave
+ 
+
+ align:start position:0%
+Australian National agency front gave
+them a lot of detail to make their data
+
+ align:start position:0%
+them a lot of detail to make their data
+ 
+
+ align:start position:0%
+them a lot of detail to make their data
+available
+
+ align:start position:0%
+available
+ 
+
+ align:start position:0%
+available
+and then I went to the library I knew
+
+ align:start position:0%
+and then I went to the library I knew
+ 
+
+ align:start position:0%
+and then I went to the library I knew
+who had implemented this program there
+
+ align:start position:0%
+who had implemented this program there
+ 
+
+ align:start position:0%
+who had implemented this program there
+was a plan the planning department I
+
+ align:start position:0%
+was a plan the planning department I
+ 
+
+ align:start position:0%
+was a plan the planning department I
+went to the library of the planning
+
+ align:start position:0%
+went to the library of the planning
+ 
+
+ align:start position:0%
+went to the library of the planning
+department I asked them would you have
+
+ align:start position:0%
+department I asked them would you have
+ 
+
+ align:start position:0%
+department I asked them would you have
+just did and they gave me like books
+
+ align:start position:0%
+just did and they gave me like books
+ 
+
+ align:start position:0%
+just did and they gave me like books
+which showed the number of the number of
+
+ align:start position:0%
+which showed the number of the number of
+ 
+
+ align:start position:0%
+which showed the number of the number of
+schools that were built in the year the
+
+ align:start position:0%
+schools that were built in the year the
+ 
+
+ align:start position:0%
+schools that were built in the year the
+the plan of the schools Etc
+
+ align:start position:0%
+the plan of the schools Etc
+ 
+
+ align:start position:0%
+the plan of the schools Etc
+I made some photocopier and I was done
+
+ align:start position:0%
+I made some photocopier and I was done
+ 
+
+ align:start position:0%
+I made some photocopier and I was done
+and then I had two more weeks to spend
+
+ align:start position:0%
+and then I had two more weeks to spend
+ 
+
+ align:start position:0%
+and then I had two more weeks to spend
+Indonesia and I got very bored that was
+
+ align:start position:0%
+Indonesia and I got very bored that was
+ 
+
+ align:start position:0%
+Indonesia and I got very bored that was
+the uh the the end of that so that's how
+
+ align:start position:0%
+the uh the the end of that so that's how
+ 
+
+ align:start position:0%
+the uh the the end of that so that's how
+I came to to that everything lined up
+
+ align:start position:0%
+I came to to that everything lined up
+ 
+
+ align:start position:0%
+I came to to that everything lined up
+quite nicely it doesn't have you know
+
+ align:start position:0%
+quite nicely it doesn't have you know
+ 
+
+ align:start position:0%
+quite nicely it doesn't have you know
+it's not always
+
+ align:start position:0%
+it's not always
+ 
+
+ align:start position:0%
+it's not always
+um like that you know there is any
+
+ align:start position:0%
+um like that you know there is any
+ 
+
+ align:start position:0%
+um like that you know there is any
+number of places where this project
+
+ align:start position:0%
+number of places where this project
+ 
+
+ align:start position:0%
+number of places where this project
+could have collapsed but in this
+
+ align:start position:0%
+could have collapsed but in this
+ 
+
+ align:start position:0%
+could have collapsed but in this
+instance like I was lucky at every step
+
+ align:start position:0%
+instance like I was lucky at every step
+ 
+
+ align:start position:0%
+instance like I was lucky at every step
+interestingly I was initially interested
+
+ align:start position:0%
+interestingly I was initially interested
+ 
+
+ align:start position:0%
+interestingly I was initially interested
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+so I had no idea how good an idea it was
+
+ align:start position:0%
+so I had no idea how good an idea it was
+ 
+
+ align:start position:0%
+so I had no idea how good an idea it was
+I just so you know this is I was I gave
+
+ align:start position:0%
+I just so you know this is I was I gave
+ 
+
+ align:start position:0%
+I just so you know this is I was I gave
+this advice to someone yesterday and I
+
+ align:start position:0%
+this advice to someone yesterday and I
+ 
+
+ align:start position:0%
+this advice to someone yesterday and I
+think it's good advice that
+
+ align:start position:0%
+think it's good advice that
+ 
+
+ align:start position:0%
+think it's good advice that
+it's very hard when you start working on
+
+ align:start position:0%
+it's very hard when you start working on
+ 
+
+ align:start position:0%
+it's very hard when you start working on
+on a research project to think about
+
+ align:start position:0%
+on a research project to think about
+ 
+
+ align:start position:0%
+on a research project to think about
+whether that's gonna be a A plus
+
+ align:start position:0%
+whether that's gonna be a A plus
+ 
+
+ align:start position:0%
+whether that's gonna be a A plus
+contribution or a B minus contribution
+
+ align:start position:0%
+contribution or a B minus contribution
+ 
+
+ align:start position:0%
+contribution or a B minus contribution
+or no contribution at all uh it's hard
+
+ align:start position:0%
+or no contribution at all uh it's hard
+ 
+
+ align:start position:0%
+or no contribution at all uh it's hard
+for you and it's even hard for people to
+
+ align:start position:0%
+for you and it's even hard for people to
+ 
+
+ align:start position:0%
+for you and it's even hard for people to
+talk to you
+
+ align:start position:0%
+talk to you
+ 
+
+ align:start position:0%
+talk to you
+so I think the best guy that I have
+
+ align:start position:0%
+so I think the best guy that I have
+ 
+
+ align:start position:0%
+so I think the best guy that I have
+found is to hide the people that I wish
+
+ align:start position:0%
+found is to hide the people that I wish
+ 
+
+ align:start position:0%
+found is to hide the people that I wish
+I had read I want to write the people
+
+ align:start position:0%
+I had read I want to write the people
+ 
+
+ align:start position:0%
+I had read I want to write the people
+that I wish to read
+
+ align:start position:0%
+that I wish to read
+ 
+
+ align:start position:0%
+that I wish to read
+and then you know that at least one
+
+ align:start position:0%
+and then you know that at least one
+ 
+
+ align:start position:0%
+and then you know that at least one
+person will like it and a pretty
+
+ align:start position:0%
+person will like it and a pretty
+ 
+
+ align:start position:0%
+person will like it and a pretty
+important person because that's yourself
+
+ align:start position:0%
+important person because that's yourself
+ 
+
+ align:start position:0%
+important person because that's yourself
+and you're going to spend a lot of time
+
+ align:start position:0%
+and you're going to spend a lot of time
+ 
+
+ align:start position:0%
+and you're going to spend a lot of time
+with that paper and the rest sort of
+
+ align:start position:0%
+with that paper and the rest sort of
+ 
+
+ align:start position:0%
+with that paper and the rest sort of
+walks itself out and I just had no idea
+
+ align:start position:0%
+walks itself out and I just had no idea
+ 
+
+ align:start position:0%
+walks itself out and I just had no idea
+that in and of itself doing all of this
+
+ align:start position:0%
+that in and of itself doing all of this
+ 
+
+ align:start position:0%
+that in and of itself doing all of this
+step was so key it seemed to me very
+
+ align:start position:0%
+step was so key it seemed to me very
+ 
+
+ align:start position:0%
+step was so key it seemed to me very
+easy I thought of it as a
+
+ align:start position:0%
+easy I thought of it as a
+ 
+
+ align:start position:0%
+easy I thought of it as a
+scales like doing skills to take a
+
+ align:start position:0%
+scales like doing skills to take a
+ 
+
+ align:start position:0%
+scales like doing skills to take a
+strategy that is very very well
+
+ align:start position:0%
+strategy that is very very well
+ 
+
+ align:start position:0%
+strategy that is very very well
+established somewhere and transpose it
+
+ align:start position:0%
+established somewhere and transpose it
+ 
+
+ align:start position:0%
+established somewhere and transpose it
+to another context
+
+ align:start position:0%
+to another context
+ 
+
+ align:start position:0%
+to another context
+and in fact in my mind it would it was
+
+ align:start position:0%
+and in fact in my mind it would it was
+ 
+
+ align:start position:0%
+and in fact in my mind it would it was
+gonna help me think about non-parametric
+
+ align:start position:0%
+gonna help me think about non-parametric
+ 
+
+ align:start position:0%
+gonna help me think about non-parametric
+returns to education I had read a paper
+
+ align:start position:0%
+returns to education I had read a paper
+ 
+
+ align:start position:0%
+returns to education I had read a paper
+which was very uh new at the time by
+
+ align:start position:0%
+which was very uh new at the time by
+ 
+
+ align:start position:0%
+which was very uh new at the time by
+Whitney newey about
+
+ align:start position:0%
+Whitney newey about
+ 
+
+ align:start position:0%
+Whitney newey about
+[Music]
+
+ align:start position:0%
+[Music]
+ 
+
+ align:start position:0%
+[Music]
+estimating non-parametric
+
+ align:start position:0%
+estimating non-parametric
+ 
+
+ align:start position:0%
+estimating non-parametric
+system with triangular
+
+ align:start position:0%
+system with triangular
+ 
+
+ align:start position:0%
+system with triangular
+with this type of situation where you
+
+ align:start position:0%
+with this type of situation where you
+ 
+
+ align:start position:0%
+with this type of situation where you
+have an instrument for for the
+
+ align:start position:0%
+have an instrument for for the
+ 
+
+ align:start position:0%
+have an instrument for for the
+environment so I thought that's where
+
+ align:start position:0%
+environment so I thought that's where
+ 
+
+ align:start position:0%
+environment so I thought that's where
+I'm going to get and at least that's
+
+ align:start position:0%
+I'm going to get and at least that's
+ 
+
+ align:start position:0%
+I'm going to get and at least that's
+going to be something new now it turned
+
+ align:start position:0%
+going to be something new now it turned
+ 
+
+ align:start position:0%
+going to be something new now it turned
+out
+
+ align:start position:0%
+out
+ 
+
+ align:start position:0%
+out
+for reason we're going to discussed very
+
+ align:start position:0%
+for reason we're going to discussed very
+ 
+
+ align:start position:0%
+for reason we're going to discussed very
+soon or if not today or on Monday that
+
+ align:start position:0%
+soon or if not today or on Monday that
+ 
+
+ align:start position:0%
+soon or if not today or on Monday that
+it was completely inappropriate to do
+
+ align:start position:0%
+it was completely inappropriate to do
+ 
+
+ align:start position:0%
+it was completely inappropriate to do
+that
+
+ align:start position:0%
+that
+ 
+
+ align:start position:0%
+that
+and I not only that but I could have
+
+ align:start position:0%
+and I not only that but I could have
+ 
+
+ align:start position:0%
+and I not only that but I could have
+entreated it from the beginning that if
+
+ align:start position:0%
+entreated it from the beginning that if
+ 
+
+ align:start position:0%
+entreated it from the beginning that if
+I had an instrument that affected people
+
+ align:start position:0%
+I had an instrument that affected people
+ 
+
+ align:start position:0%
+I had an instrument that affected people
+going to Primary School I was not going
+
+ align:start position:0%
+going to Primary School I was not going
+ 
+
+ align:start position:0%
+going to Primary School I was not going
+to be able to use it to us to to
+
+ align:start position:0%
+to be able to use it to us to to
+ 
+
+ align:start position:0%
+to be able to use it to us to to
+extrapolate to the entire distribution
+
+ align:start position:0%
+extrapolate to the entire distribution
+ 
+
+ align:start position:0%
+extrapolate to the entire distribution
+of the returns across the entire
+
+ align:start position:0%
+of the returns across the entire
+ 
+
+ align:start position:0%
+of the returns across the entire
+education Spectrum so I had thought
+
+ align:start position:0%
+education Spectrum so I had thought
+ 
+
+ align:start position:0%
+education Spectrum so I had thought
+about it I would have realized this was
+
+ align:start position:0%
+about it I would have realized this was
+ 
+
+ align:start position:0%
+about it I would have realized this was
+not this part of the project couldn't
+
+ align:start position:0%
+not this part of the project couldn't
+ 
+
+ align:start position:0%
+not this part of the project couldn't
+get done but it turned out that even
+
+ align:start position:0%
+get done but it turned out that even
+ 
+
+ align:start position:0%
+get done but it turned out that even
+without this part of the project that
+
+ align:start position:0%
+without this part of the project that
+ 
+
+ align:start position:0%
+without this part of the project that
+that was a good paper or at least a
+
+ align:start position:0%
+that was a good paper or at least a
+ 
+
+ align:start position:0%
+that was a good paper or at least a
+um understood to be a good people or got
+
+ align:start position:0%
+um understood to be a good people or got
+ 
+
+ align:start position:0%
+um understood to be a good people or got
+me a job and and so on and so forth uh
+
+ align:start position:0%
+me a job and and so on and so forth uh
+ 
+
+ align:start position:0%
+me a job and and so on and so forth uh
+so I'd like to say that it's hard to
+
+ align:start position:0%
+so I'd like to say that it's hard to
+ 
+
+ align:start position:0%
+so I'd like to say that it's hard to
+you know
+
+ align:start position:0%
+you know
+ 
+
+ align:start position:0%
+you know
+it's kind of it was a nice project
+
+ align:start position:0%
+it's kind of it was a nice project
+ 
+
+ align:start position:0%
+it's kind of it was a nice project
+because
+
+ align:start position:0%
+because
+ 
+
+ align:start position:0%
+because
+the steps were so clear
+
+ align:start position:0%
+the steps were so clear
+ 
+
+ align:start position:0%
+the steps were so clear
+to me and then you know I was lucky to
+
+ align:start position:0%
+to me and then you know I was lucky to
+ 
+
+ align:start position:0%
+to me and then you know I was lucky to
+get them done I was not stopped by the
+
+ align:start position:0%
+get them done I was not stopped by the
+ 
+
+ align:start position:0%
+get them done I was not stopped by the
+fact that I didn't know if I would find
+
+ align:start position:0%
+fact that I didn't know if I would find
+ 
+
+ align:start position:0%
+fact that I didn't know if I would find
+the data I would take some risk and then
+
+ align:start position:0%
+the data I would take some risk and then
+ 
+
+ align:start position:0%
+the data I would take some risk and then
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+even though the steps we have to clear
+
+ align:start position:0%
+even though the steps we have to clear
+ 
+
+ align:start position:0%
+even though the steps we have to clear
+it was simple at the time it was
+
+ align:start position:0%
+it was simple at the time it was
+ 
+
+ align:start position:0%
+it was simple at the time it was
+sufficient now of course everything
+
+ align:start position:0%
+sufficient now of course everything
+ 
+
+ align:start position:0%
+sufficient now of course everything
+needs to have more bells and results but
+
+ align:start position:0%
+needs to have more bells and results but
+ 
+
+ align:start position:0%
+needs to have more bells and results but
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+I think the general principle of not
+
+ align:start position:0%
+I think the general principle of not
+ 
+
+ align:start position:0%
+I think the general principle of not
+being
+
+ align:start position:0%
+being
+ 
+
+ align:start position:0%
+being
+discouraged in advanced but this is too
+
+ align:start position:0%
+discouraged in advanced but this is too
+ 
+
+ align:start position:0%
+discouraged in advanced but this is too
+easy or this is too obvious still hold
+
+ align:start position:0%
+easy or this is too obvious still hold
+ 
+
+ align:start position:0%
+easy or this is too obvious still hold
+so that's for the autobiography of
+
+ align:start position:0%
+so that's for the autobiography of
+ 
+
+ align:start position:0%
+so that's for the autobiography of
+related to this paper
+
+ align:start position:0%
+related to this paper
+ 
+
+ align:start position:0%
+related to this paper
+so it's a difference in difference we
+
+ align:start position:0%
+so it's a difference in difference we
+ 
+
+ align:start position:0%
+so it's a difference in difference we
+are going to see a lot of that you are
+
+ align:start position:0%
+are going to see a lot of that you are
+ 
+
+ align:start position:0%
+are going to see a lot of that you are
+going to see a lot of that in your
+
+ align:start position:0%
+going to see a lot of that in your
+ 
+
+ align:start position:0%
+going to see a lot of that in your
+career if you're an empirical person at
+
+ align:start position:0%
+career if you're an empirical person at
+ 
+
+ align:start position:0%
+career if you're an empirical person at
+some point you'll probably estimate some
+
+ align:start position:0%
+some point you'll probably estimate some
+ 
+
+ align:start position:0%
+some point you'll probably estimate some
+version of an event study graph or a
+
+ align:start position:0%
+version of an event study graph or a
+ 
+
+ align:start position:0%
+version of an event study graph or a
+different different div
+
+ align:start position:0%
+different different div
+ 
+
+ align:start position:0%
+different different div
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+um it's you know in the simpler setting
+
+ align:start position:0%
+um it's you know in the simpler setting
+ 
+
+ align:start position:0%
+um it's you know in the simpler setting
+it's a pretty straightforward you have
+
+ align:start position:0%
+it's a pretty straightforward you have
+ 
+
+ align:start position:0%
+it's a pretty straightforward you have
+two groups and then two periods
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um and then the group gets treated in
+
+ align:start position:0%
+um and then the group gets treated in
+ 
+
+ align:start position:0%
+um and then the group gets treated in
+the post period and not in the
+
+ align:start position:0%
+the post period and not in the
+ 
+
+ align:start position:0%
+the post period and not in the
+pre-period and your identification
+
+ align:start position:0%
+pre-period and your identification
+ 
+
+ align:start position:0%
+pre-period and your identification
+assumption can be written in this way
+
+ align:start position:0%
+assumption can be written in this way
+ 
+
+ align:start position:0%
+assumption can be written in this way
+which is if you think of it in terms of
+
+ align:start position:0%
+which is if you think of it in terms of
+ 
+
+ align:start position:0%
+which is if you think of it in terms of
+your potential outcome untreated
+
+ align:start position:0%
+your potential outcome untreated
+ 
+
+ align:start position:0%
+your potential outcome untreated
+uh it's a function possibly you know
+
+ align:start position:0%
+uh it's a function possibly you know
+ 
+
+ align:start position:0%
+uh it's a function possibly you know
+very flexible function where of You Know
+
+ align:start position:0%
+very flexible function where of You Know
+ 
+
+ align:start position:0%
+very flexible function where of You Know
+Anything could happen with respect to
+
+ align:start position:0%
+Anything could happen with respect to
+ 
+
+ align:start position:0%
+Anything could happen with respect to
+the group
+
+ align:start position:0%
+the group
+ 
+
+ align:start position:0%
+the group
+it could be related to the to the group
+
+ align:start position:0%
+it could be related to the to the group
+ 
+
+ align:start position:0%
+it could be related to the to the group
+to the time period but but what's not
+
+ align:start position:0%
+to the time period but but what's not
+ 
+
+ align:start position:0%
+to the time period but but what's not
+there that's going to help you for
+
+ align:start position:0%
+there that's going to help you for
+ 
+
+ align:start position:0%
+there that's going to help you for
+identification help us for
+
+ align:start position:0%
+identification help us for
+ 
+
+ align:start position:0%
+identification help us for
+identification
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+what did I purposefully you meet from
+
+ align:start position:0%
+what did I purposefully you meet from
+ 
+
+ align:start position:0%
+what did I purposefully you meet from
+this
+
+ align:start position:0%
+this
+ 
+
+ align:start position:0%
+this
+equation that determines yes the
+
+ align:start position:0%
+equation that determines yes the
+ 
+
+ align:start position:0%
+equation that determines yes the
+interaction between belonging to the
+
+ align:start position:0%
+interaction between belonging to the
+ 
+
+ align:start position:0%
+interaction between belonging to the
+group and exactly so we assume that uh
+
+ align:start position:0%
+group and exactly so we assume that uh
+ 
+
+ align:start position:0%
+group and exactly so we assume that uh
+you know maybe people who are younger
+
+ align:start position:0%
+you know maybe people who are younger
+ 
+
+ align:start position:0%
+you know maybe people who are younger
+will get more education because they are
+
+ align:start position:0%
+will get more education because they are
+ 
+
+ align:start position:0%
+will get more education because they are
+younger countries is richer
+
+ align:start position:0%
+younger countries is richer
+ 
+
+ align:start position:0%
+younger countries is richer
+people who are in some region will get
+
+ align:start position:0%
+people who are in some region will get
+ 
+
+ align:start position:0%
+people who are in some region will get
+more education than others but there is
+
+ align:start position:0%
+more education than others but there is
+ 
+
+ align:start position:0%
+more education than others but there is
+no the younger people in the place that
+
+ align:start position:0%
+no the younger people in the place that
+ 
+
+ align:start position:0%
+no the younger people in the place that
+are more educated would not otherwise
+
+ align:start position:0%
+are more educated would not otherwise
+ 
+
+ align:start position:0%
+are more educated would not otherwise
+have been even more even less
+
+ align:start position:0%
+have been even more even less
+ 
+
+ align:start position:0%
+have been even more even less
+so that's the Assumption we're making
+
+ align:start position:0%
+so that's the Assumption we're making
+ 
+
+ align:start position:0%
+so that's the Assumption we're making
+and that's the key identification
+
+ align:start position:0%
+and that's the key identification
+ 
+
+ align:start position:0%
+and that's the key identification
+assumption and in a lot of difference in
+
+ align:start position:0%
+assumption and in a lot of difference in
+ 
+
+ align:start position:0%
+assumption and in a lot of difference in
+different application
+
+ align:start position:0%
+different application
+ 
+
+ align:start position:0%
+different application
+the trick is going to uh both justify
+
+ align:start position:0%
+the trick is going to uh both justify
+ 
+
+ align:start position:0%
+the trick is going to uh both justify
+this assumption from a priori principle
+
+ align:start position:0%
+this assumption from a priori principle
+ 
+
+ align:start position:0%
+this assumption from a priori principle
+and kind of gather as much evidence as
+
+ align:start position:0%
+and kind of gather as much evidence as
+ 
+
+ align:start position:0%
+and kind of gather as much evidence as
+possible at the assumption is in fact
+
+ align:start position:0%
+possible at the assumption is in fact
+ 
+
+ align:start position:0%
+possible at the assumption is in fact
+real
+
+ align:start position:0%
+real
+ 
+
+ align:start position:0%
+real
+once we have that then we are in good
+
+ align:start position:0%
+once we have that then we are in good
+ 
+
+ align:start position:0%
+once we have that then we are in good
+shape so if if again if we have two
+
+ align:start position:0%
+shape so if if again if we have two
+ 
+
+ align:start position:0%
+shape so if if again if we have two
+groups to period
+
+ align:start position:0%
+groups to period
+ 
+
+ align:start position:0%
+groups to period
+then the different deep estimator is
+
+ align:start position:0%
+then the different deep estimator is
+ 
+
+ align:start position:0%
+then the different deep estimator is
+simply out of the object that we are
+
+ align:start position:0%
+simply out of the object that we are
+ 
+
+ align:start position:0%
+simply out of the object that we are
+trying to to estimate is the the
+
+ align:start position:0%
+trying to to estimate is the the
+ 
+
+ align:start position:0%
+trying to to estimate is the the
+difference in mean uh
+
+ align:start position:0%
+difference in mean uh
+ 
+
+ align:start position:0%
+difference in mean uh
+between pre and post and pre for the
+
+ align:start position:0%
+between pre and post and pre for the
+ 
+
+ align:start position:0%
+between pre and post and pre for the
+treated group minus the same thing for
+
+ align:start position:0%
+treated group minus the same thing for
+ 
+
+ align:start position:0%
+treated group minus the same thing for
+the control group and add the
+
+ align:start position:0%
+the control group and add the
+ 
+
+ align:start position:0%
+the control group and add the
+identification assumption that I laid
+
+ align:start position:0%
+identification assumption that I laid
+ 
+
+ align:start position:0%
+identification assumption that I laid
+down that's going to give you uh the the
+
+ align:start position:0%
+down that's going to give you uh the the
+ 
+
+ align:start position:0%
+down that's going to give you uh the the
+impact the average impact of the program
+
+ align:start position:0%
+impact the average impact of the program
+ 
+
+ align:start position:0%
+impact the average impact of the program
+of course we don't have this thing so we
+
+ align:start position:0%
+of course we don't have this thing so we
+ 
+
+ align:start position:0%
+of course we don't have this thing so we
+will place them by population averages
+
+ align:start position:0%
+will place them by population averages
+ 
+
+ align:start position:0%
+will place them by population averages
+uh in in our or by sample averages
+
+ align:start position:0%
+uh in in our or by sample averages
+ 
+
+ align:start position:0%
+uh in in our or by sample averages
+and uh the the different estimator is
+
+ align:start position:0%
+and uh the the different estimator is
+ 
+
+ align:start position:0%
+and uh the the different estimator is
+now going to be used to be had there is
+
+ align:start position:0%
+now going to be used to be had there is
+ 
+
+ align:start position:0%
+now going to be used to be had there is
+going to be the average uh treated
+
+ align:start position:0%
+going to be the average uh treated
+ 
+
+ align:start position:0%
+going to be the average uh treated
+treated compost minus treated good P
+
+ align:start position:0%
+treated compost minus treated good P
+ 
+
+ align:start position:0%
+treated compost minus treated good P
+minus control code post minus control
+
+ align:start position:0%
+minus control code post minus control
+ 
+
+ align:start position:0%
+minus control code post minus control
+group
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+I would like you to uh to do three lines
+
+ align:start position:0%
+I would like you to uh to do three lines
+ 
+
+ align:start position:0%
+I would like you to uh to do three lines
+of algebra when you go home ah
+
+ align:start position:0%
+of algebra when you go home ah
+ 
+
+ align:start position:0%
+of algebra when you go home ah
+which will convince you that
+
+ align:start position:0%
+which will convince you that
+ 
+
+ align:start position:0%
+which will convince you that
+this uh and this is numerically
+
+ align:start position:0%
+this uh and this is numerically
+ 
+
+ align:start position:0%
+this uh and this is numerically
+equivalent
+
+ align:start position:0%
+equivalent
+ 
+
+ align:start position:0%
+equivalent
+to estimating an OLS regression
+
+ align:start position:0%
+to estimating an OLS regression
+ 
+
+ align:start position:0%
+to estimating an OLS regression
+on a group a treated dummy a constant
+
+ align:start position:0%
+on a group a treated dummy a constant
+ 
+
+ align:start position:0%
+on a group a treated dummy a constant
+treated dummy
+
+ align:start position:0%
+treated dummy
+ 
+
+ align:start position:0%
+treated dummy
+a post dummy and the interaction of the
+
+ align:start position:0%
+a post dummy and the interaction of the
+ 
+
+ align:start position:0%
+a post dummy and the interaction of the
+two
+
+ align:start position:0%
+two
+ 
+
+ align:start position:0%
+two
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+with undergraduates I make the
+
+ align:start position:0%
+with undergraduates I make the
+ 
+
+ align:start position:0%
+with undergraduates I make the
+calculations
+
+ align:start position:0%
+calculations
+ 
+
+ align:start position:0%
+calculations
+but I'm going to assume that you can
+
+ align:start position:0%
+but I'm going to assume that you can
+ 
+
+ align:start position:0%
+but I'm going to assume that you can
+make it that's the from the OLS Formula
+
+ align:start position:0%
+make it that's the from the OLS Formula
+ 
+
+ align:start position:0%
+make it that's the from the OLS Formula
+so it takes
+
+ align:start position:0%
+so it takes
+ 
+
+ align:start position:0%
+so it takes
+lines of algebra but it's interesting
+
+ align:start position:0%
+lines of algebra but it's interesting
+ 
+
+ align:start position:0%
+lines of algebra but it's interesting
+it's you know it's good to have in mind
+
+ align:start position:0%
+it's you know it's good to have in mind
+ 
+
+ align:start position:0%
+it's you know it's good to have in mind
+you really need to know and sometimes we
+
+ align:start position:0%
+you really need to know and sometimes we
+ 
+
+ align:start position:0%
+you really need to know and sometimes we
+ask this question in the exam and not
+
+ align:start position:0%
+ask this question in the exam and not
+ 
+
+ align:start position:0%
+ask this question in the exam and not
+everybody gets it uh you really need to
+
+ align:start position:0%
+everybody gets it uh you really need to
+ 
+
+ align:start position:0%
+everybody gets it uh you really need to
+know what this is this is the difference
+
+ align:start position:0%
+know what this is this is the difference
+ 
+
+ align:start position:0%
+know what this is this is the difference
+between
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+beta1 this is the difference between
+
+ align:start position:0%
+beta1 this is the difference between
+ 
+
+ align:start position:0%
+beta1 this is the difference between
+um treated and controlled in the
+
+ align:start position:0%
+um treated and controlled in the
+ 
+
+ align:start position:0%
+um treated and controlled in the
+pre-period
+
+ align:start position:0%
+pre-period
+ 
+
+ align:start position:0%
+pre-period
+numerically
+
+ align:start position:0%
+numerically
+ 
+
+ align:start position:0%
+numerically
+and this is the difference
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+this is something
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+one needs to know in life because you
+
+ align:start position:0%
+one needs to know in life because you
+ 
+
+ align:start position:0%
+one needs to know in life because you
+get to
+
+ align:start position:0%
+get to
+ 
+
+ align:start position:0%
+get to
+so in our setting uh
+
+ align:start position:0%
+so in our setting uh
+ 
+
+ align:start position:0%
+so in our setting uh
+we have a relatively Swift School
+
+ align:start position:0%
+we have a relatively Swift School
+ 
+
+ align:start position:0%
+we have a relatively Swift School
+construction building program financed
+
+ align:start position:0%
+construction building program financed
+ 
+
+ align:start position:0%
+construction building program financed
+by the album in 1973 so someone asked
+
+ align:start position:0%
+by the album in 1973 so someone asked
+ 
+
+ align:start position:0%
+by the album in 1973 so someone asked
+how it came about that they decided to
+
+ align:start position:0%
+how it came about that they decided to
+ 
+
+ align:start position:0%
+how it came about that they decided to
+use their oil money to do that what's
+
+ align:start position:0%
+use their oil money to do that what's
+ 
+
+ align:start position:0%
+use their oil money to do that what's
+the political economy of that
+
+ align:start position:0%
+the political economy of that
+ 
+
+ align:start position:0%
+the political economy of that
+so the political economy of that is the
+
+ align:start position:0%
+so the political economy of that is the
+ 
+
+ align:start position:0%
+so the political economy of that is the
+suato came to power after a pretty
+
+ align:start position:0%
+suato came to power after a pretty
+ 
+
+ align:start position:0%
+suato came to power after a pretty
+bloody Civil War
+
+ align:start position:0%
+bloody Civil War
+ 
+
+ align:start position:0%
+bloody Civil War
+millions of Communists were killed uh
+
+ align:start position:0%
+millions of Communists were killed uh
+ 
+
+ align:start position:0%
+millions of Communists were killed uh
+the country was not in good shape
+
+ align:start position:0%
+the country was not in good shape
+ 
+
+ align:start position:0%
+the country was not in good shape
+um either politically economically when
+
+ align:start position:0%
+um either politically economically when
+ 
+
+ align:start position:0%
+um either politically economically when
+he took and Consolidated power
+
+ align:start position:0%
+he took and Consolidated power
+ 
+
+ align:start position:0%
+he took and Consolidated power
+and his view for fixing that was to try
+
+ align:start position:0%
+and his view for fixing that was to try
+ 
+
+ align:start position:0%
+and his view for fixing that was to try
+and create a national identity
+
+ align:start position:0%
+and create a national identity
+ 
+
+ align:start position:0%
+and create a national identity
+which was uniform for the whole country
+
+ align:start position:0%
+which was uniform for the whole country
+ 
+
+ align:start position:0%
+which was uniform for the whole country
+and to do that it sort of invented a
+
+ align:start position:0%
+and to do that it sort of invented a
+ 
+
+ align:start position:0%
+and to do that it sort of invented a
+whole ideology called the pankasilla uh
+
+ align:start position:0%
+whole ideology called the pankasilla uh
+ 
+
+ align:start position:0%
+whole ideology called the pankasilla uh
+really promoted the Bahasa Indonesia
+
+ align:start position:0%
+really promoted the Bahasa Indonesia
+ 
+
+ align:start position:0%
+really promoted the Bahasa Indonesia
+language which interestingly is the
+
+ align:start position:0%
+language which interestingly is the
+ 
+
+ align:start position:0%
+language which interestingly is the
+language of no one in particular it's a
+
+ align:start position:0%
+language of no one in particular it's a
+ 
+
+ align:start position:0%
+language of no one in particular it's a
+group it's a Trader language that's not
+
+ align:start position:0%
+group it's a Trader language that's not
+ 
+
+ align:start position:0%
+group it's a Trader language that's not
+spoken was not spoken in particular by
+
+ align:start position:0%
+spoken was not spoken in particular by
+ 
+
+ align:start position:0%
+spoken was not spoken in particular by
+the main ethnic group and he thought
+
+ align:start position:0%
+the main ethnic group and he thought
+ 
+
+ align:start position:0%
+the main ethnic group and he thought
+schools would be a good way to diffuse
+
+ align:start position:0%
+schools would be a good way to diffuse
+ 
+
+ align:start position:0%
+schools would be a good way to diffuse
+that ideology and to diffuse the
+
+ align:start position:0%
+that ideology and to diffuse the
+ 
+
+ align:start position:0%
+that ideology and to diffuse the
+language and therefore to create a sense
+
+ align:start position:0%
+language and therefore to create a sense
+ 
+
+ align:start position:0%
+language and therefore to create a sense
+of national Unity after what they had
+
+ align:start position:0%
+of national Unity after what they had
+ 
+
+ align:start position:0%
+of national Unity after what they had
+experienced
+
+ align:start position:0%
+experienced
+ 
+
+ align:start position:0%
+experienced
+and before that the Indonesian is an oil
+
+ align:start position:0%
+and before that the Indonesian is an oil
+ 
+
+ align:start position:0%
+and before that the Indonesian is an oil
+producing contribute before that the the
+
+ align:start position:0%
+producing contribute before that the the
+ 
+
+ align:start position:0%
+producing contribute before that the the
+oil proceeds used to go to the places
+
+ align:start position:0%
+oil proceeds used to go to the places
+ 
+
+ align:start position:0%
+oil proceeds used to go to the places
+that produce the oil
+
+ align:start position:0%
+that produce the oil
+ 
+
+ align:start position:0%
+that produce the oil
+and another thing that he thought that
+
+ align:start position:0%
+and another thing that he thought that
+ 
+
+ align:start position:0%
+and another thing that he thought that
+he would consolidate both his power and
+
+ align:start position:0%
+he would consolidate both his power and
+ 
+
+ align:start position:0%
+he would consolidate both his power and
+the whole place was to use this proceed
+
+ align:start position:0%
+the whole place was to use this proceed
+ 
+
+ align:start position:0%
+the whole place was to use this proceed
+in a more Equitable way
+
+ align:start position:0%
+in a more Equitable way
+ 
+
+ align:start position:0%
+in a more Equitable way
+so he decided that all of the money from
+
+ align:start position:0%
+so he decided that all of the money from
+ 
+
+ align:start position:0%
+so he decided that all of the money from
+the oil had to be redistributed by the
+
+ align:start position:0%
+the oil had to be redistributed by the
+ 
+
+ align:start position:0%
+the oil had to be redistributed by the
+center in Social programs
+
+ align:start position:0%
+center in Social programs
+ 
+
+ align:start position:0%
+center in Social programs
+and one of Andy School construction
+
+ align:start position:0%
+and one of Andy School construction
+ 
+
+ align:start position:0%
+and one of Andy School construction
+programs
+
+ align:start position:0%
+programs
+ 
+
+ align:start position:0%
+programs
+impressed in presidential instruction by
+
+ align:start position:0%
+impressed in presidential instruction by
+ 
+
+ align:start position:0%
+impressed in presidential instruction by
+Presidential instruction
+
+ align:start position:0%
+Presidential instruction
+ 
+
+ align:start position:0%
+Presidential instruction
+so the impressed the education the
+
+ align:start position:0%
+so the impressed the education the
+ 
+
+ align:start position:0%
+so the impressed the education the
+primary school program was the first of
+
+ align:start position:0%
+primary school program was the first of
+ 
+
+ align:start position:0%
+primary school program was the first of
+those then there was a water and
+
+ align:start position:0%
+those then there was a water and
+ 
+
+ align:start position:0%
+those then there was a water and
+sanitation program
+
+ align:start position:0%
+sanitation program
+ 
+
+ align:start position:0%
+sanitation program
+so the but when they started it was very
+
+ align:start position:0%
+so the but when they started it was very
+ 
+
+ align:start position:0%
+so the but when they started it was very
+small because they started to the first
+
+ align:start position:0%
+small because they started to the first
+ 
+
+ align:start position:0%
+small because they started to the first
+year of this is was 1972 and then the
+
+ align:start position:0%
+year of this is was 1972 and then the
+ 
+
+ align:start position:0%
+year of this is was 1972 and then the
+oil boom came in and it became I think
+
+ align:start position:0%
+oil boom came in and it became I think
+ 
+
+ align:start position:0%
+oil boom came in and it became I think
+much bigger than what they had
+
+ align:start position:0%
+much bigger than what they had
+ 
+
+ align:start position:0%
+much bigger than what they had
+anticipated
+
+ align:start position:0%
+anticipated
+ 
+
+ align:start position:0%
+anticipated
+and I kind of stuck with it both in
+
+ align:start position:0%
+and I kind of stuck with it both in
+ 
+
+ align:start position:0%
+and I kind of stuck with it both in
+terms of how to allocate the rules how
+
+ align:start position:0%
+terms of how to allocate the rules how
+ 
+
+ align:start position:0%
+terms of how to allocate the rules how
+to allocate the schools and to continue
+
+ align:start position:0%
+to allocate the schools and to continue
+ 
+
+ align:start position:0%
+to allocate the schools and to continue
+using uh our money for to this purpose
+
+ align:start position:0%
+using uh our money for to this purpose
+ 
+
+ align:start position:0%
+using uh our money for to this purpose
+so it's very different to Brazil for
+
+ align:start position:0%
+so it's very different to Brazil for
+ 
+
+ align:start position:0%
+so it's very different to Brazil for
+example where the old money is being
+
+ align:start position:0%
+example where the old money is being
+ 
+
+ align:start position:0%
+example where the old money is being
+spent in the provinces that extracted or
+
+ align:start position:0%
+spent in the provinces that extracted or
+ 
+
+ align:start position:0%
+spent in the provinces that extracted or
+in fact a lot of the oil is in the sea
+
+ align:start position:0%
+in fact a lot of the oil is in the sea
+ 
+
+ align:start position:0%
+in fact a lot of the oil is in the sea
+so it's extracted it's used in the
+
+ align:start position:0%
+so it's extracted it's used in the
+ 
+
+ align:start position:0%
+so it's extracted it's used in the
+provinces that are in line to the Sea
+
+ align:start position:0%
+provinces that are in line to the Sea
+ 
+
+ align:start position:0%
+provinces that are in line to the Sea
+and and that money there is a whole
+
+ align:start position:0%
+and and that money there is a whole
+ 
+
+ align:start position:0%
+and and that money there is a whole
+literature showing that that money is
+
+ align:start position:0%
+literature showing that that money is
+ 
+
+ align:start position:0%
+literature showing that that money is
+not very well spent by those places
+
+ align:start position:0%
+not very well spent by those places
+ 
+
+ align:start position:0%
+not very well spent by those places
+so that's the political economy of that
+
+ align:start position:0%
+so that's the political economy of that
+ 
+
+ align:start position:0%
+so that's the political economy of that
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+then they decided that they were going
+
+ align:start position:0%
+then they decided that they were going
+ 
+
+ align:start position:0%
+then they decided that they were going
+to to allocate the schools because the
+
+ align:start position:0%
+to to allocate the schools because the
+ 
+
+ align:start position:0%
+to to allocate the schools because the
+objective was to get to 85 enrollment
+
+ align:start position:0%
+objective was to get to 85 enrollment
+ 
+
+ align:start position:0%
+objective was to get to 85 enrollment
+everywhere so they were going to
+
+ align:start position:0%
+everywhere so they were going to
+ 
+
+ align:start position:0%
+everywhere so they were going to
+allocate the school as a function of the
+
+ align:start position:0%
+allocate the school as a function of the
+ 
+
+ align:start position:0%
+allocate the school as a function of the
+difference between 85 percent and
+
+ align:start position:0%
+difference between 85 percent and
+ 
+
+ align:start position:0%
+difference between 85 percent and
+wherever the school the place was
+
+ align:start position:0%
+wherever the school the place was
+ 
+
+ align:start position:0%
+wherever the school the place was
+they had their census in 1971 so they
+
+ align:start position:0%
+they had their census in 1971 so they
+ 
+
+ align:start position:0%
+they had their census in 1971 so they
+were using basically use that to say
+
+ align:start position:0%
+were using basically use that to say
+ 
+
+ align:start position:0%
+were using basically use that to say
+to basically linear increase to 85
+
+ align:start position:0%
+to basically linear increase to 85
+ 
+
+ align:start position:0%
+to basically linear increase to 85
+percent and in principally should have
+
+ align:start position:0%
+percent and in principally should have
+ 
+
+ align:start position:0%
+percent and in principally should have
+stuck at 85 percent that's another thing
+
+ align:start position:0%
+stuck at 85 percent that's another thing
+ 
+
+ align:start position:0%
+stuck at 85 percent that's another thing
+that I tried to use and didn't use to
+
+ align:start position:0%
+that I tried to use and didn't use to
+ 
+
+ align:start position:0%
+that I tried to use and didn't use to
+see whether after 85 percent it should
+
+ align:start position:0%
+see whether after 85 percent it should
+ 
+
+ align:start position:0%
+see whether after 85 percent it should
+have flattened and so one could use that
+
+ align:start position:0%
+have flattened and so one could use that
+ 
+
+ align:start position:0%
+have flattened and so one could use that
+for her
+
+ align:start position:0%
+for her
+ 
+
+ align:start position:0%
+for her
+neater identification but it didn't
+
+ align:start position:0%
+neater identification but it didn't
+ 
+
+ align:start position:0%
+neater identification but it didn't
+quite it wasn't it was too smooth so it
+
+ align:start position:0%
+quite it wasn't it was too smooth so it
+ 
+
+ align:start position:0%
+quite it wasn't it was too smooth so it
+didn't work
+
+ align:start position:0%
+didn't work
+ 
+
+ align:start position:0%
+didn't work
+so with that just it depends on the free
+
+ align:start position:0%
+so with that just it depends on the free
+ 
+
+ align:start position:0%
+so with that just it depends on the free
+campaign enrollment that gives me my
+
+ align:start position:0%
+campaign enrollment that gives me my
+ 
+
+ align:start position:0%
+campaign enrollment that gives me my
+difference in difference
+
+ align:start position:0%
+difference in difference
+ 
+
+ align:start position:0%
+difference in difference
+so I'm going to define a group of of
+
+ align:start position:0%
+so I'm going to define a group of of
+ 
+
+ align:start position:0%
+so I'm going to define a group of of
+treated people which are the young guys
+
+ align:start position:0%
+treated people which are the young guys
+ 
+
+ align:start position:0%
+treated people which are the young guys
+and then treated in control region
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um to start with we can say well let's
+
+ align:start position:0%
+um to start with we can say well let's
+ 
+
+ align:start position:0%
+um to start with we can say well let's
+say we look above the median
+
+ align:start position:0%
+say we look above the median
+ 
+
+ align:start position:0%
+say we look above the median
+and then we can do a simple definitive
+
+ align:start position:0%
+and then we can do a simple definitive
+ 
+
+ align:start position:0%
+and then we can do a simple definitive
+for year of education so this is these
+
+ align:start position:0%
+for year of education so this is these
+ 
+
+ align:start position:0%
+for year of education so this is these
+are a sample average for the high uh in
+
+ align:start position:0%
+are a sample average for the high uh in
+ 
+
+ align:start position:0%
+are a sample average for the high uh in
+program intensity and the young people
+
+ align:start position:0%
+program intensity and the young people
+ 
+
+ align:start position:0%
+program intensity and the young people
+higher program intensity and the old
+
+ align:start position:0%
+higher program intensity and the old
+ 
+
+ align:start position:0%
+higher program intensity and the old
+people the first thing we notice among
+
+ align:start position:0%
+people the first thing we notice among
+ 
+
+ align:start position:0%
+people the first thing we notice among
+the old people there was a education
+
+ align:start position:0%
+the old people there was a education
+ 
+
+ align:start position:0%
+the old people there was a education
+levels this is years of education
+
+ align:start position:0%
+levels this is years of education
+ 
+
+ align:start position:0%
+levels this is years of education
+attained by adults who were kids during
+
+ align:start position:0%
+attained by adults who were kids during
+ 
+
+ align:start position:0%
+attained by adults who were kids during
+this period is lower in the high
+
+ align:start position:0%
+this period is lower in the high
+ 
+
+ align:start position:0%
+this period is lower in the high
+intensity region that makes sense right
+
+ align:start position:0%
+intensity region that makes sense right
+ 
+
+ align:start position:0%
+intensity region that makes sense right
+because the
+
+ align:start position:0%
+because the
+ 
+
+ align:start position:0%
+because the
+because they were putting more schools
+
+ align:start position:0%
+because they were putting more schools
+ 
+
+ align:start position:0%
+because they were putting more schools
+in places that had less education to
+
+ align:start position:0%
+in places that had less education to
+ 
+
+ align:start position:0%
+in places that had less education to
+start with
+
+ align:start position:0%
+start with
+ 
+
+ align:start position:0%
+start with
+and they are still lower in for the
+
+ align:start position:0%
+and they are still lower in for the
+ 
+
+ align:start position:0%
+and they are still lower in for the
+young kids but less so
+
+ align:start position:0%
+young kids but less so
+ 
+
+ align:start position:0%
+young kids but less so
+so the difference is
+
+ align:start position:0%
+so the difference is
+ 
+
+ align:start position:0%
+so the difference is
+the difference is positive
+
+ align:start position:0%
+the difference is positive
+ 
+
+ align:start position:0%
+the difference is positive
+um although it's you know it's
+
+ align:start position:0%
+um although it's you know it's
+ 
+
+ align:start position:0%
+um although it's you know it's
+insignificant
+
+ align:start position:0%
+insignificant
+ 
+
+ align:start position:0%
+insignificant
+so this is illustrative but it's not
+
+ align:start position:0%
+so this is illustrative but it's not
+ 
+
+ align:start position:0%
+so this is illustrative but it's not
+very precise
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so that's that's good so then now we can
+
+ align:start position:0%
+so that's that's good so then now we can
+ 
+
+ align:start position:0%
+so that's that's good so then now we can
+look at uh
+
+ align:start position:0%
+look at uh
+ 
+
+ align:start position:0%
+look at uh
+we can be a bit concerned that in even
+
+ align:start position:0%
+we can be a bit concerned that in even
+ 
+
+ align:start position:0%
+we can be a bit concerned that in even
+in the absence of the program
+
+ align:start position:0%
+in the absence of the program
+ 
+
+ align:start position:0%
+in the absence of the program
+the young cohort would have converted
+
+ align:start position:0%
+the young cohort would have converted
+ 
+
+ align:start position:0%
+the young cohort would have converted
+maybe to the to the old cohorts because
+
+ align:start position:0%
+maybe to the to the old cohorts because
+ 
+
+ align:start position:0%
+maybe to the to the old cohorts because
+my
+
+ align:start position:0%
+my
+ 
+
+ align:start position:0%
+my
+go back to our basic model things
+
+ align:start position:0%
+go back to our basic model things
+ 
+
+ align:start position:0%
+go back to our basic model things
+convert and there should be one steady
+
+ align:start position:0%
+convert and there should be one steady
+ 
+
+ align:start position:0%
+convert and there should be one steady
+state to where everybody is going and
+
+ align:start position:0%
+state to where everybody is going and
+ 
+
+ align:start position:0%
+state to where everybody is going and
+it's within the country so we would
+
+ align:start position:0%
+it's within the country so we would
+ 
+
+ align:start position:0%
+it's within the country so we would
+expect conversions anyway so am I just
+
+ align:start position:0%
+expect conversions anyway so am I just
+ 
+
+ align:start position:0%
+expect conversions anyway so am I just
+capturing that
+
+ align:start position:0%
+capturing that
+ 
+
+ align:start position:0%
+capturing that
+so one easy way to do that is to compare
+
+ align:start position:0%
+so one easy way to do that is to compare
+ 
+
+ align:start position:0%
+so one easy way to do that is to compare
+the old to the very old
+
+ align:start position:0%
+the old to the very old
+ 
+
+ align:start position:0%
+the old to the very old
+um and uh
+
+ align:start position:0%
+um and uh
+ 
+
+ align:start position:0%
+um and uh
+we can do that with that kind of control
+
+ align:start position:0%
+we can do that with that kind of control
+ 
+
+ align:start position:0%
+we can do that with that kind of control
+experiment
+
+ align:start position:0%
+experiment
+ 
+
+ align:start position:0%
+experiment
+and there we can see that at least
+
+ align:start position:0%
+and there we can see that at least
+ 
+
+ align:start position:0%
+and there we can see that at least
+before it seems to be that the trend
+
+ align:start position:0%
+before it seems to be that the trend
+ 
+
+ align:start position:0%
+before it seems to be that the trend
+were in fact parallel between the two
+
+ align:start position:0%
+were in fact parallel between the two
+ 
+
+ align:start position:0%
+were in fact parallel between the two
+places
+
+ align:start position:0%
+places
+ 
+
+ align:start position:0%
+places
+so that's that's uh encouraging the the
+
+ align:start position:0%
+so that's that's uh encouraging the the
+ 
+
+ align:start position:0%
+so that's that's uh encouraging the the
+old and these are already my old and
+
+ align:start position:0%
+old and these are already my old and
+ 
+
+ align:start position:0%
+old and these are already my old and
+this is my very old and if I had done
+
+ align:start position:0%
+this is my very old and if I had done
+ 
+
+ align:start position:0%
+this is my very old and if I had done
+the differently for them I would have
+
+ align:start position:0%
+the differently for them I would have
+ 
+
+ align:start position:0%
+the differently for them I would have
+found a much smaller number
+
+ align:start position:0%
+found a much smaller number
+ 
+
+ align:start position:0%
+found a much smaller number
+and so that's
+
+ align:start position:0%
+and so that's
+ 
+
+ align:start position:0%
+and so that's
+goes in the right direction
+
+ align:start position:0%
+goes in the right direction
+ 
+
+ align:start position:0%
+goes in the right direction
+now this is all this is quite good and
+
+ align:start position:0%
+now this is all this is quite good and
+ 
+
+ align:start position:0%
+now this is all this is quite good and
+we can do better than that and that's
+
+ align:start position:0%
+we can do better than that and that's
+ 
+
+ align:start position:0%
+we can do better than that and that's
+where we have uh you know first of all
+
+ align:start position:0%
+where we have uh you know first of all
+ 
+
+ align:start position:0%
+where we have uh you know first of all
+we have many groups
+
+ align:start position:0%
+we have many groups
+ 
+
+ align:start position:0%
+we have many groups
+uh so in some places they built one
+
+ align:start position:0%
+uh so in some places they built one
+ 
+
+ align:start position:0%
+uh so in some places they built one
+school where thousand kids and two
+
+ align:start position:0%
+school where thousand kids and two
+ 
+
+ align:start position:0%
+school where thousand kids and two
+schools per thousand kids and 100 School
+
+ align:start position:0%
+schools per thousand kids and 100 School
+ 
+
+ align:start position:0%
+schools per thousand kids and 100 School
+per thousand kids or you know it doesn't
+
+ align:start position:0%
+per thousand kids or you know it doesn't
+ 
+
+ align:start position:0%
+per thousand kids or you know it doesn't
+go till 100 but so we could think of
+
+ align:start position:0%
+go till 100 but so we could think of
+ 
+
+ align:start position:0%
+go till 100 but so we could think of
+several treatments
+
+ align:start position:0%
+several treatments
+ 
+
+ align:start position:0%
+several treatments
+so in our in our case you could have one
+
+ align:start position:0%
+so in our in our case you could have one
+ 
+
+ align:start position:0%
+so in our in our case you could have one
+two three if you have not very many or
+
+ align:start position:0%
+two three if you have not very many or
+ 
+
+ align:start position:0%
+two three if you have not very many or
+you could have in our case we can say
+
+ align:start position:0%
+you could have in our case we can say
+ 
+
+ align:start position:0%
+you could have in our case we can say
+this is something discreet
+
+ align:start position:0%
+this is something discreet
+ 
+
+ align:start position:0%
+this is something discreet
+uh and I'm going to replace my uh simple
+
+ align:start position:0%
+uh and I'm going to replace my uh simple
+ 
+
+ align:start position:0%
+uh and I'm going to replace my uh simple
+defend div by by the clear regression
+
+ align:start position:0%
+defend div by by the clear regression
+ 
+
+ align:start position:0%
+defend div by by the clear regression
+uh pre and post on the number of
+
+ align:start position:0%
+uh pre and post on the number of
+ 
+
+ align:start position:0%
+uh pre and post on the number of
+Education differences
+
+ align:start position:0%
+Education differences
+ 
+
+ align:start position:0%
+Education differences
+on the
+
+ align:start position:0%
+on the
+ 
+
+ align:start position:0%
+on the
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+on the number of kids that were built
+
+ align:start position:0%
+on the number of kids that were built
+ 
+
+ align:start position:0%
+on the number of kids that were built
+so again if I had only two cohorts and I
+
+ align:start position:0%
+so again if I had only two cohorts and I
+ 
+
+ align:start position:0%
+so again if I had only two cohorts and I
+only relaxed that it gives me a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+I'm now need to control I need to put
+
+ align:start position:0%
+I'm now need to control I need to put
+ 
+
+ align:start position:0%
+I'm now need to control I need to put
+region fixed effect
+
+ align:start position:0%
+region fixed effect
+ 
+
+ align:start position:0%
+region fixed effect
+so that's control for any differences uh
+
+ align:start position:0%
+so that's control for any differences uh
+ 
+
+ align:start position:0%
+so that's control for any differences uh
+and then I'm going to assume here I make
+
+ align:start position:0%
+and then I'm going to assume here I make
+ 
+
+ align:start position:0%
+and then I'm going to assume here I make
+the assumption that the effect is linear
+
+ align:start position:0%
+the assumption that the effect is linear
+ 
+
+ align:start position:0%
+the assumption that the effect is linear
+in a number of school
+
+ align:start position:0%
+in a number of school
+ 
+
+ align:start position:0%
+in a number of school
+uh so I'm
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+regressing on an interaction not anymore
+
+ align:start position:0%
+regressing on an interaction not anymore
+ 
+
+ align:start position:0%
+regressing on an interaction not anymore
+on a treated dummy but on a number of
+
+ align:start position:0%
+on a treated dummy but on a number of
+ 
+
+ align:start position:0%
+on a treated dummy but on a number of
+school per thousand kids dummy
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and that gives me this regression again
+
+ align:start position:0%
+and that gives me this regression again
+ 
+
+ align:start position:0%
+and that gives me this regression again
+that I can do by comparing
+
+ align:start position:0%
+that I can do by comparing
+ 
+
+ align:start position:0%
+that I can do by comparing
+uh just the young to the old
+
+ align:start position:0%
+uh just the young to the old
+ 
+
+ align:start position:0%
+uh just the young to the old
+and so now this is interpret is saying
+
+ align:start position:0%
+and so now this is interpret is saying
+ 
+
+ align:start position:0%
+and so now this is interpret is saying
+that in the places that
+
+ align:start position:0%
+that in the places that
+ 
+
+ align:start position:0%
+that in the places that
+that got one more school for each extra
+
+ align:start position:0%
+that got one more school for each extra
+ 
+
+ align:start position:0%
+that got one more school for each extra
+School per thousand kids
+
+ align:start position:0%
+School per thousand kids
+ 
+
+ align:start position:0%
+School per thousand kids
+the increase in education between The
+
+ align:start position:0%
+the increase in education between The
+ 
+
+ align:start position:0%
+the increase in education between The
+Young and the old court is 0.12 years
+
+ align:start position:0%
+Young and the old court is 0.12 years
+ 
+
+ align:start position:0%
+Young and the old court is 0.12 years
+faster
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+does that make sense
+
+ align:start position:0%
+does that make sense
+ 
+
+ align:start position:0%
+does that make sense
+so this is how we
+
+ align:start position:0%
+so this is how we
+ 
+
+ align:start position:0%
+so this is how we
+we read that that's the regression
+
+ align:start position:0%
+we read that that's the regression
+ 
+
+ align:start position:0%
+we read that that's the regression
+we you can you could have read data you
+
+ align:start position:0%
+we you can you could have read data you
+ 
+
+ align:start position:0%
+we you can you could have read data you
+could have run that as a regression of
+
+ align:start position:0%
+could have run that as a regression of
+ 
+
+ align:start position:0%
+could have run that as a regression of
+the difference between The Young and the
+
+ align:start position:0%
+the difference between The Young and the
+ 
+
+ align:start position:0%
+the difference between The Young and the
+old on the number of schools per capita
+
+ align:start position:0%
+old on the number of schools per capita
+ 
+
+ align:start position:0%
+old on the number of schools per capita
+that were built in the region of birth
+
+ align:start position:0%
+that were built in the region of birth
+ 
+
+ align:start position:0%
+that were built in the region of birth
+of
+
+ align:start position:0%
+of
+ 
+
+ align:start position:0%
+of
+controlling for any differences between
+
+ align:start position:0%
+controlling for any differences between
+ 
+
+ align:start position:0%
+controlling for any differences between
+the region
+
+ align:start position:0%
+the region
+ 
+
+ align:start position:0%
+the region
+and we can do the same the same
+
+ align:start position:0%
+and we can do the same the same
+ 
+
+ align:start position:0%
+and we can do the same the same
+experiment between the
+
+ align:start position:0%
+experiment between the
+ 
+
+ align:start position:0%
+experiment between the
+between the the the old and super and
+
+ align:start position:0%
+between the the the old and super and
+ 
+
+ align:start position:0%
+between the the the old and super and
+the super old
+
+ align:start position:0%
+the super old
+ 
+
+ align:start position:0%
+the super old
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+things are now much more precise
+
+ align:start position:0%
+things are now much more precise
+ 
+
+ align:start position:0%
+things are now much more precise
+although they are too precise for
+
+ align:start position:0%
+although they are too precise for
+ 
+
+ align:start position:0%
+although they are too precise for
+residents that in that I will come in a
+
+ align:start position:0%
+residents that in that I will come in a
+ 
+
+ align:start position:0%
+residents that in that I will come in a
+minute uh my standard errors are
+
+ align:start position:0%
+minute uh my standard errors are
+ 
+
+ align:start position:0%
+minute uh my standard errors are
+completely off in that paper
+
+ align:start position:0%
+completely off in that paper
+ 
+
+ align:start position:0%
+completely off in that paper
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+I I didn't know but I didn't know any
+
+ align:start position:0%
+I I didn't know but I didn't know any
+ 
+
+ align:start position:0%
+I I didn't know but I didn't know any
+better but I now do know so I'll do so
+
+ align:start position:0%
+better but I now do know so I'll do so
+ 
+
+ align:start position:0%
+better but I now do know so I'll do so
+this is another half of for reason I'll
+
+ align:start position:0%
+this is another half of for reason I'll
+ 
+
+ align:start position:0%
+this is another half of for reason I'll
+discuss in a bit but at least it seems
+
+ align:start position:0%
+discuss in a bit but at least it seems
+ 
+
+ align:start position:0%
+discuss in a bit but at least it seems
+quite a bit more precise oh a lot more
+
+ align:start position:0%
+quite a bit more precise oh a lot more
+ 
+
+ align:start position:0%
+quite a bit more precise oh a lot more
+questions
+
+ align:start position:0%
+questions
+ 
+
+ align:start position:0%
+questions
+so that's good it looks like every
+
+ align:start position:0%
+so that's good it looks like every
+ 
+
+ align:start position:0%
+so that's good it looks like every
+thousand schools increase the number of
+
+ align:start position:0%
+thousand schools increase the number of
+ 
+
+ align:start position:0%
+thousand schools increase the number of
+year by by around 12 years and now we
+
+ align:start position:0%
+year by by around 12 years and now we
+ 
+
+ align:start position:0%
+year by by around 12 years and now we
+can do
+
+ align:start position:0%
+can do
+ 
+
+ align:start position:0%
+can do
+the we can use the fact that in fact we
+
+ align:start position:0%
+the we can use the fact that in fact we
+ 
+
+ align:start position:0%
+the we can use the fact that in fact we
+have many cohorts and also that perhaps
+
+ align:start position:0%
+have many cohorts and also that perhaps
+ 
+
+ align:start position:0%
+have many cohorts and also that perhaps
+we have a prediction
+
+ align:start position:0%
+we have a prediction
+ 
+
+ align:start position:0%
+we have a prediction
+so instead of controlling first of all
+
+ align:start position:0%
+so instead of controlling first of all
+ 
+
+ align:start position:0%
+so instead of controlling first of all
+instead of controlling for for just the
+
+ align:start position:0%
+instead of controlling for for just the
+ 
+
+ align:start position:0%
+instead of controlling for for just the
+post I could control for
+
+ align:start position:0%
+post I could control for
+ 
+
+ align:start position:0%
+post I could control for
+uh one the meter area that's not going
+
+ align:start position:0%
+uh one the meter area that's not going
+ 
+
+ align:start position:0%
+uh one the meter area that's not going
+to change anything
+
+ align:start position:0%
+to change anything
+ 
+
+ align:start position:0%
+to change anything
+but more interestingly
+
+ align:start position:0%
+but more interestingly
+ 
+
+ align:start position:0%
+but more interestingly
+I could instead of having just an
+
+ align:start position:0%
+I could instead of having just an
+ 
+
+ align:start position:0%
+I could instead of having just an
+interaction for post and and the number
+
+ align:start position:0%
+interaction for post and and the number
+ 
+
+ align:start position:0%
+interaction for post and and the number
+of schools I'm going to now
+
+ align:start position:0%
+of schools I'm going to now
+ 
+
+ align:start position:0%
+of schools I'm going to now
+control I'm going to have an interaction
+
+ align:start position:0%
+control I'm going to have an interaction
+ 
+
+ align:start position:0%
+control I'm going to have an interaction
+for every year dummy
+
+ align:start position:0%
+for every year dummy
+ 
+
+ align:start position:0%
+for every year dummy
+and uh and the number of schools
+
+ align:start position:0%
+and uh and the number of schools
+ 
+
+ align:start position:0%
+and uh and the number of schools
+which you can think to this the way this
+
+ align:start position:0%
+which you can think to this the way this
+ 
+
+ align:start position:0%
+which you can think to this the way this
+is written which starts at from the
+
+ align:start position:0%
+is written which starts at from the
+ 
+
+ align:start position:0%
+is written which starts at from the
+absolutely uh youngest people oldest
+
+ align:start position:0%
+absolutely uh youngest people oldest
+ 
+
+ align:start position:0%
+absolutely uh youngest people oldest
+people until the very end you can think
+
+ align:start position:0%
+people until the very end you can think
+ 
+
+ align:start position:0%
+people until the very end you can think
+of running a series of different diff
+
+ align:start position:0%
+of running a series of different diff
+ 
+
+ align:start position:0%
+of running a series of different diff
+where every time you're comparing other
+
+ align:start position:0%
+where every time you're comparing other
+ 
+
+ align:start position:0%
+where every time you're comparing other
+people born in 19 I think the oldest
+
+ align:start position:0%
+people born in 19 I think the oldest
+ 
+
+ align:start position:0%
+people born in 19 I think the oldest
+people are born
+
+ align:start position:0%
+people are born
+ 
+
+ align:start position:0%
+people are born
+1950 or something
+
+ align:start position:0%
+1950 or something
+ 
+
+ align:start position:0%
+1950 or something
+you compare them to people who are born
+
+ align:start position:0%
+you compare them to people who are born
+ 
+
+ align:start position:0%
+you compare them to people who are born
+you do a different diff between the 51
+
+ align:start position:0%
+you do a different diff between the 51
+ 
+
+ align:start position:0%
+you do a different diff between the 51
+core to 50. the difference between 51
+
+ align:start position:0%
+core to 50. the difference between 51
+ 
+
+ align:start position:0%
+core to 50. the difference between 51
+and 50.
+
+ align:start position:0%
+and 50.
+ 
+
+ align:start position:0%
+and 50.
+I regressed on the number of schools
+
+ align:start position:0%
+I regressed on the number of schools
+ 
+
+ align:start position:0%
+I regressed on the number of schools
+that were built and then the difference
+
+ align:start position:0%
+that were built and then the difference
+ 
+
+ align:start position:0%
+that were built and then the difference
+between 52 and 50 on the number of
+
+ align:start position:0%
+between 52 and 50 on the number of
+ 
+
+ align:start position:0%
+between 52 and 50 on the number of
+schools that were built etc etc
+
+ align:start position:0%
+schools that were built etc etc
+ 
+
+ align:start position:0%
+schools that were built etc etc
+and that builds you your
+
+ align:start position:0%
+and that builds you your
+ 
+
+ align:start position:0%
+and that builds you your
+so this first one is just Twitter and
+
+ align:start position:0%
+so this first one is just Twitter and
+ 
+
+ align:start position:0%
+so this first one is just Twitter and
+the second one is combined with the
+
+ align:start position:0%
+the second one is combined with the
+ 
+
+ align:start position:0%
+the second one is combined with the
+treatment of schools and that gives you
+
+ align:start position:0%
+treatment of schools and that gives you
+ 
+
+ align:start position:0%
+treatment of schools and that gives you
+this typical event study graph
+
+ align:start position:0%
+this typical event study graph
+ 
+
+ align:start position:0%
+this typical event study graph
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+so this is the one for education
+
+ align:start position:0%
+so this is the one for education
+ 
+
+ align:start position:0%
+so this is the one for education
+where you know I started here at zero
+
+ align:start position:0%
+where you know I started here at zero
+ 
+
+ align:start position:0%
+where you know I started here at zero
+for 24 for the oldest for the oldest
+
+ align:start position:0%
+for 24 for the oldest for the oldest
+ 
+
+ align:start position:0%
+for 24 for the oldest for the oldest
+people
+
+ align:start position:0%
+people
+ 
+
+ align:start position:0%
+people
+and so this is a different diff
+
+ align:start position:0%
+and so this is a different diff
+ 
+
+ align:start position:0%
+and so this is a different diff
+um sort of the continuous definitive for
+
+ align:start position:0%
+um sort of the continuous definitive for
+ 
+
+ align:start position:0%
+um sort of the continuous definitive for
+the 23
+
+ align:start position:0%
+the 23
+ 
+
+ align:start position:0%
+the 23
+for the 22 Etc this is one regression
+
+ align:start position:0%
+for the 22 Etc this is one regression
+ 
+
+ align:start position:0%
+for the 22 Etc this is one regression
+but this is each of this dot compares to
+
+ align:start position:0%
+but this is each of this dot compares to
+ 
+
+ align:start position:0%
+but this is each of this dot compares to
+to the oldest people
+
+ align:start position:0%
+to the oldest people
+ 
+
+ align:start position:0%
+to the oldest people
+and I do have a prediction that there
+
+ align:start position:0%
+and I do have a prediction that there
+ 
+
+ align:start position:0%
+and I do have a prediction that there
+was what wasn't any school built that
+
+ align:start position:0%
+was what wasn't any school built that
+ 
+
+ align:start position:0%
+was what wasn't any school built that
+these guys could go to if they are older
+
+ align:start position:0%
+these guys could go to if they are older
+ 
+
+ align:start position:0%
+these guys could go to if they are older
+than 12 in 1974 so I shouldn't see all
+
+ align:start position:0%
+than 12 in 1974 so I shouldn't see all
+ 
+
+ align:start position:0%
+than 12 in 1974 so I shouldn't see all
+of these guys should be zero and then as
+
+ align:start position:0%
+of these guys should be zero and then as
+ 
+
+ align:start position:0%
+of these guys should be zero and then as
+schools more schools get built and
+
+ align:start position:0%
+schools more schools get built and
+ 
+
+ align:start position:0%
+schools more schools get built and
+people are younger so they they get to
+
+ align:start position:0%
+people are younger so they they get to
+ 
+
+ align:start position:0%
+people are younger so they they get to
+enjoy them for a longer period of time
+
+ align:start position:0%
+enjoy them for a longer period of time
+ 
+
+ align:start position:0%
+enjoy them for a longer period of time
+the the prediction is that the treatment
+
+ align:start position:0%
+the the prediction is that the treatment
+ 
+
+ align:start position:0%
+the the prediction is that the treatment
+should
+
+ align:start position:0%
+should
+ 
+
+ align:start position:0%
+should
+the treatment effect should increase
+
+ align:start position:0%
+the treatment effect should increase
+ 
+
+ align:start position:0%
+the treatment effect should increase
+so at that time
+
+ align:start position:0%
+so at that time
+ 
+
+ align:start position:0%
+so at that time
+I think people really like that graph
+
+ align:start position:0%
+I think people really like that graph
+ 
+
+ align:start position:0%
+I think people really like that graph
+since then they have become very very
+
+ align:start position:0%
+since then they have become very very
+ 
+
+ align:start position:0%
+since then they have become very very
+very
+
+ align:start position:0%
+very
+ 
+
+ align:start position:0%
+very
+common and fashionable and important so
+
+ align:start position:0%
+common and fashionable and important so
+ 
+
+ align:start position:0%
+common and fashionable and important so
+I'll uh and so this graph has a lot of
+
+ align:start position:0%
+I'll uh and so this graph has a lot of
+ 
+
+ align:start position:0%
+I'll uh and so this graph has a lot of
+issues it's not funny it's not the way
+
+ align:start position:0%
+issues it's not funny it's not the way
+ 
+
+ align:start position:0%
+issues it's not funny it's not the way
+that one would construct such a graph
+
+ align:start position:0%
+that one would construct such a graph
+ 
+
+ align:start position:0%
+that one would construct such a graph
+today and I'll show you all of the
+
+ align:start position:0%
+today and I'll show you all of the
+ 
+
+ align:start position:0%
+today and I'll show you all of the
+things what need to add
+
+ align:start position:0%
+things what need to add
+ 
+
+ align:start position:0%
+things what need to add
+but at this time I you know I I it was
+
+ align:start position:0%
+but at this time I you know I I it was
+ 
+
+ align:start position:0%
+but at this time I you know I I it was
+kind of pretty satisfying that if you
+
+ align:start position:0%
+kind of pretty satisfying that if you
+ 
+
+ align:start position:0%
+kind of pretty satisfying that if you
+eyeball this looks like a straight line
+
+ align:start position:0%
+eyeball this looks like a straight line
+ 
+
+ align:start position:0%
+eyeball this looks like a straight line
+this looks like an increasing line
+
+ align:start position:0%
+this looks like an increasing line
+ 
+
+ align:start position:0%
+this looks like an increasing line
+and that's what we would expect so
+
+ align:start position:0%
+and that's what we would expect so
+ 
+
+ align:start position:0%
+and that's what we would expect so
+that's on College
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+once we have uh found this we can say
+
+ align:start position:0%
+once we have uh found this we can say
+ 
+
+ align:start position:0%
+once we have uh found this we can say
+well now that I have convinced myself
+
+ align:start position:0%
+well now that I have convinced myself
+ 
+
+ align:start position:0%
+well now that I have convinced myself
+that this is in fact zero
+
+ align:start position:0%
+that this is in fact zero
+ 
+
+ align:start position:0%
+that this is in fact zero
+I can impose it which gives me a large
+
+ align:start position:0%
+I can impose it which gives me a large
+ 
+
+ align:start position:0%
+I can impose it which gives me a large
+control cohort and now I can construct
+
+ align:start position:0%
+control cohort and now I can construct
+ 
+
+ align:start position:0%
+control cohort and now I can construct
+my defend if all with respect to the
+
+ align:start position:0%
+my defend if all with respect to the
+ 
+
+ align:start position:0%
+my defend if all with respect to the
+control cohort so all of this is going
+
+ align:start position:0%
+control cohort so all of this is going
+ 
+
+ align:start position:0%
+control cohort so all of this is going
+to be normalized
+
+ align:start position:0%
+to be normalized
+ 
+
+ align:start position:0%
+to be normalized
+now my nose is having Zero Effect
+
+ align:start position:0%
+now my nose is having Zero Effect
+ 
+
+ align:start position:0%
+now my nose is having Zero Effect
+compared to uh to them
+
+ align:start position:0%
+compared to uh to them
+ 
+
+ align:start position:0%
+compared to uh to them
+and then this is going to be compared to
+
+ align:start position:0%
+and then this is going to be compared to
+ 
+
+ align:start position:0%
+and then this is going to be compared to
+the entire group so someone asked why
+
+ align:start position:0%
+the entire group so someone asked why
+ 
+
+ align:start position:0%
+the entire group so someone asked why
+would you do that well you you do that
+
+ align:start position:0%
+would you do that well you you do that
+ 
+
+ align:start position:0%
+would you do that well you you do that
+because you get much more precise result
+
+ align:start position:0%
+because you get much more precise result
+ 
+
+ align:start position:0%
+because you get much more precise result
+if you have a control group that's much
+
+ align:start position:0%
+if you have a control group that's much
+ 
+
+ align:start position:0%
+if you have a control group that's much
+fat much larger
+
+ align:start position:0%
+fat much larger
+ 
+
+ align:start position:0%
+fat much larger
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+and oh
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so that's what I did in that table uh
+
+ align:start position:0%
+so that's what I did in that table uh
+ 
+
+ align:start position:0%
+so that's what I did in that table uh
+where I still I estimate
+
+ align:start position:0%
+where I still I estimate
+ 
+
+ align:start position:0%
+where I still I estimate
+that's what's done here we are here
+
+ align:start position:0%
+that's what's done here we are here
+ 
+
+ align:start position:0%
+that's what's done here we are here
+running aggression with only a 10 meal
+
+ align:start position:0%
+running aggression with only a 10 meal
+ 
+
+ align:start position:0%
+running aggression with only a 10 meal
+or 11 dummies which are all the people
+
+ align:start position:0%
+or 11 dummies which are all the people
+ 
+
+ align:start position:0%
+or 11 dummies which are all the people
+treated and there are various treatment
+
+ align:start position:0%
+treated and there are various treatment
+ 
+
+ align:start position:0%
+treated and there are various treatment
+effects as they each
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh and then once we've done it for wages
+
+ align:start position:0%
+uh and then once we've done it for wages
+ 
+
+ align:start position:0%
+uh and then once we've done it for wages
+we can also for Education we can also do
+
+ align:start position:0%
+we can also for Education we can also do
+ 
+
+ align:start position:0%
+we can also for Education we can also do
+it for wages which will lead to what
+
+ align:start position:0%
+it for wages which will lead to what
+ 
+
+ align:start position:0%
+it for wages which will lead to what
+we'll discuss next time for the
+
+ align:start position:0%
+we'll discuss next time for the
+ 
+
+ align:start position:0%
+we'll discuss next time for the
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+so that's all nice uh this is a very
+
+ align:start position:0%
+so that's all nice uh this is a very
+ 
+
+ align:start position:0%
+so that's all nice uh this is a very
+typical example of a different div
+
+ align:start position:0%
+typical example of a different div
+ 
+
+ align:start position:0%
+typical example of a different div
+two-way fixed effect that have become
+
+ align:start position:0%
+two-way fixed effect that have become
+ 
+
+ align:start position:0%
+two-way fixed effect that have become
+super popular in applied economics and
+
+ align:start position:0%
+super popular in applied economics and
+ 
+
+ align:start position:0%
+super popular in applied economics and
+you're gonna keep seeing them this one
+
+ align:start position:0%
+you're gonna keep seeing them this one
+ 
+
+ align:start position:0%
+you're gonna keep seeing them this one
+is a simple one because everyone got
+
+ align:start position:0%
+is a simple one because everyone got
+ 
+
+ align:start position:0%
+is a simple one because everyone got
+treated at the same time
+
+ align:start position:0%
+treated at the same time
+ 
+
+ align:start position:0%
+treated at the same time
+the only kind of complication is that
+
+ align:start position:0%
+the only kind of complication is that
+ 
+
+ align:start position:0%
+the only kind of complication is that
+the the effect that the treatment is
+
+ align:start position:0%
+the the effect that the treatment is
+ 
+
+ align:start position:0%
+the the effect that the treatment is
+introduced progressively
+
+ align:start position:0%
+introduced progressively
+ 
+
+ align:start position:0%
+introduced progressively
+so we would not expect
+
+ align:start position:0%
+so we would not expect
+ 
+
+ align:start position:0%
+so we would not expect
+no effect and then a program effect
+
+ align:start position:0%
+no effect and then a program effect
+ 
+
+ align:start position:0%
+no effect and then a program effect
+because we expect the treatment itself
+
+ align:start position:0%
+because we expect the treatment itself
+ 
+
+ align:start position:0%
+because we expect the treatment itself
+the intensity keeps increasing so the
+
+ align:start position:0%
+the intensity keeps increasing so the
+ 
+
+ align:start position:0%
+the intensity keeps increasing so the
+impact should also keep increasing
+
+ align:start position:0%
+impact should also keep increasing
+ 
+
+ align:start position:0%
+impact should also keep increasing
+there are also many cases where states
+
+ align:start position:0%
+there are also many cases where states
+ 
+
+ align:start position:0%
+there are also many cases where states
+are adopting policies in a staggered
+
+ align:start position:0%
+are adopting policies in a staggered
+ 
+
+ align:start position:0%
+are adopting policies in a staggered
+fashion or regions are adopting a policy
+
+ align:start position:0%
+fashion or regions are adopting a policy
+ 
+
+ align:start position:0%
+fashion or regions are adopting a policy
+in a staggered fashion so for example
+
+ align:start position:0%
+in a staggered fashion so for example
+ 
+
+ align:start position:0%
+in a staggered fashion so for example
+[Music]
+
+ align:start position:0%
+[Music]
+ 
+
+ align:start position:0%
+[Music]
+you could have a a you know changes the
+
+ align:start position:0%
+you could have a a you know changes the
+ 
+
+ align:start position:0%
+you could have a a you know changes the
+minimum minimum wage laws that one State
+
+ align:start position:0%
+minimum minimum wage laws that one State
+ 
+
+ align:start position:0%
+minimum minimum wage laws that one State
+uh a post and then another one and then
+
+ align:start position:0%
+uh a post and then another one and then
+ 
+
+ align:start position:0%
+uh a post and then another one and then
+another one and another one and then you
+
+ align:start position:0%
+another one and another one and then you
+ 
+
+ align:start position:0%
+another one and another one and then you
+have you you can also compare even in
+
+ align:start position:0%
+have you you can also compare even in
+ 
+
+ align:start position:0%
+have you you can also compare even in
+these settings even if everyone
+
+ align:start position:0%
+these settings even if everyone
+ 
+
+ align:start position:0%
+these settings even if everyone
+eventually adopts you can still estimate
+
+ align:start position:0%
+eventually adopts you can still estimate
+ 
+
+ align:start position:0%
+eventually adopts you can still estimate
+the impact of the policy by comparing
+
+ align:start position:0%
+the impact of the policy by comparing
+ 
+
+ align:start position:0%
+the impact of the policy by comparing
+for example people who haven't adopted
+
+ align:start position:0%
+for example people who haven't adopted
+ 
+
+ align:start position:0%
+for example people who haven't adopted
+yet that people to people who
+
+ align:start position:0%
+yet that people to people who
+ 
+
+ align:start position:0%
+yet that people to people who
+to people who have already adopted and
+
+ align:start position:0%
+to people who have already adopted and
+ 
+
+ align:start position:0%
+to people who have already adopted and
+that group keeps changing over time
+
+ align:start position:0%
+that group keeps changing over time
+ 
+
+ align:start position:0%
+that group keeps changing over time
+so in this setting so that's called the
+
+ align:start position:0%
+so in this setting so that's called the
+ 
+
+ align:start position:0%
+so in this setting so that's called the
+staggered the staggered design this is a
+
+ align:start position:0%
+staggered the staggered design this is a
+ 
+
+ align:start position:0%
+staggered the staggered design this is a
+one time one shot the policy starts
+
+ align:start position:0%
+one time one shot the policy starts
+ 
+
+ align:start position:0%
+one time one shot the policy starts
+that's those examples are staggered
+
+ align:start position:0%
+that's those examples are staggered
+ 
+
+ align:start position:0%
+that's those examples are staggered
+design and there is a whole literature
+
+ align:start position:0%
+design and there is a whole literature
+ 
+
+ align:start position:0%
+design and there is a whole literature
+for how to do these things right a first
+
+ align:start position:0%
+for how to do these things right a first
+ 
+
+ align:start position:0%
+for how to do these things right a first
+thing we staggered design is that you
+
+ align:start position:0%
+thing we staggered design is that you
+ 
+
+ align:start position:0%
+thing we staggered design is that you
+you want to to uh um
+
+ align:start position:0%
+you want to to uh um
+ 
+
+ align:start position:0%
+you want to to uh um
+put them in the right place you want to
+
+ align:start position:0%
+put them in the right place you want to
+ 
+
+ align:start position:0%
+put them in the right place you want to
+relabel them such that zero is the
+
+ align:start position:0%
+relabel them such that zero is the
+ 
+
+ align:start position:0%
+relabel them such that zero is the
+beginning of the
+
+ align:start position:0%
+beginning of the
+ 
+
+ align:start position:0%
+beginning of the
+of time is that you know it's a time
+
+ align:start position:0%
+of time is that you know it's a time
+ 
+
+ align:start position:0%
+of time is that you know it's a time
+where a particular State introduces the
+
+ align:start position:0%
+where a particular State introduces the
+ 
+
+ align:start position:0%
+where a particular State introduces the
+the policy and everything is
+
+ align:start position:0%
+the policy and everything is
+ 
+
+ align:start position:0%
+the policy and everything is
+you will draw your event study graph
+
+ align:start position:0%
+you will draw your event study graph
+ 
+
+ align:start position:0%
+you will draw your event study graph
+not in calendar time
+
+ align:start position:0%
+not in calendar time
+ 
+
+ align:start position:0%
+not in calendar time
+but in a
+
+ align:start position:0%
+but in a
+ 
+
+ align:start position:0%
+but in a
+pre and push the event time
+
+ align:start position:0%
+pre and push the event time
+ 
+
+ align:start position:0%
+pre and push the event time
+event being the policies being adopted
+
+ align:start position:0%
+event being the policies being adopted
+ 
+
+ align:start position:0%
+event being the policies being adopted
+in a particular place does that make
+
+ align:start position:0%
+in a particular place does that make
+ 
+
+ align:start position:0%
+in a particular place does that make
+sense
+
+ align:start position:0%
+sense
+ 
+
+ align:start position:0%
+sense
+I mentioned that because I'm going to
+
+ align:start position:0%
+I mentioned that because I'm going to
+ 
+
+ align:start position:0%
+I mentioned that because I'm going to
+show you an event studies graph before
+
+ align:start position:0%
+show you an event studies graph before
+ 
+
+ align:start position:0%
+show you an event studies graph before
+I'm going to understand what it means
+
+ align:start position:0%
+I'm going to understand what it means
+ 
+
+ align:start position:0%
+I'm going to understand what it means
+when the policies are staggered
+
+ align:start position:0%
+when the policies are staggered
+ 
+
+ align:start position:0%
+when the policies are staggered
+so there is an active literature on how
+
+ align:start position:0%
+so there is an active literature on how
+ 
+
+ align:start position:0%
+so there is an active literature on how
+to do it right which means that this
+
+ align:start position:0%
+to do it right which means that this
+ 
+
+ align:start position:0%
+to do it right which means that this
+paper is you know
+
+ align:start position:0%
+paper is you know
+ 
+
+ align:start position:0%
+paper is you know
+not right anymore fortunately it's the
+
+ align:start position:0%
+not right anymore fortunately it's the
+ 
+
+ align:start position:0%
+not right anymore fortunately it's the
+finding you are still mostly right but
+
+ align:start position:0%
+finding you are still mostly right but
+ 
+
+ align:start position:0%
+finding you are still mostly right but
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+there is a lot of things you would do
+
+ align:start position:0%
+there is a lot of things you would do
+ 
+
+ align:start position:0%
+there is a lot of things you would do
+differently first of all is the standard
+
+ align:start position:0%
+differently first of all is the standard
+ 
+
+ align:start position:0%
+differently first of all is the standard
+error
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+so we discussed at some point very
+
+ align:start position:0%
+so we discussed at some point very
+ 
+
+ align:start position:0%
+so we discussed at some point very
+briefly the idea of clustering standard
+
+ align:start position:0%
+briefly the idea of clustering standard
+ 
+
+ align:start position:0%
+briefly the idea of clustering standard
+errors so at the minimum
+
+ align:start position:0%
+errors so at the minimum
+ 
+
+ align:start position:0%
+errors so at the minimum
+how would you cluster the standard there
+
+ align:start position:0%
+how would you cluster the standard there
+ 
+
+ align:start position:0%
+how would you cluster the standard there
+are in a in a different div program like
+
+ align:start position:0%
+are in a in a different div program like
+ 
+
+ align:start position:0%
+are in a in a different div program like
+this one where you have individual
+
+ align:start position:0%
+this one where you have individual
+ 
+
+ align:start position:0%
+this one where you have individual
+detail but the pro the treatment the
+
+ align:start position:0%
+detail but the pro the treatment the
+ 
+
+ align:start position:0%
+detail but the pro the treatment the
+program is allocated at the district
+
+ align:start position:0%
+program is allocated at the district
+ 
+
+ align:start position:0%
+program is allocated at the district
+level
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+[Music]
+
+ align:start position:0%
+[Music]
+ 
+
+ align:start position:0%
+[Music]
+at the minimum you want to Cluster the
+
+ align:start position:0%
+at the minimum you want to Cluster the
+ 
+
+ align:start position:0%
+at the minimum you want to Cluster the
+districts of caboopa 10 times here
+
+ align:start position:0%
+districts of caboopa 10 times here
+ 
+
+ align:start position:0%
+districts of caboopa 10 times here
+and that because that's where you know
+
+ align:start position:0%
+and that because that's where you know
+ 
+
+ align:start position:0%
+and that because that's where you know
+everyone
+
+ align:start position:0%
+everyone
+ 
+
+ align:start position:0%
+everyone
+in a particular District in a particular
+
+ align:start position:0%
+in a particular District in a particular
+ 
+
+ align:start position:0%
+in a particular District in a particular
+year is has the same number of schools
+
+ align:start position:0%
+year is has the same number of schools
+ 
+
+ align:start position:0%
+year is has the same number of schools
+so that's one
+
+ align:start position:0%
+so that's one
+ 
+
+ align:start position:0%
+so that's one
+which is not done in that people but
+
+ align:start position:0%
+which is not done in that people but
+ 
+
+ align:start position:0%
+which is not done in that people but
+it's easy to do it doesn't change much
+
+ align:start position:0%
+it's easy to do it doesn't change much
+ 
+
+ align:start position:0%
+it's easy to do it doesn't change much
+but could have you know if the outcomes
+
+ align:start position:0%
+but could have you know if the outcomes
+ 
+
+ align:start position:0%
+but could have you know if the outcomes
+between people in a given District here
+
+ align:start position:0%
+between people in a given District here
+ 
+
+ align:start position:0%
+between people in a given District here
+were called
+
+ align:start position:0%
+were called
+ 
+
+ align:start position:0%
+were called
+then uh you need to then there is one
+
+ align:start position:0%
+then uh you need to then there is one
+ 
+
+ align:start position:0%
+then uh you need to then there is one
+more worry
+
+ align:start position:0%
+more worry
+ 
+
+ align:start position:0%
+more worry
+which is that
+
+ align:start position:0%
+which is that
+ 
+
+ align:start position:0%
+which is that
+suppose that instead of having annual
+
+ align:start position:0%
+suppose that instead of having annual
+ 
+
+ align:start position:0%
+suppose that instead of having annual
+data in fact I I think in that data set
+
+ align:start position:0%
+data in fact I I think in that data set
+ 
+
+ align:start position:0%
+data in fact I I think in that data set
+I have people uh exact uh birth date
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so I aggregated it by year of birth
+
+ align:start position:0%
+so I aggregated it by year of birth
+ 
+
+ align:start position:0%
+so I aggregated it by year of birth
+but in truth you know people's months of
+
+ align:start position:0%
+but in truth you know people's months of
+ 
+
+ align:start position:0%
+but in truth you know people's months of
+birth also affected the
+
+ align:start position:0%
+birth also affected the
+ 
+
+ align:start position:0%
+birth also affected the
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+instead of
+
+ align:start position:0%
+instead of
+ 
+
+ align:start position:0%
+instead of
+aggregating instead of having a great
+
+ align:start position:0%
+aggregating instead of having a great
+ 
+
+ align:start position:0%
+aggregating instead of having a great
+aggregating the data running the
+
+ align:start position:0%
+aggregating the data running the
+ 
+
+ align:start position:0%
+aggregating the data running the
+regression at the district time here
+
+ align:start position:0%
+regression at the district time here
+ 
+
+ align:start position:0%
+regression at the district time here
+level I could have said let me run it at
+
+ align:start position:0%
+level I could have said let me run it at
+ 
+
+ align:start position:0%
+level I could have said let me run it at
+the district 10 months
+
+ align:start position:0%
+the district 10 months
+ 
+
+ align:start position:0%
+the district 10 months
+right why not it should be more
+
+ align:start position:0%
+right why not it should be more
+ 
+
+ align:start position:0%
+right why not it should be more
+precisely going to give you more data
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um and suppose that I you know very
+
+ align:start position:0%
+um and suppose that I you know very
+ 
+
+ align:start position:0%
+um and suppose that I you know very
+seriously cluster my standard there are
+
+ align:start position:0%
+seriously cluster my standard there are
+ 
+
+ align:start position:0%
+seriously cluster my standard there are
+at the district a month
+
+ align:start position:0%
+at the district a month
+ 
+
+ align:start position:0%
+at the district a month
+suddenly I have many more clusters than
+
+ align:start position:0%
+suddenly I have many more clusters than
+ 
+
+ align:start position:0%
+suddenly I have many more clusters than
+in District time here so I'm going to
+
+ align:start position:0%
+in District time here so I'm going to
+ 
+
+ align:start position:0%
+in District time here so I'm going to
+get results that should be much more
+
+ align:start position:0%
+get results that should be much more
+ 
+
+ align:start position:0%
+get results that should be much more
+precise does that sound right
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+could move further I could say well I'm
+
+ align:start position:0%
+could move further I could say well I'm
+ 
+
+ align:start position:0%
+could move further I could say well I'm
+going to aggregate at the district time
+
+ align:start position:0%
+going to aggregate at the district time
+ 
+
+ align:start position:0%
+going to aggregate at the district time
+day of birth
+
+ align:start position:0%
+day of birth
+ 
+
+ align:start position:0%
+day of birth
+probably I'm back to you know very small
+
+ align:start position:0%
+probably I'm back to you know very small
+ 
+
+ align:start position:0%
+probably I'm back to you know very small
+clusters now a lot of very small
+
+ align:start position:0%
+clusters now a lot of very small
+ 
+
+ align:start position:0%
+clusters now a lot of very small
+clusters should become very precise
+
+ align:start position:0%
+clusters should become very precise
+ 
+
+ align:start position:0%
+clusters should become very precise
+uh should I want to do that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+what sounds
+
+ align:start position:0%
+what sounds
+ 
+
+ align:start position:0%
+what sounds
+but
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yes
+
+ align:start position:0%
+yes
+ 
+
+ align:start position:0%
+yes
+um you eventually run out of Freedom
+
+ align:start position:0%
+um you eventually run out of Freedom
+ 
+
+ align:start position:0%
+um you eventually run out of Freedom
+degrees with degrees of freedom I don't
+
+ align:start position:0%
+degrees with degrees of freedom I don't
+ 
+
+ align:start position:0%
+degrees with degrees of freedom I don't
+know because I'm not running I'm still
+
+ align:start position:0%
+know because I'm not running I'm still
+ 
+
+ align:start position:0%
+know because I'm not running I'm still
+running exactly the same regression so
+
+ align:start position:0%
+running exactly the same regression so
+ 
+
+ align:start position:0%
+running exactly the same regression so
+in term of the number of or I'm going to
+
+ align:start position:0%
+in term of the number of or I'm going to
+ 
+
+ align:start position:0%
+in term of the number of or I'm going to
+have more dummies for a day of birth and
+
+ align:start position:0%
+have more dummies for a day of birth and
+ 
+
+ align:start position:0%
+have more dummies for a day of birth and
+but that's not a new problem because I
+
+ align:start position:0%
+but that's not a new problem because I
+ 
+
+ align:start position:0%
+but that's not a new problem because I
+also have a lot of observations not have
+
+ align:start position:0%
+also have a lot of observations not have
+ 
+
+ align:start position:0%
+also have a lot of observations not have
+treated and control people inside the
+
+ align:start position:0%
+treated and control people inside the
+ 
+
+ align:start position:0%
+treated and control people inside the
+same cluster yeah I could have very
+
+ align:start position:0%
+same cluster yeah I could have very
+ 
+
+ align:start position:0%
+same cluster yeah I could have very
+small clusters but that's fine I'm going
+
+ align:start position:0%
+small clusters but that's fine I'm going
+ 
+
+ align:start position:0%
+small clusters but that's fine I'm going
+to have the smaller cluster the better
+
+ align:start position:0%
+to have the smaller cluster the better
+ 
+
+ align:start position:0%
+to have the smaller cluster the better
+per se
+
+ align:start position:0%
+per se
+ 
+
+ align:start position:0%
+per se
+[Music]
+
+ align:start position:0%
+[Music]
+ 
+
+ align:start position:0%
+[Music]
+exactly it sounds a bit like a
+
+ align:start position:0%
+exactly it sounds a bit like a
+ 
+
+ align:start position:0%
+exactly it sounds a bit like a
+manufacturing data I'm not manufacturing
+
+ align:start position:0%
+manufacturing data I'm not manufacturing
+ 
+
+ align:start position:0%
+manufacturing data I'm not manufacturing
+detail because the number of
+
+ align:start position:0%
+detail because the number of
+ 
+
+ align:start position:0%
+detail because the number of
+observations will be the same but I'm
+
+ align:start position:0%
+observations will be the same but I'm
+ 
+
+ align:start position:0%
+observations will be the same but I'm
+reducing the cluster size we agreed that
+
+ align:start position:0%
+reducing the cluster size we agreed that
+ 
+
+ align:start position:0%
+reducing the cluster size we agreed that
+I needed to Cluster the level of the
+
+ align:start position:0%
+I needed to Cluster the level of the
+ 
+
+ align:start position:0%
+I needed to Cluster the level of the
+unit of the treatment and we said well
+
+ align:start position:0%
+unit of the treatment and we said well
+ 
+
+ align:start position:0%
+unit of the treatment and we said well
+that's about that year time district and
+
+ align:start position:0%
+that's about that year time district and
+ 
+
+ align:start position:0%
+that's about that year time district and
+then now I'm making it well year times
+
+ align:start position:0%
+then now I'm making it well year times
+ 
+
+ align:start position:0%
+then now I'm making it well year times
+months time this trick so I have more
+
+ align:start position:0%
+months time this trick so I have more
+ 
+
+ align:start position:0%
+months time this trick so I have more
+cluster basically more effective
+
+ align:start position:0%
+cluster basically more effective
+ 
+
+ align:start position:0%
+cluster basically more effective
+observation
+
+ align:start position:0%
+observation
+ 
+
+ align:start position:0%
+observation
+sounds like a
+
+ align:start position:0%
+sounds like a
+ 
+
+ align:start position:0%
+sounds like a
+I'm creating precision
+
+ align:start position:0%
+I'm creating precision
+ 
+
+ align:start position:0%
+I'm creating precision
+that seems too good to be true and the
+
+ align:start position:0%
+that seems too good to be true and the
+ 
+
+ align:start position:0%
+that seems too good to be true and the
+issue is that
+
+ align:start position:0%
+issue is that
+ 
+
+ align:start position:0%
+issue is that
+the treatment is very correlated by your
+
+ align:start position:0%
+the treatment is very correlated by your
+ 
+
+ align:start position:0%
+the treatment is very correlated by your
+year of birth
+
+ align:start position:0%
+year of birth
+ 
+
+ align:start position:0%
+year of birth
+in particular someone born in February
+
+ align:start position:0%
+in particular someone born in February
+ 
+
+ align:start position:0%
+in particular someone born in February
+or March is treated almost the same
+
+ align:start position:0%
+or March is treated almost the same
+ 
+
+ align:start position:0%
+or March is treated almost the same
+right their level of treatment is almost
+
+ align:start position:0%
+right their level of treatment is almost
+ 
+
+ align:start position:0%
+right their level of treatment is almost
+the same
+
+ align:start position:0%
+the same
+ 
+
+ align:start position:0%
+the same
+so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that would in and of itself be fine
+
+ align:start position:0%
+that would in and of itself be fine
+ 
+
+ align:start position:0%
+that would in and of itself be fine
+except that their outcomes might also be
+
+ align:start position:0%
+except that their outcomes might also be
+ 
+
+ align:start position:0%
+except that their outcomes might also be
+correlated because they are in the state
+
+ align:start position:0%
+correlated because they are in the state
+ 
+
+ align:start position:0%
+correlated because they are in the state
+you know they are in a labor market
+
+ align:start position:0%
+you know they are in a labor market
+ 
+
+ align:start position:0%
+you know they are in a labor market
+roughly at the same time Etc so yeah
+
+ align:start position:0%
+roughly at the same time Etc so yeah
+ 
+
+ align:start position:0%
+roughly at the same time Etc so yeah
+what if it's I guess it's a similar
+
+ align:start position:0%
+what if it's I guess it's a similar
+ 
+
+ align:start position:0%
+what if it's I guess it's a similar
+scenario what if we observe multiple
+
+ align:start position:0%
+scenario what if we observe multiple
+ 
+
+ align:start position:0%
+scenario what if we observe multiple
+observations of the same person yeah
+
+ align:start position:0%
+observations of the same person yeah
+ 
+
+ align:start position:0%
+observations of the same person yeah
+likewise if we observe multiple
+
+ align:start position:0%
+likewise if we observe multiple
+ 
+
+ align:start position:0%
+likewise if we observe multiple
+observation of the same person we
+
+ align:start position:0%
+observation of the same person we
+ 
+
+ align:start position:0%
+observation of the same person we
+wouldn't want to treat them as
+
+ align:start position:0%
+wouldn't want to treat them as
+ 
+
+ align:start position:0%
+wouldn't want to treat them as
+individual observations
+
+ align:start position:0%
+individual observations
+ 
+
+ align:start position:0%
+individual observations
+exactly so the question in that case we
+
+ align:start position:0%
+exactly so the question in that case we
+ 
+
+ align:start position:0%
+exactly so the question in that case we
+would cluster by individual we would say
+
+ align:start position:0%
+would cluster by individual we would say
+ 
+
+ align:start position:0%
+would cluster by individual we would say
+you know they all come from the same
+
+ align:start position:0%
+you know they all come from the same
+ 
+
+ align:start position:0%
+you know they all come from the same
+person we would either make an
+
+ align:start position:0%
+person we would either make an
+ 
+
+ align:start position:0%
+person we would either make an
+assumption about how what the time
+
+ align:start position:0%
+assumption about how what the time
+ 
+
+ align:start position:0%
+assumption about how what the time
+series of this error is
+
+ align:start position:0%
+series of this error is
+ 
+
+ align:start position:0%
+series of this error is
+or we would just cluster by individuals
+
+ align:start position:0%
+or we would just cluster by individuals
+ 
+
+ align:start position:0%
+or we would just cluster by individuals
+saying I'm acknowledging that a rule
+
+ align:start position:0%
+saying I'm acknowledging that a rule
+ 
+
+ align:start position:0%
+saying I'm acknowledging that a rule
+coming from the same individually are
+
+ align:start position:0%
+coming from the same individually are
+ 
+
+ align:start position:0%
+coming from the same individually are
+not independent observation therefore I
+
+ align:start position:0%
+not independent observation therefore I
+ 
+
+ align:start position:0%
+not independent observation therefore I
+need to take that into account in my
+
+ align:start position:0%
+need to take that into account in my
+ 
+
+ align:start position:0%
+need to take that into account in my
+standard level similarly for people who
+
+ align:start position:0%
+standard level similarly for people who
+ 
+
+ align:start position:0%
+standard level similarly for people who
+live in the same district here we say
+
+ align:start position:0%
+live in the same district here we say
+ 
+
+ align:start position:0%
+live in the same district here we say
+well I live together they do a lot of
+
+ align:start position:0%
+well I live together they do a lot of
+ 
+
+ align:start position:0%
+well I live together they do a lot of
+thing in common
+
+ align:start position:0%
+thing in common
+ 
+
+ align:start position:0%
+thing in common
+we need to Cluster at that level because
+
+ align:start position:0%
+we need to Cluster at that level because
+ 
+
+ align:start position:0%
+we need to Cluster at that level because
+the treatment is also clustered at that
+
+ align:start position:0%
+the treatment is also clustered at that
+ 
+
+ align:start position:0%
+the treatment is also clustered at that
+level
+
+ align:start position:0%
+level
+ 
+
+ align:start position:0%
+level
+and then similarly as you both are
+
+ align:start position:0%
+and then similarly as you both are
+ 
+
+ align:start position:0%
+and then similarly as you both are
+getting to
+
+ align:start position:0%
+getting to
+ 
+
+ align:start position:0%
+getting to
+um people who are
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+living in in who are from the same year
+
+ align:start position:0%
+living in in who are from the same year
+ 
+
+ align:start position:0%
+living in in who are from the same year
+of birth or similar years of very
+
+ align:start position:0%
+of birth or similar years of very
+ 
+
+ align:start position:0%
+of birth or similar years of very
+similar months of birth I've experienced
+
+ align:start position:0%
+similar months of birth I've experienced
+ 
+
+ align:start position:0%
+similar months of birth I've experienced
+similar education condition labor market
+
+ align:start position:0%
+similar education condition labor market
+ 
+
+ align:start position:0%
+similar education condition labor market
+condition the outcomes likely to be
+
+ align:start position:0%
+condition the outcomes likely to be
+ 
+
+ align:start position:0%
+condition the outcomes likely to be
+correlated and their treatment is very
+
+ align:start position:0%
+correlated and their treatment is very
+ 
+
+ align:start position:0%
+correlated and their treatment is very
+polluted in fact with defend if it's
+
+ align:start position:0%
+polluted in fact with defend if it's
+ 
+
+ align:start position:0%
+polluted in fact with defend if it's
+really extreme because once someone is
+
+ align:start position:0%
+really extreme because once someone is
+ 
+
+ align:start position:0%
+really extreme because once someone is
+treated they're still treated forever
+
+ align:start position:0%
+treated they're still treated forever
+ 
+
+ align:start position:0%
+treated they're still treated forever
+and therefore there is a mechanical very
+
+ align:start position:0%
+and therefore there is a mechanical very
+ 
+
+ align:start position:0%
+and therefore there is a mechanical very
+strong correlation between treatment
+
+ align:start position:0%
+strong correlation between treatment
+ 
+
+ align:start position:0%
+strong correlation between treatment
+status of people who are who are born in
+
+ align:start position:0%
+status of people who are who are born in
+ 
+
+ align:start position:0%
+status of people who are who are born in
+in related years
+
+ align:start position:0%
+in related years
+ 
+
+ align:start position:0%
+in related years
+because it's not it doesn't go off on
+
+ align:start position:0%
+because it's not it doesn't go off on
+ 
+
+ align:start position:0%
+because it's not it doesn't go off on
+and off therefore we need to take that
+
+ align:start position:0%
+and off therefore we need to take that
+ 
+
+ align:start position:0%
+and off therefore we need to take that
+serial correlation over time into
+
+ align:start position:0%
+serial correlation over time into
+ 
+
+ align:start position:0%
+serial correlation over time into
+account the simplest way is to do
+
+ align:start position:0%
+account the simplest way is to do
+ 
+
+ align:start position:0%
+account the simplest way is to do
+exactly what you're saying which is
+
+ align:start position:0%
+exactly what you're saying which is
+ 
+
+ align:start position:0%
+exactly what you're saying which is
+instead of clustering at the district
+
+ align:start position:0%
+instead of clustering at the district
+ 
+
+ align:start position:0%
+instead of clustering at the district
+times here level we are going to
+
+ align:start position:0%
+times here level we are going to
+ 
+
+ align:start position:0%
+times here level we are going to
+District we're going to Cluster at the
+
+ align:start position:0%
+District we're going to Cluster at the
+ 
+
+ align:start position:0%
+District we're going to Cluster at the
+district level
+
+ align:start position:0%
+district level
+ 
+
+ align:start position:0%
+district level
+to take into account the Coalition in
+
+ align:start position:0%
+to take into account the Coalition in
+ 
+
+ align:start position:0%
+to take into account the Coalition in
+the outcomes of people who live in the
+
+ align:start position:0%
+the outcomes of people who live in the
+ 
+
+ align:start position:0%
+the outcomes of people who live in the
+same district in abundant different here
+
+ align:start position:0%
+same district in abundant different here
+ 
+
+ align:start position:0%
+same district in abundant different here
+the clustering so the condition is not
+
+ align:start position:0%
+the clustering so the condition is not
+ 
+
+ align:start position:0%
+the clustering so the condition is not
+one and but the clustering let you know
+
+ align:start position:0%
+one and but the clustering let you know
+ 
+
+ align:start position:0%
+one and but the clustering let you know
+we let the data figure out roughly what
+
+ align:start position:0%
+we let the data figure out roughly what
+ 
+
+ align:start position:0%
+we let the data figure out roughly what
+it is unless we have very few clusters
+
+ align:start position:0%
+it is unless we have very few clusters
+ 
+
+ align:start position:0%
+it is unless we have very few clusters
+in which case you start you need to do
+
+ align:start position:0%
+in which case you start you need to do
+ 
+
+ align:start position:0%
+in which case you start you need to do
+other things yeah and if you have data
+
+ align:start position:0%
+other things yeah and if you have data
+ 
+
+ align:start position:0%
+other things yeah and if you have data
+like monthly data of the construction of
+
+ align:start position:0%
+like monthly data of the construction of
+ 
+
+ align:start position:0%
+like monthly data of the construction of
+schools would it make sense to have
+
+ align:start position:0%
+schools would it make sense to have
+ 
+
+ align:start position:0%
+schools would it make sense to have
+clusters that depend on the time as well
+
+ align:start position:0%
+clusters that depend on the time as well
+ 
+
+ align:start position:0%
+clusters that depend on the time as well
+yes you could you could do that you
+
+ align:start position:0%
+yes you could you could do that you
+ 
+
+ align:start position:0%
+yes you could you could do that you
+could say if you had monthly data on
+
+ align:start position:0%
+could say if you had monthly data on
+ 
+
+ align:start position:0%
+could say if you had monthly data on
+school construction you would have your
+
+ align:start position:0%
+school construction you would have your
+ 
+
+ align:start position:0%
+school construction you would have your
+treatment defined and a month time place
+
+ align:start position:0%
+treatment defined and a month time place
+ 
+
+ align:start position:0%
+treatment defined and a month time place
+but then you would also want to Cluster
+
+ align:start position:0%
+but then you would also want to Cluster
+ 
+
+ align:start position:0%
+but then you would also want to Cluster
+the place level because for sure there
+
+ align:start position:0%
+the place level because for sure there
+ 
+
+ align:start position:0%
+the place level because for sure there
+is a lot of photo correlation in the
+
+ align:start position:0%
+is a lot of photo correlation in the
+ 
+
+ align:start position:0%
+is a lot of photo correlation in the
+number of schools constructed because it
+
+ align:start position:0%
+number of schools constructed because it
+ 
+
+ align:start position:0%
+number of schools constructed because it
+keeps going up it doesn't go down and
+
+ align:start position:0%
+keeps going up it doesn't go down and
+ 
+
+ align:start position:0%
+keeps going up it doesn't go down and
+the outcomes might also be correlated
+
+ align:start position:0%
+the outcomes might also be correlated
+ 
+
+ align:start position:0%
+the outcomes might also be correlated
+for people in similar times
+
+ align:start position:0%
+for people in similar times
+ 
+
+ align:start position:0%
+for people in similar times
+so that's the first thing we have to do
+
+ align:start position:0%
+so that's the first thing we have to do
+ 
+
+ align:start position:0%
+so that's the first thing we have to do
+that is we've known yeah put it also I
+
+ align:start position:0%
+that is we've known yeah put it also I
+ 
+
+ align:start position:0%
+that is we've known yeah put it also I
+mean this would still be I think you
+
+ align:start position:0%
+mean this would still be I think you
+ 
+
+ align:start position:0%
+mean this would still be I think you
+would still have our approach that you
+
+ align:start position:0%
+would still have our approach that you
+ 
+
+ align:start position:0%
+would still have our approach that you
+can handle once you considering the
+
+ align:start position:0%
+can handle once you considering the
+ 
+
+ align:start position:0%
+can handle once you considering the
+district level but would it be like
+
+ align:start position:0%
+district level but would it be like
+ 
+
+ align:start position:0%
+district level but would it be like
+slightly more promoting calendar year to
+
+ align:start position:0%
+slightly more promoting calendar year to
+ 
+
+ align:start position:0%
+slightly more promoting calendar year to
+use like uh school year so you're
+
+ align:start position:0%
+use like uh school year so you're
+ 
+
+ align:start position:0%
+use like uh school year so you're
+getting much closer Born Into the same
+
+ align:start position:0%
+getting much closer Born Into the same
+ 
+
+ align:start position:0%
+getting much closer Born Into the same
+uh school year yeah you could have a bit
+
+ align:start position:0%
+uh school year yeah you could have a bit
+ 
+
+ align:start position:0%
+uh school year yeah you could have a bit
+more Precision that maybe if you and you
+
+ align:start position:0%
+more Precision that maybe if you and you
+ 
+
+ align:start position:0%
+more Precision that maybe if you and you
+you could you could try playing with
+
+ align:start position:0%
+you could you could try playing with
+ 
+
+ align:start position:0%
+you could you could try playing with
+that I do think the
+
+ align:start position:0%
+that I do think the
+ 
+
+ align:start position:0%
+that I do think the
+calendar
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+in this particular instance but I'm not
+
+ align:start position:0%
+in this particular instance but I'm not
+ 
+
+ align:start position:0%
+in this particular instance but I'm not
+positive yes but that so that doesn't
+
+ align:start position:0%
+positive yes but that so that doesn't
+ 
+
+ align:start position:0%
+positive yes but that so that doesn't
+that's not about it's not just another
+
+ align:start position:0%
+that's not about it's not just another
+ 
+
+ align:start position:0%
+that's not about it's not just another
+problem it's uh Define your treatment in
+
+ align:start position:0%
+problem it's uh Define your treatment in
+ 
+
+ align:start position:0%
+problem it's uh Define your treatment in
+a more precise way so you're going
+
+ align:start position:0%
+a more precise way so you're going
+ 
+
+ align:start position:0%
+a more precise way so you're going
+that's going to give you more precision
+
+ align:start position:0%
+that's going to give you more precision
+ 
+
+ align:start position:0%
+that's going to give you more precision
+uh that is going to be reflected in your
+
+ align:start position:0%
+uh that is going to be reflected in your
+ 
+
+ align:start position:0%
+uh that is going to be reflected in your
+scenario
+
+ align:start position:0%
+scenario
+ 
+
+ align:start position:0%
+scenario
+so first thing
+
+ align:start position:0%
+so first thing
+ 
+
+ align:start position:0%
+so first thing
+that I didn't do that I now know you
+
+ align:start position:0%
+that I didn't do that I now know you
+ 
+
+ align:start position:0%
+that I didn't do that I now know you
+have to Cluster at the at the district
+
+ align:start position:0%
+have to Cluster at the at the district
+ 
+
+ align:start position:0%
+have to Cluster at the at the district
+level and when you do that actually the
+
+ align:start position:0%
+level and when you do that actually the
+ 
+
+ align:start position:0%
+level and when you do that actually the
+the estimates are less because you still
+
+ align:start position:0%
+the estimates are less because you still
+ 
+
+ align:start position:0%
+the estimates are less because you still
+have a significant impact on education
+
+ align:start position:0%
+have a significant impact on education
+ 
+
+ align:start position:0%
+have a significant impact on education
+but the the impact on wages are a bit uh
+
+ align:start position:0%
+but the the impact on wages are a bit uh
+ 
+
+ align:start position:0%
+but the the impact on wages are a bit uh
+I'll be dicey
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+then you have this uh a series of series
+
+ align:start position:0%
+then you have this uh a series of series
+ 
+
+ align:start position:0%
+then you have this uh a series of series
+of people that are much more recent that
+
+ align:start position:0%
+of people that are much more recent that
+ 
+
+ align:start position:0%
+of people that are much more recent that
+you're going to see in the you're going
+
+ align:start position:0%
+you're going to see in the you're going
+ 
+
+ align:start position:0%
+you're going to see in the you're going
+to see more investigation and in the in
+
+ align:start position:0%
+to see more investigation and in the in
+ 
+
+ align:start position:0%
+to see more investigation and in the in
+the Forum set but I'm going to make the
+
+ align:start position:0%
+the Forum set but I'm going to make the
+ 
+
+ align:start position:0%
+the Forum set but I'm going to make the
+list for you these are my understanding
+
+ align:start position:0%
+list for you these are my understanding
+ 
+
+ align:start position:0%
+list for you these are my understanding
+of the people that needs to be read now
+
+ align:start position:0%
+of the people that needs to be read now
+ 
+
+ align:start position:0%
+of the people that needs to be read now
+if you're interested in doing ever doing
+
+ align:start position:0%
+if you're interested in doing ever doing
+ 
+
+ align:start position:0%
+if you're interested in doing ever doing
+an event study or difference in
+
+ align:start position:0%
+an event study or difference in
+ 
+
+ align:start position:0%
+an event study or difference in
+difference in your life
+
+ align:start position:0%
+difference in your life
+ 
+
+ align:start position:0%
+difference in your life
+one is the good vacant point which makes
+
+ align:start position:0%
+one is the good vacant point which makes
+ 
+
+ align:start position:0%
+one is the good vacant point which makes
+this point of uh stacking the data
+
+ align:start position:0%
+this point of uh stacking the data
+ 
+
+ align:start position:0%
+this point of uh stacking the data
+appropriately if the event is staggered
+
+ align:start position:0%
+appropriately if the event is staggered
+ 
+
+ align:start position:0%
+appropriately if the event is staggered
+uh one is so this idea that it's a bit
+
+ align:start position:0%
+uh one is so this idea that it's a bit
+ 
+
+ align:start position:0%
+uh one is so this idea that it's a bit
+loose that oh there is there a pre-trend
+
+ align:start position:0%
+loose that oh there is there a pre-trend
+ 
+
+ align:start position:0%
+loose that oh there is there a pre-trend
+that everybody is testing
+
+ align:start position:0%
+that everybody is testing
+ 
+
+ align:start position:0%
+that everybody is testing
+uh that takes this paper uh takes that
+
+ align:start position:0%
+uh that takes this paper uh takes that
+ 
+
+ align:start position:0%
+uh that takes this paper uh takes that
+idea more seriously in saying first of
+
+ align:start position:0%
+idea more seriously in saying first of
+ 
+
+ align:start position:0%
+idea more seriously in saying first of
+all how would I test for Patron second
+
+ align:start position:0%
+all how would I test for Patron second
+ 
+
+ align:start position:0%
+all how would I test for Patron second
+of all
+
+ align:start position:0%
+of all
+ 
+
+ align:start position:0%
+of all
+you could not reject the patron but they
+
+ align:start position:0%
+you could not reject the patron but they
+ 
+
+ align:start position:0%
+you could not reject the patron but they
+are there anywhere so we we should
+
+ align:start position:0%
+are there anywhere so we we should
+ 
+
+ align:start position:0%
+are there anywhere so we we should
+control for them anyways so it gives you
+
+ align:start position:0%
+control for them anyways so it gives you
+ 
+
+ align:start position:0%
+control for them anyways so it gives you
+some tips for controlling for any
+
+ align:start position:0%
+some tips for controlling for any
+ 
+
+ align:start position:0%
+some tips for controlling for any
+pre-trends
+
+ align:start position:0%
+pre-trends
+ 
+
+ align:start position:0%
+pre-trends
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+this paper is great I'm gonna show you
+
+ align:start position:0%
+this paper is great I'm gonna show you
+ 
+
+ align:start position:0%
+this paper is great I'm gonna show you
+two graph from this paper but it's
+
+ align:start position:0%
+two graph from this paper but it's
+ 
+
+ align:start position:0%
+two graph from this paper but it's
+fantastic that's in your I think
+
+ align:start position:0%
+fantastic that's in your I think
+ 
+
+ align:start position:0%
+fantastic that's in your I think
+eventually probably every everything you
+
+ align:start position:0%
+eventually probably every everything you
+ 
+
+ align:start position:0%
+eventually probably every everything you
+need to know in is in here I'm willing
+
+ align:start position:0%
+need to know in is in here I'm willing
+ 
+
+ align:start position:0%
+need to know in is in here I'm willing
+to bet that that becomes the standard
+
+ align:start position:0%
+to bet that that becomes the standard
+ 
+
+ align:start position:0%
+to bet that that becomes the standard
+and everybody else is forgotten it's a
+
+ align:start position:0%
+and everybody else is forgotten it's a
+ 
+
+ align:start position:0%
+and everybody else is forgotten it's a
+review paper on how to do an event study
+
+ align:start position:0%
+review paper on how to do an event study
+ 
+
+ align:start position:0%
+review paper on how to do an event study
+graph as well as how to control for her
+
+ align:start position:0%
+graph as well as how to control for her
+ 
+
+ align:start position:0%
+graph as well as how to control for her
+for the pre-trend uh and I'll show you
+
+ align:start position:0%
+for the pre-trend uh and I'll show you
+ 
+
+ align:start position:0%
+for the pre-trend uh and I'll show you
+their event study graph we can compare
+
+ align:start position:0%
+their event study graph we can compare
+ 
+
+ align:start position:0%
+their event study graph we can compare
+it to mine
+
+ align:start position:0%
+it to mine
+ 
+
+ align:start position:0%
+it to mine
+but it's a review
+
+ align:start position:0%
+but it's a review
+ 
+
+ align:start position:0%
+but it's a review
+for the annual review or something like
+
+ align:start position:0%
+for the annual review or something like
+ 
+
+ align:start position:0%
+for the annual review or something like
+that so it's very pedagric here it's
+
+ align:start position:0%
+that so it's very pedagric here it's
+ 
+
+ align:start position:0%
+that so it's very pedagric here it's
+well done and there are stata codes to
+
+ align:start position:0%
+well done and there are stata codes to
+ 
+
+ align:start position:0%
+well done and there are stata codes to
+it so my sense is it's your One-Stop
+
+ align:start position:0%
+it so my sense is it's your One-Stop
+ 
+
+ align:start position:0%
+it so my sense is it's your One-Stop
+shop I just found out about it recently
+
+ align:start position:0%
+shop I just found out about it recently
+ 
+
+ align:start position:0%
+shop I just found out about it recently
+otherwise it would be in the in the
+
+ align:start position:0%
+otherwise it would be in the in the
+ 
+
+ align:start position:0%
+otherwise it would be in the in the
+syllabus with three stars
+
+ align:start position:0%
+syllabus with three stars
+ 
+
+ align:start position:0%
+syllabus with three stars
+uh then another issue you might get into
+
+ align:start position:0%
+uh then another issue you might get into
+ 
+
+ align:start position:0%
+uh then another issue you might get into
+is when if the treatment effect are
+
+ align:start position:0%
+is when if the treatment effect are
+ 
+
+ align:start position:0%
+is when if the treatment effect are
+heterogeneous
+
+ align:start position:0%
+heterogeneous
+ 
+
+ align:start position:0%
+heterogeneous
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+then uh what you get from just a simple
+
+ align:start position:0%
+then uh what you get from just a simple
+ 
+
+ align:start position:0%
+then uh what you get from just a simple
+difference in difference in the stack
+
+ align:start position:0%
+difference in difference in the stack
+ 
+
+ align:start position:0%
+difference in difference in the stack
+design is the weighted effect of all the
+
+ align:start position:0%
+design is the weighted effect of all the
+ 
+
+ align:start position:0%
+design is the weighted effect of all the
+treatment effects
+
+ align:start position:0%
+treatment effects
+ 
+
+ align:start position:0%
+treatment effects
+and usually that's fine but if you're
+
+ align:start position:0%
+and usually that's fine but if you're
+ 
+
+ align:start position:0%
+and usually that's fine but if you're
+unlucky some weights could be negative
+
+ align:start position:0%
+unlucky some weights could be negative
+ 
+
+ align:start position:0%
+unlucky some weights could be negative
+in which case you're a bit screwed so
+
+ align:start position:0%
+in which case you're a bit screwed so
+ 
+
+ align:start position:0%
+in which case you're a bit screwed so
+there is some work uh to correct for
+
+ align:start position:0%
+there is some work uh to correct for
+ 
+
+ align:start position:0%
+there is some work uh to correct for
+that construct the right standard there
+
+ align:start position:0%
+that construct the right standard there
+ 
+
+ align:start position:0%
+that construct the right standard there
+are
+
+ align:start position:0%
+are
+ 
+
+ align:start position:0%
+are
+um it's an issue uh probably to check I
+
+ align:start position:0%
+um it's an issue uh probably to check I
+ 
+
+ align:start position:0%
+um it's an issue uh probably to check I
+would in my sense probably less of a
+
+ align:start position:0%
+would in my sense probably less of a
+ 
+
+ align:start position:0%
+would in my sense probably less of a
+central issue than than doing that
+
+ align:start position:0%
+central issue than than doing that
+ 
+
+ align:start position:0%
+central issue than than doing that
+properly so here is their sort of
+
+ align:start position:0%
+properly so here is their sort of
+ 
+
+ align:start position:0%
+properly so here is their sort of
+after all of the suggestions have been
+
+ align:start position:0%
+after all of the suggestions have been
+ 
+
+ align:start position:0%
+after all of the suggestions have been
+implemented
+
+ align:start position:0%
+implemented
+ 
+
+ align:start position:0%
+implemented
+um so maybe you don't even need to read
+
+ align:start position:0%
+um so maybe you don't even need to read
+ 
+
+ align:start position:0%
+um so maybe you don't even need to read
+the paper you can refer to this very
+
+ align:start position:0%
+the paper you can refer to this very
+ 
+
+ align:start position:0%
+the paper you can refer to this very
+year
+
+ align:start position:0%
+year
+ 
+
+ align:start position:0%
+year
+neat summary of it I do think you should
+
+ align:start position:0%
+neat summary of it I do think you should
+ 
+
+ align:start position:0%
+neat summary of it I do think you should
+read the paper but what do we need to do
+
+ align:start position:0%
+read the paper but what do we need to do
+ 
+
+ align:start position:0%
+read the paper but what do we need to do
+well this is our Advanced study so it's
+
+ align:start position:0%
+well this is our Advanced study so it's
+ 
+
+ align:start position:0%
+well this is our Advanced study so it's
+zero is the point in our case in my my
+
+ align:start position:0%
+zero is the point in our case in my my
+ 
+
+ align:start position:0%
+zero is the point in our case in my my
+case it would be uh 12 in 1974 would be
+
+ align:start position:0%
+case it would be uh 12 in 1974 would be
+ 
+
+ align:start position:0%
+case it would be uh 12 in 1974 would be
+my zero
+
+ align:start position:0%
+my zero
+ 
+
+ align:start position:0%
+my zero
+so what did I do wrong so first of all
+
+ align:start position:0%
+so what did I do wrong so first of all
+ 
+
+ align:start position:0%
+so what did I do wrong so first of all
+let's suggests that it is better to
+
+ align:start position:0%
+let's suggests that it is better to
+ 
+
+ align:start position:0%
+let's suggests that it is better to
+normalize the year before I normalized
+
+ align:start position:0%
+normalize the year before I normalized
+ 
+
+ align:start position:0%
+normalize the year before I normalized
+here at the beginning of my period but
+
+ align:start position:0%
+here at the beginning of my period but
+ 
+
+ align:start position:0%
+here at the beginning of my period but
+of course that doesn't make much sense
+
+ align:start position:0%
+of course that doesn't make much sense
+ 
+
+ align:start position:0%
+of course that doesn't make much sense
+you would want to normalize the year
+
+ align:start position:0%
+you would want to normalize the year
+ 
+
+ align:start position:0%
+you would want to normalize the year
+before the study so I should have used
+
+ align:start position:0%
+before the study so I should have used
+ 
+
+ align:start position:0%
+before the study so I should have used
+as my omitted category people who were
+
+ align:start position:0%
+as my omitted category people who were
+ 
+
+ align:start position:0%
+as my omitted category people who were
+11 in 1972 so you normalize at at -1
+
+ align:start position:0%
+11 in 1972 so you normalize at at -1
+ 
+
+ align:start position:0%
+11 in 1972 so you normalize at at -1
+then I have no confidence interval in
+
+ align:start position:0%
+then I have no confidence interval in
+ 
+
+ align:start position:0%
+then I have no confidence interval in
+any of my graphs actually some of them
+
+ align:start position:0%
+any of my graphs actually some of them
+ 
+
+ align:start position:0%
+any of my graphs actually some of them
+have but not too much so you should have
+
+ align:start position:0%
+have but not too much so you should have
+ 
+
+ align:start position:0%
+have but not too much so you should have
+the confidence interval that everybody
+
+ align:start position:0%
+the confidence interval that everybody
+ 
+
+ align:start position:0%
+the confidence interval that everybody
+is now doing what they suggest adding as
+
+ align:start position:0%
+is now doing what they suggest adding as
+ 
+
+ align:start position:0%
+is now doing what they suggest adding as
+well are these longer this longer
+
+ align:start position:0%
+well are these longer this longer
+ 
+
+ align:start position:0%
+well are these longer this longer
+confidence interval which is a uniform
+
+ align:start position:0%
+confidence interval which is a uniform
+ 
+
+ align:start position:0%
+confidence interval which is a uniform
+confidence band so it takes into account
+
+ align:start position:0%
+confidence band so it takes into account
+ 
+
+ align:start position:0%
+confidence band so it takes into account
+the fact that you are not just testing
+
+ align:start position:0%
+the fact that you are not just testing
+ 
+
+ align:start position:0%
+the fact that you are not just testing
+one by one by one but you are testing
+
+ align:start position:0%
+one by one by one but you are testing
+ 
+
+ align:start position:0%
+one by one by one but you are testing
+all of them
+
+ align:start position:0%
+all of them
+ 
+
+ align:start position:0%
+all of them
+so the standard they are a bit wider
+
+ align:start position:0%
+so the standard they are a bit wider
+ 
+
+ align:start position:0%
+so the standard they are a bit wider
+then here they put the average of all
+
+ align:start position:0%
+then here they put the average of all
+ 
+
+ align:start position:0%
+then here they put the average of all
+these points so it's basically the
+
+ align:start position:0%
+these points so it's basically the
+ 
+
+ align:start position:0%
+these points so it's basically the
+average of your outcome in the it's
+
+ align:start position:0%
+average of your outcome in the it's
+ 
+
+ align:start position:0%
+average of your outcome in the it's
+normalized as zero in the regression but
+
+ align:start position:0%
+normalized as zero in the regression but
+ 
+
+ align:start position:0%
+normalized as zero in the regression but
+it it's not zero of course there is so
+
+ align:start position:0%
+it it's not zero of course there is so
+ 
+
+ align:start position:0%
+it it's not zero of course there is so
+it's an average of your outcome in the
+
+ align:start position:0%
+it's an average of your outcome in the
+ 
+
+ align:start position:0%
+it's an average of your outcome in the
+pre-period so it gives you a sense of
+
+ align:start position:0%
+pre-period so it gives you a sense of
+ 
+
+ align:start position:0%
+pre-period so it gives you a sense of
+magnitude and how the how the magnitude
+
+ align:start position:0%
+magnitude and how the how the magnitude
+ 
+
+ align:start position:0%
+magnitude and how the how the magnitude
+of the point estimated compare
+
+ align:start position:0%
+of the point estimated compare
+ 
+
+ align:start position:0%
+of the point estimated compare
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+what else do they propose they propose
+
+ align:start position:0%
+what else do they propose they propose
+ 
+
+ align:start position:0%
+what else do they propose they propose
+also to uh to plot what you think is the
+
+ align:start position:0%
+also to uh to plot what you think is the
+ 
+
+ align:start position:0%
+also to uh to plot what you think is the
+more restricted model so in this case
+
+ align:start position:0%
+more restricted model so in this case
+ 
+
+ align:start position:0%
+more restricted model so in this case
+the Assumption was that there is an
+
+ align:start position:0%
+the Assumption was that there is an
+ 
+
+ align:start position:0%
+the Assumption was that there is an
+effect there you know there is a
+
+ align:start position:0%
+effect there you know there is a
+ 
+
+ align:start position:0%
+effect there you know there is a
+prepared and then there is
+
+ align:start position:0%
+prepared and then there is
+ 
+
+ align:start position:0%
+prepared and then there is
+an impact so that's the restricted model
+
+ align:start position:0%
+an impact so that's the restricted model
+ 
+
+ align:start position:0%
+an impact so that's the restricted model
+so you can see you know the extent to
+
+ align:start position:0%
+so you can see you know the extent to
+ 
+
+ align:start position:0%
+so you can see you know the extent to
+which there is deviation from that
+
+ align:start position:0%
+which there is deviation from that
+ 
+
+ align:start position:0%
+which there is deviation from that
+restricted model in my case I would have
+
+ align:start position:0%
+restricted model in my case I would have
+ 
+
+ align:start position:0%
+restricted model in my case I would have
+built I would have drawn this
+
+ align:start position:0%
+built I would have drawn this
+ 
+
+ align:start position:0%
+built I would have drawn this
+or in fact I could have drawn something
+
+ align:start position:0%
+or in fact I could have drawn something
+ 
+
+ align:start position:0%
+or in fact I could have drawn something
+somewhere at some point in the paper I
+
+ align:start position:0%
+somewhere at some point in the paper I
+ 
+
+ align:start position:0%
+somewhere at some point in the paper I
+had drawn the number of school built
+
+ align:start position:0%
+had drawn the number of school built
+ 
+
+ align:start position:0%
+had drawn the number of school built
+so you could build you could construct
+
+ align:start position:0%
+so you could build you could construct
+ 
+
+ align:start position:0%
+so you could build you could construct
+for every child how many years of
+
+ align:start position:0%
+for every child how many years of
+ 
+
+ align:start position:0%
+for every child how many years of
+effective school they would enjoy
+
+ align:start position:0%
+effective school they would enjoy
+ 
+
+ align:start position:0%
+effective school they would enjoy
+and that would be your restricted
+
+ align:start position:0%
+and that would be your restricted
+ 
+
+ align:start position:0%
+and that would be your restricted
+effectively effective were only
+
+ align:start position:0%
+effectively effective were only
+ 
+
+ align:start position:0%
+effectively effective were only
+proportional to the number of school
+
+ align:start position:0%
+proportional to the number of school
+ 
+
+ align:start position:0%
+proportional to the number of school
+multiplied by the number of years you
+
+ align:start position:0%
+multiplied by the number of years you
+ 
+
+ align:start position:0%
+multiplied by the number of years you
+have to enjoy so you could compare it to
+
+ align:start position:0%
+have to enjoy so you could compare it to
+ 
+
+ align:start position:0%
+have to enjoy so you could compare it to
+the the shape of the coefficient that
+
+ align:start position:0%
+the the shape of the coefficient that
+ 
+
+ align:start position:0%
+the the shape of the coefficient that
+makes it easier for the reader to do
+
+ align:start position:0%
+makes it easier for the reader to do
+ 
+
+ align:start position:0%
+makes it easier for the reader to do
+that
+
+ align:start position:0%
+that
+ 
+
+ align:start position:0%
+that
+finally you could introduce you could
+
+ align:start position:0%
+finally you could introduce you could
+ 
+
+ align:start position:0%
+finally you could introduce you could
+put in the legend of the graph
+
+ align:start position:0%
+put in the legend of the graph
+ 
+
+ align:start position:0%
+put in the legend of the graph
+so here the the what they suggesting the
+
+ align:start position:0%
+so here the the what they suggesting the
+ 
+
+ align:start position:0%
+so here the the what they suggesting the
+people but for some reason it's not here
+
+ align:start position:0%
+people but for some reason it's not here
+ 
+
+ align:start position:0%
+people but for some reason it's not here
+it's a p-value of all these guys being
+
+ align:start position:0%
+it's a p-value of all these guys being
+ 
+
+ align:start position:0%
+it's a p-value of all these guys being
+negative
+
+ align:start position:0%
+negative
+ 
+
+ align:start position:0%
+negative
+so here you would not be able to reject
+
+ align:start position:0%
+so here you would not be able to reject
+ 
+
+ align:start position:0%
+so here you would not be able to reject
+I think they are nice and negative so a
+
+ align:start position:0%
+I think they are nice and negative so a
+ 
+
+ align:start position:0%
+I think they are nice and negative so a
+value test of all these things being
+
+ align:start position:0%
+value test of all these things being
+ 
+
+ align:start position:0%
+value test of all these things being
+negative so that's the test a formal
+
+ align:start position:0%
+negative so that's the test a formal
+ 
+
+ align:start position:0%
+negative so that's the test a formal
+test of so it being zero formal test of
+
+ align:start position:0%
+test of so it being zero formal test of
+ 
+
+ align:start position:0%
+test of so it being zero formal test of
+of uh zero quick hand
+
+ align:start position:0%
+of uh zero quick hand
+ 
+
+ align:start position:0%
+of uh zero quick hand
+and then a formal test of the
+
+ align:start position:0%
+and then a formal test of the
+ 
+
+ align:start position:0%
+and then a formal test of the
+restricting model in this case the
+
+ align:start position:0%
+restricting model in this case the
+ 
+
+ align:start position:0%
+restricting model in this case the
+restricted model is that the treatment
+
+ align:start position:0%
+restricted model is that the treatment
+ 
+
+ align:start position:0%
+restricted model is that the treatment
+effect is constant once it starts and
+
+ align:start position:0%
+effect is constant once it starts and
+ 
+
+ align:start position:0%
+effect is constant once it starts and
+here you can see that it looks like it's
+
+ align:start position:0%
+here you can see that it looks like it's
+ 
+
+ align:start position:0%
+here you can see that it looks like it's
+not and in fact they introduce here the
+
+ align:start position:0%
+not and in fact they introduce here the
+ 
+
+ align:start position:0%
+not and in fact they introduce here the
+test for a constant effect post and are
+
+ align:start position:0%
+test for a constant effect post and are
+ 
+
+ align:start position:0%
+test for a constant effect post and are
+rejected so that's in the
+
+ align:start position:0%
+rejected so that's in the
+ 
+
+ align:start position:0%
+rejected so that's in the
+that you can put that in the
+
+ align:start position:0%
+that you can put that in the
+ 
+
+ align:start position:0%
+that you can put that in the
+in The Legend So I put both the
+
+ align:start position:0%
+in The Legend So I put both the
+ 
+
+ align:start position:0%
+in The Legend So I put both the
+pre-trend and the constant treatment
+
+ align:start position:0%
+pre-trend and the constant treatment
+ 
+
+ align:start position:0%
+pre-trend and the constant treatment
+effect
+
+ align:start position:0%
+effect
+ 
+
+ align:start position:0%
+effect
+but for some reason on this graph they
+
+ align:start position:0%
+but for some reason on this graph they
+ 
+
+ align:start position:0%
+but for some reason on this graph they
+only have them
+
+ align:start position:0%
+only have them
+ 
+
+ align:start position:0%
+only have them
+so that's your state-of-the-art event
+
+ align:start position:0%
+so that's your state-of-the-art event
+ 
+
+ align:start position:0%
+so that's your state-of-the-art event
+study graph
+
+ align:start position:0%
+study graph
+ 
+
+ align:start position:0%
+study graph
+if you're a second year students you're
+
+ align:start position:0%
+if you're a second year students you're
+ 
+
+ align:start position:0%
+if you're a second year students you're
+fighting your heart
+
+ align:start position:0%
+fighting your heart
+ 
+
+ align:start position:0%
+fighting your heart
+Johan check on your paper you want
+
+ align:start position:0%
+Johan check on your paper you want
+ 
+
+ align:start position:0%
+Johan check on your paper you want
+and you have to you are planning on an
+
+ align:start position:0%
+and you have to you are planning on an
+ 
+
+ align:start position:0%
+and you have to you are planning on an
+event study graph it needs to looks like
+
+ align:start position:0%
+event study graph it needs to looks like
+ 
+
+ align:start position:0%
+event study graph it needs to looks like
+that
+
+ align:start position:0%
+that
+ 
+
+ align:start position:0%
+that
+and that's another suggestion they have
+
+ align:start position:0%
+and that's another suggestion they have
+ 
+
+ align:start position:0%
+and that's another suggestion they have
+is to uh to plot kind of the the the
+
+ align:start position:0%
+is to uh to plot kind of the the the
+ 
+
+ align:start position:0%
+is to uh to plot kind of the the the
+least Wiggly
+
+ align:start position:0%
+least Wiggly
+ 
+
+ align:start position:0%
+least Wiggly
+line
+
+ align:start position:0%
+line
+ 
+
+ align:start position:0%
+line
+uh that that fits all the points in the
+
+ align:start position:0%
+uh that that fits all the points in the
+ 
+
+ align:start position:0%
+uh that that fits all the points in the
+graph
+
+ align:start position:0%
+graph
+ 
+
+ align:start position:0%
+graph
+so here are the least wiggly line that
+
+ align:start position:0%
+so here are the least wiggly line that
+ 
+
+ align:start position:0%
+so here are the least wiggly line that
+fits all the point in the graph is a
+
+ align:start position:0%
+fits all the point in the graph is a
+ 
+
+ align:start position:0%
+fits all the point in the graph is a
+straight line
+
+ align:start position:0%
+straight line
+ 
+
+ align:start position:0%
+straight line
+so that basically is a way to tell you
+
+ align:start position:0%
+so that basically is a way to tell you
+ 
+
+ align:start position:0%
+so that basically is a way to tell you
+it doesn't fit it doesn't it does it
+
+ align:start position:0%
+it doesn't fit it doesn't it does it
+ 
+
+ align:start position:0%
+it doesn't fit it doesn't it does it
+looks like this is all pre-tran
+
+ align:start position:0%
+looks like this is all pre-tran
+ 
+
+ align:start position:0%
+looks like this is all pre-tran
+uh and here this one the least weekly
+
+ align:start position:0%
+uh and here this one the least weekly
+ 
+
+ align:start position:0%
+uh and here this one the least weekly
+line possible it's quite wiggly so seems
+
+ align:start position:0%
+line possible it's quite wiggly so seems
+ 
+
+ align:start position:0%
+line possible it's quite wiggly so seems
+very unlikely that this is
+
+ align:start position:0%
+very unlikely that this is
+ 
+
+ align:start position:0%
+very unlikely that this is
+due to
+
+ align:start position:0%
+due to
+ 
+
+ align:start position:0%
+due to
+some other thing that is moving in this
+
+ align:start position:0%
+some other thing that is moving in this
+ 
+
+ align:start position:0%
+some other thing that is moving in this
+funny way so in our case in the case of
+
+ align:start position:0%
+funny way so in our case in the case of
+ 
+
+ align:start position:0%
+funny way so in our case in the case of
+the impress program the least weekly
+
+ align:start position:0%
+the impress program the least weekly
+ 
+
+ align:start position:0%
+the impress program the least weekly
+line that fits all the point would
+
+ align:start position:0%
+line that fits all the point would
+ 
+
+ align:start position:0%
+line that fits all the point would
+probably be have been nice and like that
+
+ align:start position:0%
+probably be have been nice and like that
+ 
+
+ align:start position:0%
+probably be have been nice and like that
+and therefore quite unlikely to be
+
+ align:start position:0%
+and therefore quite unlikely to be
+ 
+
+ align:start position:0%
+and therefore quite unlikely to be
+explainable by something else but it's a
+
+ align:start position:0%
+explainable by something else but it's a
+ 
+
+ align:start position:0%
+explainable by something else but it's a
+way of making these argument in uh Less
+
+ align:start position:0%
+way of making these argument in uh Less
+ 
+
+ align:start position:0%
+way of making these argument in uh Less
+in impressionistic way
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so that's the kind of state of the art
+
+ align:start position:0%
+so that's the kind of state of the art
+ 
+
+ align:start position:0%
+so that's the kind of state of the art
+of difference in difference
+
+ align:start position:0%
+of difference in difference
+ 
+
+ align:start position:0%
+of difference in difference
+any question on that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+I thought it would be a good good
+
+ align:start position:0%
+I thought it would be a good good
+ 
+
+ align:start position:0%
+I thought it would be a good good
+occasion to put all of this on slides
+
+ align:start position:0%
+occasion to put all of this on slides
+ 
+
+ align:start position:0%
+occasion to put all of this on slides
+and you'll have a convenient way to
+
+ align:start position:0%
+and you'll have a convenient way to
+ 
+
+ align:start position:0%
+and you'll have a convenient way to
+refer to them later
+
+ align:start position:0%
+refer to them later
+ 
+
+ align:start position:0%
+refer to them later
+um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so that's also what you know what I have
+
+ align:start position:0%
+so that's also what you know what I have
+ 
+
+ align:start position:0%
+so that's also what you know what I have
+to say also on substance in terms of
+
+ align:start position:0%
+to say also on substance in terms of
+ 
+
+ align:start position:0%
+to say also on substance in terms of
+what concerns the people's reaction to
+
+ align:start position:0%
+what concerns the people's reaction to
+ 
+
+ align:start position:0%
+what concerns the people's reaction to
+the cost of Education I will go back to
+
+ align:start position:0%
+the cost of Education I will go back to
+ 
+
+ align:start position:0%
+the cost of Education I will go back to
+this paper so many people have asked
+
+ align:start position:0%
+this paper so many people have asked
+ 
+
+ align:start position:0%
+this paper so many people have asked
+about General equilibrium effect and
+
+ align:start position:0%
+about General equilibrium effect and
+ 
+
+ align:start position:0%
+about General equilibrium effect and
+I'll get back to uh
+
+ align:start position:0%
+I'll get back to uh
+ 
+
+ align:start position:0%
+I'll get back to uh
+I get back to to that when we this last
+
+ align:start position:0%
+I get back to to that when we this last
+ 
+
+ align:start position:0%
+I get back to to that when we this last
+time next time actually did write a
+
+ align:start position:0%
+time next time actually did write a
+ 
+
+ align:start position:0%
+time next time actually did write a
+paper about it so I have a paper that
+
+ align:start position:0%
+paper about it so I have a paper that
+ 
+
+ align:start position:0%
+paper about it so I have a paper that
+looks at uh
+
+ align:start position:0%
+looks at uh
+ 
+
+ align:start position:0%
+looks at uh
+the the impact of the school
+
+ align:start position:0%
+the the impact of the school
+ 
+
+ align:start position:0%
+the the impact of the school
+construction on people who were not
+
+ align:start position:0%
+construction on people who were not
+ 
+
+ align:start position:0%
+construction on people who were not
+affected by the school construction to
+
+ align:start position:0%
+affected by the school construction to
+ 
+
+ align:start position:0%
+affected by the school construction to
+get at the to get the equilibrium effect
+
+ align:start position:0%
+get at the to get the equilibrium effect
+ 
+
+ align:start position:0%
+get at the to get the equilibrium effect
+uh let me spend the last uh 10 minutes
+
+ align:start position:0%
+uh let me spend the last uh 10 minutes
+ 
+
+ align:start position:0%
+uh let me spend the last uh 10 minutes
+we have 10 15 minutes we have thinking
+
+ align:start position:0%
+we have 10 15 minutes we have thinking
+ 
+
+ align:start position:0%
+we have 10 15 minutes we have thinking
+about the other aspects of what what
+
+ align:start position:0%
+about the other aspects of what what
+ 
+
+ align:start position:0%
+about the other aspects of what what
+else enters in the in in the education
+
+ align:start position:0%
+else enters in the in in the education
+ 
+
+ align:start position:0%
+else enters in the in in the education
+production function what people seem to
+
+ align:start position:0%
+production function what people seem to
+ 
+
+ align:start position:0%
+production function what people seem to
+be responding to
+
+ align:start position:0%
+be responding to
+ 
+
+ align:start position:0%
+be responding to
+so one very nice feature of a very kind
+
+ align:start position:0%
+so one very nice feature of a very kind
+ 
+
+ align:start position:0%
+so one very nice feature of a very kind
+of specific feature of this model is
+
+ align:start position:0%
+of specific feature of this model is
+ 
+
+ align:start position:0%
+of specific feature of this model is
+people should respond to the perceived
+
+ align:start position:0%
+people should respond to the perceived
+ 
+
+ align:start position:0%
+people should respond to the perceived
+return to education
+
+ align:start position:0%
+return to education
+ 
+
+ align:start position:0%
+return to education
+so how how one would go about testing
+
+ align:start position:0%
+so how how one would go about testing
+ 
+
+ align:start position:0%
+so how how one would go about testing
+that
+
+ align:start position:0%
+that
+ 
+
+ align:start position:0%
+that
+so Rob Jensen first exploited the fact
+
+ align:start position:0%
+so Rob Jensen first exploited the fact
+ 
+
+ align:start position:0%
+so Rob Jensen first exploited the fact
+that people make mistakes on what they
+
+ align:start position:0%
+that people make mistakes on what they
+ 
+
+ align:start position:0%
+that people make mistakes on what they
+think they return to educational and
+
+ align:start position:0%
+think they return to educational and
+ 
+
+ align:start position:0%
+think they return to educational and
+therefore you can just tell them the
+
+ align:start position:0%
+therefore you can just tell them the
+ 
+
+ align:start position:0%
+therefore you can just tell them the
+truth and by telling them the truths you
+
+ align:start position:0%
+truth and by telling them the truths you
+ 
+
+ align:start position:0%
+truth and by telling them the truths you
+are affecting their uh their perceived
+
+ align:start position:0%
+are affecting their uh their perceived
+ 
+
+ align:start position:0%
+are affecting their uh their perceived
+return and you you could see whether
+
+ align:start position:0%
+return and you you could see whether
+ 
+
+ align:start position:0%
+return and you you could see whether
+therefore they react by by
+
+ align:start position:0%
+therefore they react by by
+ 
+
+ align:start position:0%
+therefore they react by by
+going to school more
+
+ align:start position:0%
+going to school more
+ 
+
+ align:start position:0%
+going to school more
+uh so he did this project in the
+
+ align:start position:0%
+uh so he did this project in the
+ 
+
+ align:start position:0%
+uh so he did this project in the
+Dominican Republic
+
+ align:start position:0%
+Dominican Republic
+ 
+
+ align:start position:0%
+Dominican Republic
+where the completion rate for high
+
+ align:start position:0%
+where the completion rate for high
+ 
+
+ align:start position:0%
+where the completion rate for high
+school is low
+
+ align:start position:0%
+school is low
+ 
+
+ align:start position:0%
+school is low
+and his first went to the students and
+
+ align:start position:0%
+and his first went to the students and
+ 
+
+ align:start position:0%
+and his first went to the students and
+asked them
+
+ align:start position:0%
+asked them
+ 
+
+ align:start position:0%
+asked them
+um their view of returning to education
+
+ align:start position:0%
+um their view of returning to education
+ 
+
+ align:start position:0%
+um their view of returning to education
+by
+
+ align:start position:0%
+by
+ 
+
+ align:start position:0%
+by
+comparing by asking them to say how much
+
+ align:start position:0%
+comparing by asking them to say how much
+ 
+
+ align:start position:0%
+comparing by asking them to say how much
+someone is
+
+ align:start position:0%
+someone is
+ 
+
+ align:start position:0%
+someone is
+for those who have complete Primary
+
+ align:start position:0%
+for those who have complete Primary
+ 
+
+ align:start position:0%
+for those who have complete Primary
+School versus those who have completed
+
+ align:start position:0%
+School versus those who have completed
+ 
+
+ align:start position:0%
+School versus those who have completed
+High School what's the difference
+
+ align:start position:0%
+High School what's the difference
+ 
+
+ align:start position:0%
+High School what's the difference
+uh by the way where what's the
+
+ align:start position:0%
+uh by the way where what's the
+ 
+
+ align:start position:0%
+uh by the way where what's the
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+let me finish that and then I'll ask you
+
+ align:start position:0%
+let me finish that and then I'll ask you
+ 
+
+ align:start position:0%
+let me finish that and then I'll ask you
+at Baseline the people seem to be people
+
+ align:start position:0%
+at Baseline the people seem to be people
+ 
+
+ align:start position:0%
+at Baseline the people seem to be people
+here seem to be underestimating the
+
+ align:start position:0%
+here seem to be underestimating the
+ 
+
+ align:start position:0%
+here seem to be underestimating the
+return to education
+
+ align:start position:0%
+return to education
+ 
+
+ align:start position:0%
+return to education
+which by the way is really not a
+
+ align:start position:0%
+which by the way is really not a
+ 
+
+ align:start position:0%
+which by the way is really not a
+generalized finding in my experience
+
+ align:start position:0%
+generalized finding in my experience
+ 
+
+ align:start position:0%
+generalized finding in my experience
+people widely overestimate the returns
+
+ align:start position:0%
+people widely overestimate the returns
+ 
+
+ align:start position:0%
+people widely overestimate the returns
+to education but it's two secondary
+
+ align:start position:0%
+to education but it's two secondary
+ 
+
+ align:start position:0%
+to education but it's two secondary
+education but in this instance they were
+
+ align:start position:0%
+education but in this instance they were
+ 
+
+ align:start position:0%
+education but in this instance they were
+underestimating them
+
+ align:start position:0%
+underestimating them
+ 
+
+ align:start position:0%
+underestimating them
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+that's what that you would get on your
+
+ align:start position:0%
+that's what that you would get on your
+ 
+
+ align:start position:0%
+that's what that you would get on your
+10 increase from uh moving from the 8th
+
+ align:start position:0%
+10 increase from uh moving from the 8th
+ 
+
+ align:start position:0%
+10 increase from uh moving from the 8th
+to the 12th when when in fact it's much
+
+ align:start position:0%
+to the 12th when when in fact it's much
+ 
+
+ align:start position:0%
+to the 12th when when in fact it's much
+bigger than that but then what they did
+
+ align:start position:0%
+bigger than that but then what they did
+ 
+
+ align:start position:0%
+bigger than that but then what they did
+is that they told them the truth
+
+ align:start position:0%
+is that they told them the truth
+ 
+
+ align:start position:0%
+is that they told them the truth
+in some schools
+
+ align:start position:0%
+in some schools
+ 
+
+ align:start position:0%
+in some schools
+so the mean Syrian return are more like
+
+ align:start position:0%
+so the mean Syrian return are more like
+ 
+
+ align:start position:0%
+so the mean Syrian return are more like
+10 percent per year so 40 for going from
+
+ align:start position:0%
+10 percent per year so 40 for going from
+ 
+
+ align:start position:0%
+10 percent per year so 40 for going from
+eighth grade to high school
+
+ align:start position:0%
+eighth grade to high school
+ 
+
+ align:start position:0%
+eighth grade to high school
+and then after some time they compared
+
+ align:start position:0%
+and then after some time they compared
+ 
+
+ align:start position:0%
+and then after some time they compared
+who stays in school but possible they
+
+ align:start position:0%
+who stays in school but possible they
+ 
+
+ align:start position:0%
+who stays in school but possible they
+show that they update their beliefs and
+
+ align:start position:0%
+show that they update their beliefs and
+ 
+
+ align:start position:0%
+show that they update their beliefs and
+I'll show you that in a minute and then
+
+ align:start position:0%
+I'll show you that in a minute and then
+ 
+
+ align:start position:0%
+I'll show you that in a minute and then
+they investigate the impact on education
+
+ align:start position:0%
+they investigate the impact on education
+ 
+
+ align:start position:0%
+they investigate the impact on education
+so before I go further what's the issue
+
+ align:start position:0%
+so before I go further what's the issue
+ 
+
+ align:start position:0%
+so before I go further what's the issue
+is doing that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+are in fact even with asking them in
+
+ align:start position:0%
+are in fact even with asking them in
+ 
+
+ align:start position:0%
+are in fact even with asking them in
+this way the difference they thought
+
+ align:start position:0%
+this way the difference they thought
+ 
+
+ align:start position:0%
+this way the difference they thought
+between in the income of someone who has
+
+ align:start position:0%
+between in the income of someone who has
+ 
+
+ align:start position:0%
+between in the income of someone who has
+completed versus not completed
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+what is potential concern in doing this
+
+ align:start position:0%
+what is potential concern in doing this
+ 
+
+ align:start position:0%
+what is potential concern in doing this
+exercise yeah
+
+ align:start position:0%
+exercise yeah
+ 
+
+ align:start position:0%
+exercise yeah
+[Music]
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah they might not understand what that
+
+ align:start position:0%
+yeah they might not understand what that
+ 
+
+ align:start position:0%
+yeah they might not understand what that
+means and in some sense
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+depending on how the question was asked
+
+ align:start position:0%
+depending on how the question was asked
+ 
+
+ align:start position:0%
+depending on how the question was asked
+it's kind of clear if it's like the
+
+ align:start position:0%
+it's kind of clear if it's like the
+ 
+
+ align:start position:0%
+it's kind of clear if it's like the
+return for like an individual who
+
+ align:start position:0%
+return for like an individual who
+ 
+
+ align:start position:0%
+return for like an individual who
+chooses to to build 13 Congress holders
+
+ align:start position:0%
+chooses to to build 13 Congress holders
+ 
+
+ align:start position:0%
+chooses to to build 13 Congress holders
+meeting her a bit like also getting into
+
+ align:start position:0%
+meeting her a bit like also getting into
+ 
+
+ align:start position:0%
+meeting her a bit like also getting into
+accountability
+
+ align:start position:0%
+accountability
+ 
+
+ align:start position:0%
+accountability
+yes exactly exactly and in what is given
+
+ align:start position:0%
+yes exactly exactly and in what is given
+ 
+
+ align:start position:0%
+yes exactly exactly and in what is given
+to them is is full of the ability by us
+
+ align:start position:0%
+to them is is full of the ability by us
+ 
+
+ align:start position:0%
+to them is is full of the ability by us
+potentially or the selection by for many
+
+ align:start position:0%
+potentially or the selection by for many
+ 
+
+ align:start position:0%
+potentially or the selection by for many
+kind
+
+ align:start position:0%
+kind
+ 
+
+ align:start position:0%
+kind
+uh you're telling them the difference
+
+ align:start position:0%
+uh you're telling them the difference
+ 
+
+ align:start position:0%
+uh you're telling them the difference
+between learning of someone who has
+
+ align:start position:0%
+between learning of someone who has
+ 
+
+ align:start position:0%
+between learning of someone who has
+completed and not completed education
+
+ align:start position:0%
+completed and not completed education
+ 
+
+ align:start position:0%
+completed and not completed education
+that's not the returns to education
+
+ align:start position:0%
+that's not the returns to education
+ 
+
+ align:start position:0%
+that's not the returns to education
+that's not the causal effect of
+
+ align:start position:0%
+that's not the causal effect of
+ 
+
+ align:start position:0%
+that's not the causal effect of
+Education
+
+ align:start position:0%
+Education
+ 
+
+ align:start position:0%
+Education
+so potentially I'm lying to people which
+
+ align:start position:0%
+so potentially I'm lying to people which
+ 
+
+ align:start position:0%
+so potentially I'm lying to people which
+is a bit problematic
+
+ align:start position:0%
+is a bit problematic
+ 
+
+ align:start position:0%
+is a bit problematic
+or not lying but giving them an
+
+ align:start position:0%
+or not lying but giving them an
+ 
+
+ align:start position:0%
+or not lying but giving them an
+information that's not
+
+ align:start position:0%
+information that's not
+ 
+
+ align:start position:0%
+information that's not
+accurate it's not accurate for the
+
+ align:start position:0%
+accurate it's not accurate for the
+ 
+
+ align:start position:0%
+accurate it's not accurate for the
+average it might and then the other kind
+
+ align:start position:0%
+average it might and then the other kind
+ 
+
+ align:start position:0%
+average it might and then the other kind
+of part of your answer is that it's not
+
+ align:start position:0%
+of part of your answer is that it's not
+ 
+
+ align:start position:0%
+of part of your answer is that it's not
+even the you know it's about an
+
+ align:start position:0%
+even the you know it's about an
+ 
+
+ align:start position:0%
+even the you know it's about an
+individual it's not necessarily the
+
+ align:start position:0%
+individual it's not necessarily the
+ 
+
+ align:start position:0%
+individual it's not necessarily the
+relevant information for any particular
+
+ align:start position:0%
+relevant information for any particular
+ 
+
+ align:start position:0%
+relevant information for any particular
+individual which of course you don't
+
+ align:start position:0%
+individual which of course you don't
+ 
+
+ align:start position:0%
+individual which of course you don't
+know
+
+ align:start position:0%
+know
+ 
+
+ align:start position:0%
+know
+so that's a little bit of a dicey
+
+ align:start position:0%
+so that's a little bit of a dicey
+ 
+
+ align:start position:0%
+so that's a little bit of a dicey
+project but again maybe you didn't know
+
+ align:start position:0%
+project but again maybe you didn't know
+ 
+
+ align:start position:0%
+project but again maybe you didn't know
+until you know this is this might be
+
+ align:start position:0%
+until you know this is this might be
+ 
+
+ align:start position:0%
+until you know this is this might be
+2020 hindsight
+
+ align:start position:0%
+2020 hindsight
+ 
+
+ align:start position:0%
+2020 hindsight
+but uh that's certainly something that
+
+ align:start position:0%
+but uh that's certainly something that
+ 
+
+ align:start position:0%
+but uh that's certainly something that
+people uh criticized they do find an
+
+ align:start position:0%
+people uh criticized they do find an
+ 
+
+ align:start position:0%
+people uh criticized they do find an
+impact uh on education they find that
+
+ align:start position:0%
+impact uh on education they find that
+ 
+
+ align:start position:0%
+impact uh on education they find that
+people generally update their belief uh
+
+ align:start position:0%
+people generally update their belief uh
+ 
+
+ align:start position:0%
+people generally update their belief uh
+positively and they find an average
+
+ align:start position:0%
+positively and they find an average
+ 
+
+ align:start position:0%
+positively and they find an average
+impact on educational let me show you
+
+ align:start position:0%
+impact on educational let me show you
+ 
+
+ align:start position:0%
+impact on educational let me show you
+the table
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+have increased on average these
+
+ align:start position:0%
+have increased on average these
+ 
+
+ align:start position:0%
+have increased on average these
+treatments regress foreign
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and then uh so this is the average
+
+ align:start position:0%
+and then uh so this is the average
+ 
+
+ align:start position:0%
+and then uh so this is the average
+effect on perceived return and then the
+
+ align:start position:0%
+effect on perceived return and then the
+ 
+
+ align:start position:0%
+effect on perceived return and then the
+average effect on various things without
+
+ align:start position:0%
+average effect on various things without
+ 
+
+ align:start position:0%
+average effect on various things without
+a return whether the uh they finished
+
+ align:start position:0%
+a return whether the uh they finished
+ 
+
+ align:start position:0%
+a return whether the uh they finished
+the years of schooling and then they
+
+ align:start position:0%
+the years of schooling and then they
+ 
+
+ align:start position:0%
+the years of schooling and then they
+actually find larger effect for the for
+
+ align:start position:0%
+actually find larger effect for the for
+ 
+
+ align:start position:0%
+actually find larger effect for the for
+for the rich household and the poor
+
+ align:start position:0%
+for the rich household and the poor
+ 
+
+ align:start position:0%
+for the rich household and the poor
+household possibly because in addition
+
+ align:start position:0%
+household possibly because in addition
+ 
+
+ align:start position:0%
+household possibly because in addition
+people you know there are also maybe
+
+ align:start position:0%
+people you know there are also maybe
+ 
+
+ align:start position:0%
+people you know there are also maybe
+constrained people can't do it
+
+ align:start position:0%
+constrained people can't do it
+ 
+
+ align:start position:0%
+constrained people can't do it
+immediately so return is not the only
+
+ align:start position:0%
+immediately so return is not the only
+ 
+
+ align:start position:0%
+immediately so return is not the only
+thing that entered the decision
+
+ align:start position:0%
+thing that entered the decision
+ 
+
+ align:start position:0%
+thing that entered the decision
+so um
+
+ align:start position:0%
+so um
+ 
+
+ align:start position:0%
+so um
+if you had to run this regression having
+
+ align:start position:0%
+if you had to run this regression having
+ 
+
+ align:start position:0%
+if you had to run this regression having
+done this experiment if you had to run
+
+ align:start position:0%
+done this experiment if you had to run
+ 
+
+ align:start position:0%
+done this experiment if you had to run
+this regression would you run it this
+
+ align:start position:0%
+this regression would you run it this
+ 
+
+ align:start position:0%
+this regression would you run it this
+way or would there be another way to run
+
+ align:start position:0%
+way or would there be another way to run
+ 
+
+ align:start position:0%
+way or would there be another way to run
+it that would make more sense
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+exactly so at the minimum you should
+
+ align:start position:0%
+exactly so at the minimum you should
+ 
+
+ align:start position:0%
+exactly so at the minimum you should
+think that the treatment
+
+ align:start position:0%
+think that the treatment
+ 
+
+ align:start position:0%
+think that the treatment
+treatment doesn't have a monotonous
+
+ align:start position:0%
+treatment doesn't have a monotonous
+ 
+
+ align:start position:0%
+treatment doesn't have a monotonous
+effect on these other things because
+
+ align:start position:0%
+effect on these other things because
+ 
+
+ align:start position:0%
+effect on these other things because
+some people
+
+ align:start position:0%
+some people
+ 
+
+ align:start position:0%
+some people
+even though on average people were
+
+ align:start position:0%
+even though on average people were
+ 
+
+ align:start position:0%
+even though on average people were
+underestimating it is likely that some
+
+ align:start position:0%
+underestimating it is likely that some
+ 
+
+ align:start position:0%
+underestimating it is likely that some
+people were overestimating and some
+
+ align:start position:0%
+people were overestimating and some
+ 
+
+ align:start position:0%
+people were overestimating and some
+people were underestimating
+
+ align:start position:0%
+people were underestimating
+ 
+
+ align:start position:0%
+people were underestimating
+so at the minimum when you are doing
+
+ align:start position:0%
+so at the minimum when you are doing
+ 
+
+ align:start position:0%
+so at the minimum when you are doing
+this kind of device in treatment and you
+
+ align:start position:0%
+this kind of device in treatment and you
+ 
+
+ align:start position:0%
+this kind of device in treatment and you
+know they have become popular we are
+
+ align:start position:0%
+know they have become popular we are
+ 
+
+ align:start position:0%
+know they have become popular we are
+going to see other examples of that you
+
+ align:start position:0%
+going to see other examples of that you
+ 
+
+ align:start position:0%
+going to see other examples of that you
+should
+
+ align:start position:0%
+should
+ 
+
+ align:start position:0%
+should
+look at you should separate the sample
+
+ align:start position:0%
+look at you should separate the sample
+ 
+
+ align:start position:0%
+look at you should separate the sample
+by the people whose prior you're moving
+
+ align:start position:0%
+by the people whose prior you're moving
+ 
+
+ align:start position:0%
+by the people whose prior you're moving
+up to the people who hire you moving
+
+ align:start position:0%
+up to the people who hire you moving
+ 
+
+ align:start position:0%
+up to the people who hire you moving
+down because you would expect the effect
+
+ align:start position:0%
+down because you would expect the effect
+ 
+
+ align:start position:0%
+down because you would expect the effect
+to go in opposite direction
+
+ align:start position:0%
+to go in opposite direction
+ 
+
+ align:start position:0%
+to go in opposite direction
+well that's just a note of
+
+ align:start position:0%
+well that's just a note of
+ 
+
+ align:start position:0%
+well that's just a note of
+how one could have done that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+uh given so this paper was criticized
+
+ align:start position:0%
+uh given so this paper was criticized
+ 
+
+ align:start position:0%
+uh given so this paper was criticized
+for what I'm telling you which is that
+
+ align:start position:0%
+for what I'm telling you which is that
+ 
+
+ align:start position:0%
+for what I'm telling you which is that
+basically you're telling people some
+
+ align:start position:0%
+basically you're telling people some
+ 
+
+ align:start position:0%
+basically you're telling people some
+junk that's a little bit uh troubling
+
+ align:start position:0%
+junk that's a little bit uh troubling
+ 
+
+ align:start position:0%
+junk that's a little bit uh troubling
+maybe we shouldn't do that
+
+ align:start position:0%
+maybe we shouldn't do that
+ 
+
+ align:start position:0%
+maybe we shouldn't do that
+um and then there are other people that
+
+ align:start position:0%
+um and then there are other people that
+ 
+
+ align:start position:0%
+um and then there are other people that
+are trying to use people that are trying
+
+ align:start position:0%
+are trying to use people that are trying
+ 
+
+ align:start position:0%
+are trying to use people that are trying
+to use the the real data data from The
+
+ align:start position:0%
+to use the the real data data from The
+ 
+
+ align:start position:0%
+to use the the real data data from The
+Real World to look at the the how people
+
+ align:start position:0%
+Real World to look at the the how people
+ 
+
+ align:start position:0%
+Real World to look at the the how people
+respond to the return to education
+
+ align:start position:0%
+respond to the return to education
+ 
+
+ align:start position:0%
+respond to the return to education
+and older people uh by Foster and
+
+ align:start position:0%
+and older people uh by Foster and
+ 
+
+ align:start position:0%
+and older people uh by Foster and
+rodents flag uh in the ER quite nice
+
+ align:start position:0%
+rodents flag uh in the ER quite nice
+ 
+
+ align:start position:0%
+rodents flag uh in the ER quite nice
+looks at the impact of high yielding
+
+ align:start position:0%
+looks at the impact of high yielding
+ 
+
+ align:start position:0%
+looks at the impact of high yielding
+variety
+
+ align:start position:0%
+variety
+ 
+
+ align:start position:0%
+variety
+and argue that high yielding variety
+
+ align:start position:0%
+and argue that high yielding variety
+ 
+
+ align:start position:0%
+and argue that high yielding variety
+grain has a large impact on returns to
+
+ align:start position:0%
+grain has a large impact on returns to
+ 
+
+ align:start position:0%
+grain has a large impact on returns to
+education because basically you need to
+
+ align:start position:0%
+education because basically you need to
+ 
+
+ align:start position:0%
+education because basically you need to
+be able to read the package and
+
+ align:start position:0%
+be able to read the package and
+ 
+
+ align:start position:0%
+be able to read the package and
+understand what it is and then have some
+
+ align:start position:0%
+understand what it is and then have some
+ 
+
+ align:start position:0%
+understand what it is and then have some
+suggesting evidence that the return to
+
+ align:start position:0%
+suggesting evidence that the return to
+ 
+
+ align:start position:0%
+suggesting evidence that the return to
+high yielding variety is very low for
+
+ align:start position:0%
+high yielding variety is very low for
+ 
+
+ align:start position:0%
+high yielding variety is very low for
+people who are not educated and very
+
+ align:start position:0%
+people who are not educated and very
+ 
+
+ align:start position:0%
+people who are not educated and very
+high for people who are educated so the
+
+ align:start position:0%
+high for people who are educated so the
+ 
+
+ align:start position:0%
+high for people who are educated so the
+introduction
+
+ align:start position:0%
+introduction
+ 
+
+ align:start position:0%
+introduction
+which is a bit sequential as well of
+
+ align:start position:0%
+which is a bit sequential as well of
+ 
+
+ align:start position:0%
+which is a bit sequential as well of
+high yielding variety across Villages
+
+ align:start position:0%
+high yielding variety across Villages
+ 
+
+ align:start position:0%
+high yielding variety across Villages
+has different impact as increases the
+
+ align:start position:0%
+has different impact as increases the
+ 
+
+ align:start position:0%
+has different impact as increases the
+return to education
+
+ align:start position:0%
+return to education
+ 
+
+ align:start position:0%
+return to education
+so that's the first thing that they say
+
+ align:start position:0%
+so that's the first thing that they say
+ 
+
+ align:start position:0%
+so that's the first thing that they say
+and then as a result when you see high
+
+ align:start position:0%
+and then as a result when you see high
+ 
+
+ align:start position:0%
+and then as a result when you see high
+yielding variety
+
+ align:start position:0%
+yielding variety
+ 
+
+ align:start position:0%
+yielding variety
+being introduced that should increase
+
+ align:start position:0%
+being introduced that should increase
+ 
+
+ align:start position:0%
+being introduced that should increase
+people uh educating their kids
+
+ align:start position:0%
+people uh educating their kids
+ 
+
+ align:start position:0%
+people uh educating their kids
+because the return to education have now
+
+ align:start position:0%
+because the return to education have now
+ 
+
+ align:start position:0%
+because the return to education have now
+gone up
+
+ align:start position:0%
+gone up
+ 
+
+ align:start position:0%
+gone up
+and they find that now one issue with
+
+ align:start position:0%
+and they find that now one issue with
+ 
+
+ align:start position:0%
+and they find that now one issue with
+that exercise is that at the same time
+
+ align:start position:0%
+that exercise is that at the same time
+ 
+
+ align:start position:0%
+that exercise is that at the same time
+that it increased the return to
+
+ align:start position:0%
+that it increased the return to
+ 
+
+ align:start position:0%
+that it increased the return to
+education and it should increase
+
+ align:start position:0%
+education and it should increase
+ 
+
+ align:start position:0%
+education and it should increase
+people's income
+
+ align:start position:0%
+people's income
+ 
+
+ align:start position:0%
+people's income
+and we've seen that in you know a richer
+
+ align:start position:0%
+and we've seen that in you know a richer
+ 
+
+ align:start position:0%
+and we've seen that in you know a richer
+model of the world income effect would
+
+ align:start position:0%
+model of the world income effect would
+ 
+
+ align:start position:0%
+model of the world income effect would
+also increase
+
+ align:start position:0%
+also increase
+ 
+
+ align:start position:0%
+also increase
+education in and of itself that's not an
+
+ align:start position:0%
+education in and of itself that's not an
+ 
+
+ align:start position:0%
+education in and of itself that's not an
+issue for them because they don't
+
+ align:start position:0%
+issue for them because they don't
+ 
+
+ align:start position:0%
+issue for them because they don't
+believe in income effect so you know the
+
+ align:start position:0%
+believe in income effect so you know the
+ 
+
+ align:start position:0%
+believe in income effect so you know the
+only thing that could possibly have
+
+ align:start position:0%
+only thing that could possibly have
+ 
+
+ align:start position:0%
+only thing that could possibly have
+happened is um is um is the response to
+
+ align:start position:0%
+happened is um is um is the response to
+ 
+
+ align:start position:0%
+happened is um is um is the response to
+return to education but one could be
+
+ align:start position:0%
+return to education but one could be
+ 
+
+ align:start position:0%
+return to education but one could be
+worried about that
+
+ align:start position:0%
+worried about that
+ 
+
+ align:start position:0%
+worried about that
+two more recent people that have which
+
+ align:start position:0%
+two more recent people that have which
+ 
+
+ align:start position:0%
+two more recent people that have which
+are on the same uh which have the same
+
+ align:start position:0%
+are on the same uh which have the same
+ 
+
+ align:start position:0%
+are on the same uh which have the same
+those two papers have a little bit the
+
+ align:start position:0%
+those two papers have a little bit the
+ 
+
+ align:start position:0%
+those two papers have a little bit the
+same mechanism at hand is a David Atkin
+
+ align:start position:0%
+same mechanism at hand is a David Atkin
+ 
+
+ align:start position:0%
+same mechanism at hand is a David Atkin
+paper and a Sarah Hernandez I was a
+
+ align:start position:0%
+paper and a Sarah Hernandez I was a
+ 
+
+ align:start position:0%
+paper and a Sarah Hernandez I was a
+graduate student Here and Now teaches at
+
+ align:start position:0%
+graduate student Here and Now teaches at
+ 
+
+ align:start position:0%
+graduate student Here and Now teaches at
+Northwestern
+
+ align:start position:0%
+Northwestern
+ 
+
+ align:start position:0%
+Northwestern
+uh they look at export jobs and Export
+
+ align:start position:0%
+uh they look at export jobs and Export
+ 
+
+ align:start position:0%
+uh they look at export jobs and Export
+jobs coming from the government sector
+
+ align:start position:0%
+jobs coming from the government sector
+ 
+
+ align:start position:0%
+jobs coming from the government sector
+mostly in Mexico and the flower sector
+
+ align:start position:0%
+mostly in Mexico and the flower sector
+ 
+
+ align:start position:0%
+mostly in Mexico and the flower sector
+in Colombia
+
+ align:start position:0%
+in Colombia
+ 
+
+ align:start position:0%
+in Colombia
+and they show that when these jobs are
+
+ align:start position:0%
+and they show that when these jobs are
+ 
+
+ align:start position:0%
+and they show that when these jobs are
+introduced it leads to dropouts of girls
+
+ align:start position:0%
+introduced it leads to dropouts of girls
+ 
+
+ align:start position:0%
+introduced it leads to dropouts of girls
+despite the fact that people are richer
+
+ align:start position:0%
+despite the fact that people are richer
+ 
+
+ align:start position:0%
+despite the fact that people are richer
+which they explained by by the fact that
+
+ align:start position:0%
+which they explained by by the fact that
+ 
+
+ align:start position:0%
+which they explained by by the fact that
+the return to education are now lower
+
+ align:start position:0%
+the return to education are now lower
+ 
+
+ align:start position:0%
+the return to education are now lower
+because you don't need to be educated to
+
+ align:start position:0%
+because you don't need to be educated to
+ 
+
+ align:start position:0%
+because you don't need to be educated to
+get any of these jobs so you can get a
+
+ align:start position:0%
+get any of these jobs so you can get a
+ 
+
+ align:start position:0%
+get any of these jobs so you can get a
+good job working in a garment Factory or
+
+ align:start position:0%
+good job working in a garment Factory or
+ 
+
+ align:start position:0%
+good job working in a garment Factory or
+you can get a good job working in a
+
+ align:start position:0%
+you can get a good job working in a
+ 
+
+ align:start position:0%
+you can get a good job working in a
+flower sector without education so
+
+ align:start position:0%
+flower sector without education so
+ 
+
+ align:start position:0%
+flower sector without education so
+people dropped out
+
+ align:start position:0%
+people dropped out
+ 
+
+ align:start position:0%
+people dropped out
+in the example of David they got
+
+ align:start position:0%
+in the example of David they got
+ 
+
+ align:start position:0%
+in the example of David they got
+schooled for it because then the sector
+
+ align:start position:0%
+schooled for it because then the sector
+ 
+
+ align:start position:0%
+schooled for it because then the sector
+disappeared and they found themselves
+
+ align:start position:0%
+disappeared and they found themselves
+ 
+
+ align:start position:0%
+disappeared and they found themselves
+without jobs and without an education
+
+ align:start position:0%
+without jobs and without an education
+ 
+
+ align:start position:0%
+without jobs and without an education
+uh that the full story of that paper but
+
+ align:start position:0%
+uh that the full story of that paper but
+ 
+
+ align:start position:0%
+uh that the full story of that paper but
+so the advantage Advantage the the
+
+ align:start position:0%
+so the advantage Advantage the the
+ 
+
+ align:start position:0%
+so the advantage Advantage the the
+advantage of that example is that the
+
+ align:start position:0%
+advantage of that example is that the
+ 
+
+ align:start position:0%
+advantage of that example is that the
+return to rejection go down at the same
+
+ align:start position:0%
+return to rejection go down at the same
+ 
+
+ align:start position:0%
+return to rejection go down at the same
+time as the income go up so we don't
+
+ align:start position:0%
+time as the income go up so we don't
+ 
+
+ align:start position:0%
+time as the income go up so we don't
+have the the income effect and the
+
+ align:start position:0%
+have the the income effect and the
+ 
+
+ align:start position:0%
+have the the income effect and the
+substitution effect going in in the same
+
+ align:start position:0%
+substitution effect going in in the same
+ 
+
+ align:start position:0%
+substitution effect going in in the same
+direction so if we find education
+
+ align:start position:0%
+direction so if we find education
+ 
+
+ align:start position:0%
+direction so if we find education
+dropping it's
+
+ align:start position:0%
+dropping it's
+ 
+
+ align:start position:0%
+dropping it's
+you know it seems likely that it's
+
+ align:start position:0%
+you know it seems likely that it's
+ 
+
+ align:start position:0%
+you know it seems likely that it's
+because of that
+
+ align:start position:0%
+because of that
+ 
+
+ align:start position:0%
+because of that
+but then Jensen went back like one step
+
+ align:start position:0%
+but then Jensen went back like one step
+ 
+
+ align:start position:0%
+but then Jensen went back like one step
+further and said well you know you
+
+ align:start position:0%
+further and said well you know you
+ 
+
+ align:start position:0%
+further and said well you know you
+didn't like my uh changing the belief so
+
+ align:start position:0%
+didn't like my uh changing the belief so
+ 
+
+ align:start position:0%
+didn't like my uh changing the belief so
+I'm gonna change the return
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um that seems like ambitious to say are
+
+ align:start position:0%
+um that seems like ambitious to say are
+ 
+
+ align:start position:0%
+um that seems like ambitious to say are
+you able to change the return to
+
+ align:start position:0%
+you able to change the return to
+ 
+
+ align:start position:0%
+you able to change the return to
+education and he had a great great idea
+
+ align:start position:0%
+education and he had a great great idea
+ 
+
+ align:start position:0%
+education and he had a great great idea
+uh which is to participate in a
+
+ align:start position:0%
+uh which is to participate in a
+ 
+
+ align:start position:0%
+uh which is to participate in a
+recruiting campaign for call centers uh
+
+ align:start position:0%
+recruiting campaign for call centers uh
+ 
+
+ align:start position:0%
+recruiting campaign for call centers uh
+you know these type of things when you
+
+ align:start position:0%
+you know these type of things when you
+ 
+
+ align:start position:0%
+you know these type of things when you
+call for your computer and typically
+
+ align:start position:0%
+call for your computer and typically
+ 
+
+ align:start position:0%
+call for your computer and typically
+it's a nice young person from
+
+ align:start position:0%
+it's a nice young person from
+ 
+
+ align:start position:0%
+it's a nice young person from
+uh suburb of the universe suburb is
+
+ align:start position:0%
+uh suburb of the universe suburb is
+ 
+
+ align:start position:0%
+uh suburb of the universe suburb is
+intended in a very broad sense who is
+
+ align:start position:0%
+intended in a very broad sense who is
+ 
+
+ align:start position:0%
+intended in a very broad sense who is
+answering the phone
+
+ align:start position:0%
+answering the phone
+ 
+
+ align:start position:0%
+answering the phone
+um so early on they were really uh
+
+ align:start position:0%
+um so early on they were really uh
+ 
+
+ align:start position:0%
+um so early on they were really uh
+recruiting Muslim Gorgan very close to
+
+ align:start position:0%
+recruiting Muslim Gorgan very close to
+ 
+
+ align:start position:0%
+recruiting Muslim Gorgan very close to
+Delhi and then
+
+ align:start position:0%
+Delhi and then
+ 
+
+ align:start position:0%
+Delhi and then
+they started extending and he worked he
+
+ align:start position:0%
+they started extending and he worked he
+ 
+
+ align:start position:0%
+they started extending and he worked he
+worked with them at the beginning of
+
+ align:start position:0%
+worked with them at the beginning of
+ 
+
+ align:start position:0%
+worked with them at the beginning of
+expansion to kind of lead them to
+
+ align:start position:0%
+expansion to kind of lead them to
+ 
+
+ align:start position:0%
+expansion to kind of lead them to
+Villages where they had never been
+
+ align:start position:0%
+Villages where they had never been
+ 
+
+ align:start position:0%
+Villages where they had never been
+in haryana or in up so basically a
+
+ align:start position:0%
+in haryana or in up so basically a
+ 
+
+ align:start position:0%
+in haryana or in up so basically a
+broader sector around up
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um it connects the the the the
+
+ align:start position:0%
+um it connects the the the the
+ 
+
+ align:start position:0%
+um it connects the the the the
+BPO the ecosystem back office processing
+
+ align:start position:0%
+BPO the ecosystem back office processing
+ 
+
+ align:start position:0%
+BPO the ecosystem back office processing
+operation with with the Villagers
+
+ align:start position:0%
+operation with with the Villagers
+ 
+
+ align:start position:0%
+operation with with the Villagers
+someone goes to the Village advertises
+
+ align:start position:0%
+someone goes to the Village advertises
+ 
+
+ align:start position:0%
+someone goes to the Village advertises
+the possibility
+
+ align:start position:0%
+the possibility
+ 
+
+ align:start position:0%
+the possibility
+uh and then
+
+ align:start position:0%
+uh and then
+ 
+
+ align:start position:0%
+uh and then
+um sees what what happens so some girls
+
+ align:start position:0%
+um sees what what happens so some girls
+ 
+
+ align:start position:0%
+um sees what what happens so some girls
+who were at the right age and had the
+
+ align:start position:0%
+who were at the right age and had the
+ 
+
+ align:start position:0%
+who were at the right age and had the
+right education which is secondary
+
+ align:start position:0%
+right education which is secondary
+ 
+
+ align:start position:0%
+right education which is secondary
+education with some English went
+
+ align:start position:0%
+education with some English went
+ 
+
+ align:start position:0%
+education with some English went
+uh and he's interested in what happened
+
+ align:start position:0%
+uh and he's interested in what happened
+ 
+
+ align:start position:0%
+uh and he's interested in what happened
+to the younger girls uh
+
+ align:start position:0%
+to the younger girls uh
+ 
+
+ align:start position:0%
+to the younger girls uh
+who could not go yet they were little
+
+ align:start position:0%
+who could not go yet they were little
+ 
+
+ align:start position:0%
+who could not go yet they were little
+and they're more likely to stay in
+
+ align:start position:0%
+and they're more likely to stay in
+ 
+
+ align:start position:0%
+and they're more likely to stay in
+school
+
+ align:start position:0%
+school
+ 
+
+ align:start position:0%
+school
+so what he finds is that
+
+ align:start position:0%
+so what he finds is that
+ 
+
+ align:start position:0%
+so what he finds is that
+women are indeed a younger women are
+
+ align:start position:0%
+women are indeed a younger women are
+ 
+
+ align:start position:0%
+women are indeed a younger women are
+indeed more likely to be working in a
+
+ align:start position:0%
+indeed more likely to be working in a
+ 
+
+ align:start position:0%
+indeed more likely to be working in a
+BPO so that's that's good there was no
+
+ align:start position:0%
+BPO so that's that's good there was no
+ 
+
+ align:start position:0%
+BPO so that's that's good there was no
+such effect for men
+
+ align:start position:0%
+such effect for men
+ 
+
+ align:start position:0%
+such effect for men
+ah
+
+ align:start position:0%
+ah
+ 
+
+ align:start position:0%
+ah
+and that both younger and both this
+
+ align:start position:0%
+and that both younger and both this
+ 
+
+ align:start position:0%
+and that both younger and both this
+woman but also the younger woman
+
+ align:start position:0%
+woman but also the younger woman
+ 
+
+ align:start position:0%
+woman but also the younger woman
+the girls were more likely to be uh in
+
+ align:start position:0%
+the girls were more likely to be uh in
+ 
+
+ align:start position:0%
+the girls were more likely to be uh in
+school
+
+ align:start position:0%
+school
+ 
+
+ align:start position:0%
+school
+and even the even younger are better fed
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so basically the parents the story is
+
+ align:start position:0%
+so basically the parents the story is
+ 
+
+ align:start position:0%
+so basically the parents the story is
+parents realized that there is more
+
+ align:start position:0%
+parents realized that there is more
+ 
+
+ align:start position:0%
+parents realized that there is more
+returns to girls in general they become
+
+ align:start position:0%
+returns to girls in general they become
+ 
+
+ align:start position:0%
+returns to girls in general they become
+more valuable in general and in
+
+ align:start position:0%
+more valuable in general and in
+ 
+
+ align:start position:0%
+more valuable in general and in
+particular more valuable if they are
+
+ align:start position:0%
+particular more valuable if they are
+ 
+
+ align:start position:0%
+particular more valuable if they are
+educated so the return to education for
+
+ align:start position:0%
+educated so the return to education for
+ 
+
+ align:start position:0%
+educated so the return to education for
+women have gone up and they start
+
+ align:start position:0%
+women have gone up and they start
+ 
+
+ align:start position:0%
+women have gone up and they start
+educating them more
+
+ align:start position:0%
+educating them more
+ 
+
+ align:start position:0%
+educating them more
+so interestingly there is no effect for
+
+ align:start position:0%
+so interestingly there is no effect for
+ 
+
+ align:start position:0%
+so interestingly there is no effect for
+men it's not discussed much in these
+
+ align:start position:0%
+men it's not discussed much in these
+ 
+
+ align:start position:0%
+men it's not discussed much in these
+people but I have another paper where
+
+ align:start position:0%
+people but I have another paper where
+ 
+
+ align:start position:0%
+people but I have another paper where
+they separate the boys between people
+
+ align:start position:0%
+they separate the boys between people
+ 
+
+ align:start position:0%
+they separate the boys between people
+who at Baseline were described to be the
+
+ align:start position:0%
+who at Baseline were described to be the
+ 
+
+ align:start position:0%
+who at Baseline were described to be the
+one who are going to take care of the
+
+ align:start position:0%
+one who are going to take care of the
+ 
+
+ align:start position:0%
+one who are going to take care of the
+family farm so usually the oldest Boy
+
+ align:start position:0%
+family farm so usually the oldest Boy
+ 
+
+ align:start position:0%
+family farm so usually the oldest Boy
+versus the younger boy and when they
+
+ align:start position:0%
+versus the younger boy and when they
+ 
+
+ align:start position:0%
+versus the younger boy and when they
+separate that they find that actually
+
+ align:start position:0%
+separate that they find that actually
+ 
+
+ align:start position:0%
+separate that they find that actually
+when the BPO recruitment started for the
+
+ align:start position:0%
+when the BPO recruitment started for the
+ 
+
+ align:start position:0%
+when the BPO recruitment started for the
+boys who are supposed to work in the
+
+ align:start position:0%
+boys who are supposed to work in the
+ 
+
+ align:start position:0%
+boys who are supposed to work in the
+Family Farm
+
+ align:start position:0%
+Family Farm
+ 
+
+ align:start position:0%
+Family Farm
+the education went down
+
+ align:start position:0%
+the education went down
+ 
+
+ align:start position:0%
+the education went down
+and for other boys it's more like girls
+
+ align:start position:0%
+and for other boys it's more like girls
+ 
+
+ align:start position:0%
+and for other boys it's more like girls
+and so the idea there is that you're
+
+ align:start position:0%
+and so the idea there is that you're
+ 
+
+ align:start position:0%
+and so the idea there is that you're
+very scared to have returned to
+
+ align:start position:0%
+very scared to have returned to
+ 
+
+ align:start position:0%
+very scared to have returned to
+education go up for the boys because you
+
+ align:start position:0%
+education go up for the boys because you
+ 
+
+ align:start position:0%
+education go up for the boys because you
+don't want them to leave because someone
+
+ align:start position:0%
+don't want them to leave because someone
+ 
+
+ align:start position:0%
+don't want them to leave because someone
+needs to stay
+
+ align:start position:0%
+needs to stay
+ 
+
+ align:start position:0%
+needs to stay
+to take care of you and to take care of
+
+ align:start position:0%
+to take care of you and to take care of
+ 
+
+ align:start position:0%
+to take care of you and to take care of
+the farm and therefore you're going to
+
+ align:start position:0%
+the farm and therefore you're going to
+ 
+
+ align:start position:0%
+the farm and therefore you're going to
+surprise education so that they don't
+
+ align:start position:0%
+surprise education so that they don't
+ 
+
+ align:start position:0%
+surprise education so that they don't
+you know hear the return to education
+
+ align:start position:0%
+you know hear the return to education
+ 
+
+ align:start position:0%
+you know hear the return to education
+for you are a negative from the point of
+
+ align:start position:0%
+for you are a negative from the point of
+ 
+
+ align:start position:0%
+for you are a negative from the point of
+view of the parents so that leads a
+
+ align:start position:0%
+view of the parents so that leads a
+ 
+
+ align:start position:0%
+view of the parents so that leads a
+little bit to the conversation we had
+
+ align:start position:0%
+little bit to the conversation we had
+ 
+
+ align:start position:0%
+little bit to the conversation we had
+with uh and others about the contract
+
+ align:start position:0%
+with uh and others about the contract
+ 
+
+ align:start position:0%
+with uh and others about the contract
+between the family
+
+ align:start position:0%
+between the family
+ 
+
+ align:start position:0%
+between the family
+as if you cannot contract to get the
+
+ align:start position:0%
+as if you cannot contract to get the
+ 
+
+ align:start position:0%
+as if you cannot contract to get the
+money back from your board and you are
+
+ align:start position:0%
+money back from your board and you are
+ 
+
+ align:start position:0%
+money back from your board and you are
+not sending them
+
+ align:start position:0%
+not sending them
+ 
+
+ align:start position:0%
+not sending them
+um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so there are there are two other
+
+ align:start position:0%
+okay so there are there are two other
+ 
+
+ align:start position:0%
+okay so there are there are two other
+things that I wanted to do that I didn't
+
+ align:start position:0%
+things that I wanted to do that I didn't
+ 
+
+ align:start position:0%
+things that I wanted to do that I didn't
+have time to do one of them I'll do
+
+ align:start position:0%
+have time to do one of them I'll do
+ 
+
+ align:start position:0%
+have time to do one of them I'll do
+later uh the when we talk about the
+
+ align:start position:0%
+later uh the when we talk about the
+ 
+
+ align:start position:0%
+later uh the when we talk about the
+family that's fine we can we can take
+
+ align:start position:0%
+family that's fine we can we can take
+ 
+
+ align:start position:0%
+family that's fine we can we can take
+that that's the Rebecca Addison Ross
+
+ align:start position:0%
+that that's the Rebecca Addison Ross
+ 
+
+ align:start position:0%
+that that's the Rebecca Addison Ross
+paper about the fact that parents have
+
+ align:start position:0%
+paper about the fact that parents have
+ 
+
+ align:start position:0%
+paper about the fact that parents have
+no idea what their kids are up to
+
+ align:start position:0%
+no idea what their kids are up to
+ 
+
+ align:start position:0%
+no idea what their kids are up to
+but this one I want to briefly uh
+
+ align:start position:0%
+but this one I want to briefly uh
+ 
+
+ align:start position:0%
+but this one I want to briefly uh
+mention
+
+ align:start position:0%
+mention
+ 
+
+ align:start position:0%
+mention
+it's a paper by uh simaja Sandra and
+
+ align:start position:0%
+it's a paper by uh simaja Sandra and
+ 
+
+ align:start position:0%
+it's a paper by uh simaja Sandra and
+Adriana erasmune
+
+ align:start position:0%
+Adriana erasmune
+ 
+
+ align:start position:0%
+Adriana erasmune
+who is looking at another returned way
+
+ align:start position:0%
+who is looking at another returned way
+ 
+
+ align:start position:0%
+who is looking at another returned way
+of affecting the return to education or
+
+ align:start position:0%
+of affecting the return to education or
+ 
+
+ align:start position:0%
+of affecting the return to education or
+the where returns are affecting is
+
+ align:start position:0%
+the where returns are affecting is
+ 
+
+ align:start position:0%
+the where returns are affecting is
+simply the fact that how long are you
+
+ align:start position:0%
+simply the fact that how long are you
+ 
+
+ align:start position:0%
+simply the fact that how long are you
+going to live
+
+ align:start position:0%
+going to live
+ 
+
+ align:start position:0%
+going to live
+so if you expect to live for a very
+
+ align:start position:0%
+so if you expect to live for a very
+ 
+
+ align:start position:0%
+so if you expect to live for a very
+short period of time then your education
+
+ align:start position:0%
+short period of time then your education
+ 
+
+ align:start position:0%
+short period of time then your education
+is not very worth it or if you expect
+
+ align:start position:0%
+is not very worth it or if you expect
+ 
+
+ align:start position:0%
+is not very worth it or if you expect
+your girl to leave for a very short time
+
+ align:start position:0%
+your girl to leave for a very short time
+ 
+
+ align:start position:0%
+your girl to leave for a very short time
+because she's going to die in childbirth
+
+ align:start position:0%
+because she's going to die in childbirth
+ 
+
+ align:start position:0%
+because she's going to die in childbirth
+anywhere then you know she's not going
+
+ align:start position:0%
+anywhere then you know she's not going
+ 
+
+ align:start position:0%
+anywhere then you know she's not going
+to experience the return for a very
+
+ align:start position:0%
+to experience the return for a very
+ 
+
+ align:start position:0%
+to experience the return for a very
+short time so that's a very Economist
+
+ align:start position:0%
+short time so that's a very Economist
+ 
+
+ align:start position:0%
+short time so that's a very Economist
+Economist way to think but uh
+
+ align:start position:0%
+Economist way to think but uh
+ 
+
+ align:start position:0%
+Economist way to think but uh
+it is quite interesting that it works
+
+ align:start position:0%
+it is quite interesting that it works
+ 
+
+ align:start position:0%
+it is quite interesting that it works
+here so what they are looking for to
+
+ align:start position:0%
+here so what they are looking for to
+ 
+
+ align:start position:0%
+here so what they are looking for to
+know whether people so in principle
+
+ align:start position:0%
+know whether people so in principle
+ 
+
+ align:start position:0%
+know whether people so in principle
+implication of this model is that if
+
+ align:start position:0%
+implication of this model is that if
+ 
+
+ align:start position:0%
+implication of this model is that if
+people expect to live longer they should
+
+ align:start position:0%
+people expect to live longer they should
+ 
+
+ align:start position:0%
+people expect to live longer they should
+or expect their daughters to to live
+
+ align:start position:0%
+or expect their daughters to to live
+ 
+
+ align:start position:0%
+or expect their daughters to to live
+longer they should really educate them
+
+ align:start position:0%
+longer they should really educate them
+ 
+
+ align:start position:0%
+longer they should really educate them
+more because they're going to enjoy the
+
+ align:start position:0%
+more because they're going to enjoy the
+ 
+
+ align:start position:0%
+more because they're going to enjoy the
+return of this education over a longer
+
+ align:start position:0%
+return of this education over a longer
+ 
+
+ align:start position:0%
+return of this education over a longer
+time period
+
+ align:start position:0%
+time period
+ 
+
+ align:start position:0%
+time period
+so you'll know you need an instrument
+
+ align:start position:0%
+so you'll know you need an instrument
+ 
+
+ align:start position:0%
+so you'll know you need an instrument
+that affects the number of years someone
+
+ align:start position:0%
+that affects the number of years someone
+ 
+
+ align:start position:0%
+that affects the number of years someone
+can expect to live without affecting
+
+ align:start position:0%
+can expect to live without affecting
+ 
+
+ align:start position:0%
+can expect to live without affecting
+anything else like the skill premium or
+
+ align:start position:0%
+anything else like the skill premium or
+ 
+
+ align:start position:0%
+anything else like the skill premium or
+the low uh or the low skill wage which
+
+ align:start position:0%
+the low uh or the low skill wage which
+ 
+
+ align:start position:0%
+the low uh or the low skill wage which
+seems like a very hard problem
+
+ align:start position:0%
+seems like a very hard problem
+ 
+
+ align:start position:0%
+seems like a very hard problem
+and what they find is to is uh in Sri
+
+ align:start position:0%
+and what they find is to is uh in Sri
+ 
+
+ align:start position:0%
+and what they find is to is uh in Sri
+Lanka a program that introduces
+
+ align:start position:0%
+Lanka a program that introduces
+ 
+
+ align:start position:0%
+Lanka a program that introduces
+ambulance uh in in all the villages
+
+ align:start position:0%
+ambulance uh in in all the villages
+ 
+
+ align:start position:0%
+ambulance uh in in all the villages
+and when they did that
+
+ align:start position:0%
+and when they did that
+ 
+
+ align:start position:0%
+and when they did that
+uh infant mortality collapsed
+
+ align:start position:0%
+uh infant mortality collapsed
+ 
+
+ align:start position:0%
+uh infant mortality collapsed
+and I did that infant mortality
+
+ align:start position:0%
+and I did that infant mortality
+ 
+
+ align:start position:0%
+and I did that infant mortality
+collapsed and in particular the drop in
+
+ align:start position:0%
+collapsed and in particular the drop in
+ 
+
+ align:start position:0%
+collapsed and in particular the drop in
+infant mortality was much larger and
+
+ align:start position:0%
+infant mortality was much larger and
+ 
+
+ align:start position:0%
+infant mortality was much larger and
+places where infant maternity was very
+
+ align:start position:0%
+places where infant maternity was very
+ 
+
+ align:start position:0%
+places where infant maternity was very
+high so basically putting the ambulance
+
+ align:start position:0%
+high so basically putting the ambulance
+ 
+
+ align:start position:0%
+high so basically putting the ambulance
+flattened out the infant mortality curve
+
+ align:start position:0%
+flattened out the infant mortality curve
+ 
+
+ align:start position:0%
+flattened out the infant mortality curve
+leading to huge decline in infant
+
+ align:start position:0%
+leading to huge decline in infant
+ 
+
+ align:start position:0%
+leading to huge decline in infant
+mortality in places that were you know
+
+ align:start position:0%
+mortality in places that were you know
+ 
+
+ align:start position:0%
+mortality in places that were you know
+really far from the hospital and people
+
+ align:start position:0%
+really far from the hospital and people
+ 
+
+ align:start position:0%
+really far from the hospital and people
+couldn't get to the hospital so the
+
+ align:start position:0%
+couldn't get to the hospital so the
+ 
+
+ align:start position:0%
+couldn't get to the hospital so the
+ambulance kind of eliminated
+
+ align:start position:0%
+ambulance kind of eliminated
+ 
+
+ align:start position:0%
+ambulance kind of eliminated
+so now they use that in saying well that
+
+ align:start position:0%
+so now they use that in saying well that
+ 
+
+ align:start position:0%
+so now they use that in saying well that
+affects that affects the the life
+
+ align:start position:0%
+affects that affects the the life
+ 
+
+ align:start position:0%
+affects that affects the the life
+expectancy of the woman but not the men
+
+ align:start position:0%
+expectancy of the woman but not the men
+ 
+
+ align:start position:0%
+expectancy of the woman but not the men
+so now I'm going to use basically the
+
+ align:start position:0%
+so now I'm going to use basically the
+ 
+
+ align:start position:0%
+so now I'm going to use basically the
+pre ambulance maternal mortality rate as
+
+ align:start position:0%
+pre ambulance maternal mortality rate as
+ 
+
+ align:start position:0%
+pre ambulance maternal mortality rate as
+an instrument for the decline in
+
+ align:start position:0%
+an instrument for the decline in
+ 
+
+ align:start position:0%
+an instrument for the decline in
+maternal mortality rate over the period
+
+ align:start position:0%
+maternal mortality rate over the period
+ 
+
+ align:start position:0%
+maternal mortality rate over the period
+to see whether people seem to respond by
+
+ align:start position:0%
+to see whether people seem to respond by
+ 
+
+ align:start position:0%
+to see whether people seem to respond by
+by educating their their girls more
+
+ align:start position:0%
+by educating their their girls more
+ 
+
+ align:start position:0%
+by educating their their girls more
+relative to the boy
+
+ align:start position:0%
+relative to the boy
+ 
+
+ align:start position:0%
+relative to the boy
+so now what we have here is a triple
+
+ align:start position:0%
+so now what we have here is a triple
+ 
+
+ align:start position:0%
+so now what we have here is a triple
+different specification
+
+ align:start position:0%
+different specification
+ 
+
+ align:start position:0%
+different specification
+and I just write down put the
+
+ align:start position:0%
+and I just write down put the
+ 
+
+ align:start position:0%
+and I just write down put the
+specification down
+
+ align:start position:0%
+specification down
+ 
+
+ align:start position:0%
+specification down
+where we have we can have a fixed effect
+
+ align:start position:0%
+where we have we can have a fixed effect
+ 
+
+ align:start position:0%
+where we have we can have a fixed effect
+we can have two effects effect whichever
+
+ align:start position:0%
+we can have two effects effect whichever
+ 
+
+ align:start position:0%
+we can have two effects effect whichever
+way District uh year District time here
+
+ align:start position:0%
+way District uh year District time here
+ 
+
+ align:start position:0%
+way District uh year District time here
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+um gender time district and gender time
+
+ align:start position:0%
+um gender time district and gender time
+ 
+
+ align:start position:0%
+um gender time district and gender time
+year so all of the double interaction
+
+ align:start position:0%
+year so all of the double interaction
+ 
+
+ align:start position:0%
+year so all of the double interaction
+can be there because what we are going
+
+ align:start position:0%
+can be there because what we are going
+ 
+
+ align:start position:0%
+can be there because what we are going
+to use is maternal mortality
+
+ align:start position:0%
+to use is maternal mortality
+ 
+
+ align:start position:0%
+to use is maternal mortality
+in a particular year like the time when
+
+ align:start position:0%
+in a particular year like the time when
+ 
+
+ align:start position:0%
+in a particular year like the time when
+they were on the you know when the
+
+ align:start position:0%
+they were on the you know when the
+ 
+
+ align:start position:0%
+they were on the you know when the
+parents could observe it times the
+
+ align:start position:0%
+parents could observe it times the
+ 
+
+ align:start position:0%
+parents could observe it times the
+female the
+
+ align:start position:0%
+female the
+ 
+
+ align:start position:0%
+female the
+and I find the uh they find that more
+
+ align:start position:0%
+and I find the uh they find that more
+ 
+
+ align:start position:0%
+and I find the uh they find that more
+maternal mortality less education
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so using just that
+
+ align:start position:0%
+so using just that
+ 
+
+ align:start position:0%
+so using just that
+they find that more maternal mortality
+
+ align:start position:0%
+they find that more maternal mortality
+ 
+
+ align:start position:0%
+they find that more maternal mortality
+leads to less education so that's kind
+
+ align:start position:0%
+leads to less education so that's kind
+ 
+
+ align:start position:0%
+leads to less education so that's kind
+of a nice paper because I think many
+
+ align:start position:0%
+of a nice paper because I think many
+ 
+
+ align:start position:0%
+of a nice paper because I think many
+people were kind of entreating that
+
+ align:start position:0%
+people were kind of entreating that
+ 
+
+ align:start position:0%
+people were kind of entreating that
+something like that might be going on
+
+ align:start position:0%
+something like that might be going on
+ 
+
+ align:start position:0%
+something like that might be going on
+but since everything is usually
+
+ align:start position:0%
+but since everything is usually
+ 
+
+ align:start position:0%
+but since everything is usually
+correlated with everything it's very
+
+ align:start position:0%
+correlated with everything it's very
+ 
+
+ align:start position:0%
+correlated with everything it's very
+hard to test and it's like ambulance
+
+ align:start position:0%
+hard to test and it's like ambulance
+ 
+
+ align:start position:0%
+hard to test and it's like ambulance
+program that was that had such a massive
+
+ align:start position:0%
+program that was that had such a massive
+ 
+
+ align:start position:0%
+program that was that had such a massive
+effect on maternal material mortality
+
+ align:start position:0%
+effect on maternal material mortality
+ 
+
+ align:start position:0%
+effect on maternal material mortality
+reduction gave them a chance to to test
+
+ align:start position:0%
+reduction gave them a chance to to test
+ 
+
+ align:start position:0%
+reduction gave them a chance to to test
+the idea
+
+ align:start position:0%
+the idea
+ 
+
+ align:start position:0%
+the idea
+right so sorry uh so we're done for
+
+ align:start position:0%
+right so sorry uh so we're done for
+ 
+
+ align:start position:0%
+right so sorry uh so we're done for
+today sorry again for uh
+
+ align:start position:0%
+today sorry again for uh
+ 
+
+ align:start position:0%
+today sorry again for uh
+slow start and uh on Monday we'll
+
+ align:start position:0%
+slow start and uh on Monday we'll
+ 
+
+ align:start position:0%
+slow start and uh on Monday we'll
+continue talking about the Indonesia
+
+ align:start position:0%
+continue talking about the Indonesia
+ 
+
+ align:start position:0%
+continue talking about the Indonesia
+paper but we'll talk about this
+
+ align:start position:0%
+paper but we'll talk about this
+ 
+
+ align:start position:0%
+paper but we'll talk about this
+estimating the return to education we
+
+ align:start position:0%
+estimating the return to education we
+ 
+
+ align:start position:0%
+estimating the return to education we
+also talk about the Ghana paper which
+
+ align:start position:0%
+also talk about the Ghana paper which
+ 
+
+ align:start position:0%
+also talk about the Ghana paper which
+I'm asking you to read as you go along
+
+ align:start position:0%
+I'm asking you to read as you go along
+ 
+
+ align:start position:0%
+I'm asking you to read as you go along
+which is another
+
+ align:start position:0%
+which is another
+ 
+
+ align:start position:0%
+which is another
+take at estimating return to education
+
+ align:start position:0%
+take at estimating return to education
+ 
+
+ align:start position:0%
+take at estimating return to education
+or impact of Education
\ No newline at end of file
diff --git a/NcPUI7aPFhA.txt b/NcPUI7aPFhA.txt
new file mode 100644
index 0000000000000000000000000000000000000000..5a3600d998a710693fc14db460861d75094be1be
--- /dev/null
+++ b/NcPUI7aPFhA.txt
@@ -0,0 +1,6219 @@
+align:start position:0%
+ 
+the following content is provided under
+
+ align:start position:0%
+the following content is provided under
+ 
+
+ align:start position:0%
+the following content is provided under
+a Creative Commons license your support
+
+ align:start position:0%
+a Creative Commons license your support
+ 
+
+ align:start position:0%
+a Creative Commons license your support
+will help MIT OpenCourseWare continue to
+
+ align:start position:0%
+will help MIT OpenCourseWare continue to
+ 
+
+ align:start position:0%
+will help MIT OpenCourseWare continue to
+offer high quality educational resources
+
+ align:start position:0%
+offer high quality educational resources
+ 
+
+ align:start position:0%
+offer high quality educational resources
+for free
+
+ align:start position:0%
+for free
+ 
+
+ align:start position:0%
+for free
+to make a donation or to view additional
+
+ align:start position:0%
+to make a donation or to view additional
+ 
+
+ align:start position:0%
+to make a donation or to view additional
+materials from hundreds of MIT courses
+
+ align:start position:0%
+materials from hundreds of MIT courses
+ 
+
+ align:start position:0%
+materials from hundreds of MIT courses
+visit MIT opencourseware at ocw.mit.edu
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so this big MIT I just came from a
+
+ align:start position:0%
+okay so this big MIT I just came from a
+ 
+
+ align:start position:0%
+okay so this big MIT I just came from a
+faculty terrific faculty member Andy low
+
+ align:start position:0%
+faculty terrific faculty member Andy low
+ 
+
+ align:start position:0%
+faculty terrific faculty member Andy low
+in in the Sloan School and I have to
+
+ align:start position:0%
+in in the Sloan School and I have to
+ 
+
+ align:start position:0%
+in in the Sloan School and I have to
+tell you what he told us and then I had
+
+ align:start position:0%
+tell you what he told us and then I had
+ 
+
+ align:start position:0%
+tell you what he told us and then I had
+I had to leave before he could explain
+
+ align:start position:0%
+I had to leave before he could explain
+ 
+
+ align:start position:0%
+I had to leave before he could explain
+why it's true but this is like an
+
+ align:start position:0%
+why it's true but this is like an
+ 
+
+ align:start position:0%
+why it's true but this is like an
+amazing fact which I don't want to
+
+ align:start position:0%
+amazing fact which I don't want to
+ 
+
+ align:start position:0%
+amazing fact which I don't want to
+forget so here you go this is everything
+
+ align:start position:0%
+forget so here you go this is everything
+ 
+
+ align:start position:0%
+forget so here you go this is everything
+will be on that board so it's it's it's
+
+ align:start position:0%
+will be on that board so it's it's it's
+ 
+
+ align:start position:0%
+will be on that board so it's it's it's
+an observation about us or other people
+
+ align:start position:0%
+an observation about us or other people
+ 
+
+ align:start position:0%
+an observation about us or other people
+maybe not us but so suppose you have a
+
+ align:start position:0%
+maybe not us but so suppose you have a
+ 
+
+ align:start position:0%
+maybe not us but so suppose you have a
+biased coin maybe you don't the people
+
+ align:start position:0%
+biased coin maybe you don't the people
+ 
+
+ align:start position:0%
+biased coin maybe you don't the people
+playing this game don't know but it's
+
+ align:start position:0%
+playing this game don't know but it's
+ 
+
+ align:start position:0%
+playing this game don't know but it's
+75% likely to produce heads 25% likely
+
+ align:start position:0%
+75% likely to produce heads 25% likely
+ 
+
+ align:start position:0%
+75% likely to produce heads 25% likely
+to produce tails and then the player has
+
+ align:start position:0%
+to produce tails and then the player has
+ 
+
+ align:start position:0%
+to produce tails and then the player has
+to guess for one flip after another
+
+ align:start position:0%
+to guess for one flip after another
+ 
+
+ align:start position:0%
+to guess for one flip after another
+heads or tails and you get a dollar if
+
+ align:start position:0%
+heads or tails and you get a dollar if
+ 
+
+ align:start position:0%
+heads or tails and you get a dollar if
+you're right you pay a dollar if you're
+
+ align:start position:0%
+you're right you pay a dollar if you're
+ 
+
+ align:start position:0%
+you're right you pay a dollar if you're
+wrong so you just want to get as many
+
+ align:start position:0%
+wrong so you just want to get as many
+ 
+
+ align:start position:0%
+wrong so you just want to get as many
+right choices as possible from this coin
+
+ align:start position:0%
+right choices as possible from this coin
+ 
+
+ align:start position:0%
+right choices as possible from this coin
+flip that continues so what should you
+
+ align:start position:0%
+flip that continues so what should you
+ 
+
+ align:start position:0%
+flip that continues so what should you
+do well what I guess I hope we would do
+
+ align:start position:0%
+do well what I guess I hope we would do
+ 
+
+ align:start position:0%
+do well what I guess I hope we would do
+is we would not know what the
+
+ align:start position:0%
+is we would not know what the
+ 
+
+ align:start position:0%
+is we would not know what the
+probabilities were so we would guess
+
+ align:start position:0%
+probabilities were so we would guess
+ 
+
+ align:start position:0%
+probabilities were so we would guess
+maybe heads the first time tails the
+
+ align:start position:0%
+maybe heads the first time tails the
+ 
+
+ align:start position:0%
+maybe heads the first time tails the
+second time heads to the third time and
+
+ align:start position:0%
+second time heads to the third time and
+ 
+
+ align:start position:0%
+second time heads to the third time and
+so on but the actual result would be
+
+ align:start position:0%
+so on but the actual result would be
+ 
+
+ align:start position:0%
+so on but the actual result would be
+mostly heads
+
+ align:start position:0%
+mostly heads
+ 
+
+ align:start position:0%
+mostly heads
+so we would learn at some point that
+
+ align:start position:0%
+so we would learn at some point that
+ 
+
+ align:start position:0%
+so we would learn at some point that
+maybe maybe not quite as soon as that we
+
+ align:start position:0%
+maybe maybe not quite as soon as that we
+ 
+
+ align:start position:0%
+maybe maybe not quite as soon as that we
+would eventually learn that we should
+
+ align:start position:0%
+would eventually learn that we should
+ 
+
+ align:start position:0%
+would eventually learn that we should
+keep guessing heads right and then we
+
+ align:start position:0%
+keep guessing heads right and then we
+ 
+
+ align:start position:0%
+keep guessing heads right and then we
+would be that would be our optimal
+
+ align:start position:0%
+would be that would be our optimal
+ 
+
+ align:start position:0%
+would be that would be our optimal
+strategy to guess heads all the time but
+
+ align:start position:0%
+strategy to guess heads all the time but
+ 
+
+ align:start position:0%
+strategy to guess heads all the time but
+what do people actually do they do start
+
+ align:start position:0%
+what do people actually do they do start
+ 
+
+ align:start position:0%
+what do people actually do they do start
+like this same way and then they're
+
+ align:start position:0%
+like this same way and then they're
+ 
+
+ align:start position:0%
+like this same way and then they're
+beginning to learn that heads is more
+
+ align:start position:0%
+beginning to learn that heads is more
+ 
+
+ align:start position:0%
+beginning to learn that heads is more
+common so maybe they do more heads than
+
+ align:start position:0%
+common so maybe they do more heads than
+ 
+
+ align:start position:0%
+common so maybe they do more heads than
+tails but sometimes tails is right and
+
+ align:start position:0%
+tails but sometimes tails is right and
+ 
+
+ align:start position:0%
+tails but sometimes tails is right and
+then after a little while they maybe see
+
+ align:start position:0%
+then after a little while they maybe see
+ 
+
+ align:start position:0%
+then after a little while they maybe see
+that it's yeah or they're just well
+
+ align:start position:0%
+that it's yeah or they're just well
+ 
+
+ align:start position:0%
+that it's yeah or they're just well
+maybe they're not counting they're just
+
+ align:start position:0%
+maybe they're not counting they're just
+ 
+
+ align:start position:0%
+maybe they're not counting they're just
+like operating like ordinary people
+
+ align:start position:0%
+like operating like ordinary people
+ 
+
+ align:start position:0%
+like operating like ordinary people
+and what do ordinary people actually do
+
+ align:start position:0%
+and what do ordinary people actually do
+ 
+
+ align:start position:0%
+and what do ordinary people actually do
+in the long run you would say guess
+
+ align:start position:0%
+in the long run you would say guess
+ 
+
+ align:start position:0%
+in the long run you would say guess
+heads every time right but they don't in
+
+ align:start position:0%
+heads every time right but they don't in
+ 
+
+ align:start position:0%
+heads every time right but they don't in
+the long run people and maybe animals
+
+ align:start position:0%
+the long run people and maybe animals
+ 
+
+ align:start position:0%
+the long run people and maybe animals
+and whatever guess heads three-quarters
+
+ align:start position:0%
+and whatever guess heads three-quarters
+ 
+
+ align:start position:0%
+and whatever guess heads three-quarters
+of the time and tails one quarter at a
+
+ align:start position:0%
+of the time and tails one quarter at a
+ 
+
+ align:start position:0%
+of the time and tails one quarter at a
+time isn't that unbelievable they're
+
+ align:start position:0%
+time isn't that unbelievable they're
+ 
+
+ align:start position:0%
+time isn't that unbelievable they're
+guessing tails a quarter of the time
+
+ align:start position:0%
+guessing tails a quarter of the time
+ 
+
+ align:start position:0%
+guessing tails a quarter of the time
+when the odds are never changing anyway
+
+ align:start position:0%
+when the odds are never changing anyway
+ 
+
+ align:start position:0%
+when the odds are never changing anyway
+that's that's something that economists
+
+ align:start position:0%
+that's that's something that economists
+ 
+
+ align:start position:0%
+that's that's something that economists
+and and other people have to explain and
+
+ align:start position:0%
+and and other people have to explain and
+ 
+
+ align:start position:0%
+and and other people have to explain and
+if I had been able to stay another hour
+
+ align:start position:0%
+if I had been able to stay another hour
+ 
+
+ align:start position:0%
+if I had been able to stay another hour
+I could tell you about the explanation
+
+ align:start position:0%
+I could tell you about the explanation
+ 
+
+ align:start position:0%
+I could tell you about the explanation
+but anyway that's that's I I see I've
+
+ align:start position:0%
+but anyway that's that's I I see I've
+ 
+
+ align:start position:0%
+but anyway that's that's I I see I've
+written that on a board that I have no
+
+ align:start position:0%
+written that on a board that I have no
+ 
+
+ align:start position:0%
+written that on a board that I have no
+way to bury so it's gonna be there and
+
+ align:start position:0%
+way to bury so it's gonna be there and
+ 
+
+ align:start position:0%
+way to bury so it's gonna be there and
+it's not the subject of 1806 five but
+
+ align:start position:0%
+it's not the subject of 1806 five but
+ 
+
+ align:start position:0%
+it's not the subject of 1806 five but
+it's kind of amazing right so there's
+
+ align:start position:0%
+it's kind of amazing right so there's
+ 
+
+ align:start position:0%
+it's kind of amazing right so there's
+good math problems everywhere okay can I
+
+ align:start position:0%
+good math problems everywhere okay can I
+ 
+
+ align:start position:0%
+good math problems everywhere okay can I
+just leave you with what I know and and
+
+ align:start position:0%
+just leave you with what I know and and
+ 
+
+ align:start position:0%
+just leave you with what I know and and
+if I learn more I'll come back to that
+
+ align:start position:0%
+if I learn more I'll come back to that
+ 
+
+ align:start position:0%
+if I learn more I'll come back to that
+question okay
+
+ align:start position:0%
+question okay
+ 
+
+ align:start position:0%
+question okay
+please turn attention this way right
+
+ align:start position:0%
+please turn attention this way right
+ 
+
+ align:start position:0%
+please turn attention this way right
+Norm's a little a few words on norms
+
+ align:start position:0%
+Norm's a little a few words on norms
+ 
+
+ align:start position:0%
+Norm's a little a few words on norms
+just like that should be a word in your
+
+ align:start position:0%
+just like that should be a word in your
+ 
+
+ align:start position:0%
+just like that should be a word in your
+language and so you should know what it
+
+ align:start position:0%
+language and so you should know what it
+ 
+
+ align:start position:0%
+language and so you should know what it
+mean and you should know they're a few
+
+ align:start position:0%
+mean and you should know they're a few
+ 
+
+ align:start position:0%
+mean and you should know they're a few
+of the important norms again a norm is a
+
+ align:start position:0%
+of the important norms again a norm is a
+ 
+
+ align:start position:0%
+of the important norms again a norm is a
+way to measure the size of a vector or
+
+ align:start position:0%
+way to measure the size of a vector or
+ 
+
+ align:start position:0%
+way to measure the size of a vector or
+the size of a matrix or the size of a
+
+ align:start position:0%
+the size of a matrix or the size of a
+ 
+
+ align:start position:0%
+the size of a matrix or the size of a
+tensor whatever we have or a function
+
+ align:start position:0%
+tensor whatever we have or a function
+ 
+
+ align:start position:0%
+tensor whatever we have or a function
+very important the norm would be a
+
+ align:start position:0%
+very important the norm would be a
+ 
+
+ align:start position:0%
+very important the norm would be a
+function like sine X from zero to PI
+
+ align:start position:0%
+function like sine X from zero to PI
+ 
+
+ align:start position:0%
+function like sine X from zero to PI
+what would be the size of that function
+
+ align:start position:0%
+what would be the size of that function
+ 
+
+ align:start position:0%
+what would be the size of that function
+well if it was two sine x the size would
+
+ align:start position:0%
+well if it was two sine x the size would
+ 
+
+ align:start position:0%
+well if it was two sine x the size would
+be twice as much so the norm should
+
+ align:start position:0%
+be twice as much so the norm should
+ 
+
+ align:start position:0%
+be twice as much so the norm should
+reflect that but so yesterday or
+
+ align:start position:0%
+reflect that but so yesterday or
+ 
+
+ align:start position:0%
+reflect that but so yesterday or
+Wednesday I told you the so there P
+
+ align:start position:0%
+Wednesday I told you the so there P
+ 
+
+ align:start position:0%
+Wednesday I told you the so there P
+equals to 1 actually infinity and then
+
+ align:start position:0%
+equals to 1 actually infinity and then
+ 
+
+ align:start position:0%
+equals to 1 actually infinity and then
+I'm gonna put in the zero norm with a
+
+ align:start position:0%
+I'm gonna put in the zero norm with a
+ 
+
+ align:start position:0%
+I'm gonna put in the zero norm with a
+question mark because you'll see it's
+
+ align:start position:0%
+question mark because you'll see it's
+ 
+
+ align:start position:0%
+question mark because you'll see it's
+that it has a problem but let me just
+
+ align:start position:0%
+that it has a problem but let me just
+ 
+
+ align:start position:0%
+that it has a problem but let me just
+recall from last time so these are the P
+
+ align:start position:0%
+recall from last time so these are the P
+ 
+
+ align:start position:0%
+recall from last time so these are the P
+equal to two is the usual sum of squares
+
+ align:start position:0%
+equal to two is the usual sum of squares
+ 
+
+ align:start position:0%
+equal to two is the usual sum of squares
+square root usual length of a vector P
+
+ align:start position:0%
+square root usual length of a vector P
+ 
+
+ align:start position:0%
+square root usual length of a vector P
+equal one is this very important norm so
+
+ align:start position:0%
+equal one is this very important norm so
+ 
+
+ align:start position:0%
+equal one is this very important norm so
+a we call that the l1 norm and we'll see
+
+ align:start position:0%
+a we call that the l1 norm and we'll see
+ 
+
+ align:start position:0%
+a we call that the l1 norm and we'll see
+a lot of that that really I mentioned
+
+ align:start position:0%
+a lot of that that really I mentioned
+ 
+
+ align:start position:0%
+a lot of that that really I mentioned
+that it plays a very significant part
+
+ align:start position:0%
+that it plays a very significant part
+ 
+
+ align:start position:0%
+that it plays a very significant part
+now in compress sensing it really was a
+
+ align:start position:0%
+now in compress sensing it really was a
+ 
+
+ align:start position:0%
+now in compress sensing it really was a
+bombshell in signal processing to
+
+ align:start position:0%
+bombshell in signal processing to
+ 
+
+ align:start position:0%
+bombshell in signal processing to
+discover and in other fields to to
+
+ align:start position:0%
+discover and in other fields to to
+ 
+
+ align:start position:0%
+discover and in other fields to to
+discover that some things really work
+
+ align:start position:0%
+discover that some things really work
+ 
+
+ align:start position:0%
+discover that some things really work
+well work best in the l1 norm the
+
+ align:start position:0%
+well work best in the l1 norm the
+ 
+
+ align:start position:0%
+well work best in the l1 norm the
+maximum norm has a natural part to play
+
+ align:start position:0%
+maximum norm has a natural part to play
+ 
+
+ align:start position:0%
+maximum norm has a natural part to play
+and we'll see that or its matrix analog
+
+ align:start position:0%
+and we'll see that or its matrix analog
+ 
+
+ align:start position:0%
+and we'll see that or its matrix analog
+so I didn't mention the l0 norm all this
+
+ align:start position:0%
+so I didn't mention the l0 norm all this
+ 
+
+ align:start position:0%
+so I didn't mention the l0 norm all this
+LP business so the LP norm
+
+ align:start position:0%
+LP business so the LP norm
+ 
+
+ align:start position:0%
+LP business so the LP norm
+or for any P is you take the piece power
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+to the piece power up here P was 2 and
+
+ align:start position:0%
+to the piece power up here P was 2 and
+ 
+
+ align:start position:0%
+to the piece power up here P was 2 and
+your take the piece root so maybe I
+
+ align:start position:0%
+your take the piece root so maybe I
+ 
+
+ align:start position:0%
+your take the piece root so maybe I
+should write it to the one over P that's
+
+ align:start position:0%
+should write it to the one over P that's
+ 
+
+ align:start position:0%
+should write it to the one over P that's
+then that way
+
+ align:start position:0%
+then that way
+ 
+
+ align:start position:0%
+then that way
+taking piece powers and piece roots we
+
+ align:start position:0%
+taking piece powers and piece roots we
+ 
+
+ align:start position:0%
+taking piece powers and piece roots we
+do get the norm of two V has a factor
+
+ align:start position:0%
+do get the norm of two V has a factor
+ 
+
+ align:start position:0%
+do get the norm of two V has a factor
+two compared to the norm of V so P equal
+
+ align:start position:0%
+two compared to the norm of V so P equal
+ 
+
+ align:start position:0%
+two compared to the norm of V so P equal
+to 2 you see that we've got it right
+
+ align:start position:0%
+to 2 you see that we've got it right
+ 
+
+ align:start position:0%
+to 2 you see that we've got it right
+there P equal one you see it here
+
+ align:start position:0%
+there P equal one you see it here
+ 
+
+ align:start position:0%
+there P equal one you see it here
+because it's just just sum of the
+
+ align:start position:0%
+because it's just just sum of the
+ 
+
+ align:start position:0%
+because it's just just sum of the
+absolute values people infinity if I if
+
+ align:start position:0%
+absolute values people infinity if I if
+ 
+
+ align:start position:0%
+absolute values people infinity if I if
+I move P up and up and up it will pick
+
+ align:start position:0%
+I move P up and up and up it will pick
+ 
+
+ align:start position:0%
+I move P up and up and up it will pick
+out you know as I increase P whichever
+
+ align:start position:0%
+out you know as I increase P whichever
+ 
+
+ align:start position:0%
+out you know as I increase P whichever
+one is biggest is going to just take
+
+ align:start position:0%
+one is biggest is going to just take
+ 
+
+ align:start position:0%
+one is biggest is going to just take
+over and that's why you get to max norm
+
+ align:start position:0%
+over and that's why you get to max norm
+ 
+
+ align:start position:0%
+over and that's why you get to max norm
+now there's zero norm where I'm using
+
+ align:start position:0%
+now there's zero norm where I'm using
+ 
+
+ align:start position:0%
+now there's zero norm where I'm using
+that word like improperly as you'll see
+
+ align:start position:0%
+that word like improperly as you'll see
+ 
+
+ align:start position:0%
+that word like improperly as you'll see
+because if so what is the 0 norm it's
+
+ align:start position:0%
+because if so what is the 0 norm it's
+ 
+
+ align:start position:0%
+because if so what is the 0 norm it's
+the so so it's the number of non-zeros
+
+ align:start position:0%
+the so so it's the number of non-zeros
+ 
+
+ align:start position:0%
+the so so it's the number of non-zeros
+of nonzero components its it it's the
+
+ align:start position:0%
+of nonzero components its it it's the
+ 
+
+ align:start position:0%
+of nonzero components its it it's the
+thing that you'd like to know about in
+
+ align:start position:0%
+thing that you'd like to know about in
+ 
+
+ align:start position:0%
+thing that you'd like to know about in
+question of sparsity does the is there
+
+ align:start position:0%
+question of sparsity does the is there
+ 
+
+ align:start position:0%
+question of sparsity does the is there
+just one nonzero component or there 11
+
+ align:start position:0%
+just one nonzero component or there 11
+ 
+
+ align:start position:0%
+just one nonzero component or there 11
+are there 101 like what that you might
+
+ align:start position:0%
+are there 101 like what that you might
+ 
+
+ align:start position:0%
+are there 101 like what that you might
+want to minimize that because sparse
+
+ align:start position:0%
+want to minimize that because sparse
+ 
+
+ align:start position:0%
+want to minimize that because sparse
+vectors and sparse matrices are much
+
+ align:start position:0%
+vectors and sparse matrices are much
+ 
+
+ align:start position:0%
+vectors and sparse matrices are much
+faster to compute with you've got good
+
+ align:start position:0%
+faster to compute with you've got good
+ 
+
+ align:start position:0%
+faster to compute with you've got good
+stuff but now i claim that's not a norm
+
+ align:start position:0%
+stuff but now i claim that's not a norm
+ 
+
+ align:start position:0%
+stuff but now i claim that's not a norm
+in the number of 0 nonzero components
+
+ align:start position:0%
+in the number of 0 nonzero components
+ 
+
+ align:start position:0%
+in the number of 0 nonzero components
+because what's the norm of to how does
+
+ align:start position:0%
+because what's the norm of to how does
+ 
+
+ align:start position:0%
+because what's the norm of to how does
+the norm of 2v compare with the norm of
+
+ align:start position:0%
+the norm of 2v compare with the norm of
+ 
+
+ align:start position:0%
+the norm of 2v compare with the norm of
+V the 0 norm it would be the same to V
+
+ align:start position:0%
+V the 0 norm it would be the same to V
+ 
+
+ align:start position:0%
+V the 0 norm it would be the same to V
+has the same number of non-zeros as
+
+ align:start position:0%
+has the same number of non-zeros as
+ 
+
+ align:start position:0%
+has the same number of non-zeros as
+so it violates the rule for a norm so I
+
+ align:start position:0%
+so it violates the rule for a norm so I
+ 
+
+ align:start position:0%
+so it violates the rule for a norm so I
+think with these norms and all the peas
+
+ align:start position:0%
+think with these norms and all the peas
+ 
+
+ align:start position:0%
+think with these norms and all the peas
+in between so actually the the math
+
+ align:start position:0%
+in between so actually the the math
+ 
+
+ align:start position:0%
+in between so actually the the math
+papers are full of let P be between 1
+
+ align:start position:0%
+papers are full of let P be between 1
+ 
+
+ align:start position:0%
+papers are full of let P be between 1
+and infinity and because that's the
+
+ align:start position:0%
+and infinity and because that's the
+ 
+
+ align:start position:0%
+and infinity and because that's the
+range where you do have a proper norm as
+
+ align:start position:0%
+range where you do have a proper norm as
+ 
+
+ align:start position:0%
+range where you do have a proper norm as
+we will see I think the good thing to do
+
+ align:start position:0%
+we will see I think the good thing to do
+ 
+
+ align:start position:0%
+we will see I think the good thing to do
+with these norms is to have a picture in
+
+ align:start position:0%
+with these norms is to have a picture in
+ 
+
+ align:start position:0%
+with these norms is to have a picture in
+your mind the geometry of a norm is real
+
+ align:start position:0%
+your mind the geometry of a norm is real
+ 
+
+ align:start position:0%
+your mind the geometry of a norm is real
+is good so the picture I'm gonna suggest
+
+ align:start position:0%
+is good so the picture I'm gonna suggest
+ 
+
+ align:start position:0%
+is good so the picture I'm gonna suggest
+is plot all the vectors let's say in 2d
+
+ align:start position:0%
+is plot all the vectors let's say in 2d
+ 
+
+ align:start position:0%
+is plot all the vectors let's say in 2d
+so two dimensional space or two so I
+
+ align:start position:0%
+so two dimensional space or two so I
+ 
+
+ align:start position:0%
+so two dimensional space or two so I
+want to plot then the vectors they have
+
+ align:start position:0%
+want to plot then the vectors they have
+ 
+
+ align:start position:0%
+want to plot then the vectors they have
+V equal one in these different norms so
+
+ align:start position:0%
+V equal one in these different norms so
+ 
+
+ align:start position:0%
+V equal one in these different norms so
+let me ask you what so here's 2d space
+
+ align:start position:0%
+let me ask you what so here's 2d space
+ 
+
+ align:start position:0%
+let me ask you what so here's 2d space
+r2 and now I want to plot all the
+
+ align:start position:0%
+r2 and now I want to plot all the
+ 
+
+ align:start position:0%
+r2 and now I want to plot all the
+vectors that have the ordinary l2
+
+ align:start position:0%
+vectors that have the ordinary l2
+ 
+
+ align:start position:0%
+vectors that have the ordinary l2
+lengths equal one so what does that
+
+ align:start position:0%
+lengths equal one so what does that
+ 
+
+ align:start position:0%
+lengths equal one so what does that
+picture look like I just think a picture
+
+ align:start position:0%
+picture look like I just think a picture
+ 
+
+ align:start position:0%
+picture look like I just think a picture
+is really worth something it's a circle
+
+ align:start position:0%
+is really worth something it's a circle
+ 
+
+ align:start position:0%
+is really worth something it's a circle
+thanks it's a circle it's a circle this
+
+ align:start position:0%
+thanks it's a circle it's a circle this
+ 
+
+ align:start position:0%
+thanks it's a circle it's a circle this
+circle is that's the equation of course
+
+ align:start position:0%
+circle is that's the equation of course
+ 
+
+ align:start position:0%
+circle is that's the equation of course
+v1 squared plus v2 squared 1 so that I
+
+ align:start position:0%
+v1 squared plus v2 squared 1 so that I
+ 
+
+ align:start position:0%
+v1 squared plus v2 squared 1 so that I
+would call that the unit ball for the
+
+ align:start position:0%
+would call that the unit ball for the
+ 
+
+ align:start position:0%
+would call that the unit ball for the
+norm or whatever is is a circle okay now
+
+ align:start position:0%
+norm or whatever is is a circle okay now
+ 
+
+ align:start position:0%
+norm or whatever is is a circle okay now
+now here comes more interesting what
+
+ align:start position:0%
+now here comes more interesting what
+ 
+
+ align:start position:0%
+now here comes more interesting what
+about in the l1 so again tell me how to
+
+ align:start position:0%
+about in the l1 so again tell me how to
+ 
+
+ align:start position:0%
+about in the l1 so again tell me how to
+plot all the points that have V 1 plus V
+
+ align:start position:0%
+plot all the points that have V 1 plus V
+ 
+
+ align:start position:0%
+plot all the points that have V 1 plus V
+2 equal 1 what what what's the boundary
+
+ align:start position:0%
+2 equal 1 what what what's the boundary
+ 
+
+ align:start position:0%
+2 equal 1 what what what's the boundary
+gonna look like now it's gonna be let's
+
+ align:start position:0%
+gonna look like now it's gonna be let's
+ 
+
+ align:start position:0%
+gonna look like now it's gonna be let's
+see well I can put in a certain number
+
+ align:start position:0%
+see well I can put in a certain number
+ 
+
+ align:start position:0%
+see well I can put in a certain number
+of points there one and there one and
+
+ align:start position:0%
+of points there one and there one and
+ 
+
+ align:start position:0%
+of points there one and there one and
+there at minus one and there
+
+ align:start position:0%
+there at minus one and there
+ 
+
+ align:start position:0%
+there at minus one and there
+this one there was that would be the
+
+ align:start position:0%
+this one there was that would be the
+ 
+
+ align:start position:0%
+this one there was that would be the
+vector that would reflect the vector 1 0
+
+ align:start position:0%
+vector that would reflect the vector 1 0
+ 
+
+ align:start position:0%
+vector that would reflect the vector 1 0
+and this would reflect the vector 0
+
+ align:start position:0%
+and this would reflect the vector 0
+ 
+
+ align:start position:0%
+and this would reflect the vector 0
+minus 1 so yeah ok so those are like
+
+ align:start position:0%
+minus 1 so yeah ok so those are like
+ 
+
+ align:start position:0%
+minus 1 so yeah ok so those are like
+four points easy to plot easy to see
+
+ align:start position:0%
+four points easy to plot easy to see
+ 
+
+ align:start position:0%
+four points easy to plot easy to see
+that the l1 norm but what's the full
+
+ align:start position:0%
+that the l1 norm but what's the full
+ 
+
+ align:start position:0%
+that the l1 norm but what's the full
+what so what's the rest of the boundary
+
+ align:start position:0%
+what so what's the rest of the boundary
+ 
+
+ align:start position:0%
+what so what's the rest of the boundary
+here it's a diamond good it's a diamond
+
+ align:start position:0%
+here it's a diamond good it's a diamond
+ 
+
+ align:start position:0%
+here it's a diamond good it's a diamond
+it's we have linear set equal to one up
+
+ align:start position:0%
+it's we have linear set equal to one up
+ 
+
+ align:start position:0%
+it's we have linear set equal to one up
+here in the positive quadrant
+
+ align:start position:0%
+here in the positive quadrant
+ 
+
+ align:start position:0%
+here in the positive quadrant
+it's just V 1 plus V 2 equal 1 in the
+
+ align:start position:0%
+it's just V 1 plus V 2 equal 1 in the
+ 
+
+ align:start position:0%
+it's just V 1 plus V 2 equal 1 in the
+graph of that is a straight line so all
+
+ align:start position:0%
+graph of that is a straight line so all
+ 
+
+ align:start position:0%
+graph of that is a straight line so all
+these guys this is all the points with V
+
+ align:start position:0%
+these guys this is all the points with V
+ 
+
+ align:start position:0%
+these guys this is all the points with V
+1 plus V 2 equal 1 and over here and
+
+ align:start position:0%
+1 plus V 2 equal 1 and over here and
+ 
+
+ align:start position:0%
+1 plus V 2 equal 1 and over here and
+over here and over here so the unit ball
+
+ align:start position:0%
+over here and over here so the unit ball
+ 
+
+ align:start position:0%
+over here and over here so the unit ball
+in the l1 norm is a diamond and that's a
+
+ align:start position:0%
+in the l1 norm is a diamond and that's a
+ 
+
+ align:start position:0%
+in the l1 norm is a diamond and that's a
+very important picture it reflects in a
+
+ align:start position:0%
+very important picture it reflects in a
+ 
+
+ align:start position:0%
+very important picture it reflects in a
+simple very simple way something
+
+ align:start position:0%
+simple very simple way something
+ 
+
+ align:start position:0%
+simple very simple way something
+important about the l1 norm and the
+
+ align:start position:0%
+important about the l1 norm and the
+ 
+
+ align:start position:0%
+important about the l1 norm and the
+reason it's just exploded him in
+
+ align:start position:0%
+reason it's just exploded him in
+ 
+
+ align:start position:0%
+reason it's just exploded him in
+importance let me continue though what
+
+ align:start position:0%
+importance let me continue though what
+ 
+
+ align:start position:0%
+importance let me continue though what
+about the max norm the Max or V infinity
+
+ align:start position:0%
+about the max norm the Max or V infinity
+ 
+
+ align:start position:0%
+about the max norm the Max or V infinity
+what so again let me plot these guys
+
+ align:start position:0%
+what so again let me plot these guys
+ 
+
+ align:start position:0%
+what so again let me plot these guys
+these guys are certainly gonna be in it
+
+ align:start position:0%
+these guys are certainly gonna be in it
+ 
+
+ align:start position:0%
+these guys are certainly gonna be in it
+again they're zero
+
+ align:start position:0%
+again they're zero
+ 
+
+ align:start position:0%
+again they're zero
+you know the plus or minus I and plus or
+
+ align:start position:0%
+you know the plus or minus I and plus or
+ 
+
+ align:start position:0%
+you know the plus or minus I and plus or
+minus J that are good friends what's the
+
+ align:start position:0%
+minus J that are good friends what's the
+ 
+
+ align:start position:0%
+minus J that are good friends what's the
+rest of the boundary look like now now
+
+ align:start position:0%
+rest of the boundary look like now now
+ 
+
+ align:start position:0%
+rest of the boundary look like now now
+this is this means max so what what are
+
+ align:start position:0%
+this is this means max so what what are
+ 
+
+ align:start position:0%
+this is this means max so what what are
+the rest of the points you see it does
+
+ align:start position:0%
+the rest of the points you see it does
+ 
+
+ align:start position:0%
+the rest of the points you see it does
+take a little thought but then you get
+
+ align:start position:0%
+take a little thought but then you get
+ 
+
+ align:start position:0%
+take a little thought but then you get
+it and you don't for forget it ok so
+
+ align:start position:0%
+it and you don't for forget it ok so
+ 
+
+ align:start position:0%
+it and you don't for forget it ok so
+what's what's up I'm looking so suppose
+
+ align:start position:0%
+what's what's up I'm looking so suppose
+ 
+
+ align:start position:0%
+what's what's up I'm looking so suppose
+the maximum is V one
+
+ align:start position:0%
+the maximum is V one
+ 
+
+ align:start position:0%
+the maximum is V one
+I think you're gonna go I I think it's
+
+ align:start position:0%
+I think you're gonna go I I think it's
+ 
+
+ align:start position:0%
+I think you're gonna go I I think it's
+gonna look like that out - out - one
+
+ align:start position:0%
+gonna look like that out - out - one
+ 
+
+ align:start position:0%
+gonna look like that out - out - one
+zero and up to zero one and up here the
+
+ align:start position:0%
+zero and up to zero one and up here the
+ 
+
+ align:start position:0%
+zero and up to zero one and up here the
+vector would be one one point for
+
+ align:start position:0%
+vector would be one one point for
+ 
+
+ align:start position:0%
+vector would be one one point for
+something so the maximum would be one is
+
+ align:start position:0%
+something so the maximum would be one is
+ 
+
+ align:start position:0%
+something so the maximum would be one is
+that okay so so so somehow what really
+
+ align:start position:0%
+that okay so so so somehow what really
+ 
+
+ align:start position:0%
+that okay so so so somehow what really
+sees as you change this number P you
+
+ align:start position:0%
+sees as you change this number P you
+ 
+
+ align:start position:0%
+sees as you change this number P you
+start with people one or daimond and it
+
+ align:start position:0%
+start with people one or daimond and it
+ 
+
+ align:start position:0%
+start with people one or daimond and it
+kind of swells out to be a circle at P
+
+ align:start position:0%
+kind of swells out to be a circle at P
+ 
+
+ align:start position:0%
+kind of swells out to be a circle at P
+equal to 2 and then it kind of keeps
+
+ align:start position:0%
+equal to 2 and then it kind of keeps
+ 
+
+ align:start position:0%
+equal to 2 and then it kind of keeps
+swelling to be a square at P equal
+
+ align:start position:0%
+swelling to be a square at P equal
+ 
+
+ align:start position:0%
+swelling to be a square at P equal
+infinity that's a that's a interesting
+
+ align:start position:0%
+infinity that's a that's a interesting
+ 
+
+ align:start position:0%
+infinity that's a that's a interesting
+thing and yeah now what's the problem
+
+ align:start position:0%
+thing and yeah now what's the problem
+ 
+
+ align:start position:0%
+thing and yeah now what's the problem
+with the 0 norm where are the points
+
+ align:start position:0%
+with the 0 norm where are the points
+ 
+
+ align:start position:0%
+with the 0 norm where are the points
+with one non zero so so so I'm plotting
+
+ align:start position:0%
+with one non zero so so so I'm plotting
+ 
+
+ align:start position:0%
+with one non zero so so so I'm plotting
+ball where are the where the where are
+
+ align:start position:0%
+ball where are the where the where are
+ 
+
+ align:start position:0%
+ball where are the where the where are
+the vectors in this thing that have one
+
+ align:start position:0%
+the vectors in this thing that have one
+ 
+
+ align:start position:0%
+the vectors in this thing that have one
+non-zero not not zero nonzero so that
+
+ align:start position:0%
+non-zero not not zero nonzero so that
+ 
+
+ align:start position:0%
+non-zero not not zero nonzero so that
+that's not included and but I but so
+
+ align:start position:0%
+that's not included and but I but so
+ 
+
+ align:start position:0%
+that's not included and but I but so
+what do I have
+
+ align:start position:0%
+what do I have
+ 
+
+ align:start position:0%
+what do I have
+I'm not allowed the vector one-third
+
+ align:start position:0%
+I'm not allowed the vector one-third
+ 
+
+ align:start position:0%
+I'm not allowed the vector one-third
+two-thirds because that has two non
+
+ align:start position:0%
+two-thirds because that has two non
+ 
+
+ align:start position:0%
+two-thirds because that has two non
+zeros so where are the points with only
+
+ align:start position:0%
+zeros so where are the points with only
+ 
+
+ align:start position:0%
+zeros so where are the points with only
+one nonzero yeah on the axes yeah that
+
+ align:start position:0%
+one nonzero yeah on the axes yeah that
+ 
+
+ align:start position:0%
+one nonzero yeah on the axes yeah that
+does tell you so he can be there and
+
+ align:start position:0%
+does tell you so he can be there and
+ 
+
+ align:start position:0%
+does tell you so he can be there and
+there okay without guy and of course so
+
+ align:start position:0%
+there okay without guy and of course so
+ 
+
+ align:start position:0%
+there okay without guy and of course so
+is just keep going out so it totally
+
+ align:start position:0%
+is just keep going out so it totally
+ 
+
+ align:start position:0%
+is just keep going out so it totally
+violates the you know so maybe the point
+
+ align:start position:0%
+violates the you know so maybe the point
+ 
+
+ align:start position:0%
+violates the you know so maybe the point
+that I should make about these figures
+
+ align:start position:0%
+that I should make about these figures
+ 
+
+ align:start position:0%
+that I should make about these figures
+so so like what's happening when I go
+
+ align:start position:0%
+so so like what's happening when I go
+ 
+
+ align:start position:0%
+so so like what's happening when I go
+down to zero I'm served it really that
+
+ align:start position:0%
+down to zero I'm served it really that
+ 
+
+ align:start position:0%
+down to zero I'm served it really that
+finger should be on the other end right
+
+ align:start position:0%
+finger should be on the other end right
+ 
+
+ align:start position:0%
+finger should be on the other end right
+oh no shoot this guy's in the middle
+
+ align:start position:0%
+oh no shoot this guy's in the middle
+ 
+
+ align:start position:0%
+oh no shoot this guy's in the middle
+this is a badly drawn finger l2 is kind
+
+ align:start position:0%
+this is a badly drawn finger l2 is kind
+ 
+
+ align:start position:0%
+this is a badly drawn finger l2 is kind
+of a center guy l1 is the at one end el
+
+ align:start position:0%
+of a center guy l1 is the at one end el
+ 
+
+ align:start position:0%
+of a center guy l1 is the at one end el
+infinities at the other end and this one
+
+ align:start position:0%
+infinities at the other end and this one
+ 
+
+ align:start position:0%
+infinities at the other end and this one
+has gone off and the left there the the
+
+ align:start position:0%
+has gone off and the left there the the
+ 
+
+ align:start position:0%
+has gone off and the left there the the
+diamond has yeah what's happened here as
+
+ align:start position:0%
+diamond has yeah what's happened here as
+ 
+
+ align:start position:0%
+diamond has yeah what's happened here as
+that one goes down towards zero none of
+
+ align:start position:0%
+that one goes down towards zero none of
+ 
+
+ align:start position:0%
+that one goes down towards zero none of
+these will be okay these these these
+
+ align:start position:0%
+these will be okay these these these
+ 
+
+ align:start position:0%
+these will be okay these these these
+balls will or these sets will lose
+
+ align:start position:0%
+balls will or these sets will lose
+ 
+
+ align:start position:0%
+balls will or these sets will lose
+weight yeah so they'll always have these
+
+ align:start position:0%
+weight yeah so they'll always have these
+ 
+
+ align:start position:0%
+weight yeah so they'll always have these
+points in but they'll be like this and
+
+ align:start position:0%
+points in but they'll be like this and
+ 
+
+ align:start position:0%
+points in but they'll be like this and
+then like this and then finally in the
+
+ align:start position:0%
+then like this and then finally in the
+ 
+
+ align:start position:0%
+then like this and then finally in the
+in the unacceptable limit but none of
+
+ align:start position:0%
+in the unacceptable limit but none of
+ 
+
+ align:start position:0%
+in the unacceptable limit but none of
+those this was not any good either this
+
+ align:start position:0%
+those this was not any good either this
+ 
+
+ align:start position:0%
+those this was not any good either this
+this was for P equal half let's say sort
+
+ align:start position:0%
+this was for P equal half let's say sort
+ 
+
+ align:start position:0%
+this was for P equal half let's say sort
+of uh that's a P equal to happen that's
+
+ align:start position:0%
+of uh that's a P equal to happen that's
+ 
+
+ align:start position:0%
+of uh that's a P equal to happen that's
+not a good norm yeah so maybe the thing
+
+ align:start position:0%
+not a good norm yeah so maybe the thing
+ 
+
+ align:start position:0%
+not a good norm yeah so maybe the thing
+you so there's a property of the circle
+
+ align:start position:0%
+you so there's a property of the circle
+ 
+
+ align:start position:0%
+you so there's a property of the circle
+the diamond and the square which is a
+
+ align:start position:0%
+the diamond and the square which is a
+ 
+
+ align:start position:0%
+the diamond and the square which is a
+nice math property of those of those
+
+ align:start position:0%
+nice math property of those of those
+ 
+
+ align:start position:0%
+nice math property of those of those
+three sets and is not possessed by this
+
+ align:start position:0%
+three sets and is not possessed by this
+ 
+
+ align:start position:0%
+three sets and is not possessed by this
+as this thing loses weight I lose the
+
+ align:start position:0%
+as this thing loses weight I lose the
+ 
+
+ align:start position:0%
+as this thing loses weight I lose the
+property and then of course that's
+
+ align:start position:0%
+property and then of course that's
+ 
+
+ align:start position:0%
+property and then of course that's
+totally lost over there do you know what
+
+ align:start position:0%
+totally lost over there do you know what
+ 
+
+ align:start position:0%
+totally lost over there do you know what
+that property would be what what it's
+
+ align:start position:0%
+that property would be what what it's
+ 
+
+ align:start position:0%
+that property would be what what it's
+for you concave convex convex I would
+
+ align:start position:0%
+for you concave convex convex I would
+ 
+
+ align:start position:0%
+for you concave convex convex I would
+say convex this is true norm has convex
+
+ align:start position:0%
+say convex this is true norm has convex
+ 
+
+ align:start position:0%
+say convex this is true norm has convex
+uni-ball maybe maybe for ball I'm taking
+
+ align:start position:0%
+uni-ball maybe maybe for ball I'm taking
+ 
+
+ align:start position:0%
+uni-ball maybe maybe for ball I'm taking
+all of these yeah so I'm allowing the
+
+ align:start position:0%
+all of these yeah so I'm allowing the
+ 
+
+ align:start position:0%
+all of these yeah so I'm allowing the
+insides of these shapes so this is not a
+
+ align:start position:0%
+insides of these shapes so this is not a
+ 
+
+ align:start position:0%
+insides of these shapes so this is not a
+convex set that set which I shouldn't
+
+ align:start position:0%
+convex set that set which I shouldn't
+ 
+
+ align:start position:0%
+convex set that set which I shouldn't
+so not not convex would be this one with
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and that reflects the fact that the oh
+
+ align:start position:0%
+and that reflects the fact that the oh
+ 
+
+ align:start position:0%
+and that reflects the fact that the oh
+the rules for a norm are broken the
+
+ align:start position:0%
+the rules for a norm are broken the
+ 
+
+ align:start position:0%
+the rules for a norm are broken the
+triangle inequality is probably broken
+
+ align:start position:0%
+triangle inequality is probably broken
+ 
+
+ align:start position:0%
+triangle inequality is probably broken
+and that yep I think that's sort of like
+
+ align:start position:0%
+and that yep I think that's sort of like
+ 
+
+ align:start position:0%
+and that yep I think that's sort of like
+worth remembering and then one more norm
+
+ align:start position:0%
+worth remembering and then one more norm
+ 
+
+ align:start position:0%
+worth remembering and then one more norm
+that's natural to think about is so s as
+
+ align:start position:0%
+that's natural to think about is so s as
+ 
+
+ align:start position:0%
+that's natural to think about is so s as
+in the Piazza question s does always
+
+ align:start position:0%
+in the Piazza question s does always
+ 
+
+ align:start position:0%
+in the Piazza question s does always
+represent a symmetric matrix in 1806
+
+ align:start position:0%
+represent a symmetric matrix in 1806
+ 
+
+ align:start position:0%
+represent a symmetric matrix in 1806
+five and now I'm gonna ask my norm is
+
+ align:start position:0%
+five and now I'm gonna ask my norm is
+ 
+
+ align:start position:0%
+five and now I'm gonna ask my norm is
+going to be so I'm gonna call it the s
+
+ align:start position:0%
+going to be so I'm gonna call it the s
+ 
+
+ align:start position:0%
+going to be so I'm gonna call it the s
+norm so asses up actually it's a
+
+ align:start position:0%
+norm so asses up actually it's a
+ 
+
+ align:start position:0%
+norm so asses up actually it's a
+positive definite symmetric matrix F is
+
+ align:start position:0%
+positive definite symmetric matrix F is
+ 
+
+ align:start position:0%
+positive definite symmetric matrix F is
+a positive definite symmetric matrix and
+
+ align:start position:0%
+a positive definite symmetric matrix and
+ 
+
+ align:start position:0%
+a positive definite symmetric matrix and
+what do I do
+
+ align:start position:0%
+what do I do
+ 
+
+ align:start position:0%
+what do I do
+I'll take V transpose AV s V sorry okay
+
+ align:start position:0%
+I'll take V transpose AV s V sorry okay
+ 
+
+ align:start position:0%
+I'll take V transpose AV s V sorry okay
+what's our word for that the energy
+
+ align:start position:0%
+what's our word for that the energy
+ 
+
+ align:start position:0%
+what's our word for that the energy
+that's the energy in the vector V and
+
+ align:start position:0%
+that's the energy in the vector V and
+ 
+
+ align:start position:0%
+that's the energy in the vector V and
+I'll take the square root so that I so
+
+ align:start position:0%
+I'll take the square root so that I so
+ 
+
+ align:start position:0%
+I'll take the square root so that I so
+that I now have the lengths of two if I
+
+ align:start position:0%
+that I now have the lengths of two if I
+ 
+
+ align:start position:0%
+that I now have the lengths of two if I
+double V from V 2 to V then I get a 2
+
+ align:start position:0%
+double V from V 2 to V then I get a 2
+ 
+
+ align:start position:0%
+double V from V 2 to V then I get a 2
+here and a 2 here and when I take this
+
+ align:start position:0%
+here and a 2 here and when I take this
+ 
+
+ align:start position:0%
+here and a 2 here and when I take this
+square root I get a overall two and
+
+ align:start position:0%
+square root I get a overall two and
+ 
+
+ align:start position:0%
+square root I get a overall two and
+that's what I want I want the norm to
+
+ align:start position:0%
+that's what I want I want the norm to
+ 
+
+ align:start position:0%
+that's what I want I want the norm to
+grow linearly with the two or three or
+
+ align:start position:0%
+grow linearly with the two or three or
+ 
+
+ align:start position:0%
+grow linearly with the two or three or
+whatever I multiply by but what is the
+
+ align:start position:0%
+whatever I multiply by but what is the
+ 
+
+ align:start position:0%
+whatever I multiply by but what is the
+shape of this thing so what is the
+
+ align:start position:0%
+shape of this thing so what is the
+ 
+
+ align:start position:0%
+shape of this thing so what is the
+what is the shape I'm gonna get a
+
+ align:start position:0%
+what is the shape I'm gonna get a
+ 
+
+ align:start position:0%
+what is the shape I'm gonna get a
+picture like that so what is the shape
+
+ align:start position:0%
+picture like that so what is the shape
+ 
+
+ align:start position:0%
+picture like that so what is the shape
+of V transpose s V equal one less or
+
+ align:start position:0%
+of V transpose s V equal one less or
+ 
+
+ align:start position:0%
+of V transpose s V equal one less or
+equal one if s is a positive symmetric
+
+ align:start position:0%
+equal one if s is a positive symmetric
+ 
+
+ align:start position:0%
+equal one if s is a positive symmetric
+positive letters tell us I'm claiming
+
+ align:start position:0%
+positive letters tell us I'm claiming
+ 
+
+ align:start position:0%
+positive letters tell us I'm claiming
+that we get a bunch of norms when do we
+
+ align:start position:0%
+that we get a bunch of norms when do we
+ 
+
+ align:start position:0%
+that we get a bunch of norms when do we
+get the l2 norm what what matrix s would
+
+ align:start position:0%
+get the l2 norm what what matrix s would
+ 
+
+ align:start position:0%
+get the l2 norm what what matrix s would
+this give us the l2 norm the identity
+
+ align:start position:0%
+this give us the l2 norm the identity
+ 
+
+ align:start position:0%
+this give us the l2 norm the identity
+certainly now what's going to happen if
+
+ align:start position:0%
+certainly now what's going to happen if
+ 
+
+ align:start position:0%
+certainly now what's going to happen if
+I use some different matrix s this
+
+ align:start position:0%
+I use some different matrix s this
+ 
+
+ align:start position:0%
+I use some different matrix s this
+circle is going to change shape I'm
+
+ align:start position:0%
+circle is going to change shape I'm
+ 
+
+ align:start position:0%
+circle is going to change shape I'm
+gonna have a different norm depending on
+
+ align:start position:0%
+gonna have a different norm depending on
+ 
+
+ align:start position:0%
+gonna have a different norm depending on
+s and a typical case would be s equal to
+
+ align:start position:0%
+s and a typical case would be s equal to
+ 
+
+ align:start position:0%
+s and a typical case would be s equal to
+3 that's a positive definite symmetric
+
+ align:start position:0%
+3 that's a positive definite symmetric
+ 
+
+ align:start position:0%
+3 that's a positive definite symmetric
+matrix and this this now I would be
+
+ align:start position:0%
+matrix and this this now I would be
+ 
+
+ align:start position:0%
+matrix and this this now I would be
+drawing the graph of 2 V 1 squared plus
+
+ align:start position:0%
+drawing the graph of 2 V 1 squared plus
+ 
+
+ align:start position:0%
+drawing the graph of 2 V 1 squared plus
+3 V 2 squared that would be the energy
+
+ align:start position:0%
+3 V 2 squared that would be the energy
+ 
+
+ align:start position:0%
+3 V 2 squared that would be the energy
+right equal one and I just want you to
+
+ align:start position:0%
+right equal one and I just want you to
+ 
+
+ align:start position:0%
+right equal one and I just want you to
+tell me what shape that is so that's a
+
+ align:start position:0%
+tell me what shape that is so that's a
+ 
+
+ align:start position:0%
+tell me what shape that is so that's a
+perfectly good norm that you could check
+
+ align:start position:0%
+perfectly good norm that you could check
+ 
+
+ align:start position:0%
+perfectly good norm that you could check
+all its properties they all come out
+
+ align:start position:0%
+all its properties they all come out
+ 
+
+ align:start position:0%
+all its properties they all come out
+easily but I get a new picture a new
+
+ align:start position:0%
+easily but I get a new picture a new
+ 
+
+ align:start position:0%
+easily but I get a new picture a new
+norm that's kind of adjustable you could
+
+ align:start position:0%
+norm that's kind of adjustable you could
+ 
+
+ align:start position:0%
+norm that's kind of adjustable you could
+say it's a weighted norm weights mean
+
+ align:start position:0%
+say it's a weighted norm weights mean
+ 
+
+ align:start position:0%
+say it's a weighted norm weights mean
+that you kind of have picked some
+
+ align:start position:0%
+that you kind of have picked some
+ 
+
+ align:start position:0%
+that you kind of have picked some
+numbers sort of appropriate to the
+
+ align:start position:0%
+numbers sort of appropriate to the
+ 
+
+ align:start position:0%
+numbers sort of appropriate to the
+particular problem well suppose those
+
+ align:start position:0%
+particular problem well suppose those
+ 
+
+ align:start position:0%
+particular problem well suppose those
+numbers are 2 and 3 what shape is the
+
+ align:start position:0%
+numbers are 2 and 3 what shape is the
+ 
+
+ align:start position:0%
+numbers are 2 and 3 what shape is the
+unit ball in this s norm it's in ellipse
+
+ align:start position:0%
+unit ball in this s norm it's in ellipse
+ 
+
+ align:start position:0%
+unit ball in this s norm it's in ellipse
+right it's an ellipse and I guess it
+
+ align:start position:0%
+right it's an ellipse and I guess it
+ 
+
+ align:start position:0%
+right it's an ellipse and I guess it
+will actually be so the larger number 3
+
+ align:start position:0%
+will actually be so the larger number 3
+ 
+
+ align:start position:0%
+will actually be so the larger number 3
+well will mean you can't go as far as
+
+ align:start position:0%
+well will mean you can't go as far as
+ 
+
+ align:start position:0%
+well will mean you can't go as far as
+a smaller number - I think it would
+
+ align:start position:0%
+a smaller number - I think it would
+ 
+
+ align:start position:0%
+a smaller number - I think it would
+probably be an ellipse like this and the
+
+ align:start position:0%
+probably be an ellipse like this and the
+ 
+
+ align:start position:0%
+probably be an ellipse like this and the
+axes axis lengths of the ellipse would
+
+ align:start position:0%
+axes axis lengths of the ellipse would
+ 
+
+ align:start position:0%
+axes axis lengths of the ellipse would
+probably have something to do with it -
+
+ align:start position:0%
+probably have something to do with it -
+ 
+
+ align:start position:0%
+probably have something to do with it -
+in the three okay so that's just now you
+
+ align:start position:0%
+in the three okay so that's just now you
+ 
+
+ align:start position:0%
+in the three okay so that's just now you
+know really all the vector norms that
+
+ align:start position:0%
+know really all the vector norms that
+ 
+
+ align:start position:0%
+know really all the vector norms that
+are sort of natural to use these come up
+
+ align:start position:0%
+are sort of natural to use these come up
+ 
+
+ align:start position:0%
+are sort of natural to use these come up
+in a natural way they're all as we said
+
+ align:start position:0%
+in a natural way they're all as we said
+ 
+
+ align:start position:0%
+in a natural way they're all as we said
+the identity matrix brings us back to
+
+ align:start position:0%
+the identity matrix brings us back to
+ 
+
+ align:start position:0%
+the identity matrix brings us back to
+the two norm so these are all sort of
+
+ align:start position:0%
+the two norm so these are all sort of
+ 
+
+ align:start position:0%
+the two norm so these are all sort of
+variations on the two norm
+
+ align:start position:0%
+variations on the two norm
+ 
+
+ align:start position:0%
+variations on the two norm
+these are variations as P runs from 1 up
+
+ align:start position:0%
+these are variations as P runs from 1 up
+ 
+
+ align:start position:0%
+these are variations as P runs from 1 up
+to 2 onto infinity and is not allowed to
+
+ align:start position:0%
+to 2 onto infinity and is not allowed to
+ 
+
+ align:start position:0%
+to 2 onto infinity and is not allowed to
+go below 1 okay that's norms and then
+
+ align:start position:0%
+go below 1 okay that's norms and then
+ 
+
+ align:start position:0%
+go below 1 okay that's norms and then
+maybe you can actually see from this
+
+ align:start position:0%
+maybe you can actually see from this
+ 
+
+ align:start position:0%
+maybe you can actually see from this
+picture here's our like somewhat hokey
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+idea of why it is that this norm
+
+ align:start position:0%
+idea of why it is that this norm
+ 
+
+ align:start position:0%
+idea of why it is that this norm
+minimizing the so minimizing there or in
+
+ align:start position:0%
+minimizing the so minimizing there or in
+ 
+
+ align:start position:0%
+minimizing the so minimizing there or in
+this norm so what do I mean by that here
+
+ align:start position:0%
+this norm so what do I mean by that here
+ 
+
+ align:start position:0%
+this norm so what do I mean by that here
+would be a typical problem minimize
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+subject to ax equal B the l1 oh sorry
+
+ align:start position:0%
+subject to ax equal B the l1 oh sorry
+ 
+
+ align:start position:0%
+subject to ax equal B the l1 oh sorry
+I'm using X now yeah one norm of the l1
+
+ align:start position:0%
+I'm using X now yeah one norm of the l1
+ 
+
+ align:start position:0%
+I'm using X now yeah one norm of the l1
+norm of X so that would be an important
+
+ align:start position:0%
+norm of X so that would be an important
+ 
+
+ align:start position:0%
+norm of X so that would be an important
+problem actually it has a name people
+
+ align:start position:0%
+problem actually it has a name people
+ 
+
+ align:start position:0%
+problem actually it has a name people
+have spent a lot of time thinking of a
+
+ align:start position:0%
+have spent a lot of time thinking of a
+ 
+
+ align:start position:0%
+have spent a lot of time thinking of a
+fast way to solve it it's almost like
+
+ align:start position:0%
+fast way to solve it it's almost like
+ 
+
+ align:start position:0%
+fast way to solve it it's almost like
+least squares what would what would make
+
+ align:start position:0%
+least squares what would what would make
+ 
+
+ align:start position:0%
+least squares what would what would make
+it more like these squares would be
+
+ align:start position:0%
+it more like these squares would be
+ 
+
+ align:start position:0%
+it more like these squares would be
+change that to two yeah yeah can I just
+
+ align:start position:0%
+change that to two yeah yeah can I just
+ 
+
+ align:start position:0%
+change that to two yeah yeah can I just
+sort of like sketch without making a big
+
+ align:start position:0%
+sort of like sketch without making a big
+ 
+
+ align:start position:0%
+sort of like sketch without making a big
+argument here the difference between L
+
+ align:start position:0%
+argument here the difference between L
+ 
+
+ align:start position:0%
+argument here the difference between L
+equal 1 or
+
+ align:start position:0%
+equal 1 or
+ 
+
+ align:start position:0%
+equal 1 or
+to here yeah just I'll just draw a
+
+ align:start position:0%
+to here yeah just I'll just draw a
+ 
+
+ align:start position:0%
+to here yeah just I'll just draw a
+picture now erase this ellipse but you
+
+ align:start position:0%
+picture now erase this ellipse but you
+ 
+
+ align:start position:0%
+picture now erase this ellipse but you
+won't forget okay so this this is our
+
+ align:start position:0%
+won't forget okay so this this is our
+ 
+
+ align:start position:0%
+won't forget okay so this this is our
+problem l with l1 it has a famous name
+
+ align:start position:0%
+problem l with l1 it has a famous name
+ 
+
+ align:start position:0%
+problem l with l1 it has a famous name
+basis pursuit
+
+ align:start position:0%
+basis pursuit
+ 
+
+ align:start position:0%
+basis pursuit
+well famous to people who work in
+
+ align:start position:0%
+well famous to people who work in
+ 
+
+ align:start position:0%
+well famous to people who work in
+optimization for l2 it has an important
+
+ align:start position:0%
+optimization for l2 it has an important
+ 
+
+ align:start position:0%
+optimization for l2 it has an important
+name well it's sort of like these
+
+ align:start position:0%
+name well it's sort of like these
+ 
+
+ align:start position:0%
+name well it's sort of like these
+squares Ridge regression all sorts of
+
+ align:start position:0%
+squares Ridge regression all sorts of
+ 
+
+ align:start position:0%
+squares Ridge regression all sorts of
+the this is like a beautiful model
+
+ align:start position:0%
+the this is like a beautiful model
+ 
+
+ align:start position:0%
+the this is like a beautiful model
+problem among all solutions to ax
+
+ align:start position:0%
+problem among all solutions to ax
+ 
+
+ align:start position:0%
+problem among all solutions to ax
+suppose this is just one equation like
+
+ align:start position:0%
+suppose this is just one equation like
+ 
+
+ align:start position:0%
+suppose this is just one equation like
+c1 x1 plus c2 x2 equals some right side
+
+ align:start position:0%
+c1 x1 plus c2 x2 equals some right side
+ 
+
+ align:start position:0%
+c1 x1 plus c2 x2 equals some right side
+B so the X's the constraint says that
+
+ align:start position:0%
+B so the X's the constraint says that
+ 
+
+ align:start position:0%
+B so the X's the constraint says that
+the vectors X have to be on a line
+
+ align:start position:0%
+the vectors X have to be on a line
+ 
+
+ align:start position:0%
+the vectors X have to be on a line
+there's suppose that's a graph of that
+
+ align:start position:0%
+there's suppose that's a graph of that
+ 
+
+ align:start position:0%
+there's suppose that's a graph of that
+line so as among all these X's which one
+
+ align:start position:0%
+line so as among all these X's which one
+ 
+
+ align:start position:0%
+line so as among all these X's which one
+yeah I never realizing what is what I'm
+
+ align:start position:0%
+yeah I never realizing what is what I'm
+ 
+
+ align:start position:0%
+yeah I never realizing what is what I'm
+gonna say is gonna be smart okay I mean
+
+ align:start position:0%
+gonna say is gonna be smart okay I mean
+ 
+
+ align:start position:0%
+gonna say is gonna be smart okay I mean
+not it's gonna be nice not gonna be
+
+ align:start position:0%
+not it's gonna be nice not gonna be
+ 
+
+ align:start position:0%
+not it's gonna be nice not gonna be
+difficult
+
+ align:start position:0%
+difficult
+ 
+
+ align:start position:0%
+difficult
+let's do the one we know best l2 so
+
+ align:start position:0%
+let's do the one we know best l2 so
+ 
+
+ align:start position:0%
+let's do the one we know best l2 so
+here's a picture of the line let me let
+
+ align:start position:0%
+here's a picture of the line let me let
+ 
+
+ align:start position:0%
+here's a picture of the line let me let
+me make it a little more tilted so so
+
+ align:start position:0%
+me make it a little more tilted so so
+ 
+
+ align:start position:0%
+me make it a little more tilted so so
+you yeah yeah yeah like like two three
+
+ align:start position:0%
+you yeah yeah yeah like like two three
+ 
+
+ align:start position:0%
+you yeah yeah yeah like like two three
+okay where this is the XY plane here's X
+
+ align:start position:0%
+okay where this is the XY plane here's X
+ 
+
+ align:start position:0%
+okay where this is the XY plane here's X
+1 there's X 2 here are the pair of the
+
+ align:start position:0%
+1 there's X 2 here are the pair of the
+ 
+
+ align:start position:0%
+1 there's X 2 here are the pair of the
+points that satisfy my condition which
+
+ align:start position:0%
+points that satisfy my condition which
+ 
+
+ align:start position:0%
+points that satisfy my condition which
+one minimizes which point on that line
+
+ align:start position:0%
+one minimizes which point on that line
+ 
+
+ align:start position:0%
+one minimizes which point on that line
+minimizes has the smallest l2 norm which
+
+ align:start position:0%
+minimizes has the smallest l2 norm which
+ 
+
+ align:start position:0%
+minimizes has the smallest l2 norm which
+point on the line has the smallest l2
+
+ align:start position:0%
+point on the line has the smallest l2
+ 
+
+ align:start position:0%
+point on the line has the smallest l2
+norm yeah you're drawing the right
+
+ align:start position:0%
+norm yeah you're drawing the right
+ 
+
+ align:start position:0%
+norm yeah you're drawing the right
+figure with your hands the smallest l2
+
+ align:start position:0%
+figure with your hands the smallest l2
+ 
+
+ align:start position:0%
+figure with your hands the smallest l2
+norm L to remember is just how far out
+
+ align:start position:0%
+norm L to remember is just how far out
+ 
+
+ align:start position:0%
+norm L to remember is just how far out
+you go
+
+ align:start position:0%
+you go
+ 
+
+ align:start position:0%
+you go
+it's it's
+
+ align:start position:0%
+it's it's
+ 
+
+ align:start position:0%
+it's it's
+circular here so it doesn't matter what
+
+ align:start position:0%
+circular here so it doesn't matter what
+ 
+
+ align:start position:0%
+circular here so it doesn't matter what
+direction they all giving the same l
+
+ align:start position:0%
+direction they all giving the same l
+ 
+
+ align:start position:0%
+direction they all giving the same l
+2-norm it's just how far so we're
+
+ align:start position:0%
+2-norm it's just how far so we're
+ 
+
+ align:start position:0%
+2-norm it's just how far so we're
+looking for the closest point on the
+
+ align:start position:0%
+looking for the closest point on the
+ 
+
+ align:start position:0%
+looking for the closest point on the
+line because we don't want to go any
+
+ align:start position:0%
+line because we don't want to go any
+ 
+
+ align:start position:0%
+line because we don't want to go any
+further we want to go a minimum distance
+
+ align:start position:0%
+further we want to go a minimum distance
+ 
+
+ align:start position:0%
+further we want to go a minimum distance
+with two now so if so where's the point
+
+ align:start position:0%
+with two now so if so where's the point
+ 
+
+ align:start position:0%
+with two now so if so where's the point
+at minimum distance yeah it's just show
+
+ align:start position:0%
+at minimum distance yeah it's just show
+ 
+
+ align:start position:0%
+at minimum distance yeah it's just show
+me again once more with hands or
+
+ align:start position:0%
+me again once more with hands or
+ 
+
+ align:start position:0%
+me again once more with hands or
+whatever it'll be that I didn't want
+
+ align:start position:0%
+whatever it'll be that I didn't want
+ 
+
+ align:start position:0%
+whatever it'll be that I didn't want
+45-degree angles there I'm gonna erase
+
+ align:start position:0%
+45-degree angles there I'm gonna erase
+ 
+
+ align:start position:0%
+45-degree angles there I'm gonna erase
+it again and really this time I'm gonna
+
+ align:start position:0%
+it again and really this time I'm gonna
+ 
+
+ align:start position:0%
+it again and really this time I'm gonna
+get angles that are not 45 all right
+
+ align:start position:0%
+get angles that are not 45 all right
+ 
+
+ align:start position:0%
+get angles that are not 45 all right
+brilliant got it okay that's my line
+
+ align:start position:0%
+brilliant got it okay that's my line
+ 
+
+ align:start position:0%
+brilliant got it okay that's my line
+okay and what's the nearest point in the
+
+ align:start position:0%
+okay and what's the nearest point in the
+ 
+
+ align:start position:0%
+okay and what's the nearest point in the
+l2 norm
+
+ align:start position:0%
+l2 norm
+ 
+
+ align:start position:0%
+l2 norm
+here's the winner in l2 right the
+
+ align:start position:0%
+here's the winner in l2 right the
+ 
+
+ align:start position:0%
+here's the winner in l2 right the
+nearest point everybody sees that
+
+ align:start position:0%
+nearest point everybody sees that
+ 
+
+ align:start position:0%
+nearest point everybody sees that
+picture so that's the that's you know
+
+ align:start position:0%
+picture so that's the that's you know
+ 
+
+ align:start position:0%
+picture so that's the that's you know
+that's a basic picture for for
+
+ align:start position:0%
+that's a basic picture for for
+ 
+
+ align:start position:0%
+that's a basic picture for for
+minimizing something with a constraint
+
+ align:start position:0%
+minimizing something with a constraint
+ 
+
+ align:start position:0%
+minimizing something with a constraint
+which is the fundamental problem of
+
+ align:start position:0%
+which is the fundamental problem of
+ 
+
+ align:start position:0%
+which is the fundamental problem of
+optimization of neural nets of
+
+ align:start position:0%
+optimization of neural nets of
+ 
+
+ align:start position:0%
+optimization of neural nets of
+everything really of life well I'm
+
+ align:start position:0%
+everything really of life well I'm
+ 
+
+ align:start position:0%
+everything really of life well I'm
+philosophical so okay that's that's but
+
+ align:start position:0%
+philosophical so okay that's that's but
+ 
+
+ align:start position:0%
+philosophical so okay that's that's but
+of course it always mean the question
+
+ align:start position:0%
+of course it always mean the question
+ 
+
+ align:start position:0%
+of course it always mean the question
+always is and maybe it's true in life to
+
+ align:start position:0%
+always is and maybe it's true in life to
+ 
+
+ align:start position:0%
+always is and maybe it's true in life to
+which norm are you using okay now count
+
+ align:start position:0%
+which norm are you using okay now count
+ 
+
+ align:start position:0%
+which norm are you using okay now count
+and show with yourself that was the
+
+ align:start position:0%
+and show with yourself that was the
+ 
+
+ align:start position:0%
+and show with yourself that was the
+minimum in l2 that's the shortest
+
+ align:start position:0%
+minimum in l2 that's the shortest
+ 
+
+ align:start position:0%
+minimum in l2 that's the shortest
+distance where a distance means what we
+
+ align:start position:0%
+distance where a distance means what we
+ 
+
+ align:start position:0%
+distance where a distance means what we
+usually think of it as meaning but now
+
+ align:start position:0%
+usually think of it as meaning but now
+ 
+
+ align:start position:0%
+usually think of it as meaning but now
+let's go for the l1 norm which point on
+
+ align:start position:0%
+let's go for the l1 norm which point on
+ 
+
+ align:start position:0%
+let's go for the l1 norm which point on
+the line has the smallest l1 norm so now
+
+ align:start position:0%
+the line has the smallest l1 norm so now
+ 
+
+ align:start position:0%
+the line has the smallest l1 norm so now
+I'm going to add the two so if this is
+
+ align:start position:0%
+I'm going to add the two so if this is
+ 
+
+ align:start position:0%
+I'm going to add the two so if this is
+some point a this is some point a zero
+
+ align:start position:0%
+some point a this is some point a zero
+ 
+
+ align:start position:0%
+some point a this is some point a zero
+and this is some point zero B right
+
+ align:start position:0%
+and this is some point zero B right
+ 
+
+ align:start position:0%
+and this is some point zero B right
+there
+
+ align:start position:0%
+there
+ 
+
+ align:start position:0%
+there
+so those two points are obviously
+
+ align:start position:0%
+so those two points are obviously
+ 
+
+ align:start position:0%
+so those two points are obviously
+important and that point we could figure
+
+ align:start position:0%
+important and that point we could figure
+ 
+
+ align:start position:0%
+important and that point we could figure
+out the formula for
+
+ align:start position:0%
+out the formula for
+ 
+
+ align:start position:0%
+out the formula for
+because it's we we know what the
+
+ align:start position:0%
+because it's we we know what the
+ 
+
+ align:start position:0%
+because it's we we know what the
+geometry is but I've just put those two
+
+ align:start position:0%
+geometry is but I've just put those two
+ 
+
+ align:start position:0%
+geometry is but I've just put those two
+points in so did I get a zero B yeah
+
+ align:start position:0%
+points in so did I get a zero B yeah
+ 
+
+ align:start position:0%
+points in so did I get a zero B yeah
+that's a zero well so let me just ask
+
+ align:start position:0%
+that's a zero well so let me just ask
+ 
+
+ align:start position:0%
+that's a zero well so let me just ask
+you that question
+
+ align:start position:0%
+you that question
+ 
+
+ align:start position:0%
+you that question
+what point on that line has the smallest
+
+ align:start position:0%
+what point on that line has the smallest
+ 
+
+ align:start position:0%
+what point on that line has the smallest
+l1 norm which has the smallest l1 norm
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+somebody said it just say it a little
+
+ align:start position:0%
+somebody said it just say it a little
+ 
+
+ align:start position:0%
+somebody said it just say it a little
+louder so that you're wrong
+
+ align:start position:0%
+louder so that you're wrong
+ 
+
+ align:start position:0%
+louder so that you're wrong
+tape forever zero B this point that's
+
+ align:start position:0%
+tape forever zero B this point that's
+ 
+
+ align:start position:0%
+tape forever zero B this point that's
+the winner
+
+ align:start position:0%
+the winner
+ 
+
+ align:start position:0%
+the winner
+this is the l1 winner and this was the
+
+ align:start position:0%
+this is the l1 winner and this was the
+ 
+
+ align:start position:0%
+this is the l1 winner and this was the
+l2 the winner and notice what I said
+
+ align:start position:0%
+l2 the winner and notice what I said
+ 
+
+ align:start position:0%
+l2 the winner and notice what I said
+earlier and I didn't see it coming but
+
+ align:start position:0%
+earlier and I didn't see it coming but
+ 
+
+ align:start position:0%
+earlier and I didn't see it coming but
+now I realize this is a finger to put in
+
+ align:start position:0%
+now I realize this is a finger to put in
+ 
+
+ align:start position:0%
+now I realize this is a finger to put in
+the notes the winner has the most zeroes
+
+ align:start position:0%
+the notes the winner has the most zeroes
+ 
+
+ align:start position:0%
+the notes the winner has the most zeroes
+it's the sparse vector it's got a zero
+
+ align:start position:0%
+it's the sparse vector it's got a zero
+ 
+
+ align:start position:0%
+it's the sparse vector it's got a zero
+well out of two components it didn't
+
+ align:start position:0%
+well out of two components it didn't
+ 
+
+ align:start position:0%
+well out of two components it didn't
+have much freedom but it has a zero
+
+ align:start position:0%
+have much freedom but it has a zero
+ 
+
+ align:start position:0%
+have much freedom but it has a zero
+component
+
+ align:start position:0%
+component
+ 
+
+ align:start position:0%
+component
+it sits on the on the on the axes it's
+
+ align:start position:0%
+it sits on the on the on the axes it's
+ 
+
+ align:start position:0%
+it sits on the on the on the axes it's
+the things on the axes that have the
+
+ align:start position:0%
+the things on the axes that have the
+ 
+
+ align:start position:0%
+the things on the axes that have the
+smallest number of components so so yes
+
+ align:start position:0%
+smallest number of components so so yes
+ 
+
+ align:start position:0%
+smallest number of components so so yes
+so this is the picture in l2 in in two
+
+ align:start position:0%
+so this is the picture in l2 in in two
+ 
+
+ align:start position:0%
+so this is the picture in l2 in in two
+sorry the picture in two dimensions so
+
+ align:start position:0%
+sorry the picture in two dimensions so
+ 
+
+ align:start position:0%
+sorry the picture in two dimensions so
+I'm in 2d and you can see that the
+
+ align:start position:0%
+I'm in 2d and you can see that the
+ 
+
+ align:start position:0%
+I'm in 2d and you can see that the
+winner is has a zero component yeah yeah
+
+ align:start position:0%
+winner is has a zero component yeah yeah
+ 
+
+ align:start position:0%
+winner is has a zero component yeah yeah
+and and that's a fact that extends into
+
+ align:start position:0%
+and and that's a fact that extends into
+ 
+
+ align:start position:0%
+and and that's a fact that extends into
+higher dimensions too and that makes the
+
+ align:start position:0%
+higher dimensions too and that makes the
+ 
+
+ align:start position:0%
+higher dimensions too and that makes the
+l1 norm special as I've said yeah is
+
+ align:start position:0%
+l1 norm special as I've said yeah is
+ 
+
+ align:start position:0%
+l1 norm special as I've said yeah is
+there more to say about that example
+
+ align:start position:0%
+there more to say about that example
+ 
+
+ align:start position:0%
+there more to say about that example
+that's for a simple 2d question that
+
+ align:start position:0%
+that's for a simple 2d question that
+ 
+
+ align:start position:0%
+that's for a simple 2d question that
+really makes the point that the l1
+
+ align:start position:0%
+really makes the point that the l1
+ 
+
+ align:start position:0%
+really makes the point that the l1
+winner is there it's not further you
+
+ align:start position:0%
+winner is there it's not further you
+ 
+
+ align:start position:0%
+winner is there it's not further you
+don't go further up the line right
+
+ align:start position:0%
+don't go further up the line right
+ 
+
+ align:start position:0%
+don't go further up the line right
+because because then you're then you
+
+ align:start position:0%
+because because then you're then you
+ 
+
+ align:start position:0%
+because because then you're then you
+have even that's bad in all ways when
+
+ align:start position:0%
+have even that's bad in all ways when
+ 
+
+ align:start position:0%
+have even that's bad in all ways when
+you go up further you're you're adding
+
+ align:start position:0%
+you go up further you're you're adding
+ 
+
+ align:start position:0%
+you go up further you're you're adding
+some nonzero
+
+ align:start position:0%
+some nonzero
+ 
+
+ align:start position:0%
+some nonzero
+first component and you're increasing
+
+ align:start position:0%
+first component and you're increasing
+ 
+
+ align:start position:0%
+first component and you're increasing
+the non zero over second component so
+
+ align:start position:0%
+the non zero over second component so
+ 
+
+ align:start position:0%
+the non zero over second component so
+your that's a bad idea
+
+ align:start position:0%
+your that's a bad idea
+ 
+
+ align:start position:0%
+your that's a bad idea
+that's a bad idea this is this is the
+
+ align:start position:0%
+that's a bad idea this is this is the
+ 
+
+ align:start position:0%
+that's a bad idea this is this is the
+winner and in a way here's the picture
+
+ align:start position:0%
+winner and in a way here's the picture
+ 
+
+ align:start position:0%
+winner and in a way here's the picture
+yeah oh yeah I should prepare these
+
+ align:start position:0%
+yeah oh yeah I should prepare these
+ 
+
+ align:start position:0%
+yeah oh yeah I should prepare these
+lectures but this one's coming out all
+
+ align:start position:0%
+lectures but this one's coming out all
+ 
+
+ align:start position:0%
+lectures but this one's coming out all
+right anyway so this so the picture
+
+ align:start position:0%
+right anyway so this so the picture
+ 
+
+ align:start position:0%
+right anyway so this so the picture
+there is the nearest ball it's at that
+
+ align:start position:0%
+there is the nearest ball it's at that
+ 
+
+ align:start position:0%
+there is the nearest ball it's at that
+point and what is it can you see that so
+
+ align:start position:0%
+point and what is it can you see that so
+ 
+
+ align:start position:0%
+point and what is it can you see that so
+that star is outside the circle this is
+
+ align:start position:0%
+that star is outside the circle this is
+ 
+
+ align:start position:0%
+that star is outside the circle this is
+the l1 winner so and that's the nearest
+
+ align:start position:0%
+the l1 winner so and that's the nearest
+ 
+
+ align:start position:0%
+the l1 winner so and that's the nearest
+that's the that's is the blow-up of the
+
+ align:start position:0%
+that's the that's is the blow-up of the
+ 
+
+ align:start position:0%
+that's the that's is the blow-up of the
+l1 norm until it hits that's the point
+
+ align:start position:0%
+l1 norm until it hits that's the point
+ 
+
+ align:start position:0%
+l1 norm until it hits that's the point
+where the l1 norm hit do you see it just
+
+ align:start position:0%
+where the l1 norm hit do you see it just
+ 
+
+ align:start position:0%
+where the l1 norm hit do you see it just
+give it a little thought that that
+
+ align:start position:0%
+give it a little thought that that
+ 
+
+ align:start position:0%
+give it a little thought that that
+another another geometric way to see the
+
+ align:start position:0%
+another another geometric way to see the
+ 
+
+ align:start position:0%
+another another geometric way to see the
+answer to this problem is you started
+
+ align:start position:0%
+answer to this problem is you started
+ 
+
+ align:start position:0%
+answer to this problem is you started
+the origin then you blow up a norm until
+
+ align:start position:0%
+the origin then you blow up a norm until
+ 
+
+ align:start position:0%
+the origin then you blow up a norm until
+you get a point on the line that
+
+ align:start position:0%
+you get a point on the line that
+ 
+
+ align:start position:0%
+you get a point on the line that
+satisfies your constraint and because
+
+ align:start position:0%
+satisfies your constraint and because
+ 
+
+ align:start position:0%
+satisfies your constraint and because
+you were blowing up a norm when it hits
+
+ align:start position:0%
+you were blowing up a norm when it hits
+ 
+
+ align:start position:0%
+you were blowing up a norm when it hits
+first that's the smallest blow-up
+
+ align:start position:0%
+first that's the smallest blow-up
+ 
+
+ align:start position:0%
+first that's the smallest blow-up
+possible
+
+ align:start position:0%
+possible
+ 
+
+ align:start position:0%
+possible
+that's the mint that's the guy that
+
+ align:start position:0%
+that's the mint that's the guy that
+ 
+
+ align:start position:0%
+that's the mint that's the guy that
+minimizes ya just think about that
+
+ align:start position:0%
+minimizes ya just think about that
+ 
+
+ align:start position:0%
+minimizes ya just think about that
+picture and I'll draw it better
+
+ align:start position:0%
+picture and I'll draw it better
+ 
+
+ align:start position:0%
+picture and I'll draw it better
+somewhere - well that's vector norms and
+
+ align:start position:0%
+somewhere - well that's vector norms and
+ 
+
+ align:start position:0%
+somewhere - well that's vector norms and
+then I introduced some matrix norms and
+
+ align:start position:0%
+then I introduced some matrix norms and
+ 
+
+ align:start position:0%
+then I introduced some matrix norms and
+let me just say a word about those
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay word about matrix norm so so the
+
+ align:start position:0%
+okay word about matrix norm so so the
+ 
+
+ align:start position:0%
+okay word about matrix norm so so the
+matrix norms were the so so now I have a
+
+ align:start position:0%
+matrix norms were the so so now I have a
+ 
+
+ align:start position:0%
+matrix norms were the so so now I have a
+matrix a and I want to define those same
+
+ align:start position:0%
+matrix a and I want to define those same
+ 
+
+ align:start position:0%
+matrix a and I want to define those same
+three norms again for a matrix and this
+
+ align:start position:0%
+three norms again for a matrix and this
+ 
+
+ align:start position:0%
+three norms again for a matrix and this
+was two norm and what was the two norm
+
+ align:start position:0%
+was two norm and what was the two norm
+ 
+
+ align:start position:0%
+was two norm and what was the two norm
+of a matrix well it was Sigma one turned
+
+ align:start position:0%
+of a matrix well it was Sigma one turned
+ 
+
+ align:start position:0%
+of a matrix well it was Sigma one turned
+out to be so what that doesn't define it
+
+ align:start position:0%
+out to be so what that doesn't define it
+ 
+
+ align:start position:0%
+out to be so what that doesn't define it
+or it could to find it just say okay the
+
+ align:start position:0%
+or it could to find it just say okay the
+ 
+
+ align:start position:0%
+or it could to find it just say okay the
+largest singular value is the two norm
+
+ align:start position:0%
+largest singular value is the two norm
+ 
+
+ align:start position:0%
+largest singular value is the two norm
+of the matrix but actually it comes from
+
+ align:start position:0%
+of the matrix but actually it comes from
+ 
+
+ align:start position:0%
+of the matrix but actually it comes from
+somewhere so I want to speak about this
+
+ align:start position:0%
+somewhere so I want to speak about this
+ 
+
+ align:start position:0%
+somewhere so I want to speak about this
+one first the tomb norm so so so it's
+
+ align:start position:0%
+one first the tomb norm so so so it's
+ 
+
+ align:start position:0%
+one first the tomb norm so so so it's
+the two norm of a matrix and one way to
+
+ align:start position:0%
+the two norm of a matrix and one way to
+ 
+
+ align:start position:0%
+the two norm of a matrix and one way to
+see the two norm of a matrix is to
+
+ align:start position:0%
+see the two norm of a matrix is to
+ 
+
+ align:start position:0%
+see the two norm of a matrix is to
+connected to the 2 norm of vectors I'd
+
+ align:start position:0%
+connected to the 2 norm of vectors I'd
+ 
+
+ align:start position:0%
+connected to the 2 norm of vectors I'd
+like to connect the two norm of matrices
+
+ align:start position:0%
+like to connect the two norm of matrices
+ 
+
+ align:start position:0%
+like to connect the two norm of matrices
+to the two norm of vectors and how shall
+
+ align:start position:0%
+to the two norm of vectors and how shall
+ 
+
+ align:start position:0%
+to the two norm of vectors and how shall
+I do that I think I'm going to look at
+
+ align:start position:0%
+I do that I think I'm going to look at
+ 
+
+ align:start position:0%
+I do that I think I'm going to look at
+the 2 norm of AX over the two norm of X
+
+ align:start position:0%
+the 2 norm of AX over the two norm of X
+ 
+
+ align:start position:0%
+the 2 norm of AX over the two norm of X
+so in a way to me that that ratio is
+
+ align:start position:0%
+so in a way to me that that ratio is
+ 
+
+ align:start position:0%
+so in a way to me that that ratio is
+like the blow up factor if a was 7 times
+
+ align:start position:0%
+like the blow up factor if a was 7 times
+ 
+
+ align:start position:0%
+like the blow up factor if a was 7 times
+the identity to take an easy case if a
+
+ align:start position:0%
+the identity to take an easy case if a
+ 
+
+ align:start position:0%
+the identity to take an easy case if a
+is 7 times the identity what would that
+
+ align:start position:0%
+is 7 times the identity what would that
+ 
+
+ align:start position:0%
+is 7 times the identity what would that
+ratio be yeah 7 if a is if a is 7 I this
+
+ align:start position:0%
+ratio be yeah 7 if a is if a is 7 I this
+ 
+
+ align:start position:0%
+ratio be yeah 7 if a is if a is 7 I this
+this will be 7 X and this will be X and
+
+ align:start position:0%
+this will be 7 X and this will be X and
+ 
+
+ align:start position:0%
+this will be 7 X and this will be X and
+norms the factor 7 comes out so that
+
+ align:start position:0%
+norms the factor 7 comes out so that
+ 
+
+ align:start position:0%
+norms the factor 7 comes out so that
+ratio will be 7 okay
+
+ align:start position:0%
+ratio will be 7 okay
+ 
+
+ align:start position:0%
+ratio will be 7 okay
+for me the norm is take that's the
+
+ align:start position:0%
+for me the norm is take that's the
+ 
+
+ align:start position:0%
+for me the norm is take that's the
+blow-up factor when so here here's my
+
+ align:start position:0%
+blow-up factor when so here here's my
+ 
+
+ align:start position:0%
+blow-up factor when so here here's my
+here's the idea of a matrix norm now I'm
+
+ align:start position:0%
+here's the idea of a matrix norm now I'm
+ 
+
+ align:start position:0%
+here's the idea of a matrix norm now I'm
+doing matrix matrix norm from vector
+
+ align:start position:0%
+doing matrix matrix norm from vector
+ 
+
+ align:start position:0%
+doing matrix matrix norm from vector
+norm and the answer will be maximum the
+
+ align:start position:0%
+norm and the answer will be maximum the
+ 
+
+ align:start position:0%
+norm and the answer will be maximum the
+maximum of this ratio I call that ratio
+
+ align:start position:0%
+maximum of this ratio I call that ratio
+ 
+
+ align:start position:0%
+maximum of this ratio I call that ratio
+of the blow up vector that's just a
+
+ align:start position:0%
+of the blow up vector that's just a
+ 
+
+ align:start position:0%
+of the blow up vector that's just a
+made-up name the maximum over all X's
+
+ align:start position:0%
+made-up name the maximum over all X's
+ 
+
+ align:start position:0%
+made-up name the maximum over all X's
+all the I look to see which vector gets
+
+ align:start position:0%
+all the I look to see which vector gets
+ 
+
+ align:start position:0%
+all the I look to see which vector gets
+blown up the most and that is the norm
+
+ align:start position:0%
+blown up the most and that is the norm
+ 
+
+ align:start position:0%
+blown up the most and that is the norm
+of the matrix
+
+ align:start position:0%
+of the matrix
+ 
+
+ align:start position:0%
+of the matrix
+I know I've I've settled on norms of
+
+ align:start position:0%
+I know I've I've settled on norms of
+ 
+
+ align:start position:0%
+I know I've I've settled on norms of
+vectors that's that's done upstairs
+
+ align:start position:0%
+vectors that's that's done upstairs
+ 
+
+ align:start position:0%
+vectors that's that's done upstairs
+there now I'm looking at norms of
+
+ align:start position:0%
+there now I'm looking at norms of
+ 
+
+ align:start position:0%
+there now I'm looking at norms of
+matrices and this is one way to get a
+
+ align:start position:0%
+matrices and this is one way to get a
+ 
+
+ align:start position:0%
+matrices and this is one way to get a
+good norm of a matrix that kind of comes
+
+ align:start position:0%
+good norm of a matrix that kind of comes
+ 
+
+ align:start position:0%
+good norm of a matrix that kind of comes
+from the two norm so there would be
+
+ align:start position:0%
+from the two norm so there would be
+ 
+
+ align:start position:0%
+from the two norm so there would be
+other norms for matrices coming from
+
+ align:start position:0%
+other norms for matrices coming from
+ 
+
+ align:start position:0%
+other norms for matrices coming from
+other vector norms and those we haven't
+
+ align:start position:0%
+other vector norms and those we haven't
+ 
+
+ align:start position:0%
+other vector norms and those we haven't
+seen but the two norm is this is a very
+
+ align:start position:0%
+seen but the two norm is this is a very
+ 
+
+ align:start position:0%
+seen but the two norm is this is a very
+important one so what is the maximum
+
+ align:start position:0%
+important one so what is the maximum
+ 
+
+ align:start position:0%
+important one so what is the maximum
+value of this of that ratio for a matrix
+
+ align:start position:0%
+value of this of that ratio for a matrix
+ 
+
+ align:start position:0%
+value of this of that ratio for a matrix
+a the claim is that it's Sigma 1 what a
+
+ align:start position:0%
+a the claim is that it's Sigma 1 what a
+ 
+
+ align:start position:0%
+a the claim is that it's Sigma 1 what a
+big equality there now can we see why is
+
+ align:start position:0%
+big equality there now can we see why is
+ 
+
+ align:start position:0%
+big equality there now can we see why is
+why is Sigma 1 the answer to this
+
+ align:start position:0%
+why is Sigma 1 the answer to this
+ 
+
+ align:start position:0%
+why is Sigma 1 the answer to this
+problem I can see a couple of ways to
+
+ align:start position:0%
+problem I can see a couple of ways to
+ 
+
+ align:start position:0%
+problem I can see a couple of ways to
+think about that but that's a very
+
+ align:start position:0%
+think about that but that's a very
+ 
+
+ align:start position:0%
+think about that but that's a very
+important fact in fact this is a way to
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+discover what Sigma 1 is without all the
+
+ align:start position:0%
+discover what Sigma 1 is without all the
+ 
+
+ align:start position:0%
+discover what Sigma 1 is without all the
+other Sigma's if I look for the X that
+
+ align:start position:0%
+other Sigma's if I look for the X that
+ 
+
+ align:start position:0%
+other Sigma's if I look for the X that
+has the biggest blow-up factor and by
+
+ align:start position:0%
+has the biggest blow-up factor and by
+ 
+
+ align:start position:0%
+has the biggest blow-up factor and by
+the way which X will it be which X will
+
+ align:start position:0%
+the way which X will it be which X will
+ 
+
+ align:start position:0%
+the way which X will it be which X will
+win the max competition here and be
+
+ align:start position:0%
+win the max competition here and be
+ 
+
+ align:start position:0%
+win the max competition here and be
+Sigma 1 times as long
+
+ align:start position:0%
+Sigma 1 times as long
+ 
+
+ align:start position:0%
+Sigma 1 times as long
+Raja's as the the ratio will be Sigma 1
+
+ align:start position:0%
+Raja's as the the ratio will be Sigma 1
+ 
+
+ align:start position:0%
+Raja's as the the ratio will be Sigma 1
+that'll be Sigma 1 when is this thing
+
+ align:start position:0%
+that'll be Sigma 1 when is this thing
+ 
+
+ align:start position:0%
+that'll be Sigma 1 when is this thing
+Sigma 1 times as large as that for which
+
+ align:start position:0%
+Sigma 1 times as large as that for which
+ 
+
+ align:start position:0%
+Sigma 1 times as large as that for which
+X naught for an eigenvector if X was an
+
+ align:start position:0%
+X naught for an eigenvector if X was an
+ 
+
+ align:start position:0%
+X naught for an eigenvector if X was an
+eigenvector what would that ratio be
+
+ align:start position:0%
+eigenvector what would that ratio be
+ 
+
+ align:start position:0%
+eigenvector what would that ratio be
+lambda but if a is not a symmetric
+
+ align:start position:0%
+lambda but if a is not a symmetric
+ 
+
+ align:start position:0%
+lambda but if a is not a symmetric
+matrix
+
+ align:start position:0%
+matrix
+ 
+
+ align:start position:0%
+matrix
+maybe the eigenvectors don't tell you
+
+ align:start position:0%
+maybe the eigenvectors don't tell you
+ 
+
+ align:start position:0%
+maybe the eigenvectors don't tell you
+the the waiter the exact way to go what
+
+ align:start position:0%
+the the waiter the exact way to go what
+ 
+
+ align:start position:0%
+the the waiter the exact way to go what
+so what vector view would you now guess
+
+ align:start position:0%
+so what vector view would you now guess
+ 
+
+ align:start position:0%
+so what vector view would you now guess
+it's not an eigenvector it is a singular
+
+ align:start position:0%
+it's not an eigenvector it is a singular
+ 
+
+ align:start position:0%
+it's not an eigenvector it is a singular
+vector and which singular vectors are
+
+ align:start position:0%
+vector and which singular vectors are
+ 
+
+ align:start position:0%
+vector and which singular vectors are
+probably going to be you v1
+
+ align:start position:0%
+probably going to be you v1
+ 
+
+ align:start position:0%
+probably going to be you v1
+yeah V one makes sense winner so the
+
+ align:start position:0%
+yeah V one makes sense winner so the
+ 
+
+ align:start position:0%
+yeah V one makes sense winner so the
+winner of this competition is X equal V
+
+ align:start position:0%
+winner of this competition is X equal V
+ 
+
+ align:start position:0%
+winner of this competition is X equal V
+1 the first the first right singular
+
+ align:start position:0%
+1 the first the first right singular
+ 
+
+ align:start position:0%
+1 the first the first right singular
+vector and we better be able to check
+
+ align:start position:0%
+vector and we better be able to check
+ 
+
+ align:start position:0%
+vector and we better be able to check
+that so again this maximization problem
+
+ align:start position:0%
+that so again this maximization problem
+ 
+
+ align:start position:0%
+that so again this maximization problem
+the answer tells you is in terms of the
+
+ align:start position:0%
+the answer tells you is in terms of the
+ 
+
+ align:start position:0%
+the answer tells you is in terms of the
+singular vectors so that's a way to find
+
+ align:start position:0%
+singular vectors so that's a way to find
+ 
+
+ align:start position:0%
+singular vectors so that's a way to find
+this first singular vector without
+
+ align:start position:0%
+this first singular vector without
+ 
+
+ align:start position:0%
+this first singular vector without
+finding them all and let's just plug in
+
+ align:start position:0%
+finding them all and let's just plug in
+ 
+
+ align:start position:0%
+finding them all and let's just plug in
+the first thing of their vector and see
+
+ align:start position:0%
+the first thing of their vector and see
+ 
+
+ align:start position:0%
+the first thing of their vector and see
+that the ratio is see what it see that
+
+ align:start position:0%
+that the ratio is see what it see that
+ 
+
+ align:start position:0%
+that the ratio is see what it see that
+the ratio is Sigma 1 so now let me plug
+
+ align:start position:0%
+the ratio is Sigma 1 so now let me plug
+ 
+
+ align:start position:0%
+the ratio is Sigma 1 so now let me plug
+it in so so what do I have I want a V 1
+
+ align:start position:0%
+it in so so what do I have I want a V 1
+ 
+
+ align:start position:0%
+it in so so what do I have I want a V 1
+over length of V 1 okay and I'm hoping
+
+ align:start position:0%
+over length of V 1 okay and I'm hoping
+ 
+
+ align:start position:0%
+over length of V 1 okay and I'm hoping
+to get that answer well what's the bout
+
+ align:start position:0%
+to get that answer well what's the bout
+ 
+
+ align:start position:0%
+to get that answer well what's the bout
+of the denominator here the length of V
+
+ align:start position:0%
+of the denominator here the length of V
+ 
+
+ align:start position:0%
+of the denominator here the length of V
+1 is what no big deal there that's one
+
+ align:start position:0%
+1 is what no big deal there that's one
+ 
+
+ align:start position:0%
+1 is what no big deal there that's one
+what what's the length of the of the top
+
+ align:start position:0%
+what what's the length of the of the top
+ 
+
+ align:start position:0%
+what what's the length of the of the top
+one so so
+
+ align:start position:0%
+one so so
+ 
+
+ align:start position:0%
+one so so
+is a v1 now what is a v1 if v1 is the
+
+ align:start position:0%
+is a v1 now what is a v1 if v1 is the
+ 
+
+ align:start position:0%
+is a v1 now what is a v1 if v1 is the
+first singular first right singular
+
+ align:start position:0%
+first singular first right singular
+ 
+
+ align:start position:0%
+first singular first right singular
+vector then a v1 is Sigma 1 times u1
+
+ align:start position:0%
+vector then a v1 is Sigma 1 times u1
+ 
+
+ align:start position:0%
+vector then a v1 is Sigma 1 times u1
+remember the singular vector deals were
+
+ align:start position:0%
+remember the singular vector deals were
+ 
+
+ align:start position:0%
+remember the singular vector deals were
+AV equals Sigma u AV k equals sigma k UK
+
+ align:start position:0%
+AV equals Sigma u AV k equals sigma k UK
+ 
+
+ align:start position:0%
+AV equals Sigma u AV k equals sigma k UK
+remember that so they're not
+
+ align:start position:0%
+remember that so they're not
+ 
+
+ align:start position:0%
+remember that so they're not
+eigenvectors their singular vectors so
+
+ align:start position:0%
+eigenvectors their singular vectors so
+ 
+
+ align:start position:0%
+eigenvectors their singular vectors so
+that's that is a v1 is the length of
+
+ align:start position:0%
+that's that is a v1 is the length of
+ 
+
+ align:start position:0%
+that's that is a v1 is the length of
+sigma 1 u 1 and it's divided by 1 and of
+
+ align:start position:0%
+sigma 1 u 1 and it's divided by 1 and of
+ 
+
+ align:start position:0%
+sigma 1 u 1 and it's divided by 1 and of
+course u 1 is also a unit vector so I
+
+ align:start position:0%
+course u 1 is also a unit vector so I
+ 
+
+ align:start position:0%
+course u 1 is also a unit vector so I
+just get signal okay so that's another
+
+ align:start position:0%
+just get signal okay so that's another
+ 
+
+ align:start position:0%
+just get signal okay so that's another
+way to say that you can find Sigma 1 by
+
+ align:start position:0%
+way to say that you can find Sigma 1 by
+ 
+
+ align:start position:0%
+way to say that you can find Sigma 1 by
+solving this maximum problem and you get
+
+ align:start position:0%
+solving this maximum problem and you get
+ 
+
+ align:start position:0%
+solving this maximum problem and you get
+that Sigma 1 ok and I could get other
+
+ align:start position:0%
+that Sigma 1 ok and I could get other
+ 
+
+ align:start position:0%
+that Sigma 1 ok and I could get other
+norms matrix norms by by maximizing that
+
+ align:start position:0%
+norms matrix norms by by maximizing that
+ 
+
+ align:start position:0%
+norms matrix norms by by maximizing that
+blow up factor in that vector norm I
+
+ align:start position:0%
+blow up factor in that vector norm I
+ 
+
+ align:start position:0%
+blow up factor in that vector norm I
+won't do that now just to keep control
+
+ align:start position:0%
+won't do that now just to keep control
+ 
+
+ align:start position:0%
+won't do that now just to keep control
+of what we've got now what were the what
+
+ align:start position:0%
+of what we've got now what were the what
+ 
+
+ align:start position:0%
+of what we've got now what were the what
+was the next matrix norm that came in
+
+ align:start position:0%
+was the next matrix norm that came in
+ 
+
+ align:start position:0%
+was the next matrix norm that came in
+last time very very important one for
+
+ align:start position:0%
+last time very very important one for
+ 
+
+ align:start position:0%
+last time very very important one for
+deep learning and neural nets somehow
+
+ align:start position:0%
+deep learning and neural nets somehow
+ 
+
+ align:start position:0%
+deep learning and neural nets somehow
+it's a little simpler than this guy and
+
+ align:start position:0%
+it's a little simpler than this guy and
+ 
+
+ align:start position:0%
+it's a little simpler than this guy and
+what's the what was that matrix norm
+
+ align:start position:0%
+what's the what was that matrix norm
+ 
+
+ align:start position:0%
+what's the what was that matrix norm
+what letter whose name goes here
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Frobenius so capital F for Frobenius and
+
+ align:start position:0%
+Frobenius so capital F for Frobenius and
+ 
+
+ align:start position:0%
+Frobenius so capital F for Frobenius and
+that and what was that that was the
+
+ align:start position:0%
+that and what was that that was the
+ 
+
+ align:start position:0%
+that and what was that that was the
+square root of the sum of the all the
+
+ align:start position:0%
+square root of the sum of the all the
+ 
+
+ align:start position:0%
+square root of the sum of the all the
+add up add all the a IJ squares for all
+
+ align:start position:0%
+add up add all the a IJ squares for all
+ 
+
+ align:start position:0%
+add up add all the a IJ squares for all
+over the matrix and then takes a square
+
+ align:start position:0%
+over the matrix and then takes a square
+ 
+
+ align:start position:0%
+over the matrix and then takes a square
+root and then somebody asked a good
+
+ align:start position:0%
+root and then somebody asked a good
+ 
+
+ align:start position:0%
+root and then somebody asked a good
+question after class on Wednesday what
+
+ align:start position:0%
+question after class on Wednesday what
+ 
+
+ align:start position:0%
+question after class on Wednesday what
+has that got to do with the Sigma's
+
+ align:start position:0%
+has that got to do with the Sigma's
+ 
+
+ align:start position:0%
+has that got to do with the Sigma's
+because I my disappoint was that these
+
+ align:start position:0%
+because I my disappoint was that these
+ 
+
+ align:start position:0%
+because I my disappoint was that these
+dorms are the guys that go with the
+
+ align:start position:0%
+dorms are the guys that go with the
+ 
+
+ align:start position:0%
+dorms are the guys that go with the
+Sigma's that does that have nice
+
+ align:start position:0%
+Sigma's that does that have nice
+ 
+
+ align:start position:0%
+Sigma's that does that have nice
+formulas for the Sigma's and here it is
+
+ align:start position:0%
+formulas for the Sigma's and here it is
+ 
+
+ align:start position:0%
+formulas for the Sigma's and here it is
+it's the square root of the sum of the
+
+ align:start position:0%
+it's the square root of the sum of the
+ 
+
+ align:start position:0%
+it's the square root of the sum of the
+squares of all the signals yes sorry let
+
+ align:start position:0%
+squares of all the signals yes sorry let
+ 
+
+ align:start position:0%
+squares of all the signals yes sorry let
+me write Frobenius again but this
+
+ align:start position:0%
+me write Frobenius again but this
+ 
+
+ align:start position:0%
+me write Frobenius again but this
+notation with an F is now pretty
+
+ align:start position:0%
+notation with an F is now pretty
+ 
+
+ align:start position:0%
+notation with an F is now pretty
+standard and we should be able to see
+
+ align:start position:0%
+standard and we should be able to see
+ 
+
+ align:start position:0%
+standard and we should be able to see
+why that number is the same as that
+
+ align:start position:0%
+why that number is the same as that
+ 
+
+ align:start position:0%
+why that number is the same as that
+number yeah I could I could give you a
+
+ align:start position:0%
+number yeah I could I could give you a
+ 
+
+ align:start position:0%
+number yeah I could I could give you a
+reason or I couldn't put it on the
+
+ align:start position:0%
+reason or I couldn't put it on the
+ 
+
+ align:start position:0%
+reason or I couldn't put it on the
+problem set yeah I think it better on
+
+ align:start position:0%
+problem set yeah I think it better on
+ 
+
+ align:start position:0%
+problem set yeah I think it better on
+the problem set because first of all
+
+ align:start position:0%
+the problem set because first of all
+ 
+
+ align:start position:0%
+the problem set because first of all
+I'll get off the hook right away and
+
+ align:start position:0%
+I'll get off the hook right away and
+ 
+
+ align:start position:0%
+I'll get off the hook right away and
+secondly this connection between in
+
+ align:start position:0%
+secondly this connection between in
+ 
+
+ align:start position:0%
+secondly this connection between in
+Probie Nia so it's like a beautiful fact
+
+ align:start position:0%
+Probie Nia so it's like a beautiful fact
+ 
+
+ align:start position:0%
+Probie Nia so it's like a beautiful fact
+about Frobenius norm that you add up all
+
+ align:start position:0%
+about Frobenius norm that you add up all
+ 
+
+ align:start position:0%
+about Frobenius norm that you add up all
+the Sigma Squared's as M times n of them
+
+ align:start position:0%
+the Sigma Squared's as M times n of them
+ 
+
+ align:start position:0%
+the Sigma Squared's as M times n of them
+because it's a all filled matrix or you
+
+ align:start position:0%
+because it's a all filled matrix or you
+ 
+
+ align:start position:0%
+because it's a all filled matrix or you
+add up so another way to say it is we
+
+ align:start position:0%
+add up so another way to say it is we
+ 
+
+ align:start position:0%
+add up so another way to say it is we
+haven't written down the SVD today's a
+
+ align:start position:0%
+haven't written down the SVD today's a
+ 
+
+ align:start position:0%
+haven't written down the SVD today's a
+whoyou Sigma V transpose and the point
+
+ align:start position:0%
+whoyou Sigma V transpose and the point
+ 
+
+ align:start position:0%
+whoyou Sigma V transpose and the point
+is that for the Frobenius norm actually
+
+ align:start position:0%
+is that for the Frobenius norm actually
+ 
+
+ align:start position:0%
+is that for the Frobenius norm actually
+for all these norms I can change you it
+
+ align:start position:0%
+for all these norms I can change you it
+ 
+
+ align:start position:0%
+for all these norms I can change you it
+doesn't change the norm so I can make
+
+ align:start position:0%
+doesn't change the norm so I can make
+ 
+
+ align:start position:0%
+doesn't change the norm so I can make
+you the identity it's you as we all know
+
+ align:start position:0%
+you the identity it's you as we all know
+ 
+
+ align:start position:0%
+you the identity it's you as we all know
+is an orthogonal matrix and what I'm
+
+ align:start position:0%
+is an orthogonal matrix and what I'm
+ 
+
+ align:start position:0%
+is an orthogonal matrix and what I'm
+saying is orthogonal matrix you doesn't
+
+ align:start position:0%
+saying is orthogonal matrix you doesn't
+ 
+
+ align:start position:0%
+saying is orthogonal matrix you doesn't
+change any of these particular norms so
+
+ align:start position:0%
+change any of these particular norms so
+ 
+
+ align:start position:0%
+change any of these particular norms so
+suppose it was the identity same here
+
+ align:start position:0%
+suppose it was the identity same here
+ 
+
+ align:start position:0%
+suppose it was the identity same here
+that could be the identity without
+
+ align:start position:0%
+that could be the identity without
+ 
+
+ align:start position:0%
+that could be the identity without
+changing the norm so we're down to the
+
+ align:start position:0%
+changing the norm so we're down to the
+ 
+
+ align:start position:0%
+changing the norm so we're down to the
+norm of the the Frobenius so what's the
+
+ align:start position:0%
+norm of the the Frobenius so what's the
+ 
+
+ align:start position:0%
+norm of the the Frobenius so what's the
+Frobenius norm
+
+ align:start position:0%
+Frobenius norm
+ 
+
+ align:start position:0%
+Frobenius norm
+of that guy what's the Probie Gnaeus
+
+ align:start position:0%
+of that guy what's the Probie Gnaeus
+ 
+
+ align:start position:0%
+of that guy what's the Probie Gnaeus
+norm of that diagonal matrix well you're
+
+ align:start position:0%
+norm of that diagonal matrix well you're
+ 
+
+ align:start position:0%
+norm of that diagonal matrix well you're
+supposed to add up the squares of all
+
+ align:start position:0%
+supposed to add up the squares of all
+ 
+
+ align:start position:0%
+supposed to add up the squares of all
+the numbers in the matrix and what do
+
+ align:start position:0%
+the numbers in the matrix and what do
+ 
+
+ align:start position:0%
+the numbers in the matrix and what do
+you get you get that right so that's why
+
+ align:start position:0%
+you get you get that right so that's why
+ 
+
+ align:start position:0%
+you get you get that right so that's why
+this is the same as this because the
+
+ align:start position:0%
+this is the same as this because the
+ 
+
+ align:start position:0%
+this is the same as this because the
+orthogonal guy there on the orthogonal
+
+ align:start position:0%
+orthogonal guy there on the orthogonal
+ 
+
+ align:start position:0%
+orthogonal guy there on the orthogonal
+guy there make no difference in the norm
+
+ align:start position:0%
+guy there make no difference in the norm
+ 
+
+ align:start position:0%
+guy there make no difference in the norm
+but that takes checking right yeah but
+
+ align:start position:0%
+but that takes checking right yeah but
+ 
+
+ align:start position:0%
+but that takes checking right yeah but
+that's another way to see why the
+
+ align:start position:0%
+that's another way to see why the
+ 
+
+ align:start position:0%
+that's another way to see why the
+provenience norm gives this and then
+
+ align:start position:0%
+provenience norm gives this and then
+ 
+
+ align:start position:0%
+provenience norm gives this and then
+finally this was the nuclear norm and
+
+ align:start position:0%
+finally this was the nuclear norm and
+ 
+
+ align:start position:0%
+finally this was the nuclear norm and
+actually just before the my lunch
+
+ align:start position:0%
+actually just before the my lunch
+ 
+
+ align:start position:0%
+actually just before the my lunch
+lecture on the subject of probably about
+
+ align:start position:0%
+lecture on the subject of probably about
+ 
+
+ align:start position:0%
+lecture on the subject of probably about
+a learning morning the lunch lecture was
+
+ align:start position:0%
+a learning morning the lunch lecture was
+ 
+
+ align:start position:0%
+a learning morning the lunch lecture was
+about this crazy way that humans behave
+
+ align:start position:0%
+about this crazy way that humans behave
+ 
+
+ align:start position:0%
+about this crazy way that humans behave
+not us but other humans other actually
+
+ align:start position:0%
+not us but other humans other actually
+ 
+
+ align:start position:0%
+not us but other humans other actually
+well take that out of the tape yeah okay
+
+ align:start position:0%
+well take that out of the tape yeah okay
+ 
+
+ align:start position:0%
+well take that out of the tape yeah okay
+anyway that was that lecture well before
+
+ align:start position:0%
+anyway that was that lecture well before
+ 
+
+ align:start position:0%
+anyway that was that lecture well before
+that was a lecture for an hour plus
+
+ align:start position:0%
+that was a lecture for an hour plus
+ 
+
+ align:start position:0%
+that was a lecture for an hour plus
+about deep learning by somebody who
+
+ align:start position:0%
+about deep learning by somebody who
+ 
+
+ align:start position:0%
+about deep learning by somebody who
+really really has begun to understand
+
+ align:start position:0%
+really really has begun to understand
+ 
+
+ align:start position:0%
+really really has begun to understand
+what is happening inside how does that
+
+ align:start position:0%
+what is happening inside how does that
+ 
+
+ align:start position:0%
+what is happening inside how does that
+gradient descent optimization algorithm
+
+ align:start position:0%
+gradient descent optimization algorithm
+ 
+
+ align:start position:0%
+gradient descent optimization algorithm
+pick out what what does it pick out as
+
+ align:start position:0%
+pick out what what does it pick out as
+ 
+
+ align:start position:0%
+pick out what what does it pick out as
+that as as the thing it learns it's
+
+ align:start position:0%
+that as as the thing it learns it's
+ 
+
+ align:start position:0%
+that as as the thing it learns it's
+gonna be the you know our goal in in
+
+ align:start position:0%
+gonna be the you know our goal in in
+ 
+
+ align:start position:0%
+gonna be the you know our goal in in
+this course we're not there yet but his
+
+ align:start position:0%
+this course we're not there yet but his
+ 
+
+ align:start position:0%
+this course we're not there yet but his
+conjecture is that that yeah so it's a
+
+ align:start position:0%
+conjecture is that that yeah so it's a
+ 
+
+ align:start position:0%
+conjecture is that that yeah so it's a
+conjecture he doesn't have our proof
+
+ align:start position:0%
+conjecture he doesn't have our proof
+ 
+
+ align:start position:0%
+conjecture he doesn't have our proof
+he's got proofs of some nice cases where
+
+ align:start position:0%
+he's got proofs of some nice cases where
+ 
+
+ align:start position:0%
+he's got proofs of some nice cases where
+things commute but he hasn't got the
+
+ align:start position:0%
+things commute but he hasn't got the
+ 
+
+ align:start position:0%
+things commute but he hasn't got the
+whole thing yet but it's pretty terrific
+
+ align:start position:0%
+whole thing yet but it's pretty terrific
+ 
+
+ align:start position:0%
+whole thing yet but it's pretty terrific
+work so this this was professor cerebro
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+in Chicago so he just announced his
+
+ align:start position:0%
+in Chicago so he just announced his
+ 
+
+ align:start position:0%
+in Chicago so he just announced his
+conjecture and his conjecture is that in
+
+ align:start position:0%
+conjecture and his conjecture is that in
+ 
+
+ align:start position:0%
+conjecture and his conjecture is that in
+a model case the deep learning that
+
+ align:start position:0%
+a model case the deep learning that
+ 
+
+ align:start position:0%
+a model case the deep learning that
+we'll learn about with a gradient
+
+ align:start position:0%
+we'll learn about with a gradient
+ 
+
+ align:start position:0%
+we'll learn about with a gradient
+descent that we'll learn about to find
+
+ align:start position:0%
+descent that we'll learn about to find
+ 
+
+ align:start position:0%
+descent that we'll learn about to find
+the best weights that the point is that
+
+ align:start position:0%
+the best weights that the point is that
+ 
+
+ align:start position:0%
+the best weights that the point is that
+they're you know typical deep learning
+
+ align:start position:0%
+they're you know typical deep learning
+ 
+
+ align:start position:0%
+they're you know typical deep learning
+problem these days there are many more
+
+ align:start position:0%
+problem these days there are many more
+ 
+
+ align:start position:0%
+problem these days there are many more
+ways than samples and so there are a lot
+
+ align:start position:0%
+ways than samples and so there are a lot
+ 
+
+ align:start position:0%
+ways than samples and so there are a lot
+of possible minima
+
+ align:start position:0%
+of possible minima
+ 
+
+ align:start position:0%
+of possible minima
+many different weights give the same
+
+ align:start position:0%
+many different weights give the same
+ 
+
+ align:start position:0%
+many different weights give the same
+minimum loss because there are so many
+
+ align:start position:0%
+minimum loss because there are so many
+ 
+
+ align:start position:0%
+minimum loss because there are so many
+weights it's the problem is like too
+
+ align:start position:0%
+weights it's the problem is like too
+ 
+
+ align:start position:0%
+weights it's the problem is like too
+many variables but it turns out to be a
+
+ align:start position:0%
+many variables but it turns out to be a
+ 
+
+ align:start position:0%
+many variables but it turns out to be a
+very very good thing that's part of the
+
+ align:start position:0%
+very very good thing that's part of the
+ 
+
+ align:start position:0%
+very very good thing that's part of the
+success and the he believes that in a
+
+ align:start position:0%
+success and the he believes that in a
+ 
+
+ align:start position:0%
+success and the he believes that in a
+model situation that the optimization by
+
+ align:start position:0%
+model situation that the optimization by
+ 
+
+ align:start position:0%
+model situation that the optimization by
+gradient descent picks out the weights
+
+ align:start position:0%
+gradient descent picks out the weights
+ 
+
+ align:start position:0%
+gradient descent picks out the weights
+that minimize the nuclear norm so this
+
+ align:start position:0%
+that minimize the nuclear norm so this
+ 
+
+ align:start position:0%
+that minimize the nuclear norm so this
+would be a norm of a lot of weights and
+
+ align:start position:0%
+would be a norm of a lot of weights and
+ 
+
+ align:start position:0%
+would be a norm of a lot of weights and
+he thinks that's where the system goes
+
+ align:start position:0%
+he thinks that's where the system goes
+ 
+
+ align:start position:0%
+he thinks that's where the system goes
+will see this this was comes up in
+
+ align:start position:0%
+will see this this was comes up in
+ 
+
+ align:start position:0%
+will see this this was comes up in
+compressed sensing as I mentioned last
+
+ align:start position:0%
+compressed sensing as I mentioned last
+ 
+
+ align:start position:0%
+compressed sensing as I mentioned last
+time so this but now I have to remember
+
+ align:start position:0%
+time so this but now I have to remember
+ 
+
+ align:start position:0%
+time so this but now I have to remember
+what was what was the definition well do
+
+ align:start position:0%
+what was what was the definition well do
+ 
+
+ align:start position:0%
+what was what was the definition well do
+you remember what the nuclear norm was
+
+ align:start position:0%
+you remember what the nuclear norm was
+ 
+
+ align:start position:0%
+you remember what the nuclear norm was
+it's also his he often used he used a
+
+ align:start position:0%
+it's also his he often used he used a
+ 
+
+ align:start position:0%
+it's also his he often used he used a
+little star instead of an end I'll put
+
+ align:start position:0%
+little star instead of an end I'll put
+ 
+
+ align:start position:0%
+little star instead of an end I'll put
+that in the notes other people call it
+
+ align:start position:0%
+that in the notes other people call it
+ 
+
+ align:start position:0%
+that in the notes other people call it
+the trace norm that's but I think this
+
+ align:start position:0%
+the trace norm that's but I think this
+ 
+
+ align:start position:0%
+the trace norm that's but I think this
+end kind of gives it a name notation you
+
+ align:start position:0%
+end kind of gives it a name notation you
+ 
+
+ align:start position:0%
+end kind of gives it a name notation you
+can remember so let's call it the
+
+ align:start position:0%
+can remember so let's call it the
+ 
+
+ align:start position:0%
+can remember so let's call it the
+nuclear norm do you remember what that
+
+ align:start position:0%
+nuclear norm do you remember what that
+ 
+
+ align:start position:0%
+nuclear norm do you remember what that
+one was
+
+ align:start position:0%
+one was
+ 
+
+ align:start position:0%
+one was
+it was yes somebody's singing it right
+
+ align:start position:0%
+it was yes somebody's singing it right
+ 
+
+ align:start position:0%
+it was yes somebody's singing it right
+add the Sigma's yeah just the sum of the
+
+ align:start position:0%
+add the Sigma's yeah just the sum of the
+ 
+
+ align:start position:0%
+add the Sigma's yeah just the sum of the
+signals like you know one norm yeah this
+
+ align:start position:0%
+signals like you know one norm yeah this
+ 
+
+ align:start position:0%
+signals like you know one norm yeah this
+is natural sort of l1 type of norm for
+
+ align:start position:0%
+is natural sort of l1 type of norm for
+ 
+
+ align:start position:0%
+is natural sort of l1 type of norm for
+matrices
+
+ align:start position:0%
+matrices
+ 
+
+ align:start position:0%
+matrices
+it's the l1 norm you have that Sigma
+
+ align:start position:0%
+it's the l1 norm you have that Sigma
+ 
+
+ align:start position:0%
+it's the l1 norm you have that Sigma
+vector this would be the l2 norm of the
+
+ align:start position:0%
+vector this would be the l2 norm of the
+ 
+
+ align:start position:0%
+vector this would be the l2 norm of the
+Sigma factor that would be the L
+
+ align:start position:0%
+Sigma factor that would be the L
+ 
+
+ align:start position:0%
+Sigma factor that would be the L
+infinity norm notice that the vector
+
+ align:start position:0%
+infinity norm notice that the vector
+ 
+
+ align:start position:0%
+infinity norm notice that the vector
+numbers infinity to 1 gets changed
+
+ align:start position:0%
+numbers infinity to 1 gets changed
+ 
+
+ align:start position:0%
+numbers infinity to 1 gets changed
+around 2 when you look at the matrix
+
+ align:start position:0%
+around 2 when you look at the matrix
+ 
+
+ align:start position:0%
+around 2 when you look at the matrix
+well so that's an exciting idea and it
+
+ align:start position:0%
+well so that's an exciting idea and it
+ 
+
+ align:start position:0%
+well so that's an exciting idea and it
+remains to be proved people are
+
+ align:start position:0%
+remains to be proved people are
+ 
+
+ align:start position:0%
+remains to be proved people are
+experimenting to see does it say is it
+
+ align:start position:0%
+experimenting to see does it say is it
+ 
+
+ align:start position:0%
+experimenting to see does it say is it
+true
+
+ align:start position:0%
+true
+ 
+
+ align:start position:0%
+true
+yep so that's a future yes okay so
+
+ align:start position:0%
+yep so that's a future yes okay so
+ 
+
+ align:start position:0%
+yep so that's a future yes okay so
+that's today we've talked about norms
+
+ align:start position:0%
+that's today we've talked about norms
+ 
+
+ align:start position:0%
+that's today we've talked about norms
+and this section of the notes will be
+
+ align:start position:0%
+and this section of the notes will be
+ 
+
+ align:start position:0%
+and this section of the notes will be
+all about norms we've taken a big leap
+
+ align:start position:0%
+all about norms we've taken a big leap
+ 
+
+ align:start position:0%
+all about norms we've taken a big leap
+in to comment about deep learning and
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this is what I want to say the most and
+
+ align:start position:0%
+this is what I want to say the most and
+ 
+
+ align:start position:0%
+this is what I want to say the most and
+I say it to every class I teach at the
+
+ align:start position:0%
+I say it to every class I teach at the
+ 
+
+ align:start position:0%
+I say it to every class I teach at the
+near the start of the semester my
+
+ align:start position:0%
+near the start of the semester my
+ 
+
+ align:start position:0%
+near the start of the semester my
+feeling about what my job is is to teach
+
+ align:start position:0%
+feeling about what my job is is to teach
+ 
+
+ align:start position:0%
+feeling about what my job is is to teach
+you things or to join you join with you
+
+ align:start position:0%
+you things or to join you join with you
+ 
+
+ align:start position:0%
+you things or to join you join with you
+in learning things as has happened today
+
+ align:start position:0%
+in learning things as has happened today
+ 
+
+ align:start position:0%
+in learning things as has happened today
+it's not to grade you I don't spend any
+
+ align:start position:0%
+it's not to grade you I don't spend any
+ 
+
+ align:start position:0%
+it's not to grade you I don't spend any
+time like like losing sleep y'all should
+
+ align:start position:0%
+time like like losing sleep y'all should
+ 
+
+ align:start position:0%
+time like like losing sleep y'all should
+should that person take up one point or
+
+ align:start position:0%
+should that person take up one point or
+ 
+
+ align:start position:0%
+should that person take up one point or
+epsilon penalty for for turning it in
+
+ align:start position:0%
+epsilon penalty for for turning it in
+ 
+
+ align:start position:0%
+epsilon penalty for for turning it in
+for minutes late
+
+ align:start position:0%
+for minutes late
+ 
+
+ align:start position:0%
+for minutes late
+hello with that right we've got a lot to
+
+ align:start position:0%
+hello with that right we've got a lot to
+ 
+
+ align:start position:0%
+hello with that right we've got a lot to
+do here and so anyway we'll get on with
+
+ align:start position:0%
+do here and so anyway we'll get on with
+ 
+
+ align:start position:0%
+do here and so anyway we'll get on with
+a job so homework three coming up and we
+
+ align:start position:0%
+a job so homework three coming up and we
+ 
+
+ align:start position:0%
+a job so homework three coming up and we
+be using the notes that you already have
+
+ align:start position:0%
+be using the notes that you already have
+ 
+
+ align:start position:0%
+be using the notes that you already have
+posted in stellar four for those
+
+ align:start position:0%
+posted in stellar four for those
+ 
+
+ align:start position:0%
+posted in stellar four for those
+sections eight and nine and so on and
+
+ align:start position:0%
+sections eight and nine and so on and
+ 
+
+ align:start position:0%
+sections eight and nine and so on and
+we'll keep going on Monday okay see you
+
+ align:start position:0%
+we'll keep going on Monday okay see you
+ 
+
+ align:start position:0%
+we'll keep going on Monday okay see you
+Monday and have a great weekend
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+you
\ No newline at end of file
diff --git a/O3hI9FdxFOM.txt b/O3hI9FdxFOM.txt
new file mode 100644
index 0000000000000000000000000000000000000000..fae17fa871da531efce94c521d63bc457097f3dd
--- /dev/null
+++ b/O3hI9FdxFOM.txt
@@ -0,0 +1,13639 @@
+align:start position:0%
+ 
+good
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+morning looks like uh 9:30 is getting
+
+ align:start position:0%
+morning looks like uh 9:30 is getting
+ 
+
+ align:start position:0%
+morning looks like uh 9:30 is getting
+earlier and earlier for everyone hello
+
+ align:start position:0%
+earlier and earlier for everyone hello
+ 
+
+ align:start position:0%
+earlier and earlier for everyone hello
+to all the people watching at
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+home I I think there should be a
+
+ align:start position:0%
+home I I think there should be a
+ 
+
+ align:start position:0%
+home I I think there should be a
+requirement that if you're watching the
+
+ align:start position:0%
+requirement that if you're watching the
+ 
+
+ align:start position:0%
+requirement that if you're watching the
+video you can only watch it 9:30 to 11:
+
+ align:start position:0%
+video you can only watch it 9:30 to 11:
+ 
+
+ align:start position:0%
+video you can only watch it 9:30 to 11:
+on
+
+ align:start position:0%
+on
+ 
+
+ align:start position:0%
+on
+somay that just to or at least start
+
+ align:start position:0%
+somay that just to or at least start
+ 
+
+ align:start position:0%
+somay that just to or at least start
+watching
+
+ align:start position:0%
+watching
+ 
+
+ align:start position:0%
+watching
+that just so you can all feel our our
+
+ align:start position:0%
+that just so you can all feel our our
+ 
+
+ align:start position:0%
+that just so you can all feel our our
+warnings um today we're going to talk
+
+ align:start position:0%
+warnings um today we're going to talk
+ 
+
+ align:start position:0%
+warnings um today we're going to talk
+about balance search trees now we've
+
+ align:start position:0%
+about balance search trees now we've
+ 
+
+ align:start position:0%
+about balance search trees now we've
+hinted at this for a while um our goal
+
+ align:start position:0%
+hinted at this for a while um our goal
+ 
+
+ align:start position:0%
+hinted at this for a while um our goal
+today is to get a search tree data
+
+ align:start position:0%
+today is to get a search tree data
+ 
+
+ align:start position:0%
+today is to get a search tree data
+structure so we can insert delete and
+
+ align:start position:0%
+structure so we can insert delete and
+ 
+
+ align:start position:0%
+structure so we can insert delete and
+search all in log n time per operation
+
+ align:start position:0%
+search all in log n time per operation
+ 
+
+ align:start position:0%
+search all in log n time per operation
+so we want a tree that's guaranteed to
+
+ align:start position:0%
+so we want a tree that's guaranteed to
+ 
+
+ align:start position:0%
+so we want a tree that's guaranteed to
+be log n in
+
+ align:start position:0%
+be log n in
+ 
+
+ align:start position:0%
+be log n in
+height so uh that's a balanced search
+
+ align:start position:0%
+height so uh that's a balanced search
+ 
+
+ align:start position:0%
+height so uh that's a balanced search
+tree data structure
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+we want a data structure that can
+
+ align:start position:0%
+we want a data structure that can
+ 
+
+ align:start position:0%
+we want a data structure that can
+maintain a dynamic set of n elements in
+
+ align:start position:0%
+maintain a dynamic set of n elements in
+ 
+
+ align:start position:0%
+maintain a dynamic set of n elements in
+log n time PR operation
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so we'll say using a tree of height
+
+ align:start position:0%
+so we'll say using a tree of height
+ 
+
+ align:start position:0%
+so we'll say using a tree of height
+order log
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+n now uh if you look very closely we
+
+ align:start position:0%
+n now uh if you look very closely we
+ 
+
+ align:start position:0%
+n now uh if you look very closely we
+haven't actually defined what a search
+
+ align:start position:0%
+haven't actually defined what a search
+ 
+
+ align:start position:0%
+haven't actually defined what a search
+tree data structure is we've defined
+
+ align:start position:0%
+tree data structure is we've defined
+ 
+
+ align:start position:0%
+tree data structure is we've defined
+what a binary search tree data structure
+
+ align:start position:0%
+what a binary search tree data structure
+ 
+
+ align:start position:0%
+what a binary search tree data structure
+is and that's one particular kind and
+
+ align:start position:0%
+is and that's one particular kind and
+ 
+
+ align:start position:0%
+is and that's one particular kind and
+that's what we'll be focusing on today
+
+ align:start position:0%
+that's what we'll be focusing on today
+ 
+
+ align:start position:0%
+that's what we'll be focusing on today
+in recitation on Friday we'll look at uh
+
+ align:start position:0%
+in recitation on Friday we'll look at uh
+ 
+
+ align:start position:0%
+in recitation on Friday we'll look at uh
+or you will look cat balance search
+
+ align:start position:0%
+or you will look cat balance search
+ 
+
+ align:start position:0%
+or you will look cat balance search
+trees that are not necessarily binary
+
+ align:start position:0%
+trees that are not necessarily binary
+ 
+
+ align:start position:0%
+trees that are not necessarily binary
+they can have each node can have a
+
+ align:start position:0%
+they can have each node can have a
+ 
+
+ align:start position:0%
+they can have each node can have a
+constant number of children not just two
+
+ align:start position:0%
+constant number of children not just two
+ 
+
+ align:start position:0%
+constant number of children not just two
+okay so I'm defining this generally
+
+ align:start position:0%
+okay so I'm defining this generally
+ 
+
+ align:start position:0%
+okay so I'm defining this generally
+you'll actually see what a search tree
+
+ align:start position:0%
+you'll actually see what a search tree
+ 
+
+ align:start position:0%
+you'll actually see what a search tree
+is in the general case later on today
+
+ align:start position:0%
+is in the general case later on today
+ 
+
+ align:start position:0%
+is in the general case later on today
+we'll just be focusing on the binary
+
+ align:start position:0%
+we'll just be focusing on the binary
+ 
+
+ align:start position:0%
+we'll just be focusing on the binary
+case so I won't Define this
+
+ align:start position:0%
+case so I won't Define this
+ 
+
+ align:start position:0%
+case so I won't Define this
+yet there are a lot of different balance
+
+ align:start position:0%
+yet there are a lot of different balance
+ 
+
+ align:start position:0%
+yet there are a lot of different balance
+search tree data
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+structures so these are the main ones
+
+ align:start position:0%
+structures so these are the main ones
+ 
+
+ align:start position:0%
+structures so these are the main ones
+that I know of the first one was AVL
+
+ align:start position:0%
+that I know of the first one was AVL
+ 
+
+ align:start position:0%
+that I know of the first one was AVL
+trees this was invented in
+
+ align:start position:0%
+trees this was invented in
+ 
+
+ align:start position:0%
+trees this was invented in
+1962 so that was the beginning of fast
+
+ align:start position:0%
+1962 so that was the beginning of fast
+ 
+
+ align:start position:0%
+1962 so that was the beginning of fast
+data
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+structures the next three sort of come
+
+ align:start position:0%
+structures the next three sort of come
+ 
+
+ align:start position:0%
+structures the next three sort of come
+together and this is what you'll cover
+
+ align:start position:0%
+together and this is what you'll cover
+ 
+
+ align:start position:0%
+together and this is what you'll cover
+in
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+recitation this week so uh these are
+
+ align:start position:0%
+recitation this week so uh these are
+ 
+
+ align:start position:0%
+recitation this week so uh these are
+non-binary trees instead of binary we
+
+ align:start position:0%
+non-binary trees instead of binary we
+ 
+
+ align:start position:0%
+non-binary trees instead of binary we
+have have maybe binary and tertiary or
+
+ align:start position:0%
+have have maybe binary and tertiary or
+ 
+
+ align:start position:0%
+have have maybe binary and tertiary or
+binary or tertiary or
+
+ align:start position:0%
+binary or tertiary or
+ 
+
+ align:start position:0%
+binary or tertiary or
+cautionary uh or a general constant
+
+ align:start position:0%
+cautionary uh or a general constant
+ 
+
+ align:start position:0%
+cautionary uh or a general constant
+degree
+
+ align:start position:0%
+degree
+ 
+
+ align:start position:0%
+degree
+B uh so that's another way you can get
+
+ align:start position:0%
+B uh so that's another way you can get
+ 
+
+ align:start position:0%
+B uh so that's another way you can get
+balance two three trees were are the
+
+ align:start position:0%
+balance two three trees were are the
+ 
+
+ align:start position:0%
+balance two three trees were are the
+second trees to be invented they were
+
+ align:start position:0%
+second trees to be invented they were
+ 
+
+ align:start position:0%
+second trees to be invented they were
+invented in
+
+ align:start position:0%
+invented in
+ 
+
+ align:start position:0%
+invented in
+1970 by
+
+ align:start position:0%
+1970 by
+ 
+
+ align:start position:0%
+1970 by
+hopcraft uh the trees we'll cover today
+
+ align:start position:0%
+hopcraft uh the trees we'll cover today
+ 
+
+ align:start position:0%
+hopcraft uh the trees we'll cover today
+are called red black
+
+ align:start position:0%
+are called red black
+ 
+
+ align:start position:0%
+are called red black
+trees these are binary search trees
+
+ align:start position:0%
+trees these are binary search trees
+ 
+
+ align:start position:0%
+trees these are binary search trees
+[Music]
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and of guaranteed logarithmic
+
+ align:start position:0%
+and of guaranteed logarithmic
+ 
+
+ align:start position:0%
+and of guaranteed logarithmic
+height um then there's some
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+others so skip lists are ones that we'll
+
+ align:start position:0%
+others so skip lists are ones that we'll
+ 
+
+ align:start position:0%
+others so skip lists are ones that we'll
+cover next
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+week it's not exactly a tree but it's
+
+ align:start position:0%
+week it's not exactly a tree but it's
+ 
+
+ align:start position:0%
+week it's not exactly a tree but it's
+more or less a tree and one that you'll
+
+ align:start position:0%
+more or less a tree and one that you'll
+ 
+
+ align:start position:0%
+more or less a tree and one that you'll
+see on your problem set this
+
+ align:start position:0%
+see on your problem set this
+ 
+
+ align:start position:0%
+see on your problem set this
+week are
+
+ align:start position:0%
+week are
+ 
+
+ align:start position:0%
+week are
+treps uh
+
+ align:start position:0%
+treps uh
+ 
+
+ align:start position:0%
+treps uh
+which I won't talk too much about here
+
+ align:start position:0%
+which I won't talk too much about here
+ 
+
+ align:start position:0%
+which I won't talk too much about here
+but they're in some sense easier to get
+
+ align:start position:0%
+but they're in some sense easier to get
+ 
+
+ align:start position:0%
+but they're in some sense easier to get
+because they essentially just rely on
+
+ align:start position:0%
+because they essentially just rely on
+ 
+
+ align:start position:0%
+because they essentially just rely on
+the material from last
+
+ align:start position:0%
+the material from last
+ 
+
+ align:start position:0%
+the material from last
+Monday right so on Monday we saw that if
+
+ align:start position:0%
+Monday right so on Monday we saw that if
+ 
+
+ align:start position:0%
+Monday right so on Monday we saw that if
+we just randomly built a binary search
+
+ align:start position:0%
+we just randomly built a binary search
+ 
+
+ align:start position:0%
+we just randomly built a binary search
+tree it's going to have log and height
+
+ align:start position:0%
+tree it's going to have log and height
+ 
+
+ align:start position:0%
+tree it's going to have log and height
+most of the time in expectation so uh
+
+ align:start position:0%
+most of the time in expectation so uh
+ 
+
+ align:start position:0%
+most of the time in expectation so uh
+treeps are a way to make that Dynamic so
+
+ align:start position:0%
+treeps are a way to make that Dynamic so
+ 
+
+ align:start position:0%
+treeps are a way to make that Dynamic so
+that instead of just having a static set
+
+ align:start position:0%
+that instead of just having a static set
+ 
+
+ align:start position:0%
+that instead of just having a static set
+of n items you can insert and delete
+
+ align:start position:0%
+of n items you can insert and delete
+ 
+
+ align:start position:0%
+of n items you can insert and delete
+into those items and still effectively
+
+ align:start position:0%
+into those items and still effectively
+ 
+
+ align:start position:0%
+into those items and still effectively
+randomly prute them and put them in a
+
+ align:start position:0%
+randomly prute them and put them in a
+ 
+
+ align:start position:0%
+randomly prute them and put them in a
+tree
+
+ align:start position:0%
+tree
+ 
+
+ align:start position:0%
+tree
+so in some sense that's the easiest it's
+
+ align:start position:0%
+so in some sense that's the easiest it's
+ 
+
+ align:start position:0%
+so in some sense that's the easiest it's
+also the most one of the most recent
+
+ align:start position:0%
+also the most one of the most recent
+ 
+
+ align:start position:0%
+also the most one of the most recent
+search tree data structures that was
+
+ align:start position:0%
+search tree data structures that was
+ 
+
+ align:start position:0%
+search tree data structures that was
+invented in
+
+ align:start position:0%
+invented in
+ 
+
+ align:start position:0%
+invented in
+1996 by a couple of
+
+ align:start position:0%
+1996 by a couple of
+ 
+
+ align:start position:0%
+1996 by a couple of
+geometers Ryman cidel and Aragon so
+
+ align:start position:0%
+geometers Ryman cidel and Aragon so
+ 
+
+ align:start position:0%
+geometers Ryman cidel and Aragon so
+those are just some search for data
+
+ align:start position:0%
+those are just some search for data
+ 
+
+ align:start position:0%
+those are just some search for data
+structures the only ones we will not
+
+ align:start position:0%
+structures the only ones we will not
+ 
+
+ align:start position:0%
+structures the only ones we will not
+cover in this class are a trees um
+
+ align:start position:0%
+cover in this class are a trees um
+ 
+
+ align:start position:0%
+cover in this class are a trees um
+they're not too hard if you're
+
+ align:start position:0%
+they're not too hard if you're
+ 
+
+ align:start position:0%
+they're not too hard if you're
+interested you should read about them
+
+ align:start position:0%
+interested you should read about them
+ 
+
+ align:start position:0%
+interested you should read about them
+because they're
+
+ align:start position:0%
+because they're
+ 
+
+ align:start position:0%
+because they're
+fun I think they're a problem in in the
+
+ align:start position:0%
+fun I think they're a problem in in the
+ 
+
+ align:start position:0%
+fun I think they're a problem in in the
+textbook okay but today we're going to
+
+ align:start position:0%
+textbook okay but today we're going to
+ 
+
+ align:start position:0%
+textbook okay but today we're going to
+focus on red black
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+trees
+
+ align:start position:0%
+trees
+ 
+
+ align:start position:0%
+trees
+which it's a fairly simple
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+idea red black trees and it's a
+
+ align:start position:0%
+idea red black trees and it's a
+ 
+
+ align:start position:0%
+idea red black trees and it's a
+particular way of guaranteeing this
+
+ align:start position:0%
+particular way of guaranteeing this
+ 
+
+ align:start position:0%
+particular way of guaranteeing this
+logarithmic height so that all the
+
+ align:start position:0%
+logarithmic height so that all the
+ 
+
+ align:start position:0%
+logarithmic height so that all the
+operations can be supported in log end
+
+ align:start position:0%
+operations can be supported in log end
+ 
+
+ align:start position:0%
+operations can be supported in log end
+time
+
+ align:start position:0%
+time
+ 
+
+ align:start position:0%
+time
+so they're binary search
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+trees
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and they have a little bit of extra
+
+ align:start position:0%
+and they have a little bit of extra
+ 
+
+ align:start position:0%
+and they have a little bit of extra
+information in each node called the
+
+ align:start position:0%
+information in each node called the
+ 
+
+ align:start position:0%
+information in each node called the
+color field
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and there's several properties that a
+
+ align:start position:0%
+and there's several properties that a
+ 
+
+ align:start position:0%
+and there's several properties that a
+tree with color field has to spec has to
+
+ align:start position:0%
+tree with color field has to spec has to
+ 
+
+ align:start position:0%
+tree with color field has to spec has to
+satisfy in order to be called the red
+
+ align:start position:0%
+satisfy in order to be called the red
+ 
+
+ align:start position:0%
+satisfy in order to be called the red
+black tree these are called the red
+
+ align:start position:0%
+black tree these are called the red
+ 
+
+ align:start position:0%
+black tree these are called the red
+black
+
+ align:start position:0%
+black
+ 
+
+ align:start position:0%
+black
+properties and this will take a little
+
+ align:start position:0%
+properties and this will take a little
+ 
+
+ align:start position:0%
+properties and this will take a little
+bit a little bit of time to write down
+
+ align:start position:0%
+bit a little bit of time to write down
+ 
+
+ align:start position:0%
+bit a little bit of time to write down
+but it's all pretty
+
+ align:start position:0%
+but it's all pretty
+ 
+
+ align:start position:0%
+but it's all pretty
+simple so once I write them down I'll
+
+ align:start position:0%
+simple so once I write them down I'll
+ 
+
+ align:start position:0%
+simple so once I write them down I'll
+say what they really mean there's four
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+properties the first one's pretty simple
+
+ align:start position:0%
+properties the first one's pretty simple
+ 
+
+ align:start position:0%
+properties the first one's pretty simple
+every node is
+
+ align:start position:0%
+every node is
+ 
+
+ align:start position:0%
+every node is
+either red or black that's the hence the
+
+ align:start position:0%
+either red or black that's the hence the
+ 
+
+ align:start position:0%
+either red or black that's the hence the
+name of red black
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+trees so the color field is just a
+
+ align:start position:0%
+trees so the color field is just a
+ 
+
+ align:start position:0%
+trees so the color field is just a
+single bit specifying red or black and
+
+ align:start position:0%
+single bit specifying red or black and
+ 
+
+ align:start position:0%
+single bit specifying red or black and
+red nodes I'm going to denote by a
+
+ align:start position:0%
+red nodes I'm going to denote by a
+ 
+
+ align:start position:0%
+red nodes I'm going to denote by a
+double circle CU I don't have colored
+
+ align:start position:0%
+double circle CU I don't have colored
+ 
+
+ align:start position:0%
+double circle CU I don't have colored
+chalk here and black nodes will be a
+
+ align:start position:0%
+chalk here and black nodes will be a
+ 
+
+ align:start position:0%
+chalk here and black nodes will be a
+single Circle and you probably don't
+
+ align:start position:0%
+single Circle and you probably don't
+ 
+
+ align:start position:0%
+single Circle and you probably don't
+have colored pens either so save us some
+
+ align:start position:0%
+have colored pens either so save us some
+ 
+
+ align:start position:0%
+have colored pens either so save us some
+grief
+
+ align:start position:0%
+grief
+ 
+
+ align:start position:0%
+grief
+um red is double circle black is single
+
+ align:start position:0%
+um red is double circle black is single
+ 
+
+ align:start position:0%
+um red is double circle black is single
+Circle and we sort of prefer black nodes
+
+ align:start position:0%
+Circle and we sort of prefer black nodes
+ 
+
+ align:start position:0%
+Circle and we sort of prefer black nodes
+in some sense red nodes are a pain as
+
+ align:start position:0%
+in some sense red nodes are a pain as
+ 
+
+ align:start position:0%
+in some sense red nodes are a pain as
+we'll
+
+ align:start position:0%
+we'll
+ 
+
+ align:start position:0%
+we'll
+see okay second
+
+ align:start position:0%
+see okay second
+ 
+
+ align:start position:0%
+see okay second
+property is that the
+
+ align:start position:0%
+property is that the
+ 
+
+ align:start position:0%
+property is that the
+root and the
+
+ align:start position:0%
+root and the
+ 
+
+ align:start position:0%
+root and the
+leaves are all
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+black and uh I'm going to pull a little
+
+ align:start position:0%
+black and uh I'm going to pull a little
+ 
+
+ align:start position:0%
+black and uh I'm going to pull a little
+trick here or uh treat binary searches a
+
+ align:start position:0%
+trick here or uh treat binary searches a
+ 
+
+ align:start position:0%
+trick here or uh treat binary searches a
+little bit differently than we have in
+
+ align:start position:0%
+little bit differently than we have in
+ 
+
+ align:start position:0%
+little bit differently than we have in
+the past um normally you think of a tree
+
+ align:start position:0%
+the past um normally you think of a tree
+ 
+
+ align:start position:0%
+the past um normally you think of a tree
+as a bunch of nodes each node could have
+
+ align:start position:0%
+as a bunch of nodes each node could have
+ 
+
+ align:start position:0%
+as a bunch of nodes each node could have
+zero or one or two children something
+
+ align:start position:0%
+zero or one or two children something
+ 
+
+ align:start position:0%
+zero or one or two children something
+like this I'm going to imagine appending
+
+ align:start position:0%
+like this I'm going to imagine appending
+ 
+
+ align:start position:0%
+like this I'm going to imagine appending
+every place where a node does not have a
+
+ align:start position:0%
+every place where a node does not have a
+ 
+
+ align:start position:0%
+every place where a node does not have a
+child I'm going to put a little dot here
+
+ align:start position:0%
+child I'm going to put a little dot here
+ 
+
+ align:start position:0%
+child I'm going to put a little dot here
+an external node which I I call a leaf
+
+ align:start position:0%
+an external node which I I call a leaf
+ 
+
+ align:start position:0%
+an external node which I I call a leaf
+so normally leaves would have been these
+
+ align:start position:0%
+so normally leaves would have been these
+ 
+
+ align:start position:0%
+so normally leaves would have been these
+items I'm just going to add to every
+
+ align:start position:0%
+items I'm just going to add to every
+ 
+
+ align:start position:0%
+items I'm just going to add to every
+absent uh child pointer a new leaf and
+
+ align:start position:0%
+absent uh child pointer a new leaf and
+ 
+
+ align:start position:0%
+absent uh child pointer a new leaf and
+these will be my leaves these are really
+
+ align:start position:0%
+these will be my leaves these are really
+ 
+
+ align:start position:0%
+these will be my leaves these are really
+the nil pointers from each of these
+
+ align:start position:0%
+the nil pointers from each of these
+ 
+
+ align:start position:0%
+the nil pointers from each of these
+nodes so now every internal node has
+
+ align:start position:0%
+nodes so now every internal node has
+ 
+
+ align:start position:0%
+nodes so now every internal node has
+exactly two children and every leaf has
+
+ align:start position:0%
+exactly two children and every leaf has
+ 
+
+ align:start position:0%
+exactly two children and every leaf has
+zero children okay so these are the noes
+
+ align:start position:0%
+zero children okay so these are the noes
+ 
+
+ align:start position:0%
+zero children okay so these are the noes
+I'm referring to these guys are black
+
+ align:start position:0%
+I'm referring to these guys are black
+ 
+
+ align:start position:0%
+I'm referring to these guys are black
+and this guy is
+
+ align:start position:0%
+and this guy is
+ 
+
+ align:start position:0%
+and this guy is
+black according to rule
+
+ align:start position:0%
+black according to rule
+ 
+
+ align:start position:0%
+black according to rule
+two now the properties get a little bit
+
+ align:start position:0%
+two now the properties get a little bit
+ 
+
+ align:start position:0%
+two now the properties get a little bit
+more
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+interesting the parent of every red node
+
+ align:start position:0%
+interesting the parent of every red node
+ 
+
+ align:start position:0%
+interesting the parent of every red node
+is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+black so whenever I have a red node its
+
+ align:start position:0%
+black so whenever I have a red node its
+ 
+
+ align:start position:0%
+black so whenever I have a red node its
+parent has to be black a single
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Circle okay so in other words if you
+
+ align:start position:0%
+Circle okay so in other words if you
+ 
+
+ align:start position:0%
+Circle okay so in other words if you
+look at a path in the tree you can never
+
+ align:start position:0%
+look at a path in the tree you can never
+ 
+
+ align:start position:0%
+look at a path in the tree you can never
+have two red nodes consecutive has to be
+
+ align:start position:0%
+have two red nodes consecutive has to be
+ 
+
+ align:start position:0%
+have two red nodes consecutive has to be
+can at most alternate red black red
+
+ align:start position:0%
+can at most alternate red black red
+ 
+
+ align:start position:0%
+can at most alternate red black red
+black you can have several black nodes
+
+ align:start position:0%
+black you can have several black nodes
+ 
+
+ align:start position:0%
+black you can have several black nodes
+consecutive but never two red nodes
+
+ align:start position:0%
+consecutive but never two red nodes
+ 
+
+ align:start position:0%
+consecutive but never two red nodes
+okay and then one more
+
+ align:start position:0%
+okay and then one more
+ 
+
+ align:start position:0%
+okay and then one more
+rule says a little bit more about such
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+paths so if we take a simple path
+
+ align:start position:0%
+paths so if we take a simple path
+ 
+
+ align:start position:0%
+paths so if we take a simple path
+meaning it doesn't repeat any
+
+ align:start position:0%
+meaning it doesn't repeat any
+ 
+
+ align:start position:0%
+meaning it doesn't repeat any
+vertices from a node X to a descendant
+
+ align:start position:0%
+vertices from a node X to a descendant
+ 
+
+ align:start position:0%
+vertices from a node X to a descendant
+leaf
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+X all such pads to all descendant leaves
+
+ align:start position:0%
+X all such pads to all descendant leaves
+ 
+
+ align:start position:0%
+X all such pads to all descendant leaves
+have the same number of black nodes on
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+them so let me draw a picture we have
+
+ align:start position:0%
+them so let me draw a picture we have
+ 
+
+ align:start position:0%
+them so let me draw a picture we have
+some tree we have some node X in the
+
+ align:start position:0%
+some tree we have some node X in the
+ 
+
+ align:start position:0%
+some tree we have some node X in the
+tree and I'm looking at all the paths
+
+ align:start position:0%
+tree and I'm looking at all the paths
+ 
+
+ align:start position:0%
+tree and I'm looking at all the paths
+from X down to some descendant Leaf down
+
+ align:start position:0%
+from X down to some descendant Leaf down
+ 
+
+ align:start position:0%
+from X down to some descendant Leaf down
+here the bottom of the tree all of these
+
+ align:start position:0%
+here the bottom of the tree all of these
+ 
+
+ align:start position:0%
+here the bottom of the tree all of these
+paths should have the same number of
+
+ align:start position:0%
+paths should have the same number of
+ 
+
+ align:start position:0%
+paths should have the same number of
+black nodes so here I'll draw that each
+
+ align:start position:0%
+black nodes so here I'll draw that each
+ 
+
+ align:start position:0%
+black nodes so here I'll draw that each
+one
+
+ align:start position:0%
+one
+ 
+
+ align:start position:0%
+one
+has uh four black nodes the leaf and
+
+ align:start position:0%
+has uh four black nodes the leaf and
+ 
+
+ align:start position:0%
+has uh four black nodes the leaf and
+three above
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+it we know that these from property
+
+ align:start position:0%
+it we know that these from property
+ 
+
+ align:start position:0%
+it we know that these from property
+three these nodes don't have at most
+
+ align:start position:0%
+three these nodes don't have at most
+ 
+
+ align:start position:0%
+three these nodes don't have at most
+half of the nodes are red because
+
+ align:start position:0%
+half of the nodes are red because
+ 
+
+ align:start position:0%
+half of the nodes are red because
+whenever I have a red node the parent
+
+ align:start position:0%
+whenever I have a red node the parent
+ 
+
+ align:start position:0%
+whenever I have a red node the parent
+must be black um but I want all of these
+
+ align:start position:0%
+must be black um but I want all of these
+ 
+
+ align:start position:0%
+must be black um but I want all of these
+paths have exactly the same number of
+
+ align:start position:0%
+paths have exactly the same number of
+ 
+
+ align:start position:0%
+paths have exactly the same number of
+black nodes one subtlety here is that
+
+ align:start position:0%
+black nodes one subtlety here is that
+ 
+
+ align:start position:0%
+black nodes one subtlety here is that
+the black height I didn't really leave
+
+ align:start position:0%
+the black height I didn't really leave
+ 
+
+ align:start position:0%
+the black height I didn't really leave
+room so I'll write it over
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+here this should be the same for all
+
+ align:start position:0%
+here this should be the same for all
+ 
+
+ align:start position:0%
+here this should be the same for all
+paths but in particular the count I'm
+
+ align:start position:0%
+paths but in particular the count I'm
+ 
+
+ align:start position:0%
+paths but in particular the count I'm
+interested in does not include x itself
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so if x is black I'm only calling
+
+ align:start position:0%
+okay so if x is black I'm only calling
+ 
+
+ align:start position:0%
+okay so if x is black I'm only calling
+the black height so the black height of
+
+ align:start position:0%
+the black height so the black height of
+ 
+
+ align:start position:0%
+the black height so the black height of
+X is this count four and even if x is
+
+ align:start position:0%
+X is this count four and even if x is
+ 
+
+ align:start position:0%
+X is this count four and even if x is
+black I'll the black height is four so
+
+ align:start position:0%
+black I'll the black height is four so
+ 
+
+ align:start position:0%
+black I'll the black height is four so
+these are just some Minor Details to get
+
+ align:start position:0%
+these are just some Minor Details to get
+ 
+
+ align:start position:0%
+these are just some Minor Details to get
+all of the algorithms a bit clean so
+
+ align:start position:0%
+all of the algorithms a bit clean so
+ 
+
+ align:start position:0%
+all of the algorithms a bit clean so
+let's look at an example of a red black
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+tree so um yeah I'll show you an example
+
+ align:start position:0%
+tree so um yeah I'll show you an example
+ 
+
+ align:start position:0%
+tree so um yeah I'll show you an example
+then I'll say why we care about these
+
+ align:start position:0%
+then I'll say why we care about these
+ 
+
+ align:start position:0%
+then I'll say why we care about these
+properties
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so this tree has several properties
+
+ align:start position:0%
+okay so this tree has several properties
+ 
+
+ align:start position:0%
+okay so this tree has several properties
+the first thing is that it's a binary
+
+ align:start position:0%
+the first thing is that it's a binary
+ 
+
+ align:start position:0%
+the first thing is that it's a binary
+search tree okay so you can check an in
+
+ align:start position:0%
+search tree okay so you can check an in
+ 
+
+ align:start position:0%
+search tree okay so you can check an in
+order traversal should give these
+
+ align:start position:0%
+order traversal should give these
+ 
+
+ align:start position:0%
+order traversal should give these
+numbers in sorted order 3 7 8 10 11 18
+
+ align:start position:0%
+numbers in sorted order 3 7 8 10 11 18
+ 
+
+ align:start position:0%
+numbers in sorted order 3 7 8 10 11 18
+22 26 so it's a valid binary search tree
+
+ align:start position:0%
+22 26 so it's a valid binary search tree
+ 
+
+ align:start position:0%
+22 26 so it's a valid binary search tree
+we've appended these leaves with no keys
+
+ align:start position:0%
+we've appended these leaves with no keys
+ 
+
+ align:start position:0%
+we've appended these leaves with no keys
+in them they're just hanging around
+
+ align:start position:0%
+in them they're just hanging around
+ 
+
+ align:start position:0%
+in them they're just hanging around
+those are the nil pointers so each of
+
+ align:start position:0%
+those are the nil pointers so each of
+ 
+
+ align:start position:0%
+those are the nil pointers so each of
+these you can call
+
+ align:start position:0%
+these you can call
+ 
+
+ align:start position:0%
+these you can call
+nil uh they're all just marked there
+
+ align:start position:0%
+nil uh they're all just marked there
+ 
+
+ align:start position:0%
+nil uh they're all just marked there
+wherever there's an absent
+
+ align:start position:0%
+wherever there's an absent
+ 
+
+ align:start position:0%
+wherever there's an absent
+child and then I've double circled some
+
+ align:start position:0%
+child and then I've double circled some
+ 
+
+ align:start position:0%
+child and then I've double circled some
+of the nodes to color them red okay if I
+
+ align:start position:0%
+of the nodes to color them red okay if I
+ 
+
+ align:start position:0%
+of the nodes to color them red okay if I
+didn't the black Heights wouldn't match
+
+ align:start position:0%
+didn't the black Heights wouldn't match
+ 
+
+ align:start position:0%
+didn't the black Heights wouldn't match
+up so have to be a little bit careful
+
+ align:start position:0%
+up so have to be a little bit careful
+ 
+
+ align:start position:0%
+up so have to be a little bit careful
+from every node we'd like to measure uh
+
+ align:start position:0%
+from every node we'd like to measure uh
+ 
+
+ align:start position:0%
+from every node we'd like to measure uh
+the number of black nodes from that node
+
+ align:start position:0%
+the number of black nodes from that node
+ 
+
+ align:start position:0%
+the number of black nodes from that node
+down to to any descendant Leaf so for
+
+ align:start position:0%
+down to to any descendant Leaf so for
+ 
+
+ align:start position:0%
+down to to any descendant Leaf so for
+example the nil pointers their black
+
+ align:start position:0%
+example the nil pointers their black
+ 
+
+ align:start position:0%
+example the nil pointers their black
+height is zero good that's always the
+
+ align:start position:0%
+height is zero good that's always the
+ 
+
+ align:start position:0%
+height is zero good that's always the
+answer so these guys all have black
+
+ align:start position:0%
+answer so these guys all have black
+ 
+
+ align:start position:0%
+answer so these guys all have black
+height zero I'll just uh represent that
+
+ align:start position:0%
+height zero I'll just uh represent that
+ 
+
+ align:start position:0%
+height zero I'll just uh represent that
+here black height equals
+
+ align:start position:0%
+here black height equals
+ 
+
+ align:start position:0%
+here black height equals
+zero okay what's the black height of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+three zero not not quite cuz these nodes
+
+ align:start position:0%
+three zero not not quite cuz these nodes
+ 
+
+ align:start position:0%
+three zero not not quite cuz these nodes
+are black so the black height is
+
+ align:start position:0%
+are black so the black height is
+ 
+
+ align:start position:0%
+are black so the black height is
+one okay you're right that we don't
+
+ align:start position:0%
+one okay you're right that we don't
+ 
+
+ align:start position:0%
+one okay you're right that we don't
+count three even though it's black uh we
+
+ align:start position:0%
+count three even though it's black uh we
+ 
+
+ align:start position:0%
+count three even though it's black uh we
+it's not included in the count but the
+
+ align:start position:0%
+it's not included in the count but the
+ 
+
+ align:start position:0%
+it's not included in the count but the
+leaves count and you there's only two
+
+ align:start position:0%
+leaves count and you there's only two
+ 
+
+ align:start position:0%
+leaves count and you there's only two
+paths here and they each have the same
+
+ align:start position:0%
+paths here and they each have the same
+ 
+
+ align:start position:0%
+paths here and they each have the same
+number of black nodes as they should uh
+
+ align:start position:0%
+number of black nodes as they should uh
+ 
+
+ align:start position:0%
+number of black nodes as they should uh
+over here let's say eight also has black
+
+ align:start position:0%
+over here let's say eight also has black
+ 
+
+ align:start position:0%
+over here let's say eight also has black
+height one even though it's
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+red okay same with
+
+ align:start position:0%
+red okay same with
+ 
+
+ align:start position:0%
+red okay same with
+11 same with
+
+ align:start position:0%
+11 same with
+ 
+
+ align:start position:0%
+11 same with
+26 each of them only has two paths each
+
+ align:start position:0%
+26 each of them only has two paths each
+ 
+
+ align:start position:0%
+26 each of them only has two paths each
+of them has each path has one black note
+
+ align:start position:0%
+of them has each path has one black note
+ 
+
+ align:start position:0%
+of them has each path has one black note
+on it uh 10
+
+ align:start position:0%
+on it uh 10
+ 
+
+ align:start position:0%
+on it uh 10
+what's the black
+
+ align:start position:0%
+what's the black
+ 
+
+ align:start position:0%
+what's the black
+height still one
+
+ align:start position:0%
+height still one
+ 
+
+ align:start position:0%
+height still one
+good cuz we don't count 10 at there's
+
+ align:start position:0%
+good cuz we don't count 10 at there's
+ 
+
+ align:start position:0%
+good cuz we don't count 10 at there's
+now four paths to leaves each of them
+
+ align:start position:0%
+now four paths to leaves each of them
+ 
+
+ align:start position:0%
+now four paths to leaves each of them
+contains exactly one black node plus the
+
+ align:start position:0%
+contains exactly one black node plus the
+ 
+
+ align:start position:0%
+contains exactly one black node plus the
+root which we don't count 22 same thing
+
+ align:start position:0%
+root which we don't count 22 same thing
+ 
+
+ align:start position:0%
+root which we don't count 22 same thing
+hopefully okay this is getting a little
+
+ align:start position:0%
+hopefully okay this is getting a little
+ 
+
+ align:start position:0%
+hopefully okay this is getting a little
+more interesting there's one path here
+
+ align:start position:0%
+more interesting there's one path here
+ 
+
+ align:start position:0%
+more interesting there's one path here
+which has one black node there's other
+
+ align:start position:0%
+which has one black node there's other
+ 
+
+ align:start position:0%
+which has one black node there's other
+paths here which are longer but they
+
+ align:start position:0%
+paths here which are longer but they
+ 
+
+ align:start position:0%
+paths here which are longer but they
+still only have one black node so if we
+
+ align:start position:0%
+still only have one black node so if we
+ 
+
+ align:start position:0%
+still only have one black node so if we
+just sort of ignore the red nodes all
+
+ align:start position:0%
+just sort of ignore the red nodes all
+ 
+
+ align:start position:0%
+just sort of ignore the red nodes all
+these pads have the same length Okay 18
+
+ align:start position:0%
+these pads have the same length Okay 18
+ 
+
+ align:start position:0%
+these pads have the same length Okay 18
+should be bigger hopefully black height
+
+ align:start position:0%
+should be bigger hopefully black height
+ 
+
+ align:start position:0%
+should be bigger hopefully black height
+of
+
+ align:start position:0%
+of
+ 
+
+ align:start position:0%
+of
+two because each of these paths now has
+
+ align:start position:0%
+two because each of these paths now has
+ 
+
+ align:start position:0%
+two because each of these paths now has
+one black note here one black note in
+
+ align:start position:0%
+one black note here one black note in
+ 
+
+ align:start position:0%
+one black note here one black note in
+the leaves or one black note here and
+
+ align:start position:0%
+the leaves or one black note here and
+ 
+
+ align:start position:0%
+the leaves or one black note here and
+one black note in the leaves and finally
+
+ align:start position:0%
+one black note in the leaves and finally
+ 
+
+ align:start position:0%
+one black note in the leaves and finally
+the root should have a black height
+
+ align:start position:0%
+the root should have a black height
+ 
+
+ align:start position:0%
+the root should have a black height
+of two easier to see over here I guess
+
+ align:start position:0%
+of two easier to see over here I guess
+ 
+
+ align:start position:0%
+of two easier to see over here I guess
+each of these pths has two black nodes
+
+ align:start position:0%
+each of these pths has two black nodes
+ 
+
+ align:start position:0%
+each of these pths has two black nodes
+same over
+
+ align:start position:0%
+same over
+ 
+
+ align:start position:0%
+same over
+here okay um
+
+ align:start position:0%
+here okay um
+ 
+
+ align:start position:0%
+here okay um
+so that's just hopefully these
+
+ align:start position:0%
+so that's just hopefully these
+ 
+
+ align:start position:0%
+so that's just hopefully these
+properties make sense we didn't check
+
+ align:start position:0%
+properties make sense we didn't check
+ 
+
+ align:start position:0%
+properties make sense we didn't check
+all of them every red node has a black
+
+ align:start position:0%
+all of them every red node has a black
+ 
+
+ align:start position:0%
+all of them every red node has a black
+parent you look at all of these paths um
+
+ align:start position:0%
+parent you look at all of these paths um
+ 
+
+ align:start position:0%
+parent you look at all of these paths um
+we sort of alternate red black at most
+
+ align:start position:0%
+we sort of alternate red black at most
+ 
+
+ align:start position:0%
+we sort of alternate red black at most
+or we have just a bunch of blacks but we
+
+ align:start position:0%
+or we have just a bunch of blacks but we
+ 
+
+ align:start position:0%
+or we have just a bunch of blacks but we
+never repeat Two Reds in a row uh the
+
+ align:start position:0%
+never repeat Two Reds in a row uh the
+ 
+
+ align:start position:0%
+never repeat Two Reds in a row uh the
+root and the leaves are black that we
+
+ align:start position:0%
+root and the leaves are black that we
+ 
+
+ align:start position:0%
+root and the leaves are black that we
+used pretty much by definition every
+
+ align:start position:0%
+used pretty much by definition every
+ 
+
+ align:start position:0%
+used pretty much by definition every
+note is red or black okay that's
+
+ align:start position:0%
+note is red or black okay that's
+ 
+
+ align:start position:0%
+note is red or black okay that's
+easy um this is a particular set of
+
+ align:start position:0%
+easy um this is a particular set of
+ 
+
+ align:start position:0%
+easy um this is a particular set of
+properties that may seem a bit arbitrary
+
+ align:start position:0%
+properties that may seem a bit arbitrary
+ 
+
+ align:start position:0%
+properties that may seem a bit arbitrary
+at this point they will make sense a lot
+
+ align:start position:0%
+at this point they will make sense a lot
+ 
+
+ align:start position:0%
+at this point they will make sense a lot
+more sense as we see what consequences
+
+ align:start position:0%
+more sense as we see what consequences
+ 
+
+ align:start position:0%
+more sense as we see what consequences
+they have but there are a couple of
+
+ align:start position:0%
+they have but there are a couple of
+ 
+
+ align:start position:0%
+they have but there are a couple of
+goals that we're trying to achieve here
+
+ align:start position:0%
+goals that we're trying to achieve here
+ 
+
+ align:start position:0%
+goals that we're trying to achieve here
+one is that these properties should
+
+ align:start position:0%
+one is that these properties should
+ 
+
+ align:start position:0%
+one is that these properties should
+force the tree to have logarithmic
+
+ align:start position:0%
+force the tree to have logarithmic
+ 
+
+ align:start position:0%
+force the tree to have logarithmic
+height order log and height and they do
+
+ align:start position:0%
+height order log and height and they do
+ 
+
+ align:start position:0%
+height order log and height and they do
+although that's probably not obvious at
+
+ align:start position:0%
+although that's probably not obvious at
+ 
+
+ align:start position:0%
+although that's probably not obvious at
+this point it follows mainly from this
+
+ align:start position:0%
+this point it follows mainly from this
+ 
+
+ align:start position:0%
+this point it follows mainly from this
+prop uh from property well from all the
+
+ align:start position:0%
+prop uh from property well from all the
+ 
+
+ align:start position:0%
+prop uh from property well from all the
+properties three and four are the main
+
+ align:start position:0%
+properties three and four are the main
+ 
+
+ align:start position:0%
+properties three and four are the main
+ones but you pretty much need all of
+
+ align:start position:0%
+ones but you pretty much need all of
+ 
+
+ align:start position:0%
+ones but you pretty much need all of
+them the other thing the other uh desire
+
+ align:start position:0%
+them the other thing the other uh desire
+ 
+
+ align:start position:0%
+them the other thing the other uh desire
+we have from these properties is that
+
+ align:start position:0%
+we have from these properties is that
+ 
+
+ align:start position:0%
+we have from these properties is that
+they're somehow easy to maintain okay I
+
+ align:start position:0%
+they're somehow easy to maintain okay I
+ 
+
+ align:start position:0%
+they're somehow easy to maintain okay I
+can create a tree in the beginning that
+
+ align:start position:0%
+can create a tree in the beginning that
+ 
+
+ align:start position:0%
+can create a tree in the beginning that
+has this property for example I could
+
+ align:start position:0%
+has this property for example I could
+ 
+
+ align:start position:0%
+has this property for example I could
+make I have to be a little bit careful
+
+ align:start position:0%
+make I have to be a little bit careful
+ 
+
+ align:start position:0%
+make I have to be a little bit careful
+but I could make certainly if I take a
+
+ align:start position:0%
+but I could make certainly if I take a
+ 
+
+ align:start position:0%
+but I could make certainly if I take a
+perfectly balanced binary tree and make
+
+ align:start position:0%
+perfectly balanced binary tree and make
+ 
+
+ align:start position:0%
+perfectly balanced binary tree and make
+all of the nodes black it will satisfy
+
+ align:start position:0%
+all of the nodes black it will satisfy
+ 
+
+ align:start position:0%
+all of the nodes black it will satisfy
+those
+
+ align:start position:0%
+those
+ 
+
+ align:start position:0%
+those
+properties okay this is a red black
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+tree okay so it's not too hard to make
+
+ align:start position:0%
+tree okay so it's not too hard to make
+ 
+
+ align:start position:0%
+tree okay so it's not too hard to make
+these properties hold just from the
+
+ align:start position:0%
+these properties hold just from the
+ 
+
+ align:start position:0%
+these properties hold just from the
+beginning
+
+ align:start position:0%
+beginning
+ 
+
+ align:start position:0%
+beginning
+the tricky part is to maintain them when
+
+ align:start position:0%
+the tricky part is to maintain them when
+ 
+
+ align:start position:0%
+the tricky part is to maintain them when
+I insert a node into this tree and
+
+ align:start position:0%
+I insert a node into this tree and
+ 
+
+ align:start position:0%
+I insert a node into this tree and
+delete a node from this tree I want to
+
+ align:start position:0%
+delete a node from this tree I want to
+ 
+
+ align:start position:0%
+delete a node from this tree I want to
+guarant I want to make it not too hard
+
+ align:start position:0%
+guarant I want to make it not too hard
+ 
+
+ align:start position:0%
+guarant I want to make it not too hard
+in login time I've got to be able to
+
+ align:start position:0%
+in login time I've got to be able to
+ 
+
+ align:start position:0%
+in login time I've got to be able to
+restore all these
+
+ align:start position:0%
+restore all these
+ 
+
+ align:start position:0%
+restore all these
+properties okay that will be the hardest
+
+ align:start position:0%
+properties okay that will be the hardest
+ 
+
+ align:start position:0%
+properties okay that will be the hardest
+part the first thing we'll do is prove
+
+ align:start position:0%
+part the first thing we'll do is prove
+ 
+
+ align:start position:0%
+part the first thing we'll do is prove
+that these properties imply that the
+
+ align:start position:0%
+that these properties imply that the
+ 
+
+ align:start position:0%
+that these properties imply that the
+tree has to have height order Logan
+
+ align:start position:0%
+tree has to have height order Logan
+ 
+
+ align:start position:0%
+tree has to have height order Logan
+therefore all searches and queries on
+
+ align:start position:0%
+therefore all searches and queries on
+ 
+
+ align:start position:0%
+therefore all searches and queries on
+that data structure will run fast then
+
+ align:start position:0%
+that data structure will run fast then
+ 
+
+ align:start position:0%
+that data structure will run fast then
+the hard part will be to make sure these
+
+ align:start position:0%
+the hard part will be to make sure these
+ 
+
+ align:start position:0%
+the hard part will be to make sure these
+properties stay true if they initially
+
+ align:start position:0%
+properties stay true if they initially
+ 
+
+ align:start position:0%
+properties stay true if they initially
+held true when we make changes to the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+tree
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so let's look at the height of a red
+
+ align:start position:0%
+so let's look at the height of a red
+ 
+
+ align:start position:0%
+so let's look at the height of a red
+black tree
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and from this we'll start to see why
+
+ align:start position:0%
+and from this we'll start to see why
+ 
+
+ align:start position:0%
+and from this we'll start to see why
+these why where these properties come
+
+ align:start position:0%
+these why where these properties come
+ 
+
+ align:start position:0%
+these why where these properties come
+from why we chose these properties
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so the claim is that a height of a red
+
+ align:start position:0%
+so the claim is that a height of a red
+ 
+
+ align:start position:0%
+so the claim is that a height of a red
+black tree with n keys so I'm not saying
+
+ align:start position:0%
+black tree with n keys so I'm not saying
+ 
+
+ align:start position:0%
+black tree with n keys so I'm not saying
+nodes here because I really only want to
+
+ align:start position:0%
+nodes here because I really only want to
+ 
+
+ align:start position:0%
+nodes here because I really only want to
+count the internal nodes not these extra
+
+ align:start position:0%
+count the internal nodes not these extra
+ 
+
+ align:start position:0%
+count the internal nodes not these extra
+leaves that we've added has height at
+
+ align:start position:0%
+leaves that we've added has height at
+ 
+
+ align:start position:0%
+leaves that we've added has height at
+most 2 * log of n plus one so order log
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+n but we have a pretty precise bound of
+
+ align:start position:0%
+n but we have a pretty precise bound of
+ 
+
+ align:start position:0%
+n but we have a pretty precise bound of
+factor of
+
+ align:start position:0%
+factor of
+ 
+
+ align:start position:0%
+factor of
+two there's a proof of this in the
+
+ align:start position:0%
+two there's a proof of this in the
+ 
+
+ align:start position:0%
+two there's a proof of this in the
+textbook uh by induction and you should
+
+ align:start position:0%
+textbook uh by induction and you should
+ 
+
+ align:start position:0%
+textbook uh by induction and you should
+read
+
+ align:start position:0%
+read
+ 
+
+ align:start position:0%
+read
+that what I'm going to give is more of a
+
+ align:start position:0%
+that what I'm going to give is more of a
+ 
+
+ align:start position:0%
+that what I'm going to give is more of a
+proof
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+sketch you should read the proof by
+
+ align:start position:0%
+sketch you should read the proof by
+ 
+
+ align:start position:0%
+sketch you should read the proof by
+induction because all the practice you
+
+ align:start position:0%
+induction because all the practice you
+ 
+
+ align:start position:0%
+induction because all the practice you
+can get with proof by induction is good
+
+ align:start position:0%
+can get with proof by induction is good
+ 
+
+ align:start position:0%
+can get with proof by induction is good
+the proof sketch on the other hand gives
+
+ align:start position:0%
+the proof sketch on the other hand gives
+ 
+
+ align:start position:0%
+the proof sketch on the other hand gives
+a lot more intuition of what's going on
+
+ align:start position:0%
+a lot more intuition of what's going on
+ 
+
+ align:start position:0%
+a lot more intuition of what's going on
+with red red black trees and connects up
+
+ align:start position:0%
+with red red black trees and connects up
+ 
+
+ align:start position:0%
+with red red black trees and connects up
+with recitation on Friday so let me tell
+
+ align:start position:0%
+with recitation on Friday so let me tell
+ 
+
+ align:start position:0%
+with recitation on Friday so let me tell
+you that
+
+ align:start position:0%
+you that
+ 
+
+ align:start position:0%
+you that
+instead um I'm going to leave that board
+
+ align:start position:0%
+instead um I'm going to leave that board
+ 
+
+ align:start position:0%
+instead um I'm going to leave that board
+blank and go over
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+here so
+
+ align:start position:0%
+here so
+ 
+
+ align:start position:0%
+here so
+uh the first thing I'm going to do this
+
+ align:start position:0%
+uh the first thing I'm going to do this
+ 
+
+ align:start position:0%
+uh the first thing I'm going to do this
+is sort of I'm going to manipulate this
+
+ align:start position:0%
+is sort of I'm going to manipulate this
+ 
+
+ align:start position:0%
+is sort of I'm going to manipulate this
+tree until it looks like something that
+
+ align:start position:0%
+tree until it looks like something that
+ 
+
+ align:start position:0%
+tree until it looks like something that
+I know the first thing I'm or the the
+
+ align:start position:0%
+I know the first thing I'm or the the
+ 
+
+ align:start position:0%
+I know the first thing I'm or the the
+main change I'm going to
+
+ align:start position:0%
+main change I'm going to
+ 
+
+ align:start position:0%
+main change I'm going to
+make is to merge each red node into its
+
+ align:start position:0%
+make is to merge each red node into its
+ 
+
+ align:start position:0%
+make is to merge each red node into its
+parent and we know that the parent of a
+
+ align:start position:0%
+parent and we know that the parent of a
+ 
+
+ align:start position:0%
+parent and we know that the parent of a
+red node must be
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+black so merge each red Noe into its
+
+ align:start position:0%
+black so merge each red Noe into its
+ 
+
+ align:start position:0%
+black so merge each red Noe into its
+black
+
+ align:start position:0%
+black
+ 
+
+ align:start position:0%
+black
+parent so let's look at that here so I'm
+
+ align:start position:0%
+parent so let's look at that here so I'm
+ 
+
+ align:start position:0%
+parent so let's look at that here so I'm
+going to take this red node merge it
+
+ align:start position:0%
+going to take this red node merge it
+ 
+
+ align:start position:0%
+going to take this red node merge it
+into its parent take this red node merge
+
+ align:start position:0%
+into its parent take this red node merge
+ 
+
+ align:start position:0%
+into its parent take this red node merge
+it into its parent and so on there's one
+
+ align:start position:0%
+it into its parent and so on there's one
+ 
+
+ align:start position:0%
+it into its parent and so on there's one
+up there which I can't reach but I'm
+
+ align:start position:0%
+up there which I can't reach but I'm
+ 
+
+ align:start position:0%
+up there which I can't reach but I'm
+going to redraw this picture now so
+
+ align:start position:0%
+going to redraw this picture now so
+ 
+
+ align:start position:0%
+going to redraw this picture now so
+seven so the top node now becomes in
+
+ align:start position:0%
+seven so the top node now becomes in
+ 
+
+ align:start position:0%
+seven so the top node now becomes in
+some sense seven and
+
+ align:start position:0%
+some sense seven and
+ 
+
+ align:start position:0%
+some sense seven and
+18 they got merged together but no one
+
+ align:start position:0%
+18 they got merged together but no one
+ 
+
+ align:start position:0%
+18 they got merged together but no one
+else joined them then on the left we
+
+ align:start position:0%
+else joined them then on the left we
+ 
+
+ align:start position:0%
+else joined them then on the left we
+have
+
+ align:start position:0%
+have
+ 
+
+ align:start position:0%
+have
+three okay nothing join that and there's
+
+ align:start position:0%
+three okay nothing join that and there's
+ 
+
+ align:start position:0%
+three okay nothing join that and there's
+some leaves as
+
+ align:start position:0%
+some leaves as
+ 
+
+ align:start position:0%
+some leaves as
+usual now if you look at maybe I'm going
+
+ align:start position:0%
+usual now if you look at maybe I'm going
+ 
+
+ align:start position:0%
+usual now if you look at maybe I'm going
+to have to draw
+
+ align:start position:0%
+to have to draw
+ 
+
+ align:start position:0%
+to have to draw
+[Music]
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this heard that sound
+
+ align:start position:0%
+this heard that sound
+ 
+
+ align:start position:0%
+this heard that sound
+before so I'm merging these nodes
+
+ align:start position:0%
+before so I'm merging these nodes
+ 
+
+ align:start position:0%
+before so I'm merging these nodes
+together and I'm merging all of these
+
+ align:start position:0%
+together and I'm merging all of these
+ 
+
+ align:start position:0%
+together and I'm merging all of these
+nodes together because each of these red
+
+ align:start position:0%
+nodes together because each of these red
+ 
+
+ align:start position:0%
+nodes together because each of these red
+nodes merges into that black node and
+
+ align:start position:0%
+nodes merges into that black node and
+ 
+
+ align:start position:0%
+nodes merges into that black node and
+I'm merging these two no no together so
+
+ align:start position:0%
+I'm merging these two no no together so
+ 
+
+ align:start position:0%
+I'm merging these two no no together so
+I'm putting this red node into that
+
+ align:start position:0%
+I'm putting this red node into that
+ 
+
+ align:start position:0%
+I'm putting this red node into that
+black node so now you can see from the
+
+ align:start position:0%
+black node so now you can see from the
+ 
+
+ align:start position:0%
+black node so now you can see from the
+root which is now
+
+ align:start position:0%
+root which is now
+ 
+
+ align:start position:0%
+root which is now
+7/18 there are three children hanging
+
+ align:start position:0%
+7/18 there are three children hanging
+ 
+
+ align:start position:0%
+7/18 there are three children hanging
+off okay so in that picture I'd like to
+
+ align:start position:0%
+off okay so in that picture I'd like to
+ 
+
+ align:start position:0%
+off okay so in that picture I'd like to
+draw that
+
+ align:start position:0%
+draw that
+ 
+
+ align:start position:0%
+draw that
+fact assuming I can get this board back
+
+ align:start position:0%
+fact assuming I can get this board back
+ 
+
+ align:start position:0%
+fact assuming I can get this board back
+down
+
+ align:start position:0%
+down
+ 
+
+ align:start position:0%
+down
+good
+
+ align:start position:0%
+good
+ 
+
+ align:start position:0%
+good
+so between 7 and 18 I have this
+
+ align:start position:0%
+so between 7 and 18 I have this
+ 
+
+ align:start position:0%
+so between 7 and 18 I have this
+conglomerate node uh 8 10
+
+ align:start position:0%
+conglomerate node uh 8 10
+ 
+
+ align:start position:0%
+conglomerate node uh 8 10
+11 and there are four leaves hanging off
+
+ align:start position:0%
+11 and there are four leaves hanging off
+ 
+
+ align:start position:0%
+11 and there are four leaves hanging off
+of that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+note and off to the right after 18 I
+
+ align:start position:0%
+note and off to the right after 18 I
+ 
+
+ align:start position:0%
+note and off to the right after 18 I
+have a conglomerate node
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+2226 and there are three leaves hanging
+
+ align:start position:0%
+2226 and there are three leaves hanging
+ 
+
+ align:start position:0%
+2226 and there are three leaves hanging
+off of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+there
+
+ align:start position:0%
+there
+ 
+
+ align:start position:0%
+there
+okay kind of a weird tree because we we
+
+ align:start position:0%
+okay kind of a weird tree because we we
+ 
+
+ align:start position:0%
+okay kind of a weird tree because we we
+dealt mainly with binary trees so far
+
+ align:start position:0%
+dealt mainly with binary trees so far
+ 
+
+ align:start position:0%
+dealt mainly with binary trees so far
+but this is a foreshadowing of what will
+
+ align:start position:0%
+but this is a foreshadowing of what will
+ 
+
+ align:start position:0%
+but this is a foreshadowing of what will
+come on Friday this is something called
+
+ align:start position:0%
+come on Friday this is something called
+ 
+
+ align:start position:0%
+come on Friday this is something called
+A 234
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+tree and he guesses why it's called A
+
+ align:start position:0%
+tree and he guesses why it's called A
+ 
+
+ align:start position:0%
+tree and he guesses why it's called A
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+tree you can have two three or four kids
+
+ align:start position:0%
+tree you can have two three or four kids
+ 
+
+ align:start position:0%
+tree you can have two three or four kids
+every node can have two three or four
+
+ align:start position:0%
+every node can have two three or four
+ 
+
+ align:start position:0%
+every node can have two three or four
+kids yeah except the leaves they have
+
+ align:start position:0%
+kids yeah except the leaves they have
+ 
+
+ align:start position:0%
+kids yeah except the leaves they have
+zero okay there's another nice property
+
+ align:start position:0%
+zero okay there's another nice property
+ 
+
+ align:start position:0%
+zero okay there's another nice property
+of two three four
+
+ align:start position:0%
+of two three four
+ 
+
+ align:start position:0%
+of two three four
+trees maybe hinted to that so there's
+
+ align:start position:0%
+trees maybe hinted to that so there's
+ 
+
+ align:start position:0%
+trees maybe hinted to that so there's
+really no control over whether you have
+
+ align:start position:0%
+really no control over whether you have
+ 
+
+ align:start position:0%
+really no control over whether you have
+uh two children or three children or
+
+ align:start position:0%
+uh two children or three children or
+ 
+
+ align:start position:0%
+uh two children or three children or
+four children but there's another nice
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+property
+
+ align:start position:0%
+property
+ 
+
+ align:start position:0%
+property
+yeah
+
+ align:start position:0%
+yeah
+ 
+
+ align:start position:0%
+yeah
+bottom all of your children have the
+
+ align:start position:0%
+bottom all of your children have the
+ 
+
+ align:start position:0%
+bottom all of your children have the
+same depth all of the all of the leaves
+
+ align:start position:0%
+same depth all of the all of the leaves
+ 
+
+ align:start position:0%
+same depth all of the all of the leaves
+have the same depth exactly all of these
+
+ align:start position:0%
+have the same depth exactly all of these
+ 
+
+ align:start position:0%
+have the same depth exactly all of these
+guys have the same depth in the tree why
+
+ align:start position:0%
+guys have the same depth in the tree why
+ 
+
+ align:start position:0%
+guys have the same depth in the tree why
+is that because of property
+
+ align:start position:0%
+is that because of property
+ 
+
+ align:start position:0%
+is that because of property
+four okay un Friday you'll see just how
+
+ align:start position:0%
+four okay un Friday you'll see just how
+ 
+
+ align:start position:0%
+four okay un Friday you'll see just how
+to maintain that property but out of
+
+ align:start position:0%
+to maintain that property but out of
+ 
+
+ align:start position:0%
+to maintain that property but out of
+this transformation we get that all of
+
+ align:start position:0%
+this transformation we get that all of
+ 
+
+ align:start position:0%
+this transformation we get that all of
+the leaves have the same depth because
+
+ align:start position:0%
+the leaves have the same depth because
+ 
+
+ align:start position:0%
+the leaves have the same depth because
+their depth now or let's say their
+
+ align:start position:0%
+their depth now or let's say their
+ 
+
+ align:start position:0%
+their depth now or let's say their
+height in the tree is their black height
+
+ align:start position:0%
+height in the tree is their black height
+ 
+
+ align:start position:0%
+height in the tree is their black height
+the the depth of these leaves will be
+
+ align:start position:0%
+the the depth of these leaves will be
+ 
+
+ align:start position:0%
+the the depth of these leaves will be
+the black height of the
+
+ align:start position:0%
+the black height of the
+ 
+
+ align:start position:0%
+the black height of the
+root okay because we sort we're erasing
+
+ align:start position:0%
+root okay because we sort we're erasing
+ 
+
+ align:start position:0%
+root okay because we sort we're erasing
+all the red nodes and we said if we look
+
+ align:start position:0%
+all the red nodes and we said if we look
+ 
+
+ align:start position:0%
+all the red nodes and we said if we look
+at a path and we ignore all the red
+
+ align:start position:0%
+at a path and we ignore all the red
+ 
+
+ align:start position:0%
+at a path and we ignore all the red
+nodes then the number of black nodes
+
+ align:start position:0%
+nodes then the number of black nodes
+ 
+
+ align:start position:0%
+nodes then the number of black nodes
+along that path is the same now we're
+
+ align:start position:0%
+along that path is the same now we're
+ 
+
+ align:start position:0%
+along that path is the same now we're
+basically just leaving all the black
+
+ align:start position:0%
+basically just leaving all the black
+ 
+
+ align:start position:0%
+basically just leaving all the black
+nodes and so along all these paths we
+
+ align:start position:0%
+nodes and so along all these paths we
+ 
+
+ align:start position:0%
+nodes and so along all these paths we
+have the same number of black nodes and
+
+ align:start position:0%
+have the same number of black nodes and
+ 
+
+ align:start position:0%
+have the same number of black nodes and
+therefore every leaf will have the same
+
+ align:start position:0%
+therefore every leaf will have the same
+ 
+
+ align:start position:0%
+therefore every leaf will have the same
+depth let me write down some of these
+
+ align:start position:0%
+depth let me write down some of these
+ 
+
+ align:start position:0%
+depth let me write down some of these
+properties so
+
+ align:start position:0%
+properties so
+ 
+
+ align:start position:0%
+properties so
+every internal
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+node has between two and four
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+children and
+
+ align:start position:0%
+children and
+ 
+
+ align:start position:0%
+children and
+and every leaf has the same
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+depth
+
+ align:start position:0%
+depth
+ 
+
+ align:start position:0%
+depth
+namely the black height of the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+root this is by property four
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+so this is telling us a lot so
+
+ align:start position:0%
+so this is telling us a lot so
+ 
+
+ align:start position:0%
+so this is telling us a lot so
+essentially what this transformation is
+
+ align:start position:0%
+essentially what this transformation is
+ 
+
+ align:start position:0%
+essentially what this transformation is
+doing is ignoring the red nodes and then
+
+ align:start position:0%
+doing is ignoring the red nodes and then
+ 
+
+ align:start position:0%
+doing is ignoring the red nodes and then
+if you just focus on the black nodes
+
+ align:start position:0%
+if you just focus on the black nodes
+ 
+
+ align:start position:0%
+if you just focus on the black nodes
+height equals black height and then
+
+ align:start position:0%
+height equals black height and then
+ 
+
+ align:start position:0%
+height equals black height and then
+black height is telling us that all the
+
+ align:start position:0%
+black height is telling us that all the
+ 
+
+ align:start position:0%
+black height is telling us that all the
+root to leaf paths have the same length
+
+ align:start position:0%
+root to leaf paths have the same length
+ 
+
+ align:start position:0%
+root to leaf paths have the same length
+therefore all these nodes are at the
+
+ align:start position:0%
+therefore all these nodes are at the
+ 
+
+ align:start position:0%
+therefore all these nodes are at the
+same
+
+ align:start position:0%
+same
+ 
+
+ align:start position:0%
+same
+level having leaves at the same level is
+
+ align:start position:0%
+level having leaves at the same level is
+ 
+
+ align:start position:0%
+level having leaves at the same level is
+a good thing because it means your tree
+
+ align:start position:0%
+a good thing because it means your tree
+ 
+
+ align:start position:0%
+a good thing because it means your tree
+is pretty much balanced if you have a
+
+ align:start position:0%
+is pretty much balanced if you have a
+ 
+
+ align:start position:0%
+is pretty much balanced if you have a
+tree where all the nodes are branching
+
+ align:start position:0%
+tree where all the nodes are branching
+ 
+
+ align:start position:0%
+tree where all the nodes are branching
+uh so they all have at least two
+
+ align:start position:0%
+uh so they all have at least two
+ 
+
+ align:start position:0%
+uh so they all have at least two
+children and all the leaves are at the
+
+ align:start position:0%
+children and all the leaves are at the
+ 
+
+ align:start position:0%
+children and all the leaves are at the
+same level that's pretty balanced okay
+
+ align:start position:0%
+same level that's pretty balanced okay
+ 
+
+ align:start position:0%
+same level that's pretty balanced okay
+we'll prove some form of that
+
+ align:start position:0%
+we'll prove some form of that
+ 
+
+ align:start position:0%
+we'll prove some form of that
+now uh I'm going to call the height of
+
+ align:start position:0%
+now uh I'm going to call the height of
+ 
+
+ align:start position:0%
+now uh I'm going to call the height of
+this tree H
+
+ align:start position:0%
+this tree H
+ 
+
+ align:start position:0%
+this tree H
+Prime the height of the original tree is
+
+ align:start position:0%
+Prime the height of the original tree is
+ 
+
+ align:start position:0%
+Prime the height of the original tree is
+H that's what we want to bound
+
+ align:start position:0%
+H that's what we want to bound
+ 
+
+ align:start position:0%
+H that's what we want to bound
+here so the first thing is to bound H
+
+ align:start position:0%
+here so the first thing is to bound H
+ 
+
+ align:start position:0%
+here so the first thing is to bound H
+Prime and then we want to relate H and H
+
+ align:start position:0%
+Prime and then we want to relate H and H
+ 
+
+ align:start position:0%
+Prime and then we want to relate H and H
+Prime
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so first question is how many
+
+ align:start position:0%
+okay so first question is how many
+ 
+
+ align:start position:0%
+okay so first question is how many
+leaves are there in this tree and it
+
+ align:start position:0%
+leaves are there in this tree and it
+ 
+
+ align:start position:0%
+leaves are there in this tree and it
+doesn't really matter which tree I'm
+
+ align:start position:0%
+doesn't really matter which tree I'm
+ 
+
+ align:start position:0%
+doesn't really matter which tree I'm
+looking at because I didn't do anything
+
+ align:start position:0%
+looking at because I didn't do anything
+ 
+
+ align:start position:0%
+looking at because I didn't do anything
+to the leaves all the leaves are black
+
+ align:start position:0%
+to the leaves all the leaves are black
+ 
+
+ align:start position:0%
+to the leaves all the leaves are black
+so the leaves didn't change how many
+
+ align:start position:0%
+so the leaves didn't change how many
+ 
+
+ align:start position:0%
+so the leaves didn't change how many
+leaves are there in this tree and
+
+ align:start position:0%
+leaves are there in this tree and
+ 
+
+ align:start position:0%
+leaves are there in this tree and
+therefore in this
+
+ align:start position:0%
+therefore in this
+ 
+
+ align:start position:0%
+therefore in this
+tree sorry nine nine indeed there are
+
+ align:start position:0%
+tree sorry nine nine indeed there are
+ 
+
+ align:start position:0%
+tree sorry nine nine indeed there are
+nine but I meant in general sorry this
+
+ align:start position:0%
+nine but I meant in general sorry this
+ 
+
+ align:start position:0%
+nine but I meant in general sorry this
+example there are nine how many keys are
+
+ align:start position:0%
+example there are nine how many keys are
+ 
+
+ align:start position:0%
+example there are nine how many keys are
+there eight so in
+
+ align:start position:0%
+there eight so in
+ 
+
+ align:start position:0%
+there eight so in
+general how do you write nine as a
+
+ align:start position:0%
+general how do you write nine as a
+ 
+
+ align:start position:0%
+general how do you write nine as a
+function of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+eight for large values of nine or
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+eight sorry plus one plus one good
+
+ align:start position:0%
+eight sorry plus one plus one good
+ 
+
+ align:start position:0%
+eight sorry plus one plus one good
+correct answer by
+
+ align:start position:0%
+correct answer by
+ 
+
+ align:start position:0%
+correct answer by
+guessing n + one okay why is it n+1
+
+ align:start position:0%
+guessing n + one okay why is it n+1
+ 
+
+ align:start position:0%
+guessing n + one okay why is it n+1
+because whenever we have let's look at
+
+ align:start position:0%
+because whenever we have let's look at
+ 
+
+ align:start position:0%
+because whenever we have let's look at
+the binary tree case where we sort of
+
+ align:start position:0%
+the binary tree case where we sort of
+ 
+
+ align:start position:0%
+the binary tree case where we sort of
+understand what's going
+
+ align:start position:0%
+understand what's going
+ 
+
+ align:start position:0%
+understand what's going
+on wherever you have a a key there are
+
+ align:start position:0%
+on wherever you have a a key there are
+ 
+
+ align:start position:0%
+on wherever you have a a key there are
+two
+
+ align:start position:0%
+two
+ 
+
+ align:start position:0%
+two
+branches and that's not a very good
+
+ align:start position:0%
+branches and that's not a very good
+ 
+
+ align:start position:0%
+branches and that's not a very good
+argument okay but we have what what is
+
+ align:start position:0%
+argument okay but we have what what is
+ 
+
+ align:start position:0%
+argument okay but we have what what is
+here called a branching binary tree
+
+ align:start position:0%
+here called a branching binary tree
+ 
+
+ align:start position:0%
+here called a branching binary tree
+every internal node has exactly two
+
+ align:start position:0%
+every internal node has exactly two
+ 
+
+ align:start position:0%
+every internal node has exactly two
+children and we're counting the number
+
+ align:start position:0%
+children and we're counting the number
+ 
+
+ align:start position:0%
+children and we're counting the number
+of leaves that you get from that process
+
+ align:start position:0%
+of leaves that you get from that process
+ 
+
+ align:start position:0%
+of leaves that you get from that process
+in terms of the number of internal nodes
+
+ align:start position:0%
+in terms of the number of internal nodes
+ 
+
+ align:start position:0%
+in terms of the number of internal nodes
+the number of leaves in a tree a
+
+ align:start position:0%
+the number of leaves in a tree a
+ 
+
+ align:start position:0%
+the number of leaves in a tree a
+branching tree is always one plus the
+
+ align:start position:0%
+branching tree is always one plus the
+ 
+
+ align:start position:0%
+branching tree is always one plus the
+number of internal nodes you should know
+
+ align:start position:0%
+number of internal nodes you should know
+ 
+
+ align:start position:0%
+number of internal nodes you should know
+that you can prove it by
+
+ align:start position:0%
+that you can prove it by
+ 
+
+ align:start position:0%
+that you can prove it by
+induction okay so the number of leaves
+
+ align:start position:0%
+induction okay so the number of leaves
+ 
+
+ align:start position:0%
+induction okay so the number of leaves
+is n plus one it doesn't hold if you
+
+ align:start position:0%
+is n plus one it doesn't hold if you
+ 
+
+ align:start position:0%
+is n plus one it doesn't hold if you
+have a single child holds if every
+
+ align:start position:0%
+have a single child holds if every
+ 
+
+ align:start position:0%
+have a single child holds if every
+internal node
+
+ align:start position:0%
+internal node
+ 
+
+ align:start position:0%
+internal node
+has uh branching factor of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+two okay this is in either
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+tree and now we want to pull out some
+
+ align:start position:0%
+tree and now we want to pull out some
+ 
+
+ align:start position:0%
+tree and now we want to pull out some
+relation between the number of leaves
+
+ align:start position:0%
+relation between the number of leaves
+ 
+
+ align:start position:0%
+relation between the number of leaves
+and the height of a
+
+ align:start position:0%
+and the height of a
+ 
+
+ align:start position:0%
+and the height of a
+tree so what's a good relation to use
+
+ align:start position:0%
+tree so what's a good relation to use
+ 
+
+ align:start position:0%
+tree so what's a good relation to use
+here we know exactly how many leaves
+
+ align:start position:0%
+here we know exactly how many leaves
+ 
+
+ align:start position:0%
+here we know exactly how many leaves
+there are that will somehow connect us
+
+ align:start position:0%
+there are that will somehow connect us
+ 
+
+ align:start position:0%
+there are that will somehow connect us
+to n what we care about is the height
+
+ align:start position:0%
+to n what we care about is the height
+ 
+
+ align:start position:0%
+to n what we care about is the height
+and let's look at the height of this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+tree so if I have a 2 three4 tree of
+
+ align:start position:0%
+tree so if I have a 2 three4 tree of
+ 
+
+ align:start position:0%
+tree so if I have a 2 three4 tree of
+height H Prime how many leaves could it
+
+ align:start position:0%
+height H Prime how many leaves could it
+ 
+
+ align:start position:0%
+height H Prime how many leaves could it
+have what's the minimum and maximum
+
+ align:start position:0%
+have what's the minimum and maximum
+ 
+
+ align:start position:0%
+have what's the minimum and maximum
+number of leaves it could
+
+ align:start position:0%
+number of leaves it could
+ 
+
+ align:start position:0%
+number of leaves it could
+have 2 to the H to four to the H or H
+
+ align:start position:0%
+have 2 to the H to four to the H or H
+ 
+
+ align:start position:0%
+have 2 to the H to four to the H or H
+Prime
+
+ align:start position:0%
+Prime
+ 
+
+ align:start position:0%
+Prime
+so we also know in the 234
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+tree the number of
+
+ align:start position:0%
+tree the number of
+ 
+
+ align:start position:0%
+tree the number of
+leaves has to be between four to the H
+
+ align:start position:0%
+leaves has to be between four to the H
+ 
+
+ align:start position:0%
+leaves has to be between four to the H
+Prime because at most I could Branch
+
+ align:start position:0%
+Prime because at most I could Branch
+ 
+
+ align:start position:0%
+Prime because at most I could Branch
+four ways in each node and it's at least
+
+ align:start position:0%
+four ways in each node and it's at least
+ 
+
+ align:start position:0%
+four ways in each node and it's at least
+2 to the H Prime because I know that
+
+ align:start position:0%
+2 to the H Prime because I know that
+ 
+
+ align:start position:0%
+2 to the H Prime because I know that
+every node branches at least two ways
+
+ align:start position:0%
+every node branches at least two ways
+ 
+
+ align:start position:0%
+every node branches at least two ways
+that's
+
+ align:start position:0%
+that's
+ 
+
+ align:start position:0%
+that's
+key so I only care about one of these I
+
+ align:start position:0%
+key so I only care about one of these I
+ 
+
+ align:start position:0%
+key so I only care about one of these I
+think this one
+
+ align:start position:0%
+think this one
+ 
+
+ align:start position:0%
+think this one
+so I get that 2 the H Prime is at most n
+
+ align:start position:0%
+so I get that 2 the H Prime is at most n
+ 
+
+ align:start position:0%
+so I get that 2 the H Prime is at most n
++ 1 because the number of leaves is n+1
+
+ align:start position:0%
++ 1 because the number of leaves is n+1
+ 
+
+ align:start position:0%
++ 1 because the number of leaves is n+1
+we know that exactly so we rewrite we
+
+ align:start position:0%
+we know that exactly so we rewrite we
+ 
+
+ align:start position:0%
+we know that exactly so we rewrite we
+take logs of both sides this says H1 is
+
+ align:start position:0%
+take logs of both sides this says H1 is
+ 
+
+ align:start position:0%
+take logs of both sides this says H1 is
+at most log of n +
+
+ align:start position:0%
+at most log of n +
+ 
+
+ align:start position:0%
+at most log of n +
+one so we have a nice balanced tree this
+
+ align:start position:0%
+one so we have a nice balanced tree this
+ 
+
+ align:start position:0%
+one so we have a nice balanced tree this
+should be intuitive if I had every node
+
+ align:start position:0%
+should be intuitive if I had every node
+ 
+
+ align:start position:0%
+should be intuitive if I had every node
+branching two ways and all the leaves at
+
+ align:start position:0%
+branching two ways and all the leaves at
+ 
+
+ align:start position:0%
+branching two ways and all the leaves at
+the same level that's a perfect tree
+
+ align:start position:0%
+the same level that's a perfect tree
+ 
+
+ align:start position:0%
+the same level that's a perfect tree
+should be exact
+
+ align:start position:0%
+should be exact
+ 
+
+ align:start position:0%
+should be exact
+log base 2 of n plus1 it turns out not
+
+ align:start position:0%
+log base 2 of n plus1 it turns out not
+ 
+
+ align:start position:0%
+log base 2 of n plus1 it turns out not
+quite n that should be the height of the
+
+ align:start position:0%
+quite n that should be the height of the
+ 
+
+ align:start position:0%
+quite n that should be the height of the
+tree here I might have even more
+
+ align:start position:0%
+tree here I might have even more
+ 
+
+ align:start position:0%
+tree here I might have even more
+branching which is making things even
+
+ align:start position:0%
+branching which is making things even
+ 
+
+ align:start position:0%
+branching which is making things even
+shallower in some sense so I get more
+
+ align:start position:0%
+shallower in some sense so I get more
+ 
+
+ align:start position:0%
+shallower in some sense so I get more
+leaves out of the same height but that's
+
+ align:start position:0%
+leaves out of the same height but that's
+ 
+
+ align:start position:0%
+leaves out of the same height but that's
+only better for me that will only
+
+ align:start position:0%
+only better for me that will only
+ 
+
+ align:start position:0%
+only better for me that will only
+decrease the height in terms of the
+
+ align:start position:0%
+decrease the height in terms of the
+ 
+
+ align:start position:0%
+decrease the height in terms of the
+number of leaves n plus one here was the
+
+ align:start position:0%
+number of leaves n plus one here was the
+ 
+
+ align:start position:0%
+number of leaves n plus one here was the
+the number of leaves so
+
+ align:start position:0%
+the number of leaves so
+ 
+
+ align:start position:0%
+the number of leaves so
+cool that's an easy upper bound on the
+
+ align:start position:0%
+cool that's an easy upper bound on the
+ 
+
+ align:start position:0%
+cool that's an easy upper bound on the
+height of this tree now what we really
+
+ align:start position:0%
+height of this tree now what we really
+ 
+
+ align:start position:0%
+height of this tree now what we really
+care about is the height of this tree so
+
+ align:start position:0%
+care about is the height of this tree so
+ 
+
+ align:start position:0%
+care about is the height of this tree so
+we want to relate H and H Prime any
+
+ align:start position:0%
+we want to relate H and H Prime any
+ 
+
+ align:start position:0%
+we want to relate H and H Prime any
+suggestions on how we might do
+
+ align:start position:0%
+suggestions on how we might do
+ 
+
+ align:start position:0%
+suggestions on how we might do
+that how do we know that the height of
+
+ align:start position:0%
+that how do we know that the height of
+ 
+
+ align:start position:0%
+that how do we know that the height of
+this reduced tree is not too much
+
+ align:start position:0%
+this reduced tree is not too much
+ 
+
+ align:start position:0%
+this reduced tree is not too much
+smaller than this one we know that this
+
+ align:start position:0%
+smaller than this one we know that this
+ 
+
+ align:start position:0%
+smaller than this one we know that this
+one is at most log n we want this one to
+
+ align:start position:0%
+one is at most log n we want this one to
+ 
+
+ align:start position:0%
+one is at most log n we want this one to
+be at most to log n plus
+
+ align:start position:0%
+be at most to log n plus
+ 
+
+ align:start position:0%
+be at most to log n plus
+one we know the answer we said the
+
+ align:start position:0%
+one we know the answer we said the
+ 
+
+ align:start position:0%
+one we know the answer we said the
+theorem
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+sorry right so property 3 tells us that
+
+ align:start position:0%
+sorry right so property 3 tells us that
+ 
+
+ align:start position:0%
+sorry right so property 3 tells us that
+we can only have one one red node for
+
+ align:start position:0%
+we can only have one one red node for
+ 
+
+ align:start position:0%
+we can only have one one red node for
+every black one we can at most alternate
+
+ align:start position:0%
+every black one we can at most alternate
+ 
+
+ align:start position:0%
+every black one we can at most alternate
+red and black so if we look at one of
+
+ align:start position:0%
+red and black so if we look at one of
+ 
+
+ align:start position:0%
+red and black so if we look at one of
+these paths that goes from a root to the
+
+ align:start position:0%
+these paths that goes from a root to the
+ 
+
+ align:start position:0%
+these paths that goes from a root to the
+to a leaf the root to a leaf the number
+
+ align:start position:0%
+to a leaf the root to a leaf the number
+ 
+
+ align:start position:0%
+to a leaf the root to a leaf the number
+of red nodes can be at most half the
+
+ align:start position:0%
+of red nodes can be at most half the
+ 
+
+ align:start position:0%
+of red nodes can be at most half the
+length of the path and that's that's if
+
+ align:start position:0%
+length of the path and that's that's if
+ 
+
+ align:start position:0%
+length of the path and that's that's if
+we take the max overall paths that's the
+
+ align:start position:0%
+we take the max overall paths that's the
+ 
+
+ align:start position:0%
+we take the max overall paths that's the
+height of the tree so we know that H is
+
+ align:start position:0%
+height of the tree so we know that H is
+ 
+
+ align:start position:0%
+height of the tree so we know that H is
+at most 2 * H
+
+ align:start position:0%
+at most 2 * H
+ 
+
+ align:start position:0%
+at most 2 * H
+prime or maybe it's easier to think of H
+
+ align:start position:0%
+prime or maybe it's easier to think of H
+ 
+
+ align:start position:0%
+prime or maybe it's easier to think of H
+Prime is at least a half H so me I got
+
+ align:start position:0%
+Prime is at least a half H so me I got
+ 
+
+ align:start position:0%
+Prime is at least a half H so me I got
+that right uh
+
+ align:start position:0%
+that right uh
+ 
+
+ align:start position:0%
+that right uh
+because at most a half of the nodes on
+
+ align:start position:0%
+because at most a half of the nodes on
+ 
+
+ align:start position:0%
+because at most a half of the nodes on
+any root to Leaf
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+path are
+
+ align:start position:0%
+path are
+ 
+
+ align:start position:0%
+path are
+red so at least half of them have to be
+
+ align:start position:0%
+red so at least half of them have to be
+ 
+
+ align:start position:0%
+red so at least half of them have to be
+black and all the black nodes are
+
+ align:start position:0%
+black and all the black nodes are
+ 
+
+ align:start position:0%
+black and all the black nodes are
+captured in this picture because we only
+
+ align:start position:0%
+captured in this picture because we only
+ 
+
+ align:start position:0%
+captured in this picture because we only
+threw away the red nodes so we have this
+
+ align:start position:0%
+threw away the red nodes so we have this
+ 
+
+ align:start position:0%
+threw away the red nodes so we have this
+relation and therefore H is at most 2 *
+
+ align:start position:0%
+relation and therefore H is at most 2 *
+ 
+
+ align:start position:0%
+relation and therefore H is at most 2 *
+log n
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
++1 okay pretty easy but have to remember
+
+ align:start position:0%
++1 okay pretty easy but have to remember
+ 
+
+ align:start position:0%
++1 okay pretty easy but have to remember
+this tree has to be balanced and that
+
+ align:start position:0%
+this tree has to be balanced and that
+ 
+
+ align:start position:0%
+this tree has to be balanced and that
+they're not too far away from each other
+
+ align:start position:0%
+they're not too far away from each other
+ 
+
+ align:start position:0%
+they're not too far away from each other
+okay so in Friday Friday's recitation
+
+ align:start position:0%
+okay so in Friday Friday's recitation
+ 
+
+ align:start position:0%
+okay so in Friday Friday's recitation
+you'll see how to manipulate trees of
+
+ align:start position:0%
+you'll see how to manipulate trees of
+ 
+
+ align:start position:0%
+you'll see how to manipulate trees of
+this form there's a cool way to do it
+
+ align:start position:0%
+this form there's a cool way to do it
+ 
+
+ align:start position:0%
+this form there's a cool way to do it
+that's 234 trees today we're going to
+
+ align:start position:0%
+that's 234 trees today we're going to
+ 
+
+ align:start position:0%
+that's 234 trees today we're going to
+see how to manipulate trees in this form
+
+ align:start position:0%
+see how to manipulate trees in this form
+ 
+
+ align:start position:0%
+see how to manipulate trees in this form
+as red black trees and you'll see
+
+ align:start position:0%
+as red black trees and you'll see
+ 
+
+ align:start position:0%
+as red black trees and you'll see
+today's lecture and you'll see Friday's
+
+ align:start position:0%
+today's lecture and you'll see Friday's
+ 
+
+ align:start position:0%
+today's lecture and you'll see Friday's
+recitation and they won't really seem to
+
+ align:start position:0%
+recitation and they won't really seem to
+ 
+
+ align:start position:0%
+recitation and they won't really seem to
+relate at all but they're the same just
+
+ align:start position:0%
+relate at all but they're the same just
+ 
+
+ align:start position:0%
+relate at all but they're the same just
+a bit
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+[Applause]
+
+ align:start position:0%
+[Applause]
+ 
+
+ align:start position:0%
+[Applause]
+hidden
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so this is good news we now know
+
+ align:start position:0%
+okay so this is good news we now know
+ 
+
+ align:start position:0%
+okay so this is good news we now know
+that all red black trees are balanced so
+
+ align:start position:0%
+that all red black trees are balanced so
+ 
+
+ align:start position:0%
+that all red black trees are balanced so
+as long as we can make sure that our
+
+ align:start position:0%
+as long as we can make sure that our
+ 
+
+ align:start position:0%
+as long as we can make sure that our
+tree stays a red black
+
+ align:start position:0%
+tree stays a red black
+ 
+
+ align:start position:0%
+tree stays a red black
+tree uh we'll be okay
+
+ align:start position:0%
+tree uh we'll be okay
+ 
+
+ align:start position:0%
+tree uh we'll be okay
+will be okay in the sense that the
+
+ align:start position:0%
+will be okay in the sense that the
+ 
+
+ align:start position:0%
+will be okay in the sense that the
+height is always log n and
+
+ align:start position:0%
+height is always log n and
+ 
+
+ align:start position:0%
+height is always log n and
+therefore uh
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+queries in a red black tree so queries
+
+ align:start position:0%
+queries in a red black tree so queries
+ 
+
+ align:start position:0%
+queries in a red black tree so queries
+are things like search find a given key
+
+ align:start position:0%
+are things like search find a given key
+ 
+
+ align:start position:0%
+are things like search find a given key
+uh find the minimum find the
+
+ align:start position:0%
+uh find the minimum find the
+ 
+
+ align:start position:0%
+uh find the minimum find the
+maximum find the
+
+ align:start position:0%
+maximum find the
+ 
+
+ align:start position:0%
+maximum find the
+successor find the predecessor these are
+
+ align:start position:0%
+successor find the predecessor these are
+ 
+
+ align:start position:0%
+successor find the predecessor these are
+all queries that we know how to support
+
+ align:start position:0%
+all queries that we know how to support
+ 
+
+ align:start position:0%
+all queries that we know how to support
+in a in a binary search tree
+
+ align:start position:0%
+in a in a binary search tree
+ 
+
+ align:start position:0%
+in a in a binary search tree
+and we know how to do them in order
+
+ align:start position:0%
+and we know how to do them in order
+ 
+
+ align:start position:0%
+and we know how to do them in order
+height
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+time and the height here is log n so we
+
+ align:start position:0%
+time and the height here is log n so we
+ 
+
+ align:start position:0%
+time and the height here is log n so we
+know that all of these operations take
+
+ align:start position:0%
+know that all of these operations take
+ 
+
+ align:start position:0%
+know that all of these operations take
+order log
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+n in a red black
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+tree okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so queries are easy we're done with
+
+ align:start position:0%
+so queries are easy we're done with
+ 
+
+ align:start position:0%
+so queries are easy we're done with
+queries just be just from balance not a
+
+ align:start position:0%
+queries just be just from balance not a
+ 
+
+ align:start position:0%
+queries just be just from balance not a
+surprise we know that balance is good
+
+ align:start position:0%
+surprise we know that balance is good
+ 
+
+ align:start position:0%
+surprise we know that balance is good
+the hard part for us will be to do
+
+ align:start position:0%
+the hard part for us will be to do
+ 
+
+ align:start position:0%
+the hard part for us will be to do
+updates
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and in this context updates means insert
+
+ align:start position:0%
+and in this context updates means insert
+ 
+
+ align:start position:0%
+and in this context updates means insert
+and
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+delete in general in a data structure we
+
+ align:start position:0%
+delete in general in a data structure we
+ 
+
+ align:start position:0%
+delete in general in a data structure we
+talk about queries that which ask ask
+
+ align:start position:0%
+talk about queries that which ask ask
+ 
+
+ align:start position:0%
+talk about queries that which ask ask
+questions about the data in the
+
+ align:start position:0%
+questions about the data in the
+ 
+
+ align:start position:0%
+questions about the data in the
+structure and updates which modify the
+
+ align:start position:0%
+structure and updates which modify the
+ 
+
+ align:start position:0%
+structure and updates which modify the
+data in the structure and most of the
+
+ align:start position:0%
+data in the structure and most of the
+ 
+
+ align:start position:0%
+data in the structure and most of the
+time here we're always thinking about
+
+ align:start position:0%
+time here we're always thinking about
+ 
+
+ align:start position:0%
+time here we're always thinking about
+Dynamic sets so you can change the
+
+ align:start position:0%
+Dynamic sets so you can change the
+ 
+
+ align:start position:0%
+Dynamic sets so you can change the
+dynamic set by adding or deleting an
+
+ align:start position:0%
+dynamic set by adding or deleting an
+ 
+
+ align:start position:0%
+dynamic set by adding or deleting an
+element you can ask all sorts of
+
+ align:start position:0%
+element you can ask all sorts of
+ 
+
+ align:start position:0%
+element you can ask all sorts of
+questions in priority cues there were
+
+ align:start position:0%
+questions in priority cues there were
+ 
+
+ align:start position:0%
+questions in priority cues there were
+other updates like delete men
+
+ align:start position:0%
+other updates like delete men
+ 
+
+ align:start position:0%
+other updates like delete men
+here we have find men but no we could
+
+ align:start position:0%
+here we have find men but no we could
+ 
+
+ align:start position:0%
+here we have find men but no we could
+then delete it okay but typically these
+
+ align:start position:0%
+then delete it okay but typically these
+ 
+
+ align:start position:0%
+then delete it okay but typically these
+are the operations we care about and
+
+ align:start position:0%
+are the operations we care about and
+ 
+
+ align:start position:0%
+are the operations we care about and
+we'll talk about updates to include both
+
+ align:start position:0%
+we'll talk about updates to include both
+ 
+
+ align:start position:0%
+we'll talk about updates to include both
+of these and queries to include all of
+
+ align:start position:0%
+of these and queries to include all of
+ 
+
+ align:start position:0%
+of these and queries to include all of
+these or whatever happens to be relevant
+
+ align:start position:0%
+these or whatever happens to be relevant
+ 
+
+ align:start position:0%
+these or whatever happens to be relevant
+in problem sets especially you'll see
+
+ align:start position:0%
+in problem sets especially you'll see
+ 
+
+ align:start position:0%
+in problem sets especially you'll see
+all sorts of different queries that you
+
+ align:start position:0%
+all sorts of different queries that you
+ 
+
+ align:start position:0%
+all sorts of different queries that you
+can
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+support okay so how do we support
+
+ align:start position:0%
+support okay so how do we support
+ 
+
+ align:start position:0%
+support okay so how do we support
+updates well we have binary search tree
+
+ align:start position:0%
+updates well we have binary search tree
+ 
+
+ align:start position:0%
+updates well we have binary search tree
+insert which we call tree insert we have
+
+ align:start position:0%
+insert which we call tree insert we have
+ 
+
+ align:start position:0%
+insert which we call tree insert we have
+we have binary search tree delete tree
+
+ align:start position:0%
+we have binary search tree delete tree
+ 
+
+ align:start position:0%
+we have binary search tree delete tree
+delete uh they will preserve the binary
+
+ align:start position:0%
+delete uh they will preserve the binary
+ 
+
+ align:start position:0%
+delete uh they will preserve the binary
+search tree property but we know they
+
+ align:start position:0%
+search tree property but we know they
+ 
+
+ align:start position:0%
+search tree property but we know they
+don't necessarily preserve balance you
+
+ align:start position:0%
+don't necessarily preserve balance you
+ 
+
+ align:start position:0%
+don't necessarily preserve balance you
+can insert a bunch of nodes just keep
+
+ align:start position:0%
+can insert a bunch of nodes just keep
+ 
+
+ align:start position:0%
+can insert a bunch of nodes just keep
+adding new minimum elements and you'll
+
+ align:start position:0%
+adding new minimum elements and you'll
+ 
+
+ align:start position:0%
+adding new minimum elements and you'll
+get a really long path off the end so
+
+ align:start position:0%
+get a really long path off the end so
+ 
+
+ align:start position:0%
+get a really long path off the end so
+presumably they do not preserve the red
+
+ align:start position:0%
+presumably they do not preserve the red
+ 
+
+ align:start position:0%
+presumably they do not preserve the red
+black properties because we know red
+
+ align:start position:0%
+black properties because we know red
+ 
+
+ align:start position:0%
+black properties because we know red
+black implies balanced in particular
+
+ align:start position:0%
+black implies balanced in particular
+ 
+
+ align:start position:0%
+black implies balanced in particular
+they won't satisfy property one which
+
+ align:start position:0%
+they won't satisfy property one which
+ 
+
+ align:start position:0%
+they won't satisfy property one which
+I've erased which is every node is red
+
+ align:start position:0%
+I've erased which is every node is red
+ 
+
+ align:start position:0%
+I've erased which is every node is red
+or black it'll add a node and not assign
+
+ align:start position:0%
+or black it'll add a node and not assign
+ 
+
+ align:start position:0%
+or black it'll add a node and not assign
+it a color so we've got to assign it a
+
+ align:start position:0%
+it a color so we've got to assign it a
+ 
+
+ align:start position:0%
+it a color so we've got to assign it a
+color
+
+ align:start position:0%
+color
+ 
+
+ align:start position:0%
+color
+and as soon as we do that we'll probably
+
+ align:start position:0%
+and as soon as we do that we'll probably
+ 
+
+ align:start position:0%
+and as soon as we do that we'll probably
+violate some other property and then we
+
+ align:start position:0%
+violate some other property and then we
+ 
+
+ align:start position:0%
+violate some other property and then we
+have to fix that property and so on so
+
+ align:start position:0%
+have to fix that property and so on so
+ 
+
+ align:start position:0%
+have to fix that property and so on so
+it's a bit tricky but you play around
+
+ align:start position:0%
+it's a bit tricky but you play around
+ 
+
+ align:start position:0%
+it's a bit tricky but you play around
+with it and it's not too
+
+ align:start position:0%
+with it and it's not too
+ 
+
+ align:start position:0%
+with it and it's not too
+hard okay
+
+ align:start position:0%
+hard okay
+ 
+
+ align:start position:0%
+hard okay
+so updates must modify the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+tree and they're going to do it in to
+
+ align:start position:0%
+tree and they're going to do it in to
+ 
+
+ align:start position:0%
+tree and they're going to do it in to
+preserve the red black properties
+
+ align:start position:0%
+preserve the red black properties
+ 
+
+ align:start position:0%
+preserve the red black properties
+they're going to do it in three
+
+ align:start position:0%
+they're going to do it in three
+ 
+
+ align:start position:0%
+they're going to do it in three
+different kinds of
+
+ align:start position:0%
+different kinds of
+ 
+
+ align:start position:0%
+different kinds of
+modifications the first thing we will
+
+ align:start position:0%
+modifications the first thing we will
+ 
+
+ align:start position:0%
+modifications the first thing we will
+indeed do is just use the BST operation
+
+ align:start position:0%
+indeed do is just use the BST operation
+ 
+
+ align:start position:0%
+indeed do is just use the BST operation
+tree insert or tree delete that's
+
+ align:start position:0%
+tree insert or tree delete that's
+ 
+
+ align:start position:0%
+tree insert or tree delete that's
+something we know how to do let's just
+
+ align:start position:0%
+something we know how to do let's just
+ 
+
+ align:start position:0%
+something we know how to do let's just
+do
+
+ align:start position:0%
+do
+ 
+
+ align:start position:0%
+do
+it we're going to have to change the
+
+ align:start position:0%
+it we're going to have to change the
+ 
+
+ align:start position:0%
+it we're going to have to change the
+colors of some of the nodes in
+
+ align:start position:0%
+colors of some of the nodes in
+ 
+
+ align:start position:0%
+colors of some of the nodes in
+particular the one that we insert better
+
+ align:start position:0%
+particular the one that we insert better
+ 
+
+ align:start position:0%
+particular the one that we insert better
+be colored somehow and in general if we
+
+ align:start position:0%
+be colored somehow and in general if we
+ 
+
+ align:start position:0%
+be colored somehow and in general if we
+just rip out a node we're going to have
+
+ align:start position:0%
+just rip out a node we're going to have
+ 
+
+ align:start position:0%
+just rip out a node we're going to have
+to recolor
+
+ align:start position:0%
+to recolor
+ 
+
+ align:start position:0%
+to recolor
+it recolor some uh nearby nodes
+
+ align:start position:0%
+it recolor some uh nearby nodes
+ 
+
+ align:start position:0%
+it recolor some uh nearby nodes
+there's one other kind of operation
+
+ align:start position:0%
+there's one other kind of operation
+ 
+
+ align:start position:0%
+there's one other kind of operation
+we're going to do so recoloring just
+
+ align:start position:0%
+we're going to do so recoloring just
+ 
+
+ align:start position:0%
+we're going to do so recoloring just
+means set to red or
+
+ align:start position:0%
+means set to red or
+ 
+
+ align:start position:0%
+means set to red or
+black the other thing you might do is
+
+ align:start position:0%
+black the other thing you might do is
+ 
+
+ align:start position:0%
+black the other thing you might do is
+rearrange the tree change the pointers
+
+ align:start position:0%
+rearrange the tree change the pointers
+ 
+
+ align:start position:0%
+rearrange the tree change the pointers
+change the links from one node to
+
+ align:start position:0%
+change the links from one node to
+ 
+
+ align:start position:0%
+change the links from one node to
+another and we're going to do that in a
+
+ align:start position:0%
+another and we're going to do that in a
+ 
+
+ align:start position:0%
+another and we're going to do that in a
+very structured way and this is one of
+
+ align:start position:0%
+very structured way and this is one of
+ 
+
+ align:start position:0%
+very structured way and this is one of
+the main reasons that uh red black trees
+
+ align:start position:0%
+the main reasons that uh red black trees
+ 
+
+ align:start position:0%
+the main reasons that uh red black trees
+are interesting the kinds of changes
+
+ align:start position:0%
+are interesting the kinds of changes
+ 
+
+ align:start position:0%
+are interesting the kinds of changes
+they make are very simple and they also
+
+ align:start position:0%
+they make are very simple and they also
+ 
+
+ align:start position:0%
+they make are very simple and they also
+don't make very many of them so they're
+
+ align:start position:0%
+don't make very many of them so they're
+ 
+
+ align:start position:0%
+don't make very many of them so they're
+called rotations
+
+ align:start position:0%
+called rotations
+ 
+
+ align:start position:0%
+called rotations
+so here's a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+rotation okay this is a way of gener
+
+ align:start position:0%
+rotation okay this is a way of gener
+ 
+
+ align:start position:0%
+rotation okay this is a way of gener
+drawing a generic part of the a tree we
+
+ align:start position:0%
+drawing a generic part of the a tree we
+ 
+
+ align:start position:0%
+drawing a generic part of the a tree we
+have two nodes A and B there's some sub
+
+ align:start position:0%
+have two nodes A and B there's some sub
+ 
+
+ align:start position:0%
+have two nodes A and B there's some sub
+trees hanging off which we draw as
+
+ align:start position:0%
+trees hanging off which we draw as
+ 
+
+ align:start position:0%
+trees hanging off which we draw as
+triangles we don't know how big they are
+
+ align:start position:0%
+triangles we don't know how big they are
+ 
+
+ align:start position:0%
+triangles we don't know how big they are
+we know they better all have the same
+
+ align:start position:0%
+we know they better all have the same
+ 
+
+ align:start position:0%
+we know they better all have the same
+black height if it's red black tree but
+
+ align:start position:0%
+black height if it's red black tree but
+ 
+
+ align:start position:0%
+black height if it's red black tree but
+in general it just looks like this
+
+ align:start position:0%
+in general it just looks like this
+ 
+
+ align:start position:0%
+in general it just looks like this
+there's some parent and there's some
+
+ align:start position:0%
+there's some parent and there's some
+ 
+
+ align:start position:0%
+there's some parent and there's some
+rest of the tree out here which we don't
+
+ align:start position:0%
+rest of the tree out here which we don't
+ 
+
+ align:start position:0%
+rest of the tree out here which we don't
+draw I'll give these sub trees names
+
+ align:start position:0%
+draw I'll give these sub trees names
+ 
+
+ align:start position:0%
+draw I'll give these sub trees names
+Greek names Alpha Beta
+
+ align:start position:0%
+Greek names Alpha Beta
+ 
+
+ align:start position:0%
+Greek names Alpha Beta
+gamma and I'll Define the Operation
+
+ align:start position:0%
+gamma and I'll Define the Operation
+ 
+
+ align:start position:0%
+gamma and I'll Define the Operation
+right
+
+ align:start position:0%
+right
+ 
+
+ align:start position:0%
+right
+rotate of
+
+ align:start position:0%
+rotate of
+ 
+
+ align:start position:0%
+rotate of
+B so in general if I have a node B I
+
+ align:start position:0%
+B so in general if I have a node B I
+ 
+
+ align:start position:0%
+B so in general if I have a node B I
+look at it and I want to do a right
+
+ align:start position:0%
+look at it and I want to do a right
+ 
+
+ align:start position:0%
+look at it and I want to do a right
+rotation I look at its left child and
+
+ align:start position:0%
+rotation I look at its left child and
+ 
+
+ align:start position:0%
+rotation I look at its left child and
+draw this picture all the sub trees of
+
+ align:start position:0%
+draw this picture all the sub trees of
+ 
+
+ align:start position:0%
+draw this picture all the sub trees of
+those two nodes
+
+ align:start position:0%
+those two nodes
+ 
+
+ align:start position:0%
+those two nodes
+and I create this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+tree so all I've done is turn this Edge
+
+ align:start position:0%
+tree so all I've done is turn this Edge
+ 
+
+ align:start position:0%
+tree so all I've done is turn this Edge
+90° the parent what was the parent of B
+
+ align:start position:0%
+90° the parent what was the parent of B
+ 
+
+ align:start position:0%
+90° the parent what was the parent of B
+is now the parent of a a is now the new
+
+ align:start position:0%
+is now the parent of a a is now the new
+ 
+
+ align:start position:0%
+is now the parent of a a is now the new
+parent of B the sub trees rearranged
+
+ align:start position:0%
+parent of B the sub trees rearranged
+ 
+
+ align:start position:0%
+parent of B the sub trees rearranged
+before they were both subt trees of
+
+ align:start position:0%
+before they were both subt trees of
+ 
+
+ align:start position:0%
+before they were both subt trees of
+these two are sub trees of a and Gamma
+
+ align:start position:0%
+these two are sub trees of a and Gamma
+ 
+
+ align:start position:0%
+these two are sub trees of a and Gamma
+was a sub tree of B gamma is still a
+
+ align:start position:0%
+was a sub tree of B gamma is still a
+ 
+
+ align:start position:0%
+was a sub tree of B gamma is still a
+subt tree of B and Alpha is still a subt
+
+ align:start position:0%
+subt tree of B and Alpha is still a subt
+ 
+
+ align:start position:0%
+subt tree of B and Alpha is still a subt
+tree of a but beta switched to being a
+
+ align:start position:0%
+tree of a but beta switched to being a
+ 
+
+ align:start position:0%
+tree of a but beta switched to being a
+sub tree of B okay the main thing we
+
+ align:start position:0%
+sub tree of B okay the main thing we
+ 
+
+ align:start position:0%
+sub tree of B okay the main thing we
+want to check here is that this
+
+ align:start position:0%
+want to check here is that this
+ 
+
+ align:start position:0%
+want to check here is that this
+operation
+
+ align:start position:0%
+operation
+ 
+
+ align:start position:0%
+operation
+preserves the binary search tree
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+property remember the binary search tree
+
+ align:start position:0%
+property remember the binary search tree
+ 
+
+ align:start position:0%
+property remember the binary search tree
+property says that all the elements in
+
+ align:start position:0%
+property says that all the elements in
+ 
+
+ align:start position:0%
+property says that all the elements in
+the left sub tree of a node are less
+
+ align:start position:0%
+the left sub tree of a node are less
+ 
+
+ align:start position:0%
+the left sub tree of a node are less
+than or equal to the node and all the
+
+ align:start position:0%
+than or equal to the node and all the
+ 
+
+ align:start position:0%
+than or equal to the node and all the
+elements in the right sub tree are
+
+ align:start position:0%
+elements in the right sub tree are
+ 
+
+ align:start position:0%
+elements in the right sub tree are
+greater than or equal to that value so
+
+ align:start position:0%
+greater than or equal to that value so
+ 
+
+ align:start position:0%
+greater than or equal to that value so
+in particular if we take some node
+
+ align:start position:0%
+in particular if we take some node
+ 
+
+ align:start position:0%
+in particular if we take some node
+little a in Alpha little B in beta and
+
+ align:start position:0%
+little a in Alpha little B in beta and
+ 
+
+ align:start position:0%
+little a in Alpha little B in beta and
+little C in gamma then a is less than or
+
+ align:start position:0%
+little C in gamma then a is less than or
+ 
+
+ align:start position:0%
+little C in gamma then a is less than or
+equal to Capital a is less than equal to
+
+ align:start position:0%
+equal to Capital a is less than equal to
+ 
+
+ align:start position:0%
+equal to Capital a is less than equal to
+Little B is less than equal to capital B
+
+ align:start position:0%
+Little B is less than equal to capital B
+ 
+
+ align:start position:0%
+Little B is less than equal to capital B
+it's less than or equal to little
+
+ align:start position:0%
+it's less than or equal to little
+ 
+
+ align:start position:0%
+it's less than or equal to little
+C okay and that this is the condition
+
+ align:start position:0%
+C okay and that this is the condition
+ 
+
+ align:start position:0%
+C okay and that this is the condition
+condition both on the left side and on
+
+ align:start position:0%
+condition both on the left side and on
+ 
+
+ align:start position:0%
+condition both on the left side and on
+the right side CU Alpha is less is left
+
+ align:start position:0%
+the right side CU Alpha is less is left
+ 
+
+ align:start position:0%
+the right side CU Alpha is less is left
+of everything beta is in between a and b
+
+ align:start position:0%
+of everything beta is in between a and b
+ 
+
+ align:start position:0%
+of everything beta is in between a and b
+and Gamma is after B the same thing is
+
+ align:start position:0%
+and Gamma is after B the same thing is
+ 
+
+ align:start position:0%
+and Gamma is after B the same thing is
+true over here beta is still supposed to
+
+ align:start position:0%
+true over here beta is still supposed to
+ 
+
+ align:start position:0%
+true over here beta is still supposed to
+be all the nodes that come between
+
+ align:start position:0%
+be all the nodes that come between
+ 
+
+ align:start position:0%
+be all the nodes that come between
+capital A and capital B so this is this
+
+ align:start position:0%
+capital A and capital B so this is this
+ 
+
+ align:start position:0%
+capital A and capital B so this is this
+is good we can definitely do this
+
+ align:start position:0%
+is good we can definitely do this
+ 
+
+ align:start position:0%
+is good we can definitely do this
+operation still have a binary search
+
+ align:start position:0%
+operation still have a binary search
+ 
+
+ align:start position:0%
+operation still have a binary search
+tree and we're going to use rotations in
+
+ align:start position:0%
+tree and we're going to use rotations in
+ 
+
+ align:start position:0%
+tree and we're going to use rotations in
+a particularly careful way to make sure
+
+ align:start position:0%
+a particularly careful way to make sure
+ 
+
+ align:start position:0%
+a particularly careful way to make sure
+that we maintain all of these properties
+
+ align:start position:0%
+that we maintain all of these properties
+ 
+
+ align:start position:0%
+that we maintain all of these properties
+that's the hard part but rotations will
+
+ align:start position:0%
+that's the hard part but rotations will
+ 
+
+ align:start position:0%
+that's the hard part but rotations will
+be our key this was the right rotate
+
+ align:start position:0%
+be our key this was the right rotate
+ 
+
+ align:start position:0%
+be our key this was the right rotate
+operation the reverse operation is left
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+rotate so this is left rotate of
+
+ align:start position:0%
+rotate so this is left rotate of
+ 
+
+ align:start position:0%
+rotate so this is left rotate of
+a in general of the two nodes that are
+
+ align:start position:0%
+a in general of the two nodes that are
+ 
+
+ align:start position:0%
+a in general of the two nodes that are
+involved we list the top one says right
+
+ align:start position:0%
+involved we list the top one says right
+ 
+
+ align:start position:0%
+involved we list the top one says right
+rotate of B will give you this left
+
+ align:start position:0%
+rotate of B will give you this left
+ 
+
+ align:start position:0%
+rotate of B will give you this left
+rotate of a will give you this so these
+
+ align:start position:0%
+rotate of a will give you this so these
+ 
+
+ align:start position:0%
+rotate of a will give you this so these
+are reversible
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+operations which feels good uh the other
+
+ align:start position:0%
+operations which feels good uh the other
+ 
+
+ align:start position:0%
+operations which feels good uh the other
+thing is that they only take constant
+
+ align:start position:0%
+thing is that they only take constant
+ 
+
+ align:start position:0%
+thing is that they only take constant
+time
+
+ align:start position:0%
+time
+ 
+
+ align:start position:0%
+time
+these are constant time
+
+ align:start position:0%
+these are constant time
+ 
+
+ align:start position:0%
+these are constant time
+operations because we're only changing a
+
+ align:start position:0%
+operations because we're only changing a
+ 
+
+ align:start position:0%
+operations because we're only changing a
+constant number of pointers as long as
+
+ align:start position:0%
+constant number of pointers as long as
+ 
+
+ align:start position:0%
+constant number of pointers as long as
+you know the node B that you're
+
+ align:start position:0%
+you know the node B that you're
+ 
+
+ align:start position:0%
+you know the node B that you're
+interested in you set the left pointer
+
+ align:start position:0%
+interested in you set the left pointer
+ 
+
+ align:start position:0%
+interested in you set the left pointer
+of B to be you want it to be beta so you
+
+ align:start position:0%
+of B to be you want it to be beta so you
+ 
+
+ align:start position:0%
+of B to be you want it to be beta so you
+set left of B to be right of a and so on
+
+ align:start position:0%
+set left of B to be right of a and so on
+ 
+
+ align:start position:0%
+set left of B to be right of a and so on
+and so on you make a constant number of
+
+ align:start position:0%
+and so on you make a constant number of
+ 
+
+ align:start position:0%
+and so on you make a constant number of
+those changes you update the parents as
+
+ align:start position:0%
+those changes you update the parents as
+ 
+
+ align:start position:0%
+those changes you update the parents as
+well it's only a constant number of
+
+ align:start position:0%
+well it's only a constant number of
+ 
+
+ align:start position:0%
+well it's only a constant number of
+links that are changing so constant
+
+ align:start position:0%
+links that are changing so constant
+ 
+
+ align:start position:0%
+links that are changing so constant
+number of assignments you need to
+
+ align:start position:0%
+number of assignments you need to
+ 
+
+ align:start position:0%
+number of assignments you need to
+do okay you've probably seen rotations
+
+ align:start position:0%
+do okay you've probably seen rotations
+ 
+
+ align:start position:0%
+do okay you've probably seen rotations
+before but we're going to use
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+them in a complicated
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+way so let's look at how to do
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+insertion we'll see it three times in
+
+ align:start position:0%
+insertion we'll see it three times in
+ 
+
+ align:start position:0%
+insertion we'll see it three times in
+some sense
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+first I'll tell you the basic idea which
+
+ align:start position:0%
+first I'll tell you the basic idea which
+ 
+
+ align:start position:0%
+first I'll tell you the basic idea which
+is pretty simple mentioned some of it
+
+ align:start position:0%
+is pretty simple mentioned some of it
+ 
+
+ align:start position:0%
+is pretty simple mentioned some of it
+already then we'll do it on an example
+
+ align:start position:0%
+already then we'll do it on an example
+ 
+
+ align:start position:0%
+already then we'll do it on an example
+feel it in our bones and then we'll give
+
+ align:start position:0%
+feel it in our bones and then we'll give
+ 
+
+ align:start position:0%
+feel it in our bones and then we'll give
+the pseudo
+
+ align:start position:0%
+the pseudo
+ 
+
+ align:start position:0%
+the pseudo
+code so that you could go home and
+
+ align:start position:0%
+code so that you could go home and
+ 
+
+ align:start position:0%
+code so that you could go home and
+implement it if you
+
+ align:start position:0%
+implement it if you
+ 
+
+ align:start position:0%
+implement it if you
+wanted okay this is I should say red
+
+ align:start position:0%
+wanted okay this is I should say red
+ 
+
+ align:start position:0%
+wanted okay this is I should say red
+black insert which in the book is called
+
+ align:start position:0%
+black insert which in the book is called
+ 
+
+ align:start position:0%
+black insert which in the book is called
+RB
+
+ align:start position:0%
+RB
+ 
+
+ align:start position:0%
+RB
+insert not for root beer but for red
+
+ align:start position:0%
+insert not for root beer but for red
+ 
+
+ align:start position:0%
+insert not for root beer but for red
+black
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so the first thing we're going to
+
+ align:start position:0%
+okay so the first thing we're going to
+ 
+
+ align:start position:0%
+okay so the first thing we're going to
+do as I said is binary search tree
+
+ align:start position:0%
+do as I said is binary search tree
+ 
+
+ align:start position:0%
+do as I said is binary search tree
+insert that node so X now becomes a new
+
+ align:start position:0%
+insert that node so X now becomes a new
+ 
+
+ align:start position:0%
+insert that node so X now becomes a new
+Leaf we search for X wherever it's
+
+ align:start position:0%
+Leaf we search for X wherever it's
+ 
+
+ align:start position:0%
+Leaf we search for X wherever it's
+supposed to go we create a new shouldn't
+
+ align:start position:0%
+supposed to go we create a new shouldn't
+ 
+
+ align:start position:0%
+supposed to go we create a new shouldn't
+call it a leaf now it's now uh a node
+
+ align:start position:0%
+call it a leaf now it's now uh a node
+ 
+
+ align:start position:0%
+call it a leaf now it's now uh a node
+hanging off it's an internal node
+
+ align:start position:0%
+hanging off it's an internal node
+ 
+
+ align:start position:0%
+hanging off it's an internal node
+hanging off one of the original nodes
+
+ align:start position:0%
+hanging off one of the original nodes
+ 
+
+ align:start position:0%
+hanging off one of the original nodes
+maybe we added it right here it now gets
+
+ align:start position:0%
+maybe we added it right here it now gets
+ 
+
+ align:start position:0%
+maybe we added it right here it now gets
+two new leaves hanging off of
+
+ align:start position:0%
+two new leaves hanging off of
+ 
+
+ align:start position:0%
+two new leaves hanging off of
+it has no internal
+
+ align:start position:0%
+it has no internal
+ 
+
+ align:start position:0%
+it has no internal
+children and we get to pick a color for
+
+ align:start position:0%
+children and we get to pick a color for
+ 
+
+ align:start position:0%
+children and we get to pick a color for
+it and
+
+ align:start position:0%
+it and
+ 
+
+ align:start position:0%
+it and
+we will pick the color
+
+ align:start position:0%
+we will pick the color
+ 
+
+ align:start position:0%
+we will pick the color
+red okay why red we definitely have to
+
+ align:start position:0%
+red okay why red we definitely have to
+ 
+
+ align:start position:0%
+red okay why red we definitely have to
+pick one of two colors we could flip a
+
+ align:start position:0%
+pick one of two colors we could flip a
+ 
+
+ align:start position:0%
+pick one of two colors we could flip a
+coin that might work but it's going to
+
+ align:start position:0%
+coin that might work but it's going to
+ 
+
+ align:start position:0%
+coin that might work but it's going to
+make our job even Messier
+
+ align:start position:0%
+make our job even Messier
+ 
+
+ align:start position:0%
+make our job even Messier
+so we're adding a new node okay it's not
+
+ align:start position:0%
+so we're adding a new node okay it's not
+ 
+
+ align:start position:0%
+so we're adding a new node okay it's not
+a root or a leaf presumably so we don't
+
+ align:start position:0%
+a root or a leaf presumably so we don't
+ 
+
+ align:start position:0%
+a root or a leaf presumably so we don't
+really need it to be Black by property
+
+ align:start position:0%
+really need it to be Black by property
+ 
+
+ align:start position:0%
+really need it to be Black by property
+two property three every red node has a
+
+ align:start position:0%
+two property three every red node has a
+ 
+
+ align:start position:0%
+two property three every red node has a
+black parent that might be a problem so
+
+ align:start position:0%
+black parent that might be a problem so
+ 
+
+ align:start position:0%
+black parent that might be a problem so
+problem is if it's parent is
+
+ align:start position:0%
+problem is if it's parent is
+ 
+
+ align:start position:0%
+problem is if it's parent is
+red then we violate Property
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+2 parent might be
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+red property three
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+sorry okay the good news is that
+
+ align:start position:0%
+sorry okay the good news is that
+ 
+
+ align:start position:0%
+sorry okay the good news is that
+property four is still true because
+
+ align:start position:0%
+property four is still true because
+ 
+
+ align:start position:0%
+property four is still true because
+property four is just counting numbers
+
+ align:start position:0%
+property four is just counting numbers
+ 
+
+ align:start position:0%
+property four is just counting numbers
+of black nodes down various paths that's
+
+ align:start position:0%
+of black nodes down various paths that's
+ 
+
+ align:start position:0%
+of black nodes down various paths that's
+really the hard property to maintain if
+
+ align:start position:0%
+really the hard property to maintain if
+ 
+
+ align:start position:0%
+really the hard property to maintain if
+we just add a new red node none of the
+
+ align:start position:0%
+we just add a new red node none of the
+ 
+
+ align:start position:0%
+we just add a new red node none of the
+black Heights change none of the number
+
+ align:start position:0%
+black Heights change none of the number
+ 
+
+ align:start position:0%
+black Heights change none of the number
+of black nodes along a path changes so
+
+ align:start position:0%
+of black nodes along a path changes so
+ 
+
+ align:start position:0%
+of black nodes along a path changes so
+this still has to hold the only thing we
+
+ align:start position:0%
+this still has to hold the only thing we
+ 
+
+ align:start position:0%
+this still has to hold the only thing we
+can violate is property 3 that's
+
+ align:start position:0%
+can violate is property 3 that's
+ 
+
+ align:start position:0%
+can violate is property 3 that's
+reasonable we know we've got to violate
+
+ align:start position:0%
+reasonable we know we've got to violate
+ 
+
+ align:start position:0%
+reasonable we know we've got to violate
+something at at the beginning just we
+
+ align:start position:0%
+something at at the beginning just we
+ 
+
+ align:start position:0%
+something at at the beginning just we
+can't just do a binary search tree
+
+ align:start position:0%
+can't just do a binary search tree
+ 
+
+ align:start position:0%
+can't just do a binary search tree
+insert
+
+ align:start position:0%
+insert
+ 
+
+ align:start position:0%
+insert
+okay so let's give it a
+
+ align:start position:0%
+okay so let's give it a
+ 
+
+ align:start position:0%
+okay so let's give it a
+try on this tree
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh I should say what we're how we're
+
+ align:start position:0%
+uh I should say what we're how we're
+ 
+
+ align:start position:0%
+uh I should say what we're how we're
+going to fix
+
+ align:start position:0%
+going to fix
+ 
+
+ align:start position:0%
+going to fix
+this how do we fix uh property
+
+ align:start position:0%
+this how do we fix uh property
+ 
+
+ align:start position:0%
+this how do we fix uh property
+three we're going to move the violation
+
+ align:start position:0%
+three we're going to move the violation
+ 
+
+ align:start position:0%
+three we're going to move the violation
+of
+
+ align:start position:0%
+of
+ 
+
+ align:start position:0%
+of
+three up the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+tree so we're going to start at node X
+
+ align:start position:0%
+tree so we're going to start at node X
+ 
+
+ align:start position:0%
+tree so we're going to start at node X
+and move up towards the
+
+ align:start position:0%
+and move up towards the
+ 
+
+ align:start position:0%
+and move up towards the
+root
+
+ align:start position:0%
+root
+ 
+
+ align:start position:0%
+root
+um this is via recoloring only thing
+
+ align:start position:0%
+um this is via recoloring only thing
+ 
+
+ align:start position:0%
+um this is via recoloring only thing
+initially we'll do is recoloring until
+
+ align:start position:0%
+initially we'll do is recoloring until
+ 
+
+ align:start position:0%
+initially we'll do is recoloring until
+we get to some
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+point where we can fix the violation
+
+ align:start position:0%
+point where we can fix the violation
+ 
+
+ align:start position:0%
+point where we can fix the violation
+using a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+rotation and probably also
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+recoloring okay so let's see this
+
+ align:start position:0%
+recoloring okay so let's see this
+ 
+
+ align:start position:0%
+recoloring okay so let's see this
+algorithm in
+
+ align:start position:0%
+algorithm in
+ 
+
+ align:start position:0%
+algorithm in
+action um I want to copy this tree and
+
+ align:start position:0%
+action um I want to copy this tree and
+ 
+
+ align:start position:0%
+action um I want to copy this tree and
+you're going to have to copy it too so
+
+ align:start position:0%
+you're going to have to copy it too so
+ 
+
+ align:start position:0%
+you're going to have to copy it too so
+I'll just redraw it instead of modifying
+
+ align:start position:0%
+I'll just redraw it instead of modifying
+ 
+
+ align:start position:0%
+I'll just redraw it instead of modifying
+that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+diagram so we have this nice red black
+
+ align:start position:0%
+diagram so we have this nice red black
+ 
+
+ align:start position:0%
+diagram so we have this nice red black
+tree and we'll try inserting a new value
+
+ align:start position:0%
+tree and we'll try inserting a new value
+ 
+
+ align:start position:0%
+tree and we'll try inserting a new value
+of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+15 22 is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+black 22 is the New
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Black okay that should be the same tree
+
+ align:start position:0%
+Black okay that should be the same tree
+ 
+
+ align:start position:0%
+Black okay that should be the same tree
+so now I'm I'm choosing the number 15 to
+
+ align:start position:0%
+so now I'm I'm choosing the number 15 to
+ 
+
+ align:start position:0%
+so now I'm I'm choosing the number 15 to
+insert because that will show a fairly
+
+ align:start position:0%
+insert because that will show a fairly
+ 
+
+ align:start position:0%
+insert because that will show a fairly
+interesting insertion sometimes
+
+ align:start position:0%
+interesting insertion sometimes
+ 
+
+ align:start position:0%
+interesting insertion sometimes
+insertion doesn't take very much work we
+
+ align:start position:0%
+insertion doesn't take very much work we
+ 
+
+ align:start position:0%
+insertion doesn't take very much work we
+just do a rotation and we're done um
+
+ align:start position:0%
+just do a rotation and we're done um
+ 
+
+ align:start position:0%
+just do a rotation and we're done um
+here I'd like to look at
+
+ align:start position:0%
+here I'd like to look at
+ 
+
+ align:start position:0%
+here I'd like to look at
+a an interesting case so we insert 15 15
+
+ align:start position:0%
+a an interesting case so we insert 15 15
+ 
+
+ align:start position:0%
+a an interesting case so we insert 15 15
+is bigger than seven it's less than 18
+
+ align:start position:0%
+is bigger than seven it's less than 18
+ 
+
+ align:start position:0%
+is bigger than seven it's less than 18
+it's bigger than 10 it's bigger than 11
+
+ align:start position:0%
+it's bigger than 10 it's bigger than 11
+ 
+
+ align:start position:0%
+it's bigger than 10 it's bigger than 11
+so 15 goes
+
+ align:start position:0%
+so 15 goes
+ 
+
+ align:start position:0%
+so 15 goes
+here so we add a new red node of 15 and
+
+ align:start position:0%
+here so we add a new red node of 15 and
+ 
+
+ align:start position:0%
+here so we add a new red node of 15 and
+it has two black leaves hanging off of
+
+ align:start position:0%
+it has two black leaves hanging off of
+ 
+
+ align:start position:0%
+it has two black leaves hanging off of
+it replaced one black Leaf now we have
+
+ align:start position:0%
+it replaced one black Leaf now we have
+ 
+
+ align:start position:0%
+it replaced one black Leaf now we have
+two okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+now we violate property three because we
+
+ align:start position:0%
+now we violate property three because we
+ 
+
+ align:start position:0%
+now we violate property three because we
+added a new red child of a red node so
+
+ align:start position:0%
+added a new red child of a red node so
+ 
+
+ align:start position:0%
+added a new red child of a red node so
+now we have two consecutive red nodes in
+
+ align:start position:0%
+now we have two consecutive red nodes in
+ 
+
+ align:start position:0%
+now we have two consecutive red nodes in
+a root to Leaf path we'd like to make
+
+ align:start position:0%
+a root to Leaf path we'd like to make
+ 
+
+ align:start position:0%
+a root to Leaf path we'd like to make
+this black but that would screw up the
+
+ align:start position:0%
+this black but that would screw up the
+ 
+
+ align:start position:0%
+this black but that would screw up the
+black Heights because now this node
+
+ align:start position:0%
+black Heights because now this node
+ 
+
+ align:start position:0%
+black Heights because now this node
+would have one black node over here and
+
+ align:start position:0%
+would have one black node over here and
+ 
+
+ align:start position:0%
+would have one black node over here and
+two black nodes down this path so that's
+
+ align:start position:0%
+two black nodes down this path so that's
+ 
+
+ align:start position:0%
+two black nodes down this path so that's
+not
+
+ align:start position:0%
+not
+ 
+
+ align:start position:0%
+not
+good what can we do well let's try to
+
+ align:start position:0%
+good what can we do well let's try to
+ 
+
+ align:start position:0%
+good what can we do well let's try to
+recolor um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+recolor
+
+ align:start position:0%
+recolor
+ 
+
+ align:start position:0%
+recolor
+yes this it's always uh takes a little
+
+ align:start position:0%
+yes this it's always uh takes a little
+ 
+
+ align:start position:0%
+yes this it's always uh takes a little
+while to remember
+
+ align:start position:0%
+while to remember
+ 
+
+ align:start position:0%
+while to remember
+so our fix is going to be to recolor and
+
+ align:start position:0%
+so our fix is going to be to recolor and
+ 
+
+ align:start position:0%
+so our fix is going to be to recolor and
+the first thing that struck me which
+
+ align:start position:0%
+the first thing that struck me which
+ 
+
+ align:start position:0%
+the first thing that struck me which
+doesn't work is we try to recolor around
+
+ align:start position:0%
+doesn't work is we try to recolor around
+ 
+
+ align:start position:0%
+doesn't work is we try to recolor around
+here it doesn't look so good cuz you
+
+ align:start position:0%
+here it doesn't look so good cuz you
+ 
+
+ align:start position:0%
+here it doesn't look so good cuz you
+know we've got red stuff down here but
+
+ align:start position:0%
+know we've got red stuff down here but
+ 
+
+ align:start position:0%
+know we've got red stuff down here but
+we've got a black note over here so we
+
+ align:start position:0%
+we've got a black note over here so we
+ 
+
+ align:start position:0%
+we've got a black note over here so we
+can't make this one red and this one
+
+ align:start position:0%
+can't make this one red and this one
+ 
+
+ align:start position:0%
+can't make this one red and this one
+black it wouldn't quite work uh if we
+
+ align:start position:0%
+black it wouldn't quite work uh if we
+ 
+
+ align:start position:0%
+black it wouldn't quite work uh if we
+look up a little higher at the
+
+ align:start position:0%
+look up a little higher at the
+ 
+
+ align:start position:0%
+look up a little higher at the
+grandparent of 15 up here we have a
+
+ align:start position:0%
+grandparent of 15 up here we have a
+ 
+
+ align:start position:0%
+grandparent of 15 up here we have a
+black node here and two red children
+
+ align:start position:0%
+black node here and two red children
+ 
+
+ align:start position:0%
+black node here and two red children
+that's actually pretty good news because
+
+ align:start position:0%
+that's actually pretty good news because
+ 
+
+ align:start position:0%
+that's actually pretty good news because
+we could instead make that two black
+
+ align:start position:0%
+we could instead make that two black
+ 
+
+ align:start position:0%
+we could instead make that two black
+children and a red parent okay locally
+
+ align:start position:0%
+children and a red parent okay locally
+ 
+
+ align:start position:0%
+children and a red parent okay locally
+that's going to be fine it's not going
+
+ align:start position:0%
+that's going to be fine it's not going
+ 
+
+ align:start position:0%
+that's going to be fine it's not going
+to change any black Heights because uh
+
+ align:start position:0%
+to change any black Heights because uh
+ 
+
+ align:start position:0%
+to change any black Heights because uh
+any path that went through these nodes
+
+ align:start position:0%
+any path that went through these nodes
+ 
+
+ align:start position:0%
+any path that went through these nodes
+before will still go through the same
+
+ align:start position:0%
+before will still go through the same
+ 
+
+ align:start position:0%
+before will still go through the same
+number of black nodes instead of going
+
+ align:start position:0%
+number of black nodes instead of going
+ 
+
+ align:start position:0%
+number of black nodes instead of going
+through a black node always here it will
+
+ align:start position:0%
+through a black node always here it will
+ 
+
+ align:start position:0%
+through a black node always here it will
+go through a black node either here or
+
+ align:start position:0%
+go through a black node either here or
+ 
+
+ align:start position:0%
+go through a black node either here or
+here CU paths always go down to the
+
+ align:start position:0%
+here CU paths always go down to the
+ 
+
+ align:start position:0%
+here CU paths always go down to the
+leaves so that's what we're going to do
+
+ align:start position:0%
+leaves so that's what we're going to do
+ 
+
+ align:start position:0%
+leaves so that's what we're going to do
+recolor these
+
+ align:start position:0%
+recolor these
+ 
+
+ align:start position:0%
+recolor these
+guys and we'll get 10 which is red we'll
+
+ align:start position:0%
+guys and we'll get 10 which is red we'll
+ 
+
+ align:start position:0%
+guys and we'll get 10 which is red we'll
+get eight which is black 11 which is
+
+ align:start position:0%
+get eight which is black 11 which is
+ 
+
+ align:start position:0%
+get eight which is black 11 which is
+black and these things don't change
+
+ align:start position:0%
+black and these things don't change
+ 
+
+ align:start position:0%
+black and these things don't change
+everything else doesn't change we're
+
+ align:start position:0%
+everything else doesn't change we're
+ 
+
+ align:start position:0%
+everything else doesn't change we're
+going to leave 15 red it's no longer in
+
+ align:start position:0%
+going to leave 15 red it's no longer in
+ 
+
+ align:start position:0%
+going to leave 15 red it's no longer in
+violation 15 is great cuz now it's
+
+ align:start position:0%
+violation 15 is great cuz now it's
+ 
+
+ align:start position:0%
+violation 15 is great cuz now it's
+parent is black we now have a new
+
+ align:start position:0%
+parent is black we now have a new
+ 
+
+ align:start position:0%
+parent is black we now have a new
+violation up here with with
+
+ align:start position:0%
+violation up here with with
+ 
+
+ align:start position:0%
+violation up here with with
+18 18 is also
+
+ align:start position:0%
+18 18 is also
+ 
+
+ align:start position:0%
+18 18 is also
+red that's the only violation we have in
+
+ align:start position:0%
+red that's the only violation we have in
+ 
+
+ align:start position:0%
+red that's the only violation we have in
+general we'll have at most one violation
+
+ align:start position:0%
+general we'll have at most one violation
+ 
+
+ align:start position:0%
+general we'll have at most one violation
+at any time till we fix it and we'll
+
+ align:start position:0%
+at any time till we fix it and we'll
+ 
+
+ align:start position:0%
+at any time till we fix it and we'll
+have zero
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+violations
+
+ align:start position:0%
+violations
+ 
+
+ align:start position:0%
+violations
+okay so now we have a violation between
+
+ align:start position:0%
+okay so now we have a violation between
+ 
+
+ align:start position:0%
+okay so now we have a violation between
+10 and 18
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+somehow always counterintuitive to me I
+
+ align:start position:0%
+somehow always counterintuitive to me I
+ 
+
+ align:start position:0%
+somehow always counterintuitive to me I
+have to look at the cheat sheet again
+
+ align:start position:0%
+have to look at the cheat sheet again
+ 
+
+ align:start position:0%
+have to look at the cheat sheet again
+all
+
+ align:start position:0%
+all
+ 
+
+ align:start position:0%
+all
+right
+
+ align:start position:0%
+right
+ 
+
+ align:start position:0%
+right
+really no okay good I was going to say
+
+ align:start position:0%
+really no okay good I was going to say
+ 
+
+ align:start position:0%
+really no okay good I was going to say
+we can't recolor anymore good I'm not
+
+ align:start position:0%
+we can't recolor anymore good I'm not
+ 
+
+ align:start position:0%
+we can't recolor anymore good I'm not
+that bad so what we'd like to do is
+
+ align:start position:0%
+that bad so what we'd like to do is
+ 
+
+ align:start position:0%
+that bad so what we'd like to do is
+again look at the grandparent of 10
+
+ align:start position:0%
+again look at the grandparent of 10
+ 
+
+ align:start position:0%
+again look at the grandparent of 10
+which is now seven the root of the tree
+
+ align:start position:0%
+which is now seven the root of the tree
+ 
+
+ align:start position:0%
+which is now seven the root of the tree
+it is black but it one of its children
+
+ align:start position:0%
+it is black but it one of its children
+ 
+
+ align:start position:0%
+it is black but it one of its children
+is black the other is red so we can't
+
+ align:start position:0%
+is black the other is red so we can't
+ 
+
+ align:start position:0%
+is black the other is red so we can't
+play the same game of taking the
+
+ align:start position:0%
+play the same game of taking the
+ 
+
+ align:start position:0%
+play the same game of taking the
+Blackness of and moving it down to the
+
+ align:start position:0%
+Blackness of and moving it down to the
+ 
+
+ align:start position:0%
+Blackness of and moving it down to the
+two children never mind that the Root's
+
+ align:start position:0%
+two children never mind that the Root's
+ 
+
+ align:start position:0%
+two children never mind that the Root's
+supposed to stay black we'll ignore that
+
+ align:start position:0%
+supposed to stay black we'll ignore that
+ 
+
+ align:start position:0%
+supposed to stay black we'll ignore that
+property for now we can't make these two
+
+ align:start position:0%
+property for now we can't make these two
+ 
+
+ align:start position:0%
+property for now we can't make these two
+black and make this one red because then
+
+ align:start position:0%
+black and make this one red because then
+ 
+
+ align:start position:0%
+black and make this one red because then
+we'd get an imbalance this one was
+
+ align:start position:0%
+we'd get an imbalance this one was
+ 
+
+ align:start position:0%
+we'd get an imbalance this one was
+already black so now paths going down
+
+ align:start position:0%
+already black so now paths going down
+ 
+
+ align:start position:0%
+already black so now paths going down
+here will have one fewer black node then
+
+ align:start position:0%
+here will have one fewer black node then
+ 
+
+ align:start position:0%
+here will have one fewer black node then
+paths going down here so we can't just
+
+ align:start position:0%
+paths going down here so we can't just
+ 
+
+ align:start position:0%
+paths going down here so we can't just
+recolor seven in its children so instead
+
+ align:start position:0%
+recolor seven in its children so instead
+ 
+
+ align:start position:0%
+recolor seven in its children so instead
+we've got to do a rotation we better be
+
+ align:start position:0%
+we've got to do a rotation we better be
+ 
+
+ align:start position:0%
+we've got to do a rotation we better be
+near the end so what I will do is rotate
+
+ align:start position:0%
+near the end so what I will do is rotate
+ 
+
+ align:start position:0%
+near the end so what I will do is rotate
+this Edge I'm going to rotate eight to
+
+ align:start position:0%
+this Edge I'm going to rotate eight to
+ 
+
+ align:start position:0%
+this Edge I'm going to rotate eight to
+to the
+
+ align:start position:0%
+to the
+ 
+
+ align:start position:0%
+to the
+right so that's the next
+
+ align:start position:0%
+right so that's the next
+ 
+
+ align:start position:0%
+right so that's the next
+operation
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+rotate right of 18
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+there'll be one more operation after
+
+ align:start position:0%
+there'll be one more operation after
+ 
+
+ align:start position:0%
+there'll be one more operation after
+this so we rotate right 18 so the root
+
+ align:start position:0%
+this so we rotate right 18 so the root
+ 
+
+ align:start position:0%
+this so we rotate right 18 so the root
+stays the same 7 three it's
+
+ align:start position:0%
+stays the same 7 three it's
+ 
+
+ align:start position:0%
+stays the same 7 three it's
+children now the right child of seven is
+
+ align:start position:0%
+children now the right child of seven is
+ 
+
+ align:start position:0%
+children now the right child of seven is
+no longer 18 is now
+
+ align:start position:0%
+no longer 18 is now
+ 
+
+ align:start position:0%
+no longer 18 is now
+10 18 becomes the right child of
+
+ align:start position:0%
+10 18 becomes the right child of
+ 
+
+ align:start position:0%
+10 18 becomes the right child of
+10 okay we have eight over
+
+ align:start position:0%
+10 okay we have eight over
+ 
+
+ align:start position:0%
+10 okay we have eight over
+here with its two children
+
+ align:start position:0%
+here with its two children
+ 
+
+ align:start position:0%
+here with its two children
+11 and 15 that sub tree fits in between
+
+ align:start position:0%
+11 and 15 that sub tree fits in between
+ 
+
+ align:start position:0%
+11 and 15 that sub tree fits in between
+10 and 18 so it goes
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+here 11 and
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+15 and then there's the right subtree
+
+ align:start position:0%
+15 and then there's the right subtree
+ 
+
+ align:start position:0%
+15 and then there's the right subtree
+everything to the right of 18 that goes
+
+ align:start position:0%
+everything to the right of 18 that goes
+ 
+
+ align:start position:0%
+everything to the right of 18 that goes
+over here
+
+ align:start position:0%
+over here
+ 
+
+ align:start position:0%
+over here
+22 and
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+26 and hopefully I'm not changing any
+
+ align:start position:0%
+26 and hopefully I'm not changing any
+ 
+
+ align:start position:0%
+26 and hopefully I'm not changing any
+colors during that
+
+ align:start position:0%
+colors during that
+ 
+
+ align:start position:0%
+colors during that
+operation if I did let me know okay
+
+ align:start position:0%
+operation if I did let me know okay
+ 
+
+ align:start position:0%
+operation if I did let me know okay
+looks good so I still have this
+
+ align:start position:0%
+looks good so I still have this
+ 
+
+ align:start position:0%
+looks good so I still have this
+violation still in trouble between 10
+
+ align:start position:0%
+violation still in trouble between 10
+ 
+
+ align:start position:0%
+violation still in trouble between 10
+and 18 but I've made this straighter
+
+ align:start position:0%
+and 18 but I've made this straighter
+ 
+
+ align:start position:0%
+and 18 but I've made this straighter
+okay that's what we want to do it turns
+
+ align:start position:0%
+okay that's what we want to do it turns
+ 
+
+ align:start position:0%
+okay that's what we want to do it turns
+out is make the connection between 18
+
+ align:start position:0%
+out is make the connection between 18
+ 
+
+ align:start position:0%
+out is make the connection between 18
+The Violator and its grandparent a
+
+ align:start position:0%
+The Violator and its grandparent a
+ 
+
+ align:start position:0%
+The Violator and its grandparent a
+straight connection two rights or two
+
+ align:start position:0%
+straight connection two rights or two
+ 
+
+ align:start position:0%
+straight connection two rights or two
+lefts here we had a zigzag right left
+
+ align:start position:0%
+lefts here we had a zigzag right left
+ 
+
+ align:start position:0%
+lefts here we had a zigzag right left
+like to make it straight okay it doesn't
+
+ align:start position:0%
+like to make it straight okay it doesn't
+ 
+
+ align:start position:0%
+like to make it straight okay it doesn't
+look like a much more balanced tree than
+
+ align:start position:0%
+look like a much more balanced tree than
+ 
+
+ align:start position:0%
+look like a much more balanced tree than
+this one in fact it looks a little worse
+
+ align:start position:0%
+this one in fact it looks a little worse
+ 
+
+ align:start position:0%
+this one in fact it looks a little worse
+but what we can do is now rotate these
+
+ align:start position:0%
+but what we can do is now rotate these
+ 
+
+ align:start position:0%
+but what we can do is now rotate these
+guys or rather rotate this Edge I'm
+
+ align:start position:0%
+guys or rather rotate this Edge I'm
+ 
+
+ align:start position:0%
+guys or rather rotate this Edge I'm
+going to rotate seven to the left make
+
+ align:start position:0%
+going to rotate seven to the left make
+ 
+
+ align:start position:0%
+going to rotate seven to the left make
+10 the root and then things will start
+
+ align:start position:0%
+10 the root and then things will start
+ 
+
+ align:start position:0%
+10 the root and then things will start
+to look
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+balanced this is a rotate
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+left of
+
+ align:start position:0%
+left of
+ 
+
+ align:start position:0%
+left of
+seven and I'm also going to do some
+
+ align:start position:0%
+seven and I'm also going to do some
+ 
+
+ align:start position:0%
+seven and I'm also going to do some
+recoloring
+
+ align:start position:0%
+recoloring
+ 
+
+ align:start position:0%
+recoloring
+at the same time just to save me drawing
+
+ align:start position:0%
+at the same time just to save me drawing
+ 
+
+ align:start position:0%
+at the same time just to save me drawing
+one more picture because the root has to
+
+ align:start position:0%
+one more picture because the root has to
+ 
+
+ align:start position:0%
+one more picture because the root has to
+be black I'm going to make 10 black
+
+ align:start position:0%
+be black I'm going to make 10 black
+ 
+
+ align:start position:0%
+be black I'm going to make 10 black
+immediately I'll make seven red that's
+
+ align:start position:0%
+immediately I'll make seven red that's
+ 
+
+ align:start position:0%
+immediately I'll make seven red that's
+the change and then the rest is just a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+rotation so we have 18 over here think I
+
+ align:start position:0%
+rotation so we have 18 over here think I
+ 
+
+ align:start position:0%
+rotation so we have 18 over here think I
+actually have to rotate in order to keep
+
+ align:start position:0%
+actually have to rotate in order to keep
+ 
+
+ align:start position:0%
+actually have to rotate in order to keep
+some red Blackness here
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+eight comes be between seven and 10 so
+
+ align:start position:0%
+eight comes be between seven and 10 so
+ 
+
+ align:start position:0%
+eight comes be between seven and 10 so
+it goes
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+here 11 goes between 10 and 18 so it
+
+ align:start position:0%
+here 11 goes between 10 and 18 so it
+ 
+
+ align:start position:0%
+here 11 goes between 10 and 18 so it
+goes
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+here 22 and 26 come after 18
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay now if I'm lucky I should satisfy
+
+ align:start position:0%
+okay now if I'm lucky I should satisfy
+ 
+
+ align:start position:0%
+okay now if I'm lucky I should satisfy
+all the properties that I want every
+
+ align:start position:0%
+all the properties that I want every
+ 
+
+ align:start position:0%
+all the properties that I want every
+node is red or black uh every red node
+
+ align:start position:0%
+node is red or black uh every red node
+ 
+
+ align:start position:0%
+node is red or black uh every red node
+has a black child this is the last place
+
+ align:start position:0%
+has a black child this is the last place
+ 
+
+ align:start position:0%
+has a black child this is the last place
+we changed red nodes have black children
+
+ align:start position:0%
+we changed red nodes have black children
+ 
+
+ align:start position:0%
+we changed red nodes have black children
+and all the black Heights should be well
+
+ align:start position:0%
+and all the black Heights should be well
+ 
+
+ align:start position:0%
+and all the black Heights should be well
+defined for for every node the number of
+
+ align:start position:0%
+defined for for every node the number of
+ 
+
+ align:start position:0%
+defined for for every node the number of
+uh black nodes along any root any node
+
+ align:start position:0%
+uh black nodes along any root any node
+ 
+
+ align:start position:0%
+uh black nodes along any root any node
+to Leaf path is the
+
+ align:start position:0%
+to Leaf path is the
+ 
+
+ align:start position:0%
+to Leaf path is the
+same and you check that was true before
+
+ align:start position:0%
+same and you check that was true before
+ 
+
+ align:start position:0%
+same and you check that was true before
+and I did a little bit of trickery with
+
+ align:start position:0%
+and I did a little bit of trickery with
+ 
+
+ align:start position:0%
+and I did a little bit of trickery with
+the recoloring here but it's still true
+
+ align:start position:0%
+the recoloring here but it's still true
+ 
+
+ align:start position:0%
+the recoloring here but it's still true
+okay and you can check that just locally
+
+ align:start position:0%
+okay and you can check that just locally
+ 
+
+ align:start position:0%
+okay and you can check that just locally
+around this rotation okay we'll do that
+
+ align:start position:0%
+around this rotation okay we'll do that
+ 
+
+ align:start position:0%
+around this rotation okay we'll do that
+in a little bit for now it's just an
+
+ align:start position:0%
+in a little bit for now it's just an
+ 
+
+ align:start position:0%
+in a little bit for now it's just an
+example it's not probably not terribly
+
+ align:start position:0%
+example it's not probably not terribly
+ 
+
+ align:start position:0%
+example it's not probably not terribly
+clear where these recoloring and
+
+ align:start position:0%
+clear where these recoloring and
+ 
+
+ align:start position:0%
+clear where these recoloring and
+rotations come from necessarily but it
+
+ align:start position:0%
+rotations come from necessarily but it
+ 
+
+ align:start position:0%
+rotations come from necessarily but it
+worked that at least convinces you that
+
+ align:start position:0%
+worked that at least convinces you that
+ 
+
+ align:start position:0%
+worked that at least convinces you that
+it it's
+
+ align:start position:0%
+it it's
+ 
+
+ align:start position:0%
+it it's
+possible and now we'll give a general
+
+ align:start position:0%
+possible and now we'll give a general
+ 
+
+ align:start position:0%
+possible and now we'll give a general
+algorithm for doing it any questions
+
+ align:start position:0%
+algorithm for doing it any questions
+ 
+
+ align:start position:0%
+algorithm for doing it any questions
+before we go
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+on
+
+ align:start position:0%
+on
+ 
+
+ align:start position:0%
+on
+so it's not exactly uh
+
+ align:start position:0%
+so it's not exactly uh
+ 
+
+ align:start position:0%
+so it's not exactly uh
+I mean just writing down the algorithm
+
+ align:start position:0%
+I mean just writing down the algorithm
+ 
+
+ align:start position:0%
+I mean just writing down the algorithm
+is not terribly
+
+ align:start position:0%
+is not terribly
+ 
+
+ align:start position:0%
+is not terribly
+intuitive it's red black trees are the
+
+ align:start position:0%
+intuitive it's red black trees are the
+ 
+
+ align:start position:0%
+intuitive it's red black trees are the
+sort of thing where you play around a
+
+ align:start position:0%
+sort of thing where you play around a
+ 
+
+ align:start position:0%
+sort of thing where you play around a
+bit you you say okay I'm going to just
+
+ align:start position:0%
+bit you you say okay I'm going to just
+ 
+
+ align:start position:0%
+bit you you say okay I'm going to just
+think about recoloring and rotations
+
+ align:start position:0%
+think about recoloring and rotations
+ 
+
+ align:start position:0%
+think about recoloring and rotations
+let's restrict myself to those
+
+ align:start position:0%
+let's restrict myself to those
+ 
+
+ align:start position:0%
+let's restrict myself to those
+operations what could I do well I try to
+
+ align:start position:0%
+operations what could I do well I try to
+ 
+
+ align:start position:0%
+operations what could I do well I try to
+recolor if that works great pushes the
+
+ align:start position:0%
+recolor if that works great pushes the
+ 
+
+ align:start position:0%
+recolor if that works great pushes the
+problem up higher and there's only log n
+
+ align:start position:0%
+problem up higher and there's only log n
+ 
+
+ align:start position:0%
+problem up higher and there's only log n
+levels order order log n levels so
+
+ align:start position:0%
+levels order order log n levels so
+ 
+
+ align:start position:0%
+levels order order log n levels so
+that's going to take order log and time
+
+ align:start position:0%
+that's going to take order log and time
+ 
+
+ align:start position:0%
+that's going to take order log and time
+at some point I'll get stuck I can't
+
+ align:start position:0%
+at some point I'll get stuck I can't
+ 
+
+ align:start position:0%
+at some point I'll get stuck I can't
+recolor anymore then it turns out a
+
+ align:start position:0%
+recolor anymore then it turns out a
+ 
+
+ align:start position:0%
+recolor anymore then it turns out a
+couple of rotations will do it always
+
+ align:start position:0%
+couple of rotations will do it always
+ 
+
+ align:start position:0%
+couple of rotations will do it always
+two rotations will
+
+ align:start position:0%
+two rotations will
+ 
+
+ align:start position:0%
+two rotations will
+suffice and you just play with it and
+
+ align:start position:0%
+suffice and you just play with it and
+ 
+
+ align:start position:0%
+suffice and you just play with it and
+and that turns out to
+
+ align:start position:0%
+and that turns out to
+ 
+
+ align:start position:0%
+and that turns out to
+work and here's
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+how Okay so let's suppose we have a a
+
+ align:start position:0%
+how Okay so let's suppose we have a a
+ 
+
+ align:start position:0%
+how Okay so let's suppose we have a a
+red black tree and an value X we want to
+
+ align:start position:0%
+red black tree and an value X we want to
+ 
+
+ align:start position:0%
+red black tree and an value X we want to
+insert here's the algorithm first we
+
+ align:start position:0%
+insert here's the algorithm first we
+ 
+
+ align:start position:0%
+insert here's the algorithm first we
+insert it into the
+
+ align:start position:0%
+insert it into the
+ 
+
+ align:start position:0%
+insert it into the
+BST so that we know
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+then we color the node red and here I'm
+
+ align:start position:0%
+then we color the node red and here I'm
+ 
+
+ align:start position:0%
+then we color the node red and here I'm
+going to use a slightly more precise
+
+ align:start position:0%
+going to use a slightly more precise
+ 
+
+ align:start position:0%
+going to use a slightly more precise
+notation color is a field of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+X and now we're going to walk our way up
+
+ align:start position:0%
+X and now we're going to walk our way up
+ 
+
+ align:start position:0%
+X and now we're going to walk our way up
+the tree with a Y Loop until we get to
+
+ align:start position:0%
+the tree with a Y Loop until we get to
+ 
+
+ align:start position:0%
+the tree with a Y Loop until we get to
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+root
+
+ align:start position:0%
+root
+ 
+
+ align:start position:0%
+root
+or until we reach a black
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+node so so in general X initially is
+
+ align:start position:0%
+node so so in general X initially is
+ 
+
+ align:start position:0%
+node so so in general X initially is
+going to be the element that we inserted
+
+ align:start position:0%
+going to be the element that we inserted
+ 
+
+ align:start position:0%
+going to be the element that we inserted
+but we're going to move X up the tree if
+
+ align:start position:0%
+but we're going to move X up the tree if
+ 
+
+ align:start position:0%
+but we're going to move X up the tree if
+ever we find that X is a black node
+
+ align:start position:0%
+ever we find that X is a black node
+ 
+
+ align:start position:0%
+ever we find that X is a black node
+we're happy because maybe it's parent is
+
+ align:start position:0%
+we're happy because maybe it's parent is
+ 
+
+ align:start position:0%
+we're happy because maybe it's parent is
+red maybe it isn't I don't care black
+
+ align:start position:0%
+red maybe it isn't I don't care black
+ 
+
+ align:start position:0%
+red maybe it isn't I don't care black
+nodes can have arbitrarily colored
+
+ align:start position:0%
+nodes can have arbitrarily colored
+ 
+
+ align:start position:0%
+nodes can have arbitrarily colored
+parents it's red nodes that we worry
+
+ align:start position:0%
+parents it's red nodes that we worry
+ 
+
+ align:start position:0%
+parents it's red nodes that we worry
+about and so if x is red we have to keep
+
+ align:start position:0%
+about and so if x is red we have to keep
+ 
+
+ align:start position:0%
+about and so if x is red we have to keep
+doing this
+
+ align:start position:0%
+doing this
+ 
+
+ align:start position:0%
+doing this
+Loop uh of course just wrote the wrong
+
+ align:start position:0%
+Loop uh of course just wrote the wrong
+ 
+
+ align:start position:0%
+Loop uh of course just wrote the wrong
+one while the color is red we're going
+
+ align:start position:0%
+one while the color is red we're going
+ 
+
+ align:start position:0%
+one while the color is red we're going
+to keep doing this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so there are three
+
+ align:start position:0%
+so there are three
+ 
+
+ align:start position:0%
+so there are three
+cases well or six depending on how you
+
+ align:start position:0%
+cases well or six depending on how you
+ 
+
+ align:start position:0%
+cases well or six depending on how you
+count that's what makes this a little
+
+ align:start position:0%
+count that's what makes this a little
+ 
+
+ align:start position:0%
+count that's what makes this a little
+bit tricky to
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+memorize okay but there are some
+
+ align:start position:0%
+memorize okay but there are some
+ 
+
+ align:start position:0%
+memorize okay but there are some
+symmetric uh situations let me draw
+
+ align:start position:0%
+symmetric uh situations let me draw
+ 
+
+ align:start position:0%
+symmetric uh situations let me draw
+them what we care about I've argued is
+
+ align:start position:0%
+them what we care about I've argued is
+ 
+
+ align:start position:0%
+them what we care about I've argued is
+between X and it's grandparent so I'm
+
+ align:start position:0%
+between X and it's grandparent so I'm
+ 
+
+ align:start position:0%
+between X and it's grandparent so I'm
+using p of X here to denote parent of X
+
+ align:start position:0%
+using p of X here to denote parent of X
+ 
+
+ align:start position:0%
+using p of X here to denote parent of X
+just because it's shorter so P of P of X
+
+ align:start position:0%
+just because it's shorter so P of P of X
+ 
+
+ align:start position:0%
+just because it's shorter so P of P of X
+is X is
+
+ align:start position:0%
+is X is
+ 
+
+ align:start position:0%
+is X is
+grandparent left of P of P of X is the
+
+ align:start position:0%
+grandparent left of P of P of X is the
+ 
+
+ align:start position:0%
+grandparent left of P of P of X is the
+left child so what I'm interested in is
+
+ align:start position:0%
+left child so what I'm interested in is
+ 
+
+ align:start position:0%
+left child so what I'm interested in is
+I look at X and if I don't assign any
+
+ align:start position:0%
+I look at X and if I don't assign any
+ 
+
+ align:start position:0%
+I look at X and if I don't assign any
+directions you know X is the child of
+
+ align:start position:0%
+directions you know X is the child of
+ 
+
+ align:start position:0%
+directions you know X is the child of
+some P of X
+
+ align:start position:0%
+some P of X
+ 
+
+ align:start position:0%
+some P of X
+and P of X is the parent of is the child
+
+ align:start position:0%
+and P of X is the parent of is the child
+ 
+
+ align:start position:0%
+and P of X is the parent of is the child
+of the grandparent P of P of X now these
+
+ align:start position:0%
+of the grandparent P of P of X now these
+ 
+
+ align:start position:0%
+of the grandparent P of P of X now these
+edges aren't vertical they're either
+
+ align:start position:0%
+edges aren't vertical they're either
+ 
+
+ align:start position:0%
+edges aren't vertical they're either
+left or right and I care about which one
+
+ align:start position:0%
+left or right and I care about which one
+ 
+
+ align:start position:0%
+left or right and I care about which one
+in particular I'm looking at whether the
+
+ align:start position:0%
+in particular I'm looking at whether the
+ 
+
+ align:start position:0%
+in particular I'm looking at whether the
+parent is the left child of of the
+
+ align:start position:0%
+parent is the left child of of the
+ 
+
+ align:start position:0%
+parent is the left child of of the
+grandparent so I want to know does it
+
+ align:start position:0%
+grandparent so I want to know does it
+ 
+
+ align:start position:0%
+grandparent so I want to know does it
+look
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+like
+
+ align:start position:0%
+like
+ 
+
+ align:start position:0%
+like
+this okay and I don't know whether X is
+
+ align:start position:0%
+this okay and I don't know whether X is
+ 
+
+ align:start position:0%
+this okay and I don't know whether X is
+to the left or to the right of the
+
+ align:start position:0%
+to the left or to the right of the
+ 
+
+ align:start position:0%
+to the left or to the right of the
+parent but is parent of X the left child
+
+ align:start position:0%
+parent but is parent of X the left child
+ 
+
+ align:start position:0%
+parent but is parent of X the left child
+of P of P of X or is it the right
+
+ align:start position:0%
+of P of P of X or is it the right
+ 
+
+ align:start position:0%
+of P of P of X or is it the right
+child and these two cases are totally
+
+ align:start position:0%
+child and these two cases are totally
+ 
+
+ align:start position:0%
+child and these two cases are totally
+symmetric but I need to assume it's one
+
+ align:start position:0%
+symmetric but I need to assume it's one
+ 
+
+ align:start position:0%
+symmetric but I need to assume it's one
+way or the other other otherwise I can't
+
+ align:start position:0%
+way or the other other otherwise I can't
+ 
+
+ align:start position:0%
+way or the other other otherwise I can't
+draw the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+pictures Okay so this will be let's call
+
+ align:start position:0%
+pictures Okay so this will be let's call
+ 
+
+ align:start position:0%
+pictures Okay so this will be let's call
+it category a and this is category B and
+
+ align:start position:0%
+it category a and this is category B and
+ 
+
+ align:start position:0%
+it category a and this is category B and
+I'm going to tell you what to do in
+
+ align:start position:0%
+I'm going to tell you what to do in
+ 
+
+ align:start position:0%
+I'm going to tell you what to do in
+category a and category B is symmetric
+
+ align:start position:0%
+category a and category B is symmetric
+ 
+
+ align:start position:0%
+category a and category B is symmetric
+you just flip left and right okay so
+
+ align:start position:0%
+you just flip left and right okay so
+ 
+
+ align:start position:0%
+you just flip left and right okay so
+this this is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+a So within category a there are three
+
+ align:start position:0%
+a So within category a there are three
+ 
+
+ align:start position:0%
+a So within category a there are three
+cases and within category B there's the
+
+ align:start position:0%
+cases and within category B there's the
+ 
+
+ align:start position:0%
+cases and within category B there's the
+same three cases just
+
+ align:start position:0%
+same three cases just
+ 
+
+ align:start position:0%
+same three cases just
+reversed so what we're going to do is
+
+ align:start position:0%
+reversed so what we're going to do is
+ 
+
+ align:start position:0%
+reversed so what we're going to do is
+look at the other child of the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+grandparent this is one reason why we
+
+ align:start position:0%
+grandparent this is one reason why we
+ 
+
+ align:start position:0%
+grandparent this is one reason why we
+sort of need to know which way we're
+
+ align:start position:0%
+sort of need to know which way we're
+ 
+
+ align:start position:0%
+sort of need to know which way we're
+looking um if the parent of X is the
+
+ align:start position:0%
+looking um if the parent of X is the
+ 
+
+ align:start position:0%
+looking um if the parent of X is the
+left child of the grandparent we're
+
+ align:start position:0%
+left child of the grandparent we're
+ 
+
+ align:start position:0%
+left child of the grandparent we're
+going to look at the other child of the
+
+ align:start position:0%
+going to look at the other child of the
+ 
+
+ align:start position:0%
+going to look at the other child of the
+grandparent which would be the right
+
+ align:start position:0%
+grandparent which would be the right
+ 
+
+ align:start position:0%
+grandparent which would be the right
+child of the grandparent call that node
+
+ align:start position:0%
+child of the grandparent call that node
+ 
+
+ align:start position:0%
+child of the grandparent call that node
+y this is also known as the uncle or the
+
+ align:start position:0%
+y this is also known as the uncle or the
+ 
+
+ align:start position:0%
+y this is also known as the uncle or the
+aunt of X depending on whether Y is male
+
+ align:start position:0%
+aunt of X depending on whether Y is male
+ 
+
+ align:start position:0%
+aunt of X depending on whether Y is male
+or
+
+ align:start position:0%
+or
+ 
+
+ align:start position:0%
+or
+female okay so this is Uncle or Aunt
+
+ align:start position:0%
+female okay so this is Uncle or Aunt
+ 
+
+ align:start position:0%
+female okay so this is Uncle or Aunt
+unfortunately in English there is no
+
+ align:start position:0%
+unfortunately in English there is no
+ 
+
+ align:start position:0%
+unfortunately in English there is no
+gender-free version of this as far as I
+
+ align:start position:0%
+gender-free version of this as far as I
+ 
+
+ align:start position:0%
+gender-free version of this as far as I
+know with parent child but no uncle aunt
+
+ align:start position:0%
+know with parent child but no uncle aunt
+ 
+
+ align:start position:0%
+know with parent child but no uncle aunt
+I'm sure we could come up with
+
+ align:start position:0%
+I'm sure we could come up with
+ 
+
+ align:start position:0%
+I'm sure we could come up with
+one I'm not going to try it's going to
+
+ align:start position:0%
+one I'm not going to try it's going to
+ 
+
+ align:start position:0%
+one I'm not going to try it's going to
+sound
+
+ align:start position:0%
+sound
+ 
+
+ align:start position:0%
+sound
+bad um all right so why do I care about
+
+ align:start position:0%
+bad um all right so why do I care about
+ 
+
+ align:start position:0%
+bad um all right so why do I care about
+why because I want to see if I can do
+
+ align:start position:0%
+why because I want to see if I can do
+ 
+
+ align:start position:0%
+why because I want to see if I can do
+this recoloring step the recoloring idea
+
+ align:start position:0%
+this recoloring step the recoloring idea
+ 
+
+ align:start position:0%
+this recoloring step the recoloring idea
+was well the grandparent is let's say
+
+ align:start position:0%
+was well the grandparent is let's say
+ 
+
+ align:start position:0%
+was well the grandparent is let's say
+it's black if I can push the Blackness
+
+ align:start position:0%
+it's black if I can push the Blackness
+ 
+
+ align:start position:0%
+it's black if I can push the Blackness
+of the parent of the grandparent down
+
+ align:start position:0%
+of the parent of the grandparent down
+ 
+
+ align:start position:0%
+of the parent of the grandparent down
+into the two
+
+ align:start position:0%
+into the two
+ 
+
+ align:start position:0%
+into the two
+children then if both of these are red
+
+ align:start position:0%
+children then if both of these are red
+ 
+
+ align:start position:0%
+children then if both of these are red
+in other words then I'd be happy then I
+
+ align:start position:0%
+in other words then I'd be happy then I
+ 
+
+ align:start position:0%
+in other words then I'd be happy then I
+push the problem up this guy's Now red
+
+ align:start position:0%
+push the problem up this guy's Now red
+ 
+
+ align:start position:0%
+push the problem up this guy's Now red
+this guy's black so these two are all
+
+ align:start position:0%
+this guy's black so these two are all
+ 
+
+ align:start position:0%
+this guy's black so these two are all
+right this one may violate the
+
+ align:start position:0%
+right this one may violate the
+ 
+
+ align:start position:0%
+right this one may violate the
+great-grandparent but we'll just keep
+
+ align:start position:0%
+great-grandparent but we'll just keep
+ 
+
+ align:start position:0%
+great-grandparent but we'll just keep
+going up and that will be fine so if
+
+ align:start position:0%
+going up and that will be fine so if
+ 
+
+ align:start position:0%
+going up and that will be fine so if
+we're lucky Y is red then we can just do
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+recoloring so if the color of
+
+ align:start position:0%
+recoloring so if the color of
+ 
+
+ align:start position:0%
+recoloring so if the color of
+Y is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+red
+
+ align:start position:0%
+red
+ 
+
+ align:start position:0%
+red
+then we will recolor and I'm going to
+
+ align:start position:0%
+then we will recolor and I'm going to
+ 
+
+ align:start position:0%
+then we will recolor and I'm going to
+defer this to a picture called case
+
+ align:start position:0%
+defer this to a picture called case
+ 
+
+ align:start position:0%
+defer this to a picture called case
+one okay let me first tell you how the
+
+ align:start position:0%
+one okay let me first tell you how the
+ 
+
+ align:start position:0%
+one okay let me first tell you how the
+cases break up and then we'll see how
+
+ align:start position:0%
+cases break up and then we'll see how
+ 
+
+ align:start position:0%
+cases break up and then we'll see how
+they
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+[Applause]
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+work so if we're not in case one so this
+
+ align:start position:0%
+work so if we're not in case one so this
+ 
+
+ align:start position:0%
+work so if we're not in case one so this
+else should be aligned with that
+
+ align:start position:0%
+else should be aligned with that
+ 
+
+ align:start position:0%
+else should be aligned with that
+then then we're either in case two or
+
+ align:start position:0%
+then then we're either in case two or
+ 
+
+ align:start position:0%
+then then we're either in case two or
+three so here's the
+
+ align:start position:0%
+three so here's the
+ 
+
+ align:start position:0%
+three so here's the
+the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+dichotomy it turns out we've actually
+
+ align:start position:0%
+dichotomy it turns out we've actually
+ 
+
+ align:start position:0%
+dichotomy it turns out we've actually
+seen all of the cases maybe not a versus
+
+ align:start position:0%
+seen all of the cases maybe not a versus
+ 
+
+ align:start position:0%
+seen all of the cases maybe not a versus
+B but we've seen the case in the very
+
+ align:start position:0%
+B but we've seen the case in the very
+ 
+
+ align:start position:0%
+B but we've seen the case in the very
+beginning where we just recolored that's
+
+ align:start position:0%
+beginning where we just recolored that's
+ 
+
+ align:start position:0%
+beginning where we just recolored that's
+case one the next thing we saw is what
+
+ align:start position:0%
+case one the next thing we saw is what
+ 
+
+ align:start position:0%
+case one the next thing we saw is what
+well it was kind of annoying that the
+
+ align:start position:0%
+well it was kind of annoying that the
+ 
+
+ align:start position:0%
+well it was kind of annoying that the
+grandparent and 10 so seven and 10 were
+
+ align:start position:0%
+grandparent and 10 so seven and 10 were
+ 
+
+ align:start position:0%
+grandparent and 10 so seven and 10 were
+not straight they were zigzagged so case
+
+ align:start position:0%
+not straight they were zigzagged so case
+ 
+
+ align:start position:0%
+not straight they were zigzagged so case
+two is when they're
+
+ align:start position:0%
+two is when they're
+ 
+
+ align:start position:0%
+two is when they're
+zigzagged turns out that's
+
+ align:start position:0%
+zigzagged turns out that's
+ 
+
+ align:start position:0%
+zigzagged turns out that's
+uh if x is the right of the you know if
+
+ align:start position:0%
+uh if x is the right of the you know if
+ 
+
+ align:start position:0%
+uh if x is the right of the you know if
+x is the right child of its parent and
+
+ align:start position:0%
+x is the right child of its parent and
+ 
+
+ align:start position:0%
+x is the right child of its parent and
+the parent is the left child of the
+
+ align:start position:0%
+the parent is the left child of the
+ 
+
+ align:start position:0%
+the parent is the left child of the
+grandparent that's what we've assumed so
+
+ align:start position:0%
+grandparent that's what we've assumed so
+ 
+
+ align:start position:0%
+grandparent that's what we've assumed so
+far that is case
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+two okay the other case is that X is the
+
+ align:start position:0%
+two okay the other case is that X is the
+ 
+
+ align:start position:0%
+two okay the other case is that X is the
+left child of its parent so then we have
+
+ align:start position:0%
+left child of its parent so then we have
+ 
+
+ align:start position:0%
+left child of its parent so then we have
+a left chain X parent of X grandparent
+
+ align:start position:0%
+a left chain X parent of X grandparent
+ 
+
+ align:start position:0%
+a left chain X parent of X grandparent
+of X that is case three
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay I did not write else here because
+
+ align:start position:0%
+okay I did not write else here because
+ 
+
+ align:start position:0%
+okay I did not write else here because
+what case two does is it reduces to case
+
+ align:start position:0%
+what case two does is it reduces to case
+ 
+
+ align:start position:0%
+what case two does is it reduces to case
+three so in case two we're going to do
+
+ align:start position:0%
+three so in case two we're going to do
+ 
+
+ align:start position:0%
+three so in case two we're going to do
+the stuff that's here and then we're
+
+ align:start position:0%
+the stuff that's here and then we're
+ 
+
+ align:start position:0%
+the stuff that's here and then we're
+going to do the stuff here we're in case
+
+ align:start position:0%
+going to do the stuff here we're in case
+ 
+
+ align:start position:0%
+going to do the stuff here we're in case
+three we just do the stuff here we're in
+
+ align:start position:0%
+three we just do the stuff here we're in
+ 
+
+ align:start position:0%
+three we just do the stuff here we're in
+case one we just do the stuff
+
+ align:start position:0%
+case one we just do the stuff
+ 
+
+ align:start position:0%
+case one we just do the stuff
+here and then that finishes the three
+
+ align:start position:0%
+here and then that finishes the three
+ 
+
+ align:start position:0%
+here and then that finishes the three
+cases on the a side then up back to this
+
+ align:start position:0%
+cases on the a side then up back to this
+ 
+
+ align:start position:0%
+cases on the a side then up back to this
+if uh we say else this is case b
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um which is the same as
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+a but reversing the Notions of left and
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+right okay in the
+
+ align:start position:0%
+right okay in the
+ 
+
+ align:start position:0%
+right okay in the
+natural natural way every time we write
+
+ align:start position:0%
+natural natural way every time we write
+ 
+
+ align:start position:0%
+natural natural way every time we write
+left of something we instead write right
+
+ align:start position:0%
+left of something we instead write right
+ 
+
+ align:start position:0%
+left of something we instead write right
+of something and vice versa so this is
+
+ align:start position:0%
+of something and vice versa so this is
+ 
+
+ align:start position:0%
+of something and vice versa so this is
+really just flipping everything over
+
+ align:start position:0%
+really just flipping everything over
+ 
+
+ align:start position:0%
+really just flipping everything over
+we'll just focus on case on
+
+ align:start position:0%
+we'll just focus on case on
+ 
+
+ align:start position:0%
+we'll just focus on case on
+category a and let's see what we do in
+
+ align:start position:0%
+category a and let's see what we do in
+ 
+
+ align:start position:0%
+category a and let's see what we do in
+each of the three cases we've seen it in
+
+ align:start position:0%
+each of the three cases we've seen it in
+ 
+
+ align:start position:0%
+each of the three cases we've seen it in
+an example but let's do it
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+generically let's do it
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+here um oh there's sorry there's a
+
+ align:start position:0%
+here um oh there's sorry there's a
+ 
+
+ align:start position:0%
+here um oh there's sorry there's a
+little there's one more line to the
+
+ align:start position:0%
+little there's one more line to the
+ 
+
+ align:start position:0%
+little there's one more line to the
+algorithm I should say so aligned with
+
+ align:start position:0%
+algorithm I should say so aligned with
+ 
+
+ align:start position:0%
+algorithm I should say so aligned with
+here we color the root there's a chance
+
+ align:start position:0%
+here we color the root there's a chance
+ 
+
+ align:start position:0%
+here we color the root there's a chance
+when you do all of this the root becomes
+
+ align:start position:0%
+when you do all of this the root becomes
+ 
+
+ align:start position:0%
+when you do all of this the root becomes
+red we always want the root to be black
+
+ align:start position:0%
+red we always want the root to be black
+ 
+
+ align:start position:0%
+red we always want the root to be black
+if it's red we set it to Black at the
+
+ align:start position:0%
+if it's red we set it to Black at the
+ 
+
+ align:start position:0%
+if it's red we set it to Black at the
+very end of the
+
+ align:start position:0%
+very end of the
+ 
+
+ align:start position:0%
+very end of the
+algorithm
+
+ align:start position:0%
+algorithm
+ 
+
+ align:start position:0%
+algorithm
+um this does not change the black height
+
+ align:start position:0%
+um this does not change the black height
+ 
+
+ align:start position:0%
+um this does not change the black height
+property everything will still be fine
+
+ align:start position:0%
+property everything will still be fine
+ 
+
+ align:start position:0%
+property everything will still be fine
+because there's I mean every path either
+
+ align:start position:0%
+because there's I mean every path either
+ 
+
+ align:start position:0%
+because there's I mean every path either
+goes to the root or it doesn't every X
+
+ align:start position:0%
+goes to the root or it doesn't every X
+ 
+
+ align:start position:0%
+goes to the root or it doesn't every X
+to Leaf path so changing the root from
+
+ align:start position:0%
+to Leaf path so changing the root from
+ 
+
+ align:start position:0%
+to Leaf path so changing the root from
+red to Black is no problem it will
+
+ align:start position:0%
+red to Black is no problem it will
+ 
+
+ align:start position:0%
+red to Black is no problem it will
+increase the black Heights of everyone
+
+ align:start position:0%
+increase the black Heights of everyone
+ 
+
+ align:start position:0%
+increase the black Heights of everyone
+but they'll all stay uh all the paths
+
+ align:start position:0%
+but they'll all stay uh all the paths
+ 
+
+ align:start position:0%
+but they'll all stay uh all the paths
+will still have the same value just
+
+ align:start position:0%
+will still have the same value just
+ 
+
+ align:start position:0%
+will still have the same value just
+it'll be one
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+larger so let's look at the three
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+cases and I'm going to use some notation
+
+ align:start position:0%
+cases and I'm going to use some notation
+ 
+
+ align:start position:0%
+cases and I'm going to use some notation
+remember we had triangles in order to
+
+ align:start position:0%
+remember we had triangles in order to
+ 
+
+ align:start position:0%
+remember we had triangles in order to
+denote uh arbitrary sub trees when we
+
+ align:start position:0%
+denote uh arbitrary sub trees when we
+ 
+
+ align:start position:0%
+denote uh arbitrary sub trees when we
+defined a rotation I'm going to use
+
+ align:start position:0%
+defined a rotation I'm going to use
+ 
+
+ align:start position:0%
+defined a rotation I'm going to use
+triangle with a DOT on top to say that
+
+ align:start position:0%
+triangle with a DOT on top to say that
+ 
+
+ align:start position:0%
+triangle with a DOT on top to say that
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+this no this subtree has a black
+
+ align:start position:0%
+this no this subtree has a black
+ 
+
+ align:start position:0%
+this no this subtree has a black
+root so this when I fill something white
+
+ align:start position:0%
+root so this when I fill something white
+ 
+
+ align:start position:0%
+root so this when I fill something white
+it means black because I'm on a black
+
+ align:start position:0%
+it means black because I'm on a black
+ 
+
+ align:start position:0%
+it means black because I'm on a black
+board
+
+ align:start position:0%
+board
+ 
+
+ align:start position:0%
+board
+sorry okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and and I also have the property that
+
+ align:start position:0%
+and and I also have the property that
+ 
+
+ align:start position:0%
+and and I also have the property that
+each of these
+
+ align:start position:0%
+each of these
+ 
+
+ align:start position:0%
+each of these
+triangles have the same black height
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so this will let me make sure that the
+
+ align:start position:0%
+so this will let me make sure that the
+ 
+
+ align:start position:0%
+so this will let me make sure that the
+black height property property four is
+
+ align:start position:0%
+black height property property four is
+ 
+
+ align:start position:0%
+black height property property four is
+being
+
+ align:start position:0%
+being
+ 
+
+ align:start position:0%
+being
+preserved so let me just show you case
+
+ align:start position:0%
+preserved so let me just show you case
+ 
+
+ align:start position:0%
+preserved so let me just show you case
+one we always want to make sure property
+
+ align:start position:0%
+one we always want to make sure property
+ 
+
+ align:start position:0%
+one we always want to make sure property
+4 is preserved because it's really hard
+
+ align:start position:0%
+4 is preserved because it's really hard
+ 
+
+ align:start position:0%
+4 is preserved because it's really hard
+to get that back it's essentially the
+
+ align:start position:0%
+to get that back it's essentially the
+ 
+
+ align:start position:0%
+to get that back it's essentially the
+balance of the
+
+ align:start position:0%
+balance of the
+ 
+
+ align:start position:0%
+balance of the
+tree so let's suppose we have some nod C
+
+ align:start position:0%
+tree so let's suppose we have some nod C
+ 
+
+ align:start position:0%
+tree so let's suppose we have some nod C
+left child a right child
+
+ align:start position:0%
+left child a right child
+ 
+
+ align:start position:0%
+left child a right child
+B and some sub trees hanging off those
+
+ align:start position:0%
+B and some sub trees hanging off those
+ 
+
+ align:start position:0%
+B and some sub trees hanging off those
+guys and all of those sub trees have the
+
+ align:start position:0%
+guys and all of those sub trees have the
+ 
+
+ align:start position:0%
+guys and all of those sub trees have the
+same black
+
+ align:start position:0%
+same black
+ 
+
+ align:start position:0%
+same black
+height so in other words these things
+
+ align:start position:0%
+height so in other words these things
+ 
+
+ align:start position:0%
+height so in other words these things
+are all at the same
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+level okay this uh is not quite what I
+
+ align:start position:0%
+level okay this uh is not quite what I
+ 
+
+ align:start position:0%
+level okay this uh is not quite what I
+wanted
+
+ align:start position:0%
+wanted
+ 
+
+ align:start position:0%
+wanted
+sorry I also so I'm considering this is
+
+ align:start position:0%
+sorry I also so I'm considering this is
+ 
+
+ align:start position:0%
+sorry I also so I'm considering this is
+node x x is red and his parent is red
+
+ align:start position:0%
+node x x is red and his parent is red
+ 
+
+ align:start position:0%
+node x x is red and his parent is red
+therefore we need to fix something we
+
+ align:start position:0%
+therefore we need to fix something we
+ 
+
+ align:start position:0%
+therefore we need to fix something we
+look at the node Y which is over here
+
+ align:start position:0%
+look at the node Y which is over here
+ 
+
+ align:start position:0%
+look at the node Y which is over here
+and I'll call it the key is D the node
+
+ align:start position:0%
+and I'll call it the key is D the node
+ 
+
+ align:start position:0%
+and I'll call it the key is D the node
+is called
+
+ align:start position:0%
+is called
+ 
+
+ align:start position:0%
+is called
+y okay it has sub trees hanging off as
+
+ align:start position:0%
+y okay it has sub trees hanging off as
+ 
+
+ align:start position:0%
+y okay it has sub trees hanging off as
+well all with the same black height so
+
+ align:start position:0%
+well all with the same black height so
+ 
+
+ align:start position:0%
+well all with the same black height so
+that will be true if if all of these
+
+ align:start position:0%
+that will be true if if all of these
+ 
+
+ align:start position:0%
+that will be true if if all of these
+nodes are red then all of these nodes
+
+ align:start position:0%
+nodes are red then all of these nodes
+ 
+
+ align:start position:0%
+nodes are red then all of these nodes
+have the same black height and therefore
+
+ align:start position:0%
+have the same black height and therefore
+ 
+
+ align:start position:0%
+have the same black height and therefore
+all of the child sub trees which have
+
+ align:start position:0%
+all of the child sub trees which have
+ 
+
+ align:start position:0%
+all of the child sub trees which have
+black roots all have to have the same
+
+ align:start position:0%
+black roots all have to have the same
+ 
+
+ align:start position:0%
+black roots all have to have the same
+black height as well okay so we're sort
+
+ align:start position:0%
+black height as well okay so we're sort
+ 
+
+ align:start position:0%
+black height as well okay so we're sort
+of looking at a big chunk of red
+
+ align:start position:0%
+of looking at a big chunk of red
+ 
+
+ align:start position:0%
+of looking at a big chunk of red
+children a red children's subtree of a
+
+ align:start position:0%
+children a red children's subtree of a
+ 
+
+ align:start position:0%
+children a red children's subtree of a
+black node looking at all all the stuff
+
+ align:start position:0%
+black node looking at all all the stuff
+ 
+
+ align:start position:0%
+black node looking at all all the stuff
+that happens to be red in case one y is
+
+ align:start position:0%
+that happens to be red in case one y is
+ 
+
+ align:start position:0%
+that happens to be red in case one y is
+red so it participates so a way to think
+
+ align:start position:0%
+red so it participates so a way to think
+ 
+
+ align:start position:0%
+red so it participates so a way to think
+of this is if we converted into the 2
+
+ align:start position:0%
+of this is if we converted into the 2
+ 
+
+ align:start position:0%
+of this is if we converted into the 2
+three4 tree or tried to we would merge
+
+ align:start position:0%
+three4 tree or tried to we would merge
+ 
+
+ align:start position:0%
+three4 tree or tried to we would merge
+all of this stuff into one node that's
+
+ align:start position:0%
+all of this stuff into one node that's
+ 
+
+ align:start position:0%
+all of this stuff into one node that's
+essentially what we're doing here this
+
+ align:start position:0%
+essentially what we're doing here this
+ 
+
+ align:start position:0%
+essentially what we're doing here this
+is not a 234 tree though we now have
+
+ align:start position:0%
+is not a 234 tree though we now have
+ 
+
+ align:start position:0%
+is not a 234 tree though we now have
+five children which is bad this is why
+
+ align:start position:0%
+five children which is bad this is why
+ 
+
+ align:start position:0%
+five children which is bad this is why
+we want to fix
+
+ align:start position:0%
+we want to fix
+ 
+
+ align:start position:0%
+we want to fix
+it so we're going to
+
+ align:start position:0%
+it so we're going to
+ 
+
+ align:start position:0%
+it so we're going to
+recolor in case one
+
+ align:start position:0%
+recolor in case one
+ 
+
+ align:start position:0%
+recolor in case one
+and we're going to take C instead of
+
+ align:start position:0%
+and we're going to take C instead of
+ 
+
+ align:start position:0%
+and we're going to take C instead of
+making C black and a and d red we're
+
+ align:start position:0%
+making C black and a and d red we're
+ 
+
+ align:start position:0%
+making C black and a and d red we're
+going to make a and D black and C
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+red so C is red a is
+
+ align:start position:0%
+red so C is red a is
+ 
+
+ align:start position:0%
+red so C is red a is
+black d is
+
+ align:start position:0%
+black d is
+ 
+
+ align:start position:0%
+black d is
+black
+
+ align:start position:0%
+black
+ 
+
+ align:start position:0%
+black
+and the subtes are the same B is the
+
+ align:start position:0%
+and the subtes are the same B is the
+ 
+
+ align:start position:0%
+and the subtes are the same B is the
+same still
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+red okay now we need to check that we
+
+ align:start position:0%
+red okay now we need to check that we
+ 
+
+ align:start position:0%
+red okay now we need to check that we
+Preserve property four that all of the
+
+ align:start position:0%
+Preserve property four that all of the
+ 
+
+ align:start position:0%
+Preserve property four that all of the
+paths have the same number of black
+
+ align:start position:0%
+paths have the same number of black
+ 
+
+ align:start position:0%
+paths have the same number of black
+nodes that follows because we know we
+
+ align:start position:0%
+nodes that follows because we know we
+ 
+
+ align:start position:0%
+nodes that follows because we know we
+didn't touch these sub trees they all
+
+ align:start position:0%
+didn't touch these sub trees they all
+ 
+
+ align:start position:0%
+didn't touch these sub trees they all
+have the same black height and uh if you
+
+ align:start position:0%
+have the same black height and uh if you
+ 
+
+ align:start position:0%
+have the same black height and uh if you
+look at any path like all the paths from
+
+ align:start position:0%
+look at any path like all the paths from
+ 
+
+ align:start position:0%
+look at any path like all the paths from
+a are going to have that black height
+
+ align:start position:0%
+a are going to have that black height
+ 
+
+ align:start position:0%
+a are going to have that black height
+all the paths from C are going to have
+
+ align:start position:0%
+all the paths from C are going to have
+ 
+
+ align:start position:0%
+all the paths from C are going to have
+that black height plus one because
+
+ align:start position:0%
+that black height plus one because
+ 
+
+ align:start position:0%
+that black height plus one because
+there's a black node in all the left
+
+ align:start position:0%
+there's a black node in all the left
+ 
+
+ align:start position:0%
+there's a black node in all the left
+paths and there's a black node in all
+
+ align:start position:0%
+paths and there's a black node in all
+ 
+
+ align:start position:0%
+paths and there's a black node in all
+the right paths so all the black Heights
+
+ align:start position:0%
+the right paths so all the black Heights
+ 
+
+ align:start position:0%
+the right paths so all the black Heights
+all the black lengths are the same so
+
+ align:start position:0%
+all the black lengths are the same so
+ 
+
+ align:start position:0%
+all the black lengths are the same so
+this preserves property 4 and it fixes
+
+ align:start position:0%
+this preserves property 4 and it fixes
+ 
+
+ align:start position:0%
+this preserves property 4 and it fixes
+property three locally cuz B used to
+
+ align:start position:0%
+property three locally cuz B used to
+ 
+
+ align:start position:0%
+property three locally cuz B used to
+violate a now B uh does not violate
+
+ align:start position:0%
+violate a now B uh does not violate
+ 
+
+ align:start position:0%
+violate a now B uh does not violate
+anything C now might have to might be
+
+ align:start position:0%
+anything C now might have to might be
+ 
+
+ align:start position:0%
+anything C now might have to might be
+violated so what we're going to do is
+
+ align:start position:0%
+violated so what we're going to do is
+ 
+
+ align:start position:0%
+violated so what we're going to do is
+set X our new value of x will be C so it
+
+ align:start position:0%
+set X our new value of x will be C so it
+ 
+
+ align:start position:0%
+set X our new value of x will be C so it
+used to be B we move it up a couple
+
+ align:start position:0%
+used to be B we move it up a couple
+ 
+
+ align:start position:0%
+used to be B we move it up a couple
+levels or in the original tree yeah we
+
+ align:start position:0%
+levels or in the original tree yeah we
+ 
+
+ align:start position:0%
+levels or in the original tree yeah we
+also move it up a couple levels so we're
+
+ align:start position:0%
+also move it up a couple levels so we're
+ 
+
+ align:start position:0%
+also move it up a couple levels so we're
+making progress up the tree and then we
+
+ align:start position:0%
+making progress up the tree and then we
+ 
+
+ align:start position:0%
+making progress up the tree and then we
+continue this
+
+ align:start position:0%
+continue this
+ 
+
+ align:start position:0%
+continue this
+Loop that's case one recolor go up C May
+
+ align:start position:0%
+Loop that's case one recolor go up C May
+ 
+
+ align:start position:0%
+Loop that's case one recolor go up C May
+violate its parent in which case we have
+
+ align:start position:0%
+violate its parent in which case we have
+ 
+
+ align:start position:0%
+violate its parent in which case we have
+to recurse so we're recursing in some
+
+ align:start position:0%
+to recurse so we're recursing in some
+ 
+
+ align:start position:0%
+to recurse so we're recursing in some
+sense or continuing on
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+C so now let's look at case two
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so I'm still in some sense defining this
+
+ align:start position:0%
+so I'm still in some sense defining this
+ 
+
+ align:start position:0%
+so I'm still in some sense defining this
+algorithm by picture this is some nice
+
+ align:start position:0%
+algorithm by picture this is some nice
+ 
+
+ align:start position:0%
+algorithm by picture this is some nice
+graphical programming language
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so let's draw case
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+two
+
+ align:start position:0%
+two
+ 
+
+ align:start position:0%
+two
+um yeah I forgot to mention something
+
+ align:start position:0%
+um yeah I forgot to mention something
+ 
+
+ align:start position:0%
+um yeah I forgot to mention something
+about case one
+
+ align:start position:0%
+about case one
+ 
+
+ align:start position:0%
+about case one
+so I I drew some things here I uh what
+
+ align:start position:0%
+so I I drew some things here I uh what
+ 
+
+ align:start position:0%
+so I I drew some things here I uh what
+what do I actually know is true so let's
+
+ align:start position:0%
+what do I actually know is true so let's
+ 
+
+ align:start position:0%
+what do I actually know is true so let's
+go let's look at the algorithm which
+
+ align:start position:0%
+go let's look at the algorithm which
+ 
+
+ align:start position:0%
+go let's look at the algorithm which
+I've now reversed but um we are assuming
+
+ align:start position:0%
+I've now reversed but um we are assuming
+ 
+
+ align:start position:0%
+I've now reversed but um we are assuming
+that we're in category a in other words
+
+ align:start position:0%
+that we're in category a in other words
+ 
+
+ align:start position:0%
+that we're in category a in other words
+the parent is the left child of the
+
+ align:start position:0%
+the parent is the left child of the
+ 
+
+ align:start position:0%
+the parent is the left child of the
+grandparent so a is the left child of C
+
+ align:start position:0%
+grandparent so a is the left child of C
+ 
+
+ align:start position:0%
+grandparent so a is the left child of C
+that much I knew therefore Y is the
+
+ align:start position:0%
+that much I knew therefore Y is the
+ 
+
+ align:start position:0%
+that much I knew therefore Y is the
+right child
+
+ align:start position:0%
+right child
+ 
+
+ align:start position:0%
+right child
+D is the right child of C I didn't
+
+ align:start position:0%
+D is the right child of C I didn't
+ 
+
+ align:start position:0%
+D is the right child of C I didn't
+actually know whether B was the right
+
+ align:start position:0%
+actually know whether B was the right
+ 
+
+ align:start position:0%
+actually know whether B was the right
+child or the left child it didn't matter
+
+ align:start position:0%
+child or the left child it didn't matter
+ 
+
+ align:start position:0%
+child or the left child it didn't matter
+in case one it doesn't matter okay so I
+
+ align:start position:0%
+in case one it doesn't matter okay so I
+ 
+
+ align:start position:0%
+in case one it doesn't matter okay so I
+should have said um the children of a
+
+ align:start position:0%
+should have said um the children of a
+ 
+
+ align:start position:0%
+should have said um the children of a
+may be
+
+ align:start position:0%
+may be
+ 
+
+ align:start position:0%
+may be
+reversed but it's just the same
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+picture okay I thought of this because
+
+ align:start position:0%
+picture okay I thought of this because
+ 
+
+ align:start position:0%
+picture okay I thought of this because
+in case two we care so case one we
+
+ align:start position:0%
+in case two we care so case one we
+ 
+
+ align:start position:0%
+in case two we care so case one we
+didn't really care in case two we say
+
+ align:start position:0%
+didn't really care in case two we say
+ 
+
+ align:start position:0%
+didn't really care in case two we say
+well uh case two is up there is X the
+
+ align:start position:0%
+well uh case two is up there is X the
+ 
+
+ align:start position:0%
+well uh case two is up there is X the
+right child of the parent or the left
+
+ align:start position:0%
+right child of the parent or the left
+ 
+
+ align:start position:0%
+right child of the parent or the left
+child if it's the right child we're in
+
+ align:start position:0%
+child if it's the right child we're in
+ 
+
+ align:start position:0%
+child if it's the right child we're in
+case two so now I really know that X
+
+ align:start position:0%
+case two so now I really know that X
+ 
+
+ align:start position:0%
+case two so now I really know that X
+here is which is B is the right child of
+
+ align:start position:0%
+here is which is B is the right child of
+ 
+
+ align:start position:0%
+here is which is B is the right child of
+a before I didn't know I didn't care now
+
+ align:start position:0%
+a before I didn't know I didn't care now
+ 
+
+ align:start position:0%
+a before I didn't know I didn't care now
+I'm assuming that it's this way okay Y
+
+ align:start position:0%
+I'm assuming that it's this way okay Y
+ 
+
+ align:start position:0%
+I'm assuming that it's this way okay Y
+is still over
+
+ align:start position:0%
+is still over
+ 
+
+ align:start position:0%
+is still over
+here and now we know that Y is black
+
+ align:start position:0%
+here and now we know that Y is black
+ 
+
+ align:start position:0%
+here and now we know that Y is black
+so y over here is a black node so now if
+
+ align:start position:0%
+so y over here is a black node so now if
+ 
+
+ align:start position:0%
+so y over here is a black node so now if
+I did the contraction trick all of these
+
+ align:start position:0%
+I did the contraction trick all of these
+ 
+
+ align:start position:0%
+I did the contraction trick all of these
+nodes a b and c would conglomerate into
+
+ align:start position:0%
+nodes a b and c would conglomerate into
+ 
+
+ align:start position:0%
+nodes a b and c would conglomerate into
+one I only have four children that
+
+ align:start position:0%
+one I only have four children that
+ 
+
+ align:start position:0%
+one I only have four children that
+actually looks pretty good why would not
+
+ align:start position:0%
+actually looks pretty good why would not
+ 
+
+ align:start position:0%
+actually looks pretty good why would not
+be involved because it's
+
+ align:start position:0%
+be involved because it's
+ 
+
+ align:start position:0%
+be involved because it's
+black
+
+ align:start position:0%
+black
+ 
+
+ align:start position:0%
+black
+okay so in this case we're going to do a
+
+ align:start position:0%
+okay so in this case we're going to do a
+ 
+
+ align:start position:0%
+okay so in this case we're going to do a
+left
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+rotation on a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so we take this Edge we turn it 90° what
+
+ align:start position:0%
+so we take this Edge we turn it 90° what
+ 
+
+ align:start position:0%
+so we take this Edge we turn it 90° what
+we get is a on the left B on the right
+
+ align:start position:0%
+we get is a on the left B on the right
+ 
+
+ align:start position:0%
+we get is a on the left B on the right
+still should preserve the in order
+
+ align:start position:0%
+still should preserve the in order
+ 
+
+ align:start position:0%
+still should preserve the in order
+traversal C up top still we have the Y
+
+ align:start position:0%
+traversal C up top still we have the Y
+ 
+
+ align:start position:0%
+traversal C up top still we have the Y
+sub tree hanging off as
+
+ align:start position:0%
+sub tree hanging off as
+ 
+
+ align:start position:0%
+sub tree hanging off as
+before uh we have one of the sub trees
+
+ align:start position:0%
+before uh we have one of the sub trees
+ 
+
+ align:start position:0%
+before uh we have one of the sub trees
+one of the other three sub trees hanging
+
+ align:start position:0%
+one of the other three sub trees hanging
+ 
+
+ align:start position:0%
+one of the other three sub trees hanging
+off B and the other two now hang off a
+
+ align:start position:0%
+off B and the other two now hang off a
+ 
+
+ align:start position:0%
+off B and the other two now hang off a
+so this was just a generic rotation
+
+ align:start position:0%
+so this was just a generic rotation
+ 
+
+ align:start position:0%
+so this was just a generic rotation
+picture applied to this
+
+ align:start position:0%
+picture applied to this
+ 
+
+ align:start position:0%
+picture applied to this
+Edge okay what that does is before we
+
+ align:start position:0%
+Edge okay what that does is before we
+ 
+
+ align:start position:0%
+Edge okay what that does is before we
+had a zigzag between X and its
+
+ align:start position:0%
+had a zigzag between X and its
+ 
+
+ align:start position:0%
+had a zigzag between X and its
+grandparent now we have a zig Zig we
+
+ align:start position:0%
+grandparent now we have a zig Zig we
+ 
+
+ align:start position:0%
+grandparent now we have a zig Zig we
+have a straight path between X so X is
+
+ align:start position:0%
+have a straight path between X so X is
+ 
+
+ align:start position:0%
+have a straight path between X so X is
+still down here I'm not changing X in
+
+ align:start position:0%
+still down here I'm not changing X in
+ 
+
+ align:start position:0%
+still down here I'm not changing X in
+this case because uh after I do case two
+
+ align:start position:0%
+this case because uh after I do case two
+ 
+
+ align:start position:0%
+this case because uh after I do case two
+I immediately do case three so this is
+
+ align:start position:0%
+I immediately do case three so this is
+ 
+
+ align:start position:0%
+I immediately do case three so this is
+what case three will look like and now I
+
+ align:start position:0%
+what case three will look like and now I
+ 
+
+ align:start position:0%
+what case three will look like and now I
+continue on to case three
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so finally here's case three and this
+
+ align:start position:0%
+so finally here's case three and this
+ 
+
+ align:start position:0%
+so finally here's case three and this
+will finally complete the insertion
+
+ align:start position:0%
+will finally complete the insertion
+ 
+
+ align:start position:0%
+will finally complete the insertion
+algorithm we have a black node C we have
+
+ align:start position:0%
+algorithm we have a black node C we have
+ 
+
+ align:start position:0%
+algorithm we have a black node C we have
+a red left child from C we have a red
+
+ align:start position:0%
+a red left child from C we have a red
+ 
+
+ align:start position:0%
+a red left child from C we have a red
+left grandchild which is
+
+ align:start position:0%
+left grandchild which is
+ 
+
+ align:start position:0%
+left grandchild which is
+X and then we have these black subt
+
+ align:start position:0%
+X and then we have these black subt
+ 
+
+ align:start position:0%
+X and then we have these black subt
+trees all of the same black height
+
+ align:start position:0%
+trees all of the same black height
+ 
+
+ align:start position:0%
+trees all of the same black height
+hanging off
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay which is exactly what we had at the
+
+ align:start position:0%
+okay which is exactly what we had at the
+ 
+
+ align:start position:0%
+okay which is exactly what we had at the
+end of case two so that definitely
+
+ align:start position:0%
+end of case two so that definitely
+ 
+
+ align:start position:0%
+end of case two so that definitely
+connects over and remember this is the
+
+ align:start position:0%
+connects over and remember this is the
+ 
+
+ align:start position:0%
+connects over and remember this is the
+only case left in category a category a
+
+ align:start position:0%
+only case left in category a category a
+ 
+
+ align:start position:0%
+only case left in category a category a
+we assumed that b was the you know the
+
+ align:start position:0%
+we assumed that b was the you know the
+ 
+
+ align:start position:0%
+we assumed that b was the you know the
+parent of X was the left child of the
+
+ align:start position:0%
+parent of X was the left child of the
+ 
+
+ align:start position:0%
+parent of X was the left child of the
+grandparent here c um so we know that we
+
+ align:start position:0%
+grandparent here c um so we know that we
+ 
+
+ align:start position:0%
+grandparent here c um so we know that we
+already did the case when y over here is
+
+ align:start position:0%
+already did the case when y over here is
+ 
+
+ align:start position:0%
+already did the case when y over here is
+red that was case one so we're assuming
+
+ align:start position:0%
+red that was case one so we're assuming
+ 
+
+ align:start position:0%
+red that was case one so we're assuming
+Y is black now we look at whether X was
+
+ align:start position:0%
+Y is black now we look at whether X was
+ 
+
+ align:start position:0%
+Y is black now we look at whether X was
+the left child or the right child if it
+
+ align:start position:0%
+the left child or the right child if it
+ 
+
+ align:start position:0%
+the left child or the right child if it
+was the right child we made it into the
+
+ align:start position:0%
+was the right child we made it into the
+ 
+
+ align:start position:0%
+was the right child we made it into the
+left child uh X actually did change here
+
+ align:start position:0%
+left child uh X actually did change here
+ 
+
+ align:start position:0%
+left child uh X actually did change here
+before X was B now X is
+
+ align:start position:0%
+before X was B now X is
+ 
+
+ align:start position:0%
+before X was B now X is
+a okay and then case three finally is
+
+ align:start position:0%
+a okay and then case three finally is
+ 
+
+ align:start position:0%
+a okay and then case three finally is
+when X is the left child of the parent
+
+ align:start position:0%
+when X is the left child of the parent
+ 
+
+ align:start position:0%
+when X is the left child of the parent
+who is the left child of the grandparent
+
+ align:start position:0%
+who is the left child of the grandparent
+ 
+
+ align:start position:0%
+who is the left child of the grandparent
+this is the last case we have to worry
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+about
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and what we do is another rot rotation
+
+ align:start position:0%
+and what we do is another rot rotation
+ 
+
+ align:start position:0%
+and what we do is another rot rotation
+just like the last rotation we did in
+
+ align:start position:0%
+just like the last rotation we did in
+ 
+
+ align:start position:0%
+just like the last rotation we did in
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+example that was case
+
+ align:start position:0%
+example that was case
+ 
+
+ align:start position:0%
+example that was case
+three so we're going to do a right
+
+ align:start position:0%
+three so we're going to do a right
+ 
+
+ align:start position:0%
+three so we're going to do a right
+rotate in this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+case
+
+ align:start position:0%
+case
+ 
+
+ align:start position:0%
+case
+of
+
+ align:start position:0%
+of
+ 
+
+ align:start position:0%
+of
+c and we're going to
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+recolor
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+what do we get well B now becomes the
+
+ align:start position:0%
+what do we get well B now becomes the
+ 
+
+ align:start position:0%
+what do we get well B now becomes the
+root and I'm going to make it black okay
+
+ align:start position:0%
+root and I'm going to make it black okay
+ 
+
+ align:start position:0%
+root and I'm going to make it black okay
+remember this this is the root of the
+
+ align:start position:0%
+remember this this is the root of the
+ 
+
+ align:start position:0%
+remember this this is the root of the
+sub tree there's other stuff hanging off
+
+ align:start position:0%
+sub tree there's other stuff hanging off
+ 
+
+ align:start position:0%
+sub tree there's other stuff hanging off
+here I really should have drawn extra
+
+ align:start position:0%
+here I really should have drawn extra
+ 
+
+ align:start position:0%
+here I really should have drawn extra
+parents in all of these pictures
+
+ align:start position:0%
+parents in all of these pictures
+ 
+
+ align:start position:0%
+parents in all of these pictures
+somewhere in the middle of the tree
+
+ align:start position:0%
+somewhere in the middle of the tree
+ 
+
+ align:start position:0%
+somewhere in the middle of the tree
+don't know where could be a rightward
+
+ align:start position:0%
+don't know where could be a rightward
+ 
+
+ align:start position:0%
+don't know where could be a rightward
+branch could be a leftward branch we
+
+ align:start position:0%
+branch could be a leftward branch we
+ 
+
+ align:start position:0%
+branch could be a leftward branch we
+don't know C becomes the child of B and
+
+ align:start position:0%
+don't know C becomes the child of B and
+ 
+
+ align:start position:0%
+don't know C becomes the child of B and
+I'm going to make it a red child a
+
+ align:start position:0%
+I'm going to make it a red child a
+ 
+
+ align:start position:0%
+I'm going to make it a red child a
+becomes a child of b as it was before
+
+ align:start position:0%
+becomes a child of b as it was before
+ 
+
+ align:start position:0%
+becomes a child of b as it was before
+keep it red
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and everything else just hangs
+
+ align:start position:0%
+and everything else just hangs
+ 
+
+ align:start position:0%
+and everything else just hangs
+off so there were
+
+ align:start position:0%
+off so there were
+ 
+
+ align:start position:0%
+off so there were
+four subtes all with the same black
+
+ align:start position:0%
+four subtes all with the same black
+ 
+
+ align:start position:0%
+four subtes all with the same black
+height and in particular this last one
+
+ align:start position:0%
+height and in particular this last one
+ 
+
+ align:start position:0%
+height and in particular this last one
+had y but we don't particularly care
+
+ align:start position:0%
+had y but we don't particularly care
+ 
+
+ align:start position:0%
+had y but we don't particularly care
+about y
+
+ align:start position:0%
+about y
+ 
+
+ align:start position:0%
+about y
+anymore now we're in really good shape
+
+ align:start position:0%
+anymore now we're in really good shape
+ 
+
+ align:start position:0%
+anymore now we're in really good shape
+because we should have no more
+
+ align:start position:0%
+because we should have no more
+ 
+
+ align:start position:0%
+because we should have no more
+violations okay before we had a
+
+ align:start position:0%
+violations okay before we had a
+ 
+
+ align:start position:0%
+violations okay before we had a
+violation between X and its parent A and
+
+ align:start position:0%
+violation between X and its parent A and
+ 
+
+ align:start position:0%
+violation between X and its parent A and
+B those aren't even uh well A and B have
+
+ align:start position:0%
+B those aren't even uh well A and B have
+ 
+
+ align:start position:0%
+B those aren't even uh well A and B have
+still have a parent child relation but B
+
+ align:start position:0%
+still have a parent child relation but B
+ 
+
+ align:start position:0%
+still have a parent child relation but B
+is now black so and B is black so we
+
+ align:start position:0%
+is now black so and B is black so we
+ 
+
+ align:start position:0%
+is now black so and B is black so we
+don't care what its parent looks like
+
+ align:start position:0%
+don't care what its parent looks like
+ 
+
+ align:start position:0%
+don't care what its parent looks like
+could be red or black both are fine
+
+ align:start position:0%
+could be red or black both are fine
+ 
+
+ align:start position:0%
+could be red or black both are fine
+we're no longer violating property 3 we
+
+ align:start position:0%
+we're no longer violating property 3 we
+ 
+
+ align:start position:0%
+we're no longer violating property 3 we
+should be done in this
+
+ align:start position:0%
+should be done in this
+ 
+
+ align:start position:0%
+should be done in this
+case see property 3 is now
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+true if you want you can say well X
+
+ align:start position:0%
+true if you want you can say well X
+ 
+
+ align:start position:0%
+true if you want you can say well X
+becomes this node and then the loop says
+
+ align:start position:0%
+becomes this node and then the loop says
+ 
+
+ align:start position:0%
+becomes this node and then the loop says
+oh X is no longer red therefore I'm done
+
+ align:start position:0%
+oh X is no longer red therefore I'm done
+ 
+
+ align:start position:0%
+oh X is no longer red therefore I'm done
+we also need to check that property 4 is
+
+ align:start position:0%
+we also need to check that property 4 is
+ 
+
+ align:start position:0%
+we also need to check that property 4 is
+preserved during this process again it's
+
+ align:start position:0%
+preserved during this process again it's
+ 
+
+ align:start position:0%
+preserved during this process again it's
+not hard because of the 234 tree
+
+ align:start position:0%
+not hard because of the 234 tree
+ 
+
+ align:start position:0%
+not hard because of the 234 tree
+transformation if I contract all the red
+
+ align:start position:0%
+transformation if I contract all the red
+ 
+
+ align:start position:0%
+transformation if I contract all the red
+things into their parents um everything
+
+ align:start position:0%
+things into their parents um everything
+ 
+
+ align:start position:0%
+things into their parents um everything
+else has a constant I mean every path in
+
+ align:start position:0%
+else has a constant I mean every path in
+ 
+
+ align:start position:0%
+else has a constant I mean every path in
+that tree and look has the same length
+
+ align:start position:0%
+that tree and look has the same length
+ 
+
+ align:start position:0%
+that tree and look has the same length
+because they have the same black length
+
+ align:start position:0%
+because they have the same black length
+ 
+
+ align:start position:0%
+because they have the same black length
+and over here that will still be true
+
+ align:start position:0%
+and over here that will still be true
+ 
+
+ align:start position:0%
+and over here that will still be true
+we're doing it's a little bit trickier
+
+ align:start position:0%
+we're doing it's a little bit trickier
+ 
+
+ align:start position:0%
+we're doing it's a little bit trickier
+here because we're recoloring at the
+
+ align:start position:0%
+here because we're recoloring at the
+ 
+
+ align:start position:0%
+here because we're recoloring at the
+same time but if you look at a path that
+
+ align:start position:0%
+same time but if you look at a path that
+ 
+
+ align:start position:0%
+same time but if you look at a path that
+comes through this tree it used to go
+
+ align:start position:0%
+comes through this tree it used to go
+ 
+
+ align:start position:0%
+comes through this tree it used to go
+through a black node C and then maybe
+
+ align:start position:0%
+through a black node C and then maybe
+ 
+
+ align:start position:0%
+through a black node C and then maybe
+some red stuff but I don't care and then
+
+ align:start position:0%
+some red stuff but I don't care and then
+ 
+
+ align:start position:0%
+some red stuff but I don't care and then
+it went through these trees which all
+
+ align:start position:0%
+it went through these trees which all
+ 
+
+ align:start position:0%
+it went through these trees which all
+have the same black height so they're
+
+ align:start position:0%
+have the same black height so they're
+ 
+
+ align:start position:0%
+have the same black height so they're
+all the same now you come in and you go
+
+ align:start position:0%
+all the same now you come in and you go
+ 
+
+ align:start position:0%
+all the same now you come in and you go
+through a black node called B and then
+
+ align:start position:0%
+through a black node called B and then
+ 
+
+ align:start position:0%
+through a black node called B and then
+you go through some red nodes doesn't
+
+ align:start position:0%
+you go through some red nodes doesn't
+ 
+
+ align:start position:0%
+you go through some red nodes doesn't
+really matter but all the trees that you
+
+ align:start position:0%
+really matter but all the trees that you
+ 
+
+ align:start position:0%
+really matter but all the trees that you
+go through down here have the same black
+
+ align:start position:0%
+go through down here have the same black
+ 
+
+ align:start position:0%
+go through down here have the same black
+height so every path through this tree
+
+ align:start position:0%
+height so every path through this tree
+ 
+
+ align:start position:0%
+height so every path through this tree
+will have the same black length Okay if
+
+ align:start position:0%
+will have the same black length Okay if
+ 
+
+ align:start position:0%
+will have the same black length Okay if
+it starts from the same
+
+ align:start position:0%
+it starts from the same
+ 
+
+ align:start position:0%
+it starts from the same
+node so we preserve property 4 we fix
+
+ align:start position:0%
+node so we preserve property 4 we fix
+ 
+
+ align:start position:0%
+node so we preserve property 4 we fix
+property three that is the insertion
+
+ align:start position:0%
+property three that is the insertion
+ 
+
+ align:start position:0%
+property three that is the insertion
+algorithm
+
+ align:start position:0%
+algorithm
+ 
+
+ align:start position:0%
+algorithm
+it's pretty
+
+ align:start position:0%
+it's pretty
+ 
+
+ align:start position:0%
+it's pretty
+long um this is something you'll
+
+ align:start position:0%
+long um this is something you'll
+ 
+
+ align:start position:0%
+long um this is something you'll
+probably just have to memorize it you've
+
+ align:start position:0%
+probably just have to memorize it you've
+ 
+
+ align:start position:0%
+probably just have to memorize it you've
+try a few examples is not so hard we can
+
+ align:start position:0%
+try a few examples is not so hard we can
+ 
+
+ align:start position:0%
+try a few examples is not so hard we can
+see that all the things we did in this
+
+ align:start position:0%
+see that all the things we did in this
+ 
+
+ align:start position:0%
+see that all the things we did in this
+example were the three cases the first
+
+ align:start position:0%
+example were the three cases the first
+ 
+
+ align:start position:0%
+example were the three cases the first
+step which unfortunately I had to erase
+
+ align:start position:0%
+step which unfortunately I had to erase
+ 
+
+ align:start position:0%
+step which unfortunately I had to erase
+for space uh all we did was recolor we
+
+ align:start position:0%
+for space uh all we did was recolor we
+ 
+
+ align:start position:0%
+for space uh all we did was recolor we
+recolored 10 and 8 and 11 that was a
+
+ align:start position:0%
+recolored 10 and 8 and 11 that was a
+ 
+
+ align:start position:0%
+recolored 10 and 8 and 11 that was a
+case one 10 was the grandparent of
+
+ align:start position:0%
+case one 10 was the grandparent of
+ 
+
+ align:start position:0%
+case one 10 was the grandparent of
+15 then we did then we looked at 10 10
+
+ align:start position:0%
+15 then we did then we looked at 10 10
+ 
+
+ align:start position:0%
+15 then we did then we looked at 10 10
+was the Violator it was a zigzag case
+
+ align:start position:0%
+was the Violator it was a zigzag case
+ 
+
+ align:start position:0%
+was the Violator it was a zigzag case
+relative to its grandparent so we did a
+
+ align:start position:0%
+relative to its grandparent so we did a
+ 
+
+ align:start position:0%
+relative to its grandparent so we did a
+right rotation to fix that took this
+
+ align:start position:0%
+right rotation to fix that took this
+ 
+
+ align:start position:0%
+right rotation to fix that took this
+Edge and turned it so that 10 became
+
+ align:start position:0%
+Edge and turned it so that 10 became
+ 
+
+ align:start position:0%
+Edge and turned it so that 10 became
+next to seven that's the picture on the
+
+ align:start position:0%
+next to seven that's the picture on the
+ 
+
+ align:start position:0%
+next to seven that's the picture on the
+top then 18 which is the new violator
+
+ align:start position:0%
+top then 18 which is the new violator
+ 
+
+ align:start position:0%
+top then 18 which is the new violator
+with its grandparent is a zig Zig it's
+
+ align:start position:0%
+with its grandparent is a zig Zig it's
+ 
+
+ align:start position:0%
+with its grandparent is a zig Zig it's
+they're both going in the same
+
+ align:start position:0%
+they're both going in the same
+ 
+
+ align:start position:0%
+they're both going in the same
+direction and now we do one more
+
+ align:start position:0%
+direction and now we do one more
+ 
+
+ align:start position:0%
+direction and now we do one more
+rotation to fix that that's that's
+
+ align:start position:0%
+rotation to fix that that's that's
+ 
+
+ align:start position:0%
+rotation to fix that that's that's
+really the only thing you have to
+
+ align:start position:0%
+really the only thing you have to
+ 
+
+ align:start position:0%
+really the only thing you have to
+remember recolor your grandparent if you
+
+ align:start position:0%
+remember recolor your grandparent if you
+ 
+
+ align:start position:0%
+remember recolor your grandparent if you
+can otherwise make it Zig Zig and then
+
+ align:start position:0%
+can otherwise make it Zig Zig and then
+ 
+
+ align:start position:0%
+can otherwise make it Zig Zig and then
+do one more one last rotation and
+
+ align:start position:0%
+do one more one last rotation and
+ 
+
+ align:start position:0%
+do one more one last rotation and
+recolor and that will work I mean if you
+
+ align:start position:0%
+recolor and that will work I mean if you
+ 
+
+ align:start position:0%
+recolor and that will work I mean if you
+remember that you can figure out the
+
+ align:start position:0%
+remember that you can figure out the
+ 
+
+ align:start position:0%
+remember that you can figure out the
+rest on any particular example we rotate
+
+ align:start position:0%
+rest on any particular example we rotate
+ 
+
+ align:start position:0%
+rest on any particular example we rotate
+10 over that better be black because in
+
+ align:start position:0%
+10 over that better be black because in
+ 
+
+ align:start position:0%
+10 over that better be black because in
+this case it's becoming the root but
+
+ align:start position:0%
+this case it's becoming the root but
+ 
+
+ align:start position:0%
+this case it's becoming the root but
+we'll make it black no matter what
+
+ align:start position:0%
+we'll make it black no matter what
+ 
+
+ align:start position:0%
+we'll make it black no matter what
+happens because there has to be one
+
+ align:start position:0%
+happens because there has to be one
+ 
+
+ align:start position:0%
+happens because there has to be one
+black node there um if we didn't recolor
+
+ align:start position:0%
+black node there um if we didn't recolor
+ 
+
+ align:start position:0%
+black node there um if we didn't recolor
+at the same time we would violate
+
+ align:start position:0%
+at the same time we would violate
+ 
+
+ align:start position:0%
+at the same time we would violate
+property
+
+ align:start position:0%
+property
+ 
+
+ align:start position:0%
+property
+
+ align:start position:0%
+ 
+
+ align:start position:0%
+um why don't I draw That Just for kicks
+
+ align:start position:0%
+um why don't I draw That Just for kicks
+ 
+
+ align:start position:0%
+um why don't I draw That Just for kicks
+and because I have a couple
+
+ align:start position:0%
+and because I have a couple
+ 
+
+ align:start position:0%
+and because I have a couple
+minutes so if we just did the rotation
+
+ align:start position:0%
+minutes so if we just did the rotation
+ 
+
+ align:start position:0%
+minutes so if we just did the rotation
+here
+
+ align:start position:0%
+here
+ 
+
+ align:start position:0%
+here
+so I say not the
+
+ align:start position:0%
+so I say not the
+ 
+
+ align:start position:0%
+so I say not the
+following we take b b is red this will
+
+ align:start position:0%
+following we take b b is red this will
+ 
+
+ align:start position:0%
+following we take b b is red this will
+give some intuition of why the algorithm
+
+ align:start position:0%
+give some intuition of why the algorithm
+ 
+
+ align:start position:0%
+give some intuition of why the algorithm
+was this way and not some other way um
+
+ align:start position:0%
+was this way and not some other way um
+ 
+
+ align:start position:0%
+was this way and not some other way um
+and C is black that's what we would have
+
+ align:start position:0%
+and C is black that's what we would have
+ 
+
+ align:start position:0%
+and C is black that's what we would have
+gotten if we just rotated this tree
+
+ align:start position:0%
+gotten if we just rotated this tree
+ 
+
+ align:start position:0%
+gotten if we just rotated this tree
+rotated b or rotated C to the right so
+
+ align:start position:0%
+rotated b or rotated C to the right so
+ 
+
+ align:start position:0%
+rotated b or rotated C to the right so
+these sub trees hang off in the same way
+
+ align:start position:0%
+these sub trees hang off in the same way
+ 
+
+ align:start position:0%
+these sub trees hang off in the same way
+sub trees look great because they all
+
+ align:start position:0%
+sub trees look great because they all
+ 
+
+ align:start position:0%
+sub trees look great because they all
+have the same black height but you see
+
+ align:start position:0%
+have the same black height but you see
+ 
+
+ align:start position:0%
+have the same black height but you see
+there's a problem if we look at all the
+
+ align:start position:0%
+there's a problem if we look at all the
+ 
+
+ align:start position:0%
+there's a problem if we look at all the
+paths starting from B and going down to
+
+ align:start position:0%
+paths starting from B and going down to
+ 
+
+ align:start position:0%
+paths starting from B and going down to
+a leaf on the left they H the number of
+
+ align:start position:0%
+a leaf on the left they H the number of
+ 
+
+ align:start position:0%
+a leaf on the left they H the number of
+black nodes is whatever the black height
+
+ align:start position:0%
+black nodes is whatever the black height
+ 
+
+ align:start position:0%
+black nodes is whatever the black height
+is over
+
+ align:start position:0%
+is over
+ 
+
+ align:start position:0%
+is over
+here label that black height um whereas
+
+ align:start position:0%
+here label that black height um whereas
+ 
+
+ align:start position:0%
+here label that black height um whereas
+all the paths on the right will be that
+
+ align:start position:0%
+all the paths on the right will be that
+ 
+
+ align:start position:0%
+all the paths on the right will be that
+black height plus one because C is black
+
+ align:start position:0%
+black height plus one because C is black
+ 
+
+ align:start position:0%
+black height plus one because C is black
+so now we violated property
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+four so we don't do this in case three
+
+ align:start position:0%
+four so we don't do this in case three
+ 
+
+ align:start position:0%
+four so we don't do this in case three
+we we after we do the rotation we also
+
+ align:start position:0%
+we we after we do the rotation we also
+ 
+
+ align:start position:0%
+we we after we do the rotation we also
+do a recoloring so we get this in other
+
+ align:start position:0%
+do a recoloring so we get this in other
+ 
+
+ align:start position:0%
+do a recoloring so we get this in other
+words we're putting the black node at
+
+ align:start position:0%
+words we're putting the black node at
+ 
+
+ align:start position:0%
+words we're putting the black node at
+the top cuz then every path has to go
+
+ align:start position:0%
+the top cuz then every path has to go
+ 
+
+ align:start position:0%
+the top cuz then every path has to go
+through that node whereas over here some
+
+ align:start position:0%
+through that node whereas over here some
+ 
+
+ align:start position:0%
+through that node whereas over here some
+of the noes went through C some of them
+
+ align:start position:0%
+of the noes went through C some of them
+ 
+
+ align:start position:0%
+of the noes went through C some of them
+went through a so this is
+
+ align:start position:0%
+went through a so this is
+ 
+
+ align:start position:0%
+went through a so this is
+bad right also we would have violated
+
+ align:start position:0%
+bad right also we would have violated
+ 
+
+ align:start position:0%
+bad right also we would have violated
+property three but the really bad thing
+
+ align:start position:0%
+property three but the really bad thing
+ 
+
+ align:start position:0%
+property three but the really bad thing
+is we're violating property 4 over
+
+ align:start position:0%
+is we're violating property 4 over
+ 
+
+ align:start position:0%
+is we're violating property 4 over
+here okay let me sum up a little bit
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so we've seen if we insert into a red
+
+ align:start position:0%
+so we've seen if we insert into a red
+ 
+
+ align:start position:0%
+so we've seen if we insert into a red
+black tree we can keep it a red black
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+tree so RB
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+insert adds x to the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+set to the dynamic set that we're trying
+
+ align:start position:0%
+set to the dynamic set that we're trying
+ 
+
+ align:start position:0%
+set to the dynamic set that we're trying
+to maintain and
+
+ align:start position:0%
+to maintain and
+ 
+
+ align:start position:0%
+to maintain and
+preserves red blackness
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so keeps the tree a red black tree which
+
+ align:start position:0%
+so keeps the tree a red black tree which
+ 
+
+ align:start position:0%
+so keeps the tree a red black tree which
+is good because that means we know then
+
+ align:start position:0%
+is good because that means we know then
+ 
+
+ align:start position:0%
+is good because that means we know then
+that it keeps logarithmic height
+
+ align:start position:0%
+that it keeps logarithmic height
+ 
+
+ align:start position:0%
+that it keeps logarithmic height
+therefore all queries and red black
+
+ align:start position:0%
+therefore all queries and red black
+ 
+
+ align:start position:0%
+therefore all queries and red black
+trees will keep taking logarithmic time
+
+ align:start position:0%
+trees will keep taking logarithmic time
+ 
+
+ align:start position:0%
+trees will keep taking logarithmic time
+how long does red black insert
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+take we know we're aiming for and for
+
+ align:start position:0%
+take we know we're aiming for and for
+ 
+
+ align:start position:0%
+take we know we're aiming for and for
+log n time per
+
+ align:start position:0%
+log n time per
+ 
+
+ align:start position:0%
+log n time per
+operation I'm not going to prove that
+
+ align:start position:0%
+operation I'm not going to prove that
+ 
+
+ align:start position:0%
+operation I'm not going to prove that
+formally but it should be pretty
+
+ align:start position:0%
+formally but it should be pretty
+ 
+
+ align:start position:0%
+formally but it should be pretty
+intuitive so cases two and three sorry
+
+ align:start position:0%
+intuitive so cases two and three sorry
+ 
+
+ align:start position:0%
+intuitive so cases two and three sorry
+pointing it the wrong place cases two
+
+ align:start position:0%
+pointing it the wrong place cases two
+ 
+
+ align:start position:0%
+pointing it the wrong place cases two
+and three are terminal when we do case
+
+ align:start position:0%
+and three are terminal when we do case
+ 
+
+ align:start position:0%
+and three are terminal when we do case
+three we're done when we do case two
+
+ align:start position:0%
+three we're done when we do case two
+ 
+
+ align:start position:0%
+three we're done when we do case two
+we're about to do case three and then
+
+ align:start position:0%
+we're about to do case three and then
+ 
+
+ align:start position:0%
+we're about to do case three and then
+we're done okay so the only thing we
+
+ align:start position:0%
+we're done okay so the only thing we
+ 
+
+ align:start position:0%
+we're done okay so the only thing we
+really have to count is case one because
+
+ align:start position:0%
+really have to count is case one because
+ 
+
+ align:start position:0%
+really have to count is case one because
+each of these operations you know
+
+ align:start position:0%
+each of these operations you know
+ 
+
+ align:start position:0%
+each of these operations you know
+recoloring rotation they all take
+
+ align:start position:0%
+recoloring rotation they all take
+ 
+
+ align:start position:0%
+recoloring rotation they all take
+constant time so it's a matter of how
+
+ align:start position:0%
+constant time so it's a matter of how
+ 
+
+ align:start position:0%
+constant time so it's a matter of how
+many are
+
+ align:start position:0%
+many are
+ 
+
+ align:start position:0%
+many are
+there uh case one does some recoloring
+
+ align:start position:0%
+there uh case one does some recoloring
+ 
+
+ align:start position:0%
+there uh case one does some recoloring
+doesn't change the tree at all
+
+ align:start position:0%
+doesn't change the tree at all
+ 
+
+ align:start position:0%
+doesn't change the tree at all
+and moves X up by two levels we know
+
+ align:start position:0%
+and moves X up by two levels we know
+ 
+
+ align:start position:0%
+and moves X up by two levels we know
+that the height of the tree is at most 2
+
+ align:start position:0%
+that the height of the tree is at most 2
+ 
+
+ align:start position:0%
+that the height of the tree is at most 2
+log n + 1 so the number of case ones is
+
+ align:start position:0%
+log n + 1 so the number of case ones is
+ 
+
+ align:start position:0%
+log n + 1 so the number of case ones is
+at most log n +
+
+ align:start position:0%
+at most log n +
+ 
+
+ align:start position:0%
+at most log n +
+one okay so the number of case ones um
+
+ align:start position:0%
+one okay so the number of case ones um
+ 
+
+ align:start position:0%
+one okay so the number of case ones um
+it's at most log
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+n so those take log n time and then the
+
+ align:start position:0%
+n so those take log n time and then the
+ 
+
+ align:start position:0%
+n so those take log n time and then the
+number of case twos and threes is at
+
+ align:start position:0%
+number of case twos and threes is at
+ 
+
+ align:start position:0%
+number of case twos and threes is at
+most one for one of these
+
+ align:start position:0%
+most one for one of these
+ 
+
+ align:start position:0%
+most one for one of these
+calls well together twos and threes is
+
+ align:start position:0%
+calls well together twos and threes is
+ 
+
+ align:start position:0%
+calls well together twos and threes is
+at most
+
+ align:start position:0%
+at most
+ 
+
+ align:start position:0%
+at most
+two okay so log n time cool uh the other
+
+ align:start position:0%
+two okay so log n time cool uh the other
+ 
+
+ align:start position:0%
+two okay so log n time cool uh the other
+thing that's interesting about red black
+
+ align:start position:0%
+thing that's interesting about red black
+ 
+
+ align:start position:0%
+thing that's interesting about red black
+insertion is that it only makes uh order
+
+ align:start position:0%
+insertion is that it only makes uh order
+ 
+
+ align:start position:0%
+insertion is that it only makes uh order
+one
+
+ align:start position:0%
+one
+ 
+
+ align:start position:0%
+one
+rotations so most of the changes are
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+recoloring um the all case one just does
+
+ align:start position:0%
+recoloring um the all case one just does
+ 
+
+ align:start position:0%
+recoloring um the all case one just does
+recoloring no rotations case two maybe
+
+ align:start position:0%
+recoloring no rotations case two maybe
+ 
+
+ align:start position:0%
+recoloring no rotations case two maybe
+does one rotation case three does one
+
+ align:start position:0%
+does one rotation case three does one
+ 
+
+ align:start position:0%
+does one rotation case three does one
+rotation if you happen to be in those
+
+ align:start position:0%
+rotation if you happen to be in those
+ 
+
+ align:start position:0%
+rotation if you happen to be in those
+cases
+
+ align:start position:0%
+cases
+ 
+
+ align:start position:0%
+cases
+so the number of rotations is at most
+
+ align:start position:0%
+so the number of rotations is at most
+ 
+
+ align:start position:0%
+so the number of rotations is at most
+two it's either one or two in an
+
+ align:start position:0%
+two it's either one or two in an
+ 
+
+ align:start position:0%
+two it's either one or two in an
+insertion it's kind of nice because uh
+
+ align:start position:0%
+insertion it's kind of nice because uh
+ 
+
+ align:start position:0%
+insertion it's kind of nice because uh
+rotating a tree is a bit more annoying
+
+ align:start position:0%
+rotating a tree is a bit more annoying
+ 
+
+ align:start position:0%
+rotating a tree is a bit more annoying
+than
+
+ align:start position:0%
+than
+ 
+
+ align:start position:0%
+than
+uh than recoloring a tree why because if
+
+ align:start position:0%
+uh than recoloring a tree why because if
+ 
+
+ align:start position:0%
+uh than recoloring a tree why because if
+you have say uh a data structure you
+
+ align:start position:0%
+you have say uh a data structure you
+ 
+
+ align:start position:0%
+you have say uh a data structure you
+have a search tree you know presumably
+
+ align:start position:0%
+have a search tree you know presumably
+ 
+
+ align:start position:0%
+have a search tree you know presumably
+people are using the search tree for
+
+ align:start position:0%
+people are using the search tree for
+ 
+
+ align:start position:0%
+people are using the search tree for
+something they're like making queries
+
+ align:start position:0%
+something they're like making queries
+ 
+
+ align:start position:0%
+something they're like making queries
+for example this search tree represents
+
+ align:start position:0%
+for example this search tree represents
+ 
+
+ align:start position:0%
+for example this search tree represents
+I don't know all the documents matching
+
+ align:start position:0%
+I don't know all the documents matching
+ 
+
+ align:start position:0%
+I don't know all the documents matching
+the word computer in Google okay we got
+
+ align:start position:0%
+the word computer in Google okay we got
+ 
+
+ align:start position:0%
+the word computer in Google okay we got
+a Google t-shirt up here so let's use a
+
+ align:start position:0%
+a Google t-shirt up here so let's use a
+ 
+
+ align:start position:0%
+a Google t-shirt up here so let's use a
+Google reference you have this search
+
+ align:start position:0%
+Google reference you have this search
+ 
+
+ align:start position:0%
+Google reference you have this search
+Tree stores all the things containing
+
+ align:start position:0%
+Tree stores all the things containing
+ 
+
+ align:start position:0%
+Tree stores all the things containing
+the word Google you'd like to search
+
+ align:start position:0%
+the word Google you'd like to search
+ 
+
+ align:start position:0%
+the word Google you'd like to search
+maybe for the ones that were modified
+
+ align:start position:0%
+maybe for the ones that were modified
+ 
+
+ align:start position:0%
+maybe for the ones that were modified
+after a certain date or whatever it is
+
+ align:start position:0%
+after a certain date or whatever it is
+ 
+
+ align:start position:0%
+after a certain date or whatever it is
+you want to do so you're doing some
+
+ align:start position:0%
+you want to do so you're doing some
+ 
+
+ align:start position:0%
+you want to do so you're doing some
+queries on this tree and people are
+
+ align:start position:0%
+queries on this tree and people are
+ 
+
+ align:start position:0%
+queries on this tree and people are
+pummeling Google like crazy with queries
+
+ align:start position:0%
+pummeling Google like crazy with queries
+ 
+
+ align:start position:0%
+pummeling Google like crazy with queries
+you know they get a zillion in a second
+
+ align:start position:0%
+you know they get a zillion in a second
+ 
+
+ align:start position:0%
+you know they get a zillion in a second
+don't quote me on that the number may
+
+ align:start position:0%
+don't quote me on that the number may
+ 
+
+ align:start position:0%
+don't quote me on that the number may
+not be accurate it's a zillion but um
+
+ align:start position:0%
+not be accurate it's a zillion but um
+ 
+
+ align:start position:0%
+not be accurate it's a zillion but um
+people are making searches all the time
+
+ align:start position:0%
+people are making searches all the time
+ 
+
+ align:start position:0%
+people are making searches all the time
+if you recolor the tree people can still
+
+ align:start position:0%
+if you recolor the tree people can still
+ 
+
+ align:start position:0%
+if you recolor the tree people can still
+make searches that's just a little bit
+
+ align:start position:0%
+make searches that's just a little bit
+ 
+
+ align:start position:0%
+make searches that's just a little bit
+you're flipping I don't care in a search
+
+ align:start position:0%
+you're flipping I don't care in a search
+ 
+
+ align:start position:0%
+you're flipping I don't care in a search
+whether a note is red or black because I
+
+ align:start position:0%
+whether a note is red or black because I
+ 
+
+ align:start position:0%
+whether a note is red or black because I
+know it will have logarithmic height so
+
+ align:start position:0%
+know it will have logarithmic height so
+ 
+
+ align:start position:0%
+know it will have logarithmic height so
+you can come along and make your
+
+ align:start position:0%
+you can come along and make your
+ 
+
+ align:start position:0%
+you can come along and make your
+occasional updates as you as your
+
+ align:start position:0%
+occasional updates as you as your
+ 
+
+ align:start position:0%
+occasional updates as you as your
+crawler surfs the webs and finds changes
+
+ align:start position:0%
+crawler surfs the webs and finds changes
+ 
+
+ align:start position:0%
+crawler surfs the webs and finds changes
+and recoloring is great rotation is a
+
+ align:start position:0%
+and recoloring is great rotation is a
+ 
+
+ align:start position:0%
+and recoloring is great rotation is a
+bit expensive because you have to lock
+
+ align:start position:0%
+bit expensive because you have to lock
+ 
+
+ align:start position:0%
+bit expensive because you have to lock
+those nodes make sure no one touches
+
+ align:start position:0%
+those nodes make sure no one touches
+ 
+
+ align:start position:0%
+those nodes make sure no one touches
+them for the duration that you rotate
+
+ align:start position:0%
+them for the duration that you rotate
+ 
+
+ align:start position:0%
+them for the duration that you rotate
+them and then unlock them so it's nice
+
+ align:start position:0%
+them and then unlock them so it's nice
+ 
+
+ align:start position:0%
+them and then unlock them so it's nice
+that the number of rotations is small
+
+ align:start position:0%
+that the number of rotations is small
+ 
+
+ align:start position:0%
+that the number of rotations is small
+really small just two whereas the time
+
+ align:start position:0%
+really small just two whereas the time
+ 
+
+ align:start position:0%
+really small just two whereas the time
+has to be log n because we're inserting
+
+ align:start position:0%
+has to be log n because we're inserting
+ 
+
+ align:start position:0%
+has to be log n because we're inserting
+into a sorted list essentially so
+
+ align:start position:0%
+into a sorted list essentially so
+ 
+
+ align:start position:0%
+into a sorted list essentially so
+there's an N logn lower if we do n
+
+ align:start position:0%
+there's an N logn lower if we do n
+ 
+
+ align:start position:0%
+there's an N logn lower if we do n
+insertions okay deletion I'm not going
+
+ align:start position:0%
+insertions okay deletion I'm not going
+ 
+
+ align:start position:0%
+insertions okay deletion I'm not going
+to cover here you should read it in the
+
+ align:start position:0%
+to cover here you should read it in the
+ 
+
+ align:start position:0%
+to cover here you should read it in the
+book it's a little bit more complicated
+
+ align:start position:0%
+book it's a little bit more complicated
+ 
+
+ align:start position:0%
+book it's a little bit more complicated
+but the same ideas it gets the same
+
+ align:start position:0%
+but the same ideas it gets the same
+ 
+
+ align:start position:0%
+but the same ideas it gets the same
+bounds log and time order one
+
+ align:start position:0%
+bounds log and time order one
+ 
+
+ align:start position:0%
+bounds log and time order one
+rotations so check it out that's red
+
+ align:start position:0%
+rotations so check it out that's red
+ 
+
+ align:start position:0%
+rotations so check it out that's red
+black trees now you can maintain data in
+
+ align:start position:0%
+black trees now you can maintain data in
+ 
+
+ align:start position:0%
+black trees now you can maintain data in
+login time per operation
+
+ align:start position:0%
+login time per operation
+ 
+
+ align:start position:0%
+login time per operation
+cool we'll now see three ways to do it
\ No newline at end of file
diff --git a/OMFpHmfC1pY.txt b/OMFpHmfC1pY.txt
new file mode 100644
index 0000000000000000000000000000000000000000..91c2cd171170854da0716eab9211b37427a4e0e6
--- /dev/null
+++ b/OMFpHmfC1pY.txt
@@ -0,0 +1,9611 @@
+align:start position:0%
+ 
+today
+
+ align:start position:0%
+today
+ 
+
+ align:start position:0%
+today
+we are talking about
+
+ align:start position:0%
+we are talking about
+ 
+
+ align:start position:0%
+we are talking about
+bonding between molecules
+
+ align:start position:0%
+bonding between molecules
+ 
+
+ align:start position:0%
+bonding between molecules
+now we have talked a lot about bonding
+
+ align:start position:0%
+now we have talked a lot about bonding
+ 
+
+ align:start position:0%
+now we have talked a lot about bonding
+within molecules
+
+ align:start position:0%
+within molecules
+ 
+
+ align:start position:0%
+within molecules
+right and that got us to saying things
+
+ align:start position:0%
+right and that got us to saying things
+ 
+
+ align:start position:0%
+right and that got us to saying things
+like well you can use electronegativity
+
+ align:start position:0%
+like well you can use electronegativity
+ 
+
+ align:start position:0%
+like well you can use electronegativity
+for example and say
+
+ align:start position:0%
+for example and say
+ 
+
+ align:start position:0%
+for example and say
+i got an ionic bond all right
+
+ align:start position:0%
+i got an ionic bond all right
+ 
+
+ align:start position:0%
+i got an ionic bond all right
+or i've got a nonpolar covalent bond or
+
+ align:start position:0%
+or i've got a nonpolar covalent bond or
+ 
+
+ align:start position:0%
+or i've got a nonpolar covalent bond or
+i've got a polar covalent bond but today
+
+ align:start position:0%
+i've got a polar covalent bond but today
+ 
+
+ align:start position:0%
+i've got a polar covalent bond but today
+what we're gonna do is talk about how
+
+ align:start position:0%
+what we're gonna do is talk about how
+ 
+
+ align:start position:0%
+what we're gonna do is talk about how
+these molecules how these molecules
+
+ align:start position:0%
+these molecules how these molecules
+ 
+
+ align:start position:0%
+these molecules how these molecules
+bond together what sorts of interactions
+
+ align:start position:0%
+bond together what sorts of interactions
+ 
+
+ align:start position:0%
+bond together what sorts of interactions
+can they have
+
+ align:start position:0%
+can they have
+ 
+
+ align:start position:0%
+can they have
+and those are really important right so
+
+ align:start position:0%
+and those are really important right so
+ 
+
+ align:start position:0%
+and those are really important right so
+so that's going to be the topic now if
+
+ align:start position:0%
+so that's going to be the topic now if
+ 
+
+ align:start position:0%
+so that's going to be the topic now if
+we just get started with what we know
+
+ align:start position:0%
+we just get started with what we know
+ 
+
+ align:start position:0%
+we just get started with what we know
+what's up there right well there's ionic
+
+ align:start position:0%
+what's up there right well there's ionic
+ 
+
+ align:start position:0%
+what's up there right well there's ionic
+so let's say
+
+ align:start position:0%
+so let's say
+ 
+
+ align:start position:0%
+so let's say
+i'm going to i'm going to fill this in
+
+ align:start position:0%
+i'm going to i'm going to fill this in
+ 
+
+ align:start position:0%
+i'm going to i'm going to fill this in
+bond
+
+ align:start position:0%
+bond
+ 
+
+ align:start position:0%
+bond
+a model you'll see what i mean i'm going
+
+ align:start position:0%
+a model you'll see what i mean i'm going
+ 
+
+ align:start position:0%
+a model you'll see what i mean i'm going
+to draw a little cartoon the
+
+ align:start position:0%
+to draw a little cartoon the
+ 
+
+ align:start position:0%
+to draw a little cartoon the
+attraction how it's attracted uh the
+
+ align:start position:0%
+attraction how it's attracted uh the
+ 
+
+ align:start position:0%
+attraction how it's attracted uh the
+energy range
+
+ align:start position:0%
+energy range
+ 
+
+ align:start position:0%
+energy range
+and an example right so for ionic bond
+
+ align:start position:0%
+and an example right so for ionic bond
+ 
+
+ align:start position:0%
+and an example right so for ionic bond
+we got ionic ionic
+
+ align:start position:0%
+we got ionic ionic
+ 
+
+ align:start position:0%
+we got ionic ionic
+okay and here we go watch this plus
+
+ align:start position:0%
+okay and here we go watch this plus
+ 
+
+ align:start position:0%
+okay and here we go watch this plus
+and minus there's my model
+
+ align:start position:0%
+and minus there's my model
+ 
+
+ align:start position:0%
+and minus there's my model
+okay and the attraction here well we'll
+
+ align:start position:0%
+okay and the attraction here well we'll
+ 
+
+ align:start position:0%
+okay and the attraction here well we'll
+get a little specific it's a cation
+
+ align:start position:0%
+get a little specific it's a cation
+ 
+
+ align:start position:0%
+get a little specific it's a cation
+and an anion and we know that that's
+
+ align:start position:0%
+and an anion and we know that that's
+ 
+
+ align:start position:0%
+and an anion and we know that that's
+gonna go like coulomb's law right so the
+
+ align:start position:0%
+gonna go like coulomb's law right so the
+ 
+
+ align:start position:0%
+gonna go like coulomb's law right so the
+attraction the energy
+
+ align:start position:0%
+attraction the energy
+ 
+
+ align:start position:0%
+attraction the energy
+not the force the energy will go like
+
+ align:start position:0%
+not the force the energy will go like
+ 
+
+ align:start position:0%
+not the force the energy will go like
+one over r
+
+ align:start position:0%
+one over r
+ 
+
+ align:start position:0%
+one over r
+roughly uh now what is the energy well
+
+ align:start position:0%
+roughly uh now what is the energy well
+ 
+
+ align:start position:0%
+roughly uh now what is the energy well
+the energy is pretty wide ranging it's
+
+ align:start position:0%
+the energy is pretty wide ranging it's
+ 
+
+ align:start position:0%
+the energy is pretty wide ranging it's
+i'm gonna do this in in kilojoules per
+
+ align:start position:0%
+i'm gonna do this in in kilojoules per
+ 
+
+ align:start position:0%
+i'm gonna do this in in kilojoules per
+mole since those are the units i have
+
+ align:start position:0%
+mole since those are the units i have
+ 
+
+ align:start position:0%
+mole since those are the units i have
+i'll write that in a second and
+
+ align:start position:0%
+i'll write that in a second and
+ 
+
+ align:start position:0%
+i'll write that in a second and
+an ionic bond can have lots and lots of
+
+ align:start position:0%
+an ionic bond can have lots and lots of
+ 
+
+ align:start position:0%
+an ionic bond can have lots and lots of
+range in here and it typically can be
+
+ align:start position:0%
+range in here and it typically can be
+ 
+
+ align:start position:0%
+range in here and it typically can be
+very strong
+
+ align:start position:0%
+very strong
+ 
+
+ align:start position:0%
+very strong
+something we've already talked about an
+
+ align:start position:0%
+something we've already talked about an
+ 
+
+ align:start position:0%
+something we've already talked about an
+example would be sodium chloride
+
+ align:start position:0%
+example would be sodium chloride
+ 
+
+ align:start position:0%
+example would be sodium chloride
+it's right there let's put the units
+
+ align:start position:0%
+it's right there let's put the units
+ 
+
+ align:start position:0%
+it's right there let's put the units
+here
+
+ align:start position:0%
+here
+ 
+
+ align:start position:0%
+here
+the energy units are in i'm going to
+
+ align:start position:0%
+the energy units are in i'm going to
+ 
+
+ align:start position:0%
+the energy units are in i'm going to
+write it here
+
+ align:start position:0%
+write it here
+ 
+
+ align:start position:0%
+write it here
+kilojoules per mole
+
+ align:start position:0%
+kilojoules per mole
+ 
+
+ align:start position:0%
+kilojoules per mole
+okay now in a covalent bond so covalent
+
+ align:start position:0%
+okay now in a covalent bond so covalent
+ 
+
+ align:start position:0%
+okay now in a covalent bond so covalent
+would be here
+
+ align:start position:0%
+would be here
+ 
+
+ align:start position:0%
+would be here
+okay so in a covalent bond remember
+
+ align:start position:0%
+okay so in a covalent bond remember
+ 
+
+ align:start position:0%
+okay so in a covalent bond remember
+we've got something very different we've
+
+ align:start position:0%
+we've got something very different we've
+ 
+
+ align:start position:0%
+we've got something very different we've
+got this carrying and sharing kind of
+
+ align:start position:0%
+got this carrying and sharing kind of
+ 
+
+ align:start position:0%
+got this carrying and sharing kind of
+thing
+
+ align:start position:0%
+thing
+ 
+
+ align:start position:0%
+thing
+and we've got maybe two atoms right two
+
+ align:start position:0%
+and we've got maybe two atoms right two
+ 
+
+ align:start position:0%
+and we've got maybe two atoms right two
+atoms like this
+
+ align:start position:0%
+atoms like this
+ 
+
+ align:start position:0%
+atoms like this
+and then the charge is sort of you know
+
+ align:start position:0%
+and then the charge is sort of you know
+ 
+
+ align:start position:0%
+and then the charge is sort of you know
+the negative charge is sort of floating
+
+ align:start position:0%
+the negative charge is sort of floating
+ 
+
+ align:start position:0%
+the negative charge is sort of floating
+around and sharing
+
+ align:start position:0%
+around and sharing
+ 
+
+ align:start position:0%
+around and sharing
+those two centers like in h2
+
+ align:start position:0%
+those two centers like in h2
+ 
+
+ align:start position:0%
+those two centers like in h2
+or cl2 i'm going to use cl so let's keep
+
+ align:start position:0%
+or cl2 i'm going to use cl so let's keep
+ 
+
+ align:start position:0%
+or cl2 i'm going to use cl so let's keep
+using cl
+
+ align:start position:0%
+using cl
+ 
+
+ align:start position:0%
+using cl
+right that would also be an example of a
+
+ align:start position:0%
+right that would also be an example of a
+ 
+
+ align:start position:0%
+right that would also be an example of a
+covalent bond
+
+ align:start position:0%
+covalent bond
+ 
+
+ align:start position:0%
+covalent bond
+and the energy range there is also quite
+
+ align:start position:0%
+and the energy range there is also quite
+ 
+
+ align:start position:0%
+and the energy range there is also quite
+large 150
+
+ align:start position:0%
+large 150
+ 
+
+ align:start position:0%
+large 150
+to 1100 are the numbers i got the
+
+ align:start position:0%
+to 1100 are the numbers i got the
+ 
+
+ align:start position:0%
+to 1100 are the numbers i got the
+attraction is shared electrons
+
+ align:start position:0%
+attraction is shared electrons
+ 
+
+ align:start position:0%
+attraction is shared electrons
+shared pair
+
+ align:start position:0%
+shared pair
+ 
+
+ align:start position:0%
+shared pair
+of electrons and
+
+ align:start position:0%
+of electrons and
+ 
+
+ align:start position:0%
+of electrons and
+i'm not putting an r dependence because
+
+ align:start position:0%
+i'm not putting an r dependence because
+ 
+
+ align:start position:0%
+i'm not putting an r dependence because
+for a covalent bond it's complicated
+
+ align:start position:0%
+for a covalent bond it's complicated
+ 
+
+ align:start position:0%
+for a covalent bond it's complicated
+it's complicated there's no it is it is
+
+ align:start position:0%
+it's complicated there's no it is it is
+ 
+
+ align:start position:0%
+it's complicated there's no it is it is
+it's a complicated but it's a very nice
+
+ align:start position:0%
+it's a complicated but it's a very nice
+ 
+
+ align:start position:0%
+it's a complicated but it's a very nice
+happy relationship but it's a
+
+ align:start position:0%
+happy relationship but it's a
+ 
+
+ align:start position:0%
+happy relationship but it's a
+complicated r
+
+ align:start position:0%
+complicated r
+ 
+
+ align:start position:0%
+complicated r
+dependence so you can't simplify it like
+
+ align:start position:0%
+dependence so you can't simplify it like
+ 
+
+ align:start position:0%
+dependence so you can't simplify it like
+you can
+
+ align:start position:0%
+you can
+ 
+
+ align:start position:0%
+you can
+with a one over r or like some of the
+
+ align:start position:0%
+with a one over r or like some of the
+ 
+
+ align:start position:0%
+with a one over r or like some of the
+other interactions we'll talk about
+
+ align:start position:0%
+other interactions we'll talk about
+ 
+
+ align:start position:0%
+other interactions we'll talk about
+today
+
+ align:start position:0%
+today
+ 
+
+ align:start position:0%
+today
+okay one over r not for covalent
+
+ align:start position:0%
+okay one over r not for covalent
+ 
+
+ align:start position:0%
+okay one over r not for covalent
+all right now that's where we've been um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+here we go here we go look at this
+
+ align:start position:0%
+here we go here we go look at this
+ 
+
+ align:start position:0%
+here we go here we go look at this
+i'm not i'm just getting started because
+
+ align:start position:0%
+i'm not i'm just getting started because
+ 
+
+ align:start position:0%
+i'm not i'm just getting started because
+the thing is
+
+ align:start position:0%
+the thing is
+ 
+
+ align:start position:0%
+the thing is
+now we got to talk about how these
+
+ align:start position:0%
+now we got to talk about how these
+ 
+
+ align:start position:0%
+now we got to talk about how these
+molecules can talk to each other
+
+ align:start position:0%
+molecules can talk to each other
+ 
+
+ align:start position:0%
+molecules can talk to each other
+and there's a variety of ways what i
+
+ align:start position:0%
+and there's a variety of ways what i
+ 
+
+ align:start position:0%
+and there's a variety of ways what i
+want to focus on
+
+ align:start position:0%
+want to focus on
+ 
+
+ align:start position:0%
+want to focus on
+first is this thing here that's that
+
+ align:start position:0%
+first is this thing here that's that
+ 
+
+ align:start position:0%
+first is this thing here that's that
+polar covalent bond
+
+ align:start position:0%
+polar covalent bond
+ 
+
+ align:start position:0%
+polar covalent bond
+that we've already talked about so we've
+
+ align:start position:0%
+that we've already talked about so we've
+ 
+
+ align:start position:0%
+that we've already talked about so we've
+already got a grounding for it right
+
+ align:start position:0%
+already got a grounding for it right
+ 
+
+ align:start position:0%
+already got a grounding for it right
+but i want to remind you of what happens
+
+ align:start position:0%
+but i want to remind you of what happens
+ 
+
+ align:start position:0%
+but i want to remind you of what happens
+right so if i have
+
+ align:start position:0%
+right so if i have
+ 
+
+ align:start position:0%
+right so if i have
+let's keep with hcl if i have hcl
+
+ align:start position:0%
+let's keep with hcl if i have hcl
+ 
+
+ align:start position:0%
+let's keep with hcl if i have hcl
+that's a nice version of a polar
+
+ align:start position:0%
+that's a nice version of a polar
+ 
+
+ align:start position:0%
+that's a nice version of a polar
+covalent bond
+
+ align:start position:0%
+covalent bond
+ 
+
+ align:start position:0%
+covalent bond
+and remember what happens there is you
+
+ align:start position:0%
+and remember what happens there is you
+ 
+
+ align:start position:0%
+and remember what happens there is you
+you got
+
+ align:start position:0%
+you got
+ 
+
+ align:start position:0%
+you got
+a sharing but sort of unfair right so
+
+ align:start position:0%
+a sharing but sort of unfair right so
+ 
+
+ align:start position:0%
+a sharing but sort of unfair right so
+one of the atoms took a little more
+
+ align:start position:0%
+one of the atoms took a little more
+ 
+
+ align:start position:0%
+one of the atoms took a little more
+of the charge and so sometimes we
+
+ align:start position:0%
+of the charge and so sometimes we
+ 
+
+ align:start position:0%
+of the charge and so sometimes we
+you know represent that with like a more
+
+ align:start position:0%
+you know represent that with like a more
+ 
+
+ align:start position:0%
+you know represent that with like a more
+of the cloud
+
+ align:start position:0%
+of the cloud
+ 
+
+ align:start position:0%
+of the cloud
+right on one side than the other but
+
+ align:start position:0%
+right on one side than the other but
+ 
+
+ align:start position:0%
+right on one side than the other but
+it's still a covalent bond
+
+ align:start position:0%
+it's still a covalent bond
+ 
+
+ align:start position:0%
+it's still a covalent bond
+yeah but the thing is that and and so
+
+ align:start position:0%
+yeah but the thing is that and and so
+ 
+
+ align:start position:0%
+yeah but the thing is that and and so
+what you're left with like in this case
+
+ align:start position:0%
+what you're left with like in this case
+ 
+
+ align:start position:0%
+what you're left with like in this case
+is some positive charge on the hydrogen
+
+ align:start position:0%
+is some positive charge on the hydrogen
+ 
+
+ align:start position:0%
+is some positive charge on the hydrogen
+atom
+
+ align:start position:0%
+atom
+ 
+
+ align:start position:0%
+atom
+and some negative charge on the chlorine
+
+ align:start position:0%
+and some negative charge on the chlorine
+ 
+
+ align:start position:0%
+and some negative charge on the chlorine
+atom and we did this already we used
+
+ align:start position:0%
+atom and we did this already we used
+ 
+
+ align:start position:0%
+atom and we did this already we used
+these symbols
+
+ align:start position:0%
+these symbols
+ 
+
+ align:start position:0%
+these symbols
+and we also talked about how that leads
+
+ align:start position:0%
+and we also talked about how that leads
+ 
+
+ align:start position:0%
+and we also talked about how that leads
+you to
+
+ align:start position:0%
+you to
+ 
+
+ align:start position:0%
+you to
+a dipole moment
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+now what is a dipole well a dipole is
+
+ align:start position:0%
+now what is a dipole well a dipole is
+ 
+
+ align:start position:0%
+now what is a dipole well a dipole is
+just
+
+ align:start position:0%
+just
+ 
+
+ align:start position:0%
+just
+the is is just the the description of
+
+ align:start position:0%
+the is is just the the description of
+ 
+
+ align:start position:0%
+the is is just the the description of
+what you have in this case where you've
+
+ align:start position:0%
+what you have in this case where you've
+ 
+
+ align:start position:0%
+what you have in this case where you've
+got
+
+ align:start position:0%
+got
+ 
+
+ align:start position:0%
+got
+two charges of opposite signs
+
+ align:start position:0%
+two charges of opposite signs
+ 
+
+ align:start position:0%
+two charges of opposite signs
+separated by some distance okay
+
+ align:start position:0%
+separated by some distance okay
+ 
+
+ align:start position:0%
+separated by some distance okay
+two charges those aren't full charges
+
+ align:start position:0%
+two charges those aren't full charges
+ 
+
+ align:start position:0%
+two charges those aren't full charges
+those are partial charges
+
+ align:start position:0%
+those are partial charges
+ 
+
+ align:start position:0%
+those are partial charges
+right they're separated by some distance
+
+ align:start position:0%
+right they're separated by some distance
+ 
+
+ align:start position:0%
+right they're separated by some distance
+the distance between these two atoms
+
+ align:start position:0%
+the distance between these two atoms
+ 
+
+ align:start position:0%
+the distance between these two atoms
+and you get a dipole moment and it has a
+
+ align:start position:0%
+and you get a dipole moment and it has a
+ 
+
+ align:start position:0%
+and you get a dipole moment and it has a
+magnitude
+
+ align:start position:0%
+magnitude
+ 
+
+ align:start position:0%
+magnitude
+and a direction and remember
+
+ align:start position:0%
+and a direction and remember
+ 
+
+ align:start position:0%
+and a direction and remember
+just so that just to remind you i did
+
+ align:start position:0%
+just so that just to remind you i did
+ 
+
+ align:start position:0%
+just so that just to remind you i did
+share this with you in a previous
+
+ align:start position:0%
+share this with you in a previous
+ 
+
+ align:start position:0%
+share this with you in a previous
+lecture but you know mu
+
+ align:start position:0%
+lecture but you know mu
+ 
+
+ align:start position:0%
+lecture but you know mu
+equals the charge times the distance
+
+ align:start position:0%
+equals the charge times the distance
+ 
+
+ align:start position:0%
+equals the charge times the distance
+between the charge
+
+ align:start position:0%
+between the charge
+ 
+
+ align:start position:0%
+between the charge
+right so that would be like the charge
+
+ align:start position:0%
+right so that would be like the charge
+ 
+
+ align:start position:0%
+right so that would be like the charge
+would be the deltas here and the
+
+ align:start position:0%
+would be the deltas here and the
+ 
+
+ align:start position:0%
+would be the deltas here and the
+distance between them
+
+ align:start position:0%
+distance between them
+ 
+
+ align:start position:0%
+distance between them
+right would be this right r um and i
+
+ align:start position:0%
+right would be this right r um and i
+ 
+
+ align:start position:0%
+right would be this right r um and i
+also and now remember the units are in
+
+ align:start position:0%
+also and now remember the units are in
+ 
+
+ align:start position:0%
+also and now remember the units are in
+dubai
+
+ align:start position:0%
+dubai
+ 
+
+ align:start position:0%
+dubai
+so for this molecule for here
+
+ align:start position:0%
+so for this molecule for here
+ 
+
+ align:start position:0%
+so for this molecule for here
+mu is around 1.8
+
+ align:start position:0%
+mu is around 1.8
+ 
+
+ align:start position:0%
+mu is around 1.8
+d and 1 d
+
+ align:start position:0%
+d and 1 d
+ 
+
+ align:start position:0%
+d and 1 d
+is equal to 3.3
+
+ align:start position:0%
+is equal to 3.3
+ 
+
+ align:start position:0%
+is equal to 3.3
+times 10 to the minus 30th
+
+ align:start position:0%
+times 10 to the minus 30th
+ 
+
+ align:start position:0%
+times 10 to the minus 30th
+coulomb meters those are the units
+
+ align:start position:0%
+coulomb meters those are the units
+ 
+
+ align:start position:0%
+coulomb meters those are the units
+charge times distance charge times
+
+ align:start position:0%
+charge times distance charge times
+ 
+
+ align:start position:0%
+charge times distance charge times
+distance right
+
+ align:start position:0%
+distance right
+ 
+
+ align:start position:0%
+distance right
+okay 3.3 times to the minus thirds
+
+ align:start position:0%
+okay 3.3 times to the minus thirds
+ 
+
+ align:start position:0%
+okay 3.3 times to the minus thirds
+coolants per meter is a dubai
+
+ align:start position:0%
+coolants per meter is a dubai
+ 
+
+ align:start position:0%
+coolants per meter is a dubai
+and again just to remind you because we
+
+ align:start position:0%
+and again just to remind you because we
+ 
+
+ align:start position:0%
+and again just to remind you because we
+did talk about this when we talked about
+
+ align:start position:0%
+did talk about this when we talked about
+ 
+
+ align:start position:0%
+did talk about this when we talked about
+polar covalent bonds
+
+ align:start position:0%
+polar covalent bonds
+ 
+
+ align:start position:0%
+polar covalent bonds
+the dipole moment of these molecules
+
+ align:start position:0%
+the dipole moment of these molecules
+ 
+
+ align:start position:0%
+the dipole moment of these molecules
+tends to range
+
+ align:start position:0%
+tends to range
+ 
+
+ align:start position:0%
+tends to range
+from zero right there
+
+ align:start position:0%
+from zero right there
+ 
+
+ align:start position:0%
+from zero right there
+right no dipole to 10 or so
+
+ align:start position:0%
+right no dipole to 10 or so
+ 
+
+ align:start position:0%
+right no dipole to 10 or so
+11. right device
+
+ align:start position:0%
+11. right device
+ 
+
+ align:start position:0%
+11. right device
+now why is this important well because
+
+ align:start position:0%
+now why is this important well because
+ 
+
+ align:start position:0%
+now why is this important well because
+if you
+
+ align:start position:0%
+if you
+ 
+
+ align:start position:0%
+if you
+if you now think well what would happen
+
+ align:start position:0%
+if you now think well what would happen
+ 
+
+ align:start position:0%
+if you now think well what would happen
+what would happen if i brought another
+
+ align:start position:0%
+what would happen if i brought another
+ 
+
+ align:start position:0%
+what would happen if i brought another
+charge
+
+ align:start position:0%
+charge
+ 
+
+ align:start position:0%
+charge
+up to the dipole what would happen right
+
+ align:start position:0%
+up to the dipole what would happen right
+ 
+
+ align:start position:0%
+up to the dipole what would happen right
+let's say that i bring a positive charge
+
+ align:start position:0%
+let's say that i bring a positive charge
+ 
+
+ align:start position:0%
+let's say that i bring a positive charge
+let's say that i have
+
+ align:start position:0%
+let's say that i have
+ 
+
+ align:start position:0%
+let's say that i have
+that i'm a sodium and i've lost that
+
+ align:start position:0%
+that i'm a sodium and i've lost that
+ 
+
+ align:start position:0%
+that i'm a sodium and i've lost that
+outer electron which we know is pretty
+
+ align:start position:0%
+outer electron which we know is pretty
+ 
+
+ align:start position:0%
+outer electron which we know is pretty
+easy to lose
+
+ align:start position:0%
+easy to lose
+ 
+
+ align:start position:0%
+easy to lose
+if you're sodium right so i'm positively
+
+ align:start position:0%
+if you're sodium right so i'm positively
+ 
+
+ align:start position:0%
+if you're sodium right so i'm positively
+charged
+
+ align:start position:0%
+charged
+ 
+
+ align:start position:0%
+charged
+and i'm coming along and i see this
+
+ align:start position:0%
+and i'm coming along and i see this
+ 
+
+ align:start position:0%
+and i'm coming along and i see this
+dipole well it turns out
+
+ align:start position:0%
+dipole well it turns out
+ 
+
+ align:start position:0%
+dipole well it turns out
+that as you can imagine i'm going to be
+
+ align:start position:0%
+that as you can imagine i'm going to be
+ 
+
+ align:start position:0%
+that as you can imagine i'm going to be
+attracted to that negative charge
+
+ align:start position:0%
+attracted to that negative charge
+ 
+
+ align:start position:0%
+attracted to that negative charge
+right so this molecule is going to
+
+ align:start position:0%
+right so this molecule is going to
+ 
+
+ align:start position:0%
+right so this molecule is going to
+orient
+
+ align:start position:0%
+orient
+ 
+
+ align:start position:0%
+orient
+in such a way that that i can actually
+
+ align:start position:0%
+in such a way that that i can actually
+ 
+
+ align:start position:0%
+in such a way that that i can actually
+bond bond to the to the molecule
+
+ align:start position:0%
+bond bond to the to the molecule
+ 
+
+ align:start position:0%
+bond bond to the to the molecule
+and and be attracted to the dipole of
+
+ align:start position:0%
+and and be attracted to the dipole of
+ 
+
+ align:start position:0%
+and and be attracted to the dipole of
+the molecule so that is actually another
+
+ align:start position:0%
+the molecule so that is actually another
+ 
+
+ align:start position:0%
+the molecule so that is actually another
+type of bond
+
+ align:start position:0%
+type of bond
+ 
+
+ align:start position:0%
+type of bond
+right and we'll call that ion
+
+ align:start position:0%
+right and we'll call that ion
+ 
+
+ align:start position:0%
+right and we'll call that ion
+dipole it's an ion dipole bond
+
+ align:start position:0%
+dipole it's an ion dipole bond
+ 
+
+ align:start position:0%
+dipole it's an ion dipole bond
+okay let's do this so that i
+
+ align:start position:0%
+okay let's do this so that i
+ 
+
+ align:start position:0%
+okay let's do this so that i
+stay within the lines
+
+ align:start position:0%
+stay within the lines
+ 
+
+ align:start position:0%
+stay within the lines
+all right now okay so what does that
+
+ align:start position:0%
+all right now okay so what does that
+ 
+
+ align:start position:0%
+all right now okay so what does that
+look like well we just said
+
+ align:start position:0%
+look like well we just said
+ 
+
+ align:start position:0%
+look like well we just said
+it's a charge i'm taking a single charge
+
+ align:start position:0%
+it's a charge i'm taking a single charge
+ 
+
+ align:start position:0%
+it's a charge i'm taking a single charge
+and i'm bringing it to this thing that
+
+ align:start position:0%
+and i'm bringing it to this thing that
+ 
+
+ align:start position:0%
+and i'm bringing it to this thing that
+has a shift of the charge within it
+
+ align:start position:0%
+has a shift of the charge within it
+ 
+
+ align:start position:0%
+has a shift of the charge within it
+that led to these two partial charges so
+
+ align:start position:0%
+that led to these two partial charges so
+ 
+
+ align:start position:0%
+that led to these two partial charges so
+as you as you can imagine it's going to
+
+ align:start position:0%
+as you as you can imagine it's going to
+ 
+
+ align:start position:0%
+as you as you can imagine it's going to
+want to orient
+
+ align:start position:0%
+want to orient
+ 
+
+ align:start position:0%
+want to orient
+to form a bond right so let's draw it
+
+ align:start position:0%
+to form a bond right so let's draw it
+ 
+
+ align:start position:0%
+to form a bond right so let's draw it
+that way right so maybe
+
+ align:start position:0%
+that way right so maybe
+ 
+
+ align:start position:0%
+that way right so maybe
+if i were to take hcl maybe i would have
+
+ align:start position:0%
+if i were to take hcl maybe i would have
+ 
+
+ align:start position:0%
+if i were to take hcl maybe i would have
+sort of like a
+
+ align:start position:0%
+sort of like a
+ 
+
+ align:start position:0%
+sort of like a
+you know a cloud like that right
+
+ align:start position:0%
+you know a cloud like that right
+ 
+
+ align:start position:0%
+you know a cloud like that right
+where it had its minus and it's plus
+
+ align:start position:0%
+where it had its minus and it's plus
+ 
+
+ align:start position:0%
+where it had its minus and it's plus
+there
+
+ align:start position:0%
+there
+ 
+
+ align:start position:0%
+there
+okay why did i i don't know why i used
+
+ align:start position:0%
+okay why did i i don't know why i used
+ 
+
+ align:start position:0%
+okay why did i i don't know why i used
+dashed lines but there you go
+
+ align:start position:0%
+dashed lines but there you go
+ 
+
+ align:start position:0%
+dashed lines but there you go
+and so and so you can see that that is
+
+ align:start position:0%
+and so and so you can see that that is
+ 
+
+ align:start position:0%
+and so and so you can see that that is
+what i wanted to put is the dashed line
+
+ align:start position:0%
+what i wanted to put is the dashed line
+ 
+
+ align:start position:0%
+what i wanted to put is the dashed line
+for the bond itself
+
+ align:start position:0%
+for the bond itself
+ 
+
+ align:start position:0%
+for the bond itself
+give myself a little space right
+
+ align:start position:0%
+give myself a little space right
+ 
+
+ align:start position:0%
+give myself a little space right
+that's the bond we're talking about
+
+ align:start position:0%
+that's the bond we're talking about
+ 
+
+ align:start position:0%
+that's the bond we're talking about
+that's the bomb we're talking now it
+
+ align:start position:0%
+that's the bomb we're talking now it
+ 
+
+ align:start position:0%
+that's the bomb we're talking now it
+turns out that this
+
+ align:start position:0%
+turns out that this
+ 
+
+ align:start position:0%
+turns out that this
+is an important type of interaction
+
+ align:start position:0%
+is an important type of interaction
+ 
+
+ align:start position:0%
+is an important type of interaction
+between molecules and ions
+
+ align:start position:0%
+between molecules and ions
+ 
+
+ align:start position:0%
+between molecules and ions
+it's an ion dipole interaction and it
+
+ align:start position:0%
+it's an ion dipole interaction and it
+ 
+
+ align:start position:0%
+it's an ion dipole interaction and it
+has a range
+
+ align:start position:0%
+has a range
+ 
+
+ align:start position:0%
+has a range
+i wrote it down it has a range
+
+ align:start position:0%
+i wrote it down it has a range
+ 
+
+ align:start position:0%
+i wrote it down it has a range
+of uh 40 to
+
+ align:start position:0%
+of uh 40 to
+ 
+
+ align:start position:0%
+of uh 40 to
+600 huge range
+
+ align:start position:0%
+600 huge range
+ 
+
+ align:start position:0%
+600 huge range
+40 to 600 and the the kind of attraction
+
+ align:start position:0%
+40 to 600 and the the kind of attraction
+ 
+
+ align:start position:0%
+40 to 600 and the the kind of attraction
+is really
+
+ align:start position:0%
+is really
+ 
+
+ align:start position:0%
+is really
+not describable in any other way than
+
+ align:start position:0%
+not describable in any other way than
+ 
+
+ align:start position:0%
+not describable in any other way than
+what we just described it's an ion and a
+
+ align:start position:0%
+what we just described it's an ion and a
+ 
+
+ align:start position:0%
+what we just described it's an ion and a
+dipole
+
+ align:start position:0%
+dipole
+ 
+
+ align:start position:0%
+dipole
+and it goes as one over r squared
+
+ align:start position:0%
+and it goes as one over r squared
+ 
+
+ align:start position:0%
+and it goes as one over r squared
+if you look at the separation the
+
+ align:start position:0%
+if you look at the separation the
+ 
+
+ align:start position:0%
+if you look at the separation the
+distance between these
+
+ align:start position:0%
+distance between these
+ 
+
+ align:start position:0%
+distance between these
+right that distance the dependence
+
+ align:start position:0%
+right that distance the dependence
+ 
+
+ align:start position:0%
+right that distance the dependence
+on the energy on the bond energy will go
+
+ align:start position:0%
+on the energy on the bond energy will go
+ 
+
+ align:start position:0%
+on the energy on the bond energy will go
+like that distance
+
+ align:start position:0%
+like that distance
+ 
+
+ align:start position:0%
+like that distance
+like one over that distance squared now
+
+ align:start position:0%
+like one over that distance squared now
+ 
+
+ align:start position:0%
+like one over that distance squared now
+these dependencies you can get from
+
+ align:start position:0%
+these dependencies you can get from
+ 
+
+ align:start position:0%
+these dependencies you can get from
+from fairly simple electrostatics okay i
+
+ align:start position:0%
+from fairly simple electrostatics okay i
+ 
+
+ align:start position:0%
+from fairly simple electrostatics okay i
+won't derive any of it i'm telling you
+
+ align:start position:0%
+won't derive any of it i'm telling you
+ 
+
+ align:start position:0%
+won't derive any of it i'm telling you
+what it is
+
+ align:start position:0%
+what it is
+ 
+
+ align:start position:0%
+what it is
+okay good okay so an ion tuple now an
+
+ align:start position:0%
+okay good okay so an ion tuple now an
+ 
+
+ align:start position:0%
+okay good okay so an ion tuple now an
+example of that would be
+
+ align:start position:0%
+example of that would be
+ 
+
+ align:start position:0%
+example of that would be
+the system that i just drew right so
+
+ align:start position:0%
+the system that i just drew right so
+ 
+
+ align:start position:0%
+the system that i just drew right so
+n a plus
+
+ align:start position:0%
+n a plus
+ 
+
+ align:start position:0%
+n a plus
+and h cl
+
+ align:start position:0%
+and h cl
+ 
+
+ align:start position:0%
+and h cl
+okay good that's a different kind of
+
+ align:start position:0%
+okay good that's a different kind of
+ 
+
+ align:start position:0%
+okay good that's a different kind of
+bond but see
+
+ align:start position:0%
+bond but see
+ 
+
+ align:start position:0%
+bond but see
+now i could also have two dipoles and i
+
+ align:start position:0%
+now i could also have two dipoles and i
+ 
+
+ align:start position:0%
+now i could also have two dipoles and i
+got a picture for that
+
+ align:start position:0%
+got a picture for that
+ 
+
+ align:start position:0%
+got a picture for that
+well what happened so here's a dipole
+
+ align:start position:0%
+well what happened so here's a dipole
+ 
+
+ align:start position:0%
+well what happened so here's a dipole
+there's my hcl dipole there it is with
+
+ align:start position:0%
+there's my hcl dipole there it is with
+ 
+
+ align:start position:0%
+there's my hcl dipole there it is with
+the negative
+
+ align:start position:0%
+the negative
+ 
+
+ align:start position:0%
+the negative
+partial charge and a positive partial
+
+ align:start position:0%
+partial charge and a positive partial
+ 
+
+ align:start position:0%
+partial charge and a positive partial
+charge and it's also color coded
+
+ align:start position:0%
+charge and it's also color coded
+ 
+
+ align:start position:0%
+charge and it's also color coded
+right okay so that's cool and there they
+
+ align:start position:0%
+right okay so that's cool and there they
+ 
+
+ align:start position:0%
+right okay so that's cool and there they
+are just floating along
+
+ align:start position:0%
+are just floating along
+ 
+
+ align:start position:0%
+are just floating along
+and i put an electric field on and i put
+
+ align:start position:0%
+and i put an electric field on and i put
+ 
+
+ align:start position:0%
+and i put an electric field on and i put
+an electric field on
+
+ align:start position:0%
+an electric field on
+ 
+
+ align:start position:0%
+an electric field on
+and and you can see that with the
+
+ align:start position:0%
+and and you can see that with the
+ 
+
+ align:start position:0%
+and and you can see that with the
+electric field so there's my positive
+
+ align:start position:0%
+electric field so there's my positive
+ 
+
+ align:start position:0%
+electric field so there's my positive
+plate my negative plate they're going to
+
+ align:start position:0%
+plate my negative plate they're going to
+ 
+
+ align:start position:0%
+plate my negative plate they're going to
+try to align
+
+ align:start position:0%
+try to align
+ 
+
+ align:start position:0%
+try to align
+right these dipoles mean that they're
+
+ align:start position:0%
+right these dipoles mean that they're
+ 
+
+ align:start position:0%
+right these dipoles mean that they're
+going to align with the field
+
+ align:start position:0%
+going to align with the field
+ 
+
+ align:start position:0%
+going to align with the field
+they're going to align with the field so
+
+ align:start position:0%
+they're going to align with the field so
+ 
+
+ align:start position:0%
+they're going to align with the field so
+all of those positive
+
+ align:start position:0%
+all of those positive
+ 
+
+ align:start position:0%
+all of those positive
+edges are going to try to turn and face
+
+ align:start position:0%
+edges are going to try to turn and face
+ 
+
+ align:start position:0%
+edges are going to try to turn and face
+the negative one and all those
+
+ align:start position:0%
+the negative one and all those
+ 
+
+ align:start position:0%
+the negative one and all those
+negative ones are going to turn and face
+
+ align:start position:0%
+negative ones are going to turn and face
+ 
+
+ align:start position:0%
+negative ones are going to turn and face
+the positive one
+
+ align:start position:0%
+the positive one
+ 
+
+ align:start position:0%
+the positive one
+um and that's exactly what we just did
+
+ align:start position:0%
+um and that's exactly what we just did
+ 
+
+ align:start position:0%
+um and that's exactly what we just did
+with this ion
+
+ align:start position:0%
+with this ion
+ 
+
+ align:start position:0%
+with this ion
+we basically did the same thing here
+
+ align:start position:0%
+we basically did the same thing here
+ 
+
+ align:start position:0%
+we basically did the same thing here
+that's what the ion did
+
+ align:start position:0%
+that's what the ion did
+ 
+
+ align:start position:0%
+that's what the ion did
+okay that's what the ion did it said hey
+
+ align:start position:0%
+okay that's what the ion did it said hey
+ 
+
+ align:start position:0%
+okay that's what the ion did it said hey
+come and face me and let's form a bond
+
+ align:start position:0%
+come and face me and let's form a bond
+ 
+
+ align:start position:0%
+come and face me and let's form a bond
+but but these these can also be
+
+ align:start position:0%
+but but these these can also be
+ 
+
+ align:start position:0%
+but but these these can also be
+attracted to each other
+
+ align:start position:0%
+attracted to each other
+ 
+
+ align:start position:0%
+attracted to each other
+right and so i've got a picture there so
+
+ align:start position:0%
+right and so i've got a picture there so
+ 
+
+ align:start position:0%
+right and so i've got a picture there so
+you can see like if i have a dipole and
+
+ align:start position:0%
+you can see like if i have a dipole and
+ 
+
+ align:start position:0%
+you can see like if i have a dipole and
+another dipole so this is not an
+
+ align:start position:0%
+another dipole so this is not an
+ 
+
+ align:start position:0%
+another dipole so this is not an
+external field and it's not an ion it's
+
+ align:start position:0%
+external field and it's not an ion it's
+ 
+
+ align:start position:0%
+external field and it's not an ion it's
+two dipoles
+
+ align:start position:0%
+two dipoles
+ 
+
+ align:start position:0%
+two dipoles
+two hcl molecules right well they each
+
+ align:start position:0%
+two hcl molecules right well they each
+ 
+
+ align:start position:0%
+two hcl molecules right well they each
+have a plus charge and a minus charge
+
+ align:start position:0%
+have a plus charge and a minus charge
+ 
+
+ align:start position:0%
+have a plus charge and a minus charge
+they each have a plus charge in the
+
+ align:start position:0%
+they each have a plus charge in the
+ 
+
+ align:start position:0%
+they each have a plus charge in the
+minus charge and a partial charge
+
+ align:start position:0%
+minus charge and a partial charge
+ 
+
+ align:start position:0%
+minus charge and a partial charge
+right polar covalent and you can see
+
+ align:start position:0%
+right polar covalent and you can see
+ 
+
+ align:start position:0%
+right polar covalent and you can see
+that those could line up actually in
+
+ align:start position:0%
+that those could line up actually in
+ 
+
+ align:start position:0%
+that those could line up actually in
+different ways to form
+
+ align:start position:0%
+different ways to form
+ 
+
+ align:start position:0%
+different ways to form
+attraction and they could also repel
+
+ align:start position:0%
+attraction and they could also repel
+ 
+
+ align:start position:0%
+attraction and they could also repel
+right but overall when they get together
+
+ align:start position:0%
+right but overall when they get together
+ 
+
+ align:start position:0%
+right but overall when they get together
+or when two of them get together they're
+
+ align:start position:0%
+or when two of them get together they're
+ 
+
+ align:start position:0%
+or when two of them get together they're
+going to find a way to attract because
+
+ align:start position:0%
+going to find a way to attract because
+ 
+
+ align:start position:0%
+going to find a way to attract because
+they can
+
+ align:start position:0%
+they can
+ 
+
+ align:start position:0%
+they can
+because they can't and so that is
+
+ align:start position:0%
+because they can't and so that is
+ 
+
+ align:start position:0%
+because they can't and so that is
+another kind of
+
+ align:start position:0%
+another kind of
+ 
+
+ align:start position:0%
+another kind of
+intermolecular attraction and it's
+
+ align:start position:0%
+intermolecular attraction and it's
+ 
+
+ align:start position:0%
+intermolecular attraction and it's
+called a dipole-dipole
+
+ align:start position:0%
+called a dipole-dipole
+ 
+
+ align:start position:0%
+called a dipole-dipole
+dipole dipole
+
+ align:start position:0%
+dipole dipole
+ 
+
+ align:start position:0%
+dipole dipole
+but let's draw this oh it's
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and if we do that we have
+
+ align:start position:0%
+and if we do that we have
+ 
+
+ align:start position:0%
+and if we do that we have
+uh let's see i'm going to try to draw
+
+ align:start position:0%
+uh let's see i'm going to try to draw
+ 
+
+ align:start position:0%
+uh let's see i'm going to try to draw
+this
+
+ align:start position:0%
+this
+ 
+
+ align:start position:0%
+this
+so i've got one dipole i'm going to
+
+ align:start position:0%
+so i've got one dipole i'm going to
+ 
+
+ align:start position:0%
+so i've got one dipole i'm going to
+stick to that picture
+
+ align:start position:0%
+stick to that picture
+ 
+
+ align:start position:0%
+stick to that picture
+i'm going to stick to this picture but
+
+ align:start position:0%
+i'm going to stick to this picture but
+ 
+
+ align:start position:0%
+i'm going to stick to this picture but
+it's the same as this picture
+
+ align:start position:0%
+it's the same as this picture
+ 
+
+ align:start position:0%
+it's the same as this picture
+right where i'm actually using the kind
+
+ align:start position:0%
+right where i'm actually using the kind
+ 
+
+ align:start position:0%
+right where i'm actually using the kind
+of shape here
+
+ align:start position:0%
+of shape here
+ 
+
+ align:start position:0%
+of shape here
+to show you that more charge has gone
+
+ align:start position:0%
+to show you that more charge has gone
+ 
+
+ align:start position:0%
+to show you that more charge has gone
+over to one side
+
+ align:start position:0%
+over to one side
+ 
+
+ align:start position:0%
+over to one side
+okay so let's go back to here right and
+
+ align:start position:0%
+okay so let's go back to here right and
+ 
+
+ align:start position:0%
+okay so let's go back to here right and
+so but if that happens
+
+ align:start position:0%
+so but if that happens
+ 
+
+ align:start position:0%
+so but if that happens
+then i've got minus and plus thank you
+
+ align:start position:0%
+then i've got minus and plus thank you
+ 
+
+ align:start position:0%
+then i've got minus and plus thank you
+okay and then i'm going to have another
+
+ align:start position:0%
+okay and then i'm going to have another
+ 
+
+ align:start position:0%
+okay and then i'm going to have another
+another one's going to want to line up
+
+ align:start position:0%
+another one's going to want to line up
+ 
+
+ align:start position:0%
+another one's going to want to line up
+like this
+
+ align:start position:0%
+like this
+ 
+
+ align:start position:0%
+like this
+oh did i do that right yeah and this is
+
+ align:start position:0%
+oh did i do that right yeah and this is
+ 
+
+ align:start position:0%
+oh did i do that right yeah and this is
+my
+
+ align:start position:0%
+my
+ 
+
+ align:start position:0%
+my
+this is the bond this dashed line here
+
+ align:start position:0%
+this is the bond this dashed line here
+ 
+
+ align:start position:0%
+this is the bond this dashed line here
+is the kind of bond that we're talking
+
+ align:start position:0%
+is the kind of bond that we're talking
+ 
+
+ align:start position:0%
+is the kind of bond that we're talking
+about
+
+ align:start position:0%
+about
+ 
+
+ align:start position:0%
+about
+yeah those are almost sort of asymmetric
+
+ align:start position:0%
+yeah those are almost sort of asymmetric
+ 
+
+ align:start position:0%
+yeah those are almost sort of asymmetric
+okay now goes in tight now that's a
+
+ align:start position:0%
+okay now goes in tight now that's a
+ 
+
+ align:start position:0%
+okay now goes in tight now that's a
+dipole dipole we don't really have a
+
+ align:start position:0%
+dipole dipole we don't really have a
+ 
+
+ align:start position:0%
+dipole dipole we don't really have a
+better way of calling that either
+
+ align:start position:0%
+better way of calling that either
+ 
+
+ align:start position:0%
+better way of calling that either
+they're dipole
+
+ align:start position:0%
+they're dipole
+ 
+
+ align:start position:0%
+they're dipole
+uh charges interacting with dipole
+
+ align:start position:0%
+uh charges interacting with dipole
+ 
+
+ align:start position:0%
+uh charges interacting with dipole
+charges and that's going to give you a
+
+ align:start position:0%
+charges and that's going to give you a
+ 
+
+ align:start position:0%
+charges and that's going to give you a
+one over
+
+ align:start position:0%
+one over
+ 
+
+ align:start position:0%
+one over
+r cubed dependence and then you know if
+
+ align:start position:0%
+r cubed dependence and then you know if
+ 
+
+ align:start position:0%
+r cubed dependence and then you know if
+you've taken some basic e
+
+ align:start position:0%
+you've taken some basic e
+ 
+
+ align:start position:0%
+you've taken some basic e
+m or if you do you'll learn this right
+
+ align:start position:0%
+m or if you do you'll learn this right
+ 
+
+ align:start position:0%
+m or if you do you'll learn this right
+you'll learn how to derive these
+
+ align:start position:0%
+you'll learn how to derive these
+ 
+
+ align:start position:0%
+you'll learn how to derive these
+these distance dependencies so i've got
+
+ align:start position:0%
+these distance dependencies so i've got
+ 
+
+ align:start position:0%
+these distance dependencies so i've got
+two dipoles
+
+ align:start position:0%
+two dipoles
+ 
+
+ align:start position:0%
+two dipoles
+right because there are two molecules
+
+ align:start position:0%
+right because there are two molecules
+ 
+
+ align:start position:0%
+right because there are two molecules
+that have
+
+ align:start position:0%
+that have
+ 
+
+ align:start position:0%
+that have
+not it's not a non-polar it's a polar
+
+ align:start position:0%
+not it's not a non-polar it's a polar
+ 
+
+ align:start position:0%
+not it's not a non-polar it's a polar
+covalent bond
+
+ align:start position:0%
+covalent bond
+ 
+
+ align:start position:0%
+covalent bond
+and those are attracted to each other in
+
+ align:start position:0%
+and those are attracted to each other in
+ 
+
+ align:start position:0%
+and those are attracted to each other in
+this way and the range of that bonding
+
+ align:start position:0%
+this way and the range of that bonding
+ 
+
+ align:start position:0%
+this way and the range of that bonding
+strength for two dipoles
+
+ align:start position:0%
+strength for two dipoles
+ 
+
+ align:start position:0%
+strength for two dipoles
+is 5 to 25 so it's a lot less
+
+ align:start position:0%
+is 5 to 25 so it's a lot less
+ 
+
+ align:start position:0%
+is 5 to 25 so it's a lot less
+right and let's well if you had
+
+ align:start position:0%
+right and let's well if you had
+ 
+
+ align:start position:0%
+right and let's well if you had
+hcl and hcl that would be an example
+
+ align:start position:0%
+hcl and hcl that would be an example
+ 
+
+ align:start position:0%
+hcl and hcl that would be an example
+no now instead of an ion i'm putting two
+
+ align:start position:0%
+no now instead of an ion i'm putting two
+ 
+
+ align:start position:0%
+no now instead of an ion i'm putting two
+polar molecules in
+
+ align:start position:0%
+polar molecules in
+ 
+
+ align:start position:0%
+polar molecules in
+right so but this could happen
+
+ align:start position:0%
+right so but this could happen
+ 
+
+ align:start position:0%
+right so but this could happen
+this could happen um from
+
+ align:start position:0%
+this could happen um from
+ 
+
+ align:start position:0%
+this could happen um from
+an atom from a molecule to a molecule it
+
+ align:start position:0%
+an atom from a molecule to a molecule it
+ 
+
+ align:start position:0%
+an atom from a molecule to a molecule it
+could happen from
+
+ align:start position:0%
+could happen from
+ 
+
+ align:start position:0%
+could happen from
+an atom to a molecule you it could
+
+ align:start position:0%
+an atom to a molecule you it could
+ 
+
+ align:start position:0%
+an atom to a molecule you it could
+happen from a molecule
+
+ align:start position:0%
+happen from a molecule
+ 
+
+ align:start position:0%
+happen from a molecule
+to an atom so so
+
+ align:start position:0%
+to an atom so so
+ 
+
+ align:start position:0%
+to an atom so so
+for for example you know i could have um
+
+ align:start position:0%
+for for example you know i could have um
+ 
+
+ align:start position:0%
+for for example you know i could have um
+if i have hcl and
+
+ align:start position:0%
+if i have hcl and
+ 
+
+ align:start position:0%
+if i have hcl and
+this has more charge has gone
+
+ align:start position:0%
+this has more charge has gone
+ 
+
+ align:start position:0%
+this has more charge has gone
+to the you know to the chlorine side
+
+ align:start position:0%
+to the you know to the chlorine side
+ 
+
+ align:start position:0%
+to the you know to the chlorine side
+right so this has my delta plus this is
+
+ align:start position:0%
+right so this has my delta plus this is
+ 
+
+ align:start position:0%
+right so this has my delta plus this is
+what i wrote over on the other side
+
+ align:start position:0%
+what i wrote over on the other side
+ 
+
+ align:start position:0%
+what i wrote over on the other side
+that's my delta minus
+
+ align:start position:0%
+that's my delta minus
+ 
+
+ align:start position:0%
+that's my delta minus
+and if i have just a single atom i'm
+
+ align:start position:0%
+and if i have just a single atom i'm
+ 
+
+ align:start position:0%
+and if i have just a single atom i'm
+going to put a xenon atom here
+
+ align:start position:0%
+going to put a xenon atom here
+ 
+
+ align:start position:0%
+going to put a xenon atom here
+well it's just sitting around happily
+
+ align:start position:0%
+well it's just sitting around happily
+ 
+
+ align:start position:0%
+well it's just sitting around happily
+you know
+
+ align:start position:0%
+you know
+ 
+
+ align:start position:0%
+you know
+minding its own business and what's
+
+ align:start position:0%
+minding its own business and what's
+ 
+
+ align:start position:0%
+minding its own business and what's
+gonna happen to that
+
+ align:start position:0%
+gonna happen to that
+ 
+
+ align:start position:0%
+gonna happen to that
+right what's gonna happen to that well
+
+ align:start position:0%
+right what's gonna happen to that well
+ 
+
+ align:start position:0%
+right what's gonna happen to that well
+see if if this comes up to
+
+ align:start position:0%
+see if if this comes up to
+ 
+
+ align:start position:0%
+see if if this comes up to
+an atom that wasn't that didn't have a
+
+ align:start position:0%
+an atom that wasn't that didn't have a
+ 
+
+ align:start position:0%
+an atom that wasn't that didn't have a
+dipole
+
+ align:start position:0%
+dipole
+ 
+
+ align:start position:0%
+dipole
+it still has feelings it still has
+
+ align:start position:0%
+it still has feelings it still has
+ 
+
+ align:start position:0%
+it still has feelings it still has
+feelings
+
+ align:start position:0%
+feelings
+ 
+
+ align:start position:0%
+feelings
+why because electrons have feelings
+
+ align:start position:0%
+why because electrons have feelings
+ 
+
+ align:start position:0%
+why because electrons have feelings
+that's why because it has electrons
+
+ align:start position:0%
+that's why because it has electrons
+ 
+
+ align:start position:0%
+that's why because it has electrons
+so those electrons are in there and it
+
+ align:start position:0%
+so those electrons are in there and it
+ 
+
+ align:start position:0%
+so those electrons are in there and it
+doesn't have a dipole
+
+ align:start position:0%
+doesn't have a dipole
+ 
+
+ align:start position:0%
+doesn't have a dipole
+but that's okay because those electrons
+
+ align:start position:0%
+but that's okay because those electrons
+ 
+
+ align:start position:0%
+but that's okay because those electrons
+still can feel
+
+ align:start position:0%
+still can feel
+ 
+
+ align:start position:0%
+still can feel
+they can feel the dipole of this
+
+ align:start position:0%
+they can feel the dipole of this
+ 
+
+ align:start position:0%
+they can feel the dipole of this
+they can feel the dipole of this
+
+ align:start position:0%
+they can feel the dipole of this
+ 
+
+ align:start position:0%
+they can feel the dipole of this
+molecule
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and when they feel that dipole they
+
+ align:start position:0%
+and when they feel that dipole they
+ 
+
+ align:start position:0%
+and when they feel that dipole they
+react to it
+
+ align:start position:0%
+react to it
+ 
+
+ align:start position:0%
+react to it
+they react to it right so there's a
+
+ align:start position:0%
+they react to it right so there's a
+ 
+
+ align:start position:0%
+they react to it right so there's a
+whole nother thing that can happen by
+
+ align:start position:0%
+whole nother thing that can happen by
+ 
+
+ align:start position:0%
+whole nother thing that can happen by
+the way it could happen
+
+ align:start position:0%
+the way it could happen
+ 
+
+ align:start position:0%
+the way it could happen
+oh that could it could happen with a
+
+ align:start position:0%
+oh that could it could happen with a
+ 
+
+ align:start position:0%
+oh that could it could happen with a
+sodium atom
+
+ align:start position:0%
+sodium atom
+ 
+
+ align:start position:0%
+sodium atom
+and a plus also is a charge
+
+ align:start position:0%
+and a plus also is a charge
+ 
+
+ align:start position:0%
+and a plus also is a charge
+that that this happy go lucky xena it
+
+ align:start position:0%
+that that this happy go lucky xena it
+ 
+
+ align:start position:0%
+that that this happy go lucky xena it
+doesn't it doesn't know what's coming
+
+ align:start position:0%
+doesn't it doesn't know what's coming
+ 
+
+ align:start position:0%
+doesn't it doesn't know what's coming
+but it's got electrons that feel charge
+
+ align:start position:0%
+but it's got electrons that feel charge
+ 
+
+ align:start position:0%
+but it's got electrons that feel charge
+and so you bring a charge to it and
+
+ align:start position:0%
+and so you bring a charge to it and
+ 
+
+ align:start position:0%
+and so you bring a charge to it and
+they're going to react to it
+
+ align:start position:0%
+they're going to react to it
+ 
+
+ align:start position:0%
+they're going to react to it
+they're going to react to it whether
+
+ align:start position:0%
+they're going to react to it whether
+ 
+
+ align:start position:0%
+they're going to react to it whether
+it's a single charge
+
+ align:start position:0%
+it's a single charge
+ 
+
+ align:start position:0%
+it's a single charge
+or whether it's a dipole these are
+
+ align:start position:0%
+or whether it's a dipole these are
+ 
+
+ align:start position:0%
+or whether it's a dipole these are
+charges
+
+ align:start position:0%
+charges
+ 
+
+ align:start position:0%
+charges
+they're going to change the charge
+
+ align:start position:0%
+they're going to change the charge
+ 
+
+ align:start position:0%
+they're going to change the charge
+around that
+
+ align:start position:0%
+around that
+ 
+
+ align:start position:0%
+around that
+atom now there's another name for that
+
+ align:start position:0%
+atom now there's another name for that
+ 
+
+ align:start position:0%
+atom now there's another name for that
+and and that leads to another kind of
+
+ align:start position:0%
+and and that leads to another kind of
+ 
+
+ align:start position:0%
+and and that leads to another kind of
+bond
+
+ align:start position:0%
+bond
+ 
+
+ align:start position:0%
+bond
+actually leads to another kind of bond
+
+ align:start position:0%
+actually leads to another kind of bond
+ 
+
+ align:start position:0%
+actually leads to another kind of bond
+let's see so i'm going to just
+
+ align:start position:0%
+let's see so i'm going to just
+ 
+
+ align:start position:0%
+let's see so i'm going to just
+let me draw the cartoon i really want to
+
+ align:start position:0%
+let me draw the cartoon i really want to
+ 
+
+ align:start position:0%
+let me draw the cartoon i really want to
+make sure you understand this
+
+ align:start position:0%
+make sure you understand this
+ 
+
+ align:start position:0%
+make sure you understand this
+because this sent sets up the next kind
+
+ align:start position:0%
+because this sent sets up the next kind
+ 
+
+ align:start position:0%
+because this sent sets up the next kind
+of bonding
+
+ align:start position:0%
+of bonding
+ 
+
+ align:start position:0%
+of bonding
+and so let's suppose i take a sodium
+
+ align:start position:0%
+and so let's suppose i take a sodium
+ 
+
+ align:start position:0%
+and so let's suppose i take a sodium
+atom
+
+ align:start position:0%
+atom
+ 
+
+ align:start position:0%
+atom
+and i'll use h2 h gazentite
+
+ align:start position:0%
+and i'll use h2 h gazentite
+ 
+
+ align:start position:0%
+and i'll use h2 h gazentite
+h i could have been a single atom it
+
+ align:start position:0%
+h i could have been a single atom it
+ 
+
+ align:start position:0%
+h i could have been a single atom it
+could have been a it could be a nonpolar
+
+ align:start position:0%
+could have been a it could be a nonpolar
+ 
+
+ align:start position:0%
+could have been a it could be a nonpolar
+molecule
+
+ align:start position:0%
+molecule
+ 
+
+ align:start position:0%
+molecule
+right so this is what this looks like
+
+ align:start position:0%
+right so this is what this looks like
+ 
+
+ align:start position:0%
+right so this is what this looks like
+and now this this is going to
+
+ align:start position:0%
+and now this this is going to
+ 
+
+ align:start position:0%
+and now this this is going to
+these are kind of walking along happily
+
+ align:start position:0%
+these are kind of walking along happily
+ 
+
+ align:start position:0%
+these are kind of walking along happily
+and then they see each other
+
+ align:start position:0%
+and then they see each other
+ 
+
+ align:start position:0%
+and then they see each other
+and all of a sudden this is going to
+
+ align:start position:0%
+and all of a sudden this is going to
+ 
+
+ align:start position:0%
+and all of a sudden this is going to
+induce a shift of the charge around
+
+ align:start position:0%
+induce a shift of the charge around
+ 
+
+ align:start position:0%
+induce a shift of the charge around
+those
+
+ align:start position:0%
+those
+ 
+
+ align:start position:0%
+those
+around that h2 molecule so what you're
+
+ align:start position:0%
+around that h2 molecule so what you're
+ 
+
+ align:start position:0%
+around that h2 molecule so what you're
+going to see is now
+
+ align:start position:0%
+going to see is now
+ 
+
+ align:start position:0%
+going to see is now
+more which way is it going to go
+
+ align:start position:0%
+more which way is it going to go
+ 
+
+ align:start position:0%
+more which way is it going to go
+which should have the bigger side the
+
+ align:start position:0%
+which should have the bigger side the
+ 
+
+ align:start position:0%
+which should have the bigger side the
+more charge right yeah here because
+
+ align:start position:0%
+more charge right yeah here because
+ 
+
+ align:start position:0%
+more charge right yeah here because
+that's positive and electrons are
+
+ align:start position:0%
+that's positive and electrons are
+ 
+
+ align:start position:0%
+that's positive and electrons are
+negative so now
+
+ align:start position:0%
+negative so now
+ 
+
+ align:start position:0%
+negative so now
+it's going to look like this now
+
+ align:start position:0%
+it's going to look like this now
+ 
+
+ align:start position:0%
+it's going to look like this now
+that was not a dipole it is not a
+
+ align:start position:0%
+that was not a dipole it is not a
+ 
+
+ align:start position:0%
+that was not a dipole it is not a
+molecule with a dipole
+
+ align:start position:0%
+molecule with a dipole
+ 
+
+ align:start position:0%
+molecule with a dipole
+but it's an induced dipole induced
+
+ align:start position:0%
+but it's an induced dipole induced
+ 
+
+ align:start position:0%
+but it's an induced dipole induced
+dipole because of feelings
+
+ align:start position:0%
+dipole because of feelings
+ 
+
+ align:start position:0%
+dipole because of feelings
+it comes down to feelings well that has
+
+ align:start position:0%
+it comes down to feelings well that has
+ 
+
+ align:start position:0%
+it comes down to feelings well that has
+a name
+
+ align:start position:0%
+a name
+ 
+
+ align:start position:0%
+a name
+right that's ion that one right there is
+
+ align:start position:0%
+right that's ion that one right there is
+ 
+
+ align:start position:0%
+right that's ion that one right there is
+ion
+
+ align:start position:0%
+ion
+ 
+
+ align:start position:0%
+ion
+induced see if i can fit it all here
+
+ align:start position:0%
+induced see if i can fit it all here
+ 
+
+ align:start position:0%
+induced see if i can fit it all here
+induced
+
+ align:start position:0%
+induced
+ 
+
+ align:start position:0%
+induced
+dipole ion induced dipole and i'm going
+
+ align:start position:0%
+dipole ion induced dipole and i'm going
+ 
+
+ align:start position:0%
+dipole ion induced dipole and i'm going
+to try to draw this now let's see
+
+ align:start position:0%
+to try to draw this now let's see
+ 
+
+ align:start position:0%
+to try to draw this now let's see
+okay hang on uh
+
+ align:start position:0%
+okay hang on uh
+ 
+
+ align:start position:0%
+okay hang on uh
+okay so the ion induced dipole
+
+ align:start position:0%
+okay so the ion induced dipole
+ 
+
+ align:start position:0%
+okay so the ion induced dipole
+i'm going to have a plus charge here and
+
+ align:start position:0%
+i'm going to have a plus charge here and
+ 
+
+ align:start position:0%
+i'm going to have a plus charge here and
+here's what i'm going to do i'm going to
+
+ align:start position:0%
+here's what i'm going to do i'm going to
+ 
+
+ align:start position:0%
+here's what i'm going to do i'm going to
+draw the
+
+ align:start position:0%
+draw the
+ 
+
+ align:start position:0%
+draw the
+original shape as what it was
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+oh boy here we go that's what it was
+
+ align:start position:0%
+oh boy here we go that's what it was
+ 
+
+ align:start position:0%
+oh boy here we go that's what it was
+but then it got induced
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay it got induced and so then once
+
+ align:start position:0%
+okay it got induced and so then once
+ 
+
+ align:start position:0%
+okay it got induced and so then once
+it's induced you've got like a minus
+
+ align:start position:0%
+it's induced you've got like a minus
+ 
+
+ align:start position:0%
+it's induced you've got like a minus
+and a plus happens
+
+ align:start position:0%
+and a plus happens
+ 
+
+ align:start position:0%
+and a plus happens
+all the time it happens all the time
+
+ align:start position:0%
+all the time it happens all the time
+ 
+
+ align:start position:0%
+all the time it happens all the time
+now um the the way that we'll we'll talk
+
+ align:start position:0%
+now um the the way that we'll we'll talk
+ 
+
+ align:start position:0%
+now um the the way that we'll we'll talk
+about this in a little bit of a
+
+ align:start position:0%
+about this in a little bit of a
+ 
+
+ align:start position:0%
+about this in a little bit of a
+different way because
+
+ align:start position:0%
+different way because
+ 
+
+ align:start position:0%
+different way because
+this attraction is between an ion by the
+
+ align:start position:0%
+this attraction is between an ion by the
+ 
+
+ align:start position:0%
+this attraction is between an ion by the
+way an ion just means an atom
+
+ align:start position:0%
+way an ion just means an atom
+ 
+
+ align:start position:0%
+way an ion just means an atom
+or something lost to charge right or has
+
+ align:start position:0%
+or something lost to charge right or has
+ 
+
+ align:start position:0%
+or something lost to charge right or has
+a charge plus or binos
+
+ align:start position:0%
+a charge plus or binos
+ 
+
+ align:start position:0%
+a charge plus or binos
+remember cation anion
+
+ align:start position:0%
+remember cation anion
+ 
+
+ align:start position:0%
+remember cation anion
+but the ion in this case is interacting
+
+ align:start position:0%
+but the ion in this case is interacting
+ 
+
+ align:start position:0%
+but the ion in this case is interacting
+with
+
+ align:start position:0%
+with
+ 
+
+ align:start position:0%
+with
+what is called a polarizable
+
+ align:start position:0%
+what is called a polarizable
+ 
+
+ align:start position:0%
+what is called a polarizable
+polarizable
+
+ align:start position:0%
+polarizable
+ 
+
+ align:start position:0%
+polarizable
+electron cloud now the electron cloud is
+
+ align:start position:0%
+electron cloud now the electron cloud is
+ 
+
+ align:start position:0%
+electron cloud now the electron cloud is
+nothing new we got
+
+ align:start position:0%
+nothing new we got
+ 
+
+ align:start position:0%
+nothing new we got
+we we got electron cloud nailed we know
+
+ align:start position:0%
+we we got electron cloud nailed we know
+ 
+
+ align:start position:0%
+we we got electron cloud nailed we know
+about electron cloud
+
+ align:start position:0%
+about electron cloud
+ 
+
+ align:start position:0%
+about electron cloud
+right because those are orbitals
+
+ align:start position:0%
+right because those are orbitals
+ 
+
+ align:start position:0%
+right because those are orbitals
+but what is this thing called
+
+ align:start position:0%
+but what is this thing called
+ 
+
+ align:start position:0%
+but what is this thing called
+polarizable right polarizable and that's
+
+ align:start position:0%
+polarizable right polarizable and that's
+ 
+
+ align:start position:0%
+polarizable right polarizable and that's
+a very important term so i'm going to
+
+ align:start position:0%
+a very important term so i'm going to
+ 
+
+ align:start position:0%
+a very important term so i'm going to
+write down
+
+ align:start position:0%
+write down
+ 
+
+ align:start position:0%
+write down
+its definition
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+because you can imagine that if
+
+ align:start position:0%
+because you can imagine that if
+ 
+
+ align:start position:0%
+because you can imagine that if
+if i have a way of being attracted to a
+
+ align:start position:0%
+if i have a way of being attracted to a
+ 
+
+ align:start position:0%
+if i have a way of being attracted to a
+nonpolar molecule
+
+ align:start position:0%
+nonpolar molecule
+ 
+
+ align:start position:0%
+nonpolar molecule
+by shifting its charge by shifting its
+
+ align:start position:0%
+by shifting its charge by shifting its
+ 
+
+ align:start position:0%
+by shifting its charge by shifting its
+cloud
+
+ align:start position:0%
+cloud
+ 
+
+ align:start position:0%
+cloud
+then how easy was that how much could i
+
+ align:start position:0%
+then how easy was that how much could i
+ 
+
+ align:start position:0%
+then how easy was that how much could i
+shift it
+
+ align:start position:0%
+shift it
+ 
+
+ align:start position:0%
+shift it
+you can tell that that's going to affect
+
+ align:start position:0%
+you can tell that that's going to affect
+ 
+
+ align:start position:0%
+you can tell that that's going to affect
+the bond strength by the way which
+
+ align:start position:0%
+the bond strength by the way which
+ 
+
+ align:start position:0%
+the bond strength by the way which
+is let's see 3 to 15
+
+ align:start position:0%
+is let's see 3 to 15
+ 
+
+ align:start position:0%
+is let's see 3 to 15
+and has a 1 over r to the 4th
+
+ align:start position:0%
+and has a 1 over r to the 4th
+ 
+
+ align:start position:0%
+and has a 1 over r to the 4th
+dependence and let's give us
+
+ align:start position:0%
+dependence and let's give us
+ 
+
+ align:start position:0%
+dependence and let's give us
+let's give the example that i gave there
+
+ align:start position:0%
+let's give the example that i gave there
+ 
+
+ align:start position:0%
+let's give the example that i gave there
+n a plus
+
+ align:start position:0%
+n a plus
+ 
+
+ align:start position:0%
+n a plus
+and h h
+
+ align:start position:0%
+and h h
+ 
+
+ align:start position:0%
+and h h
+okay nonpolar molecule again it could
+
+ align:start position:0%
+okay nonpolar molecule again it could
+ 
+
+ align:start position:0%
+okay nonpolar molecule again it could
+have been an atom
+
+ align:start position:0%
+have been an atom
+ 
+
+ align:start position:0%
+have been an atom
+but it could have been a nonpolar
+
+ align:start position:0%
+but it could have been a nonpolar
+ 
+
+ align:start position:0%
+but it could have been a nonpolar
+molecule
+
+ align:start position:0%
+molecule
+ 
+
+ align:start position:0%
+molecule
+yeah no polarizable polarizability
+
+ align:start position:0%
+yeah no polarizable polarizability
+ 
+
+ align:start position:0%
+yeah no polarizable polarizability
+is a very important concept
+
+ align:start position:0%
+is a very important concept
+ 
+
+ align:start position:0%
+is a very important concept
+polarizability
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+is the measure
+
+ align:start position:0%
+is the measure
+ 
+
+ align:start position:0%
+is the measure
+because then tight of how
+
+ align:start position:0%
+because then tight of how
+ 
+
+ align:start position:0%
+because then tight of how
+easy
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+it is to temporarily
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+temporarily distort
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the electron distribution
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that is a very important concept
+
+ align:start position:0%
+that is a very important concept
+ 
+
+ align:start position:0%
+that is a very important concept
+for these types of bonds and for a lot
+
+ align:start position:0%
+for these types of bonds and for a lot
+ 
+
+ align:start position:0%
+for these types of bonds and for a lot
+of other properties and of course for
+
+ align:start position:0%
+of other properties and of course for
+ 
+
+ align:start position:0%
+of other properties and of course for
+life in general
+
+ align:start position:0%
+life in general
+ 
+
+ align:start position:0%
+life in general
+how polarizable are my electrons i need
+
+ align:start position:0%
+how polarizable are my electrons i need
+ 
+
+ align:start position:0%
+how polarizable are my electrons i need
+to know
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+are they just willing to deform from
+
+ align:start position:0%
+are they just willing to deform from
+ 
+
+ align:start position:0%
+are they just willing to deform from
+their their happy orbitals
+
+ align:start position:0%
+their their happy orbitals
+ 
+
+ align:start position:0%
+their their happy orbitals
+temporarily temporarily because
+
+ align:start position:0%
+temporarily temporarily because
+ 
+
+ align:start position:0%
+temporarily temporarily because
+if they were going to deform permanently
+
+ align:start position:0%
+if they were going to deform permanently
+ 
+
+ align:start position:0%
+if they were going to deform permanently
+then you'd have a dipole a permanent
+
+ align:start position:0%
+then you'd have a dipole a permanent
+ 
+
+ align:start position:0%
+then you'd have a dipole a permanent
+dipole
+
+ align:start position:0%
+dipole
+ 
+
+ align:start position:0%
+dipole
+these are induced dipoles okay
+
+ align:start position:0%
+these are induced dipoles okay
+ 
+
+ align:start position:0%
+these are induced dipoles okay
+that's important okay
+
+ align:start position:0%
+that's important okay
+ 
+
+ align:start position:0%
+that's important okay
+now now okay good so that's an
+
+ align:start position:0%
+now now okay good so that's an
+ 
+
+ align:start position:0%
+now now okay good so that's an
+ion-induced dipole now
+
+ align:start position:0%
+ion-induced dipole now
+ 
+
+ align:start position:0%
+ion-induced dipole now
+you could also imagine you know this
+
+ align:start position:0%
+you could also imagine you know this
+ 
+
+ align:start position:0%
+you could also imagine you know this
+could have easily been
+
+ align:start position:0%
+could have easily been
+ 
+
+ align:start position:0%
+could have easily been
+a dipole over here it didn't have to be
+
+ align:start position:0%
+a dipole over here it didn't have to be
+ 
+
+ align:start position:0%
+a dipole over here it didn't have to be
+an ion
+
+ align:start position:0%
+an ion
+ 
+
+ align:start position:0%
+an ion
+it could have been a dipole i could have
+
+ align:start position:0%
+it could have been a dipole i could have
+ 
+
+ align:start position:0%
+it could have been a dipole i could have
+had a dipole here that came up to a
+
+ align:start position:0%
+had a dipole here that came up to a
+ 
+
+ align:start position:0%
+had a dipole here that came up to a
+nonpolar molecule or an atom
+
+ align:start position:0%
+nonpolar molecule or an atom
+ 
+
+ align:start position:0%
+nonpolar molecule or an atom
+right and it could have uh it could have
+
+ align:start position:0%
+right and it could have uh it could have
+ 
+
+ align:start position:0%
+right and it could have uh it could have
+induced the same shift in the charge
+
+ align:start position:0%
+induced the same shift in the charge
+ 
+
+ align:start position:0%
+induced the same shift in the charge
+density which then allows me to be
+
+ align:start position:0%
+density which then allows me to be
+ 
+
+ align:start position:0%
+density which then allows me to be
+attracted
+
+ align:start position:0%
+attracted
+ 
+
+ align:start position:0%
+attracted
+because there's a little bit of a
+
+ align:start position:0%
+because there's a little bit of a
+ 
+
+ align:start position:0%
+because there's a little bit of a
+fluctuation of negative charge there
+
+ align:start position:0%
+fluctuation of negative charge there
+ 
+
+ align:start position:0%
+fluctuation of negative charge there
+right let's draw so if i were to
+
+ align:start position:0%
+right let's draw so if i were to
+ 
+
+ align:start position:0%
+right let's draw so if i were to
+oh so
+
+ align:start position:0%
+oh so
+ 
+
+ align:start position:0%
+oh so
+see the thing is we've been talking
+
+ align:start position:0%
+see the thing is we've been talking
+ 
+
+ align:start position:0%
+see the thing is we've been talking
+about dimers
+
+ align:start position:0%
+about dimers
+ 
+
+ align:start position:0%
+about dimers
+but you could talk about what is the
+
+ align:start position:0%
+but you could talk about what is the
+ 
+
+ align:start position:0%
+but you could talk about what is the
+dipole of something
+
+ align:start position:0%
+dipole of something
+ 
+
+ align:start position:0%
+dipole of something
+more than a dimer right so this is polar
+
+ align:start position:0%
+more than a dimer right so this is polar
+ 
+
+ align:start position:0%
+more than a dimer right so this is polar
+what about these other things
+
+ align:start position:0%
+what about these other things
+ 
+
+ align:start position:0%
+what about these other things
+right so if i look at molecules
+
+ align:start position:0%
+right so if i look at molecules
+ 
+
+ align:start position:0%
+right so if i look at molecules
+right that are polar it's not just about
+
+ align:start position:0%
+right that are polar it's not just about
+ 
+
+ align:start position:0%
+right that are polar it's not just about
+hcl
+
+ align:start position:0%
+hcl
+ 
+
+ align:start position:0%
+hcl
+right which is that first one up there
+
+ align:start position:0%
+right which is that first one up there
+ 
+
+ align:start position:0%
+right which is that first one up there
+but that's kind of
+
+ align:start position:0%
+but that's kind of
+ 
+
+ align:start position:0%
+but that's kind of
+the obvious case but what about ccl4
+
+ align:start position:0%
+the obvious case but what about ccl4
+ 
+
+ align:start position:0%
+the obvious case but what about ccl4
+what if i take a carbon atom
+
+ align:start position:0%
+what if i take a carbon atom
+ 
+
+ align:start position:0%
+what if i take a carbon atom
+and i put four chlorines those are all
+
+ align:start position:0%
+and i put four chlorines those are all
+ 
+
+ align:start position:0%
+and i put four chlorines those are all
+polar bonds and you can see while it's
+
+ align:start position:0%
+polar bonds and you can see while it's
+ 
+
+ align:start position:0%
+polar bonds and you can see while it's
+hard to see but they've drawn in the
+
+ align:start position:0%
+hard to see but they've drawn in the
+ 
+
+ align:start position:0%
+hard to see but they've drawn in the
+dipole moment
+
+ align:start position:0%
+dipole moment
+ 
+
+ align:start position:0%
+dipole moment
+you've lost some charge from the carbon
+
+ align:start position:0%
+you've lost some charge from the carbon
+ 
+
+ align:start position:0%
+you've lost some charge from the carbon
+it's gone out to the chlorine atom
+
+ align:start position:0%
+it's gone out to the chlorine atom
+ 
+
+ align:start position:0%
+it's gone out to the chlorine atom
+there's a dipole moment within each bond
+
+ align:start position:0%
+there's a dipole moment within each bond
+ 
+
+ align:start position:0%
+there's a dipole moment within each bond
+but but now here's
+
+ align:start position:0%
+but but now here's
+ 
+
+ align:start position:0%
+but but now here's
+where vesper comes in because
+
+ align:start position:0%
+where vesper comes in because
+ 
+
+ align:start position:0%
+where vesper comes in because
+you know these are going to be
+
+ align:start position:0%
+you know these are going to be
+ 
+
+ align:start position:0%
+you know these are going to be
+tetrahedrally
+
+ align:start position:0%
+tetrahedrally
+ 
+
+ align:start position:0%
+tetrahedrally
+uh distributed and fully canceling out
+
+ align:start position:0%
+uh distributed and fully canceling out
+ 
+
+ align:start position:0%
+uh distributed and fully canceling out
+so it's like you've got all these kind
+
+ align:start position:0%
+so it's like you've got all these kind
+ 
+
+ align:start position:0%
+so it's like you've got all these kind
+of electrostatic things going on
+
+ align:start position:0%
+of electrostatic things going on
+ 
+
+ align:start position:0%
+of electrostatic things going on
+that all cancel out so this molecule is
+
+ align:start position:0%
+that all cancel out so this molecule is
+ 
+
+ align:start position:0%
+that all cancel out so this molecule is
+not a polar molecule
+
+ align:start position:0%
+not a polar molecule
+ 
+
+ align:start position:0%
+not a polar molecule
+right on the other hand molecules like
+
+ align:start position:0%
+right on the other hand molecules like
+ 
+
+ align:start position:0%
+right on the other hand molecules like
+nh3
+
+ align:start position:0%
+nh3
+ 
+
+ align:start position:0%
+nh3
+or ch3cl right now this is going to be
+
+ align:start position:0%
+or ch3cl right now this is going to be
+ 
+
+ align:start position:0%
+or ch3cl right now this is going to be
+polar because
+
+ align:start position:0%
+polar because
+ 
+
+ align:start position:0%
+polar because
+these dipoles do not cancel out within
+
+ align:start position:0%
+these dipoles do not cancel out within
+ 
+
+ align:start position:0%
+these dipoles do not cancel out within
+the molecule so you can kind of use this
+
+ align:start position:0%
+the molecule so you can kind of use this
+ 
+
+ align:start position:0%
+the molecule so you can kind of use this
+thinking there's bf3
+
+ align:start position:0%
+thinking there's bf3
+ 
+
+ align:start position:0%
+thinking there's bf3
+trigonal planar right all going to can
+
+ align:start position:0%
+trigonal planar right all going to can
+ 
+
+ align:start position:0%
+trigonal planar right all going to can
+all those dipoles cancel
+
+ align:start position:0%
+all those dipoles cancel
+ 
+
+ align:start position:0%
+all those dipoles cancel
+it's a non-polar molecule
+
+ align:start position:0%
+it's a non-polar molecule
+ 
+
+ align:start position:0%
+it's a non-polar molecule
+but if you take a classic example which
+
+ align:start position:0%
+but if you take a classic example which
+ 
+
+ align:start position:0%
+but if you take a classic example which
+we'll come back to
+
+ align:start position:0%
+we'll come back to
+ 
+
+ align:start position:0%
+we'll come back to
+of say water as a polar exam a polar
+
+ align:start position:0%
+of say water as a polar exam a polar
+ 
+
+ align:start position:0%
+of say water as a polar exam a polar
+molecule
+
+ align:start position:0%
+molecule
+ 
+
+ align:start position:0%
+molecule
+i could do the same thing right i can
+
+ align:start position:0%
+i could do the same thing right i can
+ 
+
+ align:start position:0%
+i could do the same thing right i can
+take water
+
+ align:start position:0%
+take water
+ 
+
+ align:start position:0%
+take water
+which is oxygen hydrogen hydrogen and
+
+ align:start position:0%
+which is oxygen hydrogen hydrogen and
+ 
+
+ align:start position:0%
+which is oxygen hydrogen hydrogen and
+you see you got delta plus there
+
+ align:start position:0%
+you see you got delta plus there
+ 
+
+ align:start position:0%
+you see you got delta plus there
+delta plus there and you got some minus
+
+ align:start position:0%
+delta plus there and you got some minus
+ 
+
+ align:start position:0%
+delta plus there and you got some minus
+there right
+
+ align:start position:0%
+there right
+ 
+
+ align:start position:0%
+there right
+now use it there's a dipole moment
+
+ align:start position:0%
+now use it there's a dipole moment
+ 
+
+ align:start position:0%
+now use it there's a dipole moment
+there's a dipole moment
+
+ align:start position:0%
+there's a dipole moment
+ 
+
+ align:start position:0%
+there's a dipole moment
+but they and so part of it cancels but
+
+ align:start position:0%
+but they and so part of it cancels but
+ 
+
+ align:start position:0%
+but they and so part of it cancels but
+not all of it so there is a dipole
+
+ align:start position:0%
+not all of it so there is a dipole
+ 
+
+ align:start position:0%
+not all of it so there is a dipole
+moment for the
+
+ align:start position:0%
+moment for the
+ 
+
+ align:start position:0%
+moment for the
+net water molecule the net dipole is
+
+ align:start position:0%
+net water molecule the net dipole is
+ 
+
+ align:start position:0%
+net water molecule the net dipole is
+what matters
+
+ align:start position:0%
+what matters
+ 
+
+ align:start position:0%
+what matters
+to determine if a molecule is polar or
+
+ align:start position:0%
+to determine if a molecule is polar or
+ 
+
+ align:start position:0%
+to determine if a molecule is polar or
+not right so there's a net dipole
+
+ align:start position:0%
+not right so there's a net dipole
+ 
+
+ align:start position:0%
+not right so there's a net dipole
+net dipole when you sum them all up and
+
+ align:start position:0%
+net dipole when you sum them all up and
+ 
+
+ align:start position:0%
+net dipole when you sum them all up and
+that's what's going to determine
+
+ align:start position:0%
+that's what's going to determine
+ 
+
+ align:start position:0%
+that's what's going to determine
+if this can come along to that xenon
+
+ align:start position:0%
+if this can come along to that xenon
+ 
+
+ align:start position:0%
+if this can come along to that xenon
+atom right
+
+ align:start position:0%
+atom right
+ 
+
+ align:start position:0%
+atom right
+and so here's my xenon atom just sitting
+
+ align:start position:0%
+and so here's my xenon atom just sitting
+ 
+
+ align:start position:0%
+and so here's my xenon atom just sitting
+there
+
+ align:start position:0%
+there
+ 
+
+ align:start position:0%
+there
+doing nothing and now when water comes
+
+ align:start position:0%
+doing nothing and now when water comes
+ 
+
+ align:start position:0%
+doing nothing and now when water comes
+up to xenon
+
+ align:start position:0%
+up to xenon
+ 
+
+ align:start position:0%
+up to xenon
+what's going to happen well what's going
+
+ align:start position:0%
+what's going to happen well what's going
+ 
+
+ align:start position:0%
+what's going to happen well what's going
+to happen is i've got my water molecule
+
+ align:start position:0%
+to happen is i've got my water molecule
+ 
+
+ align:start position:0%
+to happen is i've got my water molecule
+my water molecule my delta minus
+
+ align:start position:0%
+my water molecule my delta minus
+ 
+
+ align:start position:0%
+my water molecule my delta minus
+my delta plus my delta plus and because
+
+ align:start position:0%
+my delta plus my delta plus and because
+ 
+
+ align:start position:0%
+my delta plus my delta plus and because
+it's
+
+ align:start position:0%
+it's
+ 
+
+ align:start position:0%
+it's
+got a net dipole it's going to deform
+
+ align:start position:0%
+got a net dipole it's going to deform
+ 
+
+ align:start position:0%
+got a net dipole it's going to deform
+the atom right and so i'm going to have
+
+ align:start position:0%
+the atom right and so i'm going to have
+ 
+
+ align:start position:0%
+the atom right and so i'm going to have
+let's see make sure i draw this right so
+
+ align:start position:0%
+let's see make sure i draw this right so
+ 
+
+ align:start position:0%
+let's see make sure i draw this right so
+it's going to look kind of like this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+delta minus delta plus
+
+ align:start position:0%
+delta minus delta plus
+ 
+
+ align:start position:0%
+delta minus delta plus
+and that allows a water molecule to bond
+
+ align:start position:0%
+and that allows a water molecule to bond
+ 
+
+ align:start position:0%
+and that allows a water molecule to bond
+to a xenon
+
+ align:start position:0%
+to a xenon
+ 
+
+ align:start position:0%
+to a xenon
+atom it is bonding it is bonding
+
+ align:start position:0%
+atom it is bonding it is bonding
+ 
+
+ align:start position:0%
+atom it is bonding it is bonding
+with another bond which is very similar
+
+ align:start position:0%
+with another bond which is very similar
+ 
+
+ align:start position:0%
+with another bond which is very similar
+to the one i just wrote
+
+ align:start position:0%
+to the one i just wrote
+ 
+
+ align:start position:0%
+to the one i just wrote
+goes in tight but it is a dipole
+
+ align:start position:0%
+goes in tight but it is a dipole
+ 
+
+ align:start position:0%
+goes in tight but it is a dipole
+induced not ion it is a dipole
+
+ align:start position:0%
+induced not ion it is a dipole
+ 
+
+ align:start position:0%
+induced not ion it is a dipole
+induced dipole
+
+ align:start position:0%
+induced dipole
+ 
+
+ align:start position:0%
+induced dipole
+you see that because now i didn't have
+
+ align:start position:0%
+you see that because now i didn't have
+ 
+
+ align:start position:0%
+you see that because now i didn't have
+an ion i had a water molecule that had
+
+ align:start position:0%
+an ion i had a water molecule that had
+ 
+
+ align:start position:0%
+an ion i had a water molecule that had
+a dipole moment so now i've got my
+
+ align:start position:0%
+a dipole moment so now i've got my
+ 
+
+ align:start position:0%
+a dipole moment so now i've got my
+dipole induced dipole and that's going
+
+ align:start position:0%
+dipole induced dipole and that's going
+ 
+
+ align:start position:0%
+dipole induced dipole and that's going
+to look
+
+ align:start position:0%
+to look
+ 
+
+ align:start position:0%
+to look
+oh let's draw it let's see so i got my
+
+ align:start position:0%
+oh let's draw it let's see so i got my
+ 
+
+ align:start position:0%
+oh let's draw it let's see so i got my
+dipole-induced dipole so we're going to
+
+ align:start position:0%
+dipole-induced dipole so we're going to
+ 
+
+ align:start position:0%
+dipole-induced dipole so we're going to
+go
+
+ align:start position:0%
+go
+ 
+
+ align:start position:0%
+go
+kind of oh boy there we go
+
+ align:start position:0%
+kind of oh boy there we go
+ 
+
+ align:start position:0%
+kind of oh boy there we go
+okay minus plus
+
+ align:start position:0%
+okay minus plus
+ 
+
+ align:start position:0%
+okay minus plus
+and then we're gonna now that might be
+
+ align:start position:0%
+and then we're gonna now that might be
+ 
+
+ align:start position:0%
+and then we're gonna now that might be
+uh the dipole of say the water molecule
+
+ align:start position:0%
+uh the dipole of say the water molecule
+ 
+
+ align:start position:0%
+uh the dipole of say the water molecule
+or something like that and then i've got
+
+ align:start position:0%
+or something like that and then i've got
+ 
+
+ align:start position:0%
+or something like that and then i've got
+us another thing that was
+
+ align:start position:0%
+us another thing that was
+ 
+
+ align:start position:0%
+us another thing that was
+didn't have a dipole but it got induced
+
+ align:start position:0%
+didn't have a dipole but it got induced
+ 
+
+ align:start position:0%
+didn't have a dipole but it got induced
+to have one
+
+ align:start position:0%
+to have one
+ 
+
+ align:start position:0%
+to have one
+okay oh boy i went out of the lines
+
+ align:start position:0%
+okay oh boy i went out of the lines
+ 
+
+ align:start position:0%
+okay oh boy i went out of the lines
+ah i was so careful but you can't
+
+ align:start position:0%
+ah i was so careful but you can't
+ 
+
+ align:start position:0%
+ah i was so careful but you can't
+you can't hold chemistry back uh-uh
+
+ align:start position:0%
+you can't hold chemistry back uh-uh
+ 
+
+ align:start position:0%
+you can't hold chemistry back uh-uh
+no way no way
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay delta plus delta minus
+
+ align:start position:0%
+okay delta plus delta minus
+ 
+
+ align:start position:0%
+okay delta plus delta minus
+it's induced that's what that means
+
+ align:start position:0%
+it's induced that's what that means
+ 
+
+ align:start position:0%
+it's induced that's what that means
+right
+
+ align:start position:0%
+right
+ 
+
+ align:start position:0%
+right
+now it turns out that this has an even
+
+ align:start position:0%
+now it turns out that this has an even
+ 
+
+ align:start position:0%
+now it turns out that this has an even
+weaker
+
+ align:start position:0%
+weaker
+ 
+
+ align:start position:0%
+weaker
+um so this would be a dipole let's just
+
+ align:start position:0%
+um so this would be a dipole let's just
+ 
+
+ align:start position:0%
+um so this would be a dipole let's just
+write let's finish this up
+
+ align:start position:0%
+write let's finish this up
+ 
+
+ align:start position:0%
+write let's finish this up
+dipole interacting with the polarizable
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+electron cloud and the value of this
+
+ align:start position:0%
+electron cloud and the value of this
+ 
+
+ align:start position:0%
+electron cloud and the value of this
+is even lower range two to ten
+
+ align:start position:0%
+is even lower range two to ten
+ 
+
+ align:start position:0%
+is even lower range two to ten
+and the dependence is one over r to the
+
+ align:start position:0%
+and the dependence is one over r to the
+ 
+
+ align:start position:0%
+and the dependence is one over r to the
+sixth
+
+ align:start position:0%
+sixth
+ 
+
+ align:start position:0%
+sixth
+and the example let's do let's go back
+
+ align:start position:0%
+and the example let's do let's go back
+ 
+
+ align:start position:0%
+and the example let's do let's go back
+to hcl
+
+ align:start position:0%
+to hcl
+ 
+
+ align:start position:0%
+to hcl
+hcl there's my dipole coming in
+
+ align:start position:0%
+hcl there's my dipole coming in
+ 
+
+ align:start position:0%
+hcl there's my dipole coming in
+on clcl i like that because it's got
+
+ align:start position:0%
+on clcl i like that because it's got
+ 
+
+ align:start position:0%
+on clcl i like that because it's got
+three cls
+
+ align:start position:0%
+three cls
+ 
+
+ align:start position:0%
+three cls
+why not that's a non-polar molecule
+
+ align:start position:0%
+why not that's a non-polar molecule
+ 
+
+ align:start position:0%
+why not that's a non-polar molecule
+that's a that's a dipole that
+
+ align:start position:0%
+that's a that's a dipole that
+ 
+
+ align:start position:0%
+that's a that's a dipole that
+induces a dipole in this by shifting its
+
+ align:start position:0%
+induces a dipole in this by shifting its
+ 
+
+ align:start position:0%
+induces a dipole in this by shifting its
+polarizable electrons around
+
+ align:start position:0%
+polarizable electrons around
+ 
+
+ align:start position:0%
+polarizable electrons around
+right and and then it allows there to be
+
+ align:start position:0%
+right and and then it allows there to be
+ 
+
+ align:start position:0%
+right and and then it allows there to be
+a little bit of attraction
+
+ align:start position:0%
+a little bit of attraction
+ 
+
+ align:start position:0%
+a little bit of attraction
+maybe you might be saying but that's so
+
+ align:start position:0%
+maybe you might be saying but that's so
+ 
+
+ align:start position:0%
+maybe you might be saying but that's so
+little we'll get to that in a second
+
+ align:start position:0%
+little we'll get to that in a second
+ 
+
+ align:start position:0%
+little we'll get to that in a second
+that's not so little that's actually not
+
+ align:start position:0%
+that's not so little that's actually not
+ 
+
+ align:start position:0%
+that's not so little that's actually not
+so little when you got a lot of it
+
+ align:start position:0%
+so little when you got a lot of it
+ 
+
+ align:start position:0%
+so little when you got a lot of it
+okay okay dipole interaction now it
+
+ align:start position:0%
+okay okay dipole interaction now it
+ 
+
+ align:start position:0%
+okay okay dipole interaction now it
+turns out
+
+ align:start position:0%
+turns out
+ 
+
+ align:start position:0%
+turns out
+that even and this
+
+ align:start position:0%
+that even and this
+ 
+
+ align:start position:0%
+that even and this
+is what's mind-blowing you knew this was
+
+ align:start position:0%
+is what's mind-blowing you knew this was
+ 
+
+ align:start position:0%
+is what's mind-blowing you knew this was
+coming this moment today was going to
+
+ align:start position:0%
+coming this moment today was going to
+ 
+
+ align:start position:0%
+coming this moment today was going to
+come
+
+ align:start position:0%
+come
+ 
+
+ align:start position:0%
+come
+i can have an interaction
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+without any dipole to start with
+
+ align:start position:0%
+without any dipole to start with
+ 
+
+ align:start position:0%
+without any dipole to start with
+it's true i can take two nonpolar
+
+ align:start position:0%
+it's true i can take two nonpolar
+ 
+
+ align:start position:0%
+it's true i can take two nonpolar
+covalent bonds
+
+ align:start position:0%
+covalent bonds
+ 
+
+ align:start position:0%
+covalent bonds
+two nonpolar covalent molecules h2 and
+
+ align:start position:0%
+two nonpolar covalent molecules h2 and
+ 
+
+ align:start position:0%
+two nonpolar covalent molecules h2 and
+h2
+
+ align:start position:0%
+h2
+ 
+
+ align:start position:0%
+h2
+and they are attracted to each other
+
+ align:start position:0%
+and they are attracted to each other
+ 
+
+ align:start position:0%
+and they are attracted to each other
+how is that possible well it's what
+
+ align:start position:0%
+how is that possible well it's what
+ 
+
+ align:start position:0%
+how is that possible well it's what
+explains this
+
+ align:start position:0%
+explains this
+ 
+
+ align:start position:0%
+explains this
+i mean we know why does helium argon and
+
+ align:start position:0%
+i mean we know why does helium argon and
+ 
+
+ align:start position:0%
+i mean we know why does helium argon and
+xena why do these have different boiling
+
+ align:start position:0%
+xena why do these have different boiling
+ 
+
+ align:start position:0%
+xena why do these have different boiling
+points
+
+ align:start position:0%
+points
+ 
+
+ align:start position:0%
+points
+by the way the boiling point of these
+
+ align:start position:0%
+by the way the boiling point of these
+ 
+
+ align:start position:0%
+by the way the boiling point of these
+right so these can be made into liquids
+
+ align:start position:0%
+right so these can be made into liquids
+ 
+
+ align:start position:0%
+right so these can be made into liquids
+and you can boil them right
+
+ align:start position:0%
+and you can boil them right
+ 
+
+ align:start position:0%
+and you can boil them right
+uh is really different and it's a
+
+ align:start position:0%
+uh is really different and it's a
+ 
+
+ align:start position:0%
+uh is really different and it's a
+measure of how strongly
+
+ align:start position:0%
+measure of how strongly
+ 
+
+ align:start position:0%
+measure of how strongly
+they're bonded together right so this is
+
+ align:start position:0%
+they're bonded together right so this is
+ 
+
+ align:start position:0%
+they're bonded together right so this is
+a direct
+
+ align:start position:0%
+a direct
+ 
+
+ align:start position:0%
+a direct
+kind of way of thinking about of
+
+ align:start position:0%
+kind of way of thinking about of
+ 
+
+ align:start position:0%
+kind of way of thinking about of
+measuring something that's related to
+
+ align:start position:0%
+measuring something that's related to
+ 
+
+ align:start position:0%
+measuring something that's related to
+the bond strength so why do these
+
+ align:start position:0%
+the bond strength so why do these
+ 
+
+ align:start position:0%
+the bond strength so why do these
+atoms they're all just atoms
+
+ align:start position:0%
+atoms they're all just atoms
+ 
+
+ align:start position:0%
+atoms they're all just atoms
+you know they're all just like this
+
+ align:start position:0%
+you know they're all just like this
+ 
+
+ align:start position:0%
+you know they're all just like this
+they're not
+
+ align:start position:0%
+they're not
+ 
+
+ align:start position:0%
+they're not
+they don't have this this dipole right
+
+ align:start position:0%
+they don't have this this dipole right
+ 
+
+ align:start position:0%
+they don't have this this dipole right
+they're non-polar they're just atoms
+
+ align:start position:0%
+they're non-polar they're just atoms
+ 
+
+ align:start position:0%
+they're non-polar they're just atoms
+sitting there with their nice symmetric
+
+ align:start position:0%
+sitting there with their nice symmetric
+ 
+
+ align:start position:0%
+sitting there with their nice symmetric
+charge clouds
+
+ align:start position:0%
+charge clouds
+ 
+
+ align:start position:0%
+charge clouds
+how is it that they can be attracted to
+
+ align:start position:0%
+how is it that they can be attracted to
+ 
+
+ align:start position:0%
+how is it that they can be attracted to
+each other in the first place and how is
+
+ align:start position:0%
+each other in the first place and how is
+ 
+
+ align:start position:0%
+each other in the first place and how is
+it that they can have such a strong
+
+ align:start position:0%
+it that they can have such a strong
+ 
+
+ align:start position:0%
+it that they can have such a strong
+trend and that has to do with another
+
+ align:start position:0%
+trend and that has to do with another
+ 
+
+ align:start position:0%
+trend and that has to do with another
+kind of force
+
+ align:start position:0%
+kind of force
+ 
+
+ align:start position:0%
+kind of force
+and um and there's a picture so here's
+
+ align:start position:0%
+and um and there's a picture so here's
+ 
+
+ align:start position:0%
+and um and there's a picture so here's
+two examples
+
+ align:start position:0%
+two examples
+ 
+
+ align:start position:0%
+two examples
+there's two helium atoms so that's the
+
+ align:start position:0%
+there's two helium atoms so that's the
+ 
+
+ align:start position:0%
+there's two helium atoms so that's the
+first one in this list boiling point
+
+ align:start position:0%
+first one in this list boiling point
+ 
+
+ align:start position:0%
+first one in this list boiling point
+minus 269 degrees celsius is pretty cold
+
+ align:start position:0%
+minus 269 degrees celsius is pretty cold
+ 
+
+ align:start position:0%
+minus 269 degrees celsius is pretty cold
+and there's two non-polar molecules h2
+
+ align:start position:0%
+and there's two non-polar molecules h2
+ 
+
+ align:start position:0%
+and there's two non-polar molecules h2
+what happens
+
+ align:start position:0%
+what happens
+ 
+
+ align:start position:0%
+what happens
+is that you get fluctuations you get
+
+ align:start position:0%
+is that you get fluctuations you get
+ 
+
+ align:start position:0%
+is that you get fluctuations you get
+fluctuations
+
+ align:start position:0%
+fluctuations
+ 
+
+ align:start position:0%
+fluctuations
+and and what i mean by that is that just
+
+ align:start position:0%
+and and what i mean by that is that just
+ 
+
+ align:start position:0%
+and and what i mean by that is that just
+randomly literally randomly right
+
+ align:start position:0%
+randomly literally randomly right
+ 
+
+ align:start position:0%
+randomly literally randomly right
+because of collisions or thermal uh
+
+ align:start position:0%
+because of collisions or thermal uh
+ 
+
+ align:start position:0%
+because of collisions or thermal uh
+energy randomly
+
+ align:start position:0%
+energy randomly
+ 
+
+ align:start position:0%
+energy randomly
+one of those could form a dipole
+
+ align:start position:0%
+one of those could form a dipole
+ 
+
+ align:start position:0%
+one of those could form a dipole
+was that i didn't mean it it wasn't my
+
+ align:start position:0%
+was that i didn't mean it it wasn't my
+ 
+
+ align:start position:0%
+was that i didn't mean it it wasn't my
+happy place but it happened
+
+ align:start position:0%
+happy place but it happened
+ 
+
+ align:start position:0%
+happy place but it happened
+now if it happens and and your charge
+
+ align:start position:0%
+now if it happens and and your charge
+ 
+
+ align:start position:0%
+now if it happens and and your charge
+kind of goes to one side
+
+ align:start position:0%
+kind of goes to one side
+ 
+
+ align:start position:0%
+kind of goes to one side
+even if it's just for a split second
+
+ align:start position:0%
+even if it's just for a split second
+ 
+
+ align:start position:0%
+even if it's just for a split second
+that's a dipole that then if you're near
+
+ align:start position:0%
+that's a dipole that then if you're near
+ 
+
+ align:start position:0%
+that's a dipole that then if you're near
+another atom
+
+ align:start position:0%
+another atom
+ 
+
+ align:start position:0%
+another atom
+can induce a dipole and we know that if
+
+ align:start position:0%
+can induce a dipole and we know that if
+ 
+
+ align:start position:0%
+can induce a dipole and we know that if
+we can induce a dipole if we're here
+
+ align:start position:0%
+we can induce a dipole if we're here
+ 
+
+ align:start position:0%
+we can induce a dipole if we're here
+if we're at this stage we've already got
+
+ align:start position:0%
+if we're at this stage we've already got
+ 
+
+ align:start position:0%
+if we're at this stage we've already got
+that covered we already know that i can
+
+ align:start position:0%
+that covered we already know that i can
+ 
+
+ align:start position:0%
+that covered we already know that i can
+induce another dipole if i'm charged
+
+ align:start position:0%
+induce another dipole if i'm charged
+ 
+
+ align:start position:0%
+induce another dipole if i'm charged
+right and so what happens is you get
+
+ align:start position:0%
+right and so what happens is you get
+ 
+
+ align:start position:0%
+right and so what happens is you get
+this kind of fluctuation
+
+ align:start position:0%
+this kind of fluctuation
+ 
+
+ align:start position:0%
+this kind of fluctuation
+that leads literally to a bond
+
+ align:start position:0%
+that leads literally to a bond
+ 
+
+ align:start position:0%
+that leads literally to a bond
+it leads to a bond right
+
+ align:start position:0%
+it leads to a bond right
+ 
+
+ align:start position:0%
+it leads to a bond right
+and that is called london dispersion
+
+ align:start position:0%
+and that is called london dispersion
+ 
+
+ align:start position:0%
+and that is called london dispersion
+that's called the london
+
+ align:start position:0%
+that's called the london
+ 
+
+ align:start position:0%
+that's called the london
+force and the london dispersion is the
+
+ align:start position:0%
+force and the london dispersion is the
+ 
+
+ align:start position:0%
+force and the london dispersion is the
+name of
+
+ align:start position:0%
+name of
+ 
+
+ align:start position:0%
+name of
+the kind of bonding you have let me just
+
+ align:start position:0%
+the kind of bonding you have let me just
+ 
+
+ align:start position:0%
+the kind of bonding you have let me just
+make sure
+
+ align:start position:0%
+make sure
+ 
+
+ align:start position:0%
+make sure
+okay london
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+dispersion
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+notice
+
+ align:start position:0%
+notice
+ 
+
+ align:start position:0%
+notice
+notice there's room for one more it's
+
+ align:start position:0%
+notice there's room for one more it's
+ 
+
+ align:start position:0%
+notice there's room for one more it's
+coming there's more
+
+ align:start position:0%
+coming there's more
+ 
+
+ align:start position:0%
+coming there's more
+we're not done we are not done
+
+ align:start position:0%
+we're not done we are not done
+ 
+
+ align:start position:0%
+we're not done we are not done
+i can literally take two nonpolar two
+
+ align:start position:0%
+i can literally take two nonpolar two
+ 
+
+ align:start position:0%
+i can literally take two nonpolar two
+nonpolar atoms or molecules
+
+ align:start position:0%
+nonpolar atoms or molecules
+ 
+
+ align:start position:0%
+nonpolar atoms or molecules
+and i can find a way for them to be
+
+ align:start position:0%
+and i can find a way for them to be
+ 
+
+ align:start position:0%
+and i can find a way for them to be
+attracted
+
+ align:start position:0%
+attracted
+ 
+
+ align:start position:0%
+attracted
+and the way it happens is thermal
+
+ align:start position:0%
+and the way it happens is thermal
+ 
+
+ align:start position:0%
+and the way it happens is thermal
+fluctuations
+
+ align:start position:0%
+fluctuations
+ 
+
+ align:start position:0%
+fluctuations
+this is such an important force and it's
+
+ align:start position:0%
+this is such an important force and it's
+ 
+
+ align:start position:0%
+this is such an important force and it's
+such a strange one
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that i want to write down what it is
+
+ align:start position:0%
+that i want to write down what it is
+ 
+
+ align:start position:0%
+that i want to write down what it is
+it's that
+
+ align:start position:0%
+it's that
+ 
+
+ align:start position:0%
+it's that
+non-polar we've been talking about polar
+
+ align:start position:0%
+non-polar we've been talking about polar
+ 
+
+ align:start position:0%
+non-polar we've been talking about polar
+and charges but
+
+ align:start position:0%
+and charges but
+ 
+
+ align:start position:0%
+and charges but
+nonpolar molecules are
+
+ align:start position:0%
+nonpolar molecules are
+ 
+
+ align:start position:0%
+nonpolar molecules are
+attracted by fluctuations
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+fluctuations i should say
+
+ align:start position:0%
+fluctuations i should say
+ 
+
+ align:start position:0%
+fluctuations i should say
+by dipole fluctuations that's really
+
+ align:start position:0%
+by dipole fluctuations that's really
+ 
+
+ align:start position:0%
+by dipole fluctuations that's really
+what's happening
+
+ align:start position:0%
+what's happening
+ 
+
+ align:start position:0%
+what's happening
+right by dipole flux so so one of them
+
+ align:start position:0%
+right by dipole flux so so one of them
+ 
+
+ align:start position:0%
+right by dipole flux so so one of them
+gets a little shift and it's
+
+ align:start position:0%
+gets a little shift and it's
+ 
+
+ align:start position:0%
+gets a little shift and it's
+there's a dipole and then that dipole if
+
+ align:start position:0%
+there's a dipole and then that dipole if
+ 
+
+ align:start position:0%
+there's a dipole and then that dipole if
+there's another one around can induce
+
+ align:start position:0%
+there's another one around can induce
+ 
+
+ align:start position:0%
+there's another one around can induce
+a shift and then there can be a bond and
+
+ align:start position:0%
+a shift and then there can be a bond and
+ 
+
+ align:start position:0%
+a shift and then there can be a bond and
+now
+
+ align:start position:0%
+now
+ 
+
+ align:start position:0%
+now
+um this gets back to something very
+
+ align:start position:0%
+um this gets back to something very
+ 
+
+ align:start position:0%
+um this gets back to something very
+important
+
+ align:start position:0%
+important
+ 
+
+ align:start position:0%
+important
+which is that
+
+ align:start position:0%
+which is that
+ 
+
+ align:start position:0%
+which is that
+you can imagine how
+
+ align:start position:0%
+you can imagine how
+ 
+
+ align:start position:0%
+you can imagine how
+easy was it for temperature how easy was
+
+ align:start position:0%
+easy was it for temperature how easy was
+ 
+
+ align:start position:0%
+easy was it for temperature how easy was
+it
+
+ align:start position:0%
+it
+ 
+
+ align:start position:0%
+it
+to create that shift right well
+
+ align:start position:0%
+to create that shift right well
+ 
+
+ align:start position:0%
+to create that shift right well
+that's gonna have to do with your
+
+ align:start position:0%
+that's gonna have to do with your
+ 
+
+ align:start position:0%
+that's gonna have to do with your
+polarizability
+
+ align:start position:0%
+polarizability
+ 
+
+ align:start position:0%
+polarizability
+okay and now what okay so what what is
+
+ align:start position:0%
+okay and now what okay so what what is
+ 
+
+ align:start position:0%
+okay and now what okay so what what is
+it that has to do with polarizability
+
+ align:start position:0%
+it that has to do with polarizability
+ 
+
+ align:start position:0%
+it that has to do with polarizability
+right well if um i do have a board here
+
+ align:start position:0%
+right well if um i do have a board here
+ 
+
+ align:start position:0%
+right well if um i do have a board here
+ha okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+you can you can already imagine if i go
+
+ align:start position:0%
+you can you can already imagine if i go
+ 
+
+ align:start position:0%
+you can you can already imagine if i go
+back to this list here
+
+ align:start position:0%
+back to this list here
+ 
+
+ align:start position:0%
+back to this list here
+now if i go from helium to argon what
+
+ align:start position:0%
+now if i go from helium to argon what
+ 
+
+ align:start position:0%
+now if i go from helium to argon what
+have i done i've gone down
+
+ align:start position:0%
+have i done i've gone down
+ 
+
+ align:start position:0%
+have i done i've gone down
+in the periodic table and we've already
+
+ align:start position:0%
+in the periodic table and we've already
+ 
+
+ align:start position:0%
+in the periodic table and we've already
+talked about this those electrons
+
+ align:start position:0%
+talked about this those electrons
+ 
+
+ align:start position:0%
+talked about this those electrons
+that are going to do the shifting to
+
+ align:start position:0%
+that are going to do the shifting to
+ 
+
+ align:start position:0%
+that are going to do the shifting to
+cause the fluctuation
+
+ align:start position:0%
+cause the fluctuation
+ 
+
+ align:start position:0%
+cause the fluctuation
+those electrons are more loosely bound
+
+ align:start position:0%
+those electrons are more loosely bound
+ 
+
+ align:start position:0%
+those electrons are more loosely bound
+right they're further out they're more
+
+ align:start position:0%
+right they're further out they're more
+ 
+
+ align:start position:0%
+right they're further out they're more
+loosely bound
+
+ align:start position:0%
+loosely bound
+ 
+
+ align:start position:0%
+loosely bound
+we've already talked about this we
+
+ align:start position:0%
+we've already talked about this we
+ 
+
+ align:start position:0%
+we've already talked about this we
+looked at this in a lot of ways right
+
+ align:start position:0%
+looked at this in a lot of ways right
+ 
+
+ align:start position:0%
+looked at this in a lot of ways right
+whether it's radius or ionization energy
+
+ align:start position:0%
+whether it's radius or ionization energy
+ 
+
+ align:start position:0%
+whether it's radius or ionization energy
+those are if they're more loosely bound
+
+ align:start position:0%
+those are if they're more loosely bound
+ 
+
+ align:start position:0%
+those are if they're more loosely bound
+then they're easier to shift around i'm
+
+ align:start position:0%
+then they're easier to shift around i'm
+ 
+
+ align:start position:0%
+then they're easier to shift around i'm
+not taking them out
+
+ align:start position:0%
+not taking them out
+ 
+
+ align:start position:0%
+not taking them out
+all right i'm not taking them out but
+
+ align:start position:0%
+all right i'm not taking them out but
+ 
+
+ align:start position:0%
+all right i'm not taking them out but
+i'm moving them that's what london
+
+ align:start position:0%
+i'm moving them that's what london
+ 
+
+ align:start position:0%
+i'm moving them that's what london
+is right i got to fluctuate it so you
+
+ align:start position:0%
+is right i got to fluctuate it so you
+ 
+
+ align:start position:0%
+is right i got to fluctuate it so you
+can imagine now why
+
+ align:start position:0%
+can imagine now why
+ 
+
+ align:start position:0%
+can imagine now why
+if it's heavier and those electrons are
+
+ align:start position:0%
+if it's heavier and those electrons are
+ 
+
+ align:start position:0%
+if it's heavier and those electrons are
+further out they're more polarizable
+
+ align:start position:0%
+further out they're more polarizable
+ 
+
+ align:start position:0%
+further out they're more polarizable
+right so let's write that down right so
+
+ align:start position:0%
+right so let's write that down right so
+ 
+
+ align:start position:0%
+right so let's write that down right so
+the london
+
+ align:start position:0%
+the london
+ 
+
+ align:start position:0%
+the london
+so we're going to get a stronger
+
+ align:start position:0%
+so we're going to get a stronger
+ 
+
+ align:start position:0%
+so we're going to get a stronger
+stronger london
+
+ align:start position:0%
+stronger london
+ 
+
+ align:start position:0%
+stronger london
+two reasons one
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+heavier atom
+
+ align:start position:0%
+heavier atom
+ 
+
+ align:start position:0%
+heavier atom
+which really in this case right it's
+
+ align:start position:0%
+which really in this case right it's
+ 
+
+ align:start position:0%
+which really in this case right it's
+heavier but it really just means more
+
+ align:start position:0%
+heavier but it really just means more
+ 
+
+ align:start position:0%
+heavier but it really just means more
+polarizable
+
+ align:start position:0%
+polarizable
+ 
+
+ align:start position:0%
+polarizable
+if it's more polarizable that's the key
+
+ align:start position:0%
+if it's more polarizable that's the key
+ 
+
+ align:start position:0%
+if it's more polarizable that's the key
+that's the chemistry key more
+
+ align:start position:0%
+that's the chemistry key more
+ 
+
+ align:start position:0%
+that's the chemistry key more
+polarizable
+
+ align:start position:0%
+polarizable
+ 
+
+ align:start position:0%
+polarizable
+more polarizable electron cloud write it
+
+ align:start position:0%
+more polarizable electron cloud write it
+ 
+
+ align:start position:0%
+more polarizable electron cloud write it
+all out but the other thing that you can
+
+ align:start position:0%
+all out but the other thing that you can
+ 
+
+ align:start position:0%
+all out but the other thing that you can
+imagine with london
+
+ align:start position:0%
+imagine with london
+ 
+
+ align:start position:0%
+imagine with london
+right so that explains that trend the
+
+ align:start position:0%
+right so that explains that trend the
+ 
+
+ align:start position:0%
+right so that explains that trend the
+other thing that you can imagine with
+
+ align:start position:0%
+other thing that you can imagine with
+ 
+
+ align:start position:0%
+other thing that you can imagine with
+london is that
+
+ align:start position:0%
+london is that
+ 
+
+ align:start position:0%
+london is that
+these these uh interactions these
+
+ align:start position:0%
+these these uh interactions these
+ 
+
+ align:start position:0%
+these these uh interactions these
+fluctuations they're happening
+
+ align:start position:0%
+fluctuations they're happening
+ 
+
+ align:start position:0%
+fluctuations they're happening
+all over the place and the more contact
+
+ align:start position:0%
+all over the place and the more contact
+ 
+
+ align:start position:0%
+all over the place and the more contact
+i have the more places in a molecule i
+
+ align:start position:0%
+i have the more places in a molecule i
+ 
+
+ align:start position:0%
+i have the more places in a molecule i
+have
+
+ align:start position:0%
+have
+ 
+
+ align:start position:0%
+have
+to induce this to have this fluctuation
+
+ align:start position:0%
+to induce this to have this fluctuation
+ 
+
+ align:start position:0%
+to induce this to have this fluctuation
+happen the stronger these forces could
+
+ align:start position:0%
+happen the stronger these forces could
+ 
+
+ align:start position:0%
+happen the stronger these forces could
+be
+
+ align:start position:0%
+be
+ 
+
+ align:start position:0%
+be
+and this is exactly what we see look at
+
+ align:start position:0%
+and this is exactly what we see look at
+ 
+
+ align:start position:0%
+and this is exactly what we see look at
+this trend methane
+
+ align:start position:0%
+this trend methane
+ 
+
+ align:start position:0%
+this trend methane
+ethane propane and butane all i've done
+
+ align:start position:0%
+ethane propane and butane all i've done
+ 
+
+ align:start position:0%
+ethane propane and butane all i've done
+is i've added another carbon atom oh
+
+ align:start position:0%
+is i've added another carbon atom oh
+ 
+
+ align:start position:0%
+is i've added another carbon atom oh
+we're going to get to these
+
+ align:start position:0%
+we're going to get to these
+ 
+
+ align:start position:0%
+we're going to get to these
+we'll talk a little bit about orgo later
+
+ align:start position:0%
+we'll talk a little bit about orgo later
+ 
+
+ align:start position:0%
+we'll talk a little bit about orgo later
+but for now
+
+ align:start position:0%
+but for now
+ 
+
+ align:start position:0%
+but for now
+look at the boiling points of those
+
+ align:start position:0%
+look at the boiling points of those
+ 
+
+ align:start position:0%
+look at the boiling points of those
+again boiling point being a proxy
+
+ align:start position:0%
+again boiling point being a proxy
+ 
+
+ align:start position:0%
+again boiling point being a proxy
+for the bonding strength what bond could
+
+ align:start position:0%
+for the bonding strength what bond could
+ 
+
+ align:start position:0%
+for the bonding strength what bond could
+they have
+
+ align:start position:0%
+they have
+ 
+
+ align:start position:0%
+they have
+none of those only this
+
+ align:start position:0%
+none of those only this
+ 
+
+ align:start position:0%
+none of those only this
+huh i got excited only london
+
+ align:start position:0%
+huh i got excited only london
+ 
+
+ align:start position:0%
+huh i got excited only london
+because look they're non-polar molecules
+
+ align:start position:0%
+because look they're non-polar molecules
+ 
+
+ align:start position:0%
+because look they're non-polar molecules
+they got no charge on them this is the
+
+ align:start position:0%
+they got no charge on them this is the
+ 
+
+ align:start position:0%
+they got no charge on them this is the
+only way they can talk to each other
+
+ align:start position:0%
+only way they can talk to each other
+ 
+
+ align:start position:0%
+only way they can talk to each other
+but look at how much they talk to each
+
+ align:start position:0%
+but look at how much they talk to each
+ 
+
+ align:start position:0%
+but look at how much they talk to each
+other now why because of the second
+
+ align:start position:0%
+other now why because of the second
+ 
+
+ align:start position:0%
+other now why because of the second
+thing right which is that
+
+ align:start position:0%
+thing right which is that
+ 
+
+ align:start position:0%
+thing right which is that
+the greater the surface the greater the
+
+ align:start position:0%
+the greater the surface the greater the
+ 
+
+ align:start position:0%
+the greater the surface the greater the
+surface
+
+ align:start position:0%
+surface
+ 
+
+ align:start position:0%
+surface
+you can have more the more surface you
+
+ align:start position:0%
+you can have more the more surface you
+ 
+
+ align:start position:0%
+you can have more the more surface you
+have
+
+ align:start position:0%
+have
+ 
+
+ align:start position:0%
+have
+the greater surface
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+more contact area more contact area
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and that's how this bond that's how this
+
+ align:start position:0%
+and that's how this bond that's how this
+ 
+
+ align:start position:0%
+and that's how this bond that's how this
+thing works
+
+ align:start position:0%
+thing works
+ 
+
+ align:start position:0%
+thing works
+because you can have you know as as long
+
+ align:start position:0%
+because you can have you know as as long
+ 
+
+ align:start position:0%
+because you can have you know as as long
+as i've got
+
+ align:start position:0%
+as i've got
+ 
+
+ align:start position:0%
+as i've got
+more surfaces seeing each other then
+
+ align:start position:0%
+more surfaces seeing each other then
+ 
+
+ align:start position:0%
+more surfaces seeing each other then
+there can be more fluctuations
+
+ align:start position:0%
+there can be more fluctuations
+ 
+
+ align:start position:0%
+there can be more fluctuations
+right that are happening that then
+
+ align:start position:0%
+right that are happening that then
+ 
+
+ align:start position:0%
+right that are happening that then
+induce the other one to have a
+
+ align:start position:0%
+induce the other one to have a
+ 
+
+ align:start position:0%
+induce the other one to have a
+fluctuation
+
+ align:start position:0%
+fluctuation
+ 
+
+ align:start position:0%
+fluctuation
+that then create a little moment of
+
+ align:start position:0%
+that then create a little moment of
+ 
+
+ align:start position:0%
+that then create a little moment of
+bonding
+
+ align:start position:0%
+bonding
+ 
+
+ align:start position:0%
+bonding
+that dramatically changes the properties
+
+ align:start position:0%
+that dramatically changes the properties
+ 
+
+ align:start position:0%
+that dramatically changes the properties
+and look at this this is a little bit
+
+ align:start position:0%
+and look at this this is a little bit
+ 
+
+ align:start position:0%
+and look at this this is a little bit
+small but
+
+ align:start position:0%
+small but
+ 
+
+ align:start position:0%
+small but
+you know these are the so let's you know
+
+ align:start position:0%
+you know these are the so let's you know
+ 
+
+ align:start position:0%
+you know these are the so let's you know
+go all the way right ch4
+
+ align:start position:0%
+go all the way right ch4
+ 
+
+ align:start position:0%
+go all the way right ch4
+c2a okay let's go all the way and look
+
+ align:start position:0%
+c2a okay let's go all the way and look
+ 
+
+ align:start position:0%
+c2a okay let's go all the way and look
+at this it determines
+
+ align:start position:0%
+at this it determines
+ 
+
+ align:start position:0%
+at this it determines
+when you have a gas at room temperature
+
+ align:start position:0%
+when you have a gas at room temperature
+ 
+
+ align:start position:0%
+when you have a gas at room temperature
+or when you have a liquid
+
+ align:start position:0%
+or when you have a liquid
+ 
+
+ align:start position:0%
+or when you have a liquid
+at room temperature boy is that
+
+ align:start position:0%
+at room temperature boy is that
+ 
+
+ align:start position:0%
+at room temperature boy is that
+important for how we
+
+ align:start position:0%
+important for how we
+ 
+
+ align:start position:0%
+important for how we
+use these molecules right boy is that
+
+ align:start position:0%
+use these molecules right boy is that
+ 
+
+ align:start position:0%
+use these molecules right boy is that
+important
+
+ align:start position:0%
+important
+ 
+
+ align:start position:0%
+important
+it's all london there's no other option
+
+ align:start position:0%
+it's all london there's no other option
+ 
+
+ align:start position:0%
+it's all london there's no other option
+right but that's what's dictating this
+
+ align:start position:0%
+right but that's what's dictating this
+ 
+
+ align:start position:0%
+right but that's what's dictating this
+trend but it's even more
+
+ align:start position:0%
+trend but it's even more
+ 
+
+ align:start position:0%
+trend but it's even more
+mind-blowing than that because look at
+
+ align:start position:0%
+mind-blowing than that because look at
+ 
+
+ align:start position:0%
+mind-blowing than that because look at
+this this is one
+
+ align:start position:0%
+this this is one
+ 
+
+ align:start position:0%
+this this is one
+molecule that's identical
+
+ align:start position:0%
+molecule that's identical
+ 
+
+ align:start position:0%
+molecule that's identical
+this is c5 this is the five atoms of
+
+ align:start position:0%
+this is c5 this is the five atoms of
+ 
+
+ align:start position:0%
+this is c5 this is the five atoms of
+carbon
+
+ align:start position:0%
+carbon
+ 
+
+ align:start position:0%
+carbon
+and pentane same exact grams per mole
+
+ align:start position:0%
+and pentane same exact grams per mole
+ 
+
+ align:start position:0%
+and pentane same exact grams per mole
+because it's the same chemical formula
+
+ align:start position:0%
+because it's the same chemical formula
+ 
+
+ align:start position:0%
+because it's the same chemical formula
+but look here
+
+ align:start position:0%
+but look here
+ 
+
+ align:start position:0%
+but look here
+36.1 degrees c is the boiling point here
+
+ align:start position:0%
+36.1 degrees c is the boiling point here
+ 
+
+ align:start position:0%
+36.1 degrees c is the boiling point here
+it's 9.5
+
+ align:start position:0%
+it's 9.5
+ 
+
+ align:start position:0%
+it's 9.5
+why it's all this this is not the ground
+
+ align:start position:0%
+why it's all this this is not the ground
+ 
+
+ align:start position:0%
+why it's all this this is not the ground
+state
+
+ align:start position:0%
+state
+ 
+
+ align:start position:0%
+state
+this is the most stable structure is
+
+ align:start position:0%
+this is the most stable structure is
+ 
+
+ align:start position:0%
+this is the most stable structure is
+here but there is a version that's
+
+ align:start position:0%
+here but there is a version that's
+ 
+
+ align:start position:0%
+here but there is a version that's
+called neopentane
+
+ align:start position:0%
+called neopentane
+ 
+
+ align:start position:0%
+called neopentane
+it's like a nickname for it there's a
+
+ align:start position:0%
+it's like a nickname for it there's a
+ 
+
+ align:start position:0%
+it's like a nickname for it there's a
+version of it that you can make
+
+ align:start position:0%
+version of it that you can make
+ 
+
+ align:start position:0%
+version of it that you can make
+that has a different shape and because
+
+ align:start position:0%
+that has a different shape and because
+ 
+
+ align:start position:0%
+that has a different shape and because
+this shape cannot come into contact with
+
+ align:start position:0%
+this shape cannot come into contact with
+ 
+
+ align:start position:0%
+this shape cannot come into contact with
+itself look at this
+
+ align:start position:0%
+itself look at this
+ 
+
+ align:start position:0%
+itself look at this
+you can see it from the red line it's
+
+ align:start position:0%
+you can see it from the red line it's
+ 
+
+ align:start position:0%
+you can see it from the red line it's
+coming into contact with itself
+
+ align:start position:0%
+coming into contact with itself
+ 
+
+ align:start position:0%
+coming into contact with itself
+in the liquid or gas it can't have as
+
+ align:start position:0%
+in the liquid or gas it can't have as
+ 
+
+ align:start position:0%
+in the liquid or gas it can't have as
+much london
+
+ align:start position:0%
+much london
+ 
+
+ align:start position:0%
+much london
+forces london potential so it cannot
+
+ align:start position:0%
+forces london potential so it cannot
+ 
+
+ align:start position:0%
+forces london potential so it cannot
+bind as strongly and therefore the
+
+ align:start position:0%
+bind as strongly and therefore the
+ 
+
+ align:start position:0%
+bind as strongly and therefore the
+boiling point is a lot lower
+
+ align:start position:0%
+boiling point is a lot lower
+ 
+
+ align:start position:0%
+boiling point is a lot lower
+right this is a lot lower now
+
+ align:start position:0%
+right this is a lot lower now
+ 
+
+ align:start position:0%
+right this is a lot lower now
+there's a little bit of naming confusion
+
+ align:start position:0%
+there's a little bit of naming confusion
+ 
+
+ align:start position:0%
+there's a little bit of naming confusion
+i want to clear this up oh boy
+
+ align:start position:0%
+i want to clear this up oh boy
+ 
+
+ align:start position:0%
+i want to clear this up oh boy
+nowhere to go here so i'm going to get
+
+ align:start position:0%
+nowhere to go here so i'm going to get
+ 
+
+ align:start position:0%
+nowhere to go here so i'm going to get
+rid of london for a sec
+
+ align:start position:0%
+rid of london for a sec
+ 
+
+ align:start position:0%
+rid of london for a sec
+and i want to make something very clear
+
+ align:start position:0%
+and i want to make something very clear
+ 
+
+ align:start position:0%
+and i want to make something very clear
+that there's another word that's used
+
+ align:start position:0%
+that there's another word that's used
+ 
+
+ align:start position:0%
+that there's another word that's used
+which is called van der waals okay now
+
+ align:start position:0%
+which is called van der waals okay now
+ 
+
+ align:start position:0%
+which is called van der waals okay now
+this ability of a fluctuation to happen
+
+ align:start position:0%
+this ability of a fluctuation to happen
+ 
+
+ align:start position:0%
+this ability of a fluctuation to happen
+which then induces a fluctuation that
+
+ align:start position:0%
+which then induces a fluctuation that
+ 
+
+ align:start position:0%
+which then induces a fluctuation that
+can happen no matter
+
+ align:start position:0%
+can happen no matter
+ 
+
+ align:start position:0%
+can happen no matter
+what molecule you have it can happen and
+
+ align:start position:0%
+what molecule you have it can happen and
+ 
+
+ align:start position:0%
+what molecule you have it can happen and
+it does
+
+ align:start position:0%
+it does
+ 
+
+ align:start position:0%
+it does
+it's always there right so all molecules
+
+ align:start position:0%
+it's always there right so all molecules
+ 
+
+ align:start position:0%
+it's always there right so all molecules
+all molecules
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+whether they're polar or nonpolar polar
+
+ align:start position:0%
+whether they're polar or nonpolar polar
+ 
+
+ align:start position:0%
+whether they're polar or nonpolar polar
+or nonpolar
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+all molecules are attracted
+
+ align:start position:0%
+all molecules are attracted
+ 
+
+ align:start position:0%
+all molecules are attracted
+by london
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+plus any other attractive forces
+
+ align:start position:0%
+plus any other attractive forces
+ 
+
+ align:start position:0%
+plus any other attractive forces
+any other attractive forces present
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+force is present okay so that's so
+
+ align:start position:0%
+force is present okay so that's so
+ 
+
+ align:start position:0%
+force is present okay so that's so
+london is always there
+
+ align:start position:0%
+london is always there
+ 
+
+ align:start position:0%
+london is always there
+now people interchangeably
+
+ align:start position:0%
+now people interchangeably
+ 
+
+ align:start position:0%
+now people interchangeably
+use the term vanderballs
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and what van der waals encompasses
+
+ align:start position:0%
+and what van der waals encompasses
+ 
+
+ align:start position:0%
+and what van der waals encompasses
+is more than london
+
+ align:start position:0%
+is more than london
+ 
+
+ align:start position:0%
+is more than london
+so vanderballs which you will sometimes
+
+ align:start position:0%
+so vanderballs which you will sometimes
+ 
+
+ align:start position:0%
+so vanderballs which you will sometimes
+see in textbooks
+
+ align:start position:0%
+see in textbooks
+ 
+
+ align:start position:0%
+see in textbooks
+is the van der waals force
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so that is any
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+or all added
+
+ align:start position:0%
+or all added
+ 
+
+ align:start position:0%
+or all added
+together this is the combination of
+
+ align:start position:0%
+together this is the combination of
+ 
+
+ align:start position:0%
+together this is the combination of
+these weak forces
+
+ align:start position:0%
+these weak forces
+ 
+
+ align:start position:0%
+these weak forces
+of dipole dipole
+
+ align:start position:0%
+of dipole dipole
+ 
+
+ align:start position:0%
+of dipole dipole
+dipole dipole
+
+ align:start position:0%
+dipole dipole
+ 
+
+ align:start position:0%
+dipole dipole
+let's see dipole
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+induced dipole
+
+ align:start position:0%
+induced dipole
+ 
+
+ align:start position:0%
+induced dipole
+and london
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+those taken together those taken
+
+ align:start position:0%
+those taken together those taken
+ 
+
+ align:start position:0%
+those taken together those taken
+together
+
+ align:start position:0%
+together
+ 
+
+ align:start position:0%
+together
+you will sometimes see referred to as
+
+ align:start position:0%
+you will sometimes see referred to as
+ 
+
+ align:start position:0%
+you will sometimes see referred to as
+van der waals forces
+
+ align:start position:0%
+van der waals forces
+ 
+
+ align:start position:0%
+van der waals forces
+or weak forces but we know more than
+
+ align:start position:0%
+or weak forces but we know more than
+ 
+
+ align:start position:0%
+or weak forces but we know more than
+that
+
+ align:start position:0%
+that
+ 
+
+ align:start position:0%
+that
+we know the distinction
+
+ align:start position:0%
+we know the distinction
+ 
+
+ align:start position:0%
+we know the distinction
+we know that london started like this
+
+ align:start position:0%
+we know that london started like this
+ 
+
+ align:start position:0%
+we know that london started like this
+and then went like this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+ah really bad goes in tight
+
+ align:start position:0%
+ah really bad goes in tight
+ 
+
+ align:start position:0%
+ah really bad goes in tight
+right we know that it started with
+
+ align:start position:0%
+right we know that it started with
+ 
+
+ align:start position:0%
+right we know that it started with
+non-polar and that there's a difference
+
+ align:start position:0%
+non-polar and that there's a difference
+ 
+
+ align:start position:0%
+non-polar and that there's a difference
+and so this is
+
+ align:start position:0%
+and so this is
+ 
+
+ align:start position:0%
+and so this is
+all about the polarizable electron cloud
+
+ align:start position:0%
+all about the polarizable electron cloud
+ 
+
+ align:start position:0%
+all about the polarizable electron cloud
+polarizable electron cloud that's all
+
+ align:start position:0%
+polarizable electron cloud that's all
+ 
+
+ align:start position:0%
+polarizable electron cloud that's all
+you got
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+right and this can be really small 0.5
+
+ align:start position:0%
+right and this can be really small 0.5
+ 
+
+ align:start position:0%
+right and this can be really small 0.5
+to 40. oh yeah let's just keep with
+
+ align:start position:0%
+to 40. oh yeah let's just keep with
+ 
+
+ align:start position:0%
+to 40. oh yeah let's just keep with
+chlorine two
+
+ align:start position:0%
+chlorine two
+ 
+
+ align:start position:0%
+chlorine two
+chlorine two two non-polar molecules
+
+ align:start position:0%
+chlorine two two non-polar molecules
+ 
+
+ align:start position:0%
+chlorine two two non-polar molecules
+london dispersion and this also has a
+
+ align:start position:0%
+london dispersion and this also has a
+ 
+
+ align:start position:0%
+london dispersion and this also has a
+dependence of
+
+ align:start position:0%
+dependence of
+ 
+
+ align:start position:0%
+dependence of
+in terms of the distance of one over r
+
+ align:start position:0%
+in terms of the distance of one over r
+ 
+
+ align:start position:0%
+in terms of the distance of one over r
+to the sixth now in case you think
+
+ align:start position:0%
+to the sixth now in case you think
+ 
+
+ align:start position:0%
+to the sixth now in case you think
+that's small
+
+ align:start position:0%
+that's small
+ 
+
+ align:start position:0%
+that's small
+i wanna show you a little video of why
+
+ align:start position:0%
+i wanna show you a little video of why
+ 
+
+ align:start position:0%
+i wanna show you a little video of why
+this matters so
+
+ align:start position:0%
+this matters so
+ 
+
+ align:start position:0%
+this matters so
+weak forces now weak forces are really
+
+ align:start position:0%
+weak forces now weak forces are really
+ 
+
+ align:start position:0%
+weak forces now weak forces are really
+strong we know this
+
+ align:start position:0%
+strong we know this
+ 
+
+ align:start position:0%
+strong we know this
+because of mission impossible we know
+
+ align:start position:0%
+because of mission impossible we know
+ 
+
+ align:start position:0%
+because of mission impossible we know
+this
+
+ align:start position:0%
+this
+ 
+
+ align:start position:0%
+this
+also because of our own students there
+
+ align:start position:0%
+also because of our own students there
+ 
+
+ align:start position:0%
+also because of our own students there
+was one of my former students rory
+
+ align:start position:0%
+was one of my former students rory
+ 
+
+ align:start position:0%
+was one of my former students rory
+and he won all sorts of prizes because
+
+ align:start position:0%
+and he won all sorts of prizes because
+ 
+
+ align:start position:0%
+and he won all sorts of prizes because
+he was trying to be like a gecko
+
+ align:start position:0%
+he was trying to be like a gecko
+ 
+
+ align:start position:0%
+he was trying to be like a gecko
+and so he made gloves that were like
+
+ align:start position:0%
+and so he made gloves that were like
+ 
+
+ align:start position:0%
+and so he made gloves that were like
+gecko gloves and much to the delight
+
+ align:start position:0%
+gecko gloves and much to the delight
+ 
+
+ align:start position:0%
+gecko gloves and much to the delight
+of the facilities people at mit he
+
+ align:start position:0%
+of the facilities people at mit he
+ 
+
+ align:start position:0%
+of the facilities people at mit he
+actually climbed
+
+ align:start position:0%
+actually climbed
+ 
+
+ align:start position:0%
+actually climbed
+one of the buildings using these his
+
+ align:start position:0%
+one of the buildings using these his
+ 
+
+ align:start position:0%
+one of the buildings using these his
+gloves
+
+ align:start position:0%
+gloves
+ 
+
+ align:start position:0%
+gloves
+in case you are wondering it wasn't
+
+ align:start position:0%
+in case you are wondering it wasn't
+ 
+
+ align:start position:0%
+in case you are wondering it wasn't
+actually their delight
+
+ align:start position:0%
+actually their delight
+ 
+
+ align:start position:0%
+actually their delight
+um but uh but it really cool stuff so
+
+ align:start position:0%
+um but uh but it really cool stuff so
+ 
+
+ align:start position:0%
+um but uh but it really cool stuff so
+let me show you just this is like a 30
+
+ align:start position:0%
+let me show you just this is like a 30
+ 
+
+ align:start position:0%
+let me show you just this is like a 30
+second video
+
+ align:start position:0%
+second video
+ 
+
+ align:start position:0%
+second video
+he found the answer in the sheer number
+
+ align:start position:0%
+he found the answer in the sheer number
+ 
+
+ align:start position:0%
+he found the answer in the sheer number
+and design
+
+ align:start position:0%
+and design
+ 
+
+ align:start position:0%
+and design
+of the hairs on the gecko's feet
+
+ align:start position:0%
+of the hairs on the gecko's feet
+ 
+
+ align:start position:0%
+of the hairs on the gecko's feet
+geckos have millions of microscopic
+
+ align:start position:0%
+geckos have millions of microscopic
+ 
+
+ align:start position:0%
+geckos have millions of microscopic
+hairs on their toes
+
+ align:start position:0%
+hairs on their toes
+ 
+
+ align:start position:0%
+hairs on their toes
+of course we can't see this with our
+
+ align:start position:0%
+of course we can't see this with our
+ 
+
+ align:start position:0%
+of course we can't see this with our
+naked eye because each hair is only one
+
+ align:start position:0%
+naked eye because each hair is only one
+ 
+
+ align:start position:0%
+naked eye because each hair is only one
+tenth the size of a human hair
+
+ align:start position:0%
+tenth the size of a human hair
+ 
+
+ align:start position:0%
+tenth the size of a human hair
+and each of those hairs branch down to
+
+ align:start position:0%
+and each of those hairs branch down to
+ 
+
+ align:start position:0%
+and each of those hairs branch down to
+billions of little split ends
+
+ align:start position:0%
+billions of little split ends
+ 
+
+ align:start position:0%
+billions of little split ends
+and they can make such close contact
+
+ align:start position:0%
+and they can make such close contact
+ 
+
+ align:start position:0%
+and they can make such close contact
+with the surface that
+
+ align:start position:0%
+with the surface that
+ 
+
+ align:start position:0%
+with the surface that
+weak intermolecular forces can begin to
+
+ align:start position:0%
+weak intermolecular forces can begin to
+ 
+
+ align:start position:0%
+weak intermolecular forces can begin to
+add up to something really strong
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+turns out geckos exploit something
+
+ align:start position:0%
+turns out geckos exploit something
+ 
+
+ align:start position:0%
+turns out geckos exploit something
+called the van der waals force
+
+ align:start position:0%
+called the van der waals force
+ 
+
+ align:start position:0%
+called the van der waals force
+no london london if you think of an atom
+
+ align:start position:0%
+no london london if you think of an atom
+ 
+
+ align:start position:0%
+no london london if you think of an atom
+as a dancing couple
+
+ align:start position:0%
+as a dancing couple
+ 
+
+ align:start position:0%
+as a dancing couple
+when you bring two atoms into very close
+
+ align:start position:0%
+when you bring two atoms into very close
+ 
+
+ align:start position:0%
+when you bring two atoms into very close
+contact
+
+ align:start position:0%
+contact
+ 
+
+ align:start position:0%
+contact
+part of one atom can get attracted to
+
+ align:start position:0%
+part of one atom can get attracted to
+ 
+
+ align:start position:0%
+part of one atom can get attracted to
+part of the other
+
+ align:start position:0%
+part of the other
+ 
+
+ align:start position:0%
+part of the other
+that very weak bond is the van der waals
+
+ align:start position:0%
+that very weak bond is the van der waals
+ 
+
+ align:start position:0%
+that very weak bond is the van der waals
+force
+
+ align:start position:0%
+force
+ 
+
+ align:start position:0%
+force
+and it sticks atoms together proximity
+
+ align:start position:0%
+and it sticks atoms together proximity
+ 
+
+ align:start position:0%
+and it sticks atoms together proximity
+is the key
+
+ align:start position:0%
+is the key
+ 
+
+ align:start position:0%
+is the key
+but bringing two materials that near
+
+ align:start position:0%
+but bringing two materials that near
+ 
+
+ align:start position:0%
+but bringing two materials that near
+each other is harder than you'd think
+
+ align:start position:0%
+each other is harder than you'd think
+ 
+
+ align:start position:0%
+each other is harder than you'd think
+all right now obviously
+
+ align:start position:0%
+all right now obviously
+ 
+
+ align:start position:0%
+all right now obviously
+that got me very excited when i saw that
+
+ align:start position:0%
+that got me very excited when i saw that
+ 
+
+ align:start position:0%
+that got me very excited when i saw that
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+because that is how i see atoms and that
+
+ align:start position:0%
+because that is how i see atoms and that
+ 
+
+ align:start position:0%
+because that is how i see atoms and that
+is how i see electrons and i saw this
+
+ align:start position:0%
+is how i see electrons and i saw this
+ 
+
+ align:start position:0%
+is how i see electrons and i saw this
+and i almost fell over
+
+ align:start position:0%
+and i almost fell over
+ 
+
+ align:start position:0%
+and i almost fell over
+and uh and of course i've played it and
+
+ align:start position:0%
+and uh and of course i've played it and
+ 
+
+ align:start position:0%
+and uh and of course i've played it and
+i know all those moves i would suggest
+
+ align:start position:0%
+i know all those moves i would suggest
+ 
+
+ align:start position:0%
+i know all those moves i would suggest
+you guys
+
+ align:start position:0%
+you guys
+ 
+
+ align:start position:0%
+you guys
+it's a friday there's some good moves in
+
+ align:start position:0%
+it's a friday there's some good moves in
+ 
+
+ align:start position:0%
+it's a friday there's some good moves in
+there
+
+ align:start position:0%
+there
+ 
+
+ align:start position:0%
+there
+there's some good moves in there and you
+
+ align:start position:0%
+there's some good moves in there and you
+ 
+
+ align:start position:0%
+there's some good moves in there and you
+can take this on your phone and just
+
+ align:start position:0%
+can take this on your phone and just
+ 
+
+ align:start position:0%
+can take this on your phone and just
+kind of work it out at the club
+
+ align:start position:0%
+kind of work it out at the club
+ 
+
+ align:start position:0%
+kind of work it out at the club
+um and speaking of the club there's one
+
+ align:start position:0%
+um and speaking of the club there's one
+ 
+
+ align:start position:0%
+um and speaking of the club there's one
+more thing i got to teach you
+
+ align:start position:0%
+more thing i got to teach you
+ 
+
+ align:start position:0%
+more thing i got to teach you
+because it's that last line it's that
+
+ align:start position:0%
+because it's that last line it's that
+ 
+
+ align:start position:0%
+because it's that last line it's that
+last line
+
+ align:start position:0%
+last line
+ 
+
+ align:start position:0%
+last line
+um see um if you go along a trend
+
+ align:start position:0%
+um see um if you go along a trend
+ 
+
+ align:start position:0%
+um see um if you go along a trend
+like methane silane germany right these
+
+ align:start position:0%
+like methane silane germany right these
+ 
+
+ align:start position:0%
+like methane silane germany right these
+are all attract these are non-polar
+
+ align:start position:0%
+are all attract these are non-polar
+ 
+
+ align:start position:0%
+are all attract these are non-polar
+molecules
+
+ align:start position:0%
+molecules
+ 
+
+ align:start position:0%
+molecules
+they're all attracted uh to each other
+
+ align:start position:0%
+they're all attracted uh to each other
+ 
+
+ align:start position:0%
+they're all attracted uh to each other
+by these van der waals and you can see
+
+ align:start position:0%
+by these van der waals and you can see
+ 
+
+ align:start position:0%
+by these van der waals and you can see
+that
+
+ align:start position:0%
+that
+ 
+
+ align:start position:0%
+that
+the boiling point remember our proxy for
+
+ align:start position:0%
+the boiling point remember our proxy for
+ 
+
+ align:start position:0%
+the boiling point remember our proxy for
+the force the the bonding strength
+
+ align:start position:0%
+the force the the bonding strength
+ 
+
+ align:start position:0%
+the force the the bonding strength
+is going up that's what you'd expect
+
+ align:start position:0%
+is going up that's what you'd expect
+ 
+
+ align:start position:0%
+is going up that's what you'd expect
+that's because these are getting larger
+
+ align:start position:0%
+that's because these are getting larger
+ 
+
+ align:start position:0%
+that's because these are getting larger
+and they're going to be
+
+ align:start position:0%
+and they're going to be
+ 
+
+ align:start position:0%
+and they're going to be
+more polarizable electrons yeah but look
+
+ align:start position:0%
+more polarizable electrons yeah but look
+ 
+
+ align:start position:0%
+more polarizable electrons yeah but look
+at what happens
+
+ align:start position:0%
+at what happens
+ 
+
+ align:start position:0%
+at what happens
+as you go to other molecules this is the
+
+ align:start position:0%
+as you go to other molecules this is the
+ 
+
+ align:start position:0%
+as you go to other molecules this is the
+expected trend
+
+ align:start position:0%
+expected trend
+ 
+
+ align:start position:0%
+expected trend
+until you get here right nh3hf
+
+ align:start position:0%
+until you get here right nh3hf
+ 
+
+ align:start position:0%
+until you get here right nh3hf
+and that is because of one last type of
+
+ align:start position:0%
+and that is because of one last type of
+ 
+
+ align:start position:0%
+and that is because of one last type of
+bond that is because
+
+ align:start position:0%
+bond that is because
+ 
+
+ align:start position:0%
+bond that is because
+of something called a hydrogen bond it's
+
+ align:start position:0%
+of something called a hydrogen bond it's
+ 
+
+ align:start position:0%
+of something called a hydrogen bond it's
+a very unique
+
+ align:start position:0%
+a very unique
+ 
+
+ align:start position:0%
+a very unique
+uh kind of bond and so a hydrogen bond
+
+ align:start position:0%
+uh kind of bond and so a hydrogen bond
+ 
+
+ align:start position:0%
+uh kind of bond and so a hydrogen bond
+is our last intermolecular bond in
+
+ align:start position:0%
+is our last intermolecular bond in
+ 
+
+ align:start position:0%
+is our last intermolecular bond in
+hydrogen bond
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+right and it's a very particular kind of
+
+ align:start position:0%
+right and it's a very particular kind of
+ 
+
+ align:start position:0%
+right and it's a very particular kind of
+bond and it has to do with something
+
+ align:start position:0%
+bond and it has to do with something
+ 
+
+ align:start position:0%
+bond and it has to do with something
+very particular that hydrogen does
+
+ align:start position:0%
+very particular that hydrogen does
+ 
+
+ align:start position:0%
+very particular that hydrogen does
+look at those boiling points look at the
+
+ align:start position:0%
+look at those boiling points look at the
+ 
+
+ align:start position:0%
+look at those boiling points look at the
+change i mean
+
+ align:start position:0%
+change i mean
+ 
+
+ align:start position:0%
+change i mean
+h2o is h2o because of the hydrogen bond
+
+ align:start position:0%
+h2o is h2o because of the hydrogen bond
+ 
+
+ align:start position:0%
+h2o is h2o because of the hydrogen bond
+right earth's operating conditions
+
+ align:start position:0%
+right earth's operating conditions
+ 
+
+ align:start position:0%
+right earth's operating conditions
+uh are luckily right here but this is
+
+ align:start position:0%
+uh are luckily right here but this is
+ 
+
+ align:start position:0%
+uh are luckily right here but this is
+only
+
+ align:start position:0%
+only
+ 
+
+ align:start position:0%
+only
+good because of hydrogen bonds that it's
+
+ align:start position:0%
+good because of hydrogen bonds that it's
+ 
+
+ align:start position:0%
+good because of hydrogen bonds that it's
+all the way up here and not all the way
+
+ align:start position:0%
+all the way up here and not all the way
+ 
+
+ align:start position:0%
+all the way up here and not all the way
+down there
+
+ align:start position:0%
+down there
+ 
+
+ align:start position:0%
+down there
+yeah so hydrogen bonds are unique this
+
+ align:start position:0%
+yeah so hydrogen bonds are unique this
+ 
+
+ align:start position:0%
+yeah so hydrogen bonds are unique this
+is the electro negativity scale
+
+ align:start position:0%
+is the electro negativity scale
+ 
+
+ align:start position:0%
+is the electro negativity scale
+and there's something very important
+
+ align:start position:0%
+and there's something very important
+ 
+
+ align:start position:0%
+and there's something very important
+that happens for those three elements
+
+ align:start position:0%
+that happens for those three elements
+ 
+
+ align:start position:0%
+that happens for those three elements
+for those three elements those are the
+
+ align:start position:0%
+for those three elements those are the
+ 
+
+ align:start position:0%
+for those three elements those are the
+three elements that are in this trend
+
+ align:start position:0%
+three elements that are in this trend
+ 
+
+ align:start position:0%
+three elements that are in this trend
+those are the three elements see
+
+ align:start position:0%
+those are the three elements see
+ 
+
+ align:start position:0%
+those are the three elements see
+nitrogen chlorine and oxygen
+
+ align:start position:0%
+nitrogen chlorine and oxygen
+ 
+
+ align:start position:0%
+nitrogen chlorine and oxygen
+those are the three elements here and
+
+ align:start position:0%
+those are the three elements here and
+ 
+
+ align:start position:0%
+those are the three elements here and
+what's important about them is that they
+
+ align:start position:0%
+what's important about them is that they
+ 
+
+ align:start position:0%
+what's important about them is that they
+have such a huge electronegativity
+
+ align:start position:0%
+have such a huge electronegativity
+ 
+
+ align:start position:0%
+have such a huge electronegativity
+and so in a hydrogen bond what's going
+
+ align:start position:0%
+and so in a hydrogen bond what's going
+ 
+
+ align:start position:0%
+and so in a hydrogen bond what's going
+to happen
+
+ align:start position:0%
+to happen
+ 
+
+ align:start position:0%
+to happen
+what's going to happen in a hydrogen
+
+ align:start position:0%
+what's going to happen in a hydrogen
+ 
+
+ align:start position:0%
+what's going to happen in a hydrogen
+bond is they're really going to pull a
+
+ align:start position:0%
+bond is they're really going to pull a
+ 
+
+ align:start position:0%
+bond is they're really going to pull a
+lot of charge
+
+ align:start position:0%
+lot of charge
+ 
+
+ align:start position:0%
+lot of charge
+from the hydrogen so if you have
+
+ align:start position:0%
+from the hydrogen so if you have
+ 
+
+ align:start position:0%
+from the hydrogen so if you have
+so you have a very high positive charge
+
+ align:start position:0%
+so you have a very high positive charge
+ 
+
+ align:start position:0%
+so you have a very high positive charge
+on the hydrogen but there's something
+
+ align:start position:0%
+on the hydrogen but there's something
+ 
+
+ align:start position:0%
+on the hydrogen but there's something
+else that happens
+
+ align:start position:0%
+else that happens
+ 
+
+ align:start position:0%
+else that happens
+for hydrogen bonding to occur you see
+
+ align:start position:0%
+for hydrogen bonding to occur you see
+ 
+
+ align:start position:0%
+for hydrogen bonding to occur you see
+it's the
+
+ align:start position:0%
+it's the
+ 
+
+ align:start position:0%
+it's the
+h with say fluorine
+
+ align:start position:0%
+h with say fluorine
+ 
+
+ align:start position:0%
+h with say fluorine
+and you have a delta plus and a delta
+
+ align:start position:0%
+and you have a delta plus and a delta
+ 
+
+ align:start position:0%
+and you have a delta plus and a delta
+minus and this is high
+
+ align:start position:0%
+minus and this is high
+ 
+
+ align:start position:0%
+minus and this is high
+this is very high right but you also
+
+ align:start position:0%
+this is very high right but you also
+ 
+
+ align:start position:0%
+this is very high right but you also
+have
+
+ align:start position:0%
+have
+ 
+
+ align:start position:0%
+have
+a lone pair somewhere you've also got a
+
+ align:start position:0%
+a lone pair somewhere you've also got a
+ 
+
+ align:start position:0%
+a lone pair somewhere you've also got a
+lone pair
+
+ align:start position:0%
+lone pair
+ 
+
+ align:start position:0%
+lone pair
+where we know that we have that on the
+
+ align:start position:0%
+where we know that we have that on the
+ 
+
+ align:start position:0%
+where we know that we have that on the
+flurry right
+
+ align:start position:0%
+flurry right
+ 
+
+ align:start position:0%
+flurry right
+we know that and we got those too and
+
+ align:start position:0%
+we know that and we got those too and
+ 
+
+ align:start position:0%
+we know that and we got those too and
+the bond that a hydrogen bond
+
+ align:start position:0%
+the bond that a hydrogen bond
+ 
+
+ align:start position:0%
+the bond that a hydrogen bond
+represents is the fact that i've done
+
+ align:start position:0%
+represents is the fact that i've done
+ 
+
+ align:start position:0%
+represents is the fact that i've done
+two things with this same molecule
+
+ align:start position:0%
+two things with this same molecule
+ 
+
+ align:start position:0%
+two things with this same molecule
+i've taken a lot of charge off of
+
+ align:start position:0%
+i've taken a lot of charge off of
+ 
+
+ align:start position:0%
+i've taken a lot of charge off of
+hydrogen and created a very strong
+
+ align:start position:0%
+hydrogen and created a very strong
+ 
+
+ align:start position:0%
+hydrogen and created a very strong
+delta plus on the hydrogen but i've also
+
+ align:start position:0%
+delta plus on the hydrogen but i've also
+ 
+
+ align:start position:0%
+delta plus on the hydrogen but i've also
+got a lone pair somewhere
+
+ align:start position:0%
+got a lone pair somewhere
+ 
+
+ align:start position:0%
+got a lone pair somewhere
+that that can bond to and when i have
+
+ align:start position:0%
+that that can bond to and when i have
+ 
+
+ align:start position:0%
+that that can bond to and when i have
+those two things
+
+ align:start position:0%
+those two things
+ 
+
+ align:start position:0%
+those two things
+which i really have for these three
+
+ align:start position:0%
+which i really have for these three
+ 
+
+ align:start position:0%
+which i really have for these three
+elements right when i have those two
+
+ align:start position:0%
+elements right when i have those two
+ 
+
+ align:start position:0%
+elements right when i have those two
+things
+
+ align:start position:0%
+things
+ 
+
+ align:start position:0%
+things
+i can make this very special kind of
+
+ align:start position:0%
+i can make this very special kind of
+ 
+
+ align:start position:0%
+i can make this very special kind of
+bond
+
+ align:start position:0%
+bond
+ 
+
+ align:start position:0%
+bond
+now um this is what it looks like right
+
+ align:start position:0%
+now um this is what it looks like right
+ 
+
+ align:start position:0%
+now um this is what it looks like right
+so there's there's a hi
+
+ align:start position:0%
+so there's there's a hi
+ 
+
+ align:start position:0%
+so there's there's a hi
+there's an h2o molecule and i want to
+
+ align:start position:0%
+there's an h2o molecule and i want to
+ 
+
+ align:start position:0%
+there's an h2o molecule and i want to
+make a point here
+
+ align:start position:0%
+make a point here
+ 
+
+ align:start position:0%
+make a point here
+right there's the covalent bond between
+
+ align:start position:0%
+right there's the covalent bond between
+ 
+
+ align:start position:0%
+right there's the covalent bond between
+the oxygen and the hydrogen
+
+ align:start position:0%
+the oxygen and the hydrogen
+ 
+
+ align:start position:0%
+the oxygen and the hydrogen
+there's the delta plus and there's that
+
+ align:start position:0%
+there's the delta plus and there's that
+ 
+
+ align:start position:0%
+there's the delta plus and there's that
+hydrogen bond right there
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+there okay hydrogen bond that forms
+
+ align:start position:0%
+there okay hydrogen bond that forms
+ 
+
+ align:start position:0%
+there okay hydrogen bond that forms
+between the delta
+
+ align:start position:0%
+between the delta
+ 
+
+ align:start position:0%
+between the delta
+plus and the lone pair now you can see
+
+ align:start position:0%
+plus and the lone pair now you can see
+ 
+
+ align:start position:0%
+plus and the lone pair now you can see
+why water is so special
+
+ align:start position:0%
+why water is so special
+ 
+
+ align:start position:0%
+why water is so special
+you can see because unlike nh3 or hf
+
+ align:start position:0%
+you can see because unlike nh3 or hf
+ 
+
+ align:start position:0%
+you can see because unlike nh3 or hf
+you see why water had the biggest kick
+
+ align:start position:0%
+you see why water had the biggest kick
+ 
+
+ align:start position:0%
+you see why water had the biggest kick
+up
+
+ align:start position:0%
+up
+ 
+
+ align:start position:0%
+up
+from what would be expected because
+
+ align:start position:0%
+from what would be expected because
+ 
+
+ align:start position:0%
+from what would be expected because
+unlike nhh
+
+ align:start position:0%
+unlike nhh
+ 
+
+ align:start position:0%
+unlike nhh
+you have exactly the right balance
+
+ align:start position:0%
+you have exactly the right balance
+ 
+
+ align:start position:0%
+you have exactly the right balance
+i've created two of these very strong
+
+ align:start position:0%
+i've created two of these very strong
+ 
+
+ align:start position:0%
+i've created two of these very strong
+delta pluses and i've got two
+
+ align:start position:0%
+delta pluses and i've got two
+ 
+
+ align:start position:0%
+delta pluses and i've got two
+lone pairs and it all works out there's
+
+ align:start position:0%
+lone pairs and it all works out there's
+ 
+
+ align:start position:0%
+lone pairs and it all works out there's
+no extra lone pairs like here
+
+ align:start position:0%
+no extra lone pairs like here
+ 
+
+ align:start position:0%
+no extra lone pairs like here
+i've got these extra lone pairs right
+
+ align:start position:0%
+i've got these extra lone pairs right
+ 
+
+ align:start position:0%
+i've got these extra lone pairs right
+that don't don't there aren't enough
+
+ align:start position:0%
+that don't don't there aren't enough
+ 
+
+ align:start position:0%
+that don't don't there aren't enough
+moles you know each molecule only has
+
+ align:start position:0%
+moles you know each molecule only has
+ 
+
+ align:start position:0%
+moles you know each molecule only has
+one hydrogen here it's two and two
+
+ align:start position:0%
+one hydrogen here it's two and two
+ 
+
+ align:start position:0%
+one hydrogen here it's two and two
+that's why water is so special
+
+ align:start position:0%
+that's why water is so special
+ 
+
+ align:start position:0%
+that's why water is so special
+this bond is so important i know you've
+
+ align:start position:0%
+this bond is so important i know you've
+ 
+
+ align:start position:0%
+this bond is so important i know you've
+probably heard about it for water but
+
+ align:start position:0%
+probably heard about it for water but
+ 
+
+ align:start position:0%
+probably heard about it for water but
+here's my
+
+ align:start position:0%
+here's my
+ 
+
+ align:start position:0%
+here's my
+uh the example i want to give you for
+
+ align:start position:0%
+uh the example i want to give you for
+ 
+
+ align:start position:0%
+uh the example i want to give you for
+the club because some of you
+
+ align:start position:0%
+the club because some of you
+ 
+
+ align:start position:0%
+the club because some of you
+might be able to drink ethanol only if
+
+ align:start position:0%
+might be able to drink ethanol only if
+ 
+
+ align:start position:0%
+might be able to drink ethanol only if
+you're
+
+ align:start position:0%
+you're
+ 
+
+ align:start position:0%
+you're
+at the right age please of course
+
+ align:start position:0%
+at the right age please of course
+ 
+
+ align:start position:0%
+at the right age please of course
+um this is the but this is what's in
+
+ align:start position:0%
+um this is the but this is what's in
+ 
+
+ align:start position:0%
+um this is the but this is what's in
+alcohol right this is the ethanol
+
+ align:start position:0%
+alcohol right this is the ethanol
+ 
+
+ align:start position:0%
+alcohol right this is the ethanol
+molecule
+
+ align:start position:0%
+molecule
+ 
+
+ align:start position:0%
+molecule
+and it has a boiling point of 78.5
+
+ align:start position:0%
+and it has a boiling point of 78.5
+ 
+
+ align:start position:0%
+and it has a boiling point of 78.5
+degrees again
+
+ align:start position:0%
+degrees again
+ 
+
+ align:start position:0%
+degrees again
+that tells you something about the bond
+
+ align:start position:0%
+that tells you something about the bond
+ 
+
+ align:start position:0%
+that tells you something about the bond
+strength of this molecule to another
+
+ align:start position:0%
+strength of this molecule to another
+ 
+
+ align:start position:0%
+strength of this molecule to another
+molecule
+
+ align:start position:0%
+molecule
+ 
+
+ align:start position:0%
+molecule
+but look at this that's an oxygen with a
+
+ align:start position:0%
+but look at this that's an oxygen with a
+ 
+
+ align:start position:0%
+but look at this that's an oxygen with a
+hydrogen
+
+ align:start position:0%
+hydrogen
+ 
+
+ align:start position:0%
+hydrogen
+this took a lot of charge from the
+
+ align:start position:0%
+this took a lot of charge from the
+ 
+
+ align:start position:0%
+this took a lot of charge from the
+hydrogen right so you got a strong delta
+
+ align:start position:0%
+hydrogen right so you got a strong delta
+ 
+
+ align:start position:0%
+hydrogen right so you got a strong delta
+plus but you've got those two lone pairs
+
+ align:start position:0%
+plus but you've got those two lone pairs
+ 
+
+ align:start position:0%
+plus but you've got those two lone pairs
+there
+
+ align:start position:0%
+there
+ 
+
+ align:start position:0%
+there
+ready to bond to the other ethanol
+
+ align:start position:0%
+ready to bond to the other ethanol
+ 
+
+ align:start position:0%
+ready to bond to the other ethanol
+molecule but look at what happens
+
+ align:start position:0%
+molecule but look at what happens
+ 
+
+ align:start position:0%
+molecule but look at what happens
+methoxy methane is a gas at room
+
+ align:start position:0%
+methoxy methane is a gas at room
+ 
+
+ align:start position:0%
+methoxy methane is a gas at room
+temperature
+
+ align:start position:0%
+temperature
+ 
+
+ align:start position:0%
+temperature
+it's boiled off it's the exact same
+
+ align:start position:0%
+it's boiled off it's the exact same
+ 
+
+ align:start position:0%
+it's boiled off it's the exact same
+chemical formula
+
+ align:start position:0%
+chemical formula
+ 
+
+ align:start position:0%
+chemical formula
+it's the exact same chemical formula all
+
+ align:start position:0%
+it's the exact same chemical formula all
+ 
+
+ align:start position:0%
+it's the exact same chemical formula all
+i've done is shift the oxygen in
+
+ align:start position:0%
+i've done is shift the oxygen in
+ 
+
+ align:start position:0%
+i've done is shift the oxygen in
+and so now there's no hydrogen that's
+
+ align:start position:0%
+and so now there's no hydrogen that's
+ 
+
+ align:start position:0%
+and so now there's no hydrogen that's
+that's had that big of a delta on it
+
+ align:start position:0%
+that's had that big of a delta on it
+ 
+
+ align:start position:0%
+that's had that big of a delta on it
+so it cannot hydrogen bond it can we can
+
+ align:start position:0%
+so it cannot hydrogen bond it can we can
+ 
+
+ align:start position:0%
+so it cannot hydrogen bond it can we can
+london
+
+ align:start position:0%
+london
+ 
+
+ align:start position:0%
+london
+you know but it can't hydrogen it can't
+
+ align:start position:0%
+you know but it can't hydrogen it can't
+ 
+
+ align:start position:0%
+you know but it can't hydrogen it can't
+because the oxygen has the lone pairs
+
+ align:start position:0%
+because the oxygen has the lone pairs
+ 
+
+ align:start position:0%
+because the oxygen has the lone pairs
+but there's no hydrogens
+
+ align:start position:0%
+but there's no hydrogens
+ 
+
+ align:start position:0%
+but there's no hydrogens
+that have that strong of a delta so when
+
+ align:start position:0%
+that have that strong of a delta so when
+ 
+
+ align:start position:0%
+that have that strong of a delta so when
+you're at the club tonight trying out
+
+ align:start position:0%
+you're at the club tonight trying out
+ 
+
+ align:start position:0%
+you're at the club tonight trying out
+those moves
+
+ align:start position:0%
+those moves
+ 
+
+ align:start position:0%
+those moves
+go up to somebody and say it's a really
+
+ align:start position:0%
+go up to somebody and say it's a really
+ 
+
+ align:start position:0%
+go up to somebody and say it's a really
+good thing that's not
+
+ align:start position:0%
+good thing that's not
+ 
+
+ align:start position:0%
+good thing that's not
+methoxymethane isn't it really good
+
+ align:start position:0%
+methoxymethane isn't it really good
+ 
+
+ align:start position:0%
+methoxymethane isn't it really good
+thing
+
+ align:start position:0%
+thing
+ 
+
+ align:start position:0%
+thing
+and tell them about hydrogen bonds have
+
+ align:start position:0%
+and tell them about hydrogen bonds have
+ 
+
+ align:start position:0%
+and tell them about hydrogen bonds have
+a great weekend
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+you
\ No newline at end of file
diff --git a/PFfv1JnQB8Q.txt b/PFfv1JnQB8Q.txt
new file mode 100644
index 0000000000000000000000000000000000000000..7f08e75fae2e3bc0692e73c28b3aa979056577e0
--- /dev/null
+++ b/PFfv1JnQB8Q.txt
@@ -0,0 +1,14898 @@
+align:start position:0%
+ 
+the following content is provided under
+
+ align:start position:0%
+the following content is provided under
+ 
+
+ align:start position:0%
+the following content is provided under
+a Creative Commons license your support
+
+ align:start position:0%
+a Creative Commons license your support
+ 
+
+ align:start position:0%
+a Creative Commons license your support
+will help MIT open courseware continue
+
+ align:start position:0%
+will help MIT open courseware continue
+ 
+
+ align:start position:0%
+will help MIT open courseware continue
+to offer highquality educational
+
+ align:start position:0%
+to offer highquality educational
+ 
+
+ align:start position:0%
+to offer highquality educational
+resources for free to make a donation or
+
+ align:start position:0%
+resources for free to make a donation or
+ 
+
+ align:start position:0%
+resources for free to make a donation or
+to view additional materials from
+
+ align:start position:0%
+to view additional materials from
+ 
+
+ align:start position:0%
+to view additional materials from
+hundreds of MIT courses visit MIT open
+
+ align:start position:0%
+hundreds of MIT courses visit MIT open
+ 
+
+ align:start position:0%
+hundreds of MIT courses visit MIT open
+courseware at
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+ocw.mit.edu all right today we start a
+
+ align:start position:0%
+ocw.mit.edu all right today we start a
+ 
+
+ align:start position:0%
+ocw.mit.edu all right today we start a
+new section of NP Ness uh I think
+
+ align:start position:0%
+new section of NP Ness uh I think
+ 
+
+ align:start position:0%
+new section of NP Ness uh I think
+there'll just be one lecture about
+
+ align:start position:0%
+there'll just be one lecture about
+ 
+
+ align:start position:0%
+there'll just be one lecture about
+hamiltonicity
+
+ align:start position:0%
+hamiltonicity
+ 
+
+ align:start position:0%
+hamiltonicity
+so uh hamiltonian cycle and
+
+ align:start position:0%
+so uh hamiltonian cycle and
+ 
+
+ align:start position:0%
+so uh hamiltonian cycle and
+path we've talked about these briefly
+
+ align:start position:0%
+path we've talked about these briefly
+ 
+
+ align:start position:0%
+path we've talked about these briefly
+but uh cycle is just a uh cycle visiting
+
+ align:start position:0%
+but uh cycle is just a uh cycle visiting
+ 
+
+ align:start position:0%
+but uh cycle is just a uh cycle visiting
+every vertex exactly
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+once and usually
+
+ align:start position:0%
+once and usually
+ 
+
+ align:start position:0%
+once and usually
+uh when you talk about a graph being
+
+ align:start position:0%
+uh when you talk about a graph being
+ 
+
+ align:start position:0%
+uh when you talk about a graph being
+hamiltonian you mean that there's a
+
+ align:start position:0%
+hamiltonian you mean that there's a
+ 
+
+ align:start position:0%
+hamiltonian you mean that there's a
+hamiltonian cycle also called a
+
+ align:start position:0%
+hamiltonian cycle also called a
+ 
+
+ align:start position:0%
+hamiltonian cycle also called a
+hamiltonian tour or hamiltonian circuit
+
+ align:start position:0%
+hamiltonian tour or hamiltonian circuit
+ 
+
+ align:start position:0%
+hamiltonian tour or hamiltonian circuit
+uh all mean the same thing uh and then
+
+ align:start position:0%
+uh all mean the same thing uh and then
+ 
+
+ align:start position:0%
+uh all mean the same thing uh and then
+there's hamiltonian path another problem
+
+ align:start position:0%
+there's hamiltonian path another problem
+ 
+
+ align:start position:0%
+there's hamiltonian path another problem
+we have looked at before uh and same
+
+ align:start position:0%
+we have looked at before uh and same
+ 
+
+ align:start position:0%
+we have looked at before uh and same
+thing but path that visits every vertex
+
+ align:start position:0%
+thing but path that visits every vertex
+ 
+
+ align:start position:0%
+thing but path that visits every vertex
+exactly want these are pretty much the
+
+ align:start position:0%
+exactly want these are pretty much the
+ 
+
+ align:start position:0%
+exactly want these are pretty much the
+same problem but different versions are
+
+ align:start position:0%
+same problem but different versions are
+ 
+
+ align:start position:0%
+same problem but different versions are
+useful in different settings um in case
+
+ align:start position:0%
+useful in different settings um in case
+ 
+
+ align:start position:0%
+useful in different settings um in case
+you're curious where this comes from it
+
+ align:start position:0%
+you're curious where this comes from it
+ 
+
+ align:start position:0%
+you're curious where this comes from it
+comes from this game uh introduced by
+
+ align:start position:0%
+comes from this game uh introduced by
+ 
+
+ align:start position:0%
+comes from this game uh introduced by
+Hamilton in 18 1957 he was the royal
+
+ align:start position:0%
+Hamilton in 18 1957 he was the royal
+ 
+
+ align:start position:0%
+Hamilton in 18 1957 he was the royal
+astronomer of Ireland uh back then but
+
+ align:start position:0%
+astronomer of Ireland uh back then but
+ 
+
+ align:start position:0%
+astronomer of Ireland uh back then but
+he had fun with uh games as well so here
+
+ align:start position:0%
+he had fun with uh games as well so here
+ 
+
+ align:start position:0%
+he had fun with uh games as well so here
+you have something like the graph of a
+
+ align:start position:0%
+you have something like the graph of a
+ 
+
+ align:start position:0%
+you have something like the graph of a
+doc aedin The Duel is an icosahedron
+
+ align:start position:0%
+doc aedin The Duel is an icosahedron
+ 
+
+ align:start position:0%
+doc aedin The Duel is an icosahedron
+hence the name and you want to find a
+
+ align:start position:0%
+hence the name and you want to find a
+ 
+
+ align:start position:0%
+hence the name and you want to find a
+hamiltonian circuit through it or there
+
+ align:start position:0%
+hamiltonian circuit through it or there
+ 
+
+ align:start position:0%
+hamiltonian circuit through it or there
+actually a two-player game where one
+
+ align:start position:0%
+actually a two-player game where one
+ 
+
+ align:start position:0%
+actually a two-player game where one
+person chooses a subset of the graph the
+
+ align:start position:0%
+person chooses a subset of the graph the
+ 
+
+ align:start position:0%
+person chooses a subset of the graph the
+other one tries to find hamiltonian
+
+ align:start position:0%
+other one tries to find hamiltonian
+ 
+
+ align:start position:0%
+other one tries to find hamiltonian
+circuit in that
+
+ align:start position:0%
+circuit in that
+ 
+
+ align:start position:0%
+circuit in that
+subset uh so that's where hamiltonicity
+
+ align:start position:0%
+subset uh so that's where hamiltonicity
+ 
+
+ align:start position:0%
+subset uh so that's where hamiltonicity
+comes from
+
+ align:start position:0%
+comes from
+ 
+
+ align:start position:0%
+comes from
+uh but for us today it is a nice MP
+
+ align:start position:0%
+uh but for us today it is a nice MP
+ 
+
+ align:start position:0%
+uh but for us today it is a nice MP
+complete problem we've actually seen one
+
+ align:start position:0%
+complete problem we've actually seen one
+ 
+
+ align:start position:0%
+complete problem we've actually seen one
+proof that uh planer Max degree 4 I
+
+ align:start position:0%
+proof that uh planer Max degree 4 I
+ 
+
+ align:start position:0%
+proof that uh planer Max degree 4 I
+think uh hamiltonicity is hard I think
+
+ align:start position:0%
+think uh hamiltonicity is hard I think
+ 
+
+ align:start position:0%
+think uh hamiltonicity is hard I think
+uh that was in the planer sat discussion
+
+ align:start position:0%
+uh that was in the planer sat discussion
+ 
+
+ align:start position:0%
+uh that was in the planer sat discussion
+and this is the original paper that does
+
+ align:start position:0%
+and this is the original paper that does
+ 
+
+ align:start position:0%
+and this is the original paper that does
+planer 3at and there was this proof uh I
+
+ align:start position:0%
+planer 3at and there was this proof uh I
+ 
+
+ align:start position:0%
+planer 3at and there was this proof uh I
+guess it's not actually Max degree 4
+
+ align:start position:0%
+guess it's not actually Max degree 4
+ 
+
+ align:start position:0%
+guess it's not actually Max degree 4
+it's probably Max degree 6 or something
+
+ align:start position:0%
+it's probably Max degree 6 or something
+ 
+
+ align:start position:0%
+it's probably Max degree 6 or something
+uh you could get direct uh we argued the
+
+ align:start position:0%
+uh you could get direct uh we argued the
+ 
+
+ align:start position:0%
+uh you could get direct uh we argued the
+directed case this proof apparently
+
+ align:start position:0%
+directed case this proof apparently
+ 
+
+ align:start position:0%
+directed case this proof apparently
+works for the undirected case we'll get
+
+ align:start position:0%
+works for the undirected case we'll get
+ 
+
+ align:start position:0%
+works for the undirected case we'll get
+a an even stronger result here uh in
+
+ align:start position:0%
+a an even stronger result here uh in
+ 
+
+ align:start position:0%
+a an even stronger result here uh in
+general uh the problem is empty
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+complete and a lot of different special
+
+ align:start position:0%
+complete and a lot of different special
+ 
+
+ align:start position:0%
+complete and a lot of different special
+cases such as the one we saw uh for
+
+ align:start position:0%
+cases such as the one we saw uh for
+ 
+
+ align:start position:0%
+cases such as the one we saw uh for
+example if you're looking for a path and
+
+ align:start position:0%
+example if you're looking for a path and
+ 
+
+ align:start position:0%
+example if you're looking for a path and
+you're giv given uh the two end
+
+ align:start position:0%
+you're giv given uh the two end
+ 
+
+ align:start position:0%
+you're giv given uh the two end
+points so normally you say is there a
+
+ align:start position:0%
+points so normally you say is there a
+ 
+
+ align:start position:0%
+points so normally you say is there a
+hamiltonian path or is there a
+
+ align:start position:0%
+hamiltonian path or is there a
+ 
+
+ align:start position:0%
+hamiltonian path or is there a
+hamiltonian cycle those are both hard in
+
+ align:start position:0%
+hamiltonian cycle those are both hard in
+ 
+
+ align:start position:0%
+hamiltonian cycle those are both hard in
+general graphs but if I give you a graph
+
+ align:start position:0%
+general graphs but if I give you a graph
+ 
+
+ align:start position:0%
+general graphs but if I give you a graph
+and I give you two nodes s& T and I want
+
+ align:start position:0%
+and I give you two nodes s& T and I want
+ 
+
+ align:start position:0%
+and I give you two nodes s& T and I want
+to know is there uh so here's the graph
+
+ align:start position:0%
+to know is there uh so here's the graph
+ 
+
+ align:start position:0%
+to know is there uh so here's the graph
+here's S and T I want to know is there a
+
+ align:start position:0%
+here's S and T I want to know is there a
+ 
+
+ align:start position:0%
+here's S and T I want to know is there a
+path that starts at s ends at t uh this
+
+ align:start position:0%
+path that starts at s ends at t uh this
+ 
+
+ align:start position:0%
+path that starts at s ends at t uh this
+is NP hard by reduction from hamiltonian
+
+ align:start position:0%
+is NP hard by reduction from hamiltonian
+ 
+
+ align:start position:0%
+is NP hard by reduction from hamiltonian
+cycle tell me what to do
+
+ align:start position:0%
+cycle tell me what to do
+ 
+
+ align:start position:0%
+cycle tell me what to do
+you add a new node which has connection
+
+ align:start position:0%
+you add a new node which has connection
+ 
+
+ align:start position:0%
+you add a new node which has connection
+to S&T and nothing else add a new node
+
+ align:start position:0%
+to S&T and nothing else add a new node
+ 
+
+ align:start position:0%
+to S&T and nothing else add a new node
+connected to S&T and nothing else yeah
+
+ align:start position:0%
+connected to S&T and nothing else yeah
+ 
+
+ align:start position:0%
+connected to S&T and nothing else yeah
+so we'll add this new node x connect to
+
+ align:start position:0%
+so we'll add this new node x connect to
+ 
+
+ align:start position:0%
+so we'll add this new node x connect to
+S&T what's interesting about adding a
+
+ align:start position:0%
+S&T what's interesting about adding a
+ 
+
+ align:start position:0%
+S&T what's interesting about adding a
+degree 2 node is you know it has I mean
+
+ align:start position:0%
+degree 2 node is you know it has I mean
+ 
+
+ align:start position:0%
+degree 2 node is you know it has I mean
+has to be in the cycle so you know that
+
+ align:start position:0%
+has to be in the cycle so you know that
+ 
+
+ align:start position:0%
+has to be in the cycle so you know that
+these two edges have to be in the
+
+ align:start position:0%
+these two edges have to be in the
+ 
+
+ align:start position:0%
+these two edges have to be in the
+cycle also if it's directed you can
+
+ align:start position:0%
+cycle also if it's directed you can
+ 
+
+ align:start position:0%
+cycle also if it's directed you can
+direct those two so it's not
+
+ align:start position:0%
+direct those two so it's not
+ 
+
+ align:start position:0%
+direct those two so it's not
+directed uh all these are going to be
+
+ align:start position:0%
+directed uh all these are going to be
+ 
+
+ align:start position:0%
+directed uh all these are going to be
+undirected
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this would preserve directedness if you
+
+ align:start position:0%
+this would preserve directedness if you
+ 
+
+ align:start position:0%
+this would preserve directedness if you
+wanted it but yeah so uh there you go so
+
+ align:start position:0%
+wanted it but yeah so uh there you go so
+ 
+
+ align:start position:0%
+wanted it but yeah so uh there you go so
+if hamiltonian Cycle's hard then
+
+ align:start position:0%
+if hamiltonian Cycle's hard then
+ 
+
+ align:start position:0%
+if hamiltonian Cycle's hard then
+hamiltonian path given to end points is
+
+ align:start position:0%
+hamiltonian path given to end points is
+ 
+
+ align:start position:0%
+hamiltonian path given to end points is
+hard easy warmup um it's also EMP
+
+ align:start position:0%
+hard easy warmup um it's also EMP
+ 
+
+ align:start position:0%
+hard easy warmup um it's also EMP
+complete for
+
+ align:start position:0%
+complete for
+ 
+
+ align:start position:0%
+complete for
+planer three
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+regular three connected
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+graphs where every face has degree at
+
+ align:start position:0%
+graphs where every face has degree at
+ 
+
+ align:start position:0%
+graphs where every face has degree at
+least five but bother writing that down
+
+ align:start position:0%
+least five but bother writing that down
+ 
+
+ align:start position:0%
+least five but bother writing that down
+uh it's NP hard for bipar
+
+ align:start position:0%
+uh it's NP hard for bipar
+ 
+
+ align:start position:0%
+uh it's NP hard for bipar
+graphs these are all various
+
+ align:start position:0%
+graphs these are all various
+ 
+
+ align:start position:0%
+graphs these are all various
+results uh proved in the
+
+ align:start position:0%
+results uh proved in the
+ 
+
+ align:start position:0%
+results uh proved in the
+70s uh it's going be hard for squares of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+graphs squares of graphs is interesting
+
+ align:start position:0%
+graphs squares of graphs is interesting
+ 
+
+ align:start position:0%
+graphs squares of graphs is interesting
+this is whenever you have a length two
+
+ align:start position:0%
+this is whenever you have a length two
+ 
+
+ align:start position:0%
+this is whenever you have a length two
+path you add an edge that's a square uh
+
+ align:start position:0%
+path you add an edge that's a square uh
+ 
+
+ align:start position:0%
+path you add an edge that's a square uh
+that's still
+
+ align:start position:0%
+that's still
+ 
+
+ align:start position:0%
+that's still
+hard um another fun problem is Computing
+
+ align:start position:0%
+hard um another fun problem is Computing
+ 
+
+ align:start position:0%
+hard um another fun problem is Computing
+a hamiltonian cycle given a hamiltonian
+
+ align:start position:0%
+a hamiltonian cycle given a hamiltonian
+ 
+
+ align:start position:0%
+a hamiltonian cycle given a hamiltonian
+path is also
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+hard on the other hand some variations
+
+ align:start position:0%
+hard on the other hand some variations
+ 
+
+ align:start position:0%
+hard on the other hand some variations
+are easy so you have to be a little bit
+
+ align:start position:0%
+are easy so you have to be a little bit
+ 
+
+ align:start position:0%
+are easy so you have to be a little bit
+careful uh there are a lot of papers
+
+ align:start position:0%
+careful uh there are a lot of papers
+ 
+
+ align:start position:0%
+careful uh there are a lot of papers
+about various Gra s that are always
+
+ align:start position:0%
+about various Gra s that are always
+ 
+
+ align:start position:0%
+about various Gra s that are always
+hamiltonian and usually when they're
+
+ align:start position:0%
+hamiltonian and usually when they're
+ 
+
+ align:start position:0%
+hamiltonian and usually when they're
+always hamiltonian there's a good
+
+ align:start position:0%
+always hamiltonian there's a good
+ 
+
+ align:start position:0%
+always hamiltonian there's a good
+algorithm to find them here are just a
+
+ align:start position:0%
+algorithm to find them here are just a
+ 
+
+ align:start position:0%
+algorithm to find them here are just a
+couple of examples one is cubes of
+
+ align:start position:0%
+couple of examples one is cubes of
+ 
+
+ align:start position:0%
+couple of examples one is cubes of
+graphs so if you take all length three
+
+ align:start position:0%
+graphs so if you take all length three
+ 
+
+ align:start position:0%
+graphs so if you take all length three
+paths and connect them by an edge or
+
+ align:start position:0%
+paths and connect them by an edge or
+ 
+
+ align:start position:0%
+paths and connect them by an edge or
+maybe length less than or equal to three
+
+ align:start position:0%
+maybe length less than or equal to three
+ 
+
+ align:start position:0%
+maybe length less than or equal to three
+not sure exactly that's easy all such
+
+ align:start position:0%
+not sure exactly that's easy all such
+ 
+
+ align:start position:0%
+not sure exactly that's easy all such
+graphs are hamiltonian whereas squares
+
+ align:start position:0%
+graphs are hamiltonian whereas squares
+ 
+
+ align:start position:0%
+graphs are hamiltonian whereas squares
+it's still hard so that's kind of a
+
+ align:start position:0%
+it's still hard so that's kind of a
+ 
+
+ align:start position:0%
+it's still hard so that's kind of a
+limit and the other one here is planer
+
+ align:start position:0%
+limit and the other one here is planer
+ 
+
+ align:start position:0%
+limit and the other one here is planer
+three connector graphs is MP complete uh
+
+ align:start position:0%
+three connector graphs is MP complete uh
+ 
+
+ align:start position:0%
+three connector graphs is MP complete uh
+planer for connected graphs is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+polinomial this is a TTS theorem one of
+
+ align:start position:0%
+polinomial this is a TTS theorem one of
+ 
+
+ align:start position:0%
+polinomial this is a TTS theorem one of
+many TTS theorems uh all such graphs are
+
+ align:start position:0%
+many TTS theorems uh all such graphs are
+ 
+
+ align:start position:0%
+many TTS theorems uh all such graphs are
+hamiltonian so those are a few cases to
+
+ align:start position:0%
+hamiltonian so those are a few cases to
+ 
+
+ align:start position:0%
+hamiltonian so those are a few cases to
+to worry about we will see some more
+
+ align:start position:0%
+to worry about we will see some more
+ 
+
+ align:start position:0%
+to worry about we will see some more
+today and we're going to these are
+
+ align:start position:0%
+today and we're going to these are
+ 
+
+ align:start position:0%
+today and we're going to these are
+relatively simple uh we're going to
+
+ align:start position:0%
+relatively simple uh we're going to
+ 
+
+ align:start position:0%
+relatively simple uh we're going to
+prove even stricter versions of this
+
+ align:start position:0%
+prove even stricter versions of this
+ 
+
+ align:start position:0%
+prove even stricter versions of this
+problem and be complete but this starts
+
+ align:start position:0%
+problem and be complete but this starts
+ 
+
+ align:start position:0%
+problem and be complete but this starts
+to give you the flavor of what's
+
+ align:start position:0%
+to give you the flavor of what's
+ 
+
+ align:start position:0%
+to give you the flavor of what's
+there uh so in fact the first one we
+
+ align:start position:0%
+there uh so in fact the first one we
+ 
+
+ align:start position:0%
+there uh so in fact the first one we
+will
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+prove
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+is this may seem a little weird because
+
+ align:start position:0%
+is this may seem a little weird because
+ 
+
+ align:start position:0%
+is this may seem a little weird because
+I wanted to do undirected but we're
+
+ align:start position:0%
+I wanted to do undirected but we're
+ 
+
+ align:start position:0%
+I wanted to do undirected but we're
+going to make it undirected in a moment
+
+ align:start position:0%
+going to make it undirected in a moment
+ 
+
+ align:start position:0%
+going to make it undirected in a moment
+we're going to do a series of
+
+ align:start position:0%
+we're going to do a series of
+ 
+
+ align:start position:0%
+we're going to do a series of
+reductions first one we'll do is planer
+
+ align:start position:0%
+reductions first one we'll do is planer
+ 
+
+ align:start position:0%
+reductions first one we'll do is planer
+Max degree
+
+ align:start position:0%
+Max degree
+ 
+
+ align:start position:0%
+Max degree
+three
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+graphs okay so this will be um a
+
+ align:start position:0%
+graphs okay so this will be um a
+ 
+
+ align:start position:0%
+graphs okay so this will be um a
+reduction from threat so the general
+
+ align:start position:0%
+reduction from threat so the general
+ 
+
+ align:start position:0%
+reduction from threat so the general
+idea and you please wait why you should
+
+ align:start position:0%
+idea and you please wait why you should
+ 
+
+ align:start position:0%
+idea and you please wait why you should
+care about this problem we're going to
+
+ align:start position:0%
+care about this problem we're going to
+ 
+
+ align:start position:0%
+care about this problem we're going to
+reduce it to another more interesting
+
+ align:start position:0%
+reduce it to another more interesting
+ 
+
+ align:start position:0%
+reduce it to another more interesting
+version of hamiltonicity uh but here's
+
+ align:start position:0%
+version of hamiltonicity uh but here's
+ 
+
+ align:start position:0%
+version of hamiltonicity uh but here's
+one way to represent threat has
+
+ align:start position:0%
+one way to represent threat has
+ 
+
+ align:start position:0%
+one way to represent threat has
+hamiltonicity another way similar to the
+
+ align:start position:0%
+hamiltonicity another way similar to the
+ 
+
+ align:start position:0%
+hamiltonicity another way similar to the
+one we did before uh we've got Clauses
+
+ align:start position:0%
+one we did before uh we've got Clauses
+ 
+
+ align:start position:0%
+one we did before uh we've got Clauses
+here over on the left here some of the
+
+ align:start position:0%
+here over on the left here some of the
+ 
+
+ align:start position:0%
+here over on the left here some of the
+Clauses have size two but they works for
+
+ align:start position:0%
+Clauses have size two but they works for
+ 
+
+ align:start position:0%
+Clauses have size two but they works for
+the three case uh here we have the
+
+ align:start position:0%
+the three case uh here we have the
+ 
+
+ align:start position:0%
+the three case uh here we have the
+variables and the the key uh concept
+
+ align:start position:0%
+variables and the the key uh concept
+ 
+
+ align:start position:0%
+variables and the the key uh concept
+here is this notation this is notation
+
+ align:start position:0%
+here is this notation this is notation
+ 
+
+ align:start position:0%
+here is this notation this is notation
+shorthand for a more complicated Gadget
+
+ align:start position:0%
+shorthand for a more complicated Gadget
+ 
+
+ align:start position:0%
+shorthand for a more complicated Gadget
+um which is to say that these two things
+
+ align:start position:0%
+um which is to say that these two things
+ 
+
+ align:start position:0%
+um which is to say that these two things
+should not be both chosen this is an
+
+ align:start position:0%
+should not be both chosen this is an
+ 
+
+ align:start position:0%
+should not be both chosen this is an
+exclusive or uh in fact exactly one of
+
+ align:start position:0%
+exclusive or uh in fact exactly one of
+ 
+
+ align:start position:0%
+exclusive or uh in fact exactly one of
+them should be chosen so that forces X1
+
+ align:start position:0%
+them should be chosen so that forces X1
+ 
+
+ align:start position:0%
+them should be chosen so that forces X1
+to be the opposite of
+
+ align:start position:0%
+to be the opposite of
+ 
+
+ align:start position:0%
+to be the opposite of
+X1 bar and it also lets you duplicate
+
+ align:start position:0%
+X1 bar and it also lets you duplicate
+ 
+
+ align:start position:0%
+X1 bar and it also lets you duplicate
+things so here we get multiple copies of
+
+ align:start position:0%
+things so here we get multiple copies of
+ 
+
+ align:start position:0%
+things so here we get multiple copies of
+the variable you keep doing that several
+
+ align:start position:0%
+the variable you keep doing that several
+ 
+
+ align:start position:0%
+the variable you keep doing that several
+times you get many copies of variable
+
+ align:start position:0%
+times you get many copies of variable
+ 
+
+ align:start position:0%
+times you get many copies of variable
+and its complement and then we're also
+
+ align:start position:0%
+and its complement and then we're also
+ 
+
+ align:start position:0%
+and its complement and then we're also
+going to use some connections like this
+
+ align:start position:0%
+going to use some connections like this
+ 
+
+ align:start position:0%
+going to use some connections like this
+we're going to need a crossover Gadget
+
+ align:start position:0%
+we're going to need a crossover Gadget
+ 
+
+ align:start position:0%
+we're going to need a crossover Gadget
+uh but this will say that uh you well so
+
+ align:start position:0%
+uh but this will say that uh you well so
+ 
+
+ align:start position:0%
+uh but this will say that uh you well so
+this is going to be some clause which uh
+
+ align:start position:0%
+this is going to be some clause which uh
+ 
+
+ align:start position:0%
+this is going to be some clause which uh
+it's not literally as drawn again this
+
+ align:start position:0%
+it's not literally as drawn again this
+ 
+
+ align:start position:0%
+it's not literally as drawn again this
+is notation for a gadget that force is
+
+ align:start position:0%
+is notation for a gadget that force is
+ 
+
+ align:start position:0%
+is notation for a gadget that force is
+going to force at least one of these to
+
+ align:start position:0%
+going to force at least one of these to
+ 
+
+ align:start position:0%
+going to force at least one of these to
+be uh traversable
+
+ align:start position:0%
+be uh traversable
+ 
+
+ align:start position:0%
+be uh traversable
+okay so that overall should represent
+
+ align:start position:0%
+okay so that overall should represent
+ 
+
+ align:start position:0%
+okay so that overall should represent
+thre set we need a clause Gadget we need
+
+ align:start position:0%
+thre set we need a clause Gadget we need
+ 
+
+ align:start position:0%
+thre set we need a clause Gadget we need
+this exclusive or so that we can split
+
+ align:start position:0%
+this exclusive or so that we can split
+ 
+
+ align:start position:0%
+this exclusive or so that we can split
+duplicate things overall the cycle is
+
+ align:start position:0%
+duplicate things overall the cycle is
+ 
+
+ align:start position:0%
+duplicate things overall the cycle is
+going to do this so it's going to visit
+
+ align:start position:0%
+going to do this so it's going to visit
+ 
+
+ align:start position:0%
+going to do this so it's going to visit
+all the variables in order then all the
+
+ align:start position:0%
+all the variables in order then all the
+ 
+
+ align:start position:0%
+all the variables in order then all the
+Clauses in order uh so we don't we can't
+
+ align:start position:0%
+Clauses in order uh so we don't we can't
+ 
+
+ align:start position:0%
+Clauses in order uh so we don't we can't
+get anything interesting out of
+
+ align:start position:0%
+get anything interesting out of
+ 
+
+ align:start position:0%
+get anything interesting out of
+planarity because that graphs with these
+
+ align:start position:0%
+planarity because that graphs with these
+ 
+
+ align:start position:0%
+planarity because that graphs with these
+connections is not going to be planer so
+
+ align:start position:0%
+connections is not going to be planer so
+ 
+
+ align:start position:0%
+connections is not going to be planer so
+we'll need a crossover and those are the
+
+ align:start position:0%
+we'll need a crossover and those are the
+ 
+
+ align:start position:0%
+we'll need a crossover and those are the
+three gadgets we need yeah why we use
+
+ align:start position:0%
+three gadgets we need yeah why we use
+ 
+
+ align:start position:0%
+three gadgets we need yeah why we use
+the exclusive to connect
+
+ align:start position:0%
+the exclusive to connect
+ 
+
+ align:start position:0%
+the exclusive to connect
+variables uh so the idea is here there's
+
+ align:start position:0%
+variables uh so the idea is here there's
+ 
+
+ align:start position:0%
+variables uh so the idea is here there's
+a choice do I choose this Edge or this
+
+ align:start position:0%
+a choice do I choose this Edge or this
+ 
+
+ align:start position:0%
+a choice do I choose this Edge or this
+Edge in the hamiltonian cycle and I want
+
+ align:start position:0%
+Edge in the hamiltonian cycle and I want
+ 
+
+ align:start position:0%
+Edge in the hamiltonian cycle and I want
+the choice for this copy of X1 to be the
+
+ align:start position:0%
+the choice for this copy of X1 to be the
+ 
+
+ align:start position:0%
+the choice for this copy of X1 to be the
+same as for that copy of X1 so the
+
+ align:start position:0%
+same as for that copy of X1 so the
+ 
+
+ align:start position:0%
+same as for that copy of X1 so the
+exclusive or forces each instance of X1
+
+ align:start position:0%
+exclusive or forces each instance of X1
+ 
+
+ align:start position:0%
+exclusive or forces each instance of X1
+to be the same in general if there's K
+
+ align:start position:0%
+to be the same in general if there's K
+ 
+
+ align:start position:0%
+to be the same in general if there's K
+instances you'd have K of these connect
+
+ align:start position:0%
+instances you'd have K of these connect
+ 
+
+ align:start position:0%
+instances you'd have K of these connect
+that use the same Gadget to connect it
+
+ align:start position:0%
+that use the same Gadget to connect it
+ 
+
+ align:start position:0%
+that use the same Gadget to connect it
+to the instance inside the Clause
+
+ align:start position:0%
+to the instance inside the Clause
+ 
+
+ align:start position:0%
+to the instance inside the Clause
+uh I guess the the the issue the reason
+
+ align:start position:0%
+uh I guess the the the issue the reason
+ 
+
+ align:start position:0%
+uh I guess the the the issue the reason
+why we need two copies here is that you
+
+ align:start position:0%
+why we need two copies here is that you
+ 
+
+ align:start position:0%
+why we need two copies here is that you
+can't we'll see you can't have two XR
+
+ align:start position:0%
+can't we'll see you can't have two XR
+ 
+
+ align:start position:0%
+can't we'll see you can't have two XR
+gadgets going to the same place so it
+
+ align:start position:0%
+gadgets going to the same place so it
+ 
+
+ align:start position:0%
+gadgets going to the same place so it
+will be clear once we've seen the XR
+
+ align:start position:0%
+will be clear once we've seen the XR
+ 
+
+ align:start position:0%
+will be clear once we've seen the XR
+Gadget we want two distinct copies so
+
+ align:start position:0%
+Gadget we want two distinct copies so
+ 
+
+ align:start position:0%
+Gadget we want two distinct copies so
+that these two things can point to
+
+ align:start position:0%
+that these two things can point to
+ 
+
+ align:start position:0%
+that these two things can point to
+different copies of X1 that's why we're
+
+ align:start position:0%
+different copies of X1 that's why we're
+ 
+
+ align:start position:0%
+different copies of X1 that's why we're
+making a copy like that does that make
+
+ align:start position:0%
+making a copy like that does that make
+ 
+
+ align:start position:0%
+making a copy like that does that make
+sense okay next
+
+ align:start position:0%
+sense okay next
+ 
+
+ align:start position:0%
+sense okay next
+slide uh actually same slide I should
+
+ align:start position:0%
+slide uh actually same slide I should
+ 
+
+ align:start position:0%
+slide uh actually same slide I should
+just show them uh so here is maybe let's
+
+ align:start position:0%
+just show them uh so here is maybe let's
+ 
+
+ align:start position:0%
+just show them uh so here is maybe let's
+start with the XR Gadget because the
+
+ align:start position:0%
+start with the XR Gadget because the
+ 
+
+ align:start position:0%
+start with the XR Gadget because the
+Clause Clause doesn't actually use it
+
+ align:start position:0%
+Clause Clause doesn't actually use it
+ 
+
+ align:start position:0%
+Clause Clause doesn't actually use it
+but uh so the our Gadget is if we have
+
+ align:start position:0%
+but uh so the our Gadget is if we have
+ 
+
+ align:start position:0%
+but uh so the our Gadget is if we have
+two edges of opposite direction relative
+
+ align:start position:0%
+two edges of opposite direction relative
+ 
+
+ align:start position:0%
+two edges of opposite direction relative
+to the way we're being connected uh I
+
+ align:start position:0%
+to the way we're being connected uh I
+ 
+
+ align:start position:0%
+to the way we're being connected uh I
+think it also works in the other way
+
+ align:start position:0%
+think it also works in the other way
+ 
+
+ align:start position:0%
+think it also works in the other way
+because these are now these are also
+
+ align:start position:0%
+because these are now these are also
+ 
+
+ align:start position:0%
+because these are now these are also
+opposite if you redraw it this way uh
+
+ align:start position:0%
+opposite if you redraw it this way uh
+ 
+
+ align:start position:0%
+opposite if you redraw it this way uh
+we're just going to have this picture uh
+
+ align:start position:0%
+we're just going to have this picture uh
+ 
+
+ align:start position:0%
+we're just going to have this picture uh
+which can be traversed either this guy
+
+ align:start position:0%
+which can be traversed either this guy
+ 
+
+ align:start position:0%
+which can be traversed either this guy
+can come in here we're really using
+
+ align:start position:0%
+can come in here we're really using
+ 
+
+ align:start position:0%
+can come in here we're really using
+direction directionality of the graph
+
+ align:start position:0%
+direction directionality of the graph
+ 
+
+ align:start position:0%
+direction directionality of the graph
+you can Traverse the top Edge or you can
+
+ align:start position:0%
+you can Traverse the top Edge or you can
+ 
+
+ align:start position:0%
+you can Traverse the top Edge or you can
+Traverse the bottom Edge and the the
+
+ align:start position:0%
+Traverse the bottom Edge and the the
+ 
+
+ align:start position:0%
+Traverse the bottom Edge and the the
+opposite direction um but you can't you
+
+ align:start position:0%
+opposite direction um but you can't you
+ 
+
+ align:start position:0%
+opposite direction um but you can't you
+can't just turn around because then
+
+ align:start position:0%
+can't just turn around because then
+ 
+
+ align:start position:0%
+can't just turn around because then
+these vertices would be uncovered uh and
+
+ align:start position:0%
+these vertices would be uncovered uh and
+ 
+
+ align:start position:0%
+these vertices would be uncovered uh and
+if as soon as you've gone this far uh
+
+ align:start position:0%
+if as soon as you've gone this far uh
+ 
+
+ align:start position:0%
+if as soon as you've gone this far uh
+you can't come back this way so once you
+
+ align:start position:0%
+you can't come back this way so once you
+ 
+
+ align:start position:0%
+you can't come back this way so once you
+enter here you're forced to leave there
+
+ align:start position:0%
+enter here you're forced to leave there
+ 
+
+ align:start position:0%
+enter here you're forced to leave there
+once you enter here you're forced to
+
+ align:start position:0%
+once you enter here you're forced to
+ 
+
+ align:start position:0%
+once you enter here you're forced to
+leave there if you want to cover
+
+ align:start position:0%
+leave there if you want to cover
+ 
+
+ align:start position:0%
+leave there if you want to cover
+everything so that's an exclusive or and
+
+ align:start position:0%
+everything so that's an exclusive or and
+ 
+
+ align:start position:0%
+everything so that's an exclusive or and
+at least one of those better
+
+ align:start position:0%
+at least one of those better
+ 
+
+ align:start position:0%
+at least one of those better
+happen so that is what happens over
+
+ align:start position:0%
+happen so that is what happens over
+ 
+
+ align:start position:0%
+happen so that is what happens over
+there and also what we'll end up being
+
+ align:start position:0%
+there and also what we'll end up being
+ 
+
+ align:start position:0%
+there and also what we'll end up being
+doing here except we also need the
+
+ align:start position:0%
+doing here except we also need the
+ 
+
+ align:start position:0%
+doing here except we also need the
+crossing case on the other hand for the
+
+ align:start position:0%
+crossing case on the other hand for the
+ 
+
+ align:start position:0%
+crossing case on the other hand for the
+claw
+
+ align:start position:0%
+claw
+ 
+
+ align:start position:0%
+claw
+the idea
+
+ align:start position:0%
+the idea
+ 
+
+ align:start position:0%
+the idea
+is uh basically there's a cycle over
+
+ align:start position:0%
+is uh basically there's a cycle over
+ 
+
+ align:start position:0%
+is uh basically there's a cycle over
+here which is fine but somehow that
+
+ align:start position:0%
+here which is fine but somehow that
+ 
+
+ align:start position:0%
+here which is fine but somehow that
+cycle for that Clause uh has to be
+
+ align:start position:0%
+cycle for that Clause uh has to be
+ 
+
+ align:start position:0%
+cycle for that Clause uh has to be
+connected into the big cycle that we've
+
+ align:start position:0%
+connected into the big cycle that we've
+ 
+
+ align:start position:0%
+connected into the big cycle that we've
+drawn already and at least one of the
+
+ align:start position:0%
+drawn already and at least one of the
+ 
+
+ align:start position:0%
+drawn already and at least one of the
+variables needs to connect to that so um
+
+ align:start position:0%
+variables needs to connect to that so um
+ 
+
+ align:start position:0%
+variables needs to connect to that so um
+the idea is we can uh come up here uh so
+
+ align:start position:0%
+the idea is we can uh come up here uh so
+ 
+
+ align:start position:0%
+the idea is we can uh come up here uh so
+also these vertices need to be
+
+ align:start position:0%
+also these vertices need to be
+ 
+
+ align:start position:0%
+also these vertices need to be
+covered uh so we can come up here go
+
+ align:start position:0%
+covered uh so we can come up here go
+ 
+
+ align:start position:0%
+covered uh so we can come up here go
+over here loop
+
+ align:start position:0%
+over here loop
+ 
+
+ align:start position:0%
+over here loop
+around uh and be happy and then we've
+
+ align:start position:0%
+around uh and be happy and then we've
+ 
+
+ align:start position:0%
+around uh and be happy and then we've
+we've grabbed the entire
+
+ align:start position:0%
+we've grabbed the entire
+ 
+
+ align:start position:0%
+we've grabbed the entire
+cycle um also when we've grabbed this
+
+ align:start position:0%
+cycle um also when we've grabbed this
+ 
+
+ align:start position:0%
+cycle um also when we've grabbed this
+cycle we can
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+also we can also grab these
+
+ align:start position:0%
+also we can also grab these
+ 
+
+ align:start position:0%
+also we can also grab these
+vertices right all of
+
+ align:start position:0%
+vertices right all of
+ 
+
+ align:start position:0%
+vertices right all of
+them that's only going to be possible if
+
+ align:start position:0%
+them that's only going to be possible if
+ 
+
+ align:start position:0%
+them that's only going to be possible if
+this is
+
+ align:start position:0%
+this is
+ 
+
+ align:start position:0%
+this is
+possible so uh in the outer side
+
+ align:start position:0%
+possible so uh in the outer side
+ 
+
+ align:start position:0%
+possible so uh in the outer side
+uh we we can't go here and then up here
+
+ align:start position:0%
+uh we we can't go here and then up here
+ 
+
+ align:start position:0%
+uh we we can't go here and then up here
+we can go here over here that's also
+
+ align:start position:0%
+we can go here over here that's also
+ 
+
+ align:start position:0%
+we can go here over here that's also
+fine okay uh good I see so the the issue
+
+ align:start position:0%
+fine okay uh good I see so the the issue
+ 
+
+ align:start position:0%
+fine okay uh good I see so the the issue
+is so these are actually flexible these
+
+ align:start position:0%
+is so these are actually flexible these
+ 
+
+ align:start position:0%
+is so these are actually flexible these
+guys can be covered basically from the
+
+ align:start position:0%
+guys can be covered basically from the
+ 
+
+ align:start position:0%
+guys can be covered basically from the
+right side or from the left side either
+
+ align:start position:0%
+right side or from the left side either
+ 
+
+ align:start position:0%
+right side or from the left side either
+way so it doesn't matter whether you
+
+ align:start position:0%
+way so it doesn't matter whether you
+ 
+
+ align:start position:0%
+way so it doesn't matter whether you
+take this path or this
+
+ align:start position:0%
+take this path or this
+ 
+
+ align:start position:0%
+take this path or this
+path but uh at least one of them has at
+
+ align:start position:0%
+path but uh at least one of them has at
+ 
+
+ align:start position:0%
+path but uh at least one of them has at
+least one of these uh sort of pairs of
+
+ align:start position:0%
+least one of these uh sort of pairs of
+ 
+
+ align:start position:0%
+least one of these uh sort of pairs of
+edges as they're drawn over here you
+
+ align:start position:0%
+edges as they're drawn over here you
+ 
+
+ align:start position:0%
+edges as they're drawn over here you
+need to be able to choose the left
+
+ align:start position:0%
+need to be able to choose the left
+ 
+
+ align:start position:0%
+need to be able to choose the left
+choice and therefore get the big
+
+ align:start position:0%
+choice and therefore get the big
+ 
+
+ align:start position:0%
+choice and therefore get the big
+cycle and the the issue with that is
+
+ align:start position:0%
+cycle and the the issue with that is
+ 
+
+ align:start position:0%
+cycle and the the issue with that is
+because you have this X or it's an
+
+ align:start position:0%
+because you have this X or it's an
+ 
+
+ align:start position:0%
+because you have this X or it's an
+exclusive or Le exactly one of those two
+
+ align:start position:0%
+exclusive or Le exactly one of those two
+ 
+
+ align:start position:0%
+exclusive or Le exactly one of those two
+things must be true so in some cases
+
+ align:start position:0%
+things must be true so in some cases
+ 
+
+ align:start position:0%
+things must be true so in some cases
+you'll be forced to choose the right
+
+ align:start position:0%
+you'll be forced to choose the right
+ 
+
+ align:start position:0%
+you'll be forced to choose the right
+thing if this one if this variable chose
+
+ align:start position:0%
+thing if this one if this variable chose
+ 
+
+ align:start position:0%
+thing if this one if this variable chose
+the right path then this one will also
+
+ align:start position:0%
+the right path then this one will also
+ 
+
+ align:start position:0%
+the right path then this one will also
+have to choose the right path because of
+
+ align:start position:0%
+have to choose the right path because of
+ 
+
+ align:start position:0%
+have to choose the right path because of
+this exclusive ore uh and preventing you
+
+ align:start position:0%
+this exclusive ore uh and preventing you
+ 
+
+ align:start position:0%
+this exclusive ore uh and preventing you
+from grabbing the cycle you're fine in
+
+ align:start position:0%
+from grabbing the cycle you're fine in
+ 
+
+ align:start position:0%
+from grabbing the cycle you're fine in
+this Clause if at least one of them you
+
+ align:start position:0%
+this Clause if at least one of them you
+ 
+
+ align:start position:0%
+this Clause if at least one of them you
+choose the left path uh in fact this if
+
+ align:start position:0%
+choose the left path uh in fact this if
+ 
+
+ align:start position:0%
+choose the left path uh in fact this if
+you look very closely there are some
+
+ align:start position:0%
+you look very closely there are some
+ 
+
+ align:start position:0%
+you look very closely there are some
+bold edges indicating which ones got
+
+ align:start position:0%
+bold edges indicating which ones got
+ 
+
+ align:start position:0%
+bold edges indicating which ones got
+chosen here so here three of them were
+
+ align:start position:0%
+chosen here so here three of them were
+ 
+
+ align:start position:0%
+chosen here so here three of them were
+on two of them were on the right one of
+
+ align:start position:0%
+on two of them were on the right one of
+ 
+
+ align:start position:0%
+on two of them were on the right one of
+them was on the left for this clause in
+
+ align:start position:0%
+them was on the left for this clause in
+ 
+
+ align:start position:0%
+them was on the left for this clause in
+general at Le if at least one of them's
+
+ align:start position:0%
+general at Le if at least one of them's
+ 
+
+ align:start position:0%
+general at Le if at least one of them's
+on the left you're okay for the
+
+ align:start position:0%
+on the left you're okay for the
+ 
+
+ align:start position:0%
+on the left you're okay for the
+Clause clear at a high level now this
+
+ align:start position:0%
+Clause clear at a high level now this
+ 
+
+ align:start position:0%
+Clause clear at a high level now this
+would work fine if we didn't care about
+
+ align:start position:0%
+would work fine if we didn't care about
+ 
+
+ align:start position:0%
+would work fine if we didn't care about
+planarity uh but I want planer directed
+
+ align:start position:0%
+planarity uh but I want planer directed
+ 
+
+ align:start position:0%
+planarity uh but I want planer directed
+Max degree 3 at this point we should be
+
+ align:start position:0%
+Max degree 3 at this point we should be
+ 
+
+ align:start position:0%
+Max degree 3 at this point we should be
+directed Max degree 3 so the the that's
+
+ align:start position:0%
+directed Max degree 3 so the the that's
+ 
+
+ align:start position:0%
+directed Max degree 3 so the the that's
+an improvement from last last time terms
+
+ align:start position:0%
+an improvement from last last time terms
+ 
+
+ align:start position:0%
+an improvement from last last time terms
+of
+
+ align:start position:0%
+of
+ 
+
+ align:start position:0%
+of
+degrees uh and then there's this fun
+
+ align:start position:0%
+degrees uh and then there's this fun
+ 
+
+ align:start position:0%
+degrees uh and then there's this fun
+figure for the crossover so in general
+
+ align:start position:0%
+figure for the crossover so in general
+ 
+
+ align:start position:0%
+figure for the crossover so in general
+that's just a repetition of what our
+
+ align:start position:0%
+that's just a repetition of what our
+ 
+
+ align:start position:0%
+that's just a repetition of what our
+exor Gadget was now we have Crossing
+
+ align:start position:0%
+exor Gadget was now we have Crossing
+ 
+
+ align:start position:0%
+exor Gadget was now we have Crossing
+xover we have Crossing xor constraints
+
+ align:start position:0%
+xover we have Crossing xor constraints
+ 
+
+ align:start position:0%
+xover we have Crossing xor constraints
+so here's a typical example let's say we
+
+ align:start position:0%
+so here's a typical example let's say we
+ 
+
+ align:start position:0%
+so here's a typical example let's say we
+have this exor trying to go from there
+
+ align:start position:0%
+have this exor trying to go from there
+ 
+
+ align:start position:0%
+have this exor trying to go from there
+to there and it crosses these other
+
+ align:start position:0%
+to there and it crosses these other
+ 
+
+ align:start position:0%
+to there and it crosses these other
+exors uh so what we're going to do is
+
+ align:start position:0%
+exors uh so what we're going to do is
+ 
+
+ align:start position:0%
+exors uh so what we're going to do is
+build something like that gadget for the
+
+ align:start position:0%
+build something like that gadget for the
+ 
+
+ align:start position:0%
+build something like that gadget for the
+for the vertical connection with this
+
+ align:start position:0%
+for the vertical connection with this
+ 
+
+ align:start position:0%
+for the vertical connection with this
+and this and this and this and we
+
+ align:start position:0%
+and this and this and this and we
+ 
+
+ align:start position:0%
+and this and this and this and we
+duplicate these edges that doesn't help
+
+ align:start position:0%
+duplicate these edges that doesn't help
+ 
+
+ align:start position:0%
+duplicate these edges that doesn't help
+you from I mean it's the same as that
+
+ align:start position:0%
+you from I mean it's the same as that
+ 
+
+ align:start position:0%
+you from I mean it's the same as that
+picture just happen to duplicate them
+
+ align:start position:0%
+picture just happen to duplicate them
+ 
+
+ align:start position:0%
+picture just happen to duplicate them
+the reason we do that is we're going to
+
+ align:start position:0%
+the reason we do that is we're going to
+ 
+
+ align:start position:0%
+the reason we do that is we're going to
+put xor across like this and this forces
+
+ align:start position:0%
+put xor across like this and this forces
+ 
+
+ align:start position:0%
+put xor across like this and this forces
+um an alternation right so if this is in
+
+ align:start position:0%
+um an alternation right so if this is in
+ 
+
+ align:start position:0%
+um an alternation right so if this is in
+then this must be out so this must be in
+
+ align:start position:0%
+then this must be out so this must be in
+ 
+
+ align:start position:0%
+then this must be out so this must be in
+so this must be out so this must be in
+
+ align:start position:0%
+so this must be out so this must be in
+ 
+
+ align:start position:0%
+so this must be out so this must be in
+and so on all the way through and so
+
+ align:start position:0%
+and so on all the way through and so
+ 
+
+ align:start position:0%
+and so on all the way through and so
+that forces an exor between this Edge
+
+ align:start position:0%
+that forces an exor between this Edge
+ 
+
+ align:start position:0%
+that forces an exor between this Edge
+and that
+
+ align:start position:0%
+and that
+ 
+
+ align:start position:0%
+and that
+edge
+
+ align:start position:0%
+edge
+ 
+
+ align:start position:0%
+edge
+cool so that is the crossing X over X or
+
+ align:start position:0%
+cool so that is the crossing X over X or
+ 
+
+ align:start position:0%
+cool so that is the crossing X over X or
+Gadget which you plug into all of these
+
+ align:start position:0%
+Gadget which you plug into all of these
+ 
+
+ align:start position:0%
+Gadget which you plug into all of these
+pictures and you end up with planer
+
+ align:start position:0%
+pictures and you end up with planer
+ 
+
+ align:start position:0%
+pictures and you end up with planer
+directed Max degree 3 all right so far
+
+ align:start position:0%
+directed Max degree 3 all right so far
+ 
+
+ align:start position:0%
+directed Max degree 3 all right so far
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+good
+
+ align:start position:0%
+good
+ 
+
+ align:start position:0%
+good
+next I have a goal I'm still not going
+
+ align:start position:0%
+next I have a goal I'm still not going
+ 
+
+ align:start position:0%
+next I have a goal I'm still not going
+to tell you the goal uh where
+
+ align:start position:0%
+to tell you the goal uh where
+ 
+
+ align:start position:0%
+to tell you the goal uh where
+uh next one is going to be planer
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+bipartite uh Max degree
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+graphs uh
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+undirected this is going to be one of
+
+ align:start position:0%
+undirected this is going to be one of
+ 
+
+ align:start position:0%
+undirected this is going to be one of
+our simplest reductions ever there it is
+
+ align:start position:0%
+our simplest reductions ever there it is
+ 
+
+ align:start position:0%
+our simplest reductions ever there it is
+uh so the cool thing about ma degree 3
+
+ align:start position:0%
+uh so the cool thing about ma degree 3
+ 
+
+ align:start position:0%
+uh so the cool thing about ma degree 3
+directed uh I mean there are few cases
+
+ align:start position:0%
+directed uh I mean there are few cases
+ 
+
+ align:start position:0%
+directed uh I mean there are few cases
+you can exclude you can't have three
+
+ align:start position:0%
+you can exclude you can't have three
+ 
+
+ align:start position:0%
+you can exclude you can't have three
+incoming edges you can't have three
+
+ align:start position:0%
+incoming edges you can't have three
+ 
+
+ align:start position:0%
+incoming edges you can't have three
+outgoing edges be pretty hard to have a
+
+ align:start position:0%
+outgoing edges be pretty hard to have a
+ 
+
+ align:start position:0%
+outgoing edges be pretty hard to have a
+cycle that includes such vertices uh so
+
+ align:start position:0%
+cycle that includes such vertices uh so
+ 
+
+ align:start position:0%
+cycle that includes such vertices uh so
+you could have degree 2 vertices but um
+
+ align:start position:0%
+you could have degree 2 vertices but um
+ 
+
+ align:start position:0%
+you could have degree 2 vertices but um
+I don't think we even had any uh did I
+
+ align:start position:0%
+I don't think we even had any uh did I
+ 
+
+ align:start position:0%
+I don't think we even had any uh did I
+say do we have degree 3 uh degree 2 in
+
+ align:start position:0%
+say do we have degree 3 uh degree 2 in
+ 
+
+ align:start position:0%
+say do we have degree 3 uh degree 2 in
+this
+
+ align:start position:0%
+this
+ 
+
+ align:start position:0%
+this
+picture probably not I mean if we did we
+
+ align:start position:0%
+picture probably not I mean if we did we
+ 
+
+ align:start position:0%
+picture probably not I mean if we did we
+could double The Edge or something so
+
+ align:start position:0%
+could double The Edge or something so
+ 
+
+ align:start position:0%
+could double The Edge or something so
+that was probably actually planer
+
+ align:start position:0%
+that was probably actually planer
+ 
+
+ align:start position:0%
+that was probably actually planer
+directed three regular okay but now
+
+ align:start position:0%
+directed three regular okay but now
+ 
+
+ align:start position:0%
+directed three regular okay but now
+undirected but you can basically have
+
+ align:start position:0%
+undirected but you can basically have
+ 
+
+ align:start position:0%
+undirected but you can basically have
+two edges in one out or one Edge in and
+
+ align:start position:0%
+two edges in one out or one Edge in and
+ 
+
+ align:start position:0%
+two edges in one out or one Edge in and
+two
+
+ align:start position:0%
+two
+ 
+
+ align:start position:0%
+two
+out uh and we're going to repr we're
+
+ align:start position:0%
+out uh and we're going to repr we're
+ 
+
+ align:start position:0%
+out uh and we're going to repr we're
+going to convert that so the interesting
+
+ align:start position:0%
+going to convert that so the interesting
+ 
+
+ align:start position:0%
+going to convert that so the interesting
+thing here you have to visit this vertex
+
+ align:start position:0%
+thing here you have to visit this vertex
+ 
+
+ align:start position:0%
+thing here you have to visit this vertex
+which means you have to visit this
+
+ align:start position:0%
+which means you have to visit this
+ 
+
+ align:start position:0%
+which means you have to visit this
+Edge right in any hamiltonian cycle
+
+ align:start position:0%
+Edge right in any hamiltonian cycle
+ 
+
+ align:start position:0%
+Edge right in any hamiltonian cycle
+because once you come here you've got to
+
+ align:start position:0%
+because once you come here you've got to
+ 
+
+ align:start position:0%
+because once you come here you've got to
+leave on that edge similarly you have to
+
+ align:start position:0%
+leave on that edge similarly you have to
+ 
+
+ align:start position:0%
+leave on that edge similarly you have to
+visit this Edge you can tell that just
+
+ align:start position:0%
+visit this Edge you can tell that just
+ 
+
+ align:start position:0%
+visit this Edge you can tell that just
+from this picture so we call these
+
+ align:start position:0%
+from this picture so we call these
+ 
+
+ align:start position:0%
+from this picture so we call these
+forced edges
+
+ align:start position:0%
+forced edges
+ 
+
+ align:start position:0%
+forced edges
+and we can kind of represent that by
+
+ align:start position:0%
+and we can kind of represent that by
+ 
+
+ align:start position:0%
+and we can kind of represent that by
+adding a Vertex there says hey you've
+
+ align:start position:0%
+adding a Vertex there says hey you've
+ 
+
+ align:start position:0%
+adding a Vertex there says hey you've
+got to visit that edge so you're going
+
+ align:start position:0%
+got to visit that edge so you're going
+ 
+
+ align:start position:0%
+got to visit that edge so you're going
+to visit it by that little path there
+
+ align:start position:0%
+to visit it by that little path there
+ 
+
+ align:start position:0%
+to visit it by that little path there
+okay and now things are
+
+ align:start position:0%
+okay and now things are
+ 
+
+ align:start position:0%
+okay and now things are
+bipartite uh and the bipar tiess is
+
+ align:start position:0%
+bipartite uh and the bipar tiess is
+ 
+
+ align:start position:0%
+bipartite uh and the bipar tiess is
+essentially forcing the directionality
+
+ align:start position:0%
+essentially forcing the directionality
+ 
+
+ align:start position:0%
+essentially forcing the directionality
+as well so let's say when you come into
+
+ align:start position:0%
+as well so let's say when you come into
+ 
+
+ align:start position:0%
+as well so let's say when you come into
+a vertex and you're blue uh so that
+
+ align:start position:0%
+a vertex and you're blue uh so that
+ 
+
+ align:start position:0%
+a vertex and you're blue uh so that
+means these guys have had to have been
+
+ align:start position:0%
+means these guys have had to have been
+ 
+
+ align:start position:0%
+means these guys have had to have been
+red uh you're leaving whenever you leave
+
+ align:start position:0%
+red uh you're leaving whenever you leave
+ 
+
+ align:start position:0%
+red uh you're leaving whenever you leave
+you first visit a red vertex and then go
+
+ align:start position:0%
+you first visit a red vertex and then go
+ 
+
+ align:start position:0%
+you first visit a red vertex and then go
+so here you're coming in again as blue
+
+ align:start position:0%
+so here you're coming in again as blue
+ 
+
+ align:start position:0%
+so here you're coming in again as blue
+and then uh before you leave you turn
+
+ align:start position:0%
+and then uh before you leave you turn
+ 
+
+ align:start position:0%
+and then uh before you leave you turn
+red and so you will alternate always
+
+ align:start position:0%
+red and so you will alternate always
+ 
+
+ align:start position:0%
+red and so you will alternate always
+because you've satisfied directionality
+
+ align:start position:0%
+because you've satisfied directionality
+ 
+
+ align:start position:0%
+because you've satisfied directionality
+over here I mean the the outgoing edge
+
+ align:start position:0%
+over here I mean the the outgoing edge
+ 
+
+ align:start position:0%
+over here I mean the the outgoing edge
+here becomes an incoming Edge to the
+
+ align:start position:0%
+here becomes an incoming Edge to the
+ 
+
+ align:start position:0%
+here becomes an incoming Edge to the
+next vertex that means you'll be going
+
+ align:start position:0%
+next vertex that means you'll be going
+ 
+
+ align:start position:0%
+next vertex that means you'll be going
+into a blue vertex either because it's
+
+ align:start position:0%
+into a blue vertex either because it's
+ 
+
+ align:start position:0%
+into a blue vertex either because it's
+like this or like
+
+ align:start position:0%
+like this or like
+ 
+
+ align:start position:0%
+like this or like
+that okay and you
+
+ align:start position:0%
+that okay and you
+ 
+
+ align:start position:0%
+that okay and you
+are uh effectively forcing
+
+ align:start position:0%
+are uh effectively forcing
+ 
+
+ align:start position:0%
+are uh effectively forcing
+directionality um
+
+ align:start position:0%
+directionality um
+ 
+
+ align:start position:0%
+directionality um
+um I mean everything could be
+
+ align:start position:0%
+um I mean everything could be
+ 
+
+ align:start position:0%
+um I mean everything could be
+reversed but
+
+ align:start position:0%
+reversed but
+ 
+
+ align:start position:0%
+reversed but
+uh yeah because you're always coming
+
+ align:start position:0%
+uh yeah because you're always coming
+ 
+
+ align:start position:0%
+uh yeah because you're always coming
+into a blue vertex and leaving on a red
+
+ align:start position:0%
+into a blue vertex and leaving on a red
+ 
+
+ align:start position:0%
+into a blue vertex and leaving on a red
+that forces you to be going from the the
+
+ align:start position:0%
+that forces you to be going from the the
+ 
+
+ align:start position:0%
+that forces you to be going from the the
+tail of a of an arrow to the head of an
+
+ align:start position:0%
+tail of a of an arrow to the head of an
+ 
+
+ align:start position:0%
+tail of a of an arrow to the head of an
+of an arrow so same thing by symmetry
+
+ align:start position:0%
+of an arrow so same thing by symmetry
+ 
+
+ align:start position:0%
+of an arrow so same thing by symmetry
+okay so these problems are actually
+
+ align:start position:0%
+okay so these problems are actually
+ 
+
+ align:start position:0%
+okay so these problems are actually
+really close to each other and it's sort
+
+ align:start position:0%
+really close to each other and it's sort
+ 
+
+ align:start position:0%
+really close to each other and it's sort
+of uh these were done in different
+
+ align:start position:0%
+of uh these were done in different
+ 
+
+ align:start position:0%
+of uh these were done in different
+papers but uh this was an older one and
+
+ align:start position:0%
+papers but uh this was an older one and
+ 
+
+ align:start position:0%
+papers but uh this was an older one and
+then this problem was introduced for
+
+ align:start position:0%
+then this problem was introduced for
+ 
+
+ align:start position:0%
+then this problem was introduced for
+another
+
+ align:start position:0%
+another
+ 
+
+ align:start position:0%
+another
+reason which is grid
+
+ align:start position:0%
+reason which is grid
+ 
+
+ align:start position:0%
+reason which is grid
+graphs this is where I really want to
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+go so the idea with the grid graph is uh
+
+ align:start position:0%
+go so the idea with the grid graph is uh
+ 
+
+ align:start position:0%
+go so the idea with the grid graph is uh
+you let's say have a set of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+points on the Square lattice
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and then you're going to have an edge
+
+ align:start position:0%
+and then you're going to have an edge
+ 
+
+ align:start position:0%
+and then you're going to have an edge
+whenever you have two points at unit
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+distance so let me draw an
+
+ align:start position:0%
+distance so let me draw an
+ 
+
+ align:start position:0%
+distance so let me draw an
+example cheat and have some examples
+
+ align:start position:0%
+example cheat and have some examples
+ 
+
+ align:start position:0%
+example cheat and have some examples
+drawn for me uh this is in a much more
+
+ align:start position:0%
+drawn for me uh this is in a much more
+ 
+
+ align:start position:0%
+drawn for me uh this is in a much more
+recent paper but it's some nice pictures
+
+ align:start position:0%
+recent paper but it's some nice pictures
+ 
+
+ align:start position:0%
+recent paper but it's some nice pictures
+so uh we're just choosing a set of
+
+ align:start position:0%
+so uh we're just choosing a set of
+ 
+
+ align:start position:0%
+so uh we're just choosing a set of
+points in the sare grid and then
+
+ align:start position:0%
+points in the sare grid and then
+ 
+
+ align:start position:0%
+points in the sare grid and then
+whenever we have two points that are
+
+ align:start position:0%
+whenever we have two points that are
+ 
+
+ align:start position:0%
+whenever we have two points that are
+unit distance apart you're forced to
+
+ align:start position:0%
+unit distance apart you're forced to
+ 
+
+ align:start position:0%
+unit distance apart you're forced to
+have an edge there you can't say there's
+
+ align:start position:0%
+have an edge there you can't say there's
+ 
+
+ align:start position:0%
+have an edge there you can't say there's
+no Edge that would be a subgraph of a
+
+ align:start position:0%
+no Edge that would be a subgraph of a
+ 
+
+ align:start position:0%
+no Edge that would be a subgraph of a
+grid graph uh but for example when this
+
+ align:start position:0%
+grid graph uh but for example when this
+ 
+
+ align:start position:0%
+grid graph uh but for example when this
+point is absent you don't get any
+
+ align:start position:0%
+point is absent you don't get any
+ 
+
+ align:start position:0%
+point is absent you don't get any
+connections through
+
+ align:start position:0%
+connections through
+ 
+
+ align:start position:0%
+connections through
+here uh so these are all examples of
+
+ align:start position:0%
+here uh so these are all examples of
+ 
+
+ align:start position:0%
+here uh so these are all examples of
+grid
+
+ align:start position:0%
+grid
+ 
+
+ align:start position:0%
+grid
+graphs okay um now there's one special
+
+ align:start position:0%
+graphs okay um now there's one special
+ 
+
+ align:start position:0%
+graphs okay um now there's one special
+case or in general we we distinguish U
+
+ align:start position:0%
+case or in general we we distinguish U
+ 
+
+ align:start position:0%
+case or in general we we distinguish U
+there's sort of three types of Faces in
+
+ align:start position:0%
+there's sort of three types of Faces in
+ 
+
+ align:start position:0%
+there's sort of three types of Faces in
+such a planer graph there's what you
+
+ align:start position:0%
+such a planer graph there's what you
+ 
+
+ align:start position:0%
+such a planer graph there's what you
+might call pixels little one by one
+
+ align:start position:0%
+might call pixels little one by one
+ 
+
+ align:start position:0%
+might call pixels little one by one
+squares there's uh the outside face and
+
+ align:start position:0%
+squares there's uh the outside face and
+ 
+
+ align:start position:0%
+squares there's uh the outside face and
+then there's everything else which we
+
+ align:start position:0%
+then there's everything else which we
+ 
+
+ align:start position:0%
+then there's everything else which we
+call holes so any non length four um
+
+ align:start position:0%
+call holes so any non length four um
+ 
+
+ align:start position:0%
+call holes so any non length four um
+face we call a hole if there are no
+
+ align:start position:0%
+face we call a hole if there are no
+ 
+
+ align:start position:0%
+face we call a hole if there are no
+holes we call it a solid grid
+
+ align:start position:0%
+holes we call it a solid grid
+ 
+
+ align:start position:0%
+holes we call it a solid grid
+graph um this is interesting
+
+ align:start position:0%
+graph um this is interesting
+ 
+
+ align:start position:0%
+graph um this is interesting
+because solid grid graphs you can solve
+
+ align:start position:0%
+because solid grid graphs you can solve
+ 
+
+ align:start position:0%
+because solid grid graphs you can solve
+hamiltonicity and polinomial time it's
+
+ align:start position:0%
+hamiltonicity and polinomial time it's
+ 
+
+ align:start position:0%
+hamiltonicity and polinomial time it's
+not always possible but there is a
+
+ align:start position:0%
+not always possible but there is a
+ 
+
+ align:start position:0%
+not always possible but there is a
+polinomial time algorithm for solving
+
+ align:start position:0%
+polinomial time algorithm for solving
+ 
+
+ align:start position:0%
+polinomial time algorithm for solving
+the solid grid graph Case by umans and
+
+ align:start position:0%
+the solid grid graph Case by umans and
+ 
+
+ align:start position:0%
+the solid grid graph Case by umans and
+lenhard 97 it's very complicated
+
+ align:start position:0%
+lenhard 97 it's very complicated
+ 
+
+ align:start position:0%
+lenhard 97 it's very complicated
+algorithm luckily this is a hardness
+
+ align:start position:0%
+algorithm luckily this is a hardness
+ 
+
+ align:start position:0%
+algorithm luckily this is a hardness
+proof class so I don't have to cover it
+
+ align:start position:0%
+proof class so I don't have to cover it
+ 
+
+ align:start position:0%
+proof class so I don't have to cover it
+um I'm going to focus on the hardness
+
+ align:start position:0%
+um I'm going to focus on the hardness
+ 
+
+ align:start position:0%
+um I'm going to focus on the hardness
+when you allow
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+holes okay
+
+ align:start position:0%
+holes okay
+ 
+
+ align:start position:0%
+holes okay
+so this is where things get fun we are
+
+ align:start position:0%
+so this is where things get fun we are
+ 
+
+ align:start position:0%
+so this is where things get fun we are
+going to
+
+ align:start position:0%
+going to
+ 
+
+ align:start position:0%
+going to
+reduce so we did a reduction from here
+
+ align:start position:0%
+reduce so we did a reduction from here
+ 
+
+ align:start position:0%
+reduce so we did a reduction from here
+to here we're going to do reduction from
+
+ align:start position:0%
+to here we're going to do reduction from
+ 
+
+ align:start position:0%
+to here we're going to do reduction from
+here to here so we're going to suppose
+
+ align:start position:0%
+here to here so we're going to suppose
+ 
+
+ align:start position:0%
+here to here so we're going to suppose
+that we want to solve hamiltonicity in
+
+ align:start position:0%
+that we want to solve hamiltonicity in
+ 
+
+ align:start position:0%
+that we want to solve hamiltonicity in
+planer by partite Max degree 3 graphs
+
+ align:start position:0%
+planer by partite Max degree 3 graphs
+ 
+
+ align:start position:0%
+planer by partite Max degree 3 graphs
+and we're going to convert such a planer
+
+ align:start position:0%
+and we're going to convert such a planer
+ 
+
+ align:start position:0%
+and we're going to convert such a planer
+bipartite Max degree 3 graph into uh a
+
+ align:start position:0%
+bipartite Max degree 3 graph into uh a
+ 
+
+ align:start position:0%
+bipartite Max degree 3 graph into uh a
+grid graph that acts the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+same
+
+ align:start position:0%
+same
+ 
+
+ align:start position:0%
+same
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+um the first step is to draw the graph
+
+ align:start position:0%
+um the first step is to draw the graph
+ 
+
+ align:start position:0%
+um the first step is to draw the graph
+on a grd okay that's pretty pretty
+
+ align:start position:0%
+on a grd okay that's pretty pretty
+ 
+
+ align:start position:0%
+on a grd okay that's pretty pretty
+obvious
+
+ align:start position:0%
+obvious
+ 
+
+ align:start position:0%
+obvious
+um so here here's an example of what we
+
+ align:start position:0%
+um so here here's an example of what we
+ 
+
+ align:start position:0%
+um so here here's an example of what we
+want to do and then this is a picture of
+
+ align:start position:0%
+want to do and then this is a picture of
+ 
+
+ align:start position:0%
+want to do and then this is a picture of
+how to do it suppose you have a
+
+ align:start position:0%
+how to do it suppose you have a
+ 
+
+ align:start position:0%
+how to do it suppose you have a
+bipartite planer graph it's not obvious
+
+ align:start position:0%
+bipartite planer graph it's not obvious
+ 
+
+ align:start position:0%
+bipartite planer graph it's not obvious
+this is planer but it's obvious that
+
+ align:start position:0%
+this is planer but it's obvious that
+ 
+
+ align:start position:0%
+this is planer but it's obvious that
+it's bipartite it happens to be planer
+
+ align:start position:0%
+it's bipartite it happens to be planer
+ 
+
+ align:start position:0%
+it's bipartite it happens to be planer
+it's Max degree 3 and we want the
+
+ align:start position:0%
+it's Max degree 3 and we want the
+ 
+
+ align:start position:0%
+it's Max degree 3 and we want the
+vertices are labeled the X eyes and the
+
+ align:start position:0%
+vertices are labeled the X eyes and the
+ 
+
+ align:start position:0%
+vertices are labeled the X eyes and the
+Y eyes and you can see the corresponding
+
+ align:start position:0%
+Y eyes and you can see the corresponding
+ 
+
+ align:start position:0%
+Y eyes and you can see the corresponding
+labeling here so not all of the grid
+
+ align:start position:0%
+labeling here so not all of the grid
+ 
+
+ align:start position:0%
+labeling here so not all of the grid
+dots are going to be labeled some of
+
+ align:start position:0%
+dots are going to be labeled some of
+ 
+
+ align:start position:0%
+dots are going to be labeled some of
+them are just auxiliary in order to
+
+ align:start position:0%
+them are just auxiliary in order to
+ 
+
+ align:start position:0%
+them are just auxiliary in order to
+connect two vertices we're going to have
+
+ align:start position:0%
+connect two vertices we're going to have
+ 
+
+ align:start position:0%
+connect two vertices we're going to have
+to draw paths orthogonal paths on the
+
+ align:start position:0%
+to draw paths orthogonal paths on the
+ 
+
+ align:start position:0%
+to draw paths orthogonal paths on the
+grid
+
+ align:start position:0%
+grid
+ 
+
+ align:start position:0%
+grid
+uh but the key thing I want is that uh
+
+ align:start position:0%
+uh but the key thing I want is that uh
+ 
+
+ align:start position:0%
+uh but the key thing I want is that uh
+the square grid has a two coloring
+
+ align:start position:0%
+the square grid has a two coloring
+ 
+
+ align:start position:0%
+the square grid has a two coloring
+inherently and I want that two coloring
+
+ align:start position:0%
+inherently and I want that two coloring
+ 
+
+ align:start position:0%
+inherently and I want that two coloring
+to match this two coloring okay that's
+
+ align:start position:0%
+to match this two coloring okay that's
+ 
+
+ align:start position:0%
+to match this two coloring okay that's
+what I would call a parody preserving
+
+ align:start position:0%
+what I would call a parody preserving
+ 
+
+ align:start position:0%
+what I would call a parody preserving
+embedding of the
+
+ align:start position:0%
+embedding of the
+ 
+
+ align:start position:0%
+embedding of the
+graph uh how uh and you can see in this
+
+ align:start position:0%
+graph uh how uh and you can see in this
+ 
+
+ align:start position:0%
+graph uh how uh and you can see in this
+example the three x eyes are white and
+
+ align:start position:0%
+example the three x eyes are white and
+ 
+
+ align:start position:0%
+example the three x eyes are white and
+the three y eyes are black and if you
+
+ align:start position:0%
+the three y eyes are black and if you
+ 
+
+ align:start position:0%
+the three y eyes are black and if you
+check all the edges they should
+
+ align:start position:0%
+check all the edges they should
+ 
+
+ align:start position:0%
+check all the edges they should
+correspond just ignore the dash lines
+
+ align:start position:0%
+correspond just ignore the dash lines
+ 
+
+ align:start position:0%
+correspond just ignore the dash lines
+that's to show you the grid underlying
+
+ align:start position:0%
+that's to show you the grid underlying
+ 
+
+ align:start position:0%
+that's to show you the grid underlying
+uh so this is a valid embedding how do
+
+ align:start position:0%
+uh so this is a valid embedding how do
+ 
+
+ align:start position:0%
+uh so this is a valid embedding how do
+we do it well we just take any embedding
+
+ align:start position:0%
+we do it well we just take any embedding
+ 
+
+ align:start position:0%
+we do it well we just take any embedding
+in in the grid uh it's well known that
+
+ align:start position:0%
+in in the grid uh it's well known that
+ 
+
+ align:start position:0%
+in in the grid uh it's well known that
+if you have a Max deegree 4 graph you
+
+ align:start position:0%
+if you have a Max deegree 4 graph you
+ 
+
+ align:start position:0%
+if you have a Max deegree 4 graph you
+can draw it in the grid without
+
+ align:start position:0%
+can draw it in the grid without
+ 
+
+ align:start position:0%
+can draw it in the grid without
+Crossings and each Edge is some
+
+ align:start position:0%
+Crossings and each Edge is some
+ 
+
+ align:start position:0%
+Crossings and each Edge is some
+orthogonal
+
+ align:start position:0%
+orthogonal
+ 
+
+ align:start position:0%
+orthogonal
+polyline
+
+ align:start position:0%
+polyline
+ 
+
+ align:start position:0%
+polyline
+uh I won't prove that here and then um
+
+ align:start position:0%
+uh I won't prove that here and then um
+ 
+
+ align:start position:0%
+uh I won't prove that here and then um
+suppose the parody is wrong for some
+
+ align:start position:0%
+suppose the parody is wrong for some
+ 
+
+ align:start position:0%
+suppose the parody is wrong for some
+vertex suppose you draw a Vertex V and
+
+ align:start position:0%
+vertex suppose you draw a Vertex V and
+ 
+
+ align:start position:0%
+vertex suppose you draw a Vertex V and
+it happens to be black but you want it
+
+ align:start position:0%
+it happens to be black but you want it
+ 
+
+ align:start position:0%
+it happens to be black but you want it
+to be white then I'm just going to shift
+
+ align:start position:0%
+to be white then I'm just going to shift
+ 
+
+ align:start position:0%
+to be white then I'm just going to shift
+it over by one and do these kinds of
+
+ align:start position:0%
+it over by one and do these kinds of
+ 
+
+ align:start position:0%
+it over by one and do these kinds of
+Wiggles and that's it so you uh scale
+
+ align:start position:0%
+Wiggles and that's it so you uh scale
+ 
+
+ align:start position:0%
+Wiggles and that's it so you uh scale
+everything by a factor of three and
+
+ align:start position:0%
+everything by a factor of three and
+ 
+
+ align:start position:0%
+everything by a factor of three and
+you'll have room to do those Wiggles uh
+
+ align:start position:0%
+you'll have room to do those Wiggles uh
+ 
+
+ align:start position:0%
+you'll have room to do those Wiggles uh
+so you take an arbitrary orthogonal grid
+
+ align:start position:0%
+so you take an arbitrary orthogonal grid
+ 
+
+ align:start position:0%
+so you take an arbitrary orthogonal grid
+drawing and then uh add The Wiggles and
+
+ align:start position:0%
+drawing and then uh add The Wiggles and
+ 
+
+ align:start position:0%
+drawing and then uh add The Wiggles and
+you get whenever things are in the wrong
+
+ align:start position:0%
+you get whenever things are in the wrong
+ 
+
+ align:start position:0%
+you get whenever things are in the wrong
+parody and now every vertex will be in
+
+ align:start position:0%
+parody and now every vertex will be in
+ 
+
+ align:start position:0%
+parody and now every vertex will be in
+the correct parody okay that will be
+
+ align:start position:0%
+the correct parody okay that will be
+ 
+
+ align:start position:0%
+the correct parody okay that will be
+crucial for the
+
+ align:start position:0%
+crucial for the
+ 
+
+ align:start position:0%
+crucial for the
+reduction so at this point we've got an
+
+ align:start position:0%
+reduction so at this point we've got an
+ 
+
+ align:start position:0%
+reduction so at this point we've got an
+orthogonal sorry we've got an orthogonal
+
+ align:start position:0%
+orthogonal sorry we've got an orthogonal
+ 
+
+ align:start position:0%
+orthogonal sorry we've got an orthogonal
+parody preserving drawing of our given
+
+ align:start position:0%
+parody preserving drawing of our given
+ 
+
+ align:start position:0%
+parody preserving drawing of our given
+bipartite planer Max degree 3 graph and
+
+ align:start position:0%
+bipartite planer Max degree 3 graph and
+ 
+
+ align:start position:0%
+bipartite planer Max degree 3 graph and
+uh the issue is there sort of two types
+
+ align:start position:0%
+uh the issue is there sort of two types
+ 
+
+ align:start position:0%
+uh the issue is there sort of two types
+of vertices here there's the ones that
+
+ align:start position:0%
+of vertices here there's the ones that
+ 
+
+ align:start position:0%
+of vertices here there's the ones that
+we really need to visit and then there's
+
+ align:start position:0%
+we really need to visit and then there's
+ 
+
+ align:start position:0%
+we really need to visit and then there's
+these other vertices which are
+
+ align:start position:0%
+these other vertices which are
+ 
+
+ align:start position:0%
+these other vertices which are
+representing edges we don't need to
+
+ align:start position:0%
+representing edges we don't need to
+ 
+
+ align:start position:0%
+representing edges we don't need to
+visit every Edge that's the or tour
+
+ align:start position:0%
+visit every Edge that's the or tour
+ 
+
+ align:start position:0%
+visit every Edge that's the or tour
+problem hamiltonian tour we just need to
+
+ align:start position:0%
+problem hamiltonian tour we just need to
+ 
+
+ align:start position:0%
+problem hamiltonian tour we just need to
+visit every vertex which are the labeled
+
+ align:start position:0%
+visit every vertex which are the labeled
+ 
+
+ align:start position:0%
+visit every vertex which are the labeled
+dots over
+
+ align:start position:0%
+dots over
+ 
+
+ align:start position:0%
+dots over
+here so this is where things get
+
+ align:start position:0%
+here so this is where things get
+ 
+
+ align:start position:0%
+here so this is where things get
+fun uh here is a key Gadget before we
+
+ align:start position:0%
+fun uh here is a key Gadget before we
+ 
+
+ align:start position:0%
+fun uh here is a key Gadget before we
+see the overall
+
+ align:start position:0%
+see the overall
+ 
+
+ align:start position:0%
+see the overall
+architecture uh these are called
+
+ align:start position:0%
+architecture uh these are called
+ 
+
+ align:start position:0%
+architecture uh these are called
+tentacles in the original paper I'm
+
+ align:start position:0%
+tentacles in the original paper I'm
+ 
+
+ align:start position:0%
+tentacles in the original paper I'm
+calling them Edge gadgets because
+
+ align:start position:0%
+calling them Edge gadgets because
+ 
+
+ align:start position:0%
+calling them Edge gadgets because
+they're just simulating a single edge of
+
+ align:start position:0%
+they're just simulating a single edge of
+ 
+
+ align:start position:0%
+they're just simulating a single edge of
+the original graph but tentacles is
+
+ align:start position:0%
+the original graph but tentacles is
+ 
+
+ align:start position:0%
+the original graph but tentacles is
+cooler whichever you prefer uh so uh I
+
+ align:start position:0%
+cooler whichever you prefer uh so uh I
+ 
+
+ align:start position:0%
+cooler whichever you prefer uh so uh I
+mean these are the dots that haven't all
+
+ align:start position:0%
+mean these are the dots that haven't all
+ 
+
+ align:start position:0%
+mean these are the dots that haven't all
+been drawn explicitly here uh and so
+
+ align:start position:0%
+been drawn explicitly here uh and so
+ 
+
+ align:start position:0%
+been drawn explicitly here uh and so
+it's just like a 2xn sort of corridor
+
+ align:start position:0%
+it's just like a 2xn sort of corridor
+ 
+
+ align:start position:0%
+it's just like a 2xn sort of corridor
+the base version would be this uh but
+
+ align:start position:0%
+the base version would be this uh but
+ 
+
+ align:start position:0%
+the base version would be this uh but
+the if you want to have turns which
+
+ align:start position:0%
+the if you want to have turns which
+ 
+
+ align:start position:0%
+the if you want to have turns which
+we're going to need 90° turns it looks
+
+ align:start position:0%
+we're going to need 90° turns it looks
+ 
+
+ align:start position:0%
+we're going to need 90° turns it looks
+more like
+
+ align:start position:0%
+more like
+ 
+
+ align:start position:0%
+more like
+this and there's basically two ways to
+
+ align:start position:0%
+this and there's basically two ways to
+ 
+
+ align:start position:0%
+this and there's basically two ways to
+cover this sort of three ways but the
+
+ align:start position:0%
+cover this sort of three ways but the
+ 
+
+ align:start position:0%
+cover this sort of three ways but the
+way parody will work out there will only
+
+ align:start position:0%
+way parody will work out there will only
+ 
+
+ align:start position:0%
+way parody will work out there will only
+be two ways that we care about this is
+
+ align:start position:0%
+be two ways that we care about this is
+ 
+
+ align:start position:0%
+be two ways that we care about this is
+not a variable Gadget okay it's it looks
+
+ align:start position:0%
+not a variable Gadget okay it's it looks
+ 
+
+ align:start position:0%
+not a variable Gadget okay it's it looks
+like kind of maybe a variable Gadget but
+
+ align:start position:0%
+like kind of maybe a variable Gadget but
+ 
+
+ align:start position:0%
+like kind of maybe a variable Gadget but
+that's not how we're using it uh so one
+
+ align:start position:0%
+that's not how we're using it uh so one
+ 
+
+ align:start position:0%
+that's not how we're using it uh so one
+way you can visit this gadget is to
+
+ align:start position:0%
+way you can visit this gadget is to
+ 
+
+ align:start position:0%
+way you can visit this gadget is to
+zigzag like this we've seen this in
+
+ align:start position:0%
+zigzag like this we've seen this in
+ 
+
+ align:start position:0%
+zigzag like this we've seen this in
+pretty much all of our hamiltonicity
+
+ align:start position:0%
+pretty much all of our hamiltonicity
+ 
+
+ align:start position:0%
+pretty much all of our hamiltonicity
+planer hamiltonicity proof so that's the
+
+ align:start position:0%
+planer hamiltonicity proof so that's the
+ 
+
+ align:start position:0%
+planer hamiltonicity proof so that's the
+core idea is the same uh you could start
+
+ align:start position:0%
+core idea is the same uh you could start
+ 
+
+ align:start position:0%
+core idea is the same uh you could start
+at a and end at C or you could start at
+
+ align:start position:0%
+at a and end at C or you could start at
+ 
+
+ align:start position:0%
+at a and end at C or you could start at
+b and end at D and that's true in this
+
+ align:start position:0%
+b and end at D and that's true in this
+ 
+
+ align:start position:0%
+b and end at D and that's true in this
+version as well once you start
+
+ align:start position:0%
+version as well once you start
+ 
+
+ align:start position:0%
+version as well once you start
+alternating you're forced to alternate
+
+ align:start position:0%
+alternating you're forced to alternate
+ 
+
+ align:start position:0%
+alternating you're forced to alternate
+all the way through so you could imagine
+
+ align:start position:0%
+all the way through so you could imagine
+ 
+
+ align:start position:0%
+all the way through so you could imagine
+using that for a wire but we're not
+
+ align:start position:0%
+using that for a wire but we're not
+ 
+
+ align:start position:0%
+using that for a wire but we're not
+going to use the two alternations by
+
+ align:start position:0%
+going to use the two alternations by
+ 
+
+ align:start position:0%
+going to use the two alternations by
+parody we'll be forced to do it one way
+
+ align:start position:0%
+parody we'll be forced to do it one way
+ 
+
+ align:start position:0%
+parody we'll be forced to do it one way
+or the other we'll be told whether we're
+
+ align:start position:0%
+or the other we'll be told whether we're
+ 
+
+ align:start position:0%
+or the other we'll be told whether we're
+starting or ending at one of
+
+ align:start position:0%
+starting or ending at one of
+ 
+
+ align:start position:0%
+starting or ending at one of
+them uh I think well it won't matter but
+
+ align:start position:0%
+them uh I think well it won't matter but
+ 
+
+ align:start position:0%
+them uh I think well it won't matter but
+there's this other way you could visit
+
+ align:start position:0%
+there's this other way you could visit
+ 
+
+ align:start position:0%
+there's this other way you could visit
+which is to just go all the way down and
+
+ align:start position:0%
+which is to just go all the way down and
+ 
+
+ align:start position:0%
+which is to just go all the way down and
+then come all the way
+
+ align:start position:0%
+then come all the way
+ 
+
+ align:start position:0%
+then come all the way
+back okay uh this is going to correspond
+
+ align:start position:0%
+back okay uh this is going to correspond
+ 
+
+ align:start position:0%
+back okay uh this is going to correspond
+to an edge that is in the hamiltonian
+
+ align:start position:0%
+to an edge that is in the hamiltonian
+ 
+
+ align:start position:0%
+to an edge that is in the hamiltonian
+cycle because I want to start at some
+
+ align:start position:0%
+cycle because I want to start at some
+ 
+
+ align:start position:0%
+cycle because I want to start at some
+vertex up here and I want end at some
+
+ align:start position:0%
+vertex up here and I want end at some
+ 
+
+ align:start position:0%
+vertex up here and I want end at some
+vertex down here if I follow the edge
+
+ align:start position:0%
+vertex down here if I follow the edge
+ 
+
+ align:start position:0%
+vertex down here if I follow the edge
+this is going to correspond to an edge
+
+ align:start position:0%
+this is going to correspond to an edge
+ 
+
+ align:start position:0%
+this is going to correspond to an edge
+that we don't
+
+ align:start position:0%
+that we don't
+ 
+
+ align:start position:0%
+that we don't
+use right because um at this vertex I I
+
+ align:start position:0%
+use right because um at this vertex I I
+ 
+
+ align:start position:0%
+use right because um at this vertex I I
+still need to cover these vertices
+
+ align:start position:0%
+still need to cover these vertices
+ 
+
+ align:start position:0%
+still need to cover these vertices
+somehow but I don't want that to really
+
+ align:start position:0%
+somehow but I don't want that to really
+ 
+
+ align:start position:0%
+somehow but I don't want that to really
+matter I want this Edge to be coverable
+
+ align:start position:0%
+matter I want this Edge to be coverable
+ 
+
+ align:start position:0%
+matter I want this Edge to be coverable
+for free and so the idea is as I visit
+
+ align:start position:0%
+for free and so the idea is as I visit
+ 
+
+ align:start position:0%
+for free and so the idea is as I visit
+this vertex we're just going to ZIP down
+
+ align:start position:0%
+this vertex we're just going to ZIP down
+ 
+
+ align:start position:0%
+this vertex we're just going to ZIP down
+here zip back up and all these vertices
+
+ align:start position:0%
+here zip back up and all these vertices
+ 
+
+ align:start position:0%
+here zip back up and all these vertices
+get visited uh for free okay it's not
+
+ align:start position:0%
+get visited uh for free okay it's not
+ 
+
+ align:start position:0%
+get visited uh for free okay it's not
+really part of the
+
+ align:start position:0%
+really part of the
+ 
+
+ align:start position:0%
+really part of the
+tour let me show you in some more detail
+
+ align:start position:0%
+tour let me show you in some more detail
+ 
+
+ align:start position:0%
+tour let me show you in some more detail
+uh here's what a Vertex looks like
+
+ align:start position:0%
+uh here's what a Vertex looks like
+ 
+
+ align:start position:0%
+uh here's what a Vertex looks like
+vertex is just going to be a 3X3 grid of
+
+ align:start position:0%
+vertex is just going to be a 3X3 grid of
+ 
+
+ align:start position:0%
+vertex is just going to be a 3X3 grid of
+dots uh now remember there are two kinds
+
+ align:start position:0%
+dots uh now remember there are two kinds
+ 
+
+ align:start position:0%
+dots uh now remember there are two kinds
+of vertices there's the ones that were
+
+ align:start position:0%
+of vertices there's the ones that were
+ 
+
+ align:start position:0%
+of vertices there's the ones that were
+um so again we're expanding everything
+
+ align:start position:0%
+um so again we're expanding everything
+ 
+
+ align:start position:0%
+um so again we're expanding everything
+for this to work out there the vertices
+
+ align:start position:0%
+for this to work out there the vertices
+ 
+
+ align:start position:0%
+for this to work out there the vertices
+that were originally White and the
+
+ align:start position:0%
+that were originally White and the
+ 
+
+ align:start position:0%
+that were originally White and the
+vertices that were originally black
+
+ align:start position:0%
+vertices that were originally black
+ 
+
+ align:start position:0%
+vertices that were originally black
+doesn't matter which is which but
+
+ align:start position:0%
+doesn't matter which is which but
+ 
+
+ align:start position:0%
+doesn't matter which is which but
+there's two classes of vertices and
+
+ align:start position:0%
+there's two classes of vertices and
+ 
+
+ align:start position:0%
+there's two classes of vertices and
+we're going to attach the edge
+
+ align:start position:0%
+we're going to attach the edge
+ 
+
+ align:start position:0%
+we're going to attach the edge
+gadgets which were these 2xn kind of
+
+ align:start position:0%
+gadgets which were these 2xn kind of
+ 
+
+ align:start position:0%
+gadgets which were these 2xn kind of
+things uh so here this is all Edge
+
+ align:start position:0%
+things uh so here this is all Edge
+ 
+
+ align:start position:0%
+things uh so here this is all Edge
+Gadget here we're going to attach it to
+
+ align:start position:0%
+Gadget here we're going to attach it to
+ 
+
+ align:start position:0%
+Gadget here we're going to attach it to
+a Vertex that's white in this sort of
+
+ align:start position:0%
+a Vertex that's white in this sort of
+ 
+
+ align:start position:0%
+a Vertex that's white in this sort of
+flush uh length two connection so here
+
+ align:start position:0%
+flush uh length two connection so here
+ 
+
+ align:start position:0%
+flush uh length two connection so here
+this is the variable up here this 3x3
+
+ align:start position:0%
+this is the variable up here this 3x3
+ 
+
+ align:start position:0%
+this is the variable up here this 3x3
+thing and here we're add we're having
+
+ align:start position:0%
+thing and here we're add we're having
+ 
+
+ align:start position:0%
+thing and here we're add we're having
+two edges connecting to the The Edge
+
+ align:start position:0%
+two edges connecting to the The Edge
+ 
+
+ align:start position:0%
+two edges connecting to the The Edge
+gadget for the black vertices we're only
+
+ align:start position:0%
+gadget for the black vertices we're only
+ 
+
+ align:start position:0%
+gadget for the black vertices we're only
+going to have a single edge connecting
+
+ align:start position:0%
+going to have a single edge connecting
+ 
+
+ align:start position:0%
+going to have a single edge connecting
+them this is called a pin
+
+ align:start position:0%
+them this is called a pin
+ 
+
+ align:start position:0%
+them this is called a pin
+connection uh between the wire Gadget or
+
+ align:start position:0%
+connection uh between the wire Gadget or
+ 
+
+ align:start position:0%
+connection uh between the wire Gadget or
+the tentacle and the 3X3 down
+
+ align:start position:0%
+the tentacle and the 3X3 down
+ 
+
+ align:start position:0%
+the tentacle and the 3X3 down
+here okay
+
+ align:start position:0%
+here okay
+ 
+
+ align:start position:0%
+here okay
+y uh
+
+ align:start position:0%
+y uh
+ 
+
+ align:start position:0%
+y uh
+cuz um so here let's consider two
+
+ align:start position:0%
+cuz um so here let's consider two
+ 
+
+ align:start position:0%
+cuz um so here let's consider two
+vertices that are attached by an edge uh
+
+ align:start position:0%
+vertices that are attached by an edge uh
+ 
+
+ align:start position:0%
+vertices that are attached by an edge uh
+so they have opposite parity On's I've
+
+ align:start position:0%
+so they have opposite parity On's I've
+ 
+
+ align:start position:0%
+so they have opposite parity On's I've
+forgotten which is which this is white
+
+ align:start position:0%
+forgotten which is which this is white
+ 
+
+ align:start position:0%
+forgotten which is which this is white
+and this is black I think uh here we
+
+ align:start position:0%
+and this is black I think uh here we
+ 
+
+ align:start position:0%
+and this is black I think uh here we
+have the pin connection here we have the
+
+ align:start position:0%
+have the pin connection here we have the
+ 
+
+ align:start position:0%
+have the pin connection here we have the
+length two connection uh and the idea is
+
+ align:start position:0%
+length two connection uh and the idea is
+ 
+
+ align:start position:0%
+length two connection uh and the idea is
+there's exactly two ways to Traverse
+
+ align:start position:0%
+there's exactly two ways to Traverse
+ 
+
+ align:start position:0%
+there's exactly two ways to Traverse
+this Edge as we saw but now you can see
+
+ align:start position:0%
+this Edge as we saw but now you can see
+ 
+
+ align:start position:0%
+this Edge as we saw but now you can see
+the connections let me put it that way
+
+ align:start position:0%
+the connections let me put it that way
+ 
+
+ align:start position:0%
+the connections let me put it that way
+so the idea is well maybe you choose to
+
+ align:start position:0%
+so the idea is well maybe you choose to
+ 
+
+ align:start position:0%
+so the idea is well maybe you choose to
+use that edge in the cycle and so I want
+
+ align:start position:0%
+use that edge in the cycle and so I want
+ 
+
+ align:start position:0%
+use that edge in the cycle and so I want
+to be able to just Traverse it
+
+ align:start position:0%
+to be able to just Traverse it
+ 
+
+ align:start position:0%
+to be able to just Traverse it
+everything is good and so here I know
+
+ align:start position:0%
+everything is good and so here I know
+ 
+
+ align:start position:0%
+everything is good and so here I know
+that I'm entering at this point which
+
+ align:start position:0%
+that I'm entering at this point which
+ 
+
+ align:start position:0%
+that I'm entering at this point which
+means I know they'll have to be exiting
+
+ align:start position:0%
+means I know they'll have to be exiting
+ 
+
+ align:start position:0%
+means I know they'll have to be exiting
+here so the parodies are forced that
+
+ align:start position:0%
+here so the parodies are forced that
+ 
+
+ align:start position:0%
+here so the parodies are forced that
+case the zigzag parody is
+
+ align:start position:0%
+case the zigzag parody is
+ 
+
+ align:start position:0%
+case the zigzag parody is
+forced the other possibility uh because
+
+ align:start position:0%
+forced the other possibility uh because
+ 
+
+ align:start position:0%
+forced the other possibility uh because
+there's only one connection here you
+
+ align:start position:0%
+there's only one connection here you
+ 
+
+ align:start position:0%
+there's only one connection here you
+couldn't Traverse this way and then come
+
+ align:start position:0%
+couldn't Traverse this way and then come
+ 
+
+ align:start position:0%
+couldn't Traverse this way and then come
+back uh but from this side you could
+
+ align:start position:0%
+back uh but from this side you could
+ 
+
+ align:start position:0%
+back uh but from this side you could
+Traverse and then come back and it
+
+ align:start position:0%
+Traverse and then come back and it
+ 
+
+ align:start position:0%
+Traverse and then come back and it
+doesn't touch the ver Tex at all so the
+
+ align:start position:0%
+doesn't touch the ver Tex at all so the
+ 
+
+ align:start position:0%
+doesn't touch the ver Tex at all so the
+idea is you could ignore this Edge
+
+ align:start position:0%
+idea is you could ignore this Edge
+ 
+
+ align:start position:0%
+idea is you could ignore this Edge
+entirely and it gets covered for free
+
+ align:start position:0%
+entirely and it gets covered for free
+ 
+
+ align:start position:0%
+entirely and it gets covered for free
+provided once you erase this this Edge
+
+ align:start position:0%
+provided once you erase this this Edge
+ 
+
+ align:start position:0%
+provided once you erase this this Edge
+is in the hamiltonian tour and at this
+
+ align:start position:0%
+is in the hamiltonian tour and at this
+ 
+
+ align:start position:0%
+is in the hamiltonian tour and at this
+point I should mention the what all this
+
+ align:start position:0%
+point I should mention the what all this
+ 
+
+ align:start position:0%
+point I should mention the what all this
+labeling means on the vertex Gadget the
+
+ align:start position:0%
+labeling means on the vertex Gadget the
+ 
+
+ align:start position:0%
+labeling means on the vertex Gadget the
+idea is for this vertex if you start at
+
+ align:start position:0%
+idea is for this vertex if you start at
+ 
+
+ align:start position:0%
+idea is for this vertex if you start at
+any of the pis any of the Four
+
+ align:start position:0%
+any of the pis any of the Four
+ 
+
+ align:start position:0%
+any of the pis any of the Four
+Corners any of the private investigators
+
+ align:start position:0%
+Corners any of the private investigators
+ 
+
+ align:start position:0%
+Corners any of the private investigators
+then uh you can end at any other Pi PJ
+
+ align:start position:0%
+then uh you can end at any other Pi PJ
+ 
+
+ align:start position:0%
+then uh you can end at any other Pi PJ
+um in such a way that you visit all
+
+ align:start position:0%
+um in such a way that you visit all
+ 
+
+ align:start position:0%
+um in such a way that you visit all
+three of the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Eis there are four of them there are
+
+ align:start position:0%
+Eis there are four of them there are
+ 
+
+ align:start position:0%
+Eis there are four of them there are
+four of them EI EO EI EO no okay um so
+
+ align:start position:0%
+four of them EI EO EI EO no okay um so
+ 
+
+ align:start position:0%
+four of them EI EO EI EO no okay um so
+you so me skip the to the point you can
+
+ align:start position:0%
+you so me skip the to the point you can
+ 
+
+ align:start position:0%
+you so me skip the to the point you can
+start at Pi end at PJ and visit all the
+
+ align:start position:0%
+start at Pi end at PJ and visit all the
+ 
+
+ align:start position:0%
+start at Pi end at PJ and visit all the
+vertices and all of the E all the e case
+
+ align:start position:0%
+vertices and all of the E all the e case
+ 
+
+ align:start position:0%
+vertices and all of the E all the e case
+Okay so for example if I want to go from
+
+ align:start position:0%
+Okay so for example if I want to go from
+ 
+
+ align:start position:0%
+Okay so for example if I want to go from
+here to here I can go like this
+
+ align:start position:0%
+here to here I can go like this
+ 
+
+ align:start position:0%
+here to here I can go like this
+visited all the edges if I want to go
+
+ align:start position:0%
+visited all the edges if I want to go
+ 
+
+ align:start position:0%
+visited all the edges if I want to go
+from here to here I can go like this
+
+ align:start position:0%
+from here to here I can go like this
+ 
+
+ align:start position:0%
+from here to here I can go like this
+visited all the vertices visited all the
+
+ align:start position:0%
+visited all the vertices visited all the
+ 
+
+ align:start position:0%
+visited all the vertices visited all the
+e so that's good because each of these e
+
+ align:start position:0%
+e so that's good because each of these e
+ 
+
+ align:start position:0%
+e so that's good because each of these e
+e is potentially attached to some to an
+
+ align:start position:0%
+e is potentially attached to some to an
+ 
+
+ align:start position:0%
+e is potentially attached to some to an
+edge Gadget and we might want to visit
+
+ align:start position:0%
+edge Gadget and we might want to visit
+ 
+
+ align:start position:0%
+edge Gadget and we might want to visit
+all of the things out there and come
+
+ align:start position:0%
+all of the things out there and come
+ 
+
+ align:start position:0%
+all of the things out there and come
+back
+
+ align:start position:0%
+back
+ 
+
+ align:start position:0%
+back
+okay so you see the the kind of the key
+
+ align:start position:0%
+okay so you see the the kind of the key
+ 
+
+ align:start position:0%
+okay so you see the the kind of the key
+thing uh the reason why we only want a
+
+ align:start position:0%
+thing uh the reason why we only want a
+ 
+
+ align:start position:0%
+thing uh the reason why we only want a
+pin connection here here is if we had a
+
+ align:start position:0%
+pin connection here here is if we had a
+ 
+
+ align:start position:0%
+pin connection here here is if we had a
+a a full connection with with two edges
+
+ align:start position:0%
+a a full connection with with two edges
+ 
+
+ align:start position:0%
+a a full connection with with two edges
+you might imagine that you come out here
+
+ align:start position:0%
+you might imagine that you come out here
+ 
+
+ align:start position:0%
+you might imagine that you come out here
+do something eventually do other stuff
+
+ align:start position:0%
+do something eventually do other stuff
+ 
+
+ align:start position:0%
+do something eventually do other stuff
+and then come back on this path but
+
+ align:start position:0%
+and then come back on this path but
+ 
+
+ align:start position:0%
+and then come back on this path but
+because we have a pin connection always
+
+ align:start position:0%
+because we have a pin connection always
+ 
+
+ align:start position:0%
+because we have a pin connection always
+on one of the two sides uh you can't you
+
+ align:start position:0%
+on one of the two sides uh you can't you
+ 
+
+ align:start position:0%
+on one of the two sides uh you can't you
+can't have two separate traversal paths
+
+ align:start position:0%
+can't have two separate traversal paths
+ 
+
+ align:start position:0%
+can't have two separate traversal paths
+you as soon as you get here you have to
+
+ align:start position:0%
+you as soon as you get here you have to
+ 
+
+ align:start position:0%
+you as soon as you get here you have to
+turn back around if you went this way
+
+ align:start position:0%
+turn back around if you went this way
+ 
+
+ align:start position:0%
+turn back around if you went this way
+then this guy would never be visitable
+
+ align:start position:0%
+then this guy would never be visitable
+ 
+
+ align:start position:0%
+then this guy would never be visitable
+in a
+
+ align:start position:0%
+in a
+ 
+
+ align:start position:0%
+in a
+cycle okay so that's the key thing this
+
+ align:start position:0%
+cycle okay so that's the key thing this
+ 
+
+ align:start position:0%
+cycle okay so that's the key thing this
+was one of the E and so the idea is you
+
+ align:start position:0%
+was one of the E and so the idea is you
+ 
+
+ align:start position:0%
+was one of the E and so the idea is you
+can completely forget about this path
+
+ align:start position:0%
+can completely forget about this path
+ 
+
+ align:start position:0%
+can completely forget about this path
+you can just think about going from one
+
+ align:start position:0%
+you can just think about going from one
+ 
+
+ align:start position:0%
+you can just think about going from one
+of these white vertices to another in
+
+ align:start position:0%
+of these white vertices to another in
+ 
+
+ align:start position:0%
+of these white vertices to another in
+general it's going to correspond to uh
+
+ align:start position:0%
+general it's going to correspond to uh
+ 
+
+ align:start position:0%
+general it's going to correspond to uh
+which Edge gadgets that vertex Gadget is
+
+ align:start position:0%
+which Edge gadgets that vertex Gadget is
+ 
+
+ align:start position:0%
+which Edge gadgets that vertex Gadget is
+connected
+
+ align:start position:0%
+connected
+ 
+
+ align:start position:0%
+connected
+to uh and yeah so you can go from one
+
+ align:start position:0%
+to uh and yeah so you can go from one
+ 
+
+ align:start position:0%
+to uh and yeah so you can go from one
+vertex to another you will visit this
+
+ align:start position:0%
+vertex to another you will visit this
+ 
+
+ align:start position:0%
+vertex to another you will visit this
+Edge and so you can add in this part if
+
+ align:start position:0%
+Edge and so you can add in this part if
+ 
+
+ align:start position:0%
+Edge and so you can add in this part if
+you don't use the edge if you do use the
+
+ align:start position:0%
+you don't use the edge if you do use the
+ 
+
+ align:start position:0%
+you don't use the edge if you do use the
+edge then this you'll be starting from
+
+ align:start position:0%
+edge then this you'll be starting from
+ 
+
+ align:start position:0%
+edge then this you'll be starting from
+one of these white vertices and you want
+
+ align:start position:0%
+one of these white vertices and you want
+ 
+
+ align:start position:0%
+one of these white vertices and you want
+to go to this one and then you'll follow
+
+ align:start position:0%
+to go to this one and then you'll follow
+ 
+
+ align:start position:0%
+to go to this one and then you'll follow
+this path and then you get to this
+
+ align:start position:0%
+this path and then you get to this
+ 
+
+ align:start position:0%
+this path and then you get to this
+vertex and you go from one of these
+
+ align:start position:0%
+vertex and you go from one of these
+ 
+
+ align:start position:0%
+vertex and you go from one of these
+black vertices to one one of the other
+
+ align:start position:0%
+black vertices to one one of the other
+ 
+
+ align:start position:0%
+black vertices to one one of the other
+four corners and so on question should
+
+ align:start position:0%
+four corners and so on question should
+ 
+
+ align:start position:0%
+four corners and so on question should
+that line of three white dots should the
+
+ align:start position:0%
+that line of three white dots should the
+ 
+
+ align:start position:0%
+that line of three white dots should the
+middle one be in yes this should be
+
+ align:start position:0%
+middle one be in yes this should be
+ 
+
+ align:start position:0%
+middle one be in yes this should be
+black it's not my fault it could be the
+
+ align:start position:0%
+black it's not my fault it could be the
+ 
+
+ align:start position:0%
+black it's not my fault it could be the
+scanner or it could be there's a this is
+
+ align:start position:0%
+scanner or it could be there's a this is
+ 
+
+ align:start position:0%
+scanner or it could be there's a this is
+a handdrawn figure as you might guess so
+
+ align:start position:0%
+a handdrawn figure as you might guess so
+ 
+
+ align:start position:0%
+a handdrawn figure as you might guess so
+yeah that should be black everything
+
+ align:start position:0%
+yeah that should be black everything
+ 
+
+ align:start position:0%
+yeah that should be black everything
+should alternate so you see there's uh
+
+ align:start position:0%
+should alternate so you see there's uh
+ 
+
+ align:start position:0%
+should alternate so you see there's uh
+you can tell the parity of the vertex
+
+ align:start position:0%
+you can tell the parity of the vertex
+ 
+
+ align:start position:0%
+you can tell the parity of the vertex
+based on the par the color of the
+
+ align:start position:0%
+based on the par the color of the
+ 
+
+ align:start position:0%
+based on the par the color of the
+corners any other
+
+ align:start position:0%
+corners any other
+ 
+
+ align:start position:0%
+corners any other
+questions about that proof
+
+ align:start position:0%
+questions about that proof
+ 
+
+ align:start position:0%
+questions about that proof
+okay um so this is pretty cool and I
+
+ align:start position:0%
+okay um so this is pretty cool and I
+ 
+
+ align:start position:0%
+okay um so this is pretty cool and I
+would say hamiltonicity in Grid graphs
+
+ align:start position:0%
+would say hamiltonicity in Grid graphs
+ 
+
+ align:start position:0%
+would say hamiltonicity in Grid graphs
+is used a lot for as a base problem for
+
+ align:start position:0%
+is used a lot for as a base problem for
+ 
+
+ align:start position:0%
+is used a lot for as a base problem for
+reductions in computational Geometry uh
+
+ align:start position:0%
+reductions in computational Geometry uh
+ 
+
+ align:start position:0%
+reductions in computational Geometry uh
+especially tour like problems and you
+
+ align:start position:0%
+especially tour like problems and you
+ 
+
+ align:start position:0%
+especially tour like problems and you
+you'll notice the theme uh every
+
+ align:start position:0%
+you'll notice the theme uh every
+ 
+
+ align:start position:0%
+you'll notice the theme uh every
+reduction so far except the very first
+
+ align:start position:0%
+reduction so far except the very first
+ 
+
+ align:start position:0%
+reduction so far except the very first
+one I guess was from one type of
+
+ align:start position:0%
+one I guess was from one type of
+ 
+
+ align:start position:0%
+one I guess was from one type of
+hamiltonian circuit to another type of
+
+ align:start position:0%
+hamiltonian circuit to another type of
+ 
+
+ align:start position:0%
+hamiltonian circuit to another type of
+hamiltonian circuit and this tends to be
+
+ align:start position:0%
+hamiltonian circuit and this tends to be
+ 
+
+ align:start position:0%
+hamiltonian circuit and this tends to be
+common that you can work within
+
+ align:start position:0%
+common that you can work within
+ 
+
+ align:start position:0%
+common that you can work within
+hamiltonian circuit and mod your graph
+
+ align:start position:0%
+hamiltonian circuit and mod your graph
+ 
+
+ align:start position:0%
+hamiltonian circuit and mod your graph
+in all sorts of ways to get to a very
+
+ align:start position:0%
+in all sorts of ways to get to a very
+ 
+
+ align:start position:0%
+in all sorts of ways to get to a very
+simplified version of hamiltonian
+
+ align:start position:0%
+simplified version of hamiltonian
+ 
+
+ align:start position:0%
+simplified version of hamiltonian
+circuit and that's cool and so you get a
+
+ align:start position:0%
+circuit and that's cool and so you get a
+ 
+
+ align:start position:0%
+circuit and that's cool and so you get a
+lot of mileage just within the
+
+ align:start position:0%
+lot of mileage just within the
+ 
+
+ align:start position:0%
+lot of mileage just within the
+hamiltonian Circuit Family
+
+ align:start position:0%
+hamiltonian Circuit Family
+ 
+
+ align:start position:0%
+hamiltonian Circuit Family
+um cool let me give you a couple of
+
+ align:start position:0%
+um cool let me give you a couple of
+ 
+
+ align:start position:0%
+um cool let me give you a couple of
+applications right off the bat what uh
+
+ align:start position:0%
+applications right off the bat what uh
+ 
+
+ align:start position:0%
+applications right off the bat what uh
+this is going back a little bit but are
+
+ align:start position:0%
+this is going back a little bit but are
+ 
+
+ align:start position:0%
+this is going back a little bit but are
+there any sort of natural families of
+
+ align:start position:0%
+there any sort of natural families of
+ 
+
+ align:start position:0%
+there any sort of natural families of
+graphs for which finding a hamiltonian
+
+ align:start position:0%
+graphs for which finding a hamiltonian
+ 
+
+ align:start position:0%
+graphs for which finding a hamiltonian
+path is strictly easier than finding a
+
+ align:start position:0%
+path is strictly easier than finding a
+ 
+
+ align:start position:0%
+path is strictly easier than finding a
+circle uh
+
+ align:start position:0%
+circle uh
+ 
+
+ align:start position:0%
+circle uh
+I think the only this problem would be
+
+ align:start position:0%
+I think the only this problem would be
+ 
+
+ align:start position:0%
+I think the only this problem would be
+easy find a hamiltonian path given a
+
+ align:start position:0%
+easy find a hamiltonian path given a
+ 
+
+ align:start position:0%
+easy find a hamiltonian path given a
+hamiltonian path but um I'm not aware of
+
+ align:start position:0%
+hamiltonian path but um I'm not aware of
+ 
+
+ align:start position:0%
+hamiltonian path but um I'm not aware of
+any other problems where one is where
+
+ align:start position:0%
+any other problems where one is where
+ 
+
+ align:start position:0%
+any other problems where one is where
+hamiltonian path is easier than cycle um
+
+ align:start position:0%
+hamiltonian path is easier than cycle um
+ 
+
+ align:start position:0%
+hamiltonian path is easier than cycle um
+I mean in general you can reduce one to
+
+ align:start position:0%
+I mean in general you can reduce one to
+ 
+
+ align:start position:0%
+I mean in general you can reduce one to
+the other somehow it's maybe a little
+
+ align:start position:0%
+the other somehow it's maybe a little
+ 
+
+ align:start position:0%
+the other somehow it's maybe a little
+tricky without the two given end points
+
+ align:start position:0%
+tricky without the two given end points
+ 
+
+ align:start position:0%
+tricky without the two given end points
+uh and if you have lots of structure
+
+ align:start position:0%
+uh and if you have lots of structure
+ 
+
+ align:start position:0%
+uh and if you have lots of structure
+like planarity and three regularity uh
+
+ align:start position:0%
+like planarity and three regularity uh
+ 
+
+ align:start position:0%
+like planarity and three regularity uh
+it's not so clear but definitely
+
+ align:start position:0%
+it's not so clear but definitely
+ 
+
+ align:start position:0%
+it's not so clear but definitely
+Hamilton Plum path is still hard in this
+
+ align:start position:0%
+Hamilton Plum path is still hard in this
+ 
+
+ align:start position:0%
+Hamilton Plum path is still hard in this
+problem I think one easy way to do that
+
+ align:start position:0%
+problem I think one easy way to do that
+ 
+
+ align:start position:0%
+problem I think one easy way to do that
+is uh to just do the same chain of
+
+ align:start position:0%
+is uh to just do the same chain of
+ 
+
+ align:start position:0%
+is uh to just do the same chain of
+reductions but start with hiltonium path
+
+ align:start position:0%
+reductions but start with hiltonium path
+ 
+
+ align:start position:0%
+reductions but start with hiltonium path
+instead of cycle and follow through and
+
+ align:start position:0%
+instead of cycle and follow through and
+ 
+
+ align:start position:0%
+instead of cycle and follow through and
+pretty much every step should still be
+
+ align:start position:0%
+pretty much every step should still be
+ 
+
+ align:start position:0%
+pretty much every step should still be
+path-based
+
+ align:start position:0%
+path-based
+ 
+
+ align:start position:0%
+path-based
+so uh that's actually useful we'll want
+
+ align:start position:0%
+so uh that's actually useful we'll want
+ 
+
+ align:start position:0%
+so uh that's actually useful we'll want
+hamiltonian path and grid graphs also at
+
+ align:start position:0%
+hamiltonian path and grid graphs also at
+ 
+
+ align:start position:0%
+hamiltonian path and grid graphs also at
+some point but what I showed was
+
+ align:start position:0%
+some point but what I showed was
+ 
+
+ align:start position:0%
+some point but what I showed was
+hamiltonian cycle yeah so pretty much
+
+ align:start position:0%
+hamiltonian cycle yeah so pretty much
+ 
+
+ align:start position:0%
+hamiltonian cycle yeah so pretty much
+everywhere they seem to be the same but
+
+ align:start position:0%
+everywhere they seem to be the same but
+ 
+
+ align:start position:0%
+everywhere they seem to be the same but
+it'd be cool to find an example where
+
+ align:start position:0%
+it'd be cool to find an example where
+ 
+
+ align:start position:0%
+it'd be cool to find an example where
+they have different complexity
+
+ align:start position:0%
+they have different complexity
+ 
+
+ align:start position:0%
+they have different complexity
+okay uh so here's another
+
+ align:start position:0%
+okay uh so here's another
+ 
+
+ align:start position:0%
+okay uh so here's another
+problem ukan
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+tsp uh traveling salesman problem you're
+
+ align:start position:0%
+tsp uh traveling salesman problem you're
+ 
+
+ align:start position:0%
+tsp uh traveling salesman problem you're
+given a set of points in the
+
+ align:start position:0%
+given a set of points in the
+ 
+
+ align:start position:0%
+given a set of points in the
+plane better not make it too big because
+
+ align:start position:0%
+plane better not make it too big because
+ 
+
+ align:start position:0%
+plane better not make it too big because
+this is n hard um and I want to find a
+
+ align:start position:0%
+this is n hard um and I want to find a
+ 
+
+ align:start position:0%
+this is n hard um and I want to find a
+tour it visits every point exactly once
+
+ align:start position:0%
+tour it visits every point exactly once
+ 
+
+ align:start position:0%
+tour it visits every point exactly once
+and has minimum total length ukan length
+
+ align:start position:0%
+and has minimum total length ukan length
+ 
+
+ align:start position:0%
+and has minimum total length ukan length
+so it's the usual notion of
+
+ align:start position:0%
+so it's the usual notion of
+ 
+
+ align:start position:0%
+so it's the usual notion of
+length uh I claim this is NP hard now
+
+ align:start position:0%
+length uh I claim this is NP hard now
+ 
+
+ align:start position:0%
+length uh I claim this is NP hard now
+this is a little scary most of the
+
+ align:start position:0%
+this is a little scary most of the
+ 
+
+ align:start position:0%
+this is a little scary most of the
+problems we've been working with are
+
+ align:start position:0%
+problems we've been working with are
+ 
+
+ align:start position:0%
+problems we've been working with are
+very discreet I mean the output here is
+
+ align:start position:0%
+very discreet I mean the output here is
+ 
+
+ align:start position:0%
+very discreet I mean the output here is
+sort of discret you choose a permutation
+
+ align:start position:0%
+sort of discret you choose a permutation
+ 
+
+ align:start position:0%
+sort of discret you choose a permutation
+on the points uh but there's sort of it
+
+ align:start position:0%
+on the points uh but there's sort of it
+ 
+
+ align:start position:0%
+on the points uh but there's sort of it
+feels like there's almost no control
+
+ align:start position:0%
+feels like there's almost no control
+ 
+
+ align:start position:0%
+feels like there's almost no control
+here I mean how would I construct
+
+ align:start position:0%
+here I mean how would I construct
+ 
+
+ align:start position:0%
+here I mean how would I construct
+localized gadgets when I can just jump
+
+ align:start position:0%
+localized gadgets when I can just jump
+ 
+
+ align:start position:0%
+localized gadgets when I can just jump
+from any point to any other point at any
+
+ align:start position:0%
+from any point to any other point at any
+ 
+
+ align:start position:0%
+from any point to any other point at any
+time as long as that point hasn't
+
+ align:start position:0%
+time as long as that point hasn't
+ 
+
+ align:start position:0%
+time as long as that point hasn't
+already been
+
+ align:start position:0%
+already been
+ 
+
+ align:start position:0%
+already been
+used but it's really easy to prove this
+
+ align:start position:0%
+used but it's really easy to prove this
+ 
+
+ align:start position:0%
+used but it's really easy to prove this
+is NP hard given what we just did oh I
+
+ align:start position:0%
+is NP hard given what we just did oh I
+ 
+
+ align:start position:0%
+is NP hard given what we just did oh I
+should say um here's a a full worked out
+
+ align:start position:0%
+should say um here's a a full worked out
+ 
+
+ align:start position:0%
+should say um here's a a full worked out
+example so this is what I should be
+
+ align:start position:0%
+example so this is what I should be
+ 
+
+ align:start position:0%
+example so this is what I should be
+pointing at this was the parity
+
+ align:start position:0%
+pointing at this was the parity
+ 
+
+ align:start position:0%
+pointing at this was the parity
+preserving uh graph that we uh Drew
+
+ align:start position:0%
+preserving uh graph that we uh Drew
+ 
+
+ align:start position:0%
+preserving uh graph that we uh Drew
+before and this is what you get in the
+
+ align:start position:0%
+before and this is what you get in the
+ 
+
+ align:start position:0%
+before and this is what you get in the
+reduction uh along with an actual
+
+ align:start position:0%
+reduction uh along with an actual
+ 
+
+ align:start position:0%
+reduction uh along with an actual
+solution which is the one drawn in
+
+ align:start position:0%
+solution which is the one drawn in
+ 
+
+ align:start position:0%
+solution which is the one drawn in
+Orange
+
+ align:start position:0%
+Orange
+ 
+
+ align:start position:0%
+Orange
+here uh so you can see you can read that
+
+ align:start position:0%
+here uh so you can see you can read that
+ 
+
+ align:start position:0%
+here uh so you can see you can read that
+off because wherever you see zigzags
+
+ align:start position:0%
+off because wherever you see zigzags
+ 
+
+ align:start position:0%
+off because wherever you see zigzags
+that's where you're using the path here
+
+ align:start position:0%
+that's where you're using the path here
+ 
+
+ align:start position:0%
+that's where you're using the path here
+so these correspond and then this
+
+ align:start position:0%
+so these correspond and then this
+ 
+
+ align:start position:0%
+so these correspond and then this
+corresponds right and then up and over
+
+ align:start position:0%
+corresponds right and then up and over
+ 
+
+ align:start position:0%
+corresponds right and then up and over
+and then the the unused edges the the
+
+ align:start position:0%
+and then the the unused edges the the
+ 
+
+ align:start position:0%
+and then the the unused edges the the
+not orange ones that's where we get
+
+ align:start position:0%
+not orange ones that's where we get
+ 
+
+ align:start position:0%
+not orange ones that's where we get
+these kinds of Loops uh starting from
+
+ align:start position:0%
+these kinds of Loops uh starting from
+ 
+
+ align:start position:0%
+these kinds of Loops uh starting from
+the uh vertices of one parody I guess
+
+ align:start position:0%
+the uh vertices of one parody I guess
+ 
+
+ align:start position:0%
+the uh vertices of one parody I guess
+the white ones and then going to the
+
+ align:start position:0%
+the white ones and then going to the
+ 
+
+ align:start position:0%
+the white ones and then going to the
+black ones and turning around at the pin
+
+ align:start position:0%
+black ones and turning around at the pin
+ 
+
+ align:start position:0%
+black ones and turning around at the pin
+joint cool so uh given that this is hard
+
+ align:start position:0%
+joint cool so uh given that this is hard
+ 
+
+ align:start position:0%
+joint cool so uh given that this is hard
+why is this hard
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh so the decision problem let's say is
+
+ align:start position:0%
+uh so the decision problem let's say is
+ 
+
+ align:start position:0%
+uh so the decision problem let's say is
+I give you a set of points I give you
+
+ align:start position:0%
+I give you a set of points I give you
+ 
+
+ align:start position:0%
+I give you a set of points I give you
+the length the desired length of the
+
+ align:start position:0%
+the length the desired length of the
+ 
+
+ align:start position:0%
+the length the desired length of the
+tour I want to know is there a tour
+
+ align:start position:0%
+tour I want to know is there a tour
+ 
+
+ align:start position:0%
+tour I want to know is there a tour
+visits every point exactly once and has
+
+ align:start position:0%
+visits every point exactly once and has
+ 
+
+ align:start position:0%
+visits every point exactly once and has
+length at most that given
+
+ align:start position:0%
+length at most that given
+ 
+
+ align:start position:0%
+length at most that given
+length right so if you look at uh some
+
+ align:start position:0%
+length right so if you look at uh some
+ 
+
+ align:start position:0%
+length right so if you look at uh some
+grid craft it'll have some number of
+
+ align:start position:0%
+grid craft it'll have some number of
+ 
+
+ align:start position:0%
+grid craft it'll have some number of
+nodes which means the tour would have to
+
+ align:start position:0%
+nodes which means the tour would have to
+ 
+
+ align:start position:0%
+nodes which means the tour would have to
+necessarily have if you just choose
+
+ align:start position:0%
+necessarily have if you just choose
+ 
+
+ align:start position:0%
+necessarily have if you just choose
+those points the T would necessarily
+
+ align:start position:0%
+those points the T would necessarily
+ 
+
+ align:start position:0%
+those points the T would necessarily
+have at least exactly that
+
+ align:start position:0%
+have at least exactly that
+ 
+
+ align:start position:0%
+have at least exactly that
+edges and each Edge would have to have
+
+ align:start position:0%
+edges and each Edge would have to have
+ 
+
+ align:start position:0%
+edges and each Edge would have to have
+length at least one because the Clos
+
+ align:start position:0%
+length at least one because the Clos
+ 
+
+ align:start position:0%
+length at least one because the Clos
+pair of points is uh one apart Y and so
+
+ align:start position:0%
+pair of points is uh one apart Y and so
+ 
+
+ align:start position:0%
+pair of points is uh one apart Y and so
+if you just count the number of points
+
+ align:start position:0%
+if you just count the number of points
+ 
+
+ align:start position:0%
+if you just count the number of points
+and say that that's the desired uh
+
+ align:start position:0%
+and say that that's the desired uh
+ 
+
+ align:start position:0%
+and say that that's the desired uh
+length of your tour then you can only do
+
+ align:start position:0%
+length of your tour then you can only do
+ 
+
+ align:start position:0%
+length of your tour then you can only do
+that if you can get through this by
+
+ align:start position:0%
+that if you can get through this by
+ 
+
+ align:start position:0%
+that if you can get through this by
+following only edges that are length
+
+ align:start position:0%
+following only edges that are length
+ 
+
+ align:start position:0%
+following only edges that are length
+exactly so we're going to reduce from
+
+ align:start position:0%
+exactly so we're going to reduce from
+ 
+
+ align:start position:0%
+exactly so we're going to reduce from
+this
+
+ align:start position:0%
+this
+ 
+
+ align:start position:0%
+this
+problem given such a grid graph the
+
+ align:start position:0%
+problem given such a grid graph the
+ 
+
+ align:start position:0%
+problem given such a grid graph the
+reduction just looks at the vertices
+
+ align:start position:0%
+reduction just looks at the vertices
+ 
+
+ align:start position:0%
+reduction just looks at the vertices
+throws away the edges that is our input
+
+ align:start position:0%
+throws away the edges that is our input
+ 
+
+ align:start position:0%
+throws away the edges that is our input
+those points are the input to tsp then
+
+ align:start position:0%
+those points are the input to tsp then
+ 
+
+ align:start position:0%
+those points are the input to tsp then
+the claim is that every tour let's say
+
+ align:start position:0%
+the claim is that every tour let's say
+ 
+
+ align:start position:0%
+the claim is that every tour let's say
+there are end points in this picture
+
+ align:start position:0%
+there are end points in this picture
+ 
+
+ align:start position:0%
+there are end points in this picture
+every tour has to have length at least n
+
+ align:start position:0%
+every tour has to have length at least n
+ 
+
+ align:start position:0%
+every tour has to have length at least n
+as you said because they're end points
+
+ align:start position:0%
+as you said because they're end points
+ 
+
+ align:start position:0%
+as you said because they're end points
+the total number of edges is n in a
+
+ align:start position:0%
+the total number of edges is n in a
+ 
+
+ align:start position:0%
+the total number of edges is n in a
+cycle hamiltonian cycle and uh every
+
+ align:start position:0%
+cycle hamiltonian cycle and uh every
+ 
+
+ align:start position:0%
+cycle hamiltonian cycle and uh every
+Edge must have length at least one
+
+ align:start position:0%
+Edge must have length at least one
+ 
+
+ align:start position:0%
+Edge must have length at least one
+because that's the nearest pair uh and
+
+ align:start position:0%
+because that's the nearest pair uh and
+ 
+
+ align:start position:0%
+because that's the nearest pair uh and
+so that's a lower bound and then on the
+
+ align:start position:0%
+so that's a lower bound and then on the
+ 
+
+ align:start position:0%
+so that's a lower bound and then on the
+other hand if there is a tour uh that
+
+ align:start position:0%
+other hand if there is a tour uh that
+ 
+
+ align:start position:0%
+other hand if there is a tour uh that
+has length only n then it must actually
+
+ align:start position:0%
+has length only n then it must actually
+ 
+
+ align:start position:0%
+has length only n then it must actually
+be a hamian cycle in this graph because
+
+ align:start position:0%
+be a hamian cycle in this graph because
+ 
+
+ align:start position:0%
+be a hamian cycle in this graph because
+that you're then you're only using edges
+
+ align:start position:0%
+that you're then you're only using edges
+ 
+
+ align:start position:0%
+that you're then you're only using edges
+that exist in the grid graph so it's
+
+ align:start position:0%
+that exist in the grid graph so it's
+ 
+
+ align:start position:0%
+that exist in the grid graph so it's
+really the same problem ukian tsp really
+
+ align:start position:0%
+really the same problem ukian tsp really
+ 
+
+ align:start position:0%
+really the same problem ukian tsp really
+is a special case of
+
+ align:start position:0%
+is a special case of
+ 
+
+ align:start position:0%
+is a special case of
+this
+
+ align:start position:0%
+this
+ 
+
+ align:start position:0%
+this
+uh which is
+
+ align:start position:0%
+uh which is
+ 
+
+ align:start position:0%
+uh which is
+cool this problem was proved hard much
+
+ align:start position:0%
+cool this problem was proved hard much
+ 
+
+ align:start position:0%
+cool this problem was proved hard much
+earlier uh
+
+ align:start position:0%
+earlier uh
+ 
+
+ align:start position:0%
+earlier uh
+anity and grid
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+graphs but here's now a nice simple
+
+ align:start position:0%
+graphs but here's now a nice simple
+ 
+
+ align:start position:0%
+graphs but here's now a nice simple
+proof using what we
+
+ align:start position:0%
+proof using what we
+ 
+
+ align:start position:0%
+proof using what we
+know uh I'll tell you more reasons uh in
+
+ align:start position:0%
+know uh I'll tell you more reasons uh in
+ 
+
+ align:start position:0%
+know uh I'll tell you more reasons uh in
+a little bit but I have one more at this
+
+ align:start position:0%
+a little bit but I have one more at this
+ 
+
+ align:start position:0%
+a little bit but I have one more at this
+point which is platform
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+games I don't have a Graphic because
+
+ align:start position:0%
+games I don't have a Graphic because
+ 
+
+ align:start position:0%
+games I don't have a Graphic because
+there there's so many games that could
+
+ align:start position:0%
+there there's so many games that could
+ 
+
+ align:start position:0%
+there there's so many games that could
+apply here uh Super Mario Brothers among
+
+ align:start position:0%
+apply here uh Super Mario Brothers among
+ 
+
+ align:start position:0%
+apply here uh Super Mario Brothers among
+them suppose you have uh a little dude
+
+ align:start position:0%
+them suppose you have uh a little dude
+ 
+
+ align:start position:0%
+them suppose you have uh a little dude
+who can walk around and you've got some
+
+ align:start position:0%
+who can walk around and you've got some
+ 
+
+ align:start position:0%
+who can walk around and you've got some
+kind of coins I don't know how to draw
+
+ align:start position:0%
+kind of coins I don't know how to draw
+ 
+
+ align:start position:0%
+kind of coins I don't know how to draw
+coins those look like eyeballs but
+
+ align:start position:0%
+coins those look like eyeballs but
+ 
+
+ align:start position:0%
+coins those look like eyeballs but
+anyway uh you've got a bunch of coins
+
+ align:start position:0%
+anyway uh you've got a bunch of coins
+ 
+
+ align:start position:0%
+anyway uh you've got a bunch of coins
+which you want to collect and let's say
+
+ align:start position:0%
+which you want to collect and let's say
+ 
+
+ align:start position:0%
+which you want to collect and let's say
+uh and you have some way that you can
+
+ align:start position:0%
+uh and you have some way that you can
+ 
+
+ align:start position:0%
+uh and you have some way that you can
+walk around if you're top down game then
+
+ align:start position:0%
+walk around if you're top down game then
+ 
+
+ align:start position:0%
+walk around if you're top down game then
+that's pretty much the entire reduction
+
+ align:start position:0%
+that's pretty much the entire reduction
+ 
+
+ align:start position:0%
+that's pretty much the entire reduction
+um and then also you have a
+
+ align:start position:0%
+um and then also you have a
+ 
+
+ align:start position:0%
+um and then also you have a
+timer so timer plus
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Collectibles bubles or
+
+ align:start position:0%
+Collectibles bubles or
+ 
+
+ align:start position:0%
+Collectibles bubles or
+ibles say ubbles
+
+ align:start position:0%
+ibles say ubbles
+ 
+
+ align:start position:0%
+ibles say ubbles
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+and uh any such game is NP hard at least
+
+ align:start position:0%
+and uh any such game is NP hard at least
+ 
+
+ align:start position:0%
+and uh any such game is NP hard at least
+uh because if you want to get all of
+
+ align:start position:0%
+uh because if you want to get all of
+ 
+
+ align:start position:0%
+uh because if you want to get all of
+these coins that's like vertices you
+
+ align:start position:0%
+these coins that's like vertices you
+ 
+
+ align:start position:0%
+these coins that's like vertices you
+need to visit and if it's say a top down
+
+ align:start position:0%
+need to visit and if it's say a top down
+ 
+
+ align:start position:0%
+need to visit and if it's say a top down
+game you're you're walking in a grid
+
+ align:start position:0%
+game you're you're walking in a grid
+ 
+
+ align:start position:0%
+game you're you're walking in a grid
+graph the time limit will prevent us
+
+ align:start position:0%
+graph the time limit will prevent us
+ 
+
+ align:start position:0%
+graph the time limit will prevent us
+from going out into the Whit space
+
+ align:start position:0%
+from going out into the Whit space
+ 
+
+ align:start position:0%
+from going out into the Whit space
+because there's no coins there and so if
+
+ align:start position:0%
+because there's no coins there and so if
+ 
+
+ align:start position:0%
+because there's no coins there and so if
+the time limit is exactly the number of
+
+ align:start position:0%
+the time limit is exactly the number of
+ 
+
+ align:start position:0%
+the time limit is exactly the number of
+coins in every step you make you have to
+
+ align:start position:0%
+coins in every step you make you have to
+ 
+
+ align:start position:0%
+coins in every step you make you have to
+get a coin then uh that will force you
+
+ align:start position:0%
+get a coin then uh that will force you
+ 
+
+ align:start position:0%
+get a coin then uh that will force you
+to only follow these the edges in the
+
+ align:start position:0%
+to only follow these the edges in the
+ 
+
+ align:start position:0%
+to only follow these the edges in the
+grid graph can't go out
+
+ align:start position:0%
+grid graph can't go out
+ 
+
+ align:start position:0%
+grid graph can't go out
+here no obstacles needed um and you
+
+ align:start position:0%
+here no obstacles needed um and you
+ 
+
+ align:start position:0%
+here no obstacles needed um and you
+understand that in the real game of
+
+ align:start position:0%
+understand that in the real game of
+ 
+
+ align:start position:0%
+understand that in the real game of
+course there might be stuff happening
+
+ align:start position:0%
+course there might be stuff happening
+ 
+
+ align:start position:0%
+course there might be stuff happening
+here you know maybe there's a ladder so
+
+ align:start position:0%
+here you know maybe there's a ladder so
+ 
+
+ align:start position:0%
+here you know maybe there's a ladder so
+you can go up here and it's uh you just
+
+ align:start position:0%
+you can go up here and it's uh you just
+ 
+
+ align:start position:0%
+you can go up here and it's uh you just
+have to set up all of these traversal
+
+ align:start position:0%
+have to set up all of these traversal
+ 
+
+ align:start position:0%
+have to set up all of these traversal
+lengths to take the same amount of time
+
+ align:start position:0%
+lengths to take the same amount of time
+ 
+
+ align:start position:0%
+lengths to take the same amount of time
+in under optimal play and then you can
+
+ align:start position:0%
+in under optimal play and then you can
+ 
+
+ align:start position:0%
+in under optimal play and then you can
+simulate a ton of video games in this
+
+ align:start position:0%
+simulate a ton of video games in this
+ 
+
+ align:start position:0%
+simulate a ton of video games in this
+way okay this is a result this is in fun
+
+ align:start position:0%
+way okay this is a result this is in fun
+ 
+
+ align:start position:0%
+way okay this is a result this is in fun
+2010 by
+
+ align:start position:0%
+2010 by
+ 
+
+ align:start position:0%
+2010 by
+foric okay so some reasons why you care
+
+ align:start position:0%
+foric okay so some reasons why you care
+ 
+
+ align:start position:0%
+foric okay so some reasons why you care
+a lot of games map naturally onto grids
+
+ align:start position:0%
+a lot of games map naturally onto grids
+ 
+
+ align:start position:0%
+a lot of games map naturally onto grids
+uh a lot of real problems map onto can
+
+ align:start position:0%
+uh a lot of real problems map onto can
+ 
+
+ align:start position:0%
+uh a lot of real problems map onto can
+map onto
+
+ align:start position:0%
+map onto
+ 
+
+ align:start position:0%
+map onto
+grids uh but in general grids will be
+
+ align:start position:0%
+grids uh but in general grids will be
+ 
+
+ align:start position:0%
+grids uh but in general grids will be
+very
+
+ align:start position:0%
+very
+ 
+
+ align:start position:0%
+very
+helpful uh so uh next problem I want to
+
+ align:start position:0%
+helpful uh so uh next problem I want to
+ 
+
+ align:start position:0%
+helpful uh so uh next problem I want to
+solve is by solve I mean show hard as
+
+ align:start position:0%
+solve is by solve I mean show hard as
+ 
+
+ align:start position:0%
+solve is by solve I mean show hard as
+usual um let's say
+
+ align:start position:0%
+usual um let's say
+ 
+
+ align:start position:0%
+usual um let's say
+Max
+
+ align:start position:0%
+Max
+ 
+
+ align:start position:0%
+Max
+degree 3
+
+ align:start position:0%
+degree 3
+ 
+
+ align:start position:0%
+degree 3
+grid
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+graphs I don't have a great motiv well I
+
+ align:start position:0%
+graphs I don't have a great motiv well I
+ 
+
+ align:start position:0%
+graphs I don't have a great motiv well I
+have a motivation for this um there
+
+ align:start position:0%
+have a motivation for this um there
+ 
+
+ align:start position:0%
+have a motivation for this um there
+probably others that I'm not aware of I
+
+ align:start position:0%
+probably others that I'm not aware of I
+ 
+
+ align:start position:0%
+probably others that I'm not aware of I
+hadn't didn't actually know about this
+
+ align:start position:0%
+hadn't didn't actually know about this
+ 
+
+ align:start position:0%
+hadn't didn't actually know about this
+result until recently it's pretty cool
+
+ align:start position:0%
+result until recently it's pretty cool
+ 
+
+ align:start position:0%
+result until recently it's pretty cool
+uh if you look at this reduction there
+
+ align:start position:0%
+uh if you look at this reduction there
+ 
+
+ align:start position:0%
+uh if you look at this reduction there
+are some vertices that I mean here we're
+
+ align:start position:0%
+are some vertices that I mean here we're
+ 
+
+ align:start position:0%
+are some vertices that I mean here we're
+drawing the cycle but some vertices have
+
+ align:start position:0%
+drawing the cycle but some vertices have
+ 
+
+ align:start position:0%
+drawing the cycle but some vertices have
+degree four of course every grid graph
+
+ align:start position:0%
+degree four of course every grid graph
+ 
+
+ align:start position:0%
+degree four of course every grid graph
+is Max degree four uh and Max degree 2
+
+ align:start position:0%
+is Max degree four uh and Max degree 2
+ 
+
+ align:start position:0%
+is Max degree four uh and Max degree 2
+is pretty easy to solve hamiltonicity so
+
+ align:start position:0%
+is pretty easy to solve hamiltonicity so
+ 
+
+ align:start position:0%
+is pretty easy to solve hamiltonicity so
+uh what's left is Max degree 3 so
+
+ align:start position:0%
+uh what's left is Max degree 3 so
+ 
+
+ align:start position:0%
+uh what's left is Max degree 3 so
+natural question in between is can you
+
+ align:start position:0%
+natural question in between is can you
+ 
+
+ align:start position:0%
+natural question in between is can you
+do Max degree 3 grid graphs claim is
+
+ align:start position:0%
+do Max degree 3 grid graphs claim is
+ 
+
+ align:start position:0%
+do Max degree 3 grid graphs claim is
+that is also hard and it's going to be
+
+ align:start position:0%
+that is also hard and it's going to be
+ 
+
+ align:start position:0%
+that is also hard and it's going to be
+basically the same proof but we're going
+
+ align:start position:0%
+basically the same proof but we're going
+ 
+
+ align:start position:0%
+basically the same proof but we're going
+to change all the gadgets well most of
+
+ align:start position:0%
+to change all the gadgets well most of
+ 
+
+ align:start position:0%
+to change all the gadgets well most of
+them uh and so this is by there's one
+
+ align:start position:0%
+them uh and so this is by there's one
+ 
+
+ align:start position:0%
+them uh and so this is by there's one
+shared author this was e Papa Demetrio
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Ander um and then this is purion and
+
+ align:start position:0%
+Ander um and then this is purion and
+ 
+
+ align:start position:0%
+Ander um and then this is purion and
+vasani uh a couple years later so uh the
+
+ align:start position:0%
+vasani uh a couple years later so uh the
+ 
+
+ align:start position:0%
+vasani uh a couple years later so uh the
+this is actually very similar to the
+
+ align:start position:0%
+this is actually very similar to the
+ 
+
+ align:start position:0%
+this is actually very similar to the
+edge Gadget we saw before here's the old
+
+ align:start position:0%
+edge Gadget we saw before here's the old
+ 
+
+ align:start position:0%
+edge Gadget we saw before here's the old
+Edge Gadget and the turns see before
+
+ align:start position:0%
+Edge Gadget and the turns see before
+ 
+
+ align:start position:0%
+Edge Gadget and the turns see before
+when we had a turn we had a degree four
+
+ align:start position:0%
+when we had a turn we had a degree four
+ 
+
+ align:start position:0%
+when we had a turn we had a degree four
+vertex I want to get rid of that and I'm
+
+ align:start position:0%
+vertex I want to get rid of that and I'm
+ 
+
+ align:start position:0%
+vertex I want to get rid of that and I'm
+going to get rid of it by just sort of
+
+ align:start position:0%
+going to get rid of it by just sort of
+ 
+
+ align:start position:0%
+going to get rid of it by just sort of
+shifting these things apart and blowing
+
+ align:start position:0%
+shifting these things apart and blowing
+ 
+
+ align:start position:0%
+shifting these things apart and blowing
+up this circle this cycle uh so I end up
+
+ align:start position:0%
+up this circle this cycle uh so I end up
+ 
+
+ align:start position:0%
+up this circle this cycle uh so I end up
+with a bigger cycle here I end up with
+
+ align:start position:0%
+with a bigger cycle here I end up with
+ 
+
+ align:start position:0%
+with a bigger cycle here I end up with
+an edge connection there but effectively
+
+ align:start position:0%
+an edge connection there but effectively
+ 
+
+ align:start position:0%
+an edge connection there but effectively
+it's the same kind of topology um if
+
+ align:start position:0%
+it's the same kind of topology um if
+ 
+
+ align:start position:0%
+it's the same kind of topology um if
+you're coming in and
+
+ align:start position:0%
+you're coming in and
+ 
+
+ align:start position:0%
+you're coming in and
+alternating uh
+
+ align:start position:0%
+alternating uh
+ 
+
+ align:start position:0%
+alternating uh
+uh I guess you have to get the parody
+
+ align:start position:0%
+uh I guess you have to get the parody
+ 
+
+ align:start position:0%
+uh I guess you have to get the parody
+right if you're coming in from this side
+
+ align:start position:0%
+right if you're coming in from this side
+ 
+
+ align:start position:0%
+right if you're coming in from this side
+and you're alternating then you can come
+
+ align:start position:0%
+and you're alternating then you can come
+ 
+
+ align:start position:0%
+and you're alternating then you can come
+around and visit like that and
+
+ align:start position:0%
+around and visit like that and
+ 
+
+ align:start position:0%
+around and visit like that and
+everything is okay back and
+
+ align:start position:0%
+everything is okay back and
+ 
+
+ align:start position:0%
+everything is okay back and
+forth cool that it's drawn right over
+
+ align:start position:0%
+forth cool that it's drawn right over
+ 
+
+ align:start position:0%
+forth cool that it's drawn right over
+here that's the zigzag path the return
+
+ align:start position:0%
+here that's the zigzag path the return
+ 
+
+ align:start position:0%
+here that's the zigzag path the return
+path is just as before and so we can use
+
+ align:start position:0%
+path is just as before and so we can use
+ 
+
+ align:start position:0%
+path is just as before and so we can use
+this Edge Gadget exactly as we did
+
+ align:start position:0%
+this Edge Gadget exactly as we did
+ 
+
+ align:start position:0%
+this Edge Gadget exactly as we did
+before uh but now it's Max degree 3
+
+ align:start position:0%
+before uh but now it's Max degree 3
+ 
+
+ align:start position:0%
+before uh but now it's Max degree 3
+everywhere so that's easy in general
+
+ align:start position:0%
+everywhere so that's easy in general
+ 
+
+ align:start position:0%
+everywhere so that's easy in general
+using this trick that if we have uh here
+
+ align:start position:0%
+using this trick that if we have uh here
+ 
+
+ align:start position:0%
+using this trick that if we have uh here
+we had a corner uh with a vertex on it
+
+ align:start position:0%
+we had a corner uh with a vertex on it
+ 
+
+ align:start position:0%
+we had a corner uh with a vertex on it
+you can turn that into a longer path
+
+ align:start position:0%
+you can turn that into a longer path
+ 
+
+ align:start position:0%
+you can turn that into a longer path
+with various vertices on it that will
+
+ align:start position:0%
+with various vertices on it that will
+ 
+
+ align:start position:0%
+with various vertices on it that will
+act the same from a hamiltonicity
+
+ align:start position:0%
+act the same from a hamiltonicity
+ 
+
+ align:start position:0%
+act the same from a hamiltonicity
+perspective so that's the key thing
+
+ align:start position:0%
+perspective so that's the key thing
+ 
+
+ align:start position:0%
+perspective so that's the key thing
+we're doing and then uh then we're just
+
+ align:start position:0%
+we're doing and then uh then we're just
+ 
+
+ align:start position:0%
+we're doing and then uh then we're just
+it's a matter of putting things to fit
+
+ align:start position:0%
+it's a matter of putting things to fit
+ 
+
+ align:start position:0%
+it's a matter of putting things to fit
+on the
+
+ align:start position:0%
+on the
+ 
+
+ align:start position:0%
+on the
+grid okay so that's first change now the
+
+ align:start position:0%
+grid okay so that's first change now the
+ 
+
+ align:start position:0%
+grid okay so that's first change now the
+second change is going to be a little
+
+ align:start position:0%
+second change is going to be a little
+ 
+
+ align:start position:0%
+second change is going to be a little
+bit more drastic a little weirder uh the
+
+ align:start position:0%
+bit more drastic a little weirder uh the
+ 
+
+ align:start position:0%
+bit more drastic a little weirder uh the
+vertex Gadget used to be this 3x3 thing
+
+ align:start position:0%
+vertex Gadget used to be this 3x3 thing
+ 
+
+ align:start position:0%
+vertex Gadget used to be this 3x3 thing
+very hard to get rid of that vertex of
+
+ align:start position:0%
+very hard to get rid of that vertex of
+ 
+
+ align:start position:0%
+very hard to get rid of that vertex of
+degree 4 in the center uh well if you
+
+ align:start position:0%
+degree 4 in the center uh well if you
+ 
+
+ align:start position:0%
+degree 4 in the center uh well if you
+did that you would be left with a little
+
+ align:start position:0%
+did that you would be left with a little
+ 
+
+ align:start position:0%
+did that you would be left with a little
+square an empty square and uh we're
+
+ align:start position:0%
+square an empty square and uh we're
+ 
+
+ align:start position:0%
+square an empty square and uh we're
+going to need two of those so this is
+
+ align:start position:0%
+going to need two of those so this is
+ 
+
+ align:start position:0%
+going to need two of those so this is
+the dumbbell picture used in many
+
+ align:start position:0%
+the dumbbell picture used in many
+ 
+
+ align:start position:0%
+the dumbbell picture used in many
+theoretical results so we have uh two of
+
+ align:start position:0%
+theoretical results so we have uh two of
+ 
+
+ align:start position:0%
+theoretical results so we have uh two of
+these ver these squares we're going to
+
+ align:start position:0%
+these ver these squares we're going to
+ 
+
+ align:start position:0%
+these ver these squares we're going to
+separate them by a fairly long path of
+
+ align:start position:0%
+separate them by a fairly long path of
+ 
+
+ align:start position:0%
+separate them by a fairly long path of
+the right
+
+ align:start position:0%
+the right
+ 
+
+ align:start position:0%
+the right
+par and the idea is uh you can have up
+
+ align:start position:0%
+par and the idea is uh you can have up
+ 
+
+ align:start position:0%
+par and the idea is uh you can have up
+to two connections over here to edges
+
+ align:start position:0%
+to two connections over here to edges
+ 
+
+ align:start position:0%
+to two connections over here to edges
+and up to two connections over here for
+
+ align:start position:0%
+and up to two connections over here for
+ 
+
+ align:start position:0%
+and up to two connections over here for
+edges and here's a typical connections
+
+ align:start position:0%
+edges and here's a typical connections
+ 
+
+ align:start position:0%
+edges and here's a typical connections
+are going to look just like we had
+
+ align:start position:0%
+are going to look just like we had
+ 
+
+ align:start position:0%
+are going to look just like we had
+before um but it's not going to quite
+
+ align:start position:0%
+before um but it's not going to quite
+ 
+
+ align:start position:0%
+before um but it's not going to quite
+all be like this so it used to be we
+
+ align:start position:0%
+all be like this so it used to be we
+ 
+
+ align:start position:0%
+all be like this so it used to be we
+could have a full Edge connection or we
+
+ align:start position:0%
+could have a full Edge connection or we
+ 
+
+ align:start position:0%
+could have a full Edge connection or we
+can have a pin
+
+ align:start position:0%
+can have a pin
+ 
+
+ align:start position:0%
+can have a pin
+connection as before uh it's just the
+
+ align:start position:0%
+connection as before uh it's just the
+ 
+
+ align:start position:0%
+connection as before uh it's just the
+when this Edge turns it's going to use
+
+ align:start position:0%
+when this Edge turns it's going to use
+ 
+
+ align:start position:0%
+when this Edge turns it's going to use
+the weirder turn Gadget so we just the
+
+ align:start position:0%
+the weirder turn Gadget so we just the
+ 
+
+ align:start position:0%
+the weirder turn Gadget so we just the
+the the edges look basically the same as
+
+ align:start position:0%
+the the edges look basically the same as
+ 
+
+ align:start position:0%
+the the edges look basically the same as
+just the turns that we changed in the
+
+ align:start position:0%
+just the turns that we changed in the
+ 
+
+ align:start position:0%
+just the turns that we changed in the
+last
+
+ align:start position:0%
+last
+ 
+
+ align:start position:0%
+last
+slide okay uh this almost Works uh but I
+
+ align:start position:0%
+slide okay uh this almost Works uh but I
+ 
+
+ align:start position:0%
+slide okay uh this almost Works uh but I
+have to specify some details
+
+ align:start position:0%
+have to specify some details
+ 
+
+ align:start position:0%
+have to specify some details
+so for example uh let's easy case degree
+
+ align:start position:0%
+so for example uh let's easy case degree
+ 
+
+ align:start position:0%
+so for example uh let's easy case degree
+2 vertex suppose the original graph has
+
+ align:start position:0%
+2 vertex suppose the original graph has
+ 
+
+ align:start position:0%
+2 vertex suppose the original graph has
+a degree 2 vertex we had that in our
+
+ align:start position:0%
+a degree 2 vertex we had that in our
+ 
+
+ align:start position:0%
+a degree 2 vertex we had that in our
+reductions uh because in fact every
+
+ align:start position:0%
+reductions uh because in fact every
+ 
+
+ align:start position:0%
+reductions uh because in fact every
+other vertex pretty much was degree 2
+
+ align:start position:0%
+other vertex pretty much was degree 2
+ 
+
+ align:start position:0%
+other vertex pretty much was degree 2
+when if you track all of these things uh
+
+ align:start position:0%
+when if you track all of these things uh
+ 
+
+ align:start position:0%
+when if you track all of these things uh
+when we went from the directed case to
+
+ align:start position:0%
+when we went from the directed case to
+ 
+
+ align:start position:0%
+when we went from the directed case to
+the bipartite case we added in lots of
+
+ align:start position:0%
+the bipartite case we added in lots of
+ 
+
+ align:start position:0%
+the bipartite case we added in lots of
+vertices lots of degree 2 vertices so if
+
+ align:start position:0%
+vertices lots of degree 2 vertices so if
+ 
+
+ align:start position:0%
+vertices lots of degree 2 vertices so if
+we want to simulate a degree 2 vertex uh
+
+ align:start position:0%
+we want to simulate a degree 2 vertex uh
+ 
+
+ align:start position:0%
+we want to simulate a degree 2 vertex uh
+we will just have one of the edges
+
+ align:start position:0%
+we will just have one of the edges
+ 
+
+ align:start position:0%
+we will just have one of the edges
+attaching up here and one of the edges
+
+ align:start position:0%
+attaching up here and one of the edges
+ 
+
+ align:start position:0%
+attaching up here and one of the edges
+attaching down here and again up in this
+
+ align:start position:0%
+attaching down here and again up in this
+ 
+
+ align:start position:0%
+attaching down here and again up in this
+in this picture it's one on the left
+
+ align:start position:0%
+in this picture it's one on the left
+ 
+
+ align:start position:0%
+in this picture it's one on the left
+side one on the right side and again we
+
+ align:start position:0%
+side one on the right side and again we
+ 
+
+ align:start position:0%
+side one on the right side and again we
+have this feature that if we start at
+
+ align:start position:0%
+have this feature that if we start at
+ 
+
+ align:start position:0%
+have this feature that if we start at
+any of the pis we can get to uh one of
+
+ align:start position:0%
+any of the pis we can get to uh one of
+ 
+
+ align:start position:0%
+any of the pis we can get to uh one of
+the PJs by visiting all the uh EI
+
+ align:start position:0%
+the PJs by visiting all the uh EI
+ 
+
+ align:start position:0%
+the PJs by visiting all the uh EI
+edges okay so for example if we start
+
+ align:start position:0%
+edges okay so for example if we start
+ 
+
+ align:start position:0%
+edges okay so for example if we start
+here we go like this over here and we
+
+ align:start position:0%
+here we go like this over here and we
+ 
+
+ align:start position:0%
+here we go like this over here and we
+have a choice we can either go like this
+
+ align:start position:0%
+have a choice we can either go like this
+ 
+
+ align:start position:0%
+have a choice we can either go like this
+and end It P3 or go like this and end it
+
+ align:start position:0%
+and end It P3 or go like this and end it
+ 
+
+ align:start position:0%
+and end It P3 or go like this and end it
+P4 we visited all the
+
+ align:start position:0%
+P4 we visited all the
+ 
+
+ align:start position:0%
+P4 we visited all the
+e but we can't start at P1 and end at P2
+
+ align:start position:0%
+e but we can't start at P1 and end at P2
+ 
+
+ align:start position:0%
+e but we can't start at P1 and end at P2
+if we want to visit everything right
+
+ align:start position:0%
+if we want to visit everything right
+ 
+
+ align:start position:0%
+if we want to visit everything right
+start at P1 if you go out there you're
+
+ align:start position:0%
+start at P1 if you go out there you're
+ 
+
+ align:start position:0%
+start at P1 if you go out there you're
+you can never come back if you come
+
+ align:start position:0%
+you can never come back if you come
+ 
+
+ align:start position:0%
+you can never come back if you come
+around here you've already visited P2 so
+
+ align:start position:0%
+around here you've already visited P2 so
+ 
+
+ align:start position:0%
+around here you've already visited P2 so
+we cannot start an end on the left side
+
+ align:start position:0%
+we cannot start an end on the left side
+ 
+
+ align:start position:0%
+we cannot start an end on the left side
+we cannot start an end on the right side
+
+ align:start position:0%
+we cannot start an end on the right side
+ 
+
+ align:start position:0%
+we cannot start an end on the right side
+so for a degree 2 vertex that's fine we
+
+ align:start position:0%
+so for a degree 2 vertex that's fine we
+ 
+
+ align:start position:0%
+so for a degree 2 vertex that's fine we
+just put one of the connections on one
+
+ align:start position:0%
+just put one of the connections on one
+ 
+
+ align:start position:0%
+just put one of the connections on one
+side one on the other and you know we'll
+
+ align:start position:0%
+side one on the other and you know we'll
+ 
+
+ align:start position:0%
+side one on the other and you know we'll
+come in visit everything come out and
+
+ align:start position:0%
+come in visit everything come out and
+ 
+
+ align:start position:0%
+come in visit everything come out and
+because we visit all the Eis we can do
+
+ align:start position:0%
+because we visit all the Eis we can do
+ 
+
+ align:start position:0%
+because we visit all the Eis we can do
+this kind of uh traversal every time
+
+ align:start position:0%
+this kind of uh traversal every time
+ 
+
+ align:start position:0%
+this kind of uh traversal every time
+now for degree 3 vertex this is a little
+
+ align:start position:0%
+now for degree 3 vertex this is a little
+ 
+
+ align:start position:0%
+now for degree 3 vertex this is a little
+bit Troublesome um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+remember our
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+picture uh What do degree through
+
+ align:start position:0%
+picture uh What do degree through
+ 
+
+ align:start position:0%
+picture uh What do degree through
+vertices look like if you follow through
+
+ align:start position:0%
+vertices look like if you follow through
+ 
+
+ align:start position:0%
+vertices look like if you follow through
+the chain of reductions we had this case
+
+ align:start position:0%
+the chain of reductions we had this case
+ 
+
+ align:start position:0%
+the chain of reductions we had this case
+and we
+
+ align:start position:0%
+and we
+ 
+
+ align:start position:0%
+and we
+had this case and this one we converted
+
+ align:start position:0%
+had this case and this one we converted
+ 
+
+ align:start position:0%
+had this case and this one we converted
+into
+
+ align:start position:0%
+into
+ 
+
+ align:start position:0%
+into
+that and this one we converted
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+into that I
+
+ align:start position:0%
+into that I
+ 
+
+ align:start position:0%
+into that I
+think y uh because this was a forced
+
+ align:start position:0%
+think y uh because this was a forced
+ 
+
+ align:start position:0%
+think y uh because this was a forced
+Edge this was a forced Edge and so we
+
+ align:start position:0%
+Edge this was a forced Edge and so we
+ 
+
+ align:start position:0%
+Edge this was a forced Edge and so we
+added a DOT to represent that so good
+
+ align:start position:0%
+added a DOT to represent that so good
+ 
+
+ align:start position:0%
+added a DOT to represent that so good
+news is every time we have a degree 3
+
+ align:start position:0%
+news is every time we have a degree 3
+ 
+
+ align:start position:0%
+news is every time we have a degree 3
+vertex in this uh in the starting graph
+
+ align:start position:0%
+vertex in this uh in the starting graph
+ 
+
+ align:start position:0%
+vertex in this uh in the starting graph
+one of the edges is forced one of the
+
+ align:start position:0%
+one of the edges is forced one of the
+ 
+
+ align:start position:0%
+one of the edges is forced one of the
+three edges is forced so it's really a
+
+ align:start position:0%
+three edges is forced so it's really a
+ 
+
+ align:start position:0%
+three edges is forced so it's really a
+choice between do you take this one or
+
+ align:start position:0%
+choice between do you take this one or
+ 
+
+ align:start position:0%
+choice between do you take this one or
+do you take this one I mean that's of
+
+ align:start position:0%
+do you take this one I mean that's of
+ 
+
+ align:start position:0%
+do you take this one I mean that's of
+course what we had over
+
+ align:start position:0%
+course what we had over
+ 
+
+ align:start position:0%
+course what we had over
+here so what we're going to do is take
+
+ align:start position:0%
+here so what we're going to do is take
+ 
+
+ align:start position:0%
+here so what we're going to do is take
+these two edges which are exclusively
+
+ align:start position:0%
+these two edges which are exclusively
+ 
+
+ align:start position:0%
+these two edges which are exclusively
+ored together right I choose exactly one
+
+ align:start position:0%
+ored together right I choose exactly one
+ 
+
+ align:start position:0%
+ored together right I choose exactly one
+of these uh we're going to put that on
+
+ align:start position:0%
+of these uh we're going to put that on
+ 
+
+ align:start position:0%
+of these uh we're going to put that on
+one side so that one of them will go up
+
+ align:start position:0%
+one side so that one of them will go up
+ 
+
+ align:start position:0%
+one side so that one of them will go up
+here one of them will go down
+
+ align:start position:0%
+here one of them will go down
+ 
+
+ align:start position:0%
+here one of them will go down
+here and then the forced Edge we'll put
+
+ align:start position:0%
+here and then the forced Edge we'll put
+ 
+
+ align:start position:0%
+here and then the forced Edge we'll put
+over on the other side forc edge is
+
+ align:start position:0%
+over on the other side forc edge is
+ 
+
+ align:start position:0%
+over on the other side forc edge is
+always chosen so that means we'll come
+
+ align:start position:0%
+always chosen so that means we'll come
+ 
+
+ align:start position:0%
+always chosen so that means we'll come
+in on either P1 or P2 or leave on P1 or
+
+ align:start position:0%
+in on either P1 or P2 or leave on P1 or
+ 
+
+ align:start position:0%
+in on either P1 or P2 or leave on P1 or
+P2 depending on which of those two cases
+
+ align:start position:0%
+P2 depending on which of those two cases
+ 
+
+ align:start position:0%
+P2 depending on which of those two cases
+we're in and then uh we will leave or
+
+ align:start position:0%
+we're in and then uh we will leave or
+ 
+
+ align:start position:0%
+we're in and then uh we will leave or
+enter from P3 or P4 According to which
+
+ align:start position:0%
+enter from P3 or P4 According to which
+ 
+
+ align:start position:0%
+enter from P3 or P4 According to which
+of the two edges you
+
+ align:start position:0%
+of the two edges you
+ 
+
+ align:start position:0%
+of the two edges you
+choose happy no I'm understanding that
+
+ align:start position:0%
+choose happy no I'm understanding that
+ 
+
+ align:start position:0%
+choose happy no I'm understanding that
+we're actually reducing from a sub
+
+ align:start position:0%
+we're actually reducing from a sub
+ 
+
+ align:start position:0%
+we're actually reducing from a sub
+problem with cleanar bipar x 33 graphs
+
+ align:start position:0%
+problem with cleanar bipar x 33 graphs
+ 
+
+ align:start position:0%
+problem with cleanar bipar x 33 graphs
+in that every vertex is connected to at
+
+ align:start position:0%
+in that every vertex is connected to at
+ 
+
+ align:start position:0%
+in that every vertex is connected to at
+least one degre 2
+
+ align:start position:0%
+least one degre 2
+ 
+
+ align:start position:0%
+least one degre 2
+vertex yeah uh
+
+ align:start position:0%
+vertex yeah uh
+ 
+
+ align:start position:0%
+vertex yeah uh
+right so we could say at this point in
+
+ align:start position:0%
+right so we could say at this point in
+ 
+
+ align:start position:0%
+right so we could say at this point in
+fact it's planer by partite Max degree 3
+
+ align:start position:0%
+fact it's planer by partite Max degree 3
+ 
+
+ align:start position:0%
+fact it's planer by partite Max degree 3
+graphs where every degree 3 vertex is
+
+ align:start position:0%
+graphs where every degree 3 vertex is
+ 
+
+ align:start position:0%
+graphs where every degree 3 vertex is
+adjacent to at least to exactly one or
+
+ align:start position:0%
+adjacent to at least to exactly one or
+ 
+
+ align:start position:0%
+adjacent to at least to exactly one or
+no at least one degree 2 vertex uh and
+
+ align:start position:0%
+no at least one degree 2 vertex uh and
+ 
+
+ align:start position:0%
+no at least one degree 2 vertex uh and
+then we can carry that condition through
+
+ align:start position:0%
+then we can carry that condition through
+ 
+
+ align:start position:0%
+then we can carry that condition through
+all the reductions and that would make
+
+ align:start position:0%
+all the reductions and that would make
+ 
+
+ align:start position:0%
+all the reductions and that would make
+this an actual reduction or you can
+
+ align:start position:0%
+this an actual reduction or you can
+ 
+
+ align:start position:0%
+this an actual reduction or you can
+think of this as a reduction going from
+
+ align:start position:0%
+think of this as a reduction going from
+ 
+
+ align:start position:0%
+think of this as a reduction going from
+here just copying all the details yeah
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+other
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+questions okay uh I'm a little confused
+
+ align:start position:0%
+questions okay uh I'm a little confused
+ 
+
+ align:start position:0%
+questions okay uh I'm a little confused
+because there's one more Gadget but I
+
+ align:start position:0%
+because there's one more Gadget but I
+ 
+
+ align:start position:0%
+because there's one more Gadget but I
+didn't seem to use that Gadget so um
+
+ align:start position:0%
+didn't seem to use that Gadget so um
+ 
+
+ align:start position:0%
+didn't seem to use that Gadget so um
+this is a so I'm not not sure whether
+
+ align:start position:0%
+this is a so I'm not not sure whether
+ 
+
+ align:start position:0%
+this is a so I'm not not sure whether
+this is necessary uh but here's another
+
+ align:start position:0%
+this is necessary uh but here's another
+ 
+
+ align:start position:0%
+this is necessary uh but here's another
+thing you can do uh which they were
+
+ align:start position:0%
+thing you can do uh which they were
+ 
+
+ align:start position:0%
+thing you can do uh which they were
+using for the forced edges you can have
+
+ align:start position:0%
+using for the forced edges you can have
+ 
+
+ align:start position:0%
+using for the forced edges you can have
+one wire uh sorry this is the picture
+
+ align:start position:0%
+one wire uh sorry this is the picture
+ 
+
+ align:start position:0%
+one wire uh sorry this is the picture
+you can have one Edge Gadget that
+
+ align:start position:0%
+you can have one Edge Gadget that
+ 
+
+ align:start position:0%
+you can have one Edge Gadget that
+attaches to both ends of the dumbbell so
+
+ align:start position:0%
+attaches to both ends of the dumbbell so
+ 
+
+ align:start position:0%
+attaches to both ends of the dumbbell so
+then you have a choice whether you end
+
+ align:start position:0%
+then you have a choice whether you end
+ 
+
+ align:start position:0%
+then you have a choice whether you end
+up connecting that edge to the bottom of
+
+ align:start position:0%
+up connecting that edge to the bottom of
+ 
+
+ align:start position:0%
+up connecting that edge to the bottom of
+the dumbbell or to the top of the
+
+ align:start position:0%
+the dumbbell or to the top of the
+ 
+
+ align:start position:0%
+the dumbbell or to the top of the
+dumbbell uh sorry this is connecting to
+
+ align:start position:0%
+dumbbell uh sorry this is connecting to
+ 
+
+ align:start position:0%
+dumbbell uh sorry this is connecting to
+the top and this is connecting to the
+
+ align:start position:0%
+the top and this is connecting to the
+ 
+
+ align:start position:0%
+the top and this is connecting to the
+bottom the dumbbell so that's another
+
+ align:start position:0%
+bottom the dumbbell so that's another
+ 
+
+ align:start position:0%
+bottom the dumbbell so that's another
+way to do the same kind of degree 3
+
+ align:start position:0%
+way to do the same kind of degree 3
+ 
+
+ align:start position:0%
+way to do the same kind of degree 3
+vertex you could have uh this guy coming
+
+ align:start position:0%
+vertex you could have uh this guy coming
+ 
+
+ align:start position:0%
+vertex you could have uh this guy coming
+in this is the forced Edge so and the
+
+ align:start position:0%
+in this is the forced Edge so and the
+ 
+
+ align:start position:0%
+in this is the forced Edge so and the
+forc edge has to come to this vertex uh
+
+ align:start position:0%
+forc edge has to come to this vertex uh
+ 
+
+ align:start position:0%
+forc edge has to come to this vertex uh
+you get a Cho so whether you start up
+
+ align:start position:0%
+you get a Cho so whether you start up
+ 
+
+ align:start position:0%
+you get a Cho so whether you start up
+here and then leave along this nonforced
+
+ align:start position:0%
+here and then leave along this nonforced
+ 
+
+ align:start position:0%
+here and then leave along this nonforced
+Edge or you first Traverse down this way
+
+ align:start position:0%
+Edge or you first Traverse down this way
+ 
+
+ align:start position:0%
+Edge or you first Traverse down this way
+and then leave along this nonforced
+
+ align:start position:0%
+and then leave along this nonforced
+ 
+
+ align:start position:0%
+and then leave along this nonforced
+Edge so that's another way to do it but
+
+ align:start position:0%
+Edge so that's another way to do it but
+ 
+
+ align:start position:0%
+Edge so that's another way to do it but
+I it seems just as good as the way I
+
+ align:start position:0%
+I it seems just as good as the way I
+ 
+
+ align:start position:0%
+I it seems just as good as the way I
+described which was to put forced Edge
+
+ align:start position:0%
+described which was to put forced Edge
+ 
+
+ align:start position:0%
+described which was to put forced Edge
+only on one side and then the other two
+
+ align:start position:0%
+only on one side and then the other two
+ 
+
+ align:start position:0%
+only on one side and then the other two
+guys on the other side unless there's a
+
+ align:start position:0%
+guys on the other side unless there's a
+ 
+
+ align:start position:0%
+guys on the other side unless there's a
+par issue it could be that the you know
+
+ align:start position:0%
+par issue it could be that the you know
+ 
+
+ align:start position:0%
+par issue it could be that the you know
+this connection and this connection uh
+
+ align:start position:0%
+this connection and this connection uh
+ 
+
+ align:start position:0%
+this connection and this connection uh
+have the opposite opposite
+
+ align:start position:0%
+have the opposite opposite
+ 
+
+ align:start position:0%
+have the opposite opposite
+parities which is not good because we
+
+ align:start position:0%
+parities which is not good because we
+ 
+
+ align:start position:0%
+parities which is not good because we
+want the two
+
+ align:start position:0%
+want the two
+ 
+
+ align:start position:0%
+want the two
+connections um uh in this case both of
+
+ align:start position:0%
+connections um uh in this case both of
+ 
+
+ align:start position:0%
+connections um uh in this case both of
+these are going to be
+
+ align:start position:0%
+these are going to be
+ 
+
+ align:start position:0%
+these are going to be
+white and in this case both of these are
+
+ align:start position:0%
+white and in this case both of these are
+ 
+
+ align:start position:0%
+white and in this case both of these are
+going to be black so the two non-forced
+
+ align:start position:0%
+going to be black so the two non-forced
+ 
+
+ align:start position:0%
+going to be black so the two non-forced
+edges connect to vertices of the same
+
+ align:start position:0%
+edges connect to vertices of the same
+ 
+
+ align:start position:0%
+edges connect to vertices of the same
+color and I think if you try to attach
+
+ align:start position:0%
+color and I think if you try to attach
+ 
+
+ align:start position:0%
+color and I think if you try to attach
+one of them over here and one of them
+
+ align:start position:0%
+one of them over here and one of them
+ 
+
+ align:start position:0%
+one of them over here and one of them
+over here on a variable they will have
+
+ align:start position:0%
+over here on a variable they will have
+ 
+
+ align:start position:0%
+over here on a variable they will have
+the wrong colors they have opposite
+
+ align:start position:0%
+the wrong colors they have opposite
+ 
+
+ align:start position:0%
+the wrong colors they have opposite
+colors I think that's why you need this
+
+ align:start position:0%
+colors I think that's why you need this
+ 
+
+ align:start position:0%
+colors I think that's why you need this
+gadget CU now the this left connection
+
+ align:start position:0%
+gadget CU now the this left connection
+ 
+
+ align:start position:0%
+gadget CU now the this left connection
+and this other left connection will have
+
+ align:start position:0%
+and this other left connection will have
+ 
+
+ align:start position:0%
+and this other left connection will have
+the same par because this count is odd I
+
+ align:start position:0%
+the same par because this count is odd I
+ 
+
+ align:start position:0%
+the same par because this count is odd I
+think so I think that's why you need it
+
+ align:start position:0%
+think so I think that's why you need it
+ 
+
+ align:start position:0%
+think so I think that's why you need it
+and that preserves parity so it's a bit
+
+ align:start position:0%
+and that preserves parity so it's a bit
+ 
+
+ align:start position:0%
+and that preserves parity so it's a bit
+subtle you have to be careful all the
+
+ align:start position:0%
+subtle you have to be careful all the
+ 
+
+ align:start position:0%
+subtle you have to be careful all the
+connections preserve
+
+ align:start position:0%
+connections preserve
+ 
+
+ align:start position:0%
+connections preserve
+parity
+
+ align:start position:0%
+parity
+ 
+
+ align:start position:0%
+parity
+cool so that was Max degree 3 grid
+
+ align:start position:0%
+cool so that was Max degree 3 grid
+ 
+
+ align:start position:0%
+cool so that was Max degree 3 grid
+graphs any other
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+questions um here is one one motivation
+
+ align:start position:0%
+questions um here is one one motivation
+ 
+
+ align:start position:0%
+questions um here is one one motivation
+that's from this Papa Demetri vasani
+
+ align:start position:0%
+that's from this Papa Demetri vasani
+ 
+
+ align:start position:0%
+that's from this Papa Demetri vasani
+paper for this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+problem related to ukian traveling
+
+ align:start position:0%
+problem related to ukian traveling
+ 
+
+ align:start position:0%
+problem related to ukian traveling
+salesman problem
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+is this notion of degree bounded minimum
+
+ align:start position:0%
+is this notion of degree bounded minimum
+ 
+
+ align:start position:0%
+is this notion of degree bounded minimum
+spanning tree minimum spanning tree
+
+ align:start position:0%
+spanning tree minimum spanning tree
+ 
+
+ align:start position:0%
+spanning tree minimum spanning tree
+normally is a polinomial problem where
+
+ align:start position:0%
+normally is a polinomial problem where
+ 
+
+ align:start position:0%
+normally is a polinomial problem where
+you're given some graph you want to find
+
+ align:start position:0%
+you're given some graph you want to find
+ 
+
+ align:start position:0%
+you're given some graph you want to find
+a spanning tree you know tree that
+
+ align:start position:0%
+a spanning tree you know tree that
+ 
+
+ align:start position:0%
+a spanning tree you know tree that
+visits all the the vertices but it can
+
+ align:start position:0%
+visits all the the vertices but it can
+ 
+
+ align:start position:0%
+visits all the the vertices but it can
+be uh a tree instead of just a path and
+
+ align:start position:0%
+be uh a tree instead of just a path and
+ 
+
+ align:start position:0%
+be uh a tree instead of just a path and
+it's minimum and that it has minimum
+
+ align:start position:0%
+it's minimum and that it has minimum
+ 
+
+ align:start position:0%
+it's minimum and that it has minimum
+total length of all the edges so that's
+
+ align:start position:0%
+total length of all the edges so that's
+ 
+
+ align:start position:0%
+total length of all the edges so that's
+a polinomial problem uh if I say well I
+
+ align:start position:0%
+a polinomial problem uh if I say well I
+ 
+
+ align:start position:0%
+a polinomial problem uh if I say well I
+want a minimum spanning tree where all
+
+ align:start position:0%
+want a minimum spanning tree where all
+ 
+
+ align:start position:0%
+want a minimum spanning tree where all
+of the uh vertices in the tree have Max
+
+ align:start position:0%
+of the uh vertices in the tree have Max
+ 
+
+ align:start position:0%
+of the uh vertices in the tree have Max
+degree two that is hamiltonian path or I
+
+ align:start position:0%
+degree two that is hamiltonian path or I
+ 
+
+ align:start position:0%
+degree two that is hamiltonian path or I
+guess really traveling salesman problem
+
+ align:start position:0%
+guess really traveling salesman problem
+ 
+
+ align:start position:0%
+guess really traveling salesman problem
+so we already proved uh ukian Max degree
+
+ align:start position:0%
+so we already proved uh ukian Max degree
+ 
+
+ align:start position:0%
+so we already proved uh ukian Max degree
+2 uh minimum spanning tree is hard what
+
+ align:start position:0%
+2 uh minimum spanning tree is hard what
+ 
+
+ align:start position:0%
+2 uh minimum spanning tree is hard what
+about Max degree 3 does that somehow
+
+ align:start position:0%
+about Max degree 3 does that somehow
+ 
+
+ align:start position:0%
+about Max degree 3 does that somehow
+does the branching make it easier and
+
+ align:start position:0%
+does the branching make it easier and
+ 
+
+ align:start position:0%
+does the branching make it easier and
+the answer is no you start from this
+
+ align:start position:0%
+the answer is no you start from this
+ 
+
+ align:start position:0%
+the answer is no you start from this
+problem and the cool thing about a Max
+
+ align:start position:0%
+problem and the cool thing about a Max
+ 
+
+ align:start position:0%
+problem and the cool thing about a Max
+degree 3 grid graph is if you look at
+
+ align:start position:0%
+degree 3 grid graph is if you look at
+ 
+
+ align:start position:0%
+degree 3 grid graph is if you look at
+any point
+
+ align:start position:0%
+any point
+ 
+
+ align:start position:0%
+any point
+at most three of its neighboring uh
+
+ align:start position:0%
+at most three of its neighboring uh
+ 
+
+ align:start position:0%
+at most three of its neighboring uh
+spots are actual vertices one of them
+
+ align:start position:0%
+spots are actual vertices one of them
+ 
+
+ align:start position:0%
+spots are actual vertices one of them
+has to be absent in Max degree 3 so what
+
+ align:start position:0%
+has to be absent in Max degree 3 so what
+ 
+
+ align:start position:0%
+has to be absent in Max degree 3 so what
+I'm going to do is add a point really
+
+ align:start position:0%
+I'm going to do is add a point really
+ 
+
+ align:start position:0%
+I'm going to do is add a point really
+close to that
+
+ align:start position:0%
+close to that
+ 
+
+ align:start position:0%
+close to that
+one and now uh you can show in any
+
+ align:start position:0%
+one and now uh you can show in any
+ 
+
+ align:start position:0%
+one and now uh you can show in any
+minimum spaning tree these guys must be
+
+ align:start position:0%
+minimum spaning tree these guys must be
+ 
+
+ align:start position:0%
+minimum spaning tree these guys must be
+connected and uh this one basically has
+
+ align:start position:0%
+connected and uh this one basically has
+ 
+
+ align:start position:0%
+connected and uh this one basically has
+to be a leaf because everything else is
+
+ align:start position:0%
+to be a leaf because everything else is
+ 
+
+ align:start position:0%
+to be a leaf because everything else is
+quite far away I mean at at most you
+
+ align:start position:0%
+quite far away I mean at at most you
+ 
+
+ align:start position:0%
+quite far away I mean at at most you
+have have these guys
+
+ align:start position:0%
+have have these guys
+ 
+
+ align:start position:0%
+have have these guys
+occupied you know that this is
+
+ align:start position:0%
+occupied you know that this is
+ 
+
+ align:start position:0%
+occupied you know that this is
+completely absent so I add this point
+
+ align:start position:0%
+completely absent so I add this point
+ 
+
+ align:start position:0%
+completely absent so I add this point
+I'm going to have to connect this uh it
+
+ align:start position:0%
+I'm going to have to connect this uh it
+ 
+
+ align:start position:0%
+I'm going to have to connect this uh it
+won't be able to connect any other way
+
+ align:start position:0%
+won't be able to connect any other way
+ 
+
+ align:start position:0%
+won't be able to connect any other way
+if I'm if I'm using the shortest
+
+ align:start position:0%
+if I'm if I'm using the shortest
+ 
+
+ align:start position:0%
+if I'm if I'm using the shortest
+possible length and so at that point you
+
+ align:start position:0%
+possible length and so at that point you
+ 
+
+ align:start position:0%
+possible length and so at that point you
+know if this has degree three there's
+
+ align:start position:0%
+know if this has degree three there's
+ 
+
+ align:start position:0%
+know if this has degree three there's
+only two uh incident edges left and so
+
+ align:start position:0%
+only two uh incident edges left and so
+ 
+
+ align:start position:0%
+only two uh incident edges left and so
+it's hamiltonian path again in the grid
+
+ align:start position:0%
+it's hamiltonian path again in the grid
+ 
+
+ align:start position:0%
+it's hamiltonian path again in the grid
+graph so this is why they were motivated
+
+ align:start position:0%
+graph so this is why they were motivated
+ 
+
+ align:start position:0%
+graph so this is why they were motivated
+uh to Define Max degree 3 grid graphs
+
+ align:start position:0%
+uh to Define Max degree 3 grid graphs
+ 
+
+ align:start position:0%
+uh to Define Max degree 3 grid graphs
+and prove that hard
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+cool some more
+
+ align:start position:0%
+cool some more
+ 
+
+ align:start position:0%
+cool some more
+geometry all right uh so for a long time
+
+ align:start position:0%
+geometry all right uh so for a long time
+ 
+
+ align:start position:0%
+geometry all right uh so for a long time
+you know this is all done in the 80s all
+
+ align:start position:0%
+you know this is all done in the 80s all
+ 
+
+ align:start position:0%
+you know this is all done in the 80s all
+the grid graph stuff uh we only had
+
+ align:start position:0%
+the grid graph stuff uh we only had
+ 
+
+ align:start position:0%
+the grid graph stuff uh we only had
+Square
+
+ align:start position:0%
+Square
+ 
+
+ align:start position:0%
+Square
+grids uh we couldn't afford triangles
+
+ align:start position:0%
+grids uh we couldn't afford triangles
+ 
+
+ align:start position:0%
+grids uh we couldn't afford triangles
+back in the day so uh but recently uh
+
+ align:start position:0%
+back in the day so uh but recently uh
+ 
+
+ align:start position:0%
+back in the day so uh but recently uh
+people started to think about triangular
+
+ align:start position:0%
+people started to think about triangular
+ 
+
+ align:start position:0%
+people started to think about triangular
+grids and hex grids those are the only
+
+ align:start position:0%
+grids and hex grids those are the only
+ 
+
+ align:start position:0%
+grids and hex grids those are the only
+tiling regular Eng gon uh so you can
+
+ align:start position:0%
+tiling regular Eng gon uh so you can
+ 
+
+ align:start position:0%
+tiling regular Eng gon uh so you can
+Define the same kind of thing a
+
+ align:start position:0%
+Define the same kind of thing a
+ 
+
+ align:start position:0%
+Define the same kind of thing a
+triangular grid graph a hexagonal grid
+
+ align:start position:0%
+triangular grid graph a hexagonal grid
+ 
+
+ align:start position:0%
+triangular grid graph a hexagonal grid
+graph again you take a set of points in
+
+ align:start position:0%
+graph again you take a set of points in
+ 
+
+ align:start position:0%
+graph again you take a set of points in
+the Triangular lattice or the hex
+
+ align:start position:0%
+the Triangular lattice or the hex
+ 
+
+ align:start position:0%
+the Triangular lattice or the hex
+lattice is the hex actually a lattice
+
+ align:start position:0%
+lattice is the hex actually a lattice
+ 
+
+ align:start position:0%
+lattice is the hex actually a lattice
+well anyway you know what I mean the hex
+
+ align:start position:0%
+well anyway you know what I mean the hex
+ 
+
+ align:start position:0%
+well anyway you know what I mean the hex
+grid um and you um connect any two
+
+ align:start position:0%
+grid um and you um connect any two
+ 
+
+ align:start position:0%
+grid um and you um connect any two
+points when they're unit distance
+
+ align:start position:0%
+points when they're unit distance
+ 
+
+ align:start position:0%
+points when they're unit distance
+apart where that's defined to be one and
+
+ align:start position:0%
+apart where that's defined to be one and
+ 
+
+ align:start position:0%
+apart where that's defined to be one and
+one okay so again we have the notion of
+
+ align:start position:0%
+one okay so again we have the notion of
+ 
+
+ align:start position:0%
+one okay so again we have the notion of
+solid triangular or hex good graphs when
+
+ align:start position:0%
+solid triangular or hex good graphs when
+ 
+
+ align:start position:0%
+solid triangular or hex good graphs when
+there are no holes again we can
+
+ align:start position:0%
+there are no holes again we can
+ 
+
+ align:start position:0%
+there are no holes again we can
+characterize the pixels they're not
+
+ align:start position:0%
+characterize the pixels they're not
+ 
+
+ align:start position:0%
+characterize the pixels they're not
+really pixel hexel and trickles I don't
+
+ align:start position:0%
+really pixel hexel and trickles I don't
+ 
+
+ align:start position:0%
+really pixel hexel and trickles I don't
+know in the paper they're all just
+
+ align:start position:0%
+know in the paper they're all just
+ 
+
+ align:start position:0%
+know in the paper they're all just
+called pixels there's those types of
+
+ align:start position:0%
+called pixels there's those types of
+ 
+
+ align:start position:0%
+called pixels there's those types of
+faces there's the outside face and then
+
+ align:start position:0%
+faces there's the outside face and then
+ 
+
+ align:start position:0%
+faces there's the outside face and then
+there's the whole
+
+ align:start position:0%
+there's the whole
+ 
+
+ align:start position:0%
+there's the whole
+faces h o e not w h o e okay uh cool um
+
+ align:start position:0%
+faces h o e not w h o e okay uh cool um
+ 
+
+ align:start position:0%
+faces h o e not w h o e okay uh cool um
+they they Define some other terms which
+
+ align:start position:0%
+they they Define some other terms which
+ 
+
+ align:start position:0%
+they they Define some other terms which
+I will get
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+to let me tell you what's known about
+
+ align:start position:0%
+to let me tell you what's known about
+ 
+
+ align:start position:0%
+to let me tell you what's known about
+out all of these
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+problems so first thing so these
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+are other grid graphs
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so uh first thing that's known is that
+
+ align:start position:0%
+so uh first thing that's known is that
+ 
+
+ align:start position:0%
+so uh first thing that's known is that
+if you have a solid grid graph
+
+ align:start position:0%
+if you have a solid grid graph
+ 
+
+ align:start position:0%
+if you have a solid grid graph
+uh then the Triangular case is also
+
+ align:start position:0%
+uh then the Triangular case is also
+ 
+
+ align:start position:0%
+uh then the Triangular case is also
+polom so I mentioned solid Square grid
+
+ align:start position:0%
+polom so I mentioned solid Square grid
+ 
+
+ align:start position:0%
+polom so I mentioned solid Square grid
+graphs are easy to solve hamiltonicity
+
+ align:start position:0%
+graphs are easy to solve hamiltonicity
+ 
+
+ align:start position:0%
+graphs are easy to solve hamiltonicity
+in turns out solid triangular grid
+
+ align:start position:0%
+in turns out solid triangular grid
+ 
+
+ align:start position:0%
+in turns out solid triangular grid
+graphs are also easy to solve uh grid
+
+ align:start position:0%
+graphs are also easy to solve uh grid
+ 
+
+ align:start position:0%
+graphs are also easy to solve uh grid
+graphs solve hamiltonicity in almost all
+
+ align:start position:0%
+graphs solve hamiltonicity in almost all
+ 
+
+ align:start position:0%
+graphs solve hamiltonicity in almost all
+of them are hamiltonian certain sense as
+
+ align:start position:0%
+of them are hamiltonian certain sense as
+ 
+
+ align:start position:0%
+of them are hamiltonian certain sense as
+long as you check for some basic things
+
+ align:start position:0%
+long as you check for some basic things
+ 
+
+ align:start position:0%
+long as you check for some basic things
+you shouldn't have uh but hex is
+
+ align:start position:0%
+you shouldn't have uh but hex is
+ 
+
+ align:start position:0%
+you shouldn't have uh but hex is
+open so there's actually a ton of nice
+
+ align:start position:0%
+open so there's actually a ton of nice
+ 
+
+ align:start position:0%
+open so there's actually a ton of nice
+open problem
+
+ align:start position:0%
+open problem
+ 
+
+ align:start position:0%
+open problem
+still uh next
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+case is called super thin
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so what is super thin um super thin
+
+ align:start position:0%
+so what is super thin um super thin
+ 
+
+ align:start position:0%
+so what is super thin um super thin
+means uh there are no
+
+ align:start position:0%
+means uh there are no
+ 
+
+ align:start position:0%
+means uh there are no
+pixels every face is either a hole or
+
+ align:start position:0%
+pixels every face is either a hole or
+ 
+
+ align:start position:0%
+pixels every face is either a hole or
+the outside face okay I don't have an
+
+ align:start position:0%
+the outside face okay I don't have an
+ 
+
+ align:start position:0%
+the outside face okay I don't have an
+example here but this kind of connection
+
+ align:start position:0%
+example here but this kind of connection
+ 
+
+ align:start position:0%
+example here but this kind of connection
+is what you would have in super thin
+
+ align:start position:0%
+is what you would have in super thin
+ 
+
+ align:start position:0%
+is what you would have in super thin
+graphs so you've got uh a whole face
+
+ align:start position:0%
+graphs so you've got uh a whole face
+ 
+
+ align:start position:0%
+graphs so you've got uh a whole face
+here A whole face there uh you shouldn't
+
+ align:start position:0%
+here A whole face there uh you shouldn't
+ 
+
+ align:start position:0%
+here A whole face there uh you shouldn't
+have any of these pixels to be super
+
+ align:start position:0%
+have any of these pixels to be super
+ 
+
+ align:start position:0%
+have any of these pixels to be super
+thin that case turns out to be polom for
+
+ align:start position:0%
+thin that case turns out to be polom for
+ 
+
+ align:start position:0%
+thin that case turns out to be polom for
+squares and hex's open for triangles all
+
+ align:start position:0%
+squares and hex's open for triangles all
+ 
+
+ align:start position:0%
+squares and hex's open for triangles all
+right next
+
+ align:start position:0%
+right next
+ 
+
+ align:start position:0%
+right next
+case is called
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+thin WR the
+
+ align:start position:0%
+thin WR the
+ 
+
+ align:start position:0%
+thin WR the
+implies in the thin case uh both the
+
+ align:start position:0%
+implies in the thin case uh both the
+ 
+
+ align:start position:0%
+implies in the thin case uh both the
+triangle and the square problems are
+
+ align:start position:0%
+triangle and the square problems are
+ 
+
+ align:start position:0%
+triangle and the square problems are
+empty hard hex's are open what does thin
+
+ align:start position:0%
+empty hard hex's are open what does thin
+ 
+
+ align:start position:0%
+empty hard hex's are open what does thin
+mean thin means every vertex is on the
+
+ align:start position:0%
+mean thin means every vertex is on the
+ 
+
+ align:start position:0%
+mean thin means every vertex is on the
+boundary
+
+ align:start position:0%
+boundary
+ 
+
+ align:start position:0%
+boundary
+okay so super thin is something like
+
+ align:start position:0%
+okay so super thin is something like
+ 
+
+ align:start position:0%
+okay so super thin is something like
+every Edge is on the boundary thin is
+
+ align:start position:0%
+every Edge is on the boundary thin is
+ 
+
+ align:start position:0%
+every Edge is on the boundary thin is
+that every vertex is on the boundary so
+
+ align:start position:0%
+that every vertex is on the boundary so
+ 
+
+ align:start position:0%
+that every vertex is on the boundary so
+for example this part here is thin the
+
+ align:start position:0%
+for example this part here is thin the
+ 
+
+ align:start position:0%
+for example this part here is thin the
+boundar is actually drawn in bold here
+
+ align:start position:0%
+boundar is actually drawn in bold here
+ 
+
+ align:start position:0%
+boundar is actually drawn in bold here
+so if if every vertex has bold edges
+
+ align:start position:0%
+so if if every vertex has bold edges
+ 
+
+ align:start position:0%
+so if if every vertex has bold edges
+incident to it then we call that thin so
+
+ align:start position:0%
+incident to it then we call that thin so
+ 
+
+ align:start position:0%
+incident to it then we call that thin so
+it's a little bit thicker than super
+
+ align:start position:0%
+it's a little bit thicker than super
+ 
+
+ align:start position:0%
+it's a little bit thicker than super
+thin uh so uh it's maybe it's also
+
+ align:start position:0%
+thin uh so uh it's maybe it's also
+ 
+
+ align:start position:0%
+thin uh so uh it's maybe it's also
+easier to think in the duel if you if
+
+ align:start position:0%
+easier to think in the duel if you if
+ 
+
+ align:start position:0%
+easier to think in the duel if you if
+you care to if you draw a Vertex for
+
+ align:start position:0%
+you care to if you draw a Vertex for
+ 
+
+ align:start position:0%
+you care to if you draw a Vertex for
+every pixel in the super thin case there
+
+ align:start position:0%
+every pixel in the super thin case there
+ 
+
+ align:start position:0%
+every pixel in the super thin case there
+are no vertices in the duel in the thin
+
+ align:start position:0%
+are no vertices in the duel in the thin
+ 
+
+ align:start position:0%
+are no vertices in the duel in the thin
+case uh The Duel is super
+
+ align:start position:0%
+case uh The Duel is super
+ 
+
+ align:start position:0%
+case uh The Duel is super
+thin I don't know if that's easier to
+
+ align:start position:0%
+thin I don't know if that's easier to
+ 
+
+ align:start position:0%
+thin I don't know if that's easier to
+think about uh but these cases are
+
+ align:start position:0%
+think about uh but these cases are
+ 
+
+ align:start position:0%
+think about uh but these cases are
+actually hard at least in two out of the
+
+ align:start position:0%
+actually hard at least in two out of the
+ 
+
+ align:start position:0%
+actually hard at least in two out of the
+three pictures one of them we have
+
+ align:start position:0%
+three pictures one of them we have
+ 
+
+ align:start position:0%
+three pictures one of them we have
+already proved
+
+ align:start position:0%
+already proved
+ 
+
+ align:start position:0%
+already proved
+um if you have a Max degree 3 grid graph
+
+ align:start position:0%
+um if you have a Max degree 3 grid graph
+ 
+
+ align:start position:0%
+um if you have a Max degree 3 grid graph
+uh it's degree Max degree is three then
+
+ align:start position:0%
+uh it's degree Max degree is three then
+ 
+
+ align:start position:0%
+uh it's degree Max degree is three then
+it it must be on the boundary because of
+
+ align:start position:0%
+it it must be on the boundary because of
+ 
+
+ align:start position:0%
+it it must be on the boundary because of
+that absent pixel so so we already
+
+ align:start position:0%
+that absent pixel so so we already
+ 
+
+ align:start position:0%
+that absent pixel so so we already
+showed the thin case for squares is hard
+
+ align:start position:0%
+showed the thin case for squares is hard
+ 
+
+ align:start position:0%
+showed the thin case for squares is hard
+Max degree 3 implies uh thin for squares
+
+ align:start position:0%
+Max degree 3 implies uh thin for squares
+ 
+
+ align:start position:0%
+Max degree 3 implies uh thin for squares
+and uh so you might ask what about
+
+ align:start position:0%
+and uh so you might ask what about
+ 
+
+ align:start position:0%
+and uh so you might ask what about
+triangles okay so triangles is so
+
+ align:start position:0%
+triangles okay so triangles is so
+ 
+
+ align:start position:0%
+triangles okay so triangles is so
+finally we get to an actual proof um
+
+ align:start position:0%
+finally we get to an actual proof um
+ 
+
+ align:start position:0%
+finally we get to an actual proof um
+it's going to be the same kind of thing
+
+ align:start position:0%
+it's going to be the same kind of thing
+ 
+
+ align:start position:0%
+it's going to be the same kind of thing
+I'll skip this detail but this is the uh
+
+ align:start position:0%
+I'll skip this detail but this is the uh
+ 
+
+ align:start position:0%
+I'll skip this detail but this is the uh
+planer embedding part so you again we're
+
+ align:start position:0%
+planer embedding part so you again we're
+ 
+
+ align:start position:0%
+planer embedding part so you again we're
+going to reduce from bipartite Max to
+
+ align:start position:0%
+going to reduce from bipartite Max to
+ 
+
+ align:start position:0%
+going to reduce from bipartite Max to
+degre 3 planer hamiltonicity as we did
+
+ align:start position:0%
+degre 3 planer hamiltonicity as we did
+ 
+
+ align:start position:0%
+degre 3 planer hamiltonicity as we did
+before and then we're going to draw it
+
+ align:start position:0%
+before and then we're going to draw it
+ 
+
+ align:start position:0%
+before and then we're going to draw it
+in the plane in some kind of parody
+
+ align:start position:0%
+in the plane in some kind of parody
+ 
+
+ align:start position:0%
+in the plane in some kind of parody
+preserving sense with uh edges routed on
+
+ align:start position:0%
+preserving sense with uh edges routed on
+ 
+
+ align:start position:0%
+preserving sense with uh edges routed on
+the Triangular
+
+ align:start position:0%
+the Triangular
+ 
+
+ align:start position:0%
+the Triangular
+grid okay that's not
+
+ align:start position:0%
+grid okay that's not
+ 
+
+ align:start position:0%
+grid okay that's not
+hard then we have uh very similar
+
+ align:start position:0%
+hard then we have uh very similar
+ 
+
+ align:start position:0%
+hard then we have uh very similar
+looking gadgets although in this case a
+
+ align:start position:0%
+looking gadgets although in this case a
+ 
+
+ align:start position:0%
+looking gadgets although in this case a
+Vertex uh can just be a little triangle
+
+ align:start position:0%
+Vertex uh can just be a little triangle
+ 
+
+ align:start position:0%
+Vertex uh can just be a little triangle
+of dots uh The Edge gadg is going to
+
+ align:start position:0%
+of dots uh The Edge gadg is going to
+ 
+
+ align:start position:0%
+of dots uh The Edge gadg is going to
+look pretty similar it's like a ladder
+
+ align:start position:0%
+look pretty similar it's like a ladder
+ 
+
+ align:start position:0%
+look pretty similar it's like a ladder
+but now the ladder has funny rungs on it
+
+ align:start position:0%
+but now the ladder has funny rungs on it
+ 
+
+ align:start position:0%
+but now the ladder has funny rungs on it
+uh turns are just what you would
+
+ align:start position:0%
+uh turns are just what you would
+ 
+
+ align:start position:0%
+uh turns are just what you would
+expect uh notice we get degree five
+
+ align:start position:0%
+expect uh notice we get degree five
+ 
+
+ align:start position:0%
+expect uh notice we get degree five
+here uh but otherwise things are the
+
+ align:start position:0%
+here uh but otherwise things are the
+ 
+
+ align:start position:0%
+here uh but otherwise things are the
+same you can Traverse either in the loop
+
+ align:start position:0%
+same you can Traverse either in the loop
+ 
+
+ align:start position:0%
+same you can Traverse either in the loop
+back configuration when you have this
+
+ align:start position:0%
+back configuration when you have this
+ 
+
+ align:start position:0%
+back configuration when you have this
+pin joint there you'll be forced to turn
+
+ align:start position:0%
+pin joint there you'll be forced to turn
+ 
+
+ align:start position:0%
+pin joint there you'll be forced to turn
+around there or you do or you zigzag all
+
+ align:start position:0%
+around there or you do or you zigzag all
+ 
+
+ align:start position:0%
+around there or you do or you zigzag all
+the way through and then that's used for
+
+ align:start position:0%
+the way through and then that's used for
+ 
+
+ align:start position:0%
+the way through and then that's used for
+present edges so these are the edges you
+
+ align:start position:0%
+present edges so these are the edges you
+ 
+
+ align:start position:0%
+present edges so these are the edges you
+don't use in the hamiltonan these are
+
+ align:start position:0%
+don't use in the hamiltonan these are
+ 
+
+ align:start position:0%
+don't use in the hamiltonan these are
+edges you do use and there are two types
+
+ align:start position:0%
+edges you do use and there are two types
+ 
+
+ align:start position:0%
+edges you do use and there are two types
+of vertices there's the ones uh of one
+
+ align:start position:0%
+of vertices there's the ones uh of one
+ 
+
+ align:start position:0%
+of vertices there's the ones uh of one
+parody where you always meet here you're
+
+ align:start position:0%
+parody where you always meet here you're
+ 
+
+ align:start position:0%
+parody where you always meet here you're
+kind of meeting with three edges but
+
+ align:start position:0%
+kind of meeting with three edges but
+ 
+
+ align:start position:0%
+kind of meeting with three edges but
+you're kind of meeting on a whole Edge
+
+ align:start position:0%
+you're kind of meeting on a whole Edge
+ 
+
+ align:start position:0%
+you're kind of meeting on a whole Edge
+like that and from here you have the
+
+ align:start position:0%
+like that and from here you have the
+ 
+
+ align:start position:0%
+like that and from here you have the
+choice whether you do this or do this
+
+ align:start position:0%
+choice whether you do this or do this
+ 
+
+ align:start position:0%
+choice whether you do this or do this
+two of them will be zigzags one of them
+
+ align:start position:0%
+two of them will be zigzags one of them
+ 
+
+ align:start position:0%
+two of them will be zigzags one of them
+will be uh double back and then there's
+
+ align:start position:0%
+will be uh double back and then there's
+ 
+
+ align:start position:0%
+will be uh double back and then there's
+the other parody class where you only
+
+ align:start position:0%
+the other parody class where you only
+ 
+
+ align:start position:0%
+the other parody class where you only
+have pin joints these are again just
+
+ align:start position:0%
+have pin joints these are again just
+ 
+
+ align:start position:0%
+have pin joints these are again just
+connected by single edges so they act
+
+ align:start position:0%
+connected by single edges so they act
+ 
+
+ align:start position:0%
+connected by single edges so they act
+just like like we had before okay so
+
+ align:start position:0%
+just like like we had before okay so
+ 
+
+ align:start position:0%
+just like like we had before okay so
+pretty much the same reduction but with
+
+ align:start position:0%
+pretty much the same reduction but with
+ 
+
+ align:start position:0%
+pretty much the same reduction but with
+different in some ways this is an even
+
+ align:start position:0%
+different in some ways this is an even
+ 
+
+ align:start position:0%
+different in some ways this is an even
+easier reduction I
+
+ align:start position:0%
+easier reduction I
+ 
+
+ align:start position:0%
+easier reduction I
+think uh cool now that was Max degree
+
+ align:start position:0%
+think uh cool now that was Max degree
+ 
+
+ align:start position:0%
+think uh cool now that was Max degree
+five what about Max degree 4 so here we
+
+ align:start position:0%
+five what about Max degree 4 so here we
+ 
+
+ align:start position:0%
+five what about Max degree 4 so here we
+had degree 5 vertex there if we kind of
+
+ align:start position:0%
+had degree 5 vertex there if we kind of
+ 
+
+ align:start position:0%
+had degree 5 vertex there if we kind of
+do our same trick of spreading them
+
+ align:start position:0%
+do our same trick of spreading them
+ 
+
+ align:start position:0%
+do our same trick of spreading them
+around you end up with degree four at
+
+ align:start position:0%
+around you end up with degree four at
+ 
+
+ align:start position:0%
+around you end up with degree four at
+most and it Act the same and
+
+ align:start position:0%
+most and it Act the same and
+ 
+
+ align:start position:0%
+most and it Act the same and
+the uh vertices we going to explode into
+
+ align:start position:0%
+the uh vertices we going to explode into
+ 
+
+ align:start position:0%
+the uh vertices we going to explode into
+a
+
+ align:start position:0%
+a
+ 
+
+ align:start position:0%
+a
+hexagon and it
+
+ align:start position:0%
+hexagon and it
+ 
+
+ align:start position:0%
+hexagon and it
+works okay so
+
+ align:start position:0%
+works okay so
+ 
+
+ align:start position:0%
+works okay so
+uh I should
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+say Max degree
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+4 triangle is NP
+
+ align:start position:0%
+4 triangle is NP
+ 
+
+ align:start position:0%
+4 triangle is NP
+hard this red should also be thin
+
+ align:start position:0%
+hard this red should also be thin
+ 
+
+ align:start position:0%
+hard this red should also be thin
+previous one may have also been thin but
+
+ align:start position:0%
+previous one may have also been thin but
+ 
+
+ align:start position:0%
+previous one may have also been thin but
+uh again all of the vertices are on the
+
+ align:start position:0%
+uh again all of the vertices are on the
+ 
+
+ align:start position:0%
+uh again all of the vertices are on the
+boundary so this is the thin triangle is
+
+ align:start position:0%
+boundary so this is the thin triangle is
+ 
+
+ align:start position:0%
+boundary so this is the thin triangle is
+hard Max degree four triangle is hard we
+
+ align:start position:0%
+hard Max degree four triangle is hard we
+ 
+
+ align:start position:0%
+hard Max degree four triangle is hard we
+did this one so we've done all the
+
+ align:start position:0%
+did this one so we've done all the
+ 
+
+ align:start position:0%
+did this one so we've done all the
+hardness
+
+ align:start position:0%
+hardness
+ 
+
+ align:start position:0%
+hardness
+proofs okay that will cease to be the
+
+ align:start position:0%
+proofs okay that will cease to be the
+ 
+
+ align:start position:0%
+proofs okay that will cease to be the
+case in a moment uh okay
+
+ align:start position:0%
+case in a moment uh okay
+ 
+
+ align:start position:0%
+case in a moment uh okay
+here's one more thing Max so what about
+
+ align:start position:0%
+here's one more thing Max so what about
+ 
+
+ align:start position:0%
+here's one more thing Max so what about
+hex grids is there any I hav't mention
+
+ align:start position:0%
+hex grids is there any I hav't mention
+ 
+
+ align:start position:0%
+hex grids is there any I hav't mention
+any hardness for hex grids yet uh and
+
+ align:start position:0%
+any hardness for hex grids yet uh and
+ 
+
+ align:start position:0%
+any hardness for hex grids yet uh and
+one thing we know is Max degree 3
+
+ align:start position:0%
+one thing we know is Max degree 3
+ 
+
+ align:start position:0%
+one thing we know is Max degree 3
+already knew squares but also
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+hexagons are NP hard now this is not so
+
+ align:start position:0%
+hexagons are NP hard now this is not so
+ 
+
+ align:start position:0%
+hexagons are NP hard now this is not so
+impressive uh every vertex in HEX grid
+
+ align:start position:0%
+impressive uh every vertex in HEX grid
+ 
+
+ align:start position:0%
+impressive uh every vertex in HEX grid
+has a degree at most three but you can't
+
+ align:start position:0%
+has a degree at most three but you can't
+ 
+
+ align:start position:0%
+has a degree at most three but you can't
+hope for two so that's the best you can
+
+ align:start position:0%
+hope for two so that's the best you can
+ 
+
+ align:start position:0%
+hope for two so that's the best you can
+hope for Max degree characterization
+
+ align:start position:0%
+hope for Max degree characterization
+ 
+
+ align:start position:0%
+hope for Max degree characterization
+with respect to hex grid okay uh this
+
+ align:start position:0%
+with respect to hex grid okay uh this
+ 
+
+ align:start position:0%
+with respect to hex grid okay uh this
+proof is tricky
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um maybe uh before I go there let me
+
+ align:start position:0%
+um maybe uh before I go there let me
+ 
+
+ align:start position:0%
+um maybe uh before I go there let me
+just mention one other result so this is
+
+ align:start position:0%
+just mention one other result so this is
+ 
+
+ align:start position:0%
+just mention one other result so this is
+delayed one other thing is uh one other
+
+ align:start position:0%
+delayed one other thing is uh one other
+ 
+
+ align:start position:0%
+delayed one other thing is uh one other
+notion you can think about for a grid
+
+ align:start position:0%
+notion you can think about for a grid
+ 
+
+ align:start position:0%
+notion you can think about for a grid
+graphs is called polygonal grid graphs
+
+ align:start position:0%
+graphs is called polygonal grid graphs
+ 
+
+ align:start position:0%
+graphs is called polygonal grid graphs
+and that's what's supposed to be
+
+ align:start position:0%
+and that's what's supposed to be
+ 
+
+ align:start position:0%
+and that's what's supposed to be
+Illustrated here polygonal is kind of
+
+ align:start position:0%
+Illustrated here polygonal is kind of
+ 
+
+ align:start position:0%
+Illustrated here polygonal is kind of
+the opposite of super thin so super thin
+
+ align:start position:0%
+the opposite of super thin so super thin
+ 
+
+ align:start position:0%
+the opposite of super thin so super thin
+we had an an edge that had uh non pixel
+
+ align:start position:0%
+we had an an edge that had uh non pixel
+ 
+
+ align:start position:0%
+we had an an edge that had uh non pixel
+on both
+
+ align:start position:0%
+on both
+ 
+
+ align:start position:0%
+on both
+sides in polygonal every Edge has a
+
+ align:start position:0%
+sides in polygonal every Edge has a
+ 
+
+ align:start position:0%
+sides in polygonal every Edge has a
+pixel on at least one of the two sides
+
+ align:start position:0%
+pixel on at least one of the two sides
+ 
+
+ align:start position:0%
+pixel on at least one of the two sides
+okay so you never have you never have an
+
+ align:start position:0%
+okay so you never have you never have an
+ 
+
+ align:start position:0%
+okay so you never have you never have an
+edge between two holes or a hole on the
+
+ align:start position:0%
+edge between two holes or a hole on the
+ 
+
+ align:start position:0%
+edge between two holes or a hole on the
+outside face that's the polygonal
+
+ align:start position:0%
+outside face that's the polygonal
+ 
+
+ align:start position:0%
+outside face that's the polygonal
+situation uh and so that's something you
+
+ align:start position:0%
+situation uh and so that's something you
+ 
+
+ align:start position:0%
+situation uh and so that's something you
+might assume it's sort of like saying
+
+ align:start position:0%
+might assume it's sort of like saying
+ 
+
+ align:start position:0%
+might assume it's sort of like saying
+you had a polygon and then you sort of
+
+ align:start position:0%
+you had a polygon and then you sort of
+ 
+
+ align:start position:0%
+you had a polygon and then you sort of
+took the interior of the polygon whereas
+
+ align:start position:0%
+took the interior of the polygon whereas
+ 
+
+ align:start position:0%
+took the interior of the polygon whereas
+here this was not really a polygon
+
+ align:start position:0%
+here this was not really a polygon
+ 
+
+ align:start position:0%
+here this was not really a polygon
+because it's like there was a doubled
+
+ align:start position:0%
+because it's like there was a doubled
+ 
+
+ align:start position:0%
+because it's like there was a doubled
+Edge there or something that's not
+
+ align:start position:0%
+Edge there or something that's not
+ 
+
+ align:start position:0%
+Edge there or something that's not
+really a nice picture so polygonal is
+
+ align:start position:0%
+really a nice picture so polygonal is
+ 
+
+ align:start position:0%
+really a nice picture so polygonal is
+something you might hope for in in the
+
+ align:start position:0%
+something you might hope for in in the
+ 
+
+ align:start position:0%
+something you might hope for in in the
+Practical applications which we will get
+
+ align:start position:0%
+Practical applications which we will get
+ 
+
+ align:start position:0%
+Practical applications which we will get
+to
+
+ align:start position:0%
+to
+ 
+
+ align:start position:0%
+to
+soon funny thing is uh for polygonal
+
+ align:start position:0%
+soon funny thing is uh for polygonal
+ 
+
+ align:start position:0%
+soon funny thing is uh for polygonal
+triangular grid graphs the problem is
+
+ align:start position:0%
+triangular grid graphs the problem is
+ 
+
+ align:start position:0%
+triangular grid graphs the problem is
+polinomial and for
+
+ align:start position:0%
+polinomial and for
+ 
+
+ align:start position:0%
+polinomial and for
+polygonal uh hex grid graphs the problem
+
+ align:start position:0%
+polygonal uh hex grid graphs the problem
+ 
+
+ align:start position:0%
+polygonal uh hex grid graphs the problem
+is NP
+
+ align:start position:0%
+is NP
+ 
+
+ align:start position:0%
+is NP
+hard and for polygonal Square grid
+
+ align:start position:0%
+hard and for polygonal Square grid
+ 
+
+ align:start position:0%
+hard and for polygonal Square grid
+graphs we don't
+
+ align:start position:0%
+graphs we don't
+ 
+
+ align:start position:0%
+graphs we don't
+know so another open problem
+
+ align:start position:0%
+know so another open problem
+ 
+
+ align:start position:0%
+know so another open problem
+okay I I won't prove this I think again
+
+ align:start position:0%
+okay I I won't prove this I think again
+ 
+
+ align:start position:0%
+okay I I won't prove this I think again
+this is almost always feasible there's
+
+ align:start position:0%
+this is almost always feasible there's
+ 
+
+ align:start position:0%
+this is almost always feasible there's
+almost always a hamiltonian path uh for
+
+ align:start position:0%
+almost always a hamiltonian path uh for
+ 
+
+ align:start position:0%
+almost always a hamiltonian path uh for
+this I'm guessing it follows from the
+
+ align:start position:0%
+this I'm guessing it follows from the
+ 
+
+ align:start position:0%
+this I'm guessing it follows from the
+same proof but uh let's go into this
+
+ align:start position:0%
+same proof but uh let's go into this
+ 
+
+ align:start position:0%
+same proof but uh let's go into this
+this proof Max degree well hex grid
+
+ align:start position:0%
+this proof Max degree well hex grid
+ 
+
+ align:start position:0%
+this proof Max degree well hex grid
+hardness again there's a drawing step
+
+ align:start position:0%
+hardness again there's a drawing step
+ 
+
+ align:start position:0%
+hardness again there's a drawing step
+you're given some bipartite Max degree 3
+
+ align:start position:0%
+you're given some bipartite Max degree 3
+ 
+
+ align:start position:0%
+you're given some bipartite Max degree 3
+graph uh and bipartite planer Max degree
+
+ align:start position:0%
+graph uh and bipartite planer Max degree
+ 
+
+ align:start position:0%
+graph uh and bipartite planer Max degree
+3 graph uh and then we're going to draw
+
+ align:start position:0%
+3 graph uh and then we're going to draw
+ 
+
+ align:start position:0%
+3 graph uh and then we're going to draw
+it on the hex grid um in this case we're
+
+ align:start position:0%
+it on the hex grid um in this case we're
+ 
+
+ align:start position:0%
+it on the hex grid um in this case we're
+going to represent variables by sort of
+
+ align:start position:0%
+going to represent variables by sort of
+ 
+
+ align:start position:0%
+going to represent variables by sort of
+horizontal
+
+ align:start position:0%
+horizontal
+ 
+
+ align:start position:0%
+horizontal
+strips uh just because that's what is a
+
+ align:start position:0%
+strips uh just because that's what is a
+ 
+
+ align:start position:0%
+strips uh just because that's what is a
+little bit easier to do so it turns out
+
+ align:start position:0%
+little bit easier to do so it turns out
+ 
+
+ align:start position:0%
+little bit easier to do so it turns out
+uh I think turns are really annoying on
+
+ align:start position:0%
+uh I think turns are really annoying on
+ 
+
+ align:start position:0%
+uh I think turns are really annoying on
+the hex Grid it's hard to do a turn so
+
+ align:start position:0%
+the hex Grid it's hard to do a turn so
+ 
+
+ align:start position:0%
+the hex Grid it's hard to do a turn so
+uh we're going to focus our turn
+
+ align:start position:0%
+uh we're going to focus our turn
+ 
+
+ align:start position:0%
+uh we're going to focus our turn
+attention Within These Little rectangles
+
+ align:start position:0%
+attention Within These Little rectangles
+ 
+
+ align:start position:0%
+attention Within These Little rectangles
+and turns out you can draw everything in
+
+ align:start position:0%
+and turns out you can draw everything in
+ 
+
+ align:start position:0%
+and turns out you can draw everything in
+such a way that all of the edges are
+
+ align:start position:0%
+such a way that all of the edges are
+ 
+
+ align:start position:0%
+such a way that all of the edges are
+straight lines straight line segments if
+
+ align:start position:0%
+straight lines straight line segments if
+ 
+
+ align:start position:0%
+straight lines straight line segments if
+if you grow the vertices to be these
+
+ align:start position:0%
+if you grow the vertices to be these
+ 
+
+ align:start position:0%
+if you grow the vertices to be these
+longer horizontal things okay so believe
+
+ align:start position:0%
+longer horizontal things okay so believe
+ 
+
+ align:start position:0%
+longer horizontal things okay so believe
+believe
+
+ align:start position:0%
+believe
+ 
+
+ align:start position:0%
+believe
+that uh
+
+ align:start position:0%
+that uh
+ 
+
+ align:start position:0%
+that uh
+then main idea is is a very similar kind
+
+ align:start position:0%
+then main idea is is a very similar kind
+ 
+
+ align:start position:0%
+then main idea is is a very similar kind
+of thing uh in general they in this case
+
+ align:start position:0%
+of thing uh in general they in this case
+ 
+
+ align:start position:0%
+of thing uh in general they in this case
+they're going to draw the pictures and
+
+ align:start position:0%
+they're going to draw the pictures and
+ 
+
+ align:start position:0%
+they're going to draw the pictures and
+they're going to draw all of the forced
+
+ align:start position:0%
+they're going to draw all of the forced
+ 
+
+ align:start position:0%
+they're going to draw all of the forced
+edges that must be in there uh and here
+
+ align:start position:0%
+edges that must be in there uh and here
+ 
+
+ align:start position:0%
+edges that must be in there uh and here
+they haven't drawn the part in the
+
+ align:start position:0%
+they haven't drawn the part in the
+ 
+
+ align:start position:0%
+they haven't drawn the part in the
+middle there's two ways to fill it in
+
+ align:start position:0%
+middle there's two ways to fill it in
+ 
+
+ align:start position:0%
+middle there's two ways to fill it in
+essentially you could zigzag back and
+
+ align:start position:0%
+essentially you could zigzag back and
+ 
+
+ align:start position:0%
+essentially you could zigzag back and
+forth just like before or you could go
+
+ align:start position:0%
+forth just like before or you could go
+ 
+
+ align:start position:0%
+forth just like before or you could go
+there and come back just like before so
+
+ align:start position:0%
+there and come back just like before so
+ 
+
+ align:start position:0%
+there and come back just like before so
+Edge Gadget looks pretty
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+reasonable uh these are some more
+
+ align:start position:0%
+reasonable uh these are some more
+ 
+
+ align:start position:0%
+reasonable uh these are some more
+gadgets uh these are like subroutines
+
+ align:start position:0%
+gadgets uh these are like subroutines
+ 
+
+ align:start position:0%
+gadgets uh these are like subroutines
+they're going to use uh they're named
+
+ align:start position:0%
+they're going to use uh they're named
+ 
+
+ align:start position:0%
+they're going to use uh they're named
+and they have color patterns to give you
+
+ align:start position:0%
+and they have color patterns to give you
+ 
+
+ align:start position:0%
+and they have color patterns to give you
+a sense this is going to be the center
+
+ align:start position:0%
+a sense this is going to be the center
+ 
+
+ align:start position:0%
+a sense this is going to be the center
+of a
+
+ align:start position:0%
+of a
+ 
+
+ align:start position:0%
+of a
+Vertex uh and there's a few different
+
+ align:start position:0%
+Vertex uh and there's a few different
+ 
+
+ align:start position:0%
+Vertex uh and there's a few different
+things you could do with that uh this is
+
+ align:start position:0%
+things you could do with that uh this is
+ 
+
+ align:start position:0%
+things you could do with that uh this is
+some kind of turn Gadget that's what I
+
+ align:start position:0%
+some kind of turn Gadget that's what I
+ 
+
+ align:start position:0%
+some kind of turn Gadget that's what I
+called it they call it uh something a
+
+ align:start position:0%
+called it they call it uh something a
+ 
+
+ align:start position:0%
+called it they call it uh something a
+little different I think a rosette but
+
+ align:start position:0%
+little different I think a rosette but
+ 
+
+ align:start position:0%
+little different I think a rosette but
+uh you can sort of zigzag
+
+ align:start position:0%
+uh you can sort of zigzag
+ 
+
+ align:start position:0%
+uh you can sort of zigzag
+or you can kind of go there and double
+
+ align:start position:0%
+or you can kind of go there and double
+ 
+
+ align:start position:0%
+or you can kind of go there and double
+back but you end up with different
+
+ align:start position:0%
+back but you end up with different
+ 
+
+ align:start position:0%
+back but you end up with different
+orientations at the ends this is what
+
+ align:start position:0%
+orientations at the ends this is what
+ 
+
+ align:start position:0%
+orientations at the ends this is what
+they call a U-turn um again these edges
+
+ align:start position:0%
+they call a U-turn um again these edges
+ 
+
+ align:start position:0%
+they call a U-turn um again these edges
+are forced you can either use it as a
+
+ align:start position:0%
+are forced you can either use it as a
+ 
+
+ align:start position:0%
+are forced you can either use it as a
+zigzag or they could both kind of cancel
+
+ align:start position:0%
+zigzag or they could both kind of cancel
+ 
+
+ align:start position:0%
+zigzag or they could both kind of cancel
+each other out sort of don't don't meet
+
+ align:start position:0%
+each other out sort of don't don't meet
+ 
+
+ align:start position:0%
+each other out sort of don't don't meet
+each other so you get different kind of
+
+ align:start position:0%
+each other so you get different kind of
+ 
+
+ align:start position:0%
+each other so you get different kind of
+connectivity okay with that in mind here
+
+ align:start position:0%
+connectivity okay with that in mind here
+ 
+
+ align:start position:0%
+connectivity okay with that in mind here
+is all the vertex
+
+ align:start position:0%
+is all the vertex
+ 
+
+ align:start position:0%
+is all the vertex
+gadgets uh so I I I I don't know all the
+
+ align:start position:0%
+gadgets uh so I I I I don't know all the
+ 
+
+ align:start position:0%
+gadgets uh so I I I I don't know all the
+details here
+
+ align:start position:0%
+details here
+ 
+
+ align:start position:0%
+details here
+um I think there's a lot of uh cases
+
+ align:start position:0%
+um I think there's a lot of uh cases
+ 
+
+ align:start position:0%
+um I think there's a lot of uh cases
+because of the different ways things
+
+ align:start position:0%
+because of the different ways things
+ 
+
+ align:start position:0%
+because of the different ways things
+could be connected you could have like
+
+ align:start position:0%
+could be connected you could have like
+ 
+
+ align:start position:0%
+could be connected you could have like
+one on top of the notice the dash things
+
+ align:start position:0%
+one on top of the notice the dash things
+ 
+
+ align:start position:0%
+one on top of the notice the dash things
+are the rectangles that I had before
+
+ align:start position:0%
+are the rectangles that I had before
+ 
+
+ align:start position:0%
+are the rectangles that I had before
+normally they'd be really spread out uh
+
+ align:start position:0%
+normally they'd be really spread out uh
+ 
+
+ align:start position:0%
+normally they'd be really spread out uh
+so maybe you have two on the bottom one
+
+ align:start position:0%
+so maybe you have two on the bottom one
+ 
+
+ align:start position:0%
+so maybe you have two on the bottom one
+on the top here we have two on the top
+
+ align:start position:0%
+on the top here we have two on the top
+ 
+
+ align:start position:0%
+on the top here we have two on the top
+one on the bottom and they could be
+
+ align:start position:0%
+one on the bottom and they could be
+ 
+
+ align:start position:0%
+one on the bottom and they could be
+oriented like this or oriented like that
+
+ align:start position:0%
+oriented like this or oriented like that
+ 
+
+ align:start position:0%
+oriented like this or oriented like that
+so there's a lot of different cases as a
+
+ align:start position:0%
+so there's a lot of different cases as a
+ 
+
+ align:start position:0%
+so there's a lot of different cases as a
+result the the core part in the middle
+
+ align:start position:0%
+result the the core part in the middle
+ 
+
+ align:start position:0%
+result the the core part in the middle
+is the same it's pretty much like the
+
+ align:start position:0%
+is the same it's pretty much like the
+ 
+
+ align:start position:0%
+is the same it's pretty much like the
+examples we had before
+
+ align:start position:0%
+examples we had before
+ 
+
+ align:start position:0%
+examples we had before
+of
+
+ align:start position:0%
+of
+ 
+
+ align:start position:0%
+of
+uh essentially like a little 3x3 Square
+
+ align:start position:0%
+uh essentially like a little 3x3 Square
+ 
+
+ align:start position:0%
+uh essentially like a little 3x3 Square
+for the square case or a little triangle
+
+ align:start position:0%
+for the square case or a little triangle
+ 
+
+ align:start position:0%
+for the square case or a little triangle
+in the Triangle case little bit bigger
+
+ align:start position:0%
+in the Triangle case little bit bigger
+ 
+
+ align:start position:0%
+in the Triangle case little bit bigger
+in a hex it's basically a cycle with an
+
+ align:start position:0%
+in a hex it's basically a cycle with an
+ 
+
+ align:start position:0%
+in a hex it's basically a cycle with an
+extra dot in the middle um but then
+
+ align:start position:0%
+extra dot in the middle um but then
+ 
+
+ align:start position:0%
+extra dot in the middle um but then
+there's this is this was a U-turn Gadget
+
+ align:start position:0%
+there's this is this was a U-turn Gadget
+ 
+
+ align:start position:0%
+there's this is this was a U-turn Gadget
+so if something was coming up here uh
+
+ align:start position:0%
+so if something was coming up here uh
+ 
+
+ align:start position:0%
+so if something was coming up here uh
+you could just sort of turn back around
+
+ align:start position:0%
+you could just sort of turn back around
+ 
+
+ align:start position:0%
+you could just sort of turn back around
+if you don't want to use the edge uh I
+
+ align:start position:0%
+if you don't want to use the edge uh I
+ 
+
+ align:start position:0%
+if you don't want to use the edge uh I
+think these are prob well yeah so
+
+ align:start position:0%
+think these are prob well yeah so
+ 
+
+ align:start position:0%
+think these are prob well yeah so
+there's probably also two parody classes
+
+ align:start position:0%
+there's probably also two parody classes
+ 
+
+ align:start position:0%
+there's probably also two parody classes
+uh there's these turn gadgets
+
+ align:start position:0%
+uh there's these turn gadgets
+ 
+
+ align:start position:0%
+uh there's these turn gadgets
+and it
+
+ align:start position:0%
+and it
+ 
+
+ align:start position:0%
+and it
+works okay so but it's
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+complicated I think that's I all I'll
+
+ align:start position:0%
+complicated I think that's I all I'll
+ 
+
+ align:start position:0%
+complicated I think that's I all I'll
+say about various grid graphs yeah I
+
+ align:start position:0%
+say about various grid graphs yeah I
+ 
+
+ align:start position:0%
+say about various grid graphs yeah I
+think you said that thin hexagonal grids
+
+ align:start position:0%
+think you said that thin hexagonal grids
+ 
+
+ align:start position:0%
+think you said that thin hexagonal grids
+were open so th means the vertex every
+
+ align:start position:0%
+were open so th means the vertex every
+ 
+
+ align:start position:0%
+were open so th means the vertex every
+vertex on the
+
+ align:start position:0%
+vertex on the
+ 
+
+ align:start position:0%
+vertex on the
+boundary nebor right no that's it's not
+
+ align:start position:0%
+boundary nebor right no that's it's not
+ 
+
+ align:start position:0%
+boundary nebor right no that's it's not
+necessarily the same so if you have hex
+
+ align:start position:0%
+necessarily the same so if you have hex
+ 
+
+ align:start position:0%
+necessarily the same so if you have hex
+grid I mean this could still be a
+
+ align:start position:0%
+grid I mean this could still be a
+ 
+
+ align:start position:0%
+grid I mean this could still be a
+boundary cycle and you still have degree
+
+ align:start position:0%
+boundary cycle and you still have degree
+ 
+
+ align:start position:0%
+boundary cycle and you still have degree
+3 vertex X something like this part is
+
+ align:start position:0%
+3 vertex X something like this part is
+ 
+
+ align:start position:0%
+3 vertex X something like this part is
+thin I'm guessing you could complete
+
+ align:start position:0%
+thin I'm guessing you could complete
+ 
+
+ align:start position:0%
+thin I'm guessing you could complete
+that so they're probably very special so
+
+ align:start position:0%
+that so they're probably very special so
+ 
+
+ align:start position:0%
+that so they're probably very special so
+I could imagine the thin hex grids are a
+
+ align:start position:0%
+I could imagine the thin hex grids are a
+ 
+
+ align:start position:0%
+I could imagine the thin hex grids are a
+polinomial but it's not known okay uh
+
+ align:start position:0%
+polinomial but it's not known okay uh
+ 
+
+ align:start position:0%
+polinomial but it's not known okay uh
+one more picture this is an actual
+
+ align:start position:0%
+one more picture this is an actual
+ 
+
+ align:start position:0%
+one more picture this is an actual
+explicitly constructed example from that
+
+ align:start position:0%
+explicitly constructed example from that
+ 
+
+ align:start position:0%
+explicitly constructed example from that
+graph to this uh crazy gadgets but now
+
+ align:start position:0%
+graph to this uh crazy gadgets but now
+ 
+
+ align:start position:0%
+graph to this uh crazy gadgets but now
+you can see a little better what the
+
+ align:start position:0%
+you can see a little better what the
+ 
+
+ align:start position:0%
+you can see a little better what the
+rectangles look like if you want to
+
+ align:start position:0%
+rectangles look like if you want to
+ 
+
+ align:start position:0%
+rectangles look like if you want to
+stretch something out you just make
+
+ align:start position:0%
+stretch something out you just make
+ 
+
+ align:start position:0%
+stretch something out you just make
+there's always horizontal wires that you
+
+ align:start position:0%
+there's always horizontal wires that you
+ 
+
+ align:start position:0%
+there's always horizontal wires that you
+can stretch out and I keep them wires
+
+ align:start position:0%
+can stretch out and I keep them wires
+ 
+
+ align:start position:0%
+can stretch out and I keep them wires
+there's horizontal pieces of edge
+
+ align:start position:0%
+there's horizontal pieces of edge
+ 
+
+ align:start position:0%
+there's horizontal pieces of edge
+gadgets that you can just stretch out uh
+
+ align:start position:0%
+gadgets that you can just stretch out uh
+ 
+
+ align:start position:0%
+gadgets that you can just stretch out uh
+so that you end up firing and hitting
+
+ align:start position:0%
+so that you end up firing and hitting
+ 
+
+ align:start position:0%
+so that you end up firing and hitting
+the the next vertex which is this
+
+ align:start position:0%
+the the next vertex which is this
+ 
+
+ align:start position:0%
+the the next vertex which is this
+rectangle and when you spread out the
+
+ align:start position:0%
+rectangle and when you spread out the
+ 
+
+ align:start position:0%
+rectangle and when you spread out the
+rectangles you have to stretch out these
+
+ align:start position:0%
+rectangles you have to stretch out these
+ 
+
+ align:start position:0%
+rectangles you have to stretch out these
+diagonal
+
+ align:start position:0%
+diagonal
+ 
+
+ align:start position:0%
+diagonal
+shots cool that was hex grid graphs why
+
+ align:start position:0%
+shots cool that was hex grid graphs why
+ 
+
+ align:start position:0%
+shots cool that was hex grid graphs why
+do we care about hex grid graphs so much
+
+ align:start position:0%
+do we care about hex grid graphs so much
+ 
+
+ align:start position:0%
+do we care about hex grid graphs so much
+because Settlers of
+
+ align:start position:0%
+because Settlers of
+ 
+
+ align:start position:0%
+because Settlers of
+Katan and various other board games that
+
+ align:start position:0%
+Katan and various other board games that
+ 
+
+ align:start position:0%
+Katan and various other board games that
+have a hex grid um now has anyone here
+
+ align:start position:0%
+have a hex grid um now has anyone here
+ 
+
+ align:start position:0%
+have a hex grid um now has anyone here
+not played of Katon okay a few um Bas
+
+ align:start position:0%
+not played of Katon okay a few um Bas
+ 
+
+ align:start position:0%
+not played of Katon okay a few um Bas
+there there's there's a whole game to it
+
+ align:start position:0%
+there there's there's a whole game to it
+ 
+
+ align:start position:0%
+there there's there's a whole game to it
+but uh
+
+ align:start position:0%
+but uh
+ 
+
+ align:start position:0%
+but uh
+what what I'm going to focus on is uh
+
+ align:start position:0%
+what what I'm going to focus on is uh
+ 
+
+ align:start position:0%
+what what I'm going to focus on is uh
+this card it's called longest
+
+ align:start position:0%
+this card it's called longest
+ 
+
+ align:start position:0%
+this card it's called longest
+road so um in general you're
+
+ align:start position:0%
+road so um in general you're
+ 
+
+ align:start position:0%
+road so um in general you're
+constructing cities don't worry about
+
+ align:start position:0%
+constructing cities don't worry about
+ 
+
+ align:start position:0%
+constructing cities don't worry about
+cities uh but you're constructing these
+
+ align:start position:0%
+cities uh but you're constructing these
+ 
+
+ align:start position:0%
+cities uh but you're constructing these
+Road segments they are edges on the hex
+
+ align:start position:0%
+Road segments they are edges on the hex
+ 
+
+ align:start position:0%
+Road segments they are edges on the hex
+grid and longest road says that you get
+
+ align:start position:0%
+grid and longest road says that you get
+ 
+
+ align:start position:0%
+grid and longest road says that you get
+two points two victory points if you
+
+ align:start position:0%
+two points two victory points if you
+ 
+
+ align:start position:0%
+two points two victory points if you
+have the longest Road meaning the
+
+ align:start position:0%
+have the longest Road meaning the
+ 
+
+ align:start position:0%
+have the longest Road meaning the
+longest path that can be formed using
+
+ align:start position:0%
+longest path that can be formed using
+ 
+
+ align:start position:0%
+longest path that can be formed using
+edges of your color versus edges of
+
+ align:start position:0%
+edges of your color versus edges of
+ 
+
+ align:start position:0%
+edges of your color versus edges of
+anyone else's color then you get two
+
+ align:start position:0%
+anyone else's color then you get two
+ 
+
+ align:start position:0%
+anyone else's color then you get two
+points so here's the idea uh for
+
+ align:start position:0%
+points so here's the idea uh for
+ 
+
+ align:start position:0%
+points so here's the idea uh for
+Settlers of Katan has Randomness and
+
+ align:start position:0%
+Settlers of Katan has Randomness and
+ 
+
+ align:start position:0%
+Settlers of Katan has Randomness and
+stuff like that but again if we look at
+
+ align:start position:0%
+stuff like that but again if we look at
+ 
+
+ align:start position:0%
+stuff like that but again if we look at
+a mate in one problem uh that that goes
+
+ align:start position:0%
+a mate in one problem uh that that goes
+ 
+
+ align:start position:0%
+a mate in one problem uh that that goes
+out the window it's just can I win in
+
+ align:start position:0%
+out the window it's just can I win in
+ 
+
+ align:start position:0%
+out the window it's just can I win in
+this one move there's no Randomness to
+
+ align:start position:0%
+this one move there's no Randomness to
+ 
+
+ align:start position:0%
+this one move there's no Randomness to
+that uh let's suppose you have tons of
+
+ align:start position:0%
+that uh let's suppose you have tons of
+ 
+
+ align:start position:0%
+that uh let's suppose you have tons of
+resources this is what you need to build
+
+ align:start position:0%
+resources this is what you need to build
+ 
+
+ align:start position:0%
+resources this is what you need to build
+a road and inconveniently your opponents
+
+ align:start position:0%
+a road and inconveniently your opponents
+ 
+
+ align:start position:0%
+a road and inconveniently your opponents
+have built cities and things in all of
+
+ align:start position:0%
+have built cities and things in all of
+ 
+
+ align:start position:0%
+have built cities and things in all of
+these white spots
+
+ align:start position:0%
+these white spots
+ 
+
+ align:start position:0%
+these white spots
+so you're not allowed to build roads
+
+ align:start position:0%
+so you're not allowed to build roads
+ 
+
+ align:start position:0%
+so you're not allowed to build roads
+there that's just part of the rules uh
+
+ align:start position:0%
+there that's just part of the rules uh
+ 
+
+ align:start position:0%
+there that's just part of the rules uh
+so that's the opponents form obstacles
+
+ align:start position:0%
+so that's the opponents form obstacles
+ 
+
+ align:start position:0%
+so that's the opponents form obstacles
+and then uh because you have infinite
+
+ align:start position:0%
+and then uh because you have infinite
+ 
+
+ align:start position:0%
+and then uh because you have infinite
+cache you can basically build the entire
+
+ align:start position:0%
+cache you can basically build the entire
+ 
+
+ align:start position:0%
+cache you can basically build the entire
+grid graph here and then to figure out
+
+ align:start position:0%
+grid graph here and then to figure out
+ 
+
+ align:start position:0%
+grid graph here and then to figure out
+whether there's a really long road
+
+ align:start position:0%
+whether there's a really long road
+ 
+
+ align:start position:0%
+whether there's a really long road
+namely uh a road length n where n is the
+
+ align:start position:0%
+namely uh a road length n where n is the
+ 
+
+ align:start position:0%
+namely uh a road length n where n is the
+number of pixels that were not occupied
+
+ align:start position:0%
+number of pixels that were not occupied
+ 
+
+ align:start position:0%
+number of pixels that were not occupied
+by opponents number of dots that are not
+
+ align:start position:0%
+by opponents number of dots that are not
+ 
+
+ align:start position:0%
+by opponents number of dots that are not
+occupied by opponents uh is MP
+
+ align:start position:0%
+occupied by opponents uh is MP
+ 
+
+ align:start position:0%
+occupied by opponents uh is MP
+complete cool and your opponent has a a
+
+ align:start position:0%
+complete cool and your opponent has a a
+ 
+
+ align:start position:0%
+complete cool and your opponent has a a
+slightly shorter road so you really have
+
+ align:start position:0%
+slightly shorter road so you really have
+ 
+
+ align:start position:0%
+slightly shorter road so you really have
+to distinguish uh whether you've uh
+
+ align:start position:0%
+to distinguish uh whether you've uh
+ 
+
+ align:start position:0%
+to distinguish uh whether you've uh
+whether you have the longest road in
+
+ align:start position:0%
+whether you have the longest road in
+ 
+
+ align:start position:0%
+whether you have the longest road in
+fact I like to say Main in zero is MP
+
+ align:start position:0%
+fact I like to say Main in zero is MP
+ 
+
+ align:start position:0%
+fact I like to say Main in zero is MP
+complete deciding whether you've already
+
+ align:start position:0%
+complete deciding whether you've already
+ 
+
+ align:start position:0%
+complete deciding whether you've already
+won the game is MP complete right now
+
+ align:start position:0%
+won the game is MP complete right now
+ 
+
+ align:start position:0%
+won the game is MP complete right now
+you don't even need cash it's just I
+
+ align:start position:0%
+you don't even need cash it's just I
+ 
+
+ align:start position:0%
+you don't even need cash it's just I
+give you a configuration do you have the
+
+ align:start position:0%
+give you a configuration do you have the
+ 
+
+ align:start position:0%
+give you a configuration do you have the
+longest road is empty hard so it's the
+
+ align:start position:0%
+longest road is empty hard so it's the
+ 
+
+ align:start position:0%
+longest road is empty hard so it's the
+only main zero hardness result I know of
+
+ align:start position:0%
+only main zero hardness result I know of
+ 
+
+ align:start position:0%
+only main zero hardness result I know of
+maybe we can find
+
+ align:start position:0%
+maybe we can find
+ 
+
+ align:start position:0%
+maybe we can find
+more okay so that's why hex grids are
+
+ align:start position:0%
+more okay so that's why hex grids are
+ 
+
+ align:start position:0%
+more okay so that's why hex grids are
+cool
+
+ align:start position:0%
+cool
+ 
+
+ align:start position:0%
+cool
+let's do some more games uh here's
+
+ align:start position:0%
+let's do some more games uh here's
+ 
+
+ align:start position:0%
+let's do some more games uh here's
+another Nick puzzle slitherlink their
+
+ align:start position:0%
+another Nick puzzle slitherlink their
+ 
+
+ align:start position:0%
+another Nick puzzle slitherlink their
+more famous ones uh so you're given a
+
+ align:start position:0%
+more famous ones uh so you're given a
+ 
+
+ align:start position:0%
+more famous ones uh so you're given a
+grid of squares each square is either
+
+ align:start position:0%
+grid of squares each square is either
+ 
+
+ align:start position:0%
+grid of squares each square is either
+blank meaning no constraint or there's a
+
+ align:start position:0%
+blank meaning no constraint or there's a
+ 
+
+ align:start position:0%
+blank meaning no constraint or there's a
+number saying there should be exactly
+
+ align:start position:0%
+number saying there should be exactly
+ 
+
+ align:start position:0%
+number saying there should be exactly
+two edges among those four and there
+
+ align:start position:0%
+two edges among those four and there
+ 
+
+ align:start position:0%
+two edges among those four and there
+should be exactly three edges among
+
+ align:start position:0%
+should be exactly three edges among
+ 
+
+ align:start position:0%
+should be exactly three edges among
+those four your goal is to find a cycle
+
+ align:start position:0%
+those four your goal is to find a cycle
+ 
+
+ align:start position:0%
+those four your goal is to find a cycle
+not hamiltonian but just a cycle it
+
+ align:start position:0%
+not hamiltonian but just a cycle it
+ 
+
+ align:start position:0%
+not hamiltonian but just a cycle it
+doesn't visit all the dots uh that
+
+ align:start position:0%
+doesn't visit all the dots uh that
+ 
+
+ align:start position:0%
+doesn't visit all the dots uh that
+satisfies that neighboring constraint so
+
+ align:start position:0%
+satisfies that neighboring constraint so
+ 
+
+ align:start position:0%
+satisfies that neighboring constraint so
+here there were exactly two here there
+
+ align:start position:0%
+here there were exactly two here there
+ 
+
+ align:start position:0%
+here there were exactly two here there
+exactly three uh edges in your
+
+ align:start position:0%
+exactly three uh edges in your
+ 
+
+ align:start position:0%
+exactly three uh edges in your
+cycle okay this is the very first puzzle
+
+ align:start position:0%
+cycle okay this is the very first puzzle
+ 
+
+ align:start position:0%
+cycle okay this is the very first puzzle
+on the website again there are books of
+
+ align:start position:0%
+on the website again there are books of
+ 
+
+ align:start position:0%
+on the website again there are books of
+slitherlink puzzles and here is uh a
+
+ align:start position:0%
+slitherlink puzzles and here is uh a
+ 
+
+ align:start position:0%
+slitherlink puzzles and here is uh a
+little over Overkill of hardness proof
+
+ align:start position:0%
+little over Overkill of hardness proof
+ 
+
+ align:start position:0%
+little over Overkill of hardness proof
+but in one slide uh so this is a
+
+ align:start position:0%
+but in one slide uh so this is a
+ 
+
+ align:start position:0%
+but in one slide uh so this is a
+reduction from hamiltonicity
+
+ align:start position:0%
+reduction from hamiltonicity
+ 
+
+ align:start position:0%
+reduction from hamiltonicity
+in planer graphs so you take any planer
+
+ align:start position:0%
+in planer graphs so you take any planer
+ 
+
+ align:start position:0%
+in planer graphs so you take any planer
+graph and draw it in the grid this is
+
+ align:start position:0%
+graph and draw it in the grid this is
+ 
+
+ align:start position:0%
+graph and draw it in the grid this is
+one of the very first steps we did
+
+ align:start position:0%
+one of the very first steps we did
+ 
+
+ align:start position:0%
+one of the very first steps we did
+today um and then if you do that there
+
+ align:start position:0%
+today um and then if you do that there
+ 
+
+ align:start position:0%
+today um and then if you do that there
+are two types of vertices there's the
+
+ align:start position:0%
+are two types of vertices there's the
+ 
+
+ align:start position:0%
+are two types of vertices there's the
+ones you have to visit and there's the
+
+ align:start position:0%
+ones you have to visit and there's the
+ 
+
+ align:start position:0%
+ones you have to visit and there's the
+ones you don't have to visit now we know
+
+ align:start position:0%
+ones you don't have to visit now we know
+ 
+
+ align:start position:0%
+ones you don't have to visit now we know
+grid graphs are hard so we could
+
+ align:start position:0%
+grid graphs are hard so we could
+ 
+
+ align:start position:0%
+grid graphs are hard so we could
+actually assume all of the vertices have
+
+ align:start position:0%
+actually assume all of the vertices have
+ 
+
+ align:start position:0%
+actually assume all of the vertices have
+to be visited but uh for whatever reason
+
+ align:start position:0%
+to be visited but uh for whatever reason
+ 
+
+ align:start position:0%
+to be visited but uh for whatever reason
+this proof did not do that probably at
+
+ align:start position:0%
+this proof did not do that probably at
+ 
+
+ align:start position:0%
+this proof did not do that probably at
+that this was back in 2000 so at that
+
+ align:start position:0%
+that this was back in 2000 so at that
+ 
+
+ align:start position:0%
+that this was back in 2000 so at that
+point maybe it was not so well
+
+ align:start position:0%
+point maybe it was not so well
+ 
+
+ align:start position:0%
+point maybe it was not so well
+known uh but these days grid graph
+
+ align:start position:0%
+known uh but these days grid graph
+ 
+
+ align:start position:0%
+known uh but these days grid graph
+Hamilton is used a lot but probably not
+
+ align:start position:0%
+Hamilton is used a lot but probably not
+ 
+
+ align:start position:0%
+Hamilton is used a lot but probably not
+so much then uh so anyway there's this
+
+ align:start position:0%
+so much then uh so anyway there's this
+ 
+
+ align:start position:0%
+so much then uh so anyway there's this
+gadget which is uh you can do whatever
+
+ align:start position:0%
+gadget which is uh you can do whatever
+ 
+
+ align:start position:0%
+gadget which is uh you can do whatever
+you want basically uh these are the
+
+ align:start position:0%
+you want basically uh these are the
+ 
+
+ align:start position:0%
+you want basically uh these are the
+vertices that don't need to be visited
+
+ align:start position:0%
+vertices that don't need to be visited
+ 
+
+ align:start position:0%
+vertices that don't need to be visited
+the key Gadget is this one so let's
+
+ align:start position:0%
+the key Gadget is this one so let's
+ 
+
+ align:start position:0%
+the key Gadget is this one so let's
+focus our attention here we have these
+
+ align:start position:0%
+focus our attention here we have these
+ 
+
+ align:start position:0%
+focus our attention here we have these
+ones which means the cycle must come
+
+ align:start position:0%
+ones which means the cycle must come
+ 
+
+ align:start position:0%
+ones which means the cycle must come
+here and so collectively these are going
+
+ align:start position:0%
+here and so collectively these are going
+ 
+
+ align:start position:0%
+here and so collectively these are going
+to form hamiltonian cycle constraints
+
+ align:start position:0%
+to form hamiltonian cycle constraints
+ 
+
+ align:start position:0%
+to form hamiltonian cycle constraints
+you're building a cycle and you have to
+
+ align:start position:0%
+you're building a cycle and you have to
+ 
+
+ align:start position:0%
+you're building a cycle and you have to
+visit these ones now it turns out no
+
+ align:start position:0%
+visit these ones now it turns out no
+ 
+
+ align:start position:0%
+visit these ones now it turns out no
+matter which end you come in and which
+
+ align:start position:0%
+matter which end you come in and which
+ 
+
+ align:start position:0%
+matter which end you come in and which
+end you leave you can visit all of the
+
+ align:start position:0%
+end you leave you can visit all of the
+ 
+
+ align:start position:0%
+end you leave you can visit all of the
+ones you can be adjacent to all of the
+
+ align:start position:0%
+ones you can be adjacent to all of the
+ 
+
+ align:start position:0%
+ones you can be adjacent to all of the
+ones so with different turns are going
+
+ align:start position:0%
+ones so with different turns are going
+ 
+
+ align:start position:0%
+ones so with different turns are going
+straight and so if there is a
+
+ align:start position:0%
+straight and so if there is a
+ 
+
+ align:start position:0%
+straight and so if there is a
+hamiltonian cycle you'll be able to
+
+ align:start position:0%
+hamiltonian cycle you'll be able to
+ 
+
+ align:start position:0%
+hamiltonian cycle you'll be able to
+visit all the
+
+ align:start position:0%
+visit all the
+ 
+
+ align:start position:0%
+visit all the
+ones and conversely if you can visit all
+
+ align:start position:0%
+ones and conversely if you can visit all
+ 
+
+ align:start position:0%
+ones and conversely if you can visit all
+the ones that must be a hamiltonian
+
+ align:start position:0%
+the ones that must be a hamiltonian
+ 
+
+ align:start position:0%
+the ones that must be a hamiltonian
+cycle the one extra thing we need to say
+
+ align:start position:0%
+cycle the one extra thing we need to say
+ 
+
+ align:start position:0%
+cycle the one extra thing we need to say
+uh if you just glue these gadgets
+
+ align:start position:0%
+uh if you just glue these gadgets
+ 
+
+ align:start position:0%
+uh if you just glue these gadgets
+together then there's no uh you can go
+
+ align:start position:0%
+together then there's no uh you can go
+ 
+
+ align:start position:0%
+together then there's no uh you can go
+from anywhere to anywhere uh so you just
+
+ align:start position:0%
+from anywhere to anywhere uh so you just
+ 
+
+ align:start position:0%
+from anywhere to anywhere uh so you just
+add in some zeros here if you don't want
+
+ align:start position:0%
+add in some zeros here if you don't want
+ 
+
+ align:start position:0%
+add in some zeros here if you don't want
+there to be a connection from left to
+
+ align:start position:0%
+there to be a connection from left to
+ 
+
+ align:start position:0%
+there to be a connection from left to
+right so you can use that to delineate
+
+ align:start position:0%
+right so you can use that to delineate
+ 
+
+ align:start position:0%
+right so you can use that to delineate
+the boundary so this could actually do a
+
+ align:start position:0%
+the boundary so this could actually do a
+ 
+
+ align:start position:0%
+the boundary so this could actually do a
+subgraph of a grid graph even more
+
+ align:start position:0%
+subgraph of a grid graph even more
+ 
+
+ align:start position:0%
+subgraph of a grid graph even more
+special uh or you leave it clear if
+
+ align:start position:0%
+special uh or you leave it clear if
+ 
+
+ align:start position:0%
+special uh or you leave it clear if
+there's an edge so you get a picture
+
+ align:start position:0%
+there's an edge so you get a picture
+ 
+
+ align:start position:0%
+there's an edge so you get a picture
+like this in this case they're using
+
+ align:start position:0%
+like this in this case they're using
+ 
+
+ align:start position:0%
+like this in this case they're using
+these bunch of zeros to say well you you
+
+ align:start position:0%
+these bunch of zeros to say well you you
+ 
+
+ align:start position:0%
+these bunch of zeros to say well you you
+don't have to visit these pixels uh
+
+ align:start position:0%
+don't have to visit these pixels uh
+ 
+
+ align:start position:0%
+don't have to visit these pixels uh
+because they're just simulating a big
+
+ align:start position:0%
+because they're just simulating a big
+ 
+
+ align:start position:0%
+because they're just simulating a big
+Edge but we already have infrastructure
+
+ align:start position:0%
+Edge but we already have infrastructure
+ 
+
+ align:start position:0%
+Edge but we already have infrastructure
+to simulate edges we don't really need
+
+ align:start position:0%
+to simulate edges we don't really need
+ 
+
+ align:start position:0%
+to simulate edges we don't really need
+that okay so that's really easy
+
+ align:start position:0%
+that okay so that's really easy
+ 
+
+ align:start position:0%
+that okay so that's really easy
+proof uh I would say in general what you
+
+ align:start position:0%
+proof uh I would say in general what you
+ 
+
+ align:start position:0%
+proof uh I would say in general what you
+have to be careful about here is that
+
+ align:start position:0%
+have to be careful about here is that
+ 
+
+ align:start position:0%
+have to be careful about here is that
+edges are free because in hamiltonian
+
+ align:start position:0%
+edges are free because in hamiltonian
+ 
+
+ align:start position:0%
+edges are free because in hamiltonian
+cycle you're not supposed to pay for the
+
+ align:start position:0%
+cycle you're not supposed to pay for the
+ 
+
+ align:start position:0%
+cycle you're not supposed to pay for the
+edges you just have to visit every
+
+ align:start position:0%
+edges you just have to visit every
+ 
+
+ align:start position:0%
+edges you just have to visit every
+vertex uh but that's really easy in this
+
+ align:start position:0%
+vertex uh but that's really easy in this
+ 
+
+ align:start position:0%
+vertex uh but that's really easy in this
+kind of setup uh another Nick puzzle uh
+
+ align:start position:0%
+kind of setup uh another Nick puzzle uh
+ 
+
+ align:start position:0%
+kind of setup uh another Nick puzzle uh
+Hashi kako uh bridge building you have a
+
+ align:start position:0%
+Hashi kako uh bridge building you have a
+ 
+
+ align:start position:0%
+Hashi kako uh bridge building you have a
+bunch of dots in the plane each dot has
+
+ align:start position:0%
+bunch of dots in the plane each dot has
+ 
+
+ align:start position:0%
+bunch of dots in the plane each dot has
+a number on it uh specifying a degree
+
+ align:start position:0%
+a number on it uh specifying a degree
+ 
+
+ align:start position:0%
+a number on it uh specifying a degree
+request and your goal is to make a
+
+ align:start position:0%
+request and your goal is to make a
+ 
+
+ align:start position:0%
+request and your goal is to make a
+connected
+
+ align:start position:0%
+connected
+ 
+
+ align:start position:0%
+connected
+structure uh it looks like it's usually
+
+ align:start position:0%
+structure uh it looks like it's usually
+ 
+
+ align:start position:0%
+structure uh it looks like it's usually
+a tree but that's not part of the
+
+ align:start position:0%
+a tree but that's not part of the
+ 
+
+ align:start position:0%
+a tree but that's not part of the
+constraints uh where every vertex has
+
+ align:start position:0%
+constraints uh where every vertex has
+ 
+
+ align:start position:0%
+constraints uh where every vertex has
+that degree you can use multiple edges
+
+ align:start position:0%
+that degree you can use multiple edges
+ 
+
+ align:start position:0%
+that degree you can use multiple edges
+you can build multiple Bridges between
+
+ align:start position:0%
+you can build multiple Bridges between
+ 
+
+ align:start position:0%
+you can build multiple Bridges between
+the same two cities uh and so there's
+
+ align:start position:0%
+the same two cities uh and so there's
+ 
+
+ align:start position:0%
+the same two cities uh and so there's
+four here incident to that eight
+
+ align:start position:0%
+four here incident to that eight
+ 
+
+ align:start position:0%
+four here incident to that eight
+incident to that and everything's
+
+ align:start position:0%
+incident to that and everything's
+ 
+
+ align:start position:0%
+incident to that and everything's
+orthogonal you can only build horizontal
+
+ align:start position:0%
+orthogonal you can only build horizontal
+ 
+
+ align:start position:0%
+orthogonal you can only build horizontal
+vertical you can't build a bridge like
+
+ align:start position:0%
+vertical you can't build a bridge like
+ 
+
+ align:start position:0%
+vertical you can't build a bridge like
+this hard to make not allowed to make
+
+ align:start position:0%
+this hard to make not allowed to make
+ 
+
+ align:start position:0%
+this hard to make not allowed to make
+turns yeah think the standard posing you
+
+ align:start position:0%
+turns yeah think the standard posing you
+ 
+
+ align:start position:0%
+turns yeah think the standard posing you
+only get two parallel edges per pair ah
+
+ align:start position:0%
+only get two parallel edges per pair ah
+ 
+
+ align:start position:0%
+only get two parallel edges per pair ah
+and okay so also standard is that Max uh
+
+ align:start position:0%
+and okay so also standard is that Max uh
+ 
+
+ align:start position:0%
+and okay so also standard is that Max uh
+double edge no Triple Edge thank you I
+
+ align:start position:0%
+double edge no Triple Edge thank you I
+ 
+
+ align:start position:0%
+double edge no Triple Edge thank you I
+obviously haven't actually played um it
+
+ align:start position:0%
+obviously haven't actually played um it
+ 
+
+ align:start position:0%
+obviously haven't actually played um it
+won't matter in this reduction so here
+
+ align:start position:0%
+won't matter in this reduction so here
+ 
+
+ align:start position:0%
+won't matter in this reduction so here
+we are reducing from Hamilton in Grid
+
+ align:start position:0%
+we are reducing from Hamilton in Grid
+ 
+
+ align:start position:0%
+we are reducing from Hamilton in Grid
+graphs so these are edges that we might
+
+ align:start position:0%
+graphs so these are edges that we might
+ 
+
+ align:start position:0%
+graphs so these are edges that we might
+want to allow uh in general we're going
+
+ align:start position:0%
+want to allow uh in general we're going
+ 
+
+ align:start position:0%
+want to allow uh in general we're going
+to use these little ones to delineate
+
+ align:start position:0%
+to use these little ones to delineate
+ 
+
+ align:start position:0%
+to use these little ones to delineate
+the boundary it's just the same kind of
+
+ align:start position:0%
+the boundary it's just the same kind of
+ 
+
+ align:start position:0%
+the boundary it's just the same kind of
+trick we use uh here with ukian degree 3
+
+ align:start position:0%
+trick we use uh here with ukian degree 3
+ 
+
+ align:start position:0%
+trick we use uh here with ukian degree 3
+MST we added the little dot just off to
+
+ align:start position:0%
+MST we added the little dot just off to
+ 
+
+ align:start position:0%
+MST we added the little dot just off to
+the side uh there it's not a metric
+
+ align:start position:0%
+the side uh there it's not a metric
+ 
+
+ align:start position:0%
+the side uh there it's not a metric
+problem here so we're just adding it one
+
+ align:start position:0%
+problem here so we're just adding it one
+ 
+
+ align:start position:0%
+problem here so we're just adding it one
+unit over that delineates the boundary
+
+ align:start position:0%
+unit over that delineates the boundary
+ 
+
+ align:start position:0%
+unit over that delineates the boundary
+that basically is forced to connect into
+
+ align:start position:0%
+that basically is forced to connect into
+ 
+
+ align:start position:0%
+that basically is forced to connect into
+the only uh neighbor you if you tried to
+
+ align:start position:0%
+the only uh neighbor you if you tried to
+ 
+
+ align:start position:0%
+the only uh neighbor you if you tried to
+do this kind of connection you'd end up
+
+ align:start position:0%
+do this kind of connection you'd end up
+ 
+
+ align:start position:0%
+do this kind of connection you'd end up
+being disconnected you just get sing
+
+ align:start position:0%
+being disconnected you just get sing
+ 
+
+ align:start position:0%
+being disconnected you just get sing
+single edge there because ones will only
+
+ align:start position:0%
+single edge there because ones will only
+ 
+
+ align:start position:0%
+single edge there because ones will only
+face ones so uh sorry the other
+
+ align:start position:0%
+face ones so uh sorry the other
+ 
+
+ align:start position:0%
+face ones so uh sorry the other
+constraint is uh you're not allowed of
+
+ align:start position:0%
+constraint is uh you're not allowed of
+ 
+
+ align:start position:0%
+constraint is uh you're not allowed of
+Crossing
+
+ align:start position:0%
+Crossing
+ 
+
+ align:start position:0%
+Crossing
+Bridges uh that won't matter here uh so
+
+ align:start position:0%
+Bridges uh that won't matter here uh so
+ 
+
+ align:start position:0%
+Bridges uh that won't matter here uh so
+we delineate the boundary at the ones
+
+ align:start position:0%
+we delineate the boundary at the ones
+ 
+
+ align:start position:0%
+we delineate the boundary at the ones
+and then every other vertex is going to
+
+ align:start position:0%
+and then every other vertex is going to
+ 
+
+ align:start position:0%
+and then every other vertex is going to
+have value two plus the number of
+
+ align:start position:0%
+have value two plus the number of
+ 
+
+ align:start position:0%
+have value two plus the number of
+boundary edges incident to it so here it
+
+ align:start position:0%
+boundary edges incident to it so here it
+ 
+
+ align:start position:0%
+boundary edges incident to it so here it
+happens to be four here it happens to be
+
+ align:start position:0%
+happens to be four here it happens to be
+ 
+
+ align:start position:0%
+happens to be four here it happens to be
+three so I could have gone like this
+
+ align:start position:0%
+three so I could have gone like this
+ 
+
+ align:start position:0%
+three so I could have gone like this
+that would have been fine but in this
+
+ align:start position:0%
+that would have been fine but in this
+ 
+
+ align:start position:0%
+that would have been fine but in this
+cycle I happened to go around that
+
+ align:start position:0%
+cycle I happened to go around that
+ 
+
+ align:start position:0%
+cycle I happened to go around that
+way okay that's representing this cycle
+
+ align:start position:0%
+way okay that's representing this cycle
+ 
+
+ align:start position:0%
+way okay that's representing this cycle
+so again very easy this shows you how
+
+ align:start position:0%
+so again very easy this shows you how
+ 
+
+ align:start position:0%
+so again very easy this shows you how
+useful it is once you have grid graphs
+
+ align:start position:0%
+useful it is once you have grid graphs
+ 
+
+ align:start position:0%
+useful it is once you have grid graphs
+you can do any problem on any grid
+
+ align:start position:0%
+you can do any problem on any grid
+ 
+
+ align:start position:0%
+you can do any problem on any grid
+pretty much that has any kind of tour
+
+ align:start position:0%
+pretty much that has any kind of tour
+ 
+
+ align:start position:0%
+pretty much that has any kind of tour
+like thing uh that will be hard using
+
+ align:start position:0%
+like thing uh that will be hard using
+ 
+
+ align:start position:0%
+like thing uh that will be hard using
+these reductions so that's why we
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+care all right uh here's some practical
+
+ align:start position:0%
+care all right uh here's some practical
+ 
+
+ align:start position:0%
+care all right uh here's some practical
+motivation well I have a game here but
+
+ align:start position:0%
+motivation well I have a game here but
+ 
+
+ align:start position:0%
+motivation well I have a game here but
+suppose you're mowing your lawn and so
+
+ align:start position:0%
+suppose you're mowing your lawn and so
+ 
+
+ align:start position:0%
+suppose you're mowing your lawn and so
+usually a lawnmower has a circular
+
+ align:start position:0%
+usually a lawnmower has a circular
+ 
+
+ align:start position:0%
+usually a lawnmower has a circular
+cutting tool but uh in this game it
+
+ align:start position:0%
+cutting tool but uh in this game it
+ 
+
+ align:start position:0%
+cutting tool but uh in this game it
+happens to be a square cutting tool it's
+
+ align:start position:0%
+happens to be a square cutting tool it's
+ 
+
+ align:start position:0%
+happens to be a square cutting tool it's
+basically the same and you have some
+
+ align:start position:0%
+basically the same and you have some
+ 
+
+ align:start position:0%
+basically the same and you have some
+polygon with holes that you want to uh
+
+ align:start position:0%
+polygon with holes that you want to uh
+ 
+
+ align:start position:0%
+polygon with holes that you want to uh
+mow uh there's actually two versions of
+
+ align:start position:0%
+mow uh there's actually two versions of
+ 
+
+ align:start position:0%
+mow uh there's actually two versions of
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+problem
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh and they were introduced by Aran Fe
+
+ align:start position:0%
+uh and they were introduced by Aran Fe
+ 
+
+ align:start position:0%
+uh and they were introduced by Aran Fe
+and Mitchell 2000 uh one's called lawn
+
+ align:start position:0%
+and Mitchell 2000 uh one's called lawn
+ 
+
+ align:start position:0%
+and Mitchell 2000 uh one's called lawn
+mowing
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so lawn mowing you're given a a polygon
+
+ align:start position:0%
+so lawn mowing you're given a a polygon
+ 
+
+ align:start position:0%
+so lawn mowing you're given a a polygon
+you you have to visit let's say if we're
+
+ align:start position:0%
+you you have to visit let's say if we're
+ 
+
+ align:start position:0%
+you you have to visit let's say if we're
+using a square cutter you have to visit
+
+ align:start position:0%
+using a square cutter you have to visit
+ 
+
+ align:start position:0%
+using a square cutter you have to visit
+every pixel of the polygon you have to
+
+ align:start position:0%
+every pixel of the polygon you have to
+ 
+
+ align:start position:0%
+every pixel of the polygon you have to
+visit the entire you're moving a square
+
+ align:start position:0%
+visit the entire you're moving a square
+ 
+
+ align:start position:0%
+visit the entire you're moving a square
+unit square around you've got to visit
+
+ align:start position:0%
+unit square around you've got to visit
+ 
+
+ align:start position:0%
+unit square around you've got to visit
+everything to cut the entire lawn but
+
+ align:start position:0%
+everything to cut the entire lawn but
+ 
+
+ align:start position:0%
+everything to cut the entire lawn but
+you're also allowed to leave the polygon
+
+ align:start position:0%
+you're also allowed to leave the polygon
+ 
+
+ align:start position:0%
+you're also allowed to leave the polygon
+because would for lawnmower you can go
+
+ align:start position:0%
+because would for lawnmower you can go
+ 
+
+ align:start position:0%
+because would for lawnmower you can go
+outside the grass you can go onto the
+
+ align:start position:0%
+outside the grass you can go onto the
+ 
+
+ align:start position:0%
+outside the grass you can go onto the
+pavement most lawnmowers that doesn't
+
+ align:start position:0%
+pavement most lawnmowers that doesn't
+ 
+
+ align:start position:0%
+pavement most lawnmowers that doesn't
+break it so that's called lawn mowing uh
+
+ align:start position:0%
+break it so that's called lawn mowing uh
+ 
+
+ align:start position:0%
+break it so that's called lawn mowing uh
+you can go outside if you want
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and the other problem is called
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+milling and with Milling you can't go
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+outside okay that video game is probably
+
+ align:start position:0%
+outside okay that video game is probably
+ 
+
+ align:start position:0%
+outside okay that video game is probably
+some hybrid between these two problems
+
+ align:start position:0%
+some hybrid between these two problems
+ 
+
+ align:start position:0%
+some hybrid between these two problems
+but both problems have been considered a
+
+ align:start position:0%
+but both problems have been considered a
+ 
+
+ align:start position:0%
+but both problems have been considered a
+lot especially from an approximation
+
+ align:start position:0%
+lot especially from an approximation
+ 
+
+ align:start position:0%
+lot especially from an approximation
+standpoint uh but just from a uh there
+
+ align:start position:0%
+standpoint uh but just from a uh there
+ 
+
+ align:start position:0%
+standpoint uh but just from a uh there
+are lots of situations where this kind
+
+ align:start position:0%
+are lots of situations where this kind
+ 
+
+ align:start position:0%
+are lots of situations where this kind
+of problem comes up suppose you're laser
+
+ align:start position:0%
+of problem comes up suppose you're laser
+ 
+
+ align:start position:0%
+of problem comes up suppose you're laser
+cutting uh this is one of the first
+
+ align:start position:0%
+cutting uh this is one of the first
+ 
+
+ align:start position:0%
+cutting uh this is one of the first
+laser cutter projects we did with George
+
+ align:start position:0%
+laser cutter projects we did with George
+ 
+
+ align:start position:0%
+laser cutter projects we did with George
+Hart back in 2003
+
+ align:start position:0%
+Hart back in 2003
+ 
+
+ align:start position:0%
+Hart back in 2003
+um where cutting out these double
+
+ align:start position:0%
+um where cutting out these double
+ 
+
+ align:start position:0%
+um where cutting out these double
+two-headed salamanders like that and
+
+ align:start position:0%
+two-headed salamanders like that and
+ 
+
+ align:start position:0%
+two-headed salamanders like that and
+then assembling them if you've ever been
+
+ align:start position:0%
+then assembling them if you've ever been
+ 
+
+ align:start position:0%
+then assembling them if you've ever been
+to G6 in sta it's hanging there uh so
+
+ align:start position:0%
+to G6 in sta it's hanging there uh so
+ 
+
+ align:start position:0%
+to G6 in sta it's hanging there uh so
+you can think of this laser cutting
+
+ align:start position:0%
+you can think of this laser cutting
+ 
+
+ align:start position:0%
+you can think of this laser cutting
+problem is you have a lot of dots and
+
+ align:start position:0%
+problem is you have a lot of dots and
+ 
+
+ align:start position:0%
+problem is you have a lot of dots and
+you have to cut them all um that is
+
+ align:start position:0%
+you have to cut them all um that is
+ 
+
+ align:start position:0%
+you have to cut them all um that is
+pretty literally what happens to the
+
+ align:start position:0%
+pretty literally what happens to the
+ 
+
+ align:start position:0%
+pretty literally what happens to the
+laser cutter is pulsing with little dots
+
+ align:start position:0%
+laser cutter is pulsing with little dots
+ 
+
+ align:start position:0%
+laser cutter is pulsing with little dots
+um and in this case it looks pretty
+
+ align:start position:0%
+um and in this case it looks pretty
+ 
+
+ align:start position:0%
+um and in this case it looks pretty
+clear how to connect them together but
+
+ align:start position:0%
+clear how to connect them together but
+ 
+
+ align:start position:0%
+clear how to connect them together but
+uh if you're cutting many salamanders
+
+ align:start position:0%
+uh if you're cutting many salamanders
+ 
+
+ align:start position:0%
+uh if you're cutting many salamanders
+out of one sheet and you think of the
+
+ align:start position:0%
+out of one sheet and you think of the
+ 
+
+ align:start position:0%
+out of one sheet and you think of the
+salamanders is pretty small uh that's
+
+ align:start position:0%
+salamanders is pretty small uh that's
+ 
+
+ align:start position:0%
+salamanders is pretty small uh that's
+like a tsp problem or or really a
+
+ align:start position:0%
+like a tsp problem or or really a
+ 
+
+ align:start position:0%
+like a tsp problem or or really a
+Milling problem you have to visit all
+
+ align:start position:0%
+Milling problem you have to visit all
+ 
+
+ align:start position:0%
+Milling problem you have to visit all
+these things uh using the shortest uh
+
+ align:start position:0%
+these things uh using the shortest uh
+ 
+
+ align:start position:0%
+these things uh using the shortest uh
+it's really a lawn mowing problem so you
+
+ align:start position:0%
+it's really a lawn mowing problem so you
+ 
+
+ align:start position:0%
+it's really a lawn mowing problem so you
+can turn off the laser and you can move
+
+ align:start position:0%
+can turn off the laser and you can move
+ 
+
+ align:start position:0%
+can turn off the laser and you can move
+around to somewhere else that you don't
+
+ align:start position:0%
+around to somewhere else that you don't
+ 
+
+ align:start position:0%
+around to somewhere else that you don't
+want to
+
+ align:start position:0%
+want to
+ 
+
+ align:start position:0%
+want to
+visit uh 3D printing is like a lawn
+
+ align:start position:0%
+visit uh 3D printing is like a lawn
+ 
+
+ align:start position:0%
+visit uh 3D printing is like a lawn
+mowing problem in each layer so 3D
+
+ align:start position:0%
+mowing problem in each layer so 3D
+ 
+
+ align:start position:0%
+mowing problem in each layer so 3D
+printing is done by printing each layer
+
+ align:start position:0%
+printing is done by printing each layer
+ 
+
+ align:start position:0%
+printing is done by printing each layer
+and then stacking them up one at a time
+
+ align:start position:0%
+and then stacking them up one at a time
+ 
+
+ align:start position:0%
+and then stacking them up one at a time
+so in each layer you have to deposit
+
+ align:start position:0%
+so in each layer you have to deposit
+ 
+
+ align:start position:0%
+so in each layer you have to deposit
+material in fdm say we're additive
+
+ align:start position:0%
+material in fdm say we're additive
+ 
+
+ align:start position:0%
+material in fdm say we're additive
+printing uh you have to deposit material
+
+ align:start position:0%
+printing uh you have to deposit material
+ 
+
+ align:start position:0%
+printing uh you have to deposit material
+uh if you're doing laser curing same
+
+ align:start position:0%
+uh if you're doing laser curing same
+ 
+
+ align:start position:0%
+uh if you're doing laser curing same
+kind of thing how do you move the laser
+
+ align:start position:0%
+kind of thing how do you move the laser
+ 
+
+ align:start position:0%
+kind of thing how do you move the laser
+with the shortest amount of work uh it's
+
+ align:start position:0%
+with the shortest amount of work uh it's
+ 
+
+ align:start position:0%
+with the shortest amount of work uh it's
+called Milling I don't have an image for
+
+ align:start position:0%
+called Milling I don't have an image for
+ 
+
+ align:start position:0%
+called Milling I don't have an image for
+this because if you're doing NC Milling
+
+ align:start position:0%
+this because if you're doing NC Milling
+ 
+
+ align:start position:0%
+this because if you're doing NC Milling
+you have a drill and you're moving the
+
+ align:start position:0%
+you have a drill and you're moving the
+ 
+
+ align:start position:0%
+you have a drill and you're moving the
+drill around to cut out some shape you
+
+ align:start position:0%
+drill around to cut out some shape you
+ 
+
+ align:start position:0%
+drill around to cut out some shape you
+uh or to cut a
+
+ align:start position:0%
+uh or to cut a
+ 
+
+ align:start position:0%
+uh or to cut a
+region
+
+ align:start position:0%
+region
+ 
+
+ align:start position:0%
+region
+um you there you're not allowed to go
+
+ align:start position:0%
+um you there you're not allowed to go
+ 
+
+ align:start position:0%
+um you there you're not allowed to go
+outside the shape you want to cut
+
+ align:start position:0%
+outside the shape you want to cut
+ 
+
+ align:start position:0%
+outside the shape you want to cut
+because if you go outside you cut too
+
+ align:start position:0%
+because if you go outside you cut too
+ 
+
+ align:start position:0%
+because if you go outside you cut too
+much and you don't want to have to pay
+
+ align:start position:0%
+much and you don't want to have to pay
+ 
+
+ align:start position:0%
+much and you don't want to have to pay
+to retract there are other versions of
+
+ align:start position:0%
+to retract there are other versions of
+ 
+
+ align:start position:0%
+to retract there are other versions of
+the problem where you can retract the
+
+ align:start position:0%
+the problem where you can retract the
+ 
+
+ align:start position:0%
+the problem where you can retract the
+cut bit and so on uh so um of course we
+
+ align:start position:0%
+cut bit and so on uh so um of course we
+ 
+
+ align:start position:0%
+cut bit and so on uh so um of course we
+proved Milling is hard that is exactly
+
+ align:start position:0%
+proved Milling is hard that is exactly
+ 
+
+ align:start position:0%
+proved Milling is hard that is exactly
+the Hamilton see and grid graphs if
+
+ align:start position:0%
+the Hamilton see and grid graphs if
+ 
+
+ align:start position:0%
+the Hamilton see and grid graphs if
+you're not allowed to leave the region
+
+ align:start position:0%
+you're not allowed to leave the region
+ 
+
+ align:start position:0%
+you're not allowed to leave the region
+of course that also shows lawn mowing is
+
+ align:start position:0%
+of course that also shows lawn mowing is
+ 
+
+ align:start position:0%
+of course that also shows lawn mowing is
+hard because you never want to go
+
+ align:start position:0%
+hard because you never want to go
+ 
+
+ align:start position:0%
+hard because you never want to go
+outside the region one fun result is
+
+ align:start position:0%
+outside the region one fun result is
+ 
+
+ align:start position:0%
+outside the region one fun result is
+lawn mowing is hard even when you have
+
+ align:start position:0%
+lawn mowing is hard even when you have
+ 
+
+ align:start position:0%
+lawn mowing is hard even when you have
+no holes in your region so if you cut
+
+ align:start position:0%
+no holes in your region so if you cut
+ 
+
+ align:start position:0%
+no holes in your region so if you cut
+these little slits from a lawn mowing
+
+ align:start position:0%
+these little slits from a lawn mowing
+ 
+
+ align:start position:0%
+these little slits from a lawn mowing
+perspective it basically makes no
+
+ align:start position:0%
+perspective it basically makes no
+ 
+
+ align:start position:0%
+perspective it basically makes no
+difference because you can still go over
+
+ align:start position:0%
+difference because you can still go over
+ 
+
+ align:start position:0%
+difference because you can still go over
+it uh and it doesn't really save you
+
+ align:start position:0%
+it uh and it doesn't really save you
+ 
+
+ align:start position:0%
+it uh and it doesn't really save you
+anything to not have to cut that so
+
+ align:start position:0%
+anything to not have to cut that so
+ 
+
+ align:start position:0%
+anything to not have to cut that so
+lawnmowing is hard even without
+
+ align:start position:0%
+lawnmowing is hard even without
+ 
+
+ align:start position:0%
+lawnmowing is hard even without
+holes
+
+ align:start position:0%
+holes
+ 
+
+ align:start position:0%
+holes
+uh cool I have one more problem do you
+
+ align:start position:0%
+uh cool I have one more problem do you
+ 
+
+ align:start position:0%
+uh cool I have one more problem do you
+want to see
+
+ align:start position:0%
+want to see
+ 
+
+ align:start position:0%
+want to see
+it okay uh so here's uh sorry a brief
+
+ align:start position:0%
+it okay uh so here's uh sorry a brief
+ 
+
+ align:start position:0%
+it okay uh so here's uh sorry a brief
+warmup suppose you have a grid graph you
+
+ align:start position:0%
+warmup suppose you have a grid graph you
+ 
+
+ align:start position:0%
+warmup suppose you have a grid graph you
+rotate at 45° you can represent each of
+
+ align:start position:0%
+rotate at 45° you can represent each of
+ 
+
+ align:start position:0%
+rotate at 45° you can represent each of
+these vertices as a vertical segment if
+
+ align:start position:0%
+these vertices as a vertical segment if
+ 
+
+ align:start position:0%
+these vertices as a vertical segment if
+they're black parody or horizontal
+
+ align:start position:0%
+they're black parody or horizontal
+ 
+
+ align:start position:0%
+they're black parody or horizontal
+segment if they're white parody such
+
+ align:start position:0%
+segment if they're white parody such
+ 
+
+ align:start position:0%
+segment if they're white parody such
+that segments intersect if and only if
+
+ align:start position:0%
+that segments intersect if and only if
+ 
+
+ align:start position:0%
+that segments intersect if and only if
+there's an edge joining okay so these
+
+ align:start position:0%
+there's an edge joining okay so these
+ 
+
+ align:start position:0%
+there's an edge joining okay so these
+are unit orthogonal segments this is
+
+ align:start position:0%
+are unit orthogonal segments this is
+ 
+
+ align:start position:0%
+are unit orthogonal segments this is
+called an intersection graph where you
+
+ align:start position:0%
+called an intersection graph where you
+ 
+
+ align:start position:0%
+called an intersection graph where you
+the vertices are the objects and the
+
+ align:start position:0%
+the vertices are the objects and the
+ 
+
+ align:start position:0%
+the vertices are the objects and the
+edges are whether things
+
+ align:start position:0%
+edges are whether things
+ 
+
+ align:start position:0%
+edges are whether things
+intersect okay that I need that so
+
+ align:start position:0%
+intersect okay that I need that so
+ 
+
+ align:start position:0%
+intersect okay that I need that so
+hamiltonicity in these graphs is
+
+ align:start position:0%
+hamiltonicity in these graphs is
+ 
+
+ align:start position:0%
+hamiltonicity in these graphs is
+hard uh here's a problem called minimum
+
+ align:start position:0%
+hard uh here's a problem called minimum
+ 
+
+ align:start position:0%
+hard uh here's a problem called minimum
+turn Milling so a big issue for 3D
+
+ align:start position:0%
+turn Milling so a big issue for 3D
+ 
+
+ align:start position:0%
+turn Milling so a big issue for 3D
+printing uh for Milling usually when
+
+ align:start position:0%
+printing uh for Milling usually when
+ 
+
+ align:start position:0%
+printing uh for Milling usually when
+you're when you're cutting or you're
+
+ align:start position:0%
+you're when you're cutting or you're
+ 
+
+ align:start position:0%
+you're when you're cutting or you're
+depositing material you can move really
+
+ align:start position:0%
+depositing material you can move really
+ 
+
+ align:start position:0%
+depositing material you can move really
+fast in a straight line
+
+ align:start position:0%
+fast in a straight line
+ 
+
+ align:start position:0%
+fast in a straight line
+but when you need to make a turn you
+
+ align:start position:0%
+but when you need to make a turn you
+ 
+
+ align:start position:0%
+but when you need to make a turn you
+have to basically come to a stop and
+
+ align:start position:0%
+have to basically come to a stop and
+ 
+
+ align:start position:0%
+have to basically come to a stop and
+then speed up again so suppose you have
+
+ align:start position:0%
+then speed up again so suppose you have
+ 
+
+ align:start position:0%
+then speed up again so suppose you have
+infinite
+
+ align:start position:0%
+infinite
+ 
+
+ align:start position:0%
+infinite
+acceleration uh so to speak or close to
+
+ align:start position:0%
+acceleration uh so to speak or close to
+ 
+
+ align:start position:0%
+acceleration uh so to speak or close to
+infinite acceleration so once you're
+
+ align:start position:0%
+infinite acceleration so once you're
+ 
+
+ align:start position:0%
+infinite acceleration so once you're
+going straight you can go arbitrarily
+
+ align:start position:0%
+going straight you can go arbitrarily
+ 
+
+ align:start position:0%
+going straight you can go arbitrarily
+far for the same cost and what you
+
+ align:start position:0%
+far for the same cost and what you
+ 
+
+ align:start position:0%
+far for the same cost and what you
+really pay for is the slowing down and
+
+ align:start position:0%
+really pay for is the slowing down and
+ 
+
+ align:start position:0%
+really pay for is the slowing down and
+speeding back up at every corner so then
+
+ align:start position:0%
+speeding back up at every corner so then
+ 
+
+ align:start position:0%
+speeding back up at every corner so then
+you want to minimize the number of turns
+
+ align:start position:0%
+you want to minimize the number of turns
+ 
+
+ align:start position:0%
+you want to minimize the number of turns
+not the length this is one of my first
+
+ align:start position:0%
+not the length this is one of my first
+ 
+
+ align:start position:0%
+not the length this is one of my first
+hardness proofs that it was not about
+
+ align:start position:0%
+hardness proofs that it was not about
+ 
+
+ align:start position:0%
+hardness proofs that it was not about
+puzzles um I think the original paper
+
+ align:start position:0%
+puzzles um I think the original paper
+ 
+
+ align:start position:0%
+puzzles um I think the original paper
+was 2,000 then Journal version 2005 uh
+
+ align:start position:0%
+was 2,000 then Journal version 2005 uh
+ 
+
+ align:start position:0%
+was 2,000 then Journal version 2005 uh
+so suppose you have one of these
+
+ align:start position:0%
+so suppose you have one of these
+ 
+
+ align:start position:0%
+so suppose you have one of these
+rectangle intersection graphs what we're
+
+ align:start position:0%
+rectangle intersection graphs what we're
+ 
+
+ align:start position:0%
+rectangle intersection graphs what we're
+going to do is explode it replace each
+
+ align:start position:0%
+going to do is explode it replace each
+ 
+
+ align:start position:0%
+going to do is explode it replace each
+of these things with a a cycle and then
+
+ align:start position:0%
+of these things with a a cycle and then
+ 
+
+ align:start position:0%
+of these things with a a cycle and then
+thicken that cycle this is
+
+ align:start position:0%
+thicken that cycle this is
+ 
+
+ align:start position:0%
+thicken that cycle this is
+a thin grid graph not super thin maybe
+
+ align:start position:0%
+a thin grid graph not super thin maybe
+ 
+
+ align:start position:0%
+a thin grid graph not super thin maybe
+maybe super thin uh here it's super thin
+
+ align:start position:0%
+maybe super thin uh here it's super thin
+ 
+
+ align:start position:0%
+maybe super thin uh here it's super thin
+and here it's you have a little square
+
+ align:start position:0%
+and here it's you have a little square
+ 
+
+ align:start position:0%
+and here it's you have a little square
+that you're cutting with so each of
+
+ align:start position:0%
+that you're cutting with so each of
+ 
+
+ align:start position:0%
+that you're cutting with so each of
+these things you have to make four turns
+
+ align:start position:0%
+these things you have to make four turns
+ 
+
+ align:start position:0%
+these things you have to make four turns
+okay then also to go from one of these
+
+ align:start position:0%
+okay then also to go from one of these
+ 
+
+ align:start position:0%
+okay then also to go from one of these
+to one of these to go from one vertex to
+
+ align:start position:0%
+to one of these to go from one vertex to
+ 
+
+ align:start position:0%
+to one of these to go from one vertex to
+the next you need a turn so generally
+
+ align:start position:0%
+the next you need a turn so generally
+ 
+
+ align:start position:0%
+the next you need a turn so generally
+you're going to need five n turns in
+
+ align:start position:0%
+you're going to need five n turns in
+ 
+
+ align:start position:0%
+you're going to need five n turns in
+order to visit n of these original
+
+ align:start position:0%
+order to visit n of these original
+ 
+
+ align:start position:0%
+order to visit n of these original
+segments and you can do that if and only
+
+ align:start position:0%
+segments and you can do that if and only
+ 
+
+ align:start position:0%
+segments and you can do that if and only
+if there's a hamiltonian cycle in the
+
+ align:start position:0%
+if there's a hamiltonian cycle in the
+ 
+
+ align:start position:0%
+if there's a hamiltonian cycle in the
+original graph which was this picture uh
+
+ align:start position:0%
+original graph which was this picture uh
+ 
+
+ align:start position:0%
+original graph which was this picture uh
+basically if you come in one position uh
+
+ align:start position:0%
+basically if you come in one position uh
+ 
+
+ align:start position:0%
+basically if you come in one position uh
+so here's a uh cycle you're trying to or
+
+ align:start position:0%
+so here's a uh cycle you're trying to or
+ 
+
+ align:start position:0%
+so here's a uh cycle you're trying to or
+one of these um rectangles you want to
+
+ align:start position:0%
+one of these um rectangles you want to
+ 
+
+ align:start position:0%
+one of these um rectangles you want to
+visit you come in one place and you know
+
+ align:start position:0%
+visit you come in one place and you know
+ 
+
+ align:start position:0%
+visit you come in one place and you know
+you want leave on some other place so
+
+ align:start position:0%
+you want leave on some other place so
+ 
+
+ align:start position:0%
+you want leave on some other place so
+you double this Edge you're going to cut
+
+ align:start position:0%
+you double this Edge you're going to cut
+ 
+
+ align:start position:0%
+you double this Edge you're going to cut
+it twice that's allowed in this model
+
+ align:start position:0%
+it twice that's allowed in this model
+ 
+
+ align:start position:0%
+it twice that's allowed in this model
+and then you loop around and the number
+
+ align:start position:0%
+and then you loop around and the number
+ 
+
+ align:start position:0%
+and then you loop around and the number
+of turns here is exactly one to come in
+
+ align:start position:0%
+of turns here is exactly one to come in
+ 
+
+ align:start position:0%
+of turns here is exactly one to come in
+four to go around and then one to come
+
+ align:start position:0%
+four to go around and then one to come
+ 
+
+ align:start position:0%
+four to go around and then one to come
+out in general it's one per Edge in the
+
+ align:start position:0%
+out in general it's one per Edge in the
+ 
+
+ align:start position:0%
+out in general it's one per Edge in the
+cycle and four per vertex in the cycle
+
+ align:start position:0%
+cycle and four per vertex in the cycle
+ 
+
+ align:start position:0%
+cycle and four per vertex in the cycle
+so again uh hamiltonicity gives us what
+
+ align:start position:0%
+so again uh hamiltonicity gives us what
+ 
+
+ align:start position:0%
+so again uh hamiltonicity gives us what
+we want even when we're minimizing
+
+ align:start position:0%
+we want even when we're minimizing
+ 
+
+ align:start position:0%
+we want even when we're minimizing
+number of turns we can simulate that by
+
+ align:start position:0%
+number of turns we can simulate that by
+ 
+
+ align:start position:0%
+number of turns we can simulate that by
+counting vertices as turns basically
+
+ align:start position:0%
+counting vertices as turns basically
+ 
+
+ align:start position:0%
+counting vertices as turns basically
+and that's it for hamity
\ No newline at end of file
diff --git a/Q8p2q9GFBMk.txt b/Q8p2q9GFBMk.txt
new file mode 100644
index 0000000000000000000000000000000000000000..50bc13e4d9b4c3dd2a6a5ab78202e77ed0b7ed98
--- /dev/null
+++ b/Q8p2q9GFBMk.txt
@@ -0,0 +1,7283 @@
+align:start position:0%
+ 
+the following content is provided under
+
+ align:start position:0%
+the following content is provided under
+ 
+
+ align:start position:0%
+the following content is provided under
+a Creative Commons license your support
+
+ align:start position:0%
+a Creative Commons license your support
+ 
+
+ align:start position:0%
+a Creative Commons license your support
+will help MIT open courseware continue
+
+ align:start position:0%
+will help MIT open courseware continue
+ 
+
+ align:start position:0%
+will help MIT open courseware continue
+to offer highquality educational
+
+ align:start position:0%
+to offer highquality educational
+ 
+
+ align:start position:0%
+to offer highquality educational
+resources for free to make a donation or
+
+ align:start position:0%
+resources for free to make a donation or
+ 
+
+ align:start position:0%
+resources for free to make a donation or
+view additional materials from hundreds
+
+ align:start position:0%
+view additional materials from hundreds
+ 
+
+ align:start position:0%
+view additional materials from hundreds
+of MIT courses visit MIT open courseware
+
+ align:start position:0%
+of MIT courses visit MIT open courseware
+ 
+
+ align:start position:0%
+of MIT courses visit MIT open courseware
+at
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+ocw.mit.edu maybe a few of you were
+
+ align:start position:0%
+ocw.mit.edu maybe a few of you were
+ 
+
+ align:start position:0%
+ocw.mit.edu maybe a few of you were
+expecting a quiz today but I actually
+
+ align:start position:0%
+expecting a quiz today but I actually
+ 
+
+ align:start position:0%
+expecting a quiz today but I actually
+said on class on Friday that I wouldn't
+
+ align:start position:0%
+said on class on Friday that I wouldn't
+ 
+
+ align:start position:0%
+said on class on Friday that I wouldn't
+give the quiz this week
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so uh sticking with
+
+ align:start position:0%
+so uh sticking with
+ 
+
+ align:start position:0%
+so uh sticking with
+that I'm not giving it it was to be on
+
+ align:start position:0%
+that I'm not giving it it was to be on
+ 
+
+ align:start position:0%
+that I'm not giving it it was to be on
+the Wilson notes but
+
+ align:start position:0%
+the Wilson notes but
+ 
+
+ align:start position:0%
+the Wilson notes but
+uh I don't well if we can fit it in
+
+ align:start position:0%
+uh I don't well if we can fit it in
+ 
+
+ align:start position:0%
+uh I don't well if we can fit it in
+later we might but I want you to focus
+
+ align:start position:0%
+later we might but I want you to focus
+ 
+
+ align:start position:0%
+later we might but I want you to focus
+on your
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+projects because the reading is not very
+
+ align:start position:0%
+projects because the reading is not very
+ 
+
+ align:start position:0%
+projects because the reading is not very
+heavy this
+
+ align:start position:0%
+heavy this
+ 
+
+ align:start position:0%
+heavy this
+week first is his chapter on cultural
+
+ align:start position:0%
+week first is his chapter on cultural
+ 
+
+ align:start position:0%
+week first is his chapter on cultural
+determinism so we'll talk about that
+
+ align:start position:0%
+determinism so we'll talk about that
+ 
+
+ align:start position:0%
+determinism so we'll talk about that
+today
+
+ align:start position:0%
+today
+ 
+
+ align:start position:0%
+today
+and then the remaining
+
+ align:start position:0%
+and then the remaining
+ 
+
+ align:start position:0%
+and then the remaining
+matters on Friday and
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Monday sorry the left projector the the
+
+ align:start position:0%
+Monday sorry the left projector the the
+ 
+
+ align:start position:0%
+Monday sorry the left projector the the
+bulb won't come
+
+ align:start position:0%
+bulb won't come
+ 
+
+ align:start position:0%
+bulb won't come
+on at least not from
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+here this is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+how Alcock starts this chapter on
+
+ align:start position:0%
+how Alcock starts this chapter on
+ 
+
+ align:start position:0%
+how Alcock starts this chapter on
+cultural determin is in he quotes this
+
+ align:start position:0%
+cultural determin is in he quotes this
+ 
+
+ align:start position:0%
+cultural determin is in he quotes this
+soci sociology
+
+ align:start position:0%
+soci sociology
+ 
+
+ align:start position:0%
+soci sociology
+book human biology does nothing to
+
+ align:start position:0%
+book human biology does nothing to
+ 
+
+ align:start position:0%
+book human biology does nothing to
+structure human
+
+ align:start position:0%
+structure human
+ 
+
+ align:start position:0%
+structure human
+society and that's common
+
+ align:start position:0%
+society and that's common
+ 
+
+ align:start position:0%
+society and that's common
+um belief among sociologists and
+
+ align:start position:0%
+um belief among sociologists and
+ 
+
+ align:start position:0%
+um belief among sociologists and
+cultural anthropologists as we shall
+
+ align:start position:0%
+cultural anthropologists as we shall
+ 
+
+ align:start position:0%
+cultural anthropologists as we shall
+see they don't like social biology
+
+ align:start position:0%
+see they don't like social biology
+ 
+
+ align:start position:0%
+see they don't like social biology
+and some of that is still true U the
+
+ align:start position:0%
+and some of that is still true U the
+ 
+
+ align:start position:0%
+and some of that is still true U the
+arguments
+
+ align:start position:0%
+arguments
+ 
+
+ align:start position:0%
+arguments
+I think are more against biology in
+
+ align:start position:0%
+I think are more against biology in
+ 
+
+ align:start position:0%
+I think are more against biology in
+general if when it concerns Evolution
+
+ align:start position:0%
+general if when it concerns Evolution
+ 
+
+ align:start position:0%
+general if when it concerns Evolution
+applied to human
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+beings
+
+ align:start position:0%
+beings
+ 
+
+ align:start position:0%
+beings
+Dennis in 95 called it Darwin's
+
+ align:start position:0%
+Dennis in 95 called it Darwin's
+ 
+
+ align:start position:0%
+Dennis in 95 called it Darwin's
+dangerous
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+idea it's not just due to
+
+ align:start position:0%
+idea it's not just due to
+ 
+
+ align:start position:0%
+idea it's not just due to
+interpretations that are common among
+
+ align:start position:0%
+interpretations that are common among
+ 
+
+ align:start position:0%
+interpretations that are common among
+followers of religions it's
+
+ align:start position:0%
+followers of religions it's
+ 
+
+ align:start position:0%
+followers of religions it's
+uh also Al found in
+
+ align:start position:0%
+uh also Al found in
+ 
+
+ align:start position:0%
+uh also Al found in
+Academia in these groups and I mentioned
+
+ align:start position:0%
+Academia in these groups and I mentioned
+ 
+
+ align:start position:0%
+Academia in these groups and I mentioned
+and then Educators as
+
+ align:start position:0%
+and then Educators as
+ 
+
+ align:start position:0%
+and then Educators as
+well but there's certain errors that are
+
+ align:start position:0%
+well but there's certain errors that are
+ 
+
+ align:start position:0%
+well but there's certain errors that are
+repeated in their statements and one is
+
+ align:start position:0%
+repeated in their statements and one is
+ 
+
+ align:start position:0%
+repeated in their statements and one is
+you could say the error of the false
+
+ align:start position:0%
+you could say the error of the false
+ 
+
+ align:start position:0%
+you could say the error of the false
+dichotomy so what is the
+
+ align:start position:0%
+dichotomy so what is the
+ 
+
+ align:start position:0%
+dichotomy so what is the
+dichotomy that they're they're saying
+
+ align:start position:0%
+dichotomy that they're they're saying
+ 
+
+ align:start position:0%
+dichotomy that they're they're saying
+they favor one side not the other side
+
+ align:start position:0%
+they favor one side not the other side
+ 
+
+ align:start position:0%
+they favor one side not the other side
+the either culture or
+
+ align:start position:0%
+the either culture or
+ 
+
+ align:start position:0%
+the either culture or
+biology either learned or innate either
+
+ align:start position:0%
+biology either learned or innate either
+ 
+
+ align:start position:0%
+biology either learned or innate either
+nature or nurture we've talked about
+
+ align:start position:0%
+nature or nurture we've talked about
+ 
+
+ align:start position:0%
+nature or nurture we've talked about
+this before it's actually always both
+
+ align:start position:0%
+this before it's actually always both
+ 
+
+ align:start position:0%
+this before it's actually always both
+the same is true for culture biolog uh
+
+ align:start position:0%
+the same is true for culture biolog uh
+ 
+
+ align:start position:0%
+the same is true for culture biolog uh
+evolutionary influences and cultural
+
+ align:start position:0%
+evolutionary influences and cultural
+ 
+
+ align:start position:0%
+evolutionary influences and cultural
+influences on human behavior it's just a
+
+ align:start position:0%
+influences on human behavior it's just a
+ 
+
+ align:start position:0%
+influences on human behavior it's just a
+nature nurture
+
+ align:start position:0%
+nature nurture
+ 
+
+ align:start position:0%
+nature nurture
+issue they
+
+ align:start position:0%
+issue they
+ 
+
+ align:start position:0%
+issue they
+also confuse approximate and
+
+ align:start position:0%
+also confuse approximate and
+ 
+
+ align:start position:0%
+also confuse approximate and
+evolutionary or ultimate hypotheses
+
+ align:start position:0%
+evolutionary or ultimate hypotheses
+ 
+
+ align:start position:0%
+evolutionary or ultimate hypotheses
+that's also very common in their
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+statements
+
+ align:start position:0%
+statements
+ 
+
+ align:start position:0%
+statements
+uh Alcock tells the story of Frank Boaz
+
+ align:start position:0%
+uh Alcock tells the story of Frank Boaz
+ 
+
+ align:start position:0%
+uh Alcock tells the story of Frank Boaz
+and his students Boaz
+
+ align:start position:0%
+and his students Boaz
+ 
+
+ align:start position:0%
+and his students Boaz
+was very well known as a he calls him
+
+ align:start position:0%
+was very well known as a he calls him
+ 
+
+ align:start position:0%
+was very well known as a he calls him
+the first modern cultural Anthropologist
+
+ align:start position:0%
+the first modern cultural Anthropologist
+ 
+
+ align:start position:0%
+the first modern cultural Anthropologist
+of
+
+ align:start position:0%
+of
+ 
+
+ align:start position:0%
+of
+note and he
+
+ align:start position:0%
+note and he
+ 
+
+ align:start position:0%
+note and he
+asserted what he his belief in the
+
+ align:start position:0%
+asserted what he his belief in the
+ 
+
+ align:start position:0%
+asserted what he his belief in the
+autonomy of culture from biology
+
+ align:start position:0%
+autonomy of culture from biology
+ 
+
+ align:start position:0%
+autonomy of culture from biology
+thereby according to elcock bringing the
+
+ align:start position:0%
+thereby according to elcock bringing the
+ 
+
+ align:start position:0%
+thereby according to elcock bringing the
+study of human behavior from
+
+ align:start position:0%
+study of human behavior from
+ 
+
+ align:start position:0%
+study of human behavior from
+evolutionary
+
+ align:start position:0%
+evolutionary
+ 
+
+ align:start position:0%
+evolutionary
+biology which had become admittedly
+
+ align:start position:0%
+biology which had become admittedly
+ 
+
+ align:start position:0%
+biology which had become admittedly
+tainted
+
+ align:start position:0%
+tainted
+ 
+
+ align:start position:0%
+tainted
+by many people who Associated it with
+
+ align:start position:0%
+by many people who Associated it with
+ 
+
+ align:start position:0%
+by many people who Associated it with
+racism social Darwinism and
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Eugenics they were used as you know from
+
+ align:start position:0%
+Eugenics they were used as you know from
+ 
+
+ align:start position:0%
+Eugenics they were used as you know from
+Reading earlier in the book used by
+
+ align:start position:0%
+Reading earlier in the book used by
+ 
+
+ align:start position:0%
+Reading earlier in the book used by
+critics of socio biology
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so Boaz in
+
+ align:start position:0%
+so Boaz in
+ 
+
+ align:start position:0%
+so Boaz in
+his at least according to his students
+
+ align:start position:0%
+his at least according to his students
+ 
+
+ align:start position:0%
+his at least according to his students
+uh uh promoted this idea that the
+
+ align:start position:0%
+uh uh promoted this idea that the
+ 
+
+ align:start position:0%
+uh uh promoted this idea that the
+cultural practices are Limitless in
+
+ align:start position:0%
+cultural practices are Limitless in
+ 
+
+ align:start position:0%
+cultural practices are Limitless in
+essentially arbitrary in nature and one
+
+ align:start position:0%
+essentially arbitrary in nature and one
+ 
+
+ align:start position:0%
+essentially arbitrary in nature and one
+of those students became very well known
+
+ align:start position:0%
+of those students became very well known
+ 
+
+ align:start position:0%
+of those students became very well known
+Margaret me I remember meeting a friend
+
+ align:start position:0%
+Margaret me I remember meeting a friend
+ 
+
+ align:start position:0%
+Margaret me I remember meeting a friend
+of mine in high
+
+ align:start position:0%
+of mine in high
+ 
+
+ align:start position:0%
+of mine in high
+school a girl who had mapped out her
+
+ align:start position:0%
+school a girl who had mapped out her
+ 
+
+ align:start position:0%
+school a girl who had mapped out her
+career based on the career of Margaret
+
+ align:start position:0%
+career based on the career of Margaret
+ 
+
+ align:start position:0%
+career based on the career of Margaret
+me she was going to become a cultural
+
+ align:start position:0%
+me she was going to become a cultural
+ 
+
+ align:start position:0%
+me she was going to become a cultural
+Anthropologist she was going to travel
+
+ align:start position:0%
+Anthropologist she was going to travel
+ 
+
+ align:start position:0%
+Anthropologist she was going to travel
+give lectures get paid for them and so
+
+ align:start position:0%
+give lectures get paid for them and so
+ 
+
+ align:start position:0%
+give lectures get paid for them and so
+on and so forth just like Margaret
+
+ align:start position:0%
+on and so forth just like Margaret
+ 
+
+ align:start position:0%
+on and so forth just like Margaret
+me
+
+ align:start position:0%
+me
+ 
+
+ align:start position:0%
+me
+uh I don't know what how that turned out
+
+ align:start position:0%
+uh I don't know what how that turned out
+ 
+
+ align:start position:0%
+uh I don't know what how that turned out
+but anyway this this was the book this
+
+ align:start position:0%
+but anyway this this was the book this
+ 
+
+ align:start position:0%
+but anyway this this was the book this
+was the book she Margaret me wrote this
+
+ align:start position:0%
+was the book she Margaret me wrote this
+ 
+
+ align:start position:0%
+was the book she Margaret me wrote this
+book entitled coming of age in Samoa was
+
+ align:start position:0%
+book entitled coming of age in Samoa was
+ 
+
+ align:start position:0%
+book entitled coming of age in Samoa was
+written in 28 or published in 28
+
+ align:start position:0%
+written in 28 or published in 28
+ 
+
+ align:start position:0%
+written in 28 or published in 28
+was very widely quoted it certainly was
+
+ align:start position:0%
+was very widely quoted it certainly was
+ 
+
+ align:start position:0%
+was very widely quoted it certainly was
+well known up to about 1975 and I think
+
+ align:start position:0%
+well known up to about 1975 and I think
+ 
+
+ align:start position:0%
+well known up to about 1975 and I think
+it's declined somewhat since then and
+
+ align:start position:0%
+it's declined somewhat since then and
+ 
+
+ align:start position:0%
+it's declined somewhat since then and
+there are good reasons for that so let's
+
+ align:start position:0%
+there are good reasons for that so let's
+ 
+
+ align:start position:0%
+there are good reasons for that so let's
+look at why would people be interested
+
+ align:start position:0%
+look at why would people be interested
+ 
+
+ align:start position:0%
+look at why would people be interested
+in
+
+ align:start position:0%
+in
+ 
+
+ align:start position:0%
+in
+somoa because she claimed that the
+
+ align:start position:0%
+somoa because she claimed that the
+ 
+
+ align:start position:0%
+somoa because she claimed that the
+society there was very different from
+
+ align:start position:0%
+society there was very different from
+ 
+
+ align:start position:0%
+society there was very different from
+American
+
+ align:start position:0%
+American
+ 
+
+ align:start position:0%
+American
+society she said they
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+were sexually free there was no conflict
+
+ align:start position:0%
+were sexually free there was no conflict
+ 
+
+ align:start position:0%
+were sexually free there was no conflict
+between kids and parents they were
+
+ align:start position:0%
+between kids and parents they were
+ 
+
+ align:start position:0%
+between kids and parents they were
+allowed to do whatever they wanted there
+
+ align:start position:0%
+allowed to do whatever they wanted there
+ 
+
+ align:start position:0%
+allowed to do whatever they wanted there
+was no rape and so on and so forth and
+
+ align:start position:0%
+was no rape and so on and so forth and
+ 
+
+ align:start position:0%
+was no rape and so on and so forth and
+one of these ID idilic
+
+ align:start position:0%
+one of these ID idilic
+ 
+
+ align:start position:0%
+one of these ID idilic
+societies
+
+ align:start position:0%
+societies
+ 
+
+ align:start position:0%
+societies
+well Derek
+
+ align:start position:0%
+well Derek
+ 
+
+ align:start position:0%
+well Derek
+Freeman went there and did she was only
+
+ align:start position:0%
+Freeman went there and did she was only
+ 
+
+ align:start position:0%
+Freeman went there and did she was only
+there for 12
+
+ align:start position:0%
+there for 12
+ 
+
+ align:start position:0%
+there for 12
+weeks and interviewed a group of young
+
+ align:start position:0%
+weeks and interviewed a group of young
+ 
+
+ align:start position:0%
+weeks and interviewed a group of young
+women there that was the she quickly
+
+ align:start position:0%
+women there that was the she quickly
+ 
+
+ align:start position:0%
+women there that was the she quickly
+learned
+
+ align:start position:0%
+learned
+ 
+
+ align:start position:0%
+learned
+enough of the language she could
+
+ align:start position:0%
+enough of the language she could
+ 
+
+ align:start position:0%
+enough of the language she could
+communicate with
+
+ align:start position:0%
+communicate with
+ 
+
+ align:start position:0%
+communicate with
+them but that was the extent of her
+
+ align:start position:0%
+them but that was the extent of her
+ 
+
+ align:start position:0%
+them but that was the extent of her
+actual study
+
+ align:start position:0%
+actual study
+ 
+
+ align:start position:0%
+actual study
+well Derek Freeman went there much later
+
+ align:start position:0%
+well Derek Freeman went there much later
+ 
+
+ align:start position:0%
+well Derek Freeman went there much later
+and it led to a book in 1983 he he spent
+
+ align:start position:0%
+and it led to a book in 1983 he he spent
+ 
+
+ align:start position:0%
+and it led to a book in 1983 he he spent
+I don't remember how long but it was a
+
+ align:start position:0%
+I don't remember how long but it was a
+ 
+
+ align:start position:0%
+I don't remember how long but it was a
+couple of years I think uh and he wrote
+
+ align:start position:0%
+couple of years I think uh and he wrote
+ 
+
+ align:start position:0%
+couple of years I think uh and he wrote
+a book in 1983 very critical of me so
+
+ align:start position:0%
+a book in 1983 very critical of me so
+ 
+
+ align:start position:0%
+a book in 1983 very critical of me so
+let's just go through Margaret me's
+
+ align:start position:0%
+let's just go through Margaret me's
+ 
+
+ align:start position:0%
+let's just go through Margaret me's
+claims that turned out to be much too
+
+ align:start position:0%
+claims that turned out to be much too
+ 
+
+ align:start position:0%
+claims that turned out to be much too
+extreme so we want to know how did she
+
+ align:start position:0%
+extreme so we want to know how did she
+ 
+
+ align:start position:0%
+extreme so we want to know how did she
+come to believe those claims why did she
+
+ align:start position:0%
+come to believe those claims why did she
+ 
+
+ align:start position:0%
+come to believe those claims why did she
+make errors
+
+ align:start position:0%
+make errors
+ 
+
+ align:start position:0%
+make errors
+uh and we've already talked about Frank
+
+ align:start position:0%
+uh and we've already talked about Frank
+ 
+
+ align:start position:0%
+uh and we've already talked about Frank
+Boaz and what he believed and she was
+
+ align:start position:0%
+Boaz and what he believed and she was
+ 
+
+ align:start position:0%
+Boaz and what he believed and she was
+his student and she promoted those ideas
+
+ align:start position:0%
+his student and she promoted those ideas
+ 
+
+ align:start position:0%
+his student and she promoted those ideas
+in this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+book she claimed that Samoa Samoan
+
+ align:start position:0%
+book she claimed that Samoa Samoan
+ 
+
+ align:start position:0%
+book she claimed that Samoa Samoan
+Society is very
+
+ align:start position:0%
+Society is very
+ 
+
+ align:start position:0%
+Society is very
+different from our society having very
+
+ align:start position:0%
+different from our society having very
+ 
+
+ align:start position:0%
+different from our society having very
+relaxed attitudes towards premarital sex
+
+ align:start position:0%
+relaxed attitudes towards premarital sex
+ 
+
+ align:start position:0%
+relaxed attitudes towards premarital sex
+by young women uh and that used to be
+
+ align:start position:0%
+by young women uh and that used to be
+ 
+
+ align:start position:0%
+by young women uh and that used to be
+much stricter U at the time she wrote
+
+ align:start position:0%
+much stricter U at the time she wrote
+ 
+
+ align:start position:0%
+much stricter U at the time she wrote
+that book Far stricter than than it is
+
+ align:start position:0%
+that book Far stricter than than it is
+ 
+
+ align:start position:0%
+that book Far stricter than than it is
+now in modern American
+
+ align:start position:0%
+now in modern American
+ 
+
+ align:start position:0%
+now in modern American
+society he also claimed an absence of
+
+ align:start position:0%
+society he also claimed an absence of
+ 
+
+ align:start position:0%
+society he also claimed an absence of
+rape freedom from emotional turbulence
+
+ align:start position:0%
+rape freedom from emotional turbulence
+ 
+
+ align:start position:0%
+rape freedom from emotional turbulence
+during adolescence and remember these
+
+ align:start position:0%
+during adolescence and remember these
+ 
+
+ align:start position:0%
+during adolescence and remember these
+were adolescent girls who was
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+interviewing so this is what she had
+
+ align:start position:0%
+interviewing so this is what she had
+ 
+
+ align:start position:0%
+interviewing so this is what she had
+done she at age
+
+ align:start position:0%
+done she at age
+ 
+
+ align:start position:0%
+done she at age
+23 because of being told by another
+
+ align:start position:0%
+23 because of being told by another
+ 
+
+ align:start position:0%
+23 because of being told by another
+cultural Anthropologist about Samo and
+
+ align:start position:0%
+cultural Anthropologist about Samo and
+ 
+
+ align:start position:0%
+cultural Anthropologist about Samo and
+Society she wanted to verify what they
+
+ align:start position:0%
+Society she wanted to verify what they
+ 
+
+ align:start position:0%
+Society she wanted to verify what they
+were
+
+ align:start position:0%
+were
+ 
+
+ align:start position:0%
+were
+believing
+
+ align:start position:0%
+believing
+ 
+
+ align:start position:0%
+believing
+uh so she based the study on
+
+ align:start position:0%
+uh so she based the study on
+ 
+
+ align:start position:0%
+uh so she based the study on
+interviewing 25 young
+
+ align:start position:0%
+interviewing 25 young
+ 
+
+ align:start position:0%
+interviewing 25 young
+women now those 25 women many of them
+
+ align:start position:0%
+women now those 25 women many of them
+ 
+
+ align:start position:0%
+women now those 25 women many of them
+most of them were still alive when Derek
+
+ align:start position:0%
+most of them were still alive when Derek
+ 
+
+ align:start position:0%
+most of them were still alive when Derek
+Freeman went there so he talked to the
+
+ align:start position:0%
+Freeman went there so he talked to the
+ 
+
+ align:start position:0%
+Freeman went there so he talked to the
+very same women when they were much
+
+ align:start position:0%
+very same women when they were much
+ 
+
+ align:start position:0%
+very same women when they were much
+older
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and as Freeman describes she didn't stay
+
+ align:start position:0%
+and as Freeman describes she didn't stay
+ 
+
+ align:start position:0%
+and as Freeman describes she didn't stay
+in Soma for really extensive
+
+ align:start position:0%
+in Soma for really extensive
+ 
+
+ align:start position:0%
+in Soma for really extensive
+observations she just believed what the
+
+ align:start position:0%
+observations she just believed what the
+ 
+
+ align:start position:0%
+observations she just believed what the
+girls told her and they were often
+
+ align:start position:0%
+girls told her and they were often
+ 
+
+ align:start position:0%
+girls told her and they were often
+kidding
+
+ align:start position:0%
+kidding
+ 
+
+ align:start position:0%
+kidding
+her she heard what she wanted to hear
+
+ align:start position:0%
+her she heard what she wanted to hear
+ 
+
+ align:start position:0%
+her she heard what she wanted to hear
+she didn't wasn't critical in her
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+method and this belief of
+
+ align:start position:0%
+method and this belief of
+ 
+
+ align:start position:0%
+method and this belief of
+Boaz uh is what she wanted to promote
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+they're certainly the same issues faced
+
+ align:start position:0%
+they're certainly the same issues faced
+ 
+
+ align:start position:0%
+they're certainly the same issues faced
+by
+
+ align:start position:0%
+by
+ 
+
+ align:start position:0%
+by
+sociobiologists since then when they
+
+ align:start position:0%
+sociobiologists since then when they
+ 
+
+ align:start position:0%
+sociobiologists since then when they
+have applied the ideas and methods to
+
+ align:start position:0%
+have applied the ideas and methods to
+ 
+
+ align:start position:0%
+have applied the ideas and methods to
+human that's what got EO Wilson we say
+
+ align:start position:0%
+human that's what got EO Wilson we say
+ 
+
+ align:start position:0%
+human that's what got EO Wilson we say
+in such
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+trouble he was in trouble because he put
+
+ align:start position:0%
+trouble he was in trouble because he put
+ 
+
+ align:start position:0%
+trouble he was in trouble because he put
+a chapter on human society and the very
+
+ align:start position:0%
+a chapter on human society and the very
+ 
+
+ align:start position:0%
+a chapter on human society and the very
+last chapter of the book applying
+
+ align:start position:0%
+last chapter of the book applying
+ 
+
+ align:start position:0%
+last chapter of the book applying
+sociobiology ideas to Human
+
+ align:start position:0%
+sociobiology ideas to Human
+ 
+
+ align:start position:0%
+sociobiology ideas to Human
+to
+
+ align:start position:0%
+to
+ 
+
+ align:start position:0%
+to
+humans the I mean the bulk of the book
+
+ align:start position:0%
+humans the I mean the bulk of the book
+ 
+
+ align:start position:0%
+humans the I mean the bulk of the book
+is about animal
+
+ align:start position:0%
+is about animal
+ 
+
+ align:start position:0%
+is about animal
+behavior animal social behavior in
+
+ align:start position:0%
+behavior animal social behavior in
+ 
+
+ align:start position:0%
+behavior animal social behavior in
+particular so this is how I would
+
+ align:start position:0%
+particular so this is how I would
+ 
+
+ align:start position:0%
+particular so this is how I would
+summarize it all she tried to do a
+
+ align:start position:0%
+summarize it all she tried to do a
+ 
+
+ align:start position:0%
+summarize it all she tried to do a
+scientific study she was young
+
+ align:start position:0%
+scientific study she was young
+ 
+
+ align:start position:0%
+scientific study she was young
+inexperienced 23 years old she made big
+
+ align:start position:0%
+inexperienced 23 years old she made big
+ 
+
+ align:start position:0%
+inexperienced 23 years old she made big
+mistakes but her book became very
+
+ align:start position:0%
+mistakes but her book became very
+ 
+
+ align:start position:0%
+mistakes but her book became very
+popular and had a wide influence despite
+
+ align:start position:0%
+popular and had a wide influence despite
+ 
+
+ align:start position:0%
+popular and had a wide influence despite
+those
+
+ align:start position:0%
+those
+ 
+
+ align:start position:0%
+those
+erors and they didn't really be the
+
+ align:start position:0%
+erors and they didn't really be the
+ 
+
+ align:start position:0%
+erors and they didn't really be the
+erors didn't really become well known
+
+ align:start position:0%
+erors didn't really become well known
+ 
+
+ align:start position:0%
+erors didn't really become well known
+until and I don't think they're well
+
+ align:start position:0%
+until and I don't think they're well
+ 
+
+ align:start position:0%
+until and I don't think they're well
+known now except among
+
+ align:start position:0%
+known now except among
+ 
+
+ align:start position:0%
+known now except among
+academics U and that took many
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+years
+
+ align:start position:0%
+years
+ 
+
+ align:start position:0%
+years
+so if we they obviously these cultural
+
+ align:start position:0%
+so if we they obviously these cultural
+ 
+
+ align:start position:0%
+so if we they obviously these cultural
+anthropologists had a blank slate view
+
+ align:start position:0%
+anthropologists had a blank slate view
+ 
+
+ align:start position:0%
+anthropologists had a blank slate view
+of human
+
+ align:start position:0%
+of human
+ 
+
+ align:start position:0%
+of human
+nature and we have we've talked about
+
+ align:start position:0%
+nature and we have we've talked about
+ 
+
+ align:start position:0%
+nature and we have we've talked about
+that conflicts with sociobiological
+
+ align:start position:0%
+that conflicts with sociobiological
+ 
+
+ align:start position:0%
+that conflicts with sociobiological
+views but what do Blank Slate views of
+
+ align:start position:0%
+views but what do Blank Slate views of
+ 
+
+ align:start position:0%
+views but what do Blank Slate views of
+human nature actually predict about
+
+ align:start position:0%
+human nature actually predict about
+ 
+
+ align:start position:0%
+human nature actually predict about
+social structure and
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+practices and as we summarize that just
+
+ align:start position:0%
+practices and as we summarize that just
+ 
+
+ align:start position:0%
+practices and as we summarize that just
+note that it's it's
+
+ align:start position:0%
+note that it's it's
+ 
+
+ align:start position:0%
+note that it's it's
+easy to make these ideas believable
+
+ align:start position:0%
+easy to make these ideas believable
+ 
+
+ align:start position:0%
+easy to make these ideas believable
+about humans but not for Animals it's
+
+ align:start position:0%
+about humans but not for Animals it's
+ 
+
+ align:start position:0%
+about humans but not for Animals it's
+much more hard to make these predictions
+
+ align:start position:0%
+much more hard to make these predictions
+ 
+
+ align:start position:0%
+much more hard to make these predictions
+about
+
+ align:start position:0%
+about
+ 
+
+ align:start position:0%
+about
+animals
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+there's two new things here about this
+
+ align:start position:0%
+there's two new things here about this
+ 
+
+ align:start position:0%
+there's two new things here about this
+whole discussion one is G's claim that
+
+ align:start position:0%
+whole discussion one is G's claim that
+ 
+
+ align:start position:0%
+whole discussion one is G's claim that
+uh bi he he was criticized by
+
+ align:start position:0%
+uh bi he he was criticized by
+ 
+
+ align:start position:0%
+uh bi he he was criticized by
+sociobiologists for talking so much
+
+ align:start position:0%
+sociobiologists for talking so much
+ 
+
+ align:start position:0%
+sociobiologists for talking so much
+about biological determinism that he
+
+ align:start position:0%
+about biological determinism that he
+ 
+
+ align:start position:0%
+about biological determinism that he
+changed it to biological
+
+ align:start position:0%
+changed it to biological
+ 
+
+ align:start position:0%
+changed it to biological
+potentiality so he claimed that a human
+
+ align:start position:0%
+potentiality so he claimed that a human
+ 
+
+ align:start position:0%
+potentiality so he claimed that a human
+has a brain capable of a full range of
+
+ align:start position:0%
+has a brain capable of a full range of
+ 
+
+ align:start position:0%
+has a brain capable of a full range of
+human behaviors and predisposed towards
+
+ align:start position:0%
+human behaviors and predisposed towards
+ 
+
+ align:start position:0%
+human behaviors and predisposed towards
+none
+
+ align:start position:0%
+none
+ 
+
+ align:start position:0%
+none
+he made that he was a biologist an
+
+ align:start position:0%
+he made that he was a biologist an
+ 
+
+ align:start position:0%
+he made that he was a biologist an
+evolutionary biologist writing regularly
+
+ align:start position:0%
+evolutionary biologist writing regularly
+ 
+
+ align:start position:0%
+evolutionary biologist writing regularly
+in the magazine natural history and he
+
+ align:start position:0%
+in the magazine natural history and he
+ 
+
+ align:start position:0%
+in the magazine natural history and he
+was very well
+
+ align:start position:0%
+was very well
+ 
+
+ align:start position:0%
+was very well
+known and he sort of becomes a Whipping
+
+ align:start position:0%
+known and he sort of becomes a Whipping
+ 
+
+ align:start position:0%
+known and he sort of becomes a Whipping
+Boy in alcock's
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+book The problem is there was a lack of
+
+ align:start position:0%
+book The problem is there was a lack of
+ 
+
+ align:start position:0%
+book The problem is there was a lack of
+rigorous tests of the predictions of
+
+ align:start position:0%
+rigorous tests of the predictions of
+ 
+
+ align:start position:0%
+rigorous tests of the predictions of
+cultural
+
+ align:start position:0%
+cultural
+ 
+
+ align:start position:0%
+cultural
+determinism and
+
+ align:start position:0%
+determinism and
+ 
+
+ align:start position:0%
+determinism and
+elcock tries to suggest some predictions
+
+ align:start position:0%
+elcock tries to suggest some predictions
+ 
+
+ align:start position:0%
+elcock tries to suggest some predictions
+that the critic should be testing and
+
+ align:start position:0%
+that the critic should be testing and
+ 
+
+ align:start position:0%
+that the critic should be testing and
+given you where he does
+
+ align:start position:0%
+given you where he does
+ 
+
+ align:start position:0%
+given you where he does
+that he basically says human behavior
+
+ align:start position:0%
+that he basically says human behavior
+ 
+
+ align:start position:0%
+that he basically says human behavior
+should differ greatly and arbitrarily
+
+ align:start position:0%
+should differ greatly and arbitrarily
+ 
+
+ align:start position:0%
+should differ greatly and arbitrarily
+from society to society and he gives
+
+ align:start position:0%
+from society to society and he gives
+ 
+
+ align:start position:0%
+from society to society and he gives
+examples of that do you think that's
+
+ align:start position:0%
+examples of that do you think that's
+ 
+
+ align:start position:0%
+examples of that do you think that's
+true should societies differ
+
+ align:start position:0%
+true should societies differ
+ 
+
+ align:start position:0%
+true should societies differ
+arbitrarily well there got to be some
+
+ align:start position:0%
+arbitrarily well there got to be some
+ 
+
+ align:start position:0%
+arbitrarily well there got to be some
+constraints right but they claim there's
+
+ align:start position:0%
+constraints right but they claim there's
+ 
+
+ align:start position:0%
+constraints right but they claim there's
+no inheritance of
+
+ align:start position:0%
+no inheritance of
+ 
+
+ align:start position:0%
+no inheritance of
+behavior in humans only in animals or at
+
+ align:start position:0%
+behavior in humans only in animals or at
+ 
+
+ align:start position:0%
+behavior in humans only in animals or at
+least not you know when you start
+
+ align:start position:0%
+least not you know when you start
+ 
+
+ align:start position:0%
+least not you know when you start
+thinking about it does that mean they
+
+ align:start position:0%
+thinking about it does that mean they
+ 
+
+ align:start position:0%
+thinking about it does that mean they
+don't believe that we inherit the
+
+ align:start position:0%
+don't believe that we inherit the
+ 
+
+ align:start position:0%
+don't believe that we inherit the
+ability to
+
+ align:start position:0%
+ability to
+ 
+
+ align:start position:0%
+ability to
+walk I don't think
+
+ align:start position:0%
+walk I don't think
+ 
+
+ align:start position:0%
+walk I don't think
+so but actually most of them do believe
+
+ align:start position:0%
+so but actually most of them do believe
+ 
+
+ align:start position:0%
+so but actually most of them do believe
+we have to learn to
+
+ align:start position:0%
+we have to learn to
+ 
+
+ align:start position:0%
+we have to learn to
+walk as I pointed out a number of
+
+ align:start position:0%
+walk as I pointed out a number of
+ 
+
+ align:start position:0%
+walk as I pointed out a number of
+times even though it's actually a fixed
+
+ align:start position:0%
+times even though it's actually a fixed
+ 
+
+ align:start position:0%
+times even though it's actually a fixed
+action
+
+ align:start position:0%
+action
+ 
+
+ align:start position:0%
+action
+pattern uh as many other things are in
+
+ align:start position:0%
+pattern uh as many other things are in
+ 
+
+ align:start position:0%
+pattern uh as many other things are in
+human as well as in animal
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+behavior so elcock tries to apply that
+
+ align:start position:0%
+behavior so elcock tries to apply that
+ 
+
+ align:start position:0%
+behavior so elcock tries to apply that
+and and uh I think it's pretty
+
+ align:start position:0%
+and and uh I think it's pretty
+ 
+
+ align:start position:0%
+and and uh I think it's pretty
+interesting when you actually make the
+
+ align:start position:0%
+interesting when you actually make the
+ 
+
+ align:start position:0%
+interesting when you actually make the
+predictions and you look from society to
+
+ align:start position:0%
+predictions and you look from society to
+ 
+
+ align:start position:0%
+predictions and you look from society to
+society and you find out that they
+
+ align:start position:0%
+society and you find out that they
+ 
+
+ align:start position:0%
+society and you find out that they
+don't there are wide differences but
+
+ align:start position:0%
+don't there are wide differences but
+ 
+
+ align:start position:0%
+don't there are wide differences but
+they don't they're not arbitrary random
+
+ align:start position:0%
+they don't they're not arbitrary random
+ 
+
+ align:start position:0%
+they don't they're not arbitrary random
+differences at
+
+ align:start position:0%
+differences at
+ 
+
+ align:start position:0%
+differences at
+all so read that and you will see
+
+ align:start position:0%
+all so read that and you will see
+ 
+
+ align:start position:0%
+all so read that and you will see
+exactly what I'm talking about I'm not
+
+ align:start position:0%
+exactly what I'm talking about I'm not
+ 
+
+ align:start position:0%
+exactly what I'm talking about I'm not
+going to go over them now it's very
+
+ align:start position:0%
+going to go over them now it's very
+ 
+
+ align:start position:0%
+going to go over them now it's very
+clear in alcock's book and uh you should
+
+ align:start position:0%
+clear in alcock's book and uh you should
+ 
+
+ align:start position:0%
+clear in alcock's book and uh you should
+be familiar with you know how difficult
+
+ align:start position:0%
+be familiar with you know how difficult
+ 
+
+ align:start position:0%
+be familiar with you know how difficult
+those predictions
+
+ align:start position:0%
+those predictions
+ 
+
+ align:start position:0%
+those predictions
+are
+
+ align:start position:0%
+are
+ 
+
+ align:start position:0%
+are
+to to to
+
+ align:start position:0%
+to to to
+ 
+
+ align:start position:0%
+to to to
+test I'm sorry they're not difficult to
+
+ align:start position:0%
+test I'm sorry they're not difficult to
+ 
+
+ align:start position:0%
+test I'm sorry they're not difficult to
+test they're difficult to verify any of
+
+ align:start position:0%
+test they're difficult to verify any of
+ 
+
+ align:start position:0%
+test they're difficult to verify any of
+them
+
+ align:start position:0%
+them
+ 
+
+ align:start position:0%
+them
+okay although we might not want to say
+
+ align:start position:0%
+okay although we might not want to say
+ 
+
+ align:start position:0%
+okay although we might not want to say
+there is completely arbitrary I don't
+
+ align:start position:0%
+there is completely arbitrary I don't
+ 
+
+ align:start position:0%
+there is completely arbitrary I don't
+know if any of them would claim that but
+
+ align:start position:0%
+know if any of them would claim that but
+ 
+
+ align:start position:0%
+know if any of them would claim that but
+the way they talk maybe it's partly in
+
+ align:start position:0%
+the way they talk maybe it's partly in
+ 
+
+ align:start position:0%
+the way they talk maybe it's partly in
+their the strength of their the vehement
+
+ align:start position:0%
+their the strength of their the vehement
+ 
+
+ align:start position:0%
+their the strength of their the vehement
+of their opposition to sociobiology that
+
+ align:start position:0%
+of their opposition to sociobiology that
+ 
+
+ align:start position:0%
+of their opposition to sociobiology that
+they make these strong claims
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+but all
+
+ align:start position:0%
+but all
+ 
+
+ align:start position:0%
+but all
+right let's talk about male female
+
+ align:start position:0%
+right let's talk about male female
+ 
+
+ align:start position:0%
+right let's talk about male female
+attraction because this is something
+
+ align:start position:0%
+attraction because this is something
+ 
+
+ align:start position:0%
+attraction because this is something
+that sociobiologists have dealt with and
+
+ align:start position:0%
+that sociobiologists have dealt with and
+ 
+
+ align:start position:0%
+that sociobiologists have dealt with and
+dealt with it as you know in many
+
+ align:start position:0%
+dealt with it as you know in many
+ 
+
+ align:start position:0%
+dealt with it as you know in many
+animals we've talked about sexual
+
+ align:start position:0%
+animals we've talked about sexual
+ 
+
+ align:start position:0%
+animals we've talked about sexual
+selection we've shown examples of it
+
+ align:start position:0%
+selection we've shown examples of it
+ 
+
+ align:start position:0%
+selection we've shown examples of it
+from especially bird
+
+ align:start position:0%
+from especially bird
+ 
+
+ align:start position:0%
+from especially bird
+Behavior Uh there's a whole program on
+
+ align:start position:0%
+Behavior Uh there's a whole program on
+ 
+
+ align:start position:0%
+Behavior Uh there's a whole program on
+WGBH on love in animals and many many
+
+ align:start position:0%
+WGBH on love in animals and many many
+ 
+
+ align:start position:0%
+WGBH on love in animals and many many
+examples not just from
+
+ align:start position:0%
+examples not just from
+ 
+
+ align:start position:0%
+examples not just from
+Birds uh about things males will do to
+
+ align:start position:0%
+Birds uh about things males will do to
+ 
+
+ align:start position:0%
+Birds uh about things males will do to
+be chosen by females and a little bit on
+
+ align:start position:0%
+be chosen by females and a little bit on
+ 
+
+ align:start position:0%
+be chosen by females and a little bit on
+the other side though it's often it's
+
+ align:start position:0%
+the other side though it's often it's
+ 
+
+ align:start position:0%
+the other side though it's often it's
+more on that than on the uh mailmate
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+choice I just want you to know when we
+
+ align:start position:0%
+choice I just want you to know when we
+ 
+
+ align:start position:0%
+choice I just want you to know when we
+go over this it's not what's
+
+ align:start position:0%
+go over this it's not what's
+ 
+
+ align:start position:0%
+go over this it's not what's
+fashionable that matches What Men
+
+ align:start position:0%
+fashionable that matches What Men
+ 
+
+ align:start position:0%
+fashionable that matches What Men
+actually prefer in a
+
+ align:start position:0%
+actually prefer in a
+ 
+
+ align:start position:0%
+actually prefer in a
+mate and yet what men actually prefer is
+
+ align:start position:0%
+mate and yet what men actually prefer is
+ 
+
+ align:start position:0%
+mate and yet what men actually prefer is
+the only thing of real interest to
+
+ align:start position:0%
+the only thing of real interest to
+ 
+
+ align:start position:0%
+the only thing of real interest to
+sociobiologist not what they say not
+
+ align:start position:0%
+sociobiologist not what they say not
+ 
+
+ align:start position:0%
+sociobiologist not what they say not
+what modern fashion dictates and so
+
+ align:start position:0%
+what modern fashion dictates and so
+ 
+
+ align:start position:0%
+what modern fashion dictates and so
+forth as a very easy example of that
+
+ align:start position:0%
+forth as a very easy example of that
+ 
+
+ align:start position:0%
+forth as a very easy example of that
+look at the difference
+
+ align:start position:0%
+look at the difference
+ 
+
+ align:start position:0%
+look at the difference
+between women that are pictured in
+
+ align:start position:0%
+between women that are pictured in
+ 
+
+ align:start position:0%
+between women that are pictured in
+fashion magazines and women that are
+
+ align:start position:0%
+fashion magazines and women that are
+ 
+
+ align:start position:0%
+fashion magazines and women that are
+pictured in the male pinup magazines or
+
+ align:start position:0%
+pictured in the male pinup magazines or
+ 
+
+ align:start position:0%
+pictured in the male pinup magazines or
+whatever you want to call
+
+ align:start position:0%
+whatever you want to call
+ 
+
+ align:start position:0%
+whatever you want to call
+them big
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+differences okay
+
+ align:start position:0%
+differences okay
+ 
+
+ align:start position:0%
+differences okay
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+also we should note that there are
+
+ align:start position:0%
+also we should note that there are
+ 
+
+ align:start position:0%
+also we should note that there are
+societal differences for example in the
+
+ align:start position:0%
+societal differences for example in the
+ 
+
+ align:start position:0%
+societal differences for example in the
+poorer Society
+
+ align:start position:0%
+poorer Society
+ 
+
+ align:start position:0%
+poorer Society
+women that are heavier that is a higher
+
+ align:start position:0%
+women that are heavier that is a higher
+ 
+
+ align:start position:0%
+women that are heavier that is a higher
+body mass index and we'll talk about
+
+ align:start position:0%
+body mass index and we'll talk about
+ 
+
+ align:start position:0%
+body mass index and we'll talk about
+that in a minute U the higher body mass
+
+ align:start position:0%
+that in a minute U the higher body mass
+ 
+
+ align:start position:0%
+that in a minute U the higher body mass
+index May indicate greater wealth and
+
+ align:start position:0%
+index May indicate greater wealth and
+ 
+
+ align:start position:0%
+index May indicate greater wealth and
+therefore be
+
+ align:start position:0%
+therefore be
+ 
+
+ align:start position:0%
+therefore be
+attractive when I first went to India I
+
+ align:start position:0%
+attractive when I first went to India I
+ 
+
+ align:start position:0%
+attractive when I first went to India I
+realized that at least at uh doesn't
+
+ align:start position:0%
+realized that at least at uh doesn't
+ 
+
+ align:start position:0%
+realized that at least at uh doesn't
+apply so much to
+
+ align:start position:0%
+apply so much to
+ 
+
+ align:start position:0%
+apply so much to
+the the very wealthy in India but if you
+
+ align:start position:0%
+the the very wealthy in India but if you
+ 
+
+ align:start position:0%
+the the very wealthy in India but if you
+deal with the bulk of the people
+
+ align:start position:0%
+deal with the bulk of the people
+ 
+
+ align:start position:0%
+deal with the bulk of the people
+um women that are heavier are often
+
+ align:start position:0%
+um women that are heavier are often
+ 
+
+ align:start position:0%
+um women that are heavier are often
+preferred uh because it indicates that
+
+ align:start position:0%
+preferred uh because it indicates that
+ 
+
+ align:start position:0%
+preferred uh because it indicates that
+they must have more
+
+ align:start position:0%
+they must have more
+ 
+
+ align:start position:0%
+they must have more
+resources you think that would apply
+
+ align:start position:0%
+resources you think that would apply
+ 
+
+ align:start position:0%
+resources you think that would apply
+even more to men men be heavier but they
+
+ align:start position:0%
+even more to men men be heavier but they
+ 
+
+ align:start position:0%
+even more to men men be heavier but they
+always talk about the
+
+ align:start position:0%
+always talk about the
+ 
+
+ align:start position:0%
+always talk about the
+women all
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+right in Alcock this one I we'll take a
+
+ align:start position:0%
+right in Alcock this one I we'll take a
+ 
+
+ align:start position:0%
+right in Alcock this one I we'll take a
+look at since I didn't actually copy the
+
+ align:start position:0%
+look at since I didn't actually copy the
+ 
+
+ align:start position:0%
+look at since I didn't actually copy the
+table for the sleds but many of you have
+
+ align:start position:0%
+table for the sleds but many of you have
+ 
+
+ align:start position:0%
+table for the sleds but many of you have
+looked at it if you've read this chapter
+
+ align:start position:0%
+looked at it if you've read this chapter
+ 
+
+ align:start position:0%
+looked at it if you've read this chapter
+table 71 that's on page 138 he goes
+
+ align:start position:0%
+table 71 that's on page 138 he goes
+ 
+
+ align:start position:0%
+table 71 that's on page 138 he goes
+through attributes in women that men
+
+ align:start position:0%
+through attributes in women that men
+ 
+
+ align:start position:0%
+through attributes in women that men
+find attractive and what is their
+
+ align:start position:0%
+find attractive and what is their
+ 
+
+ align:start position:0%
+find attractive and what is their
+meaning what is their signal value what
+
+ align:start position:0%
+meaning what is their signal value what
+ 
+
+ align:start position:0%
+meaning what is their signal value what
+is that
+
+ align:start position:0%
+is that
+ 
+
+ align:start position:0%
+is that
+property of a woman's body
+
+ align:start position:0%
+property of a woman's body
+ 
+
+ align:start position:0%
+property of a woman's body
+signal and he says all the attributes
+
+ align:start position:0%
+signal and he says all the attributes
+ 
+
+ align:start position:0%
+signal and he says all the attributes
+listed indicate Health fertility sexual
+
+ align:start position:0%
+listed indicate Health fertility sexual
+ 
+
+ align:start position:0%
+listed indicate Health fertility sexual
+maturity and youth okay they're all
+
+ align:start position:0%
+maturity and youth okay they're all
+ 
+
+ align:start position:0%
+maturity and youth okay they're all
+together predictors of Lifetime
+
+ align:start position:0%
+together predictors of Lifetime
+ 
+
+ align:start position:0%
+together predictors of Lifetime
+reproductive potential and you must keep
+
+ align:start position:0%
+reproductive potential and you must keep
+ 
+
+ align:start position:0%
+reproductive potential and you must keep
+in mind when you look at these things
+
+ align:start position:0%
+in mind when you look at these things
+ 
+
+ align:start position:0%
+in mind when you look at these things
+that there's always a range there's
+
+ align:start position:0%
+that there's always a range there's
+ 
+
+ align:start position:0%
+that there's always a range there's
+always exceptions to the general rule
+
+ align:start position:0%
+always exceptions to the general rule
+ 
+
+ align:start position:0%
+always exceptions to the general rule
+sociobiological hypotheses are not about
+
+ align:start position:0%
+sociobiological hypotheses are not about
+ 
+
+ align:start position:0%
+sociobiological hypotheses are not about
+always and they're not disproved by
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+sometimes so this first attribute is
+
+ align:start position:0%
+sometimes so this first attribute is
+ 
+
+ align:start position:0%
+sometimes so this first attribute is
+smoothed unblemished skin indicates
+
+ align:start position:0%
+smoothed unblemished skin indicates
+ 
+
+ align:start position:0%
+smoothed unblemished skin indicates
+youthfulness and good health
+
+ align:start position:0%
+youthfulness and good health
+ 
+
+ align:start position:0%
+youthfulness and good health
+and he lists he gives references for
+
+ align:start position:0%
+and he lists he gives references for
+ 
+
+ align:start position:0%
+and he lists he gives references for
+studies of that that have been done
+
+ align:start position:0%
+studies of that that have been done
+ 
+
+ align:start position:0%
+studies of that that have been done
+symmetrical faces and limbs indicates
+
+ align:start position:0%
+symmetrical faces and limbs indicates
+ 
+
+ align:start position:0%
+symmetrical faces and limbs indicates
+developmental stability good genes good
+
+ align:start position:0%
+developmental stability good genes good
+ 
+
+ align:start position:0%
+developmental stability good genes good
+nutritional experience during
+
+ align:start position:0%
+nutritional experience during
+ 
+
+ align:start position:0%
+nutritional experience during
+development then one he calls facial
+
+ align:start position:0%
+development then one he calls facial
+ 
+
+ align:start position:0%
+development then one he calls facial
+averageness Optimum optim indicates
+
+ align:start position:0%
+averageness Optimum optim indicates
+ 
+
+ align:start position:0%
+averageness Optimum optim indicates
+Optimum normal
+
+ align:start position:0%
+Optimum normal
+ 
+
+ align:start position:0%
+Optimum normal
+development and resistance to
+
+ align:start position:0%
+development and resistance to
+ 
+
+ align:start position:0%
+development and resistance to
+parasites
+
+ align:start position:0%
+parasites
+ 
+
+ align:start position:0%
+parasites
+prominent you know you don't think much
+
+ align:start position:0%
+prominent you know you don't think much
+ 
+
+ align:start position:0%
+prominent you know you don't think much
+we don't have that much trouble with
+
+ align:start position:0%
+we don't have that much trouble with
+ 
+
+ align:start position:0%
+we don't have that much trouble with
+parasites and but it's big problems for
+
+ align:start position:0%
+parasites and but it's big problems for
+ 
+
+ align:start position:0%
+parasites and but it's big problems for
+many groups humans groups and certainly
+
+ align:start position:0%
+many groups humans groups and certainly
+ 
+
+ align:start position:0%
+many groups humans groups and certainly
+was in our
+
+ align:start position:0%
+was in our
+ 
+
+ align:start position:0%
+was in our
+Evolution prominent cheekbones indicate
+
+ align:start position:0%
+Evolution prominent cheekbones indicate
+ 
+
+ align:start position:0%
+Evolution prominent cheekbones indicate
+sexual maturity cheekbones of mature
+
+ align:start position:0%
+sexual maturity cheekbones of mature
+ 
+
+ align:start position:0%
+sexual maturity cheekbones of mature
+women are quite different than when they
+
+ align:start position:0%
+women are quite different than when they
+ 
+
+ align:start position:0%
+women are quite different than when they
+were
+
+ align:start position:0%
+were
+ 
+
+ align:start position:0%
+were
+younger small chin small nose large eyes
+
+ align:start position:0%
+younger small chin small nose large eyes
+ 
+
+ align:start position:0%
+younger small chin small nose large eyes
+full lips indicates high estrogen levels
+
+ align:start position:0%
+full lips indicates high estrogen levels
+ 
+
+ align:start position:0%
+full lips indicates high estrogen levels
+during development and
+
+ align:start position:0%
+during development and
+ 
+
+ align:start position:0%
+during development and
+muths waste to hip ratio of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+0.7 indicates current high estrogen
+
+ align:start position:0%
+0.7 indicates current high estrogen
+ 
+
+ align:start position:0%
+0.7 indicates current high estrogen
+levels ample fat reserves in good health
+
+ align:start position:0%
+levels ample fat reserves in good health
+ 
+
+ align:start position:0%
+levels ample fat reserves in good health
+higher probability of becoming pregnant
+
+ align:start position:0%
+higher probability of becoming pregnant
+ 
+
+ align:start position:0%
+higher probability of becoming pregnant
+lower probability of early
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+mortality there's been many studies of
+
+ align:start position:0%
+mortality there's been many studies of
+ 
+
+ align:start position:0%
+mortality there's been many studies of
+that and arguments about
+
+ align:start position:0%
+that and arguments about
+ 
+
+ align:start position:0%
+that and arguments about
+it but the average in what men prefer
+
+ align:start position:0%
+it but the average in what men prefer
+ 
+
+ align:start position:0%
+it but the average in what men prefer
+always comes out to be about 0.7
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay I remember reading one of the very
+
+ align:start position:0%
+okay I remember reading one of the very
+ 
+
+ align:start position:0%
+okay I remember reading one of the very
+early studies of that it was done by a
+
+ align:start position:0%
+early studies of that it was done by a
+ 
+
+ align:start position:0%
+early studies of that it was done by a
+woman from India uh very nice study
+
+ align:start position:0%
+woman from India uh very nice study
+ 
+
+ align:start position:0%
+woman from India uh very nice study
+where she made this whole science into a
+
+ align:start position:0%
+where she made this whole science into a
+ 
+
+ align:start position:0%
+where she made this whole science into a
+quantitative
+
+ align:start position:0%
+quantitative
+ 
+
+ align:start position:0%
+quantitative
+science large firm symmetrical breasts
+
+ align:start position:0%
+science large firm symmetrical breasts
+ 
+
+ align:start position:0%
+science large firm symmetrical breasts
+indicates developmental stability
+
+ align:start position:0%
+indicates developmental stability
+ 
+
+ align:start position:0%
+indicates developmental stability
+youthfulness and immune system
+
+ align:start position:0%
+youthfulness and immune system
+ 
+
+ align:start position:0%
+youthfulness and immune system
+competence in a body mass
+
+ align:start position:0%
+competence in a body mass
+ 
+
+ align:start position:0%
+competence in a body mass
+index in his table he says 20 to 24 the
+
+ align:start position:0%
+index in his table he says 20 to 24 the
+ 
+
+ align:start position:0%
+index in his table he says 20 to 24 the
+preferred range is actually 17 to 24
+
+ align:start position:0%
+preferred range is actually 17 to 24
+ 
+
+ align:start position:0%
+preferred range is actually 17 to 24
+indicates high fertility and low
+
+ align:start position:0%
+indicates high fertility and low
+ 
+
+ align:start position:0%
+indicates high fertility and low
+mortality rates and you notice that is a
+
+ align:start position:0%
+mortality rates and you notice that is a
+ 
+
+ align:start position:0%
+mortality rates and you notice that is a
+big range 17 to
+
+ align:start position:0%
+big range 17 to
+ 
+
+ align:start position:0%
+big range 17 to
+24 um we'll talk a little more about
+
+ align:start position:0%
+24 um we'll talk a little more about
+ 
+
+ align:start position:0%
+24 um we'll talk a little more about
+this body mass
+
+ align:start position:0%
+this body mass
+ 
+
+ align:start position:0%
+this body mass
+index but
+
+ align:start position:0%
+index but
+ 
+
+ align:start position:0%
+index but
+uh right here I put I pulled a table out
+
+ align:start position:0%
+uh right here I put I pulled a table out
+ 
+
+ align:start position:0%
+uh right here I put I pulled a table out
+of
+
+ align:start position:0%
+of
+ 
+
+ align:start position:0%
+of
+Wikipedia
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+I point out here at the top there's
+
+ align:start position:0%
+I point out here at the top there's
+ 
+
+ align:start position:0%
+I point out here at the top there's
+variability in measures of the relative
+
+ align:start position:0%
+variability in measures of the relative
+ 
+
+ align:start position:0%
+variability in measures of the relative
+importance
+
+ align:start position:0%
+importance
+ 
+
+ align:start position:0%
+importance
+of different factors especially in these
+
+ align:start position:0%
+of different factors especially in these
+ 
+
+ align:start position:0%
+of different factors especially in these
+two body mass index and the waist to hip
+
+ align:start position:0%
+two body mass index and the waist to hip
+ 
+
+ align:start position:0%
+two body mass index and the waist to hip
+ratio so we'll talk a little more about
+
+ align:start position:0%
+ratio so we'll talk a little more about
+ 
+
+ align:start position:0%
+ratio so we'll talk a little more about
+that but and he these are the class
+
+ align:start position:0%
+that but and he these are the class
+ 
+
+ align:start position:0%
+that but and he these are the class
+usual
+
+ align:start position:0%
+usual
+ 
+
+ align:start position:0%
+usual
+classifications from severely
+
+ align:start position:0%
+classifications from severely
+ 
+
+ align:start position:0%
+classifications from severely
+underweight and underweight to normal
+
+ align:start position:0%
+underweight and underweight to normal
+ 
+
+ align:start position:0%
+underweight and underweight to normal
+and then over and notice the normal
+
+ align:start position:0%
+and then over and notice the normal
+ 
+
+ align:start position:0%
+and then over and notice the normal
+ranges pretty big 185 to 25 how do you
+
+ align:start position:0%
+ranges pretty big 185 to 25 how do you
+ 
+
+ align:start position:0%
+ranges pretty big 185 to 25 how do you
+compute your body mass index since you
+
+ align:start position:0%
+compute your body mass index since you
+ 
+
+ align:start position:0%
+compute your body mass index since you
+Mar all be curious what your body mass
+
+ align:start position:0%
+Mar all be curious what your body mass
+ 
+
+ align:start position:0%
+Mar all be curious what your body mass
+is okay well notice it's it's in
+
+ align:start position:0%
+is okay well notice it's it's in
+ 
+
+ align:start position:0%
+is okay well notice it's it's in
+kilograms per meter squared meter of
+
+ align:start position:0%
+kilograms per meter squared meter of
+ 
+
+ align:start position:0%
+kilograms per meter squared meter of
+height
+
+ align:start position:0%
+height
+ 
+
+ align:start position:0%
+height
+okay so you have to convert your weight
+
+ align:start position:0%
+okay so you have to convert your weight
+ 
+
+ align:start position:0%
+okay so you have to convert your weight
+in pounds to kilogram to get this
+
+ align:start position:0%
+in pounds to kilogram to get this
+ 
+
+ align:start position:0%
+in pounds to kilogram to get this
+measure con convert your height
+
+ align:start position:0%
+measure con convert your height
+ 
+
+ align:start position:0%
+measure con convert your height
+to
+
+ align:start position:0%
+to
+ 
+
+ align:start position:0%
+to
+uh to
+
+ align:start position:0%
+uh to
+ 
+
+ align:start position:0%
+uh to
+meters and then you come out with these
+
+ align:start position:0%
+meters and then you come out with these
+ 
+
+ align:start position:0%
+meters and then you come out with these
+numbers you know and most of you I'm
+
+ align:start position:0%
+numbers you know and most of you I'm
+ 
+
+ align:start position:0%
+numbers you know and most of you I'm
+sure will fall in this range 18 and half
+
+ align:start position:0%
+sure will fall in this range 18 and half
+ 
+
+ align:start position:0%
+sure will fall in this range 18 and half
+to
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+25 and yes I'm not underweight I'm
+
+ align:start position:0%
+25 and yes I'm not underweight I'm
+ 
+
+ align:start position:0%
+25 and yes I'm not underweight I'm
+actually in this range I'm at the low
+
+ align:start position:0%
+actually in this range I'm at the low
+ 
+
+ align:start position:0%
+actually in this range I'm at the low
+end okay and
+
+ align:start position:0%
+end okay and
+ 
+
+ align:start position:0%
+end okay and
+U and then notice all these categories
+
+ align:start position:0%
+U and then notice all these categories
+ 
+
+ align:start position:0%
+U and then notice all these categories
+for being over overweight overweight
+
+ align:start position:0%
+for being over overweight overweight
+ 
+
+ align:start position:0%
+for being over overweight overweight
+obese class one obese class 2 severely
+
+ align:start position:0%
+obese class one obese class 2 severely
+ 
+
+ align:start position:0%
+obese class one obese class 2 severely
+obese morbidly obese super obese and
+
+ align:start position:0%
+obese morbidly obese super obese and
+ 
+
+ align:start position:0%
+obese morbidly obese super obese and
+Hyper
+
+ align:start position:0%
+Hyper
+ 
+
+ align:start position:0%
+Hyper
+obese and notice these are the
+
+ align:start position:0%
+obese and notice these are the
+ 
+
+ align:start position:0%
+obese and notice these are the
+weights
+
+ align:start position:0%
+weights
+ 
+
+ align:start position:0%
+weights
+of someone
+
+ align:start position:0%
+of someone
+ 
+
+ align:start position:0%
+of someone
+with that's U 5' 11 1.8
+
+ align:start position:0%
+with that's U 5' 11 1.8
+ 
+
+ align:start position:0%
+with that's U 5' 11 1.8
+m okay so if they're
+
+ align:start position:0%
+m okay so if they're
+ 
+
+ align:start position:0%
+m okay so if they're
+5'11 okay very tall woman
+
+ align:start position:0%
+5'11 okay very tall woman
+ 
+
+ align:start position:0%
+5'11 okay very tall woman
+[Music]
+
+ align:start position:0%
+[Music]
+ 
+
+ align:start position:0%
+[Music]
+an average man these are the weights
+
+ align:start position:0%
+an average man these are the weights
+ 
+
+ align:start position:0%
+an average man these are the weights
+they have to be to have that body mass
+
+ align:start position:0%
+they have to be to have that body mass
+ 
+
+ align:start position:0%
+they have to be to have that body mass
+index and the males always prefer as I
+
+ align:start position:0%
+index and the males always prefer as I
+ 
+
+ align:start position:0%
+index and the males always prefer as I
+pointed out before 17 to
+
+ align:start position:0%
+pointed out before 17 to
+ 
+
+ align:start position:0%
+pointed out before 17 to
+24 okay so they
+
+ align:start position:0%
+24 okay so they
+ 
+
+ align:start position:0%
+24 okay so they
+prefer women to be from at the top end
+
+ align:start position:0%
+prefer women to be from at the top end
+ 
+
+ align:start position:0%
+prefer women to be from at the top end
+of the underweight range uh to near the
+
+ align:start position:0%
+of the underweight range uh to near the
+ 
+
+ align:start position:0%
+of the underweight range uh to near the
+top of
+
+ align:start position:0%
+top of
+ 
+
+ align:start position:0%
+top of
+normal
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so then he cites this British study
+
+ align:start position:0%
+okay so then he cites this British study
+ 
+
+ align:start position:0%
+okay so then he cites this British study
+1998 of preferences shown by British
+
+ align:start position:0%
+1998 of preferences shown by British
+ 
+
+ align:start position:0%
+1998 of preferences shown by British
+male
+
+ align:start position:0%
+male
+ 
+
+ align:start position:0%
+male
+undergraduates this is the title Optimum
+
+ align:start position:0%
+undergraduates this is the title Optimum
+ 
+
+ align:start position:0%
+undergraduates this is the title Optimum
+body mass index and maximum sexual
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+attractiveness and they claim and this
+
+ align:start position:0%
+attractiveness and they claim and this
+ 
+
+ align:start position:0%
+attractiveness and they claim and this
+is shows you the controversy because
+
+ align:start position:0%
+is shows you the controversy because
+ 
+
+ align:start position:0%
+is shows you the controversy because
+there's been many studies of waste to
+
+ align:start position:0%
+there's been many studies of waste to
+ 
+
+ align:start position:0%
+there's been many studies of waste to
+hip ratios the big factor for
+
+ align:start position:0%
+hip ratios the big factor for
+ 
+
+ align:start position:0%
+hip ratios the big factor for
+attractiveness they found that the BMI
+
+ align:start position:0%
+attractiveness they found that the BMI
+ 
+
+ align:start position:0%
+attractiveness they found that the BMI
+was a much better predictable in the
+
+ align:start position:0%
+was a much better predictable in the
+ 
+
+ align:start position:0%
+was a much better predictable in the
+ways to hip
+
+ align:start position:0%
+ways to hip
+ 
+
+ align:start position:0%
+ways to hip
+ratio even though other studies haven't
+
+ align:start position:0%
+ratio even though other studies haven't
+ 
+
+ align:start position:0%
+ratio even though other studies haven't
+shown such a difference in fact the
+
+ align:start position:0%
+shown such a difference in fact the
+ 
+
+ align:start position:0%
+shown such a difference in fact the
+ratio's been often been reported to be
+
+ align:start position:0%
+ratio's been often been reported to be
+ 
+
+ align:start position:0%
+ratio's been often been reported to be
+the most important so I'm going to go
+
+ align:start position:0%
+the most important so I'm going to go
+ 
+
+ align:start position:0%
+the most important so I'm going to go
+through one of those interesting studies
+
+ align:start position:0%
+through one of those interesting studies
+ 
+
+ align:start position:0%
+through one of those interesting studies
+next I think both factors there's plenty
+
+ align:start position:0%
+next I think both factors there's plenty
+ 
+
+ align:start position:0%
+next I think both factors there's plenty
+of evidence that both factors are
+
+ align:start position:0%
+of evidence that both factors are
+ 
+
+ align:start position:0%
+of evidence that both factors are
+important but in their study the the
+
+ align:start position:0%
+important but in their study the the
+ 
+
+ align:start position:0%
+important but in their study the the
+range was 17 to
+
+ align:start position:0%
+range was 17 to
+ 
+
+ align:start position:0%
+range was 17 to
+24 uh and I point out the numbers there
+
+ align:start position:0%
+24 uh and I point out the numbers there
+ 
+
+ align:start position:0%
+24 uh and I point out the numbers there
+for both those both those type of
+
+ align:start position:0%
+for both those both those type of
+ 
+
+ align:start position:0%
+for both those both those type of
+values but there are
+
+ align:start position:0%
+values but there are
+ 
+
+ align:start position:0%
+values but there are
+exceptions and one is this the group of
+
+ align:start position:0%
+exceptions and one is this the group of
+ 
+
+ align:start position:0%
+exceptions and one is this the group of
+yomi okay South American
+
+ align:start position:0%
+yomi okay South American
+ 
+
+ align:start position:0%
+yomi okay South American
+tribe U was found that they tend to
+
+ align:start position:0%
+tribe U was found that they tend to
+ 
+
+ align:start position:0%
+tribe U was found that they tend to
+prefer females with a figure that's
+
+ align:start position:0%
+prefer females with a figure that's
+ 
+
+ align:start position:0%
+prefer females with a figure that's
+heavier with a larger waste to hip
+
+ align:start position:0%
+heavier with a larger waste to hip
+ 
+
+ align:start position:0%
+heavier with a larger waste to hip
+ratio than pre than what is preferred by
+
+ align:start position:0%
+ratio than pre than what is preferred by
+ 
+
+ align:start position:0%
+ratio than pre than what is preferred by
+most men and and most in what we call
+
+ align:start position:0%
+most men and and most in what we call
+ 
+
+ align:start position:0%
+most men and and most in what we call
+Advanced
+
+ align:start position:0%
+Advanced
+ 
+
+ align:start position:0%
+Advanced
+cultures Advanced technically
+
+ align:start position:0%
+cultures Advanced technically
+ 
+
+ align:start position:0%
+cultures Advanced technically
+educationally so forth okay
+
+ align:start position:0%
+educationally so forth okay
+ 
+
+ align:start position:0%
+educationally so forth okay
+and I didn't bring the pictures they
+
+ align:start position:0%
+and I didn't bring the pictures they
+ 
+
+ align:start position:0%
+and I didn't bring the pictures they
+show silhouettes of the kind of women
+
+ align:start position:0%
+show silhouettes of the kind of women
+ 
+
+ align:start position:0%
+show silhouettes of the kind of women
+they they were basically these men in
+
+ align:start position:0%
+they they were basically these men in
+ 
+
+ align:start position:0%
+they they were basically these men in
+the test were shown little drawings of
+
+ align:start position:0%
+the test were shown little drawings of
+ 
+
+ align:start position:0%
+the test were shown little drawings of
+women uh sort of front view mostly front
+
+ align:start position:0%
+women uh sort of front view mostly front
+ 
+
+ align:start position:0%
+women uh sort of front view mostly front
+view so you can see their shape and they
+
+ align:start position:0%
+view so you can see their shape and they
+ 
+
+ align:start position:0%
+view so you can see their shape and they
+chose the heavy slightly heavier than
+
+ align:start position:0%
+chose the heavy slightly heavier than
+ 
+
+ align:start position:0%
+chose the heavy slightly heavier than
+the what people in USA or Europe would
+
+ align:start position:0%
+the what people in USA or Europe would
+ 
+
+ align:start position:0%
+the what people in USA or Europe would
+choose So He suggests I think his
+
+ align:start position:0%
+choose So He suggests I think his
+ 
+
+ align:start position:0%
+choose So He suggests I think his
+argument it's a little bit fuzzy but it
+
+ align:start position:0%
+argument it's a little bit fuzzy but it
+ 
+
+ align:start position:0%
+argument it's a little bit fuzzy but it
+and it hasn't been fully tested
+
+ align:start position:0%
+and it hasn't been fully tested
+ 
+
+ align:start position:0%
+and it hasn't been fully tested
+but he points out that obesity was all
+
+ align:start position:0%
+but he points out that obesity was all
+ 
+
+ align:start position:0%
+but he points out that obesity was all
+but impossible in pre-colonial Amar
+
+ align:start position:0%
+but impossible in pre-colonial Amar
+ 
+
+ align:start position:0%
+but impossible in pre-colonial Amar
+Indian groups these were American an
+
+ align:start position:0%
+Indian groups these were American an
+ 
+
+ align:start position:0%
+Indian groups these were American an
+American Indian group in South America
+
+ align:start position:0%
+American Indian group in South America
+ 
+
+ align:start position:0%
+American Indian group in South America
+uh being underweight was probably more
+
+ align:start position:0%
+uh being underweight was probably more
+ 
+
+ align:start position:0%
+uh being underweight was probably more
+common and if a woman was slightly
+
+ align:start position:0%
+common and if a woman was slightly
+ 
+
+ align:start position:0%
+common and if a woman was slightly
+overweight
+
+ align:start position:0%
+overweight
+ 
+
+ align:start position:0%
+overweight
+He suggests that there was a greater
+
+ align:start position:0%
+He suggests that there was a greater
+ 
+
+ align:start position:0%
+He suggests that there was a greater
+probability of her being
+
+ align:start position:0%
+probability of her being
+ 
+
+ align:start position:0%
+probability of her being
+fertile and also the probability would
+
+ align:start position:0%
+fertile and also the probability would
+ 
+
+ align:start position:0%
+fertile and also the probability would
+be greater that she doesn't have a
+
+ align:start position:0%
+be greater that she doesn't have a
+ 
+
+ align:start position:0%
+be greater that she doesn't have a
+problem with parasites which are common
+
+ align:start position:0%
+problem with parasites which are common
+ 
+
+ align:start position:0%
+problem with parasites which are common
+down in
+
+ align:start position:0%
+down in
+ 
+
+ align:start position:0%
+down in
+there uh and with their living
+
+ align:start position:0%
+there uh and with their living
+ 
+
+ align:start position:0%
+there uh and with their living
+style and of course that suggestion
+
+ align:start position:0%
+style and of course that suggestion
+ 
+
+ align:start position:0%
+style and of course that suggestion
+should apply to other groups that should
+
+ align:start position:0%
+should apply to other groups that should
+ 
+
+ align:start position:0%
+should apply to other groups that should
+be more
+
+ align:start position:0%
+be more
+ 
+
+ align:start position:0%
+be more
+tested
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh and it should at least be true for
+
+ align:start position:0%
+uh and it should at least be true for
+ 
+
+ align:start position:0%
+uh and it should at least be true for
+groups that have been isolated from
+
+ align:start position:0%
+groups that have been isolated from
+ 
+
+ align:start position:0%
+groups that have been isolated from
+Modern
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+societies we don't know he's probably
+
+ align:start position:0%
+societies we don't know he's probably
+ 
+
+ align:start position:0%
+societies we don't know he's probably
+right about this but you know you need
+
+ align:start position:0%
+right about this but you know you need
+ 
+
+ align:start position:0%
+right about this but you know you need
+to test any of these
+
+ align:start position:0%
+to test any of these
+ 
+
+ align:start position:0%
+to test any of these
+ideas and but you could also just say
+
+ align:start position:0%
+ideas and but you could also just say
+ 
+
+ align:start position:0%
+ideas and but you could also just say
+well okay one one exception doesn't
+
+ align:start position:0%
+well okay one one exception doesn't
+ 
+
+ align:start position:0%
+well okay one one exception doesn't
+disprove the general finding and even
+
+ align:start position:0%
+disprove the general finding and even
+ 
+
+ align:start position:0%
+disprove the general finding and even
+though that's true when you get a
+
+ align:start position:0%
+though that's true when you get a
+ 
+
+ align:start position:0%
+though that's true when you get a
+consistent finding like that in one
+
+ align:start position:0%
+consistent finding like that in one
+ 
+
+ align:start position:0%
+consistent finding like that in one
+Society there's got to be some reason
+
+ align:start position:0%
+Society there's got to be some reason
+ 
+
+ align:start position:0%
+Society there's got to be some reason
+for it and so it's worthy of more
+
+ align:start position:0%
+for it and so it's worthy of more
+ 
+
+ align:start position:0%
+for it and so it's worthy of more
+investigation
+
+ align:start position:0%
+investigation
+ 
+
+ align:start position:0%
+investigation
+but not just with the yomi but with
+
+ align:start position:0%
+but not just with the yomi but with
+ 
+
+ align:start position:0%
+but not just with the yomi but with
+other groups where similar conditions
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+apply okay now this is a
+
+ align:start position:0%
+apply okay now this is a
+ 
+
+ align:start position:0%
+apply okay now this is a
+study uh where they paid attention to
+
+ align:start position:0%
+study uh where they paid attention to
+ 
+
+ align:start position:0%
+study uh where they paid attention to
+both of these
+
+ align:start position:0%
+both of these
+ 
+
+ align:start position:0%
+both of these
+measures this is the article male
+
+ align:start position:0%
+measures this is the article male
+ 
+
+ align:start position:0%
+measures this is the article male
+preferences for female waist to hip
+
+ align:start position:0%
+preferences for female waist to hip
+ 
+
+ align:start position:0%
+preferences for female waist to hip
+ratio and body mass index in the
+
+ align:start position:0%
+ratio and body mass index in the
+ 
+
+ align:start position:0%
+ratio and body mass index in the
+highlands of Papua New
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Guinea
+
+ align:start position:0%
+Guinea
+ 
+
+ align:start position:0%
+Guinea
+it was published in the American Journal
+
+ align:start position:0%
+it was published in the American Journal
+ 
+
+ align:start position:0%
+it was published in the American Journal
+of physical anthropology a few years
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+ago they were using 100 men in three
+
+ align:start position:0%
+ago they were using 100 men in three
+ 
+
+ align:start position:0%
+ago they were using 100 men in three
+villages in this remote
+
+ align:start position:0%
+villages in this remote
+ 
+
+ align:start position:0%
+villages in this remote
+region they were asked to judge
+
+ align:start position:0%
+region they were asked to judge
+ 
+
+ align:start position:0%
+region they were asked to judge
+attractiveness of women who had
+
+ align:start position:0%
+attractiveness of women who had
+ 
+
+ align:start position:0%
+attractiveness of women who had
+undergone micrograph surgery to reduce
+
+ align:start position:0%
+undergone micrograph surgery to reduce
+ 
+
+ align:start position:0%
+undergone micrograph surgery to reduce
+their waste to hip ratio they'd
+
+ align:start position:0%
+their waste to hip ratio they'd
+ 
+
+ align:start position:0%
+their waste to hip ratio they'd
+undergone a kind of plastic
+
+ align:start position:0%
+undergone a kind of plastic
+ 
+
+ align:start position:0%
+undergone a kind of plastic
+surgery
+
+ align:start position:0%
+surgery
+ 
+
+ align:start position:0%
+surgery
+so what they do is they take the fatty
+
+ align:start position:0%
+so what they do is they take the fatty
+ 
+
+ align:start position:0%
+so what they do is they take the fatty
+tissue the adapost tissue from the waist
+
+ align:start position:0%
+tissue the adapost tissue from the waist
+ 
+
+ align:start position:0%
+tissue the adapost tissue from the waist
+and reshape the buttocks with it so the
+
+ align:start position:0%
+and reshape the buttocks with it so the
+ 
+
+ align:start position:0%
+and reshape the buttocks with it so the
+weight the average weight anyway of
+
+ align:start position:0%
+weight the average weight anyway of
+ 
+
+ align:start position:0%
+weight the average weight anyway of
+these women doesn't change
+
+ align:start position:0%
+these women doesn't change
+ 
+
+ align:start position:0%
+these women doesn't change
+much but their shape
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+changes they get more of an hourglass
+
+ align:start position:0%
+changes they get more of an hourglass
+ 
+
+ align:start position:0%
+changes they get more of an hourglass
+figure and the men consistently chose
+
+ align:start position:0%
+figure and the men consistently chose
+ 
+
+ align:start position:0%
+figure and the men consistently chose
+postoperative photographs as being more
+
+ align:start position:0%
+postoperative photographs as being more
+ 
+
+ align:start position:0%
+postoperative photographs as being more
+attractive than pre-operative
+
+ align:start position:0%
+attractive than pre-operative
+ 
+
+ align:start position:0%
+attractive than pre-operative
+photographs of the same women
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and it didn't seem to be the body mass
+
+ align:start position:0%
+and it didn't seem to be the body mass
+ 
+
+ align:start position:0%
+and it didn't seem to be the body mass
+index that made a difference these These
+
+ align:start position:0%
+index that made a difference these These
+ 
+
+ align:start position:0%
+index that made a difference these These
+are the actual numbers from the study so
+
+ align:start position:0%
+are the actual numbers from the study so
+ 
+
+ align:start position:0%
+are the actual numbers from the study so
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+uh the were they did it twice these are
+
+ align:start position:0%
+uh the were they did it twice these are
+ 
+
+ align:start position:0%
+uh the were they did it twice these are
+the two groups of women undergoing this
+
+ align:start position:0%
+the two groups of women undergoing this
+ 
+
+ align:start position:0%
+the two groups of women undergoing this
+surgery uh this is these
+
+ align:start position:0%
+surgery uh this is these
+ 
+
+ align:start position:0%
+surgery uh this is these
+are G gives the patients uh ethnicity
+
+ align:start position:0%
+are G gives the patients uh ethnicity
+ 
+
+ align:start position:0%
+are G gives the patients uh ethnicity
+and you can see that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+varied
+
+ align:start position:0%
+varied
+ 
+
+ align:start position:0%
+varied
+and the in this group
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh you can see that the body mass index
+
+ align:start position:0%
+uh you can see that the body mass index
+ 
+
+ align:start position:0%
+uh you can see that the body mass index
+was not change one group they were
+
+ align:start position:0%
+was not change one group they were
+ 
+
+ align:start position:0%
+was not change one group they were
+changing more the other one group
+
+ align:start position:0%
+changing more the other one group
+ 
+
+ align:start position:0%
+changing more the other one group
+actually went up a little bit the other
+
+ align:start position:0%
+actually went up a little bit the other
+ 
+
+ align:start position:0%
+actually went up a little bit the other
+group went down a little bit the body
+
+ align:start position:0%
+group went down a little bit the body
+ 
+
+ align:start position:0%
+group went down a little bit the body
+mass index but the waste hip ratios that
+
+ align:start position:0%
+mass index but the waste hip ratios that
+ 
+
+ align:start position:0%
+mass index but the waste hip ratios that
+you can see would
+
+ align:start position:0%
+you can see would
+ 
+
+ align:start position:0%
+you can see would
+consistently uh
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+reduced
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+all right so that was the data they had
+
+ align:start position:0%
+all right so that was the data they had
+ 
+
+ align:start position:0%
+all right so that was the data they had
+and they the men were tested on
+
+ align:start position:0%
+and they the men were tested on
+ 
+
+ align:start position:0%
+and they the men were tested on
+photographs these were the the nature of
+
+ align:start position:0%
+photographs these were the the nature of
+ 
+
+ align:start position:0%
+photographs these were the the nature of
+the photographs so here's a preop here's
+
+ align:start position:0%
+the photographs so here's a preop here's
+ 
+
+ align:start position:0%
+the photographs so here's a preop here's
+postop and this is the oblike view preop
+
+ align:start position:0%
+postop and this is the oblike view preop
+ 
+
+ align:start position:0%
+postop and this is the oblike view preop
+and postop so it shows what the surgeons
+
+ align:start position:0%
+and postop so it shows what the surgeons
+ 
+
+ align:start position:0%
+and postop so it shows what the surgeons
+were doing and these are the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+preferences much greater preference for
+
+ align:start position:0%
+preferences much greater preference for
+ 
+
+ align:start position:0%
+preferences much greater preference for
+the postoperative C ly for that
+
+ align:start position:0%
+the postoperative C ly for that
+ 
+
+ align:start position:0%
+the postoperative C ly for that
+view so that was one study that because
+
+ align:start position:0%
+view so that was one study that because
+ 
+
+ align:start position:0%
+view so that was one study that because
+they were the very same women involved
+
+ align:start position:0%
+they were the very same women involved
+ 
+
+ align:start position:0%
+they were the very same women involved
+the only thing that was changing in an
+
+ align:start position:0%
+the only thing that was changing in an
+ 
+
+ align:start position:0%
+the only thing that was changing in an
+obvious way was simply that that shape
+
+ align:start position:0%
+obvious way was simply that that shape
+ 
+
+ align:start position:0%
+obvious way was simply that that shape
+that affected their wayist to hip ratio
+
+ align:start position:0%
+that affected their wayist to hip ratio
+ 
+
+ align:start position:0%
+that affected their wayist to hip ratio
+the body mass index um when it did go
+
+ align:start position:0%
+the body mass index um when it did go
+ 
+
+ align:start position:0%
+the body mass index um when it did go
+down didn't seem to make any difference
+
+ align:start position:0%
+down didn't seem to make any difference
+ 
+
+ align:start position:0%
+down didn't seem to make any difference
+in that particular
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+study so what about reference is shown
+
+ align:start position:0%
+study so what about reference is shown
+ 
+
+ align:start position:0%
+study so what about reference is shown
+by females choosing mates this has been
+
+ align:start position:0%
+by females choosing mates this has been
+ 
+
+ align:start position:0%
+by females choosing mates this has been
+studied also and as we know
+
+ align:start position:0%
+studied also and as we know
+ 
+
+ align:start position:0%
+studied also and as we know
+from uh when we were talking about
+
+ align:start position:0%
+from uh when we were talking about
+ 
+
+ align:start position:0%
+from uh when we were talking about
+Scott's
+
+ align:start position:0%
+Scott's
+ 
+
+ align:start position:0%
+Scott's
+chapters that females tend to make their
+
+ align:start position:0%
+chapters that females tend to make their
+ 
+
+ align:start position:0%
+chapters that females tend to make their
+decisions by different kinds of
+
+ align:start position:0%
+decisions by different kinds of
+ 
+
+ align:start position:0%
+decisions by different kinds of
+means
+
+ align:start position:0%
+means
+ 
+
+ align:start position:0%
+means
+uh it doesn't mean that physical
+
+ align:start position:0%
+uh it doesn't mean that physical
+ 
+
+ align:start position:0%
+uh it doesn't mean that physical
+attractiveness does not make some
+
+ align:start position:0%
+attractiveness does not make some
+ 
+
+ align:start position:0%
+attractiveness does not make some
+difference but it is often not as nearly
+
+ align:start position:0%
+difference but it is often not as nearly
+ 
+
+ align:start position:0%
+difference but it is often not as nearly
+as important for a woman as it is for a
+
+ align:start position:0%
+as important for a woman as it is for a
+ 
+
+ align:start position:0%
+as important for a woman as it is for a
+man and there's reasons evolutionary
+
+ align:start position:0%
+man and there's reasons evolutionary
+ 
+
+ align:start position:0%
+man and there's reasons evolutionary
+reasons for that
+
+ align:start position:0%
+reasons for that
+ 
+
+ align:start position:0%
+reasons for that
+women
+
+ align:start position:0%
+women
+ 
+
+ align:start position:0%
+women
+prefer resource
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+potential and so You' predict that well
+
+ align:start position:0%
+potential and so You' predict that well
+ 
+
+ align:start position:0%
+potential and so You' predict that well
+they might prer like older men more
+
+ align:start position:0%
+they might prer like older men more
+ 
+
+ align:start position:0%
+they might prer like older men more
+likely to have more
+
+ align:start position:0%
+likely to have more
+ 
+
+ align:start position:0%
+likely to have more
+resources uh they more likely to produce
+
+ align:start position:0%
+resources uh they more likely to produce
+ 
+
+ align:start position:0%
+resources uh they more likely to produce
+preer rich men and so forth uh men with
+
+ align:start position:0%
+preer rich men and so forth uh men with
+ 
+
+ align:start position:0%
+preer rich men and so forth uh men with
+property most men at the age when these
+
+ align:start position:0%
+property most men at the age when these
+ 
+
+ align:start position:0%
+property most men at the age when these
+choices are made don't actually have
+
+ align:start position:0%
+choices are made don't actually have
+ 
+
+ align:start position:0%
+choices are made don't actually have
+property in our society but
+
+ align:start position:0%
+property in our society but
+ 
+
+ align:start position:0%
+property in our society but
+but anyway that's how I would expect
+
+ align:start position:0%
+but anyway that's how I would expect
+ 
+
+ align:start position:0%
+but anyway that's how I would expect
+them to differ and this is if you look
+
+ align:start position:0%
+them to differ and this is if you look
+ 
+
+ align:start position:0%
+them to differ and this is if you look
+at
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh the term maximum reproductive
+
+ align:start position:0%
+uh the term maximum reproductive
+ 
+
+ align:start position:0%
+uh the term maximum reproductive
+potential just has a different a
+
+ align:start position:0%
+potential just has a different a
+ 
+
+ align:start position:0%
+potential just has a different a
+different meaning for women and men and
+
+ align:start position:0%
+different meaning for women and men and
+ 
+
+ align:start position:0%
+different meaning for women and men and
+this is the difference in age
+
+ align:start position:0%
+this is the difference in age
+ 
+
+ align:start position:0%
+this is the difference in age
+preferences uh the mean age this this is
+
+ align:start position:0%
+preferences uh the mean age this this is
+ 
+
+ align:start position:0%
+preferences uh the mean age this this is
+the age
+
+ align:start position:0%
+the age
+ 
+
+ align:start position:0%
+the age
+difference
+
+ align:start position:0%
+difference
+ 
+
+ align:start position:0%
+difference
+uh male greater than
+
+ align:start position:0%
+uh male greater than
+ 
+
+ align:start position:0%
+uh male greater than
+female it's only these to the left of
+
+ align:start position:0%
+female it's only these to the left of
+ 
+
+ align:start position:0%
+female it's only these to the left of
+that vertical line there where
+
+ align:start position:0%
+that vertical line there where
+ 
+
+ align:start position:0%
+that vertical line there where
+the in actual marriages the male uh is
+
+ align:start position:0%
+the in actual marriages the male uh is
+ 
+
+ align:start position:0%
+the in actual marriages the male uh is
+younger than the female these are all
+
+ align:start position:0%
+younger than the female these are all
+ 
+
+ align:start position:0%
+younger than the female these are all
+the ones where the male is older and
+
+ align:start position:0%
+the ones where the male is older and
+ 
+
+ align:start position:0%
+the ones where the male is older and
+note that the peak is roughly 3
+
+ align:start position:0%
+note that the peak is roughly 3
+ 
+
+ align:start position:0%
+note that the peak is roughly 3
+years that's consistent finding in these
+
+ align:start position:0%
+years that's consistent finding in these
+ 
+
+ align:start position:0%
+years that's consistent finding in these
+studies but no notice also a huge range
+
+ align:start position:0%
+studies but no notice also a huge range
+ 
+
+ align:start position:0%
+studies but no notice also a huge range
+okay it goes up of course some women
+
+ align:start position:0%
+okay it goes up of course some women
+ 
+
+ align:start position:0%
+okay it goes up of course some women
+will marry a man that's more than twice
+
+ align:start position:0%
+will marry a man that's more than twice
+ 
+
+ align:start position:0%
+will marry a man that's more than twice
+their age and this does occur so it's
+
+ align:start position:0%
+their age and this does occur so it's
+ 
+
+ align:start position:0%
+their age and this does occur so it's
+all that kind of data is on this this
+
+ align:start position:0%
+all that kind of data is on this this
+ 
+
+ align:start position:0%
+all that kind of data is on this this
+type of curve but you can see it's a
+
+ align:start position:0%
+type of curve but you can see it's a
+ 
+
+ align:start position:0%
+type of curve but you can see it's a
+small small percentage
+
+ align:start position:0%
+small small percentage
+ 
+
+ align:start position:0%
+small small percentage
+there so it's explained by just it's
+
+ align:start position:0%
+there so it's explained by just it's
+ 
+
+ align:start position:0%
+there so it's explained by just it's
+it's predicted by this expectation that
+
+ align:start position:0%
+it's predicted by this expectation that
+ 
+
+ align:start position:0%
+it's predicted by this expectation that
+women are looking more for potential or
+
+ align:start position:0%
+women are looking more for potential or
+ 
+
+ align:start position:0%
+women are looking more for potential or
+actual
+
+ align:start position:0%
+actual
+ 
+
+ align:start position:0%
+actual
+resources all right
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+humans also have this tendency to stay
+
+ align:start position:0%
+humans also have this tendency to stay
+ 
+
+ align:start position:0%
+humans also have this tendency to stay
+and act within
+
+ align:start position:0%
+and act within
+ 
+
+ align:start position:0%
+and act within
+groups and different groups May compete
+
+ align:start position:0%
+groups and different groups May compete
+ 
+
+ align:start position:0%
+groups and different groups May compete
+with each other sometimes
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+violently remember the story of Romeo
+
+ align:start position:0%
+violently remember the story of Romeo
+ 
+
+ align:start position:0%
+violently remember the story of Romeo
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+Juliet so uh
+
+ align:start position:0%
+Juliet so uh
+ 
+
+ align:start position:0%
+Juliet so uh
+I I want to try to specify a list of
+
+ align:start position:0%
+I I want to try to specify a list of
+ 
+
+ align:start position:0%
+I I want to try to specify a list of
+evolutionary fit winess benefits of
+
+ align:start position:0%
+evolutionary fit winess benefits of
+ 
+
+ align:start position:0%
+evolutionary fit winess benefits of
+these groupism
+
+ align:start position:0%
+these groupism
+ 
+
+ align:start position:0%
+these groupism
+feelings why do we like to measure to to
+
+ align:start position:0%
+feelings why do we like to measure to to
+ 
+
+ align:start position:0%
+feelings why do we like to measure to to
+choose someone within our group
+
+ align:start position:0%
+choose someone within our group
+ 
+
+ align:start position:0%
+choose someone within our group
+especially if think of earlier Society
+
+ align:start position:0%
+especially if think of earlier Society
+ 
+
+ align:start position:0%
+especially if think of earlier Society
+during our
+
+ align:start position:0%
+during our
+ 
+
+ align:start position:0%
+during our
+Evolution okay and these are the things
+
+ align:start position:0%
+Evolution okay and these are the things
+ 
+
+ align:start position:0%
+Evolution okay and these are the things
+I could come up
+
+ align:start position:0%
+I could come up
+ 
+
+ align:start position:0%
+I could come up
+with higher probability of finding a
+
+ align:start position:0%
+with higher probability of finding a
+ 
+
+ align:start position:0%
+with higher probability of finding a
+mate
+
+ align:start position:0%
+mate
+ 
+
+ align:start position:0%
+mate
+okay higher probability of rescue and
+
+ align:start position:0%
+okay higher probability of rescue and
+ 
+
+ align:start position:0%
+okay higher probability of rescue and
+survival if you lit the stay within that
+
+ align:start position:0%
+survival if you lit the stay within that
+ 
+
+ align:start position:0%
+survival if you lit the stay within that
+group higher probability of better
+
+ align:start position:0%
+group higher probability of better
+ 
+
+ align:start position:0%
+group higher probability of better
+defense against
+
+ align:start position:0%
+defense against
+ 
+
+ align:start position:0%
+defense against
+predators if there's a predator people
+
+ align:start position:0%
+predators if there's a predator people
+ 
+
+ align:start position:0%
+predators if there's a predator people
+in the same
+
+ align:start position:0%
+in the same
+ 
+
+ align:start position:0%
+in the same
+group get together help each other not
+
+ align:start position:0%
+group get together help each other not
+ 
+
+ align:start position:0%
+group get together help each other not
+as likely to help the
+
+ align:start position:0%
+as likely to help the
+ 
+
+ align:start position:0%
+as likely to help the
+outsider higher probability of better
+
+ align:start position:0%
+outsider higher probability of better
+ 
+
+ align:start position:0%
+outsider higher probability of better
+defense against hostile human
+
+ align:start position:0%
+defense against hostile human
+ 
+
+ align:start position:0%
+defense against hostile human
+groups advantages in food acquisition
+
+ align:start position:0%
+groups advantages in food acquisition
+ 
+
+ align:start position:0%
+groups advantages in food acquisition
+Gathering hunting with sharing and
+
+ align:start position:0%
+Gathering hunting with sharing and
+ 
+
+ align:start position:0%
+Gathering hunting with sharing and
+specialization these are all advantages
+
+ align:start position:0%
+specialization these are all advantages
+ 
+
+ align:start position:0%
+specialization these are all advantages
+of being in a group help in child
+
+ align:start position:0%
+of being in a group help in child
+ 
+
+ align:start position:0%
+of being in a group help in child
+rearing and
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+education and advantages in learning
+
+ align:start position:0%
+education and advantages in learning
+ 
+
+ align:start position:0%
+education and advantages in learning
+from older more experienced group
+
+ align:start position:0%
+from older more experienced group
+ 
+
+ align:start position:0%
+from older more experienced group
+members much more like it's much easier
+
+ align:start position:0%
+members much more like it's much easier
+ 
+
+ align:start position:0%
+members much more like it's much easier
+that's within your group and someone
+
+ align:start position:0%
+that's within your group and someone
+ 
+
+ align:start position:0%
+that's within your group and someone
+from another
+
+ align:start position:0%
+from another
+ 
+
+ align:start position:0%
+from another
+group of course now we formalized
+
+ align:start position:0%
+group of course now we formalized
+ 
+
+ align:start position:0%
+group of course now we formalized
+education so much we cross these
+
+ align:start position:0%
+education so much we cross these
+ 
+
+ align:start position:0%
+education so much we cross these
+boundaries all the time it's not but at
+
+ align:start position:0%
+boundaries all the time it's not but at
+ 
+
+ align:start position:0%
+boundaries all the time it's not but at
+least during our Evolution these are
+
+ align:start position:0%
+least during our Evolution these are
+ 
+
+ align:start position:0%
+least during our Evolution these are
+probably all
+
+ align:start position:0%
+probably all
+ 
+
+ align:start position:0%
+probably all
+uh probably all would be
+
+ align:start position:0%
+uh probably all would be
+ 
+
+ align:start position:0%
+uh probably all would be
+true which would simply explain why
+
+ align:start position:0%
+true which would simply explain why
+ 
+
+ align:start position:0%
+true which would simply explain why
+we've evolved these kinds of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+feelings okay then we get to his
+
+ align:start position:0%
+feelings okay then we get to his
+ 
+
+ align:start position:0%
+feelings okay then we get to his
+appendix
+
+ align:start position:0%
+appendix
+ 
+
+ align:start position:0%
+appendix
+questions
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh about the biological basis for
+
+ align:start position:0%
+uh about the biological basis for
+ 
+
+ align:start position:0%
+uh about the biological basis for
+reciprocity among humans the claim is it
+
+ align:start position:0%
+reciprocity among humans the claim is it
+ 
+
+ align:start position:0%
+reciprocity among humans the claim is it
+remains unproven General self and here
+
+ align:start position:0%
+remains unproven General self and here
+ 
+
+ align:start position:0%
+remains unproven General self and here
+the statement is that General
+
+ align:start position:0%
+the statement is that General
+ 
+
+ align:start position:0%
+the statement is that General
+self-interest and an ability to see
+
+ align:start position:0%
+self-interest and an ability to see
+ 
+
+ align:start position:0%
+self-interest and an ability to see
+beyond the short term may be all that's
+
+ align:start position:0%
+beyond the short term may be all that's
+ 
+
+ align:start position:0%
+beyond the short term may be all that's
+required to generate such Behavior so
+
+ align:start position:0%
+required to generate such Behavior so
+ 
+
+ align:start position:0%
+required to generate such Behavior so
+what's the misunderstanding in that kind
+
+ align:start position:0%
+what's the misunderstanding in that kind
+ 
+
+ align:start position:0%
+what's the misunderstanding in that kind
+of statement is very simple they can use
+
+ align:start position:0%
+of statement is very simple they can use
+ 
+
+ align:start position:0%
+of statement is very simple they can use
+approximate and ultimate issues you know
+
+ align:start position:0%
+approximate and ultimate issues you know
+ 
+
+ align:start position:0%
+approximate and ultimate issues you know
+you as we know from before you have to
+
+ align:start position:0%
+you as we know from before you have to
+ 
+
+ align:start position:0%
+you as we know from before you have to
+deal with those things separately
+
+ align:start position:0%
+deal with those things separately
+ 
+
+ align:start position:0%
+deal with those things separately
+understand that there are separate kinds
+
+ align:start position:0%
+understand that there are separate kinds
+ 
+
+ align:start position:0%
+understand that there are separate kinds
+of qu of
+
+ align:start position:0%
+of qu of
+ 
+
+ align:start position:0%
+of qu of
+issues uh
+
+ align:start position:0%
+issues uh
+ 
+
+ align:start position:0%
+issues uh
+what about the idea of languages
+
+ align:start position:0%
+what about the idea of languages
+ 
+
+ align:start position:0%
+what about the idea of languages
+languages vary greatly among human
+
+ align:start position:0%
+languages vary greatly among human
+ 
+
+ align:start position:0%
+languages vary greatly among human
+sociey so if someone claims that this
+
+ align:start position:0%
+sociey so if someone claims that this
+ 
+
+ align:start position:0%
+sociey so if someone claims that this
+fact clearly demonstrates the greater
+
+ align:start position:0%
+fact clearly demonstrates the greater
+ 
+
+ align:start position:0%
+fact clearly demonstrates the greater
+importance of culture than biology in
+
+ align:start position:0%
+importance of culture than biology in
+ 
+
+ align:start position:0%
+importance of culture than biology in
+the control of human behavior how do a
+
+ align:start position:0%
+the control of human behavior how do a
+ 
+
+ align:start position:0%
+the control of human behavior how do a
+sociobiologist deal with that very
+
+ align:start position:0%
+sociobiologist deal with that very
+ 
+
+ align:start position:0%
+sociobiologist deal with that very
+simply the important issue is language
+
+ align:start position:0%
+simply the important issue is language
+ 
+
+ align:start position:0%
+simply the important issue is language
+versus no language not the details of a
+
+ align:start position:0%
+versus no language not the details of a
+ 
+
+ align:start position:0%
+versus no language not the details of a
+particular language that's where chsky
+
+ align:start position:0%
+particular language that's where chsky
+ 
+
+ align:start position:0%
+particular language that's where chsky
+made great contribution pointing out the
+
+ align:start position:0%
+made great contribution pointing out the
+ 
+
+ align:start position:0%
+made great contribution pointing out the
+the form of grammar that's the same one
+
+ align:start position:0%
+the form of grammar that's the same one
+ 
+
+ align:start position:0%
+the form of grammar that's the same one
+language after another after
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+another so we're born with an innate
+
+ align:start position:0%
+another so we're born with an innate
+ 
+
+ align:start position:0%
+another so we're born with an innate
+ability to learn any language that's
+
+ align:start position:0%
+ability to learn any language that's
+ 
+
+ align:start position:0%
+ability to learn any language that's
+what we
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+inherit and here's one of Steph j
+
+ align:start position:0%
+inherit and here's one of Steph j
+ 
+
+ align:start position:0%
+inherit and here's one of Steph j
+gr's u statements men are not programmed
+
+ align:start position:0%
+gr's u statements men are not programmed
+ 
+
+ align:start position:0%
+gr's u statements men are not programmed
+by genes to maximize matings nor are
+
+ align:start position:0%
+by genes to maximize matings nor are
+ 
+
+ align:start position:0%
+by genes to maximize matings nor are
+women devoted to monogamy by un
+
+ align:start position:0%
+women devoted to monogamy by un
+ 
+
+ align:start position:0%
+women devoted to monogamy by un
+inalterable nature we can speak only of
+
+ align:start position:0%
+inalterable nature we can speak only of
+ 
+
+ align:start position:0%
+inalterable nature we can speak only of
+capacities not requirements or even
+
+ align:start position:0%
+capacities not requirements or even
+ 
+
+ align:start position:0%
+capacities not requirements or even
+determining propensities therefore our
+
+ align:start position:0%
+determining propensities therefore our
+ 
+
+ align:start position:0%
+determining propensities therefore our
+biology does not make us do
+
+ align:start position:0%
+biology does not make us do
+ 
+
+ align:start position:0%
+biology does not make us do
+it so how do you deal with that kind of
+
+ align:start position:0%
+it so how do you deal with that kind of
+ 
+
+ align:start position:0%
+it so how do you deal with that kind of
+criticism
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+sociobiology he's pitting culture
+
+ align:start position:0%
+sociobiology he's pitting culture
+ 
+
+ align:start position:0%
+sociobiology he's pitting culture
+against biology culture versus biology
+
+ align:start position:0%
+against biology culture versus biology
+ 
+
+ align:start position:0%
+against biology culture versus biology
+is it's not an either or matter at
+
+ align:start position:0%
+is it's not an either or matter at
+ 
+
+ align:start position:0%
+is it's not an either or matter at
+all as we pointed out both are always
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+involved okay now this is an
+
+ align:start position:0%
+involved okay now this is an
+ 
+
+ align:start position:0%
+involved okay now this is an
+interesting this is a critique of Alcock
+
+ align:start position:0%
+interesting this is a critique of Alcock
+ 
+
+ align:start position:0%
+interesting this is a critique of Alcock
+in the final paragraph of chapter 7 he
+
+ align:start position:0%
+in the final paragraph of chapter 7 he
+ 
+
+ align:start position:0%
+in the final paragraph of chapter 7 he
+sums up his conclusions about the
+
+ align:start position:0%
+sums up his conclusions about the
+ 
+
+ align:start position:0%
+sums up his conclusions about the
+unlikely philosophy that goul needs and
+
+ align:start position:0%
+unlikely philosophy that goul needs and
+ 
+
+ align:start position:0%
+unlikely philosophy that goul needs and
+many social scientists and some
+
+ align:start position:0%
+many social scientists and some
+ 
+
+ align:start position:0%
+many social scientists and some
+feminists would have a accept largely on
+
+ align:start position:0%
+feminists would have a accept largely on
+ 
+
+ align:start position:0%
+feminists would have a accept largely on
+ideological grounds but then he suddenly
+
+ align:start position:0%
+ideological grounds but then he suddenly
+ 
+
+ align:start position:0%
+ideological grounds but then he suddenly
+shifts the argument and listen to what
+
+ align:start position:0%
+shifts the argument and listen to what
+ 
+
+ align:start position:0%
+shifts the argument and listen to what
+he
+
+ align:start position:0%
+he
+ 
+
+ align:start position:0%
+he
+says that this position has any residual
+
+ align:start position:0%
+says that this position has any residual
+ 
+
+ align:start position:0%
+says that this position has any residual
+credibility can be attributed largely to
+
+ align:start position:0%
+credibility can be attributed largely to
+ 
+
+ align:start position:0%
+credibility can be attributed largely to
+the power of wishful thinking that some
+
+ align:start position:0%
+the power of wishful thinking that some
+ 
+
+ align:start position:0%
+the power of wishful thinking that some
+special meaning occurs to human
+
+ align:start position:0%
+special meaning occurs to human
+ 
+
+ align:start position:0%
+special meaning occurs to human
+existence and this is this is a quote
+
+ align:start position:0%
+existence and this is this is a quote
+ 
+
+ align:start position:0%
+existence and this is this is a quote
+now it is not easy to accept that
+
+ align:start position:0%
+now it is not easy to accept that
+ 
+
+ align:start position:0%
+now it is not easy to accept that
+evolution is a meaningless tale told by
+
+ align:start position:0%
+evolution is a meaningless tale told by
+ 
+
+ align:start position:0%
+evolution is a meaningless tale told by
+an idiot
+
+ align:start position:0%
+an idiot
+ 
+
+ align:start position:0%
+an idiot
+his conclusion is then stated indeed
+
+ align:start position:0%
+his conclusion is then stated indeed
+ 
+
+ align:start position:0%
+his conclusion is then stated indeed
+most people find it hard to believe that
+
+ align:start position:0%
+most people find it hard to believe that
+ 
+
+ align:start position:0%
+most people find it hard to believe that
+blind evolutionary processes have
+
+ align:start position:0%
+blind evolutionary processes have
+ 
+
+ align:start position:0%
+blind evolutionary processes have
+created us a creature whose unconscious
+
+ align:start position:0%
+created us a creature whose unconscious
+ 
+
+ align:start position:0%
+created us a creature whose unconscious
+ultimate goal is no different from that
+
+ align:start position:0%
+ultimate goal is no different from that
+ 
+
+ align:start position:0%
+ultimate goal is no different from that
+of the slime mold the arvar the pine
+
+ align:start position:0%
+of the slime mold the arvar the pine
+ 
+
+ align:start position:0%
+of the slime mold the arvar the pine
+tree and the
+
+ align:start position:0%
+tree and the
+ 
+
+ align:start position:0%
+tree and the
+earthworm although this point is
+
+ align:start position:0%
+earthworm although this point is
+ 
+
+ align:start position:0%
+earthworm although this point is
+evitably U evidently unpalatable it is
+
+ align:start position:0%
+evitably U evidently unpalatable it is
+ 
+
+ align:start position:0%
+evitably U evidently unpalatable it is
+true
+
+ align:start position:0%
+true
+ 
+
+ align:start position:0%
+true
+nevertheless so my criticism of alock
+
+ align:start position:0%
+nevertheless so my criticism of alock
+ 
+
+ align:start position:0%
+nevertheless so my criticism of alock
+here is just that it's very narrow
+
+ align:start position:0%
+here is just that it's very narrow
+ 
+
+ align:start position:0%
+here is just that it's very narrow
+definition of what you mean by an
+
+ align:start position:0%
+definition of what you mean by an
+ 
+
+ align:start position:0%
+definition of what you mean by an
+ultimate
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+goal there's a the ultimate reason we
+
+ align:start position:0%
+goal there's a the ultimate reason we
+ 
+
+ align:start position:0%
+goal there's a the ultimate reason we
+evolve this way is certainly this very
+
+ align:start position:0%
+evolve this way is certainly this very
+ 
+
+ align:start position:0%
+evolve this way is certainly this very
+simple rule
+
+ align:start position:0%
+simple rule
+ 
+
+ align:start position:0%
+simple rule
+of
+
+ align:start position:0%
+of
+ 
+
+ align:start position:0%
+of
+maximizing genetic
+
+ align:start position:0%
+maximizing genetic
+ 
+
+ align:start position:0%
+maximizing genetic
+fitness so is it really a meaningless
+
+ align:start position:0%
+fitness so is it really a meaningless
+ 
+
+ align:start position:0%
+fitness so is it really a meaningless
+tale told by an idot
+
+ align:start position:0%
+tale told by an idot
+ 
+
+ align:start position:0%
+tale told by an idot
+idiot in my view what is really
+
+ align:start position:0%
+idiot in my view what is really
+ 
+
+ align:start position:0%
+idiot in my view what is really
+incredible and amazing is that the
+
+ align:start position:0%
+incredible and amazing is that the
+ 
+
+ align:start position:0%
+incredible and amazing is that the
+simple and repeated process of genetic
+
+ align:start position:0%
+simple and repeated process of genetic
+ 
+
+ align:start position:0%
+simple and repeated process of genetic
+spread and change following the
+
+ align:start position:0%
+spread and change following the
+ 
+
+ align:start position:0%
+spread and change following the
+biological law of natural selection has
+
+ align:start position:0%
+biological law of natural selection has
+ 
+
+ align:start position:0%
+biological law of natural selection has
+led to such complex creatures with such
+
+ align:start position:0%
+led to such complex creatures with such
+ 
+
+ align:start position:0%
+led to such complex creatures with such
+cognitive capacities with such an
+
+ align:start position:0%
+cognitive capacities with such an
+ 
+
+ align:start position:0%
+cognitive capacities with such an
+ability to ponder the nature of the
+
+ align:start position:0%
+ability to ponder the nature of the
+ 
+
+ align:start position:0%
+ability to ponder the nature of the
+world and its beings and beyond that I
+
+ align:start position:0%
+world and its beings and beyond that I
+ 
+
+ align:start position:0%
+world and its beings and beyond that I
+would add that conscious
+
+ align:start position:0%
+would add that conscious
+ 
+
+ align:start position:0%
+would add that conscious
+beings the sociobiologists the
+
+ align:start position:0%
+beings the sociobiologists the
+ 
+
+ align:start position:0%
+beings the sociobiologists the
+evolutionists have no explanation for
+
+ align:start position:0%
+evolutionists have no explanation for
+ 
+
+ align:start position:0%
+evolutionists have no explanation for
+even existence of
+
+ align:start position:0%
+even existence of
+ 
+
+ align:start position:0%
+even existence of
+Consciousness it's outside their Realm
+
+ align:start position:0%
+Consciousness it's outside their Realm
+ 
+
+ align:start position:0%
+Consciousness it's outside their Realm
+as I pointed out
+
+ align:start position:0%
+as I pointed out
+ 
+
+ align:start position:0%
+as I pointed out
+before okay here's a final topic we have
+
+ align:start position:0%
+before okay here's a final topic we have
+ 
+
+ align:start position:0%
+before okay here's a final topic we have
+four
+
+ align:start position:0%
+four
+ 
+
+ align:start position:0%
+four
+minutes romantic
+
+ align:start position:0%
+minutes romantic
+ 
+
+ align:start position:0%
+minutes romantic
+love is the phenomenon of romantic love
+
+ align:start position:0%
+love is the phenomenon of romantic love
+ 
+
+ align:start position:0%
+love is the phenomenon of romantic love
+the falling in love experience an
+
+ align:start position:0%
+the falling in love experience an
+ 
+
+ align:start position:0%
+the falling in love experience an
+invention of medieval Court life as has
+
+ align:start position:0%
+invention of medieval Court life as has
+ 
+
+ align:start position:0%
+invention of medieval Court life as has
+been repeatedly
+
+ align:start position:0%
+been repeatedly
+ 
+
+ align:start position:0%
+been repeatedly
+asserted in in the in literature and and
+
+ align:start position:0%
+asserted in in the in literature and and
+ 
+
+ align:start position:0%
+asserted in in the in literature and and
+it it's a very popular belief after it
+
+ align:start position:0%
+it it's a very popular belief after it
+ 
+
+ align:start position:0%
+it it's a very popular belief after it
+was first
+
+ align:start position:0%
+was first
+ 
+
+ align:start position:0%
+was first
+propose does it only occur in certain
+
+ align:start position:0%
+propose does it only occur in certain
+ 
+
+ align:start position:0%
+propose does it only occur in certain
+cultures so I want to State a sociu a
+
+ align:start position:0%
+cultures so I want to State a sociu a
+ 
+
+ align:start position:0%
+cultures so I want to State a sociu a
+biological hypothesis concerning its
+
+ align:start position:0%
+biological hypothesis concerning its
+ 
+
+ align:start position:0%
+biological hypothesis concerning its
+Origins because you're working on
+
+ align:start position:0%
+Origins because you're working on
+ 
+
+ align:start position:0%
+Origins because you're working on
+another homework on your topics I'm not
+
+ align:start position:0%
+another homework on your topics I'm not
+ 
+
+ align:start position:0%
+another homework on your topics I'm not
+going to give this as a homework I'm
+
+ align:start position:0%
+going to give this as a homework I'm
+ 
+
+ align:start position:0%
+going to give this as a homework I'm
+going to give you what I would say about
+
+ align:start position:0%
+going to give you what I would say about
+ 
+
+ align:start position:0%
+going to give you what I would say about
+it uh first of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+all I would say that the idea was in
+
+ align:start position:0%
+all I would say that the idea was in
+ 
+
+ align:start position:0%
+all I would say that the idea was in
+invented by people who could not accept
+
+ align:start position:0%
+invented by people who could not accept
+ 
+
+ align:start position:0%
+invented by people who could not accept
+the role of innate motivations in humans
+
+ align:start position:0%
+the role of innate motivations in humans
+ 
+
+ align:start position:0%
+the role of innate motivations in humans
+at all and there are many people like
+
+ align:start position:0%
+at all and there are many people like
+ 
+
+ align:start position:0%
+at all and there are many people like
+that okay does it occur only in certain
+
+ align:start position:0%
+that okay does it occur only in certain
+ 
+
+ align:start position:0%
+that okay does it occur only in certain
+cultures it appears to occur in all
+
+ align:start position:0%
+cultures it appears to occur in all
+ 
+
+ align:start position:0%
+cultures it appears to occur in all
+cultures to some degree and there are
+
+ align:start position:0%
+cultures to some degree and there are
+ 
+
+ align:start position:0%
+cultures to some degree and there are
+many cultures that have
+
+ align:start position:0%
+many cultures that have
+ 
+
+ align:start position:0%
+many cultures that have
+um marriages that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+are made by the basically deci all the
+
+ align:start position:0%
+are made by the basically deci all the
+ 
+
+ align:start position:0%
+are made by the basically deci all the
+decisions are by the parents and the
+
+ align:start position:0%
+decisions are by the parents and the
+ 
+
+ align:start position:0%
+decisions are by the parents and the
+relatives but even in those
+
+ align:start position:0%
+relatives but even in those
+ 
+
+ align:start position:0%
+relatives but even in those
+cultures they they end up having to
+
+ align:start position:0%
+cultures they they end up having to
+ 
+
+ align:start position:0%
+cultures they they end up having to
+separate well this was an arranged
+
+ align:start position:0%
+separate well this was an arranged
+ 
+
+ align:start position:0%
+separate well this was an arranged
+marriage and that is a love marriage
+
+ align:start position:0%
+marriage and that is a love marriage
+ 
+
+ align:start position:0%
+marriage and that is a love marriage
+they separate them okay and you find
+
+ align:start position:0%
+they separate them okay and you find
+ 
+
+ align:start position:0%
+they separate them okay and you find
+that in all these
+
+ align:start position:0%
+that in all these
+ 
+
+ align:start position:0%
+that in all these
+cultures
+
+ align:start position:0%
+cultures
+ 
+
+ align:start position:0%
+cultures
+uh it's because falling in love still
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+happens fortunately in societies where
+
+ align:start position:0%
+happens fortunately in societies where
+ 
+
+ align:start position:0%
+happens fortunately in societies where
+the marriages are decided by parents
+
+ align:start position:0%
+the marriages are decided by parents
+ 
+
+ align:start position:0%
+the marriages are decided by parents
+they often work out better when
+
+ align:start position:0%
+they often work out better when
+ 
+
+ align:start position:0%
+they often work out better when
+marriages here where the
+
+ align:start position:0%
+marriages here where the
+ 
+
+ align:start position:0%
+marriages here where the
+rate of divorce is now greater than
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+50% but let's State a sociobiological
+
+ align:start position:0%
+50% but let's State a sociobiological
+ 
+
+ align:start position:0%
+50% but let's State a sociobiological
+hypothesis about the
+
+ align:start position:0%
+hypothesis about the
+ 
+
+ align:start position:0%
+hypothesis about the
+origins of that feeling it's clearly
+
+ align:start position:0%
+origins of that feeling it's clearly
+ 
+
+ align:start position:0%
+origins of that feeling it's clearly
+instinctive when it if you haven't
+
+ align:start position:0%
+instinctive when it if you haven't
+ 
+
+ align:start position:0%
+instinctive when it if you haven't
+experienced
+
+ align:start position:0%
+experienced
+ 
+
+ align:start position:0%
+experienced
+it uh you will realize when it does
+
+ align:start position:0%
+it uh you will realize when it does
+ 
+
+ align:start position:0%
+it uh you will realize when it does
+occur that you're it's in innate
+
+ align:start position:0%
+occur that you're it's in innate
+ 
+
+ align:start position:0%
+occur that you're it's in innate
+something's happening to you
+
+ align:start position:0%
+something's happening to you
+ 
+
+ align:start position:0%
+something's happening to you
+okay does it occur only in young people
+
+ align:start position:0%
+okay does it occur only in young people
+ 
+
+ align:start position:0%
+okay does it occur only in young people
+no are prominent leaders in the
+
+ align:start position:0%
+no are prominent leaders in the
+ 
+
+ align:start position:0%
+no are prominent leaders in the
+community exempt there's plenty of
+
+ align:start position:0%
+community exempt there's plenty of
+ 
+
+ align:start position:0%
+community exempt there's plenty of
+examples in the news where that's not
+
+ align:start position:0%
+examples in the news where that's not
+ 
+
+ align:start position:0%
+examples in the news where that's not
+true uh if it is evolved as a human
+
+ align:start position:0%
+true uh if it is evolved as a human
+ 
+
+ align:start position:0%
+true uh if it is evolved as a human
+fixed action pattern it's got to be
+
+ align:start position:0%
+fixed action pattern it's got to be
+ 
+
+ align:start position:0%
+fixed action pattern it's got to be
+adaptive in a sociobiological
+
+ align:start position:0%
+adaptive in a sociobiological
+ 
+
+ align:start position:0%
+adaptive in a sociobiological
+sense like many evolved Tendencies it
+
+ align:start position:0%
+sense like many evolved Tendencies it
+ 
+
+ align:start position:0%
+sense like many evolved Tendencies it
+can produce conflicts not only in the
+
+ align:start position:0%
+can produce conflicts not only in the
+ 
+
+ align:start position:0%
+can produce conflicts not only in the
+society but within the individual and
+
+ align:start position:0%
+society but within the individual and
+ 
+
+ align:start position:0%
+society but within the individual and
+this can cause what we call cognitive
+
+ align:start position:0%
+this can cause what we call cognitive
+ 
+
+ align:start position:0%
+this can cause what we call cognitive
+dissonance which the individual will
+
+ align:start position:0%
+dissonance which the individual will
+ 
+
+ align:start position:0%
+dissonance which the individual will
+struggle to resolve in one way or the
+
+ align:start position:0%
+struggle to resolve in one way or the
+ 
+
+ align:start position:0%
+struggle to resolve in one way or the
+other okay so consider why it it must
+
+ align:start position:0%
+other okay so consider why it it must
+ 
+
+ align:start position:0%
+other okay so consider why it it must
+have had to evolve in early human
+
+ align:start position:0%
+have had to evolve in early human
+ 
+
+ align:start position:0%
+have had to evolve in early human
+groups think of the close bonds acquired
+
+ align:start position:0%
+groups think of the close bonds acquired
+ 
+
+ align:start position:0%
+groups think of the close bonds acquired
+in growing up in an extended
+
+ align:start position:0%
+in growing up in an extended
+ 
+
+ align:start position:0%
+in growing up in an extended
+family within which there
+
+ align:start position:0%
+family within which there
+ 
+
+ align:start position:0%
+family within which there
+were very bad consequences of inbreeding
+
+ align:start position:0%
+were very bad consequences of inbreeding
+ 
+
+ align:start position:0%
+were very bad consequences of inbreeding
+it was necessary for genetic fitness to
+
+ align:start position:0%
+it was necessary for genetic fitness to
+ 
+
+ align:start position:0%
+it was necessary for genetic fitness to
+have a motivation that could occur in
+
+ align:start position:0%
+have a motivation that could occur in
+ 
+
+ align:start position:0%
+have a motivation that could occur in
+strength after sexual maturity strong
+
+ align:start position:0%
+strength after sexual maturity strong
+ 
+
+ align:start position:0%
+strength after sexual maturity strong
+enough to cause a young person to leave
+
+ align:start position:0%
+enough to cause a young person to leave
+ 
+
+ align:start position:0%
+enough to cause a young person to leave
+his natal
+
+ align:start position:0%
+his natal
+ 
+
+ align:start position:0%
+his natal
+GOP and the result was what
+
+ align:start position:0%
+GOP and the result was what
+ 
+
+ align:start position:0%
+GOP and the result was what
+we they call often call Roaming In
+
+ align:start position:0%
+we they call often call Roaming In
+ 
+
+ align:start position:0%
+we they call often call Roaming In
+Search of a mate a very common tradition
+
+ align:start position:0%
+Search of a mate a very common tradition
+ 
+
+ align:start position:0%
+Search of a mate a very common tradition
+usually the male but not always just the
+
+ align:start position:0%
+usually the male but not always just the
+ 
+
+ align:start position:0%
+usually the male but not always just the
+male will go off in search of a mate he
+
+ align:start position:0%
+male will go off in search of a mate he
+ 
+
+ align:start position:0%
+male will go off in search of a mate he
+leaves home till he finds a woman he can
+
+ align:start position:0%
+leaves home till he finds a woman he can
+ 
+
+ align:start position:0%
+leaves home till he finds a woman he can
+fall
+
+ align:start position:0%
+fall
+ 
+
+ align:start position:0%
+fall
+for you also have secret Liaisons
+
+ align:start position:0%
+for you also have secret Liaisons
+ 
+
+ align:start position:0%
+for you also have secret Liaisons
+eloping all the other characteristics of
+
+ align:start position:0%
+eloping all the other characteristics of
+ 
+
+ align:start position:0%
+eloping all the other characteristics of
+the falling in love phenomenon including
+
+ align:start position:0%
+the falling in love phenomenon including
+ 
+
+ align:start position:0%
+the falling in love phenomenon including
+behaving stupidly and irrationally
+
+ align:start position:0%
+behaving stupidly and irrationally
+ 
+
+ align:start position:0%
+behaving stupidly and irrationally
+disregarding long-established habits and
+
+ align:start position:0%
+disregarding long-established habits and
+ 
+
+ align:start position:0%
+disregarding long-established habits and
+okay it has a biological reason
+
+ align:start position:0%
+okay it has a biological reason
+ 
+
+ align:start position:0%
+okay it has a biological reason
+okay and then I'll let you just read
+
+ align:start position:0%
+okay and then I'll let you just read
+ 
+
+ align:start position:0%
+okay and then I'll let you just read
+these I put a few summaries of recent
+
+ align:start position:0%
+these I put a few summaries of recent
+ 
+
+ align:start position:0%
+these I put a few summaries of recent
+research and they're very very easy to
+
+ align:start position:0%
+research and they're very very easy to
+ 
+
+ align:start position:0%
+research and they're very very easy to
+find
\ No newline at end of file
diff --git a/QCGJVKaCDuI.txt b/QCGJVKaCDuI.txt
new file mode 100644
index 0000000000000000000000000000000000000000..ae01710cd22074dc78ac14bac14b1391f6a459f0
--- /dev/null
+++ b/QCGJVKaCDuI.txt
@@ -0,0 +1,419 @@
+align:start position:0%
+ 
+hello and welcome back to recitation I'd
+
+ align:start position:0%
+hello and welcome back to recitation I'd
+ 
+
+ align:start position:0%
+hello and welcome back to recitation I'd
+like to uh work on a problem with you
+
+ align:start position:0%
+like to uh work on a problem with you
+ 
+
+ align:start position:0%
+like to uh work on a problem with you
+which is to compute the volume of a
+
+ align:start position:0%
+which is to compute the volume of a
+ 
+
+ align:start position:0%
+which is to compute the volume of a
+parallel pipid using 3x3 determinants so
+
+ align:start position:0%
+parallel pipid using 3x3 determinants so
+ 
+
+ align:start position:0%
+parallel pipid using 3x3 determinants so
+here we've got the parallel pipid drawn
+
+ align:start position:0%
+here we've got the parallel pipid drawn
+ 
+
+ align:start position:0%
+here we've got the parallel pipid drawn
+it has one of its vertices is at the
+
+ align:start position:0%
+it has one of its vertices is at the
+ 
+
+ align:start position:0%
+it has one of its vertices is at the
+origin 0000 0 and the other three edges
+
+ align:start position:0%
+origin 0000 0 and the other three edges
+ 
+
+ align:start position:0%
+origin 0000 0 and the other three edges
+are given to us uh with these
+
+ align:start position:0%
+are given to us uh with these
+ 
+
+ align:start position:0%
+are given to us uh with these
+coordinates here so why don't you take
+
+ align:start position:0%
+coordinates here so why don't you take
+ 
+
+ align:start position:0%
+coordinates here so why don't you take
+some time to work out this problem pause
+
+ align:start position:0%
+some time to work out this problem pause
+ 
+
+ align:start position:0%
+some time to work out this problem pause
+the video and check back with me and
+
+ align:start position:0%
+the video and check back with me and
+ 
+
+ align:start position:0%
+the video and check back with me and
+I'll show you how I solved
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+it okay welcome back let's get started
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so uh the first thing that we uh need to
+
+ align:start position:0%
+so uh the first thing that we uh need to
+ 
+
+ align:start position:0%
+so uh the first thing that we uh need to
+do is we need to remember that Computing
+
+ align:start position:0%
+do is we need to remember that Computing
+ 
+
+ align:start position:0%
+do is we need to remember that Computing
+volumes of parallel pipids is the same
+
+ align:start position:0%
+volumes of parallel pipids is the same
+ 
+
+ align:start position:0%
+volumes of parallel pipids is the same
+thing as Computing 3x3 determinants so
+
+ align:start position:0%
+thing as Computing 3x3 determinants so
+ 
+
+ align:start position:0%
+thing as Computing 3x3 determinants so
+the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+volume is just equal to the determinant
+
+ align:start position:0%
+volume is just equal to the determinant
+ 
+
+ align:start position:0%
+volume is just equal to the determinant
+uh which is built out of the vectors uh
+
+ align:start position:0%
+uh which is built out of the vectors uh
+ 
+
+ align:start position:0%
+uh which is built out of the vectors uh
+the row vectors determining the edges so
+
+ align:start position:0%
+the row vectors determining the edges so
+ 
+
+ align:start position:0%
+the row vectors determining the edges so
+we
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+have well that's almost true um this
+
+ align:start position:0%
+have well that's almost true um this
+ 
+
+ align:start position:0%
+have well that's almost true um this
+determinant will be uh either a positive
+
+ align:start position:0%
+determinant will be uh either a positive
+ 
+
+ align:start position:0%
+determinant will be uh either a positive
+or A negative number and we always want
+
+ align:start position:0%
+or A negative number and we always want
+ 
+
+ align:start position:0%
+or A negative number and we always want
+to take the positive number so I'm going
+
+ align:start position:0%
+to take the positive number so I'm going
+ 
+
+ align:start position:0%
+to take the positive number so I'm going
+to write plus or minus here and we'll
+
+ align:start position:0%
+to write plus or minus here and we'll
+ 
+
+ align:start position:0%
+to write plus or minus here and we'll
+have to remember at the end that we want
+
+ align:start position:0%
+have to remember at the end that we want
+ 
+
+ align:start position:0%
+have to remember at the end that we want
+a positive number so we can compute this
+
+ align:start position:0%
+a positive number so we can compute this
+ 
+
+ align:start position:0%
+a positive number so we can compute this
+determinant using lass expansion as we
+
+ align:start position:0%
+determinant using lass expansion as we
+ 
+
+ align:start position:0%
+determinant using lass expansion as we
+did in the last
+
+ align:start position:0%
+did in the last
+ 
+
+ align:start position:0%
+did in the last
+video so for lla expansion we take the
+
+ align:start position:0%
+video so for lla expansion we take the
+ 
+
+ align:start position:0%
+video so for lla expansion we take the
+we can do lass expansion on the first
+
+ align:start position:0%
+we can do lass expansion on the first
+ 
+
+ align:start position:0%
+we can do lass expansion on the first
+row and that will again be nice because
+
+ align:start position:0%
+row and that will again be nice because
+ 
+
+ align:start position:0%
+row and that will again be nice because
+uh this zero here will make our
+
+ align:start position:0%
+uh this zero here will make our
+ 
+
+ align:start position:0%
+uh this zero here will make our
+computation simpler and so remember
+
+ align:start position:0%
+computation simpler and so remember
+ 
+
+ align:start position:0%
+computation simpler and so remember
+remember what we do is we take the first
+
+ align:start position:0%
+remember what we do is we take the first
+ 
+
+ align:start position:0%
+remember what we do is we take the first
+entry in the row and then we need to
+
+ align:start position:0%
+entry in the row and then we need to
+ 
+
+ align:start position:0%
+entry in the row and then we need to
+multiply by the minor that we get by
+
+ align:start position:0%
+multiply by the minor that we get by
+ 
+
+ align:start position:0%
+multiply by the minor that we get by
+covering up that row and that column so
+
+ align:start position:0%
+covering up that row and that column so
+ 
+
+ align:start position:0%
+covering up that row and that column so
+we have this this little 2x two
+
+ align:start position:0%
+we have this this little 2x two
+ 
+
+ align:start position:0%
+we have this this little 2x two
+determinant which looks like minus
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+one and now we need to
+
+ align:start position:0%
+one and now we need to
+ 
+
+ align:start position:0%
+one and now we need to
+subtract uh the next entry in the row
+
+ align:start position:0%
+subtract uh the next entry in the row
+ 
+
+ align:start position:0%
+subtract uh the next entry in the row
+times uh its minor which is now this
+
+ align:start position:0%
+times uh its minor which is now this
+ 
+
+ align:start position:0%
+times uh its minor which is now this
+Matrix 1 1 0
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+1 so take that determinant we get 1 uh
+
+ align:start position:0%
+1 so take that determinant we get 1 uh
+ 
+
+ align:start position:0%
+1 so take that determinant we get 1 uh
+minus 0 so Al together we get one so
+
+ align:start position:0%
+minus 0 so Al together we get one so
+ 
+
+ align:start position:0%
+minus 0 so Al together we get one so
+what that tells us is that our uh our uh
+
+ align:start position:0%
+what that tells us is that our uh our uh
+ 
+
+ align:start position:0%
+what that tells us is that our uh our uh
+determinant is uh Min
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+-4 but then that tells us that our
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+volume
+
+ align:start position:0%
+volume
+ 
+
+ align:start position:0%
+volume
+is+ 4 and I'll leave it at that
\ No newline at end of file
diff --git a/QCo-RtfLzyc.txt b/QCo-RtfLzyc.txt
new file mode 100644
index 0000000000000000000000000000000000000000..f0eb0f202b035543105f24603bde3466d8a5eabc
--- /dev/null
+++ b/QCo-RtfLzyc.txt
@@ -0,0 +1,241 @@
+For some applications, data naturally comes
+in vector or matrix form.
+
+For example, a vector of digitized samples
+representing an audio waveform over time,
+
+or a matrix of pixel colors in a 2D image
+from a camera.
+
+When processing that data, it's common to
+perform the same sequence of operations on
+
+each data element.
+
+The example code shown here is computing a
+vector sum, where each component of one vector
+
+is added to the corresponding component of
+another vector.
+
+By replicating the datapath portion of our
+CPU, we can design special-purpose vector
+
+processors capable of performing the same
+operation on many data elements in parallel.
+
+Here we see that the register file and ALU
+have been replicated and the control signals
+
+from decoding the current instruction are
+shared by all the datapaths.
+
+Data is fetched from memory in big blocks
+(very much like fetching a cache line) and
+
+the specified register in each datapath is
+loaded with one of the words from the block.
+
+Similarly each datapath can contribute a word
+to be stored as a contiguous block in main
+
+memory.
+
+In such machines, the width of the data buses
+to and from main memory is many words wide,
+
+so a single memory access provides data for
+all the datapaths in parallel.
+
+Executing a single instruction on a machine
+with N datapaths is equivalent to executing
+
+N instructions on a conventional machine with
+a single datapath.
+
+The result achieves a lot of parallelism without
+the complexities of out-of-order superscalar
+
+execution.
+
+Suppose we had a vector processor with 16
+datapaths.
+
+Let's compare its performance on a vector-sum
+operation to that of a conventional pipelined
+
+Beta processor.
+
+Here's the Beta code, carefully organized
+to avoid any data hazards during execution.
+
+There are 9 instructions in the loop, taking
+10 cycles to execute if we count the NOP introduced
+
+into the pipeline when the BNE at the end
+of the loop is taken.
+
+It takes 160 cycles to sum all 16 elements
+assuming no additional cycles are required
+
+due to cache misses.
+
+And here's the corresponding code for a vector
+processor where we've assumed constant-sized
+
+16-element vectors.
+
+Note that "V" registers refer to a particular
+location in the register file associated with
+
+each datapath, while the "R" registers are
+the conventional Beta registers used for address
+
+computations, etc.
+
+It would only take 4 cycles for the vector
+processor to complete the desired operations,
+
+a speed-up of 40.
+
+This example shows the best-possible speed-up.
+
+The key to a good speed-up is our ability
+to "vectorize" the code and take advantage
+
+of all the datapaths operating in parallel.
+
+This isn't possible for every application,
+but for tasks like audio or video encoding
+
+and decoding, and all sorts of digital signal
+processing, vectorization is very doable.
+
+Memory operations enjoy a similar performance
+improvement since the access overhead is amortized
+
+over large blocks of data.
+
+You might wonder if it's possible to efficiently
+perform data-dependent operations on a vector
+
+processor.
+
+Data-dependent operations appear as conditional
+statements on conventional machines, where
+
+the body of the statement is executed if the
+condition is true.
+
+If testing and branching is under the control
+of the single-instruction execution engine,
+
+how can we take advantage of the parallel
+datapaths?
+
+The trick is provide each datapath with a
+local predicate flag.
+
+Use a vectorized compare instruction (CMPLT.V)
+to perform the a[i] < b[i] comparisons in
+
+parallel and remember the result locally in
+each datapath's predicate flag.
+
+Then extend the vector ISA to include "predicated
+instructions" which check the local predicate
+
+to see if they should execute or do nothing.
+
+In this example, ADDC.V.iftrue only performs
+the ADDC on the local data if the local predicate
+
+flag is true.
+
+Instruction predication is also used in many
+non-vector architectures to avoid the execution-time
+
+penalties associated with mis-predicted conditional
+branches.
+
+They are particularly useful for simple arithmetic
+and boolean operations (i.e., very short instruction
+
+sequences) that should be executed only if
+a condition is met.
+
+The x86 ISA includes a conditional move instruction,
+and in the 32-bit ARM ISA almost all instructions
+
+can be conditionally executed.
+
+The power of vector processors comes from
+having 1 instruction initiate N parallel operations
+
+on N pairs of operands.
+
+Most modern CPUs incorporate vector extensions
+that operate in parallel on 8-, 16-, 32- or
+
+64-bit operands organized as blocks of 128-,
+256-, or 512-bit data.
+
+Often all that's needed is some simple additional
+logic on an ALU designed to process full-width
+
+operands.
+
+The parallelism is baked into the vector program,
+not discovered on-the-fly by the instruction
+
+dispatch and execution machinery.
+
+Writing the specialized vector programs is
+a worthwhile investment for certain library
+
+functions which see a lot use in processing
+today's information streams with their heavy
+
+use of images, and A/V material.
+
+Perhaps the best example of architectures
+with many datapaths operating in parallel
+
+are the graphics processing units (GPUs) found
+in almost all computer graphics systems.
+
+GPU datapaths are typically specialized for
+32- and 64-bit floating point operations found
+
+in the algorithms needed to display in real-time
+a 3D scene represented as billions of triangular
+
+patches as a 2D image on the computer screen.
+
+Coordinate transformation, pixel shading and
+antialiasing, texture mapping, etc., are examples
+
+of "embarrassingly parallel" computations
+where the parallelism comes from having to
+
+perform the same computation independently
+on millions of different data objects.
+
+Similar problems can be found in the fields
+of bioinformatics, big data processing, neural
+
+net emulation used in deep machine learning,
+and so on.
+
+Increasingly, GPUs are used in many interesting
+scientific and engineering calculations and
+
+not just as graphics engines.
+
+Data-level parallelism provides significant
+performance improvements in a variety of useful
+
+situations.
+
+So current and future ISAs will almost certainly
+include support for vector operations.
\ No newline at end of file
diff --git a/RDvMzWDzZkc.txt b/RDvMzWDzZkc.txt
new file mode 100644
index 0000000000000000000000000000000000000000..b936c143ef6c3e28cb6f524bdb1dfe79e99cb007
--- /dev/null
+++ b/RDvMzWDzZkc.txt
@@ -0,0 +1,13131 @@
+align:start position:0%
+ 
+the following content is provided under
+
+ align:start position:0%
+the following content is provided under
+ 
+
+ align:start position:0%
+the following content is provided under
+a Creative Commons license your support
+
+ align:start position:0%
+a Creative Commons license your support
+ 
+
+ align:start position:0%
+a Creative Commons license your support
+will help MIT OpenCourseWare continue to
+
+ align:start position:0%
+will help MIT OpenCourseWare continue to
+ 
+
+ align:start position:0%
+will help MIT OpenCourseWare continue to
+offer high quality educational resources
+
+ align:start position:0%
+offer high quality educational resources
+ 
+
+ align:start position:0%
+offer high quality educational resources
+for free
+
+ align:start position:0%
+for free
+ 
+
+ align:start position:0%
+for free
+to make a donation or to view additional
+
+ align:start position:0%
+to make a donation or to view additional
+ 
+
+ align:start position:0%
+to make a donation or to view additional
+materials from hundreds of MIT courses
+
+ align:start position:0%
+materials from hundreds of MIT courses
+ 
+
+ align:start position:0%
+materials from hundreds of MIT courses
+visit MIT opencourseware at ocw.mit.edu
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+let me just introduce myself and then
+
+ align:start position:0%
+let me just introduce myself and then
+ 
+
+ align:start position:0%
+let me just introduce myself and then
+maybe you all can introduce yourself
+
+ align:start position:0%
+maybe you all can introduce yourself
+ 
+
+ align:start position:0%
+maybe you all can introduce yourself
+yourselves to me and to each other so
+
+ align:start position:0%
+yourselves to me and to each other so
+ 
+
+ align:start position:0%
+yourselves to me and to each other so
+I'm bill bond villian and for the last
+
+ align:start position:0%
+I'm bill bond villian and for the last
+ 
+
+ align:start position:0%
+I'm bill bond villian and for the last
+11 years I have been director of mi
+
+ align:start position:0%
+11 years I have been director of mi
+ 
+
+ align:start position:0%
+11 years I have been director of mi
+t--'s Washington DC office and I've
+
+ align:start position:0%
+t--'s Washington DC office and I've
+ 
+
+ align:start position:0%
+t--'s Washington DC office and I've
+taught at Georgetown University of
+
+ align:start position:0%
+taught at Georgetown University of
+ 
+
+ align:start position:0%
+taught at Georgetown University of
+course on science and tech policy for
+
+ align:start position:0%
+course on science and tech policy for
+ 
+
+ align:start position:0%
+course on science and tech policy for
+about 12 years and I teach different
+
+ align:start position:0%
+about 12 years and I teach different
+ 
+
+ align:start position:0%
+about 12 years and I teach different
+course on energy technology policy at
+
+ align:start position:0%
+course on energy technology policy at
+ 
+
+ align:start position:0%
+course on energy technology policy at
+Johns Hopkins sighs so I'm on the edge
+
+ align:start position:0%
+Johns Hopkins sighs so I'm on the edge
+ 
+
+ align:start position:0%
+Johns Hopkins sighs so I'm on the edge
+I'm faculty at Georgetown and Hopkins
+
+ align:start position:0%
+I'm faculty at Georgetown and Hopkins
+ 
+
+ align:start position:0%
+I'm faculty at Georgetown and Hopkins
+ice and after 11 years of being director
+
+ align:start position:0%
+ice and after 11 years of being director
+ 
+
+ align:start position:0%
+ice and after 11 years of being director
+the Washington office I've stepped down
+
+ align:start position:0%
+the Washington office I've stepped down
+ 
+
+ align:start position:0%
+the Washington office I've stepped down
+from that job so I'm now a lecturer up
+
+ align:start position:0%
+from that job so I'm now a lecturer up
+ 
+
+ align:start position:0%
+from that job so I'm now a lecturer up
+here and I've got a an attachment to mi
+
+ align:start position:0%
+here and I've got a an attachment to mi
+ 
+
+ align:start position:0%
+here and I've got a an attachment to mi
+t--'s Industrial Policy Center which is
+
+ align:start position:0%
+t--'s Industrial Policy Center which is
+ 
+
+ align:start position:0%
+t--'s Industrial Policy Center which is
+one of its policy centers and I'm
+
+ align:start position:0%
+one of its policy centers and I'm
+ 
+
+ align:start position:0%
+one of its policy centers and I'm
+finishing my third book actually just
+
+ align:start position:0%
+finishing my third book actually just
+ 
+
+ align:start position:0%
+finishing my third book actually just
+now at MIT press on advanced
+
+ align:start position:0%
+now at MIT press on advanced
+ 
+
+ align:start position:0%
+now at MIT press on advanced
+manufacturing so you're gonna hear more
+
+ align:start position:0%
+manufacturing so you're gonna hear more
+ 
+
+ align:start position:0%
+manufacturing so you're gonna hear more
+than your share about manufacturing for
+
+ align:start position:0%
+than your share about manufacturing for
+ 
+
+ align:start position:0%
+than your share about manufacturing for
+this all over you're stuck with those
+
+ align:start position:0%
+this all over you're stuck with those
+ 
+
+ align:start position:0%
+this all over you're stuck with those
+realities and you know I had a kind of a
+
+ align:start position:0%
+realities and you know I had a kind of a
+ 
+
+ align:start position:0%
+realities and you know I had a kind of a
+background in I was in the executive
+
+ align:start position:0%
+background in I was in the executive
+ 
+
+ align:start position:0%
+background in I was in the executive
+branch as a child and I was a Deputy
+
+ align:start position:0%
+branch as a child and I was a Deputy
+ 
+
+ align:start position:0%
+branch as a child and I was a Deputy
+Assistant Secretary of Transportation of
+
+ align:start position:0%
+Assistant Secretary of Transportation of
+ 
+
+ align:start position:0%
+Assistant Secretary of Transportation of
+my youth long before any of you were
+
+ align:start position:0%
+my youth long before any of you were
+ 
+
+ align:start position:0%
+my youth long before any of you were
+born and got to really engage in the
+
+ align:start position:0%
+born and got to really engage in the
+ 
+
+ align:start position:0%
+born and got to really engage in the
+development of major legislation that
+
+ align:start position:0%
+development of major legislation that
+ 
+
+ align:start position:0%
+development of major legislation that
+deregulated most of the big
+
+ align:start position:0%
+deregulated most of the big
+ 
+
+ align:start position:0%
+deregulated most of the big
+transportation sectors so aviation
+
+ align:start position:0%
+transportation sectors so aviation
+ 
+
+ align:start position:0%
+transportation sectors so aviation
+trucking and railroads and then did a
+
+ align:start position:0%
+trucking and railroads and then did a
+ 
+
+ align:start position:0%
+trucking and railroads and then did a
+lot of work on Surface Transportation
+
+ align:start position:0%
+lot of work on Surface Transportation
+ 
+
+ align:start position:0%
+lot of work on Surface Transportation
+then practice law because I've been
+
+ align:start position:0%
+then practice law because I've been
+ 
+
+ align:start position:0%
+then practice law because I've been
+trained as a lawyer so practice law for
+
+ align:start position:0%
+trained as a lawyer so practice law for
+ 
+
+ align:start position:0%
+trained as a lawyer so practice law for
+a decade and then somebody I knew and
+
+ align:start position:0%
+a decade and then somebody I knew and
+ 
+
+ align:start position:0%
+a decade and then somebody I knew and
+had worked with at an earlier stage
+
+ align:start position:0%
+had worked with at an earlier stage
+ 
+
+ align:start position:0%
+had worked with at an earlier stage
+became US senators so I got one of those
+
+ align:start position:0%
+became US senators so I got one of those
+ 
+
+ align:start position:0%
+became US senators so I got one of those
+proverbial Washington phone calls you
+
+ align:start position:0%
+proverbial Washington phone calls you
+ 
+
+ align:start position:0%
+proverbial Washington phone calls you
+know why don't you come up and we'll
+
+ align:start position:0%
+know why don't you come up and we'll
+ 
+
+ align:start position:0%
+know why don't you come up and we'll
+talk bill and that conversation lasted
+
+ align:start position:0%
+talk bill and that conversation lasted
+ 
+
+ align:start position:0%
+talk bill and that conversation lasted
+for over 15 years so I couldn't resist
+
+ align:start position:0%
+for over 15 years so I couldn't resist
+ 
+
+ align:start position:0%
+for over 15 years so I couldn't resist
+staying up there it was much too
+
+ align:start position:0%
+staying up there it was much too
+ 
+
+ align:start position:0%
+staying up there it was much too
+interesting and fun so had a long
+
+ align:start position:0%
+interesting and fun so had a long
+ 
+
+ align:start position:0%
+interesting and fun so had a long
+we're working in the US Senate and
+
+ align:start position:0%
+we're working in the US Senate and
+ 
+
+ align:start position:0%
+we're working in the US Senate and
+worked on lots of legislation but
+
+ align:start position:0%
+worked on lots of legislation but
+ 
+
+ align:start position:0%
+worked on lots of legislation but
+including a lot of work on innovation
+
+ align:start position:0%
+including a lot of work on innovation
+ 
+
+ align:start position:0%
+including a lot of work on innovation
+policy and science policy and R&D policy
+
+ align:start position:0%
+policy and science policy and R&D policy
+ 
+
+ align:start position:0%
+policy and science policy and R&D policy
+so that's kind of where I got my
+
+ align:start position:0%
+so that's kind of where I got my
+ 
+
+ align:start position:0%
+so that's kind of where I got my
+training in this territory it was very
+
+ align:start position:0%
+training in this territory it was very
+ 
+
+ align:start position:0%
+training in this territory it was very
+much learning by doing and then 11 years
+
+ align:start position:0%
+much learning by doing and then 11 years
+ 
+
+ align:start position:0%
+much learning by doing and then 11 years
+ago I went to MIT to run their
+
+ align:start position:0%
+ago I went to MIT to run their
+ 
+
+ align:start position:0%
+ago I went to MIT to run their
+Washington office which has been a great
+
+ align:start position:0%
+Washington office which has been a great
+ 
+
+ align:start position:0%
+Washington office which has been a great
+joy so anyway that's kind of and then I
+
+ align:start position:0%
+joy so anyway that's kind of and then I
+ 
+
+ align:start position:0%
+joy so anyway that's kind of and then I
+just as I said just stepped down so from
+
+ align:start position:0%
+just as I said just stepped down so from
+ 
+
+ align:start position:0%
+just as I said just stepped down so from
+that very activist kind of job to this
+
+ align:start position:0%
+that very activist kind of job to this
+ 
+
+ align:start position:0%
+that very activist kind of job to this
+life of leisurely MIT faculty you know
+
+ align:start position:0%
+life of leisurely MIT faculty you know
+ 
+
+ align:start position:0%
+life of leisurely MIT faculty you know
+supposedly I'm quasi retired I doubt it
+
+ align:start position:0%
+supposedly I'm quasi retired I doubt it
+ 
+
+ align:start position:0%
+supposedly I'm quasi retired I doubt it
+but in anyway that's my background let
+
+ align:start position:0%
+but in anyway that's my background let
+ 
+
+ align:start position:0%
+but in anyway that's my background let
+me let me just say a few things about
+
+ align:start position:0%
+me let me just say a few things about
+ 
+
+ align:start position:0%
+me let me just say a few things about
+how this course is going to work you
+
+ align:start position:0%
+how this course is going to work you
+ 
+
+ align:start position:0%
+how this course is going to work you
+know we know from a lot of studies and
+
+ align:start position:0%
+know we know from a lot of studies and
+ 
+
+ align:start position:0%
+know we know from a lot of studies and
+MIT s online crowd is now doing about
+
+ align:start position:0%
+MIT s online crowd is now doing about
+ 
+
+ align:start position:0%
+MIT s online crowd is now doing about
+learning science that the talking head
+
+ align:start position:0%
+learning science that the talking head
+ 
+
+ align:start position:0%
+learning science that the talking head
+is not an efficient way to learn so we
+
+ align:start position:0%
+is not an efficient way to learn so we
+ 
+
+ align:start position:0%
+is not an efficient way to learn so we
+really need you all participating in a
+
+ align:start position:0%
+really need you all participating in a
+ 
+
+ align:start position:0%
+really need you all participating in a
+class and coming into the discussions so
+
+ align:start position:0%
+class and coming into the discussions so
+ 
+
+ align:start position:0%
+class and coming into the discussions so
+to further that and you saw my email
+
+ align:start position:0%
+to further that and you saw my email
+ 
+
+ align:start position:0%
+to further that and you saw my email
+kind of introducing the course and
+
+ align:start position:0%
+kind of introducing the course and
+ 
+
+ align:start position:0%
+kind of introducing the course and
+you've seen the discussion the syllabus
+
+ align:start position:0%
+you've seen the discussion the syllabus
+ 
+
+ align:start position:0%
+you've seen the discussion the syllabus
+those of you who haven't been able to
+
+ align:start position:0%
+those of you who haven't been able to
+ 
+
+ align:start position:0%
+those of you who haven't been able to
+get online yet let's stick around for
+
+ align:start position:0%
+get online yet let's stick around for
+ 
+
+ align:start position:0%
+get online yet let's stick around for
+after class let's make sure you get
+
+ align:start position:0%
+after class let's make sure you get
+ 
+
+ align:start position:0%
+after class let's make sure you get
+registered and get access to the online
+
+ align:start position:0%
+registered and get access to the online
+ 
+
+ align:start position:0%
+registered and get access to the online
+materials in the background materials so
+
+ align:start position:0%
+materials in the background materials so
+ 
+
+ align:start position:0%
+materials in the background materials so
+let's talk for a few minutes after class
+
+ align:start position:0%
+let's talk for a few minutes after class
+ 
+
+ align:start position:0%
+let's talk for a few minutes after class
+but essentially we're going to use a
+
+ align:start position:0%
+but essentially we're going to use a
+ 
+
+ align:start position:0%
+but essentially we're going to use a
+discussion leader system and what that
+
+ align:start position:0%
+discussion leader system and what that
+ 
+
+ align:start position:0%
+discussion leader system and what that
+means is that we'll all have you know
+
+ align:start position:0%
+means is that we'll all have you know
+ 
+
+ align:start position:0%
+means is that we'll all have you know
+five readings or so for each class and
+
+ align:start position:0%
+five readings or so for each class and
+ 
+
+ align:start position:0%
+five readings or so for each class and
+I'm gonna ask all of you to do those
+
+ align:start position:0%
+I'm gonna ask all of you to do those
+ 
+
+ align:start position:0%
+I'm gonna ask all of you to do those
+readings and then do a short doesn't
+
+ align:start position:0%
+readings and then do a short doesn't
+ 
+
+ align:start position:0%
+readings and then do a short doesn't
+need me more than a page it shouldn't
+
+ align:start position:0%
+need me more than a page it shouldn't
+ 
+
+ align:start position:0%
+need me more than a page it shouldn't
+really be more than a page and a half
+
+ align:start position:0%
+really be more than a page and a half
+ 
+
+ align:start position:0%
+really be more than a page and a half
+some key bullet points on the key
+
+ align:start position:0%
+some key bullet points on the key
+ 
+
+ align:start position:0%
+some key bullet points on the key
+findings that you drew from those
+
+ align:start position:0%
+findings that you drew from those
+ 
+
+ align:start position:0%
+findings that you drew from those
+readings and a couple of questions right
+
+ align:start position:0%
+readings and a couple of questions right
+ 
+
+ align:start position:0%
+readings and a couple of questions right
+so that kind of gets all of you thinking
+
+ align:start position:0%
+so that kind of gets all of you thinking
+ 
+
+ align:start position:0%
+so that kind of gets all of you thinking
+about the readings on the way in and
+
+ align:start position:0%
+about the readings on the way in and
+ 
+
+ align:start position:0%
+about the readings on the way in and
+some cute questions you've got about the
+
+ align:start position:0%
+some cute questions you've got about the
+ 
+
+ align:start position:0%
+some cute questions you've got about the
+so that you can help own the class right
+
+ align:start position:0%
+so that you can help own the class right
+ 
+
+ align:start position:0%
+so that you can help own the class right
+because it only works if you all own it
+
+ align:start position:0%
+because it only works if you all own it
+ 
+
+ align:start position:0%
+because it only works if you all own it
+and then in turn will do this discussion
+
+ align:start position:0%
+and then in turn will do this discussion
+ 
+
+ align:start position:0%
+and then in turn will do this discussion
+leader thing so each week I'll ask a
+
+ align:start position:0%
+leader thing so each week I'll ask a
+ 
+
+ align:start position:0%
+leader thing so each week I'll ask a
+couple of you to be leaders of the Q&A
+
+ align:start position:0%
+couple of you to be leaders of the Q&A
+ 
+
+ align:start position:0%
+couple of you to be leaders of the Q&A
+part of the class so here's here's how
+
+ align:start position:0%
+part of the class so here's here's how
+ 
+
+ align:start position:0%
+part of the class so here's here's how
+it will work so I'll talk about any
+
+ align:start position:0%
+it will work so I'll talk about any
+ 
+
+ align:start position:0%
+it will work so I'll talk about any
+given reading for maybe 10 minutes maybe
+
+ align:start position:0%
+given reading for maybe 10 minutes maybe
+ 
+
+ align:start position:0%
+given reading for maybe 10 minutes maybe
+a little more than that right and then
+
+ align:start position:0%
+a little more than that right and then
+ 
+
+ align:start position:0%
+a little more than that right and then
+I'm going to turn it over to the
+
+ align:start position:0%
+I'm going to turn it over to the
+ 
+
+ align:start position:0%
+I'm going to turn it over to the
+discussion leader to kind of bring you
+
+ align:start position:0%
+discussion leader to kind of bring you
+ 
+
+ align:start position:0%
+discussion leader to kind of bring you
+all into the review of the reading right
+
+ align:start position:0%
+all into the review of the reading right
+ 
+
+ align:start position:0%
+all into the review of the reading right
+so that you get to participate in this
+
+ align:start position:0%
+so that you get to participate in this
+ 
+
+ align:start position:0%
+so that you get to participate in this
+and get you get your thoughts out on the
+
+ align:start position:0%
+and get you get your thoughts out on the
+ 
+
+ align:start position:0%
+and get you get your thoughts out on the
+table and importantly in terms of your
+
+ align:start position:0%
+table and importantly in terms of your
+ 
+
+ align:start position:0%
+table and importantly in terms of your
+learning process you're thinking you're
+
+ align:start position:0%
+learning process you're thinking you're
+ 
+
+ align:start position:0%
+learning process you're thinking you're
+learning you're speaking all of those
+
+ align:start position:0%
+learning you're speaking all of those
+ 
+
+ align:start position:0%
+learning you're speaking all of those
+are key to the learning process one
+
+ align:start position:0%
+are key to the learning process one
+ 
+
+ align:start position:0%
+are key to the learning process one
+thing which we know from MIT is online
+
+ align:start position:0%
+thing which we know from MIT is online
+ 
+
+ align:start position:0%
+thing which we know from MIT is online
+classes and the learning science that's
+
+ align:start position:0%
+classes and the learning science that's
+ 
+
+ align:start position:0%
+classes and the learning science that's
+work that's been going with them is that
+
+ align:start position:0%
+work that's been going with them is that
+ 
+
+ align:start position:0%
+work that's been going with them is that
+the human memory fades after more than
+
+ align:start position:0%
+the human memory fades after more than
+ 
+
+ align:start position:0%
+the human memory fades after more than
+ten minutes of the talking head I mean
+
+ align:start position:0%
+ten minutes of the talking head I mean
+ 
+
+ align:start position:0%
+ten minutes of the talking head I mean
+it is just not rememberable right and
+
+ align:start position:0%
+it is just not rememberable right and
+ 
+
+ align:start position:0%
+it is just not rememberable right and
+it's very important to change settings
+
+ align:start position:0%
+it's very important to change settings
+ 
+
+ align:start position:0%
+it's very important to change settings
+after that so we're gonna change
+
+ align:start position:0%
+after that so we're gonna change
+ 
+
+ align:start position:0%
+after that so we're gonna change
+settings and it's going to be you and
+
+ align:start position:0%
+settings and it's going to be you and
+ 
+
+ align:start position:0%
+settings and it's going to be you and
+you all are gonna kind of lead the next
+
+ align:start position:0%
+you all are gonna kind of lead the next
+ 
+
+ align:start position:0%
+you all are gonna kind of lead the next
+phase and then we'll go to the next
+
+ align:start position:0%
+phase and then we'll go to the next
+ 
+
+ align:start position:0%
+phase and then we'll go to the next
+reading after we talked about the
+
+ align:start position:0%
+reading after we talked about the
+ 
+
+ align:start position:0%
+reading after we talked about the
+initial one for awhile we'll go to the
+
+ align:start position:0%
+initial one for awhile we'll go to the
+ 
+
+ align:start position:0%
+initial one for awhile we'll go to the
+next reading and follow this pattern
+
+ align:start position:0%
+next reading and follow this pattern
+ 
+
+ align:start position:0%
+next reading and follow this pattern
+through and then I will always try to
+
+ align:start position:0%
+through and then I will always try to
+ 
+
+ align:start position:0%
+through and then I will always try to
+summarize either at the beginning of the
+
+ align:start position:0%
+summarize either at the beginning of the
+ 
+
+ align:start position:0%
+summarize either at the beginning of the
+end of the class where we are because we
+
+ align:start position:0%
+end of the class where we are because we
+ 
+
+ align:start position:0%
+end of the class where we are because we
+also know that repetition is key to
+
+ align:start position:0%
+also know that repetition is key to
+ 
+
+ align:start position:0%
+also know that repetition is key to
+learning too so just a few elementary
+
+ align:start position:0%
+learning too so just a few elementary
+ 
+
+ align:start position:0%
+learning too so just a few elementary
+points about learning science there
+
+ align:start position:0%
+points about learning science there
+ 
+
+ align:start position:0%
+points about learning science there
+really is actually some design here the
+
+ align:start position:0%
+really is actually some design here the
+ 
+
+ align:start position:0%
+really is actually some design here the
+discussion leader stuff is going to be
+
+ align:start position:0%
+discussion leader stuff is going to be
+ 
+
+ align:start position:0%
+discussion leader stuff is going to be
+very informal this is going to be very
+
+ align:start position:0%
+very informal this is going to be very
+ 
+
+ align:start position:0%
+very informal this is going to be very
+relaxed I don't want you to be concerned
+
+ align:start position:0%
+relaxed I don't want you to be concerned
+ 
+
+ align:start position:0%
+relaxed I don't want you to be concerned
+about have to do fancy presentations
+
+ align:start position:0%
+about have to do fancy presentations
+ 
+
+ align:start position:0%
+about have to do fancy presentations
+just you know speak for a few minutes
+
+ align:start position:0%
+just you know speak for a few minutes
+ 
+
+ align:start position:0%
+just you know speak for a few minutes
+about some key things that you found
+
+ align:start position:0%
+about some key things that you found
+ 
+
+ align:start position:0%
+about some key things that you found
+about the particular reading and then
+
+ align:start position:0%
+about the particular reading and then
+ 
+
+ align:start position:0%
+about the particular reading and then
+try and draw out your classmates now
+
+ align:start position:0%
+try and draw out your classmates now
+ 
+
+ align:start position:0%
+try and draw out your classmates now
+you'll get there one-pagers their
+
+ align:start position:0%
+you'll get there one-pagers their
+ 
+
+ align:start position:0%
+you'll get there one-pagers their
+reading summaries in advance they'll get
+
+ align:start position:0%
+reading summaries in advance they'll get
+ 
+
+ align:start position:0%
+reading summaries in advance they'll get
+you cut through those the day in advance
+
+ align:start position:0%
+you cut through those the day in advance
+ 
+
+ align:start position:0%
+you cut through those the day in advance
+I'll get a copy to write so I'm going to
+
+ align:start position:0%
+I'll get a copy to write so I'm going to
+ 
+
+ align:start position:0%
+I'll get a copy to write so I'm going to
+set up a rough discussion leader agenda
+
+ align:start position:0%
+set up a rough discussion leader agenda
+ 
+
+ align:start position:0%
+set up a rough discussion leader agenda
+for the first few classes and then we'll
+
+ align:start position:0%
+for the first few classes and then we'll
+ 
+
+ align:start position:0%
+for the first few classes and then we'll
+formalize it for the whole class but
+
+ align:start position:0%
+formalize it for the whole class but
+ 
+
+ align:start position:0%
+formalize it for the whole class but
+all of you will be discussion leaders
+
+ align:start position:0%
+all of you will be discussion leaders
+ 
+
+ align:start position:0%
+all of you will be discussion leaders
+probably at least a couple of times but
+
+ align:start position:0%
+probably at least a couple of times but
+ 
+
+ align:start position:0%
+probably at least a couple of times but
+again it's very relaxed it's very
+
+ align:start position:0%
+again it's very relaxed it's very
+ 
+
+ align:start position:0%
+again it's very relaxed it's very
+informal and you know we're just gonna
+
+ align:start position:0%
+informal and you know we're just gonna
+ 
+
+ align:start position:0%
+informal and you know we're just gonna
+be sitting around the table and I want
+
+ align:start position:0%
+be sitting around the table and I want
+ 
+
+ align:start position:0%
+be sitting around the table and I want
+you to kind of really work to bring your
+
+ align:start position:0%
+you to kind of really work to bring your
+ 
+
+ align:start position:0%
+you to kind of really work to bring your
+classmates you know into the into the
+
+ align:start position:0%
+classmates you know into the into the
+ 
+
+ align:start position:0%
+classmates you know into the into the
+talking so questions about this let me
+
+ align:start position:0%
+talking so questions about this let me
+ 
+
+ align:start position:0%
+talking so questions about this let me
+talk about where this class is going to
+
+ align:start position:0%
+talk about where this class is going to
+ 
+
+ align:start position:0%
+talk about where this class is going to
+go so you get a sense of the pieces that
+
+ align:start position:0%
+go so you get a sense of the pieces that
+ 
+
+ align:start position:0%
+go so you get a sense of the pieces that
+lie ahead so the first couple of classes
+
+ align:start position:0%
+lie ahead so the first couple of classes
+ 
+
+ align:start position:0%
+lie ahead so the first couple of classes
+are really introductory and you know
+
+ align:start position:0%
+are really introductory and you know
+ 
+
+ align:start position:0%
+are really introductory and you know
+today's class as those of you were able
+
+ align:start position:0%
+today's class as those of you were able
+ 
+
+ align:start position:0%
+today's class as those of you were able
+to get to the site saw is really about
+
+ align:start position:0%
+to get to the site saw is really about
+ 
+
+ align:start position:0%
+to get to the site saw is really about
+economic growth theory
+
+ align:start position:0%
+economic growth theory
+ 
+
+ align:start position:0%
+economic growth theory
+all right so innovation growth theory
+
+ align:start position:0%
+all right so innovation growth theory
+ 
+
+ align:start position:0%
+all right so innovation growth theory
+and that's foundational in other words
+
+ align:start position:0%
+and that's foundational in other words
+ 
+
+ align:start position:0%
+and that's foundational in other words
+why do we what are the pillars on which
+
+ align:start position:0%
+why do we what are the pillars on which
+ 
+
+ align:start position:0%
+why do we what are the pillars on which
+studying innovation rests clearly the
+
+ align:start position:0%
+studying innovation rests clearly the
+ 
+
+ align:start position:0%
+studying innovation rests clearly the
+economic justification is one of the
+
+ align:start position:0%
+economic justification is one of the
+ 
+
+ align:start position:0%
+economic justification is one of the
+absolute central and probably the
+
+ align:start position:0%
+absolute central and probably the
+ 
+
+ align:start position:0%
+absolute central and probably the
+critical one so what does innovation
+
+ align:start position:0%
+critical one so what does innovation
+ 
+
+ align:start position:0%
+critical one so what does innovation
+growth policy how does it think how is
+
+ align:start position:0%
+growth policy how does it think how is
+ 
+
+ align:start position:0%
+growth policy how does it think how is
+it organized and we're going to be
+
+ align:start position:0%
+it organized and we're going to be
+ 
+
+ align:start position:0%
+it organized and we're going to be
+reading two very famous growth
+
+ align:start position:0%
+reading two very famous growth
+ 
+
+ align:start position:0%
+reading two very famous growth
+economists and talking about them three
+
+ align:start position:0%
+economists and talking about them three
+ 
+
+ align:start position:0%
+economists and talking about them three
+actually and kind of trying to put
+
+ align:start position:0%
+actually and kind of trying to put
+ 
+
+ align:start position:0%
+actually and kind of trying to put
+together what the basics of growth
+
+ align:start position:0%
+together what the basics of growth
+ 
+
+ align:start position:0%
+together what the basics of growth
+theory so that we understand that it can
+
+ align:start position:0%
+theory so that we understand that it can
+ 
+
+ align:start position:0%
+theory so that we understand that it can
+use that then the second class moves
+
+ align:start position:0%
+use that then the second class moves
+ 
+
+ align:start position:0%
+use that then the second class moves
+into kind of a second part of growth
+
+ align:start position:0%
+into kind of a second part of growth
+ 
+
+ align:start position:0%
+into kind of a second part of growth
+theory and we could call this innovation
+
+ align:start position:0%
+theory and we could call this innovation
+ 
+
+ align:start position:0%
+theory and we could call this innovation
+systems in other words innovation occurs
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+in a system and you have to understand
+
+ align:start position:0%
+in a system and you have to understand
+ 
+
+ align:start position:0%
+in a system and you have to understand
+the elements of that system so we're
+
+ align:start position:0%
+the elements of that system so we're
+ 
+
+ align:start position:0%
+the elements of that system so we're
+going to talk about that systems
+
+ align:start position:0%
+going to talk about that systems
+ 
+
+ align:start position:0%
+going to talk about that systems
+approach in next week's class and then
+
+ align:start position:0%
+approach in next week's class and then
+ 
+
+ align:start position:0%
+approach in next week's class and then
+I'll give you two kind of key tools to
+
+ align:start position:0%
+I'll give you two kind of key tools to
+ 
+
+ align:start position:0%
+I'll give you two kind of key tools to
+work with
+
+ align:start position:0%
+work with
+ 
+
+ align:start position:0%
+work with
+in other words based on the first couple
+
+ align:start position:0%
+in other words based on the first couple
+ 
+
+ align:start position:0%
+in other words based on the first couple
+of classes you're going to be able to
+
+ align:start position:0%
+of classes you're going to be able to
+ 
+
+ align:start position:0%
+of classes you're going to be able to
+look at another country at a state at a
+
+ align:start position:0%
+look at another country at a state at a
+ 
+
+ align:start position:0%
+look at another country at a state at a
+region and you're going to be able to
+
+ align:start position:0%
+region and you're going to be able to
+ 
+
+ align:start position:0%
+region and you're going to be able to
+see how you can evaluate
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that areas innovation system what are
+
+ align:start position:0%
+that areas innovation system what are
+ 
+
+ align:start position:0%
+that areas innovation system what are
+the factors you'd you look for what are
+
+ align:start position:0%
+the factors you'd you look for what are
+ 
+
+ align:start position:0%
+the factors you'd you look for what are
+the capabilities that you look for how
+
+ align:start position:0%
+the capabilities that you look for how
+ 
+
+ align:start position:0%
+the capabilities that you look for how
+do you assess them and then in
+
+ align:start position:0%
+do you assess them and then in
+ 
+
+ align:start position:0%
+do you assess them and then in
+particular at the end of next week's
+
+ align:start position:0%
+particular at the end of next week's
+ 
+
+ align:start position:0%
+particular at the end of next week's
+class how do you look at them as a
+
+ align:start position:0%
+class how do you look at them as a
+ 
+
+ align:start position:0%
+class how do you look at them as a
+system and then we'll take that
+
+ align:start position:0%
+system and then we'll take that
+ 
+
+ align:start position:0%
+system and then we'll take that
+framework and we're going to apply that
+
+ align:start position:0%
+framework and we're going to apply that
+ 
+
+ align:start position:0%
+framework and we're going to apply that
+framework and add pieces to it through
+
+ align:start position:0%
+framework and add pieces to it through
+ 
+
+ align:start position:0%
+framework and add pieces to it through
+the rest of the class so the next two
+
+ align:start position:0%
+the rest of the class so the next two
+ 
+
+ align:start position:0%
+the rest of the class so the next two
+classes are really about manufacturing
+
+ align:start position:0%
+classes are really about manufacturing
+ 
+
+ align:start position:0%
+classes are really about manufacturing
+so just in case you got the idea that
+
+ align:start position:0%
+so just in case you got the idea that
+ 
+
+ align:start position:0%
+so just in case you got the idea that
+this is just policy esoterica we're
+
+ align:start position:0%
+this is just policy esoterica we're
+ 
+
+ align:start position:0%
+this is just policy esoterica we're
+gonna have a very real dive and do some
+
+ align:start position:0%
+gonna have a very real dive and do some
+ 
+
+ align:start position:0%
+gonna have a very real dive and do some
+very real problems that are frankly at
+
+ align:start position:0%
+very real problems that are frankly at
+ 
+
+ align:start position:0%
+very real problems that are frankly at
+the heart of the political disruption
+
+ align:start position:0%
+the heart of the political disruption
+ 
+
+ align:start position:0%
+the heart of the political disruption
+that's going on now in the United States
+
+ align:start position:0%
+that's going on now in the United States
+ 
+
+ align:start position:0%
+that's going on now in the United States
+and elsewhere so we're gonna do two
+
+ align:start position:0%
+and elsewhere so we're gonna do two
+ 
+
+ align:start position:0%
+and elsewhere so we're gonna do two
+classes on that right so a deep very
+
+ align:start position:0%
+classes on that right so a deep very
+ 
+
+ align:start position:0%
+classes on that right so a deep very
+practical very real dive into a really
+
+ align:start position:0%
+practical very real dive into a really
+ 
+
+ align:start position:0%
+practical very real dive into a really
+important and very current innovation
+
+ align:start position:0%
+important and very current innovation
+ 
+
+ align:start position:0%
+important and very current innovation
+system problem and then we're gonna go
+
+ align:start position:0%
+system problem and then we're gonna go
+ 
+
+ align:start position:0%
+system problem and then we're gonna go
+back and pick up some pieces we started
+
+ align:start position:0%
+back and pick up some pieces we started
+ 
+
+ align:start position:0%
+back and pick up some pieces we started
+with at the first couple of classes so
+
+ align:start position:0%
+with at the first couple of classes so
+ 
+
+ align:start position:0%
+with at the first couple of classes so
+we're going to look hard at the u.s.
+
+ align:start position:0%
+we're going to look hard at the u.s.
+ 
+
+ align:start position:0%
+we're going to look hard at the u.s.
+innovation system particularly the
+
+ align:start position:0%
+innovation system particularly the
+ 
+
+ align:start position:0%
+innovation system particularly the
+federal pieces of it right the federal
+
+ align:start position:0%
+federal pieces of it right the federal
+ 
+
+ align:start position:0%
+federal pieces of it right the federal
+R&D agencies and organizations that are
+
+ align:start position:0%
+R&D agencies and organizations that are
+ 
+
+ align:start position:0%
+R&D agencies and organizations that are
+part of the u.s. innovation system
+
+ align:start position:0%
+part of the u.s. innovation system
+ 
+
+ align:start position:0%
+part of the u.s. innovation system
+research and development okay
+
+ align:start position:0%
+research and development okay
+ 
+
+ align:start position:0%
+research and development okay
+don't hesitate to ask questions by the
+
+ align:start position:0%
+don't hesitate to ask questions by the
+ 
+
+ align:start position:0%
+don't hesitate to ask questions by the
+way please you know bring those forward
+
+ align:start position:0%
+way please you know bring those forward
+ 
+
+ align:start position:0%
+way please you know bring those forward
+so we'll look at the research and
+
+ align:start position:0%
+so we'll look at the research and
+ 
+
+ align:start position:0%
+so we'll look at the research and
+development system it's done it's
+
+ align:start position:0%
+development system it's done it's
+ 
+
+ align:start position:0%
+development system it's done it's
+daunting
+
+ align:start position:0%
+daunting
+ 
+
+ align:start position:0%
+daunting
+Steff that is easier okay
+
+ align:start position:0%
+Steff that is easier okay
+ 
+
+ align:start position:0%
+Steff that is easier okay
+thanks Steph and you know where did it
+
+ align:start position:0%
+thanks Steph and you know where did it
+ 
+
+ align:start position:0%
+thanks Steph and you know where did it
+come from how does it think how is it
+
+ align:start position:0%
+come from how does it think how is it
+ 
+
+ align:start position:0%
+come from how does it think how is it
+organized what are its origins because
+
+ align:start position:0%
+organized what are its origins because
+ 
+
+ align:start position:0%
+organized what are its origins because
+worried MIT I'll give you a lot of
+
+ align:start position:0%
+worried MIT I'll give you a lot of
+ 
+
+ align:start position:0%
+worried MIT I'll give you a lot of
+insider and mighty stuff because MIT
+
+ align:start position:0%
+insider and mighty stuff because MIT
+ 
+
+ align:start position:0%
+insider and mighty stuff because MIT
+historically was involved in a lot of
+
+ align:start position:0%
+historically was involved in a lot of
+ 
+
+ align:start position:0%
+historically was involved in a lot of
+this so you'll collect some good MIT
+
+ align:start position:0%
+this so you'll collect some good MIT
+ 
+
+ align:start position:0%
+this so you'll collect some good MIT
+stories
+
+ align:start position:0%
+stories
+ 
+
+ align:start position:0%
+stories
+I hope particularly in that class but
+
+ align:start position:0%
+I hope particularly in that class but
+ 
+
+ align:start position:0%
+I hope particularly in that class but
+you know MIT greats like veneer Bush and
+
+ align:start position:0%
+you know MIT greats like veneer Bush and
+ 
+
+ align:start position:0%
+you know MIT greats like veneer Bush and
+Alfred Loomis will come up in that class
+
+ align:start position:0%
+Alfred Loomis will come up in that class
+ 
+
+ align:start position:0%
+Alfred Loomis will come up in that class
+then in the sixth class we're going to
+
+ align:start position:0%
+then in the sixth class we're going to
+ 
+
+ align:start position:0%
+then in the sixth class we're going to
+talk about kind of the major policy
+
+ align:start position:0%
+talk about kind of the major policy
+ 
+
+ align:start position:0%
+talk about kind of the major policy
+focus
+
+ align:start position:0%
+focus
+ 
+
+ align:start position:0%
+focus
+in science technology policy which is
+
+ align:start position:0%
+in science technology policy which is
+ 
+
+ align:start position:0%
+in science technology policy which is
+called the valley of death how do you
+
+ align:start position:0%
+called the valley of death how do you
+ 
+
+ align:start position:0%
+called the valley of death how do you
+get from the research side over to later
+
+ align:start position:0%
+get from the research side over to later
+ 
+
+ align:start position:0%
+get from the research side over to later
+stage development right and that's been
+
+ align:start position:0%
+stage development right and that's been
+ 
+
+ align:start position:0%
+stage development right and that's been
+the major policy emphasis in the u.s.
+
+ align:start position:0%
+the major policy emphasis in the u.s.
+ 
+
+ align:start position:0%
+the major policy emphasis in the u.s.
+system is a big chasm there a valley
+
+ align:start position:0%
+system is a big chasm there a valley
+ 
+
+ align:start position:0%
+system is a big chasm there a valley
+building the bridging mechanisms across
+
+ align:start position:0%
+building the bridging mechanisms across
+ 
+
+ align:start position:0%
+building the bridging mechanisms across
+it's been a big policy preoccupation so
+
+ align:start position:0%
+it's been a big policy preoccupation so
+ 
+
+ align:start position:0%
+it's been a big policy preoccupation so
+we'll dive into that literature and we
+
+ align:start position:0%
+we'll dive into that literature and we
+ 
+
+ align:start position:0%
+we'll dive into that literature and we
+will also look at the fact that the
+
+ align:start position:0%
+will also look at the fact that the
+ 
+
+ align:start position:0%
+will also look at the fact that the
+United States actually runs to
+
+ align:start position:0%
+United States actually runs to
+ 
+
+ align:start position:0%
+United States actually runs to
+innovation systems so we run the
+
+ align:start position:0%
+innovation systems so we run the
+ 
+
+ align:start position:0%
+innovation systems so we run the
+innovation system probably most of you
+
+ align:start position:0%
+innovation system probably most of you
+ 
+
+ align:start position:0%
+innovation system probably most of you
+are familiar with places like NSF right
+
+ align:start position:0%
+are familiar with places like NSF right
+ 
+
+ align:start position:0%
+are familiar with places like NSF right
+the Office of Science at the Department
+
+ align:start position:0%
+the Office of Science at the Department
+ 
+
+ align:start position:0%
+the Office of Science at the Department
+of Energy NIH right so that's the kind
+
+ align:start position:0%
+of Energy NIH right so that's the kind
+ 
+
+ align:start position:0%
+of Energy NIH right so that's the kind
+of civilian side but then there's a
+
+ align:start position:0%
+of civilian side but then there's a
+ 
+
+ align:start position:0%
+of civilian side but then there's a
+whole defense innovation system that
+
+ align:start position:0%
+whole defense innovation system that
+ 
+
+ align:start position:0%
+whole defense innovation system that
+it's organized very differently Lilly is
+
+ align:start position:0%
+it's organized very differently Lilly is
+ 
+
+ align:start position:0%
+it's organized very differently Lilly is
+not in our head because we spent time on
+
+ align:start position:0%
+not in our head because we spent time on
+ 
+
+ align:start position:0%
+not in our head because we spent time on
+this in the first class so we'll talk
+
+ align:start position:0%
+this in the first class so we'll talk
+ 
+
+ align:start position:0%
+this in the first class so we'll talk
+about that system too and kind of how
+
+ align:start position:0%
+about that system too and kind of how
+ 
+
+ align:start position:0%
+about that system too and kind of how
+that works and then all up until class
+
+ align:start position:0%
+that works and then all up until class
+ 
+
+ align:start position:0%
+that works and then all up until class
+seven we've been talking about
+
+ align:start position:0%
+seven we've been talking about
+ 
+
+ align:start position:0%
+seven we've been talking about
+innovation as though it's has to do with
+
+ align:start position:0%
+innovation as though it's has to do with
+ 
+
+ align:start position:0%
+innovation as though it's has to do with
+institutions but people innovate not
+
+ align:start position:0%
+institutions but people innovate not
+ 
+
+ align:start position:0%
+institutions but people innovate not
+institutions so innovation is owned by
+
+ align:start position:0%
+institutions so innovation is owned by
+ 
+
+ align:start position:0%
+institutions so innovation is owned by
+people it occurs in a very face-to-face
+
+ align:start position:0%
+people it occurs in a very face-to-face
+ 
+
+ align:start position:0%
+people it occurs in a very face-to-face
+environment right
+
+ align:start position:0%
+environment right
+ 
+
+ align:start position:0%
+environment right
+you can't just understand innovation by
+
+ align:start position:0%
+you can't just understand innovation by
+ 
+
+ align:start position:0%
+you can't just understand innovation by
+understanding the institutions that are
+
+ align:start position:0%
+understanding the institutions that are
+ 
+
+ align:start position:0%
+understanding the institutions that are
+sticking their hands into it in the end
+
+ align:start position:0%
+sticking their hands into it in the end
+ 
+
+ align:start position:0%
+sticking their hands into it in the end
+it's a people system and how do people
+
+ align:start position:0%
+it's a people system and how do people
+ 
+
+ align:start position:0%
+it's a people system and how do people
+what does innovation look like when
+
+ align:start position:0%
+what does innovation look like when
+ 
+
+ align:start position:0%
+what does innovation look like when
+people are running it at the
+
+ align:start position:0%
+people are running it at the
+ 
+
+ align:start position:0%
+people are running it at the
+face-to-face level and it turns out
+
+ align:start position:0%
+face-to-face level and it turns out
+ 
+
+ align:start position:0%
+face-to-face level and it turns out
+there's literature on this there's some
+
+ align:start position:0%
+there's literature on this there's some
+ 
+
+ align:start position:0%
+there's literature on this there's some
+rules that innovation groups tend to
+
+ align:start position:0%
+rules that innovation groups tend to
+ 
+
+ align:start position:0%
+rules that innovation groups tend to
+follow when they're undertaking their
+
+ align:start position:0%
+follow when they're undertaking their
+ 
+
+ align:start position:0%
+follow when they're undertaking their
+process of trying to get to a
+
+ align:start position:0%
+process of trying to get to a
+ 
+
+ align:start position:0%
+process of trying to get to a
+breakthrough so we'll look at the
+
+ align:start position:0%
+breakthrough so we'll look at the
+ 
+
+ align:start position:0%
+breakthrough so we'll look at the
+organization of innovation systems at
+
+ align:start position:0%
+organization of innovation systems at
+ 
+
+ align:start position:0%
+organization of innovation systems at
+the face-to-face level as well as the
+
+ align:start position:0%
+the face-to-face level as well as the
+ 
+
+ align:start position:0%
+the face-to-face level as well as the
+institutional level and that class you
+
+ align:start position:0%
+institutional level and that class you
+ 
+
+ align:start position:0%
+institutional level and that class you
+all will own because I'm gonna have you
+
+ align:start position:0%
+all will own because I'm gonna have you
+ 
+
+ align:start position:0%
+all will own because I'm gonna have you
+all present a group of you on great
+
+ align:start position:0%
+all present a group of you on great
+ 
+
+ align:start position:0%
+all present a group of you on great
+innovation groups and then we've got the
+
+ align:start position:0%
+innovation groups and then we've got the
+ 
+
+ align:start position:0%
+innovation groups and then we've got the
+foundations all set and we're gonna
+
+ align:start position:0%
+foundations all set and we're gonna
+ 
+
+ align:start position:0%
+foundations all set and we're gonna
+start to look at particular segments so
+
+ align:start position:0%
+start to look at particular segments so
+ 
+
+ align:start position:0%
+start to look at particular segments so
+we'll take a deep dive into DARPA the
+
+ align:start position:0%
+we'll take a deep dive into DARPA the
+ 
+
+ align:start position:0%
+we'll take a deep dive into DARPA the
+Defense Advanced Research
+
+ align:start position:0%
+Defense Advanced Research
+ 
+
+ align:start position:0%
+Defense Advanced Research
+Church agency and its innovation model
+
+ align:start position:0%
+Church agency and its innovation model
+ 
+
+ align:start position:0%
+Church agency and its innovation model
+so that'll be kind of a case study we're
+
+ align:start position:0%
+so that'll be kind of a case study we're
+ 
+
+ align:start position:0%
+so that'll be kind of a case study we're
+gonna take a close look at at energy
+
+ align:start position:0%
+gonna take a close look at at energy
+ 
+
+ align:start position:0%
+gonna take a close look at at energy
+technology and here Martha will help us
+
+ align:start position:0%
+technology and here Martha will help us
+ 
+
+ align:start position:0%
+technology and here Martha will help us
+get through the class cuz she'll know
+
+ align:start position:0%
+get through the class cuz she'll know
+ 
+
+ align:start position:0%
+get through the class cuz she'll know
+much more than me and we're gonna look
+
+ align:start position:0%
+much more than me and we're gonna look
+ 
+
+ align:start position:0%
+much more than me and we're gonna look
+very closely at the life science
+
+ align:start position:0%
+very closely at the life science
+ 
+
+ align:start position:0%
+very closely at the life science
+innovation system that on the federal
+
+ align:start position:0%
+innovation system that on the federal
+ 
+
+ align:start position:0%
+innovation system that on the federal
+side is led by the National Institutes
+
+ align:start position:0%
+side is led by the National Institutes
+ 
+
+ align:start position:0%
+side is led by the National Institutes
+of Health and some of the big challenges
+
+ align:start position:0%
+of Health and some of the big challenges
+ 
+
+ align:start position:0%
+of Health and some of the big challenges
+in that system we're gonna develop an
+
+ align:start position:0%
+in that system we're gonna develop an
+ 
+
+ align:start position:0%
+in that system we're gonna develop an
+idea of how do legacy sectors innovate
+
+ align:start position:0%
+idea of how do legacy sectors innovate
+ 
+
+ align:start position:0%
+idea of how do legacy sectors innovate
+right because you know the computing
+
+ align:start position:0%
+right because you know the computing
+ 
+
+ align:start position:0%
+right because you know the computing
+revolution was brought about by a new
+
+ align:start position:0%
+revolution was brought about by a new
+ 
+
+ align:start position:0%
+revolution was brought about by a new
+frontier creating a new frontier
+
+ align:start position:0%
+frontier creating a new frontier
+ 
+
+ align:start position:0%
+frontier creating a new frontier
+territory and innovation but most of the
+
+ align:start position:0%
+territory and innovation but most of the
+ 
+
+ align:start position:0%
+territory and innovation but most of the
+economy more than 80% is owned by these
+
+ align:start position:0%
+economy more than 80% is owned by these
+ 
+
+ align:start position:0%
+economy more than 80% is owned by these
+established sectors and it's much harder
+
+ align:start position:0%
+established sectors and it's much harder
+ 
+
+ align:start position:0%
+established sectors and it's much harder
+to bring innovation into those sectors
+
+ align:start position:0%
+to bring innovation into those sectors
+ 
+
+ align:start position:0%
+to bring innovation into those sectors
+so energy is like the poster child for
+
+ align:start position:0%
+so energy is like the poster child for
+ 
+
+ align:start position:0%
+so energy is like the poster child for
+that problem and we'll take a real look
+
+ align:start position:0%
+that problem and we'll take a real look
+ 
+
+ align:start position:0%
+that problem and we'll take a real look
+at that and then at the close the class
+
+ align:start position:0%
+at that and then at the close the class
+ 
+
+ align:start position:0%
+at that and then at the close the class
+we're gonna do a couple of I think more
+
+ align:start position:0%
+we're gonna do a couple of I think more
+ 
+
+ align:start position:0%
+we're gonna do a couple of I think more
+fun and interesting you know out of the
+
+ align:start position:0%
+fun and interesting you know out of the
+ 
+
+ align:start position:0%
+fun and interesting you know out of the
+blue categories so we're gonna look at
+
+ align:start position:0%
+blue categories so we're gonna look at
+ 
+
+ align:start position:0%
+blue categories so we're gonna look at
+the talent base and science and
+
+ align:start position:0%
+the talent base and science and
+ 
+
+ align:start position:0%
+the talent base and science and
+technology education and all the
+
+ align:start position:0%
+technology education and all the
+ 
+
+ align:start position:0%
+technology education and all the
+challenge is embedded in that developing
+
+ align:start position:0%
+challenge is embedded in that developing
+ 
+
+ align:start position:0%
+challenge is embedded in that developing
+as strong as in detail at base and then
+
+ align:start position:0%
+as strong as in detail at base and then
+ 
+
+ align:start position:0%
+as strong as in detail at base and then
+we're gonna take a look at what we could
+
+ align:start position:0%
+we're gonna take a look at what we could
+ 
+
+ align:start position:0%
+we're gonna take a look at what we could
+call the future of work so are you gonna
+
+ align:start position:0%
+call the future of work so are you gonna
+ 
+
+ align:start position:0%
+call the future of work so are you gonna
+have any jobs right are you gonna be
+
+ align:start position:0%
+have any jobs right are you gonna be
+ 
+
+ align:start position:0%
+have any jobs right are you gonna be
+displaced by MIT developed robotics
+
+ align:start position:0%
+displaced by MIT developed robotics
+ 
+
+ align:start position:0%
+displaced by MIT developed robotics
+right that will be you aren't don't
+
+ align:start position:0%
+right that will be you aren't don't
+ 
+
+ align:start position:0%
+right that will be you aren't don't
+worry but that'll be one of the
+
+ align:start position:0%
+worry but that'll be one of the
+ 
+
+ align:start position:0%
+worry but that'll be one of the
+challenges that we're going to look at
+
+ align:start position:0%
+challenges that we're going to look at
+ 
+
+ align:start position:0%
+challenges that we're going to look at
+now tell me your name so I get to know
+
+ align:start position:0%
+now tell me your name so I get to know
+ 
+
+ align:start position:0%
+now tell me your name so I get to know
+everybody
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay Martina you know we'll look at I
+
+ align:start position:0%
+okay Martina you know we'll look at I
+ 
+
+ align:start position:0%
+okay Martina you know we'll look at I
+tell you who will look at will look at
+
+ align:start position:0%
+tell you who will look at will look at
+ 
+
+ align:start position:0%
+tell you who will look at will look at
+the kind of techno dystopia movement
+
+ align:start position:0%
+the kind of techno dystopia movement
+ 
+
+ align:start position:0%
+the kind of techno dystopia movement
+which Erik Brynjolfsson and Andrew
+
+ align:start position:0%
+which Erik Brynjolfsson and Andrew
+ 
+
+ align:start position:0%
+which Erik Brynjolfsson and Andrew
+McAfee at Sloan have been doing a lot of
+
+ align:start position:0%
+McAfee at Sloan have been doing a lot of
+ 
+
+ align:start position:0%
+McAfee at Sloan have been doing a lot of
+work on and that's you know IT is going
+
+ align:start position:0%
+work on and that's you know IT is going
+ 
+
+ align:start position:0%
+work on and that's you know IT is going
+to replace
+
+ align:start position:0%
+to replace
+ 
+
+ align:start position:0%
+to replace
+a lot of work theory we're gonna look at
+
+ align:start position:0%
+a lot of work theory we're gonna look at
+ 
+
+ align:start position:0%
+a lot of work theory we're gonna look at
+David otter
+
+ align:start position:0%
+David otter
+ 
+
+ align:start position:0%
+David otter
+who's a wonderful MIT economist and
+
+ align:start position:0%
+who's a wonderful MIT economist and
+ 
+
+ align:start position:0%
+who's a wonderful MIT economist and
+we'll read several things from David but
+
+ align:start position:0%
+we'll read several things from David but
+ 
+
+ align:start position:0%
+we'll read several things from David but
+he's looking at all kinds of an economic
+
+ align:start position:0%
+he's looking at all kinds of an economic
+ 
+
+ align:start position:0%
+he's looking at all kinds of an economic
+effects on job creation including from
+
+ align:start position:0%
+effects on job creation including from
+ 
+
+ align:start position:0%
+effects on job creation including from
+manufacturing and you know we're gonna
+
+ align:start position:0%
+manufacturing and you know we're gonna
+ 
+
+ align:start position:0%
+manufacturing and you know we're gonna
+look at some studies that try to take a
+
+ align:start position:0%
+look at some studies that try to take a
+ 
+
+ align:start position:0%
+look at some studies that try to take a
+deep dive into you know how much work is
+
+ align:start position:0%
+deep dive into you know how much work is
+ 
+
+ align:start position:0%
+deep dive into you know how much work is
+actually gonna be displaced right and
+
+ align:start position:0%
+actually gonna be displaced right and
+ 
+
+ align:start position:0%
+actually gonna be displaced right and
+there's a fairly interesting new OECD
+
+ align:start position:0%
+there's a fairly interesting new OECD
+ 
+
+ align:start position:0%
+there's a fairly interesting new OECD
+study that came out this summer that
+
+ align:start position:0%
+study that came out this summer that
+ 
+
+ align:start position:0%
+study that came out this summer that
+indicates it's not going to be that bad
+
+ align:start position:0%
+indicates it's not going to be that bad
+ 
+
+ align:start position:0%
+indicates it's not going to be that bad
+so we're gonna look at all these kinds
+
+ align:start position:0%
+so we're gonna look at all these kinds
+ 
+
+ align:start position:0%
+so we're gonna look at all these kinds
+of issues and kind of play them out but
+
+ align:start position:0%
+of issues and kind of play them out but
+ 
+
+ align:start position:0%
+of issues and kind of play them out but
+I think it'll be you know particularly
+
+ align:start position:0%
+I think it'll be you know particularly
+ 
+
+ align:start position:0%
+I think it'll be you know particularly
+interesting and a kind of challenging
+
+ align:start position:0%
+interesting and a kind of challenging
+ 
+
+ align:start position:0%
+interesting and a kind of challenging
+session one more thing we'll do as David
+
+ align:start position:0%
+session one more thing we'll do as David
+ 
+
+ align:start position:0%
+session one more thing we'll do as David
+Mindell who's teaches at STS who is a
+
+ align:start position:0%
+Mindell who's teaches at STS who is a
+ 
+
+ align:start position:0%
+Mindell who's teaches at STS who is a
+wonderful technology historian but also
+
+ align:start position:0%
+wonderful technology historian but also
+ 
+
+ align:start position:0%
+wonderful technology historian but also
+a terrific engineer so David is on leave
+
+ align:start position:0%
+a terrific engineer so David is on leave
+ 
+
+ align:start position:0%
+a terrific engineer so David is on leave
+from MIT this semester because he's
+
+ align:start position:0%
+from MIT this semester because he's
+ 
+
+ align:start position:0%
+from MIT this semester because he's
+doing his robotics startup but he has a
+
+ align:start position:0%
+doing his robotics startup but he has a
+ 
+
+ align:start position:0%
+doing his robotics startup but he has a
+book called our robots ourselves
+
+ align:start position:0%
+book called our robots ourselves
+ 
+
+ align:start position:0%
+book called our robots ourselves
+and he takes a really deep look if
+
+ align:start position:0%
+and he takes a really deep look if
+ 
+
+ align:start position:0%
+and he takes a really deep look if
+robotics in a way is the most
+
+ align:start position:0%
+robotics in a way is the most
+ 
+
+ align:start position:0%
+robotics in a way is the most
+threatening entry to human work what
+
+ align:start position:0%
+threatening entry to human work what
+ 
+
+ align:start position:0%
+threatening entry to human work what
+does that actually look like right what
+
+ align:start position:0%
+does that actually look like right what
+ 
+
+ align:start position:0%
+does that actually look like right what
+is actually going on and he comes up
+
+ align:start position:0%
+is actually going on and he comes up
+ 
+
+ align:start position:0%
+is actually going on and he comes up
+with a thesis that's much more about
+
+ align:start position:0%
+with a thesis that's much more about
+ 
+
+ align:start position:0%
+with a thesis that's much more about
+assistive robotics and Co bot X then
+
+ align:start position:0%
+assistive robotics and Co bot X then
+ 
+
+ align:start position:0%
+assistive robotics and Co bot X then
+about people displacement so we'll look
+
+ align:start position:0%
+about people displacement so we'll look
+ 
+
+ align:start position:0%
+about people displacement so we'll look
+at all this stuff and try and lay it out
+
+ align:start position:0%
+at all this stuff and try and lay it out
+ 
+
+ align:start position:0%
+at all this stuff and try and lay it out
+anything anything so far questions so
+
+ align:start position:0%
+anything anything so far questions so
+ 
+
+ align:start position:0%
+anything anything so far questions so
+far yeah so we're gonna do snapshots on
+
+ align:start position:0%
+far yeah so we're gonna do snapshots on
+ 
+
+ align:start position:0%
+far yeah so we're gonna do snapshots on
+international issues kind of throughout
+
+ align:start position:0%
+international issues kind of throughout
+ 
+
+ align:start position:0%
+international issues kind of throughout
+so the basic focus will be in the US but
+
+ align:start position:0%
+so the basic focus will be in the US but
+ 
+
+ align:start position:0%
+so the basic focus will be in the US but
+Matt coming back to your question
+
+ align:start position:0%
+Matt coming back to your question
+ 
+
+ align:start position:0%
+Matt coming back to your question
+there'll be a lot of underlying
+
+ align:start position:0%
+there'll be a lot of underlying
+ 
+
+ align:start position:0%
+there'll be a lot of underlying
+questions about how economic growth
+
+ align:start position:0%
+questions about how economic growth
+ 
+
+ align:start position:0%
+questions about how economic growth
+innovation based growth works that's
+
+ align:start position:0%
+innovation based growth works that's
+ 
+
+ align:start position:0%
+innovation based growth works that's
+going to have a lot more applicability
+
+ align:start position:0%
+going to have a lot more applicability
+ 
+
+ align:start position:0%
+going to have a lot more applicability
+worldwide including the development of
+
+ align:start position:0%
+worldwide including the development of
+ 
+
+ align:start position:0%
+worldwide including the development of
+developing world so you're gonna get a
+
+ align:start position:0%
+developing world so you're gonna get a
+ 
+
+ align:start position:0%
+developing world so you're gonna get a
+toolset that will enable you
+
+ align:start position:0%
+toolset that will enable you
+ 
+
+ align:start position:0%
+toolset that will enable you
+to look at innovation much more broadly
+
+ align:start position:0%
+to look at innovation much more broadly
+ 
+
+ align:start position:0%
+to look at innovation much more broadly
+than just the US you're gonna pick up a
+
+ align:start position:0%
+than just the US you're gonna pick up a
+ 
+
+ align:start position:0%
+than just the US you're gonna pick up a
+lot of pieces about the US but it's a
+
+ align:start position:0%
+lot of pieces about the US but it's a
+ 
+
+ align:start position:0%
+lot of pieces about the US but it's a
+much broader toolset than that which I
+
+ align:start position:0%
+much broader toolset than that which I
+ 
+
+ align:start position:0%
+much broader toolset than that which I
+think you'll be able to apply and we'll
+
+ align:start position:0%
+think you'll be able to apply and we'll
+ 
+
+ align:start position:0%
+think you'll be able to apply and we'll
+have a number of readings that will pull
+
+ align:start position:0%
+have a number of readings that will pull
+ 
+
+ align:start position:0%
+have a number of readings that will pull
+us into the international issues what
+
+ align:start position:0%
+us into the international issues what
+ 
+
+ align:start position:0%
+us into the international issues what
+else our team I'm always open to current
+
+ align:start position:0%
+else our team I'm always open to current
+ 
+
+ align:start position:0%
+else our team I'm always open to current
+events so when we talk about
+
+ align:start position:0%
+events so when we talk about
+ 
+
+ align:start position:0%
+events so when we talk about
+manufacturing I'll try and give you a
+
+ align:start position:0%
+manufacturing I'll try and give you a
+ 
+
+ align:start position:0%
+manufacturing I'll try and give you a
+backdrop on some of that so that's
+
+ align:start position:0%
+backdrop on some of that so that's
+ 
+
+ align:start position:0%
+backdrop on some of that so that's
+that's the third class and you know it's
+
+ align:start position:0%
+that's the third class and you know it's
+ 
+
+ align:start position:0%
+that's the third class and you know it's
+been a lot of social disruption in the
+
+ align:start position:0%
+been a lot of social disruption in the
+ 
+
+ align:start position:0%
+been a lot of social disruption in the
+US and we'll try and through a reading
+
+ align:start position:0%
+US and we'll try and through a reading
+ 
+
+ align:start position:0%
+US and we'll try and through a reading
+but we'll talk about David autor and
+
+ align:start position:0%
+but we'll talk about David autor and
+ 
+
+ align:start position:0%
+but we'll talk about David autor and
+some of his work and findings in that
+
+ align:start position:0%
+some of his work and findings in that
+ 
+
+ align:start position:0%
+some of his work and findings in that
+area in particular and there'll be a lot
+
+ align:start position:0%
+area in particular and there'll be a lot
+ 
+
+ align:start position:0%
+area in particular and there'll be a lot
+of stories developing as the year goes
+
+ align:start position:0%
+of stories developing as the year goes
+ 
+
+ align:start position:0%
+of stories developing as the year goes
+on I know anything else to start yeah
+
+ align:start position:0%
+on I know anything else to start yeah
+ 
+
+ align:start position:0%
+on I know anything else to start yeah
+fleshie Rasheed right yeah it's good you
+
+ align:start position:0%
+fleshie Rasheed right yeah it's good you
+ 
+
+ align:start position:0%
+fleshie Rasheed right yeah it's good you
+bet you bet none of this stuff is locked
+
+ align:start position:0%
+bet you bet none of this stuff is locked
+ 
+
+ align:start position:0%
+bet you bet none of this stuff is locked
+in stone you know I hope all of you will
+
+ align:start position:0%
+in stone you know I hope all of you will
+ 
+
+ align:start position:0%
+in stone you know I hope all of you will
+do startups at some point in your career
+
+ align:start position:0%
+do startups at some point in your career
+ 
+
+ align:start position:0%
+do startups at some point in your career
+I hope all of you will be involved in
+
+ align:start position:0%
+I hope all of you will be involved in
+ 
+
+ align:start position:0%
+I hope all of you will be involved in
+innovation policy and issues and part of
+
+ align:start position:0%
+innovation policy and issues and part of
+ 
+
+ align:start position:0%
+innovation policy and issues and part of
+the tool set you're going to get is how
+
+ align:start position:0%
+the tool set you're going to get is how
+ 
+
+ align:start position:0%
+the tool set you're going to get is how
+to think about those innovation systems
+
+ align:start position:0%
+to think about those innovation systems
+ 
+
+ align:start position:0%
+to think about those innovation systems
+and how to think about organizing them
+
+ align:start position:0%
+and how to think about organizing them
+ 
+
+ align:start position:0%
+and how to think about organizing them
+in an optimal way if anything that's the
+
+ align:start position:0%
+in an optimal way if anything that's the
+ 
+
+ align:start position:0%
+in an optimal way if anything that's the
+key thing I won't want to convey in this
+
+ align:start position:0%
+key thing I won't want to convey in this
+ 
+
+ align:start position:0%
+key thing I won't want to convey in this
+course so then when you're running this
+
+ align:start position:0%
+course so then when you're running this
+ 
+
+ align:start position:0%
+course so then when you're running this
+country you got a you got an agenda
+
+ align:start position:0%
+country you got a you got an agenda
+ 
+
+ align:start position:0%
+country you got a you got an agenda
+ready to go anything else
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+alright so I'm gonna do more talking in
+
+ align:start position:0%
+alright so I'm gonna do more talking in
+ 
+
+ align:start position:0%
+alright so I'm gonna do more talking in
+this class I'll do less talking in
+
+ align:start position:0%
+this class I'll do less talking in
+ 
+
+ align:start position:0%
+this class I'll do less talking in
+future classes hold me to that but let
+
+ align:start position:0%
+future classes hold me to that but let
+ 
+
+ align:start position:0%
+future classes hold me to that but let
+me kind of summarize what we're gonna
+
+ align:start position:0%
+me kind of summarize what we're gonna
+ 
+
+ align:start position:0%
+me kind of summarize what we're gonna
+see in today's class so we're gonna talk
+
+ align:start position:0%
+see in today's class so we're gonna talk
+ 
+
+ align:start position:0%
+see in today's class so we're gonna talk
+about Robert Solow and his contribution
+
+ align:start position:0%
+about Robert Solow and his contribution
+ 
+
+ align:start position:0%
+about Robert Solow and his contribution
+is to think about a critical factor in
+
+ align:start position:0%
+is to think about a critical factor in
+ 
+
+ align:start position:0%
+is to think about a critical factor in
+innovation right a direct innovation
+
+ align:start position:0%
+innovation right a direct innovation
+ 
+
+ align:start position:0%
+innovation right a direct innovation
+factor which he refers to as
+
+ align:start position:0%
+factor which he refers to as
+ 
+
+ align:start position:0%
+factor which he refers to as
+technological and related innovation so
+
+ align:start position:0%
+technological and related innovation so
+ 
+
+ align:start position:0%
+technological and related innovation so
+that's a term that I want you all to
+
+ align:start position:0%
+that's a term that I want you all to
+ 
+
+ align:start position:0%
+that's a term that I want you all to
+recall technological and related
+
+ align:start position:0%
+recall technological and related
+ 
+
+ align:start position:0%
+recall technological and related
+innovation we're gonna use that a lot
+
+ align:start position:0%
+innovation we're gonna use that a lot
+ 
+
+ align:start position:0%
+innovation we're gonna use that a lot
+and we'll talk in a minute about what it
+
+ align:start position:0%
+and we'll talk in a minute about what it
+ 
+
+ align:start position:0%
+and we'll talk in a minute about what it
+means and then we're gonna talk about
+
+ align:start position:0%
+means and then we're gonna talk about
+ 
+
+ align:start position:0%
+means and then we're gonna talk about
+another great growth economist Paul
+
+ align:start position:0%
+another great growth economist Paul
+ 
+
+ align:start position:0%
+another great growth economist Paul
+Romer he was in MIT for about a year and
+
+ align:start position:0%
+Romer he was in MIT for about a year and
+ 
+
+ align:start position:0%
+Romer he was in MIT for about a year and
+then ran out he's a character and we'll
+
+ align:start position:0%
+then ran out he's a character and we'll
+ 
+
+ align:start position:0%
+then ran out he's a character and we'll
+talk about him too but he comes up with
+
+ align:start position:0%
+talk about him too but he comes up with
+ 
+
+ align:start position:0%
+talk about him too but he comes up with
+our second direct innovation factor
+
+ align:start position:0%
+our second direct innovation factor
+ 
+
+ align:start position:0%
+our second direct innovation factor
+human capital engaged in research and
+
+ align:start position:0%
+human capital engaged in research and
+ 
+
+ align:start position:0%
+human capital engaged in research and
+we'll talk about what that means and
+
+ align:start position:0%
+we'll talk about what that means and
+ 
+
+ align:start position:0%
+we'll talk about what that means and
+then third do these factors actually
+
+ align:start position:0%
+then third do these factors actually
+ 
+
+ align:start position:0%
+then third do these factors actually
+make sense
+
+ align:start position:0%
+make sense
+ 
+
+ align:start position:0%
+make sense
+so Dale Jorgenson is a Harvard economics
+
+ align:start position:0%
+so Dale Jorgenson is a Harvard economics
+ 
+
+ align:start position:0%
+so Dale Jorgenson is a Harvard economics
+professor of note another great growth
+
+ align:start position:0%
+professor of note another great growth
+ 
+
+ align:start position:0%
+professor of note another great growth
+economist then he takes a deep dive into
+
+ align:start position:0%
+economist then he takes a deep dive into
+ 
+
+ align:start position:0%
+economist then he takes a deep dive into
+the IT revolution of the 90s and the
+
+ align:start position:0%
+the IT revolution of the 90s and the
+ 
+
+ align:start position:0%
+the IT revolution of the 90s and the
+period leading up to that and he
+
+ align:start position:0%
+period leading up to that and he
+ 
+
+ align:start position:0%
+period leading up to that and he
+essentially concludes yeah this was
+
+ align:start position:0%
+essentially concludes yeah this was
+ 
+
+ align:start position:0%
+essentially concludes yeah this was
+technological driven innovation based
+
+ align:start position:0%
+technological driven innovation based
+ 
+
+ align:start position:0%
+technological driven innovation based
+growth it drove a huge growth in the
+
+ align:start position:0%
+growth it drove a huge growth in the
+ 
+
+ align:start position:0%
+growth it drove a huge growth in the
+economy and then we'll have fun with a
+
+ align:start position:0%
+economy and then we'll have fun with a
+ 
+
+ align:start position:0%
+economy and then we'll have fun with a
+little study by Merrill Lynch which is
+
+ align:start position:0%
+little study by Merrill Lynch which is
+ 
+
+ align:start position:0%
+little study by Merrill Lynch which is
+an investor's look at innovation and how
+
+ align:start position:0%
+an investor's look at innovation and how
+ 
+
+ align:start position:0%
+an investor's look at innovation and how
+do investors think about investing in
+
+ align:start position:0%
+do investors think about investing in
+ 
+
+ align:start position:0%
+do investors think about investing in
+innovation and then we'll look at some I
+
+ align:start position:0%
+innovation and then we'll look at some I
+ 
+
+ align:start position:0%
+innovation and then we'll look at some I
+asked you all to look at NSF indicators
+
+ align:start position:0%
+asked you all to look at NSF indicators
+ 
+
+ align:start position:0%
+asked you all to look at NSF indicators
+I'll explain what that is in a bit but
+
+ align:start position:0%
+I'll explain what that is in a bit but
+ 
+
+ align:start position:0%
+I'll explain what that is in a bit but
+we'll look at some ways of looking at
+
+ align:start position:0%
+we'll look at some ways of looking at
+ 
+
+ align:start position:0%
+we'll look at some ways of looking at
+those two facing innovation factors the
+
+ align:start position:0%
+those two facing innovation factors the
+ 
+
+ align:start position:0%
+those two facing innovation factors the
+technology R&D factor the talent factor
+
+ align:start position:0%
+technology R&D factor the talent factor
+ 
+
+ align:start position:0%
+technology R&D factor the talent factor
+and where do those if you look at those
+
+ align:start position:0%
+and where do those if you look at those
+ 
+
+ align:start position:0%
+and where do those if you look at those
+what do those look like in the US so
+
+ align:start position:0%
+what do those look like in the US so
+ 
+
+ align:start position:0%
+what do those look like in the US so
+part one here is you know the
+
+ align:start position:0%
+part one here is you know the
+ 
+
+ align:start position:0%
+part one here is you know the
+kind of fundamental factors of
+
+ align:start position:0%
+kind of fundamental factors of
+ 
+
+ align:start position:0%
+kind of fundamental factors of
+innovation but let me get some general
+
+ align:start position:0%
+innovation but let me get some general
+ 
+
+ align:start position:0%
+innovation but let me get some general
+terms on the table and I will post by
+
+ align:start position:0%
+terms on the table and I will post by
+ 
+
+ align:start position:0%
+terms on the table and I will post by
+the way the lectures after on the
+
+ align:start position:0%
+the way the lectures after on the
+ 
+
+ align:start position:0%
+the way the lectures after on the
+stellar website so you all have access
+
+ align:start position:0%
+stellar website so you all have access
+ 
+
+ align:start position:0%
+stellar website so you all have access
+to them but there's some terms that will
+
+ align:start position:0%
+to them but there's some terms that will
+ 
+
+ align:start position:0%
+to them but there's some terms that will
+recur here and you no need to memorize
+
+ align:start position:0%
+recur here and you no need to memorize
+ 
+
+ align:start position:0%
+recur here and you no need to memorize
+them now but they'll be you know posted
+
+ align:start position:0%
+them now but they'll be you know posted
+ 
+
+ align:start position:0%
+them now but they'll be you know posted
+today or tomorrow so science science
+
+ align:start position:0%
+today or tomorrow so science science
+ 
+
+ align:start position:0%
+today or tomorrow so science science
+evolved as a way of understanding the
+
+ align:start position:0%
+evolved as a way of understanding the
+ 
+
+ align:start position:0%
+evolved as a way of understanding the
+natural world it came out of natural
+
+ align:start position:0%
+natural world it came out of natural
+ 
+
+ align:start position:0%
+natural world it came out of natural
+philosophy it's an 18th 19th century
+
+ align:start position:0%
+philosophy it's an 18th 19th century
+ 
+
+ align:start position:0%
+philosophy it's an 18th 19th century
+kind of conceptual framework it is
+
+ align:start position:0%
+kind of conceptual framework it is
+ 
+
+ align:start position:0%
+kind of conceptual framework it is
+observational at heart it observes the
+
+ align:start position:0%
+observational at heart it observes the
+ 
+
+ align:start position:0%
+observational at heart it observes the
+natural world and attempts to understand
+
+ align:start position:0%
+natural world and attempts to understand
+ 
+
+ align:start position:0%
+natural world and attempts to understand
+how it's put together and it's organized
+
+ align:start position:0%
+how it's put together and it's organized
+ 
+
+ align:start position:0%
+how it's put together and it's organized
+around discovery about that natural
+
+ align:start position:0%
+around discovery about that natural
+ 
+
+ align:start position:0%
+around discovery about that natural
+world and it's order technology is
+
+ align:start position:0%
+world and it's order technology is
+ 
+
+ align:start position:0%
+world and it's order technology is
+really different it is a system to
+
+ align:start position:0%
+really different it is a system to
+ 
+
+ align:start position:0%
+really different it is a system to
+organize scientific and technical
+
+ align:start position:0%
+organize scientific and technical
+ 
+
+ align:start position:0%
+organize scientific and technical
+knowledge to go after a more practical
+
+ align:start position:0%
+knowledge to go after a more practical
+ 
+
+ align:start position:0%
+knowledge to go after a more practical
+purpose and the system's includes the
+
+ align:start position:0%
+purpose and the system's includes the
+ 
+
+ align:start position:0%
+purpose and the system's includes the
+technical advance plus models to
+
+ align:start position:0%
+technical advance plus models to
+ 
+
+ align:start position:0%
+technical advance plus models to
+implement that advance so you move from
+
+ align:start position:0%
+implement that advance so you move from
+ 
+
+ align:start position:0%
+implement that advance so you move from
+observation to implementation right and
+
+ align:start position:0%
+observation to implementation right and
+ 
+
+ align:start position:0%
+observation to implementation right and
+this is obviously the historical
+
+ align:start position:0%
+this is obviously the historical
+ 
+
+ align:start position:0%
+this is obviously the historical
+boundary between science and engineering
+
+ align:start position:0%
+boundary between science and engineering
+ 
+
+ align:start position:0%
+boundary between science and engineering
+right and research another term we'll
+
+ align:start position:0%
+right and research another term we'll
+ 
+
+ align:start position:0%
+right and research another term we'll
+use constantly means increasing the
+
+ align:start position:0%
+use constantly means increasing the
+ 
+
+ align:start position:0%
+use constantly means increasing the
+scientific or technical knowledge or
+
+ align:start position:0%
+scientific or technical knowledge or
+ 
+
+ align:start position:0%
+scientific or technical knowledge or
+both right so research can pursue either
+
+ align:start position:0%
+both right so research can pursue either
+ 
+
+ align:start position:0%
+both right so research can pursue either
+of these historic ends or both
+
+ align:start position:0%
+of these historic ends or both
+ 
+
+ align:start position:0%
+of these historic ends or both
+simultaneously invention is about
+
+ align:start position:0%
+simultaneously invention is about
+ 
+
+ align:start position:0%
+simultaneously invention is about
+applying research knowledge to create a
+
+ align:start position:0%
+applying research knowledge to create a
+ 
+
+ align:start position:0%
+applying research knowledge to create a
+practical idea or device in a vention is
+
+ align:start position:0%
+practical idea or device in a vention is
+ 
+
+ align:start position:0%
+practical idea or device in a vention is
+really different than innovation right
+
+ align:start position:0%
+really different than innovation right
+ 
+
+ align:start position:0%
+really different than innovation right
+innovation is built on scientific
+
+ align:start position:0%
+innovation is built on scientific
+ 
+
+ align:start position:0%
+innovation is built on scientific
+discovery and on breakthrough invention
+
+ align:start position:0%
+discovery and on breakthrough invention
+ 
+
+ align:start position:0%
+discovery and on breakthrough invention
+or inventions
+
+ align:start position:0%
+or inventions
+ 
+
+ align:start position:0%
+or inventions
+but it is the system of research
+
+ align:start position:0%
+but it is the system of research
+ 
+
+ align:start position:0%
+but it is the system of research
+invention development that uses both
+
+ align:start position:0%
+invention development that uses both
+ 
+
+ align:start position:0%
+invention development that uses both
+scientific background scientific
+
+ align:start position:0%
+scientific background scientific
+ 
+
+ align:start position:0%
+scientific background scientific
+knowledge and technology knowledge to
+
+ align:start position:0%
+knowledge and technology knowledge to
+ 
+
+ align:start position:0%
+knowledge and technology knowledge to
+lead to the implementation and
+
+ align:start position:0%
+lead to the implementation and
+ 
+
+ align:start position:0%
+lead to the implementation and
+widespread applicability of you know a
+
+ align:start position:0%
+widespread applicability of you know a
+ 
+
+ align:start position:0%
+widespread applicability of you know a
+technology area right so typically in
+
+ align:start position:0%
+technology area right so typically in
+ 
+
+ align:start position:0%
+technology area right so typically in
+our society that means commercialization
+
+ align:start position:0%
+our society that means commercialization
+ 
+
+ align:start position:0%
+our society that means commercialization
+so this class is about this right that's
+
+ align:start position:0%
+so this class is about this right that's
+ 
+
+ align:start position:0%
+so this class is about this right that's
+the stage we're most focused on but
+
+ align:start position:0%
+the stage we're most focused on but
+ 
+
+ align:start position:0%
+the stage we're most focused on but
+remember all the input above that that
+
+ align:start position:0%
+remember all the input above that that
+ 
+
+ align:start position:0%
+remember all the input above that that
+goes into this now an innovation system
+
+ align:start position:0%
+goes into this now an innovation system
+ 
+
+ align:start position:0%
+goes into this now an innovation system
+we talked about this briefly before is
+
+ align:start position:0%
+we talked about this briefly before is
+ 
+
+ align:start position:0%
+we talked about this briefly before is
+the ecosystem for developing innovation
+
+ align:start position:0%
+the ecosystem for developing innovation
+ 
+
+ align:start position:0%
+the ecosystem for developing innovation
+and as we discussed briefly it operates
+
+ align:start position:0%
+and as we discussed briefly it operates
+ 
+
+ align:start position:0%
+and as we discussed briefly it operates
+at at least two levels it operates at
+
+ align:start position:0%
+at at least two levels it operates at
+ 
+
+ align:start position:0%
+at at least two levels it operates at
+the institutional level of supporting
+
+ align:start position:0%
+the institutional level of supporting
+ 
+
+ align:start position:0%
+the institutional level of supporting
+the development of the inventions and
+
+ align:start position:0%
+the development of the inventions and
+ 
+
+ align:start position:0%
+the development of the inventions and
+discovery that go into innovation but it
+
+ align:start position:0%
+discovery that go into innovation but it
+ 
+
+ align:start position:0%
+discovery that go into innovation but it
+also operates at the personal
+
+ align:start position:0%
+also operates at the personal
+ 
+
+ align:start position:0%
+also operates at the personal
+face-to-face level right because in the
+
+ align:start position:0%
+face-to-face level right because in the
+ 
+
+ align:start position:0%
+face-to-face level right because in the
+end people you all innovate not some
+
+ align:start position:0%
+end people you all innovate not some
+ 
+
+ align:start position:0%
+end people you all innovate not some
+fancy institution innovation wave theory
+
+ align:start position:0%
+fancy institution innovation wave theory
+ 
+
+ align:start position:0%
+fancy institution innovation wave theory
+okay and economics this is called Condry
+
+ align:start position:0%
+okay and economics this is called Condry
+ 
+
+ align:start position:0%
+okay and economics this is called Condry
+F theory and we'll talk more about this
+
+ align:start position:0%
+F theory and we'll talk more about this
+ 
+
+ align:start position:0%
+F theory and we'll talk more about this
+you know as the class goes on but let me
+
+ align:start position:0%
+you know as the class goes on but let me
+ 
+
+ align:start position:0%
+you know as the class goes on but let me
+just give you a kind of a snapshot on
+
+ align:start position:0%
+just give you a kind of a snapshot on
+ 
+
+ align:start position:0%
+just give you a kind of a snapshot on
+what I'm talking about innovation tends
+
+ align:start position:0%
+what I'm talking about innovation tends
+ 
+
+ align:start position:0%
+what I'm talking about innovation tends
+to come in a wave and in your lifetime
+
+ align:start position:0%
+to come in a wave and in your lifetime
+ 
+
+ align:start position:0%
+to come in a wave and in your lifetime
+the big wave has been the IT revolution
+
+ align:start position:0%
+the big wave has been the IT revolution
+ 
+
+ align:start position:0%
+the big wave has been the IT revolution
+right if we if we were born in 1800 well
+
+ align:start position:0%
+right if we if we were born in 1800 well
+ 
+
+ align:start position:0%
+right if we if we were born in 1800 well
+roads right would be like a big
+
+ align:start position:0%
+roads right would be like a big
+ 
+
+ align:start position:0%
+roads right would be like a big
+innovation wave early Telegraph based
+
+ align:start position:0%
+innovation wave early Telegraph based
+ 
+
+ align:start position:0%
+innovation wave early Telegraph based
+communication would be a big innovation
+
+ align:start position:0%
+communication would be a big innovation
+ 
+
+ align:start position:0%
+communication would be a big innovation
+wave right electricity would be a big
+
+ align:start position:0%
+wave right electricity would be a big
+ 
+
+ align:start position:0%
+wave right electricity would be a big
+innovation with right and you tend to
+
+ align:start position:0%
+innovation with right and you tend to
+ 
+
+ align:start position:0%
+innovation with right and you tend to
+have a core technology advance you pile
+
+ align:start position:0%
+have a core technology advance you pile
+ 
+
+ align:start position:0%
+have a core technology advance you pile
+on applications and it begins to move
+
+ align:start position:0%
+on applications and it begins to move
+ 
+
+ align:start position:0%
+on applications and it begins to move
+through an entire society and in effect
+
+ align:start position:0%
+through an entire society and in effect
+ 
+
+ align:start position:0%
+through an entire society and in effect
+the whole society and to some extent the
+
+ align:start position:0%
+the whole society and to some extent the
+ 
+
+ align:start position:0%
+the whole society and to some extent the
+technology drives the nature of the
+
+ align:start position:0%
+technology drives the nature of the
+ 
+
+ align:start position:0%
+technology drives the nature of the
+society so that's what Karl Marx
+
+ align:start position:0%
+society so that's what Karl Marx
+ 
+
+ align:start position:0%
+society so that's what Karl Marx
+believed that's called determinism right
+
+ align:start position:0%
+believed that's called determinism right
+ 
+
+ align:start position:0%
+believed that's called determinism right
+that the technology plays a determinist
+
+ align:start position:0%
+that the technology plays a determinist
+ 
+
+ align:start position:0%
+that the technology plays a determinist
+stick role in the organization of
+
+ align:start position:0%
+stick role in the organization of
+ 
+
+ align:start position:0%
+stick role in the organization of
+society so it's big it is very big it's
+
+ align:start position:0%
+society so it's big it is very big it's
+ 
+
+ align:start position:0%
+society so it's big it is very big it's
+not just a pile of new technology stuff
+
+ align:start position:0%
+not just a pile of new technology stuff
+ 
+
+ align:start position:0%
+not just a pile of new technology stuff
+it is fundamentally changing the way in
+
+ align:start position:0%
+it is fundamentally changing the way in
+ 
+
+ align:start position:0%
+it is fundamentally changing the way in
+which the society is organized as well
+
+ align:start position:0%
+which the society is organized as well
+ 
+
+ align:start position:0%
+which the society is organized as well
+so that's also part of these innovation
+
+ align:start position:0%
+so that's also part of these innovation
+ 
+
+ align:start position:0%
+so that's also part of these innovation
+ways okay so a wave hits an economy
+
+ align:start position:0%
+ways okay so a wave hits an economy
+ 
+
+ align:start position:0%
+ways okay so a wave hits an economy
+takes a long time to grow eventually it
+
+ align:start position:0%
+takes a long time to grow eventually it
+ 
+
+ align:start position:0%
+takes a long time to grow eventually it
+scales up and affects a good part of the
+
+ align:start position:0%
+scales up and affects a good part of the
+ 
+
+ align:start position:0%
+scales up and affects a good part of the
+economy in any given time eventually you
+
+ align:start position:0%
+economy in any given time eventually you
+ 
+
+ align:start position:0%
+economy in any given time eventually you
+run out of the technology menu and it
+
+ align:start position:0%
+run out of the technology menu and it
+ 
+
+ align:start position:0%
+run out of the technology menu and it
+stabilizes right but it doesn't
+
+ align:start position:0%
+stabilizes right but it doesn't
+ 
+
+ align:start position:0%
+stabilizes right but it doesn't
+disappear it creates a new plateau in
+
+ align:start position:0%
+disappear it creates a new plateau in
+ 
+
+ align:start position:0%
+disappear it creates a new plateau in
+your economy and then you do another
+
+ align:start position:0%
+your economy and then you do another
+ 
+
+ align:start position:0%
+your economy and then you do another
+wave yeah let me see if there's I know
+
+ align:start position:0%
+wave yeah let me see if there's I know
+ 
+
+ align:start position:0%
+wave yeah let me see if there's I know
+is there any chalk down at that end
+
+ align:start position:0%
+is there any chalk down at that end
+ 
+
+ align:start position:0%
+is there any chalk down at that end
+Martha I don't see any it's all right oh
+
+ align:start position:0%
+Martha I don't see any it's all right oh
+ 
+
+ align:start position:0%
+Martha I don't see any it's all right oh
+there is great we'll come back to this
+
+ align:start position:0%
+there is great we'll come back to this
+ 
+
+ align:start position:0%
+there is great we'll come back to this
+but it's an important enough idea so
+
+ align:start position:0%
+but it's an important enough idea so
+ 
+
+ align:start position:0%
+but it's an important enough idea so
+there's a slow build-up and then there's
+
+ align:start position:0%
+there's a slow build-up and then there's
+ 
+
+ align:start position:0%
+there's a slow build-up and then there's
+a rapid buildup then there's a bubble
+
+ align:start position:0%
+a rapid buildup then there's a bubble
+ 
+
+ align:start position:0%
+a rapid buildup then there's a bubble
+then there's slower scaling and then
+
+ align:start position:0%
+then there's slower scaling and then
+ 
+
+ align:start position:0%
+then there's slower scaling and then
+eventually you reach technological
+
+ align:start position:0%
+eventually you reach technological
+ 
+
+ align:start position:0%
+eventually you reach technological
+maturity right sort of three scales this
+
+ align:start position:0%
+maturity right sort of three scales this
+ 
+
+ align:start position:0%
+maturity right sort of three scales this
+is where the bubble is right so the IT
+
+ align:start position:0%
+is where the bubble is right so the IT
+ 
+
+ align:start position:0%
+is where the bubble is right so the IT
+wave right somebody I don't know where
+
+ align:start position:0%
+wave right somebody I don't know where
+ 
+
+ align:start position:0%
+wave right somebody I don't know where
+this starts maybe it starts with Babbage
+
+ align:start position:0%
+this starts maybe it starts with Babbage
+ 
+
+ align:start position:0%
+this starts maybe it starts with Babbage
+in the 19th century right but let's
+
+ align:start position:0%
+in the 19th century right but let's
+ 
+
+ align:start position:0%
+in the 19th century right but let's
+start it with the anti computers at the
+
+ align:start position:0%
+start it with the anti computers at the
+ 
+
+ align:start position:0%
+start it with the anti computers at the
+end of lowered to 1945-46 right slow
+
+ align:start position:0%
+end of lowered to 1945-46 right slow
+ 
+
+ align:start position:0%
+end of lowered to 1945-46 right slow
+scale-up then you hit the 1990s and then
+
+ align:start position:0%
+scale-up then you hit the 1990s and then
+ 
+
+ align:start position:0%
+scale-up then you hit the 1990s and then
+you have very rapid scale up right and
+
+ align:start position:0%
+you have very rapid scale up right and
+ 
+
+ align:start position:0%
+you have very rapid scale up right and
+you've probably had some sense for what
+
+ align:start position:0%
+you've probably had some sense for what
+ 
+
+ align:start position:0%
+you've probably had some sense for what
+that era was like but it was a period of
+
+ align:start position:0%
+that era was like but it was a period of
+ 
+
+ align:start position:0%
+that era was like but it was a period of
+remarkably big growth rise big increase
+
+ align:start position:0%
+remarkably big growth rise big increase
+ 
+
+ align:start position:0%
+remarkably big growth rise big increase
+in GDP growth rate accompanied and
+
+ align:start position:0%
+in GDP growth rate accompanied and
+ 
+
+ align:start position:0%
+in GDP growth rate accompanied and
+driven by a big gain in productivity
+
+ align:start position:0%
+driven by a big gain in productivity
+ 
+
+ align:start position:0%
+driven by a big gain in productivity
+we'll come back to that term in a bit
+
+ align:start position:0%
+we'll come back to that term in a bit
+ 
+
+ align:start position:0%
+we'll come back to that term in a bit
+too
+
+ align:start position:0%
+too
+ 
+
+ align:start position:0%
+too
+then there's always a bubble right so if
+
+ align:start position:0%
+then there's always a bubble right so if
+ 
+
+ align:start position:0%
+then there's always a bubble right so if
+you all are investing in innovation
+
+ align:start position:0%
+you all are investing in innovation
+ 
+
+ align:start position:0%
+you all are investing in innovation
+waves right if you go into the financial
+
+ align:start position:0%
+waves right if you go into the financial
+ 
+
+ align:start position:0%
+waves right if you go into the financial
+sector and you're investing in
+
+ align:start position:0%
+sector and you're investing in
+ 
+
+ align:start position:0%
+sector and you're investing in
+innovation ways trying to ride them you
+
+ align:start position:0%
+innovation ways trying to ride them you
+ 
+
+ align:start position:0%
+innovation ways trying to ride them you
+want to start about here ride it all the
+
+ align:start position:0%
+want to start about here ride it all the
+ 
+
+ align:start position:0%
+want to start about here ride it all the
+way up but never forget that there's
+
+ align:start position:0%
+way up but never forget that there's
+ 
+
+ align:start position:0%
+way up but never forget that there's
+going to be a bubble there is always a
+
+ align:start position:0%
+going to be a bubble there is always a
+ 
+
+ align:start position:0%
+going to be a bubble there is always a
+bubble in every innovation wave so far
+
+ align:start position:0%
+bubble in every innovation wave so far
+ 
+
+ align:start position:0%
+bubble in every innovation wave so far
+there's always been a bubble so in the
+
+ align:start position:0%
+there's always been a bubble so in the
+ 
+
+ align:start position:0%
+there's always been a bubble so in the
+IT revolution that was the dot-com bust
+
+ align:start position:0%
+IT revolution that was the dot-com bust
+ 
+
+ align:start position:0%
+IT revolution that was the dot-com bust
+of 2001 right and then we're in a long
+
+ align:start position:0%
+of 2001 right and then we're in a long
+ 
+
+ align:start position:0%
+of 2001 right and then we're in a long
+period of continued technological
+
+ align:start position:0%
+period of continued technological
+ 
+
+ align:start position:0%
+period of continued technological
+advance but not at the rate of the 1990s
+
+ align:start position:0%
+advance but not at the rate of the 1990s
+ 
+
+ align:start position:0%
+advance but not at the rate of the 1990s
+growth period right and you can think
+
+ align:start position:0%
+growth period right and you can think
+ 
+
+ align:start position:0%
+growth period right and you can think
+about different generations of companies
+
+ align:start position:0%
+about different generations of companies
+ 
+
+ align:start position:0%
+about different generations of companies
+that come along and play different roles
+
+ align:start position:0%
+that come along and play different roles
+ 
+
+ align:start position:0%
+that come along and play different roles
+here and then it's some day and IT may
+
+ align:start position:0%
+here and then it's some day and IT may
+ 
+
+ align:start position:0%
+here and then it's some day and IT may
+be different but some day will reach a
+
+ align:start position:0%
+be different but some day will reach a
+ 
+
+ align:start position:0%
+be different but some day will reach a
+certain amount of technological maturity
+
+ align:start position:0%
+certain amount of technological maturity
+ 
+
+ align:start position:0%
+certain amount of technological maturity
+and the growth rate will stabilize and
+
+ align:start position:0%
+and the growth rate will stabilize and
+ 
+
+ align:start position:0%
+and the growth rate will stabilize and
+then we'll do something else right so
+
+ align:start position:0%
+then we'll do something else right so
+ 
+
+ align:start position:0%
+then we'll do something else right so
+that's kind of what a wave looks like
+
+ align:start position:0%
+that's kind of what a wave looks like
+ 
+
+ align:start position:0%
+that's kind of what a wave looks like
+and again you build into your economy a
+
+ align:start position:0%
+and again you build into your economy a
+ 
+
+ align:start position:0%
+and again you build into your economy a
+series of mesas or plateaus which don't
+
+ align:start position:0%
+series of mesas or plateaus which don't
+ 
+
+ align:start position:0%
+series of mesas or plateaus which don't
+disappear you just go on to the next
+
+ align:start position:0%
+disappear you just go on to the next
+ 
+
+ align:start position:0%
+disappear you just go on to the next
+innovation way this is the way economies
+
+ align:start position:0%
+innovation way this is the way economies
+ 
+
+ align:start position:0%
+innovation way this is the way economies
+grow right through these innovation
+
+ align:start position:0%
+grow right through these innovation
+ 
+
+ align:start position:0%
+grow right through these innovation
+waves so it's a pretty important concept
+
+ align:start position:0%
+waves so it's a pretty important concept
+ 
+
+ align:start position:0%
+waves so it's a pretty important concept
+and if you can get your technology
+
+ align:start position:0%
+and if you can get your technology
+ 
+
+ align:start position:0%
+and if you can get your technology
+advanced into an innovation wave then it
+
+ align:start position:0%
+advanced into an innovation wave then it
+ 
+
+ align:start position:0%
+advanced into an innovation wave then it
+kind of goes on autopilot right and all
+
+ align:start position:0%
+kind of goes on autopilot right and all
+ 
+
+ align:start position:0%
+kind of goes on autopilot right and all
+these things start to occur so that's
+
+ align:start position:0%
+these things start to occur so that's
+ 
+
+ align:start position:0%
+these things start to occur so that's
+where desperately trying to do for
+
+ align:start position:0%
+where desperately trying to do for
+ 
+
+ align:start position:0%
+where desperately trying to do for
+energy we're trying to get it scaled up
+
+ align:start position:0%
+energy we're trying to get it scaled up
+ 
+
+ align:start position:0%
+energy we're trying to get it scaled up
+enough so that it can take off go on
+
+ align:start position:0%
+enough so that it can take off go on
+ 
+
+ align:start position:0%
+enough so that it can take off go on
+autopilot and just kind of happen yeah
+
+ align:start position:0%
+autopilot and just kind of happen yeah
+ 
+
+ align:start position:0%
+autopilot and just kind of happen yeah
+it wipes out lots of the dot-com
+
+ align:start position:0%
+it wipes out lots of the dot-com
+ 
+
+ align:start position:0%
+it wipes out lots of the dot-com
+startups right they die right and only
+
+ align:start position:0%
+startups right they die right and only
+ 
+
+ align:start position:0%
+startups right they die right and only
+the stronger companies with more solid
+
+ align:start position:0%
+the stronger companies with more solid
+ 
+
+ align:start position:0%
+the stronger companies with more solid
+and during models survive right so
+
+ align:start position:0%
+and during models survive right so
+ 
+
+ align:start position:0%
+and during models survive right so
+always anticipate the bubble and get out
+
+ align:start position:0%
+always anticipate the bubble and get out
+ 
+
+ align:start position:0%
+always anticipate the bubble and get out
+in time that's the key
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+these have a different perspective they
+
+ align:start position:0%
+these have a different perspective they
+ 
+
+ align:start position:0%
+these have a different perspective they
+seen as two bucks they see as one baby
+
+ align:start position:0%
+seen as two bucks they see as one baby
+ 
+
+ align:start position:0%
+seen as two bucks they see as one baby
+bump so for the 90s it was like it cost
+
+ align:start position:0%
+bump so for the 90s it was like it cost
+ 
+
+ align:start position:0%
+bump so for the 90s it was like it cost
+you like $70,000 to buy servers so like
+
+ align:start position:0%
+you like $70,000 to buy servers so like
+ 
+
+ align:start position:0%
+you like $70,000 to buy servers so like
+a lot of capital start and so people get
+
+ align:start position:0%
+a lot of capital start and so people get
+ 
+
+ align:start position:0%
+a lot of capital start and so people get
+really really excited and then they
+
+ align:start position:0%
+really really excited and then they
+ 
+
+ align:start position:0%
+really really excited and then they
+people keep innovating right and you can
+
+ align:start position:0%
+people keep innovating right and you can
+ 
+
+ align:start position:0%
+people keep innovating right and you can
+look at this as a couple of months but
+
+ align:start position:0%
+look at this as a couple of months but
+ 
+
+ align:start position:0%
+look at this as a couple of months but
+not quite in the way Martine that you're
+
+ align:start position:0%
+not quite in the way Martine that you're
+ 
+
+ align:start position:0%
+not quite in the way Martine that you're
+describing but you could look at this
+
+ align:start position:0%
+describing but you could look at this
+ 
+
+ align:start position:0%
+describing but you could look at this
+rise and then this phase that's kind of
+
+ align:start position:0%
+rise and then this phase that's kind of
+ 
+
+ align:start position:0%
+rise and then this phase that's kind of
+two different pieces too so that's
+
+ align:start position:0%
+two different pieces too so that's
+ 
+
+ align:start position:0%
+two different pieces too so that's
+another way of looking at this rapid
+
+ align:start position:0%
+another way of looking at this rapid
+ 
+
+ align:start position:0%
+another way of looking at this rapid
+growth more stable growth with different
+
+ align:start position:0%
+growth more stable growth with different
+ 
+
+ align:start position:0%
+growth more stable growth with different
+firms typically involved in the two
+
+ align:start position:0%
+firms typically involved in the two
+ 
+
+ align:start position:0%
+firms typically involved in the two
+we're gonna do we're gonna dig into this
+
+ align:start position:0%
+we're gonna do we're gonna dig into this
+ 
+
+ align:start position:0%
+we're gonna do we're gonna dig into this
+right so but go ahead you're getting
+
+ align:start position:0%
+right so but go ahead you're getting
+ 
+
+ align:start position:0%
+right so but go ahead you're getting
+rich right a lot of people are getting
+
+ align:start position:0%
+rich right a lot of people are getting
+ 
+
+ align:start position:0%
+rich right a lot of people are getting
+rich right that's the key indicator in
+
+ align:start position:0%
+rich right that's the key indicator in
+ 
+
+ align:start position:0%
+rich right that's the key indicator in
+the IT revolution everybody got a lot
+
+ align:start position:0%
+the IT revolution everybody got a lot
+ 
+
+ align:start position:0%
+the IT revolution everybody got a lot
+better off so all quintiles of the
+
+ align:start position:0%
+better off so all quintiles of the
+ 
+
+ align:start position:0%
+better off so all quintiles of the
+society ended up with a significant game
+
+ align:start position:0%
+society ended up with a significant game
+ 
+
+ align:start position:0%
+society ended up with a significant game
+you know the upper-middle class as usual
+
+ align:start position:0%
+you know the upper-middle class as usual
+ 
+
+ align:start position:0%
+you know the upper-middle class as usual
+gets the biggest game but everybody went
+
+ align:start position:0%
+gets the biggest game but everybody went
+ 
+
+ align:start position:0%
+gets the biggest game but everybody went
+up in that time period
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+I'm stealing mail and thunder from later
+
+ align:start position:0%
+I'm stealing mail and thunder from later
+ 
+
+ align:start position:0%
+I'm stealing mail and thunder from later
+in the class but I actually will deal
+
+ align:start position:0%
+in the class but I actually will deal
+ 
+
+ align:start position:0%
+in the class but I actually will deal
+with some of this when we talk about
+
+ align:start position:0%
+with some of this when we talk about
+ 
+
+ align:start position:0%
+with some of this when we talk about
+Jorgenson we'll get into productivity
+
+ align:start position:0%
+Jorgenson we'll get into productivity
+ 
+
+ align:start position:0%
+Jorgenson we'll get into productivity
+and GDP growth so make me come back to
+
+ align:start position:0%
+and GDP growth so make me come back to
+ 
+
+ align:start position:0%
+and GDP growth so make me come back to
+this all right so we got through
+
+ align:start position:0%
+this all right so we got through
+ 
+
+ align:start position:0%
+this all right so we got through
+innovation weighs more or less with more
+
+ align:start position:0%
+innovation weighs more or less with more
+ 
+
+ align:start position:0%
+innovation weighs more or less with more
+to come and then we talked earlier about
+
+ align:start position:0%
+to come and then we talked earlier about
+ 
+
+ align:start position:0%
+to come and then we talked earlier about
+this valley of death concept right the
+
+ align:start position:0%
+this valley of death concept right the
+ 
+
+ align:start position:0%
+this valley of death concept right the
+gap between research and later stage
+
+ align:start position:0%
+gap between research and later stage
+ 
+
+ align:start position:0%
+gap between research and later stage
+development that has been the main focus
+
+ align:start position:0%
+development that has been the main focus
+ 
+
+ align:start position:0%
+development that has been the main focus
+of public policy in the innovation field
+
+ align:start position:0%
+of public policy in the innovation field
+ 
+
+ align:start position:0%
+of public policy in the innovation field
+one of the things about this class is
+
+ align:start position:0%
+one of the things about this class is
+ 
+
+ align:start position:0%
+one of the things about this class is
+that you're gonna realize this is only
+
+ align:start position:0%
+that you're gonna realize this is only
+ 
+
+ align:start position:0%
+that you're gonna realize this is only
+one part of a much more complicated in
+
+ align:start position:0%
+one part of a much more complicated in
+ 
+
+ align:start position:0%
+one part of a much more complicated in
+Richards stories so we're gonna be
+
+ align:start position:0%
+Richards stories so we're gonna be
+ 
+
+ align:start position:0%
+Richards stories so we're gonna be
+telling a lot of stories in addition to
+
+ align:start position:0%
+telling a lot of stories in addition to
+ 
+
+ align:start position:0%
+telling a lot of stories in addition to
+this story but that's one of the stories
+
+ align:start position:0%
+this story but that's one of the stories
+ 
+
+ align:start position:0%
+this story but that's one of the stories
+we're gonna tell
+
+ align:start position:0%
+we're gonna tell
+ 
+
+ align:start position:0%
+we're gonna tell
+so any further questions about this I
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+just wanted to get some basic vocabulary
+
+ align:start position:0%
+just wanted to get some basic vocabulary
+ 
+
+ align:start position:0%
+just wanted to get some basic vocabulary
+kind of out on the table let me say a
+
+ align:start position:0%
+kind of out on the table let me say a
+ 
+
+ align:start position:0%
+kind of out on the table let me say a
+few more introductory things the
+
+ align:start position:0%
+few more introductory things the
+ 
+
+ align:start position:0%
+few more introductory things the
+relationship between science and
+
+ align:start position:0%
+relationship between science and
+ 
+
+ align:start position:0%
+relationship between science and
+technology really before the mid 19th
+
+ align:start position:0%
+technology really before the mid 19th
+ 
+
+ align:start position:0%
+technology really before the mid 19th
+century technology was wasn't really
+
+ align:start position:0%
+century technology was wasn't really
+ 
+
+ align:start position:0%
+century technology was wasn't really
+based on science it was based in a way
+
+ align:start position:0%
+based on science it was based in a way
+ 
+
+ align:start position:0%
+based on science it was based in a way
+on tinkering and that's not to say that
+
+ align:start position:0%
+on tinkering and that's not to say that
+ 
+
+ align:start position:0%
+on tinkering and that's not to say that
+science didn't enter at some critical
+
+ align:start position:0%
+science didn't enter at some critical
+ 
+
+ align:start position:0%
+science didn't enter at some critical
+stages it does but the initial invention
+
+ align:start position:0%
+stages it does but the initial invention
+ 
+
+ align:start position:0%
+stages it does but the initial invention
+moments our technology types fiddling
+
+ align:start position:0%
+moments our technology types fiddling
+ 
+
+ align:start position:0%
+moments our technology types fiddling
+around in the 19th century in late 18th
+
+ align:start position:0%
+around in the 19th century in late 18th
+ 
+
+ align:start position:0%
+around in the 19th century in late 18th
+century equivalent of a garage right so
+
+ align:start position:0%
+century equivalent of a garage right so
+ 
+
+ align:start position:0%
+century equivalent of a garage right so
+science is not far enough along to be
+
+ align:start position:0%
+science is not far enough along to be
+ 
+
+ align:start position:0%
+science is not far enough along to be
+able to give birth to technology for at
+
+ align:start position:0%
+able to give birth to technology for at
+ 
+
+ align:start position:0%
+able to give birth to technology for at
+least a large part of the 19th century
+
+ align:start position:0%
+least a large part of the 19th century
+ 
+
+ align:start position:0%
+least a large part of the 19th century
+but now we're in an era where basic
+
+ align:start position:0%
+but now we're in an era where basic
+ 
+
+ align:start position:0%
+but now we're in an era where basic
+science definitely can give rise to
+
+ align:start position:0%
+science definitely can give rise to
+ 
+
+ align:start position:0%
+science definitely can give rise to
+technology now somebody a friend I know
+
+ align:start position:0%
+technology now somebody a friend I know
+ 
+
+ align:start position:0%
+technology now somebody a friend I know
+pretty well named Lee Buchanan it was a
+
+ align:start position:0%
+pretty well named Lee Buchanan it was a
+ 
+
+ align:start position:0%
+pretty well named Lee Buchanan it was a
+former deputy director of DARPA would
+
+ align:start position:0%
+former deputy director of DARPA would
+ 
+
+ align:start position:0%
+former deputy director of DARPA would
+always insist that yeah that's all fine
+
+ align:start position:0%
+always insist that yeah that's all fine
+ 
+
+ align:start position:0%
+always insist that yeah that's all fine
+but I'm running DARPA and I get nothing
+
+ align:start position:0%
+but I'm running DARPA and I get nothing
+ 
+
+ align:start position:0%
+but I'm running DARPA and I get nothing
+out of basic science I could drop all
+
+ align:start position:0%
+out of basic science I could drop all
+ 
+
+ align:start position:0%
+out of basic science I could drop all
+that funding I never miss it he
+
+ align:start position:0%
+that funding I never miss it he
+ 
+
+ align:start position:0%
+that funding I never miss it he
+explained to me one day so you know I
+
+ align:start position:0%
+explained to me one day so you know I
+ 
+
+ align:start position:0%
+explained to me one day so you know I
+think he's wrong but you should know
+
+ align:start position:0%
+think he's wrong but you should know
+ 
+
+ align:start position:0%
+think he's wrong but you should know
+there's a debate about this including in
+
+ align:start position:0%
+there's a debate about this including in
+ 
+
+ align:start position:0%
+there's a debate about this including in
+our most famous advanced technology
+
+ align:start position:0%
+our most famous advanced technology
+ 
+
+ align:start position:0%
+our most famous advanced technology
+agency but I think in the end the
+
+ align:start position:0%
+agency but I think in the end the
+ 
+
+ align:start position:0%
+agency but I think in the end the
+evidence is strong that science can now
+
+ align:start position:0%
+evidence is strong that science can now
+ 
+
+ align:start position:0%
+evidence is strong that science can now
+give rise to technology but keep in mind
+
+ align:start position:0%
+give rise to technology but keep in mind
+ 
+
+ align:start position:0%
+give rise to technology but keep in mind
+that technology still gives rise to
+
+ align:start position:0%
+that technology still gives rise to
+ 
+
+ align:start position:0%
+that technology still gives rise to
+science and we'll talk about what that
+
+ align:start position:0%
+science and we'll talk about what that
+ 
+
+ align:start position:0%
+science and we'll talk about what that
+means in a bit now here's our first MIT
+
+ align:start position:0%
+means in a bit now here's our first MIT
+ 
+
+ align:start position:0%
+means in a bit now here's our first MIT
+great forgive the MIT centric focus here
+
+ align:start position:0%
+great forgive the MIT centric focus here
+ 
+
+ align:start position:0%
+great forgive the MIT centric focus here
+for our colleagues from other
+
+ align:start position:0%
+for our colleagues from other
+ 
+
+ align:start position:0%
+for our colleagues from other
+institutions you'll have to bear with me
+
+ align:start position:0%
+institutions you'll have to bear with me
+ 
+
+ align:start position:0%
+institutions you'll have to bear with me
+Robert Solow won the Nobel Prize in
+
+ align:start position:0%
+Robert Solow won the Nobel Prize in
+ 
+
+ align:start position:0%
+Robert Solow won the Nobel Prize in
+Economics in 1980
+
+ align:start position:0%
+Economics in 1980
+ 
+
+ align:start position:0%
+Economics in 1980
+for essentially developing growth
+
+ align:start position:0%
+for essentially developing growth
+ 
+
+ align:start position:0%
+for essentially developing growth
+economics I mean he created an entire
+
+ align:start position:0%
+economics I mean he created an entire
+ 
+
+ align:start position:0%
+economics I mean he created an entire
+field of economics and he's a just a
+
+ align:start position:0%
+field of economics and he's a just a
+ 
+
+ align:start position:0%
+field of economics and he's a just a
+wonderful human being he's still around
+
+ align:start position:0%
+wonderful human being he's still around
+ 
+
+ align:start position:0%
+wonderful human being he's still around
+if you ever get a chance to meet him or
+
+ align:start position:0%
+if you ever get a chance to meet him or
+ 
+
+ align:start position:0%
+if you ever get a chance to meet him or
+listen to him don't miss it it's one of
+
+ align:start position:0%
+listen to him don't miss it it's one of
+ 
+
+ align:start position:0%
+listen to him don't miss it it's one of
+the greats
+
+ align:start position:0%
+the greats
+ 
+
+ align:start position:0%
+the greats
+forget the Nobel Prize the really
+
+ align:start position:0%
+forget the Nobel Prize the really
+ 
+
+ align:start position:0%
+forget the Nobel Prize the really
+important prize is the President's Medal
+
+ align:start position:0%
+important prize is the President's Medal
+ 
+
+ align:start position:0%
+important prize is the President's Medal
+of Technology right
+
+ align:start position:0%
+of Technology right
+ 
+
+ align:start position:0%
+of Technology right
+the only economist who's ever won the
+
+ align:start position:0%
+the only economist who's ever won the
+ 
+
+ align:start position:0%
+the only economist who's ever won the
+President's Medal of Technology there is
+
+ align:start position:0%
+President's Medal of Technology there is
+ 
+
+ align:start position:0%
+President's Medal of Technology there is
+getting it from Clinton it's really
+
+ align:start position:0%
+getting it from Clinton it's really
+ 
+
+ align:start position:0%
+getting it from Clinton it's really
+unusual his work is so important in its
+
+ align:start position:0%
+unusual his work is so important in its
+ 
+
+ align:start position:0%
+unusual his work is so important in its
+implications for technology development
+
+ align:start position:0%
+implications for technology development
+ 
+
+ align:start position:0%
+implications for technology development
+that he gets the technology prize too
+
+ align:start position:0%
+that he gets the technology prize too
+ 
+
+ align:start position:0%
+that he gets the technology prize too
+from the president I can't tell you what
+
+ align:start position:0%
+from the president I can't tell you what
+ 
+
+ align:start position:0%
+from the president I can't tell you what
+a nice person he is
+
+ align:start position:0%
+a nice person he is
+ 
+
+ align:start position:0%
+a nice person he is
+I once watched him testify in front of
+
+ align:start position:0%
+I once watched him testify in front of
+ 
+
+ align:start position:0%
+I once watched him testify in front of
+the House Science Committee and you know
+
+ align:start position:0%
+the House Science Committee and you know
+ 
+
+ align:start position:0%
+the House Science Committee and you know
+it was like you know God has entered the
+
+ align:start position:0%
+it was like you know God has entered the
+ 
+
+ align:start position:0%
+it was like you know God has entered the
+room solos come into the room
+
+ align:start position:0%
+room solos come into the room
+ 
+
+ align:start position:0%
+room solos come into the room
+and the committee all knew that
+
+ align:start position:0%
+and the committee all knew that
+ 
+
+ align:start position:0%
+and the committee all knew that
+innovation base growth theory comes from
+
+ align:start position:0%
+innovation base growth theory comes from
+ 
+
+ align:start position:0%
+innovation base growth theory comes from
+this guy and you know they were just
+
+ align:start position:0%
+this guy and you know they were just
+ 
+
+ align:start position:0%
+this guy and you know they were just
+incredibly complimentary and the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+congressman who was like the number two
+
+ align:start position:0%
+congressman who was like the number two
+ 
+
+ align:start position:0%
+congressman who was like the number two
+or three and the committee server
+
+ align:start position:0%
+or three and the committee server
+ 
+
+ align:start position:0%
+or three and the committee server
+question he was fairly early and she
+
+ align:start position:0%
+question he was fairly early and she
+ 
+
+ align:start position:0%
+question he was fairly early and she
+turned to him and said you know doctor
+
+ align:start position:0%
+turned to him and said you know doctor
+ 
+
+ align:start position:0%
+turned to him and said you know doctor
+you know for the purpose of this hearing
+
+ align:start position:0%
+you know for the purpose of this hearing
+ 
+
+ align:start position:0%
+you know for the purpose of this hearing
+you know what what what should we call
+
+ align:start position:0%
+you know what what what should we call
+ 
+
+ align:start position:0%
+you know what what what should we call
+you noblest you know what terms should
+
+ align:start position:0%
+you noblest you know what terms should
+ 
+
+ align:start position:0%
+you noblest you know what terms should
+we use for you and he kind of leans back
+
+ align:start position:0%
+we use for you and he kind of leans back
+ 
+
+ align:start position:0%
+we use for you and he kind of leans back
+and he says well you know I was a tech
+
+ align:start position:0%
+and he says well you know I was a tech
+ 
+
+ align:start position:0%
+and he says well you know I was a tech
+sergeant in the army
+
+ align:start position:0%
+sergeant in the army
+ 
+
+ align:start position:0%
+sergeant in the army
+and during the Korean War and I really
+
+ align:start position:0%
+and during the Korean War and I really
+ 
+
+ align:start position:0%
+and during the Korean War and I really
+came to like the title Sarge so maybe he
+
+ align:start position:0%
+came to like the title Sarge so maybe he
+ 
+
+ align:start position:0%
+came to like the title Sarge so maybe he
+could call me Sarge and there's this you
+
+ align:start position:0%
+could call me Sarge and there's this you
+ 
+
+ align:start position:0%
+could call me Sarge and there's this you
+know fancy congressional you know
+
+ align:start position:0%
+know fancy congressional you know
+ 
+
+ align:start position:0%
+know fancy congressional you know
+committee calling Robert Solow Sarge for
+
+ align:start position:0%
+committee calling Robert Solow Sarge for
+ 
+
+ align:start position:0%
+committee calling Robert Solow Sarge for
+the rest of the hearing was absolutely
+
+ align:start position:0%
+the rest of the hearing was absolutely
+ 
+
+ align:start position:0%
+the rest of the hearing was absolutely
+just they he had them eating out of his
+
+ align:start position:0%
+just they he had them eating out of his
+ 
+
+ align:start position:0%
+just they he had them eating out of his
+hands he was just funny and charming and
+
+ align:start position:0%
+hands he was just funny and charming and
+ 
+
+ align:start position:0%
+hands he was just funny and charming and
+incredibly thoughtful all at the same
+
+ align:start position:0%
+incredibly thoughtful all at the same
+ 
+
+ align:start position:0%
+incredibly thoughtful all at the same
+time so he's quite an amazing figure
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+he wins the Nobel Prize for essentially
+
+ align:start position:0%
+he wins the Nobel Prize for essentially
+ 
+
+ align:start position:0%
+he wins the Nobel Prize for essentially
+blowing up a large part of classical
+
+ align:start position:0%
+blowing up a large part of classical
+ 
+
+ align:start position:0%
+blowing up a large part of classical
+economics and the problem with classical
+
+ align:start position:0%
+economics and the problem with classical
+ 
+
+ align:start position:0%
+economics and the problem with classical
+economics and look I asked you to read
+
+ align:start position:0%
+economics and look I asked you to read
+ 
+
+ align:start position:0%
+economics and look I asked you to read
+this and it's his Nobel Prize talks so
+
+ align:start position:0%
+this and it's his Nobel Prize talks so
+ 
+
+ align:start position:0%
+this and it's his Nobel Prize talks so
+it's for economics writing it's fairly
+
+ align:start position:0%
+it's for economics writing it's fairly
+ 
+
+ align:start position:0%
+it's for economics writing it's fairly
+accessible but even then it's not simple
+
+ align:start position:0%
+accessible but even then it's not simple
+ 
+
+ align:start position:0%
+accessible but even then it's not simple
+when if you all haven't if you're going
+
+ align:start position:0%
+when if you all haven't if you're going
+ 
+
+ align:start position:0%
+when if you all haven't if you're going
+to be reading it and I'm gonna ask
+
+ align:start position:0%
+to be reading it and I'm gonna ask
+ 
+
+ align:start position:0%
+to be reading it and I'm gonna ask
+everybody who hasn't done the readings
+
+ align:start position:0%
+everybody who hasn't done the readings
+ 
+
+ align:start position:0%
+everybody who hasn't done the readings
+yet for this class because I know it's
+
+ align:start position:0%
+yet for this class because I know it's
+ 
+
+ align:start position:0%
+yet for this class because I know it's
+your first time with access to the
+
+ align:start position:0%
+your first time with access to the
+ 
+
+ align:start position:0%
+your first time with access to the
+stellar site but just blow by the
+
+ align:start position:0%
+stellar site but just blow by the
+ 
+
+ align:start position:0%
+stellar site but just blow by the
+economics formulation period just blow
+
+ align:start position:0%
+economics formulation period just blow
+ 
+
+ align:start position:0%
+economics formulation period just blow
+by the econometrics just get the basic
+
+ align:start position:0%
+by the econometrics just get the basic
+ 
+
+ align:start position:0%
+by the econometrics just get the basic
+ideas down for both solo and for Romer
+
+ align:start position:0%
+ideas down for both solo and for Romer
+ 
+
+ align:start position:0%
+ideas down for both solo and for Romer
+particular Romer when it's a
+
+ align:start position:0%
+particular Romer when it's a
+ 
+
+ align:start position:0%
+particular Romer when it's a
+particularly complicated reading for
+
+ align:start position:0%
+particularly complicated reading for
+ 
+
+ align:start position:0%
+particularly complicated reading for
+those of you who have not studied
+
+ align:start position:0%
+those of you who have not studied
+ 
+
+ align:start position:0%
+those of you who have not studied
+economics but he goes after classical
+
+ align:start position:0%
+economics but he goes after classical
+ 
+
+ align:start position:0%
+economics but he goes after classical
+economic theory and just to summarize in
+
+ align:start position:0%
+economic theory and just to summarize in
+ 
+
+ align:start position:0%
+economic theory and just to summarize in
+a simpler way than is really fair to
+
+ align:start position:0%
+a simpler way than is really fair to
+ 
+
+ align:start position:0%
+a simpler way than is really fair to
+classical economics classical economics
+
+ align:start position:0%
+classical economics classical economics
+ 
+
+ align:start position:0%
+classical economics classical economics
+asked when an economy is capable of
+
+ align:start position:0%
+asked when an economy is capable of
+ 
+
+ align:start position:0%
+asked when an economy is capable of
+steady economic growth and they never
+
+ align:start position:0%
+steady economic growth and they never
+ 
+
+ align:start position:0%
+steady economic growth and they never
+came up with a good answer they the
+
+ align:start position:0%
+came up with a good answer they the
+ 
+
+ align:start position:0%
+came up with a good answer they the
+formulation was when the national
+
+ align:start position:0%
+formulation was when the national
+ 
+
+ align:start position:0%
+formulation was when the national
+savings rate which means income saved in
+
+ align:start position:0%
+savings rate which means income saved in
+ 
+
+ align:start position:0%
+savings rate which means income saved in
+the economy equals the capital supply
+
+ align:start position:0%
+the economy equals the capital supply
+ 
+
+ align:start position:0%
+the economy equals the capital supply
+capital output ratio and the rate of
+
+ align:start position:0%
+capital output ratio and the rate of
+ 
+
+ align:start position:0%
+capital output ratio and the rate of
+labor force growth that's labor supply
+
+ align:start position:0%
+labor force growth that's labor supply
+ 
+
+ align:start position:0%
+labor force growth that's labor supply
+right then you get growth that was the
+
+ align:start position:0%
+right then you get growth that was the
+ 
+
+ align:start position:0%
+right then you get growth that was the
+theory right so let me simplify that
+
+ align:start position:0%
+theory right so let me simplify that
+ 
+
+ align:start position:0%
+theory right so let me simplify that
+even more
+
+ align:start position:0%
+even more
+ 
+
+ align:start position:0%
+even more
+essentially they've got two factors
+
+ align:start position:0%
+essentially they've got two factors
+ 
+
+ align:start position:0%
+essentially they've got two factors
+Capital supply and labor supply and it's
+
+ align:start position:0%
+Capital supply and labor supply and it's
+ 
+
+ align:start position:0%
+Capital supply and labor supply and it's
+not capitalist and part like all the
+
+ align:start position:0%
+not capitalist and part like all the
+ 
+
+ align:start position:0%
+not capitalist and part like all the
+money it's capitalist like plant
+
+ align:start position:0%
+money it's capitalist like plant
+ 
+
+ align:start position:0%
+money it's capitalist like plant
+equipment as well as resources that's
+
+ align:start position:0%
+equipment as well as resources that's
+ 
+
+ align:start position:0%
+equipment as well as resources that's
+available and labor supply includes not
+
+ align:start position:0%
+available and labor supply includes not
+ 
+
+ align:start position:0%
+available and labor supply includes not
+just you know the number of workers but
+
+ align:start position:0%
+just you know the number of workers but
+ 
+
+ align:start position:0%
+just you know the number of workers but
+education health systems and the
+
+ align:start position:0%
+education health systems and the
+ 
+
+ align:start position:0%
+education health systems and the
+supporting systems for that too so it's
+
+ align:start position:0%
+supporting systems for that too so it's
+ 
+
+ align:start position:0%
+supporting systems for that too so it's
+these are bigger concepts so essentially
+
+ align:start position:0%
+these are bigger concepts so essentially
+ 
+
+ align:start position:0%
+these are bigger concepts so essentially
+their theory was that these are the
+
+ align:start position:0%
+their theory was that these are the
+ 
+
+ align:start position:0%
+their theory was that these are the
+contributing factors capital supply and
+
+ align:start position:0%
+contributing factors capital supply and
+ 
+
+ align:start position:0%
+contributing factors capital supply and
+labor supply and when you get those in
+
+ align:start position:0%
+labor supply and when you get those in
+ 
+
+ align:start position:0%
+labor supply and when you get those in
+the right balance supported by your
+
+ align:start position:0%
+the right balance supported by your
+ 
+
+ align:start position:0%
+the right balance supported by your
+national saving rate which is
+
+ align:start position:0%
+national saving rate which is
+ 
+
+ align:start position:0%
+national saving rate which is
+essentially
+
+ align:start position:0%
+essentially
+ 
+
+ align:start position:0%
+essentially
+the funder of those systems then you
+
+ align:start position:0%
+the funder of those systems then you
+ 
+
+ align:start position:0%
+the funder of those systems then you
+will get economic growth it's a static
+
+ align:start position:0%
+will get economic growth it's a static
+ 
+
+ align:start position:0%
+will get economic growth it's a static
+view okay it's an equilibrium system and
+
+ align:start position:0%
+view okay it's an equilibrium system and
+ 
+
+ align:start position:0%
+view okay it's an equilibrium system and
+these factors have to be in the right
+
+ align:start position:0%
+these factors have to be in the right
+ 
+
+ align:start position:0%
+these factors have to be in the right
+balance they constantly tend to throw
+
+ align:start position:0%
+balance they constantly tend to throw
+ 
+
+ align:start position:0%
+balance they constantly tend to throw
+each other off for growth to occur so
+
+ align:start position:0%
+each other off for growth to occur so
+ 
+
+ align:start position:0%
+each other off for growth to occur so
+you explain a business cycle from this I
+
+ align:start position:0%
+you explain a business cycle from this I
+ 
+
+ align:start position:0%
+you explain a business cycle from this I
+mean not really but that's what it
+
+ align:start position:0%
+mean not really but that's what it
+ 
+
+ align:start position:0%
+mean not really but that's what it
+attempts to do and capitalism becomes
+
+ align:start position:0%
+attempts to do and capitalism becomes
+ 
+
+ align:start position:0%
+attempts to do and capitalism becomes
+just periods of alternating you know
+
+ align:start position:0%
+just periods of alternating you know
+ 
+
+ align:start position:0%
+just periods of alternating you know
+improvement and gain and decline right
+
+ align:start position:0%
+improvement and gain and decline right
+ 
+
+ align:start position:0%
+improvement and gain and decline right
+so it's a business cycle kind of
+
+ align:start position:0%
+so it's a business cycle kind of
+ 
+
+ align:start position:0%
+so it's a business cycle kind of
+explanation we're seeing unemployment
+
+ align:start position:0%
+explanation we're seeing unemployment
+ 
+
+ align:start position:0%
+explanation we're seeing unemployment
+and then labor shortages right
+
+ align:start position:0%
+and then labor shortages right
+ 
+
+ align:start position:0%
+and then labor shortages right
+everything is throwing each other
+
+ align:start position:0%
+everything is throwing each other
+ 
+
+ align:start position:0%
+everything is throwing each other
+overtime out of balance it is not a
+
+ align:start position:0%
+overtime out of balance it is not a
+ 
+
+ align:start position:0%
+overtime out of balance it is not a
+dynamic model I should explain that
+
+ align:start position:0%
+dynamic model I should explain that
+ 
+
+ align:start position:0%
+dynamic model I should explain that
+classical economics you know it
+
+ align:start position:0%
+classical economics you know it
+ 
+
+ align:start position:0%
+classical economics you know it
+basically starts with Adam Smith and
+
+ align:start position:0%
+basically starts with Adam Smith and
+ 
+
+ align:start position:0%
+basically starts with Adam Smith and
+lasts until really the post-war - period
+
+ align:start position:0%
+lasts until really the post-war - period
+ 
+
+ align:start position:0%
+lasts until really the post-war - period
+and the problem with economics that was
+
+ align:start position:0%
+and the problem with economics that was
+ 
+
+ align:start position:0%
+and the problem with economics that was
+so frustrating to economists as well as
+
+ align:start position:0%
+so frustrating to economists as well as
+ 
+
+ align:start position:0%
+so frustrating to economists as well as
+policymakers was that it wasn't it
+
+ align:start position:0%
+policymakers was that it wasn't it
+ 
+
+ align:start position:0%
+policymakers was that it wasn't it
+didn't really have a foundational set of
+
+ align:start position:0%
+didn't really have a foundational set of
+ 
+
+ align:start position:0%
+didn't really have a foundational set of
+operating and working assumptions that
+
+ align:start position:0%
+operating and working assumptions that
+ 
+
+ align:start position:0%
+operating and working assumptions that
+were reliable it didn't have a reliable
+
+ align:start position:0%
+were reliable it didn't have a reliable
+ 
+
+ align:start position:0%
+were reliable it didn't have a reliable
+base so if you had you know 15 of you
+
+ align:start position:0%
+base so if you had you know 15 of you
+ 
+
+ align:start position:0%
+base so if you had you know 15 of you
+were economists sitting around trying to
+
+ align:start position:0%
+were economists sitting around trying to
+ 
+
+ align:start position:0%
+were economists sitting around trying to
+explain to me a policymaker
+
+ align:start position:0%
+explain to me a policymaker
+ 
+
+ align:start position:0%
+explain to me a policymaker
+how come there was a Great Depression
+
+ align:start position:0%
+how come there was a Great Depression
+ 
+
+ align:start position:0%
+how come there was a Great Depression
+you would have at least thirty ideas on
+
+ align:start position:0%
+you would have at least thirty ideas on
+ 
+
+ align:start position:0%
+you would have at least thirty ideas on
+the table right it wasn't really
+
+ align:start position:0%
+the table right it wasn't really
+ 
+
+ align:start position:0%
+the table right it wasn't really
+terribly helpful to me right there were
+
+ align:start position:0%
+terribly helpful to me right there were
+ 
+
+ align:start position:0%
+terribly helpful to me right there were
+just too many variables so social
+
+ align:start position:0%
+just too many variables so social
+ 
+
+ align:start position:0%
+just too many variables so social
+science in the course of war - saw what
+
+ align:start position:0%
+science in the course of war - saw what
+ 
+
+ align:start position:0%
+science in the course of war - saw what
+physics did right I'm staring in our to
+
+ align:start position:0%
+physics did right I'm staring in our to
+ 
+
+ align:start position:0%
+physics did right I'm staring in our to
+physics guys here oh there's more
+
+ align:start position:0%
+physics guys here oh there's more
+ 
+
+ align:start position:0%
+physics guys here oh there's more
+several physics those physics in that
+
+ align:start position:0%
+several physics those physics in that
+ 
+
+ align:start position:0%
+several physics those physics in that
+pre-warp one or two period attempts to
+
+ align:start position:0%
+pre-warp one or two period attempts to
+ 
+
+ align:start position:0%
+pre-warp one or two period attempts to
+get down to basic known scientifically
+
+ align:start position:0%
+get down to basic known scientifically
+ 
+
+ align:start position:0%
+get down to basic known scientifically
+established you know currents
+
+ align:start position:0%
+established you know currents
+ 
+
+ align:start position:0%
+established you know currents
+of fact that can be demonstrated and
+
+ align:start position:0%
+of fact that can be demonstrated and
+ 
+
+ align:start position:0%
+of fact that can be demonstrated and
+known so that's the whole particle
+
+ align:start position:0%
+known so that's the whole particle
+ 
+
+ align:start position:0%
+known so that's the whole particle
+physics endeavor right we're gonna weed
+
+ align:start position:0%
+physics endeavor right we're gonna weed
+ 
+
+ align:start position:0%
+physics endeavor right we're gonna weed
+out extraneous stuff get down to a
+
+ align:start position:0%
+out extraneous stuff get down to a
+ 
+
+ align:start position:0%
+out extraneous stuff get down to a
+fairly small subset of stuff that we
+
+ align:start position:0%
+fairly small subset of stuff that we
+ 
+
+ align:start position:0%
+fairly small subset of stuff that we
+really know and then work with those is
+
+ align:start position:0%
+really know and then work with those is
+ 
+
+ align:start position:0%
+really know and then work with those is
+building blocks so all of the social
+
+ align:start position:0%
+building blocks so all of the social
+ 
+
+ align:start position:0%
+building blocks so all of the social
+sciences watch what happens to physics
+
+ align:start position:0%
+sciences watch what happens to physics
+ 
+
+ align:start position:0%
+sciences watch what happens to physics
+in that pre-world War two period and
+
+ align:start position:0%
+in that pre-world War two period and
+ 
+
+ align:start position:0%
+in that pre-world War two period and
+that World War two period we're
+
+ align:start position:0%
+that World War two period we're
+ 
+
+ align:start position:0%
+that World War two period we're
+eventually things like nuclear weapons
+
+ align:start position:0%
+eventually things like nuclear weapons
+ 
+
+ align:start position:0%
+eventually things like nuclear weapons
+and power come about and they think gee
+
+ align:start position:0%
+and power come about and they think gee
+ 
+
+ align:start position:0%
+and power come about and they think gee
+maybe they're onto something maybe
+
+ align:start position:0%
+maybe they're onto something maybe
+ 
+
+ align:start position:0%
+maybe they're onto something maybe
+that's a practice that we ought to do
+
+ align:start position:0%
+that's a practice that we ought to do
+ 
+
+ align:start position:0%
+that's a practice that we ought to do
+can we get down to a relatively small
+
+ align:start position:0%
+can we get down to a relatively small
+ 
+
+ align:start position:0%
+can we get down to a relatively small
+number of known variables and in effect
+
+ align:start position:0%
+number of known variables and in effect
+ 
+
+ align:start position:0%
+number of known variables and in effect
+create a known system here that's much
+
+ align:start position:0%
+create a known system here that's much
+ 
+
+ align:start position:0%
+create a known system here that's much
+more reliable than the kind of pre-war
+
+ align:start position:0%
+more reliable than the kind of pre-war
+ 
+
+ align:start position:0%
+more reliable than the kind of pre-war
+to guesswork in economics that everybody
+
+ align:start position:0%
+to guesswork in economics that everybody
+ 
+
+ align:start position:0%
+to guesswork in economics that everybody
+would be working from a similar kind of
+
+ align:start position:0%
+would be working from a similar kind of
+ 
+
+ align:start position:0%
+would be working from a similar kind of
+problem set so that's the enterprise
+
+ align:start position:0%
+problem set so that's the enterprise
+ 
+
+ align:start position:0%
+problem set so that's the enterprise
+solo is a neoclassical economist so he's
+
+ align:start position:0%
+solo is a neoclassical economist so he's
+ 
+
+ align:start position:0%
+solo is a neoclassical economist so he's
+post classical economics he's Troy which
+
+ align:start position:0%
+post classical economics he's Troy which
+ 
+
+ align:start position:0%
+post classical economics he's Troy which
+Paul Samuelson here is you know one of
+
+ align:start position:0%
+Paul Samuelson here is you know one of
+ 
+
+ align:start position:0%
+Paul Samuelson here is you know one of
+the tiny handful of great leaders of
+
+ align:start position:0%
+the tiny handful of great leaders of
+ 
+
+ align:start position:0%
+the tiny handful of great leaders of
+that tries to get economics down to a
+
+ align:start position:0%
+that tries to get economics down to a
+ 
+
+ align:start position:0%
+that tries to get economics down to a
+subset of known factors and known
+
+ align:start position:0%
+subset of known factors and known
+ 
+
+ align:start position:0%
+subset of known factors and known
+realities that can be demonstrated
+
+ align:start position:0%
+realities that can be demonstrated
+ 
+
+ align:start position:0%
+realities that can be demonstrated
+mathlab met and mathematically proven so
+
+ align:start position:0%
+mathlab met and mathematically proven so
+ 
+
+ align:start position:0%
+mathlab met and mathematically proven so
+that's what neoclassical economics is up
+
+ align:start position:0%
+that's what neoclassical economics is up
+ 
+
+ align:start position:0%
+that's what neoclassical economics is up
+against that's what they're trying to do
+
+ align:start position:0%
+against that's what they're trying to do
+ 
+
+ align:start position:0%
+against that's what they're trying to do
+solo is a neoclassical economist and he
+
+ align:start position:0%
+solo is a neoclassical economist and he
+ 
+
+ align:start position:0%
+solo is a neoclassical economist and he
+is working through this problem of
+
+ align:start position:0%
+is working through this problem of
+ 
+
+ align:start position:0%
+is working through this problem of
+growth so you know we had what 150 200
+
+ align:start position:0%
+growth so you know we had what 150 200
+ 
+
+ align:start position:0%
+growth so you know we had what 150 200
+years worth of economics and they didn't
+
+ align:start position:0%
+years worth of economics and they didn't
+ 
+
+ align:start position:0%
+years worth of economics and they didn't
+have a viable growth theory I mean
+
+ align:start position:0%
+have a viable growth theory I mean
+ 
+
+ align:start position:0%
+have a viable growth theory I mean
+what's with this right so fortunately
+
+ align:start position:0%
+what's with this right so fortunately
+ 
+
+ align:start position:0%
+what's with this right so fortunately
+solo comes along and he forms one and he
+
+ align:start position:0%
+solo comes along and he forms one and he
+ 
+
+ align:start position:0%
+solo comes along and he forms one and he
+said the story told by these classical
+
+ align:start position:0%
+said the story told by these classical
+ 
+
+ align:start position:0%
+said the story told by these classical
+models felt wrong and he noted that and
+
+ align:start position:0%
+models felt wrong and he noted that and
+ 
+
+ align:start position:0%
+models felt wrong and he noted that and
+one of the classical economists Harry
+
+ align:start position:0%
+one of the classical economists Harry
+ 
+
+ align:start position:0%
+one of the classical economists Harry
+there was a hint of and generalizations
+
+ align:start position:0%
+there was a hint of and generalizations
+ 
+
+ align:start position:0%
+there was a hint of and generalizations
+about not the proneural behavior and he
+
+ align:start position:0%
+about not the proneural behavior and he
+ 
+
+ align:start position:0%
+about not the proneural behavior and he
+decided that he could think about
+
+ align:start position:0%
+decided that he could think about
+ 
+
+ align:start position:0%
+decided that he could think about
+replacing the capital and labour output
+
+ align:start position:0%
+replacing the capital and labour output
+ 
+
+ align:start position:0%
+replacing the capital and labour output
+with a richer and more realistic
+
+ align:start position:0%
+with a richer and more realistic
+ 
+
+ align:start position:0%
+with a richer and more realistic
+representation of technology
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+which would be a new theory of
+
+ align:start position:0%
+which would be a new theory of
+ 
+
+ align:start position:0%
+which would be a new theory of
+production not just an assessment of
+
+ align:start position:0%
+production not just an assessment of
+ 
+
+ align:start position:0%
+production not just an assessment of
+output levels that's the key thought
+
+ align:start position:0%
+output levels that's the key thought
+ 
+
+ align:start position:0%
+output levels that's the key thought
+pattern here so it's not that capital
+
+ align:start position:0%
+pattern here so it's not that capital
+ 
+
+ align:start position:0%
+pattern here so it's not that capital
+supply and labor supply aren't important
+
+ align:start position:0%
+supply and labor supply aren't important
+ 
+
+ align:start position:0%
+supply and labor supply aren't important
+right they remain important factors but
+
+ align:start position:0%
+right they remain important factors but
+ 
+
+ align:start position:0%
+right they remain important factors but
+they are not close to as important as
+
+ align:start position:0%
+they are not close to as important as
+ 
+
+ align:start position:0%
+they are not close to as important as
+this more realistic representation of
+
+ align:start position:0%
+this more realistic representation of
+ 
+
+ align:start position:0%
+this more realistic representation of
+technology which we also calls as I said
+
+ align:start position:0%
+technology which we also calls as I said
+ 
+
+ align:start position:0%
+technology which we also calls as I said
+earlier technological and related
+
+ align:start position:0%
+earlier technological and related
+ 
+
+ align:start position:0%
+earlier technological and related
+innovation so it's not just the
+
+ align:start position:0%
+innovation so it's not just the
+ 
+
+ align:start position:0%
+innovation so it's not just the
+technology right it includes that bundle
+
+ align:start position:0%
+technology right it includes that bundle
+ 
+
+ align:start position:0%
+technology right it includes that bundle
+of stuff around the technology like
+
+ align:start position:0%
+of stuff around the technology like
+ 
+
+ align:start position:0%
+of stuff around the technology like
+process and business models that enable
+
+ align:start position:0%
+process and business models that enable
+ 
+
+ align:start position:0%
+process and business models that enable
+it okay but in the end it's
+
+ align:start position:0%
+it okay but in the end it's
+ 
+
+ align:start position:0%
+it okay but in the end it's
+technology-based innovation that becomes
+
+ align:start position:0%
+technology-based innovation that becomes
+ 
+
+ align:start position:0%
+technology-based innovation that becomes
+the heart of economic growth and soullow
+
+ align:start position:0%
+the heart of economic growth and soullow
+ 
+
+ align:start position:0%
+the heart of economic growth and soullow
+does a 50-year review of the US economy
+
+ align:start position:0%
+does a 50-year review of the US economy
+ 
+
+ align:start position:0%
+does a 50-year review of the US economy
+and he concludes that in that 50 year
+
+ align:start position:0%
+and he concludes that in that 50 year
+ 
+
+ align:start position:0%
+and he concludes that in that 50 year
+time period technological and related
+
+ align:start position:0%
+time period technological and related
+ 
+
+ align:start position:0%
+time period technological and related
+innovation is the dominant causative
+
+ align:start position:0%
+innovation is the dominant causative
+ 
+
+ align:start position:0%
+innovation is the dominant causative
+factor of US economic growth to the tune
+
+ align:start position:0%
+factor of US economic growth to the tune
+ 
+
+ align:start position:0%
+factor of US economic growth to the tune
+of about two thirds so in that range
+
+ align:start position:0%
+of about two thirds so in that range
+ 
+
+ align:start position:0%
+of about two thirds so in that range
+somewhere between 50% and higher we may
+
+ align:start position:0%
+somewhere between 50% and higher we may
+ 
+
+ align:start position:0%
+somewhere between 50% and higher we may
+be on the higher end of that now in this
+
+ align:start position:0%
+be on the higher end of that now in this
+ 
+
+ align:start position:0%
+be on the higher end of that now in this
+era they were in now and that's his
+
+ align:start position:0%
+era they were in now and that's his
+ 
+
+ align:start position:0%
+era they were in now and that's his
+that's his key breakthrough so capital
+
+ align:start position:0%
+that's his key breakthrough so capital
+ 
+
+ align:start position:0%
+that's his key breakthrough so capital
+supply and labor supply are significant
+
+ align:start position:0%
+supply and labor supply are significant
+ 
+
+ align:start position:0%
+supply and labor supply are significant
+but they're down in the teens now he
+
+ align:start position:0%
+but they're down in the teens now he
+ 
+
+ align:start position:0%
+but they're down in the teens now he
+acknowledges that the rate of growth is
+
+ align:start position:0%
+acknowledges that the rate of growth is
+ 
+
+ align:start position:0%
+acknowledges that the rate of growth is
+going to depend upon the investment rate
+
+ align:start position:0%
+going to depend upon the investment rate
+ 
+
+ align:start position:0%
+going to depend upon the investment rate
+because that'll be effective that help
+
+ align:start position:0%
+because that'll be effective that help
+ 
+
+ align:start position:0%
+because that'll be effective that help
+drives it so capital supplier is still
+
+ align:start position:0%
+drives it so capital supplier is still
+ 
+
+ align:start position:0%
+drives it so capital supplier is still
+significant but old growth theory
+
+ align:start position:0%
+significant but old growth theory
+ 
+
+ align:start position:0%
+significant but old growth theory
+classical growth theory is mechanical it
+
+ align:start position:0%
+classical growth theory is mechanical it
+ 
+
+ align:start position:0%
+classical growth theory is mechanical it
+is an equilibrium system it's constantly
+
+ align:start position:0%
+is an equilibrium system it's constantly
+ 
+
+ align:start position:0%
+is an equilibrium system it's constantly
+going in and out of balance hence those
+
+ align:start position:0%
+going in and out of balance hence those
+ 
+
+ align:start position:0%
+going in and out of balance hence those
+business cycles the great thing about
+
+ align:start position:0%
+business cycles the great thing about
+ 
+
+ align:start position:0%
+business cycles the great thing about
+what solo comes up with is that he
+
+ align:start position:0%
+what solo comes up with is that he
+ 
+
+ align:start position:0%
+what solo comes up with is that he
+brings a dynamic factor into
+
+ align:start position:0%
+brings a dynamic factor into
+ 
+
+ align:start position:0%
+brings a dynamic factor into
+understanding growth
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+I'll skip some of this this can be very
+
+ align:start position:0%
+I'll skip some of this this can be very
+ 
+
+ align:start position:0%
+I'll skip some of this this can be very
+good news okay so economics goes from
+
+ align:start position:0%
+good news okay so economics goes from
+ 
+
+ align:start position:0%
+good news okay so economics goes from
+like this kind of dark and dismal
+
+ align:start position:0%
+like this kind of dark and dismal
+ 
+
+ align:start position:0%
+like this kind of dark and dismal
+science to a way in which a society can
+
+ align:start position:0%
+science to a way in which a society can
+ 
+
+ align:start position:0%
+science to a way in which a society can
+grow right and increase its well-being
+
+ align:start position:0%
+grow right and increase its well-being
+ 
+
+ align:start position:0%
+grow right and increase its well-being
+by introducing more technological and
+
+ align:start position:0%
+by introducing more technological and
+ 
+
+ align:start position:0%
+by introducing more technological and
+related innovation that's you know
+
+ align:start position:0%
+related innovation that's you know
+ 
+
+ align:start position:0%
+related innovation that's you know
+profoundly good news it gets us out of
+
+ align:start position:0%
+profoundly good news it gets us out of
+ 
+
+ align:start position:0%
+profoundly good news it gets us out of
+this old equilibrium system this old
+
+ align:start position:0%
+this old equilibrium system this old
+ 
+
+ align:start position:0%
+this old equilibrium system this old
+dismal science one two what if you can
+
+ align:start position:0%
+dismal science one two what if you can
+ 
+
+ align:start position:0%
+dismal science one two what if you can
+get it going what can be a dynamic
+
+ align:start position:0%
+get it going what can be a dynamic
+ 
+
+ align:start position:0%
+get it going what can be a dynamic
+pattern and improve societal well-being
+
+ align:start position:0%
+pattern and improve societal well-being
+ 
+
+ align:start position:0%
+pattern and improve societal well-being
+we can see these technological
+
+ align:start position:0%
+we can see these technological
+ 
+
+ align:start position:0%
+we can see these technological
+innovations and the way they change
+
+ align:start position:0%
+innovations and the way they change
+ 
+
+ align:start position:0%
+innovations and the way they change
+society in the past right so we think
+
+ align:start position:0%
+society in the past right so we think
+ 
+
+ align:start position:0%
+society in the past right so we think
+about what the 19th century looks like
+
+ align:start position:0%
+about what the 19th century looks like
+ 
+
+ align:start position:0%
+about what the 19th century looks like
+and I mentioned some of these before but
+
+ align:start position:0%
+and I mentioned some of these before but
+ 
+
+ align:start position:0%
+and I mentioned some of these before but
+you know canals and railroads and
+
+ align:start position:0%
+you know canals and railroads and
+ 
+
+ align:start position:0%
+you know canals and railroads and
+electricity and the Telegraph and the
+
+ align:start position:0%
+electricity and the Telegraph and the
+ 
+
+ align:start position:0%
+electricity and the Telegraph and the
+telephone and more recent times
+
+ align:start position:0%
+telephone and more recent times
+ 
+
+ align:start position:0%
+telephone and more recent times
+aerospace and computing and the Internet
+
+ align:start position:0%
+aerospace and computing and the Internet
+ 
+
+ align:start position:0%
+aerospace and computing and the Internet
+these are all growth transformers right
+
+ align:start position:0%
+these are all growth transformers right
+ 
+
+ align:start position:0%
+these are all growth transformers right
+and you've seen a couple of these you've
+
+ align:start position:0%
+and you've seen a couple of these you've
+ 
+
+ align:start position:0%
+and you've seen a couple of these you've
+seen the IT revolution in your lifetime
+
+ align:start position:0%
+seen the IT revolution in your lifetime
+ 
+
+ align:start position:0%
+seen the IT revolution in your lifetime
+and you've seen a smaller scale but
+
+ align:start position:0%
+and you've seen a smaller scale but
+ 
+
+ align:start position:0%
+and you've seen a smaller scale but
+still significant biotech revolution
+
+ align:start position:0%
+still significant biotech revolution
+ 
+
+ align:start position:0%
+still significant biotech revolution
+right which is still both of what you're
+
+ align:start position:0%
+right which is still both of what you're
+ 
+
+ align:start position:0%
+right which is still both of what you're
+still playing out so you can get a feel
+
+ align:start position:0%
+still playing out so you can get a feel
+ 
+
+ align:start position:0%
+still playing out so you can get a feel
+for what these things look like we kind
+
+ align:start position:0%
+for what these things look like we kind
+ 
+
+ align:start position:0%
+for what these things look like we kind
+of know they're real
+
+ align:start position:0%
+of know they're real
+ 
+
+ align:start position:0%
+of know they're real
+right this is not just some solo
+
+ align:start position:0%
+right this is not just some solo
+ 
+
+ align:start position:0%
+right this is not just some solo
+construct we feel these because we see
+
+ align:start position:0%
+construct we feel these because we see
+ 
+
+ align:start position:0%
+construct we feel these because we see
+them around us so what's the pattern so
+
+ align:start position:0%
+them around us so what's the pattern so
+ 
+
+ align:start position:0%
+them around us so what's the pattern so
+there's a core technology advance that
+
+ align:start position:0%
+there's a core technology advance that
+ 
+
+ align:start position:0%
+there's a core technology advance that
+yields opportunities for new
+
+ align:start position:0%
+yields opportunities for new
+ 
+
+ align:start position:0%
+yields opportunities for new
+applications which can pile on to that
+
+ align:start position:0%
+applications which can pile on to that
+ 
+
+ align:start position:0%
+applications which can pile on to that
+core technology advanced and then that
+
+ align:start position:0%
+core technology advanced and then that
+ 
+
+ align:start position:0%
+core technology advanced and then that
+in turn can become big enough that it
+
+ align:start position:0%
+in turn can become big enough that it
+ 
+
+ align:start position:0%
+in turn can become big enough that it
+enters society at scale right and we
+
+ align:start position:0%
+enters society at scale right and we
+ 
+
+ align:start position:0%
+enters society at scale right and we
+also the IT revolution spreading into
+
+ align:start position:0%
+also the IT revolution spreading into
+ 
+
+ align:start position:0%
+also the IT revolution spreading into
+different parts of the economy and then
+
+ align:start position:0%
+different parts of the economy and then
+ 
+
+ align:start position:0%
+different parts of the economy and then
+that can yield productivity gain so
+
+ align:start position:0%
+that can yield productivity gain so
+ 
+
+ align:start position:0%
+that can yield productivity gain so
+productivity gains for you non
+
+ align:start position:0%
+productivity gains for you non
+ 
+
+ align:start position:0%
+productivity gains for you non
+economists are when you're producing
+
+ align:start position:0%
+economists are when you're producing
+ 
+
+ align:start position:0%
+economists are when you're producing
+more with less labor input so more for
+
+ align:start position:0%
+more with less labor input so more for
+ 
+
+ align:start position:0%
+more with less labor input so more for
+less
+
+ align:start position:0%
+less
+ 
+
+ align:start position:0%
+less
+right workers spend less time on the
+
+ align:start position:0%
+right workers spend less time on the
+ 
+
+ align:start position:0%
+right workers spend less time on the
+production stage and they produce more
+
+ align:start position:0%
+production stage and they produce more
+ 
+
+ align:start position:0%
+production stage and they produce more
+right so those are the efficiencies that
+
+ align:start position:0%
+right so those are the efficiencies that
+ 
+
+ align:start position:0%
+right so those are the efficiencies that
+come out of technology enable these
+
+ align:start position:0%
+come out of technology enable these
+ 
+
+ align:start position:0%
+come out of technology enable these
+productivity gains the productivity
+
+ align:start position:0%
+productivity gains the productivity
+ 
+
+ align:start position:0%
+productivity gains the productivity
+gains that is a real gain in the society
+
+ align:start position:0%
+gains that is a real gain in the society
+ 
+
+ align:start position:0%
+gains that is a real gain in the society
+right that creates real wealth because
+
+ align:start position:0%
+right that creates real wealth because
+ 
+
+ align:start position:0%
+right that creates real wealth because
+you're producing more with less so
+
+ align:start position:0%
+you're producing more with less so
+ 
+
+ align:start position:0%
+you're producing more with less so
+there's a real game and then depending
+
+ align:start position:0%
+there's a real game and then depending
+ 
+
+ align:start position:0%
+there's a real game and then depending
+on how your societies organized you can
+
+ align:start position:0%
+on how your societies organized you can
+ 
+
+ align:start position:0%
+on how your societies organized you can
+distribute that wealth and the society
+
+ align:start position:0%
+distribute that wealth and the society
+ 
+
+ align:start position:0%
+distribute that wealth and the society
+can move ahead so that's what we saw
+
+ align:start position:0%
+can move ahead so that's what we saw
+ 
+
+ align:start position:0%
+can move ahead so that's what we saw
+happening in that amazing 1990s period
+
+ align:start position:0%
+happening in that amazing 1990s period
+ 
+
+ align:start position:0%
+happening in that amazing 1990s period
+right and we'll talk about Jorgenson and
+
+ align:start position:0%
+right and we'll talk about Jorgenson and
+ 
+
+ align:start position:0%
+right and we'll talk about Jorgenson and
+the pictures of that in a minute
+
+ align:start position:0%
+the pictures of that in a minute
+ 
+
+ align:start position:0%
+the pictures of that in a minute
+follow me you with me so great we're out
+
+ align:start position:0%
+follow me you with me so great we're out
+ 
+
+ align:start position:0%
+follow me you with me so great we're out
+of the dismal science there's really
+
+ align:start position:0%
+of the dismal science there's really
+ 
+
+ align:start position:0%
+of the dismal science there's really
+good news here you can do this
+
+ align:start position:0%
+good news here you can do this
+ 
+
+ align:start position:0%
+good news here you can do this
+innovation stuff and grow your society
+
+ align:start position:0%
+innovation stuff and grow your society
+ 
+
+ align:start position:0%
+innovation stuff and grow your society
+grow your economy and grow SAS Lydell
+
+ align:start position:0%
+grow your economy and grow SAS Lydell
+ 
+
+ align:start position:0%
+grow your economy and grow SAS Lydell
+well Bing right that's the good news the
+
+ align:start position:0%
+well Bing right that's the good news the
+ 
+
+ align:start position:0%
+well Bing right that's the good news the
+bad news is how the heck do you do that
+
+ align:start position:0%
+bad news is how the heck do you do that
+ 
+
+ align:start position:0%
+bad news is how the heck do you do that
+how do you do that and that's what this
+
+ align:start position:0%
+how do you do that and that's what this
+ 
+
+ align:start position:0%
+how do you do that and that's what this
+course is about how do you do that for a
+
+ align:start position:0%
+course is about how do you do that for a
+ 
+
+ align:start position:0%
+course is about how do you do that for a
+long time
+
+ align:start position:0%
+long time
+ 
+
+ align:start position:0%
+long time
+economists thought that this
+
+ align:start position:0%
+economists thought that this
+ 
+
+ align:start position:0%
+economists thought that this
+technological and unrelated innovation
+
+ align:start position:0%
+technological and unrelated innovation
+ 
+
+ align:start position:0%
+technological and unrelated innovation
+stuff was the way in which rich nations
+
+ align:start position:0%
+stuff was the way in which rich nations
+ 
+
+ align:start position:0%
+stuff was the way in which rich nations
+got much richer and that's pretty much
+
+ align:start position:0%
+got much richer and that's pretty much
+ 
+
+ align:start position:0%
+got much richer and that's pretty much
+the way it looked for a long period of
+
+ align:start position:0%
+the way it looked for a long period of
+ 
+
+ align:start position:0%
+the way it looked for a long period of
+time but then funny things started
+
+ align:start position:0%
+time but then funny things started
+ 
+
+ align:start position:0%
+time but then funny things started
+happening right countries like Korea
+
+ align:start position:0%
+happening right countries like Korea
+ 
+
+ align:start position:0%
+happening right countries like Korea
+Taiwan but then really importantly India
+
+ align:start position:0%
+Taiwan but then really importantly India
+ 
+
+ align:start position:0%
+Taiwan but then really importantly India
+and China hit on aspects of a
+
+ align:start position:0%
+and China hit on aspects of a
+ 
+
+ align:start position:0%
+and China hit on aspects of a
+technological based innovation model and
+
+ align:start position:0%
+technological based innovation model and
+ 
+
+ align:start position:0%
+technological based innovation model and
+began to significantly grow the middle
+
+ align:start position:0%
+began to significantly grow the middle
+ 
+
+ align:start position:0%
+began to significantly grow the middle
+classes in their society so we now know
+
+ align:start position:0%
+classes in their society so we now know
+ 
+
+ align:start position:0%
+classes in their society so we now know
+this is not only Malthus view this is
+
+ align:start position:0%
+this is not only Malthus view this is
+ 
+
+ align:start position:0%
+this is not only Malthus view this is
+not only a model for developed countries
+
+ align:start position:0%
+not only a model for developed countries
+ 
+
+ align:start position:0%
+not only a model for developed countries
+this is a developing country model -
+
+ align:start position:0%
+this is a developing country model -
+ 
+
+ align:start position:0%
+this is a developing country model -
+this is really important right
+
+ align:start position:0%
+this is really important right
+ 
+
+ align:start position:0%
+this is really important right
+so technological progress is key capital
+
+ align:start position:0%
+so technological progress is key capital
+ 
+
+ align:start position:0%
+so technological progress is key capital
+is a supporting role but still important
+
+ align:start position:0%
+is a supporting role but still important
+ 
+
+ align:start position:0%
+is a supporting role but still important
+right labor supply is a supporting role
+
+ align:start position:0%
+right labor supply is a supporting role
+ 
+
+ align:start position:0%
+right labor supply is a supporting role
+if it's still important and solo brings
+
+ align:start position:0%
+if it's still important and solo brings
+ 
+
+ align:start position:0%
+if it's still important and solo brings
+us this whole new set of ideas but then
+
+ align:start position:0%
+us this whole new set of ideas but then
+ 
+
+ align:start position:0%
+us this whole new set of ideas but then
+he runs into a problem because remember
+
+ align:start position:0%
+he runs into a problem because remember
+ 
+
+ align:start position:0%
+he runs into a problem because remember
+he's a neoclassical economist he wants
+
+ align:start position:0%
+he's a neoclassical economist he wants
+ 
+
+ align:start position:0%
+he's a neoclassical economist he wants
+to get down to a small number of
+
+ align:start position:0%
+to get down to a small number of
+ 
+
+ align:start position:0%
+to get down to a small number of
+variables that you really know right
+
+ align:start position:0%
+variables that you really know right
+ 
+
+ align:start position:0%
+variables that you really know right
+good luck with trying to understand an
+
+ align:start position:0%
+good luck with trying to understand an
+ 
+
+ align:start position:0%
+good luck with trying to understand an
+innovation system based upon
+
+ align:start position:0%
+innovation system based upon
+ 
+
+ align:start position:0%
+innovation system based upon
+mathematically proven small numbers of
+
+ align:start position:0%
+mathematically proven small numbers of
+ 
+
+ align:start position:0%
+mathematically proven small numbers of
+variables it is much too rich and
+
+ align:start position:0%
+variables it is much too rich and
+ 
+
+ align:start position:0%
+variables it is much too rich and
+complex system you can't put an
+
+ align:start position:0%
+complex system you can't put an
+ 
+
+ align:start position:0%
+complex system you can't put an
+innovation system in to supply and
+
+ align:start position:0%
+innovation system in to supply and
+ 
+
+ align:start position:0%
+innovation system in to supply and
+demand curves so Sola sees the power of
+
+ align:start position:0%
+demand curves so Sola sees the power of
+ 
+
+ align:start position:0%
+demand curves so Sola sees the power of
+technological advance but he doesn't see
+
+ align:start position:0%
+technological advance but he doesn't see
+ 
+
+ align:start position:0%
+technological advance but he doesn't see
+how to measure it
+
+ align:start position:0%
+how to measure it
+ 
+
+ align:start position:0%
+how to measure it
+so we can't put it into his neoclassical
+
+ align:start position:0%
+so we can't put it into his neoclassical
+ 
+
+ align:start position:0%
+so we can't put it into his neoclassical
+economic model so he treats
+
+ align:start position:0%
+economic model so he treats
+ 
+
+ align:start position:0%
+economic model so he treats
+technological innovation as exogenous
+
+ align:start position:0%
+technological innovation as exogenous
+ 
+
+ align:start position:0%
+technological innovation as exogenous
+outside of the economic analytical
+
+ align:start position:0%
+outside of the economic analytical
+ 
+
+ align:start position:0%
+outside of the economic analytical
+modeling process that he's involved in
+
+ align:start position:0%
+modeling process that he's involved in
+ 
+
+ align:start position:0%
+modeling process that he's involved in
+that's pretty amazing right when you
+
+ align:start position:0%
+that's pretty amazing right when you
+ 
+
+ align:start position:0%
+that's pretty amazing right when you
+think about it the guy figures out the
+
+ align:start position:0%
+think about it the guy figures out the
+ 
+
+ align:start position:0%
+think about it the guy figures out the
+dominant causative factor of growth
+
+ align:start position:0%
+dominant causative factor of growth
+ 
+
+ align:start position:0%
+dominant causative factor of growth
+which is needless to say a pretty
+
+ align:start position:0%
+which is needless to say a pretty
+ 
+
+ align:start position:0%
+which is needless to say a pretty
+important thing in economics and then he
+
+ align:start position:0%
+important thing in economics and then he
+ 
+
+ align:start position:0%
+important thing in economics and then he
+can't play with it right because it's
+
+ align:start position:0%
+can't play with it right because it's
+ 
+
+ align:start position:0%
+can't play with it right because it's
+outside his system so that brings us to
+
+ align:start position:0%
+outside his system so that brings us to
+ 
+
+ align:start position:0%
+outside his system so that brings us to
+this character and this is Paul Romer
+
+ align:start position:0%
+this character and this is Paul Romer
+ 
+
+ align:start position:0%
+this character and this is Paul Romer
+and you can see you know very California
+
+ align:start position:0%
+and you can see you know very California
+ 
+
+ align:start position:0%
+and you can see you know very California
+right and he's got that laid book laid
+
+ align:start position:0%
+right and he's got that laid book laid
+ 
+
+ align:start position:0%
+right and he's got that laid book laid
+back kind of relaxed look in his eyes
+
+ align:start position:0%
+back kind of relaxed look in his eyes
+ 
+
+ align:start position:0%
+back kind of relaxed look in his eyes
+and he's he is a remarkable figure he is
+
+ align:start position:0%
+and he's he is a remarkable figure he is
+ 
+
+ align:start position:0%
+and he's he is a remarkable figure he is
+a maverick trouble maker
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+you know I got to know him by actually
+
+ align:start position:0%
+you know I got to know him by actually
+ 
+
+ align:start position:0%
+you know I got to know him by actually
+working on some legislation with him
+
+ align:start position:0%
+working on some legislation with him
+ 
+
+ align:start position:0%
+working on some legislation with him
+back when I was working in the Senate
+
+ align:start position:0%
+back when I was working in the Senate
+ 
+
+ align:start position:0%
+back when I was working in the Senate
+and you know we knew we needed to
+
+ align:start position:0%
+and you know we knew we needed to
+ 
+
+ align:start position:0%
+and you know we knew we needed to
+improve the STEM education science and
+
+ align:start position:0%
+improve the STEM education science and
+ 
+
+ align:start position:0%
+improve the STEM education science and
+technology work base that was going to
+
+ align:start position:0%
+technology work base that was going to
+ 
+
+ align:start position:0%
+technology work base that was going to
+be pretty important for reasons I'll
+
+ align:start position:0%
+be pretty important for reasons I'll
+ 
+
+ align:start position:0%
+be pretty important for reasons I'll
+explain in a minute and how would you do
+
+ align:start position:0%
+explain in a minute and how would you do
+ 
+
+ align:start position:0%
+explain in a minute and how would you do
+that right so I'm a Senate staffer I'm
+
+ align:start position:0%
+that right so I'm a Senate staffer I'm
+ 
+
+ align:start position:0%
+that right so I'm a Senate staffer I'm
+thinking gee were already spending you
+
+ align:start position:0%
+thinking gee were already spending you
+ 
+
+ align:start position:0%
+thinking gee were already spending you
+know X billions of dollars on
+
+ align:start position:0%
+know X billions of dollars on
+ 
+
+ align:start position:0%
+know X billions of dollars on
+fellowships for you guys and you know
+
+ align:start position:0%
+fellowships for you guys and you know
+ 
+
+ align:start position:0%
+fellowships for you guys and you know
+then we're gonna have to find billions
+
+ align:start position:0%
+then we're gonna have to find billions
+ 
+
+ align:start position:0%
+then we're gonna have to find billions
+more and increase the number and expand
+
+ align:start position:0%
+more and increase the number and expand
+ 
+
+ align:start position:0%
+more and increase the number and expand
+the base and it's gonna be incredibly
+
+ align:start position:0%
+the base and it's gonna be incredibly
+ 
+
+ align:start position:0%
+the base and it's gonna be incredibly
+costly and I never get this past so you
+
+ align:start position:0%
+costly and I never get this past so you
+ 
+
+ align:start position:0%
+costly and I never get this past so you
+know rumor is thinking about all this
+
+ align:start position:0%
+know rumor is thinking about all this
+ 
+
+ align:start position:0%
+know rumor is thinking about all this
+stuff and writing about it and we'll
+
+ align:start position:0%
+stuff and writing about it and we'll
+ 
+
+ align:start position:0%
+stuff and writing about it and we'll
+read something else of his late in the
+
+ align:start position:0%
+read something else of his late in the
+ 
+
+ align:start position:0%
+read something else of his late in the
+class but sit down with him and I said
+
+ align:start position:0%
+class but sit down with him and I said
+ 
+
+ align:start position:0%
+class but sit down with him and I said
+bill none of you know you're not
+
+ align:start position:0%
+bill none of you know you're not
+ 
+
+ align:start position:0%
+bill none of you know you're not
+thinking about this right said think
+
+ align:start position:0%
+thinking about this right said think
+ 
+
+ align:start position:0%
+thinking about this right said think
+like an economist said you don't have to
+
+ align:start position:0%
+like an economist said you don't have to
+ 
+
+ align:start position:0%
+like an economist said you don't have to
+subsidize everything he just bribed the
+
+ align:start position:0%
+subsidize everything he just bribed the
+ 
+
+ align:start position:0%
+subsidize everything he just bribed the
+gatekeepers right that was his phrase
+
+ align:start position:0%
+gatekeepers right that was his phrase
+ 
+
+ align:start position:0%
+gatekeepers right that was his phrase
+and his point was you don't have to
+
+ align:start position:0%
+and his point was you don't have to
+ 
+
+ align:start position:0%
+and his point was you don't have to
+throw a huge amount of money and build
+
+ align:start position:0%
+throw a huge amount of money and build
+ 
+
+ align:start position:0%
+throw a huge amount of money and build
+up all kinds of programmatic elements
+
+ align:start position:0%
+up all kinds of programmatic elements
+ 
+
+ align:start position:0%
+up all kinds of programmatic elements
+you just figure out who's not doing
+
+ align:start position:0%
+you just figure out who's not doing
+ 
+
+ align:start position:0%
+you just figure out who's not doing
+their job and expanding the number of
+
+ align:start position:0%
+their job and expanding the number of
+ 
+
+ align:start position:0%
+their job and expanding the number of
+scientists and engineers studying at
+
+ align:start position:0%
+scientists and engineers studying at
+ 
+
+ align:start position:0%
+scientists and engineers studying at
+universities and you bribed them to
+
+ align:start position:0%
+universities and you bribed them to
+ 
+
+ align:start position:0%
+universities and you bribed them to
+change their ways that's the way you do
+
+ align:start position:0%
+change their ways that's the way you do
+ 
+
+ align:start position:0%
+change their ways that's the way you do
+it right much cheaper and sure enough we
+
+ align:start position:0%
+it right much cheaper and sure enough we
+ 
+
+ align:start position:0%
+it right much cheaper and sure enough we
+fashioned legislation and eventually get
+
+ align:start position:0%
+fashioned legislation and eventually get
+ 
+
+ align:start position:0%
+fashioned legislation and eventually get
+it passed I'm not sure it changed all
+
+ align:start position:0%
+it passed I'm not sure it changed all
+ 
+
+ align:start position:0%
+it passed I'm not sure it changed all
+that much but it was a fun exercise
+
+ align:start position:0%
+that much but it was a fun exercise
+ 
+
+ align:start position:0%
+that much but it was a fun exercise
+working with him because he definitely
+
+ align:start position:0%
+working with him because he definitely
+ 
+
+ align:start position:0%
+working with him because he definitely
+has this maverick troublemaking
+
+ align:start position:0%
+has this maverick troublemaking
+ 
+
+ align:start position:0%
+has this maverick troublemaking
+perspective at one point in his career
+
+ align:start position:0%
+perspective at one point in his career
+ 
+
+ align:start position:0%
+perspective at one point in his career
+at Stanford he he realizes the
+
+ align:start position:0%
+at Stanford he he realizes the
+ 
+
+ align:start position:0%
+at Stanford he he realizes the
+incredible inefficiency of economics
+
+ align:start position:0%
+incredible inefficiency of economics
+ 
+
+ align:start position:0%
+incredible inefficiency of economics
+education that his students just aren't
+
+ align:start position:0%
+education that his students just aren't
+ 
+
+ align:start position:0%
+education that his students just aren't
+getting the big ideas by listening to
+
+ align:start position:0%
+getting the big ideas by listening to
+ 
+
+ align:start position:0%
+getting the big ideas by listening to
+lectures and reading textbooks it's just
+
+ align:start position:0%
+lectures and reading textbooks it's just
+ 
+
+ align:start position:0%
+lectures and reading textbooks it's just
+not happening so he walks out of
+
+ align:start position:0%
+not happening so he walks out of
+ 
+
+ align:start position:0%
+not happening so he walks out of
+Stanford and sets up his own economics
+
+ align:start position:0%
+Stanford and sets up his own economics
+ 
+
+ align:start position:0%
+Stanford and sets up his own economics
+textbook company which is anti textbook
+
+ align:start position:0%
+textbook company which is anti textbook
+ 
+
+ align:start position:0%
+textbook company which is anti textbook
+right and essentially develops a whole
+
+ align:start position:0%
+right and essentially develops a whole
+ 
+
+ align:start position:0%
+right and essentially develops a whole
+set of modules of learn
+
+ align:start position:0%
+set of modules of learn
+ 
+
+ align:start position:0%
+set of modules of learn
+by doing exercises and problem sets and
+
+ align:start position:0%
+by doing exercises and problem sets and
+ 
+
+ align:start position:0%
+by doing exercises and problem sets and
+online elements right and so you don't
+
+ align:start position:0%
+online elements right and so you don't
+ 
+
+ align:start position:0%
+online elements right and so you don't
+get a textbook yeah you get something
+
+ align:start position:0%
+get a textbook yeah you get something
+ 
+
+ align:start position:0%
+get a textbook yeah you get something
+with the textbook but you get all kinds
+
+ align:start position:0%
+with the textbook but you get all kinds
+ 
+
+ align:start position:0%
+with the textbook but you get all kinds
+of online pieces that you do constantly
+
+ align:start position:0%
+of online pieces that you do constantly
+ 
+
+ align:start position:0%
+of online pieces that you do constantly
+and getting through this so he
+
+ align:start position:0%
+and getting through this so he
+ 
+
+ align:start position:0%
+and getting through this so he
+completely blew up the whole economics
+
+ align:start position:0%
+completely blew up the whole economics
+ 
+
+ align:start position:0%
+completely blew up the whole economics
+textbook industry and has forced an
+
+ align:start position:0%
+textbook industry and has forced an
+ 
+
+ align:start position:0%
+textbook industry and has forced an
+absolutely fundamental reform and then
+
+ align:start position:0%
+absolutely fundamental reform and then
+ 
+
+ align:start position:0%
+absolutely fundamental reform and then
+he went out and proved yes my new system
+
+ align:start position:0%
+he went out and proved yes my new system
+ 
+
+ align:start position:0%
+he went out and proved yes my new system
+here works better than Paul Samuelson's
+
+ align:start position:0%
+here works better than Paul Samuelson's
+ 
+
+ align:start position:0%
+here works better than Paul Samuelson's
+and everybody else's textbooks because
+
+ align:start position:0%
+and everybody else's textbooks because
+ 
+
+ align:start position:0%
+and everybody else's textbooks because
+people are absorbing the core ideas and
+
+ align:start position:0%
+people are absorbing the core ideas and
+ 
+
+ align:start position:0%
+people are absorbing the core ideas and
+be able to work with them much more
+
+ align:start position:0%
+be able to work with them much more
+ 
+
+ align:start position:0%
+be able to work with them much more
+efficiently it's a whole learning by
+
+ align:start position:0%
+efficiently it's a whole learning by
+ 
+
+ align:start position:0%
+efficiently it's a whole learning by
+doing problem-based learning set that he
+
+ align:start position:0%
+doing problem-based learning set that he
+ 
+
+ align:start position:0%
+doing problem-based learning set that he
+brings in economics so you know he just
+
+ align:start position:0%
+brings in economics so you know he just
+ 
+
+ align:start position:0%
+brings in economics so you know he just
+walks out of his economics job at
+
+ align:start position:0%
+walks out of his economics job at
+ 
+
+ align:start position:0%
+walks out of his economics job at
+Stanford and does this for four years so
+
+ align:start position:0%
+Stanford and does this for four years so
+ 
+
+ align:start position:0%
+Stanford and does this for four years so
+he's and now he's on the latest of his
+
+ align:start position:0%
+he's and now he's on the latest of his
+ 
+
+ align:start position:0%
+he's and now he's on the latest of his
+exercises which is he's walked out if he
+
+ align:start position:0%
+exercises which is he's walked out if he
+ 
+
+ align:start position:0%
+exercises which is he's walked out if he
+went to NYU a few years ago to work on
+
+ align:start position:0%
+went to NYU a few years ago to work on
+ 
+
+ align:start position:0%
+went to NYU a few years ago to work on
+sort of cluster development theory and
+
+ align:start position:0%
+sort of cluster development theory and
+ 
+
+ align:start position:0%
+sort of cluster development theory and
+cities in metropolitan areas and growth
+
+ align:start position:0%
+cities in metropolitan areas and growth
+ 
+
+ align:start position:0%
+cities in metropolitan areas and growth
+but then he left that so he's now chief
+
+ align:start position:0%
+but then he left that so he's now chief
+ 
+
+ align:start position:0%
+but then he left that so he's now chief
+economist for the World Bank and look
+
+ align:start position:0%
+economist for the World Bank and look
+ 
+
+ align:start position:0%
+economist for the World Bank and look
+out right this there's gonna be trouble
+
+ align:start position:0%
+out right this there's gonna be trouble
+ 
+
+ align:start position:0%
+out right this there's gonna be trouble
+ahead here he's gonna he's gonna change
+
+ align:start position:0%
+ahead here he's gonna he's gonna change
+ 
+
+ align:start position:0%
+ahead here he's gonna he's gonna change
+that place I'm confident but let's talk
+
+ align:start position:0%
+that place I'm confident but let's talk
+ 
+
+ align:start position:0%
+that place I'm confident but let's talk
+about the ideas that he brings to our
+
+ align:start position:0%
+about the ideas that he brings to our
+ 
+
+ align:start position:0%
+about the ideas that he brings to our
+problem this past summer I think that's
+
+ align:start position:0%
+problem this past summer I think that's
+ 
+
+ align:start position:0%
+problem this past summer I think that's
+when he started I haven't seen him since
+
+ align:start position:0%
+when he started I haven't seen him since
+ 
+
+ align:start position:0%
+when he started I haven't seen him since
+he started but sure enough one thing he
+
+ align:start position:0%
+he started but sure enough one thing he
+ 
+
+ align:start position:0%
+he started but sure enough one thing he
+does he writes this attack on economists
+
+ align:start position:0%
+does he writes this attack on economists
+ 
+
+ align:start position:0%
+does he writes this attack on economists
+saying they're completely in love with
+
+ align:start position:0%
+saying they're completely in love with
+ 
+
+ align:start position:0%
+saying they're completely in love with
+you know metrics and mathematics and
+
+ align:start position:0%
+you know metrics and mathematics and
+ 
+
+ align:start position:0%
+you know metrics and mathematics and
+it's not gonna get him anywhere these
+
+ align:start position:0%
+it's not gonna get him anywhere these
+ 
+
+ align:start position:0%
+it's not gonna get him anywhere these
+systems are too complex and it's just an
+
+ align:start position:0%
+systems are too complex and it's just an
+ 
+
+ align:start position:0%
+systems are too complex and it's just an
+assault on the profession because this
+
+ align:start position:0%
+assault on the profession because this
+ 
+
+ align:start position:0%
+assault on the profession because this
+is a profession like all professions it
+
+ align:start position:0%
+is a profession like all professions it
+ 
+
+ align:start position:0%
+is a profession like all professions it
+doesn't attack itself right this that's
+
+ align:start position:0%
+doesn't attack itself right this that's
+ 
+
+ align:start position:0%
+doesn't attack itself right this that's
+not polite right so Romer just you know
+
+ align:start position:0%
+not polite right so Romer just you know
+ 
+
+ align:start position:0%
+not polite right so Romer just you know
+lifts the veil of trouble and it's quite
+
+ align:start position:0%
+lifts the veil of trouble and it's quite
+ 
+
+ align:start position:0%
+lifts the veil of trouble and it's quite
+a piece it hasn't formally been
+
+ align:start position:0%
+a piece it hasn't formally been
+ 
+
+ align:start position:0%
+a piece it hasn't formally been
+published how much or any journal darest
+
+ align:start position:0%
+published how much or any journal darest
+ 
+
+ align:start position:0%
+published how much or any journal darest
+publish it but it's it's definitely
+
+ align:start position:0%
+publish it but it's it's definitely
+ 
+
+ align:start position:0%
+publish it but it's it's definitely
+circulating around I'll try and find it
+
+ align:start position:0%
+circulating around I'll try and find it
+ 
+
+ align:start position:0%
+circulating around I'll try and find it
+for you because it's a fun read it's
+
+ align:start position:0%
+for you because it's a fun read it's
+ 
+
+ align:start position:0%
+for you because it's a fun read it's
+really something
+
+ align:start position:0%
+really something
+ 
+
+ align:start position:0%
+really something
+anyway that's Romer and Romer is on this
+
+ align:start position:0%
+anyway that's Romer and Romer is on this
+ 
+
+ align:start position:0%
+anyway that's Romer and Romer is on this
+project his his famous 1990 piece which
+
+ align:start position:0%
+project his his famous 1990 piece which
+ 
+
+ align:start position:0%
+project his his famous 1990 piece which
+frankly probably should win him the
+
+ align:start position:0%
+frankly probably should win him the
+ 
+
+ align:start position:0%
+frankly probably should win him the
+Nobel Prize in Economics but he's such a
+
+ align:start position:0%
+Nobel Prize in Economics but he's such a
+ 
+
+ align:start position:0%
+Nobel Prize in Economics but he's such a
+troublemaker that it probably won't is
+
+ align:start position:0%
+troublemaker that it probably won't is
+ 
+
+ align:start position:0%
+troublemaker that it probably won't is
+called endogenous
+
+ align:start position:0%
+called endogenous
+ 
+
+ align:start position:0%
+called endogenous
+logical change so he's trying to reverse
+
+ align:start position:0%
+logical change so he's trying to reverse
+ 
+
+ align:start position:0%
+logical change so he's trying to reverse
+solos exogenous change and make it go
+
+ align:start position:0%
+solos exogenous change and make it go
+ 
+
+ align:start position:0%
+solos exogenous change and make it go
+back get these ideas of economic growth
+
+ align:start position:0%
+back get these ideas of economic growth
+ 
+
+ align:start position:0%
+back get these ideas of economic growth
+back into an economics thinking
+
+ align:start position:0%
+back into an economics thinking
+ 
+
+ align:start position:0%
+back into an economics thinking
+framework that's his project here right
+
+ align:start position:0%
+framework that's his project here right
+ 
+
+ align:start position:0%
+framework that's his project here right
+and he starts on this pathway so he
+
+ align:start position:0%
+and he starts on this pathway so he
+ 
+
+ align:start position:0%
+and he starts on this pathway so he
+agrees I mean let me just summarize the
+
+ align:start position:0%
+agrees I mean let me just summarize the
+ 
+
+ align:start position:0%
+agrees I mean let me just summarize the
+basic points he agrees was so low that
+
+ align:start position:0%
+basic points he agrees was so low that
+ 
+
+ align:start position:0%
+basic points he agrees was so low that
+growth is driven by technological change
+
+ align:start position:0%
+growth is driven by technological change
+ 
+
+ align:start position:0%
+growth is driven by technological change
+and then he argues that that in turn is
+
+ align:start position:0%
+and then he argues that that in turn is
+ 
+
+ align:start position:0%
+and then he argues that that in turn is
+driven by researchers who he describes
+
+ align:start position:0%
+driven by researchers who he describes
+ 
+
+ align:start position:0%
+driven by researchers who he describes
+as economic agents profit maximizing
+
+ align:start position:0%
+as economic agents profit maximizing
+ 
+
+ align:start position:0%
+as economic agents profit maximizing
+agents and then he looks at how
+
+ align:start position:0%
+agents and then he looks at how
+ 
+
+ align:start position:0%
+agents and then he looks at how
+technology isn't really a conventional
+
+ align:start position:0%
+technology isn't really a conventional
+ 
+
+ align:start position:0%
+technology isn't really a conventional
+good in the normal sense of economic
+
+ align:start position:0%
+good in the normal sense of economic
+ 
+
+ align:start position:0%
+good in the normal sense of economic
+goods but it has its own set of unique
+
+ align:start position:0%
+goods but it has its own set of unique
+ 
+
+ align:start position:0%
+goods but it has its own set of unique
+properties that make it really quite
+
+ align:start position:0%
+properties that make it really quite
+ 
+
+ align:start position:0%
+properties that make it really quite
+different but most important for us he
+
+ align:start position:0%
+different but most important for us he
+ 
+
+ align:start position:0%
+different but most important for us he
+looks at when he calls human capital
+
+ align:start position:0%
+looks at when he calls human capital
+ 
+
+ align:start position:0%
+looks at when he calls human capital
+engaged in research in other words you
+
+ align:start position:0%
+engaged in research in other words you
+ 
+
+ align:start position:0%
+engaged in research in other words you
+don't just have to do R&D to loosely
+
+ align:start position:0%
+don't just have to do R&D to loosely
+ 
+
+ align:start position:0%
+don't just have to do R&D to loosely
+summarize so long you've got to have a
+
+ align:start position:0%
+summarize so long you've got to have a
+ 
+
+ align:start position:0%
+summarize so long you've got to have a
+talent base doing that R&D this whole
+
+ align:start position:0%
+talent base doing that R&D this whole
+ 
+
+ align:start position:0%
+talent base doing that R&D this whole
+project is to take all these concepts
+
+ align:start position:0%
+project is to take all these concepts
+ 
+
+ align:start position:0%
+project is to take all these concepts
+and move them into an endogenous theory
+
+ align:start position:0%
+and move them into an endogenous theory
+ 
+
+ align:start position:0%
+and move them into an endogenous theory
+of of growth so his growth model is
+
+ align:start position:0%
+of of growth so his growth model is
+ 
+
+ align:start position:0%
+of of growth so his growth model is
+similar to you know two solos he's
+
+ align:start position:0%
+similar to you know two solos he's
+ 
+
+ align:start position:0%
+similar to you know two solos he's
+picking up on solos work you know he
+
+ align:start position:0%
+picking up on solos work you know he
+ 
+
+ align:start position:0%
+picking up on solos work you know he
+sees that technological change is the
+
+ align:start position:0%
+sees that technological change is the
+ 
+
+ align:start position:0%
+sees that technological change is the
+heart of economic growth as we've
+
+ align:start position:0%
+heart of economic growth as we've
+ 
+
+ align:start position:0%
+heart of economic growth as we've
+discussed he sees that technological
+
+ align:start position:0%
+discussed he sees that technological
+ 
+
+ align:start position:0%
+discussed he sees that technological
+change occurs in turn in a large part
+
+ align:start position:0%
+change occurs in turn in a large part
+ 
+
+ align:start position:0%
+change occurs in turn in a large part
+because of people responding to market
+
+ align:start position:0%
+because of people responding to market
+ 
+
+ align:start position:0%
+because of people responding to market
+incentives again he's trying to get this
+
+ align:start position:0%
+incentives again he's trying to get this
+ 
+
+ align:start position:0%
+incentives again he's trying to get this
+into economic thinking and this
+
+ align:start position:0%
+into economic thinking and this
+ 
+
+ align:start position:0%
+into economic thinking and this
+technological knowledge which is
+
+ align:start position:0%
+technological knowledge which is
+ 
+
+ align:start position:0%
+technological knowledge which is
+instructions for working with materials
+
+ align:start position:0%
+instructions for working with materials
+ 
+
+ align:start position:0%
+instructions for working with materials
+is inherently different from other
+
+ align:start position:0%
+is inherently different from other
+ 
+
+ align:start position:0%
+is inherently different from other
+economic models so developing a new and
+
+ align:start position:0%
+economic models so developing a new and
+ 
+
+ align:start position:0%
+economic models so developing a new and
+better set of instructions he argues is
+
+ align:start position:0%
+better set of instructions he argues is
+ 
+
+ align:start position:0%
+better set of instructions he argues is
+a can be treated as a fixed cost in
+
+ align:start position:0%
+a can be treated as a fixed cost in
+ 
+
+ align:start position:0%
+a can be treated as a fixed cost in
+economic terms and it's therefore a
+
+ align:start position:0%
+economic terms and it's therefore a
+ 
+
+ align:start position:0%
+economic terms and it's therefore a
+defining characteristic economics
+
+ align:start position:0%
+defining characteristic economics
+ 
+
+ align:start position:0%
+defining characteristic economics
+characteristic of innovation so just for
+
+ align:start position:0%
+characteristic of innovation so just for
+ 
+
+ align:start position:0%
+characteristic of innovation so just for
+an example right I mean there's article
+
+ align:start position:0%
+an example right I mean there's article
+ 
+
+ align:start position:0%
+an example right I mean there's article
+is richer than this but I'll just cite a
+
+ align:start position:0%
+is richer than this but I'll just cite a
+ 
+
+ align:start position:0%
+is richer than this but I'll just cite a
+few examples of what he
+
+ align:start position:0%
+few examples of what he
+ 
+
+ align:start position:0%
+few examples of what he
+trying to think about a rival good is
+
+ align:start position:0%
+trying to think about a rival good is
+ 
+
+ align:start position:0%
+trying to think about a rival good is
+property that if used by one person or
+
+ align:start position:0%
+property that if used by one person or
+ 
+
+ align:start position:0%
+property that if used by one person or
+firm precludes use by another and a non
+
+ align:start position:0%
+firm precludes use by another and a non
+ 
+
+ align:start position:0%
+firm precludes use by another and a non
+rival good is a kind of property that if
+
+ align:start position:0%
+rival good is a kind of property that if
+ 
+
+ align:start position:0%
+rival good is a kind of property that if
+used by one person or firm in no way
+
+ align:start position:0%
+used by one person or firm in no way
+ 
+
+ align:start position:0%
+used by one person or firm in no way
+limits the use by the others so
+
+ align:start position:0%
+limits the use by the others so
+ 
+
+ align:start position:0%
+limits the use by the others so
+technology he argues is naturally
+
+ align:start position:0%
+technology he argues is naturally
+ 
+
+ align:start position:0%
+technology he argues is naturally
+non-rival right because it can be
+
+ align:start position:0%
+non-rival right because it can be
+ 
+
+ align:start position:0%
+non-rival right because it can be
+readily shared and adopted by others in
+
+ align:start position:0%
+readily shared and adopted by others in
+ 
+
+ align:start position:0%
+readily shared and adopted by others in
+other words once you see this thing and
+
+ align:start position:0%
+other words once you see this thing and
+ 
+
+ align:start position:0%
+other words once you see this thing and
+understand how it works then you can
+
+ align:start position:0%
+understand how it works then you can
+ 
+
+ align:start position:0%
+understand how it works then you can
+make your own version of it right but
+
+ align:start position:0%
+make your own version of it right but
+ 
+
+ align:start position:0%
+make your own version of it right but
+there's obviously an how would you get
+
+ align:start position:0%
+there's obviously an how would you get
+ 
+
+ align:start position:0%
+there's obviously an how would you get
+rich off this if it's completely non
+
+ align:start position:0%
+rich off this if it's completely non
+ 
+
+ align:start position:0%
+rich off this if it's completely non
+rival so capitalists move to make it
+
+ align:start position:0%
+rival so capitalists move to make it
+ 
+
+ align:start position:0%
+rival so capitalists move to make it
+excludable right where the owner of the
+
+ align:start position:0%
+excludable right where the owner of the
+ 
+
+ align:start position:0%
+excludable right where the owner of the
+good Steve Jobs and his crew try to
+
+ align:start position:0%
+good Steve Jobs and his crew try to
+ 
+
+ align:start position:0%
+good Steve Jobs and his crew try to
+prevent others from using it through for
+
+ align:start position:0%
+prevent others from using it through for
+ 
+
+ align:start position:0%
+prevent others from using it through for
+example through trade secret serve
+
+ align:start position:0%
+example through trade secret serve
+ 
+
+ align:start position:0%
+example through trade secret serve
+patents right so technology can be made
+
+ align:start position:0%
+patents right so technology can be made
+ 
+
+ align:start position:0%
+patents right so technology can be made
+partially excludable but in the end
+
+ align:start position:0%
+partially excludable but in the end
+ 
+
+ align:start position:0%
+partially excludable but in the end
+technology has these remember this term
+
+ align:start position:0%
+technology has these remember this term
+ 
+
+ align:start position:0%
+technology has these remember this term
+spillover features knowledge spillover
+
+ align:start position:0%
+spillover features knowledge spillover
+ 
+
+ align:start position:0%
+spillover features knowledge spillover
+features that make it pretty accessible
+
+ align:start position:0%
+features that make it pretty accessible
+ 
+
+ align:start position:0%
+features that make it pretty accessible
+because you get to see the technology
+
+ align:start position:0%
+because you get to see the technology
+ 
+
+ align:start position:0%
+because you get to see the technology
+and you can derive ideas about how its
+
+ align:start position:0%
+and you can derive ideas about how its
+ 
+
+ align:start position:0%
+and you can derive ideas about how its
+put together so technology is unlike any
+
+ align:start position:0%
+put together so technology is unlike any
+ 
+
+ align:start position:0%
+put together so technology is unlike any
+other kind of economic good because it
+
+ align:start position:0%
+other kind of economic good because it
+ 
+
+ align:start position:0%
+other kind of economic good because it
+can be both excludable and
+
+ align:start position:0%
+can be both excludable and
+ 
+
+ align:start position:0%
+can be both excludable and
+non-excludable rival and nonrival right
+
+ align:start position:0%
+non-excludable rival and nonrival right
+ 
+
+ align:start position:0%
+non-excludable rival and nonrival right
+it's not like anything else it's not
+
+ align:start position:0%
+it's not like anything else it's not
+ 
+
+ align:start position:0%
+it's not like anything else it's not
+like owning a farm right and you are mad
+
+ align:start position:0%
+like owning a farm right and you are mad
+ 
+
+ align:start position:0%
+like owning a farm right and you are mad
+max' good technology in general so he's
+
+ align:start position:0%
+max' good technology in general so he's
+ 
+
+ align:start position:0%
+max' good technology in general so he's
+developing a broader way of looking at
+
+ align:start position:0%
+developing a broader way of looking at
+ 
+
+ align:start position:0%
+developing a broader way of looking at
+this whole category all right so that's
+
+ align:start position:0%
+this whole category all right so that's
+ 
+
+ align:start position:0%
+this whole category all right so that's
+one I core idea let's try and develop
+
+ align:start position:0%
+one I core idea let's try and develop
+ 
+
+ align:start position:0%
+one I core idea let's try and develop
+theories of economics that by which we
+
+ align:start position:0%
+theories of economics that by which we
+ 
+
+ align:start position:0%
+theories of economics that by which we
+can better describe what technology is
+
+ align:start position:0%
+can better describe what technology is
+ 
+
+ align:start position:0%
+can better describe what technology is
+since it's so key to growth but his
+
+ align:start position:0%
+since it's so key to growth but his
+ 
+
+ align:start position:0%
+since it's so key to growth but his
+really important contribution is around
+
+ align:start position:0%
+really important contribution is around
+ 
+
+ align:start position:0%
+really important contribution is around
+the role of human capital and that's
+
+ align:start position:0%
+the role of human capital and that's
+ 
+
+ align:start position:0%
+the role of human capital and that's
+what I want you to really remember today
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+not gonna explain this so it's Rome
+
+ align:start position:0%
+not gonna explain this so it's Rome
+ 
+
+ align:start position:0%
+not gonna explain this so it's Rome
+right whatever it is 200 right it's
+
+ align:start position:0%
+right whatever it is 200 right it's
+ 
+
+ align:start position:0%
+right whatever it is 200 right it's
+wrong and Romans they're terrific
+
+ align:start position:0%
+wrong and Romans they're terrific
+ 
+
+ align:start position:0%
+wrong and Romans they're terrific
+engineers they figured out these amazing
+
+ align:start position:0%
+engineers they figured out these amazing
+ 
+
+ align:start position:0%
+engineers they figured out these amazing
+roads right and they stuck them around
+
+ align:start position:0%
+roads right and they stuck them around
+ 
+
+ align:start position:0%
+roads right and they stuck them around
+all over Europe and that's a technology
+
+ align:start position:0%
+all over Europe and that's a technology
+ 
+
+ align:start position:0%
+all over Europe and that's a technology
+advanced and it improves communication
+
+ align:start position:0%
+advanced and it improves communication
+ 
+
+ align:start position:0%
+advanced and it improves communication
+systems and transports so it carries
+
+ align:start position:0%
+systems and transports so it carries
+ 
+
+ align:start position:0%
+systems and transports so it carries
+with it its technological advance that
+
+ align:start position:0%
+with it its technological advance that
+ 
+
+ align:start position:0%
+with it its technological advance that
+carries with it some game now the width
+
+ align:start position:0%
+carries with it some game now the width
+ 
+
+ align:start position:0%
+carries with it some game now the width
+of the Roman Road is the defining
+
+ align:start position:0%
+of the Roman Road is the defining
+ 
+
+ align:start position:0%
+of the Roman Road is the defining
+characteristic of the width of railroads
+
+ align:start position:0%
+characteristic of the width of railroads
+ 
+
+ align:start position:0%
+characteristic of the width of railroads
+right that's the width that's the
+
+ align:start position:0%
+right that's the width that's the
+ 
+
+ align:start position:0%
+right that's the width that's the
+distance between the rail rails is
+
+ align:start position:0%
+distance between the rail rails is
+ 
+
+ align:start position:0%
+distance between the rail rails is
+defined by the Roman Road distances
+
+ align:start position:0%
+defined by the Roman Road distances
+ 
+
+ align:start position:0%
+defined by the Roman Road distances
+interestingly enough the Romans had a
+
+ align:start position:0%
+interestingly enough the Romans had a
+ 
+
+ align:start position:0%
+interestingly enough the Romans had a
+very primitive kind of toy steam engine
+
+ align:start position:0%
+very primitive kind of toy steam engine
+ 
+
+ align:start position:0%
+very primitive kind of toy steam engine
+that Roman kids would play with and you
+
+ align:start position:0%
+that Roman kids would play with and you
+ 
+
+ align:start position:0%
+that Roman kids would play with and you
+know it had an axle and had this you
+
+ align:start position:0%
+know it had an axle and had this you
+ 
+
+ align:start position:0%
+know it had an axle and had this you
+know little you heated up with a candle
+
+ align:start position:0%
+know little you heated up with a candle
+ 
+
+ align:start position:0%
+know little you heated up with a candle
+or something and then this little thing
+
+ align:start position:0%
+or something and then this little thing
+ 
+
+ align:start position:0%
+or something and then this little thing
+would spin around puffing away because
+
+ align:start position:0%
+would spin around puffing away because
+ 
+
+ align:start position:0%
+would spin around puffing away because
+it would you know water would boil and
+
+ align:start position:0%
+it would you know water would boil and
+ 
+
+ align:start position:0%
+it would you know water would boil and
+so forth and would sort of spin around
+
+ align:start position:0%
+so forth and would sort of spin around
+ 
+
+ align:start position:0%
+so forth and would sort of spin around
+Romer would say that the reason why
+
+ align:start position:0%
+Romer would say that the reason why
+ 
+
+ align:start position:0%
+Romer would say that the reason why
+Romans didn't take the step of putting
+
+ align:start position:0%
+Romans didn't take the step of putting
+ 
+
+ align:start position:0%
+Romans didn't take the step of putting
+rails on their roads and sticking the
+
+ align:start position:0%
+rails on their roads and sticking the
+ 
+
+ align:start position:0%
+rails on their roads and sticking the
+steam engines on the rails was that they
+
+ align:start position:0%
+steam engines on the rails was that they
+ 
+
+ align:start position:0%
+steam engines on the rails was that they
+did not have enough human capital
+
+ align:start position:0%
+did not have enough human capital
+ 
+
+ align:start position:0%
+did not have enough human capital
+engaged in research in other words they
+
+ align:start position:0%
+engaged in research in other words they
+ 
+
+ align:start position:0%
+engaged in research in other words they
+didn't have a big enough group of people
+
+ align:start position:0%
+didn't have a big enough group of people
+ 
+
+ align:start position:0%
+didn't have a big enough group of people
+that were talented and well-educated
+
+ align:start position:0%
+that were talented and well-educated
+ 
+
+ align:start position:0%
+that were talented and well-educated
+that were figuring out how to move this
+
+ align:start position:0%
+that were figuring out how to move this
+ 
+
+ align:start position:0%
+that were figuring out how to move this
+toy steam system to an actual technology
+
+ align:start position:0%
+toy steam system to an actual technology
+ 
+
+ align:start position:0%
+toy steam system to an actual technology
+advanced you know moving through the
+
+ align:start position:0%
+advanced you know moving through the
+ 
+
+ align:start position:0%
+advanced you know moving through the
+innovation and invention and innovation
+
+ align:start position:0%
+innovation and invention and innovation
+ 
+
+ align:start position:0%
+innovation and invention and innovation
+stages so the human human capital
+
+ align:start position:0%
+stages so the human human capital
+ 
+
+ align:start position:0%
+stages so the human human capital
+engaged in research would have been was
+
+ align:start position:0%
+engaged in research would have been was
+ 
+
+ align:start position:0%
+engaged in research would have been was
+the critical determinant factor about
+
+ align:start position:0%
+the critical determinant factor about
+ 
+
+ align:start position:0%
+the critical determinant factor about
+why they didn't put these pieces
+
+ align:start position:0%
+why they didn't put these pieces
+ 
+
+ align:start position:0%
+why they didn't put these pieces
+together right so it's not just doing a
+
+ align:start position:0%
+together right so it's not just doing a
+ 
+
+ align:start position:0%
+together right so it's not just doing a
+bunch of research
+
+ align:start position:0%
+bunch of research
+ 
+
+ align:start position:0%
+bunch of research
+you've got to have the talent base doing
+
+ align:start position:0%
+you've got to have the talent base doing
+ 
+
+ align:start position:0%
+you've got to have the talent base doing
+that research and that that will be a
+
+ align:start position:0%
+that research and that that will be a
+ 
+
+ align:start position:0%
+that research and that that will be a
+determining factor in whether or not
+
+ align:start position:0%
+determining factor in whether or not
+ 
+
+ align:start position:0%
+determining factor in whether or not
+you're going to get to the stage of
+
+ align:start position:0%
+you're going to get to the stage of
+ 
+
+ align:start position:0%
+you're going to get to the stage of
+technological advance so you follow me
+
+ align:start position:0%
+technological advance so you follow me
+ 
+
+ align:start position:0%
+technological advance so you follow me
+so it's again that phrasing is human
+
+ align:start position:0%
+so it's again that phrasing is human
+ 
+
+ align:start position:0%
+so it's again that phrasing is human
+capital engagement research if you lack
+
+ align:start position:0%
+capital engagement research if you lack
+ 
+
+ align:start position:0%
+capital engagement research if you lack
+human capital engaged in research you
+
+ align:start position:0%
+human capital engaged in research you
+ 
+
+ align:start position:0%
+human capital engaged in research you
+get economic stagnation all right let's
+
+ align:start position:0%
+get economic stagnation all right let's
+ 
+
+ align:start position:0%
+get economic stagnation all right let's
+do another picture medieval Europe right
+
+ align:start position:0%
+do another picture medieval Europe right
+ 
+
+ align:start position:0%
+do another picture medieval Europe right
+let's face it there's no human capital
+
+ align:start position:0%
+let's face it there's no human capital
+ 
+
+ align:start position:0%
+let's face it there's no human capital
+engagement research maybe a few
+
+ align:start position:0%
+engagement research maybe a few
+ 
+
+ align:start position:0%
+engagement research maybe a few
+alchemists you know poking around in
+
+ align:start position:0%
+alchemists you know poking around in
+ 
+
+ align:start position:0%
+alchemists you know poking around in
+dungeons right that's it all right so
+
+ align:start position:0%
+dungeons right that's it all right so
+ 
+
+ align:start position:0%
+dungeons right that's it all right so
+what is their economic growth in
+
+ align:start position:0%
+what is their economic growth in
+ 
+
+ align:start position:0%
+what is their economic growth in
+medieval Europe not really right I mean
+
+ align:start position:0%
+medieval Europe not really right I mean
+ 
+
+ align:start position:0%
+medieval Europe not really right I mean
+they learn something about castle
+
+ align:start position:0%
+they learn something about castle
+ 
+
+ align:start position:0%
+they learn something about castle
+building but a lot of that came from the
+
+ align:start position:0%
+building but a lot of that came from the
+ 
+
+ align:start position:0%
+building but a lot of that came from the
+Romans anyway economic growth basically
+
+ align:start position:0%
+Romans anyway economic growth basically
+ 
+
+ align:start position:0%
+Romans anyway economic growth basically
+consisted of you know hiring a
+
+ align:start position:0%
+consisted of you know hiring a
+ 
+
+ align:start position:0%
+consisted of you know hiring a
+motorcycle gang and you know putting on
+
+ align:start position:0%
+motorcycle gang and you know putting on
+ 
+
+ align:start position:0%
+motorcycle gang and you know putting on
+a horses and riding over to the next
+
+ align:start position:0%
+a horses and riding over to the next
+ 
+
+ align:start position:0%
+a horses and riding over to the next
+guy's castle and looting the place
+
+ align:start position:0%
+guy's castle and looting the place
+ 
+
+ align:start position:0%
+guy's castle and looting the place
+that's how you got gained right that was
+
+ align:start position:0%
+that's how you got gained right that was
+ 
+
+ align:start position:0%
+that's how you got gained right that was
+the economic growth model it was
+
+ align:start position:0%
+the economic growth model it was
+ 
+
+ align:start position:0%
+the economic growth model it was
+stealing right it was like piracy right
+
+ align:start position:0%
+stealing right it was like piracy right
+ 
+
+ align:start position:0%
+stealing right it was like piracy right
+there was no economic growth model so
+
+ align:start position:0%
+there was no economic growth model so
+ 
+
+ align:start position:0%
+there was no economic growth model so
+it's not until the Industrial Revolution
+
+ align:start position:0%
+it's not until the Industrial Revolution
+ 
+
+ align:start position:0%
+it's not until the Industrial Revolution
+that you get a significant amount of
+
+ align:start position:0%
+that you get a significant amount of
+ 
+
+ align:start position:0%
+that you get a significant amount of
+human capital engaged in research that's
+
+ align:start position:0%
+human capital engaged in research that's
+ 
+
+ align:start position:0%
+human capital engaged in research that's
+going to be able to nurture these
+
+ align:start position:0%
+going to be able to nurture these
+ 
+
+ align:start position:0%
+going to be able to nurture these
+technology advances so we know we have
+
+ align:start position:0%
+technology advances so we know we have
+ 
+
+ align:start position:0%
+technology advances so we know we have
+our second innovation factor now the
+
+ align:start position:0%
+our second innovation factor now the
+ 
+
+ align:start position:0%
+our second innovation factor now the
+first factor solo and again I'm
+
+ align:start position:0%
+first factor solo and again I'm
+ 
+
+ align:start position:0%
+first factor solo and again I'm
+summarizing here you got to do R&D right
+
+ align:start position:0%
+summarizing here you got to do R&D right
+ 
+
+ align:start position:0%
+summarizing here you got to do R&D right
+technological and related innovation you
+
+ align:start position:0%
+technological and related innovation you
+ 
+
+ align:start position:0%
+technological and related innovation you
+got to do some R&D Romer second factor
+
+ align:start position:0%
+got to do some R&D Romer second factor
+ 
+
+ align:start position:0%
+got to do some R&D Romer second factor
+human capital engagement research you
+
+ align:start position:0%
+human capital engagement research you
+ 
+
+ align:start position:0%
+human capital engagement research you
+kind of have the talent base behind that
+
+ align:start position:0%
+kind of have the talent base behind that
+ 
+
+ align:start position:0%
+kind of have the talent base behind that
+or indecent behind that technological
+
+ align:start position:0%
+or indecent behind that technological
+ 
+
+ align:start position:0%
+or indecent behind that technological
+advance is going to be the talent base
+
+ align:start position:0%
+advance is going to be the talent base
+ 
+
+ align:start position:0%
+advance is going to be the talent base
+so that gives us two factors and you
+
+ align:start position:0%
+so that gives us two factors and you
+ 
+
+ align:start position:0%
+so that gives us two factors and you
+guys can now look at any country or a
+
+ align:start position:0%
+guys can now look at any country or a
+ 
+
+ align:start position:0%
+guys can now look at any country or a
+society or region and you can now say oh
+
+ align:start position:0%
+society or region and you can now say oh
+ 
+
+ align:start position:0%
+society or region and you can now say oh
+I can start to look at that I can look
+
+ align:start position:0%
+I can start to look at that I can look
+ 
+
+ align:start position:0%
+I can start to look at that I can look
+at hey are they doing
+
+ align:start position:0%
+at hey are they doing
+ 
+
+ align:start position:0%
+at hey are they doing
+a bunch of R&D and to what's their
+
+ align:start position:0%
+a bunch of R&D and to what's their
+ 
+
+ align:start position:0%
+a bunch of R&D and to what's their
+talent base like right Romer develops
+
+ align:start position:0%
+talent base like right Romer develops
+ 
+
+ align:start position:0%
+talent base like right Romer develops
+something that he calls prospector
+
+ align:start position:0%
+something that he calls prospector
+ 
+
+ align:start position:0%
+something that he calls prospector
+theory now that's not in this reading
+
+ align:start position:0%
+theory now that's not in this reading
+ 
+
+ align:start position:0%
+theory now that's not in this reading
+since some of us somewhat later work but
+
+ align:start position:0%
+since some of us somewhat later work but
+ 
+
+ align:start position:0%
+since some of us somewhat later work but
+it's a really it's an intriguing idea
+
+ align:start position:0%
+it's a really it's an intriguing idea
+ 
+
+ align:start position:0%
+it's a really it's an intriguing idea
+and it's very simple and straightforward
+
+ align:start position:0%
+and it's very simple and straightforward
+ 
+
+ align:start position:0%
+and it's very simple and straightforward
+but it'll help you in making these
+
+ align:start position:0%
+but it'll help you in making these
+ 
+
+ align:start position:0%
+but it'll help you in making these
+assessments so Romer looks at the
+
+ align:start position:0%
+assessments so Romer looks at the
+ 
+
+ align:start position:0%
+assessments so Romer looks at the
+chemical engineering industry in Europe
+
+ align:start position:0%
+chemical engineering industry in Europe
+ 
+
+ align:start position:0%
+chemical engineering industry in Europe
+in the late 1800s and he notices that
+
+ align:start position:0%
+in the late 1800s and he notices that
+ 
+
+ align:start position:0%
+in the late 1800s and he notices that
+there are two countries that dominate
+
+ align:start position:0%
+there are two countries that dominate
+ 
+
+ align:start position:0%
+there are two countries that dominate
+these early chemical industries Germany
+
+ align:start position:0%
+these early chemical industries Germany
+ 
+
+ align:start position:0%
+these early chemical industries Germany
+and Britain they have the big emerging
+
+ align:start position:0%
+and Britain they have the big emerging
+ 
+
+ align:start position:0%
+and Britain they have the big emerging
+chemical industries and other countries
+
+ align:start position:0%
+chemical industries and other countries
+ 
+
+ align:start position:0%
+chemical industries and other countries
+are doing stuff in this area they don't
+
+ align:start position:0%
+are doing stuff in this area they don't
+ 
+
+ align:start position:0%
+are doing stuff in this area they don't
+have anything like what Germany and
+
+ align:start position:0%
+have anything like what Germany and
+ 
+
+ align:start position:0%
+have anything like what Germany and
+Britain are up to stemming looks behind
+
+ align:start position:0%
+Britain are up to stemming looks behind
+ 
+
+ align:start position:0%
+Britain are up to stemming looks behind
+those industries and finds that both
+
+ align:start position:0%
+those industries and finds that both
+ 
+
+ align:start position:0%
+those industries and finds that both
+Germany and Britain have very strong
+
+ align:start position:0%
+Germany and Britain have very strong
+ 
+
+ align:start position:0%
+Germany and Britain have very strong
+education systems for chemical engineers
+
+ align:start position:0%
+education systems for chemical engineers
+ 
+
+ align:start position:0%
+education systems for chemical engineers
+so they are creating a talent base that
+
+ align:start position:0%
+so they are creating a talent base that
+ 
+
+ align:start position:0%
+so they are creating a talent base that
+enables the advances that they are
+
+ align:start position:0%
+enables the advances that they are
+ 
+
+ align:start position:0%
+enables the advances that they are
+making in in chemical engineering so the
+
+ align:start position:0%
+making in in chemical engineering so the
+ 
+
+ align:start position:0%
+making in in chemical engineering so the
+idea is you got a field of prospectors
+
+ align:start position:0%
+idea is you got a field of prospectors
+ 
+
+ align:start position:0%
+idea is you got a field of prospectors
+so let's take it back to the origin of
+
+ align:start position:0%
+so let's take it back to the origin of
+ 
+
+ align:start position:0%
+so let's take it back to the origin of
+the idea so it's the California Gold
+
+ align:start position:0%
+the idea so it's the California Gold
+ 
+
+ align:start position:0%
+the idea so it's the California Gold
+Rush and it's 1848 it's not 18-49 yet
+
+ align:start position:0%
+Rush and it's 1848 it's not 18-49 yet
+ 
+
+ align:start position:0%
+Rush and it's 1848 it's not 18-49 yet
+right it's 1848 and you've got you know
+
+ align:start position:0%
+right it's 1848 and you've got you know
+ 
+
+ align:start position:0%
+right it's 1848 and you've got you know
+five or six people hanging around the
+
+ align:start position:0%
+five or six people hanging around the
+ 
+
+ align:start position:0%
+five or six people hanging around the
+Sacramento River occasionally sticking a
+
+ align:start position:0%
+Sacramento River occasionally sticking a
+ 
+
+ align:start position:0%
+Sacramento River occasionally sticking a
+pan into the river
+
+ align:start position:0%
+pan into the river
+ 
+
+ align:start position:0%
+pan into the river
+alright then a year later 18-49
+
+ align:start position:0%
+alright then a year later 18-49
+ 
+
+ align:start position:0%
+alright then a year later 18-49
+you've got 250,000 people sticking pans
+
+ align:start position:0%
+you've got 250,000 people sticking pans
+ 
+
+ align:start position:0%
+you've got 250,000 people sticking pans
+into the Sacramento River and every
+
+ align:start position:0%
+into the Sacramento River and every
+ 
+
+ align:start position:0%
+into the Sacramento River and every
+trace of bowls you know part of that
+
+ align:start position:0%
+trace of bowls you know part of that
+ 
+
+ align:start position:0%
+trace of bowls you know part of that
+river system up every Creek what do you
+
+ align:start position:0%
+river system up every Creek what do you
+ 
+
+ align:start position:0%
+river system up every Creek what do you
+think you find more gold with 250,000
+
+ align:start position:0%
+think you find more gold with 250,000
+ 
+
+ align:start position:0%
+think you find more gold with 250,000
+people you bet
+
+ align:start position:0%
+people you bet
+ 
+
+ align:start position:0%
+people you bet
+right staggering amount of gold gets
+
+ align:start position:0%
+right staggering amount of gold gets
+ 
+
+ align:start position:0%
+right staggering amount of gold gets
+down that's prospector Theory
+
+ align:start position:0%
+down that's prospector Theory
+ 
+
+ align:start position:0%
+down that's prospector Theory
+in other words and it's a little more
+
+ align:start position:0%
+in other words and it's a little more
+ 
+
+ align:start position:0%
+in other words and it's a little more
+sophisticated than that but you're gonna
+
+ align:start position:0%
+sophisticated than that but you're gonna
+ 
+
+ align:start position:0%
+sophisticated than that but you're gonna
+find more gold if you've got more
+
+ align:start position:0%
+find more gold if you've got more
+ 
+
+ align:start position:0%
+find more gold if you've got more
+prospectors on the problem now you have
+
+ align:start position:0%
+prospectors on the problem now you have
+ 
+
+ align:start position:0%
+prospectors on the problem now you have
+to train those prospectors it can't be
+
+ align:start position:0%
+to train those prospectors it can't be
+ 
+
+ align:start position:0%
+to train those prospectors it can't be
+totally amateur hour it's much better if
+
+ align:start position:0%
+totally amateur hour it's much better if
+ 
+
+ align:start position:0%
+totally amateur hour it's much better if
+you have trained sophisticated
+
+ align:start position:0%
+you have trained sophisticated
+ 
+
+ align:start position:0%
+you have trained sophisticated
+prospectors like Britain in German
+
+ align:start position:0%
+prospectors like Britain in German
+ 
+
+ align:start position:0%
+prospectors like Britain in German
+Britain and Germany did with the
+
+ align:start position:0%
+Britain and Germany did with the
+ 
+
+ align:start position:0%
+Britain and Germany did with the
+chemical engineering sector so you need
+
+ align:start position:0%
+chemical engineering sector so you need
+ 
+
+ align:start position:0%
+chemical engineering sector so you need
+that human capital engaged in the
+
+ align:start position:0%
+that human capital engaged in the
+ 
+
+ align:start position:0%
+that human capital engaged in the
+research system if the human capital is
+
+ align:start position:0%
+research system if the human capital is
+ 
+
+ align:start position:0%
+research system if the human capital is
+driving cabs it doesn't do any good
+
+ align:start position:0%
+driving cabs it doesn't do any good
+ 
+
+ align:start position:0%
+driving cabs it doesn't do any good
+you've got to have that human capital
+
+ align:start position:0%
+you've got to have that human capital
+ 
+
+ align:start position:0%
+you've got to have that human capital
+engaged in that system of research so
+
+ align:start position:0%
+engaged in that system of research so
+ 
+
+ align:start position:0%
+engaged in that system of research so
+you can then now make a further
+
+ align:start position:0%
+you can then now make a further
+ 
+
+ align:start position:0%
+you can then now make a further
+extrapolation on what roamers thinking
+
+ align:start position:0%
+extrapolation on what roamers thinking
+ 
+
+ align:start position:0%
+extrapolation on what roamers thinking
+about right you have a way now of
+
+ align:start position:0%
+about right you have a way now of
+ 
+
+ align:start position:0%
+about right you have a way now of
+looking at fundamental strengths of
+
+ align:start position:0%
+looking at fundamental strengths of
+ 
+
+ align:start position:0%
+looking at fundamental strengths of
+innovation system its R&D system and the
+
+ align:start position:0%
+innovation system its R&D system and the
+ 
+
+ align:start position:0%
+innovation system its R&D system and the
+talent in that system
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+questions
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+two weeks don't disappear you include
+
+ align:start position:0%
+two weeks don't disappear you include
+ 
+
+ align:start position:0%
+two weeks don't disappear you include
+questions of include really good and
+
+ align:start position:0%
+questions of include really good and
+ 
+
+ align:start position:0%
+questions of include really good and
+timely point so if Romer is right and
+
+ align:start position:0%
+timely point so if Romer is right and
+ 
+
+ align:start position:0%
+timely point so if Romer is right and
+you want a large number of well-trained
+
+ align:start position:0%
+you want a large number of well-trained
+ 
+
+ align:start position:0%
+you want a large number of well-trained
+prospectors and you're fencing off
+
+ align:start position:0%
+prospectors and you're fencing off
+ 
+
+ align:start position:0%
+prospectors and you're fencing off
+significant parts you society from that
+
+ align:start position:0%
+significant parts you society from that
+ 
+
+ align:start position:0%
+significant parts you society from that
+prospector pool you're doing something
+
+ align:start position:0%
+prospector pool you're doing something
+ 
+
+ align:start position:0%
+prospector pool you're doing something
+really stupid right just fundamental
+
+ align:start position:0%
+really stupid right just fundamental
+ 
+
+ align:start position:0%
+really stupid right just fundamental
+isn't that that's how simple and
+
+ align:start position:0%
+isn't that that's how simple and
+ 
+
+ align:start position:0%
+isn't that that's how simple and
+straightforward prospector theory is
+
+ align:start position:0%
+straightforward prospector theory is
+ 
+
+ align:start position:0%
+straightforward prospector theory is
+right that's why what's been happening
+
+ align:start position:0%
+right that's why what's been happening
+ 
+
+ align:start position:0%
+right that's why what's been happening
+over the last few weeks makes me so
+
+ align:start position:0%
+over the last few weeks makes me so
+ 
+
+ align:start position:0%
+over the last few weeks makes me so
+nervous because the u.s. developed an
+
+ align:start position:0%
+nervous because the u.s. developed an
+ 
+
+ align:start position:0%
+nervous because the u.s. developed an
+innovation system that worked on
+
+ align:start position:0%
+innovation system that worked on
+ 
+
+ align:start position:0%
+innovation system that worked on
+encouraging talent from everywhere to
+
+ align:start position:0%
+encouraging talent from everywhere to
+ 
+
+ align:start position:0%
+encouraging talent from everywhere to
+come here and it's a huge innovation
+
+ align:start position:0%
+come here and it's a huge innovation
+ 
+
+ align:start position:0%
+come here and it's a huge innovation
+advantage right it's huge in other words
+
+ align:start position:0%
+advantage right it's huge in other words
+ 
+
+ align:start position:0%
+advantage right it's huge in other words
+if you're running an innovation system
+
+ align:start position:0%
+if you're running an innovation system
+ 
+
+ align:start position:0%
+if you're running an innovation system
+and sucking in talent from everywhere to
+
+ align:start position:0%
+and sucking in talent from everywhere to
+ 
+
+ align:start position:0%
+and sucking in talent from everywhere to
+help field it right to help staff it
+
+ align:start position:0%
+help field it right to help staff it
+ 
+
+ align:start position:0%
+help field it right to help staff it
+that's really interesting compared to
+
+ align:start position:0%
+that's really interesting compared to
+ 
+
+ align:start position:0%
+that's really interesting compared to
+running an innovation system where you
+
+ align:start position:0%
+running an innovation system where you
+ 
+
+ align:start position:0%
+running an innovation system where you
+put fences around your borders not very
+
+ align:start position:0%
+put fences around your borders not very
+ 
+
+ align:start position:0%
+put fences around your borders not very
+smart
+
+ align:start position:0%
+smart
+ 
+
+ align:start position:0%
+smart
+that's why 400 tech companies have
+
+ align:start position:0%
+that's why 400 tech companies have
+ 
+
+ align:start position:0%
+that's why 400 tech companies have
+joined the amicus brief in the case
+
+ align:start position:0%
+joined the amicus brief in the case
+ 
+
+ align:start position:0%
+joined the amicus brief in the case
+that's being argued today right because
+
+ align:start position:0%
+that's being argued today right because
+ 
+
+ align:start position:0%
+that's being argued today right because
+they understand this so there is a huge
+
+ align:start position:0%
+they understand this so there is a huge
+ 
+
+ align:start position:0%
+they understand this so there is a huge
+inclusion piece to this fundamental idea
+
+ align:start position:0%
+inclusion piece to this fundamental idea
+ 
+
+ align:start position:0%
+inclusion piece to this fundamental idea
+Russia yeah I don't think we're there
+
+ align:start position:0%
+Russia yeah I don't think we're there
+ 
+
+ align:start position:0%
+Russia yeah I don't think we're there
+yet that's it's always an important
+
+ align:start position:0%
+yet that's it's always an important
+ 
+
+ align:start position:0%
+yet that's it's always an important
+question does a society have too much
+
+ align:start position:0%
+question does a society have too much
+ 
+
+ align:start position:0%
+question does a society have too much
+innovation going on right and I think
+
+ align:start position:0%
+innovation going on right and I think
+ 
+
+ align:start position:0%
+innovation going on right and I think
+we're not remotely close to that I don't
+
+ align:start position:0%
+we're not remotely close to that I don't
+ 
+
+ align:start position:0%
+we're not remotely close to that I don't
+think we're close to that right in other
+
+ align:start position:0%
+think we're close to that right in other
+ 
+
+ align:start position:0%
+think we're close to that right in other
+words we've got if technological and
+
+ align:start position:0%
+words we've got if technological and
+ 
+
+ align:start position:0%
+words we've got if technological and
+related innovation is the key driver for
+
+ align:start position:0%
+related innovation is the key driver for
+ 
+
+ align:start position:0%
+related innovation is the key driver for
+growth and we've got you know 2% growth
+
+ align:start position:0%
+growth and we've got you know 2% growth
+ 
+
+ align:start position:0%
+growth and we've got you know 2% growth
+at the moment maybe improving the
+
+ align:start position:0%
+at the moment maybe improving the
+ 
+
+ align:start position:0%
+at the moment maybe improving the
+innovation system might be a way to
+
+ align:start position:0%
+innovation system might be a way to
+ 
+
+ align:start position:0%
+innovation system might be a way to
+improve our growth rate therefore one
+
+ align:start position:0%
+improve our growth rate therefore one
+ 
+
+ align:start position:0%
+improve our growth rate therefore one
+way of looking at that is to get more
+
+ align:start position:0%
+way of looking at that is to get more
+ 
+
+ align:start position:0%
+way of looking at that is to get more
+prospectors on the problem right so I
+
+ align:start position:0%
+prospectors on the problem right so I
+ 
+
+ align:start position:0%
+prospectors on the problem right so I
+mean that's a simple-minded idea but the
+
+ align:start position:0%
+mean that's a simple-minded idea but the
+ 
+
+ align:start position:0%
+mean that's a simple-minded idea but the
+prospector theory is pretty
+
+ align:start position:0%
+prospector theory is pretty
+ 
+
+ align:start position:0%
+prospector theory is pretty
+straightforward
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+it's supposed to be didn't have too many
+
+ align:start position:0%
+it's supposed to be didn't have too many
+ 
+
+ align:start position:0%
+it's supposed to be didn't have too many
+Vikings
+
+ align:start position:0%
+Vikings
+ 
+
+ align:start position:0%
+Vikings
+I think we're just so far away from this
+
+ align:start position:0%
+I think we're just so far away from this
+ 
+
+ align:start position:0%
+I think we're just so far away from this
+that we it's it's not really worthy of
+
+ align:start position:0%
+that we it's it's not really worthy of
+ 
+
+ align:start position:0%
+that we it's it's not really worthy of
+thought I mean look periodically in the
+
+ align:start position:0%
+thought I mean look periodically in the
+ 
+
+ align:start position:0%
+thought I mean look periodically in the
+science community there's panic about
+
+ align:start position:0%
+science community there's panic about
+ 
+
+ align:start position:0%
+science community there's panic about
+heavens we've trained too many
+
+ align:start position:0%
+heavens we've trained too many
+ 
+
+ align:start position:0%
+heavens we've trained too many
+physicists right they're only going to
+
+ align:start position:0%
+physicists right they're only going to
+ 
+
+ align:start position:0%
+physicists right they're only going to
+be able to drive cabs right that we're
+
+ align:start position:0%
+be able to drive cabs right that we're
+ 
+
+ align:start position:0%
+be able to drive cabs right that we're
+over we're in an oversupply situation
+
+ align:start position:0%
+over we're in an oversupply situation
+ 
+
+ align:start position:0%
+over we're in an oversupply situation
+and every once in a while you get you
+
+ align:start position:0%
+and every once in a while you get you
+ 
+
+ align:start position:0%
+and every once in a while you get you
+know cycles that frankly largely
+
+ align:start position:0%
+know cycles that frankly largely
+ 
+
+ align:start position:0%
+know cycles that frankly largely
+resemble the business cycles that tell
+
+ align:start position:0%
+resemble the business cycles that tell
+ 
+
+ align:start position:0%
+resemble the business cycles that tell
+us that we're at those were we may be at
+
+ align:start position:0%
+us that we're at those were we may be at
+ 
+
+ align:start position:0%
+us that we're at those were we may be at
+those stages and panic hits the science
+
+ align:start position:0%
+those stages and panic hits the science
+ 
+
+ align:start position:0%
+those stages and panic hits the science
+community that we're over we're training
+
+ align:start position:0%
+community that we're over we're training
+ 
+
+ align:start position:0%
+community that we're over we're training
+too many numbers but if we go back and
+
+ align:start position:0%
+too many numbers but if we go back and
+ 
+
+ align:start position:0%
+too many numbers but if we go back and
+think about what we've been learning
+
+ align:start position:0%
+think about what we've been learning
+ 
+
+ align:start position:0%
+think about what we've been learning
+here which is that technological and
+
+ align:start position:0%
+here which is that technological and
+ 
+
+ align:start position:0%
+here which is that technological and
+related innovation is a dynamic factor
+
+ align:start position:0%
+related innovation is a dynamic factor
+ 
+
+ align:start position:0%
+related innovation is a dynamic factor
+in your society in your economy right it
+
+ align:start position:0%
+in your society in your economy right it
+ 
+
+ align:start position:0%
+in your society in your economy right it
+is core to the way in which you grow
+
+ align:start position:0%
+is core to the way in which you grow
+ 
+
+ align:start position:0%
+is core to the way in which you grow
+then the talent base is a dynamic factor
+
+ align:start position:0%
+then the talent base is a dynamic factor
+ 
+
+ align:start position:0%
+then the talent base is a dynamic factor
+too and you don't want to restrict a
+
+ align:start position:0%
+too and you don't want to restrict a
+ 
+
+ align:start position:0%
+too and you don't want to restrict a
+dynamic factor because you're gonna
+
+ align:start position:0%
+dynamic factor because you're gonna
+ 
+
+ align:start position:0%
+dynamic factor because you're gonna
+limit your dynamism right don't shut
+
+ align:start position:0%
+limit your dynamism right don't shut
+ 
+
+ align:start position:0%
+limit your dynamism right don't shut
+down dynamic factors let them thrive the
+
+ align:start position:0%
+down dynamic factors let them thrive the
+ 
+
+ align:start position:0%
+down dynamic factors let them thrive the
+key here is not the problem science has
+
+ align:start position:0%
+key here is not the problem science has
+ 
+
+ align:start position:0%
+key here is not the problem science has
+it's not able to extrapolate to a larger
+
+ align:start position:0%
+it's not able to extrapolate to a larger
+ 
+
+ align:start position:0%
+it's not able to extrapolate to a larger
+use of its talent base right just
+
+ align:start position:0%
+use of its talent base right just
+ 
+
+ align:start position:0%
+use of its talent base right just
+because there may not be enough jobs in
+
+ align:start position:0%
+because there may not be enough jobs in
+ 
+
+ align:start position:0%
+because there may not be enough jobs in
+formal academia for all of the
+
+ align:start position:0%
+formal academia for all of the
+ 
+
+ align:start position:0%
+formal academia for all of the
+scientists we're training doesn't mean
+
+ align:start position:0%
+scientists we're training doesn't mean
+ 
+
+ align:start position:0%
+scientists we're training doesn't mean
+that there aren't really important
+
+ align:start position:0%
+that there aren't really important
+ 
+
+ align:start position:0%
+that there aren't really important
+functions and roles they can play
+
+ align:start position:0%
+functions and roles they can play
+ 
+
+ align:start position:0%
+functions and roles they can play
+elsewhere right so two-thirds of US
+
+ align:start position:0%
+elsewhere right so two-thirds of US
+ 
+
+ align:start position:0%
+elsewhere right so two-thirds of US
+scientists and engineers are employed by
+
+ align:start position:0%
+scientists and engineers are employed by
+ 
+
+ align:start position:0%
+scientists and engineers are employed by
+manufacturing industries right that's
+
+ align:start position:0%
+manufacturing industries right that's
+ 
+
+ align:start position:0%
+manufacturing industries right that's
+where actually most of the jobs are
+
+ align:start position:0%
+where actually most of the jobs are
+ 
+
+ align:start position:0%
+where actually most of the jobs are
+right not in the Academy and yet the
+
+ align:start position:0%
+right not in the Academy and yet the
+ 
+
+ align:start position:0%
+right not in the Academy and yet the
+scientific community views it as oh it's
+
+ align:start position:0%
+scientific community views it as oh it's
+ 
+
+ align:start position:0%
+scientific community views it as oh it's
+the Academy and that's where the
+
+ align:start position:0%
+the Academy and that's where the
+ 
+
+ align:start position:0%
+the Academy and that's where the
+oversupply problem is but maybe the key
+
+ align:start position:0%
+oversupply problem is but maybe the key
+ 
+
+ align:start position:0%
+oversupply problem is but maybe the key
+here is equipping that talent base with
+
+ align:start position:0%
+here is equipping that talent base with
+ 
+
+ align:start position:0%
+here is equipping that talent base with
+a whole new set of tools that enable
+
+ align:start position:0%
+a whole new set of tools that enable
+ 
+
+ align:start position:0%
+a whole new set of tools that enable
+them to play a broader role than simply
+
+ align:start position:0%
+them to play a broader role than simply
+ 
+
+ align:start position:0%
+them to play a broader role than simply
+supporting an academy right maybe that
+
+ align:start position:0%
+supporting an academy right maybe that
+ 
+
+ align:start position:0%
+supporting an academy right maybe that
+would be a smarter talent based
+
+ align:start position:0%
+would be a smarter talent based
+ 
+
+ align:start position:0%
+would be a smarter talent based
+trainings idea right
+
+ align:start position:0%
+trainings idea right
+ 
+
+ align:start position:0%
+trainings idea right
+maybe you give him you know
+
+ align:start position:0%
+maybe you give him you know
+ 
+
+ align:start position:0%
+maybe you give him you know
+entrepreneurship classes so they can
+
+ align:start position:0%
+entrepreneurship classes so they can
+ 
+
+ align:start position:0%
+entrepreneurship classes so they can
+think about starting their own startups
+
+ align:start position:0%
+think about starting their own startups
+ 
+
+ align:start position:0%
+think about starting their own startups
+maybe they get business miners right so
+
+ align:start position:0%
+maybe they get business miners right so
+ 
+
+ align:start position:0%
+maybe they get business miners right so
+they can do startup stuff maybe they get
+
+ align:start position:0%
+they can do startup stuff maybe they get
+ 
+
+ align:start position:0%
+they can do startup stuff maybe they get
+other kinds of training that gives them
+
+ align:start position:0%
+other kinds of training that gives them
+ 
+
+ align:start position:0%
+other kinds of training that gives them
+additional skill sets in addition to
+
+ align:start position:0%
+additional skill sets in addition to
+ 
+
+ align:start position:0%
+additional skill sets in addition to
+kind of classical research skill sets I
+
+ align:start position:0%
+kind of classical research skill sets I
+ 
+
+ align:start position:0%
+kind of classical research skill sets I
+think that would probably be a better
+
+ align:start position:0%
+think that would probably be a better
+ 
+
+ align:start position:0%
+think that would probably be a better
+answer than attempting to restrict the
+
+ align:start position:0%
+answer than attempting to restrict the
+ 
+
+ align:start position:0%
+answer than attempting to restrict the
+supply the historical US growth rate is
+
+ align:start position:0%
+supply the historical US growth rate is
+ 
+
+ align:start position:0%
+supply the historical US growth rate is
+3% that's starting to look pretty good
+
+ align:start position:0%
+3% that's starting to look pretty good
+ 
+
+ align:start position:0%
+3% that's starting to look pretty good
+cuz we haven't been there for quite some
+
+ align:start position:0%
+cuz we haven't been there for quite some
+ 
+
+ align:start position:0%
+cuz we haven't been there for quite some
+time it makes a big difference you all
+
+ align:start position:0%
+time it makes a big difference you all
+ 
+
+ align:start position:0%
+time it makes a big difference you all
+probably don't remember this too well
+
+ align:start position:0%
+probably don't remember this too well
+ 
+
+ align:start position:0%
+probably don't remember this too well
+but the dynamic quality and feel of the
+
+ align:start position:0%
+but the dynamic quality and feel of the
+ 
+
+ align:start position:0%
+but the dynamic quality and feel of the
+US economy in the 1990s was very
+
+ align:start position:0%
+US economy in the 1990s was very
+ 
+
+ align:start position:0%
+US economy in the 1990s was very
+different the sense of opportunity that
+
+ align:start position:0%
+different the sense of opportunity that
+ 
+
+ align:start position:0%
+different the sense of opportunity that
+was there was very powerful and it was
+
+ align:start position:0%
+was there was very powerful and it was
+ 
+
+ align:start position:0%
+was there was very powerful and it was
+pretty pervasive about society and if
+
+ align:start position:0%
+pretty pervasive about society and if
+ 
+
+ align:start position:0%
+pretty pervasive about society and if
+technological and related innovation
+
+ align:start position:0%
+technological and related innovation
+ 
+
+ align:start position:0%
+technological and related innovation
+tries growth and it's key to our growth
+
+ align:start position:0%
+tries growth and it's key to our growth
+ 
+
+ align:start position:0%
+tries growth and it's key to our growth
+rate then we the task is not how do you
+
+ align:start position:0%
+rate then we the task is not how do you
+ 
+
+ align:start position:0%
+rate then we the task is not how do you
+shut that down but how do you get back
+
+ align:start position:0%
+shut that down but how do you get back
+ 
+
+ align:start position:0%
+shut that down but how do you get back
+to a higher level growth rate I'd argue
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+[Music]
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+[Music]
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah I mean it's an interesting idea
+
+ align:start position:0%
+yeah I mean it's an interesting idea
+ 
+
+ align:start position:0%
+yeah I mean it's an interesting idea
+right and I do think that we do have too
+
+ align:start position:0%
+right and I do think that we do have too
+ 
+
+ align:start position:0%
+right and I do think that we do have too
+many empty kitchens at this point right
+
+ align:start position:0%
+many empty kitchens at this point right
+ 
+
+ align:start position:0%
+many empty kitchens at this point right
+that needs staffing up frankly they need
+
+ align:start position:0%
+that needs staffing up frankly they need
+ 
+
+ align:start position:0%
+that needs staffing up frankly they need
+a path to growth and you know getting to
+
+ align:start position:0%
+a path to growth and you know getting to
+ 
+
+ align:start position:0%
+a path to growth and you know getting to
+fourth generation nuclear power I mean
+
+ align:start position:0%
+fourth generation nuclear power I mean
+ 
+
+ align:start position:0%
+fourth generation nuclear power I mean
+that's you know that's an absolute core
+
+ align:start position:0%
+that's you know that's an absolute core
+ 
+
+ align:start position:0%
+that's you know that's an absolute core
+climate strategy in my view but I think
+
+ align:start position:0%
+climate strategy in my view but I think
+ 
+
+ align:start position:0%
+climate strategy in my view but I think
+it's increasingly widespread at MIT
+
+ align:start position:0%
+it's increasingly widespread at MIT
+ 
+
+ align:start position:0%
+it's increasingly widespread at MIT
+right and we're not staffing that
+
+ align:start position:0%
+right and we're not staffing that
+ 
+
+ align:start position:0%
+right and we're not staffing that
+revolution up in Romer's terms I'm not
+
+ align:start position:0%
+revolution up in Romer's terms I'm not
+ 
+
+ align:start position:0%
+revolution up in Romer's terms I'm not
+putting enough prospectors on the
+
+ align:start position:0%
+putting enough prospectors on the
+ 
+
+ align:start position:0%
+putting enough prospectors on the
+problem it's increasingly hard to
+
+ align:start position:0%
+problem it's increasingly hard to
+ 
+
+ align:start position:0%
+problem it's increasingly hard to
+organize startups that do something
+
+ align:start position:0%
+organize startups that do something
+ 
+
+ align:start position:0%
+organize startups that do something
+other than software in biotech because
+
+ align:start position:0%
+other than software in biotech because
+ 
+
+ align:start position:0%
+other than software in biotech because
+venture capital is just doing too well
+
+ align:start position:0%
+venture capital is just doing too well
+ 
+
+ align:start position:0%
+venture capital is just doing too well
+with those models and look there's
+
+ align:start position:0%
+with those models and look there's
+ 
+
+ align:start position:0%
+with those models and look there's
+nothing wrong with software in biotech
+
+ align:start position:0%
+nothing wrong with software in biotech
+ 
+
+ align:start position:0%
+nothing wrong with software in biotech
+it's you know it's important stuff so
+
+ align:start position:0%
+it's you know it's important stuff so
+ 
+
+ align:start position:0%
+it's you know it's important stuff so
+it's nothing wrong with what they're
+
+ align:start position:0%
+it's nothing wrong with what they're
+ 
+
+ align:start position:0%
+it's nothing wrong with what they're
+doing but we are not funding other
+
+ align:start position:0%
+doing but we are not funding other
+ 
+
+ align:start position:0%
+doing but we are not funding other
+technology sectors so we don't have a
+
+ align:start position:0%
+technology sectors so we don't have a
+ 
+
+ align:start position:0%
+technology sectors so we don't have a
+broad-based approach on technology
+
+ align:start position:0%
+broad-based approach on technology
+ 
+
+ align:start position:0%
+broad-based approach on technology
+advance so your metaphor Marteen of some
+
+ align:start position:0%
+advance so your metaphor Marteen of some
+ 
+
+ align:start position:0%
+advance so your metaphor Marteen of some
+empty kitchens we're emptying our
+
+ align:start position:0%
+empty kitchens we're emptying our
+ 
+
+ align:start position:0%
+empty kitchens we're emptying our
+kitchens on quote hard technologies
+
+ align:start position:0%
+kitchens on quote hard technologies
+ 
+
+ align:start position:0%
+kitchens on quote hard technologies
+where you'd have to manufacture
+
+ align:start position:0%
+where you'd have to manufacture
+ 
+
+ align:start position:0%
+where you'd have to manufacture
+something because the scale-up process
+
+ align:start position:0%
+something because the scale-up process
+ 
+
+ align:start position:0%
+something because the scale-up process
+is much harder for that financing system
+
+ align:start position:0%
+is much harder for that financing system
+ 
+
+ align:start position:0%
+is much harder for that financing system
+to muster then scaling up you know a
+
+ align:start position:0%
+to muster then scaling up you know a
+ 
+
+ align:start position:0%
+to muster then scaling up you know a
+software startup where it's
+
+ align:start position:0%
+software startup where it's
+ 
+
+ align:start position:0%
+software startup where it's
+infrastructures in the cloud and doesn't
+
+ align:start position:0%
+infrastructures in the cloud and doesn't
+ 
+
+ align:start position:0%
+infrastructures in the cloud and doesn't
+cost anything and can stale scale up
+
+ align:start position:0%
+cost anything and can stale scale up
+ 
+
+ align:start position:0%
+cost anything and can stale scale up
+very quickly with very limited amounts
+
+ align:start position:0%
+very quickly with very limited amounts
+ 
+
+ align:start position:0%
+very quickly with very limited amounts
+of capital it's much more complicated to
+
+ align:start position:0%
+of capital it's much more complicated to
+ 
+
+ align:start position:0%
+of capital it's much more complicated to
+stand up a new energy technology it's a
+
+ align:start position:0%
+stand up a new energy technology it's a
+ 
+
+ align:start position:0%
+stand up a new energy technology it's a
+longer term project than some more
+
+ align:start position:0%
+longer term project than some more
+ 
+
+ align:start position:0%
+longer term project than some more
+expensive scalar process so we're not
+
+ align:start position:0%
+expensive scalar process so we're not
+ 
+
+ align:start position:0%
+expensive scalar process so we're not
+doing those so we've got a gap and we'll
+
+ align:start position:0%
+doing those so we've got a gap and we'll
+ 
+
+ align:start position:0%
+doing those so we've got a gap and we'll
+talk about this in the next class in the
+
+ align:start position:0%
+talk about this in the next class in the
+ 
+
+ align:start position:0%
+talk about this in the next class in the
+innovation system that's yielding a
+
+ align:start position:0%
+innovation system that's yielding a
+ 
+
+ align:start position:0%
+innovation system that's yielding a
+bunch of empty kitchens around our
+
+ align:start position:0%
+bunch of empty kitchens around our
+ 
+
+ align:start position:0%
+bunch of empty kitchens around our
+economy whereas I'd argue what we want
+
+ align:start position:0%
+economy whereas I'd argue what we want
+ 
+
+ align:start position:0%
+economy whereas I'd argue what we want
+to do is fill those kitchens up but
+
+ align:start position:0%
+to do is fill those kitchens up but
+ 
+
+ align:start position:0%
+to do is fill those kitchens up but
+they've got to have a pathway to success
+
+ align:start position:0%
+they've got to have a pathway to success
+ 
+
+ align:start position:0%
+they've got to have a pathway to success
+as part of that that you follow me said
+
+ align:start position:0%
+as part of that that you follow me said
+ 
+
+ align:start position:0%
+as part of that that you follow me said
+add up is that what you're after Tara
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+they're going up the kitchen set no
+
+ align:start position:0%
+they're going up the kitchen set no
+ 
+
+ align:start position:0%
+they're going up the kitchen set no
+one's going to right now right and look
+
+ align:start position:0%
+one's going to right now right and look
+ 
+
+ align:start position:0%
+one's going to right now right and look
+if we could get energy onto the wave
+
+ align:start position:0%
+if we could get energy onto the wave
+ 
+
+ align:start position:0%
+if we could get energy onto the wave
+right it would make all the difference
+
+ align:start position:0%
+right it would make all the difference
+ 
+
+ align:start position:0%
+right it would make all the difference
+we could do it right so if we could
+
+ align:start position:0%
+we could do it right so if we could
+ 
+
+ align:start position:0%
+we could do it right so if we could
+manage to get it into this phase and
+
+ align:start position:0%
+manage to get it into this phase and
+ 
+
+ align:start position:0%
+manage to get it into this phase and
+we're not we're strolling the build-up
+
+ align:start position:0%
+we're not we're strolling the build-up
+ 
+
+ align:start position:0%
+we're not we're strolling the build-up
+phase but if we could get here that gets
+
+ align:start position:0%
+phase but if we could get here that gets
+ 
+
+ align:start position:0%
+phase but if we could get here that gets
+to be really interesting yeah max I
+
+ align:start position:0%
+to be really interesting yeah max I
+ 
+
+ align:start position:0%
+to be really interesting yeah max I
+follow fusion a lot because MIT has been
+
+ align:start position:0%
+follow fusion a lot because MIT has been
+ 
+
+ align:start position:0%
+follow fusion a lot because MIT has been
+so involved in this so it's been one of
+
+ align:start position:0%
+so involved in this so it's been one of
+ 
+
+ align:start position:0%
+so involved in this so it's been one of
+my more fun adventures in recent years
+
+ align:start position:0%
+my more fun adventures in recent years
+ 
+
+ align:start position:0%
+my more fun adventures in recent years
+is working with your fusion team on some
+
+ align:start position:0%
+is working with your fusion team on some
+ 
+
+ align:start position:0%
+is working with your fusion team on some
+of these issues but you're right that
+
+ align:start position:0%
+of these issues but you're right that
+ 
+
+ align:start position:0%
+of these issues but you're right that
+technological advances that could
+
+ align:start position:0%
+technological advances that could
+ 
+
+ align:start position:0%
+technological advances that could
+actually scale this thing actually now I
+
+ align:start position:0%
+actually scale this thing actually now I
+ 
+
+ align:start position:0%
+actually scale this thing actually now I
+think for the first time is great
+
+ align:start position:0%
+think for the first time is great
+ 
+
+ align:start position:0%
+think for the first time is great
+concern to me exciting yeah you to find
+
+ align:start position:0%
+concern to me exciting yeah you to find
+ 
+
+ align:start position:0%
+concern to me exciting yeah you to find
+you you're right on a whole series of
+
+ align:start position:0%
+you you're right on a whole series of
+ 
+
+ align:start position:0%
+you you're right on a whole series of
+big important problems that we need to
+
+ align:start position:0%
+big important problems that we need to
+ 
+
+ align:start position:0%
+big important problems that we need to
+keep bringing into this class discussion
+
+ align:start position:0%
+keep bringing into this class discussion
+ 
+
+ align:start position:0%
+keep bringing into this class discussion
+and you know creating a culture around
+
+ align:start position:0%
+and you know creating a culture around
+ 
+
+ align:start position:0%
+and you know creating a culture around
+science and creating culture around
+
+ align:start position:0%
+science and creating culture around
+ 
+
+ align:start position:0%
+science and creating culture around
+technology development a culture around
+
+ align:start position:0%
+technology development a culture around
+ 
+
+ align:start position:0%
+technology development a culture around
+entrepreneurship and a culture around
+
+ align:start position:0%
+entrepreneurship and a culture around
+ 
+
+ align:start position:0%
+entrepreneurship and a culture around
+startups those turned out to be fairly
+
+ align:start position:0%
+startups those turned out to be fairly
+ 
+
+ align:start position:0%
+startups those turned out to be fairly
+key it's hard for economics that's
+
+ align:start position:0%
+key it's hard for economics that's
+ 
+
+ align:start position:0%
+key it's hard for economics that's
+trying to do mathematical modeling to
+
+ align:start position:0%
+trying to do mathematical modeling to
+ 
+
+ align:start position:0%
+trying to do mathematical modeling to
+capture these cultural historical issues
+
+ align:start position:0%
+capture these cultural historical issues
+ 
+
+ align:start position:0%
+capture these cultural historical issues
+but they're there and you know part of
+
+ align:start position:0%
+but they're there and you know part of
+ 
+
+ align:start position:0%
+but they're there and you know part of
+what makes innovation systems Theory so
+
+ align:start position:0%
+what makes innovation systems Theory so
+ 
+
+ align:start position:0%
+what makes innovation systems Theory so
+interesting is just the sheer complexity
+
+ align:start position:0%
+interesting is just the sheer complexity
+ 
+
+ align:start position:0%
+interesting is just the sheer complexity
+of that system and the number of
+
+ align:start position:0%
+of that system and the number of
+ 
+
+ align:start position:0%
+of that system and the number of
+variables operating there and you're
+
+ align:start position:0%
+variables operating there and you're
+ 
+
+ align:start position:0%
+variables operating there and you're
+right on an important point
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+understanding the historical context for
+
+ align:start position:0%
+understanding the historical context for
+ 
+
+ align:start position:0%
+understanding the historical context for
+example turns out to be pretty key when
+
+ align:start position:0%
+example turns out to be pretty key when
+ 
+
+ align:start position:0%
+example turns out to be pretty key when
+you look at innovation systems in
+
+ align:start position:0%
+you look at innovation systems in
+ 
+
+ align:start position:0%
+you look at innovation systems in
+different regions of the world right
+
+ align:start position:0%
+different regions of the world right
+ 
+
+ align:start position:0%
+different regions of the world right
+different regions have different ways of
+
+ align:start position:0%
+different regions have different ways of
+ 
+
+ align:start position:0%
+different regions have different ways of
+organizing innovation systems the
+
+ align:start position:0%
+organizing innovation systems the
+ 
+
+ align:start position:0%
+organizing innovation systems the
+innovation system that got organized in
+
+ align:start position:0%
+innovation system that got organized in
+ 
+
+ align:start position:0%
+innovation system that got organized in
+Japan coming out of the second world war
+
+ align:start position:0%
+Japan coming out of the second world war
+ 
+
+ align:start position:0%
+Japan coming out of the second world war
+it's a very different innovation system
+
+ align:start position:0%
+it's a very different innovation system
+ 
+
+ align:start position:0%
+it's a very different innovation system
+than the u.s. organized and we'll try
+
+ align:start position:0%
+than the u.s. organized and we'll try
+ 
+
+ align:start position:0%
+than the u.s. organized and we'll try
+and talk about some of that actually in
+
+ align:start position:0%
+and talk about some of that actually in
+ 
+
+ align:start position:0%
+and talk about some of that actually in
+the next class but keep bringing us back
+
+ align:start position:0%
+the next class but keep bringing us back
+ 
+
+ align:start position:0%
+the next class but keep bringing us back
+to these two these cultural factors
+
+ align:start position:0%
+to these two these cultural factors
+ 
+
+ align:start position:0%
+to these two these cultural factors
+Thank You Martha you've got a question
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+what have been useful right right right
+
+ align:start position:0%
+what have been useful right right right
+ 
+
+ align:start position:0%
+what have been useful right right right
+and there's you know I mean in a society
+
+ align:start position:0%
+and there's you know I mean in a society
+ 
+
+ align:start position:0%
+and there's you know I mean in a society
+there in the end there is no substitute
+
+ align:start position:0%
+there in the end there is no substitute
+ 
+
+ align:start position:0%
+there in the end there is no substitute
+for leadership right you really need a
+
+ align:start position:0%
+for leadership right you really need a
+ 
+
+ align:start position:0%
+for leadership right you really need a
+big dose of that as well and you know we
+
+ align:start position:0%
+big dose of that as well and you know we
+ 
+
+ align:start position:0%
+big dose of that as well and you know we
+will talk more about innovation systems
+
+ align:start position:0%
+will talk more about innovation systems
+ 
+
+ align:start position:0%
+will talk more about innovation systems
+and how can you nurture change agents
+
+ align:start position:0%
+and how can you nurture change agents
+ 
+
+ align:start position:0%
+and how can you nurture change agents
+particularly for innovation in these
+
+ align:start position:0%
+particularly for innovation in these
+ 
+
+ align:start position:0%
+particularly for innovation in these
+legacy established complex sectors like
+
+ align:start position:0%
+legacy established complex sectors like
+ 
+
+ align:start position:0%
+legacy established complex sectors like
+energy how can you introduce change
+
+ align:start position:0%
+energy how can you introduce change
+ 
+
+ align:start position:0%
+energy how can you introduce change
+agents and what tool sets can they use
+
+ align:start position:0%
+agents and what tool sets can they use
+ 
+
+ align:start position:0%
+agents and what tool sets can they use
+to actually drive change so we'll talk
+
+ align:start position:0%
+to actually drive change so we'll talk
+ 
+
+ align:start position:0%
+to actually drive change so we'll talk
+about that particularly in the energy
+
+ align:start position:0%
+about that particularly in the energy
+ 
+
+ align:start position:0%
+about that particularly in the energy
+class but it's relevant to many others
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+you
\ No newline at end of file
diff --git a/RgScJ20EnW8.txt b/RgScJ20EnW8.txt
new file mode 100644
index 0000000000000000000000000000000000000000..23ec601994954003fa5aa463cd69e15f2d46b0a9
--- /dev/null
+++ b/RgScJ20EnW8.txt
@@ -0,0 +1,3866 @@
+The following
+content is provided
+
+under a Creative
+Commons license.
+
+Your support will help MIT
+OpenCourseWare continue
+
+to offer high-quality
+educational resources for free.
+
+To make a donation, or to
+view additional materials
+
+from hundreds of MIT courses,
+visit MIT OpenCourseWare
+
+at ocw.mit.edu.
+
+PROFESSOR: OK, in that case,
+let's begin in our usual way
+
+by going through a review
+of last time's lecture.
+
+Last time, we talked
+really about two
+
+calculational problems.
+
+One was the calculation of
+the age of the universe,
+
+taking into account a
+universe model which
+
+has matter, radiation,
+vacuum energy, and curvature.
+
+And we got the general formula.
+
+And then for the same type
+of cosmological model,
+
+we also calculated how
+one finds the brightness
+
+of a distant source--
+the energy flux in terms
+
+of the redshift of that source.
+
+So first, the age of the
+universe calculation--
+
+that really just depends on the
+first-order Friedman equation,
+
+which I've rewritten here.
+
+We put three terms
+on the right hand
+
+side for the mass density-- a
+matter term, a radiation term,
+
+and a vacuum energy term.
+
+And we know-- and this is
+the important ingredient--
+
+we know how each depend
+on the scale factor.
+
+Non-relativistic
+matter falls off like 1
+
+over the cube of
+the scale factor.
+
+Radiation falls off like
+1 over the fourth power
+
+of the scale factor.
+
+And vacuum energy
+is just constant.
+
+Next step that we did was just
+to rewrite this equation, where
+
+we put in the explicit
+time dependence
+
+in the form of this x
+which is the ratio of a
+
+of t to the present value of
+the scale factor-- a of t 0.
+
+And furthermore, we
+expressed the matter density
+
+in terms of the present
+contribution to omega.
+
+And rewriting equation in that
+language, it takes that form.
+
+And then, I pulled a fast one.
+
+I said we could also
+write this last term
+
+to look pretty much
+like the others.
+
+It just is a constant that
+falls off like 1 over a squared.
+
+So if you define
+omega sub k 0, which
+
+is exactly what you need to
+make this look like that,
+
+and in terms of omega
+sub k 0, all four terms
+
+have the same characteristic.
+
+They're just a constant
+times a power of x.
+
+So this is, then, the rewriting
+of the Friedman equation one
+
+more time, just using this
+new definition of how we're
+
+going to treat the
+curvature of the universe.
+
+And simply by looking
+at this formula
+
+and applying it
+to x equals 1, you
+
+can see that that
+becomes then 1 is
+
+equal to the sum
+of these omegas.
+
+And that can be thought
+of as a clearer, perhaps,
+
+definition of what
+omega sub k 0 is.
+
+It's just 1 minus all of the
+other contributions to omega.
+
+So it's how much the actual
+mass density of the universe
+
+differs from the
+critical density.
+
+Then once we have
+this equation, which
+
+is the equation
+which tells us what
+
+x dot is as a function of x,
+we could just rewrite that
+
+by bringing dt to one
+side of the equation
+
+and dx to the other and
+integrating both sides.
+
+And that leads to
+our final result.
+
+The age of the universe is
+simply given by that integral.
+
+And this is a very
+neat expression
+
+for the age of the
+universe in terms
+
+of the present value of
+the Hubble expansion rate
+
+and each contribution to omega
+in terms of its present value.
+
+And you just plug those
+into this formula.
+
+In general, you have to do
+the integral numerically,
+
+because the integral's
+a little too complicated
+
+to have an analytic expression.
+
+And that will give you
+the age of universe
+
+for any model that
+meets this description.
+
+So any questions about that
+calculation before we go on?
+
+OK, very good.
+
+The next calculation
+we did last time
+
+was the calculation of
+radiation flux versus redshift.
+
+And this is exactly
+what the astronomers
+
+were measuring in 1998
+when they concluded
+
+that the universe
+was accelerating.
+
+They were looking at distant
+supernova type 1a explosions.
+
+They made the assumption
+that all supernova type
+
+1a explosions have the same
+intrinsic power output.
+
+That's based roughly on
+observation and guesswork.
+
+There's not really a
+good theory for it,
+
+so it's mostly a matter of being
+consistent with observations.
+
+But then they could
+calculate for any given model
+
+in terms of these different
+omegas what you expect in terms
+
+of received radiation as
+a function of redshift.
+
+And they compared their
+data with the models--
+
+and I'll show you
+that data shortly--
+
+and found that the
+models only fit
+
+if one had a significant
+component of vacuum
+
+energy causing
+universe to accelerate.
+
+So to do the calculation, we
+need a metric for the universe.
+
+And I considered only
+the closed universe case.
+
+There's also the flat
+case and the open case,
+
+which are similar.
+
+And you'll actually be asked to
+do those on the homework set.
+
+So the metric for
+a closed universe
+
+can be written this
+way, where sine psi is
+
+the square root of k
+times r, to relate it
+
+to the other way-- the more
+standard way-- of writing
+
+the Robertson Walker metric.
+
+But for our purposes
+for this calculation,
+
+it's easiest to do it
+this way, because we're
+
+going to be interested in
+radio trajectories of photons.
+
+And this metric simplifies
+the radial direction
+
+as much as it can be.
+
+It's just d psi squared.
+
+Oh, it's the
+computer that froze.
+
+You never know with Windows.
+
+I think we're in business now.
+
+Back to where we were.
+
+We have the metric.
+
+Now what we want to do
+is imagine a light source
+
+being received by a detector.
+
+And we put the light
+source in the center
+
+of our coordinate system.
+
+We put the detector at some
+distance corresponding to psi
+
+equals psi sub D, where psi is
+our radial coordinate and psi
+
+sub D is the radial
+coordinate of the detector.
+
+We imagine a whole sphere
+with the same radius
+
+as the detector,
+because we expect
+
+the source to be
+spherically symmetric.
+
+And therefore, the light
+emitted by the source
+
+will be uniformly
+spread over that sphere.
+
+And that will allow us to
+calculate how much of it
+
+will hit the detector.
+
+The fraction
+hitting the detector
+
+will just be the area
+of the detector divided
+
+by the area of the sphere.
+
+The area of the detector
+is whatever it is.
+
+We call it capital A.
+The area of the sphere
+
+is 4 pi times the
+radius of the sphere.
+
+And the radius of the sphere
+in physical coordinates
+
+is the scale factor squared
+times the sine squared
+
+of psi sub D, coming
+from the metric.
+
+It's the radius that appears
+in the angular part that
+
+counts, because it's the angles
+that we're integrating over
+
+to get the area of the sphere.
+
+So the radius is
+just a tilde squared
+
+times sine squared is
+the radius squared.
+
+Then we also need to
+remember something
+
+we've said a number of times
+previously in this class, which
+
+is that when the photons
+travel from the source
+
+to the detector, their
+intensity is suppressed
+
+by two powers of 1 plus z,
+two powers of the redshift.
+
+And one of those
+factors in 1 plus z
+
+comes from redshifting
+each photon.
+
+The frequency of each
+photon is redshifted,
+
+and that means that the energy
+of each photon is redshifted--
+
+goes down by a
+factor of 1 plus z.
+
+But in addition, the rate
+of arrival of the photons
+
+is essentially a clock
+which is also time dilated.
+
+So the rate of arrival of the
+photons as seen by the observer
+
+is suppressed by another
+factor of 1 plus z.
+
+So putting all that together,
+the received energy flux,
+
+which is the power received
+divided by the area,
+
+is just the power emitted by
+the source divided by 4 pi.
+
+We get this factor
+of 1 plus z squared,
+
+due to what we just discussed.
+
+And then the a squared of
+t sine squared psi sub D.
+
+So it's just the total
+power times that fraction
+
+that we receive times the two
+factors of 1 over 1 plus z.
+
+And this then is essentially
+the final answer,
+
+except we want to know how to
+evaluate a tilde squared of t 0
+
+and sine squared of psi
+sub D in terms of things
+
+that we more directly measure.
+
+So to do that, a
+tilde of t 0 turns out
+
+to be easy, because
+it really is just
+
+related by the definition of
+omega sub k 0 to omega sub k 0.
+
+So this formula is
+just a rewriting
+
+of the definition
+of omega sub k 0.
+
+To figure out what
+psi is, we want
+
+to integrate along
+the line of sight
+
+to be able to figure
+out the time of emission
+
+in terms of psi.
+
+And that time of
+emission could then
+
+be related to the redshift,
+because the redshift is just
+
+the ratio of the scale factors
+between reception and emission.
+
+So we look first at the metric.
+
+And say we're
+going to be looking
+
+at null geodesics in
+the radial direction.
+
+And null means ds
+squared equals 0,
+
+and that's minus c
+squared dt squared
+
+plus a tilde squared of
+t times d psi squared.
+
+And that implies
+immediately that the psi dt
+
+is just equal to the speed
+of light divided by a tilde.
+
+And then we can get
+the total increment
+
+in psi between the source
+and us by integrating
+
+between the time of
+emission-- the time
+
+of the source-- to the
+present time-- t sub 0.
+
+And then it's just a matter
+of changing variables
+
+to express the variable
+of integration.
+
+Instead of st, we could express
+it as z-- the redshift itself.
+
+And that brings in a factor of
+h, because h is a dot over a.
+
+And I showed the
+manipulations last time,
+
+but it brings in a factor of h.
+
+But we know what h is
+as a function of z.
+
+It comes from the
+Friedman equation.
+
+And that then gives us an
+expression for psi of z sub
+
+s as an integral over z.
+
+And writing in what h of
+z is and what a tilde of z
+
+is from that expression,
+the expression for psi of z
+
+becomes the equation
+that's boxed.
+
+Just a matter of algebraic
+substitutions involving
+
+the Friedman equation, which
+determines what h of z is.
+
+And then putting
+everything together,
+
+J is just given by this
+expression, where all I've done
+
+is to substitute the
+expression for a tilde of c 0.
+
+And sine squared
+psi is still here,
+
+but it gets evaluated
+according to that formula.
+
+And putting these together,
+we have a complete calculation
+
+of the received radiation
+flux as a function
+
+of cosmological parameters--
+the omegas and the h 0--
+
+and the redshift of the source.
+
+And that's the end
+of the calculation.
+
+And that's where we
+finished last time.
+
+So any questions about
+that calculation?
+
+OK, fine.
+
+In that case, moving on, the
+next thing I wanted to show you
+
+was some real data.
+
+So here are some real data
+from one of those two teams
+
+that made the original
+announcements in 1998.
+
+This is from the High-Z
+Supernova Search Team.
+
+And I should write some
+definitions on the blackboard.
+
+The vertical axis there
+is essentially brightness.
+
+But you wouldn't expect the
+astronomers to just call
+
+it brightness, because they
+like to use fancier words.
+
+So they write it as
+little m minus capital
+
+M-- measured in magnitudes,
+they put in parentheses.
+
+And little m minus
+capital M has the name,
+
+it's called the
+distance modulus,
+
+meaning it's a way of
+measuring distance.
+
+They think of brightness as
+a way of measuring distance,
+
+which indeed is what
+it's being used for.
+
+And it's defined as
+5 times the logarithm
+
+base 10 of d sub L
+over 1 megaparsec,
+
+which means the luminosity
+distance-- I'll define this
+
+in more detail in
+a second-- d sub L
+
+is the luminosity distance--
+distance as inferred
+
+from the luminosity.
+
+And they're measuring
+it in megaparsecs
+
+and taking the
+logarithm base 10.
+
+And then, by convention,
+there's an offset here of 25.
+
+Why not?
+
+So this is the definition
+of the distance modulus.
+
+And d sub L is defined by
+the relationship of what
+
+J would be in a flat
+Euclidean universe
+
+if you were receiving
+that luminosity.
+
+So J is equal to
+the actual power
+
+output of the source divided
+by 4 pi d sub L squared.
+
+This defines d sub L. So
+d sub L is the distance
+
+that that source would have
+to be at in a static Euclidean
+
+universe for you to see
+it with the brightness
+
+that you actually see.
+
+This, I guess, completes
+the definitions,
+
+but we can put these together.
+
+And m minus M is then
+equal to minus 5/2
+
+times the logarithm
+base 10 of 4 pi J times
+
+1 megaparsec squared,
+divided by the actual power
+
+output of the source, and
+then, of course, plus 25.
+
+So this relates this
+distance modulus
+
+to the energy flux and the power
+output of the original source.
+
+There's also on this
+slide the acronym MLCS.
+
+MLCS stand for multi-color
+light curve shape.
+
+And what that refers to is the
+High-Z Supernova Search Team
+
+invented a method of
+compensating, to some extent,
+
+for small variations
+in the actual power
+
+output of the
+supernovae type 1a.
+
+Instead of assuming
+that they all
+
+have exactly the
+same brightness,
+
+they discovered by looking at
+nearby supernovae of this type
+
+that there's a correlation
+between the absolute brightness
+
+of the supernovae and the
+shape of the light curve--
+
+that is, light versus time.
+
+So they were careful to
+measure the light versus time
+
+for the supernovae that
+they used in this study.
+
+And they used that as a way
+of applying a small correction
+
+to what they interpreted
+as the intrinsic brightness
+
+of each supernova.
+
+And the results
+are these points.
+
+[INAUDIBLE] the top
+are the raw points,
+
+and three different curves
+for three different models.
+
+And they characterize the
+models in the same way
+
+we would-- in terms of different
+contributions to omega.
+
+So the top model is the
+cosmological constant dominated
+
+model, where omega
+sub lambda, which
+
+is what we've been calling
+omega sub vac is 0.76.
+
+And it's a flat model,
+so 0.24 for omega matter.
+
+And radiation is ignorable.
+
+They compared that with the
+middle model of these three,
+
+which was a model that
+had no vacuum energy,
+
+and omega matter of 0.2.
+
+That was essentially
+the dominant model
+
+at the time, the belief that
+the universe was open then
+
+had about a critical
+density of 1/5 or 1/4.
+
+And then they also
+compared it with a model
+
+where omega was 1-- entirely of
+matter with no vacuum energy.
+
+And that was this
+dashed curve, which
+
+is the lower of
+these three curves.
+
+And when the data
+is just plotted,
+
+it's a little hard to see
+how much difference there
+
+is between the three curves.
+
+So they re-plotted the data,
+plotting the middle curve
+
+as a straight line
+by construction.
+
+And then they plotted
+deviations from that line.
+
+And they did that for both
+the theoretical curves
+
+and the data.
+
+And in this magnified
+picture, you
+
+can see a little bit better
+that this top curve fits
+
+things the best.
+
+And that's what they call
+the lambda CDM model.
+
+It corresponds to
+omega m equals 0.24.
+
+Omega lambda equals 0.76.
+
+So it's the model with
+a cosmological constant,
+
+with a vacuum energy.
+
+And lambda CDM stands for
+lambda and cold, dark matter.
+
+And cold, dark
+matter is just what
+
+we've been calling
+non-relativistic matter.
+
+So the claim is that these data
+points, even though there's
+
+a fair amount of scatter,
+fit the top curve much,
+
+much better than they
+fit the middle curve
+
+or the bottom curve.
+
+And statistically, that's true.
+
+It really is a much better
+fit, even though by eye, it's
+
+not that clear what's going on.
+
+I think by eye it looks clear
+that the top one fits it better
+
+than others, but
+it's not that clear
+
+how important the difference is.
+
+But nonetheless, the astronomers
+were thoroughly convinced
+
+that this was a real effect.
+
+There was considerable
+discussion
+
+about possible
+systematic errors.
+
+And I guess next, I'll say
+a few words about that.
+
+First of all, I
+should maybe just
+
+clarify a little bit
+better what's being seen.
+
+What's being seen is that for
+a given redshift, this curve,
+
+which basically shows brightness
+in a funny, funny way, where
+
+dimmer is upward, larger
+values of little m minus M--
+
+there's a minus sign
+in this formula--
+
+means a dimmer galaxy, one
+that looks further away.
+
+And basically, when astronomers
+see this, they think distance.
+
+So larger values
+means further away.
+
+So what's being seen is that
+these distant supernovae
+
+are a little bit
+dimmer than what
+
+you would expect in either
+of the other two models,
+
+either of the models that
+do not have vacuum energy.
+
+And the amount by
+which they're dimmer
+
+is a few tenths of a magnitude.
+
+And each tenth of a magnitude
+corresponds to about 10%
+
+in brightness.
+
+So what they're saying is that
+these distant if supernovae,
+
+if we assume they
+really fit this curve,
+
+are 20% to 30%
+dimmer than you would
+
+have expected in other models.
+
+It might be worth saying a
+little bit about why dimmer
+
+is the right sign to correspond
+to acceleration, which
+
+is by no means totally
+obvious, I don't think.
+
+So we're plotting--
+
+AUDIENCE: What year is this?
+
+PROFESSOR: What year?
+
+This was old data that
+was published in 1998.
+
+It has gotten better.
+
+Now it's much more
+unambiguous that this works.
+
+So this is distance as
+inferred by brightness.
+
+So this is basically
+what's being plotted.
+
+If one thinks about a
+fixed z in which way
+
+that you go-- up or down--
+I find that totally cryptic.
+
+I don't really parse that
+very well in my own head.
+
+But it's much clearer if you
+think about the other way.
+
+You could think about a
+galaxy-- or a supernova
+
+in this case-- at a
+fixed distance, and ask,
+
+suppose I compare different
+models-- ones that accelerate
+
+and models that
+don't accelerate.
+
+So if we fix the distance
+and say, what would we
+
+expect for the
+redshift of a given
+
+galaxy, in an accelerating
+model versus a non-accelerating
+
+model-- remember, the
+redshift is basically
+
+a measure of the
+velocity, or at least it's
+
+strongly influenced by the
+velocity of the object.
+
+So if the universe
+is accelerating,
+
+it means that the universe was
+expanding slower in the past
+
+than you would have
+thought otherwise.
+
+It's speeded up to reach
+its present expansion rate.
+
+So an accelerating
+universe is a universe
+
+that was expanding
+slower in the past.
+
+And slower in the past means
+that a galaxy at a given
+
+distance would have
+been moving slower,
+
+and hence would have
+had a lower value of z.
+
+So the effect of acceleration
+for a given distance-- we'll
+
+fix the distance-- should be
+to move the line that way,
+
+towards lower z.
+
+And by moving the dot that way,
+it puts it above the curve.
+
+So it's the same as
+shifting things up,
+
+which is the more
+natural way of describing
+
+what's seen in the graph.
+
+The points are higher
+than the curve.
+
+So the bottom line, though,
+is that what they're saying
+
+is distant supernovae are
+20%, 30% dimmer than you
+
+might have thought.
+
+And from that, they want to
+infer that the universe is
+
+accelerating, which is a
+rather dramatic conclusion.
+
+So naturally, you
+want to ask, are there
+
+other things that can cause
+supernovae to look dimmer?
+
+And of course, there
+are other things
+
+that can cause
+supernovae to look dimmer
+
+than you might have thought.
+
+And there are two
+main ideas that
+
+were discussed at the time.
+
+One of them is just plain dust.
+
+If you're looking at something
+through a dusty atmosphere,
+
+it looks dimmer than
+it would otherwise.
+
+And that is a
+genuine possibility
+
+that was strongly considered.
+
+The arguments against
+dust were mainly twofold.
+
+The first is that
+dust very rarely
+
+absorbs uniformly
+across the spectrum.
+
+Dust usually-- depending on
+the size of the dust grains--
+
+absorbs more blue
+light than red light,
+
+leaving more red
+light coming through.
+
+So the effect of seeing
+something through dust
+
+is normally to cause
+it to look more red.
+
+And this reddening was not seen.
+
+The spectrum of the light
+from the existing supernovae
+
+was analyzed very carefully.
+
+And the spectrum
+of the distant ones
+
+looked just like the spectrum of
+the nearby ones-- appropriately
+
+redshifted, of course, but
+otherwise not distorted
+
+in any way.
+
+There was no sign
+of this reddening.
+
+Now, it's possible to have
+what the astronomers refer
+
+to as gray dust, which is by
+definition dust that absorbs
+
+uniformly across the spectrum
+of what you're looking at.
+
+But the grains have
+to be unusually large.
+
+And nobody was ever
+able to figure out
+
+a source for dust
+grains of that sort.
+
+So based partly on
+theoretical grounds
+
+and partly on what
+nobody has ever found,
+
+there's no evidence
+for dust grains
+
+that would possibly
+cause dimming
+
+that would look this way,
+that would be dimming
+
+that was uniform
+across the spectrum.
+
+Yes?
+
+AUDIENCE: How do you
+tell the difference
+
+between reddened light from
+dust and redshifted light?
+
+PROFESSOR: OK, how do
+you tell the difference
+
+between reddened light from
+dust and plain old redshift?
+
+The difference is that the
+plain old redshift uniformly
+
+shifts everything
+by the same factor.
+
+So the whole spectrum is
+just moved down uniformly
+
+towards the red.
+
+This reddening
+effect really means
+
+that the blue part
+of the spectrum
+
+is depressed relative
+to the red part.
+
+So the shape of the
+spectrum is changed.
+
+So one argument is that
+we don't see reddening,
+
+and we don't know any way to
+make dust that would be gray.
+
+The second argument is that
+if dust was a major factor,
+
+presumably most of the
+dust that would be relevant
+
+would be dust in the same galaxy
+as the supernova explosion
+
+itself, because there's
+not that much dust
+
+in intergalactic space.
+
+And if dust in the galaxy of the
+supernova itself were relevant,
+
+then-- let me draw a
+little picture here.
+
+So if dust in what's
+called the host
+
+galaxy-- the galaxy which
+has the supernova in it--
+
+then you would have
+a picture where
+
+there would be a ball of
+dust filling the galaxy.
+
+And the supernova that you're
+looking at might be there,
+
+or it might be there.
+
+And let's say we're
+looking from over here.
+
+So depending on where the
+supernova was in the galaxy,
+
+we would see very different
+amounts of intervening dust.
+
+And if dust were
+causing this dimming,
+
+it would mean we would be
+seeing a significant scatter
+
+in the amount of dimming
+depending on where
+
+the supernova happened
+to be in its host galaxy.
+
+And that spread was not seen.
+
+The spread that one
+sees in that curve
+
+could be measured and calibrated
+against known uncertainties
+
+in the brightness of
+supernovae and then
+
+the detection apparatus.
+
+And the spread that
+was seen was just what
+
+you expect without any
+additional spread associated
+
+with a dusty galaxy
+acting as the host.
+
+So no evidence for the
+spread of brightnesses
+
+that would be expected
+from a dusty host.
+
+Another item that
+was considered--
+
+these are the main
+arguments against dust--
+
+another argument
+that was considered,
+
+another possible source of
+dimming, is galactic evolution.
+
+And there, the main effect
+that people worried about
+
+was the production of
+heavy chemical elements
+
+during the life of a galaxy.
+
+As you've certainly learned
+about from your reading--
+
+I don't know if we've talked
+about it in class or not--
+
+the early universe was essential
+all hydrogen and helium.
+
+Heavier elements were
+made later in stars
+
+that produce
+supernovae explosions.
+
+And these supernovae
+explosions gradually
+
+cause galaxies to become
+more and more enriched
+
+with heavy elements.
+
+And by heavy, I mean
+anything heavier than helium.
+
+And that could
+affect, in principle,
+
+the behavior of
+supernovae explosions.
+
+So the evidence
+against that was simply
+
+that every other
+characteristic that astronomers
+
+could measure of
+these supernovae
+
+in the distant
+galaxies looked exactly
+
+like what was seen
+for nearby galaxies.
+
+So no evidence for any
+kind of evolution was seen.
+
+And there are many
+properties you
+
+could measure that are
+independent of distance,
+
+like the shape of the
+spectrum and things like that,
+
+and the pattern of the
+light curve versus time.
+
+So all those characteristics
+that astronomers can measure
+
+seem to be exactly the same
+for the very distant supernovae
+
+which happened
+billions of years ago,
+
+and the more nearby ones
+that happened recently.
+
+And furthermore,
+among the nearby ones,
+
+there's a big spread of
+abundances of heavy chemical
+
+elements, just because
+different galaxies
+
+have had different histories.
+
+So among the nearby
+ones, you could
+
+look for is there
+an effect caused
+
+by the relative abundance
+of heavy elements,
+
+and astronomers didn't find any.
+
+So there was no sign
+that galactic evolution
+
+could be playing a role
+here, even though one
+
+does need to worry about it.
+
+So the point is that
+distant supernovae 1a
+
+look like nearby ones.
+
+I'll call that a in my outline.
+
+And b is that among the nearby
+1a's, heavy element abundance
+
+had no perceptible effect.
+
+So the dominant opinion
+gradually shifted,
+
+and now I think it's almost 100%
+that this acceleration is real.
+
+The acceleration, by
+the way, is further
+
+confirmed by measurements
+of fluctuations
+
+in the cosmic background
+radiation measurements that
+
+have been done by some
+ground-based experiments,
+
+and also the satellite
+experiments of WMAP
+
+and now Planck, which
+measure the anisotropies--
+
+the ripples-- in the cosmic
+background radiation.
+
+It's hard to see what
+those ripples would
+
+have to do with the
+amount of vacuum energy.
+
+But it does turn out-- and
+we'll talk more about this
+
+a little bit later--
+that we really
+
+do have a detailed theory
+of what makes these ripples.
+
+We can calculate what the
+spectrum of those ripples
+
+should look like.
+
+And the calculations
+depend on parameters
+
+which include the
+amount of vacuum energy.
+
+And in order to
+make things work,
+
+one does have to put
+in essentially exactly
+
+the same amount of vacuum
+energy as has been detected
+
+in these supernova
+1a observations.
+
+So everything fits
+together very tightly.
+
+And I think now, just about
+everybody is convinced
+
+that the universe
+really is accelerating.
+
+The acceleration
+could, in principle,
+
+have at least two different
+causes that we can talk about.
+
+One is vacuum energy, which is
+the one that I'm focusing on,
+
+which is the
+simplest explanation.
+
+The other possibility that is
+discussed in the literature
+
+is something called
+quintessence,
+
+which is a made-up word.
+
+And what it refers
+to is the possibility
+
+that the acceleration
+of the universe today
+
+could be caused by a mechanism
+which is really in principle
+
+exactly the same as what
+we talk about for inflation
+
+in the early universe and
+will be talking about later.
+
+Specifically, there could be
+a slowly evolving scalar field
+
+which is essentially uniform
+throughout the universe,
+
+and changing slowly with time so
+it looks like it's a constant.
+
+And it could be the energy
+density of that scalar field
+
+that is looking to us as
+if it were vacuum energy.
+
+But that's the
+minority point of view.
+
+And that introduces
+extra parameters
+
+that don't seem to be necessary.
+
+But it's up for grabs.
+
+Nobody really knows.
+
+OK, any questions about
+what we just talked about?
+
+In that case, let me go
+on to my next topic, which
+
+is I want to talk
+a little bit more
+
+about the physics
+of vacuum energy.
+
+What is it that we
+understand about it,
+
+and why is it that
+most physicists say
+
+it's the least understood
+issue in physics?
+
+We really don't
+understand vacuum energy,
+
+even though we do understand
+why it might be nonzero.
+
+Where we're totally at a loss
+is trying to make any sense out
+
+of the value of the energy
+density that is actually
+
+observed.
+
+So where does vacuum energy come
+from in a quantum field theory?
+
+There are basically, I would
+say, three contributions.
+
+Maybe I should say in
+quantum field theory.
+
+The other context in which
+this might be discussed
+
+would be string theory.
+
+I may or may not say
+something about string theory,
+
+but I won't say much.
+
+But in quantum field
+theory, there are basically,
+
+I think, three contributions.
+
+The first is the
+easiest to understand,
+
+which is quantum fluctuations
+in bosonic fields,
+
+where the best
+example is the photon,
+
+or the electromagnetic field.
+
+Now, in a classical
+vacuum, e and b-- the
+
+the electric and
+magnetic fields--
+
+would just be 0, because that's
+the lowest possible energy
+
+density.
+
+But just as you are
+probably aware that
+
+there's an uncertainty principle
+in quantum mechanics which
+
+tells you that the momentum and
+position of a particle cannot
+
+be well-defined
+at the same time,
+
+it is also true that e and
+b cannot be well-defined
+
+at the same time.
+
+So the uncertainty principles
+applied to the field theory
+
+imply that e and b cannot
+just be 0 and stay 0.
+
+E and b are constantly
+fluctuating.
+
+And that means
+that there's energy
+
+associated with
+those fluctuations.
+
+And the mathematics of it is
+actually incredibly simple.
+
+If one imagines the
+fields inside a box,
+
+to be able to at least
+avoid the infinity of space,
+
+the fields inside a
+box could be described
+
+in terms of standing waves,
+where each standing wave is
+
+either a half wavelength or
+a full wavelength across.
+
+And by the way, you'll be doing
+a homework problem on this.
+
+And each standing
+wave has the physics
+
+of a harmonic oscillator.
+
+It oscillates sinusoidally
+with time, the wave.
+
+And when one works out
+the mathematics, and even
+
+the quantum mechanics,
+it's exactly the same
+
+as a harmonic oscillator.
+
+So each standing wave
+has a zero-point energy.
+
+You may know that the zero-point
+energy of a harmonic oscillator
+
+is not 0, but it's 1/2 h
+bar omega, or 1/2 h nu,
+
+depending on whether you're
+using nu or omega to describe
+
+the frequency of the oscillator.
+
+So each standing wave
+contributes 1/2 h bar omega.
+
+And then the problem is how
+many standing waves are there?
+
+And the answer is, there's
+an infinite number of them,
+
+because there's no limit to how
+short the wavelength can be.
+
+So there's no limit to
+how many ups and downs you
+
+can have in your
+standing wave from one
+
+end of the box to the next.
+
+So the answer you
+get is infinite.
+
+It diverges.
+
+Now, the fact that it
+diverges at short distances
+
+can be used as an excuse for
+getting the problem wrong.
+
+Obviously, it's wrong.
+
+The answer's not infinite.
+
+But we have an excuse,
+because we certainly
+
+know there are wavelengths
+that are short enough
+
+that we don't understand the
+physics at those length scales
+
+anymore.
+
+We're basing everything on
+extrapolating from wavelengths
+
+that we can actually
+measure in the laboratory.
+
+So one could
+imagine that there's
+
+some wavelength beyond which
+everything we're saying here
+
+is nonsense, and we don't have
+to keep adding up 1/2 h bar
+
+omega anymore,
+because the arguments
+
+that justify the 1/2 h
+bar omega no longer apply.
+
+So we can use that as a
+cutoff for the calculation.
+
+And a typical
+cutoff-- by typical, I
+
+mean typical in arguments
+that physicists talk about, so
+
+typical in physics speak.
+
+So a cutoff that's
+often invoked here
+
+is the Planck scale,
+which is the square root
+
+of h bar times G
+divided by c cubed.
+
+And that has units
+of length, and it's
+
+equal to about 1.6 times 10
+to the minus 33 centimeters.
+
+And what makes the
+scale significant
+
+is it's the scale at which we
+expect the effects of quantum
+
+gravity to start
+to be important.
+
+And we know that
+this quantum field
+
+theory that we're
+talking about does not
+
+include the effects of gravity.
+
+And we don't really
+even know how
+
+to modify it so that it would
+include the effects of gravity.
+
+So the quantum
+effects of gravity
+
+are still something
+of a mystery.
+
+So it makes sense to
+cut the theory off,
+
+if not earlier, at least
+at the Planck scale.
+
+Yes?
+
+AUDIENCE: So I would imagine
+what we're doing, in order
+
+to say that we have a standing
+wave, we have to have a box.
+
+And then in order to realize
+the fact that the universe may
+
+be large, you just take the
+limit as the box gets large.
+
+But is it really OK to do that?
+
+I mean, to treat
+an infinite system
+
+as the limit of a finite system?
+
+PROFESSOR: OK, the
+question is-- what
+
+we're going to be
+doing here is I
+
+talked about putting the
+standing waves in a box.
+
+And then at the end, we're
+going to take the limit
+
+as the box gets
+bigger and bigger.
+
+And the question is, is
+that really a valid way
+
+of treating the infinite space?
+
+And the answer is,
+in this case, it is.
+
+I'm not sure how solid
+an argument I can make.
+
+Certainly what one does
+find is what you'd expect,
+
+that as you make the
+box bigger and bigger,
+
+the energy that you get is
+proportional to the size
+
+of the box.
+
+So you're calculating
+an energy density.
+
+And probably the most precise
+thing I can say at the moment
+
+is that if it were not true,
+if the answer you got really
+
+depended on the way in which
+the space was infinite,
+
+then you'd be learning something
+about the infinite universe
+
+by doing an experiment
+in the lab, which
+
+is a little far-fetched.
+
+That is, if you do an
+experiment in a lab,
+
+it really doesn't
+tell you anything
+
+about whether the universe
+is infinite or turns back
+
+on itself and is closed.
+
+And calculations
+certainly do show
+
+that you get the
+same-- you could do,
+
+for example, a closed
+universe without a box.
+
+And you get the
+same energy density,
+
+as long as the universe was
+big, as we're getting this way.
+
+So I think there's a pretty
+solid calculational evidence
+
+that what you get does
+not depend on the box.
+
+Yes?
+
+AUDIENCE: Going
+off that question,
+
+do we use the maximum
+size of our box
+
+as the size of our
+observable universe, then?
+
+PROFESSOR: OK, the
+question is, what do we
+
+use as the maximum
+size of the box?
+
+Is it the size of the
+observable universe?
+
+The answer really is
+that what you find
+
+is that you get an energy
+density that's independent
+
+of the size of the box,
+as long as the box is big.
+
+And it's that energy density
+that we're looking for.
+
+We don't claim to know anything
+about the total energy.
+
+And we don't really
+need to know anything
+
+about the total energy.
+
+Everything that we formulated
+here in terms of energy
+
+densities.
+
+Now, the catch is, that
+if one puts in this cutoff
+
+and takes into account only
+the energies of 1/2 h bar
+
+omega going up to this cutoff
+and stopping there-- or down
+
+to the cutoff if one's thinking
+of length as the measure--
+
+you could then ask, do
+we get an energy density
+
+that's in any way close to
+what the astronomers tell us
+
+the vacuum energy actually is?
+
+And the answer is
+emphatically no.
+
+We don't get anything close.
+
+We're in fact off by about
+120 orders of magnitude,
+
+which even in cosmology is
+a significant embarrassment,
+
+which is why physicists consider
+this question of the vacuum
+
+energy density to be such
+an incredible mystery.
+
+We really have no
+idea how to get
+
+a number as small
+as what we observe.
+
+Let us go on to talk
+about other contributions,
+
+because they are certainly
+important in the way we
+
+think about things.
+
+So far I have number one, right?
+
+So next comes two.
+
+And that is the quantum
+fluctuations of Fermi fields,
+
+where the best-known example
+here is the electron.
+
+Now, in quantum field
+theory, I should point out
+
+that all particles are described
+by fields, not just the photon.
+
+The electron is described
+by a field also.
+
+It's called the electron field.
+
+And because the electron is
+a fermion and not a boson,
+
+the electron field has
+somewhat different properties
+
+than bosonic fields,
+reflecting the fact
+
+that the fermions themselves
+obey the exclusion principle.
+
+It turns out that
+for fermions, there
+
+are also quantum fluctuations.
+
+They're also of order
+1/2 h bar omega.
+
+But actually, it's a
+little bit different.
+
+They're in some sense h
+bar omega and not 1/2.
+
+But what's peculiar is that
+for electrons, the contribution
+
+is negative.
+
+And the origin of this
+negativity I think
+
+has a fairly simple
+explanations,
+
+although the explanation is
+not ever given, actually.
+
+The exploration that's used
+in quantum field theory books
+
+involves looking at
+equation 47 and seeing
+
+that there's an
+anticommutator there.
+
+And because the
+fields anticommute,
+
+there's a minus sign.
+
+And that means the
+energy is negative.
+
+And that is basically the way
+it's described in textbooks.
+
+That certainly says
+where the minus sign
+
+appears in which equation.
+
+But I don't think it's
+really an explanation of what
+
+the minus sign is talking about.
+
+But I think there is an
+explanation of what the minus
+
+sign is talking about, which
+goes back to the old picture
+
+that Dirac himself
+introduced when he first
+
+invented the Dirac equation.
+
+When Dirac first invented
+the Dirac equation,
+
+he was trying to
+interpret it more or less
+
+in the same language as
+the Schrodinger equation.
+
+We don't quite do that anymore.
+
+But in doing that,
+Dirac discovered
+
+that his Dirac
+equation, which was
+
+the natural relativistic
+generalization
+
+of the Schrodinger equation
+to a particle which
+
+has spin 1/2, which I'm not sure
+how Dirac knew it had spin 1/2,
+
+but in any case,
+it's the equation
+
+for a particle of spin 1/2.
+
+And what he found was that if
+you just look at the energy
+
+the spectrum that the
+equation itself gives you,
+
+it's symmetric about 0.
+
+So if we plot energy going this
+way, if there's a state here,
+
+there's also a state
+there at negative energy.
+
+And if there's a
+state there, there's
+
+another state there,
+exactly opposite it.
+
+It's completely
+symmetric up and down.
+
+Now, the interpretation
+that Dirac gave to that
+
+was not that there are a lot of
+ways of making negative energy.
+
+He realized that the
+vacuum is by definition
+
+the state of lowest
+possible energy.
+
+And if you can lower the
+energy by adding a particle
+
+to these negative
+energy states, that
+
+would mean that there'd be a
+way of lowering the energy,
+
+and the state would
+not be the vacuum.
+
+So the vacuum, Dirac
+proposed, is the state
+
+in which all of these negative
+energy levels are filled.
+
+And the action of putting
+all these x's on the picture
+
+is often called
+filling the Dirac sea.
+
+S-E-A-- sea, where sea refers
+to this ocean of negative energy
+
+states, which is infinite.
+
+It just keeps going down.
+
+You can imagine filling all of
+them to describe the vacuum.
+
+Then if you ask what is
+the physics after you've
+
+done that-- what are
+the possible excitations
+
+of the vacuum, what
+states does this theory
+
+contain other than the vacuum?
+
+And the answer is that
+there could be occupations
+
+of these positive energy states,
+and those are called electrons.
+
+It's also possible
+to remove-- if you
+
+put in the right
+amount of energy--
+
+one of the negative energy
+states, which is filled,
+
+but we could take away
+the particle that's there.
+
+And the absence of a
+particle there-- a hole
+
+in the negative energy
+sea-- is a positron.
+
+So electrons are there.
+
+The e plus is a hole
+in the Dirac sea.
+
+Now, the difficulty
+with this picture,
+
+and the reason why it's
+not often use these days,
+
+is that it makes it
+look like there's
+
+an intrinsic difference between
+electrons and positrons.
+
+Nonetheless, Dirac
+was perfectly aware
+
+that when you went
+through the math,
+
+they were completely symmetric.
+
+The fact that you
+described it this way
+
+is just really a feature
+of your description,
+
+but it doesn't make any
+measurable difference.
+
+So a positron really is just a
+perfect image of an electron,
+
+but with the opposite
+charge, with otherwise
+
+all the same
+physical properties.
+
+And there's ways
+of describing it
+
+where you don't make this
+distinction between particles
+
+and holes.
+
+But the particle hole way
+is I think the easiest
+
+way of understanding where the
+negative energy is coming from.
+
+The negative energy came by
+saying that the energy was 0
+
+before we filled
+any of these levels.
+
+And as you fill the
+negative energy sea,
+
+you're lowering
+energy all the time.
+
+And it's that contribution
+which makes up
+
+the infinite negative
+contribution coming
+
+from the Fermi fields.
+
+And the algebra is
+certainly exactly right.
+
+The energy that
+people write down
+
+for the negative energy
+of the Fermi fields--
+
+what they get by anticommuting
+two operators in equation 37--
+
+is exactly the
+expression you get
+
+for what it takes to
+fill the Dirac sea.
+
+Yes?
+
+AUDIENCE: Are we
+pretty confident
+
+that the smallness
+of the vacuum energy
+
+can't come from cancellations
+between the bosonic
+
+and the Fermi fields?
+
+PROFESSOR: OK, the question
+is, are we confident that
+
+the cancellation cannot come
+from the cancellations between
+
+the Fermi fields and
+the bosonic fields.
+
+No, we're all confident that
+it cannot come from that.
+
+it very likely does
+come from that.
+
+But we are confident that we
+have no idea why that happens.
+
+And therefore,
+it's a big mystery.
+
+Certainly our ignorance
+allows for any answer.
+
+Because we have a positive
+infinite contribution,
+
+we're just going to cut
+off and make it large.
+
+And we're going to have a
+negative contribution, which
+
+we're going to cut off and
+make it large in magnitude
+
+but negative.
+
+And then we're
+going to add them,
+
+and we have no idea
+what we're going to get.
+
+But the fact that
+we get something
+
+that gets incredibly close to
+0, and not something that's
+
+at all the same magnitude as the
+pieces you're adding together--
+
+the positive piece or
+the negative piece--
+
+means there's something going
+on that we don't understand.
+
+There's a cancellation that's
+happening that we cannot
+
+explain.
+
+Now, I should maybe
+add that there's
+
+one context where we would
+expect a cancellation.
+
+And that is, there
+are theories that
+
+are what are called
+supersymmetric,
+
+which have a perfect symmetry
+between bosons and fermions,
+
+which would relate the
+positive energy from the photon
+
+to the infinite negative energy
+you would get from particles
+
+called photinos, which would
+be the supersymmetric partner
+
+of the photons-- a
+spin 1/2 particle
+
+that's a mirror
+image of a photon
+
+but has a fermionic character.
+
+So in an exactly
+supersymmetric theory,
+
+you would get an
+exact cancellation
+
+between the positive and
+the negative contributions.
+
+And the answer has to be 0 in an
+exactly supersymmetric theory.
+
+However, the world is clearly
+not exactly supersymmetric.
+
+This photino has
+never been seen.
+
+And there'd be a particle
+called the selectron, which
+
+would be the scalar partner
+of the electron, which
+
+also has not been seen.
+
+And every known
+particle would have
+
+a partner, which
+has not been seen.
+
+There are no supersymmetric
+pairs which are known.
+
+So supersymmetry is
+still a possibility
+
+as a broken symmetry of nature.
+
+And a lot of people think-- for
+pretty good reasons, I thin--
+
+that it's very likely
+that the world does
+
+have an underlying
+supersymmetry.
+
+But as long as the
+supersymmetry is broken,
+
+it no longer guarantees
+this cancellation.
+
+And you could estimate
+what the mismatch is.
+
+And it does make things
+a little bit better here.
+
+If we just take this
+Planck scale cutoff,
+
+we miss an energy density by a
+factor of about 10 to the 120.
+
+If we apply
+supersymmetry and make
+
+an estimate of what the
+supersymmetry breaking scale is
+
+and what effect that has on the
+mismatch of these calculations,
+
+then it gets reduced.
+
+Instead of being 120 order
+of magnitude problems,
+
+it's got a 50 order of
+magnitude problem, which
+
+is a lot better,
+but not good enough.
+
+Now, I do want to mention
+a third contribution here
+
+for completeness.
+
+The third one is
+likely be finite,
+
+so it's not as problematic
+as the other two.
+
+AUDIENCE: [INAUDIBLE]
+
+PROFESSOR: Same thing.
+
+Planck scale.
+
+AUDIENCE: Oh, OK.
+
+PROFESSOR: The
+third contribution
+
+is that some fields
+are believed to have
+
+nonzero values in the vacuum.
+
+And the famous example of
+that is the Higgs field,
+
+for which the particle
+associated with the Higgs
+
+was discovered a
+year ago at CERN,
+
+after over 50 years
+of looking for it.
+
+And the Higgs field is
+maybe the only field
+
+that's part of the
+standard model that
+
+has a nonzero expectation value,
+a nonzero value in the vacuum.
+
+But in more
+sophisticated theories
+
+like grand unified
+theories, there
+
+are many more fields that have
+nonzero values in the vacuum.
+
+So that's a likely extension
+of our standard model
+
+of particle physics.
+
+So the bottom line is that it's
+easy for particle physicists
+
+to understand why the vacuum
+energy should be nonzero,
+
+but damned hard to have any
+idea of why it has the value
+
+that it has.
+
+We'll talk maybe at
+the end of the course
+
+about the possibility that
+the value of the vacuum energy
+
+density is, quote,
+"anthropically selected."
+
+That is one possible
+explanation,
+
+which maybe shows how
+desperate physicists
+
+are to look for an
+explanation here.
+
+One possible explanation
+begins with ideas
+
+from string theory, where
+string theory tells us
+
+that there isn't just
+one kind of vacuum,
+
+but in fact, a huge number
+of different types of vacuum,
+
+perhaps 10 to the 500.
+
+And that would
+mean that if there
+
+were sort of random values for
+these infinite numbers that
+
+get cut off, that get cut
+off with different values--
+
+and there are other ways
+of looking at the vacuum
+
+energy in string
+theories-- you'd
+
+expect coming out
+of string theory
+
+that the typical vacuum energy
+would be about the same as what
+
+you get when you
+cut off the quantum
+
+fluctuations of the
+electromagnetic field
+
+at the Planck scale.
+
+That is, the typical
+vacuum energy coming out
+
+of a string theory would be
+at the Planck scale, which
+
+is this huge number
+compared to what we observe.
+
+But string theory
+would be predict
+
+that there would be a spread
+of numbers going essentially
+
+from plus the Planck scale
+to minus the Planck scale,
+
+with everything in between.
+
+There'd be a tiny fraction
+of those vacua that
+
+would have a very small vacuum
+energy like what we observe.
+
+That's what you'd expect
+from string theory--
+
+a large number, but a tiny
+fraction of vacua that
+
+would be in that integral.
+
+And then the only
+problem would be
+
+to explain why we might likely
+be living in such an unusually
+
+small fraction of the set
+of all possible vacuums.
+
+And the answer to
+that that's discussed
+
+is that it may be
+anthropically selected.
+
+That is, life may only
+form when the vacuum
+
+energy is incredibly small.
+
+And that is not built
+entirely from whole cloth.
+
+There is some
+physics behind that.
+
+We know that this vacuum energy
+affects the Friedman equation,
+
+which means it affects the
+expansion rate of the universe.
+
+So if we had a Planck
+scale vacuum energy,
+
+that would cause the
+universe to essentially blow
+
+apart at the time scale of the
+Planck scale, which is about 10
+
+to the minus 40
+something seconds,
+
+due to the huge repulsion
+that would be created
+
+by that positive vacuum energy.
+
+And conversely, if there
+was a huge negative vacuum
+
+energy on the order
+of the Planck scale,
+
+the universe would just
+implode on a time scale
+
+of order of the
+Planck scale-- 10
+
+to the minus 40
+something seconds.
+
+So assuming that life takes
+billions of years to evolve
+
+and assuming nothing
+else about life,
+
+one can conclude that
+life can only exist
+
+in the very narrow band
+of possible vacuum energy
+
+densities which are
+incredibly small, like the one
+
+that we're living in.
+
+So it could be that we're
+here only because there
+
+isn't any life anyplace else.
+
+So all living things see a very,
+very small value of this vacuum
+
+energy density, even though
+if you plunk yourself down
+
+at a random place
+in this multiverse,
+
+you'd be likely to see
+a vacuum energy that's
+
+near the Planck scale.
+
+OK, I'm done talking
+about this for now.
+
+Any further questions about
+it before we leave the topic?
+
+I had suggested that we go
+on to talk about problems
+
+with the conventional
+big bang model,
+
+but, there is actually
+something else I wanted to do.
+
+I don't know how long
+it will take exactly,
+
+but I have a little historical
+interlude to talk about here.
+
+We've been talking about
+the Friedman equations
+
+and how they're modified by the
+cosmological constant, which
+
+of course is an item that was
+very dear to Einstein's heart.
+
+So I'd like to tell
+you a little history
+
+story about Albert Einstein
+and Alexander Friedman,
+
+which I think is
+very interesting.
+
+The punchline of the story is
+that Einstein made pretty much
+
+of a fool out of
+himself on this.
+
+And the reason why I like
+the story is maybe twofold.
+
+One is, I find it
+very comforting
+
+to know that even perhaps the
+greatest physicist of all time
+
+can make dumb mistakes
+just like the rest of us
+
+make dumb mistakes.
+
+I think that's a very comforting
+thing to keep in mind.
+
+And the other moral
+of the story is,
+
+I think, the
+importance of trying
+
+to be open-minded about
+issues in physics.
+
+Einstein was very much convinced
+that the universe was static,
+
+and so convinced that,
+in fact, he really made
+
+stupid mistakes trying to
+defend his static universe.
+
+So this will be a story
+of such a mistake.
+
+So those are the two people.
+
+Friedman was a Russian natural--
+he was really a meteorologist.
+
+They didn't really have that
+many theoretical physicists
+
+back in those days.
+
+But as a meteorologist,
+he was an expert
+
+in solving partial
+differential equations,
+
+and got himself interested
+in general relativity, which
+
+was a new theory at this point.
+
+And in 1922, he published
+an actual physics paper,
+
+I think the first physics
+paper he ever published,
+
+and one of two.
+
+He wrote basically two papers
+about the Friedman equations--
+
+one for closed universes,
+and one for open universes.
+
+So the first of those
+papers was published
+
+in June 29, 1922 in the premier
+physics journal of the day--
+
+the Zeitschrift fur
+Physik, a German journal.
+
+And almost immediately--
+or a few months later,
+
+when Einstein noticed
+this article--
+
+Einstein submitted a comment
+about the article claiming
+
+that the article was
+entirely wrong, just
+
+mathematically wrong.
+
+And the article was titled
+"Remark on the Work of A.
+
+Friedmann 'On the Curvature
+of Space' " by A. Einstein,
+
+Berlin, received
+September 18, 1922.
+
+Looking at these dates--
+the original article
+
+was received in June
+1922, and Einstein
+
+was responding by September
+18, a few months later.
+
+And this is a translation,
+which comes from a book called
+
+Cosmological Constants,
+which is basically
+
+a book of famous
+articles in cosmology,
+
+like Friedman's, and all
+these original articles.
+
+It's a great book if you
+can still get a copy of it.
+
+It's no doubt out of print.
+
+It was written by Jeremy
+Bernstein and Gary Feinberg.
+
+And I'm taking the
+translation from there,
+
+because this was
+written in German.
+
+I don't know German.
+
+"The works cited contains
+a result concerning
+
+a non-stationary world
+which seems suspect to me.
+
+Indeed, those
+solutions do not appear
+
+compatible with the
+field equations."
+
+And I guess A is the label
+of the field equations
+
+as they appeared in
+Friedman's paper.
+
+"From the field equation,
+it follows necessarily
+
+that the divergence of the
+matter tensor Tik vanishes."
+
+That is, energy
+momentum is conserved
+
+as a four-vector quantity.
+
+"This along with ansatzes C and
+D"-- equations from the paper--
+
+leads, according to Einstein,
+to an equation which we can all
+
+recognize the meaning of-- the
+partial of rho with respect
+
+to x sub 4-- time-- is 0.
+
+Einstein convinced himself
+that the equations of general
+
+relativity led to the conclusion
+that rho cannot change with
+
+time.
+
+And he then goes on to
+say "which together with 8
+
+implies that the world radius
+R"-- that's the scale factor.
+
+That's what we call a of
+t-- "is constant in time.
+
+The significance of
+the work, therefore,
+
+is to demonstrate
+this constancy."
+
+All Friedman does
+once you correct
+
+his equations,
+according to Einstein,
+
+was prove that the only
+cosmological solution is rho
+
+equals a constant, which was
+Einstein's static solution.
+
+This was entirely wrong-- no
+basis whatever in mathematics.
+
+But it took a while
+before Einstein
+
+got himself straightened out.
+
+And he did actually
+publish this.
+
+The sequence of events was, June
+29, Friedman submits his paper.
+
+September 18, Einstein submits
+his rebuttal to the paper.
+
+Friedman didn't learn about this
+until the following December.
+
+Friedman had a friend who played
+a key role in this story-- Yrui
+
+Krutkov, who was visiting
+in Berlin during this time.
+
+And Friedman actually
+learned from Krutkov
+
+that Einstein had
+submitted a rebuttal.
+
+So Friedman apparently was able
+to track it down and read it.
+
+And he wrote a detailed
+letter to Einstein
+
+explaining to Einstein
+what he got wrong,
+
+which is a gutsy thing
+to do, but Friedman
+
+was right in this case.
+
+But Einstein was traveling and
+actually never read the letter,
+
+at least not until much later.
+
+Then the following May,
+Krutkov and Einstein
+
+are both at a conference in
+Leiden, a conference that they
+
+were both attending, which was
+a farewell lecture by Lorentz,
+
+who was retiring at that time.
+
+So they met and started
+talking, and continued talking.
+
+And we know most about it
+from a series of letters
+
+that Krutkov wrote to his
+sister back in Saint Petersburg.
+
+And according to those
+letters-- and I'm now
+
+quoting from a rather lovely
+book called Alexander A.
+
+Friedmann-- The Man who
+Made the Universe Expand,
+
+by Tropp, Frenkel, and Chernin.
+
+Krutkov wrote to his sister
+that on Monday, May 7,
+
+1923, "I was reading,
+together with Einstein,
+
+Friedman's article in the
+Zeitschrift fur Physik.
+
+And then on May 18, he
+wrote, "I defeated Einstein
+
+in the argument about Friedmann.
+
+Petrograd's honor is saved!"
+
+Petrograd is what we now
+call Saint Petersburg,
+
+and where they were all from--
+that is, Friedman and Krutkov.
+
+And then shortly
+after that, on May 31,
+
+Einstein submitted a
+retraction of his refutation
+
+of Friedman's paper.
+
+And the retraction
+is-- again, I'm
+
+quoting from Cosmological
+Constant, which
+
+translates all these
+nice papers into English.
+
+Einstein wrote, very briefly,
+"I have in an earlier note
+
+criticized the cited
+work-- Friedmann 1922.
+
+My objection rested
+however, as Mr. Krutkov
+
+off in person and a
+letter from Mr. Friedmann
+
+convinced me, on a
+calculational error.
+
+I am convinced that
+Mr. Friedmann's results
+
+are both correct and clarifying.
+
+They show that in addition
+to the static solution
+
+to the field
+equations, there are
+
+time varying solutions with a
+spatially symmetric structure."
+
+Anyway, the expanding universe
+that we now talk about.
+
+Einstein did have to
+admit, ultimately,
+
+that algebra is algebra, and you
+can't really futz with algebra.
+
+And the Einstein equations
+do not imply that rho cannot
+
+change with time, and
+that Friedman was right.
+
+There's an interesting twist
+on this retraction letter.
+
+This is just a photo of
+Einstein at this time period,
+
+and Krutkov.
+
+There's an interesting twist
+on the retraction letter, which
+
+is that the original
+draft still exists.
+
+I forget what museum it's in.
+
+But it's quoted in
+another marvelous book
+
+about this history
+called The Invented
+
+Universe, by Pierre Kerzberg.
+
+And I Xeroxed this
+from the book.
+
+And this is the original draft.
+
+And notice there
+are some cross-outs.
+
+And the last cross-out, which
+followed this explanation
+
+that there is this expanding
+solution-- in Einstein's
+
+original draft, he wrote
+but then crossed out
+
+"a physical significance can
+hardly be ascribed to them."
+
+So his initial instinct,
+even after having
+
+been convinced that these
+were a valid solution
+
+to the equations, was to say
+that they couldn't possibly
+
+be physical, because
+they're not physical.
+
+The universe is static.
+
+But somehow, before
+he submitted it,
+
+he did realize that
+there wasn't actually
+
+any solid logic
+behind that reasoning.
+
+So logic did prevail, and
+he decided that he really
+
+had no right to say
+that the solution has
+
+no physical significance, which
+is a good thing, because now,
+
+of course, it is the
+solution that we consider
+
+physically significant-- the
+expanding solution of Friedman.
+
+So [INAUDIBLE] is
+a mystery, I think.
+
+OK, we have just a couple
+minutes left in the class.
+
+So I think that is
+nearly enough time for me
+
+to at least introduce what
+I want to talk about next.
+
+What we'll be talking about next
+time-- and I'll just introduce
+
+it now-- are a set of
+two problems associated
+
+with the conventional
+big bang theory.
+
+And by the conventional
+bang big bang theory,
+
+I mean basically the theory
+we've been talking about,
+
+but in particular,
+the big bang theory
+
+without inflation, which we
+will be talking about later.
+
+But so far, we've been talking
+about the big bang theory
+
+without inflation.
+
+And the two problems
+that we'll talk about
+
+are called the horizon
+or horizon homogeneity
+
+problem, and the
+flatness problem.
+
+Both of these are
+problems connected
+
+with the initial conditions
+necessary to make the model
+
+work.
+
+So this horizon
+homogeneity problem
+
+is a problem about
+trying to understand
+
+the uniformity of the observed
+universe, which we've just
+
+put in as part of our
+initial conditions.
+
+The model that we've
+constructed was just completely
+
+homogeneous and isotropic
+from start to present.
+
+The evidence for the
+uniformity of the universe
+
+shows up most strongly,
+as I think we said before,
+
+in the cosmic background
+radiation, which
+
+can be measured to
+fantastic precision.
+
+And this radiation is known to
+be uniform in all directions
+
+to an accuracy of
+one part in 100,000,
+
+which is really a phenomenal
+level of accuracy.
+
+Now, what makes this
+hard to understand
+
+in the conventional
+big bang theory is
+
+that if instead
+of just putting it
+
+in as an assumption about
+the initial conditions,
+
+you try to get it out
+of any kind of dynamics,
+
+that turns out to be impossible.
+
+And in particular, a calculation
+that we'll do next time
+
+is we'll imagine
+tracing back photons
+
+from the cosmic background
+radiation arriving at the Earth
+
+today from two opposite
+directions in the sky.
+
+Now, the phenomenology is
+that those photons come
+
+with exactly the same
+temperature to an accuracy
+
+of one part in
+100,000, and that's
+
+what we're trying to explain.
+
+Now, we all do know
+that systems do
+
+come to a uniform temperature.
+
+If you heated the air
+in this room in a corner
+
+and then let the
+room stand, the heat
+
+would scatter
+throughout the room,
+
+and the room would come
+to a uniform temperature.
+
+If you take a hot slice
+of pizza out of the oven,
+
+it gets cool, as
+everybody knows.
+
+So there is this
+so-called zeroth law
+
+of thermodynamics which
+says that everything tends
+
+to come to a
+uniform temperature.
+
+And it's a fair question to
+ask, can we perhaps explain
+
+the uniformity of the
+universe by invoking
+
+this zeroth law
+of thermodynamcs?
+
+Maybe the universe
+just had time to come
+
+to a uniform temperature.
+
+But one can see immediately
+when one looks at details
+
+that that's not the case.
+
+Within the context of
+our conventional model
+
+of cosmology, the
+universe definitely
+
+did not have time to come
+to a uniform temperature.
+
+And the easiest way
+to drive that home
+
+will be a calculation that we
+will do first thing next time,
+
+which is that we will
+trace back photons coming
+
+from opposite
+directions in the sky
+
+and ask, what would
+it take for them
+
+to have been set equal
+to the same temperature
+
+when they were first emitted?
+
+And what we'll find is
+that when we trace them
+
+back to their emission sources,
+that those emissions took place
+
+at two points which were
+separated from each other
+
+by about 50 horizon distances.
+
+So assuming that physical
+influences are limited
+
+by the speed of
+light-- and according
+
+to everything that we know about
+the laws of physics, that's
+
+true-- there is no way that the
+emission of that photon coming
+
+from that direction could
+have had any causal connection
+
+with the emission
+of the photon coming
+
+from the other direction.
+
+So if the uniformity
+had to be set up
+
+by physical processes
+that happened
+
+after the initial singularity,
+there's just no way
+
+that that emission could
+have known anything
+
+about what was
+going on over there,
+
+and no way they could have
+arranged to be emitting photons
+
+at the same energy
+at the same time.
+
+Now, everything
+does work if you're
+
+willing to just assume that
+everything started at uniform.
+
+But if you're not
+willing to assume that,
+
+and want to try to derive the
+uniformity of the universe
+
+as a dynamical
+consequence of processes
+
+in the early
+universe, there's just
+
+no way to do it in the
+conventional big bang
+
+theory because of this
+causality argument.
+
+And later, we'll see that
+inflation gets around that.
+
+Yes?
+
+AUDIENCE: How do we know
+that the homogeneity wasn't
+
+just created when the
+universe was smaller,
+
+in such a way that the
+speed of light limit
+
+wouldn't be violated, and
+that it would just maintain
+
+[INAUDIBLE]?
+
+PROFESSOR: OK, the
+question is, how do we
+
+know that the uniformity
+wasn't established when
+
+the universe was very small,
+and then the speed of light
+
+might not have to be violated?
+
+Well, the point is
+that if the dynamics is
+
+the conventional big bang
+model, what we'll show
+
+is that there's
+not really enough.
+
+No matter how early you
+imagine it happening,
+
+it still is 50 horizon
+distances apart.
+
+And there's no way that those
+points could've communicated,
+
+no matter how close
+you come to t equals 0.
+
+Now, you are of course
+free to assuming anything
+
+you want about the
+singularity at t equals 0.
+
+So if you want to just assume
+that somehow the singularity
+
+homogenized
+everything, that's OK.
+
+But there's no theory behind it.
+
+That's just speculation.
+
+But it is satisfactory
+speculation.
+
+There's nothing it contradicts.
+
+But the beauty of inflation
+is that it does, in fact,
+
+provide a dynamical explanation
+for how this uniformity could
+
+have been created, which,
+at least to many people,
+
+is better than just
+speculating that somehow it
+
+happened in the singularity.
+
+OK, I think that's it for now.
+
+I will tell you about
+the other problem
+
+we'll talk about
+next time next time.
+
+And I will see you
+all next Tuesday.
\ No newline at end of file
diff --git a/TTArY7ojshU.txt b/TTArY7ojshU.txt
new file mode 100644
index 0000000000000000000000000000000000000000..8abcd86745aad556b41293ac0e5be358dbe5a103
--- /dev/null
+++ b/TTArY7ojshU.txt
@@ -0,0 +1,13872 @@
+align:start position:0%
+ 
+okay everyone let's get started uh
+
+ align:start position:0%
+okay everyone let's get started uh
+ 
+
+ align:start position:0%
+okay everyone let's get started uh
+welcome back um to uh theory of
+
+ align:start position:0%
+welcome back um to uh theory of
+ 
+
+ align:start position:0%
+welcome back um to uh theory of
+computation lecture number
+
+ align:start position:0%
+computation lecture number
+ 
+
+ align:start position:0%
+computation lecture number
+six um
+
+ align:start position:0%
+six um
+ 
+
+ align:start position:0%
+six um
+so we have
+
+ align:start position:0%
+so we have
+ 
+
+ align:start position:0%
+so we have
+been
+
+ align:start position:0%
+been
+ 
+
+ align:start position:0%
+been
+um looking
+
+ align:start position:0%
+um looking
+ 
+
+ align:start position:0%
+um looking
+at a number of different models of
+
+ align:start position:0%
+at a number of different models of
+ 
+
+ align:start position:0%
+at a number of different models of
+computation and um last lecture actually
+
+ align:start position:0%
+computation and um last lecture actually
+ 
+
+ align:start position:0%
+computation and um last lecture actually
+was an important one for us because we
+
+ align:start position:0%
+was an important one for us because we
+ 
+
+ align:start position:0%
+was an important one for us because we
+shifted gears um from our restricted
+
+ align:start position:0%
+shifted gears um from our restricted
+ 
+
+ align:start position:0%
+shifted gears um from our restricted
+model
+
+ align:start position:0%
+model
+ 
+
+ align:start position:0%
+model
+um finite autometer push down autometer
+
+ align:start position:0%
+um finite autometer push down autometer
+ 
+
+ align:start position:0%
+um finite autometer push down autometer
+and their
+
+ align:start position:0%
+and their
+ 
+
+ align:start position:0%
+and their
+Associated um generative models regular
+
+ align:start position:0%
+Associated um generative models regular
+ 
+
+ align:start position:0%
+Associated um generative models regular
+expressions and uh and context free
+
+ align:start position:0%
+expressions and uh and context free
+ 
+
+ align:start position:0%
+expressions and uh and context free
+grammars to touring machines which are
+
+ align:start position:0%
+grammars to touring machines which are
+ 
+
+ align:start position:0%
+grammars to touring machines which are
+going to be the model that we're going
+
+ align:start position:0%
+going to be the model that we're going
+ 
+
+ align:start position:0%
+going to be the model that we're going
+to which is the model that we're going
+
+ align:start position:0%
+to which is the model that we're going
+ 
+
+ align:start position:0%
+to which is the model that we're going
+to be sticking with for the rest of the
+
+ align:start position:0%
+to be sticking with for the rest of the
+ 
+
+ align:start position:0%
+to be sticking with for the rest of the
+semester because that's going to be our
+
+ align:start position:0%
+semester because that's going to be our
+ 
+
+ align:start position:0%
+semester because that's going to be our
+model as we're going to argue today for
+
+ align:start position:0%
+model as we're going to argue today for
+ 
+
+ align:start position:0%
+model as we're going to argue today for
+a general purpose
+
+ align:start position:0%
+a general purpose
+ 
+
+ align:start position:0%
+a general purpose
+computer so in a sense everything we've
+
+ align:start position:0%
+computer so in a sense everything we've
+ 
+
+ align:start position:0%
+computer so in a sense everything we've
+been doing up till now has or up until
+
+ align:start position:0%
+been doing up till now has or up until
+ 
+
+ align:start position:0%
+been doing up till now has or up until
+that point has been kind of a warm-up um
+
+ align:start position:0%
+that point has been kind of a warm-up um
+ 
+
+ align:start position:0%
+that point has been kind of a warm-up um
+but it's been um nevertheless has gotten
+
+ align:start position:0%
+but it's been um nevertheless has gotten
+ 
+
+ align:start position:0%
+but it's been um nevertheless has gotten
+chance for us to introduce some
+
+ align:start position:0%
+chance for us to introduce some
+ 
+
+ align:start position:0%
+chance for us to introduce some
+important Concepts uh that are um used
+
+ align:start position:0%
+important Concepts uh that are um used
+ 
+
+ align:start position:0%
+important Concepts uh that are um used
+in practice and also will serve as good
+
+ align:start position:0%
+in practice and also will serve as good
+ 
+
+ align:start position:0%
+in practice and also will serve as good
+examples for us moving forward and also
+
+ align:start position:0%
+examples for us moving forward and also
+ 
+
+ align:start position:0%
+examples for us moving forward and also
+just to get our you know get kind of um
+
+ align:start position:0%
+just to get our you know get kind of um
+ 
+
+ align:start position:0%
+just to get our you know get kind of um
+uh you know in in a sense on the same
+
+ align:start position:0%
+uh you know in in a sense on the same
+ 
+
+ align:start position:0%
+uh you know in in a sense on the same
+page uh
+
+ align:start position:0%
+page uh
+ 
+
+ align:start position:0%
+page uh
+so um what we're going to be doing today
+
+ align:start position:0%
+so um what we're going to be doing today
+ 
+
+ align:start position:0%
+so um what we're going to be doing today
+is um uh
+
+ align:start position:0%
+is um uh
+ 
+
+ align:start position:0%
+is um uh
+uh looking at the touring Machine model
+
+ align:start position:0%
+uh looking at the touring Machine model
+ 
+
+ align:start position:0%
+uh looking at the touring Machine model
+in a little bit more depth um one can
+
+ align:start position:0%
+in a little bit more depth um one can
+ 
+
+ align:start position:0%
+in a little bit more depth um one can
+Define touring machines in all sorts of
+
+ align:start position:0%
+Define touring machines in all sorts of
+ 
+
+ align:start position:0%
+Define touring machines in all sorts of
+different ways but it's going to turn
+
+ align:start position:0%
+different ways but it's going to turn
+ 
+
+ align:start position:0%
+different ways but it's going to turn
+out not to matter because all of those
+
+ align:start position:0%
+out not to matter because all of those
+ 
+
+ align:start position:0%
+out not to matter because all of those
+different ways are going to be
+
+ align:start position:0%
+different ways are going to be
+ 
+
+ align:start position:0%
+different ways are going to be
+equivalent to one another and so we are
+
+ align:start position:0%
+equivalent to one another and so we are
+ 
+
+ align:start position:0%
+equivalent to one another and so we are
+going to uh stick with the very simplest
+
+ align:start position:0%
+going to uh stick with the very simplest
+ 
+
+ align:start position:0%
+going to uh stick with the very simplest
+version the one we've already defined
+
+ align:start position:0%
+version the one we've already defined
+ 
+
+ align:start position:0%
+version the one we've already defined
+namely this uh the simple one tape
+
+ align:start position:0%
+namely this uh the simple one tape
+ 
+
+ align:start position:0%
+namely this uh the simple one tape
+turing machine but um where going to
+
+ align:start position:0%
+turing machine but um where going to
+ 
+
+ align:start position:0%
+turing machine but um where going to
+basically justify that by looking at
+
+ align:start position:0%
+basically justify that by looking at
+ 
+
+ align:start position:0%
+basically justify that by looking at
+some of these other models and proving
+
+ align:start position:0%
+some of these other models and proving
+ 
+
+ align:start position:0%
+some of these other models and proving
+equivalent so uh we can we look of at
+
+ align:start position:0%
+equivalent so uh we can we look of at
+ 
+
+ align:start position:0%
+equivalent so uh we can we look of at
+multi-tape touring machines we'll look
+
+ align:start position:0%
+multi-tape touring machines we'll look
+ 
+
+ align:start position:0%
+multi-tape touring machines we'll look
+at non-deterministic touring machines
+
+ align:start position:0%
+at non-deterministic touring machines
+ 
+
+ align:start position:0%
+at non-deterministic touring machines
+and we'll look at another model which is
+
+ align:start position:0%
+and we'll look at another model which is
+ 
+
+ align:start position:0%
+and we'll look at another model which is
+slightly different but is still based on
+
+ align:start position:0%
+slightly different but is still based on
+ 
+
+ align:start position:0%
+slightly different but is still based on
+tour machines called an
+
+ align:start position:0%
+tour machines called an
+ 
+
+ align:start position:0%
+tour machines called an
+enumerator and we'll show that those all
+
+ align:start position:0%
+enumerator and we'll show that those all
+ 
+
+ align:start position:0%
+enumerator and we'll show that those all
+in the end um give you the same class of
+
+ align:start position:0%
+in the end um give you the same class of
+ 
+
+ align:start position:0%
+in the end um give you the same class of
+languages and so in that sense they're
+
+ align:start position:0%
+languages and so in that sense they're
+ 
+
+ align:start position:0%
+languages and so in that sense they're
+all equivalent to one another and that's
+
+ align:start position:0%
+all equivalent to one another and that's
+ 
+
+ align:start position:0%
+all equivalent to one another and that's
+going to be serve as a kind of a
+
+ align:start position:0%
+going to be serve as a kind of a
+ 
+
+ align:start position:0%
+going to be serve as a kind of a
+motivator um kind of to in a sense
+
+ align:start position:0%
+motivator um kind of to in a sense
+ 
+
+ align:start position:0%
+motivator um kind of to in a sense
+recapitulate some of the history of the
+
+ align:start position:0%
+recapitulate some of the history of the
+ 
+
+ align:start position:0%
+recapitulate some of the history of the
+subject um and going to lead to our um
+
+ align:start position:0%
+subject um and going to lead to our um
+ 
+
+ align:start position:0%
+subject um and going to lead to our um
+discussion of what's called The Church
+
+ align:start position:0%
+discussion of what's called The Church
+ 
+
+ align:start position:0%
+discussion of what's called The Church
+Turing thesis so we will uh I'll get to
+
+ align:start position:0%
+Turing thesis so we will uh I'll get to
+ 
+
+ align:start position:0%
+Turing thesis so we will uh I'll get to
+that in due course um and we'll also
+
+ align:start position:0%
+that in due course um and we'll also
+ 
+
+ align:start position:0%
+that in due course um and we'll also
+talk about uh some notation
+
+ align:start position:0%
+talk about uh some notation
+ 
+
+ align:start position:0%
+talk about uh some notation
+for um languages and notations for
+
+ align:start position:0%
+for um languages and notations for
+ 
+
+ align:start position:0%
+for um languages and notations for
+touring machines and for coding objects
+
+ align:start position:0%
+touring machines and for coding objects
+ 
+
+ align:start position:0%
+touring machines and for coding objects
+to feed into touring machines as input
+
+ align:start position:0%
+to feed into touring machines as input
+ 
+
+ align:start position:0%
+to feed into touring machines as input
+but we'll get to that shortly as well uh
+
+ align:start position:0%
+but we'll get to that shortly as well uh
+ 
+
+ align:start position:0%
+but we'll get to that shortly as well uh
+so let's move on then we will um next um
+
+ align:start position:0%
+so let's move on then we will um next um
+ 
+
+ align:start position:0%
+so let's move on then we will um next um
+go into uh a little review of what we
+
+ align:start position:0%
+go into uh a little review of what we
+ 
+
+ align:start position:0%
+go into uh a little review of what we
+did with with for touring machines and
+
+ align:start position:0%
+did with with for touring machines and
+ 
+
+ align:start position:0%
+did with with for touring machines and
+um just want to make sure we're all
+
+ align:start position:0%
+um just want to make sure we're all
+ 
+
+ align:start position:0%
+um just want to make sure we're all
+together on that it's a very important
+
+ align:start position:0%
+together on that it's a very important
+ 
+
+ align:start position:0%
+together on that it's a very important
+concept for us this term so the turing
+
+ align:start position:0%
+concept for us this term so the turing
+ 
+
+ align:start position:0%
+concept for us this term so the turing
+machine model looks like there's going
+
+ align:start position:0%
+machine model looks like there's going
+ 
+
+ align:start position:0%
+machine model looks like there's going
+to be this finite control there's a tape
+
+ align:start position:0%
+to be this finite control there's a tape
+ 
+
+ align:start position:0%
+to be this finite control there's a tape
+with a head that can read and write on
+
+ align:start position:0%
+with a head that can read and write on
+ 
+
+ align:start position:0%
+with a head that can read and write on
+the tape can move in both directions the
+
+ align:start position:0%
+the tape can move in both directions the
+ 
+
+ align:start position:0%
+the tape can move in both directions the
+tape is infinite to the to to one side
+
+ align:start position:0%
+tape is infinite to the to to one side
+ 
+
+ align:start position:0%
+tape is infinite to the to to one side
+and so on as I've mentioned last time
+
+ align:start position:0%
+and so on as I've mentioned last time
+ 
+
+ align:start position:0%
+and so on as I've mentioned last time
+um the output of the touring machine is
+
+ align:start position:0%
+um the output of the touring machine is
+ 
+
+ align:start position:0%
+um the output of the touring machine is
+either going to be a halt accepting or
+
+ align:start position:0%
+either going to be a halt accepting or
+ 
+
+ align:start position:0%
+either going to be a halt accepting or
+rejecting or Loop that the machine may
+
+ align:start position:0%
+rejecting or Loop that the machine may
+ 
+
+ align:start position:0%
+rejecting or Loop that the machine may
+run forever with three possible outcomes
+
+ align:start position:0%
+run forever with three possible outcomes
+ 
+
+ align:start position:0%
+run forever with three possible outcomes
+for any particular input the machine May
+
+ align:start position:0%
+for any particular input the machine May
+ 
+
+ align:start position:0%
+for any particular input the machine May
+accept that input by entering Q accept
+
+ align:start position:0%
+accept that input by entering Q accept
+ 
+
+ align:start position:0%
+accept that input by entering Q accept
+May Halt and reject by entering Q reject
+
+ align:start position:0%
+May Halt and reject by entering Q reject
+ 
+
+ align:start position:0%
+May Halt and reject by entering Q reject
+and it might reject by looping which
+
+ align:start position:0%
+and it might reject by looping which
+ 
+
+ align:start position:0%
+and it might reject by looping which
+means it just never gets to the accept
+
+ align:start position:0%
+means it just never gets to the accept
+ 
+
+ align:start position:0%
+means it just never gets to the accept
+state or the uh it never gets to any
+
+ align:start position:0%
+state or the uh it never gets to any
+ 
+
+ align:start position:0%
+state or the uh it never gets to any
+halting state it just goes forever but
+
+ align:start position:0%
+halting state it just goes forever but
+ 
+
+ align:start position:0%
+halting state it just goes forever but
+we still consider that to be rejecting
+
+ align:start position:0%
+we still consider that to be rejecting
+ 
+
+ align:start position:0%
+we still consider that to be rejecting
+the input just it's rejecting by
+
+ align:start position:0%
+the input just it's rejecting by
+ 
+
+ align:start position:0%
+the input just it's rejecting by
+looping okay um and as we defined last
+
+ align:start position:0%
+looping okay um and as we defined last
+ 
+
+ align:start position:0%
+looping okay um and as we defined last
+time a language is touring recognizable
+
+ align:start position:0%
+time a language is touring recognizable
+ 
+
+ align:start position:0%
+time a language is touring recognizable
+as or as we typically write T
+
+ align:start position:0%
+as or as we typically write T
+ 
+
+ align:start position:0%
+as or as we typically write T
+recognizable if it's the language of
+
+ align:start position:0%
+recognizable if it's the language of
+ 
+
+ align:start position:0%
+recognizable if it's the language of
+some touring machine the collection of
+
+ align:start position:0%
+some touring machine the collection of
+ 
+
+ align:start position:0%
+some touring machine the collection of
+accepted strings from that touring
+
+ align:start position:0%
+accepted strings from that touring
+ 
+
+ align:start position:0%
+accepted strings from that touring
+machine again just as before machine May
+
+ align:start position:0%
+machine again just as before machine May
+ 
+
+ align:start position:0%
+machine again just as before machine May
+accept zero strings one string many
+
+ align:start position:0%
+accept zero strings one string many
+ 
+
+ align:start position:0%
+accept zero strings one string many
+strings but it always has one language
+
+ align:start position:0%
+strings but it always has one language
+ 
+
+ align:start position:0%
+strings but it always has one language
+um the collection of all accepted
+
+ align:start position:0%
+um the collection of all accepted
+ 
+
+ align:start position:0%
+um the collection of all accepted
+strings um now if you have a decider
+
+ align:start position:0%
+strings um now if you have a decider
+ 
+
+ align:start position:0%
+strings um now if you have a decider
+which is a machine that never Loops
+
+ align:start position:0%
+which is a machine that never Loops
+ 
+
+ align:start position:0%
+which is a machine that never Loops
+which always halts on every input then
+
+ align:start position:0%
+which always halts on every input then
+ 
+
+ align:start position:0%
+which always halts on every input then
+we say its language is a decidable
+
+ align:start position:0%
+we say its language is a decidable
+ 
+
+ align:start position:0%
+we say its language is a decidable
+language so we'll say a language is
+
+ align:start position:0%
+language so we'll say a language is
+ 
+
+ align:start position:0%
+language so we'll say a language is
+turning decidable or simply decidable if
+
+ align:start position:0%
+turning decidable or simply decidable if
+ 
+
+ align:start position:0%
+turning decidable or simply decidable if
+it's the language of some
+
+ align:start position:0%
+it's the language of some
+ 
+
+ align:start position:0%
+it's the language of some
+decider which is a touring machine that
+
+ align:start position:0%
+decider which is a touring machine that
+ 
+
+ align:start position:0%
+decider which is a touring machine that
+always hals on all
+
+ align:start position:0%
+always hals on all
+ 
+
+ align:start position:0%
+always hals on all
+inputs so we have those two distinct
+
+ align:start position:0%
+inputs so we have those two distinct
+ 
+
+ align:start position:0%
+inputs so we have those two distinct
+Notions touring recognizable languages
+
+ align:start position:0%
+Notions touring recognizable languages
+ 
+
+ align:start position:0%
+Notions touring recognizable languages
+and touring decidable
+
+ align:start position:0%
+and touring decidable
+ 
+
+ align:start position:0%
+and touring decidable
+languages
+
+ align:start position:0%
+languages
+ 
+
+ align:start position:0%
+languages
+um now as we're going to argue this
+
+ align:start position:0%
+um now as we're going to argue this
+ 
+
+ align:start position:0%
+um now as we're going to argue this
+lecture touring machines are going to be
+
+ align:start position:0%
+lecture touring machines are going to be
+ 
+
+ align:start position:0%
+lecture touring machines are going to be
+our model of a general general purpose
+
+ align:start position:0%
+our model of a general general purpose
+ 
+
+ align:start position:0%
+our model of a general general purpose
+computer so that's the way we're going
+
+ align:start position:0%
+computer so that's the way we're going
+ 
+
+ align:start position:0%
+computer so that's the way we're going
+to think of computers as touring
+
+ align:start position:0%
+to think of computers as touring
+ 
+
+ align:start position:0%
+to think of computers as touring
+machines
+
+ align:start position:0%
+machines
+ 
+
+ align:start position:0%
+machines
+um and um why touring machines why
+
+ align:start position:0%
+um and um why touring machines why
+ 
+
+ align:start position:0%
+um and um why touring machines why
+didn't we pick something else well the
+
+ align:start position:0%
+didn't we pick something else well the
+ 
+
+ align:start position:0%
+didn't we pick something else well the
+fact is it doesn't matter and that's
+
+ align:start position:0%
+fact is it doesn't matter and that's
+ 
+
+ align:start position:0%
+fact is it doesn't matter and that's
+going to be the point of this lecture um
+
+ align:start position:0%
+going to be the point of this lecture um
+ 
+
+ align:start position:0%
+going to be the point of this lecture um
+all reasonable models of general purpose
+
+ align:start position:0%
+all reasonable models of general purpose
+ 
+
+ align:start position:0%
+all reasonable models of general purpose
+computation um you know unrestricted um
+
+ align:start position:0%
+computation um you know unrestricted um
+ 
+
+ align:start position:0%
+computation um you know unrestricted um
+computation in the sense of not limited
+
+ align:start position:0%
+computation in the sense of not limited
+ 
+
+ align:start position:0%
+computation in the sense of not limited
+memory um are all going to be are all
+
+ align:start position:0%
+memory um are all going to be are all
+ 
+
+ align:start position:0%
+memory um are all going to be are all
+have been shown um all the models that
+
+ align:start position:0%
+have been shown um all the models that
+ 
+
+ align:start position:0%
+have been shown um all the models that
+we've ever encountered have all been
+
+ align:start position:0%
+we've ever encountered have all been
+ 
+
+ align:start position:0%
+we've ever encountered have all been
+shown to be equivalent to one another um
+
+ align:start position:0%
+shown to be equivalent to one another um
+ 
+
+ align:start position:0%
+shown to be equivalent to one another um
+and so you you're free to pick anyone
+
+ align:start position:0%
+and so you you're free to pick anyone
+ 
+
+ align:start position:0%
+and so you you're free to pick anyone
+you like and so for this course we going
+
+ align:start position:0%
+you like and so for this course we going
+ 
+
+ align:start position:0%
+you like and so for this course we going
+to pick touring machines because they're
+
+ align:start position:0%
+to pick touring machines because they're
+ 
+
+ align:start position:0%
+to pick touring machines because they're
+very simple to argue about
+
+ align:start position:0%
+very simple to argue about
+ 
+
+ align:start position:0%
+very simple to argue about
+mathematically and also they have a sort
+
+ align:start position:0%
+mathematically and also they have a sort
+ 
+
+ align:start position:0%
+mathematically and also they have a sort
+of a some element of
+
+ align:start position:0%
+of a some element of
+ 
+
+ align:start position:0%
+of a some element of
+familiarity in that you know they're
+
+ align:start position:0%
+familiarity in that you know they're
+ 
+
+ align:start position:0%
+familiarity in that you know they're
+they they feel like um you You Well they
+
+ align:start position:0%
+they they feel like um you You Well they
+ 
+
+ align:start position:0%
+they they feel like um you You Well they
+um they're more familiar than some of
+
+ align:start position:0%
+um they're more familiar than some of
+ 
+
+ align:start position:0%
+um they're more familiar than some of
+the other models that have been proposed
+
+ align:start position:0%
+the other models that have been proposed
+ 
+
+ align:start position:0%
+the other models that have been proposed
+that are out there um you know such as
+
+ align:start position:0%
+that are out there um you know such as
+ 
+
+ align:start position:0%
+that are out there um you know such as
+you know re rewriting systems Lambda
+
+ align:start position:0%
+you know re rewriting systems Lambda
+ 
+
+ align:start position:0%
+you know re rewriting systems Lambda
+calculus and so on Turing machines Feel
+
+ align:start position:0%
+calculus and so on Turing machines Feel
+ 
+
+ align:start position:0%
+calculus and so on Turing machines Feel
+Like A Primitive kind of computer and
+
+ align:start position:0%
+Like A Primitive kind of computer and
+ 
+
+ align:start position:0%
+Like A Primitive kind of computer and
+that sense they have a certain
+
+ align:start position:0%
+that sense they have a certain
+ 
+
+ align:start position:0%
+that sense they have a certain
+familiarity okay um so let's start
+
+ align:start position:0%
+familiarity okay um so let's start
+ 
+
+ align:start position:0%
+familiarity okay um so let's start
+talking about variations on the touring
+
+ align:start position:0%
+talking about variations on the touring
+ 
+
+ align:start position:0%
+talking about variations on the touring
+Machine model and we're going to argue
+
+ align:start position:0%
+Machine model and we're going to argue
+ 
+
+ align:start position:0%
+Machine model and we're going to argue
+that it doesn't make it doesn't make any
+
+ align:start position:0%
+that it doesn't make it doesn't make any
+ 
+
+ align:start position:0%
+that it doesn't make it doesn't make any
+difference
+
+ align:start position:0%
+difference
+ 
+
+ align:start position:0%
+difference
+um and then where this is going to be
+
+ align:start position:0%
+um and then where this is going to be
+ 
+
+ align:start position:0%
+um and then where this is going to be
+kind of a precursor to a discussion of a
+
+ align:start position:0%
+kind of a precursor to a discussion of a
+ 
+
+ align:start position:0%
+kind of a precursor to a discussion of a
+bit of the history of the subject that
+
+ align:start position:0%
+bit of the history of the subject that
+ 
+
+ align:start position:0%
+bit of the history of the subject that
+we going and get to in the second half
+
+ align:start position:0%
+we going and get to in the second half
+ 
+
+ align:start position:0%
+we going and get to in the second half
+of the lecture so um a multi-tape
+
+ align:start position:0%
+of the lecture so um a multi-tape
+ 
+
+ align:start position:0%
+of the lecture so um a multi-tape
+turning machine is a turning machine as
+
+ align:start position:0%
+turning machine is a turning machine as
+ 
+
+ align:start position:0%
+turning machine is a turning machine as
+you might imagine that has more than one
+
+ align:start position:0%
+you might imagine that has more than one
+ 
+
+ align:start position:0%
+you might imagine that has more than one
+well it has one or possibly more tapes
+
+ align:start position:0%
+well it has one or possibly more tapes
+ 
+
+ align:start position:0%
+well it has one or possibly more tapes
+so a single tape touring machine would
+
+ align:start position:0%
+so a single tape touring machine would
+ 
+
+ align:start position:0%
+so a single tape touring machine would
+be a
+
+ align:start position:0%
+be a
+ 
+
+ align:start position:0%
+be a
+special version of a multitape turing
+
+ align:start position:0%
+special version of a multitape turing
+ 
+
+ align:start position:0%
+special version of a multitape turing
+machine that's okay uh but you might
+
+ align:start position:0%
+machine that's okay uh but you might
+ 
+
+ align:start position:0%
+machine that's okay uh but you might
+have more than one tape um as I've shown
+
+ align:start position:0%
+have more than one tape um as I've shown
+ 
+
+ align:start position:0%
+have more than one tape um as I've shown
+in this
+
+ align:start position:0%
+in this
+ 
+
+ align:start position:0%
+in this
+diagram now uh how do we actually use a
+
+ align:start position:0%
+diagram now uh how do we actually use a
+ 
+
+ align:start position:0%
+diagram now uh how do we actually use a
+multi-tape touring machine well you
+
+ align:start position:0%
+multi-tape touring machine well you
+ 
+
+ align:start position:0%
+multi-tape touring machine well you
+present the in and we're going to see
+
+ align:start position:0%
+present the in and we're going to see
+ 
+
+ align:start position:0%
+present the in and we're going to see
+these coming up for convenience
+
+ align:start position:0%
+these coming up for convenience
+ 
+
+ align:start position:0%
+these coming up for convenience
+sometimes it's it's it's nice to be
+
+ align:start position:0%
+sometimes it's it's it's nice to be
+ 
+
+ align:start position:0%
+sometimes it's it's it's nice to be
+working with multiple tapes uh so we're
+
+ align:start position:0%
+working with multiple tapes uh so we're
+ 
+
+ align:start position:0%
+working with multiple tapes uh so we're
+going to see these later on in the
+
+ align:start position:0%
+going to see these later on in the
+ 
+
+ align:start position:0%
+going to see these later on in the
+semester a couple of times as well
+
+ align:start position:0%
+semester a couple of times as well
+ 
+
+ align:start position:0%
+semester a couple of times as well
+but for now um you know we'll we're
+
+ align:start position:0%
+but for now um you know we'll we're
+ 
+
+ align:start position:0%
+but for now um you know we'll we're
+setting the model up so that the input
+
+ align:start position:0%
+setting the model up so that the input
+ 
+
+ align:start position:0%
+setting the model up so that the input
+is going to be presented on a special
+
+ align:start position:0%
+is going to be presented on a special
+ 
+
+ align:start position:0%
+is going to be presented on a special
+input tape um so that's where the input
+
+ align:start position:0%
+input tape um so that's where the input
+ 
+
+ align:start position:0%
+input tape um so that's where the input
+appears and it's going to be followed by
+
+ align:start position:0%
+appears and it's going to be followed by
+ 
+
+ align:start position:0%
+appears and it's going to be followed by
+blanks just as we had before and now we
+
+ align:start position:0%
+blanks just as we had before and now we
+ 
+
+ align:start position:0%
+blanks just as we had before and now we
+have these potentially other tapes
+
+ align:start position:0%
+have these potentially other tapes
+ 
+
+ align:start position:0%
+have these potentially other tapes
+possibly other tapes which are we call
+
+ align:start position:0%
+possibly other tapes which are we call
+ 
+
+ align:start position:0%
+possibly other tapes which are we call
+them work tapes where the machine can uh
+
+ align:start position:0%
+them work tapes where the machine can uh
+ 
+
+ align:start position:0%
+them work tapes where the machine can uh
+write other stuff as it wishes and those
+
+ align:start position:0%
+write other stuff as it wishes and those
+ 
+
+ align:start position:0%
+write other stuff as it wishes and those
+tapes are going to be initially blank uh
+
+ align:start position:0%
+tapes are going to be initially blank uh
+ 
+
+ align:start position:0%
+tapes are going to be initially blank uh
+so just all blanks on
+
+ align:start position:0%
+so just all blanks on
+ 
+
+ align:start position:0%
+so just all blanks on
+them all of the tapes are going to be
+
+ align:start position:0%
+them all of the tapes are going to be
+ 
+
+ align:start position:0%
+them all of the tapes are going to be
+read and write so you can write on the
+
+ align:start position:0%
+read and write so you can write on the
+ 
+
+ align:start position:0%
+read and write so you can write on the
+input tape obviously you can read on
+
+ align:start position:0%
+input tape obviously you can read on
+ 
+
+ align:start position:0%
+input tape obviously you can read on
+from the input tape and you can read and
+
+ align:start position:0%
+from the input tape and you can read and
+ 
+
+ align:start position:0%
+from the input tape and you can read and
+write on the other tapes as
+
+ align:start position:0%
+write on the other tapes as
+ 
+
+ align:start position:0%
+write on the other tapes as
+well um so what we want to First
+
+ align:start position:0%
+well um so what we want to First
+ 
+
+ align:start position:0%
+well um so what we want to First
+establish that by having these
+
+ align:start position:0%
+establish that by having these
+ 
+
+ align:start position:0%
+establish that by having these
+additional tapes you don't get
+
+ align:start position:0%
+additional tapes you don't get
+ 
+
+ align:start position:0%
+additional tapes you don't get
+additional power for the machine in the
+
+ align:start position:0%
+additional power for the machine in the
+ 
+
+ align:start position:0%
+additional power for the machine in the
+sense that you're not going to
+
+ align:start position:0%
+sense that you're not going to
+ 
+
+ align:start position:0%
+sense that you're not going to
+have um uh you won't have
+
+ align:start position:0%
+have um uh you won't have
+ 
+
+ align:start position:0%
+have um uh you won't have
+additional uh um languages that you can
+
+ align:start position:0%
+additional uh um languages that you can
+ 
+
+ align:start position:0%
+additional uh um languages that you can
+recognize by virtue of having these
+
+ align:start position:0%
+recognize by virtue of having these
+ 
+
+ align:start position:0%
+recognize by virtue of having these
+additional tapes me you you could
+
+ align:start position:0%
+additional tapes me you you could
+ 
+
+ align:start position:0%
+additional tapes me you you could
+imagine that having more tapes will
+
+ align:start position:0%
+imagine that having more tapes will
+ 
+
+ align:start position:0%
+imagine that having more tapes will
+allow you to do more things um you know
+
+ align:start position:0%
+allow you to do more things um you know
+ 
+
+ align:start position:0%
+allow you to do more things um you know
+for example if you have a push down
+
+ align:start position:0%
+for example if you have a push down
+ 
+
+ align:start position:0%
+for example if you have a push down
+automaton with two stacks you can do
+
+ align:start position:0%
+automaton with two stacks you can do
+ 
+
+ align:start position:0%
+automaton with two stacks you can do
+more languages than you can with one
+
+ align:start position:0%
+more languages than you can with one
+ 
+
+ align:start position:0%
+more languages than you can with one
+stack so it's conceivable that by having
+
+ align:start position:0%
+stack so it's conceivable that by having
+ 
+
+ align:start position:0%
+stack so it's conceivable that by having
+more tapes you can do more languages
+
+ align:start position:0%
+more tapes you can do more languages
+ 
+
+ align:start position:0%
+more tapes you can do more languages
+than you could with one with one
+
+ align:start position:0%
+than you could with one with one
+ 
+
+ align:start position:0%
+than you could with one with one
+tape but in fact that's not the case one
+
+ align:start position:0%
+tape but in fact that's not the case one
+ 
+
+ align:start position:0%
+tape but in fact that's not the case one
+one tape is as good as having many tapes
+
+ align:start position:0%
+one tape is as good as having many tapes
+ 
+
+ align:start position:0%
+one tape is as good as having many tapes
+uh and we're going to prove that you
+
+ align:start position:0%
+uh and we're going to prove that you
+ 
+
+ align:start position:0%
+uh and we're going to prove that you
+know uh we're going to quickly sketch
+
+ align:start position:0%
+know uh we're going to quickly sketch
+ 
+
+ align:start position:0%
+know uh we're going to quickly sketch
+through the proof of that fact um so uh
+
+ align:start position:0%
+through the proof of that fact um so uh
+ 
+
+ align:start position:0%
+through the proof of that fact um so uh
+the theorem is that a touring machine a
+
+ align:start position:0%
+the theorem is that a touring machine a
+ 
+
+ align:start position:0%
+the theorem is that a touring machine a
+language is touring recognizable and
+
+ align:start position:0%
+language is touring recognizable and
+ 
+
+ align:start position:0%
+language is touring recognizable and
+when we say touring recognizable for now
+
+ align:start position:0%
+when we say touring recognizable for now
+ 
+
+ align:start position:0%
+when we say touring recognizable for now
+we mean just with one tape um so um
+
+ align:start position:0%
+we mean just with one tape um so um
+ 
+
+ align:start position:0%
+we mean just with one tape um so um
+that's the way we've defined it so a
+
+ align:start position:0%
+that's the way we've defined it so a
+ 
+
+ align:start position:0%
+that's the way we've defined it so a
+language is touring recognizable if and
+
+ align:start position:0%
+language is touring recognizable if and
+ 
+
+ align:start position:0%
+language is touring recognizable if and
+only if some multi-tape touring machine
+
+ align:start position:0%
+only if some multi-tape touring machine
+ 
+
+ align:start position:0%
+only if some multi-tape touring machine
+recognizes that language
+
+ align:start position:0%
+recognizes that language
+ 
+
+ align:start position:0%
+recognizes that language
+okay so really that another way of
+
+ align:start position:0%
+okay so really that another way of
+ 
+
+ align:start position:0%
+okay so really that another way of
+saying that is um if you have a language
+
+ align:start position:0%
+saying that is um if you have a language
+ 
+
+ align:start position:0%
+saying that is um if you have a language
+that you can do with a single tape you
+
+ align:start position:0%
+that you can do with a single tape you
+ 
+
+ align:start position:0%
+that you can do with a single tape you
+can do it with a multi-tape and vice
+
+ align:start position:0%
+can do it with a multi-tape and vice
+ 
+
+ align:start position:0%
+can do it with a multi-tape and vice
+versa so One Direction of that is
+
+ align:start position:0%
+versa so One Direction of that is
+ 
+
+ align:start position:0%
+versa so One Direction of that is
+immediate because a single tape touring
+
+ align:start position:0%
+immediate because a single tape touring
+ 
+
+ align:start position:0%
+immediate because a single tape touring
+machine is already a multi-tape touring
+
+ align:start position:0%
+machine is already a multi-tape touring
+ 
+
+ align:start position:0%
+machine is already a multi-tape touring
+machine that just happens to have one
+
+ align:start position:0%
+machine that just happens to have one
+ 
+
+ align:start position:0%
+machine that just happens to have one
+tape uh so the forward direction of that
+
+ align:start position:0%
+tape uh so the forward direction of that
+ 
+
+ align:start position:0%
+tape uh so the forward direction of that
+is is um there's nothing to say that's
+
+ align:start position:0%
+is is um there's nothing to say that's
+ 
+
+ align:start position:0%
+is is um there's nothing to say that's
+just immediately true um but if we want
+
+ align:start position:0%
+just immediately true um but if we want
+ 
+
+ align:start position:0%
+just immediately true um but if we want
+to prove the reverse then we're going to
+
+ align:start position:0%
+to prove the reverse then we're going to
+ 
+
+ align:start position:0%
+to prove the reverse then we're going to
+have to do some work um and the work is
+
+ align:start position:0%
+have to do some work um and the work is
+ 
+
+ align:start position:0%
+have to do some work um and the work is
+going to be showing how do you convert a
+
+ align:start position:0%
+going to be showing how do you convert a
+ 
+
+ align:start position:0%
+going to be showing how do you convert a
+multi-tape touring machine to a single
+
+ align:start position:0%
+multi-tape touring machine to a single
+ 
+
+ align:start position:0%
+multi-tape touring machine to a single
+tape touring machine so if we have
+
+ align:start position:0%
+tape touring machine so if we have
+ 
+
+ align:start position:0%
+tape touring machine so if we have
+something that's recognized by a
+
+ align:start position:0%
+something that's recognized by a
+ 
+
+ align:start position:0%
+something that's recognized by a
+multi-tape touring machine it's still
+
+ align:start position:0%
+multi-tape touring machine it's still
+ 
+
+ align:start position:0%
+multi-tape touring machine it's still
+touring recognizable and what that means
+
+ align:start position:0%
+touring recognizable and what that means
+ 
+
+ align:start position:0%
+touring recognizable and what that means
+is you can do it with a single tape
+
+ align:start position:0%
+is you can do it with a single tape
+ 
+
+ align:start position:0%
+is you can do it with a single tape
+touring machine so we have to show how
+
+ align:start position:0%
+touring machine so we have to show how
+ 
+
+ align:start position:0%
+touring machine so we have to show how
+to do the
+
+ align:start position:0%
+to do the
+ 
+
+ align:start position:0%
+to do the
+conversion and I'll kind of you know I
+
+ align:start position:0%
+conversion and I'll kind of you know I
+ 
+
+ align:start position:0%
+conversion and I'll kind of you know I
+I'll I I'll show you that I think in a
+
+ align:start position:0%
+I'll I I'll show you that I think in a
+ 
+
+ align:start position:0%
+I'll I I'll show you that I think in a
+convincing way but you know without
+
+ align:start position:0%
+convincing way but you know without
+ 
+
+ align:start position:0%
+convincing way but you know without
+getting into too much detail um so
+
+ align:start position:0%
+getting into too much detail um so
+ 
+
+ align:start position:0%
+getting into too much detail um so
+here's an image of a multi-tape touring
+
+ align:start position:0%
+here's an image of a multi-tape touring
+ 
+
+ align:start position:0%
+here's an image of a multi-tape touring
+machine in during the course of its
+
+ align:start position:0%
+machine in during the course of its
+ 
+
+ align:start position:0%
+machine in during the course of its
+input so it has already we've already
+
+ align:start position:0%
+input so it has already we've already
+ 
+
+ align:start position:0%
+input so it has already we've already
+started it off um you know initially it
+
+ align:start position:0%
+started it off um you know initially it
+ 
+
+ align:start position:0%
+started it off um you know initially it
+starts off with the um other tapes the
+
+ align:start position:0%
+starts off with the um other tapes the
+ 
+
+ align:start position:0%
+starts off with the um other tapes the
+work tapes being all blank but now it's
+
+ align:start position:0%
+work tapes being all blank but now it's
+ 
+
+ align:start position:0%
+work tapes being all blank but now it's
+processed for a while and you know the
+
+ align:start position:0%
+processed for a while and you know the
+ 
+
+ align:start position:0%
+processed for a while and you know the
+head on the input tape is now has moved
+
+ align:start position:0%
+head on the input tape is now has moved
+ 
+
+ align:start position:0%
+head on the input tape is now has moved
+off from its starting position at the
+
+ align:start position:0%
+off from its starting position at the
+ 
+
+ align:start position:0%
+off from its starting position at the
+left end it's somewhere in the middle
+
+ align:start position:0%
+left end it's somewhere in the middle
+ 
+
+ align:start position:0%
+left end it's somewhere in the middle
+it's written stuff on the other
+
+ align:start position:0%
+it's written stuff on the other
+ 
+
+ align:start position:0%
+it's written stuff on the other
+tapes and what we want to is show how to
+
+ align:start position:0%
+tapes and what we want to is show how to
+ 
+
+ align:start position:0%
+tapes and what we want to is show how to
+represent that same
+
+ align:start position:0%
+represent that same
+ 
+
+ align:start position:0%
+represent that same
+information on a single tape touring
+
+ align:start position:0%
+information on a single tape touring
+ 
+
+ align:start position:0%
+information on a single tape touring
+machine in a way which allows the single
+
+ align:start position:0%
+machine in a way which allows the single
+ 
+
+ align:start position:0%
+machine in a way which allows the single
+tape touring machine to carry out the
+
+ align:start position:0%
+tape touring machine to carry out the
+ 
+
+ align:start position:0%
+tape touring machine to carry out the
+steps of the multi-tape touring machine
+
+ align:start position:0%
+steps of the multi-tape touring machine
+ 
+
+ align:start position:0%
+steps of the multi-tape touring machine
+but using only its single tape by virtue
+
+ align:start position:0%
+but using only its single tape by virtue
+ 
+
+ align:start position:0%
+but using only its single tape by virtue
+of some kind of a data structure which
+
+ align:start position:0%
+of some kind of a data structure which
+ 
+
+ align:start position:0%
+of some kind of a data structure which
+allows for the simulation to to go
+
+ align:start position:0%
+allows for the simulation to to go
+ 
+
+ align:start position:0%
+allows for the simulation to to go
+forward okay so how is the simul the
+
+ align:start position:0%
+forward okay so how is the simul the
+ 
+
+ align:start position:0%
+forward okay so how is the simul the
+single tape touring machine going to be
+
+ align:start position:0%
+single tape touring machine going to be
+ 
+
+ align:start position:0%
+single tape touring machine going to be
+simulating going to be carrying out the
+
+ align:start position:0%
+simulating going to be carrying out the
+ 
+
+ align:start position:0%
+simulating going to be carrying out the
+the the same effect of having these
+
+ align:start position:0%
+the the same effect of having these
+ 
+
+ align:start position:0%
+the the same effect of having these
+multiple types on the multi-tape touring
+
+ align:start position:0%
+multiple types on the multi-tape touring
+ 
+
+ align:start position:0%
+multiple types on the multi-tape touring
+machine so here's a picture of the
+
+ align:start position:0%
+machine so here's a picture of the
+ 
+
+ align:start position:0%
+machine so here's a picture of the
+single tape touring machine it just has
+
+ align:start position:0%
+single tape touring machine it just has
+ 
+
+ align:start position:0%
+single tape touring machine it just has
+one
+
+ align:start position:0%
+one
+ 
+
+ align:start position:0%
+one
+tape by the way I should mention that
+
+ align:start position:0%
+tape by the way I should mention that
+ 
+
+ align:start position:0%
+tape by the way I should mention that
+all of the tapes are infinite to the
+
+ align:start position:0%
+all of the tapes are infinite to the
+ 
+
+ align:start position:0%
+all of the tapes are infinite to the
+right um in the multi-tape touring
+
+ align:start position:0%
+right um in the multi-tape touring
+ 
+
+ align:start position:0%
+right um in the multi-tape touring
+machine just as we had for the single
+
+ align:start position:0%
+machine just as we had for the single
+ 
+
+ align:start position:0%
+machine just as we had for the single
+tape touring machine and now uh with
+
+ align:start position:0%
+tape touring machine and now uh with
+ 
+
+ align:start position:0%
+tape touring machine and now uh with
+this uh single tape turning machine it's
+
+ align:start position:0%
+this uh single tape turning machine it's
+ 
+
+ align:start position:0%
+this uh single tape turning machine it's
+going to represent the information that
+
+ align:start position:0%
+going to represent the information that
+ 
+
+ align:start position:0%
+going to represent the information that
+was on that's present on these multiple
+
+ align:start position:0%
+was on that's present on these multiple
+ 
+
+ align:start position:0%
+was on that's present on these multiple
+tapes but using only the single tape and
+
+ align:start position:0%
+tapes but using only the single tape and
+ 
+
+ align:start position:0%
+tapes but using only the single tape and
+the way I'm choosing to do that is going
+
+ align:start position:0%
+the way I'm choosing to do that is going
+ 
+
+ align:start position:0%
+the way I'm choosing to do that is going
+to be particularly simple um I'm going
+
+ align:start position:0%
+to be particularly simple um I'm going
+ 
+
+ align:start position:0%
+to be particularly simple um I'm going
+to just divide up so here I'm saying it
+
+ align:start position:0%
+to just divide up so here I'm saying it
+ 
+
+ align:start position:0%
+to just divide up so here I'm saying it
+in words uh it's going to simulate in by
+
+ align:start position:0%
+in words uh it's going to simulate in by
+ 
+
+ align:start position:0%
+in words uh it's going to simulate in by
+storing the contents of the multitape on
+
+ align:start position:0%
+storing the contents of the multitape on
+ 
+
+ align:start position:0%
+storing the contents of the multitape on
+the single tape in separate blocks so
+
+ align:start position:0%
+the single tape in separate blocks so
+ 
+
+ align:start position:0%
+the single tape in separate blocks so
+I'm basically going to divide up the
+
+ align:start position:0%
+I'm basically going to divide up the
+ 
+
+ align:start position:0%
+I'm basically going to divide up the
+single tape uh touring machines tape
+
+ align:start position:0%
+single tape uh touring machines tape
+ 
+
+ align:start position:0%
+single tape uh touring machines tape
+into separate regions where each one of
+
+ align:start position:0%
+into separate regions where each one of
+ 
+
+ align:start position:0%
+into separate regions where each one of
+those regions is going to have the
+
+ align:start position:0%
+those regions is going to have the
+ 
+
+ align:start position:0%
+those regions is going to have the
+information that was on one of the
+
+ align:start position:0%
+information that was on one of the
+ 
+
+ align:start position:0%
+information that was on one of the
+tapes in the um multi-tape
+
+ align:start position:0%
+tapes in the um multi-tape
+ 
+
+ align:start position:0%
+tapes in the um multi-tape
+machine so for example here is on the
+
+ align:start position:0%
+machine so for example here is on the
+ 
+
+ align:start position:0%
+machine so for example here is on the
+first tape it's got a a BBA well that's
+
+ align:start position:0%
+first tape it's got a a BBA well that's
+ 
+
+ align:start position:0%
+first tape it's got a a BBA well that's
+going to appear here in that first block
+
+ align:start position:0%
+going to appear here in that first block
+ 
+
+ align:start position:0%
+going to appear here in that first block
+on the single tape turning machine
+
+ align:start position:0%
+on the single tape turning machine
+ 
+
+ align:start position:0%
+on the single tape turning machine
+okay sort of seeing it float down to
+
+ align:start position:0%
+okay sort of seeing it float down to
+ 
+
+ align:start position:0%
+okay sort of seeing it float down to
+suggest that it's coming from this
+
+ align:start position:0%
+suggest that it's coming from this
+ 
+
+ align:start position:0%
+suggest that it's coming from this
+multi-tape touring machine but that's
+
+ align:start position:0%
+multi-tape touring machine but that's
+ 
+
+ align:start position:0%
+multi-tape touring machine but that's
+really been developed by the simulation
+
+ align:start position:0%
+really been developed by the simulation
+ 
+
+ align:start position:0%
+really been developed by the simulation
+that the single tape touring machine has
+
+ align:start position:0%
+that the single tape touring machine has
+ 
+
+ align:start position:0%
+that the single tape touring machine has
+obviously the single tape turning
+
+ align:start position:0%
+obviously the single tape turning
+ 
+
+ align:start position:0%
+obviously the single tape turning
+machine doesn't have any direct access
+
+ align:start position:0%
+machine doesn't have any direct access
+ 
+
+ align:start position:0%
+machine doesn't have any direct access
+to the multitape machine but it's going
+
+ align:start position:0%
+to the multitape machine but it's going
+ 
+
+ align:start position:0%
+to the multitape machine but it's going
+to be
+
+ align:start position:0%
+to be
+ 
+
+ align:start position:0%
+to be
+simulating so this is how we're showing
+
+ align:start position:0%
+simulating so this is how we're showing
+ 
+
+ align:start position:0%
+simulating so this is how we're showing
+the data is being stored on the single
+
+ align:start position:0%
+the data is being stored on the single
+ 
+
+ align:start position:0%
+the data is being stored on the single
+tape machine's tape so in the second
+
+ align:start position:0%
+tape machine's tape so in the second
+ 
+
+ align:start position:0%
+tape machine's tape so in the second
+Block it's going to have the contents of
+
+ align:start position:0%
+Block it's going to have the contents of
+ 
+
+ align:start position:0%
+Block it's going to have the contents of
+the second uh tape of the touring
+
+ align:start position:0%
+the second uh tape of the touring
+ 
+
+ align:start position:0%
+the second uh tape of the touring
+multitape
+
+ align:start position:0%
+multitape
+ 
+
+ align:start position:0%
+multitape
+machine and the uh the final um uh
+
+ align:start position:0%
+machine and the uh the final um uh
+ 
+
+ align:start position:0%
+machine and the uh the final um uh
+region of the single tapes the final
+
+ align:start position:0%
+region of the single tapes the final
+ 
+
+ align:start position:0%
+region of the single tapes the final
+block so-called of the single tapes tape
+
+ align:start position:0%
+block so-called of the single tapes tape
+ 
+
+ align:start position:0%
+block so-called of the single tapes tape
+is going to have single tape machine's
+
+ align:start position:0%
+is going to have single tape machine's
+ 
+
+ align:start position:0%
+is going to have single tape machine's
+tape is going to have the the rest of
+
+ align:start position:0%
+tape is going to have the the rest of
+ 
+
+ align:start position:0%
+tape is going to have the the rest of
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+um the contents of the last tape of of M
+
+ align:start position:0%
+um the contents of the last tape of of M
+ 
+
+ align:start position:0%
+um the contents of the last tape of of M
+and then it's going to be followed by
+
+ align:start position:0%
+and then it's going to be followed by
+ 
+
+ align:start position:0%
+and then it's going to be followed by
+the same infinitely many blanks that
+
+ align:start position:0%
+the same infinitely many blanks that
+ 
+
+ align:start position:0%
+the same infinitely many blanks that
+each of these um uh tapes are going to
+
+ align:start position:0%
+each of these um uh tapes are going to
+ 
+
+ align:start position:0%
+each of these um uh tapes are going to
+have uh following the portion that they
+
+ align:start position:0%
+have uh following the portion that they
+ 
+
+ align:start position:0%
+have uh following the portion that they
+may have written during the course of
+
+ align:start position:0%
+may have written during the course of
+ 
+
+ align:start position:0%
+may have written during the course of
+their
+
+ align:start position:0%
+their
+ 
+
+ align:start position:0%
+their
+computation okay um so that's what the
+
+ align:start position:0%
+computation okay um so that's what the
+ 
+
+ align:start position:0%
+computation okay um so that's what the
+single tape touring machine's tape is
+
+ align:start position:0%
+single tape touring machine's tape is
+ 
+
+ align:start position:0%
+single tape touring machine's tape is
+going to look like during the course of
+
+ align:start position:0%
+going to look like during the course of
+ 
+
+ align:start position:0%
+going to look like during the course of
+its computation it's going to have the
+
+ align:start position:0%
+its computation it's going to have the
+ 
+
+ align:start position:0%
+its computation it's going to have the
+information represented in these blocks
+
+ align:start position:0%
+information represented in these blocks
+ 
+
+ align:start position:0%
+information represented in these blocks
+capturing all of the information that
+
+ align:start position:0%
+capturing all of the information that
+ 
+
+ align:start position:0%
+capturing all of the information that
+the multi-tape touring machine has in a
+
+ align:start position:0%
+the multi-tape touring machine has in a
+ 
+
+ align:start position:0%
+the multi-tape touring machine has in a
+perhaps somewhat less convenient way
+
+ align:start position:0%
+perhaps somewhat less convenient way
+ 
+
+ align:start position:0%
+perhaps somewhat less convenient way
+because the multi-tape touring machine
+
+ align:start position:0%
+because the multi-tape touring machine
+ 
+
+ align:start position:0%
+because the multi-tape touring machine
+you know we didn't really make this
+
+ align:start position:0%
+you know we didn't really make this
+ 
+
+ align:start position:0%
+you know we didn't really make this
+explicit and in part because it doesn't
+
+ align:start position:0%
+explicit and in part because it doesn't
+ 
+
+ align:start position:0%
+explicit and in part because it doesn't
+really matter we didn't say exactly how
+
+ align:start position:0%
+really matter we didn't say exactly how
+ 
+
+ align:start position:0%
+really matter we didn't say exactly how
+the multi-tape touring machine operates
+
+ align:start position:0%
+the multi-tape touring machine operates
+ 
+
+ align:start position:0%
+the multi-tape touring machine operates
+what I have in mind is that the
+
+ align:start position:0%
+what I have in mind is that the
+ 
+
+ align:start position:0%
+what I have in mind is that the
+multi-tape touring machine can read and
+
+ align:start position:0%
+multi-tape touring machine can read and
+ 
+
+ align:start position:0%
+multi-tape touring machine can read and
+move all of its heads from all of its
+
+ align:start position:0%
+move all of its heads from all of its
+ 
+
+ align:start position:0%
+move all of its heads from all of its
+heads in one step
+
+ align:start position:0%
+heads in one step
+ 
+
+ align:start position:0%
+heads in one step
+so in a single step of the multitape
+
+ align:start position:0%
+so in a single step of the multitape
+ 
+
+ align:start position:0%
+so in a single step of the multitape
+machine it can it can obtain the
+
+ align:start position:0%
+machine it can it can obtain the
+ 
+
+ align:start position:0%
+machine it can it can obtain the
+information that's underneath each of
+
+ align:start position:0%
+information that's underneath each of
+ 
+
+ align:start position:0%
+information that's underneath each of
+its heads feed that into its transition
+
+ align:start position:0%
+its heads feed that into its transition
+ 
+
+ align:start position:0%
+its heads feed that into its transition
+function and then together with the
+
+ align:start position:0%
+function and then together with the
+ 
+
+ align:start position:0%
+function and then together with the
+state of the multitape machine decide
+
+ align:start position:0%
+state of the multitape machine decide
+ 
+
+ align:start position:0%
+state of the multitape machine decide
+how to change each of those locations
+
+ align:start position:0%
+how to change each of those locations
+ 
+
+ align:start position:0%
+how to change each of those locations
+and then how to move each one of those
+
+ align:start position:0%
+and then how to move each one of those
+ 
+
+ align:start position:0%
+and then how to move each one of those
+heads so it's kind of operating on all
+
+ align:start position:0%
+heads so it's kind of operating on all
+ 
+
+ align:start position:0%
+heads so it's kind of operating on all
+of the tapes in
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+parallel okay so now uh how how does the
+
+ align:start position:0%
+parallel okay so now uh how how does the
+ 
+
+ align:start position:0%
+parallel okay so now uh how how does the
+actual steps of the simulation of the
+
+ align:start position:0%
+actual steps of the simulation of the
+ 
+
+ align:start position:0%
+actual steps of the simulation of the
+single tape you know by the single tape
+
+ align:start position:0%
+single tape you know by the single tape
+ 
+
+ align:start position:0%
+single tape you know by the single tape
+um machine had as a go so first of
+
+ align:start position:0%
+um machine had as a go so first of
+ 
+
+ align:start position:0%
+um machine had as a go so first of
+all besides storing the contents of each
+
+ align:start position:0%
+all besides storing the contents of each
+ 
+
+ align:start position:0%
+all besides storing the contents of each
+of the tapes in in s's single
+
+ align:start position:0%
+of the tapes in in s's single
+ 
+
+ align:start position:0%
+of the tapes in in s's single
+tape there's some additional information
+
+ align:start position:0%
+tape there's some additional information
+ 
+
+ align:start position:0%
+tape there's some additional information
+that it needs to record
+
+ align:start position:0%
+that it needs to record
+ 
+
+ align:start position:0%
+that it needs to record
+namely um M has a head for each one of
+
+ align:start position:0%
+namely um M has a head for each one of
+ 
+
+ align:start position:0%
+namely um M has a head for each one of
+its tapes
+
+ align:start position:0%
+its tapes
+ 
+
+ align:start position:0%
+its tapes
+but s has just a single
+
+ align:start position:0%
+but s has just a single
+ 
+
+ align:start position:0%
+but s has just a single
+head and each of M's heads could be in
+
+ align:start position:0%
+head and each of M's heads could be in
+ 
+
+ align:start position:0%
+head and each of M's heads could be in
+some different location you know in this
+
+ align:start position:0%
+some different location you know in this
+ 
+
+ align:start position:0%
+some different location you know in this
+case as I've shown it on the first tape
+
+ align:start position:0%
+case as I've shown it on the first tape
+ 
+
+ align:start position:0%
+case as I've shown it on the first tape
+it's headed in location three on the
+
+ align:start position:0%
+it's headed in location three on the
+ 
+
+ align:start position:0%
+it's headed in location three on the
+second tape it's in location two on the
+
+ align:start position:0%
+second tape it's in location two on the
+ 
+
+ align:start position:0%
+second tape it's in location two on the
+third tape it's on location on the last
+
+ align:start position:0%
+third tape it's on location on the last
+ 
+
+ align:start position:0%
+third tape it's on location on the last
+tape it's in location one uh so where
+
+ align:start position:0%
+tape it's in location one uh so where
+ 
+
+ align:start position:0%
+tape it's in location one uh so where
+were we we were simulating the
+
+ align:start position:0%
+were we we were simulating the
+ 
+
+ align:start position:0%
+were we we were simulating the
+multi-tape touring machine with the
+
+ align:start position:0%
+multi-tape touring machine with the
+ 
+
+ align:start position:0%
+multi-tape touring machine with the
+single tape touring machine and we had
+
+ align:start position:0%
+single tape touring machine and we had
+ 
+
+ align:start position:0%
+single tape touring machine and we had
+to keep track of where the heads are
+
+ align:start position:0%
+to keep track of where the heads are
+ 
+
+ align:start position:0%
+to keep track of where the heads are
+um and so we're going to do that by
+
+ align:start position:0%
+um and so we're going to do that by
+ 
+
+ align:start position:0%
+um and so we're going to do that by
+writing the locations on those
+
+ align:start position:0%
+writing the locations on those
+ 
+
+ align:start position:0%
+writing the locations on those
+blocks okay so we're going to have a
+
+ align:start position:0%
+blocks okay so we're going to have a
+ 
+
+ align:start position:0%
+blocks okay so we're going to have a
+special dot as I've shown here to
+
+ align:start position:0%
+special dot as I've shown here to
+ 
+
+ align:start position:0%
+special dot as I've shown here to
+represent the location of the head in
+
+ align:start position:0%
+represent the location of the head in
+ 
+
+ align:start position:0%
+represent the location of the head in
+that very first block so the head's on
+
+ align:start position:0%
+that very first block so the head's on
+ 
+
+ align:start position:0%
+that very first block so the head's on
+the B I'm going to dot the B and I'm
+
+ align:start position:0%
+the B I'm going to dot the B and I'm
+ 
+
+ align:start position:0%
+the B I'm going to dot the B and I'm
+going to do the same thing for the
+
+ align:start position:0%
+going to do the same thing for the
+ 
+
+ align:start position:0%
+going to do the same thing for the
+locations of the others um
+
+ align:start position:0%
+locations of the others um
+ 
+
+ align:start position:0%
+locations of the others um
+heads and how am I getting that effect
+
+ align:start position:0%
+heads and how am I getting that effect
+ 
+
+ align:start position:0%
+heads and how am I getting that effect
+well we've had seen something like that
+
+ align:start position:0%
+well we've had seen something like that
+ 
+
+ align:start position:0%
+well we've had seen something like that
+before where we just expand the tape
+
+ align:start position:0%
+before where we just expand the tape
+ 
+
+ align:start position:0%
+before where we just expand the tape
+alphabet of s to allow for these dotted
+
+ align:start position:0%
+alphabet of s to allow for these dotted
+ 
+
+ align:start position:0%
+alphabet of s to allow for these dotted
+symbols as well as the uh irregular
+
+ align:start position:0%
+symbols as well as the uh irregular
+ 
+
+ align:start position:0%
+symbols as well as the uh irregular
+symbols we also have expanded it to
+
+ align:start position:0%
+symbols we also have expanded it to
+ 
+
+ align:start position:0%
+symbols we also have expanded it to
+include the the limiter markers that
+
+ align:start position:0%
+include the the limiter markers that
+ 
+
+ align:start position:0%
+include the the limiter markers that
+separate the blocks one one another
+
+ align:start position:0%
+separate the blocks one one another
+ 
+
+ align:start position:0%
+separate the blocks one one another
+which I'm writing as a pound sign um so
+
+ align:start position:0%
+which I'm writing as a pound sign um so
+ 
+
+ align:start position:0%
+which I'm writing as a pound sign um so
+we can just get that effect simply by
+
+ align:start position:0%
+we can just get that effect simply by
+ 
+
+ align:start position:0%
+we can just get that effect simply by
+expanding the tape alphabet of s okay a
+
+ align:start position:0%
+expanding the tape alphabet of s okay a
+ 
+
+ align:start position:0%
+expanding the tape alphabet of s okay a
+few more details of s that are just
+
+ align:start position:0%
+few more details of s that are just
+ 
+
+ align:start position:0%
+few more details of s that are just
+worth looking at just to make sure we're
+
+ align:start position:0%
+worth looking at just to make sure we're
+ 
+
+ align:start position:0%
+worth looking at just to make sure we're
+kind of all understanding what's
+
+ align:start position:0%
+kind of all understanding what's
+ 
+
+ align:start position:0%
+kind of all understanding what's
+happening so for every time M takes one
+
+ align:start position:0%
+happening so for every time M takes one
+ 
+
+ align:start position:0%
+happening so for every time M takes one
+step s has actually a lot of work to do
+
+ align:start position:0%
+step s has actually a lot of work to do
+ 
+
+ align:start position:0%
+step s has actually a lot of work to do
+because one step of M it can move all of
+
+ align:start position:0%
+because one step of M it can move all of
+ 
+
+ align:start position:0%
+because one step of M it can move all of
+those read read and move all of those
+
+ align:start position:0%
+those read read and move all of those
+ 
+
+ align:start position:0%
+those read read and move all of those
+heads all at one shot s has to scan the
+
+ align:start position:0%
+heads all at one shot s has to scan the
+ 
+
+ align:start position:0%
+heads all at one shot s has to scan the
+entire tape to see what those what's
+
+ align:start position:0%
+entire tape to see what those what's
+ 
+
+ align:start position:0%
+entire tape to see what those what's
+underneath those in effect virtual heads
+
+ align:start position:0%
+underneath those in effect virtual heads
+ 
+
+ align:start position:0%
+underneath those in effect virtual heads
+which are the locations of the dotted
+
+ align:start position:0%
+which are the locations of the dotted
+ 
+
+ align:start position:0%
+which are the locations of the dotted
+symbols it has to see what's underneath
+
+ align:start position:0%
+symbols it has to see what's underneath
+ 
+
+ align:start position:0%
+symbols it has to see what's underneath
+each one of those
+
+ align:start position:0%
+each one of those
+ 
+
+ align:start position:0%
+each one of those
+heads um uh to see how to update the
+
+ align:start position:0%
+heads um uh to see how to update the
+ 
+
+ align:start position:0%
+heads um uh to see how to update the
+transition you know update its state to
+
+ align:start position:0%
+transition you know update its state to
+ 
+
+ align:start position:0%
+transition you know update its state to
+the next state and then it has to scan
+
+ align:start position:0%
+the next state and then it has to scan
+ 
+
+ align:start position:0%
+the next state and then it has to scan
+again to um change the the location
+
+ align:start position:0%
+again to um change the the location
+ 
+
+ align:start position:0%
+again to um change the the location
+change the contents of those of those
+
+ align:start position:0%
+change the contents of those of those
+ 
+
+ align:start position:0%
+change the contents of those of those
+tape locations and also to move the head
+
+ align:start position:0%
+tape locations and also to move the head
+ 
+
+ align:start position:0%
+tape locations and also to move the head
+left or right by moving the effectively
+
+ align:start position:0%
+left or right by moving the effectively
+ 
+
+ align:start position:0%
+left or right by moving the effectively
+now moving the dot left or right so
+
+ align:start position:0%
+now moving the dot left or right so
+ 
+
+ align:start position:0%
+now moving the dot left or right so
+that's pretty straightforward
+
+ align:start position:0%
+that's pretty straightforward
+ 
+
+ align:start position:0%
+that's pretty straightforward
+uh uh there's one application that can
+
+ align:start position:0%
+uh uh there's one application that can
+ 
+
+ align:start position:0%
+uh uh there's one application that can
+occur however um which is that what
+
+ align:start position:0%
+occur however um which is that what
+ 
+
+ align:start position:0%
+occur however um which is that what
+happens if um on one of the tapes let's
+
+ align:start position:0%
+happens if um on one of the tapes let's
+ 
+
+ align:start position:0%
+happens if um on one of the tapes let's
+say m starts using writing more content
+
+ align:start position:0%
+say m starts using writing more content
+ 
+
+ align:start position:0%
+say m starts using writing more content
+then you have room in that
+
+ align:start position:0%
+then you have room in that
+ 
+
+ align:start position:0%
+then you have room in that
+block uh to store that
+
+ align:start position:0%
+block uh to store that
+ 
+
+ align:start position:0%
+block uh to store that
+information you know so if M like moves
+
+ align:start position:0%
+information you know so if M like moves
+ 
+
+ align:start position:0%
+information you know so if M like moves
+it has one1 suppose M you know after a
+
+ align:start position:0%
+it has one1 suppose M you know after a
+ 
+
+ align:start position:0%
+it has one1 suppose M you know after a
+few steps moves its head into the
+
+ align:start position:0%
+few steps moves its head into the
+ 
+
+ align:start position:0%
+few steps moves its head into the
+original blank portion of the tape and
+
+ align:start position:0%
+original blank portion of the tape and
+ 
+
+ align:start position:0%
+original blank portion of the tape and
+writes another symbol there we we have
+
+ align:start position:0%
+writes another symbol there we we have
+ 
+
+ align:start position:0%
+writes another symbol there we we have
+to put that symbol somewhere because we
+
+ align:start position:0%
+to put that symbol somewhere because we
+ 
+
+ align:start position:0%
+to put that symbol somewhere because we
+have to record all that information and
+
+ align:start position:0%
+have to record all that information and
+ 
+
+ align:start position:0%
+have to record all that information and
+the block is like full so what do we do
+
+ align:start position:0%
+the block is like full so what do we do
+ 
+
+ align:start position:0%
+the block is like full so what do we do
+well in that case s goes to like a
+
+ align:start position:0%
+well in that case s goes to like a
+ 
+
+ align:start position:0%
+well in that case s goes to like a
+little interrupt routine and
+
+ align:start position:0%
+little interrupt routine and
+ 
+
+ align:start position:0%
+little interrupt routine and
+uh moves shifts all of the symbols um to
+
+ align:start position:0%
+uh moves shifts all of the symbols um to
+ 
+
+ align:start position:0%
+uh moves shifts all of the symbols um to
+the right one place to make open up um a
+
+ align:start position:0%
+the right one place to make open up um a
+ 
+
+ align:start position:0%
+the right one place to make open up um a
+location here where it can write a new
+
+ align:start position:0%
+location here where it can write a new
+ 
+
+ align:start position:0%
+location here where it can write a new
+symbol for uh carrying continuing the
+
+ align:start position:0%
+symbol for uh carrying continuing the
+ 
+
+ align:start position:0%
+symbol for uh carrying continuing the
+simulation so with that in mind uh s can
+
+ align:start position:0%
+simulation so with that in mind uh s can
+ 
+
+ align:start position:0%
+simulation so with that in mind uh s can
+maintain the current contents of each of
+
+ align:start position:0%
+maintain the current contents of each of
+ 
+
+ align:start position:0%
+maintain the current contents of each of
+M's tapes and um let me just note that
+
+ align:start position:0%
+M's tapes and um let me just note that
+ 
+
+ align:start position:0%
+M's tapes and um let me just note that
+here shift to add room is
+
+ align:start position:0%
+here shift to add room is
+ 
+
+ align:start position:0%
+here shift to add room is
+needed and that's all that happens in
+
+ align:start position:0%
+needed and that's all that happens in
+ 
+
+ align:start position:0%
+needed and that's all that happens in
+this during the course of the simulation
+
+ align:start position:0%
+this during the course of the simulation
+ 
+
+ align:start position:0%
+this during the course of the simulation
+okay and if of course if S as it's
+
+ align:start position:0%
+okay and if of course if S as it's
+ 
+
+ align:start position:0%
+okay and if of course if S as it's
+simulating m observes that M comes to an
+
+ align:start position:0%
+simulating m observes that M comes to an
+ 
+
+ align:start position:0%
+simulating m observes that M comes to an
+accept or rejects
+
+ align:start position:0%
+accept or rejects
+ 
+
+ align:start position:0%
+accept or rejects
+uh s should do the
+
+ align:start position:0%
+uh s should do the
+ 
+
+ align:start position:0%
+uh s should do the
+same okay so that that's our description
+
+ align:start position:0%
+same okay so that that's our description
+ 
+
+ align:start position:0%
+same okay so that that's our description
+of how the simulation of the the single
+
+ align:start position:0%
+of how the simulation of the the single
+ 
+
+ align:start position:0%
+of how the simulation of the the single
+tape simulation of the multi-tape
+
+ align:start position:0%
+tape simulation of the multi-tape
+ 
+
+ align:start position:0%
+tape simulation of the multi-tape
+machine works right okay let's turn to
+
+ align:start position:0%
+machine works right okay let's turn to
+ 
+
+ align:start position:0%
+machine works right okay let's turn to
+non-deterministic machines
+
+ align:start position:0%
+non-deterministic machines
+ 
+
+ align:start position:0%
+non-deterministic machines
+now if you remember for find out and I
+
+ align:start position:0%
+now if you remember for find out and I
+ 
+
+ align:start position:0%
+now if you remember for find out and I
+hope you do for find out atoma we had
+
+ align:start position:0%
+hope you do for find out atoma we had
+ 
+
+ align:start position:0%
+hope you do for find out atoma we had
+equivalence between non-deterministic
+
+ align:start position:0%
+equivalence between non-deterministic
+ 
+
+ align:start position:0%
+equivalence between non-deterministic
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+deterministic um find autometer for push
+
+ align:start position:0%
+deterministic um find autometer for push
+ 
+
+ align:start position:0%
+deterministic um find autometer for push
+down autometer we did not have
+
+ align:start position:0%
+down autometer we did not have
+ 
+
+ align:start position:0%
+down autometer we did not have
+equivalence we didn't prove that but we
+
+ align:start position:0%
+equivalence we didn't prove that but we
+ 
+
+ align:start position:0%
+equivalence we didn't prove that but we
+just stated it as a fact there are
+
+ align:start position:0%
+just stated it as a fact there are
+ 
+
+ align:start position:0%
+just stated it as a fact there are
+certain languages that you can do with
+
+ align:start position:0%
+certain languages that you can do with
+ 
+
+ align:start position:0%
+certain languages that you can do with
+non-deterministic push down autometer
+
+ align:start position:0%
+non-deterministic push down autometer
+ 
+
+ align:start position:0%
+non-deterministic push down autometer
+which is the model we typically hold as
+
+ align:start position:0%
+which is the model we typically hold as
+ 
+
+ align:start position:0%
+which is the model we typically hold as
+our standard so that some things you can
+
+ align:start position:0%
+our standard so that some things you can
+ 
+
+ align:start position:0%
+our standard so that some things you can
+do with non-deterministic push down
+
+ align:start position:0%
+do with non-deterministic push down
+ 
+
+ align:start position:0%
+do with non-deterministic push down
+automa that you cannot do with
+
+ align:start position:0%
+automa that you cannot do with
+ 
+
+ align:start position:0%
+automa that you cannot do with
+deterministic push down autom um you
+
+ align:start position:0%
+deterministic push down autom um you
+ 
+
+ align:start position:0%
+deterministic push down autom um you
+really need the non-determinism they're
+
+ align:start position:0%
+really need the non-determinism they're
+ 
+
+ align:start position:0%
+really need the non-determinism they're
+not not equivalent for Turing machines
+
+ align:start position:0%
+not not equivalent for Turing machines
+ 
+
+ align:start position:0%
+not not equivalent for Turing machines
+uh we're going to get the equivalents
+
+ align:start position:0%
+uh we're going to get the equivalents
+ 
+
+ align:start position:0%
+uh we're going to get the equivalents
+back so we show that anything you can do
+
+ align:start position:0%
+back so we show that anything you can do
+ 
+
+ align:start position:0%
+back so we show that anything you can do
+with a non-deterministic touring machine
+
+ align:start position:0%
+with a non-deterministic touring machine
+ 
+
+ align:start position:0%
+with a non-deterministic touring machine
+in terms of language recognition you can
+
+ align:start position:0%
+in terms of language recognition you can
+ 
+
+ align:start position:0%
+in terms of language recognition you can
+also do with a deterministic turning
+
+ align:start position:0%
+also do with a deterministic turning
+ 
+
+ align:start position:0%
+also do with a deterministic turning
+machine so remember we kind of mentioned
+
+ align:start position:0%
+machine so remember we kind of mentioned
+ 
+
+ align:start position:0%
+machine so remember we kind of mentioned
+this briefly last time the
+
+ align:start position:0%
+this briefly last time the
+ 
+
+ align:start position:0%
+this briefly last time the
+non-deterministic turning machine looks
+
+ align:start position:0%
+non-deterministic turning machine looks
+ 
+
+ align:start position:0%
+non-deterministic turning machine looks
+exactly like a deterministic turning
+
+ align:start position:0%
+exactly like a deterministic turning
+ 
+
+ align:start position:0%
+exactly like a deterministic turning
+machine except for the transition
+
+ align:start position:0%
+machine except for the transition
+ 
+
+ align:start position:0%
+machine except for the transition
+function where we have this power set
+
+ align:start position:0%
+function where we have this power set
+ 
+
+ align:start position:0%
+function where we have this power set
+which allows for multiple different
+
+ align:start position:0%
+which allows for multiple different
+ 
+
+ align:start position:0%
+which allows for multiple different
+outcomes at a given step instead of just
+
+ align:start position:0%
+outcomes at a given step instead of just
+ 
+
+ align:start position:0%
+outcomes at a given step instead of just
+a single outcome that you would have in
+
+ align:start position:0%
+a single outcome that you would have in
+ 
+
+ align:start position:0%
+a single outcome that you would have in
+a deterministic uh machine so we
+
+ align:start position:0%
+a deterministic uh machine so we
+ 
+
+ align:start position:0%
+a deterministic uh machine so we
+represent that with this power set here
+
+ align:start position:0%
+represent that with this power set here
+ 
+
+ align:start position:0%
+represent that with this power set here
+um uh applied to the possibilities that
+
+ align:start position:0%
+um uh applied to the possibilities that
+ 
+
+ align:start position:0%
+um uh applied to the possibilities that
+um the machine would have as the um next
+
+ align:start position:0%
+um the machine would have as the um next
+ 
+
+ align:start position:0%
+um the machine would have as the um next
+uh Next
+
+ align:start position:0%
+uh Next
+ 
+
+ align:start position:0%
+uh Next
+Step okay um so now we're going to prove
+
+ align:start position:0%
+Step okay um so now we're going to prove
+ 
+
+ align:start position:0%
+Step okay um so now we're going to prove
+a very similar theorem that a is touring
+
+ align:start position:0%
+a very similar theorem that a is touring
+ 
+
+ align:start position:0%
+a very similar theorem that a is touring
+recognizable by an ordinary one tape
+
+ align:start position:0%
+recognizable by an ordinary one tape
+ 
+
+ align:start position:0%
+recognizable by an ordinary one tape
+touring machine that kind of goes
+
+ align:start position:0%
+touring machine that kind of goes
+ 
+
+ align:start position:0%
+touring machine that kind of goes
+without saying so that's we how we
+
+ align:start position:0%
+without saying so that's we how we
+ 
+
+ align:start position:0%
+without saying so that's we how we
+defined it a is touring recognizable if
+
+ align:start position:0%
+defined it a is touring recognizable if
+ 
+
+ align:start position:0%
+defined it a is touring recognizable if
+and only if some non-deterministic
+
+ align:start position:0%
+and only if some non-deterministic
+ 
+
+ align:start position:0%
+and only if some non-deterministic
+touring machine recognizes that
+
+ align:start position:0%
+touring machine recognizes that
+ 
+
+ align:start position:0%
+touring machine recognizes that
+language
+
+ align:start position:0%
+language
+ 
+
+ align:start position:0%
+language
+okay um again remember we're using
+
+ align:start position:0%
+okay um again remember we're using
+ 
+
+ align:start position:0%
+okay um again remember we're using
+non-determinism in the way we always do
+
+ align:start position:0%
+non-determinism in the way we always do
+ 
+
+ align:start position:0%
+non-determinism in the way we always do
+namely that uh a non-deterministic
+
+ align:start position:0%
+namely that uh a non-deterministic
+ 
+
+ align:start position:0%
+namely that uh a non-deterministic
+machine accepts if there is some Branch
+
+ align:start position:0%
+machine accepts if there is some Branch
+ 
+
+ align:start position:0%
+machine accepts if there is some Branch
+or some thread of it's not computation
+
+ align:start position:0%
+or some thread of it's not computation
+ 
+
+ align:start position:0%
+or some thread of it's not computation
+ends up at an accept other branches
+
+ align:start position:0%
+ends up at an accept other branches
+ 
+
+ align:start position:0%
+ends up at an accept other branches
+might go forever or might reject part
+
+ align:start position:0%
+might go forever or might reject part
+ 
+
+ align:start position:0%
+might go forever or might reject part
+way part of the way through um but
+
+ align:start position:0%
+way part of the way through um but
+ 
+
+ align:start position:0%
+way part of the way through um but
+acceptance always overrules them if any
+
+ align:start position:0%
+acceptance always overrules them if any
+ 
+
+ align:start position:0%
+acceptance always overrules them if any
+branch accepts that's how
+
+ align:start position:0%
+branch accepts that's how
+ 
+
+ align:start position:0%
+branch accepts that's how
+non-determinism works for us okay so
+
+ align:start position:0%
+non-determinism works for us okay so
+ 
+
+ align:start position:0%
+non-determinism works for us okay so
+now the forward direction of this is
+
+ align:start position:0%
+now the forward direction of this is
+ 
+
+ align:start position:0%
+now the forward direction of this is
+again just like before immediate because
+
+ align:start position:0%
+again just like before immediate because
+ 
+
+ align:start position:0%
+again just like before immediate because
+a deterministic turing machine is a
+
+ align:start position:0%
+a deterministic turing machine is a
+ 
+
+ align:start position:0%
+a deterministic turing machine is a
+special kind of non-deterministic turing
+
+ align:start position:0%
+special kind of non-deterministic turing
+ 
+
+ align:start position:0%
+special kind of non-deterministic turing
+machine which never branches U
+
+ align:start position:0%
+machine which never branches U
+ 
+
+ align:start position:0%
+machine which never branches U
+non-deterministically on any of its
+
+ align:start position:0%
+non-deterministically on any of its
+ 
+
+ align:start position:0%
+non-deterministically on any of its
+steps um so that forward direction is
+
+ align:start position:0%
+steps um so that forward direction is
+ 
+
+ align:start position:0%
+steps um so that forward direction is
+immediate the backwards definition is
+
+ align:start position:0%
+immediate the backwards definition is
+ 
+
+ align:start position:0%
+immediate the backwards definition is
+where we're going to have to do some
+
+ align:start position:0%
+where we're going to have to do some
+ 
+
+ align:start position:0%
+where we're going to have to do some
+work converting our non-deterministic
+
+ align:start position:0%
+work converting our non-deterministic
+ 
+
+ align:start position:0%
+work converting our non-deterministic
+turning machine to a deterministic
+
+ align:start position:0%
+turning machine to a deterministic
+ 
+
+ align:start position:0%
+turning machine to a deterministic
+turning machine and we'll do so as
+
+ align:start position:0%
+turning machine and we'll do so as
+ 
+
+ align:start position:0%
+turning machine and we'll do so as
+follows we'll take a non-deterministic
+
+ align:start position:0%
+follows we'll take a non-deterministic
+ 
+
+ align:start position:0%
+follows we'll take a non-deterministic
+turning machine uh here's our picture
+
+ align:start position:0%
+turning machine uh here's our picture
+ 
+
+ align:start position:0%
+turning machine uh here's our picture
+and we're going to now um imagine its
+
+ align:start position:0%
+and we're going to now um imagine its
+ 
+
+ align:start position:0%
+and we're going to now um imagine its
+computation in terms of a tree um and so
+
+ align:start position:0%
+computation in terms of a tree um and so
+ 
+
+ align:start position:0%
+computation in terms of a tree um and so
+here the non-deterministic computation
+
+ align:start position:0%
+here the non-deterministic computation
+ 
+
+ align:start position:0%
+here the non-deterministic computation
+tree for n on some input W so n for
+
+ align:start position:0%
+tree for n on some input W so n for
+ 
+
+ align:start position:0%
+tree for n on some input W so n for
+non-deterministic
+
+ align:start position:0%
+non-deterministic
+ 
+
+ align:start position:0%
+non-deterministic
+uh here is the tree um somewhere down
+
+ align:start position:0%
+uh here is the tree um somewhere down
+ 
+
+ align:start position:0%
+uh here is the tree um somewhere down
+here it might end up accepting and as I
+
+ align:start position:0%
+here it might end up accepting and as I
+ 
+
+ align:start position:0%
+here it might end up accepting and as I
+mentioned that is going to be uh
+
+ align:start position:0%
+mentioned that is going to be uh
+ 
+
+ align:start position:0%
+mentioned that is going to be uh
+defining the overall computation to be
+
+ align:start position:0%
+defining the overall computation to be
+ 
+
+ align:start position:0%
+defining the overall computation to be
+accepting if there is some place here
+
+ align:start position:0%
+accepting if there is some place here
+ 
+
+ align:start position:0%
+accepting if there is some place here
+that's accepting and the only way it can
+
+ align:start position:0%
+that's accepting and the only way it can
+ 
+
+ align:start position:0%
+that's accepting and the only way it can
+be non-accepting computation if there is
+
+ align:start position:0%
+be non-accepting computation if there is
+ 
+
+ align:start position:0%
+be non-accepting computation if there is
+no accept that occurs anywhere
+
+ align:start position:0%
+no accept that occurs anywhere
+ 
+
+ align:start position:0%
+no accept that occurs anywhere
+and somehow if you're going to convert
+
+ align:start position:0%
+and somehow if you're going to convert
+ 
+
+ align:start position:0%
+and somehow if you're going to convert
+this non- deterministic machine to a
+
+ align:start position:0%
+this non- deterministic machine to a
+ 
+
+ align:start position:0%
+this non- deterministic machine to a
+deterministic machine the deterministic
+
+ align:start position:0%
+deterministic machine the deterministic
+ 
+
+ align:start position:0%
+deterministic machine the deterministic
+machine is going to have to get that
+
+ align:start position:0%
+machine is going to have to get that
+ 
+
+ align:start position:0%
+machine is going to have to get that
+same effect though it only has determin
+
+ align:start position:0%
+same effect though it only has determin
+ 
+
+ align:start position:0%
+same effect though it only has determin
+you know doesn't have the
+
+ align:start position:0%
+you know doesn't have the
+ 
+
+ align:start position:0%
+you know doesn't have the
+non-determinism so how does it manage
+
+ align:start position:0%
+non-determinism so how does it manage
+ 
+
+ align:start position:0%
+non-determinism so how does it manage
+that well it's really going to be
+
+ align:start position:0%
+that well it's really going to be
+ 
+
+ align:start position:0%
+that well it's really going to be
+carrying out the simulation you know um
+
+ align:start position:0%
+carrying out the simulation you know um
+ 
+
+ align:start position:0%
+carrying out the simulation you know um
+kind of as you would imagine doing it
+
+ align:start position:0%
+kind of as you would imagine doing it
+ 
+
+ align:start position:0%
+kind of as you would imagine doing it
+yourself if you were told you had to
+
+ align:start position:0%
+yourself if you were told you had to
+ 
+
+ align:start position:0%
+yourself if you were told you had to
+simulate a non-deterministic turing
+
+ align:start position:0%
+simulate a non-deterministic turing
+ 
+
+ align:start position:0%
+simulate a non-deterministic turing
+machine which is you're going to search
+
+ align:start position:0%
+machine which is you're going to search
+ 
+
+ align:start position:0%
+machine which is you're going to search
+that tree of possibility ities looking
+
+ align:start position:0%
+that tree of possibility ities looking
+ 
+
+ align:start position:0%
+that tree of possibility ities looking
+to see if you find and accept if you do
+
+ align:start position:0%
+to see if you find and accept if you do
+ 
+
+ align:start position:0%
+to see if you find and accept if you do
+then you accept if you if you don't well
+
+ align:start position:0%
+then you accept if you if you don't well
+ 
+
+ align:start position:0%
+then you accept if you if you don't well
+maybe you'll go forever or maybe you'll
+
+ align:start position:0%
+maybe you'll go forever or maybe you'll
+ 
+
+ align:start position:0%
+maybe you'll go forever or maybe you'll
+manage to search the entire tree and
+
+ align:start position:0%
+manage to search the entire tree and
+ 
+
+ align:start position:0%
+manage to search the entire tree and
+then you will um say no I accept uh no I
+
+ align:start position:0%
+then you will um say no I accept uh no I
+ 
+
+ align:start position:0%
+then you will um say no I accept uh no I
+reject um okay so let's just see again
+
+ align:start position:0%
+reject um okay so let's just see again
+ 
+
+ align:start position:0%
+reject um okay so let's just see again
+what the data structure of that
+
+ align:start position:0%
+what the data structure of that
+ 
+
+ align:start position:0%
+what the data structure of that
+deterministic machine's tape is going to
+
+ align:start position:0%
+deterministic machine's tape is going to
+ 
+
+ align:start position:0%
+deterministic machine's tape is going to
+look like um so the way this simulation
+
+ align:start position:0%
+look like um so the way this simulation
+ 
+
+ align:start position:0%
+look like um so the way this simulation
+is going to carry out and and you know
+
+ align:start position:0%
+is going to carry out and and you know
+ 
+
+ align:start position:0%
+is going to carry out and and you know
+you could program this in a of different
+
+ align:start position:0%
+you could program this in a of different
+ 
+
+ align:start position:0%
+you could program this in a of different
+ways and in fact the textbook has a
+
+ align:start position:0%
+ways and in fact the textbook has a
+ 
+
+ align:start position:0%
+ways and in fact the textbook has a
+somewhat different simulation but I
+
+ align:start position:0%
+somewhat different simulation but I
+ 
+
+ align:start position:0%
+somewhat different simulation but I
+think this one here is uh lends itself a
+
+ align:start position:0%
+think this one here is uh lends itself a
+ 
+
+ align:start position:0%
+think this one here is uh lends itself a
+little bit better um and maybe it's a
+
+ align:start position:0%
+little bit better um and maybe it's a
+ 
+
+ align:start position:0%
+little bit better um and maybe it's a
+little simpler for description um in
+
+ align:start position:0%
+little simpler for description um in
+ 
+
+ align:start position:0%
+little simpler for description um in
+this in this setting uh but there's lots
+
+ align:start position:0%
+this in this setting uh but there's lots
+ 
+
+ align:start position:0%
+this in this setting uh but there's lots
+of different ways of improving these
+
+ align:start position:0%
+of different ways of improving these
+ 
+
+ align:start position:0%
+of different ways of improving these
+things um so we're g to m is going to
+
+ align:start position:0%
+things um so we're g to m is going to
+ 
+
+ align:start position:0%
+things um so we're g to m is going to
+simulate n kind of a little bit similar
+
+ align:start position:0%
+simulate n kind of a little bit similar
+ 
+
+ align:start position:0%
+simulate n kind of a little bit similar
+to the previous uh simulation it's going
+
+ align:start position:0%
+to the previous uh simulation it's going
+ 
+
+ align:start position:0%
+to the previous uh simulation it's going
+to break the tape up into
+
+ align:start position:0%
+to break the tape up into
+ 
+
+ align:start position:0%
+to break the tape up into
+blocks and it's going to now store in
+
+ align:start position:0%
+blocks and it's going to now store in
+ 
+
+ align:start position:0%
+blocks and it's going to now store in
+each
+
+ align:start position:0%
+each
+ 
+
+ align:start position:0%
+each
+block um a different thread at a
+
+ align:start position:0%
+block um a different thread at a
+ 
+
+ align:start position:0%
+block um a different thread at a
+particular point in time of n's
+
+ align:start position:0%
+particular point in time of n's
+ 
+
+ align:start position:0%
+particular point in time of n's
+computation so you imagine where m is
+
+ align:start position:0%
+computation so you imagine where m is
+ 
+
+ align:start position:0%
+computation so you imagine where m is
+going to be simulating n sort
+
+ align:start position:0%
+going to be simulating n sort
+ 
+
+ align:start position:0%
+going to be simulating n sort
+of um doing the same
+
+ align:start position:0%
+of um doing the same
+ 
+
+ align:start position:0%
+of um doing the same
+parallelism but doing the getting the
+
+ align:start position:0%
+parallelism but doing the getting the
+ 
+
+ align:start position:0%
+parallelism but doing the getting the
+effect of the parallelism not through
+
+ align:start position:0%
+effect of the parallelism not through
+ 
+
+ align:start position:0%
+effect of the parallelism not through
+the non-determinism but by maintaining
+
+ align:start position:0%
+the non-determinism but by maintaining
+ 
+
+ align:start position:0%
+the non-determinism but by maintaining
+cop C of each of the threads on its tape
+
+ align:start position:0%
+cop C of each of the threads on its tape
+ 
+
+ align:start position:0%
+cop C of each of the threads on its tape
+and then updating them
+
+ align:start position:0%
+and then updating them
+ 
+
+ align:start position:0%
+and then updating them
+accordingly so the idea is I think not
+
+ align:start position:0%
+accordingly so the idea is I think not
+ 
+
+ align:start position:0%
+accordingly so the idea is I think not
+not too complicated
+
+ align:start position:0%
+not too complicated
+ 
+
+ align:start position:0%
+not too complicated
+um so let's just see some of the some of
+
+ align:start position:0%
+um so let's just see some of the some of
+ 
+
+ align:start position:0%
+um so let's just see some of the some of
+the details here so here here populating
+
+ align:start position:0%
+the details here so here here populating
+ 
+
+ align:start position:0%
+the details here so here here populating
+those blocks with the contents of um
+
+ align:start position:0%
+those blocks with the contents of um
+ 
+
+ align:start position:0%
+those blocks with the contents of um
+ends tape on different threads at at a s
+
+ align:start position:0%
+ends tape on different threads at at a s
+ 
+
+ align:start position:0%
+ends tape on different threads at at a s
+you know maybe that corresponds to um
+
+ align:start position:0%
+you know maybe that corresponds to um
+ 
+
+ align:start position:0%
+you know maybe that corresponds to um
+ends tape you know after the fifth step
+
+ align:start position:0%
+ends tape you know after the fifth step
+ 
+
+ align:start position:0%
+ends tape you know after the fifth step
+of end
+
+ align:start position:0%
+of end
+ 
+
+ align:start position:0%
+of end
+um you know on each of those threads you
+
+ align:start position:0%
+um you know on each of those threads you
+ 
+
+ align:start position:0%
+um you know on each of those threads you
+have these three possibilities let's say
+
+ align:start position:0%
+have these three possibilities let's say
+ 
+
+ align:start position:0%
+have these three possibilities let's say
+written down as three different
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+blocks um now
+
+ align:start position:0%
+blocks um now
+ 
+
+ align:start position:0%
+blocks um now
+uh remember in the case of the
+
+ align:start position:0%
+uh remember in the case of the
+ 
+
+ align:start position:0%
+uh remember in the case of the
+multi-tape simulation we needed to
+
+ align:start position:0%
+multi-tape simulation we needed to
+ 
+
+ align:start position:0%
+multi-tape simulation we needed to
+record some extra inform extra
+
+ align:start position:0%
+record some extra inform extra
+ 
+
+ align:start position:0%
+record some extra inform extra
+information in particular we had to
+
+ align:start position:0%
+information in particular we had to
+ 
+
+ align:start position:0%
+information in particular we had to
+record the location of the heads by
+
+ align:start position:0%
+record the location of the heads by
+ 
+
+ align:start position:0%
+record the location of the heads by
+using those dotted symbols we're going
+
+ align:start position:0%
+using those dotted symbols we're going
+ 
+
+ align:start position:0%
+using those dotted symbols we're going
+to do that again because each one of
+
+ align:start position:0%
+to do that again because each one of
+ 
+
+ align:start position:0%
+to do that again because each one of
+these threads might have their head in
+
+ align:start position:0%
+these threads might have their head in
+ 
+
+ align:start position:0%
+these threads might have their head in
+some different location but we're going
+
+ align:start position:0%
+some different location but we're going
+ 
+
+ align:start position:0%
+some different location but we're going
+to have to do more but let actually so
+
+ align:start position:0%
+to have to do more but let actually so
+ 
+
+ align:start position:0%
+to have to do more but let actually so
+let's do one one thing at a time we're
+
+ align:start position:0%
+let's do one one thing at a time we're
+ 
+
+ align:start position:0%
+let's do one one thing at a time we're
+going to store the head
+
+ align:start position:0%
+going to store the head
+ 
+
+ align:start position:0%
+going to store the head
+location here they are all written down
+
+ align:start position:0%
+location here they are all written down
+ 
+
+ align:start position:0%
+location here they are all written down
+as dotted symbols but now there's
+
+ align:start position:0%
+as dotted symbols but now there's
+ 
+
+ align:start position:0%
+as dotted symbols but now there's
+something that goes further because in
+
+ align:start position:0%
+something that goes further because in
+ 
+
+ align:start position:0%
+something that goes further because in
+the multi-tape
+
+ align:start position:0%
+the multi-tape
+ 
+
+ align:start position:0%
+the multi-tape
+case there was one Global
+
+ align:start position:0%
+case there was one Global
+ 
+
+ align:start position:0%
+case there was one Global
+state that the multi-tape machine was in
+
+ align:start position:0%
+state that the multi-tape machine was in
+ 
+
+ align:start position:0%
+state that the multi-tape machine was in
+of course at any given time it's just
+
+ align:start position:0%
+of course at any given time it's just
+ 
+
+ align:start position:0%
+of course at any given time it's just
+one has one finite control it's in one
+
+ align:start position:0%
+one has one finite control it's in one
+ 
+
+ align:start position:0%
+one has one finite control it's in one
+state um and
+
+ align:start position:0%
+state um and
+ 
+
+ align:start position:0%
+state um and
+uh but but but in the case of the
+
+ align:start position:0%
+uh but but but in the case of the
+ 
+
+ align:start position:0%
+uh but but but in the case of the
+non-deterministic machine that we're
+
+ align:start position:0%
+non-deterministic machine that we're
+ 
+
+ align:start position:0%
+non-deterministic machine that we're
+simulating now each thread can be in a
+
+ align:start position:0%
+simulating now each thread can be in a
+ 
+
+ align:start position:0%
+simulating now each thread can be in a
+different
+
+ align:start position:0%
+different
+ 
+
+ align:start position:0%
+different
+state um so whereas before we could keep
+
+ align:start position:0%
+state um so whereas before we could keep
+ 
+
+ align:start position:0%
+state um so whereas before we could keep
+track of the multi tapes tur the
+
+ align:start position:0%
+track of the multi tapes tur the
+ 
+
+ align:start position:0%
+track of the multi tapes tur the
+multitape machine State inside the
+
+ align:start position:0%
+multitape machine State inside the
+ 
+
+ align:start position:0%
+multitape machine State inside the
+single tape machine's finite control now
+
+ align:start position:0%
+single tape machine's finite control now
+ 
+
+ align:start position:0%
+single tape machine's finite control now
+there could be many many different
+
+ align:start position:0%
+there could be many many different
+ 
+
+ align:start position:0%
+there could be many many different
+states to keep track of so you won't be
+
+ align:start position:0%
+states to keep track of so you won't be
+ 
+
+ align:start position:0%
+states to keep track of so you won't be
+able to store that in a finite control
+
+ align:start position:0%
+able to store that in a finite control
+ 
+
+ align:start position:0%
+able to store that in a finite control
+anymore because there could be some huge
+
+ align:start position:0%
+anymore because there could be some huge
+ 
+
+ align:start position:0%
+anymore because there could be some huge
+number of threads active at any given
+
+ align:start position:0%
+number of threads active at any given
+ 
+
+ align:start position:0%
+number of threads active at any given
+stage and some of them can be in one
+
+ align:start position:0%
+stage and some of them can be in one
+ 
+
+ align:start position:0%
+stage and some of them can be in one
+state others can be in different state
+
+ align:start position:0%
+state others can be in different state
+ 
+
+ align:start position:0%
+state others can be in different state
+and you know how do you keep track of
+
+ align:start position:0%
+and you know how do you keep track of
+ 
+
+ align:start position:0%
+and you know how do you keep track of
+all that so we're going to have to use
+
+ align:start position:0%
+all that so we're going to have to use
+ 
+
+ align:start position:0%
+all that so we're going to have to use
+the tape we're going to actually write
+
+ align:start position:0%
+the tape we're going to actually write
+ 
+
+ align:start position:0%
+the tape we're going to actually write
+down which state a given thread is in on
+
+ align:start position:0%
+down which state a given thread is in on
+ 
+
+ align:start position:0%
+down which state a given thread is in on
+that block and we'll do that I'll show
+
+ align:start position:0%
+that block and we'll do that I'll show
+ 
+
+ align:start position:0%
+that block and we'll do that I'll show
+it like this um so writing down the
+
+ align:start position:0%
+it like this um so writing down the
+ 
+
+ align:start position:0%
+it like this um so writing down the
+state of each in the
+
+ align:start position:0%
+state of each in the
+ 
+
+ align:start position:0%
+state of each in the
+block by writing down symbols which
+
+ align:start position:0%
+block by writing down symbols which
+ 
+
+ align:start position:0%
+block by writing down symbols which
+correspond to those uh
+
+ align:start position:0%
+correspond to those uh
+ 
+
+ align:start position:0%
+correspond to those uh
+States so we're actually in a sense
+
+ align:start position:0%
+States so we're actually in a sense
+ 
+
+ align:start position:0%
+States so we're actually in a sense
+writing the state down right on top of
+
+ align:start position:0%
+writing the state down right on top of
+ 
+
+ align:start position:0%
+writing the state down right on top of
+the block using symbols that correspond
+
+ align:start position:0%
+the block using symbols that correspond
+ 
+
+ align:start position:0%
+the block using symbols that correspond
+to those States so again we're doing
+
+ align:start position:0%
+to those States so again we're doing
+ 
+
+ align:start position:0%
+to those States so again we're doing
+getting that effect by increasing the
+
+ align:start position:0%
+getting that effect by increasing the
+ 
+
+ align:start position:0%
+getting that effect by increasing the
+tape alphabet of M to
+
+ align:start position:0%
+tape alphabet of M to
+ 
+
+ align:start position:0%
+tape alphabet of M to
+include um symbols that correspond to
+
+ align:start position:0%
+include um symbols that correspond to
+ 
+
+ align:start position:0%
+include um symbols that correspond to
+each of its
+
+ align:start position:0%
+each of its
+ 
+
+ align:start position:0%
+each of its
+states and we're going to write those
+
+ align:start position:0%
+states and we're going to write those
+ 
+
+ align:start position:0%
+states and we're going to write those
+symbols down so here's the symbol for
+
+ align:start position:0%
+symbols down so here's the symbol for
+ 
+
+ align:start position:0%
+symbols down so here's the symbol for
+State Q8 that says well one of that very
+
+ align:start position:0%
+State Q8 that says well one of that very
+ 
+
+ align:start position:0%
+State Q8 that says well one of that very
+first thread of n's computation is in
+
+ align:start position:0%
+first thread of n's computation is in
+ 
+
+ align:start position:0%
+first thread of n's computation is in
+state Q8 it's in this third position of
+
+ align:start position:0%
+state Q8 it's in this third position of
+ 
+
+ align:start position:0%
+state Q8 it's in this third position of
+its t um on its tape uh the head is on
+
+ align:start position:0%
+its t um on its tape uh the head is on
+ 
+
+ align:start position:0%
+its t um on its tape uh the head is on
+the third position there and the tape
+
+ align:start position:0%
+the third position there and the tape
+ 
+
+ align:start position:0%
+the third position there and the tape
+contents is
+
+ align:start position:0%
+contents is
+ 
+
+ align:start position:0%
+contents is
+aaba that's how we represent that thread
+
+ align:start position:0%
+aaba that's how we represent that thread
+ 
+
+ align:start position:0%
+aaba that's how we represent that thread
+of the
+
+ align:start position:0%
+of the
+ 
+
+ align:start position:0%
+of the
+computation um including the
+
+ align:start position:0%
+computation um including the
+ 
+
+ align:start position:0%
+computation um including the
+state okay now um so am is going to
+
+ align:start position:0%
+state okay now um so am is going to
+ 
+
+ align:start position:0%
+state okay now um so am is going to
+carry out that step by step maintaining
+
+ align:start position:0%
+carry out that step by step maintaining
+ 
+
+ align:start position:0%
+carry out that step by step maintaining
+that information on its tape they're
+
+ align:start position:0%
+that information on its tape they're
+ 
+
+ align:start position:0%
+that information on its tape they're
+again similar to before there might be
+
+ align:start position:0%
+again similar to before there might be
+ 
+
+ align:start position:0%
+again similar to before there might be
+some special situations arising so for
+
+ align:start position:0%
+some special situations arising so for
+ 
+
+ align:start position:0%
+some special situations arising so for
+example n is not non-deterministic so a
+
+ align:start position:0%
+example n is not non-deterministic so a
+ 
+
+ align:start position:0%
+example n is not non-deterministic so a
+rad might Fork into uh two threads what
+
+ align:start position:0%
+rad might Fork into uh two threads what
+ 
+
+ align:start position:0%
+rad might Fork into uh two threads what
+do we do then um well sort of
+
+ align:start position:0%
+do we do then um well sort of
+ 
+
+ align:start position:0%
+do we do then um well sort of
+the you know the reasonable thing if
+
+ align:start position:0%
+the you know the reasonable thing if
+ 
+
+ align:start position:0%
+the you know the reasonable thing if
+there's a forking thread M then copies
+
+ align:start position:0%
+there's a forking thread M then copies
+ 
+
+ align:start position:0%
+there's a forking thread M then copies
+that block makes two copies of the block
+
+ align:start position:0%
+that block makes two copies of the block
+ 
+
+ align:start position:0%
+that block makes two copies of the block
+to correspond to the two or however many
+
+ align:start position:0%
+to correspond to the two or however many
+ 
+
+ align:start position:0%
+to correspond to the two or however many
+copies you need to correspond to the
+
+ align:start position:0%
+copies you need to correspond to the
+ 
+
+ align:start position:0%
+copies you need to correspond to the
+possibilities that um that that thread
+
+ align:start position:0%
+possibilities that um that that thread
+ 
+
+ align:start position:0%
+possibilities that um that that thread
+is branching into so you want to
+
+ align:start position:0%
+is branching into so you want to
+ 
+
+ align:start position:0%
+is branching into so you want to
+represent them all on different blocks
+
+ align:start position:0%
+represent them all on different blocks
+ 
+
+ align:start position:0%
+represent them all on different blocks
+of M's tape
+
+ align:start position:0%
+of M's tape
+ 
+
+ align:start position:0%
+of M's tape
+all right um and then if M ever finds
+
+ align:start position:0%
+all right um and then if M ever finds
+ 
+
+ align:start position:0%
+all right um and then if M ever finds
+out that on one of the threads it's
+
+ align:start position:0%
+out that on one of the threads it's
+ 
+
+ align:start position:0%
+out that on one of the threads it's
+entering the accept state it can just
+
+ align:start position:0%
+entering the accept state it can just
+ 
+
+ align:start position:0%
+entering the accept state it can just
+shut down the whole computation at that
+
+ align:start position:0%
+shut down the whole computation at that
+ 
+
+ align:start position:0%
+shut down the whole computation at that
+point and say
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+accept Okay so perhaps a little
+
+ align:start position:0%
+accept Okay so perhaps a little
+ 
+
+ align:start position:0%
+accept Okay so perhaps a little
+elaborate but I think conceptually
+
+ align:start position:0%
+elaborate but I think conceptually
+ 
+
+ align:start position:0%
+elaborate but I think conceptually
+hopefully um not too bad um now uh uh
+
+ align:start position:0%
+hopefully um not too bad um now uh uh
+ 
+
+ align:start position:0%
+hopefully um not too bad um now uh uh
+let's move on then to talk about uh
+
+ align:start position:0%
+let's move on then to talk about uh
+ 
+
+ align:start position:0%
+let's move on then to talk about uh
+somewhat of a different uh looking well
+
+ align:start position:0%
+somewhat of a different uh looking well
+ 
+
+ align:start position:0%
+somewhat of a different uh looking well
+sort of a different model in a way um uh
+
+ align:start position:0%
+sort of a different model in a way um uh
+ 
+
+ align:start position:0%
+sort of a different model in a way um uh
+which has some historical significance
+
+ align:start position:0%
+which has some historical significance
+ 
+
+ align:start position:0%
+which has some historical significance
+and sometimes is a helpful way to look
+
+ align:start position:0%
+and sometimes is a helpful way to look
+ 
+
+ align:start position:0%
+and sometimes is a helpful way to look
+at uh touring recognizability and you
+
+ align:start position:0%
+at uh touring recognizability and you
+ 
+
+ align:start position:0%
+at uh touring recognizability and you
+and incidentally you have a homework
+
+ align:start position:0%
+and incidentally you have a homework
+ 
+
+ align:start position:0%
+and incidentally you have a homework
+problem uh on this um model called an
+
+ align:start position:0%
+problem uh on this um model called an
+ 
+
+ align:start position:0%
+problem uh on this um model called an
+enumerator or Turing
+
+ align:start position:0%
+enumerator or Turing
+ 
+
+ align:start position:0%
+enumerator or Turing
+enumerator um
+
+ align:start position:0%
+enumerator um
+ 
+
+ align:start position:0%
+enumerator um
+so uh here uh it's going to operate some
+
+ align:start position:0%
+so uh here uh it's going to operate some
+ 
+
+ align:start position:0%
+so uh here uh it's going to operate some
+much differently um first of all we're
+
+ align:start position:0%
+much differently um first of all we're
+ 
+
+ align:start position:0%
+much differently um first of all we're
+going to enhance the touring Machine
+
+ align:start position:0%
+going to enhance the touring Machine
+ 
+
+ align:start position:0%
+going to enhance the touring Machine
+model it's going to now have just a
+
+ align:start position:0%
+model it's going to now have just a
+ 
+
+ align:start position:0%
+model it's going to now have just a
+single tape but it's going to also have
+
+ align:start position:0%
+single tape but it's going to also have
+ 
+
+ align:start position:0%
+single tape but it's going to also have
+a
+
+ align:start position:0%
+a
+ 
+
+ align:start position:0%
+a
+printer okay so we're now adding in this
+
+ align:start position:0%
+printer okay so we're now adding in this
+ 
+
+ align:start position:0%
+printer okay so we're now adding in this
+new device into the touring machine
+
+ align:start position:0%
+new device into the touring machine
+ 
+
+ align:start position:0%
+new device into the touring machine
+called the printer um and
+
+ align:start position:0%
+called the printer um and
+ 
+
+ align:start position:0%
+called the printer um and
+um the touring machine has uh tape as
+
+ align:start position:0%
+um the touring machine has uh tape as
+ 
+
+ align:start position:0%
+um the touring machine has uh tape as
+before except we never provide any input
+
+ align:start position:0%
+before except we never provide any input
+ 
+
+ align:start position:0%
+before except we never provide any input
+to the machine
+
+ align:start position:0%
+to the machine
+ 
+
+ align:start position:0%
+to the machine
+um the tape always starts out fully
+
+ align:start position:0%
+um the tape always starts out fully
+ 
+
+ align:start position:0%
+um the tape always starts out fully
+blank it's only used for reading and
+
+ align:start position:0%
+blank it's only used for reading and
+ 
+
+ align:start position:0%
+blank it's only used for reading and
+writing uh only used for for like the
+
+ align:start position:0%
+writing uh only used for for like the
+ 
+
+ align:start position:0%
+writing uh only used for for like the
+keeping TR for uh for for work um it's
+
+ align:start position:0%
+keeping TR for uh for for work um it's
+ 
+
+ align:start position:0%
+keeping TR for uh for for work um it's
+not where you present the input so how
+
+ align:start position:0%
+not where you present the input so how
+ 
+
+ align:start position:0%
+not where you present the input so how
+do you talk about the language of the
+
+ align:start position:0%
+do you talk about the language of the
+ 
+
+ align:start position:0%
+do you talk about the language of the
+machine well what the way you work this
+
+ align:start position:0%
+machine well what the way you work this
+ 
+
+ align:start position:0%
+machine well what the way you work this
+machine is you take this enumerator uh
+
+ align:start position:0%
+machine is you take this enumerator uh
+ 
+
+ align:start position:0%
+machine is you take this enumerator uh
+it's a deterministic Mach with a printer
+
+ align:start position:0%
+it's a deterministic Mach with a printer
+ 
+
+ align:start position:0%
+it's a deterministic Mach with a printer
+as I mentioned you start it off in blank
+
+ align:start position:0%
+as I mentioned you start it off in blank
+ 
+
+ align:start position:0%
+as I mentioned you start it off in blank
+tape and it you it runs and runs and
+
+ align:start position:0%
+tape and it you it runs and runs and
+ 
+
+ align:start position:0%
+tape and it you it runs and runs and
+runs and periodically it can print a
+
+ align:start position:0%
+runs and periodically it can print a
+ 
+
+ align:start position:0%
+runs and periodically it can print a
+string Under some sort of program
+
+ align:start position:0%
+string Under some sort of program
+ 
+
+ align:start position:0%
+string Under some sort of program
+control which I'm not going to spell out
+
+ align:start position:0%
+control which I'm not going to spell out
+ 
+
+ align:start position:0%
+control which I'm not going to spell out
+for you but you can imagine you might
+
+ align:start position:0%
+for you but you can imagine you might
+ 
+
+ align:start position:0%
+for you but you can imagine you might
+have to define the machine in such a way
+
+ align:start position:0%
+have to define the machine in such a way
+ 
+
+ align:start position:0%
+have to define the machine in such a way
+that when it goes into a certain print
+
+ align:start position:0%
+that when it goes into a certain print
+ 
+
+ align:start position:0%
+that when it goes into a certain print
+state so we're not going to set that all
+
+ align:start position:0%
+state so we're not going to set that all
+ 
+
+ align:start position:0%
+state so we're not going to set that all
+up then whatever string is in a certain
+
+ align:start position:0%
+up then whatever string is in a certain
+ 
+
+ align:start position:0%
+up then whatever string is in a certain
+region of the tape maybe from the the
+
+ align:start position:0%
+region of the tape maybe from the the
+ 
+
+ align:start position:0%
+region of the tape maybe from the the
+start point up to the head location that
+
+ align:start position:0%
+start point up to the head location that
+ 
+
+ align:start position:0%
+start point up to the head location that
+gets printed out on the printer and then
+
+ align:start position:0%
+gets printed out on the printer and then
+ 
+
+ align:start position:0%
+gets printed out on the printer and then
+it can print out other strings in due
+
+ align:start position:0%
+it can print out other strings in due
+ 
+
+ align:start position:0%
+it can print out other strings in due
+course and so periodically you think of
+
+ align:start position:0%
+course and so periodically you think of
+ 
+
+ align:start position:0%
+course and so periodically you think of
+this printer as printing out a string um
+
+ align:start position:0%
+this printer as printing out a string um
+ 
+
+ align:start position:0%
+this printer as printing out a string um
+under the control of the uh the turing
+
+ align:start position:0%
+under the control of the uh the turing
+ 
+
+ align:start position:0%
+under the control of the uh the turing
+machine enumerator um and so these print
+
+ align:start position:0%
+machine enumerator um and so these print
+ 
+
+ align:start position:0%
+machine enumerator um and so these print
+strings these strings it could print out
+
+ align:start position:0%
+strings these strings it could print out
+ 
+
+ align:start position:0%
+strings these strings it could print out
+W1 W2 they
+
+ align:start position:0%
+W1 W2 they
+ 
+
+ align:start position:0%
+W1 W2 they
+appear and uh the machine might possibly
+
+ align:start position:0%
+appear and uh the machine might possibly
+ 
+
+ align:start position:0%
+appear and uh the machine might possibly
+go forever and print infinitely many
+
+ align:start position:0%
+go forever and print infinitely many
+ 
+
+ align:start position:0%
+go forever and print infinitely many
+strings or it might uh go forever and
+
+ align:start position:0%
+strings or it might uh go forever and
+ 
+
+ align:start position:0%
+strings or it might uh go forever and
+only print finally many strings or it
+
+ align:start position:0%
+only print finally many strings or it
+ 
+
+ align:start position:0%
+only print finally many strings or it
+might stop after a while by entering a a
+
+ align:start position:0%
+might stop after a while by entering a a
+ 
+
+ align:start position:0%
+might stop after a while by entering a a
+halting state accepting and rejecting is
+
+ align:start position:0%
+halting state accepting and rejecting is
+ 
+
+ align:start position:0%
+halting state accepting and rejecting is
+irrelevant but enters a halting state
+
+ align:start position:0%
+irrelevant but enters a halting state
+ 
+
+ align:start position:0%
+irrelevant but enters a halting state
+and then U the number the strings that
+
+ align:start position:0%
+and then U the number the strings that
+ 
+
+ align:start position:0%
+and then U the number the strings that
+it's printed out the finitely many
+
+ align:start position:0%
+it's printed out the finitely many
+ 
+
+ align:start position:0%
+it's printed out the finitely many
+strings are printed out or just that's
+
+ align:start position:0%
+strings are printed out or just that's
+ 
+
+ align:start position:0%
+strings are printed out or just that's
+the output of the machine now the
+
+ align:start position:0%
+the output of the machine now the
+ 
+
+ align:start position:0%
+the output of the machine now the
+language of the machine is the
+
+ align:start position:0%
+language of the machine is the
+ 
+
+ align:start position:0%
+language of the machine is the
+collection of all strings that it ever
+
+ align:start position:0%
+collection of all strings that it ever
+ 
+
+ align:start position:0%
+collection of all strings that it ever
+prints
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+out so we're defining language in a
+
+ align:start position:0%
+out so we're defining language in a
+ 
+
+ align:start position:0%
+out so we're defining language in a
+somewhat different way here it's not the
+
+ align:start position:0%
+somewhat different way here it's not the
+ 
+
+ align:start position:0%
+somewhat different way here it's not the
+strings that it accepts it's the strings
+
+ align:start position:0%
+strings that it accepts it's the strings
+ 
+
+ align:start position:0%
+strings that it accepts it's the strings
+that it
+
+ align:start position:0%
+that it
+ 
+
+ align:start position:0%
+that it
+prints so we think of this mean Sheen
+
+ align:start position:0%
+prints so we think of this mean Sheen
+ 
+
+ align:start position:0%
+prints so we think of this mean Sheen
+almost a little bit analogous to like
+
+ align:start position:0%
+almost a little bit analogous to like
+ 
+
+ align:start position:0%
+almost a little bit analogous to like
+the regular expression or the grammar in
+
+ align:start position:0%
+the regular expression or the grammar in
+ 
+
+ align:start position:0%
+the regular expression or the grammar in
+the sense that it's a generative model
+
+ align:start position:0%
+the sense that it's a generative model
+ 
+
+ align:start position:0%
+the sense that it's a generative model
+it produces the language rather than
+
+ align:start position:0%
+it produces the language rather than
+ 
+
+ align:start position:0%
+it produces the language rather than
+accepts the strings in the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+language so it's not really a recognizer
+
+ align:start position:0%
+language so it's not really a recognizer
+ 
+
+ align:start position:0%
+language so it's not really a recognizer
+it's a generator and the language of the
+
+ align:start position:0%
+it's a generator and the language of the
+ 
+
+ align:start position:0%
+it's a generator and the language of the
+machine as I'm writing over here for
+
+ align:start position:0%
+machine as I'm writing over here for
+ 
+
+ align:start position:0%
+machine as I'm writing over here for
+enumerator here we say that its language
+
+ align:start position:0%
+enumerator here we say that its language
+ 
+
+ align:start position:0%
+enumerator here we say that its language
+is a collection of strings at it
+
+ align:start position:0%
+is a collection of strings at it
+ 
+
+ align:start position:0%
+is a collection of strings at it
+prints okay now we will show that a
+
+ align:start position:0%
+prints okay now we will show that a
+ 
+
+ align:start position:0%
+prints okay now we will show that a
+language is touring recognizable in the
+
+ align:start position:0%
+language is touring recognizable in the
+ 
+
+ align:start position:0%
+language is touring recognizable in the
+previous sense you know you recognized
+
+ align:start position:0%
+previous sense you know you recognized
+ 
+
+ align:start position:0%
+previous sense you know you recognized
+by some ordinary touring machine if only
+
+ align:start position:0%
+by some ordinary touring machine if only
+ 
+
+ align:start position:0%
+by some ordinary touring machine if only
+if it's the language of some
+
+ align:start position:0%
+if it's the language of some
+ 
+
+ align:start position:0%
+if it's the language of some
+enumerate and actually this is kind of a
+
+ align:start position:0%
+enumerate and actually this is kind of a
+ 
+
+ align:start position:0%
+enumerate and actually this is kind of a
+little bit of an interesting proof uh
+
+ align:start position:0%
+little bit of an interesting proof uh
+ 
+
+ align:start position:0%
+little bit of an interesting proof uh
+you have to do some work it's an if and
+
+ align:start position:0%
+you have to do some work it's an if and
+ 
+
+ align:start position:0%
+you have to do some work it's an if and
+only if now neither direction is
+
+ align:start position:0%
+only if now neither direction is
+ 
+
+ align:start position:0%
+only if now neither direction is
+immediate you're going to have to do
+
+ align:start position:0%
+immediate you're going to have to do
+ 
+
+ align:start position:0%
+immediate you're going to have to do
+some work uh in both directions One
+
+ align:start position:0%
+some work uh in both directions One
+ 
+
+ align:start position:0%
+some work uh in both directions One
+Direction is a little harder then the
+
+ align:start position:0%
+Direction is a little harder then the
+ 
+
+ align:start position:0%
+Direction is a little harder then the
+other will start off with the easier
+
+ align:start position:0%
+other will start off with the easier
+ 
+
+ align:start position:0%
+other will start off with the easier
+Direction let's say we have an
+
+ align:start position:0%
+Direction let's say we have an
+ 
+
+ align:start position:0%
+Direction let's say we have an
+enumerator
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+hope you hopefully you got this concept
+
+ align:start position:0%
+hope you hopefully you got this concept
+ 
+
+ align:start position:0%
+hope you hopefully you got this concept
+of this touring machine which
+
+ align:start position:0%
+of this touring machine which
+ 
+
+ align:start position:0%
+of this touring machine which
+periodically P prints strings when
+
+ align:start position:0%
+periodically P prints strings when
+ 
+
+ align:start position:0%
+periodically P prints strings when
+you've started it off on the empty tape
+
+ align:start position:0%
+you've started it off on the empty tape
+ 
+
+ align:start position:0%
+you've started it off on the empty tape
+um uh so now what I'm going to construct
+
+ align:start position:0%
+um uh so now what I'm going to construct
+ 
+
+ align:start position:0%
+um uh so now what I'm going to construct
+for you um is the touring machine
+
+ align:start position:0%
+for you um is the touring machine
+ 
+
+ align:start position:0%
+for you um is the touring machine
+recognizer defined from the enumerator
+
+ align:start position:0%
+recognizer defined from the enumerator
+ 
+
+ align:start position:0%
+recognizer defined from the enumerator
+so this recognizer is going to be
+
+ align:start position:0%
+so this recognizer is going to be
+ 
+
+ align:start position:0%
+so this recognizer is going to be
+simulating the
+
+ align:start position:0%
+simulating the
+ 
+
+ align:start position:0%
+simulating the
+enumerator um so it's basically the
+
+ align:start position:0%
+enumerator um so it's basically the
+ 
+
+ align:start position:0%
+enumerator um so it's basically the
+recognizer you're going to launch the
+
+ align:start position:0%
+recognizer you're going to launch the
+ 
+
+ align:start position:0%
+recognizer you're going to launch the
+enumerator it's going to start off
+
+ align:start position:0%
+enumerator it's going to start off
+ 
+
+ align:start position:0%
+enumerator it's going to start off
+simulating it
+
+ align:start position:0%
+simulating it
+ 
+
+ align:start position:0%
+simulating it
+um now if you want if it's convenient we
+
+ align:start position:0%
+um now if you want if it's convenient we
+ 
+
+ align:start position:0%
+um now if you want if it's convenient we
+we could use several tapes we can use
+
+ align:start position:0%
+we could use several tapes we can use
+ 
+
+ align:start position:0%
+we could use several tapes we can use
+one tape to simulate the recognizer and
+
+ align:start position:0%
+one tape to simulate the recognizer and
+ 
+
+ align:start position:0%
+one tape to simulate the recognizer and
+you have other tapes available for
+
+ align:start position:0%
+you have other tapes available for
+ 
+
+ align:start position:0%
+you have other tapes available for
+convenience if you want because we
+
+ align:start position:0%
+convenience if you want because we
+ 
+
+ align:start position:0%
+convenience if you want because we
+already showed multi-tape and single
+
+ align:start position:0%
+already showed multi-tape and single
+ 
+
+ align:start position:0%
+already showed multi-tape and single
+tape are equivalent so if you want to
+
+ align:start position:0%
+tape are equivalent so if you want to
+ 
+
+ align:start position:0%
+tape are equivalent so if you want to
+think of M as having multiple tapes it's
+
+ align:start position:0%
+think of M as having multiple tapes it's
+ 
+
+ align:start position:0%
+think of M as having multiple tapes it's
+not going to really be that important
+
+ align:start position:0%
+not going to really be that important
+ 
+
+ align:start position:0%
+not going to really be that important
+relevant to my conversation um but
+
+ align:start position:0%
+relevant to my conversation um but
+ 
+
+ align:start position:0%
+relevant to my conversation um but
+you're going to simulate e starting on
+
+ align:start position:0%
+you're going to simulate e starting on
+ 
+
+ align:start position:0%
+you're going to simulate e starting on
+the blank input as you're supposed to
+
+ align:start position:0%
+the blank input as you're supposed to
+ 
+
+ align:start position:0%
+the blank input as you're supposed to
+and then you're going to see whenever e
+
+ align:start position:0%
+and then you're going to see whenever e
+ 
+
+ align:start position:0%
+and then you're going to see whenever e
+prints an X you're going to see if x is
+
+ align:start position:0%
+prints an X you're going to see if x is
+ 
+
+ align:start position:0%
+prints an X you're going to see if x is
+the same as the input to the
+
+ align:start position:0%
+the same as the input to the
+ 
+
+ align:start position:0%
+the same as the input to the
+recognizer you you get the idea so we
+
+ align:start position:0%
+recognizer you you get the idea so we
+ 
+
+ align:start position:0%
+recognizer you you get the idea so we
+have a recognizer it has an input string
+
+ align:start position:0%
+have a recognizer it has an input string
+ 
+
+ align:start position:0%
+have a recognizer it has an input string
+maybe like one
+
+ align:start position:0%
+maybe like one
+ 
+
+ align:start position:0%
+maybe like one
+one01 and I want to know I want to
+
+ align:start position:0%
+one01 and I want to know I want to
+ 
+
+ align:start position:0%
+one01 and I want to know I want to
+accept that string if it's one of the
+
+ align:start position:0%
+accept that string if it's one of the
+ 
+
+ align:start position:0%
+accept that string if it's one of the
+strings that the enumerator e prints out
+
+ align:start position:0%
+strings that the enumerator e prints out
+ 
+
+ align:start position:0%
+strings that the enumerator e prints out
+because that's what the recognizer do
+
+ align:start position:0%
+because that's what the recognizer do
+ 
+
+ align:start position:0%
+because that's what the recognizer do
+it's supposed to accept all the strings
+
+ align:start position:0%
+it's supposed to accept all the strings
+ 
+
+ align:start position:0%
+it's supposed to accept all the strings
+that the enumerator prints out so I got
+
+ align:start position:0%
+that the enumerator prints out so I got
+ 
+
+ align:start position:0%
+that the enumerator prints out so I got
+this one one 01 what do I do I launch I
+
+ align:start position:0%
+this one one 01 what do I do I launch I
+ 
+
+ align:start position:0%
+this one one 01 what do I do I launch I
+fire up that numerator I get it going
+
+ align:start position:0%
+fire up that numerator I get it going
+ 
+
+ align:start position:0%
+fire up that numerator I get it going
+and I start watching the strings that
+
+ align:start position:0%
+and I start watching the strings that
+ 
+
+ align:start position:0%
+and I start watching the strings that
+prints out comparing them with my input
+
+ align:start position:0%
+prints out comparing them with my input
+ 
+
+ align:start position:0%
+prints out comparing them with my input
+string
+
+ align:start position:0%
+string
+ 
+
+ align:start position:0%
+string
+1101 if I ever see it print out a
+
+ align:start position:0%
+1101 if I ever see it print out a
+ 
+
+ align:start position:0%
+1101 if I ever see it print out a
+
+ align:start position:0%
+ 
+
+ align:start position:0%
+great I I know I can accept because I
+
+ align:start position:0%
+great I I know I can accept because I
+ 
+
+ align:start position:0%
+great I I know I can accept because I
+know it's in the enumerator
+
+ align:start position:0%
+know it's in the enumerator
+ 
+
+ align:start position:0%
+know it's in the enumerator
+language but if I compare and compare
+
+ align:start position:0%
+language but if I compare and compare
+ 
+
+ align:start position:0%
+language but if I compare and compare
+and compare I never see uh the
+
+ align:start position:0%
+and compare I never see uh the
+ 
+
+ align:start position:0%
+and compare I never see uh the
+enumerator ever printing out uh my input
+
+ align:start position:0%
+enumerator ever printing out uh my input
+ 
+
+ align:start position:0%
+enumerator ever printing out uh my input
+string 1101 uh well I just keep
+
+ align:start position:0%
+string 1101 uh well I just keep
+ 
+
+ align:start position:0%
+string 1101 uh well I just keep
+simulating e if e holds well then I can
+
+ align:start position:0%
+simulating e if e holds well then I can
+ 
+
+ align:start position:0%
+simulating e if e holds well then I can
+hold and reject um if I've never seen
+
+ align:start position:0%
+hold and reject um if I've never seen
+ 
+
+ align:start position:0%
+hold and reject um if I've never seen
+that string coming out as an output um
+
+ align:start position:0%
+that string coming out as an output um
+ 
+
+ align:start position:0%
+that string coming out as an output um
+if e doesn't hold well I'm just not
+
+ align:start position:0%
+if e doesn't hold well I'm just not
+ 
+
+ align:start position:0%
+if e doesn't hold well I'm just not
+going to holdt either I'm going to go
+
+ align:start position:0%
+going to holdt either I'm going to go
+ 
+
+ align:start position:0%
+going to holdt either I'm going to go
+forever but then I'm going to be
+
+ align:start position:0%
+forever but then I'm going to be
+ 
+
+ align:start position:0%
+forever but then I'm going to be
+rejecting my input by
+
+ align:start position:0%
+rejecting my input by
+ 
+
+ align:start position:0%
+rejecting my input by
+looping okay so that's the proof of
+
+ align:start position:0%
+looping okay so that's the proof of
+ 
+
+ align:start position:0%
+looping okay so that's the proof of
+converting in this uh backward Direction
+
+ align:start position:0%
+converting in this uh backward Direction
+ 
+
+ align:start position:0%
+converting in this uh backward Direction
+which is the easier Direction now let's
+
+ align:start position:0%
+which is the easier Direction now let's
+ 
+
+ align:start position:0%
+which is the easier Direction now let's
+look at the forward Direction which has
+
+ align:start position:0%
+look at the forward Direction which has
+ 
+
+ align:start position:0%
+look at the forward Direction which has
+a certain wrinkle that in it that we're
+
+ align:start position:0%
+a certain wrinkle that in it that we're
+ 
+
+ align:start position:0%
+a certain wrinkle that in it that we're
+going to have to get
+
+ align:start position:0%
+going to have to get
+ 
+
+ align:start position:0%
+going to have to get
+to so now we're going to be building our
+
+ align:start position:0%
+to so now we're going to be building our
+ 
+
+ align:start position:0%
+to so now we're going to be building our
+enumerator to simulate our
+
+ align:start position:0%
+enumerator to simulate our
+ 
+
+ align:start position:0%
+enumerator to simulate our
+recognizer okay and the way we'll do
+
+ align:start position:0%
+recognizer okay and the way we'll do
+ 
+
+ align:start position:0%
+recognizer okay and the way we'll do
+that is the enumerator has to print out
+
+ align:start position:0%
+that is the enumerator has to print out
+ 
+
+ align:start position:0%
+that is the enumerator has to print out
+all of the strings that the recognizer
+
+ align:start position:0%
+all of the strings that the recognizer
+ 
+
+ align:start position:0%
+all of the strings that the recognizer
+would ever
+
+ align:start position:0%
+would ever
+ 
+
+ align:start position:0%
+would ever
+accept so you can to do the obvious
+
+ align:start position:0%
+accept so you can to do the obvious
+ 
+
+ align:start position:0%
+accept so you can to do the obvious
+thing you're going to take the
+
+ align:start position:0%
+thing you're going to take the
+ 
+
+ align:start position:0%
+thing you're going to take the
+enumerator is going to start simulating
+
+ align:start position:0%
+enumerator is going to start simulating
+ 
+
+ align:start position:0%
+enumerator is going to start simulating
+the recognizer M on all possible strings
+
+ align:start position:0%
+the recognizer M on all possible strings
+ 
+
+ align:start position:0%
+the recognizer M on all possible strings
+sort of you know one by one using doing
+
+ align:start position:0%
+sort of you know one by one using doing
+ 
+
+ align:start position:0%
+sort of you know one by one using doing
+them in parallel taking turns you never
+
+ align:start position:0%
+them in parallel taking turns you never
+ 
+
+ align:start position:0%
+them in parallel taking turns you never
+not you know we um maybe we didn't make
+
+ align:start position:0%
+not you know we um maybe we didn't make
+ 
+
+ align:start position:0%
+not you know we um maybe we didn't make
+this so explicit but you don't have you
+
+ align:start position:0%
+this so explicit but you don't have you
+ 
+
+ align:start position:0%
+this so explicit but you don't have you
+know you can sort of time share among
+
+ align:start position:0%
+know you can sort of time share among
+ 
+
+ align:start position:0%
+know you can sort of time share among
+several different possibilities you run
+
+ align:start position:0%
+several different possibilities you run
+ 
+
+ align:start position:0%
+several different possibilities you run
+you know sort of like having different
+
+ align:start position:0%
+you know sort of like having different
+ 
+
+ align:start position:0%
+you know sort of like having different
+blocks uh for the machine diff you're
+
+ align:start position:0%
+blocks uh for the machine diff you're
+ 
+
+ align:start position:0%
+blocks uh for the machine diff you're
+going to run
+
+ align:start position:0%
+going to run
+ 
+
+ align:start position:0%
+going to run
+um uh the enumerator is going to run the
+
+ align:start position:0%
+um uh the enumerator is going to run the
+ 
+
+ align:start position:0%
+um uh the enumerator is going to run the
+recognizer on um it's you know well
+
+ align:start position:0%
+recognizer on um it's you know well
+ 
+
+ align:start position:0%
+recognizer on um it's you know well
+let's just say it does it sequentially
+
+ align:start position:0%
+let's just say it does it sequentially
+ 
+
+ align:start position:0%
+let's just say it does it sequentially
+it runs it on the empty string it runs
+
+ align:start position:0%
+it runs it on the empty string it runs
+ 
+
+ align:start position:0%
+it runs it on the empty string it runs
+it on the string zero it runs it on the
+
+ align:start position:0%
+it on the string zero it runs it on the
+ 
+
+ align:start position:0%
+it on the string zero it runs it on the
+string one one runs it on the string 0 0
+
+ align:start position:0%
+string one one runs it on the string 0 0
+ 
+
+ align:start position:0%
+string one one runs it on the string 0 0
+these are all the possible strings in
+
+ align:start position:0%
+these are all the possible strings in
+ 
+
+ align:start position:0%
+these are all the possible strings in
+Sigma star you you run on all of them
+
+ align:start position:0%
+Sigma star you you run on all of them
+ 
+
+ align:start position:0%
+Sigma star you you run on all of them
+and uh whenever the
+
+ align:start position:0%
+and uh whenever the
+ 
+
+ align:start position:0%
+and uh whenever the
+enumerator
+
+ align:start position:0%
+enumerator
+ 
+
+ align:start position:0%
+enumerator
+uh uh
+
+ align:start position:0%
+uh uh
+ 
+
+ align:start position:0%
+uh uh
+oh this is wrong
+
+ align:start position:0%
+oh this is wrong
+ 
+
+ align:start position:0%
+oh this is wrong
+whenever
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um so whenever
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh M
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+accepts then print I can't right very
+
+ align:start position:0%
+accepts then print I can't right very
+ 
+
+ align:start position:0%
+accepts then print I can't right very
+well
+
+ align:start position:0%
+well
+ 
+
+ align:start position:0%
+well
+print
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+W um wi
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+oops okay so I'm going just say it in
+
+ align:start position:0%
+oops okay so I'm going just say it in
+ 
+
+ align:start position:0%
+oops okay so I'm going just say it in
+words you're going to simulate Emma on
+
+ align:start position:0%
+words you're going to simulate Emma on
+ 
+
+ align:start position:0%
+words you're going to simulate Emma on
+hwi whenever you notice and accepting wi
+
+ align:start position:0%
+hwi whenever you notice and accepting wi
+ 
+
+ align:start position:0%
+hwi whenever you notice and accepting wi
+you just print out
+
+ align:start position:0%
+you just print out
+ 
+
+ align:start position:0%
+you just print out
+wi um because you want to print out all
+
+ align:start position:0%
+wi um because you want to print out all
+ 
+
+ align:start position:0%
+wi um because you want to print out all
+of the strings that M
+
+ align:start position:0%
+of the strings that M
+ 
+
+ align:start position:0%
+of the strings that M
+accepts now what H the pro there is a
+
+ align:start position:0%
+accepts now what H the pro there is a
+ 
+
+ align:start position:0%
+accepts now what H the pro there is a
+problem here so hopefully you're not
+
+ align:start position:0%
+problem here so hopefully you're not
+ 
+
+ align:start position:0%
+problem here so hopefully you're not
+confused by this typo
+
+ align:start position:0%
+confused by this typo
+ 
+
+ align:start position:0%
+confused by this typo
+um uh doing it sequentially like I just
+
+ align:start position:0%
+um uh doing it sequentially like I just
+ 
+
+ align:start position:0%
+um uh doing it sequentially like I just
+described doesn't quite work so let me
+
+ align:start position:0%
+described doesn't quite work so let me
+ 
+
+ align:start position:0%
+described doesn't quite work so let me
+just back that up here doing it
+
+ align:start position:0%
+just back that up here doing it
+ 
+
+ align:start position:0%
+just back that up here doing it
+sequentially doesn't quite work because
+
+ align:start position:0%
+sequentially doesn't quite work because
+ 
+
+ align:start position:0%
+sequentially doesn't quite work because
+Emma might get stuck looping on one of
+
+ align:start position:0%
+Emma might get stuck looping on one of
+ 
+
+ align:start position:0%
+Emma might get stuck looping on one of
+the wi like you know maybe when I feed W
+
+ align:start position:0%
+the wi like you know maybe when I feed W
+ 
+
+ align:start position:0%
+the wi like you know maybe when I feed W
+zero into W into m m goes
+
+ align:start position:0%
+zero into W into m m goes
+ 
+
+ align:start position:0%
+zero into W into m m goes
+forever because m is rejecting the Zero
+
+ align:start position:0%
+forever because m is rejecting the Zero
+ 
+
+ align:start position:0%
+forever because m is rejecting the Zero
+by looping but maybe it also accepts one
+
+ align:start position:0%
+by looping but maybe it also accepts one
+ 
+
+ align:start position:0%
+by looping but maybe it also accepts one
+this next string in the list the string
+
+ align:start position:0%
+this next string in the list the string
+ 
+
+ align:start position:0%
+this next string in the list the string
+one I'll never get to one by just
+
+ align:start position:0%
+one I'll never get to one by just
+ 
+
+ align:start position:0%
+one I'll never get to one by just
+feeding the strings into m one by one
+
+ align:start position:0%
+feeding the strings into m one by one
+ 
+
+ align:start position:0%
+feeding the strings into m one by one
+like this what I really have to do is
+
+ align:start position:0%
+like this what I really have to do is
+ 
+
+ align:start position:0%
+like this what I really have to do is
+run all of the strings in m in
+
+ align:start position:0%
+run all of the strings in m in
+ 
+
+ align:start position:0%
+run all of the strings in m in
+parallel and the way I'm going to
+
+ align:start position:0%
+parallel and the way I'm going to
+ 
+
+ align:start position:0%
+parallel and the way I'm going to
+indicate that is I'm going to simulate M
+
+ align:start position:0%
+indicate that is I'm going to simulate M
+ 
+
+ align:start position:0%
+indicate that is I'm going to simulate M
+on W1 to Wi for I steps for each
+
+ align:start position:0%
+on W1 to Wi for I steps for each
+ 
+
+ align:start position:0%
+on W1 to Wi for I steps for each
+possible I so I'm going to run
+
+ align:start position:0%
+possible I so I'm going to run
+ 
+
+ align:start position:0%
+possible I so I'm going to run
+M
+
+ align:start position:0%
+M
+ 
+
+ align:start position:0%
+M
+on uh more and more strings for more and
+
+ align:start position:0%
+on uh more and more strings for more and
+ 
+
+ align:start position:0%
+on uh more and more strings for more and
+more
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+steps okay until and every time I notice
+
+ align:start position:0%
+steps okay until and every time I notice
+ 
+
+ align:start position:0%
+steps okay until and every time I notice
+an mxf something I print it
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+out
+
+ align:start position:0%
+out
+ 
+
+ align:start position:0%
+out
+um uh
+
+ align:start position:0%
+um uh
+ 
+
+ align:start position:0%
+um uh
+so I will fix this in the um version of
+
+ align:start position:0%
+so I will fix this in the um version of
+ 
+
+ align:start position:0%
+so I will fix this in the um version of
+the uh file that I um published on the
+
+ align:start position:0%
+the uh file that I um published on the
+ 
+
+ align:start position:0%
+the uh file that I um published on the
+website so if you're still not getting
+
+ align:start position:0%
+website so if you're still not getting
+ 
+
+ align:start position:0%
+website so if you're still not getting
+it you can look there um uh but just to
+
+ align:start position:0%
+it you can look there um uh but just to
+ 
+
+ align:start position:0%
+it you can look there um uh but just to
+make things even worse I have a check in
+
+ align:start position:0%
+make things even worse I have a check in
+ 
+
+ align:start position:0%
+make things even worse I have a check in
+which is going to be about this one
+
+ align:start position:0%
+which is going to be about this one
+ 
+
+ align:start position:0%
+which is going to be about this one
+little Point here um so I got a question
+
+ align:start position:0%
+little Point here um so I got a question
+ 
+
+ align:start position:0%
+little Point here um so I got a question
+where do we get the wi strings the wi
+
+ align:start position:0%
+where do we get the wi strings the wi
+ 
+
+ align:start position:0%
+where do we get the wi strings the wi
+strings are simply the list of all
+
+ align:start position:0%
+strings are simply the list of all
+ 
+
+ align:start position:0%
+strings are simply the list of all
+strings in Sigma
+
+ align:start position:0%
+strings in Sigma
+ 
+
+ align:start position:0%
+strings in Sigma
+star so we can under program control
+
+ align:start position:0%
+star so we can under program control
+ 
+
+ align:start position:0%
+star so we can under program control
+we can make M go through every possible
+
+ align:start position:0%
+we can make M go through every possible
+ 
+
+ align:start position:0%
+we can make M go through every possible
+string like if you had an odometer
+
+ align:start position:0%
+string like if you had an odometer
+ 
+
+ align:start position:0%
+string like if you had an odometer
+you're going to first get to the empty
+
+ align:start position:0%
+you're going to first get to the empty
+ 
+
+ align:start position:0%
+you're going to first get to the empty
+string then you go to the string zero
+
+ align:start position:0%
+string then you go to the string zero
+ 
+
+ align:start position:0%
+string then you go to the string zero
+then the string one you can write a
+
+ align:start position:0%
+then the string one you can write a
+ 
+
+ align:start position:0%
+then the string one you can write a
+program which is going to do that um uh
+
+ align:start position:0%
+program which is going to do that um uh
+ 
+
+ align:start position:0%
+program which is going to do that um uh
+and the touring machine can simil write
+
+ align:start position:0%
+and the touring machine can simil write
+ 
+
+ align:start position:0%
+and the touring machine can simil write
+write code to do that um to get to each
+
+ align:start position:0%
+write code to do that um to get to each
+ 
+
+ align:start position:0%
+write code to do that um to get to each
+possible string one by one and then
+
+ align:start position:0%
+possible string one by one and then
+ 
+
+ align:start position:0%
+possible string one by one and then
+that's what the um enumerator is doing
+
+ align:start position:0%
+that's what the um enumerator is doing
+ 
+
+ align:start position:0%
+that's what the um enumerator is doing
+it's obtaining each of those strings and
+
+ align:start position:0%
+it's obtaining each of those strings and
+ 
+
+ align:start position:0%
+it's obtaining each of those strings and
+then feeding them into M seeing what M
+
+ align:start position:0%
+then feeding them into M seeing what M
+ 
+
+ align:start position:0%
+then feeding them into M seeing what M
+does
+
+ align:start position:0%
+does
+ 
+
+ align:start position:0%
+does
+what I'm trying to get at here is that
+
+ align:start position:0%
+what I'm trying to get at here is that
+ 
+
+ align:start position:0%
+what I'm trying to get at here is that
+it's not good to feed them in run M to
+
+ align:start position:0%
+it's not good to feed them in run M to
+ 
+
+ align:start position:0%
+it's not good to feed them in run M to
+completion on each one before we go into
+
+ align:start position:0%
+completion on each one before we go into
+ 
+
+ align:start position:0%
+completion on each one before we go into
+the next one you really kind of have to
+
+ align:start position:0%
+the next one you really kind of have to
+ 
+
+ align:start position:0%
+the next one you really kind of have to
+do them all in
+
+ align:start position:0%
+do them all in
+ 
+
+ align:start position:0%
+do them all in
+parallel uh um to avoid the problem of
+
+ align:start position:0%
+parallel uh um to avoid the problem of
+ 
+
+ align:start position:0%
+parallel uh um to avoid the problem of
+getting stuck on one string that m is
+
+ align:start position:0%
+getting stuck on one string that m is
+ 
+
+ align:start position:0%
+getting stuck on one string that m is
+looping on um all right so uh this is
+
+ align:start position:0%
+looping on um all right so uh this is
+ 
+
+ align:start position:0%
+looping on um all right so uh this is
+relevant to your homework in fact if I
+
+ align:start position:0%
+relevant to your homework in fact if I
+ 
+
+ align:start position:0%
+relevant to your homework in fact if I
+convert M to an
+
+ align:start position:0%
+convert M to an
+ 
+
+ align:start position:0%
+convert M to an
+enumerator um in this way
+
+ align:start position:0%
+enumerator um in this way
+ 
+
+ align:start position:0%
+enumerator um in this way
+does that enumerator always print the
+
+ align:start position:0%
+does that enumerator always print the
+ 
+
+ align:start position:0%
+does that enumerator always print the
+strings out in string order string order
+
+ align:start position:0%
+strings out in string order string order
+ 
+
+ align:start position:0%
+strings out in string order string order
+is this order here um having them uh the
+
+ align:start position:0%
+is this order here um having them uh the
+ 
+
+ align:start position:0%
+is this order here um having them uh the
+having the shorter strings coming up
+
+ align:start position:0%
+having the shorter strings coming up
+ 
+
+ align:start position:0%
+having the shorter strings coming up
+before the longer strings and within
+
+ align:start position:0%
+before the longer strings and within
+ 
+
+ align:start position:0%
+before the longer strings and within
+strings of a certain length just doing
+
+ align:start position:0%
+strings of a certain length just doing
+ 
+
+ align:start position:0%
+strings of a certain length just doing
+them in lexic graphic
+
+ align:start position:0%
+them in lexic graphic
+ 
+
+ align:start position:0%
+them in lexic graphic
+order um uh so um hopefully you follow
+
+ align:start position:0%
+order um uh so um hopefully you follow
+ 
+
+ align:start position:0%
+order um uh so um hopefully you follow
+that but since you're you know these are
+
+ align:start position:0%
+that but since you're you know these are
+ 
+
+ align:start position:0%
+that but since you're you know these are
+not uh correctness is that doesn't
+
+ align:start position:0%
+not uh correctness is that doesn't
+ 
+
+ align:start position:0%
+not uh correctness is that doesn't
+matter uh for us let me launch that pull
+
+ align:start position:0%
+matter uh for us let me launch that pull
+ 
+
+ align:start position:0%
+matter uh for us let me launch that pull
+let's I'll see how confused how random
+
+ align:start position:0%
+let's I'll see how confused how random
+ 
+
+ align:start position:0%
+let's I'll see how confused how random
+the answer is here
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh so a fair amount of confusion if
+
+ align:start position:0%
+uh so a fair amount of confusion if
+ 
+
+ align:start position:0%
+uh so a fair amount of confusion if
+you're confused obviously you're in good
+
+ align:start position:0%
+you're confused obviously you're in good
+ 
+
+ align:start position:0%
+you're confused obviously you're in good
+company there um okay about to shut this
+
+ align:start position:0%
+company there um okay about to shut this
+ 
+
+ align:start position:0%
+company there um okay about to shut this
+down uh five seconds to
+
+ align:start position:0%
+down uh five seconds to
+ 
+
+ align:start position:0%
+down uh five seconds to
+go okay ending in
+
+ align:start position:0%
+go okay ending in
+ 
+
+ align:start position:0%
+go okay ending in
+now
+
+ align:start position:0%
+now
+ 
+
+ align:start position:0%
+now
+uh all right so the correct answer as
+
+ align:start position:0%
+uh all right so the correct answer as
+ 
+
+ align:start position:0%
+uh all right so the correct answer as
+the majority of you did get is in fact
+
+ align:start position:0%
+the majority of you did get is in fact
+ 
+
+ align:start position:0%
+the majority of you did get is in fact
+that the order is not going to be uh
+
+ align:start position:0%
+that the order is not going to be uh
+ 
+
+ align:start position:0%
+that the order is not going to be uh
+respected here when e uh prints things
+
+ align:start position:0%
+respected here when e uh prints things
+ 
+
+ align:start position:0%
+respected here when e uh prints things
+out it might print out some things later
+
+ align:start position:0%
+out it might print out some things later
+ 
+
+ align:start position:0%
+out it might print out some things later
+in the order before earlier things in
+
+ align:start position:0%
+in the order before earlier things in
+ 
+
+ align:start position:0%
+in the order before earlier things in
+the order what's going to control how um
+
+ align:start position:0%
+the order what's going to control how um
+ 
+
+ align:start position:0%
+the order what's going to control how um
+when m is going to print it out it
+
+ align:start position:0%
+when m is going to print it out it
+ 
+
+ align:start position:0%
+when m is going to print it out it
+really is if M accepts some strings more
+
+ align:start position:0%
+really is if M accepts some strings more
+ 
+
+ align:start position:0%
+really is if M accepts some strings more
+quickly in fewer
+
+ align:start position:0%
+quickly in fewer
+ 
+
+ align:start position:0%
+quickly in fewer
+steps then e might end up printing out
+
+ align:start position:0%
+steps then e might end up printing out
+ 
+
+ align:start position:0%
+steps then e might end up printing out
+though that string earlier in the
+
+ align:start position:0%
+though that string earlier in the
+ 
+
+ align:start position:0%
+though that string earlier in the
+list um than some other string that
+
+ align:start position:0%
+list um than some other string that
+ 
+
+ align:start position:0%
+list um than some other string that
+might be a shorter
+
+ align:start position:0%
+might be a shorter
+ 
+
+ align:start position:0%
+might be a shorter
+string um
+
+ align:start position:0%
+string um
+ 
+
+ align:start position:0%
+string um
+because uh the order in which e is going
+
+ align:start position:0%
+because uh the order in which e is going
+ 
+
+ align:start position:0%
+because uh the order in which e is going
+going to now identify that m is is
+
+ align:start position:0%
+going to now identify that m is is
+ 
+
+ align:start position:0%
+going to now identify that m is is
+accepting those strings is is the um
+
+ align:start position:0%
+accepting those strings is is the um
+ 
+
+ align:start position:0%
+accepting those strings is is the um
+depends upon the speed with which m is
+
+ align:start position:0%
+depends upon the speed with which m is
+ 
+
+ align:start position:0%
+depends upon the speed with which m is
+do actually doing the
+
+ align:start position:0%
+do actually doing the
+ 
+
+ align:start position:0%
+do actually doing the
+accepting so you have to um this is
+
+ align:start position:0%
+accepting so you have to um this is
+ 
+
+ align:start position:0%
+accepting so you have to um this is
+relevant to one of your homeworks
+
+ align:start position:0%
+relevant to one of your homeworks
+ 
+
+ align:start position:0%
+relevant to one of your homeworks
+because if uh what you're going to be at
+
+ align:start position:0%
+because if uh what you're going to be at
+ 
+
+ align:start position:0%
+because if uh what you're going to be at
+to show is that if you start with a
+
+ align:start position:0%
+to show is that if you start with a
+ 
+
+ align:start position:0%
+to show is that if you start with a
+decidable language instead of a
+
+ align:start position:0%
+decidable language instead of a
+ 
+
+ align:start position:0%
+decidable language instead of a
+recognizable language then you can make
+
+ align:start position:0%
+recognizable language then you can make
+ 
+
+ align:start position:0%
+recognizable language then you can make
+an then then you can make an enumerator
+
+ align:start position:0%
+an then then you can make an enumerator
+ 
+
+ align:start position:0%
+an then then you can make an enumerator
+which always prints out things in order
+
+ align:start position:0%
+which always prints out things in order
+ 
+
+ align:start position:0%
+which always prints out things in order
+in the string
+
+ align:start position:0%
+in the string
+ 
+
+ align:start position:0%
+in the string
+order okay and um and vice versa so if
+
+ align:start position:0%
+order okay and um and vice versa so if
+ 
+
+ align:start position:0%
+order okay and um and vice versa so if
+you have and if you have a string which
+
+ align:start position:0%
+you have and if you have a string which
+ 
+
+ align:start position:0%
+you have and if you have a string which
+a numerator which prints things out in
+
+ align:start position:0%
+a numerator which prints things out in
+ 
+
+ align:start position:0%
+a numerator which prints things out in
+string order then the language is
+
+ align:start position:0%
+string order then the language is
+ 
+
+ align:start position:0%
+string order then the language is
+decidable okay so you need to think
+
+ align:start position:0%
+decidable okay so you need to think
+ 
+
+ align:start position:0%
+decidable okay so you need to think
+about
+
+ align:start position:0%
+about
+ 
+
+ align:start position:0%
+about
+that uh One Direction is a fairly simple
+
+ align:start position:0%
+that uh One Direction is a fairly simple
+ 
+
+ align:start position:0%
+that uh One Direction is a fairly simple
+modification of what I just showed um
+
+ align:start position:0%
+modification of what I just showed um
+ 
+
+ align:start position:0%
+modification of what I just showed um
+the other direction is a little bit of
+
+ align:start position:0%
+the other direction is a little bit of
+ 
+
+ align:start position:0%
+the other direction is a little bit of
+more work um so um anyway why don't we
+
+ align:start position:0%
+more work um so um anyway why don't we
+ 
+
+ align:start position:0%
+more work um so um anyway why don't we
+uh uh take our little coffee break here
+
+ align:start position:0%
+uh uh take our little coffee break here
+ 
+
+ align:start position:0%
+uh uh take our little coffee break here
+uh okay so that's an interesting
+
+ align:start position:0%
+uh okay so that's an interesting
+ 
+
+ align:start position:0%
+uh okay so that's an interesting
+question so one question is if there's
+
+ align:start position:0%
+question so one question is if there's
+ 
+
+ align:start position:0%
+question so one question is if there's
+because you know we Sigma has an
+
+ align:start position:0%
+because you know we Sigma has an
+ 
+
+ align:start position:0%
+because you know we Sigma has an
+infinite Sigma star is
+
+ align:start position:0%
+infinite Sigma star is
+ 
+
+ align:start position:0%
+infinite Sigma star is
+infinite um uh if I understand this
+
+ align:start position:0%
+infinite um uh if I understand this
+ 
+
+ align:start position:0%
+infinite um uh if I understand this
+question quite correctly which says you
+
+ align:start position:0%
+question quite correctly which says you
+ 
+
+ align:start position:0%
+question quite correctly which says you
+know it's an infinite number of strings
+
+ align:start position:0%
+know it's an infinite number of strings
+ 
+
+ align:start position:0%
+know it's an infinite number of strings
+here uh how H how does the machine even
+
+ align:start position:0%
+here uh how H how does the machine even
+ 
+
+ align:start position:0%
+here uh how H how does the machine even
+get started because it has to go through
+
+ align:start position:0%
+get started because it has to go through
+ 
+
+ align:start position:0%
+get started because it has to go through
+and enumerate all of it no it's not
+
+ align:start position:0%
+and enumerate all of it no it's not
+ 
+
+ align:start position:0%
+and enumerate all of it no it's not
+first writing down all of those strings
+
+ align:start position:0%
+first writing down all of those strings
+ 
+
+ align:start position:0%
+first writing down all of those strings
+um because yeah you can't write down an
+
+ align:start position:0%
+um because yeah you can't write down an
+ 
+
+ align:start position:0%
+um because yeah you can't write down an
+you can't do this infinite step of
+
+ align:start position:0%
+you can't do this infinite step of
+ 
+
+ align:start position:0%
+you can't do this infinite step of
+writing down all the strings what I had
+
+ align:start position:0%
+writing down all the strings what I had
+ 
+
+ align:start position:0%
+writing down all the strings what I had
+in mind is you're going to take each
+
+ align:start position:0%
+in mind is you're going to take each
+ 
+
+ align:start position:0%
+in mind is you're going to take each
+string in turn first you're going to
+
+ align:start position:0%
+string in turn first you're going to
+ 
+
+ align:start position:0%
+string in turn first you're going to
+take the first string on the list uh of
+
+ align:start position:0%
+take the first string on the list uh of
+ 
+
+ align:start position:0%
+take the first string on the list uh of
+Sigma star run M uh on that string and
+
+ align:start position:0%
+Sigma star run M uh on that string and
+ 
+
+ align:start position:0%
+Sigma star run M uh on that string and
+then the next string in Sigma star run
+
+ align:start position:0%
+then the next string in Sigma star run
+ 
+
+ align:start position:0%
+then the next string in Sigma star run
+it on that string and so on string after
+
+ align:start position:0%
+it on that string and so on string after
+ 
+
+ align:start position:0%
+it on that string and so on string after
+string um and so you're never going to
+
+ align:start position:0%
+string um and so you're never going to
+ 
+
+ align:start position:0%
+string um and so you're never going to
+have infinitely many strings to deal
+
+ align:start position:0%
+have infinitely many strings to deal
+ 
+
+ align:start position:0%
+have infinitely many strings to deal
+with it's just going to be more and more
+
+ align:start position:0%
+with it's just going to be more and more
+ 
+
+ align:start position:0%
+with it's just going to be more and more
+strings as you're going along and uh the
+
+ align:start position:0%
+strings as you're going along and uh the
+ 
+
+ align:start position:0%
+strings as you're going along and uh the
+question I was trying to get at is
+
+ align:start position:0%
+question I was trying to get at is
+ 
+
+ align:start position:0%
+question I was trying to get at is
+whether you're going
+
+ align:start position:0%
+whether you're going
+ 
+
+ align:start position:0%
+whether you're going
+to run each one to compl completion
+
+ align:start position:0%
+to run each one to compl completion
+ 
+
+ align:start position:0%
+to run each one to compl completion
+before you get to the next one or you're
+
+ align:start position:0%
+before you get to the next one or you're
+ 
+
+ align:start position:0%
+before you get to the next one or you're
+going to kind of try to do them all in
+
+ align:start position:0%
+going to kind of try to do them all in
+ 
+
+ align:start position:0%
+going to kind of try to do them all in
+parallel which is what you need to do uh
+
+ align:start position:0%
+parallel which is what you need to do uh
+ 
+
+ align:start position:0%
+parallel which is what you need to do uh
+for to prove this uh this there um won't
+
+ align:start position:0%
+for to prove this uh this there um won't
+ 
+
+ align:start position:0%
+for to prove this uh this there um won't
+there be infinitely many W yes so there
+
+ align:start position:0%
+there be infinitely many W yes so there
+ 
+
+ align:start position:0%
+there be infinitely many W yes so there
+are a similar question infinitely many W
+
+ align:start position:0%
+are a similar question infinitely many W
+ 
+
+ align:start position:0%
+are a similar question infinitely many W
+there are infinitely many W but you know
+
+ align:start position:0%
+there are infinitely many W but you know
+ 
+
+ align:start position:0%
+there are infinitely many W but you know
+it's just an infinite Loop that we're in
+
+ align:start position:0%
+it's just an infinite Loop that we're in
+ 
+
+ align:start position:0%
+it's just an infinite Loop that we're in
+one by one you're taking care of more
+
+ align:start position:0%
+one by one you're taking care of more
+ 
+
+ align:start position:0%
+one by one you're taking care of more
+and more uh wi as you're going um
+
+ align:start position:0%
+and more uh wi as you're going um
+ 
+
+ align:start position:0%
+and more uh wi as you're going um
+uh let's see
+
+ align:start position:0%
+uh let's see
+ 
+
+ align:start position:0%
+uh let's see
+here yes so e is another question is are
+
+ align:start position:0%
+here yes so e is another question is are
+ 
+
+ align:start position:0%
+here yes so e is another question is are
+we running it all all the strings in
+
+ align:start position:0%
+we running it all all the strings in
+ 
+
+ align:start position:0%
+we running it all all the strings in
+parallel yes we are running things all
+
+ align:start position:0%
+parallel yes we are running things all
+ 
+
+ align:start position:0%
+parallel yes we are running things all
+all on running all of the strings in
+
+ align:start position:0%
+all on running all of the strings in
+ 
+
+ align:start position:0%
+all on running all of the strings in
+parallel but you know it's running them
+
+ align:start position:0%
+parallel but you know it's running them
+ 
+
+ align:start position:0%
+parallel but you know it's running them
+in parallel but um these
+
+ align:start position:0%
+in parallel but um these
+ 
+
+ align:start position:0%
+in parallel but um these
+are
+
+ align:start position:0%
+are
+ 
+
+ align:start position:0%
+are
+um uh you know it's we're not defining a
+
+ align:start position:0%
+um uh you know it's we're not defining a
+ 
+
+ align:start position:0%
+um uh you know it's we're not defining a
+parallel touring machine it's running
+
+ align:start position:0%
+parallel touring machine it's running
+ 
+
+ align:start position:0%
+parallel touring machine it's running
+them in parallel using time sharing you
+
+ align:start position:0%
+them in parallel using time sharing you
+ 
+
+ align:start position:0%
+them in parallel using time sharing you
+know it runs a little bit in this block
+
+ align:start position:0%
+know it runs a little bit in this block
+ 
+
+ align:start position:0%
+know it runs a little bit in this block
+runs a little bit in that block and then
+
+ align:start position:0%
+runs a little bit in that block and then
+ 
+
+ align:start position:0%
+runs a little bit in that block and then
+another block and sort of shifts around
+
+ align:start position:0%
+another block and sort of shifts around
+ 
+
+ align:start position:0%
+another block and sort of shifts around
+and sort of does a few steps of each and
+
+ align:start position:0%
+and sort of does a few steps of each and
+ 
+
+ align:start position:0%
+and sort of does a few steps of each and
+that's how it's getting the effect of
+
+ align:start position:0%
+that's how it's getting the effect of
+ 
+
+ align:start position:0%
+that's how it's getting the effect of
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+parallelism
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um uh
+
+ align:start position:0%
+um uh
+ 
+
+ align:start position:0%
+um uh
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um question is would the enumerator
+
+ align:start position:0%
+um question is would the enumerator
+ 
+
+ align:start position:0%
+um question is would the enumerator
+essentially have a print tape and a work
+
+ align:start position:0%
+essentially have a print tape and a work
+ 
+
+ align:start position:0%
+essentially have a print tape and a work
+tape yeah you could think of it as
+
+ align:start position:0%
+tape yeah you could think of it as
+ 
+
+ align:start position:0%
+tape yeah you could think of it as
+having a print tape you know however you
+
+ align:start position:0%
+having a print tape you know however you
+ 
+
+ align:start position:0%
+having a print tape you know however you
+want to formalize it it's it it doesn't
+
+ align:start position:0%
+want to formalize it it's it it doesn't
+ 
+
+ align:start position:0%
+want to formalize it it's it it doesn't
+matter I mean I'm being a little
+
+ align:start position:0%
+matter I mean I'm being a little
+ 
+
+ align:start position:0%
+matter I mean I'm being a little
+Whimsical with attaching it to a picture
+
+ align:start position:0%
+Whimsical with attaching it to a picture
+ 
+
+ align:start position:0%
+Whimsical with attaching it to a picture
+of
+
+ align:start position:0%
+of
+ 
+
+ align:start position:0%
+of
+a a real printer but yeah it just you
+
+ align:start position:0%
+a a real printer but yeah it just you
+ 
+
+ align:start position:0%
+a a real printer but yeah it just you
+think conceptually can a print tape
+
+ align:start position:0%
+think conceptually can a print tape
+ 
+
+ align:start position:0%
+think conceptually can a print tape
+however you like to to think about it
+
+ align:start position:0%
+however you like to to think about it
+ 
+
+ align:start position:0%
+however you like to to think about it
+it's fine um um how can we directly say
+
+ align:start position:0%
+it's fine um um how can we directly say
+ 
+
+ align:start position:0%
+it's fine um um how can we directly say
+that without knowing the program of the
+
+ align:start position:0%
+that without knowing the program of the
+ 
+
+ align:start position:0%
+that without knowing the program of the
+printer
+
+ align:start position:0%
+printer
+ 
+
+ align:start position:0%
+printer
+uh the printer is just there's no we
+
+ align:start position:0%
+uh the printer is just there's no we
+ 
+
+ align:start position:0%
+uh the printer is just there's no we
+don't have to get into the code the
+
+ align:start position:0%
+don't have to get into the code the
+ 
+
+ align:start position:0%
+don't have to get into the code the
+structure of the printer the printer is
+
+ align:start position:0%
+structure of the printer the printer is
+ 
+
+ align:start position:0%
+structure of the printer the printer is
+just uh something where you say print a
+
+ align:start position:0%
+just uh something where you say print a
+ 
+
+ align:start position:0%
+just uh something where you say print a
+string and a and a string comes out
+
+ align:start position:0%
+string and a and a string comes out
+ 
+
+ align:start position:0%
+string and a and a string comes out
+that's all we know about the printer and
+
+ align:start position:0%
+that's all we know about the printer and
+ 
+
+ align:start position:0%
+that's all we know about the printer and
+that's all we need to know um so there's
+
+ align:start position:0%
+that's all we need to know um so there's
+ 
+
+ align:start position:0%
+that's all we need to know um so there's
+no program for the printer uh sorry if I
+
+ align:start position:0%
+no program for the printer uh sorry if I
+ 
+
+ align:start position:0%
+no program for the printer uh sorry if I
+not understanding your question your
+
+ align:start position:0%
+not understanding your question your
+ 
+
+ align:start position:0%
+not understanding your question your
+question but the question literally says
+
+ align:start position:0%
+question but the question literally says
+ 
+
+ align:start position:0%
+question but the question literally says
+how can we say that without knowing the
+
+ align:start position:0%
+how can we say that without knowing the
+ 
+
+ align:start position:0%
+how can we say that without knowing the
+program of the printer
+
+ align:start position:0%
+program of the printer
+ 
+
+ align:start position:0%
+program of the printer
+um so if the machine is decidable why
+
+ align:start position:0%
+um so if the machine is decidable why
+ 
+
+ align:start position:0%
+um so if the machine is decidable why
+does it have to print all strings in
+
+ align:start position:0%
+does it have to print all strings in
+ 
+
+ align:start position:0%
+does it have to print all strings in
+order for example if one string is
+
+ align:start position:0%
+order for example if one string is
+ 
+
+ align:start position:0%
+order for example if one string is
+shorter and it can it be decided
+
+ align:start position:0%
+shorter and it can it be decided
+ 
+
+ align:start position:0%
+shorter and it can it be decided
+later we well yeah if the uh the reason
+
+ align:start position:0%
+later we well yeah if the uh the reason
+ 
+
+ align:start position:0%
+later we well yeah if the uh the reason
+why we want uh so the question is if the
+
+ align:start position:0%
+why we want uh so the question is if the
+ 
+
+ align:start position:0%
+why we want uh so the question is if the
+machine is decidable why why does it
+
+ align:start position:0%
+machine is decidable why why does it
+ 
+
+ align:start position:0%
+machine is decidable why why does it
+have to print all strings in
+
+ align:start position:0%
+have to print all strings in
+ 
+
+ align:start position:0%
+have to print all strings in
+order uh because that's what I'm asking
+
+ align:start position:0%
+order uh because that's what I'm asking
+ 
+
+ align:start position:0%
+order uh because that's what I'm asking
+you to do in the problem that's what the
+
+ align:start position:0%
+you to do in the problem that's what the
+ 
+
+ align:start position:0%
+you to do in the problem that's what the
+if you read the problem I think it's
+
+ align:start position:0%
+if you read the problem I think it's
+ 
+
+ align:start position:0%
+if you read the problem I think it's
+number five on the pet that's what I'm
+
+ align:start position:0%
+number five on the pet that's what I'm
+ 
+
+ align:start position:0%
+number five on the pet that's what I'm
+asking you to do that's why you have to
+
+ align:start position:0%
+asking you to do that's why you have to
+ 
+
+ align:start position:0%
+asking you to do that's why you have to
+print it in order uh otherwise you
+
+ align:start position:0%
+print it in order uh otherwise you
+ 
+
+ align:start position:0%
+print it in order uh otherwise you
+wouldn't have to worry about printing in
+
+ align:start position:0%
+wouldn't have to worry about printing in
+ 
+
+ align:start position:0%
+wouldn't have to worry about printing in
+order it's just because I'm asking you
+
+ align:start position:0%
+order it's just because I'm asking you
+ 
+
+ align:start position:0%
+order it's just because I'm asking you
+to um okay so I think we're at a time
+
+ align:start position:0%
+to um okay so I think we're at a time
+ 
+
+ align:start position:0%
+to um okay so I think we're at a time
+let's um let us move back into um our
+
+ align:start position:0%
+let's um let us move back into um our
+ 
+
+ align:start position:0%
+let's um let us move back into um our
+our material um um okay second half
+
+ align:start position:0%
+our material um um okay second half
+ 
+
+ align:start position:0%
+our material um um okay second half
+Church Turing
+
+ align:start position:0%
+Church Turing
+ 
+
+ align:start position:0%
+Church Turing
+thesis um so Church uh this is going
+
+ align:start position:0%
+thesis um so Church uh this is going
+ 
+
+ align:start position:0%
+thesis um so Church uh this is going
+back into the bit of the history of the
+
+ align:start position:0%
+back into the bit of the history of the
+ 
+
+ align:start position:0%
+back into the bit of the history of the
+subject back to the 1930s
+
+ align:start position:0%
+subject back to the 1930s
+ 
+
+ align:start position:0%
+subject back to the 1930s
+um back then people were uh interested
+
+ align:start position:0%
+um back then people were uh interested
+ 
+
+ align:start position:0%
+um back then people were uh interested
+in formulating the notion of what do we
+
+ align:start position:0%
+in formulating the notion of what do we
+ 
+
+ align:start position:0%
+in formulating the notion of what do we
+mean by algorithm they didn't even call
+
+ align:start position:0%
+mean by algorithm they didn't even call
+ 
+
+ align:start position:0%
+mean by algorithm they didn't even call
+it algorithm um and those they call it
+
+ align:start position:0%
+it algorithm um and those they call it
+ 
+
+ align:start position:0%
+it algorithm um and those they call it
+some people call it procedure some
+
+ align:start position:0%
+some people call it procedure some
+ 
+
+ align:start position:0%
+some people call it procedure some
+people call it effective procedure um
+
+ align:start position:0%
+people call it effective procedure um
+ 
+
+ align:start position:0%
+people call it effective procedure um
+some people call it um uh effective
+
+ align:start position:0%
+some people call it um uh effective
+ 
+
+ align:start position:0%
+some people call it um uh effective
+calculation um but you know people had
+
+ align:start position:0%
+calculation um but you know people had
+ 
+
+ align:start position:0%
+calculation um but you know people had
+in their minds mathematicians have been
+
+ align:start position:0%
+in their minds mathematicians have been
+ 
+
+ align:start position:0%
+in their minds mathematicians have been
+dealing for centuries thousands of years
+
+ align:start position:0%
+dealing for centuries thousands of years
+ 
+
+ align:start position:0%
+dealing for centuries thousands of years
+with procedures for doing things that's
+
+ align:start position:0%
+with procedures for doing things that's
+ 
+
+ align:start position:0%
+with procedures for doing things that's
+a very natural thing and mathematical
+
+ align:start position:0%
+a very natural thing and mathematical
+ 
+
+ align:start position:0%
+a very natural thing and mathematical
+logicians in particular church and
+
+ align:start position:0%
+logicians in particular church and
+ 
+
+ align:start position:0%
+logicians in particular church and
+Turing uh Turing is somebody you surely
+
+ align:start position:0%
+Turing uh Turing is somebody you surely
+ 
+
+ align:start position:0%
+Turing uh Turing is somebody you surely
+obviously have heard of church maybe not
+
+ align:start position:0%
+obviously have heard of church maybe not
+ 
+
+ align:start position:0%
+obviously have heard of church maybe not
+um uh church was touring's thesis
+
+ align:start position:0%
+um uh church was touring's thesis
+ 
+
+ align:start position:0%
+um uh church was touring's thesis
+advisor in fact um and they both were
+
+ align:start position:0%
+advisor in fact um and they both were
+ 
+
+ align:start position:0%
+advisor in fact um and they both were
+coming out of the uh mathematical logic
+
+ align:start position:0%
+coming out of the uh mathematical logic
+ 
+
+ align:start position:0%
+coming out of the uh mathematical logic
+field of mathematics and uh using trying
+
+ align:start position:0%
+field of mathematics and uh using trying
+ 
+
+ align:start position:0%
+field of mathematics and uh using trying
+to use mathematical logic to formalize
+
+ align:start position:0%
+to use mathematical logic to formalize
+ 
+
+ align:start position:0%
+to use mathematical logic to formalize
+this intuitive notion of what we have
+
+ align:start position:0%
+this intuitive notion of what we have
+ 
+
+ align:start position:0%
+this intuitive notion of what we have
+had for for centuries about what a what
+
+ align:start position:0%
+had for for centuries about what a what
+ 
+
+ align:start position:0%
+had for for centuries about what a what
+a procedure is what is it what what is
+
+ align:start position:0%
+a procedure is what is it what what is
+ 
+
+ align:start position:0%
+a procedure is what is it what what is
+what is an algorithm
+
+ align:start position:0%
+what is an algorithm
+ 
+
+ align:start position:0%
+what is an algorithm
+U and um back in those days you know
+
+ align:start position:0%
+U and um back in those days you know
+ 
+
+ align:start position:0%
+U and um back in those days you know
+they came up with different ways of of
+
+ align:start position:0%
+they came up with different ways of of
+ 
+
+ align:start position:0%
+they came up with different ways of of
+formalizing it um uh so you know here we
+
+ align:start position:0%
+formalizing it um uh so you know here we
+ 
+
+ align:start position:0%
+formalizing it um uh so you know here we
+had this notion of algorithm which is
+
+ align:start position:0%
+had this notion of algorithm which is
+ 
+
+ align:start position:0%
+had this notion of algorithm which is
+kind of intuitive concept
+
+ align:start position:0%
+kind of intuitive concept
+ 
+
+ align:start position:0%
+kind of intuitive concept
+touring proposed touring machine as a
+
+ align:start position:0%
+touring proposed touring machine as a
+ 
+
+ align:start position:0%
+touring proposed touring machine as a
+way of capturing that in a formal way
+
+ align:start position:0%
+way of capturing that in a formal way
+ 
+
+ align:start position:0%
+way of capturing that in a formal way
+for mathematically precise way other
+
+ align:start position:0%
+for mathematically precise way other
+ 
+
+ align:start position:0%
+for mathematically precise way other
+people came up with other ways of doing
+
+ align:start position:0%
+people came up with other ways of doing
+ 
+
+ align:start position:0%
+people came up with other ways of doing
+it
+
+ align:start position:0%
+it
+ 
+
+ align:start position:0%
+it
+um and back then it wasn't obvious that
+
+ align:start position:0%
+um and back then it wasn't obvious that
+ 
+
+ align:start position:0%
+um and back then it wasn't obvious that
+all of those different formulations
+
+ align:start position:0%
+all of those different formulations
+ 
+
+ align:start position:0%
+all of those different formulations
+would end up giving you equivalent
+
+ align:start position:0%
+would end up giving you equivalent
+ 
+
+ align:start position:0%
+would end up giving you equivalent
+Concepts equivalent Notions um and in
+
+ align:start position:0%
+Concepts equivalent Notions um and in
+ 
+
+ align:start position:0%
+Concepts equivalent Notions um and in
+fact they proved in Fairly elaborate
+
+ align:start position:0%
+fact they proved in Fairly elaborate
+ 
+
+ align:start position:0%
+fact they proved in Fairly elaborate
+detail that the different methods that
+
+ align:start position:0%
+detail that the different methods that
+ 
+
+ align:start position:0%
+detail that the different methods that
+people came up with it was the Lambda
+
+ align:start position:0%
+people came up with it was the Lambda
+ 
+
+ align:start position:0%
+people came up with it was the Lambda
+calculus there was rewriting systems
+
+ align:start position:0%
+calculus there was rewriting systems
+ 
+
+ align:start position:0%
+calculus there was rewriting systems
+there were several methods that were
+
+ align:start position:0%
+there were several methods that were
+ 
+
+ align:start position:0%
+there were several methods that were
+proposed for formalizing this notion and
+
+ align:start position:0%
+proposed for formalizing this notion and
+ 
+
+ align:start position:0%
+proposed for formalizing this notion and
+they all turned out to be equivalent to
+
+ align:start position:0%
+they all turned out to be equivalent to
+ 
+
+ align:start position:0%
+they all turned out to be equivalent to
+one another um in today that seems kind
+
+ align:start position:0%
+one another um in today that seems kind
+ 
+
+ align:start position:0%
+one another um in today that seems kind
+of obvious even though I went through
+
+ align:start position:0%
+of obvious even though I went through
+ 
+
+ align:start position:0%
+of obvious even though I went through
+some effort to prove that uh just to
+
+ align:start position:0%
+some effort to prove that uh just to
+ 
+
+ align:start position:0%
+some effort to prove that uh just to
+give you a feeling for how those things
+
+ align:start position:0%
+give you a feeling for how those things
+ 
+
+ align:start position:0%
+give you a feeling for how those things
+uh go you know that you know if you have
+
+ align:start position:0%
+uh go you know that you know if you have
+ 
+
+ align:start position:0%
+uh go you know that you know if you have
+programs if you have Pascal and Java say
+
+ align:start position:0%
+programs if you have Pascal and Java say
+ 
+
+ align:start position:0%
+programs if you have Pascal and Java say
+and thinking about what you can do
+
+ align:start position:0%
+and thinking about what you can do
+ 
+
+ align:start position:0%
+and thinking about what you can do
+mathematically in in those I'm not
+
+ align:start position:0%
+mathematically in in those I'm not
+ 
+
+ align:start position:0%
+mathematically in in those I'm not
+talking about their ability to inter
+
+ align:start position:0%
+talking about their ability to inter
+ 
+
+ align:start position:0%
+talking about their ability to inter
+face with you know windows and so on but
+
+ align:start position:0%
+face with you know windows and so on but
+ 
+
+ align:start position:0%
+face with you know windows and so on but
+just the mathematical
+
+ align:start position:0%
+just the mathematical
+ 
+
+ align:start position:0%
+just the mathematical
+capabilities the capability of doing
+
+ align:start position:0%
+capabilities the capability of doing
+ 
+
+ align:start position:0%
+capabilities the capability of doing
+mathematical calculations or functions
+
+ align:start position:0%
+mathematical calculations or functions
+ 
+
+ align:start position:0%
+mathematical calculations or functions
+with a a pascal program or a Java
+
+ align:start position:0%
+with a a pascal program or a Java
+ 
+
+ align:start position:0%
+with a a pascal program or a Java
+program you know it would be absurd to
+
+ align:start position:0%
+program you know it would be absurd to
+ 
+
+ align:start position:0%
+program you know it would be absurd to
+think there's some program that you can
+
+ align:start position:0%
+think there's some program that you can
+ 
+
+ align:start position:0%
+think there's some program that you can
+write in Java that you can't write in
+
+ align:start position:0%
+write in Java that you can't write in
+ 
+
+ align:start position:0%
+write in Java that you can't write in
+Pascal um or python
+
+ align:start position:0%
+Pascal um or python
+ 
+
+ align:start position:0%
+Pascal um or python
+uh uh and the reason is we know you can
+
+ align:start position:0%
+uh uh and the reason is we know you can
+ 
+
+ align:start position:0%
+uh uh and the reason is we know you can
+compile python into Java and you can
+
+ align:start position:0%
+compile python into Java and you can
+ 
+
+ align:start position:0%
+compile python into Java and you can
+compile Java back into python that tells
+
+ align:start position:0%
+compile Java back into python that tells
+ 
+
+ align:start position:0%
+compile Java back into python that tells
+you that the two systems of two
+
+ align:start position:0%
+you that the two systems of two
+ 
+
+ align:start position:0%
+you that the two systems of two
+programming languages are equivalent in
+
+ align:start position:0%
+programming languages are equivalent in
+ 
+
+ align:start position:0%
+programming languages are equivalent in
+power um that wasn't obvious that from
+
+ align:start position:0%
+power um that wasn't obvious that from
+ 
+
+ align:start position:0%
+power um that wasn't obvious that from
+the get-go to these folks so they um
+
+ align:start position:0%
+the get-go to these folks so they um
+ 
+
+ align:start position:0%
+the get-go to these folks so they um
+observed that uh all of the different
+
+ align:start position:0%
+observed that uh all of the different
+ 
+
+ align:start position:0%
+observed that uh all of the different
+efforts they came at formalizing
+
+ align:start position:0%
+efforts they came at formalizing
+ 
+
+ align:start position:0%
+efforts they came at formalizing
+algorithm all were equivalent to one
+
+ align:start position:0%
+algorithm all were equivalent to one
+ 
+
+ align:start position:0%
+algorithm all were equivalent to one
+another that was that that was a kind of
+
+ align:start position:0%
+another that was that that was a kind of
+ 
+
+ align:start position:0%
+another that was that that was a kind of
+a breakthrough moment when they realized
+
+ align:start position:0%
+a breakthrough moment when they realized
+ 
+
+ align:start position:0%
+a breakthrough moment when they realized
+that they're all that not all the ways
+
+ align:start position:0%
+that they're all that not all the ways
+ 
+
+ align:start position:0%
+that they're all that not all the ways
+that they've come up with and once they
+
+ align:start position:0%
+that they've come up with and once they
+ 
+
+ align:start position:0%
+that they've come up with and once they
+got the idea they realize all reasonable
+
+ align:start position:0%
+got the idea they realize all reasonable
+ 
+
+ align:start position:0%
+got the idea they realize all reasonable
+ways of doing it are always going to be
+
+ align:start position:0%
+ways of doing it are always going to be
+ 
+
+ align:start position:0%
+ways of doing it are always going to be
+equivalent um and so that suggested that
+
+ align:start position:0%
+equivalent um and so that suggested that
+ 
+
+ align:start position:0%
+equivalent um and so that suggested that
+they've really captured this notion of
+
+ align:start position:0%
+they've really captured this notion of
+ 
+
+ align:start position:0%
+they've really captured this notion of
+algorithm by any one of those methods
+
+ align:start position:0%
+algorithm by any one of those methods
+ 
+
+ align:start position:0%
+algorithm by any one of those methods
+say a touring machine and that's what
+
+ align:start position:0%
+say a touring machine and that's what
+ 
+
+ align:start position:0%
+say a touring machine and that's what
+they took you can't prove that because
+
+ align:start position:0%
+they took you can't prove that because
+ 
+
+ align:start position:0%
+they took you can't prove that because
+algorithms are an intuitive notion but
+
+ align:start position:0%
+algorithms are an intuitive notion but
+ 
+
+ align:start position:0%
+algorithms are an intuitive notion but
+the fact that we're able to capture that
+
+ align:start position:0%
+the fact that we're able to capture that
+ 
+
+ align:start position:0%
+the fact that we're able to capture that
+in a formal way that's what we call
+
+ align:start position:0%
+in a formal way that's what we call
+ 
+
+ align:start position:0%
+in a formal way that's what we call
+today the church touring
+
+ align:start position:0%
+today the church touring
+ 
+
+ align:start position:0%
+today the church touring
+thesis okay um so um that is uh um so
+
+ align:start position:0%
+thesis okay um so um that is uh um so
+ 
+
+ align:start position:0%
+thesis okay um so um that is uh um so
+any of these methods um uh capture the
+
+ align:start position:0%
+any of these methods um uh capture the
+ 
+
+ align:start position:0%
+any of these methods um uh capture the
+notion of algorithm as we
+
+ align:start position:0%
+notion of algorithm as we
+ 
+
+ align:start position:0%
+notion of algorithm as we
+described and that has had a big impact
+
+ align:start position:0%
+described and that has had a big impact
+ 
+
+ align:start position:0%
+described and that has had a big impact
+on mathematics uh so now I just want
+
+ align:start position:0%
+on mathematics uh so now I just want
+ 
+
+ align:start position:0%
+on mathematics uh so now I just want
+to just give me one second
+
+ align:start position:0%
+to just give me one second
+ 
+
+ align:start position:0%
+to just give me one second
+here all right here's a checkin on this
+
+ align:start position:0%
+here all right here's a checkin on this
+ 
+
+ align:start position:0%
+here all right here's a checkin on this
+one um so you know Alan Turing so here
+
+ align:start position:0%
+one um so you know Alan Turing so here
+ 
+
+ align:start position:0%
+one um so you know Alan Turing so here
+are some facts which may or may not be
+
+ align:start position:0%
+are some facts which may or may not be
+ 
+
+ align:start position:0%
+are some facts which may or may not be
+true about Allen tur um so uh now you
+
+ align:start position:0%
+true about Allen tur um so uh now you
+ 
+
+ align:start position:0%
+true about Allen tur um so uh now you
+get to pick all of the ones that apply
+
+ align:start position:0%
+get to pick all of the ones that apply
+ 
+
+ align:start position:0%
+get to pick all of the ones that apply
+um based on your knowledge obviously
+
+ align:start position:0%
+um based on your knowledge obviously
+ 
+
+ align:start position:0%
+um based on your knowledge obviously
+this is
+
+ align:start position:0%
+this is
+ 
+
+ align:start position:0%
+this is
+not uh something this is more for fun
+
+ align:start position:0%
+not uh something this is more for fun
+ 
+
+ align:start position:0%
+not uh something this is more for fun
+but um or historical interest um but
+
+ align:start position:0%
+but um or historical interest um but
+ 
+
+ align:start position:0%
+but um or historical interest um but
+here is uh let's launch that poll see
+
+ align:start position:0%
+here is uh let's launch that poll see
+ 
+
+ align:start position:0%
+here is uh let's launch that poll see
+what how much you know about uh Mr
+
+ align:start position:0%
+what how much you know about uh Mr
+ 
+
+ align:start position:0%
+what how much you know about uh Mr
+Turing
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um check all that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+apply okay almost done please
+
+ align:start position:0%
+apply okay almost done please
+ 
+
+ align:start position:0%
+apply okay almost done please
+please let's wrap it up I think that's
+
+ align:start position:0%
+please let's wrap it up I think that's
+ 
+
+ align:start position:0%
+please let's wrap it up I think that's
+everybody okay two seconds please get
+
+ align:start position:0%
+everybody okay two seconds please get
+ 
+
+ align:start position:0%
+everybody okay two seconds please get
+credit for doing this and polling in
+
+ align:start position:0%
+credit for doing this and polling in
+ 
+
+ align:start position:0%
+credit for doing this and polling in
+fact it's kind of interesting here
+
+ align:start position:0%
+fact it's kind of interesting here
+ 
+
+ align:start position:0%
+fact it's kind of interesting here
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+[Music]
+
+ align:start position:0%
+[Music]
+ 
+
+ align:start position:0%
+[Music]
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+uh you all do know that he was a code
+
+ align:start position:0%
+uh you all do know that he was a code
+ 
+
+ align:start position:0%
+uh you all do know that he was a code
+breaker uh he was a um worked uh in fact
+
+ align:start position:0%
+breaker uh he was a um worked uh in fact
+ 
+
+ align:start position:0%
+breaker uh he was a um worked uh in fact
+did was part of a team I think led the
+
+ align:start position:0%
+did was part of a team I think led the
+ 
+
+ align:start position:0%
+did was part of a team I think led the
+team which broke the the German code um
+
+ align:start position:0%
+team which broke the the German code um
+ 
+
+ align:start position:0%
+team which broke the the German code um
+during World War II you know the Turing
+
+ align:start position:0%
+during World War II you know the Turing
+ 
+
+ align:start position:0%
+during World War II you know the Turing
+test is a famous uh thing for how do you
+
+ align:start position:0%
+test is a famous uh thing for how do you
+ 
+
+ align:start position:0%
+test is a famous uh thing for how do you
+characterize when you have an
+
+ align:start position:0%
+characterize when you have an
+ 
+
+ align:start position:0%
+characterize when you have an
+intelligent machine um so he definitely
+
+ align:start position:0%
+intelligent machine um so he definitely
+ 
+
+ align:start position:0%
+intelligent machine um so he definitely
+worked in AI he worked in biology as
+
+ align:start position:0%
+worked in AI he worked in biology as
+ 
+
+ align:start position:0%
+worked in AI he worked in biology as
+well um he has a paper that less well
+
+ align:start position:0%
+well um he has a paper that less well
+ 
+
+ align:start position:0%
+well um he has a paper that less well
+known to computer scientists but if you
+
+ align:start position:0%
+known to computer scientists but if you
+ 
+
+ align:start position:0%
+known to computer scientists but if you
+look him up um on Wikipedia where I get
+
+ align:start position:0%
+look him up um on Wikipedia where I get
+ 
+
+ align:start position:0%
+look him up um on Wikipedia where I get
+all my information
+
+ align:start position:0%
+all my information
+ 
+
+ align:start position:0%
+all my information
+uh he actually and I knew this anyway uh
+
+ align:start position:0%
+uh he actually and I knew this anyway uh
+ 
+
+ align:start position:0%
+uh he actually and I knew this anyway uh
+he has a very famous paper an
+
+ align:start position:0%
+he has a very famous paper an
+ 
+
+ align:start position:0%
+he has a very famous paper an
+influential paper on how
+
+ align:start position:0%
+influential paper on how
+ 
+
+ align:start position:0%
+influential paper on how
+um for example spots arise on um on
+
+ align:start position:0%
+um for example spots arise on um on
+ 
+
+ align:start position:0%
+um for example spots arise on um on
+tiger on on leopards and stripes on
+
+ align:start position:0%
+tiger on on leopards and stripes on
+ 
+
+ align:start position:0%
+tiger on on leopards and stripes on
+tigers and so on um gave a kind of
+
+ align:start position:0%
+tigers and so on um gave a kind of
+ 
+
+ align:start position:0%
+tigers and so on um gave a kind of
+mathematical model for that which
+
+ align:start position:0%
+mathematical model for that which
+ 
+
+ align:start position:0%
+mathematical model for that which
+actually proves actually is uh quite
+
+ align:start position:0%
+actually proves actually is uh quite
+ 
+
+ align:start position:0%
+actually proves actually is uh quite
+does capture things in an accurate way
+
+ align:start position:0%
+does capture things in an accurate way
+ 
+
+ align:start position:0%
+does capture things in an accurate way
+uh as as was shown subsequent to that uh
+
+ align:start position:0%
+uh as as was shown subsequent to that uh
+ 
+
+ align:start position:0%
+uh as as was shown subsequent to that uh
+was imprisoned for being gay in fact as
+
+ align:start position:0%
+was imprisoned for being gay in fact as
+ 
+
+ align:start position:0%
+was imprisoned for being gay in fact as
+far as I know from his history he was
+
+ align:start position:0%
+far as I know from his history he was
+ 
+
+ align:start position:0%
+far as I know from his history he was
+not imprisoned for being gay um he was
+
+ align:start position:0%
+not imprisoned for being gay um he was
+ 
+
+ align:start position:0%
+not imprisoned for being gay um he was
+convicted of being gay um and was given
+
+ align:start position:0%
+convicted of being gay um and was given
+ 
+
+ align:start position:0%
+convicted of being gay um and was given
+a choice to go to prison or to take
+
+ align:start position:0%
+a choice to go to prison or to take
+ 
+
+ align:start position:0%
+a choice to go to prison or to take
+chemicals to
+
+ align:start position:0%
+chemicals to
+ 
+
+ align:start position:0%
+chemicals to
+cure him from being gay and he opted not
+
+ align:start position:0%
+cure him from being gay and he opted not
+ 
+
+ align:start position:0%
+cure him from being gay and he opted not
+to go to prison and take the
+
+ align:start position:0%
+to go to prison and take the
+ 
+
+ align:start position:0%
+to go to prison and take the
+chemicals uh and sadly he committed
+
+ align:start position:0%
+chemicals uh and sadly he committed
+ 
+
+ align:start position:0%
+chemicals uh and sadly he committed
+suicide um two years after that so um he
+
+ align:start position:0%
+suicide um two years after that so um he
+ 
+
+ align:start position:0%
+suicide um two years after that so um he
+was
+
+ align:start position:0%
+was
+ 
+
+ align:start position:0%
+was
+um treated very treated very badly by uh
+
+ align:start position:0%
+um treated very treated very badly by uh
+ 
+
+ align:start position:0%
+um treated very treated very badly by uh
+the British society and British
+
+ align:start position:0%
+the British society and British
+ 
+
+ align:start position:0%
+the British society and British
+government uh despite having the great
+
+ align:start position:0%
+government uh despite having the great
+ 
+
+ align:start position:0%
+government uh despite having the great
+work that he had done um
+
+ align:start position:0%
+work that he had done um
+ 
+
+ align:start position:0%
+work that he had done um
+and um you might think that he has been
+
+ align:start position:0%
+and um you might think that he has been
+ 
+
+ align:start position:0%
+and um you might think that he has been
+honored by appearing on a British bank
+
+ align:start position:0%
+honored by appearing on a British bank
+ 
+
+ align:start position:0%
+honored by appearing on a British bank
+note that's also not true um uh but the
+
+ align:start position:0%
+note that's also not true um uh but the
+ 
+
+ align:start position:0%
+note that's also not true um uh but the
+good news is he's not uh currently on a
+
+ align:start position:0%
+good news is he's not uh currently on a
+ 
+
+ align:start position:0%
+good news is he's not uh currently on a
+British bank note but he's going to be
+
+ align:start position:0%
+British bank note but he's going to be
+ 
+
+ align:start position:0%
+British bank note but he's going to be
+on a British bank note starting next
+
+ align:start position:0%
+on a British bank note starting next
+ 
+
+ align:start position:0%
+on a British bank note starting next
+year um so that is uh um so that's uh
+
+ align:start position:0%
+year um so that is uh um so that's uh
+ 
+
+ align:start position:0%
+year um so that is uh um so that's uh
+you know along with um Winston Churchill
+
+ align:start position:0%
+you know along with um Winston Churchill
+ 
+
+ align:start position:0%
+you know along with um Winston Churchill
+and a number of other notable Brits he's
+
+ align:start position:0%
+and a number of other notable Brits he's
+ 
+
+ align:start position:0%
+and a number of other notable Brits he's
+going to be on the the 50 pound b Bank
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay um so let us continue
+
+ align:start position:0%
+okay um so let us continue
+ 
+
+ align:start position:0%
+okay um so let us continue
+um so as I mentioned uh the church
+
+ align:start position:0%
+um so as I mentioned uh the church
+ 
+
+ align:start position:0%
+um so as I mentioned uh the church
+string thesis is important for
+
+ align:start position:0%
+string thesis is important for
+ 
+
+ align:start position:0%
+string thesis is important for
+mathematics um and it has to do with
+
+ align:start position:0%
+mathematics um and it has to do with
+ 
+
+ align:start position:0%
+mathematics um and it has to do with
+these Hilbert problems I don't know how
+
+ align:start position:0%
+these Hilbert problems I don't know how
+ 
+
+ align:start position:0%
+these Hilbert problems I don't know how
+many of you have encountered that David
+
+ align:start position:0%
+many of you have encountered that David
+ 
+
+ align:start position:0%
+many of you have encountered that David
+Hilbert was widely considered to be the
+
+ align:start position:0%
+Hilbert was widely considered to be the
+ 
+
+ align:start position:0%
+Hilbert was widely considered to be the
+perhaps the greatest mathematician of
+
+ align:start position:0%
+perhaps the greatest mathematician of
+ 
+
+ align:start position:0%
+perhaps the greatest mathematician of
+his day um and um you know every four
+
+ align:start position:0%
+his day um and um you know every four
+ 
+
+ align:start position:0%
+his day um and um you know every four
+years mathematicians get together for an
+
+ align:start position:0%
+years mathematicians get together for an
+ 
+
+ align:start position:0%
+years mathematicians get together for an
+international Congress called the
+
+ align:start position:0%
+international Congress called the
+ 
+
+ align:start position:0%
+international Congress called the
+international Congress of mathematicians
+
+ align:start position:0%
+international Congress of mathematicians
+ 
+
+ align:start position:0%
+international Congress of mathematicians
+it was you know even that's been going
+
+ align:start position:0%
+it was you know even that's been going
+ 
+
+ align:start position:0%
+it was you know even that's been going
+on for over a hundred years and he was
+
+ align:start position:0%
+on for over a hundred years and he was
+ 
+
+ align:start position:0%
+on for over a hundred years and he was
+invited to the
+
+ align:start position:0%
+invited to the
+ 
+
+ align:start position:0%
+invited to the
+1900 uh meeting to give a talk about
+
+ align:start position:0%
+1900 uh meeting to give a talk about
+ 
+
+ align:start position:0%
+1900 uh meeting to give a talk about
+anything he wanted and what he decided
+
+ align:start position:0%
+anything he wanted and what he decided
+ 
+
+ align:start position:0%
+anything he wanted and what he decided
+to do in during that presentation is
+
+ align:start position:0%
+to do in during that presentation is
+ 
+
+ align:start position:0%
+to do in during that presentation is
+give it is present
+
+ align:start position:0%
+give it is present
+ 
+
+ align:start position:0%
+give it is present
+23 uh
+
+ align:start position:0%
+23 uh
+ 
+
+ align:start position:0%
+23 uh
+problems that would be a challenge for
+
+ align:start position:0%
+problems that would be a challenge for
+ 
+
+ align:start position:0%
+problems that would be a challenge for
+mathematicians for the coming
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Century um and um uh you know we're
+
+ align:start position:0%
+Century um and um uh you know we're
+ 
+
+ align:start position:0%
+Century um and um uh you know we're
+running a little short on time so I'm
+
+ align:start position:0%
+running a little short on time so I'm
+ 
+
+ align:start position:0%
+running a little short on time so I'm
+not going to go into them some of these
+
+ align:start position:0%
+not going to go into them some of these
+ 
+
+ align:start position:0%
+not going to go into them some of these
+we'll talk about later uh but the 10th
+
+ align:start position:0%
+we'll talk about later uh but the 10th
+ 
+
+ align:start position:0%
+we'll talk about later uh but the 10th
+problem here is about algorithms the
+
+ align:start position:0%
+problem here is about algorithms the
+ 
+
+ align:start position:0%
+problem here is about algorithms the
+10th problem on Hilbert's list of called
+
+ align:start position:0%
+10th problem on Hilbert's list of called
+ 
+
+ align:start position:0%
+10th problem on Hilbert's list of called
+called Hilbert's 10th problem is a
+
+ align:start position:0%
+called Hilbert's 10th problem is a
+ 
+
+ align:start position:0%
+called Hilbert's 10th problem is a
+problem about algorithms and it says
+
+ align:start position:0%
+problem about algorithms and it says
+ 
+
+ align:start position:0%
+problem about algorithms and it says
+give an algorithm for solving what are
+
+ align:start position:0%
+give an algorithm for solving what are
+ 
+
+ align:start position:0%
+give an algorithm for solving what are
+called di Fantine
+
+ align:start position:0%
+called di Fantine
+ 
+
+ align:start position:0%
+called di Fantine
+equations um he didn't call it an
+
+ align:start position:0%
+equations um he didn't call it an
+ 
+
+ align:start position:0%
+equations um he didn't call it an
+algorithm he call it some uh you know
+
+ align:start position:0%
+algorithm he call it some uh you know
+ 
+
+ align:start position:0%
+algorithm he call it some uh you know
+finite procedure or something like that
+
+ align:start position:0%
+finite procedure or something like that
+ 
+
+ align:start position:0%
+finite procedure or something like that
+but you know you what are diophantine
+
+ align:start position:0%
+but you know you what are diophantine
+ 
+
+ align:start position:0%
+but you know you what are diophantine
+equations I'm glad you asked
+
+ align:start position:0%
+equations I'm glad you asked
+ 
+
+ align:start position:0%
+equations I'm glad you asked
+uh Dian equations uh what are they well
+
+ align:start position:0%
+uh Dian equations uh what are they well
+ 
+
+ align:start position:0%
+uh Dian equations uh what are they well
+they're very simple they're just
+
+ align:start position:0%
+they're very simple they're just
+ 
+
+ align:start position:0%
+they're very simple they're just
+polinomial equations like you know does
+
+ align:start position:0%
+polinomial equations like you know does
+ 
+
+ align:start position:0%
+polinomial equations like you know does
+this polinomial equal some constant for
+
+ align:start position:0%
+this polinomial equal some constant for
+ 
+
+ align:start position:0%
+this polinomial equal some constant for
+example um but where you're looking for
+
+ align:start position:0%
+example um but where you're looking for
+ 
+
+ align:start position:0%
+example um but where you're looking for
+the solutions you know the polinomial
+
+ align:start position:0%
+the solutions you know the polinomial
+ 
+
+ align:start position:0%
+the solutions you know the polinomial
+are variables you're looking for the
+
+ align:start position:0%
+are variables you're looking for the
+ 
+
+ align:start position:0%
+are variables you're looking for the
+solutions but you're only allowing the
+
+ align:start position:0%
+solutions but you're only allowing the
+ 
+
+ align:start position:0%
+solutions but you're only allowing the
+solutions to be
+
+ align:start position:0%
+solutions to be
+ 
+
+ align:start position:0%
+solutions to be
+integers so here's an example um so I
+
+ align:start position:0%
+integers so here's an example um so I
+ 
+
+ align:start position:0%
+integers so here's an example um so I
+give you this polinomial um here I'm
+
+ align:start position:0%
+give you this polinomial um here I'm
+ 
+
+ align:start position:0%
+give you this polinomial um here I'm
+setting it equal to seven and I want to
+
+ align:start position:0%
+setting it equal to seven and I want to
+ 
+
+ align:start position:0%
+setting it equal to seven and I want to
+solve that equation
+
+ align:start position:0%
+solve that equation
+ 
+
+ align:start position:0%
+solve that equation
+so it has these three variables X Y and
+
+ align:start position:0%
+so it has these three variables X Y and
+ 
+
+ align:start position:0%
+so it has these three variables X Y and
+Z so you have to find a solution there
+
+ align:start position:0%
+Z so you have to find a solution there
+ 
+
+ align:start position:0%
+Z so you have to find a solution there
+but I'm only going to allow you to have
+
+ align:start position:0%
+but I'm only going to allow you to have
+ 
+
+ align:start position:0%
+but I'm only going to allow you to have
+plugin Z integers and in fact there is a
+
+ align:start position:0%
+plugin Z integers and in fact there is a
+ 
+
+ align:start position:0%
+plugin Z integers and in fact there is a
+solution in integers one two and minus
+
+ align:start position:0%
+solution in integers one two and minus
+ 
+
+ align:start position:0%
+solution in integers one two and minus
+two if you plug it in you'll see it
+
+ align:start position:0%
+two if you plug it in you'll see it
+ 
+
+ align:start position:0%
+two if you plug it in you'll see it
+works all right um now the general
+
+ align:start position:0%
+works all right um now the general
+ 
+
+ align:start position:0%
+works all right um now the general
+problem that Hilbert was addressing is
+
+ align:start position:0%
+problem that Hilbert was addressing is
+ 
+
+ align:start position:0%
+problem that Hilbert was addressing is
+suppose I give you a
+
+ align:start position:0%
+suppose I give you a
+ 
+
+ align:start position:0%
+suppose I give you a
+polinomial um let's say it set it it set
+
+ align:start position:0%
+polinomial um let's say it set it it set
+ 
+
+ align:start position:0%
+polinomial um let's say it set it it set
+to zero so we're looking for roots of
+
+ align:start position:0%
+to zero so we're looking for roots of
+ 
+
+ align:start position:0%
+to zero so we're looking for roots of
+the polinomial but just some polinomial
+
+ align:start position:0%
+the polinomial but just some polinomial
+ 
+
+ align:start position:0%
+the polinomial but just some polinomial
+equation you can always put it in this
+
+ align:start position:0%
+equation you can always put it in this
+ 
+
+ align:start position:0%
+equation you can always put it in this
+form and I want to know uh does it have
+
+ align:start position:0%
+form and I want to know uh does it have
+ 
+
+ align:start position:0%
+form and I want to know uh does it have
+a solution in
+
+ align:start position:0%
+a solution in
+ 
+
+ align:start position:0%
+a solution in
+integers um and what I want what I'm
+
+ align:start position:0%
+integers um and what I want what I'm
+ 
+
+ align:start position:0%
+integers um and what I want what I'm
+looking for is a procedure which will
+
+ align:start position:0%
+looking for is a procedure which will
+ 
+
+ align:start position:0%
+looking for is a procedure which will
+tell me yes or no I want to know um give
+
+ align:start position:0%
+tell me yes or no I want to know um give
+ 
+
+ align:start position:0%
+tell me yes or no I want to know um give
+an algorithm to answer that question for
+
+ align:start position:0%
+an algorithm to answer that question for
+ 
+
+ align:start position:0%
+an algorithm to answer that question for
+a given polinomial or the or using the
+
+ align:start position:0%
+a given polinomial or the or using the
+ 
+
+ align:start position:0%
+a given polinomial or the or using the
+language of this course defining this in
+
+ align:start position:0%
+language of this course defining this in
+ 
+
+ align:start position:0%
+language of this course defining this in
+terms of a
+
+ align:start position:0%
+terms of a
+ 
+
+ align:start position:0%
+terms of a
+language uh decide this language give a
+
+ align:start position:0%
+language uh decide this language give a
+ 
+
+ align:start position:0%
+language uh decide this language give a
+give a turing machine which will decide
+
+ align:start position:0%
+give a turing machine which will decide
+ 
+
+ align:start position:0%
+give a turing machine which will decide
+yes or no for any given polinomial yes
+
+ align:start position:0%
+yes or no for any given polinomial yes
+ 
+
+ align:start position:0%
+yes or no for any given polinomial yes
+there is a solution in integers no there
+
+ align:start position:0%
+there is a solution in integers no there
+ 
+
+ align:start position:0%
+there is a solution in integers no there
+is no solution in
+
+ align:start position:0%
+is no solution in
+ 
+
+ align:start position:0%
+is no solution in
+okay and um uh that is a um uh um uh
+
+ align:start position:0%
+okay and um uh that is a um uh um uh
+ 
+
+ align:start position:0%
+okay and um uh that is a um uh um uh
+that that was what um Hilbert asked in
+
+ align:start position:0%
+that that was what um Hilbert asked in
+ 
+
+ align:start position:0%
+that that was what um Hilbert asked in
+his 10th problem given algorithm now as
+
+ align:start position:0%
+his 10th problem given algorithm now as
+ 
+
+ align:start position:0%
+his 10th problem given algorithm now as
+we know now took um 70 years to get the
+
+ align:start position:0%
+we know now took um 70 years to get the
+ 
+
+ align:start position:0%
+we know now took um 70 years to get the
+answer that um uh that there is no such
+
+ align:start position:0%
+answer that um uh that there is no such
+ 
+
+ align:start position:0%
+answer that um uh that there is no such
+algorithm it's an undecidable problem
+
+ align:start position:0%
+algorithm it's an undecidable problem
+ 
+
+ align:start position:0%
+algorithm it's an undecidable problem
+and we'll talk about that a little bit
+
+ align:start position:0%
+and we'll talk about that a little bit
+ 
+
+ align:start position:0%
+and we'll talk about that a little bit
+later in the term but um there is D is
+
+ align:start position:0%
+later in the term but um there is D is
+ 
+
+ align:start position:0%
+later in the term but um there is D is
+not a decidable
+
+ align:start position:0%
+not a decidable
+ 
+
+ align:start position:0%
+not a decidable
+language now um there was no hope of
+
+ align:start position:0%
+language now um there was no hope of
+ 
+
+ align:start position:0%
+language now um there was no hope of
+coming up with that answer in 1900 or
+
+ align:start position:0%
+coming up with that answer in 1900 or
+ 
+
+ align:start position:0%
+coming up with that answer in 1900 or
+even in
+
+ align:start position:0%
+even in
+ 
+
+ align:start position:0%
+even in
+1910 because we didn't have a formal
+
+ align:start position:0%
+1910 because we didn't have a formal
+ 
+
+ align:start position:0%
+1910 because we didn't have a formal
+idea of what an algorithm is that had to
+
+ align:start position:0%
+idea of what an algorithm is that had to
+ 
+
+ align:start position:0%
+idea of what an algorithm is that had to
+wait until the church Turing thesis told
+
+ align:start position:0%
+wait until the church Turing thesis told
+ 
+
+ align:start position:0%
+wait until the church Turing thesis told
+us that algorithms really are touring
+
+ align:start position:0%
+us that algorithms really are touring
+ 
+
+ align:start position:0%
+us that algorithms really are touring
+machines that there is a formal way of
+
+ align:start position:0%
+machines that there is a formal way of
+ 
+
+ align:start position:0%
+machines that there is a formal way of
+saying what an algorithm is
+
+ align:start position:0%
+saying what an algorithm is
+ 
+
+ align:start position:0%
+saying what an algorithm is
+and once you had that notion then you
+
+ align:start position:0%
+and once you had that notion then you
+ 
+
+ align:start position:0%
+and once you had that notion then you
+could prove that there is no touring
+
+ align:start position:0%
+could prove that there is no touring
+ 
+
+ align:start position:0%
+could prove that there is no touring
+machine but before that you had only
+
+ align:start position:0%
+machine but before that you had only
+ 
+
+ align:start position:0%
+machine but before that you had only
+this vague notion intuitive notion of
+
+ align:start position:0%
+this vague notion intuitive notion of
+ 
+
+ align:start position:0%
+this vague notion intuitive notion of
+what an algorithm is and so there was no
+
+ align:start position:0%
+what an algorithm is and so there was no
+ 
+
+ align:start position:0%
+what an algorithm is and so there was no
+hope of ever answering that because the
+
+ align:start position:0%
+hope of ever answering that because the
+ 
+
+ align:start position:0%
+hope of ever answering that because the
+in fact the answer is there is no such
+
+ align:start position:0%
+in fact the answer is there is no such
+ 
+
+ align:start position:0%
+in fact the answer is there is no such
+algorithm okay now um I'll give this as
+
+ align:start position:0%
+algorithm okay now um I'll give this as
+ 
+
+ align:start position:0%
+algorithm okay now um I'll give this as
+a little exercise to you we're a little
+
+ align:start position:0%
+a little exercise to you we're a little
+ 
+
+ align:start position:0%
+a little exercise to you we're a little
+bit running short on time but this
+
+ align:start position:0%
+bit running short on time but this
+ 
+
+ align:start position:0%
+bit running short on time but this
+language D is in fact a recognizable
+
+ align:start position:0%
+language D is in fact a recognizable
+ 
+
+ align:start position:0%
+language D is in fact a recognizable
+language so I would suggest you think
+
+ align:start position:0%
+language so I would suggest you think
+ 
+
+ align:start position:0%
+language so I would suggest you think
+about that offline um but basically you
+
+ align:start position:0%
+about that offline um but basically you
+ 
+
+ align:start position:0%
+about that offline um but basically you
+know you can try plugging in different
+
+ align:start position:0%
+know you can try plugging in different
+ 
+
+ align:start position:0%
+know you can try plugging in different
+values for these variables and if you
+
+ align:start position:0%
+values for these variables and if you
+ 
+
+ align:start position:0%
+values for these variables and if you
+ever find a you know the um that it
+
+ align:start position:0%
+ever find a you know the um that it
+ 
+
+ align:start position:0%
+ever find a you know the um that it
+evaluates a zero then you can accept but
+
+ align:start position:0%
+evaluates a zero then you can accept but
+ 
+
+ align:start position:0%
+evaluates a zero then you can accept but
+otherwise you just have to keep going
+
+ align:start position:0%
+otherwise you just have to keep going
+ 
+
+ align:start position:0%
+otherwise you just have to keep going
+and looking so showing recognizability
+
+ align:start position:0%
+and looking so showing recognizability
+ 
+
+ align:start position:0%
+and looking so showing recognizability
+is very simple but decidability is
+
+ align:start position:0%
+is very simple but decidability is
+ 
+
+ align:start position:0%
+is very simple but decidability is
+false okay now let's talk a little bit
+
+ align:start position:0%
+false okay now let's talk a little bit
+ 
+
+ align:start position:0%
+false okay now let's talk a little bit
+about encodings for touring machines um
+
+ align:start position:0%
+about encodings for touring machines um
+ 
+
+ align:start position:0%
+about encodings for touring machines um
+so uh we're going to be working
+
+ align:start position:0%
+so uh we're going to be working
+ 
+
+ align:start position:0%
+so uh we're going to be working
+encodings and touring machines so we're
+
+ align:start position:0%
+encodings and touring machines so we're
+ 
+
+ align:start position:0%
+encodings and touring machines so we're
+now going to be working with um uh
+
+ align:start position:0%
+now going to be working with um uh
+ 
+
+ align:start position:0%
+now going to be working with um uh
+touring machines going forward um we're
+
+ align:start position:0%
+touring machines going forward um we're
+ 
+
+ align:start position:0%
+touring machines going forward um we're
+going as I you know we're going
+
+ align:start position:0%
+going as I you know we're going
+ 
+
+ align:start position:0%
+going as I you know we're going
+to the input to those touring machines
+
+ align:start position:0%
+to the input to those touring machines
+ 
+
+ align:start position:0%
+to the input to those touring machines
+might be pols Might Be Strings they
+
+ align:start position:0%
+might be pols Might Be Strings they
+ 
+
+ align:start position:0%
+might be pols Might Be Strings they
+might be other things too we might want
+
+ align:start position:0%
+might be other things too we might want
+ 
+
+ align:start position:0%
+might be other things too we might want
+to feed autometer into the tourning
+
+ align:start position:0%
+to feed autometer into the tourning
+ 
+
+ align:start position:0%
+to feed autometer into the tourning
+machines so the touring machine can
+
+ align:start position:0%
+machines so the touring machine can
+ 
+
+ align:start position:0%
+machines so the touring machine can
+answer questions about the autometer
+
+ align:start position:0%
+answer questions about the autometer
+ 
+
+ align:start position:0%
+answer questions about the autometer
+well don't forget touring machines take
+
+ align:start position:0%
+well don't forget touring machines take
+ 
+
+ align:start position:0%
+well don't forget touring machines take
+as their input just strings so we have
+
+ align:start position:0%
+as their input just strings so we have
+ 
+
+ align:start position:0%
+as their input just strings so we have
+to think about how we're going to
+
+ align:start position:0%
+to think about how we're going to
+ 
+
+ align:start position:0%
+to think about how we're going to
+represent something more comp licated
+
+ align:start position:0%
+represent something more comp licated
+ 
+
+ align:start position:0%
+represent something more comp licated
+like an automaton as a string and I'm
+
+ align:start position:0%
+like an automaton as a string and I'm
+ 
+
+ align:start position:0%
+like an automaton as a string and I'm
+not going to get into the details of
+
+ align:start position:0%
+not going to get into the details of
+ 
+
+ align:start position:0%
+not going to get into the details of
+that you could spell it out in detail um
+
+ align:start position:0%
+that you could spell it out in detail um
+ 
+
+ align:start position:0%
+that you could spell it out in detail um
+but I think that's not too interesting
+
+ align:start position:0%
+but I think that's not too interesting
+ 
+
+ align:start position:0%
+but I think that's not too interesting
+to get into that we're just going to
+
+ align:start position:0%
+to get into that we're just going to
+ 
+
+ align:start position:0%
+to get into that we're just going to
+develop a notation that says if you have
+
+ align:start position:0%
+develop a notation that says if you have
+ 
+
+ align:start position:0%
+develop a notation that says if you have
+some object o it could be a polinomial
+
+ align:start position:0%
+some object o it could be a polinomial
+ 
+
+ align:start position:0%
+some object o it could be a polinomial
+it could be an automaton it could be a
+
+ align:start position:0%
+it could be an automaton it could be a
+ 
+
+ align:start position:0%
+it could be an automaton it could be a
+graph it could be whatever you're
+
+ align:start position:0%
+graph it could be whatever you're
+ 
+
+ align:start position:0%
+graph it could be whatever you're
+working with a table um I'm going to
+
+ align:start position:0%
+working with a table um I'm going to
+ 
+
+ align:start position:0%
+working with a table um I'm going to
+write that o in these brackets to mean
+
+ align:start position:0%
+write that o in these brackets to mean
+ 
+
+ align:start position:0%
+write that o in these brackets to mean
+an encoding of that object into a string
+
+ align:start position:0%
+an encoding of that object into a string
+ 
+
+ align:start position:0%
+an encoding of that object into a string
+and then you can feed the string into
+
+ align:start position:0%
+and then you can feed the string into
+ 
+
+ align:start position:0%
+and then you can feed the string into
+the touring
+
+ align:start position:0%
+the touring
+ 
+
+ align:start position:0%
+the touring
+machine okay um uh so that's how we're
+
+ align:start position:0%
+machine okay um uh so that's how we're
+ 
+
+ align:start position:0%
+machine okay um uh so that's how we're
+going to be thinking of presenting
+
+ align:start position:0%
+going to be thinking of presenting
+ 
+
+ align:start position:0%
+going to be thinking of presenting
+touring machines with more complicated
+
+ align:start position:0%
+touring machines with more complicated
+ 
+
+ align:start position:0%
+touring machines with more complicated
+objects and strings as input because
+
+ align:start position:0%
+objects and strings as input because
+ 
+
+ align:start position:0%
+objects and strings as input because
+we're just going to represent them as
+
+ align:start position:0%
+we're just going to represent them as
+ 
+
+ align:start position:0%
+we're just going to represent them as
+strings using some ways in which I'm
+
+ align:start position:0%
+strings using some ways in which I'm
+ 
+
+ align:start position:0%
+strings using some ways in which I'm
+sure you're all familiar and that's how
+
+ align:start position:0%
+sure you're all familiar and that's how
+ 
+
+ align:start position:0%
+sure you're all familiar and that's how
+you deal with representing stuff when
+
+ align:start position:0%
+you deal with representing stuff when
+ 
+
+ align:start position:0%
+you deal with representing stuff when
+you're you know have write your programs
+
+ align:start position:0%
+you're you know have write your programs
+ 
+
+ align:start position:0%
+you're you know have write your programs
+anyway um but just to make it formal and
+
+ align:start position:0%
+anyway um but just to make it formal and
+ 
+
+ align:start position:0%
+anyway um but just to make it formal and
+that's the way we're going to write it
+
+ align:start position:0%
+that's the way we're going to write it
+ 
+
+ align:start position:0%
+that's the way we're going to write it
+down in these brackets and if you have a
+
+ align:start position:0%
+down in these brackets and if you have a
+ 
+
+ align:start position:0%
+down in these brackets and if you have a
+list of several objects that you want to
+
+ align:start position:0%
+list of several objects that you want to
+ 
+
+ align:start position:0%
+list of several objects that you want to
+present together um to a touring machine
+
+ align:start position:0%
+present together um to a touring machine
+ 
+
+ align:start position:0%
+present together um to a touring machine
+we'll just write them together within
+
+ align:start position:0%
+we'll just write them together within
+ 
+
+ align:start position:0%
+we'll just write them together within
+brackets like this um now for writing
+
+ align:start position:0%
+brackets like this um now for writing
+ 
+
+ align:start position:0%
+brackets like this um now for writing
+touring machines
+
+ align:start position:0%
+touring machines
+ 
+
+ align:start position:0%
+touring machines
+down we're going to going forward going
+
+ align:start position:0%
+down we're going to going forward going
+ 
+
+ align:start position:0%
+down we're going to going forward going
+to be using high level English
+
+ align:start position:0%
+to be using high level English
+ 
+
+ align:start position:0%
+to be using high level English
+descriptions um we're not going to be
+
+ align:start position:0%
+descriptions um we're not going to be
+ 
+
+ align:start position:0%
+descriptions um we're not going to be
+worrying about managing the te like the
+
+ align:start position:0%
+worrying about managing the te like the
+ 
+
+ align:start position:0%
+worrying about managing the te like the
+stuff we've been doing up till now I'm
+
+ align:start position:0%
+stuff we've been doing up till now I'm
+ 
+
+ align:start position:0%
+stuff we've been doing up till now I'm
+not going to ask you to do it we're not
+
+ align:start position:0%
+not going to ask you to do it we're not
+ 
+
+ align:start position:0%
+not going to ask you to do it we're not
+going to do that anymore and I'm not
+
+ align:start position:0%
+going to do that anymore and I'm not
+ 
+
+ align:start position:0%
+going to do that anymore and I'm not
+going to ask you to do it managing where
+
+ align:start position:0%
+going to ask you to do it managing where
+ 
+
+ align:start position:0%
+going to ask you to do it managing where
+stuff goes on the tapes and all that
+
+ align:start position:0%
+stuff goes on the tapes and all that
+ 
+
+ align:start position:0%
+stuff goes on the tapes and all that
+stuff that's too low level um because
+
+ align:start position:0%
+stuff that's too low level um because
+ 
+
+ align:start position:0%
+stuff that's too low level um because
+really now that we have the church
+
+ align:start position:0%
+really now that we have the church
+ 
+
+ align:start position:0%
+really now that we have the church
+touring thesis we really interested in
+
+ align:start position:0%
+touring thesis we really interested in
+ 
+
+ align:start position:0%
+touring thesis we really interested in
+talking about algorithms we're not that
+
+ align:start position:0%
+talking about algorithms we're not that
+ 
+
+ align:start position:0%
+talking about algorithms we're not that
+interested talk talking about touring
+
+ align:start position:0%
+interested talk talking about touring
+ 
+
+ align:start position:0%
+interested talk talking about touring
+machines per se We Men algorithms um and
+
+ align:start position:0%
+machines per se We Men algorithms um and
+ 
+
+ align:start position:0%
+machines per se We Men algorithms um and
+what the power of computation is so um
+
+ align:start position:0%
+what the power of computation is so um
+ 
+
+ align:start position:0%
+what the power of computation is so um
+we're going to only be talking about
+
+ align:start position:0%
+we're going to only be talking about
+ 
+
+ align:start position:0%
+we're going to only be talking about
+touring machines now in a high higher
+
+ align:start position:0%
+touring machines now in a high higher
+ 
+
+ align:start position:0%
+touring machines now in a high higher
+level way and only when we need to prove
+
+ align:start position:0%
+level way and only when we need to prove
+ 
+
+ align:start position:0%
+level way and only when we need to prove
+something about uh capabilities we're
+
+ align:start position:0%
+something about uh capabilities we're
+ 
+
+ align:start position:0%
+something about uh capabilities we're
+going to come back to touring machines
+
+ align:start position:0%
+going to come back to touring machines
+ 
+
+ align:start position:0%
+going to come back to touring machines
+I'm going to be proving things you know
+
+ align:start position:0%
+I'm going to be proving things you know
+ 
+
+ align:start position:0%
+I'm going to be proving things you know
+about their limitations and so on so our
+
+ align:start position:0%
+about their limitations and so on so our
+ 
+
+ align:start position:0%
+about their limitations and so on so our
+notation for running touring machines is
+
+ align:start position:0%
+notation for running touring machines is
+ 
+
+ align:start position:0%
+notation for running touring machines is
+going to
+
+ align:start position:0%
+going to
+ 
+
+ align:start position:0%
+going to
+be basically going to put the touring
+
+ align:start position:0%
+be basically going to put the touring
+ 
+
+ align:start position:0%
+be basically going to put the touring
+machine inside these quotation marks and
+
+ align:start position:0%
+machine inside these quotation marks and
+ 
+
+ align:start position:0%
+machine inside these quotation marks and
+we're going to know
+
+ align:start position:0%
+we're going to know
+ 
+
+ align:start position:0%
+we're going to know
+that we could if in principle write out
+
+ align:start position:0%
+that we could if in principle write out
+ 
+
+ align:start position:0%
+that we could if in principle write out
+the touring machine in a precise way in
+
+ align:start position:0%
+the touring machine in a precise way in
+ 
+
+ align:start position:0%
+the touring machine in a precise way in
+terms of states and transition function
+
+ align:start position:0%
+terms of states and transition function
+ 
+
+ align:start position:0%
+terms of states and transition function
+and so on but we'll never actually go
+
+ align:start position:0%
+and so on but we'll never actually go
+ 
+
+ align:start position:0%
+and so on but we'll never actually go
+ahead and do that lengthy
+
+ align:start position:0%
+ahead and do that lengthy
+ 
+
+ align:start position:0%
+ahead and do that lengthy
+exercise um so quick check in
+
+ align:start position:0%
+exercise um so quick check in
+ 
+
+ align:start position:0%
+exercise um so quick check in
+here so one of the features well okay
+
+ align:start position:0%
+here so one of the features well okay
+ 
+
+ align:start position:0%
+here so one of the features well okay
+let me not give this away so if X and Y
+
+ align:start position:0%
+let me not give this away so if X and Y
+ 
+
+ align:start position:0%
+let me not give this away so if X and Y
+are
+
+ align:start position:0%
+are
+ 
+
+ align:start position:0%
+are
+strings you know I want to now have a
+
+ align:start position:0%
+strings you know I want to now have a
+ 
+
+ align:start position:0%
+strings you know I want to now have a
+way of presenting two strings as a
+
+ align:start position:0%
+way of presenting two strings as a
+ 
+
+ align:start position:0%
+way of presenting two strings as a
+single string as input to my machine
+
+ align:start position:0%
+single string as input to my machine
+ 
+
+ align:start position:0%
+single string as input to my machine
+because it's I always think of my
+
+ align:start position:0%
+because it's I always think of my
+ 
+
+ align:start position:0%
+because it's I always think of my
+machine is getting a single
+
+ align:start position:0%
+machine is getting a single
+ 
+
+ align:start position:0%
+machine is getting a single
+input so would you suggest one way of
+
+ align:start position:0%
+input so would you suggest one way of
+ 
+
+ align:start position:0%
+input so would you suggest one way of
+combining two strings into one which we
+
+ align:start position:0%
+combining two strings into one which we
+ 
+
+ align:start position:0%
+combining two strings into one which we
+would be a good encoding is just to
+
+ align:start position:0%
+would be a good encoding is just to
+ 
+
+ align:start position:0%
+would be a good encoding is just to
+concatenate those two strings
+
+ align:start position:0%
+concatenate those two strings
+ 
+
+ align:start position:0%
+concatenate those two strings
+together it's would it be that would
+
+ align:start position:0%
+together it's would it be that would
+ 
+
+ align:start position:0%
+together it's would it be that would
+would that be the way you would do it is
+
+ align:start position:0%
+would that be the way you would do it is
+ 
+
+ align:start position:0%
+would that be the way you would do it is
+that a good way to do it or or not such
+
+ align:start position:0%
+that a good way to do it or or not such
+ 
+
+ align:start position:0%
+that a good way to do it or or not such
+a good way to do it um so let's
+
+ align:start position:0%
+a good way to do it um so let's
+ 
+
+ align:start position:0%
+a good way to do it um so let's
+uh um let's see here
+
+ align:start position:0%
+uh um let's see here
+ 
+
+ align:start position:0%
+uh um let's see here
+I can get to that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+next and think of what you would want to
+
+ align:start position:0%
+next and think of what you would want to
+ 
+
+ align:start position:0%
+next and think of what you would want to
+have happened in a good
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+encoding
+
+ align:start position:0%
+encoding
+ 
+
+ align:start position:0%
+encoding
+okay ready set
+
+ align:start position:0%
+okay ready set
+ 
+
+ align:start position:0%
+okay ready set
+sold uh share
+
+ align:start position:0%
+sold uh share
+ 
+
+ align:start position:0%
+sold uh share
+results yeah I think most of you got the
+
+ align:start position:0%
+results yeah I think most of you got the
+ 
+
+ align:start position:0%
+results yeah I think most of you got the
+idea that this is not a good way of
+
+ align:start position:0%
+idea that this is not a good way of
+ 
+
+ align:start position:0%
+idea that this is not a good way of
+combining two strings into one um
+
+ align:start position:0%
+combining two strings into one um
+ 
+
+ align:start position:0%
+combining two strings into one um
+because the problem is it's kind of
+
+ align:start position:0%
+because the problem is it's kind of
+ 
+
+ align:start position:0%
+because the problem is it's kind of
+ambiguous in a sense
+
+ align:start position:0%
+ambiguous in a sense
+ 
+
+ align:start position:0%
+ambiguous in a sense
+you know that you could if you combine
+
+ align:start position:0%
+you know that you could if you combine
+ 
+
+ align:start position:0%
+you know that you could if you combine
+two strings this way what's what's
+
+ align:start position:0%
+two strings this way what's what's
+ 
+
+ align:start position:0%
+two strings this way what's what's
+important in an encoding is that the
+
+ align:start position:0%
+important in an encoding is that the
+ 
+
+ align:start position:0%
+important in an encoding is that the
+machine when it gets the encoding it can
+
+ align:start position:0%
+machine when it gets the encoding it can
+ 
+
+ align:start position:0%
+machine when it gets the encoding it can
+decode them back into the original
+
+ align:start position:0%
+decode them back into the original
+ 
+
+ align:start position:0%
+decode them back into the original
+objects and if you're just going to be
+
+ align:start position:0%
+objects and if you're just going to be
+ 
+
+ align:start position:0%
+objects and if you're just going to be
+sticking the two strings together you
+
+ align:start position:0%
+sticking the two strings together you
+ 
+
+ align:start position:0%
+sticking the two strings together you
+don't know where one string ends and the
+
+ align:start position:0%
+don't know where one string ends and the
+ 
+
+ align:start position:0%
+don't know where one string ends and the
+next string begins and so it's not going
+
+ align:start position:0%
+next string begins and so it's not going
+ 
+
+ align:start position:0%
+next string begins and so it's not going
+to be a good way of combining things you
+
+ align:start position:0%
+to be a good way of combining things you
+ 
+
+ align:start position:0%
+to be a good way of combining things you
+you should F find a little bit more
+
+ align:start position:0%
+you should F find a little bit more
+ 
+
+ align:start position:0%
+you should F find a little bit more
+clever way of either introducing another
+
+ align:start position:0%
+clever way of either introducing another
+ 
+
+ align:start position:0%
+clever way of either introducing another
+symbol or doing something a little bit
+
+ align:start position:0%
+symbol or doing something a little bit
+ 
+
+ align:start position:0%
+symbol or doing something a little bit
+more sophisticated which allow you to be
+
+ align:start position:0%
+more sophisticated which allow you to be
+ 
+
+ align:start position:0%
+more sophisticated which allow you to be
+a ble to do the decoding as well as the
+
+ align:start position:0%
+a ble to do the decoding as well as the
+ 
+
+ align:start position:0%
+a ble to do the decoding as well as the
+encoding in a unique
+
+ align:start position:0%
+encoding in a unique
+ 
+
+ align:start position:0%
+encoding in a unique
+way okay so uh getting back to that
+
+ align:start position:0%
+way okay so uh getting back to that
+ 
+
+ align:start position:0%
+way okay so uh getting back to that
+notation for turing machine so here is
+
+ align:start position:0%
+notation for turing machine so here is
+ 
+
+ align:start position:0%
+notation for turing machine so here is
+the machine we've already seen once
+
+ align:start position:0%
+the machine we've already seen once
+ 
+
+ align:start position:0%
+the machine we've already seen once
+before uh for a to the k b to the K C to
+
+ align:start position:0%
+before uh for a to the k b to the K C to
+ 
+
+ align:start position:0%
+before uh for a to the k b to the K C to
+the K I would write it now more simply
+
+ align:start position:0%
+the K I would write it now more simply
+ 
+
+ align:start position:0%
+the K I would write it now more simply
+than managing all of the tapes that we
+
+ align:start position:0%
+than managing all of the tapes that we
+ 
+
+ align:start position:0%
+than managing all of the tapes that we
+had the first time around which we did
+
+ align:start position:0%
+had the first time around which we did
+ 
+
+ align:start position:0%
+had the first time around which we did
+last lecture I would just say given an
+
+ align:start position:0%
+last lecture I would just say given an
+ 
+
+ align:start position:0%
+last lecture I would just say given an
+input W check if W is of the right form
+
+ align:start position:0%
+input W check if W is of the right form
+ 
+
+ align:start position:0%
+input W check if W is of the right form
+with the things in the right order
+
+ align:start position:0%
+with the things in the right order
+ 
+
+ align:start position:0%
+with the things in the right order
+reject if it's not count the number of
+
+ align:start position:0%
+reject if it's not count the number of
+ 
+
+ align:start position:0%
+reject if it's not count the number of
+A's BS and C's and W except if all the
+
+ align:start position:0%
+A's BS and C's and W except if all the
+ 
+
+ align:start position:0%
+A's BS and C's and W except if all the
+counts are equal and reject if not we're
+
+ align:start position:0%
+counts are equal and reject if not we're
+ 
+
+ align:start position:0%
+counts are equal and reject if not we're
+not going to be that's going to be good
+
+ align:start position:0%
+not going to be that's going to be good
+ 
+
+ align:start position:0%
+not going to be that's going to be good
+enough to be writing things at that
+
+ align:start position:0%
+enough to be writing things at that
+ 
+
+ align:start position:0%
+enough to be writing things at that
+higher level when you're going to be
+
+ align:start position:0%
+higher level when you're going to be
+ 
+
+ align:start position:0%
+higher level when you're going to be
+writing your algorithm descriptions you
+
+ align:start position:0%
+writing your algorithm descriptions you
+ 
+
+ align:start position:0%
+writing your algorithm descriptions you
+just have to make sure that whatever
+
+ align:start position:0%
+just have to make sure that whatever
+ 
+
+ align:start position:0%
+just have to make sure that whatever
+you're doing you can Implement um you
+
+ align:start position:0%
+you're doing you can Implement um you
+ 
+
+ align:start position:0%
+you're doing you can Implement um you
+know you you can't make uh you don't you
+
+ align:start position:0%
+know you you can't make uh you don't you
+ 
+
+ align:start position:0%
+know you you can't make uh you don't you
+you don't want to be doing tests which
+
+ align:start position:0%
+you don't want to be doing tests which
+ 
+
+ align:start position:0%
+you don't want to be doing tests which
+are impossible or doing infinite
+
+ align:start position:0%
+are impossible or doing infinite
+ 
+
+ align:start position:0%
+are impossible or doing infinite
+infinitely much work in one stage that's
+
+ align:start position:0%
+infinitely much work in one stage that's
+ 
+
+ align:start position:0%
+infinitely much work in one stage that's
+not good um but as long as it's clear
+
+ align:start position:0%
+not good um but as long as it's clear
+ 
+
+ align:start position:0%
+not good um but as long as it's clear
+that what you doing has doing only a
+
+ align:start position:0%
+that what you doing has doing only a
+ 
+
+ align:start position:0%
+that what you doing has doing only a
+finite amount of work in every stage and
+
+ align:start position:0%
+finite amount of work in every stage and
+ 
+
+ align:start position:0%
+finite amount of work in every stage and
+it's something that you could really
+
+ align:start position:0%
+it's something that you could really
+ 
+
+ align:start position:0%
+it's something that you could really
+Implement you can write it at a high in
+
+ align:start position:0%
+Implement you can write it at a high in
+ 
+
+ align:start position:0%
+Implement you can write it at a high in
+a high level um okay I wanted to spend a
+
+ align:start position:0%
+a high level um okay I wanted to spend a
+ 
+
+ align:start position:0%
+a high level um okay I wanted to spend a
+few minutes talking about problem set
+
+ align:start position:0%
+few minutes talking about problem set
+ 
+
+ align:start position:0%
+few minutes talking about problem set
+two but we a little bit running out of
+
+ align:start position:0%
+two but we a little bit running out of
+ 
+
+ align:start position:0%
+two but we a little bit running out of
+time here um uh in particular there was
+
+ align:start position:0%
+time here um uh in particular there was
+ 
+
+ align:start position:0%
+time here um uh in particular there was
+this problem number five where you show
+
+ align:start position:0%
+this problem number five where you show
+ 
+
+ align:start position:0%
+this problem number five where you show
+that language of touring recognizable if
+
+ align:start position:0%
+that language of touring recognizable if
+ 
+
+ align:start position:0%
+that language of touring recognizable if
+and only if there's a decidable D um
+
+ align:start position:0%
+and only if there's a decidable D um
+ 
+
+ align:start position:0%
+and only if there's a decidable D um
+where C is touring recognizable where D
+
+ align:start position:0%
+where C is touring recognizable where D
+ 
+
+ align:start position:0%
+where C is touring recognizable where D
+is now collection of pairs we got some
+
+ align:start position:0%
+is now collection of pairs we got some
+ 
+
+ align:start position:0%
+is now collection of pairs we got some
+questions about the notation which I've
+
+ align:start position:0%
+questions about the notation which I've
+ 
+
+ align:start position:0%
+questions about the notation which I've
+hope hopefully answered now so um
+
+ align:start position:0%
+hope hopefully answered now so um
+ 
+
+ align:start position:0%
+hope hopefully answered now so um
+C uh is a set of x's such that there
+
+ align:start position:0%
+C uh is a set of x's such that there
+ 
+
+ align:start position:0%
+C uh is a set of x's such that there
+exists a string you can pair it with so
+
+ align:start position:0%
+exists a string you can pair it with so
+ 
+
+ align:start position:0%
+exists a string you can pair it with so
+that the string X Y is in
+
+ align:start position:0%
+that the string X Y is in
+ 
+
+ align:start position:0%
+that the string X Y is in
+D um let me try to give you a picture of
+
+ align:start position:0%
+D um let me try to give you a picture of
+ 
+
+ align:start position:0%
+D um let me try to give you a picture of
+that uh
+
+ align:start position:0%
+that uh
+ 
+
+ align:start position:0%
+that uh
+um so I'm going to think of d as a
+
+ align:start position:0%
+um so I'm going to think of d as a
+ 
+
+ align:start position:0%
+um so I'm going to think of d as a
+collection of pairs of strings and it
+
+ align:start position:0%
+collection of pairs of strings and it
+ 
+
+ align:start position:0%
+collection of pairs of strings and it
+might be helpful to think of D kind of
+
+ align:start position:0%
+might be helpful to think of D kind of
+ 
+
+ align:start position:0%
+might be helpful to think of D kind of
+you know on the axes here so if we have
+
+ align:start position:0%
+you know on the axes here so if we have
+ 
+
+ align:start position:0%
+you know on the axes here so if we have
+a pair of strings XY which I have not
+
+ align:start position:0%
+a pair of strings XY which I have not
+ 
+
+ align:start position:0%
+a pair of strings XY which I have not
+yet packaged into a single string I'm
+
+ align:start position:0%
+yet packaged into a single string I'm
+ 
+
+ align:start position:0%
+yet packaged into a single string I'm
+thinking of them as a pair of two
+
+ align:start position:0%
+thinking of them as a pair of two
+ 
+
+ align:start position:0%
+thinking of them as a pair of two
+objects at this moment uh think of d as
+
+ align:start position:0%
+objects at this moment uh think of d as
+ 
+
+ align:start position:0%
+objects at this moment uh think of d as
+so you know Ju Just the X part is just
+
+ align:start position:0%
+so you know Ju Just the X part is just
+ 
+
+ align:start position:0%
+so you know Ju Just the X part is just
+below here on the x-axis um D you might
+
+ align:start position:0%
+below here on the x-axis um D you might
+ 
+
+ align:start position:0%
+below here on the x-axis um D you might
+want to think just conceptually want to
+
+ align:start position:0%
+want to think just conceptually want to
+ 
+
+ align:start position:0%
+want to think just conceptually want to
+think of it as a collection of pairs so
+
+ align:start position:0%
+think of it as a collection of pairs so
+ 
+
+ align:start position:0%
+think of it as a collection of pairs so
+it's like a subset of all of these pairs
+
+ align:start position:0%
+it's like a subset of all of these pairs
+ 
+
+ align:start position:0%
+it's like a subset of all of these pairs
+and C
+
+ align:start position:0%
+and C
+ 
+
+ align:start position:0%
+and C
+is all of the the X's that correspond to
+
+ align:start position:0%
+is all of the the X's that correspond to
+ 
+
+ align:start position:0%
+is all of the the X's that correspond to
+any pair in here um sometimes we call
+
+ align:start position:0%
+any pair in here um sometimes we call
+ 
+
+ align:start position:0%
+any pair in here um sometimes we call
+that the projection because it's all the
+
+ align:start position:0%
+that the projection because it's all the
+ 
+
+ align:start position:0%
+that the projection because it's all the
+things that are below or the shadow if
+
+ align:start position:0%
+things that are below or the shadow if
+ 
+
+ align:start position:0%
+things that are below or the shadow if
+you had a light sitting up here it's all
+
+ align:start position:0%
+you had a light sitting up here it's all
+ 
+
+ align:start position:0%
+you had a light sitting up here it's all
+the things that are kind of underneath a
+
+ align:start position:0%
+the things that are kind of underneath a
+ 
+
+ align:start position:0%
+the things that are kind of underneath a
+D um so I've written C here kind of a
+
+ align:start position:0%
+D um so I've written C here kind of a
+ 
+
+ align:start position:0%
+D um so I've written C here kind of a
+little thicker if you can see that so
+
+ align:start position:0%
+little thicker if you can see that so
+ 
+
+ align:start position:0%
+little thicker if you can see that so
+that's the C language and
+
+ align:start position:0%
+that's the C language and
+ 
+
+ align:start position:0%
+that's the C language and
+um what you're going to what there's two
+
+ align:start position:0%
+um what you're going to what there's two
+ 
+
+ align:start position:0%
+um what you're going to what there's two
+directions here one is a lot easier than
+
+ align:start position:0%
+directions here one is a lot easier than
+ 
+
+ align:start position:0%
+directions here one is a lot easier than
+the other if I give you a decidable
+
+ align:start position:0%
+the other if I give you a decidable
+ 
+
+ align:start position:0%
+the other if I give you a decidable
+d and I want to test whether something's
+
+ align:start position:0%
+d and I want to test whether something's
+ 
+
+ align:start position:0%
+d and I want to test whether something's
+in C so I give you an X I want to know
+
+ align:start position:0%
+in C so I give you an X I want to know
+ 
+
+ align:start position:0%
+in C so I give you an X I want to know
+is it is x in
+
+ align:start position:0%
+is it is x in
+ 
+
+ align:start position:0%
+is it is x in
+C well you now have to test is there
+
+ align:start position:0%
+C well you now have to test is there
+ 
+
+ align:start position:0%
+C well you now have to test is there
+some y that I can pair with X where the
+
+ align:start position:0%
+some y that I can pair with X where the
+ 
+
+ align:start position:0%
+some y that I can pair with X where the
+pair is in
+
+ align:start position:0%
+pair is in
+ 
+
+ align:start position:0%
+pair is in
+D um so you know you can start looking
+
+ align:start position:0%
+D um so you know you can start looking
+ 
+
+ align:start position:0%
+D um so you know you can start looking
+for that y if you ever find one you know
+
+ align:start position:0%
+for that y if you ever find one you know
+ 
+
+ align:start position:0%
+for that y if you ever find one you know
+that X is in C there are infinitely many
+
+ align:start position:0%
+that X is in C there are infinitely many
+ 
+
+ align:start position:0%
+that X is in C there are infinitely many
+y to to look for but don't forget you
+
+ align:start position:0%
+y to to look for but don't forget you
+ 
+
+ align:start position:0%
+y to to look for but don't forget you
+know you're only looking for a
+
+ align:start position:0%
+know you're only looking for a
+ 
+
+ align:start position:0%
+know you're only looking for a
+recognizer for
+
+ align:start position:0%
+recognizer for
+ 
+
+ align:start position:0%
+recognizer for
+C so you know on the rejecting side
+
+ align:start position:0%
+C so you know on the rejecting side
+ 
+
+ align:start position:0%
+C so you know on the rejecting side
+you're allowed to go forever so I I'm
+
+ align:start position:0%
+you're allowed to go forever so I I'm
+ 
+
+ align:start position:0%
+you're allowed to go forever so I I'm
+kind of giving you a way to think about
+
+ align:start position:0%
+kind of giving you a way to think about
+ 
+
+ align:start position:0%
+kind of giving you a way to think about
+the easy Direction the hard Direction um
+
+ align:start position:0%
+the easy Direction the hard Direction um
+ 
+
+ align:start position:0%
+the easy Direction the hard Direction um
+you need to think about um how are you
+
+ align:start position:0%
+you need to think about um how are you
+ 
+
+ align:start position:0%
+you need to think about um how are you
+going to come up with that decidable
+
+ align:start position:0%
+going to come up with that decidable
+ 
+
+ align:start position:0%
+going to come up with that decidable
+date if I give you C you have to find a
+
+ align:start position:0%
+date if I give you C you have to find a
+ 
+
+ align:start position:0%
+date if I give you C you have to find a
+decidable d and now you're you're
+
+ align:start position:0%
+decidable d and now you're you're
+ 
+
+ align:start position:0%
+decidable d and now you're you're
+bringing something down lower you're
+
+ align:start position:0%
+bringing something down lower you're
+ 
+
+ align:start position:0%
+bringing something down lower you're
+starting with a recognizing recognizable
+
+ align:start position:0%
+starting with a recognizing recognizable
+ 
+
+ align:start position:0%
+starting with a recognizing recognizable
+language and a decidable language which
+
+ align:start position:0%
+language and a decidable language which
+ 
+
+ align:start position:0%
+language and a decidable language which
+is going to sort of be counterpart to
+
+ align:start position:0%
+is going to sort of be counterpart to
+ 
+
+ align:start position:0%
+is going to sort of be counterpart to
+that in a sense is a simpler language
+
+ align:start position:0%
+that in a sense is a simpler language
+ 
+
+ align:start position:0%
+that in a sense is a simpler language
+and the way it becomes simpler is that Y
+
+ align:start position:0%
+and the way it becomes simpler is that Y
+ 
+
+ align:start position:0%
+and the way it becomes simpler is that Y
+is going to help you determine whether X
+
+ align:start position:0%
+is going to help you determine whether X
+ 
+
+ align:start position:0%
+is going to help you determine whether X
+is in
+
+ align:start position:0%
+is in
+ 
+
+ align:start position:0%
+is in
+C um and I guess the thing that you
+
+ align:start position:0%
+C um and I guess the thing that you
+ 
+
+ align:start position:0%
+C um and I guess the thing that you
+should I'll leave you with is and maybe
+
+ align:start position:0%
+should I'll leave you with is and maybe
+ 
+
+ align:start position:0%
+should I'll leave you with is and maybe
+we can talk about this a little bit more
+
+ align:start position:0%
+we can talk about this a little bit more
+ 
+
+ align:start position:0%
+we can talk about this a little bit more
+uh on Tuesday I'll I'll try to leave it
+
+ align:start position:0%
+uh on Tuesday I'll I'll try to leave it
+ 
+
+ align:start position:0%
+uh on Tuesday I'll I'll try to leave it
+a little bit more time
+
+ align:start position:0%
+a little bit more time
+ 
+
+ align:start position:0%
+a little bit more time
+uh if you want to test if something's in
+
+ align:start position:0%
+uh if you want to test if something's in
+ 
+
+ align:start position:0%
+uh if you want to test if something's in
+c x is in C but I don't want to let you
+
+ align:start position:0%
+c x is in C but I don't want to let you
+ 
+
+ align:start position:0%
+c x is in C but I don't want to let you
+go forever anymore because I want to be
+
+ align:start position:0%
+go forever anymore because I want to be
+ 
+
+ align:start position:0%
+go forever anymore because I want to be
+a decidable language and I'm going to
+
+ align:start position:0%
+a decidable language and I'm going to
+ 
+
+ align:start position:0%
+a decidable language and I'm going to
+use y to help you what information would
+
+ align:start position:0%
+use y to help you what information would
+ 
+
+ align:start position:0%
+use y to help you what information would
+help you guarantee you get the right
+
+ align:start position:0%
+help you guarantee you get the right
+ 
+
+ align:start position:0%
+help you guarantee you get the right
+answer for X being in C um but that you
+
+ align:start position:0%
+answer for X being in C um but that you
+ 
+
+ align:start position:0%
+answer for X being in C um but that you
+would um have to be sure you're getting
+
+ align:start position:0%
+would um have to be sure you're getting
+ 
+
+ align:start position:0%
+would um have to be sure you're getting
+the right answer so it's you know why
+
+ align:start position:0%
+the right answer so it's you know why
+ 
+
+ align:start position:0%
+the right answer so it's you know why
+could just be the answer but then you
+
+ align:start position:0%
+could just be the answer but then you
+ 
+
+ align:start position:0%
+could just be the answer but then you
+know you don't know that that's you you
+
+ align:start position:0%
+know you don't know that that's you you
+ 
+
+ align:start position:0%
+know you don't know that that's you you
+have to be convinced that you have the
+
+ align:start position:0%
+have to be convinced that you have the
+ 
+
+ align:start position:0%
+have to be convinced that you have the
+right answer you know why just saying
+
+ align:start position:0%
+right answer you know why just saying
+ 
+
+ align:start position:0%
+right answer you know why just saying
+what it is I mean you could why could
+
+ align:start position:0%
+what it is I mean you could why could
+ 
+
+ align:start position:0%
+what it is I mean you could why could
+say it that X is in D even when it's not
+
+ align:start position:0%
+say it that X is in D even when it's not
+ 
+
+ align:start position:0%
+say it that X is in D even when it's not
+true X is in C even when it's not true
+
+ align:start position:0%
+true X is in C even when it's not true
+ 
+
+ align:start position:0%
+true X is in C even when it's not true
+but so what information would allow you
+
+ align:start position:0%
+but so what information would allow you
+ 
+
+ align:start position:0%
+but so what information would allow you
+to check that X is in C what would be
+
+ align:start position:0%
+to check that X is in C what would be
+ 
+
+ align:start position:0%
+to check that X is in C what would be
+helpful information to check the x's and
+
+ align:start position:0%
+helpful information to check the x's and
+ 
+
+ align:start position:0%
+helpful information to check the x's and
+C where you would avoid ever having to
+
+ align:start position:0%
+C where you would avoid ever having to
+ 
+
+ align:start position:0%
+C where you would avoid ever having to
+go
+
+ align:start position:0%
+go
+ 
+
+ align:start position:0%
+go
+forever little bit too rushed here to
+
+ align:start position:0%
+forever little bit too rushed here to
+ 
+
+ align:start position:0%
+forever little bit too rushed here to
+for that to be helpful anyway let's just
+
+ align:start position:0%
+for that to be helpful anyway let's just
+ 
+
+ align:start position:0%
+for that to be helpful anyway let's just
+uh conclude what we've done um just
+
+ align:start position:0%
+uh conclude what we've done um just
+ 
+
+ align:start position:0%
+uh conclude what we've done um just
+brief summary here
+
+ align:start position:0%
+brief summary here
+ 
+
+ align:start position:0%
+brief summary here
+um and I I I don't want to
+
+ align:start position:0%
+um and I I I don't want to
+ 
+
+ align:start position:0%
+um and I I I don't want to
+uh um keep you in keep you over time so
+
+ align:start position:0%
+uh um keep you in keep you over time so
+ 
+
+ align:start position:0%
+uh um keep you in keep you over time so
+I'll just leave this up on the board um
+
+ align:start position:0%
+I'll just leave this up on the board um
+ 
+
+ align:start position:0%
+I'll just leave this up on the board um
+I will uh
+
+ align:start position:0%
+I will uh
+ 
+
+ align:start position:0%
+I will uh
+um uh see if there's any so what the
+
+ align:start position:0%
+um uh see if there's any so what the
+ 
+
+ align:start position:0%
+um uh see if there's any so what the
+lecture is over uh and you can take off
+
+ align:start position:0%
+lecture is over uh and you can take off
+ 
+
+ align:start position:0%
+lecture is over uh and you can take off
+as you wish um I will stick around for a
+
+ align:start position:0%
+as you wish um I will stick around for a
+ 
+
+ align:start position:0%
+as you wish um I will stick around for a
+couple of minutes I have another meeting
+
+ align:start position:0%
+couple of minutes I have another meeting
+ 
+
+ align:start position:0%
+couple of minutes I have another meeting
+soon um but I'll answer try to answer
+
+ align:start position:0%
+soon um but I'll answer try to answer
+ 
+
+ align:start position:0%
+soon um but I'll answer try to answer
+some
+
+ align:start position:0%
+some
+ 
+
+ align:start position:0%
+some
+chats uh
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+all right um people are commenting about
+
+ align:start position:0%
+all right um people are commenting about
+ 
+
+ align:start position:0%
+all right um people are commenting about
+this movie about touring the imitation
+
+ align:start position:0%
+this movie about touring the imitation
+ 
+
+ align:start position:0%
+this movie about touring the imitation
+game uh you know if you haven't seen
+
+ align:start position:0%
+game uh you know if you haven't seen
+ 
+
+ align:start position:0%
+game uh you know if you haven't seen
+that I recommend it
+
+ align:start position:0%
+that I recommend it
+ 
+
+ align:start position:0%
+that I recommend it
+um um and
+
+ align:start position:0%
+um um and
+ 
+
+ align:start position:0%
+um um and
+uh is it a good idea to make y to be
+
+ align:start position:0%
+uh is it a good idea to make y to be
+ 
+
+ align:start position:0%
+uh is it a good idea to make y to be
+equal to the repeated Loop stram H I'm
+
+ align:start position:0%
+equal to the repeated Loop stram H I'm
+ 
+
+ align:start position:0%
+equal to the repeated Loop stram H I'm
+not sure about that uh thank you for the
+
+ align:start position:0%
+not sure about that uh thank you for the
+ 
+
+ align:start position:0%
+not sure about that uh thank you for the
+uh thank you everybody for sending your
+
+ align:start position:0%
+uh thank you everybody for sending your
+ 
+
+ align:start position:0%
+uh thank you everybody for sending your
+kind notes um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+is church Turing thesis the question is
+
+ align:start position:0%
+is church Turing thesis the question is
+ 
+
+ align:start position:0%
+is church Turing thesis the question is
+is it in the book yes it's in the book
+
+ align:start position:0%
+is it in the book yes it's in the book
+ 
+
+ align:start position:0%
+is it in the book yes it's in the book
+kind of similar to what I've already
+
+ align:start position:0%
+kind of similar to what I've already
+ 
+
+ align:start position:0%
+kind of similar to what I've already
+said but
+
+ align:start position:0%
+said but
+ 
+
+ align:start position:0%
+said but
+yes
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um okay this is a good question here um
+
+ align:start position:0%
+um okay this is a good question here um
+ 
+
+ align:start position:0%
+um okay this is a good question here um
+the church touring thesis somebody asked
+
+ align:start position:0%
+the church touring thesis somebody asked
+ 
+
+ align:start position:0%
+the church touring thesis somebody asked
+me is it proved in the book there's
+
+ align:start position:0%
+me is it proved in the book there's
+ 
+
+ align:start position:0%
+me is it proved in the book there's
+nothing to prove
+
+ align:start position:0%
+nothing to prove
+ 
+
+ align:start position:0%
+nothing to prove
+the church touring thesis is an
+
+ align:start position:0%
+the church touring thesis is an
+ 
+
+ align:start position:0%
+the church touring thesis is an
+equivalence between the intuitive and
+
+ align:start position:0%
+equivalence between the intuitive and
+ 
+
+ align:start position:0%
+equivalence between the intuitive and
+the formal you can't prove something
+
+ align:start position:0%
+the formal you can't prove something
+ 
+
+ align:start position:0%
+the formal you can't prove something
+like that um you can just make it's
+
+ align:start position:0%
+like that um you can just make it's
+ 
+
+ align:start position:0%
+like that um you can just make it's
+really in a sense a hypothesis that the
+
+ align:start position:0%
+really in a sense a hypothesis that the
+ 
+
+ align:start position:0%
+really in a sense a hypothesis that the
+only thing you'll ever be able to
+
+ align:start position:0%
+only thing you'll ever be able to
+ 
+
+ align:start position:0%
+only thing you'll ever be able to
+compute um is something that you can do
+
+ align:start position:0%
+compute um is something that you can do
+ 
+
+ align:start position:0%
+compute um is something that you can do
+with a touring machine um I mean that
+
+ align:start position:0%
+with a touring machine um I mean that
+ 
+
+ align:start position:0%
+with a touring machine um I mean that
+has something to do with the nature of
+
+ align:start position:0%
+has something to do with the nature of
+ 
+
+ align:start position:0%
+has something to do with the nature of
+the physical world and I'm sure I don't
+
+ align:start position:0%
+the physical world and I'm sure I don't
+ 
+
+ align:start position:0%
+the physical world and I'm sure I don't
+really think that's what people had in
+
+ align:start position:0%
+really think that's what people had in
+ 
+
+ align:start position:0%
+really think that's what people had in
+mind it's that you know the the kinds of
+
+ align:start position:0%
+mind it's that you know the the kinds of
+ 
+
+ align:start position:0%
+mind it's that you know the the kinds of
+things that we nor think of being able
+
+ align:start position:0%
+things that we nor think of being able
+ 
+
+ align:start position:0%
+things that we nor think of being able
+to do with a with a rest with a
+
+ align:start position:0%
+to do with a with a rest with a
+ 
+
+ align:start position:0%
+to do with a with a rest with a
+procedure mathematically is exactly the
+
+ align:start position:0%
+procedure mathematically is exactly the
+ 
+
+ align:start position:0%
+procedure mathematically is exactly the
+kinds of things that you can do with a
+
+ align:start position:0%
+kinds of things that you can do with a
+ 
+
+ align:start position:0%
+kinds of things that you can do with a
+touring machine
+
+ align:start position:0%
+touring machine
+ 
+
+ align:start position:0%
+touring machine
+um so somebody's pointing I will trying
+
+ align:start position:0%
+um so somebody's pointing I will trying
+ 
+
+ align:start position:0%
+um so somebody's pointing I will trying
+to be helpful here maybe these folks are
+
+ align:start position:0%
+to be helpful here maybe these folks are
+ 
+
+ align:start position:0%
+to be helpful here maybe these folks are
+asking about equivalence of various
+
+ align:start position:0%
+asking about equivalence of various
+ 
+
+ align:start position:0%
+asking about equivalence of various
+different computation models being
+
+ align:start position:0%
+different computation models being
+ 
+
+ align:start position:0%
+different computation models being
+proved in the book not the church during
+
+ align:start position:0%
+proved in the book not the church during
+ 
+
+ align:start position:0%
+proved in the book not the church during
+thesis itself well I mean that's the the
+
+ align:start position:0%
+thesis itself well I mean that's the the
+ 
+
+ align:start position:0%
+thesis itself well I mean that's the the
+things that we proved in lecture are
+
+ align:start position:0%
+things that we proved in lecture are
+ 
+
+ align:start position:0%
+things that we proved in lecture are
+also proved in the book um about the
+
+ align:start position:0%
+also proved in the book um about the
+ 
+
+ align:start position:0%
+also proved in the book um about the
+equivalent of single tape machines
+
+ align:start position:0%
+equivalent of single tape machines
+ 
+
+ align:start position:0%
+equivalent of single tape machines
+multi-tape machines non-deterministic
+
+ align:start position:0%
+multi-tape machines non-deterministic
+ 
+
+ align:start position:0%
+multi-tape machines non-deterministic
+machines um those are all proved in the
+
+ align:start position:0%
+machines um those are all proved in the
+ 
+
+ align:start position:0%
+machines um those are all proved in the
+book we don't those I mean there's lots
+
+ align:start position:0%
+book we don't those I mean there's lots
+ 
+
+ align:start position:0%
+book we don't those I mean there's lots
+of models out there so we could spend a
+
+ align:start position:0%
+of models out there so we could spend a
+ 
+
+ align:start position:0%
+of models out there so we could spend a
+lot of time proving equivalences um and
+
+ align:start position:0%
+lot of time proving equivalences um and
+ 
+
+ align:start position:0%
+lot of time proving equivalences um and
+there are books that do spend a lot of
+
+ align:start position:0%
+there are books that do spend a lot of
+ 
+
+ align:start position:0%
+there are books that do spend a lot of
+time proving equivalences but I
+
+ align:start position:0%
+time proving equivalences but I
+ 
+
+ align:start position:0%
+time proving equivalences but I
+think you know
+
+ align:start position:0%
+think you know
+ 
+
+ align:start position:0%
+think you know
+uh we yeah I think what we've given is
+
+ align:start position:0%
+uh we yeah I think what we've given is
+ 
+
+ align:start position:0%
+uh we yeah I think what we've given is
+probably enough
+
+ align:start position:0%
+probably enough
+ 
+
+ align:start position:0%
+probably enough
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+uh so somebody that's a good question if
+
+ align:start position:0%
+uh so somebody that's a good question if
+ 
+
+ align:start position:0%
+uh so somebody that's a good question if
+if you give an
+
+ align:start position:0%
+if you give an
+ 
+
+ align:start position:0%
+if you give an
+algorithm okay if you give an algorithm
+
+ align:start position:0%
+algorithm okay if you give an algorithm
+ 
+
+ align:start position:0%
+algorithm okay if you give an algorithm
+you don't need to give the actual
+
+ align:start position:0%
+you don't need to give the actual
+ 
+
+ align:start position:0%
+you don't need to give the actual
+machine uh going forward unless somebody
+
+ align:start position:0%
+machine uh going forward unless somebody
+ 
+
+ align:start position:0%
+machine uh going forward unless somebody
+unless you're explicitly asked to um uh
+
+ align:start position:0%
+unless you're explicitly asked to um uh
+ 
+
+ align:start position:0%
+unless you're explicitly asked to um uh
+but yes you don't you don't have to give
+
+ align:start position:0%
+but yes you don't you don't have to give
+ 
+
+ align:start position:0%
+but yes you don't you don't have to give
+um the states and transitions anymore
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um okay so it's a little after four I
+
+ align:start position:0%
+um okay so it's a little after four I
+ 
+
+ align:start position:0%
+um okay so it's a little after four I
+think we're going
+
+ align:start position:0%
+think we're going
+ 
+
+ align:start position:0%
+think we're going
+to I think I'm going to move on to my
+
+ align:start position:0%
+to I think I'm going to move on to my
+ 
+
+ align:start position:0%
+to I think I'm going to move on to my
+next meeting uh so I uh thank you for
+
+ align:start position:0%
+next meeting uh so I uh thank you for
+ 
+
+ align:start position:0%
+next meeting uh so I uh thank you for
+being here and I will see you um on
+
+ align:start position:0%
+being here and I will see you um on
+ 
+
+ align:start position:0%
+being here and I will see you um on
+Tuesday
\ No newline at end of file
diff --git a/Tpaw_dE9LyY.txt b/Tpaw_dE9LyY.txt
new file mode 100644
index 0000000000000000000000000000000000000000..fa4004820d3accde79ff1080f86a36b98f62cf68
--- /dev/null
+++ b/Tpaw_dE9LyY.txt
@@ -0,0 +1,675 @@
+align:start position:0%
+ 
+I'm pleased to know that our colleagues
+
+ align:start position:0%
+I'm pleased to know that our colleagues
+ 
+
+ align:start position:0%
+I'm pleased to know that our colleagues
+at MIT are reaching out to people all
+
+ align:start position:0%
+at MIT are reaching out to people all
+ 
+
+ align:start position:0%
+at MIT are reaching out to people all
+over the world to engage them in this
+
+ align:start position:0%
+over the world to engage them in this
+ 
+
+ align:start position:0%
+over the world to engage them in this
+important discussion about the future of
+
+ align:start position:0%
+important discussion about the future of
+ 
+
+ align:start position:0%
+important discussion about the future of
+work we are launching our own future of
+
+ align:start position:0%
+work we are launching our own future of
+ 
+
+ align:start position:0%
+work we are launching our own future of
+work initiative here at the io and this
+
+ align:start position:0%
+work initiative here at the io and this
+ 
+
+ align:start position:0%
+work initiative here at the io and this
+course will fit very well with our
+
+ align:start position:0%
+course will fit very well with our
+ 
+
+ align:start position:0%
+course will fit very well with our
+initiative look I think that our future
+
+ align:start position:0%
+initiative look I think that our future
+ 
+
+ align:start position:0%
+initiative look I think that our future
+of work initiative responds to to two
+
+ align:start position:0%
+of work initiative responds to to two
+ 
+
+ align:start position:0%
+of work initiative responds to to two
+essential things one's got to do with
+
+ align:start position:0%
+essential things one's got to do with
+ 
+
+ align:start position:0%
+essential things one's got to do with
+need one's got to do with opportunity uh
+
+ align:start position:0%
+need one's got to do with opportunity uh
+ 
+
+ align:start position:0%
+need one's got to do with opportunity uh
+the need comes from the fact and we're
+
+ align:start position:0%
+the need comes from the fact and we're
+ 
+
+ align:start position:0%
+the need comes from the fact and we're
+all conscious of this in our everyday
+
+ align:start position:0%
+all conscious of this in our everyday
+ 
+
+ align:start position:0%
+all conscious of this in our everyday
+lives that there is massive change
+
+ align:start position:0%
+lives that there is massive change
+ 
+
+ align:start position:0%
+lives that there is massive change
+taking place in the world of work
+
+ align:start position:0%
+taking place in the world of work
+ 
+
+ align:start position:0%
+taking place in the world of work
+transformative change at a Pac and at a
+
+ align:start position:0%
+transformative change at a Pac and at a
+ 
+
+ align:start position:0%
+transformative change at a Pac and at a
+depth that we don't really have
+
+ align:start position:0%
+depth that we don't really have
+ 
+
+ align:start position:0%
+depth that we don't really have
+experience of in the past so we think
+
+ align:start position:0%
+experience of in the past so we think
+ 
+
+ align:start position:0%
+experience of in the past so we think
+that we need to study these big changes
+
+ align:start position:0%
+that we need to study these big changes
+ 
+
+ align:start position:0%
+that we need to study these big changes
+to understand them better as a way of
+
+ align:start position:0%
+to understand them better as a way of
+ 
+
+ align:start position:0%
+to understand them better as a way of
+working out what we should do about them
+
+ align:start position:0%
+working out what we should do about them
+ 
+
+ align:start position:0%
+working out what we should do about them
+uh in order order to make sure that the
+
+ align:start position:0%
+uh in order order to make sure that the
+ 
+
+ align:start position:0%
+uh in order order to make sure that the
+world of work responds to the ilo's
+
+ align:start position:0%
+world of work responds to the ilo's
+ 
+
+ align:start position:0%
+world of work responds to the ilo's
+ideas of social justice fairness at work
+
+ align:start position:0%
+ideas of social justice fairness at work
+ 
+
+ align:start position:0%
+ideas of social justice fairness at work
+and then there is the opportunity and
+
+ align:start position:0%
+and then there is the opportunity and
+ 
+
+ align:start position:0%
+and then there is the opportunity and
+the opportunity comes from the fact that
+
+ align:start position:0%
+the opportunity comes from the fact that
+ 
+
+ align:start position:0%
+the opportunity comes from the fact that
+in in three years time in
+
+ align:start position:0%
+in in three years time in
+ 
+
+ align:start position:0%
+in in three years time in
+2019 the io will celebrate its 100th
+
+ align:start position:0%
+2019 the io will celebrate its 100th
+ 
+
+ align:start position:0%
+2019 the io will celebrate its 100th
+birthday it's centinary so what better
+
+ align:start position:0%
+birthday it's centinary so what better
+ 
+
+ align:start position:0%
+birthday it's centinary so what better
+opportunity they don't come around that
+
+ align:start position:0%
+opportunity they don't come around that
+ 
+
+ align:start position:0%
+opportunity they don't come around that
+frequently what better opportunity than
+
+ align:start position:0%
+frequently what better opportunity than
+ 
+
+ align:start position:0%
+frequently what better opportunity than
+that to have this in-depth reflection
+
+ align:start position:0%
+that to have this in-depth reflection
+ 
+
+ align:start position:0%
+that to have this in-depth reflection
+about the direction that the world of
+
+ align:start position:0%
+about the direction that the world of
+ 
+
+ align:start position:0%
+about the direction that the world of
+work is taking and what we can can do to
+
+ align:start position:0%
+work is taking and what we can can do to
+ 
+
+ align:start position:0%
+work is taking and what we can can do to
+shape it to move it towards these ideals
+
+ align:start position:0%
+shape it to move it towards these ideals
+ 
+
+ align:start position:0%
+shape it to move it towards these ideals
+of social justice we are proposing uh to
+
+ align:start position:0%
+of social justice we are proposing uh to
+ 
+
+ align:start position:0%
+of social justice we are proposing uh to
+Our member states that they structure
+
+ align:start position:0%
+Our member states that they structure
+ 
+
+ align:start position:0%
+Our member states that they structure
+their National dialogues around four
+
+ align:start position:0%
+their National dialogues around four
+ 
+
+ align:start position:0%
+their National dialogues around four
+conversations and very quickly uh one is
+
+ align:start position:0%
+conversations and very quickly uh one is
+ 
+
+ align:start position:0%
+conversations and very quickly uh one is
+to do with work and Society sounds a bit
+
+ align:start position:0%
+to do with work and Society sounds a bit
+ 
+
+ align:start position:0%
+to do with work and Society sounds a bit
+philosophical but I think there are some
+
+ align:start position:0%
+philosophical but I think there are some
+ 
+
+ align:start position:0%
+philosophical but I think there are some
+really deep questions out there about
+
+ align:start position:0%
+really deep questions out there about
+ 
+
+ align:start position:0%
+really deep questions out there about
+what work means to each and every one of
+
+ align:start position:0%
+what work means to each and every one of
+ 
+
+ align:start position:0%
+what work means to each and every one of
+us in terms not only of earning our
+
+ align:start position:0%
+us in terms not only of earning our
+ 
+
+ align:start position:0%
+us in terms not only of earning our
+living but also of self-realization of
+
+ align:start position:0%
+living but also of self-realization of
+ 
+
+ align:start position:0%
+living but also of self-realization of
+our you know what our lives mean and and
+
+ align:start position:0%
+our you know what our lives mean and and
+ 
+
+ align:start position:0%
+our you know what our lives mean and and
+how we want to proceed with them
+
+ align:start position:0%
+how we want to proceed with them
+ 
+
+ align:start position:0%
+how we want to proceed with them
+secondly and it's the most frequently
+
+ align:start position:0%
+secondly and it's the most frequently
+ 
+
+ align:start position:0%
+secondly and it's the most frequently
+Asked question that I at least get about
+
+ align:start position:0%
+Asked question that I at least get about
+ 
+
+ align:start position:0%
+Asked question that I at least get about
+the future is decent work of Tomorrow
+
+ align:start position:0%
+the future is decent work of Tomorrow
+ 
+
+ align:start position:0%
+the future is decent work of Tomorrow
+the decent jobs of tomorrow where are
+
+ align:start position:0%
+the decent jobs of tomorrow where are
+ 
+
+ align:start position:0%
+the decent jobs of tomorrow where are
+those jobs coming from we're having to
+
+ align:start position:0%
+those jobs coming from we're having to
+ 
+
+ align:start position:0%
+those jobs coming from we're having to
+create 40 million jobs every year just
+
+ align:start position:0%
+create 40 million jobs every year just
+ 
+
+ align:start position:0%
+create 40 million jobs every year just
+to absorb the new people coming onto the
+
+ align:start position:0%
+to absorb the new people coming onto the
+ 
+
+ align:start position:0%
+to absorb the new people coming onto the
+labor markets uh and frankly we're not
+
+ align:start position:0%
+labor markets uh and frankly we're not
+ 
+
+ align:start position:0%
+labor markets uh and frankly we're not
+able to do it at the moment so we have
+
+ align:start position:0%
+able to do it at the moment so we have
+ 
+
+ align:start position:0%
+able to do it at the moment so we have
+to be able to discuss the nature and the
+
+ align:start position:0%
+to be able to discuss the nature and the
+ 
+
+ align:start position:0%
+to be able to discuss the nature and the
+origin of work in the future
+
+ align:start position:0%
+origin of work in the future
+ 
+
+ align:start position:0%
+origin of work in the future
+the third item is about the organization
+
+ align:start position:0%
+the third item is about the organization
+ 
+
+ align:start position:0%
+the third item is about the organization
+the organization of work and production
+
+ align:start position:0%
+the organization of work and production
+ 
+
+ align:start position:0%
+the organization of work and production
+you know we're seeing the digital
+
+ align:start position:0%
+you know we're seeing the digital
+ 
+
+ align:start position:0%
+you know we're seeing the digital
+economy take off we're seeing the way
+
+ align:start position:0%
+economy take off we're seeing the way
+ 
+
+ align:start position:0%
+economy take off we're seeing the way
+that the internet is mediating work in
+
+ align:start position:0%
+that the internet is mediating work in
+ 
+
+ align:start position:0%
+that the internet is mediating work in
+entirely new ways uh maybe the
+
+ align:start position:0%
+entirely new ways uh maybe the
+ 
+
+ align:start position:0%
+entirely new ways uh maybe the
+Enterprise is going to look very
+
+ align:start position:0%
+Enterprise is going to look very
+ 
+
+ align:start position:0%
+Enterprise is going to look very
+different in the future from what it
+
+ align:start position:0%
+different in the future from what it
+ 
+
+ align:start position:0%
+different in the future from what it
+looks like today we're seeing the
+
+ align:start position:0%
+looks like today we're seeing the
+ 
+
+ align:start position:0%
+looks like today we're seeing the
+fragmentation and globalization of
+
+ align:start position:0%
+fragmentation and globalization of
+ 
+
+ align:start position:0%
+fragmentation and globalization of
+production systems in Global Supply
+
+ align:start position:0%
+production systems in Global Supply
+ 
+
+ align:start position:0%
+production systems in Global Supply
+chains we need to understand what the
+
+ align:start position:0%
+chains we need to understand what the
+ 
+
+ align:start position:0%
+chains we need to understand what the
+full implications are of this new
+
+ align:start position:0%
+full implications are of this new
+ 
+
+ align:start position:0%
+full implications are of this new
+organization and Global division of
+
+ align:start position:0%
+organization and Global division of
+ 
+
+ align:start position:0%
+organization and Global division of
+labor and the fourth point and this is
+
+ align:start position:0%
+labor and the fourth point and this is
+ 
+
+ align:start position:0%
+labor and the fourth point and this is
+the culminating point of the of the
+
+ align:start position:0%
+the culminating point of the of the
+ 
+
+ align:start position:0%
+the culminating point of the of the
+whole thing we have to say well what are
+
+ align:start position:0%
+whole thing we have to say well what are
+ 
+
+ align:start position:0%
+whole thing we have to say well what are
+the consequences of these changes for
+
+ align:start position:0%
+the consequences of these changes for
+ 
+
+ align:start position:0%
+the consequences of these changes for
+the ilo's Mandate uh for social justice
+
+ align:start position:0%
+the ilo's Mandate uh for social justice
+ 
+
+ align:start position:0%
+the ilo's Mandate uh for social justice
+how can we shape manage all of these
+
+ align:start position:0%
+how can we shape manage all of these
+ 
+
+ align:start position:0%
+how can we shape manage all of these
+changes so that we keep the world moving
+
+ align:start position:0%
+changes so that we keep the world moving
+ 
+
+ align:start position:0%
+changes so that we keep the world moving
+in this direction of social justice so
+
+ align:start position:0%
+in this direction of social justice so
+ 
+
+ align:start position:0%
+in this direction of social justice so
+let me end by encouraging everyone to
+
+ align:start position:0%
+let me end by encouraging everyone to
+ 
+
+ align:start position:0%
+let me end by encouraging everyone to
+join us in using the ideas and the
+
+ align:start position:0%
+join us in using the ideas and the
+ 
+
+ align:start position:0%
+join us in using the ideas and the
+information presented in this course to
+
+ align:start position:0%
+information presented in this course to
+ 
+
+ align:start position:0%
+information presented in this course to
+improve the future of work for people
+
+ align:start position:0%
+improve the future of work for people
+ 
+
+ align:start position:0%
+improve the future of work for people
+all around the world
\ No newline at end of file
diff --git a/UGiED1HPB08.txt b/UGiED1HPB08.txt
new file mode 100644
index 0000000000000000000000000000000000000000..43f0daf047bf8dad950cbdb7f2c2ad93fdd4a63d
--- /dev/null
+++ b/UGiED1HPB08.txt
@@ -0,0 +1,5907 @@
+align:start position:0%
+ 
+the following content is provided under
+
+ align:start position:0%
+the following content is provided under
+ 
+
+ align:start position:0%
+the following content is provided under
+a Creative Commons license your support
+
+ align:start position:0%
+a Creative Commons license your support
+ 
+
+ align:start position:0%
+a Creative Commons license your support
+will help MIT open courseware continue
+
+ align:start position:0%
+will help MIT open courseware continue
+ 
+
+ align:start position:0%
+will help MIT open courseware continue
+to offer highquality educational
+
+ align:start position:0%
+to offer highquality educational
+ 
+
+ align:start position:0%
+to offer highquality educational
+resources for free to make a donation or
+
+ align:start position:0%
+resources for free to make a donation or
+ 
+
+ align:start position:0%
+resources for free to make a donation or
+view additional materials from hundreds
+
+ align:start position:0%
+view additional materials from hundreds
+ 
+
+ align:start position:0%
+view additional materials from hundreds
+of MIT courses visit mitop courseware at
+
+ align:start position:0%
+of MIT courses visit mitop courseware at
+ 
+
+ align:start position:0%
+of MIT courses visit mitop courseware at
+ocw.mit.edu
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+hi today we tackle another facet of
+
+ align:start position:0%
+hi today we tackle another facet of
+ 
+
+ align:start position:0%
+hi today we tackle another facet of
+applications of complex numbers in our
+
+ align:start position:0%
+applications of complex numbers in our
+ 
+
+ align:start position:0%
+applications of complex numbers in our
+survey of our complex variable mini
+
+ align:start position:0%
+survey of our complex variable mini
+ 
+
+ align:start position:0%
+survey of our complex variable mini
+course and in particular what we're
+
+ align:start position:0%
+course and in particular what we're
+ 
+
+ align:start position:0%
+course and in particular what we're
+going to study today is the role of
+
+ align:start position:0%
+going to study today is the role of
+ 
+
+ align:start position:0%
+going to study today is the role of
+infinite series and sequences in complex
+
+ align:start position:0%
+infinite series and sequences in complex
+ 
+
+ align:start position:0%
+infinite series and sequences in complex
+numbers and I call today's lesson
+
+ align:start position:0%
+numbers and I call today's lesson
+ 
+
+ align:start position:0%
+numbers and I call today's lesson
+therefore sequences and series now among
+
+ align:start position:0%
+therefore sequences and series now among
+ 
+
+ align:start position:0%
+therefore sequences and series now among
+other things let's take a look at a p a
+
+ align:start position:0%
+other things let's take a look at a p a
+ 
+
+ align:start position:0%
+other things let's take a look at a p a
+purely pedagogical problem for example
+
+ align:start position:0%
+purely pedagogical problem for example
+ 
+
+ align:start position:0%
+purely pedagogical problem for example
+at this stage of the game notice that I
+
+ align:start position:0%
+at this stage of the game notice that I
+ 
+
+ align:start position:0%
+at this stage of the game notice that I
+can't even talk meaningfully about what
+
+ align:start position:0%
+can't even talk meaningfully about what
+ 
+
+ align:start position:0%
+can't even talk meaningfully about what
+I mean by e to the Z nor by what I mean
+
+ align:start position:0%
+I mean by e to the Z nor by what I mean
+ 
+
+ align:start position:0%
+I mean by e to the Z nor by what I mean
+by sinine Z I can not visualize Z as an
+
+ align:start position:0%
+by sinine Z I can not visualize Z as an
+ 
+
+ align:start position:0%
+by sinine Z I can not visualize Z as an
+angle because it may be imaginary I
+
+ align:start position:0%
+angle because it may be imaginary I
+ 
+
+ align:start position:0%
+angle because it may be imaginary I
+can't visualize it uh as a length in the
+
+ align:start position:0%
+can't visualize it uh as a length in the
+ 
+
+ align:start position:0%
+can't visualize it uh as a length in the
+traditional sense uh that we viewed
+
+ align:start position:0%
+traditional sense uh that we viewed
+ 
+
+ align:start position:0%
+traditional sense uh that we viewed
+functions from real variables into uh
+
+ align:start position:0%
+functions from real variables into uh
+ 
+
+ align:start position:0%
+functions from real variables into uh
+real
+
+ align:start position:0%
+real
+ 
+
+ align:start position:0%
+real
+variables and the question that comes up
+
+ align:start position:0%
+variables and the question that comes up
+ 
+
+ align:start position:0%
+variables and the question that comes up
+is how could I Define e to the Z and sin
+
+ align:start position:0%
+is how could I Define e to the Z and sin
+ 
+
+ align:start position:0%
+is how could I Define e to the Z and sin
+Z in fact the cynic might say why would
+
+ align:start position:0%
+Z in fact the cynic might say why would
+ 
+
+ align:start position:0%
+Z in fact the cynic might say why would
+you want to Define e to the Z and sin Z
+
+ align:start position:0%
+you want to Define e to the Z and sin Z
+ 
+
+ align:start position:0%
+you want to Define e to the Z and sin Z
+Now one very cynical answer to the synic
+
+ align:start position:0%
+Now one very cynical answer to the synic
+ 
+
+ align:start position:0%
+Now one very cynical answer to the synic
+would simply be that one of the most
+
+ align:start position:0%
+would simply be that one of the most
+ 
+
+ align:start position:0%
+would simply be that one of the most
+practical reasons for knowing how to
+
+ align:start position:0%
+practical reasons for knowing how to
+ 
+
+ align:start position:0%
+practical reasons for knowing how to
+define e to the Z and sin Z is that they
+
+ align:start position:0%
+define e to the Z and sin Z is that they
+ 
+
+ align:start position:0%
+define e to the Z and sin Z is that they
+will be on the quiz at the end of this
+
+ align:start position:0%
+will be on the quiz at the end of this
+ 
+
+ align:start position:0%
+will be on the quiz at the end of this
+particular block but that's hardly a
+
+ align:start position:0%
+particular block but that's hardly a
+ 
+
+ align:start position:0%
+particular block but that's hardly a
+fair motivation I will go into this in
+
+ align:start position:0%
+fair motivation I will go into this in
+ 
+
+ align:start position:0%
+fair motivation I will go into this in
+more detail later in the lecture let me
+
+ align:start position:0%
+more detail later in the lecture let me
+ 
+
+ align:start position:0%
+more detail later in the lecture let me
+simply point out that every time we have
+
+ align:start position:0%
+simply point out that every time we have
+ 
+
+ align:start position:0%
+simply point out that every time we have
+an analytic function its real and
+
+ align:start position:0%
+an analytic function its real and
+ 
+
+ align:start position:0%
+an analytic function its real and
+imaginary Parts Define a conformal
+
+ align:start position:0%
+imaginary Parts Define a conformal
+ 
+
+ align:start position:0%
+imaginary Parts Define a conformal
+mapping and consequently every time we
+
+ align:start position:0%
+mapping and consequently every time we
+ 
+
+ align:start position:0%
+mapping and consequently every time we
+can meaningfully invent an analytic
+
+ align:start position:0%
+can meaningfully invent an analytic
+ 
+
+ align:start position:0%
+can meaningfully invent an analytic
+function we have automatically invented
+
+ align:start position:0%
+function we have automatically invented
+ 
+
+ align:start position:0%
+function we have automatically invented
+a new conformal mapping as I say we'll
+
+ align:start position:0%
+a new conformal mapping as I say we'll
+ 
+
+ align:start position:0%
+a new conformal mapping as I say we'll
+go into that in more detail as we go
+
+ align:start position:0%
+go into that in more detail as we go
+ 
+
+ align:start position:0%
+go into that in more detail as we go
+along but the question that now comes up
+
+ align:start position:0%
+along but the question that now comes up
+ 
+
+ align:start position:0%
+along but the question that now comes up
+is how can I define e to the Z how can I
+
+ align:start position:0%
+is how can I define e to the Z how can I
+ 
+
+ align:start position:0%
+is how can I define e to the Z how can I
+define s z Kos Z all of these things and
+
+ align:start position:0%
+define s z Kos Z all of these things and
+ 
+
+ align:start position:0%
+define s z Kos Z all of these things and
+one of the best ways of beginning is
+
+ align:start position:0%
+one of the best ways of beginning is
+ 
+
+ align:start position:0%
+one of the best ways of beginning is
+again again to emphasize something that
+
+ align:start position:0%
+again again to emphasize something that
+ 
+
+ align:start position:0%
+again again to emphasize something that
+we said in one of our earlier lectures
+
+ align:start position:0%
+we said in one of our earlier lectures
+ 
+
+ align:start position:0%
+we said in one of our earlier lectures
+on complex numbers that whatever
+
+ align:start position:0%
+on complex numbers that whatever
+ 
+
+ align:start position:0%
+on complex numbers that whatever
+definitions we invent we want to make
+
+ align:start position:0%
+definitions we invent we want to make
+ 
+
+ align:start position:0%
+definitions we invent we want to make
+sure that the new definition does not
+
+ align:start position:0%
+sure that the new definition does not
+ 
+
+ align:start position:0%
+sure that the new definition does not
+contradict the old one in other words
+
+ align:start position:0%
+contradict the old one in other words
+ 
+
+ align:start position:0%
+contradict the old one in other words
+whatever definition I give of e to the Z
+
+ align:start position:0%
+whatever definition I give of e to the Z
+ 
+
+ align:start position:0%
+whatever definition I give of e to the Z
+I want to make sure that if Z happens to
+
+ align:start position:0%
+I want to make sure that if Z happens to
+ 
+
+ align:start position:0%
+I want to make sure that if Z happens to
+be real if I replace Z by X that e to
+
+ align:start position:0%
+be real if I replace Z by X that e to
+ 
+
+ align:start position:0%
+be real if I replace Z by X that e to
+the X has the same meaning whether I
+
+ align:start position:0%
+the X has the same meaning whether I
+ 
+
+ align:start position:0%
+the X has the same meaning whether I
+view X as a real number or whether I
+
+ align:start position:0%
+view X as a real number or whether I
+ 
+
+ align:start position:0%
+view X as a real number or whether I
+view it as a complex number now now one
+
+ align:start position:0%
+view it as a complex number now now one
+ 
+
+ align:start position:0%
+view it as a complex number now now one
+of the standard ways of doing something
+
+ align:start position:0%
+of the standard ways of doing something
+ 
+
+ align:start position:0%
+of the standard ways of doing something
+like this is the following we in part
+
+ align:start position:0%
+like this is the following we in part
+ 
+
+ align:start position:0%
+like this is the following we in part
+one of our course had shown that the
+
+ align:start position:0%
+one of our course had shown that the
+ 
+
+ align:start position:0%
+one of our course had shown that the
+power series representation for e to the
+
+ align:start position:0%
+power series representation for e to the
+ 
+
+ align:start position:0%
+power series representation for e to the
+X was given by this infinite Series
+
+ align:start position:0%
+X was given by this infinite Series
+ 
+
+ align:start position:0%
+X was given by this infinite Series
+where this infinite series converged to
+
+ align:start position:0%
+where this infinite series converged to
+ 
+
+ align:start position:0%
+where this infinite series converged to
+e to the X for all real values of X now
+
+ align:start position:0%
+e to the X for all real values of X now
+ 
+
+ align:start position:0%
+e to the X for all real values of X now
+what we can therefore say is look at if
+
+ align:start position:0%
+what we can therefore say is look at if
+ 
+
+ align:start position:0%
+what we can therefore say is look at if
+I just verbatim every place I see an X
+
+ align:start position:0%
+I just verbatim every place I see an X
+ 
+
+ align:start position:0%
+I just verbatim every place I see an X
+replace that by a z and and now make up
+
+ align:start position:0%
+replace that by a z and and now make up
+ 
+
+ align:start position:0%
+replace that by a z and and now make up
+the definition that e to the Z will be
+
+ align:start position:0%
+the definition that e to the Z will be
+ 
+
+ align:start position:0%
+the definition that e to the Z will be
+summation n goes from 0 to Infinity Z to
+
+ align:start position:0%
+summation n goes from 0 to Infinity Z to
+ 
+
+ align:start position:0%
+summation n goes from 0 to Infinity Z to
+the N / n factorial then no matter what
+
+ align:start position:0%
+the N / n factorial then no matter what
+ 
+
+ align:start position:0%
+the N / n factorial then no matter what
+else happens I'm sure that my definition
+
+ align:start position:0%
+else happens I'm sure that my definition
+ 
+
+ align:start position:0%
+else happens I'm sure that my definition
+of e to the Z must agree with my
+
+ align:start position:0%
+of e to the Z must agree with my
+ 
+
+ align:start position:0%
+of e to the Z must agree with my
+definition of e to the X whenever Z and
+
+ align:start position:0%
+definition of e to the X whenever Z and
+ 
+
+ align:start position:0%
+definition of e to the X whenever Z and
+X are equal in other words whenever Z
+
+ align:start position:0%
+X are equal in other words whenever Z
+ 
+
+ align:start position:0%
+X are equal in other words whenever Z
+happens to denote a real number why is
+
+ align:start position:0%
+happens to denote a real number why is
+ 
+
+ align:start position:0%
+happens to denote a real number why is
+that the case because I got the new
+
+ align:start position:0%
+that the case because I got the new
+ 
+
+ align:start position:0%
+that the case because I got the new
+definition by lifting it from the old
+
+ align:start position:0%
+definition by lifting it from the old
+ 
+
+ align:start position:0%
+definition by lifting it from the old
+just replacing X by a z the question
+
+ align:start position:0%
+just replacing X by a z the question
+ 
+
+ align:start position:0%
+just replacing X by a z the question
+that comes up of course is what do you
+
+ align:start position:0%
+that comes up of course is what do you
+ 
+
+ align:start position:0%
+that comes up of course is what do you
+mean by this expression what do you mean
+
+ align:start position:0%
+mean by this expression what do you mean
+ 
+
+ align:start position:0%
+mean by this expression what do you mean
+by a series when you're dealing with
+
+ align:start position:0%
+by a series when you're dealing with
+ 
+
+ align:start position:0%
+by a series when you're dealing with
+complex numbers in particular what it
+
+ align:start position:0%
+complex numbers in particular what it
+ 
+
+ align:start position:0%
+complex numbers in particular what it
+means is is that given a sequence of
+
+ align:start position:0%
+means is is that given a sequence of
+ 
+
+ align:start position:0%
+means is is that given a sequence of
+complex numbers I must Define what I
+
+ align:start position:0%
+complex numbers I must Define what I
+ 
+
+ align:start position:0%
+complex numbers I must Define what I
+mean by a limit and then go through this
+
+ align:start position:0%
+mean by a limit and then go through this
+ 
+
+ align:start position:0%
+mean by a limit and then go through this
+idea of defining a series to be a
+
+ align:start position:0%
+idea of defining a series to be a
+ 
+
+ align:start position:0%
+idea of defining a series to be a
+sequence of partial sums and going
+
+ align:start position:0%
+sequence of partial sums and going
+ 
+
+ align:start position:0%
+sequence of partial sums and going
+through the same bit structurally that I
+
+ align:start position:0%
+through the same bit structurally that I
+ 
+
+ align:start position:0%
+through the same bit structurally that I
+went through in the real case
+
+ align:start position:0%
+went through in the real case
+ 
+
+ align:start position:0%
+went through in the real case
+now let's do something that I think is
+
+ align:start position:0%
+now let's do something that I think is
+ 
+
+ align:start position:0%
+now let's do something that I think is
+very interesting over here let's just
+
+ align:start position:0%
+very interesting over here let's just
+ 
+
+ align:start position:0%
+very interesting over here let's just
+write down what the diff the definition
+
+ align:start position:0%
+write down what the diff the definition
+ 
+
+ align:start position:0%
+write down what the diff the definition
+was for a limit of a sequence a subn to
+
+ align:start position:0%
+was for a limit of a sequence a subn to
+ 
+
+ align:start position:0%
+was for a limit of a sequence a subn to
+equal L as n went to Infinity what was
+
+ align:start position:0%
+equal L as n went to Infinity what was
+ 
+
+ align:start position:0%
+equal L as n went to Infinity what was
+that definition in the real case limit
+
+ align:start position:0%
+that definition in the real case limit
+ 
+
+ align:start position:0%
+that definition in the real case limit
+as n approaches Infinity a subn equals l
+
+ align:start position:0%
+as n approaches Infinity a subn equals l
+ 
+
+ align:start position:0%
+as n approaches Infinity a subn equals l
+means given any Epsilon greater than
+
+ align:start position:0%
+means given any Epsilon greater than
+ 
+
+ align:start position:0%
+means given any Epsilon greater than
+zero there exists a capital N such that
+
+ align:start position:0%
+zero there exists a capital N such that
+ 
+
+ align:start position:0%
+zero there exists a capital N such that
+whenever little n exceeds capital N the
+
+ align:start position:0%
+whenever little n exceeds capital N the
+ 
+
+ align:start position:0%
+whenever little n exceeds capital N the
+absolute value of a subn minus L is less
+
+ align:start position:0%
+absolute value of a subn minus L is less
+ 
+
+ align:start position:0%
+absolute value of a subn minus L is less
+than Epsilon I hope this is very
+
+ align:start position:0%
+than Epsilon I hope this is very
+ 
+
+ align:start position:0%
+than Epsilon I hope this is very
+familiar to you if not feel free to
+
+ align:start position:0%
+familiar to you if not feel free to
+ 
+
+ align:start position:0%
+familiar to you if not feel free to
+review it but here is the interesting
+
+ align:start position:0%
+review it but here is the interesting
+ 
+
+ align:start position:0%
+review it but here is the interesting
+point no place in here do I mention that
+
+ align:start position:0%
+point no place in here do I mention that
+ 
+
+ align:start position:0%
+point no place in here do I mention that
+as sa Ben and L have to be real numbers
+
+ align:start position:0%
+as sa Ben and L have to be real numbers
+ 
+
+ align:start position:0%
+as sa Ben and L have to be real numbers
+in other words when I made up this
+
+ align:start position:0%
+in other words when I made up this
+ 
+
+ align:start position:0%
+in other words when I made up this
+definition I assumed that they were but
+
+ align:start position:0%
+definition I assumed that they were but
+ 
+
+ align:start position:0%
+definition I assumed that they were but
+notice that no place in here in this
+
+ align:start position:0%
+notice that no place in here in this
+ 
+
+ align:start position:0%
+notice that no place in here in this
+definition do I say that Asen and L are
+
+ align:start position:0%
+definition do I say that Asen and L are
+ 
+
+ align:start position:0%
+definition do I say that Asen and L are
+real in fact where are the only places
+
+ align:start position:0%
+real in fact where are the only places
+ 
+
+ align:start position:0%
+real in fact where are the only places
+that I use realness that since Epsilon
+
+ align:start position:0%
+that I use realness that since Epsilon
+ 
+
+ align:start position:0%
+that I use realness that since Epsilon
+is real I would like to believe that no
+
+ align:start position:0%
+is real I would like to believe that no
+ 
+
+ align:start position:0%
+is real I would like to believe that no
+matter what Ace and LR that the
+
+ align:start position:0%
+matter what Ace and LR that the
+ 
+
+ align:start position:0%
+matter what Ace and LR that the
+magnitude the absolute value of a subn
+
+ align:start position:0%
+magnitude the absolute value of a subn
+ 
+
+ align:start position:0%
+magnitude the absolute value of a subn
+minus L must be less than Epsilon means
+
+ align:start position:0%
+minus L must be less than Epsilon means
+ 
+
+ align:start position:0%
+minus L must be less than Epsilon means
+that the magnitude of a subn minus L
+
+ align:start position:0%
+that the magnitude of a subn minus L
+ 
+
+ align:start position:0%
+that the magnitude of a subn minus L
+must be a real number among other things
+
+ align:start position:0%
+must be a real number among other things
+ 
+
+ align:start position:0%
+must be a real number among other things
+in fact preferably a positive real
+
+ align:start position:0%
+in fact preferably a positive real
+ 
+
+ align:start position:0%
+in fact preferably a positive real
+number notice that the magnitude of a
+
+ align:start position:0%
+number notice that the magnitude of a
+ 
+
+ align:start position:0%
+number notice that the magnitude of a
+complex number is still a non- negative
+
+ align:start position:0%
+complex number is still a non- negative
+ 
+
+ align:start position:0%
+complex number is still a non- negative
+real consequently even if a subn and L
+
+ align:start position:0%
+real consequently even if a subn and L
+ 
+
+ align:start position:0%
+real consequently even if a subn and L
+are complex this definition still holds
+
+ align:start position:0%
+are complex this definition still holds
+ 
+
+ align:start position:0%
+are complex this definition still holds
+and in fact the pictorial interpretation
+
+ align:start position:0%
+and in fact the pictorial interpretation
+ 
+
+ align:start position:0%
+and in fact the pictorial interpretation
+of the definition holds precisely the
+
+ align:start position:0%
+of the definition holds precisely the
+ 
+
+ align:start position:0%
+of the definition holds precisely the
+same as the did in the real case except
+
+ align:start position:0%
+same as the did in the real case except
+ 
+
+ align:start position:0%
+same as the did in the real case except
+that an Epsilon neighborhood of L is an
+
+ align:start position:0%
+that an Epsilon neighborhood of L is an
+ 
+
+ align:start position:0%
+that an Epsilon neighborhood of L is an
+interval in the real case and it's a
+
+ align:start position:0%
+interval in the real case and it's a
+ 
+
+ align:start position:0%
+interval in the real case and it's a
+circle a disc I shouldn't say a circle
+
+ align:start position:0%
+circle a disc I shouldn't say a circle
+ 
+
+ align:start position:0%
+circle a disc I shouldn't say a circle
+remember the circle is the circum the
+
+ align:start position:0%
+remember the circle is the circum the
+ 
+
+ align:start position:0%
+remember the circle is the circum the
+thing we call the circumference the dis
+
+ align:start position:0%
+thing we call the circumference the dis
+ 
+
+ align:start position:0%
+thing we call the circumference the dis
+is the inside of the circle the uh the
+
+ align:start position:0%
+is the inside of the circle the uh the
+ 
+
+ align:start position:0%
+is the inside of the circle the uh the
+neighborhood is a dis in the complex
+
+ align:start position:0%
+neighborhood is a dis in the complex
+ 
+
+ align:start position:0%
+neighborhood is a dis in the complex
+case namely notice that to say that the
+
+ align:start position:0%
+case namely notice that to say that the
+ 
+
+ align:start position:0%
+case namely notice that to say that the
+absolute value of a subn minus L is less
+
+ align:start position:0%
+absolute value of a subn minus L is less
+ 
+
+ align:start position:0%
+absolute value of a subn minus L is less
+than Epsilon still means that a subn is
+
+ align:start position:0%
+than Epsilon still means that a subn is
+ 
+
+ align:start position:0%
+than Epsilon still means that a subn is
+with an Epsilon of L the difference is
+
+ align:start position:0%
+with an Epsilon of L the difference is
+ 
+
+ align:start position:0%
+with an Epsilon of L the difference is
+that the domain of L is now the XY plane
+
+ align:start position:0%
+that the domain of L is now the XY plane
+ 
+
+ align:start position:0%
+that the domain of L is now the XY plane
+the Aon diagram so to be with an Epsilon
+
+ align:start position:0%
+the Aon diagram so to be with an Epsilon
+ 
+
+ align:start position:0%
+the Aon diagram so to be with an Epsilon
+of l i now take a circle centered at L
+
+ align:start position:0%
+of l i now take a circle centered at L
+ 
+
+ align:start position:0%
+of l i now take a circle centered at L
+with radius Epsilon and draw that Circle
+
+ align:start position:0%
+with radius Epsilon and draw that Circle
+ 
+
+ align:start position:0%
+with radius Epsilon and draw that Circle
+and what I'm saying is that if the limit
+
+ align:start position:0%
+and what I'm saying is that if the limit
+ 
+
+ align:start position:0%
+and what I'm saying is that if the limit
+of the sequence is L after a certain
+
+ align:start position:0%
+of the sequence is L after a certain
+ 
+
+ align:start position:0%
+of the sequence is L after a certain
+number of terms all the remaining terms
+
+ align:start position:0%
+number of terms all the remaining terms
+ 
+
+ align:start position:0%
+number of terms all the remaining terms
+are inside this circle in other words
+
+ align:start position:0%
+are inside this circle in other words
+ 
+
+ align:start position:0%
+are inside this circle in other words
+just as in the real case in the complex
+
+ align:start position:0%
+just as in the real case in the complex
+ 
+
+ align:start position:0%
+just as in the real case in the complex
+case the limit replaces an infinite
+
+ align:start position:0%
+case the limit replaces an infinite
+ 
+
+ align:start position:0%
+case the limit replaces an infinite
+number of points DOT uh numbers you see
+
+ align:start position:0%
+number of points DOT uh numbers you see
+ 
+
+ align:start position:0%
+number of points DOT uh numbers you see
+an infinite number of points by a finite
+
+ align:start position:0%
+an infinite number of points by a finite
+ 
+
+ align:start position:0%
+an infinite number of points by a finite
+number plus one dot in other words
+
+ align:start position:0%
+number plus one dot in other words
+ 
+
+ align:start position:0%
+number plus one dot in other words
+there's a bunch of numbers that may lie
+
+ align:start position:0%
+there's a bunch of numbers that may lie
+ 
+
+ align:start position:0%
+there's a bunch of numbers that may lie
+outside the circle but after a point
+
+ align:start position:0%
+outside the circle but after a point
+ 
+
+ align:start position:0%
+outside the circle but after a point
+after a certain term all of the
+
+ align:start position:0%
+after a certain term all of the
+ 
+
+ align:start position:0%
+after a certain term all of the
+remaining terms lie inside this
+
+ align:start position:0%
+remaining terms lie inside this
+ 
+
+ align:start position:0%
+remaining terms lie inside this
+particular dis and structurally you see
+
+ align:start position:0%
+particular dis and structurally you see
+ 
+
+ align:start position:0%
+particular dis and structurally you see
+that's exactly the same thing that
+
+ align:start position:0%
+that's exactly the same thing that
+ 
+
+ align:start position:0%
+that's exactly the same thing that
+happen in the real case consequently
+
+ align:start position:0%
+happen in the real case consequently
+ 
+
+ align:start position:0%
+happen in the real case consequently
+since the structural definition is the
+
+ align:start position:0%
+since the structural definition is the
+ 
+
+ align:start position:0%
+since the structural definition is the
+same since the geometric interpretation
+
+ align:start position:0%
+same since the geometric interpretation
+ 
+
+ align:start position:0%
+same since the geometric interpretation
+is the same except that diss have
+
+ align:start position:0%
+is the same except that diss have
+ 
+
+ align:start position:0%
+is the same except that diss have
+replaced
+
+ align:start position:0%
+replaced
+ 
+
+ align:start position:0%
+replaced
+intervals I would expect that all the
+
+ align:start position:0%
+intervals I would expect that all the
+ 
+
+ align:start position:0%
+intervals I would expect that all the
+limit theorems held just as in the real
+
+ align:start position:0%
+limit theorems held just as in the real
+ 
+
+ align:start position:0%
+limit theorems held just as in the real
+case and indeed they do and we'll talk
+
+ align:start position:0%
+case and indeed they do and we'll talk
+ 
+
+ align:start position:0%
+case and indeed they do and we'll talk
+about those in the exercises in a
+
+ align:start position:0%
+about those in the exercises in a
+ 
+
+ align:start position:0%
+about those in the exercises in a
+similar way though that we went from
+
+ align:start position:0%
+similar way though that we went from
+ 
+
+ align:start position:0%
+similar way though that we went from
+sequences to Series in the real case we
+
+ align:start position:0%
+sequences to Series in the real case we
+ 
+
+ align:start position:0%
+sequences to Series in the real case we
+can now do the same thing in the complex
+
+ align:start position:0%
+can now do the same thing in the complex
+ 
+
+ align:start position:0%
+can now do the same thing in the complex
+case namely suppose C1 C2 C3 ETC
+
+ align:start position:0%
+case namely suppose C1 C2 C3 ETC
+ 
+
+ align:start position:0%
+case namely suppose C1 C2 C3 ETC
+represent a sequence of complex numbers
+
+ align:start position:0%
+represent a sequence of complex numbers
+ 
+
+ align:start position:0%
+represent a sequence of complex numbers
+by the infinite sum n goes from 1 to
+
+ align:start position:0%
+by the infinite sum n goes from 1 to
+ 
+
+ align:start position:0%
+by the infinite sum n goes from 1 to
+Infinity C subn I simply mean the limit
+
+ align:start position:0%
+Infinity C subn I simply mean the limit
+ 
+
+ align:start position:0%
+Infinity C subn I simply mean the limit
+as n goes to Infinity C1 plus Etc CN
+
+ align:start position:0%
+as n goes to Infinity C1 plus Etc CN
+ 
+
+ align:start position:0%
+as n goes to Infinity C1 plus Etc CN
+noticing that this is what one number it
+
+ align:start position:0%
+noticing that this is what one number it
+ 
+
+ align:start position:0%
+noticing that this is what one number it
+depends on n and it's what you call the
+
+ align:start position:0%
+depends on n and it's what you call the
+ 
+
+ align:start position:0%
+depends on n and it's what you call the
+nth partial sum of the series that we've
+
+ align:start position:0%
+nth partial sum of the series that we've
+ 
+
+ align:start position:0%
+nth partial sum of the series that we've
+added up C1 through CN the next term
+
+ align:start position:0%
+added up C1 through CN the next term
+ 
+
+ align:start position:0%
+added up C1 through CN the next term
+would be obtained by adding on CN C subn
+
+ align:start position:0%
+would be obtained by adding on CN C subn
+ 
+
+ align:start position:0%
+would be obtained by adding on CN C subn
+plus 1 Etc but notice again the similar
+
+ align:start position:0%
+plus 1 Etc but notice again the similar
+ 
+
+ align:start position:0%
+plus 1 Etc but notice again the similar
+structure and consequently the usual
+
+ align:start position:0%
+structure and consequently the usual
+ 
+
+ align:start position:0%
+structure and consequently the usual
+theorems for series that apply to the
+
+ align:start position:0%
+theorems for series that apply to the
+ 
+
+ align:start position:0%
+theorems for series that apply to the
+real variable case apply to the complex
+
+ align:start position:0%
+real variable case apply to the complex
+ 
+
+ align:start position:0%
+real variable case apply to the complex
+variable case again what's the only
+
+ align:start position:0%
+variable case again what's the only
+ 
+
+ align:start position:0%
+variable case again what's the only
+difference the only difference will be
+
+ align:start position:0%
+difference the only difference will be
+ 
+
+ align:start position:0%
+difference the only difference will be
+that intervals of convergence will be
+
+ align:start position:0%
+that intervals of convergence will be
+ 
+
+ align:start position:0%
+that intervals of convergence will be
+replaced by diss or Circles of
+
+ align:start position:0%
+replaced by diss or Circles of
+ 
+
+ align:start position:0%
+replaced by diss or Circles of
+convergence in particular if we let s
+
+ align:start position:0%
+convergence in particular if we let s
+ 
+
+ align:start position:0%
+convergence in particular if we let s
+denote the set of all complex numberers
+
+ align:start position:0%
+denote the set of all complex numberers
+ 
+
+ align:start position:0%
+denote the set of all complex numberers
+Z for which the power series summation a
+
+ align:start position:0%
+Z for which the power series summation a
+ 
+
+ align:start position:0%
+Z for which the power series summation a
+n z to the N converges then just as in
+
+ align:start position:0%
+n z to the N converges then just as in
+ 
+
+ align:start position:0%
+n z to the N converges then just as in
+the real case one of three things must
+
+ align:start position:0%
+the real case one of three things must
+ 
+
+ align:start position:0%
+the real case one of three things must
+happen namely either s consists solely
+
+ align:start position:0%
+happen namely either s consists solely
+ 
+
+ align:start position:0%
+happen namely either s consists solely
+of zero see obviously if I replace Z by
+
+ align:start position:0%
+of zero see obviously if I replace Z by
+ 
+
+ align:start position:0%
+of zero see obviously if I replace Z by
+Zer this thing converges it's
+
+ align:start position:0%
+Zer this thing converges it's
+ 
+
+ align:start position:0%
+Zer this thing converges it's
+identically zero in fact or it may be
+
+ align:start position:0%
+identically zero in fact or it may be
+ 
+
+ align:start position:0%
+identically zero in fact or it may be
+such that these terms go to zero so
+
+ align:start position:0%
+such that these terms go to zero so
+ 
+
+ align:start position:0%
+such that these terms go to zero so
+rapidly that this will converge for all
+
+ align:start position:0%
+rapidly that this will converge for all
+ 
+
+ align:start position:0%
+rapidly that this will converge for all
+complex numb C in other words that the
+
+ align:start position:0%
+complex numb C in other words that the
+ 
+
+ align:start position:0%
+complex numb C in other words that the
+in that the set s can be all complex
+
+ align:start position:0%
+in that the set s can be all complex
+ 
+
+ align:start position:0%
+in that the set s can be all complex
+numbers usually you'll get something in
+
+ align:start position:0%
+numbers usually you'll get something in
+ 
+
+ align:start position:0%
+numbers usually you'll get something in
+between these two extremes and that's
+
+ align:start position:0%
+between these two extremes and that's
+ 
+
+ align:start position:0%
+between these two extremes and that's
+the case like just in the real case
+
+ align:start position:0%
+the case like just in the real case
+ 
+
+ align:start position:0%
+the case like just in the real case
+there exists a number capital r than
+
+ align:start position:0%
+there exists a number capital r than
+ 
+
+ align:start position:0%
+there exists a number capital r than
+zero such that the set s consists of all
+
+ align:start position:0%
+zero such that the set s consists of all
+ 
+
+ align:start position:0%
+zero such that the set s consists of all
+of those Z's such that the absolute
+
+ align:start position:0%
+of those Z's such that the absolute
+ 
+
+ align:start position:0%
+of those Z's such that the absolute
+value of Z is less than R and by the way
+
+ align:start position:0%
+value of Z is less than R and by the way
+ 
+
+ align:start position:0%
+value of Z is less than R and by the way
+what does this mean geometrically the
+
+ align:start position:0%
+what does this mean geometrically the
+ 
+
+ align:start position:0%
+what does this mean geometrically the
+absolute value of Z is the magnitude of
+
+ align:start position:0%
+absolute value of Z is the magnitude of
+ 
+
+ align:start position:0%
+absolute value of Z is the magnitude of
+Z that's the distance of Z from the
+
+ align:start position:0%
+Z that's the distance of Z from the
+ 
+
+ align:start position:0%
+Z that's the distance of Z from the
+origin this says that Z is within
+
+ align:start position:0%
+origin this says that Z is within
+ 
+
+ align:start position:0%
+origin this says that Z is within
+capital r of the origin that means
+
+ align:start position:0%
+capital r of the origin that means
+ 
+
+ align:start position:0%
+capital r of the origin that means
+you're inside the circle centered at the
+
+ align:start position:0%
+you're inside the circle centered at the
+ 
+
+ align:start position:0%
+you're inside the circle centered at the
+origin with radius r at any rate going
+
+ align:start position:0%
+origin with radius r at any rate going
+ 
+
+ align:start position:0%
+origin with radius r at any rate going
+on the convergence is both absolute and
+
+ align:start position:0%
+on the convergence is both absolute and
+ 
+
+ align:start position:0%
+on the convergence is both absolute and
+uniform in any interior disc in other
+
+ align:start position:0%
+uniform in any interior disc in other
+ 
+
+ align:start position:0%
+uniform in any interior disc in other
+words inside the disc absolute value of
+
+ align:start position:0%
+words inside the disc absolute value of
+ 
+
+ align:start position:0%
+words inside the disc absolute value of
+Z is less than or equal to little r
+
+ align:start position:0%
+Z is less than or equal to little r
+ 
+
+ align:start position:0%
+Z is less than or equal to little r
+where little r is less than capital r
+
+ align:start position:0%
+where little r is less than capital r
+ 
+
+ align:start position:0%
+where little r is less than capital r
+again in terms of a picture what we're
+
+ align:start position:0%
+again in terms of a picture what we're
+ 
+
+ align:start position:0%
+again in terms of a picture what we're
+saying is if the first two conditions
+
+ align:start position:0%
+saying is if the first two conditions
+ 
+
+ align:start position:0%
+saying is if the first two conditions
+don't hold given a power series at the
+
+ align:start position:0%
+don't hold given a power series at the
+ 
+
+ align:start position:0%
+don't hold given a power series at the
+origin I draw a circle I don't draw a
+
+ align:start position:0%
+origin I draw a circle I don't draw a
+ 
+
+ align:start position:0%
+origin I draw a circle I don't draw a
+circle what I'm saying is there exists a
+
+ align:start position:0%
+circle what I'm saying is there exists a
+ 
+
+ align:start position:0%
+circle what I'm saying is there exists a
+circle such that the power series will
+
+ align:start position:0%
+circle such that the power series will
+ 
+
+ align:start position:0%
+circle such that the power series will
+converge every place inside here it will
+
+ align:start position:0%
+converge every place inside here it will
+ 
+
+ align:start position:0%
+converge every place inside here it will
+diverge every place outside here and
+
+ align:start position:0%
+diverge every place outside here and
+ 
+
+ align:start position:0%
+diverge every place outside here and
+what happens on the boundary must be
+
+ align:start position:0%
+what happens on the boundary must be
+ 
+
+ align:start position:0%
+what happens on the boundary must be
+investigated separately again just as in
+
+ align:start position:0%
+investigated separately again just as in
+ 
+
+ align:start position:0%
+investigated separately again just as in
+the real case okay that's what the key
+
+ align:start position:0%
+the real case okay that's what the key
+ 
+
+ align:start position:0%
+the real case okay that's what the key
+theorem is and again you'll have time to
+
+ align:start position:0%
+theorem is and again you'll have time to
+ 
+
+ align:start position:0%
+theorem is and again you'll have time to
+reread this and to digest it in your
+
+ align:start position:0%
+reread this and to digest it in your
+ 
+
+ align:start position:0%
+reread this and to digest it in your
+leisure before you try the
+
+ align:start position:0%
+leisure before you try the
+ 
+
+ align:start position:0%
+leisure before you try the
+exercises now once we've defined what we
+
+ align:start position:0%
+exercises now once we've defined what we
+ 
+
+ align:start position:0%
+exercises now once we've defined what we
+mean by a power series and notice by the
+
+ align:start position:0%
+mean by a power series and notice by the
+ 
+
+ align:start position:0%
+mean by a power series and notice by the
+way that absolute convergence goes
+
+ align:start position:0%
+way that absolute convergence goes
+ 
+
+ align:start position:0%
+way that absolute convergence goes
+through word for word in the complex
+
+ align:start position:0%
+through word for word in the complex
+ 
+
+ align:start position:0%
+through word for word in the complex
+valued case because after all in terms
+
+ align:start position:0%
+valued case because after all in terms
+ 
+
+ align:start position:0%
+valued case because after all in terms
+of absolute convergence we look at
+
+ align:start position:0%
+of absolute convergence we look at
+ 
+
+ align:start position:0%
+of absolute convergence we look at
+absolute values and absolute values are
+
+ align:start position:0%
+absolute values and absolute values are
+ 
+
+ align:start position:0%
+absolute values and absolute values are
+non- negative reals regardless of
+
+ align:start position:0%
+non- negative reals regardless of
+ 
+
+ align:start position:0%
+non- negative reals regardless of
+whether the thing that we're looking at
+
+ align:start position:0%
+whether the thing that we're looking at
+ 
+
+ align:start position:0%
+whether the thing that we're looking at
+happen to be complex numbers or real
+
+ align:start position:0%
+happen to be complex numbers or real
+ 
+
+ align:start position:0%
+happen to be complex numbers or real
+numbers to begin with magnitudes are
+
+ align:start position:0%
+numbers to begin with magnitudes are
+ 
+
+ align:start position:0%
+numbers to begin with magnitudes are
+non- negative at any rate one can then
+
+ align:start position:0%
+non- negative at any rate one can then
+ 
+
+ align:start position:0%
+non- negative at any rate one can then
+show in precisely the same way that we
+
+ align:start position:0%
+show in precisely the same way that we
+ 
+
+ align:start position:0%
+show in precisely the same way that we
+did it in the real variable case that
+
+ align:start position:0%
+did it in the real variable case that
+ 
+
+ align:start position:0%
+did it in the real variable case that
+this particular power series see forget
+
+ align:start position:0%
+this particular power series see forget
+ 
+
+ align:start position:0%
+this particular power series see forget
+about this being e to the Z right now I
+
+ align:start position:0%
+about this being e to the Z right now I
+ 
+
+ align:start position:0%
+about this being e to the Z right now I
+make up this power series I use the
+
+ align:start position:0%
+make up this power series I use the
+ 
+
+ align:start position:0%
+make up this power series I use the
+ratio test and I can show by the ratio
+
+ align:start position:0%
+ratio test and I can show by the ratio
+ 
+
+ align:start position:0%
+ratio test and I can show by the ratio
+test that this series converges
+
+ align:start position:0%
+test that this series converges
+ 
+
+ align:start position:0%
+test that this series converges
+uniformly and absolutely for all real
+
+ align:start position:0%
+uniformly and absolutely for all real
+ 
+
+ align:start position:0%
+uniformly and absolutely for all real
+values of Z which I I'm sorry for all
+
+ align:start position:0%
+values of Z which I I'm sorry for all
+ 
+
+ align:start position:0%
+values of Z which I I'm sorry for all
+finite values of Z I don't mean real
+
+ align:start position:0%
+finite values of Z I don't mean real
+ 
+
+ align:start position:0%
+finite values of Z I don't mean real
+values I mean finite values Z does not
+
+ align:start position:0%
+values I mean finite values Z does not
+ 
+
+ align:start position:0%
+values I mean finite values Z does not
+have to be real okay now what I say is
+
+ align:start position:0%
+have to be real okay now what I say is
+ 
+
+ align:start position:0%
+have to be real okay now what I say is
+because this is uniformly convergent
+
+ align:start position:0%
+because this is uniformly convergent
+ 
+
+ align:start position:0%
+because this is uniformly convergent
+this power series behaves like a
+
+ align:start position:0%
+this power series behaves like a
+ 
+
+ align:start position:0%
+this power series behaves like a
+polinomial I can differentiate a term by
+
+ align:start position:0%
+polinomial I can differentiate a term by
+ 
+
+ align:start position:0%
+polinomial I can differentiate a term by
+term I can integrate a term by term Etc
+
+ align:start position:0%
+term I can integrate a term by term Etc
+ 
+
+ align:start position:0%
+term I can integrate a term by term Etc
+ET etc etc I'll now give this a name and
+
+ align:start position:0%
+ET etc etc I'll now give this a name and
+ 
+
+ align:start position:0%
+ET etc etc I'll now give this a name and
+being very very judicious what name do I
+
+ align:start position:0%
+being very very judicious what name do I
+ 
+
+ align:start position:0%
+being very very judicious what name do I
+pick I pick e to the Z because that's
+
+ align:start position:0%
+pick I pick e to the Z because that's
+ 
+
+ align:start position:0%
+pick I pick e to the Z because that's
+what motivated my inventing this
+
+ align:start position:0%
+what motivated my inventing this
+ 
+
+ align:start position:0%
+what motivated my inventing this
+function this series in the first place
+
+ align:start position:0%
+function this series in the first place
+ 
+
+ align:start position:0%
+function this series in the first place
+and what am I now sure of I'm sure of
+
+ align:start position:0%
+and what am I now sure of I'm sure of
+ 
+
+ align:start position:0%
+and what am I now sure of I'm sure of
+the fact that if I replace Z by X in
+
+ align:start position:0%
+the fact that if I replace Z by X in
+ 
+
+ align:start position:0%
+the fact that if I replace Z by X in
+other words if Z is real that this must
+
+ align:start position:0%
+other words if Z is real that this must
+ 
+
+ align:start position:0%
+other words if Z is real that this must
+still be the same as what e to the X was
+
+ align:start position:0%
+still be the same as what e to the X was
+ 
+
+ align:start position:0%
+still be the same as what e to the X was
+before and what's the best proof of that
+
+ align:start position:0%
+before and what's the best proof of that
+ 
+
+ align:start position:0%
+before and what's the best proof of that
+replace Z by x what you get is summation
+
+ align:start position:0%
+replace Z by x what you get is summation
+ 
+
+ align:start position:0%
+replace Z by x what you get is summation
+n goes from 0 To infinity x to the N / n
+
+ align:start position:0%
+n goes from 0 To infinity x to the N / n
+ 
+
+ align:start position:0%
+n goes from 0 To infinity x to the N / n
+factorial and we saw in part one of our
+
+ align:start position:0%
+factorial and we saw in part one of our
+ 
+
+ align:start position:0%
+factorial and we saw in part one of our
+course that that was precisely e to X
+
+ align:start position:0%
+course that that was precisely e to X
+ 
+
+ align:start position:0%
+course that that was precisely e to X
+well since exponentials May bother you a
+
+ align:start position:0%
+well since exponentials May bother you a
+ 
+
+ align:start position:0%
+well since exponentials May bother you a
+little bit more than SS and cosiness
+
+ align:start position:0%
+little bit more than SS and cosiness
+ 
+
+ align:start position:0%
+little bit more than SS and cosiness
+let's revisit the same problem in terms
+
+ align:start position:0%
+let's revisit the same problem in terms
+ 
+
+ align:start position:0%
+let's revisit the same problem in terms
+of s z what I do is is I Define sin Z to
+
+ align:start position:0%
+of s z what I do is is I Define sin Z to
+ 
+
+ align:start position:0%
+of s z what I do is is I Define sin Z to
+be this uniformly absolutely convergent
+
+ align:start position:0%
+be this uniformly absolutely convergent
+ 
+
+ align:start position:0%
+be this uniformly absolutely convergent
+power series see I use again using
+
+ align:start position:0%
+power series see I use again using
+ 
+
+ align:start position:0%
+power series see I use again using
+hindsight knowing that in the case of
+
+ align:start position:0%
+hindsight knowing that in the case of
+ 
+
+ align:start position:0%
+hindsight knowing that in the case of
+sinx this was the convergent power
+
+ align:start position:0%
+sinx this was the convergent power
+ 
+
+ align:start position:0%
+sinx this was the convergent power
+series I simply replace X by Z up
+
+ align:start position:0%
+series I simply replace X by Z up
+ 
+
+ align:start position:0%
+series I simply replace X by Z up
+here all right I replace X by z i now
+
+ align:start position:0%
+here all right I replace X by z i now
+ 
+
+ align:start position:0%
+here all right I replace X by z i now
+use the ratio test on this to show that
+
+ align:start position:0%
+use the ratio test on this to show that
+ 
+
+ align:start position:0%
+use the ratio test on this to show that
+this does converge for all finite Z in
+
+ align:start position:0%
+this does converge for all finite Z in
+ 
+
+ align:start position:0%
+this does converge for all finite Z in
+fact that's sort of redundant to do that
+
+ align:start position:0%
+fact that's sort of redundant to do that
+ 
+
+ align:start position:0%
+fact that's sort of redundant to do that
+I know Dar well that's going to happen
+
+ align:start position:0%
+I know Dar well that's going to happen
+ 
+
+ align:start position:0%
+I know Dar well that's going to happen
+because it happened here and
+
+ align:start position:0%
+because it happened here and
+ 
+
+ align:start position:0%
+because it happened here and
+structurally these are the same but I
+
+ align:start position:0%
+structurally these are the same but I
+ 
+
+ align:start position:0%
+structurally these are the same but I
+now then after showing that I say okay
+
+ align:start position:0%
+now then after showing that I say okay
+ 
+
+ align:start position:0%
+now then after showing that I say okay
+this converges for all Z let's give it a
+
+ align:start position:0%
+this converges for all Z let's give it a
+ 
+
+ align:start position:0%
+this converges for all Z let's give it a
+name I'll call it sin Z and what
+
+ align:start position:0%
+name I'll call it sin Z and what
+ 
+
+ align:start position:0%
+name I'll call it sin Z and what
+guarantee do I have that sin Z is the
+
+ align:start position:0%
+guarantee do I have that sin Z is the
+ 
+
+ align:start position:0%
+guarantee do I have that sin Z is the
+same as sin x whenever Z is real and
+
+ align:start position:0%
+same as sin x whenever Z is real and
+ 
+
+ align:start position:0%
+same as sin x whenever Z is real and
+again let me point out something notice
+
+ align:start position:0%
+again let me point out something notice
+ 
+
+ align:start position:0%
+again let me point out something notice
+in the real case we started knowing what
+
+ align:start position:0%
+in the real case we started knowing what
+ 
+
+ align:start position:0%
+in the real case we started knowing what
+sinx was but not knowing what its power
+
+ align:start position:0%
+sinx was but not knowing what its power
+ 
+
+ align:start position:0%
+sinx was but not knowing what its power
+series expansion was and we developed
+
+ align:start position:0%
+series expansion was and we developed
+ 
+
+ align:start position:0%
+series expansion was and we developed
+the power series expansion and by the
+
+ align:start position:0%
+the power series expansion and by the
+ 
+
+ align:start position:0%
+the power series expansion and by the
+way notice that when you want to compute
+
+ align:start position:0%
+way notice that when you want to compute
+ 
+
+ align:start position:0%
+way notice that when you want to compute
+sinx to any number of decimal places
+
+ align:start position:0%
+sinx to any number of decimal places
+ 
+
+ align:start position:0%
+sinx to any number of decimal places
+whether you doing it by hand or by the
+
+ align:start position:0%
+whether you doing it by hand or by the
+ 
+
+ align:start position:0%
+whether you doing it by hand or by the
+computer notice that it's the power
+
+ align:start position:0%
+computer notice that it's the power
+ 
+
+ align:start position:0%
+computer notice that it's the power
+series that you use you see and you
+
+ align:start position:0%
+series that you use you see and you
+ 
+
+ align:start position:0%
+series that you use you see and you
+you chop this off after a certain number
+
+ align:start position:0%
+you chop this off after a certain number
+ 
+
+ align:start position:0%
+you chop this off after a certain number
+of terms if you wish but one does use
+
+ align:start position:0%
+of terms if you wish but one does use
+ 
+
+ align:start position:0%
+of terms if you wish but one does use
+the power series idea what I am saying
+
+ align:start position:0%
+the power series idea what I am saying
+ 
+
+ align:start position:0%
+the power series idea what I am saying
+though is had I wish to from a purely
+
+ align:start position:0%
+though is had I wish to from a purely
+ 
+
+ align:start position:0%
+though is had I wish to from a purely
+pedagogical point of view I could have
+
+ align:start position:0%
+pedagogical point of view I could have
+ 
+
+ align:start position:0%
+pedagogical point of view I could have
+said look at let me now forget about
+
+ align:start position:0%
+said look at let me now forget about
+ 
+
+ align:start position:0%
+said look at let me now forget about
+this definition of sinx and Define sinx
+
+ align:start position:0%
+this definition of sinx and Define sinx
+ 
+
+ align:start position:0%
+this definition of sinx and Define sinx
+just by this particular power series
+
+ align:start position:0%
+just by this particular power series
+ 
+
+ align:start position:0%
+just by this particular power series
+that would have been artificial to do at
+
+ align:start position:0%
+that would have been artificial to do at
+ 
+
+ align:start position:0%
+that would have been artificial to do at
+that time what I'm saying now though is
+
+ align:start position:0%
+that time what I'm saying now though is
+ 
+
+ align:start position:0%
+that time what I'm saying now though is
+this start with sinx in the real case
+
+ align:start position:0%
+this start with sinx in the real case
+ 
+
+ align:start position:0%
+this start with sinx in the real case
+develop its convergent power series take
+
+ align:start position:0%
+develop its convergent power series take
+ 
+
+ align:start position:0%
+develop its convergent power series take
+that power series
+
+ align:start position:0%
+that power series
+ 
+
+ align:start position:0%
+that power series
+replace X by Z and Define that new
+
+ align:start position:0%
+replace X by Z and Define that new
+ 
+
+ align:start position:0%
+replace X by Z and Define that new
+complex power series to be what sin Z is
+
+ align:start position:0%
+complex power series to be what sin Z is
+ 
+
+ align:start position:0%
+complex power series to be what sin Z is
+and that gets the job done for you now
+
+ align:start position:0%
+and that gets the job done for you now
+ 
+
+ align:start position:0%
+and that gets the job done for you now
+the interesting thing is that one can
+
+ align:start position:0%
+the interesting thing is that one can
+ 
+
+ align:start position:0%
+the interesting thing is that one can
+now show that all of the trigonometric
+
+ align:start position:0%
+now show that all of the trigonometric
+ 
+
+ align:start position:0%
+now show that all of the trigonometric
+functions be they hyperbolic or circular
+
+ align:start position:0%
+functions be they hyperbolic or circular
+ 
+
+ align:start position:0%
+functions be they hyperbolic or circular
+functions are related to e to the Z well
+
+ align:start position:0%
+functions are related to e to the Z well
+ 
+
+ align:start position:0%
+functions are related to e to the Z well
+why that's interesting is not very
+
+ align:start position:0%
+why that's interesting is not very
+ 
+
+ align:start position:0%
+why that's interesting is not very
+important right now it's we'll mention
+
+ align:start position:0%
+important right now it's we'll mention
+ 
+
+ align:start position:0%
+important right now it's we'll mention
+that in more detail on other occasions
+
+ align:start position:0%
+that in more detail on other occasions
+ 
+
+ align:start position:0%
+that in more detail on other occasions
+hopefully but the idea is this by using
+
+ align:start position:0%
+hopefully but the idea is this by using
+ 
+
+ align:start position:0%
+hopefully but the idea is this by using
+the fact that these various series are
+
+ align:start position:0%
+the fact that these various series are
+ 
+
+ align:start position:0%
+the fact that these various series are
+absolutely and uniformly convergent so I
+
+ align:start position:0%
+absolutely and uniformly convergent so I
+ 
+
+ align:start position:0%
+absolutely and uniformly convergent so I
+can manipulate them term by term and
+
+ align:start position:0%
+can manipulate them term by term and
+ 
+
+ align:start position:0%
+can manipulate them term by term and
+these things are done in detail in the
+
+ align:start position:0%
+these things are done in detail in the
+ 
+
+ align:start position:0%
+these things are done in detail in the
+text and I will give you other ones to
+
+ align:start position:0%
+text and I will give you other ones to
+ 
+
+ align:start position:0%
+text and I will give you other ones to
+do for homework so that you get the
+
+ align:start position:0%
+do for homework so that you get the
+ 
+
+ align:start position:0%
+do for homework so that you get the
+drill on this one can show the very
+
+ align:start position:0%
+drill on this one can show the very
+ 
+
+ align:start position:0%
+drill on this one can show the very
+amazing result that e to the i z is
+
+ align:start position:0%
+amazing result that e to the i z is
+ 
+
+ align:start position:0%
+amazing result that e to the i z is
+cosine Z plus I sin z a very amazing
+
+ align:start position:0%
+cosine Z plus I sin z a very amazing
+ 
+
+ align:start position:0%
+cosine Z plus I sin z a very amazing
+result it relates the cosine and the
+
+ align:start position:0%
+result it relates the cosine and the
+ 
+
+ align:start position:0%
+result it relates the cosine and the
+sign to an exponential in fact to stress
+
+ align:start position:0%
+sign to an exponential in fact to stress
+ 
+
+ align:start position:0%
+sign to an exponential in fact to stress
+this from a different point of view if I
+
+ align:start position:0%
+this from a different point of view if I
+ 
+
+ align:start position:0%
+this from a different point of view if I
+take the special case that Z is real
+
+ align:start position:0%
+take the special case that Z is real
+ 
+
+ align:start position:0%
+take the special case that Z is real
+notice that this says what e to the iix
+
+ align:start position:0%
+notice that this says what e to the iix
+ 
+
+ align:start position:0%
+notice that this says what e to the iix
+see replace Z byx is cinx plus I
+
+ align:start position:0%
+see replace Z byx is cinx plus I
+ 
+
+ align:start position:0%
+see replace Z byx is cinx plus I
+sinx okay in particular what this then
+
+ align:start position:0%
+sinx okay in particular what this then
+ 
+
+ align:start position:0%
+sinx okay in particular what this then
+says is let's go back to the Aon diagram
+
+ align:start position:0%
+says is let's go back to the Aon diagram
+ 
+
+ align:start position:0%
+says is let's go back to the Aon diagram
+where we take the complex number view it
+
+ align:start position:0%
+where we take the complex number view it
+ 
+
+ align:start position:0%
+where we take the complex number view it
+in polar coordinates as R comma Theta
+
+ align:start position:0%
+in polar coordinates as R comma Theta
+ 
+
+ align:start position:0%
+in polar coordinates as R comma Theta
+which means what R cosine theta plus i r
+
+ align:start position:0%
+which means what R cosine theta plus i r
+ 
+
+ align:start position:0%
+which means what R cosine theta plus i r
+sin Theta factor out the R so R * cosine
+
+ align:start position:0%
+sin Theta factor out the R so R * cosine
+ 
+
+ align:start position:0%
+sin Theta factor out the R so R * cosine
+theta plus I sin Theta but cine theta
+
+ align:start position:0%
+theta plus I sin Theta but cine theta
+ 
+
+ align:start position:0%
+theta plus I sin Theta but cine theta
+plus I sin Theta is e to the I Theta and
+
+ align:start position:0%
+plus I sin Theta is e to the I Theta and
+ 
+
+ align:start position:0%
+plus I sin Theta is e to the I Theta and
+what that says is that if you really
+
+ align:start position:0%
+what that says is that if you really
+ 
+
+ align:start position:0%
+what that says is that if you really
+wanted a nice name for this R comma
+
+ align:start position:0%
+wanted a nice name for this R comma
+ 
+
+ align:start position:0%
+wanted a nice name for this R comma
+Theta does turn out in the language of
+
+ align:start position:0%
+Theta does turn out in the language of
+ 
+
+ align:start position:0%
+Theta does turn out in the language of
+polar coordinates using complex
+
+ align:start position:0%
+polar coordinates using complex
+ 
+
+ align:start position:0%
+polar coordinates using complex
+variables without cartisian reference is
+
+ align:start position:0%
+variables without cartisian reference is
+ 
+
+ align:start position:0%
+variables without cartisian reference is
+re e to the I Theta which by the way
+
+ align:start position:0%
+re e to the I Theta which by the way
+ 
+
+ align:start position:0%
+re e to the I Theta which by the way
+would explain very nicely why when you
+
+ align:start position:0%
+would explain very nicely why when you
+ 
+
+ align:start position:0%
+would explain very nicely why when you
+multiply complex numbers you multiply
+
+ align:start position:0%
+multiply complex numbers you multiply
+ 
+
+ align:start position:0%
+multiply complex numbers you multiply
+the magnitude and add the arguments
+
+ align:start position:0%
+the magnitude and add the arguments
+ 
+
+ align:start position:0%
+the magnitude and add the arguments
+namely notice that the magnitudes are
+
+ align:start position:0%
+namely notice that the magnitudes are
+ 
+
+ align:start position:0%
+namely notice that the magnitudes are
+these scal factors in front of the
+
+ align:start position:0%
+these scal factors in front of the
+ 
+
+ align:start position:0%
+these scal factors in front of the
+exponential the arguments occur as
+
+ align:start position:0%
+exponential the arguments occur as
+ 
+
+ align:start position:0%
+exponential the arguments occur as
+exponents and when you multiply two
+
+ align:start position:0%
+exponents and when you multiply two
+ 
+
+ align:start position:0%
+exponents and when you multiply two
+numbers to the base e you add the
+
+ align:start position:0%
+numbers to the base e you add the
+ 
+
+ align:start position:0%
+numbers to the base e you add the
+exponents in fact when you multiply
+
+ align:start position:0%
+exponents in fact when you multiply
+ 
+
+ align:start position:0%
+exponents in fact when you multiply
+numbers to any base you add the
+
+ align:start position:0%
+numbers to any base you add the
+ 
+
+ align:start position:0%
+numbers to any base you add the
+exponents and that's why you add the
+
+ align:start position:0%
+exponents and that's why you add the
+ 
+
+ align:start position:0%
+exponents and that's why you add the
+angles over here uh again a very
+
+ align:start position:0%
+angles over here uh again a very
+ 
+
+ align:start position:0%
+angles over here uh again a very
+interesting side which is worth
+
+ align:start position:0%
+interesting side which is worth
+ 
+
+ align:start position:0%
+interesting side which is worth
+absolutely nothing but I always I think
+
+ align:start position:0%
+absolutely nothing but I always I think
+ 
+
+ align:start position:0%
+absolutely nothing but I always I think
+it was the first thing that ever turned
+
+ align:start position:0%
+it was the first thing that ever turned
+ 
+
+ align:start position:0%
+it was the first thing that ever turned
+me on in mathematics that get my
+
+ align:start position:0%
+me on in mathematics that get my
+ 
+
+ align:start position:0%
+me on in mathematics that get my
+metaphysical mathematical dander up was
+
+ align:start position:0%
+metaphysical mathematical dander up was
+ 
+
+ align:start position:0%
+metaphysical mathematical dander up was
+if you replace X
+
+ align:start position:0%
+if you replace X
+ 
+
+ align:start position:0%
+if you replace X
+by pi over here see what does that mean
+
+ align:start position:0%
+by pi over here see what does that mean
+ 
+
+ align:start position:0%
+by pi over here see what does that mean
+if I replace X by pi the magnitude is
+
+ align:start position:0%
+if I replace X by pi the magnitude is
+ 
+
+ align:start position:0%
+if I replace X by pi the magnitude is
+one the angle is pi e to the I
+
+ align:start position:0%
+one the angle is pi e to the I
+ 
+
+ align:start position:0%
+one the angle is pi e to the I
+Pi e to the I
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Pi is just another way of writing minus
+
+ align:start position:0%
+Pi is just another way of writing minus
+ 
+
+ align:start position:0%
+Pi is just another way of writing minus
+one see what is e to the I Pi the
+
+ align:start position:0%
+one see what is e to the I Pi the
+ 
+
+ align:start position:0%
+one see what is e to the I Pi the
+argument is pi that means 180° the
+
+ align:start position:0%
+argument is pi that means 180° the
+ 
+
+ align:start position:0%
+argument is pi that means 180° the
+argument is one and the number which is
+
+ align:start position:0%
+argument is one and the number which is
+ 
+
+ align:start position:0%
+argument is one and the number which is
+one unit from the origin in the Aon
+
+ align:start position:0%
+one unit from the origin in the Aon
+ 
+
+ align:start position:0%
+one unit from the origin in the Aon
+diagram at an angle of 180° is the real
+
+ align:start position:0%
+diagram at an angle of 180° is the real
+ 
+
+ align:start position:0%
+diagram at an angle of 180° is the real
+number minus one and I've always been
+
+ align:start position:0%
+number minus one and I've always been
+ 
+
+ align:start position:0%
+number minus one and I've always been
+mystified by the three most remarkable
+
+ align:start position:0%
+mystified by the three most remarkable
+ 
+
+ align:start position:0%
+mystified by the three most remarkable
+numbers constants in mathematics seem to
+
+ align:start position:0%
+numbers constants in mathematics seem to
+ 
+
+ align:start position:0%
+numbers constants in mathematics seem to
+be EI I and pi and e to the I Pi turns
+
+ align:start position:0%
+be EI I and pi and e to the I Pi turns
+ 
+
+ align:start position:0%
+be EI I and pi and e to the I Pi turns
+out to be minus one I just mentioned
+
+ align:start position:0%
+out to be minus one I just mentioned
+ 
+
+ align:start position:0%
+out to be minus one I just mentioned
+this to show you how complicated things
+
+ align:start position:0%
+this to show you how complicated things
+ 
+
+ align:start position:0%
+this to show you how complicated things
+can get if you try to read too much
+
+ align:start position:0%
+can get if you try to read too much
+ 
+
+ align:start position:0%
+can get if you try to read too much
+meaning into things but don't worry
+
+ align:start position:0%
+meaning into things but don't worry
+ 
+
+ align:start position:0%
+meaning into things but don't worry
+about that right now I couldn't resist
+
+ align:start position:0%
+about that right now I couldn't resist
+ 
+
+ align:start position:0%
+about that right now I couldn't resist
+the comment what I would like to do
+
+ align:start position:0%
+the comment what I would like to do
+ 
+
+ align:start position:0%
+the comment what I would like to do
+though is to show you now how this is
+
+ align:start position:0%
+though is to show you now how this is
+ 
+
+ align:start position:0%
+though is to show you now how this is
+used to define other functions and get
+
+ align:start position:0%
+used to define other functions and get
+ 
+
+ align:start position:0%
+used to define other functions and get
+us other results among other things
+
+ align:start position:0%
+us other results among other things
+ 
+
+ align:start position:0%
+us other results among other things
+notice that the first bad thing that
+
+ align:start position:0%
+notice that the first bad thing that
+ 
+
+ align:start position:0%
+notice that the first bad thing that
+happens with the polar coordinate
+
+ align:start position:0%
+happens with the polar coordinate
+ 
+
+ align:start position:0%
+happens with the polar coordinate
+representation is if the complex number
+
+ align:start position:0%
+representation is if the complex number
+ 
+
+ align:start position:0%
+representation is if the complex number
+Z can be written as re e to the I Theta
+
+ align:start position:0%
+Z can be written as re e to the I Theta
+ 
+
+ align:start position:0%
+Z can be written as re e to the I Theta
+it can also be written as re e to the I
+
+ align:start position:0%
+it can also be written as re e to the I
+ 
+
+ align:start position:0%
+it can also be written as re e to the I
+Theta + 2 pi K because every time I
+
+ align:start position:0%
+Theta + 2 pi K because every time I
+ 
+
+ align:start position:0%
+Theta + 2 pi K because every time I
+change my angle by 2 pi or
+
+ align:start position:0%
+change my angle by 2 pi or
+ 
+
+ align:start position:0%
+change my angle by 2 pi or
+360° I come back to the same Point again
+
+ align:start position:0%
+360° I come back to the same Point again
+ 
+
+ align:start position:0%
+360° I come back to the same Point again
+at any rate forgetting about that
+
+ align:start position:0%
+at any rate forgetting about that
+ 
+
+ align:start position:0%
+at any rate forgetting about that
+problem for the time being notice how I
+
+ align:start position:0%
+problem for the time being notice how I
+ 
+
+ align:start position:0%
+problem for the time being notice how I
+can now Define a logarithm for a complex
+
+ align:start position:0%
+can now Define a logarithm for a complex
+ 
+
+ align:start position:0%
+can now Define a logarithm for a complex
+number in fact the logarithm will turn
+
+ align:start position:0%
+number in fact the logarithm will turn
+ 
+
+ align:start position:0%
+number in fact the logarithm will turn
+out to be the inverse of e to the Z the
+
+ align:start position:0%
+out to be the inverse of e to the Z the
+ 
+
+ align:start position:0%
+out to be the inverse of e to the Z the
+same as before but we won't worry about
+
+ align:start position:0%
+same as before but we won't worry about
+ 
+
+ align:start position:0%
+same as before but we won't worry about
+that here either let's see how we could
+
+ align:start position:0%
+that here either let's see how we could
+ 
+
+ align:start position:0%
+that here either let's see how we could
+Define log Z from this now we would like
+
+ align:start position:0%
+Define log Z from this now we would like
+ 
+
+ align:start position:0%
+Define log Z from this now we would like
+the log to have the usual logarithmic
+
+ align:start position:0%
+the log to have the usual logarithmic
+ 
+
+ align:start position:0%
+the log to have the usual logarithmic
+properties the log of a product should
+
+ align:start position:0%
+properties the log of a product should
+ 
+
+ align:start position:0%
+properties the log of a product should
+be the sum of the logi the the sum of
+
+ align:start position:0%
+be the sum of the logi the the sum of
+ 
+
+ align:start position:0%
+be the sum of the logi the the sum of
+the logs so log Z should be log R plus
+
+ align:start position:0%
+the logs so log Z should be log R plus
+ 
+
+ align:start position:0%
+the logs so log Z should be log R plus
+log e to the I Theta + 2 pi k now R is a
+
+ align:start position:0%
+log e to the I Theta + 2 pi k now R is a
+ 
+
+ align:start position:0%
+log e to the I Theta + 2 pi k now R is a
+positive real number we already know
+
+ align:start position:0%
+positive real number we already know
+ 
+
+ align:start position:0%
+positive real number we already know
+that the natural log applies there so
+
+ align:start position:0%
+that the natural log applies there so
+ 
+
+ align:start position:0%
+that the natural log applies there so
+the N so what we say is okay the log of
+
+ align:start position:0%
+the N so what we say is okay the log of
+ 
+
+ align:start position:0%
+the N so what we say is okay the log of
+R is just natural log R log e to
+
+ align:start position:0%
+R is just natural log R log e to
+ 
+
+ align:start position:0%
+R is just natural log R log e to
+anything the log and the E are inverse
+
+ align:start position:0%
+anything the log and the E are inverse
+ 
+
+ align:start position:0%
+anything the log and the E are inverse
+of one another so they should cancel and
+
+ align:start position:0%
+of one another so they should cancel and
+ 
+
+ align:start position:0%
+of one another so they should cancel and
+this should just be I Theta + 2 pi K in
+
+ align:start position:0%
+this should just be I Theta + 2 pi K in
+ 
+
+ align:start position:0%
+this should just be I Theta + 2 pi K in
+other words to find the log of the
+
+ align:start position:0%
+other words to find the log of the
+ 
+
+ align:start position:0%
+other words to find the log of the
+complex number Z you simply take the log
+
+ align:start position:0%
+complex number Z you simply take the log
+ 
+
+ align:start position:0%
+complex number Z you simply take the log
+of its magnitude and add on as the
+
+ align:start position:0%
+of its magnitude and add on as the
+ 
+
+ align:start position:0%
+of its magnitude and add on as the
+imaginary part what the argument
+
+ align:start position:0%
+imaginary part what the argument
+ 
+
+ align:start position:0%
+imaginary part what the argument
+noticing by the way that the argument is
+
+ align:start position:0%
+noticing by the way that the argument is
+ 
+
+ align:start position:0%
+noticing by the way that the argument is
+multivalued see log Z is multivalued
+
+ align:start position:0%
+multivalued see log Z is multivalued
+ 
+
+ align:start position:0%
+multivalued see log Z is multivalued
+consequently we must get into the idea
+
+ align:start position:0%
+consequently we must get into the idea
+ 
+
+ align:start position:0%
+consequently we must get into the idea
+of principal values and one usually
+
+ align:start position:0%
+of principal values and one usually
+ 
+
+ align:start position:0%
+of principal values and one usually
+assumes unless otherwise stated that the
+
+ align:start position:0%
+assumes unless otherwise stated that the
+ 
+
+ align:start position:0%
+assumes unless otherwise stated that the
+argument is at no greater than Pi but
+
+ align:start position:0%
+argument is at no greater than Pi but
+ 
+
+ align:start position:0%
+argument is at no greater than Pi but
+greater than minus Pi if we don't mean
+
+ align:start position:0%
+greater than minus Pi if we don't mean
+ 
+
+ align:start position:0%
+greater than minus Pi if we don't mean
+that we have to state that separately
+
+ align:start position:0%
+that we have to state that separately
+ 
+
+ align:start position:0%
+that we have to state that separately
+again we will drill on that in the
+
+ align:start position:0%
+again we will drill on that in the
+ 
+
+ align:start position:0%
+again we will drill on that in the
+exercises by the way another application
+
+ align:start position:0%
+exercises by the way another application
+ 
+
+ align:start position:0%
+exercises by the way another application
+that relates the hyperbolic functions to
+
+ align:start position:0%
+that relates the hyperbolic functions to
+ 
+
+ align:start position:0%
+that relates the hyperbolic functions to
+the tri metric to the circular functions
+
+ align:start position:0%
+the tri metric to the circular functions
+ 
+
+ align:start position:0%
+the tri metric to the circular functions
+notice that if we wanted to Define
+
+ align:start position:0%
+notice that if we wanted to Define
+ 
+
+ align:start position:0%
+notice that if we wanted to Define
+hyperbolic cosine of IX mimicking what
+
+ align:start position:0%
+hyperbolic cosine of IX mimicking what
+ 
+
+ align:start position:0%
+hyperbolic cosine of IX mimicking what
+happened in the real case this would be
+
+ align:start position:0%
+happened in the real case this would be
+ 
+
+ align:start position:0%
+happened in the real case this would be
+e to the IX plus e to minus IX over 2 we
+
+ align:start position:0%
+e to the IX plus e to minus IX over 2 we
+ 
+
+ align:start position:0%
+e to the IX plus e to minus IX over 2 we
+already saw that e to the IX was cinx +
+
+ align:start position:0%
+already saw that e to the IX was cinx +
+ 
+
+ align:start position:0%
+already saw that e to the IX was cinx +
+i sinx e to Theus IX is e to the I of -
+
+ align:start position:0%
+i sinx e to Theus IX is e to the I of -
+ 
+
+ align:start position:0%
+i sinx e to Theus IX is e to the I of -
+x that's cosine - x plus I sin - x by
+
+ align:start position:0%
+x that's cosine - x plus I sin - x by
+ 
+
+ align:start position:0%
+x that's cosine - x plus I sin - x by
+the way I hope that's clear to you when
+
+ align:start position:0%
+the way I hope that's clear to you when
+ 
+
+ align:start position:0%
+the way I hope that's clear to you when
+I say that e to the iix is cine X plus I
+
+ align:start position:0%
+I say that e to the iix is cine X plus I
+ 
+
+ align:start position:0%
+I say that e to the iix is cine X plus I
+sinx what I really mean is or even up
+
+ align:start position:0%
+sinx what I really mean is or even up
+ 
+
+ align:start position:0%
+sinx what I really mean is or even up
+here what I really mean is that e to the
+
+ align:start position:0%
+here what I really mean is that e to the
+ 
+
+ align:start position:0%
+here what I really mean is that e to the
+I anything is cosine of that anything
+
+ align:start position:0%
+I anything is cosine of that anything
+ 
+
+ align:start position:0%
+I anything is cosine of that anything
+plus I S of that anything in particular
+
+ align:start position:0%
+plus I S of that anything in particular
+ 
+
+ align:start position:0%
+plus I S of that anything in particular
+if I replace Z by minus X I get e to the
+
+ align:start position:0%
+if I replace Z by minus X I get e to the
+ 
+
+ align:start position:0%
+if I replace Z by minus X I get e to the
+i - x in other words- IX is cosine - x
+
+ align:start position:0%
+i - x in other words- IX is cosine - x
+ 
+
+ align:start position:0%
+i - x in other words- IX is cosine - x
+plus I sin -
+
+ align:start position:0%
+plus I sin -
+ 
+
+ align:start position:0%
+plus I sin -
+x okay and notice that cosine of - x
+
+ align:start position:0%
+x okay and notice that cosine of - x
+ 
+
+ align:start position:0%
+x okay and notice that cosine of - x
+equal cosine X X sin - x is- sin x these
+
+ align:start position:0%
+equal cosine X X sin - x is- sin x these
+ 
+
+ align:start position:0%
+equal cosine X X sin - x is- sin x these
+terms cancel this becomes 2 cosine x 2
+
+ align:start position:0%
+terms cancel this becomes 2 cosine x 2
+ 
+
+ align:start position:0%
+terms cancel this becomes 2 cosine x 2
+cosine X ID 2 is cosine X and we have
+
+ align:start position:0%
+cosine X ID 2 is cosine X and we have
+ 
+
+ align:start position:0%
+cosine X ID 2 is cosine X and we have
+the rather amazing identity that K IX is
+
+ align:start position:0%
+the rather amazing identity that K IX is
+ 
+
+ align:start position:0%
+the rather amazing identity that K IX is
+cine X in other words a very interesting
+
+ align:start position:0%
+cine X in other words a very interesting
+ 
+
+ align:start position:0%
+cine X in other words a very interesting
+relationship between the hyperbolic and
+
+ align:start position:0%
+relationship between the hyperbolic and
+ 
+
+ align:start position:0%
+relationship between the hyperbolic and
+the circular functions and by the way
+
+ align:start position:0%
+the circular functions and by the way
+ 
+
+ align:start position:0%
+the circular functions and by the way
+this shouldn't be too
+
+ align:start position:0%
+this shouldn't be too
+ 
+
+ align:start position:0%
+this shouldn't be too
+surprising notice that the circular
+
+ align:start position:0%
+surprising notice that the circular
+ 
+
+ align:start position:0%
+surprising notice that the circular
+functions come from studying x²
+
+ align:start position:0%
+functions come from studying x²
+ 
+
+ align:start position:0%
+functions come from studying x²
++
+
+ align:start position:0%
++
+ 
+
+ align:start position:0%
++
+y^2 = 1 the hyperbolic functions come
+
+ align:start position:0%
+y^2 = 1 the hyperbolic functions come
+ 
+
+ align:start position:0%
+y^2 = 1 the hyperbolic functions come
+from studying x^2 - Y2 = 1 and x^2 - y^2
+
+ align:start position:0%
+from studying x^2 - Y2 = 1 and x^2 - y^2
+ 
+
+ align:start position:0%
+from studying x^2 - Y2 = 1 and x^2 - y^2
+can be written as x^2 plus the quantity
+
+ align:start position:0%
+can be written as x^2 plus the quantity
+ 
+
+ align:start position:0%
+can be written as x^2 plus the quantity
+I y^2 so what would be a a hyperbola in
+
+ align:start position:0%
+I y^2 so what would be a a hyperbola in
+ 
+
+ align:start position:0%
+I y^2 so what would be a a hyperbola in
+the XY plane would be a circle in the x
+
+ align:start position:0%
+the XY plane would be a circle in the x
+ 
+
+ align:start position:0%
+the XY plane would be a circle in the x
+i y plane whatever that might be but
+
+ align:start position:0%
+i y plane whatever that might be but
+ 
+
+ align:start position:0%
+i y plane whatever that might be but
+again that's just in the form of an
+
+ align:start position:0%
+again that's just in the form of an
+ 
+
+ align:start position:0%
+again that's just in the form of an
+aside and now we'll come back to we mean
+
+ align:start position:0%
+aside and now we'll come back to we mean
+ 
+
+ align:start position:0%
+aside and now we'll come back to we mean
+by saying that we can use these new
+
+ align:start position:0%
+by saying that we can use these new
+ 
+
+ align:start position:0%
+by saying that we can use these new
+analytic functions to do conformal
+
+ align:start position:0%
+analytic functions to do conformal
+ 
+
+ align:start position:0%
+analytic functions to do conformal
+mappings let's come back to the question
+
+ align:start position:0%
+mappings let's come back to the question
+ 
+
+ align:start position:0%
+mappings let's come back to the question
+that we raised at the very beginning of
+
+ align:start position:0%
+that we raised at the very beginning of
+ 
+
+ align:start position:0%
+that we raised at the very beginning of
+our lecture about e to the
+
+ align:start position:0%
+our lecture about e to the
+ 
+
+ align:start position:0%
+our lecture about e to the
+Z certainly because Z is X+ i y e to the
+
+ align:start position:0%
+Z certainly because Z is X+ i y e to the
+ 
+
+ align:start position:0%
+Z certainly because Z is X+ i y e to the
+Z will be e to X Plus i y because of the
+
+ align:start position:0%
+Z will be e to X Plus i y because of the
+ 
+
+ align:start position:0%
+Z will be e to X Plus i y because of the
+properties that the exponential will
+
+ align:start position:0%
+properties that the exponential will
+ 
+
+ align:start position:0%
+properties that the exponential will
+have and by the way all of these
+
+ align:start position:0%
+have and by the way all of these
+ 
+
+ align:start position:0%
+have and by the way all of these
+exponential properties can be proven
+
+ align:start position:0%
+exponential properties can be proven
+ 
+
+ align:start position:0%
+exponential properties can be proven
+from the power series you see we don't
+
+ align:start position:0%
+from the power series you see we don't
+ 
+
+ align:start position:0%
+from the power series you see we don't
+need the real interpretation the power
+
+ align:start position:0%
+need the real interpretation the power
+ 
+
+ align:start position:0%
+need the real interpretation the power
+series will give us all the these
+
+ align:start position:0%
+series will give us all the these
+ 
+
+ align:start position:0%
+series will give us all the these
+results but again we'll drill on those
+
+ align:start position:0%
+results but again we'll drill on those
+ 
+
+ align:start position:0%
+results but again we'll drill on those
+in the exercises I just want to get the
+
+ align:start position:0%
+in the exercises I just want to get the
+ 
+
+ align:start position:0%
+in the exercises I just want to get the
+Highlights here this is e to x * e to
+
+ align:start position:0%
+Highlights here this is e to x * e to
+ 
+
+ align:start position:0%
+Highlights here this is e to x * e to
+the i y but notice here you see that Y
+
+ align:start position:0%
+the i y but notice here you see that Y
+ 
+
+ align:start position:0%
+the i y but notice here you see that Y
+is real and for even if it wasn't real
+
+ align:start position:0%
+is real and for even if it wasn't real
+ 
+
+ align:start position:0%
+is real and for even if it wasn't real
+it doesn't make any difference e to the
+
+ align:start position:0%
+it doesn't make any difference e to the
+ 
+
+ align:start position:0%
+it doesn't make any difference e to the
+i y is cosine y + I sin y multiplying
+
+ align:start position:0%
+i y is cosine y + I sin y multiplying
+ 
+
+ align:start position:0%
+i y is cosine y + I sin y multiplying
+this out e to the Z is e to x cosine y
+
+ align:start position:0%
+this out e to the Z is e to x cosine y
+ 
+
+ align:start position:0%
+this out e to the Z is e to x cosine y
+plus I E to X sin y the important thing
+
+ align:start position:0%
+plus I E to X sin y the important thing
+ 
+
+ align:start position:0%
+plus I E to X sin y the important thing
+being that because Y is real e to the x
+
+ align:start position:0%
+being that because Y is real e to the x
+ 
+
+ align:start position:0%
+being that because Y is real e to the x
+cosine y and e to X X sin y are both
+
+ align:start position:0%
+cosine y and e to X X sin y are both
+ 
+
+ align:start position:0%
+cosine y and e to X X sin y are both
+real and consequently if I let U denote
+
+ align:start position:0%
+real and consequently if I let U denote
+ 
+
+ align:start position:0%
+real and consequently if I let U denote
+the real part and V denote the imaginary
+
+ align:start position:0%
+the real part and V denote the imaginary
+ 
+
+ align:start position:0%
+the real part and V denote the imaginary
+part as usual what I have is that u = e
+
+ align:start position:0%
+part as usual what I have is that u = e
+ 
+
+ align:start position:0%
+part as usual what I have is that u = e
+to x cosine y v = e to X sin Y Must Be a
+
+ align:start position:0%
+to x cosine y v = e to X sin Y Must Be a
+ 
+
+ align:start position:0%
+to x cosine y v = e to X sin Y Must Be a
+Real conformal mapping why because the
+
+ align:start position:0%
+Real conformal mapping why because the
+ 
+
+ align:start position:0%
+Real conformal mapping why because the
+real and the imaginary Parts the real
+
+ align:start position:0%
+real and the imaginary Parts the real
+ 
+
+ align:start position:0%
+real and the imaginary Parts the real
+and the imaginary parts make up an
+
+ align:start position:0%
+and the imaginary parts make up an
+ 
+
+ align:start position:0%
+and the imaginary parts make up an
+analytic function how do I know this
+
+ align:start position:0%
+analytic function how do I know this
+ 
+
+ align:start position:0%
+analytic function how do I know this
+function is analytic because its power
+
+ align:start position:0%
+function is analytic because its power
+ 
+
+ align:start position:0%
+function is analytic because its power
+series exists and the fact that it's
+
+ align:start position:0%
+series exists and the fact that it's
+ 
+
+ align:start position:0%
+series exists and the fact that it's
+power series exists means that all the
+
+ align:start position:0%
+power series exists means that all the
+ 
+
+ align:start position:0%
+power series exists means that all the
+derivatives must exist now again I
+
+ align:start position:0%
+derivatives must exist now again I
+ 
+
+ align:start position:0%
+derivatives must exist now again I
+didn't write this in here but maybe it's
+
+ align:start position:0%
+didn't write this in here but maybe it's
+ 
+
+ align:start position:0%
+didn't write this in here but maybe it's
+a worthwhile asside to show you what
+
+ align:start position:0%
+a worthwhile asside to show you what
+ 
+
+ align:start position:0%
+a worthwhile asside to show you what
+this conformal mapping looks like for
+
+ align:start position:0%
+this conformal mapping looks like for
+ 
+
+ align:start position:0%
+this conformal mapping looks like for
+example notice that if I Square both
+
+ align:start position:0%
+example notice that if I Square both
+ 
+
+ align:start position:0%
+example notice that if I Square both
+sides of each equation here and add if I
+
+ align:start position:0%
+sides of each equation here and add if I
+ 
+
+ align:start position:0%
+sides of each equation here and add if I
+square and add what do I get on one side
+
+ align:start position:0%
+square and add what do I get on one side
+ 
+
+ align:start position:0%
+square and add what do I get on one side
+I get u^2 + v^2 on the other side I get
+
+ align:start position:0%
+I get u^2 + v^2 on the other side I get
+ 
+
+ align:start position:0%
+I get u^2 + v^2 on the other side I get
+e 2x cosine 2 y plus e 2x sin^2 y i I
+
+ align:start position:0%
+e 2x cosine 2 y plus e 2x sin^2 y i I
+ 
+
+ align:start position:0%
+e 2x cosine 2 y plus e 2x sin^2 y i I
+factor out e 2X and that gives me e 2x
+
+ align:start position:0%
+factor out e 2X and that gives me e 2x
+ 
+
+ align:start position:0%
+factor out e 2X and that gives me e 2x
+sin^2 y + cosine ^ 2 Y which is 1 so
+
+ align:start position:0%
+sin^2 y + cosine ^ 2 Y which is 1 so
+ 
+
+ align:start position:0%
+sin^2 y + cosine ^ 2 Y which is 1 so
+this is just U ^2 + v^2 is e 2x to
+
+ align:start position:0%
+this is just U ^2 + v^2 is e 2x to
+ 
+
+ align:start position:0%
+this is just U ^2 + v^2 is e 2x to
+eliminate X from the equations I can
+
+ align:start position:0%
+eliminate X from the equations I can
+ 
+
+ align:start position:0%
+eliminate X from the equations I can
+divide the Bottom by the top and I get
+
+ align:start position:0%
+divide the Bottom by the top and I get
+ 
+
+ align:start position:0%
+divide the Bottom by the top and I get
+that V over
+
+ align:start position:0%
+that V over
+ 
+
+ align:start position:0%
+that V over
+u v/ u is equal to tangent
+
+ align:start position:0%
+u v/ u is equal to tangent
+ 
+
+ align:start position:0%
+u v/ u is equal to tangent
+Y and by the way notice what this thing
+
+ align:start position:0%
+Y and by the way notice what this thing
+ 
+
+ align:start position:0%
+Y and by the way notice what this thing
+tells me this tells me see what are the
+
+ align:start position:0%
+tells me this tells me see what are the
+ 
+
+ align:start position:0%
+tells me this tells me see what are the
+uh basic lines in the XY plane that the
+
+ align:start position:0%
+uh basic lines in the XY plane that the
+ 
+
+ align:start position:0%
+uh basic lines in the XY plane that the
+lines x equal a constant y equals a
+
+ align:start position:0%
+lines x equal a constant y equals a
+ 
+
+ align:start position:0%
+lines x equal a constant y equals a
+constant notice that if x is a constant
+
+ align:start position:0%
+constant notice that if x is a constant
+ 
+
+ align:start position:0%
+constant notice that if x is a constant
+this says that U ^2 + v^2 = e to a
+
+ align:start position:0%
+this says that U ^2 + v^2 = e to a
+ 
+
+ align:start position:0%
+this says that U ^2 + v^2 = e to a
+constant power that's u^2 + v^2 is a
+
+ align:start position:0%
+constant power that's u^2 + v^2 is a
+ 
+
+ align:start position:0%
+constant power that's u^2 + v^2 is a
+constant that's a circle centered at the
+
+ align:start position:0%
+constant that's a circle centered at the
+ 
+
+ align:start position:0%
+constant that's a circle centered at the
+origin in other words the lines x equal
+
+ align:start position:0%
+origin in other words the lines x equal
+ 
+
+ align:start position:0%
+origin in other words the lines x equal
+a constant map into concentric circles
+
+ align:start position:0%
+a constant map into concentric circles
+ 
+
+ align:start position:0%
+a constant map into concentric circles
+on the other hand if Y is a constant
+
+ align:start position:0%
+on the other hand if Y is a constant
+ 
+
+ align:start position:0%
+on the other hand if Y is a constant
+this says that v/ U is a constant in the
+
+ align:start position:0%
+this says that v/ U is a constant in the
+ 
+
+ align:start position:0%
+this says that v/ U is a constant in the
+UV V plane v/ U is a constant is a
+
+ align:start position:0%
+UV V plane v/ U is a constant is a
+ 
+
+ align:start position:0%
+UV V plane v/ U is a constant is a
+straight line that goes through the
+
+ align:start position:0%
+straight line that goes through the
+ 
+
+ align:start position:0%
+straight line that goes through the
+origin see V is a constant times U now
+
+ align:start position:0%
+origin see V is a constant times U now
+ 
+
+ align:start position:0%
+origin see V is a constant times U now
+what that means pictorially let's see if
+
+ align:start position:0%
+what that means pictorially let's see if
+ 
+
+ align:start position:0%
+what that means pictorially let's see if
+I have some room to squeeze this in here
+
+ align:start position:0%
+I have some room to squeeze this in here
+ 
+
+ align:start position:0%
+I have some room to squeeze this in here
+what this means pictorially is that this
+
+ align:start position:0%
+what this means pictorially is that this
+ 
+
+ align:start position:0%
+what this means pictorially is that this
+kind of a
+
+ align:start position:0%
+kind of a
+ 
+
+ align:start position:0%
+kind of a
+network see in the XY
+
+ align:start position:0%
+network see in the XY
+ 
+
+ align:start position:0%
+network see in the XY
+plane this kind of a network in the XY
+
+ align:start position:0%
+plane this kind of a network in the XY
+ 
+
+ align:start position:0%
+plane this kind of a network in the XY
+plane is mapped into what this network
+
+ align:start position:0%
+plane is mapped into what this network
+ 
+
+ align:start position:0%
+plane is mapped into what this network
+is mapped into a what the vertical lines
+
+ align:start position:0%
+is mapped into a what the vertical lines
+ 
+
+ align:start position:0%
+is mapped into a what the vertical lines
+go into concentric circles and the
+
+ align:start position:0%
+go into concentric circles and the
+ 
+
+ align:start position:0%
+go into concentric circles and the
+horizontal lines go in into lines
+
+ align:start position:0%
+horizontal lines go in into lines
+ 
+
+ align:start position:0%
+horizontal lines go in into lines
+through the origin here and not
+
+ align:start position:0%
+through the origin here and not
+ 
+
+ align:start position:0%
+through the origin here and not
+okay notice by the way that every line
+
+ align:start position:0%
+okay notice by the way that every line
+ 
+
+ align:start position:0%
+okay notice by the way that every line
+through the origin meets The Circle at
+
+ align:start position:0%
+through the origin meets The Circle at
+ 
+
+ align:start position:0%
+through the origin meets The Circle at
+right
+
+ align:start position:0%
+right
+ 
+
+ align:start position:0%
+right
+angles notice that these lines were at
+
+ align:start position:0%
+angles notice that these lines were at
+ 
+
+ align:start position:0%
+angles notice that these lines were at
+right angles here notice the conformal
+
+ align:start position:0%
+right angles here notice the conformal
+ 
+
+ align:start position:0%
+right angles here notice the conformal
+property here in other words lines that
+
+ align:start position:0%
+property here in other words lines that
+ 
+
+ align:start position:0%
+property here in other words lines that
+meet at right angle in the XY plane must
+
+ align:start position:0%
+meet at right angle in the XY plane must
+ 
+
+ align:start position:0%
+meet at right angle in the XY plane must
+meet at right angles in the UV plane and
+
+ align:start position:0%
+meet at right angles in the UV plane and
+ 
+
+ align:start position:0%
+meet at right angles in the UV plane and
+let me separate this out from anything
+
+ align:start position:0%
+let me separate this out from anything
+ 
+
+ align:start position:0%
+let me separate this out from anything
+else that I've done so that we don't get
+
+ align:start position:0%
+else that I've done so that we don't get
+ 
+
+ align:start position:0%
+else that I've done so that we don't get
+too mixed up with this by the way one of
+
+ align:start position:0%
+too mixed up with this by the way one of
+ 
+
+ align:start position:0%
+too mixed up with this by the way one of
+the ways that this is used in
+
+ align:start position:0%
+the ways that this is used in
+ 
+
+ align:start position:0%
+the ways that this is used in
+application is with the inverse mapping
+
+ align:start position:0%
+application is with the inverse mapping
+ 
+
+ align:start position:0%
+application is with the inverse mapping
+that in certain cases where we have to
+
+ align:start position:0%
+that in certain cases where we have to
+ 
+
+ align:start position:0%
+that in certain cases where we have to
+deal with regions that have this kind of
+
+ align:start position:0%
+deal with regions that have this kind of
+ 
+
+ align:start position:0%
+deal with regions that have this kind of
+a
+
+ align:start position:0%
+a
+ 
+
+ align:start position:0%
+a
+shape we back map this region and what
+
+ align:start position:0%
+shape we back map this region and what
+ 
+
+ align:start position:0%
+shape we back map this region and what
+will it go into it'll go into a
+
+ align:start position:0%
+will it go into it'll go into a
+ 
+
+ align:start position:0%
+will it go into it'll go into a
+rectangle here and for example in
+
+ align:start position:0%
+rectangle here and for example in
+ 
+
+ align:start position:0%
+rectangle here and for example in
+solving Lassa equation it might be a lot
+
+ align:start position:0%
+solving Lassa equation it might be a lot
+ 
+
+ align:start position:0%
+solving Lassa equation it might be a lot
+easier to solve lass's equation on the
+
+ align:start position:0%
+easier to solve lass's equation on the
+ 
+
+ align:start position:0%
+easier to solve lass's equation on the
+boundary of a rectangle than on the
+
+ align:start position:0%
+boundary of a rectangle than on the
+ 
+
+ align:start position:0%
+boundary of a rectangle than on the
+boundary of a region of this particular
+
+ align:start position:0%
+boundary of a region of this particular
+ 
+
+ align:start position:0%
+boundary of a region of this particular
+type again I don't want to go into too
+
+ align:start position:0%
+type again I don't want to go into too
+ 
+
+ align:start position:0%
+type again I don't want to go into too
+much detail here because it obscures
+
+ align:start position:0%
+much detail here because it obscures
+ 
+
+ align:start position:0%
+much detail here because it obscures
+what the main overview is namely every
+
+ align:start position:0%
+what the main overview is namely every
+ 
+
+ align:start position:0%
+what the main overview is namely every
+time we invent an analytic function like
+
+ align:start position:0%
+time we invent an analytic function like
+ 
+
+ align:start position:0%
+time we invent an analytic function like
+e to the Z sin Z cos Z Etc we have
+
+ align:start position:0%
+e to the Z sin Z cos Z Etc we have
+ 
+
+ align:start position:0%
+e to the Z sin Z cos Z Etc we have
+invented a new conformal mapping where
+
+ align:start position:0%
+invented a new conformal mapping where
+ 
+
+ align:start position:0%
+invented a new conformal mapping where
+that conformal mapping will help us in a
+
+ align:start position:0%
+that conformal mapping will help us in a
+ 
+
+ align:start position:0%
+that conformal mapping will help us in a
+particular application or not depends on
+
+ align:start position:0%
+particular application or not depends on
+ 
+
+ align:start position:0%
+particular application or not depends on
+the application but what the meaning of
+
+ align:start position:0%
+the application but what the meaning of
+ 
+
+ align:start position:0%
+the application but what the meaning of
+it is is independent of any application
+
+ align:start position:0%
+it is is independent of any application
+ 
+
+ align:start position:0%
+it is is independent of any application
+okay now let's take one more important
+
+ align:start position:0%
+okay now let's take one more important
+ 
+
+ align:start position:0%
+okay now let's take one more important
+reason you see what I'm afraid of now is
+
+ align:start position:0%
+reason you see what I'm afraid of now is
+ 
+
+ align:start position:0%
+reason you see what I'm afraid of now is
+I'm giving you the impression that
+
+ align:start position:0%
+I'm giving you the impression that
+ 
+
+ align:start position:0%
+I'm giving you the impression that
+complex numbers have value only if
+
+ align:start position:0%
+complex numbers have value only if
+ 
+
+ align:start position:0%
+complex numbers have value only if
+you're doing conformal mappings you see
+
+ align:start position:0%
+you're doing conformal mappings you see
+ 
+
+ align:start position:0%
+you're doing conformal mappings you see
+con complex numbers give you a degree of
+
+ align:start position:0%
+con complex numbers give you a degree of
+ 
+
+ align:start position:0%
+con complex numbers give you a degree of
+Consciousness so to speak above the real
+
+ align:start position:0%
+Consciousness so to speak above the real
+ 
+
+ align:start position:0%
+Consciousness so to speak above the real
+numbers let me give you an example of
+
+ align:start position:0%
+numbers let me give you an example of
+ 
+
+ align:start position:0%
+numbers let me give you an example of
+another problem that used to hang me up
+
+ align:start position:0%
+another problem that used to hang me up
+ 
+
+ align:start position:0%
+another problem that used to hang me up
+when I was an undergraduate student
+
+ align:start position:0%
+when I was an undergraduate student
+ 
+
+ align:start position:0%
+when I was an undergraduate student
+learning calculus I'm going to apply
+
+ align:start position:0%
+learning calculus I'm going to apply
+ 
+
+ align:start position:0%
+learning calculus I'm going to apply
+complex Val results to real series now
+
+ align:start position:0%
+complex Val results to real series now
+ 
+
+ align:start position:0%
+complex Val results to real series now
+remember the geometric series 1/ 1 - U
+
+ align:start position:0%
+remember the geometric series 1/ 1 - U
+ 
+
+ align:start position:0%
+remember the geometric series 1/ 1 - U
+is 1 + U + U ^2 Etc in other words
+
+ align:start position:0%
+is 1 + U + U ^2 Etc in other words
+ 
+
+ align:start position:0%
+is 1 + U + U ^2 Etc in other words
+summation n goes from 0 to Infinity U
+
+ align:start position:0%
+summation n goes from 0 to Infinity U
+ 
+
+ align:start position:0%
+summation n goes from 0 to Infinity U
+the n and that converges for the
+
+ align:start position:0%
+the n and that converges for the
+ 
+
+ align:start position:0%
+the n and that converges for the
+absolute value of U less than one let's
+
+ align:start position:0%
+absolute value of U less than one let's
+ 
+
+ align:start position:0%
+absolute value of U less than one let's
+suppose now I replace U by - x^2 if I do
+
+ align:start position:0%
+suppose now I replace U by - x^2 if I do
+ 
+
+ align:start position:0%
+suppose now I replace U by - x^2 if I do
+that I get 1 over 1 + x^2 is 1 - x^2 + x
+
+ align:start position:0%
+that I get 1 over 1 + x^2 is 1 - x^2 + x
+ 
+
+ align:start position:0%
+that I get 1 over 1 + x^2 is 1 - x^2 + x
+4 - x 6 Etc in other words summation n
+
+ align:start position:0%
+4 - x 6 Etc in other words summation n
+ 
+
+ align:start position:0%
+4 - x 6 Etc in other words summation n
+goes from 0 to Infinity I want my signs
+
+ align:start position:0%
+goes from 0 to Infinity I want my signs
+ 
+
+ align:start position:0%
+goes from 0 to Infinity I want my signs
+to alternate with the first one being
+
+ align:start position:0%
+to alternate with the first one being
+ 
+
+ align:start position:0%
+to alternate with the first one being
+positive so I put in minus1 the n x the
+
+ align:start position:0%
+positive so I put in minus1 the n x the
+ 
+
+ align:start position:0%
+positive so I put in minus1 the n x the
+2 N and that converges for the absolute
+
+ align:start position:0%
+2 N and that converges for the absolute
+ 
+
+ align:start position:0%
+2 N and that converges for the absolute
+value of x less than one now let me just
+
+ align:start position:0%
+value of x less than one now let me just
+ 
+
+ align:start position:0%
+value of x less than one now let me just
+focus my attention on a question for you
+
+ align:start position:0%
+focus my attention on a question for you
+ 
+
+ align:start position:0%
+focus my attention on a question for you
+here and I'll come back to this I want
+
+ align:start position:0%
+here and I'll come back to this I want
+ 
+
+ align:start position:0%
+here and I'll come back to this I want
+to come back here in a second but the
+
+ align:start position:0%
+to come back here in a second but the
+ 
+
+ align:start position:0%
+to come back here in a second but the
+idea is what goes wrong when x equals
+
+ align:start position:0%
+idea is what goes wrong when x equals
+ 
+
+ align:start position:0%
+idea is what goes wrong when x equals
+plus or minus one you see let me show
+
+ align:start position:0%
+plus or minus one you see let me show
+ 
+
+ align:start position:0%
+plus or minus one you see let me show
+you what I mean by that when I saw this
+
+ align:start position:0%
+you what I mean by that when I saw this
+ 
+
+ align:start position:0%
+you what I mean by that when I saw this
+series for the first time and somebody
+
+ align:start position:0%
+series for the first time and somebody
+ 
+
+ align:start position:0%
+series for the first time and somebody
+says look at you got to be careful when
+
+ align:start position:0%
+says look at you got to be careful when
+ 
+
+ align:start position:0%
+says look at you got to be careful when
+the absolute value of U is equal to one
+
+ align:start position:0%
+the absolute value of U is equal to one
+ 
+
+ align:start position:0%
+the absolute value of U is equal to one
+that was be careful when U equals 1 or
+
+ align:start position:0%
+that was be careful when U equals 1 or
+ 
+
+ align:start position:0%
+that was be careful when U equals 1 or
+minus one well minus one didn't bother
+
+ align:start position:0%
+minus one well minus one didn't bother
+ 
+
+ align:start position:0%
+minus one well minus one didn't bother
+me that much but one I could see right
+
+ align:start position:0%
+me that much but one I could see right
+ 
+
+ align:start position:0%
+me that much but one I could see right
+away what went wrong namely When U is 1
+
+ align:start position:0%
+away what went wrong namely When U is 1
+ 
+
+ align:start position:0%
+away what went wrong namely When U is 1
+here 1 over 1 minus U is 1 over Z which
+
+ align:start position:0%
+here 1 over 1 minus U is 1 over Z which
+ 
+
+ align:start position:0%
+here 1 over 1 minus U is 1 over Z which
+is undefined and I expect trouble over
+
+ align:start position:0%
+is undefined and I expect trouble over
+ 
+
+ align:start position:0%
+is undefined and I expect trouble over
+here on the other hand when the absolute
+
+ align:start position:0%
+here on the other hand when the absolute
+ 
+
+ align:start position:0%
+here on the other hand when the absolute
+value of x equals 1 here that means that
+
+ align:start position:0%
+value of x equals 1 here that means that
+ 
+
+ align:start position:0%
+value of x equals 1 here that means that
+x^2 is 1 I mean whether X is 1 or minus
+
+ align:start position:0%
+x^2 is 1 I mean whether X is 1 or minus
+ 
+
+ align:start position:0%
+x^2 is 1 I mean whether X is 1 or minus
+one x^2 is 1 look at nothing goes wrong
+
+ align:start position:0%
+one x^2 is 1 look at nothing goes wrong
+ 
+
+ align:start position:0%
+one x^2 is 1 look at nothing goes wrong
+over here 1/ 1 + x squ is perfectly well
+
+ align:start position:0%
+over here 1/ 1 + x squ is perfectly well
+ 
+
+ align:start position:0%
+over here 1/ 1 + x squ is perfectly well
+defined at the at xal 1 I would expect
+
+ align:start position:0%
+defined at the at xal 1 I would expect
+ 
+
+ align:start position:0%
+defined at the at xal 1 I would expect
+because my upbringing was such that I
+
+ align:start position:0%
+because my upbringing was such that I
+ 
+
+ align:start position:0%
+because my upbringing was such that I
+always thought that the bad points
+
+ align:start position:0%
+always thought that the bad points
+ 
+
+ align:start position:0%
+always thought that the bad points
+occurred where the denominator blew up
+
+ align:start position:0%
+occurred where the denominator blew up
+ 
+
+ align:start position:0%
+occurred where the denominator blew up
+but see this denominator never blows up
+
+ align:start position:0%
+but see this denominator never blows up
+ 
+
+ align:start position:0%
+but see this denominator never blows up
+because 1 + x^2 is always at least as
+
+ align:start position:0%
+because 1 + x^2 is always at least as
+ 
+
+ align:start position:0%
+because 1 + x^2 is always at least as
+big as
+
+ align:start position:0%
+big as
+ 
+
+ align:start position:0%
+big as
+one provided what of course that X is
+
+ align:start position:0%
+one provided what of course that X is
+ 
+
+ align:start position:0%
+one provided what of course that X is
+real because a square of a real number
+
+ align:start position:0%
+real because a square of a real number
+ 
+
+ align:start position:0%
+real because a square of a real number
+can't be negative that's the hint by the
+
+ align:start position:0%
+can't be negative that's the hint by the
+ 
+
+ align:start position:0%
+can't be negative that's the hint by the
+way the square of a complex number could
+
+ align:start position:0%
+way the square of a complex number could
+ 
+
+ align:start position:0%
+way the square of a complex number could
+certainly be negative
+
+ align:start position:0%
+certainly be negative
+ 
+
+ align:start position:0%
+certainly be negative
+and here's what I'm saying if I now take
+
+ align:start position:0%
+and here's what I'm saying if I now take
+ 
+
+ align:start position:0%
+and here's what I'm saying if I now take
+this real valued
+
+ align:start position:0%
+this real valued
+ 
+
+ align:start position:0%
+this real valued
+series and convert it to a complex
+
+ align:start position:0%
+series and convert it to a complex
+ 
+
+ align:start position:0%
+series and convert it to a complex
+valued series by replacing X by Z all
+
+ align:start position:0%
+valued series by replacing X by Z all
+ 
+
+ align:start position:0%
+valued series by replacing X by Z all
+right using the same ratio test Etc that
+
+ align:start position:0%
+right using the same ratio test Etc that
+ 
+
+ align:start position:0%
+right using the same ratio test Etc that
+we did before I can prove that this
+
+ align:start position:0%
+we did before I can prove that this
+ 
+
+ align:start position:0%
+we did before I can prove that this
+infinite Series this power series
+
+ align:start position:0%
+infinite Series this power series
+ 
+
+ align:start position:0%
+infinite Series this power series
+converges to one over 1 + z^ 2 provided
+
+ align:start position:0%
+converges to one over 1 + z^ 2 provided
+ 
+
+ align:start position:0%
+converges to one over 1 + z^ 2 provided
+the absolute value of Z is less than one
+
+ align:start position:0%
+the absolute value of Z is less than one
+ 
+
+ align:start position:0%
+the absolute value of Z is less than one
+now by the way what does it mean to say
+
+ align:start position:0%
+now by the way what does it mean to say
+ 
+
+ align:start position:0%
+now by the way what does it mean to say
+the absolute value of Z is less than one
+
+ align:start position:0%
+the absolute value of Z is less than one
+ 
+
+ align:start position:0%
+the absolute value of Z is less than one
+it means that Z is less than one unit
+
+ align:start position:0%
+it means that Z is less than one unit
+ 
+
+ align:start position:0%
+it means that Z is less than one unit
+from the origin It means that in the Aon
+
+ align:start position:0%
+from the origin It means that in the Aon
+ 
+
+ align:start position:0%
+from the origin It means that in the Aon
+diagram Z is inside the circle centered
+
+ align:start position:0%
+diagram Z is inside the circle centered
+ 
+
+ align:start position:0%
+diagram Z is inside the circle centered
+at the origin with radius equal to one
+
+ align:start position:0%
+at the origin with radius equal to one
+ 
+
+ align:start position:0%
+at the origin with radius equal to one
+but here's the key point when I look at
+
+ align:start position:0%
+but here's the key point when I look at
+ 
+
+ align:start position:0%
+but here's the key point when I look at
+this I'm not at all upset that something
+
+ align:start position:0%
+this I'm not at all upset that something
+ 
+
+ align:start position:0%
+this I'm not at all upset that something
+can go wrong on this circle namely 1
+
+ align:start position:0%
+can go wrong on this circle namely 1
+ 
+
+ align:start position:0%
+can go wrong on this circle namely 1
+over 1 + z^2 factors into 1 / Z + I * Z
+
+ align:start position:0%
+over 1 + z^2 factors into 1 / Z + I * Z
+ 
+
+ align:start position:0%
+over 1 + z^2 factors into 1 / Z + I * Z
+minus I and certainly I am Leary of
+
+ align:start position:0%
+minus I and certainly I am Leary of
+ 
+
+ align:start position:0%
+minus I and certainly I am Leary of
+letting Z either equal minus I or I
+
+ align:start position:0%
+letting Z either equal minus I or I
+ 
+
+ align:start position:0%
+letting Z either equal minus I or I
+because it's going to make my
+
+ align:start position:0%
+because it's going to make my
+ 
+
+ align:start position:0%
+because it's going to make my
+denominator vanish and even in the
+
+ align:start position:0%
+denominator vanish and even in the
+ 
+
+ align:start position:0%
+denominator vanish and even in the
+complex numbers as you recall from our
+
+ align:start position:0%
+complex numbers as you recall from our
+ 
+
+ align:start position:0%
+complex numbers as you recall from our
+first lecture on complex numbers you
+
+ align:start position:0%
+first lecture on complex numbers you
+ 
+
+ align:start position:0%
+first lecture on complex numbers you
+cannot divide by zero in other words at
+
+ align:start position:0%
+cannot divide by zero in other words at
+ 
+
+ align:start position:0%
+cannot divide by zero in other words at
+a glance I recognize that Z equals plus
+
+ align:start position:0%
+a glance I recognize that Z equals plus
+ 
+
+ align:start position:0%
+a glance I recognize that Z equals plus
+or minus I is trouble in other words
+
+ align:start position:0%
+or minus I is trouble in other words
+ 
+
+ align:start position:0%
+or minus I is trouble in other words
+going to the agon diagram in this
+
+ align:start position:0%
+going to the agon diagram in this
+ 
+
+ align:start position:0%
+going to the agon diagram in this
+picture I know I'm in trouble at these
+
+ align:start position:0%
+picture I know I'm in trouble at these
+ 
+
+ align:start position:0%
+picture I know I'm in trouble at these
+two points on the circle absolute value
+
+ align:start position:0%
+two points on the circle absolute value
+ 
+
+ align:start position:0%
+two points on the circle absolute value
+of Z equals 1 remember this is a circle
+
+ align:start position:0%
+of Z equals 1 remember this is a circle
+ 
+
+ align:start position:0%
+of Z equals 1 remember this is a circle
+it's the locus of all points in the
+
+ align:start position:0%
+it's the locus of all points in the
+ 
+
+ align:start position:0%
+it's the locus of all points in the
+diagram one unit from the origin now
+
+ align:start position:0%
+diagram one unit from the origin now
+ 
+
+ align:start position:0%
+diagram one unit from the origin now
+remember what we said about the circle
+
+ align:start position:0%
+remember what we said about the circle
+ 
+
+ align:start position:0%
+remember what we said about the circle
+of convergence that that set s where the
+
+ align:start position:0%
+of convergence that that set s where the
+ 
+
+ align:start position:0%
+of convergence that that set s where the
+power series converges there is a circle
+
+ align:start position:0%
+power series converges there is a circle
+ 
+
+ align:start position:0%
+power series converges there is a circle
+such that inside the circle the thing
+
+ align:start position:0%
+such that inside the circle the thing
+ 
+
+ align:start position:0%
+such that inside the circle the thing
+always converges outside it always
+
+ align:start position:0%
+always converges outside it always
+ 
+
+ align:start position:0%
+always converges outside it always
+diverges consequently the fact that I
+
+ align:start position:0%
+diverges consequently the fact that I
+ 
+
+ align:start position:0%
+diverges consequently the fact that I
+have two bad spots over here tells me
+
+ align:start position:0%
+have two bad spots over here tells me
+ 
+
+ align:start position:0%
+have two bad spots over here tells me
+that I cannot go beyond this circle in
+
+ align:start position:0%
+that I cannot go beyond this circle in
+ 
+
+ align:start position:0%
+that I cannot go beyond this circle in
+talking about what happened with the
+
+ align:start position:0%
+talking about what happened with the
+ 
+
+ align:start position:0%
+talking about what happened with the
+power series expansion for 1 over 1+ z^2
+
+ align:start position:0%
+power series expansion for 1 over 1+ z^2
+ 
+
+ align:start position:0%
+power series expansion for 1 over 1+ z^2
+notice that all I require is that
+
+ align:start position:0%
+notice that all I require is that
+ 
+
+ align:start position:0%
+notice that all I require is that
+something go wrong on the circle there
+
+ align:start position:0%
+something go wrong on the circle there
+ 
+
+ align:start position:0%
+something go wrong on the circle there
+are infinitely many points on this
+
+ align:start position:0%
+are infinitely many points on this
+ 
+
+ align:start position:0%
+are infinitely many points on this
+circle and the likelihood that the point
+
+ align:start position:0%
+circle and the likelihood that the point
+ 
+
+ align:start position:0%
+circle and the likelihood that the point
+at which things went bad happened to be
+
+ align:start position:0%
+at which things went bad happened to be
+ 
+
+ align:start position:0%
+at which things went bad happened to be
+at the point where the circle crossed
+
+ align:start position:0%
+at the point where the circle crossed
+ 
+
+ align:start position:0%
+at the point where the circle crossed
+the x-axis is particularly small in
+
+ align:start position:0%
+the x-axis is particularly small in
+ 
+
+ align:start position:0%
+the x-axis is particularly small in
+other words speaking from another point
+
+ align:start position:0%
+other words speaking from another point
+ 
+
+ align:start position:0%
+other words speaking from another point
+of view if I have the Good Fortune to be
+
+ align:start position:0%
+of view if I have the Good Fortune to be
+ 
+
+ align:start position:0%
+of view if I have the Good Fortune to be
+able to be standing in the complex
+
+ align:start position:0%
+able to be standing in the complex
+ 
+
+ align:start position:0%
+able to be standing in the complex
+number world looking down at this circle
+
+ align:start position:0%
+number world looking down at this circle
+ 
+
+ align:start position:0%
+number world looking down at this circle
+I see what went wrong if my perspective
+
+ align:start position:0%
+I see what went wrong if my perspective
+ 
+
+ align:start position:0%
+I see what went wrong if my perspective
+is limited to the xais I can't see
+
+ align:start position:0%
+is limited to the xais I can't see
+ 
+
+ align:start position:0%
+is limited to the xais I can't see
+anything that went wrong and I can't
+
+ align:start position:0%
+anything that went wrong and I can't
+ 
+
+ align:start position:0%
+anything that went wrong and I can't
+understand why I can't expand this
+
+ align:start position:0%
+understand why I can't expand this
+ 
+
+ align:start position:0%
+understand why I can't expand this
+circle further in other words the bad
+
+ align:start position:0%
+circle further in other words the bad
+ 
+
+ align:start position:0%
+circle further in other words the bad
+spots are on the magnitude of Z equals 1
+
+ align:start position:0%
+spots are on the magnitude of Z equals 1
+ 
+
+ align:start position:0%
+spots are on the magnitude of Z equals 1
+but not at the point zal
+
+ align:start position:0%
+but not at the point zal
+ 
+
+ align:start position:0%
+but not at the point zal
+1 or zal minus one these were good
+
+ align:start position:0%
+1 or zal minus one these were good
+ 
+
+ align:start position:0%
+1 or zal minus one these were good
+points see these were good points these
+
+ align:start position:0%
+points see these were good points these
+ 
+
+ align:start position:0%
+points see these were good points these
+were the bad ones but all you needed was
+
+ align:start position:0%
+were the bad ones but all you needed was
+ 
+
+ align:start position:0%
+were the bad ones but all you needed was
+One Bad Apple to spoil the whole circle
+
+ align:start position:0%
+One Bad Apple to spoil the whole circle
+ 
+
+ align:start position:0%
+One Bad Apple to spoil the whole circle
+so to speak at any rate I think that's
+
+ align:start position:0%
+so to speak at any rate I think that's
+ 
+
+ align:start position:0%
+so to speak at any rate I think that's
+enough to make my point the point being
+
+ align:start position:0%
+enough to make my point the point being
+ 
+
+ align:start position:0%
+enough to make my point the point being
+that by studying complex series we do
+
+ align:start position:0%
+that by studying complex series we do
+ 
+
+ align:start position:0%
+that by studying complex series we do
+two things one is we get a larger hold
+
+ align:start position:0%
+two things one is we get a larger hold
+ 
+
+ align:start position:0%
+two things one is we get a larger hold
+on the set of analytic functions which
+
+ align:start position:0%
+on the set of analytic functions which
+ 
+
+ align:start position:0%
+on the set of analytic functions which
+help us in things like conformal
+
+ align:start position:0%
+help us in things like conformal
+ 
+
+ align:start position:0%
+help us in things like conformal
+mappings and other things which we
+
+ align:start position:0%
+mappings and other things which we
+ 
+
+ align:start position:0%
+mappings and other things which we
+haven't gone into and secondly it gives
+
+ align:start position:0%
+haven't gone into and secondly it gives
+ 
+
+ align:start position:0%
+haven't gone into and secondly it gives
+us A New Perspective at series involving
+
+ align:start position:0%
+us A New Perspective at series involving
+ 
+
+ align:start position:0%
+us A New Perspective at series involving
+real power series because we now have an
+
+ align:start position:0%
+real power series because we now have an
+ 
+
+ align:start position:0%
+real power series because we now have an
+extra Dimension from which to view the
+
+ align:start position:0%
+extra Dimension from which to view the
+ 
+
+ align:start position:0%
+extra Dimension from which to view the
+power series at any rate we'll talk
+
+ align:start position:0%
+power series at any rate we'll talk
+ 
+
+ align:start position:0%
+power series at any rate we'll talk
+about other aspects of complex variables
+
+ align:start position:0%
+about other aspects of complex variables
+ 
+
+ align:start position:0%
+about other aspects of complex variables
+namely integration next time for the
+
+ align:start position:0%
+namely integration next time for the
+ 
+
+ align:start position:0%
+namely integration next time for the
+time being do the exercises in this unit
+
+ align:start position:0%
+time being do the exercises in this unit
+ 
+
+ align:start position:0%
+time being do the exercises in this unit
+and until next time
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+goodbye funding for the publication of
+
+ align:start position:0%
+goodbye funding for the publication of
+ 
+
+ align:start position:0%
+goodbye funding for the publication of
+this video was provided by the Gabriella
+
+ align:start position:0%
+this video was provided by the Gabriella
+ 
+
+ align:start position:0%
+this video was provided by the Gabriella
+and Paul rosenbom
+
+ align:start position:0%
+and Paul rosenbom
+ 
+
+ align:start position:0%
+and Paul rosenbom
+foundation help ocw continue to provide
+
+ align:start position:0%
+foundation help ocw continue to provide
+ 
+
+ align:start position:0%
+foundation help ocw continue to provide
+free and open access to MIT courses by
+
+ align:start position:0%
+free and open access to MIT courses by
+ 
+
+ align:start position:0%
+free and open access to MIT courses by
+making a donation at ocw.mit.edu/donate
\ No newline at end of file
diff --git a/UsGBIfjUK7U.txt b/UsGBIfjUK7U.txt
new file mode 100644
index 0000000000000000000000000000000000000000..1cd4a48f73aad09ca085386aba9b01fdd8817c9c
--- /dev/null
+++ b/UsGBIfjUK7U.txt
@@ -0,0 +1,3416 @@
+align:start position:0%
+ 
+hi welcome back to recitation you've
+
+ align:start position:0%
+hi welcome back to recitation you've
+ 
+
+ align:start position:0%
+hi welcome back to recitation you've
+been talking in class about partial
+
+ align:start position:0%
+been talking in class about partial
+ 
+
+ align:start position:0%
+been talking in class about partial
+fraction decomposition as a as a tool
+
+ align:start position:0%
+fraction decomposition as a as a tool
+ 
+
+ align:start position:0%
+fraction decomposition as a as a tool
+for integration so remember that the the
+
+ align:start position:0%
+for integration so remember that the the
+ 
+
+ align:start position:0%
+for integration so remember that the the
+point of partial fraction decomposition
+
+ align:start position:0%
+point of partial fraction decomposition
+ 
+
+ align:start position:0%
+point of partial fraction decomposition
+is that whenever you have a rational
+
+ align:start position:0%
+is that whenever you have a rational
+ 
+
+ align:start position:0%
+is that whenever you have a rational
+function that is one polinomial divided
+
+ align:start position:0%
+function that is one polinomial divided
+ 
+
+ align:start position:0%
+function that is one polinomial divided
+by another that in principle partial
+
+ align:start position:0%
+by another that in principle partial
+ 
+
+ align:start position:0%
+by another that in principle partial
+fraction decomposition lets you write
+
+ align:start position:0%
+fraction decomposition lets you write
+ 
+
+ align:start position:0%
+fraction decomposition lets you write
+any such expression as a sum of things
+
+ align:start position:0%
+any such expression as a sum of things
+ 
+
+ align:start position:0%
+any such expression as a sum of things
+Each of which is relatively easy to
+
+ align:start position:0%
+Each of which is relatively easy to
+ 
+
+ align:start position:0%
+Each of which is relatively easy to
+integrate so the the technique here is
+
+ align:start position:0%
+integrate so the the technique here is
+ 
+
+ align:start position:0%
+integrate so the the technique here is
+is purely algebraic um and then and then
+
+ align:start position:0%
+is purely algebraic um and then and then
+ 
+
+ align:start position:0%
+is purely algebraic um and then and then
+you just apply integral rules that we've
+
+ align:start position:0%
+you just apply integral rules that we've
+ 
+
+ align:start position:0%
+you just apply integral rules that we've
+already learned U so I have here four uh
+
+ align:start position:0%
+already learned U so I have here four uh
+ 
+
+ align:start position:0%
+already learned U so I have here four uh
+four rational functions for you and what
+
+ align:start position:0%
+four rational functions for you and what
+ 
+
+ align:start position:0%
+four rational functions for you and what
+I'd like you to do in each case is try
+
+ align:start position:0%
+I'd like you to do in each case is try
+ 
+
+ align:start position:0%
+I'd like you to do in each case is try
+to decompose it into the into the
+
+ align:start position:0%
+to decompose it into the into the
+ 
+
+ align:start position:0%
+to decompose it into the into the
+general form that Professor jarrison
+
+ align:start position:0%
+general form that Professor jarrison
+ 
+
+ align:start position:0%
+general form that Professor jarrison
+taught you um so don't I'm I'm not
+
+ align:start position:0%
+taught you um so don't I'm I'm not
+ 
+
+ align:start position:0%
+taught you um so don't I'm I'm not
+asking you to you know if if you like
+
+ align:start position:0%
+asking you to you know if if you like
+ 
+
+ align:start position:0%
+asking you to you know if if you like
+you're you're certainly welcome to go
+
+ align:start position:0%
+you're you're certainly welcome to go
+ 
+
+ align:start position:0%
+you're you're certainly welcome to go
+ahead and compute the the
+
+ align:start position:0%
+ahead and compute the the
+ 
+
+ align:start position:0%
+ahead and compute the the
+anti-derivatives after you do that but
+
+ align:start position:0%
+anti-derivatives after you do that but
+ 
+
+ align:start position:0%
+anti-derivatives after you do that but
+I'm not going to gonna do it for you or
+
+ align:start position:0%
+I'm not going to gonna do it for you or
+ 
+
+ align:start position:0%
+I'm not going to gonna do it for you or
+I'm I'm not gonna ask you to do it um so
+
+ align:start position:0%
+I'm I'm not gonna ask you to do it um so
+ 
+
+ align:start position:0%
+I'm I'm not gonna ask you to do it um so
+what I'd like you to do though is is is
+
+ align:start position:0%
+what I'd like you to do though is is is
+ 
+
+ align:start position:0%
+what I'd like you to do though is is is
+to for each of these four Expressions to
+
+ align:start position:0%
+to for each of these four Expressions to
+ 
+
+ align:start position:0%
+to for each of these four Expressions to
+to break it out into the into the form
+
+ align:start position:0%
+to break it out into the into the form
+ 
+
+ align:start position:0%
+to break it out into the into the form
+of the the partial fraction
+
+ align:start position:0%
+of the the partial fraction
+ 
+
+ align:start position:0%
+of the the partial fraction
+decomposition so why don't you take a
+
+ align:start position:0%
+decomposition so why don't you take a
+ 
+
+ align:start position:0%
+decomposition so why don't you take a
+few minutes to do that come back and you
+
+ align:start position:0%
+few minutes to do that come back and you
+ 
+
+ align:start position:0%
+few minutes to do that come back and you
+can check your work against
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+mine all right welcome back hopefully
+
+ align:start position:0%
+mine all right welcome back hopefully
+ 
+
+ align:start position:0%
+mine all right welcome back hopefully
+you had some fun working on these uh
+
+ align:start position:0%
+you had some fun working on these uh
+ 
+
+ align:start position:0%
+you had some fun working on these uh
+they're they're a little bit tricky I
+
+ align:start position:0%
+they're they're a little bit tricky I
+ 
+
+ align:start position:0%
+they're they're a little bit tricky I
+think or I picked them to be a little
+
+ align:start position:0%
+think or I picked them to be a little
+ 
+
+ align:start position:0%
+think or I picked them to be a little
+bit tricky so let's let's go through
+
+ align:start position:0%
+bit tricky so let's let's go through
+ 
+
+ align:start position:0%
+bit tricky so let's let's go through
+them one by one I guess I'll I'll start
+
+ align:start position:0%
+them one by one I guess I'll I'll start
+ 
+
+ align:start position:0%
+them one by one I guess I'll I'll start
+with the first one
+
+ align:start position:0%
+with the first one
+ 
+
+ align:start position:0%
+with the first one
+um so for the first
+
+ align:start position:0%
+um so for the first
+ 
+
+ align:start position:0%
+um so for the first
+one I have
+
+ align:start position:0%
+one I have
+ 
+
+ align:start position:0%
+one I have
+X2 - 4x +
+
+ align:start position:0%
+X2 - 4x +
+ 
+
+ align:start position:0%
+X2 - 4x +
+
+ align:start position:0%
+ 
+
+ align:start position:0%
+over x^2 - 8 x now the first thing to do
+
+ align:start position:0%
+over x^2 - 8 x now the first thing to do
+ 
+
+ align:start position:0%
+over x^2 - 8 x now the first thing to do
+when you start the partial fraction
+
+ align:start position:0%
+when you start the partial fraction
+ 
+
+ align:start position:0%
+when you start the partial fraction
+method is that you have to check that
+
+ align:start position:0%
+method is that you have to check that
+ 
+
+ align:start position:0%
+method is that you have to check that
+the degree
+
+ align:start position:0%
+the degree
+ 
+
+ align:start position:0%
+the degree
+of the numerator is smaller than the
+
+ align:start position:0%
+of the numerator is smaller than the
+ 
+
+ align:start position:0%
+of the numerator is smaller than the
+degree of the denominator now in this
+
+ align:start position:0%
+degree of the denominator now in this
+ 
+
+ align:start position:0%
+degree of the denominator now in this
+case that's not true the the it's the
+
+ align:start position:0%
+case that's not true the the it's the
+ 
+
+ align:start position:0%
+case that's not true the the it's the
+degree on top is two and the degree on
+
+ align:start position:0%
+degree on top is two and the degree on
+ 
+
+ align:start position:0%
+degree on top is two and the degree on
+bottom is two so we need to do long
+
+ align:start position:0%
+bottom is two so we need to do long
+ 
+
+ align:start position:0%
+bottom is two so we need to do long
+division or you know we need to do
+
+ align:start position:0%
+division or you know we need to do
+ 
+
+ align:start position:0%
+division or you know we need to do
+something well long division is the
+
+ align:start position:0%
+something well long division is the
+ 
+
+ align:start position:0%
+something well long division is the
+usual and and always usual way and
+
+ align:start position:0%
+usual and and always usual way and
+ 
+
+ align:start position:0%
+usual and and always usual way and
+always works in order to reduce the the
+
+ align:start position:0%
+always works in order to reduce the the
+ 
+
+ align:start position:0%
+always works in order to reduce the the
+degree of the top here so that so that
+
+ align:start position:0%
+degree of the top here so that so that
+ 
+
+ align:start position:0%
+degree of the top here so that so that
+it's smaller than the degree of the
+
+ align:start position:0%
+it's smaller than the degree of the
+ 
+
+ align:start position:0%
+it's smaller than the degree of the
+Bottom now I've I've done this ahead of
+
+ align:start position:0%
+Bottom now I've I've done this ahead of
+ 
+
+ align:start position:0%
+Bottom now I've I've done this ahead of
+time um and it's and it's not too hard
+
+ align:start position:0%
+time um and it's and it's not too hard
+ 
+
+ align:start position:0%
+time um and it's and it's not too hard
+to check that this is equal to 1
+
+ align:start position:0%
+to check that this is equal to 1
+ 
+
+ align:start position:0%
+to check that this is equal to 1
++ 4x + 4
+
+ align:start position:0%
++ 4x + 4
+ 
+
+ align:start position:0%
++ 4x + 4
+over x^2 - 8X it's a relatively easy
+
+ align:start position:0%
+over x^2 - 8X it's a relatively easy
+ 
+
+ align:start position:0%
+over x^2 - 8X it's a relatively easy
+long division to do in any case um so
+
+ align:start position:0%
+long division to do in any case um so
+ 
+
+ align:start position:0%
+long division to do in any case um so
+okay so what we get after we do that
+
+ align:start position:0%
+okay so what we get after we do that
+ 
+
+ align:start position:0%
+okay so what we get after we do that
+process is we get something in front
+
+ align:start position:0%
+process is we get something in front
+ 
+
+ align:start position:0%
+process is we get something in front
+that's always a polom and that's good
+
+ align:start position:0%
+that's always a polom and that's good
+ 
+
+ align:start position:0%
+that's always a polom and that's good
+because remember our goal is to you know
+
+ align:start position:0%
+because remember our goal is to you know
+ 
+
+ align:start position:0%
+because remember our goal is to you know
+manipulate this into a form where we can
+
+ align:start position:0%
+manipulate this into a form where we can
+ 
+
+ align:start position:0%
+manipulate this into a form where we can
+integrate it and and polinomial are easy
+
+ align:start position:0%
+integrate it and and polinomial are easy
+ 
+
+ align:start position:0%
+integrate it and and polinomial are easy
+to integrate so then then we usually
+
+ align:start position:0%
+to integrate so then then we usually
+ 
+
+ align:start position:0%
+to integrate so then then we usually
+just forget about this for the time
+
+ align:start position:0%
+just forget about this for the time
+ 
+
+ align:start position:0%
+just forget about this for the time
+being and and what we want to do is
+
+ align:start position:0%
+being and and what we want to do is
+ 
+
+ align:start position:0%
+being and and what we want to do is
+partial fraction decompose the second
+
+ align:start position:0%
+partial fraction decompose the second
+ 
+
+ align:start position:0%
+partial fraction decompose the second
+part so to do that the first thing you
+
+ align:start position:0%
+part so to do that the first thing you
+ 
+
+ align:start position:0%
+part so to do that the first thing you
+need to do once you once you've got a
+
+ align:start position:0%
+need to do once you once you've got a
+ 
+
+ align:start position:0%
+need to do once you once you've got a
+smaller degree on top than downstairs is
+
+ align:start position:0%
+smaller degree on top than downstairs is
+ 
+
+ align:start position:0%
+smaller degree on top than downstairs is
+that you factor the the denominator so
+
+ align:start position:0%
+that you factor the the denominator so
+ 
+
+ align:start position:0%
+that you factor the the denominator so
+in this case I'm going to keep the one
+
+ align:start position:0%
+in this case I'm going to keep the one
+ 
+
+ align:start position:0%
+in this case I'm going to keep the one
+plus just so I can keep writing equals
+
+ align:start position:0%
+plus just so I can keep writing equals
+ 
+
+ align:start position:0%
+plus just so I can keep writing equals
+signs and be honest about it um but you
+
+ align:start position:0%
+signs and be honest about it um but you
+ 
+
+ align:start position:0%
+signs and be honest about it um but you
+know but but really our Focus now is
+
+ align:start position:0%
+know but but really our Focus now is
+ 
+
+ align:start position:0%
+know but but really our Focus now is
+just entirely on this on this second sum
+
+ align:start position:0%
+just entirely on this on this second sum
+ 
+
+ align:start position:0%
+just entirely on this on this second sum
+and so this is equal to 1
+
+ align:start position:0%
+and so this is equal to 1
+ 
+
+ align:start position:0%
+and so this is equal to 1
++ 4x + 4 is on top and okay so we need
+
+ align:start position:0%
++ 4x + 4 is on top and okay so we need
+ 
+
+ align:start position:0%
++ 4x + 4 is on top and okay so we need
+to factor the the denominator if
+
+ align:start position:0%
+to factor the the denominator if
+ 
+
+ align:start position:0%
+to factor the the denominator if
+possible and in this case that it that's
+
+ align:start position:0%
+possible and in this case that it that's
+ 
+
+ align:start position:0%
+possible and in this case that it that's
+that's not only possible it's it's
+
+ align:start position:0%
+that's not only possible it's it's
+ 
+
+ align:start position:0%
+that's not only possible it's it's
+pretty straightforward we can factor out
+
+ align:start position:0%
+pretty straightforward we can factor out
+ 
+
+ align:start position:0%
+pretty straightforward we can factor out
+an X from both terms and we see that the
+
+ align:start position:0%
+an X from both terms and we see that the
+ 
+
+ align:start position:0%
+an X from both terms and we see that the
+denominator is
+
+ align:start position:0%
+denominator is
+ 
+
+ align:start position:0%
+denominator is
+x * X whoops minus
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+8 okay now in this case this is the the
+
+ align:start position:0%
+8 okay now in this case this is the the
+ 
+
+ align:start position:0%
+8 okay now in this case this is the the
+simplest situation for partial fraction
+
+ align:start position:0%
+simplest situation for partial fraction
+ 
+
+ align:start position:0%
+simplest situation for partial fraction
+decomposition we have the denominator is
+
+ align:start position:0%
+decomposition we have the denominator is
+ 
+
+ align:start position:0%
+decomposition we have the denominator is
+a product of distinct linear factors so
+
+ align:start position:0%
+a product of distinct linear factors so
+ 
+
+ align:start position:0%
+a product of distinct linear factors so
+when the denominator is a product of
+
+ align:start position:0%
+when the denominator is a product of
+ 
+
+ align:start position:0%
+when the denominator is a product of
+distinct linear factors what we get this
+
+ align:start position:0%
+distinct linear factors what we get this
+ 
+
+ align:start position:0%
+distinct linear factors what we get this
+is equal to what the partial fraction
+
+ align:start position:0%
+is equal to what the partial fraction
+ 
+
+ align:start position:0%
+is equal to what the partial fraction
+theorem tells us we can write is that
+
+ align:start position:0%
+theorem tells us we can write is that
+ 
+
+ align:start position:0%
+theorem tells us we can write is that
+this is equal
+
+ align:start position:0%
+this is equal
+ 
+
+ align:start position:0%
+this is equal
+to something some constant over the
+
+ align:start position:0%
+to something some constant over the
+ 
+
+ align:start position:0%
+to something some constant over the
+first Factor plus some constant over
+
+ align:start position:0%
+first Factor plus some constant over
+ 
+
+ align:start position:0%
+first Factor plus some constant over
+the the second Factor now if you if you
+
+ align:start position:0%
+the the second Factor now if you if you
+ 
+
+ align:start position:0%
+the the second Factor now if you if you
+had you know three factors then you
+
+ align:start position:0%
+had you know three factors then you
+ 
+
+ align:start position:0%
+had you know three factors then you
+would have three of these terms one for
+
+ align:start position:0%
+would have three of these terms one for
+ 
+
+ align:start position:0%
+would have three of these terms one for
+one for each factor if they were
+
+ align:start position:0%
+one for each factor if they were
+ 
+
+ align:start position:0%
+one for each factor if they were
+distinct linear factors so great okay
+
+ align:start position:0%
+distinct linear factors so great okay
+ 
+
+ align:start position:0%
+distinct linear factors so great okay
+now we can apply the the the coverup
+
+ align:start position:0%
+now we can apply the the the coverup
+ 
+
+ align:start position:0%
+now we can apply the the the coverup
+method that Professor jarrison taught us
+
+ align:start position:0%
+method that Professor jarrison taught us
+ 
+
+ align:start position:0%
+method that Professor jarrison taught us
+so again the one doesn't really matter
+
+ align:start position:0%
+so again the one doesn't really matter
+ 
+
+ align:start position:0%
+so again the one doesn't really matter
+here and you can just ignore it um so we
+
+ align:start position:0%
+here and you can just ignore it um so we
+ 
+
+ align:start position:0%
+here and you can just ignore it um so we
+have this is equal to this sum and we
+
+ align:start position:0%
+have this is equal to this sum and we
+ 
+
+ align:start position:0%
+have this is equal to this sum and we
+want to find the values of A and B that
+
+ align:start position:0%
+want to find the values of A and B that
+ 
+
+ align:start position:0%
+want to find the values of A and B that
+make this true and then once we have
+
+ align:start position:0%
+make this true and then once we have
+ 
+
+ align:start position:0%
+make this true and then once we have
+values of A and B that make this true
+
+ align:start position:0%
+values of A and B that make this true
+ 
+
+ align:start position:0%
+values of A and B that make this true
+the resulting expression will be all set
+
+ align:start position:0%
+the resulting expression will be all set
+ 
+
+ align:start position:0%
+the resulting expression will be all set
+to integrate right you this will just be
+
+ align:start position:0%
+to integrate right you this will just be
+ 
+
+ align:start position:0%
+to integrate right you this will just be
+easy it's just a polinomial in fact just
+
+ align:start position:0%
+easy it's just a polinomial in fact just
+ 
+
+ align:start position:0%
+easy it's just a polinomial in fact just
+a constant this is going to give us a
+
+ align:start position:0%
+a constant this is going to give us a
+ 
+
+ align:start position:0%
+a constant this is going to give us a
+logarithm and this is going to give us a
+
+ align:start position:0%
+logarithm and this is going to give us a
+ 
+
+ align:start position:0%
+logarithm and this is going to give us a
+logarithm so so once we find these
+
+ align:start position:0%
+logarithm so so once we find these
+ 
+
+ align:start position:0%
+logarithm so so once we find these
+constants A and B we're all set to
+
+ align:start position:0%
+constants A and B we're all set to
+ 
+
+ align:start position:0%
+constants A and B we're all set to
+integrate so okay so how does the cover
+
+ align:start position:0%
+integrate so okay so how does the cover
+ 
+
+ align:start position:0%
+integrate so okay so how does the cover
+up method work well so you cover
+
+ align:start position:0%
+up method work well so you cover
+ 
+
+ align:start position:0%
+up method work well so you cover
+up one of the factors in this case
+
+ align:start position:0%
+up one of the factors in this case
+ 
+
+ align:start position:0%
+up one of the factors in this case
+X and you cover up on the other side
+
+ align:start position:0%
+X and you cover up on the other side
+ 
+
+ align:start position:0%
+X and you cover up on the other side
+everything that doesn't have X in the
+
+ align:start position:0%
+everything that doesn't have X in the
+ 
+
+ align:start position:0%
+everything that doesn't have X in the
+denominator and also X and then you go
+
+ align:start position:0%
+denominator and also X and then you go
+ 
+
+ align:start position:0%
+denominator and also X and then you go
+back here and you plug in the
+
+ align:start position:0%
+back here and you plug in the
+ 
+
+ align:start position:0%
+back here and you plug in the
+appropriate value the you know the X
+
+ align:start position:0%
+appropriate value the you know the X
+ 
+
+ align:start position:0%
+appropriate value the you know the X
+minus whatever so in this case that's
+
+ align:start position:0%
+minus whatever so in this case that's
+ 
+
+ align:start position:0%
+minus whatever so in this case that's
+that's xal 0 and so over here you get 4
+
+ align:start position:0%
+that's xal 0 and so over here you get 4
+ 
+
+ align:start position:0%
+that's xal 0 and so over here you get 4
+over - 8 so that gives us
+
+ align:start position:0%
+over - 8 so that gives us
+ 
+
+ align:start position:0%
+over - 8 so that gives us
+a is equal to 4
+
+ align:start position:0%
+a is equal to 4
+ 
+
+ align:start position:0%
+a is equal to 4
+/
+
+ align:start position:0%
+/
+ 
+
+ align:start position:0%
+/
+8 which is minus a half and now we can
+
+ align:start position:0%
+8 which is minus a half and now we can
+ 
+
+ align:start position:0%
+8 which is minus a half and now we can
+do the same thing with the x - 8 part so
+
+ align:start position:0%
+do the same thing with the x - 8 part so
+ 
+
+ align:start position:0%
+do the same thing with the x - 8 part so
+we cover up x - 8 we cover up everything
+
+ align:start position:0%
+we cover up x - 8 we cover up everything
+ 
+
+ align:start position:0%
+we cover up x - 8 we cover up everything
+that doesn't have an x - 8 in it so
+
+ align:start position:0%
+that doesn't have an x - 8 in it so
+ 
+
+ align:start position:0%
+that doesn't have an x - 8 in it so
+we've got on the right hand side we get
+
+ align:start position:0%
+we've got on the right hand side we get
+ 
+
+ align:start position:0%
+we've got on the right hand side we get
+B and on the left hand side we have have
+
+ align:start position:0%
+B and on the left hand side we have have
+ 
+
+ align:start position:0%
+B and on the left hand side we have have
+to plug in 8 here so we plug 4 * 8 + 4
+
+ align:start position:0%
+to plug in 8 here so we plug 4 * 8 + 4
+ 
+
+ align:start position:0%
+to plug in 8 here so we plug 4 * 8 + 4
+which is 32 is 36 and divided by 8 so
+
+ align:start position:0%
+which is 32 is 36 and divided by 8 so
+ 
+
+ align:start position:0%
+which is 32 is 36 and divided by 8 so
+that's 36 divided 8 is 9 /
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+2 so once you've got these values of A
+
+ align:start position:0%
+2 so once you've got these values of A
+ 
+
+ align:start position:0%
+2 so once you've got these values of A
+and B okay so so so our original
+
+ align:start position:0%
+and B okay so so so our original
+ 
+
+ align:start position:0%
+and B okay so so so our original
+expression now we substitute in these
+
+ align:start position:0%
+expression now we substitute in these
+ 
+
+ align:start position:0%
+expression now we substitute in these
+values of A and B then we know that this
+
+ align:start position:0%
+values of A and B then we know that this
+ 
+
+ align:start position:0%
+values of A and B then we know that this
+is a true equality and then the
+
+ align:start position:0%
+is a true equality and then the
+ 
+
+ align:start position:0%
+is a true equality and then the
+integration of this expression is just
+
+ align:start position:0%
+integration of this expression is just
+ 
+
+ align:start position:0%
+integration of this expression is just
+reduced completely to the integration of
+
+ align:start position:0%
+reduced completely to the integration of
+ 
+
+ align:start position:0%
+reduced completely to the integration of
+this easy to integrate expression okay
+
+ align:start position:0%
+this easy to integrate expression okay
+ 
+
+ align:start position:0%
+this easy to integrate expression okay
+and so this is the partial fraction
+
+ align:start position:0%
+and so this is the partial fraction
+ 
+
+ align:start position:0%
+and so this is the partial fraction
+decomposition here with with you know
+
+ align:start position:0%
+decomposition here with with you know
+ 
+
+ align:start position:0%
+decomposition here with with you know
+with a equals minus a half and b equals
+
+ align:start position:0%
+with a equals minus a half and b equals
+ 
+
+ align:start position:0%
+with a equals minus a half and b equals
+9 halfes so that's part A let's go on to
+
+ align:start position:0%
+9 halfes so that's part A let's go on to
+ 
+
+ align:start position:0%
+9 halfes so that's part A let's go on to
+Part
+
+ align:start position:0%
+Part
+ 
+
+ align:start position:0%
+Part
+B I have to remind myself what part B is
+
+ align:start position:0%
+B I have to remind myself what part B is
+ 
+
+ align:start position:0%
+B I have to remind myself what part B is
+ah okay so Part B is x^2 / x + 1 4th
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so in this case in the denominator we
+
+ align:start position:0%
+so in this case in the denominator we
+ 
+
+ align:start position:0%
+so in this case in the denominator we
+still have only linear factors but we
+
+ align:start position:0%
+still have only linear factors but we
+ 
+
+ align:start position:0%
+still have only linear factors but we
+have repeated factors and I mean this
+
+ align:start position:0%
+have repeated factors and I mean this
+ 
+
+ align:start position:0%
+have repeated factors and I mean this
+this is actually a particularly simple
+
+ align:start position:0%
+this is actually a particularly simple
+ 
+
+ align:start position:0%
+this is actually a particularly simple
+example where we have only one factor
+
+ align:start position:0%
+example where we have only one factor
+ 
+
+ align:start position:0%
+example where we have only one factor
+but it's repeated four times right
+
+ align:start position:0%
+but it's repeated four times right
+ 
+
+ align:start position:0%
+but it's repeated four times right
+fourth power so when you have that
+
+ align:start position:0%
+fourth power so when you have that
+ 
+
+ align:start position:0%
+fourth power so when you have that
+situation the partial fraction
+
+ align:start position:0%
+situation the partial fraction
+ 
+
+ align:start position:0%
+situation the partial fraction
+decomposition looks a little bit
+
+ align:start position:0%
+decomposition looks a little bit
+ 
+
+ align:start position:0%
+decomposition looks a little bit
+different and so what you get is that
+
+ align:start position:0%
+different and so what you get is that
+ 
+
+ align:start position:0%
+different and so what you get is that
+you have for every repeated power
+
+ align:start position:0%
+you have for every repeated power
+ 
+
+ align:start position:0%
+you have for every repeated power
+so for each this this one appears four
+
+ align:start position:0%
+so for each this this one appears four
+ 
+
+ align:start position:0%
+so for each this this one appears four
+times so you get four sum ANS on the
+
+ align:start position:0%
+times so you get four sum ANS on the
+ 
+
+ align:start position:0%
+times so you get four sum ANS on the
+right hand side with increasing powers
+
+ align:start position:0%
+right hand side with increasing powers
+ 
+
+ align:start position:0%
+right hand side with increasing powers
+of of this this linear Factor so with
+
+ align:start position:0%
+of of this this linear Factor so with
+ 
+
+ align:start position:0%
+of of this this linear Factor so with
+increasing powers of xus one so this is
+
+ align:start position:0%
+increasing powers of xus one so this is
+ 
+
+ align:start position:0%
+increasing powers of xus one so this is
+going to be a or sorry x + 1 um a over x
+
+ align:start position:0%
+going to be a or sorry x + 1 um a over x
+ 
+
+ align:start position:0%
+going to be a or sorry x + 1 um a over x
++ 1 plus b over x + 1
+
+ align:start position:0%
++ 1 plus b over x + 1
+ 
+
+ align:start position:0%
++ 1 plus b over x + 1
+squared plus
+
+ align:start position:0%
+squared plus
+ 
+
+ align:start position:0%
+squared plus
+C over x + 1 cubed plus
+
+ align:start position:0%
+C over x + 1 cubed plus
+ 
+
+ align:start position:0%
+C over x + 1 cubed plus
+d over x + 1 to the 4th now remember
+
+ align:start position:0%
+d over x + 1 to the 4th now remember
+ 
+
+ align:start position:0%
+d over x + 1 to the 4th now remember
+even though the degree here goes up in
+
+ align:start position:0%
+even though the degree here goes up in
+ 
+
+ align:start position:0%
+even though the degree here goes up in
+these in these later sums what stays on
+
+ align:start position:0%
+these in these later sums what stays on
+ 
+
+ align:start position:0%
+these in these later sums what stays on
+top is is the same it's it just stays a
+
+ align:start position:0%
+top is is the same it's it just stays a
+ 
+
+ align:start position:0%
+top is is the same it's it just stays a
+constant If This Were a quadratic Factor
+
+ align:start position:0%
+constant If This Were a quadratic Factor
+ 
+
+ align:start position:0%
+constant If This Were a quadratic Factor
+it would it would stay linear it doesn't
+
+ align:start position:0%
+it would it would stay linear it doesn't
+ 
+
+ align:start position:0%
+it would it would stay linear it doesn't
+it the top doesn't increase in degree
+
+ align:start position:0%
+it the top doesn't increase in degree
+ 
+
+ align:start position:0%
+it the top doesn't increase in degree
+when you do this um and a good a good
+
+ align:start position:0%
+when you do this um and a good a good
+ 
+
+ align:start position:0%
+when you do this um and a good a good
+simple way to check that you've you've
+
+ align:start position:0%
+simple way to check that you've you've
+ 
+
+ align:start position:0%
+simple way to check that you've you've
+got the right AB you know before you
+
+ align:start position:0%
+got the right AB you know before you
+ 
+
+ align:start position:0%
+got the right AB you know before you
+solve for the constant make sure you've
+
+ align:start position:0%
+solve for the constant make sure you've
+ 
+
+ align:start position:0%
+solve for the constant make sure you've
+got the right abstract decomposition is
+
+ align:start position:0%
+got the right abstract decomposition is
+ 
+
+ align:start position:0%
+got the right abstract decomposition is
+is to count the number of of these these
+
+ align:start position:0%
+is to count the number of of these these
+ 
+
+ align:start position:0%
+is to count the number of of these these
+constants that you're looking for it
+
+ align:start position:0%
+constants that you're looking for it
+ 
+
+ align:start position:0%
+constants that you're looking for it
+should be it should always match the the
+
+ align:start position:0%
+should be it should always match the the
+ 
+
+ align:start position:0%
+should be it should always match the the
+degree of the denominator over here so
+
+ align:start position:0%
+degree of the denominator over here so
+ 
+
+ align:start position:0%
+degree of the denominator over here so
+in this case the degree of the
+
+ align:start position:0%
+in this case the degree of the
+ 
+
+ align:start position:0%
+in this case the degree of the
+denominator is four and there are four
+
+ align:start position:0%
+denominator is four and there are four
+ 
+
+ align:start position:0%
+denominator is four and there are four
+constants so we've so so so that's a
+
+ align:start position:0%
+constants so we've so so so that's a
+ 
+
+ align:start position:0%
+constants so we've so so so that's a
+good way to check that that you set the
+
+ align:start position:0%
+good way to check that that you set the
+ 
+
+ align:start position:0%
+good way to check that that you set the
+problem up right okay so now um what do
+
+ align:start position:0%
+problem up right okay so now um what do
+ 
+
+ align:start position:0%
+problem up right okay so now um what do
+we do in this case well the coverup
+
+ align:start position:0%
+we do in this case well the coverup
+ 
+
+ align:start position:0%
+we do in this case well the coverup
+method works but it only works to find
+
+ align:start position:0%
+method works but it only works to find
+ 
+
+ align:start position:0%
+method works but it only works to find
+the the highest degree term right so we
+
+ align:start position:0%
+the the highest degree term right so we
+ 
+
+ align:start position:0%
+the the highest degree term right so we
+cover up x + 1 4th and we cover up
+
+ align:start position:0%
+cover up x + 1 4th and we cover up
+ 
+
+ align:start position:0%
+cover up x + 1 4th and we cover up
+everything with a smaller power of X+
+
+ align:start position:0%
+everything with a smaller power of X+
+ 
+
+ align:start position:0%
+everything with a smaller power of X+
+one and then we plug in uh negative 1
+
+ align:start position:0%
+one and then we plug in uh negative 1
+ 
+
+ align:start position:0%
+one and then we plug in uh negative 1
+right because we need X plus one to be
+
+ align:start position:0%
+right because we need X plus one to be
+ 
+
+ align:start position:0%
+right because we need X plus one to be
+to be zero so okay so over here we get
+
+ align:start position:0%
+to be zero so okay so over here we get
+ 
+
+ align:start position:0%
+to be zero so okay so over here we get
+netive 1^2 is 1 so we get right away
+
+ align:start position:0%
+netive 1^2 is 1 so we get right away
+ 
+
+ align:start position:0%
+netive 1^2 is 1 so we get right away
+that D is equal to
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+one okay but that doesn't give us a b or
+
+ align:start position:0%
+one okay but that doesn't give us a b or
+ 
+
+ align:start position:0%
+one okay but that doesn't give us a b or
+c we can't get a b or c by the coverup
+
+ align:start position:0%
+c we can't get a b or c by the coverup
+ 
+
+ align:start position:0%
+c we can't get a b or c by the coverup
+method now there are couple different
+
+ align:start position:0%
+method now there are couple different
+ 
+
+ align:start position:0%
+method now there are couple different
+ways you can proceed at this
+
+ align:start position:0%
+ways you can proceed at this
+ 
+
+ align:start position:0%
+ways you can proceed at this
+point one thing you can do which is
+
+ align:start position:0%
+point one thing you can do which is
+ 
+
+ align:start position:0%
+point one thing you can do which is
+something that often Works um is you
+
+ align:start position:0%
+something that often Works um is you
+ 
+
+ align:start position:0%
+something that often Works um is you
+could uh plug in values well so this
+
+ align:start position:0%
+could uh plug in values well so this
+ 
+
+ align:start position:0%
+could uh plug in values well so this
+will always work I shouldn't say often
+
+ align:start position:0%
+will always work I shouldn't say often
+ 
+
+ align:start position:0%
+will always work I shouldn't say often
+works you can start plugging in other
+
+ align:start position:0%
+works you can start plugging in other
+ 
+
+ align:start position:0%
+works you can start plugging in other
+values for x and as you plug in other
+
+ align:start position:0%
+values for x and as you plug in other
+ 
+
+ align:start position:0%
+values for x and as you plug in other
+values for X what you'll see is that for
+
+ align:start position:0%
+values for X what you'll see is that for
+ 
+
+ align:start position:0%
+values for X what you'll see is that for
+every value you plug in you'll get a
+
+ align:start position:0%
+every value you plug in you'll get a
+ 
+
+ align:start position:0%
+every value you plug in you'll get a
+linear equation
+
+ align:start position:0%
+linear equation
+ 
+
+ align:start position:0%
+linear equation
+relating your variables a b c and
+
+ align:start position:0%
+relating your variables a b c and
+ 
+
+ align:start position:0%
+relating your variables a b c and
+whatever in this case that's all we've
+
+ align:start position:0%
+whatever in this case that's all we've
+ 
+
+ align:start position:0%
+whatever in this case that's all we've
+got left a b and c to each other and so
+
+ align:start position:0%
+got left a b and c to each other and so
+ 
+
+ align:start position:0%
+got left a b and c to each other and so
+if you plug in three different values of
+
+ align:start position:0%
+if you plug in three different values of
+ 
+
+ align:start position:0%
+if you plug in three different values of
+X say you'll get three different linear
+
+ align:start position:0%
+X say you'll get three different linear
+ 
+
+ align:start position:0%
+X say you'll get three different linear
+equations with three different variables
+
+ align:start position:0%
+equations with three different variables
+ 
+
+ align:start position:0%
+equations with three different variables
+and then you can solve them that's one
+
+ align:start position:0%
+and then you can solve them that's one
+ 
+
+ align:start position:0%
+and then you can solve them that's one
+thing you can do another thing you could
+
+ align:start position:0%
+thing you can do another thing you could
+ 
+
+ align:start position:0%
+thing you can do another thing you could
+do is you can multiply through by x + 1
+
+ align:start position:0%
+do is you can multiply through by x + 1
+ 
+
+ align:start position:0%
+do is you can multiply through by x + 1
+4th so if you do that you'll have on the
+
+ align:start position:0%
+4th so if you do that you'll have on the
+ 
+
+ align:start position:0%
+4th so if you do that you'll have on the
+left you'll just have X squ and on the
+
+ align:start position:0%
+left you'll just have X squ and on the
+ 
+
+ align:start position:0%
+left you'll just have X squ and on the
+right you'll have well you have a * x +
+
+ align:start position:0%
+right you'll have well you have a * x +
+ 
+
+ align:start position:0%
+right you'll have well you have a * x +
+1 cubed plus b * x + 1^ 2 plus C * X+ 1
+
+ align:start position:0%
+1 cubed plus b * x + 1^ 2 plus C * X+ 1
+ 
+
+ align:start position:0%
+1 cubed plus b * x + 1^ 2 plus C * X+ 1
+plus d and we already know that D is
+
+ align:start position:0%
+plus d and we already know that D is
+ 
+
+ align:start position:0%
+plus d and we already know that D is
+equal to one okay and so then for those
+
+ align:start position:0%
+equal to one okay and so then for those
+ 
+
+ align:start position:0%
+equal to one okay and so then for those
+two things to be equal they're equal as
+
+ align:start position:0%
+two things to be equal they're equal as
+ 
+
+ align:start position:0%
+two things to be equal they're equal as
+pols all their coefficients have to be
+
+ align:start position:0%
+pols all their coefficients have to be
+ 
+
+ align:start position:0%
+pols all their coefficients have to be
+equal so you can just look at the
+
+ align:start position:0%
+equal so you can just look at the
+ 
+
+ align:start position:0%
+equal so you can just look at the
+coefficients in that resulting
+
+ align:start position:0%
+coefficients in that resulting
+ 
+
+ align:start position:0%
+coefficients in that resulting
+expression and ask um you know which
+
+ align:start position:0%
+expression and ask um you know which
+ 
+
+ align:start position:0%
+expression and ask um you know which
+which
+
+ align:start position:0%
+which
+ 
+
+ align:start position:0%
+which
+coefficients uh sorry and you can you
+
+ align:start position:0%
+coefficients uh sorry and you can you
+ 
+
+ align:start position:0%
+coefficients uh sorry and you can you
+can set coefficients on the two sides
+
+ align:start position:0%
+can set coefficients on the two sides
+ 
+
+ align:start position:0%
+can set coefficients on the two sides
+equal if the two Pol are equal all their
+
+ align:start position:0%
+equal if the two Pol are equal all their
+ 
+
+ align:start position:0%
+equal if the two Pol are equal all their
+corresponding coefficients are equal so
+
+ align:start position:0%
+corresponding coefficients are equal so
+ 
+
+ align:start position:0%
+corresponding coefficients are equal so
+you could look you know at this side and
+
+ align:start position:0%
+you could look you know at this side and
+ 
+
+ align:start position:0%
+you could look you know at this side and
+you'll say oh okay so the coefficient of
+
+ align:start position:0%
+you'll say oh okay so the coefficient of
+ 
+
+ align:start position:0%
+you'll say oh okay so the coefficient of
+x cubed has to be the same as whatever
+
+ align:start position:0%
+x cubed has to be the same as whatever
+ 
+
+ align:start position:0%
+x cubed has to be the same as whatever
+the coefficient of x cubed over here is
+
+ align:start position:0%
+the coefficient of x cubed over here is
+ 
+
+ align:start position:0%
+the coefficient of x cubed over here is
+and the coefficient of x squ has to be
+
+ align:start position:0%
+and the coefficient of x squ has to be
+ 
+
+ align:start position:0%
+and the coefficient of x squ has to be
+the same as the coefficient of x squ and
+
+ align:start position:0%
+the same as the coefficient of x squ and
+ 
+
+ align:start position:0%
+the same as the coefficient of x squ and
+and so on so that's another way to
+
+ align:start position:0%
+and so on so that's another way to
+ 
+
+ align:start position:0%
+and so on so that's another way to
+proceed um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+a yeah all right th those are really
+
+ align:start position:0%
+a yeah all right th those are really
+ 
+
+ align:start position:0%
+a yeah all right th those are really
+your your two your two best options um I
+
+ align:start position:0%
+your your two your two best options um I
+ 
+
+ align:start position:0%
+your your two your two best options um I
+like I like to multiply through
+
+ align:start position:0%
+like I like to multiply through
+ 
+
+ align:start position:0%
+like I like to multiply through
+personally um so okay so so if I were to
+
+ align:start position:0%
+personally um so okay so so if I were to
+ 
+
+ align:start position:0%
+personally um so okay so so if I were to
+do that in this case on the left hand
+
+ align:start position:0%
+do that in this case on the left hand
+ 
+
+ align:start position:0%
+do that in this case on the left hand
+side I'd get x^2 = a * x + 1 cubed + B *
+
+ align:start position:0%
+side I'd get x^2 = a * x + 1 cubed + B *
+ 
+
+ align:start position:0%
+side I'd get x^2 = a * x + 1 cubed + B *
+x + 1
+
+ align:start position:0%
+x + 1
+ 
+
+ align:start position:0%
+x + 1
+2 +
+
+ align:start position:0%
+2 +
+ 
+
+ align:start position:0%
+2 +
+C * x + 1 plus d except we already know
+
+ align:start position:0%
+C * x + 1 plus d except we already know
+ 
+
+ align:start position:0%
+C * x + 1 plus d except we already know
+that D is equal to one so I'm just going
+
+ align:start position:0%
+that D is equal to one so I'm just going
+ 
+
+ align:start position:0%
+that D is equal to one so I'm just going
+to write + one
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so okay so actually let me let me say
+
+ align:start position:0%
+so okay so actually let me let me say
+ 
+
+ align:start position:0%
+so okay so actually let me let me say
+that there there are other things you
+
+ align:start position:0%
+that there there are other things you
+ 
+
+ align:start position:0%
+that there there are other things you
+could do which is you could you could
+
+ align:start position:0%
+could do which is you could you could
+ 
+
+ align:start position:0%
+could do which is you could you could
+rearrange things and and simplify
+
+ align:start position:0%
+rearrange things and and simplify
+ 
+
+ align:start position:0%
+rearrange things and and simplify
+algebraically before plugging in values
+
+ align:start position:0%
+algebraically before plugging in values
+ 
+
+ align:start position:0%
+algebraically before plugging in values
+or before comparing coefficients um so
+
+ align:start position:0%
+or before comparing coefficients um so
+ 
+
+ align:start position:0%
+or before comparing coefficients um so
+let me give you one example of of each
+
+ align:start position:0%
+let me give you one example of of each
+ 
+
+ align:start position:0%
+let me give you one example of of each
+of those three possibilities so for
+
+ align:start position:0%
+of those three possibilities so for
+ 
+
+ align:start position:0%
+of those three possibilities so for
+example um one thing you can do is you
+
+ align:start position:0%
+example um one thing you can do is you
+ 
+
+ align:start position:0%
+example um one thing you can do is you
+can look at look at the highest degree
+
+ align:start position:0%
+can look at look at the highest degree
+ 
+
+ align:start position:0%
+can look at look at the highest degree
+coefficient so as professor jarrison
+
+ align:start position:0%
+coefficient so as professor jarrison
+ 
+
+ align:start position:0%
+coefficient so as professor jarrison
+said the easiest coefficients are
+
+ align:start position:0%
+said the easiest coefficients are
+ 
+
+ align:start position:0%
+said the easiest coefficients are
+usually the high order terms and and the
+
+ align:start position:0%
+usually the high order terms and and the
+ 
+
+ align:start position:0%
+usually the high order terms and and the
+low order terms so in this case the high
+
+ align:start position:0%
+low order terms so in this case the high
+ 
+
+ align:start position:0%
+low order terms so in this case the high
+order term would be that this is a third
+
+ align:start position:0%
+order term would be that this is a third
+ 
+
+ align:start position:0%
+order term would be that this is a third
+degree polinomial on the right hand side
+
+ align:start position:0%
+degree polinomial on the right hand side
+ 
+
+ align:start position:0%
+degree polinomial on the right hand side
+and it's a second degree polinomial on
+
+ align:start position:0%
+and it's a second degree polinomial on
+ 
+
+ align:start position:0%
+and it's a second degree polinomial on
+the left um so the the the highest order
+
+ align:start position:0%
+the left um so the the the highest order
+ 
+
+ align:start position:0%
+the left um so the the the highest order
+term here x cubed it just appears in
+
+ align:start position:0%
+term here x cubed it just appears in
+ 
+
+ align:start position:0%
+term here x cubed it just appears in
+this one place as coefficient a right
+
+ align:start position:0%
+this one place as coefficient a right
+ 
+
+ align:start position:0%
+this one place as coefficient a right
+this is ax cubed plus something time x s
+
+ align:start position:0%
+this is ax cubed plus something time x s
+ 
+
+ align:start position:0%
+this is ax cubed plus something time x s
+plus blah blah blah blah blah and over
+
+ align:start position:0%
+plus blah blah blah blah blah and over
+ 
+
+ align:start position:0%
+plus blah blah blah blah blah and over
+here we have no X
+
+ align:start position:0%
+here we have no X
+ 
+
+ align:start position:0%
+here we have no X
+cubes so you have X cubes here but no X
+
+ align:start position:0%
+cubes so you have X cubes here but no X
+ 
+
+ align:start position:0%
+cubes so you have X cubes here but no X
+cubes here that means the coefficient of
+
+ align:start position:0%
+cubes here that means the coefficient of
+ 
+
+ align:start position:0%
+cubes here that means the coefficient of
+x Cub here has to be zero so a has to be
+
+ align:start position:0%
+x Cub here has to be zero so a has to be
+ 
+
+ align:start position:0%
+x Cub here has to be zero so a has to be
+zero
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so a has to be equal to zero and
+
+ align:start position:0%
+okay so a has to be equal to zero and
+ 
+
+ align:start position:0%
+okay so a has to be equal to zero and
+that simplifies everything a little bit
+
+ align:start position:0%
+that simplifies everything a little bit
+ 
+
+ align:start position:0%
+that simplifies everything a little bit
+so now we get x^2 equal B * x + 1 2 + C
+
+ align:start position:0%
+so now we get x^2 equal B * x + 1 2 + C
+ 
+
+ align:start position:0%
+so now we get x^2 equal B * x + 1 2 + C
+* x +
+
+ align:start position:0%
+* x +
+ 
+
+ align:start position:0%
+* x +
+1 plus
+
+ align:start position:0%
+1 plus
+ 
+
+ align:start position:0%
+1 plus
+one now let me show you what I mean
+
+ align:start position:0%
+one now let me show you what I mean
+ 
+
+ align:start position:0%
+one now let me show you what I mean
+about
+
+ align:start position:0%
+about
+ 
+
+ align:start position:0%
+about
+algebraic uh manipulation this one if
+
+ align:start position:0%
+algebraic uh manipulation this one if
+ 
+
+ align:start position:0%
+algebraic uh manipulation this one if
+you wanted you could you could always
+
+ align:start position:0%
+you wanted you could you could always
+ 
+
+ align:start position:0%
+you wanted you could you could always
+just subtract it over to the other side
+
+ align:start position:0%
+just subtract it over to the other side
+ 
+
+ align:start position:0%
+just subtract it over to the other side
+right and so then you'll have on the
+
+ align:start position:0%
+right and so then you'll have on the
+ 
+
+ align:start position:0%
+right and so then you'll have on the
+left you'll have x^2 - 1 and x^2 - 1 you
+
+ align:start position:0%
+left you'll have x^2 - 1 and x^2 - 1 you
+ 
+
+ align:start position:0%
+left you'll have x^2 - 1 and x^2 - 1 you
+can write as x -1 * x + 1
+
+ align:start position:0%
+can write as x -1 * x + 1
+ 
+
+ align:start position:0%
+can write as x -1 * x + 1
+= B * x + 1^ 2 + C
+
+ align:start position:0%
+= B * x + 1^ 2 + C
+ 
+
+ align:start position:0%
+= B * x + 1^ 2 + C
+* x + one and now you could divide out
+
+ align:start position:0%
+* x + one and now you could divide out
+ 
+
+ align:start position:0%
+* x + one and now you could divide out
+by an X plus one everywhere it appears
+
+ align:start position:0%
+by an X plus one everywhere it appears
+ 
+
+ align:start position:0%
+by an X plus one everywhere it appears
+in all terms so you get x -1 = B * x +
+
+ align:start position:0%
+in all terms so you get x -1 = B * x +
+ 
+
+ align:start position:0%
+in all terms so you get x -1 = B * x +
+1 plus c
+
+ align:start position:0%
+1 plus c
+ 
+
+ align:start position:0%
+1 plus c
+and now what this does for you is is you
+
+ align:start position:0%
+and now what this does for you is is you
+ 
+
+ align:start position:0%
+and now what this does for you is is you
+sort of just reduced the degree
+
+ align:start position:0%
+sort of just reduced the degree
+ 
+
+ align:start position:0%
+sort of just reduced the degree
+everywhere and actually you you could
+
+ align:start position:0%
+everywhere and actually you you could
+ 
+
+ align:start position:0%
+everywhere and actually you you could
+you could substitute xals minus one
+
+ align:start position:0%
+you could substitute xals minus one
+ 
+
+ align:start position:0%
+you could substitute xals minus one
+again if you wanted to for example um
+
+ align:start position:0%
+again if you wanted to for example um
+ 
+
+ align:start position:0%
+again if you wanted to for example um
+and here so for example if you
+
+ align:start position:0%
+and here so for example if you
+ 
+
+ align:start position:0%
+and here so for example if you
+substitute xal minus one this that's
+
+ align:start position:0%
+substitute xal minus one this that's
+ 
+
+ align:start position:0%
+substitute xal minus one this that's
+that's the same as it's the same idea as
+
+ align:start position:0%
+that's the same as it's the same idea as
+ 
+
+ align:start position:0%
+that's the same as it's the same idea as
+what you do in the coverup method um
+
+ align:start position:0%
+what you do in the coverup method um
+ 
+
+ align:start position:0%
+what you do in the coverup method um
+this this B term will just die
+
+ align:start position:0%
+this this B term will just die
+ 
+
+ align:start position:0%
+this this B term will just die
+completely and you'll be left with
+
+ align:start position:0%
+completely and you'll be left with
+ 
+
+ align:start position:0%
+completely and you'll be left with
+negative -2 on the left so you get C I'm
+
+ align:start position:0%
+negative -2 on the left so you get C I'm
+ 
+
+ align:start position:0%
+negative -2 on the left so you get C I'm
+going to have to move over here sorry so
+
+ align:start position:0%
+going to have to move over here sorry so
+ 
+
+ align:start position:0%
+going to have to move over here sorry so
+C is equal to -2 then and also you can
+
+ align:start position:0%
+C is equal to -2 then and also you can
+ 
+
+ align:start position:0%
+C is equal to -2 then and also you can
+do the the the one thing I haven't done
+
+ align:start position:0%
+do the the the one thing I haven't done
+ 
+
+ align:start position:0%
+do the the the one thing I haven't done
+so far is this plugging in nice choices
+
+ align:start position:0%
+so far is this plugging in nice choices
+ 
+
+ align:start position:0%
+so far is this plugging in nice choices
+of values so another nice choice of
+
+ align:start position:0%
+of values so another nice choice of
+ 
+
+ align:start position:0%
+of values so another nice choice of
+value for x that we haven't used is xals
+
+ align:start position:0%
+value for x that we haven't used is xals
+ 
+
+ align:start position:0%
+value for x that we haven't used is xals
+0 so if you plug in xal 0 you get minus1
+
+ align:start position:0%
+0 so if you plug in xal 0 you get minus1
+ 
+
+ align:start position:0%
+0 so if you plug in xal 0 you get minus1
+= b + C so -1 = b + C and since we just
+
+ align:start position:0%
+= b + C so -1 = b + C and since we just
+ 
+
+ align:start position:0%
+= b + C so -1 = b + C and since we just
+found C that means that b is equal to
+
+ align:start position:0%
+found C that means that b is equal to
+ 
+
+ align:start position:0%
+found C that means that b is equal to
+1 all right
+
+ align:start position:0%
+1 all right
+ 
+
+ align:start position:0%
+1 all right
+so oh boy I'm using a lot of space
+
+ align:start position:0%
+so oh boy I'm using a lot of space
+ 
+
+ align:start position:0%
+so oh boy I'm using a lot of space
+aren't I all right right so in this case
+
+ align:start position:0%
+aren't I all right right so in this case
+ 
+
+ align:start position:0%
+aren't I all right right so in this case
+we've got our coefficients AAL 0 d = 1
+
+ align:start position:0%
+we've got our coefficients AAL 0 d = 1
+ 
+
+ align:start position:0%
+we've got our coefficients AAL 0 d = 1
+Bal 1 Cal min-2 and that gives us the
+
+ align:start position:0%
+Bal 1 Cal min-2 and that gives us the
+ 
+
+ align:start position:0%
+Bal 1 Cal min-2 and that gives us the
+partial fraction
+
+ align:start position:0%
+partial fraction
+ 
+
+ align:start position:0%
+partial fraction
+decomposition um let's go back over here
+
+ align:start position:0%
+decomposition um let's go back over here
+ 
+
+ align:start position:0%
+decomposition um let's go back over here
+then and and look at question C so for C
+
+ align:start position:0%
+then and and look at question C so for C
+ 
+
+ align:start position:0%
+then and and look at question C so for C
+the question is what is the partial
+
+ align:start position:0%
+the question is what is the partial
+ 
+
+ align:start position:0%
+the question is what is the partial
+fraction decomposition of 2x + 2 divided
+
+ align:start position:0%
+fraction decomposition of 2x + 2 divided
+ 
+
+ align:start position:0%
+fraction decomposition of 2x + 2 divided
+the quantity 4x^2 + 1^
+
+ align:start position:0%
+the quantity 4x^2 + 1^
+ 
+
+ align:start position:0%
+the quantity 4x^2 + 1^
+2 uh this one's really easy this one is
+
+ align:start position:0%
+2 uh this one's really easy this one is
+ 
+
+ align:start position:0%
+2 uh this one's really easy this one is
+n this is already partial fraction
+
+ align:start position:0%
+n this is already partial fraction
+ 
+
+ align:start position:0%
+n this is already partial fraction
+decomposed right when you when you when
+
+ align:start position:0%
+decomposed right when you when you when
+ 
+
+ align:start position:0%
+decomposed right when you when you when
+you have so so here we have an
+
+ align:start position:0%
+you have so so here we have an
+ 
+
+ align:start position:0%
+you have so so here we have an
+irreducible quadratic in the denominator
+
+ align:start position:0%
+irreducible quadratic in the denominator
+ 
+
+ align:start position:0%
+irreducible quadratic in the denominator
+you can't you can't Factor this any
+
+ align:start position:0%
+you can't you can't Factor this any
+ 
+
+ align:start position:0%
+you can't you can't Factor this any
+further than it's than it's gone it it
+
+ align:start position:0%
+further than it's than it's gone it it
+ 
+
+ align:start position:0%
+further than it's than it's gone it it
+also occurs to to a higher power so when
+
+ align:start position:0%
+also occurs to to a higher power so when
+ 
+
+ align:start position:0%
+also occurs to to a higher power so when
+you when you partial fraction decompose
+
+ align:start position:0%
+you when you partial fraction decompose
+ 
+
+ align:start position:0%
+you when you partial fraction decompose
+something like this you want something
+
+ align:start position:0%
+something like this you want something
+ 
+
+ align:start position:0%
+something like this you want something
+linear over 4x^2 + 1 plus something
+
+ align:start position:0%
+linear over 4x^2 + 1 plus something
+ 
+
+ align:start position:0%
+linear over 4x^2 + 1 plus something
+linear over 4x^2 + 1^
+
+ align:start position:0%
+linear over 4x^2 + 1^
+ 
+
+ align:start position:0%
+linear over 4x^2 + 1^
+2 but we already have that right the the
+
+ align:start position:0%
+2 but we already have that right the the
+ 
+
+ align:start position:0%
+2 but we already have that right the the
+the the first linear part is zero and
+
+ align:start position:0%
+the the first linear part is zero and
+ 
+
+ align:start position:0%
+the the first linear part is zero and
+the second is is something linear over
+
+ align:start position:0%
+the second is is something linear over
+ 
+
+ align:start position:0%
+the second is is something linear over
+4x^2 + 1^2 so to integrate this it's
+
+ align:start position:0%
+4x^2 + 1^2 so to integrate this it's
+ 
+
+ align:start position:0%
+4x^2 + 1^2 so to integrate this it's
+already in a pretty good form now you're
+
+ align:start position:0%
+already in a pretty good form now you're
+ 
+
+ align:start position:0%
+already in a pretty good form now you're
+actually going to right if you wanted to
+
+ align:start position:0%
+actually going to right if you wanted to
+ 
+
+ align:start position:0%
+actually going to right if you wanted to
+integrate this you would you would split
+
+ align:start position:0%
+integrate this you would you would split
+ 
+
+ align:start position:0%
+integrate this you would you would split
+it into into two pieces one with the 2X
+
+ align:start position:0%
+it into into two pieces one with the 2X
+ 
+
+ align:start position:0%
+it into into two pieces one with the 2X
+and then one with the two and the first
+
+ align:start position:0%
+and then one with the two and the first
+ 
+
+ align:start position:0%
+and then one with the two and the first
+one you would just be a usual U
+
+ align:start position:0%
+one you would just be a usual U
+ 
+
+ align:start position:0%
+one you would just be a usual U
+substitution and the second one you
+
+ align:start position:0%
+substitution and the second one you
+ 
+
+ align:start position:0%
+substitution and the second one you
+would want some sort of trigonometric
+
+ align:start position:0%
+would want some sort of trigonometric
+ 
+
+ align:start position:0%
+would want some sort of trigonometric
+substitution um but but it but this one
+
+ align:start position:0%
+substitution um but but it but this one
+ 
+
+ align:start position:0%
+substitution um but but it but this one
+is already ready for for methods where
+
+ align:start position:0%
+is already ready for for methods where
+ 
+
+ align:start position:0%
+is already ready for for methods where
+already should be comfortable with okay
+
+ align:start position:0%
+already should be comfortable with okay
+ 
+
+ align:start position:0%
+already should be comfortable with okay
+so see that's that's easy it's done
+
+ align:start position:0%
+so see that's that's easy it's done
+ 
+
+ align:start position:0%
+so see that's that's easy it's done
+already I'll put a check mark there
+
+ align:start position:0%
+already I'll put a check mark there
+ 
+
+ align:start position:0%
+already I'll put a check mark there
+because that makes me happy okay and so
+
+ align:start position:0%
+because that makes me happy okay and so
+ 
+
+ align:start position:0%
+because that makes me happy okay and so
+for the all right for this last one um
+
+ align:start position:0%
+for the all right for this last one um
+ 
+
+ align:start position:0%
+for the all right for this last one um
+I'm I'm also not going to write this one
+
+ align:start position:0%
+I'm I'm also not going to write this one
+ 
+
+ align:start position:0%
+I'm I'm also not going to write this one
+out uh but the thing to notice here is
+
+ align:start position:0%
+out uh but the thing to notice here is
+ 
+
+ align:start position:0%
+out uh but the thing to notice here is
+that the way I wrote it this was really
+
+ align:start position:0%
+that the way I wrote it this was really
+ 
+
+ align:start position:0%
+that the way I wrote it this was really
+mean of me right I wrote it as x^2 minus
+
+ align:start position:0%
+mean of me right I wrote it as x^2 minus
+ 
+
+ align:start position:0%
+mean of me right I wrote it as x^2 minus
+1^ s so a natural instinct is say aha
+
+ align:start position:0%
+1^ s so a natural instinct is say aha
+ 
+
+ align:start position:0%
+1^ s so a natural instinct is say aha
+it's a quadratic repeated factor in the
+
+ align:start position:0%
+it's a quadratic repeated factor in the
+ 
+
+ align:start position:0%
+it's a quadratic repeated factor in the
+denominator right but but that but
+
+ align:start position:0%
+denominator right but but that but
+ 
+
+ align:start position:0%
+denominator right but but that but
+that's just because I was mean and I
+
+ align:start position:0%
+that's just because I was mean and I
+ 
+
+ align:start position:0%
+that's just because I was mean and I
+wrote it this way that's not actually
+
+ align:start position:0%
+wrote it this way that's not actually
+ 
+
+ align:start position:0%
+wrote it this way that's not actually
+what this is this this is not
+
+ align:start position:0%
+what this is this this is not
+ 
+
+ align:start position:0%
+what this is this this is not
+irreducible this factors you can
+
+ align:start position:0%
+irreducible this factors you can
+ 
+
+ align:start position:0%
+irreducible this factors you can
+rewrite let me let me come back over
+
+ align:start position:0%
+rewrite let me let me come back over
+ 
+
+ align:start position:0%
+rewrite let me let me come back over
+here so this is for question D so you
+
+ align:start position:0%
+here so this is for question D so you
+ 
+
+ align:start position:0%
+here so this is for question D so you
+can rewrite x^2 - one squared as x -1 2
+
+ align:start position:0%
+can rewrite x^2 - one squared as x -1 2
+ 
+
+ align:start position:0%
+can rewrite x^2 - one squared as x -1 2
+* x + 1 squar you can you can Factor
+
+ align:start position:0%
+* x + 1 squar you can you can Factor
+ 
+
+ align:start position:0%
+* x + 1 squar you can you can Factor
+this x^2 -
+
+ align:start position:0%
+this x^2 -
+ 
+
+ align:start position:0%
+this x^2 -
+one um so when you factor this x -1 what
+
+ align:start position:0%
+one um so when you factor this x -1 what
+ 
+
+ align:start position:0%
+one um so when you factor this x -1 what
+you see is this isn't a problem that has
+
+ align:start position:0%
+you see is this isn't a problem that has
+ 
+
+ align:start position:0%
+you see is this isn't a problem that has
+one irreducible quadratic Factor
+
+ align:start position:0%
+one irreducible quadratic Factor
+ 
+
+ align:start position:0%
+one irreducible quadratic Factor
+appearing to the second power what it
+
+ align:start position:0%
+appearing to the second power what it
+ 
+
+ align:start position:0%
+appearing to the second power what it
+has is two linear factors each appearing
+
+ align:start position:0%
+has is two linear factors each appearing
+ 
+
+ align:start position:0%
+has is two linear factors each appearing
+to the second power so the partial
+
+ align:start position:0%
+to the second power so the partial
+ 
+
+ align:start position:0%
+to the second power so the partial
+fraction decomposition in this problem
+
+ align:start position:0%
+fraction decomposition in this problem
+ 
+
+ align:start position:0%
+fraction decomposition in this problem
+will be something like a over x
+
+ align:start position:0%
+will be something like a over x
+ 
+
+ align:start position:0%
+will be something like a over x
+-1 + B over x -1 2ar + C over x + 1 plus
+
+ align:start position:0%
+-1 + B over x -1 2ar + C over x + 1 plus
+ 
+
+ align:start position:0%
+-1 + B over x -1 2ar + C over x + 1 plus
+D
+
+ align:start position:0%
+D
+ 
+
+ align:start position:0%
+D
+over x + 1
+
+ align:start position:0%
+over x + 1
+ 
+
+ align:start position:0%
+over x + 1
+2 that's what we you'll get when you
+
+ align:start position:0%
+2 that's what we you'll get when you
+ 
+
+ align:start position:0%
+2 that's what we you'll get when you
+when you apply partial fraction
+
+ align:start position:0%
+when you apply partial fraction
+ 
+
+ align:start position:0%
+when you apply partial fraction
+decomposition to this problem and then
+
+ align:start position:0%
+decomposition to this problem and then
+ 
+
+ align:start position:0%
+decomposition to this problem and then
+you have to solve for the for the
+
+ align:start position:0%
+you have to solve for the for the
+ 
+
+ align:start position:0%
+you have to solve for the for the
+coefficients a b c and d so I'm not
+
+ align:start position:0%
+coefficients a b c and d so I'm not
+ 
+
+ align:start position:0%
+coefficients a b c and d so I'm not
+going to write that out myself but I but
+
+ align:start position:0%
+going to write that out myself but I but
+ 
+
+ align:start position:0%
+going to write that out myself but I but
+I cleverly did it uh before before I
+
+ align:start position:0%
+I cleverly did it uh before before I
+ 
+
+ align:start position:0%
+I cleverly did it uh before before I
+came on camera so I can tell you what
+
+ align:start position:0%
+came on camera so I can tell you what
+ 
+
+ align:start position:0%
+came on camera so I can tell you what
+the answer is if if you want to check
+
+ align:start position:0%
+the answer is if if you want to check
+ 
+
+ align:start position:0%
+the answer is if if you want to check
+your work so here we have a is equal to
+
+ align:start position:0%
+your work so here we have a is equal to
+ 
+
+ align:start position:0%
+your work so here we have a is equal to
+zero B is equal
+
+ align:start position:0%
+zero B is equal
+ 
+
+ align:start position:0%
+zero B is equal
+1 C is equal to 1 and D is equal to
+
+ align:start position:0%
+1 C is equal to 1 and D is equal to
+ 
+
+ align:start position:0%
+1 C is equal to 1 and D is equal to
+minus 3 so that's for the I didn't write
+
+ align:start position:0%
+minus 3 so that's for the I didn't write
+ 
+
+ align:start position:0%
+minus 3 so that's for the I didn't write
+it over here that's for this particular
+
+ align:start position:0%
+it over here that's for this particular
+ 
+
+ align:start position:0%
+it over here that's for this particular
+numerator that we that we started with
+
+ align:start position:0%
+numerator that we that we started with
+ 
+
+ align:start position:0%
+numerator that we that we started with
+back over here the for so for this
+
+ align:start position:0%
+back over here the for so for this
+ 
+
+ align:start position:0%
+back over here the for so for this
+particular fraction if you if you carry
+
+ align:start position:0%
+particular fraction if you if you carry
+ 
+
+ align:start position:0%
+particular fraction if you if you carry
+out the partial fraction decomposition
+
+ align:start position:0%
+out the partial fraction decomposition
+ 
+
+ align:start position:0%
+out the partial fraction decomposition
+what you
+
+ align:start position:0%
+what you
+ 
+
+ align:start position:0%
+what you
+get is is right here so okay so those
+
+ align:start position:0%
+get is is right here so okay so those
+ 
+
+ align:start position:0%
+get is is right here so okay so those
+are that was a few more examples of the
+
+ align:start position:0%
+are that was a few more examples of the
+ 
+
+ align:start position:0%
+are that was a few more examples of the
+partial fraction decomposition um I hope
+
+ align:start position:0%
+partial fraction decomposition um I hope
+ 
+
+ align:start position:0%
+partial fraction decomposition um I hope
+hope you enjoyed them and I'm going to
+
+ align:start position:0%
+hope you enjoyed them and I'm going to
+ 
+
+ align:start position:0%
+hope you enjoyed them and I'm going to
+end there
\ No newline at end of file
diff --git a/UzMEzYQOFRA.txt b/UzMEzYQOFRA.txt
new file mode 100644
index 0000000000000000000000000000000000000000..ba05c5251a4e70a9cfc93b40b2f9a7fc612be973
--- /dev/null
+++ b/UzMEzYQOFRA.txt
@@ -0,0 +1,8355 @@
+align:start position:0%
+ 
+the following content is provided under
+
+ align:start position:0%
+the following content is provided under
+ 
+
+ align:start position:0%
+the following content is provided under
+a Creative Commons license your support
+
+ align:start position:0%
+a Creative Commons license your support
+ 
+
+ align:start position:0%
+a Creative Commons license your support
+will help MIT OpenCourseWare continue to
+
+ align:start position:0%
+will help MIT OpenCourseWare continue to
+ 
+
+ align:start position:0%
+will help MIT OpenCourseWare continue to
+offer high quality educational resources
+
+ align:start position:0%
+offer high quality educational resources
+ 
+
+ align:start position:0%
+offer high quality educational resources
+for free
+
+ align:start position:0%
+for free
+ 
+
+ align:start position:0%
+for free
+to make a donation or view additional
+
+ align:start position:0%
+to make a donation or view additional
+ 
+
+ align:start position:0%
+to make a donation or view additional
+materials from hundreds of MIT courses
+
+ align:start position:0%
+materials from hundreds of MIT courses
+ 
+
+ align:start position:0%
+materials from hundreds of MIT courses
+visit MIT opencourseware at ocw.mit.edu
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+iron homeostasis and module six and then
+
+ align:start position:0%
+iron homeostasis and module six and then
+ 
+
+ align:start position:0%
+iron homeostasis and module six and then
+we're going to move on to module 7 and
+
+ align:start position:0%
+we're going to move on to module 7 and
+ 
+
+ align:start position:0%
+we're going to move on to module 7 and
+the readings have been posted and the
+
+ align:start position:0%
+the readings have been posted and the
+ 
+
+ align:start position:0%
+the readings have been posted and the
+PowerPoint has been posted for today's
+
+ align:start position:0%
+PowerPoint has been posted for today's
+ 
+
+ align:start position:0%
+PowerPoint has been posted for today's
+lecture as well okay so we were talking
+
+ align:start position:0%
+lecture as well okay so we were talking
+ 
+
+ align:start position:0%
+lecture as well okay so we were talking
+about last time peptidoglycan x' and
+
+ align:start position:0%
+about last time peptidoglycan x' and
+ 
+
+ align:start position:0%
+about last time peptidoglycan x' and
+gram-positive bacteria and they're
+
+ align:start position:0%
+gram-positive bacteria and they're
+ 
+
+ align:start position:0%
+gram-positive bacteria and they're
+actually quite thick depending on the
+
+ align:start position:0%
+actually quite thick depending on the
+ 
+
+ align:start position:0%
+actually quite thick depending on the
+organism and so what is the strategy
+
+ align:start position:0%
+organism and so what is the strategy
+ 
+
+ align:start position:0%
+organism and so what is the strategy
+nature uses to be able to pick up iron
+
+ align:start position:0%
+nature uses to be able to pick up iron
+ 
+
+ align:start position:0%
+nature uses to be able to pick up iron
+where you have WIC where you have a
+
+ align:start position:0%
+where you have WIC where you have a
+ 
+
+ align:start position:0%
+where you have WIC where you have a
+bacteria surrounded by this huge pet
+
+ align:start position:0%
+bacteria surrounded by this huge pet
+ 
+
+ align:start position:0%
+bacteria surrounded by this huge pet
+that okhla I can and the strategy and
+
+ align:start position:0%
+that okhla I can and the strategy and
+ 
+
+ align:start position:0%
+that okhla I can and the strategy and
+staph aureus that has evolved is they
+
+ align:start position:0%
+staph aureus that has evolved is they
+ 
+
+ align:start position:0%
+staph aureus that has evolved is they
+attach everything almost everything
+
+ align:start position:0%
+attach everything almost everything
+ 
+
+ align:start position:0%
+attach everything almost everything
+covalently to the peptidoglycan itself
+
+ align:start position:0%
+covalently to the peptidoglycan itself
+ 
+
+ align:start position:0%
+covalently to the peptidoglycan itself
+so at the end of the last lecture we
+
+ align:start position:0%
+so at the end of the last lecture we
+ 
+
+ align:start position:0%
+so at the end of the last lecture we
+were looking at we introduced you to the
+
+ align:start position:0%
+were looking at we introduced you to the
+ 
+
+ align:start position:0%
+were looking at we introduced you to the
+operon and staph aureus and there were
+
+ align:start position:0%
+operon and staph aureus and there were
+ 
+
+ align:start position:0%
+operon and staph aureus and there were
+proteins called sore cases which are
+
+ align:start position:0%
+proteins called sore cases which are
+ 
+
+ align:start position:0%
+proteins called sore cases which are
+transpeptidase is really basically and
+
+ align:start position:0%
+transpeptidase is really basically and
+ 
+
+ align:start position:0%
+transpeptidase is really basically and
+they have different sequence
+
+ align:start position:0%
+they have different sequence
+ 
+
+ align:start position:0%
+they have different sequence
+specificities and just go back one so
+
+ align:start position:0%
+specificities and just go back one so
+ 
+
+ align:start position:0%
+specificities and just go back one so
+where we were last time we have this
+
+ align:start position:0%
+where we were last time we have this
+ 
+
+ align:start position:0%
+where we were last time we have this
+operon and all of the proteins that are
+
+ align:start position:0%
+operon and all of the proteins that are
+ 
+
+ align:start position:0%
+operon and all of the proteins that are
+going to be involved in uptake of heme
+
+ align:start position:0%
+going to be involved in uptake of heme
+ 
+
+ align:start position:0%
+going to be involved in uptake of heme
+into the cell are called the isd
+
+ align:start position:0%
+into the cell are called the isd
+ 
+
+ align:start position:0%
+into the cell are called the isd
+proteins and so here's the operon and
+
+ align:start position:0%
+proteins and so here's the operon and
+ 
+
+ align:start position:0%
+proteins and so here's the operon and
+you could see that each part of this
+
+ align:start position:0%
+you could see that each part of this
+ 
+
+ align:start position:0%
+you could see that each part of this
+operon is activated by a fur box of fur
+
+ align:start position:0%
+operon is activated by a fur box of fur
+ 
+
+ align:start position:0%
+operon is activated by a fur box of fur
+boxes the transcriptional factor that
+
+ align:start position:0%
+boxes the transcriptional factor that
+ 
+
+ align:start position:0%
+boxes the transcriptional factor that
+turns off or on regulation at the
+
+ align:start position:0%
+turns off or on regulation at the
+ 
+
+ align:start position:0%
+turns off or on regulation at the
+transcriptional level by the presence or
+
+ align:start position:0%
+transcriptional level by the presence or
+ 
+
+ align:start position:0%
+transcriptional level by the presence or
+absence of iron which we're not going to
+
+ align:start position:0%
+absence of iron which we're not going to
+ 
+
+ align:start position:0%
+absence of iron which we're not going to
+talk about further and what I wanted to
+
+ align:start position:0%
+talk about further and what I wanted to
+ 
+
+ align:start position:0%
+talk about further and what I wanted to
+point out here before we move on is that
+
+ align:start position:0%
+point out here before we move on is that
+ 
+
+ align:start position:0%
+point out here before we move on is that
+all of the yellow anchors are proteins
+
+ align:start position:0%
+all of the yellow anchors are proteins
+ 
+
+ align:start position:0%
+all of the yellow anchors are proteins
+that are couch covalently by sort a they
+
+ align:start position:0%
+that are couch covalently by sort a they
+ 
+
+ align:start position:0%
+that are couch covalently by sort a they
+okay which has a defined zip code the
+
+ align:start position:0%
+okay which has a defined zip code the
+ 
+
+ align:start position:0%
+okay which has a defined zip code the
+blue in is d c has its own sort a sort
+
+ align:start position:0%
+blue in is d c has its own sort a sort
+ 
+
+ align:start position:0%
+blue in is d c has its own sort a sort
+a's b and is de is not attached
+
+ align:start position:0%
+a's b and is de is not attached
+ 
+
+ align:start position:0%
+a's b and is de is not attached
+covalently to the peptidoglycan but
+
+ align:start position:0%
+covalently to the peptidoglycan but
+ 
+
+ align:start position:0%
+covalently to the peptidoglycan but
+actually has membrane
+
+ align:start position:0%
+actually has membrane
+ 
+
+ align:start position:0%
+actually has membrane
+covalently to a lipid which is then
+
+ align:start position:0%
+covalently to a lipid which is then
+ 
+
+ align:start position:0%
+covalently to a lipid which is then
+inserted into the membrane which is the
+
+ align:start position:0%
+inserted into the membrane which is the
+ 
+
+ align:start position:0%
+inserted into the membrane which is the
+other strategy that's used in these
+
+ align:start position:0%
+other strategy that's used in these
+ 
+
+ align:start position:0%
+other strategy that's used in these
+systems and let me just point out you
+
+ align:start position:0%
+systems and let me just point out you
+ 
+
+ align:start position:0%
+systems and let me just point out you
+saw this I'm not going to spend much
+
+ align:start position:0%
+saw this I'm not going to spend much
+ 
+
+ align:start position:0%
+saw this I'm not going to spend much
+time on this today because you've
+
+ align:start position:0%
+time on this today because you've
+ 
+
+ align:start position:0%
+time on this today because you've
+already had a problem and your last
+
+ align:start position:0%
+already had a problem and your last
+ 
+
+ align:start position:0%
+already had a problem and your last
+problem was set on this but you have
+
+ align:start position:0%
+problem was set on this but you have
+ 
+
+ align:start position:0%
+problem was set on this but you have
+these little n domains and the neat
+
+ align:start position:0%
+these little n domains and the neat
+ 
+
+ align:start position:0%
+these little n domains and the neat
+domains which are 120 amino acid domains
+
+ align:start position:0%
+domains which are 120 amino acid domains
+ 
+
+ align:start position:0%
+domains which are 120 amino acid domains
+that allow you to pick up team and are
+
+ align:start position:0%
+that allow you to pick up team and are
+ 
+
+ align:start position:0%
+that allow you to pick up team and are
+involved and transfer of heme down a
+
+ align:start position:0%
+involved and transfer of heme down a
+ 
+
+ align:start position:0%
+involved and transfer of heme down a
+brach bucket for grade so what we're
+
+ align:start position:0%
+brach bucket for grade so what we're
+ 
+
+ align:start position:0%
+brach bucket for grade so what we're
+trying to do is attach these ISDN
+
+ align:start position:0%
+trying to do is attach these ISDN
+ 
+
+ align:start position:0%
+trying to do is attach these ISDN
+proteins to the peptidoglycan how it
+
+ align:start position:0%
+proteins to the peptidoglycan how it
+ 
+
+ align:start position:0%
+proteins to the peptidoglycan how it
+does that how they end up being
+
+ align:start position:0%
+does that how they end up being
+ 
+
+ align:start position:0%
+does that how they end up being
+organized how many there are is all an
+
+ align:start position:0%
+organized how many there are is all an
+ 
+
+ align:start position:0%
+organized how many there are is all an
+active area of research we don't really
+
+ align:start position:0%
+active area of research we don't really
+ 
+
+ align:start position:0%
+active area of research we don't really
+know that somebody might know it but
+
+ align:start position:0%
+know that somebody might know it but
+ 
+
+ align:start position:0%
+know that somebody might know it but
+it's not in the published literature and
+
+ align:start position:0%
+it's not in the published literature and
+ 
+
+ align:start position:0%
+it's not in the published literature and
+so the idea is again you can see all of
+
+ align:start position:0%
+so the idea is again you can see all of
+ 
+
+ align:start position:0%
+so the idea is again you can see all of
+these proteins in some way of tethered
+
+ align:start position:0%
+these proteins in some way of tethered
+ 
+
+ align:start position:0%
+these proteins in some way of tethered
+via usually a single trans membrane
+
+ align:start position:0%
+via usually a single trans membrane
+ 
+
+ align:start position:0%
+via usually a single trans membrane
+spanning region in the protein and
+
+ align:start position:0%
+spanning region in the protein and
+ 
+
+ align:start position:0%
+spanning region in the protein and
+here's one ISD protein here with a
+
+ align:start position:0%
+here's one ISD protein here with a
+ 
+
+ align:start position:0%
+here's one ISD protein here with a
+little zip code and it involves two
+
+ align:start position:0%
+little zip code and it involves two
+ 
+
+ align:start position:0%
+little zip code and it involves two
+sorties a which you've now seen over and
+
+ align:start position:0%
+sorties a which you've now seen over and
+ 
+
+ align:start position:0%
+sorties a which you've now seen over and
+over again happens to have a cysteine in
+
+ align:start position:0%
+over again happens to have a cysteine in
+ 
+
+ align:start position:0%
+over again happens to have a cysteine in
+its active site to go through a covalent
+
+ align:start position:0%
+its active site to go through a covalent
+ 
+
+ align:start position:0%
+its active site to go through a covalent
+bond formation and you're going to be
+
+ align:start position:0%
+bond formation and you're going to be
+ 
+
+ align:start position:0%
+bond formation and you're going to be
+cleaving one peptide bond and forming
+
+ align:start position:0%
+cleaving one peptide bond and forming
+ 
+
+ align:start position:0%
+cleaving one peptide bond and forming
+another peptide bond where have you seen
+
+ align:start position:0%
+another peptide bond where have you seen
+ 
+
+ align:start position:0%
+another peptide bond where have you seen
+that before
+
+ align:start position:0%
+that before
+ 
+
+ align:start position:0%
+that before
+that's how you did cross linking the
+
+ align:start position:0%
+that's how you did cross linking the
+ 
+
+ align:start position:0%
+that's how you did cross linking the
+transpeptidase it transpeptidase in
+
+ align:start position:0%
+transpeptidase it transpeptidase in
+ 
+
+ align:start position:0%
+transpeptidase it transpeptidase in
+reaction we talked about last time that
+
+ align:start position:0%
+reaction we talked about last time that
+ 
+
+ align:start position:0%
+reaction we talked about last time that
+allows you to form the bag and the bag
+
+ align:start position:0%
+allows you to form the bag and the bag
+ 
+
+ align:start position:0%
+allows you to form the bag and the bag
+of peptidoglycan x' becomes cross-linked
+
+ align:start position:0%
+of peptidoglycan x' becomes cross-linked
+ 
+
+ align:start position:0%
+of peptidoglycan x' becomes cross-linked
+and that's the key to survival of the
+
+ align:start position:0%
+and that's the key to survival of the
+ 
+
+ align:start position:0%
+and that's the key to survival of the
+organism and so you cleave this bond
+
+ align:start position:0%
+organism and so you cleave this bond
+ 
+
+ align:start position:0%
+organism and so you cleave this bond
+between t and g the specificity is
+
+ align:start position:0%
+between t and g the specificity is
+ 
+
+ align:start position:0%
+between t and g the specificity is
+understood and people in the Penta
+
+ align:start position:0%
+understood and people in the Penta
+ 
+
+ align:start position:0%
+understood and people in the Penta
+Lutece lab use sortase quite a bit but
+
+ align:start position:0%
+Lutece lab use sortase quite a bit but
+ 
+
+ align:start position:0%
+Lutece lab use sortase quite a bit but
+it has been engineered by the Luo lab to
+
+ align:start position:0%
+it has been engineered by the Luo lab to
+ 
+
+ align:start position:0%
+it has been engineered by the Luo lab to
+be more efficient as a catalyst so this
+
+ align:start position:0%
+be more efficient as a catalyst so this
+ 
+
+ align:start position:0%
+be more efficient as a catalyst so this
+is a natural catalyst you do a trance
+
+ align:start position:0%
+is a natural catalyst you do a trance
+ 
+
+ align:start position:0%
+is a natural catalyst you do a trance
+peptide pected asian reaction and then
+
+ align:start position:0%
+peptide pected asian reaction and then
+ 
+
+ align:start position:0%
+peptide pected asian reaction and then
+you have this is to me what's amazing
+
+ align:start position:0%
+you have this is to me what's amazing
+ 
+
+ align:start position:0%
+you have this is to me what's amazing
+you have this lipid 2 which is that c55
+
+ align:start position:0%
+you have this lipid 2 which is that c55
+ 
+
+ align:start position:0%
+you have this lipid 2 which is that c55
+isoprene system with the pentacle I seen
+
+ align:start position:0%
+isoprene system with the pentacle I seen
+ 
+
+ align:start position:0%
+isoprene system with the pentacle I seen
+hanging
+
+ align:start position:0%
+hanging
+ 
+
+ align:start position:0%
+hanging
+the pentapeptide all of which is
+
+ align:start position:0%
+the pentapeptide all of which is
+ 
+
+ align:start position:0%
+the pentapeptide all of which is
+generated on the inside of the cell and
+
+ align:start position:0%
+generated on the inside of the cell and
+ 
+
+ align:start position:0%
+generated on the inside of the cell and
+gets transferred to the outside of the
+
+ align:start position:0%
+gets transferred to the outside of the
+ 
+
+ align:start position:0%
+gets transferred to the outside of the
+cell one then is set up to do peptide
+
+ align:start position:0%
+cell one then is set up to do peptide
+ 
+
+ align:start position:0%
+cell one then is set up to do peptide
+bond formation just like just like we
+
+ align:start position:0%
+bond formation just like just like we
+ 
+
+ align:start position:0%
+bond formation just like just like we
+saw with the transpeptidase reaction and
+
+ align:start position:0%
+saw with the transpeptidase reaction and
+ 
+
+ align:start position:0%
+saw with the transpeptidase reaction and
+so you end up with in this lipid lipid
+
+ align:start position:0%
+so you end up with in this lipid lipid
+ 
+
+ align:start position:0%
+so you end up with in this lipid lipid
+too attached to the ISDN protein okay
+
+ align:start position:0%
+too attached to the ISDN protein okay
+ 
+
+ align:start position:0%
+too attached to the ISDN protein okay
+and then that's taken the so this is the
+
+ align:start position:0%
+and then that's taken the so this is the
+ 
+
+ align:start position:0%
+and then that's taken the so this is the
+detailed chemistry that we just
+
+ align:start position:0%
+detailed chemistry that we just
+ 
+
+ align:start position:0%
+detailed chemistry that we just
+discussed and you can go through it
+
+ align:start position:0%
+discussed and you can go through it
+ 
+
+ align:start position:0%
+discussed and you can go through it
+again if you don't remember it but it's
+
+ align:start position:0%
+again if you don't remember it but it's
+ 
+
+ align:start position:0%
+again if you don't remember it but it's
+very similar to the things we've now
+
+ align:start position:0%
+very similar to the things we've now
+ 
+
+ align:start position:0%
+very similar to the things we've now
+seen many many times in this course so
+
+ align:start position:0%
+seen many many times in this course so
+ 
+
+ align:start position:0%
+seen many many times in this course so
+once you attach this what happens is it
+
+ align:start position:0%
+once you attach this what happens is it
+ 
+
+ align:start position:0%
+once you attach this what happens is it
+gets transferred the whole thing now
+
+ align:start position:0%
+gets transferred the whole thing now
+ 
+
+ align:start position:0%
+gets transferred the whole thing now
+gets transferred by the mechanism
+
+ align:start position:0%
+gets transferred by the mechanism
+ 
+
+ align:start position:0%
+gets transferred by the mechanism
+similar to forming the polymer but now
+
+ align:start position:0%
+similar to forming the polymer but now
+ 
+
+ align:start position:0%
+similar to forming the polymer but now
+you have the pentacle I seen with an
+
+ align:start position:0%
+you have the pentacle I seen with an
+ 
+
+ align:start position:0%
+you have the pentacle I seen with an
+ISDN protein attached as well and so you
+
+ align:start position:0%
+ISDN protein attached as well and so you
+ 
+
+ align:start position:0%
+ISDN protein attached as well and so you
+can see then this is the growing
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+peptidoglycan with alternating units of
+
+ align:start position:0%
+peptidoglycan with alternating units of
+ 
+
+ align:start position:0%
+peptidoglycan with alternating units of
+an acetyl glucosamine and SAT Lee Remick
+
+ align:start position:0%
+an acetyl glucosamine and SAT Lee Remick
+ 
+
+ align:start position:0%
+an acetyl glucosamine and SAT Lee Remick
+acid we talked about last time and now
+
+ align:start position:0%
+acid we talked about last time and now
+ 
+
+ align:start position:0%
+acid we talked about last time and now
+we have the ISDN protein covalently
+
+ align:start position:0%
+we have the ISDN protein covalently
+ 
+
+ align:start position:0%
+we have the ISDN protein covalently
+attached so this is a pretty amazing
+
+ align:start position:0%
+attached so this is a pretty amazing
+ 
+
+ align:start position:0%
+attached so this is a pretty amazing
+strategy and you can imagine trying to
+
+ align:start position:0%
+strategy and you can imagine trying to
+ 
+
+ align:start position:0%
+strategy and you can imagine trying to
+study this under natural systems with
+
+ align:start position:0%
+study this under natural systems with
+ 
+
+ align:start position:0%
+study this under natural systems with
+everything attached is quite challenging
+
+ align:start position:0%
+everything attached is quite challenging
+ 
+
+ align:start position:0%
+everything attached is quite challenging
+and so the problem you had on the
+
+ align:start position:0%
+and so the problem you had on the
+ 
+
+ align:start position:0%
+and so the problem you had on the
+problem set what do they do they cut
+
+ align:start position:0%
+problem set what do they do they cut
+ 
+
+ align:start position:0%
+problem set what do they do they cut
+everything off and all you're looking at
+
+ align:start position:0%
+everything off and all you're looking at
+ 
+
+ align:start position:0%
+everything off and all you're looking at
+is a little piece of the protein not the
+
+ align:start position:0%
+is a little piece of the protein not the
+ 
+
+ align:start position:0%
+is a little piece of the protein not the
+whole protein anchored in this way with
+
+ align:start position:0%
+whole protein anchored in this way with
+ 
+
+ align:start position:0%
+whole protein anchored in this way with
+the right topology in the active site so
+
+ align:start position:0%
+the right topology in the active site so
+ 
+
+ align:start position:0%
+the right topology in the active site so
+to me even thinking about how you make a
+
+ align:start position:0%
+to me even thinking about how you make a
+ 
+
+ align:start position:0%
+to me even thinking about how you make a
+peptidoglycan that's 50 50 nanometers
+
+ align:start position:0%
+peptidoglycan that's 50 50 nanometers
+ 
+
+ align:start position:0%
+peptidoglycan that's 50 50 nanometers
+thick you know
+
+ align:start position:0%
+thick you know
+ 
+
+ align:start position:0%
+thick you know
+so you add things how does it construct
+
+ align:start position:0%
+so you add things how does it construct
+ 
+
+ align:start position:0%
+so you add things how does it construct
+yourself a cyclist around this system
+
+ align:start position:0%
+yourself a cyclist around this system
+ 
+
+ align:start position:0%
+yourself a cyclist around this system
+and build up I think nobody knows that
+
+ align:start position:0%
+and build up I think nobody knows that
+ 
+
+ align:start position:0%
+and build up I think nobody knows that
+and recent studies have been able to the
+
+ align:start position:0%
+and recent studies have been able to the
+ 
+
+ align:start position:0%
+and recent studies have been able to the
+first time to in staph.aureus
+
+ align:start position:0%
+first time to in staph.aureus
+ 
+
+ align:start position:0%
+first time to in staph.aureus
+reconstitute transpeptidase in and the
+
+ align:start position:0%
+reconstitute transpeptidase in and the
+ 
+
+ align:start position:0%
+reconstitute transpeptidase in and the
+glycosyl transferase reaction so maybe
+
+ align:start position:0%
+glycosyl transferase reaction so maybe
+ 
+
+ align:start position:0%
+glycosyl transferase reaction so maybe
+that with a sort of an imaging
+
+ align:start position:0%
+that with a sort of an imaging
+ 
+
+ align:start position:0%
+that with a sort of an imaging
+technology we have maybe in the next
+
+ align:start position:0%
+technology we have maybe in the next
+ 
+
+ align:start position:0%
+technology we have maybe in the next
+five or six years somebody
+
+ align:start position:0%
+five or six years somebody
+ 
+
+ align:start position:0%
+five or six years somebody
+we'll figure out how this amazing thing
+
+ align:start position:0%
+we'll figure out how this amazing thing
+ 
+
+ align:start position:0%
+we'll figure out how this amazing thing
+is organized so anyhow we were able to
+
+ align:start position:0%
+is organized so anyhow we were able to
+ 
+
+ align:start position:0%
+is organized so anyhow we were able to
+attach these things covalently and so
+
+ align:start position:0%
+attach these things covalently and so
+ 
+
+ align:start position:0%
+attach these things covalently and so
+here we are we've got these all all of
+
+ align:start position:0%
+here we are we've got these all all of
+ 
+
+ align:start position:0%
+here we are we've got these all all of
+these things anchored and then in your
+
+ align:start position:0%
+these things anchored and then in your
+ 
+
+ align:start position:0%
+these things anchored and then in your
+problem set and in the last part of this
+
+ align:start position:0%
+problem set and in the last part of this
+ 
+
+ align:start position:0%
+problem set and in the last part of this
+I just wanted to very briefly go through
+
+ align:start position:0%
+I just wanted to very briefly go through
+ 
+
+ align:start position:0%
+I just wanted to very briefly go through
+how are people trying to study how the
+
+ align:start position:0%
+how are people trying to study how the
+ 
+
+ align:start position:0%
+how are people trying to study how the
+heme that appear gets transferred and so
+
+ align:start position:0%
+heme that appear gets transferred and so
+ 
+
+ align:start position:0%
+heme that appear gets transferred and so
+this is a cartoon model and so we have
+
+ align:start position:0%
+this is a cartoon model and so we have
+ 
+
+ align:start position:0%
+this is a cartoon model and so we have
+hemoglobin we've been able to get we've
+
+ align:start position:0%
+hemoglobin we've been able to get we've
+ 
+
+ align:start position:0%
+hemoglobin we've been able to get we've
+been able to lyse red blood cells get
+
+ align:start position:0%
+been able to lyse red blood cells get
+ 
+
+ align:start position:0%
+been able to lyse red blood cells get
+the get hemoglobin to come out or have
+
+ align:start position:0%
+the get hemoglobin to come out or have
+ 
+
+ align:start position:0%
+the get hemoglobin to come out or have
+to get globin hemoglobin and now somehow
+
+ align:start position:0%
+to get globin hemoglobin and now somehow
+ 
+
+ align:start position:0%
+to get globin hemoglobin and now somehow
+you have to extract the heme and that's
+
+ align:start position:0%
+you have to extract the heme and that's
+ 
+
+ align:start position:0%
+you have to extract the heme and that's
+done by two proteins is B B and H and
+
+ align:start position:0%
+done by two proteins is B B and H and
+ 
+
+ align:start position:0%
+done by two proteins is B B and H and
+then we somehow have to get it to the
+
+ align:start position:0%
+then we somehow have to get it to the
+ 
+
+ align:start position:0%
+then we somehow have to get it to the
+plasma membrane and so the model is that
+
+ align:start position:0%
+plasma membrane and so the model is that
+ 
+
+ align:start position:0%
+plasma membrane and so the model is that
+this is transferred from IsdB through a
+
+ align:start position:0%
+this is transferred from IsdB through a
+ 
+
+ align:start position:0%
+this is transferred from IsdB through a
+neat domain okay so all of these
+
+ align:start position:0%
+neat domain okay so all of these
+ 
+
+ align:start position:0%
+neat domain okay so all of these
+transfers up to here are through these
+
+ align:start position:0%
+transfers up to here are through these
+ 
+
+ align:start position:0%
+transfers up to here are through these
+little domains that can bind him and we
+
+ align:start position:0%
+little domains that can bind him and we
+ 
+
+ align:start position:0%
+little domains that can bind him and we
+have a structure of it I'll briefly show
+
+ align:start position:0%
+have a structure of it I'll briefly show
+ 
+
+ align:start position:0%
+have a structure of it I'll briefly show
+you that and then the question is there
+
+ align:start position:0%
+you that and then the question is there
+ 
+
+ align:start position:0%
+you that and then the question is there
+in order if you get it out of is DB vs.
+
+ align:start position:0%
+in order if you get it out of is DB vs.
+ 
+
+ align:start position:0%
+in order if you get it out of is DB vs.
+is th is it transferred you know here we
+
+ align:start position:0%
+is th is it transferred you know here we
+ 
+
+ align:start position:0%
+is th is it transferred you know here we
+have a closer to this than B but is is C
+
+ align:start position:0%
+have a closer to this than B but is is C
+ 
+
+ align:start position:0%
+have a closer to this than B but is is C
+closer than a I mean what is the
+
+ align:start position:0%
+closer than a I mean what is the
+ 
+
+ align:start position:0%
+closer than a I mean what is the
+organization how many of these guys are
+
+ align:start position:0%
+organization how many of these guys are
+ 
+
+ align:start position:0%
+organization how many of these guys are
+there can they be transferred back and
+
+ align:start position:0%
+there can they be transferred back and
+ 
+
+ align:start position:0%
+there can they be transferred back and
+forth between the is das I mean there's
+
+ align:start position:0%
+forth between the is das I mean there's
+ 
+
+ align:start position:0%
+forth between the is das I mean there's
+a hundred questions you can ask and I
+
+ align:start position:0%
+a hundred questions you can ask and I
+ 
+
+ align:start position:0%
+a hundred questions you can ask and I
+think we don't know the answer to any of
+
+ align:start position:0%
+think we don't know the answer to any of
+ 
+
+ align:start position:0%
+think we don't know the answer to any of
+them and the methodology the problems
+
+ align:start position:0%
+them and the methodology the problems
+ 
+
+ align:start position:0%
+them and the methodology the problems
+that you looked at again they were
+
+ align:start position:0%
+that you looked at again they were
+ 
+
+ align:start position:0%
+that you looked at again they were
+looking at something that wasn't the
+
+ align:start position:0%
+looking at something that wasn't the
+ 
+
+ align:start position:0%
+looking at something that wasn't the
+intact system and the key to all of this
+
+ align:start position:0%
+intact system and the key to all of this
+ 
+
+ align:start position:0%
+intact system and the key to all of this
+of course is a kinetics and I think when
+
+ align:start position:0%
+of course is a kinetics and I think when
+ 
+
+ align:start position:0%
+of course is a kinetics and I think when
+you start taking apart the pieces so you
+
+ align:start position:0%
+you start taking apart the pieces so you
+ 
+
+ align:start position:0%
+you start taking apart the pieces so you
+have this piece and this piece and half
+
+ align:start position:0%
+have this piece and this piece and half
+ 
+
+ align:start position:0%
+have this piece and this piece and half
+the spinach is is missing then you have
+
+ align:start position:0%
+the spinach is is missing then you have
+ 
+
+ align:start position:0%
+the spinach is is missing then you have
+this issue of how do you design the
+
+ align:start position:0%
+this issue of how do you design the
+ 
+
+ align:start position:0%
+this issue of how do you design the
+experiment so you have the right
+
+ align:start position:0%
+experiment so you have the right
+ 
+
+ align:start position:0%
+experiment so you have the right
+concentrations so they meet
+
+ align:start position:0%
+concentrations so they meet
+ 
+
+ align:start position:0%
+concentrations so they meet
+um in an efficient facet fashion and so
+
+ align:start position:0%
+um in an efficient facet fashion and so
+ 
+
+ align:start position:0%
+um in an efficient facet fashion and so
+the kinetics of what you were looking at
+
+ align:start position:0%
+the kinetics of what you were looking at
+ 
+
+ align:start position:0%
+the kinetics of what you were looking at
+and your problems that are not realistic
+
+ align:start position:0%
+and your problems that are not realistic
+ 
+
+ align:start position:0%
+and your problems that are not realistic
+because things aren't covalently
+
+ align:start position:0%
+because things aren't covalently
+ 
+
+ align:start position:0%
+because things aren't covalently
+attached and so the question is does it
+
+ align:start position:0%
+attached and so the question is does it
+ 
+
+ align:start position:0%
+attached and so the question is does it
+really give you a good representation of
+
+ align:start position:0%
+really give you a good representation of
+ 
+
+ align:start position:0%
+really give you a good representation of
+what's going on in the intact system so
+
+ align:start position:0%
+what's going on in the intact system so
+ 
+
+ align:start position:0%
+what's going on in the intact system so
+the model has been from studies like the
+
+ align:start position:0%
+the model has been from studies like the
+ 
+
+ align:start position:0%
+the model has been from studies like the
+ones that you saw in your problem set
+
+ align:start position:0%
+ones that you saw in your problem set
+ 
+
+ align:start position:0%
+ones that you saw in your problem set
+that there is a pathway that this
+
+ align:start position:0%
+that there is a pathway that this
+ 
+
+ align:start position:0%
+that there is a pathway that this
+protein can extract the B and the H
+
+ align:start position:0%
+protein can extract the B and the H
+ 
+
+ align:start position:0%
+protein can extract the B and the H
+proteins can extract the heme it's
+
+ align:start position:0%
+proteins can extract the heme it's
+ 
+
+ align:start position:0%
+proteins can extract the heme it's
+transferred to the a protein and so here
+
+ align:start position:0%
+transferred to the a protein and so here
+ 
+
+ align:start position:0%
+transferred to the a protein and so here
+we have can it be transferred directly
+
+ align:start position:0%
+we have can it be transferred directly
+ 
+
+ align:start position:0%
+we have can it be transferred directly
+to the C protein or it doesn't need to
+
+ align:start position:0%
+to the C protein or it doesn't need to
+ 
+
+ align:start position:0%
+to the C protein or it doesn't need to
+go through the a protein so then you can
+
+ align:start position:0%
+go through the a protein so then you can
+ 
+
+ align:start position:0%
+go through the a protein so then you can
+start doing experiments like that you
+
+ align:start position:0%
+start doing experiments like that you
+ 
+
+ align:start position:0%
+start doing experiments like that you
+can take this protein and look for
+
+ align:start position:0%
+can take this protein and look for
+ 
+
+ align:start position:0%
+can take this protein and look for
+transfer to this protein or you can add
+
+ align:start position:0%
+transfer to this protein or you can add
+ 
+
+ align:start position:0%
+transfer to this protein or you can add
+in this protein and see if the rate if
+
+ align:start position:0%
+in this protein and see if the rate if
+ 
+
+ align:start position:0%
+in this protein and see if the rate if
+you set the experimental correctly
+
+ align:start position:0%
+you set the experimental correctly
+ 
+
+ align:start position:0%
+you set the experimental correctly
+increases you can also ask the question
+
+ align:start position:0%
+increases you can also ask the question
+ 
+
+ align:start position:0%
+increases you can also ask the question
+are these reactions stoichiometric or
+
+ align:start position:0%
+are these reactions stoichiometric or
+ 
+
+ align:start position:0%
+are these reactions stoichiometric or
+catalytic which was also asked in the
+
+ align:start position:0%
+catalytic which was also asked in the
+ 
+
+ align:start position:0%
+catalytic which was also asked in the
+problem set you were looking at if you
+
+ align:start position:0%
+problem set you were looking at if you
+ 
+
+ align:start position:0%
+problem set you were looking at if you
+if this if there is an order how fast is
+
+ align:start position:0%
+if this if there is an order how fast is
+ 
+
+ align:start position:0%
+if this if there is an order how fast is
+the transfer from here to here versus
+
+ align:start position:0%
+the transfer from here to here versus
+ 
+
+ align:start position:0%
+the transfer from here to here versus
+here to here and if it's really fast
+
+ align:start position:0%
+here to here and if it's really fast
+ 
+
+ align:start position:0%
+here to here and if it's really fast
+what can happen is you don't need
+
+ align:start position:0%
+what can happen is you don't need
+ 
+
+ align:start position:0%
+what can happen is you don't need
+stoichiometric amounts of this you can
+
+ align:start position:0%
+stoichiometric amounts of this you can
+ 
+
+ align:start position:0%
+stoichiometric amounts of this you can
+use small amounts of this to get the
+
+ align:start position:0%
+use small amounts of this to get the
+ 
+
+ align:start position:0%
+use small amounts of this to get the
+transfer to work and those are the kinds
+
+ align:start position:0%
+transfer to work and those are the kinds
+ 
+
+ align:start position:0%
+transfer to work and those are the kinds
+of questions that people are actually
+
+ align:start position:0%
+of questions that people are actually
+ 
+
+ align:start position:0%
+of questions that people are actually
+focused on so this is one model that
+
+ align:start position:0%
+focused on so this is one model that
+ 
+
+ align:start position:0%
+focused on so this is one model that
+came out are the types of studies that
+
+ align:start position:0%
+came out are the types of studies that
+ 
+
+ align:start position:0%
+came out are the types of studies that
+you guys had on your problem set and
+
+ align:start position:0%
+you guys had on your problem set and
+ 
+
+ align:start position:0%
+you guys had on your problem set and
+eventually you need to get down here to
+
+ align:start position:0%
+eventually you need to get down here to
+ 
+
+ align:start position:0%
+eventually you need to get down here to
+transfer this to the ATP A's which
+
+ align:start position:0%
+transfer this to the ATP A's which
+ 
+
+ align:start position:0%
+transfer this to the ATP A's which
+allows the heme to be transferred into
+
+ align:start position:0%
+allows the heme to be transferred into
+ 
+
+ align:start position:0%
+allows the heme to be transferred into
+the cytosol so these proteins are
+
+ align:start position:0%
+the cytosol so these proteins are
+ 
+
+ align:start position:0%
+the cytosol so these proteins are
+structurally distinct from this protein
+
+ align:start position:0%
+structurally distinct from this protein
+ 
+
+ align:start position:0%
+structurally distinct from this protein
+which is structurally distinct from that
+
+ align:start position:0%
+which is structurally distinct from that
+ 
+
+ align:start position:0%
+which is structurally distinct from that
+protein we have structures of always
+
+ align:start position:0%
+protein we have structures of always
+ 
+
+ align:start position:0%
+protein we have structures of always
+these things and they all do heme
+
+ align:start position:0%
+these things and they all do heme
+ 
+
+ align:start position:0%
+these things and they all do heme
+transfer I mean that's what their
+
+ align:start position:0%
+transfer I mean that's what their
+ 
+
+ align:start position:0%
+transfer I mean that's what their
+function actually is and so the details
+
+ align:start position:0%
+function actually is and so the details
+ 
+
+ align:start position:0%
+function actually is and so the details
+the molecular details of how the heme is
+
+ align:start position:0%
+the molecular details of how the heme is
+ 
+
+ align:start position:0%
+the molecular details of how the heme is
+transferred is a major focus of a lot of
+
+ align:start position:0%
+transferred is a major focus of a lot of
+ 
+
+ align:start position:0%
+transferred is a major focus of a lot of
+energy right now and so if you actually
+
+ align:start position:0%
+energy right now and so if you actually
+ 
+
+ align:start position:0%
+energy right now and so if you actually
+look at this
+
+ align:start position:0%
+look at this
+ 
+
+ align:start position:0%
+look at this
+I wanted to say a few things about how
+
+ align:start position:0%
+I wanted to say a few things about how
+ 
+
+ align:start position:0%
+I wanted to say a few things about how
+this happens and so one of the things
+
+ align:start position:0%
+this happens and so one of the things
+ 
+
+ align:start position:0%
+this happens and so one of the things
+that you need to think about so what are
+
+ align:start position:0%
+that you need to think about so what are
+ 
+
+ align:start position:0%
+that you need to think about so what are
+the methods to examine i SD team
+
+ align:start position:0%
+the methods to examine i SD team
+ 
+
+ align:start position:0%
+the methods to examine i SD team
+transfer and this is through these neat
+
+ align:start position:0%
+transfer and this is through these neat
+ 
+
+ align:start position:0%
+transfer and this is through these neat
+domains which I defined before and so
+
+ align:start position:0%
+domains which I defined before and so
+ 
+
+ align:start position:0%
+domains which I defined before and so
+one of the first things that people did
+
+ align:start position:0%
+one of the first things that people did
+ 
+
+ align:start position:0%
+one of the first things that people did
+was number one you need to you need to
+
+ align:start position:0%
+was number one you need to you need to
+ 
+
+ align:start position:0%
+was number one you need to you need to
+clone Express purify the the ISDN
+
+ align:start position:0%
+clone Express purify the the ISDN
+ 
+
+ align:start position:0%
+clone Express purify the the ISDN
+proteins and most of these studies have
+
+ align:start position:0%
+proteins and most of these studies have
+ 
+
+ align:start position:0%
+proteins and most of these studies have
+been done in pieces versus foam lengths
+
+ align:start position:0%
+been done in pieces versus foam lengths
+ 
+
+ align:start position:0%
+been done in pieces versus foam lengths
+okay and when you do so you could try to
+
+ align:start position:0%
+okay and when you do so you could try to
+ 
+
+ align:start position:0%
+okay and when you do so you could try to
+do the whole thing some of these things
+
+ align:start position:0%
+do the whole thing some of these things
+ 
+
+ align:start position:0%
+do the whole thing some of these things
+have three neat domains some have one
+
+ align:start position:0%
+have three neat domains some have one
+ 
+
+ align:start position:0%
+have three neat domains some have one
+neat domain if you look in those
+
+ align:start position:0%
+neat domain if you look in those
+ 
+
+ align:start position:0%
+neat domain if you look in those
+cartoons I gave you the number of neat
+
+ align:start position:0%
+cartoons I gave you the number of neat
+ 
+
+ align:start position:0%
+cartoons I gave you the number of neat
+domains are defined by sequences so you
+
+ align:start position:0%
+domains are defined by sequences so you
+ 
+
+ align:start position:0%
+domains are defined by sequences so you
+can study the full length thing or the
+
+ align:start position:0%
+can study the full length thing or the
+ 
+
+ align:start position:0%
+can study the full length thing or the
+other one and in fact I think in your
+
+ align:start position:0%
+other one and in fact I think in your
+ 
+
+ align:start position:0%
+other one and in fact I think in your
+problem said I can't remember but the
+
+ align:start position:0%
+problem said I can't remember but the
+ 
+
+ align:start position:0%
+problem said I can't remember but the
+problem said I think you actually you
+
+ align:start position:0%
+problem said I think you actually you
+ 
+
+ align:start position:0%
+problem said I think you actually you
+actually didn't expect was an experiment
+
+ align:start position:0%
+actually didn't expect was an experiment
+ 
+
+ align:start position:0%
+actually didn't expect was an experiment
+that you had one at one neat domain
+
+ align:start position:0%
+that you had one at one neat domain
+ 
+
+ align:start position:0%
+that you had one at one neat domain
+versus two and what was the differences
+
+ align:start position:0%
+versus two and what was the differences
+ 
+
+ align:start position:0%
+versus two and what was the differences
+in the transfer so you can make these
+
+ align:start position:0%
+in the transfer so you can make these
+ 
+
+ align:start position:0%
+in the transfer so you can make these
+things but when you make some hemas
+
+ align:start position:0%
+things but when you make some hemas
+ 
+
+ align:start position:0%
+things but when you make some hemas
+quite often because their bio synthetic
+
+ align:start position:0%
+quite often because their bio synthetic
+ 
+
+ align:start position:0%
+quite often because their bio synthetic
+machinery like there is to insert iron
+
+ align:start position:0%
+machinery like there is to insert iron
+ 
+
+ align:start position:0%
+machinery like there is to insert iron
+clusters biosynthetic on your clusters
+
+ align:start position:0%
+clusters biosynthetic on your clusters
+ 
+
+ align:start position:0%
+clusters biosynthetic on your clusters
+is also bio synthetic machinery to
+
+ align:start position:0%
+is also bio synthetic machinery to
+ 
+
+ align:start position:0%
+is also bio synthetic machinery to
+insert teams so it comes out these come
+
+ align:start position:0%
+insert teams so it comes out these come
+ 
+
+ align:start position:0%
+insert teams so it comes out these come
+out to be April ok so then what you need
+
+ align:start position:0%
+out to be April ok so then what you need
+ 
+
+ align:start position:0%
+out to be April ok so then what you need
+to do is you need to add a PO plus
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+protoporphyrin 9 to get presumably hello
+
+ align:start position:0%
+protoporphyrin 9 to get presumably hello
+ 
+
+ align:start position:0%
+protoporphyrin 9 to get presumably hello
+ok
+
+ align:start position:0%
+ok
+ 
+
+ align:start position:0%
+ok
+holo whatever ISDN is
+
+ align:start position:0%
+holo whatever ISDN is
+ 
+
+ align:start position:0%
+holo whatever ISDN is
+and then you need to purify that you can
+
+ align:start position:0%
+and then you need to purify that you can
+ 
+
+ align:start position:0%
+and then you need to purify that you can
+get rid of any heme you don't have a
+
+ align:start position:0%
+get rid of any heme you don't have a
+ 
+
+ align:start position:0%
+get rid of any heme you don't have a
+bunch of heme floating around so it's an
+
+ align:start position:0%
+bunch of heme floating around so it's an
+ 
+
+ align:start position:0%
+bunch of heme floating around so it's an
+again yet another purification to look
+
+ align:start position:0%
+again yet another purification to look
+ 
+
+ align:start position:0%
+again yet another purification to look
+at all of this stuff that may or may not
+
+ align:start position:0%
+at all of this stuff that may or may not
+ 
+
+ align:start position:0%
+at all of this stuff that may or may not
+be easy and so then after you do that
+
+ align:start position:0%
+be easy and so then after you do that
+ 
+
+ align:start position:0%
+be easy and so then after you do that
+what you want to do is you need to
+
+ align:start position:0%
+what you want to do is you need to
+ 
+
+ align:start position:0%
+what you want to do is you need to
+characterize the spectra of the isd
+
+ align:start position:0%
+characterize the spectra of the isd
+ 
+
+ align:start position:0%
+characterize the spectra of the isd
+proteins loaded with him and so this is
+
+ align:start position:0%
+proteins loaded with him and so this is
+ 
+
+ align:start position:0%
+proteins loaded with him and so this is
+the key to the solution of the problem
+
+ align:start position:0%
+the key to the solution of the problem
+ 
+
+ align:start position:0%
+the key to the solution of the problem
+which is the same thing you saw in in
+
+ align:start position:0%
+which is the same thing you saw in in
+ 
+
+ align:start position:0%
+which is the same thing you saw in in
+your problem set but if you look at heme
+
+ align:start position:0%
+your problem set but if you look at heme
+ 
+
+ align:start position:0%
+your problem set but if you look at heme
+and I'll show you one set of data a
+
+ align:start position:0%
+and I'll show you one set of data a
+ 
+
+ align:start position:0%
+and I'll show you one set of data a
+different one from what you had in your
+
+ align:start position:0%
+different one from what you had in your
+ 
+
+ align:start position:0%
+different one from what you had in your
+problem set but heme you all know this
+
+ align:start position:0%
+problem set but heme you all know this
+ 
+
+ align:start position:0%
+problem set but heme you all know this
+from looking at hemoglobin when you
+
+ align:start position:0%
+from looking at hemoglobin when you
+ 
+
+ align:start position:0%
+from looking at hemoglobin when you
+bring your pick yourself and your
+
+ align:start position:0%
+bring your pick yourself and your
+ 
+
+ align:start position:0%
+bring your pick yourself and your
+bleeder thread or it's blue depending on
+
+ align:start position:0%
+bleeder thread or it's blue depending on
+ 
+
+ align:start position:0%
+bleeder thread or it's blue depending on
+the oxygenation state they have a very
+
+ align:start position:0%
+the oxygenation state they have a very
+ 
+
+ align:start position:0%
+the oxygenation state they have a very
+strong band called the sarey band at 400
+
+ align:start position:0%
+strong band called the sarey band at 400
+ 
+
+ align:start position:0%
+strong band called the sarey band at 400
+nanometers okay about 100 okay and
+
+ align:start position:0%
+nanometers okay about 100 okay and
+ 
+
+ align:start position:0%
+nanometers okay about 100 okay and
+that's a key thing why do they like the
+
+ align:start position:0%
+that's a key thing why do they like the
+ 
+
+ align:start position:0%
+that's a key thing why do they like the
+Sylvania being because it has extremely
+
+ align:start position:0%
+Sylvania being because it has extremely
+ 
+
+ align:start position:0%
+Sylvania being because it has extremely
+high extinction coefficient I don't know
+
+ align:start position:0%
+high extinction coefficient I don't know
+ 
+
+ align:start position:0%
+high extinction coefficient I don't know
+what the number is but its extinction
+
+ align:start position:0%
+what the number is but its extinction
+ 
+
+ align:start position:0%
+what the number is but its extinction
+coefficient at 400 is approximately 10
+
+ align:start position:0%
+coefficient at 400 is approximately 10
+ 
+
+ align:start position:0%
+coefficient at 400 is approximately 10
+to the fifth okay so it's easy to see
+
+ align:start position:0%
+to the fifth okay so it's easy to see
+ 
+
+ align:start position:0%
+to the fifth okay so it's easy to see
+that's why people have studied teams
+
+ align:start position:0%
+that's why people have studied teams
+ 
+
+ align:start position:0%
+that's why people have studied teams
+over the years because team is so much
+
+ align:start position:0%
+over the years because team is so much
+ 
+
+ align:start position:0%
+over the years because team is so much
+easier to see than any non heme iron
+
+ align:start position:0%
+easier to see than any non heme iron
+ 
+
+ align:start position:0%
+easier to see than any non heme iron
+systems and what you can see here what
+
+ align:start position:0%
+systems and what you can see here what
+ 
+
+ align:start position:0%
+systems and what you can see here what
+you're also turn out to be quite useful
+
+ align:start position:0%
+you're also turn out to be quite useful
+ 
+
+ align:start position:0%
+you're also turn out to be quite useful
+is these much weaker bands between 500
+
+ align:start position:0%
+is these much weaker bands between 500
+ 
+
+ align:start position:0%
+is these much weaker bands between 500
+and 650 and those bands can also be used
+
+ align:start position:0%
+and 650 and those bands can also be used
+ 
+
+ align:start position:0%
+and 650 and those bands can also be used
+if you have enough sample to look at
+
+ align:start position:0%
+if you have enough sample to look at
+ 
+
+ align:start position:0%
+if you have enough sample to look at
+this and they're more distinct they're
+
+ align:start position:0%
+this and they're more distinct they're
+ 
+
+ align:start position:0%
+this and they're more distinct they're
+indicative of the coordination
+
+ align:start position:0%
+indicative of the coordination
+ 
+
+ align:start position:0%
+indicative of the coordination
+environment ahim whether it's whether
+
+ align:start position:0%
+environment ahim whether it's whether
+ 
+
+ align:start position:0%
+environment ahim whether it's whether
+it's hexa coordinated or whether it's
+
+ align:start position:0%
+it's hexa coordinated or whether it's
+ 
+
+ align:start position:0%
+it's hexa coordinated or whether it's
+Penta coordinate so all of this I'm not
+
+ align:start position:0%
+Penta coordinate so all of this I'm not
+ 
+
+ align:start position:0%
+Penta coordinate so all of this I'm not
+going to talk about the spectroscopy the
+
+ align:start position:0%
+going to talk about the spectroscopy the
+ 
+
+ align:start position:0%
+going to talk about the spectroscopy the
+spectroscopy of Hulme's has been
+
+ align:start position:0%
+spectroscopy of Hulme's has been
+ 
+
+ align:start position:0%
+spectroscopy of Hulme's has been
+extremely well studied and has extremely
+
+ align:start position:0%
+extremely well studied and has extremely
+ 
+
+ align:start position:0%
+extremely well studied and has extremely
+rich and so you need to do that you need
+
+ align:start position:0%
+rich and so you need to do that you need
+ 
+
+ align:start position:0%
+rich and so you need to do that you need
+to have your little proteins
+
+ align:start position:0%
+to have your little proteins
+ 
+
+ align:start position:0%
+to have your little proteins
+characterized and
+
+ align:start position:0%
+characterized and
+ 
+
+ align:start position:0%
+characterized and
+loaded with emu need to quantitate the
+
+ align:start position:0%
+loaded with emu need to quantitate the
+ 
+
+ align:start position:0%
+loaded with emu need to quantitate the
+amount of heme bones they want to make
+
+ align:start position:0%
+amount of heme bones they want to make
+ 
+
+ align:start position:0%
+amount of heme bones they want to make
+sure you don't have any free heme around
+
+ align:start position:0%
+sure you don't have any free heme around
+ 
+
+ align:start position:0%
+sure you don't have any free heme around
+which could interfere with all of your
+
+ align:start position:0%
+which could interfere with all of your
+ 
+
+ align:start position:0%
+which could interfere with all of your
+experiments and then you can ask the
+
+ align:start position:0%
+experiments and then you can ask the
+ 
+
+ align:start position:0%
+experiments and then you can ask the
+question you can start asking your
+
+ align:start position:0%
+question you can start asking your
+ 
+
+ align:start position:0%
+question you can start asking your
+questions once you've got that
+
+ align:start position:0%
+questions once you've got that
+ 
+
+ align:start position:0%
+questions once you've got that
+information if you start out with ISD a
+
+ align:start position:0%
+information if you start out with ISD a
+ 
+
+ align:start position:0%
+information if you start out with ISD a
+loaded with him does it gets transferred
+
+ align:start position:0%
+loaded with him does it gets transferred
+ 
+
+ align:start position:0%
+loaded with him does it gets transferred
+to is DC in the a po form okay and so
+
+ align:start position:0%
+to is DC in the a po form okay and so
+ 
+
+ align:start position:0%
+to is DC in the a po form okay and so
+how do you monitor this reaction anybody
+
+ align:start position:0%
+how do you monitor this reaction anybody
+ 
+
+ align:start position:0%
+how do you monitor this reaction anybody
+got any suggestions one way would be say
+
+ align:start position:0%
+got any suggestions one way would be say
+ 
+
+ align:start position:0%
+got any suggestions one way would be say
+one of the question that they're focused
+
+ align:start position:0%
+one of the question that they're focused
+ 
+
+ align:start position:0%
+one of the question that they're focused
+on here is does is da with a heme plus a
+
+ align:start position:0%
+on here is does is da with a heme plus a
+ 
+
+ align:start position:0%
+on here is does is da with a heme plus a
+PO is DC does it transfer the heme to
+
+ align:start position:0%
+PO is DC does it transfer the heme to
+ 
+
+ align:start position:0%
+PO is DC does it transfer the heme to
+give you a po i SG a + hm is DC and the
+
+ align:start position:0%
+give you a po i SG a + hm is DC and the
+ 
+
+ align:start position:0%
+give you a po i SG a + hm is DC and the
+question is what's the mechanism of this
+
+ align:start position:0%
+question is what's the mechanism of this
+ 
+
+ align:start position:0%
+question is what's the mechanism of this
+transfer so I just told you we have
+
+ align:start position:0%
+transfer so I just told you we have
+ 
+
+ align:start position:0%
+transfer so I just told you we have
+spectroscopy okay so I'm going to show
+
+ align:start position:0%
+spectroscopy okay so I'm going to show
+ 
+
+ align:start position:0%
+spectroscopy okay so I'm going to show
+you you could potentially do that that's
+
+ align:start position:0%
+you you could potentially do that that's
+ 
+
+ align:start position:0%
+you you could potentially do that that's
+not so easy to do but is there another
+
+ align:start position:0%
+not so easy to do but is there another
+ 
+
+ align:start position:0%
+not so easy to do but is there another
+method you can think of so we could
+
+ align:start position:0%
+method you can think of so we could
+ 
+
+ align:start position:0%
+method you can think of so we could
+monitor the reaction you need an assay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay and that's what you saw in your
+
+ align:start position:0%
+okay and that's what you saw in your
+ 
+
+ align:start position:0%
+okay and that's what you saw in your
+problem set so we can take advantage of
+
+ align:start position:0%
+problem set so we can take advantage of
+ 
+
+ align:start position:0%
+problem set so we can take advantage of
+the region of the saw a band or perhaps
+
+ align:start position:0%
+the region of the saw a band or perhaps
+ 
+
+ align:start position:0%
+the region of the saw a band or perhaps
+in the longer wavelength what other
+
+ align:start position:0%
+in the longer wavelength what other
+ 
+
+ align:start position:0%
+in the longer wavelength what other
+method might you be able to use to
+
+ align:start position:0%
+method might you be able to use to
+ 
+
+ align:start position:0%
+method might you be able to use to
+monitor this reaction that we've learned
+
+ align:start position:0%
+monitor this reaction that we've learned
+ 
+
+ align:start position:0%
+monitor this reaction that we've learned
+about recently in recitations which
+
+ align:start position:0%
+about recently in recitations which
+ 
+
+ align:start position:0%
+about recently in recitations which
+hasn't been used in the papers that
+
+ align:start position:0%
+hasn't been used in the papers that
+ 
+
+ align:start position:0%
+hasn't been used in the papers that
+you've read but actually has been used
+
+ align:start position:0%
+you've read but actually has been used
+ 
+
+ align:start position:0%
+you've read but actually has been used
+to study these systems
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah mass spec and so what people have
+
+ align:start position:0%
+yeah mass spec and so what people have
+ 
+
+ align:start position:0%
+yeah mass spec and so what people have
+done so you have to carry which what you
+
+ align:start position:0%
+done so you have to carry which what you
+ 
+
+ align:start position:0%
+done so you have to carry which what you
+will see is that if you look at the
+
+ align:start position:0%
+will see is that if you look at the
+ 
+
+ align:start position:0%
+will see is that if you look at the
+sizes of these things some have two neat
+
+ align:start position:0%
+sizes of these things some have two neat
+ 
+
+ align:start position:0%
+sizes of these things some have two neat
+domains want some have one the a PO also
+
+ align:start position:0%
+domains want some have one the a PO also
+ 
+
+ align:start position:0%
+domains want some have one the a PO also
+is distinct in size from the non a PO so
+
+ align:start position:0%
+is distinct in size from the non a PO so
+ 
+
+ align:start position:0%
+is distinct in size from the non a PO so
+theoretically if you do all of your
+
+ align:start position:0%
+theoretically if you do all of your
+ 
+
+ align:start position:0%
+theoretically if you do all of your
+homework you can use mass spec
+
+ align:start position:0%
+homework you can use mass spec
+ 
+
+ align:start position:0%
+homework you can use mass spec
+quantitatively to measure these
+
+ align:start position:0%
+quantitatively to measure these
+ 
+
+ align:start position:0%
+quantitatively to measure these
+reactions and a lot of people have
+
+ align:start position:0%
+reactions and a lot of people have
+ 
+
+ align:start position:0%
+reactions and a lot of people have
+recently gone to that that method
+
+ align:start position:0%
+recently gone to that that method
+ 
+
+ align:start position:0%
+recently gone to that that method
+because this method is challenging now
+
+ align:start position:0%
+because this method is challenging now
+ 
+
+ align:start position:0%
+because this method is challenging now
+again the caveat is so you always need
+
+ align:start position:0%
+again the caveat is so you always need
+ 
+
+ align:start position:0%
+again the caveat is so you always need
+to remember this is that all the ISD
+
+ align:start position:0%
+to remember this is that all the ISD
+ 
+
+ align:start position:0%
+to remember this is that all the ISD
+proteins are not covalently attached to
+
+ align:start position:0%
+proteins are not covalently attached to
+ 
+
+ align:start position:0%
+proteins are not covalently attached to
+the peptidoglycan okay so to me this
+
+ align:start position:0%
+the peptidoglycan okay so to me this
+ 
+
+ align:start position:0%
+the peptidoglycan okay so to me this
+immediately raises this issue of how do
+
+ align:start position:0%
+immediately raises this issue of how do
+ 
+
+ align:start position:0%
+immediately raises this issue of how do
+you decide how to do your experiments
+
+ align:start position:0%
+you decide how to do your experiments
+ 
+
+ align:start position:0%
+you decide how to do your experiments
+you know so how much do use micro molar
+
+ align:start position:0%
+you know so how much do use micro molar
+ 
+
+ align:start position:0%
+you know so how much do use micro molar
+do use do you use milli molar do you is
+
+ align:start position:0%
+do use do you use milli molar do you is
+ 
+
+ align:start position:0%
+do use do you use milli molar do you is
+it is it widely different depending on
+
+ align:start position:0%
+it is it widely different depending on
+ 
+
+ align:start position:0%
+it is it widely different depending on
+whether it's attached or not attached
+
+ align:start position:0%
+whether it's attached or not attached
+ 
+
+ align:start position:0%
+whether it's attached or not attached
+and all of that is going to affect the
+
+ align:start position:0%
+and all of that is going to affect the
+ 
+
+ align:start position:0%
+and all of that is going to affect the
+kinetics of this transfer so you can see
+
+ align:start position:0%
+kinetics of this transfer so you can see
+ 
+
+ align:start position:0%
+kinetics of this transfer so you can see
+transfer but what you really want is the
+
+ align:start position:0%
+transfer but what you really want is the
+ 
+
+ align:start position:0%
+transfer but what you really want is the
+rate constants for transfer so you have
+
+ align:start position:0%
+rate constants for transfer so you have
+ 
+
+ align:start position:0%
+rate constants for transfer so you have
+two questions is do you see transfer so
+
+ align:start position:0%
+two questions is do you see transfer so
+ 
+
+ align:start position:0%
+two questions is do you see transfer so
+that's the first question and so one
+
+ align:start position:0%
+that's the first question and so one
+ 
+
+ align:start position:0%
+that's the first question and so one
+could tell that by either of these two
+
+ align:start position:0%
+could tell that by either of these two
+ 
+
+ align:start position:0%
+could tell that by either of these two
+assays so you could use one and two and
+
+ align:start position:0%
+assays so you could use one and two and
+ 
+
+ align:start position:0%
+assays so you could use one and two and
+what you really want are the rate
+
+ align:start position:0%
+what you really want are the rate
+ 
+
+ align:start position:0%
+what you really want are the rate
+constants for transfer okay and the rate
+
+ align:start position:0%
+constants for transfer okay and the rate
+ 
+
+ align:start position:0%
+constants for transfer okay and the rate
+constants for transfer are dependent on
+
+ align:start position:0%
+constants for transfer are dependent on
+ 
+
+ align:start position:0%
+constants for transfer are dependent on
+the concentrations okay so how you set
+
+ align:start position:0%
+the concentrations okay so how you set
+ 
+
+ align:start position:0%
+the concentrations okay so how you set
+this up is something you've got to do a
+
+ align:start position:0%
+this up is something you've got to do a
+ 
+
+ align:start position:0%
+this up is something you've got to do a
+lot of messing around with and so if you
+
+ align:start position:0%
+lot of messing around with and so if you
+ 
+
+ align:start position:0%
+lot of messing around with and so if you
+look at this model you can ask the
+
+ align:start position:0%
+look at this model you can ask the
+ 
+
+ align:start position:0%
+look at this model you can ask the
+question how is this transfer occurred
+
+ align:start position:0%
+question how is this transfer occurred
+ 
+
+ align:start position:0%
+question how is this transfer occurred
+do you go through a ternary complex so
+
+ align:start position:0%
+do you go through a ternary complex so
+ 
+
+ align:start position:0%
+do you go through a ternary complex so
+does this form a complex with this and
+
+ align:start position:0%
+does this form a complex with this and
+ 
+
+ align:start position:0%
+does this form a complex with this and
+then the transfer occurs through the
+
+ align:start position:0%
+then the transfer occurs through the
+ 
+
+ align:start position:0%
+then the transfer occurs through the
+complex or you can ask a question does
+
+ align:start position:0%
+complex or you can ask a question does
+ 
+
+ align:start position:0%
+complex or you can ask a question does
+the Hien dissociate
+
+ align:start position:0%
+the Hien dissociate
+ 
+
+ align:start position:0%
+the Hien dissociate
+and then the heem get picked up so you
+
+ align:start position:0%
+and then the heem get picked up so you
+ 
+
+ align:start position:0%
+and then the heem get picked up so you
+can ask the question is what is the
+
+ align:start position:0%
+can ask the question is what is the
+ 
+
+ align:start position:0%
+can ask the question is what is the
+order of addition so you look and look
+
+ align:start position:0%
+order of addition so you look and look
+ 
+
+ align:start position:0%
+order of addition so you look and look
+at the mechanism of transfer and
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+specifically the order of addition do
+
+ align:start position:0%
+specifically the order of addition do
+ 
+
+ align:start position:0%
+specifically the order of addition do
+you need the second protein there to see
+
+ align:start position:0%
+you need the second protein there to see
+ 
+
+ align:start position:0%
+you need the second protein there to see
+transfers so they've done a whole bunch
+
+ align:start position:0%
+transfers so they've done a whole bunch
+ 
+
+ align:start position:0%
+transfers so they've done a whole bunch
+of experiments like this I'll show you
+
+ align:start position:0%
+of experiments like this I'll show you
+ 
+
+ align:start position:0%
+of experiments like this I'll show you
+using I'll show you using the UM the
+
+ align:start position:0%
+using I'll show you using the UM the
+ 
+
+ align:start position:0%
+using I'll show you using the UM the
+sarey band what they they actually want
+
+ align:start position:0%
+sarey band what they they actually want
+ 
+
+ align:start position:0%
+sarey band what they they actually want
+it or in this particular reaction but
+
+ align:start position:0%
+it or in this particular reaction but
+ 
+
+ align:start position:0%
+it or in this particular reaction but
+they did a experiment where they just
+
+ align:start position:0%
+they did a experiment where they just
+ 
+
+ align:start position:0%
+they did a experiment where they just
+took is da is da loaded with him and
+
+ align:start position:0%
+took is da is da loaded with him and
+ 
+
+ align:start position:0%
+took is da is da loaded with him and
+asked the question does heme go in to
+
+ align:start position:0%
+asked the question does heme go in to
+ 
+
+ align:start position:0%
+asked the question does heme go in to
+solution okay so that's not a trivial
+
+ align:start position:0%
+solution okay so that's not a trivial
+ 
+
+ align:start position:0%
+solution okay so that's not a trivial
+experiment either because it can rebind
+
+ align:start position:0%
+experiment either because it can rebind
+ 
+
+ align:start position:0%
+experiment either because it can rebind
+it depends on the on rate and the off
+
+ align:start position:0%
+it depends on the on rate and the off
+ 
+
+ align:start position:0%
+it depends on the on rate and the off
+rate so you have to have a way of making
+
+ align:start position:0%
+rate so you have to have a way of making
+ 
+
+ align:start position:0%
+rate so you have to have a way of making
+sure that if it comes off you pull it to
+
+ align:start position:0%
+sure that if it comes off you pull it to
+ 
+
+ align:start position:0%
+sure that if it comes off you pull it to
+the right to be able to measure the rate
+
+ align:start position:0%
+the right to be able to measure the rate
+ 
+
+ align:start position:0%
+the right to be able to measure the rate
+constants so this whole problem is
+
+ align:start position:0%
+constants so this whole problem is
+ 
+
+ align:start position:0%
+constants so this whole problem is
+really associated with thinking about
+
+ align:start position:0%
+really associated with thinking about
+ 
+
+ align:start position:0%
+really associated with thinking about
+detailed kinetic models which I'm not
+
+ align:start position:0%
+detailed kinetic models which I'm not
+ 
+
+ align:start position:0%
+detailed kinetic models which I'm not
+gonna go into but if you look at the
+
+ align:start position:0%
+gonna go into but if you look at the
+ 
+
+ align:start position:0%
+gonna go into but if you look at the
+data that's what you need to think about
+
+ align:start position:0%
+data that's what you need to think about
+ 
+
+ align:start position:0%
+data that's what you need to think about
+to believe the data whether the data has
+
+ align:start position:0%
+to believe the data whether the data has
+ 
+
+ align:start position:0%
+to believe the data whether the data has
+been interpreted correctly that I'm very
+
+ align:start position:0%
+been interpreted correctly that I'm very
+ 
+
+ align:start position:0%
+been interpreted correctly that I'm very
+briefly going to show you need to derive
+
+ align:start position:0%
+briefly going to show you need to derive
+ 
+
+ align:start position:0%
+briefly going to show you need to derive
+the equations and look at what your
+
+ align:start position:0%
+the equations and look at what your
+ 
+
+ align:start position:0%
+the equations and look at what your
+expectations are are they consistent
+
+ align:start position:0%
+expectations are are they consistent
+ 
+
+ align:start position:0%
+expectations are are they consistent
+with a kinetic analysis of what's going
+
+ align:start position:0%
+with a kinetic analysis of what's going
+ 
+
+ align:start position:0%
+with a kinetic analysis of what's going
+on so here they see a rate constant so
+
+ align:start position:0%
+on so here they see a rate constant so
+ 
+
+ align:start position:0%
+on so here they see a rate constant so
+here they're just looking simply at this
+
+ align:start position:0%
+here they're just looking simply at this
+ 
+
+ align:start position:0%
+here they're just looking simply at this
+reaction does this go to i SD a a po +
+
+ align:start position:0%
+reaction does this go to i SD a a po +
+ 
+
+ align:start position:0%
+reaction does this go to i SD a a po +
+heme okay and if they look at that rate
+
+ align:start position:0%
+heme okay and if they look at that rate
+ 
+
+ align:start position:0%
+heme okay and if they look at that rate
+constant is 0.07 per second okay so it's
+
+ align:start position:0%
+constant is 0.07 per second okay so it's
+ 
+
+ align:start position:0%
+constant is 0.07 per second okay so it's
+really slow okay so then the question is
+
+ align:start position:0%
+really slow okay so then the question is
+ 
+
+ align:start position:0%
+really slow okay so then the question is
+is this transfer D does anybody remember
+
+ align:start position:0%
+is this transfer D does anybody remember
+ 
+
+ align:start position:0%
+is this transfer D does anybody remember
+what the rate constants were for
+
+ align:start position:0%
+what the rate constants were for
+ 
+
+ align:start position:0%
+what the rate constants were for
+transfer in the problem you worked at
+
+ align:start position:0%
+transfer in the problem you worked at
+ 
+
+ align:start position:0%
+transfer in the problem you worked at
+who is it seconds was it minutes did you
+
+ align:start position:0%
+who is it seconds was it minutes did you
+ 
+
+ align:start position:0%
+who is it seconds was it minutes did you
+think about it I don't remember what the
+
+ align:start position:0%
+think about it I don't remember what the
+ 
+
+ align:start position:0%
+think about it I don't remember what the
+numbers are at the top
+
+ align:start position:0%
+numbers are at the top
+ 
+
+ align:start position:0%
+numbers are at the top
+yeah so that's much faster than this and
+
+ align:start position:0%
+yeah so that's much faster than this and
+ 
+
+ align:start position:0%
+yeah so that's much faster than this and
+so this is a really low number but the
+
+ align:start position:0%
+so this is a really low number but the
+ 
+
+ align:start position:0%
+so this is a really low number but the
+question is how remember we're missing
+
+ align:start position:0%
+question is how remember we're missing
+ 
+
+ align:start position:0%
+question is how remember we're missing
+part of the whole system and so could be
+
+ align:start position:0%
+part of the whole system and so could be
+ 
+
+ align:start position:0%
+part of the whole system and so could be
+really low just because we don't have
+
+ align:start position:0%
+really low just because we don't have
+ 
+
+ align:start position:0%
+really low just because we don't have
+the system set up to be to mimic what we
+
+ align:start position:0%
+the system set up to be to mimic what we
+ 
+
+ align:start position:0%
+the system set up to be to mimic what we
+see in the native organism so that's the
+
+ align:start position:0%
+see in the native organism so that's the
+ 
+
+ align:start position:0%
+see in the native organism so that's the
+problem you always face and so if you
+
+ align:start position:0%
+problem you always face and so if you
+ 
+
+ align:start position:0%
+problem you always face and so if you
+look at the data here's what they're
+
+ align:start position:0%
+look at the data here's what they're
+ 
+
+ align:start position:0%
+look at the data here's what they're
+monitoring so here's the soiree band at
+
+ align:start position:0%
+monitoring so here's the soiree band at
+ 
+
+ align:start position:0%
+monitoring so here's the soiree band at
+400 and so you need to get a good
+
+ align:start position:0%
+400 and so you need to get a good
+ 
+
+ align:start position:0%
+400 and so you need to get a good
+spectrum and convince yourself you're
+
+ align:start position:0%
+spectrum and convince yourself you're
+ 
+
+ align:start position:0%
+spectrum and convince yourself you're
+looking at the stoichiometric loading so
+
+ align:start position:0%
+looking at the stoichiometric loading so
+ 
+
+ align:start position:0%
+looking at the stoichiometric loading so
+you need to know how much he may it's
+
+ align:start position:0%
+you need to know how much he may it's
+ 
+
+ align:start position:0%
+you need to know how much he may it's
+going to affect your absorption spectrum
+
+ align:start position:0%
+going to affect your absorption spectrum
+ 
+
+ align:start position:0%
+going to affect your absorption spectrum
+okay so you need to know how much is
+
+ align:start position:0%
+okay so you need to know how much is
+ 
+
+ align:start position:0%
+okay so you need to know how much is
+loaded and then you could do the
+
+ align:start position:0%
+loaded and then you could do the
+ 
+
+ align:start position:0%
+loaded and then you could do the
+experiment outlined over there and what
+
+ align:start position:0%
+experiment outlined over there and what
+ 
+
+ align:start position:0%
+experiment outlined over there and what
+they're monitoring is these small
+
+ align:start position:0%
+they're monitoring is these small
+ 
+
+ align:start position:0%
+they're monitoring is these small
+changes okay
+
+ align:start position:0%
+changes okay
+ 
+
+ align:start position:0%
+changes okay
+and so when they do that they come up
+
+ align:start position:0%
+and so when they do that they come up
+ 
+
+ align:start position:0%
+and so when they do that they come up
+with if you look at the analysis and
+
+ align:start position:0%
+with if you look at the analysis and
+ 
+
+ align:start position:0%
+with if you look at the analysis and
+I'll show you a few pieces of data they
+
+ align:start position:0%
+I'll show you a few pieces of data they
+ 
+
+ align:start position:0%
+I'll show you a few pieces of data they
+come up with them they favor the model
+
+ align:start position:0%
+come up with them they favor the model
+ 
+
+ align:start position:0%
+come up with them they favor the model
+associated with the kinetic analysis of
+
+ align:start position:0%
+associated with the kinetic analysis of
+ 
+
+ align:start position:0%
+associated with the kinetic analysis of
+all of their data that you form a
+
+ align:start position:0%
+all of their data that you form a
+ 
+
+ align:start position:0%
+all of their data that you form a
+tertiary complex sorry a binary complex
+
+ align:start position:0%
+tertiary complex sorry a binary complex
+ 
+
+ align:start position:0%
+tertiary complex sorry a binary complex
+of the two proteins and that the heme is
+
+ align:start position:0%
+of the two proteins and that the heme is
+ 
+
+ align:start position:0%
+of the two proteins and that the heme is
+transferred from one to the other and
+
+ align:start position:0%
+transferred from one to the other and
+ 
+
+ align:start position:0%
+transferred from one to the other and
+then the a PO is da dissociates okay so
+
+ align:start position:0%
+then the a PO is da dissociates okay so
+ 
+
+ align:start position:0%
+then the a PO is da dissociates okay so
+this is analogous to what you've seen
+
+ align:start position:0%
+this is analogous to what you've seen
+ 
+
+ align:start position:0%
+this is analogous to what you've seen
+and here's some data so they've done it
+
+ align:start position:0%
+and here's some data so they've done it
+ 
+
+ align:start position:0%
+and here's some data so they've done it
+with every single pair in this
+
+ align:start position:0%
+with every single pair in this
+ 
+
+ align:start position:0%
+with every single pair in this
+particular paper and what you can go do
+
+ align:start position:0%
+particular paper and what you can go do
+ 
+
+ align:start position:0%
+particular paper and what you can go do
+what you can do and they've done all the
+
+ align:start position:0%
+what you can do and they've done all the
+ 
+
+ align:start position:0%
+what you can do and they've done all the
+experiments the same way I've been able
+
+ align:start position:0%
+experiments the same way I've been able
+ 
+
+ align:start position:0%
+experiments the same way I've been able
+to see differences and so array bands
+
+ align:start position:0%
+to see differences and so array bands
+ 
+
+ align:start position:0%
+to see differences and so array bands
+these were all done with changes in the
+
+ align:start position:0%
+these were all done with changes in the
+ 
+
+ align:start position:0%
+these were all done with changes in the
+spectra the visible spectra but if you
+
+ align:start position:0%
+spectra the visible spectra but if you
+ 
+
+ align:start position:0%
+spectra the visible spectra but if you
+look at this for example from the
+
+ align:start position:0%
+look at this for example from the
+ 
+
+ align:start position:0%
+look at this for example from the
+transfer of the heme from met hemoglobin
+
+ align:start position:0%
+transfer of the heme from met hemoglobin
+ 
+
+ align:start position:0%
+transfer of the heme from met hemoglobin
+okay so that's the first step up here
+
+ align:start position:0%
+okay so that's the first step up here
+ 
+
+ align:start position:0%
+okay so that's the first step up here
+and you look at all the rate constants
+
+ align:start position:0%
+and you look at all the rate constants
+ 
+
+ align:start position:0%
+and you look at all the rate constants
+they measured they the fastest number is
+
+ align:start position:0%
+they measured they the fastest number is
+ 
+
+ align:start position:0%
+they measured they the fastest number is
+zero point three one per second okay so
+
+ align:start position:0%
+zero point three one per second okay so
+ 
+
+ align:start position:0%
+zero point three one per second okay so
+that's slow but you might expect it
+
+ align:start position:0%
+that's slow but you might expect it
+ 
+
+ align:start position:0%
+that's slow but you might expect it
+might not be so easy to extract the heme
+
+ align:start position:0%
+might not be so easy to extract the heme
+ 
+
+ align:start position:0%
+might not be so easy to extract the heme
+of hemoglobin okay so what you might
+
+ align:start position:0%
+of hemoglobin okay so what you might
+ 
+
+ align:start position:0%
+of hemoglobin okay so what you might
+expect this to be slow but again if you
+
+ align:start position:0%
+expect this to be slow but again if you
+ 
+
+ align:start position:0%
+expect this to be slow but again if you
+look here and this is the thing that
+
+ align:start position:0%
+look here and this is the thing that
+ 
+
+ align:start position:0%
+look here and this is the thing that
+I think hopefully some of you thought
+
+ align:start position:0%
+I think hopefully some of you thought
+ 
+
+ align:start position:0%
+I think hopefully some of you thought
+about if you look at the rate constants
+
+ align:start position:0%
+about if you look at the rate constants
+ 
+
+ align:start position:0%
+about if you look at the rate constants
+these reactions are all by molecular
+
+ align:start position:0%
+these reactions are all by molecular
+ 
+
+ align:start position:0%
+these reactions are all by molecular
+okay but what do they have up there they
+
+ align:start position:0%
+okay but what do they have up there they
+ 
+
+ align:start position:0%
+okay but what do they have up there they
+have first-order processes so that has
+
+ align:start position:0%
+have first-order processes so that has
+ 
+
+ align:start position:0%
+have first-order processes so that has
+got to be telling you something about
+
+ align:start position:0%
+got to be telling you something about
+ 
+
+ align:start position:0%
+got to be telling you something about
+the interaction let's compare whether
+
+ align:start position:0%
+the interaction let's compare whether
+ 
+
+ align:start position:0%
+the interaction let's compare whether
+this interaction is rapid and reversible
+
+ align:start position:0%
+this interaction is rapid and reversible
+ 
+
+ align:start position:0%
+this interaction is rapid and reversible
+okay and in the paper describing this
+
+ align:start position:0%
+okay and in the paper describing this
+ 
+
+ align:start position:0%
+okay and in the paper describing this
+work in detail and I give you the
+
+ align:start position:0%
+work in detail and I give you the
+ 
+
+ align:start position:0%
+work in detail and I give you the
+reference in the PowerPoint for those if
+
+ align:start position:0%
+reference in the PowerPoint for those if
+ 
+
+ align:start position:0%
+reference in the PowerPoint for those if
+you want to look at it you need to think
+
+ align:start position:0%
+you want to look at it you need to think
+ 
+
+ align:start position:0%
+you want to look at it you need to think
+about the kinetic analysis so when
+
+ align:start position:0%
+about the kinetic analysis so when
+ 
+
+ align:start position:0%
+about the kinetic analysis so when
+you're looking at rate constants you
+
+ align:start position:0%
+you're looking at rate constants you
+ 
+
+ align:start position:0%
+you're looking at rate constants you
+need to think about whether it's first
+
+ align:start position:0%
+need to think about whether it's first
+ 
+
+ align:start position:0%
+need to think about whether it's first
+or second order or somehow they have to
+
+ align:start position:0%
+or second order or somehow they have to
+ 
+
+ align:start position:0%
+or second order or somehow they have to
+get together if this is due when it
+
+ align:start position:0%
+get together if this is due when it
+ 
+
+ align:start position:0%
+get together if this is due when it
+happened rapid and reversible you still
+
+ align:start position:0%
+happened rapid and reversible you still
+ 
+
+ align:start position:0%
+happened rapid and reversible you still
+have a term for that equilibrium step
+
+ align:start position:0%
+have a term for that equilibrium step
+ 
+
+ align:start position:0%
+have a term for that equilibrium step
+but then you're looking at a first order
+
+ align:start position:0%
+but then you're looking at a first order
+ 
+
+ align:start position:0%
+but then you're looking at a first order
+process okay
+
+ align:start position:0%
+process okay
+ 
+
+ align:start position:0%
+process okay
+so if you look I'm not going to go
+
+ align:start position:0%
+so if you look I'm not going to go
+ 
+
+ align:start position:0%
+so if you look I'm not going to go
+through the whole thing but if you look
+
+ align:start position:0%
+through the whole thing but if you look
+ 
+
+ align:start position:0%
+through the whole thing but if you look
+at the transfer from hollo is DB so
+
+ align:start position:0%
+at the transfer from hollo is DB so
+ 
+
+ align:start position:0%
+at the transfer from hollo is DB so
+that's the second step it got the B got
+
+ align:start position:0%
+that's the second step it got the B got
+ 
+
+ align:start position:0%
+that's the second step it got the B got
+the heme out of the hemoglobin and then
+
+ align:start position:0%
+the heme out of the hemoglobin and then
+ 
+
+ align:start position:0%
+the heme out of the hemoglobin and then
+you can look at the transfer to all the
+
+ align:start position:0%
+you can look at the transfer to all the
+ 
+
+ align:start position:0%
+you can look at the transfer to all the
+other proteins you see that in this case
+
+ align:start position:0%
+other proteins you see that in this case
+ 
+
+ align:start position:0%
+other proteins you see that in this case
+one is 114 per second so that's a fast
+
+ align:start position:0%
+one is 114 per second so that's a fast
+ 
+
+ align:start position:0%
+one is 114 per second so that's a fast
+transfer okay so you can look down
+
+ align:start position:0%
+transfer okay so you can look down
+ 
+
+ align:start position:0%
+transfer okay so you can look down
+they've done every single one of these
+
+ align:start position:0%
+they've done every single one of these
+ 
+
+ align:start position:0%
+they've done every single one of these
+steps and they've also then also asked
+
+ align:start position:0%
+steps and they've also then also asked
+ 
+
+ align:start position:0%
+steps and they've also then also asked
+the question 10 these proteins have
+
+ align:start position:0%
+the question 10 these proteins have
+ 
+
+ align:start position:0%
+the question 10 these proteins have
+catalytically so then they put in a
+
+ align:start position:0%
+catalytically so then they put in a
+ 
+
+ align:start position:0%
+catalytically so then they put in a
+small amount of one and look at the rate
+
+ align:start position:0%
+small amount of one and look at the rate
+ 
+
+ align:start position:0%
+small amount of one and look at the rate
+constants in the presence of the absence
+
+ align:start position:0%
+constants in the presence of the absence
+ 
+
+ align:start position:0%
+constants in the presence of the absence
+of one and they conclude that these
+
+ align:start position:0%
+of one and they conclude that these
+ 
+
+ align:start position:0%
+of one and they conclude that these
+proteins can act catalytically as well
+
+ align:start position:0%
+proteins can act catalytically as well
+ 
+
+ align:start position:0%
+proteins can act catalytically as well
+so these are the kinds I don't want to
+
+ align:start position:0%
+so these are the kinds I don't want to
+ 
+
+ align:start position:0%
+so these are the kinds I don't want to
+spend a lot of time discussing this
+
+ align:start position:0%
+spend a lot of time discussing this
+ 
+
+ align:start position:0%
+spend a lot of time discussing this
+detailed set up because I think you
+
+ align:start position:0%
+detailed set up because I think you
+ 
+
+ align:start position:0%
+detailed set up because I think you
+still have to worry about being
+
+ align:start position:0%
+still have to worry about being
+ 
+
+ align:start position:0%
+still have to worry about being
+covalently attached to the peptidoglycan
+
+ align:start position:0%
+covalently attached to the peptidoglycan
+ 
+
+ align:start position:0%
+covalently attached to the peptidoglycan
+but these rate constants are pretty darn
+
+ align:start position:0%
+but these rate constants are pretty darn
+ 
+
+ align:start position:0%
+but these rate constants are pretty darn
+fast okay and so then the other thing
+
+ align:start position:0%
+fast okay and so then the other thing
+ 
+
+ align:start position:0%
+fast okay and so then the other thing
+that's interesting is why does it have
+
+ align:start position:0%
+that's interesting is why does it have
+ 
+
+ align:start position:0%
+that's interesting is why does it have
+an order does it have an order so if you
+
+ align:start position:0%
+an order does it have an order so if you
+ 
+
+ align:start position:0%
+an order does it have an order so if you
+were going to take B can I transfer it
+
+ align:start position:0%
+were going to take B can I transfer it
+ 
+
+ align:start position:0%
+were going to take B can I transfer it
+to C and what are the differences in the
+
+ align:start position:0%
+to C and what are the differences in the
+ 
+
+ align:start position:0%
+to C and what are the differences in the
+rate constants and here it's 114 versus
+
+ align:start position:0%
+rate constants and here it's 114 versus
+ 
+
+ align:start position:0%
+rate constants and here it's 114 versus
+15 okay so now the question is did they
+
+ align:start position:0%
+15 okay so now the question is did they
+ 
+
+ align:start position:0%
+15 okay so now the question is did they
+set up the experiment correctly you know
+
+ align:start position:0%
+set up the experiment correctly you know
+ 
+
+ align:start position:0%
+set up the experiment correctly you know
+they probably used all the same constant
+
+ align:start position:0%
+they probably used all the same constant
+ 
+
+ align:start position:0%
+they probably used all the same constant
+trations in the experiment but one might
+
+ align:start position:0%
+trations in the experiment but one might
+ 
+
+ align:start position:0%
+trations in the experiment but one might
+have an higher affinity than the other
+
+ align:start position:0%
+have an higher affinity than the other
+ 
+
+ align:start position:0%
+have an higher affinity than the other
+and so you need to take you need to
+
+ align:start position:0%
+and so you need to take you need to
+ 
+
+ align:start position:0%
+and so you need to take you need to
+think about all that stuff and if they
+
+ align:start position:0%
+think about all that stuff and if they
+ 
+
+ align:start position:0%
+think about all that stuff and if they
+thought about that correctly they really
+
+ align:start position:0%
+thought about that correctly they really
+ 
+
+ align:start position:0%
+thought about that correctly they really
+have learned something about the order
+
+ align:start position:0%
+have learned something about the order
+ 
+
+ align:start position:0%
+have learned something about the order
+of addition and the ability of these
+
+ align:start position:0%
+of addition and the ability of these
+ 
+
+ align:start position:0%
+of addition and the ability of these
+proteins to act catalytically so this is
+
+ align:start position:0%
+proteins to act catalytically so this is
+ 
+
+ align:start position:0%
+proteins to act catalytically so this is
+a way this is state-of-the-art right now
+
+ align:start position:0%
+a way this is state-of-the-art right now
+ 
+
+ align:start position:0%
+a way this is state-of-the-art right now
+the way people are studying this and
+
+ align:start position:0%
+the way people are studying this and
+ 
+
+ align:start position:0%
+the way people are studying this and
+this kinetic mod the kinetic data has
+
+ align:start position:0%
+this kinetic mod the kinetic data has
+ 
+
+ align:start position:0%
+this kinetic mod the kinetic data has
+allowed us to come up with that model I
+
+ align:start position:0%
+allowed us to come up with that model I
+ 
+
+ align:start position:0%
+allowed us to come up with that model I
+just showed you that there is an ordered
+
+ align:start position:0%
+just showed you that there is an ordered
+ 
+
+ align:start position:0%
+just showed you that there is an ordered
+way to transfer these systems and then I
+
+ align:start position:0%
+way to transfer these systems and then I
+ 
+
+ align:start position:0%
+way to transfer these systems and then I
+just want to say very briefly I just
+
+ align:start position:0%
+just want to say very briefly I just
+ 
+
+ align:start position:0%
+just want to say very briefly I just
+want to show you very briefly the
+
+ align:start position:0%
+want to show you very briefly the
+ 
+
+ align:start position:0%
+want to show you very briefly the
+structures of these and just show you
+
+ align:start position:0%
+structures of these and just show you
+ 
+
+ align:start position:0%
+structures of these and just show you
+with again where the state of the art is
+
+ align:start position:0%
+with again where the state of the art is
+ 
+
+ align:start position:0%
+with again where the state of the art is
+in this area all of these neat domains
+
+ align:start position:0%
+in this area all of these neat domains
+ 
+
+ align:start position:0%
+in this area all of these neat domains
+so neat domains are the heme binding
+
+ align:start position:0%
+so neat domains are the heme binding
+ 
+
+ align:start position:0%
+so neat domains are the heme binding
+domains 120 amino acids they're found in
+
+ align:start position:0%
+domains 120 amino acids they're found in
+ 
+
+ align:start position:0%
+domains 120 amino acids they're found in
+a b c and h they found in four different
+
+ align:start position:0%
+a b c and h they found in four different
+ 
+
+ align:start position:0%
+a b c and h they found in four different
+proteins okay they all this is
+
+ align:start position:0%
+proteins okay they all this is
+ 
+
+ align:start position:0%
+proteins okay they all this is
+superposition of all the neat domains
+
+ align:start position:0%
+superposition of all the neat domains
+ 
+
+ align:start position:0%
+superposition of all the neat domains
+you can see they all look alike okay
+
+ align:start position:0%
+you can see they all look alike okay
+ 
+
+ align:start position:0%
+you can see they all look alike okay
+furthermore if you go down here and you
+
+ align:start position:0%
+furthermore if you go down here and you
+ 
+
+ align:start position:0%
+furthermore if you go down here and you
+look at binding they all have a Penta
+
+ align:start position:0%
+look at binding they all have a Penta
+ 
+
+ align:start position:0%
+look at binding they all have a Penta
+coordinate heme with one axial again
+
+ align:start position:0%
+coordinate heme with one axial again
+ 
+
+ align:start position:0%
+coordinate heme with one axial again
+being a tyrosine the other one the top
+
+ align:start position:0%
+being a tyrosine the other one the top
+ 
+
+ align:start position:0%
+being a tyrosine the other one the top
+face is a PO and in this version of it
+
+ align:start position:0%
+face is a PO and in this version of it
+ 
+
+ align:start position:0%
+face is a PO and in this version of it
+so they also have a structure of two of
+
+ align:start position:0%
+so they also have a structure of two of
+ 
+
+ align:start position:0%
+so they also have a structure of two of
+these things bound together
+
+ align:start position:0%
+these things bound together
+ 
+
+ align:start position:0%
+these things bound together
+all right again these are little domains
+
+ align:start position:0%
+all right again these are little domains
+ 
+
+ align:start position:0%
+all right again these are little domains
+and so the question that you have to ask
+
+ align:start position:0%
+and so the question that you have to ask
+ 
+
+ align:start position:0%
+and so the question that you have to ask
+yourself which is this question of
+
+ align:start position:0%
+yourself which is this question of
+ 
+
+ align:start position:0%
+yourself which is this question of
+ligand rates of exchange of ligands how
+
+ align:start position:0%
+ligand rates of exchange of ligands how
+ 
+
+ align:start position:0%
+ligand rates of exchange of ligands how
+is this transferred do you have how how
+
+ align:start position:0%
+is this transferred do you have how how
+ 
+
+ align:start position:0%
+is this transferred do you have how how
+does this interface help this guy move
+
+ align:start position:0%
+does this interface help this guy move
+ 
+
+ align:start position:0%
+does this interface help this guy move
+from this protein to that protein and
+
+ align:start position:0%
+from this protein to that protein and
+ 
+
+ align:start position:0%
+from this protein to that protein and
+that's what people are focusing their
+
+ align:start position:0%
+that's what people are focusing their
+ 
+
+ align:start position:0%
+that's what people are focusing their
+energies on trying to think about the
+
+ align:start position:0%
+energies on trying to think about the
+ 
+
+ align:start position:0%
+energies on trying to think about the
+detailed structures to come up with a
+
+ align:start position:0%
+detailed structures to come up with a
+ 
+
+ align:start position:0%
+detailed structures to come up with a
+model for how this transfer occurs and
+
+ align:start position:0%
+model for how this transfer occurs and
+ 
+
+ align:start position:0%
+model for how this transfer occurs and
+I'll just show you this is a if you go
+
+ align:start position:0%
+I'll just show you this is a if you go
+ 
+
+ align:start position:0%
+I'll just show you this is a if you go
+all the way down you're going from C
+
+ align:start position:0%
+all the way down you're going from C
+ 
+
+ align:start position:0%
+all the way down you're going from C
+you're going to go from C to e e has a
+
+ align:start position:0%
+you're going to go from C to e e has a
+ 
+
+ align:start position:0%
+you're going to go from C to e e has a
+different structure so the mechanism of
+
+ align:start position:0%
+different structure so the mechanism of
+ 
+
+ align:start position:0%
+different structure so the mechanism of
+heat transfer is different people have a
+
+ align:start position:0%
+heat transfer is different people have a
+ 
+
+ align:start position:0%
+heat transfer is different people have a
+model for that you need to think about
+
+ align:start position:0%
+model for that you need to think about
+ 
+
+ align:start position:0%
+model for that you need to think about
+the details and now furthermore
+
+ align:start position:0%
+the details and now furthermore
+ 
+
+ align:start position:0%
+the details and now furthermore
+you can go from E to F all the way
+
+ align:start position:0%
+you can go from E to F all the way
+ 
+
+ align:start position:0%
+you can go from E to F all the way
+through the plasma membrane to the
+
+ align:start position:0%
+through the plasma membrane to the
+ 
+
+ align:start position:0%
+through the plasma membrane to the
+ATPase which then helped you get the
+
+ align:start position:0%
+ATPase which then helped you get the
+ 
+
+ align:start position:0%
+ATPase which then helped you get the
+heme provides the driving force getting
+
+ align:start position:0%
+heme provides the driving force getting
+ 
+
+ align:start position:0%
+heme provides the driving force getting
+him into the into the cytosol so we have
+
+ align:start position:0%
+him into the into the cytosol so we have
+ 
+
+ align:start position:0%
+him into the into the cytosol so we have
+a lot of structural data but what's
+
+ align:start position:0%
+a lot of structural data but what's
+ 
+
+ align:start position:0%
+a lot of structural data but what's
+disappointing I think from reading those
+
+ align:start position:0%
+disappointing I think from reading those
+ 
+
+ align:start position:0%
+disappointing I think from reading those
+papers which I have read is we still
+
+ align:start position:0%
+papers which I have read is we still
+ 
+
+ align:start position:0%
+papers which I have read is we still
+really don't have a good model for how
+
+ align:start position:0%
+really don't have a good model for how
+ 
+
+ align:start position:0%
+really don't have a good model for how
+these transfers actually work so this is
+
+ align:start position:0%
+these transfers actually work so this is
+ 
+
+ align:start position:0%
+these transfers actually work so this is
+an active area of research research and
+
+ align:start position:0%
+an active area of research research and
+ 
+
+ align:start position:0%
+an active area of research research and
+the people interested in the
+
+ align:start position:0%
+the people interested in the
+ 
+
+ align:start position:0%
+the people interested in the
+bioinorganic chemistry and how you get
+
+ align:start position:0%
+bioinorganic chemistry and how you get
+ 
+
+ align:start position:0%
+bioinorganic chemistry and how you get
+heme into cells okay so that is the end
+
+ align:start position:0%
+heme into cells okay so that is the end
+ 
+
+ align:start position:0%
+heme into cells okay so that is the end
+of module 6 I think we've learned a lot
+
+ align:start position:0%
+of module 6 I think we've learned a lot
+ 
+
+ align:start position:0%
+of module 6 I think we've learned a lot
+in the last few years about these
+
+ align:start position:0%
+in the last few years about these
+ 
+
+ align:start position:0%
+in the last few years about these
+proteins but as you can see we still
+
+ align:start position:0%
+proteins but as you can see we still
+ 
+
+ align:start position:0%
+proteins but as you can see we still
+have a long way to go in terms of
+
+ align:start position:0%
+have a long way to go in terms of
+ 
+
+ align:start position:0%
+have a long way to go in terms of
+molecular understanding okay and so the
+
+ align:start position:0%
+molecular understanding okay and so the
+ 
+
+ align:start position:0%
+molecular understanding okay and so the
+next module module cell 7 is going to be
+
+ align:start position:0%
+next module module cell 7 is going to be
+ 
+
+ align:start position:0%
+next module module cell 7 is going to be
+the shortest module and I'll give you an
+
+ align:start position:0%
+the shortest module and I'll give you an
+ 
+
+ align:start position:0%
+the shortest module and I'll give you an
+outline of what I'm going to be what I'm
+
+ align:start position:0%
+outline of what I'm going to be what I'm
+ 
+
+ align:start position:0%
+outline of what I'm going to be what I'm
+gonna be and then today's the first
+
+ align:start position:0%
+gonna be and then today's the first
+ 
+
+ align:start position:0%
+gonna be and then today's the first
+lecture is much longer than the second
+
+ align:start position:0%
+lecture is much longer than the second
+ 
+
+ align:start position:0%
+lecture is much longer than the second
+lecture and we'll see the second lecture
+
+ align:start position:0%
+lecture and we'll see the second lecture
+ 
+
+ align:start position:0%
+lecture and we'll see the second lecture
+is going to be focused a lot on what
+
+ align:start position:0%
+is going to be focused a lot on what
+ 
+
+ align:start position:0%
+is going to be focused a lot on what
+we're doing in recitation this week so
+
+ align:start position:0%
+we're doing in recitation this week so
+ 
+
+ align:start position:0%
+we're doing in recitation this week so
+if you notice maybe you you haven't but
+
+ align:start position:0%
+if you notice maybe you you haven't but
+ 
+
+ align:start position:0%
+if you notice maybe you you haven't but
+we posted the readings and one of the
+
+ align:start position:0%
+we posted the readings and one of the
+ 
+
+ align:start position:0%
+we posted the readings and one of the
+papers for the course this part of the
+
+ align:start position:0%
+papers for the course this part of the
+ 
+
+ align:start position:0%
+papers for the course this part of the
+course the lecture part of the course is
+
+ align:start position:0%
+course the lecture part of the course is
+ 
+
+ align:start position:0%
+course the lecture part of the course is
+a Carroll paper you're supposed to read
+
+ align:start position:0%
+a Carroll paper you're supposed to read
+ 
+
+ align:start position:0%
+a Carroll paper you're supposed to read
+for recitation so there's a lot of
+
+ align:start position:0%
+for recitation so there's a lot of
+ 
+
+ align:start position:0%
+for recitation so there's a lot of
+overlap and so the second lecture will
+
+ align:start position:0%
+overlap and so the second lecture will
+ 
+
+ align:start position:0%
+overlap and so the second lecture will
+be much shorter because we're going to
+
+ align:start position:0%
+be much shorter because we're going to
+ 
+
+ align:start position:0%
+be much shorter because we're going to
+draw on what we're doing in recitation
+
+ align:start position:0%
+draw on what we're doing in recitation
+ 
+
+ align:start position:0%
+draw on what we're doing in recitation
+actually today so okay so let me give
+
+ align:start position:0%
+actually today so okay so let me give
+ 
+
+ align:start position:0%
+actually today so okay so let me give
+you the outline so module 7 ok is a
+
+ align:start position:0%
+you the outline so module 7 ok is a
+ 
+
+ align:start position:0%
+you the outline so module 7 ok is a
+shortest and this is the required
+
+ align:start position:0%
+shortest and this is the required
+ 
+
+ align:start position:0%
+shortest and this is the required
+reading so we posted a review article by
+
+ align:start position:0%
+reading so we posted a review article by
+ 
+
+ align:start position:0%
+reading so we posted a review article by
+Winterbourne who in my opinion this area
+
+ align:start position:0%
+Winterbourne who in my opinion this area
+ 
+
+ align:start position:0%
+Winterbourne who in my opinion this area
+of rare reactive oxygen species and how
+
+ align:start position:0%
+of rare reactive oxygen species and how
+ 
+
+ align:start position:0%
+of rare reactive oxygen species and how
+romeo's to how you control reactive
+
+ align:start position:0%
+romeo's to how you control reactive
+ 
+
+ align:start position:0%
+romeo's to how you control reactive
+oxygen species I'm going to show
+
+ align:start position:0%
+oxygen species I'm going to show
+ 
+
+ align:start position:0%
+oxygen species I'm going to show
+they could be good they can be bad just
+
+ align:start position:0%
+they could be good they can be bad just
+ 
+
+ align:start position:0%
+they could be good they can be bad just
+like we saw with iron it's all a
+
+ align:start position:0%
+like we saw with iron it's all a
+ 
+
+ align:start position:0%
+like we saw with iron it's all a
+question of homeostasis the most cycles
+
+ align:start position:0%
+question of homeostasis the most cycles
+ 
+
+ align:start position:0%
+question of homeostasis the most cycles
+the most thoughtful discussions have
+
+ align:start position:0%
+the most thoughtful discussions have
+ 
+
+ align:start position:0%
+the most thoughtful discussions have
+been described by Winterbourne who is in
+
+ align:start position:0%
+been described by Winterbourne who is in
+ 
+
+ align:start position:0%
+been described by Winterbourne who is in
+New Zealand who really thinks about the
+
+ align:start position:0%
+New Zealand who really thinks about the
+ 
+
+ align:start position:0%
+New Zealand who really thinks about the
+kinetics of what's going on and I would
+
+ align:start position:0%
+kinetics of what's going on and I would
+ 
+
+ align:start position:0%
+kinetics of what's going on and I would
+argue you can't do anything in this
+
+ align:start position:0%
+argue you can't do anything in this
+ 
+
+ align:start position:0%
+argue you can't do anything in this
+field without thinking about kinetics
+
+ align:start position:0%
+field without thinking about kinetics
+ 
+
+ align:start position:0%
+field without thinking about kinetics
+which most people most MDS in this field
+
+ align:start position:0%
+which most people most MDS in this field
+ 
+
+ align:start position:0%
+which most people most MDS in this field
+don't think about it all okay so the
+
+ align:start position:0%
+don't think about it all okay so the
+ 
+
+ align:start position:0%
+don't think about it all okay so the
+literature is a mess okay and so but I
+
+ align:start position:0%
+literature is a mess okay and so but I
+ 
+
+ align:start position:0%
+literature is a mess okay and so but I
+think the last few years it's become
+
+ align:start position:0%
+think the last few years it's become
+ 
+
+ align:start position:0%
+think the last few years it's become
+it's become it's starting to get my
+
+ align:start position:0%
+it's become it's starting to get my
+ 
+
+ align:start position:0%
+it's become it's starting to get my
+money okay and I think it's an
+
+ align:start position:0%
+money okay and I think it's an
+ 
+
+ align:start position:0%
+money okay and I think it's an
+incredibly important area I guarantee
+
+ align:start position:0%
+incredibly important area I guarantee
+ 
+
+ align:start position:0%
+incredibly important area I guarantee
+you that that's true so unmod an
+
+ align:start position:0%
+you that that's true so unmod an
+ 
+
+ align:start position:0%
+you that that's true so unmod an
+incredibly important the area is going
+
+ align:start position:0%
+incredibly important the area is going
+ 
+
+ align:start position:0%
+incredibly important the area is going
+to be up to you guys but I think it's
+
+ align:start position:0%
+to be up to you guys but I think it's
+ 
+
+ align:start position:0%
+to be up to you guys but I think it's
+going to happen in the next five years
+
+ align:start position:0%
+going to happen in the next five years
+ 
+
+ align:start position:0%
+going to happen in the next five years
+or something I think we're gonna we've
+
+ align:start position:0%
+or something I think we're gonna we've
+ 
+
+ align:start position:0%
+or something I think we're gonna we've
+already learned a lot in the last couple
+
+ align:start position:0%
+already learned a lot in the last couple
+ 
+
+ align:start position:0%
+already learned a lot in the last couple
+of years so I'm gonna have an outline so
+
+ align:start position:0%
+of years so I'm gonna have an outline so
+ 
+
+ align:start position:0%
+of years so I'm gonna have an outline so
+we have that paper and then we have the
+
+ align:start position:0%
+we have that paper and then we have the
+ 
+
+ align:start position:0%
+we have that paper and then we have the
+Carroll paper that you guys hopefully
+
+ align:start position:0%
+Carroll paper that you guys hopefully
+ 
+
+ align:start position:0%
+Carroll paper that you guys hopefully
+have already looked at in some form all
+
+ align:start position:0%
+have already looked at in some form all
+ 
+
+ align:start position:0%
+have already looked at in some form all
+right so here I need to switch okay so
+
+ align:start position:0%
+right so here I need to switch okay so
+ 
+
+ align:start position:0%
+right so here I need to switch okay so
+where are we going and so we're gonna
+
+ align:start position:0%
+where are we going and so we're gonna
+ 
+
+ align:start position:0%
+where are we going and so we're gonna
+have a couple of lectures first of all
+
+ align:start position:0%
+have a couple of lectures first of all
+ 
+
+ align:start position:0%
+have a couple of lectures first of all
+what is our OS so our OS our reactive
+
+ align:start position:0%
+what is our OS so our OS our reactive
+ 
+
+ align:start position:0%
+what is our OS so our OS our reactive
+oxygen species
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so automatically they're a bunch of
+
+ align:start position:0%
+okay so automatically they're a bunch of
+ 
+
+ align:start position:0%
+okay so automatically they're a bunch of
+molecules that are reactive and so what
+
+ align:start position:0%
+molecules that are reactive and so what
+ 
+
+ align:start position:0%
+molecules that are reactive and so what
+you need to think about is what is
+
+ align:start position:0%
+you need to think about is what is
+ 
+
+ align:start position:0%
+you need to think about is what is
+reactive me okay so the first thing is
+
+ align:start position:0%
+reactive me okay so the first thing is
+ 
+
+ align:start position:0%
+reactive me okay so the first thing is
+we're going to identify them okay the
+
+ align:start position:0%
+we're going to identify them okay the
+ 
+
+ align:start position:0%
+we're going to identify them okay the
+second thing is we're going to look at
+
+ align:start position:0%
+second thing is we're going to look at
+ 
+
+ align:start position:0%
+second thing is we're going to look at
+the chemical reactivity and again the
+
+ align:start position:0%
+the chemical reactivity and again the
+ 
+
+ align:start position:0%
+the chemical reactivity and again the
+question of chemical reactivity can be
+
+ align:start position:0%
+question of chemical reactivity can be
+ 
+
+ align:start position:0%
+question of chemical reactivity can be
+quite complex but I'm going to give you
+
+ align:start position:0%
+quite complex but I'm going to give you
+ 
+
+ align:start position:0%
+quite complex but I'm going to give you
+my view of the chemical reactivity and
+
+ align:start position:0%
+my view of the chemical reactivity and
+ 
+
+ align:start position:0%
+my view of the chemical reactivity and
+what that view is based on and then
+
+ align:start position:0%
+what that view is based on and then
+ 
+
+ align:start position:0%
+what that view is based on and then
+we'll very briefly look at over since we
+
+ align:start position:0%
+we'll very briefly look at over since we
+ 
+
+ align:start position:0%
+we'll very briefly look at over since we
+move
+
+ align:start position:0%
+move
+ 
+
+ align:start position:0%
+move
+an anaerobic world whatever a billion
+
+ align:start position:0%
+an anaerobic world whatever a billion
+ 
+
+ align:start position:0%
+an anaerobic world whatever a billion
+years ago into anaerobic world like we
+
+ align:start position:0%
+years ago into anaerobic world like we
+ 
+
+ align:start position:0%
+years ago into anaerobic world like we
+learned from the last module the
+
+ align:start position:0%
+learned from the last module the
+ 
+
+ align:start position:0%
+learned from the last module the
+question is how do we defend ourselves
+
+ align:start position:0%
+question is how do we defend ourselves
+ 
+
+ align:start position:0%
+question is how do we defend ourselves
+against the presence of oxygen with
+
+ align:start position:0%
+against the presence of oxygen with
+ 
+
+ align:start position:0%
+against the presence of oxygen with
+reduced metals okay and that's the issue
+
+ align:start position:0%
+reduced metals okay and that's the issue
+ 
+
+ align:start position:0%
+reduced metals okay and that's the issue
+we raised last time so what are our
+
+ align:start position:0%
+we raised last time so what are our
+ 
+
+ align:start position:0%
+we raised last time so what are our
+defense mechanisms because we saw we had
+
+ align:start position:0%
+defense mechanisms because we saw we had
+ 
+
+ align:start position:0%
+defense mechanisms because we saw we had
+copper we had iron and now we have
+
+ align:start position:0%
+copper we had iron and now we have
+ 
+
+ align:start position:0%
+copper we had iron and now we have
+oxygen and we'll see that that can be a
+
+ align:start position:0%
+oxygen and we'll see that that can be a
+ 
+
+ align:start position:0%
+oxygen and we'll see that that can be a
+recipe for disaster and once you can
+
+ align:start position:0%
+recipe for disaster and once you can
+ 
+
+ align:start position:0%
+recipe for disaster and once you can
+figure out how to control all of that so
+
+ align:start position:0%
+figure out how to control all of that so
+ 
+
+ align:start position:0%
+figure out how to control all of that so
+again it's all homeostasis so that's the
+
+ align:start position:0%
+again it's all homeostasis so that's the
+ 
+
+ align:start position:0%
+again it's all homeostasis so that's the
+second that will be the first part of
+
+ align:start position:0%
+second that will be the first part of
+ 
+
+ align:start position:0%
+second that will be the first part of
+today's lecture then we're going to move
+
+ align:start position:0%
+today's lecture then we're going to move
+ 
+
+ align:start position:0%
+today's lecture then we're going to move
+into the question of the battle between
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+bacteria or viruses or parasites in
+
+ align:start position:0%
+bacteria or viruses or parasites in
+ 
+
+ align:start position:0%
+bacteria or viruses or parasites in
+humans and what I'm going to talk about
+
+ align:start position:0%
+humans and what I'm going to talk about
+ 
+
+ align:start position:0%
+humans and what I'm going to talk about
+specifically is destruction of bacteria
+
+ align:start position:0%
+specifically is destruction of bacteria
+ 
+
+ align:start position:0%
+specifically is destruction of bacteria
+by neutrophils and we'll see that
+
+ align:start position:0%
+by neutrophils and we'll see that
+ 
+
+ align:start position:0%
+by neutrophils and we'll see that
+neutrophils are white blood cells and we
+
+ align:start position:0%
+neutrophils are white blood cells and we
+ 
+
+ align:start position:0%
+neutrophils are white blood cells and we
+will see that they're the first
+
+ align:start position:0%
+will see that they're the first
+ 
+
+ align:start position:0%
+will see that they're the first
+responders so if you have a bacteria and
+
+ align:start position:0%
+responders so if you have a bacteria and
+ 
+
+ align:start position:0%
+responders so if you have a bacteria and
+our blood stream the first guys they are
+
+ align:start position:0%
+our blood stream the first guys they are
+ 
+
+ align:start position:0%
+our blood stream the first guys they are
+the neutrophils and that's what we're
+
+ align:start position:0%
+the neutrophils and that's what we're
+ 
+
+ align:start position:0%
+the neutrophils and that's what we're
+gonna focus on okay so let me see
+
+ align:start position:0%
+gonna focus on okay so let me see
+ 
+
+ align:start position:0%
+gonna focus on okay so let me see
+alright I'll go over here
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so neutrophils are the first
+
+ align:start position:0%
+okay so neutrophils are the first
+ 
+
+ align:start position:0%
+okay so neutrophils are the first
+responders and all we know quite a bit
+
+ align:start position:0%
+responders and all we know quite a bit
+ 
+
+ align:start position:0%
+responders and all we know quite a bit
+about this and really what we're going
+
+ align:start position:0%
+about this and really what we're going
+ 
+
+ align:start position:0%
+about this and really what we're going
+to be focusing on and both today's
+
+ align:start position:0%
+to be focusing on and both today's
+ 
+
+ align:start position:0%
+to be focusing on and both today's
+lecture and in the next lecture is one
+
+ align:start position:0%
+lecture and in the next lecture is one
+ 
+
+ align:start position:0%
+lecture and in the next lecture is one
+prote the group of isozymes called knox
+
+ align:start position:0%
+prote the group of isozymes called knox
+ 
+
+ align:start position:0%
+prote the group of isozymes called knox
+proteins and o-x NADPH oxidase --is and
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay we're going to talk about that
+
+ align:start position:0%
+okay we're going to talk about that
+ 
+
+ align:start position:0%
+okay we're going to talk about that
+particular protein and we're going to be
+
+ align:start position:0%
+particular protein and we're going to be
+ 
+
+ align:start position:0%
+particular protein and we're going to be
+specifically focused on Knox two and
+
+ align:start position:0%
+specifically focused on Knox two and
+ 
+
+ align:start position:0%
+specifically focused on Knox two and
+we'll see that Knox twos professional
+
+ align:start position:0%
+we'll see that Knox twos professional
+ 
+
+ align:start position:0%
+we'll see that Knox twos professional
+job we'll talk about that is to generate
+
+ align:start position:0%
+job we'll talk about that is to generate
+ 
+
+ align:start position:0%
+job we'll talk about that is to generate
+a reactive oxygen species superoxide
+
+ align:start position:0%
+a reactive oxygen species superoxide
+ 
+
+ align:start position:0%
+a reactive oxygen species superoxide
+which is then going to be used in some
+
+ align:start position:0%
+which is then going to be used in some
+ 
+
+ align:start position:0%
+which is then going to be used in some
+way to kill bacteria okay so we're gonna
+
+ align:start position:0%
+way to kill bacteria okay so we're gonna
+ 
+
+ align:start position:0%
+way to kill bacteria okay so we're gonna
+be talking about neutrophils we're going
+
+ align:start position:0%
+be talking about neutrophils we're going
+ 
+
+ align:start position:0%
+be talking about neutrophils we're going
+to be talking about the knox protein
+
+ align:start position:0%
+to be talking about the knox protein
+ 
+
+ align:start position:0%
+to be talking about the knox protein
+also if you've read the recitation paper
+
+ align:start position:0%
+also if you've read the recitation paper
+ 
+
+ align:start position:0%
+also if you've read the recitation paper
+for today what are we talking about in
+
+ align:start position:0%
+for today what are we talking about in
+ 
+
+ align:start position:0%
+for today what are we talking about in
+signaling that's oxygen-dependent the
+
+ align:start position:0%
+signaling that's oxygen-dependent the
+ 
+
+ align:start position:0%
+signaling that's oxygen-dependent the
+knox proteins so here we have bad we're
+
+ align:start position:0%
+knox proteins so here we have bad we're
+ 
+
+ align:start position:0%
+knox proteins so here we have bad we're
+killing the bacteria here we have good
+
+ align:start position:0%
+killing the bacteria here we have good
+ 
+
+ align:start position:0%
+killing the bacteria here we have good
+we're using the knox proteins for
+
+ align:start position:0%
+we're using the knox proteins for
+ 
+
+ align:start position:0%
+we're using the knox proteins for
+signaling so that's sort of the
+
+ align:start position:0%
+signaling so that's sort of the
+ 
+
+ align:start position:0%
+signaling so that's sort of the
+take-home message is homeostasis how do
+
+ align:start position:0%
+take-home message is homeostasis how do
+ 
+
+ align:start position:0%
+take-home message is homeostasis how do
+you control it for bad versus for good
+
+ align:start position:0%
+you control it for bad versus for good
+ 
+
+ align:start position:0%
+you control it for bad versus for good
+we've already seen that in the case of
+
+ align:start position:0%
+we've already seen that in the case of
+ 
+
+ align:start position:0%
+we've already seen that in the case of
+the iron systems so so the other protein
+
+ align:start position:0%
+the iron systems so so the other protein
+ 
+
+ align:start position:0%
+the iron systems so so the other protein
+we're gonna talk about today or probably
+
+ align:start position:0%
+we're gonna talk about today or probably
+ 
+
+ align:start position:0%
+we're gonna talk about today or probably
+won't get that far today how bad am i
+
+ align:start position:0%
+won't get that far today how bad am i
+ 
+
+ align:start position:0%
+won't get that far today how bad am i
+okay so we have another protein called
+
+ align:start position:0%
+okay so we have another protein called
+ 
+
+ align:start position:0%
+okay so we have another protein called
+milo peroxidase and we're gonna see that
+
+ align:start position:0%
+milo peroxidase and we're gonna see that
+ 
+
+ align:start position:0%
+milo peroxidase and we're gonna see that
+this so this guy is going to be involved
+
+ align:start position:0%
+this so this guy is going to be involved
+ 
+
+ align:start position:0%
+this so this guy is going to be involved
+with superoxide this guy is involved in
+
+ align:start position:0%
+with superoxide this guy is involved in
+ 
+
+ align:start position:0%
+with superoxide this guy is involved in
+the neutrophils Jenner with generating
+
+ align:start position:0%
+the neutrophils Jenner with generating
+ 
+
+ align:start position:0%
+the neutrophils Jenner with generating
+hypochlorous acid so these are the
+
+ align:start position:0%
+hypochlorous acid so these are the
+ 
+
+ align:start position:0%
+hypochlorous acid so these are the
+proteins and these proteins together
+
+ align:start position:0%
+proteins and these proteins together
+ 
+
+ align:start position:0%
+proteins and these proteins together
+I'll give you the model the current
+
+ align:start position:0%
+I'll give you the model the current
+ 
+
+ align:start position:0%
+I'll give you the model the current
+model but the current model I'm going to
+
+ align:start position:0%
+model but the current model I'm going to
+ 
+
+ align:start position:0%
+model but the current model I'm going to
+give you as much simpler than reality
+
+ align:start position:0%
+give you as much simpler than reality
+ 
+
+ align:start position:0%
+give you as much simpler than reality
+okay but those are the proteins we're
+
+ align:start position:0%
+okay but those are the proteins we're
+ 
+
+ align:start position:0%
+okay but those are the proteins we're
+going to
+
+ align:start position:0%
+going to
+ 
+
+ align:start position:0%
+going to
+focus on and those are two of the
+
+ align:start position:0%
+focus on and those are two of the
+ 
+
+ align:start position:0%
+focus on and those are two of the
+reactive species were going to be
+
+ align:start position:0%
+reactive species were going to be
+ 
+
+ align:start position:0%
+reactive species were going to be
+focusing on and then the second lecture
+
+ align:start position:0%
+focusing on and then the second lecture
+ 
+
+ align:start position:0%
+focusing on and then the second lecture
+goes back to the NOx to proteins and the
+
+ align:start position:0%
+goes back to the NOx to proteins and the
+ 
+
+ align:start position:0%
+goes back to the NOx to proteins and the
+question now of not killing but
+
+ align:start position:0%
+question now of not killing but
+ 
+
+ align:start position:0%
+question now of not killing but
+signaling and as we already saw in the
+
+ align:start position:0%
+signaling and as we already saw in the
+ 
+
+ align:start position:0%
+signaling and as we already saw in the
+last in the last recitation how are we
+
+ align:start position:0%
+last in the last recitation how are we
+ 
+
+ align:start position:0%
+last in the last recitation how are we
+sickening we were signaling by from a
+
+ align:start position:0%
+sickening we were signaling by from a
+ 
+
+ align:start position:0%
+sickening we were signaling by from a
+reaction of self fighter groups with
+
+ align:start position:0%
+reaction of self fighter groups with
+ 
+
+ align:start position:0%
+reaction of self fighter groups with
+hydrogen peroxide which can be generated
+
+ align:start position:0%
+hydrogen peroxide which can be generated
+ 
+
+ align:start position:0%
+hydrogen peroxide which can be generated
+from superoxide I'll show you how that
+
+ align:start position:0%
+from superoxide I'll show you how that
+ 
+
+ align:start position:0%
+from superoxide I'll show you how that
+happens
+
+ align:start position:0%
+happens
+ 
+
+ align:start position:0%
+happens
+so signaling and we're focusing on
+
+ align:start position:0%
+so signaling and we're focusing on
+ 
+
+ align:start position:0%
+so signaling and we're focusing on
+signaling by self-immolation which again
+
+ align:start position:0%
+signaling by self-immolation which again
+ 
+
+ align:start position:0%
+signaling by self-immolation which again
+is the topic of today's recitation of
+
+ align:start position:0%
+is the topic of today's recitation of
+ 
+
+ align:start position:0%
+is the topic of today's recitation of
+the epidermal growth factor receptor
+
+ align:start position:0%
+the epidermal growth factor receptor
+ 
+
+ align:start position:0%
+the epidermal growth factor receptor
+okay so that's what we're going okay and
+
+ align:start position:0%
+okay so that's what we're going okay and
+ 
+
+ align:start position:0%
+okay so that's what we're going okay and
+I'm going to give you that we're gonna
+
+ align:start position:0%
+I'm going to give you that we're gonna
+ 
+
+ align:start position:0%
+I'm going to give you that we're gonna
+follow this outline and I think you'll
+
+ align:start position:0%
+follow this outline and I think you'll
+ 
+
+ align:start position:0%
+follow this outline and I think you'll
+get a pretty good feeling for an
+
+ align:start position:0%
+get a pretty good feeling for an
+ 
+
+ align:start position:0%
+get a pretty good feeling for an
+overview of reactive oxygen species even
+
+ align:start position:0%
+overview of reactive oxygen species even
+ 
+
+ align:start position:0%
+overview of reactive oxygen species even
+though we're not going through it in a
+
+ align:start position:0%
+though we're not going through it in a
+ 
+
+ align:start position:0%
+though we're not going through it in a
+lot of details it's really complicated
+
+ align:start position:0%
+lot of details it's really complicated
+ 
+
+ align:start position:0%
+lot of details it's really complicated
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+so what I want to do before I get to
+
+ align:start position:0%
+so what I want to do before I get to
+ 
+
+ align:start position:0%
+so what I want to do before I get to
+this slide is give you the big picture
+
+ align:start position:0%
+this slide is give you the big picture
+ 
+
+ align:start position:0%
+this slide is give you the big picture
+[Applause]
+
+ align:start position:0%
+[Applause]
+ 
+
+ align:start position:0%
+[Applause]
+okay so this is the take-home message so
+
+ align:start position:0%
+okay so this is the take-home message so
+ 
+
+ align:start position:0%
+okay so this is the take-home message so
+we have a big picture okay and so here
+
+ align:start position:0%
+we have a big picture okay and so here
+ 
+
+ align:start position:0%
+we have a big picture okay and so here
+we have cell okay and in this cell we
+
+ align:start position:0%
+we have cell okay and in this cell we
+ 
+
+ align:start position:0%
+we have cell okay and in this cell we
+have reactive oxygen species and there
+
+ align:start position:0%
+have reactive oxygen species and there
+ 
+
+ align:start position:0%
+have reactive oxygen species and there
+were also things called reactive
+
+ align:start position:0%
+were also things called reactive
+ 
+
+ align:start position:0%
+were also things called reactive
+nitrogen species and you'll see that in
+
+ align:start position:0%
+nitrogen species and you'll see that in
+ 
+
+ align:start position:0%
+nitrogen species and you'll see that in
+some of the slides in the PowerPoint
+
+ align:start position:0%
+some of the slides in the PowerPoint
+ 
+
+ align:start position:0%
+some of the slides in the PowerPoint
+presentation we're not going to talk
+
+ align:start position:0%
+presentation we're not going to talk
+ 
+
+ align:start position:0%
+presentation we're not going to talk
+about that chemistry it's interesting if
+
+ align:start position:0%
+about that chemistry it's interesting if
+ 
+
+ align:start position:0%
+about that chemistry it's interesting if
+I had an extra three or four lectures I
+
+ align:start position:0%
+I had an extra three or four lectures I
+ 
+
+ align:start position:0%
+I had an extra three or four lectures I
+would also be talking about that it's
+
+ align:start position:0%
+would also be talking about that it's
+ 
+
+ align:start position:0%
+would also be talking about that it's
+central it's as important as reactive
+
+ align:start position:0%
+central it's as important as reactive
+ 
+
+ align:start position:0%
+central it's as important as reactive
+oxygen species but I've decided to focus
+
+ align:start position:0%
+oxygen species but I've decided to focus
+ 
+
+ align:start position:0%
+oxygen species but I've decided to focus
+on that's what I've decided to focus on
+
+ align:start position:0%
+on that's what I've decided to focus on
+ 
+
+ align:start position:0%
+on that's what I've decided to focus on
+so we have hydroxide radical we have
+
+ align:start position:0%
+so we have hydroxide radical we have
+ 
+
+ align:start position:0%
+so we have hydroxide radical we have
+hydrogen peroxide
+
+ align:start position:0%
+hydrogen peroxide
+ 
+
+ align:start position:0%
+hydrogen peroxide
+we have superoxide and we have
+
+ align:start position:0%
+we have superoxide and we have
+ 
+
+ align:start position:0%
+we have superoxide and we have
+hypochlorous acid okay so these are the
+
+ align:start position:0%
+hypochlorous acid okay so these are the
+ 
+
+ align:start position:0%
+hypochlorous acid okay so these are the
+four species that we're gonna be focused
+
+ align:start position:0%
+four species that we're gonna be focused
+ 
+
+ align:start position:0%
+four species that we're gonna be focused
+on and you can already see that some of
+
+ align:start position:0%
+on and you can already see that some of
+ 
+
+ align:start position:0%
+on and you can already see that some of
+them are radical and some of them are
+
+ align:start position:0%
+them are radical and some of them are
+ 
+
+ align:start position:0%
+them are radical and some of them are
+not okay so reactive oxygen species
+
+ align:start position:0%
+not okay so reactive oxygen species
+ 
+
+ align:start position:0%
+not okay so reactive oxygen species
+doesn't mean they have a free radical
+
+ align:start position:0%
+doesn't mean they have a free radical
+ 
+
+ align:start position:0%
+doesn't mean they have a free radical
+they can do one electron or two electron
+
+ align:start position:0%
+they can do one electron or two electron
+ 
+
+ align:start position:0%
+they can do one electron or two electron
+chemistry and we'll talk briefly about
+
+ align:start position:0%
+chemistry and we'll talk briefly about
+ 
+
+ align:start position:0%
+chemistry and we'll talk briefly about
+that and so the question is where did
+
+ align:start position:0%
+that and so the question is where did
+ 
+
+ align:start position:0%
+that and so the question is where did
+these come from okay so remember we made
+
+ align:start position:0%
+these come from okay so remember we made
+ 
+
+ align:start position:0%
+these come from okay so remember we made
+a transition from an anaerobic to an
+
+ align:start position:0%
+a transition from an anaerobic to an
+ 
+
+ align:start position:0%
+a transition from an anaerobic to an
+aerobic world a billion years ago and
+
+ align:start position:0%
+aerobic world a billion years ago and
+ 
+
+ align:start position:0%
+aerobic world a billion years ago and
+during that process we have a
+
+ align:start position:0%
+during that process we have a
+ 
+
+ align:start position:0%
+during that process we have a
+respiratory chain in humans the
+
+ align:start position:0%
+respiratory chain in humans the
+ 
+
+ align:start position:0%
+respiratory chain in humans the
+respiratory chain is found in the
+
+ align:start position:0%
+respiratory chain is found in the
+ 
+
+ align:start position:0%
+respiratory chain is found in the
+mitochondria otherwise it's found in the
+
+ align:start position:0%
+mitochondria otherwise it's found in the
+ 
+
+ align:start position:0%
+mitochondria otherwise it's found in the
+plasma membrane so we have complexes 1 2
+
+ align:start position:0%
+plasma membrane so we have complexes 1 2
+ 
+
+ align:start position:0%
+plasma membrane so we have complexes 1 2
+& 3 and these guys do chemistry their
+
+ align:start position:0%
+& 3 and these guys do chemistry their
+ 
+
+ align:start position:0%
+& 3 and these guys do chemistry their
+ultimate goal if you're in an oxygen
+
+ align:start position:0%
+ultimate goal if you're in an oxygen
+ 
+
+ align:start position:0%
+ultimate goal if you're in an oxygen
+oxygen dependent world is to reduce
+
+ align:start position:0%
+oxygen dependent world is to reduce
+ 
+
+ align:start position:0%
+oxygen dependent world is to reduce
+oxygen to water okay so this is a goal
+
+ align:start position:0%
+oxygen to water okay so this is a goal
+ 
+
+ align:start position:0%
+oxygen to water okay so this is a goal
+is oxygen to water although you all know
+
+ align:start position:0%
+is oxygen to water although you all know
+ 
+
+ align:start position:0%
+is oxygen to water although you all know
+in bacteria if there's no oxygen you
+
+ align:start position:0%
+in bacteria if there's no oxygen you
+ 
+
+ align:start position:0%
+in bacteria if there's no oxygen you
+have to have some other terminal
+
+ align:start position:0%
+have to have some other terminal
+ 
+
+ align:start position:0%
+have to have some other terminal
+electron acceptor and so what you get
+
+ align:start position:0%
+electron acceptor and so what you get
+ 
+
+ align:start position:0%
+electron acceptor and so what you get
+from these complexes is uncoupling okay
+
+ align:start position:0%
+from these complexes is uncoupling okay
+ 
+
+ align:start position:0%
+from these complexes is uncoupling okay
+so 100 percent of the time it doesn't do
+
+ align:start position:0%
+so 100 percent of the time it doesn't do
+ 
+
+ align:start position:0%
+so 100 percent of the time it doesn't do
+what you want it to do and so you have
+
+ align:start position:0%
+what you want it to do and so you have
+ 
+
+ align:start position:0%
+what you want it to do and so you have
+to you you get a side reactions that you
+
+ align:start position:0%
+to you you get a side reactions that you
+ 
+
+ align:start position:0%
+to you you get a side reactions that you
+have to deal with you know what I do
+
+ align:start position:0%
+have to deal with you know what I do
+ 
+
+ align:start position:0%
+have to deal with you know what I do
+with my chalk anyhow so you get
+
+ align:start position:0%
+with my chalk anyhow so you get
+ 
+
+ align:start position:0%
+with my chalk anyhow so you get
+uncoupling okay so that's one way if
+
+ align:start position:0%
+uncoupling okay so that's one way if
+ 
+
+ align:start position:0%
+uncoupling okay so that's one way if
+they're generated a second way that
+
+ align:start position:0%
+they're generated a second way that
+ 
+
+ align:start position:0%
+they're generated a second way that
+generated we've already been through we
+
+ align:start position:0%
+generated we've already been through we
+ 
+
+ align:start position:0%
+generated we've already been through we
+went from an anaerobic world to an
+
+ align:start position:0%
+went from an anaerobic world to an
+ 
+
+ align:start position:0%
+went from an anaerobic world to an
+aerobic world what do we have under
+
+ align:start position:0%
+aerobic world what do we have under
+ 
+
+ align:start position:0%
+aerobic world what do we have under
+those conditions we have iron and we
+
+ align:start position:0%
+those conditions we have iron and we
+ 
+
+ align:start position:0%
+those conditions we have iron and we
+have copper and again we have oxygen and
+
+ align:start position:0%
+have copper and again we have oxygen and
+ 
+
+ align:start position:0%
+have copper and again we have oxygen and
+so we can generate reactive oxygen
+
+ align:start position:0%
+so we can generate reactive oxygen
+ 
+
+ align:start position:0%
+so we can generate reactive oxygen
+species we've already talked about the
+
+ align:start position:0%
+species we've already talked about the
+ 
+
+ align:start position:0%
+species we've already talked about the
+fact that iron just isn't freely
+
+ align:start position:0%
+fact that iron just isn't freely
+ 
+
+ align:start position:0%
+fact that iron just isn't freely
+floating around inside the cell but if
+
+ align:start position:0%
+floating around inside the cell but if
+ 
+
+ align:start position:0%
+floating around inside the cell but if
+something happens
+
+ align:start position:0%
+something happens
+ 
+
+ align:start position:0%
+something happens
+and you have been balance in iron
+
+ align:start position:0%
+and you have been balance in iron
+ 
+
+ align:start position:0%
+and you have been balance in iron
+homeostasis it leads to imbalance in
+
+ align:start position:0%
+homeostasis it leads to imbalance in
+ 
+
+ align:start position:0%
+homeostasis it leads to imbalance in
+oxygen homeostasis and hopefully you
+
+ align:start position:0%
+oxygen homeostasis and hopefully you
+ 
+
+ align:start position:0%
+oxygen homeostasis and hopefully you
+remember that one of the proteins
+
+ align:start position:0%
+remember that one of the proteins
+ 
+
+ align:start position:0%
+remember that one of the proteins
+regulated by the iron responsive element
+
+ align:start position:0%
+regulated by the iron responsive element
+ 
+
+ align:start position:0%
+regulated by the iron responsive element
+iron responsive binding proteins was up
+
+ align:start position:0%
+iron responsive binding proteins was up
+ 
+
+ align:start position:0%
+iron responsive binding proteins was up
+the oxygen transcription oxygen sensing
+
+ align:start position:0%
+the oxygen transcription oxygen sensing
+ 
+
+ align:start position:0%
+the oxygen transcription oxygen sensing
+trans transcription factor another way
+
+ align:start position:0%
+trans transcription factor another way
+ 
+
+ align:start position:0%
+trans transcription factor another way
+that we get these things are from
+
+ align:start position:0%
+that we get these things are from
+ 
+
+ align:start position:0%
+that we get these things are from
+xenobiotics or environmental pollutants
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+if you smoke which I guess people don't
+
+ align:start position:0%
+if you smoke which I guess people don't
+ 
+
+ align:start position:0%
+if you smoke which I guess people don't
+do but when I was in graduate school
+
+ align:start position:0%
+do but when I was in graduate school
+ 
+
+ align:start position:0%
+do but when I was in graduate school
+everybody smoked and they smoked in the
+
+ align:start position:0%
+everybody smoked and they smoked in the
+ 
+
+ align:start position:0%
+everybody smoked and they smoked in the
+lab anyhow you can say so pollutants can
+
+ align:start position:0%
+lab anyhow you can say so pollutants can
+ 
+
+ align:start position:0%
+lab anyhow you can say so pollutants can
+react generate reactive oxygen species
+
+ align:start position:0%
+react generate reactive oxygen species
+ 
+
+ align:start position:0%
+react generate reactive oxygen species
+okay so so that's how we get them what
+
+ align:start position:0%
+okay so so that's how we get them what
+ 
+
+ align:start position:0%
+okay so so that's how we get them what
+do we do with them okay so there's some
+
+ align:start position:0%
+do we do with them okay so there's some
+ 
+
+ align:start position:0%
+do we do with them okay so there's some
+important things that we can do with
+
+ align:start position:0%
+important things that we can do with
+ 
+
+ align:start position:0%
+important things that we can do with
+them so what are we gonna do with them
+
+ align:start position:0%
+them so what are we gonna do with them
+ 
+
+ align:start position:0%
+them so what are we gonna do with them
+so one of the things we can do is we
+
+ align:start position:0%
+so one of the things we can do is we
+ 
+
+ align:start position:0%
+so one of the things we can do is we
+have white blood cells and neutrophils
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and we kill bacteria or viruses or
+
+ align:start position:0%
+and we kill bacteria or viruses or
+ 
+
+ align:start position:0%
+and we kill bacteria or viruses or
+parasites okay so that's one of the good
+
+ align:start position:0%
+parasites okay so that's one of the good
+ 
+
+ align:start position:0%
+parasites okay so that's one of the good
+things we can do with them a second
+
+ align:start position:0%
+things we can do with them a second
+ 
+
+ align:start position:0%
+things we can do with them a second
+thing we're gonna do with them which is
+
+ align:start position:0%
+thing we're gonna do with them which is
+ 
+
+ align:start position:0%
+thing we're gonna do with them which is
+what we're focusing on is signaling and
+
+ align:start position:0%
+what we're focusing on is signaling and
+ 
+
+ align:start position:0%
+what we're focusing on is signaling and
+we'll see that while we are looking at
+
+ align:start position:0%
+we'll see that while we are looking at
+ 
+
+ align:start position:0%
+we'll see that while we are looking at
+signaling of growth factors or home
+
+ align:start position:0%
+signaling of growth factors or home
+ 
+
+ align:start position:0%
+signaling of growth factors or home
+hormones or cytokines which is good
+
+ align:start position:0%
+hormones or cytokines which is good
+ 
+
+ align:start position:0%
+hormones or cytokines which is good
+signaling we'll see that you can have
+
+ align:start position:0%
+signaling we'll see that you can have
+ 
+
+ align:start position:0%
+signaling we'll see that you can have
+all kinds of signaling okay so it's not
+
+ align:start position:0%
+all kinds of signaling okay so it's not
+ 
+
+ align:start position:0%
+all kinds of signaling okay so it's not
+limited to the one system we're going to
+
+ align:start position:0%
+limited to the one system we're going to
+ 
+
+ align:start position:0%
+limited to the one system we're going to
+be studying so it's very broadly defined
+
+ align:start position:0%
+be studying so it's very broadly defined
+ 
+
+ align:start position:0%
+be studying so it's very broadly defined
+this is a huge area of research right
+
+ align:start position:0%
+this is a huge area of research right
+ 
+
+ align:start position:0%
+this is a huge area of research right
+now people looking at this and the third
+
+ align:start position:0%
+now people looking at this and the third
+ 
+
+ align:start position:0%
+now people looking at this and the third
+thing that happens when this is
+
+ align:start position:0%
+thing that happens when this is
+ 
+
+ align:start position:0%
+thing that happens when this is
+completely out of control is you modify
+
+ align:start position:0%
+completely out of control is you modify
+ 
+
+ align:start position:0%
+completely out of control is you modify
+you damage all the macromolecules and so
+
+ align:start position:0%
+you damage all the macromolecules and so
+ 
+
+ align:start position:0%
+you damage all the macromolecules and so
+molecules inside the cell so you have
+
+ align:start position:0%
+molecules inside the cell so you have
+ 
+
+ align:start position:0%
+molecules inside the cell so you have
+extensive damage you can have extensive
+
+ align:start position:0%
+extensive damage you can have extensive
+ 
+
+ align:start position:0%
+extensive damage you can have extensive
+damage of you know DNA it's not writing
+
+ align:start position:0%
+damage of you know DNA it's not writing
+ 
+
+ align:start position:0%
+damage of you know DNA it's not writing
+very well proteins but it's not a little
+
+ align:start position:0%
+very well proteins but it's not a little
+ 
+
+ align:start position:0%
+very well proteins but it's not a little
+bit to that you have lipids lipids are
+
+ align:start position:0%
+bit to that you have lipids lipids are
+ 
+
+ align:start position:0%
+bit to that you have lipids lipids are
+modified by hydrogen peroxide and so
+
+ align:start position:0%
+modified by hydrogen peroxide and so
+ 
+
+ align:start position:0%
+modified by hydrogen peroxide and so
+that's the big picture that's where
+
+ align:start position:0%
+that's the big picture that's where
+ 
+
+ align:start position:0%
+that's the big picture that's where
+we're going we're focusing on these guys
+
+ align:start position:0%
+we're going we're focusing on these guys
+ 
+
+ align:start position:0%
+we're going we're focusing on these guys
+and we're focusing on good things that
+
+ align:start position:0%
+and we're focusing on good things that
+ 
+
+ align:start position:0%
+and we're focusing on good things that
+we're focusing on bad things and how do
+
+ align:start position:0%
+we're focusing on bad things and how do
+ 
+
+ align:start position:0%
+we're focusing on bad things and how do
+we control all of that okay okay so in
+
+ align:start position:0%
+we control all of that okay okay so in
+ 
+
+ align:start position:0%
+we control all of that okay okay so in
+the next what I want to do is show you
+
+ align:start position:0%
+the next what I want to do is show you
+ 
+
+ align:start position:0%
+the next what I want to do is show you
+why this is why I decided to talk about
+
+ align:start position:0%
+why this is why I decided to talk about
+ 
+
+ align:start position:0%
+why this is why I decided to talk about
+this I've always found this area
+
+ align:start position:0%
+this I've always found this area
+ 
+
+ align:start position:0%
+this I've always found this area
+fascinating um and I must say I've been
+
+ align:start position:0%
+fascinating um and I must say I've been
+ 
+
+ align:start position:0%
+fascinating um and I must say I've been
+going to meetings off and on for decades
+
+ align:start position:0%
+going to meetings off and on for decades
+ 
+
+ align:start position:0%
+going to meetings off and on for decades
+and I said up quit going because I lost
+
+ align:start position:0%
+and I said up quit going because I lost
+ 
+
+ align:start position:0%
+and I said up quit going because I lost
+information every time I went to a
+
+ align:start position:0%
+information every time I went to a
+ 
+
+ align:start position:0%
+information every time I went to a
+meeting because it was so confusing
+
+ align:start position:0%
+meeting because it was so confusing
+ 
+
+ align:start position:0%
+meeting because it was so confusing
+because everybody used different cell
+
+ align:start position:0%
+because everybody used different cell
+ 
+
+ align:start position:0%
+because everybody used different cell
+types and they have different kinds of
+
+ align:start position:0%
+types and they have different kinds of
+ 
+
+ align:start position:0%
+types and they have different kinds of
+assays and they didn't pay attention to
+
+ align:start position:0%
+assays and they didn't pay attention to
+ 
+
+ align:start position:0%
+assays and they didn't pay attention to
+what the assays were really telling them
+
+ align:start position:0%
+what the assays were really telling them
+ 
+
+ align:start position:0%
+what the assays were really telling them
+but now I think we're at the time when
+
+ align:start position:0%
+but now I think we're at the time when
+ 
+
+ align:start position:0%
+but now I think we're at the time when
+people really need the people are doing
+
+ align:start position:0%
+people really need the people are doing
+ 
+
+ align:start position:0%
+people really need the people are doing
+good experiments I think we've turned a
+
+ align:start position:0%
+good experiments I think we've turned a
+ 
+
+ align:start position:0%
+good experiments I think we've turned a
+corner and so one of the things that is
+
+ align:start position:0%
+corner and so one of the things that is
+ 
+
+ align:start position:0%
+corner and so one of the things that is
+been in the front pages of all the
+
+ align:start position:0%
+been in the front pages of all the
+ 
+
+ align:start position:0%
+been in the front pages of all the
+newspapers since 2007 it was we actually
+
+ align:start position:0%
+newspapers since 2007 it was we actually
+ 
+
+ align:start position:0%
+newspapers since 2007 it was we actually
+there was Jim Collins who was at Boston
+
+ align:start position:0%
+there was Jim Collins who was at Boston
+ 
+
+ align:start position:0%
+there was Jim Collins who was at Boston
+University had received a huge amount of
+
+ align:start position:0%
+University had received a huge amount of
+ 
+
+ align:start position:0%
+University had received a huge amount of
+press on a paper he published in 2007
+
+ align:start position:0%
+press on a paper he published in 2007
+ 
+
+ align:start position:0%
+press on a paper he published in 2007
+and since that time has been extremely
+
+ align:start position:0%
+and since that time has been extremely
+ 
+
+ align:start position:0%
+and since that time has been extremely
+controversial and so I think you it
+
+ align:start position:0%
+controversial and so I think you it
+ 
+
+ align:start position:0%
+controversial and so I think you it
+brings up a lot of issues about again
+
+ align:start position:0%
+brings up a lot of issues about again
+ 
+
+ align:start position:0%
+brings up a lot of issues about again
+how you do controlled experiments so his
+
+ align:start position:0%
+how you do controlled experiments so his
+ 
+
+ align:start position:0%
+how you do controlled experiments so his
+observation his conclusions were from
+
+ align:start position:0%
+observation his conclusions were from
+ 
+
+ align:start position:0%
+observation his conclusions were from
+the experiments he published were very
+
+ align:start position:0%
+the experiments he published were very
+ 
+
+ align:start position:0%
+the experiments he published were very
+interesting so we just talked about
+
+ align:start position:0%
+interesting so we just talked about
+ 
+
+ align:start position:0%
+interesting so we just talked about
+antibiotics right what did they target
+
+ align:start position:0%
+antibiotics right what did they target
+ 
+
+ align:start position:0%
+antibiotics right what did they target
+they target cell walls we have
+
+ align:start position:0%
+they target cell walls we have
+ 
+
+ align:start position:0%
+they target cell walls we have
+penicillin vancomycin they can target
+
+ align:start position:0%
+penicillin vancomycin they can target
+ 
+
+ align:start position:0%
+penicillin vancomycin they can target
+the ribosome you saw that in the first
+
+ align:start position:0%
+the ribosome you saw that in the first
+ 
+
+ align:start position:0%
+the ribosome you saw that in the first
+part of the course you have amino
+
+ align:start position:0%
+part of the course you have amino
+ 
+
+ align:start position:0%
+part of the course you have amino
+glycosides they can target DNA
+
+ align:start position:0%
+glycosides they can target DNA
+ 
+
+ align:start position:0%
+glycosides they can target DNA
+replication so those are the three sort
+
+ align:start position:0%
+replication so those are the three sort
+ 
+
+ align:start position:0%
+replication so those are the three sort
+of major targets you have the clonal ins
+
+ align:start position:0%
+of major targets you have the clonal ins
+ 
+
+ align:start position:0%
+of major targets you have the clonal ins
+that do that
+
+ align:start position:0%
+that do that
+ 
+
+ align:start position:0%
+that do that
+his conclusion from the paper is that
+
+ align:start position:0%
+his conclusion from the paper is that
+ 
+
+ align:start position:0%
+his conclusion from the paper is that
+all of these things the mechanism of
+
+ align:start position:0%
+all of these things the mechanism of
+ 
+
+ align:start position:0%
+all of these things the mechanism of
+cell killed
+
+ align:start position:0%
+cell killed
+ 
+
+ align:start position:0%
+cell killed
+it's not involved with the primary
+
+ align:start position:0%
+it's not involved with the primary
+ 
+
+ align:start position:0%
+it's not involved with the primary
+targets at all but it's involved with a
+
+ align:start position:0%
+targets at all but it's involved with a
+ 
+
+ align:start position:0%
+targets at all but it's involved with a
+downstream target that somehow these
+
+ align:start position:0%
+downstream target that somehow these
+ 
+
+ align:start position:0%
+downstream target that somehow these
+guys undo oxygen homeostasis resulting
+
+ align:start position:0%
+guys undo oxygen homeostasis resulting
+ 
+
+ align:start position:0%
+guys undo oxygen homeostasis resulting
+in bad radicals reactive oxygen species
+
+ align:start position:0%
+in bad radicals reactive oxygen species
+ 
+
+ align:start position:0%
+in bad radicals reactive oxygen species
+that end up damaging macromolecules
+
+ align:start position:0%
+that end up damaging macromolecules
+ 
+
+ align:start position:0%
+that end up damaging macromolecules
+damaging the cell and resulting in
+
+ align:start position:0%
+damaging the cell and resulting in
+ 
+
+ align:start position:0%
+damaging the cell and resulting in
+bacterial cell death okay so that's the
+
+ align:start position:0%
+bacterial cell death okay so that's the
+ 
+
+ align:start position:0%
+bacterial cell death okay so that's the
+model this has been quite controversial
+
+ align:start position:0%
+model this has been quite controversial
+ 
+
+ align:start position:0%
+model this has been quite controversial
+I've given you some papers to read the
+
+ align:start position:0%
+I've given you some papers to read the
+ 
+
+ align:start position:0%
+I've given you some papers to read the
+latest paper was just published online
+
+ align:start position:0%
+latest paper was just published online
+ 
+
+ align:start position:0%
+latest paper was just published online
+saying reactive oxygen species play an
+
+ align:start position:0%
+saying reactive oxygen species play an
+ 
+
+ align:start position:0%
+saying reactive oxygen species play an
+important role in bacterial seidel
+
+ align:start position:0%
+important role in bacterial seidel
+ 
+
+ align:start position:0%
+important role in bacterial seidel
+activity of the Quinlan's that targets
+
+ align:start position:0%
+activity of the Quinlan's that targets
+ 
+
+ align:start position:0%
+activity of the Quinlan's that targets
+topoisomerase in DNA replication but
+
+ align:start position:0%
+topoisomerase in DNA replication but
+ 
+
+ align:start position:0%
+topoisomerase in DNA replication but
+we've had two articles published in
+
+ align:start position:0%
+we've had two articles published in
+ 
+
+ align:start position:0%
+we've had two articles published in
+science saying killing by bacterial
+
+ align:start position:0%
+science saying killing by bacterial
+ 
+
+ align:start position:0%
+science saying killing by bacterial
+antibiotics does not depend on reactive
+
+ align:start position:0%
+antibiotics does not depend on reactive
+ 
+
+ align:start position:0%
+antibiotics does not depend on reactive
+oxygen species so we've had quite
+
+ align:start position:0%
+oxygen species so we've had quite
+ 
+
+ align:start position:0%
+oxygen species so we've had quite
+inflammatory responses to this paper
+
+ align:start position:0%
+inflammatory responses to this paper
+ 
+
+ align:start position:0%
+inflammatory responses to this paper
+which I at one stage didn't believe
+
+ align:start position:0%
+which I at one stage didn't believe
+ 
+
+ align:start position:0%
+which I at one stage didn't believe
+anything that he did because I think if
+
+ align:start position:0%
+anything that he did because I think if
+ 
+
+ align:start position:0%
+anything that he did because I think if
+you look at the original a lot of the
+
+ align:start position:0%
+you look at the original a lot of the
+ 
+
+ align:start position:0%
+you look at the original a lot of the
+original experiments they use reagents
+
+ align:start position:0%
+original experiments they use reagents
+ 
+
+ align:start position:0%
+original experiments they use reagents
+that were completely non specific for
+
+ align:start position:0%
+that were completely non specific for
+ 
+
+ align:start position:0%
+that were completely non specific for
+what they thought they were okay but I
+
+ align:start position:0%
+what they thought they were okay but I
+ 
+
+ align:start position:0%
+what they thought they were okay but I
+think I am now I think his observations
+
+ align:start position:0%
+think I am now I think his observations
+ 
+
+ align:start position:0%
+think I am now I think his observations
+in fact were correct but not some of his
+
+ align:start position:0%
+in fact were correct but not some of his
+ 
+
+ align:start position:0%
+in fact were correct but not some of his
+observations were correct but the
+
+ align:start position:0%
+observations were correct but the
+ 
+
+ align:start position:0%
+observations were correct but the
+reasoning behind the observations has
+
+ align:start position:0%
+reasoning behind the observations has
+ 
+
+ align:start position:0%
+reasoning behind the observations has
+changed and I think there is something
+
+ align:start position:0%
+changed and I think there is something
+ 
+
+ align:start position:0%
+changed and I think there is something
+about this you do signaling up here and
+
+ align:start position:0%
+about this you do signaling up here and
+ 
+
+ align:start position:0%
+about this you do signaling up here and
+then where do you see something way down
+
+ align:start position:0%
+then where do you see something way down
+ 
+
+ align:start position:0%
+then where do you see something way down
+here because you trigger off a signaling
+
+ align:start position:0%
+here because you trigger off a signaling
+ 
+
+ align:start position:0%
+here because you trigger off a signaling
+cascade and that's the way the world
+
+ align:start position:0%
+cascade and that's the way the world
+ 
+
+ align:start position:0%
+cascade and that's the way the world
+works inside the cell so a second
+
+ align:start position:0%
+works inside the cell so a second
+ 
+
+ align:start position:0%
+works inside the cell so a second
+example of this which also received a
+
+ align:start position:0%
+example of this which also received a
+ 
+
+ align:start position:0%
+example of this which also received a
+lot of press this guy everybody know who
+
+ align:start position:0%
+lot of press this guy everybody know who
+ 
+
+ align:start position:0%
+lot of press this guy everybody know who
+this guy is you know the DNA guy the
+
+ align:start position:0%
+this guy is you know the DNA guy the
+ 
+
+ align:start position:0%
+this guy is you know the DNA guy the
+famous these Emil chauvinist pig but the
+
+ align:start position:0%
+famous these Emil chauvinist pig but the
+ 
+
+ align:start position:0%
+famous these Emil chauvinist pig but the
+DNA guys anyhow what he you know there's
+
+ align:start position:0%
+DNA guys anyhow what he you know there's
+ 
+
+ align:start position:0%
+DNA guys anyhow what he you know there's
+been a big fight our reactive oxygen
+
+ align:start position:0%
+been a big fight our reactive oxygen
+ 
+
+ align:start position:0%
+been a big fight our reactive oxygen
+species good or bad and fighting cancer
+
+ align:start position:0%
+species good or bad and fighting cancer
+ 
+
+ align:start position:0%
+species good or bad and fighting cancer
+so some people say again it's the
+
+ align:start position:0%
+so some people say again it's the
+ 
+
+ align:start position:0%
+so some people say again it's the
+reactive oxygen species that eventually
+
+ align:start position:0%
+reactive oxygen species that eventually
+ 
+
+ align:start position:0%
+reactive oxygen species that eventually
+kill the cancer cells again you do
+
+ align:start position:0%
+kill the cancer cells again you do
+ 
+
+ align:start position:0%
+kill the cancer cells again you do
+something up here you trigger off a set
+
+ align:start position:0%
+something up here you trigger off a set
+ 
+
+ align:start position:0%
+something up here you trigger off a set
+of events you generate a pathway that
+
+ align:start position:0%
+of events you generate a pathway that
+ 
+
+ align:start position:0%
+of events you generate a pathway that
+generates react about
+
+ align:start position:0%
+generates react about
+ 
+
+ align:start position:0%
+generates react about
+oxygen species that helps kill the tumor
+
+ align:start position:0%
+oxygen species that helps kill the tumor
+ 
+
+ align:start position:0%
+oxygen species that helps kill the tumor
+cells or do they stimulate growth
+
+ align:start position:0%
+cells or do they stimulate growth
+ 
+
+ align:start position:0%
+cells or do they stimulate growth
+reactive oxygen species stimulate growth
+
+ align:start position:0%
+reactive oxygen species stimulate growth
+ 
+
+ align:start position:0%
+reactive oxygen species stimulate growth
+or do they trigger apoptosis okay so
+
+ align:start position:0%
+or do they trigger apoptosis okay so
+ 
+
+ align:start position:0%
+or do they trigger apoptosis okay so
+people are still debating that and
+
+ align:start position:0%
+people are still debating that and
+ 
+
+ align:start position:0%
+people are still debating that and
+there's probably some truth in both of
+
+ align:start position:0%
+there's probably some truth in both of
+ 
+
+ align:start position:0%
+there's probably some truth in both of
+these statements depending on how you
+
+ align:start position:0%
+these statements depending on how you
+ 
+
+ align:start position:0%
+these statements depending on how you
+look at it anyhow that's just to get you
+
+ align:start position:0%
+look at it anyhow that's just to get you
+ 
+
+ align:start position:0%
+look at it anyhow that's just to get you
+thinking about the fact that this is an
+
+ align:start position:0%
+thinking about the fact that this is an
+ 
+
+ align:start position:0%
+thinking about the fact that this is an
+important area um that a lot of people
+
+ align:start position:0%
+important area um that a lot of people
+ 
+
+ align:start position:0%
+important area um that a lot of people
+are actually focusing energy on okay so
+
+ align:start position:0%
+are actually focusing energy on okay so
+ 
+
+ align:start position:0%
+are actually focusing energy on okay so
+what I want to do now is we've you've
+
+ align:start position:0%
+what I want to do now is we've you've
+ 
+
+ align:start position:0%
+what I want to do now is we've you've
+given a big overview what I want to do
+
+ align:start position:0%
+given a big overview what I want to do
+ 
+
+ align:start position:0%
+given a big overview what I want to do
+now is look at what are the species
+
+ align:start position:0%
+now is look at what are the species
+ 
+
+ align:start position:0%
+now is look at what are the species
+identification of the species and the
+
+ align:start position:0%
+identification of the species and the
+ 
+
+ align:start position:0%
+identification of the species and the
+species we're gonna be focusing on again
+
+ align:start position:0%
+species we're gonna be focusing on again
+ 
+
+ align:start position:0%
+species we're gonna be focusing on again
+or superoxide I write this down later
+
+ align:start position:0%
+or superoxide I write this down later
+ 
+
+ align:start position:0%
+or superoxide I write this down later
+hydrogen peroxide h2o2 hypochlorous acid
+
+ align:start position:0%
+hydrogen peroxide h2o2 hypochlorous acid
+ 
+
+ align:start position:0%
+hydrogen peroxide h2o2 hypochlorous acid
+and hydroxide radical okay so this is
+
+ align:start position:0%
+and hydroxide radical okay so this is
+ 
+
+ align:start position:0%
+and hydroxide radical okay so this is
+this is a scheme that was taken from a
+
+ align:start position:0%
+this is a scheme that was taken from a
+ 
+
+ align:start position:0%
+this is a scheme that was taken from a
+Winterbourne articles so it's in all of
+
+ align:start position:0%
+Winterbourne articles so it's in all of
+ 
+
+ align:start position:0%
+Winterbourne articles so it's in all of
+her papers I don't know if it's I don't
+
+ align:start position:0%
+her papers I don't know if it's I don't
+ 
+
+ align:start position:0%
+her papers I don't know if it's I don't
+know if it's the exact same scheme and
+
+ align:start position:0%
+know if it's the exact same scheme and
+ 
+
+ align:start position:0%
+know if it's the exact same scheme and
+the reading assignment but you'll see
+
+ align:start position:0%
+the reading assignment but you'll see
+ 
+
+ align:start position:0%
+the reading assignment but you'll see
+something similar and we're not a told
+
+ align:start position:0%
+something similar and we're not a told
+ 
+
+ align:start position:0%
+something similar and we're not a told
+you we're not going to talk about
+
+ align:start position:0%
+you we're not going to talk about
+ 
+
+ align:start position:0%
+you we're not going to talk about
+reactive oxygen species we're only
+
+ align:start position:0%
+reactive oxygen species we're only
+ 
+
+ align:start position:0%
+reactive oxygen species we're only
+focusing on reactive sorry reactive
+
+ align:start position:0%
+focusing on reactive sorry reactive
+ 
+
+ align:start position:0%
+focusing on reactive sorry reactive
+nitrogen species we're only focusing on
+
+ align:start position:0%
+nitrogen species we're only focusing on
+ 
+
+ align:start position:0%
+nitrogen species we're only focusing on
+reactive oxygen species but this gives
+
+ align:start position:0%
+reactive oxygen species but this gives
+ 
+
+ align:start position:0%
+reactive oxygen species but this gives
+you the big picture with both okay so
+
+ align:start position:0%
+you the big picture with both okay so
+ 
+
+ align:start position:0%
+you the big picture with both okay so
+where are we going to be focusing oxygen
+
+ align:start position:0%
+where are we going to be focusing oxygen
+ 
+
+ align:start position:0%
+where are we going to be focusing oxygen
+I picks up an electron and goes to
+
+ align:start position:0%
+I picks up an electron and goes to
+ 
+
+ align:start position:0%
+I picks up an electron and goes to
+superoxide superoxide and the presence
+
+ align:start position:0%
+superoxide superoxide and the presence
+ 
+
+ align:start position:0%
+superoxide superoxide and the presence
+of another electron and protons goes to
+
+ align:start position:0%
+of another electron and protons goes to
+ 
+
+ align:start position:0%
+of another electron and protons goes to
+hydrogen peroxide so we're going to be
+
+ align:start position:0%
+hydrogen peroxide so we're going to be
+ 
+
+ align:start position:0%
+hydrogen peroxide so we're going to be
+focusing here hydrogen peroxide in the
+
+ align:start position:0%
+focusing here hydrogen peroxide in the
+ 
+
+ align:start position:0%
+focusing here hydrogen peroxide in the
+presence of iron - okay if we want we've
+
+ align:start position:0%
+presence of iron - okay if we want we've
+ 
+
+ align:start position:0%
+presence of iron - okay if we want we've
+somehow screwed up our iron and we're in
+
+ align:start position:0%
+somehow screwed up our iron and we're in
+ 
+
+ align:start position:0%
+somehow screwed up our iron and we're in
+the reduced state generates hydroxide
+
+ align:start position:0%
+the reduced state generates hydroxide
+ 
+
+ align:start position:0%
+the reduced state generates hydroxide
+radical okay hydrogen peroxide with my
+
+ align:start position:0%
+radical okay hydrogen peroxide with my
+ 
+
+ align:start position:0%
+radical okay hydrogen peroxide with my
+low peroxidase in in the neutrophils
+
+ align:start position:0%
+low peroxidase in in the neutrophils
+ 
+
+ align:start position:0%
+low peroxidase in in the neutrophils
+forms hypochlorous acid and so at which
+
+ align:start position:0%
+forms hypochlorous acid and so at which
+ 
+
+ align:start position:0%
+forms hypochlorous acid and so at which
+eventually can chlorinate everything
+
+ align:start position:0%
+eventually can chlorinate everything
+ 
+
+ align:start position:0%
+eventually can chlorinate everything
+they chlorinate amino acids a chlorinate
+
+ align:start position:0%
+they chlorinate amino acids a chlorinate
+ 
+
+ align:start position:0%
+they chlorinate amino acids a chlorinate
+slippage
+
+ align:start position:0%
+slippage
+ 
+
+ align:start position:0%
+slippage
+and can result in extensive damage to
+
+ align:start position:0%
+and can result in extensive damage to
+ 
+
+ align:start position:0%
+and can result in extensive damage to
+whatever hypochlorous accident acid is
+
+ align:start position:0%
+whatever hypochlorous accident acid is
+ 
+
+ align:start position:0%
+whatever hypochlorous accident acid is
+adjacent to so this is what this is
+
+ align:start position:0%
+adjacent to so this is what this is
+ 
+
+ align:start position:0%
+adjacent to so this is what this is
+where we're gonna be focusing okay this
+
+ align:start position:0%
+where we're gonna be focusing okay this
+ 
+
+ align:start position:0%
+where we're gonna be focusing okay this
+part of the scheme those of you who has
+
+ align:start position:0%
+part of the scheme those of you who has
+ 
+
+ align:start position:0%
+part of the scheme those of you who has
+seen reactive nitrogen species can look
+
+ align:start position:0%
+seen reactive nitrogen species can look
+ 
+
+ align:start position:0%
+seen reactive nitrogen species can look
+at how that gets integrated into this
+
+ align:start position:0%
+at how that gets integrated into this
+ 
+
+ align:start position:0%
+at how that gets integrated into this
+big picture okay so I just want to write
+
+ align:start position:0%
+big picture okay so I just want to write
+ 
+
+ align:start position:0%
+big picture okay so I just want to write
+down one of these things I think it's
+
+ align:start position:0%
+down one of these things I think it's
+ 
+
+ align:start position:0%
+down one of these things I think it's
+important to think about ultimately
+
+ align:start position:0%
+important to think about ultimately
+ 
+
+ align:start position:0%
+important to think about ultimately
+we're doing chemistry this whoops I mean
+
+ align:start position:0%
+we're doing chemistry this whoops I mean
+ 
+
+ align:start position:0%
+we're doing chemistry this whoops I mean
+this is like it's terrible it's all of a
+
+ align:start position:0%
+this is like it's terrible it's all of a
+ 
+
+ align:start position:0%
+this is like it's terrible it's all of a
+sudden I look up I it's a good thing I
+
+ align:start position:0%
+sudden I look up I it's a good thing I
+ 
+
+ align:start position:0%
+sudden I look up I it's a good thing I
+looked up because I would have kept
+
+ align:start position:0%
+looked up because I would have kept
+ 
+
+ align:start position:0%
+looked up because I would have kept
+going anyhow sorry the time is over but
+
+ align:start position:0%
+going anyhow sorry the time is over but
+ 
+
+ align:start position:0%
+going anyhow sorry the time is over but
+next time we will come back and we will
+
+ align:start position:0%
+next time we will come back and we will
+ 
+
+ align:start position:0%
+next time we will come back and we will
+talk about what I outlined on the board
+
+ align:start position:0%
+talk about what I outlined on the board
+ 
+
+ align:start position:0%
+talk about what I outlined on the board
+and I didn't even digress today I'm just
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+you
\ No newline at end of file
diff --git a/VieMadwoNNs.txt b/VieMadwoNNs.txt
new file mode 100644
index 0000000000000000000000000000000000000000..c7797a2c0b4b1dcaaf96910f4fde3c2f8059537e
--- /dev/null
+++ b/VieMadwoNNs.txt
@@ -0,0 +1,1395 @@
+align:start position:0%
+ 
+since you are enrolled in this course
+
+ align:start position:0%
+since you are enrolled in this course
+ 
+
+ align:start position:0%
+since you are enrolled in this course
+let's assume that you have decided on or
+
+ align:start position:0%
+let's assume that you have decided on or
+ 
+
+ align:start position:0%
+let's assume that you have decided on or
+perhaps are already engaged in a
+
+ align:start position:0%
+perhaps are already engaged in a
+ 
+
+ align:start position:0%
+perhaps are already engaged in a
+managerial or professional
+
+ align:start position:0%
+managerial or professional
+ 
+
+ align:start position:0%
+managerial or professional
+career and that you are developing or
+
+ align:start position:0%
+career and that you are developing or
+ 
+
+ align:start position:0%
+career and that you are developing or
+have already developed the Knowledge and
+
+ align:start position:0%
+have already developed the Knowledge and
+ 
+
+ align:start position:0%
+have already developed the Knowledge and
+Skills necessary to do the job that's
+
+ align:start position:0%
+Skills necessary to do the job that's
+ 
+
+ align:start position:0%
+Skills necessary to do the job that's
+great but don't stop there experts agree
+
+ align:start position:0%
+great but don't stop there experts agree
+ 
+
+ align:start position:0%
+great but don't stop there experts agree
+that it will take a special set of
+
+ align:start position:0%
+that it will take a special set of
+ 
+
+ align:start position:0%
+that it will take a special set of
+competencies to succeed in tomorrow's
+
+ align:start position:0%
+competencies to succeed in tomorrow's
+ 
+
+ align:start position:0%
+competencies to succeed in tomorrow's
+organizations which will be even more
+
+ align:start position:0%
+organizations which will be even more
+ 
+
+ align:start position:0%
+organizations which will be even more
+globalized digitized collaborative and
+
+ align:start position:0%
+globalized digitized collaborative and
+ 
+
+ align:start position:0%
+globalized digitized collaborative and
+agile than those we see
+
+ align:start position:0%
+agile than those we see
+ 
+
+ align:start position:0%
+agile than those we see
+today many have written on this topic
+
+ align:start position:0%
+today many have written on this topic
+ 
+
+ align:start position:0%
+today many have written on this topic
+one of the best sources we think is a
+
+ align:start position:0%
+one of the best sources we think is a
+ 
+
+ align:start position:0%
+one of the best sources we think is a
+small monograph published by The
+
+ align:start position:0%
+small monograph published by The
+ 
+
+ align:start position:0%
+small monograph published by The
+Institute of the future titled future of
+
+ align:start position:0%
+Institute of the future titled future of
+ 
+
+ align:start position:0%
+Institute of the future titled future of
+work skills 2020
+
+ align:start position:0%
+work skills 2020
+ 
+
+ align:start position:0%
+work skills 2020
+here is a brief synopsis of the 10
+
+ align:start position:0%
+here is a brief synopsis of the 10
+ 
+
+ align:start position:0%
+here is a brief synopsis of the 10
+competencies that the Institute suggests
+
+ align:start position:0%
+competencies that the Institute suggests
+ 
+
+ align:start position:0%
+competencies that the Institute suggests
+will be essential for your career
+
+ align:start position:0%
+will be essential for your career
+ 
+
+ align:start position:0%
+will be essential for your career
+success in the years
+
+ align:start position:0%
+success in the years
+ 
+
+ align:start position:0%
+success in the years
+ahead first relating to
+
+ align:start position:0%
+ahead first relating to
+ 
+
+ align:start position:0%
+ahead first relating to
+globalization The Institute stresses the
+
+ align:start position:0%
+globalization The Institute stresses the
+ 
+
+ align:start position:0%
+globalization The Institute stresses the
+need for cross-cultural competency which
+
+ align:start position:0%
+need for cross-cultural competency which
+ 
+
+ align:start position:0%
+need for cross-cultural competency which
+has a couple of key components one is
+
+ align:start position:0%
+has a couple of key components one is
+ 
+
+ align:start position:0%
+has a couple of key components one is
+the ability to work effectively with
+
+ align:start position:0%
+the ability to work effectively with
+ 
+
+ align:start position:0%
+the ability to work effectively with
+those from other cultures perhaps in
+
+ align:start position:0%
+those from other cultures perhaps in
+ 
+
+ align:start position:0%
+those from other cultures perhaps in
+teams made up of many different
+
+ align:start position:0%
+teams made up of many different
+ 
+
+ align:start position:0%
+teams made up of many different
+nationalities and the other is the
+
+ align:start position:0%
+nationalities and the other is the
+ 
+
+ align:start position:0%
+nationalities and the other is the
+ability to work effectively outside of
+
+ align:start position:0%
+ability to work effectively outside of
+ 
+
+ align:start position:0%
+ability to work effectively outside of
+your native land and while most business
+
+ align:start position:0%
+your native land and while most business
+ 
+
+ align:start position:0%
+your native land and while most business
+probably will continue to be conducted
+
+ align:start position:0%
+probably will continue to be conducted
+ 
+
+ align:start position:0%
+probably will continue to be conducted
+in English it certainly wouldn't hurt to
+
+ align:start position:0%
+in English it certainly wouldn't hurt to
+ 
+
+ align:start position:0%
+in English it certainly wouldn't hurt to
+have a familiarity with other languages
+
+ align:start position:0%
+have a familiarity with other languages
+ 
+
+ align:start position:0%
+have a familiarity with other languages
+as
+
+ align:start position:0%
+as
+ 
+
+ align:start position:0%
+as
+well turning to the circle label
+
+ align:start position:0%
+well turning to the circle label
+ 
+
+ align:start position:0%
+well turning to the circle label
+digitization we see that there are four
+
+ align:start position:0%
+digitization we see that there are four
+ 
+
+ align:start position:0%
+digitization we see that there are four
+key competencies involved one is sense
+
+ align:start position:0%
+key competencies involved one is sense
+ 
+
+ align:start position:0%
+key competencies involved one is sense
+making
+
+ align:start position:0%
+making
+ 
+
+ align:start position:0%
+making
+the future will be all about Mass data
+
+ align:start position:0%
+the future will be all about Mass data
+ 
+
+ align:start position:0%
+the future will be all about Mass data
+we will be even more inundated than we
+
+ align:start position:0%
+we will be even more inundated than we
+ 
+
+ align:start position:0%
+we will be even more inundated than we
+are now so it will be necessary to have
+
+ align:start position:0%
+are now so it will be necessary to have
+ 
+
+ align:start position:0%
+are now so it will be necessary to have
+the capacity to work through tons of
+
+ align:start position:0%
+the capacity to work through tons of
+ 
+
+ align:start position:0%
+the capacity to work through tons of
+information and see the big picture
+
+ align:start position:0%
+information and see the big picture
+ 
+
+ align:start position:0%
+information and see the big picture
+we'll have to be critical thinkers but
+
+ align:start position:0%
+we'll have to be critical thinkers but
+ 
+
+ align:start position:0%
+we'll have to be critical thinkers but
+we also have to keep in mind that
+
+ align:start position:0%
+we also have to keep in mind that
+ 
+
+ align:start position:0%
+we also have to keep in mind that
+technology isn't good for everything so
+
+ align:start position:0%
+technology isn't good for everything so
+ 
+
+ align:start position:0%
+technology isn't good for everything so
+we need to develop the capacity to
+
+ align:start position:0%
+we need to develop the capacity to
+ 
+
+ align:start position:0%
+we need to develop the capacity to
+decide when to rely on computers for
+
+ align:start position:0%
+decide when to rely on computers for
+ 
+
+ align:start position:0%
+decide when to rely on computers for
+assistance and answers and just as
+
+ align:start position:0%
+assistance and answers and just as
+ 
+
+ align:start position:0%
+assistance and answers and just as
+important when not
+
+ align:start position:0%
+important when not
+ 
+
+ align:start position:0%
+important when not
+to a second competency in this area is
+
+ align:start position:0%
+to a second competency in this area is
+ 
+
+ align:start position:0%
+to a second competency in this area is
+computational thinking this includes
+
+ align:start position:0%
+computational thinking this includes
+ 
+
+ align:start position:0%
+computational thinking this includes
+developing a basic understanding of
+
+ align:start position:0%
+developing a basic understanding of
+ 
+
+ align:start position:0%
+developing a basic understanding of
+computer programming and simulation
+
+ align:start position:0%
+computer programming and simulation
+ 
+
+ align:start position:0%
+computer programming and simulation
+modeling it doesn't mean that we all
+
+ align:start position:0%
+modeling it doesn't mean that we all
+ 
+
+ align:start position:0%
+modeling it doesn't mean that we all
+have to become computer geeks in the era
+
+ align:start position:0%
+have to become computer geeks in the era
+ 
+
+ align:start position:0%
+have to become computer geeks in the era
+of big data we can rely on specially
+
+ align:start position:0%
+of big data we can rely on specially
+ 
+
+ align:start position:0%
+of big data we can rely on specially
+trained data scientists to do the heavy
+
+ align:start position:0%
+trained data scientists to do the heavy
+ 
+
+ align:start position:0%
+trained data scientists to do the heavy
+lifting but the rest of us will need to
+
+ align:start position:0%
+lifting but the rest of us will need to
+ 
+
+ align:start position:0%
+lifting but the rest of us will need to
+know enough about what the experts are
+
+ align:start position:0%
+know enough about what the experts are
+ 
+
+ align:start position:0%
+know enough about what the experts are
+doing to be actively involved in the
+
+ align:start position:0%
+doing to be actively involved in the
+ 
+
+ align:start position:0%
+doing to be actively involved in the
+process in two ways one is on the front
+
+ align:start position:0%
+process in two ways one is on the front
+ 
+
+ align:start position:0%
+process in two ways one is on the front
+end to frame questions and problems in
+
+ align:start position:0%
+end to frame questions and problems in
+ 
+
+ align:start position:0%
+end to frame questions and problems in
+ways that the data scientist can analyze
+
+ align:start position:0%
+ways that the data scientist can analyze
+ 
+
+ align:start position:0%
+ways that the data scientist can analyze
+or model and two on the back end to be
+
+ align:start position:0%
+or model and two on the back end to be
+ 
+
+ align:start position:0%
+or model and two on the back end to be
+the ones who interpret the results and
+
+ align:start position:0%
+the ones who interpret the results and
+ 
+
+ align:start position:0%
+the ones who interpret the results and
+come up with value added answers and
+
+ align:start position:0%
+come up with value added answers and
+ 
+
+ align:start position:0%
+come up with value added answers and
+solutions third in this context there is
+
+ align:start position:0%
+solutions third in this context there is
+ 
+
+ align:start position:0%
+solutions third in this context there is
+the issue of new media literacy here the
+
+ align:start position:0%
+the issue of new media literacy here the
+ 
+
+ align:start position:0%
+the issue of new media literacy here the
+reference is to becoming expert in the
+
+ align:start position:0%
+reference is to becoming expert in the
+ 
+
+ align:start position:0%
+reference is to becoming expert in the
+use of social media tools internets
+
+ align:start position:0%
+use of social media tools internets
+ 
+
+ align:start position:0%
+use of social media tools internets
+blogs podcasts videos and so forth in
+
+ align:start position:0%
+blogs podcasts videos and so forth in
+ 
+
+ align:start position:0%
+blogs podcasts videos and so forth in
+the future many folks will be working
+
+ align:start position:0%
+the future many folks will be working
+ 
+
+ align:start position:0%
+the future many folks will be working
+remotely and will be called upon to
+
+ align:start position:0%
+remotely and will be called upon to
+ 
+
+ align:start position:0%
+remotely and will be called upon to
+create and share content through these
+
+ align:start position:0%
+create and share content through these
+ 
+
+ align:start position:0%
+create and share content through these
+Technologies and to do so in ways that
+
+ align:start position:0%
+Technologies and to do so in ways that
+ 
+
+ align:start position:0%
+Technologies and to do so in ways that
+not only help solve complex problems but
+
+ align:start position:0%
+not only help solve complex problems but
+ 
+
+ align:start position:0%
+not only help solve complex problems but
+also engage and persuade our colleagues
+
+ align:start position:0%
+also engage and persuade our colleagues
+ 
+
+ align:start position:0%
+also engage and persuade our colleagues
+and other important people such as
+
+ align:start position:0%
+and other important people such as
+ 
+
+ align:start position:0%
+and other important people such as
+customers and
+
+ align:start position:0%
+customers and
+ 
+
+ align:start position:0%
+customers and
+clients finally in this area is
+
+ align:start position:0%
+clients finally in this area is
+ 
+
+ align:start position:0%
+clients finally in this area is
+cognitive load Management in tomorrow's
+
+ align:start position:0%
+cognitive load Management in tomorrow's
+ 
+
+ align:start position:0%
+cognitive load Management in tomorrow's
+World it will be very easy to get
+
+ align:start position:0%
+World it will be very easy to get
+ 
+
+ align:start position:0%
+World it will be very easy to get
+overwhelmed by the mass of information
+
+ align:start position:0%
+overwhelmed by the mass of information
+ 
+
+ align:start position:0%
+overwhelmed by the mass of information
+that's bound to come our way we need to
+
+ align:start position:0%
+that's bound to come our way we need to
+ 
+
+ align:start position:0%
+that's bound to come our way we need to
+learn how to avoid this how to evaluate
+
+ align:start position:0%
+learn how to avoid this how to evaluate
+ 
+
+ align:start position:0%
+learn how to avoid this how to evaluate
+Rank and tag content so that we keep our
+
+ align:start position:0%
+Rank and tag content so that we keep our
+ 
+
+ align:start position:0%
+Rank and tag content so that we keep our
+eyes on what's really important and let
+
+ align:start position:0%
+eyes on what's really important and let
+ 
+
+ align:start position:0%
+eyes on what's really important and let
+the rest
+
+ align:start position:0%
+the rest
+ 
+
+ align:start position:0%
+the rest
+go some somewhat ironically computer
+
+ align:start position:0%
+go some somewhat ironically computer
+ 
+
+ align:start position:0%
+go some somewhat ironically computer
+programs are already available to help
+
+ align:start position:0%
+programs are already available to help
+ 
+
+ align:start position:0%
+programs are already available to help
+with this they have the ability to sense
+
+ align:start position:0%
+with this they have the ability to sense
+ 
+
+ align:start position:0%
+with this they have the ability to sense
+when we are becoming overloaded or tired
+
+ align:start position:0%
+when we are becoming overloaded or tired
+ 
+
+ align:start position:0%
+when we are becoming overloaded or tired
+and then to automatically intervene to
+
+ align:start position:0%
+and then to automatically intervene to
+ 
+
+ align:start position:0%
+and then to automatically intervene to
+slow down or simplify the flow of
+
+ align:start position:0%
+slow down or simplify the flow of
+ 
+
+ align:start position:0%
+slow down or simplify the flow of
+information we're
+
+ align:start position:0%
+information we're
+ 
+
+ align:start position:0%
+information we're
+getting third let's turn to the issue of
+
+ align:start position:0%
+getting third let's turn to the issue of
+ 
+
+ align:start position:0%
+getting third let's turn to the issue of
+collaboration one essential competency
+
+ align:start position:0%
+collaboration one essential competency
+ 
+
+ align:start position:0%
+collaboration one essential competency
+here is social
+
+ align:start position:0%
+here is social
+ 
+
+ align:start position:0%
+here is social
+intelligence this refers to the ability
+
+ align:start position:0%
+intelligence this refers to the ability
+ 
+
+ align:start position:0%
+intelligence this refers to the ability
+to connect with with others in an
+
+ align:start position:0%
+to connect with with others in an
+ 
+
+ align:start position:0%
+to connect with with others in an
+emotional and deeply personal way to
+
+ align:start position:0%
+emotional and deeply personal way to
+ 
+
+ align:start position:0%
+emotional and deeply personal way to
+quickly assess the feelings of others
+
+ align:start position:0%
+quickly assess the feelings of others
+ 
+
+ align:start position:0%
+quickly assess the feelings of others
+and then adapt our words tone and
+
+ align:start position:0%
+and then adapt our words tone and
+ 
+
+ align:start position:0%
+and then adapt our words tone and
+gestures accordingly everyone agrees
+
+ align:start position:0%
+gestures accordingly everyone agrees
+ 
+
+ align:start position:0%
+gestures accordingly everyone agrees
+that this is a uniquely human competency
+
+ align:start position:0%
+that this is a uniquely human competency
+ 
+
+ align:start position:0%
+that this is a uniquely human competency
+that so far at least gives us a leg up
+
+ align:start position:0%
+that so far at least gives us a leg up
+ 
+
+ align:start position:0%
+that so far at least gives us a leg up
+on
+
+ align:start position:0%
+on
+ 
+
+ align:start position:0%
+on
+robots further The Institute talks about
+
+ align:start position:0%
+robots further The Institute talks about
+ 
+
+ align:start position:0%
+robots further The Institute talks about
+virtual collaboration meaning the
+
+ align:start position:0%
+virtual collaboration meaning the
+ 
+
+ align:start position:0%
+virtual collaboration meaning the
+ability to work effectively with and
+
+ align:start position:0%
+ability to work effectively with and
+ 
+
+ align:start position:0%
+ability to work effectively with and
+eventually perhap perhaps lead teammates
+
+ align:start position:0%
+eventually perhap perhaps lead teammates
+ 
+
+ align:start position:0%
+eventually perhap perhaps lead teammates
+we may never meet or even see in person
+
+ align:start position:0%
+we may never meet or even see in person
+ 
+
+ align:start position:0%
+we may never meet or even see in person
+this involves becoming really good at
+
+ align:start position:0%
+this involves becoming really good at
+ 
+
+ align:start position:0%
+this involves becoming really good at
+turning in-house networks and New Media
+
+ align:start position:0%
+turning in-house networks and New Media
+ 
+
+ align:start position:0%
+turning in-house networks and New Media
+into what some call social water coolers
+
+ align:start position:0%
+into what some call social water coolers
+ 
+
+ align:start position:0%
+into what some call social water coolers
+important tools helping to enhance a
+
+ align:start position:0%
+important tools helping to enhance a
+ 
+
+ align:start position:0%
+important tools helping to enhance a
+sense of
+
+ align:start position:0%
+sense of
+ 
+
+ align:start position:0%
+sense of
+camaraderie and social presence among
+
+ align:start position:0%
+camaraderie and social presence among
+ 
+
+ align:start position:0%
+camaraderie and social presence among
+colleagues who are all over the
+
+ align:start position:0%
+colleagues who are all over the
+ 
+
+ align:start position:0%
+colleagues who are all over the
+map online Gamers already have a leg up
+
+ align:start position:0%
+map online Gamers already have a leg up
+ 
+
+ align:start position:0%
+map online Gamers already have a leg up
+on developing this competency
+
+ align:start position:0%
+on developing this competency
+ 
+
+ align:start position:0%
+on developing this competency
+since this is in large part what they
+
+ align:start position:0%
+since this is in large part what they
+ 
+
+ align:start position:0%
+since this is in large part what they
+are learning to
+
+ align:start position:0%
+are learning to
+ 
+
+ align:start position:0%
+are learning to
+do and finally let's consider agility
+
+ align:start position:0%
+do and finally let's consider agility
+ 
+
+ align:start position:0%
+do and finally let's consider agility
+which really is the capacity to be
+
+ align:start position:0%
+which really is the capacity to be
+ 
+
+ align:start position:0%
+which really is the capacity to be
+comfortable with change three
+
+ align:start position:0%
+comfortable with change three
+ 
+
+ align:start position:0%
+comfortable with change three
+competencies are stressed here one is
+
+ align:start position:0%
+competencies are stressed here one is
+ 
+
+ align:start position:0%
+competencies are stressed here one is
+novel and adaptive thinking in a world
+
+ align:start position:0%
+novel and adaptive thinking in a world
+ 
+
+ align:start position:0%
+novel and adaptive thinking in a world
+of Rapid change it is essential that we
+
+ align:start position:0%
+of Rapid change it is essential that we
+ 
+
+ align:start position:0%
+of Rapid change it is essential that we
+never let the tried and true get in the
+
+ align:start position:0%
+never let the tried and true get in the
+ 
+
+ align:start position:0%
+never let the tried and true get in the
+way of being open to new ways of doing
+
+ align:start position:0%
+way of being open to new ways of doing
+ 
+
+ align:start position:0%
+way of being open to new ways of doing
+things in the future all of us will be
+
+ align:start position:0%
+things in the future all of us will be
+ 
+
+ align:start position:0%
+things in the future all of us will be
+expected to keep our eyes on
+
+ align:start position:0%
+expected to keep our eyes on
+ 
+
+ align:start position:0%
+expected to keep our eyes on
+developments that are going on in the
+
+ align:start position:0%
+developments that are going on in the
+ 
+
+ align:start position:0%
+developments that are going on in the
+world so that we can anticipate upcoming
+
+ align:start position:0%
+world so that we can anticipate upcoming
+ 
+
+ align:start position:0%
+world so that we can anticipate upcoming
+challenges and most important be on the
+
+ align:start position:0%
+challenges and most important be on the
+ 
+
+ align:start position:0%
+challenges and most important be on the
+Leading Edge of developing unique and
+
+ align:start position:0%
+Leading Edge of developing unique and
+ 
+
+ align:start position:0%
+Leading Edge of developing unique and
+creative ideas and solutions to deal
+
+ align:start position:0%
+creative ideas and solutions to deal
+ 
+
+ align:start position:0%
+creative ideas and solutions to deal
+with these challenges in real
+
+ align:start position:0%
+with these challenges in real
+ 
+
+ align:start position:0%
+with these challenges in real
+time second The Institute talks about
+
+ align:start position:0%
+time second The Institute talks about
+ 
+
+ align:start position:0%
+time second The Institute talks about
+design mindset this is closely related
+
+ align:start position:0%
+design mindset this is closely related
+ 
+
+ align:start position:0%
+design mindset this is closely related
+to novel and adaptive thinking
+
+ align:start position:0%
+to novel and adaptive thinking
+ 
+
+ align:start position:0%
+to novel and adaptive thinking
+it refers to being super familiar with
+
+ align:start position:0%
+it refers to being super familiar with
+ 
+
+ align:start position:0%
+it refers to being super familiar with
+our work situation so that we can see
+
+ align:start position:0%
+our work situation so that we can see
+ 
+
+ align:start position:0%
+our work situation so that we can see
+when changes need to be made but even
+
+ align:start position:0%
+when changes need to be made but even
+ 
+
+ align:start position:0%
+when changes need to be made but even
+more important it refers to having the
+
+ align:start position:0%
+more important it refers to having the
+ 
+
+ align:start position:0%
+more important it refers to having the
+ability to make useful recommendations
+
+ align:start position:0%
+ability to make useful recommendations
+ 
+
+ align:start position:0%
+ability to make useful recommendations
+for redesigning the work environment as
+
+ align:start position:0%
+for redesigning the work environment as
+ 
+
+ align:start position:0%
+for redesigning the work environment as
+well as the processes and procedures
+
+ align:start position:0%
+well as the processes and procedures
+ 
+
+ align:start position:0%
+well as the processes and procedures
+being used to get the work
+
+ align:start position:0%
+being used to get the work
+ 
+
+ align:start position:0%
+being used to get the work
+done and then there is what the
+
+ align:start position:0%
+done and then there is what the
+ 
+
+ align:start position:0%
+done and then there is what the
+Institute calls transdisciplinarity
+
+ align:start position:0%
+Institute calls transdisciplinarity
+ 
+
+ align:start position:0%
+Institute calls transdisciplinarity
+which is a big word for a simple idea in
+
+ align:start position:0%
+which is a big word for a simple idea in
+ 
+
+ align:start position:0%
+which is a big word for a simple idea in
+the future the ideal worker will be
+
+ align:start position:0%
+the future the ideal worker will be
+ 
+
+ align:start position:0%
+the future the ideal worker will be
+t-shaped that is deeply expert in one or
+
+ align:start position:0%
+t-shaped that is deeply expert in one or
+ 
+
+ align:start position:0%
+t-shaped that is deeply expert in one or
+more disciplines which is the vertical
+
+ align:start position:0%
+more disciplines which is the vertical
+ 
+
+ align:start position:0%
+more disciplines which is the vertical
+part of the te but also knowledgeable
+
+ align:start position:0%
+part of the te but also knowledgeable
+ 
+
+ align:start position:0%
+part of the te but also knowledgeable
+about and comfortable with many other
+
+ align:start position:0%
+about and comfortable with many other
+ 
+
+ align:start position:0%
+about and comfortable with many other
+disciplines the horizontal part of the
+
+ align:start position:0%
+disciplines the horizontal part of the
+ 
+
+ align:start position:0%
+disciplines the horizontal part of the
+tea in other words once you're world
+
+ align:start position:0%
+tea in other words once you're world
+ 
+
+ align:start position:0%
+tea in other words once you're world
+class at one thing make sure you keep
+
+ align:start position:0%
+class at one thing make sure you keep
+ 
+
+ align:start position:0%
+class at one thing make sure you keep
+right on learning about a lot of other
+
+ align:start position:0%
+right on learning about a lot of other
+ 
+
+ align:start position:0%
+right on learning about a lot of other
+things success in the future will depend
+
+ align:start position:0%
+things success in the future will depend
+ 
+
+ align:start position:0%
+things success in the future will depend
+on our willingness and ability to keep
+
+ align:start position:0%
+on our willingness and ability to keep
+ 
+
+ align:start position:0%
+on our willingness and ability to keep
+growing and
+
+ align:start position:0%
+growing and
+ 
+
+ align:start position:0%
+growing and
+developing to become more Global in our
+
+ align:start position:0%
+developing to become more Global in our
+ 
+
+ align:start position:0%
+developing to become more Global in our
+thinking more comfortable with the
+
+ align:start position:0%
+thinking more comfortable with the
+ 
+
+ align:start position:0%
+thinking more comfortable with the
+digitization of everything ever better
+
+ align:start position:0%
+digitization of everything ever better
+ 
+
+ align:start position:0%
+digitization of everything ever better
+at collaborating with colleagues and
+
+ align:start position:0%
+at collaborating with colleagues and
+ 
+
+ align:start position:0%
+at collaborating with colleagues and
+others and above all staying deeply
+
+ align:start position:0%
+others and above all staying deeply
+ 
+
+ align:start position:0%
+others and above all staying deeply
+committed to being adaptive lifelong
+
+ align:start position:0%
+committed to being adaptive lifelong
+ 
+
+ align:start position:0%
+committed to being adaptive lifelong
+learners
\ No newline at end of file
diff --git a/WMDXIL3IvBg.txt b/WMDXIL3IvBg.txt
new file mode 100644
index 0000000000000000000000000000000000000000..ccc95461407455582cbb7026ca58c4b71f6d2432
--- /dev/null
+++ b/WMDXIL3IvBg.txt
@@ -0,0 +1,12115 @@
+align:start position:0%
+ 
+the following content is provided under
+
+ align:start position:0%
+the following content is provided under
+ 
+
+ align:start position:0%
+the following content is provided under
+a Creative Commons license your support
+
+ align:start position:0%
+a Creative Commons license your support
+ 
+
+ align:start position:0%
+a Creative Commons license your support
+will help MIT open courseware continue
+
+ align:start position:0%
+will help MIT open courseware continue
+ 
+
+ align:start position:0%
+will help MIT open courseware continue
+to offer highquality educational
+
+ align:start position:0%
+to offer highquality educational
+ 
+
+ align:start position:0%
+to offer highquality educational
+resources for free to make a donation or
+
+ align:start position:0%
+resources for free to make a donation or
+ 
+
+ align:start position:0%
+resources for free to make a donation or
+view additional materials from hundreds
+
+ align:start position:0%
+view additional materials from hundreds
+ 
+
+ align:start position:0%
+view additional materials from hundreds
+of MIT courses visit MIT opencourseware
+
+ align:start position:0%
+of MIT courses visit MIT opencourseware
+ 
+
+ align:start position:0%
+of MIT courses visit MIT opencourseware
+at
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+ocw.mit.edu I hope you're getting
+
+ align:start position:0%
+ocw.mit.edu I hope you're getting
+ 
+
+ align:start position:0%
+ocw.mit.edu I hope you're getting
+excited about the
+
+ align:start position:0%
+excited about the
+ 
+
+ align:start position:0%
+excited about the
+trip um so there are a few things that I
+
+ align:start position:0%
+trip um so there are a few things that I
+ 
+
+ align:start position:0%
+trip um so there are a few things that I
+managed to skip over last time one is
+
+ align:start position:0%
+managed to skip over last time one is
+ 
+
+ align:start position:0%
+managed to skip over last time one is
+solar cookers somehow got dropped from
+
+ align:start position:0%
+solar cookers somehow got dropped from
+ 
+
+ align:start position:0%
+solar cookers somehow got dropped from
+my presentation and they're kind of key
+
+ align:start position:0%
+my presentation and they're kind of key
+ 
+
+ align:start position:0%
+my presentation and they're kind of key
+part of cooking that I wanted to talk
+
+ align:start position:0%
+part of cooking that I wanted to talk
+ 
+
+ align:start position:0%
+part of cooking that I wanted to talk
+about um at least most of you guys have
+
+ align:start position:0%
+about um at least most of you guys have
+ 
+
+ align:start position:0%
+about um at least most of you guys have
+investigated a little bit on your own
+
+ align:start position:0%
+investigated a little bit on your own
+ 
+
+ align:start position:0%
+investigated a little bit on your own
+and then we also just talking about the
+
+ align:start position:0%
+and then we also just talking about the
+ 
+
+ align:start position:0%
+and then we also just talking about the
+energy to boil water so in terms of
+
+ align:start position:0%
+energy to boil water so in terms of
+ 
+
+ align:start position:0%
+energy to boil water so in terms of
+solar cookers there as uh groupo Phoenix
+
+ align:start position:0%
+solar cookers there as uh groupo Phoenix
+ 
+
+ align:start position:0%
+solar cookers there as uh groupo Phoenix
+mentioned there are three types so
+
+ align:start position:0%
+mentioned there are three types so
+ 
+
+ align:start position:0%
+mentioned there are three types so
+there's
+
+ align:start position:0%
+there's
+ 
+
+ align:start position:0%
+there's
+the concentrator par parabolic method
+
+ align:start position:0%
+the concentrator par parabolic method
+ 
+
+ align:start position:0%
+the concentrator par parabolic method
+where you have some sort of parabolic
+
+ align:start position:0%
+where you have some sort of parabolic
+ 
+
+ align:start position:0%
+where you have some sort of parabolic
+collector that's aiming the heat onto
+
+ align:start position:0%
+collector that's aiming the heat onto
+ 
+
+ align:start position:0%
+collector that's aiming the heat onto
+your cooking cook stove which is then
+
+ align:start position:0%
+your cooking cook stove which is then
+ 
+
+ align:start position:0%
+your cooking cook stove which is then
+heating up the material you have the box
+
+ align:start position:0%
+heating up the material you have the box
+ 
+
+ align:start position:0%
+heating up the material you have the box
+method which is using a greenhouse
+
+ align:start position:0%
+method which is using a greenhouse
+ 
+
+ align:start position:0%
+method which is using a greenhouse
+method um where you have a reflective
+
+ align:start position:0%
+method um where you have a reflective
+ 
+
+ align:start position:0%
+method um where you have a reflective
+device uh reflecting into the greenhouse
+
+ align:start position:0%
+device uh reflecting into the greenhouse
+ 
+
+ align:start position:0%
+device uh reflecting into the greenhouse
+and that's pretty much the design that
+
+ align:start position:0%
+and that's pretty much the design that
+ 
+
+ align:start position:0%
+and that's pretty much the design that
+um group of Phoenix uses I wouldn't call
+
+ align:start position:0%
+um group of Phoenix uses I wouldn't call
+ 
+
+ align:start position:0%
+um group of Phoenix uses I wouldn't call
+it a hybrid because the hybrid has both
+
+ align:start position:0%
+it a hybrid because the hybrid has both
+ 
+
+ align:start position:0%
+it a hybrid because the hybrid has both
+that Greenhouse but also uses some
+
+ align:start position:0%
+that Greenhouse but also uses some
+ 
+
+ align:start position:0%
+that Greenhouse but also uses some
+parabolic features to collect the energy
+
+ align:start position:0%
+parabolic features to collect the energy
+ 
+
+ align:start position:0%
+parabolic features to collect the energy
+um and you can see that the cost you can
+
+ align:start position:0%
+um and you can see that the cost you can
+ 
+
+ align:start position:0%
+um and you can see that the cost you can
+imagine the cost of these three devices
+
+ align:start position:0%
+imagine the cost of these three devices
+ 
+
+ align:start position:0%
+imagine the cost of these three devices
+shown varies and so you can get very
+
+ align:start position:0%
+shown varies and so you can get very
+ 
+
+ align:start position:0%
+shown varies and so you can get very
+inexpensive versions of all of these but
+
+ align:start position:0%
+inexpensive versions of all of these but
+ 
+
+ align:start position:0%
+inexpensive versions of all of these but
+the parabolic is definitely the hardest
+
+ align:start position:0%
+the parabolic is definitely the hardest
+ 
+
+ align:start position:0%
+the parabolic is definitely the hardest
+to get super cheap um and very expensive
+
+ align:start position:0%
+to get super cheap um and very expensive
+ 
+
+ align:start position:0%
+to get super cheap um and very expensive
+versions so I wanted to start by just um
+
+ align:start position:0%
+versions so I wanted to start by just um
+ 
+
+ align:start position:0%
+versions so I wanted to start by just um
+talking about what you think might be
+
+ align:start position:0%
+talking about what you think might be
+ 
+
+ align:start position:0%
+talking about what you think might be
+some pros and cons of solar cookers
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+I a question yeah is the refle material
+
+ align:start position:0%
+I a question yeah is the refle material
+ 
+
+ align:start position:0%
+I a question yeah is the refle material
+that they use what is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+it just she metal
+
+ align:start position:0%
+it just she metal
+ 
+
+ align:start position:0%
+it just she metal
+or like aluminum foil so sheet metal is
+
+ align:start position:0%
+or like aluminum foil so sheet metal is
+ 
+
+ align:start position:0%
+or like aluminum foil so sheet metal is
+pretty
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh yeah yeah it's hard to get a really
+
+ align:start position:0%
+uh yeah yeah it's hard to get a really
+ 
+
+ align:start position:0%
+uh yeah yeah it's hard to get a really
+good reflection off of it so I think
+
+ align:start position:0%
+good reflection off of it so I think
+ 
+
+ align:start position:0%
+good reflection off of it so I think
+I've seen some that are like basically
+
+ align:start position:0%
+I've seen some that are like basically
+ 
+
+ align:start position:0%
+I've seen some that are like basically
+mirrors so um is I think what that is um
+
+ align:start position:0%
+mirrors so um is I think what that is um
+ 
+
+ align:start position:0%
+mirrors so um is I think what that is um
+this
+
+ align:start position:0%
+this
+ 
+
+ align:start position:0%
+this
+is um like a plastic that's super shiny
+
+ align:start position:0%
+is um like a plastic that's super shiny
+ 
+
+ align:start position:0%
+is um like a plastic that's super shiny
+that's just laminated onto the cardboard
+
+ align:start position:0%
+that's just laminated onto the cardboard
+ 
+
+ align:start position:0%
+that's just laminated onto the cardboard
+so a whole range from expensive to
+
+ align:start position:0%
+so a whole range from expensive to
+ 
+
+ align:start position:0%
+so a whole range from expensive to
+non I have a question um so the one that
+
+ align:start position:0%
+non I have a question um so the one that
+ 
+
+ align:start position:0%
+non I have a question um so the one that
+uh is the concentrator where does what
+
+ align:start position:0%
+uh is the concentrator where does what
+ 
+
+ align:start position:0%
+uh is the concentrator where does what
+is it concentrating towards the box or
+
+ align:start position:0%
+is it concentrating towards the box or
+ 
+
+ align:start position:0%
+is it concentrating towards the box or
+towards no so this is an open pan so
+
+ align:start position:0%
+towards no so this is an open pan so
+ 
+
+ align:start position:0%
+towards no so this is an open pan so
+this just concentrating it on the
+
+ align:start position:0%
+this just concentrating it on the
+ 
+
+ align:start position:0%
+this just concentrating it on the
+pan so that these this is the difference
+
+ align:start position:0%
+pan so that these this is the difference
+ 
+
+ align:start position:0%
+pan so that these this is the difference
+the concentrator is is just you know
+
+ align:start position:0%
+the concentrator is is just you know
+ 
+
+ align:start position:0%
+the concentrator is is just you know
+shining a strong Ray of heat onto
+
+ align:start position:0%
+shining a strong Ray of heat onto
+ 
+
+ align:start position:0%
+shining a strong Ray of heat onto
+something mostly just not Electric solar
+
+ align:start position:0%
+something mostly just not Electric solar
+ 
+
+ align:start position:0%
+something mostly just not Electric solar
+cookers are very rarely electrical I've
+
+ align:start position:0%
+cookers are very rarely electrical I've
+ 
+
+ align:start position:0%
+cookers are very rarely electrical I've
+never seen one of we talking about was
+
+ align:start position:0%
+never seen one of we talking about was
+ 
+
+ align:start position:0%
+never seen one of we talking about was
+like having a bigger panel maybe each
+
+ align:start position:0%
+like having a bigger panel maybe each
+ 
+
+ align:start position:0%
+like having a bigger panel maybe each
+house Community where you can charge the
+
+ align:start position:0%
+house Community where you can charge the
+ 
+
+ align:start position:0%
+house Community where you can charge the
+cell phone and you can also um cook but
+
+ align:start position:0%
+cell phone and you can also um cook but
+ 
+
+ align:start position:0%
+cell phone and you can also um cook but
+then that would have that like we were
+
+ align:start position:0%
+then that would have that like we were
+ 
+
+ align:start position:0%
+then that would have that like we were
+thinking about like the panel outside on
+
+ align:start position:0%
+thinking about like the panel outside on
+ 
+
+ align:start position:0%
+thinking about like the panel outside on
+the roof
+
+ align:start position:0%
+the roof
+ 
+
+ align:start position:0%
+the roof
+collecting collecting the Rays
+
+ align:start position:0%
+collecting collecting the Rays
+ 
+
+ align:start position:0%
+collecting collecting the Rays
+collecting the like solar energy
+
+ align:start position:0%
+collecting the like solar energy
+ 
+
+ align:start position:0%
+collecting the like solar energy
+transferring it into like
+
+ align:start position:0%
+transferring it into like
+ 
+
+ align:start position:0%
+transferring it into like
+electrical energy and uh getting it to
+
+ align:start position:0%
+electrical energy and uh getting it to
+ 
+
+ align:start position:0%
+electrical energy and uh getting it to
+to the solar cooker and the so I think
+
+ align:start position:0%
+to the solar cooker and the so I think
+ 
+
+ align:start position:0%
+to the solar cooker and the so I think
+that would be a really good estimation
+
+ align:start position:0%
+that would be a really good estimation
+ 
+
+ align:start position:0%
+that would be a really good estimation
+exercise to figure out what it takes to
+
+ align:start position:0%
+exercise to figure out what it takes to
+ 
+
+ align:start position:0%
+exercise to figure out what it takes to
+make a solar cooker that's an electrical
+
+ align:start position:0%
+make a solar cooker that's an electrical
+ 
+
+ align:start position:0%
+make a solar cooker that's an electrical
+solar cooker um because do you remember
+
+ align:start position:0%
+solar cooker um because do you remember
+ 
+
+ align:start position:0%
+solar cooker um because do you remember
+how many watts a
+
+ align:start position:0%
+how many watts a
+ 
+
+ align:start position:0%
+how many watts a
+typical stove or oven
+
+ align:start position:0%
+typical stove or oven
+ 
+
+ align:start position:0%
+typical stove or oven
+is yeah
+
+ align:start position:0%
+is yeah
+ 
+
+ align:start position:0%
+is yeah
+and so like a typical like burner is
+
+ align:start position:0%
+and so like a typical like burner is
+ 
+
+ align:start position:0%
+and so like a typical like burner is
+1,000 to 1500 watts a typical oven is
+
+ align:start position:0%
+1,000 to 1500 watts a typical oven is
+ 
+
+ align:start position:0%
+1,000 to 1500 watts a typical oven is
+3,000 Watts so we're talking really
+
+ align:start position:0%
+3,000 Watts so we're talking really
+ 
+
+ align:start position:0%
+3,000 Watts so we're talking really
+different Scopes in terms of what a cell
+
+ align:start position:0%
+different Scopes in terms of what a cell
+ 
+
+ align:start position:0%
+different Scopes in terms of what a cell
+phone charger is and what cooking is
+
+ align:start position:0%
+phone charger is and what cooking is
+ 
+
+ align:start position:0%
+phone charger is and what cooking is
+needs to be and so um that's a high
+
+ align:start position:0%
+needs to be and so um that's a high
+ 
+
+ align:start position:0%
+needs to be and so um that's a high
+barrier to entry so you need to look
+
+ align:start position:0%
+barrier to entry so you need to look
+ 
+
+ align:start position:0%
+barrier to entry so you need to look
+into the viability of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that okay so can we make a list of what
+
+ align:start position:0%
+that okay so can we make a list of what
+ 
+
+ align:start position:0%
+that okay so can we make a list of what
+you think are the bonuses of Sor cookers
+
+ align:start position:0%
+you think are the bonuses of Sor cookers
+ 
+
+ align:start position:0%
+you think are the bonuses of Sor cookers
+and what are some of the drawbacks Benji
+
+ align:start position:0%
+and what are some of the drawbacks Benji
+ 
+
+ align:start position:0%
+and what are some of the drawbacks Benji
+um it's free after you buy it yeah so
+
+ align:start position:0%
+um it's free after you buy it yeah so
+ 
+
+ align:start position:0%
+um it's free after you buy it yeah so
+it's free
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+energy zero emissions y
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+a con is that you might not be able to
+
+ align:start position:0%
+a con is that you might not be able to
+ 
+
+ align:start position:0%
+a con is that you might not be able to
+have it right outside your home like
+
+ align:start position:0%
+have it right outside your home like
+ 
+
+ align:start position:0%
+have it right outside your home like
+that girl standing in a river which is
+
+ align:start position:0%
+that girl standing in a river which is
+ 
+
+ align:start position:0%
+that girl standing in a river which is
+probably not
+
+ align:start position:0%
+probably not
+ 
+
+ align:start position:0%
+probably not
+outside um so
+
+ align:start position:0%
+outside um so
+ 
+
+ align:start position:0%
+outside um so
+uh how do we so it needs to be like it
+
+ align:start position:0%
+uh how do we so it needs to be like it
+ 
+
+ align:start position:0%
+uh how do we so it needs to be like it
+needs to be out to find a sunny location
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah it's depending on weather and time
+
+ align:start position:0%
+yeah it's depending on weather and time
+ 
+
+ align:start position:0%
+yeah it's depending on weather and time
+of day
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+said um apart from the conator cookers
+
+ align:start position:0%
+said um apart from the conator cookers
+ 
+
+ align:start position:0%
+said um apart from the conator cookers
+they can't fry food yeah so your your
+
+ align:start position:0%
+they can't fry food yeah so your your
+ 
+
+ align:start position:0%
+they can't fry food yeah so your your
+your cooking options are limited
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so yeah you can absolutely fry food with
+
+ align:start position:0%
+so yeah you can absolutely fry food with
+ 
+
+ align:start position:0%
+so yeah you can absolutely fry food with
+the concentrator but it can be hard to
+
+ align:start position:0%
+the concentrator but it can be hard to
+ 
+
+ align:start position:0%
+the concentrator but it can be hard to
+get a low heat if you want a low heat in
+
+ align:start position:0%
+get a low heat if you want a low heat in
+ 
+
+ align:start position:0%
+get a low heat if you want a low heat in
+a
+
+ align:start position:0%
+a
+ 
+
+ align:start position:0%
+a
+concentrator Carter excuse me
+
+ align:start position:0%
+concentrator Carter excuse me
+ 
+
+ align:start position:0%
+concentrator Carter excuse me
+portability
+
+ align:start position:0%
+portability
+ 
+
+ align:start position:0%
+portability
+portability yeah so I'll put that in the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+middle well and there's a real guility
+
+ align:start position:0%
+middle well and there's a real guility
+ 
+
+ align:start position:0%
+middle well and there's a real guility
+would
+
+ align:start position:0%
+would
+ 
+
+ align:start position:0%
+would
+be uh but
+
+ align:start position:0%
+be uh but
+ 
+
+ align:start position:0%
+be uh but
+scale that you can move it around but
+
+ align:start position:0%
+scale that you can move it around but
+ 
+
+ align:start position:0%
+scale that you can move it around but
+only to a certain size well but you can
+
+ align:start position:0%
+only to a certain size well but you can
+ 
+
+ align:start position:0%
+only to a certain size well but you can
+see here so like this is a highly
+
+ align:start position:0%
+see here so like this is a highly
+ 
+
+ align:start position:0%
+see here so like this is a highly
+portable solar cooker that that parabell
+
+ align:start position:0%
+portable solar cooker that that parabell
+ 
+
+ align:start position:0%
+portable solar cooker that that parabell
+concentrator actually folds up into
+
+ align:start position:0%
+concentrator actually folds up into
+ 
+
+ align:start position:0%
+concentrator actually folds up into
+something that's not much bigger like
+
+ align:start position:0%
+something that's not much bigger like
+ 
+
+ align:start position:0%
+something that's not much bigger like
+it's significantly smaller than this so
+
+ align:start position:0%
+it's significantly smaller than this so
+ 
+
+ align:start position:0%
+it's significantly smaller than this so
+that is super portable whereas the
+
+ align:start position:0%
+that is super portable whereas the
+ 
+
+ align:start position:0%
+that is super portable whereas the
+concentr that concentrator is a fixed
+
+ align:start position:0%
+concentr that concentrator is a fixed
+ 
+
+ align:start position:0%
+concentr that concentrator is a fixed
+location so some are portable some are
+
+ align:start position:0%
+location so some are portable some are
+ 
+
+ align:start position:0%
+location so some are portable some are
+not um and then if they're portable that
+
+ align:start position:0%
+not um and then if they're portable that
+ 
+
+ align:start position:0%
+not um and then if they're portable that
+can be helpful but then it's limited by
+
+ align:start position:0%
+can be helpful but then it's limited by
+ 
+
+ align:start position:0%
+can be helpful but then it's limited by
+size so I think actually leaving it in
+
+ align:start position:0%
+size so I think actually leaving it in
+ 
+
+ align:start position:0%
+size so I think actually leaving it in
+the middle is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+reasonable
+
+ align:start position:0%
+reasonable
+ 
+
+ align:start position:0%
+reasonable
+c yeah
+
+ align:start position:0%
+c yeah
+ 
+
+ align:start position:0%
+c yeah
+um I don't know if that is TR any more
+
+ align:start position:0%
+um I don't know if that is TR any more
+ 
+
+ align:start position:0%
+um I don't know if that is TR any more
+true than it is for any
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+stove any other thoughts
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah let me see
+
+ align:start position:0%
+yeah let me see
+ 
+
+ align:start position:0%
+yeah let me see
+obviously haveit
+
+ align:start position:0%
+obviously haveit
+ 
+
+ align:start position:0%
+obviously haveit
+impr yeah so no emissions which
+
+ align:start position:0%
+impr yeah so no emissions which
+ 
+
+ align:start position:0%
+impr yeah so no emissions which
+yields this better
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+health there's also no preparation time
+
+ align:start position:0%
+health there's also no preparation time
+ 
+
+ align:start position:0%
+health there's also no preparation time
+like you don't need to collect fuel yeah
+
+ align:start position:0%
+like you don't need to collect fuel yeah
+ 
+
+ align:start position:0%
+like you don't need to collect fuel yeah
+so no no fuel
+
+ align:start position:0%
+so no no fuel
+ 
+
+ align:start position:0%
+so no no fuel
+collection which sort of links to that
+
+ align:start position:0%
+collection which sort of links to that
+ 
+
+ align:start position:0%
+collection which sort of links to that
+one so cuz it's either time or money
+
+ align:start position:0%
+one so cuz it's either time or money
+ 
+
+ align:start position:0%
+one so cuz it's either time or money
+generally Sid I guess our would be that
+
+ align:start position:0%
+generally Sid I guess our would be that
+ 
+
+ align:start position:0%
+generally Sid I guess our would be that
+you constantly like change the Angles
+
+ align:start position:0%
+you constantly like change the Angles
+ 
+
+ align:start position:0%
+you constantly like change the Angles
+and you're cooking for for a long period
+
+ align:start position:0%
+and you're cooking for for a long period
+ 
+
+ align:start position:0%
+and you're cooking for for a long period
+of time so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um okay yeah
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Beni so if someone you know if someone
+
+ align:start position:0%
+Beni so if someone you know if someone
+ 
+
+ align:start position:0%
+Beni so if someone you know if someone
+wants to have I don't
+
+ align:start position:0%
+wants to have I don't
+ 
+
+ align:start position:0%
+wants to have I don't
+know you're not using
+
+ align:start position:0%
+know you're not using
+ 
+
+ align:start position:0%
+know you're not using
+any yep so because people do use their
+
+ align:start position:0%
+any yep so because people do use their
+ 
+
+ align:start position:0%
+any yep so because people do use their
+Fires for heating for mosquito
+
+ align:start position:0%
+Fires for heating for mosquito
+ 
+
+ align:start position:0%
+Fires for heating for mosquito
+control for light sometimes yeah
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay super so I think that's a pretty
+
+ align:start position:0%
+okay super so I think that's a pretty
+ 
+
+ align:start position:0%
+okay super so I think that's a pretty
+good list to give you some background
+
+ align:start position:0%
+good list to give you some background
+ 
+
+ align:start position:0%
+good list to give you some background
+solar cookers were invented in the mid
+
+ align:start position:0%
+solar cookers were invented in the mid
+ 
+
+ align:start position:0%
+solar cookers were invented in the mid
+1700s so they've been around for a
+
+ align:start position:0%
+1700s so they've been around for a
+ 
+
+ align:start position:0%
+1700s so they've been around for a
+really long time and I think that
+
+ align:start position:0%
+really long time and I think that
+ 
+
+ align:start position:0%
+really long time and I think that
+is an indicator of how this is a great
+
+ align:start position:0%
+is an indicator of how this is a great
+ 
+
+ align:start position:0%
+is an indicator of how this is a great
+technology in some cases but isn't ever
+
+ align:start position:0%
+technology in some cases but isn't ever
+ 
+
+ align:start position:0%
+technology in some cases but isn't ever
+going to be the killer app that solves
+
+ align:start position:0%
+going to be the killer app that solves
+ 
+
+ align:start position:0%
+going to be the killer app that solves
+the world's cooking challenges uh
+
+ align:start position:0%
+the world's cooking challenges uh
+ 
+
+ align:start position:0%
+the world's cooking challenges uh
+because one would think if they been
+
+ align:start position:0%
+because one would think if they been
+ 
+
+ align:start position:0%
+because one would think if they been
+around since the 1700s that the
+
+ align:start position:0%
+around since the 1700s that the
+ 
+
+ align:start position:0%
+around since the 1700s that the
+refinement that takes it to killer app
+
+ align:start position:0%
+refinement that takes it to killer app
+ 
+
+ align:start position:0%
+refinement that takes it to killer app
+would have been developed already but
+
+ align:start position:0%
+would have been developed already but
+ 
+
+ align:start position:0%
+would have been developed already but
+the cons of it weather dependent it's
+
+ align:start position:0%
+the cons of it weather dependent it's
+ 
+
+ align:start position:0%
+the cons of it weather dependent it's
+time dependent you need to be in a sunny
+
+ align:start position:0%
+time dependent you need to be in a sunny
+ 
+
+ align:start position:0%
+time dependent you need to be in a sunny
+location you need to be outside are all
+
+ align:start position:0%
+location you need to be outside are all
+ 
+
+ align:start position:0%
+location you need to be outside are all
+really huge um so some of the challenges
+
+ align:start position:0%
+really huge um so some of the challenges
+ 
+
+ align:start position:0%
+really huge um so some of the challenges
+with the concentrators are the glare and
+
+ align:start position:0%
+with the concentrators are the glare and
+ 
+
+ align:start position:0%
+with the concentrators are the glare and
+just how hot it is so it's kind of hard
+
+ align:start position:0%
+just how hot it is so it's kind of hard
+ 
+
+ align:start position:0%
+just how hot it is so it's kind of hard
+to see cuz the um quality of the picture
+
+ align:start position:0%
+to see cuz the um quality of the picture
+ 
+
+ align:start position:0%
+to see cuz the um quality of the picture
+has gone down going through the
+
+ align:start position:0%
+has gone down going through the
+ 
+
+ align:start position:0%
+has gone down going through the
+projector but this woman is sort of
+
+ align:start position:0%
+projector but this woman is sort of
+ 
+
+ align:start position:0%
+projector but this woman is sort of
+grimac
+
+ align:start position:0%
+grimac
+ 
+
+ align:start position:0%
+grimac
+because it's so bright that it's
+
+ align:start position:0%
+because it's so bright that it's
+ 
+
+ align:start position:0%
+because it's so bright that it's
+actually hard to um to deal with and
+
+ align:start position:0%
+actually hard to um to deal with and
+ 
+
+ align:start position:0%
+actually hard to um to deal with and
+it's also
+
+ align:start position:0%
+it's also
+ 
+
+ align:start position:0%
+it's also
+um very hot where it is yeah is it
+
+ align:start position:0%
+um very hot where it is yeah is it
+ 
+
+ align:start position:0%
+um very hot where it is yeah is it
+dangerous yeah so the the concentrators
+
+ align:start position:0%
+dangerous yeah so the the concentrators
+ 
+
+ align:start position:0%
+dangerous yeah so the the concentrators
+in particular are dangerous and so
+
+ align:start position:0%
+in particular are dangerous and so
+ 
+
+ align:start position:0%
+in particular are dangerous and so
+people are really concerned especially
+
+ align:start position:0%
+people are really concerned especially
+ 
+
+ align:start position:0%
+people are really concerned especially
+with kids um you know it's getting not
+
+ align:start position:0%
+with kids um you know it's getting not
+ 
+
+ align:start position:0%
+with kids um you know it's getting not
+permanently but temporary blinded or
+
+ align:start position:0%
+permanently but temporary blinded or
+ 
+
+ align:start position:0%
+permanently but temporary blinded or
+burned um there's also issues that you
+
+ align:start position:0%
+burned um there's also issues that you
+ 
+
+ align:start position:0%
+burned um there's also issues that you
+can imagine how easy that would
+
+ align:start position:0%
+can imagine how easy that would
+ 
+
+ align:start position:0%
+can imagine how easy that would
+be voila
+
+ align:start position:0%
+be voila
+ 
+
+ align:start position:0%
+be voila
+so I have a really quick question for
+
+ align:start position:0%
+so I have a really quick question for
+ 
+
+ align:start position:0%
+so I have a really quick question for
+all of you anyone wearing shoes with
+
+ align:start position:0%
+all of you anyone wearing shoes with
+ 
+
+ align:start position:0%
+all of you anyone wearing shoes with
+laces can you please stand
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+up and the rest of you just look around
+
+ align:start position:0%
+up and the rest of you just look around
+ 
+
+ align:start position:0%
+up and the rest of you just look around
+get a good look at
+
+ align:start position:0%
+get a good look at
+ 
+
+ align:start position:0%
+get a good look at
+uh who who has laces and who
+
+ align:start position:0%
+uh who who has laces and who
+ 
+
+ align:start position:0%
+uh who who has laces and who
+doesn't this thing clipped on here
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay thank you guys you can sit
+
+ align:start position:0%
+okay thank you guys you can sit
+ 
+
+ align:start position:0%
+okay thank you guys you can sit
+down
+
+ align:start position:0%
+down
+ 
+
+ align:start position:0%
+down
+um so I I hate to break it to you like
+
+ align:start position:0%
+um so I I hate to break it to you like
+ 
+
+ align:start position:0%
+um so I I hate to break it to you like
+this um but you know I can see a lot of
+
+ align:start position:0%
+this um but you know I can see a lot of
+ 
+
+ align:start position:0%
+this um but you know I can see a lot of
+the way you tied your laces and a lot of
+
+ align:start position:0%
+the way you tied your laces and a lot of
+ 
+
+ align:start position:0%
+the way you tied your laces and a lot of
+you just use like the simple like bunny
+
+ align:start position:0%
+you just use like the simple like bunny
+ 
+
+ align:start position:0%
+you just use like the simple like bunny
+ears kind of knot you learned when you
+
+ align:start position:0%
+ears kind of knot you learned when you
+ 
+
+ align:start position:0%
+ears kind of knot you learned when you
+were like five or six you know which was
+
+ align:start position:0%
+were like five or six you know which was
+ 
+
+ align:start position:0%
+were like five or six you know which was
+great when you learned it and worked
+
+ align:start position:0%
+great when you learned it and worked
+ 
+
+ align:start position:0%
+great when you learned it and worked
+well um but honestly now it's kind of a
+
+ align:start position:0%
+well um but honestly now it's kind of a
+ 
+
+ align:start position:0%
+well um but honestly now it's kind of a
+dumb knot to
+
+ align:start position:0%
+dumb knot to
+ 
+
+ align:start position:0%
+dumb knot to
+use uh I you've been using your whole
+
+ align:start position:0%
+use uh I you've been using your whole
+ 
+
+ align:start position:0%
+use uh I you've been using your whole
+life but um you know I I can stand up
+
+ align:start position:0%
+life but um you know I I can stand up
+ 
+
+ align:start position:0%
+life but um you know I I can stand up
+here and tell you that because uh so I'm
+
+ align:start position:0%
+here and tell you that because uh so I'm
+ 
+
+ align:start position:0%
+here and tell you that because uh so I'm
+I'm a graduate student here mechanical
+
+ align:start position:0%
+I'm a graduate student here mechanical
+ 
+
+ align:start position:0%
+I'm a graduate student here mechanical
+engineering um which if you haven't
+
+ align:start position:0%
+engineering um which if you haven't
+ 
+
+ align:start position:0%
+engineering um which if you haven't
+heard is probably the best mechanical
+
+ align:start position:0%
+heard is probably the best mechanical
+ 
+
+ align:start position:0%
+heard is probably the best mechanical
+engineering department in the
+
+ align:start position:0%
+engineering department in the
+ 
+
+ align:start position:0%
+engineering department in the
+world um so you know I've learned all
+
+ align:start position:0%
+world um so you know I've learned all
+ 
+
+ align:start position:0%
+world um so you know I've learned all
+about design and like good designs and
+
+ align:start position:0%
+about design and like good designs and
+ 
+
+ align:start position:0%
+about design and like good designs and
+bad designs um and these bunny ear knots
+
+ align:start position:0%
+bad designs um and these bunny ear knots
+ 
+
+ align:start position:0%
+bad designs um and these bunny ear knots
+are are pretty bad
+
+ align:start position:0%
+are are pretty bad
+ 
+
+ align:start position:0%
+are are pretty bad
+designs um you know if you want we could
+
+ align:start position:0%
+designs um you know if you want we could
+ 
+
+ align:start position:0%
+designs um you know if you want we could
+sit here and analyze the stresses in
+
+ align:start position:0%
+sit here and analyze the stresses in
+ 
+
+ align:start position:0%
+sit here and analyze the stresses in
+them and and kind of of where are the
+
+ align:start position:0%
+them and and kind of of where are the
+ 
+
+ align:start position:0%
+them and and kind of of where are the
+equilibrium points and why does it stay
+
+ align:start position:0%
+equilibrium points and why does it stay
+ 
+
+ align:start position:0%
+equilibrium points and why does it stay
+tied and why does it always come untied
+
+ align:start position:0%
+tied and why does it always come untied
+ 
+
+ align:start position:0%
+tied and why does it always come untied
+um but you know the summary of all that
+
+ align:start position:0%
+um but you know the summary of all that
+ 
+
+ align:start position:0%
+um but you know the summary of all that
+is just it's a bad not and you guys
+
+ align:start position:0%
+is just it's a bad not and you guys
+ 
+
+ align:start position:0%
+is just it's a bad not and you guys
+should learn a new one uh but thankfully
+
+ align:start position:0%
+should learn a new one uh but thankfully
+ 
+
+ align:start position:0%
+should learn a new one uh but thankfully
+I'm I'm here and I'm going to go through
+
+ align:start position:0%
+I'm I'm here and I'm going to go through
+ 
+
+ align:start position:0%
+I'm I'm here and I'm going to go through
+and teach you how to tie it better or
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+not okay so I'm going to kind of step
+
+ align:start position:0%
+not okay so I'm going to kind of step
+ 
+
+ align:start position:0%
+not okay so I'm going to kind of step
+out of that character and ask you just
+
+ align:start position:0%
+out of that character and ask you just
+ 
+
+ align:start position:0%
+out of that character and ask you just
+real quickly to share kind of thoughts
+
+ align:start position:0%
+real quickly to share kind of thoughts
+ 
+
+ align:start position:0%
+real quickly to share kind of thoughts
+or feelings of that experience and kind
+
+ align:start position:0%
+or feelings of that experience and kind
+ 
+
+ align:start position:0%
+or feelings of that experience and kind
+of what I said or what I did that made
+
+ align:start position:0%
+of what I said or what I did that made
+ 
+
+ align:start position:0%
+of what I said or what I did that made
+you think or feel the way you are now I
+
+ align:start position:0%
+you think or feel the way you are now I
+ 
+
+ align:start position:0%
+you think or feel the way you are now I
+don't actually
+
+ align:start position:0%
+don't actually
+ 
+
+ align:start position:0%
+don't actually
+use okay that
+
+ align:start position:0%
+use okay that
+ 
+
+ align:start position:0%
+use okay that
+work other anyone else yeah he whispered
+
+ align:start position:0%
+work other anyone else yeah he whispered
+ 
+
+ align:start position:0%
+work other anyone else yeah he whispered
+to me he's like I don't should have my
+
+ align:start position:0%
+to me he's like I don't should have my
+ 
+
+ align:start position:0%
+to me he's like I don't should have my
+shoes
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+tied you pointed out the people who were
+
+ align:start position:0%
+tied you pointed out the people who were
+ 
+
+ align:start position:0%
+tied you pointed out the people who were
+doing it wrong which might make them
+
+ align:start position:0%
+doing it wrong which might make them
+ 
+
+ align:start position:0%
+doing it wrong which might make them
+feel bad though I don't think people
+
+ align:start position:0%
+feel bad though I don't think people
+ 
+
+ align:start position:0%
+feel bad though I don't think people
+here actually feel too bad about the way
+
+ align:start position:0%
+here actually feel too bad about the way
+ 
+
+ align:start position:0%
+here actually feel too bad about the way
+they tie their shoes
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah goe how you been say again how have
+
+ align:start position:0%
+yeah goe how you been say again how have
+ 
+
+ align:start position:0%
+yeah goe how you been say again how have
+you been D I've been well
+
+ align:start position:0%
+you been D I've been well
+ 
+
+ align:start position:0%
+you been D I've been well
+um so yeah
+
+ align:start position:0%
+um so yeah
+ 
+
+ align:start position:0%
+um so yeah
+so any other thoughts about how I came
+
+ align:start position:0%
+so any other thoughts about how I came
+ 
+
+ align:start position:0%
+so any other thoughts about how I came
+across I I obviously have this idea that
+
+ align:start position:0%
+across I I obviously have this idea that
+ 
+
+ align:start position:0%
+across I I obviously have this idea that
+I want to get you to learn how to tie
+
+ align:start position:0%
+I want to get you to learn how to tie
+ 
+
+ align:start position:0%
+I want to get you to learn how to tie
+your shoes differently do you think that
+
+ align:start position:0%
+your shoes differently do you think that
+ 
+
+ align:start position:0%
+your shoes differently do you think that
+was the best
+
+ align:start position:0%
+was the best
+ 
+
+ align:start position:0%
+was the best
+approach so it was good cuz you're
+
+ align:start position:0%
+approach so it was good cuz you're
+ 
+
+ align:start position:0%
+approach so it was good cuz you're
+really confident and so it was easy to
+
+ align:start position:0%
+really confident and so it was easy to
+ 
+
+ align:start position:0%
+really confident and so it was easy to
+listen to you and your kind of argument
+
+ align:start position:0%
+listen to you and your kind of argument
+ 
+
+ align:start position:0%
+listen to you and your kind of argument
+and the flow of your conversation was
+
+ align:start position:0%
+and the flow of your conversation was
+ 
+
+ align:start position:0%
+and the flow of your conversation was
+really easy to follow but
+
+ align:start position:0%
+really easy to follow but
+ 
+
+ align:start position:0%
+really easy to follow but
+also think you were overconfident for
+
+ align:start position:0%
+also think you were overconfident for
+ 
+
+ align:start position:0%
+also think you were overconfident for
+such a simple topic and in fact Al you
+
+ align:start position:0%
+such a simple topic and in fact Al you
+ 
+
+ align:start position:0%
+such a simple topic and in fact Al you
+brought uh the whole MIT thing I think
+
+ align:start position:0%
+brought uh the whole MIT thing I think
+ 
+
+ align:start position:0%
+brought uh the whole MIT thing I think
+for us it's good cuz we're all the MIT
+
+ align:start position:0%
+for us it's good cuz we're all the MIT
+ 
+
+ align:start position:0%
+for us it's good cuz we're all the MIT
+of course but I don't know how that
+
+ align:start position:0%
+of course but I don't know how that
+ 
+
+ align:start position:0%
+of course but I don't know how that
+would go with other people like so you
+
+ align:start position:0%
+would go with other people like so you
+ 
+
+ align:start position:0%
+would go with other people like so you
+think you're I don't know it seemed like
+
+ align:start position:0%
+think you're I don't know it seemed like
+ 
+
+ align:start position:0%
+think you're I don't know it seemed like
+you just you thought you were better
+
+ align:start position:0%
+you just you thought you were better
+ 
+
+ align:start position:0%
+you just you thought you were better
+than us cuz like arrogant exactly yeah I
+
+ align:start position:0%
+than us cuz like arrogant exactly yeah I
+ 
+
+ align:start position:0%
+than us cuz like arrogant exactly yeah I
+was trying to be
+
+ align:start position:0%
+was trying to be
+ 
+
+ align:start position:0%
+was trying to be
+um right I mean I also I assumed there's
+
+ align:start position:0%
+um right I mean I also I assumed there's
+ 
+
+ align:start position:0%
+um right I mean I also I assumed there's
+a problem right I assumed that you're
+
+ align:start position:0%
+a problem right I assumed that you're
+ 
+
+ align:start position:0%
+a problem right I assumed that you're
+not happy with the way you're tying your
+
+ align:start position:0%
+not happy with the way you're tying your
+ 
+
+ align:start position:0%
+not happy with the way you're tying your
+shoes right and it said have a better
+
+ align:start position:0%
+shoes right and it said have a better
+ 
+
+ align:start position:0%
+shoes right and it said have a better
+way um like you said I ostracized
+
+ align:start position:0%
+way um like you said I ostracized
+ 
+
+ align:start position:0%
+way um like you said I ostracized
+someone who tied their shoes differently
+
+ align:start position:0%
+someone who tied their shoes differently
+ 
+
+ align:start position:0%
+someone who tied their shoes differently
+um I didn't introduce myself at all I
+
+ align:start position:0%
+um I didn't introduce myself at all I
+ 
+
+ align:start position:0%
+um I didn't introduce myself at all I
+just kind of barged in here and said hey
+
+ align:start position:0%
+just kind of barged in here and said hey
+ 
+
+ align:start position:0%
+just kind of barged in here and said hey
+let me tell you about this right just
+
+ align:start position:0%
+let me tell you about this right just
+ 
+
+ align:start position:0%
+let me tell you about this right just
+the personal connection is a pretty
+
+ align:start position:0%
+the personal connection is a pretty
+ 
+
+ align:start position:0%
+the personal connection is a pretty
+important thing when you're working with
+
+ align:start position:0%
+important thing when you're working with
+ 
+
+ align:start position:0%
+important thing when you're working with
+people
+
+ align:start position:0%
+people
+ 
+
+ align:start position:0%
+people
+um you know also I didn't really ask any
+
+ align:start position:0%
+um you know also I didn't really ask any
+ 
+
+ align:start position:0%
+um you know also I didn't really ask any
+information from you other than could
+
+ align:start position:0%
+information from you other than could
+ 
+
+ align:start position:0%
+information from you other than could
+you stand up if you have shoes that tie
+
+ align:start position:0%
+you stand up if you have shoes that tie
+ 
+
+ align:start position:0%
+you stand up if you have shoes that tie
+with laces right there was no other
+
+ align:start position:0%
+with laces right there was no other
+ 
+
+ align:start position:0%
+with laces right there was no other
+exchange of information right and so if
+
+ align:start position:0%
+exchange of information right and so if
+ 
+
+ align:start position:0%
+exchange of information right and so if
+I'm coming in here and I'm trying to
+
+ align:start position:0%
+I'm coming in here and I'm trying to
+ 
+
+ align:start position:0%
+I'm coming in here and I'm trying to
+help you with what I assume is a problem
+
+ align:start position:0%
+help you with what I assume is a problem
+ 
+
+ align:start position:0%
+help you with what I assume is a problem
+you know it's good to interact and get
+
+ align:start position:0%
+you know it's good to interact and get
+ 
+
+ align:start position:0%
+you know it's good to interact and get
+some kind of information from you guys
+
+ align:start position:0%
+some kind of information from you guys
+ 
+
+ align:start position:0%
+some kind of information from you guys
+um and and also I kind of imposed my
+
+ align:start position:0%
+um and and also I kind of imposed my
+ 
+
+ align:start position:0%
+um and and also I kind of imposed my
+value of keeping shoes tied for a long
+
+ align:start position:0%
+value of keeping shoes tied for a long
+ 
+
+ align:start position:0%
+value of keeping shoes tied for a long
+time over what might be a value of ease
+
+ align:start position:0%
+time over what might be a value of ease
+ 
+
+ align:start position:0%
+time over what might be a value of ease
+to tie your shoe or ease to untie your
+
+ align:start position:0%
+to tie your shoe or ease to untie your
+ 
+
+ align:start position:0%
+to tie your shoe or ease to untie your
+shoe or just familiarity or the way the
+
+ align:start position:0%
+shoe or just familiarity or the way the
+ 
+
+ align:start position:0%
+shoe or just familiarity or the way the
+knot looks you like the way it looks so
+
+ align:start position:0%
+knot looks you like the way it looks so
+ 
+
+ align:start position:0%
+knot looks you like the way it looks so
+you're going to tie the bunny ears over
+
+ align:start position:0%
+you're going to tie the bunny ears over
+ 
+
+ align:start position:0%
+you're going to tie the bunny ears over
+some other not right so I kind of just
+
+ align:start position:0%
+some other not right so I kind of just
+ 
+
+ align:start position:0%
+some other not right so I kind of just
+assumed all these things and just put
+
+ align:start position:0%
+assumed all these things and just put
+ 
+
+ align:start position:0%
+assumed all these things and just put
+them on you and said hey here's a better
+
+ align:start position:0%
+them on you and said hey here's a better
+ 
+
+ align:start position:0%
+them on you and said hey here's a better
+way of doing
+
+ align:start position:0%
+way of doing
+ 
+
+ align:start position:0%
+way of doing
+it so I wanted to use it as a simple
+
+ align:start position:0%
+it so I wanted to use it as a simple
+ 
+
+ align:start position:0%
+it so I wanted to use it as a simple
+illustration of some circumstances you
+
+ align:start position:0%
+illustration of some circumstances you
+ 
+
+ align:start position:0%
+illustration of some circumstances you
+might find yourself in going to
+
+ align:start position:0%
+might find yourself in going to
+ 
+
+ align:start position:0%
+might find yourself in going to
+Nicaragua soon um when you're working
+
+ align:start position:0%
+Nicaragua soon um when you're working
+ 
+
+ align:start position:0%
+Nicaragua soon um when you're working
+with uh people there on the projects
+
+ align:start position:0%
+with uh people there on the projects
+ 
+
+ align:start position:0%
+with uh people there on the projects
+that you've you've been working on so
+
+ align:start position:0%
+that you've you've been working on so
+ 
+
+ align:start position:0%
+that you've you've been working on so
+far where you're going into an entirely
+
+ align:start position:0%
+far where you're going into an entirely
+ 
+
+ align:start position:0%
+far where you're going into an entirely
+different culture right working in
+
+ align:start position:0%
+different culture right working in
+ 
+
+ align:start position:0%
+different culture right working in
+communities where you really don't know
+
+ align:start position:0%
+communities where you really don't know
+ 
+
+ align:start position:0%
+communities where you really don't know
+how everything works um and it it'd be
+
+ align:start position:0%
+how everything works um and it it'd be
+ 
+
+ align:start position:0%
+how everything works um and it it'd be
+really easy to come across in these same
+
+ align:start position:0%
+really easy to come across in these same
+ 
+
+ align:start position:0%
+really easy to come across in these same
+kinds of ways um so I wanted to just
+
+ align:start position:0%
+kinds of ways um so I wanted to just
+ 
+
+ align:start position:0%
+kinds of ways um so I wanted to just
+take a minute if we can to divide up
+
+ align:start position:0%
+take a minute if we can to divide up
+ 
+
+ align:start position:0%
+take a minute if we can to divide up
+into the teams right you guys have been
+
+ align:start position:0%
+into the teams right you guys have been
+ 
+
+ align:start position:0%
+into the teams right you guys have been
+working in teams um and just talk about
+
+ align:start position:0%
+working in teams um and just talk about
+ 
+
+ align:start position:0%
+working in teams um and just talk about
+how you might approach a situation where
+
+ align:start position:0%
+how you might approach a situation where
+ 
+
+ align:start position:0%
+how you might approach a situation where
+you show up to a community you have a
+
+ align:start position:0%
+you show up to a community you have a
+ 
+
+ align:start position:0%
+you show up to a community you have a
+community partner and you know you have
+
+ align:start position:0%
+community partner and you know you have
+ 
+
+ align:start position:0%
+community partner and you know you have
+the project that you've been working on
+
+ align:start position:0%
+the project that you've been working on
+ 
+
+ align:start position:0%
+the project that you've been working on
+all
+
+ align:start position:0%
+all
+ 
+
+ align:start position:0%
+all
+term and um guess how would you go about
+
+ align:start position:0%
+term and um guess how would you go about
+ 
+
+ align:start position:0%
+term and um guess how would you go about
+approaching the situation where you just
+
+ align:start position:0%
+approaching the situation where you just
+ 
+
+ align:start position:0%
+approaching the situation where you just
+show up you get out of the van or you
+
+ align:start position:0%
+show up you get out of the van or you
+ 
+
+ align:start position:0%
+show up you get out of the van or you
+get off the back of the truck and you're
+
+ align:start position:0%
+get off the back of the truck and you're
+ 
+
+ align:start position:0%
+get off the back of the truck and you're
+all right you show up
+
+ align:start position:0%
+all right you show up
+ 
+
+ align:start position:0%
+all right you show up
+up what do you do how do you approach
+
+ align:start position:0%
+up what do you do how do you approach
+ 
+
+ align:start position:0%
+up what do you do how do you approach
+the the leaders that you interact with
+
+ align:start position:0%
+the the leaders that you interact with
+ 
+
+ align:start position:0%
+the the leaders that you interact with
+or just the the people there um and so I
+
+ align:start position:0%
+or just the the people there um and so I
+ 
+
+ align:start position:0%
+or just the the people there um and so I
+I remember last year we had about four
+
+ align:start position:0%
+I remember last year we had about four
+ 
+
+ align:start position:0%
+I remember last year we had about four
+teams or so this's three okay so three
+
+ align:start position:0%
+teams or so this's three okay so three
+ 
+
+ align:start position:0%
+teams or so this's three okay so three
+teams that actually works perfectly um
+
+ align:start position:0%
+teams that actually works perfectly um
+ 
+
+ align:start position:0%
+teams that actually works perfectly um
+and right before we do this I'll
+
+ align:start position:0%
+and right before we do this I'll
+ 
+
+ align:start position:0%
+and right before we do this I'll
+introduce myself a little more I'm Steve
+
+ align:start position:0%
+introduce myself a little more I'm Steve
+ 
+
+ align:start position:0%
+introduce myself a little more I'm Steve
+Ray I know some some of you I'm a PhD
+
+ align:start position:0%
+Ray I know some some of you I'm a PhD
+ 
+
+ align:start position:0%
+Ray I know some some of you I'm a PhD
+suud mechanical engineer here and helped
+
+ align:start position:0%
+suud mechanical engineer here and helped
+ 
+
+ align:start position:0%
+suud mechanical engineer here and helped
+out with DB energy last year uh but in
+
+ align:start position:0%
+out with DB energy last year uh but in
+ 
+
+ align:start position:0%
+out with DB energy last year uh but in
+order to graduate I need to spend a
+
+ align:start position:0%
+order to graduate I need to spend a
+ 
+
+ align:start position:0%
+order to graduate I need to spend a
+little more time on my dissert ation
+
+ align:start position:0%
+little more time on my dissert ation
+ 
+
+ align:start position:0%
+little more time on my dissert ation
+this year so I couldn't help out more
+
+ align:start position:0%
+this year so I couldn't help out more
+ 
+
+ align:start position:0%
+this year so I couldn't help out more
+than this um but yeah that's it I went
+
+ align:start position:0%
+than this um but yeah that's it I went
+ 
+
+ align:start position:0%
+than this um but yeah that's it I went
+to to nicod last year and it was a great
+
+ align:start position:0%
+to to nicod last year and it was a great
+ 
+
+ align:start position:0%
+to to nicod last year and it was a great
+time so you guys should be pumped you
+
+ align:start position:0%
+time so you guys should be pumped you
+ 
+
+ align:start position:0%
+time so you guys should be pumped you
+leave like Friday or Saturday Sunday
+
+ align:start position:0%
+leave like Friday or Saturday Sunday
+ 
+
+ align:start position:0%
+leave like Friday or Saturday Sunday
+Sunday Okay cool so let's just break up
+
+ align:start position:0%
+Sunday Okay cool so let's just break up
+ 
+
+ align:start position:0%
+Sunday Okay cool so let's just break up
+and then we can quickly talk about it
+
+ align:start position:0%
+and then we can quickly talk about it
+ 
+
+ align:start position:0%
+and then we can quickly talk about it
+and the three of us will kind of just
+
+ align:start position:0%
+and the three of us will kind of just
+ 
+
+ align:start position:0%
+and the three of us will kind of just
+help facilitate and help you guys think
+
+ align:start position:0%
+help facilitate and help you guys think
+ 
+
+ align:start position:0%
+help facilitate and help you guys think
+about how you could kind of approach
+
+ align:start position:0%
+about how you could kind of approach
+ 
+
+ align:start position:0%
+about how you could kind of approach
+this in a in a positive way I just want
+
+ align:start position:0%
+this in a in a positive way I just want
+ 
+
+ align:start position:0%
+this in a in a positive way I just want
+to mention that the twoo timeing I think
+
+ align:start position:0%
+to mention that the twoo timeing I think
+ 
+
+ align:start position:0%
+to mention that the twoo timeing I think
+it's very comparable to cooking so you
+
+ align:start position:0%
+it's very comparable to cooking so you
+ 
+
+ align:start position:0%
+it's very comparable to cooking so you
+guys have been cook chewing tin your
+
+ align:start position:0%
+guys have been cook chewing tin your
+ 
+
+ align:start position:0%
+guys have been cook chewing tin your
+shoes since kindergarten is and most
+
+ align:start position:0%
+shoes since kindergarten is and most
+ 
+
+ align:start position:0%
+shoes since kindergarten is and most
+people have been in the kitchen since
+
+ align:start position:0%
+people have been in the kitchen since
+ 
+
+ align:start position:0%
+people have been in the kitchen since
+before they could walk um and cooking
+
+ align:start position:0%
+before they could walk um and cooking
+ 
+
+ align:start position:0%
+before they could walk um and cooking
+you know from seven or8 years old and so
+
+ align:start position:0%
+you know from seven or8 years old and so
+ 
+
+ align:start position:0%
+you know from seven or8 years old and so
+coming in and saying you're cooking
+
+ align:start position:0%
+coming in and saying you're cooking
+ 
+
+ align:start position:0%
+coming in and saying you're cooking
+wrong um which is somewhat what some of
+
+ align:start position:0%
+wrong um which is somewhat what some of
+ 
+
+ align:start position:0%
+wrong um which is somewhat what some of
+us are saying you know hopefully not the
+
+ align:start position:0%
+us are saying you know hopefully not the
+ 
+
+ align:start position:0%
+us are saying you know hopefully not the
+EXP um but fundamentally suggesting
+
+ align:start position:0%
+EXP um but fundamentally suggesting
+ 
+
+ align:start position:0%
+EXP um but fundamentally suggesting
+changes is comparable that you know like
+
+ align:start position:0%
+changes is comparable that you know like
+ 
+
+ align:start position:0%
+changes is comparable that you know like
+it sounds ludicrous and what are you
+
+ align:start position:0%
+it sounds ludicrous and what are you
+ 
+
+ align:start position:0%
+it sounds ludicrous and what are you
+talking about
+
+ align:start position:0%
+talking about
+ 
+
+ align:start position:0%
+talking about
+yeah and sometimes if there's like a
+
+ align:start position:0%
+yeah and sometimes if there's like a
+ 
+
+ align:start position:0%
+yeah and sometimes if there's like a
+something that's relatively new you
+
+ align:start position:0%
+something that's relatively new you
+ 
+
+ align:start position:0%
+something that's relatively new you
+might not even be aware of the problems
+
+ align:start position:0%
+might not even be aware of the problems
+ 
+
+ align:start position:0%
+might not even be aware of the problems
+with it because you've just been doing
+
+ align:start position:0%
+with it because you've just been doing
+ 
+
+ align:start position:0%
+with it because you've just been doing
+it the same way the whole time um so if
+
+ align:start position:0%
+it the same way the whole time um so if
+ 
+
+ align:start position:0%
+it the same way the whole time um so if
+You observe something and they and you
+
+ align:start position:0%
+You observe something and they and you
+ 
+
+ align:start position:0%
+You observe something and they and you
+ask them you have any problems with this
+
+ align:start position:0%
+ask them you have any problems with this
+ 
+
+ align:start position:0%
+ask them you have any problems with this
+so things you can improve and they say h
+
+ align:start position:0%
+so things you can improve and they say h
+ 
+
+ align:start position:0%
+so things you can improve and they say h
+not really like it works pretty well and
+
+ align:start position:0%
+not really like it works pretty well and
+ 
+
+ align:start position:0%
+not really like it works pretty well and
+if you see things that are that you
+
+ align:start position:0%
+if you see things that are that you
+ 
+
+ align:start position:0%
+if you see things that are that you
+think could be improved you could ask
+
+ align:start position:0%
+think could be improved you could ask
+ 
+
+ align:start position:0%
+think could be improved you could ask
+them well you know what do you think
+
+ align:start position:0%
+them well you know what do you think
+ 
+
+ align:start position:0%
+them well you know what do you think
+about decreasing the time for this to to
+
+ align:start position:0%
+about decreasing the time for this to to
+ 
+
+ align:start position:0%
+about decreasing the time for this to to
+work by making this change or something
+
+ align:start position:0%
+work by making this change or something
+ 
+
+ align:start position:0%
+work by making this change or something
+like that where um you it might not be
+
+ align:start position:0%
+like that where um you it might not be
+ 
+
+ align:start position:0%
+like that where um you it might not be
+totally apparent but you can still ask
+
+ align:start position:0%
+totally apparent but you can still ask
+ 
+
+ align:start position:0%
+totally apparent but you can still ask
+him how they would view
+
+ align:start position:0%
+him how they would view
+ 
+
+ align:start position:0%
+him how they would view
+it but starting with what they see is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+huge really
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+proud being cutting carefully there so
+
+ align:start position:0%
+proud being cutting carefully there so
+ 
+
+ align:start position:0%
+proud being cutting carefully there so
+that people be respecting what they've
+
+ align:start position:0%
+that people be respecting what they've
+ 
+
+ align:start position:0%
+that people be respecting what they've
+accomplished while providing
+
+ align:start position:0%
+accomplished while providing
+ 
+
+ align:start position:0%
+accomplished while providing
+positive ideas
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+for thanks so I know that was kind of
+
+ align:start position:0%
+for thanks so I know that was kind of
+ 
+
+ align:start position:0%
+for thanks so I know that was kind of
+bizarre and weird but um for some of the
+
+ align:start position:0%
+bizarre and weird but um for some of the
+ 
+
+ align:start position:0%
+bizarre and weird but um for some of the
+communities they sort of walking in
+
+ align:start position:0%
+communities they sort of walking in
+ 
+
+ align:start position:0%
+communities they sort of walking in
+while they're going about their daily
+
+ align:start position:0%
+while they're going about their daily
+ 
+
+ align:start position:0%
+while they're going about their daily
+lives and getting completely interrupted
+
+ align:start position:0%
+lives and getting completely interrupted
+ 
+
+ align:start position:0%
+lives and getting completely interrupted
+so that you could talk to them um and so
+
+ align:start position:0%
+so that you could talk to them um and so
+ 
+
+ align:start position:0%
+so that you could talk to them um and so
+just thinking about how awkward and
+
+ align:start position:0%
+just thinking about how awkward and
+ 
+
+ align:start position:0%
+just thinking about how awkward and
+weird that felt and therefore what you
+
+ align:start position:0%
+weird that felt and therefore what you
+ 
+
+ align:start position:0%
+weird that felt and therefore what you
+can do that wasn't like what Steve did
+
+ align:start position:0%
+can do that wasn't like what Steve did
+ 
+
+ align:start position:0%
+can do that wasn't like what Steve did
+because he was definitely doing worst
+
+ align:start position:0%
+because he was definitely doing worst
+ 
+
+ align:start position:0%
+because he was definitely doing worst
+case scenario in order to minimize that
+
+ align:start position:0%
+case scenario in order to minimize that
+ 
+
+ align:start position:0%
+case scenario in order to minimize that
+awkwardness and weirdness
+
+ align:start position:0%
+awkwardness and weirdness
+ 
+
+ align:start position:0%
+awkwardness and weirdness
+um so back to solar
+
+ align:start position:0%
+um so back to solar
+ 
+
+ align:start position:0%
+um so back to solar
+cookers uh so yeah so we're talking
+
+ align:start position:0%
+cookers uh so yeah so we're talking
+ 
+
+ align:start position:0%
+cookers uh so yeah so we're talking
+about the concentrator it can be so hot
+
+ align:start position:0%
+about the concentrator it can be so hot
+ 
+
+ align:start position:0%
+about the concentrator it can be so hot
+as to be dangerous especially for kids
+
+ align:start position:0%
+as to be dangerous especially for kids
+ 
+
+ align:start position:0%
+as to be dangerous especially for kids
+but really for everyone um you can see
+
+ align:start position:0%
+but really for everyone um you can see
+ 
+
+ align:start position:0%
+but really for everyone um you can see
+that is a big wind catcher so they can
+
+ align:start position:0%
+that is a big wind catcher so they can
+ 
+
+ align:start position:0%
+that is a big wind catcher so they can
+blow over pretty easily that's actually
+
+ align:start position:0%
+blow over pretty easily that's actually
+ 
+
+ align:start position:0%
+blow over pretty easily that's actually
+an issue with the group of Phoenix uh
+
+ align:start position:0%
+an issue with the group of Phoenix uh
+ 
+
+ align:start position:0%
+an issue with the group of Phoenix uh
+silic cookers too because this panel is
+
+ align:start position:0%
+silic cookers too because this panel is
+ 
+
+ align:start position:0%
+silic cookers too because this panel is
+so big that it catches in the wind um
+
+ align:start position:0%
+so big that it catches in the wind um
+ 
+
+ align:start position:0%
+so big that it catches in the wind um
+and then you C it's there's also a risk
+
+ align:start position:0%
+and then you C it's there's also a risk
+ 
+
+ align:start position:0%
+and then you C it's there's also a risk
+of when you're stirring spilling food
+
+ align:start position:0%
+of when you're stirring spilling food
+ 
+
+ align:start position:0%
+of when you're stirring spilling food
+onto the reflector and then damaging the
+
+ align:start position:0%
+onto the reflector and then damaging the
+ 
+
+ align:start position:0%
+onto the reflector and then damaging the
+reflector and how well it works so
+
+ align:start position:0%
+reflector and how well it works so
+ 
+
+ align:start position:0%
+reflector and how well it works so
+there's some real drawbacks from the
+
+ align:start position:0%
+there's some real drawbacks from the
+ 
+
+ align:start position:0%
+there's some real drawbacks from the
+parabolic from the greenhouse um it's a
+
+ align:start position:0%
+parabolic from the greenhouse um it's a
+ 
+
+ align:start position:0%
+parabolic from the greenhouse um it's a
+lower temperature and so you can really
+
+ align:start position:0%
+lower temperature and so you can really
+ 
+
+ align:start position:0%
+lower temperature and so you can really
+only cook certain things um but there's
+
+ align:start position:0%
+only cook certain things um but there's
+ 
+
+ align:start position:0%
+only cook certain things um but there's
+no burning happening and you really
+
+ align:start position:0%
+no burning happening and you really
+ 
+
+ align:start position:0%
+no burning happening and you really
+don't need to pay much attention to it
+
+ align:start position:0%
+don't need to pay much attention to it
+ 
+
+ align:start position:0%
+don't need to pay much attention to it
+apart from adjusting the the angle to
+
+ align:start position:0%
+apart from adjusting the the angle to
+ 
+
+ align:start position:0%
+apart from adjusting the the angle to
+the sun
+
+ align:start position:0%
+the sun
+ 
+
+ align:start position:0%
+the sun
+um and then the combo has some of the
+
+ align:start position:0%
+um and then the combo has some of the
+ 
+
+ align:start position:0%
+um and then the combo has some of the
+pros and some of the cons of the
+
+ align:start position:0%
+pros and some of the cons of the
+ 
+
+ align:start position:0%
+pros and some of the cons of the
+others uh so we talked about the
+
+ align:start position:0%
+others uh so we talked about the
+ 
+
+ align:start position:0%
+others uh so we talked about the
+benefits are pretty um oh and the other
+
+ align:start position:0%
+benefits are pretty um oh and the other
+ 
+
+ align:start position:0%
+benefits are pretty um oh and the other
+thing here is like you really can't stir
+
+ align:start position:0%
+thing here is like you really can't stir
+ 
+
+ align:start position:0%
+thing here is like you really can't stir
+this right because as soon as you open
+
+ align:start position:0%
+this right because as soon as you open
+ 
+
+ align:start position:0%
+this right because as soon as you open
+it up uh you you're losing all your your
+
+ align:start position:0%
+it up uh you you're losing all your your
+ 
+
+ align:start position:0%
+it up uh you you're losing all your your
+heat and you have to start all over
+
+ align:start position:0%
+heat and you have to start all over
+ 
+
+ align:start position:0%
+heat and you have to start all over
+again so it's it's a challenging device
+
+ align:start position:0%
+again so it's it's a challenging device
+ 
+
+ align:start position:0%
+again so it's it's a challenging device
+the uh so boxes are made out of almost
+
+ align:start position:0%
+the uh so boxes are made out of almost
+ 
+
+ align:start position:0%
+the uh so boxes are made out of almost
+anything like I've seen plastic I've
+
+ align:start position:0%
+anything like I've seen plastic I've
+ 
+
+ align:start position:0%
+anything like I've seen plastic I've
+seen wood I've seen metal so yeah um so
+
+ align:start position:0%
+seen wood I've seen metal so yeah um so
+ 
+
+ align:start position:0%
+seen wood I've seen metal so yeah um so
+so some of the challenges that people
+
+ align:start position:0%
+so some of the challenges that people
+ 
+
+ align:start position:0%
+so some of the challenges that people
+can be frustrated about in addition so
+
+ align:start position:0%
+can be frustrated about in addition so
+ 
+
+ align:start position:0%
+can be frustrated about in addition so
+one is that you have to cook outdoors
+
+ align:start position:0%
+one is that you have to cook outdoors
+ 
+
+ align:start position:0%
+one is that you have to cook outdoors
+and so in cultures where cooking indoors
+
+ align:start position:0%
+and so in cultures where cooking indoors
+ 
+
+ align:start position:0%
+and so in cultures where cooking indoors
+is standard cooking Outdoors po poses a
+
+ align:start position:0%
+is standard cooking Outdoors po poses a
+ 
+
+ align:start position:0%
+is standard cooking Outdoors po poses a
+lot of challenges so one is just the
+
+ align:start position:0%
+lot of challenges so one is just the
+ 
+
+ align:start position:0%
+lot of challenges so one is just the
+need for privacy another is just risks
+
+ align:start position:0%
+need for privacy another is just risks
+ 
+
+ align:start position:0%
+need for privacy another is just risks
+of theft of either your food and or your
+
+ align:start position:0%
+of theft of either your food and or your
+ 
+
+ align:start position:0%
+of theft of either your food and or your
+cooker um and it's also for people who
+
+ align:start position:0%
+cooker um and it's also for people who
+ 
+
+ align:start position:0%
+cooker um and it's also for people who
+are used to cooking around a fire it's a
+
+ align:start position:0%
+are used to cooking around a fire it's a
+ 
+
+ align:start position:0%
+are used to cooking around a fire it's a
+little less social uh or can be and so
+
+ align:start position:0%
+little less social uh or can be and so
+ 
+
+ align:start position:0%
+little less social uh or can be and so
+that can be a flip side of frust ation
+
+ align:start position:0%
+that can be a flip side of frust ation
+ 
+
+ align:start position:0%
+that can be a flip side of frust ation
+um the super affordable ones like this
+
+ align:start position:0%
+um the super affordable ones like this
+ 
+
+ align:start position:0%
+um the super affordable ones like this
+one is made out of cardboard and so they
+
+ align:start position:0%
+one is made out of cardboard and so they
+ 
+
+ align:start position:0%
+one is made out of cardboard and so they
+don't last very long CU termites tend to
+
+ align:start position:0%
+don't last very long CU termites tend to
+ 
+
+ align:start position:0%
+don't last very long CU termites tend to
+eat them or other
+
+ align:start position:0%
+eat them or other
+ 
+
+ align:start position:0%
+eat them or other
+insects uh but they're very inexpensive
+
+ align:start position:0%
+insects uh but they're very inexpensive
+ 
+
+ align:start position:0%
+insects uh but they're very inexpensive
+um and then they use a plastic bag just
+
+ align:start position:0%
+um and then they use a plastic bag just
+ 
+
+ align:start position:0%
+um and then they use a plastic bag just
+as your cover for your greenhouse and
+
+ align:start position:0%
+as your cover for your greenhouse and
+ 
+
+ align:start position:0%
+as your cover for your greenhouse and
+again very inexpensive but pretty short
+
+ align:start position:0%
+again very inexpensive but pretty short
+ 
+
+ align:start position:0%
+again very inexpensive but pretty short
+life um and so then you have with all
+
+ align:start position:0%
+life um and so then you have with all
+ 
+
+ align:start position:0%
+life um and so then you have with all
+these things breaking down and you have
+
+ align:start position:0%
+these things breaking down and you have
+ 
+
+ align:start position:0%
+these things breaking down and you have
+a supply chain issue of you need to make
+
+ align:start position:0%
+a supply chain issue of you need to make
+ 
+
+ align:start position:0%
+a supply chain issue of you need to make
+sure that people are able to get
+
+ align:start position:0%
+sure that people are able to get
+ 
+
+ align:start position:0%
+sure that people are able to get
+Replacements um and able to afford
+
+ align:start position:0%
+Replacements um and able to afford
+ 
+
+ align:start position:0%
+Replacements um and able to afford
+replacement
+
+ align:start position:0%
+replacement
+ 
+
+ align:start position:0%
+replacement
+um the size often times uh I sort of
+
+ align:start position:0%
+um the size often times uh I sort of
+ 
+
+ align:start position:0%
+um the size often times uh I sort of
+gave you a hard time Carter about the
+
+ align:start position:0%
+gave you a hard time Carter about the
+ 
+
+ align:start position:0%
+gave you a hard time Carter about the
+size thing um but it's true that
+
+ align:start position:0%
+size thing um but it's true that
+ 
+
+ align:start position:0%
+size thing um but it's true that
+actually a lot of the times they're
+
+ align:start position:0%
+actually a lot of the times they're
+ 
+
+ align:start position:0%
+actually a lot of the times they're
+relatively small for how much they can
+
+ align:start position:0%
+relatively small for how much they can
+ 
+
+ align:start position:0%
+relatively small for how much they can
+cook and so you can't always cook for
+
+ align:start position:0%
+cook and so you can't always cook for
+ 
+
+ align:start position:0%
+cook and so you can't always cook for
+all of your family members that's
+
+ align:start position:0%
+all of your family members that's
+ 
+
+ align:start position:0%
+all of your family members that's
+frustrating there was an interesting
+
+ align:start position:0%
+frustrating there was an interesting
+ 
+
+ align:start position:0%
+frustrating there was an interesting
+sort of case study where solar cookers
+
+ align:start position:0%
+sort of case study where solar cookers
+ 
+
+ align:start position:0%
+sort of case study where solar cookers
+were brought uh to kakuma which is a
+
+ align:start position:0%
+were brought uh to kakuma which is a
+ 
+
+ align:start position:0%
+were brought uh to kakuma which is a
+Kenyon refugee camp for uh refugees from
+
+ align:start position:0%
+Kenyon refugee camp for uh refugees from
+ 
+
+ align:start position:0%
+Kenyon refugee camp for uh refugees from
+the Sudan and the solar cookers
+
+ align:start position:0%
+the Sudan and the solar cookers
+ 
+
+ align:start position:0%
+the Sudan and the solar cookers
+International gave away a bunch of
+
+ align:start position:0%
+International gave away a bunch of
+ 
+
+ align:start position:0%
+International gave away a bunch of
+cookers
+
+ align:start position:0%
+cookers
+ 
+
+ align:start position:0%
+cookers
+and they it was it actually this cooker
+
+ align:start position:0%
+and they it was it actually this cooker
+ 
+
+ align:start position:0%
+and they it was it actually this cooker
+right here and um so they people were
+
+ align:start position:0%
+right here and um so they people were
+ 
+
+ align:start position:0%
+right here and um so they people were
+getting their solar cookers for free and
+
+ align:start position:0%
+getting their solar cookers for free and
+ 
+
+ align:start position:0%
+getting their solar cookers for free and
+cooking was a huge issue in these
+
+ align:start position:0%
+cooking was a huge issue in these
+ 
+
+ align:start position:0%
+cooking was a huge issue in these
+refugee camps because women were having
+
+ align:start position:0%
+refugee camps because women were having
+ 
+
+ align:start position:0%
+refugee camps because women were having
+to leave the camp in order to get
+
+ align:start position:0%
+to leave the camp in order to get
+ 
+
+ align:start position:0%
+to leave the camp in order to get
+firewood and when they were they were
+
+ align:start position:0%
+firewood and when they were they were
+ 
+
+ align:start position:0%
+firewood and when they were they were
+regularly raped and so they needed an
+
+ align:start position:0%
+regularly raped and so they needed an
+ 
+
+ align:start position:0%
+regularly raped and so they needed an
+alternative um pretty sever severely
+
+ align:start position:0%
+alternative um pretty sever severely
+ 
+
+ align:start position:0%
+alternative um pretty sever severely
+because there was no safe option for
+
+ align:start position:0%
+because there was no safe option for
+ 
+
+ align:start position:0%
+because there was no safe option for
+cooking and they also were spending over
+
+ align:start position:0%
+cooking and they also were spending over
+ 
+
+ align:start position:0%
+cooking and they also were spending over
+50% of their income on firewood um if
+
+ align:start position:0%
+50% of their income on firewood um if
+ 
+
+ align:start position:0%
+50% of their income on firewood um if
+they were buying it uh so really
+
+ align:start position:0%
+they were buying it uh so really
+ 
+
+ align:start position:0%
+they were buying it uh so really
+outrageous and in the end what they
+
+ align:start position:0%
+outrageous and in the end what they
+ 
+
+ align:start position:0%
+outrageous and in the end what they
+found is that less than 20% of people
+
+ align:start position:0%
+found is that less than 20% of people
+ 
+
+ align:start position:0%
+found is that less than 20% of people
+ended up using the solar cookers more
+
+ align:start position:0%
+ended up using the solar cookers more
+ 
+
+ align:start position:0%
+ended up using the solar cookers more
+than one or two days per week so that's
+
+ align:start position:0%
+than one or two days per week so that's
+ 
+
+ align:start position:0%
+than one or two days per week so that's
+a pretty low rate of usage um for
+
+ align:start position:0%
+a pretty low rate of usage um for
+ 
+
+ align:start position:0%
+a pretty low rate of usage um for
+something when you're facing really
+
+ align:start position:0%
+something when you're facing really
+ 
+
+ align:start position:0%
+something when you're facing really
+severe costs either to your bodily
+
+ align:start position:0%
+severe costs either to your bodily
+ 
+
+ align:start position:0%
+severe costs either to your bodily
+well-being or your income um that severe
+
+ align:start position:0%
+well-being or your income um that severe
+ 
+
+ align:start position:0%
+well-being or your income um that severe
+so I think that speaks to the challenges
+
+ align:start position:0%
+so I think that speaks to the challenges
+ 
+
+ align:start position:0%
+so I think that speaks to the challenges
+of solar cooker adoption that um people
+
+ align:start position:0%
+of solar cooker adoption that um people
+ 
+
+ align:start position:0%
+of solar cooker adoption that um people
+don't love to use them
+
+ align:start position:0%
+don't love to use them
+ 
+
+ align:start position:0%
+don't love to use them
+was that just because they were not used
+
+ align:start position:0%
+was that just because they were not used
+ 
+
+ align:start position:0%
+was that just because they were not used
+to it or were there any major kind of
+
+ align:start position:0%
+to it or were there any major kind of
+ 
+
+ align:start position:0%
+to it or were there any major kind of
+design flaws that made them useless or
+
+ align:start position:0%
+design flaws that made them useless or
+ 
+
+ align:start position:0%
+design flaws that made them useless or
+well so people really don't like them
+
+ align:start position:0%
+well so people really don't like them
+ 
+
+ align:start position:0%
+well so people really don't like them
+like these cookers work um but all these
+
+ align:start position:0%
+like these cookers work um but all these
+ 
+
+ align:start position:0%
+like these cookers work um but all these
+real issues like you can only cook
+
+ align:start position:0%
+real issues like you can only cook
+ 
+
+ align:start position:0%
+real issues like you can only cook
+during Lun for lunch basically you can't
+
+ align:start position:0%
+during Lun for lunch basically you can't
+ 
+
+ align:start position:0%
+during Lun for lunch basically you can't
+cook for breakfast you can't cook for
+
+ align:start position:0%
+cook for breakfast you can't cook for
+ 
+
+ align:start position:0%
+cook for breakfast you can't cook for
+dinner um you can only cook C certain
+
+ align:start position:0%
+dinner um you can only cook C certain
+ 
+
+ align:start position:0%
+dinner um you can only cook C certain
+types of foods etc etc make them a
+
+ align:start position:0%
+types of foods etc etc make them a
+ 
+
+ align:start position:0%
+types of foods etc etc make them a
+really limit of limited value um so on
+
+ align:start position:0%
+really limit of limited value um so on
+ 
+
+ align:start position:0%
+really limit of limited value um so on
+the flip side uh at kakuma is that there
+
+ align:start position:0%
+the flip side uh at kakuma is that there
+ 
+
+ align:start position:0%
+the flip side uh at kakuma is that there
+were a bunch of single men there um who
+
+ align:start position:0%
+were a bunch of single men there um who
+ 
+
+ align:start position:0%
+were a bunch of single men there um who
+were separated from their families so
+
+ align:start position:0%
+were separated from their families so
+ 
+
+ align:start position:0%
+were separated from their families so
+normally um in the
+
+ align:start position:0%
+normally um in the
+ 
+
+ align:start position:0%
+normally um in the
+Sudan I am talking about Sudan yeah um
+
+ align:start position:0%
+Sudan I am talking about Sudan yeah um
+ 
+
+ align:start position:0%
+Sudan I am talking about Sudan yeah um
+in the Sudan um if you're a single guy
+
+ align:start position:0%
+in the Sudan um if you're a single guy
+ 
+
+ align:start position:0%
+in the Sudan um if you're a single guy
+your mom cooks for you and it's not
+
+ align:start position:0%
+your mom cooks for you and it's not
+ 
+
+ align:start position:0%
+your mom cooks for you and it's not
+normal for men to cook at all so either
+
+ align:start position:0%
+normal for men to cook at all so either
+ 
+
+ align:start position:0%
+normal for men to cook at all so either
+your wife or your mom is cooking for you
+
+ align:start position:0%
+your wife or your mom is cooking for you
+ 
+
+ align:start position:0%
+your wife or your mom is cooking for you
+and so these single men were separated
+
+ align:start position:0%
+and so these single men were separated
+ 
+
+ align:start position:0%
+and so these single men were separated
+from their mom so they didn't have
+
+ align:start position:0%
+from their mom so they didn't have
+ 
+
+ align:start position:0%
+from their mom so they didn't have
+anyone to cook with and it was really
+
+ align:start position:0%
+anyone to cook with and it was really
+ 
+
+ align:start position:0%
+anyone to cook with and it was really
+socially inappropriate for them to cook
+
+ align:start position:0%
+socially inappropriate for them to cook
+ 
+
+ align:start position:0%
+socially inappropriate for them to cook
+with wood and so they were actually the
+
+ align:start position:0%
+with wood and so they were actually the
+ 
+
+ align:start position:0%
+with wood and so they were actually the
+adopters who used the solar cookers
+
+ align:start position:0%
+adopters who used the solar cookers
+ 
+
+ align:start position:0%
+adopters who used the solar cookers
+because it was appropriate for them to
+
+ align:start position:0%
+because it was appropriate for them to
+ 
+
+ align:start position:0%
+because it was appropriate for them to
+use these because they're really not
+
+ align:start position:0%
+use these because they're really not
+ 
+
+ align:start position:0%
+use these because they're really not
+considered stoves the way uh firewood
+
+ align:start position:0%
+considered stoves the way uh firewood
+ 
+
+ align:start position:0%
+considered stoves the way uh firewood
+stove would be considered a stove so
+
+ align:start position:0%
+stove would be considered a stove so
+ 
+
+ align:start position:0%
+stove would be considered a stove so
+that was the success story was that when
+
+ align:start position:0%
+that was the success story was that when
+ 
+
+ align:start position:0%
+that was the success story was that when
+you needed a radically different um
+
+ align:start position:0%
+you needed a radically different um
+ 
+
+ align:start position:0%
+you needed a radically different um
+option it was it was relatively well
+
+ align:start position:0%
+option it was it was relatively well
+ 
+
+ align:start position:0%
+option it was it was relatively well
+adopted um so yeah so and the other
+
+ align:start position:0%
+adopted um so yeah so and the other
+ 
+
+ align:start position:0%
+adopted um so yeah so and the other
+aspect is
+
+ align:start position:0%
+aspect is
+ 
+
+ align:start position:0%
+aspect is
+that the in this Camp there was a food
+
+ align:start position:0%
+that the in this Camp there was a food
+ 
+
+ align:start position:0%
+that the in this Camp there was a food
+scarcity also which is unsurprising and
+
+ align:start position:0%
+scarcity also which is unsurprising and
+ 
+
+ align:start position:0%
+scarcity also which is unsurprising and
+so asking people to uh experiment with
+
+ align:start position:0%
+so asking people to uh experiment with
+ 
+
+ align:start position:0%
+so asking people to uh experiment with
+how they cook when they don't know if
+
+ align:start position:0%
+how they cook when they don't know if
+ 
+
+ align:start position:0%
+how they cook when they don't know if
+they have enough food is a huge um
+
+ align:start position:0%
+they have enough food is a huge um
+ 
+
+ align:start position:0%
+they have enough food is a huge um
+request best of people and so I think
+
+ align:start position:0%
+request best of people and so I think
+ 
+
+ align:start position:0%
+request best of people and so I think
+that's part of the reason for the lack
+
+ align:start position:0%
+that's part of the reason for the lack
+ 
+
+ align:start position:0%
+that's part of the reason for the lack
+of adoption was that I'm not willing to
+
+ align:start position:0%
+of adoption was that I'm not willing to
+ 
+
+ align:start position:0%
+of adoption was that I'm not willing to
+try this wacky stove because what if I
+
+ align:start position:0%
+try this wacky stove because what if I
+ 
+
+ align:start position:0%
+try this wacky stove because what if I
+ruin my food that means I don't eat
+
+ align:start position:0%
+ruin my food that means I don't eat
+ 
+
+ align:start position:0%
+ruin my food that means I don't eat
+today and I don't know when I'll be
+
+ align:start position:0%
+today and I don't know when I'll be
+ 
+
+ align:start position:0%
+today and I don't know when I'll be
+eating very much um so that was the the
+
+ align:start position:0%
+eating very much um so that was the the
+ 
+
+ align:start position:0%
+eating very much um so that was the the
+summer summary of solar cookers there
+
+ align:start position:0%
+summer summary of solar cookers there
+ 
+
+ align:start position:0%
+summer summary of solar cookers there
+any questions on solar
+
+ align:start position:0%
+any questions on solar
+ 
+
+ align:start position:0%
+any questions on solar
+cookers I'm sorry I dropped that over
+
+ align:start position:0%
+cookers I'm sorry I dropped that over
+ 
+
+ align:start position:0%
+cookers I'm sorry I dropped that over
+the charcoal lecture that or stove
+
+ align:start position:0%
+the charcoal lecture that or stove
+ 
+
+ align:start position:0%
+the charcoal lecture that or stove
+lecture that would have been the time to
+
+ align:start position:0%
+lecture that would have been the time to
+ 
+
+ align:start position:0%
+lecture that would have been the time to
+do it I don't know how it got lost okay
+
+ align:start position:0%
+do it I don't know how it got lost okay
+ 
+
+ align:start position:0%
+do it I don't know how it got lost okay
+so now we're finally going to talk about
+
+ align:start position:0%
+so now we're finally going to talk about
+ 
+
+ align:start position:0%
+so now we're finally going to talk about
+the trip
+
+ align:start position:0%
+the trip
+ 
+
+ align:start position:0%
+the trip
+a bit um sort of reverting back to what
+
+ align:start position:0%
+a bit um sort of reverting back to what
+ 
+
+ align:start position:0%
+a bit um sort of reverting back to what
+Steve was talking about this lectures a
+
+ align:start position:0%
+Steve was talking about this lectures a
+ 
+
+ align:start position:0%
+Steve was talking about this lectures a
+little bouncing around intentionally so
+
+ align:start position:0%
+little bouncing around intentionally so
+ 
+
+ align:start position:0%
+little bouncing around intentionally so
+that Steve could interrupt us um so uh
+
+ align:start position:0%
+that Steve could interrupt us um so uh
+ 
+
+ align:start position:0%
+that Steve could interrupt us um so uh
+the trip goals are number one to have
+
+ align:start position:0%
+the trip goals are number one to have
+ 
+
+ align:start position:0%
+the trip goals are number one to have
+some well identified well understood and
+
+ align:start position:0%
+some well identified well understood and
+ 
+
+ align:start position:0%
+some well identified well understood and
+well documented projects um ideally
+
+ align:start position:0%
+well documented projects um ideally
+ 
+
+ align:start position:0%
+well documented projects um ideally
+highly relevant to daab energy however
+
+ align:start position:0%
+highly relevant to daab energy however
+ 
+
+ align:start position:0%
+highly relevant to daab energy however
+if you find some that are not at all
+
+ align:start position:0%
+if you find some that are not at all
+ 
+
+ align:start position:0%
+if you find some that are not at all
+energy projects but are seem like
+
+ align:start position:0%
+energy projects but are seem like
+ 
+
+ align:start position:0%
+energy projects but are seem like
+interesting projects we can often take
+
+ align:start position:0%
+interesting projects we can often take
+ 
+
+ align:start position:0%
+interesting projects we can often take
+these projects and feed them into daab
+
+ align:start position:0%
+these projects and feed them into daab
+ 
+
+ align:start position:0%
+these projects and feed them into daab
+design or other daab classes so if you
+
+ align:start position:0%
+design or other daab classes so if you
+ 
+
+ align:start position:0%
+design or other daab classes so if you
+learn about some others feel free to
+
+ align:start position:0%
+learn about some others feel free to
+ 
+
+ align:start position:0%
+learn about some others feel free to
+document them it's really helpful to
+
+ align:start position:0%
+document them it's really helpful to
+ 
+
+ align:start position:0%
+document them it's really helpful to
+daab as a community to have those extra
+
+ align:start position:0%
+daab as a community to have those extra
+ 
+
+ align:start position:0%
+daab as a community to have those extra
+projects um and then we've talked about
+
+ align:start position:0%
+projects um and then we've talked about
+ 
+
+ align:start position:0%
+projects um and then we've talked about
+a few projects for you guys there may be
+
+ align:start position:0%
+a few projects for you guys there may be
+ 
+
+ align:start position:0%
+a few projects for you guys there may be
+others that come up that are either
+
+ align:start position:0%
+others that come up that are either
+ 
+
+ align:start position:0%
+others that come up that are either
+ideal for you to work on this semester
+
+ align:start position:0%
+ideal for you to work on this semester
+ 
+
+ align:start position:0%
+ideal for you to work on this semester
+and that's fine to change course like
+
+ align:start position:0%
+and that's fine to change course like
+ 
+
+ align:start position:0%
+and that's fine to change course like
+that and or for you to um for future
+
+ align:start position:0%
+that and or for you to um for future
+ 
+
+ align:start position:0%
+that and or for you to um for future
+generations of DB energy students to
+
+ align:start position:0%
+generations of DB energy students to
+ 
+
+ align:start position:0%
+generations of DB energy students to
+work on so please document any projects
+
+ align:start position:0%
+work on so please document any projects
+ 
+
+ align:start position:0%
+work on so please document any projects
+you come across um and I will be getting
+
+ align:start position:0%
+you come across um and I will be getting
+ 
+
+ align:start position:0%
+you come across um and I will be getting
+you on Friday the sheet of how to
+
+ align:start position:0%
+you on Friday the sheet of how to
+ 
+
+ align:start position:0%
+you on Friday the sheet of how to
+document so that you have a good sense
+
+ align:start position:0%
+document so that you have a good sense
+ 
+
+ align:start position:0%
+document so that you have a good sense
+of what information you need to gather
+
+ align:start position:0%
+of what information you need to gather
+ 
+
+ align:start position:0%
+of what information you need to gather
+but hopefully we're also getting that
+
+ align:start position:0%
+but hopefully we're also getting that
+ 
+
+ align:start position:0%
+but hopefully we're also getting that
+today um second is to really understand
+
+ align:start position:0%
+today um second is to really understand
+ 
+
+ align:start position:0%
+today um second is to really understand
+the communities are working in so you
+
+ align:start position:0%
+the communities are working in so you
+ 
+
+ align:start position:0%
+the communities are working in so you
+can do a good job of Designing with and
+
+ align:start position:0%
+can do a good job of Designing with and
+ 
+
+ align:start position:0%
+can do a good job of Designing with and
+for them um what are their needs what
+
+ align:start position:0%
+for them um what are their needs what
+ 
+
+ align:start position:0%
+for them um what are their needs what
+are their finances what is their health
+
+ align:start position:0%
+are their finances what is their health
+ 
+
+ align:start position:0%
+are their finances what is their health
+their education culture government um
+
+ align:start position:0%
+their education culture government um
+ 
+
+ align:start position:0%
+their education culture government um
+both you know less critically though
+
+ align:start position:0%
+both you know less critically though
+ 
+
+ align:start position:0%
+both you know less critically though
+some somewhat critically in terms of
+
+ align:start position:0%
+some somewhat critically in terms of
+ 
+
+ align:start position:0%
+some somewhat critically in terms of
+understanding when grids arrive the
+
+ align:start position:0%
+understanding when grids arrive the
+ 
+
+ align:start position:0%
+understanding when grids arrive the
+formal government but also like the
+
+ align:start position:0%
+formal government but also like the
+ 
+
+ align:start position:0%
+formal government but also like the
+informal Community government that
+
+ align:start position:0%
+informal Community government that
+ 
+
+ align:start position:0%
+informal Community government that
+exists um and along those lines formal
+
+ align:start position:0%
+exists um and along those lines formal
+ 
+
+ align:start position:0%
+exists um and along those lines formal
+informal leaders Lifestyles um work etc
+
+ align:start position:0%
+informal leaders Lifestyles um work etc
+ 
+
+ align:start position:0%
+informal leaders Lifestyles um work etc
+and then doing the charcoal trainings SL
+
+ align:start position:0%
+and then doing the charcoal trainings SL
+ 
+
+ align:start position:0%
+and then doing the charcoal trainings SL
+creative capacity building as
+
+ align:start position:0%
+creative capacity building as
+ 
+
+ align:start position:0%
+creative capacity building as
+appropriate so I want to talk a little
+
+ align:start position:0%
+appropriate so I want to talk a little
+ 
+
+ align:start position:0%
+appropriate so I want to talk a little
+bit about creative capacity building
+
+ align:start position:0%
+bit about creative capacity building
+ 
+
+ align:start position:0%
+bit about creative capacity building
+which is a term that Amy Smith coined
+
+ align:start position:0%
+which is a term that Amy Smith coined
+ 
+
+ align:start position:0%
+which is a term that Amy Smith coined
+for the way that she um hopes that all
+
+ align:start position:0%
+for the way that she um hopes that all
+ 
+
+ align:start position:0%
+for the way that she um hopes that all
+daab groups can work so I want to talk
+
+ align:start position:0%
+daab groups can work so I want to talk
+ 
+
+ align:start position:0%
+daab groups can work so I want to talk
+about what she did um at a refugee camp
+
+ align:start position:0%
+about what she did um at a refugee camp
+ 
+
+ align:start position:0%
+about what she did um at a refugee camp
+in Uganda as an example uh so this is a
+
+ align:start position:0%
+in Uganda as an example uh so this is a
+ 
+
+ align:start position:0%
+in Uganda as an example uh so this is a
+relief camp for refugees in Uganda it
+
+ align:start position:0%
+relief camp for refugees in Uganda it
+ 
+
+ align:start position:0%
+relief camp for refugees in Uganda it
+looks kind of picturesque but each one
+
+ align:start position:0%
+looks kind of picturesque but each one
+ 
+
+ align:start position:0%
+looks kind of picturesque but each one
+of those Huts uh is about 10 or 12 ft in
+
+ align:start position:0%
+of those Huts uh is about 10 or 12 ft in
+ 
+
+ align:start position:0%
+of those Huts uh is about 10 or 12 ft in
+diameter and houses 20 people generally
+
+ align:start position:0%
+diameter and houses 20 people generally
+ 
+
+ align:start position:0%
+diameter and houses 20 people generally
+and they've been living there for 20 to
+
+ align:start position:0%
+and they've been living there for 20 to
+ 
+
+ align:start position:0%
+and they've been living there for 20 to
+30 years um so there's plenty of people
+
+ align:start position:0%
+30 years um so there's plenty of people
+ 
+
+ align:start position:0%
+30 years um so there's plenty of people
+who have grown up in this refugee camp
+
+ align:start position:0%
+who have grown up in this refugee camp
+ 
+
+ align:start position:0%
+who have grown up in this refugee camp
+um it's their choice is to be there are
+
+ align:start position:0%
+um it's their choice is to be there are
+ 
+
+ align:start position:0%
+um it's their choice is to be there are
+to be completely unsafe if they're not
+
+ align:start position:0%
+to be completely unsafe if they're not
+ 
+
+ align:start position:0%
+to be completely unsafe if they're not
+in the refugee camp um either getting
+
+ align:start position:0%
+in the refugee camp um either getting
+ 
+
+ align:start position:0%
+in the refugee camp um either getting
+killed or getting um enlisted into the
+
+ align:start position:0%
+killed or getting um enlisted into the
+ 
+
+ align:start position:0%
+killed or getting um enlisted into the
+army um and because they're in a camp
+
+ align:start position:0%
+army um and because they're in a camp
+ 
+
+ align:start position:0%
+army um and because they're in a camp
+there's really no natural resources or
+
+ align:start position:0%
+there's really no natural resources or
+ 
+
+ align:start position:0%
+there's really no natural resources or
+ability to do work so there's a real
+
+ align:start position:0%
+ability to do work so there's a real
+ 
+
+ align:start position:0%
+ability to do work so there's a real
+culture of dependency um things are
+
+ align:start position:0%
+culture of dependency um things are
+ 
+
+ align:start position:0%
+culture of dependency um things are
+finally safe enough that this group of
+
+ align:start position:0%
+finally safe enough that this group of
+ 
+
+ align:start position:0%
+finally safe enough that this group of
+people is getting and it's about 100,000
+
+ align:start position:0%
+people is getting and it's about 100,000
+ 
+
+ align:start position:0%
+people is getting and it's about 100,000
+people um group of people is getting
+
+ align:start position:0%
+people um group of people is getting
+ 
+
+ align:start position:0%
+people um group of people is getting
+ready to get repatriated back to um
+
+ align:start position:0%
+ready to get repatriated back to um
+ 
+
+ align:start position:0%
+ready to get repatriated back to um
+their original homes um but people have
+
+ align:start position:0%
+their original homes um but people have
+ 
+
+ align:start position:0%
+their original homes um but people have
+basically lived there their whole lives
+
+ align:start position:0%
+basically lived there their whole lives
+ 
+
+ align:start position:0%
+basically lived there their whole lives
+and so there's this culture of
+
+ align:start position:0%
+and so there's this culture of
+ 
+
+ align:start position:0%
+and so there's this culture of
+dependency how are we going to adjust
+
+ align:start position:0%
+dependency how are we going to adjust
+ 
+
+ align:start position:0%
+dependency how are we going to adjust
+back to home um they're used to a very
+
+ align:start position:0%
+back to home um they're used to a very
+ 
+
+ align:start position:0%
+back to home um they're used to a very
+centralized life in Camp um and
+
+ align:start position:0%
+centralized life in Camp um and
+ 
+
+ align:start position:0%
+centralized life in Camp um and
+adjusting back and especially the burden
+
+ align:start position:0%
+adjusting back and especially the burden
+ 
+
+ align:start position:0%
+adjusting back and especially the burden
+on the women going back is very high
+
+ align:start position:0%
+on the women going back is very high
+ 
+
+ align:start position:0%
+on the women going back is very high
+because all of a sudden they now have to
+
+ align:start position:0%
+because all of a sudden they now have to
+ 
+
+ align:start position:0%
+because all of a sudden they now have to
+be figuring out how to cook all the food
+
+ align:start position:0%
+be figuring out how to cook all the food
+ 
+
+ align:start position:0%
+be figuring out how to cook all the food
+get all the water get all the wood Etc
+
+ align:start position:0%
+get all the water get all the wood Etc
+ 
+
+ align:start position:0%
+get all the water get all the wood Etc
+um and there's been very little capacity
+
+ align:start position:0%
+um and there's been very little capacity
+ 
+
+ align:start position:0%
+um and there's been very little capacity
+building in this Camp up to now um so
+
+ align:start position:0%
+building in this Camp up to now um so
+ 
+
+ align:start position:0%
+building in this Camp up to now um so
+what Amy did when she was invited there
+
+ align:start position:0%
+what Amy did when she was invited there
+ 
+
+ align:start position:0%
+what Amy did when she was invited there
+um was initially do a technology
+
+ align:start position:0%
+um was initially do a technology
+ 
+
+ align:start position:0%
+um was initially do a technology
+demonstration with a sort of classic DB
+
+ align:start position:0%
+demonstration with a sort of classic DB
+ 
+
+ align:start position:0%
+demonstration with a sort of classic DB
+technology which is corn shellers and if
+
+ align:start position:0%
+technology which is corn shellers and if
+ 
+
+ align:start position:0%
+technology which is corn shellers and if
+you're curious about them they're on the
+
+ align:start position:0%
+you're curious about them they're on the
+ 
+
+ align:start position:0%
+you're curious about them they're on the
+back shelf back there so you can check
+
+ align:start position:0%
+back shelf back there so you can check
+ 
+
+ align:start position:0%
+back shelf back there so you can check
+them out but basically
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um the corn sheller uh people generally
+
+ align:start position:0%
+um the corn sheller uh people generally
+ 
+
+ align:start position:0%
+um the corn sheller uh people generally
+shell corn by hand it's really labor
+
+ align:start position:0%
+shell corn by hand it's really labor
+ 
+
+ align:start position:0%
+shell corn by hand it's really labor
+intensive and relatively painful to do
+
+ align:start position:0%
+intensive and relatively painful to do
+ 
+
+ align:start position:0%
+intensive and relatively painful to do
+because the corn is dry and it's really
+
+ align:start position:0%
+because the corn is dry and it's really
+ 
+
+ align:start position:0%
+because the corn is dry and it's really
+hard to get off um and so daab
+
+ align:start position:0%
+hard to get off um and so daab
+ 
+
+ align:start position:0%
+hard to get off um and so daab
+identified this injection molded corn
+
+ align:start position:0%
+identified this injection molded corn
+ 
+
+ align:start position:0%
+identified this injection molded corn
+sheller or something that could work in
+
+ align:start position:0%
+sheller or something that could work in
+ 
+
+ align:start position:0%
+sheller or something that could work in
+a lot of communities really well but
+
+ align:start position:0%
+a lot of communities really well but
+ 
+
+ align:start position:0%
+a lot of communities really well but
+it's really hard to injection mold at
+
+ align:start position:0%
+it's really hard to injection mold at
+ 
+
+ align:start position:0%
+it's really hard to injection mold at
+the community level it requires really
+
+ align:start position:0%
+the community level it requires really
+ 
+
+ align:start position:0%
+the community level it requires really
+high pressure and plastic neither of
+
+ align:start position:0%
+high pressure and plastic neither of
+ 
+
+ align:start position:0%
+high pressure and plastic neither of
+which are available and so daab
+
+ align:start position:0%
+which are available and so daab
+ 
+
+ align:start position:0%
+which are available and so daab
+developed two ways of making that corn
+
+ align:start position:0%
+developed two ways of making that corn
+ 
+
+ align:start position:0%
+developed two ways of making that corn
+sheller either by welding or by bending
+
+ align:start position:0%
+sheller either by welding or by bending
+ 
+
+ align:start position:0%
+sheller either by welding or by bending
+sheet metal that are really easy to make
+
+ align:start position:0%
+sheet metal that are really easy to make
+ 
+
+ align:start position:0%
+sheet metal that are really easy to make
+basically anywhere and allow people to
+
+ align:start position:0%
+basically anywhere and allow people to
+ 
+
+ align:start position:0%
+basically anywhere and allow people to
+Shell their own corn very quickly very
+
+ align:start position:0%
+Shell their own corn very quickly very
+ 
+
+ align:start position:0%
+Shell their own corn very quickly very
+affordable
+
+ align:start position:0%
+affordable
+ 
+
+ align:start position:0%
+affordable
+um and people really loved it so they
+
+ align:start position:0%
+um and people really loved it so they
+ 
+
+ align:start position:0%
+um and people really loved it so they
+they really excited um and so this is
+
+ align:start position:0%
+they really excited um and so this is
+ 
+
+ align:start position:0%
+they really excited um and so this is
+Kofi who traveled with Amy and is
+
+ align:start position:0%
+Kofi who traveled with Amy and is
+ 
+
+ align:start position:0%
+Kofi who traveled with Amy and is
+another DB staff member um they taught
+
+ align:start position:0%
+another DB staff member um they taught
+ 
+
+ align:start position:0%
+another DB staff member um they taught
+them how to make their own corn shellers
+
+ align:start position:0%
+them how to make their own corn shellers
+ 
+
+ align:start position:0%
+them how to make their own corn shellers
+and people were really pumped and so
+
+ align:start position:0%
+and people were really pumped and so
+ 
+
+ align:start position:0%
+and people were really pumped and so
+this was both just a tech transfer sort
+
+ align:start position:0%
+this was both just a tech transfer sort
+ 
+
+ align:start position:0%
+this was both just a tech transfer sort
+of like doing a charcoal demonstration
+
+ align:start position:0%
+of like doing a charcoal demonstration
+ 
+
+ align:start position:0%
+of like doing a charcoal demonstration
+I'm teaching you how to make these corn
+
+ align:start position:0%
+I'm teaching you how to make these corn
+ 
+
+ align:start position:0%
+I'm teaching you how to make these corn
+shellers and hopefully you can start
+
+ align:start position:0%
+shellers and hopefully you can start
+ 
+
+ align:start position:0%
+shellers and hopefully you can start
+making them for yourselves and using
+
+ align:start position:0%
+making them for yourselves and using
+ 
+
+ align:start position:0%
+making them for yourselves and using
+them awesome but also to start inspiring
+
+ align:start position:0%
+them awesome but also to start inspiring
+ 
+
+ align:start position:0%
+them awesome but also to start inspiring
+conversation about well what else do you
+
+ align:start position:0%
+conversation about well what else do you
+ 
+
+ align:start position:0%
+conversation about well what else do you
+need and how else could it be how could
+
+ align:start position:0%
+need and how else could it be how could
+ 
+
+ align:start position:0%
+need and how else could it be how could
+those needs be dress together um and so
+
+ align:start position:0%
+those needs be dress together um and so
+ 
+
+ align:start position:0%
+those needs be dress together um and so
+one of the projects that was discussed
+
+ align:start position:0%
+one of the projects that was discussed
+ 
+
+ align:start position:0%
+one of the projects that was discussed
+was uh grinding so grinding their corn
+
+ align:start position:0%
+was uh grinding so grinding their corn
+ 
+
+ align:start position:0%
+was uh grinding so grinding their corn
+this is a traditional grinding stone you
+
+ align:start position:0%
+this is a traditional grinding stone you
+ 
+
+ align:start position:0%
+this is a traditional grinding stone you
+can imagine how hard it is to use this
+
+ align:start position:0%
+can imagine how hard it is to use this
+ 
+
+ align:start position:0%
+can imagine how hard it is to use this
+Stone to successfully grind dried corn
+
+ align:start position:0%
+Stone to successfully grind dried corn
+ 
+
+ align:start position:0%
+Stone to successfully grind dried corn
+um how labor intensive it is and people
+
+ align:start position:0%
+um how labor intensive it is and people
+ 
+
+ align:start position:0%
+um how labor intensive it is and people
+found it uh they also or actually not
+
+ align:start position:0%
+found it uh they also or actually not
+ 
+
+ align:start position:0%
+found it uh they also or actually not
+corn excuse me they grind Sesame and
+
+ align:start position:0%
+corn excuse me they grind Sesame and
+ 
+
+ align:start position:0%
+corn excuse me they grind Sesame and
+groundnuts which are peanuts in it um
+
+ align:start position:0%
+groundnuts which are peanuts in it um
+ 
+
+ align:start position:0%
+groundnuts which are peanuts in it um
+and again it's very labor intensive so
+
+ align:start position:0%
+and again it's very labor intensive so
+ 
+
+ align:start position:0%
+and again it's very labor intensive so
+first so that was the issue posed was
+
+ align:start position:0%
+first so that was the issue posed was
+ 
+
+ align:start position:0%
+first so that was the issue posed was
+how do we grind our our uh Sesame and
+
+ align:start position:0%
+how do we grind our our uh Sesame and
+ 
+
+ align:start position:0%
+how do we grind our our uh Sesame and
+peanuts more easily and so first they
+
+ align:start position:0%
+peanuts more easily and so first they
+ 
+
+ align:start position:0%
+peanuts more easily and so first they
+looked at what the commercial method is
+
+ align:start position:0%
+looked at what the commercial method is
+ 
+
+ align:start position:0%
+looked at what the commercial method is
+in that area is a commercial grinder
+
+ align:start position:0%
+in that area is a commercial grinder
+ 
+
+ align:start position:0%
+in that area is a commercial grinder
+which requires diesel um and is totally
+
+ align:start position:0%
+which requires diesel um and is totally
+ 
+
+ align:start position:0%
+which requires diesel um and is totally
+unaffordable for this community so they
+
+ align:start position:0%
+unaffordable for this community so they
+ 
+
+ align:start position:0%
+unaffordable for this community so they
+said all right that's not going to work
+
+ align:start position:0%
+said all right that's not going to work
+ 
+
+ align:start position:0%
+said all right that's not going to work
+so let's design our own and so in a day
+
+ align:start position:0%
+so let's design our own and so in a day
+ 
+
+ align:start position:0%
+so let's design our own and so in a day
+they found a meat grinder and put
+
+ align:start position:0%
+they found a meat grinder and put
+ 
+
+ align:start position:0%
+they found a meat grinder and put
+together this really basic crappy
+
+ align:start position:0%
+together this really basic crappy
+ 
+
+ align:start position:0%
+together this really basic crappy
+prototype um and partly it was crappy
+
+ align:start position:0%
+prototype um and partly it was crappy
+ 
+
+ align:start position:0%
+prototype um and partly it was crappy
+because they had a day and partly was is
+
+ align:start position:0%
+because they had a day and partly was is
+ 
+
+ align:start position:0%
+because they had a day and partly was is
+cra happy intentionally because they
+
+ align:start position:0%
+cra happy intentionally because they
+ 
+
+ align:start position:0%
+cra happy intentionally because they
+built this with Community Partners um
+
+ align:start position:0%
+built this with Community Partners um
+ 
+
+ align:start position:0%
+built this with Community Partners um
+Amy and Kofi really took the lead but
+
+ align:start position:0%
+Amy and Kofi really took the lead but
+ 
+
+ align:start position:0%
+Amy and Kofi really took the lead but
+working very closely with the local
+
+ align:start position:0%
+working very closely with the local
+ 
+
+ align:start position:0%
+working very closely with the local
+Builders as well as the local people and
+
+ align:start position:0%
+Builders as well as the local people and
+ 
+
+ align:start position:0%
+Builders as well as the local people and
+so people got a really good sense of how
+
+ align:start position:0%
+so people got a really good sense of how
+ 
+
+ align:start position:0%
+so people got a really good sense of how
+one could develop this project really
+
+ align:start position:0%
+one could develop this project really
+ 
+
+ align:start position:0%
+one could develop this project really
+fast without the fancy MIT education
+
+ align:start position:0%
+fast without the fancy MIT education
+ 
+
+ align:start position:0%
+fast without the fancy MIT education
+that Amy brings to the table but just
+
+ align:start position:0%
+that Amy brings to the table but just
+ 
+
+ align:start position:0%
+that Amy brings to the table but just
+they got their head around oh this is
+
+ align:start position:0%
+they got their head around oh this is
+ 
+
+ align:start position:0%
+they got their head around oh this is
+how I could do this and got really
+
+ align:start position:0%
+how I could do this and got really
+ 
+
+ align:start position:0%
+how I could do this and got really
+excited and they also saw how relatively
+
+ align:start position:0%
+excited and they also saw how relatively
+ 
+
+ align:start position:0%
+excited and they also saw how relatively
+crappy this was and how there need to be
+
+ align:start position:0%
+crappy this was and how there need to be
+ 
+
+ align:start position:0%
+crappy this was and how there need to be
+improvements and so they started saying
+
+ align:start position:0%
+improvements and so they started saying
+ 
+
+ align:start position:0%
+improvements and so they started saying
+things like when I build mine I'm going
+
+ align:start position:0%
+things like when I build mine I'm going
+ 
+
+ align:start position:0%
+things like when I build mine I'm going
+to do this which is a really good
+
+ align:start position:0%
+to do this which is a really good
+ 
+
+ align:start position:0%
+to do this which is a really good
+indicator that they're now feeling
+
+ align:start position:0%
+indicator that they're now feeling
+ 
+
+ align:start position:0%
+indicator that they're now feeling
+empowered to build their own rather than
+
+ align:start position:0%
+empowered to build their own rather than
+ 
+
+ align:start position:0%
+empowered to build their own rather than
+when you come back and build me another
+
+ align:start position:0%
+when you come back and build me another
+ 
+
+ align:start position:0%
+when you come back and build me another
+one it's going to look like this right
+
+ align:start position:0%
+one it's going to look like this right
+ 
+
+ align:start position:0%
+one it's going to look like this right
+and that's that's the goal is right when
+
+ align:start position:0%
+and that's that's the goal is right when
+ 
+
+ align:start position:0%
+and that's that's the goal is right when
+I build mine rather than when you come
+
+ align:start position:0%
+I build mine rather than when you come
+ 
+
+ align:start position:0%
+I build mine rather than when you come
+back and Build Me Mine uh so people got
+
+ align:start position:0%
+back and Build Me Mine uh so people got
+ 
+
+ align:start position:0%
+back and Build Me Mine uh so people got
+really excited um and just tried it out
+
+ align:start position:0%
+really excited um and just tried it out
+ 
+
+ align:start position:0%
+really excited um and just tried it out
+um and it was a great
+
+ align:start position:0%
+um and it was a great
+ 
+
+ align:start position:0%
+um and it was a great
+outcome so uh this sort of experience
+
+ align:start position:0%
+outcome so uh this sort of experience
+ 
+
+ align:start position:0%
+outcome so uh this sort of experience
+helped Amy solidify her thinking about
+
+ align:start position:0%
+helped Amy solidify her thinking about
+ 
+
+ align:start position:0%
+helped Amy solidify her thinking about
+creative capacity building which is
+
+ align:start position:0%
+creative capacity building which is
+ 
+
+ align:start position:0%
+creative capacity building which is
+we're not there for just for Tex
+
+ align:start position:0%
+we're not there for just for Tex
+ 
+
+ align:start position:0%
+we're not there for just for Tex
+transfer we're not there just to
+
+ align:start position:0%
+transfer we're not there just to
+ 
+
+ align:start position:0%
+transfer we're not there just to
+identify problems and then come back to
+
+ align:start position:0%
+identify problems and then come back to
+ 
+
+ align:start position:0%
+identify problems and then come back to
+MIT and fix them but working with people
+
+ align:start position:0%
+MIT and fix them but working with people
+ 
+
+ align:start position:0%
+MIT and fix them but working with people
+side by side through all areas of the
+
+ align:start position:0%
+side by side through all areas of the
+ 
+
+ align:start position:0%
+side by side through all areas of the
+design process to help them develop
+
+ align:start position:0%
+design process to help them develop
+ 
+
+ align:start position:0%
+design process to help them develop
+their own solutions to problems and work
+
+ align:start position:0%
+their own solutions to problems and work
+ 
+
+ align:start position:0%
+their own solutions to problems and work
+together with them and the nature of a
+
+ align:start position:0%
+together with them and the nature of a
+ 
+
+ align:start position:0%
+together with them and the nature of a
+dlab trip going for a week and spring
+
+ align:start position:0%
+dlab trip going for a week and spring
+ 
+
+ align:start position:0%
+dlab trip going for a week and spring
+break is we can't fully achieve all of
+
+ align:start position:0%
+break is we can't fully achieve all of
+ 
+
+ align:start position:0%
+break is we can't fully achieve all of
+this but at least if we have this in
+
+ align:start position:0%
+this but at least if we have this in
+ 
+
+ align:start position:0%
+this but at least if we have this in
+mind we can achieve as much of it as
+
+ align:start position:0%
+mind we can achieve as much of it as
+ 
+
+ align:start position:0%
+mind we can achieve as much of it as
+possible um some of the amazing things
+
+ align:start position:0%
+possible um some of the amazing things
+ 
+
+ align:start position:0%
+possible um some of the amazing things
+that happened on this trip is that um
+
+ align:start position:0%
+that happened on this trip is that um
+ 
+
+ align:start position:0%
+that happened on this trip is that um
+the translator they were working with
+
+ align:start position:0%
+the translator they were working with
+ 
+
+ align:start position:0%
+the translator they were working with
+told them that they they were the first
+
+ align:start position:0%
+told them that they they were the first
+ 
+
+ align:start position:0%
+told them that they they were the first
+um foreigners that this Camp had ever
+
+ align:start position:0%
+um foreigners that this Camp had ever
+ 
+
+ align:start position:0%
+um foreigners that this Camp had ever
+seen who actually did work because most
+
+ align:start position:0%
+seen who actually did work because most
+ 
+
+ align:start position:0%
+seen who actually did work because most
+people who come to do relief work come
+
+ align:start position:0%
+people who come to do relief work come
+ 
+
+ align:start position:0%
+people who come to do relief work come
+with clipboards and do a lot of
+
+ align:start position:0%
+with clipboards and do a lot of
+ 
+
+ align:start position:0%
+with clipboards and do a lot of
+interviews and ask a lot of questions um
+
+ align:start position:0%
+interviews and ask a lot of questions um
+ 
+
+ align:start position:0%
+interviews and ask a lot of questions um
+this is not to attack all relief work
+
+ align:start position:0%
+this is not to attack all relief work
+ 
+
+ align:start position:0%
+this is not to attack all relief work
+right there's a lot of groly work that
+
+ align:start position:0%
+right there's a lot of groly work that
+ 
+
+ align:start position:0%
+right there's a lot of groly work that
+goes on but there's also a lot of
+
+ align:start position:0%
+goes on but there's also a lot of
+ 
+
+ align:start position:0%
+goes on but there's also a lot of
+clipboard question asking and there's a
+
+ align:start position:0%
+clipboard question asking and there's a
+ 
+
+ align:start position:0%
+clipboard question asking and there's a
+need for that but um actually having
+
+ align:start position:0%
+need for that but um actually having
+ 
+
+ align:start position:0%
+need for that but um actually having
+people come and do work and work side by
+
+ align:start position:0%
+people come and do work and work side by
+ 
+
+ align:start position:0%
+people come and do work and work side by
+side is pretty
+
+ align:start position:0%
+side is pretty
+ 
+
+ align:start position:0%
+side is pretty
+valuable so for example here's Kofi
+
+ align:start position:0%
+valuable so for example here's Kofi
+ 
+
+ align:start position:0%
+valuable so for example here's Kofi
+chopping wood for making fires because
+
+ align:start position:0%
+chopping wood for making fires because
+ 
+
+ align:start position:0%
+chopping wood for making fires because
+that's what needed to be done so he
+
+ align:start position:0%
+that's what needed to be done so he
+ 
+
+ align:start position:0%
+that's what needed to be done so he
+helped out doing it and that's the kind
+
+ align:start position:0%
+helped out doing it and that's the kind
+ 
+
+ align:start position:0%
+helped out doing it and that's the kind
+of thing that you might start to do when
+
+ align:start position:0%
+of thing that you might start to do when
+ 
+
+ align:start position:0%
+of thing that you might start to do when
+you're in your community next week um
+
+ align:start position:0%
+you're in your community next week um
+ 
+
+ align:start position:0%
+you're in your community next week um
+however you don't see a picture of Amy
+
+ align:start position:0%
+however you don't see a picture of Amy
+ 
+
+ align:start position:0%
+however you don't see a picture of Amy
+chopping wood but you do see a picture
+
+ align:start position:0%
+chopping wood but you do see a picture
+ 
+
+ align:start position:0%
+chopping wood but you do see a picture
+of Amy helping sweep up after their
+
+ align:start position:0%
+of Amy helping sweep up after their
+ 
+
+ align:start position:0%
+of Amy helping sweep up after their
+demonstration um and why is that well
+
+ align:start position:0%
+demonstration um and why is that well
+ 
+
+ align:start position:0%
+demonstration um and why is that well
+it's totally culturally inappropriate
+
+ align:start position:0%
+it's totally culturally inappropriate
+ 
+
+ align:start position:0%
+it's totally culturally inappropriate
+for Amy to chop wood this would be
+
+ align:start position:0%
+for Amy to chop wood this would be
+ 
+
+ align:start position:0%
+for Amy to chop wood this would be
+inappropriate for Kofi to help sweep up
+
+ align:start position:0%
+inappropriate for Kofi to help sweep up
+ 
+
+ align:start position:0%
+inappropriate for Kofi to help sweep up
+and so while it's great to break down
+
+ align:start position:0%
+and so while it's great to break down
+ 
+
+ align:start position:0%
+and so while it's great to break down
+gender barriers at some level you also
+
+ align:start position:0%
+gender barriers at some level you also
+ 
+
+ align:start position:0%
+gender barriers at some level you also
+need to be respectful and so Amy will
+
+ align:start position:0%
+need to be respectful and so Amy will
+ 
+
+ align:start position:0%
+need to be respectful and so Amy will
+happily chop firewood when given the
+
+ align:start position:0%
+happily chop firewood when given the
+ 
+
+ align:start position:0%
+happily chop firewood when given the
+opportunity but if it's totally
+
+ align:start position:0%
+opportunity but if it's totally
+ 
+
+ align:start position:0%
+opportunity but if it's totally
+inappropriate she won't and vice versa
+
+ align:start position:0%
+inappropriate she won't and vice versa
+ 
+
+ align:start position:0%
+inappropriate she won't and vice versa
+so it's a balancing act about helping
+
+ align:start position:0%
+so it's a balancing act about helping
+ 
+
+ align:start position:0%
+so it's a balancing act about helping
+people um but also being respectful of
+
+ align:start position:0%
+people um but also being respectful of
+ 
+
+ align:start position:0%
+people um but also being respectful of
+what's appropriate so it can be very
+
+ align:start position:0%
+what's appropriate so it can be very
+ 
+
+ align:start position:0%
+what's appropriate so it can be very
+easy in communities to let people just
+
+ align:start position:0%
+easy in communities to let people just
+ 
+
+ align:start position:0%
+easy in communities to let people just
+help you people will be really kind and
+
+ align:start position:0%
+help you people will be really kind and
+ 
+
+ align:start position:0%
+help you people will be really kind and
+gracious and serve you and it's really
+
+ align:start position:0%
+gracious and serve you and it's really
+ 
+
+ align:start position:0%
+gracious and serve you and it's really
+important to make sure that you're
+
+ align:start position:0%
+important to make sure that you're
+ 
+
+ align:start position:0%
+important to make sure that you're
+acting as a community member working
+
+ align:start position:0%
+acting as a community member working
+ 
+
+ align:start position:0%
+acting as a community member working
+rather than someone who's a visitor or
+
+ align:start position:0%
+rather than someone who's a visitor or
+ 
+
+ align:start position:0%
+rather than someone who's a visitor or
+guest even though you are um only being
+
+ align:start position:0%
+guest even though you are um only being
+ 
+
+ align:start position:0%
+guest even though you are um only being
+helped
+
+ align:start position:0%
+helped
+ 
+
+ align:start position:0%
+helped
+um and the general rule of thumb is that
+
+ align:start position:0%
+um and the general rule of thumb is that
+ 
+
+ align:start position:0%
+um and the general rule of thumb is that
+Amy likes to say is people are people so
+
+ align:start position:0%
+Amy likes to say is people are people so
+ 
+
+ align:start position:0%
+Amy likes to say is people are people so
+if you you would help someone out here
+
+ align:start position:0%
+if you you would help someone out here
+ 
+
+ align:start position:0%
+if you you would help someone out here
+doing something you should do it there
+
+ align:start position:0%
+doing something you should do it there
+ 
+
+ align:start position:0%
+doing something you should do it there
+um and vice versa if you'd be really
+
+ align:start position:0%
+um and vice versa if you'd be really
+ 
+
+ align:start position:0%
+um and vice versa if you'd be really
+uncomfortable helping X here then you
+
+ align:start position:0%
+uncomfortable helping X here then you
+ 
+
+ align:start position:0%
+uncomfortable helping X here then you
+don't need to be force yourself to be
+
+ align:start position:0%
+don't need to be force yourself to be
+ 
+
+ align:start position:0%
+don't need to be force yourself to be
+super uncomfortable there um some of the
+
+ align:start position:0%
+super uncomfortable there um some of the
+ 
+
+ align:start position:0%
+super uncomfortable there um some of the
+advantages of doing this sort of
+
+ align:start position:0%
+advantages of doing this sort of
+ 
+
+ align:start position:0%
+advantages of doing this sort of
+participatory work are it's efficient
+
+ align:start position:0%
+participatory work are it's efficient
+ 
+
+ align:start position:0%
+participatory work are it's efficient
+and that's a sort of deceptive thing to
+
+ align:start position:0%
+and that's a sort of deceptive thing to
+ 
+
+ align:start position:0%
+and that's a sort of deceptive thing to
+say it's efficient because it takes a
+
+ align:start position:0%
+say it's efficient because it takes a
+ 
+
+ align:start position:0%
+say it's efficient because it takes a
+long time and can be really frustrating
+
+ align:start position:0%
+long time and can be really frustrating
+ 
+
+ align:start position:0%
+long time and can be really frustrating
+however if you're delivering a product
+
+ align:start position:0%
+however if you're delivering a product
+ 
+
+ align:start position:0%
+however if you're delivering a product
+that no one actually needs or is excited
+
+ align:start position:0%
+that no one actually needs or is excited
+ 
+
+ align:start position:0%
+that no one actually needs or is excited
+about then there's a real loss of
+
+ align:start position:0%
+about then there's a real loss of
+ 
+
+ align:start position:0%
+about then there's a real loss of
+efficiency there by not working with
+
+ align:start position:0%
+efficiency there by not working with
+ 
+
+ align:start position:0%
+efficiency there by not working with
+them in the first place um and similarly
+
+ align:start position:0%
+them in the first place um and similarly
+ 
+
+ align:start position:0%
+them in the first place um and similarly
+it can be effective to really work with
+
+ align:start position:0%
+it can be effective to really work with
+ 
+
+ align:start position:0%
+it can be effective to really work with
+people and get something that's really
+
+ align:start position:0%
+people and get something that's really
+ 
+
+ align:start position:0%
+people and get something that's really
+valuable um it can help transition
+
+ align:start position:0%
+valuable um it can help transition
+ 
+
+ align:start position:0%
+valuable um it can help transition
+people to a level of self-reliance they
+
+ align:start position:0%
+people to a level of self-reliance they
+ 
+
+ align:start position:0%
+people to a level of self-reliance they
+didn't have previously and help um your
+
+ align:start position:0%
+didn't have previously and help um your
+ 
+
+ align:start position:0%
+didn't have previously and help um your
+projects and the work become sustainable
+
+ align:start position:0%
+projects and the work become sustainable
+ 
+
+ align:start position:0%
+projects and the work become sustainable
+um some of the disadvantages are it's
+
+ align:start position:0%
+um some of the disadvantages are it's
+ 
+
+ align:start position:0%
+um some of the disadvantages are it's
+slow it takes a long time um it requires
+
+ align:start position:0%
+slow it takes a long time um it requires
+ 
+
+ align:start position:0%
+slow it takes a long time um it requires
+a lot of human and material resources
+
+ align:start position:0%
+a lot of human and material resources
+ 
+
+ align:start position:0%
+a lot of human and material resources
+potentially there's a lot of
+
+ align:start position:0%
+potentially there's a lot of
+ 
+
+ align:start position:0%
+potentially there's a lot of
+unpredictability as most teams have
+
+ align:start position:0%
+unpredictability as most teams have
+ 
+
+ align:start position:0%
+unpredictability as most teams have
+already experienced and if you haven't
+
+ align:start position:0%
+already experienced and if you haven't
+ 
+
+ align:start position:0%
+already experienced and if you haven't
+you will experience um and you have to
+
+ align:start position:0%
+you will experience um and you have to
+ 
+
+ align:start position:0%
+you will experience um and you have to
+be able to just roll with that
+
+ align:start position:0%
+be able to just roll with that
+ 
+
+ align:start position:0%
+be able to just roll with that
+unpredictability rather than getting
+
+ align:start position:0%
+unpredictability rather than getting
+ 
+
+ align:start position:0%
+unpredictability rather than getting
+super frustrated by it I mean you will
+
+ align:start position:0%
+super frustrated by it I mean you will
+ 
+
+ align:start position:0%
+super frustrated by it I mean you will
+get super frustrated by it but not
+
+ align:start position:0%
+get super frustrated by it but not
+ 
+
+ align:start position:0%
+get super frustrated by it but not
+letting that frustration be the dominant
+
+ align:start position:0%
+letting that frustration be the dominant
+ 
+
+ align:start position:0%
+letting that frustration be the dominant
+experience um and then finally ex
+
+ align:start position:0%
+experience um and then finally ex
+ 
+
+ align:start position:0%
+experience um and then finally ex
+managing expectations both of not um
+
+ align:start position:0%
+managing expectations both of not um
+ 
+
+ align:start position:0%
+managing expectations both of not um
+getting your Community Partners thinking
+
+ align:start position:0%
+getting your Community Partners thinking
+ 
+
+ align:start position:0%
+getting your Community Partners thinking
+that you're going to do something
+
+ align:start position:0%
+that you're going to do something
+ 
+
+ align:start position:0%
+that you're going to do something
+magical that isn't actually Within in
+
+ align:start position:0%
+magical that isn't actually Within in
+ 
+
+ align:start position:0%
+magical that isn't actually Within in
+your power or vice versa you yourself
+
+ align:start position:0%
+your power or vice versa you yourself
+ 
+
+ align:start position:0%
+your power or vice versa you yourself
+thinking you're going to be doing
+
+ align:start position:0%
+thinking you're going to be doing
+ 
+
+ align:start position:0%
+thinking you're going to be doing
+something amazing that's actually not
+
+ align:start position:0%
+something amazing that's actually not
+ 
+
+ align:start position:0%
+something amazing that's actually not
+reasonable to expect in the time and
+
+ align:start position:0%
+reasonable to expect in the time and
+ 
+
+ align:start position:0%
+reasonable to expect in the time and
+with the resources you
+
+ align:start position:0%
+with the resources you
+ 
+
+ align:start position:0%
+with the resources you
+have
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh so the typical design process is
+
+ align:start position:0%
+uh so the typical design process is
+ 
+
+ align:start position:0%
+uh so the typical design process is
+you're trying to go from a problem to
+
+ align:start position:0%
+you're trying to go from a problem to
+ 
+
+ align:start position:0%
+you're trying to go from a problem to
+solution and you generally go through
+
+ align:start position:0%
+solution and you generally go through
+ 
+
+ align:start position:0%
+solution and you generally go through
+generating ideas evaluating them
+
+ align:start position:0%
+generating ideas evaluating them
+ 
+
+ align:start position:0%
+generating ideas evaluating them
+designing in more detail actually
+
+ align:start position:0%
+designing in more detail actually
+ 
+
+ align:start position:0%
+designing in more detail actually
+building testing and evaluation it's not
+
+ align:start position:0%
+building testing and evaluation it's not
+ 
+
+ align:start position:0%
+building testing and evaluation it's not
+actually the L linear of course but
+
+ align:start position:0%
+actually the L linear of course but
+ 
+
+ align:start position:0%
+actually the L linear of course but
+that's the general idea and so
+
+ align:start position:0%
+that's the general idea and so
+ 
+
+ align:start position:0%
+that's the general idea and so
+traditionally
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um you would involve communities just at
+
+ align:start position:0%
+um you would involve communities just at
+ 
+
+ align:start position:0%
+um you would involve communities just at
+the end um and that's obviously not
+
+ align:start position:0%
+the end um and that's obviously not
+ 
+
+ align:start position:0%
+the end um and that's obviously not
+ideal for all the reasons we've talked
+
+ align:start position:0%
+ideal for all the reasons we've talked
+ 
+
+ align:start position:0%
+ideal for all the reasons we've talked
+about and so then hopefully you involve
+
+ align:start position:0%
+about and so then hopefully you involve
+ 
+
+ align:start position:0%
+about and so then hopefully you involve
+them in the beginning and the idea of
+
+ align:start position:0%
+them in the beginning and the idea of
+ 
+
+ align:start position:0%
+them in the beginning and the idea of
+co-creation is that you're involving
+
+ align:start position:0%
+co-creation is that you're involving
+ 
+
+ align:start position:0%
+co-creation is that you're involving
+your community throughout all stages and
+
+ align:start position:0%
+your community throughout all stages and
+ 
+
+ align:start position:0%
+your community throughout all stages and
+so one thing to talk about when you are
+
+ align:start position:0%
+so one thing to talk about when you are
+ 
+
+ align:start position:0%
+so one thing to talk about when you are
+there is all right I'm not going to be
+
+ align:start position:0%
+there is all right I'm not going to be
+ 
+
+ align:start position:0%
+there is all right I'm not going to be
+here for the next few weeks while I'm
+
+ align:start position:0%
+here for the next few weeks while I'm
+ 
+
+ align:start position:0%
+here for the next few weeks while I'm
+doing all these steps how can I stay
+
+ align:start position:0%
+doing all these steps how can I stay
+ 
+
+ align:start position:0%
+doing all these steps how can I stay
+connected with you what's the best way
+
+ align:start position:0%
+connected with you what's the best way
+ 
+
+ align:start position:0%
+connected with you what's the best way
+way to be in contact with you um so that
+
+ align:start position:0%
+way to be in contact with you um so that
+ 
+
+ align:start position:0%
+way to be in contact with you um so that
+you can involve your Community Partners
+
+ align:start position:0%
+you can involve your Community Partners
+ 
+
+ align:start position:0%
+you can involve your Community Partners
+as much as
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+possible there any questions about all
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that yeah you like with the like we have
+
+ align:start position:0%
+that yeah you like with the like we have
+ 
+
+ align:start position:0%
+that yeah you like with the like we have
+Lindsay do you mean with the people
+
+ align:start position:0%
+Lindsay do you mean with the people
+ 
+
+ align:start position:0%
+Lindsay do you mean with the people
+there like with so everyone so Lindsay
+
+ align:start position:0%
+there like with so everyone so Lindsay
+ 
+
+ align:start position:0%
+there like with so everyone so Lindsay
+is both really useful as a goet um but
+
+ align:start position:0%
+is both really useful as a goet um but
+ 
+
+ align:start position:0%
+is both really useful as a goet um but
+she also can't answer all the questions
+
+ align:start position:0%
+she also can't answer all the questions
+ 
+
+ align:start position:0%
+she also can't answer all the questions
+that you are going to have um because L
+
+ align:start position:0%
+that you are going to have um because L
+ 
+
+ align:start position:0%
+that you are going to have um because L
+Lindsay is one of the organizers of
+
+ align:start position:0%
+Lindsay is one of the organizers of
+ 
+
+ align:start position:0%
+Lindsay is one of the organizers of
+group of Phoenix um and so Lindsay may
+
+ align:start position:0%
+group of Phoenix um and so Lindsay may
+ 
+
+ align:start position:0%
+group of Phoenix um and so Lindsay may
+be the person you need to use to get the
+
+ align:start position:0%
+be the person you need to use to get the
+ 
+
+ align:start position:0%
+be the person you need to use to get the
+answers from the women you're working
+
+ align:start position:0%
+answers from the women you're working
+ 
+
+ align:start position:0%
+answers from the women you're working
+with but you can't just rely on Lindsay
+
+ align:start position:0%
+with but you can't just rely on Lindsay
+ 
+
+ align:start position:0%
+with but you can't just rely on Lindsay
+um reasonably but she may be the best
+
+ align:start position:0%
+um reasonably but she may be the best
+ 
+
+ align:start position:0%
+um reasonably but she may be the best
+way to get
+
+ align:start position:0%
+way to get
+ 
+
+ align:start position:0%
+way to get
+information so speaking of information
+
+ align:start position:0%
+information so speaking of information
+ 
+
+ align:start position:0%
+information so speaking of information
+um I want to talk a little bit about
+
+ align:start position:0%
+um I want to talk a little bit about
+ 
+
+ align:start position:0%
+um I want to talk a little bit about
+what the barriers are to getting in good
+
+ align:start position:0%
+what the barriers are to getting in good
+ 
+
+ align:start position:0%
+what the barriers are to getting in good
+information and some of the methods so
+
+ align:start position:0%
+information and some of the methods so
+ 
+
+ align:start position:0%
+information and some of the methods so
+what makes getting good information hard
+
+ align:start position:0%
+what makes getting good information hard
+ 
+
+ align:start position:0%
+what makes getting good information hard
+and what would you do to get good
+
+ align:start position:0%
+and what would you do to get good
+ 
+
+ align:start position:0%
+and what would you do to get good
+information and by information I mean
+
+ align:start position:0%
+information and by information I mean
+ 
+
+ align:start position:0%
+information and by information I mean
+learning you know is this uh solar
+
+ align:start position:0%
+learning you know is this uh solar
+ 
+
+ align:start position:0%
+learning you know is this uh solar
+cooker design actually a good idea uh
+
+ align:start position:0%
+cooker design actually a good idea uh
+ 
+
+ align:start position:0%
+cooker design actually a good idea uh
+how often do you cook with the solar
+
+ align:start position:0%
+how often do you cook with the solar
+ 
+
+ align:start position:0%
+how often do you cook with the solar
+cooker etc etc so
+
+ align:start position:0%
+cooker etc etc so
+ 
+
+ align:start position:0%
+cooker etc etc so
+yeah language language
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah what else
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+whichever reiteration of ask the
+
+ align:start position:0%
+whichever reiteration of ask the
+ 
+
+ align:start position:0%
+whichever reiteration of ask the
+question multiple times to make sure you
+
+ align:start position:0%
+question multiple times to make sure you
+ 
+
+ align:start position:0%
+question multiple times to make sure you
+get
+
+ align:start position:0%
+get
+ 
+
+ align:start position:0%
+get
+answer another way that would be
+
+ align:start position:0%
+answer another way that would be
+ 
+
+ align:start position:0%
+answer another way that would be
+physical experience firstand experience
+
+ align:start position:0%
+physical experience firstand experience
+ 
+
+ align:start position:0%
+physical experience firstand experience
+not firstand but
+
+ align:start position:0%
+not firstand but
+ 
+
+ align:start position:0%
+not firstand but
+just well I think both actually
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+what
+
+ align:start position:0%
+what
+ 
+
+ align:start position:0%
+what
+else cultural
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yep
+
+ align:start position:0%
+yep
+ 
+
+ align:start position:0%
+yep
+that teaming
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+I think sometimes you might run into
+
+ align:start position:0%
+I think sometimes you might run into
+ 
+
+ align:start position:0%
+I think sometimes you might run into
+like some people think one thing but
+
+ align:start position:0%
+like some people think one thing but
+ 
+
+ align:start position:0%
+like some people think one thing but
+some people think another so having to
+
+ align:start position:0%
+some people think another so having to
+ 
+
+ align:start position:0%
+some people think another so having to
+like figure out get an over El
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+just yeah
+
+ align:start position:0%
+just yeah
+ 
+
+ align:start position:0%
+just yeah
+absolutely I think time is an issue
+
+ align:start position:0%
+absolutely I think time is an issue
+ 
+
+ align:start position:0%
+absolutely I think time is an issue
+since what we did for one week and we're
+
+ align:start position:0%
+since what we did for one week and we're
+ 
+
+ align:start position:0%
+since what we did for one week and we're
+all very ambitious we want to get the
+
+ align:start position:0%
+all very ambitious we want to get the
+ 
+
+ align:start position:0%
+all very ambitious we want to get the
+most out of it
+
+ align:start position:0%
+most out of it
+ 
+
+ align:start position:0%
+most out of it
+and maybe like we'll want to like kind
+
+ align:start position:0%
+and maybe like we'll want to like kind
+ 
+
+ align:start position:0%
+and maybe like we'll want to like kind
+of bypass small little things into them
+
+ align:start position:0%
+of bypass small little things into them
+ 
+
+ align:start position:0%
+of bypass small little things into them
+may make a big difference like
+
+ align:start position:0%
+may make a big difference like
+ 
+
+ align:start position:0%
+may make a big difference like
+introducing ourselves and making that
+
+ align:start position:0%
+introducing ourselves and making that
+ 
+
+ align:start position:0%
+introducing ourselves and making that
+establishing the personal contact that
+
+ align:start position:0%
+establishing the personal contact that
+ 
+
+ align:start position:0%
+establishing the personal contact that
+this guy didn't have yeah yeah you can
+
+ align:start position:0%
+this guy didn't have yeah yeah you can
+ 
+
+ align:start position:0%
+this guy didn't have yeah yeah you can
+get much better information from people
+
+ align:start position:0%
+get much better information from people
+ 
+
+ align:start position:0%
+get much better information from people
+if you actually spend the time to do the
+
+ align:start position:0%
+if you actually spend the time to do the
+ 
+
+ align:start position:0%
+if you actually spend the time to do the
+introductions and thankfully for you
+
+ align:start position:0%
+introductions and thankfully for you
+ 
+
+ align:start position:0%
+introductions and thankfully for you
+guys you're not in a community where
+
+ align:start position:0%
+guys you're not in a community where
+ 
+
+ align:start position:0%
+guys you're not in a community where
+it's traditional to spend like an hour
+
+ align:start position:0%
+it's traditional to spend like an hour
+ 
+
+ align:start position:0%
+it's traditional to spend like an hour
+doing the introd introductions and how
+
+ align:start position:0%
+doing the introd introductions and how
+ 
+
+ align:start position:0%
+doing the introd introductions and how
+is your family and this and that in
+
+ align:start position:0%
+is your family and this and that in
+ 
+
+ align:start position:0%
+is your family and this and that in
+Nicaragua at least in these areas is
+
+ align:start position:0%
+Nicaragua at least in these areas is
+ 
+
+ align:start position:0%
+Nicaragua at least in these areas is
+people are used to doing things a little
+
+ align:start position:0%
+people are used to doing things a little
+ 
+
+ align:start position:0%
+people are used to doing things a little
+more quickly but doing the Steve Ray
+
+ align:start position:0%
+more quickly but doing the Steve Ray
+ 
+
+ align:start position:0%
+more quickly but doing the Steve Ray
+approach not his approach but what he
+
+ align:start position:0%
+approach not his approach but what he
+ 
+
+ align:start position:0%
+approach not his approach but what he
+did of barging right in and being like
+
+ align:start position:0%
+did of barging right in and being like
+ 
+
+ align:start position:0%
+did of barging right in and being like
+oh let me see your shoelaces is probably
+
+ align:start position:0%
+oh let me see your shoelaces is probably
+ 
+
+ align:start position:0%
+oh let me see your shoelaces is probably
+not the best um spending the time to
+
+ align:start position:0%
+not the best um spending the time to
+ 
+
+ align:start position:0%
+not the best um spending the time to
+introduce yourself and get to know
+
+ align:start position:0%
+introduce yourself and get to know
+ 
+
+ align:start position:0%
+introduce yourself and get to know
+people a little bit it's definitely
+
+ align:start position:0%
+people a little bit it's definitely
+ 
+
+ align:start position:0%
+people a little bit it's definitely
+going to
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+help okay
+
+ align:start position:0%
+help okay
+ 
+
+ align:start position:0%
+help okay
+so gender
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yep n doesn't have very much of like men
+
+ align:start position:0%
+yep n doesn't have very much of like men
+ 
+
+ align:start position:0%
+yep n doesn't have very much of like men
+over women kind of
+
+ align:start position:0%
+over women kind of
+ 
+
+ align:start position:0%
+over women kind of
+it depends who you talk to um but I
+
+ align:start position:0%
+it depends who you talk to um but I
+ 
+
+ align:start position:0%
+it depends who you talk to um but I
+would say it's not as Extreme as other
+
+ align:start position:0%
+would say it's not as Extreme as other
+ 
+
+ align:start position:0%
+would say it's not as Extreme as other
+places age going be a problem like are
+
+ align:start position:0%
+places age going be a problem like are
+ 
+
+ align:start position:0%
+places age going be a problem like are
+they going to have trouble respect
+
+ align:start position:0%
+they going to have trouble respect
+ 
+
+ align:start position:0%
+they going to have trouble respect
+people that are younger than them um I
+
+ align:start position:0%
+people that are younger than them um I
+ 
+
+ align:start position:0%
+people that are younger than them um I
+don't know it could be I didn't
+
+ align:start position:0%
+don't know it could be I didn't
+ 
+
+ align:start position:0%
+don't know it could be I didn't
+encounter it as a big issue but it's
+
+ align:start position:0%
+encounter it as a big issue but it's
+ 
+
+ align:start position:0%
+encounter it as a big issue but it's
+it's always a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+possibility so some of the issues I have
+
+ align:start position:0%
+possibility so some of the issues I have
+ 
+
+ align:start position:0%
+possibility so some of the issues I have
+encountered myself are so yes the
+
+ align:start position:0%
+encountered myself are so yes the
+ 
+
+ align:start position:0%
+encountered myself are so yes the
+language and some sometimes you deal
+
+ align:start position:0%
+language and some sometimes you deal
+ 
+
+ align:start position:0%
+language and some sometimes you deal
+with that with the translator whether
+
+ align:start position:0%
+with that with the translator whether
+ 
+
+ align:start position:0%
+with that with the translator whether
+it's someone on your team or someone on
+
+ align:start position:0%
+it's someone on your team or someone on
+ 
+
+ align:start position:0%
+it's someone on your team or someone on
+your in your community organization is
+
+ align:start position:0%
+your in your community organization is
+ 
+
+ align:start position:0%
+your in your community organization is
+helping um educational backgrounds are
+
+ align:start position:0%
+helping um educational backgrounds are
+ 
+
+ align:start position:0%
+helping um educational backgrounds are
+different cultural backgrounds are
+
+ align:start position:0%
+different cultural backgrounds are
+ 
+
+ align:start position:0%
+different cultural backgrounds are
+different people tell you what you want
+
+ align:start position:0%
+different people tell you what you want
+ 
+
+ align:start position:0%
+different people tell you what you want
+to hear what they think you want to hear
+
+ align:start position:0%
+to hear what they think you want to hear
+ 
+
+ align:start position:0%
+to hear what they think you want to hear
+as opposed to what you actually want to
+
+ align:start position:0%
+as opposed to what you actually want to
+ 
+
+ align:start position:0%
+as opposed to what you actually want to
+hear um and you may be easily talking to
+
+ align:start position:0%
+hear um and you may be easily talking to
+ 
+
+ align:start position:0%
+hear um and you may be easily talking to
+the wrong person so to get into those a
+
+ align:start position:0%
+the wrong person so to get into those a
+ 
+
+ align:start position:0%
+the wrong person so to get into those a
+little more so language obviously um is
+
+ align:start position:0%
+little more so language obviously um is
+ 
+
+ align:start position:0%
+little more so language obviously um is
+challenging and when you use a
+
+ align:start position:0%
+challenging and when you use a
+ 
+
+ align:start position:0%
+challenging and when you use a
+translator there's often times where you
+
+ align:start position:0%
+translator there's often times where you
+ 
+
+ align:start position:0%
+translator there's often times where you
+ask a question that you know Tak you 2
+
+ align:start position:0%
+ask a question that you know Tak you 2
+ 
+
+ align:start position:0%
+ask a question that you know Tak you 2
+minutes to say and the translator asks a
+
+ align:start position:0%
+minutes to say and the translator asks a
+ 
+
+ align:start position:0%
+minutes to say and the translator asks a
+1 second question and then the person
+
+ align:start position:0%
+1 second question and then the person
+ 
+
+ align:start position:0%
+1 second question and then the person
+responds by talking for three minutes
+
+ align:start position:0%
+responds by talking for three minutes
+ 
+
+ align:start position:0%
+responds by talking for three minutes
+and the translator says
+
+ align:start position:0%
+and the translator says
+ 
+
+ align:start position:0%
+and the translator says
+yes um and that can be really
+
+ align:start position:0%
+yes um and that can be really
+ 
+
+ align:start position:0%
+yes um and that can be really
+frustrating and at the same time you're
+
+ align:start position:0%
+frustrating and at the same time you're
+ 
+
+ align:start position:0%
+frustrating and at the same time you're
+completely beholden to your translator
+
+ align:start position:0%
+completely beholden to your translator
+ 
+
+ align:start position:0%
+completely beholden to your translator
+so if you take them outside and yell at
+
+ align:start position:0%
+so if you take them outside and yell at
+ 
+
+ align:start position:0%
+so if you take them outside and yell at
+them I mean I don't think that's going
+
+ align:start position:0%
+them I mean I don't think that's going
+ 
+
+ align:start position:0%
+them I mean I don't think that's going
+to happen right but if that you know if
+
+ align:start position:0%
+to happen right but if that you know if
+ 
+
+ align:start position:0%
+to happen right but if that you know if
+you took a really pissed-off approach to
+
+ align:start position:0%
+you took a really pissed-off approach to
+ 
+
+ align:start position:0%
+you took a really pissed-off approach to
+this the effect would be um even worse
+
+ align:start position:0%
+this the effect would be um even worse
+ 
+
+ align:start position:0%
+this the effect would be um even worse
+response from your translation
+
+ align:start position:0%
+response from your translation
+ 
+
+ align:start position:0%
+response from your translation
+um educational backgrounds so what I
+
+ align:start position:0%
+um educational backgrounds so what I
+ 
+
+ align:start position:0%
+um educational backgrounds so what I
+mean by that is that most of us are
+
+ align:start position:0%
+mean by that is that most of us are
+ 
+
+ align:start position:0%
+mean by that is that most of us are
+pretty used to talking in watts in
+
+ align:start position:0%
+pretty used to talking in watts in
+ 
+
+ align:start position:0%
+pretty used to talking in watts in
+jewels in inches whatever in units and
+
+ align:start position:0%
+jewels in inches whatever in units and
+ 
+
+ align:start position:0%
+jewels in inches whatever in units and
+just with a math sense and if you
+
+ align:start position:0%
+just with a math sense and if you
+ 
+
+ align:start position:0%
+just with a math sense and if you
+haven't had a math education you may
+
+ align:start position:0%
+haven't had a math education you may
+ 
+
+ align:start position:0%
+haven't had a math education you may
+have a really intuitive understanding of
+
+ align:start position:0%
+have a really intuitive understanding of
+ 
+
+ align:start position:0%
+have a really intuitive understanding of
+all those Concepts but you don't
+
+ align:start position:0%
+all those Concepts but you don't
+ 
+
+ align:start position:0%
+all those Concepts but you don't
+actually have the language the same
+
+ align:start position:0%
+actually have the language the same
+ 
+
+ align:start position:0%
+actually have the language the same
+language um so it's not a Spanish versus
+
+ align:start position:0%
+language um so it's not a Spanish versus
+ 
+
+ align:start position:0%
+language um so it's not a Spanish versus
+English barrier it's a educational
+
+ align:start position:0%
+English barrier it's a educational
+ 
+
+ align:start position:0%
+English barrier it's a educational
+language barrier and so you are it's
+
+ align:start position:0%
+language barrier and so you are it's
+ 
+
+ align:start position:0%
+language barrier and so you are it's
+beholden on you when some you say well
+
+ align:start position:0%
+beholden on you when some you say well
+ 
+
+ align:start position:0%
+beholden on you when some you say well
+how long long is that expecting 3 in and
+
+ align:start position:0%
+how long long is that expecting 3 in and
+ 
+
+ align:start position:0%
+how long long is that expecting 3 in and
+someone you know answers like you know
+
+ align:start position:0%
+someone you know answers like you know
+ 
+
+ align:start position:0%
+someone you know answers like you know
+some other analogy figuring out how to
+
+ align:start position:0%
+some other analogy figuring out how to
+ 
+
+ align:start position:0%
+some other analogy figuring out how to
+translate that rather than saying well
+
+ align:start position:0%
+translate that rather than saying well
+ 
+
+ align:start position:0%
+translate that rather than saying well
+is that 6 in or 8 in right because
+
+ align:start position:0%
+is that 6 in or 8 in right because
+ 
+
+ align:start position:0%
+is that 6 in or 8 in right because
+that's not going to give you very useful
+
+ align:start position:0%
+that's not going to give you very useful
+ 
+
+ align:start position:0%
+that's not going to give you very useful
+information and they do
+
+ align:start position:0%
+information and they do
+ 
+
+ align:start position:0%
+information and they do
+cim I saw both really
+
+ align:start position:0%
+cim I saw both really
+ 
+
+ align:start position:0%
+cim I saw both really
+yeah um but a lot of it is without
+
+ align:start position:0%
+yeah um but a lot of it is without
+ 
+
+ align:start position:0%
+yeah um but a lot of it is without
+standard units too like a lot of people
+
+ align:start position:0%
+standard units too like a lot of people
+ 
+
+ align:start position:0%
+standard units too like a lot of people
+just aren't used to units and units of
+
+ align:start position:0%
+just aren't used to units and units of
+ 
+
+ align:start position:0%
+just aren't used to units and units of
+measure like um what you're used to um
+
+ align:start position:0%
+measure like um what you're used to um
+ 
+
+ align:start position:0%
+measure like um what you're used to um
+cultural background of course um and
+
+ align:start position:0%
+cultural background of course um and
+ 
+
+ align:start position:0%
+cultural background of course um and
+then telling you what you want to hear
+
+ align:start position:0%
+then telling you what you want to hear
+ 
+
+ align:start position:0%
+then telling you what you want to hear
+it's really common if you say so what do
+
+ align:start position:0%
+it's really common if you say so what do
+ 
+
+ align:start position:0%
+it's really common if you say so what do
+you think of my design right people be
+
+ align:start position:0%
+you think of my design right people be
+ 
+
+ align:start position:0%
+you think of my design right people be
+like oh it's great yeah we totally use
+
+ align:start position:0%
+like oh it's great yeah we totally use
+ 
+
+ align:start position:0%
+like oh it's great yeah we totally use
+that awesome love it yeah it's good mhm
+
+ align:start position:0%
+that awesome love it yeah it's good mhm
+ 
+
+ align:start position:0%
+that awesome love it yeah it's good mhm
+and unless you both ask your question
+
+ align:start position:0%
+and unless you both ask your question
+ 
+
+ align:start position:0%
+and unless you both ask your question
+more carefully and keep probing you'll
+
+ align:start position:0%
+more carefully and keep probing you'll
+ 
+
+ align:start position:0%
+more carefully and keep probing you'll
+never hear beyond that and it's really
+
+ align:start position:0%
+never hear beyond that and it's really
+ 
+
+ align:start position:0%
+never hear beyond that and it's really
+easy when you're proud of something to
+
+ align:start position:0%
+easy when you're proud of something to
+ 
+
+ align:start position:0%
+easy when you're proud of something to
+be like well they said do they love it
+
+ align:start position:0%
+be like well they said do they love it
+ 
+
+ align:start position:0%
+be like well they said do they love it
+awesome and so working through that is
+
+ align:start position:0%
+awesome and so working through that is
+ 
+
+ align:start position:0%
+awesome and so working through that is
+is important and then also talking to
+
+ align:start position:0%
+is important and then also talking to
+ 
+
+ align:start position:0%
+is important and then also talking to
+the wrong person so it can be really
+
+ align:start position:0%
+the wrong person so it can be really
+ 
+
+ align:start position:0%
+the wrong person so it can be really
+easy to ask all questions of Lindsay for
+
+ align:start position:0%
+easy to ask all questions of Lindsay for
+ 
+
+ align:start position:0%
+easy to ask all questions of Lindsay for
+example is the community or organizer
+
+ align:start position:0%
+example is the community or organizer
+ 
+
+ align:start position:0%
+example is the community or organizer
+and she speaks English Etc and she'll
+
+ align:start position:0%
+and she speaks English Etc and she'll
+ 
+
+ align:start position:0%
+and she speaks English Etc and she'll
+give you some really good insights but
+
+ align:start position:0%
+give you some really good insights but
+ 
+
+ align:start position:0%
+give you some really good insights but
+if you just talk to her you won't get
+
+ align:start position:0%
+if you just talk to her you won't get
+ 
+
+ align:start position:0%
+if you just talk to her you won't get
+the right information or you can
+
+ align:start position:0%
+the right information or you can
+ 
+
+ align:start position:0%
+the right information or you can
+interview someone about cooking habits
+
+ align:start position:0%
+interview someone about cooking habits
+ 
+
+ align:start position:0%
+interview someone about cooking habits
+and then if you forget to ask how often
+
+ align:start position:0%
+and then if you forget to ask how often
+ 
+
+ align:start position:0%
+and then if you forget to ask how often
+do you cook and find out actually they
+
+ align:start position:0%
+do you cook and find out actually they
+ 
+
+ align:start position:0%
+do you cook and find out actually they
+aren't the cook but they'll answer
+
+ align:start position:0%
+aren't the cook but they'll answer
+ 
+
+ align:start position:0%
+aren't the cook but they'll answer
+because you're asking these questions if
+
+ align:start position:0%
+because you're asking these questions if
+ 
+
+ align:start position:0%
+because you're asking these questions if
+you don't ask the right questions you're
+
+ align:start position:0%
+you don't ask the right questions you're
+ 
+
+ align:start position:0%
+you don't ask the right questions you're
+just never going to get the right
+
+ align:start position:0%
+just never going to get the right
+ 
+
+ align:start position:0%
+just never going to get the right
+information and there's classic examples
+
+ align:start position:0%
+information and there's classic examples
+ 
+
+ align:start position:0%
+information and there's classic examples
+of that in terms of talking to the male
+
+ align:start position:0%
+of that in terms of talking to the male
+ 
+
+ align:start position:0%
+of that in terms of talking to the male
+leaders in the community and never
+
+ align:start position:0%
+leaders in the community and never
+ 
+
+ align:start position:0%
+leaders in the community and never
+talking to the women in the community I
+
+ align:start position:0%
+talking to the women in the community I
+ 
+
+ align:start position:0%
+talking to the women in the community I
+think that'll be less of an issue for
+
+ align:start position:0%
+think that'll be less of an issue for
+ 
+
+ align:start position:0%
+think that'll be less of an issue for
+most of you guys given who you're
+
+ align:start position:0%
+most of you guys given who you're
+ 
+
+ align:start position:0%
+most of you guys given who you're
+working with but it's something to keep
+
+ align:start position:0%
+working with but it's something to keep
+ 
+
+ align:start position:0%
+working with but it's something to keep
+in
+
+ align:start position:0%
+in
+ 
+
+ align:start position:0%
+in
+mind so I sort of got to this and you
+
+ align:start position:0%
+mind so I sort of got to this and you
+ 
+
+ align:start position:0%
+mind so I sort of got to this and you
+got to it too so one some of the methods
+
+ align:start position:0%
+got to it too so one some of the methods
+ 
+
+ align:start position:0%
+got to it too so one some of the methods
+to manage this are asking the same
+
+ align:start position:0%
+to manage this are asking the same
+ 
+
+ align:start position:0%
+to manage this are asking the same
+person the same question in many
+
+ align:start position:0%
+person the same question in many
+ 
+
+ align:start position:0%
+person the same question in many
+different ways multiple times as well as
+
+ align:start position:0%
+different ways multiple times as well as
+ 
+
+ align:start position:0%
+different ways multiple times as well as
+asking different people the same
+
+ align:start position:0%
+asking different people the same
+ 
+
+ align:start position:0%
+asking different people the same
+question multiple times anticipating
+
+ align:start position:0%
+question multiple times anticipating
+ 
+
+ align:start position:0%
+question multiple times anticipating
+that you're going to get some variation
+
+ align:start position:0%
+that you're going to get some variation
+ 
+
+ align:start position:0%
+that you're going to get some variation
+another thing you can do is ask some
+
+ align:start position:0%
+another thing you can do is ask some
+ 
+
+ align:start position:0%
+another thing you can do is ask some
+questions that you kind of already know
+
+ align:start position:0%
+questions that you kind of already know
+ 
+
+ align:start position:0%
+questions that you kind of already know
+the answer to um if if you do so that
+
+ align:start position:0%
+the answer to um if if you do so that
+ 
+
+ align:start position:0%
+the answer to um if if you do so that
+you can get an indicator of how reliable
+
+ align:start position:0%
+you can get an indicator of how reliable
+ 
+
+ align:start position:0%
+you can get an indicator of how reliable
+this person is in terms of giving you
+
+ align:start position:0%
+this person is in terms of giving you
+ 
+
+ align:start position:0%
+this person is in terms of giving you
+useful information because some people
+
+ align:start position:0%
+useful information because some people
+ 
+
+ align:start position:0%
+useful information because some people
+are much more on the telling you what
+
+ align:start position:0%
+are much more on the telling you what
+ 
+
+ align:start position:0%
+are much more on the telling you what
+you want way they think you want to hear
+
+ align:start position:0%
+you want way they think you want to hear
+ 
+
+ align:start position:0%
+you want way they think you want to hear
+sigh than others and there's some Pro
+
+ align:start position:0%
+sigh than others and there's some Pro
+ 
+
+ align:start position:0%
+sigh than others and there's some Pro
+probing questions you might be able to
+
+ align:start position:0%
+probing questions you might be able to
+ 
+
+ align:start position:0%
+probing questions you might be able to
+develop that um can help you get around
+
+ align:start position:0%
+develop that um can help you get around
+ 
+
+ align:start position:0%
+develop that um can help you get around
+that um demonstrating an openness to
+
+ align:start position:0%
+that um demonstrating an openness to
+ 
+
+ align:start position:0%
+that um demonstrating an openness to
+criticism and that generally does not
+
+ align:start position:0%
+criticism and that generally does not
+ 
+
+ align:start position:0%
+criticism and that generally does not
+mean saying oh you won't offend me tell
+
+ align:start position:0%
+mean saying oh you won't offend me tell
+ 
+
+ align:start position:0%
+mean saying oh you won't offend me tell
+me whatever you want but can mean
+
+ align:start position:0%
+me whatever you want but can mean
+ 
+
+ align:start position:0%
+me whatever you want but can mean
+something like you know I've talked to
+
+ align:start position:0%
+something like you know I've talked to
+ 
+
+ align:start position:0%
+something like you know I've talked to
+some people who've criticized or you
+
+ align:start position:0%
+some people who've criticized or you
+ 
+
+ align:start position:0%
+some people who've criticized or you
+know have said they don't like this idea
+
+ align:start position:0%
+know have said they don't like this idea
+ 
+
+ align:start position:0%
+know have said they don't like this idea
+because of this you know is that
+
+ align:start position:0%
+because of this you know is that
+ 
+
+ align:start position:0%
+because of this you know is that
+something that you you think might be a
+
+ align:start position:0%
+something that you you think might be a
+ 
+
+ align:start position:0%
+something that you you think might be a
+problem too why or why not um and just
+
+ align:start position:0%
+problem too why or why not um and just
+ 
+
+ align:start position:0%
+problem too why or why not um and just
+repeatedly attacking yourself so that
+
+ align:start position:0%
+repeatedly attacking yourself so that
+ 
+
+ align:start position:0%
+repeatedly attacking yourself so that
+that you actually get some criticisms
+
+ align:start position:0%
+that you actually get some criticisms
+ 
+
+ align:start position:0%
+that you actually get some criticisms
+from them because as great as you all
+
+ align:start position:0%
+from them because as great as you all
+ 
+
+ align:start position:0%
+from them because as great as you all
+are I'm sure there's going to be some
+
+ align:start position:0%
+are I'm sure there's going to be some
+ 
+
+ align:start position:0%
+are I'm sure there's going to be some
+flaws in every approach and so getting
+
+ align:start position:0%
+flaws in every approach and so getting
+ 
+
+ align:start position:0%
+flaws in every approach and so getting
+to those flaws helps you get to a really
+
+ align:start position:0%
+to those flaws helps you get to a really
+ 
+
+ align:start position:0%
+to those flaws helps you get to a really
+great product faster um repeating
+
+ align:start position:0%
+great product faster um repeating
+ 
+
+ align:start position:0%
+great product faster um repeating
+answers back is sort of a classic method
+
+ align:start position:0%
+answers back is sort of a classic method
+ 
+
+ align:start position:0%
+answers back is sort of a classic method
+for making sure that there's
+
+ align:start position:0%
+for making sure that there's
+ 
+
+ align:start position:0%
+for making sure that there's
+understanding on both sides encouraging
+
+ align:start position:0%
+understanding on both sides encouraging
+ 
+
+ align:start position:0%
+understanding on both sides encouraging
+questions very explicitly saying you
+
+ align:start position:0%
+questions very explicitly saying you
+ 
+
+ align:start position:0%
+questions very explicitly saying you
+know what questions do you have for me
+
+ align:start position:0%
+know what questions do you have for me
+ 
+
+ align:start position:0%
+know what questions do you have for me
+what can I tell you um is pretty
+
+ align:start position:0%
+what can I tell you um is pretty
+ 
+
+ align:start position:0%
+what can I tell you um is pretty
+important uh verifying expertise so sort
+
+ align:start position:0%
+important uh verifying expertise so sort
+ 
+
+ align:start position:0%
+important uh verifying expertise so sort
+of as I mentioned with the wrong person
+
+ align:start position:0%
+of as I mentioned with the wrong person
+ 
+
+ align:start position:0%
+of as I mentioned with the wrong person
+if you talk to someone about cooking
+
+ align:start position:0%
+if you talk to someone about cooking
+ 
+
+ align:start position:0%
+if you talk to someone about cooking
+actually making sure that they cook
+
+ align:start position:0%
+actually making sure that they cook
+ 
+
+ align:start position:0%
+actually making sure that they cook
+would be a good good thing to do um and
+
+ align:start position:0%
+would be a good good thing to do um and
+ 
+
+ align:start position:0%
+would be a good good thing to do um and
+then finally dealing with the translator
+
+ align:start position:0%
+then finally dealing with the translator
+ 
+
+ align:start position:0%
+then finally dealing with the translator
+spending some time beforehand talking
+
+ align:start position:0%
+spending some time beforehand talking
+ 
+
+ align:start position:0%
+spending some time beforehand talking
+about what your goals are what your
+
+ align:start position:0%
+about what your goals are what your
+ 
+
+ align:start position:0%
+about what your goals are what your
+preferences are um because translators
+
+ align:start position:0%
+preferences are um because translators
+ 
+
+ align:start position:0%
+preferences are um because translators
+have choices in terms of do they give
+
+ align:start position:0%
+have choices in terms of do they give
+ 
+
+ align:start position:0%
+have choices in terms of do they give
+you the detailed response or do they
+
+ align:start position:0%
+you the detailed response or do they
+ 
+
+ align:start position:0%
+you the detailed response or do they
+just give you the yes and if you're on a
+
+ align:start position:0%
+just give you the yes and if you're on a
+ 
+
+ align:start position:0%
+just give you the yes and if you're on a
+time crunch you may just want the yes
+
+ align:start position:0%
+time crunch you may just want the yes
+ 
+
+ align:start position:0%
+time crunch you may just want the yes
+but if you have the time you probably
+
+ align:start position:0%
+but if you have the time you probably
+ 
+
+ align:start position:0%
+but if you have the time you probably
+want the detailed um answer with the
+
+ align:start position:0%
+want the detailed um answer with the
+ 
+
+ align:start position:0%
+want the detailed um answer with the
+subtleties even if it's more painful to
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+translate so one of the challenges is
+
+ align:start position:0%
+translate so one of the challenges is
+ 
+
+ align:start position:0%
+translate so one of the challenges is
+when you're working on engineering
+
+ align:start position:0%
+when you're working on engineering
+ 
+
+ align:start position:0%
+when you're working on engineering
+projects is getting to the core problem
+
+ align:start position:0%
+projects is getting to the core problem
+ 
+
+ align:start position:0%
+projects is getting to the core problem
+um and that sort of ties in to the
+
+ align:start position:0%
+um and that sort of ties in to the
+ 
+
+ align:start position:0%
+um and that sort of ties in to the
+project spec specifications so someone
+
+ align:start position:0%
+project spec specifications so someone
+ 
+
+ align:start position:0%
+project spec specifications so someone
+will say I need a new stove instead of I
+
+ align:start position:0%
+will say I need a new stove instead of I
+ 
+
+ align:start position:0%
+will say I need a new stove instead of I
+need to not have such a smoky
+
+ align:start position:0%
+need to not have such a smoky
+ 
+
+ align:start position:0%
+need to not have such a smoky
+environment in my kitchen and you need
+
+ align:start position:0%
+environment in my kitchen and you need
+ 
+
+ align:start position:0%
+environment in my kitchen and you need
+to make sure you're asking the questions
+
+ align:start position:0%
+to make sure you're asking the questions
+ 
+
+ align:start position:0%
+to make sure you're asking the questions
+to get to smoking environment not new
+
+ align:start position:0%
+to get to smoking environment not new
+ 
+
+ align:start position:0%
+to get to smoking environment not new
+stove right and be really easy to
+
+ align:start position:0%
+stove right and be really easy to
+ 
+
+ align:start position:0%
+stove right and be really easy to
+specify that brand new stove without um
+
+ align:start position:0%
+specify that brand new stove without um
+ 
+
+ align:start position:0%
+specify that brand new stove without um
+getting uh the right and question
+
+ align:start position:0%
+getting uh the right and question
+ 
+
+ align:start position:0%
+getting uh the right and question
+answered which is the smoking
+
+ align:start position:0%
+answered which is the smoking
+ 
+
+ align:start position:0%
+answered which is the smoking
+environment so partly it's making sure
+
+ align:start position:0%
+environment so partly it's making sure
+ 
+
+ align:start position:0%
+environment so partly it's making sure
+that you're not letting them design for
+
+ align:start position:0%
+that you're not letting them design for
+ 
+
+ align:start position:0%
+that you're not letting them design for
+you which everyone does it's really hard
+
+ align:start position:0%
+you which everyone does it's really hard
+ 
+
+ align:start position:0%
+you which everyone does it's really hard
+to describe what you need in terms of
+
+ align:start position:0%
+to describe what you need in terms of
+ 
+
+ align:start position:0%
+to describe what you need in terms of
+specifications as you probably just
+
+ align:start position:0%
+specifications as you probably just
+ 
+
+ align:start position:0%
+specifications as you probably just
+found out um or saw in that 29 lecture I
+
+ align:start position:0%
+found out um or saw in that 29 lecture I
+ 
+
+ align:start position:0%
+found out um or saw in that 29 lecture I
+linked to when trying to describe a
+
+ align:start position:0%
+linked to when trying to describe a
+ 
+
+ align:start position:0%
+linked to when trying to describe a
+lemon or a piece of fruit um um as a
+
+ align:start position:0%
+lemon or a piece of fruit um um as a
+ 
+
+ align:start position:0%
+lemon or a piece of fruit um um as a
+project specification rather than I need
+
+ align:start position:0%
+project specification rather than I need
+ 
+
+ align:start position:0%
+project specification rather than I need
+a lemon right um that's much harder but
+
+ align:start position:0%
+a lemon right um that's much harder but
+ 
+
+ align:start position:0%
+a lemon right um that's much harder but
+that's what you this is actually the
+
+ align:start position:0%
+that's what you this is actually the
+ 
+
+ align:start position:0%
+that's what you this is actually the
+information you need to make a good
+
+ align:start position:0%
+information you need to make a good
+ 
+
+ align:start position:0%
+information you need to make a good
+design so that you're not going down the
+
+ align:start position:0%
+design so that you're not going down the
+ 
+
+ align:start position:0%
+design so that you're not going down the
+path of a design that may not actually
+
+ align:start position:0%
+path of a design that may not actually
+ 
+
+ align:start position:0%
+path of a design that may not actually
+match the real needs um because it's
+
+ align:start position:0%
+match the real needs um because it's
+ 
+
+ align:start position:0%
+match the real needs um because it's
+easier to think in products than in
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+specifications uh so getting to the core
+
+ align:start position:0%
+specifications uh so getting to the core
+ 
+
+ align:start position:0%
+specifications uh so getting to the core
+problem some ways you can do that in
+
+ align:start position:0%
+problem some ways you can do that in
+ 
+
+ align:start position:0%
+problem some ways you can do that in
+addition to just being patient when
+
+ align:start position:0%
+addition to just being patient when
+ 
+
+ align:start position:0%
+addition to just being patient when
+people talk about what they want in
+
+ align:start position:0%
+people talk about what they want in
+ 
+
+ align:start position:0%
+people talk about what they want in
+terms of a product and then you
+
+ align:start position:0%
+terms of a product and then you
+ 
+
+ align:start position:0%
+terms of a product and then you
+translating back into the specifications
+
+ align:start position:0%
+translating back into the specifications
+ 
+
+ align:start position:0%
+translating back into the specifications
+is so tell me what would happen when you
+
+ align:start position:0%
+is so tell me what would happen when you
+ 
+
+ align:start position:0%
+is so tell me what would happen when you
+use this new thing tell me a story about
+
+ align:start position:0%
+use this new thing tell me a story about
+ 
+
+ align:start position:0%
+use this new thing tell me a story about
+what that would be like and have them
+
+ align:start position:0%
+what that would be like and have them
+ 
+
+ align:start position:0%
+what that would be like and have them
+sort of walk you through what life is
+
+ align:start position:0%
+sort of walk you through what life is
+ 
+
+ align:start position:0%
+sort of walk you through what life is
+like with this new Option um talk you
+
+ align:start position:0%
+like with this new Option um talk you
+ 
+
+ align:start position:0%
+like with this new Option um talk you
+know when you're trying to find out more
+
+ align:start position:0%
+know when you're trying to find out more
+ 
+
+ align:start position:0%
+know when you're trying to find out more
+about what those specifications are
+
+ align:start position:0%
+about what those specifications are
+ 
+
+ align:start position:0%
+about what those specifications are
+rather than saying how big should it be
+
+ align:start position:0%
+rather than saying how big should it be
+ 
+
+ align:start position:0%
+rather than saying how big should it be
+saying well how big is too big is 10et
+
+ align:start position:0%
+saying well how big is too big is 10et
+ 
+
+ align:start position:0%
+saying well how big is too big is 10et
+you know is is this big too big is this
+
+ align:start position:0%
+you know is is this big too big is this
+ 
+
+ align:start position:0%
+you know is is this big too big is this
+big too big and again I just said 10 ft
+
+ align:start position:0%
+big too big and again I just said 10 ft
+ 
+
+ align:start position:0%
+big too big and again I just said 10 ft
+and that's probably not what you want to
+
+ align:start position:0%
+and that's probably not what you want to
+ 
+
+ align:start position:0%
+and that's probably not what you want to
+say you want to use your hands to
+
+ align:start position:0%
+say you want to use your hands to
+ 
+
+ align:start position:0%
+say you want to use your hands to
+gesture or use some other things to
+
+ align:start position:0%
+gesture or use some other things to
+ 
+
+ align:start position:0%
+gesture or use some other things to
+compare because 10 ft even for us is a
+
+ align:start position:0%
+compare because 10 ft even for us is a
+ 
+
+ align:start position:0%
+compare because 10 ft even for us is a
+little hard to imagine exactly how big
+
+ align:start position:0%
+little hard to imagine exactly how big
+ 
+
+ align:start position:0%
+little hard to imagine exactly how big
+10t is and for someone who hasn't grown
+
+ align:start position:0%
+10t is and for someone who hasn't grown
+ 
+
+ align:start position:0%
+10t is and for someone who hasn't grown
+up using um rulers and tape measures Etc
+
+ align:start position:0%
+up using um rulers and tape measures Etc
+ 
+
+ align:start position:0%
+up using um rulers and tape measures Etc
+it's harder um and so I put big and
+
+ align:start position:0%
+it's harder um and so I put big and
+ 
+
+ align:start position:0%
+it's harder um and so I put big and
+small in parenthesis because it could be
+
+ align:start position:0%
+small in parenthesis because it could be
+ 
+
+ align:start position:0%
+small in parenthesis because it could be
+like how hot how cold how whatever all
+
+ align:start position:0%
+like how hot how cold how whatever all
+ 
+
+ align:start position:0%
+like how hot how cold how whatever all
+sorts of different things um challenge
+
+ align:start position:0%
+sorts of different things um challenge
+ 
+
+ align:start position:0%
+sorts of different things um challenge
+challenge their requests so like if they
+
+ align:start position:0%
+challenge their requests so like if they
+ 
+
+ align:start position:0%
+challenge their requests so like if they
+say oh no it has to be you know it can't
+
+ align:start position:0%
+say oh no it has to be you know it can't
+ 
+
+ align:start position:0%
+say oh no it has to be you know it can't
+be bigger than this say well what would
+
+ align:start position:0%
+be bigger than this say well what would
+ 
+
+ align:start position:0%
+be bigger than this say well what would
+happen if it was this big why would that
+
+ align:start position:0%
+happen if it was this big why would that
+ 
+
+ align:start position:0%
+happen if it was this big why would that
+be a bad thing so that you really
+
+ align:start position:0%
+be a bad thing so that you really
+ 
+
+ align:start position:0%
+be a bad thing so that you really
+understand what they're getting at um
+
+ align:start position:0%
+understand what they're getting at um
+ 
+
+ align:start position:0%
+understand what they're getting at um
+and then get getting feedback on your
+
+ align:start position:0%
+and then get getting feedback on your
+ 
+
+ align:start position:0%
+and then get getting feedback on your
+own ideas including ones that you know
+
+ align:start position:0%
+own ideas including ones that you know
+ 
+
+ align:start position:0%
+own ideas including ones that you know
+are problematic so showing them a design
+
+ align:start position:0%
+are problematic so showing them a design
+ 
+
+ align:start position:0%
+are problematic so showing them a design
+that you know has some issues and
+
+ align:start position:0%
+that you know has some issues and
+ 
+
+ align:start position:0%
+that you know has some issues and
+getting feedback on it trying to get
+
+ align:start position:0%
+getting feedback on it trying to get
+ 
+
+ align:start position:0%
+getting feedback on it trying to get
+them comfortable with criticizing um so
+
+ align:start position:0%
+them comfortable with criticizing um so
+ 
+
+ align:start position:0%
+them comfortable with criticizing um so
+that you can and then also listening to
+
+ align:start position:0%
+that you can and then also listening to
+ 
+
+ align:start position:0%
+that you can and then also listening to
+the way they're criticizing what they're
+
+ align:start position:0%
+the way they're criticizing what they're
+ 
+
+ align:start position:0%
+the way they're criticizing what they're
+C catching maybe open up some
+
+ align:start position:0%
+C catching maybe open up some
+ 
+
+ align:start position:0%
+C catching maybe open up some
+information for you um and then finally
+
+ align:start position:0%
+information for you um and then finally
+ 
+
+ align:start position:0%
+information for you um and then finally
+as you're engaged in these questions and
+
+ align:start position:0%
+as you're engaged in these questions and
+ 
+
+ align:start position:0%
+as you're engaged in these questions and
+conversations taking time mentally um to
+
+ align:start position:0%
+conversations taking time mentally um to
+ 
+
+ align:start position:0%
+conversations taking time mentally um to
+view what you know and sort of do a
+
+ align:start position:0%
+view what you know and sort of do a
+ 
+
+ align:start position:0%
+view what you know and sort of do a
+mental design process of writing down
+
+ align:start position:0%
+mental design process of writing down
+ 
+
+ align:start position:0%
+mental design process of writing down
+the specifications and being like okay I
+
+ align:start position:0%
+the specifications and being like okay I
+ 
+
+ align:start position:0%
+the specifications and being like okay I
+know these things what else don't I know
+
+ align:start position:0%
+know these things what else don't I know
+ 
+
+ align:start position:0%
+know these things what else don't I know
+so that you make sure to get to all the
+
+ align:start position:0%
+so that you make sure to get to all the
+ 
+
+ align:start position:0%
+so that you make sure to get to all the
+questions you need to ask and it's kind
+
+ align:start position:0%
+questions you need to ask and it's kind
+ 
+
+ align:start position:0%
+questions you need to ask and it's kind
+of hard and takes practice but you guys
+
+ align:start position:0%
+of hard and takes practice but you guys
+ 
+
+ align:start position:0%
+of hard and takes practice but you guys
+will uh do
+
+ align:start position:0%
+will uh do
+ 
+
+ align:start position:0%
+will uh do
+great so now
+
+ align:start position:0%
+great so now
+ 
+
+ align:start position:0%
+great so now
+um I'm G to save that till Friday
+
+ align:start position:0%
+um I'm G to save that till Friday
+ 
+
+ align:start position:0%
+um I'm G to save that till Friday
+because we're running out of
+
+ align:start position:0%
+because we're running out of
+ 
+
+ align:start position:0%
+because we're running out of
+time
+
+ align:start position:0%
+time
+ 
+
+ align:start position:0%
+time
+um so I just wanted to go over or maybe
+
+ align:start position:0%
+um so I just wanted to go over or maybe
+ 
+
+ align:start position:0%
+um so I just wanted to go over or maybe
+I'll get back to it if I have time um
+
+ align:start position:0%
+I'll get back to it if I have time um
+ 
+
+ align:start position:0%
+I'll get back to it if I have time um
+the packing list and trip uh advice
+
+ align:start position:0%
+the packing list and trip uh advice
+ 
+
+ align:start position:0%
+the packing list and trip uh advice
+which is all posted on Stellar but in
+
+ align:start position:0%
+which is all posted on Stellar but in
+ 
+
+ align:start position:0%
+which is all posted on Stellar but in
+case you haven't had a chance to read it
+
+ align:start position:0%
+case you haven't had a chance to read it
+ 
+
+ align:start position:0%
+case you haven't had a chance to read it
+I know they're kind of long um so some
+
+ align:start position:0%
+I know they're kind of long um so some
+ 
+
+ align:start position:0%
+I know they're kind of long um so some
+people were earlier asking me do I need
+
+ align:start position:0%
+people were earlier asking me do I need
+ 
+
+ align:start position:0%
+people were earlier asking me do I need
+to buy a new X um probably not so there
+
+ align:start position:0%
+to buy a new X um probably not so there
+ 
+
+ align:start position:0%
+to buy a new X um probably not so there
+might be one or two things you want to
+
+ align:start position:0%
+might be one or two things you want to
+ 
+
+ align:start position:0%
+might be one or two things you want to
+buy but generally the goal of daab is
+
+ align:start position:0%
+buy but generally the goal of daab is
+ 
+
+ align:start position:0%
+buy but generally the goal of daab is
+not to make yourself broke going to
+
+ align:start position:0%
+not to make yourself broke going to
+ 
+
+ align:start position:0%
+not to make yourself broke going to
+travel to a developing country um so
+
+ align:start position:0%
+travel to a developing country um so
+ 
+
+ align:start position:0%
+travel to a developing country um so
+very little needs to be bought new and
+
+ align:start position:0%
+very little needs to be bought new and
+ 
+
+ align:start position:0%
+very little needs to be bought new and
+pack lightly which is in direct
+
+ align:start position:0%
+pack lightly which is in direct
+ 
+
+ align:start position:0%
+pack lightly which is in direct
+contradiction to the two-page packing
+
+ align:start position:0%
+contradiction to the two-page packing
+ 
+
+ align:start position:0%
+contradiction to the two-page packing
+list that I provided you but basically
+
+ align:start position:0%
+list that I provided you but basically
+ 
+
+ align:start position:0%
+list that I provided you but basically
+that two-page packing list is the list
+
+ align:start position:0%
+that two-page packing list is the list
+ 
+
+ align:start position:0%
+that two-page packing list is the list
+of all things that someone at daab
+
+ align:start position:0%
+of all things that someone at daab
+ 
+
+ align:start position:0%
+of all things that someone at daab
+really likes bringing and so some people
+
+ align:start position:0%
+really likes bringing and so some people
+ 
+
+ align:start position:0%
+really likes bringing and so some people
+really value certain things other people
+
+ align:start position:0%
+really value certain things other people
+ 
+
+ align:start position:0%
+really value certain things other people
+bring value other things you sort of
+
+ align:start position:0%
+bring value other things you sort of
+ 
+
+ align:start position:0%
+bring value other things you sort of
+have to know yourself what are the
+
+ align:start position:0%
+have to know yourself what are the
+ 
+
+ align:start position:0%
+have to know yourself what are the
+objects that are going to be important
+
+ align:start position:0%
+objects that are going to be important
+ 
+
+ align:start position:0%
+objects that are going to be important
+for you to have and what are the ones
+
+ align:start position:0%
+for you to have and what are the ones
+ 
+
+ align:start position:0%
+for you to have and what are the ones
+that you can skip so there's just a
+
+ align:start position:0%
+that you can skip so there's just a
+ 
+
+ align:start position:0%
+that you can skip so there's just a
+couple that I have on that packing list
+
+ align:start position:0%
+couple that I have on that packing list
+ 
+
+ align:start position:0%
+couple that I have on that packing list
+that are in blue I didn't even put
+
+ align:start position:0%
+that are in blue I didn't even put
+ 
+
+ align:start position:0%
+that are in blue I didn't even put
+underwear in blue right just the ones
+
+ align:start position:0%
+underwear in blue right just the ones
+ 
+
+ align:start position:0%
+underwear in blue right just the ones
+like a flashlight that if you don't have
+
+ align:start position:0%
+like a flashlight that if you don't have
+ 
+
+ align:start position:0%
+like a flashlight that if you don't have
+it's going to be really hard for you to
+
+ align:start position:0%
+it's going to be really hard for you to
+ 
+
+ align:start position:0%
+it's going to be really hard for you to
+function so things like that you have to
+
+ align:start position:0%
+function so things like that you have to
+ 
+
+ align:start position:0%
+function so things like that you have to
+have everything else is sort of your
+
+ align:start position:0%
+have everything else is sort of your
+ 
+
+ align:start position:0%
+have everything else is sort of your
+call so if you don't have Tas you don't
+
+ align:start position:0%
+call so if you don't have Tas you don't
+ 
+
+ align:start position:0%
+call so if you don't have Tas you don't
+have boots you don't have whatever don't
+
+ align:start position:0%
+have boots you don't have whatever don't
+ 
+
+ align:start position:0%
+have boots you don't have whatever don't
+worry about it um don't go out and buy
+
+ align:start position:0%
+worry about it um don't go out and buy
+ 
+
+ align:start position:0%
+worry about it um don't go out and buy
+yourself a 200 pair of hiking boots um
+
+ align:start position:0%
+yourself a 200 pair of hiking boots um
+ 
+
+ align:start position:0%
+yourself a 200 pair of hiking boots um
+that you'll never wear again just for
+
+ align:start position:0%
+that you'll never wear again just for
+ 
+
+ align:start position:0%
+that you'll never wear again just for
+this trip that's not necessary um so
+
+ align:start position:0%
+this trip that's not necessary um so
+ 
+
+ align:start position:0%
+this trip that's not necessary um so
+pack lightly um with that being said it
+
+ align:start position:0%
+pack lightly um with that being said it
+ 
+
+ align:start position:0%
+pack lightly um with that being said it
+can be as cold as like 50° at night so
+
+ align:start position:0%
+can be as cold as like 50° at night so
+ 
+
+ align:start position:0%
+can be as cold as like 50° at night so
+you might want a light fleece or
+
+ align:start position:0%
+you might want a light fleece or
+ 
+
+ align:start position:0%
+you might want a light fleece or
+something like that and then in the
+
+ align:start position:0%
+something like that and then in the
+ 
+
+ align:start position:0%
+something like that and then in the
+middle of the day it's wicked hot and
+
+ align:start position:0%
+middle of the day it's wicked hot and
+ 
+
+ align:start position:0%
+middle of the day it's wicked hot and
+humid um relatively conservative dress
+
+ align:start position:0%
+humid um relatively conservative dress
+ 
+
+ align:start position:0%
+humid um relatively conservative dress
+again um for a lot of these things I'm
+
+ align:start position:0%
+again um for a lot of these things I'm
+ 
+
+ align:start position:0%
+again um for a lot of these things I'm
+asking you to be more conservative than
+
+ align:start position:0%
+asking you to be more conservative than
+ 
+
+ align:start position:0%
+asking you to be more conservative than
+you may see most people being not most
+
+ align:start position:0%
+you may see most people being not most
+ 
+
+ align:start position:0%
+you may see most people being not most
+but many people in Nicaragua being um
+
+ align:start position:0%
+but many people in Nicaragua being um
+ 
+
+ align:start position:0%
+but many people in Nicaragua being um
+because again we're representing MIT and
+
+ align:start position:0%
+because again we're representing MIT and
+ 
+
+ align:start position:0%
+because again we're representing MIT and
+daab and the Y yada and so we want to be
+
+ align:start position:0%
+daab and the Y yada and so we want to be
+ 
+
+ align:start position:0%
+daab and the Y yada and so we want to be
+respectful to the people who are on the
+
+ align:start position:0%
+respectful to the people who are on the
+ 
+
+ align:start position:0%
+respectful to the people who are on the
+conservative side in terms of dress Etc
+
+ align:start position:0%
+conservative side in terms of dress Etc
+ 
+
+ align:start position:0%
+conservative side in terms of dress Etc
+um toiletries so if you have any
+
+ align:start position:0%
+um toiletries so if you have any
+ 
+
+ align:start position:0%
+um toiletries so if you have any
+medications that you need to take you
+
+ align:start position:0%
+medications that you need to take you
+ 
+
+ align:start position:0%
+medications that you need to take you
+should take twice as many as you need
+
+ align:start position:0%
+should take twice as many as you need
+ 
+
+ align:start position:0%
+should take twice as many as you need
+and keep them in two separate places so
+
+ align:start position:0%
+and keep them in two separate places so
+ 
+
+ align:start position:0%
+and keep them in two separate places so
+that if a bag gets stolen or lost you
+
+ align:start position:0%
+that if a bag gets stolen or lost you
+ 
+
+ align:start position:0%
+that if a bag gets stolen or lost you
+have your meds um you definitely want to
+
+ align:start position:0%
+have your meds um you definitely want to
+ 
+
+ align:start position:0%
+have your meds um you definitely want to
+bring toilet paper or tissues or
+
+ align:start position:0%
+bring toilet paper or tissues or
+ 
+
+ align:start position:0%
+bring toilet paper or tissues or
+something like that you can use for
+
+ align:start position:0%
+something like that you can use for
+ 
+
+ align:start position:0%
+something like that you can use for
+toilet paper cuz not all places will
+
+ align:start position:0%
+toilet paper cuz not all places will
+ 
+
+ align:start position:0%
+toilet paper cuz not all places will
+have it um you won't be offered a towel
+
+ align:start position:0%
+have it um you won't be offered a towel
+ 
+
+ align:start position:0%
+have it um you won't be offered a towel
+so if you want to have a towel for
+
+ align:start position:0%
+so if you want to have a towel for
+ 
+
+ align:start position:0%
+so if you want to have a towel for
+showering which will be bucket showers
+
+ align:start position:0%
+showering which will be bucket showers
+ 
+
+ align:start position:0%
+showering which will be bucket showers
+um so taking a scoop of water from a
+
+ align:start position:0%
+um so taking a scoop of water from a
+ 
+
+ align:start position:0%
+um so taking a scoop of water from a
+bucket and pouring it on your head um
+
+ align:start position:0%
+bucket and pouring it on your head um
+ 
+
+ align:start position:0%
+bucket and pouring it on your head um
+you should bring one but I would bring a
+
+ align:start position:0%
+you should bring one but I would bring a
+ 
+
+ align:start position:0%
+you should bring one but I would bring a
+small one because they're pretty bulky
+
+ align:start position:0%
+small one because they're pretty bulky
+ 
+
+ align:start position:0%
+small one because they're pretty bulky
+um you'll definitely want bug repellent
+
+ align:start position:0%
+um you'll definitely want bug repellent
+ 
+
+ align:start position:0%
+um you'll definitely want bug repellent
+and sunscreen the sun is much stronger
+
+ align:start position:0%
+and sunscreen the sun is much stronger
+ 
+
+ align:start position:0%
+and sunscreen the sun is much stronger
+and um you will sunburn if you don't
+
+ align:start position:0%
+and um you will sunburn if you don't
+ 
+
+ align:start position:0%
+and um you will sunburn if you don't
+wear sunscreen if you're fair skinned um
+
+ align:start position:0%
+wear sunscreen if you're fair skinned um
+ 
+
+ align:start position:0%
+wear sunscreen if you're fair skinned um
+flashlight again is key having a photoc
+
+ align:start position:0%
+flashlight again is key having a photoc
+ 
+
+ align:start position:0%
+flashlight again is key having a photoc
+copy of your passport um bringing a
+
+ align:start position:0%
+copy of your passport um bringing a
+ 
+
+ align:start position:0%
+copy of your passport um bringing a
+notebook like I mentioned um and then
+
+ align:start position:0%
+notebook like I mentioned um and then
+ 
+
+ align:start position:0%
+notebook like I mentioned um and then
+nothing of value so you shouldn't be
+
+ align:start position:0%
+nothing of value so you shouldn't be
+ 
+
+ align:start position:0%
+nothing of value so you shouldn't be
+wearing your brass rats um you could
+
+ align:start position:0%
+wearing your brass rats um you could
+ 
+
+ align:start position:0%
+wearing your brass rats um you could
+skip earrings or wear really small
+
+ align:start position:0%
+skip earrings or wear really small
+ 
+
+ align:start position:0%
+skip earrings or wear really small
+subtle ones um cameras like a small
+
+ align:start position:0%
+subtle ones um cameras like a small
+ 
+
+ align:start position:0%
+subtle ones um cameras like a small
+junky point and shoot is fine but a dlsr
+
+ align:start position:0%
+junky point and shoot is fine but a dlsr
+ 
+
+ align:start position:0%
+junky point and shoot is fine but a dlsr
+is not ideal um again you'll see some
+
+ align:start position:0%
+is not ideal um again you'll see some
+ 
+
+ align:start position:0%
+is not ideal um again you'll see some
+people in Nicaragua with the lsrs but
+
+ align:start position:0%
+people in Nicaragua with the lsrs but
+ 
+
+ align:start position:0%
+people in Nicaragua with the lsrs but
+they're making the choice for themselves
+
+ align:start position:0%
+they're making the choice for themselves
+ 
+
+ align:start position:0%
+they're making the choice for themselves
+about having that and therefore bringing
+
+ align:start position:0%
+about having that and therefore bringing
+ 
+
+ align:start position:0%
+about having that and therefore bringing
+the potential crime associated with
+
+ align:start position:0%
+the potential crime associated with
+ 
+
+ align:start position:0%
+the potential crime associated with
+having a fancy device there and it's not
+
+ align:start position:0%
+having a fancy device there and it's not
+ 
+
+ align:start position:0%
+having a fancy device there and it's not
+fair for you to make that call for your
+
+ align:start position:0%
+fair for you to make that call for your
+ 
+
+ align:start position:0%
+fair for you to make that call for your
+entire team um on that camera yeah what
+
+ align:start position:0%
+entire team um on that camera yeah what
+ 
+
+ align:start position:0%
+entire team um on that camera yeah what
+kind of risk are you talking about like
+
+ align:start position:0%
+kind of risk are you talking about like
+ 
+
+ align:start position:0%
+kind of risk are you talking about like
+m is actually waterproof and shockproof
+
+ align:start position:0%
+m is actually waterproof and shockproof
+ 
+
+ align:start position:0%
+m is actually waterproof and shockproof
+or it theft
+
+ align:start position:0%
+or it theft
+ 
+
+ align:start position:0%
+or it theft
+theft so even if we so do you have a
+
+ align:start position:0%
+theft so even if we so do you have a
+ 
+
+ align:start position:0%
+theft so even if we so do you have a
+point do you have a waterproof sock
+
+ align:start position:0%
+point do you have a waterproof sock
+ 
+
+ align:start position:0%
+point do you have a waterproof sock
+prooof dlsr what's the dlsr there like
+
+ align:start position:0%
+prooof dlsr what's the dlsr there like
+ 
+
+ align:start position:0%
+prooof dlsr what's the dlsr there like
+the big no not the big one so a point
+
+ align:start position:0%
+the big no not the big one so a point
+ 
+
+ align:start position:0%
+the big no not the big one so a point
+shoot totally fine yeah yeah so this is
+
+ align:start position:0%
+shoot totally fine yeah yeah so this is
+ 
+
+ align:start position:0%
+shoot totally fine yeah yeah so this is
+what I'm saying so like a camera that's
+
+ align:start position:0%
+what I'm saying so like a camera that's
+ 
+
+ align:start position:0%
+what I'm saying so like a camera that's
+this size is fine a camera that's that
+
+ align:start position:0%
+this size is fine a camera that's that
+ 
+
+ align:start position:0%
+this size is fine a camera that's that
+size not
+
+ align:start position:0%
+size not
+ 
+
+ align:start position:0%
+size not
+fine is what I'm saying um ones that
+
+ align:start position:0%
+fine is what I'm saying um ones that
+ 
+
+ align:start position:0%
+fine is what I'm saying um ones that
+have like the switch out a lenses a dlsr
+
+ align:start position:0%
+have like the switch out a lenses a dlsr
+ 
+
+ align:start position:0%
+have like the switch out a lenses a dlsr
+you know fancy nice camera that's what
+
+ align:start position:0%
+you know fancy nice camera that's what
+ 
+
+ align:start position:0%
+you know fancy nice camera that's what
+I'm asking you not to take point and
+
+ align:start position:0%
+I'm asking you not to take point and
+ 
+
+ align:start position:0%
+I'm asking you not to take point and
+shoot you should totally take
+
+ align:start position:0%
+shoot you should totally take
+ 
+
+ align:start position:0%
+shoot you should totally take
+um and then yeah laptops um your team
+
+ align:start position:0%
+um and then yeah laptops um your team
+ 
+
+ align:start position:0%
+um and then yeah laptops um your team
+probably shouldn't bring any laptops if
+
+ align:start position:0%
+probably shouldn't bring any laptops if
+ 
+
+ align:start position:0%
+probably shouldn't bring any laptops if
+you need to you should bring one um but
+
+ align:start position:0%
+you need to you should bring one um but
+ 
+
+ align:start position:0%
+you need to you should bring one um but
+definitely not more than that um yeah do
+
+ align:start position:0%
+definitely not more than that um yeah do
+ 
+
+ align:start position:0%
+definitely not more than that um yeah do
+you recommend bringing more than one
+
+ align:start position:0%
+you recommend bringing more than one
+ 
+
+ align:start position:0%
+you recommend bringing more than one
+card for camera yes so I recommend
+
+ align:start position:0%
+card for camera yes so I recommend
+ 
+
+ align:start position:0%
+card for camera yes so I recommend
+bringing as much memory and battery
+
+ align:start position:0%
+bringing as much memory and battery
+ 
+
+ align:start position:0%
+bringing as much memory and battery
+charging capability as you can um both
+
+ align:start position:0%
+charging capability as you can um both
+ 
+
+ align:start position:0%
+charging capability as you can um both
+because you'll have limited access to
+
+ align:start position:0%
+because you'll have limited access to
+ 
+
+ align:start position:0%
+because you'll have limited access to
+electricity for battery charging and
+
+ align:start position:0%
+electricity for battery charging and
+ 
+
+ align:start position:0%
+electricity for battery charging and
+then you may be taking a lot of pictures
+
+ align:start position:0%
+then you may be taking a lot of pictures
+ 
+
+ align:start position:0%
+then you may be taking a lot of pictures
+and um you may not have a laptop and be
+
+ align:start position:0%
+and um you may not have a laptop and be
+ 
+
+ align:start position:0%
+and um you may not have a laptop and be
+able to download them until you get
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+home I'm not sure why
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that's
+
+ align:start position:0%
+that's
+ 
+
+ align:start position:0%
+that's
+yeah um
+
+ align:start position:0%
+yeah um
+ 
+
+ align:start position:0%
+yeah um
+so the thing that's complicated is so
+
+ align:start position:0%
+so the thing that's complicated is so
+ 
+
+ align:start position:0%
+so the thing that's complicated is so
+every trip leader will have a cell phone
+
+ align:start position:0%
+every trip leader will have a cell phone
+ 
+
+ align:start position:0%
+every trip leader will have a cell phone
+with them so for emergencies there's a
+
+ align:start position:0%
+with them so for emergencies there's a
+ 
+
+ align:start position:0%
+with them so for emergencies there's a
+way to call the states or a way to call
+
+ align:start position:0%
+way to call the states or a way to call
+ 
+
+ align:start position:0%
+way to call the states or a way to call
+within your country or whatever you need
+
+ align:start position:0%
+within your country or whatever you need
+ 
+
+ align:start position:0%
+within your country or whatever you need
+um I can't see why you'd need a cell
+
+ align:start position:0%
+um I can't see why you'd need a cell
+ 
+
+ align:start position:0%
+um I can't see why you'd need a cell
+phone um like it might be nice to have
+
+ align:start position:0%
+phone um like it might be nice to have
+ 
+
+ align:start position:0%
+phone um like it might be nice to have
+during your layovers or whatever so you
+
+ align:start position:0%
+during your layovers or whatever so you
+ 
+
+ align:start position:0%
+during your layovers or whatever so you
+might want to bring it for that reason
+
+ align:start position:0%
+might want to bring it for that reason
+ 
+
+ align:start position:0%
+might want to bring it for that reason
+but if it's anything at all nice and I'm
+
+ align:start position:0%
+but if it's anything at all nice and I'm
+ 
+
+ align:start position:0%
+but if it's anything at all nice and I'm
+concluding like my junkie phone is nice
+
+ align:start position:0%
+concluding like my junkie phone is nice
+ 
+
+ align:start position:0%
+concluding like my junkie phone is nice
+um but anything that looks fancier than
+
+ align:start position:0%
+um but anything that looks fancier than
+ 
+
+ align:start position:0%
+um but anything that looks fancier than
+like flip phones that people had like 10
+
+ align:start position:0%
+like flip phones that people had like 10
+ 
+
+ align:start position:0%
+like flip phones that people had like 10
+years ago um should never be visible in
+
+ align:start position:0%
+years ago um should never be visible in
+ 
+
+ align:start position:0%
+years ago um should never be visible in
+Nicaragua so if you're going to bring it
+
+ align:start position:0%
+Nicaragua so if you're going to bring it
+ 
+
+ align:start position:0%
+Nicaragua so if you're going to bring it
+pack it in the bottom of your bag you
+
+ align:start position:0%
+pack it in the bottom of your bag you
+ 
+
+ align:start position:0%
+pack it in the bottom of your bag you
+know as soon as you get to Miami um and
+
+ align:start position:0%
+know as soon as you get to Miami um and
+ 
+
+ align:start position:0%
+know as soon as you get to Miami um and
+leave it there um rather than taking it
+
+ align:start position:0%
+leave it there um rather than taking it
+ 
+
+ align:start position:0%
+leave it there um rather than taking it
+out so and again like you'll see a few
+
+ align:start position:0%
+out so and again like you'll see a few
+ 
+
+ align:start position:0%
+out so and again like you'll see a few
+people with iPhones but in Nicaragua but
+
+ align:start position:0%
+people with iPhones but in Nicaragua but
+ 
+
+ align:start position:0%
+people with iPhones but in Nicaragua but
+they're taking a risk and you shouldn't
+
+ align:start position:0%
+they're taking a risk and you shouldn't
+ 
+
+ align:start position:0%
+they're taking a risk and you shouldn't
+have yours out and about while you're
+
+ align:start position:0%
+have yours out and about while you're
+ 
+
+ align:start position:0%
+have yours out and about while you're
+there um but the one thing is that most
+
+ align:start position:0%
+there um but the one thing is that most
+ 
+
+ align:start position:0%
+there um but the one thing is that most
+of you are leaving super super early on
+
+ align:start position:0%
+of you are leaving super super early on
+ 
+
+ align:start position:0%
+of you are leaving super super early on
+Sunday so you do want to have your cell
+
+ align:start position:0%
+Sunday so you do want to have your cell
+ 
+
+ align:start position:0%
+Sunday so you do want to have your cell
+phone out that morning that middle of
+
+ align:start position:0%
+phone out that morning that middle of
+ 
+
+ align:start position:0%
+phone out that morning that middle of
+the night just to make sure you're awake
+
+ align:start position:0%
+the night just to make sure you're awake
+ 
+
+ align:start position:0%
+the night just to make sure you're awake
+um I don't know at 3:00 am like I feel
+
+ align:start position:0%
+um I don't know at 3:00 am like I feel
+ 
+
+ align:start position:0%
+um I don't know at 3:00 am like I feel
+like most of you probably won't even
+
+ align:start position:0%
+like most of you probably won't even
+ 
+
+ align:start position:0%
+like most of you probably won't even
+sleep right like I don't I don't go to
+
+ align:start position:0%
+sleep right like I don't I don't go to
+ 
+
+ align:start position:0%
+sleep right like I don't I don't go to
+sleep if I have to leave at 3: um but
+
+ align:start position:0%
+sleep if I have to leave at 3: um but
+ 
+
+ align:start position:0%
+sleep if I have to leave at 3: um but
+yeah we want to make sure you get there
+
+ align:start position:0%
+yeah we want to make sure you get there
+ 
+
+ align:start position:0%
+yeah we want to make sure you get there
+um so one other thing you want to bring
+
+ align:start position:0%
+um so one other thing you want to bring
+ 
+
+ align:start position:0%
+um so one other thing you want to bring
+is gifts for your Community Partners um
+
+ align:start position:0%
+is gifts for your Community Partners um
+ 
+
+ align:start position:0%
+is gifts for your Community Partners um
+and so some criteria for what makes a
+
+ align:start position:0%
+and so some criteria for what makes a
+ 
+
+ align:start position:0%
+and so some criteria for what makes a
+good gift is one that is not
+
+ align:start position:0%
+good gift is one that is not
+ 
+
+ align:start position:0%
+good gift is one that is not
+extravagantly over-the toop expensive
+
+ align:start position:0%
+extravagantly over-the toop expensive
+ 
+
+ align:start position:0%
+extravagantly over-the toop expensive
+because it can sort of set up
+
+ align:start position:0%
+because it can sort of set up
+ 
+
+ align:start position:0%
+because it can sort of set up
+a the disparity between wealth can be
+
+ align:start position:0%
+a the disparity between wealth can be
+ 
+
+ align:start position:0%
+a the disparity between wealth can be
+more um significant and make people feel
+
+ align:start position:0%
+more um significant and make people feel
+ 
+
+ align:start position:0%
+more um significant and make people feel
+uncomfortable um also you may well be on
+
+ align:start position:0%
+uncomfortable um also you may well be on
+ 
+
+ align:start position:0%
+uncomfortable um also you may well be on
+a budget and I don't want you to go
+
+ align:start position:0%
+a budget and I don't want you to go
+ 
+
+ align:start position:0%
+a budget and I don't want you to go
+broke buying gifts for your family um
+
+ align:start position:0%
+broke buying gifts for your family um
+ 
+
+ align:start position:0%
+broke buying gifts for your family um
+other things are will they actually use
+
+ align:start position:0%
+other things are will they actually use
+ 
+
+ align:start position:0%
+other things are will they actually use
+it will this just become some piece of
+
+ align:start position:0%
+it will this just become some piece of
+ 
+
+ align:start position:0%
+it will this just become some piece of
+trash that um adds trash to the
+
+ align:start position:0%
+trash that um adds trash to the
+ 
+
+ align:start position:0%
+trash that um adds trash to the
+community um in places where they're
+
+ align:start position:0%
+community um in places where they're
+ 
+
+ align:start position:0%
+community um in places where they're
+relatively pristine and we or not but we
+
+ align:start position:0%
+relatively pristine and we or not but we
+ 
+
+ align:start position:0%
+relatively pristine and we or not but we
+don't want to be adding to the trash
+
+ align:start position:0%
+don't want to be adding to the trash
+ 
+
+ align:start position:0%
+don't want to be adding to the trash
+load Etc um so daab has a few things
+
+ align:start position:0%
+load Etc um so daab has a few things
+ 
+
+ align:start position:0%
+load Etc um so daab has a few things
+that we um buy that are branded as daab
+
+ align:start position:0%
+that we um buy that are branded as daab
+ 
+
+ align:start position:0%
+that we um buy that are branded as daab
+objects that you can um buy from daab so
+
+ align:start position:0%
+objects that you can um buy from daab so
+ 
+
+ align:start position:0%
+objects that you can um buy from daab so
+gifts are not something that daab pays
+
+ align:start position:0%
+gifts are not something that daab pays
+ 
+
+ align:start position:0%
+gifts are not something that daab pays
+for it's something that you pay for as a
+
+ align:start position:0%
+for it's something that you pay for as a
+ 
+
+ align:start position:0%
+for it's something that you pay for as a
+team or an individual um because they're
+
+ align:start position:0%
+team or an individual um because they're
+ 
+
+ align:start position:0%
+team or an individual um because they're
+from you um and so it's up to you to
+
+ align:start position:0%
+from you um and so it's up to you to
+ 
+
+ align:start position:0%
+from you um and so it's up to you to
+decide how much but I think something is
+
+ align:start position:0%
+decide how much but I think something is
+ 
+
+ align:start position:0%
+decide how much but I think something is
+appropriate um so Sports bottles are $5
+
+ align:start position:0%
+appropriate um so Sports bottles are $5
+ 
+
+ align:start position:0%
+appropriate um so Sports bottles are $5
+these hats maybe six or 8 um hats I
+
+ align:start position:0%
+these hats maybe six or 8 um hats I
+ 
+
+ align:start position:0%
+these hats maybe six or 8 um hats I
+think are a pretty good gift because
+
+ align:start position:0%
+think are a pretty good gift because
+ 
+
+ align:start position:0%
+think are a pretty good gift because
+people can wear them and they like them
+
+ align:start position:0%
+people can wear them and they like them
+ 
+
+ align:start position:0%
+people can wear them and they like them
+and a lot of people wear baseball caps
+
+ align:start position:0%
+and a lot of people wear baseball caps
+ 
+
+ align:start position:0%
+and a lot of people wear baseball caps
+um but don't bring them Red Sox caps cuz
+
+ align:start position:0%
+um but don't bring them Red Sox caps cuz
+ 
+
+ align:start position:0%
+um but don't bring them Red Sox caps cuz
+most them like
+
+ align:start position:0%
+most them like
+ 
+
+ align:start position:0%
+most them like
+Yankees and those are the only two teams
+
+ align:start position:0%
+Yankees and those are the only two teams
+ 
+
+ align:start position:0%
+Yankees and those are the only two teams
+that are basically known from what I saw
+
+ align:start position:0%
+that are basically known from what I saw
+ 
+
+ align:start position:0%
+that are basically known from what I saw
+um we also have these little flashlights
+
+ align:start position:0%
+um we also have these little flashlights
+ 
+
+ align:start position:0%
+um we also have these little flashlights
+um oh I think the battery is blocked so
+
+ align:start position:0%
+um oh I think the battery is blocked so
+ 
+
+ align:start position:0%
+um oh I think the battery is blocked so
+I can't turn it on but yeah um the the
+
+ align:start position:0%
+I can't turn it on but yeah um the the
+ 
+
+ align:start position:0%
+I can't turn it on but yeah um the the
+challenge with these flashlights it
+
+ align:start position:0%
+challenge with these flashlights it
+ 
+
+ align:start position:0%
+challenge with these flashlights it
+means the battery has to be replaced and
+
+ align:start position:0%
+means the battery has to be replaced and
+ 
+
+ align:start position:0%
+means the battery has to be replaced and
+things like that so it's a mixed bag um
+
+ align:start position:0%
+things like that so it's a mixed bag um
+ 
+
+ align:start position:0%
+things like that so it's a mixed bag um
+how valuable it is but they're they're
+
+ align:start position:0%
+how valuable it is but they're they're
+ 
+
+ align:start position:0%
+how valuable it is but they're they're
+fun um these little drawstring bags um
+
+ align:start position:0%
+fun um these little drawstring bags um
+ 
+
+ align:start position:0%
+fun um these little drawstring bags um
+which people like um I often bring
+
+ align:start position:0%
+which people like um I often bring
+ 
+
+ align:start position:0%
+which people like um I often bring
+chocolate to share with my like I'll
+
+ align:start position:0%
+chocolate to share with my like I'll
+ 
+
+ align:start position:0%
+chocolate to share with my like I'll
+bring a couple hats to bring for like
+
+ align:start position:0%
+bring a couple hats to bring for like
+ 
+
+ align:start position:0%
+bring a couple hats to bring for like
+someone like Lindsay or someone who's
+
+ align:start position:0%
+someone like Lindsay or someone who's
+ 
+
+ align:start position:0%
+someone like Lindsay or someone who's
+helping you a lot and then for the
+
+ align:start position:0%
+helping you a lot and then for the
+ 
+
+ align:start position:0%
+helping you a lot and then for the
+family just bring chocolate that you can
+
+ align:start position:0%
+family just bring chocolate that you can
+ 
+
+ align:start position:0%
+family just bring chocolate that you can
+share with them um Trader Joe sells
+
+ align:start position:0%
+share with them um Trader Joe sells
+ 
+
+ align:start position:0%
+share with them um Trader Joe sells
+pretty good pretty cheap chocolate that
+
+ align:start position:0%
+pretty good pretty cheap chocolate that
+ 
+
+ align:start position:0%
+pretty good pretty cheap chocolate that
+travels pretty well some chocolate melts
+
+ align:start position:0%
+travels pretty well some chocolate melts
+ 
+
+ align:start position:0%
+travels pretty well some chocolate melts
+really easily and that's not ideal for
+
+ align:start position:0%
+really easily and that's not ideal for
+ 
+
+ align:start position:0%
+really easily and that's not ideal for
+given how hot it is um but some of the
+
+ align:start position:0%
+given how hot it is um but some of the
+ 
+
+ align:start position:0%
+given how hot it is um but some of the
+nicer chocolate comes in like three
+
+ align:start position:0%
+nicer chocolate comes in like three
+ 
+
+ align:start position:0%
+nicer chocolate comes in like three
+packs for like two bucks um and just
+
+ align:start position:0%
+packs for like two bucks um and just
+ 
+
+ align:start position:0%
+packs for like two bucks um and just
+sharing that with your family it means
+
+ align:start position:0%
+sharing that with your family it means
+ 
+
+ align:start position:0%
+sharing that with your family it means
+something you can share with all the
+
+ align:start position:0%
+something you can share with all the
+ 
+
+ align:start position:0%
+something you can share with all the
+members um and is nice and is from your
+
+ align:start position:0%
+members um and is nice and is from your
+ 
+
+ align:start position:0%
+members um and is nice and is from your
+home country chocolate in Nicaragua in
+
+ align:start position:0%
+home country chocolate in Nicaragua in
+ 
+
+ align:start position:0%
+home country chocolate in Nicaragua in
+my opinion is far inferior to Chate in
+
+ align:start position:0%
+my opinion is far inferior to Chate in
+ 
+
+ align:start position:0%
+my opinion is far inferior to Chate in
+the states um and uh a lot of people I
+
+ align:start position:0%
+the states um and uh a lot of people I
+ 
+
+ align:start position:0%
+the states um and uh a lot of people I
+know agree um and so something like that
+
+ align:start position:0%
+know agree um and so something like that
+ 
+
+ align:start position:0%
+know agree um and so something like that
+is also appropriate so are there any
+
+ align:start position:0%
+is also appropriate so are there any
+ 
+
+ align:start position:0%
+is also appropriate so are there any
+questions on gifts want to get any of
+
+ align:start position:0%
+questions on gifts want to get any of
+ 
+
+ align:start position:0%
+questions on gifts want to get any of
+these um so I'm trying to leave a little
+
+ align:start position:0%
+these um so I'm trying to leave a little
+ 
+
+ align:start position:0%
+these um so I'm trying to leave a little
+time at the end of this class so that
+
+ align:start position:0%
+time at the end of this class so that
+ 
+
+ align:start position:0%
+time at the end of this class so that
+your team can make a list of all the
+
+ align:start position:0%
+your team can make a list of all the
+ 
+
+ align:start position:0%
+your team can make a list of all the
+things you need from daab and these gift
+
+ align:start position:0%
+things you need from daab and these gift
+ 
+
+ align:start position:0%
+things you need from daab and these gift
+things are among
+
+ align:start position:0%
+things are among
+ 
+
+ align:start position:0%
+things are among
+them um in terms of money that you might
+
+ align:start position:0%
+them um in terms of money that you might
+ 
+
+ align:start position:0%
+them um in terms of money that you might
+need uh so you should bring your Charlie
+
+ align:start position:0%
+need uh so you should bring your Charlie
+ 
+
+ align:start position:0%
+need uh so you should bring your Charlie
+card because you'll probably be coming
+
+ align:start position:0%
+card because you'll probably be coming
+ 
+
+ align:start position:0%
+card because you'll probably be coming
+back on the tea if not going there um
+
+ align:start position:0%
+back on the tea if not going there um
+ 
+
+ align:start position:0%
+back on the tea if not going there um
+there's an entry Visa cost to get into
+
+ align:start position:0%
+there's an entry Visa cost to get into
+ 
+
+ align:start position:0%
+there's an entry Visa cost to get into
+Nicaragua of $10 and if you just have a
+
+ align:start position:0%
+Nicaragua of $10 and if you just have a
+ 
+
+ align:start position:0%
+Nicaragua of $10 and if you just have a
+$10 bill on you it's nice to not have to
+
+ align:start position:0%
+$10 bill on you it's nice to not have to
+ 
+
+ align:start position:0%
+$10 bill on you it's nice to not have to
+deal with the Customs agent making
+
+ align:start position:0%
+deal with the Customs agent making
+ 
+
+ align:start position:0%
+deal with the Customs agent making
+change um if you're bringing cash so you
+
+ align:start position:0%
+change um if you're bringing cash so you
+ 
+
+ align:start position:0%
+change um if you're bringing cash so you
+may want some cash um for food that's
+
+ align:start position:0%
+may want some cash um for food that's
+ 
+
+ align:start position:0%
+may want some cash um for food that's
+not already prepaid um which you guys
+
+ align:start position:0%
+not already prepaid um which you guys
+ 
+
+ align:start position:0%
+not already prepaid um which you guys
+will reimburse us for after the trip or
+
+ align:start position:0%
+will reimburse us for after the trip or
+ 
+
+ align:start position:0%
+will reimburse us for after the trip or
+um for gifts for yourself to bring home
+
+ align:start position:0%
+um for gifts for yourself to bring home
+ 
+
+ align:start position:0%
+um for gifts for yourself to bring home
+to for yourself or family members um at
+
+ align:start position:0%
+to for yourself or family members um at
+ 
+
+ align:start position:0%
+to for yourself or family members um at
+the airport if not while you're
+
+ align:start position:0%
+the airport if not while you're
+ 
+
+ align:start position:0%
+the airport if not while you're
+traveling there'll be opportunities to
+
+ align:start position:0%
+traveling there'll be opportunities to
+ 
+
+ align:start position:0%
+traveling there'll be opportunities to
+do a little shopping um so you shouldn't
+
+ align:start position:0%
+do a little shopping um so you shouldn't
+ 
+
+ align:start position:0%
+do a little shopping um so you shouldn't
+bring anything bigger than a $20 bill um
+
+ align:start position:0%
+bring anything bigger than a $20 bill um
+ 
+
+ align:start position:0%
+bring anything bigger than a $20 bill um
+and smaller bills are nicer generally
+
+ align:start position:0%
+and smaller bills are nicer generally
+ 
+
+ align:start position:0%
+and smaller bills are nicer generally
+because it's hard for people to make
+
+ align:start position:0%
+because it's hard for people to make
+ 
+
+ align:start position:0%
+because it's hard for people to make
+change um but the Bills should be in
+
+ align:start position:0%
+change um but the Bills should be in
+ 
+
+ align:start position:0%
+change um but the Bills should be in
+decent condition if they're really ratty
+
+ align:start position:0%
+decent condition if they're really ratty
+ 
+
+ align:start position:0%
+decent condition if they're really ratty
+people won't take them um and then if
+
+ align:start position:0%
+people won't take them um and then if
+ 
+
+ align:start position:0%
+people won't take them um and then if
+you expect to be needing to use your
+
+ align:start position:0%
+you expect to be needing to use your
+ 
+
+ align:start position:0%
+you expect to be needing to use your
+bank or credit card debit card for
+
+ align:start position:0%
+bank or credit card debit card for
+ 
+
+ align:start position:0%
+bank or credit card debit card for
+either for general just getting money
+
+ align:start position:0%
+either for general just getting money
+ 
+
+ align:start position:0%
+either for general just getting money
+out of an ATM or for an emergency you
+
+ align:start position:0%
+out of an ATM or for an emergency you
+ 
+
+ align:start position:0%
+out of an ATM or for an emergency you
+should call them to warn them that
+
+ align:start position:0%
+should call them to warn them that
+ 
+
+ align:start position:0%
+should call them to warn them that
+you're traveling so that if you do need
+
+ align:start position:0%
+you're traveling so that if you do need
+ 
+
+ align:start position:0%
+you're traveling so that if you do need
+it you can CU usually they'll block any
+
+ align:start position:0%
+it you can CU usually they'll block any
+ 
+
+ align:start position:0%
+it you can CU usually they'll block any
+charges and unless youve told them ahead
+
+ align:start position:0%
+charges and unless youve told them ahead
+ 
+
+ align:start position:0%
+charges and unless youve told them ahead
+of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+time um some tips so you should assume
+
+ align:start position:0%
+time um some tips so you should assume
+ 
+
+ align:start position:0%
+time um some tips so you should assume
+that drinking water is unsafe um which
+
+ align:start position:0%
+that drinking water is unsafe um which
+ 
+
+ align:start position:0%
+that drinking water is unsafe um which
+means that any vegetables or fruits that
+
+ align:start position:0%
+means that any vegetables or fruits that
+ 
+
+ align:start position:0%
+means that any vegetables or fruits that
+aren't cooked are also unsafe because
+
+ align:start position:0%
+aren't cooked are also unsafe because
+ 
+
+ align:start position:0%
+aren't cooked are also unsafe because
+they were probably washed in that unsafe
+
+ align:start position:0%
+they were probably washed in that unsafe
+ 
+
+ align:start position:0%
+they were probably washed in that unsafe
+drinking water um so uh each team me
+
+ align:start position:0%
+drinking water um so uh each team me
+ 
+
+ align:start position:0%
+drinking water um so uh each team me
+team trip leader will have a water
+
+ align:start position:0%
+team trip leader will have a water
+ 
+
+ align:start position:0%
+team trip leader will have a water
+filter that you guys can use to filter
+
+ align:start position:0%
+filter that you guys can use to filter
+ 
+
+ align:start position:0%
+filter that you guys can use to filter
+your own water which means you really do
+
+ align:start position:0%
+your own water which means you really do
+ 
+
+ align:start position:0%
+your own water which means you really do
+want to bring a water bottle so that you
+
+ align:start position:0%
+want to bring a water bottle so that you
+ 
+
+ align:start position:0%
+want to bring a water bottle so that you
+can um clean have clean water in that
+
+ align:start position:0%
+can um clean have clean water in that
+ 
+
+ align:start position:0%
+can um clean have clean water in that
+water bottle um but this is definitely
+
+ align:start position:0%
+water bottle um but this is definitely
+ 
+
+ align:start position:0%
+water bottle um but this is definitely
+something to be cautious on so you stay
+
+ align:start position:0%
+something to be cautious on so you stay
+ 
+
+ align:start position:0%
+something to be cautious on so you stay
+healthy for the trip because it's such a
+
+ align:start position:0%
+healthy for the trip because it's such a
+ 
+
+ align:start position:0%
+healthy for the trip because it's such a
+short trip that if you get sick for a
+
+ align:start position:0%
+short trip that if you get sick for a
+ 
+
+ align:start position:0%
+short trip that if you get sick for a
+few days that's half your
+
+ align:start position:0%
+few days that's half your
+ 
+
+ align:start position:0%
+few days that's half your
+trip um NE nothing nothing expensive at
+
+ align:start position:0%
+trip um NE nothing nothing expensive at
+ 
+
+ align:start position:0%
+trip um NE nothing nothing expensive at
+least in site or brought so you know
+
+ align:start position:0%
+least in site or brought so you know
+ 
+
+ align:start position:0%
+least in site or brought so you know
+like a brass rat or nice jewelry or
+
+ align:start position:0%
+like a brass rat or nice jewelry or
+ 
+
+ align:start position:0%
+like a brass rat or nice jewelry or
+watch or whatever leave here if you need
+
+ align:start position:0%
+watch or whatever leave here if you need
+ 
+
+ align:start position:0%
+watch or whatever leave here if you need
+to bring that cell phone so you have it
+
+ align:start position:0%
+to bring that cell phone so you have it
+ 
+
+ align:start position:0%
+to bring that cell phone so you have it
+while you're in the states while you're
+
+ align:start position:0%
+while you're in the states while you're
+ 
+
+ align:start position:0%
+while you're in the states while you're
+traveling just keep it hidden in your
+
+ align:start position:0%
+traveling just keep it hidden in your
+ 
+
+ align:start position:0%
+traveling just keep it hidden in your
+bag so that um it's not brought
+
+ align:start position:0%
+bag so that um it's not brought
+ 
+
+ align:start position:0%
+bag so that um it's not brought
+attention to being brought attention to
+
+ align:start position:0%
+attention to being brought attention to
+ 
+
+ align:start position:0%
+attention to being brought attention to
+at all um you should always be travel in
+
+ align:start position:0%
+at all um you should always be travel in
+ 
+
+ align:start position:0%
+at all um you should always be travel in
+groups ideally um but especially at
+
+ align:start position:0%
+groups ideally um but especially at
+ 
+
+ align:start position:0%
+groups ideally um but especially at
+night um there's going to be some cases
+
+ align:start position:0%
+night um there's going to be some cases
+ 
+
+ align:start position:0%
+night um there's going to be some cases
+where that'll be tricky but um do your
+
+ align:start position:0%
+where that'll be tricky but um do your
+ 
+
+ align:start position:0%
+where that'll be tricky but um do your
+best to be as safe as possible um as I
+
+ align:start position:0%
+best to be as safe as possible um as I
+ 
+
+ align:start position:0%
+best to be as safe as possible um as I
+mentioned flexibility and Patience are
+
+ align:start position:0%
+mentioned flexibility and Patience are
+ 
+
+ align:start position:0%
+mentioned flexibility and Patience are
+really great assets to have um so just
+
+ align:start position:0%
+really great assets to have um so just
+ 
+
+ align:start position:0%
+really great assets to have um so just
+sort of go in not expecting to be as
+
+ align:start position:0%
+sort of go in not expecting to be as
+ 
+
+ align:start position:0%
+sort of go in not expecting to be as
+efficient or effective as you NE
+
+ align:start position:0%
+efficient or effective as you NE
+ 
+
+ align:start position:0%
+efficient or effective as you NE
+necessarily hoped and sort of expect
+
+ align:start position:0%
+necessarily hoped and sort of expect
+ 
+
+ align:start position:0%
+necessarily hoped and sort of expect
+that things are going to change at the
+
+ align:start position:0%
+that things are going to change at the
+ 
+
+ align:start position:0%
+that things are going to change at the
+last minute and that'll help make the
+
+ align:start position:0%
+last minute and that'll help make the
+ 
+
+ align:start position:0%
+last minute and that'll help make the
+trip more fun rather than frustrating um
+
+ align:start position:0%
+trip more fun rather than frustrating um
+ 
+
+ align:start position:0%
+trip more fun rather than frustrating um
+and then managing expectations with the
+
+ align:start position:0%
+and then managing expectations with the
+ 
+
+ align:start position:0%
+and then managing expectations with the
+Community Partners um it's really easy
+
+ align:start position:0%
+Community Partners um it's really easy
+ 
+
+ align:start position:0%
+Community Partners um it's really easy
+for Community Partners to be like when
+
+ align:start position:0%
+for Community Partners to be like when
+ 
+
+ align:start position:0%
+for Community Partners to be like when
+are you coming back and you're so pumped
+
+ align:start position:0%
+are you coming back and you're so pumped
+ 
+
+ align:start position:0%
+are you coming back and you're so pumped
+and you're having such a great time and
+
+ align:start position:0%
+and you're having such a great time and
+ 
+
+ align:start position:0%
+and you're having such a great time and
+you're like I'll be back this summer
+
+ align:start position:0%
+you're like I'll be back this summer
+ 
+
+ align:start position:0%
+you're like I'll be back this summer
+like not thinking about well actually I
+
+ align:start position:0%
+like not thinking about well actually I
+ 
+
+ align:start position:0%
+like not thinking about well actually I
+have that internship at whoever and I'm
+
+ align:start position:0%
+have that internship at whoever and I'm
+ 
+
+ align:start position:0%
+have that internship at whoever and I'm
+not going to be back this summer and may
+
+ align:start position:0%
+not going to be back this summer and may
+ 
+
+ align:start position:0%
+not going to be back this summer and may
+never be back and so you don't want to
+
+ align:start position:0%
+never be back and so you don't want to
+ 
+
+ align:start position:0%
+never be back and so you don't want to
+make any promises that you can't keep
+
+ align:start position:0%
+make any promises that you can't keep
+ 
+
+ align:start position:0%
+make any promises that you can't keep
+that's really important um because that
+
+ align:start position:0%
+that's really important um because that
+ 
+
+ align:start position:0%
+that's really important um because that
+can ruin our relationship with our
+
+ align:start position:0%
+can ruin our relationship with our
+ 
+
+ align:start position:0%
+can ruin our relationship with our
+Community
+
+ align:start position:0%
+Community
+ 
+
+ align:start position:0%
+Community
+Partners um so just a reminder a few of
+
+ align:start position:0%
+Partners um so just a reminder a few of
+ 
+
+ align:start position:0%
+Partners um so just a reminder a few of
+you still owe me at least some of these
+
+ align:start position:0%
+you still owe me at least some of these
+ 
+
+ align:start position:0%
+you still owe me at least some of these
+things and so please get them to me
+
+ align:start position:0%
+things and so please get them to me
+ 
+
+ align:start position:0%
+things and so please get them to me
+today or tell me why you can't and what
+
+ align:start position:0%
+today or tell me why you can't and what
+ 
+
+ align:start position:0%
+today or tell me why you can't and what
+you're going to do if you haven't
+
+ align:start position:0%
+you're going to do if you haven't
+ 
+
+ align:start position:0%
+you're going to do if you haven't
+already um and so for the remainder of
+
+ align:start position:0%
+already um and so for the remainder of
+ 
+
+ align:start position:0%
+already um and so for the remainder of
+the class um I need to do micro
+
+ align:start position:0%
+the class um I need to do micro
+ 
+
+ align:start position:0%
+the class um I need to do micro
+interviews with everyone who's traveling
+
+ align:start position:0%
+interviews with everyone who's traveling
+ 
+
+ align:start position:0%
+interviews with everyone who's traveling
+um it's just a daab thing that we do we
+
+ align:start position:0%
+um it's just a daab thing that we do we
+ 
+
+ align:start position:0%
+um it's just a daab thing that we do we
+just talk oneon-one really briefly
+
+ align:start position:0%
+just talk oneon-one really briefly
+ 
+
+ align:start position:0%
+just talk oneon-one really briefly
+um you may want to revise your plan a
+
+ align:start position:0%
+um you may want to revise your plan a
+ 
+
+ align:start position:0%
+um you may want to revise your plan a
+little bit based on feedback from the
+
+ align:start position:0%
+little bit based on feedback from the
+ 
+
+ align:start position:0%
+little bit based on feedback from the
+presentations um you probably want to
+
+ align:start position:0%
+presentations um you probably want to
+ 
+
+ align:start position:0%
+presentations um you probably want to
+talk in your group about how much
+
+ align:start position:0%
+talk in your group about how much
+ 
+
+ align:start position:0%
+talk in your group about how much
+checked luggage you're having versus
+
+ align:start position:0%
+checked luggage you're having versus
+ 
+
+ align:start position:0%
+checked luggage you're having versus
+carryon who's carrying what for any
+
+ align:start position:0%
+carryon who's carrying what for any
+ 
+
+ align:start position:0%
+carryon who's carrying what for any
+bulky items you have have things that
+
+ align:start position:0%
+bulky items you have have things that
+ 
+
+ align:start position:0%
+bulky items you have have things that
+you might need from daab I need you to
+
+ align:start position:0%
+you might need from daab I need you to
+ 
+
+ align:start position:0%
+you might need from daab I need you to
+tell me by the end of class today so you
+
+ align:start position:0%
+tell me by the end of class today so you
+ 
+
+ align:start position:0%
+tell me by the end of class today so you
+might need tools you might need cameras
+
+ align:start position:0%
+might need tools you might need cameras
+ 
+
+ align:start position:0%
+might need tools you might need cameras
+we have some that we can lend um
+
+ align:start position:0%
+we have some that we can lend um
+ 
+
+ align:start position:0%
+we have some that we can lend um
+mosquito Nets hammocks other it'd be
+
+ align:start position:0%
+mosquito Nets hammocks other it'd be
+ 
+
+ align:start position:0%
+mosquito Nets hammocks other it'd be
+nice if at least a few people have
+
+ align:start position:0%
+nice if at least a few people have
+ 
+
+ align:start position:0%
+nice if at least a few people have
+cameras so that um you can get different
+
+ align:start position:0%
+cameras so that um you can get different
+ 
+
+ align:start position:0%
+cameras so that um you can get different
+angles of shots when you're all taking
+
+ align:start position:0%
+angles of shots when you're all taking
+ 
+
+ align:start position:0%
+angles of shots when you're all taking
+pictures together and also um if one
+
+ align:start position:0%
+pictures together and also um if one
+ 
+
+ align:start position:0%
+pictures together and also um if one
+dies you're not unable to take pictures
+
+ align:start position:0%
+dies you're not unable to take pictures
+ 
+
+ align:start position:0%
+dies you're not unable to take pictures
+because pictures are really important
+
+ align:start position:0%
+because pictures are really important
+ 
+
+ align:start position:0%
+because pictures are really important
+for the projects um and then anything
+
+ align:start position:0%
+for the projects um and then anything
+ 
+
+ align:start position:0%
+for the projects um and then anything
+else you might need
+
+ align:start position:0%
+else you might need
+ 
+
+ align:start position:0%
+else you might need
+so are there any questions about all
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that okay cool
\ No newline at end of file
diff --git a/Wb34zGvpC3E.txt b/Wb34zGvpC3E.txt
new file mode 100644
index 0000000000000000000000000000000000000000..d95e8ff13ada9dba8e247c1aa9b70da3dd9121fa
--- /dev/null
+++ b/Wb34zGvpC3E.txt
@@ -0,0 +1,9024 @@
+align:start position:0%
+ 
+the following content is provided under
+
+ align:start position:0%
+the following content is provided under
+ 
+
+ align:start position:0%
+the following content is provided under
+a Creative Commons license your support
+
+ align:start position:0%
+a Creative Commons license your support
+ 
+
+ align:start position:0%
+a Creative Commons license your support
+will help MIT open courseware continue
+
+ align:start position:0%
+will help MIT open courseware continue
+ 
+
+ align:start position:0%
+will help MIT open courseware continue
+to offer highquality educational
+
+ align:start position:0%
+to offer highquality educational
+ 
+
+ align:start position:0%
+to offer highquality educational
+resources for free to make a donation or
+
+ align:start position:0%
+resources for free to make a donation or
+ 
+
+ align:start position:0%
+resources for free to make a donation or
+to view additional materials from
+
+ align:start position:0%
+to view additional materials from
+ 
+
+ align:start position:0%
+to view additional materials from
+hundreds of MIT courses visit MIT open
+
+ align:start position:0%
+hundreds of MIT courses visit MIT open
+ 
+
+ align:start position:0%
+hundreds of MIT courses visit MIT open
+courseware at
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+ocw.mit.edu let's see a couple of
+
+ align:start position:0%
+ocw.mit.edu let's see a couple of
+ 
+
+ align:start position:0%
+ocw.mit.edu let's see a couple of
+announcements uh tomorrow there'll be a
+
+ align:start position:0%
+announcements uh tomorrow there'll be a
+ 
+
+ align:start position:0%
+announcements uh tomorrow there'll be a
+quiz 6 based on homework 6 just on the
+
+ align:start position:0%
+quiz 6 based on homework 6 just on the
+ 
+
+ align:start position:0%
+quiz 6 based on homework 6 just on the
+um crystallography there's a little bit
+
+ align:start position:0%
+um crystallography there's a little bit
+ 
+
+ align:start position:0%
+um crystallography there's a little bit
+at the end of homework six on X-rays and
+
+ align:start position:0%
+at the end of homework six on X-rays and
+ 
+
+ align:start position:0%
+at the end of homework six on X-rays and
+we will just start to talk about x-rays
+
+ align:start position:0%
+we will just start to talk about x-rays
+ 
+
+ align:start position:0%
+we will just start to talk about x-rays
+today so I think that uh we'll leave
+
+ align:start position:0%
+today so I think that uh we'll leave
+ 
+
+ align:start position:0%
+today so I think that uh we'll leave
+that out so just be based on
+
+ align:start position:0%
+that out so just be based on
+ 
+
+ align:start position:0%
+that out so just be based on
+crystallography um and I've asked the
+
+ align:start position:0%
+crystallography um and I've asked the
+ 
+
+ align:start position:0%
+crystallography um and I've asked the
+recitation instructors to administer the
+
+ align:start position:0%
+recitation instructors to administer the
+ 
+
+ align:start position:0%
+recitation instructors to administer the
+test at the end of the period so you can
+
+ align:start position:0%
+test at the end of the period so you can
+ 
+
+ align:start position:0%
+test at the end of the period so you can
+have some chance to ask uh
+
+ align:start position:0%
+have some chance to ask uh
+ 
+
+ align:start position:0%
+have some chance to ask uh
+questions um last day we talked about uh
+
+ align:start position:0%
+questions um last day we talked about uh
+ 
+
+ align:start position:0%
+questions um last day we talked about uh
+crystallography we were introduced to
+
+ align:start position:0%
+crystallography we were introduced to
+ 
+
+ align:start position:0%
+crystallography we were introduced to
+the seven Crystal systems and the 14 bra
+
+ align:start position:0%
+the seven Crystal systems and the 14 bra
+ 
+
+ align:start position:0%
+the seven Crystal systems and the 14 bra
+lates which are showing up on the uh
+
+ align:start position:0%
+lates which are showing up on the uh
+ 
+
+ align:start position:0%
+lates which are showing up on the uh
+slide taken from the lecture notes and
+
+ align:start position:0%
+slide taken from the lecture notes and
+ 
+
+ align:start position:0%
+slide taken from the lecture notes and
+we saw that if we wanted to describe the
+
+ align:start position:0%
+we saw that if we wanted to describe the
+ 
+
+ align:start position:0%
+we saw that if we wanted to describe the
+arrangement of atoms in a crystal we
+
+ align:start position:0%
+arrangement of atoms in a crystal we
+ 
+
+ align:start position:0%
+arrangement of atoms in a crystal we
+could do so by combining the notion of
+
+ align:start position:0%
+could do so by combining the notion of
+ 
+
+ align:start position:0%
+could do so by combining the notion of
+the brav latus of which there are 14
+
+ align:start position:0%
+the brav latus of which there are 14
+ 
+
+ align:start position:0%
+the brav latus of which there are 14
+distinct types with a basis the basis
+
+ align:start position:0%
+distinct types with a basis the basis
+ 
+
+ align:start position:0%
+distinct types with a basis the basis
+could be a single atom could be a group
+
+ align:start position:0%
+could be a single atom could be a group
+ 
+
+ align:start position:0%
+could be a single atom could be a group
+of atoms could be an ion pair could be
+
+ align:start position:0%
+of atoms could be an ion pair could be
+ 
+
+ align:start position:0%
+of atoms could be an ion pair could be
+uh atom pair and uh we saw that got us
+
+ align:start position:0%
+uh atom pair and uh we saw that got us
+ 
+
+ align:start position:0%
+uh atom pair and uh we saw that got us
+through an elaborate set of uh crystals
+
+ align:start position:0%
+through an elaborate set of uh crystals
+ 
+
+ align:start position:0%
+through an elaborate set of uh crystals
+and then towards the end we focused on
+
+ align:start position:0%
+and then towards the end we focused on
+ 
+
+ align:start position:0%
+and then towards the end we focused on
+on cubic crystals because cubic crystals
+
+ align:start position:0%
+on cubic crystals because cubic crystals
+ 
+
+ align:start position:0%
+on cubic crystals because cubic crystals
+are representative of a large number of
+
+ align:start position:0%
+are representative of a large number of
+ 
+
+ align:start position:0%
+are representative of a large number of
+metals in the periodic table and it's
+
+ align:start position:0%
+metals in the periodic table and it's
+ 
+
+ align:start position:0%
+metals in the periodic table and it's
+much more tractable mathematically so
+
+ align:start position:0%
+much more tractable mathematically so
+ 
+
+ align:start position:0%
+much more tractable mathematically so
+we're going to focus on cubic crystals
+
+ align:start position:0%
+we're going to focus on cubic crystals
+ 
+
+ align:start position:0%
+we're going to focus on cubic crystals
+and I'm going to continue along with
+
+ align:start position:0%
+and I'm going to continue along with
+ 
+
+ align:start position:0%
+and I'm going to continue along with
+that today and in particular I want to
+
+ align:start position:0%
+that today and in particular I want to
+ 
+
+ align:start position:0%
+that today and in particular I want to
+start looking at uh notation and the
+
+ align:start position:0%
+start looking at uh notation and the
+ 
+
+ align:start position:0%
+start looking at uh notation and the
+reason I want to look at notation is I
+
+ align:start position:0%
+reason I want to look at notation is I
+ 
+
+ align:start position:0%
+reason I want to look at notation is I
+want to be able to define a point a line
+
+ align:start position:0%
+want to be able to define a point a line
+ 
+
+ align:start position:0%
+want to be able to define a point a line
+and a plane so that when we start
+
+ align:start position:0%
+and a plane so that when we start
+ 
+
+ align:start position:0%
+and a plane so that when we start
+characterizing crystals I can give you a
+
+ align:start position:0%
+characterizing crystals I can give you a
+ 
+
+ align:start position:0%
+characterizing crystals I can give you a
+mathematical notation that represents
+
+ align:start position:0%
+mathematical notation that represents
+ 
+
+ align:start position:0%
+mathematical notation that represents
+the face of the cube the body diagonal
+
+ align:start position:0%
+the face of the cube the body diagonal
+ 
+
+ align:start position:0%
+the face of the cube the body diagonal
+of the cube a line going on the body
+
+ align:start position:0%
+of the cube a line going on the body
+ 
+
+ align:start position:0%
+of the cube a line going on the body
+diagonal a line going along the edge
+
+ align:start position:0%
+diagonal a line going along the edge
+ 
+
+ align:start position:0%
+diagonal a line going along the edge
+instead of writing it in words I want to
+
+ align:start position:0%
+instead of writing it in words I want to
+ 
+
+ align:start position:0%
+instead of writing it in words I want to
+be able to do so mathematically and so
+
+ align:start position:0%
+be able to do so mathematically and so
+ 
+
+ align:start position:0%
+be able to do so mathematically and so
+for that we're going to turn to this
+
+ align:start position:0%
+for that we're going to turn to this
+ 
+
+ align:start position:0%
+for that we're going to turn to this
+handout which has the elements of
+
+ align:start position:0%
+handout which has the elements of
+ 
+
+ align:start position:0%
+handout which has the elements of
+crystallographic notation I'm going to
+
+ align:start position:0%
+crystallographic notation I'm going to
+ 
+
+ align:start position:0%
+crystallographic notation I'm going to
+quickly go through this I think last day
+
+ align:start position:0%
+quickly go through this I think last day
+ 
+
+ align:start position:0%
+quickly go through this I think last day
+we started talking about position so
+
+ align:start position:0%
+we started talking about position so
+ 
+
+ align:start position:0%
+we started talking about position so
+I've drawn a little uh sketch here this
+
+ align:start position:0%
+I've drawn a little uh sketch here this
+ 
+
+ align:start position:0%
+I've drawn a little uh sketch here this
+is the unit cell the unit cell is the
+
+ align:start position:0%
+is the unit cell the unit cell is the
+ 
+
+ align:start position:0%
+is the unit cell the unit cell is the
+cube because we're talking about a cubic
+
+ align:start position:0%
+cube because we're talking about a cubic
+ 
+
+ align:start position:0%
+cube because we're talking about a cubic
+system and this is just the lattice I
+
+ align:start position:0%
+system and this is just the lattice I
+ 
+
+ align:start position:0%
+system and this is just the lattice I
+haven't put atoms here okay so I'm just
+
+ align:start position:0%
+haven't put atoms here okay so I'm just
+ 
+
+ align:start position:0%
+haven't put atoms here okay so I'm just
+talking about lattice points in space
+
+ align:start position:0%
+talking about lattice points in space
+ 
+
+ align:start position:0%
+talking about lattice points in space
+and just to remind us a B and C are the
+
+ align:start position:0%
+and just to remind us a B and C are the
+ 
+
+ align:start position:0%
+and just to remind us a B and C are the
+unit vectors and in a cubic system a
+
+ align:start position:0%
+unit vectors and in a cubic system a
+ 
+
+ align:start position:0%
+unit vectors and in a cubic system a
+equal bals C and each of them is equal
+
+ align:start position:0%
+equal bals C and each of them is equal
+ 
+
+ align:start position:0%
+equal bals C and each of them is equal
+to a the lattice constant this is the
+
+ align:start position:0%
+to a the lattice constant this is the
+ 
+
+ align:start position:0%
+to a the lattice constant this is the
+lattice constant
+
+ align:start position:0%
+lattice constant
+ 
+
+ align:start position:0%
+lattice constant
+a and that's that's the dimension a the
+
+ align:start position:0%
+a and that's that's the dimension a the
+ 
+
+ align:start position:0%
+a and that's that's the dimension a the
+lattice constant and all angles are
+
+ align:start position:0%
+lattice constant and all angles are
+ 
+
+ align:start position:0%
+lattice constant and all angles are
+right angles so Alpha equals betaal g
+
+ align:start position:0%
+right angles so Alpha equals betaal g
+ 
+
+ align:start position:0%
+right angles so Alpha equals betaal g
+equals 90° so just to just to practice
+
+ align:start position:0%
+equals 90° so just to just to practice
+ 
+
+ align:start position:0%
+equals 90° so just to just to practice
+the origin as I've shown here the origin
+
+ align:start position:0%
+the origin as I've shown here the origin
+ 
+
+ align:start position:0%
+the origin as I've shown here the origin
+all we do is write 0 0 Z as you would in
+
+ align:start position:0%
+all we do is write 0 0 Z as you would in
+ 
+
+ align:start position:0%
+all we do is write 0 0 Z as you would in
+your math class but don't put
+
+ align:start position:0%
+your math class but don't put
+ 
+
+ align:start position:0%
+your math class but don't put
+parentheses around it because
+
+ align:start position:0%
+parentheses around it because
+ 
+
+ align:start position:0%
+parentheses around it because
+parentheses are reserved for planes
+
+ align:start position:0%
+parentheses are reserved for planes
+ 
+
+ align:start position:0%
+parentheses are reserved for planes
+we're going to use parentheses later on
+
+ align:start position:0%
+we're going to use parentheses later on
+ 
+
+ align:start position:0%
+we're going to use parentheses later on
+the crystallographers have their own
+
+ align:start position:0%
+the crystallographers have their own
+ 
+
+ align:start position:0%
+the crystallographers have their own
+notation okay so here's point a here's
+
+ align:start position:0%
+notation okay so here's point a here's
+ 
+
+ align:start position:0%
+notation okay so here's point a here's
+point a what do we see it's
+
+ align:start position:0%
+point a what do we see it's
+ 
+
+ align:start position:0%
+point a what do we see it's
+out uh it's on it's in the the YZ plane
+
+ align:start position:0%
+out uh it's on it's in the the YZ plane
+ 
+
+ align:start position:0%
+out uh it's on it's in the the YZ plane
+by the way I've chosen a um a set of
+
+ align:start position:0%
+by the way I've chosen a um a set of
+ 
+
+ align:start position:0%
+by the way I've chosen a um a set of
+coordinate axes that are in Conformity
+
+ align:start position:0%
+coordinate axes that are in Conformity
+ 
+
+ align:start position:0%
+coordinate axes that are in Conformity
+with the right hand rule I don't care
+
+ align:start position:0%
+with the right hand rule I don't care
+ 
+
+ align:start position:0%
+with the right hand rule I don't care
+which axis you choose to be X it doesn't
+
+ align:start position:0%
+which axis you choose to be X it doesn't
+ 
+
+ align:start position:0%
+which axis you choose to be X it doesn't
+matter I generally like to make Z
+
+ align:start position:0%
+matter I generally like to make Z
+ 
+
+ align:start position:0%
+matter I generally like to make Z
+vertical but I don't care as long as you
+
+ align:start position:0%
+vertical but I don't care as long as you
+ 
+
+ align:start position:0%
+vertical but I don't care as long as you
+use the right hand rule you need to
+
+ align:start position:0%
+use the right hand rule you need to
+ 
+
+ align:start position:0%
+use the right hand rule you need to
+observe the right hand rule because in
+
+ align:start position:0%
+observe the right hand rule because in
+ 
+
+ align:start position:0%
+observe the right hand rule because in
+physics you're going to find that there
+
+ align:start position:0%
+physics you're going to find that there
+ 
+
+ align:start position:0%
+physics you're going to find that there
+are certain Vector forces that are the
+
+ align:start position:0%
+are certain Vector forces that are the
+ 
+
+ align:start position:0%
+are certain Vector forces that are the
+product cross product and if you don't
+
+ align:start position:0%
+product cross product and if you don't
+ 
+
+ align:start position:0%
+product cross product and if you don't
+use the right-and rule convention you'll
+
+ align:start position:0%
+use the right-and rule convention you'll
+ 
+
+ align:start position:0%
+use the right-and rule convention you'll
+get things identically backwards so the
+
+ align:start position:0%
+get things identically backwards so the
+ 
+
+ align:start position:0%
+get things identically backwards so the
+thumb is your x axis y AIS z-axis
+
+ align:start position:0%
+thumb is your x axis y AIS z-axis
+ 
+
+ align:start position:0%
+thumb is your x axis y AIS z-axis
+however you want to do it so I've got
+
+ align:start position:0%
+however you want to do it so I've got
+ 
+
+ align:start position:0%
+however you want to do it so I've got
+the x-axis coming out of the board the y
+
+ align:start position:0%
+the x-axis coming out of the board the y
+ 
+
+ align:start position:0%
+the x-axis coming out of the board the y
+axis and the z-axis are in the plane of
+
+ align:start position:0%
+axis and the z-axis are in the plane of
+ 
+
+ align:start position:0%
+axis and the z-axis are in the plane of
+the board um so if we come here this
+
+ align:start position:0%
+the board um so if we come here this
+ 
+
+ align:start position:0%
+the board um so if we come here this
+point a is zero units out on the x axis
+
+ align:start position:0%
+point a is zero units out on the x axis
+ 
+
+ align:start position:0%
+point a is zero units out on the x axis
+it's one unit out on the y axis one unit
+
+ align:start position:0%
+it's one unit out on the y axis one unit
+ 
+
+ align:start position:0%
+it's one unit out on the y axis one unit
+up on z-axis so this would be 011 and B
+
+ align:start position:0%
+up on z-axis so this would be 011 and B
+ 
+
+ align:start position:0%
+up on z-axis so this would be 011 and B
+as I've drawn it looks like it's uh one
+
+ align:start position:0%
+as I've drawn it looks like it's uh one
+ 
+
+ align:start position:0%
+as I've drawn it looks like it's uh one
+unit out on the um x axis it's uh no
+
+ align:start position:0%
+unit out on the um x axis it's uh no
+ 
+
+ align:start position:0%
+unit out on the um x axis it's uh no
+units out on the y axis and a half a
+
+ align:start position:0%
+units out on the y axis and a half a
+ 
+
+ align:start position:0%
+units out on the y axis and a half a
+unit up on the z-axis so that's 1 z a
+
+ align:start position:0%
+unit up on the z-axis so that's 1 z a
+ 
+
+ align:start position:0%
+unit up on the z-axis so that's 1 z a
+half so that's that's about the last
+
+ align:start position:0%
+half so that's that's about the last
+ 
+
+ align:start position:0%
+half so that's that's about the last
+time I'm going to want to talk about
+
+ align:start position:0%
+time I'm going to want to talk about
+ 
+
+ align:start position:0%
+time I'm going to want to talk about
+these things it's more interesting to
+
+ align:start position:0%
+these things it's more interesting to
+ 
+
+ align:start position:0%
+these things it's more interesting to
+talk about lines so for lines I'm going
+
+ align:start position:0%
+talk about lines so for lines I'm going
+ 
+
+ align:start position:0%
+talk about lines so for lines I'm going
+to say let's just follow along the slide
+
+ align:start position:0%
+to say let's just follow along the slide
+ 
+
+ align:start position:0%
+to say let's just follow along the slide
+and the slide uh imitates what's going
+
+ align:start position:0%
+and the slide uh imitates what's going
+ 
+
+ align:start position:0%
+and the slide uh imitates what's going
+on here so let's see I've got a couple
+
+ align:start position:0%
+on here so let's see I've got a couple
+ 
+
+ align:start position:0%
+on here so let's see I've got a couple
+of them I want to try let's look at uh
+
+ align:start position:0%
+of them I want to try let's look at uh
+ 
+
+ align:start position:0%
+of them I want to try let's look at uh
+for starters OB we want to look at uh OB
+
+ align:start position:0%
+for starters OB we want to look at uh OB
+ 
+
+ align:start position:0%
+for starters OB we want to look at uh OB
+so I'm going to start at the origin and
+
+ align:start position:0%
+so I'm going to start at the origin and
+ 
+
+ align:start position:0%
+so I'm going to start at the origin and
+I'm going to come out to the point B and
+
+ align:start position:0%
+I'm going to come out to the point B and
+ 
+
+ align:start position:0%
+I'm going to come out to the point B and
+I've got a vector on this it's emanating
+
+ align:start position:0%
+I've got a vector on this it's emanating
+ 
+
+ align:start position:0%
+I've got a vector on this it's emanating
+from the origin out to B and what does
+
+ align:start position:0%
+from the origin out to B and what does
+ 
+
+ align:start position:0%
+from the origin out to B and what does
+it say to do it says Uh define a vector
+
+ align:start position:0%
+it say to do it says Uh define a vector
+ 
+
+ align:start position:0%
+it say to do it says Uh define a vector
+from origin of the point on the line
+
+ align:start position:0%
+from origin of the point on the line
+ 
+
+ align:start position:0%
+from origin of the point on the line
+choose the smallest set of integers andc
+
+ align:start position:0%
+choose the smallest set of integers andc
+ 
+
+ align:start position:0%
+choose the smallest set of integers andc
+no commas so I put the origin which
+
+ align:start position:0%
+no commas so I put the origin which
+ 
+
+ align:start position:0%
+no commas so I put the origin which
+conveniently here is the origin out to
+
+ align:start position:0%
+conveniently here is the origin out to
+ 
+
+ align:start position:0%
+conveniently here is the origin out to
+the point along that direction so the
+
+ align:start position:0%
+the point along that direction so the
+ 
+
+ align:start position:0%
+the point along that direction so the
+vector OB as written will go from there
+
+ align:start position:0%
+vector OB as written will go from there
+ 
+
+ align:start position:0%
+vector OB as written will go from there
+out to what is it goes to 1 z a half but
+
+ align:start position:0%
+out to what is it goes to 1 z a half but
+ 
+
+ align:start position:0%
+out to what is it goes to 1 z a half but
+then it says on
+
+ align:start position:0%
+then it says on
+ 
+
+ align:start position:0%
+then it says on
+uh let's see no commas and closing
+
+ align:start position:0%
+uh let's see no commas and closing
+ 
+
+ align:start position:0%
+uh let's see no commas and closing
+brackets and clear the fractions they
+
+ align:start position:0%
+brackets and clear the fractions they
+ 
+
+ align:start position:0%
+brackets and clear the fractions they
+don't like to have fractions when you're
+
+ align:start position:0%
+don't like to have fractions when you're
+ 
+
+ align:start position:0%
+don't like to have fractions when you're
+talking about lines so clear the
+
+ align:start position:0%
+talking about lines so clear the
+ 
+
+ align:start position:0%
+talking about lines so clear the
+fractions multiply through so then
+
+ align:start position:0%
+fractions multiply through so then
+ 
+
+ align:start position:0%
+fractions multiply through so then
+that'll just double it two 01 and you
+
+ align:start position:0%
+that'll just double it two 01 and you
+ 
+
+ align:start position:0%
+that'll just double it two 01 and you
+could say well what are they doing
+
+ align:start position:0%
+could say well what are they doing
+ 
+
+ align:start position:0%
+could say well what are they doing
+actually if you can imagine going out
+
+ align:start position:0%
+actually if you can imagine going out
+ 
+
+ align:start position:0%
+actually if you can imagine going out
+one more one more unit cell this line
+
+ align:start position:0%
+one more one more unit cell this line
+ 
+
+ align:start position:0%
+one more one more unit cell this line
+would actually go through the point 2011
+
+ align:start position:0%
+would actually go through the point 2011
+ 
+
+ align:start position:0%
+would actually go through the point 2011
+so you're just looking at the projection
+
+ align:start position:0%
+so you're just looking at the projection
+ 
+
+ align:start position:0%
+so you're just looking at the projection
+along here you're just multiplying it
+
+ align:start position:0%
+along here you're just multiplying it
+ 
+
+ align:start position:0%
+along here you're just multiplying it
+and then it says no commas and enclosing
+
+ align:start position:0%
+and then it says no commas and enclosing
+ 
+
+ align:start position:0%
+and then it says no commas and enclosing
+brackets
+
+ align:start position:0%
+brackets
+ 
+
+ align:start position:0%
+brackets
+okay this is called a bracket these
+
+ align:start position:0%
+okay this is called a bracket these
+ 
+
+ align:start position:0%
+okay this is called a bracket these
+staple like things are called
+
+ align:start position:0%
+staple like things are called
+ 
+
+ align:start position:0%
+staple like things are called
+brackets so that's a direction the
+
+ align:start position:0%
+brackets so that's a direction the
+ 
+
+ align:start position:0%
+brackets so that's a direction the
+direction o let's do the uh let's see
+
+ align:start position:0%
+direction o let's do the uh let's see
+ 
+
+ align:start position:0%
+direction o let's do the uh let's see
+what's the other one we're going to do
+
+ align:start position:0%
+what's the other one we're going to do
+ 
+
+ align:start position:0%
+what's the other one we're going to do
+what is it AO
+
+ align:start position:0%
+what is it AO
+ 
+
+ align:start position:0%
+what is it AO
+AO all right so it says you have to move
+
+ align:start position:0%
+AO all right so it says you have to move
+ 
+
+ align:start position:0%
+AO all right so it says you have to move
+the origin to the base of the vector so
+
+ align:start position:0%
+the origin to the base of the vector so
+ 
+
+ align:start position:0%
+the origin to the base of the vector so
+if I want to do AO I have to I have to
+
+ align:start position:0%
+if I want to do AO I have to I have to
+ 
+
+ align:start position:0%
+if I want to do AO I have to I have to
+put the origin up here at the tail of
+
+ align:start position:0%
+put the origin up here at the tail of
+ 
+
+ align:start position:0%
+put the origin up here at the tail of
+the vector so if this is the origin I'm
+
+ align:start position:0%
+the vector so if this is the origin I'm
+ 
+
+ align:start position:0%
+the vector so if this is the origin I'm
+moving actually what I'm not moving
+
+ align:start position:0%
+moving actually what I'm not moving
+ 
+
+ align:start position:0%
+moving actually what I'm not moving
+anywhere in the x- axis but I'm moving
+
+ align:start position:0%
+anywhere in the x- axis but I'm moving
+ 
+
+ align:start position:0%
+anywhere in the x- axis but I'm moving
+minus one in the Y AIS and minus one in
+
+ align:start position:0%
+minus one in the Y AIS and minus one in
+ 
+
+ align:start position:0%
+minus one in the Y AIS and minus one in
+the z-axis in order to get this
+
+ align:start position:0%
+the z-axis in order to get this
+ 
+
+ align:start position:0%
+the z-axis in order to get this
+direction so I'm really going zero in
+
+ align:start position:0%
+direction so I'm really going zero in
+ 
+
+ align:start position:0%
+direction so I'm really going zero in
+the X I'm going minus one in the Y and
+
+ align:start position:0%
+the X I'm going minus one in the Y and
+ 
+
+ align:start position:0%
+the X I'm going minus one in the Y and
+minus one in the Z and you can see since
+
+ align:start position:0%
+minus one in the Z and you can see since
+ 
+
+ align:start position:0%
+minus one in the Z and you can see since
+we don't use commas putting minus signs
+
+ align:start position:0%
+we don't use commas putting minus signs
+ 
+
+ align:start position:0%
+we don't use commas putting minus signs
+would look cumbersome so in
+
+ align:start position:0%
+would look cumbersome so in
+ 
+
+ align:start position:0%
+would look cumbersome so in
+crystallographic notation the minus sign
+
+ align:start position:0%
+crystallographic notation the minus sign
+ 
+
+ align:start position:0%
+crystallographic notation the minus sign
+is represented as a macron a macron is a
+
+ align:start position:0%
+is represented as a macron a macron is a
+ 
+
+ align:start position:0%
+is represented as a macron a macron is a
+line over so this is z one bar one bar
+
+ align:start position:0%
+line over so this is z one bar one bar
+ 
+
+ align:start position:0%
+line over so this is z one bar one bar
+that's equal to minus one but in Crystal
+
+ align:start position:0%
+that's equal to minus one but in Crystal
+ 
+
+ align:start position:0%
+that's equal to minus one but in Crystal
+crystallographers use the term one bar
+
+ align:start position:0%
+crystallographers use the term one bar
+ 
+
+ align:start position:0%
+crystallographers use the term one bar
+so this is o one bar one bar for this
+
+ align:start position:0%
+so this is o one bar one bar for this
+ 
+
+ align:start position:0%
+so this is o one bar one bar for this
+line uh a down to origin so that's
+
+ align:start position:0%
+line uh a down to origin so that's
+ 
+
+ align:start position:0%
+line uh a down to origin so that's
+that's how that's done and then it says
+
+ align:start position:0%
+that's how that's done and then it says
+ 
+
+ align:start position:0%
+that's how that's done and then it says
+uh let's see we can denote an entire
+
+ align:start position:0%
+uh let's see we can denote an entire
+ 
+
+ align:start position:0%
+uh let's see we can denote an entire
+family of directions by carrots so let's
+
+ align:start position:0%
+family of directions by carrots so let's
+ 
+
+ align:start position:0%
+family of directions by carrots so let's
+do that if I want to suppose I wanted to
+
+ align:start position:0%
+do that if I want to suppose I wanted to
+ 
+
+ align:start position:0%
+do that if I want to suppose I wanted to
+say um what have I got up there all of
+
+ align:start position:0%
+say um what have I got up there all of
+ 
+
+ align:start position:0%
+say um what have I got up there all of
+the body diagonals well how would I get
+
+ align:start position:0%
+the body diagonals well how would I get
+ 
+
+ align:start position:0%
+the body diagonals well how would I get
+a body diagonal
+
+ align:start position:0%
+a body diagonal
+ 
+
+ align:start position:0%
+a body diagonal
+a body
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+diagonal if this is the origin and I
+
+ align:start position:0%
+diagonal if this is the origin and I
+ 
+
+ align:start position:0%
+diagonal if this is the origin and I
+want to go up the body diagonal it would
+
+ align:start position:0%
+want to go up the body diagonal it would
+ 
+
+ align:start position:0%
+want to go up the body diagonal it would
+be out one unit out one unit out one
+
+ align:start position:0%
+be out one unit out one unit out one
+ 
+
+ align:start position:0%
+be out one unit out one unit out one
+unit so it would be 11 one one would be
+
+ align:start position:0%
+unit so it would be 11 one one would be
+ 
+
+ align:start position:0%
+unit so it would be 11 one one would be
+a body diagonal all right but suppose I
+
+ align:start position:0%
+a body diagonal all right but suppose I
+ 
+
+ align:start position:0%
+a body diagonal all right but suppose I
+want to say all body diagonals that's
+
+ align:start position:0%
+want to say all body diagonals that's
+ 
+
+ align:start position:0%
+want to say all body diagonals that's
+111 this direction one1 that direction I
+
+ align:start position:0%
+111 this direction one1 that direction I
+ 
+
+ align:start position:0%
+111 this direction one1 that direction I
+want to get this body diagonal I want to
+
+ align:start position:0%
+want to get this body diagonal I want to
+ 
+
+ align:start position:0%
+want to get this body diagonal I want to
+get that body diagonal how do I do that
+
+ align:start position:0%
+get that body diagonal how do I do that
+ 
+
+ align:start position:0%
+get that body diagonal how do I do that
+I can do that by putting carrots these
+
+ align:start position:0%
+I can do that by putting carrots these
+ 
+
+ align:start position:0%
+I can do that by putting carrots these
+are called carrots those of you who have
+
+ align:start position:0%
+are called carrots those of you who have
+ 
+
+ align:start position:0%
+are called carrots those of you who have
+done some editing and proof reading know
+
+ align:start position:0%
+done some editing and proof reading know
+ 
+
+ align:start position:0%
+done some editing and proof reading know
+these terms okay so carrots so this is
+
+ align:start position:0%
+these terms okay so carrots so this is
+ 
+
+ align:start position:0%
+these terms okay so carrots so this is
+all body
+
+ align:start position:0%
+all body
+ 
+
+ align:start position:0%
+all body
+diagonals this is all body
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+diagonals we could do a few others while
+
+ align:start position:0%
+diagonals we could do a few others while
+ 
+
+ align:start position:0%
+diagonals we could do a few others while
+we're at it suppose I wanted to do uh
+
+ align:start position:0%
+we're at it suppose I wanted to do uh
+ 
+
+ align:start position:0%
+we're at it suppose I wanted to do uh
+all of the face
+
+ align:start position:0%
+all of the face
+ 
+
+ align:start position:0%
+all of the face
+diagonals all of the face diagonals like
+
+ align:start position:0%
+diagonals all of the face diagonals like
+ 
+
+ align:start position:0%
+diagonals all of the face diagonals like
+this like this and then over here like
+
+ align:start position:0%
+this like this and then over here like
+ 
+
+ align:start position:0%
+this like this and then over here like
+this like this well what's a face
+
+ align:start position:0%
+this like this well what's a face
+ 
+
+ align:start position:0%
+this like this well what's a face
+diagonal 0 1 0 1 1 right so all the face
+
+ align:start position:0%
+diagonal 0 1 0 1 1 right so all the face
+ 
+
+ align:start position:0%
+diagonal 0 1 0 1 1 right so all the face
+diagonals would be okay all face
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+diagonals um what about all Cube edges
+
+ align:start position:0%
+diagonals um what about all Cube edges
+ 
+
+ align:start position:0%
+diagonals um what about all Cube edges
+what's a cube Edge Cube Edge could be
+
+ align:start position:0%
+what's a cube Edge Cube Edge could be
+ 
+
+ align:start position:0%
+what's a cube Edge Cube Edge could be
+this one 0 01 so this would be all
+
+ align:start position:0%
+this one 0 01 so this would be all
+ 
+
+ align:start position:0%
+this one 0 01 so this would be all
+Cube
+
+ align:start position:0%
+Cube
+ 
+
+ align:start position:0%
+Cube
+edges so what does it mean it means
+
+ align:start position:0%
+edges so what does it mean it means
+ 
+
+ align:start position:0%
+edges so what does it mean it means
+write this out in full so that's O
+
+ align:start position:0%
+write this out in full so that's O
+ 
+
+ align:start position:0%
+write this out in full so that's O
+pardon me
+
+ align:start position:0%
+pardon me
+ 
+
+ align:start position:0%
+pardon me
+o1 okay o1 bar
+
+ align:start position:0%
+o1 okay o1 bar
+ 
+
+ align:start position:0%
+o1 okay o1 bar
+R
+
+ align:start position:0%
+R
+ 
+
+ align:start position:0%
+R
+o10 see I'm using o for zero I'm I'm
+
+ align:start position:0%
+o10 see I'm using o for zero I'm I'm
+ 
+
+ align:start position:0%
+o10 see I'm using o for zero I'm I'm
+cluing you into crystallographers talk
+
+ align:start position:0%
+cluing you into crystallographers talk
+ 
+
+ align:start position:0%
+cluing you into crystallographers talk
+that's how they talk o in one bar so
+
+ align:start position:0%
+that's how they talk o in one bar so
+ 
+
+ align:start position:0%
+that's how they talk o in one bar so
+you're going to be really hip if you end
+
+ align:start position:0%
+you're going to be really hip if you end
+ 
+
+ align:start position:0%
+you're going to be really hip if you end
+up in an elevator with a bunch of
+
+ align:start position:0%
+up in an elevator with a bunch of
+ 
+
+ align:start position:0%
+up in an elevator with a bunch of
+crystallographers okay and there's two
+
+ align:start position:0%
+crystallographers okay and there's two
+ 
+
+ align:start position:0%
+crystallographers okay and there's two
+others here
+
+ align:start position:0%
+others here
+ 
+
+ align:start position:0%
+others here
+10 and one bar
+
+ align:start position:0%
+10 and one bar
+ 
+
+ align:start position:0%
+10 and one bar
+o well how many faces are there six how
+
+ align:start position:0%
+o well how many faces are there six how
+ 
+
+ align:start position:0%
+o well how many faces are there six how
+many face edges six and look just going
+
+ align:start position:0%
+many face edges six and look just going
+ 
+
+ align:start position:0%
+many face edges six and look just going
+through the permutations and
+
+ align:start position:0%
+through the permutations and
+ 
+
+ align:start position:0%
+through the permutations and
+combinations gives you exactly the
+
+ align:start position:0%
+combinations gives you exactly the
+ 
+
+ align:start position:0%
+combinations gives you exactly the
+number that you should have this is
+
+ align:start position:0%
+number that you should have this is
+ 
+
+ align:start position:0%
+number that you should have this is
+mathematics imitating reality that's
+
+ align:start position:0%
+mathematics imitating reality that's
+ 
+
+ align:start position:0%
+mathematics imitating reality that's
+good that's good and likewise here if
+
+ align:start position:0%
+good that's good and likewise here if
+ 
+
+ align:start position:0%
+good that's good and likewise here if
+you go through all the permutation
+
+ align:start position:0%
+you go through all the permutation
+ 
+
+ align:start position:0%
+you go through all the permutation
+combinations of 01 and one bar you'll
+
+ align:start position:0%
+combinations of 01 and one bar you'll
+ 
+
+ align:start position:0%
+combinations of 01 and one bar you'll
+end up with all of the possibilities for
+
+ align:start position:0%
+end up with all of the possibilities for
+ 
+
+ align:start position:0%
+end up with all of the possibilities for
+face diagonals all the possibility for
+
+ align:start position:0%
+face diagonals all the possibility for
+ 
+
+ align:start position:0%
+face diagonals all the possibility for
+body diagonals I think I've got a a
+
+ align:start position:0%
+body diagonals I think I've got a a
+ 
+
+ align:start position:0%
+body diagonals I think I've got a a
+cartoon here that shows there it is it
+
+ align:start position:0%
+cartoon here that shows there it is it
+ 
+
+ align:start position:0%
+cartoon here that shows there it is it
+shows all of the different uh diagonals
+
+ align:start position:0%
+shows all of the different uh diagonals
+ 
+
+ align:start position:0%
+shows all of the different uh diagonals
+that are possible when you mix one and
+
+ align:start position:0%
+that are possible when you mix one and
+ 
+
+ align:start position:0%
+that are possible when you mix one and
+one are okay that's good so that's so
+
+ align:start position:0%
+one are okay that's good so that's so
+ 
+
+ align:start position:0%
+one are okay that's good so that's so
+far so good that's pretty simple now
+
+ align:start position:0%
+far so good that's pretty simple now
+ 
+
+ align:start position:0%
+far so good that's pretty simple now
+let's look at planes let's look at
+
+ align:start position:0%
+let's look at planes let's look at
+ 
+
+ align:start position:0%
+let's look at planes let's look at
+planes for planes we use something
+
+ align:start position:0%
+planes for planes we use something
+ 
+
+ align:start position:0%
+planes for planes we use something
+called the Miller
+
+ align:start position:0%
+called the Miller
+ 
+
+ align:start position:0%
+called the Miller
+indices Miller indices for describing
+
+ align:start position:0%
+indices Miller indices for describing
+ 
+
+ align:start position:0%
+indices Miller indices for describing
+planes and they're named after the uh
+
+ align:start position:0%
+planes and they're named after the uh
+ 
+
+ align:start position:0%
+planes and they're named after the uh
+British minology
+
+ align:start position:0%
+British minology
+ 
+
+ align:start position:0%
+British minology
+williiam hallow Miller who back in the
+
+ align:start position:0%
+williiam hallow Miller who back in the
+ 
+
+ align:start position:0%
+williiam hallow Miller who back in the
+1830s gave us this uh means of
+
+ align:start position:0%
+1830s gave us this uh means of
+ 
+
+ align:start position:0%
+1830s gave us this uh means of
+describing a plane and I think I would
+
+ align:start position:0%
+describing a plane and I think I would
+ 
+
+ align:start position:0%
+describing a plane and I think I would
+rather than write it down just just
+
+ align:start position:0%
+rather than write it down just just
+ 
+
+ align:start position:0%
+rather than write it down just just
+follow along here because you got the
+
+ align:start position:0%
+follow along here because you got the
+ 
+
+ align:start position:0%
+follow along here because you got the
+notes in front of you you know from your
+
+ align:start position:0%
+notes in front of you you know from your
+ 
+
+ align:start position:0%
+notes in front of you you know from your
+math that the uh equation of a plane is
+
+ align:start position:0%
+math that the uh equation of a plane is
+ 
+
+ align:start position:0%
+math that the uh equation of a plane is
+X over a + y over B plus Z over Cal 1
+
+ align:start position:0%
+X over a + y over B plus Z over Cal 1
+ 
+
+ align:start position:0%
+X over a + y over B plus Z over Cal 1
+and a B and C are the intercepts with
+
+ align:start position:0%
+and a B and C are the intercepts with
+ 
+
+ align:start position:0%
+and a B and C are the intercepts with
+the X Y and Z axis respectively so what
+
+ align:start position:0%
+the X Y and Z axis respectively so what
+ 
+
+ align:start position:0%
+the X Y and Z axis respectively so what
+what um what Miller did is he said let's
+
+ align:start position:0%
+what um what Miller did is he said let's
+ 
+
+ align:start position:0%
+what um what Miller did is he said let's
+let H be 1 over a k be one over B and
+
+ align:start position:0%
+let H be 1 over a k be one over B and
+ 
+
+ align:start position:0%
+let H be 1 over a k be one over B and
+Lal 1 / C so this becomes the equation
+
+ align:start position:0%
+Lal 1 / C so this becomes the equation
+ 
+
+ align:start position:0%
+Lal 1 / C so this becomes the equation
+of the plane HX + KY + LZ = one and now
+
+ align:start position:0%
+of the plane HX + KY + LZ = one and now
+ 
+
+ align:start position:0%
+of the plane HX + KY + LZ = one and now
+what you do is you take the h k and l
+
+ align:start position:0%
+what you do is you take the h k and l
+ 
+
+ align:start position:0%
+what you do is you take the h k and l
+and enclose those in parentheses so in
+
+ align:start position:0%
+and enclose those in parentheses so in
+ 
+
+ align:start position:0%
+and enclose those in parentheses so in
+other words he's taking the plane index
+
+ align:start position:0%
+other words he's taking the plane index
+ 
+
+ align:start position:0%
+other words he's taking the plane index
+to be the reciprocals of the intercepts
+
+ align:start position:0%
+to be the reciprocals of the intercepts
+ 
+
+ align:start position:0%
+to be the reciprocals of the intercepts
+with the three axes and you'll see why
+
+ align:start position:0%
+with the three axes and you'll see why
+ 
+
+ align:start position:0%
+with the three axes and you'll see why
+in a second you'll see why in a second
+
+ align:start position:0%
+in a second you'll see why in a second
+ 
+
+ align:start position:0%
+in a second you'll see why in a second
+why do it that way well because every
+
+ align:start position:0%
+why do it that way well because every
+ 
+
+ align:start position:0%
+why do it that way well because every
+once in a while something like this
+
+ align:start position:0%
+once in a while something like this
+ 
+
+ align:start position:0%
+once in a while something like this
+happens so here's a simple one just to
+
+ align:start position:0%
+happens so here's a simple one just to
+ 
+
+ align:start position:0%
+happens so here's a simple one just to
+get our feet wet so here A B and C are
+
+ align:start position:0%
+get our feet wet so here A B and C are
+ 
+
+ align:start position:0%
+get our feet wet so here A B and C are
+the unit vectors so this is the x axis
+
+ align:start position:0%
+the unit vectors so this is the x axis
+ 
+
+ align:start position:0%
+the unit vectors so this is the x axis
+in the same convention I've chosen X is
+
+ align:start position:0%
+in the same convention I've chosen X is
+ 
+
+ align:start position:0%
+in the same convention I've chosen X is
+coming out of the plane of the slide Y
+
+ align:start position:0%
+coming out of the plane of the slide Y
+ 
+
+ align:start position:0%
+coming out of the plane of the slide Y
+is moving to the right and Z is moving
+
+ align:start position:0%
+is moving to the right and Z is moving
+ 
+
+ align:start position:0%
+is moving to the right and Z is moving
+up okay so here's a plane that's shaded
+
+ align:start position:0%
+up okay so here's a plane that's shaded
+ 
+
+ align:start position:0%
+up okay so here's a plane that's shaded
+in and what do you see it cuts the x
+
+ align:start position:0%
+in and what do you see it cuts the x
+ 
+
+ align:start position:0%
+in and what do you see it cuts the x
+axis at xal plus a half it cuts the Y
+
+ align:start position:0%
+axis at xal plus a half it cuts the Y
+ 
+
+ align:start position:0%
+axis at xal plus a half it cuts the Y
+AIS at yal +1 and it never cuts the Z
+
+ align:start position:0%
+AIS at yal +1 and it never cuts the Z
+ 
+
+ align:start position:0%
+AIS at yal +1 and it never cuts the Z
+axis it's parallel to the Z axis so
+
+ align:start position:0%
+axis it's parallel to the Z axis so
+ 
+
+ align:start position:0%
+axis it's parallel to the Z axis so
+mathematically we would say the Z
+
+ align:start position:0%
+mathematically we would say the Z
+ 
+
+ align:start position:0%
+mathematically we would say the Z
+intercept is infinity and who wants to
+
+ align:start position:0%
+intercept is infinity and who wants to
+ 
+
+ align:start position:0%
+intercept is infinity and who wants to
+have Infinity so now you see the wisdom
+
+ align:start position:0%
+have Infinity so now you see the wisdom
+ 
+
+ align:start position:0%
+have Infinity so now you see the wisdom
+of of Miller Miller said let's describe
+
+ align:start position:0%
+of of Miller Miller said let's describe
+ 
+
+ align:start position:0%
+of of Miller Miller said let's describe
+this in terms of the reciprocals so
+
+ align:start position:0%
+this in terms of the reciprocals so
+ 
+
+ align:start position:0%
+this in terms of the reciprocals so
+what's the reciprocal of a half it's two
+
+ align:start position:0%
+what's the reciprocal of a half it's two
+ 
+
+ align:start position:0%
+what's the reciprocal of a half it's two
+what's the reciprocal of one it's one
+
+ align:start position:0%
+what's the reciprocal of one it's one
+ 
+
+ align:start position:0%
+what's the reciprocal of one it's one
+and what's the reciprocal of infinity
+
+ align:start position:0%
+and what's the reciprocal of infinity
+ 
+
+ align:start position:0%
+and what's the reciprocal of infinity
+zero so we can describe this plane as
+
+ align:start position:0%
+zero so we can describe this plane as
+ 
+
+ align:start position:0%
+zero so we can describe this plane as
+the 2 one0
+
+ align:start position:0%
+the 2 one0
+ 
+
+ align:start position:0%
+the 2 one0
+plane whenever you see a zero whatever
+
+ align:start position:0%
+plane whenever you see a zero whatever
+ 
+
+ align:start position:0%
+plane whenever you see a zero whatever
+place the zero lies that means that
+
+ align:start position:0%
+place the zero lies that means that
+ 
+
+ align:start position:0%
+place the zero lies that means that
+plane is parallel to that axis so right
+
+ align:start position:0%
+plane is parallel to that axis so right
+ 
+
+ align:start position:0%
+plane is parallel to that axis so right
+away I can say that's a plane that's
+
+ align:start position:0%
+away I can say that's a plane that's
+ 
+
+ align:start position:0%
+away I can say that's a plane that's
+parallel to the z-axis it doesn't cross
+
+ align:start position:0%
+parallel to the z-axis it doesn't cross
+ 
+
+ align:start position:0%
+parallel to the z-axis it doesn't cross
+the z- axis so there it is so there's
+
+ align:start position:0%
+the z- axis so there it is so there's
+ 
+
+ align:start position:0%
+the z- axis so there it is so there's
+the uh formula you take the reciprocal
+
+ align:start position:0%
+the uh formula you take the reciprocal
+ 
+
+ align:start position:0%
+the uh formula you take the reciprocal
+of the intercepts put them side by side
+
+ align:start position:0%
+of the intercepts put them side by side
+ 
+
+ align:start position:0%
+of the intercepts put them side by side
+no commas and this is why we Sav the
+
+ align:start position:0%
+no commas and this is why we Sav the
+ 
+
+ align:start position:0%
+no commas and this is why we Sav the
+parentheses and that's why we don't put
+
+ align:start position:0%
+parentheses and that's why we don't put
+ 
+
+ align:start position:0%
+parentheses and that's why we don't put
+our uh position in parenthesis because
+
+ align:start position:0%
+our uh position in parenthesis because
+ 
+
+ align:start position:0%
+our uh position in parenthesis because
+we're saving parentheses for the plane
+
+ align:start position:0%
+we're saving parentheses for the plane
+ 
+
+ align:start position:0%
+we're saving parentheses for the plane
+oh let's do a few more this is W it's a
+
+ align:start position:0%
+oh let's do a few more this is W it's a
+ 
+
+ align:start position:0%
+oh let's do a few more this is W it's a
+lot of fun on a Monday see you're
+
+ align:start position:0%
+lot of fun on a Monday see you're
+ 
+
+ align:start position:0%
+lot of fun on a Monday see you're
+excited to be back in class and man
+
+ align:start position:0%
+excited to be back in class and man
+ 
+
+ align:start position:0%
+excited to be back in class and man
+there's a cool thing that happens when
+
+ align:start position:0%
+there's a cool thing that happens when
+ 
+
+ align:start position:0%
+there's a cool thing that happens when
+you use Miller indices you see what I
+
+ align:start position:0%
+you use Miller indices you see what I
+ 
+
+ align:start position:0%
+you use Miller indices you see what I
+just did I just drew a Direction and
+
+ align:start position:0%
+just did I just drew a Direction and
+ 
+
+ align:start position:0%
+just did I just drew a Direction and
+that direction is the 210 Direction and
+
+ align:start position:0%
+that direction is the 210 Direction and
+ 
+
+ align:start position:0%
+that direction is the 210 Direction and
+what do you notice about the position of
+
+ align:start position:0%
+what do you notice about the position of
+ 
+
+ align:start position:0%
+what do you notice about the position of
+210 versus the 210 plane when you write
+
+ align:start position:0%
+210 versus the 210 plane when you write
+ 
+
+ align:start position:0%
+210 versus the 210 plane when you write
+directions according to this formula and
+
+ align:start position:0%
+directions according to this formula and
+ 
+
+ align:start position:0%
+directions according to this formula and
+planes according to Miller indices the
+
+ align:start position:0%
+planes according to Miller indices the
+ 
+
+ align:start position:0%
+planes according to Miller indices the
+210 direction is perpendicular to the
+
+ align:start position:0%
+210 direction is perpendicular to the
+ 
+
+ align:start position:0%
+210 direction is perpendicular to the
+
+ align:start position:0%
+ 
+
+ align:start position:0%
+plane 210 direction is perpendicular to
+
+ align:start position:0%
+plane 210 direction is perpendicular to
+ 
+
+ align:start position:0%
+plane 210 direction is perpendicular to
+the 210 plane let's do another one oh
+
+ align:start position:0%
+the 210 plane let's do another one oh
+ 
+
+ align:start position:0%
+the 210 plane let's do another one oh
+this is a good one this is uh this is a
+
+ align:start position:0%
+this is a good one this is uh this is a
+ 
+
+ align:start position:0%
+this is a good one this is uh this is a
+plane
+
+ align:start position:0%
+plane
+ 
+
+ align:start position:0%
+plane
+that cuts the Y AIS at y equal 1 it's
+
+ align:start position:0%
+that cuts the Y AIS at y equal 1 it's
+ 
+
+ align:start position:0%
+that cuts the Y AIS at y equal 1 it's
+parallel to the x-axis parallel to the
+
+ align:start position:0%
+parallel to the x-axis parallel to the
+ 
+
+ align:start position:0%
+parallel to the x-axis parallel to the
+z-axis never cuts the x or the
+
+ align:start position:0%
+z-axis never cuts the x or the
+ 
+
+ align:start position:0%
+z-axis never cuts the x or the
+z-axis so that's an 010 plane I mean you
+
+ align:start position:0%
+z-axis so that's an 010 plane I mean you
+ 
+
+ align:start position:0%
+z-axis so that's an 010 plane I mean you
+can do that in your head right so that's
+
+ align:start position:0%
+can do that in your head right so that's
+ 
+
+ align:start position:0%
+can do that in your head right so that's
+an 01 plane that's an o10 plane and so
+
+ align:start position:0%
+an 01 plane that's an o10 plane and so
+ 
+
+ align:start position:0%
+an 01 plane that's an o10 plane and so
+on and so forth here's an o2o plane why
+
+ align:start position:0%
+on and so forth here's an o2o plane why
+ 
+
+ align:start position:0%
+on and so forth here's an o2o plane why
+well because it cuts the y axis at y
+
+ align:start position:0%
+well because it cuts the y axis at y
+ 
+
+ align:start position:0%
+well because it cuts the y axis at y
+equals a half and take the reciprocal is
+
+ align:start position:0%
+equals a half and take the reciprocal is
+ 
+
+ align:start position:0%
+equals a half and take the reciprocal is
+two so o20
+
+ align:start position:0%
+two so o20
+ 
+
+ align:start position:0%
+two so o20
+o2o and let's try again well there's 010
+
+ align:start position:0%
+o2o and let's try again well there's 010
+ 
+
+ align:start position:0%
+o2o and let's try again well there's 010
+Direction and what do you know the o10
+
+ align:start position:0%
+Direction and what do you know the o10
+ 
+
+ align:start position:0%
+Direction and what do you know the o10
+direction is normal to the o10 plane and
+
+ align:start position:0%
+direction is normal to the o10 plane and
+ 
+
+ align:start position:0%
+direction is normal to the o10 plane and
+o2o direction is normal to the o2o plane
+
+ align:start position:0%
+o2o direction is normal to the o2o plane
+ 
+
+ align:start position:0%
+o2o direction is normal to the o2o plane
+what do you know about the o10 direction
+
+ align:start position:0%
+what do you know about the o10 direction
+ 
+
+ align:start position:0%
+what do you know about the o10 direction
+the o2o direction they're the same
+
+ align:start position:0%
+the o2o direction they're the same
+ 
+
+ align:start position:0%
+the o2o direction they're the same
+direction o anything o is going to be
+
+ align:start position:0%
+direction o anything o is going to be
+ 
+
+ align:start position:0%
+direction o anything o is going to be
+along the y
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+axis that's an o2o plane I could shift
+
+ align:start position:0%
+axis that's an o2o plane I could shift
+ 
+
+ align:start position:0%
+axis that's an o2o plane I could shift
+the origin to here couldn't I so then
+
+ align:start position:0%
+the origin to here couldn't I so then
+ 
+
+ align:start position:0%
+the origin to here couldn't I so then
+that would be an O2 plane and that would
+
+ align:start position:0%
+that would be an O2 plane and that would
+ 
+
+ align:start position:0%
+that would be an O2 plane and that would
+be an O2
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+plane well here's some more
+
+ align:start position:0%
+plane well here's some more
+ 
+
+ align:start position:0%
+plane well here's some more
+111 well look at this plane here it cuts
+
+ align:start position:0%
+111 well look at this plane here it cuts
+ 
+
+ align:start position:0%
+111 well look at this plane here it cuts
+the x axis at x equals 1 the y axis at y
+
+ align:start position:0%
+the x axis at x equals 1 the y axis at y
+ 
+
+ align:start position:0%
+the x axis at x equals 1 the y axis at y
+equals 1 the z-axis at Z equals 1 so
+
+ align:start position:0%
+equals 1 the z-axis at Z equals 1 so
+ 
+
+ align:start position:0%
+equals 1 the z-axis at Z equals 1 so
+shade that in that's the 111 plane but
+
+ align:start position:0%
+shade that in that's the 111 plane but
+ 
+
+ align:start position:0%
+shade that in that's the 111 plane but
+that's also a 111 plane we can keep
+
+ align:start position:0%
+that's also a 111 plane we can keep
+ 
+
+ align:start position:0%
+that's also a 111 plane we can keep
+Shifting the origin I don't know where
+
+ align:start position:0%
+Shifting the origin I don't know where
+ 
+
+ align:start position:0%
+Shifting the origin I don't know where
+the origin of the universe is so I can
+
+ align:start position:0%
+the origin of the universe is so I can
+ 
+
+ align:start position:0%
+the origin of the universe is so I can
+move this anywhere along
+
+ align:start position:0%
+move this anywhere along
+ 
+
+ align:start position:0%
+move this anywhere along
+now here's one here's backwards see this
+
+ align:start position:0%
+now here's one here's backwards see this
+ 
+
+ align:start position:0%
+now here's one here's backwards see this
+now is one one one bar because if I put
+
+ align:start position:0%
+now is one one one bar because if I put
+ 
+
+ align:start position:0%
+now is one one one bar because if I put
+the uh if I put the origin here I'm
+
+ align:start position:0%
+the uh if I put the origin here I'm
+ 
+
+ align:start position:0%
+the uh if I put the origin here I'm
+cutting the x- axis at + one I'm cutting
+
+ align:start position:0%
+cutting the x- axis at + one I'm cutting
+ 
+
+ align:start position:0%
+cutting the x- axis at + one I'm cutting
+the Y AIS at + one but I've got a
+
+ align:start position:0%
+the Y AIS at + one but I've got a
+ 
+
+ align:start position:0%
+the Y AIS at + one but I've got a
+negative tilt to this plane so the
+
+ align:start position:0%
+negative tilt to this plane so the
+ 
+
+ align:start position:0%
+negative tilt to this plane so the
+z-axis is being cut at minus one so
+
+ align:start position:0%
+z-axis is being cut at minus one so
+ 
+
+ align:start position:0%
+z-axis is being cut at minus one so
+again we try to use the minus sign uh
+
+ align:start position:0%
+again we try to use the minus sign uh
+ 
+
+ align:start position:0%
+again we try to use the minus sign uh
+avoid the minus sign rather and instead
+
+ align:start position:0%
+avoid the minus sign rather and instead
+ 
+
+ align:start position:0%
+avoid the minus sign rather and instead
+we put the macron over the number and in
+
+ align:start position:0%
+we put the macron over the number and in
+ 
+
+ align:start position:0%
+we put the macron over the number and in
+that way we give the uh minus indication
+
+ align:start position:0%
+that way we give the uh minus indication
+ 
+
+ align:start position:0%
+that way we give the uh minus indication
+on a number no par no commas in
+
+ align:start position:0%
+on a number no par no commas in
+ 
+
+ align:start position:0%
+on a number no par no commas in
+parentheses now let's do the test here's
+
+ align:start position:0%
+parentheses now let's do the test here's
+ 
+
+ align:start position:0%
+parentheses now let's do the test here's
+the 111 Direction and sure enough the
+
+ align:start position:0%
+the 111 Direction and sure enough the
+ 
+
+ align:start position:0%
+the 111 Direction and sure enough the
+111 Direction cuts the 111 plane
+
+ align:start position:0%
+111 Direction cuts the 111 plane
+ 
+
+ align:start position:0%
+111 Direction cuts the 111 plane
+normally let's try over here there's the
+
+ align:start position:0%
+normally let's try over here there's the
+ 
+
+ align:start position:0%
+normally let's try over here there's the
+111 bar Direction Boom cuts through the
+
+ align:start position:0%
+111 bar Direction Boom cuts through the
+ 
+
+ align:start position:0%
+111 bar Direction Boom cuts through the
+111 bar plane
+
+ align:start position:0%
+111 bar plane
+ 
+
+ align:start position:0%
+111 bar plane
+normally it's fantastic fantastic and we
+
+ align:start position:0%
+normally it's fantastic fantastic and we
+ 
+
+ align:start position:0%
+normally it's fantastic fantastic and we
+can do families we can do families of
+
+ align:start position:0%
+can do families we can do families of
+ 
+
+ align:start position:0%
+can do families we can do families of
+planes as well so let's look at families
+
+ align:start position:0%
+planes as well so let's look at families
+ 
+
+ align:start position:0%
+planes as well so let's look at families
+of planes what kind of families could we
+
+ align:start position:0%
+of planes what kind of families could we
+ 
+
+ align:start position:0%
+of planes what kind of families could we
+we could come up with if we want to do
+
+ align:start position:0%
+we could come up with if we want to do
+ 
+
+ align:start position:0%
+we could come up with if we want to do
+families families of planes with brace
+
+ align:start position:0%
+families families of planes with brace
+ 
+
+ align:start position:0%
+families families of planes with brace
+brackets
+
+ align:start position:0%
+brackets
+ 
+
+ align:start position:0%
+brackets
+right families of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+planes
+
+ align:start position:0%
+planes
+ 
+
+ align:start position:0%
+planes
+use
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+braces so if I want to say all Cube
+
+ align:start position:0%
+braces so if I want to say all Cube
+ 
+
+ align:start position:0%
+braces so if I want to say all Cube
+faces all Cube faces that would be
+
+ align:start position:0%
+faces all Cube faces that would be
+ 
+
+ align:start position:0%
+faces all Cube faces that would be
+o1 because 010 we saw was the was
+
+ align:start position:0%
+o1 because 010 we saw was the was
+ 
+
+ align:start position:0%
+o1 because 010 we saw was the was
+parallel to the cuts the y axis parallel
+
+ align:start position:0%
+parallel to the cuts the y axis parallel
+ 
+
+ align:start position:0%
+parallel to the cuts the y axis parallel
+to the XZ plane so that's going to tell
+
+ align:start position:0%
+to the XZ plane so that's going to tell
+ 
+
+ align:start position:0%
+to the XZ plane so that's going to tell
+you to roll over 0 01 and one bar in
+
+ align:start position:0%
+you to roll over 0 01 and one bar in
+ 
+
+ align:start position:0%
+you to roll over 0 01 and one bar in
+this manner only instead of brackets
+
+ align:start position:0%
+this manner only instead of brackets
+ 
+
+ align:start position:0%
+this manner only instead of brackets
+you've got braces how many faces on a
+
+ align:start position:0%
+you've got braces how many faces on a
+ 
+
+ align:start position:0%
+you've got braces how many faces on a
+cube there's six how many combinations
+
+ align:start position:0%
+cube there's six how many combinations
+ 
+
+ align:start position:0%
+cube there's six how many combinations
+of zero one and one bar are there six so
+
+ align:start position:0%
+of zero one and one bar are there six so
+ 
+
+ align:start position:0%
+of zero one and one bar are there six so
+there you go and by the way one other
+
+ align:start position:0%
+there you go and by the way one other
+ 
+
+ align:start position:0%
+there you go and by the way one other
+thing if you want to be hip with the
+
+ align:start position:0%
+thing if you want to be hip with the
+ 
+
+ align:start position:0%
+thing if you want to be hip with the
+crystallographers this is one way of
+
+ align:start position:0%
+crystallographers this is one way of
+ 
+
+ align:start position:0%
+crystallographers this is one way of
+writing it another way of writing it is
+
+ align:start position:0%
+writing it another way of writing it is
+ 
+
+ align:start position:0%
+writing it another way of writing it is
+10 10 is equivalent to 1 but
+
+ align:start position:0%
+10 10 is equivalent to 1 but
+ 
+
+ align:start position:0%
+10 10 is equivalent to 1 but
+crystallographers like to put things in
+
+ align:start position:0%
+crystallographers like to put things in
+ 
+
+ align:start position:0%
+crystallographers like to put things in
+ascending order so the crystallographer
+
+ align:start position:0%
+ascending order so the crystallographer
+ 
+
+ align:start position:0%
+ascending order so the crystallographer
+would never write 10 crystallographer
+
+ align:start position:0%
+would never write 10 crystallographer
+ 
+
+ align:start position:0%
+would never write 10 crystallographer
+write o1 so that's that's cool Factor
+
+ align:start position:0%
+write o1 so that's that's cool Factor
+ 
+
+ align:start position:0%
+write o1 so that's that's cool Factor
+there if you want to get you you never
+
+ align:start position:0%
+there if you want to get you you never
+ 
+
+ align:start position:0%
+there if you want to get you you never
+know when you're going to meet a
+
+ align:start position:0%
+know when you're going to meet a
+ 
+
+ align:start position:0%
+know when you're going to meet a
+crystallographer on an elevator it could
+
+ align:start position:0%
+crystallographer on an elevator it could
+ 
+
+ align:start position:0%
+crystallographer on an elevator it could
+come in it could be the ice breaker
+
+ align:start position:0%
+come in it could be the ice breaker
+ 
+
+ align:start position:0%
+come in it could be the ice breaker
+because they might be shy you know okay
+
+ align:start position:0%
+because they might be shy you know okay
+ 
+
+ align:start position:0%
+because they might be shy you know okay
+and the last thing the last thing I want
+
+ align:start position:0%
+and the last thing the last thing I want
+ 
+
+ align:start position:0%
+and the last thing the last thing I want
+to do is talk about the distance
+
+ align:start position:0%
+to do is talk about the distance
+ 
+
+ align:start position:0%
+to do is talk about the distance
+calculation another virtue of using
+
+ align:start position:0%
+calculation another virtue of using
+ 
+
+ align:start position:0%
+calculation another virtue of using
+Miller indices I want to put this up
+
+ align:start position:0%
+Miller indices I want to put this up
+ 
+
+ align:start position:0%
+Miller indices I want to put this up
+here because it's it's on the handout
+
+ align:start position:0%
+here because it's it's on the handout
+ 
+
+ align:start position:0%
+here because it's it's on the handout
+but I want to make sure that it gets on
+
+ align:start position:0%
+but I want to make sure that it gets on
+ 
+
+ align:start position:0%
+but I want to make sure that it gets on
+the board the hkl plane is perpendicular
+
+ align:start position:0%
+the board the hkl plane is perpendicular
+ 
+
+ align:start position:0%
+the board the hkl plane is perpendicular
+to the
+
+ align:start position:0%
+to the
+ 
+
+ align:start position:0%
+to the
+hkl direction when we use such a
+
+ align:start position:0%
+hkl direction when we use such a
+ 
+
+ align:start position:0%
+hkl direction when we use such a
+notation and then I want to show let's
+
+ align:start position:0%
+notation and then I want to show let's
+ 
+
+ align:start position:0%
+notation and then I want to show let's
+go back to the previous slide uh go back
+
+ align:start position:0%
+go back to the previous slide uh go back
+ 
+
+ align:start position:0%
+go back to the previous slide uh go back
+two of them because it's easier to see
+
+ align:start position:0%
+two of them because it's easier to see
+ 
+
+ align:start position:0%
+two of them because it's easier to see
+here I want to calculate the distance
+
+ align:start position:0%
+here I want to calculate the distance
+ 
+
+ align:start position:0%
+here I want to calculate the distance
+between adjacent planes of the same
+
+ align:start position:0%
+between adjacent planes of the same
+ 
+
+ align:start position:0%
+between adjacent planes of the same
+index so we can calculate the distance
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the distance between adjacent
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+planes between adjacent planes of the
+
+ align:start position:0%
+planes between adjacent planes of the
+ 
+
+ align:start position:0%
+planes between adjacent planes of the
+same
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+index
+
+ align:start position:0%
+index
+ 
+
+ align:start position:0%
+index
+so what's the distance between two
+
+ align:start position:0%
+so what's the distance between two
+ 
+
+ align:start position:0%
+so what's the distance between two
+adjacent planes of some value hkl and
+
+ align:start position:0%
+adjacent planes of some value hkl and
+ 
+
+ align:start position:0%
+adjacent planes of some value hkl and
+that's given by the the
+
+ align:start position:0%
+that's given by the the
+ 
+
+ align:start position:0%
+that's given by the the
+following formula which again is a
+
+ align:start position:0%
+following formula which again is a
+ 
+
+ align:start position:0%
+following formula which again is a
+testimony to uh to Miller the the
+
+ align:start position:0%
+testimony to uh to Miller the the
+ 
+
+ align:start position:0%
+testimony to uh to Miller the the
+distance and I'm going to subscript it
+
+ align:start position:0%
+distance and I'm going to subscript it
+ 
+
+ align:start position:0%
+distance and I'm going to subscript it
+hkl because they're all the same index
+
+ align:start position:0%
+hkl because they're all the same index
+ 
+
+ align:start position:0%
+hkl because they're all the same index
+is given
+
+ align:start position:0%
+is given
+ 
+
+ align:start position:0%
+is given
+by a which is the lce constant divided
+
+ align:start position:0%
+by a which is the lce constant divided
+ 
+
+ align:start position:0%
+by a which is the lce constant divided
+by the square root of h^2 + K2 +
+
+ align:start position:0%
+by the square root of h^2 + K2 +
+ 
+
+ align:start position:0%
+by the square root of h^2 + K2 +
+L2 where a is the lattice
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+constant okay so let's test it if hkl is
+
+ align:start position:0%
+constant okay so let's test it if hkl is
+ 
+
+ align:start position:0%
+constant okay so let's test it if hkl is
+010 well trivially that separation
+
+ align:start position:0%
+010 well trivially that separation
+ 
+
+ align:start position:0%
+010 well trivially that separation
+should be a the lattice constant and I
+
+ align:start position:0%
+should be a the lattice constant and I
+ 
+
+ align:start position:0%
+should be a the lattice constant and I
+think you can see that quite nicely up
+
+ align:start position:0%
+think you can see that quite nicely up
+ 
+
+ align:start position:0%
+think you can see that quite nicely up
+on the the screen here it's one lattice
+
+ align:start position:0%
+on the the screen here it's one lattice
+ 
+
+ align:start position:0%
+on the the screen here it's one lattice
+constant between successive o10 planes
+
+ align:start position:0%
+constant between successive o10 planes
+ 
+
+ align:start position:0%
+constant between successive o10 planes
+let's try it with o20 well it's going to
+
+ align:start position:0%
+let's try it with o20 well it's going to
+ 
+
+ align:start position:0%
+let's try it with o20 well it's going to
+be the square root of 2^2 which is a
+
+ align:start position:0%
+be the square root of 2^2 which is a
+ 
+
+ align:start position:0%
+be the square root of 2^2 which is a
+over two and sure enough what's the
+
+ align:start position:0%
+over two and sure enough what's the
+ 
+
+ align:start position:0%
+over two and sure enough what's the
+distance between o20 and the adjacent
+
+ align:start position:0%
+distance between o20 and the adjacent
+ 
+
+ align:start position:0%
+distance between o20 and the adjacent
+plane comparable to it it's a it's only
+
+ align:start position:0%
+plane comparable to it it's a it's only
+ 
+
+ align:start position:0%
+plane comparable to it it's a it's only
+half a lattice constant so in essence if
+
+ align:start position:0%
+half a lattice constant so in essence if
+ 
+
+ align:start position:0%
+half a lattice constant so in essence if
+you look here every o2o plane every o2o
+
+ align:start position:0%
+you look here every o2o plane every o2o
+ 
+
+ align:start position:0%
+you look here every o2o plane every o2o
+plane plane is only half a lattice
+
+ align:start position:0%
+plane plane is only half a lattice
+ 
+
+ align:start position:0%
+plane plane is only half a lattice
+constant away every 010 plane is a full
+
+ align:start position:0%
+constant away every 010 plane is a full
+ 
+
+ align:start position:0%
+constant away every 010 plane is a full
+lattice constant so what you're really
+
+ align:start position:0%
+lattice constant so what you're really
+ 
+
+ align:start position:0%
+lattice constant so what you're really
+seeing then is that the the distance d
+
+ align:start position:0%
+seeing then is that the the distance d
+ 
+
+ align:start position:0%
+seeing then is that the the distance d
+goes down the distance between planes
+
+ align:start position:0%
+goes down the distance between planes
+ 
+
+ align:start position:0%
+goes down the distance between planes
+goes down
+
+ align:start position:0%
+goes down
+ 
+
+ align:start position:0%
+goes down
+as the Miller index goes up and what's
+
+ align:start position:0%
+as the Miller index goes up and what's
+ 
+
+ align:start position:0%
+as the Miller index goes up and what's
+that what's the lowest Miller index the
+
+ align:start position:0%
+that what's the lowest Miller index the
+ 
+
+ align:start position:0%
+that what's the lowest Miller index the
+lowest Miller index is
+
+ align:start position:0%
+lowest Miller index is
+ 
+
+ align:start position:0%
+lowest Miller index is
+o1 lowest Miller index is o1 so that's a
+
+ align:start position:0%
+o1 lowest Miller index is o1 so that's a
+ 
+
+ align:start position:0%
+o1 lowest Miller index is o1 so that's a
+lattice constant that's the max maximum
+
+ align:start position:0%
+lattice constant that's the max maximum
+ 
+
+ align:start position:0%
+lattice constant that's the max maximum
+separation and I think you can see that
+
+ align:start position:0%
+separation and I think you can see that
+ 
+
+ align:start position:0%
+separation and I think you can see that
+as you move hkl to higher values what
+
+ align:start position:0%
+as you move hkl to higher values what
+ 
+
+ align:start position:0%
+as you move hkl to higher values what
+you're doing is you're cutting at a
+
+ align:start position:0%
+you're doing is you're cutting at a
+ 
+
+ align:start position:0%
+you're doing is you're cutting at a
+higher angular slice and as you cut for
+
+ align:start position:0%
+higher angular slice and as you cut for
+ 
+
+ align:start position:0%
+higher angular slice and as you cut for
+a higher angular slice the distance
+
+ align:start position:0%
+a higher angular slice the distance
+ 
+
+ align:start position:0%
+a higher angular slice the distance
+between successive planes is going to be
+
+ align:start position:0%
+between successive planes is going to be
+ 
+
+ align:start position:0%
+between successive planes is going to be
+reduced mathematically what's going on
+
+ align:start position:0%
+reduced mathematically what's going on
+ 
+
+ align:start position:0%
+reduced mathematically what's going on
+this is getting larger in the
+
+ align:start position:0%
+this is getting larger in the
+ 
+
+ align:start position:0%
+this is getting larger in the
+denominator this is remaining the same
+
+ align:start position:0%
+denominator this is remaining the same
+ 
+
+ align:start position:0%
+denominator this is remaining the same
+so that distance becomes closer and
+
+ align:start position:0%
+so that distance becomes closer and
+ 
+
+ align:start position:0%
+so that distance becomes closer and
+closer together and why am i showing you
+
+ align:start position:0%
+closer together and why am i showing you
+ 
+
+ align:start position:0%
+closer together and why am i showing you
+this because we're going to use it in
+
+ align:start position:0%
+this because we're going to use it in
+ 
+
+ align:start position:0%
+this because we're going to use it in
+the very next unit not three years from
+
+ align:start position:0%
+the very next unit not three years from
+ 
+
+ align:start position:0%
+the very next unit not three years from
+now we're going to use it in the next
+
+ align:start position:0%
+now we're going to use it in the next
+ 
+
+ align:start position:0%
+now we're going to use it in the next
+unit when we take this information and
+
+ align:start position:0%
+unit when we take this information and
+ 
+
+ align:start position:0%
+unit when we take this information and
+characterize crystals and we're going to
+
+ align:start position:0%
+characterize crystals and we're going to
+ 
+
+ align:start position:0%
+characterize crystals and we're going to
+characterize atomic structure by the use
+
+ align:start position:0%
+characterize atomic structure by the use
+ 
+
+ align:start position:0%
+characterize atomic structure by the use
+of something that is comparable in
+
+ align:start position:0%
+of something that is comparable in
+ 
+
+ align:start position:0%
+of something that is comparable in
+dimension right if we're going to
+
+ align:start position:0%
+dimension right if we're going to
+ 
+
+ align:start position:0%
+dimension right if we're going to
+measure the dimension of the human hair
+
+ align:start position:0%
+measure the dimension of the human hair
+ 
+
+ align:start position:0%
+measure the dimension of the human hair
+we're not going to use a yard stick what
+
+ align:start position:0%
+we're not going to use a yard stick what
+ 
+
+ align:start position:0%
+we're not going to use a yard stick what
+kind of numbers are we looking at for
+
+ align:start position:0%
+kind of numbers are we looking at for
+ 
+
+ align:start position:0%
+kind of numbers are we looking at for
+these distances we're looking at
+
+ align:start position:0%
+these distances we're looking at
+ 
+
+ align:start position:0%
+these distances we're looking at
+something down
+
+ align:start position:0%
+something down
+ 
+
+ align:start position:0%
+something down
+around some number of angstroms so we
+
+ align:start position:0%
+around some number of angstroms so we
+ 
+
+ align:start position:0%
+around some number of angstroms so we
+better find some tool that gives me
+
+ align:start position:0%
+better find some tool that gives me
+ 
+
+ align:start position:0%
+better find some tool that gives me
+units of some number of angrum and that
+
+ align:start position:0%
+units of some number of angrum and that
+ 
+
+ align:start position:0%
+units of some number of angrum and that
+tool will be x-rays x-rays so now let's
+
+ align:start position:0%
+tool will be x-rays x-rays so now let's
+ 
+
+ align:start position:0%
+tool will be x-rays x-rays so now let's
+look at
+
+ align:start position:0%
+look at
+ 
+
+ align:start position:0%
+look at
+characterization
+
+ align:start position:0%
+characterization
+ 
+
+ align:start position:0%
+characterization
+characterization of atomic
+
+ align:start position:0%
+characterization of atomic
+ 
+
+ align:start position:0%
+characterization of atomic
+structure by
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+x-rays so today I want to talk about
+
+ align:start position:0%
+x-rays so today I want to talk about
+ 
+
+ align:start position:0%
+x-rays so today I want to talk about
+this the discovery of X-rays and the
+
+ align:start position:0%
+this the discovery of X-rays and the
+ 
+
+ align:start position:0%
+this the discovery of X-rays and the
+underlying physics and then next day
+
+ align:start position:0%
+underlying physics and then next day
+ 
+
+ align:start position:0%
+underlying physics and then next day
+we're going to look at applications so
+
+ align:start position:0%
+we're going to look at applications so
+ 
+
+ align:start position:0%
+we're going to look at applications so
+first of all what are X-rays x-rays are
+
+ align:start position:0%
+first of all what are X-rays x-rays are
+ 
+
+ align:start position:0%
+first of all what are X-rays x-rays are
+a form of electromagnetic
+
+ align:start position:0%
+a form of electromagnetic
+ 
+
+ align:start position:0%
+a form of electromagnetic
+radiation they're a form of
+
+ align:start position:0%
+radiation they're a form of
+ 
+
+ align:start position:0%
+radiation they're a form of
+electromagnetic
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+radiation electromagnetic
+
+ align:start position:0%
+radiation electromagnetic
+ 
+
+ align:start position:0%
+radiation electromagnetic
+radiation so what's that mean that means
+
+ align:start position:0%
+radiation so what's that mean that means
+ 
+
+ align:start position:0%
+radiation so what's that mean that means
+all of these formulas apply eal H new
+
+ align:start position:0%
+all of these formulas apply eal H new
+ 
+
+ align:start position:0%
+all of these formulas apply eal H new
+equals HC over Lambda equal HC new bar
+
+ align:start position:0%
+equals HC over Lambda equal HC new bar
+ 
+
+ align:start position:0%
+equals HC over Lambda equal HC new bar
+that applies that applies
+
+ align:start position:0%
+that applies that applies
+ 
+
+ align:start position:0%
+that applies that applies
+and the special characteristic of x-rays
+
+ align:start position:0%
+and the special characteristic of x-rays
+ 
+
+ align:start position:0%
+and the special characteristic of x-rays
+is Lambda is very short and typically
+
+ align:start position:0%
+is Lambda is very short and typically
+ 
+
+ align:start position:0%
+is Lambda is very short and typically
+there's no hard rule on this but just in
+
+ align:start position:0%
+there's no hard rule on this but just in
+ 
+
+ align:start position:0%
+there's no hard rule on this but just in
+round numbers we're looking at between
+
+ align:start position:0%
+round numbers we're looking at between
+ 
+
+ align:start position:0%
+round numbers we're looking at between
+1/ 100th to 100 angstroms it's centered
+
+ align:start position:0%
+1/ 100th to 100 angstroms it's centered
+ 
+
+ align:start position:0%
+1/ 100th to 100 angstroms it's centered
+at about one angstrom where one angstrom
+
+ align:start position:0%
+at about one angstrom where one angstrom
+ 
+
+ align:start position:0%
+at about one angstrom where one angstrom
+is equal to 10us 10 meters I know it's
+
+ align:start position:0%
+is equal to 10us 10 meters I know it's
+ 
+
+ align:start position:0%
+is equal to 10us 10 meters I know it's
+not an SI unit and you know my aversion
+
+ align:start position:0%
+not an SI unit and you know my aversion
+ 
+
+ align:start position:0%
+not an SI unit and you know my aversion
+to the nanometer but I'll put it up here
+
+ align:start position:0%
+to the nanometer but I'll put it up here
+ 
+
+ align:start position:0%
+to the nanometer but I'll put it up here
+because I'm required by the
+
+ align:start position:0%
+because I'm required by the
+ 
+
+ align:start position:0%
+because I'm required by the
+international Union of pure and applied
+
+ align:start position:0%
+international Union of pure and applied
+ 
+
+ align:start position:0%
+international Union of pure and applied
+chemistry and the system international
+
+ align:start position:0%
+chemistry and the system international
+ 
+
+ align:start position:0%
+chemistry and the system international
+to put this cont temptable unit here but
+
+ align:start position:0%
+to put this cont temptable unit here but
+ 
+
+ align:start position:0%
+to put this cont temptable unit here but
+I love the angstrom so this is just my
+
+ align:start position:0%
+I love the angstrom so this is just my
+ 
+
+ align:start position:0%
+I love the angstrom so this is just my
+personal preference okay so let's let's
+
+ align:start position:0%
+personal preference okay so let's let's
+ 
+
+ align:start position:0%
+personal preference okay so let's let's
+plug in a value suppose we have one
+
+ align:start position:0%
+plug in a value suppose we have one
+ 
+
+ align:start position:0%
+plug in a value suppose we have one
+angstrom as the wavelength if I use HC
+
+ align:start position:0%
+angstrom as the wavelength if I use HC
+ 
+
+ align:start position:0%
+angstrom as the wavelength if I use HC
+over Lambda where Lambda equals 1
+
+ align:start position:0%
+over Lambda where Lambda equals 1
+ 
+
+ align:start position:0%
+over Lambda where Lambda equals 1
+angstrom or 10us 10 m I end up with 12,4
+
+ align:start position:0%
+angstrom or 10us 10 m I end up with 12,4
+ 
+
+ align:start position:0%
+angstrom or 10us 10 m I end up with 12,4
+00 electron volts per
+
+ align:start position:0%
+00 electron volts per
+ 
+
+ align:start position:0%
+00 electron volts per
+photon per photon 12,400 electron volts
+
+ align:start position:0%
+photon per photon 12,400 electron volts
+ 
+
+ align:start position:0%
+photon per photon 12,400 electron volts
+per photon and this is clearly going to
+
+ align:start position:0%
+per photon and this is clearly going to
+ 
+
+ align:start position:0%
+per photon and this is clearly going to
+be powerful radiation let's take a look
+
+ align:start position:0%
+be powerful radiation let's take a look
+ 
+
+ align:start position:0%
+be powerful radiation let's take a look
+here I pulled this out of the back of
+
+ align:start position:0%
+here I pulled this out of the back of
+ 
+
+ align:start position:0%
+here I pulled this out of the back of
+the text this has um ionization energies
+
+ align:start position:0%
+the text this has um ionization energies
+ 
+
+ align:start position:0%
+the text this has um ionization energies
+for the first uh Seven Elements so if
+
+ align:start position:0%
+for the first uh Seven Elements so if
+ 
+
+ align:start position:0%
+for the first uh Seven Elements so if
+you if you look here this is the in
+
+ align:start position:0%
+you if you look here this is the in
+ 
+
+ align:start position:0%
+you if you look here this is the in
+green I'm showing the first ionization
+
+ align:start position:0%
+green I'm showing the first ionization
+ 
+
+ align:start position:0%
+green I'm showing the first ionization
+energy and this is right off your
+
+ align:start position:0%
+energy and this is right off your
+ 
+
+ align:start position:0%
+energy and this is right off your
+periodic table right 13.6 electron volts
+
+ align:start position:0%
+periodic table right 13.6 electron volts
+ 
+
+ align:start position:0%
+periodic table right 13.6 electron volts
+I've rounded it to two significant
+
+ align:start position:0%
+I've rounded it to two significant
+ 
+
+ align:start position:0%
+I've rounded it to two significant
+figures so it's 13.6 for hydrogen it's
+
+ align:start position:0%
+figures so it's 13.6 for hydrogen it's
+ 
+
+ align:start position:0%
+figures so it's 13.6 for hydrogen it's
+25 for helium it's five um for lithium
+
+ align:start position:0%
+25 for helium it's five um for lithium
+ 
+
+ align:start position:0%
+25 for helium it's five um for lithium
+and so on so these are these are tiny
+
+ align:start position:0%
+and so on so these are these are tiny
+ 
+
+ align:start position:0%
+and so on so these are these are tiny
+tiny numbers these are electron volts
+
+ align:start position:0%
+tiny numbers these are electron volts
+ 
+
+ align:start position:0%
+tiny numbers these are electron volts
+all right now what we can do is look
+
+ align:start position:0%
+all right now what we can do is look
+ 
+
+ align:start position:0%
+all right now what we can do is look
+down this row this is this is the last
+
+ align:start position:0%
+down this row this is this is the last
+ 
+
+ align:start position:0%
+down this row this is this is the last
+electron to come off okay so the second
+
+ align:start position:0%
+electron to come off okay so the second
+ 
+
+ align:start position:0%
+electron to come off okay so the second
+ionization energy of helium is for a one
+
+ align:start position:0%
+ionization energy of helium is for a one
+ 
+
+ align:start position:0%
+ionization energy of helium is for a one
+electron atom right helium has two
+
+ align:start position:0%
+electron atom right helium has two
+ 
+
+ align:start position:0%
+electron atom right helium has two
+electrons if it loses one it only has
+
+ align:start position:0%
+electrons if it loses one it only has
+ 
+
+ align:start position:0%
+electrons if it loses one it only has
+one left so this is a one electron atom
+
+ align:start position:0%
+one left so this is a one electron atom
+ 
+
+ align:start position:0%
+one left so this is a one electron atom
+this is a one electron atom this is a
+
+ align:start position:0%
+this is a one electron atom this is a
+ 
+
+ align:start position:0%
+this is a one electron atom this is a
+one electron atom and look at the
+
+ align:start position:0%
+one electron atom and look at the
+ 
+
+ align:start position:0%
+one electron atom and look at the
+energies this is for the innermost
+
+ align:start position:0%
+energies this is for the innermost
+ 
+
+ align:start position:0%
+energies this is for the innermost
+electron well one electron atom that'll
+
+ align:start position:0%
+electron well one electron atom that'll
+ 
+
+ align:start position:0%
+electron well one electron atom that'll
+conform to the bore model and sure
+
+ align:start position:0%
+conform to the bore model and sure
+ 
+
+ align:start position:0%
+conform to the bore model and sure
+enough look at the ratios of these
+
+ align:start position:0%
+enough look at the ratios of these
+ 
+
+ align:start position:0%
+enough look at the ratios of these
+numbers these are determined by x-ray
+
+ align:start position:0%
+numbers these are determined by x-ray
+ 
+
+ align:start position:0%
+numbers these are determined by x-ray
+photo electron spectroscopy and roughly
+
+ align:start position:0%
+photo electron spectroscopy and roughly
+ 
+
+ align:start position:0%
+photo electron spectroscopy and roughly
+14 * 4 is 56 so there it is 1 to 4 to 9
+
+ align:start position:0%
+14 * 4 is 56 so there it is 1 to 4 to 9
+ 
+
+ align:start position:0%
+14 * 4 is 56 so there it is 1 to 4 to 9
+to 16 and it's just a manifestation of
+
+ align:start position:0%
+to 16 and it's just a manifestation of
+ 
+
+ align:start position:0%
+to 16 and it's just a manifestation of
+what you've seen as the ground state
+
+ align:start position:0%
+what you've seen as the ground state
+ 
+
+ align:start position:0%
+what you've seen as the ground state
+energy in the bore model goes as the
+
+ align:start position:0%
+energy in the bore model goes as the
+ 
+
+ align:start position:0%
+energy in the bore model goes as the
+square of the atomic number so
+
+ align:start position:0%
+square of the atomic number so
+ 
+
+ align:start position:0%
+square of the atomic number so
+everything's making sense but what I
+
+ align:start position:0%
+everything's making sense but what I
+ 
+
+ align:start position:0%
+everything's making sense but what I
+draw your attention to is look this is
+
+ align:start position:0%
+draw your attention to is look this is
+ 
+
+ align:start position:0%
+draw your attention to is look this is
+the innermost held electron of nitrogen
+
+ align:start position:0%
+the innermost held electron of nitrogen
+ 
+
+ align:start position:0%
+the innermost held electron of nitrogen
+it's 668 electron volts and I've got
+
+ align:start position:0%
+it's 668 electron volts and I've got
+ 
+
+ align:start position:0%
+it's 668 electron volts and I've got
+12,400 this has enormous power this has
+
+ align:start position:0%
+12,400 this has enormous power this has
+ 
+
+ align:start position:0%
+12,400 this has enormous power this has
+the power to
+
+ align:start position:0%
+the power to
+ 
+
+ align:start position:0%
+the power to
+ionize ionize inner shell
+
+ align:start position:0%
+ionize ionize inner shell
+ 
+
+ align:start position:0%
+ionize ionize inner shell
+electrons this is like a bowling alley
+
+ align:start position:0%
+electrons this is like a bowling alley
+ 
+
+ align:start position:0%
+electrons this is like a bowling alley
+this is like a bowling alley and all the
+
+ align:start position:0%
+this is like a bowling alley and all the
+ 
+
+ align:start position:0%
+this is like a bowling alley and all the
+pins are going flying here this is
+
+ align:start position:0%
+pins are going flying here this is
+ 
+
+ align:start position:0%
+pins are going flying here this is
+incredible
+
+ align:start position:0%
+incredible
+ 
+
+ align:start position:0%
+incredible
+energy so what's the what's the
+
+ align:start position:0%
+energy so what's the what's the
+ 
+
+ align:start position:0%
+energy so what's the what's the
+underlying principles here well I think
+
+ align:start position:0%
+underlying principles here well I think
+ 
+
+ align:start position:0%
+underlying principles here well I think
+we have to start with a history lesson
+
+ align:start position:0%
+we have to start with a history lesson
+ 
+
+ align:start position:0%
+we have to start with a history lesson
+so we'll start with a history lesson
+
+ align:start position:0%
+so we'll start with a history lesson
+ 
+
+ align:start position:0%
+so we'll start with a history lesson
+we'll go back to November 8th 1895 it
+
+ align:start position:0%
+we'll go back to November 8th 1895 it
+ 
+
+ align:start position:0%
+we'll go back to November 8th 1895 it
+was a dark and stormy night really it
+
+ align:start position:0%
+was a dark and stormy night really it
+ 
+
+ align:start position:0%
+was a dark and stormy night really it
+was a dark and stormy night on November
+
+ align:start position:0%
+was a dark and stormy night on November
+ 
+
+ align:start position:0%
+was a dark and stormy night on November
+8th 189 95 in
+
+ align:start position:0%
+8th 189 95 in
+ 
+
+ align:start position:0%
+8th 189 95 in
+verburg verburg in
+
+ align:start position:0%
+verburg verburg in
+ 
+
+ align:start position:0%
+verburg verburg in
+Bavaria which is now part of Germany and
+
+ align:start position:0%
+Bavaria which is now part of Germany and
+ 
+
+ align:start position:0%
+Bavaria which is now part of Germany and
+there was a physics Professor there
+
+ align:start position:0%
+there was a physics Professor there
+ 
+
+ align:start position:0%
+there was a physics Professor there
+physics Professor there by the name of
+
+ align:start position:0%
+physics Professor there by the name of
+ 
+
+ align:start position:0%
+physics Professor there by the name of
+Willam
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+renen William
+
+ align:start position:0%
+renen William
+ 
+
+ align:start position:0%
+renen William
+renin and he was doing research as many
+
+ align:start position:0%
+renin and he was doing research as many
+ 
+
+ align:start position:0%
+renin and he was doing research as many
+people were at that time on gas
+
+ align:start position:0%
+people were at that time on gas
+ 
+
+ align:start position:0%
+people were at that time on gas
+discharge tub we've seen gas discharge
+
+ align:start position:0%
+discharge tub we've seen gas discharge
+ 
+
+ align:start position:0%
+discharge tub we've seen gas discharge
+tubes a number of times in 3091 and
+
+ align:start position:0%
+tubes a number of times in 3091 and
+ 
+
+ align:start position:0%
+tubes a number of times in 3091 and
+renen was part of that army of
+
+ align:start position:0%
+renen was part of that army of
+ 
+
+ align:start position:0%
+renen was part of that army of
+researchers and what Ren's specialty was
+
+ align:start position:0%
+researchers and what Ren's specialty was
+ 
+
+ align:start position:0%
+researchers and what Ren's specialty was
+he was pursuing gas discharge spectral
+
+ align:start position:0%
+he was pursuing gas discharge spectral
+ 
+
+ align:start position:0%
+he was pursuing gas discharge spectral
+analysis under reduced
+
+ align:start position:0%
+analysis under reduced
+ 
+
+ align:start position:0%
+analysis under reduced
+pressure so he was pumping down with a
+
+ align:start position:0%
+pressure so he was pumping down with a
+ 
+
+ align:start position:0%
+pressure so he was pumping down with a
+vacuum pump to get the gas pressure very
+
+ align:start position:0%
+vacuum pump to get the gas pressure very
+ 
+
+ align:start position:0%
+vacuum pump to get the gas pressure very
+very low and very very high voltage
+
+ align:start position:0%
+very low and very very high voltage
+ 
+
+ align:start position:0%
+very low and very very high voltage
+that's what his take was he wanted to
+
+ align:start position:0%
+that's what his take was he wanted to
+ 
+
+ align:start position:0%
+that's what his take was he wanted to
+look at high voltage and very very low
+
+ align:start position:0%
+look at high voltage and very very low
+ 
+
+ align:start position:0%
+look at high voltage and very very low
+pressure pressure and let's take a look
+
+ align:start position:0%
+pressure pressure and let's take a look
+ 
+
+ align:start position:0%
+pressure pressure and let's take a look
+at what his his apparatus looked like um
+
+ align:start position:0%
+at what his his apparatus looked like um
+ 
+
+ align:start position:0%
+at what his his apparatus looked like um
+well we'll start with the the tube as
+
+ align:start position:0%
+well we'll start with the the tube as
+ 
+
+ align:start position:0%
+well we'll start with the the tube as
+you've seen many times we'll put a we'll
+
+ align:start position:0%
+you've seen many times we'll put a we'll
+ 
+
+ align:start position:0%
+you've seen many times we'll put a we'll
+put the cathode to the left we'll put
+
+ align:start position:0%
+put the cathode to the left we'll put
+ 
+
+ align:start position:0%
+put the cathode to the left we'll put
+the anode to the
+
+ align:start position:0%
+the anode to the
+ 
+
+ align:start position:0%
+the anode to the
+right and he had the laboratory on the
+
+ align:start position:0%
+right and he had the laboratory on the
+ 
+
+ align:start position:0%
+right and he had the laboratory on the
+second floor laboratory in the second
+
+ align:start position:0%
+second floor laboratory in the second
+ 
+
+ align:start position:0%
+second floor laboratory in the second
+floor his apartment was on the first
+
+ align:start position:0%
+floor his apartment was on the first
+ 
+
+ align:start position:0%
+floor his apartment was on the first
+floor and down in the basement he had a
+
+ align:start position:0%
+floor and down in the basement he had a
+ 
+
+ align:start position:0%
+floor and down in the basement he had a
+bunch of uh uh batteries chromic acid
+
+ align:start position:0%
+bunch of uh uh batteries chromic acid
+ 
+
+ align:start position:0%
+bunch of uh uh batteries chromic acid
+chromic acid in open beakers uh down in
+
+ align:start position:0%
+chromic acid in open beakers uh down in
+ 
+
+ align:start position:0%
+chromic acid in open beakers uh down in
+the basement so let's indicate that with
+
+ align:start position:0%
+the basement so let's indicate that with
+ 
+
+ align:start position:0%
+the basement so let's indicate that with
+the classical symbol and this altogether
+
+ align:start position:0%
+the classical symbol and this altogether
+ 
+
+ align:start position:0%
+the classical symbol and this altogether
+put out about 20 volts and then what he
+
+ align:start position:0%
+put out about 20 volts and then what he
+ 
+
+ align:start position:0%
+put out about 20 volts and then what he
+did is he was a professor of physics who
+
+ align:start position:0%
+did is he was a professor of physics who
+ 
+
+ align:start position:0%
+did is he was a professor of physics who
+understood some electrical engineering
+
+ align:start position:0%
+understood some electrical engineering
+ 
+
+ align:start position:0%
+understood some electrical engineering
+so he had a choke coil here so the choke
+
+ align:start position:0%
+so he had a choke coil here so the choke
+ 
+
+ align:start position:0%
+so he had a choke coil here so the choke
+coil would would take the the current
+
+ align:start position:0%
+coil would would take the the current
+ 
+
+ align:start position:0%
+coil would would take the the current
+store up and eight times a second eight
+
+ align:start position:0%
+store up and eight times a second eight
+ 
+
+ align:start position:0%
+store up and eight times a second eight
+times a second
+
+ align:start position:0%
+times a second
+ 
+
+ align:start position:0%
+times a second
+it would discharge and it would
+
+ align:start position:0%
+it would discharge and it would
+ 
+
+ align:start position:0%
+it would discharge and it would
+discharge at 35,000 volts so he could
+
+ align:start position:0%
+discharge at 35,000 volts so he could
+ 
+
+ align:start position:0%
+discharge at 35,000 volts so he could
+take 20 volts and up it to uh 35,000 by
+
+ align:start position:0%
+take 20 volts and up it to uh 35,000 by
+ 
+
+ align:start position:0%
+take 20 volts and up it to uh 35,000 by
+the use of this choke coil so eight
+
+ align:start position:0%
+the use of this choke coil so eight
+ 
+
+ align:start position:0%
+the use of this choke coil so eight
+times a second he had 35,000 volts
+
+ align:start position:0%
+times a second he had 35,000 volts
+ 
+
+ align:start position:0%
+times a second he had 35,000 volts
+coming off the cathode here so you've
+
+ align:start position:0%
+coming off the cathode here so you've
+ 
+
+ align:start position:0%
+coming off the cathode here so you've
+got Bam Bam Bam Bam but speed that up
+
+ align:start position:0%
+got Bam Bam Bam Bam but speed that up
+ 
+
+ align:start position:0%
+got Bam Bam Bam Bam but speed that up
+about eight times and that's what that's
+
+ align:start position:0%
+about eight times and that's what that's
+ 
+
+ align:start position:0%
+about eight times and that's what that's
+what's going on and so with 35,000 volts
+
+ align:start position:0%
+what's going on and so with 35,000 volts
+ 
+
+ align:start position:0%
+what's going on and so with 35,000 volts
+he launches electrons off the cathode
+
+ align:start position:0%
+he launches electrons off the cathode
+ 
+
+ align:start position:0%
+he launches electrons off the cathode
+and they go zooming across what is very
+
+ align:start position:0%
+and they go zooming across what is very
+ 
+
+ align:start position:0%
+and they go zooming across what is very
+very low pressure gas and crash into the
+
+ align:start position:0%
+very low pressure gas and crash into the
+ 
+
+ align:start position:0%
+very low pressure gas and crash into the
+anode and in the meantime to keep this
+
+ align:start position:0%
+anode and in the meantime to keep this
+ 
+
+ align:start position:0%
+anode and in the meantime to keep this
+thing dynamically at low pressure this
+
+ align:start position:0%
+thing dynamically at low pressure this
+ 
+
+ align:start position:0%
+thing dynamically at low pressure this
+goes to a vacuum
+
+ align:start position:0%
+goes to a vacuum
+ 
+
+ align:start position:0%
+goes to a vacuum
+pump vacuum pump to keep this thing
+
+ align:start position:0%
+pump vacuum pump to keep this thing
+ 
+
+ align:start position:0%
+pump vacuum pump to keep this thing
+pumped down as low as he
+
+ align:start position:0%
+pumped down as low as he
+ 
+
+ align:start position:0%
+pumped down as low as he
+can and he was measuring what was going
+
+ align:start position:0%
+can and he was measuring what was going
+ 
+
+ align:start position:0%
+can and he was measuring what was going
+on inside this gas tube and so he had a
+
+ align:start position:0%
+on inside this gas tube and so he had a
+ 
+
+ align:start position:0%
+on inside this gas tube and so he had a
+detector and his detector was over here
+
+ align:start position:0%
+detector and his detector was over here
+ 
+
+ align:start position:0%
+detector and his detector was over here
+the detector was off to the side and the
+
+ align:start position:0%
+the detector was off to the side and the
+ 
+
+ align:start position:0%
+the detector was off to the side and the
+detector consisted of of either a piece
+
+ align:start position:0%
+detector consisted of of either a piece
+ 
+
+ align:start position:0%
+detector consisted of of either a piece
+of cloth or a paper towel which had been
+
+ align:start position:0%
+of cloth or a paper towel which had been
+ 
+
+ align:start position:0%
+of cloth or a paper towel which had been
+painted with a a chemical that would
+
+ align:start position:0%
+painted with a a chemical that would
+ 
+
+ align:start position:0%
+painted with a a chemical that would
+glow when it was struck by something
+
+ align:start position:0%
+glow when it was struck by something
+ 
+
+ align:start position:0%
+glow when it was struck by something
+what would the something be it something
+
+ align:start position:0%
+what would the something be it something
+ 
+
+ align:start position:0%
+what would the something be it something
+would
+
+ align:start position:0%
+would
+ 
+
+ align:start position:0%
+would
+be electrons or photons that have an
+
+ align:start position:0%
+be electrons or photons that have an
+ 
+
+ align:start position:0%
+be electrons or photons that have an
+energy high enough to cause excitation
+
+ align:start position:0%
+energy high enough to cause excitation
+ 
+
+ align:start position:0%
+energy high enough to cause excitation
+of something in the paint and then
+
+ align:start position:0%
+of something in the paint and then
+ 
+
+ align:start position:0%
+of something in the paint and then
+reemission in the visible doesn't do any
+
+ align:start position:0%
+reemission in the visible doesn't do any
+ 
+
+ align:start position:0%
+reemission in the visible doesn't do any
+good to excite electrons in the detector
+
+ align:start position:0%
+good to excite electrons in the detector
+ 
+
+ align:start position:0%
+good to excite electrons in the detector
+to have them Reit outside the visible
+
+ align:start position:0%
+to have them Reit outside the visible
+ 
+
+ align:start position:0%
+to have them Reit outside the visible
+okay so that's what's going on so this
+
+ align:start position:0%
+okay so that's what's going on so this
+ 
+
+ align:start position:0%
+okay so that's what's going on so this
+is this was paper or
+
+ align:start position:0%
+is this was paper or
+ 
+
+ align:start position:0%
+is this was paper or
+cloth and it was painted with an aquous
+
+ align:start position:0%
+cloth and it was painted with an aquous
+ 
+
+ align:start position:0%
+cloth and it was painted with an aquous
+solution of
+
+ align:start position:0%
+solution of
+ 
+
+ align:start position:0%
+solution of
+barium platino
+
+ align:start position:0%
+barium platino
+ 
+
+ align:start position:0%
+barium platino
+cyanide yummy stuff barium platino
+
+ align:start position:0%
+cyanide yummy stuff barium platino
+ 
+
+ align:start position:0%
+cyanide yummy stuff barium platino
+cyanide which glows
+
+ align:start position:0%
+cyanide which glows
+ 
+
+ align:start position:0%
+cyanide which glows
+green it glows green when it's
+
+ align:start position:0%
+green it glows green when it's
+ 
+
+ align:start position:0%
+green it glows green when it's
+excited and uh this is called a
+
+ align:start position:0%
+excited and uh this is called a
+ 
+
+ align:start position:0%
+excited and uh this is called a
+scintillation screen scintillation
+
+ align:start position:0%
+scintillation screen scintillation
+ 
+
+ align:start position:0%
+scintillation screen scintillation
+screen comes from the Latin word for
+
+ align:start position:0%
+screen comes from the Latin word for
+ 
+
+ align:start position:0%
+screen comes from the Latin word for
+spark cintilla means spark in Latin so
+
+ align:start position:0%
+spark cintilla means spark in Latin so
+ 
+
+ align:start position:0%
+spark cintilla means spark in Latin so
+when the screen is struck by some form
+
+ align:start position:0%
+when the screen is struck by some form
+ 
+
+ align:start position:0%
+when the screen is struck by some form
+of energy uh it will glow and so he' had
+
+ align:start position:0%
+of energy uh it will glow and so he' had
+ 
+
+ align:start position:0%
+of energy uh it will glow and so he' had
+dinner and it was up in the up on the
+
+ align:start position:0%
+dinner and it was up in the up on the
+ 
+
+ align:start position:0%
+dinner and it was up in the up on the
+second floor cranking away after dinner
+
+ align:start position:0%
+second floor cranking away after dinner
+ 
+
+ align:start position:0%
+second floor cranking away after dinner
+and it was uh it was dark it was raining
+
+ align:start position:0%
+and it was uh it was dark it was raining
+ 
+
+ align:start position:0%
+and it was uh it was dark it was raining
+had the windows open and a street light
+
+ align:start position:0%
+had the windows open and a street light
+ 
+
+ align:start position:0%
+had the windows open and a street light
+was was coming in oh by the way renen
+
+ align:start position:0%
+was was coming in oh by the way renen
+ 
+
+ align:start position:0%
+was was coming in oh by the way renen
+suffered from daltonism he was red green
+
+ align:start position:0%
+suffered from daltonism he was red green
+ 
+
+ align:start position:0%
+suffered from daltonism he was red green
+colorblind and this was a green screen
+
+ align:start position:0%
+colorblind and this was a green screen
+ 
+
+ align:start position:0%
+colorblind and this was a green screen
+and and with 35,000 volts even at
+
+ align:start position:0%
+and and with 35,000 volts even at
+ 
+
+ align:start position:0%
+and and with 35,000 volts even at
+reduced pressure given the capacity of
+
+ align:start position:0%
+reduced pressure given the capacity of
+ 
+
+ align:start position:0%
+reduced pressure given the capacity of
+those days for vacuum pumps he still had
+
+ align:start position:0%
+those days for vacuum pumps he still had
+ 
+
+ align:start position:0%
+those days for vacuum pumps he still had
+a lot of glow from the the the tube so
+
+ align:start position:0%
+a lot of glow from the the the tube so
+ 
+
+ align:start position:0%
+a lot of glow from the the the tube so
+the tube is glowing um he's got a street
+
+ align:start position:0%
+the tube is glowing um he's got a street
+ 
+
+ align:start position:0%
+the tube is glowing um he's got a street
+light in the background so he decides to
+
+ align:start position:0%
+light in the background so he decides to
+ 
+
+ align:start position:0%
+light in the background so he decides to
+close the drapes and and uh take out the
+
+ align:start position:0%
+close the drapes and and uh take out the
+ 
+
+ align:start position:0%
+close the drapes and and uh take out the
+street light and then furthermore he
+
+ align:start position:0%
+street light and then furthermore he
+ 
+
+ align:start position:0%
+street light and then furthermore he
+decides to darken darken the the room so
+
+ align:start position:0%
+decides to darken darken the the room so
+ 
+
+ align:start position:0%
+decides to darken darken the the room so
+he he puts a cardboard box over the a
+
+ align:start position:0%
+he he puts a cardboard box over the a
+ 
+
+ align:start position:0%
+he he puts a cardboard box over the a
+tube so now the tube is enclosed in a
+
+ align:start position:0%
+tube so now the tube is enclosed in a
+ 
+
+ align:start position:0%
+tube so now the tube is enclosed in a
+cardboard box so it's it's not glowing
+
+ align:start position:0%
+cardboard box so it's it's not glowing
+ 
+
+ align:start position:0%
+cardboard box so it's it's not glowing
+visibly to him it's glowing inside the
+
+ align:start position:0%
+visibly to him it's glowing inside the
+ 
+
+ align:start position:0%
+visibly to him it's glowing inside the
+box and he continues to see
+
+ align:start position:0%
+box and he continues to see
+ 
+
+ align:start position:0%
+box and he continues to see
+scintillation continues to see things
+
+ align:start position:0%
+scintillation continues to see things
+ 
+
+ align:start position:0%
+scintillation continues to see things
+glowing so he says
+
+ align:start position:0%
+glowing so he says
+ 
+
+ align:start position:0%
+glowing so he says
+hm something that's something
+
+ align:start position:0%
+hm something that's something
+ 
+
+ align:start position:0%
+hm something that's something
+interesting the other thing that
+
+ align:start position:0%
+interesting the other thing that
+ 
+
+ align:start position:0%
+interesting the other thing that
+happened was kind of interesting his
+
+ align:start position:0%
+happened was kind of interesting his
+ 
+
+ align:start position:0%
+happened was kind of interesting his
+graduate student who had prepared some
+
+ align:start position:0%
+graduate student who had prepared some
+ 
+
+ align:start position:0%
+graduate student who had prepared some
+of the apparatus I guess he was
+
+ align:start position:0%
+of the apparatus I guess he was
+ 
+
+ align:start position:0%
+of the apparatus I guess he was
+practicing painting the scintillation
+
+ align:start position:0%
+practicing painting the scintillation
+ 
+
+ align:start position:0%
+practicing painting the scintillation
+screen so what the student had done was
+
+ align:start position:0%
+screen so what the student had done was
+ 
+
+ align:start position:0%
+screen so what the student had done was
+to uh paint the letter
+
+ align:start position:0%
+to uh paint the letter
+ 
+
+ align:start position:0%
+to uh paint the letter
+A on a paper towel and he left the paper
+
+ align:start position:0%
+A on a paper towel and he left the paper
+ 
+
+ align:start position:0%
+A on a paper towel and he left the paper
+towel on the lab bench so now rin's got
+
+ align:start position:0%
+towel on the lab bench so now rin's got
+ 
+
+ align:start position:0%
+towel on the lab bench so now rin's got
+the the tube enclosed in cardboard this
+
+ align:start position:0%
+the the tube enclosed in cardboard this
+ 
+
+ align:start position:0%
+the the tube enclosed in cardboard this
+thing's glowing he looks down he sees
+
+ align:start position:0%
+thing's glowing he looks down he sees
+ 
+
+ align:start position:0%
+thing's glowing he looks down he sees
+the letter A the letter a is glowing and
+
+ align:start position:0%
+the letter A the letter a is glowing and
+ 
+
+ align:start position:0%
+the letter A the letter a is glowing and
+he's going wait a minute this is crazy
+
+ align:start position:0%
+he's going wait a minute this is crazy
+ 
+
+ align:start position:0%
+he's going wait a minute this is crazy
+so he says all right so he takes a piece
+
+ align:start position:0%
+so he says all right so he takes a piece
+ 
+
+ align:start position:0%
+so he says all right so he takes a piece
+of black paper and he puts it here in
+
+ align:start position:0%
+of black paper and he puts it here in
+ 
+
+ align:start position:0%
+of black paper and he puts it here in
+between the tube and the screen and the
+
+ align:start position:0%
+between the tube and the screen and the
+ 
+
+ align:start position:0%
+between the tube and the screen and the
+screen continues to glow and then he
+
+ align:start position:0%
+screen continues to glow and then he
+ 
+
+ align:start position:0%
+screen continues to glow and then he
+says uh he takes out he had a deck of
+
+ align:start position:0%
+says uh he takes out he had a deck of
+ 
+
+ align:start position:0%
+says uh he takes out he had a deck of
+playing cards in his in his uh lab so
+
+ align:start position:0%
+playing cards in his in his uh lab so
+ 
+
+ align:start position:0%
+playing cards in his in his uh lab so
+don't laugh that's how mlay have
+
+ align:start position:0%
+don't laugh that's how mlay have
+ 
+
+ align:start position:0%
+don't laugh that's how mlay have
+discovered periodicity so so he takes a
+
+ align:start position:0%
+discovered periodicity so so he takes a
+ 
+
+ align:start position:0%
+discovered periodicity so so he takes a
+playing card he puts the playing card in
+
+ align:start position:0%
+playing card he puts the playing card in
+ 
+
+ align:start position:0%
+playing card he puts the playing card in
+front and the tube continues to glow and
+
+ align:start position:0%
+front and the tube continues to glow and
+ 
+
+ align:start position:0%
+front and the tube continues to glow and
+then he takes a book and he puts a book
+
+ align:start position:0%
+then he takes a book and he puts a book
+ 
+
+ align:start position:0%
+then he takes a book and he puts a book
+in between and the tube continues to
+
+ align:start position:0%
+in between and the tube continues to
+ 
+
+ align:start position:0%
+in between and the tube continues to
+Glow so he's getting wait a minute so
+
+ align:start position:0%
+Glow so he's getting wait a minute so
+ 
+
+ align:start position:0%
+Glow so he's getting wait a minute so
+then he grabs a piece of lead foil and
+
+ align:start position:0%
+then he grabs a piece of lead foil and
+ 
+
+ align:start position:0%
+then he grabs a piece of lead foil and
+he puts the lead foil in here and what
+
+ align:start position:0%
+he puts the lead foil in here and what
+ 
+
+ align:start position:0%
+he puts the lead foil in here and what
+happens is that where the lead foil is
+
+ align:start position:0%
+happens is that where the lead foil is
+ 
+
+ align:start position:0%
+happens is that where the lead foil is
+the screen is not glowing but then he
+
+ align:start position:0%
+the screen is not glowing but then he
+ 
+
+ align:start position:0%
+the screen is not glowing but then he
+sees the outline of the bones of his
+
+ align:start position:0%
+sees the outline of the bones of his
+ 
+
+ align:start position:0%
+sees the outline of the bones of his
+hand on the lead holding the lead
+
+ align:start position:0%
+hand on the lead holding the lead
+ 
+
+ align:start position:0%
+hand on the lead holding the lead
+foil so all of this stuff is going on
+
+ align:start position:0%
+foil so all of this stuff is going on
+ 
+
+ align:start position:0%
+foil so all of this stuff is going on
+and he just he just goes goes to town he
+
+ align:start position:0%
+and he just he just goes goes to town he
+ 
+
+ align:start position:0%
+and he just he just goes goes to town he
+says you know what I've got to I've got
+
+ align:start position:0%
+says you know what I've got to I've got
+ 
+
+ align:start position:0%
+says you know what I've got to I've got
+to this can't be electrons because
+
+ align:start position:0%
+to this can't be electrons because
+ 
+
+ align:start position:0%
+to this can't be electrons because
+electrons can't live in air they'll be
+
+ align:start position:0%
+electrons can't live in air they'll be
+ 
+
+ align:start position:0%
+electrons can't live in air they'll be
+stopped by air so he knew about radio
+
+ align:start position:0%
+stopped by air so he knew about radio
+ 
+
+ align:start position:0%
+stopped by air so he knew about radio
+waves from Herz and he said could this
+
+ align:start position:0%
+waves from Herz and he said could this
+ 
+
+ align:start position:0%
+waves from Herz and he said could this
+be some form of mysterious radiation
+
+ align:start position:0%
+be some form of mysterious radiation
+ 
+
+ align:start position:0%
+be some form of mysterious radiation
+that's capable and he was really afraid
+
+ align:start position:0%
+that's capable and he was really afraid
+ 
+
+ align:start position:0%
+that's capable and he was really afraid
+to say this a form of radiation that's
+
+ align:start position:0%
+to say this a form of radiation that's
+ 
+
+ align:start position:0%
+to say this a form of radiation that's
+capable of penetrating
+
+ align:start position:0%
+capable of penetrating
+ 
+
+ align:start position:0%
+capable of penetrating
+matter it's 1895 you're going to come
+
+ align:start position:0%
+matter it's 1895 you're going to come
+ 
+
+ align:start position:0%
+matter it's 1895 you're going to come
+out publicly and say I have a form of
+
+ align:start position:0%
+out publicly and say I have a form of
+ 
+
+ align:start position:0%
+out publicly and say I have a form of
+radiation that can penetrate matter so
+
+ align:start position:0%
+radiation that can penetrate matter so
+ 
+
+ align:start position:0%
+radiation that can penetrate matter so
+he gets a magnet out he moves a magnet
+
+ align:start position:0%
+he gets a magnet out he moves a magnet
+ 
+
+ align:start position:0%
+he gets a magnet out he moves a magnet
+it doesn't change so the stuff isn't
+
+ align:start position:0%
+it doesn't change so the stuff isn't
+ 
+
+ align:start position:0%
+it doesn't change so the stuff isn't
+sensitive to magnetic field but if he
+
+ align:start position:0%
+sensitive to magnetic field but if he
+ 
+
+ align:start position:0%
+sensitive to magnetic field but if he
+puts a magnet here of course he gets
+
+ align:start position:0%
+puts a magnet here of course he gets
+ 
+
+ align:start position:0%
+puts a magnet here of course he gets
+changes uh he can't see this stuff he
+
+ align:start position:0%
+changes uh he can't see this stuff he
+ 
+
+ align:start position:0%
+changes uh he can't see this stuff he
+can only see evidence of it it's
+
+ align:start position:0%
+can only see evidence of it it's
+ 
+
+ align:start position:0%
+can only see evidence of it it's
+mysterious it's mysterious so he calls
+
+ align:start position:0%
+mysterious it's mysterious so he calls
+ 
+
+ align:start position:0%
+mysterious it's mysterious so he calls
+it X the unknown quantity it's X
+
+ align:start position:0%
+it X the unknown quantity it's X
+ 
+
+ align:start position:0%
+it X the unknown quantity it's X
+radiation X radiation this is November
+
+ align:start position:0%
+radiation X radiation this is November
+ 
+
+ align:start position:0%
+radiation X radiation this is November
+8th
+
+ align:start position:0%
+8th
+ 
+
+ align:start position:0%
+8th
+1895 and to show you what a what a great
+
+ align:start position:0%
+1895 and to show you what a what a great
+ 
+
+ align:start position:0%
+1895 and to show you what a what a great
+scientist he was rather than rushing to
+
+ align:start position:0%
+scientist he was rather than rushing to
+ 
+
+ align:start position:0%
+scientist he was rather than rushing to
+publication he spends all of November
+
+ align:start position:0%
+publication he spends all of November
+ 
+
+ align:start position:0%
+publication he spends all of November
+and December repeating the experiment
+
+ align:start position:0%
+and December repeating the experiment
+ 
+
+ align:start position:0%
+and December repeating the experiment
+and trying it in different ways until
+
+ align:start position:0%
+and trying it in different ways until
+ 
+
+ align:start position:0%
+and trying it in different ways until
+he's convinced that the effect is real
+
+ align:start position:0%
+he's convinced that the effect is real
+ 
+
+ align:start position:0%
+he's convinced that the effect is real
+and then around Christmas time of 1895
+
+ align:start position:0%
+and then around Christmas time of 1895
+ 
+
+ align:start position:0%
+and then around Christmas time of 1895
+he sends off a manuscript and it's
+
+ align:start position:0%
+he sends off a manuscript and it's
+ 
+
+ align:start position:0%
+he sends off a manuscript and it's
+published in the first week of January
+
+ align:start position:0%
+published in the first week of January
+ 
+
+ align:start position:0%
+published in the first week of January
+of
+
+ align:start position:0%
+of
+ 
+
+ align:start position:0%
+of
+1896 and it takes the World by storm
+
+ align:start position:0%
+1896 and it takes the World by storm
+ 
+
+ align:start position:0%
+1896 and it takes the World by storm
+he's announcing that there's a form of
+
+ align:start position:0%
+he's announcing that there's a form of
+ 
+
+ align:start position:0%
+he's announcing that there's a form of
+radiation that can penetrate matter and
+
+ align:start position:0%
+radiation that can penetrate matter and
+ 
+
+ align:start position:0%
+radiation that can penetrate matter and
+furthermore he's got an x-ray of a human
+
+ align:start position:0%
+furthermore he's got an x-ray of a human
+ 
+
+ align:start position:0%
+furthermore he's got an x-ray of a human
+hand you know this is the 1890s so PE
+
+ align:start position:0%
+hand you know this is the 1890s so PE
+ 
+
+ align:start position:0%
+hand you know this is the 1890s so PE
+people are you know very prude very
+
+ align:start position:0%
+people are you know very prude very
+ 
+
+ align:start position:0%
+people are you know very prude very
+private he's got a form of radiation
+
+ align:start position:0%
+private he's got a form of radiation
+ 
+
+ align:start position:0%
+private he's got a form of radiation
+that can look inside the human body this
+
+ align:start position:0%
+that can look inside the human body this
+ 
+
+ align:start position:0%
+that can look inside the human body this
+is really shocking
+
+ align:start position:0%
+is really shocking
+ 
+
+ align:start position:0%
+is really shocking
+stuff so already uh on January
+
+ align:start position:0%
+stuff so already uh on January
+ 
+
+ align:start position:0%
+stuff so already uh on January
+16th January 16th
+
+ align:start position:0%
+16th January 16th
+ 
+
+ align:start position:0%
+16th January 16th
+1896 was an article in New York Times
+
+ align:start position:0%
+1896 was an article in New York Times
+ 
+
+ align:start position:0%
+1896 was an article in New York Times
+article in New York Times about this
+
+ align:start position:0%
+article in New York Times about this
+ 
+
+ align:start position:0%
+article in New York Times about this
+stuff mysterious form of
+
+ align:start position:0%
+stuff mysterious form of
+ 
+
+ align:start position:0%
+stuff mysterious form of
+radiation well by the way you know he
+
+ align:start position:0%
+radiation well by the way you know he
+ 
+
+ align:start position:0%
+radiation well by the way you know he
+was doing his experiments how was he
+
+ align:start position:0%
+was doing his experiments how was he
+ 
+
+ align:start position:0%
+was doing his experiments how was he
+recording his results he was recording
+
+ align:start position:0%
+recording his results he was recording
+ 
+
+ align:start position:0%
+recording his results he was recording
+his results on photographic film and his
+
+ align:start position:0%
+his results on photographic film and his
+ 
+
+ align:start position:0%
+his results on photographic film and his
+photographic film was fogging he had his
+
+ align:start position:0%
+photographic film was fogging he had his
+ 
+
+ align:start position:0%
+photographic film was fogging he had his
+photographic film stored in a cabinet on
+
+ align:start position:0%
+photographic film stored in a cabinet on
+ 
+
+ align:start position:0%
+photographic film stored in a cabinet on
+the other side of the lab and half of
+
+ align:start position:0%
+the other side of the lab and half of
+ 
+
+ align:start position:0%
+the other side of the lab and half of
+the time he take the photographic film
+
+ align:start position:0%
+the time he take the photographic film
+ 
+
+ align:start position:0%
+the time he take the photographic film
+out and it was fogged so whatever this
+
+ align:start position:0%
+out and it was fogged so whatever this
+ 
+
+ align:start position:0%
+out and it was fogged so whatever this
+stuff is it's it's penetrating
+
+ align:start position:0%
+stuff is it's it's penetrating
+ 
+
+ align:start position:0%
+stuff is it's it's penetrating
+everything it's penetrating the doors of
+
+ align:start position:0%
+everything it's penetrating the doors of
+ 
+
+ align:start position:0%
+everything it's penetrating the doors of
+his file cabinet they weren't steel case
+
+ align:start position:0%
+his file cabinet they weren't steel case
+ 
+
+ align:start position:0%
+his file cabinet they weren't steel case
+they were probably wooden file cabinets
+
+ align:start position:0%
+they were probably wooden file cabinets
+ 
+
+ align:start position:0%
+they were probably wooden file cabinets
+right so widespread widespread
+
+ align:start position:0%
+right so widespread widespread
+ 
+
+ align:start position:0%
+right so widespread widespread
+adoption widespread adoption some of
+
+ align:start position:0%
+adoption widespread adoption some of
+ 
+
+ align:start position:0%
+adoption widespread adoption some of
+it
+
+ align:start position:0%
+it
+ 
+
+ align:start position:0%
+it
+silly uh what's some of the silly ones
+
+ align:start position:0%
+silly uh what's some of the silly ones
+ 
+
+ align:start position:0%
+silly uh what's some of the silly ones
+in London there was a manufacture
+
+ align:start position:0%
+in London there was a manufacture
+ 
+
+ align:start position:0%
+in London there was a manufacture
+announced remember this is prudish
+
+ align:start position:0%
+announced remember this is prudish
+ 
+
+ align:start position:0%
+announced remember this is prudish
+Victorian England that he could uh sell
+
+ align:start position:0%
+Victorian England that he could uh sell
+ 
+
+ align:start position:0%
+Victorian England that he could uh sell
+you X-ray proof ladies
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+underwear in France there was no such
+
+ align:start position:0%
+underwear in France there was no such
+ 
+
+ align:start position:0%
+underwear in France there was no such
+thing the French don't care about such
+
+ align:start position:0%
+thing the French don't care about such
+ 
+
+ align:start position:0%
+thing the French don't care about such
+matters so instead this was uh remember
+
+ align:start position:0%
+matters so instead this was uh remember
+ 
+
+ align:start position:0%
+matters so instead this was uh remember
+the French uh deare had invented haly
+
+ align:start position:0%
+the French uh deare had invented haly
+ 
+
+ align:start position:0%
+the French uh deare had invented haly
+photography so someone in France offered
+
+ align:start position:0%
+photography so someone in France offered
+ 
+
+ align:start position:0%
+photography so someone in France offered
+to ex-ray the human soul this is very
+
+ align:start position:0%
+to ex-ray the human soul this is very
+ 
+
+ align:start position:0%
+to ex-ray the human soul this is very
+good um I'm ashamed to say what happened
+
+ align:start position:0%
+good um I'm ashamed to say what happened
+ 
+
+ align:start position:0%
+good um I'm ashamed to say what happened
+in the United States the New York uh
+
+ align:start position:0%
+in the United States the New York uh
+ 
+
+ align:start position:0%
+in the United States the New York uh
+City College of Physicians and surgeons
+
+ align:start position:0%
+City College of Physicians and surgeons
+ 
+
+ align:start position:0%
+City College of Physicians and surgeons
+announced that they would use x-ray to
+
+ align:start position:0%
+announced that they would use x-ray to
+ 
+
+ align:start position:0%
+announced that they would use x-ray to
+project um anatomical diagrams from
+
+ align:start position:0%
+project um anatomical diagrams from
+ 
+
+ align:start position:0%
+project um anatomical diagrams from
+textbooks onto the brains of medical
+
+ align:start position:0%
+textbooks onto the brains of medical
+ 
+
+ align:start position:0%
+textbooks onto the brains of medical
+students thereby creating and I quote an
+
+ align:start position:0%
+students thereby creating and I quote an
+ 
+
+ align:start position:0%
+students thereby creating and I quote an
+enduring
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+impression in Iowa somebody offered to
+
+ align:start position:0%
+impression in Iowa somebody offered to
+ 
+
+ align:start position:0%
+impression in Iowa somebody offered to
+x-ray copper pennies and thereby turn
+
+ align:start position:0%
+x-ray copper pennies and thereby turn
+ 
+
+ align:start position:0%
+x-ray copper pennies and thereby turn
+them into gold so that's that's what
+
+ align:start position:0%
+them into gold so that's that's what
+ 
+
+ align:start position:0%
+them into gold so that's that's what
+happened but seriously what what really
+
+ align:start position:0%
+happened but seriously what what really
+ 
+
+ align:start position:0%
+happened but seriously what what really
+did happen very quickly was the use of
+
+ align:start position:0%
+did happen very quickly was the use of
+ 
+
+ align:start position:0%
+did happen very quickly was the use of
+x-rays as a diagnostic tool already in
+
+ align:start position:0%
+x-rays as a diagnostic tool already in
+ 
+
+ align:start position:0%
+x-rays as a diagnostic tool already in
+February of uh 1896 there was a Scottish
+
+ align:start position:0%
+February of uh 1896 there was a Scottish
+ 
+
+ align:start position:0%
+February of uh 1896 there was a Scottish
+physician who used X-rays and look it's
+
+ align:start position:0%
+physician who used X-rays and look it's
+ 
+
+ align:start position:0%
+physician who used X-rays and look it's
+simple it's just that you could do this
+
+ align:start position:0%
+simple it's just that you could do this
+ 
+
+ align:start position:0%
+simple it's just that you could do this
+in a high school I mean what is it you
+
+ align:start position:0%
+in a high school I mean what is it you
+ 
+
+ align:start position:0%
+in a high school I mean what is it you
+know it's just a gas discharge tube pair
+
+ align:start position:0%
+know it's just a gas discharge tube pair
+ 
+
+ align:start position:0%
+know it's just a gas discharge tube pair
+of electrodes with a feed through and
+
+ align:start position:0%
+of electrodes with a feed through and
+ 
+
+ align:start position:0%
+of electrodes with a feed through and
+you know he's got 35,000 volts I mean
+
+ align:start position:0%
+you know he's got 35,000 volts I mean
+ 
+
+ align:start position:0%
+you know he's got 35,000 volts I mean
+that's kind of stuff that comes off the
+
+ align:start position:0%
+that's kind of stuff that comes off the
+ 
+
+ align:start position:0%
+that's kind of stuff that comes off the
+chassis of your your television set this
+
+ align:start position:0%
+chassis of your your television set this
+ 
+
+ align:start position:0%
+chassis of your your television set this
+is trivial stuff know so people are
+
+ align:start position:0%
+is trivial stuff know so people are
+ 
+
+ align:start position:0%
+is trivial stuff know so people are
+putting these things everywhere they're
+
+ align:start position:0%
+putting these things everywhere they're
+ 
+
+ align:start position:0%
+putting these things everywhere they're
+sitting in offices an open view nobody
+
+ align:start position:0%
+sitting in offices an open view nobody
+ 
+
+ align:start position:0%
+sitting in offices an open view nobody
+knew so this physician uh had a
+
+ align:start position:0%
+knew so this physician uh had a
+ 
+
+ align:start position:0%
+knew so this physician uh had a
+seamstress come to him she was involved
+
+ align:start position:0%
+seamstress come to him she was involved
+ 
+
+ align:start position:0%
+seamstress come to him she was involved
+in an industrial accident in a mill uh a
+
+ align:start position:0%
+in an industrial accident in a mill uh a
+ 
+
+ align:start position:0%
+in an industrial accident in a mill uh a
+needle broke off in her hand now how
+
+ align:start position:0%
+needle broke off in her hand now how
+ 
+
+ align:start position:0%
+needle broke off in her hand now how
+would you find the needle in a hand you
+
+ align:start position:0%
+would you find the needle in a hand you
+ 
+
+ align:start position:0%
+would you find the needle in a hand you
+can't well x-ray they identifi the
+
+ align:start position:0%
+can't well x-ray they identifi the
+ 
+
+ align:start position:0%
+can't well x-ray they identifi the
+location of the needle performed the
+
+ align:start position:0%
+location of the needle performed the
+ 
+
+ align:start position:0%
+location of the needle performed the
+surgery Boom for dental applications it
+
+ align:start position:0%
+surgery Boom for dental applications it
+ 
+
+ align:start position:0%
+surgery Boom for dental applications it
+was immediately adopted they were
+
+ align:start position:0%
+was immediately adopted they were
+ 
+
+ align:start position:0%
+was immediately adopted they were
+already using it in 1899 as a form of
+
+ align:start position:0%
+already using it in 1899 as a form of
+ 
+
+ align:start position:0%
+already using it in 1899 as a form of
+treatment for
+
+ align:start position:0%
+treatment for
+ 
+
+ align:start position:0%
+treatment for
+cancer very interesting took over so
+
+ align:start position:0%
+cancer very interesting took over so
+ 
+
+ align:start position:0%
+cancer very interesting took over so
+what's the relative physics what's going
+
+ align:start position:0%
+what's the relative physics what's going
+ 
+
+ align:start position:0%
+what's the relative physics what's going
+on here so where do we have to go I said
+
+ align:start position:0%
+on here so where do we have to go I said
+ 
+
+ align:start position:0%
+on here so where do we have to go I said
+we have to look at the anode because
+
+ align:start position:0%
+we have to look at the anode because
+ 
+
+ align:start position:0%
+we have to look at the anode because
+that's where the electrons are crashing
+
+ align:start position:0%
+that's where the electrons are crashing
+ 
+
+ align:start position:0%
+that's where the electrons are crashing
+into that's the site of the Collision
+
+ align:start position:0%
+into that's the site of the Collision
+ 
+
+ align:start position:0%
+into that's the site of the Collision
+isn't it something's happening at that
+
+ align:start position:0%
+isn't it something's happening at that
+ 
+
+ align:start position:0%
+isn't it something's happening at that
+anode so let's look inside the anode and
+
+ align:start position:0%
+anode so let's look inside the anode and
+ 
+
+ align:start position:0%
+anode so let's look inside the anode and
+suppose it's copper what could we say
+
+ align:start position:0%
+suppose it's copper what could we say
+ 
+
+ align:start position:0%
+suppose it's copper what could we say
+about
+
+ align:start position:0%
+about
+ 
+
+ align:start position:0%
+about
+it the
+
+ align:start position:0%
+it the
+ 
+
+ align:start position:0%
+it the
+anode this is where the electron
+
+ align:start position:0%
+anode this is where the electron
+ 
+
+ align:start position:0%
+anode this is where the electron
+Collision that's the Maximum Impact
+
+ align:start position:0%
+Collision that's the Maximum Impact
+ 
+
+ align:start position:0%
+Collision that's the Maximum Impact
+isn't it so let's just see what might be
+
+ align:start position:0%
+isn't it so let's just see what might be
+ 
+
+ align:start position:0%
+isn't it so let's just see what might be
+going on I want to show you the power of
+
+ align:start position:0%
+going on I want to show you the power of
+ 
+
+ align:start position:0%
+going on I want to show you the power of
+estimation okay um how far how far down
+
+ align:start position:0%
+estimation okay um how far how far down
+ 
+
+ align:start position:0%
+estimation okay um how far how far down
+I've shown you that with nitrogen at
+
+ align:start position:0%
+I've shown you that with nitrogen at
+ 
+
+ align:start position:0%
+I've shown you that with nitrogen at
+668 uh electron volts to get to the
+
+ align:start position:0%
+668 uh electron volts to get to the
+ 
+
+ align:start position:0%
+668 uh electron volts to get to the
+inner shell electrons what about in The
+
+ align:start position:0%
+inner shell electrons what about in The
+ 
+
+ align:start position:0%
+inner shell electrons what about in The
+Case of the anode well um what's going
+
+ align:start position:0%
+Case of the anode well um what's going
+ 
+
+ align:start position:0%
+Case of the anode well um what's going
+on there well I can say what's the
+
+ align:start position:0%
+on there well I can say what's the
+ 
+
+ align:start position:0%
+on there well I can say what's the
+energy of the 1s electron in Copper 28
+
+ align:start position:0%
+energy of the 1s electron in Copper 28
+ 
+
+ align:start position:0%
+energy of the 1s electron in Copper 28
+plus that's a one electron system okay
+
+ align:start position:0%
+plus that's a one electron system okay
+ 
+
+ align:start position:0%
+plus that's a one electron system okay
+and you know that in real copper with
+
+ align:start position:0%
+and you know that in real copper with
+ 
+
+ align:start position:0%
+and you know that in real copper with
+all of its electrons this value is going
+
+ align:start position:0%
+all of its electrons this value is going
+ 
+
+ align:start position:0%
+all of its electrons this value is going
+to be an overestimate because the
+
+ align:start position:0%
+to be an overestimate because the
+ 
+
+ align:start position:0%
+to be an overestimate because the
+presence of all the other electrons is
+
+ align:start position:0%
+presence of all the other electrons is
+ 
+
+ align:start position:0%
+presence of all the other electrons is
+going to sap some of the protonic uh
+
+ align:start position:0%
+going to sap some of the protonic uh
+ 
+
+ align:start position:0%
+going to sap some of the protonic uh
+culic Force so this will be a an upper
+
+ align:start position:0%
+culic Force so this will be a an upper
+ 
+
+ align:start position:0%
+culic Force so this will be a an upper
+bound of what that energy could be we
+
+ align:start position:0%
+bound of what that energy could be we
+ 
+
+ align:start position:0%
+bound of what that energy could be we
+know that's simply equal to the energy
+
+ align:start position:0%
+know that's simply equal to the energy
+ 
+
+ align:start position:0%
+know that's simply equal to the energy
+of the 1s in hydrogen right times
+
+ align:start position:0%
+of the 1s in hydrogen right times
+ 
+
+ align:start position:0%
+of the 1s in hydrogen right times
+z^2 so if I take 13.6 electron volts
+
+ align:start position:0%
+z^2 so if I take 13.6 electron volts
+ 
+
+ align:start position:0%
+z^2 so if I take 13.6 electron volts
+time
+
+ align:start position:0%
+time
+ 
+
+ align:start position:0%
+time
+29 squared I get
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+114,000 electron volts which is still
+
+ align:start position:0%
+114,000 electron volts which is still
+ 
+
+ align:start position:0%
+114,000 electron volts which is still
+less than the 35,000
+
+ align:start position:0%
+less than the 35,000
+ 
+
+ align:start position:0%
+less than the 35,000
+electron volts that renen had so renen
+
+ align:start position:0%
+electron volts that renen had so renen
+ 
+
+ align:start position:0%
+electron volts that renen had so renen
+is running a a huge bowling alley here
+
+ align:start position:0%
+is running a a huge bowling alley here
+ 
+
+ align:start position:0%
+is running a a huge bowling alley here
+he's able to knock out 1s electrons from
+
+ align:start position:0%
+he's able to knock out 1s electrons from
+ 
+
+ align:start position:0%
+he's able to knock out 1s electrons from
+copper and what happens when you knock
+
+ align:start position:0%
+copper and what happens when you knock
+ 
+
+ align:start position:0%
+copper and what happens when you knock
+out electrons intershell electrons
+
+ align:start position:0%
+out electrons intershell electrons
+ 
+
+ align:start position:0%
+out electrons intershell electrons
+what's the next thing that
+
+ align:start position:0%
+what's the next thing that
+ 
+
+ align:start position:0%
+what's the next thing that
+happens now let's look at an energy
+
+ align:start position:0%
+happens now let's look at an energy
+ 
+
+ align:start position:0%
+happens now let's look at an energy
+level diagram so let's let's suppose
+
+ align:start position:0%
+level diagram so let's let's suppose
+ 
+
+ align:start position:0%
+level diagram so let's let's suppose
+this is a the anode so this is the anode
+
+ align:start position:0%
+this is a the anode so this is the anode
+ 
+
+ align:start position:0%
+this is a the anode so this is the anode
+in the gas tube it's energy level
+
+ align:start position:0%
+in the gas tube it's energy level
+ 
+
+ align:start position:0%
+in the gas tube it's energy level
+diagram so this is going to be n equal
+
+ align:start position:0%
+diagram so this is going to be n equal
+ 
+
+ align:start position:0%
+diagram so this is going to be n equal
+infinity and we'll just do a few of them
+
+ align:start position:0%
+infinity and we'll just do a few of them
+ 
+
+ align:start position:0%
+infinity and we'll just do a few of them
+so this is n = 4 n = 3 Nal 2 and n
+
+ align:start position:0%
+so this is n = 4 n = 3 Nal 2 and n
+ 
+
+ align:start position:0%
+so this is n = 4 n = 3 Nal 2 and n
+equals 1 not to scale I'm trying to show
+
+ align:start position:0%
+equals 1 not to scale I'm trying to show
+ 
+
+ align:start position:0%
+equals 1 not to scale I'm trying to show
+that they're a little bit farther apart
+
+ align:start position:0%
+that they're a little bit farther apart
+ 
+
+ align:start position:0%
+that they're a little bit farther apart
+as you go lower and lower and so this is
+
+ align:start position:0%
+as you go lower and lower and so this is
+ 
+
+ align:start position:0%
+as you go lower and lower and so this is
+ground state energy E1 this is Nal 2
+
+ align:start position:0%
+ground state energy E1 this is Nal 2
+ 
+
+ align:start position:0%
+ground state energy E1 this is Nal 2
+shell Nal 3 shell Nal 4 shell and out
+
+ align:start position:0%
+shell Nal 3 shell Nal 4 shell and out
+ 
+
+ align:start position:0%
+shell Nal 3 shell Nal 4 shell and out
+here it's zero isn't it and so what do I
+
+ align:start position:0%
+here it's zero isn't it and so what do I
+ 
+
+ align:start position:0%
+here it's zero isn't it and so what do I
+have I've got some instent electron that
+
+ align:start position:0%
+have I've got some instent electron that
+ 
+
+ align:start position:0%
+have I've got some instent electron that
+comes zooming in here zooming in here
+
+ align:start position:0%
+comes zooming in here zooming in here
+ 
+
+ align:start position:0%
+comes zooming in here zooming in here
+this is
+
+ align:start position:0%
+this is
+ 
+
+ align:start position:0%
+this is
+incident this is the one that's been
+
+ align:start position:0%
+incident this is the one that's been
+ 
+
+ align:start position:0%
+incident this is the one that's been
+accelerated right so the energy of this
+
+ align:start position:0%
+accelerated right so the energy of this
+ 
+
+ align:start position:0%
+accelerated right so the energy of this
+electron it's all kinetic and that's
+
+ align:start position:0%
+electron it's all kinetic and that's
+ 
+
+ align:start position:0%
+electron it's all kinetic and that's
+equal to product of the charge on the
+
+ align:start position:0%
+equal to product of the charge on the
+ 
+
+ align:start position:0%
+equal to product of the charge on the
+electron which is Elemental e times a
+
+ align:start position:0%
+electron which is Elemental e times a
+ 
+
+ align:start position:0%
+electron which is Elemental e times a
+plate voltage which is 35,000 volts
+
+ align:start position:0%
+plate voltage which is 35,000 volts
+ 
+
+ align:start position:0%
+plate voltage which is 35,000 volts
+that's how I get 35,000 electron volts
+
+ align:start position:0%
+that's how I get 35,000 electron volts
+ 
+
+ align:start position:0%
+that's how I get 35,000 electron volts
+is the energy and it can come in and
+
+ align:start position:0%
+is the energy and it can come in and
+ 
+
+ align:start position:0%
+is the energy and it can come in and
+we've just showing that it's got enough
+
+ align:start position:0%
+we've just showing that it's got enough
+ 
+
+ align:start position:0%
+we've just showing that it's got enough
+energy that it can even knock out an
+
+ align:start position:0%
+energy that it can even knock out an
+ 
+
+ align:start position:0%
+energy that it can even knock out an
+inner shell
+
+ align:start position:0%
+inner shell
+ 
+
+ align:start position:0%
+inner shell
+electron it can even dislodge an inner
+
+ align:start position:0%
+electron it can even dislodge an inner
+ 
+
+ align:start position:0%
+electron it can even dislodge an inner
+shell electron so let's see what would
+
+ align:start position:0%
+shell electron so let's see what would
+ 
+
+ align:start position:0%
+shell electron so let's see what would
+happen if that were the case it
+
+ align:start position:0%
+happen if that were the case it
+ 
+
+ align:start position:0%
+happen if that were the case it
+dislodges an inner shell electron what's
+
+ align:start position:0%
+dislodges an inner shell electron what's
+ 
+
+ align:start position:0%
+dislodges an inner shell electron what's
+the next thing well I've got a vacancy
+
+ align:start position:0%
+the next thing well I've got a vacancy
+ 
+
+ align:start position:0%
+the next thing well I've got a vacancy
+down here so what will happen well
+
+ align:start position:0%
+down here so what will happen well
+ 
+
+ align:start position:0%
+down here so what will happen well
+electron will fall from n equals 2 to n
+
+ align:start position:0%
+electron will fall from n equals 2 to n
+ 
+
+ align:start position:0%
+electron will fall from n equals 2 to n
+equals 1 and when it does
+
+ align:start position:0%
+equals 1 and when it does
+ 
+
+ align:start position:0%
+equals 1 and when it does
+so it gives off radiation it gives off
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+radiation well if it falls from n equals
+
+ align:start position:0%
+radiation well if it falls from n equals
+ 
+
+ align:start position:0%
+radiation well if it falls from n equals
+2 Nal 1 there's a slim chance it might
+
+ align:start position:0%
+2 Nal 1 there's a slim chance it might
+ 
+
+ align:start position:0%
+2 Nal 1 there's a slim chance it might
+even fall from Nal 3 to Nal 1 or maybe
+
+ align:start position:0%
+even fall from Nal 3 to Nal 1 or maybe
+ 
+
+ align:start position:0%
+even fall from Nal 3 to Nal 1 or maybe
+even Nal 4 to Nal 1 well heck if it can
+
+ align:start position:0%
+even Nal 4 to Nal 1 well heck if it can
+ 
+
+ align:start position:0%
+even Nal 4 to Nal 1 well heck if it can
+go from two to one there's a vacancy in
+
+ align:start position:0%
+go from two to one there's a vacancy in
+ 
+
+ align:start position:0%
+go from two to one there's a vacancy in
+two so I might get 3 to two I might get
+
+ align:start position:0%
+two so I might get 3 to two I might get
+ 
+
+ align:start position:0%
+two so I might get 3 to two I might get
+four to two and you get the picture you
+
+ align:start position:0%
+four to two and you get the picture you
+ 
+
+ align:start position:0%
+four to two and you get the picture you
+get a whole Cascade here you get a whole
+
+ align:start position:0%
+get a whole Cascade here you get a whole
+ 
+
+ align:start position:0%
+get a whole Cascade here you get a whole
+Cascade each one of these gives off
+
+ align:start position:0%
+Cascade each one of these gives off
+ 
+
+ align:start position:0%
+Cascade each one of these gives off
+photons Photon emissions so you have you
+
+ align:start position:0%
+photons Photon emissions so you have you
+ 
+
+ align:start position:0%
+photons Photon emissions so you have you
+have
+
+ align:start position:0%
+have
+ 
+
+ align:start position:0%
+have
+expulsion expulsion
+
+ align:start position:0%
+expulsion expulsion
+ 
+
+ align:start position:0%
+expulsion expulsion
+of K
+
+ align:start position:0%
+of K
+ 
+
+ align:start position:0%
+of K
+shell all of the electrons but you can
+
+ align:start position:0%
+shell all of the electrons but you can
+ 
+
+ align:start position:0%
+shell all of the electrons but you can
+go all the way down to the kshell kshell
+
+ align:start position:0%
+go all the way down to the kshell kshell
+ 
+
+ align:start position:0%
+go all the way down to the kshell kshell
+electrons and then
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Cascade and accompanied by photo
+
+ align:start position:0%
+Cascade and accompanied by photo
+ 
+
+ align:start position:0%
+Cascade and accompanied by photo
+emission
+
+ align:start position:0%
+emission
+ 
+
+ align:start position:0%
+emission
+photoemission the difference is that
+
+ align:start position:0%
+photoemission the difference is that
+ 
+
+ align:start position:0%
+photoemission the difference is that
+instead of being in the visible or the
+
+ align:start position:0%
+instead of being in the visible or the
+ 
+
+ align:start position:0%
+instead of being in the visible or the
+infrared these energy levels are so
+
+ align:start position:0%
+infrared these energy levels are so
+ 
+
+ align:start position:0%
+infrared these energy levels are so
+so tightly bounded that this is in the X
+
+ align:start position:0%
+so tightly bounded that this is in the X
+ 
+
+ align:start position:0%
+so tightly bounded that this is in the X
+region of the spectrum this is in the X
+
+ align:start position:0%
+region of the spectrum this is in the X
+ 
+
+ align:start position:0%
+region of the spectrum this is in the X
+region of the spectrum and we have
+
+ align:start position:0%
+region of the spectrum and we have
+ 
+
+ align:start position:0%
+region of the spectrum and we have
+labels for these different uh for these
+
+ align:start position:0%
+labels for these different uh for these
+ 
+
+ align:start position:0%
+labels for these different uh for these
+different uh photons um and first of all
+
+ align:start position:0%
+different uh photons um and first of all
+ 
+
+ align:start position:0%
+different uh photons um and first of all
+you know that the spectroscopists don't
+
+ align:start position:0%
+you know that the spectroscopists don't
+ 
+
+ align:start position:0%
+you know that the spectroscopists don't
+like the numbers this is the chemist
+
+ align:start position:0%
+like the numbers this is the chemist
+ 
+
+ align:start position:0%
+like the numbers this is the chemist
+notation Nal 1 Nal 2 Nal 3 Nal 4 the
+
+ align:start position:0%
+notation Nal 1 Nal 2 Nal 3 Nal 4 the
+ 
+
+ align:start position:0%
+notation Nal 1 Nal 2 Nal 3 Nal 4 the
+spectroscopists call the ground state
+
+ align:start position:0%
+spectroscopists call the ground state
+ 
+
+ align:start position:0%
+spectroscopists call the ground state
+kshell this is mshell this is n shell
+
+ align:start position:0%
+kshell this is mshell this is n shell
+ 
+
+ align:start position:0%
+kshell this is mshell this is n shell
+okay I left out a letter in the alphabet
+
+ align:start position:0%
+okay I left out a letter in the alphabet
+ 
+
+ align:start position:0%
+okay I left out a letter in the alphabet
+k l L shell mshell n shell so we can
+
+ align:start position:0%
+k l L shell mshell n shell so we can
+ 
+
+ align:start position:0%
+k l L shell mshell n shell so we can
+label this as a photon that came from a
+
+ align:start position:0%
+label this as a photon that came from a
+ 
+
+ align:start position:0%
+label this as a photon that came from a
+Cascade down to the K shell and to
+
+ align:start position:0%
+Cascade down to the K shell and to
+ 
+
+ align:start position:0%
+Cascade down to the K shell and to
+distinguish this kshell electron from
+
+ align:start position:0%
+distinguish this kshell electron from
+ 
+
+ align:start position:0%
+distinguish this kshell electron from
+the kshell electron involving a
+
+ align:start position:0%
+the kshell electron involving a
+ 
+
+ align:start position:0%
+the kshell electron involving a
+transition from Nal 3 down to nals 1 we
+
+ align:start position:0%
+transition from Nal 3 down to nals 1 we
+ 
+
+ align:start position:0%
+transition from Nal 3 down to nals 1 we
+have a
+
+ align:start position:0%
+have a
+ 
+
+ align:start position:0%
+have a
+second indicator and that's the
+
+ align:start position:0%
+second indicator and that's the
+ 
+
+ align:start position:0%
+second indicator and that's the
+subscript Alpha so this means the
+
+ align:start position:0%
+subscript Alpha so this means the
+ 
+
+ align:start position:0%
+subscript Alpha so this means the
+Cascade
+
+ align:start position:0%
+Cascade
+ 
+
+ align:start position:0%
+Cascade
+Cascade down to
+
+ align:start position:0%
+Cascade down to
+ 
+
+ align:start position:0%
+Cascade down to
+kshell and the alpha
+
+ align:start position:0%
+kshell and the alpha
+ 
+
+ align:start position:0%
+kshell and the alpha
+represents how far the electron traveled
+
+ align:start position:0%
+represents how far the electron traveled
+ 
+
+ align:start position:0%
+represents how far the electron traveled
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+from one shell away so that means from
+
+ align:start position:0%
+from one shell away so that means from
+ 
+
+ align:start position:0%
+from one shell away so that means from
+Nal 2 to Nal 1 this is a
+
+ align:start position:0%
+Nal 2 to Nal 1 this is a
+ 
+
+ align:start position:0%
+Nal 2 to Nal 1 this is a
+k beta
+
+ align:start position:0%
+k beta
+ 
+
+ align:start position:0%
+k beta
+Photon this is a k gamma photon so this
+
+ align:start position:0%
+Photon this is a k gamma photon so this
+ 
+
+ align:start position:0%
+Photon this is a k gamma photon so this
+is like a Lyman series all right this is
+
+ align:start position:0%
+is like a Lyman series all right this is
+ 
+
+ align:start position:0%
+is like a Lyman series all right this is
+like a Balmer series because it always
+
+ align:start position:0%
+like a Balmer series because it always
+ 
+
+ align:start position:0%
+like a Balmer series because it always
+ends at nals 2 Nal 3 to Nal 2 gives us a
+
+ align:start position:0%
+ends at nals 2 Nal 3 to Nal 2 gives us a
+ 
+
+ align:start position:0%
+ends at nals 2 Nal 3 to Nal 2 gives us a
+photon and that photon is going to be
+
+ align:start position:0%
+photon and that photon is going to be
+ 
+
+ align:start position:0%
+photon and that photon is going to be
+called L Alpha Nal 4 to Nal 2 will give
+
+ align:start position:0%
+called L Alpha Nal 4 to Nal 2 will give
+ 
+
+ align:start position:0%
+called L Alpha Nal 4 to Nal 2 will give
+us a photon and that's going to be
+
+ align:start position:0%
+us a photon and that's going to be
+ 
+
+ align:start position:0%
+us a photon and that's going to be
+called L beta so I'm going to get a
+
+ align:start position:0%
+called L beta so I'm going to get a
+ 
+
+ align:start position:0%
+called L beta so I'm going to get a
+whole Spectrum I'm going to get a whole
+
+ align:start position:0%
+whole Spectrum I'm going to get a whole
+ 
+
+ align:start position:0%
+whole Spectrum I'm going to get a whole
+Spectrum let's take a look at what that
+
+ align:start position:0%
+Spectrum let's take a look at what that
+ 
+
+ align:start position:0%
+Spectrum let's take a look at what that
+Spectrum might look like uh I could
+
+ align:start position:0%
+Spectrum might look like uh I could
+ 
+
+ align:start position:0%
+Spectrum might look like uh I could
+calculate any one of these I could say
+
+ align:start position:0%
+calculate any one of these I could say
+ 
+
+ align:start position:0%
+calculate any one of these I could say
+Lambda of copper K Alpha would equal
+
+ align:start position:0%
+Lambda of copper K Alpha would equal
+ 
+
+ align:start position:0%
+Lambda of copper K Alpha would equal
+what it's the same as you've seen before
+
+ align:start position:0%
+what it's the same as you've seen before
+ 
+
+ align:start position:0%
+what it's the same as you've seen before
+HC over what the
+
+ align:start position:0%
+HC over what the
+ 
+
+ align:start position:0%
+HC over what the
+energy of Nal 2 shell to energy of n
+
+ align:start position:0%
+energy of Nal 2 shell to energy of n
+ 
+
+ align:start position:0%
+energy of Nal 2 shell to energy of n
+equals 1 shell so what can we do we can
+
+ align:start position:0%
+equals 1 shell so what can we do we can
+ 
+
+ align:start position:0%
+equals 1 shell so what can we do we can
+measure this we know H and C we can
+
+ align:start position:0%
+measure this we know H and C we can
+ 
+
+ align:start position:0%
+measure this we know H and C we can
+calculate what those energy levels are
+
+ align:start position:0%
+calculate what those energy levels are
+ 
+
+ align:start position:0%
+calculate what those energy levels are
+right so let's plot this out I could
+
+ align:start position:0%
+right so let's plot this out I could
+ 
+
+ align:start position:0%
+right so let's plot this out I could
+make a plot of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+wavelength intensity and I will get an
+
+ align:start position:0%
+wavelength intensity and I will get an
+ 
+
+ align:start position:0%
+wavelength intensity and I will get an
+entire spectrum of lines I'll have first
+
+ align:start position:0%
+entire spectrum of lines I'll have first
+ 
+
+ align:start position:0%
+entire spectrum of lines I'll have first
+the this is high wavelength so that
+
+ align:start position:0%
+the this is high wavelength so that
+ 
+
+ align:start position:0%
+the this is high wavelength so that
+means energy is increasing from right to
+
+ align:start position:0%
+means energy is increasing from right to
+ 
+
+ align:start position:0%
+means energy is increasing from right to
+left so the highest energy is over here
+
+ align:start position:0%
+left so the highest energy is over here
+ 
+
+ align:start position:0%
+left so the highest energy is over here
+so what's the highest energy up there
+
+ align:start position:0%
+so what's the highest energy up there
+ 
+
+ align:start position:0%
+so what's the highest energy up there
+the highest energy looks like Nal 4 down
+
+ align:start position:0%
+the highest energy looks like Nal 4 down
+ 
+
+ align:start position:0%
+the highest energy looks like Nal 4 down
+to Nal 1 so that's going to be over here
+
+ align:start position:0%
+to Nal 1 so that's going to be over here
+ 
+
+ align:start position:0%
+to Nal 1 so that's going to be over here
+so this could be K gamma then K beta
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay Alpha then the L lines are 3:2 4:2
+
+ align:start position:0%
+okay Alpha then the L lines are 3:2 4:2
+ 
+
+ align:start position:0%
+okay Alpha then the L lines are 3:2 4:2
+so they're over here so this is L Alpha
+
+ align:start position:0%
+so they're over here so this is L Alpha
+ 
+
+ align:start position:0%
+so they're over here so this is L Alpha
+L beta and so on and these different
+
+ align:start position:0%
+L beta and so on and these different
+ 
+
+ align:start position:0%
+L beta and so on and these different
+wavelengths are associated with
+
+ align:start position:0%
+wavelengths are associated with
+ 
+
+ align:start position:0%
+wavelengths are associated with
+different
+
+ align:start position:0%
+different
+ 
+
+ align:start position:0%
+different
+energies and these different energies
+
+ align:start position:0%
+energies and these different energies
+ 
+
+ align:start position:0%
+energies and these different energies
+are associated with what they're
+
+ align:start position:0%
+are associated with what they're
+ 
+
+ align:start position:0%
+are associated with what they're
+associated with The
+
+ align:start position:0%
+associated with The
+ 
+
+ align:start position:0%
+associated with The
+Binding inside the atom inside the
+
+ align:start position:0%
+Binding inside the atom inside the
+ 
+
+ align:start position:0%
+Binding inside the atom inside the
+target
+
+ align:start position:0%
+target
+ 
+
+ align:start position:0%
+target
+so every target has its own number of
+
+ align:start position:0%
+so every target has its own number of
+ 
+
+ align:start position:0%
+so every target has its own number of
+protons its own number of electrons so
+
+ align:start position:0%
+protons its own number of electrons so
+ 
+
+ align:start position:0%
+protons its own number of electrons so
+this set of lines is characteristic of
+
+ align:start position:0%
+this set of lines is characteristic of
+ 
+
+ align:start position:0%
+this set of lines is characteristic of
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+target it's characteristic of the
+
+ align:start position:0%
+target it's characteristic of the
+ 
+
+ align:start position:0%
+target it's characteristic of the
+Target and I had to do a whole year of
+
+ align:start position:0%
+Target and I had to do a whole year of
+ 
+
+ align:start position:0%
+Target and I had to do a whole year of
+X-ray crystallography as a junior back
+
+ align:start position:0%
+X-ray crystallography as a junior back
+ 
+
+ align:start position:0%
+X-ray crystallography as a junior back
+at the University of Toronto we used
+
+ align:start position:0%
+at the University of Toronto we used
+ 
+
+ align:start position:0%
+at the University of Toronto we used
+copper as the target I will
+
+ align:start position:0%
+copper as the target I will
+ 
+
+ align:start position:0%
+copper as the target I will
+know on my deathbed that the wavelength
+
+ align:start position:0%
+know on my deathbed that the wavelength
+ 
+
+ align:start position:0%
+know on my deathbed that the wavelength
+of copper K Alpha is 1.54
+
+ align:start position:0%
+of copper K Alpha is 1.54
+ 
+
+ align:start position:0%
+of copper K Alpha is 1.54
+18 angstroms okay so if I walk into the
+
+ align:start position:0%
+18 angstroms okay so if I walk into the
+ 
+
+ align:start position:0%
+18 angstroms okay so if I walk into the
+room and I see 1.54 one8 angstroms
+
+ align:start position:0%
+room and I see 1.54 one8 angstroms
+ 
+
+ align:start position:0%
+room and I see 1.54 one8 angstroms
+that's
+
+ align:start position:0%
+that's
+ 
+
+ align:start position:0%
+that's
+copper it comes from copper and any
+
+ align:start position:0%
+copper it comes from copper and any
+ 
+
+ align:start position:0%
+copper it comes from copper and any
+other element is going to give me a
+
+ align:start position:0%
+other element is going to give me a
+ 
+
+ align:start position:0%
+other element is going to give me a
+different set of lines so what I'm
+
+ align:start position:0%
+different set of lines so what I'm
+ 
+
+ align:start position:0%
+different set of lines so what I'm
+learning here is I have a way of
+
+ align:start position:0%
+learning here is I have a way of
+ 
+
+ align:start position:0%
+learning here is I have a way of
+identifying elements so this is now
+
+ align:start position:0%
+identifying elements so this is now
+ 
+
+ align:start position:0%
+identifying elements so this is now
+turning into something that could be a
+
+ align:start position:0%
+turning into something that could be a
+ 
+
+ align:start position:0%
+turning into something that could be a
+technique of chemical analysis and we'll
+
+ align:start position:0%
+technique of chemical analysis and we'll
+ 
+
+ align:start position:0%
+technique of chemical analysis and we'll
+return next day to see what else we can
+
+ align:start position:0%
+return next day to see what else we can
+ 
+
+ align:start position:0%
+return next day to see what else we can
+do with it uh so so uh just for the last
+
+ align:start position:0%
+do with it uh so so uh just for the last
+ 
+
+ align:start position:0%
+do with it uh so so uh just for the last
+five minutes I'm going to show you a
+
+ align:start position:0%
+five minutes I'm going to show you a
+ 
+
+ align:start position:0%
+five minutes I'm going to show you a
+little bit more about uh uh renen and
+
+ align:start position:0%
+little bit more about uh uh renen and
+ 
+
+ align:start position:0%
+little bit more about uh uh renen and
+his Discovery but I wanted to uh pay uh
+
+ align:start position:0%
+his Discovery but I wanted to uh pay uh
+ 
+
+ align:start position:0%
+his Discovery but I wanted to uh pay uh
+um just uh draw attention to our winner
+
+ align:start position:0%
+um just uh draw attention to our winner
+ 
+
+ align:start position:0%
+um just uh draw attention to our winner
+from Friday Who U was unable to attend
+
+ align:start position:0%
+from Friday Who U was unable to attend
+ 
+
+ align:start position:0%
+from Friday Who U was unable to attend
+the lecture and uh so I want to ask uh n
+
+ align:start position:0%
+the lecture and uh so I want to ask uh n
+ 
+
+ align:start position:0%
+the lecture and uh so I want to ask uh n
+Gabriel to stand and uh accept her uh
+
+ align:start position:0%
+Gabriel to stand and uh accept her uh
+ 
+
+ align:start position:0%
+Gabriel to stand and uh accept her uh
+acknowledgement for the fine job she did
+
+ align:start position:0%
+acknowledgement for the fine job she did
+ 
+
+ align:start position:0%
+acknowledgement for the fine job she did
+on the actinide uh thing and she's
+
+ align:start position:0%
+on the actinide uh thing and she's
+ 
+
+ align:start position:0%
+on the actinide uh thing and she's
+wearing her scarf why don't you come
+
+ align:start position:0%
+wearing her scarf why don't you come
+ 
+
+ align:start position:0%
+wearing her scarf why don't you come
+down and people can see you wearing the
+
+ align:start position:0%
+down and people can see you wearing the
+ 
+
+ align:start position:0%
+down and people can see you wearing the
+really super hot American Chemical
+
+ align:start position:0%
+really super hot American Chemical
+ 
+
+ align:start position:0%
+really super hot American Chemical
+Society
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+scarf thank
+
+ align:start position:0%
+scarf thank
+ 
+
+ align:start position:0%
+scarf thank
+you good good now here's the dark and
+
+ align:start position:0%
+you good good now here's the dark and
+ 
+
+ align:start position:0%
+you good good now here's the dark and
+stormy night uh the following morning
+
+ align:start position:0%
+stormy night uh the following morning
+ 
+
+ align:start position:0%
+stormy night uh the following morning
+it's sunny this is Ren's laboratory on
+
+ align:start position:0%
+it's sunny this is Ren's laboratory on
+ 
+
+ align:start position:0%
+it's sunny this is Ren's laboratory on
+the second floor of his flat in bburg
+
+ align:start position:0%
+the second floor of his flat in bburg
+ 
+
+ align:start position:0%
+the second floor of his flat in bburg
+it's a museum today and you can see the
+
+ align:start position:0%
+it's a museum today and you can see the
+ 
+
+ align:start position:0%
+it's a museum today and you can see the
+tubes and the the lead wires going down
+
+ align:start position:0%
+tubes and the the lead wires going down
+ 
+
+ align:start position:0%
+tubes and the the lead wires going down
+to the basement and so on now hold it I
+
+ align:start position:0%
+to the basement and so on now hold it I
+ 
+
+ align:start position:0%
+to the basement and so on now hold it I
+don't I don't want a lot of noise you
+
+ align:start position:0%
+don't I don't want a lot of noise you
+ 
+
+ align:start position:0%
+don't I don't want a lot of noise you
+know
+
+ align:start position:0%
+know
+ 
+
+ align:start position:0%
+know
+just all right this is the first
+
+ align:start position:0%
+just all right this is the first
+ 
+
+ align:start position:0%
+just all right this is the first
+radiograph ever this is rin's wife
+
+ align:start position:0%
+radiograph ever this is rin's wife
+ 
+
+ align:start position:0%
+radiograph ever this is rin's wife
+Bera yes you know he noticed that there
+
+ align:start position:0%
+Bera yes you know he noticed that there
+ 
+
+ align:start position:0%
+Bera yes you know he noticed that there
+was a shadow with the lead but renin I
+
+ align:start position:0%
+was a shadow with the lead but renin I
+ 
+
+ align:start position:0%
+was a shadow with the lead but renin I
+mean he was smart I mean he was he was
+
+ align:start position:0%
+mean he was smart I mean he was he was
+ 
+
+ align:start position:0%
+mean he was smart I mean he was he was
+he had to share the glory so he said
+
+ align:start position:0%
+he had to share the glory so he said
+ 
+
+ align:start position:0%
+he had to share the glory so he said
+honey uh would you mind coming upstairs
+
+ align:start position:0%
+honey uh would you mind coming upstairs
+ 
+
+ align:start position:0%
+honey uh would you mind coming upstairs
+I'd like to take your picture and so
+
+ align:start position:0%
+I'd like to take your picture and so
+ 
+
+ align:start position:0%
+I'd like to take your picture and so
+Bertha put her hand in the path of the
+
+ align:start position:0%
+Bertha put her hand in the path of the
+ 
+
+ align:start position:0%
+Bertha put her hand in the path of the
+X-ray and for 15 full minutes uh waited
+
+ align:start position:0%
+X-ray and for 15 full minutes uh waited
+ 
+
+ align:start position:0%
+X-ray and for 15 full minutes uh waited
+while those x-rays uh went through you
+
+ align:start position:0%
+while those x-rays uh went through you
+ 
+
+ align:start position:0%
+while those x-rays uh went through you
+can see the ring on her finger and so on
+
+ align:start position:0%
+can see the ring on her finger and so on
+ 
+
+ align:start position:0%
+can see the ring on her finger and so on
+she endured in that 15 minutes uh
+
+ align:start position:0%
+she endured in that 15 minutes uh
+ 
+
+ align:start position:0%
+she endured in that 15 minutes uh
+greater than a lifetime dose of what we
+
+ align:start position:0%
+greater than a lifetime dose of what we
+ 
+
+ align:start position:0%
+greater than a lifetime dose of what we
+would consider safe today U people just
+
+ align:start position:0%
+would consider safe today U people just
+ 
+
+ align:start position:0%
+would consider safe today U people just
+didn't know anyways um this gave birth
+
+ align:start position:0%
+didn't know anyways um this gave birth
+ 
+
+ align:start position:0%
+didn't know anyways um this gave birth
+to Medical radiography and I would uh
+
+ align:start position:0%
+to Medical radiography and I would uh
+ 
+
+ align:start position:0%
+to Medical radiography and I would uh
+just out of curiosity like to know is is
+
+ align:start position:0%
+just out of curiosity like to know is is
+ 
+
+ align:start position:0%
+just out of curiosity like to know is is
+there there anybody in this room who's
+
+ align:start position:0%
+there there anybody in this room who's
+ 
+
+ align:start position:0%
+there there anybody in this room who's
+never had a medical or dental
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+x-ray I see a very few I see a few hands
+
+ align:start position:0%
+x-ray I see a very few I see a few hands
+ 
+
+ align:start position:0%
+x-ray I see a very few I see a few hands
+few hands to you I say congratulations
+
+ align:start position:0%
+few hands to you I say congratulations
+ 
+
+ align:start position:0%
+few hands to you I say congratulations
+and I hope you keep up the good work um
+
+ align:start position:0%
+and I hope you keep up the good work um
+ 
+
+ align:start position:0%
+and I hope you keep up the good work um
+okay here's a second thing so we have we
+
+ align:start position:0%
+okay here's a second thing so we have we
+ 
+
+ align:start position:0%
+okay here's a second thing so we have we
+have radiography that came out of Ren's
+
+ align:start position:0%
+have radiography that came out of Ren's
+ 
+
+ align:start position:0%
+have radiography that came out of Ren's
+Discovery renen had a beam um a torsion
+
+ align:start position:0%
+Discovery renen had a beam um a torsion
+ 
+
+ align:start position:0%
+Discovery renen had a beam um a torsion
+balance okay you know like the Justice
+
+ align:start position:0%
+balance okay you know like the Justice
+ 
+
+ align:start position:0%
+balance okay you know like the Justice
+she's got the two scales so the one
+
+ align:start position:0%
+she's got the two scales so the one
+ 
+
+ align:start position:0%
+she's got the two scales so the one
+scale you put the unknown in the other
+
+ align:start position:0%
+scale you put the unknown in the other
+ 
+
+ align:start position:0%
+scale you put the unknown in the other
+scale you put the calibrated Mass so he
+
+ align:start position:0%
+scale you put the calibrated Mass so he
+ 
+
+ align:start position:0%
+scale you put the calibrated Mass so he
+had a set of brass weights here in a
+
+ align:start position:0%
+had a set of brass weights here in a
+ 
+
+ align:start position:0%
+had a set of brass weights here in a
+wooden box and he closed the wooden box
+
+ align:start position:0%
+wooden box and he closed the wooden box
+ 
+
+ align:start position:0%
+wooden box and he closed the wooden box
+and he irradiated the box with the
+
+ align:start position:0%
+and he irradiated the box with the
+ 
+
+ align:start position:0%
+and he irradiated the box with the
+x-rays and took this
+
+ align:start position:0%
+x-rays and took this
+ 
+
+ align:start position:0%
+x-rays and took this
+Photograph and what do you see you see
+
+ align:start position:0%
+Photograph and what do you see you see
+ 
+
+ align:start position:0%
+Photograph and what do you see you see
+that different materials have different
+
+ align:start position:0%
+that different materials have different
+ 
+
+ align:start position:0%
+that different materials have different
+electron
+
+ align:start position:0%
+electron
+ 
+
+ align:start position:0%
+electron
+densities and therefore the wood is
+
+ align:start position:0%
+densities and therefore the wood is
+ 
+
+ align:start position:0%
+densities and therefore the wood is
+transparent more or less to x-rays
+
+ align:start position:0%
+transparent more or less to x-rays
+ 
+
+ align:start position:0%
+transparent more or less to x-rays
+whereas the brass is less so so you have
+
+ align:start position:0%
+whereas the brass is less so so you have
+ 
+
+ align:start position:0%
+whereas the brass is less so so you have
+a differentiation you know the way we
+
+ align:start position:0%
+a differentiation you know the way we
+ 
+
+ align:start position:0%
+a differentiation you know the way we
+see things is by
+
+ align:start position:0%
+see things is by
+ 
+
+ align:start position:0%
+see things is by
+differentiation so here you have a
+
+ align:start position:0%
+differentiation so here you have a
+ 
+
+ align:start position:0%
+differentiation so here you have a
+differentiation so he could identify
+
+ align:start position:0%
+differentiation so he could identify
+ 
+
+ align:start position:0%
+differentiation so he could identify
+what was in the box when the box was
+
+ align:start position:0%
+what was in the box when the box was
+ 
+
+ align:start position:0%
+what was in the box when the box was
+closed so that gives rise
+
+ align:start position:0%
+closed so that gives rise
+ 
+
+ align:start position:0%
+closed so that gives rise
+to security technology every time you go
+
+ align:start position:0%
+to security technology every time you go
+ 
+
+ align:start position:0%
+to security technology every time you go
+to the airport you are subjected to this
+
+ align:start position:0%
+to the airport you are subjected to this
+ 
+
+ align:start position:0%
+to the airport you are subjected to this
+and it started with
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+renen renen also had a
+
+ align:start position:0%
+renen renen also had a
+ 
+
+ align:start position:0%
+renen renen also had a
+gun it was a musket come on he wasn't
+
+ align:start position:0%
+gun it was a musket come on he wasn't
+ 
+
+ align:start position:0%
+gun it was a musket come on he wasn't
+wasn't holding up convenience stores
+
+ align:start position:0%
+wasn't holding up convenience stores
+ 
+
+ align:start position:0%
+wasn't holding up convenience stores
+what do you laughing you know he had a
+
+ align:start position:0%
+what do you laughing you know he had a
+ 
+
+ align:start position:0%
+what do you laughing you know he had a
+gun right he went hunting so he he took
+
+ align:start position:0%
+gun right he went hunting so he he took
+ 
+
+ align:start position:0%
+gun right he went hunting so he he took
+an X Raph of his
+
+ align:start position:0%
+an X Raph of his
+ 
+
+ align:start position:0%
+an X Raph of his
+gun and this is used today it gives
+
+ align:start position:0%
+gun and this is used today it gives
+ 
+
+ align:start position:0%
+gun and this is used today it gives
+birth to the technology of failure
+
+ align:start position:0%
+birth to the technology of failure
+ 
+
+ align:start position:0%
+birth to the technology of failure
+analysis in fact there are certain um
+
+ align:start position:0%
+analysis in fact there are certain um
+ 
+
+ align:start position:0%
+analysis in fact there are certain um
+types of
+
+ align:start position:0%
+types of
+ 
+
+ align:start position:0%
+types of
+weld typically involving very dangerous
+
+ align:start position:0%
+weld typically involving very dangerous
+ 
+
+ align:start position:0%
+weld typically involving very dangerous
+uh circumstances such as pressure
+
+ align:start position:0%
+uh circumstances such as pressure
+ 
+
+ align:start position:0%
+uh circumstances such as pressure
+vessels that are going to contain steam
+
+ align:start position:0%
+vessels that are going to contain steam
+ 
+
+ align:start position:0%
+vessels that are going to contain steam
+at very very high pressures the code is
+
+ align:start position:0%
+at very very high pressures the code is
+ 
+
+ align:start position:0%
+at very very high pressures the code is
+is that every inch of the welded seam
+
+ align:start position:0%
+is that every inch of the welded seam
+ 
+
+ align:start position:0%
+is that every inch of the welded seam
+must be inspected by X radiation in
+
+ align:start position:0%
+must be inspected by X radiation in
+ 
+
+ align:start position:0%
+must be inspected by X radiation in
+order to find what internal cracks
+
+ align:start position:0%
+order to find what internal cracks
+ 
+
+ align:start position:0%
+order to find what internal cracks
+because if there's a crack there's a
+
+ align:start position:0%
+because if there's a crack there's a
+ 
+
+ align:start position:0%
+because if there's a crack there's a
+difference in in electron density and so
+
+ align:start position:0%
+difference in in electron density and so
+ 
+
+ align:start position:0%
+difference in in electron density and so
+you'll see contrast in the X-ray
+
+ align:start position:0%
+you'll see contrast in the X-ray
+ 
+
+ align:start position:0%
+you'll see contrast in the X-ray
+photograph so from that experiment come
+
+ align:start position:0%
+photograph so from that experiment come
+ 
+
+ align:start position:0%
+photograph so from that experiment come
+three Technologies three
+
+ align:start position:0%
+three Technologies three
+ 
+
+ align:start position:0%
+three Technologies three
+Technologies and for his work
+
+ align:start position:0%
+Technologies and for his work
+ 
+
+ align:start position:0%
+Technologies and for his work
+renen was the recipient of the very
+
+ align:start position:0%
+renen was the recipient of the very
+ 
+
+ align:start position:0%
+renen was the recipient of the very
+first Nobel Prize in physics it was
+
+ align:start position:0%
+first Nobel Prize in physics it was
+ 
+
+ align:start position:0%
+first Nobel Prize in physics it was
+awarded in 1901 and he was the unanimous
+
+ align:start position:0%
+awarded in 1901 and he was the unanimous
+ 
+
+ align:start position:0%
+awarded in 1901 and he was the unanimous
+choice of the world physics Community
+
+ align:start position:0%
+choice of the world physics Community
+ 
+
+ align:start position:0%
+choice of the world physics Community
+for the for what he had done and you're
+
+ align:start position:0%
+for the for what he had done and you're
+ 
+
+ align:start position:0%
+for the for what he had done and you're
+going to see next day more that uh the
+
+ align:start position:0%
+going to see next day more that uh the
+ 
+
+ align:start position:0%
+going to see next day more that uh the
+the discovery of x-rays enabl but one
+
+ align:start position:0%
+the discovery of x-rays enabl but one
+ 
+
+ align:start position:0%
+the discovery of x-rays enabl but one
+last
+
+ align:start position:0%
+last
+ 
+
+ align:start position:0%
+last
+thing what a what a fine human being he
+
+ align:start position:0%
+thing what a what a fine human being he
+ 
+
+ align:start position:0%
+thing what a what a fine human being he
+was you know what he did with his
+
+ align:start position:0%
+was you know what he did with his
+ 
+
+ align:start position:0%
+was you know what he did with his
+winnings he donated them to the
+
+ align:start position:0%
+winnings he donated them to the
+ 
+
+ align:start position:0%
+winnings he donated them to the
+University of wburg to be made an
+
+ align:start position:0%
+University of wburg to be made an
+ 
+
+ align:start position:0%
+University of wburg to be made an
+endowment for student scholarships and
+
+ align:start position:0%
+endowment for student scholarships and
+ 
+
+ align:start position:0%
+endowment for student scholarships and
+to this day physics students at the
+
+ align:start position:0%
+to this day physics students at the
+ 
+
+ align:start position:0%
+to this day physics students at the
+University of verburg are recipience of
+
+ align:start position:0%
+University of verburg are recipience of
+ 
+
+ align:start position:0%
+University of verburg are recipience of
+scholarships that were endowed by renen
+
+ align:start position:0%
+scholarships that were endowed by renen
+ 
+
+ align:start position:0%
+scholarships that were endowed by renen
+with his Nobel Prize winnings in 1901
+
+ align:start position:0%
+with his Nobel Prize winnings in 1901
+ 
+
+ align:start position:0%
+with his Nobel Prize winnings in 1901
+I'll see you on Wednesday
\ No newline at end of file
diff --git a/WbQYpeXWKHI.txt b/WbQYpeXWKHI.txt
new file mode 100644
index 0000000000000000000000000000000000000000..8347df4e5af5db454f4e3f179d0bb747bb309746
--- /dev/null
+++ b/WbQYpeXWKHI.txt
@@ -0,0 +1,18771 @@
+align:start position:0%
+ 
+the following content is provided by MIT
+
+ align:start position:0%
+the following content is provided by MIT
+ 
+
+ align:start position:0%
+the following content is provided by MIT
+open courseware under a Creative Commons
+
+ align:start position:0%
+open courseware under a Creative Commons
+ 
+
+ align:start position:0%
+open courseware under a Creative Commons
+license additional information about our
+
+ align:start position:0%
+license additional information about our
+ 
+
+ align:start position:0%
+license additional information about our
+license and MIT open course Weare in
+
+ align:start position:0%
+license and MIT open course Weare in
+ 
+
+ align:start position:0%
+license and MIT open course Weare in
+general is available at
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+ocw.mit.edu okay good morning today the
+
+ align:start position:0%
+ocw.mit.edu okay good morning today the
+ 
+
+ align:start position:0%
+ocw.mit.edu okay good morning today the
+last day of our
+
+ align:start position:0%
+last day of our
+ 
+
+ align:start position:0%
+last day of our
+[Laughter]
+
+ align:start position:0%
+[Laughter]
+ 
+
+ align:start position:0%
+[Laughter]
+CSE we we do basically two two
+
+ align:start position:0%
+CSE we we do basically two two
+ 
+
+ align:start position:0%
+CSE we we do basically two two
+activities we will make again the
+
+ align:start position:0%
+activities we will make again the
+ 
+
+ align:start position:0%
+activities we will make again the
+exercise of critical moments reflection
+
+ align:start position:0%
+exercise of critical moments reflection
+ 
+
+ align:start position:0%
+exercise of critical moments reflection
+methodology that we made in the second
+
+ align:start position:0%
+methodology that we made in the second
+ 
+
+ align:start position:0%
+methodology that we made in the second
+day of the
+
+ align:start position:0%
+day of the
+ 
+
+ align:start position:0%
+day of the
+course and we will talk about the future
+
+ align:start position:0%
+course and we will talk about the future
+ 
+
+ align:start position:0%
+course and we will talk about the future
+of reflective practice in this new world
+
+ align:start position:0%
+of reflective practice in this new world
+ 
+
+ align:start position:0%
+of reflective practice in this new world
+that is
+
+ align:start position:0%
+that is
+ 
+
+ align:start position:0%
+that is
+emerging
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay I will try to make you to remember
+
+ align:start position:0%
+okay I will try to make you to remember
+ 
+
+ align:start position:0%
+okay I will try to make you to remember
+to help you to remember the methodology
+
+ align:start position:0%
+to help you to remember the methodology
+ 
+
+ align:start position:0%
+to help you to remember the methodology
+the first step of the methodology is
+
+ align:start position:0%
+the first step of the methodology is
+ 
+
+ align:start position:0%
+the first step of the methodology is
+to formulate a question a question that
+
+ align:start position:0%
+to formulate a question a question that
+ 
+
+ align:start position:0%
+to formulate a question a question that
+will guide my mind in the analysis that
+
+ align:start position:0%
+will guide my mind in the analysis that
+ 
+
+ align:start position:0%
+will guide my mind in the analysis that
+I will be trying to to
+
+ align:start position:0%
+I will be trying to to
+ 
+
+ align:start position:0%
+I will be trying to to
+do and once we have the question we name
+
+ align:start position:0%
+do and once we have the question we name
+ 
+
+ align:start position:0%
+do and once we have the question we name
+it inquiring
+
+ align:start position:0%
+it inquiring
+ 
+
+ align:start position:0%
+it inquiring
+question we we step back to the
+
+ align:start position:0%
+question we we step back to the
+ 
+
+ align:start position:0%
+question we we step back to the
+experience trying to identify
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+critical
+
+ align:start position:0%
+critical
+ 
+
+ align:start position:0%
+critical
+moments I will explain better what
+
+ align:start position:0%
+moments I will explain better what
+ 
+
+ align:start position:0%
+moments I will explain better what
+critical moments
+
+ align:start position:0%
+critical moments
+ 
+
+ align:start position:0%
+critical moments
+means and we will con reconstruct the
+
+ align:start position:0%
+means and we will con reconstruct the
+ 
+
+ align:start position:0%
+means and we will con reconstruct the
+experience through the critical moments
+
+ align:start position:0%
+experience through the critical moments
+ 
+
+ align:start position:0%
+experience through the critical moments
+and we will make an analysis of that
+
+ align:start position:0%
+and we will make an analysis of that
+ 
+
+ align:start position:0%
+and we will make an analysis of that
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so the first step is the inquiry
+
+ align:start position:0%
+so the first step is the inquiry
+ 
+
+ align:start position:0%
+so the first step is the inquiry
+question
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+what you need to think about
+
+ align:start position:0%
+what you need to think about
+ 
+
+ align:start position:0%
+what you need to think about
+for defining your inquiry question is
+
+ align:start position:0%
+for defining your inquiry question is
+ 
+
+ align:start position:0%
+for defining your inquiry question is
+what
+
+ align:start position:0%
+what
+ 
+
+ align:start position:0%
+what
+questions if you had an answer
+
+ align:start position:0%
+questions if you had an answer
+ 
+
+ align:start position:0%
+questions if you had an answer
+to would help
+
+ align:start position:0%
+to would help
+ 
+
+ align:start position:0%
+to would help
+you to better apply reflective
+
+ align:start position:0%
+you to better apply reflective
+ 
+
+ align:start position:0%
+you to better apply reflective
+practice in your future
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+activities okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the issue
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+is reflective practice in my future
+
+ align:start position:0%
+is reflective practice in my future
+ 
+
+ align:start position:0%
+is reflective practice in my future
+activities how I can improve
+
+ align:start position:0%
+activities how I can improve
+ 
+
+ align:start position:0%
+activities how I can improve
+it and the question
+
+ align:start position:0%
+it and the question
+ 
+
+ align:start position:0%
+it and the question
+is what I need to answer for improving
+
+ align:start position:0%
+is what I need to answer for improving
+ 
+
+ align:start position:0%
+is what I need to answer for improving
+the application of reflective practice
+
+ align:start position:0%
+the application of reflective practice
+ 
+
+ align:start position:0%
+the application of reflective practice
+in my future activi
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay each one we formulate one question
+
+ align:start position:0%
+okay each one we formulate one question
+ 
+
+ align:start position:0%
+okay each one we formulate one question
+and we will collect as we did the second
+
+ align:start position:0%
+and we will collect as we did the second
+ 
+
+ align:start position:0%
+and we will collect as we did the second
+day of the course please write down what
+
+ align:start position:0%
+day of the course please write down what
+ 
+
+ align:start position:0%
+day of the course please write down what
+question you would like to
+
+ align:start position:0%
+question you would like to
+ 
+
+ align:start position:0%
+question you would like to
+to answer with the
+
+ align:start position:0%
+to answer with the
+ 
+
+ align:start position:0%
+to answer with the
+exercise about anything no about about
+
+ align:start position:0%
+exercise about anything no about about
+ 
+
+ align:start position:0%
+exercise about anything no about about
+anything that will help you to
+
+ align:start position:0%
+anything that will help you to
+ 
+
+ align:start position:0%
+anything that will help you to
+improve or to better apply reflective
+
+ align:start position:0%
+improve or to better apply reflective
+ 
+
+ align:start position:0%
+improve or to better apply reflective
+practice in your future
+
+ align:start position:0%
+practice in your future
+ 
+
+ align:start position:0%
+practice in your future
+activity
+
+ align:start position:0%
+activity
+ 
+
+ align:start position:0%
+activity
+okay thinking about your experience
+
+ align:start position:0%
+okay thinking about your experience
+ 
+
+ align:start position:0%
+okay thinking about your experience
+throughout the course what you would
+
+ align:start position:0%
+throughout the course what you would
+ 
+
+ align:start position:0%
+throughout the course what you would
+like to understand better for applying
+
+ align:start position:0%
+like to understand better for applying
+ 
+
+ align:start position:0%
+like to understand better for applying
+refle Ive
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+practice okay go into your mind think on
+
+ align:start position:0%
+practice okay go into your mind think on
+ 
+
+ align:start position:0%
+practice okay go into your mind think on
+the challenges of applying reflective
+
+ align:start position:0%
+the challenges of applying reflective
+ 
+
+ align:start position:0%
+the challenges of applying reflective
+practice what you already know and what
+
+ align:start position:0%
+practice what you already know and what
+ 
+
+ align:start position:0%
+practice what you already know and what
+you are not so clear about and what
+
+ align:start position:0%
+you are not so clear about and what
+ 
+
+ align:start position:0%
+you are not so clear about and what
+question you would like to answer to
+
+ align:start position:0%
+question you would like to answer to
+ 
+
+ align:start position:0%
+question you would like to answer to
+have an answer okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+she will come
+
+ align:start position:0%
+she will come
+ 
+
+ align:start position:0%
+she will come
+back see fore
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+second
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+we're thinking about the inquiry
+
+ align:start position:0%
+we're thinking about the inquiry
+ 
+
+ align:start position:0%
+we're thinking about the inquiry
+question yes okay
+
+ align:start position:0%
+question yes okay
+ 
+
+ align:start position:0%
+question yes okay
+yeah okay morning we have already begun
+
+ align:start position:0%
+yeah okay morning we have already begun
+ 
+
+ align:start position:0%
+yeah okay morning we have already begun
+we are trying to formulate an inquiry
+
+ align:start position:0%
+we are trying to formulate an inquiry
+ 
+
+ align:start position:0%
+we are trying to formulate an inquiry
+question for a reflection
+
+ align:start position:0%
+question for a reflection
+ 
+
+ align:start position:0%
+question for a reflection
+exercise
+
+ align:start position:0%
+exercise
+ 
+
+ align:start position:0%
+exercise
+okay where you will put in front of you
+
+ align:start position:0%
+okay where you will put in front of you
+ 
+
+ align:start position:0%
+okay where you will put in front of you
+for
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+speech
+
+ align:start position:0%
+speech
+ 
+
+ align:start position:0%
+speech
+foreign foreign speech
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+now now let's begin
+
+ align:start position:0%
+now now let's begin
+ 
+
+ align:start position:0%
+now now let's begin
+[Music]
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay okay let's begin
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+your
+
+ align:start position:0%
+your
+ 
+
+ align:start position:0%
+your
+question um we had two do I just use one
+
+ align:start position:0%
+question um we had two do I just use one
+ 
+
+ align:start position:0%
+question um we had two do I just use one
+or okay one at a time my first thought
+
+ align:start position:0%
+or okay one at a time my first thought
+ 
+
+ align:start position:0%
+or okay one at a time my first thought
+was how to and this is what I thought I
+
+ align:start position:0%
+was how to and this is what I thought I
+ 
+
+ align:start position:0%
+was how to and this is what I thought I
+don't know what it means how to make
+
+ align:start position:0%
+don't know what it means how to make
+ 
+
+ align:start position:0%
+don't know what it means how to make
+reflective practice more practical okay
+
+ align:start position:0%
+reflective practice more practical okay
+ 
+
+ align:start position:0%
+reflective practice more practical okay
+how to make reflective practice more
+
+ align:start position:0%
+how to make reflective practice more
+ 
+
+ align:start position:0%
+how to make reflective practice more
+practical
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay um how can I engage a community in
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+learning from
+
+ align:start position:0%
+learning from
+ 
+
+ align:start position:0%
+learning from
+their
+
+ align:start position:0%
+their
+ 
+
+ align:start position:0%
+their
+organiz how
+
+ align:start position:0%
+organiz how
+ 
+
+ align:start position:0%
+organiz how
+can engage
+
+ align:start position:0%
+can engage
+ 
+
+ align:start position:0%
+can engage
+Community how can I best
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+engage and learning and learning from
+
+ align:start position:0%
+engage and learning and learning from
+ 
+
+ align:start position:0%
+engage and learning and learning from
+their organiz
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Rel how can I use reflective practice
+
+ align:start position:0%
+Rel how can I use reflective practice
+ 
+
+ align:start position:0%
+Rel how can I use reflective practice
+skills
+
+ align:start position:0%
+skills
+ 
+
+ align:start position:0%
+skills
+in CL
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Rel to develop a close
+
+ align:start position:0%
+Rel to develop a close
+ 
+
+ align:start position:0%
+Rel to develop a close
+relation with the
+
+ align:start position:0%
+relation with the
+ 
+
+ align:start position:0%
+relation with the
+groups with the groups I am involved
+
+ align:start position:0%
+groups with the groups I am involved
+ 
+
+ align:start position:0%
+groups with the groups I am involved
+okay how can you apply with effective
+
+ align:start position:0%
+okay how can you apply with effective
+ 
+
+ align:start position:0%
+okay how can you apply with effective
+practice to Community
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Development how can we apply effective
+
+ align:start position:0%
+Development how can we apply effective
+ 
+
+ align:start position:0%
+Development how can we apply effective
+practice to Community Development to
+
+ align:start position:0%
+practice to Community Development to
+ 
+
+ align:start position:0%
+practice to Community Development to
+Community
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Development effective
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+practice
+
+ align:start position:0%
+practice
+ 
+
+ align:start position:0%
+practice
+development um I'm not sure if I did
+
+ align:start position:0%
+development um I'm not sure if I did
+ 
+
+ align:start position:0%
+development um I'm not sure if I did
+this correctly okay I wrote down I
+
+ align:start position:0%
+this correctly okay I wrote down I
+ 
+
+ align:start position:0%
+this correctly okay I wrote down I
+understand the importance in respect of
+
+ align:start position:0%
+understand the importance in respect of
+ 
+
+ align:start position:0%
+understand the importance in respect of
+of individuals with disabilities in our
+
+ align:start position:0%
+of individuals with disabilities in our
+ 
+
+ align:start position:0%
+of individuals with disabilities in our
+workplaces members of the board of
+
+ align:start position:0%
+workplaces members of the board of
+ 
+
+ align:start position:0%
+workplaces members of the board of
+directors and participants in community
+
+ align:start position:0%
+directors and participants in community
+ 
+
+ align:start position:0%
+directors and participants in community
+organizations should I say it again yes
+
+ align:start position:0%
+organizations should I say it again yes
+ 
+
+ align:start position:0%
+organizations should I say it again yes
+okay question because this is an
+
+ align:start position:0%
+okay question because this is an
+ 
+
+ align:start position:0%
+okay question because this is an
+statement you need to formulate a
+
+ align:start position:0%
+statement you need to formulate a
+ 
+
+ align:start position:0%
+statement you need to formulate a
+question okay and then I wrote how do
+
+ align:start position:0%
+question okay and then I wrote how do
+ 
+
+ align:start position:0%
+question okay and then I wrote how do
+you educate people about the
+
+ align:start position:0%
+you educate people about the
+ 
+
+ align:start position:0%
+you educate people about the
+contributions of individuals with
+
+ align:start position:0%
+contributions of individuals with
+ 
+
+ align:start position:0%
+contributions of individuals with
+disabilities ensure their participation
+
+ align:start position:0%
+disabilities ensure their participation
+ 
+
+ align:start position:0%
+disabilities ensure their participation
+not so fast for en I wrote how do you
+
+ align:start position:0%
+not so fast for en I wrote how do you
+ 
+
+ align:start position:0%
+not so fast for en I wrote how do you
+educate people about the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+contributions can you synthesize a bit
+
+ align:start position:0%
+contributions can you synthesize a bit
+ 
+
+ align:start position:0%
+contributions can you synthesize a bit
+because we not be easy to okay can I
+
+ align:start position:0%
+because we not be easy to okay can I
+ 
+
+ align:start position:0%
+because we not be easy to okay can I
+think about it for a couple minutes
+
+ align:start position:0%
+think about it for a couple minutes
+ 
+
+ align:start position:0%
+think about it for a couple minutes
+while you're going around okay yes I
+
+ align:start position:0%
+while you're going around okay yes I
+ 
+
+ align:start position:0%
+while you're going around okay yes I
+wrote it too long maybe okay how to
+
+ align:start position:0%
+wrote it too long maybe okay how to
+ 
+
+ align:start position:0%
+wrote it too long maybe okay how to
+implement uh uh
+
+ align:start position:0%
+implement uh uh
+ 
+
+ align:start position:0%
+implement uh uh
+democracy uh on the reflection on the
+
+ align:start position:0%
+democracy uh on the reflection on the
+ 
+
+ align:start position:0%
+democracy uh on the reflection on the
+reflection PL yeah well
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+democracy in into the reflection
+
+ align:start position:0%
+democracy in into the reflection
+ 
+
+ align:start position:0%
+democracy in into the reflection
+practice into the reflection of
+
+ align:start position:0%
+practice into the reflection of
+ 
+
+ align:start position:0%
+practice into the reflection of
+practice exercise more
+
+ align:start position:0%
+practice exercise more
+ 
+
+ align:start position:0%
+practice exercise more
+like what the difference how
+
+ align:start position:0%
+like what the difference how
+ 
+
+ align:start position:0%
+like what the difference how
+that how like democracy and
+
+ align:start position:0%
+that how like democracy and
+ 
+
+ align:start position:0%
+that how like democracy and
+reflection sometimes it's very confused
+
+ align:start position:0%
+reflection sometimes it's very confused
+ 
+
+ align:start position:0%
+reflection sometimes it's very confused
+with democracy is it can we can change
+
+ align:start position:0%
+with democracy is it can we can change
+ 
+
+ align:start position:0%
+with democracy is it can we can change
+the order should be how I can apply
+
+ align:start position:0%
+the order should be how I can apply
+ 
+
+ align:start position:0%
+the order should be how I can apply
+reflective practice in democracy okay on
+
+ align:start position:0%
+reflective practice in democracy okay on
+ 
+
+ align:start position:0%
+reflective practice in democracy okay on
+Democracy issues in democracy on the
+
+ align:start position:0%
+Democracy issues in democracy on the
+ 
+
+ align:start position:0%
+Democracy issues in democracy on the
+issues of
+
+ align:start position:0%
+issues of
+ 
+
+ align:start position:0%
+issues of
+democracy how we can Implement
+
+ align:start position:0%
+democracy how we can Implement
+ 
+
+ align:start position:0%
+democracy how we can Implement
+reflective
+
+ align:start position:0%
+reflective
+ 
+
+ align:start position:0%
+reflective
+practice to the issues of democracy okay
+
+ align:start position:0%
+practice to the issues of democracy okay
+ 
+
+ align:start position:0%
+practice to the issues of democracy okay
+thank
+
+ align:start position:0%
+thank
+ 
+
+ align:start position:0%
+thank
+you um I had three so I don't know I'll
+
+ align:start position:0%
+you um I had three so I don't know I'll
+ 
+
+ align:start position:0%
+you um I had three so I don't know I'll
+read what um what are the areas in which
+
+ align:start position:0%
+read what um what are the areas in which
+ 
+
+ align:start position:0%
+read what um what are the areas in which
+the group oh wait for
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh what are the areas in which the group
+
+ align:start position:0%
+uh what are the areas in which the group
+ 
+
+ align:start position:0%
+uh what are the areas in which the group
+had the hardest time doing successfully
+
+ align:start position:0%
+had the hardest time doing successfully
+ 
+
+ align:start position:0%
+had the hardest time doing successfully
+and why how can we merge individual
+
+ align:start position:0%
+and why how can we merge individual
+ 
+
+ align:start position:0%
+and why how can we merge individual
+frames better and how can we more
+
+ align:start position:0%
+frames better and how can we more
+ 
+
+ align:start position:0%
+frames better and how can we more
+effectively become aware of our tcid
+
+ align:start position:0%
+effectively become aware of our tcid
+ 
+
+ align:start position:0%
+effectively become aware of our tcid
+assumptions so I don't know we could
+
+ align:start position:0%
+assumptions so I don't know we could
+ 
+
+ align:start position:0%
+assumptions so I don't know we could
+pick one out of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+those so what are the areas in which the
+
+ align:start position:0%
+those so what are the areas in which the
+ 
+
+ align:start position:0%
+those so what are the areas in which the
+group had
+
+ align:start position:0%
+group had
+ 
+
+ align:start position:0%
+group had
+difficulty uh
+
+ align:start position:0%
+difficulty uh
+ 
+
+ align:start position:0%
+difficulty uh
+a difficulty doing
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+successfully and why or is that two
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+questions
+
+ align:start position:0%
+questions
+ 
+
+ align:start position:0%
+questions
+okay um I was trying to figure out how
+
+ align:start position:0%
+okay um I was trying to figure out how
+ 
+
+ align:start position:0%
+okay um I was trying to figure out how
+to take this knowledge about reflective
+
+ align:start position:0%
+to take this knowledge about reflective
+ 
+
+ align:start position:0%
+to take this knowledge about reflective
+practice and implement it at an
+
+ align:start position:0%
+practice and implement it at an
+ 
+
+ align:start position:0%
+practice and implement it at an
+organizational how do I take the
+
+ align:start position:0%
+organizational how do I take the
+ 
+
+ align:start position:0%
+organizational how do I take the
+knowledge that I have and
+
+ align:start position:0%
+knowledge that I have and
+ 
+
+ align:start position:0%
+knowledge that I have and
+okay how to apply the knowledge about
+
+ align:start position:0%
+okay how to apply the knowledge about
+ 
+
+ align:start position:0%
+okay how to apply the knowledge about
+reflective practice in at a larger scale
+
+ align:start position:0%
+reflective practice in at a larger scale
+ 
+
+ align:start position:0%
+reflective practice in at a larger scale
+with either Community or organization or
+
+ align:start position:0%
+with either Community or organization or
+ 
+
+ align:start position:0%
+with either Community or organization or
+if I'm working in a group with a number
+
+ align:start position:0%
+if I'm working in a group with a number
+ 
+
+ align:start position:0%
+if I'm working in a group with a number
+of different people how do
+
+ align:start position:0%
+of different people how do
+ 
+
+ align:start position:0%
+of different people how do
+I if that's not already part of the
+
+ align:start position:0%
+I if that's not already part of the
+ 
+
+ align:start position:0%
+I if that's not already part of the
+process how do I bring that into the
+
+ align:start position:0%
+process how do I bring that into the
+ 
+
+ align:start position:0%
+process how do I bring that into the
+process
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+MH that's this practice that allows your
+
+ align:start position:0%
+MH that's this practice that allows your
+ 
+
+ align:start position:0%
+MH that's this practice that allows your
+Escape okay you
+
+ align:start position:0%
+Escape okay you
+ 
+
+ align:start position:0%
+Escape okay you
+um is about how do we what steps
+
+ align:start position:0%
+um is about how do we what steps
+ 
+
+ align:start position:0%
+um is about how do we what steps
+necessary to make
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+reflec how is it necessary for steps are
+
+ align:start position:0%
+reflec how is it necessary for steps are
+ 
+
+ align:start position:0%
+reflec how is it necessary for steps are
+necessary to make practice a habit a
+
+ align:start position:0%
+necessary to make practice a habit a
+ 
+
+ align:start position:0%
+necessary to make practice a habit a
+habit okay that it comes naturally
+
+ align:start position:0%
+habit okay that it comes naturally
+ 
+
+ align:start position:0%
+habit okay that it comes naturally
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+okay to make effective practice
+
+ align:start position:0%
+okay to make effective practice
+ 
+
+ align:start position:0%
+okay to make effective practice
+habit
+
+ align:start position:0%
+habit
+ 
+
+ align:start position:0%
+habit
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+natural um I think me I see like three
+
+ align:start position:0%
+natural um I think me I see like three
+ 
+
+ align:start position:0%
+natural um I think me I see like three
+of them up there that I would reiterate
+
+ align:start position:0%
+of them up there that I would reiterate
+ 
+
+ align:start position:0%
+of them up there that I would reiterate
+like Ezra's comment about how you you
+
+ align:start position:0%
+like Ezra's comment about how you you
+ 
+
+ align:start position:0%
+like Ezra's comment about how you you
+know integrate this into you know
+
+ align:start position:0%
+know integrate this into you know
+ 
+
+ align:start position:0%
+know integrate this into you know
+organizations that you work with in so I
+
+ align:start position:0%
+organizations that you work with in so I
+ 
+
+ align:start position:0%
+organizations that you work with in so I
+think that would be the biggest one for
+
+ align:start position:0%
+think that would be the biggest one for
+ 
+
+ align:start position:0%
+think that would be the biggest one for
+me okay this one
+
+ align:start position:0%
+me okay this one
+ 
+
+ align:start position:0%
+me okay this one
+okay now we need to select one of them
+
+ align:start position:0%
+okay now we need to select one of them
+ 
+
+ align:start position:0%
+okay now we need to select one of them
+oh as a grou as a group
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yes I yes Ed have you yeah I I made it a
+
+ align:start position:0%
+yes I yes Ed have you yeah I I made it a
+ 
+
+ align:start position:0%
+yes I yes Ed have you yeah I I made it a
+little shorter okay um this what I wrote
+
+ align:start position:0%
+little shorter okay um this what I wrote
+ 
+
+ align:start position:0%
+little shorter okay um this what I wrote
+I wrote how do I continue to include
+
+ align:start position:0%
+I wrote how do I continue to include
+ 
+
+ align:start position:0%
+I wrote how do I continue to include
+people with disabilities within
+
+ align:start position:0%
+people with disabilities within
+ 
+
+ align:start position:0%
+people with disabilities within
+Community organizations As
+
+ align:start position:0%
+Community organizations As
+ 
+
+ align:start position:0%
+Community organizations As
+Leaders yeah you want me say slowly how
+
+ align:start position:0%
+Leaders yeah you want me say slowly how
+ 
+
+ align:start position:0%
+Leaders yeah you want me say slowly how
+is that related to this yes the problem
+
+ align:start position:0%
+is that related to this yes the problem
+ 
+
+ align:start position:0%
+is that related to this yes the problem
+you you need a question that if you had
+
+ align:start position:0%
+you you need a question that if you had
+ 
+
+ align:start position:0%
+you you need a question that if you had
+an answer
+
+ align:start position:0%
+an answer
+ 
+
+ align:start position:0%
+an answer
+to it would help you apply reflective
+
+ align:start position:0%
+to it would help you apply reflective
+ 
+
+ align:start position:0%
+to it would help you apply reflective
+practice in your work in your future
+
+ align:start position:0%
+practice in your work in your future
+ 
+
+ align:start position:0%
+practice in your work in your future
+activities
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+well I let me just say this maybe just
+
+ align:start position:0%
+well I let me just say this maybe just
+ 
+
+ align:start position:0%
+well I let me just say this maybe just
+say like I I've done a lot of work with
+
+ align:start position:0%
+say like I I've done a lot of work with
+ 
+
+ align:start position:0%
+say like I I've done a lot of work with
+including people with disabilities in my
+
+ align:start position:0%
+including people with disabilities in my
+ 
+
+ align:start position:0%
+including people with disabilities in my
+practice so I want to include more
+
+ align:start position:0%
+practice so I want to include more
+ 
+
+ align:start position:0%
+practice so I want to include more
+people with disabilities in
+
+ align:start position:0%
+people with disabilities in
+ 
+
+ align:start position:0%
+people with disabilities in
+organizations As Leaders because a lot
+
+ align:start position:0%
+organizations As Leaders because a lot
+ 
+
+ align:start position:0%
+organizations As Leaders because a lot
+of times they don't have equal
+
+ align:start position:0%
+of times they don't have equal
+ 
+
+ align:start position:0%
+of times they don't have equal
+opportunity you would like to apply
+
+ align:start position:0%
+opportunity you would like to apply
+ 
+
+ align:start position:0%
+opportunity you would like to apply
+reflective practice to this kind of
+
+ align:start position:0%
+reflective practice to this kind of
+ 
+
+ align:start position:0%
+reflective practice to this kind of
+issue yes okay or how to apply refective
+
+ align:start position:0%
+issue yes okay or how to apply refective
+ 
+
+ align:start position:0%
+issue yes okay or how to apply refective
+practice for including individuals with
+
+ align:start position:0%
+practice for including individuals with
+ 
+
+ align:start position:0%
+practice for including individuals with
+disabilities individuals with disability
+
+ align:start position:0%
+disabilities individuals with disability
+ 
+
+ align:start position:0%
+disabilities individuals with disability
+okay I'm think it's
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so do you do you see any here that
+
+ align:start position:0%
+okay so do you do you see any here that
+ 
+
+ align:start position:0%
+okay so do you do you see any here that
+can be combined that are similar that
+
+ align:start position:0%
+can be combined that are similar that
+ 
+
+ align:start position:0%
+can be combined that are similar that
+are the same let's look first for for
+
+ align:start position:0%
+are the same let's look first for for
+ 
+
+ align:start position:0%
+are the same let's look first for for
+any any questions that may
+
+ align:start position:0%
+any any questions that may
+ 
+
+ align:start position:0%
+any any questions that may
+be
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+duplicates yes I think um the maybe make
+
+ align:start position:0%
+duplicates yes I think um the maybe make
+ 
+
+ align:start position:0%
+duplicates yes I think um the maybe make
+reflective practice more practical and
+
+ align:start position:0%
+reflective practice more practical and
+ 
+
+ align:start position:0%
+reflective practice more practical and
+making it a habit or
+
+ align:start position:0%
+making it a habit or
+ 
+
+ align:start position:0%
+making it a habit or
+similar okay okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+I think they're actually a little
+
+ align:start position:0%
+I think they're actually a little
+ 
+
+ align:start position:0%
+I think they're actually a little
+different I they're related but I don't
+
+ align:start position:0%
+different I they're related but I don't
+ 
+
+ align:start position:0%
+different I they're related but I don't
+think they're the exact same question I
+
+ align:start position:0%
+think they're the exact same question I
+ 
+
+ align:start position:0%
+think they're the exact same question I
+mean practical means it's making it kind
+
+ align:start position:0%
+mean practical means it's making it kind
+ 
+
+ align:start position:0%
+mean practical means it's making it kind
+of convenient and simple or is making it
+
+ align:start position:0%
+of convenient and simple or is making it
+ 
+
+ align:start position:0%
+of convenient and simple or is making it
+a habit of sort of doing it
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+consistently similar okay let's go do we
+
+ align:start position:0%
+consistently similar okay let's go do we
+ 
+
+ align:start position:0%
+consistently similar okay let's go do we
+find any any
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+I go
+
+ align:start position:0%
+I go
+ 
+
+ align:start position:0%
+I go
+another
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+question what were you saying
+
+ align:start position:0%
+question what were you saying
+ 
+
+ align:start position:0%
+question what were you saying
+cine I'm
+
+ align:start position:0%
+cine I'm
+ 
+
+ align:start position:0%
+cine I'm
+thinking see with i i
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+MH f and g are like the same
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+statement
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah if is the same G is a phrase of f
+
+ align:start position:0%
+yeah if is the same G is a phrase of f
+ 
+
+ align:start position:0%
+yeah if is the same G is a phrase of f
+you can eliminate
+
+ align:start position:0%
+you can eliminate
+ 
+
+ align:start position:0%
+you can eliminate
+F I think c and d c would kind of fall
+
+ align:start position:0%
+F I think c and d c would kind of fall
+ 
+
+ align:start position:0%
+F I think c and d c would kind of fall
+not no I'm sorry not c um B I think B
+
+ align:start position:0%
+not no I'm sorry not c um B I think B
+ 
+
+ align:start position:0%
+not no I'm sorry not c um B I think B
+and D are
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+related how can I apply reflective
+
+ align:start position:0%
+related how can I apply reflective
+ 
+
+ align:start position:0%
+related how can I apply reflective
+practice to Community Development and
+
+ align:start position:0%
+practice to Community Development and
+ 
+
+ align:start position:0%
+practice to Community Development and
+how
+
+ align:start position:0%
+how
+ 
+
+ align:start position:0%
+how
+can can I engage a community in learning
+
+ align:start position:0%
+can can I engage a community in learning
+ 
+
+ align:start position:0%
+can can I engage a community in learning
+from their organizing work b b and
+
+ align:start position:0%
+from their organizing work b b and
+ 
+
+ align:start position:0%
+from their organizing work b b and
+yes and is more General than right
+
+ align:start position:0%
+yes and is more General than right
+ 
+
+ align:start position:0%
+yes and is more General than right
+exactly both of those could be a subset
+
+ align:start position:0%
+exactly both of those could be a subset
+ 
+
+ align:start position:0%
+exactly both of those could be a subset
+of I because they're types of
+
+ align:start position:0%
+of I because they're types of
+ 
+
+ align:start position:0%
+of I because they're types of
+organizations okay yeah appage do you
+
+ align:start position:0%
+organizations okay yeah appage do you
+ 
+
+ align:start position:0%
+organizations okay yeah appage do you
+see another kind
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+of sort of like a topic
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+area that's even more
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay wish
+
+ align:start position:0%
+okay wish
+ 
+
+ align:start position:0%
+okay wish
+could a right now that we're kind of
+
+ align:start position:0%
+could a right now that we're kind of
+ 
+
+ align:start position:0%
+could a right now that we're kind of
+able to combine with
+
+ align:start position:0%
+able to combine with
+ 
+
+ align:start position:0%
+able to combine with
+J B and
+
+ align:start position:0%
+J B and
+ 
+
+ align:start position:0%
+J B and
+D with I anything with regards to H and
+
+ align:start position:0%
+D with I anything with regards to H and
+ 
+
+ align:start position:0%
+D with I anything with regards to H and
+G
+
+ align:start position:0%
+G
+ 
+
+ align:start position:0%
+G
+and
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+see I think how can we apply the
+
+ align:start position:0%
+see I think how can we apply the
+ 
+
+ align:start position:0%
+see I think how can we apply the
+knowledge about practice at a larger
+
+ align:start position:0%
+knowledge about practice at a larger
+ 
+
+ align:start position:0%
+knowledge about practice at a larger
+scale and how can we Implement
+
+ align:start position:0%
+scale and how can we Implement
+ 
+
+ align:start position:0%
+scale and how can we Implement
+reflective practice to the issues of
+
+ align:start position:0%
+reflective practice to the issues of
+ 
+
+ align:start position:0%
+reflective practice to the issues of
+democracy
+
+ align:start position:0%
+democracy
+ 
+
+ align:start position:0%
+democracy
+Rel larg
+
+ align:start position:0%
+Rel larg
+ 
+
+ align:start position:0%
+Rel larg
+scale are related the question is that
+
+ align:start position:0%
+scale are related the question is that
+ 
+
+ align:start position:0%
+scale are related the question is that
+in G it's tost in specific issue and the
+
+ align:start position:0%
+in G it's tost in specific issue and the
+ 
+
+ align:start position:0%
+in G it's tost in specific issue and the
+other
+
+ align:start position:0%
+other
+ 
+
+ align:start position:0%
+other
+is to different kind of issues
+
+ align:start position:0%
+is to different kind of issues
+ 
+
+ align:start position:0%
+is to different kind of issues
+no that B and D were under
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+I okay okay so if you were then to try
+
+ align:start position:0%
+I okay okay so if you were then to try
+ 
+
+ align:start position:0%
+I okay okay so if you were then to try
+if if you were then to try to combine A
+
+ align:start position:0%
+if if you were then to try to combine A
+ 
+
+ align:start position:0%
+if if you were then to try to combine A
+and J how would you combine it
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+mean in One
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+S how can we make reflective practice
+
+ align:start position:0%
+S how can we make reflective practice
+ 
+
+ align:start position:0%
+S how can we make reflective practice
+common
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+practice mhm
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+but then you don't include the Practical
+
+ align:start position:0%
+but then you don't include the Practical
+ 
+
+ align:start position:0%
+but then you don't include the Practical
+part
+
+ align:start position:0%
+part
+ 
+
+ align:start position:0%
+part
+right I guess it's somewhat impli what
+
+ align:start position:0%
+right I guess it's somewhat impli what
+ 
+
+ align:start position:0%
+right I guess it's somewhat impli what
+do you
+
+ align:start position:0%
+do you
+ 
+
+ align:start position:0%
+do you
+think more
+
+ align:start position:0%
+think more
+ 
+
+ align:start position:0%
+think more
+practical and natural how that okay is
+
+ align:start position:0%
+practical and natural how that okay is
+ 
+
+ align:start position:0%
+practical and natural how that okay is
+that good okay good all right yeah now
+
+ align:start position:0%
+that good okay good all right yeah now
+ 
+
+ align:start position:0%
+that good okay good all right yeah now
+this one here B andd how can we engage
+
+ align:start position:0%
+this one here B andd how can we engage
+ 
+
+ align:start position:0%
+this one here B andd how can we engage
+community in learning from their
+
+ align:start position:0%
+community in learning from their
+ 
+
+ align:start position:0%
+community in learning from their
+organizing work and how can we apply
+
+ align:start position:0%
+organizing work and how can we apply
+ 
+
+ align:start position:0%
+organizing work and how can we apply
+reflective practice to Community
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Development how do you prefer to and
+
+ align:start position:0%
+Development how do you prefer to and
+ 
+
+ align:start position:0%
+Development how do you prefer to and
+then you've got the element here of how
+
+ align:start position:0%
+then you've got the element here of how
+ 
+
+ align:start position:0%
+then you've got the element here of how
+to how to take reflective practice to a
+
+ align:start position:0%
+to how to take reflective practice to a
+ 
+
+ align:start position:0%
+to how to take reflective practice to a
+larger scale
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+how can we apply we could to take the d
+
+ align:start position:0%
+how can we apply we could to take the d
+ 
+
+ align:start position:0%
+how can we apply we could to take the d
+as starting
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+point or not I mean I don't know I have
+
+ align:start position:0%
+point or not I mean I don't know I have
+ 
+
+ align:start position:0%
+point or not I mean I don't know I have
+a question about where we're trying to
+
+ align:start position:0%
+a question about where we're trying to
+ 
+
+ align:start position:0%
+a question about where we're trying to
+get to maybe that's my question if if we
+
+ align:start position:0%
+get to maybe that's my question if if we
+ 
+
+ align:start position:0%
+get to maybe that's my question if if we
+could rephrase the questions in a way
+
+ align:start position:0%
+could rephrase the questions in a way
+ 
+
+ align:start position:0%
+could rephrase the questions in a way
+that integrate the interest of everybody
+
+ align:start position:0%
+that integrate the interest of everybody
+ 
+
+ align:start position:0%
+that integrate the interest of everybody
+no of the two persons who formate no no
+
+ align:start position:0%
+no of the two persons who formate no no
+ 
+
+ align:start position:0%
+no of the two persons who formate no no
+that's our that's our immediate step
+
+ align:start position:0%
+that's our that's our immediate step
+ 
+
+ align:start position:0%
+that's our that's our immediate step
+what's our second step after that we
+
+ align:start position:0%
+what's our second step after that we
+ 
+
+ align:start position:0%
+what's our second step after that we
+will s two or three of these two or
+
+ align:start position:0%
+will s two or three of these two or
+ 
+
+ align:start position:0%
+will s two or three of these two or
+three
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay I think that there's a thing
+
+ align:start position:0%
+okay I think that there's a thing
+ 
+
+ align:start position:0%
+okay I think that there's a thing
+about I think that uh D could
+
+ align:start position:0%
+about I think that uh D could
+ 
+
+ align:start position:0%
+about I think that uh D could
+be
+
+ align:start position:0%
+be
+ 
+
+ align:start position:0%
+be
+the it could be the the general
+
+ align:start position:0%
+the it could be the the general
+ 
+
+ align:start position:0%
+the it could be the the general
+organizing could fall under D so it
+
+ align:start position:0%
+organizing could fall under D so it
+ 
+
+ align:start position:0%
+organizing could fall under D so it
+could be a natural Evolution from from
+
+ align:start position:0%
+could be a natural Evolution from from
+ 
+
+ align:start position:0%
+could be a natural Evolution from from
+Community Development rather so I guess
+
+ align:start position:0%
+Community Development rather so I guess
+ 
+
+ align:start position:0%
+Community Development rather so I guess
+I'm saying that
+
+ align:start position:0%
+I'm saying that
+ 
+
+ align:start position:0%
+I'm saying that
+um how can
+
+ align:start position:0%
+um how can
+ 
+
+ align:start position:0%
+um how can
+app
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+engage how can we engage community in
+
+ align:start position:0%
+engage how can we engage community in
+ 
+
+ align:start position:0%
+engage how can we engage community in
+using refective practice for their
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+development is it like a change from I
+
+ align:start position:0%
+development is it like a change from I
+ 
+
+ align:start position:0%
+development is it like a change from I
+to D to B like I is the least specific
+
+ align:start position:0%
+to D to B like I is the least specific
+ 
+
+ align:start position:0%
+to D to B like I is the least specific
+General D is Community Development is
+
+ align:start position:0%
+General D is Community Development is
+ 
+
+ align:start position:0%
+General D is Community Development is
+specific element development okay
+
+ align:start position:0%
+specific element development okay
+ 
+
+ align:start position:0%
+specific element development okay
+because I is so General I could see the
+
+ align:start position:0%
+because I is so General I could see the
+ 
+
+ align:start position:0%
+because I is so General I could see the
+AJ falling under ey my suggestion is
+
+ align:start position:0%
+AJ falling under ey my suggestion is
+ 
+
+ align:start position:0%
+AJ falling under ey my suggestion is
+please
+
+ align:start position:0%
+please
+ 
+
+ align:start position:0%
+please
+propose
+
+ align:start position:0%
+propose
+ 
+
+ align:start position:0%
+propose
+phrases
+
+ align:start position:0%
+phrases
+ 
+
+ align:start position:0%
+phrases
+okay did you say what you what you just
+
+ align:start position:0%
+okay did you say what you what you just
+ 
+
+ align:start position:0%
+okay did you say what you what you just
+said could you repeat what you just said
+
+ align:start position:0%
+said could you repeat what you just said
+ 
+
+ align:start position:0%
+said could you repeat what you just said
+in terms of combining them how can we
+
+ align:start position:0%
+in terms of combining them how can we
+ 
+
+ align:start position:0%
+in terms of combining them how can we
+engage communities in the in the use of
+
+ align:start position:0%
+engage communities in the in the use of
+ 
+
+ align:start position:0%
+engage communities in the in the use of
+reflective practice for their
+
+ align:start position:0%
+reflective practice for their
+ 
+
+ align:start position:0%
+reflective practice for their
+development
+
+ align:start position:0%
+development
+ 
+
+ align:start position:0%
+development
+yes
+
+ align:start position:0%
+yes
+ 
+
+ align:start position:0%
+yes
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+okay so does that take in
+
+ align:start position:0%
+okay so does that take in
+ 
+
+ align:start position:0%
+okay so does that take in
+I does that cover
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+I does that include I
+
+ align:start position:0%
+I does that include I
+ 
+
+ align:start position:0%
+I does that include I
+that no I I'm not trying
+
+ align:start position:0%
+that no I I'm not trying
+ 
+
+ align:start position:0%
+that no I I'm not trying
+to yes
+
+ align:start position:0%
+to yes
+ 
+
+ align:start position:0%
+to yes
+okay how can we engage communities to
+
+ align:start position:0%
+okay how can we engage communities to
+ 
+
+ align:start position:0%
+okay how can we engage communities to
+use effective practice for their
+
+ align:start position:0%
+use effective practice for their
+ 
+
+ align:start position:0%
+use effective practice for their
+development okay so can we put new new
+
+ align:start position:0%
+development okay so can we put new new
+ 
+
+ align:start position:0%
+development okay so can we put new new
+new letters for
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+okay now please select
+
+ align:start position:0%
+okay now please select
+ 
+
+ align:start position:0%
+okay now please select
+two of these that you would like to to
+
+ align:start position:0%
+two of these that you would like to to
+ 
+
+ align:start position:0%
+two of these that you would like to to
+answer first silently no as
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+always any two on the yes any
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+two she's eliminating the question that
+
+ align:start position:0%
+two she's eliminating the question that
+ 
+
+ align:start position:0%
+two she's eliminating the question that
+are already
+
+ align:start position:0%
+are already
+ 
+
+ align:start position:0%
+are already
+reformulated what numbers did the top so
+
+ align:start position:0%
+reformulated what numbers did the top so
+ 
+
+ align:start position:0%
+reformulated what numbers did the top so
+I'm leaving I okay cuz we never yeah
+
+ align:start position:0%
+I'm leaving I okay cuz we never yeah
+ 
+
+ align:start position:0%
+I'm leaving I okay cuz we never yeah
+in
+
+ align:start position:0%
+in
+ 
+
+ align:start position:0%
+in
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay can you repeat that c for me how to
+
+ align:start position:0%
+okay can you repeat that c for me how to
+ 
+
+ align:start position:0%
+okay can you repeat that c for me how to
+use effective
+
+ align:start position:0%
+use effective
+ 
+
+ align:start position:0%
+use effective
+practice skills to develop a closer
+
+ align:start position:0%
+practice skills to develop a closer
+ 
+
+ align:start position:0%
+practice skills to develop a closer
+relationship with the group I'm involved
+
+ align:start position:0%
+relationship with the group I'm involved
+ 
+
+ align:start position:0%
+relationship with the group I'm involved
+with
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay let's
+
+ align:start position:0%
+okay let's
+ 
+
+ align:start position:0%
+okay let's
+me your
+
+ align:start position:0%
+me your
+ 
+
+ align:start position:0%
+me your
+letters which one I want to work on huh
+
+ align:start position:0%
+letters which one I want to work on huh
+ 
+
+ align:start position:0%
+letters which one I want to work on huh
+just one two two
+
+ align:start position:0%
+just one two two
+ 
+
+ align:start position:0%
+just one two two
+okay I or
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+l i i
+
+ align:start position:0%
+l i i
+ 
+
+ align:start position:0%
+l i i
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+you um l or l or
+
+ align:start position:0%
+you um l or l or
+ 
+
+ align:start position:0%
+you um l or l or
+l l l you can have another choice if you
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+want I m I m I
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay I wrote down mc
+
+ align:start position:0%
+okay I wrote down mc
+ 
+
+ align:start position:0%
+okay I wrote down mc
+mc
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+CC okay I would say MC as well C and
+
+ align:start position:0%
+CC okay I would say MC as well C and
+ 
+
+ align:start position:0%
+CC okay I would say MC as well C and
+what m m okay H and I H and
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+I gosh all
+
+ align:start position:0%
+I gosh all
+ 
+
+ align:start position:0%
+I gosh all
+right l i l and
+
+ align:start position:0%
+right l i l and
+ 
+
+ align:start position:0%
+right l i l and
+i l
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+i m and I M and I I didn't realize M and
+
+ align:start position:0%
+i m and I M and I I didn't realize M and
+ 
+
+ align:start position:0%
+i m and I M and I I didn't realize M and
+I you um l and i l and i
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yes okay
+
+ align:start position:0%
+yes okay
+ 
+
+ align:start position:0%
+yes okay
+you okay so we
+
+ align:start position:0%
+you okay so we
+ 
+
+ align:start position:0%
+you okay so we
+have basically three questions
+
+ align:start position:0%
+have basically three questions
+ 
+
+ align:start position:0%
+have basically three questions
+no we can work with how we
+
+ align:start position:0%
+no we can work with how we
+ 
+
+ align:start position:0%
+no we can work with how we
+make common
+
+ align:start position:0%
+make common
+ 
+
+ align:start position:0%
+make common
+practice reflective practice a common
+
+ align:start position:0%
+practice reflective practice a common
+ 
+
+ align:start position:0%
+practice reflective practice a common
+practice to make it practical and
+
+ align:start position:0%
+practice to make it practical and
+ 
+
+ align:start position:0%
+practice to make it practical and
+natural natural no yes how we can engage
+
+ align:start position:0%
+natural natural no yes how we can engage
+ 
+
+ align:start position:0%
+natural natural no yes how we can engage
+communities to use reflective practice
+
+ align:start position:0%
+communities to use reflective practice
+ 
+
+ align:start position:0%
+communities to use reflective practice
+for their
+
+ align:start position:0%
+for their
+ 
+
+ align:start position:0%
+for their
+development and how do you
+
+ align:start position:0%
+development and how do you
+ 
+
+ align:start position:0%
+development and how do you
+do apply the knowledge about reflective
+
+ align:start position:0%
+do apply the knowledge about reflective
+ 
+
+ align:start position:0%
+do apply the knowledge about reflective
+practice at a larger scale
+
+ align:start position:0%
+practice at a larger scale
+ 
+
+ align:start position:0%
+practice at a larger scale
+okay we will write these questions in a
+
+ align:start position:0%
+okay we will write these questions in a
+ 
+
+ align:start position:0%
+okay we will write these questions in a
+sheet of
+
+ align:start position:0%
+sheet of
+ 
+
+ align:start position:0%
+sheet of
+paper
+
+ align:start position:0%
+paper
+ 
+
+ align:start position:0%
+paper
+and we we watch The Next
+
+ align:start position:0%
+and we we watch The Next
+ 
+
+ align:start position:0%
+and we we watch The Next
+[Music]
+
+ align:start position:0%
+[Music]
+ 
+
+ align:start position:0%
+[Music]
+Step the next step is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+[Applause]
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+[Music]
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+no try to remember the
+
+ align:start position:0%
+no try to remember the
+ 
+
+ align:start position:0%
+no try to remember the
+course okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and try
+
+ align:start position:0%
+and try
+ 
+
+ align:start position:0%
+and try
+to recover your critical
+
+ align:start position:0%
+to recover your critical
+ 
+
+ align:start position:0%
+to recover your critical
+moments are moments that you perceive as
+
+ align:start position:0%
+moments are moments that you perceive as
+ 
+
+ align:start position:0%
+moments are moments that you perceive as
+important because they have they
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+was positive or negative
+
+ align:start position:0%
+was positive or negative
+ 
+
+ align:start position:0%
+was positive or negative
+because they was meaningful for you in a
+
+ align:start position:0%
+because they was meaningful for you in a
+ 
+
+ align:start position:0%
+because they was meaningful for you in a
+positive way or negative
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+way not
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+necessarily in the in the
+
+ align:start position:0%
+necessarily in the in the
+ 
+
+ align:start position:0%
+necessarily in the in the
+CSE but related to the C you may have a
+
+ align:start position:0%
+CSE but related to the C you may have a
+ 
+
+ align:start position:0%
+CSE but related to the C you may have a
+critical moment in your house thinking
+
+ align:start position:0%
+critical moment in your house thinking
+ 
+
+ align:start position:0%
+critical moment in your house thinking
+about the
+
+ align:start position:0%
+about the
+ 
+
+ align:start position:0%
+about the
+curse okay or trying to make a task for
+
+ align:start position:0%
+curse okay or trying to make a task for
+ 
+
+ align:start position:0%
+curse okay or trying to make a task for
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+course okay but should be critical
+
+ align:start position:0%
+course okay but should be critical
+ 
+
+ align:start position:0%
+course okay but should be critical
+moments of your learning
+
+ align:start position:0%
+moments of your learning
+ 
+
+ align:start position:0%
+moments of your learning
+process relative to the related to
+
+ align:start position:0%
+process relative to the related to
+ 
+
+ align:start position:0%
+process relative to the related to
+reflective reflective
+
+ align:start position:0%
+reflective reflective
+ 
+
+ align:start position:0%
+reflective reflective
+prce okay then we should come up with
+
+ align:start position:0%
+prce okay then we should come up with
+ 
+
+ align:start position:0%
+prce okay then we should come up with
+you need to write eight eight eight yes
+
+ align:start position:0%
+you need to write eight eight eight yes
+ 
+
+ align:start position:0%
+you need to write eight eight eight yes
+the you have a with eight
+
+ align:start position:0%
+the you have a with eight
+ 
+
+ align:start position:0%
+the you have a with eight
+and as you can see first of all you will
+
+ align:start position:0%
+and as you can see first of all you will
+ 
+
+ align:start position:0%
+and as you can see first of all you will
+write the name of the critical moment
+
+ align:start position:0%
+write the name of the critical moment
+ 
+
+ align:start position:0%
+write the name of the critical moment
+after that a brief phrase describing
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+it and once you have all the critical
+
+ align:start position:0%
+it and once you have all the critical
+ 
+
+ align:start position:0%
+it and once you have all the critical
+moments already
+
+ align:start position:0%
+moments already
+ 
+
+ align:start position:0%
+moments already
+identified try to
+
+ align:start position:0%
+identified try to
+ 
+
+ align:start position:0%
+identified try to
+establish the level of importance for
+
+ align:start position:0%
+establish the level of importance for
+ 
+
+ align:start position:0%
+establish the level of importance for
+you let's work with two levels
+
+ align:start position:0%
+you let's work with two levels
+ 
+
+ align:start position:0%
+you let's work with two levels
+one and two and notice that on the Forum
+
+ align:start position:0%
+one and two and notice that on the Forum
+ 
+
+ align:start position:0%
+one and two and notice that on the Forum
+there's a for your
+
+ align:start position:0%
+there's a for your
+ 
+
+ align:start position:0%
+there's a for your
+name and what group you belong
+
+ align:start position:0%
+name and what group you belong
+ 
+
+ align:start position:0%
+name and what group you belong
+to we
+
+ align:start position:0%
+to we
+ 
+
+ align:start position:0%
+to we
+are just put a if you're an mCP student
+
+ align:start position:0%
+are just put a if you're an mCP student
+ 
+
+ align:start position:0%
+are just put a if you're an mCP student
+B if you're crcp affiliate and C if
+
+ align:start position:0%
+B if you're crcp affiliate and C if
+ 
+
+ align:start position:0%
+B if you're crcp affiliate and C if
+you're
+
+ align:start position:0%
+you're
+ 
+
+ align:start position:0%
+you're
+other
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay and then are we
+
+ align:start position:0%
+okay and then are we
+ 
+
+ align:start position:0%
+okay and then are we
+same yeah the same thing the same thing
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay the same
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+thing there's two priority levels yes
+
+ align:start position:0%
+thing there's two priority levels yes
+ 
+
+ align:start position:0%
+thing there's two priority levels yes
+which is the highest you decide which
+
+ align:start position:0%
+which is the highest you decide which
+ 
+
+ align:start position:0%
+which is the highest you decide which
+one you think that are more meaningful
+
+ align:start position:0%
+one you think that are more meaningful
+ 
+
+ align:start position:0%
+one you think that are more meaningful
+for your process no is a one a higher or
+
+ align:start position:0%
+for your process no is a one a higher or
+ 
+
+ align:start position:0%
+for your process no is a one a higher or
+two a
+
+ align:start position:0%
+two a
+ 
+
+ align:start position:0%
+two a
+Higher One higher in terms of what
+
+ align:start position:0%
+Higher One higher in terms of what
+ 
+
+ align:start position:0%
+Higher One higher in terms of what
+importance for you personally
+
+ align:start position:0%
+importance for you personally
+ 
+
+ align:start position:0%
+importance for you personally
+what do you think
+
+ align:start position:0%
+what do you think
+ 
+
+ align:start position:0%
+what do you think
+that
+
+ align:start position:0%
+that
+ 
+
+ align:start position:0%
+that
+ER were more meaningful for you and one
+
+ align:start position:0%
+ER were more meaningful for you and one
+ 
+
+ align:start position:0%
+ER were more meaningful for you and one
+is high one is high
+
+ align:start position:0%
+is high one is high
+ 
+
+ align:start position:0%
+is high one is high
+okay Sebastian I have a question yes can
+
+ align:start position:0%
+okay Sebastian I have a question yes can
+ 
+
+ align:start position:0%
+okay Sebastian I have a question yes can
+it be connected to your your
+
+ align:start position:0%
+it be connected to your your
+ 
+
+ align:start position:0%
+it be connected to your your
+professional
+
+ align:start position:0%
+professional
+ 
+
+ align:start position:0%
+professional
+work talk what you learn from the class
+
+ align:start position:0%
+work talk what you learn from the class
+ 
+
+ align:start position:0%
+work talk what you learn from the class
+can it be applied to experiences in
+
+ align:start position:0%
+can it be applied to experiences in
+ 
+
+ align:start position:0%
+can it be applied to experiences in
+community organizing is that okay I'm
+
+ align:start position:0%
+community organizing is that okay I'm
+ 
+
+ align:start position:0%
+community organizing is that okay I'm
+not quite clear enough it myself
+
+ align:start position:0%
+not quite clear enough it myself
+ 
+
+ align:start position:0%
+not quite clear enough it myself
+the timeline is critical moments for
+
+ align:start position:0%
+the timeline is critical moments for
+ 
+
+ align:start position:0%
+the timeline is critical moments for
+your learning process related to
+
+ align:start position:0%
+your learning process related to
+ 
+
+ align:start position:0%
+your learning process related to
+reflective practice okay over the last
+
+ align:start position:0%
+reflective practice okay over the last
+ 
+
+ align:start position:0%
+reflective practice okay over the last
+two weeks last two weeks or as long as
+
+ align:start position:0%
+two weeks last two weeks or as long as
+ 
+
+ align:start position:0%
+two weeks last two weeks or as long as
+I've been here and the days you have
+
+ align:start position:0%
+I've been here and the days you have
+ 
+
+ align:start position:0%
+I've been here and the days you have
+been here I think okay okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay and
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+you
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+write we have 10 days in the course okay
+
+ align:start position:0%
+write we have 10 days in the course okay
+ 
+
+ align:start position:0%
+write we have 10 days in the course okay
+day one day two 3 4
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+5 six for the
+
+ align:start position:0%
+5 six for the
+ 
+
+ align:start position:0%
+5 six for the
+weekend if you have some thing in the
+
+ align:start position:0%
+weekend if you have some thing in the
+ 
+
+ align:start position:0%
+weekend if you have some thing in the
+weekend okay okay
+
+ align:start position:0%
+weekend okay okay
+ 
+
+ align:start position:0%
+weekend okay okay
+7 8 9 10 and 11
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+10 days of the course and the weekend it
+
+ align:start position:0%
+10 days of the course and the weekend it
+ 
+
+ align:start position:0%
+10 days of the course and the weekend it
+may happen that you have some okay I'm
+
+ align:start position:0%
+may happen that you have some okay I'm
+ 
+
+ align:start position:0%
+may happen that you have some okay I'm
+not sure
+
+ align:start position:0%
+not sure
+ 
+
+ align:start position:0%
+not sure
+about but I need to give you this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+possibility your
+
+ align:start position:0%
+possibility your
+ 
+
+ align:start position:0%
+possibility your
+moment okay
+
+ align:start position:0%
+moment okay
+ 
+
+ align:start position:0%
+moment okay
+because this will help us
+
+ align:start position:0%
+because this will help us
+ 
+
+ align:start position:0%
+because this will help us
+to create the timeline
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay how long we have for this we
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+have 10 minutes
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so it's necessary to go
+
+ align:start position:0%
+so it's necessary to go
+ 
+
+ align:start position:0%
+so it's necessary to go
+through one phrase a brief
+
+ align:start position:0%
+through one phrase a brief
+ 
+
+ align:start position:0%
+through one phrase a brief
+phrase just enough you know exactly to
+
+ align:start position:0%
+phrase just enough you know exactly to
+ 
+
+ align:start position:0%
+phrase just enough you know exactly to
+know what is it about okay describe why
+
+ align:start position:0%
+know what is it about okay describe why
+ 
+
+ align:start position:0%
+know what is it about okay describe why
+it's an important event or just what it
+
+ align:start position:0%
+it's an important event or just what it
+ 
+
+ align:start position:0%
+it's an important event or just what it
+is what it is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay yes just what is it
+
+ align:start position:0%
+okay yes just what is it
+ 
+
+ align:start position:0%
+okay yes just what is it
+because ER if I go to
+
+ align:start position:0%
+because ER if I go to
+ 
+
+ align:start position:0%
+because ER if I go to
+tce I will
+
+ align:start position:0%
+tce I will
+ 
+
+ align:start position:0%
+tce I will
+open okay new level
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+of in some cases you may
+
+ align:start position:0%
+of in some cases you may
+ 
+
+ align:start position:0%
+of in some cases you may
+consider necessary to explain why you
+
+ align:start position:0%
+consider necessary to explain why you
+ 
+
+ align:start position:0%
+consider necessary to explain why you
+can use it but not the core content
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+you can go through your emotions in the
+
+ align:start position:0%
+you can go through your emotions in the
+ 
+
+ align:start position:0%
+you can go through your emotions in the
+course okay critical moments are highly
+
+ align:start position:0%
+course okay critical moments are highly
+ 
+
+ align:start position:0%
+course okay critical moments are highly
+related with our how we were f
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+speee
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+foreign
+
+ align:start position:0%
+foreign
+ 
+
+ align:start position:0%
+foreign
+speee
+
+ align:start position:0%
+speee
+ 
+
+ align:start position:0%
+speee
+spee fo
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+I BR my
+
+ align:start position:0%
+I BR my
+ 
+
+ align:start position:0%
+I BR my
+daughter
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yes experience with
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+English
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+India yes
+
+ align:start position:0%
+India yes
+ 
+
+ align:start position:0%
+India yes
+she's she had
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yes now
+
+ align:start position:0%
+yes now
+ 
+
+ align:start position:0%
+yes now
+she she's preparing
+
+ align:start position:0%
+she she's preparing
+ 
+
+ align:start position:0%
+she she's preparing
+for you to apply
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+psychology app
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+[Applause]
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay don't SPS too much time in just one
+
+ align:start position:0%
+okay don't SPS too much time in just one
+ 
+
+ align:start position:0%
+okay don't SPS too much time in just one
+critical moment once it's clear just go
+
+ align:start position:0%
+critical moment once it's clear just go
+ 
+
+ align:start position:0%
+critical moment once it's clear just go
+to the next one
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+don't try to be to be
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+precise you
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+what it's a process of retrieving of our
+
+ align:start position:0%
+what it's a process of retrieving of our
+ 
+
+ align:start position:0%
+what it's a process of retrieving of our
+memory
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+good
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+need
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+see be better
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+we
+
+ align:start position:0%
+we
+ 
+
+ align:start position:0%
+we
+are privity level and then here here the
+
+ align:start position:0%
+are privity level and then here here the
+ 
+
+ align:start position:0%
+are privity level and then here here the
+priority
+
+ align:start position:0%
+priority
+ 
+
+ align:start position:0%
+priority
+level
+
+ align:start position:0%
+level
+ 
+
+ align:start position:0%
+level
+oh the date the the day you can put in
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+place please because other people will
+
+ align:start position:0%
+place please because other people will
+ 
+
+ align:start position:0%
+place please because other people will
+read after
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+no it's okay you need to put the name
+
+ align:start position:0%
+no it's okay you need to put the name
+ 
+
+ align:start position:0%
+no it's okay you need to put the name
+but if
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+you what's
+
+ align:start position:0%
+you what's
+ 
+
+ align:start position:0%
+you what's
+this your own assumption this one
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+oh
+
+ align:start position:0%
+oh
+ 
+
+ align:start position:0%
+oh
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+yes
+
+ align:start position:0%
+yes
+ 
+
+ align:start position:0%
+yes
+events oh okay only EV small it's the
+
+ align:start position:0%
+events oh okay only EV small it's the
+ 
+
+ align:start position:0%
+events oh okay only EV small it's the
+tit of a newspaper oh okay like a
+
+ align:start position:0%
+tit of a newspaper oh okay like a
+ 
+
+ align:start position:0%
+tit of a newspaper oh okay like a
+headline head oh I
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+WR yes
+
+ align:start position:0%
+WR yes
+ 
+
+ align:start position:0%
+WR yes
+okay the name put the name of okay the
+
+ align:start position:0%
+okay the name put the name of okay the
+ 
+
+ align:start position:0%
+okay the name put the name of okay the
+begin of
+
+ align:start position:0%
+begin of
+ 
+
+ align:start position:0%
+begin of
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+okay so you need WR
+
+ align:start position:0%
+okay so you need WR
+ 
+
+ align:start position:0%
+okay so you need WR
+yes okay
+
+ align:start position:0%
+yes okay
+ 
+
+ align:start position:0%
+yes okay
+and and only for I think
+
+ align:start position:0%
+and and only for I think
+ 
+
+ align:start position:0%
+and and only for I think
+the only the days right well that's what
+
+ align:start position:0%
+the only the days right well that's what
+ 
+
+ align:start position:0%
+the only the days right well that's what
+I'm doing just four days I can
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay okay how
+
+ align:start position:0%
+okay okay how
+ 
+
+ align:start position:0%
+okay okay how
+many don't okay you
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+how many has
+
+ align:start position:0%
+how many has
+ 
+
+ align:start position:0%
+how many has
+it
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay choose your top
+
+ align:start position:0%
+okay choose your top
+ 
+
+ align:start position:0%
+okay choose your top
+four all right and when you say priority
+
+ align:start position:0%
+four all right and when you say priority
+ 
+
+ align:start position:0%
+four all right and when you say priority
+level you prioritize possible you mean
+
+ align:start position:0%
+level you prioritize possible you mean
+ 
+
+ align:start position:0%
+level you prioritize possible you mean
+from 1 to four on you pull up we didn't
+
+ align:start position:0%
+from 1 to four on you pull up we didn't
+ 
+
+ align:start position:0%
+from 1 to four on you pull up we didn't
+explain
+
+ align:start position:0%
+explain
+ 
+
+ align:start position:0%
+explain
+already you said pick one or two level
+
+ align:start position:0%
+already you said pick one or two level
+ 
+
+ align:start position:0%
+already you said pick one or two level
+one or
+
+ align:start position:0%
+one or
+ 
+
+ align:start position:0%
+one or
+two
+
+ align:start position:0%
+two
+ 
+
+ align:start position:0%
+two
+really
+
+ align:start position:0%
+really
+ 
+
+ align:start position:0%
+really
+great so here pick your top four that
+
+ align:start position:0%
+great so here pick your top four that
+ 
+
+ align:start position:0%
+great so here pick your top four that
+you'd like to share okay how do what are
+
+ align:start position:0%
+you'd like to share okay how do what are
+ 
+
+ align:start position:0%
+you'd like to share okay how do what are
+your
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+crer the ones that seem most um
+
+ align:start position:0%
+crer the ones that seem most um
+ 
+
+ align:start position:0%
+crer the ones that seem most um
+important for you in terms of your
+
+ align:start position:0%
+important for you in terms of your
+ 
+
+ align:start position:0%
+important for you in terms of your
+learning
+
+ align:start position:0%
+learning
+ 
+
+ align:start position:0%
+learning
+process that
+
+ align:start position:0%
+process that
+ 
+
+ align:start position:0%
+process that
+necessar the name of the critical
+
+ align:start position:0%
+necessar the name of the critical
+ 
+
+ align:start position:0%
+necessar the name of the critical
+moments I thought so but if not don't
+
+ align:start position:0%
+moments I thought so but if not don't
+ 
+
+ align:start position:0%
+moments I thought so but if not don't
+worry about it is the name of an
+
+ align:start position:0%
+worry about it is the name of an
+ 
+
+ align:start position:0%
+worry about it is the name of an
+event
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay it's similar
+
+ align:start position:0%
+okay it's similar
+ 
+
+ align:start position:0%
+okay it's similar
+to if I am reading a
+
+ align:start position:0%
+to if I am reading a
+ 
+
+ align:start position:0%
+to if I am reading a
+newspaper
+
+ align:start position:0%
+newspaper
+ 
+
+ align:start position:0%
+newspaper
+the the first
+
+ align:start position:0%
+the the first
+ 
+
+ align:start position:0%
+the the first
+line head the headline thing like this I
+
+ align:start position:0%
+line head the headline thing like this I
+ 
+
+ align:start position:0%
+line head the headline thing like this I
+I read and I know what is it about ch's
+
+ align:start position:0%
+I read and I know what is it about ch's
+ 
+
+ align:start position:0%
+I read and I know what is it about ch's
+your top four in terms of the
+
+ align:start position:0%
+your top four in terms of the
+ 
+
+ align:start position:0%
+your top four in terms of the
+significant in your learning process
+
+ align:start position:0%
+significant in your learning process
+ 
+
+ align:start position:0%
+significant in your learning process
+yeah this is the just the title of the
+
+ align:start position:0%
+yeah this is the just the title of the
+ 
+
+ align:start position:0%
+yeah this is the just the title of the
+critical moment people who writes I know
+
+ align:start position:0%
+critical moment people who writes I know
+ 
+
+ align:start position:0%
+critical moment people who writes I know
+here I'm going to
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+write right
+
+ align:start position:0%
+write right
+ 
+
+ align:start position:0%
+write right
+[Music]
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+one okay four for each
+
+ align:start position:0%
+one okay four for each
+ 
+
+ align:start position:0%
+one okay four for each
+one yes four
+
+ align:start position:0%
+one yes four
+ 
+
+ align:start position:0%
+one yes four
+four four critical moments yes four
+
+ align:start position:0%
+four four critical moments yes four
+ 
+
+ align:start position:0%
+four four critical moments yes four
+critical Moments One critical moment in
+
+ align:start position:0%
+critical Moments One critical moment in
+ 
+
+ align:start position:0%
+critical Moments One critical moment in
+each index card
+
+ align:start position:0%
+each index card
+ 
+
+ align:start position:0%
+each index card
+with big
+
+ align:start position:0%
+with big
+ 
+
+ align:start position:0%
+with big
+letters for helping us to read so here
+
+ align:start position:0%
+letters for helping us to read so here
+ 
+
+ align:start position:0%
+letters for helping us to read so here
+you have your new s mark
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+no no
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+here oh we were going to talk to you and
+
+ align:start position:0%
+here oh we were going to talk to you and
+ 
+
+ align:start position:0%
+here oh we were going to talk to you and
+ask you because you've been here
+
+ align:start position:0%
+ask you because you've been here
+ 
+
+ align:start position:0%
+ask you because you've been here
+days interesting for
+
+ align:start position:0%
+days interesting for
+ 
+
+ align:start position:0%
+days interesting for
+you that be
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+better veryt great
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah like you did
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+before this you put your
+
+ align:start position:0%
+before this you put your
+ 
+
+ align:start position:0%
+before this you put your
+name this the critical moment
+
+ align:start position:0%
+name this the critical moment
+ 
+
+ align:start position:0%
+name this the critical moment
+name your
+
+ align:start position:0%
+name your
+ 
+
+ align:start position:0%
+name your
+name plus or
+
+ align:start position:0%
+name plus or
+ 
+
+ align:start position:0%
+name plus or
+minus and the date like the day the DAT
+
+ align:start position:0%
+minus and the date like the day the DAT
+ 
+
+ align:start position:0%
+minus and the date like the day the DAT
+will be 0 1 2 3 4 5
+
+ align:start position:0%
+will be 0 1 2 3 4 5
+ 
+
+ align:start position:0%
+will be 0 1 2 3 4 5
+five
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay if you think that you have you had
+
+ align:start position:0%
+okay if you think that you have you had
+ 
+
+ align:start position:0%
+okay if you think that you have you had
+some critical moments before the course
+
+ align:start position:0%
+some critical moments before the course
+ 
+
+ align:start position:0%
+some critical moments before the course
+only
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+one no it's an event an event happens in
+
+ align:start position:0%
+one no it's an event an event happens in
+ 
+
+ align:start position:0%
+one no it's an event an event happens in
+one day this was the
+
+ align:start position:0%
+one day this was the
+ 
+
+ align:start position:0%
+one day this was the
+weekend Oh weekends included was only
+
+ align:start position:0%
+weekend Oh weekends included was only
+ 
+
+ align:start position:0%
+weekend Oh weekends included was only
+six weekend is only six ah I told them
+
+ align:start position:0%
+six weekend is only six ah I told them
+ 
+
+ align:start position:0%
+six weekend is only six ah I told them
+six for the weekend
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay no
+
+ align:start position:0%
+okay no
+ 
+
+ align:start position:0%
+okay no
+problem six okay but we need to change
+
+ align:start position:0%
+problem six okay but we need to change
+ 
+
+ align:start position:0%
+problem six okay but we need to change
+all the other on the other
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay the best
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+six
+
+ align:start position:0%
+six
+ 
+
+ align:start position:0%
+six
+yeah yeah
+
+ align:start position:0%
+yeah yeah
+ 
+
+ align:start position:0%
+yeah yeah
+seven so we 8 9 and we have until 11
+
+ align:start position:0%
+seven so we 8 9 and we have until 11
+ 
+
+ align:start position:0%
+seven so we 8 9 and we have until 11
+okay now six is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+weend remember EV has a
+
+ align:start position:0%
+weend remember EV has a
+ 
+
+ align:start position:0%
+weend remember EV has a
+date process may be
+
+ align:start position:0%
+date process may be
+ 
+
+ align:start position:0%
+date process may be
+longer but we are talking about
+
+ align:start position:0%
+longer but we are talking about
+ 
+
+ align:start position:0%
+longer but we are talking about
+events critical moments are
+
+ align:start position:0%
+events critical moments are
+ 
+
+ align:start position:0%
+events critical moments are
+moments not
+
+ align:start position:0%
+moments not
+ 
+
+ align:start position:0%
+moments not
+processes and now we from these eight we
+
+ align:start position:0%
+processes and now we from these eight we
+ 
+
+ align:start position:0%
+processes and now we from these eight we
+choose yeah yes you select the four more
+
+ align:start position:0%
+choose yeah yes you select the four more
+ 
+
+ align:start position:0%
+choose yeah yes you select the four more
+more important most important in terms
+
+ align:start position:0%
+more important most important in terms
+ 
+
+ align:start position:0%
+more important most important in terms
+of your learning process yes they're all
+
+ align:start position:0%
+of your learning process yes they're all
+ 
+
+ align:start position:0%
+of your learning process yes they're all
+going to be
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+one they will all be
+
+ align:start position:0%
+one they will all be
+ 
+
+ align:start position:0%
+one they will all be
+one all be number one yes yeah they
+
+ align:start position:0%
+one all be number one yes yeah they
+ 
+
+ align:start position:0%
+one all be number one yes yeah they
+should
+
+ align:start position:0%
+should
+ 
+
+ align:start position:0%
+should
+be of the highest priority if you have
+
+ align:start position:0%
+be of the highest priority if you have
+ 
+
+ align:start position:0%
+be of the highest priority if you have
+more than
+
+ align:start position:0%
+more than
+ 
+
+ align:start position:0%
+more than
+four okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+event is also process right H an event
+
+ align:start position:0%
+event is also process right H an event
+ 
+
+ align:start position:0%
+event is also process right H an event
+is part of a process it's a part of a
+
+ align:start position:0%
+is part of a process it's a part of a
+ 
+
+ align:start position:0%
+is part of a process it's a part of a
+process we will construct the
+
+ align:start position:0%
+process we will construct the
+ 
+
+ align:start position:0%
+process we will construct the
+process and in the process you select
+
+ align:start position:0%
+process and in the process you select
+ 
+
+ align:start position:0%
+process and in the process you select
+the key event the key event of your
+
+ align:start position:0%
+the key event the key event of your
+ 
+
+ align:start position:0%
+the key event the key event of your
+process will be the critical
+
+ align:start position:0%
+process will be the critical
+ 
+
+ align:start position:0%
+process will be the critical
+moment but critical moments are
+
+ align:start position:0%
+moment but critical moments are
+ 
+
+ align:start position:0%
+moment but critical moments are
+events okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+I suggest you to use three to six words
+
+ align:start position:0%
+I suggest you to use three to six words
+ 
+
+ align:start position:0%
+I suggest you to use three to six words
+for describing for naming the critical
+
+ align:start position:0%
+for describing for naming the critical
+ 
+
+ align:start position:0%
+for describing for naming the critical
+moment three to six
+
+ align:start position:0%
+moment three to six
+ 
+
+ align:start position:0%
+moment three to six
+words we make easier for us
+
+ align:start position:0%
+words we make easier for us
+ 
+
+ align:start position:0%
+words we make easier for us
+to to pick up the idea of the critical
+
+ align:start position:0%
+to to pick up the idea of the critical
+ 
+
+ align:start position:0%
+to to pick up the idea of the critical
+moment
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+for the index card in
+
+ align:start position:0%
+for the index card in
+ 
+
+ align:start position:0%
+for the index card in
+your sheet of paper you
+
+ align:start position:0%
+your sheet of paper you
+ 
+
+ align:start position:0%
+your sheet of paper you
+can be much
+
+ align:start position:0%
+can be much
+ 
+
+ align:start position:0%
+can be much
+more
+
+ align:start position:0%
+more
+ 
+
+ align:start position:0%
+more
+detated okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+for spee
+
+ align:start position:0%
+for spee
+ 
+
+ align:start position:0%
+for spee
+speech
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+speech
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+see okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+foree
+
+ align:start position:0%
+foree
+ 
+
+ align:start position:0%
+foree
+for okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+achievements areas of improvement of
+
+ align:start position:0%
+achievements areas of improvement of
+ 
+
+ align:start position:0%
+achievements areas of improvement of
+the is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+who is not have not finished
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yet those of you who are ready no no no
+
+ align:start position:0%
+yet those of you who are ready no no no
+ 
+
+ align:start position:0%
+yet those of you who are ready no no no
+we can wait everyone to finish
+
+ align:start position:0%
+we can wait everyone to finish
+ 
+
+ align:start position:0%
+we can wait everyone to finish
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+what four four okay the form more
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+[Music]
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+important have you finished we are just
+
+ align:start position:0%
+important have you finished we are just
+ 
+
+ align:start position:0%
+important have you finished we are just
+waiting for you put here I just
+
+ align:start position:0%
+waiting for you put here I just
+ 
+
+ align:start position:0%
+waiting for you put here I just
+yeah please at the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+back more beautiful with
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+thisan just the title the title just the
+
+ align:start position:0%
+thisan just the title the title just the
+ 
+
+ align:start position:0%
+thisan just the title the title just the
+title of the event of what happened this
+
+ align:start position:0%
+title of the event of what happened this
+ 
+
+ align:start position:0%
+title of the event of what happened this
+day okay
+
+ align:start position:0%
+day okay
+ 
+
+ align:start position:0%
+day okay
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+okay we I we know that some of you have
+
+ align:start position:0%
+okay we I we know that some of you have
+ 
+
+ align:start position:0%
+okay we I we know that some of you have
+already finished but we need to wait
+
+ align:start position:0%
+already finished but we need to wait
+ 
+
+ align:start position:0%
+already finished but we need to wait
+everyone to finish before to
+
+ align:start position:0%
+everyone to finish before to
+ 
+
+ align:start position:0%
+everyone to finish before to
+begin the next
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+step and remember to to put the date of
+
+ align:start position:0%
+step and remember to to put the date of
+ 
+
+ align:start position:0%
+step and remember to to put the date of
+the event in this
+
+ align:start position:0%
+the event in this
+ 
+
+ align:start position:0%
+the event in this
+way in
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this if it was before the course you put
+
+ align:start position:0%
+this if it was before the course you put
+ 
+
+ align:start position:0%
+this if it was before the course you put
+zero if it was in the first week of the
+
+ align:start position:0%
+zero if it was in the first week of the
+ 
+
+ align:start position:0%
+zero if it was in the first week of the
+course 1 2 3 4 or five if it was in the
+
+ align:start position:0%
+course 1 2 3 4 or five if it was in the
+ 
+
+ align:start position:0%
+course 1 2 3 4 or five if it was in the
+weekend six and the other days of the
+
+ align:start position:0%
+weekend six and the other days of the
+ 
+
+ align:start position:0%
+weekend six and the other days of the
+course are 7 8 9 10 and 11 okay one
+
+ align:start position:0%
+course are 7 8 9 10 and 11 okay one
+ 
+
+ align:start position:0%
+course are 7 8 9 10 and 11 okay one
+number more than the day of the
+
+ align:start position:0%
+number more than the day of the
+ 
+
+ align:start position:0%
+number more than the day of the
+course okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay and to maintain the number listen
+
+ align:start position:0%
+okay and to maintain the number listen
+ 
+
+ align:start position:0%
+okay and to maintain the number listen
+[Laughter]
+
+ align:start position:0%
+[Laughter]
+ 
+
+ align:start position:0%
+[Laughter]
+Le
+
+ align:start position:0%
+Le
+ 
+
+ align:start position:0%
+Le
+okay yeah
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+you
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+what Happ
+
+ align:start position:0%
+what Happ
+ 
+
+ align:start position:0%
+what Happ
+[Music]
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+right okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay you
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+it's fore
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+[Music]
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah okay let's begin who wants to
+
+ align:start position:0%
+yeah okay let's begin who wants to
+ 
+
+ align:start position:0%
+yeah okay let's begin who wants to
+start the person who each person will
+
+ align:start position:0%
+start the person who each person will
+ 
+
+ align:start position:0%
+start the person who each person will
+come here and
+
+ align:start position:0%
+come here and
+ 
+
+ align:start position:0%
+come here and
+we put the kit come on it and
+
+ align:start position:0%
+we put the kit come on it and
+ 
+
+ align:start position:0%
+we put the kit come on it and
+before it read for us and put the
+
+ align:start position:0%
+before it read for us and put the
+ 
+
+ align:start position:0%
+before it read for us and put the
+critical moment if it's positive in the
+
+ align:start position:0%
+critical moment if it's positive in the
+ 
+
+ align:start position:0%
+critical moment if it's positive in the
+upper side negative at the down side
+
+ align:start position:0%
+upper side negative at the down side
+ 
+
+ align:start position:0%
+upper side negative at the down side
+like the
+
+ align:start position:0%
+like the
+ 
+
+ align:start position:0%
+like the
+the last day the first day can you what
+
+ align:start position:0%
+the last day the first day can you what
+ 
+
+ align:start position:0%
+the last day the first day can you what
+to begin okay can I I suggest you to
+
+ align:start position:0%
+to begin okay can I I suggest you to
+ 
+
+ align:start position:0%
+to begin okay can I I suggest you to
+take your four with you and begin to
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Yes um one positive was the exercise
+
+ align:start position:0%
+Yes um one positive was the exercise
+ 
+
+ align:start position:0%
+Yes um one positive was the exercise
+around reframing that the problem
+
+ align:start position:0%
+around reframing that the problem
+ 
+
+ align:start position:0%
+around reframing that the problem
+statement
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay and then
+
+ align:start position:0%
+okay and then
+ 
+
+ align:start position:0%
+okay and then
+um I have to about the same exercise the
+
+ align:start position:0%
+um I have to about the same exercise the
+ 
+
+ align:start position:0%
+um I have to about the same exercise the
+whole reframing exercise
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh and then the assumptions
+
+ align:start position:0%
+uh and then the assumptions
+ 
+
+ align:start position:0%
+uh and then the assumptions
+um this means
+
+ align:start position:0%
+um this means
+ 
+
+ align:start position:0%
+um this means
+the the awareness that was raised of how
+
+ align:start position:0%
+the the awareness that was raised of how
+ 
+
+ align:start position:0%
+the the awareness that was raised of how
+many assumptions I operate from and how
+
+ align:start position:0%
+many assumptions I operate from and how
+ 
+
+ align:start position:0%
+many assumptions I operate from and how
+hard it is to defend
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+them and then the last one is um the
+
+ align:start position:0%
+them and then the last one is um the
+ 
+
+ align:start position:0%
+them and then the last one is um the
+mental modeling that we did of MIT and
+
+ align:start position:0%
+mental modeling that we did of MIT and
+ 
+
+ align:start position:0%
+mental modeling that we did of MIT and
+the realization of how I can see it
+
+ align:start position:0%
+the realization of how I can see it
+ 
+
+ align:start position:0%
+the realization of how I can see it
+being used to identify areas of conflict
+
+ align:start position:0%
+being used to identify areas of conflict
+ 
+
+ align:start position:0%
+being used to identify areas of conflict
+and agreement
+
+ align:start position:0%
+and agreement
+ 
+
+ align:start position:0%
+and agreement
+okay okay thank you that okay okay
+
+ align:start position:0%
+okay okay thank you that okay okay
+ 
+
+ align:start position:0%
+okay okay thank you that okay okay
+that's okay the this was Tuesday no no
+
+ align:start position:0%
+that's okay the this was Tuesday no no
+ 
+
+ align:start position:0%
+that's okay the this was Tuesday no no
+it the framing the original framing
+
+ align:start position:0%
+it the framing the original framing
+ 
+
+ align:start position:0%
+it the framing the original framing
+exercise was on Monday wasn't it Monday
+
+ align:start position:0%
+exercise was on Monday wasn't it Monday
+ 
+
+ align:start position:0%
+exercise was on Monday wasn't it Monday
+yeah yes okay okay yes yes correct the
+
+ align:start position:0%
+yeah yes okay okay yes yes correct the
+ 
+
+ align:start position:0%
+yeah yes okay okay yes yes correct the
+first exercise was framing okay the next
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+one
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay describing um mental models as
+
+ align:start position:0%
+okay describing um mental models as
+ 
+
+ align:start position:0%
+okay describing um mental models as
+possible
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and identifying features for framing I
+
+ align:start position:0%
+and identifying features for framing I
+ 
+
+ align:start position:0%
+and identifying features for framing I
+very
+
+ align:start position:0%
+very
+ 
+
+ align:start position:0%
+very
+critical day
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+eight and using assumptions being
+
+ align:start position:0%
+eight and using assumptions being
+ 
+
+ align:start position:0%
+eight and using assumptions being
+careful for writing questions using
+
+ align:start position:0%
+careful for writing questions using
+ 
+
+ align:start position:0%
+careful for writing questions using
+assumptions and your own values that
+
+ align:start position:0%
+assumptions and your own values that
+ 
+
+ align:start position:0%
+assumptions and your own values that
+exercise was
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+very okay thank you very
+
+ align:start position:0%
+very okay thank you very
+ 
+
+ align:start position:0%
+very okay thank you very
+much another person
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+walk
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+off day four um how stuck we are in our
+
+ align:start position:0%
+off day four um how stuck we are in our
+ 
+
+ align:start position:0%
+off day four um how stuck we are in our
+theories of or spoused and theories of
+
+ align:start position:0%
+theories of or spoused and theories of
+ 
+
+ align:start position:0%
+theories of or spoused and theories of
+action same day I had a so what
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+moment
+
+ align:start position:0%
+moment
+ 
+
+ align:start position:0%
+moment
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+H where's the modeling one the modeling
+
+ align:start position:0%
+H where's the modeling one the modeling
+ 
+
+ align:start position:0%
+H where's the modeling one the modeling
+five
+
+ align:start position:0%
+five
+ 
+
+ align:start position:0%
+five
+I enjoyed MIT model and my moment of
+
+ align:start position:0%
+I enjoyed MIT model and my moment of
+ 
+
+ align:start position:0%
+I enjoyed MIT model and my moment of
+looking at an MIT model as if I were a
+
+ align:start position:0%
+looking at an MIT model as if I were a
+ 
+
+ align:start position:0%
+looking at an MIT model as if I were a
+squirrel or if I were a bird help me
+
+ align:start position:0%
+squirrel or if I were a bird help me
+ 
+
+ align:start position:0%
+squirrel or if I were a bird help me
+give me an AA
+
+ align:start position:0%
+give me an AA
+ 
+
+ align:start position:0%
+give me an AA
+moment you know it's weird that I was
+
+ align:start position:0%
+moment you know it's weird that I was
+ 
+
+ align:start position:0%
+moment you know it's weird that I was
+probably on something that morning um
+
+ align:start position:0%
+probably on something that morning um
+ 
+
+ align:start position:0%
+probably on something that morning um
+and then 10 I guess yesterday yesterday
+
+ align:start position:0%
+and then 10 I guess yesterday yesterday
+ 
+
+ align:start position:0%
+and then 10 I guess yesterday yesterday
+yes um how we can combine some
+
+ align:start position:0%
+yes um how we can combine some
+ 
+
+ align:start position:0%
+yes um how we can combine some
+creativity with rationality ah okay
+
+ align:start position:0%
+creativity with rationality ah okay
+ 
+
+ align:start position:0%
+creativity with rationality ah okay
+thank you
+
+ align:start position:0%
+thank you
+ 
+
+ align:start position:0%
+thank you
+who you
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Le's a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+tape okay my first one was um the
+
+ align:start position:0%
+tape okay my first one was um the
+ 
+
+ align:start position:0%
+tape okay my first one was um the
+reframing
+
+ align:start position:0%
+reframing
+ 
+
+ align:start position:0%
+reframing
+exercise um the reframing yep which day
+
+ align:start position:0%
+exercise um the reframing yep which day
+ 
+
+ align:start position:0%
+exercise um the reframing yep which day
+was that was day
+
+ align:start position:0%
+was that was day
+ 
+
+ align:start position:0%
+was that was day
+four that was yeah that was that and
+
+ align:start position:0%
+four that was yeah that was that and
+ 
+
+ align:start position:0%
+four that was yeah that was that and
+justice for all my issue was this
+
+ align:start position:0%
+justice for all my issue was this
+ 
+
+ align:start position:0%
+justice for all my issue was this
+exercise
+
+ align:start position:0%
+exercise
+ 
+
+ align:start position:0%
+exercise
+um day
+
+ align:start position:0%
+um day
+ 
+
+ align:start position:0%
+um day
+10 positive uh revisiting concepts with
+
+ align:start position:0%
+10 positive uh revisiting concepts with
+ 
+
+ align:start position:0%
+10 positive uh revisiting concepts with
+reframing a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+frame um day
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+four um again well this is positive um
+
+ align:start position:0%
+four um again well this is positive um
+ 
+
+ align:start position:0%
+four um again well this is positive um
+day for yeah it was after going back and
+
+ align:start position:0%
+day for yeah it was after going back and
+ 
+
+ align:start position:0%
+day for yeah it was after going back and
+thinking about it um being able to
+
+ align:start position:0%
+thinking about it um being able to
+ 
+
+ align:start position:0%
+thinking about it um being able to
+separate the issue from the the purpose
+
+ align:start position:0%
+separate the issue from the the purpose
+ 
+
+ align:start position:0%
+separate the issue from the the purpose
+of the
+
+ align:start position:0%
+of the
+ 
+
+ align:start position:0%
+of the
+workshop um and day five mental
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+models you know my actualization how I
+
+ align:start position:0%
+models you know my actualization how I
+ 
+
+ align:start position:0%
+models you know my actualization how I
+actually use
+
+ align:start position:0%
+actually use
+ 
+
+ align:start position:0%
+actually use
+MIT my RO here at MIT okay thank you
+
+ align:start position:0%
+MIT my RO here at MIT okay thank you
+ 
+
+ align:start position:0%
+MIT my RO here at MIT okay thank you
+very much I will try to move this
+
+ align:start position:0%
+very much I will try to move this
+ 
+
+ align:start position:0%
+very much I will try to move this
+for able to make
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the next
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+one the first one about the mental
+
+ align:start position:0%
+one the first one about the mental
+ 
+
+ align:start position:0%
+one the first one about the mental
+models class um was actually never clear
+
+ align:start position:0%
+models class um was actually never clear
+ 
+
+ align:start position:0%
+models class um was actually never clear
+to me how you identify and build a
+
+ align:start position:0%
+to me how you identify and build a
+ 
+
+ align:start position:0%
+to me how you identify and build a
+mental
+
+ align:start position:0%
+mental
+ 
+
+ align:start position:0%
+mental
+model yes five
+
+ align:start position:0%
+model yes five
+ 
+
+ align:start position:0%
+model yes five
+for um the conceptualization
+
+ align:start position:0%
+for um the conceptualization
+ 
+
+ align:start position:0%
+for um the conceptualization
+class about related to the reframing it
+
+ align:start position:0%
+class about related to the reframing it
+ 
+
+ align:start position:0%
+class about related to the reframing it
+was
+
+ align:start position:0%
+was
+ 
+
+ align:start position:0%
+was
+actually was yesterday yesterday it was
+
+ align:start position:0%
+actually was yesterday yesterday it was
+ 
+
+ align:start position:0%
+actually was yesterday yesterday it was
+10 I think 10 right yes so it was
+
+ align:start position:0%
+10 I think 10 right yes so it was
+ 
+
+ align:start position:0%
+10 I think 10 right yes so it was
+positive
+
+ align:start position:0%
+positive
+ 
+
+ align:start position:0%
+positive
+um the reframing
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+class the class the first Monday this
+
+ align:start position:0%
+class the class the first Monday this
+ 
+
+ align:start position:0%
+class the class the first Monday this
+this week Monday yes is actually very
+
+ align:start position:0%
+this week Monday yes is actually very
+ 
+
+ align:start position:0%
+this week Monday yes is actually very
+enlightening also POS the importance of
+
+ align:start position:0%
+enlightening also POS the importance of
+ 
+
+ align:start position:0%
+enlightening also POS the importance of
+refraining yes okay and then I thought
+
+ align:start position:0%
+refraining yes okay and then I thought
+ 
+
+ align:start position:0%
+refraining yes okay and then I thought
+there was not enough reflective dialogue
+
+ align:start position:0%
+there was not enough reflective dialogue
+ 
+
+ align:start position:0%
+there was not enough reflective dialogue
+related to mental
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+models okay thank you very
+
+ align:start position:0%
+models okay thank you very
+ 
+
+ align:start position:0%
+models okay thank you very
+much
+
+ align:start position:0%
+much
+ 
+
+ align:start position:0%
+much
+okay please
+
+ align:start position:0%
+okay please
+ 
+
+ align:start position:0%
+okay please
+please
+
+ align:start position:0%
+please
+ 
+
+ align:start position:0%
+please
+uh no particular
+
+ align:start position:0%
+uh no particular
+ 
+
+ align:start position:0%
+uh no particular
+order
+
+ align:start position:0%
+order
+ 
+
+ align:start position:0%
+order
+um dissecting assumptions in the problem
+
+ align:start position:0%
+um dissecting assumptions in the problem
+ 
+
+ align:start position:0%
+um dissecting assumptions in the problem
+frame I thought was really helpful
+
+ align:start position:0%
+frame I thought was really helpful
+ 
+
+ align:start position:0%
+frame I thought was really helpful
+exercise um I also thought the framing
+
+ align:start position:0%
+exercise um I also thought the framing
+ 
+
+ align:start position:0%
+exercise um I also thought the framing
+the problem exercise was also very
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+good no one else mentioned this so far
+
+ align:start position:0%
+good no one else mentioned this so far
+ 
+
+ align:start position:0%
+good no one else mentioned this so far
+but I thought was really
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+cool help me help me get clear about
+
+ align:start position:0%
+cool help me help me get clear about
+ 
+
+ align:start position:0%
+cool help me help me get clear about
+type of knowledge and how think about
+
+ align:start position:0%
+type of knowledge and how think about
+ 
+
+ align:start position:0%
+type of knowledge and how think about
+issues and s the cycle
+
+ align:start position:0%
+issues and s the cycle
+ 
+
+ align:start position:0%
+issues and s the cycle
+okay yeah and uh I just like hearing
+
+ align:start position:0%
+okay yeah and uh I just like hearing
+ 
+
+ align:start position:0%
+okay yeah and uh I just like hearing
+about Sean's conception of reflective
+
+ align:start position:0%
+about Sean's conception of reflective
+ 
+
+ align:start position:0%
+about Sean's conception of reflective
+practice ah okay thank
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+you um so none of mine were about the
+
+ align:start position:0%
+you um so none of mine were about the
+ 
+
+ align:start position:0%
+you um so none of mine were about the
+content or the uh exercises they were
+
+ align:start position:0%
+content or the uh exercises they were
+ 
+
+ align:start position:0%
+content or the uh exercises they were
+mostly about
+
+ align:start position:0%
+mostly about
+ 
+
+ align:start position:0%
+mostly about
+just um stuff that got me here and got
+
+ align:start position:0%
+just um stuff that got me here and got
+ 
+
+ align:start position:0%
+just um stuff that got me here and got
+me motivated to be here
+
+ align:start position:0%
+me motivated to be here
+ 
+
+ align:start position:0%
+me motivated to be here
+yes so the first
+
+ align:start position:0%
+yes so the first
+ 
+
+ align:start position:0%
+yes so the first
+um first thing was just seeing the
+
+ align:start position:0%
+um first thing was just seeing the
+ 
+
+ align:start position:0%
+um first thing was just seeing the
+poster of the David
+
+ align:start position:0%
+poster of the David
+ 
+
+ align:start position:0%
+poster of the David
+score remembering that this is something
+
+ align:start position:0%
+score remembering that this is something
+ 
+
+ align:start position:0%
+score remembering that this is something
+I was interested in and that I should
+
+ align:start position:0%
+I was interested in and that I should
+ 
+
+ align:start position:0%
+I was interested in and that I should
+get up in the
+
+ align:start position:0%
+get up in the
+ 
+
+ align:start position:0%
+get up in the
+[Laughter]
+
+ align:start position:0%
+[Laughter]
+ 
+
+ align:start position:0%
+[Laughter]
+morning none of
+
+ align:start position:0%
+morning none of
+ 
+
+ align:start position:0%
+morning none of
+the then the second thing of related was
+
+ align:start position:0%
+the then the second thing of related was
+ 
+
+ align:start position:0%
+the then the second thing of related was
+I was going to do this GIS course and I
+
+ align:start position:0%
+I was going to do this GIS course and I
+ 
+
+ align:start position:0%
+I was going to do this GIS course and I
+was like oh may have to do that too and
+
+ align:start position:0%
+was like oh may have to do that too and
+ 
+
+ align:start position:0%
+was like oh may have to do that too and
+well maybe I can kind of do both and
+
+ align:start position:0%
+well maybe I can kind of do both and
+ 
+
+ align:start position:0%
+well maybe I can kind of do both and
+well you know kind of do an hour of this
+
+ align:start position:0%
+well you know kind of do an hour of this
+ 
+
+ align:start position:0%
+well you know kind of do an hour of this
+and then run off the other class and do
+
+ align:start position:0%
+and then run off the other class and do
+ 
+
+ align:start position:0%
+and then run off the other class and do
+this crazy thing and I was like no this
+
+ align:start position:0%
+this crazy thing and I was like no this
+ 
+
+ align:start position:0%
+this crazy thing and I was like no this
+is more interesting I'm going to skip
+
+ align:start position:0%
+is more interesting I'm going to skip
+ 
+
+ align:start position:0%
+is more interesting I'm going to skip
+the G course this is more important I
+
+ align:start position:0%
+the G course this is more important I
+ 
+
+ align:start position:0%
+the G course this is more important I
+can G
+
+ align:start position:0%
+can G
+ 
+
+ align:start position:0%
+can G
+anytime um which continued throughout
+
+ align:start position:0%
+anytime um which continued throughout
+ 
+
+ align:start position:0%
+anytime um which continued throughout
+the week by the way to the first GIS
+
+ align:start position:0%
+the week by the way to the first GIS
+ 
+
+ align:start position:0%
+the week by the way to the first GIS
+course then there were a number of other
+
+ align:start position:0%
+course then there were a number of other
+ 
+
+ align:start position:0%
+course then there were a number of other
+things that I thought I was going to do
+
+ align:start position:0%
+things that I thought I was going to do
+ 
+
+ align:start position:0%
+things that I thought I was going to do
+instead of this class and then I ended
+
+ align:start position:0%
+instead of this class and then I ended
+ 
+
+ align:start position:0%
+instead of this class and then I ended
+up still coming to every class I was
+
+ align:start position:0%
+up still coming to every class I was
+ 
+
+ align:start position:0%
+up still coming to every class I was
+going to go to New York for a long
+
+ align:start position:0%
+going to go to New York for a long
+ 
+
+ align:start position:0%
+going to go to New York for a long
+weekend that didn't happen no different
+
+ align:start position:0%
+weekend that didn't happen no different
+ 
+
+ align:start position:0%
+weekend that didn't happen no different
+things so that was sort of the first
+
+ align:start position:0%
+things so that was sort of the first
+ 
+
+ align:start position:0%
+things so that was sort of the first
+seed of like well you know this is more
+
+ align:start position:0%
+seed of like well you know this is more
+ 
+
+ align:start position:0%
+seed of like well you know this is more
+important um was that okay uh
+
+ align:start position:0%
+important um was that okay uh
+ 
+
+ align:start position:0%
+important um was that okay uh
+then
+
+ align:start position:0%
+then
+ 
+
+ align:start position:0%
+then
+um uh Claudia and sebastio invited me to
+
+ align:start position:0%
+um uh Claudia and sebastio invited me to
+ 
+
+ align:start position:0%
+um uh Claudia and sebastio invited me to
+come and do the mental mapping exercise
+
+ align:start position:0%
+come and do the mental mapping exercise
+ 
+
+ align:start position:0%
+come and do the mental mapping exercise
+with before class yes and so I learned a
+
+ align:start position:0%
+with before class yes and so I learned a
+ 
+
+ align:start position:0%
+with before class yes and so I learned a
+lot about new ways of thinking about um
+
+ align:start position:0%
+lot about new ways of thinking about um
+ 
+
+ align:start position:0%
+lot about new ways of thinking about um
+cognitive mapping and I just really
+
+ align:start position:0%
+cognitive mapping and I just really
+ 
+
+ align:start position:0%
+cognitive mapping and I just really
+enjoyed that that was really helpful for
+
+ align:start position:0%
+enjoyed that that was really helpful for
+ 
+
+ align:start position:0%
+enjoyed that that was really helpful for
+me just going thinking my own thinking
+
+ align:start position:0%
+me just going thinking my own thinking
+ 
+
+ align:start position:0%
+me just going thinking my own thinking
+the work that I'm involved with and then
+
+ align:start position:0%
+the work that I'm involved with and then
+ 
+
+ align:start position:0%
+the work that I'm involved with and then
+um I met with you guys after class and
+
+ align:start position:0%
+um I met with you guys after class and
+ 
+
+ align:start position:0%
+um I met with you guys after class and
+that was really
+
+ align:start position:0%
+that was really
+ 
+
+ align:start position:0%
+that was really
+um got me excited about stuff on the
+
+ align:start position:0%
+um got me excited about stuff on the
+ 
+
+ align:start position:0%
+um got me excited about stuff on the
+same day okay
+
+ align:start position:0%
+same day okay
+ 
+
+ align:start position:0%
+same day okay
+so just for not
+
+ align:start position:0%
+so just for not
+ 
+
+ align:start position:0%
+so just for not
+block okay let
+
+ align:start position:0%
+block okay let
+ 
+
+ align:start position:0%
+block okay let
+let here we we assume that I connected
+
+ align:start position:0%
+let here we we assume that I connected
+ 
+
+ align:start position:0%
+let here we we assume that I connected
+with okay thank
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+you so I'm really bad at remembering
+
+ align:start position:0%
+you so I'm really bad at remembering
+ 
+
+ align:start position:0%
+you so I'm really bad at remembering
+like what day it is
+
+ align:start position:0%
+like what day it is
+ 
+
+ align:start position:0%
+like what day it is
+so um you'll have to help me okay
+
+ align:start position:0%
+so um you'll have to help me okay
+ 
+
+ align:start position:0%
+so um you'll have to help me okay
+um I think it was day 10 learning that
+
+ align:start position:0%
+um I think it was day 10 learning that
+ 
+
+ align:start position:0%
+um I think it was day 10 learning that
+um the key is conceptual Innovation and
+
+ align:start position:0%
+um the key is conceptual Innovation and
+ 
+
+ align:start position:0%
+um the key is conceptual Innovation and
+not Technic day 10 day 10 conceptual
+
+ align:start position:0%
+not Technic day 10 day 10 conceptual
+ 
+
+ align:start position:0%
+not Technic day 10 day 10 conceptual
+Innovation and not and not technical
+
+ align:start position:0%
+Innovation and not and not technical
+ 
+
+ align:start position:0%
+Innovation and not and not technical
+Innovation yes
+
+ align:start position:0%
+Innovation yes
+ 
+
+ align:start position:0%
+Innovation yes
+okay um learning that lack of is not a
+
+ align:start position:0%
+okay um learning that lack of is not a
+ 
+
+ align:start position:0%
+okay um learning that lack of is not a
+way to State the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+problem
+
+ align:start position:0%
+problem
+ 
+
+ align:start position:0%
+problem
+the of
+
+ align:start position:0%
+the of
+ 
+
+ align:start position:0%
+the of
+money eight eight eight okay positive or
+
+ align:start position:0%
+money eight eight eight okay positive or
+ 
+
+ align:start position:0%
+money eight eight eight okay positive or
+negative
+
+ align:start position:0%
+negative
+ 
+
+ align:start position:0%
+negative
+it was it was positive and negative I
+
+ align:start position:0%
+it was it was positive and negative I
+ 
+
+ align:start position:0%
+it was it was positive and negative I
+was like oh okay it isn't you know so
+
+ align:start position:0%
+was like oh okay it isn't you know so
+ 
+
+ align:start position:0%
+was like oh okay it isn't you know so
+that was kind of negative CU I always
+
+ align:start position:0%
+that was kind of negative CU I always
+ 
+
+ align:start position:0%
+that was kind of negative CU I always
+just thought like I knew had a state of
+
+ align:start position:0%
+just thought like I knew had a state of
+ 
+
+ align:start position:0%
+just thought like I knew had a state of
+problem you
+
+ align:start position:0%
+problem you
+ 
+
+ align:start position:0%
+problem you
+know had a lot of lack of problem
+
+ align:start position:0%
+know had a lot of lack of problem
+ 
+
+ align:start position:0%
+know had a lot of lack of problem
+state but um but it was positive because
+
+ align:start position:0%
+state but um but it was positive because
+ 
+
+ align:start position:0%
+state but um but it was positive because
+now it forces me to think more you know
+
+ align:start position:0%
+now it forces me to think more you know
+ 
+
+ align:start position:0%
+now it forces me to think more you know
+when someone says what's the problem
+
+ align:start position:0%
+when someone says what's the problem
+ 
+
+ align:start position:0%
+when someone says what's the problem
+here now I have to think more so it was
+
+ align:start position:0%
+here now I have to think more so it was
+ 
+
+ align:start position:0%
+here now I have to think more so it was
+good kind
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+of um and then I like when um Cesar was
+
+ align:start position:0%
+of um and then I like when um Cesar was
+ 
+
+ align:start position:0%
+of um and then I like when um Cesar was
+telling us the story about
+
+ align:start position:0%
+telling us the story about
+ 
+
+ align:start position:0%
+telling us the story about
+Framingham the
+
+ align:start position:0%
+Framingham the
+ 
+
+ align:start position:0%
+Framingham the
+first
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+sevening about fing when told us the
+
+ align:start position:0%
+sevening about fing when told us the
+ 
+
+ align:start position:0%
+sevening about fing when told us the
+story 77 Monday 7 for he told the story
+
+ align:start position:0%
+story 77 Monday 7 for he told the story
+ 
+
+ align:start position:0%
+story 77 Monday 7 for he told the story
+for helping us to frame the situation of
+
+ align:start position:0%
+for helping us to frame the situation of
+ 
+
+ align:start position:0%
+for helping us to frame the situation of
+Framingham okay um you know I thought
+
+ align:start position:0%
+Framingham okay um you know I thought
+ 
+
+ align:start position:0%
+Framingham okay um you know I thought
+that was positive and negative like it
+
+ align:start position:0%
+that was positive and negative like it
+ 
+
+ align:start position:0%
+that was positive and negative like it
+was positive because I felt like I
+
+ align:start position:0%
+was positive because I felt like I
+ 
+
+ align:start position:0%
+was positive because I felt like I
+learned a lot about the situation and
+
+ align:start position:0%
+learned a lot about the situation and
+ 
+
+ align:start position:0%
+learned a lot about the situation and
+what went on and it was kind of negative
+
+ align:start position:0%
+what went on and it was kind of negative
+ 
+
+ align:start position:0%
+what went on and it was kind of negative
+cuz and I thought oh my gosh like these
+
+ align:start position:0%
+cuz and I thought oh my gosh like these
+ 
+
+ align:start position:0%
+cuz and I thought oh my gosh like these
+are some of the challenges and issues
+
+ align:start position:0%
+are some of the challenges and issues
+ 
+
+ align:start position:0%
+are some of the challenges and issues
+that I'm going to have to deal with like
+
+ align:start position:0%
+that I'm going to have to deal with like
+ 
+
+ align:start position:0%
+that I'm going to have to deal with like
+as a planner and
+
+ align:start position:0%
+as a planner and
+ 
+
+ align:start position:0%
+as a planner and
+so um and
+
+ align:start position:0%
+so um and
+ 
+
+ align:start position:0%
+so um and
+then the day um having the class disturb
+
+ align:start position:0%
+then the day um having the class disturb
+ 
+
+ align:start position:0%
+then the day um having the class disturb
+my assumptions when they question me on
+
+ align:start position:0%
+my assumptions when they question me on
+ 
+
+ align:start position:0%
+my assumptions when they question me on
+the race
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+exercise great that was four four so
+
+ align:start position:0%
+exercise great that was four four so
+ 
+
+ align:start position:0%
+exercise great that was four four so
+that was actually it started off as a
+
+ align:start position:0%
+that was actually it started off as a
+ 
+
+ align:start position:0%
+that was actually it started off as a
+negative CU I was like what are you
+
+ align:start position:0%
+negative CU I was like what are you
+ 
+
+ align:start position:0%
+negative CU I was like what are you
+doing like why are you you know I I
+
+ align:start position:0%
+doing like why are you you know I I
+ 
+
+ align:start position:0%
+doing like why are you you know I I
+don't I didn't really understand yeah
+
+ align:start position:0%
+don't I didn't really understand yeah
+ 
+
+ align:start position:0%
+don't I didn't really understand yeah
+you know as yet like what really the
+
+ align:start position:0%
+you know as yet like what really the
+ 
+
+ align:start position:0%
+you know as yet like what really the
+point of it was and so you get kind of
+
+ align:start position:0%
+point of it was and so you get kind of
+ 
+
+ align:start position:0%
+point of it was and so you get kind of
+defensive and like you have to like
+
+ align:start position:0%
+defensive and like you have to like
+ 
+
+ align:start position:0%
+defensive and like you have to like
+defend what you're saying but I mean now
+
+ align:start position:0%
+defend what you're saying but I mean now
+ 
+
+ align:start position:0%
+defend what you're saying but I mean now
+I think it's positive because I realize
+
+ align:start position:0%
+I think it's positive because I realize
+ 
+
+ align:start position:0%
+I think it's positive because I realize
+like it was you know this whole process
+
+ align:start position:0%
+like it was you know this whole process
+ 
+
+ align:start position:0%
+like it was you know this whole process
+of just uncovering our assumptions which
+
+ align:start position:0%
+of just uncovering our assumptions which
+ 
+
+ align:start position:0%
+of just uncovering our assumptions which
+I now see is a good thing we don't have
+
+ align:start position:0%
+I now see is a good thing we don't have
+ 
+
+ align:start position:0%
+I now see is a good thing we don't have
+to hold on
+
+ align:start position:0%
+to hold on
+ 
+
+ align:start position:0%
+to hold on
+okay we are oh
+
+ align:start position:0%
+okay we are oh
+ 
+
+ align:start position:0%
+okay we are oh
+you but what I try to do in the back
+
+ align:start position:0%
+you but what I try to do in the back
+ 
+
+ align:start position:0%
+you but what I try to do in the back
+which you will see later I I don't know
+
+ align:start position:0%
+which you will see later I I don't know
+ 
+
+ align:start position:0%
+which you will see later I I don't know
+if I remember the
+
+ align:start position:0%
+if I remember the
+ 
+
+ align:start position:0%
+if I remember the
+days
+
+ align:start position:0%
+days
+ 
+
+ align:start position:0%
+days
+but first I start with reflex and PR
+
+ align:start position:0%
+but first I start with reflex and PR
+ 
+
+ align:start position:0%
+but first I start with reflex and PR
+because I was not I had one idea about
+
+ align:start position:0%
+because I was not I had one idea about
+ 
+
+ align:start position:0%
+because I was not I had one idea about
+it and then when I got here and started
+
+ align:start position:0%
+it and then when I got here and started
+ 
+
+ align:start position:0%
+it and then when I got here and started
+to see it I was like I had to completely
+
+ align:start position:0%
+to see it I was like I had to completely
+ 
+
+ align:start position:0%
+to see it I was like I had to completely
+change my way of thinking what
+
+ align:start position:0%
+change my way of thinking what
+ 
+
+ align:start position:0%
+change my way of thinking what
+reflecting practice of you was so the
+
+ align:start position:0%
+reflecting practice of you was so the
+ 
+
+ align:start position:0%
+reflecting practice of you was so the
+positive is on the
+
+ align:start position:0%
+positive is on the
+ 
+
+ align:start position:0%
+positive is on the
+top okay when did you realize that
+
+ align:start position:0%
+top okay when did you realize that
+ 
+
+ align:start position:0%
+top okay when did you realize that
+yesterday no I think was a process was
+
+ align:start position:0%
+yesterday no I think was a process was
+ 
+
+ align:start position:0%
+yesterday no I think was a process was
+throughout the course and I felt every I
+
+ align:start position:0%
+throughout the course and I felt every I
+ 
+
+ align:start position:0%
+throughout the course and I felt every I
+was learning different you know in the
+
+ align:start position:0%
+was learning different you know in the
+ 
+
+ align:start position:0%
+was learning different you know in the
+process and then on the back I put a
+
+ align:start position:0%
+process and then on the back I put a
+ 
+
+ align:start position:0%
+process and then on the back I put a
+little bit about what was happening
+
+ align:start position:0%
+little bit about what was happening
+ 
+
+ align:start position:0%
+little bit about what was happening
+around that time and my community from
+
+ align:start position:0%
+around that time and my community from
+ 
+
+ align:start position:0%
+around that time and my community from
+him is what was discussing that was
+
+ align:start position:0%
+him is what was discussing that was
+ 
+
+ align:start position:0%
+him is what was discussing that was
+making me thinking of that so you can
+
+ align:start position:0%
+making me thinking of that so you can
+ 
+
+ align:start position:0%
+making me thinking of that so you can
+see that later uh and then I found the
+
+ align:start position:0%
+see that later uh and then I found the
+ 
+
+ align:start position:0%
+see that later uh and then I found the
+frame and reframe the and of course the
+
+ align:start position:0%
+frame and reframe the and of course the
+ 
+
+ align:start position:0%
+frame and reframe the and of course the
+frame and reframe was really what helped
+
+ align:start position:0%
+frame and reframe was really what helped
+ 
+
+ align:start position:0%
+frame and reframe was really what helped
+me to see what the reflection practicing
+
+ align:start position:0%
+me to see what the reflection practicing
+ 
+
+ align:start position:0%
+me to see what the reflection practicing
+was wasse because to trying to do the
+
+ align:start position:0%
+was wasse because to trying to do the
+ 
+
+ align:start position:0%
+was wasse because to trying to do the
+frame and reframe was when I could
+
+ align:start position:0%
+frame and reframe was when I could
+ 
+
+ align:start position:0%
+frame and reframe was when I could
+better understand what reflection to was
+
+ align:start position:0%
+better understand what reflection to was
+ 
+
+ align:start position:0%
+better understand what reflection to was
+does that make sense to you yes which
+
+ align:start position:0%
+does that make sense to you yes which
+ 
+
+ align:start position:0%
+does that make sense to you yes which
+day the day when we we we did a refra I
+
+ align:start position:0%
+day the day when we we we did a refra I
+ 
+
+ align:start position:0%
+day the day when we we we did a refra I
+think was it started on Monday that
+
+ align:start position:0%
+think was it started on Monday that
+ 
+
+ align:start position:0%
+think was it started on Monday that
+would really get into small what day was
+
+ align:start position:0%
+would really get into small what day was
+ 
+
+ align:start position:0%
+would really get into small what day was
+that Monday is here this is Monday it's
+
+ align:start position:0%
+that Monday is here this is Monday it's
+ 
+
+ align:start position:0%
+that Monday is here this is Monday it's
+positive or negative it's positive okay
+
+ align:start position:0%
+positive or negative it's positive okay
+ 
+
+ align:start position:0%
+positive or negative it's positive okay
+let's put I'm a own
+
+ align:start position:0%
+let's put I'm a own
+ 
+
+ align:start position:0%
+let's put I'm a own
+positive okay but actually the framing
+
+ align:start position:0%
+positive okay but actually the framing
+ 
+
+ align:start position:0%
+positive okay but actually the framing
+for her was
+
+ align:start position:0%
+for her was
+ 
+
+ align:start position:0%
+for her was
+Tuesday she was a listen she put Framing
+
+ align:start position:0%
+Tuesday she was a listen she put Framing
+ 
+
+ align:start position:0%
+Tuesday she was a listen she put Framing
+and reframing you need to
+
+ align:start position:0%
+and reframing you need to
+ 
+
+ align:start position:0%
+and reframing you need to
+choose okay uh Tuesday right Tuesday
+
+ align:start position:0%
+choose okay uh Tuesday right Tuesday
+ 
+
+ align:start position:0%
+choose okay uh Tuesday right Tuesday
+Tuesday was the when I we could size we
+
+ align:start position:0%
+Tuesday was the when I we could size we
+ 
+
+ align:start position:0%
+Tuesday was the when I we could size we
+analyze we analyze the framewor the
+
+ align:start position:0%
+analyze we analyze the framewor the
+ 
+
+ align:start position:0%
+analyze we analyze the framewor the
+frame it was Tuesday and we discover how
+
+ align:start position:0%
+frame it was Tuesday and we discover how
+ 
+
+ align:start position:0%
+frame it was Tuesday and we discover how
+it was stated how if the assumptions
+
+ align:start position:0%
+it was stated how if the assumptions
+ 
+
+ align:start position:0%
+it was stated how if the assumptions
+really were MH and the question of the
+
+ align:start position:0%
+really were MH and the question of the
+ 
+
+ align:start position:0%
+really were MH and the question of the
+lack of mhm no so that's Tuesday right
+
+ align:start position:0%
+lack of mhm no so that's Tuesday right
+ 
+
+ align:start position:0%
+lack of mhm no so that's Tuesday right
+Tu
+
+ align:start position:0%
+Tu
+ 
+
+ align:start position:0%
+Tu
+here and then Wednesday was when when we
+
+ align:start position:0%
+here and then Wednesday was when when we
+ 
+
+ align:start position:0%
+here and then Wednesday was when when we
+were looking at
+
+ align:start position:0%
+were looking at
+ 
+
+ align:start position:0%
+were looking at
+how coherent the models the frames okay
+
+ align:start position:0%
+how coherent the models the frames okay
+ 
+
+ align:start position:0%
+how coherent the models the frames okay
+I think that was the mental models and
+
+ align:start position:0%
+I think that was the mental models and
+ 
+
+ align:start position:0%
+I think that was the mental models and
+dialogue that was less so the theories
+
+ align:start position:0%
+dialogue that was less so the theories
+ 
+
+ align:start position:0%
+dialogue that was less so the theories
+in the concept of the ideas I think I
+
+ align:start position:0%
+in the concept of the ideas I think I
+ 
+
+ align:start position:0%
+in the concept of the ideas I think I
+got when I understood the frame and
+
+ align:start position:0%
+got when I understood the frame and
+ 
+
+ align:start position:0%
+got when I understood the frame and
+reframe was when I really could see the
+
+ align:start position:0%
+reframe was when I really could see the
+ 
+
+ align:start position:0%
+reframe was when I really could see the
+concept of the ideas and things coming
+
+ align:start position:0%
+concept of the ideas and things coming
+ 
+
+ align:start position:0%
+concept of the ideas and things coming
+together and I and I I think I'm very
+
+ align:start position:0%
+together and I and I I think I'm very
+ 
+
+ align:start position:0%
+together and I and I I think I'm very
+visual because I was really using this
+
+ align:start position:0%
+visual because I was really using this
+ 
+
+ align:start position:0%
+visual because I was really using this
+models that was learning here is the
+
+ align:start position:0%
+models that was learning here is the
+ 
+
+ align:start position:0%
+models that was learning here is the
+work I was doing in but I put it in the
+
+ align:start position:0%
+work I was doing in but I put it in the
+ 
+
+ align:start position:0%
+work I was doing in but I put it in the
+back of here you can take a look and I
+
+ align:start position:0%
+back of here you can take a look and I
+ 
+
+ align:start position:0%
+back of here you can take a look and I
+think I had a better understand it was
+
+ align:start position:0%
+think I had a better understand it was
+ 
+
+ align:start position:0%
+think I had a better understand it was
+more positive than it was negative when
+
+ align:start position:0%
+more positive than it was negative when
+ 
+
+ align:start position:0%
+more positive than it was negative when
+I was watching when I was here thinking
+
+ align:start position:0%
+I was watching when I was here thinking
+ 
+
+ align:start position:0%
+I was watching when I was here thinking
+I didn't feel as positive when I had to
+
+ align:start position:0%
+I didn't feel as positive when I had to
+ 
+
+ align:start position:0%
+I didn't feel as positive when I had to
+implement in a community so that was on
+
+ align:start position:0%
+implement in a community so that was on
+ 
+
+ align:start position:0%
+implement in a community so that was on
+Thursday
+
+ align:start position:0%
+Thursday
+ 
+
+ align:start position:0%
+Thursday
+Thursday yes here this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+night
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay and the ment Mar I think that was
+
+ align:start position:0%
+okay and the ment Mar I think that was
+ 
+
+ align:start position:0%
+okay and the ment Mar I think that was
+before the mental Mar and the difficult
+
+ align:start position:0%
+before the mental Mar and the difficult
+ 
+
+ align:start position:0%
+before the mental Mar and the difficult
+of the dialogue and to put in the St
+
+ align:start position:0%
+of the dialogue and to put in the St
+ 
+
+ align:start position:0%
+of the dialogue and to put in the St
+together that was very I really still
+
+ align:start position:0%
+together that was very I really still
+ 
+
+ align:start position:0%
+together that was very I really still
+not quite get that okay what is the
+
+ align:start position:0%
+not quite get that okay what is the
+ 
+
+ align:start position:0%
+not quite get that okay what is the
+mental model was I think that
+
+ align:start position:0%
+mental model was I think that
+ 
+
+ align:start position:0%
+mental model was I think that
+was five it's negative yeah okay okay
+
+ align:start position:0%
+was five it's negative yeah okay okay
+ 
+
+ align:start position:0%
+was five it's negative yeah okay okay
+thank you very much let's move it a bit
+
+ align:start position:0%
+thank you very much let's move it a bit
+ 
+
+ align:start position:0%
+thank you very much let's move it a bit
+for not to block the other one
+
+ align:start position:0%
+for not to block the other one
+ 
+
+ align:start position:0%
+for not to block the other one
+okay so we have here a brief description
+
+ align:start position:0%
+okay so we have here a brief description
+ 
+
+ align:start position:0%
+okay so we have here a brief description
+a very brief description of what
+
+ align:start position:0%
+a very brief description of what
+ 
+
+ align:start position:0%
+a very brief description of what
+happened
+
+ align:start position:0%
+happened
+ 
+
+ align:start position:0%
+happened
+what I would like to talk with you is
+
+ align:start position:0%
+what I would like to talk with you is
+ 
+
+ align:start position:0%
+what I would like to talk with you is
+can I sit
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+here
+
+ align:start position:0%
+here
+ 
+
+ align:start position:0%
+here
+okay thank
+
+ align:start position:0%
+okay thank
+ 
+
+ align:start position:0%
+okay thank
+you because if I I'm there I will be
+
+ align:start position:0%
+you because if I I'm there I will be
+ 
+
+ align:start position:0%
+you because if I I'm there I will be
+blocking you okay let's
+
+ align:start position:0%
+blocking you okay let's
+ 
+
+ align:start position:0%
+blocking you okay let's
+see
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+first
+
+ align:start position:0%
+first
+ 
+
+ align:start position:0%
+first
+ER we have the perceptions of all the
+
+ align:start position:0%
+ER we have the perceptions of all the
+ 
+
+ align:start position:0%
+ER we have the perceptions of all the
+participants during the course
+
+ align:start position:0%
+participants during the course
+ 
+
+ align:start position:0%
+participants during the course
+what are the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+main the mean find this what are you
+
+ align:start position:0%
+main the mean find this what are you
+ 
+
+ align:start position:0%
+main the mean find this what are you
+seeing in
+
+ align:start position:0%
+seeing in
+ 
+
+ align:start position:0%
+seeing in
+this what can you see in this group of
+
+ align:start position:0%
+this what can you see in this group of
+ 
+
+ align:start position:0%
+this what can you see in this group of
+critical
+
+ align:start position:0%
+critical
+ 
+
+ align:start position:0%
+critical
+moments yes it it seems like to me that
+
+ align:start position:0%
+moments yes it it seems like to me that
+ 
+
+ align:start position:0%
+moments yes it it seems like to me that
+uh people rated the the highest um
+
+ align:start position:0%
+uh people rated the the highest um
+ 
+
+ align:start position:0%
+uh people rated the the highest um
+things that
+
+ align:start position:0%
+things that
+ 
+
+ align:start position:0%
+things that
+were of particular relevance to them
+
+ align:start position:0%
+were of particular relevance to them
+ 
+
+ align:start position:0%
+were of particular relevance to them
+um in their work so like for me the
+
+ align:start position:0%
+um in their work so like for me the
+ 
+
+ align:start position:0%
+um in their work so like for me the
+mental mapping was really important just
+
+ align:start position:0%
+mental mapping was really important just
+ 
+
+ align:start position:0%
+mental mapping was really important just
+in terms of what I what I've been doing
+
+ align:start position:0%
+in terms of what I what I've been doing
+ 
+
+ align:start position:0%
+in terms of what I what I've been doing
+for my research and I think for a lot of
+
+ align:start position:0%
+for my research and I think for a lot of
+ 
+
+ align:start position:0%
+for my research and I think for a lot of
+people throughout the course I keep
+
+ align:start position:0%
+people throughout the course I keep
+ 
+
+ align:start position:0%
+people throughout the course I keep
+hearing that reframing is something that
+
+ align:start position:0%
+hearing that reframing is something that
+ 
+
+ align:start position:0%
+hearing that reframing is something that
+people are interested in and so it's not
+
+ align:start position:0%
+people are interested in and so it's not
+ 
+
+ align:start position:0%
+people are interested in and so it's not
+terribly surprising to me that a lot of
+
+ align:start position:0%
+terribly surprising to me that a lot of
+ 
+
+ align:start position:0%
+terribly surprising to me that a lot of
+people really congregated around the
+
+ align:start position:0%
+people really congregated around the
+ 
+
+ align:start position:0%
+people really congregated around the
+reframing exercise as being the most
+
+ align:start position:0%
+reframing exercise as being the most
+ 
+
+ align:start position:0%
+reframing exercise as being the most
+important part because it's something
+
+ align:start position:0%
+important part because it's something
+ 
+
+ align:start position:0%
+important part because it's something
+that they already felt was valuable and
+
+ align:start position:0%
+that they already felt was valuable and
+ 
+
+ align:start position:0%
+that they already felt was valuable and
+necessary for their work and I feel like
+
+ align:start position:0%
+necessary for their work and I feel like
+ 
+
+ align:start position:0%
+necessary for their work and I feel like
+the negative ones are largely when
+
+ align:start position:0%
+the negative ones are largely when
+ 
+
+ align:start position:0%
+the negative ones are largely when
+people weren't quite
+
+ align:start position:0%
+people weren't quite
+ 
+
+ align:start position:0%
+people weren't quite
+understanding why why to do the exercise
+
+ align:start position:0%
+understanding why why to do the exercise
+ 
+
+ align:start position:0%
+understanding why why to do the exercise
+or or what the concept was that they
+
+ align:start position:0%
+or or what the concept was that they
+ 
+
+ align:start position:0%
+or or what the concept was that they
+were supposed to be getting it's when
+
+ align:start position:0%
+were supposed to be getting it's when
+ 
+
+ align:start position:0%
+were supposed to be getting it's when
+there was some confusion or a sense of
+
+ align:start position:0%
+there was some confusion or a sense of
+ 
+
+ align:start position:0%
+there was some confusion or a sense of
+um that they weren't like they weren't
+
+ align:start position:0%
+um that they weren't like they weren't
+ 
+
+ align:start position:0%
+um that they weren't like they weren't
+getting the material perhaps but those
+
+ align:start position:0%
+getting the material perhaps but those
+ 
+
+ align:start position:0%
+getting the material perhaps but those
+seem like maybe a lot of the
+
+ align:start position:0%
+seem like maybe a lot of the
+ 
+
+ align:start position:0%
+seem like maybe a lot of the
+problems okay thank you another
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+comment
+
+ align:start position:0%
+comment
+ 
+
+ align:start position:0%
+comment
+yes uh it seems like the turning point
+
+ align:start position:0%
+yes uh it seems like the turning point
+ 
+
+ align:start position:0%
+yes uh it seems like the turning point
+for people was the end of last week in
+
+ align:start position:0%
+for people was the end of last week in
+ 
+
+ align:start position:0%
+for people was the end of last week in
+the beginning of the second week because
+
+ align:start position:0%
+the beginning of the second week because
+ 
+
+ align:start position:0%
+the beginning of the second week because
+there's a lot of a lot of negative but
+
+ align:start position:0%
+there's a lot of a lot of negative but
+ 
+
+ align:start position:0%
+there's a lot of a lot of negative but
+also a lot of positive within that that
+
+ align:start position:0%
+also a lot of positive within that that
+ 
+
+ align:start position:0%
+also a lot of positive within that that
+frame of time between Friday and Monday
+
+ align:start position:0%
+frame of time between Friday and Monday
+ 
+
+ align:start position:0%
+frame of time between Friday and Monday
+I mean the beginning of the second week
+
+ align:start position:0%
+I mean the beginning of the second week
+ 
+
+ align:start position:0%
+I mean the beginning of the second week
+I think it's an
+
+ align:start position:0%
+I think it's an
+ 
+
+ align:start position:0%
+I think it's an
+important um
+
+ align:start position:0%
+important um
+ 
+
+ align:start position:0%
+important um
+mhm there there was an important change
+
+ align:start position:0%
+mhm there there was an important change
+ 
+
+ align:start position:0%
+mhm there there was an important change
+within people's identification of
+
+ align:start position:0%
+within people's identification of
+ 
+
+ align:start position:0%
+within people's identification of
+critical moments either if they are
+
+ align:start position:0%
+critical moments either if they are
+ 
+
+ align:start position:0%
+critical moments either if they are
+positive or negative mhm building on
+
+ align:start position:0%
+positive or negative mhm building on
+ 
+
+ align:start position:0%
+positive or negative mhm building on
+that point it seems like the first first
+
+ align:start position:0%
+that point it seems like the first first
+ 
+
+ align:start position:0%
+that point it seems like the first first
+couple of days people kind of maybe
+
+ align:start position:0%
+couple of days people kind of maybe
+ 
+
+ align:start position:0%
+couple of days people kind of maybe
+weren't getting it or everyone's kind of
+
+ align:start position:0%
+weren't getting it or everyone's kind of
+ 
+
+ align:start position:0%
+weren't getting it or everyone's kind of
+getting their feet wet slow sorry the
+
+ align:start position:0%
+getting their feet wet slow sorry the
+ 
+
+ align:start position:0%
+getting their feet wet slow sorry the
+first couple of days everyone sort of
+
+ align:start position:0%
+first couple of days everyone sort of
+ 
+
+ align:start position:0%
+first couple of days everyone sort of
+starting to get their feet wet and you
+
+ align:start position:0%
+starting to get their feet wet and you
+ 
+
+ align:start position:0%
+starting to get their feet wet and you
+know they're sort of just trying to
+
+ align:start position:0%
+know they're sort of just trying to
+ 
+
+ align:start position:0%
+know they're sort of just trying to
+figure stuff out and then we started to
+
+ align:start position:0%
+figure stuff out and then we started to
+ 
+
+ align:start position:0%
+figure stuff out and then we started to
+employ it on the fourth and fifth day
+
+ align:start position:0%
+employ it on the fourth and fifth day
+ 
+
+ align:start position:0%
+employ it on the fourth and fifth day
+and people sort of struggled with that
+
+ align:start position:0%
+and people sort of struggled with that
+ 
+
+ align:start position:0%
+and people sort of struggled with that
+and had a hard time so we had a mix of
+
+ align:start position:0%
+and had a hard time so we had a mix of
+ 
+
+ align:start position:0%
+and had a hard time so we had a mix of
+reactions but then in the second week
+
+ align:start position:0%
+reactions but then in the second week
+ 
+
+ align:start position:0%
+reactions but then in the second week
+maybe people started to come together
+
+ align:start position:0%
+maybe people started to come together
+ 
+
+ align:start position:0%
+maybe people started to come together
+and understand better and really kind of
+
+ align:start position:0%
+and understand better and really kind of
+ 
+
+ align:start position:0%
+and understand better and really kind of
+get it at a deeper Lev maybe which then
+
+ align:start position:0%
+get it at a deeper Lev maybe which then
+ 
+
+ align:start position:0%
+get it at a deeper Lev maybe which then
+made it make more sense okay thank
+
+ align:start position:0%
+made it make more sense okay thank
+ 
+
+ align:start position:0%
+made it make more sense okay thank
+you other
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+comment if you want we can compare your
+
+ align:start position:0%
+comment if you want we can compare your
+ 
+
+ align:start position:0%
+comment if you want we can compare your
+own experience with the experience of
+
+ align:start position:0%
+own experience with the experience of
+ 
+
+ align:start position:0%
+own experience with the experience of
+the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+group you
+
+ align:start position:0%
+group you
+ 
+
+ align:start position:0%
+group you
+can talk about surprises you have
+
+ align:start position:0%
+can talk about surprises you have
+ 
+
+ align:start position:0%
+can talk about surprises you have
+looking
+
+ align:start position:0%
+looking
+ 
+
+ align:start position:0%
+looking
+this distribution of critical moments
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+or question you have in our minds Esra I
+
+ align:start position:0%
+or question you have in our minds Esra I
+ 
+
+ align:start position:0%
+or question you have in our minds Esra I
+was just wondering how much um
+
+ align:start position:0%
+was just wondering how much um
+ 
+
+ align:start position:0%
+was just wondering how much um
+background of other things that are
+
+ align:start position:0%
+background of other things that are
+ 
+
+ align:start position:0%
+background of other things that are
+going on our lives that's where we put
+
+ align:start position:0%
+going on our lives that's where we put
+ 
+
+ align:start position:0%
+going on our lives that's where we put
+critical moments and how we we can talk
+
+ align:start position:0%
+critical moments and how we we can talk
+ 
+
+ align:start position:0%
+critical moments and how we we can talk
+about this later because it should open
+
+ align:start position:0%
+about this later because it should open
+ 
+
+ align:start position:0%
+about this later because it should open
+a new vein of conversation okay let's
+
+ align:start position:0%
+a new vein of conversation okay let's
+ 
+
+ align:start position:0%
+a new vein of conversation okay let's
+see just the course this
+
+ align:start position:0%
+see just the course this
+ 
+
+ align:start position:0%
+see just the course this
+moment how we live live the course yes
+
+ align:start position:0%
+moment how we live live the course yes
+ 
+
+ align:start position:0%
+moment how we live live the course yes
+Rec confirms what I had seen SE in the
+
+ align:start position:0%
+Rec confirms what I had seen SE in the
+ 
+
+ align:start position:0%
+Rec confirms what I had seen SE in the
+other critical moments exercise that we
+
+ align:start position:0%
+other critical moments exercise that we
+ 
+
+ align:start position:0%
+other critical moments exercise that we
+did and the one that was done at at care
+
+ align:start position:0%
+did and the one that was done at at care
+ 
+
+ align:start position:0%
+did and the one that was done at at care
+that the groups critical moments tend to
+
+ align:start position:0%
+that the groups critical moments tend to
+ 
+
+ align:start position:0%
+that the groups critical moments tend to
+Cluster in the same areas it's still
+
+ align:start position:0%
+Cluster in the same areas it's still
+ 
+
+ align:start position:0%
+Cluster in the same areas it's still
+interesting to me that you know working
+
+ align:start position:0%
+interesting to me that you know working
+ 
+
+ align:start position:0%
+interesting to me that you know working
+totally independently that it comes out
+
+ align:start position:0%
+totally independently that it comes out
+ 
+
+ align:start position:0%
+totally independently that it comes out
+that way and now it's it's still 100% of
+
+ align:start position:0%
+that way and now it's it's still 100% of
+ 
+
+ align:start position:0%
+that way and now it's it's still 100% of
+of the three little experiences I've
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+had okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yes yes yes thank you about I agree with
+
+ align:start position:0%
+yes yes yes thank you about I agree with
+ 
+
+ align:start position:0%
+yes yes yes thank you about I agree with
+was Chris said we were just trying to
+
+ align:start position:0%
+was Chris said we were just trying to
+ 
+
+ align:start position:0%
+was Chris said we were just trying to
+understand what was going
+
+ align:start position:0%
+understand what was going
+ 
+
+ align:start position:0%
+understand what was going
+on I I think it also relates to when we
+
+ align:start position:0%
+on I I think it also relates to when we
+ 
+
+ align:start position:0%
+on I I think it also relates to when we
+began to do more
+
+ align:start position:0%
+began to do more
+ 
+
+ align:start position:0%
+began to do more
+involved
+
+ align:start position:0%
+involved
+ 
+
+ align:start position:0%
+involved
+um involving exercises where we all
+
+ align:start position:0%
+um involving exercises where we all
+ 
+
+ align:start position:0%
+um involving exercises where we all
+participated at a greater and had a
+
+ align:start position:0%
+participated at a greater and had a
+ 
+
+ align:start position:0%
+participated at a greater and had a
+little bit more indepth discussions
+
+ align:start position:0%
+little bit more indepth discussions
+ 
+
+ align:start position:0%
+little bit more indepth discussions
+about what we were doing it involved us
+
+ align:start position:0%
+about what we were doing it involved us
+ 
+
+ align:start position:0%
+about what we were doing it involved us
+more therefore my assumption would be
+
+ align:start position:0%
+more therefore my assumption would be
+ 
+
+ align:start position:0%
+more therefore my assumption would be
+that that what caused those to be a
+
+ align:start position:0%
+that that what caused those to be a
+ 
+
+ align:start position:0%
+that that what caused those to be a
+little bit more critical okay at the
+
+ align:start position:0%
+little bit more critical okay at the
+ 
+
+ align:start position:0%
+little bit more critical okay at the
+when at the outset I didn't feel very
+
+ align:start position:0%
+when at the outset I didn't feel very
+ 
+
+ align:start position:0%
+when at the outset I didn't feel very
+involved okay and I'm realizing that I
+
+ align:start position:0%
+involved okay and I'm realizing that I
+ 
+
+ align:start position:0%
+involved okay and I'm realizing that I
+made my my critical moments were more
+
+ align:start position:0%
+made my my critical moments were more
+ 
+
+ align:start position:0%
+made my my critical moments were more
+like aha positives but perhaps I should
+
+ align:start position:0%
+like aha positives but perhaps I should
+ 
+
+ align:start position:0%
+like aha positives but perhaps I should
+have put one that went the the whole
+
+ align:start position:0%
+have put one that went the the whole
+ 
+
+ align:start position:0%
+have put one that went the the whole
+length because I still felt that we
+
+ align:start position:0%
+length because I still felt that we
+ 
+
+ align:start position:0%
+length because I still felt that we
+missed opportunities to to do what we
+
+ align:start position:0%
+missed opportunities to to do what we
+ 
+
+ align:start position:0%
+missed opportunities to to do what we
+did yesterday and have a group
+
+ align:start position:0%
+did yesterday and have a group
+ 
+
+ align:start position:0%
+did yesterday and have a group
+discussion where others could say how it
+
+ align:start position:0%
+discussion where others could say how it
+ 
+
+ align:start position:0%
+discussion where others could say how it
+would how they were thinking about it in
+
+ align:start position:0%
+would how they were thinking about it in
+ 
+
+ align:start position:0%
+would how they were thinking about it in
+their own
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+lives
+
+ align:start position:0%
+lives
+ 
+
+ align:start position:0%
+lives
+okay she
+
+ align:start position:0%
+okay she
+ 
+
+ align:start position:0%
+okay she
+after I totally agree with her is when
+
+ align:start position:0%
+after I totally agree with her is when
+ 
+
+ align:start position:0%
+after I totally agree with her is when
+we I agree with her because that
+
+ align:start position:0%
+we I agree with her because that
+ 
+
+ align:start position:0%
+we I agree with her because that
+particular time Friday was the first day
+
+ align:start position:0%
+particular time Friday was the first day
+ 
+
+ align:start position:0%
+particular time Friday was the first day
+and you had um breakout groups and we
+
+ align:start position:0%
+and you had um breakout groups and we
+ 
+
+ align:start position:0%
+and you had um breakout groups and we
+had a lot of discussion and a lot of
+
+ align:start position:0%
+had a lot of discussion and a lot of
+ 
+
+ align:start position:0%
+had a lot of discussion and a lot of
+interaction that Friday and Monday and I
+
+ align:start position:0%
+interaction that Friday and Monday and I
+ 
+
+ align:start position:0%
+interaction that Friday and Monday and I
+think that touched on that's what most
+
+ align:start position:0%
+think that touched on that's what most
+ 
+
+ align:start position:0%
+think that touched on that's what most
+of us really remember and I think um
+
+ align:start position:0%
+of us really remember and I think um
+ 
+
+ align:start position:0%
+of us really remember and I think um
+Tuesday we also had a break out we have
+
+ align:start position:0%
+Tuesday we also had a break out we have
+ 
+
+ align:start position:0%
+Tuesday we also had a break out we have
+groups exercises we all
+
+ align:start position:0%
+groups exercises we all
+ 
+
+ align:start position:0%
+groups exercises we all
+interacted back and shared deers and um
+
+ align:start position:0%
+interacted back and shared deers and um
+ 
+
+ align:start position:0%
+interacted back and shared deers and um
+I know that's what goes in the moment
+
+ align:start position:0%
+I know that's what goes in the moment
+ 
+
+ align:start position:0%
+I know that's what goes in the moment
+particular days okay thank you yes es uh
+
+ align:start position:0%
+particular days okay thank you yes es uh
+ 
+
+ align:start position:0%
+particular days okay thank you yes es uh
+I was just going to say that it seems
+
+ align:start position:0%
+I was just going to say that it seems
+ 
+
+ align:start position:0%
+I was just going to say that it seems
+like the days that people remember the
+
+ align:start position:0%
+like the days that people remember the
+ 
+
+ align:start position:0%
+like the days that people remember the
+most are also at least in my
+
+ align:start position:0%
+most are also at least in my
+ 
+
+ align:start position:0%
+most are also at least in my
+recollection of the two weeks those were
+
+ align:start position:0%
+recollection of the two weeks those were
+ 
+
+ align:start position:0%
+recollection of the two weeks those were
+the days where we really dug in deepest
+
+ align:start position:0%
+the days where we really dug in deepest
+ 
+
+ align:start position:0%
+the days where we really dug in deepest
+with the exercises and really tried
+
+ align:start position:0%
+with the exercises and really tried
+ 
+
+ align:start position:0%
+with the exercises and really tried
+tried to pull out the
+
+ align:start position:0%
+tried to pull out the
+ 
+
+ align:start position:0%
+tried to pull out the
+assumptions but what is interesting is
+
+ align:start position:0%
+assumptions but what is interesting is
+ 
+
+ align:start position:0%
+assumptions but what is interesting is
+that at the at the beginning when the
+
+ align:start position:0%
+that at the at the beginning when the
+ 
+
+ align:start position:0%
+that at the at the beginning when the
+exercise require by
+
+ align:start position:0%
+exercise require by
+ 
+
+ align:start position:0%
+exercise require by
+more involvement engagement of each one
+
+ align:start position:0%
+more involvement engagement of each one
+ 
+
+ align:start position:0%
+more involvement engagement of each one
+we have more negative critical moments
+
+ align:start position:0%
+we have more negative critical moments
+ 
+
+ align:start position:0%
+we have more negative critical moments
+no and after a
+
+ align:start position:0%
+no and after a
+ 
+
+ align:start position:0%
+no and after a
+while know people got
+
+ align:start position:0%
+while know people got
+ 
+
+ align:start position:0%
+while know people got
+to I think
+
+ align:start position:0%
+to I think
+ 
+
+ align:start position:0%
+to I think
+to control better their I think that
+
+ align:start position:0%
+to control better their I think that
+ 
+
+ align:start position:0%
+to control better their I think that
+also has to do with how people interact
+
+ align:start position:0%
+also has to do with how people interact
+ 
+
+ align:start position:0%
+also has to do with how people interact
+with each other within a group how they
+
+ align:start position:0%
+with each other within a group how they
+ 
+
+ align:start position:0%
+with each other within a group how they
+get to meet each other and be more
+
+ align:start position:0%
+get to meet each other and be more
+ 
+
+ align:start position:0%
+get to meet each other and be more
+comfortable with each other so there's a
+
+ align:start position:0%
+comfortable with each other so there's a
+ 
+
+ align:start position:0%
+comfortable with each other so there's a
+period of time where for the adapation
+
+ align:start position:0%
+period of time where for the adapation
+ 
+
+ align:start position:0%
+period of time where for the adapation
+process implicates positive and negative
+
+ align:start position:0%
+process implicates positive and negative
+ 
+
+ align:start position:0%
+process implicates positive and negative
+effects and that is a consequence of
+
+ align:start position:0%
+effects and that is a consequence of
+ 
+
+ align:start position:0%
+effects and that is a consequence of
+being more aware of the group and of the
+
+ align:start position:0%
+being more aware of the group and of the
+ 
+
+ align:start position:0%
+being more aware of the group and of the
+people and how they think and how you
+
+ align:start position:0%
+people and how they think and how you
+ 
+
+ align:start position:0%
+people and how they think and how you
+have to relate with
+
+ align:start position:0%
+have to relate with
+ 
+
+ align:start position:0%
+have to relate with
+them so I think that's why that can
+
+ align:start position:0%
+them so I think that's why that can
+ 
+
+ align:start position:0%
+them so I think that's why that can
+explain a lot about the negative
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+also but the the critical moment that
+
+ align:start position:0%
+also but the the critical moment that
+ 
+
+ align:start position:0%
+also but the the critical moment that
+don't refer to
+
+ align:start position:0%
+don't refer to
+ 
+
+ align:start position:0%
+don't refer to
+group relation they refer to relation
+
+ align:start position:0%
+group relation they refer to relation
+ 
+
+ align:start position:0%
+group relation they refer to relation
+between the person and some issues of
+
+ align:start position:0%
+between the person and some issues of
+ 
+
+ align:start position:0%
+between the person and some issues of
+the course no no no because if
+
+ align:start position:0%
+the course no no no because if
+ 
+
+ align:start position:0%
+the course no no no because if
+you I
+
+ align:start position:0%
+you I
+ 
+
+ align:start position:0%
+you I
+mean if you know you're stuck you're
+
+ align:start position:0%
+mean if you know you're stuck you're
+ 
+
+ align:start position:0%
+mean if you know you're stuck you're
+feeling stuck in certain situations and
+
+ align:start position:0%
+feeling stuck in certain situations and
+ 
+
+ align:start position:0%
+feeling stuck in certain situations and
+it may be related to your inability to
+
+ align:start position:0%
+it may be related to your inability to
+ 
+
+ align:start position:0%
+it may be related to your inability to
+connect to the other people in your
+
+ align:start position:0%
+connect to the other people in your
+ 
+
+ align:start position:0%
+connect to the other people in your
+group with whom you're doing an exercise
+
+ align:start position:0%
+group with whom you're doing an exercise
+ 
+
+ align:start position:0%
+group with whom you're doing an exercise
+you
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+know how comfortable you
+
+ align:start position:0%
+know how comfortable you
+ 
+
+ align:start position:0%
+know how comfortable you
+feel okay should be an explanation but
+
+ align:start position:0%
+feel okay should be an explanation but
+ 
+
+ align:start position:0%
+feel okay should be an explanation but
+not stated there in the words well yeah
+
+ align:start position:0%
+not stated there in the words well yeah
+ 
+
+ align:start position:0%
+not stated there in the words well yeah
+agreed
+
+ align:start position:0%
+agreed
+ 
+
+ align:start position:0%
+agreed
+that my
+
+ align:start position:0%
+that my
+ 
+
+ align:start position:0%
+that my
+reasons part of my
+
+ align:start position:0%
+reasons part of my
+ 
+
+ align:start position:0%
+reasons part of my
+reasons I I think that I began to have
+
+ align:start position:0%
+reasons I I think that I began to have
+ 
+
+ align:start position:0%
+reasons I I think that I began to have
+more positive more it is the group
+
+ align:start position:0%
+more positive more it is the group
+ 
+
+ align:start position:0%
+more positive more it is the group
+dynamic and and getting okay more you
+
+ align:start position:0%
+dynamic and and getting okay more you
+ 
+
+ align:start position:0%
+dynamic and and getting okay more you
+know when you look around the room you
+
+ align:start position:0%
+know when you look around the room you
+ 
+
+ align:start position:0%
+know when you look around the room you
+feel like I kind of know some of these
+
+ align:start position:0%
+feel like I kind of know some of these
+ 
+
+ align:start position:0%
+feel like I kind of know some of these
+okay you're right that it's not stated
+
+ align:start position:0%
+okay you're right that it's not stated
+ 
+
+ align:start position:0%
+okay you're right that it's not stated
+but that wasn't the question we were
+
+ align:start position:0%
+but that wasn't the question we were
+ 
+
+ align:start position:0%
+but that wasn't the question we were
+asked to express we were asked to
+
+ align:start position:0%
+asked to express we were asked to
+ 
+
+ align:start position:0%
+asked to express we were asked to
+express the critical moment not why it
+
+ align:start position:0%
+express the critical moment not why it
+ 
+
+ align:start position:0%
+express the critical moment not why it
+was a critical moment okay I think you
+
+ align:start position:0%
+was a critical moment okay I think you
+ 
+
+ align:start position:0%
+was a critical moment okay I think you
+express behind what yes it's behind the
+
+ align:start position:0%
+express behind what yes it's behind the
+ 
+
+ align:start position:0%
+express behind what yes it's behind the
+these critical moments we have the
+
+ align:start position:0%
+these critical moments we have the
+ 
+
+ align:start position:0%
+these critical moments we have the
+process of
+
+ align:start position:0%
+process of
+ 
+
+ align:start position:0%
+process of
+group dynamic dynamic okay well just
+
+ align:start position:0%
+group dynamic dynamic okay well just
+ 
+
+ align:start position:0%
+group dynamic dynamic okay well just
+like your your
+
+ align:start position:0%
+like your your
+ 
+
+ align:start position:0%
+like your your
+assumption that um that the first
+
+ align:start position:0%
+assumption that um that the first
+ 
+
+ align:start position:0%
+assumption that um that the first
+experience was the first time we let
+
+ align:start position:0%
+experience was the first time we let
+ 
+
+ align:start position:0%
+experience was the first time we let
+ourselves be uh vulnerable and and then
+
+ align:start position:0%
+ourselves be uh vulnerable and and then
+ 
+
+ align:start position:0%
+ourselves be uh vulnerable and and then
+it was it was better that's your
+
+ align:start position:0%
+it was it was better that's your
+ 
+
+ align:start position:0%
+it was it was better that's your
+assumption about why these were critical
+
+ align:start position:0%
+assumption about why these were critical
+ 
+
+ align:start position:0%
+assumption about why these were critical
+moments exactly it's not there it's not
+
+ align:start position:0%
+moments exactly it's not there it's not
+ 
+
+ align:start position:0%
+moments exactly it's not there it's not
+there we are assuming you are assuming I
+
+ align:start position:0%
+there we are assuming you are assuming I
+ 
+
+ align:start position:0%
+there we are assuming you are assuming I
+know
+
+ align:start position:0%
+know
+ 
+
+ align:start position:0%
+know
+you I haven't considered it if you want
+
+ align:start position:0%
+you I haven't considered it if you want
+ 
+
+ align:start position:0%
+you I haven't considered it if you want
+me to I can come up with with an
+
+ align:start position:0%
+me to I can come up with with an
+ 
+
+ align:start position:0%
+me to I can come up with with an
+assumption as
+
+ align:start position:0%
+assumption as
+ 
+
+ align:start position:0%
+assumption as
+well so good I I try to to read to
+
+ align:start position:0%
+well so good I I try to to read to
+ 
+
+ align:start position:0%
+well so good I I try to to read to
+interpret what people are telling me I
+
+ align:start position:0%
+interpret what people are telling me I
+ 
+
+ align:start position:0%
+interpret what people are telling me I
+have no opinion about this yet yes you
+
+ align:start position:0%
+have no opinion about this yet yes you
+ 
+
+ align:start position:0%
+have no opinion about this yet yes you
+created an opinion maybe but she she
+
+ align:start position:0%
+created an opinion maybe but she she
+ 
+
+ align:start position:0%
+created an opinion maybe but she she
+expressed that there was a group dynamic
+
+ align:start position:0%
+expressed that there was a group dynamic
+ 
+
+ align:start position:0%
+expressed that there was a group dynamic
+and jod also express it and Claudia also
+
+ align:start position:0%
+and jod also express it and Claudia also
+ 
+
+ align:start position:0%
+and jod also express it and Claudia also
+expressed the same feeling so
+
+ align:start position:0%
+expressed the same feeling so
+ 
+
+ align:start position:0%
+expressed the same feeling so
+I to it for me I have not opinion about
+
+ align:start position:0%
+I to it for me I have not opinion about
+ 
+
+ align:start position:0%
+I to it for me I have not opinion about
+this yet yeah okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Le yes she she has a question okay okay
+
+ align:start position:0%
+Le yes she she has a question okay okay
+ 
+
+ align:start position:0%
+Le yes she she has a question okay okay
+oh I was about to ask I here on the
+
+ align:start position:0%
+oh I was about to ask I here on the
+ 
+
+ align:start position:0%
+oh I was about to ask I here on the
+first 4 days is that the first day of
+
+ align:start position:0%
+first 4 days is that the first day of
+ 
+
+ align:start position:0%
+first 4 days is that the first day of
+exercise of
+
+ align:start position:0%
+exercise of
+ 
+
+ align:start position:0%
+exercise of
+exercises when was the first the first
+
+ align:start position:0%
+exercises when was the first the first
+ 
+
+ align:start position:0%
+exercises when was the first the first
+day was about learning and that was
+
+ align:start position:0%
+day was about learning and that was
+ 
+
+ align:start position:0%
+day was about learning and that was
+there was a group exercise there was a
+
+ align:start position:0%
+there was a group exercise there was a
+ 
+
+ align:start position:0%
+there was a group exercise there was a
+for every
+
+ align:start position:0%
+for every
+ 
+
+ align:start position:0%
+for every
+day yes yes all the days there were a
+
+ align:start position:0%
+day yes yes all the days there were a
+ 
+
+ align:start position:0%
+day yes yes all the days there were a
+group
+
+ align:start position:0%
+group
+ 
+
+ align:start position:0%
+group
+exercises
+
+ align:start position:0%
+exercises
+ 
+
+ align:start position:0%
+exercises
+okay I just going to say that and I'm
+
+ align:start position:0%
+okay I just going to say that and I'm
+ 
+
+ align:start position:0%
+okay I just going to say that and I'm
+I'm speaking strictly on my own behalf
+
+ align:start position:0%
+I'm speaking strictly on my own behalf
+ 
+
+ align:start position:0%
+I'm speaking strictly on my own behalf
+um for me emotional feel I think the the
+
+ align:start position:0%
+um for me emotional feel I think the the
+ 
+
+ align:start position:0%
+um for me emotional feel I think the the
+negative um leading up to Friday
+
+ align:start position:0%
+negative um leading up to Friday
+ 
+
+ align:start position:0%
+negative um leading up to Friday
+Thursday the fourth um I agree that we
+
+ align:start position:0%
+Thursday the fourth um I agree that we
+ 
+
+ align:start position:0%
+Thursday the fourth um I agree that we
+were kind of getting Concepts and
+
+ align:start position:0%
+were kind of getting Concepts and
+ 
+
+ align:start position:0%
+were kind of getting Concepts and
+understanding feeling you know trying to
+
+ align:start position:0%
+understanding feeling you know trying to
+ 
+
+ align:start position:0%
+understanding feeling you know trying to
+see where the work was going but for me
+
+ align:start position:0%
+see where the work was going but for me
+ 
+
+ align:start position:0%
+see where the work was going but for me
+on Thursday the exercise that was
+
+ align:start position:0%
+on Thursday the exercise that was
+ 
+
+ align:start position:0%
+on Thursday the exercise that was
+chosen really um it bubbled up a lot of
+
+ align:start position:0%
+chosen really um it bubbled up a lot of
+ 
+
+ align:start position:0%
+chosen really um it bubbled up a lot of
+emotions that come out certainly for me
+
+ align:start position:0%
+emotions that come out certainly for me
+ 
+
+ align:start position:0%
+emotions that come out certainly for me
+when you talk about issues of race and I
+
+ align:start position:0%
+when you talk about issues of race and I
+ 
+
+ align:start position:0%
+when you talk about issues of race and I
+think that that exercise that was
+
+ align:start position:0%
+think that that exercise that was
+ 
+
+ align:start position:0%
+think that that exercise that was
+chosen um made me go back and really
+
+ align:start position:0%
+chosen um made me go back and really
+ 
+
+ align:start position:0%
+chosen um made me go back and really
+look
+
+ align:start position:0%
+look
+ 
+
+ align:start position:0%
+look
+at how important how when you're trying
+
+ align:start position:0%
+at how important how when you're trying
+ 
+
+ align:start position:0%
+at how important how when you're trying
+to sort of articulate or um and not that
+
+ align:start position:0%
+to sort of articulate or um and not that
+ 
+
+ align:start position:0%
+to sort of articulate or um and not that
+you even have to own it but when you're
+
+ align:start position:0%
+you even have to own it but when you're
+ 
+
+ align:start position:0%
+you even have to own it but when you're
+trying to
+
+ align:start position:0%
+trying to
+ 
+
+ align:start position:0%
+trying to
+articulate um Concepts or get
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um theories across how difficult it is
+
+ align:start position:0%
+um theories across how difficult it is
+ 
+
+ align:start position:0%
+um theories across how difficult it is
+to use issues around race to convey that
+
+ align:start position:0%
+to use issues around race to convey that
+ 
+
+ align:start position:0%
+to use issues around race to convey that
+concept if you know what I mean and I
+
+ align:start position:0%
+concept if you know what I mean and I
+ 
+
+ align:start position:0%
+concept if you know what I mean and I
+think it it just it it really Disturbed
+
+ align:start position:0%
+think it it just it it really Disturbed
+ 
+
+ align:start position:0%
+think it it just it it really Disturbed
+me in a way that I had to really
+
+ align:start position:0%
+me in a way that I had to really
+ 
+
+ align:start position:0%
+me in a way that I had to really
+reconsider why am I here and so that's
+
+ align:start position:0%
+reconsider why am I here and so that's
+ 
+
+ align:start position:0%
+reconsider why am I here and so that's
+why I put negative and positive because
+
+ align:start position:0%
+why I put negative and positive because
+ 
+
+ align:start position:0%
+why I put negative and positive because
+I think that the whole notion of the
+
+ align:start position:0%
+I think that the whole notion of the
+ 
+
+ align:start position:0%
+I think that the whole notion of the
+concept you know the that we were
+
+ align:start position:0%
+concept you know the that we were
+ 
+
+ align:start position:0%
+concept you know the that we were
+talking about on that day
+
+ align:start position:0%
+talking about on that day
+ 
+
+ align:start position:0%
+talking about on that day
+was trying to understand framing or
+
+ align:start position:0%
+was trying to understand framing or
+ 
+
+ align:start position:0%
+was trying to understand framing or
+reframing theor and use theories and use
+
+ align:start position:0%
+reframing theor and use theories and use
+ 
+
+ align:start position:0%
+reframing theor and use theories and use
+and but because we're dealing with an
+
+ align:start position:0%
+and but because we're dealing with an
+ 
+
+ align:start position:0%
+and but because we're dealing with an
+issue that's so complex in this
+
+ align:start position:0%
+issue that's so complex in this
+ 
+
+ align:start position:0%
+issue that's so complex in this
+society and so emotional it just
+
+ align:start position:0%
+society and so emotional it just
+ 
+
+ align:start position:0%
+society and so emotional it just
+barricaded my ability to really get it
+
+ align:start position:0%
+barricaded my ability to really get it
+ 
+
+ align:start position:0%
+barricaded my ability to really get it
+and I had to go home and really think
+
+ align:start position:0%
+and I had to go home and really think
+ 
+
+ align:start position:0%
+and I had to go home and really think
+about it and really sort of understand
+
+ align:start position:0%
+about it and really sort of understand
+ 
+
+ align:start position:0%
+about it and really sort of understand
+that I had to separate the issue so I
+
+ align:start position:0%
+that I had to separate the issue so I
+ 
+
+ align:start position:0%
+that I had to separate the issue so I
+think it's by it certainly opened up
+
+ align:start position:0%
+think it's by it certainly opened up
+ 
+
+ align:start position:0%
+think it's by it certainly opened up
+my my mind and my openness to receiving
+
+ align:start position:0%
+my my mind and my openness to receiving
+ 
+
+ align:start position:0%
+my my mind and my openness to receiving
+the information and understanding what
+
+ align:start position:0%
+the information and understanding what
+ 
+
+ align:start position:0%
+the information and understanding what
+it was you're here to do what I'm here
+
+ align:start position:0%
+it was you're here to do what I'm here
+ 
+
+ align:start position:0%
+it was you're here to do what I'm here
+to do why I'm here
+
+ align:start position:0%
+to do why I'm here
+ 
+
+ align:start position:0%
+to do why I'm here
+so thank you please isn't that is that I
+
+ align:start position:0%
+so thank you please isn't that is that I
+ 
+
+ align:start position:0%
+so thank you please isn't that is that I
+kind of feel like is not a great
+
+ align:start position:0%
+kind of feel like is not a great
+ 
+
+ align:start position:0%
+kind of feel like is not a great
+exercise though to have I mean it's hard
+
+ align:start position:0%
+exercise though to have I mean it's hard
+ 
+
+ align:start position:0%
+exercise though to have I mean it's hard
+it's much harder to do it with race but
+
+ align:start position:0%
+it's much harder to do it with race but
+ 
+
+ align:start position:0%
+it's much harder to do it with race but
+to have that charge cuz I mean you know
+
+ align:start position:0%
+to have that charge cuz I mean you know
+ 
+
+ align:start position:0%
+to have that charge cuz I mean you know
+these are the situations that happen in
+
+ align:start position:0%
+these are the situations that happen in
+ 
+
+ align:start position:0%
+these are the situations that happen in
+the real world people get really charged
+
+ align:start position:0%
+the real world people get really charged
+ 
+
+ align:start position:0%
+the real world people get really charged
+about issues and you can't you can't
+
+ align:start position:0%
+about issues and you can't you can't
+ 
+
+ align:start position:0%
+about issues and you can't you can't
+just separate your emotions you know on
+
+ align:start position:0%
+just separate your emotions you know on
+ 
+
+ align:start position:0%
+just separate your emotions you know on
+something like race or I don't class
+
+ align:start position:0%
+something like race or I don't class
+ 
+
+ align:start position:0%
+something like race or I don't class
+issues or postwar I mean whatever the
+
+ align:start position:0%
+issues or postwar I mean whatever the
+ 
+
+ align:start position:0%
+issues or postwar I mean whatever the
+issue is you know I mean are you saying
+
+ align:start position:0%
+issue is you know I mean are you saying
+ 
+
+ align:start position:0%
+issue is you know I mean are you saying
+do you think it was good to have it so
+
+ align:start position:0%
+do you think it was good to have it so
+ 
+
+ align:start position:0%
+do you think it was good to have it so
+early you think it would have been
+
+ align:start position:0%
+early you think it would have been
+ 
+
+ align:start position:0%
+early you think it would have been
+better to have it later on or not at all
+
+ align:start position:0%
+better to have it later on or not at all
+ 
+
+ align:start position:0%
+better to have it later on or not at all
+I think it would be better not to have
+
+ align:start position:0%
+I think it would be better not to have
+ 
+
+ align:start position:0%
+I think it would be better not to have
+it at
+
+ align:start position:0%
+it at
+ 
+
+ align:start position:0%
+it at
+all for me I mean because the impact
+
+ align:start position:0%
+all for me I mean because the impact
+ 
+
+ align:start position:0%
+all for me I mean because the impact
+that it had on me was just not a
+
+ align:start position:0%
+that it had on me was just not a
+ 
+
+ align:start position:0%
+that it had on me was just not a
+positive impact and it it almost
+
+ align:start position:0%
+positive impact and it it almost
+ 
+
+ align:start position:0%
+positive impact and it it almost
+Disturbed me to the point where I didn't
+
+ align:start position:0%
+Disturbed me to the point where I didn't
+ 
+
+ align:start position:0%
+Disturbed me to the point where I didn't
+even want to
+
+ align:start position:0%
+even want to
+ 
+
+ align:start position:0%
+even want to
+come back and that was so ridiculous go
+
+ align:start position:0%
+come back and that was so ridiculous go
+ 
+
+ align:start position:0%
+come back and that was so ridiculous go
+back and really think about what that
+
+ align:start position:0%
+back and really think about what that
+ 
+
+ align:start position:0%
+back and really think about what that
+meant for me and I actually had a
+
+ align:start position:0%
+meant for me and I actually had a
+ 
+
+ align:start position:0%
+meant for me and I actually had a
+conversation with Caesar about it
+
+ align:start position:0%
+conversation with Caesar about it
+ 
+
+ align:start position:0%
+conversation with Caesar about it
+because I was just really so disturbed
+
+ align:start position:0%
+because I was just really so disturbed
+ 
+
+ align:start position:0%
+because I was just really so disturbed
+by the whole thing and it wasn't it
+
+ align:start position:0%
+by the whole thing and it wasn't it
+ 
+
+ align:start position:0%
+by the whole thing and it wasn't it
+wasn't anything anyone said it was just
+
+ align:start position:0%
+wasn't anything anyone said it was just
+ 
+
+ align:start position:0%
+wasn't anything anyone said it was just
+the circumstances of the world that
+
+ align:start position:0%
+the circumstances of the world that
+ 
+
+ align:start position:0%
+the circumstances of the world that
+we're living in and working in and
+
+ align:start position:0%
+we're living in and working in and
+ 
+
+ align:start position:0%
+we're living in and working in and
+trying to fight for justice um so it
+
+ align:start position:0%
+trying to fight for justice um so it
+ 
+
+ align:start position:0%
+trying to fight for justice um so it
+wasn't the class it was
+
+ align:start position:0%
+wasn't the class it was
+ 
+
+ align:start position:0%
+wasn't the class it was
+just you know I guess I was society and
+
+ align:start position:0%
+just you know I guess I was society and
+ 
+
+ align:start position:0%
+just you know I guess I was society and
+I it just really Disturbed my spirit so
+
+ align:start position:0%
+I it just really Disturbed my spirit so
+ 
+
+ align:start position:0%
+I it just really Disturbed my spirit so
+what made you tell us about this
+
+ align:start position:0%
+what made you tell us about this
+ 
+
+ align:start position:0%
+what made you tell us about this
+critical moment
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+here what made you tell what what made
+
+ align:start position:0%
+here what made you tell what what made
+ 
+
+ align:start position:0%
+here what made you tell what what made
+me tell so you're telling us you know
+
+ align:start position:0%
+me tell so you're telling us you know
+ 
+
+ align:start position:0%
+me tell so you're telling us you know
+you're telling us about this like you
+
+ align:start position:0%
+you're telling us about this like you
+ 
+
+ align:start position:0%
+you're telling us about this like you
+being very disturbed that day but then
+
+ align:start position:0%
+being very disturbed that day but then
+ 
+
+ align:start position:0%
+being very disturbed that day but then
+something I think your conversation with
+
+ align:start position:0%
+something I think your conversation with
+ 
+
+ align:start position:0%
+something I think your conversation with
+Caesar all tell us about what happened
+
+ align:start position:0%
+Caesar all tell us about what happened
+ 
+
+ align:start position:0%
+Caesar all tell us about what happened
+here no it was a conversation with
+
+ align:start position:0%
+here no it was a conversation with
+ 
+
+ align:start position:0%
+here no it was a conversation with
+myself when I went home that night and
+
+ align:start position:0%
+myself when I went home that night and
+ 
+
+ align:start position:0%
+myself when I went home that night and
+then Contin with Caesar the following
+
+ align:start position:0%
+then Contin with Caesar the following
+ 
+
+ align:start position:0%
+then Contin with Caesar the following
+day really made
+
+ align:start position:0%
+day really made
+ 
+
+ align:start position:0%
+day really made
+me
+
+ align:start position:0%
+me
+ 
+
+ align:start position:0%
+me
+separate the purpose of while we're here
+
+ align:start position:0%
+separate the purpose of while we're here
+ 
+
+ align:start position:0%
+separate the purpose of while we're here
+and what value can come out of a process
+
+ align:start position:0%
+and what value can come out of a process
+ 
+
+ align:start position:0%
+and what value can come out of a process
+like this and giv some hope for working
+
+ align:start position:0%
+like this and giv some hope for working
+ 
+
+ align:start position:0%
+like this and giv some hope for working
+through hard issues that communities
+
+ align:start position:0%
+through hard issues that communities
+ 
+
+ align:start position:0%
+through hard issues that communities
+face with every day um I thought that
+
+ align:start position:0%
+face with every day um I thought that
+ 
+
+ align:start position:0%
+face with every day um I thought that
+this this process could maybe help
+
+ align:start position:0%
+this this process could maybe help
+ 
+
+ align:start position:0%
+this this process could maybe help
+others understand some of the
+
+ align:start position:0%
+others understand some of the
+ 
+
+ align:start position:0%
+others understand some of the
+complicated issues that we're deing with
+
+ align:start position:0%
+complicated issues that we're deing with
+ 
+
+ align:start position:0%
+complicated issues that we're deing with
+every day so I had to really dig deep
+
+ align:start position:0%
+every day so I had to really dig deep
+ 
+
+ align:start position:0%
+every day so I had to really dig deep
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+separate my emotions
+
+ align:start position:0%
+separate my emotions
+ 
+
+ align:start position:0%
+separate my emotions
+from the issue and the purpose and look
+
+ align:start position:0%
+from the issue and the purpose and look
+ 
+
+ align:start position:0%
+from the issue and the purpose and look
+at this this series of this class as an
+
+ align:start position:0%
+at this this series of this class as an
+ 
+
+ align:start position:0%
+at this this series of this class as an
+opportunity to perhaps use in my work to
+
+ align:start position:0%
+opportunity to perhaps use in my work to
+ 
+
+ align:start position:0%
+opportunity to perhaps use in my work to
+have others who are struggl the same
+
+ align:start position:0%
+have others who are struggl the same
+ 
+
+ align:start position:0%
+have others who are struggl the same
+issues race and class and all those
+
+ align:start position:0%
+issues race and class and all those
+ 
+
+ align:start position:0%
+issues race and class and all those
+things that the is that
+
+ align:start position:0%
+things that the is that
+ 
+
+ align:start position:0%
+things that the is that
+we okay thank you
+
+ align:start position:0%
+we okay thank you
+ 
+
+ align:start position:0%
+we okay thank you
+please oh no any other comment about
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this okay I just said one thing I was oh
+
+ align:start position:0%
+this okay I just said one thing I was oh
+ 
+
+ align:start position:0%
+this okay I just said one thing I was oh
+yes I thought when we did the Framingham
+
+ align:start position:0%
+yes I thought when we did the Framingham
+ 
+
+ align:start position:0%
+yes I thought when we did the Framingham
+when we heard c talk about the
+
+ align:start position:0%
+when we heard c talk about the
+ 
+
+ align:start position:0%
+when we heard c talk about the
+Framingham k no situation and then we
+
+ align:start position:0%
+Framingham k no situation and then we
+ 
+
+ align:start position:0%
+Framingham k no situation and then we
+did the problem solving together that
+
+ align:start position:0%
+did the problem solving together that
+ 
+
+ align:start position:0%
+did the problem solving together that
+was a very rich experience for me you
+
+ align:start position:0%
+was a very rich experience for me you
+ 
+
+ align:start position:0%
+was a very rich experience for me you
+know where we all contributed what we
+
+ align:start position:0%
+know where we all contributed what we
+ 
+
+ align:start position:0%
+know where we all contributed what we
+knew or heard or experienced our own
+
+ align:start position:0%
+knew or heard or experienced our own
+ 
+
+ align:start position:0%
+knew or heard or experienced our own
+practice I thought that was an excellent
+
+ align:start position:0%
+practice I thought that was an excellent
+ 
+
+ align:start position:0%
+practice I thought that was an excellent
+day particularly for
+
+ align:start position:0%
+day particularly for
+ 
+
+ align:start position:0%
+day particularly for
+me okay so um yes so the question um one
+
+ align:start position:0%
+me okay so um yes so the question um one
+ 
+
+ align:start position:0%
+me okay so um yes so the question um one
+of the questions that you guys picked
+
+ align:start position:0%
+of the questions that you guys picked
+ 
+
+ align:start position:0%
+of the questions that you guys picked
+today was how to make reflective
+
+ align:start position:0%
+today was how to make reflective
+ 
+
+ align:start position:0%
+today was how to make reflective
+practice common practice like more
+
+ align:start position:0%
+practice common practice like more
+ 
+
+ align:start position:0%
+practice common practice like more
+practical and natur
+
+ align:start position:0%
+practical and natur
+ 
+
+ align:start position:0%
+practical and natur
+for our for
+
+ align:start position:0%
+for our for
+ 
+
+ align:start position:0%
+for our for
+us if we were to do this whole
+
+ align:start position:0%
+us if we were to do this whole
+ 
+
+ align:start position:0%
+us if we were to do this whole
+methodology and finish we what we would
+
+ align:start position:0%
+methodology and finish we what we would
+ 
+
+ align:start position:0%
+methodology and finish we what we would
+do at this point is see which of these
+
+ align:start position:0%
+do at this point is see which of these
+ 
+
+ align:start position:0%
+do at this point is see which of these
+critical moments if we if we understood
+
+ align:start position:0%
+critical moments if we if we understood
+ 
+
+ align:start position:0%
+critical moments if we if we understood
+better if we could
+
+ align:start position:0%
+better if we could
+ 
+
+ align:start position:0%
+better if we could
+analyze in more depth we would begin to
+
+ align:start position:0%
+analyze in more depth we would begin to
+ 
+
+ align:start position:0%
+analyze in more depth we would begin to
+answer this
+
+ align:start position:0%
+answer this
+ 
+
+ align:start position:0%
+answer this
+question
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay no
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+looking at
+
+ align:start position:0%
+looking at
+ 
+
+ align:start position:0%
+looking at
+the yes looking at
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the no I'm describing the methodology as
+
+ align:start position:0%
+the no I'm describing the methodology as
+ 
+
+ align:start position:0%
+the no I'm describing the methodology as
+as it's not what we're going to do now
+
+ align:start position:0%
+as it's not what we're going to do now
+ 
+
+ align:start position:0%
+as it's not what we're going to do now
+as so I think it's important for you to
+
+ align:start position:0%
+as so I think it's important for you to
+ 
+
+ align:start position:0%
+as so I think it's important for you to
+know what it is so that you know that
+
+ align:start position:0%
+know what it is so that you know that
+ 
+
+ align:start position:0%
+know what it is so that you know that
+we're making a change okay so how it
+
+ align:start position:0%
+we're making a change okay so how it
+ 
+
+ align:start position:0%
+we're making a change okay so how it
+usually works is you look at all these
+
+ align:start position:0%
+usually works is you look at all these
+ 
+
+ align:start position:0%
+usually works is you look at all these
+critical moments and you begin to
+
+ align:start position:0%
+critical moments and you begin to
+ 
+
+ align:start position:0%
+critical moments and you begin to
+identify the ones that if you analyze in
+
+ align:start position:0%
+identify the ones that if you analyze in
+ 
+
+ align:start position:0%
+identify the ones that if you analyze in
+depth through storytelling you would be
+
+ align:start position:0%
+depth through storytelling you would be
+ 
+
+ align:start position:0%
+depth through storytelling you would be
+able to begin to answer this ingry
+
+ align:start position:0%
+able to begin to answer this ingry
+ 
+
+ align:start position:0%
+able to begin to answer this ingry
+question okay we're not going to do that
+
+ align:start position:0%
+question okay we're not going to do that
+ 
+
+ align:start position:0%
+question okay we're not going to do that
+what we're going to do is just in
+
+ align:start position:0%
+what we're going to do is just in
+ 
+
+ align:start position:0%
+what we're going to do is just in
+general if you look at the distribution
+
+ align:start position:0%
+general if you look at the distribution
+ 
+
+ align:start position:0%
+general if you look at the distribution
+of these critical moments and what we
+
+ align:start position:0%
+of these critical moments and what we
+ 
+
+ align:start position:0%
+of these critical moments and what we
+just discussed is there anything that
+
+ align:start position:0%
+just discussed is there anything that
+ 
+
+ align:start position:0%
+just discussed is there anything that
+comes to your mind that could help you
+
+ align:start position:0%
+comes to your mind that could help you
+ 
+
+ align:start position:0%
+comes to your mind that could help you
+begin to answer this question what ideas
+
+ align:start position:0%
+begin to answer this question what ideas
+ 
+
+ align:start position:0%
+begin to answer this question what ideas
+do
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+you okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+one question we have two questions no
+
+ align:start position:0%
+one question we have two questions no
+ 
+
+ align:start position:0%
+one question we have two questions no
+we're just going to focus because of
+
+ align:start position:0%
+we're just going to focus because of
+ 
+
+ align:start position:0%
+we're just going to focus because of
+time we're just going to focus on this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+question okay CL
+
+ align:start position:0%
+question okay CL
+ 
+
+ align:start position:0%
+question okay CL
+suggesting we're we're going to focus on
+
+ align:start position:0%
+suggesting we're we're going to focus on
+ 
+
+ align:start position:0%
+suggesting we're we're going to focus on
+this question of all the question
+
+ align:start position:0%
+this question of all the question
+ 
+
+ align:start position:0%
+this question of all the question
+questions okay if that's okay with you
+
+ align:start position:0%
+questions okay if that's okay with you
+ 
+
+ align:start position:0%
+questions okay if that's okay with you
+guys because of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+time okay how to
+
+ align:start position:0%
+time okay how to
+ 
+
+ align:start position:0%
+time okay how to
+make reflective practice common
+
+ align:start position:0%
+make reflective practice common
+ 
+
+ align:start position:0%
+make reflective practice common
+practice
+
+ align:start position:0%
+practice
+ 
+
+ align:start position:0%
+practice
+okay thinking about
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this thinking about your own experience
+
+ align:start position:0%
+this thinking about your own experience
+ 
+
+ align:start position:0%
+this thinking about your own experience
+and the experience that you saw from the
+
+ align:start position:0%
+and the experience that you saw from the
+ 
+
+ align:start position:0%
+and the experience that you saw from the
+other people
+
+ align:start position:0%
+other people
+ 
+
+ align:start position:0%
+other people
+these days you are try to learn
+
+ align:start position:0%
+these days you are try to learn
+ 
+
+ align:start position:0%
+these days you are try to learn
+reflective practice you are trying to
+
+ align:start position:0%
+reflective practice you are trying to
+ 
+
+ align:start position:0%
+reflective practice you are trying to
+apply reflective practice and now
+
+ align:start position:0%
+apply reflective practice and now
+ 
+
+ align:start position:0%
+apply reflective practice and now
+from this reconstruction we have made
+
+ align:start position:0%
+from this reconstruction we have made
+ 
+
+ align:start position:0%
+from this reconstruction we have made
+what you can find that should be useful
+
+ align:start position:0%
+what you can find that should be useful
+ 
+
+ align:start position:0%
+what you can find that should be useful
+for having ideas about how to make a
+
+ align:start position:0%
+for having ideas about how to make a
+ 
+
+ align:start position:0%
+for having ideas about how to make a
+common
+
+ align:start position:0%
+common
+ 
+
+ align:start position:0%
+common
+practice how to make ref reflective
+
+ align:start position:0%
+practice how to make ref reflective
+ 
+
+ align:start position:0%
+practice how to make ref reflective
+practice a common practice like more
+
+ align:start position:0%
+practice a common practice like more
+ 
+
+ align:start position:0%
+practice a common practice like more
+practical and natural yes there have
+
+ align:start position:0%
+practical and natural yes there have
+ 
+
+ align:start position:0%
+practical and natural yes there have
+been a lot of theories thrown out about
+
+ align:start position:0%
+been a lot of theories thrown out about
+ 
+
+ align:start position:0%
+been a lot of theories thrown out about
+why these clustered in a way that they
+
+ align:start position:0%
+why these clustered in a way that they
+ 
+
+ align:start position:0%
+why these clustered in a way that they
+did if we take the assumption that it's
+
+ align:start position:0%
+did if we take the assumption that it's
+ 
+
+ align:start position:0%
+did if we take the assumption that it's
+because uh your your analysis which I
+
+ align:start position:0%
+because uh your your analysis which I
+ 
+
+ align:start position:0%
+because uh your your analysis which I
+like about it was hard at the beginning
+
+ align:start position:0%
+like about it was hard at the beginning
+ 
+
+ align:start position:0%
+like about it was hard at the beginning
+for people to really analyze their
+
+ align:start position:0%
+for people to really analyze their
+ 
+
+ align:start position:0%
+for people to really analyze their
+assumptions and then as they gotten more
+
+ align:start position:0%
+assumptions and then as they gotten more
+ 
+
+ align:start position:0%
+assumptions and then as they gotten more
+and more practice they started to be
+
+ align:start position:0%
+and more practice they started to be
+ 
+
+ align:start position:0%
+and more practice they started to be
+more and more comfortable with being in
+
+ align:start position:0%
+more and more comfortable with being in
+ 
+
+ align:start position:0%
+more and more comfortable with being in
+that limbo land that you talking about
+
+ align:start position:0%
+that limbo land that you talking about
+ 
+
+ align:start position:0%
+that limbo land that you talking about
+not quite knowing where they stood in
+
+ align:start position:0%
+not quite knowing where they stood in
+ 
+
+ align:start position:0%
+not quite knowing where they stood in
+terms of their
+
+ align:start position:0%
+terms of their
+ 
+
+ align:start position:0%
+terms of their
+assumptions that when we're dealing with
+
+ align:start position:0%
+assumptions that when we're dealing with
+ 
+
+ align:start position:0%
+assumptions that when we're dealing with
+people out in the real world who haven't
+
+ align:start position:0%
+people out in the real world who haven't
+ 
+
+ align:start position:0%
+people out in the real world who haven't
+taken this 10day course we're going to
+
+ align:start position:0%
+taken this 10day course we're going to
+ 
+
+ align:start position:0%
+taken this 10day course we're going to
+get people who are not even at day four
+
+ align:start position:0%
+get people who are not even at day four
+ 
+
+ align:start position:0%
+get people who are not even at day four
+they're they're at day one okay and so
+
+ align:start position:0%
+they're they're at day one okay and so
+ 
+
+ align:start position:0%
+they're they're at day one okay and so
+not even if they're day zero even seen
+
+ align:start position:0%
+not even if they're day zero even seen
+ 
+
+ align:start position:0%
+not even if they're day zero even seen
+the post
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so the closest thing out of all of those
+
+ align:start position:0%
+so the closest thing out of all of those
+ 
+
+ align:start position:0%
+so the closest thing out of all of those
+days the closest thing that gets to day
+
+ align:start position:0%
+days the closest thing that gets to day
+ 
+
+ align:start position:0%
+days the closest thing that gets to day
+Zero is all these problems people had at
+
+ align:start position:0%
+Zero is all these problems people had at
+ 
+
+ align:start position:0%
+Zero is all these problems people had at
+day four and so I feel like if we
+
+ align:start position:0%
+day four and so I feel like if we
+ 
+
+ align:start position:0%
+day four and so I feel like if we
+analyzed what's going on with all those
+
+ align:start position:0%
+analyzed what's going on with all those
+ 
+
+ align:start position:0%
+analyzed what's going on with all those
+problems in day four we'd have a better
+
+ align:start position:0%
+problems in day four we'd have a better
+ 
+
+ align:start position:0%
+problems in day four we'd have a better
+sense of what problems we might
+
+ align:start position:0%
+sense of what problems we might
+ 
+
+ align:start position:0%
+sense of what problems we might
+encounter with others when we try and
+
+ align:start position:0%
+encounter with others when we try and
+ 
+
+ align:start position:0%
+encounter with others when we try and
+integrate this into our work and that
+
+ align:start position:0%
+integrate this into our work and that
+ 
+
+ align:start position:0%
+integrate this into our work and that
+might help us answer the question of how
+
+ align:start position:0%
+might help us answer the question of how
+ 
+
+ align:start position:0%
+might help us answer the question of how
+do we do it on a daily basis at least in
+
+ align:start position:0%
+do we do it on a daily basis at least in
+ 
+
+ align:start position:0%
+do we do it on a daily basis at least in
+terms but could you synthesize your idea
+
+ align:start position:0%
+terms but could you synthesize your idea
+ 
+
+ align:start position:0%
+terms but could you synthesize your idea
+in just one phrase one yes the idea that
+
+ align:start position:0%
+in just one phrase one yes the idea that
+ 
+
+ align:start position:0%
+in just one phrase one yes the idea that
+you think that make may help
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+to
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+why it gets a little bit back to Chris's
+
+ align:start position:0%
+why it gets a little bit back to Chris's
+ 
+
+ align:start position:0%
+why it gets a little bit back to Chris's
+question why people struggled with that
+
+ align:start position:0%
+question why people struggled with that
+ 
+
+ align:start position:0%
+question why people struggled with that
+exercise okay and if we could understand
+
+ align:start position:0%
+exercise okay and if we could understand
+ 
+
+ align:start position:0%
+exercise okay and if we could understand
+why then it struggled with that exercise
+
+ align:start position:0%
+why then it struggled with that exercise
+ 
+
+ align:start position:0%
+why then it struggled with that exercise
+we might be able to understand how we
+
+ align:start position:0%
+we might be able to understand how we
+ 
+
+ align:start position:0%
+we might be able to understand how we
+could okay practice in use this in our
+
+ align:start position:0%
+could okay practice in use this in our
+ 
+
+ align:start position:0%
+could okay practice in use this in our
+daily practice and it would also help
+
+ align:start position:0%
+daily practice and it would also help
+ 
+
+ align:start position:0%
+daily practice and it would also help
+address the question that I had about
+
+ align:start position:0%
+address the question that I had about
+ 
+
+ align:start position:0%
+address the question that I had about
+how do you bring this into a larger
+
+ align:start position:0%
+how do you bring this into a larger
+ 
+
+ align:start position:0%
+how do you bring this into a larger
+scale of working with other people and
+
+ align:start position:0%
+scale of working with other people and
+ 
+
+ align:start position:0%
+scale of working with other people and
+getting them to think in the same terms
+
+ align:start position:0%
+getting them to think in the same terms
+ 
+
+ align:start position:0%
+getting them to think in the same terms
+which I think
+
+ align:start position:0%
+which I think
+ 
+
+ align:start position:0%
+which I think
+also okay I think I think Chris's
+
+ align:start position:0%
+also okay I think I think Chris's
+ 
+
+ align:start position:0%
+also okay I think I think Chris's
+question how what what can we learn from
+
+ align:start position:0%
+question how what what can we learn from
+ 
+
+ align:start position:0%
+question how what what can we learn from
+analyzing the problems people had with
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+exercise anyone have ideas about this
+
+ align:start position:0%
+exercise anyone have ideas about this
+ 
+
+ align:start position:0%
+exercise anyone have ideas about this
+question yes I I'm not sure if that even
+
+ align:start position:0%
+question yes I I'm not sure if that even
+ 
+
+ align:start position:0%
+question yes I I'm not sure if that even
+makes sense but I think based on what
+
+ align:start position:0%
+makes sense but I think based on what
+ 
+
+ align:start position:0%
+makes sense but I think based on what
+Lee had say and the impact of this
+
+ align:start position:0%
+Lee had say and the impact of this
+ 
+
+ align:start position:0%
+Lee had say and the impact of this
+exercise has caused on her and Bas off
+
+ align:start position:0%
+exercise has caused on her and Bas off
+ 
+
+ align:start position:0%
+exercise has caused on her and Bas off
+some of the experience I have and what
+
+ align:start position:0%
+some of the experience I have and what
+ 
+
+ align:start position:0%
+some of the experience I have and what
+you saying Ben sentence at the beginning
+
+ align:start position:0%
+you saying Ben sentence at the beginning
+ 
+
+ align:start position:0%
+you saying Ben sentence at the beginning
+it's so critical if you have to go in a
+
+ align:start position:0%
+it's so critical if you have to go in a
+ 
+
+ align:start position:0%
+it's so critical if you have to go in a
+community and you only have half an hour
+
+ align:start position:0%
+community and you only have half an hour
+ 
+
+ align:start position:0%
+community and you only have half an hour
+an hour to to bring an idea to bring a
+
+ align:start position:0%
+an hour to to bring an idea to bring a
+ 
+
+ align:start position:0%
+an hour to to bring an idea to bring a
+uh something that's going to touch many
+
+ align:start position:0%
+uh something that's going to touch many
+ 
+
+ align:start position:0%
+uh something that's going to touch many
+sensitive people there who might be the
+
+ align:start position:0%
+sensitive people there who might be the
+ 
+
+ align:start position:0%
+sensitive people there who might be the
+ones who make things happen how can you
+
+ align:start position:0%
+ones who make things happen how can you
+ 
+
+ align:start position:0%
+ones who make things happen how can you
+deal with that and I find that basic on
+
+ align:start position:0%
+deal with that and I find that basic on
+ 
+
+ align:start position:0%
+deal with that and I find that basic on
+what we see here is to be able to
+
+ align:start position:0%
+what we see here is to be able to
+ 
+
+ align:start position:0%
+what we see here is to be able to
+describe this kind of practice in a very
+
+ align:start position:0%
+describe this kind of practice in a very
+ 
+
+ align:start position:0%
+describe this kind of practice in a very
+small way when you come to a place when
+
+ align:start position:0%
+small way when you come to a place when
+ 
+
+ align:start position:0%
+small way when you come to a place when
+you're trying to identify is be able to
+
+ align:start position:0%
+you're trying to identify is be able to
+ 
+
+ align:start position:0%
+you're trying to identify is be able to
+be to have a dialogue and I think we go
+
+ align:start position:0%
+be to have a dialogue and I think we go
+ 
+
+ align:start position:0%
+be to have a dialogue and I think we go
+back to the dialogue of of bring this
+
+ align:start position:0%
+back to the dialogue of of bring this
+ 
+
+ align:start position:0%
+back to the dialogue of of bring this
+kind of understanding to whatever way
+
+ align:start position:0%
+kind of understanding to whatever way
+ 
+
+ align:start position:0%
+kind of understanding to whatever way
+you're going to work so you won't have
+
+ align:start position:0%
+you're going to work so you won't have
+ 
+
+ align:start position:0%
+you're going to work so you won't have
+reaction like that when people walk away
+
+ align:start position:0%
+reaction like that when people walk away
+ 
+
+ align:start position:0%
+reaction like that when people walk away
+because what you're trying where you're
+
+ align:start position:0%
+because what you're trying where you're
+ 
+
+ align:start position:0%
+because what you're trying where you're
+trying to get does that make sense okay
+
+ align:start position:0%
+trying to get does that make sense okay
+ 
+
+ align:start position:0%
+trying to get does that make sense okay
+thank you
+
+ align:start position:0%
+thank you
+ 
+
+ align:start position:0%
+thank you
+CIA she asked it first I
+
+ align:start position:0%
+CIA she asked it first I
+ 
+
+ align:start position:0%
+CIA she asked it first I
+said common practice implicates a
+
+ align:start position:0%
+said common practice implicates a
+ 
+
+ align:start position:0%
+said common practice implicates a
+certain maturity of group dynamics to
+
+ align:start position:0%
+certain maturity of group dynamics to
+ 
+
+ align:start position:0%
+certain maturity of group dynamics to
+happen Okay in terms of individual
+
+ align:start position:0%
+happen Okay in terms of individual
+ 
+
+ align:start position:0%
+happen Okay in terms of individual
+dynamic or individual dynamic in the
+
+ align:start position:0%
+dynamic or individual dynamic in the
+ 
+
+ align:start position:0%
+dynamic or individual dynamic in the
+relationship with the people that you
+
+ align:start position:0%
+relationship with the people that you
+ 
+
+ align:start position:0%
+relationship with the people that you
+are working with are the people that are
+
+ align:start position:0%
+are working with are the people that are
+ 
+
+ align:start position:0%
+are working with are the people that are
+part of the community that you intend to
+
+ align:start position:0%
+part of the community that you intend to
+ 
+
+ align:start position:0%
+part of the community that you intend to
+where you intend to
+
+ align:start position:0%
+where you intend to
+ 
+
+ align:start position:0%
+where you intend to
+implement the reflective practice or a
+
+ align:start position:0%
+implement the reflective practice or a
+ 
+
+ align:start position:0%
+implement the reflective practice or a
+culture of reflective practice it's not
+
+ align:start position:0%
+culture of reflective practice it's not
+ 
+
+ align:start position:0%
+culture of reflective practice it's not
+what I mean is it's just not something
+
+ align:start position:0%
+what I mean is it's just not something
+ 
+
+ align:start position:0%
+what I mean is it's just not something
+that happens in the first day it
+
+ align:start position:0%
+that happens in the first day it
+ 
+
+ align:start position:0%
+that happens in the first day it
+replicates certain process
+
+ align:start position:0%
+replicates certain process
+ 
+
+ align:start position:0%
+replicates certain process
+of familiarization with the groups the
+
+ align:start position:0%
+of familiarization with the groups the
+ 
+
+ align:start position:0%
+of familiarization with the groups the
+group of
+
+ align:start position:0%
+group of
+ 
+
+ align:start position:0%
+group of
+okay people need to feel comfortable
+
+ align:start position:0%
+okay people need to feel comfortable
+ 
+
+ align:start position:0%
+okay people need to feel comfortable
+with the others they need to trust each
+
+ align:start position:0%
+with the others they need to trust each
+ 
+
+ align:start position:0%
+with the others they need to trust each
+others things like that they need to
+
+ align:start position:0%
+others things like that they need to
+ 
+
+ align:start position:0%
+others things like that they need to
+construct some kind of relation among
+
+ align:start position:0%
+construct some kind of relation among
+ 
+
+ align:start position:0%
+construct some kind of relation among
+them for feel comfortable sharing this
+
+ align:start position:0%
+them for feel comfortable sharing this
+ 
+
+ align:start position:0%
+them for feel comfortable sharing this
+kind of
+
+ align:start position:0%
+kind of
+ 
+
+ align:start position:0%
+kind of
+effort okay Chris I I would almost
+
+ align:start position:0%
+effort okay Chris I I would almost
+ 
+
+ align:start position:0%
+effort okay Chris I I would almost
+phrase what you're saying like I agree
+
+ align:start position:0%
+phrase what you're saying like I agree
+ 
+
+ align:start position:0%
+phrase what you're saying like I agree
+with what you're saying I almost phrase
+
+ align:start position:0%
+with what you're saying I almost phrase
+ 
+
+ align:start position:0%
+with what you're saying I almost phrase
+it as Unity like you know it's like
+
+ align:start position:0%
+it as Unity like you know it's like
+ 
+
+ align:start position:0%
+it as Unity like you know it's like
+there's sort of a sense of shared Spirit
+
+ align:start position:0%
+there's sort of a sense of shared Spirit
+ 
+
+ align:start position:0%
+there's sort of a sense of shared Spirit
+or common like there's a common energy
+
+ align:start position:0%
+or common like there's a common energy
+ 
+
+ align:start position:0%
+or common like there's a common energy
+that sort of develops over time that you
+
+ align:start position:0%
+that sort of develops over time that you
+ 
+
+ align:start position:0%
+that sort of develops over time that you
+don't get in the first day and or two
+
+ align:start position:0%
+don't get in the first day and or two
+ 
+
+ align:start position:0%
+don't get in the first day and or two
+days the first two or 3 days which maybe
+
+ align:start position:0%
+days the first two or 3 days which maybe
+ 
+
+ align:start position:0%
+days the first two or 3 days which maybe
+you know I mean once you start working
+
+ align:start position:0%
+you know I mean once you start working
+ 
+
+ align:start position:0%
+you know I mean once you start working
+on stuff you know that tends to open up
+
+ align:start position:0%
+on stuff you know that tends to open up
+ 
+
+ align:start position:0%
+on stuff you know that tends to open up
+and I don't know so maybe maybe that' be
+
+ align:start position:0%
+and I don't know so maybe maybe that' be
+ 
+
+ align:start position:0%
+and I don't know so maybe maybe that' be
+it maybe I could ask a question which
+
+ align:start position:0%
+it maybe I could ask a question which
+ 
+
+ align:start position:0%
+it maybe I could ask a question which
+was what are the contextual conditions
+
+ align:start position:0%
+was what are the contextual conditions
+ 
+
+ align:start position:0%
+was what are the contextual conditions
+needed for I don't know reflective
+
+ align:start position:0%
+needed for I don't know reflective
+ 
+
+ align:start position:0%
+needed for I don't know reflective
+practice to work work well okay so we
+
+ align:start position:0%
+practice to work work well okay so we
+ 
+
+ align:start position:0%
+practice to work work well okay so we
+should put attention to the contextual
+
+ align:start position:0%
+should put attention to the contextual
+ 
+
+ align:start position:0%
+should put attention to the contextual
+conditions like maybe it doesn't work in
+
+ align:start position:0%
+conditions like maybe it doesn't work in
+ 
+
+ align:start position:0%
+conditions like maybe it doesn't work in
+the first two days making this process
+
+ align:start position:0%
+the first two days making this process
+ 
+
+ align:start position:0%
+the first two days making this process
+going
+
+ align:start position:0%
+going
+ 
+
+ align:start position:0%
+going
+forward that is a much better phrasing
+
+ align:start position:0%
+forward that is a much better phrasing
+ 
+
+ align:start position:0%
+forward that is a much better phrasing
+of what I intended to say
+
+ align:start position:0%
+of what I intended to say
+ 
+
+ align:start position:0%
+of what I intended to say
+actually about the context where you do
+
+ align:start position:0%
+actually about the context where you do
+ 
+
+ align:start position:0%
+actually about the context where you do
+it which I think is very important okay
+
+ align:start position:0%
+it which I think is very important okay
+ 
+
+ align:start position:0%
+it which I think is very important okay
+but what if you only have one
+
+ align:start position:0%
+but what if you only have one
+ 
+
+ align:start position:0%
+but what if you only have one
+day
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay but we cannot we cannot solve this
+
+ align:start position:0%
+okay but we cannot we cannot solve this
+ 
+
+ align:start position:0%
+okay but we cannot we cannot solve this
+question this
+
+ align:start position:0%
+question this
+ 
+
+ align:start position:0%
+question this
+moment learning to ask the right
+
+ align:start position:0%
+moment learning to ask the right
+ 
+
+ align:start position:0%
+moment learning to ask the right
+questions learning to ask the right
+
+ align:start position:0%
+questions learning to ask the right
+ 
+
+ align:start position:0%
+questions learning to ask the right
+questions if we can learn how to ask the
+
+ align:start position:0%
+questions if we can learn how to ask the
+ 
+
+ align:start position:0%
+questions if we can learn how to ask the
+right
+
+ align:start position:0%
+right
+ 
+
+ align:start position:0%
+right
+questions yes okay great thank you very
+
+ align:start position:0%
+questions yes okay great thank you very
+ 
+
+ align:start position:0%
+questions yes okay great thank you very
+much yeah that's that's what because we
+
+ align:start position:0%
+much yeah that's that's what because we
+ 
+
+ align:start position:0%
+much yeah that's that's what because we
+can only control what we do do so if we
+
+ align:start position:0%
+can only control what we do do so if we
+ 
+
+ align:start position:0%
+can only control what we do do so if we
+if we have a problem to address in a
+
+ align:start position:0%
+if we have a problem to address in a
+ 
+
+ align:start position:0%
+if we have a problem to address in a
+community we're going we can only do we
+
+ align:start position:0%
+community we're going we can only do we
+ 
+
+ align:start position:0%
+community we're going we can only do we
+can only control our own approach so how
+
+ align:start position:0%
+can only control our own approach so how
+ 
+
+ align:start position:0%
+can only control our own approach so how
+do we make this common practice for
+
+ align:start position:0%
+do we make this common practice for
+ 
+
+ align:start position:0%
+do we make this common practice for
+us by asking the right questions how do
+
+ align:start position:0%
+us by asking the right questions how do
+ 
+
+ align:start position:0%
+us by asking the right questions how do
+we remember to ask the right questions
+
+ align:start position:0%
+we remember to ask the right questions
+ 
+
+ align:start position:0%
+we remember to ask the right questions
+to ourselves right yeah because I can't
+
+ align:start position:0%
+to ourselves right yeah because I can't
+ 
+
+ align:start position:0%
+to ourselves right yeah because I can't
+okay to think about going into community
+
+ align:start position:0%
+okay to think about going into community
+ 
+
+ align:start position:0%
+okay to think about going into community
+and get them all to do this is
+
+ align:start position:0%
+and get them all to do this is
+ 
+
+ align:start position:0%
+and get them all to do this is
+overwhelming for me right now cuz I my
+
+ align:start position:0%
+overwhelming for me right now cuz I my
+ 
+
+ align:start position:0%
+overwhelming for me right now cuz I my
+question was how do I make this a habit
+
+ align:start position:0%
+question was how do I make this a habit
+ 
+
+ align:start position:0%
+question was how do I make this a habit
+for me first you know if I can ask the
+
+ align:start position:0%
+for me first you know if I can ask the
+ 
+
+ align:start position:0%
+for me first you know if I can ask the
+right question maybe I can bring
+
+ align:start position:0%
+right question maybe I can bring
+ 
+
+ align:start position:0%
+right question maybe I can bring
+somebody on board with going into this
+
+ align:start position:0%
+somebody on board with going into this
+ 
+
+ align:start position:0%
+somebody on board with going into this
+whole process okay if I don't approach
+
+ align:start position:0%
+whole process okay if I don't approach
+ 
+
+ align:start position:0%
+whole process okay if I don't approach
+it you
+
+ align:start position:0%
+it you
+ 
+
+ align:start position:0%
+it you
+know okay so the the the capacity
+
+ align:start position:0%
+know okay so the the the capacity
+ 
+
+ align:start position:0%
+know okay so the the the capacity
+for asking the the right question is
+
+ align:start position:0%
+for asking the the right question is
+ 
+
+ align:start position:0%
+for asking the the right question is
+something that we make
+
+ align:start position:0%
+something that we make
+ 
+
+ align:start position:0%
+something that we make
+easier for one to reflect no to remember
+
+ align:start position:0%
+easier for one to reflect no to remember
+ 
+
+ align:start position:0%
+easier for one to reflect no to remember
+ask the right
+
+ align:start position:0%
+ask the right
+ 
+
+ align:start position:0%
+ask the right
+question okay and also to understand
+
+ align:start position:0%
+question okay and also to understand
+ 
+
+ align:start position:0%
+question okay and also to understand
+what is the yeah what is the right yeah
+
+ align:start position:0%
+what is the yeah what is the right yeah
+ 
+
+ align:start position:0%
+what is the yeah what is the right yeah
+how to ask the right question okay we
+
+ align:start position:0%
+how to ask the right question okay we
+ 
+
+ align:start position:0%
+how to ask the right question okay we
+have a new question here how to ask the
+
+ align:start position:0%
+have a new question here how to ask the
+ 
+
+ align:start position:0%
+have a new question here how to ask the
+right question but it's a good one we
+
+ align:start position:0%
+right question but it's a good one we
+ 
+
+ align:start position:0%
+right question but it's a good one we
+think should think about
+
+ align:start position:0%
+think should think about
+ 
+
+ align:start position:0%
+think should think about
+it that you you know the group that your
+
+ align:start position:0%
+it that you you know the group that your
+ 
+
+ align:start position:0%
+it that you you know the group that your
+work have some familiarity to the people
+
+ align:start position:0%
+work have some familiarity to the people
+ 
+
+ align:start position:0%
+work have some familiarity to the people
+you're working with um would that help
+
+ align:start position:0%
+you're working with um would that help
+ 
+
+ align:start position:0%
+you're working with um would that help
+you address them in a different way if
+
+ align:start position:0%
+you address them in a different way if
+ 
+
+ align:start position:0%
+you address them in a different way if
+you know the group have some idea the
+
+ align:start position:0%
+you know the group have some idea the
+ 
+
+ align:start position:0%
+you know the group have some idea the
+background of people that you're working
+
+ align:start position:0%
+background of people that you're working
+ 
+
+ align:start position:0%
+background of people that you're working
+with the the experience of scissor is
+
+ align:start position:0%
+with the the experience of scissor is
+ 
+
+ align:start position:0%
+with the the experience of scissor is
+that it's a almost a requirement people
+
+ align:start position:0%
+that it's a almost a requirement people
+ 
+
+ align:start position:0%
+that it's a almost a requirement people
+to share some kind of experience before
+
+ align:start position:0%
+to share some kind of experience before
+ 
+
+ align:start position:0%
+to share some kind of experience before
+for making the process as a group not
+
+ align:start position:0%
+for making the process as a group not
+ 
+
+ align:start position:0%
+for making the process as a group not
+necessarily
+
+ align:start position:0%
+necessarily
+ 
+
+ align:start position:0%
+necessarily
+for for working individually but for
+
+ align:start position:0%
+for for working individually but for
+ 
+
+ align:start position:0%
+for for working individually but for
+working as a group is required to share
+
+ align:start position:0%
+working as a group is required to share
+ 
+
+ align:start position:0%
+working as a group is required to share
+the same kind of experience or the same
+
+ align:start position:0%
+the same kind of experience or the same
+ 
+
+ align:start position:0%
+the same kind of experience or the same
+experience so I I think this if you
+
+ align:start position:0%
+experience so I I think this if you
+ 
+
+ align:start position:0%
+experience so I I think this if you
+think about this question how to make
+
+ align:start position:0%
+think about this question how to make
+ 
+
+ align:start position:0%
+think about this question how to make
+reflective practice common practice for
+
+ align:start position:0%
+reflective practice common practice for
+ 
+
+ align:start position:0%
+reflective practice common practice for
+ourselves from an individual level you
+
+ align:start position:0%
+ourselves from an individual level you
+ 
+
+ align:start position:0%
+ourselves from an individual level you
+know this what what nikisha and JY just
+
+ align:start position:0%
+know this what what nikisha and JY just
+ 
+
+ align:start position:0%
+know this what what nikisha and JY just
+mentioned really it's it's a learning
+
+ align:start position:0%
+mentioned really it's it's a learning
+ 
+
+ align:start position:0%
+mentioned really it's it's a learning
+from from this from what we've we see in
+
+ align:start position:0%
+from from this from what we've we see in
+ 
+
+ align:start position:0%
+from from this from what we've we see in
+these critical moments you know the
+
+ align:start position:0%
+these critical moments you know the
+ 
+
+ align:start position:0%
+these critical moments you know the
+questions some of these things help
+
+ align:start position:0%
+questions some of these things help
+ 
+
+ align:start position:0%
+questions some of these things help
+that's that's a lesson we get that's
+
+ align:start position:0%
+that's that's a lesson we get that's
+ 
+
+ align:start position:0%
+that's that's a lesson we get that's
+something we get that helps us begin to
+
+ align:start position:0%
+something we get that helps us begin to
+ 
+
+ align:start position:0%
+something we get that helps us begin to
+answer this question so try to focus on
+
+ align:start position:0%
+answer this question so try to focus on
+ 
+
+ align:start position:0%
+answer this question so try to focus on
+those types of
+
+ align:start position:0%
+those types of
+ 
+
+ align:start position:0%
+those types of
+things okay for name um and you said
+
+ align:start position:0%
+things okay for name um and you said
+ 
+
+ align:start position:0%
+things okay for name um and you said
+where we would where would we look um
+
+ align:start position:0%
+where we would where would we look um
+ 
+
+ align:start position:0%
+where we would where would we look um
+for these things and I think one of the
+
+ align:start position:0%
+for these things and I think one of the
+ 
+
+ align:start position:0%
+for these things and I think one of the
+of the things that I heard might Ezra
+
+ align:start position:0%
+of the things that I heard might Ezra
+ 
+
+ align:start position:0%
+of the things that I heard might Ezra
+who said it was um the critical moments
+
+ align:start position:0%
+who said it was um the critical moments
+ 
+
+ align:start position:0%
+who said it was um the critical moments
+were related to when the moment was
+
+ align:start position:0%
+were related to when the moment was
+ 
+
+ align:start position:0%
+were related to when the moment was
+relevant to the
+
+ align:start position:0%
+relevant to the
+ 
+
+ align:start position:0%
+relevant to the
+individual and so that's what I that's
+
+ align:start position:0%
+individual and so that's what I that's
+ 
+
+ align:start position:0%
+individual and so that's what I that's
+where I would
+
+ align:start position:0%
+where I would
+ 
+
+ align:start position:0%
+where I would
+look figure out how to
+
+ align:start position:0%
+look figure out how to
+ 
+
+ align:start position:0%
+look figure out how to
+make can you repeat please yeah that's
+
+ align:start position:0%
+make can you repeat please yeah that's
+ 
+
+ align:start position:0%
+make can you repeat please yeah that's
+um if we can you repeat please um you
+
+ align:start position:0%
+um if we can you repeat please um you
+ 
+
+ align:start position:0%
+um if we can you repeat please um you
+asked us where we would look yes to
+
+ align:start position:0%
+asked us where we would look yes to
+ 
+
+ align:start position:0%
+asked us where we would look yes to
+figure out how to make common practice
+
+ align:start position:0%
+figure out how to make common practice
+ 
+
+ align:start position:0%
+figure out how to make common practice
+more practical mhm uh I would look to
+
+ align:start position:0%
+more practical mhm uh I would look to
+ 
+
+ align:start position:0%
+more practical mhm uh I would look to
+moments of relevance for the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+individual okay any other idea
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+[Music]
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so you feel comfortable with this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+answers some other things come in mind
+
+ align:start position:0%
+answers some other things come in mind
+ 
+
+ align:start position:0%
+answers some other things come in mind
+for example X Esra had a question at the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+beginning remember should we come to
+
+ align:start position:0%
+beginning remember should we come to
+ 
+
+ align:start position:0%
+beginning remember should we come to
+class or not huh should he come to class
+
+ align:start position:0%
+class or not huh should he come to class
+ 
+
+ align:start position:0%
+class or not huh should he come to class
+or
+
+ align:start position:0%
+or
+ 
+
+ align:start position:0%
+or
+not okay I don't remember but you had a
+
+ align:start position:0%
+not okay I don't remember but you had a
+ 
+
+ align:start position:0%
+not okay I don't remember but you had a
+question I ask you wait for a moment
+
+ align:start position:0%
+question I ask you wait for a moment
+ 
+
+ align:start position:0%
+question I ask you wait for a moment
+because we are now trying to answer uh
+
+ align:start position:0%
+because we are now trying to answer uh
+ 
+
+ align:start position:0%
+because we are now trying to answer uh
+no it was about the the background the
+
+ align:start position:0%
+no it was about the the background the
+ 
+
+ align:start position:0%
+no it was about the the background the
+context of what's happening in our daily
+
+ align:start position:0%
+context of what's happening in our daily
+ 
+
+ align:start position:0%
+context of what's happening in our daily
+lives outside of class that affects
+
+ align:start position:0%
+lives outside of class that affects
+ 
+
+ align:start position:0%
+lives outside of class that affects
+where we
+
+ align:start position:0%
+where we
+ 
+
+ align:start position:0%
+where we
+the critical moments how we okay it's
+
+ align:start position:0%
+the critical moments how we okay it's
+ 
+
+ align:start position:0%
+the critical moments how we okay it's
+only about how how we Define the
+
+ align:start position:0%
+only about how how we Define the
+ 
+
+ align:start position:0%
+only about how how we Define the
+critical moments no it's about what we
+
+ align:start position:0%
+critical moments no it's about what we
+ 
+
+ align:start position:0%
+critical moments no it's about what we
+were what we're going through personally
+
+ align:start position:0%
+were what we're going through personally
+ 
+
+ align:start position:0%
+were what we're going through personally
+in our lives that may have impacted the
+
+ align:start position:0%
+in our lives that may have impacted the
+ 
+
+ align:start position:0%
+in our lives that may have impacted the
+yes IDE I I got it okay
+
+ align:start position:0%
+yes IDE I I got it okay
+ 
+
+ align:start position:0%
+yes IDE I I got it okay
+okay yes qu I had a thought on Rene's
+
+ align:start position:0%
+okay yes qu I had a thought on Rene's
+ 
+
+ align:start position:0%
+okay yes qu I had a thought on Rene's
+point which was maybe maybe we can't
+
+ align:start position:0%
+point which was maybe maybe we can't
+ 
+
+ align:start position:0%
+point which was maybe maybe we can't
+really go through the whole process of
+
+ align:start position:0%
+really go through the whole process of
+ 
+
+ align:start position:0%
+really go through the whole process of
+reflective practice quickly but is there
+
+ align:start position:0%
+reflective practice quickly but is there
+ 
+
+ align:start position:0%
+reflective practice quickly but is there
+a way convey the value of it quickly at
+
+ align:start position:0%
+a way convey the value of it quickly at
+ 
+
+ align:start position:0%
+a way convey the value of it quickly at
+least so at least people at least you
+
+ align:start position:0%
+least so at least people at least you
+ 
+
+ align:start position:0%
+least so at least people at least you
+get them hooked and like they kind of
+
+ align:start position:0%
+get them hooked and like they kind of
+ 
+
+ align:start position:0%
+get them hooked and like they kind of
+you know raises people's curiosity and
+
+ align:start position:0%
+you know raises people's curiosity and
+ 
+
+ align:start position:0%
+you know raises people's curiosity and
+say well H that's interesting maybe I'll
+
+ align:start position:0%
+say well H that's interesting maybe I'll
+ 
+
+ align:start position:0%
+say well H that's interesting maybe I'll
+stick it out for two days or whatever it
+
+ align:start position:0%
+stick it out for two days or whatever it
+ 
+
+ align:start position:0%
+stick it out for two days or whatever it
+takes to really start to get into it to
+
+ align:start position:0%
+takes to really start to get into it to
+ 
+
+ align:start position:0%
+takes to really start to get into it to
+the point where you can feel you can
+
+ align:start position:0%
+the point where you can feel you can
+ 
+
+ align:start position:0%
+the point where you can feel you can
+feel the value you know maybe like our
+
+ align:start position:0%
+feel the value you know maybe like our
+ 
+
+ align:start position:0%
+feel the value you know maybe like our
+day four period when you kind of you
+
+ align:start position:0%
+day four period when you kind of you
+ 
+
+ align:start position:0%
+day four period when you kind of you
+know really
+
+ align:start position:0%
+know really
+ 
+
+ align:start position:0%
+know really
+engage I don't know yeah I'm not sure
+
+ align:start position:0%
+engage I don't know yeah I'm not sure
+ 
+
+ align:start position:0%
+engage I don't know yeah I'm not sure
+how to do that but
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so I think that we
+
+ align:start position:0%
+okay so I think that we
+ 
+
+ align:start position:0%
+okay so I think that we
+have um it's related actually with the
+
+ align:start position:0%
+have um it's related actually with the
+ 
+
+ align:start position:0%
+have um it's related actually with the
+type of language that you use to
+
+ align:start position:0%
+type of language that you use to
+ 
+
+ align:start position:0%
+type of language that you use to
+communicate what is reflective practice
+
+ align:start position:0%
+communicate what is reflective practice
+ 
+
+ align:start position:0%
+communicate what is reflective practice
+my question is there a way to
+
+ align:start position:0%
+my question is there a way to
+ 
+
+ align:start position:0%
+my question is there a way to
+communicate in a different way that can
+
+ align:start position:0%
+communicate in a different way that can
+ 
+
+ align:start position:0%
+communicate in a different way that can
+attract more
+
+ align:start position:0%
+attract more
+ 
+
+ align:start position:0%
+attract more
+people to understand and to to
+
+ align:start position:0%
+people to understand and to to
+ 
+
+ align:start position:0%
+people to understand and to to
+understand and to make it a more common
+
+ align:start position:0%
+understand and to make it a more common
+ 
+
+ align:start position:0%
+understand and to make it a more common
+and useful thing in people's lives and
+
+ align:start position:0%
+and useful thing in people's lives and
+ 
+
+ align:start position:0%
+and useful thing in people's lives and
+not so much an abstract thinking about a
+
+ align:start position:0%
+not so much an abstract thinking about a
+ 
+
+ align:start position:0%
+not so much an abstract thinking about a
+situation and then you need to
+
+ align:start position:0%
+situation and then you need to
+ 
+
+ align:start position:0%
+situation and then you need to
+just thinking about the the way you
+
+ align:start position:0%
+just thinking about the the way you
+ 
+
+ align:start position:0%
+just thinking about the the way you
+communicate the way the way that you use
+
+ align:start position:0%
+communicate the way the way that you use
+ 
+
+ align:start position:0%
+communicate the way the way that you use
+to communicate what you want
+
+ align:start position:0%
+to communicate what you want
+ 
+
+ align:start position:0%
+to communicate what you want
+to develop at a common practice okay the
+
+ align:start position:0%
+to develop at a common practice okay the
+ 
+
+ align:start position:0%
+to develop at a common practice okay the
+vocabulary the kind of words are uses no
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay not the vocabulary the mediums you
+
+ align:start position:0%
+okay not the vocabulary the mediums you
+ 
+
+ align:start position:0%
+okay not the vocabulary the mediums you
+use to
+
+ align:start position:0%
+use to
+ 
+
+ align:start position:0%
+use to
+address the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the mediums you use it's not only the
+
+ align:start position:0%
+the mediums you use it's not only the
+ 
+
+ align:start position:0%
+the mediums you use it's not only the
+vocabulary it's how how you communicate
+
+ align:start position:0%
+vocabulary it's how how you communicate
+ 
+
+ align:start position:0%
+vocabulary it's how how you communicate
+if you communicate through workshops if
+
+ align:start position:0%
+if you communicate through workshops if
+ 
+
+ align:start position:0%
+if you communicate through workshops if
+you communicate through media
+
+ align:start position:0%
+you communicate through media
+ 
+
+ align:start position:0%
+you communicate through media
+um commun type of communication if you
+
+ align:start position:0%
+um commun type of communication if you
+ 
+
+ align:start position:0%
+um commun type of communication if you
+just what is what is
+
+ align:start position:0%
+just what is what is
+ 
+
+ align:start position:0%
+just what is what is
+the is the the channel the channel to
+
+ align:start position:0%
+the is the the channel the channel to
+ 
+
+ align:start position:0%
+the is the the channel the channel to
+get to people and okay what is the would
+
+ align:start position:0%
+get to people and okay what is the would
+ 
+
+ align:start position:0%
+get to people and okay what is the would
+that be models would that be the
+
+ align:start position:0%
+that be models would that be the
+ 
+
+ align:start position:0%
+that be models would that be the
+different models they use
+
+ align:start position:0%
+different models they use
+ 
+
+ align:start position:0%
+different models they use
+[Music]
+
+ align:start position:0%
+[Music]
+ 
+
+ align:start position:0%
+[Music]
+depending on the
+
+ align:start position:0%
+depending on the
+ 
+
+ align:start position:0%
+depending on the
+group we should be aware of that because
+
+ align:start position:0%
+group we should be aware of that because
+ 
+
+ align:start position:0%
+group we should be aware of that because
+different people prefer different ways
+
+ align:start position:0%
+different people prefer different ways
+ 
+
+ align:start position:0%
+different people prefer different ways
+of expressions in in media yes okay
+
+ align:start position:0%
+of expressions in in media yes okay
+ 
+
+ align:start position:0%
+of expressions in in media yes okay
+thank you very much the best one um I
+
+ align:start position:0%
+thank you very much the best one um I
+ 
+
+ align:start position:0%
+thank you very much the best one um I
+was just going to say that maybe one way
+
+ align:start position:0%
+was just going to say that maybe one way
+ 
+
+ align:start position:0%
+was just going to say that maybe one way
+to try to answer this question of how to
+
+ align:start position:0%
+to try to answer this question of how to
+ 
+
+ align:start position:0%
+to try to answer this question of how to
+make the practice more something that
+
+ align:start position:0%
+make the practice more something that
+ 
+
+ align:start position:0%
+make the practice more something that
+comes in your daily life would be to try
+
+ align:start position:0%
+comes in your daily life would be to try
+ 
+
+ align:start position:0%
+comes in your daily life would be to try
+and figure
+
+ align:start position:0%
+and figure
+ 
+
+ align:start position:0%
+and figure
+out which of the exercises or what of
+
+ align:start position:0%
+out which of the exercises or what of
+ 
+
+ align:start position:0%
+out which of the exercises or what of
+the exercises you found to be most
+
+ align:start position:0%
+the exercises you found to be most
+ 
+
+ align:start position:0%
+the exercises you found to be most
+valuable and start with trying to
+
+ align:start position:0%
+valuable and start with trying to
+ 
+
+ align:start position:0%
+valuable and start with trying to
+incorporate those kinds of things into
+
+ align:start position:0%
+incorporate those kinds of things into
+ 
+
+ align:start position:0%
+incorporate those kinds of things into
+your dat like which are the ones that
+
+ align:start position:0%
+your dat like which are the ones that
+ 
+
+ align:start position:0%
+your dat like which are the ones that
+you could do on on a regular
+
+ align:start position:0%
+you could do on on a regular
+ 
+
+ align:start position:0%
+you could do on on a regular
+basis that that would have the most the
+
+ align:start position:0%
+basis that that would have the most the
+ 
+
+ align:start position:0%
+basis that that would have the most the
+most impact
+
+ align:start position:0%
+most impact
+ 
+
+ align:start position:0%
+most impact
+on okay the actual
+
+ align:start position:0%
+on okay the actual
+ 
+
+ align:start position:0%
+on okay the actual
+exercises you are thinking about the
+
+ align:start position:0%
+exercises you are thinking about the
+ 
+
+ align:start position:0%
+exercises you are thinking about the
+exercise we made in the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+course like with framing or model
+
+ align:start position:0%
+course like with framing or model
+ 
+
+ align:start position:0%
+course like with framing or model
+models things like that and try to to
+
+ align:start position:0%
+models things like that and try to to
+ 
+
+ align:start position:0%
+models things like that and try to to
+use what we have learned with this
+
+ align:start position:0%
+use what we have learned with this
+ 
+
+ align:start position:0%
+use what we have learned with this
+exercise in Practical situation we are
+
+ align:start position:0%
+exercise in Practical situation we are
+ 
+
+ align:start position:0%
+exercise in Practical situation we are
+facing okay like which of those do you
+
+ align:start position:0%
+facing okay like which of those do you
+ 
+
+ align:start position:0%
+facing okay like which of those do you
+feel like you got the most value out of
+
+ align:start position:0%
+feel like you got the most value out of
+ 
+
+ align:start position:0%
+feel like you got the most value out of
+because each one is going to take you
+
+ align:start position:0%
+because each one is going to take you
+ 
+
+ align:start position:0%
+because each one is going to take you
+some time to do so which one did you
+
+ align:start position:0%
+some time to do so which one did you
+ 
+
+ align:start position:0%
+some time to do so which one did you
+feel like really gave you the most bank
+
+ align:start position:0%
+feel like really gave you the most bank
+ 
+
+ align:start position:0%
+feel like really gave you the most bank
+for your buck that you could then go and
+
+ align:start position:0%
+for your buck that you could then go and
+ 
+
+ align:start position:0%
+for your buck that you could then go and
+Implement okay great because this is the
+
+ align:start position:0%
+Implement okay great because this is the
+ 
+
+ align:start position:0%
+Implement okay great because this is the
+starting point no you need a starting
+
+ align:start position:0%
+starting point no you need a starting
+ 
+
+ align:start position:0%
+starting point no you need a starting
+point for improving your the use of
+
+ align:start position:0%
+point for improving your the use of
+ 
+
+ align:start position:0%
+point for improving your the use of
+refective practice not not the theory in
+
+ align:start position:0%
+refective practice not not the theory in
+ 
+
+ align:start position:0%
+refective practice not not the theory in
+general but one point where you began to
+
+ align:start position:0%
+general but one point where you began to
+ 
+
+ align:start position:0%
+general but one point where you began to
+practice this it's no okay thank you
+
+ align:start position:0%
+practice this it's no okay thank you
+ 
+
+ align:start position:0%
+practice this it's no okay thank you
+very much let's go for a break a very
+
+ align:start position:0%
+very much let's go for a break a very
+ 
+
+ align:start position:0%
+very much let's go for a break a very
+brief break because we need to make
+
+ align:start position:0%
+brief break because we need to make
+ 
+
+ align:start position:0%
+brief break because we need to make
+another exercise before to end the
+
+ align:start position:0%
+another exercise before to end the
+ 
+
+ align:start position:0%
+another exercise before to end the
+course okay so do we have how long five
+
+ align:start position:0%
+course okay so do we have how long five
+ 
+
+ align:start position:0%
+course okay so do we have how long five
+minutes please yeah really five minutes
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the the
+
+ align:start position:0%
+the the
+ 
+
+ align:start position:0%
+the the
+purpose the
+
+ align:start position:0%
+purpose the
+ 
+
+ align:start position:0%
+purpose the
+purpose is not to give
+
+ align:start position:0%
+purpose is not to give
+ 
+
+ align:start position:0%
+purpose is not to give
+you
+
+ align:start position:0%
+you
+ 
+
+ align:start position:0%
+you
+a
+
+ align:start position:0%
+a
+ 
+
+ align:start position:0%
+a
+extensive vision of what is happening
+
+ align:start position:0%
+extensive vision of what is happening
+ 
+
+ align:start position:0%
+extensive vision of what is happening
+just try
+
+ align:start position:0%
+just try
+ 
+
+ align:start position:0%
+just try
+to to understand the context
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+where reflective practice emerged
+
+ align:start position:0%
+where reflective practice emerged
+ 
+
+ align:start position:0%
+where reflective practice emerged
+and what kind of context we are facing
+
+ align:start position:0%
+and what kind of context we are facing
+ 
+
+ align:start position:0%
+and what kind of context we are facing
+now okay yes we we need each one
+
+ align:start position:0%
+now okay yes we we need each one
+ 
+
+ align:start position:0%
+now okay yes we we need each one
+please yeah you can no no no let's wait
+
+ align:start position:0%
+please yeah you can no no no let's wait
+ 
+
+ align:start position:0%
+please yeah you can no no no let's wait
+okay the question is the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+first the question is that reflective
+
+ align:start position:0%
+first the question is that reflective
+ 
+
+ align:start position:0%
+first the question is that reflective
+practice is something that was
+
+ align:start position:0%
+practice is something that was
+ 
+
+ align:start position:0%
+practice is something that was
+invented in these' 70s and 80s and the
+
+ align:start position:0%
+invented in these' 70s and 80s and the
+ 
+
+ align:start position:0%
+invented in these' 70s and 80s and the
+beginning of the '90s
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+99s
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+and in the last 10 years it begins to to
+
+ align:start position:0%
+and in the last 10 years it begins to to
+ 
+
+ align:start position:0%
+and in the last 10 years it begins to to
+be applied but a lot of people
+
+ align:start position:0%
+be applied but a lot of people
+ 
+
+ align:start position:0%
+be applied but a lot of people
+worldwide in the last 10 years let's
+
+ align:start position:0%
+worldwide in the last 10 years let's
+ 
+
+ align:start position:0%
+worldwide in the last 10 years let's
+go after reflective practice was created
+
+ align:start position:0%
+go after reflective practice was created
+ 
+
+ align:start position:0%
+go after reflective practice was created
+a lot of things happened
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+web this new Global communicational
+
+ align:start position:0%
+web this new Global communicational
+ 
+
+ align:start position:0%
+web this new Global communicational
+platform that connect China India United
+
+ align:start position:0%
+platform that connect China India United
+ 
+
+ align:start position:0%
+platform that connect China India United
+States Latin America and enable us to
+
+ align:start position:0%
+States Latin America and enable us to
+ 
+
+ align:start position:0%
+States Latin America and enable us to
+be in contact
+
+ align:start position:0%
+be in contact
+ 
+
+ align:start position:0%
+be in contact
+worldwide the cell phones and the the
+
+ align:start position:0%
+worldwide the cell phones and the the
+ 
+
+ align:start position:0%
+worldwide the cell phones and the the
+OIP communication like
+
+ align:start position:0%
+OIP communication like
+ 
+
+ align:start position:0%
+OIP communication like
+Skype and the fact that the market at
+
+ align:start position:0%
+Skype and the fact that the market at
+ 
+
+ align:start position:0%
+Skype and the fact that the market at
+the world almost doubled in 10
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+years so
+
+ align:start position:0%
+years so
+ 
+
+ align:start position:0%
+years so
+in in the last 10 years we begin to see
+
+ align:start position:0%
+in in the last 10 years we begin to see
+ 
+
+ align:start position:0%
+in in the last 10 years we begin to see
+some of these things that are
+
+ align:start position:0%
+some of these things that are
+ 
+
+ align:start position:0%
+some of these things that are
+emerging one is Wikipedia and the
+
+ align:start position:0%
+emerging one is Wikipedia and the
+ 
+
+ align:start position:0%
+emerging one is Wikipedia and the
+concept of
+
+ align:start position:0%
+concept of
+ 
+
+ align:start position:0%
+concept of
+Wiki no the gradual construction of
+
+ align:start position:0%
+Wiki no the gradual construction of
+ 
+
+ align:start position:0%
+Wiki no the gradual construction of
+knowledge
+
+ align:start position:0%
+knowledge
+ 
+
+ align:start position:0%
+knowledge
+where many
+
+ align:start position:0%
+where many
+ 
+
+ align:start position:0%
+where many
+people collaborate for constructing a
+
+ align:start position:0%
+people collaborate for constructing a
+ 
+
+ align:start position:0%
+people collaborate for constructing a
+knowledge
+
+ align:start position:0%
+knowledge
+ 
+
+ align:start position:0%
+knowledge
+base okay and A New Concept
+
+ align:start position:0%
+base okay and A New Concept
+ 
+
+ align:start position:0%
+base okay and A New Concept
+of Encyclopedia it is an evolving
+
+ align:start position:0%
+of Encyclopedia it is an evolving
+ 
+
+ align:start position:0%
+of Encyclopedia it is an evolving
+encyclopedia but it's not only Wikipedia
+
+ align:start position:0%
+encyclopedia but it's not only Wikipedia
+ 
+
+ align:start position:0%
+encyclopedia but it's not only Wikipedia
+but not only the idea of an evolving
+
+ align:start position:0%
+but not only the idea of an evolving
+ 
+
+ align:start position:0%
+but not only the idea of an evolving
+cyclopedia but also of an evolving
+
+ align:start position:0%
+cyclopedia but also of an evolving
+ 
+
+ align:start position:0%
+cyclopedia but also of an evolving
+knowledge base for
+
+ align:start position:0%
+knowledge base for
+ 
+
+ align:start position:0%
+knowledge base for
+each a interest I
+
+ align:start position:0%
+each a interest I
+ 
+
+ align:start position:0%
+each a interest I
+have the search and
+
+ align:start position:0%
+have the search and
+ 
+
+ align:start position:0%
+have the search and
+gole
+
+ align:start position:0%
+gole
+ 
+
+ align:start position:0%
+gole
+Yahoo the
+
+ align:start position:0%
+Yahoo the
+ 
+
+ align:start position:0%
+Yahoo the
+Chinese I don't remember its
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+name
+
+ align:start position:0%
+name
+ 
+
+ align:start position:0%
+name
+what v
+
+ align:start position:0%
+what v
+ 
+
+ align:start position:0%
+what v
+no
+
+ align:start position:0%
+no
+ 
+
+ align:start position:0%
+no
+and this these search engines are
+
+ align:start position:0%
+and this these search engines are
+ 
+
+ align:start position:0%
+and this these search engines are
+changing the way we access to
+
+ align:start position:0%
+changing the way we access to
+ 
+
+ align:start position:0%
+changing the way we access to
+information for us it's almost
+
+ align:start position:0%
+information for us it's almost
+ 
+
+ align:start position:0%
+information for us it's almost
+impossible to work without use engines
+
+ align:start position:0%
+impossible to work without use engines
+ 
+
+ align:start position:0%
+impossible to work without use engines
+this moment this will change our Prof
+
+ align:start position:0%
+this moment this will change our Prof
+ 
+
+ align:start position:0%
+this moment this will change our Prof
+work the other idea is I don't know if
+
+ align:start position:0%
+work the other idea is I don't know if
+ 
+
+ align:start position:0%
+work the other idea is I don't know if
+you know that the Iowa electronic
+
+ align:start position:0%
+you know that the Iowa electronic
+ 
+
+ align:start position:0%
+you know that the Iowa electronic
+Market
+
+ align:start position:0%
+Market
+ 
+
+ align:start position:0%
+Market
+the it's in the book The Wisdom of
+
+ align:start position:0%
+the it's in the book The Wisdom of
+ 
+
+ align:start position:0%
+the it's in the book The Wisdom of
+crowds it's about M exclusively in their
+
+ align:start position:0%
+crowds it's about M exclusively in their
+ 
+
+ align:start position:0%
+crowds it's about M exclusively in their
+minds and not other people don't share
+
+ align:start position:0%
+minds and not other people don't share
+ 
+
+ align:start position:0%
+minds and not other people don't share
+this knowledge and combining all this to
+
+ align:start position:0%
+this knowledge and combining all this to
+ 
+
+ align:start position:0%
+this knowledge and combining all this to
+make
+
+ align:start position:0%
+make
+ 
+
+ align:start position:0%
+make
+decisions it's very interesting you can
+
+ align:start position:0%
+decisions it's very interesting you can
+ 
+
+ align:start position:0%
+decisions it's very interesting you can
+go into the
+
+ align:start position:0%
+go into the
+ 
+
+ align:start position:0%
+go into the
+I electronic Market to understand how it
+
+ align:start position:0%
+I electronic Market to understand how it
+ 
+
+ align:start position:0%
+I electronic Market to understand how it
+works okay it's like people take make
+
+ align:start position:0%
+works okay it's like people take make
+ 
+
+ align:start position:0%
+works okay it's like people take make
+decisions in downtown downtown now
+
+ align:start position:0%
+decisions in downtown downtown now
+ 
+
+ align:start position:0%
+decisions in downtown downtown now
+in the B of New
+
+ align:start position:0%
+in the B of New
+ 
+
+ align:start position:0%
+in the B of New
+York the stock
+
+ align:start position:0%
+York the stock
+ 
+
+ align:start position:0%
+York the stock
+exchange yes
+
+ align:start position:0%
+exchange yes
+ 
+
+ align:start position:0%
+exchange yes
+okay did yes
+
+ align:start position:0%
+okay did yes
+ 
+
+ align:start position:0%
+okay did yes
+and one one less than 20 than than
+
+ align:start position:0%
+and one one less than 20 than than
+ 
+
+ align:start position:0%
+and one one less than 20 than than
+200 minutes after the accident of the
+
+ align:start position:0%
+200 minutes after the accident of the
+ 
+
+ align:start position:0%
+200 minutes after the accident of the
+Challenger they knew the reasons of the
+
+ align:start position:0%
+Challenger they knew the reasons of the
+ 
+
+ align:start position:0%
+Challenger they knew the reasons of the
+accident in the boards of New York the
+
+ align:start position:0%
+accident in the boards of New York the
+ 
+
+ align:start position:0%
+accident in the boards of New York the
+committee spent eight or six or eight
+
+ align:start position:0%
+committee spent eight or six or eight
+ 
+
+ align:start position:0%
+committee spent eight or six or eight
+months I'm not sure about that for
+
+ align:start position:0%
+months I'm not sure about that for
+ 
+
+ align:start position:0%
+months I'm not sure about that for
+arriving to the same conclusion and less
+
+ align:start position:0%
+arriving to the same conclusion and less
+ 
+
+ align:start position:0%
+arriving to the same conclusion and less
+than two hours after they was clear
+
+ align:start position:0%
+than two hours after they was clear
+ 
+
+ align:start position:0%
+than two hours after they was clear
+about who was the responsible and the
+
+ align:start position:0%
+about who was the responsible and the
+ 
+
+ align:start position:0%
+about who was the responsible and the
+price of the share of this company fell
+
+ align:start position:0%
+price of the share of this company fell
+ 
+
+ align:start position:0%
+price of the share of this company fell
+12%
+
+ align:start position:0%
+12%
+ 
+
+ align:start position:0%
+12%
+the conclusion was that the ring was
+
+ align:start position:0%
+the conclusion was that the ring was
+ 
+
+ align:start position:0%
+the conclusion was that the ring was
+that produced the accident was produced
+
+ align:start position:0%
+that produced the accident was produced
+ 
+
+ align:start position:0%
+that produced the accident was produced
+by this company it was clear less than 2
+
+ align:start position:0%
+by this company it was clear less than 2
+ 
+
+ align:start position:0%
+by this company it was clear less than 2
+hours after the accident so the the the
+
+ align:start position:0%
+hours after the accident so the the the
+ 
+
+ align:start position:0%
+hours after the accident so the the the
+use of private knowledge for making
+
+ align:start position:0%
+use of private knowledge for making
+ 
+
+ align:start position:0%
+use of private knowledge for making
+decisions is a very powerful
+
+ align:start position:0%
+decisions is a very powerful
+ 
+
+ align:start position:0%
+decisions is a very powerful
+tool the other thing is the concept of
+
+ align:start position:0%
+tool the other thing is the concept of
+ 
+
+ align:start position:0%
+tool the other thing is the concept of
+collective
+
+ align:start position:0%
+collective
+ 
+
+ align:start position:0%
+collective
+intelligence it's a bit wide broader
+
+ align:start position:0%
+intelligence it's a bit wide broader
+ 
+
+ align:start position:0%
+intelligence it's a bit wide broader
+than this one is how I can combine
+
+ align:start position:0%
+than this one is how I can combine
+ 
+
+ align:start position:0%
+than this one is how I can combine
+capacities of people around a share
+
+ align:start position:0%
+capacities of people around a share
+ 
+
+ align:start position:0%
+capacities of people around a share
+issue or share area of Interest similar
+
+ align:start position:0%
+issue or share area of Interest similar
+ 
+
+ align:start position:0%
+issue or share area of Interest similar
+to this is community of
+
+ align:start position:0%
+to this is community of
+ 
+
+ align:start position:0%
+to this is community of
+practice are small groups community of
+
+ align:start position:0%
+practice are small groups community of
+ 
+
+ align:start position:0%
+practice are small groups community of
+practice not open collective
+
+ align:start position:0%
+practice not open collective
+ 
+
+ align:start position:0%
+practice not open collective
+intelligence more open so socially open
+
+ align:start position:0%
+intelligence more open so socially open
+ 
+
+ align:start position:0%
+intelligence more open so socially open
+and community of practice
+
+ align:start position:0%
+and community of practice
+ 
+
+ align:start position:0%
+and community of practice
+are groups normally in internal to an
+
+ align:start position:0%
+are groups normally in internal to an
+ 
+
+ align:start position:0%
+are groups normally in internal to an
+organization or institution that are
+
+ align:start position:0%
+organization or institution that are
+ 
+
+ align:start position:0%
+organization or institution that are
+working together for exploring for for
+
+ align:start position:0%
+working together for exploring for for
+ 
+
+ align:start position:0%
+working together for exploring for for
+learning for sharing knowledge
+
+ align:start position:0%
+learning for sharing knowledge
+ 
+
+ align:start position:0%
+learning for sharing knowledge
+okay the concept
+
+ align:start position:0%
+okay the concept
+ 
+
+ align:start position:0%
+okay the concept
+of
+
+ align:start position:0%
+of
+ 
+
+ align:start position:0%
+of
+innovation is something that Ares in the
+
+ align:start position:0%
+innovation is something that Ares in the
+ 
+
+ align:start position:0%
+innovation is something that Ares in the
+mind of one person of in the mind of a
+
+ align:start position:0%
+mind of one person of in the mind of a
+ 
+
+ align:start position:0%
+mind of one person of in the mind of a
+small group is being changed for
+
+ align:start position:0%
+small group is being changed for
+ 
+
+ align:start position:0%
+small group is being changed for
+distributed
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Innovation there is a book of a teacher
+
+ align:start position:0%
+Innovation there is a book of a teacher
+ 
+
+ align:start position:0%
+Innovation there is a book of a teacher
+of MIT about about democratizing
+
+ align:start position:0%
+of MIT about about democratizing
+ 
+
+ align:start position:0%
+of MIT about about democratizing
+Innovation it's about how customers
+
+ align:start position:0%
+Innovation it's about how customers
+ 
+
+ align:start position:0%
+Innovation it's about how customers
+develop Innovation for
+
+ align:start position:0%
+develop Innovation for
+ 
+
+ align:start position:0%
+develop Innovation for
+companies if you go to internet you find
+
+ align:start position:0%
+companies if you go to internet you find
+ 
+
+ align:start position:0%
+companies if you go to internet you find
+groups of people who are interested in
+
+ align:start position:0%
+groups of people who are interested in
+ 
+
+ align:start position:0%
+groups of people who are interested in
+Social Innovation how groups innovate at
+
+ align:start position:0%
+Social Innovation how groups innovate at
+ 
+
+ align:start position:0%
+Social Innovation how groups innovate at
+Social level and how they how they can
+
+ align:start position:0%
+Social level and how they how they can
+ 
+
+ align:start position:0%
+Social level and how they how they can
+combine their Innovations and they can
+
+ align:start position:0%
+combine their Innovations and they can
+ 
+
+ align:start position:0%
+combine their Innovations and they can
+share their experiences and more and
+
+ align:start position:0%
+share their experiences and more and
+ 
+
+ align:start position:0%
+share their experiences and more and
+more research is being doing in
+
+ align:start position:0%
+more research is being doing in
+ 
+
+ align:start position:0%
+more research is being doing in
+networks okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+some authors think that the art of
+
+ align:start position:0%
+some authors think that the art of
+ 
+
+ align:start position:0%
+some authors think that the art of
+conceptual Innovation is the
+
+ align:start position:0%
+conceptual Innovation is the
+ 
+
+ align:start position:0%
+conceptual Innovation is the
+driver
+
+ align:start position:0%
+driver
+ 
+
+ align:start position:0%
+driver
+what's pulling the process forward
+
+ align:start position:0%
+what's pulling the process forward
+ 
+
+ align:start position:0%
+what's pulling the process forward
+is the capacity of combining a
+
+ align:start position:0%
+is the capacity of combining a
+ 
+
+ align:start position:0%
+is the capacity of combining a
+different different kinds of of
+
+ align:start position:0%
+different different kinds of of
+ 
+
+ align:start position:0%
+different different kinds of of
+Technologies and this combination is
+
+ align:start position:0%
+Technologies and this combination is
+ 
+
+ align:start position:0%
+Technologies and this combination is
+made
+
+ align:start position:0%
+made
+ 
+
+ align:start position:0%
+made
+in is made by
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the creation of New Concept of products
+
+ align:start position:0%
+the creation of New Concept of products
+ 
+
+ align:start position:0%
+the creation of New Concept of products
+or New Concept of services or idea that
+
+ align:start position:0%
+or New Concept of services or idea that
+ 
+
+ align:start position:0%
+or New Concept of services or idea that
+enable to reframe a lot many different
+
+ align:start position:0%
+enable to reframe a lot many different
+ 
+
+ align:start position:0%
+enable to reframe a lot many different
+things what do we discussed yesterday
+
+ align:start position:0%
+things what do we discussed yesterday
+ 
+
+ align:start position:0%
+things what do we discussed yesterday
+conceptual Innovation is becoming the
+
+ align:start position:0%
+conceptual Innovation is becoming the
+ 
+
+ align:start position:0%
+conceptual Innovation is becoming the
+the driver okay and for people who are
+
+ align:start position:0%
+the driver okay and for people who are
+ 
+
+ align:start position:0%
+the driver okay and for people who are
+in the market the
+
+ align:start position:0%
+in the market the
+ 
+
+ align:start position:0%
+in the market the
+third phrase is important we have
+
+ align:start position:0%
+third phrase is important we have
+ 
+
+ align:start position:0%
+third phrase is important we have
+millions of people innovating
+
+ align:start position:0%
+millions of people innovating
+ 
+
+ align:start position:0%
+millions of people innovating
+systematically the only way to get an
+
+ align:start position:0%
+systematically the only way to get an
+ 
+
+ align:start position:0%
+systematically the only way to get an
+edge and maintain the edge is innovating
+
+ align:start position:0%
+edge and maintain the edge is innovating
+ 
+
+ align:start position:0%
+edge and maintain the edge is innovating
+the concepts I am working with okay and
+
+ align:start position:0%
+the concepts I am working with okay and
+ 
+
+ align:start position:0%
+the concepts I am working with okay and
+after3 Ary will be much more important
+
+ align:start position:0%
+after3 Ary will be much more important
+ 
+
+ align:start position:0%
+after3 Ary will be much more important
+in the future okay let's
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+go new requirements of collaborative
+
+ align:start position:0%
+go new requirements of collaborative
+ 
+
+ align:start position:0%
+go new requirements of collaborative
+work Global and local issues are getting
+
+ align:start position:0%
+work Global and local issues are getting
+ 
+
+ align:start position:0%
+work Global and local issues are getting
+mixing new issues are
+
+ align:start position:0%
+mixing new issues are
+ 
+
+ align:start position:0%
+mixing new issues are
+emerging that not fit in any
+
+ align:start position:0%
+emerging that not fit in any
+ 
+
+ align:start position:0%
+emerging that not fit in any
+profession
+
+ align:start position:0%
+profession
+ 
+
+ align:start position:0%
+profession
+okay local problems may be combined at
+
+ align:start position:0%
+okay local problems may be combined at
+ 
+
+ align:start position:0%
+okay local problems may be combined at
+Global
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+level
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and more and more we need combine
+
+ align:start position:0%
+and more and more we need combine
+ 
+
+ align:start position:0%
+and more and more we need combine
+different kind of profession for
+
+ align:start position:0%
+different kind of profession for
+ 
+
+ align:start position:0%
+different kind of profession for
+tackling the same
+
+ align:start position:0%
+tackling the same
+ 
+
+ align:start position:0%
+tackling the same
+problem
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yes
+
+ align:start position:0%
+yes
+ 
+
+ align:start position:0%
+yes
+so any professions will any profession
+
+ align:start position:0%
+so any professions will any profession
+ 
+
+ align:start position:0%
+so any professions will any profession
+will face the challenge of getting
+
+ align:start position:0%
+will face the challenge of getting
+ 
+
+ align:start position:0%
+will face the challenge of getting
+updated to expand for applying to new
+
+ align:start position:0%
+updated to expand for applying to new
+ 
+
+ align:start position:0%
+updated to expand for applying to new
+fields to adapt to change
+
+ align:start position:0%
+fields to adapt to change
+ 
+
+ align:start position:0%
+fields to adapt to change
+situations to reinvent its practice
+
+ align:start position:0%
+situations to reinvent its practice
+ 
+
+ align:start position:0%
+situations to reinvent its practice
+I'm not Reinventing my profession but
+
+ align:start position:0%
+I'm not Reinventing my profession but
+ 
+
+ align:start position:0%
+I'm not Reinventing my profession but
+the way I do my profession I need to
+
+ align:start position:0%
+the way I do my profession I need to
+ 
+
+ align:start position:0%
+the way I do my profession I need to
+reinvent it and in some cases I need to
+
+ align:start position:0%
+reinvent it and in some cases I need to
+ 
+
+ align:start position:0%
+reinvent it and in some cases I need to
+reinvent or create new
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+professions
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay what has this all this with
+
+ align:start position:0%
+okay what has this all this with
+ 
+
+ align:start position:0%
+okay what has this all this with
+reflective
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+practice
+
+ align:start position:0%
+practice
+ 
+
+ align:start position:0%
+practice
+and I try to to show you some people who
+
+ align:start position:0%
+and I try to to show you some people who
+ 
+
+ align:start position:0%
+and I try to to show you some people who
+are go
+
+ align:start position:0%
+are go
+ 
+
+ align:start position:0%
+are go
+going forward in this of reflective
+
+ align:start position:0%
+going forward in this of reflective
+ 
+
+ align:start position:0%
+going forward in this of reflective
+practice from their own perspective
+
+ align:start position:0%
+practice from their own perspective
+ 
+
+ align:start position:0%
+practice from their own perspective
+okay the first books of
+
+ align:start position:0%
+okay the first books of
+ 
+
+ align:start position:0%
+okay the first books of
+the in the ground no are the books of
+
+ align:start position:0%
+the in the ground no are the books of
+ 
+
+ align:start position:0%
+the in the ground no are the books of
+Sean okay and after that we have the
+
+ align:start position:0%
+Sean okay and after that we have the
+ 
+
+ align:start position:0%
+Sean okay and after that we have the
+medic
+
+ align:start position:0%
+medic
+ 
+
+ align:start position:0%
+medic
+effect how to trigger creativity in
+
+ align:start position:0%
+effect how to trigger creativity in
+ 
+
+ align:start position:0%
+effect how to trigger creativity in
+groups of
+
+ align:start position:0%
+groups of
+ 
+
+ align:start position:0%
+groups of
+people democratize Innovation the
+
+ align:start position:0%
+people democratize Innovation the
+ 
+
+ align:start position:0%
+people democratize Innovation the
+teacher of MIT how customers can
+
+ align:start position:0%
+teacher of MIT how customers can
+ 
+
+ align:start position:0%
+teacher of MIT how customers can
+innovate much better than the R&D
+
+ align:start position:0%
+innovate much better than the R&D
+ 
+
+ align:start position:0%
+innovate much better than the R&D
+divisions of
+
+ align:start position:0%
+divisions of
+ 
+
+ align:start position:0%
+divisions of
+company customers H customers customers
+
+ align:start position:0%
+company customers H customers customers
+ 
+
+ align:start position:0%
+company customers H customers customers
+thank you
+
+ align:start position:0%
+thank you
+ 
+
+ align:start position:0%
+thank you
+customers the 10 phases of
+
+ align:start position:0%
+customers the 10 phases of
+ 
+
+ align:start position:0%
+customers the 10 phases of
+innovation from
+
+ align:start position:0%
+innovation from
+ 
+
+ align:start position:0%
+innovation from
+id id Ido no
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yes in Spanish I say Ideo it's Tom
+
+ align:start position:0%
+yes in Spanish I say Ideo it's Tom
+ 
+
+ align:start position:0%
+yes in Spanish I say Ideo it's Tom
+Kelly the number one in innovation in
+
+ align:start position:0%
+Kelly the number one in innovation in
+ 
+
+ align:start position:0%
+Kelly the number one in innovation in
+the United States you can see that the
+
+ align:start position:0%
+the United States you can see that the
+ 
+
+ align:start position:0%
+the United States you can see that the
+way they think has a lot of the way we
+
+ align:start position:0%
+way they think has a lot of the way we
+ 
+
+ align:start position:0%
+way they think has a lot of the way we
+think in reflective practice
+
+ align:start position:0%
+think in reflective practice
+ 
+
+ align:start position:0%
+think in reflective practice
+okay how to combine ideas how to
+
+ align:start position:0%
+okay how to combine ideas how to
+ 
+
+ align:start position:0%
+okay how to combine ideas how to
+construct on partial
+
+ align:start position:0%
+construct on partial
+ 
+
+ align:start position:0%
+construct on partial
+ideas how to reinterpret the ideas that
+
+ align:start position:0%
+ideas how to reinterpret the ideas that
+ 
+
+ align:start position:0%
+ideas how to reinterpret the ideas that
+other people brought to make it to fit
+
+ align:start position:0%
+other people brought to make it to fit
+ 
+
+ align:start position:0%
+other people brought to make it to fit
+with my idea or how may I to reinterpret
+
+ align:start position:0%
+with my idea or how may I to reinterpret
+ 
+
+ align:start position:0%
+with my idea or how may I to reinterpret
+my idea to make it to fit with the
+
+ align:start position:0%
+my idea to make it to fit with the
+ 
+
+ align:start position:0%
+my idea to make it to fit with the
+others how to be flexible interacting
+
+ align:start position:0%
+others how to be flexible interacting
+ 
+
+ align:start position:0%
+others how to be flexible interacting
+professionally how to adapt mentally to
+
+ align:start position:0%
+professionally how to adapt mentally to
+ 
+
+ align:start position:0%
+professionally how to adapt mentally to
+the different situation that I am
+
+ align:start position:0%
+the different situation that I am
+ 
+
+ align:start position:0%
+the different situation that I am
+facing the other one is source of power
+
+ align:start position:0%
+facing the other one is source of power
+ 
+
+ align:start position:0%
+facing the other one is source of power
+is the most similar book I have read to
+
+ align:start position:0%
+is the most similar book I have read to
+ 
+
+ align:start position:0%
+is the most similar book I have read to
+the reflective
+
+ align:start position:0%
+the reflective
+ 
+
+ align:start position:0%
+the reflective
+practitioner it's about how people think
+
+ align:start position:0%
+practitioner it's about how people think
+ 
+
+ align:start position:0%
+practitioner it's about how people think
+think in
+
+ align:start position:0%
+think in
+ 
+
+ align:start position:0%
+think in
+action it's about the firefighters I
+
+ align:start position:0%
+action it's about the firefighters I
+ 
+
+ align:start position:0%
+action it's about the firefighters I
+showed the first day okay and the word
+
+ align:start position:0%
+showed the first day okay and the word
+ 
+
+ align:start position:0%
+showed the first day okay and the word
+is flat there is a part of the
+
+ align:start position:0%
+is flat there is a part of the
+ 
+
+ align:start position:0%
+is flat there is a part of the
+reflection of Thomas fredman dedicated
+
+ align:start position:0%
+reflection of Thomas fredman dedicated
+ 
+
+ align:start position:0%
+reflection of Thomas fredman dedicated
+to conceptual
+
+ align:start position:0%
+to conceptual
+ 
+
+ align:start position:0%
+to conceptual
+Innovation a whole new mind is about the
+
+ align:start position:0%
+Innovation a whole new mind is about the
+ 
+
+ align:start position:0%
+Innovation a whole new mind is about the
+role of
+
+ align:start position:0%
+role of
+ 
+
+ align:start position:0%
+role of
+concept in the process of create
+
+ align:start position:0%
+concept in the process of create
+ 
+
+ align:start position:0%
+concept in the process of create
+creation infotopia is the new
+
+ align:start position:0%
+creation infotopia is the new
+ 
+
+ align:start position:0%
+creation infotopia is the new
+environment that is emerging and how we
+
+ align:start position:0%
+environment that is emerging and how we
+ 
+
+ align:start position:0%
+environment that is emerging and how we
+need
+
+ align:start position:0%
+need
+ 
+
+ align:start position:0%
+need
+to to be aware of our the way we are
+
+ align:start position:0%
+to to be aware of our the way we are
+ 
+
+ align:start position:0%
+to to be aware of our the way we are
+framing the problems the way we are
+
+ align:start position:0%
+framing the problems the way we are
+ 
+
+ align:start position:0%
+framing the problems the way we are
+thinking about the situation for
+
+ align:start position:0%
+thinking about the situation for
+ 
+
+ align:start position:0%
+thinking about the situation for
+combining with other people and I am
+
+ align:start position:0%
+combining with other people and I am
+ 
+
+ align:start position:0%
+combining with other people and I am
+sure that we could have another examples
+
+ align:start position:0%
+sure that we could have another examples
+ 
+
+ align:start position:0%
+sure that we could have another examples
+of
+
+ align:start position:0%
+of
+ 
+
+ align:start position:0%
+of
+that
+
+ align:start position:0%
+that
+ 
+
+ align:start position:0%
+that
+my assumption
+
+ align:start position:0%
+my assumption
+ 
+
+ align:start position:0%
+my assumption
+hypothesis in this case because I am
+
+ align:start position:0%
+hypothesis in this case because I am
+ 
+
+ align:start position:0%
+hypothesis in this case because I am
+aware of that is that main idea many
+
+ align:start position:0%
+aware of that is that main idea many
+ 
+
+ align:start position:0%
+aware of that is that main idea many
+ideas of reflective practice are being
+
+ align:start position:0%
+ideas of reflective practice are being
+ 
+
+ align:start position:0%
+ideas of reflective practice are being
+used by these authors and they are find
+
+ align:start position:0%
+used by these authors and they are find
+ 
+
+ align:start position:0%
+used by these authors and they are find
+finding very very powerful for
+
+ align:start position:0%
+finding very very powerful for
+ 
+
+ align:start position:0%
+finding very very powerful for
+them okay so in spite of that reflective
+
+ align:start position:0%
+them okay so in spite of that reflective
+ 
+
+ align:start position:0%
+them okay so in spite of that reflective
+practice was developed in the 60s 70s
+
+ align:start position:0%
+practice was developed in the 60s 70s
+ 
+
+ align:start position:0%
+practice was developed in the 60s 70s
+and 80s its importance is growing in
+
+ align:start position:0%
+and 80s its importance is growing in
+ 
+
+ align:start position:0%
+and 80s its importance is growing in
+this
+
+ align:start position:0%
+this
+ 
+
+ align:start position:0%
+this
+Century okay yes are those other setting
+
+ align:start position:0%
+Century okay yes are those other setting
+ 
+
+ align:start position:0%
+Century okay yes are those other setting
+sh no no one
+
+ align:start position:0%
+sh no no one
+ 
+
+ align:start position:0%
+sh no no one
+SES but it doesn't matter because if you
+
+ align:start position:0%
+SES but it doesn't matter because if you
+ 
+
+ align:start position:0%
+SES but it doesn't matter because if you
+analyze the way they
+
+ align:start position:0%
+analyze the way they
+ 
+
+ align:start position:0%
+analyze the way they
+are presented their ideas you can find
+
+ align:start position:0%
+are presented their ideas you can find
+ 
+
+ align:start position:0%
+are presented their ideas you can find
+similarities but they they the people
+
+ align:start position:0%
+similarities but they they the people
+ 
+
+ align:start position:0%
+similarities but they they the people
+who sites Shan is the people who are
+
+ align:start position:0%
+who sites Shan is the people who are
+ 
+
+ align:start position:0%
+who sites Shan is the people who are
+dedicated to reflection methodology
+
+ align:start position:0%
+dedicated to reflection methodology
+ 
+
+ align:start position:0%
+dedicated to reflection methodology
+most of them because
+
+ align:start position:0%
+most of them because
+ 
+
+ align:start position:0%
+most of them because
+the the idea of reflective practice was
+
+ align:start position:0%
+the the idea of reflective practice was
+ 
+
+ align:start position:0%
+the the idea of reflective practice was
+interpreted as the practice of
+
+ align:start position:0%
+interpreted as the practice of
+ 
+
+ align:start position:0%
+interpreted as the practice of
+reflection that's not exactly the same
+
+ align:start position:0%
+reflection that's not exactly the same
+ 
+
+ align:start position:0%
+reflection that's not exactly the same
+it's just one part of reflective
+
+ align:start position:0%
+it's just one part of reflective
+ 
+
+ align:start position:0%
+it's just one part of reflective
+practice the practice of
+
+ align:start position:0%
+practice the practice of
+ 
+
+ align:start position:0%
+practice the practice of
+reflection okay the practice of
+
+ align:start position:0%
+reflection okay the practice of
+ 
+
+ align:start position:0%
+reflection okay the practice of
+reflection is the stepping back to one
+
+ align:start position:0%
+reflection is the stepping back to one
+ 
+
+ align:start position:0%
+reflection is the stepping back to one
+experience to retrieve knowledge and for
+
+ align:start position:0%
+experience to retrieve knowledge and for
+ 
+
+ align:start position:0%
+experience to retrieve knowledge and for
+for understanding better it's very
+
+ align:start position:0%
+for understanding better it's very
+ 
+
+ align:start position:0%
+for understanding better it's very
+useful for these two purpose and it's
+
+ align:start position:0%
+useful for these two purpose and it's
+ 
+
+ align:start position:0%
+useful for these two purpose and it's
+very useful to for learning to be a
+
+ align:start position:0%
+very useful to for learning to be a
+ 
+
+ align:start position:0%
+very useful to for learning to be a
+reflective practitioner to think in
+
+ align:start position:0%
+reflective practitioner to think in
+ 
+
+ align:start position:0%
+reflective practitioner to think in
+action to improve the way we think in
+
+ align:start position:0%
+action to improve the way we think in
+ 
+
+ align:start position:0%
+action to improve the way we think in
+action but the idea of Shan is basically
+
+ align:start position:0%
+action but the idea of Shan is basically
+ 
+
+ align:start position:0%
+action but the idea of Shan is basically
+this last phrase how to improve the way
+
+ align:start position:0%
+this last phrase how to improve the way
+ 
+
+ align:start position:0%
+this last phrase how to improve the way
+we think in
+
+ align:start position:0%
+we think in
+ 
+
+ align:start position:0%
+we think in
+action
+
+ align:start position:0%
+action
+ 
+
+ align:start position:0%
+action
+okay yeah and I have some question for
+
+ align:start position:0%
+okay yeah and I have some question for
+ 
+
+ align:start position:0%
+okay yeah and I have some question for
+you about this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+how many cards you may
+
+ align:start position:0%
+how many cards you may
+ 
+
+ align:start position:0%
+how many cards you may
+receive we we we need to simplify the
+
+ align:start position:0%
+receive we we we need to simplify the
+ 
+
+ align:start position:0%
+receive we we we need to simplify the
+exercise
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+no yeah okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+please each one of
+
+ align:start position:0%
+please each one of
+ 
+
+ align:start position:0%
+please each one of
+you with we have thought during the
+
+ align:start position:0%
+you with we have thought during the
+ 
+
+ align:start position:0%
+you with we have thought during the
+course combining with some of these
+
+ align:start position:0%
+course combining with some of these
+ 
+
+ align:start position:0%
+course combining with some of these
+ideas I
+
+ align:start position:0%
+ideas I
+ 
+
+ align:start position:0%
+ideas I
+presented
+
+ align:start position:0%
+presented
+ 
+
+ align:start position:0%
+presented
+each one will write three
+
+ align:start position:0%
+each one will write three
+ 
+
+ align:start position:0%
+each one will write three
+cards yes this course will required
+
+ align:start position:0%
+cards yes this course will required
+ 
+
+ align:start position:0%
+cards yes this course will required
+to to think hard until the last minute
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay how do you see the
+
+ align:start position:0%
+okay how do you see the
+ 
+
+ align:start position:0%
+okay how do you see the
+future of this the ideas of this
+
+ align:start position:0%
+future of this the ideas of this
+ 
+
+ align:start position:0%
+future of this the ideas of this
+course in your practice or
+
+ align:start position:0%
+course in your practice or
+ 
+
+ align:start position:0%
+course in your practice or
+[Music]
+
+ align:start position:0%
+[Music]
+ 
+
+ align:start position:0%
+[Music]
+in
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yes in
+
+ align:start position:0%
+yes in
+ 
+
+ align:start position:0%
+yes in
+the this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+one to visual is the future of reflect
+
+ align:start position:0%
+one to visual is the future of reflect
+ 
+
+ align:start position:0%
+one to visual is the future of reflect
+of reflective
+
+ align:start position:0%
+of reflective
+ 
+
+ align:start position:0%
+of reflective
+practice what possibilities are open for
+
+ align:start position:0%
+practice what possibilities are open for
+ 
+
+ align:start position:0%
+practice what possibilities are open for
+reflective pract in this new environment
+
+ align:start position:0%
+reflective pract in this new environment
+ 
+
+ align:start position:0%
+reflective pract in this new environment
+it's
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay okay what future do you see for the
+
+ align:start position:0%
+okay okay what future do you see for the
+ 
+
+ align:start position:0%
+okay okay what future do you see for the
+ideas this ideas developed that
+
+ align:start position:0%
+ideas this ideas developed that
+ 
+
+ align:start position:0%
+ideas this ideas developed that
+time okay three three cards
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+please three you can put your name if
+
+ align:start position:0%
+please three you can put your name if
+ 
+
+ align:start position:0%
+please three you can put your name if
+you
+
+ align:start position:0%
+you
+ 
+
+ align:start position:0%
+you
+want okay but how you see the future of
+
+ align:start position:0%
+want okay but how you see the future of
+ 
+
+ align:start position:0%
+want okay but how you see the future of
+reflective practice
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+with
+
+ align:start position:0%
+with
+ 
+
+ align:start position:0%
+with
+Mark you can use you can write as you
+
+ align:start position:0%
+Mark you can use you can write as you
+ 
+
+ align:start position:0%
+Mark you can use you can write as you
+wish
+
+ align:start position:0%
+wish
+ 
+
+ align:start position:0%
+wish
+because we will not work with the cards
+
+ align:start position:0%
+because we will not work with the cards
+ 
+
+ align:start position:0%
+because we will not work with the cards
+you give us the cards and we after you
+
+ align:start position:0%
+you give us the cards and we after you
+ 
+
+ align:start position:0%
+you give us the cards and we after you
+write the cards you express with vocally
+
+ align:start position:0%
+write the cards you express with vocally
+ 
+
+ align:start position:0%
+write the cards you express with vocally
+the main ideas as you have
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+wrote connect your own own you can
+
+ align:start position:0%
+wrote connect your own own you can
+ 
+
+ align:start position:0%
+wrote connect your own own you can
+connect to your own practice as a
+
+ align:start position:0%
+connect to your own practice as a
+ 
+
+ align:start position:0%
+connect to your own practice as a
+reference okay okay but we are trying to
+
+ align:start position:0%
+reference okay okay but we are trying to
+ 
+
+ align:start position:0%
+reference okay okay but we are trying to
+to understand the future of of
+
+ align:start position:0%
+to understand the future of of
+ 
+
+ align:start position:0%
+to understand the future of of
+reflective practice in general okay the
+
+ align:start position:0%
+reflective practice in general okay the
+ 
+
+ align:start position:0%
+reflective practice in general okay the
+idea of this course okay okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+please please you have five
+
+ align:start position:0%
+please please you have five
+ 
+
+ align:start position:0%
+please please you have five
+minutes yes you know that the production
+
+ align:start position:0%
+minutes yes you know that the production
+ 
+
+ align:start position:0%
+minutes yes you know that the production
+of ideas doesn't depend of
+
+ align:start position:0%
+of ideas doesn't depend of
+ 
+
+ align:start position:0%
+of ideas doesn't depend of
+time it's a great
+
+ align:start position:0%
+time it's a great
+ 
+
+ align:start position:0%
+time it's a great
+thing
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yes very fast they question is that we
+
+ align:start position:0%
+yes very fast they question is that we
+ 
+
+ align:start position:0%
+yes very fast they question is that we
+just don't pick them at the moment okay
+
+ align:start position:0%
+just don't pick them at the moment okay
+ 
+
+ align:start position:0%
+just don't pick them at the moment okay
+okay the first glance that
+
+ align:start position:0%
+okay the first glance that
+ 
+
+ align:start position:0%
+okay the first glance that
+you the first fragment of idea that pass
+
+ align:start position:0%
+you the first fragment of idea that pass
+ 
+
+ align:start position:0%
+you the first fragment of idea that pass
+through your mind just write okay just
+
+ align:start position:0%
+through your mind just write okay just
+ 
+
+ align:start position:0%
+through your mind just write okay just
+pick
+
+ align:start position:0%
+pick
+ 
+
+ align:start position:0%
+pick
+it don't s much because the first glance
+
+ align:start position:0%
+it don't s much because the first glance
+ 
+
+ align:start position:0%
+it don't s much because the first glance
+is the best idea most of the times okay
+
+ align:start position:0%
+is the best idea most of the times okay
+ 
+
+ align:start position:0%
+is the best idea most of the times okay
+yes yes for because the inconscious is
+
+ align:start position:0%
+yes yes for because the inconscious is
+ 
+
+ align:start position:0%
+yes yes for because the inconscious is
+very very powerful in these things in
+
+ align:start position:0%
+very very powerful in these things in
+ 
+
+ align:start position:0%
+very very powerful in these things in
+very fast
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay the best way I find for doing this
+
+ align:start position:0%
+okay the best way I find for doing this
+ 
+
+ align:start position:0%
+okay the best way I find for doing this
+very fast is the first the first idea I
+
+ align:start position:0%
+very fast is the first the first idea I
+ 
+
+ align:start position:0%
+very fast is the first the first idea I
+just write it and just and after that I
+
+ align:start position:0%
+just write it and just and after that I
+ 
+
+ align:start position:0%
+just write it and just and after that I
+discard it if it was not it if it were
+
+ align:start position:0%
+discard it if it was not it if it were
+ 
+
+ align:start position:0%
+discard it if it was not it if it were
+not this idea what new idea should be so
+
+ align:start position:0%
+not this idea what new idea should be so
+ 
+
+ align:start position:0%
+not this idea what new idea should be so
+I put my mind blank again and a new idea
+
+ align:start position:0%
+I put my mind blank again and a new idea
+ 
+
+ align:start position:0%
+I put my mind blank again and a new idea
+comes
+
+ align:start position:0%
+comes
+ 
+
+ align:start position:0%
+comes
+up rapid prototyping mean huh rapid
+
+ align:start position:0%
+up rapid prototyping mean huh rapid
+ 
+
+ align:start position:0%
+up rapid prototyping mean huh rapid
+prototyping I don't know the the the
+
+ align:start position:0%
+prototyping I don't know the the the
+ 
+
+ align:start position:0%
+prototyping I don't know the the the
+name I is the the method I use in my
+
+ align:start position:0%
+name I is the the method I use in my
+ 
+
+ align:start position:0%
+name I is the the method I use in my
+workshops
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay the question is I formulate an idea
+
+ align:start position:0%
+okay the question is I formulate an idea
+ 
+
+ align:start position:0%
+okay the question is I formulate an idea
+and I eliminate it from my mind after I
+
+ align:start position:0%
+and I eliminate it from my mind after I
+ 
+
+ align:start position:0%
+and I eliminate it from my mind after I
+have formulated for my might be able to
+
+ align:start position:0%
+have formulated for my might be able to
+ 
+
+ align:start position:0%
+have formulated for my might be able to
+go to a new idea to create the condition
+
+ align:start position:0%
+go to a new idea to create the condition
+ 
+
+ align:start position:0%
+go to a new idea to create the condition
+for the create and drop create and drop
+
+ align:start position:0%
+for the create and drop create and drop
+ 
+
+ align:start position:0%
+for the create and drop create and drop
+yes yes
+
+ align:start position:0%
+yes yes
+ 
+
+ align:start position:0%
+yes yes
+okay La
+
+ align:start position:0%
+okay La
+ 
+
+ align:start position:0%
+okay La
+see lapis
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+no okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah it's the only way you can produce
+
+ align:start position:0%
+yeah it's the only way you can produce
+ 
+
+ align:start position:0%
+yeah it's the only way you can produce
+100 ideas in one
+
+ align:start position:0%
+100 ideas in one
+ 
+
+ align:start position:0%
+100 ideas in one
+hour okay
+
+ align:start position:0%
+hour okay
+ 
+
+ align:start position:0%
+hour okay
+you you look
+
+ align:start position:0%
+you you look
+ 
+
+ align:start position:0%
+you you look
+at
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay foree
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+excuse
+
+ align:start position:0%
+excuse
+ 
+
+ align:start position:0%
+excuse
+me we had to stop it forgive
+
+ align:start position:0%
+me we had to stop it forgive
+ 
+
+ align:start position:0%
+me we had to stop it forgive
+me
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+fore
+
+ align:start position:0%
+fore
+ 
+
+ align:start position:0%
+fore
+speech
+
+ align:start position:0%
+speech
+ 
+
+ align:start position:0%
+speech
+fore foreign
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+speech for
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+for for
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+I'm not sure if I'm answering the
+
+ align:start position:0%
+I'm not sure if I'm answering the
+ 
+
+ align:start position:0%
+I'm not sure if I'm answering the
+question I'm more talking about
+
+ align:start position:0%
+question I'm more talking about
+ 
+
+ align:start position:0%
+question I'm more talking about
+consequences of
+
+ align:start position:0%
+consequences of
+ 
+
+ align:start position:0%
+consequences of
+us yeah you can there some way to
+
+ align:start position:0%
+us yeah you can there some way to
+ 
+
+ align:start position:0%
+us yeah you can there some way to
+express an idea
+
+ align:start position:0%
+express an idea
+ 
+
+ align:start position:0%
+express an idea
+you can express an idea by from
+
+ align:start position:0%
+you can express an idea by from
+ 
+
+ align:start position:0%
+you can express an idea by from
+different
+
+ align:start position:0%
+different
+ 
+
+ align:start position:0%
+different
+sources okay
+
+ align:start position:0%
+sources okay
+ 
+
+ align:start position:0%
+sources okay
+yes the way the idea in your mind great
+
+ align:start position:0%
+yes the way the idea in your mind great
+ 
+
+ align:start position:0%
+yes the way the idea in your mind great
+just put
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+it no p no
+
+ align:start position:0%
+it no p no
+ 
+
+ align:start position:0%
+it no p no
+P SC no P
+
+ align:start position:0%
+P SC no P
+ 
+
+ align:start position:0%
+P SC no P
+SC you have don't think just
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+right I real the question I answering
+
+ align:start position:0%
+right I real the question I answering
+ 
+
+ align:start position:0%
+right I real the question I answering
+more is what what possibilities does
+
+ align:start position:0%
+more is what what possibilities does
+ 
+
+ align:start position:0%
+more is what what possibilities does
+reflective practice open in the
+
+ align:start position:0%
+reflective practice open in the
+ 
+
+ align:start position:0%
+reflective practice open in the
+environment is that okay
+
+ align:start position:0%
+environment is that okay
+ 
+
+ align:start position:0%
+environment is that okay
+okay yes
+
+ align:start position:0%
+okay yes
+ 
+
+ align:start position:0%
+okay yes
+I yes it's the same it's it's another
+
+ align:start position:0%
+I yes it's the same it's it's another
+ 
+
+ align:start position:0%
+I yes it's the same it's it's another
+door for looking at the same idea we
+
+ align:start position:0%
+door for looking at the same idea we
+ 
+
+ align:start position:0%
+door for looking at the same idea we
+were trying to to
+
+ align:start position:0%
+were trying to to
+ 
+
+ align:start position:0%
+were trying to to
+obser it's more reflective
+
+ align:start position:0%
+obser it's more reflective
+ 
+
+ align:start position:0%
+obser it's more reflective
+pring refective practices sort of okay
+
+ align:start position:0%
+pring refective practices sort of okay
+ 
+
+ align:start position:0%
+pring refective practices sort of okay
+but if it is the c it will it will be
+
+ align:start position:0%
+but if it is the c it will it will be
+ 
+
+ align:start position:0%
+but if it is the c it will it will be
+part of this reality and this part will
+
+ align:start position:0%
+part of this reality and this part will
+ 
+
+ align:start position:0%
+part of this reality and this part will
+be a new possibility for it okay yeah
+
+ align:start position:0%
+be a new possibility for it okay yeah
+ 
+
+ align:start position:0%
+be a new possibility for it okay yeah
+already
+
+ align:start position:0%
+already
+ 
+
+ align:start position:0%
+already
+Yes can
+
+ align:start position:0%
+Yes can
+ 
+
+ align:start position:0%
+Yes can
+we okay we we need to work
+
+ align:start position:0%
+we okay we we need to work
+ 
+
+ align:start position:0%
+we okay we we need to work
+very no we have not we have eight
+
+ align:start position:0%
+very no we have not we have eight
+ 
+
+ align:start position:0%
+very no we have not we have eight
+minutes okay we we'll
+
+ align:start position:0%
+minutes okay we we'll
+ 
+
+ align:start position:0%
+minutes okay we we'll
+finish 12 less 15 because you need to
+
+ align:start position:0%
+finish 12 less 15 because you need to
+ 
+
+ align:start position:0%
+finish 12 less 15 because you need to
+make the evaluation of the curse and we
+
+ align:start position:0%
+make the evaluation of the curse and we
+ 
+
+ align:start position:0%
+make the evaluation of the curse and we
+will not be here in the in the classroom
+
+ align:start position:0%
+will not be here in the in the classroom
+ 
+
+ align:start position:0%
+will not be here in the in the classroom
+as you are evaluating the course okay so
+
+ align:start position:0%
+as you are evaluating the course okay so
+ 
+
+ align:start position:0%
+as you are evaluating the course okay so
+we have only 8 minutes okay let's talk
+
+ align:start position:0%
+we have only 8 minutes okay let's talk
+ 
+
+ align:start position:0%
+we have only 8 minutes okay let's talk
+about
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that must faay with
+
+ align:start position:0%
+that must faay with
+ 
+
+ align:start position:0%
+that must faay with
+that yes can you move it
+
+ align:start position:0%
+that yes can you move it
+ 
+
+ align:start position:0%
+that yes can you move it
+okay okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+let's you will give us your cards after
+
+ align:start position:0%
+let's you will give us your cards after
+ 
+
+ align:start position:0%
+let's you will give us your cards after
+okay but
+
+ align:start position:0%
+okay but
+ 
+
+ align:start position:0%
+okay but
+please the most important idea of the
+
+ align:start position:0%
+please the most important idea of the
+ 
+
+ align:start position:0%
+please the most important idea of the
+three
+
+ align:start position:0%
+three
+ 
+
+ align:start position:0%
+three
+cards please tell
+
+ align:start position:0%
+cards please tell
+ 
+
+ align:start position:0%
+cards please tell
+us one yes if you want you can talk
+
+ align:start position:0%
+us one yes if you want you can talk
+ 
+
+ align:start position:0%
+us one yes if you want you can talk
+about more than one but first one idea
+
+ align:start position:0%
+about more than one but first one idea
+ 
+
+ align:start position:0%
+about more than one but first one idea
+of the three
+
+ align:start position:0%
+of the three
+ 
+
+ align:start position:0%
+of the three
+we will work with the cars after the
+
+ align:start position:0%
+we will work with the cars after the
+ 
+
+ align:start position:0%
+we will work with the cars after the
+first I'm not clear what just share one
+
+ align:start position:0%
+first I'm not clear what just share one
+ 
+
+ align:start position:0%
+first I'm not clear what just share one
+of okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay oh you're asking no no I don't no I
+
+ align:start position:0%
+okay oh you're asking no no I don't no I
+ 
+
+ align:start position:0%
+okay oh you're asking no no I don't no I
+I I I was looking at you because you we
+
+ align:start position:0%
+I I I was looking at you because you we
+ 
+
+ align:start position:0%
+I I I was looking at you because you we
+were trying to understand what I'm
+
+ align:start position:0%
+were trying to understand what I'm
+ 
+
+ align:start position:0%
+were trying to understand what I'm
+supposed to do okay and who wants to
+
+ align:start position:0%
+supposed to do okay and who wants to
+ 
+
+ align:start position:0%
+supposed to do okay and who wants to
+begin I'll begin okay um I think that um
+
+ align:start position:0%
+begin I'll begin okay um I think that um
+ 
+
+ align:start position:0%
+begin I'll begin okay um I think that um
+reflective practice can improve
+
+ align:start position:0%
+reflective practice can improve
+ 
+
+ align:start position:0%
+reflective practice can improve
+organizational institutional
+
+ align:start position:0%
+organizational institutional
+ 
+
+ align:start position:0%
+organizational institutional
+efficiency can improve organizational
+
+ align:start position:0%
+efficiency can improve organizational
+ 
+
+ align:start position:0%
+efficiency can improve organizational
+and institutional
+
+ align:start position:0%
+and institutional
+ 
+
+ align:start position:0%
+and institutional
+efficiency okay thank
+
+ align:start position:0%
+efficiency okay thank
+ 
+
+ align:start position:0%
+efficiency okay thank
+you it's similar to the kind of
+
+ align:start position:0%
+you it's similar to the kind of
+ 
+
+ align:start position:0%
+you it's similar to the kind of
+formulation you was thinking before
+
+ align:start position:0%
+formulation you was thinking before
+ 
+
+ align:start position:0%
+formulation you was thinking before
+okay is a possible to
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+build can you um is a possible blueprint
+
+ align:start position:0%
+build can you um is a possible blueprint
+ 
+
+ align:start position:0%
+build can you um is a possible blueprint
+to be used for building the Str
+
+ align:start position:0%
+to be used for building the Str
+ 
+
+ align:start position:0%
+to be used for building the Str
+Community organization um a what
+
+ align:start position:0%
+Community organization um a what
+ 
+
+ align:start position:0%
+Community organization um a what
+community a strengthen strengthen okay
+
+ align:start position:0%
+community a strengthen strengthen okay
+ 
+
+ align:start position:0%
+community a strengthen strengthen okay
+great okay CIA
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um reflective reflective practice um
+
+ align:start position:0%
+um reflective reflective practice um
+ 
+
+ align:start position:0%
+um reflective reflective practice um
+would cause can cause or is
+
+ align:start position:0%
+would cause can cause or is
+ 
+
+ align:start position:0%
+would cause can cause or is
+causing an intermediate process of
+
+ align:start position:0%
+causing an intermediate process of
+ 
+
+ align:start position:0%
+causing an intermediate process of
+conflict of
+
+ align:start position:0%
+conflict of
+ 
+
+ align:start position:0%
+conflict of
+paradigms par paradig paradig okay
+
+ align:start position:0%
+paradigms par paradig paradig okay
+ 
+
+ align:start position:0%
+paradigms par paradig paradig okay
+paradig
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yes I wrote
+
+ align:start position:0%
+yes I wrote
+ 
+
+ align:start position:0%
+yes I wrote
+down to write to finish to write
+
+ align:start position:0%
+down to write to finish to write
+ 
+
+ align:start position:0%
+down to write to finish to write
+intermediate process mhm of conflict of
+
+ align:start position:0%
+intermediate process mhm of conflict of
+ 
+
+ align:start position:0%
+intermediate process mhm of conflict of
+paradigms I want to say that it's not
+
+ align:start position:0%
+paradigms I want to say that it's not
+ 
+
+ align:start position:0%
+paradigms I want to say that it's not
+it's not
+
+ align:start position:0%
+it's not
+ 
+
+ align:start position:0%
+it's not
+an it's not a process that will take
+
+ align:start position:0%
+an it's not a process that will take
+ 
+
+ align:start position:0%
+an it's not a process that will take
+forever it's it's
+
+ align:start position:0%
+forever it's it's
+ 
+
+ align:start position:0%
+forever it's it's
+a it's an intermediate process to get
+
+ align:start position:0%
+a it's an intermediate process to get
+ 
+
+ align:start position:0%
+a it's an intermediate process to get
+somewhere after
+
+ align:start position:0%
+somewhere after
+ 
+
+ align:start position:0%
+somewhere after
+I don't know if it's the right word that
+
+ align:start position:0%
+I don't know if it's the right word that
+ 
+
+ align:start position:0%
+I don't know if it's the right word that
+mean the right
+
+ align:start position:0%
+mean the right
+ 
+
+ align:start position:0%
+mean the right
+word
+
+ align:start position:0%
+word
+ 
+
+ align:start position:0%
+word
+intermediate inter
+
+ align:start position:0%
+intermediate inter
+ 
+
+ align:start position:0%
+intermediate inter
+mediate it's a process that has it's a
+
+ align:start position:0%
+mediate it's a process that has it's a
+ 
+
+ align:start position:0%
+mediate it's a process that has it's a
+it's a stage of development exactly
+
+ align:start position:0%
+it's a stage of development exactly
+ 
+
+ align:start position:0%
+it's a stage of development exactly
+exactly okay it's a how do you say that
+
+ align:start position:0%
+exactly okay it's a how do you say that
+ 
+
+ align:start position:0%
+exactly okay it's a how do you say that
+is that a word for that immedate intered
+
+ align:start position:0%
+is that a word for that immedate intered
+ 
+
+ align:start position:0%
+is that a word for that immedate intered
+intermediate stage intermediate stage
+
+ align:start position:0%
+intermediate stage intermediate stage
+ 
+
+ align:start position:0%
+intermediate stage intermediate stage
+intermediate stage yes it
+
+ align:start position:0%
+intermediate stage yes it
+ 
+
+ align:start position:0%
+intermediate stage yes it
+is towards what a change in
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+paradig
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay in par okay um I wrote down
+
+ align:start position:0%
+okay in par okay um I wrote down
+ 
+
+ align:start position:0%
+okay in par okay um I wrote down
+demystifying
+
+ align:start position:0%
+demystifying
+ 
+
+ align:start position:0%
+demystifying
+demystifying reflective practice in a
+
+ align:start position:0%
+demystifying reflective practice in a
+ 
+
+ align:start position:0%
+demystifying reflective practice in a
+community Through facilitation can
+
+ align:start position:0%
+community Through facilitation can
+ 
+
+ align:start position:0%
+community Through facilitation can
+result in collective decision
+
+ align:start position:0%
+result in collective decision
+ 
+
+ align:start position:0%
+result in collective decision
+making should I say it's slower no okay
+
+ align:start position:0%
+making should I say it's slower no okay
+ 
+
+ align:start position:0%
+making should I say it's slower no okay
+[Applause]
+
+ align:start position:0%
+[Applause]
+ 
+
+ align:start position:0%
+[Applause]
+mhm
+
+ align:start position:0%
+mhm
+ 
+
+ align:start position:0%
+mhm
+Community dis mystifying effective
+
+ align:start position:0%
+Community dis mystifying effective
+ 
+
+ align:start position:0%
+Community dis mystifying effective
+practice in communities in a in a
+
+ align:start position:0%
+practice in communities in a in a
+ 
+
+ align:start position:0%
+practice in communities in a in a
+community Through facilitation resulting
+
+ align:start position:0%
+community Through facilitation resulting
+ 
+
+ align:start position:0%
+community Through facilitation resulting
+in collective decision
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+making okay you I'm not done okay please
+
+ align:start position:0%
+making okay you I'm not done okay please
+ 
+
+ align:start position:0%
+making okay you I'm not done okay please
+uh reflective practice can change the
+
+ align:start position:0%
+uh reflective practice can change the
+ 
+
+ align:start position:0%
+uh reflective practice can change the
+way we sorry I wait
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+for um reflective practice can change
+
+ align:start position:0%
+for um reflective practice can change
+ 
+
+ align:start position:0%
+for um reflective practice can change
+the way we think feel and act as we
+
+ align:start position:0%
+the way we think feel and act as we
+ 
+
+ align:start position:0%
+the way we think feel and act as we
+evolve through our lives into higher
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+beings respective
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+practice change the way we think feel
+
+ align:start position:0%
+practice change the way we think feel
+ 
+
+ align:start position:0%
+practice change the way we think feel
+and act think feel and act as we evolve
+
+ align:start position:0%
+and act think feel and act as we evolve
+ 
+
+ align:start position:0%
+and act think feel and act as we evolve
+through our lives as we evolve
+
+ align:start position:0%
+through our lives as we evolve
+ 
+
+ align:start position:0%
+through our lives as we evolve
+all life into higher
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+beings okay thank you Esra uh so all
+
+ align:start position:0%
+beings okay thank you Esra uh so all
+ 
+
+ align:start position:0%
+beings okay thank you Esra uh so all
+three of mine were actually sort of one
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+long so basically I was thinking that
+
+ align:start position:0%
+long so basically I was thinking that
+ 
+
+ align:start position:0%
+long so basically I was thinking that
+reflective practice could enable um
+
+ align:start position:0%
+reflective practice could enable um
+ 
+
+ align:start position:0%
+reflective practice could enable um
+conception of new uh hybrid
+
+ align:start position:0%
+conception of new uh hybrid
+ 
+
+ align:start position:0%
+conception of new uh hybrid
+interdisiplinary
+
+ align:start position:0%
+interdisiplinary
+ 
+
+ align:start position:0%
+interdisiplinary
+teams which would then also enable those
+
+ align:start position:0%
+teams which would then also enable those
+ 
+
+ align:start position:0%
+teams which would then also enable those
+hybrid teams to improve their
+
+ align:start position:0%
+hybrid teams to improve their
+ 
+
+ align:start position:0%
+hybrid teams to improve their
+effectiveness as they work
+
+ align:start position:0%
+effectiveness as they work
+ 
+
+ align:start position:0%
+effectiveness as they work
+together which would then enable the
+
+ align:start position:0%
+together which would then enable the
+ 
+
+ align:start position:0%
+together which would then enable the
+development of new conceptual
+
+ align:start position:0%
+development of new conceptual
+ 
+
+ align:start position:0%
+development of new conceptual
+Innovations enabling Solutions of
+
+ align:start position:0%
+Innovations enabling Solutions of
+ 
+
+ align:start position:0%
+Innovations enabling Solutions of
+intractable problems problems that were
+
+ align:start position:0%
+intractable problems problems that were
+ 
+
+ align:start position:0%
+intractable problems problems that were
+previously intract okay work better
+
+ align:start position:0%
+previously intract okay work better
+ 
+
+ align:start position:0%
+previously intract okay work better
+together and what else uh so enable the
+
+ align:start position:0%
+together and what else uh so enable the
+ 
+
+ align:start position:0%
+together and what else uh so enable the
+teams to come to come together and then
+
+ align:start position:0%
+teams to come to come together and then
+ 
+
+ align:start position:0%
+teams to come to come together and then
+to work better together so the creation
+
+ align:start position:0%
+to work better together so the creation
+ 
+
+ align:start position:0%
+to work better together so the creation
+of
+
+ align:start position:0%
+of
+ 
+
+ align:start position:0%
+of
+team and then uh getting them to work
+
+ align:start position:0%
+team and then uh getting them to work
+ 
+
+ align:start position:0%
+team and then uh getting them to work
+better once they're actually together
+
+ align:start position:0%
+better once they're actually together
+ 
+
+ align:start position:0%
+better once they're actually together
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+then uh which would then enable the
+
+ align:start position:0%
+then uh which would then enable the
+ 
+
+ align:start position:0%
+then uh which would then enable the
+development of new conceptual
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Innovations okay thank
+
+ align:start position:0%
+Innovations okay thank
+ 
+
+ align:start position:0%
+Innovations okay thank
+you um I
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+put okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+I put um reflective practice can help
+
+ align:start position:0%
+I put um reflective practice can help
+ 
+
+ align:start position:0%
+I put um reflective practice can help
+build
+
+ align:start position:0%
+build
+ 
+
+ align:start position:0%
+build
+consensus in a complex society where an
+
+ align:start position:0%
+consensus in a complex society where an
+ 
+
+ align:start position:0%
+consensus in a complex society where an
+increasing number of Interest must be
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+balanced where there's an increasing
+
+ align:start position:0%
+balanced where there's an increasing
+ 
+
+ align:start position:0%
+balanced where there's an increasing
+where an increasing number of Interest
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+really well one of my couple of my
+
+ align:start position:0%
+really well one of my couple of my
+ 
+
+ align:start position:0%
+really well one of my couple of my
+thoughts are already up there so I'll
+
+ align:start position:0%
+thoughts are already up there so I'll
+ 
+
+ align:start position:0%
+thoughts are already up there so I'll
+play Devil's Advocate and say that the
+
+ align:start position:0%
+play Devil's Advocate and say that the
+ 
+
+ align:start position:0%
+play Devil's Advocate and say that the
+new environment with the massive amount
+
+ align:start position:0%
+new environment with the massive amount
+ 
+
+ align:start position:0%
+new environment with the massive amount
+of information and the ability to share
+
+ align:start position:0%
+of information and the ability to share
+ 
+
+ align:start position:0%
+of information and the ability to share
+it so fast will make reflective practice
+
+ align:start position:0%
+it so fast will make reflective practice
+ 
+
+ align:start position:0%
+it so fast will make reflective practice
+ever more difficult
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+[Applause]
+
+ align:start position:0%
+[Applause]
+ 
+
+ align:start position:0%
+[Applause]
+yeah
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+[Applause]
+
+ align:start position:0%
+[Applause]
+ 
+
+ align:start position:0%
+[Applause]
+okay we make effective practice even
+
+ align:start position:0%
+okay we make effective practice even
+ 
+
+ align:start position:0%
+okay we make effective practice even
+more difficult
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay no
+
+ align:start position:0%
+okay no
+ 
+
+ align:start position:0%
+okay no
+way the increasing amounts of you know
+
+ align:start position:0%
+way the increasing amounts of you know
+ 
+
+ align:start position:0%
+way the increasing amounts of you know
+information
+
+ align:start position:0%
+information
+ 
+
+ align:start position:0%
+information
+and like groups
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+blogging yeah to answer the question of
+
+ align:start position:0%
+blogging yeah to answer the question of
+ 
+
+ align:start position:0%
+blogging yeah to answer the question of
+what possibilities are opening for
+
+ align:start position:0%
+what possibilities are opening for
+ 
+
+ align:start position:0%
+what possibilities are opening for
+reflective practice I think I think that
+
+ align:start position:0%
+reflective practice I think I think that
+ 
+
+ align:start position:0%
+reflective practice I think I think that
+um the new discoveries are challenging
+
+ align:start position:0%
+um the new discoveries are challenging
+ 
+
+ align:start position:0%
+um the new discoveries are challenging
+assumptions mhm so that opens
+
+ align:start position:0%
+assumptions mhm so that opens
+ 
+
+ align:start position:0%
+assumptions mhm so that opens
+opportunities for reflective practice
+
+ align:start position:0%
+opportunities for reflective practice
+ 
+
+ align:start position:0%
+opportunities for reflective practice
+mhm
+
+ align:start position:0%
+mhm
+ 
+
+ align:start position:0%
+mhm
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+okay yes
+
+ align:start position:0%
+okay yes
+ 
+
+ align:start position:0%
+okay yes
+okay let's wait just a second
+
+ align:start position:0%
+okay let's wait just a second
+ 
+
+ align:start position:0%
+okay let's wait just a second
+for to finish to
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+WR
+
+ align:start position:0%
+WR
+ 
+
+ align:start position:0%
+WR
+scoll
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah yes she can she has space there to
+
+ align:start position:0%
+yeah yes she can she has space there to
+ 
+
+ align:start position:0%
+yeah yes she can she has space there to
+reflection prac we can find a common
+
+ align:start position:0%
+reflection prac we can find a common
+ 
+
+ align:start position:0%
+reflection prac we can find a common
+solution for local communities and
+
+ align:start position:0%
+solution for local communities and
+ 
+
+ align:start position:0%
+solution for local communities and
+Global problems through theory and
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+practice
+
+ align:start position:0%
+practice
+ 
+
+ align:start position:0%
+practice
+Comm
+
+ align:start position:0%
+Comm
+ 
+
+ align:start position:0%
+Comm
+[Music]
+
+ align:start position:0%
+[Music]
+ 
+
+ align:start position:0%
+[Music]
+solutions
+
+ align:start position:0%
+solutions
+ 
+
+ align:start position:0%
+solutions
+for local
+
+ align:start position:0%
+for local
+ 
+
+ align:start position:0%
+for local
+problems
+
+ align:start position:0%
+problems
+ 
+
+ align:start position:0%
+problems
+problems okay okay thank you very much
+
+ align:start position:0%
+problems okay okay thank you very much
+ 
+
+ align:start position:0%
+problems okay okay thank you very much
+okay so these are the ideas you can
+
+ align:start position:0%
+okay so these are the ideas you can
+ 
+
+ align:start position:0%
+okay so these are the ideas you can
+visualize for the future of effective
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+practice
+
+ align:start position:0%
+practice
+ 
+
+ align:start position:0%
+practice
+see
+
+ align:start position:0%
+see
+ 
+
+ align:start position:0%
+see
+okay my on view about that is
+
+ align:start position:0%
+okay my on view about that is
+ 
+
+ align:start position:0%
+okay my on view about that is
+that in the next time I think that
+
+ align:start position:0%
+that in the next time I think that
+ 
+
+ align:start position:0%
+that in the next time I think that
+people will recreate reflective practice
+
+ align:start position:0%
+people will recreate reflective practice
+ 
+
+ align:start position:0%
+people will recreate reflective practice
+in a way for to do it much more
+
+ align:start position:0%
+in a way for to do it much more
+ 
+
+ align:start position:0%
+in a way for to do it much more
+practical okay and Powerful
+
+ align:start position:0%
+practical okay and Powerful
+ 
+
+ align:start position:0%
+practical okay and Powerful
+for solving this kind of problems like
+
+ align:start position:0%
+for solving this kind of problems like
+ 
+
+ align:start position:0%
+for solving this kind of problems like
+conceptual
+
+ align:start position:0%
+conceptual
+ 
+
+ align:start position:0%
+conceptual
+Innovation ER
+
+ align:start position:0%
+Innovation ER
+ 
+
+ align:start position:0%
+Innovation ER
+different ER perspectives of different
+
+ align:start position:0%
+different ER perspectives of different
+ 
+
+ align:start position:0%
+different ER perspectives of different
+groups things like that I think that
+
+ align:start position:0%
+groups things like that I think that
+ 
+
+ align:start position:0%
+groups things like that I think that
+reflective practice will
+
+ align:start position:0%
+reflective practice will
+ 
+
+ align:start position:0%
+reflective practice will
+be recreated in the next years
\ No newline at end of file
diff --git a/WwBaQCy4jfk.txt b/WwBaQCy4jfk.txt
new file mode 100644
index 0000000000000000000000000000000000000000..939a79153cd0f100b45899bddaebc30acd9999f4
--- /dev/null
+++ b/WwBaQCy4jfk.txt
@@ -0,0 +1,3280 @@
+align:start position:0%
+ 
+hi welcome back to recitation in lecture
+
+ align:start position:0%
+hi welcome back to recitation in lecture
+ 
+
+ align:start position:0%
+hi welcome back to recitation in lecture
+you've been learning about the
+
+ align:start position:0%
+you've been learning about the
+ 
+
+ align:start position:0%
+you've been learning about the
+Divergence Theorem also known as gauss's
+
+ align:start position:0%
+Divergence Theorem also known as gauss's
+ 
+
+ align:start position:0%
+Divergence Theorem also known as gauss's
+theorem and flux and all that good stuff
+
+ align:start position:0%
+theorem and flux and all that good stuff
+ 
+
+ align:start position:0%
+theorem and flux and all that good stuff
+so I have a a nice exercise on it for
+
+ align:start position:0%
+so I have a a nice exercise on it for
+ 
+
+ align:start position:0%
+so I have a a nice exercise on it for
+you here um so what I want is I want you
+
+ align:start position:0%
+you here um so what I want is I want you
+ 
+
+ align:start position:0%
+you here um so what I want is I want you
+to take F I want it to be the field
+
+ align:start position:0%
+to take F I want it to be the field
+ 
+
+ align:start position:0%
+to take F I want it to be the field
+whose components are X over row cubed y
+
+ align:start position:0%
+whose components are X over row cubed y
+ 
+
+ align:start position:0%
+whose components are X over row cubed y
+overow row cubed and Z over row cubed so
+
+ align:start position:0%
+overow row cubed and Z over row cubed so
+ 
+
+ align:start position:0%
+overow row cubed and Z over row cubed so
+here row is your usual Row from
+
+ align:start position:0%
+here row is your usual Row from
+ 
+
+ align:start position:0%
+here row is your usual Row from
+spherical coordinates row is equal to
+
+ align:start position:0%
+spherical coordinates row is equal to
+ 
+
+ align:start position:0%
+spherical coordinates row is equal to
+the otk of x^2 plus y^ S Plus z^2 um and
+
+ align:start position:0%
+the otk of x^2 plus y^ S Plus z^2 um and
+ 
+
+ align:start position:0%
+the otk of x^2 plus y^ S Plus z^2 um and
+I want s to be the surface of the Box
+
+ align:start position:0%
+I want s to be the surface of the Box
+ 
+
+ align:start position:0%
+I want s to be the surface of the Box
+whose vertices are plus or- 2 plus or -2
+
+ align:start position:0%
+whose vertices are plus or- 2 plus or -2
+ 
+
+ align:start position:0%
+whose vertices are plus or- 2 plus or -2
+Plus or min-2 um so it's a a cubical box
+
+ align:start position:0%
+Plus or min-2 um so it's a a cubical box
+ 
+
+ align:start position:0%
+Plus or min-2 um so it's a a cubical box
+um so what I'd like you to do is first
+
+ align:start position:0%
+um so what I'd like you to do is first
+ 
+
+ align:start position:0%
+um so what I'd like you to do is first
+in part A I'd like you to show that the
+
+ align:start position:0%
+in part A I'd like you to show that the
+ 
+
+ align:start position:0%
+in part A I'd like you to show that the
+Divergence of f is zero wherever the
+
+ align:start position:0%
+Divergence of f is zero wherever the
+ 
+
+ align:start position:0%
+Divergence of f is zero wherever the
+field f is defined um in Part B what I'd
+
+ align:start position:0%
+field f is defined um in Part B what I'd
+ 
+
+ align:start position:0%
+field f is defined um in Part B what I'd
+like you to think about is whether we
+
+ align:start position:0%
+like you to think about is whether we
+ 
+
+ align:start position:0%
+like you to think about is whether we
+can conclude from that that the the the
+
+ align:start position:0%
+can conclude from that that the the the
+ 
+
+ align:start position:0%
+can conclude from that that the the the
+flux through the surface of s is equal
+
+ align:start position:0%
+flux through the surface of s is equal
+ 
+
+ align:start position:0%
+flux through the surface of s is equal
+to zero all right and in part
+
+ align:start position:0%
+to zero all right and in part
+ 
+
+ align:start position:0%
+to zero all right and in part
+three or C um what I'd like you to do is
+
+ align:start position:0%
+three or C um what I'd like you to do is
+ 
+
+ align:start position:0%
+three or C um what I'd like you to do is
+to use the extended version of gauss's
+
+ align:start position:0%
+to use the extended version of gauss's
+ 
+
+ align:start position:0%
+to use the extended version of gauss's
+theorem or the extended version of the
+
+ align:start position:0%
+theorem or the extended version of the
+ 
+
+ align:start position:0%
+theorem or the extended version of the
+Divergence Theorem um in order to to
+
+ align:start position:0%
+Divergence Theorem um in order to to
+ 
+
+ align:start position:0%
+Divergence Theorem um in order to to
+actually compute the flux through S by
+
+ align:start position:0%
+actually compute the flux through S by
+ 
+
+ align:start position:0%
+actually compute the flux through S by
+Computing an integral so uh why why
+
+ align:start position:0%
+Computing an integral so uh why why
+ 
+
+ align:start position:0%
+Computing an integral so uh why why
+don't you pause the video for a couple
+
+ align:start position:0%
+don't you pause the video for a couple
+ 
+
+ align:start position:0%
+don't you pause the video for a couple
+of minutes come back we can uh work jeez
+
+ align:start position:0%
+of minutes come back we can uh work jeez
+ 
+
+ align:start position:0%
+of minutes come back we can uh work jeez
+pause the video for a couple minutes
+
+ align:start position:0%
+pause the video for a couple minutes
+ 
+
+ align:start position:0%
+pause the video for a couple minutes
+work out this problem come back and we
+
+ align:start position:0%
+work out this problem come back and we
+ 
+
+ align:start position:0%
+work out this problem come back and we
+can work it out
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+together hopefully you had some luck
+
+ align:start position:0%
+together hopefully you had some luck
+ 
+
+ align:start position:0%
+together hopefully you had some luck
+with this problem let's get started part
+
+ align:start position:0%
+with this problem let's get started part
+ 
+
+ align:start position:0%
+with this problem let's get started part
+A asks you to compute the Divergence of
+
+ align:start position:0%
+A asks you to compute the Divergence of
+ 
+
+ align:start position:0%
+A asks you to compute the Divergence of
+f so in order to compute that well we're
+
+ align:start position:0%
+f so in order to compute that well we're
+ 
+
+ align:start position:0%
+f so in order to compute that well we're
+going to need to take the partial
+
+ align:start position:0%
+going to need to take the partial
+ 
+
+ align:start position:0%
+going to need to take the partial
+derivatives of the components of F and
+
+ align:start position:0%
+derivatives of the components of F and
+ 
+
+ align:start position:0%
+derivatives of the components of F and
+in order to do that at some point I'm
+
+ align:start position:0%
+in order to do that at some point I'm
+ 
+
+ align:start position:0%
+in order to do that at some point I'm
+going to need to take a partial
+
+ align:start position:0%
+going to need to take a partial
+ 
+
+ align:start position:0%
+going to need to take a partial
+derivative of row so let me first
+
+ align:start position:0%
+derivative of row so let me first
+ 
+
+ align:start position:0%
+derivative of row so let me first
+compute the partial derivatives of row
+
+ align:start position:0%
+compute the partial derivatives of row
+ 
+
+ align:start position:0%
+compute the partial derivatives of row
+and that'll save me a tiny bit of work
+
+ align:start position:0%
+and that'll save me a tiny bit of work
+ 
+
+ align:start position:0%
+and that'll save me a tiny bit of work
+later so row is equal to the < TK of x^2
+
+ align:start position:0%
+later so row is equal to the < TK of x^2
+ 
+
+ align:start position:0%
+later so row is equal to the < TK of x^2
++ y^ 2 plus z^
+
+ align:start position:0%
++ y^ 2 plus z^
+ 
+
+ align:start position:0%
++ y^ 2 plus z^
+
+ align:start position:0%
+ 
+
+ align:start position:0%
+so partial
+
+ align:start position:0%
+so partial
+ 
+
+ align:start position:0%
+so partial
+row partial X well you just apply your
+
+ align:start position:0%
+row partial X well you just apply your
+ 
+
+ align:start position:0%
+row partial X well you just apply your
+usual chain rule here and I guess we get
+
+ align:start position:0%
+usual chain rule here and I guess we get
+ 
+
+ align:start position:0%
+usual chain rule here and I guess we get
+a half but then we get a two that
+
+ align:start position:0%
+a half but then we get a two that
+ 
+
+ align:start position:0%
+a half but then we get a two that
+cancels it so I think this works out to
+
+ align:start position:0%
+cancels it so I think this works out to
+ 
+
+ align:start position:0%
+cancels it so I think this works out to
+x / the < TK of x^2 + y^2 + z^2 so
+
+ align:start position:0%
+x / the < TK of x^2 + y^2 + z^2 so
+ 
+
+ align:start position:0%
+x / the < TK of x^2 + y^2 + z^2 so
+that's x / row all right and we're I'm
+
+ align:start position:0%
+that's x / row all right and we're I'm
+ 
+
+ align:start position:0%
+that's x / row all right and we're I'm
+just going to keep row around here
+
+ align:start position:0%
+just going to keep row around here
+ 
+
+ align:start position:0%
+just going to keep row around here
+because it you know because otherwise I
+
+ align:start position:0%
+because it you know because otherwise I
+ 
+
+ align:start position:0%
+because it you know because otherwise I
+have to write out the square root of x s
+
+ align:start position:0%
+have to write out the square root of x s
+ 
+
+ align:start position:0%
+have to write out the square root of x s
+plus y squ plus z s over and over again
+
+ align:start position:0%
+plus y squ plus z s over and over again
+ 
+
+ align:start position:0%
+plus y squ plus z s over and over again
+and this is going to save me um some
+
+ align:start position:0%
+and this is going to save me um some
+ 
+
+ align:start position:0%
+and this is going to save me um some
+effort and would save you some effort um
+
+ align:start position:0%
+effort and would save you some effort um
+ 
+
+ align:start position:0%
+effort and would save you some effort um
+as well so okay so row this is row so
+
+ align:start position:0%
+as well so okay so row this is row so
+ 
+
+ align:start position:0%
+as well so okay so row this is row so
+this is D DX um so the component of
+
+ align:start position:0%
+this is D DX um so the component of
+ 
+
+ align:start position:0%
+this is D DX um so the component of
+F that we want to take the partial of so
+
+ align:start position:0%
+F that we want to take the partial of so
+ 
+
+ align:start position:0%
+F that we want to take the partial of so
+we want to take the X partial of the
+
+ align:start position:0%
+we want to take the X partial of the
+ 
+
+ align:start position:0%
+we want to take the X partial of the
+first component of f so that's the X
+
+ align:start position:0%
+first component of f so that's the X
+ 
+
+ align:start position:0%
+first component of f so that's the X
+partial of X over row
+
+ align:start position:0%
+partial of X over row
+ 
+
+ align:start position:0%
+partial of X over row
+cubed okay and you just apply your usual
+
+ align:start position:0%
+cubed okay and you just apply your usual
+ 
+
+ align:start position:0%
+cubed okay and you just apply your usual
+quotient rule so what do we get we get
+
+ align:start position:0%
+quotient rule so what do we get we get
+ 
+
+ align:start position:0%
+quotient rule so what do we get we get
+the derivative of the top so that's row
+
+ align:start position:0%
+the derivative of the top so that's row
+ 
+
+ align:start position:0%
+the derivative of the top so that's row
+cubed minus okay so the top is x times
+
+ align:start position:0%
+cubed minus okay so the top is x times
+ 
+
+ align:start position:0%
+cubed minus okay so the top is x times
+the derivative of the bottom is going to
+
+ align:start position:0%
+the derivative of the bottom is going to
+ 
+
+ align:start position:0%
+the derivative of the bottom is going to
+be 3 row 2ar * X over row so that's
+
+ align:start position:0%
+be 3 row 2ar * X over row so that's
+ 
+
+ align:start position:0%
+be 3 row 2ar * X over row so that's
+three so we have an X so it's
+
+ align:start position:0%
+three so we have an X so it's
+ 
+
+ align:start position:0%
+three so we have an X so it's
+3x^2 row / the bottom squar which is row
+
+ align:start position:0%
+3x^2 row / the bottom squar which is row
+ 
+
+ align:start position:0%
+3x^2 row / the bottom squar which is row
+to the 6 and I guess there's a common
+
+ align:start position:0%
+to the 6 and I guess there's a common
+ 
+
+ align:start position:0%
+to the 6 and I guess there's a common
+factor of row everywhere that we can
+
+ align:start position:0%
+factor of row everywhere that we can
+ 
+
+ align:start position:0%
+factor of row everywhere that we can
+cancel out so this is equal to Row 2 - 3
+
+ align:start position:0%
+cancel out so this is equal to Row 2 - 3
+ 
+
+ align:start position:0%
+cancel out so this is equal to Row 2 - 3
+x^2 / row to the 5th okay so that's the
+
+ align:start position:0%
+x^2 / row to the 5th okay so that's the
+ 
+
+ align:start position:0%
+x^2 / row to the 5th okay so that's the
+partial the X partial derivative of the
+
+ align:start position:0%
+partial the X partial derivative of the
+ 
+
+ align:start position:0%
+partial the X partial derivative of the
+first component of f now we need the Y
+
+ align:start position:0%
+first component of f now we need the Y
+ 
+
+ align:start position:0%
+first component of f now we need the Y
+partial derivative of the second
+
+ align:start position:0%
+partial derivative of the second
+ 
+
+ align:start position:0%
+partial derivative of the second
+component of F and the Z partial
+
+ align:start position:0%
+component of F and the Z partial
+ 
+
+ align:start position:0%
+component of F and the Z partial
+derivative of the third component of f
+
+ align:start position:0%
+derivative of the third component of f
+ 
+
+ align:start position:0%
+derivative of the third component of f
+but if you go and look back at what the
+
+ align:start position:0%
+but if you go and look back at what the
+ 
+
+ align:start position:0%
+but if you go and look back at what the
+formula for f was you see that this is a
+
+ align:start position:0%
+formula for f was you see that this is a
+ 
+
+ align:start position:0%
+formula for f was you see that this is a
+very very symmetric formula so in order
+
+ align:start position:0%
+very very symmetric formula so in order
+ 
+
+ align:start position:0%
+very very symmetric formula so in order
+to get from the first component to the
+
+ align:start position:0%
+to get from the first component to the
+ 
+
+ align:start position:0%
+to get from the first component to the
+second component we just change X to Y
+
+ align:start position:0%
+second component we just change X to Y
+ 
+
+ align:start position:0%
+second component we just change X to Y
+and to get from the second component to
+
+ align:start position:0%
+and to get from the second component to
+ 
+
+ align:start position:0%
+and to get from the second component to
+the third we just change y to Z because
+
+ align:start position:0%
+the third we just change y to Z because
+ 
+
+ align:start position:0%
+the third we just change y to Z because
+of course row is treats X Y and Z the
+
+ align:start position:0%
+of course row is treats X Y and Z the
+ 
+
+ align:start position:0%
+of course row is treats X Y and Z the
+same um so what does that mean well that
+
+ align:start position:0%
+same um so what does that mean well that
+ 
+
+ align:start position:0%
+same um so what does that mean well that
+means that the partial derivatives are
+
+ align:start position:0%
+means that the partial derivatives are
+ 
+
+ align:start position:0%
+means that the partial derivatives are
+easy to compute having computed this x
+
+ align:start position:0%
+easy to compute having computed this x
+ 
+
+ align:start position:0%
+easy to compute having computed this x
+partial derivative we also get um that
+
+ align:start position:0%
+partial derivative we also get um that
+ 
+
+ align:start position:0%
+partial derivative we also get um that
+partial
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh over partial y of the second
+
+ align:start position:0%
+uh over partial y of the second
+ 
+
+ align:start position:0%
+uh over partial y of the second
+component which is y over row cubed is
+
+ align:start position:0%
+component which is y over row cubed is
+ 
+
+ align:start position:0%
+component which is y over row cubed is
+equal to Row 2 - 3 y^ 2 over row 5th and
+
+ align:start position:0%
+equal to Row 2 - 3 y^ 2 over row 5th and
+ 
+
+ align:start position:0%
+equal to Row 2 - 3 y^ 2 over row 5th and
+the last one we get partial over partial
+
+ align:start position:0%
+the last one we get partial over partial
+ 
+
+ align:start position:0%
+the last one we get partial over partial
+Z of Z over row
+
+ align:start position:0%
+Z of Z over row
+ 
+
+ align:start position:0%
+Z of Z over row
+cubed is equal to Row 2 minus sorry I'm
+
+ align:start position:0%
+cubed is equal to Row 2 minus sorry I'm
+ 
+
+ align:start position:0%
+cubed is equal to Row 2 minus sorry I'm
+getting a little cramped here 3 z^ 2
+
+ align:start position:0%
+getting a little cramped here 3 z^ 2
+ 
+
+ align:start position:0%
+getting a little cramped here 3 z^ 2
+over row to the
+
+ align:start position:0%
+over row to the
+ 
+
+ align:start position:0%
+over row to the
+5th and so adding these up we get
+
+ align:start position:0%
+5th and so adding these up we get
+ 
+
+ align:start position:0%
+5th and so adding these up we get
+that div f is equal to well it's just
+
+ align:start position:0%
+that div f is equal to well it's just
+ 
+
+ align:start position:0%
+that div f is equal to well it's just
+equal to the sum of those three things
+
+ align:start position:0%
+equal to the sum of those three things
+ 
+
+ align:start position:0%
+equal to the sum of those three things
+so that's let's see what we've got we've
+
+ align:start position:0%
+so that's let's see what we've got we've
+ 
+
+ align:start position:0%
+so that's let's see what we've got we've
+got a three so the denominators are all
+
+ align:start position:0%
+got a three so the denominators are all
+ 
+
+ align:start position:0%
+got a three so the denominators are all
+row to the 5th and we've got 3 Row 2 -
+
+ align:start position:0%
+row to the 5th and we've got 3 Row 2 -
+ 
+
+ align:start position:0%
+row to the 5th and we've got 3 Row 2 -
+3x^ 2 - 3 y^ 2 - 3 Z 2 so this is equal
+
+ align:start position:0%
+3x^ 2 - 3 y^ 2 - 3 Z 2 so this is equal
+ 
+
+ align:start position:0%
+3x^ 2 - 3 y^ 2 - 3 Z 2 so this is equal
+to 3 Row 2 - 3 x^ 2 - 3 y^ 2 - 3 z^2 all
+
+ align:start position:0%
+to 3 Row 2 - 3 x^ 2 - 3 y^ 2 - 3 z^2 all
+ 
+
+ align:start position:0%
+to 3 Row 2 - 3 x^ 2 - 3 y^ 2 - 3 z^2 all
+over row to the 5th but of course Row 2
+
+ align:start position:0%
+over row to the 5th but of course Row 2
+ 
+
+ align:start position:0%
+over row to the 5th but of course Row 2
+is x^2 + y^2 + z^2 so this numerator is
+
+ align:start position:0%
+is x^2 + y^2 + z^2 so this numerator is
+ 
+
+ align:start position:0%
+is x^2 + y^2 + z^2 so this numerator is
+just zero so this is equal to
+
+ align:start position:0%
+just zero so this is equal to
+ 
+
+ align:start position:0%
+just zero so this is equal to
+zero okay which is what we thought it
+
+ align:start position:0%
+zero okay which is what we thought it
+ 
+
+ align:start position:0%
+zero okay which is what we thought it
+should be all right good so so that's
+
+ align:start position:0%
+should be all right good so so that's
+ 
+
+ align:start position:0%
+should be all right good so so that's
+part A we just computed the partial
+
+ align:start position:0%
+part A we just computed the partial
+ 
+
+ align:start position:0%
+part A we just computed the partial
+derivatives of F and then added them
+
+ align:start position:0%
+derivatives of F and then added them
+ 
+
+ align:start position:0%
+derivatives of F and then added them
+together to get the Divergence and we we
+
+ align:start position:0%
+together to get the Divergence and we we
+ 
+
+ align:start position:0%
+together to get the Divergence and we we
+found that in fact yes the Divergence
+
+ align:start position:0%
+found that in fact yes the Divergence
+ 
+
+ align:start position:0%
+found that in fact yes the Divergence
+was equal to zero great so that's part A
+
+ align:start position:0%
+was equal to zero great so that's part A
+ 
+
+ align:start position:0%
+was equal to zero great so that's part A
+so let's go look at what part B was Part
+
+ align:start position:0%
+so let's go look at what part B was Part
+ 
+
+ align:start position:0%
+so let's go look at what part B was Part
+B asked can we conclude that the flux
+
+ align:start position:0%
+B asked can we conclude that the flux
+ 
+
+ align:start position:0%
+B asked can we conclude that the flux
+through the surface s is zero all right
+
+ align:start position:0%
+through the surface s is zero all right
+ 
+
+ align:start position:0%
+through the surface s is zero all right
+now remember what the Divergence Theorem
+
+ align:start position:0%
+now remember what the Divergence Theorem
+ 
+
+ align:start position:0%
+now remember what the Divergence Theorem
+says the Divergence Theorem says that
+
+ align:start position:0%
+says the Divergence Theorem says that
+ 
+
+ align:start position:0%
+says the Divergence Theorem says that
+the flux through a surface of a field is
+
+ align:start position:0%
+the flux through a surface of a field is
+ 
+
+ align:start position:0%
+the flux through a surface of a field is
+equal to the triple integral of the
+
+ align:start position:0%
+equal to the triple integral of the
+ 
+
+ align:start position:0%
+equal to the triple integral of the
+Divergence of that field over the
+
+ align:start position:0%
+Divergence of that field over the
+ 
+
+ align:start position:0%
+Divergence of that field over the
+interior provided the field is defined
+
+ align:start position:0%
+interior provided the field is defined
+ 
+
+ align:start position:0%
+interior provided the field is defined
+and differentiable and nice or whatever
+
+ align:start position:0%
+and differentiable and nice or whatever
+ 
+
+ align:start position:0%
+and differentiable and nice or whatever
+everywhere
+
+ align:start position:0%
+everywhere
+ 
+
+ align:start position:0%
+everywhere
+inside okay but this field has a problem
+
+ align:start position:0%
+inside okay but this field has a problem
+ 
+
+ align:start position:0%
+inside okay but this field has a problem
+almost everywhere this field is nicely
+
+ align:start position:0%
+almost everywhere this field is nicely
+ 
+
+ align:start position:0%
+almost everywhere this field is nicely
+behaved but at zero we have a real
+
+ align:start position:0%
+behaved but at zero we have a real
+ 
+
+ align:start position:0%
+behaved but at zero we have a real
+problem we're dividing by zero right so
+
+ align:start position:0%
+problem we're dividing by zero right so
+ 
+
+ align:start position:0%
+problem we're dividing by zero right so
+this field is not defined at zero so
+
+ align:start position:0%
+this field is not defined at zero so
+ 
+
+ align:start position:0%
+this field is not defined at zero so
+there's a single point in the middle of
+
+ align:start position:0%
+there's a single point in the middle of
+ 
+
+ align:start position:0%
+there's a single point in the middle of
+this Cube where this where this field
+
+ align:start position:0%
+this Cube where this where this field
+ 
+
+ align:start position:0%
+this Cube where this where this field
+behaves badly and that means we can't
+
+ align:start position:0%
+behaves badly and that means we can't
+ 
+
+ align:start position:0%
+behaves badly and that means we can't
+apply the Divergence Theorem inside this
+
+ align:start position:0%
+apply the Divergence Theorem inside this
+ 
+
+ align:start position:0%
+apply the Divergence Theorem inside this
+Cube so since we can't apply the
+
+ align:start position:0%
+Cube so since we can't apply the
+ 
+
+ align:start position:0%
+Cube so since we can't apply the
+Divergence Theorem we aren't allowed to
+
+ align:start position:0%
+Divergence Theorem we aren't allowed to
+ 
+
+ align:start position:0%
+Divergence Theorem we aren't allowed to
+conclude immediately
+
+ align:start position:0%
+conclude immediately
+ 
+
+ align:start position:0%
+conclude immediately
+that that the diver that the flux
+
+ align:start position:0%
+that that the diver that the flux
+ 
+
+ align:start position:0%
+that that the diver that the flux
+through this surface is zero okay so the
+
+ align:start position:0%
+through this surface is zero okay so the
+ 
+
+ align:start position:0%
+through this surface is zero okay so the
+answer is no we can't conclude that the
+
+ align:start position:0%
+answer is no we can't conclude that the
+ 
+
+ align:start position:0%
+answer is no we can't conclude that the
+flux through S is zero because one of
+
+ align:start position:0%
+flux through S is zero because one of
+ 
+
+ align:start position:0%
+flux through S is zero because one of
+the hypotheses of the Divergence Theorem
+
+ align:start position:0%
+the hypotheses of the Divergence Theorem
+ 
+
+ align:start position:0%
+the hypotheses of the Divergence Theorem
+isn't satisfied namely the field isn't
+
+ align:start position:0%
+isn't satisfied namely the field isn't
+ 
+
+ align:start position:0%
+isn't satisfied namely the field isn't
+defined everywhere inside the region or
+
+ align:start position:0%
+defined everywhere inside the region or
+ 
+
+ align:start position:0%
+defined everywhere inside the region or
+inside the surface um okay so so the
+
+ align:start position:0%
+inside the surface um okay so so the
+ 
+
+ align:start position:0%
+inside the surface um okay so so the
+answer to
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+B is no okay I'm just going to write
+
+ align:start position:0%
+B is no okay I'm just going to write
+ 
+
+ align:start position:0%
+B is no okay I'm just going to write
+that but it's no because the hypotheses
+
+ align:start position:0%
+that but it's no because the hypotheses
+ 
+
+ align:start position:0%
+that but it's no because the hypotheses
+aren't satisfied ified okay so now let's
+
+ align:start position:0%
+aren't satisfied ified okay so now let's
+ 
+
+ align:start position:0%
+aren't satisfied ified okay so now let's
+look at Pro Part c um so part C suggests
+
+ align:start position:0%
+look at Pro Part c um so part C suggests
+ 
+
+ align:start position:0%
+look at Pro Part c um so part C suggests
+okay so we couldn't we can't conclude
+
+ align:start position:0%
+okay so we couldn't we can't conclude
+ 
+
+ align:start position:0%
+okay so we couldn't we can't conclude
+that that the flux is zero so okay so so
+
+ align:start position:0%
+that that the flux is zero so okay so so
+ 
+
+ align:start position:0%
+that that the flux is zero so okay so so
+we still want to know what the flux is
+
+ align:start position:0%
+we still want to know what the flux is
+ 
+
+ align:start position:0%
+we still want to know what the flux is
+right then that's still an interesting
+
+ align:start position:0%
+right then that's still an interesting
+ 
+
+ align:start position:0%
+right then that's still an interesting
+question so so part C suggests maybe you
+
+ align:start position:0%
+question so so part C suggests maybe you
+ 
+
+ align:start position:0%
+question so so part C suggests maybe you
+can still use the Divergence Theorem
+
+ align:start position:0%
+can still use the Divergence Theorem
+ 
+
+ align:start position:0%
+can still use the Divergence Theorem
+well now it's we're calling it Gus's
+
+ align:start position:0%
+well now it's we're calling it Gus's
+ 
+
+ align:start position:0%
+well now it's we're calling it Gus's
+theorem extended gauss's theorem to
+
+ align:start position:0%
+theorem extended gauss's theorem to
+ 
+
+ align:start position:0%
+theorem extended gauss's theorem to
+compute what this flux is so let's let's
+
+ align:start position:0%
+compute what this flux is so let's let's
+ 
+
+ align:start position:0%
+compute what this flux is so let's let's
+think about how we could do that so
+
+ align:start position:0%
+think about how we could do that so
+ 
+
+ align:start position:0%
+think about how we could do that so
+remember what extended Gus's theorem
+
+ align:start position:0%
+remember what extended Gus's theorem
+ 
+
+ align:start position:0%
+remember what extended Gus's theorem
+says or extended Divergence Theorem it's
+
+ align:start position:0%
+says or extended Divergence Theorem it's
+ 
+
+ align:start position:0%
+says or extended Divergence Theorem it's
+I'm I'm just going to I'm going to try
+
+ align:start position:0%
+I'm I'm just going to I'm going to try
+ 
+
+ align:start position:0%
+I'm I'm just going to I'm going to try
+and just say gauss's theorem from now on
+
+ align:start position:0%
+and just say gauss's theorem from now on
+ 
+
+ align:start position:0%
+and just say gauss's theorem from now on
+so I stop having to say both but I mean
+
+ align:start position:0%
+so I stop having to say both but I mean
+ 
+
+ align:start position:0%
+so I stop having to say both but I mean
+both I mean they're the same theorem
+
+ align:start position:0%
+both I mean they're the same theorem
+ 
+
+ align:start position:0%
+both I mean they're the same theorem
+right okay so so extended Gus's theorem
+
+ align:start position:0%
+right okay so so extended Gus's theorem
+ 
+
+ align:start position:0%
+right okay so so extended Gus's theorem
+what that says so so Gus's theorem says
+
+ align:start position:0%
+what that says so so Gus's theorem says
+ 
+
+ align:start position:0%
+what that says so so Gus's theorem says
+when you have a when you have a surface
+
+ align:start position:0%
+when you have a when you have a surface
+ 
+
+ align:start position:0%
+when you have a when you have a surface
+bounding a region the flux through the
+
+ align:start position:0%
+bounding a region the flux through the
+ 
+
+ align:start position:0%
+bounding a region the flux through the
+surface is equal to the triple integral
+
+ align:start position:0%
+surface is equal to the triple integral
+ 
+
+ align:start position:0%
+surface is equal to the triple integral
+of Divergence over the region provided
+
+ align:start position:0%
+of Divergence over the region provided
+ 
+
+ align:start position:0%
+of Divergence over the region provided
+everything is well defined and nice um
+
+ align:start position:0%
+everything is well defined and nice um
+ 
+
+ align:start position:0%
+everything is well defined and nice um
+Extended gauss's theorem says this is
+
+ align:start position:0%
+Extended gauss's theorem says this is
+ 
+
+ align:start position:0%
+Extended gauss's theorem says this is
+still true if your if your region has
+
+ align:start position:0%
+still true if your if your region has
+ 
+
+ align:start position:0%
+still true if your if your region has
+more than one boundary so for example if
+
+ align:start position:0%
+more than one boundary so for example if
+ 
+
+ align:start position:0%
+more than one boundary so for example if
+your region is is a is a hollow
+
+ align:start position:0%
+your region is is a is a hollow
+ 
+
+ align:start position:0%
+your region is is a is a hollow
+something so if it you know it's a
+
+ align:start position:0%
+something so if it you know it's a
+ 
+
+ align:start position:0%
+something so if it you know it's a
+spherical shell that has an outside
+
+ align:start position:0%
+spherical shell that has an outside
+ 
+
+ align:start position:0%
+spherical shell that has an outside
+sphere and an inside sphere then then
+
+ align:start position:0%
+sphere and an inside sphere then then
+ 
+
+ align:start position:0%
+sphere and an inside sphere then then
+extended gauss's theorem says okay so
+
+ align:start position:0%
+extended gauss's theorem says okay so
+ 
+
+ align:start position:0%
+extended gauss's theorem says okay so
+you do the same thing you take the
+
+ align:start position:0%
+you do the same thing you take the
+ 
+
+ align:start position:0%
+you do the same thing you take the
+triple integral of the Divergence over
+
+ align:start position:0%
+triple integral of the Divergence over
+ 
+
+ align:start position:0%
+triple integral of the Divergence over
+the solid region and then you take the
+
+ align:start position:0%
+the solid region and then you take the
+ 
+
+ align:start position:0%
+the solid region and then you take the
+flux but you add up the flux over all of
+
+ align:start position:0%
+flux but you add up the flux over all of
+ 
+
+ align:start position:0%
+flux but you add up the flux over all of
+the boundary pieces so you add up the
+
+ align:start position:0%
+the boundary pieces so you add up the
+ 
+
+ align:start position:0%
+the boundary pieces so you add up the
+flux over the the outside boundary
+
+ align:start position:0%
+flux over the the outside boundary
+ 
+
+ align:start position:0%
+flux over the the outside boundary
+surface and also if there is one through
+
+ align:start position:0%
+surface and also if there is one through
+ 
+
+ align:start position:0%
+surface and also if there is one through
+any other boundary surfaces okay so
+
+ align:start position:0%
+any other boundary surfaces okay so
+ 
+
+ align:start position:0%
+any other boundary surfaces okay so
+that's and and those two things are
+
+ align:start position:0%
+that's and and those two things are
+ 
+
+ align:start position:0%
+that's and and those two things are
+equal the so the flux the total flux
+
+ align:start position:0%
+equal the so the flux the total flux
+ 
+
+ align:start position:0%
+equal the so the flux the total flux
+through all of the boundary surfaces is
+
+ align:start position:0%
+through all of the boundary surfaces is
+ 
+
+ align:start position:0%
+through all of the boundary surfaces is
+equal to the integral of Divergence over
+
+ align:start position:0%
+equal to the integral of Divergence over
+ 
+
+ align:start position:0%
+equal to the integral of Divergence over
+the whole region bounded by those
+
+ align:start position:0%
+the whole region bounded by those
+ 
+
+ align:start position:0%
+the whole region bounded by those
+surfaces all right so how are we going
+
+ align:start position:0%
+surfaces all right so how are we going
+ 
+
+ align:start position:0%
+surfaces all right so how are we going
+to use this so we're trying to compute
+
+ align:start position:0%
+to use this so we're trying to compute
+ 
+
+ align:start position:0%
+to use this so we're trying to compute
+the the surface the integral of we're
+
+ align:start position:0%
+the the surface the integral of we're
+ 
+
+ align:start position:0%
+the the surface the integral of we're
+trying to compute the flux through a
+
+ align:start position:0%
+trying to compute the flux through a
+ 
+
+ align:start position:0%
+trying to compute the flux through a
+Surface by
+
+ align:start position:0%
+Surface by
+ 
+
+ align:start position:0%
+Surface by
+okay but we don't want to compute a
+
+ align:start position:0%
+okay but we don't want to compute a
+ 
+
+ align:start position:0%
+okay but we don't want to compute a
+double integral if we could if we can
+
+ align:start position:0%
+double integral if we could if we can
+ 
+
+ align:start position:0%
+double integral if we could if we can
+avoid it we don't want to compute the
+
+ align:start position:0%
+avoid it we don't want to compute the
+ 
+
+ align:start position:0%
+avoid it we don't want to compute the
+surface integral um so what we'd like to
+
+ align:start position:0%
+surface integral um so what we'd like to
+ 
+
+ align:start position:0%
+surface integral um so what we'd like to
+do is we'd like to find a convenient
+
+ align:start position:0%
+do is we'd like to find a convenient
+ 
+
+ align:start position:0%
+do is we'd like to find a convenient
+region over which to compute this this
+
+ align:start position:0%
+region over which to compute this this
+ 
+
+ align:start position:0%
+region over which to compute this this
+uh this integral to put us in a
+
+ align:start position:0%
+uh this integral to put us in a
+ 
+
+ align:start position:0%
+uh this integral to put us in a
+situation where we can apply extended
+
+ align:start position:0%
+situation where we can apply extended
+ 
+
+ align:start position:0%
+situation where we can apply extended
+gases theorem so we can't use just the
+
+ align:start position:0%
+gases theorem so we can't use just the
+ 
+
+ align:start position:0%
+gases theorem so we can't use just the
+inside of the cube so we want some other
+
+ align:start position:0%
+inside of the cube so we want some other
+ 
+
+ align:start position:0%
+inside of the cube so we want some other
+region so what we're going to do is
+
+ align:start position:0%
+region so what we're going to do is
+ 
+
+ align:start position:0%
+region so what we're going to do is
+we're going to walk over here and we're
+
+ align:start position:0%
+we're going to walk over here and we're
+ 
+
+ align:start position:0%
+we're going to walk over here and we're
+going to do one well I mean there are
+
+ align:start position:0%
+going to do one well I mean there are
+ 
+
+ align:start position:0%
+going to do one well I mean there are
+many possible things you could do but
+
+ align:start position:0%
+many possible things you could do but
+ 
+
+ align:start position:0%
+many possible things you could do but
+this is a nice one all right one thing
+
+ align:start position:0%
+this is a nice one all right one thing
+ 
+
+ align:start position:0%
+this is a nice one all right one thing
+you could do is you could take a big
+
+ align:start position:0%
+you could do is you could take a big
+ 
+
+ align:start position:0%
+you could do is you could take a big
+sphere take a big sphere so we've got
+
+ align:start position:0%
+sphere take a big sphere so we've got
+ 
+
+ align:start position:0%
+sphere take a big sphere so we've got
+our Cube here these you know this is the
+
+ align:start position:0%
+our Cube here these you know this is the
+ 
+
+ align:start position:0%
+our Cube here these you know this is the
+point 222 and this is the point 22 minus
+
+ align:start position:0%
+point 222 and this is the point 22 minus
+ 
+
+ align:start position:0%
+point 222 and this is the point 22 minus
+2 and so on um so we've taken a big
+
+ align:start position:0%
+2 and so on um so we've taken a big
+ 
+
+ align:start position:0%
+2 and so on um so we've taken a big
+sphere of radius R for some Big R um
+
+ align:start position:0%
+sphere of radius R for some Big R um
+ 
+
+ align:start position:0%
+sphere of radius R for some Big R um
+that contains this this uh our surface s
+
+ align:start position:0%
+that contains this this uh our surface s
+ 
+
+ align:start position:0%
+that contains this this uh our surface s
+that we're interested in that completely
+
+ align:start position:0%
+that we're interested in that completely
+ 
+
+ align:start position:0%
+that we're interested in that completely
+contains the cube okay so so why have we
+
+ align:start position:0%
+contains the cube okay so so why have we
+ 
+
+ align:start position:0%
+contains the cube okay so so why have we
+done that well extended gauss's theorem
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+says okay so what does extended Gus's
+
+ align:start position:0%
+says okay so what does extended Gus's
+ 
+
+ align:start position:0%
+says okay so what does extended Gus's
+theorem say for the region between the
+
+ align:start position:0%
+theorem say for the region between the
+ 
+
+ align:start position:0%
+theorem say for the region between the
+sphere and this Cube all right so so our
+
+ align:start position:0%
+sphere and this Cube all right so so our
+ 
+
+ align:start position:0%
+sphere and this Cube all right so so our
+our cube is named s let's call our
+
+ align:start position:0%
+our cube is named s let's call our
+ 
+
+ align:start position:0%
+our cube is named s let's call our
+sphere
+
+ align:start position:0%
+sphere
+ 
+
+ align:start position:0%
+sphere
+S2 because why not um okay and let's
+
+ align:start position:0%
+S2 because why not um okay and let's
+ 
+
+ align:start position:0%
+S2 because why not um okay and let's
+call the solid region between them
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+between the
+
+ align:start position:0%
+between the
+ 
+
+ align:start position:0%
+between the
+cube and sphere well we you know we just
+
+ align:start position:0%
+cube and sphere well we you know we just
+ 
+
+ align:start position:0%
+cube and sphere well we you know we just
+just for convenience let's give it a
+
+ align:start position:0%
+just for convenience let's give it a
+ 
+
+ align:start position:0%
+just for convenience let's give it a
+name so I don't know we often call solid
+
+ align:start position:0%
+name so I don't know we often call solid
+ 
+
+ align:start position:0%
+name so I don't know we often call solid
+regions D so let's call it D so that's
+
+ align:start position:0%
+regions D so let's call it D so that's
+ 
+
+ align:start position:0%
+regions D so let's call it D so that's
+this it's this spherical region but it
+
+ align:start position:0%
+this it's this spherical region but it
+ 
+
+ align:start position:0%
+this it's this spherical region but it
+has a cubical hole in the middle of it
+
+ align:start position:0%
+has a cubical hole in the middle of it
+ 
+
+ align:start position:0%
+has a cubical hole in the middle of it
+okay so what does extended gauss's
+
+ align:start position:0%
+okay so what does extended gauss's
+ 
+
+ align:start position:0%
+okay so what does extended gauss's
+theorem say so extended Gus's theorem
+
+ align:start position:0%
+theorem say so extended Gus's theorem
+ 
+
+ align:start position:0%
+theorem say so extended Gus's theorem
+says that the tripal triple
+
+ align:start position:0%
+says that the tripal triple
+ 
+
+ align:start position:0%
+says that the tripal triple
+integral over D of the Divergence of
+
+ align:start position:0%
+integral over D of the Divergence of
+ 
+
+ align:start position:0%
+integral over D of the Divergence of
+f
+
+ align:start position:0%
+f
+ 
+
+ align:start position:0%
+f
+DV is equal to it's equal to okay the
+
+ align:start position:0%
+DV is equal to it's equal to okay the
+ 
+
+ align:start position:0%
+DV is equal to it's equal to okay the
+sum of the fluxes through each of the
+
+ align:start position:0%
+sum of the fluxes through each of the
+ 
+
+ align:start position:0%
+sum of the fluxes through each of the
+surfaces but we for this we want the
+
+ align:start position:0%
+surfaces but we for this we want the
+ 
+
+ align:start position:0%
+surfaces but we for this we want the
+flux out of the solid region so what
+
+ align:start position:0%
+flux out of the solid region so what
+ 
+
+ align:start position:0%
+flux out of the solid region so what
+that means is so for the sphere the flux
+
+ align:start position:0%
+that means is so for the sphere the flux
+ 
+
+ align:start position:0%
+that means is so for the sphere the flux
+out of the inside of of the sphere is
+
+ align:start position:0%
+out of the inside of of the sphere is
+ 
+
+ align:start position:0%
+out of the inside of of the sphere is
+the flux out of the sphere so
+
+ align:start position:0%
+the flux out of the sphere so
+ 
+
+ align:start position:0%
+the flux out of the sphere so
+that's integral over
+
+ align:start position:0%
+that's integral over
+ 
+
+ align:start position:0%
+that's integral over
+S2 of
+
+ align:start position:0%
+S2 of
+ 
+
+ align:start position:0%
+S2 of
+f do
+
+ align:start position:0%
+f do
+ 
+
+ align:start position:0%
+f do
+n d surface area but for the cube the
+
+ align:start position:0%
+n d surface area but for the cube the
+ 
+
+ align:start position:0%
+n d surface area but for the cube the
+flux out of this region is the flux into
+
+ align:start position:0%
+flux out of this region is the flux into
+ 
+
+ align:start position:0%
+flux out of this region is the flux into
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+cube right you're out here you're living
+
+ align:start position:0%
+cube right you're out here you're living
+ 
+
+ align:start position:0%
+cube right you're out here you're living
+in a region outside the cube so when you
+
+ align:start position:0%
+in a region outside the cube so when you
+ 
+
+ align:start position:0%
+in a region outside the cube so when you
+leave that region you're going into the
+
+ align:start position:0%
+leave that region you're going into the
+ 
+
+ align:start position:0%
+leave that region you're going into the
+cube so this is the negative of the flux
+
+ align:start position:0%
+cube so this is the negative of the flux
+ 
+
+ align:start position:0%
+cube so this is the negative of the flux
+that we really want so this is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+minus the flux through the cube of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+FN with respect to surface area so
+
+ align:start position:0%
+FN with respect to surface area so
+ 
+
+ align:start position:0%
+FN with respect to surface area so
+remember the signs here are different
+
+ align:start position:0%
+remember the signs here are different
+ 
+
+ align:start position:0%
+remember the signs here are different
+because what I'm take I'm taking this
+
+ align:start position:0%
+because what I'm take I'm taking this
+ 
+
+ align:start position:0%
+because what I'm take I'm taking this
+normal to be the outward pointing normal
+
+ align:start position:0%
+normal to be the outward pointing normal
+ 
+
+ align:start position:0%
+normal to be the outward pointing normal
+to both surfaces the normal that points
+
+ align:start position:0%
+to both surfaces the normal that points
+ 
+
+ align:start position:0%
+to both surfaces the normal that points
+away from the origin but the normal
+
+ align:start position:0%
+away from the origin but the normal
+ 
+
+ align:start position:0%
+away from the origin but the normal
+pointing away from the
+
+ align:start position:0%
+pointing away from the
+ 
+
+ align:start position:0%
+pointing away from the
+origin at on the cube is the normal that
+
+ align:start position:0%
+origin at on the cube is the normal that
+ 
+
+ align:start position:0%
+origin at on the cube is the normal that
+points into the solid region instead of
+
+ align:start position:0%
+points into the solid region instead of
+ 
+
+ align:start position:0%
+points into the solid region instead of
+the normal that points out of the solid
+
+ align:start position:0%
+the normal that points out of the solid
+ 
+
+ align:start position:0%
+the normal that points out of the solid
+region so that's why this minus sign is
+
+ align:start position:0%
+region so that's why this minus sign is
+ 
+
+ align:start position:0%
+region so that's why this minus sign is
+here okay all right so what does this
+
+ align:start position:0%
+here okay all right so what does this
+ 
+
+ align:start position:0%
+here okay all right so what does this
+mean well we we've already computed in
+
+ align:start position:0%
+mean well we we've already computed in
+ 
+
+ align:start position:0%
+mean well we we've already computed in
+part A that the diver so first of all f
+
+ align:start position:0%
+part A that the diver so first of all f
+ 
+
+ align:start position:0%
+part A that the diver so first of all f
+is well defined everywhere in this
+
+ align:start position:0%
+is well defined everywhere in this
+ 
+
+ align:start position:0%
+is well defined everywhere in this
+region D the only place F was badly
+
+ align:start position:0%
+region D the only place F was badly
+ 
+
+ align:start position:0%
+region D the only place F was badly
+behaved was the origin and this region
+
+ align:start position:0%
+behaved was the origin and this region
+ 
+
+ align:start position:0%
+behaved was the origin and this region
+doesn't contain it which is why this
+
+ align:start position:0%
+doesn't contain it which is why this
+ 
+
+ align:start position:0%
+doesn't contain it which is why this
+trick works so we already computed that
+
+ align:start position:0%
+trick works so we already computed that
+ 
+
+ align:start position:0%
+trick works so we already computed that
+the Divergence of f is zero everywhere
+
+ align:start position:0%
+the Divergence of f is zero everywhere
+ 
+
+ align:start position:0%
+the Divergence of f is zero everywhere
+it's defined so it's zero on all of D
+
+ align:start position:0%
+it's defined so it's zero on all of D
+ 
+
+ align:start position:0%
+it's defined so it's zero on all of D
+and so this triple integral is just zero
+
+ align:start position:0%
+and so this triple integral is just zero
+ 
+
+ align:start position:0%
+and so this triple integral is just zero
+so if this triple integral is zero that
+
+ align:start position:0%
+so if this triple integral is zero that
+ 
+
+ align:start position:0%
+so if this triple integral is zero that
+means we can just add um this other or
+
+ align:start position:0%
+means we can just add um this other or
+ 
+
+ align:start position:0%
+means we can just add um this other or
+the thing that we're interested in to
+
+ align:start position:0%
+the thing that we're interested in to
+ 
+
+ align:start position:0%
+the thing that we're interested in to
+both sides and we get
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that the surface integral over the cube
+
+ align:start position:0%
+that the surface integral over the cube
+ 
+
+ align:start position:0%
+that the surface integral over the cube
+of f.n with respect to surface area is
+
+ align:start position:0%
+of f.n with respect to surface area is
+ 
+
+ align:start position:0%
+of f.n with respect to surface area is
+equal to the surface integral over the
+
+ align:start position:0%
+equal to the surface integral over the
+ 
+
+ align:start position:0%
+equal to the surface integral over the
+sphere of
+
+ align:start position:0%
+sphere of
+ 
+
+ align:start position:0%
+sphere of
+f.n with respect to surface area okay so
+
+ align:start position:0%
+f.n with respect to surface area okay so
+ 
+
+ align:start position:0%
+f.n with respect to surface area okay so
+all right so we've we've
+
+ align:start position:0%
+all right so we've we've
+ 
+
+ align:start position:0%
+all right so we've we've
+converted this uh our original integral
+
+ align:start position:0%
+converted this uh our original integral
+ 
+
+ align:start position:0%
+converted this uh our original integral
+our flux integral that we're interested
+
+ align:start position:0%
+our flux integral that we're interested
+ 
+
+ align:start position:0%
+our flux integral that we're interested
+in and we've found that it's equal to
+
+ align:start position:0%
+in and we've found that it's equal to
+ 
+
+ align:start position:0%
+in and we've found that it's equal to
+this separate uh flux integral over a
+
+ align:start position:0%
+this separate uh flux integral over a
+ 
+
+ align:start position:0%
+this separate uh flux integral over a
+different surface this time over a big
+
+ align:start position:0%
+different surface this time over a big
+ 
+
+ align:start position:0%
+different surface this time over a big
+sphere okay so that's that's nice um why
+
+ align:start position:0%
+sphere okay so that's that's nice um why
+ 
+
+ align:start position:0%
+sphere okay so that's that's nice um why
+do we want to do that well we want to do
+
+ align:start position:0%
+do we want to do that well we want to do
+ 
+
+ align:start position:0%
+do we want to do that well we want to do
+that because f is a really nicely
+
+ align:start position:0%
+that because f is a really nicely
+ 
+
+ align:start position:0%
+that because f is a really nicely
+behaved field with respect to a sphere f
+
+ align:start position:0%
+behaved field with respect to a sphere f
+ 
+
+ align:start position:0%
+behaved field with respect to a sphere f
+is a radial field so F do
+
+ align:start position:0%
+is a radial field so F do
+ 
+
+ align:start position:0%
+is a radial field so F do
+n is really easy to understand
+
+ align:start position:0%
+n is really easy to understand
+ 
+
+ align:start position:0%
+n is really easy to understand
+FN is just well N is a unit normal and F
+
+ align:start position:0%
+FN is just well N is a unit normal and F
+ 
+
+ align:start position:0%
+FN is just well N is a unit normal and F
+is a radial field so on a sphere the the
+
+ align:start position:0%
+is a radial field so on a sphere the the
+ 
+
+ align:start position:0%
+is a radial field so on a sphere the the
+normal is radial right it it's it's
+
+ align:start position:0%
+normal is radial right it it's it's
+ 
+
+ align:start position:0%
+normal is radial right it it's it's
+parallel to the position vector and F is
+
+ align:start position:0%
+parallel to the position vector and F is
+ 
+
+ align:start position:0%
+parallel to the position vector and F is
+radial so they're both pointing in
+
+ align:start position:0%
+radial so they're both pointing in
+ 
+
+ align:start position:0%
+radial so they're both pointing in
+exactly the same direction so when you
+
+ align:start position:0%
+exactly the same direction so when you
+ 
+
+ align:start position:0%
+exactly the same direction so when you
+take that dot product n is the unit
+
+ align:start position:0%
+take that dot product n is the unit
+ 
+
+ align:start position:0%
+take that dot product n is the unit
+Vector in the same direction as F so
+
+ align:start position:0%
+Vector in the same direction as F so
+ 
+
+ align:start position:0%
+Vector in the same direction as F so
+when you dot that with f you just get
+
+ align:start position:0%
+when you dot that with f you just get
+ 
+
+ align:start position:0%
+when you dot that with f you just get
+the length of f okay so so what does
+
+ align:start position:0%
+the length of f okay so so what does
+ 
+
+ align:start position:0%
+the length of f okay so so what does
+that mean that means over
+
+ align:start position:0%
+that mean that means over
+ 
+
+ align:start position:0%
+that mean that means over
+here this integrand is really easy to
+
+ align:start position:0%
+here this integrand is really easy to
+ 
+
+ align:start position:0%
+here this integrand is really easy to
+understand okay this
+
+ align:start position:0%
+understand okay this
+ 
+
+ align:start position:0%
+understand okay this
+integrand f.n on the sphere is just
+
+ align:start position:0%
+integrand f.n on the sphere is just
+ 
+
+ align:start position:0%
+integrand f.n on the sphere is just
+equal to the
+
+ align:start position:0%
+equal to the
+ 
+
+ align:start position:0%
+equal to the
+length of the vector F now what is the
+
+ align:start position:0%
+length of the vector F now what is the
+ 
+
+ align:start position:0%
+length of the vector F now what is the
+length of the vector F well we know what
+
+ align:start position:0%
+length of the vector F well we know what
+ 
+
+ align:start position:0%
+length of the vector F well we know what
+f is it's X over row cubed I hat plus y
+
+ align:start position:0%
+f is it's X over row cubed I hat plus y
+ 
+
+ align:start position:0%
+f is it's X over row cubed I hat plus y
+over row cubed J hat plus Z over row
+
+ align:start position:0%
+over row cubed J hat plus Z over row
+ 
+
+ align:start position:0%
+over row cubed J hat plus Z over row
+cubed K hat so okay so you compute the
+
+ align:start position:0%
+cubed K hat so okay so you compute the
+ 
+
+ align:start position:0%
+cubed K hat so okay so you compute the
+length of that vector and what do you
+
+ align:start position:0%
+length of that vector and what do you
+ 
+
+ align:start position:0%
+length of that vector and what do you
+get well it's exactly 1 over row squared
+
+ align:start position:0%
+get well it's exactly 1 over row squared
+ 
+
+ align:start position:0%
+get well it's exactly 1 over row squared
+okay and but we said that this is a
+
+ align:start position:0%
+okay and but we said that this is a
+ 
+
+ align:start position:0%
+okay and but we said that this is a
+sphere I guess I didn't write it down so
+
+ align:start position:0%
+sphere I guess I didn't write it down so
+ 
+
+ align:start position:0%
+sphere I guess I didn't write it down so
+this is a sphere let me write it down
+
+ align:start position:0%
+this is a sphere let me write it down
+ 
+
+ align:start position:0%
+this is a sphere let me write it down
+right here this is a sphere whose radius
+
+ align:start position:0%
+right here this is a sphere whose radius
+ 
+
+ align:start position:0%
+right here this is a sphere whose radius
+is Big R it doesn't really matter very
+
+ align:start position:0%
+is Big R it doesn't really matter very
+ 
+
+ align:start position:0%
+is Big R it doesn't really matter very
+much what what R we choose we just want
+
+ align:start position:0%
+much what what R we choose we just want
+ 
+
+ align:start position:0%
+much what what R we choose we just want
+it to be big enough so that it contains
+
+ align:start position:0%
+it to be big enough so that it contains
+ 
+
+ align:start position:0%
+it to be big enough so that it contains
+the whole Cube if you said this is a
+
+ align:start position:0%
+the whole Cube if you said this is a
+ 
+
+ align:start position:0%
+the whole Cube if you said this is a
+sphere of radius 10 that would
+
+ align:start position:0%
+sphere of radius 10 that would
+ 
+
+ align:start position:0%
+sphere of radius 10 that would
+completely do the trick that would be
+
+ align:start position:0%
+completely do the trick that would be
+ 
+
+ align:start position:0%
+completely do the trick that would be
+totally fine
+
+ align:start position:0%
+totally fine
+ 
+
+ align:start position:0%
+totally fine
+okay so the radius of the sphere is Big
+
+ align:start position:0%
+okay so the radius of the sphere is Big
+ 
+
+ align:start position:0%
+okay so the radius of the sphere is Big
+R so the length of the field we said
+
+ align:start position:0%
+R so the length of the field we said
+ 
+
+ align:start position:0%
+R so the length of the field we said
+back over here is 1
+
+ align:start position:0%
+back over here is 1
+ 
+
+ align:start position:0%
+back over here is 1
+over R 2 the the length of the vector
+
+ align:start position:0%
+over R 2 the the length of the vector
+ 
+
+ align:start position:0%
+over R 2 the the length of the vector
+F so this integral this this flux
+
+ align:start position:0%
+F so this integral this this flux
+ 
+
+ align:start position:0%
+F so this integral this this flux
+integral then is the integral over the
+
+ align:start position:0%
+integral then is the integral over the
+ 
+
+ align:start position:0%
+integral then is the integral over the
+sphere S2 of a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+constant so it's the integral over the
+
+ align:start position:0%
+constant so it's the integral over the
+ 
+
+ align:start position:0%
+constant so it's the integral over the
+sphere of 1/ R 2 DS
+
+ align:start position:0%
+sphere of 1/ R 2 DS
+ 
+
+ align:start position:0%
+sphere of 1/ R 2 DS
+but when you integrate a constant over a
+
+ align:start position:0%
+but when you integrate a constant over a
+ 
+
+ align:start position:0%
+but when you integrate a constant over a
+surface what you get is just that
+
+ align:start position:0%
+surface what you get is just that
+ 
+
+ align:start position:0%
+surface what you get is just that
+constant times the surface area well
+
+ align:start position:0%
+constant times the surface area well
+ 
+
+ align:start position:0%
+constant times the surface area well
+what's the surface area this is a sphere
+
+ align:start position:0%
+what's the surface area this is a sphere
+ 
+
+ align:start position:0%
+what's the surface area this is a sphere
+it's easy to understand its surface area
+
+ align:start position:0%
+it's easy to understand its surface area
+ 
+
+ align:start position:0%
+it's easy to understand its surface area
+its surface area is
+
+ align:start position:0%
+its surface area is
+ 
+
+ align:start position:0%
+its surface area is
+4 piir 2 right so this is equal to the
+
+ align:start position:0%
+4 piir 2 right so this is equal to the
+ 
+
+ align:start position:0%
+4 piir 2 right so this is equal to the
+surface area so that's 4 pi r 2times
+
+ align:start position:0%
+surface area so that's 4 pi r 2times
+ 
+
+ align:start position:0%
+surface area so that's 4 pi r 2times
+whatever that constant was so the
+
+ align:start position:0%
+whatever that constant was so the
+ 
+
+ align:start position:0%
+whatever that constant was so the
+constant was 1 / R 2 and so the r squs
+
+ align:start position:0%
+constant was 1 / R 2 and so the r squs
+ 
+
+ align:start position:0%
+constant was 1 / R 2 and so the r squs
+cancel right this is why it didn't
+
+ align:start position:0%
+cancel right this is why it didn't
+ 
+
+ align:start position:0%
+cancel right this is why it didn't
+matter what R we chose because it's just
+
+ align:start position:0%
+matter what R we chose because it's just
+ 
+
+ align:start position:0%
+matter what R we chose because it's just
+going to cancel at the end
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+anyhow okay so those cancel and we're
+
+ align:start position:0%
+anyhow okay so those cancel and we're
+ 
+
+ align:start position:0%
+anyhow okay so those cancel and we're
+left with 4 Pi so let's let's just
+
+ align:start position:0%
+left with 4 Pi so let's let's just
+ 
+
+ align:start position:0%
+left with 4 Pi so let's let's just
+quickly recap what we did in this part
+
+ align:start position:0%
+quickly recap what we did in this part
+ 
+
+ align:start position:0%
+quickly recap what we did in this part
+C we're looking to compute the flux over
+
+ align:start position:0%
+C we're looking to compute the flux over
+ 
+
+ align:start position:0%
+C we're looking to compute the flux over
+the cube but it's a kind of unpleasant
+
+ align:start position:0%
+the cube but it's a kind of unpleasant
+ 
+
+ align:start position:0%
+the cube but it's a kind of unpleasant
+integral we'd have to compute to to
+
+ align:start position:0%
+integral we'd have to compute to to
+ 
+
+ align:start position:0%
+integral we'd have to compute to to
+total up the fluxes over these various
+
+ align:start position:0%
+total up the fluxes over these various
+ 
+
+ align:start position:0%
+total up the fluxes over these various
+different faces and so on so instead we
+
+ align:start position:0%
+different faces and so on so instead we
+ 
+
+ align:start position:0%
+different faces and so on so instead we
+had this clever idea that will apply the
+
+ align:start position:0%
+had this clever idea that will apply the
+ 
+
+ align:start position:0%
+had this clever idea that will apply the
+Divergence Theorem to replace the cube
+
+ align:start position:0%
+Divergence Theorem to replace the cube
+ 
+
+ align:start position:0%
+Divergence Theorem to replace the cube
+with a more congenial surface so the
+
+ align:start position:0%
+with a more congenial surface so the
+ 
+
+ align:start position:0%
+with a more congenial surface so the
+surface we choose because this is a nice
+
+ align:start position:0%
+surface we choose because this is a nice
+ 
+
+ align:start position:0%
+surface we choose because this is a nice
+radial Vector fi field that's our main
+
+ align:start position:0%
+radial Vector fi field that's our main
+ 
+
+ align:start position:0%
+radial Vector fi field that's our main
+hint because there was you know a row
+
+ align:start position:0%
+hint because there was you know a row
+ 
+
+ align:start position:0%
+hint because there was you know a row
+involved in the problem if you will um
+
+ align:start position:0%
+involved in the problem if you will um
+ 
+
+ align:start position:0%
+involved in the problem if you will um
+so our this the surface that we choose
+
+ align:start position:0%
+so our this the surface that we choose
+ 
+
+ align:start position:0%
+so our this the surface that we choose
+is some big sphere and then we apply the
+
+ align:start position:0%
+is some big sphere and then we apply the
+ 
+
+ align:start position:0%
+is some big sphere and then we apply the
+the extended gausses theorem to the
+
+ align:start position:0%
+the extended gausses theorem to the
+ 
+
+ align:start position:0%
+the extended gausses theorem to the
+solid region between the cube and the
+
+ align:start position:0%
+solid region between the cube and the
+ 
+
+ align:start position:0%
+solid region between the cube and the
+sphere outside the cube but inside the
+
+ align:start position:0%
+sphere outside the cube but inside the
+ 
+
+ align:start position:0%
+sphere outside the cube but inside the
+sphere so because the Divergence of the
+
+ align:start position:0%
+sphere so because the Divergence of the
+ 
+
+ align:start position:0%
+sphere so because the Divergence of the
+field is
+
+ align:start position:0%
+field is
+ 
+
+ align:start position:0%
+field is
+zero the extended guses theorem tells us
+
+ align:start position:0%
+zero the extended guses theorem tells us
+ 
+
+ align:start position:0%
+zero the extended guses theorem tells us
+that the two fluxes the flux over the
+
+ align:start position:0%
+that the two fluxes the flux over the
+ 
+
+ align:start position:0%
+that the two fluxes the flux over the
+cube the flux out of the cube and the
+
+ align:start position:0%
+cube the flux out of the cube and the
+ 
+
+ align:start position:0%
+cube the flux out of the cube and the
+flux out of the sphere actually equal to
+
+ align:start position:0%
+flux out of the sphere actually equal to
+ 
+
+ align:start position:0%
+flux out of the sphere actually equal to
+each other but since the fluxes are
+
+ align:start position:0%
+each other but since the fluxes are
+ 
+
+ align:start position:0%
+each other but since the fluxes are
+actually equal to each other that means
+
+ align:start position:0%
+actually equal to each other that means
+ 
+
+ align:start position:0%
+actually equal to each other that means
+we can just in order to compute the flux
+
+ align:start position:0%
+we can just in order to compute the flux
+ 
+
+ align:start position:0%
+we can just in order to compute the flux
+out of the cube it's enough to compute
+
+ align:start position:0%
+out of the cube it's enough to compute
+ 
+
+ align:start position:0%
+out of the cube it's enough to compute
+the flux out of the sphere okay but
+
+ align:start position:0%
+the flux out of the sphere okay but
+ 
+
+ align:start position:0%
+the flux out of the sphere okay but
+Computing the flux out of the sphere is
+
+ align:start position:0%
+Computing the flux out of the sphere is
+ 
+
+ align:start position:0%
+Computing the flux out of the sphere is
+relatively easy because on the sphere
+
+ align:start position:0%
+relatively easy because on the sphere
+ 
+
+ align:start position:0%
+relatively easy because on the sphere
+the Grand f.n is just
+
+ align:start position:0%
+the Grand f.n is just
+ 
+
+ align:start position:0%
+the Grand f.n is just
+constant and so then we're integrating a
+
+ align:start position:0%
+constant and so then we're integrating a
+ 
+
+ align:start position:0%
+constant and so then we're integrating a
+surface a constant over the surface of a
+
+ align:start position:0%
+surface a constant over the surface of a
+ 
+
+ align:start position:0%
+surface a constant over the surface of a
+sphere and that just gives us the
+
+ align:start position:0%
+sphere and that just gives us the
+ 
+
+ align:start position:0%
+sphere and that just gives us the
+surface area of the sphere times that
+
+ align:start position:0%
+surface area of the sphere times that
+ 
+
+ align:start position:0%
+surface area of the sphere times that
+constant which is 4 Pi r^ 2 * 1 r^ 2
+
+ align:start position:0%
+constant which is 4 Pi r^ 2 * 1 r^ 2
+ 
+
+ align:start position:0%
+constant which is 4 Pi r^ 2 * 1 r^ 2
+which is 4 Pi so the flux out of the
+
+ align:start position:0%
+which is 4 Pi so the flux out of the
+ 
+
+ align:start position:0%
+which is 4 Pi so the flux out of the
+cube then is also equal to 4
+
+ align:start position:0%
+cube then is also equal to 4
+ 
+
+ align:start position:0%
+cube then is also equal to 4
+Pi I'll stop there
\ No newline at end of file
diff --git a/X3_SfVMyE3k.txt b/X3_SfVMyE3k.txt
new file mode 100644
index 0000000000000000000000000000000000000000..3cf216afc33d897d5ae353228037c1e8cde24fad
--- /dev/null
+++ b/X3_SfVMyE3k.txt
@@ -0,0 +1,3209 @@
+The following content is
+provided under a Creative
+
+Commons license.
+
+Your support will help MIT
+OpenCourseWare continue to
+
+offer high quality educational
+resources for free.
+
+To make a donation or view
+additional materials from
+
+hundreds of MIT courses, visit
+MIT OpenCourseWare at
+
+ocw.mit.edu.
+
+PROFESSOR: I guess [OBSCURED]
+
+Let's get going.
+
+OK, should I introduce you?
+
+BRADLEY KUSZMAUL: If you want.
+
+I can introduce myself.
+
+PROFESSOR: We have Bradley
+Kuszmaul who's been doing
+
+articles on Cilk?
+
+He's a very interesting
+paralleling and also what you
+
+can say about the program It's
+a very interesting project
+
+that coming for a while, and
+there's a lot of interesting
+
+things he's developed,
+and multi core
+
+becoming very important.
+
+BRADLEY KUSZMAUL: So how
+many of you people have
+
+ever heard of Cilk?
+
+Have used it?
+
+So those of you who have
+used it may find
+
+this talk old or whatever.
+
+So Cilk is a system that
+runs on a shared-memory
+
+multiprocessor.
+
+So this is not like the system
+you've been programming for
+
+this class.
+
+This kind of machine you have
+processors, which each have
+
+cache and some sort of a network
+and a bunch of memory
+
+and when the processors do
+memory operations they are all
+
+on the same address space
+and it's typically--
+
+the memory system provides some
+sort of coherence like
+
+strong consistency or maybe
+released consistency.
+
+We're interested in the case
+where the distance from
+
+processors to other processors
+into a processors to memory
+
+may be nonuniform and so it's
+important to use the cache
+
+well in this kind of machine
+because you can't
+
+just ignore the cache.
+
+So sort of the technology that
+I'm going to talk about for
+
+this kind of system
+is called Cilk.
+
+Cilk is a C language and it does
+dynamic multithreading
+
+and it has a provably
+good runtime system.
+
+So I'll talk about what
+those all mean.
+
+Cilk runs on shared-memory
+machines like Suns and SGIs
+
+and well, you probably can't
+find Alphaservers anymore.
+
+It runs on SMPs like that are
+in everybody's laptops now.
+
+There's been several interesting
+applications
+
+written in Cilk including virus
+shell assembly, graphics
+
+rendering, n-body simulation.
+
+We did a bunch of chess programs
+because they were
+
+sort of the raison
+d'etre for Cilk.
+
+One of the features about Cilk
+is that it automatically
+
+manages a lot of the
+low-level issues.
+
+You don't have to do load
+balancing, you don't have to
+
+write in protocols.
+
+You basically write programs
+that look a lot more like the
+
+ordinary Cilk programs instead
+of saying first I'm going to
+
+do this and then I'm going to
+set this variable and then
+
+somebody else is going to read
+that variable and that's a
+
+protocol and those are very
+difficult to get right.
+
+AUDIENCE: [OBSCURED]
+
+BRADLEY KUSZMAUL: Yeah,
+I'll mention that
+
+a little bit later.
+
+We had award-winning
+chess player.
+
+So to explain what Cilk's about
+
+I'll talk about Fibonacci.
+
+Now Fibonacci, this is just to
+review in case you don't know
+
+C. You all know C right?
+
+So Fibonacci is the function
+that each number is the sum of
+
+the previous two Fibonacci
+numbers.
+
+And this is an implementation
+that basically does that
+
+computation directly.
+
+The Fibonacci of n if n is
+less than 2, it's just n.
+
+So Fibonacci of zero
+is zero, 1 is 1.
+
+2, the Fibonacci's--
+
+well, then you have to do the
+recursion, so you compute
+
+Fibonacci of n minus 1 and
+Fibonacci of n minus 2 and sum
+
+them together and that's
+Fibonacci of n.
+
+One observation about this
+function is it's a really slow
+
+implementation of Fibonacci.
+
+You all know how to
+do this faster?
+
+How fast can you do Fibonacci?
+
+You all know this, How
+fast is this one?
+
+AUDIENCE: [OBSCURED].
+
+BRADLEY KUSZMAUL: So for those
+of you who don't know--
+
+certainly know how to compute
+Fibonacci in linear time just
+
+by keeping track of the
+most recent two.
+
+1, 1, 2, 3, 5, you just do it.
+
+This is exponential time and
+there's an algorithm that does
+
+it in logarithmic time.
+
+So this implementation is
+doubly, exponentially bad.
+
+But it's good as a didactic
+example because it's easy to
+
+understand.
+
+So to turn this into Cilk we
+just add some key words and
+
+I'll talk about what the key
+words are in a minute, but the
+
+key thing to understand about
+this is if you delete the key
+
+words you have a C program and
+Cilk programs have the
+
+property that one of the legal
+semantics for the Cilk program
+
+is the C program that you get
+by deleting the key words.
+
+Now there's other possible
+semantics
+
+you could get because--
+
+not for this function, this
+function always produces the
+
+same answer because there's
+no race conditions in it.
+
+But for programs that have
+races you may have other
+
+semantics that the system
+could provide.
+
+And so this kind of a language
+extension where you can sort
+
+of delete the extensions and get
+a correct implementation
+
+of the parallel program is
+called a faithful extension.
+
+A lot of languages like OpenMP
+have properties that if you
+
+had these directives and if
+you delete them, it will
+
+change the semantics of your
+program and so you have to be
+
+very careful.
+
+Now if you're careful about
+programming OpenMP you can
+
+make it so that it's faithful,
+that has this property.
+
+But that's not always
+the case that it is.
+
+Sure.
+
+AUDIENCE: Is it built
+on the different..
+
+BRADLEY KUSZMAUL: C 77.
+
+No, C 89.
+
+AUDIENCE: OK, so there's
+no presumption
+
+or any alias involved?
+
+It's assumed that
+the [OBSCURED].
+
+BRADLEY KUSZMAUL: So the
+issue of restricted
+
+pointers, for example?
+
+AUDIENCE: Restricted pointers.
+
+BRADLEY KUSZMAUL: So Cilk
+turns out to work
+
+with C 99 as well.
+
+AUDIENCE: But is the presumption
+though for a
+
+pointer that it could alias?
+
+BRADLEY KUSZMAUL: The Cilk
+compiler makes no assumptions
+
+about that.
+
+If you write a program
+and the back end--
+
+Cilk works and I'll talk about
+this in a couple minutes.
+
+Cilk works by transforming
+this into a C
+
+program that has--
+
+when you run it on one processor
+it's just the
+
+original C program in effect.
+
+And so if you have a dialect
+of C that has restricted
+
+pointers and a compiler that--
+
+PROFESSOR: You're taking
+the assumptions that
+
+if you make a mistake--
+
+BRADLEY KUSZMAUL: If you make a
+mistake the language doens't
+
+stop you from making
+the mistake.
+
+AUDIENCE: Well, but in C 89
+there's not a mistake.
+
+There's no assumption about
+aliasing, right?
+
+It could alias.
+
+So if I said --
+
+BRADLEY KUSZMAUL: Because of
+the aliasing you write a
+
+program that has a race
+condition in it, which is
+
+erroneous--
+
+AUDIENCE: It would be valid?
+
+BRADLEY KUSZMAUL: No,
+it'd still be valid.
+
+It would just have a race in
+it and you would have a
+
+non-determinate result.
+
+PROFESSOR: It may not
+do what you want.
+
+BRADLEY KUSZMAUL: It may not do
+what you want, but one of
+
+the legal executions of that
+parallel program is the
+
+original C program.
+
+AUDIENCE: So there's no extra.
+
+BRADLEY KUSZMAUL: At the sort
+of level of doing analysis,
+
+Cilk doesn't do analysis.
+
+Cilk is a compiler that compiles
+this language and the
+
+semantics are what they are,
+which is you the spawn is
+
+its-- and I'll talk about
+the semantics.
+
+The spawn means you can run the
+function in parallel and
+
+if that doesn't give you the
+same answer every time it's
+
+not the compilers fault.
+
+AUDIENCE: [OBSCURED]
+
+BRADLEY KUSZMAUL: Pardon?
+
+AUDIENCE: There has to be some
+guarantee [OBSCURED].
+
+[OBSCURED]
+
+PROFESSOR: How in a race
+condition you get some
+
+[OBSCURED].
+
+BRADLEY KUSZMAUL: One of the
+legal things the Cilk system
+
+could do is just run this,
+run that program.
+
+Now if you're running it on
+multiple processors that's not
+
+what happens because the other
+thing is there's some
+
+performance guarantees we get.
+
+So there's actually
+parallelism.
+
+But on one processor in fact,
+that's exactly what the
+
+execution does.
+
+So Cilk does dynamic
+multithreading and this is
+
+different from p threads for
+example where you have this
+
+very heavyweight thread that
+costs tens of thousands of
+
+instructions to create.
+
+Cilk threads are really small,
+so in this program there's a
+
+Cilk thread that runs basically
+from when the fib
+
+starts to here and then--
+
+I feel like there's a missing
+slide in here.
+
+I didn't tell you about spawn.
+
+OK, well let me tell you about
+spawn because what the spawn
+
+means is that this function
+can run in parallel.
+
+That's very simple.
+
+What the sync means is that all
+the functions that were
+
+spawned off in this function all
+have to finish before this
+
+function can proceed.
+
+So in a normal execution of C,
+when you call a function the
+
+parent stops.
+
+In Cilk the parent can keep
+running, so while that's
+
+running the parent-- this can
+spawn off this and then the
+
+sync happens and now the
+parent has to stop.
+
+And this key word basically just
+says that this function
+
+can be spawned.
+
+AUDIENCE: Is the sync in that
+scope or the children scope?
+
+BRADLEY KUSZMAUL: The sync is
+scoped within the function.
+
+So you could have a 4 loop
+that spawned off a
+
+whole bunch of stuff.
+
+AUDIENCE: You could call the
+function instead of moving
+
+some spawns, but
+then [OBSCURED]
+
+in the sync.
+
+BRADLEY KUSZMAUL: There's an
+explicit sync at the end of
+
+every function.
+
+So Cilk functions are strict.
+
+PROFESSOR: [NOISE]
+
+BRADLEY KUSZMAUL: You know,
+there's children down inside
+
+here, but this function can't
+return-- well, if I had
+
+omitted the sync and down in
+some leaf the compiler puts
+
+one in before the function
+returns.
+
+There's some languages that are
+like this where somehow
+
+the intermediate function can go
+away and then you can sync
+
+directly with your
+grandparent.
+
+AUDIENCE: Otherwise
+it would stop.
+
+BRADLEY KUSZMAUL: So this gives
+you this dag, so you
+
+have this part of the program
+that runs up to the first
+
+spawn and then part of the
+program that runs between the
+
+spawns and the part of the
+program that runs after--
+
+well, after the last spawn to
+the sync and then from there
+
+to the return.
+
+So I've got this drawing
+that shows this
+
+function sort of running.
+
+So first the purple code runs
+at it gets to the spawn, it
+
+spawns of this guy, but now the
+second piece of code can
+
+start running.
+
+He does a spawn, so these two
+are running in parallel.
+
+Meanwhile.
+
+This guy started that pff.
+
+This is a base case, so he's
+going to not do anything.
+
+Just feels like there's
+something
+
+missing in this slide.
+
+Oh well.
+
+Essentially now this
+guy couldn't run
+
+going back to here.
+
+This part of the code couldn't
+run until after sync so this
+
+thing's sitting here waiting.
+
+So when these guys finally
+return then this can run.
+
+This guy's getting stuck here.
+
+He runs and he runs.
+
+These two return and the
+value comes up here.
+
+And now basically the
+function is done.
+
+One observation here is that
+there's no mention of the
+
+number of processors
+in this code.
+
+You haven't specified how
+to schedule or how many
+
+processors.
+
+All you've specified is this
+directed acyclic graph that
+
+unfolds dynamically and it's
+up to us to schedule those
+
+onto the processors.
+
+So this code is processor
+oblivious.
+
+It's oblivious to the number
+of processors.
+
+PROFESSOR: But because we're
+using the language we're
+
+probably have to create, write
+as many spawns depending on--
+
+BRADLEY KUSZMAUL: No, what you
+do is you write as many spawns
+
+as you can.
+
+You expose all the parallelism
+in your code.
+
+So you want this dag to have
+millions of threads in it
+
+concurrently.
+
+And then it's up to us to
+schedule that efficiently.
+
+So it's a different mindset
+then, I have 4 processors, let
+
+me create 4 things to do.
+
+I have 4 processors, let me
+create a million things to do.
+
+And then the Cilk scheduler
+guarantees to give you-- you
+
+have 4 processors, I'll give
+you 4 fold speed up.
+
+PROFESSOR: I guess what you'd
+like to avoid is the mindset
+
+of the programmer has to change
+or find the changing
+
+tuning the parameters
+for the performance.
+
+BRADLEY KUSZMAUL: There's some
+tuning that you do in order to
+
+make the leaf code.
+
+There's some overhead for
+doing function calls.
+
+So it's small overhead.
+
+It turns out the cost
+of the spawn is like
+
+three function calls.
+
+If you were actually trying to
+make this code run faster you
+
+make the base case bigger and do
+something, trying to speed
+
+things up a little bit with
+the leaves of this call.
+
+So there's this call tree
+and inside the call
+
+tree is this dag.
+
+So it supports C's rule
+for pointers.
+
+For whatever dialect you have.
+If you have a pointer to a
+
+stack and then you have a
+pointer to the stack and then
+
+you call, you're allowed to use
+that pointer in C. So in
+
+Cilk you are as well.
+
+If you have a parallel thing
+going on where normally in C
+
+you would call A, then B
+returns, then C and D. So C
+
+and D can refer to anything on
+A, but C can't legally refer
+
+to something on B and the same
+rule applies to Cilk.
+
+So we have a data structure that
+implements this cactus
+
+stack is what it's called, after
+the sugauro cactus--
+
+the view of the imagery
+there and it lets you
+
+support that rule.
+
+There's some advanced features
+in Cilk that have to do with
+
+speculative execution and I'm
+going to skip over those today
+
+because it turns out that sort
+of 99% of the time you don't
+
+need this stuff.
+
+We have some debugger support,
+so if you've written code that
+
+relied on some semantics that
+maybe you didn't like when you
+
+went to the parallel world,
+you'd like to find out.
+
+This is a tool that basically
+takes a Cilk program and an
+
+input data set and it runs and
+it tells you is there any
+
+schedule that I could have
+chosen-- so it's that directed
+
+acyclic graph.
+
+So there's a whole bunch of
+possible schedules I could
+
+have chosen.
+
+Is there any schedule that
+changes the order of two
+
+concurrent memory operations
+where one of them is right?
+
+So we call this the
+non-determinator because it
+
+finds all the determinacy
+races in your program.
+
+And Cilk guarantees-- the Cilk
+race detector is guaranteed to
+
+find those.
+
+There's a lot of race detectors
+where if the race
+
+doesn't actually occur you
+have two things that are
+
+logically in parallel, but if
+they don't actually run on
+
+different processors a lot of
+race detectors out there in
+
+the world won't report
+the race.
+
+So you get false negatives and
+there's a bunch of false
+
+positives that show up.
+
+This basically only gives
+you the real ones.
+
+AUDIENCE: That might be
+indicatiors there might be
+
+still a data to arrays.
+
+BRADLEY KUSZMAUL: So this
+doesn't analyze the program.
+
+It analyzes the execution.
+
+So it's not trying to solve some
+MP complete problem or
+
+Turing complete problem.
+
+And so this reduces the problem
+of finding data races
+
+to the situation that's just
+like when you're trying to do
+
+code release and quality control
+for serial programs.
+
+You write tests.
+
+If you don't test your program
+you don't know what it does
+
+and that's the same
+property here.
+
+If you do find some race someday
+later then you can
+
+write a test for it and know
+that you're testing to make
+
+sure that race didn't creep
+back into your code.
+
+That's what you want out of a
+software release strategy.
+
+AUDIENCE: [NOISE]
+
+BRADLEY KUSZMAUL: If you start
+putting in sync than maybe the
+
+race goes away because
+of that.
+
+But if just put in
+instrumentation to try to
+
+figure out what's going,
+it's still there.
+
+And the race detector sort of
+says, this variable in this
+
+function, this variable in this
+function, you look at it
+
+and say, how could
+that happen?
+
+And finally you figured out and
+you fix it and then you
+
+put it-- if you're trying to do
+software release you build
+
+a regression test that will
+verify that has that input.
+
+AUDIENCE: What if you have a
+situation where the spawn
+
+graph falls into a terminal.
+
+So it's not a radius, but
+monitoring spawn is there but
+
+it spawns a graph a
+little bit deeper.
+
+BRADLEY KUSZMAUL: Yes.
+
+For example, our race detector
+understands locks.
+
+So part of the rule is it
+doesn't report a race if the
+
+two memory accesses--
+
+if there was a lock that they
+both held in common.
+
+Now you now you can write buggy
+programs because you can
+
+essentially do the memory at
+lock, you know, read the
+
+memory, unlock, lock,
+write the memory.
+
+Now the interleave happens
+and there's a race.
+
+So the assumption of this race
+detector is that if you put
+
+locks in there that you've
+sort of thought about.
+
+This is finding races that you
+forgot about rather than races
+
+that you ostensibly
+thought about.
+
+There are some races that
+are actually correct.
+
+For example, in the chess
+programs there's this big
+
+table that remembers all
+the chess positions
+
+that have been seen.
+
+And if you don't get the right
+answer out of the table it
+
+doesn't matter because you
+search it again anyway.
+
+Not getting the right
+answer means you
+
+don't get any answer.
+
+You look something up and it's
+not there so you search again.
+
+If you just waited a little
+longer maybe somebody else
+
+would have put the value
+in, you could have
+
+saved a little work.
+
+And so in that case, well it
+turns out to be there's no
+
+parallel way to do that.
+
+So I'm willing to tolerate that
+race because that gives
+
+me performance and so you have
+what we call fake locks, which
+
+are basically things that look
+like lock calls, but they
+
+don't do anything except tell
+the race detector, pretend
+
+there was a lock
+held in common.
+
+Yeah?
+
+AUDIENCE:
+[UNINTELLIGIBLE PHRASE]
+
+BRADLEY KUSZMAUL: If it says
+there's no race it means that
+
+for every possible
+scheduling that--
+
+AUDIENCE:
+[UNINTELLIGIBLE PHRASE].
+
+BRADLEY KUSZMAUL: Well,
+you have that dag.
+
+And imagine running it
+on one processor.
+
+There's a lot of possible
+orders in
+
+which to run the dag.
+
+And the rule is well, was there
+a load in a store or a
+
+store in a store that switched
+orders in some possible
+
+schedule and that's
+the definition.
+
+AUDIENCE: So, in practice,
+sorry, one of the [INAUDIBLE]
+
+techniques is loss.
+
+Assuming, dependent on the
+processor, that you have
+
+atomic rights, we want to
+deal with that data
+
+[UNINTELLIGIBLE] in
+the background --
+
+BRADLEY KUSZMAUL: Those
+protocols are really hard to
+
+get right, but yes, it's
+an important trick.
+
+AUDIENCE: Certainly
+[INAUDIBLE].
+
+BRADLEY KUSZMAUL: So to convince
+the race detector not
+
+to complain you put fake
+locks around it.
+
+You've programmed a
+sophisticated algorithm it's
+
+up to you to get the
+details right.
+
+The other property about this
+race detector is that it's
+
+fast. It runs almost
+in liear time.
+
+A lot of the race detectors that
+you find out there run in
+
+quadratic time.
+
+So if you want to run a million
+instructions it has to
+
+compare every instruction to
+every other instruction.
+
+Turns out we don't
+have to do that.
+
+We run in time, which is n times
+alpha of n where alpha's
+
+the inverse Ackermann
+function.
+
+Anybody remember that from
+the union-find algorithm.
+
+It's got that graded So it's
+like the almost linear time.
+
+We actually now have a linear
+timed one that has performance
+
+advantages.
+
+So let me do a little
+theory in practice.
+
+In Cilk we have some fundamental
+complexity
+
+measures that we worry about.
+
+So we're interested in knowing
+and being able to predict the
+
+runtime of a Cilk program
+on P processors.
+
+So we want to know T sub p,
+which is the execution time on
+
+P processors.
+
+That's the goal.
+
+What we've got to work with is
+some directed acyclic graph
+
+that is for a particular input
+set and if the program
+
+determines it and everything
+else it's a well defined graph
+
+and we can come up with some
+basic measures of this graph.
+
+So T sub 1 is the work of the
+graph, which is the total time
+
+it would take to run that
+graph on one processor.
+
+Or if you assume that these
+things are all cost unit
+
+times, just the number
+of nodes.
+
+So for this graph
+what's the work?
+
+I heard teen, but something--
+
+18?
+
+And the critical path
+is the longest path.
+
+And if these nodes weren't unit
+time you'd have to weight
+
+the things according
+to actually how
+
+much time they run.
+
+So the critical path
+here is what?
+
+9.
+
+So I think those are right.
+
+The lower bounds then that you
+know is that you don't expect
+
+the runtime on P processes to be
+faster than linear speedup.
+
+In this model that
+doesn't happen.
+
+It turns out cache
+does things.
+
+It's adding more than
+just processors.
+
+You're adding more cache too.
+
+So all sorts of things or maybe
+it means that there's a
+
+better algorithm you
+should have used.
+
+So there's some funny things
+that happen if you have bad
+
+algorithms and so forth.
+
+But in this model you can't have
+more than linear speedup.
+
+You also can't get things done
+faster than in linear time.
+
+This model assumes basically
+that these costs of running
+
+these things are fixed and the
+cache has the property that
+
+changing the order of execution
+means that the
+
+actual costs of the nodes in
+the graph change costs.
+
+So those are lower bounds and
+the things that we want to
+
+know are speedups, so that's
+T sub 1 over T sub p.
+
+And the parallelism of
+the graph is T sub
+
+1 over T sub infinity.
+
+So the work over the critical
+path and we've been calling
+
+this span sometimes lately.
+
+Some people call that depth.
+
+Span is easier to say than
+critical path, depth has too
+
+many other meanings so
+I kind of like span.
+
+So what's the parallelism
+for this program?
+
+18/9.
+
+We said that T sub 1 was what?
+
+18.
+
+The infinity is 9.
+
+So on average and if you had
+an infinite number of
+
+processors and you scheduled
+this as greedy as you good, it
+
+would take you 9 steps to run
+and you would you be doing 18
+
+things worth of work.
+
+So on average there's
+two things to do.
+
+You know, 1 plus 1 plus 1 plus
+3 plus 4 plus 4 plus 1 plus 1
+
+plus 1 divided by 9
+turns out to be 2.
+
+So the average parallelism or
+just the parallelism of the
+
+program is T sub 1 over
+T sub infinity.
+
+And this property is something
+that's not dependent on the
+
+scheduler, it's a property
+of the program.
+
+Doesn't depend on how many
+processors you have.
+
+AUDIENCE: [OBSCURED]
+
+You're saying, you're calling
+that the span now?
+
+Is that the one for
+us [OBSCURED]
+
+BRADLEY KUSZMAUL: That's
+too long to say.
+
+I might as well say critical
+path length.
+
+Critical path length, longest
+trace span is a mathematical
+
+sounding name.
+
+AUDIENCE: We just like
+to steal terminology.
+
+BRADLEY KUSZMAUL: Well, yeah.
+
+So there's a theorem due to--
+
+Graham and Brent said that
+there's some schedule that can
+
+actually achieve the sum of
+those two lower bounds.
+
+This linear speedup is one lower
+bound of the runtime and
+
+the critical path
+is the other.
+
+So there's some schedule that
+basically achieves the sum of
+
+those and how does that
+theorem work?
+
+Well, at each time
+step either--
+
+suppose we had 3 processors.
+
+Either there's at least 3 things
+ready to run and so
+
+what you do is you do
+a greedy schedule.
+
+You grab any 3 of them.
+
+If there's fewer than p things
+to run, like here we have a
+
+situation where these
+have all run.
+
+The green ones are
+ready to go.
+
+Those are the only 2 that
+are ready to go.
+
+So what do you do then
+in a greedy schedule?
+
+You run them all.
+
+And the argument goes, well, how
+many times steps could you
+
+execute 3 things?
+
+At most you could do it the work
+divided by the number of
+
+processors times because
+then after that you've
+
+used up all the work.
+
+Well how many times could you
+execute less than p things?
+
+Well, every time you execute
+less than p things you're
+
+reducing the length of the
+remaining critical path.
+
+You can't do that more
+than the span times.
+
+And so a greedy scheduler will
+achieve some runtime which is
+
+within the sum of these 2.
+
+It's actually the sum
+of these 2 minus 1.
+
+It turns out that there has to
+be at least one node that's on
+
+both work and critical path.
+
+And so that means that you're
+guaranteed to be within a
+
+factor of 2 of optimal with
+a greedy schedule.
+
+And it turns out that if you
+have a lot of parallelism
+
+compared to the number
+processors, so if you have a
+
+graph that has a million fold
+parallelism and a thousand
+
+fold processors Well, if this
+is really small compared to
+
+the work, if you have a graph
+with a million fold
+
+parallelism that means the
+critical path is small.
+
+If you only had 1000 processors
+that means this
+
+term's big.
+
+And that means that this term is
+very close to this term, so
+
+essentially the corollary to
+this is that you get linear
+
+speedup, perfect linear speed
+asymptotically if you have
+
+fewer processors then you have
+parallelism in your program.
+
+So the game here at this level
+of understanding, I haven't
+
+told you how the scheduler
+actually works-- is to write a
+
+program that's got a lot of
+parallelism that you can get
+
+linear speedup.
+
+Well, the work-stealing
+scheduler we actually use.
+
+The problem is the greedy
+schedulers can be hard to
+
+compute-- especially if you
+imagine having a million
+
+processors in a program with
+a billion fold parallelism.
+
+Finding on every clock cycle,
+finding something for each of
+
+the million guys to do is
+conceptually difficult, so
+
+instead we have a work-stealing
+scheduler.
+
+I'll talk about that
+in a second.
+
+It achieves bounds which are
+not quite as good as those.
+
+This bound is the same.
+
+It's the sum of two terms. One
+is the linear speedup term,
+
+but instead of it being T sub
+infinity it's big O of T sub
+
+infinity because you actually
+have to do communication
+
+sometimes if the critical
+path length is long.
+
+Basically, you can
+sort of imagine.
+
+If you have a lot of things to
+do, a lot of tasks and people
+
+to do it, it's easy to do that
+in parallel if there's no
+
+interdependencies
+among the tasks.
+
+But as soon as there's
+dependencies you end up having
+
+to coordinate a lot and that
+communication costs--
+
+there's lots of lore about
+adding programmers to a task
+
+and it slowing you down.
+
+Because basically communication
+gets you.
+
+What we found empirically--
+
+there's a theorem for this--
+
+empirically the runtime is
+actually still very close to
+
+the sum of those terms. Or maybe
+it's those terms plus 2
+
+times T sub infinity or
+something like that.
+
+And again, we basically get
+near-perfect speedup as long
+
+as the number of processors
+is a lot less than the
+
+parallelism.
+
+Should be sort of a less
+than less than.
+
+The compiler has the mode where
+you basically can insert
+
+instrumentations.
+
+So you can run your program,
+it'll tell you the critical
+
+path length.
+
+You can compute these numbers.
+
+Clear how to compute work, you
+just sum up the runtime of all
+
+the threads.
+
+To compute the critical path
+length, well you have to do
+
+some max's and stuff as you
+go through the graph.
+
+And the average cost of a spawn
+these days is about 3 on
+
+like a dual core pentium.
+
+Three times the cost
+of a function call.
+
+And most of that cost actually
+has to do with the memory
+
+barrier that we do at the spawn
+because that machine
+
+doesn't have strong
+consistencies.
+
+So you have to put this memory
+barrier in and that just
+
+empties all the pipelines.
+
+It does better on like an SGI
+machine, which has strong--
+
+well, traditional.
+
+A MIPS machine that has strong
+consistency actually does
+
+better for the cost
+of that overhead.
+
+Let me talk a little
+bit about chess.
+
+And we had a bunch of chess
+programs. I wrote one in 1994,
+
+which placed third at the
+International Computer Chess
+
+Championship and that was
+running on a big connection
+
+machine CM5.
+
+I was one of the architects
+of that machine, so
+
+it was double fun.
+
+We wrote another program that
+placed second in '95 and that
+
+was running on an 1800 node
+Paragon and that was a big
+
+computer back then.
+
+We built another program called
+Cilk chess, which
+
+placed first in '96 running on
+a relatively smaller machine.
+
+And then on a larger SGI origin
+we ran some more and
+
+then at the World Computer Chess
+Championship in 1999 we
+
+beat Deep Blue and
+lost to a PC.
+
+And people don't realize this,
+but at the time that Deep Blue
+
+beat Kasparov it was not the
+World Computer Chess
+
+Champion, a PC was.
+
+So what?
+
+It's running a program.
+
+You know, there's this
+head and a tape.
+
+I don't know what it did.
+
+So this was a program called
+Fritz, which is a commercially
+
+available program.
+
+And those guys were very good,
+the PC guys playing were very
+
+good at getting on sort
+of the algorithm side.
+
+We got advantage
+by brute force.
+
+And we also had some real chess
+expertise on our team,
+
+but those guys were spending
+full time on things like
+
+pruning away sub-searches that
+they were convinced weren't
+
+going to pan out.
+
+Computer chess programs spend
+most of their time looking at
+
+situations that any person would
+look at and say, ah,
+
+blacks won.
+
+Why are you even looking
+at this?
+
+And it keeps searching.
+
+It's like, well maybe there's
+a way to get the queen.
+
+So computers are pretty
+dumb at that.
+
+So basically these guys put a
+lot more chess intelligence in
+
+and we also lost due to what--
+in this particular game, we
+
+were tied for first place and we
+decided to do a runoff game
+
+to find out who would win and
+we lost due to a classic
+
+horizon effect.
+
+So it turns out that we were
+searching to depth 12 in the
+
+tree and Fritz was searching
+to depth 11.
+
+Even with all these heuristics
+and stuff they had in it, they
+
+were still not searching
+as deeply as we were.
+
+But there was a move that was a
+good move that looked OK at
+
+depth 11 and looked bad at depth
+11 and at depth 13 it
+
+looked really good again.
+
+So they saw the move and made
+it for the wrong reason, we
+
+saw the move and didn't make it
+for the right reason, but
+
+it was wrong and the right
+move-- if we'd been able to
+
+search a little deeper, we would
+have seen that it was
+
+really the wrong thing to do.
+
+This happens all the
+time in chess.
+
+There's a little randomness
+in there.
+
+This horizon effect shows up
+and again, it boils down to
+
+the programs are not
+intelligent.
+
+A human would look at it and
+say, eventually that knight's
+
+going to fall.
+
+But if the computer can't see
+it with a search, you know?
+
+We plotted the speedup of star
+Socrates, which was the first
+
+one on this funny graph.
+
+So this looks sort of like a
+typical linear speedup graph.
+
+Sort of when you're down here
+with few numbers processors
+
+you get good linear speedup
+and eventually you stop
+
+getting linear speedup.
+
+That's sort of in broad
+strokes what
+
+this graph looks like.
+
+But the axes are
+kind of funny.
+
+The axes aren't the number of
+processors and the speedup--
+
+it's the number processors
+divided by the parallelism of
+
+the program.
+
+And here is the speedup divided
+by the parallelism of
+
+the program.
+
+And the reason we did that is
+the each of these data points
+
+is a different program with
+different work in span.
+
+If I'm trying to run a
+particular problem on a bunch
+
+of different processors I can
+just draw that curve and see
+
+what happens as get
+more processors.
+
+I'm not getting any advantage
+because I've got too many
+
+processors.
+
+I've exceeded the parallelism
+of the program.
+
+But if I'm running, trying
+to compare two different
+
+programs, how do I do that?
+
+Well, you can do that by
+normalizing by the
+
+parallelism.
+
+So down in this domain the
+number of processors is small
+
+compared to the average
+parallelism and we get good
+
+linear speedups.
+
+And up in this the domain the
+number of processors is large
+
+and it starts asymptoting to
+the point where the speedup
+
+approaches the parallelism and
+that's sort of what happened.
+
+You get some noise out here so
+one of the things down here,
+
+it's nice and tight.
+
+And that's because we're in
+that domain where the
+
+communication costs are
+infrequently paid because
+
+there's lots of work to do.
+
+You don't have to communicate
+very much.
+
+Up here there's a lot of
+communication that happens and
+
+so the noise is showing
+up more in the data.
+
+This curve here is the
+T sub 1 over P plus T
+
+sub infinity curve.
+
+The T sub P equals T sub
+infinity curve and that's the
+
+linear speedup curve
+on this graph.
+
+So I think there's an important
+lesson in this graph
+
+besides the data itself, which
+is if you're careful about
+
+choosing the axes, you can take
+a whole bunch of data
+
+that you couldn't see how to
+plot it together and you can
+
+plot it together and get
+something meaningful.
+
+So in my Ph.D. thesis I had
+hundreds of little plots for
+
+each chess position and I didn't
+figure out how-- it's
+
+like they all look
+the same, right?
+
+But I didn't sort of figure out
+that if I was careful I
+
+could actually make
+them be the same.
+
+That happened after I
+published my thesis.
+
+Oh, we could just
+overlay them.
+
+Well, what's the normalization
+that makes that work?
+
+So there's a speedup paradox
+that happened.
+
+Pardon?
+
+AUDIENCE: [OBSCURED]
+
+BRADLEY KUSZMAUL: Yeah, OK.
+
+There was a speedup paradox that
+happened while we were
+
+developing star Socrates.
+
+We were developing this for
+512 processor connection
+
+machine that was at University
+of Illinois, but we only had a
+
+smaller machine on which
+to do our development.
+
+We had a 128 processor machine
+at MIT and most days I could
+
+only get 32 processors
+because the machine
+
+was in heavy demand.
+
+So we had this program
+and it ran on 32
+
+processors in 65 seconds.
+
+And one of the developers said,
+here's a variation on
+
+the algorithm, it
+changes the dag.
+
+It's a heuristic.
+
+It makes the program
+run more efficient.
+
+Look, it runs in only 40 seconds
+on 32 processors.
+
+And so is that a good idea?
+
+It sure seemed like a good idea,
+but we were worried that
+
+we knew that the transformation
+increased the
+
+critical path length of the
+program, so we weren't sure it
+
+was a good idea.
+
+So we did some calculation.
+
+We measured the work
+and the speedup.
+
+And so the work here--
+
+these numbers have been cooked
+a little bit to make the math
+
+easy, but the numbers--
+
+this really did happen, but not
+with these exact numbers.
+
+So we had a work which was 2048
+seconds and only 1 second
+
+of critical path.
+
+And over this new program had
+only 1/2 as much work to do,
+
+but the critical path
+length was longer.
+
+It was 8 seconds long.
+
+If you predict on 32 processors
+what the runtime's
+
+going to be that formula
+says well, 65 seconds.
+
+If you predict it on 32
+processors this-- well, it's
+
+40 seconds and that looks good,
+but we were going to be
+
+running the tournament on 512
+processors where this term
+
+would start being less important
+than this term.
+
+So this really did happen and
+we actually went back and
+
+validated that these numbers
+were right after we did the
+
+calculation and it allowed us to
+do the engineering to make
+
+the right decision and not be
+misled by something that
+
+looked good in the
+test environment.
+
+We were able to predict what was
+going to happen on the big
+
+machine without actually having
+access to the big
+
+machine and that was
+very important.
+
+Let me do some algorithms. You
+guys probably have done some
+
+matrix multipliers over the
+past 3 weeks, right?
+
+That's probably the only thing
+you've been able to do would
+
+be my guess.
+
+So matrix multiplication
+is this operation.
+
+I won't talk about it, but
+you know what it is.
+
+In Cilk instead of doing the
+standard triply nested loops
+
+you do divide and conquer.
+
+We don't parallelize loops we
+parallelize function calls, so
+
+you want to express a
+loops as recursion.
+
+So to multipliy two big matrices
+you do a whole bunch
+
+of little matrix multiplications
+of the
+
+sub-blocks and then you express
+those little matrix
+
+multiplications themselves and
+go off and recursively do
+
+smaller matrix multiplications.
+
+So this requires 8
+multiplications of matrices
+
+these of 1/2 the number of
+rows and 1/2 the number
+
+columns an one edition at the
+end where you add these two
+
+matrices together.
+
+That's the algorithm that we do,
+it's the same total work
+
+as the standard one, but it's
+just expressed recursively.
+
+So a matrix multiply is you
+do these 8 multiplies.
+
+I had to create a temporary
+variable, so the first four
+
+multiplies the A's and B's
+into C. The second four
+
+multiply the A's and B's into
+T and then I have to add T
+
+into C. So I do all those
+spawns, do all the multiplies.
+
+I do a sync because I better not
+start using the results on
+
+the multiplies and adding them
+until the multiplies are done.
+
+AUDIENCE: Which four
+do you add?
+
+BRADLEY KUSZMAUL: What?
+
+There's parallelism in add.
+
+Matrix addition.
+
+AUDIENCE: Yeah, but it doesn't
+add spawn extent
+
+BRADLEY KUSZMAUL: Well,
+we spawn off add.
+
+I don't understand--
+
+[INTERPOSING VOICES]
+
+BRADLEY KUSZMAUL: So you have
+to spawn Cilk functions even
+
+if you're only executing
+one of them at a time.
+
+Cilk functions are spawned,
+C functions are called.
+
+It's a decision that's built
+into the language.
+
+It's not really a fundamental
+decision.
+
+It's just that's the
+way we did it.
+
+AUDIENCE: Why'd you choose to
+have the key word then?
+
+That's just documentation
+from the caller side?
+
+BRADLEY KUSZMAUL: Yeah, we found
+we were less likely to
+
+make a mistake if we sort of
+built it into the type system
+
+in this way.
+
+But I'm not convinced that this
+is the best way to do
+
+this type system.
+
+AUDIENCE: Can the C functions
+spawn a Cilk function.
+
+BRADLEY KUSZMAUL: No.
+
+You can only call spawn, spawn,
+spawn, spawn then you
+
+can call C functions
+at the leaves.
+
+It turns out you can actually
+spawn Cilk functions if you're
+
+a little clever about-- there's
+a mechanism for a Cilk
+
+system running in the background
+and if you're
+
+running C you can
+say OK, do this
+
+Cilk function in parallel.
+
+So we have that, but that's
+not didactic.
+
+AUDIENCE: Sorry, I
+have a question
+
+about the sync spawning.
+
+Is the sync actually doing a
+whole wave or -- like, in the
+
+case of-- maybe not in the case
+of the add here, but in
+
+plenty of other practical
+functions you get inside the
+
+spawn function looking
+at the tendencies of
+
+the parameters, right?
+
+Based on how those
+were built from
+
+previous spawned funcitons.
+
+You can actually just start
+processing so long as it's
+
+guaranteed that the results
+are available before you
+
+actually read them.
+
+BRADLEY KUSZMAUL: So there's
+this other style of expressing
+
+parallelism which you see
+in some of the data flow
+
+languages where you say well,
+I've computed this first
+
+multiply, why can't I get
+started on the corresponding
+
+part of the addition.
+
+And it turns out that in those
+models there's no performance
+
+guarantees.
+
+The real issue is you
+run out of memory.
+
+It's a long topic, let's not
+go into it, but there's a
+
+serious technical issue with
+those programming models.
+
+We have very tight memory
+bounds as well, so we
+
+simultaneously get these good
+scheduling bounds and good
+
+memory bounds and if you are
+doing that you could have sort
+
+of a really large number of
+temporaries required and run
+
+out of memory.
+
+The data flow machine used to
+have this number-- there was a
+
+student, Ken Traub, who was
+working on Monsoon when Greg
+
+Papadapolous was here and he
+came up with this term which
+
+we called Traub's constant,
+which was how long the machine
+
+could be guaranteed to run
+before it crashed from being
+
+out of memory.
+
+And that was-- well, he took
+the rate at which it Kahn's
+
+divided by the amount of
+memory and that was it.
+
+And many data flow programs had
+that property that Monsoon
+
+could run for 40 seconds
+and then after
+
+that you never knew.
+
+It might start crashing at any
+moment, so everybody wrote
+
+short data flow programs.
+
+So one of the things you
+actually do when you're
+
+implementing, when you're trying
+to engineer this to go
+
+fast, is you course in the
+base case, which I didn't
+
+describe up there.
+
+You don't just do a 1 by 1
+matrix multiplied down there
+
+at the leaves of
+this recursion.
+
+Because then you're not using
+the processor pipeline
+
+efficiently.
+
+You call the Intel Math Kernel
+Library or something on an 8
+
+by 8 matrix so that it really
+gets the pipeline a
+
+chance to chug away.
+
+So analysis.
+
+This matrix addition operation--
+well, what's the
+
+work for matrix addition?
+
+Well the work to do a matrix
+operation on n rows is well,
+
+you have to do 4 additions
+of size n over 2.
+
+Plus there's order 1 work
+here for the sync.
+
+And that recurrence has solution
+order n squared.
+
+Well, that's not surprising.
+
+You have to add up 2 matrices
+which are n by n.
+
+That's going to be n squared
+so that's a good result.
+
+The critical path for this is
+well, you have to do all of
+
+these in parallel.
+
+So whatever the critical path of
+the longest one is, they're
+
+all the same so it's just the
+critical path of the size n
+
+over 2 plus quarter 1, so the
+critical path is order log n.
+
+For matrix multiplication,
+sort of the reason I
+
+do this is I can.
+
+This is a model which I can
+do this analysis, so
+
+I have to do it.
+
+But really, being able to do
+this analysis is important
+
+when you're trying to make
+things run faster.
+
+Matrix multiplication, well,
+the work is I have to do 8
+
+little matrix multiplies plus
+I have to do the matrix add.
+
+The work has solution order n
+cubed and everybody knows that
+
+there's order n cubed multiply
+adds in a matrix multiplier,
+
+so that's not very surprising.
+
+The critical path is-- well, I
+have to do a add so that takes
+
+log n, plus I have to do a
+multiply on a matrix that's
+
+1/2 the size.
+
+So the critical path length of
+the whole thing has solution
+
+order log squared n.
+
+So the total parallelism of
+matrix multiplication is the
+
+work over the span, which is
+n cubed over log squared n.
+
+So if you have a 1000 by 1000
+matrix that means your
+
+parallelism is close
+to 10 million.
+
+There's a lot of parallelism
+and in fact, we see perfect
+
+linear speedup on matrix
+multiply because there's so
+
+much parallelism in it.
+
+It turns out that this stack
+temporary that I created so
+
+that I could do these multiplies
+all in parallel is
+
+actually costing me work because
+I'm on a machine that
+
+has cache and I want to use
+the cache effectively.
+
+So I really don't want to create
+a whole big temporary
+
+matrix and blow my cache
+out if I can avoid it.
+
+So I proposed the following
+matrix multiply, which is I
+
+first do 4 of the matrix
+multiplies into C1 then I do a
+
+sync and then I do the other
+4 into C1 and another sync.
+
+And I forgot to do the add-- oh,
+no those are multiply adds
+
+so they're multiplying
+and adding in.
+
+And this saves space because it
+doesn't need a temporary,
+
+but it increases the
+critical path.
+
+So is that a good idea
+about or a bad idea?
+
+Well, we can answer part of that
+question with analysis.
+
+Saving space we know is going
+to save something.
+
+What does it do to the work
+in critical path?
+
+Well, the work is still the
+same, it's n cubed because we
+
+didn't change the number of
+flops that we're doing.
+
+But the critical
+path has grown.
+
+Instead of doing 1 times a
+matrix multiply, we have to do
+
+one and then sync and
+then do another one.
+
+So it's 2 matrix multiplies of
+1/2 the size plus the order 1
+
+and that recurrence has solution
+order n instead of
+
+order log squared n.
+
+So that sounds bad, we've made
+the critical path longer.
+
+AUDIENCE: [OBSCURED]
+
+BRADLEY KUSZMAUL: What?
+
+Yeah.
+
+So parallelism is now order n
+squared instead of n cubed
+
+over log squared n and for a
+1000 by 1000 matrix that means
+
+you still have a million
+fold parallelism.
+
+So for relatively modest sized
+matrices you still have plenty
+
+of work to do this
+optimization.
+
+So this is a good transformation
+to do it.
+
+One of the advantages of Cilk
+is that you can do this kind
+
+of You could say, let me
+do an optimization.
+
+I can do an optimization in my
+C code and I get to take
+
+advantage of it in
+the Cilk code.
+
+I could do this kind of
+optimization of trading work
+
+for parallelism.
+
+If I have a lot of work that
+sometimes is a good idea.
+
+Ordinary matrix multiplication
+just is really bad.
+
+Basically you can imagine
+spawning off the n squared
+
+inner dot products here and
+
+computing them all in parallel.
+
+It has work n cubed
+parallelism log n.
+
+I mean, critical path log n so
+the parallelism's even better.
+
+It's n cubed over log n
+instead of n squared.
+
+That looks better theoretically,
+but it's really
+
+bad in practice because it has
+such poor cache behavior.
+
+So we don't do that.
+
+I'll just briefly talk
+about how it works.
+
+So Cilk does work-stealing.
+
+We had did double ended
+queue-like decque.
+
+So at the bottom of the queue
+is the stack where you push
+
+and pop things and the top is
+something where you can pop
+
+things off if you want to.
+
+And so what's running is all
+these processors are running
+
+each on their own stack.
+
+They're all running the
+ordinary serial code.
+
+That's sort of the
+basic situation.
+
+They're pretty much
+running the serial
+
+code most of the time.
+
+So some processor runs.
+
+It pushes.
+
+Well, it doesn't spawn,
+so what does it do?
+
+It pushes something onto its
+stack because it's just a
+
+function call.
+
+And it does another couple more
+spawns so things pop off.
+
+Somebody returns so
+he pops his stack.
+
+So far everything's going on,
+they're not communicating,
+
+they're completely independent
+computations.
+
+This guy spawns and now
+he's out of work.
+
+Now he has to do something.
+
+What he does is he goes and
+picks another processor at
+
+random and he steals
+the thing from the
+
+other end of the stack.
+
+So he's unlikely to conflict
+because this guy's pushing and
+
+popping down here, but there's
+a lock in there, thers's a
+
+little algorithm.
+
+A non-blocking algorithm
+actually, it's not lock.
+
+And so he goes and he steals
+something and come on, slide
+
+over there.
+
+Whoa.
+
+Yes, that's animation, right?
+
+That's the extent
+of my animation.
+
+And then he starts
+working away.
+
+And the theorem is that a
+work-stealing scheduler like
+
+this gives expected running
+time with high probability
+
+actually of T sub 1 over P
+plus T sub infinity on P
+
+processors.
+
+And the pseudoproof is a little
+bit like the proof for
+
+Brent's Theorem,
+which is either
+
+you're working or stealing.
+
+If you're working well, that
+goes against T sub 1 over P.
+
+You can't do that very much
+or you run out of work.
+
+If you're stealing well, each
+steal has a chance that it
+
+steals the thing that's
+on the critical path.
+
+You may actually steal the wrong
+thing, but you actually
+
+have a 1 in P chance that you're
+the one who steals the
+
+thing that it's on the critical
+path and then in
+
+which case the expected
+number--
+
+so you had this chance of
+1 over P of reducing the
+
+critical path length by 1, so
+after this many steals the
+
+critical path is all gone.
+
+So you can only do P times
+T infinity steals.
+
+This high probability
+it comes out.
+
+And that gives you
+these bounds.
+
+OK, I'm not going to give
+you all this stuff.
+
+Message passing sucks,
+you know.
+
+You guys know.
+
+There's probably nothing
+else in here.
+
+So basically the pitch here is
+that you get some high level
+
+linguistics support for these
+very fine-grained parallelism.
+
+It's an algorithmic programming
+model so that
+
+means that you can do
+engineering for performance.
+
+There's fairly easy conversion
+of existing code, especially
+
+when you combine it with
+the race detector.
+
+You've got this factorization
+of the debugging problem and
+
+to debugging your serial code
+is you run it with all the
+
+Cilk stuff turned off.
+
+You allied the program and make
+sure your program works.
+
+Then you run it with the rate
+detector to make sure you get
+
+the same answer in parallel
+and then you're done.
+
+Applications in Cilk don't just
+scale to large number of
+
+processors, they scale down
+to small numbers, which is
+
+important if you only have
+two processors or one.
+
+You don't suddenly want to pay
+a factor of 10 to get off the
+
+ground, which happens
+sometimes on
+
+clusters running MPI.
+
+You have to pay a big
+overhead before
+
+you've made any progress.
+
+And one of the advantages for
+example is that the number of
+
+processors might change
+dynamically.
+
+In this model that's
+OK because it's
+
+not part of the program.
+
+So you may have the operating
+system reduce the number of
+
+actual worker threads that you
+have doing that work-stealing
+
+and that can work.
+
+One of the bad things about
+Cilk is that it doesn't
+
+support sort of data parallel
+or program model kind of
+
+parallelism.
+
+You really have to think of
+things as this divide and
+
+conquer kind of the world.
+
+And if you have trouble
+expressing that--
+
+situations where you're doing
+Jacobi update and you very
+
+carefully put things on, had
+each processor work on its
+
+local memory and then they only
+have to communicate at
+
+the boundaries.
+
+That's difficult to do right
+in Cilk because essentially
+
+every time you go around the
+loop of I have all these
+
+things to do.
+
+All the work-stealing happens
+randomly and it happens on a
+
+different processor.
+
+So it's not very good at that
+sort of thing, although it
+
+turns out Jacobi update's not
+a very good example for that
+
+because there are more
+sophisticated algorithms that
+
+use cache effectively that you
+can express in Cilk and I
+
+would have no idea how to no
+say those in some of these
+
+sort of data parallel
+languages.
+
+Using the cache efficiently is
+really important on modern
+
+processors.
+
+PROFESSOR: Thank you.
+
+Questions?
+
+BRADLEY KUSZMAUL: You can
+download Cilk, there's a bunch
+
+of contributors.
+
+Those are the Cilk worms
+and you can download
+
+Cilk off our webpage.
+
+Just Google for Cilk
+and you'll find it.
+
+It's a great language,
+you'll love it.
+
+You'll love it much more than
+what you've been doing.
+
+AUDIENCE: How does the Cilk
+play with processor
+
+[OBSCURED]?
+
+BRADLEY KUSZMAUL: Well, you
+have to have a language, a
+
+compiler that can
+generate those.
+
+If you have an assembly command
+or you have some other
+
+complier that can
+generate those.
+
+So I just won the HPC challenge,
+which is this
+
+challenge where everybody tries
+to run parallel programs
+
+and argue that they
+get productivity.
+
+For that there were some codes
+like matrix multiply and LUD
+
+composition with pivoting.
+
+Basically at the leads of the
+computation I call the Intel
+
+Math Kernel Library.
+
+Which in turn uses the
+SSE instructions.
+
+You could do anything you can do
+in C in the C parts of the
+
+code because Cilk compiler just
+passes those through.
+
+So if you have some really
+efficient pipeline code for
+
+doing something, up to
+some point it made
+
+sense to use that.
+
+AUDIENCE: [OBSCURED]
+
+BRADLEY KUSZMAUL: So I ran
+it on NASIS Columbia.
+
+So the benchmark consists of--
+well, there's 7 applications
+
+they have. 6 of which are
+actually well-defined.
+
+One of them is this thing that
+just measures network
+
+performance or something,
+so it doesn't
+
+have any real semantics.
+
+There's 6 benchmarks.
+
+One of them is LUD composition,
+one of them is
+
+DJEM matrix multiplication and
+this FFT and 3 others.
+
+So I implemented all 6, nobody
+else implemented all 6.
+
+It turns out that you had to
+implement 3 in order to enter.
+
+Almost everybody implemented 3
+or 4, but I did all 6 which is
+
+part of why I won.
+
+So I could argue that in
+a weeks work I just
+
+implemented--
+
+AUDIENCE: What is [OBSCURED]?
+
+BRADLEY KUSZMAUL: So the prize
+has two components.
+
+Performance and productivity or
+elegance or something and
+
+it's completely whatever the
+judges want that to be.
+
+So it was up to me as a
+presenter to make the case
+
+that I was elegant.
+
+Because I had my performance
+numbers, which were pretty
+
+good and it turned out that the
+IBM entry for x10 did me
+
+more good than I did, I think.
+
+Because they got up there and
+they compared the performance
+
+of x10 to their Cilk
+implementation and their x10
+
+thing was almost as
+good as Cilk.
+
+So after that I think the judges
+said they had to give
+
+me the prize.
+
+So basically, it went down to
+supercomputing and each of us
+
+got 5 minutes to present and
+there were 5 finalists.
+
+We did our presentation and
+then they gave out the --
+
+So they divided the prize three
+ways: the people who got
+
+the absolute best performance,
+which were some people running
+
+UPC and the people who had the
+most elegance based on minimal
+
+number of lines of codes and
+that was Cleve at --
+
+what's his name?
+
+The Mathworks guy, MATLAB guy.
+
+Who said, look, matrix,
+LUD composition.
+
+LU of P. It's very elegant,
+but I don't think that it
+
+really sort of explains what
+you have to do to solve the
+
+problems. So he won the prize
+for most elegant and I got the
+
+prize for best combination,
+which they then changed--
+
+in the final citation for the
+prize they said, most
+
+productivity.
+
+That was the prize.
+
+So I actually won the contest
+because that was what the
+
+contest was supposed to be
+was most productivity.
+
+But I only won 1/3 of the
+prize money because they
+
+divided it three ways.
+
+PROFESSOR: Any other question?
+
+Thank you.
+
+BRADLEY KUSZMAUL: Thank you.
+
+PROFESSOR: We'll take a 5 minute
+break and since you had
+
+guest lecturer I do
+have [OBSCURED]
\ No newline at end of file
diff --git a/X4Y9n_c1ej8.txt b/X4Y9n_c1ej8.txt
new file mode 100644
index 0000000000000000000000000000000000000000..3ef495a7e6be9c3008215f8dfbc58d12481c1a08
--- /dev/null
+++ b/X4Y9n_c1ej8.txt
@@ -0,0 +1,180 @@
+PROFESSOR: Hello,
+welcome again to 8701.
+
+In this short video, I'll talk
+about the books we are using
+
+and the literature we
+are using in this class.
+
+So let's dive right into.
+
+There's a sequence
+of textbooks I
+
+go back to when I prepare
+the material for the class.
+
+You know, the one
+which I use in order
+
+to derive the outline or
+the schedule for the class
+
+is Introduction to High
+Energy Physics by Perkins.
+
+But again, I use
+material from a sequence
+
+of textbooks and reading
+material for you guys as well.
+
+Nuclear physics is not
+covered in Perkins,
+
+so we have here Samuel Wong's
+book on Introductory Nuclear
+
+Physics.
+
+We spend about two weeks
+talking about nuclear physics
+
+towards the second
+part of the class.
+
+And a couple of basics, we talk
+about the introductory material
+
+really in the sequence.
+
+A book I like a lot
+is the Introduction
+
+to Elementary
+Particles by Griffiths.
+
+And you see me using examples
+out of that book a bit.
+
+Then on the nuclear physics
+side there is Kenneth Krane.
+
+It's an MIT book
+and a book which
+
+has been put together by
+MIT faculty and research
+
+scientists.
+
+And then there's Techniques for
+Nuclear and Particle Physics
+
+by Leo, which I like a lot.
+
+It's a little bit
+of an older book,
+
+but it goes into some
+of the technical details
+
+and material details which
+are important to understand
+
+how we build detectors.
+
+And then a more recent book
+is Modern Particle Physics
+
+by Mark Thomson.
+
+It dives right into particle
+physics, the energy frontier.
+
+And it's really nice to read.
+
+It's a modern book.
+
+And it's easy to
+read and comprehend.
+
+I recommend to have a look
+at the review articles
+
+by the particle data group.
+
+They are really
+concise articles which
+
+are for beginners or for
+introductory level maybe
+
+a little bit
+difficult. But as we
+
+go through the
+material in this class,
+
+you should be able to take
+those articles to review
+
+certain sections of this class.
+
+For example, QCD, or
+electroweak interactions,
+
+the Higgs mechanism.
+
+And while you do
+this, you also learn
+
+one of the latest results
+and measurement in this area.
+
+I'll be posting a set of papers
+as we go through the class.
+
+And you'll see in the
+course organization
+
+that I'll ask you to
+actually summarize
+
+some of those papers in
+our recitation section.
+
+So those are going to be
+important papers, for example,
+
+describing the
+experiment which was used
+
+to measure parity violation,
+or the paper on the Higgs
+
+discovery.
+
+That's it for literature.
+
+Please as always go ahead
+and ask me questions.
+
+You know this.
+
+You know if you Google particle
+physics or nuclear physics,
+
+you will find tons of
+literature available
+
+on as many good books.
+
+And you might find
+a different one
+
+from this listing which
+suits your appetite
+
+for reading and learning.
\ No newline at end of file
diff --git a/XAt0dX5M-TA.txt b/XAt0dX5M-TA.txt
new file mode 100644
index 0000000000000000000000000000000000000000..5c653d9cff078755d8e582c5899b29691d25fdc5
--- /dev/null
+++ b/XAt0dX5M-TA.txt
@@ -0,0 +1,1323 @@
+align:start position:0%
+ 
+welcome back to
+
+ align:start position:0%
+welcome back to
+ 
+
+ align:start position:0%
+welcome back to
+age 20 special relativity in this video
+
+ align:start position:0%
+age 20 special relativity in this video
+ 
+
+ align:start position:0%
+age 20 special relativity in this video
+we talk about galilean transformation so
+
+ align:start position:0%
+we talk about galilean transformation so
+ 
+
+ align:start position:0%
+we talk about galilean transformation so
+what is it you're going to do you want
+
+ align:start position:0%
+what is it you're going to do you want
+ 
+
+ align:start position:0%
+what is it you're going to do you want
+to describe our event p
+
+ align:start position:0%
+to describe our event p
+ 
+
+ align:start position:0%
+to describe our event p
+maybe professor cluj exploding
+
+ align:start position:0%
+maybe professor cluj exploding
+ 
+
+ align:start position:0%
+maybe professor cluj exploding
+um it's two different reference frame we
+
+ align:start position:0%
+um it's two different reference frame we
+ 
+
+ align:start position:0%
+um it's two different reference frame we
+can call one of the reference frame our
+
+ align:start position:0%
+can call one of the reference frame our
+ 
+
+ align:start position:0%
+can call one of the reference frame our
+laboratory frame
+
+ align:start position:0%
+laboratory frame
+ 
+
+ align:start position:0%
+laboratory frame
+maybe that's the frame in which
+
+ align:start position:0%
+maybe that's the frame in which
+ 
+
+ align:start position:0%
+maybe that's the frame in which
+professor clutter was stationary it has
+
+ align:start position:0%
+professor clutter was stationary it has
+ 
+
+ align:start position:0%
+professor clutter was stationary it has
+an origin and has axis x y and z
+
+ align:start position:0%
+an origin and has axis x y and z
+ 
+
+ align:start position:0%
+an origin and has axis x y and z
+and then we have a moving frame which is
+
+ align:start position:0%
+and then we have a moving frame which is
+ 
+
+ align:start position:0%
+and then we have a moving frame which is
+moving with a constant velocity
+
+ align:start position:0%
+moving with a constant velocity
+ 
+
+ align:start position:0%
+moving with a constant velocity
+with respect to the laboratory frame
+
+ align:start position:0%
+with respect to the laboratory frame
+ 
+
+ align:start position:0%
+with respect to the laboratory frame
+the origin is o prime the axes are x
+
+ align:start position:0%
+the origin is o prime the axes are x
+ 
+
+ align:start position:0%
+the origin is o prime the axes are x
+prime y prime and z prime
+
+ align:start position:0%
+prime y prime and z prime
+ 
+
+ align:start position:0%
+prime y prime and z prime
+all right so now what did we learn from
+
+ align:start position:0%
+all right so now what did we learn from
+ 
+
+ align:start position:0%
+all right so now what did we learn from
+this let's think about an example
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+an example most of you have experienced
+
+ align:start position:0%
+an example most of you have experienced
+ 
+
+ align:start position:0%
+an example most of you have experienced
+before is the one where you sit in a
+
+ align:start position:0%
+before is the one where you sit in a
+ 
+
+ align:start position:0%
+before is the one where you sit in a
+train car and if it's not a train car it
+
+ align:start position:0%
+train car and if it's not a train car it
+ 
+
+ align:start position:0%
+train car and if it's not a train car it
+can be a
+
+ align:start position:0%
+can be a
+ 
+
+ align:start position:0%
+can be a
+car or a plane something which is moving
+
+ align:start position:0%
+car or a plane something which is moving
+ 
+
+ align:start position:0%
+car or a plane something which is moving
+with respect to earth
+
+ align:start position:0%
+with respect to earth
+ 
+
+ align:start position:0%
+with respect to earth
+if you look out of the window
+
+ align:start position:0%
+if you look out of the window
+ 
+
+ align:start position:0%
+if you look out of the window
+and you know the acceleration is very
+
+ align:start position:0%
+and you know the acceleration is very
+ 
+
+ align:start position:0%
+and you know the acceleration is very
+very minor
+
+ align:start position:0%
+very minor
+ 
+
+ align:start position:0%
+very minor
+it's often not clear whether or not the
+
+ align:start position:0%
+it's often not clear whether or not the
+ 
+
+ align:start position:0%
+it's often not clear whether or not the
+earth the train station or the train car
+
+ align:start position:0%
+earth the train station or the train car
+ 
+
+ align:start position:0%
+earth the train station or the train car
+is moving and so you have
+
+ align:start position:0%
+is moving and so you have
+ 
+
+ align:start position:0%
+is moving and so you have
+this this kind of
+
+ align:start position:0%
+this this kind of
+ 
+
+ align:start position:0%
+this this kind of
+weird feeling that you know i don't know
+
+ align:start position:0%
+weird feeling that you know i don't know
+ 
+
+ align:start position:0%
+weird feeling that you know i don't know
+if maybe the neighboring train started
+
+ align:start position:0%
+if maybe the neighboring train started
+ 
+
+ align:start position:0%
+if maybe the neighboring train started
+moving or i'm i'm moving um but what you
+
+ align:start position:0%
+moving or i'm i'm moving um but what you
+ 
+
+ align:start position:0%
+moving or i'm i'm moving um but what you
+want to do here is describe
+
+ align:start position:0%
+want to do here is describe
+ 
+
+ align:start position:0%
+want to do here is describe
+you sitting in the train car
+
+ align:start position:0%
+you sitting in the train car
+ 
+
+ align:start position:0%
+you sitting in the train car
+um you know reading a newspaper uh once
+
+ align:start position:0%
+um you know reading a newspaper uh once
+ 
+
+ align:start position:0%
+um you know reading a newspaper uh once
+with
+
+ align:start position:0%
+with
+ 
+
+ align:start position:0%
+with
+within your laboratory frame within the
+
+ align:start position:0%
+within your laboratory frame within the
+ 
+
+ align:start position:0%
+within your laboratory frame within the
+frame of the train and then you want to
+
+ align:start position:0%
+frame of the train and then you want to
+ 
+
+ align:start position:0%
+frame of the train and then you want to
+describe the very same events or
+
+ align:start position:0%
+describe the very same events or
+ 
+
+ align:start position:0%
+describe the very same events or
+sequence of events
+
+ align:start position:0%
+sequence of events
+ 
+
+ align:start position:0%
+sequence of events
+in
+
+ align:start position:0%
+in
+ 
+
+ align:start position:0%
+in
+the frame of the stationary train
+
+ align:start position:0%
+the frame of the stationary train
+ 
+
+ align:start position:0%
+the frame of the stationary train
+station
+
+ align:start position:0%
+station
+ 
+
+ align:start position:0%
+station
+all right let's look at a specific
+
+ align:start position:0%
+all right let's look at a specific
+ 
+
+ align:start position:0%
+all right let's look at a specific
+example
+
+ align:start position:0%
+example
+ 
+
+ align:start position:0%
+example
+here again our professor is exploding at
+
+ align:start position:0%
+here again our professor is exploding at
+ 
+
+ align:start position:0%
+here again our professor is exploding at
+a time
+
+ align:start position:0%
+a time
+ 
+
+ align:start position:0%
+a time
+tp
+
+ align:start position:0%
+tp
+ 
+
+ align:start position:0%
+tp
+at xp yp and zp
+
+ align:start position:0%
+at xp yp and zp
+ 
+
+ align:start position:0%
+at xp yp and zp
+to make this a little bit easier
+
+ align:start position:0%
+to make this a little bit easier
+ 
+
+ align:start position:0%
+to make this a little bit easier
+we define at time t equals zero the
+
+ align:start position:0%
+we define at time t equals zero the
+ 
+
+ align:start position:0%
+we define at time t equals zero the
+origin of the two frames coincide that
+
+ align:start position:0%
+origin of the two frames coincide that
+ 
+
+ align:start position:0%
+origin of the two frames coincide that
+just means that
+
+ align:start position:0%
+just means that
+ 
+
+ align:start position:0%
+just means that
+at the origin we have two clocks two
+
+ align:start position:0%
+at the origin we have two clocks two
+ 
+
+ align:start position:0%
+at the origin we have two clocks two
+watches and we make sure that they're
+
+ align:start position:0%
+watches and we make sure that they're
+ 
+
+ align:start position:0%
+watches and we make sure that they're
+synchronized
+
+ align:start position:0%
+synchronized
+ 
+
+ align:start position:0%
+synchronized
+right and then you know my watch stays
+
+ align:start position:0%
+right and then you know my watch stays
+ 
+
+ align:start position:0%
+right and then you know my watch stays
+with me and then there's a second watch
+
+ align:start position:0%
+with me and then there's a second watch
+ 
+
+ align:start position:0%
+with me and then there's a second watch
+maybe with you um
+
+ align:start position:0%
+maybe with you um
+ 
+
+ align:start position:0%
+maybe with you um
+which
+
+ align:start position:0%
+which
+ 
+
+ align:start position:0%
+which
+you know
+
+ align:start position:0%
+you know
+ 
+
+ align:start position:0%
+you know
+moves along and those are great watches
+
+ align:start position:0%
+moves along and those are great watches
+ 
+
+ align:start position:0%
+moves along and those are great watches
+they're synchronized
+
+ align:start position:0%
+they're synchronized
+ 
+
+ align:start position:0%
+they're synchronized
+you also want to simplify you can always
+
+ align:start position:0%
+you also want to simplify you can always
+ 
+
+ align:start position:0%
+you also want to simplify you can always
+define the
+
+ align:start position:0%
+define the
+ 
+
+ align:start position:0%
+define the
+direction of our coordinate system such
+
+ align:start position:0%
+direction of our coordinate system such
+ 
+
+ align:start position:0%
+direction of our coordinate system such
+that the velocity
+
+ align:start position:0%
+that the velocity
+ 
+
+ align:start position:0%
+that the velocity
+the relative velocity between the two
+
+ align:start position:0%
+the relative velocity between the two
+ 
+
+ align:start position:0%
+the relative velocity between the two
+reference frame is in one specific
+
+ align:start position:0%
+reference frame is in one specific
+ 
+
+ align:start position:0%
+reference frame is in one specific
+direction here i decided to use x i
+
+ align:start position:0%
+direction here i decided to use x i
+ 
+
+ align:start position:0%
+direction here i decided to use x i
+could have used y and z and i could
+
+ align:start position:0%
+could have used y and z and i could
+ 
+
+ align:start position:0%
+could have used y and z and i could
+rotate them
+
+ align:start position:0%
+rotate them
+ 
+
+ align:start position:0%
+rotate them
+rotate the coordinate systems or the
+
+ align:start position:0%
+rotate the coordinate systems or the
+ 
+
+ align:start position:0%
+rotate the coordinate systems or the
+relative movement of the coordinate
+
+ align:start position:0%
+relative movement of the coordinate
+ 
+
+ align:start position:0%
+relative movement of the coordinate
+systems in any way it's just a
+
+ align:start position:0%
+systems in any way it's just a
+ 
+
+ align:start position:0%
+systems in any way it's just a
+simplification here
+
+ align:start position:0%
+simplification here
+ 
+
+ align:start position:0%
+simplification here
+when i do that i can rewrite this event
+
+ align:start position:0%
+when i do that i can rewrite this event
+ 
+
+ align:start position:0%
+when i do that i can rewrite this event
+p
+
+ align:start position:0%
+p
+ 
+
+ align:start position:0%
+p
+in the s s
+
+ align:start position:0%
+in the s s
+ 
+
+ align:start position:0%
+in the s s
+prime frame through the s frame in the
+
+ align:start position:0%
+prime frame through the s frame in the
+ 
+
+ align:start position:0%
+prime frame through the s frame in the
+following way so for x we find
+
+ align:start position:0%
+following way so for x we find
+ 
+
+ align:start position:0%
+following way so for x we find
+that x p is given by x prime p is given
+
+ align:start position:0%
+that x p is given by x prime p is given
+ 
+
+ align:start position:0%
+that x p is given by x prime p is given
+by x p minus v the velocity relative
+
+ align:start position:0%
+by x p minus v the velocity relative
+ 
+
+ align:start position:0%
+by x p minus v the velocity relative
+velocity
+
+ align:start position:0%
+velocity
+ 
+
+ align:start position:0%
+velocity
+i could put a little label x here
+
+ align:start position:0%
+i could put a little label x here
+ 
+
+ align:start position:0%
+i could put a little label x here
+times t p
+
+ align:start position:0%
+times t p
+ 
+
+ align:start position:0%
+times t p
+and then for the y coordinates and the z
+
+ align:start position:0%
+and then for the y coordinates and the z
+ 
+
+ align:start position:0%
+and then for the y coordinates and the z
+coordinates there's no change
+
+ align:start position:0%
+coordinates there's no change
+ 
+
+ align:start position:0%
+coordinates there's no change
+for the time intuitively you say that
+
+ align:start position:0%
+for the time intuitively you say that
+ 
+
+ align:start position:0%
+for the time intuitively you say that
+just two watches they run with the same
+
+ align:start position:0%
+just two watches they run with the same
+ 
+
+ align:start position:0%
+just two watches they run with the same
+speed
+
+ align:start position:0%
+speed
+ 
+
+ align:start position:0%
+speed
+um meaning that the time in both frames
+
+ align:start position:0%
+um meaning that the time in both frames
+ 
+
+ align:start position:0%
+um meaning that the time in both frames
+for the same events are the same
+
+ align:start position:0%
+for the same events are the same
+ 
+
+ align:start position:0%
+for the same events are the same
+so now i'm asking you if you're watching
+
+ align:start position:0%
+so now i'm asking you if you're watching
+ 
+
+ align:start position:0%
+so now i'm asking you if you're watching
+this video
+
+ align:start position:0%
+this video
+ 
+
+ align:start position:0%
+this video
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+to find the velocity and acceleration it
+
+ align:start position:0%
+to find the velocity and acceleration it
+ 
+
+ align:start position:0%
+to find the velocity and acceleration it
+might be good to stop and just write
+
+ align:start position:0%
+might be good to stop and just write
+ 
+
+ align:start position:0%
+might be good to stop and just write
+this down
+
+ align:start position:0%
+this down
+ 
+
+ align:start position:0%
+this down
+so find the velocity and acceleration of
+
+ align:start position:0%
+so find the velocity and acceleration of
+ 
+
+ align:start position:0%
+so find the velocity and acceleration of
+the s prime of s prime expressed by the
+
+ align:start position:0%
+the s prime of s prime expressed by the
+ 
+
+ align:start position:0%
+the s prime of s prime expressed by the
+s coordinates let's try to do that
+
+ align:start position:0%
+s coordinates let's try to do that
+ 
+
+ align:start position:0%
+s coordinates let's try to do that
+so first we built the derivative
+
+ align:start position:0%
+so first we built the derivative
+ 
+
+ align:start position:0%
+so first we built the derivative
+dx prime dt prime which is our velocity
+
+ align:start position:0%
+dx prime dt prime which is our velocity
+ 
+
+ align:start position:0%
+dx prime dt prime which is our velocity
+that's the velocity of an object in my
+
+ align:start position:0%
+that's the velocity of an object in my
+ 
+
+ align:start position:0%
+that's the velocity of an object in my
+prime frame
+
+ align:start position:0%
+prime frame
+ 
+
+ align:start position:0%
+prime frame
+and that's given by d dt
+
+ align:start position:0%
+and that's given by d dt
+ 
+
+ align:start position:0%
+and that's given by d dt
+i can just
+
+ align:start position:0%
+i can just
+ 
+
+ align:start position:0%
+i can just
+do that here because the times are the
+
+ align:start position:0%
+do that here because the times are the
+ 
+
+ align:start position:0%
+do that here because the times are the
+same
+
+ align:start position:0%
+same
+ 
+
+ align:start position:0%
+same
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+times x minus vt
+
+ align:start position:0%
+times x minus vt
+ 
+
+ align:start position:0%
+times x minus vt
+that's
+
+ align:start position:0%
+that's
+ 
+
+ align:start position:0%
+that's
+x u x the velocity in my s frame minus v
+
+ align:start position:0%
+x u x the velocity in my s frame minus v
+ 
+
+ align:start position:0%
+x u x the velocity in my s frame minus v
+that's really what you expect you just
+
+ align:start position:0%
+that's really what you expect you just
+ 
+
+ align:start position:0%
+that's really what you expect you just
+subtract or add the velocities
+
+ align:start position:0%
+subtract or add the velocities
+ 
+
+ align:start position:0%
+subtract or add the velocities
+if i then build the acceleration i have
+
+ align:start position:0%
+if i then build the acceleration i have
+ 
+
+ align:start position:0%
+if i then build the acceleration i have
+to build the derivative of u x prime
+
+ align:start position:0%
+to build the derivative of u x prime
+ 
+
+ align:start position:0%
+to build the derivative of u x prime
+which is our acceleration
+
+ align:start position:0%
+which is our acceleration
+ 
+
+ align:start position:0%
+which is our acceleration
+in the prime frame
+
+ align:start position:0%
+in the prime frame
+ 
+
+ align:start position:0%
+in the prime frame
+um here again i just do this in x
+
+ align:start position:0%
+um here again i just do this in x
+ 
+
+ align:start position:0%
+um here again i just do this in x
+direction because the solution for the y
+
+ align:start position:0%
+direction because the solution for the y
+ 
+
+ align:start position:0%
+direction because the solution for the y
+direction and z direction by trivial so
+
+ align:start position:0%
+direction and z direction by trivial so
+ 
+
+ align:start position:0%
+direction and z direction by trivial so
+now i find d u x
+
+ align:start position:0%
+now i find d u x
+ 
+
+ align:start position:0%
+now i find d u x
+dt minus dv dt
+
+ align:start position:0%
+dt minus dv dt
+ 
+
+ align:start position:0%
+dt minus dv dt
+now the velocity as we defined between
+
+ align:start position:0%
+now the velocity as we defined between
+ 
+
+ align:start position:0%
+now the velocity as we defined between
+the two reference frame is constant
+
+ align:start position:0%
+the two reference frame is constant
+ 
+
+ align:start position:0%
+the two reference frame is constant
+therefore this is zero meaning that the
+
+ align:start position:0%
+therefore this is zero meaning that the
+ 
+
+ align:start position:0%
+therefore this is zero meaning that the
+velocity of the accelerations in the two
+
+ align:start position:0%
+velocity of the accelerations in the two
+ 
+
+ align:start position:0%
+velocity of the accelerations in the two
+frames are the same
+
+ align:start position:0%
+frames are the same
+ 
+
+ align:start position:0%
+frames are the same
+the accelerations are the same
+
+ align:start position:0%
+the accelerations are the same
+ 
+
+ align:start position:0%
+the accelerations are the same
+that means that
+
+ align:start position:0%
+that means that
+ 
+
+ align:start position:0%
+that means that
+the uh forces in the two frames are the
+
+ align:start position:0%
+the uh forces in the two frames are the
+ 
+
+ align:start position:0%
+the uh forces in the two frames are the
+same and that means that the forces
+
+ align:start position:0%
+same and that means that the forces
+ 
+
+ align:start position:0%
+same and that means that the forces
+or the accelerations are invariant they
+
+ align:start position:0%
+or the accelerations are invariant they
+ 
+
+ align:start position:0%
+or the accelerations are invariant they
+do not change
+
+ align:start position:0%
+do not change
+ 
+
+ align:start position:0%
+do not change
+based on the reference frame i use
+
+ align:start position:0%
+based on the reference frame i use
+ 
+
+ align:start position:0%
+based on the reference frame i use
+so now
+
+ align:start position:0%
+so now
+ 
+
+ align:start position:0%
+so now
+coming back to the example we discussed
+
+ align:start position:0%
+coming back to the example we discussed
+ 
+
+ align:start position:0%
+coming back to the example we discussed
+in our very first lecture
+
+ align:start position:0%
+in our very first lecture
+ 
+
+ align:start position:0%
+in our very first lecture
+uh your experiment in the train car
+
+ align:start position:0%
+uh your experiment in the train car
+ 
+
+ align:start position:0%
+uh your experiment in the train car
+as
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the velocity
+
+ align:start position:0%
+the velocity
+ 
+
+ align:start position:0%
+the velocity
+between those two frames
+
+ align:start position:0%
+between those two frames
+ 
+
+ align:start position:0%
+between those two frames
+the frame
+
+ align:start position:0%
+the frame
+ 
+
+ align:start position:0%
+the frame
+in your car
+
+ align:start position:0%
+in your car
+ 
+
+ align:start position:0%
+in your car
+or a second frame
+
+ align:start position:0%
+or a second frame
+ 
+
+ align:start position:0%
+or a second frame
+are constant there is no way to tell
+
+ align:start position:0%
+are constant there is no way to tell
+ 
+
+ align:start position:0%
+are constant there is no way to tell
+whether or not your train car is moving
+
+ align:start position:0%
+whether or not your train car is moving
+ 
+
+ align:start position:0%
+whether or not your train car is moving
+or not
+
+ align:start position:0%
+or not
+ 
+
+ align:start position:0%
+or not
+that is only true as long as the
+
+ align:start position:0%
+that is only true as long as the
+ 
+
+ align:start position:0%
+that is only true as long as the
+velocities are constant and and and
+
+ align:start position:0%
+velocities are constant and and and
+ 
+
+ align:start position:0%
+velocities are constant and and and
+unchanged constantly
+
+ align:start position:0%
+unchanged constantly
+ 
+
+ align:start position:0%
+unchanged constantly
+so in summary
+
+ align:start position:0%
+so in summary
+ 
+
+ align:start position:0%
+so in summary
+in newton's mechanics time
+
+ align:start position:0%
+in newton's mechanics time
+ 
+
+ align:start position:0%
+in newton's mechanics time
+and accelerations are invariant and
+
+ align:start position:0%
+and accelerations are invariant and
+ 
+
+ align:start position:0%
+and accelerations are invariant and
+therefore also the forces there is no
+
+ align:start position:0%
+therefore also the forces there is no
+ 
+
+ align:start position:0%
+therefore also the forces there is no
+inertial frame which is above another
+
+ align:start position:0%
+inertial frame which is above another
+ 
+
+ align:start position:0%
+inertial frame which is above another
+one
+
+ align:start position:0%
+one
+ 
+
+ align:start position:0%
+one
+so you can pick one or you can pick
+
+ align:start position:0%
+so you can pick one or you can pick
+ 
+
+ align:start position:0%
+so you can pick one or you can pick
+another one there is no difference in
+
+ align:start position:0%
+another one there is no difference in
+ 
+
+ align:start position:0%
+another one there is no difference in
+the descriptions of the physics between
+
+ align:start position:0%
+the descriptions of the physics between
+ 
+
+ align:start position:0%
+the descriptions of the physics between
+those two frames
\ No newline at end of file
diff --git a/Y9r9dO7KQj4.txt b/Y9r9dO7KQj4.txt
new file mode 100644
index 0000000000000000000000000000000000000000..b31699f014d59dfbe0988a91a9acbdaac1908949
--- /dev/null
+++ b/Y9r9dO7KQj4.txt
@@ -0,0 +1,834 @@
+PROFESSOR: Hi.
+
+Today I'd like to talk to you
+about some notable aspects of
+
+Python that you'll encounter in
+the 6.01 software, as well
+
+as in the general sense when
+working with Python.
+
+A lot of these little tidbits
+of Python have some
+
+interesting history associated
+with them, especially related
+
+to the history of computer
+science.
+
+And also, I want to indicate
+some things that tend to mess
+
+up, especially, first time
+programmers, but also
+
+especially people that
+are new to Python.
+
+First, I'd like to bring
+us back to last week.
+
+We were talking about
+object-oriented programming
+
+and inheritance.
+
+Object-oriented programming
+is a programming paradigm.
+
+It's in the same category as
+imperative programming or
+
+functional programming.
+
+And you might say I have a good
+sense of the fact that in
+
+object-oriented programming,
+everything is an object.
+
+But I don't really have a good
+sense of what constitutes
+
+imperative programming or
+functional programming.
+
+I'm going to focus on functional
+programming right
+
+now, because it has more of a
+historic root in the academic
+
+development of computer
+science.
+
+Functional programming is like
+object-oriented programming in
+
+that everything is a function.
+
+It refers to the idea that you
+want to write as much of your
+
+code as possible in a purely
+functional manner.
+
+And in particular, you're
+looking for the ability to
+
+avoid things like side-effects
+or enable many different kinds
+
+of evaluation.
+
+Those kinds of things are not
+the subject of this course,
+
+but I think they're worth noting
+to figure out why we're
+
+bothering learning about things
+like lambdas and list
+
+comprehensions in
+the first place.
+
+Speaking of which, the first
+thing we need to talk about
+
+before we even talk about things
+like lambdas and list
+
+comprehensions, is the concept
+that in Python,
+
+everything is an object.
+
+But because functions are
+first-class objects, we can
+
+also treat Python to a large
+extent like a functional
+
+programming language.
+
+What do I mean when
+I say functions
+
+are first class objects?
+
+I mean that a function
+can be the return
+
+value of another function.
+
+I mean that the function can be
+passed in as an argument to
+
+a function.
+
+And I mean that functions can be
+assigned variable names and
+
+manipulated the same way that we
+manipulate any other piece
+
+of data structure.
+
+This is important, because
+if you want higher order
+
+functions or functions that
+actually modify or use other
+
+functions as a part of you know,
+whatever it is they do,
+
+then you need to be able to
+interact with the function
+
+like it's any other object,
+in part pass it in
+
+or return it out.
+
+Let's look at an example.
+
+So let's say I start off with a
+very basic function, right?
+
+If you want to square some
+sort of value, probably
+
+numeric in this case, then
+all you have to do is
+
+multiply it by itself.
+
+Pretty simple.
+
+Good place to start.
+
+As a consequence of the idea
+that functions are first class
+
+objects, I can write a function
+that takes in a
+
+function as an argument and
+then develops a return
+
+function that uses the
+function that I
+
+passed in, on itself.
+
+So any arguments that I would
+pass to someFunction, I would
+
+pass into someFunction, take
+the return value of this
+
+function call, and then pass
+that into someFunction again.
+
+That's what returnFunction
+does.
+
+And down here, I return
+returnFunction.
+
+Note that the object
+type of this
+
+return value is a function.
+
+So once I have returnFunction,
+I can actually pass it
+
+arguments, have them run through
+someFunction, not once
+
+but twice, and then get out a
+value that's of the return
+
+type of someFunction.
+
+Note that I made some
+assumptions while
+
+writing this function.
+
+First, I've assumed that
+someFunction returns out the
+
+same number of arguments, and
+either accept an arbitrary
+
+number of arguments or accepts
+the same number of arguments
+
+as it puts out.
+
+The other assumption that I've
+made is that the data type
+
+that someFunction returns is
+the same as the data types
+
+that someFunction accepts.
+
+Or the things that someFunction
+does to its
+
+arguments can be done to
+multiple kinds of arguments.
+
+But that's a whole different
+argument.
+
+Right now, we're just focusing
+on the fact that we pass in
+
+some arbitrary number of
+arguments, call someFunction
+
+on it, call someFunction again
+on the return value of this,
+
+and return that as something you
+can do to whatever it is,
+
+someFunction operates on.
+
+OK.
+
+Let's review an example, because
+I promise it'll be
+
+more clear.
+
+Let's say f is going to be the
+
+composition, a square on itself.
+
+If I do that, I end up with a
+function that operates on an
+
+arbitrary number
+of arguments--
+
+that's not true.
+
+I end up with a copy of square
+that takes in the same number
+
+of arguments as square
+called on itself.
+
+So here a square is substituted
+for someFunction.
+
+Here a square is called on
+that call of square.
+
+And here is what f
+is assigned to.
+
+So when I call f of
+2, I'm going to
+
+substitute 2 in for args.
+
+I'm going to call
+square on args.
+
+If I call square on
+args, I get out 4.
+
+And if I call square on args
+again, or if I call square of
+
+args where args is defined as
+the return value of this, then
+
+I'm going to call square
+on 4, I'll square 4,
+
+and I'll get 16.
+
+Take a second to type it into
+IDLE, and make it make sense
+
+to yourself.
+
+All of this code
+should compile.
+
+Mess around with the parameters,
+if you're having
+
+trouble convincing yourself
+that it does.
+
+Ok.
+
+Now I think we're ready
+to talk about lambdas.
+
+If you can pass in functions as
+arguments or return them as
+
+values or assign them to
+variable names and just treat
+
+them like any other data type,
+then you should be able to
+
+treat them as some sort
+of raw value.
+
+And that's where lambdas
+come in.
+
+Lambda is a key word in Python
+that tells you you're about to
+
+use a function that you have not
+given any sort of name or
+
+defined in any place in your
+code or environment
+
+beforehand.
+
+You're just going to start
+talking about something that
+
+you would like to do to a given
+number of arguments, and
+
+then what you want
+to return out.
+
+Lambda has roots in lambda
+calculus which, if you're
+
+familiar with the history of
+computer science, you've
+
+probably heard of.
+
+Now might be a good time to look
+up lambda calculus, if
+
+you've never heard it before
+or possibly Alonzo Church.
+
+But it's still available in code
+today, which is really
+
+cool, and speaks to the
+continuing power or at least
+
+recognition of importance of
+functional programming.
+
+As I said before, the idea with
+lambda is that you could
+
+write an anonymous function.
+
+Over here, in order to write a
+function that's squared, I had
+
+to write out a define line.
+
+And because Python uses
+indentation, because in
+
+Python, indentation carries
+meaning, I'd have to enter and
+
+return over to a next line--
+
+I'm actually not sure if
+that's strictly true.
+
+I think you can do def
+square x, return
+
+x, but I'm not positive.
+
+I've only seen it written
+like this.
+
+And I think it's because in the
+general sense, people try
+
+to respect things like
+convention and
+
+readability in Python.
+
+If you're using lambda, people
+already know that you want to
+
+describe a function
+really quickly.
+
+Or you want to describe
+function without
+
+assigning it any name.
+
+Therefore, the two most common
+uses you'll see of lambda is
+
+when you want a really fast
+function and you don't want to
+
+spend extra time or lines
+writing out that function.
+
+It's pretty clear what
+this is going to do.
+
+Or if, in a particular
+sense, you need
+
+an anonymous function.
+
+You don't want to assign
+a name or memory space
+
+associated with that function.
+
+Note instead of using square,
+I can just write out this.
+
+So I saved two lines of
+code defining square.
+
+And then I don't have to refer
+back to some earlier part of
+
+the code in order to understand
+
+what this line does.
+
+Pretty cool.
+
+All right.
+
+So there's functions of
+first class objects.
+
+There's lambda.
+
+Let's talk about how to
+use lambdas on lists.
+
+In Python, you'll end up doing
+a lot of list manipulation.
+
+One of the best uses of
+anonymized functions in any
+
+functional programming language
+is the ability to
+
+manipulate lists in a line.
+
+If I've defined just a pretty
+straightforward list right
+
+here, I can use functions like
+map filter and reduce to--
+
+in one line--
+
+take a list, apply a function to
+every element in that list,
+
+and then return a copy of
+the result of that list.
+
+I didn't have to write a
+separate function to do the
+
+list handling.
+
+I didn't have to write a
+separate function to multiply
+
+the list by two.
+
+And I've communicated what I'm
+doing effectively to people
+
+that are used to functional
+programming.
+
+So if you type this line in,
+you should end up with a
+
+return in interactive mode of
+every element in this list
+
+multiplied by two.
+
+Now's a good time to try.
+
+Once you've done that, I also
+recommend looking at the
+
+original copied demolist.
+
+Note that this is unaltered.
+
+Map actually returned a new data
+structure that represents
+
+performing this function
+on this list.
+
+This becomes important later
+when I explain aliasing, but I
+
+will do that in about
+two minutes.
+
+If we want to get even more
+elegant, we can use list
+
+comprehensions.
+
+List comprehensions--
+
+if you ask somebody where list
+comprehensions are from,
+
+they'll probably say Haskell,
+because that is the most
+
+popular use of list
+comprehensions, in terms of
+
+pure lazy functional
+programming.
+
+But it actually goes back
+further than that, and is in
+
+Small Talk, and then something
+from the '60s.
+
+I can't remember the name
+of it right now.
+
+They're really nice because
+they borrow a syntactic
+
+approach from mathematicians.
+
+This looks a lot like
+set notation.
+
+And when you read this, you
+can probably tell that the
+
+list listComprehension is going
+to describe a set of
+
+points from 1 to 4.
+
+But you accomplish that in
+possibly one line of code.
+
+I've written it on three here
+because I wanted to keep it in
+
+this space.
+
+But it's really concise.
+
+If you type this into IDLE,
+you should see the kind of
+
+list that it returns,
+and also what's
+
+listComprehension is now--
+
+what now constitutes
+listComprehension.
+
+You can use listComprehensions
+with functions like map and
+
+filter and reduce.
+
+And, along with the anonymized
+functions, all of these tools
+
+provide you with a lot of
+functionality in a very short
+
+amount of space.
+
+It's also good to be able to
+recognize what's going on when
+
+you see something like this
+or something like this.
+
+Because you'll probably run into
+it in, in particular, a
+
+lot with Lisp code, but also in
+the artificial intelligence
+
+community in particular.
+
+Ok.
+
+We've talked about all that.
+
+Let's take a second to talk
+about the fact that lists are
+
+actually mutable, and what that
+means, and what things
+
+you have to be careful about if
+you're going to be working
+
+with mutable objects.
+
+If you're new to programming,
+or you're new to Python,
+
+you've probably already
+worked with some of
+
+these data types, right?
+
+Any numbers, any strings,
+any tuples,
+
+are going to be immutable.
+
+What that means is if you have
+a variable and you have a
+
+second variable that has a
+different assignment line
+
+associated with it-- right?
+
+I haven't assigned
+g to h here.
+
+I've just signed g to "hello"
+and h to "hello."
+
+If you look at the space in
+memory that Python associates
+
+with both objects, they point
+to the same place.
+
+This is the definition of
+an immutable object.
+
+When g points to "hello" and h
+points to "hello," they both
+
+point to the same place.
+
+If x points to 5 and y points to
+5, they're both pointing to
+
+the same place.
+
+If you point x at 6,
+it now points to a
+
+different memory address.
+
+This gets confounded
+when you're talking
+
+about mutable objects.
+
+The problem with mutable objects
+is that you select a
+
+memory space to contain the
+object or memory ID in Python
+
+to contain the object.
+
+And then that object is
+changed in place.
+
+You can use this to your
+advantage but it can
+
+also mess with you.
+
+And here's how.
+
+Let's say I assigned
+a to a small list.
+
+And I also assigned b to a.
+
+b and a now point at
+the same place.
+
+If I manipulate b, and I'm--
+
+excuse me-- still working with
+an immutable object, or excuse
+
+me, if I'm still working with
+a mutable object, the object
+
+in that memory address
+has been altered.
+
+And b and a still point to
+the same place in memory.
+
+So if I look at a, it's going to
+look like b, which is going
+
+to look like 1, 2, 3, 4 --
+
+which is not what I assigned
+a to originally.
+
+Again, can be powerful, but you
+have to keep it in mind.
+
+And it might start to mess with,
+in particular, the 6.01
+
+software when you're dealing
+with state machines.
+
+In order to get around this, you
+can create a copy of the
+
+list and then modify the copy.
+
+This is actually
+what map does.
+
+If you want to do it, the
+easiest way to do it on the
+
+first layer is to specify
+the index into the
+
+list with no bounce.
+
+It'll copy the whole thing.
+
+There's also a Python library
+copy or deep copy, if you want
+
+to copy lists of lists of
+lists of lists of lists.
+
+And just to clarify, you'll note
+that after you assign c
+
+to a copy of a, c and a occupy
+different memory places.
+
+So if you modify c, a will
+retain its original value.
+
+I think that's all the
+notable things I have
+
+to say about Python.
+
+and gives us enough power to do
+some really powerful list
+
+manipulation or array
+manipulation, and covers what
+
+we want to say about functional
+programming before
+
+we get into the notion
+of state, which I'll
+
+talk about next time.
\ No newline at end of file
diff --git a/YS-o3X0tazU.txt b/YS-o3X0tazU.txt
new file mode 100644
index 0000000000000000000000000000000000000000..bfd9657975a4b8a46d53267a2fb20f11be88ebb2
--- /dev/null
+++ b/YS-o3X0tazU.txt
@@ -0,0 +1,987 @@
+align:start position:0%
+ 
+okay very briefly I sports a project we
+
+ align:start position:0%
+okay very briefly I sports a project we
+ 
+
+ align:start position:0%
+okay very briefly I sports a project we
+are doing it the sensible City lab but
+
+ align:start position:0%
+are doing it the sensible City lab but
+ 
+
+ align:start position:0%
+are doing it the sensible City lab but
+let me tell you a couple words about
+
+ align:start position:0%
+let me tell you a couple words about
+ 
+
+ align:start position:0%
+let me tell you a couple words about
+sensible city lab it's a new research
+
+ align:start position:0%
+sensible city lab it's a new research
+ 
+
+ align:start position:0%
+sensible city lab it's a new research
+group here at MIT it's in between the
+
+ align:start position:0%
+group here at MIT it's in between the
+ 
+
+ align:start position:0%
+group here at MIT it's in between the
+media lab and urban tourism planning
+
+ align:start position:0%
+media lab and urban tourism planning
+ 
+
+ align:start position:0%
+media lab and urban tourism planning
+well what do we do there what we do is a
+
+ align:start position:0%
+well what do we do there what we do is a
+ 
+
+ align:start position:0%
+well what do we do there what we do is a
+look at this that's that's yesterday's
+
+ align:start position:0%
+look at this that's that's yesterday's
+ 
+
+ align:start position:0%
+look at this that's that's yesterday's
+wireless that's varco knees Cape Cod
+
+ align:start position:0%
+wireless that's varco knees Cape Cod
+ 
+
+ align:start position:0%
+wireless that's varco knees Cape Cod
+station look at all of that steel and
+
+ align:start position:0%
+station look at all of that steel and
+ 
+
+ align:start position:0%
+station look at all of that steel and
+engine and energy and the amount of
+
+ align:start position:0%
+engine and energy and the amount of
+ 
+
+ align:start position:0%
+engine and energy and the amount of
+effort just to transmit a few bits of
+
+ align:start position:0%
+effort just to transmit a few bits of
+ 
+
+ align:start position:0%
+effort just to transmit a few bits of
+information across the Atlantic now look
+
+ align:start position:0%
+information across the Atlantic now look
+ 
+
+ align:start position:0%
+information across the Atlantic now look
+at today's wireless it's more like this
+
+ align:start position:0%
+at today's wireless it's more like this
+ 
+
+ align:start position:0%
+at today's wireless it's more like this
+and you can actually transmit much more
+
+ align:start position:0%
+and you can actually transmit much more
+ 
+
+ align:start position:0%
+and you can actually transmit much more
+information using that and what we're
+
+ align:start position:0%
+information using that and what we're
+ 
+
+ align:start position:0%
+information using that and what we're
+doing is sort of we think in a creative
+
+ align:start position:0%
+doing is sort of we think in a creative
+ 
+
+ align:start position:0%
+doing is sort of we think in a creative
+way the interface between people mobile
+
+ align:start position:0%
+way the interface between people mobile
+ 
+
+ align:start position:0%
+way the interface between people mobile
+technology and the city now concerning I
+
+ align:start position:0%
+technology and the city now concerning I
+ 
+
+ align:start position:0%
+technology and the city now concerning I
+spots this project is based on the MIT
+
+ align:start position:0%
+spots this project is based on the MIT
+ 
+
+ align:start position:0%
+spots this project is based on the MIT
+campus that's what you see there so you
+
+ align:start position:0%
+campus that's what you see there so you
+ 
+
+ align:start position:0%
+campus that's what you see there so you
+most of you I'm sure familiar Bob stone
+
+ align:start position:0%
+most of you I'm sure familiar Bob stone
+ 
+
+ align:start position:0%
+most of you I'm sure familiar Bob stone
+MIT and the interesting thing is that if
+
+ align:start position:0%
+MIT and the interesting thing is that if
+ 
+
+ align:start position:0%
+MIT and the interesting thing is that if
+you talk to anybody at MIT they will
+
+ align:start position:0%
+you talk to anybody at MIT they will
+ 
+
+ align:start position:0%
+you talk to anybody at MIT they will
+tell you there's a big revolution
+
+ align:start position:0%
+tell you there's a big revolution
+ 
+
+ align:start position:0%
+tell you there's a big revolution
+happening and this revolution is in the
+
+ align:start position:0%
+happening and this revolution is in the
+ 
+
+ align:start position:0%
+happening and this revolution is in the
+way people live and work and it's
+
+ align:start position:0%
+way people live and work and it's
+ 
+
+ align:start position:0%
+way people live and work and it's
+brought by laptop computers and Wi-Fi so
+
+ align:start position:0%
+brought by laptop computers and Wi-Fi so
+ 
+
+ align:start position:0%
+brought by laptop computers and Wi-Fi so
+if you look at this this is how people
+
+ align:start position:0%
+if you look at this this is how people
+ 
+
+ align:start position:0%
+if you look at this this is how people
+used to work here and this is more like
+
+ align:start position:0%
+used to work here and this is more like
+ 
+
+ align:start position:0%
+used to work here and this is more like
+today now this is a bit biased as you
+
+ align:start position:0%
+today now this is a bit biased as you
+ 
+
+ align:start position:0%
+today now this is a bit biased as you
+see we we could find the worst possible
+
+ align:start position:0%
+see we we could find the worst possible
+ 
+
+ align:start position:0%
+see we we could find the worst possible
+image of a computer room dull boring no
+
+ align:start position:0%
+image of a computer room dull boring no
+ 
+
+ align:start position:0%
+image of a computer room dull boring no
+natural light and and this like a sunny
+
+ align:start position:0%
+natural light and and this like a sunny
+ 
+
+ align:start position:0%
+natural light and and this like a sunny
+day it's not like today but the thing is
+
+ align:start position:0%
+day it's not like today but the thing is
+ 
+
+ align:start position:0%
+day it's not like today but the thing is
+that there's a big change and what we
+
+ align:start position:0%
+that there's a big change and what we
+ 
+
+ align:start position:0%
+that there's a big change and what we
+are trying to do with I sports is try to
+
+ align:start position:0%
+are trying to do with I sports is try to
+ 
+
+ align:start position:0%
+are trying to do with I sports is try to
+define and see how the change is
+
+ align:start position:0%
+define and see how the change is
+ 
+
+ align:start position:0%
+define and see how the change is
+happening and quantify this by allowing
+
+ align:start position:0%
+happening and quantify this by allowing
+ 
+
+ align:start position:0%
+happening and quantify this by allowing
+people to locate themselves actually
+
+ align:start position:0%
+people to locate themselves actually
+ 
+
+ align:start position:0%
+people to locate themselves actually
+with a few meter accuracy using the
+
+ align:start position:0%
+with a few meter accuracy using the
+ 
+
+ align:start position:0%
+with a few meter accuracy using the
+Wi-Fi network and so it's a unique case
+
+ align:start position:0%
+Wi-Fi network and so it's a unique case
+ 
+
+ align:start position:0%
+Wi-Fi network and so it's a unique case
+study that you are starting to monitor
+
+ align:start position:0%
+study that you are starting to monitor
+ 
+
+ align:start position:0%
+study that you are starting to monitor
+where we got 20,000 people in the MIT
+
+ align:start position:0%
+where we got 20,000 people in the MIT
+ 
+
+ align:start position:0%
+where we got 20,000 people in the MIT
+campus a big chunk urban chunk with
+
+ align:start position:0%
+campus a big chunk urban chunk with
+ 
+
+ align:start position:0%
+campus a big chunk urban chunk with
+3,000 access points that's quite a bit
+
+ align:start position:0%
+3,000 access points that's quite a bit
+ 
+
+ align:start position:0%
+3,000 access points that's quite a bit
+if you think that cities like
+
+ align:start position:0%
+if you think that cities like
+ 
+
+ align:start position:0%
+if you think that cities like
+Philadelphia actually are planning to
+
+ align:start position:0%
+Philadelphia actually are planning to
+ 
+
+ align:start position:0%
+Philadelphia actually are planning to
+cover all of this
+
+ align:start position:0%
+cover all of this
+ 
+
+ align:start position:0%
+cover all of this
+with Wi-Fi in the can in the next couple
+
+ align:start position:0%
+with Wi-Fi in the can in the next couple
+ 
+
+ align:start position:0%
+with Wi-Fi in the can in the next couple
+of years and that's less than three
+
+ align:start position:0%
+of years and that's less than three
+ 
+
+ align:start position:0%
+of years and that's less than three
+thousand less than the number we have of
+
+ align:start position:0%
+thousand less than the number we have of
+ 
+
+ align:start position:0%
+thousand less than the number we have of
+access point this high density means
+
+ align:start position:0%
+access point this high density means
+ 
+
+ align:start position:0%
+access point this high density means
+that we can locate everybody with just a
+
+ align:start position:0%
+that we can locate everybody with just a
+ 
+
+ align:start position:0%
+that we can locate everybody with just a
+few meters accuracy this is just a map
+
+ align:start position:0%
+few meters accuracy this is just a map
+ 
+
+ align:start position:0%
+few meters accuracy this is just a map
+with some of the access points and
+
+ align:start position:0%
+with some of the access points and
+ 
+
+ align:start position:0%
+with some of the access points and
+actually i'll show you the two marks for
+
+ align:start position:0%
+actually i'll show you the two marks for
+ 
+
+ align:start position:0%
+actually i'll show you the two marks for
+for the project you'll see at the museum
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+oops the first type of map is a map that
+
+ align:start position:0%
+oops the first type of map is a map that
+ 
+
+ align:start position:0%
+oops the first type of map is a map that
+shows you in real time the activity
+
+ align:start position:0%
+shows you in real time the activity
+ 
+
+ align:start position:0%
+shows you in real time the activity
+going on on the network and how many
+
+ align:start position:0%
+going on on the network and how many
+ 
+
+ align:start position:0%
+going on on the network and how many
+people are working in different parts of
+
+ align:start position:0%
+people are working in different parts of
+ 
+
+ align:start position:0%
+people are working in different parts of
+the campus so you get this type of map
+
+ align:start position:0%
+the campus so you get this type of map
+ 
+
+ align:start position:0%
+the campus so you get this type of map
+changing you don't see very well here
+
+ align:start position:0%
+changing you don't see very well here
+ 
+
+ align:start position:0%
+changing you don't see very well here
+but you see better the museum and the
+
+ align:start position:0%
+but you see better the museum and the
+ 
+
+ align:start position:0%
+but you see better the museum and the
+second map is this one that's like oops
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that's like the heartbeat of MIT now
+
+ align:start position:0%
+that's like the heartbeat of MIT now
+ 
+
+ align:start position:0%
+that's like the heartbeat of MIT now
+what you see here is total activity
+
+ align:start position:0%
+what you see here is total activity
+ 
+
+ align:start position:0%
+what you see here is total activity
+going on on the campus in real time and
+
+ align:start position:0%
+going on on the campus in real time and
+ 
+
+ align:start position:0%
+going on on the campus in real time and
+you see the past week so what you see
+
+ align:start position:0%
+you see the past week so what you see
+ 
+
+ align:start position:0%
+you see the past week so what you see
+here is all of MIT and that's actually a
+
+ align:start position:0%
+here is all of MIT and that's actually a
+ 
+
+ align:start position:0%
+here is all of MIT and that's actually a
+standard day you see people come in
+
+ align:start position:0%
+standard day you see people come in
+ 
+
+ align:start position:0%
+standard day you see people come in
+working nine to five and then actually
+
+ align:start position:0%
+working nine to five and then actually
+ 
+
+ align:start position:0%
+working nine to five and then actually
+students keeping them working quite late
+
+ align:start position:0%
+students keeping them working quite late
+ 
+
+ align:start position:0%
+students keeping them working quite late
+even even during iap and then you got a
+
+ align:start position:0%
+even even during iap and then you got a
+ 
+
+ align:start position:0%
+even even during iap and then you got a
+peek a peek and a minimum at 6am and
+
+ align:start position:0%
+peek a peek and a minimum at 6am and
+ 
+
+ align:start position:0%
+peek a peek and a minimum at 6am and
+then you got the next day it's
+
+ align:start position:0%
+then you got the next day it's
+ 
+
+ align:start position:0%
+then you got the next day it's
+interesting Friday Saturday and Sunday
+
+ align:start position:0%
+interesting Friday Saturday and Sunday
+ 
+
+ align:start position:0%
+interesting Friday Saturday and Sunday
+when most of the activity 925 activity
+
+ align:start position:0%
+when most of the activity 925 activity
+ 
+
+ align:start position:0%
+when most of the activity 925 activity
+disappears and actually you got just the
+
+ align:start position:0%
+disappears and actually you got just the
+ 
+
+ align:start position:0%
+disappears and actually you got just the
+remaining part of the curve happening
+
+ align:start position:0%
+remaining part of the curve happening
+ 
+
+ align:start position:0%
+remaining part of the curve happening
+activity is sweeping down in on friday
+
+ align:start position:0%
+activity is sweeping down in on friday
+ 
+
+ align:start position:0%
+activity is sweeping down in on friday
+evening people going out and on sunday
+
+ align:start position:0%
+evening people going out and on sunday
+ 
+
+ align:start position:0%
+evening people going out and on sunday
+when you're starting to panic again
+
+ align:start position:0%
+when you're starting to panic again
+ 
+
+ align:start position:0%
+when you're starting to panic again
+about monday in the next week then
+
+ align:start position:0%
+about monday in the next week then
+ 
+
+ align:start position:0%
+about monday in the next week then
+there's another peak and then what you
+
+ align:start position:0%
+there's another peak and then what you
+ 
+
+ align:start position:0%
+there's another peak and then what you
+see here you can do this in cui every
+
+ align:start position:0%
+see here you can do this in cui every
+ 
+
+ align:start position:0%
+see here you can do this in cui every
+room on the campus and what you see here
+
+ align:start position:0%
+room on the campus and what you see here
+ 
+
+ align:start position:0%
+room on the campus and what you see here
+for instance is this actual room and you
+
+ align:start position:0%
+for instance is this actual room and you
+ 
+
+ align:start position:0%
+for instance is this actual room and you
+see most of the week it was pretty no
+
+ align:start position:0%
+see most of the week it was pretty no
+ 
+
+ align:start position:0%
+see most of the week it was pretty no
+activity and look at today and today you
+
+ align:start position:0%
+activity and look at today and today you
+ 
+
+ align:start position:0%
+activity and look at today and today you
+can get that you get actually up to 25
+
+ align:start position:0%
+can get that you get actually up to 25
+ 
+
+ align:start position:0%
+can get that you get actually up to 25
+users which is the number of laptop i
+
+ align:start position:0%
+users which is the number of laptop i
+ 
+
+ align:start position:0%
+users which is the number of laptop i
+counted
+
+ align:start position:0%
+counted
+ 
+
+ align:start position:0%
+counted
+accounted earlier today of people
+
+ align:start position:0%
+accounted earlier today of people
+ 
+
+ align:start position:0%
+accounted earlier today of people
+connected to the wireless internet here
+
+ align:start position:0%
+connected to the wireless internet here
+ 
+
+ align:start position:0%
+connected to the wireless internet here
+and you sit here that's today Monday it
+
+ align:start position:0%
+and you sit here that's today Monday it
+ 
+
+ align:start position:0%
+and you sit here that's today Monday it
+will appear in a minute anyway you see
+
+ align:start position:0%
+will appear in a minute anyway you see
+ 
+
+ align:start position:0%
+will appear in a minute anyway you see
+the demo at yeah here you see the spike
+
+ align:start position:0%
+the demo at yeah here you see the spike
+ 
+
+ align:start position:0%
+the demo at yeah here you see the spike
+today today's activity and you see the
+
+ align:start position:0%
+today today's activity and you see the
+ 
+
+ align:start position:0%
+today today's activity and you see the
+demo at the museum just a couple of just
+
+ align:start position:0%
+demo at the museum just a couple of just
+ 
+
+ align:start position:0%
+demo at the museum just a couple of just
+a couple of things about just to
+
+ align:start position:0%
+a couple of things about just to
+ 
+
+ align:start position:0%
+a couple of things about just to
+conclude another project we have is
+
+ align:start position:0%
+conclude another project we have is
+ 
+
+ align:start position:0%
+conclude another project we have is
+actually with with a soccer team being
+
+ align:start position:0%
+actually with with a soccer team being
+ 
+
+ align:start position:0%
+actually with with a soccer team being
+Italian I am very proud of this project
+
+ align:start position:0%
+Italian I am very proud of this project
+ 
+
+ align:start position:0%
+Italian I am very proud of this project
+and it's with AC Milan and he were
+
+ align:start position:0%
+and it's with AC Milan and he were
+ 
+
+ align:start position:0%
+and it's with AC Milan and he were
+tracking actually players with a couple
+
+ align:start position:0%
+tracking actually players with a couple
+ 
+
+ align:start position:0%
+tracking actually players with a couple
+of centimeter accuracy in real time and
+
+ align:start position:0%
+of centimeter accuracy in real time and
+ 
+
+ align:start position:0%
+of centimeter accuracy in real time and
+then developing artificial intelligence
+
+ align:start position:0%
+then developing artificial intelligence
+ 
+
+ align:start position:0%
+then developing artificial intelligence
+algorithms in order to study the
+
+ align:start position:0%
+algorithms in order to study the
+ 
+
+ align:start position:0%
+algorithms in order to study the
+movement and optimize strategy so we get
+
+ align:start position:0%
+movement and optimize strategy so we get
+ 
+
+ align:start position:0%
+movement and optimize strategy so we get
+this type of traces and then analyze
+
+ align:start position:0%
+this type of traces and then analyze
+ 
+
+ align:start position:0%
+this type of traces and then analyze
+them and then because a number of other
+
+ align:start position:0%
+them and then because a number of other
+ 
+
+ align:start position:0%
+them and then because a number of other
+projects really dealing with technology
+
+ align:start position:0%
+projects really dealing with technology
+ 
+
+ align:start position:0%
+projects really dealing with technology
+and space how technology in space
+
+ align:start position:0%
+and space how technology in space
+ 
+
+ align:start position:0%
+and space how technology in space
+interface we also started this is funded
+
+ align:start position:0%
+interface we also started this is funded
+ 
+
+ align:start position:0%
+interface we also started this is funded
+through a sensible City consortium
+
+ align:start position:0%
+through a sensible City consortium
+ 
+
+ align:start position:0%
+through a sensible City consortium
+that's sort of bringing together the
+
+ align:start position:0%
+that's sort of bringing together the
+ 
+
+ align:start position:0%
+that's sort of bringing together the
+different the key actors being part of
+
+ align:start position:0%
+different the key actors being part of
+ 
+
+ align:start position:0%
+different the key actors being part of
+this revolution from network operators
+
+ align:start position:0%
+this revolution from network operators
+ 
+
+ align:start position:0%
+this revolution from network operators
+hardware companies urban hardware and in
+
+ align:start position:0%
+hardware companies urban hardware and in
+ 
+
+ align:start position:0%
+hardware companies urban hardware and in
+public administration but that's it i
+
+ align:start position:0%
+public administration but that's it i
+ 
+
+ align:start position:0%
+public administration but that's it i
+think if you dry to have a chat will be
+
+ align:start position:0%
+think if you dry to have a chat will be
+ 
+
+ align:start position:0%
+think if you dry to have a chat will be
+at the museum thanks a lot
\ No newline at end of file
diff --git a/YzZUIYRCE38.txt b/YzZUIYRCE38.txt
new file mode 100644
index 0000000000000000000000000000000000000000..a4aae501f207b2aaf4fc5e70624845bfe5d54697
--- /dev/null
+++ b/YzZUIYRCE38.txt
@@ -0,0 +1,7253 @@
+align:start position:0%
+ 
+okay uh cameras are rolling this is
+
+ align:start position:0%
+okay uh cameras are rolling this is
+ 
+
+ align:start position:0%
+okay uh cameras are rolling this is
+lecture
+
+ align:start position:0%
+lecture
+ 
+
+ align:start position:0%
+lecture
+14 starting a new
+
+ align:start position:0%
+14 starting a new
+ 
+
+ align:start position:0%
+14 starting a new
+chapter chapter about
+
+ align:start position:0%
+chapter chapter about
+ 
+
+ align:start position:0%
+chapter chapter about
+orthogonality what it means for vectors
+
+ align:start position:0%
+orthogonality what it means for vectors
+ 
+
+ align:start position:0%
+orthogonality what it means for vectors
+to be
+
+ align:start position:0%
+to be
+ 
+
+ align:start position:0%
+to be
+orthogonal what it means for subspaces
+
+ align:start position:0%
+orthogonal what it means for subspaces
+ 
+
+ align:start position:0%
+orthogonal what it means for subspaces
+to be orthogonal what it means for bases
+
+ align:start position:0%
+to be orthogonal what it means for bases
+ 
+
+ align:start position:0%
+to be orthogonal what it means for bases
+to be
+
+ align:start position:0%
+to be
+ 
+
+ align:start position:0%
+to be
+orthogonal so 90° this is a this is a 90
+
+ align:start position:0%
+orthogonal so 90° this is a this is a 90
+ 
+
+ align:start position:0%
+orthogonal so 90° this is a this is a 90
+Dee
+
+ align:start position:0%
+Dee
+ 
+
+ align:start position:0%
+Dee
+chapter so what does it
+
+ align:start position:0%
+chapter so what does it
+ 
+
+ align:start position:0%
+chapter so what does it
+mean uh let me let me jump to
+
+ align:start position:0%
+mean uh let me let me jump to
+ 
+
+ align:start position:0%
+mean uh let me let me jump to
+subspaces because I've drawn here the
+
+ align:start position:0%
+subspaces because I've drawn here the
+ 
+
+ align:start position:0%
+subspaces because I've drawn here the
+big picture this is the this is the 1806
+
+ align:start position:0%
+big picture this is the this is the 1806
+ 
+
+ align:start position:0%
+big picture this is the this is the 1806
+picture here and and uh hold it down
+
+ align:start position:0%
+picture here and and uh hold it down
+ 
+
+ align:start position:0%
+picture here and and uh hold it down
+guys uh so this is the picture and we
+
+ align:start position:0%
+guys uh so this is the picture and we
+ 
+
+ align:start position:0%
+guys uh so this is the picture and we
+know a lot about that picture already we
+
+ align:start position:0%
+know a lot about that picture already we
+ 
+
+ align:start position:0%
+know a lot about that picture already we
+know the dimension of every Subspace we
+
+ align:start position:0%
+know the dimension of every Subspace we
+ 
+
+ align:start position:0%
+know the dimension of every Subspace we
+know that these dimensions
+
+ align:start position:0%
+know that these dimensions
+ 
+
+ align:start position:0%
+know that these dimensions
+are R and N minus r we know that these
+
+ align:start position:0%
+are R and N minus r we know that these
+ 
+
+ align:start position:0%
+are R and N minus r we know that these
+dimensions are R and M minus
+
+ align:start position:0%
+dimensions are R and M minus
+ 
+
+ align:start position:0%
+dimensions are R and M minus
+r what we what I want to show now is
+
+ align:start position:0%
+r what we what I want to show now is
+ 
+
+ align:start position:0%
+r what we what I want to show now is
+what this figure is saying that the
+
+ align:start position:0%
+what this figure is saying that the
+ 
+
+ align:start position:0%
+what this figure is saying that the
+angle with the figure is like just my
+
+ align:start position:0%
+angle with the figure is like just my
+ 
+
+ align:start position:0%
+angle with the figure is like just my
+attempt to draw what I'm now going to
+
+ align:start position:0%
+attempt to draw what I'm now going to
+ 
+
+ align:start position:0%
+attempt to draw what I'm now going to
+say that the angle between these
+
+ align:start position:0%
+say that the angle between these
+ 
+
+ align:start position:0%
+say that the angle between these
+subspaces is
+
+ align:start position:0%
+subspaces is
+ 
+
+ align:start position:0%
+subspaces is
+90° and the angle between these
+
+ align:start position:0%
+90° and the angle between these
+ 
+
+ align:start position:0%
+90° and the angle between these
+subspaces is 90° now I have to say what
+
+ align:start position:0%
+subspaces is 90° now I have to say what
+ 
+
+ align:start position:0%
+subspaces is 90° now I have to say what
+does that mean what does it mean for
+
+ align:start position:0%
+does that mean what does it mean for
+ 
+
+ align:start position:0%
+does that mean what does it mean for
+subspaces to be orthogonal
+
+ align:start position:0%
+subspaces to be orthogonal
+ 
+
+ align:start position:0%
+subspaces to be orthogonal
+but I hope you appreciate
+
+ align:start position:0%
+but I hope you appreciate
+ 
+
+ align:start position:0%
+but I hope you appreciate
+the beauty of this
+
+ align:start position:0%
+the beauty of this
+ 
+
+ align:start position:0%
+the beauty of this
+picture that that those subspaces are
+
+ align:start position:0%
+picture that that those subspaces are
+ 
+
+ align:start position:0%
+picture that that those subspaces are
+going to come out to be
+
+ align:start position:0%
+going to come out to be
+ 
+
+ align:start position:0%
+going to come out to be
+orthogonal those two and also those two
+
+ align:start position:0%
+orthogonal those two and also those two
+ 
+
+ align:start position:0%
+orthogonal those two and also those two
+so that's like one
+
+ align:start position:0%
+so that's like one
+ 
+
+ align:start position:0%
+so that's like one
+point one important point to step
+
+ align:start position:0%
+point one important point to step
+ 
+
+ align:start position:0%
+point one important point to step
+forward in understanding those subspaces
+
+ align:start position:0%
+forward in understanding those subspaces
+ 
+
+ align:start position:0%
+forward in understanding those subspaces
+we knew what each Subspace was like we
+
+ align:start position:0%
+we knew what each Subspace was like we
+ 
+
+ align:start position:0%
+we knew what each Subspace was like we
+could compute bases for them now we know
+
+ align:start position:0%
+could compute bases for them now we know
+ 
+
+ align:start position:0%
+could compute bases for them now we know
+more or we will in a few
+
+ align:start position:0%
+more or we will in a few
+ 
+
+ align:start position:0%
+more or we will in a few
+minutes okay I have to say first of all
+
+ align:start position:0%
+minutes okay I have to say first of all
+ 
+
+ align:start position:0%
+minutes okay I have to say first of all
+what does it mean for two vectors to be
+
+ align:start position:0%
+what does it mean for two vectors to be
+ 
+
+ align:start position:0%
+what does it mean for two vectors to be
+orthogonal so let me start with
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that orthogonal
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+vectors the word orthogonal is is just
+
+ align:start position:0%
+vectors the word orthogonal is is just
+ 
+
+ align:start position:0%
+vectors the word orthogonal is is just
+just another word for
+
+ align:start position:0%
+just another word for
+ 
+
+ align:start position:0%
+just another word for
+perpendicular it means that in N
+
+ align:start position:0%
+perpendicular it means that in N
+ 
+
+ align:start position:0%
+perpendicular it means that in N
+dimensional space the angle between
+
+ align:start position:0%
+dimensional space the angle between
+ 
+
+ align:start position:0%
+dimensional space the angle between
+those vectors is
+
+ align:start position:0%
+those vectors is
+ 
+
+ align:start position:0%
+those vectors is
+90° it means that they form a right
+
+ align:start position:0%
+90° it means that they form a right
+ 
+
+ align:start position:0%
+90° it means that they form a right
+triangle it even means that the going
+
+ align:start position:0%
+triangle it even means that the going
+ 
+
+ align:start position:0%
+triangle it even means that the going
+way back to the Greeks that this uh
+
+ align:start position:0%
+way back to the Greeks that this uh
+ 
+
+ align:start position:0%
+way back to the Greeks that this uh
+angle that this triangle a vector
+
+ align:start position:0%
+angle that this triangle a vector
+ 
+
+ align:start position:0%
+angle that this triangle a vector
+x a vector
+
+ align:start position:0%
+x a vector
+ 
+
+ align:start position:0%
+x a vector
+y and the vector x + y of course that'll
+
+ align:start position:0%
+y and the vector x + y of course that'll
+ 
+
+ align:start position:0%
+y and the vector x + y of course that'll
+be the
+
+ align:start position:0%
+be the
+ 
+
+ align:start position:0%
+be the
+hypotenuse so what was it the Greeks
+
+ align:start position:0%
+hypotenuse so what was it the Greeks
+ 
+
+ align:start position:0%
+hypotenuse so what was it the Greeks
+figured out and it's neat it's the fact
+
+ align:start position:0%
+figured out and it's neat it's the fact
+ 
+
+ align:start position:0%
+figured out and it's neat it's the fact
+that the so these are orthogonal this is
+
+ align:start position:0%
+that the so these are orthogonal this is
+ 
+
+ align:start position:0%
+that the so these are orthogonal this is
+a right angle if so so let me put the
+
+ align:start position:0%
+a right angle if so so let me put the
+ 
+
+ align:start position:0%
+a right angle if so so let me put the
+great name down
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Pythagoras I'm I'm looking for what am I
+
+ align:start position:0%
+Pythagoras I'm I'm looking for what am I
+ 
+
+ align:start position:0%
+Pythagoras I'm I'm looking for what am I
+looking for for I'm looking for the
+
+ align:start position:0%
+looking for for I'm looking for the
+ 
+
+ align:start position:0%
+looking for for I'm looking for the
+condition if you give me two vectors how
+
+ align:start position:0%
+condition if you give me two vectors how
+ 
+
+ align:start position:0%
+condition if you give me two vectors how
+do I know if they're
+
+ align:start position:0%
+do I know if they're
+ 
+
+ align:start position:0%
+do I know if they're
+orthogonal how can I tell two
+
+ align:start position:0%
+orthogonal how can I tell two
+ 
+
+ align:start position:0%
+orthogonal how can I tell two
+perpendicular vectors and actually you
+
+ align:start position:0%
+perpendicular vectors and actually you
+ 
+
+ align:start position:0%
+perpendicular vectors and actually you
+probably know the answer let me write
+
+ align:start position:0%
+probably know the answer let me write
+ 
+
+ align:start position:0%
+probably know the answer let me write
+the answer down orthogonal vectors
+
+ align:start position:0%
+the answer down orthogonal vectors
+ 
+
+ align:start position:0%
+the answer down orthogonal vectors
+what's the test for
+
+ align:start position:0%
+what's the test for
+ 
+
+ align:start position:0%
+what's the test for
+orthogonality I take the dotproduct
+
+ align:start position:0%
+orthogonality I take the dotproduct
+ 
+
+ align:start position:0%
+orthogonality I take the dotproduct
+which I tend to write as X transpose y
+
+ align:start position:0%
+which I tend to write as X transpose y
+ 
+
+ align:start position:0%
+which I tend to write as X transpose y
+because that's a row times a column and
+
+ align:start position:0%
+because that's a row times a column and
+ 
+
+ align:start position:0%
+because that's a row times a column and
+that matrix multiplication just gives me
+
+ align:start position:0%
+that matrix multiplication just gives me
+ 
+
+ align:start position:0%
+that matrix multiplication just gives me
+the right thing that X1 y1 plus X2 Y2
+
+ align:start position:0%
+the right thing that X1 y1 plus X2 Y2
+ 
+
+ align:start position:0%
+the right thing that X1 y1 plus X2 Y2
+and so on so these vectors are
+
+ align:start position:0%
+and so on so these vectors are
+ 
+
+ align:start position:0%
+and so on so these vectors are
+orthogonal if
+
+ align:start position:0%
+orthogonal if
+ 
+
+ align:start position:0%
+orthogonal if
+this result X transpose Y
+
+ align:start position:0%
+this result X transpose Y
+ 
+
+ align:start position:0%
+this result X transpose Y
+is zero that's the test okay can I
+
+ align:start position:0%
+is zero that's the test okay can I
+ 
+
+ align:start position:0%
+is zero that's the test okay can I
+connect that to other things
+
+ align:start position:0%
+connect that to other things
+ 
+
+ align:start position:0%
+connect that to other things
+I mean it's like it's amazing it's it's
+
+ align:start position:0%
+I mean it's like it's amazing it's it's
+ 
+
+ align:start position:0%
+I mean it's like it's amazing it's it's
+just beautiful that here we have we're
+
+ align:start position:0%
+just beautiful that here we have we're
+ 
+
+ align:start position:0%
+just beautiful that here we have we're
+in N
+
+ align:start position:0%
+in N
+ 
+
+ align:start position:0%
+in N
+Dimensions we've got a couple of vectors
+
+ align:start position:0%
+Dimensions we've got a couple of vectors
+ 
+
+ align:start position:0%
+Dimensions we've got a couple of vectors
+we want to know the angle between them
+
+ align:start position:0%
+we want to know the angle between them
+ 
+
+ align:start position:0%
+we want to know the angle between them
+and the right thing to look at is the
+
+ align:start position:0%
+and the right thing to look at is the
+ 
+
+ align:start position:0%
+and the right thing to look at is the
+simplest thing you can imagine the dot
+
+ align:start position:0%
+simplest thing you can imagine the dot
+ 
+
+ align:start position:0%
+simplest thing you can imagine the dot
+product okay now why so I'm answering
+
+ align:start position:0%
+product okay now why so I'm answering
+ 
+
+ align:start position:0%
+product okay now why so I'm answering
+the question now why let's just some
+
+ align:start position:0%
+the question now why let's just some
+ 
+
+ align:start position:0%
+the question now why let's just some
+let's add some uh justification to this
+
+ align:start position:0%
+let's add some uh justification to this
+ 
+
+ align:start position:0%
+let's add some uh justification to this
+fact that that's the test okay so
+
+ align:start position:0%
+fact that that's the test okay so
+ 
+
+ align:start position:0%
+fact that that's the test okay so
+Pythagoras would say we've got a right
+
+ align:start position:0%
+Pythagoras would say we've got a right
+ 
+
+ align:start position:0%
+Pythagoras would say we've got a right
+triangle if that length squared plus
+
+ align:start position:0%
+triangle if that length squared plus
+ 
+
+ align:start position:0%
+triangle if that length squared plus
+that length squared equals that length
+
+ align:start position:0%
+that length squared equals that length
+ 
+
+ align:start position:0%
+that length squared equals that length
+squared okay can I write it as
+
+ align:start position:0%
+squared okay can I write it as
+ 
+
+ align:start position:0%
+squared okay can I write it as
+X2 +
+
+ align:start position:0%
+X2 +
+ 
+
+ align:start position:0%
+X2 +
+y^2
+
+ align:start position:0%
+y^2
+ 
+
+ align:start position:0%
+y^2
+= x +
+
+ align:start position:0%
+= x +
+ 
+
+ align:start position:0%
+= x +
+Y2 now don't please don't think that
+
+ align:start position:0%
+Y2 now don't please don't think that
+ 
+
+ align:start position:0%
+Y2 now don't please don't think that
+this is always
+
+ align:start position:0%
+this is always
+ 
+
+ align:start position:0%
+this is always
+true this is only going to be true in
+
+ align:start position:0%
+true this is only going to be true in
+ 
+
+ align:start position:0%
+true this is only going to be true in
+this it's going to be equivalent to
+
+ align:start position:0%
+this it's going to be equivalent to
+ 
+
+ align:start position:0%
+this it's going to be equivalent to
+orthogonality for other triangles of
+
+ align:start position:0%
+orthogonality for other triangles of
+ 
+
+ align:start position:0%
+orthogonality for other triangles of
+course it's not true for other triangles
+
+ align:start position:0%
+course it's not true for other triangles
+ 
+
+ align:start position:0%
+course it's not true for other triangles
+it's not but for a right triangle
+
+ align:start position:0%
+it's not but for a right triangle
+ 
+
+ align:start position:0%
+it's not but for a right triangle
+somehow that fact should connect to that
+
+ align:start position:0%
+somehow that fact should connect to that
+ 
+
+ align:start position:0%
+somehow that fact should connect to that
+fact can we just make that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+connection what's the connection between
+
+ align:start position:0%
+connection what's the connection between
+ 
+
+ align:start position:0%
+connection what's the connection between
+this test for orthogonality and this
+
+ align:start position:0%
+this test for orthogonality and this
+ 
+
+ align:start position:0%
+this test for orthogonality and this
+statement of orthogonality well I guess
+
+ align:start position:0%
+statement of orthogonality well I guess
+ 
+
+ align:start position:0%
+statement of orthogonality well I guess
+I have to say what is the length squared
+
+ align:start position:0%
+I have to say what is the length squared
+ 
+
+ align:start position:0%
+I have to say what is the length squared
+so let's continue on the board
+
+ align:start position:0%
+so let's continue on the board
+ 
+
+ align:start position:0%
+so let's continue on the board
+underneath with that equation give me
+
+ align:start position:0%
+underneath with that equation give me
+ 
+
+ align:start position:0%
+underneath with that equation give me
+another way to express the length
+
+ align:start position:0%
+another way to express the length
+ 
+
+ align:start position:0%
+another way to express the length
+squared of a
+
+ align:start position:0%
+squared of a
+ 
+
+ align:start position:0%
+squared of a
+vector let me just give you a vector the
+
+ align:start position:0%
+vector let me just give you a vector the
+ 
+
+ align:start position:0%
+vector let me just give you a vector the
+vector 1 two
+
+ align:start position:0%
+vector 1 two
+ 
+
+ align:start position:0%
+vector 1 two
+3 that's in three
+
+ align:start position:0%
+3 that's in three
+ 
+
+ align:start position:0%
+3 that's in three
+dimensions what is the length squared of
+
+ align:start position:0%
+dimensions what is the length squared of
+ 
+
+ align:start position:0%
+dimensions what is the length squared of
+the vector X equal 1 2
+
+ align:start position:0%
+the vector X equal 1 2
+ 
+
+ align:start position:0%
+the vector X equal 1 2
+3 so how do you find the length
+
+ align:start position:0%
+3 so how do you find the length
+ 
+
+ align:start position:0%
+3 so how do you find the length
+squared well really you're just you want
+
+ align:start position:0%
+squared well really you're just you want
+ 
+
+ align:start position:0%
+squared well really you're just you want
+the length of that Vector that goes
+
+ align:start position:0%
+the length of that Vector that goes
+ 
+
+ align:start position:0%
+the length of that Vector that goes
+along one up two and out three and and
+
+ align:start position:0%
+along one up two and out three and and
+ 
+
+ align:start position:0%
+along one up two and out three and and
+we'll come come back to that right
+
+ align:start position:0%
+we'll come come back to that right
+ 
+
+ align:start position:0%
+we'll come come back to that right
+triangle stuff the length squared is
+
+ align:start position:0%
+triangle stuff the length squared is
+ 
+
+ align:start position:0%
+triangle stuff the length squared is
+this is
+
+ align:start position:0%
+this is
+ 
+
+ align:start position:0%
+this is
+exactly X transpose
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+X whenever I d x transpose X I know I've
+
+ align:start position:0%
+X whenever I d x transpose X I know I've
+ 
+
+ align:start position:0%
+X whenever I d x transpose X I know I've
+got a number that's positive it's a
+
+ align:start position:0%
+got a number that's positive it's a
+ 
+
+ align:start position:0%
+got a number that's positive it's a
+length squared unless it unless X
+
+ align:start position:0%
+length squared unless it unless X
+ 
+
+ align:start position:0%
+length squared unless it unless X
+happens to be the zero Vector that's the
+
+ align:start position:0%
+happens to be the zero Vector that's the
+ 
+
+ align:start position:0%
+happens to be the zero Vector that's the
+one case where the length is
+
+ align:start position:0%
+one case where the length is
+ 
+
+ align:start position:0%
+one case where the length is
+zero so right this is just X1 2 plus X2
+
+ align:start position:0%
+zero so right this is just X1 2 plus X2
+ 
+
+ align:start position:0%
+zero so right this is just X1 2 plus X2
+2ar plus so on plus xn^ 2 so one in the
+
+ align:start position:0%
+2ar plus so on plus xn^ 2 so one in the
+ 
+
+ align:start position:0%
+2ar plus so on plus xn^ 2 so one in the
+example I gave you what was the length
+
+ align:start position:0%
+example I gave you what was the length
+ 
+
+ align:start position:0%
+example I gave you what was the length
+squar of that Vector 1 2
+
+ align:start position:0%
+squar of that Vector 1 2
+ 
+
+ align:start position:0%
+squar of that Vector 1 2
+3 so so you square those you get 1 4 and
+
+ align:start position:0%
+3 so so you square those you get 1 4 and
+ 
+
+ align:start position:0%
+3 so so you square those you get 1 4 and
+9 you add you get
+
+ align:start position:0%
+9 you add you get
+ 
+
+ align:start position:0%
+9 you add you get
+14 so the vector 1 2 3 has length
+
+ align:start position:0%
+14 so the vector 1 2 3 has length
+ 
+
+ align:start position:0%
+14 so the vector 1 2 3 has length
+14 so let me just let let me just put
+
+ align:start position:0%
+14 so let me just let let me just put
+ 
+
+ align:start position:0%
+14 so let me just let let me just put
+down a vector here uh let X be the
+
+ align:start position:0%
+down a vector here uh let X be the
+ 
+
+ align:start position:0%
+down a vector here uh let X be the
+vector one
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+23 let me cook up a vector that's
+
+ align:start position:0%
+23 let me cook up a vector that's
+ 
+
+ align:start position:0%
+23 let me cook up a vector that's
+orthogonal to
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+it so what's the vector that's
+
+ align:start position:0%
+it so what's the vector that's
+ 
+
+ align:start position:0%
+it so what's the vector that's
+orthogonal so write down here
+
+ align:start position:0%
+orthogonal so write down here
+ 
+
+ align:start position:0%
+orthogonal so write down here
+x^2 is 1 + 4 + 9
+
+ align:start position:0%
+x^2 is 1 + 4 + 9
+ 
+
+ align:start position:0%
+x^2 is 1 + 4 + 9
+14 uh let me cook up a vector that's
+
+ align:start position:0%
+14 uh let me cook up a vector that's
+ 
+
+ align:start position:0%
+14 uh let me cook up a vector that's
+orthogonal to it we'll
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+get right that that those two vectors
+
+ align:start position:0%
+get right that that those two vectors
+ 
+
+ align:start position:0%
+get right that that those two vectors
+are orthogonal the length of y^2
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+is
+
+ align:start position:0%
+is
+ 
+
+ align:start position:0%
+is
+5 and x +
+
+ align:start position:0%
+5 and x +
+ 
+
+ align:start position:0%
+5 and x +
+y is is 1 and two making three 2 and Min
+
+ align:start position:0%
+y is is 1 and two making three 2 and Min
+ 
+
+ align:start position:0%
+y is is 1 and two making three 2 and Min
+- one making 1 3 and zero making three
+
+ align:start position:0%
+- one making 1 3 and zero making three
+ 
+
+ align:start position:0%
+- one making 1 3 and zero making three
+and the length of this
+
+ align:start position:0%
+and the length of this
+ 
+
+ align:start position:0%
+and the length of this
+squared is 9 + 1 + 9
+
+ align:start position:0%
+squared is 9 + 1 + 9
+ 
+
+ align:start position:0%
+squared is 9 + 1 + 9
+19 and sure
+
+ align:start position:0%
+19 and sure
+ 
+
+ align:start position:0%
+19 and sure
+enough I I haven't proved anything I'm
+
+ align:start position:0%
+enough I I haven't proved anything I'm
+ 
+
+ align:start position:0%
+enough I I haven't proved anything I'm
+just
+
+ align:start position:0%
+just
+ 
+
+ align:start position:0%
+just
+like check to see that my my my test X
+
+ align:start position:0%
+like check to see that my my my test X
+ 
+
+ align:start position:0%
+like check to see that my my my test X
+transpose y equal 0 which is true right
+
+ align:start position:0%
+transpose y equal 0 which is true right
+ 
+
+ align:start position:0%
+transpose y equal 0 which is true right
+everybody sees that X transpose Y is
+
+ align:start position:0%
+everybody sees that X transpose Y is
+ 
+
+ align:start position:0%
+everybody sees that X transpose Y is
+zero here that that's maybe the main
+
+ align:start position:0%
+zero here that that's maybe the main
+ 
+
+ align:start position:0%
+zero here that that's maybe the main
+point that you should get really quick
+
+ align:start position:0%
+point that you should get really quick
+ 
+
+ align:start position:0%
+point that you should get really quick
+at doing X transpose y so it's just this
+
+ align:start position:0%
+at doing X transpose y so it's just this
+ 
+
+ align:start position:0%
+at doing X transpose y so it's just this
+plus this plus this and that's zero and
+
+ align:start position:0%
+plus this plus this and that's zero and
+ 
+
+ align:start position:0%
+plus this plus this and that's zero and
+sure enough that clicks with uh 14 + 5
+
+ align:start position:0%
+sure enough that clicks with uh 14 + 5
+ 
+
+ align:start position:0%
+sure enough that clicks with uh 14 + 5
+agreeing with 19 now let me just do that
+
+ align:start position:0%
+agreeing with 19 now let me just do that
+ 
+
+ align:start position:0%
+agreeing with 19 now let me just do that
+in
+
+ align:start position:0%
+in
+ 
+
+ align:start position:0%
+in
+letters so that's y transpose y
+
+ align:start position:0%
+letters so that's y transpose y
+ 
+
+ align:start position:0%
+letters so that's y transpose y
+Y and this is x + y transpose x +
+
+ align:start position:0%
+Y and this is x + y transpose x +
+ 
+
+ align:start position:0%
+Y and this is x + y transpose x +
+y okay so I'm looking again this isn't
+
+ align:start position:0%
+y okay so I'm looking again this isn't
+ 
+
+ align:start position:0%
+y okay so I'm looking again this isn't
+always true I repeat this is going to be
+
+ align:start position:0%
+always true I repeat this is going to be
+ 
+
+ align:start position:0%
+always true I repeat this is going to be
+true when we have a right
+
+ align:start position:0%
+true when we have a right
+ 
+
+ align:start position:0%
+true when we have a right
+angle and let's just well of course I'm
+
+ align:start position:0%
+angle and let's just well of course I'm
+ 
+
+ align:start position:0%
+angle and let's just well of course I'm
+just going to simplify this stuff here
+
+ align:start position:0%
+just going to simplify this stuff here
+ 
+
+ align:start position:0%
+just going to simplify this stuff here
+there's an X transpose X there and
+
+ align:start position:0%
+there's an X transpose X there and
+ 
+
+ align:start position:0%
+there's an X transpose X there and
+there's a y transpose y there
+
+ align:start position:0%
+there's a y transpose y there
+ 
+
+ align:start position:0%
+there's a y transpose y there
+and there's an X transpose
+
+ align:start position:0%
+and there's an X transpose
+ 
+
+ align:start position:0%
+and there's an X transpose
+Y and there's a y transpose
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+X I knew I could do that simplification
+
+ align:start position:0%
+X I knew I could do that simplification
+ 
+
+ align:start position:0%
+X I knew I could do that simplification
+because I'm just doing matrix
+
+ align:start position:0%
+because I'm just doing matrix
+ 
+
+ align:start position:0%
+because I'm just doing matrix
+multiplication and I've just followed
+
+ align:start position:0%
+multiplication and I've just followed
+ 
+
+ align:start position:0%
+multiplication and I've just followed
+the rules okay so X transpose X is
+
+ align:start position:0%
+the rules okay so X transpose X is
+ 
+
+ align:start position:0%
+the rules okay so X transpose X is
+cancel y transpose y's cancel and what
+
+ align:start position:0%
+cancel y transpose y's cancel and what
+ 
+
+ align:start position:0%
+cancel y transpose y's cancel and what
+about these guys what can what can you
+
+ align:start position:0%
+about these guys what can what can you
+ 
+
+ align:start position:0%
+about these guys what can what can you
+tell me about
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the inner product of X with Y and the
+
+ align:start position:0%
+the inner product of X with Y and the
+ 
+
+ align:start position:0%
+the inner product of X with Y and the
+inner product of Y with
+
+ align:start position:0%
+inner product of Y with
+ 
+
+ align:start position:0%
+inner product of Y with
+X is there a
+
+ align:start position:0%
+X is there a
+ 
+
+ align:start position:0%
+X is there a
+difference I think if we while we're
+
+ align:start position:0%
+difference I think if we while we're
+ 
+
+ align:start position:0%
+difference I think if we while we're
+doing
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+real vectors which is all we're doing
+
+ align:start position:0%
+real vectors which is all we're doing
+ 
+
+ align:start position:0%
+real vectors which is all we're doing
+now there isn't a difference there's no
+
+ align:start position:0%
+now there isn't a difference there's no
+ 
+
+ align:start position:0%
+now there isn't a difference there's no
+difference if I take X transpose y
+
+ align:start position:0%
+difference if I take X transpose y
+ 
+
+ align:start position:0%
+difference if I take X transpose y
+that'll give me zero if I took y
+
+ align:start position:0%
+that'll give me zero if I took y
+ 
+
+ align:start position:0%
+that'll give me zero if I took y
+transpose X I would have the same X1 y1
+
+ align:start position:0%
+transpose X I would have the same X1 y1
+ 
+
+ align:start position:0%
+transpose X I would have the same X1 y1
+and X2 Y2 and X3 Y3 it would be the same
+
+ align:start position:0%
+and X2 Y2 and X3 Y3 it would be the same
+ 
+
+ align:start position:0%
+and X2 Y2 and X3 Y3 it would be the same
+so this is this is this is the same as
+
+ align:start position:0%
+so this is this is this is the same as
+ 
+
+ align:start position:0%
+so this is this is this is the same as
+that this is really I'll I'll knock that
+
+ align:start position:0%
+that this is really I'll I'll knock that
+ 
+
+ align:start position:0%
+that this is really I'll I'll knock that
+guy out and say two of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+these so actually that's the this this
+
+ align:start position:0%
+these so actually that's the this this
+ 
+
+ align:start position:0%
+these so actually that's the this this
+equation boiled down to this thing being
+
+ align:start position:0%
+equation boiled down to this thing being
+ 
+
+ align:start position:0%
+equation boiled down to this thing being
+zero right everything else cancelled and
+
+ align:start position:0%
+zero right everything else cancelled and
+ 
+
+ align:start position:0%
+zero right everything else cancelled and
+this equation boiled down to that one so
+
+ align:start position:0%
+this equation boiled down to that one so
+ 
+
+ align:start position:0%
+this equation boiled down to that one so
+that's really all I wanted
+
+ align:start position:0%
+that's really all I wanted
+ 
+
+ align:start position:0%
+that's really all I wanted
+I just wanted to check
+
+ align:start position:0%
+I just wanted to check
+ 
+
+ align:start position:0%
+I just wanted to check
+that
+
+ align:start position:0%
+that
+ 
+
+ align:start position:0%
+that
+Pythagoras for a right
+
+ align:start position:0%
+Pythagoras for a right
+ 
+
+ align:start position:0%
+Pythagoras for a right
+triangle led me to this of course I
+
+ align:start position:0%
+triangle led me to this of course I
+ 
+
+ align:start position:0%
+triangle led me to this of course I
+cancel the two now no problem to X
+
+ align:start position:0%
+cancel the two now no problem to X
+ 
+
+ align:start position:0%
+cancel the two now no problem to X
+transpose yal 0 as the
+
+ align:start position:0%
+transpose yal 0 as the
+ 
+
+ align:start position:0%
+transpose yal 0 as the
+test fair enough okay you knew it was
+
+ align:start position:0%
+test fair enough okay you knew it was
+ 
+
+ align:start position:0%
+test fair enough okay you knew it was
+coming the dotproduct of orthogonal
+
+ align:start position:0%
+coming the dotproduct of orthogonal
+ 
+
+ align:start position:0%
+coming the dotproduct of orthogonal
+vectors is zero it's just I just want to
+
+ align:start position:0%
+vectors is zero it's just I just want to
+ 
+
+ align:start position:0%
+vectors is zero it's just I just want to
+say that's really neat it comes that it
+
+ align:start position:0%
+say that's really neat it comes that it
+ 
+
+ align:start position:0%
+say that's really neat it comes that it
+comes out so well all
+
+ align:start position:0%
+comes out so well all
+ 
+
+ align:start position:0%
+comes out so well all
+right now what about so now I know if
+
+ align:start position:0%
+right now what about so now I know if
+ 
+
+ align:start position:0%
+right now what about so now I know if
+two vect what it means when two vectors
+
+ align:start position:0%
+two vect what it means when two vectors
+ 
+
+ align:start position:0%
+two vect what it means when two vectors
+are orthogonal by the way what about if
+
+ align:start position:0%
+are orthogonal by the way what about if
+ 
+
+ align:start position:0%
+are orthogonal by the way what about if
+one of these guys is the zero
+
+ align:start position:0%
+one of these guys is the zero
+ 
+
+ align:start position:0%
+one of these guys is the zero
+Vector suppose X is the zero vector and
+
+ align:start position:0%
+Vector suppose X is the zero vector and
+ 
+
+ align:start position:0%
+Vector suppose X is the zero vector and
+Y is
+
+ align:start position:0%
+Y is
+ 
+
+ align:start position:0%
+Y is
+whatever are they
+
+ align:start position:0%
+whatever are they
+ 
+
+ align:start position:0%
+whatever are they
+orthogonal
+
+ align:start position:0%
+orthogonal
+ 
+
+ align:start position:0%
+orthogonal
+sure in math the one thing about math is
+
+ align:start position:0%
+sure in math the one thing about math is
+ 
+
+ align:start position:0%
+sure in math the one thing about math is
+you're supposed to follow the
+
+ align:start position:0%
+you're supposed to follow the
+ 
+
+ align:start position:0%
+you're supposed to follow the
+rules so you're supposed to if if x is
+
+ align:start position:0%
+rules so you're supposed to if if x is
+ 
+
+ align:start position:0%
+rules so you're supposed to if if x is
+the zero Vector you're supposed to take
+
+ align:start position:0%
+the zero Vector you're supposed to take
+ 
+
+ align:start position:0%
+the zero Vector you're supposed to take
+the zero Vector dotted with Y and of
+
+ align:start position:0%
+the zero Vector dotted with Y and of
+ 
+
+ align:start position:0%
+the zero Vector dotted with Y and of
+course you get always get zero so just
+
+ align:start position:0%
+course you get always get zero so just
+ 
+
+ align:start position:0%
+course you get always get zero so just
+so we're all sure the zero Vector is
+
+ align:start position:0%
+so we're all sure the zero Vector is
+ 
+
+ align:start position:0%
+so we're all sure the zero Vector is
+orthogonal to
+
+ align:start position:0%
+orthogonal to
+ 
+
+ align:start position:0%
+orthogonal to
+everybody but what I want
+
+ align:start position:0%
+everybody but what I want
+ 
+
+ align:start position:0%
+everybody but what I want
+to what I now want
+
+ align:start position:0%
+to what I now want
+ 
+
+ align:start position:0%
+to what I now want
+to uh speak about about is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+subspaces what does it mean for me to
+
+ align:start position:0%
+subspaces what does it mean for me to
+ 
+
+ align:start position:0%
+subspaces what does it mean for me to
+say that some Subspace is orthogonal to
+
+ align:start position:0%
+say that some Subspace is orthogonal to
+ 
+
+ align:start position:0%
+say that some Subspace is orthogonal to
+some other
+
+ align:start position:0%
+some other
+ 
+
+ align:start position:0%
+some other
+Subspace so okay now I've got to write
+
+ align:start position:0%
+Subspace so okay now I've got to write
+ 
+
+ align:start position:0%
+Subspace so okay now I've got to write
+this down so because we're defining
+
+ align:start position:0%
+this down so because we're defining
+ 
+
+ align:start position:0%
+this down so because we're defining
+definition of
+
+ align:start position:0%
+definition of
+ 
+
+ align:start position:0%
+definition of
+Subspace
+
+ align:start position:0%
+Subspace
+ 
+
+ align:start position:0%
+Subspace
+s is orthogonal
+
+ align:start position:0%
+s is orthogonal
+ 
+
+ align:start position:0%
+s is orthogonal
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+to
+
+ align:start position:0%
+to
+ 
+
+ align:start position:0%
+to
+Subspace
+
+ align:start position:0%
+Subspace
+ 
+
+ align:start position:0%
+Subspace
+let's say
+
+ align:start position:0%
+let's say
+ 
+
+ align:start position:0%
+let's say
+t so I've got a couple of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+subspaces and what should it mean for
+
+ align:start position:0%
+subspaces and what should it mean for
+ 
+
+ align:start position:0%
+subspaces and what should it mean for
+those guys to be
+
+ align:start position:0%
+those guys to be
+ 
+
+ align:start position:0%
+those guys to be
+orthogonal it's just a n sort of what's
+
+ align:start position:0%
+orthogonal it's just a n sort of what's
+ 
+
+ align:start position:0%
+orthogonal it's just a n sort of what's
+the natural extension from orthogonal
+
+ align:start position:0%
+the natural extension from orthogonal
+ 
+
+ align:start position:0%
+the natural extension from orthogonal
+vectors to orthogonal
+
+ align:start position:0%
+vectors to orthogonal
+ 
+
+ align:start position:0%
+vectors to orthogonal
+subspaces well and in
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+particular let's think of some
+
+ align:start position:0%
+particular let's think of some
+ 
+
+ align:start position:0%
+particular let's think of some
+orthogonal subspaces like like
+
+ align:start position:0%
+orthogonal subspaces like like
+ 
+
+ align:start position:0%
+orthogonal subspaces like like
+uh uh this
+
+ align:start position:0%
+uh uh this
+ 
+
+ align:start position:0%
+uh uh this
+wall let's say in three
+
+ align:start position:0%
+wall let's say in three
+ 
+
+ align:start position:0%
+wall let's say in three
+dimensions so the Blackboard extended to
+
+ align:start position:0%
+dimensions so the Blackboard extended to
+ 
+
+ align:start position:0%
+dimensions so the Blackboard extended to
+Infinity right is a is a Subspace a
+
+ align:start position:0%
+Infinity right is a is a Subspace a
+ 
+
+ align:start position:0%
+Infinity right is a is a Subspace a
+plane a two-dimensional
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Subspace it's a little bumpy but anyway
+
+ align:start position:0%
+Subspace it's a little bumpy but anyway
+ 
+
+ align:start position:0%
+Subspace it's a little bumpy but anyway
+it's a think of it as a
+
+ align:start position:0%
+it's a think of it as a
+ 
+
+ align:start position:0%
+it's a think of it as a
+Subspace um let me take the floor as
+
+ align:start position:0%
+Subspace um let me take the floor as
+ 
+
+ align:start position:0%
+Subspace um let me take the floor as
+another
+
+ align:start position:0%
+another
+ 
+
+ align:start position:0%
+another
+Subspace
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+again it's not uh great Subspace MIT
+
+ align:start position:0%
+again it's not uh great Subspace MIT
+ 
+
+ align:start position:0%
+again it's not uh great Subspace MIT
+only Built it like so so but
+
+ align:start position:0%
+only Built it like so so but
+ 
+
+ align:start position:0%
+only Built it like so so but
+uh and I'll put the origin right here so
+
+ align:start position:0%
+uh and I'll put the origin right here so
+ 
+
+ align:start position:0%
+uh and I'll put the origin right here so
+the origin of the world is right
+
+ align:start position:0%
+the origin of the world is right
+ 
+
+ align:start position:0%
+the origin of the world is right
+there
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay thereby giving linear algebra it's
+
+ align:start position:0%
+okay thereby giving linear algebra it's
+ 
+
+ align:start position:0%
+okay thereby giving linear algebra it's
+proper importance in in this okay so
+
+ align:start position:0%
+proper importance in in this okay so
+ 
+
+ align:start position:0%
+proper importance in in this okay so
+there's one Subspace there's another one
+
+ align:start position:0%
+there's one Subspace there's another one
+ 
+
+ align:start position:0%
+there's one Subspace there's another one
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+floor
+
+ align:start position:0%
+floor
+ 
+
+ align:start position:0%
+floor
+and are they
+
+ align:start position:0%
+and are they
+ 
+
+ align:start position:0%
+and are they
+orthogon what does it mean for two
+
+ align:start position:0%
+orthogon what does it mean for two
+ 
+
+ align:start position:0%
+orthogon what does it mean for two
+subspaces to be orthogonal and and in
+
+ align:start position:0%
+subspaces to be orthogonal and and in
+ 
+
+ align:start position:0%
+subspaces to be orthogonal and and in
+that special case are they orthogonal
+
+ align:start position:0%
+that special case are they orthogonal
+ 
+
+ align:start position:0%
+that special case are they orthogonal
+all right let let's finish this sentence
+
+ align:start position:0%
+all right let let's finish this sentence
+ 
+
+ align:start position:0%
+all right let let's finish this sentence
+what does it mean
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+means we have to have to know what what
+
+ align:start position:0%
+means we have to have to know what what
+ 
+
+ align:start position:0%
+means we have to have to know what what
+we're talking about here so what would
+
+ align:start position:0%
+we're talking about here so what would
+ 
+
+ align:start position:0%
+we're talking about here so what would
+be a reasonable idea of
+
+ align:start position:0%
+be a reasonable idea of
+ 
+
+ align:start position:0%
+be a reasonable idea of
+orthography well let me put the right
+
+ align:start position:0%
+orthography well let me put the right
+ 
+
+ align:start position:0%
+orthography well let me put the right
+thing up it means that every Vector in
+
+ align:start position:0%
+thing up it means that every Vector in
+ 
+
+ align:start position:0%
+thing up it means that every Vector in
+s
+
+ align:start position:0%
+s
+ 
+
+ align:start position:0%
+s
+every
+
+ align:start position:0%
+every
+ 
+
+ align:start position:0%
+every
+Vector in
+
+ align:start position:0%
+Vector in
+ 
+
+ align:start position:0%
+Vector in
+S is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+orthogonal
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+to to what am I going to say
+
+ align:start position:0%
+to to what am I going to say
+ 
+
+ align:start position:0%
+to to what am I going to say
+every Vector in
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+P
+
+ align:start position:0%
+P
+ 
+
+ align:start position:0%
+P
+that that's a reasonable and it's a good
+
+ align:start position:0%
+that that's a reasonable and it's a good
+ 
+
+ align:start position:0%
+that that's a reasonable and it's a good
+and it's the right definition for two
+
+ align:start position:0%
+and it's the right definition for two
+ 
+
+ align:start position:0%
+and it's the right definition for two
+subspaces to be orthogonal but I just
+
+ align:start position:0%
+subspaces to be orthogonal but I just
+ 
+
+ align:start position:0%
+subspaces to be orthogonal but I just
+want you to see hey what does that
+
+ align:start position:0%
+want you to see hey what does that
+ 
+
+ align:start position:0%
+want you to see hey what does that
+mean so answer the question about the
+
+ align:start position:0%
+mean so answer the question about the
+ 
+
+ align:start position:0%
+mean so answer the question about the
+the Blackboard and the
+
+ align:start position:0%
+the Blackboard and the
+ 
+
+ align:start position:0%
+the Blackboard and the
+floor are those two subspaces they're
+
+ align:start position:0%
+floor are those two subspaces they're
+ 
+
+ align:start position:0%
+floor are those two subspaces they're
+they're two-dimensional right and we're
+
+ align:start position:0%
+they're two-dimensional right and we're
+ 
+
+ align:start position:0%
+they're two-dimensional right and we're
+in
+
+ align:start position:0%
+in
+ 
+
+ align:start position:0%
+in
+R3 it's like the XZ plane or something
+
+ align:start position:0%
+R3 it's like the XZ plane or something
+ 
+
+ align:start position:0%
+R3 it's like the XZ plane or something
+and the XY
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+plane are they
+
+ align:start position:0%
+plane are they
+ 
+
+ align:start position:0%
+plane are they
+orthogonal is every Vector in the black
+
+ align:start position:0%
+orthogonal is every Vector in the black
+ 
+
+ align:start position:0%
+orthogonal is every Vector in the black
+board orthogonal to every Vector in the
+
+ align:start position:0%
+board orthogonal to every Vector in the
+ 
+
+ align:start position:0%
+board orthogonal to every Vector in the
+floor starting from the origin right
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+there yes or no I could take a
+
+ align:start position:0%
+there yes or no I could take a
+ 
+
+ align:start position:0%
+there yes or no I could take a
+vote probably get some yeses and some
+
+ align:start position:0%
+vote probably get some yeses and some
+ 
+
+ align:start position:0%
+vote probably get some yeses and some
+NOS no is the answer they're not you can
+
+ align:start position:0%
+NOS no is the answer they're not you can
+ 
+
+ align:start position:0%
+NOS no is the answer they're not you can
+tell me a vector in the Blackboard and a
+
+ align:start position:0%
+tell me a vector in the Blackboard and a
+ 
+
+ align:start position:0%
+tell me a vector in the Blackboard and a
+vector in the floor that are not
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+orthogonal uh which which well you can
+
+ align:start position:0%
+orthogonal uh which which well you can
+ 
+
+ align:start position:0%
+orthogonal uh which which well you can
+tell me quite a few I guess maybe like I
+
+ align:start position:0%
+tell me quite a few I guess maybe like I
+ 
+
+ align:start position:0%
+tell me quite a few I guess maybe like I
+could take some 45° guy in the
+
+ align:start position:0%
+could take some 45° guy in the
+ 
+
+ align:start position:0%
+could take some 45° guy in the
+Blackboard and some thing in the
+
+ align:start position:0%
+Blackboard and some thing in the
+ 
+
+ align:start position:0%
+Blackboard and some thing in the
+floor that that aren't at 90° right in
+
+ align:start position:0%
+floor that that aren't at 90° right in
+ 
+
+ align:start position:0%
+floor that that aren't at 90° right in
+fact even more you could tell me a
+
+ align:start position:0%
+fact even more you could tell me a
+ 
+
+ align:start position:0%
+fact even more you could tell me a
+vector that's in both the Blackboard
+
+ align:start position:0%
+vector that's in both the Blackboard
+ 
+
+ align:start position:0%
+vector that's in both the Blackboard
+plane and the floor plane so it's
+
+ align:start position:0%
+plane and the floor plane so it's
+ 
+
+ align:start position:0%
+plane and the floor plane so it's
+certainly not orthogonal to itself so
+
+ align:start position:0%
+certainly not orthogonal to itself so
+ 
+
+ align:start position:0%
+certainly not orthogonal to itself so
+for sure those two planes aren't
+
+ align:start position:0%
+for sure those two planes aren't
+ 
+
+ align:start position:0%
+for sure those two planes aren't
+orthog what would that be so what's a
+
+ align:start position:0%
+orthog what would that be so what's a
+ 
+
+ align:start position:0%
+orthog what would that be so what's a
+vector that's in the
+
+ align:start position:0%
+vector that's in the
+ 
+
+ align:start position:0%
+vector that's in the
+like in in both of those
+
+ align:start position:0%
+like in in both of those
+ 
+
+ align:start position:0%
+like in in both of those
+planes this this guy running along the
+
+ align:start position:0%
+planes this this guy running along the
+ 
+
+ align:start position:0%
+planes this this guy running along the
+crack there where the intersection the
+
+ align:start position:0%
+crack there where the intersection the
+ 
+
+ align:start position:0%
+crack there where the intersection the
+intersection a
+
+ align:start position:0%
+intersection a
+ 
+
+ align:start position:0%
+intersection a
+vector if two subspaces meet some Vector
+
+ align:start position:0%
+vector if two subspaces meet some Vector
+ 
+
+ align:start position:0%
+vector if two subspaces meet some Vector
+well then for sure they're not
+
+ align:start position:0%
+well then for sure they're not
+ 
+
+ align:start position:0%
+well then for sure they're not
+orthogonal
+
+ align:start position:0%
+orthogonal
+ 
+
+ align:start position:0%
+orthogonal
+because that Vector is in one and it's
+
+ align:start position:0%
+because that Vector is in one and it's
+ 
+
+ align:start position:0%
+because that Vector is in one and it's
+in the other and it's not orthogonal to
+
+ align:start position:0%
+in the other and it's not orthogonal to
+ 
+
+ align:start position:0%
+in the other and it's not orthogonal to
+itself unless it's zero so the only I
+
+ align:start position:0%
+itself unless it's zero so the only I
+ 
+
+ align:start position:0%
+itself unless it's zero so the only I
+mean so or
+
+ align:start position:0%
+mean so or
+ 
+
+ align:start position:0%
+mean so or
+oral if for me to say these two
+
+ align:start position:0%
+oral if for me to say these two
+ 
+
+ align:start position:0%
+oral if for me to say these two
+subspaces are orthogonal first of all
+
+ align:start position:0%
+subspaces are orthogonal first of all
+ 
+
+ align:start position:0%
+subspaces are orthogonal first of all
+I'm certainly saying that they don't
+
+ align:start position:0%
+I'm certainly saying that they don't
+ 
+
+ align:start position:0%
+I'm certainly saying that they don't
+intersect in
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+any uh nonzero B but also I mean more
+
+ align:start position:0%
+any uh nonzero B but also I mean more
+ 
+
+ align:start position:0%
+any uh nonzero B but also I mean more
+than that just not intersecting isn't
+
+ align:start position:0%
+than that just not intersecting isn't
+ 
+
+ align:start position:0%
+than that just not intersecting isn't
+good enough so give me an
+
+ align:start position:0%
+good enough so give me an
+ 
+
+ align:start position:0%
+good enough so give me an
+example oh that's say in the
+
+ align:start position:0%
+example oh that's say in the
+ 
+
+ align:start position:0%
+example oh that's say in the
+plane oh what when do we have orthog
+
+ align:start position:0%
+plane oh what when do we have orthog
+ 
+
+ align:start position:0%
+plane oh what when do we have orthog
+subspaces in the plane yeah tell me in
+
+ align:start position:0%
+subspaces in the plane yeah tell me in
+ 
+
+ align:start position:0%
+subspaces in the plane yeah tell me in
+the plane so we don't there aren't that
+
+ align:start position:0%
+the plane so we don't there aren't that
+ 
+
+ align:start position:0%
+the plane so we don't there aren't that
+many different subspaces in the plane
+
+ align:start position:0%
+many different subspaces in the plane
+ 
+
+ align:start position:0%
+many different subspaces in the plane
+what what have we got in the plane as
+
+ align:start position:0%
+what what have we got in the plane as
+ 
+
+ align:start position:0%
+what what have we got in the plane as
+possible sub
+
+ align:start position:0%
+possible sub
+ 
+
+ align:start position:0%
+possible sub
+spaces the zero Vector real
+
+ align:start position:0%
+spaces the zero Vector real
+ 
+
+ align:start position:0%
+spaces the zero Vector real
+small uh aign through the
+
+ align:start position:0%
+small uh aign through the
+ 
+
+ align:start position:0%
+small uh aign through the
+origin or the whole
+
+ align:start position:0%
+origin or the whole
+ 
+
+ align:start position:0%
+origin or the whole
+plane okay now so when is a line through
+
+ align:start position:0%
+plane okay now so when is a line through
+ 
+
+ align:start position:0%
+plane okay now so when is a line through
+the origin orthogonal to the whole
+
+ align:start position:0%
+the origin orthogonal to the whole
+ 
+
+ align:start position:0%
+the origin orthogonal to the whole
+plane
+
+ align:start position:0%
+plane
+ 
+
+ align:start position:0%
+plane
+never right never when is a line through
+
+ align:start position:0%
+never right never when is a line through
+ 
+
+ align:start position:0%
+never right never when is a line through
+the origin orthogonal to the zero
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Subspace always right when is a line
+
+ align:start position:0%
+Subspace always right when is a line
+ 
+
+ align:start position:0%
+Subspace always right when is a line
+through the origin orthogonal to a a
+
+ align:start position:0%
+through the origin orthogonal to a a
+ 
+
+ align:start position:0%
+through the origin orthogonal to a a
+different line through the origin well
+
+ align:start position:0%
+different line through the origin well
+ 
+
+ align:start position:0%
+different line through the origin well
+that's the case that we all have a clear
+
+ align:start position:0%
+that's the case that we all have a clear
+ 
+
+ align:start position:0%
+that's the case that we all have a clear
+picture of they the two lines have to
+
+ align:start position:0%
+picture of they the two lines have to
+ 
+
+ align:start position:0%
+picture of they the two lines have to
+meet at 90° they have only the so that
+
+ align:start position:0%
+meet at 90° they have only the so that
+ 
+
+ align:start position:0%
+meet at 90° they have only the so that
+so that's like this simple case I'm
+
+ align:start position:0%
+so that's like this simple case I'm
+ 
+
+ align:start position:0%
+so that's like this simple case I'm
+talking about there's one Subspace
+
+ align:start position:0%
+talking about there's one Subspace
+ 
+
+ align:start position:0%
+talking about there's one Subspace
+there's the other Subspace they only
+
+ align:start position:0%
+there's the other Subspace they only
+ 
+
+ align:start position:0%
+there's the other Subspace they only
+meet at zero and they're orthog okay
+
+ align:start position:0%
+meet at zero and they're orthog okay
+ 
+
+ align:start position:0%
+meet at zero and they're orthog okay
+now so we now know what it means for two
+
+ align:start position:0%
+now so we now know what it means for two
+ 
+
+ align:start position:0%
+now so we now know what it means for two
+subspaces to be orthogonal and now I
+
+ align:start position:0%
+subspaces to be orthogonal and now I
+ 
+
+ align:start position:0%
+subspaces to be orthogonal and now I
+want to say that this is true for the
+
+ align:start position:0%
+want to say that this is true for the
+ 
+
+ align:start position:0%
+want to say that this is true for the
+row space and the null space okay so
+
+ align:start position:0%
+row space and the null space okay so
+ 
+
+ align:start position:0%
+row space and the null space okay so
+that's the that's the neat fact so row
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+space is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+orthogonal to the null space now how did
+
+ align:start position:0%
+orthogonal to the null space now how did
+ 
+
+ align:start position:0%
+orthogonal to the null space now how did
+I come up with
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that but you see the like it's great
+
+ align:start position:0%
+that but you see the like it's great
+ 
+
+ align:start position:0%
+that but you see the like it's great
+that means that these that these
+
+ align:start position:0%
+that means that these that these
+ 
+
+ align:start position:0%
+that means that these that these
+subspaces are just the right things
+
+ align:start position:0%
+subspaces are just the right things
+ 
+
+ align:start position:0%
+subspaces are just the right things
+they're just cutting the cutting the
+
+ align:start position:0%
+they're just cutting the cutting the
+ 
+
+ align:start position:0%
+they're just cutting the cutting the
+whole Space up into two perpendicular
+
+ align:start position:0%
+whole Space up into two perpendicular
+ 
+
+ align:start position:0%
+whole Space up into two perpendicular
+subspaces Okay so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+why well what have I
+
+ align:start position:0%
+why well what have I
+ 
+
+ align:start position:0%
+why well what have I
+got to work with all I know is the null
+
+ align:start position:0%
+got to work with all I know is the null
+ 
+
+ align:start position:0%
+got to work with all I know is the null
+space the null space has vectors that
+
+ align:start position:0%
+space the null space has vectors that
+ 
+
+ align:start position:0%
+space the null space has vectors that
+solve a x = z so this is a this is a guy
+
+ align:start position:0%
+solve a x = z so this is a this is a guy
+ 
+
+ align:start position:0%
+solve a x = z so this is a this is a guy
+x x is in the null
+
+ align:start position:0%
+x x is in the null
+ 
+
+ align:start position:0%
+x x is in the null
+space then ax is
+
+ align:start position:0%
+space then ax is
+ 
+
+ align:start position:0%
+space then ax is
+zero so why
+
+ align:start position:0%
+zero so why
+ 
+
+ align:start position:0%
+zero so why
+is an orthogonal to the rows of
+
+ align:start position:0%
+is an orthogonal to the rows of
+ 
+
+ align:start position:0%
+is an orthogonal to the rows of
+a if I write down axal Z which is all I
+
+ align:start position:0%
+a if I write down axal Z which is all I
+ 
+
+ align:start position:0%
+a if I write down axal Z which is all I
+know about the null
+
+ align:start position:0%
+know about the null
+ 
+
+ align:start position:0%
+know about the null
+space
+
+ align:start position:0%
+space
+ 
+
+ align:start position:0%
+space
+then I guess I want you to see that
+
+ align:start position:0%
+then I guess I want you to see that
+ 
+
+ align:start position:0%
+then I guess I want you to see that
+that's telling me just that equation
+
+ align:start position:0%
+that's telling me just that equation
+ 
+
+ align:start position:0%
+that's telling me just that equation
+right there is telling
+
+ align:start position:0%
+right there is telling
+ 
+
+ align:start position:0%
+right there is telling
+me that the rows of a let me write it
+
+ align:start position:0%
+me that the rows of a let me write it
+ 
+
+ align:start position:0%
+me that the rows of a let me write it
+out there's Row one of
+
+ align:start position:0%
+out there's Row one of
+ 
+
+ align:start position:0%
+out there's Row one of
+a row
+
+ align:start position:0%
+a row
+ 
+
+ align:start position:0%
+a row
+two row M
+
+ align:start position:0%
+two row M
+ 
+
+ align:start position:0%
+two row M
+of a that that's a and it's multiplying
+
+ align:start position:0%
+of a that that's a and it's multiplying
+ 
+
+ align:start position:0%
+of a that that's a and it's multiplying
+X and it's
+
+ align:start position:0%
+X and it's
+ 
+
+ align:start position:0%
+X and it's
+producing
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+zero okay written out that way you'll
+
+ align:start position:0%
+zero okay written out that way you'll
+ 
+
+ align:start position:0%
+zero okay written out that way you'll
+see
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+it so I'm saying that a vector in the
+
+ align:start position:0%
+it so I'm saying that a vector in the
+ 
+
+ align:start position:0%
+it so I'm saying that a vector in the
+row space is perpendicular to this guy X
+
+ align:start position:0%
+row space is perpendicular to this guy X
+ 
+
+ align:start position:0%
+row space is perpendicular to this guy X
+in the null space and you see
+
+ align:start position:0%
+in the null space and you see
+ 
+
+ align:start position:0%
+in the null space and you see
+why because this equation equation is
+
+ align:start position:0%
+why because this equation equation is
+ 
+
+ align:start position:0%
+why because this equation equation is
+telling you that Row one of
+
+ align:start position:0%
+telling you that Row one of
+ 
+
+ align:start position:0%
+telling you that Row one of
+a multiplying that's a that's a DOT
+
+ align:start position:0%
+a multiplying that's a that's a DOT
+ 
+
+ align:start position:0%
+a multiplying that's a that's a DOT
+product right Row one away dot product
+
+ align:start position:0%
+product right Row one away dot product
+ 
+
+ align:start position:0%
+product right Row one away dot product
+with this x is producing this
+
+ align:start position:0%
+with this x is producing this
+ 
+
+ align:start position:0%
+with this x is producing this
+zero so X is orthogonal to the first
+
+ align:start position:0%
+zero so X is orthogonal to the first
+ 
+
+ align:start position:0%
+zero so X is orthogonal to the first
+row and to the second row row 2 of a x
+
+ align:start position:0%
+row and to the second row row 2 of a x
+ 
+
+ align:start position:0%
+row and to the second row row 2 of a x
+is giving that zero row M of a * X is
+
+ align:start position:0%
+is giving that zero row M of a * X is
+ 
+
+ align:start position:0%
+is giving that zero row M of a * X is
+giving that zero so X is the equation is
+
+ align:start position:0%
+giving that zero so X is the equation is
+ 
+
+ align:start position:0%
+giving that zero so X is the equation is
+telling me that X is orth to all the
+
+ align:start position:0%
+telling me that X is orth to all the
+ 
+
+ align:start position:0%
+telling me that X is orth to all the
+rows right it's just sitting there
+
+ align:start position:0%
+rows right it's just sitting there
+ 
+
+ align:start position:0%
+rows right it's just sitting there
+that's all we we it had to be sitting
+
+ align:start position:0%
+that's all we we it had to be sitting
+ 
+
+ align:start position:0%
+that's all we we it had to be sitting
+there because we didn't know anything
+
+ align:start position:0%
+there because we didn't know anything
+ 
+
+ align:start position:0%
+there because we didn't know anything
+more about the no space than this and
+
+ align:start position:0%
+more about the no space than this and
+ 
+
+ align:start position:0%
+more about the no space than this and
+now I guess to be
+
+ align:start position:0%
+now I guess to be
+ 
+
+ align:start position:0%
+now I guess to be
+totally complete here I've now checked
+
+ align:start position:0%
+totally complete here I've now checked
+ 
+
+ align:start position:0%
+totally complete here I've now checked
+that X is orthogonal to each separate
+
+ align:start position:0%
+that X is orthogonal to each separate
+ 
+
+ align:start position:0%
+that X is orthogonal to each separate
+row but what else strictly speaking do I
+
+ align:start position:0%
+row but what else strictly speaking do I
+ 
+
+ align:start position:0%
+row but what else strictly speaking do I
+have to
+
+ align:start position:0%
+have to
+ 
+
+ align:start position:0%
+have to
+do
+
+ align:start position:0%
+do
+ 
+
+ align:start position:0%
+do
+that that what to show that those
+
+ align:start position:0%
+that that what to show that those
+ 
+
+ align:start position:0%
+that that what to show that those
+subspaces are orthogonal I have to take
+
+ align:start position:0%
+subspaces are orthogonal I have to take
+ 
+
+ align:start position:0%
+subspaces are orthogonal I have to take
+this X in the null space and show that
+
+ align:start position:0%
+this X in the null space and show that
+ 
+
+ align:start position:0%
+this X in the null space and show that
+it's orthogonal to
+
+ align:start position:0%
+it's orthogonal to
+ 
+
+ align:start position:0%
+it's orthogonal to
+every Vector in the row space every
+
+ align:start position:0%
+every Vector in the row space every
+ 
+
+ align:start position:0%
+every Vector in the row space every
+Vector in the row space so what what
+
+ align:start position:0%
+Vector in the row space so what what
+ 
+
+ align:start position:0%
+Vector in the row space so what what
+else is in the row
+
+ align:start position:0%
+else is in the row
+ 
+
+ align:start position:0%
+else is in the row
+space the this row is in the row space
+
+ align:start position:0%
+space the this row is in the row space
+ 
+
+ align:start position:0%
+space the this row is in the row space
+that row is in the row space they
+
+ align:start position:0%
+that row is in the row space they
+ 
+
+ align:start position:0%
+that row is in the row space they
+they're all there but that's not the
+
+ align:start position:0%
+they're all there but that's not the
+ 
+
+ align:start position:0%
+they're all there but that's not the
+whole row space right we just have to
+
+ align:start position:0%
+whole row space right we just have to
+ 
+
+ align:start position:0%
+whole row space right we just have to
+like remember what does it mean what
+
+ align:start position:0%
+like remember what does it mean what
+ 
+
+ align:start position:0%
+like remember what does it mean what
+does that word space telling
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and what else is in the row
+
+ align:start position:0%
+and what else is in the row
+ 
+
+ align:start position:0%
+and what else is in the row
+space besides the
+
+ align:start position:0%
+space besides the
+ 
+
+ align:start position:0%
+space besides the
+rows all
+
+ align:start position:0%
+rows all
+ 
+
+ align:start position:0%
+rows all
+their
+
+ align:start position:0%
+their
+ 
+
+ align:start position:0%
+their
+combination so I really have to check
+
+ align:start position:0%
+combination so I really have to check
+ 
+
+ align:start position:0%
+combination so I really have to check
+that sure enough if x is perpendicular
+
+ align:start position:0%
+that sure enough if x is perpendicular
+ 
+
+ align:start position:0%
+that sure enough if x is perpendicular
+Row one row two all the all the
+
+ align:start position:0%
+Row one row two all the all the
+ 
+
+ align:start position:0%
+Row one row two all the all the
+different separate rows then also X is
+
+ align:start position:0%
+different separate rows then also X is
+ 
+
+ align:start position:0%
+different separate rows then also X is
+perpendicular to a combination of the
+
+ align:start position:0%
+perpendicular to a combination of the
+ 
+
+ align:start position:0%
+perpendicular to a combination of the
+rows and that's just matrix
+
+ align:start position:0%
+rows and that's just matrix
+ 
+
+ align:start position:0%
+rows and that's just matrix
+multiplication again you know I have
+
+ align:start position:0%
+multiplication again you know I have
+ 
+
+ align:start position:0%
+multiplication again you know I have
+Row
+
+ align:start position:0%
+Row
+ 
+
+ align:start position:0%
+Row
+one transpose X is
+
+ align:start position:0%
+one transpose X is
+ 
+
+ align:start position:0%
+one transpose X is
+zero so on row two transpose X is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+zero so I'm entitled to multiply that by
+
+ align:start position:0%
+zero so I'm entitled to multiply that by
+ 
+
+ align:start position:0%
+zero so I'm entitled to multiply that by
+some C1 this by some C2 I still have
+
+ align:start position:0%
+some C1 this by some C2 I still have
+ 
+
+ align:start position:0%
+some C1 this by some C2 I still have
+zeros I'm entitled to add so I have C1
+
+ align:start position:0%
+zeros I'm entitled to add so I have C1
+ 
+
+ align:start position:0%
+zeros I'm entitled to add so I have C1
+Row one so so all this when I put that
+
+ align:start position:0%
+Row one so so all this when I put that
+ 
+
+ align:start position:0%
+Row one so so all this when I put that
+together
+
+ align:start position:0%
+together
+ 
+
+ align:start position:0%
+together
+that's big parentheses see C1 Row one
+
+ align:start position:0%
+that's big parentheses see C1 Row one
+ 
+
+ align:start position:0%
+that's big parentheses see C1 Row one
+plus C2 row2 and so on transpose X is
+
+ align:start position:0%
+plus C2 row2 and so on transpose X is
+ 
+
+ align:start position:0%
+plus C2 row2 and so on transpose X is
+zero right I just added the zeros and
+
+ align:start position:0%
+zero right I just added the zeros and
+ 
+
+ align:start position:0%
+zero right I just added the zeros and
+got zero and I just added these
+
+ align:start position:0%
+got zero and I just added these
+ 
+
+ align:start position:0%
+got zero and I just added these
+following the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+rules no no big deal the whole point was
+
+ align:start position:0%
+rules no no big deal the whole point was
+ 
+
+ align:start position:0%
+rules no no big deal the whole point was
+right sitting in that
+
+ align:start position:0%
+right sitting in that
+ 
+
+ align:start position:0%
+right sitting in that
+okay so if I come back to this figure
+
+ align:start position:0%
+okay so if I come back to this figure
+ 
+
+ align:start position:0%
+okay so if I come back to this figure
+now
+
+ align:start position:0%
+now
+ 
+
+ align:start position:0%
+now
+now I'm like a happier person cuz I have
+
+ align:start position:0%
+now I'm like a happier person cuz I have
+ 
+
+ align:start position:0%
+now I'm like a happier person cuz I have
+this uh the I now see how those
+
+ align:start position:0%
+this uh the I now see how those
+ 
+
+ align:start position:0%
+this uh the I now see how those
+subspaces are oriented and these
+
+ align:start position:0%
+subspaces are oriented and these
+ 
+
+ align:start position:0%
+subspaces are oriented and these
+subspaces are also oriented well
+
+ align:start position:0%
+subspaces are also oriented well
+ 
+
+ align:start position:0%
+subspaces are also oriented well
+actually why why is that
+
+ align:start position:0%
+actually why why is that
+ 
+
+ align:start position:0%
+actually why why is that
+orthogonality well it's the same
+
+ align:start position:0%
+orthogonality well it's the same
+ 
+
+ align:start position:0%
+orthogonality well it's the same
+statement for a transpose that that one
+
+ align:start position:0%
+statement for a transpose that that one
+ 
+
+ align:start position:0%
+statement for a transpose that that one
+was for a so I won't take time to prove
+
+ align:start position:0%
+was for a so I won't take time to prove
+ 
+
+ align:start position:0%
+was for a so I won't take time to prove
+it again because
+
+ align:start position:0%
+it again because
+ 
+
+ align:start position:0%
+it again because
+it's cuz we checked it for every Matrix
+
+ align:start position:0%
+it's cuz we checked it for every Matrix
+ 
+
+ align:start position:0%
+it's cuz we checked it for every Matrix
+and a transposes just as good a matrix
+
+ align:start position:0%
+and a transposes just as good a matrix
+ 
+
+ align:start position:0%
+and a transposes just as good a matrix
+as a so we're orthogonal over there so
+
+ align:start position:0%
+as a so we're orthogonal over there so
+ 
+
+ align:start position:0%
+as a so we're orthogonal over there so
+we really
+
+ align:start position:0%
+we really
+ 
+
+ align:start position:0%
+we really
+have carved up this these this this was
+
+ align:start position:0%
+have carved up this these this this was
+ 
+
+ align:start position:0%
+have carved up this these this this was
+like carving up M dimensional space into
+
+ align:start position:0%
+like carving up M dimensional space into
+ 
+
+ align:start position:0%
+like carving up M dimensional space into
+two
+
+ align:start position:0%
+two
+ 
+
+ align:start position:0%
+two
+subspaces and this one was carving Up N
+
+ align:start position:0%
+subspaces and this one was carving Up N
+ 
+
+ align:start position:0%
+subspaces and this one was carving Up N
+dimensional space
+
+ align:start position:0%
+dimensional space
+ 
+
+ align:start position:0%
+dimensional space
+into two
+
+ align:start position:0%
+into two
+ 
+
+ align:start position:0%
+into two
+subspaces
+
+ align:start position:0%
+subspaces
+ 
+
+ align:start position:0%
+subspaces
+and well one more thing here one more
+
+ align:start position:0%
+and well one more thing here one more
+ 
+
+ align:start position:0%
+and well one more thing here one more
+important
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+thing let let me move into into into
+
+ align:start position:0%
+thing let let me move into into into
+ 
+
+ align:start position:0%
+thing let let me move into into into
+three
+
+ align:start position:0%
+three
+ 
+
+ align:start position:0%
+three
+dimensions tell me a couple of
+
+ align:start position:0%
+dimensions tell me a couple of
+ 
+
+ align:start position:0%
+dimensions tell me a couple of
+orthogonal
+
+ align:start position:0%
+orthogonal
+ 
+
+ align:start position:0%
+orthogonal
+subspaces in three
+
+ align:start position:0%
+subspaces in three
+ 
+
+ align:start position:0%
+subspaces in three
+dimensions that somehow don't carve up
+
+ align:start position:0%
+dimensions that somehow don't carve up
+ 
+
+ align:start position:0%
+dimensions that somehow don't carve up
+the whole Space stuff left
+
+ align:start position:0%
+the whole Space stuff left
+ 
+
+ align:start position:0%
+the whole Space stuff left
+there I'm thinking of a couple of
+
+ align:start position:0%
+there I'm thinking of a couple of
+ 
+
+ align:start position:0%
+there I'm thinking of a couple of
+orthogonal
+
+ align:start position:0%
+orthogonal
+ 
+
+ align:start position:0%
+orthogonal
+lines if I suppose I'm in three
+
+ align:start position:0%
+lines if I suppose I'm in three
+ 
+
+ align:start position:0%
+lines if I suppose I'm in three
+dimensions
+
+ align:start position:0%
+dimensions
+ 
+
+ align:start position:0%
+dimensions
+R3 and I have one line one
+
+ align:start position:0%
+R3 and I have one line one
+ 
+
+ align:start position:0%
+R3 and I have one line one
+onedimensional Subspace and a
+
+ align:start position:0%
+onedimensional Subspace and a
+ 
+
+ align:start position:0%
+onedimensional Subspace and a
+perpendicular one could those be the row
+
+ align:start position:0%
+perpendicular one could those be the row
+ 
+
+ align:start position:0%
+perpendicular one could those be the row
+space and the null
+
+ align:start position:0%
+space and the null
+ 
+
+ align:start position:0%
+space and the null
+space could those be the row space and
+
+ align:start position:0%
+space could those be the row space and
+ 
+
+ align:start position:0%
+space could those be the row space and
+the null space could I could I be in
+
+ align:start position:0%
+the null space could I could I be in
+ 
+
+ align:start position:0%
+the null space could I could I be in
+three
+
+ align:start position:0%
+three
+ 
+
+ align:start position:0%
+three
+dimensions
+
+ align:start position:0%
+dimensions
+ 
+
+ align:start position:0%
+dimensions
+and have a row space that's a line and a
+
+ align:start position:0%
+and have a row space that's a line and a
+ 
+
+ align:start position:0%
+and have a row space that's a line and a
+null space that's a
+
+ align:start position:0%
+null space that's a
+ 
+
+ align:start position:0%
+null space that's a
+line no why
+
+ align:start position:0%
+line no why
+ 
+
+ align:start position:0%
+line no why
+not because the dimensions aren't right
+
+ align:start position:0%
+not because the dimensions aren't right
+ 
+
+ align:start position:0%
+not because the dimensions aren't right
+right the dimensions are no good the the
+
+ align:start position:0%
+right the dimensions are no good the the
+ 
+
+ align:start position:0%
+right the dimensions are no good the the
+dimensions here R and N minus r they add
+
+ align:start position:0%
+dimensions here R and N minus r they add
+ 
+
+ align:start position:0%
+dimensions here R and N minus r they add
+up to three they add up to
+
+ align:start position:0%
+up to three they add up to
+ 
+
+ align:start position:0%
+up to three they add up to
+n if I take it's just if I just follow
+
+ align:start position:0%
+n if I take it's just if I just follow
+ 
+
+ align:start position:0%
+n if I take it's just if I just follow
+that
+
+ align:start position:0%
+that
+ 
+
+ align:start position:0%
+that
+example if if if
+
+ align:start position:0%
+example if if if
+ 
+
+ align:start position:0%
+example if if if
+if the row space is onedimensional
+
+ align:start position:0%
+if the row space is onedimensional
+ 
+
+ align:start position:0%
+if the row space is onedimensional
+suppose a is what's a good in I'm in R3
+
+ align:start position:0%
+suppose a is what's a good in I'm in R3
+ 
+
+ align:start position:0%
+suppose a is what's a good in I'm in R3
+I want a one-dimensional row space let
+
+ align:start position:0%
+I want a one-dimensional row space let
+ 
+
+ align:start position:0%
+I want a one-dimensional row space let
+me take 1 25 2
+
+ align:start position:0%
+me take 1 25 2
+ 
+
+ align:start position:0%
+me take 1 25 2
+41 what's the dimension of that row
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+space
+
+ align:start position:0%
+space
+ 
+
+ align:start position:0%
+space
+one what's the dimension of the null
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+space tell what's the null space look
+
+ align:start position:0%
+space tell what's the null space look
+ 
+
+ align:start position:0%
+space tell what's the null space look
+look like in that case the row space is
+
+ align:start position:0%
+look like in that case the row space is
+ 
+
+ align:start position:0%
+look like in that case the row space is
+a line right onedimensional it's just a
+
+ align:start position:0%
+a line right onedimensional it's just a
+ 
+
+ align:start position:0%
+a line right onedimensional it's just a
+line through
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+125 geometrically what's the row space
+
+ align:start position:0%
+125 geometrically what's the row space
+ 
+
+ align:start position:0%
+125 geometrically what's the row space
+look
+
+ align:start position:0%
+look
+ 
+
+ align:start position:0%
+look
+like it's
+
+ align:start position:0%
+like it's
+ 
+
+ align:start position:0%
+like it's
+a what's its Dimension so so here our
+
+ align:start position:0%
+a what's its Dimension so so here our
+ 
+
+ align:start position:0%
+a what's its Dimension so so here our
+here n is
+
+ align:start position:0%
+here n is
+ 
+
+ align:start position:0%
+here n is
+three the rank is
+
+ align:start position:0%
+three the rank is
+ 
+
+ align:start position:0%
+three the rank is
+one so the dimension of the null space
+
+ align:start position:0%
+one so the dimension of the null space
+ 
+
+ align:start position:0%
+one so the dimension of the null space
+so I'm looking
+
+ align:start position:0%
+so I'm looking
+ 
+
+ align:start position:0%
+so I'm looking
+at this x X1 X2 X3 to give
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+zero so the dimension of the null space
+
+ align:start position:0%
+zero so the dimension of the null space
+ 
+
+ align:start position:0%
+zero so the dimension of the null space
+is we all know is two right it's a plane
+
+ align:start position:0%
+is we all know is two right it's a plane
+ 
+
+ align:start position:0%
+is we all know is two right it's a plane
+and now actually we know we see better
+
+ align:start position:0%
+and now actually we know we see better
+ 
+
+ align:start position:0%
+and now actually we know we see better
+what plane is it what plane is
+
+ align:start position:0%
+what plane is it what plane is
+ 
+
+ align:start position:0%
+what plane is it what plane is
+it it's the plane that's perpendicular
+
+ align:start position:0%
+it it's the plane that's perpendicular
+ 
+
+ align:start position:0%
+it it's the plane that's perpendicular
+to when
+
+ align:start position:0%
+to when
+ 
+
+ align:start position:0%
+to when
+25 right we now see in fact the 2410
+
+ align:start position:0%
+25 right we now see in fact the 2410
+ 
+
+ align:start position:0%
+25 right we now see in fact the 2410
+didn't actually have any effect at all I
+
+ align:start position:0%
+didn't actually have any effect at all I
+ 
+
+ align:start position:0%
+didn't actually have any effect at all I
+could have just ignored that that didn't
+
+ align:start position:0%
+could have just ignored that that didn't
+ 
+
+ align:start position:0%
+could have just ignored that that didn't
+change the row space or the null
+
+ align:start position:0%
+change the row space or the null
+ 
+
+ align:start position:0%
+change the row space or the null
+space I'll just make that one
+
+ align:start position:0%
+space I'll just make that one
+ 
+
+ align:start position:0%
+space I'll just make that one
+equation yeah okay sure that's that's
+
+ align:start position:0%
+equation yeah okay sure that's that's
+ 
+
+ align:start position:0%
+equation yeah okay sure that's that's
+the easiest to deal with one
+
+ align:start position:0%
+the easiest to deal with one
+ 
+
+ align:start position:0%
+the easiest to deal with one
+equation three
+
+ align:start position:0%
+equation three
+ 
+
+ align:start position:0%
+equation three
+unknowns and
+
+ align:start position:0%
+unknowns and
+ 
+
+ align:start position:0%
+unknowns and
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+I want to ask
+
+ align:start position:0%
+I want to ask
+ 
+
+ align:start position:0%
+I want to ask
+uh what's what does the equation give me
+
+ align:start position:0%
+uh what's what does the equation give me
+ 
+
+ align:start position:0%
+uh what's what does the equation give me
+it gives me the null
+
+ align:start position:0%
+it gives me the null
+ 
+
+ align:start position:0%
+it gives me the null
+space and you would have
+
+ align:start position:0%
+space and you would have
+ 
+
+ align:start position:0%
+space and you would have
+said back in September you would have
+
+ align:start position:0%
+said back in September you would have
+ 
+
+ align:start position:0%
+said back in September you would have
+said it gives you a plane and we're
+
+ align:start position:0%
+said it gives you a plane and we're
+ 
+
+ align:start position:0%
+said it gives you a plane and we're
+we're completely right and the plane it
+
+ align:start position:0%
+we're completely right and the plane it
+ 
+
+ align:start position:0%
+we're completely right and the plane it
+gives you the normal Vector you remember
+
+ align:start position:0%
+gives you the normal Vector you remember
+ 
+
+ align:start position:0%
+gives you the normal Vector you remember
+in calculus there was this D normal
+
+ align:start position:0%
+in calculus there was this D normal
+ 
+
+ align:start position:0%
+in calculus there was this D normal
+Vector called n well there it is
+
+ align:start position:0%
+Vector called n well there it is
+ 
+
+ align:start position:0%
+Vector called n well there it is
+
+ align:start position:0%
+ 
+
+ align:start position:0%
+okay so
+
+ align:start position:0%
+okay so
+ 
+
+ align:start position:0%
+okay so
+uh that what what is the what's the
+
+ align:start position:0%
+uh that what what is the what's the
+ 
+
+ align:start position:0%
+uh that what what is the what's the
+point I want to make here I want to make
+
+ align:start position:0%
+point I want to make here I want to make
+ 
+
+ align:start position:0%
+point I want to make here I want to make
+I want to emphasize that not only are
+
+ align:start position:0%
+I want to emphasize that not only are
+ 
+
+ align:start position:0%
+I want to emphasize that not only are
+the let me write it in
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+words so I want to write the null
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+space and the row space
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+are
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+orthogonal that's that's this neat fact
+
+ align:start position:0%
+orthogonal that's that's this neat fact
+ 
+
+ align:start position:0%
+orthogonal that's that's this neat fact
+which we we've just checked from axal Z
+
+ align:start position:0%
+which we we've just checked from axal Z
+ 
+
+ align:start position:0%
+which we we've just checked from axal Z
+but now I want to say I want to say more
+
+ align:start position:0%
+but now I want to say I want to say more
+ 
+
+ align:start position:0%
+but now I want to say I want to say more
+because there's a little more that's
+
+ align:start position:0%
+because there's a little more that's
+ 
+
+ align:start position:0%
+because there's a little more that's
+true their Dimensions add to the whole
+
+ align:start position:0%
+true their Dimensions add to the whole
+ 
+
+ align:start position:0%
+true their Dimensions add to the whole
+Space so that's like a little extra
+
+ align:start position:0%
+Space so that's like a little extra
+ 
+
+ align:start position:0%
+Space so that's like a little extra
+information
+
+ align:start position:0%
+information
+ 
+
+ align:start position:0%
+information
+that it's not like I could I couldn't
+
+ align:start position:0%
+that it's not like I could I couldn't
+ 
+
+ align:start position:0%
+that it's not like I could I couldn't
+have a line and a line in three
+
+ align:start position:0%
+have a line and a line in three
+ 
+
+ align:start position:0%
+have a line and a line in three
+dimensions those those don't add up one
+
+ align:start position:0%
+dimensions those those don't add up one
+ 
+
+ align:start position:0%
+dimensions those those don't add up one
+and one don't add to three so I use the
+
+ align:start position:0%
+and one don't add to three so I use the
+ 
+
+ align:start position:0%
+and one don't add to three so I use the
+word orthogonal
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+complement
+
+ align:start position:0%
+complement
+ 
+
+ align:start position:0%
+complement
+in RN and the idea of this word
+
+ align:start position:0%
+in RN and the idea of this word
+ 
+
+ align:start position:0%
+in RN and the idea of this word
+compliment is
+
+ align:start position:0%
+compliment is
+ 
+
+ align:start position:0%
+compliment is
+that the orthogonal complement of a row
+
+ align:start position:0%
+that the orthogonal complement of a row
+ 
+
+ align:start position:0%
+that the orthogonal complement of a row
+space contains not just some vectors
+
+ align:start position:0%
+space contains not just some vectors
+ 
+
+ align:start position:0%
+space contains not just some vectors
+that are orthogonal to it but all so so
+
+ align:start position:0%
+that are orthogonal to it but all so so
+ 
+
+ align:start position:0%
+that are orthogonal to it but all so so
+what does that mean that means that the
+
+ align:start position:0%
+what does that mean that means that the
+ 
+
+ align:start position:0%
+what does that mean that means that the
+null
+
+ align:start position:0%
+null
+ 
+
+ align:start position:0%
+null
+space contains
+
+ align:start position:0%
+space contains
+ 
+
+ align:start position:0%
+space contains
+all not just some but all
+
+ align:start position:0%
+all not just some but all
+ 
+
+ align:start position:0%
+all not just some but all
+vectors that are perpendicular to the
+
+ align:start position:0%
+vectors that are perpendicular to the
+ 
+
+ align:start position:0%
+vectors that are perpendicular to the
+row
+
+ align:start position:0%
+row
+ 
+
+ align:start position:0%
+row
+space
+
+ align:start position:0%
+space
+ 
+
+ align:start position:0%
+space
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+really what I've done in this half of
+
+ align:start position:0%
+really what I've done in this half of
+ 
+
+ align:start position:0%
+really what I've done in this half of
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+lecture is
+
+ align:start position:0%
+lecture is
+ 
+
+ align:start position:0%
+lecture is
+just
+
+ align:start position:0%
+just
+ 
+
+ align:start position:0%
+just
+notice some of the nice geometry that
+
+ align:start position:0%
+notice some of the nice geometry that
+ 
+
+ align:start position:0%
+notice some of the nice geometry that
+that we didn't pick up before because we
+
+ align:start position:0%
+that we didn't pick up before because we
+ 
+
+ align:start position:0%
+that we didn't pick up before because we
+didn't discuss perpendicular vectors
+
+ align:start position:0%
+didn't discuss perpendicular vectors
+ 
+
+ align:start position:0%
+didn't discuss perpendicular vectors
+before but it was all sitting there and
+
+ align:start position:0%
+before but it was all sitting there and
+ 
+
+ align:start position:0%
+before but it was all sitting there and
+now we picked it up that these vectors
+
+ align:start position:0%
+now we picked it up that these vectors
+ 
+
+ align:start position:0%
+now we picked it up that these vectors
+are orthogonal complements and I guess I
+
+ align:start position:0%
+are orthogonal complements and I guess I
+ 
+
+ align:start position:0%
+are orthogonal complements and I guess I
+even call
+
+ align:start position:0%
+even call
+ 
+
+ align:start position:0%
+even call
+this part one of the fun FAL theorem of
+
+ align:start position:0%
+this part one of the fun FAL theorem of
+ 
+
+ align:start position:0%
+this part one of the fun FAL theorem of
+linear algebra the fundamental theorem
+
+ align:start position:0%
+linear algebra the fundamental theorem
+ 
+
+ align:start position:0%
+linear algebra the fundamental theorem
+of linear algebra is about these four
+
+ align:start position:0%
+of linear algebra is about these four
+ 
+
+ align:start position:0%
+of linear algebra is about these four
+subspaces so part one is about their
+
+ align:start position:0%
+subspaces so part one is about their
+ 
+
+ align:start position:0%
+subspaces so part one is about their
+Dimension maybe I should call it part
+
+ align:start position:0%
+Dimension maybe I should call it part
+ 
+
+ align:start position:0%
+Dimension maybe I should call it part
+two
+
+ align:start position:0%
+two
+ 
+
+ align:start position:0%
+two
+now their Dimensions we
+
+ align:start position:0%
+now their Dimensions we
+ 
+
+ align:start position:0%
+now their Dimensions we
+got now we're getting their
+
+ align:start position:0%
+got now we're getting their
+ 
+
+ align:start position:0%
+got now we're getting their
+orthogonality that's part
+
+ align:start position:0%
+orthogonality that's part
+ 
+
+ align:start position:0%
+orthogonality that's part
+two and part
+
+ align:start position:0%
+two and part
+ 
+
+ align:start position:0%
+two and part
+three will be about bases for orthogonal
+
+ align:start position:0%
+three will be about bases for orthogonal
+ 
+
+ align:start position:0%
+three will be about bases for orthogonal
+bases so that's uh coming up okay so I'm
+
+ align:start position:0%
+bases so that's uh coming up okay so I'm
+ 
+
+ align:start position:0%
+bases so that's uh coming up okay so I'm
+I'm
+
+ align:start position:0%
+I'm
+ 
+
+ align:start position:0%
+I'm
+uh I'm happy with that uh geometry right
+
+ align:start position:0%
+uh I'm happy with that uh geometry right
+ 
+
+ align:start position:0%
+uh I'm happy with that uh geometry right
+now
+
+ align:start position:0%
+now
+ 
+
+ align:start position:0%
+now
+okay okay now what's my next goal in
+
+ align:start position:0%
+okay okay now what's my next goal in
+ 
+
+ align:start position:0%
+okay okay now what's my next goal in
+this chapter here's the it's the main
+
+ align:start position:0%
+this chapter here's the it's the main
+ 
+
+ align:start position:0%
+this chapter here's the it's the main
+problem of the
+
+ align:start position:0%
+problem of the
+ 
+
+ align:start position:0%
+problem of the
+chapter the main problem of the chapter
+
+ align:start position:0%
+chapter the main problem of the chapter
+ 
+
+ align:start position:0%
+chapter the main problem of the chapter
+is so this is
+
+ align:start position:0%
+is so this is
+ 
+
+ align:start position:0%
+is so this is
+coming coming
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+attraction this is this is the very last
+
+ align:start position:0%
+attraction this is this is the very last
+ 
+
+ align:start position:0%
+attraction this is this is the very last
+chapter that's about axal
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+B I would like to solve that system of
+
+ align:start position:0%
+B I would like to solve that system of
+ 
+
+ align:start position:0%
+B I would like to solve that system of
+equations when there is no
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+solution you may say what a ridiculous
+
+ align:start position:0%
+solution you may say what a ridiculous
+ 
+
+ align:start position:0%
+solution you may say what a ridiculous
+thing to do but but I have to say I it's
+
+ align:start position:0%
+thing to do but but I have to say I it's
+ 
+
+ align:start position:0%
+thing to do but but I have to say I it's
+done all the time in fact it has to be
+
+ align:start position:0%
+done all the time in fact it has to be
+ 
+
+ align:start position:0%
+done all the time in fact it has to be
+done you get so so the problem is
+
+ align:start position:0%
+done you get so so the problem is
+ 
+
+ align:start position:0%
+done you get so so the problem is
+solve as the best possible solve I'll
+
+ align:start position:0%
+solve as the best possible solve I'll
+ 
+
+ align:start position:0%
+solve as the best possible solve I'll
+put
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+quote ax B
+
+ align:start position:0%
+quote ax B
+ 
+
+ align:start position:0%
+quote ax B
+when there
+
+ align:start position:0%
+when there
+ 
+
+ align:start position:0%
+when there
+is no
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+solution and of course what does that
+
+ align:start position:0%
+solution and of course what does that
+ 
+
+ align:start position:0%
+solution and of course what does that
+mean b isn't in the in the column
+
+ align:start position:0%
+mean b isn't in the in the column
+ 
+
+ align:start position:0%
+mean b isn't in the in the column
+space and it's quite typical if this
+
+ align:start position:0%
+space and it's quite typical if this
+ 
+
+ align:start position:0%
+space and it's quite typical if this
+Matrix a is rectangular if I maybe I
+
+ align:start position:0%
+Matrix a is rectangular if I maybe I
+ 
+
+ align:start position:0%
+Matrix a is rectangular if I maybe I
+have M equations and that's bigger than
+
+ align:start position:0%
+have M equations and that's bigger than
+ 
+
+ align:start position:0%
+have M equations and that's bigger than
+the number of
+
+ align:start position:0%
+the number of
+ 
+
+ align:start position:0%
+the number of
+unknowns then for sure the
+
+ align:start position:0%
+unknowns then for sure the
+ 
+
+ align:start position:0%
+unknowns then for sure the
+rank is not M the rank couldn't be M now
+
+ align:start position:0%
+rank is not M the rank couldn't be M now
+ 
+
+ align:start position:0%
+rank is not M the rank couldn't be M now
+so there will be a lot of right hand
+
+ align:start position:0%
+so there will be a lot of right hand
+ 
+
+ align:start position:0%
+so there will be a lot of right hand
+sides with no solution
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+but it here's an
+
+ align:start position:0%
+but it here's an
+ 
+
+ align:start position:0%
+but it here's an
+example some satellite is buzzing along
+
+ align:start position:0%
+example some satellite is buzzing along
+ 
+
+ align:start position:0%
+example some satellite is buzzing along
+you measure its
+
+ align:start position:0%
+you measure its
+ 
+
+ align:start position:0%
+you measure its
+position you make a th
+
+ align:start position:0%
+position you make a th
+ 
+
+ align:start position:0%
+position you make a th
+measurements so that gives you a th
+
+ align:start position:0%
+measurements so that gives you a th
+ 
+
+ align:start position:0%
+measurements so that gives you a th
+equations for the for the parameters
+
+ align:start position:0%
+equations for the for the parameters
+ 
+
+ align:start position:0%
+equations for the for the parameters
+that that that give the position but
+
+ align:start position:0%
+that that that give the position but
+ 
+
+ align:start position:0%
+that that that give the position but
+there aren't a thousand parameters it's
+
+ align:start position:0%
+there aren't a thousand parameters it's
+ 
+
+ align:start position:0%
+there aren't a thousand parameters it's
+just maybe
+
+ align:start position:0%
+just maybe
+ 
+
+ align:start position:0%
+just maybe
+six or you're measuring the you're doing
+
+ align:start position:0%
+six or you're measuring the you're doing
+ 
+
+ align:start position:0%
+six or you're measuring the you're doing
+question
+
+ align:start position:0%
+question
+ 
+
+ align:start position:0%
+question
+eres you're you're measuring uh uh
+
+ align:start position:0%
+eres you're you're measuring uh uh
+ 
+
+ align:start position:0%
+eres you're you're measuring uh uh
+resistances you're taking pulses you
+
+ align:start position:0%
+resistances you're taking pulses you
+ 
+
+ align:start position:0%
+resistances you're taking pulses you
+you're measuring somebody's pulse rate
+
+ align:start position:0%
+you're measuring somebody's pulse rate
+ 
+
+ align:start position:0%
+you're measuring somebody's pulse rate
+okay there's just one unknown the pulse
+
+ align:start position:0%
+okay there's just one unknown the pulse
+ 
+
+ align:start position:0%
+okay there's just one unknown the pulse
+rate so you measure it once okay fine
+
+ align:start position:0%
+rate so you measure it once okay fine
+ 
+
+ align:start position:0%
+rate so you measure it once okay fine
+but if you really want to know it you
+
+ align:start position:0%
+but if you really want to know it you
+ 
+
+ align:start position:0%
+but if you really want to know it you
+measure it multiple
+
+ align:start position:0%
+measure it multiple
+ 
+
+ align:start position:0%
+measure it multiple
+times but then the measurements have
+
+ align:start position:0%
+times but then the measurements have
+ 
+
+ align:start position:0%
+times but then the measurements have
+noise in them so there's the problem is
+
+ align:start position:0%
+noise in them so there's the problem is
+ 
+
+ align:start position:0%
+noise in them so there's the problem is
+that in many many problems we got too
+
+ align:start position:0%
+that in many many problems we got too
+ 
+
+ align:start position:0%
+that in many many problems we got too
+many equations and they've got noise in
+
+ align:start position:0%
+many equations and they've got noise in
+ 
+
+ align:start position:0%
+many equations and they've got noise in
+the right hand side so axal
+
+ align:start position:0%
+the right hand side so axal
+ 
+
+ align:start position:0%
+the right hand side so axal
+B I can't expect to solve it exactly
+
+ align:start position:0%
+B I can't expect to solve it exactly
+ 
+
+ align:start position:0%
+B I can't expect to solve it exactly
+right because I don't even know what the
+
+ align:start position:0%
+right because I don't even know what the
+ 
+
+ align:start position:0%
+right because I don't even know what the
+ER there's error there's there's a
+
+ align:start position:0%
+ER there's error there's there's a
+ 
+
+ align:start position:0%
+ER there's error there's there's a
+measurement mistake in B but there's
+
+ align:start position:0%
+measurement mistake in B but there's
+ 
+
+ align:start position:0%
+measurement mistake in B but there's
+information
+
+ align:start position:0%
+information
+ 
+
+ align:start position:0%
+information
+too there's a lot of information about X
+
+ align:start position:0%
+too there's a lot of information about X
+ 
+
+ align:start position:0%
+too there's a lot of information about X
+in there and what I want to do is like
+
+ align:start position:0%
+in there and what I want to do is like
+ 
+
+ align:start position:0%
+in there and what I want to do is like
+separate the noise the
+
+ align:start position:0%
+separate the noise the
+ 
+
+ align:start position:0%
+separate the noise the
+junk from the
+
+ align:start position:0%
+junk from the
+ 
+
+ align:start position:0%
+junk from the
+information and so this is a
+
+ align:start position:0%
+information and so this is a
+ 
+
+ align:start position:0%
+information and so this is a
+straightforward linear algebra problem
+
+ align:start position:0%
+straightforward linear algebra problem
+ 
+
+ align:start position:0%
+straightforward linear algebra problem
+how do I solve what's the best
+
+ align:start position:0%
+how do I solve what's the best
+ 
+
+ align:start position:0%
+how do I solve what's the best
+solution
+
+ align:start position:0%
+solution
+ 
+
+ align:start position:0%
+solution
+okay now let
+
+ align:start position:0%
+okay now let
+ 
+
+ align:start position:0%
+okay now let
+me um I I want to say so that's like
+
+ align:start position:0%
+me um I I want to say so that's like
+ 
+
+ align:start position:0%
+me um I I want to say so that's like
+describes the problem in a algebraic way
+
+ align:start position:0%
+describes the problem in a algebraic way
+ 
+
+ align:start position:0%
+describes the problem in a algebraic way
+I've got some equations
+
+ align:start position:0%
+I've got some equations
+ 
+
+ align:start position:0%
+I've got some equations
+I'm looking for the best solution well
+
+ align:start position:0%
+I'm looking for the best solution well
+ 
+
+ align:start position:0%
+I'm looking for the best solution well
+one way to find it is one one way sorry
+
+ align:start position:0%
+one way to find it is one one way sorry
+ 
+
+ align:start position:0%
+one way to find it is one one way sorry
+one way to find a solution is throw
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+away equations until you've got a nice
+
+ align:start position:0%
+away equations until you've got a nice
+ 
+
+ align:start position:0%
+away equations until you've got a nice
+Square invertible system and solve
+
+ align:start position:0%
+Square invertible system and solve
+ 
+
+ align:start position:0%
+Square invertible system and solve
+that that's not
+
+ align:start position:0%
+that that's not
+ 
+
+ align:start position:0%
+that that's not
+satisfactory there's no reason in these
+
+ align:start position:0%
+satisfactory there's no reason in these
+ 
+
+ align:start position:0%
+satisfactory there's no reason in these
+measurements to say these measurements
+
+ align:start position:0%
+measurements to say these measurements
+ 
+
+ align:start position:0%
+measurements to say these measurements
+are perfect and these measurements are
+
+ align:start position:0%
+are perfect and these measurements are
+ 
+
+ align:start position:0%
+are perfect and these measurements are
+useless we want to use use all the
+
+ align:start position:0%
+useless we want to use use all the
+ 
+
+ align:start position:0%
+useless we want to use use all the
+measurements to get the best information
+
+ align:start position:0%
+measurements to get the best information
+ 
+
+ align:start position:0%
+measurements to get the best information
+to get the maximum information but how
+
+ align:start position:0%
+to get the maximum information but how
+ 
+
+ align:start position:0%
+to get the maximum information but how
+okay let me anticipate a matrix that's
+
+ align:start position:0%
+okay let me anticipate a matrix that's
+ 
+
+ align:start position:0%
+okay let me anticipate a matrix that's
+going to show up this a is typically
+
+ align:start position:0%
+going to show up this a is typically
+ 
+
+ align:start position:0%
+going to show up this a is typically
+rectangular but a matrix that shows up
+
+ align:start position:0%
+rectangular but a matrix that shows up
+ 
+
+ align:start position:0%
+rectangular but a matrix that shows up
+whenever you have and we've chapter 3
+
+ align:start position:0%
+whenever you have and we've chapter 3
+ 
+
+ align:start position:0%
+whenever you have and we've chapter 3
+was all about rectangular
+
+ align:start position:0%
+was all about rectangular
+ 
+
+ align:start position:0%
+was all about rectangular
+maty and we know when this is solvable
+
+ align:start position:0%
+maty and we know when this is solvable
+ 
+
+ align:start position:0%
+maty and we know when this is solvable
+you could do elimination on it right but
+
+ align:start position:0%
+you could do elimination on it right but
+ 
+
+ align:start position:0%
+you could do elimination on it right but
+I'm thinking hey you do elimination and
+
+ align:start position:0%
+I'm thinking hey you do elimination and
+ 
+
+ align:start position:0%
+I'm thinking hey you do elimination and
+you get equation 0 equal other nonzeros
+
+ align:start position:0%
+you get equation 0 equal other nonzeros
+ 
+
+ align:start position:0%
+you get equation 0 equal other nonzeros
+I'm thinking we really elimination is
+
+ align:start position:0%
+I'm thinking we really elimination is
+ 
+
+ align:start position:0%
+I'm thinking we really elimination is
+going to
+
+ align:start position:0%
+going to
+ 
+
+ align:start position:0%
+going to
+fail so that's our question elimination
+
+ align:start position:0%
+fail so that's our question elimination
+ 
+
+ align:start position:0%
+fail so that's our question elimination
+will get us down to to will tell us if
+
+ align:start position:0%
+will get us down to to will tell us if
+ 
+
+ align:start position:0%
+will get us down to to will tell us if
+there is a solution or not but I'm now
+
+ align:start position:0%
+there is a solution or not but I'm now
+ 
+
+ align:start position:0%
+there is a solution or not but I'm now
+thinking
+
+ align:start position:0%
+thinking
+ 
+
+ align:start position:0%
+thinking
+not okay so what are we going to do all
+
+ align:start position:0%
+not okay so what are we going to do all
+ 
+
+ align:start position:0%
+not okay so what are we going to do all
+right I want to I want to tell you
+
+ align:start position:0%
+right I want to I want to tell you
+ 
+
+ align:start position:0%
+right I want to I want to tell you
+to jump ahead to The Matrix that will
+
+ align:start position:0%
+to jump ahead to The Matrix that will
+ 
+
+ align:start position:0%
+to jump ahead to The Matrix that will
+play a key role so this is the Matrix
+
+ align:start position:0%
+play a key role so this is the Matrix
+ 
+
+ align:start position:0%
+play a key role so this is the Matrix
+that you want to understand for this
+
+ align:start position:0%
+that you want to understand for this
+ 
+
+ align:start position:0%
+that you want to understand for this
+chapter 4 and it's the Matrix a
+
+ align:start position:0%
+chapter 4 and it's the Matrix a
+ 
+
+ align:start position:0%
+chapter 4 and it's the Matrix a
+transpose
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+a
+
+ align:start position:0%
+a
+ 
+
+ align:start position:0%
+a
+what's tell me some things about that
+
+ align:start position:0%
+what's tell me some things about that
+ 
+
+ align:start position:0%
+what's tell me some things about that
+Matrix so a is this m byn Matrix
+
+ align:start position:0%
+Matrix so a is this m byn Matrix
+ 
+
+ align:start position:0%
+Matrix so a is this m byn Matrix
+rectangular but now I'm saying that the
+
+ align:start position:0%
+rectangular but now I'm saying that the
+ 
+
+ align:start position:0%
+rectangular but now I'm saying that the
+good Matrix that shows up in the end is
+
+ align:start position:0%
+good Matrix that shows up in the end is
+ 
+
+ align:start position:0%
+good Matrix that shows up in the end is
+a transpose a so tell me something about
+
+ align:start position:0%
+a transpose a so tell me something about
+ 
+
+ align:start position:0%
+a transpose a so tell me something about
+that is it yeah tell me what's the first
+
+ align:start position:0%
+that is it yeah tell me what's the first
+ 
+
+ align:start position:0%
+that is it yeah tell me what's the first
+thing you know about a
+
+ align:start position:0%
+thing you know about a
+ 
+
+ align:start position:0%
+thing you know about a
+transpose it's square right Square
+
+ align:start position:0%
+transpose it's square right Square
+ 
+
+ align:start position:0%
+transpose it's square right Square
+because this is M byn and this is n by m
+
+ align:start position:0%
+because this is M byn and this is n by m
+ 
+
+ align:start position:0%
+because this is M byn and this is n by m
+so this is the result is n byn good
+
+ align:start position:0%
+so this is the result is n byn good
+ 
+
+ align:start position:0%
+so this is the result is n byn good
+Square what
+
+ align:start position:0%
+Square what
+ 
+
+ align:start position:0%
+Square what
+else it's symmetric good it's
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+symmetric cuz you remember how to do
+
+ align:start position:0%
+symmetric cuz you remember how to do
+ 
+
+ align:start position:0%
+symmetric cuz you remember how to do
+that if we transpose that
+
+ align:start position:0%
+that if we transpose that
+ 
+
+ align:start position:0%
+that if we transpose that
+Matrix let's transpose it a transpose a
+
+ align:start position:0%
+Matrix let's transpose it a transpose a
+ 
+
+ align:start position:0%
+Matrix let's transpose it a transpose a
+if I transpose it then that comes first
+
+ align:start position:0%
+if I transpose it then that comes first
+ 
+
+ align:start position:0%
+if I transpose it then that comes first
+transpose this comes
+
+ align:start position:0%
+transpose this comes
+ 
+
+ align:start position:0%
+transpose this comes
+second transpose
+
+ align:start position:0%
+second transpose
+ 
+
+ align:start position:0%
+second transpose
+and then transposing twice is leaves it
+
+ align:start position:0%
+and then transposing twice is leaves it
+ 
+
+ align:start position:0%
+and then transposing twice is leaves it
+brings it back to the same so it's
+
+ align:start position:0%
+brings it back to the same so it's
+ 
+
+ align:start position:0%
+brings it back to the same so it's
+aetric good
+
+ align:start position:0%
+aetric good
+ 
+
+ align:start position:0%
+aetric good
+now we now know how to ask more about a
+
+ align:start position:0%
+now we now know how to ask more about a
+ 
+
+ align:start position:0%
+now we now know how to ask more about a
+maker I'm interested
+
+ align:start position:0%
+maker I'm interested
+ 
+
+ align:start position:0%
+maker I'm interested
+in is it
+
+ align:start position:0%
+in is it
+ 
+
+ align:start position:0%
+in is it
+invertible if not what's its null
+
+ align:start position:0%
+invertible if not what's its null
+ 
+
+ align:start position:0%
+invertible if not what's its null
+space so I want to know about cuz cuz
+
+ align:start position:0%
+space so I want to know about cuz cuz
+ 
+
+ align:start position:0%
+space so I want to know about cuz cuz
+you're to see well let me let me
+
+ align:start position:0%
+you're to see well let me let me
+ 
+
+ align:start position:0%
+you're to see well let me let me
+even well I shouldn't do this but I will
+
+ align:start position:0%
+even well I shouldn't do this but I will
+ 
+
+ align:start position:0%
+even well I shouldn't do this but I will
+let me tell you what equation to
+
+ align:start position:0%
+let me tell you what equation to
+ 
+
+ align:start position:0%
+let me tell you what equation to
+solve when you can't solve that
+
+ align:start position:0%
+solve when you can't solve that
+ 
+
+ align:start position:0%
+solve when you can't solve that
+one the good equation comes from
+
+ align:start position:0%
+one the good equation comes from
+ 
+
+ align:start position:0%
+one the good equation comes from
+multiplying both sides by a
+
+ align:start position:0%
+multiplying both sides by a
+ 
+
+ align:start position:0%
+multiplying both sides by a
+transpose so the the the good equation
+
+ align:start position:0%
+transpose so the the the good equation
+ 
+
+ align:start position:0%
+transpose so the the the good equation
+that you get to is this one a transpose
+
+ align:start position:0%
+that you get to is this one a transpose
+ 
+
+ align:start position:0%
+that you get to is this one a transpose
+a x = a transpose
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+B that will be the central equation in
+
+ align:start position:0%
+B that will be the central equation in
+ 
+
+ align:start position:0%
+B that will be the central equation in
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+chapter so I think why not tell it to
+
+ align:start position:0%
+chapter so I think why not tell it to
+ 
+
+ align:start position:0%
+chapter so I think why not tell it to
+why not admit it right away okay I have
+
+ align:start position:0%
+why not admit it right away okay I have
+ 
+
+ align:start position:0%
+why not admit it right away okay I have
+to I should really give
+
+ align:start position:0%
+to I should really give
+ 
+
+ align:start position:0%
+to I should really give
+x uh I I want to sort of indicate that
+
+ align:start position:0%
+x uh I I want to sort of indicate that
+ 
+
+ align:start position:0%
+x uh I I want to sort of indicate that
+this x isn't I mean this X
+
+ align:start position:0%
+this x isn't I mean this X
+ 
+
+ align:start position:0%
+this x isn't I mean this X
+was the solution to that equation if it
+
+ align:start position:0%
+was the solution to that equation if it
+ 
+
+ align:start position:0%
+was the solution to that equation if it
+existed but probably
+
+ align:start position:0%
+existed but probably
+ 
+
+ align:start position:0%
+existed but probably
+didn't now let me give this a different
+
+ align:start position:0%
+didn't now let me give this a different
+ 
+
+ align:start position:0%
+didn't now let me give this a different
+name X
+
+ align:start position:0%
+name X
+ 
+
+ align:start position:0%
+name X
+hat because I'm
+
+ align:start position:0%
+hat because I'm
+ 
+
+ align:start position:0%
+hat because I'm
+hoping this one will have a
+
+ align:start position:0%
+hoping this one will have a
+ 
+
+ align:start position:0%
+hoping this one will have a
+solution and I'm saying that it's my
+
+ align:start position:0%
+solution and I'm saying that it's my
+ 
+
+ align:start position:0%
+solution and I'm saying that it's my
+best
+
+ align:start position:0%
+best
+ 
+
+ align:start position:0%
+best
+solution I'll have to say what does best
+
+ align:start position:0%
+solution I'll have to say what does best
+ 
+
+ align:start position:0%
+solution I'll have to say what does best
+mean but that's going to be my my my
+
+ align:start position:0%
+mean but that's going to be my my my
+ 
+
+ align:start position:0%
+mean but that's going to be my my my
+plan I'm going to say that the best
+
+ align:start position:0%
+plan I'm going to say that the best
+ 
+
+ align:start position:0%
+plan I'm going to say that the best
+solution solves this equation so you see
+
+ align:start position:0%
+solution solves this equation so you see
+ 
+
+ align:start position:0%
+solution solves this equation so you see
+right away why I'm so interested in this
+
+ align:start position:0%
+right away why I'm so interested in this
+ 
+
+ align:start position:0%
+right away why I'm so interested in this
+Matrix a transpose a and in its
+
+ align:start position:0%
+Matrix a transpose a and in its
+ 
+
+ align:start position:0%
+Matrix a transpose a and in its
+invertibility okay now when is it
+
+ align:start position:0%
+invertibility okay now when is it
+ 
+
+ align:start position:0%
+invertibility okay now when is it
+invertible okay let me take a case let
+
+ align:start position:0%
+invertible okay let me take a case let
+ 
+
+ align:start position:0%
+invertible okay let me take a case let
+let me just do an example and then uh uh
+
+ align:start position:0%
+let me just do an example and then uh uh
+ 
+
+ align:start position:0%
+let me just do an example and then uh uh
+I I'll just pick a matrix
+
+ align:start position:0%
+I I'll just pick a matrix
+ 
+
+ align:start position:0%
+I I'll just pick a matrix
+here just so we see what a transpose a
+
+ align:start position:0%
+here just so we see what a transpose a
+ 
+
+ align:start position:0%
+here just so we see what a transpose a
+looks like so let me take a matrix a 1 1
+
+ align:start position:0%
+looks like so let me take a matrix a 1 1
+ 
+
+ align:start position:0%
+looks like so let me take a matrix a 1 1
+1 1 2 five just to invent a matrix so
+
+ align:start position:0%
+1 1 2 five just to invent a matrix so
+ 
+
+ align:start position:0%
+1 1 2 five just to invent a matrix so
+there's a matrix
+
+ align:start position:0%
+there's a matrix
+ 
+
+ align:start position:0%
+there's a matrix
+a notice that it has Nal 3 rows and Nal
+
+ align:start position:0%
+a notice that it has Nal 3 rows and Nal
+ 
+
+ align:start position:0%
+a notice that it has Nal 3 rows and Nal
+
+ align:start position:0%
+ 
+
+ align:start position:0%
+columns its rank
+
+ align:start position:0%
+columns its rank
+ 
+
+ align:start position:0%
+columns its rank
+is the rank of that Matrix
+
+ align:start position:0%
+is the rank of that Matrix
+ 
+
+ align:start position:0%
+is the rank of that Matrix
+is two right yeah The Columns are
+
+ align:start position:0%
+is two right yeah The Columns are
+ 
+
+ align:start position:0%
+is two right yeah The Columns are
+independent does ax equal B if I look at
+
+ align:start position:0%
+independent does ax equal B if I look at
+ 
+
+ align:start position:0%
+independent does ax equal B if I look at
+ax equal B so X is just X1
+
+ align:start position:0%
+ax equal B so X is just X1
+ 
+
+ align:start position:0%
+ax equal B so X is just X1
+X2 and B is B1 B2
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+B3 do I expect to solve ax equal B what
+
+ align:start position:0%
+B3 do I expect to solve ax equal B what
+ 
+
+ align:start position:0%
+B3 do I expect to solve ax equal B what
+what's no way right I mean linear
+
+ align:start position:0%
+what's no way right I mean linear
+ 
+
+ align:start position:0%
+what's no way right I mean linear
+algebra is great but solving three
+
+ align:start position:0%
+algebra is great but solving three
+ 
+
+ align:start position:0%
+algebra is great but solving three
+equations with only two unknowns usually
+
+ align:start position:0%
+equations with only two unknowns usually
+ 
+
+ align:start position:0%
+equations with only two unknowns usually
+we can't do it we can only solve it if
+
+ align:start position:0%
+we can't do it we can only solve it if
+ 
+
+ align:start position:0%
+we can't do it we can only solve it if
+this Vector B is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+what I can solve that equation if that
+
+ align:start position:0%
+what I can solve that equation if that
+ 
+
+ align:start position:0%
+what I can solve that equation if that
+Vector B1 B2 B3 is in
+
+ align:start position:0%
+Vector B1 B2 B3 is in
+ 
+
+ align:start position:0%
+Vector B1 B2 B3 is in
+the column space if if it's a
+
+ align:start position:0%
+the column space if if it's a
+ 
+
+ align:start position:0%
+the column space if if it's a
+combination of those columns then fine
+
+ align:start position:0%
+combination of those columns then fine
+ 
+
+ align:start position:0%
+combination of those columns then fine
+but usually it won't be though the
+
+ align:start position:0%
+but usually it won't be though the
+ 
+
+ align:start position:0%
+but usually it won't be though the
+combinations just fill up a plane and
+
+ align:start position:0%
+combinations just fill up a plane and
+ 
+
+ align:start position:0%
+combinations just fill up a plane and
+most vectors aren't on that plane so
+
+ align:start position:0%
+most vectors aren't on that plane so
+ 
+
+ align:start position:0%
+most vectors aren't on that plane so
+what I'm saying is that I'm going to
+
+ align:start position:0%
+what I'm saying is that I'm going to
+ 
+
+ align:start position:0%
+what I'm saying is that I'm going to
+work with the Matrix a transpose a and I
+
+ align:start position:0%
+work with the Matrix a transpose a and I
+ 
+
+ align:start position:0%
+work with the Matrix a transpose a and I
+just want to figure out in this example
+
+ align:start position:0%
+just want to figure out in this example
+ 
+
+ align:start position:0%
+just want to figure out in this example
+what a transpose a
+
+ align:start position:0%
+what a transpose a
+ 
+
+ align:start position:0%
+what a transpose a
+is so it's 2 by two the first entry is a
+
+ align:start position:0%
+is so it's 2 by two the first entry is a
+ 
+
+ align:start position:0%
+is so it's 2 by two the first entry is a
+three the next entry is an eight this
+
+ align:start position:0%
+three the next entry is an eight this
+ 
+
+ align:start position:0%
+three the next entry is an eight this
+entry is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+a what's that
+
+ align:start position:0%
+a what's that
+ 
+
+ align:start position:0%
+a what's that
+entry eight for sure we knew it had to
+
+ align:start position:0%
+entry eight for sure we knew it had to
+ 
+
+ align:start position:0%
+entry eight for sure we knew it had to
+be and this entry is
+
+ align:start position:0%
+be and this entry is
+ 
+
+ align:start position:0%
+be and this entry is
+what that now getting out my trusting
+
+ align:start position:0%
+what that now getting out my trusting
+ 
+
+ align:start position:0%
+what that now getting out my trusting
+calculator 30 is that
+
+ align:start position:0%
+calculator 30 is that
+ 
+
+ align:start position:0%
+calculator 30 is that
+right 30 and is that Matrix invertible
+
+ align:start position:0%
+right 30 and is that Matrix invertible
+ 
+
+ align:start position:0%
+right 30 and is that Matrix invertible
+there's an a transpose
+
+ align:start position:0%
+there's an a transpose
+ 
+
+ align:start position:0%
+there's an a transpose
+a and it is invertible right 38 is not a
+
+ align:start position:0%
+a and it is invertible right 38 is not a
+ 
+
+ align:start position:0%
+a and it is invertible right 38 is not a
+multiple of 830 and and it's invertible
+
+ align:start position:0%
+multiple of 830 and and it's invertible
+ 
+
+ align:start position:0%
+multiple of 830 and and it's invertible
+and that's the normal that's what I
+
+ align:start position:0%
+and that's the normal that's what I
+ 
+
+ align:start position:0%
+and that's the normal that's what I
+expect so this is what I what I want to
+
+ align:start position:0%
+expect so this is what I what I want to
+ 
+
+ align:start position:0%
+expect so this is what I what I want to
+I want to show
+
+ align:start position:0%
+I want to show
+ 
+
+ align:start position:0%
+I want to show
+so here's the final here's the key point
+
+ align:start position:0%
+so here's the final here's the key point
+ 
+
+ align:start position:0%
+so here's the final here's the key point
+the null space of a transpose a it it
+
+ align:start position:0%
+the null space of a transpose a it it
+ 
+
+ align:start position:0%
+the null space of a transpose a it it
+it's not going to be always
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+invertible tell me a matrix yeah now I
+
+ align:start position:0%
+invertible tell me a matrix yeah now I
+ 
+
+ align:start position:0%
+invertible tell me a matrix yeah now I
+have to I have to say that I can't say a
+
+ align:start position:0%
+have to I have to say that I can't say a
+ 
+
+ align:start position:0%
+have to I have to say that I can't say a
+transpose a is always invertible because
+
+ align:start position:0%
+transpose a is always invertible because
+ 
+
+ align:start position:0%
+transpose a is always invertible because
+that's asking too much I mean what could
+
+ align:start position:0%
+that's asking too much I mean what could
+ 
+
+ align:start position:0%
+that's asking too much I mean what could
+The Matrix a be for example so that a
+
+ align:start position:0%
+The Matrix a be for example so that a
+ 
+
+ align:start position:0%
+The Matrix a be for example so that a
+transpose a was not invertible
+
+ align:start position:0%
+transpose a was not invertible
+ 
+
+ align:start position:0%
+transpose a was not invertible
+well even could be the zero Matrix I
+
+ align:start position:0%
+well even could be the zero Matrix I
+ 
+
+ align:start position:0%
+well even could be the zero Matrix I
+mean that's like extreme case suppose I
+
+ align:start position:0%
+mean that's like extreme case suppose I
+ 
+
+ align:start position:0%
+mean that's like extreme case suppose I
+make this
+
+ align:start position:0%
+make this
+ 
+
+ align:start position:0%
+make this
+rank suppose I change to that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+a now I figure out a transpose a again
+
+ align:start position:0%
+a now I figure out a transpose a again
+ 
+
+ align:start position:0%
+a now I figure out a transpose a again
+and I get what do I
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+get I Get
+
+ align:start position:0%
+get I Get
+ 
+
+ align:start position:0%
+get I Get
+Nine I get nine of course and here I
+
+ align:start position:0%
+Nine I get nine of course and here I
+ 
+
+ align:start position:0%
+Nine I get nine of course and here I
+get what's that
+
+ align:start position:0%
+get what's that
+ 
+
+ align:start position:0%
+get what's that
+entry
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+27 and is that Matrix invertible
+
+ align:start position:0%
+27 and is that Matrix invertible
+ 
+
+ align:start position:0%
+27 and is that Matrix invertible
+no and why do I I I I knew it wouldn't
+
+ align:start position:0%
+no and why do I I I I knew it wouldn't
+ 
+
+ align:start position:0%
+no and why do I I I I knew it wouldn't
+be invertible anyway because this Matrix
+
+ align:start position:0%
+be invertible anyway because this Matrix
+ 
+
+ align:start position:0%
+be invertible anyway because this Matrix
+only has
+
+ align:start position:0%
+only has
+ 
+
+ align:start position:0%
+only has
+[Music]
+
+ align:start position:0%
+[Music]
+ 
+
+ align:start position:0%
+[Music]
+rank
+
+ align:start position:0%
+rank
+ 
+
+ align:start position:0%
+rank
+one and if I have a product of matrices
+
+ align:start position:0%
+one and if I have a product of matrices
+ 
+
+ align:start position:0%
+one and if I have a product of matrices
+of rank one the product is not going to
+
+ align:start position:0%
+of rank one the product is not going to
+ 
+
+ align:start position:0%
+of rank one the product is not going to
+have a rank bigger than
+
+ align:start position:0%
+have a rank bigger than
+ 
+
+ align:start position:0%
+have a rank bigger than
+one so I'm not surprised that the answer
+
+ align:start position:0%
+one so I'm not surprised that the answer
+ 
+
+ align:start position:0%
+one so I'm not surprised that the answer
+only has rank one and that's what
+
+ align:start position:0%
+only has rank one and that's what
+ 
+
+ align:start position:0%
+only has rank one and that's what
+I'm always happens that the rank of a
+
+ align:start position:0%
+I'm always happens that the rank of a
+ 
+
+ align:start position:0%
+I'm always happens that the rank of a
+transpose a comes out to equal the rank
+
+ align:start position:0%
+transpose a comes out to equal the rank
+ 
+
+ align:start position:0%
+transpose a comes out to equal the rank
+of
+
+ align:start position:0%
+of
+ 
+
+ align:start position:0%
+of
+a so uh yeah so the null space of a
+
+ align:start position:0%
+a so uh yeah so the null space of a
+ 
+
+ align:start position:0%
+a so uh yeah so the null space of a
+transpose a equals the null space of a
+
+ align:start position:0%
+transpose a equals the null space of a
+ 
+
+ align:start position:0%
+transpose a equals the null space of a
+the rank of a transpose
+
+ align:start position:0%
+the rank of a transpose
+ 
+
+ align:start position:0%
+the rank of a transpose
+a
+
+ align:start position:0%
+a
+ 
+
+ align:start position:0%
+a
+equals the rank of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+a so
+
+ align:start position:0%
+a so
+ 
+
+ align:start position:0%
+a so
+let's I I'll tell you in a as soon as I
+
+ align:start position:0%
+let's I I'll tell you in a as soon as I
+ 
+
+ align:start position:0%
+let's I I'll tell you in a as soon as I
+can why that's true but
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+let's draw from that what the fact that
+
+ align:start position:0%
+let's draw from that what the fact that
+ 
+
+ align:start position:0%
+let's draw from that what the fact that
+I want this tells me that this Square
+
+ align:start position:0%
+I want this tells me that this Square
+ 
+
+ align:start position:0%
+I want this tells me that this Square
+symmetric Matrix is invertible if
+
+ align:start position:0%
+symmetric Matrix is invertible if
+ 
+
+ align:start position:0%
+symmetric Matrix is invertible if
+so here's my conclusion a transpose a is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+invertible if exactly when exactly
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+if this null space is only got the zero
+
+ align:start position:0%
+if this null space is only got the zero
+ 
+
+ align:start position:0%
+if this null space is only got the zero
+back which means The Columns of a are
+
+ align:start position:0%
+back which means The Columns of a are
+ 
+
+ align:start position:0%
+back which means The Columns of a are
+independent so a transpose a is
+
+ align:start position:0%
+independent so a transpose a is
+ 
+
+ align:start position:0%
+independent so a transpose a is
+invertible exactly if a a
+
+ align:start position:0%
+invertible exactly if a a
+ 
+
+ align:start position:0%
+invertible exactly if a a
+has
+
+ align:start position:0%
+has
+ 
+
+ align:start position:0%
+has
+independent
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+columns that's
+
+ align:start position:0%
+columns that's
+ 
+
+ align:start position:0%
+columns that's
+the that's the that's the the the fact
+
+ align:start position:0%
+the that's the that's the the the fact
+ 
+
+ align:start position:0%
+the that's the that's the the the fact
+that I need about a transpose a and then
+
+ align:start position:0%
+that I need about a transpose a and then
+ 
+
+ align:start position:0%
+that I need about a transpose a and then
+you'll see next
+
+ align:start position:0%
+you'll see next
+ 
+
+ align:start position:0%
+you'll see next
+time how a transpose a enters everything
+
+ align:start position:0%
+time how a transpose a enters everything
+ 
+
+ align:start position:0%
+time how a transpose a enters everything
+next next lecture is actually a crucial
+
+ align:start position:0%
+next next lecture is actually a crucial
+ 
+
+ align:start position:0%
+next next lecture is actually a crucial
+one here I'm preparing for it by getting
+
+ align:start position:0%
+one here I'm preparing for it by getting
+ 
+
+ align:start position:0%
+one here I'm preparing for it by getting
+us thinking about a transpose a and its
+
+ align:start position:0%
+us thinking about a transpose a and its
+ 
+
+ align:start position:0%
+us thinking about a transpose a and its
+rank is the same as the rank of a and we
+
+ align:start position:0%
+rank is the same as the rank of a and we
+ 
+
+ align:start position:0%
+rank is the same as the rank of a and we
+can decide when it's inverted okay so
+
+ align:start position:0%
+can decide when it's inverted okay so
+ 
+
+ align:start position:0%
+can decide when it's inverted okay so
+I'll see you
+
+ align:start position:0%
+I'll see you
+ 
+
+ align:start position:0%
+I'll see you
+Friday
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+thanks
\ No newline at end of file
diff --git a/Zl92WCm30bU.txt b/Zl92WCm30bU.txt
new file mode 100644
index 0000000000000000000000000000000000000000..015ea1d167885d53b5479657cf16c23b1bfd0688
--- /dev/null
+++ b/Zl92WCm30bU.txt
@@ -0,0 +1,10066 @@
+align:start position:0%
+ 
+all right uh let's continue our
+
+ align:start position:0%
+all right uh let's continue our
+ 
+
+ align:start position:0%
+all right uh let's continue our
+discussion of factor markets uh remember
+
+ align:start position:0%
+discussion of factor markets uh remember
+ 
+
+ align:start position:0%
+discussion of factor markets uh remember
+to set the stage we are now in the
+
+ align:start position:0%
+to set the stage we are now in the
+ 
+
+ align:start position:0%
+to set the stage we are now in the
+second half of the course talking about
+
+ align:start position:0%
+second half of the course talking about
+ 
+
+ align:start position:0%
+second half of the course talking about
+the various elements that underly the
+
+ align:start position:0%
+the various elements that underly the
+ 
+
+ align:start position:0%
+the various elements that underly the
+supply and demand model that we
+
+ align:start position:0%
+supply and demand model that we
+ 
+
+ align:start position:0%
+supply and demand model that we
+developed in the first half of the
+
+ align:start position:0%
+developed in the first half of the
+ 
+
+ align:start position:0%
+developed in the first half of the
+course and the first question we're
+
+ align:start position:0%
+course and the first question we're
+ 
+
+ align:start position:0%
+course and the first question we're
+tackling is where to W andr come from
+
+ align:start position:0%
+tackling is where to W andr come from
+ 
+
+ align:start position:0%
+tackling is where to W andr come from
+where do these prices that are the price
+
+ align:start position:0%
+where do these prices that are the price
+ 
+
+ align:start position:0%
+where do these prices that are the price
+of firm inputs where do they come from
+
+ align:start position:0%
+of firm inputs where do they come from
+ 
+
+ align:start position:0%
+of firm inputs where do they come from
+and they come of course from markets
+
+ align:start position:0%
+and they come of course from markets
+ 
+
+ align:start position:0%
+and they come of course from markets
+markets of demand and Supply markets
+
+ align:start position:0%
+markets of demand and Supply markets
+ 
+
+ align:start position:0%
+markets of demand and Supply markets
+four factors so let's start by doing the
+
+ align:start position:0%
+four factors so let's start by doing the
+ 
+
+ align:start position:0%
+four factors so let's start by doing the
+labor market
+
+ align:start position:0%
+labor market
+ 
+
+ align:start position:0%
+labor market
+equilibrium let's start by doing the
+
+ align:start position:0%
+equilibrium let's start by doing the
+ 
+
+ align:start position:0%
+equilibrium let's start by doing the
+labor market
+
+ align:start position:0%
+labor market
+ 
+
+ align:start position:0%
+labor market
+equilibrium and then we'll talk about
+
+ align:start position:0%
+equilibrium and then we'll talk about
+ 
+
+ align:start position:0%
+equilibrium and then we'll talk about
+what effect a minimum
+
+ align:start position:0%
+what effect a minimum
+ 
+
+ align:start position:0%
+what effect a minimum
+wage has in that
+
+ align:start position:0%
+wage has in that
+ 
+
+ align:start position:0%
+wage has in that
+equilibrium okay so let's look at figure
+
+ align:start position:0%
+equilibrium okay so let's look at figure
+ 
+
+ align:start position:0%
+equilibrium okay so let's look at figure
+
+ align:start position:0%
+ 
+
+ align:start position:0%
+1 figure 161 puts together the labor
+
+ align:start position:0%
+1 figure 161 puts together the labor
+ 
+
+ align:start position:0%
+1 figure 161 puts together the labor
+market
+
+ align:start position:0%
+market
+ 
+
+ align:start position:0%
+market
+equilibrium we have a a demand
+
+ align:start position:0%
+equilibrium we have a a demand
+ 
+
+ align:start position:0%
+equilibrium we have a a demand
+curve the demand curve comes from firms
+
+ align:start position:0%
+curve the demand curve comes from firms
+ 
+
+ align:start position:0%
+curve the demand curve comes from firms
+because in Factor markets firms are now
+
+ align:start position:0%
+because in Factor markets firms are now
+ 
+
+ align:start position:0%
+because in Factor markets firms are now
+the demanders and people are the
+
+ align:start position:0%
+the demanders and people are the
+ 
+
+ align:start position:0%
+the demanders and people are the
+suppliers so we flipped the tables from
+
+ align:start position:0%
+suppliers so we flipped the tables from
+ 
+
+ align:start position:0%
+suppliers so we flipped the tables from
+a typical Market in a typical Market
+
+ align:start position:0%
+a typical Market in a typical Market
+ 
+
+ align:start position:0%
+a typical Market in a typical Market
+cons in a consumer goods Market I'm
+
+ align:start position:0%
+cons in a consumer goods Market I'm
+ 
+
+ align:start position:0%
+cons in a consumer goods Market I'm
+consumer goods Market firms Drive the
+
+ align:start position:0%
+consumer goods Market firms Drive the
+ 
+
+ align:start position:0%
+consumer goods Market firms Drive the
+supply curve and consumers Drive the
+
+ align:start position:0%
+supply curve and consumers Drive the
+ 
+
+ align:start position:0%
+supply curve and consumers Drive the
+demand curve that's no longer true true
+
+ align:start position:0%
+demand curve that's no longer true true
+ 
+
+ align:start position:0%
+demand curve that's no longer true true
+now firms Drive the domain curve and
+
+ align:start position:0%
+now firms Drive the domain curve and
+ 
+
+ align:start position:0%
+now firms Drive the domain curve and
+consumers Drive the supply curve so the
+
+ align:start position:0%
+consumers Drive the supply curve so the
+ 
+
+ align:start position:0%
+consumers Drive the supply curve so the
+domain curve comes from the marginal
+
+ align:start position:0%
+domain curve comes from the marginal
+ 
+
+ align:start position:0%
+domain curve comes from the marginal
+product of labor okay so we have uh a
+
+ align:start position:0%
+product of labor okay so we have uh a
+ 
+
+ align:start position:0%
+product of labor okay so we have uh a
+demand curve in labor market equilibrium
+
+ align:start position:0%
+demand curve in labor market equilibrium
+ 
+
+ align:start position:0%
+demand curve in labor market equilibrium
+here we're saying the demand curve is 70
+
+ align:start position:0%
+here we're saying the demand curve is 70
+ 
+
+ align:start position:0%
+here we're saying the demand curve is 70
+minus
+
+ align:start position:0%
+minus
+ 
+
+ align:start position:0%
+minus
+W we're saying that as the wage goes up
+
+ align:start position:0%
+W we're saying that as the wage goes up
+ 
+
+ align:start position:0%
+W we're saying that as the wage goes up
+firms want fewer workers and we could
+
+ align:start position:0%
+firms want fewer workers and we could
+ 
+
+ align:start position:0%
+firms want fewer workers and we could
+see that from our earlier firm
+
+ align:start position:0%
+see that from our earlier firm
+ 
+
+ align:start position:0%
+see that from our earlier firm
+optimization okay but there's also
+
+ align:start position:0%
+optimization okay but there's also
+ 
+
+ align:start position:0%
+optimization okay but there's also
+supply curve now we talked about last
+
+ align:start position:0%
+supply curve now we talked about last
+ 
+
+ align:start position:0%
+supply curve now we talked about last
+time is the shape of the supply curve
+
+ align:start position:0%
+time is the shape of the supply curve
+ 
+
+ align:start position:0%
+time is the shape of the supply curve
+here is indeterminant and that's because
+
+ align:start position:0%
+here is indeterminant and that's because
+ 
+
+ align:start position:0%
+here is indeterminant and that's because
+income effects offset substitution
+
+ align:start position:0%
+income effects offset substitution
+ 
+
+ align:start position:0%
+income effects offset substitution
+effects when Leisure is a normal good
+
+ align:start position:0%
+effects when Leisure is a normal good
+ 
+
+ align:start position:0%
+effects when Leisure is a normal good
+okay that's the key lesson from last
+
+ align:start position:0%
+okay that's the key lesson from last
+ 
+
+ align:start position:0%
+okay that's the key lesson from last
+lecture is that even when Leisure a
+
+ align:start position:0%
+lecture is that even when Leisure a
+ 
+
+ align:start position:0%
+lecture is that even when Leisure a
+normal good income effects offset
+
+ align:start position:0%
+normal good income effects offset
+ 
+
+ align:start position:0%
+normal good income effects offset
+substitution effects so we don't know
+
+ align:start position:0%
+substitution effects so we don't know
+ 
+
+ align:start position:0%
+substitution effects so we don't know
+the shape of supply curve that said
+
+ align:start position:0%
+the shape of supply curve that said
+ 
+
+ align:start position:0%
+the shape of supply curve that said
+we're going to pretty much for the rest
+
+ align:start position:0%
+we're going to pretty much for the rest
+ 
+
+ align:start position:0%
+we're going to pretty much for the rest
+of the semester assume upward sloping
+
+ align:start position:0%
+of the semester assume upward sloping
+ 
+
+ align:start position:0%
+of the semester assume upward sloping
+labor Supply curves we're going to
+
+ align:start position:0%
+labor Supply curves we're going to
+ 
+
+ align:start position:0%
+labor Supply curves we're going to
+pretty much assume substitution effects
+
+ align:start position:0%
+pretty much assume substitution effects
+ 
+
+ align:start position:0%
+pretty much assume substitution effects
+offset income effects because they hell
+
+ align:start position:0%
+offset income effects because they hell
+ 
+
+ align:start position:0%
+offset income effects because they hell
+of a lot each to work with it's a mess
+
+ align:start position:0%
+of a lot each to work with it's a mess
+ 
+
+ align:start position:0%
+of a lot each to work with it's a mess
+when they both slope down so we're
+
+ align:start position:0%
+when they both slope down so we're
+ 
+
+ align:start position:0%
+when they both slope down so we're
+pretty much going to assume that
+
+ align:start position:0%
+pretty much going to assume that
+ 
+
+ align:start position:0%
+pretty much going to assume that
+substitution effects Dominate and the
+
+ align:start position:0%
+substitution effects Dominate and the
+ 
+
+ align:start position:0%
+substitution effects Dominate and the
+labor supply curve is upward sloping so
+
+ align:start position:0%
+labor supply curve is upward sloping so
+ 
+
+ align:start position:0%
+labor supply curve is upward sloping so
+here for example we have a labor supply
+
+ align:start position:0%
+here for example we have a labor supply
+ 
+
+ align:start position:0%
+here for example we have a labor supply
+curve um uh of the
+
+ align:start position:0%
+curve um uh of the
+ 
+
+ align:start position:0%
+curve um uh of the
+form uh that uh labor equals um uh wus
+
+ align:start position:0%
+form uh that uh labor equals um uh wus
+ 
+
+ align:start position:0%
+form uh that uh labor equals um uh wus
+10 so a higher wage leads to more labor
+
+ align:start position:0%
+10 so a higher wage leads to more labor
+ 
+
+ align:start position:0%
+10 so a higher wage leads to more labor
+Supply okay so this uh uh so a higher
+
+ align:start position:0%
+Supply okay so this uh uh so a higher
+ 
+
+ align:start position:0%
+Supply okay so this uh uh so a higher
+wage leads to more labor SL it should be
+
+ align:start position:0%
+wage leads to more labor SL it should be
+ 
+
+ align:start position:0%
+wage leads to more labor SL it should be
+L equal 70 so this is the demand curve
+
+ align:start position:0%
+L equal 70 so this is the demand curve
+ 
+
+ align:start position:0%
+L equal 70 so this is the demand curve
+the demand curve is L equal 70 minus W
+
+ align:start position:0%
+the demand curve is L equal 70 minus W
+ 
+
+ align:start position:0%
+the demand curve is L equal 70 minus W
+the supply curve is uh Lal wus 10 so to
+
+ align:start position:0%
+the supply curve is uh Lal wus 10 so to
+ 
+
+ align:start position:0%
+the supply curve is uh Lal wus 10 so to
+solve for equilibrium we simply set
+
+ align:start position:0%
+solve for equilibrium we simply set
+ 
+
+ align:start position:0%
+solve for equilibrium we simply set
+those equal we know how to do that now
+
+ align:start position:0%
+those equal we know how to do that now
+ 
+
+ align:start position:0%
+those equal we know how to do that now
+and you find the equilibrium is at 30
+
+ align:start position:0%
+and you find the equilibrium is at 30
+ 
+
+ align:start position:0%
+and you find the equilibrium is at 30
+units of Labor with a wage of 40 that's
+
+ align:start position:0%
+units of Labor with a wage of 40 that's
+ 
+
+ align:start position:0%
+units of Labor with a wage of 40 that's
+the point at which firms are happy to
+
+ align:start position:0%
+the point at which firms are happy to
+ 
+
+ align:start position:0%
+the point at which firms are happy to
+hire workers and workers are happy to
+
+ align:start position:0%
+hire workers and workers are happy to
+ 
+
+ align:start position:0%
+hire workers and workers are happy to
+work so it's the same kind of
+
+ align:start position:0%
+work so it's the same kind of
+ 
+
+ align:start position:0%
+work so it's the same kind of
+equilibrium of goods markets
+
+ align:start position:0%
+equilibrium of goods markets
+ 
+
+ align:start position:0%
+equilibrium of goods markets
+now it's just in a factor market
+
+ align:start position:0%
+now it's just in a factor market
+ 
+
+ align:start position:0%
+now it's just in a factor market
+okay now let's ask what happens when we
+
+ align:start position:0%
+okay now let's ask what happens when we
+ 
+
+ align:start position:0%
+okay now let's ask what happens when we
+add a minimum
+
+ align:start position:0%
+add a minimum
+ 
+
+ align:start position:0%
+add a minimum
+wage what happens we add a minimum wage
+
+ align:start position:0%
+wage what happens we add a minimum wage
+ 
+
+ align:start position:0%
+wage what happens we add a minimum wage
+which is a standard labor market
+
+ align:start position:0%
+which is a standard labor market
+ 
+
+ align:start position:0%
+which is a standard labor market
+intervention all around the world okay
+
+ align:start position:0%
+intervention all around the world okay
+ 
+
+ align:start position:0%
+intervention all around the world okay
+some of you may even enjoyed minimum
+
+ align:start position:0%
+some of you may even enjoyed minimum
+ 
+
+ align:start position:0%
+some of you may even enjoyed minimum
+wage jobs at some point in your past
+
+ align:start position:0%
+wage jobs at some point in your past
+ 
+
+ align:start position:0%
+wage jobs at some point in your past
+lives or hopefully not in your future
+
+ align:start position:0%
+lives or hopefully not in your future
+ 
+
+ align:start position:0%
+lives or hopefully not in your future
+lives but some point in your past lives
+
+ align:start position:0%
+lives but some point in your past lives
+ 
+
+ align:start position:0%
+lives but some point in your past lives
+uh it's a common feature of the
+
+ align:start position:0%
+uh it's a common feature of the
+ 
+
+ align:start position:0%
+uh it's a common feature of the
+developed worlds have minimum wages the
+
+ align:start position:0%
+developed worlds have minimum wages the
+ 
+
+ align:start position:0%
+developed worlds have minimum wages the
+way minimum wage work is the government
+
+ align:start position:0%
+way minimum wage work is the government
+ 
+
+ align:start position:0%
+way minimum wage work is the government
+just sets a wage floor below which
+
+ align:start position:0%
+just sets a wage floor below which
+ 
+
+ align:start position:0%
+just sets a wage floor below which
+employers cannot pay their employees
+
+ align:start position:0%
+employers cannot pay their employees
+ 
+
+ align:start position:0%
+employers cannot pay their employees
+they set a wage floor so for example
+
+ align:start position:0%
+they set a wage floor so for example
+ 
+
+ align:start position:0%
+they set a wage floor so for example
+imagine the government came in and set a
+
+ align:start position:0%
+imagine the government came in and set a
+ 
+
+ align:start position:0%
+imagine the government came in and set a
+wage floor of 50 set a minimum wage of
+
+ align:start position:0%
+wage floor of 50 set a minimum wage of
+ 
+
+ align:start position:0%
+wage floor of 50 set a minimum wage of
+50 above the market equilibrium
+
+ align:start position:0%
+50 above the market equilibrium
+ 
+
+ align:start position:0%
+50 above the market equilibrium
+wage
+
+ align:start position:0%
+wage
+ 
+
+ align:start position:0%
+wage
+okay so the new equilibrium
+
+ align:start position:0%
+okay so the new equilibrium
+ 
+
+ align:start position:0%
+okay so the new equilibrium
+now is the new outcome the new market
+
+ align:start position:0%
+now is the new outcome the new market
+ 
+
+ align:start position:0%
+now is the new outcome the new market
+outcome is actually at 0 two
+
+ align:start position:0%
+outcome is actually at 0 two
+ 
+
+ align:start position:0%
+outcome is actually at 0 two
+why well because that higher wage firms
+
+ align:start position:0%
+why well because that higher wage firms
+ 
+
+ align:start position:0%
+why well because that higher wage firms
+want to hire fewer
+
+ align:start position:0%
+want to hire fewer
+ 
+
+ align:start position:0%
+want to hire fewer
+workers it doesn't matter what workers
+
+ align:start position:0%
+workers it doesn't matter what workers
+ 
+
+ align:start position:0%
+workers it doesn't matter what workers
+want there's no jobs for them so firms
+
+ align:start position:0%
+want there's no jobs for them so firms
+ 
+
+ align:start position:0%
+want there's no jobs for them so firms
+say fine if that higher wage I only want
+
+ align:start position:0%
+say fine if that higher wage I only want
+ 
+
+ align:start position:0%
+say fine if that higher wage I only want
+
+ align:start position:0%
+ 
+
+ align:start position:0%
+workers workers say well gee at that
+
+ align:start position:0%
+workers workers say well gee at that
+ 
+
+ align:start position:0%
+workers workers say well gee at that
+higher wage I want to work actually uh I
+
+ align:start position:0%
+higher wage I want to work actually uh I
+ 
+
+ align:start position:0%
+higher wage I want to work actually uh I
+want to work much more than
+
+ align:start position:0%
+want to work much more than
+ 
+
+ align:start position:0%
+want to work much more than
+that okay um Andrew in the future uh
+
+ align:start position:0%
+that okay um Andrew in the future uh
+ 
+
+ align:start position:0%
+that okay um Andrew in the future uh
+diagram we should have the Y inter the x
+
+ align:start position:0%
+diagram we should have the Y inter the x
+ 
+
+ align:start position:0%
+diagram we should have the Y inter the x
+intercept for the excess Supply um they
+
+ align:start position:0%
+intercept for the excess Supply um they
+ 
+
+ align:start position:0%
+intercept for the excess Supply um they
+want to work much more than that so you
+
+ align:start position:0%
+want to work much more than that so you
+ 
+
+ align:start position:0%
+want to work much more than that so you
+end up with an excess supply of
+
+ align:start position:0%
+end up with an excess supply of
+ 
+
+ align:start position:0%
+end up with an excess supply of
+labor now when we talked about supply
+
+ align:start position:0%
+labor now when we talked about supply
+ 
+
+ align:start position:0%
+labor now when we talked about supply
+and demand equilibrium we talked about
+
+ align:start position:0%
+and demand equilibrium we talked about
+ 
+
+ align:start position:0%
+and demand equilibrium we talked about
+us how disequilibrium outcomes resolve
+
+ align:start position:0%
+us how disequilibrium outcomes resolve
+ 
+
+ align:start position:0%
+us how disequilibrium outcomes resolve
+themselves through Market adjustments
+
+ align:start position:0%
+themselves through Market adjustments
+ 
+
+ align:start position:0%
+themselves through Market adjustments
+well here this disequilibrium outcome
+
+ align:start position:0%
+well here this disequilibrium outcome
+ 
+
+ align:start position:0%
+well here this disequilibrium outcome
+cannot resolve itself the market can't
+
+ align:start position:0%
+cannot resolve itself the market can't
+ 
+
+ align:start position:0%
+cannot resolve itself the market can't
+adjust the Market's stuck because of the
+
+ align:start position:0%
+adjust the Market's stuck because of the
+ 
+
+ align:start position:0%
+adjust the Market's stuck because of the
+regulation so we end up in a situation
+
+ align:start position:0%
+regulation so we end up in a situation
+ 
+
+ align:start position:0%
+regulation so we end up in a situation
+we're out of equilibrium we have excess
+
+ align:start position:0%
+we're out of equilibrium we have excess
+ 
+
+ align:start position:0%
+we're out of equilibrium we have excess
+Supply okay in in in layman's terms we
+
+ align:start position:0%
+Supply okay in in in layman's terms we
+ 
+
+ align:start position:0%
+Supply okay in in in layman's terms we
+call that
+
+ align:start position:0%
+call that
+ 
+
+ align:start position:0%
+call that
+unemployment we end up with unemployment
+
+ align:start position:0%
+unemployment we end up with unemployment
+ 
+
+ align:start position:0%
+unemployment we end up with unemployment
+we end up with people who want to work
+
+ align:start position:0%
+we end up with people who want to work
+ 
+
+ align:start position:0%
+we end up with people who want to work
+but can't
+
+ align:start position:0%
+but can't
+ 
+
+ align:start position:0%
+but can't
+work okay and that causes an
+
+ align:start position:0%
+work okay and that causes an
+ 
+
+ align:start position:0%
+work okay and that causes an
+inefficiency or dead weight loss you see
+
+ align:start position:0%
+inefficiency or dead weight loss you see
+ 
+
+ align:start position:0%
+inefficiency or dead weight loss you see
+before the
+
+ align:start position:0%
+before the
+ 
+
+ align:start position:0%
+before the
+policy worker
+
+ align:start position:0%
+policy worker
+ 
+
+ align:start position:0%
+policy worker
+Surplus okay was um or I'm sorry firm
+
+ align:start position:0%
+Surplus okay was um or I'm sorry firm
+ 
+
+ align:start position:0%
+Surplus okay was um or I'm sorry firm
+Surplus I'm sorry for the policy firm
+
+ align:start position:0%
+Surplus I'm sorry for the policy firm
+ 
+
+ align:start position:0%
+Surplus I'm sorry for the policy firm
+Surplus cuz firms the consumers here was
+
+ align:start position:0%
+Surplus cuz firms the consumers here was
+ 
+
+ align:start position:0%
+Surplus cuz firms the consumers here was
+a plus b plus C that was the consumer
+
+ align:start position:0%
+a plus b plus C that was the consumer
+ 
+
+ align:start position:0%
+a plus b plus C that was the consumer
+surplus or in this case consumers are
+
+ align:start position:0%
+surplus or in this case consumers are
+ 
+
+ align:start position:0%
+surplus or in this case consumers are
+firms they really call that more the
+
+ align:start position:0%
+firms they really call that more the
+ 
+
+ align:start position:0%
+firms they really call that more the
+demander Surplus the supplier Surplus
+
+ align:start position:0%
+demander Surplus the supplier Surplus
+ 
+
+ align:start position:0%
+demander Surplus the supplier Surplus
+was D plus e with the minimum wage we've
+
+ align:start position:0%
+was D plus e with the minimum wage we've
+ 
+
+ align:start position:0%
+was D plus e with the minimum wage we've
+now transferred the area
+
+ align:start position:0%
+now transferred the area
+ 
+
+ align:start position:0%
+now transferred the area
+B from firms to workers so the firm
+
+ align:start position:0%
+B from firms to workers so the firm
+ 
+
+ align:start position:0%
+B from firms to workers so the firm
+Surplus this the demander Surplus has
+
+ align:start position:0%
+Surplus this the demander Surplus has
+ 
+
+ align:start position:0%
+Surplus this the demander Surplus has
+fallen all the way to
+
+ align:start position:0%
+fallen all the way to
+ 
+
+ align:start position:0%
+fallen all the way to
+a so we've transferred the area B but
+
+ align:start position:0%
+a so we've transferred the area B but
+ 
+
+ align:start position:0%
+a so we've transferred the area B but
+we've created in doing so a dead weight
+
+ align:start position:0%
+we've created in doing so a dead weight
+ 
+
+ align:start position:0%
+we've created in doing so a dead weight
+loss of C plus a
+
+ align:start position:0%
+loss of C plus a
+ 
+
+ align:start position:0%
+loss of C plus a
+standard kind of welfare analys we've
+
+ align:start position:0%
+standard kind of welfare analys we've
+ 
+
+ align:start position:0%
+standard kind of welfare analys we've
+done so several times before now okay so
+
+ align:start position:0%
+done so several times before now okay so
+ 
+
+ align:start position:0%
+done so several times before now okay so
+what we've done with this policy is
+
+ align:start position:0%
+what we've done with this policy is
+ 
+
+ align:start position:0%
+what we've done with this policy is
+we've transferred the area
+
+ align:start position:0%
+we've transferred the area
+ 
+
+ align:start position:0%
+we've transferred the area
+B from the demanders who are firms to
+
+ align:start position:0%
+B from the demanders who are firms to
+ 
+
+ align:start position:0%
+B from the demanders who are firms to
+the suppliers who are workers but in
+
+ align:start position:0%
+the suppliers who are workers but in
+ 
+
+ align:start position:0%
+the suppliers who are workers but in
+doing so we've created a deadweight loss
+
+ align:start position:0%
+doing so we've created a deadweight loss
+ 
+
+ align:start position:0%
+doing so we've created a deadweight loss
+C plus e why because those are trades
+
+ align:start position:0%
+C plus e why because those are trades
+ 
+
+ align:start position:0%
+C plus e why because those are trades
+that would be efficient to make they're
+
+ align:start position:0%
+that would be efficient to make they're
+ 
+
+ align:start position:0%
+that would be efficient to make they're
+not being made there are workers that
+
+ align:start position:0%
+not being made there are workers that
+ 
+
+ align:start position:0%
+not being made there are workers that
+would happily
+
+ align:start position:0%
+would happily
+ 
+
+ align:start position:0%
+would happily
+work at a wage below 50 and firms would
+
+ align:start position:0%
+work at a wage below 50 and firms would
+ 
+
+ align:start position:0%
+work at a wage below 50 and firms would
+be happy to H them at a wage below 50
+
+ align:start position:0%
+be happy to H them at a wage below 50
+ 
+
+ align:start position:0%
+be happy to H them at a wage below 50
+but we're not letting that transaction
+
+ align:start position:0%
+but we're not letting that transaction
+ 
+
+ align:start position:0%
+but we're not letting that transaction
+happen that's wasted economic efficiency
+
+ align:start position:0%
+happen that's wasted economic efficiency
+ 
+
+ align:start position:0%
+happen that's wasted economic efficiency
+or dead weight
+
+ align:start position:0%
+or dead weight
+ 
+
+ align:start position:0%
+or dead weight
+loss this is the pretty standard an of
+
+ align:start position:0%
+loss this is the pretty standard an of
+ 
+
+ align:start position:0%
+loss this is the pretty standard an of
+minimum wage and this says that well
+
+ align:start position:0%
+minimum wage and this says that well
+ 
+
+ align:start position:0%
+minimum wage and this says that well
+look when you put a minimum wage you get
+
+ align:start position:0%
+look when you put a minimum wage you get
+ 
+
+ align:start position:0%
+look when you put a minimum wage you get
+a
+
+ align:start position:0%
+a
+ 
+
+ align:start position:0%
+a
+trade-off you get a transfer to workers
+
+ align:start position:0%
+trade-off you get a transfer to workers
+ 
+
+ align:start position:0%
+trade-off you get a transfer to workers
+which you may like but you create a dead
+
+ align:start position:0%
+which you may like but you create a dead
+ 
+
+ align:start position:0%
+which you may like but you create a dead
+weight loss because you create
+
+ align:start position:0%
+weight loss because you create
+ 
+
+ align:start position:0%
+weight loss because you create
+unemployment but actually starting about
+
+ align:start position:0%
+unemployment but actually starting about
+ 
+
+ align:start position:0%
+unemployment but actually starting about
+30 years ago research started finding
+
+ align:start position:0%
+30 years ago research started finding
+ 
+
+ align:start position:0%
+30 years ago research started finding
+that minimum wages didn't cause
+
+ align:start position:0%
+that minimum wages didn't cause
+ 
+
+ align:start position:0%
+that minimum wages didn't cause
+unemployment actually some research
+
+ align:start position:0%
+unemployment actually some research
+ 
+
+ align:start position:0%
+unemployment actually some research
+studies suggest you put a minimum wage
+
+ align:start position:0%
+studies suggest you put a minimum wage
+ 
+
+ align:start position:0%
+studies suggest you put a minimum wage
+employment goes
+
+ align:start position:0%
+employment goes
+ 
+
+ align:start position:0%
+employment goes
+up but certainly there was very little
+
+ align:start position:0%
+up but certainly there was very little
+ 
+
+ align:start position:0%
+up but certainly there was very little
+evidence that goes
+
+ align:start position:0%
+evidence that goes
+ 
+
+ align:start position:0%
+evidence that goes
+down this was quite striking because how
+
+ align:start position:0%
+down this was quite striking because how
+ 
+
+ align:start position:0%
+down this was quite striking because how
+could that happen now one way it could
+
+ align:start position:0%
+could that happen now one way it could
+ 
+
+ align:start position:0%
+could that happen now one way it could
+happen of course could be if the demand
+
+ align:start position:0%
+happen of course could be if the demand
+ 
+
+ align:start position:0%
+happen of course could be if the demand
+curve was perfectly
+
+ align:start position:0%
+curve was perfectly
+ 
+
+ align:start position:0%
+curve was perfectly
+inelastic then a minimum wage would not
+
+ align:start position:0%
+inelastic then a minimum wage would not
+ 
+
+ align:start position:0%
+inelastic then a minimum wage would not
+lower employment
+
+ align:start position:0%
+lower employment
+ 
+
+ align:start position:0%
+lower employment
+you can see that in this graph it's I
+
+ align:start position:0%
+you can see that in this graph it's I
+ 
+
+ align:start position:0%
+you can see that in this graph it's I
+haven't drawn this out but you see the
+
+ align:start position:0%
+haven't drawn this out but you see the
+ 
+
+ align:start position:0%
+haven't drawn this out but you see the
+162 imagine taking that blue line and
+
+ align:start position:0%
+162 imagine taking that blue line and
+ 
+
+ align:start position:0%
+162 imagine taking that blue line and
+making it vertical you'll see the
+
+ align:start position:0%
+making it vertical you'll see the
+ 
+
+ align:start position:0%
+making it vertical you'll see the
+minimum wage wouldn't cause unemployment
+
+ align:start position:0%
+minimum wage wouldn't cause unemployment
+ 
+
+ align:start position:0%
+minimum wage wouldn't cause unemployment
+so one thing that could be going on is
+
+ align:start position:0%
+so one thing that could be going on is
+ 
+
+ align:start position:0%
+so one thing that could be going on is
+demand could be perfectly in elastic but
+
+ align:start position:0%
+demand could be perfectly in elastic but
+ 
+
+ align:start position:0%
+demand could be perfectly in elastic but
+in fact there's lots of studies which
+
+ align:start position:0%
+in fact there's lots of studies which
+ 
+
+ align:start position:0%
+in fact there's lots of studies which
+say that's not true demand for labor is
+
+ align:start position:0%
+say that's not true demand for labor is
+ 
+
+ align:start position:0%
+say that's not true demand for labor is
+not perfectly in elastic so that can't
+
+ align:start position:0%
+not perfectly in elastic so that can't
+ 
+
+ align:start position:0%
+not perfectly in elastic so that can't
+be the explanation so we said an
+
+ align:start position:0%
+be the explanation so we said an
+ 
+
+ align:start position:0%
+be the explanation so we said an
+alternative explanation which is that
+
+ align:start position:0%
+alternative explanation which is that
+ 
+
+ align:start position:0%
+alternative explanation which is that
+just like Goods markets can be
+
+ align:start position:0%
+just like Goods markets can be
+ 
+
+ align:start position:0%
+just like Goods markets can be
+non-competitive labor markets can also
+
+ align:start position:0%
+non-competitive labor markets can also
+ 
+
+ align:start position:0%
+non-competitive labor markets can also
+be non-competitive
+
+ align:start position:0%
+be non-competitive
+ 
+
+ align:start position:0%
+be non-competitive
+and so we think the explanation is
+
+ align:start position:0%
+and so we think the explanation is
+ 
+
+ align:start position:0%
+and so we think the explanation is
+non-competitive labor
+
+ align:start position:0%
+non-competitive labor
+ 
+
+ align:start position:0%
+non-competitive labor
+markets okay so when we when we thought
+
+ align:start position:0%
+markets okay so when we when we thought
+ 
+
+ align:start position:0%
+markets okay so when we when we thought
+about firms selling Goods we said look
+
+ align:start position:0%
+about firms selling Goods we said look
+ 
+
+ align:start position:0%
+about firms selling Goods we said look
+at a competitive market firms face
+
+ align:start position:0%
+at a competitive market firms face
+ 
+
+ align:start position:0%
+at a competitive market firms face
+perfectly elastic demand any given firm
+
+ align:start position:0%
+perfectly elastic demand any given firm
+ 
+
+ align:start position:0%
+perfectly elastic demand any given firm
+faces perfectly elastic
+
+ align:start position:0%
+faces perfectly elastic
+ 
+
+ align:start position:0%
+faces perfectly elastic
+demand okay well
+
+ align:start position:0%
+demand okay well
+ 
+
+ align:start position:0%
+demand okay well
+likewise when we think about a firm
+
+ align:start position:0%
+likewise when we think about a firm
+ 
+
+ align:start position:0%
+likewise when we think about a firm
+hiring workers we think that in a we if
+
+ align:start position:0%
+hiring workers we think that in a we if
+ 
+
+ align:start position:0%
+hiring workers we think that in a we if
+labor markets are competitive
+
+ align:start position:0%
+labor markets are competitive
+ 
+
+ align:start position:0%
+labor markets are competitive
+any given firm faed a perfectly elastic
+
+ align:start position:0%
+any given firm faed a perfectly elastic
+ 
+
+ align:start position:0%
+any given firm faed a perfectly elastic
+supply curve think about the intuition
+
+ align:start position:0%
+supply curve think about the intuition
+ 
+
+ align:start position:0%
+supply curve think about the intuition
+the interest perfectly competitive
+
+ align:start position:0%
+the interest perfectly competitive
+ 
+
+ align:start position:0%
+the interest perfectly competitive
+market is look if I'm selling chachis
+
+ align:start position:0%
+market is look if I'm selling chachis
+ 
+
+ align:start position:0%
+market is look if I'm selling chachis
+next to the other guy selling
+
+ align:start position:0%
+next to the other guy selling
+ 
+
+ align:start position:0%
+next to the other guy selling
+chachis then I can't raise my price
+
+ align:start position:0%
+chachis then I can't raise my price
+ 
+
+ align:start position:0%
+chachis then I can't raise my price
+above or below his because if I raise it
+
+ align:start position:0%
+above or below his because if I raise it
+ 
+
+ align:start position:0%
+above or below his because if I raise it
+above I'll sell zero below I'll sell I
+
+ align:start position:0%
+above I'll sell zero below I'll sell I
+ 
+
+ align:start position:0%
+above I'll sell zero below I'll sell I
+won't I won't be able to meet
+
+ align:start position:0%
+won't I won't be able to meet
+ 
+
+ align:start position:0%
+won't I won't be able to meet
+demand well it's the same thing when
+
+ align:start position:0%
+demand well it's the same thing when
+ 
+
+ align:start position:0%
+demand well it's the same thing when
+hiring workers a perfectly competitive
+
+ align:start position:0%
+hiring workers a perfectly competitive
+ 
+
+ align:start position:0%
+hiring workers a perfectly competitive
+market imagine a perfectly competitive
+
+ align:start position:0%
+market imagine a perfectly competitive
+ 
+
+ align:start position:0%
+market imagine a perfectly competitive
+labor market which is fast food
+
+ align:start position:0%
+labor market which is fast food
+ 
+
+ align:start position:0%
+labor market which is fast food
+workers okay there's a bunch of fast
+
+ align:start position:0%
+workers okay there's a bunch of fast
+ 
+
+ align:start position:0%
+workers okay there's a bunch of fast
+food restaurants near each other if
+
+ align:start position:0%
+food restaurants near each other if
+ 
+
+ align:start position:0%
+food restaurants near each other if
+McDonald's pays 50 cents more than
+
+ align:start position:0%
+McDonald's pays 50 cents more than
+ 
+
+ align:start position:0%
+McDonald's pays 50 cents more than
+Burger King everyone leaves Burger King
+
+ align:start position:0%
+Burger King everyone leaves Burger King
+ 
+
+ align:start position:0%
+Burger King everyone leaves Burger King
+and works at McDonald's if Burger King
+
+ align:start position:0%
+and works at McDonald's if Burger King
+ 
+
+ align:start position:0%
+and works at McDonald's if Burger King
+pays 50 cents more than McDonald's vice
+
+ align:start position:0%
+pays 50 cents more than McDonald's vice
+ 
+
+ align:start position:0%
+pays 50 cents more than McDonald's vice
+versa so you have essentially each firm
+
+ align:start position:0%
+versa so you have essentially each firm
+ 
+
+ align:start position:0%
+versa so you have essentially each firm
+faces a flat supply curve because
+
+ align:start position:0%
+faces a flat supply curve because
+ 
+
+ align:start position:0%
+faces a flat supply curve because
+workers can just move it's an easy
+
+ align:start position:0%
+workers can just move it's an easy
+ 
+
+ align:start position:0%
+workers can just move it's an easy
+substitution between them just like it's
+
+ align:start position:0%
+substitution between them just like it's
+ 
+
+ align:start position:0%
+substitution between them just like it's
+EAS a substitute between statues of the
+
+ align:start position:0%
+EAS a substitute between statues of the
+ 
+
+ align:start position:0%
+EAS a substitute between statues of the
+eiel tower little mini statues it's easy
+
+ align:start position:0%
+eiel tower little mini statues it's easy
+ 
+
+ align:start position:0%
+eiel tower little mini statues it's easy
+substitute between working mcdonal and
+
+ align:start position:0%
+substitute between working mcdonal and
+ 
+
+ align:start position:0%
+substitute between working mcdonal and
+Burger King it's the same job and
+
+ align:start position:0%
+Burger King it's the same job and
+ 
+
+ align:start position:0%
+Burger King it's the same job and
+they're near each
+
+ align:start position:0%
+they're near each
+ 
+
+ align:start position:0%
+they're near each
+other okay however
+
+ align:start position:0%
+other okay however
+ 
+
+ align:start position:0%
+other okay however
+what we've realized is that may in fact
+
+ align:start position:0%
+what we've realized is that may in fact
+ 
+
+ align:start position:0%
+what we've realized is that may in fact
+not be
+
+ align:start position:0%
+not be
+ 
+
+ align:start position:0%
+not be
+true what if just like Goods markets can
+
+ align:start position:0%
+true what if just like Goods markets can
+ 
+
+ align:start position:0%
+true what if just like Goods markets can
+be
+
+ align:start position:0%
+be
+ 
+
+ align:start position:0%
+be
+non-competitive what if labor markets
+
+ align:start position:0%
+non-competitive what if labor markets
+ 
+
+ align:start position:0%
+non-competitive what if labor markets
+can be
+
+ align:start position:0%
+can be
+ 
+
+ align:start position:0%
+can be
+non-competitive remember the assumptions
+
+ align:start position:0%
+non-competitive remember the assumptions
+ 
+
+ align:start position:0%
+non-competitive remember the assumptions
+we required for a perfectly competitive
+
+ align:start position:0%
+we required for a perfectly competitive
+ 
+
+ align:start position:0%
+we required for a perfectly competitive
+Goods Market we required perfect
+
+ align:start position:0%
+Goods Market we required perfect
+ 
+
+ align:start position:0%
+Goods Market we required perfect
+information and no transaction costs and
+
+ align:start position:0%
+information and no transaction costs and
+ 
+
+ align:start position:0%
+information and no transaction costs and
+all Goods being the same well for a
+
+ align:start position:0%
+all Goods being the same well for a
+ 
+
+ align:start position:0%
+all Goods being the same well for a
+perfectly competitive labor market the
+
+ align:start position:0%
+perfectly competitive labor market the
+ 
+
+ align:start position:0%
+perfectly competitive labor market the
+same requirements are in place
+
+ align:start position:0%
+same requirements are in place
+ 
+
+ align:start position:0%
+same requirements are in place
+you need perfect
+
+ align:start position:0%
+you need perfect
+ 
+
+ align:start position:0%
+you need perfect
+information you need no transaction
+
+ align:start position:0%
+information you need no transaction
+ 
+
+ align:start position:0%
+information you need no transaction
+costs and all jobs to be the same well
+
+ align:start position:0%
+costs and all jobs to be the same well
+ 
+
+ align:start position:0%
+costs and all jobs to be the same well
+that's not true in particular the first
+
+ align:start position:0%
+that's not true in particular the first
+ 
+
+ align:start position:0%
+that's not true in particular the first
+isn't true we don't have perfect
+
+ align:start position:0%
+isn't true we don't have perfect
+ 
+
+ align:start position:0%
+isn't true we don't have perfect
+information because jobs don't always
+
+ align:start position:0%
+information because jobs don't always
+ 
+
+ align:start position:0%
+information because jobs don't always
+post their wages typically don't post
+
+ align:start position:0%
+post their wages typically don't post
+ 
+
+ align:start position:0%
+post their wages typically don't post
+their wages and typically you don't know
+
+ align:start position:0%
+their wages and typically you don't know
+ 
+
+ align:start position:0%
+their wages and typically you don't know
+what you can make in another
+
+ align:start position:0%
+what you can make in another
+ 
+
+ align:start position:0%
+what you can make in another
+firm okay once you don't know what you
+
+ align:start position:0%
+firm okay once you don't know what you
+ 
+
+ align:start position:0%
+firm okay once you don't know what you
+can make in another firm once it's
+
+ align:start position:0%
+can make in another firm once it's
+ 
+
+ align:start position:0%
+can make in another firm once it's
+costly to learn that that's a
+
+ align:start position:0%
+costly to learn that that's a
+ 
+
+ align:start position:0%
+costly to learn that that's a
+transaction cost that interferes
+
+ align:start position:0%
+transaction cost that interferes
+ 
+
+ align:start position:0%
+transaction cost that interferes
+okay that's one form of transaction
+
+ align:start position:0%
+okay that's one form of transaction
+ 
+
+ align:start position:0%
+okay that's one form of transaction
+costs that could interfere what we think
+
+ align:start position:0%
+costs that could interfere what we think
+ 
+
+ align:start position:0%
+costs that could interfere what we think
+is a fairly competitive
+
+ align:start position:0%
+is a fairly competitive
+ 
+
+ align:start position:0%
+is a fairly competitive
+market okay now let's go further let's
+
+ align:start position:0%
+market okay now let's go further let's
+ 
+
+ align:start position:0%
+market okay now let's go further let's
+think about the most extreme case which
+
+ align:start position:0%
+think about the most extreme case which
+ 
+
+ align:start position:0%
+think about the most extreme case which
+was the old mining towns we used to have
+
+ align:start position:0%
+was the old mining towns we used to have
+ 
+
+ align:start position:0%
+was the old mining towns we used to have
+in the West in the US in the US the way
+
+ align:start position:0%
+in the West in the US in the US the way
+ 
+
+ align:start position:0%
+in the West in the US in the US the way
+it work is you discovered gold you'd set
+
+ align:start position:0%
+it work is you discovered gold you'd set
+ 
+
+ align:start position:0%
+it work is you discovered gold you'd set
+up a town to around the gold mine and
+
+ align:start position:0%
+up a town to around the gold mine and
+ 
+
+ align:start position:0%
+up a town to around the gold mine and
+everyone in that town would work in the
+
+ align:start position:0%
+everyone in that town would work in the
+ 
+
+ align:start position:0%
+everyone in that town would work in the
+gold mine or they would work selling
+
+ align:start position:0%
+gold mine or they would work selling
+ 
+
+ align:start position:0%
+gold mine or they would work selling
+stuff to worked in the gold mine okay
+
+ align:start position:0%
+stuff to worked in the gold mine okay
+ 
+
+ align:start position:0%
+stuff to worked in the gold mine okay
+well in that case you definitely didn't
+
+ align:start position:0%
+well in that case you definitely didn't
+ 
+
+ align:start position:0%
+well in that case you definitely didn't
+face a competitive labor market because
+
+ align:start position:0%
+face a competitive labor market because
+ 
+
+ align:start position:0%
+face a competitive labor market because
+that was the only place to work there
+
+ align:start position:0%
+that was the only place to work there
+ 
+
+ align:start position:0%
+that was the only place to work there
+was one employer the gold
+
+ align:start position:0%
+was one employer the gold
+ 
+
+ align:start position:0%
+was one employer the gold
+mine and they had and if you want to
+
+ align:start position:0%
+mine and they had and if you want to
+ 
+
+ align:start position:0%
+mine and they had and if you want to
+work you had to work for that one
+
+ align:start position:0%
+work you had to work for that one
+ 
+
+ align:start position:0%
+work you had to work for that one
+employer so instead of the case of a
+
+ align:start position:0%
+employer so instead of the case of a
+ 
+
+ align:start position:0%
+employer so instead of the case of a
+monopoly we had a case of a
+
+ align:start position:0%
+monopoly we had a case of a
+ 
+
+ align:start position:0%
+monopoly we had a case of a
+monopsony a monopsony a
+
+ align:start position:0%
+monopsony a monopsony a
+ 
+
+ align:start position:0%
+monopsony a monopsony a
+monopoly is when only one firm sells the
+
+ align:start position:0%
+monopoly is when only one firm sells the
+ 
+
+ align:start position:0%
+monopoly is when only one firm sells the
+good a
+
+ align:start position:0%
+good a
+ 
+
+ align:start position:0%
+good a
+monopsony is when only one firm hires
+
+ align:start position:0%
+monopsony is when only one firm hires
+ 
+
+ align:start position:0%
+monopsony is when only one firm hires
+the workers
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay let's suppose further let's just s
+
+ align:start position:0%
+okay let's suppose further let's just s
+ 
+
+ align:start position:0%
+okay let's suppose further let's just s
+is having a bunch of Gold Mine Workers
+
+ align:start position:0%
+is having a bunch of Gold Mine Workers
+ 
+
+ align:start position:0%
+is having a bunch of Gold Mine Workers
+let's suppose further that just as we
+
+ align:start position:0%
+let's suppose further that just as we
+ 
+
+ align:start position:0%
+let's suppose further that just as we
+assume initially the monopolies can't
+
+ align:start position:0%
+assume initially the monopolies can't
+ 
+
+ align:start position:0%
+assume initially the monopolies can't
+price
+
+ align:start position:0%
+price
+ 
+
+ align:start position:0%
+price
+discriminate let's assume monopsonies
+
+ align:start position:0%
+discriminate let's assume monopsonies
+ 
+
+ align:start position:0%
+discriminate let's assume monopsonies
+can't wage discriminate this is actually
+
+ align:start position:0%
+can't wage discriminate this is actually
+ 
+
+ align:start position:0%
+can't wage discriminate this is actually
+kind of a more reasonable assumption it
+
+ align:start position:0%
+kind of a more reasonable assumption it
+ 
+
+ align:start position:0%
+kind of a more reasonable assumption it
+was always sort of weird to say why
+
+ align:start position:0%
+was always sort of weird to say why
+ 
+
+ align:start position:0%
+was always sort of weird to say why
+could monopolis charge different people
+
+ align:start position:0%
+could monopolis charge different people
+ 
+
+ align:start position:0%
+could monopolis charge different people
+different prices it's a more reasonable
+
+ align:start position:0%
+different prices it's a more reasonable
+ 
+
+ align:start position:0%
+different prices it's a more reasonable
+sub to think firms can't pay similar
+
+ align:start position:0%
+sub to think firms can't pay similar
+ 
+
+ align:start position:0%
+sub to think firms can't pay similar
+worker different way wages they'd be
+
+ align:start position:0%
+worker different way wages they'd be
+ 
+
+ align:start position:0%
+worker different way wages they'd be
+pissed right it's sort of you know if if
+
+ align:start position:0%
+pissed right it's sort of you know if if
+ 
+
+ align:start position:0%
+pissed right it's sort of you know if if
+if you're paying two Works doing the
+
+ align:start position:0%
+if you're paying two Works doing the
+ 
+
+ align:start position:0%
+if you're paying two Works doing the
+same job different wages they're going
+
+ align:start position:0%
+same job different wages they're going
+ 
+
+ align:start position:0%
+same job different wages they're going
+to get upset people care about Equity
+
+ align:start position:0%
+to get upset people care about Equity
+ 
+
+ align:start position:0%
+to get upset people care about Equity
+it's sort of more reasonable think for
+
+ align:start position:0%
+it's sort of more reasonable think for
+ 
+
+ align:start position:0%
+it's sort of more reasonable think for
+the same job you sort of have to pay the
+
+ align:start position:0%
+the same job you sort of have to pay the
+ 
+
+ align:start position:0%
+the same job you sort of have to pay the
+same wage I think that's a much sort of
+
+ align:start position:0%
+same wage I think that's a much sort of
+ 
+
+ align:start position:0%
+same wage I think that's a much sort of
+more reasonable assumption than it is a
+
+ align:start position:0%
+more reasonable assumption than it is a
+ 
+
+ align:start position:0%
+more reasonable assumption than it is a
+monopoly
+
+ align:start position:0%
+monopoly
+ 
+
+ align:start position:0%
+monopoly
+case okay I mean you can pay managers
+
+ align:start position:0%
+case okay I mean you can pay managers
+ 
+
+ align:start position:0%
+case okay I mean you can pay managers
+more than M workers but it's sort of
+
+ align:start position:0%
+more than M workers but it's sort of
+ 
+
+ align:start position:0%
+more than M workers but it's sort of
+reasonable to think you kind of have to
+
+ align:start position:0%
+reasonable to think you kind of have to
+ 
+
+ align:start position:0%
+reasonable to think you kind of have to
+pay all the M workers the same
+
+ align:start position:0%
+pay all the M workers the same
+ 
+
+ align:start position:0%
+pay all the M workers the same
+thing what that means is that just as
+
+ align:start position:0%
+thing what that means is that just as
+ 
+
+ align:start position:0%
+thing what that means is that just as
+when you're a
+
+ align:start position:0%
+when you're a
+ 
+
+ align:start position:0%
+when you're a
+monopoly lowering your price might hurt
+
+ align:start position:0%
+monopoly lowering your price might hurt
+ 
+
+ align:start position:0%
+monopoly lowering your price might hurt
+your profits through the poisoning
+
+ align:start position:0%
+your profits through the poisoning
+ 
+
+ align:start position:0%
+your profits through the poisoning
+effect when your M
+
+ align:start position:0%
+effect when your M
+ 
+
+ align:start position:0%
+effect when your M
+monopsony raising the wage will hurt
+
+ align:start position:0%
+monopsony raising the wage will hurt
+ 
+
+ align:start position:0%
+monopsony raising the wage will hurt
+your profits through an equivalent
+
+ align:start position:0%
+your profits through an equivalent
+ 
+
+ align:start position:0%
+your profits through an equivalent
+poisoning
+
+ align:start position:0%
+poisoning
+ 
+
+ align:start position:0%
+poisoning
+effect so let's think about the firm's
+
+ align:start position:0%
+effect so let's think about the firm's
+ 
+
+ align:start position:0%
+effect so let's think about the firm's
+decision okay the firm wants to set the
+
+ align:start position:0%
+decision okay the firm wants to set the
+ 
+
+ align:start position:0%
+decision okay the firm wants to set the
+marginal cost of the next worker equal
+
+ align:start position:0%
+marginal cost of the next worker equal
+ 
+
+ align:start position:0%
+marginal cost of the next worker equal
+to the marginal benefit of the next
+
+ align:start position:0%
+to the marginal benefit of the next
+ 
+
+ align:start position:0%
+to the marginal benefit of the next
+worker okay what is the marginal
+
+ align:start position:0%
+worker okay what is the marginal
+ 
+
+ align:start position:0%
+worker okay what is the marginal
+benefit well the marginal benefit is
+
+ align:start position:0%
+benefit well the marginal benefit is
+ 
+
+ align:start position:0%
+benefit well the marginal benefit is
+still the marginal revenue product of
+
+ align:start position:0%
+still the marginal revenue product of
+ 
+
+ align:start position:0%
+still the marginal revenue product of
+labor that hasn't changed that's true
+
+ align:start position:0%
+labor that hasn't changed that's true
+ 
+
+ align:start position:0%
+labor that hasn't changed that's true
+regardless of the market the next worker
+
+ align:start position:0%
+regardless of the market the next worker
+ 
+
+ align:start position:0%
+regardless of the market the next worker
+produces the next marginal revenue
+
+ align:start position:0%
+produces the next marginal revenue
+ 
+
+ align:start position:0%
+produces the next marginal revenue
+produc the marginal product of labor
+
+ align:start position:0%
+produc the marginal product of labor
+ 
+
+ align:start position:0%
+produc the marginal product of labor
+what changes the marginal
+
+ align:start position:0%
+what changes the marginal
+ 
+
+ align:start position:0%
+what changes the marginal
+cost before the marginal cost was the
+
+ align:start position:0%
+cost before the marginal cost was the
+ 
+
+ align:start position:0%
+cost before the marginal cost was the
+wage in a perfectly competitive labor
+
+ align:start position:0%
+wage in a perfectly competitive labor
+ 
+
+ align:start position:0%
+wage in a perfectly competitive labor
+market I didn't say last time I was
+
+ align:start position:0%
+market I didn't say last time I was
+ 
+
+ align:start position:0%
+market I didn't say last time I was
+assuming that but I was in a perfectly
+
+ align:start position:0%
+assuming that but I was in a perfectly
+ 
+
+ align:start position:0%
+assuming that but I was in a perfectly
+competitive labor market the wage is the
+
+ align:start position:0%
+competitive labor market the wage is the
+ 
+
+ align:start position:0%
+competitive labor market the wage is the
+cost but in a monop market that's no
+
+ align:start position:0%
+cost but in a monop market that's no
+ 
+
+ align:start position:0%
+cost but in a monop market that's no
+longer true and to see that want to say
+
+ align:start position:0%
+longer true and to see that want to say
+ 
+
+ align:start position:0%
+longer true and to see that want to say
+what's the marginal cost the mar cost is
+
+ align:start position:0%
+what's the marginal cost the mar cost is
+ 
+
+ align:start position:0%
+what's the marginal cost the mar cost is
+the marginal expenditure to get another
+
+ align:start position:0%
+the marginal expenditure to get another
+ 
+
+ align:start position:0%
+the marginal expenditure to get another
+unit of
+
+ align:start position:0%
+unit of
+ 
+
+ align:start position:0%
+unit of
+Labor well what's the expenditure to get
+
+ align:start position:0%
+Labor well what's the expenditure to get
+ 
+
+ align:start position:0%
+Labor well what's the expenditure to get
+another unit of Labor your expenditure
+
+ align:start position:0%
+another unit of Labor your expenditure
+ 
+
+ align:start position:0%
+another unit of Labor your expenditure
+is your what's your total what's your
+
+ align:start position:0%
+is your what's your total what's your
+ 
+
+ align:start position:0%
+is your what's your total what's your
+total wage Bill I'm sorry what's your
+
+ align:start position:0%
+total wage Bill I'm sorry what's your
+ 
+
+ align:start position:0%
+total wage Bill I'm sorry what's your
+total wage bill it's the wage you pay by
+
+ align:start position:0%
+total wage bill it's the wage you pay by
+ 
+
+ align:start position:0%
+total wage bill it's the wage you pay by
+times the number of workers you have but
+
+ align:start position:0%
+times the number of workers you have but
+ 
+
+ align:start position:0%
+times the number of workers you have but
+the number of workers you have is a
+
+ align:start position:0%
+the number of workers you have is a
+ 
+
+ align:start position:0%
+the number of workers you have is a
+function of the wage you pay right the
+
+ align:start position:0%
+function of the wage you pay right the
+ 
+
+ align:start position:0%
+function of the wage you pay right the
+more you pay the more workers will kind
+
+ align:start position:0%
+more you pay the more workers will kind
+ 
+
+ align:start position:0%
+more you pay the more workers will kind
+of want to work with you so if we
+
+ align:start position:0%
+of want to work with you so if we
+ 
+
+ align:start position:0%
+of want to work with you so if we
+differentiate this and get marginal
+
+ align:start position:0%
+differentiate this and get marginal
+ 
+
+ align:start position:0%
+differentiate this and get marginal
+expenditure which is sort of the firm's
+
+ align:start position:0%
+expenditure which is sort of the firm's
+ 
+
+ align:start position:0%
+expenditure which is sort of the firm's
+marginal cost of hiring another unit of
+
+ align:start position:0%
+marginal cost of hiring another unit of
+ 
+
+ align:start position:0%
+marginal cost of hiring another unit of
+Labor the marginal
+
+ align:start position:0%
+Labor the marginal
+ 
+
+ align:start position:0%
+Labor the marginal
+expenditure is W plus DW DL time
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+l in other
+
+ align:start position:0%
+l in other
+ 
+
+ align:start position:0%
+l in other
+words it's this term which is positive
+
+ align:start position:0%
+words it's this term which is positive
+ 
+
+ align:start position:0%
+words it's this term which is positive
+the marginal expenditure is the wage
+
+ align:start position:0%
+the marginal expenditure is the wage
+ 
+
+ align:start position:0%
+the marginal expenditure is the wage
+plus this second term which is how much
+
+ align:start position:0%
+plus this second term which is how much
+ 
+
+ align:start position:0%
+plus this second term which is how much
+do you have to raise the wage to get
+
+ align:start position:0%
+do you have to raise the wage to get
+ 
+
+ align:start position:0%
+do you have to raise the wage to get
+another worker
+
+ align:start position:0%
+another worker
+ 
+
+ align:start position:0%
+another worker
+it's a flip side of the poisoning effect
+
+ align:start position:0%
+it's a flip side of the poisoning effect
+ 
+
+ align:start position:0%
+it's a flip side of the poisoning effect
+the poisoning effect was as a monopolist
+
+ align:start position:0%
+the poisoning effect was as a monopolist
+ 
+
+ align:start position:0%
+the poisoning effect was as a monopolist
+if I want to sell one more unit I face a
+
+ align:start position:0%
+if I want to sell one more unit I face a
+ 
+
+ align:start position:0%
+if I want to sell one more unit I face a
+tradeoff I sell the additional unit
+
+ align:start position:0%
+tradeoff I sell the additional unit
+ 
+
+ align:start position:0%
+tradeoff I sell the additional unit
+that's good but I have to lower my price
+
+ align:start position:0%
+that's good but I have to lower my price
+ 
+
+ align:start position:0%
+that's good but I have to lower my price
+to sell it that's bad here if I want to
+
+ align:start position:0%
+to sell it that's bad here if I want to
+ 
+
+ align:start position:0%
+to sell it that's bad here if I want to
+hire one more unit of Labor there's an
+
+ align:start position:0%
+hire one more unit of Labor there's an
+ 
+
+ align:start position:0%
+hire one more unit of Labor there's an
+equivalent tradeoff I get one more
+
+ align:start position:0%
+equivalent tradeoff I get one more
+ 
+
+ align:start position:0%
+equivalent tradeoff I get one more
+worker that's
+
+ align:start position:0%
+worker that's
+ 
+
+ align:start position:0%
+worker that's
+good but I have to pay all my workers
+
+ align:start position:0%
+good but I have to pay all my workers
+ 
+
+ align:start position:0%
+good but I have to pay all my workers
+more to get him that's bad
+
+ align:start position:0%
+more to get him that's bad
+ 
+
+ align:start position:0%
+more to get him that's bad
+why because I can't wage
+
+ align:start position:0%
+why because I can't wage
+ 
+
+ align:start position:0%
+why because I can't wage
+discriminate and it sort of makes sense
+
+ align:start position:0%
+discriminate and it sort of makes sense
+ 
+
+ align:start position:0%
+discriminate and it sort of makes sense
+if I want to expand the number of it's I
+
+ align:start position:0%
+if I want to expand the number of it's I
+ 
+
+ align:start position:0%
+if I want to expand the number of it's I
+once again I think it's much more intive
+
+ align:start position:0%
+once again I think it's much more intive
+ 
+
+ align:start position:0%
+once again I think it's much more intive
+the Monopoly case if I want more workers
+
+ align:start position:0%
+the Monopoly case if I want more workers
+ 
+
+ align:start position:0%
+the Monopoly case if I want more workers
+I got to raise the
+
+ align:start position:0%
+I got to raise the
+ 
+
+ align:start position:0%
+I got to raise the
+wage okay why was this not an issue for
+
+ align:start position:0%
+wage okay why was this not an issue for
+ 
+
+ align:start position:0%
+wage okay why was this not an issue for
+the perfectly competitive firm it's not
+
+ align:start position:0%
+the perfectly competitive firm it's not
+ 
+
+ align:start position:0%
+the perfectly competitive firm it's not
+an issue firm because they faced a
+
+ align:start position:0%
+an issue firm because they faced a
+ 
+
+ align:start position:0%
+an issue firm because they faced a
+perfectly elastic firm labor supply
+
+ align:start position:0%
+perfectly elastic firm labor supply
+ 
+
+ align:start position:0%
+perfectly elastic firm labor supply
+curve workers were different McDonald's
+
+ align:start position:0%
+curve workers were different McDonald's
+ 
+
+ align:start position:0%
+curve workers were different McDonald's
+and Burger King so they could just go
+
+ align:start position:0%
+and Burger King so they could just go
+ 
+
+ align:start position:0%
+and Burger King so they could just go
+back and forth but a a monopsonist
+
+ align:start position:0%
+back and forth but a a monopsonist
+ 
+
+ align:start position:0%
+back and forth but a a monopsonist
+doesn't face that anymore they face the
+
+ align:start position:0%
+doesn't face that anymore they face the
+ 
+
+ align:start position:0%
+doesn't face that anymore they face the
+true market labor supply curve which is
+
+ align:start position:0%
+true market labor supply curve which is
+ 
+
+ align:start position:0%
+true market labor supply curve which is
+not perfectly elastic so to see this
+
+ align:start position:0%
+not perfectly elastic so to see this
+ 
+
+ align:start position:0%
+not perfectly elastic so to see this
+let's go to figure 164 so
+
+ align:start position:0%
+let's go to figure 164 so
+ 
+
+ align:start position:0%
+let's go to figure 164 so
+163 that's a perfectly competitive
+
+ align:start position:0%
+163 that's a perfectly competitive
+ 
+
+ align:start position:0%
+163 that's a perfectly competitive
+case the marginal benefit of hiring
+
+ align:start position:0%
+case the marginal benefit of hiring
+ 
+
+ align:start position:0%
+case the marginal benefit of hiring
+another worker is the marginal revenue
+
+ align:start position:0%
+another worker is the marginal revenue
+ 
+
+ align:start position:0%
+another worker is the marginal revenue
+product of labor 163 the marginal
+
+ align:start position:0%
+product of labor 163 the marginal
+ 
+
+ align:start position:0%
+product of labor 163 the marginal
+benefit the marginal revenue product of
+
+ align:start position:0%
+benefit the marginal revenue product of
+ 
+
+ align:start position:0%
+benefit the marginal revenue product of
+labor the marginal cost is expressed by
+
+ align:start position:0%
+labor the marginal cost is expressed by
+ 
+
+ align:start position:0%
+labor the marginal cost is expressed by
+the wage which is determined by a
+
+ align:start position:0%
+the wage which is determined by a
+ 
+
+ align:start position:0%
+the wage which is determined by a
+perfectly competitive
+
+ align:start position:0%
+perfectly competitive
+ 
+
+ align:start position:0%
+perfectly competitive
+market but 164 is a mopsy now we have
+
+ align:start position:0%
+market but 164 is a mopsy now we have
+ 
+
+ align:start position:0%
+market but 164 is a mopsy now we have
+the same marginal revenue product of
+
+ align:start position:0%
+the same marginal revenue product of
+ 
+
+ align:start position:0%
+the same marginal revenue product of
+labor which we defined as 70 minus L we
+
+ align:start position:0%
+labor which we defined as 70 minus L we
+ 
+
+ align:start position:0%
+labor which we defined as 70 minus L we
+use the same example did before 70 minus
+
+ align:start position:0%
+use the same example did before 70 minus
+ 
+
+ align:start position:0%
+use the same example did before 70 minus
+L uh well we're flipping this so the
+
+ align:start position:0%
+L uh well we're flipping this so the
+ 
+
+ align:start position:0%
+L uh well we're flipping this so the
+marginal so now we can write the
+
+ align:start position:0%
+marginal so now we can write the
+ 
+
+ align:start position:0%
+marginal so now we can write the
+marginal revenue product of labor curve
+
+ align:start position:0%
+marginal revenue product of labor curve
+ 
+
+ align:start position:0%
+marginal revenue product of labor curve
+as simply W equal 70 minus l so just
+
+ align:start position:0%
+as simply W equal 70 minus l so just
+ 
+
+ align:start position:0%
+as simply W equal 70 minus l so just
+inverting
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that okay that's that's the firm's
+
+ align:start position:0%
+that okay that's that's the firm's
+ 
+
+ align:start position:0%
+that okay that's that's the firm's
+demand curve or margin product of labor
+
+ align:start position:0%
+demand curve or margin product of labor
+ 
+
+ align:start position:0%
+demand curve or margin product of labor
+curve but what about its marginal
+
+ align:start position:0%
+curve but what about its marginal
+ 
+
+ align:start position:0%
+curve but what about its marginal
+expenditure curve well if you look at
+
+ align:start position:0%
+expenditure curve well if you look at
+ 
+
+ align:start position:0%
+expenditure curve well if you look at
+the supply curve the supply curve was w
+
+ align:start position:0%
+the supply curve the supply curve was w
+ 
+
+ align:start position:0%
+the supply curve the supply curve was w
+= l + 10 right so we can now say expend
+
+ align:start position:0%
+= l + 10 right so we can now say expend
+ 
+
+ align:start position:0%
+= l + 10 right so we can now say expend
+the firm's expenditure
+
+ align:start position:0%
+the firm's expenditure
+ 
+
+ align:start position:0%
+the firm's expenditure
+function labor is W I'm sorry uh the
+
+ align:start position:0%
+function labor is W I'm sorry uh the
+ 
+
+ align:start position:0%
+function labor is W I'm sorry uh the
+firm's expenditure
+
+ align:start position:0%
+firm's expenditure
+ 
+
+ align:start position:0%
+firm's expenditure
+function is L time L + 10 that's its
+
+ align:start position:0%
+function is L time L + 10 that's its
+ 
+
+ align:start position:0%
+function is L time L + 10 that's its
+labor expenditures right stare at that
+
+ align:start position:0%
+labor expenditures right stare at that
+ 
+
+ align:start position:0%
+labor expenditures right stare at that
+for a minute the number of workers times
+
+ align:start position:0%
+for a minute the number of workers times
+ 
+
+ align:start position:0%
+for a minute the number of workers times
+the wage the wage comes from this
+
+ align:start position:0%
+the wage the wage comes from this
+ 
+
+ align:start position:0%
+the wage the wage comes from this
+equation differentiate that with respect
+
+ align:start position:0%
+equation differentiate that with respect
+ 
+
+ align:start position:0%
+equation differentiate that with respect
+to L and what do you
+
+ align:start position:0%
+to L and what do you
+ 
+
+ align:start position:0%
+to L and what do you
+get if you different if you differ
+
+ align:start position:0%
+get if you different if you differ
+ 
+
+ align:start position:0%
+get if you different if you differ
+respect to L you get that you get two
+
+ align:start position:0%
+respect to L you get that you get two
+ 
+
+ align:start position:0%
+respect to L you get that you get two
+you get uh 2 L +
+
+ align:start position:0%
+you get uh 2 L +
+ 
+
+ align:start position:0%
+you get uh 2 L +
+10 and that is the firm's marginal
+
+ align:start position:0%
+10 and that is the firm's marginal
+ 
+
+ align:start position:0%
+10 and that is the firm's marginal
+expenditure
+
+ align:start position:0%
+expenditure
+ 
+
+ align:start position:0%
+expenditure
+curve which is
+
+ align:start position:0%
+curve which is
+ 
+
+ align:start position:0%
+curve which is
+above the F the supply curve as you see
+
+ align:start position:0%
+above the F the supply curve as you see
+ 
+
+ align:start position:0%
+above the F the supply curve as you see
+in figure
+
+ align:start position:0%
+in figure
+ 
+
+ align:start position:0%
+in figure
+164 so what does a monopsonist do the
+
+ align:start position:0%
+164 so what does a monopsonist do the
+ 
+
+ align:start position:0%
+164 so what does a monopsonist do the
+monopsonist set
+
+ align:start position:0%
+monopsonist set
+ 
+
+ align:start position:0%
+monopsonist set
+goes to the point where marginal cost
+
+ align:start position:0%
+goes to the point where marginal cost
+ 
+
+ align:start position:0%
+goes to the point where marginal cost
+equals marginal benefits what's the
+
+ align:start position:0%
+equals marginal benefits what's the
+ 
+
+ align:start position:0%
+equals marginal benefits what's the
+marginal cost the marginal cost is the
+
+ align:start position:0%
+marginal cost the marginal cost is the
+ 
+
+ align:start position:0%
+marginal cost the marginal cost is the
+marginal expenditure curve what's the
+
+ align:start position:0%
+marginal expenditure curve what's the
+ 
+
+ align:start position:0%
+marginal expenditure curve what's the
+marginal benefit the marginal revenue
+
+ align:start position:0%
+marginal benefit the marginal revenue
+ 
+
+ align:start position:0%
+marginal benefit the marginal revenue
+product curve so it says I want to hire
+
+ align:start position:0%
+product curve so it says I want to hire
+ 
+
+ align:start position:0%
+product curve so it says I want to hire
+
+ align:start position:0%
+ 
+
+ align:start position:0%
+workers not the 30 I was hiring in the
+
+ align:start position:0%
+workers not the 30 I was hiring in the
+ 
+
+ align:start position:0%
+workers not the 30 I was hiring in the
+market was competitive but
+
+ align:start position:0%
+market was competitive but
+ 
+
+ align:start position:0%
+market was competitive but
+20 what wage am I going to pay them well
+
+ align:start position:0%
+20 what wage am I going to pay them well
+ 
+
+ align:start position:0%
+20 what wage am I going to pay them well
+just like the monopolist needs to
+
+ align:start position:0%
+just like the monopolist needs to
+ 
+
+ align:start position:0%
+just like the monopolist needs to
+respect the demand curve the monopsonist
+
+ align:start position:0%
+respect the demand curve the monopsonist
+ 
+
+ align:start position:0%
+respect the demand curve the monopsonist
+needs to respect the supply curve so
+
+ align:start position:0%
+needs to respect the supply curve so
+ 
+
+ align:start position:0%
+needs to respect the supply curve so
+ways you can pay them when we read off
+
+ align:start position:0%
+ways you can pay them when we read off
+ 
+
+ align:start position:0%
+ways you can pay them when we read off
+the supply curve you're going to pay
+
+ align:start position:0%
+the supply curve you're going to pay
+ 
+
+ align:start position:0%
+the supply curve you're going to pay
+them 30 instead of
+
+ align:start position:0%
+them 30 instead of
+ 
+
+ align:start position:0%
+them 30 instead of
+40 so what's going on here you're hiring
+
+ align:start position:0%
+40 so what's going on here you're hiring
+ 
+
+ align:start position:0%
+40 so what's going on here you're hiring
+fewer workers at a lower
+
+ align:start position:0%
+fewer workers at a lower
+ 
+
+ align:start position:0%
+fewer workers at a lower
+wage than the equilibrium would dictate
+
+ align:start position:0%
+wage than the equilibrium would dictate
+ 
+
+ align:start position:0%
+wage than the equilibrium would dictate
+why because if you want more workers you
+
+ align:start position:0%
+why because if you want more workers you
+ 
+
+ align:start position:0%
+why because if you want more workers you
+got to raise the wage and that's not
+
+ align:start position:0%
+got to raise the wage and that's not
+ 
+
+ align:start position:0%
+got to raise the wage and that's not
+profitable so if you're if you're at the
+
+ align:start position:0%
+profitable so if you're if you're at the
+ 
+
+ align:start position:0%
+profitable so if you're if you're at the
+point where you're paying 30 to get 20
+
+ align:start position:0%
+point where you're paying 30 to get 20
+ 
+
+ align:start position:0%
+point where you're paying 30 to get 20
+workers and from that point you want to
+
+ align:start position:0%
+workers and from that point you want to
+ 
+
+ align:start position:0%
+workers and from that point you want to
+hire more workers say well look you know
+
+ align:start position:0%
+hire more workers say well look you know
+ 
+
+ align:start position:0%
+hire more workers say well look you know
+even at that point it's you know I'm
+
+ align:start position:0%
+even at that point it's you know I'm
+ 
+
+ align:start position:0%
+even at that point it's you know I'm
+making money on the next
+
+ align:start position:0%
+making money on the next
+ 
+
+ align:start position:0%
+making money on the next
+worker but the problem is to hire that
+
+ align:start position:0%
+worker but the problem is to hire that
+ 
+
+ align:start position:0%
+worker but the problem is to hire that
+next work you have to pay higher wages
+
+ align:start position:0%
+next work you have to pay higher wages
+ 
+
+ align:start position:0%
+next work you have to pay higher wages
+to all your previous workers and it's
+
+ align:start position:0%
+to all your previous workers and it's
+ 
+
+ align:start position:0%
+to all your previous workers and it's
+not worth it this is a hard intuition
+
+ align:start position:0%
+not worth it this is a hard intuition
+ 
+
+ align:start position:0%
+not worth it this is a hard intuition
+but it's the flip side of the poisoning
+
+ align:start position:0%
+but it's the flip side of the poisoning
+ 
+
+ align:start position:0%
+but it's the flip side of the poisoning
+intuition so go back to your Monopoly
+
+ align:start position:0%
+intuition so go back to your Monopoly
+ 
+
+ align:start position:0%
+intuition so go back to your Monopoly
+case and work it through you'll see it's
+
+ align:start position:0%
+case and work it through you'll see it's
+ 
+
+ align:start position:0%
+case and work it through you'll see it's
+all just the
+
+ align:start position:0%
+all just the
+ 
+
+ align:start position:0%
+all just the
+opposite okay now while I need to teach
+
+ align:start position:0%
+opposite okay now while I need to teach
+ 
+
+ align:start position:0%
+opposite okay now while I need to teach
+you the math and the graphs because
+
+ align:start position:0%
+you the math and the graphs because
+ 
+
+ align:start position:0%
+you the math and the graphs because
+that's what we test you on the intuition
+
+ align:start position:0%
+that's what we test you on the intuition
+ 
+
+ align:start position:0%
+that's what we test you on the intuition
+here is actually pretty clear I think
+
+ align:start position:0%
+here is actually pretty clear I think
+ 
+
+ align:start position:0%
+here is actually pretty clear I think
+clearer than the Monopoly case just
+
+ align:start position:0%
+clearer than the Monopoly case just
+ 
+
+ align:start position:0%
+clearer than the Monopoly case just
+think about the intuition for a second
+
+ align:start position:0%
+think about the intuition for a second
+ 
+
+ align:start position:0%
+think about the intuition for a second
+think about me at
+
+ align:start position:0%
+think about me at
+ 
+
+ align:start position:0%
+think about me at
+MIT there's many universities I could
+
+ align:start position:0%
+MIT there's many universities I could
+ 
+
+ align:start position:0%
+MIT there's many universities I could
+work for okay I mean it sound arrogant
+
+ align:start position:0%
+work for okay I mean it sound arrogant
+ 
+
+ align:start position:0%
+work for okay I mean it sound arrogant
+but there's a lot of universities out
+
+ align:start position:0%
+but there's a lot of universities out
+ 
+
+ align:start position:0%
+but there's a lot of universities out
+there presumably some others would want
+
+ align:start position:0%
+there presumably some others would want
+ 
+
+ align:start position:0%
+there presumably some others would want
+to hire me
+
+ align:start position:0%
+to hire me
+ 
+
+ align:start position:0%
+to hire me
+okay yet MIT has monopsony power over me
+
+ align:start position:0%
+okay yet MIT has monopsony power over me
+ 
+
+ align:start position:0%
+okay yet MIT has monopsony power over me
+why what gives MIT monopsony power over
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+me it's nothing nefarious think about
+
+ align:start position:0%
+me it's nothing nefarious think about
+ 
+
+ align:start position:0%
+me it's nothing nefarious think about
+typically any but any firm has Monopoly
+
+ align:start position:0%
+typically any but any firm has Monopoly
+ 
+
+ align:start position:0%
+typically any but any firm has Monopoly
+power over their employees
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+why well
+
+ align:start position:0%
+why well
+ 
+
+ align:start position:0%
+why well
+yeah I don't know how much I get paid
+
+ align:start position:0%
+yeah I don't know how much I get paid
+ 
+
+ align:start position:0%
+yeah I don't know how much I get paid
+anywhere else that's one reason so
+
+ align:start position:0%
+anywhere else that's one reason so
+ 
+
+ align:start position:0%
+anywhere else that's one reason so
+there's an information
+
+ align:start position:0%
+there's an information
+ 
+
+ align:start position:0%
+there's an information
+reason what else now let's actually
+
+ align:start position:0%
+reason what else now let's actually
+ 
+
+ align:start position:0%
+reason what else now let's actually
+let's compare that actually I know how
+
+ align:start position:0%
+let's compare that actually I know how
+ 
+
+ align:start position:0%
+let's compare that actually I know how
+to get paid in California because
+
+ align:start position:0%
+to get paid in California because
+ 
+
+ align:start position:0%
+to get paid in California because
+California public schools have to make
+
+ align:start position:0%
+California public schools have to make
+ 
+
+ align:start position:0%
+California public schools have to make
+their wages public so let's say I could
+
+ align:start position:0%
+their wages public so let's say I could
+ 
+
+ align:start position:0%
+their wages public so let's say I could
+overcome that actually if you go online
+
+ align:start position:0%
+overcome that actually if you go online
+ 
+
+ align:start position:0%
+overcome that actually if you go online
+you want know when it's paid at a public
+
+ align:start position:0%
+you want know when it's paid at a public
+ 
+
+ align:start position:0%
+you want know when it's paid at a public
+university in America you can figure
+
+ align:start position:0%
+university in America you can figure
+ 
+
+ align:start position:0%
+university in America you can figure
+that out okay so let's say I could solve
+
+ align:start position:0%
+that out okay so let's say I could solve
+ 
+
+ align:start position:0%
+that out okay so let's say I could solve
+that problem but there's other reasons
+
+ align:start position:0%
+that problem but there's other reasons
+ 
+
+ align:start position:0%
+that problem but there's other reasons
+why MIT is monop power let's say if they
+
+ align:start position:0%
+why MIT is monop power let's say if they
+ 
+
+ align:start position:0%
+why MIT is monop power let's say if they
+mov to California
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah well I'm established I I have to
+
+ align:start position:0%
+yeah well I'm established I I have to
+ 
+
+ align:start position:0%
+yeah well I'm established I I have to
+ move right like if I want to go
+
+ align:start position:0%
+ move right like if I want to go
+ 
+
+ align:start position:0%
+ move right like if I want to go
+to California I gotta move that sucks I
+
+ align:start position:0%
+to California I gotta move that sucks I
+ 
+
+ align:start position:0%
+to California I gotta move that sucks I
+gotta pack up the house I got to leave
+
+ align:start position:0%
+gotta pack up the house I got to leave
+ 
+
+ align:start position:0%
+gotta pack up the house I got to leave
+all my friends uh in particular my wife
+
+ align:start position:0%
+all my friends uh in particular my wife
+ 
+
+ align:start position:0%
+all my friends uh in particular my wife
+might have a job that she likes here my
+
+ align:start position:0%
+might have a job that she likes here my
+ 
+
+ align:start position:0%
+might have a job that she likes here my
+kids might like being in school here so
+
+ align:start position:0%
+kids might like being in school here so
+ 
+
+ align:start position:0%
+kids might like being in school here so
+there's a huge transaction cost
+
+ align:start position:0%
+there's a huge transaction cost
+ 
+
+ align:start position:0%
+there's a huge transaction cost
+transaction costs create monopsony power
+
+ align:start position:0%
+transaction costs create monopsony power
+ 
+
+ align:start position:0%
+transaction costs create monopsony power
+it's not a mining town me it's not a
+
+ align:start position:0%
+it's not a mining town me it's not a
+ 
+
+ align:start position:0%
+it's not a mining town me it's not a
+mining town but it still has Market
+
+ align:start position:0%
+mining town but it still has Market
+ 
+
+ align:start position:0%
+mining town but it still has Market
+power over me because of transaction
+
+ align:start position:0%
+power over me because of transaction
+ 
+
+ align:start position:0%
+power over me because of transaction
+costs do also the fact I like teaching
+
+ align:start position:0%
+costs do also the fact I like teaching
+ 
+
+ align:start position:0%
+costs do also the fact I like teaching
+MIT I've got my lecture set the to some
+
+ align:start position:0%
+MIT I've got my lecture set the to some
+ 
+
+ align:start position:0%
+MIT I've got my lecture set the to some
+other univers I have to dumb them down
+
+ align:start position:0%
+other univers I have to dumb them down
+ 
+
+ align:start position:0%
+other univers I have to dumb them down
+because the students aren't as smart as
+
+ align:start position:0%
+because the students aren't as smart as
+ 
+
+ align:start position:0%
+because the students aren't as smart as
+MIT I don't want to do that I've got I
+
+ align:start position:0%
+MIT I don't want to do that I've got I
+ 
+
+ align:start position:0%
+MIT I don't want to do that I've got I
+my office has a window view it's pretty
+
+ align:start position:0%
+my office has a window view it's pretty
+ 
+
+ align:start position:0%
+my office has a window view it's pretty
+awesome my window has an has a river
+
+ align:start position:0%
+awesome my window has an has a river
+ 
+
+ align:start position:0%
+awesome my window has an has a river
+view my office has a window view Jesus
+
+ align:start position:0%
+view my office has a window view Jesus
+ 
+
+ align:start position:0%
+view my office has a window view Jesus
+my my office has a Riverview through the
+
+ align:start position:0%
+my my office has a Riverview through the
+ 
+
+ align:start position:0%
+my my office has a Riverview through the
+window okay that's pretty awesome that'
+
+ align:start position:0%
+window okay that's pretty awesome that'
+ 
+
+ align:start position:0%
+window okay that's pretty awesome that'
+be hard to replicate a lot of other
+
+ align:start position:0%
+be hard to replicate a lot of other
+ 
+
+ align:start position:0%
+be hard to replicate a lot of other
+universities
+
+ align:start position:0%
+universities
+ 
+
+ align:start position:0%
+universities
+basically every job change in jobs comes
+
+ align:start position:0%
+basically every job change in jobs comes
+ 
+
+ align:start position:0%
+basically every job change in jobs comes
+with transaction costs transaction costs
+
+ align:start position:0%
+with transaction costs transaction costs
+ 
+
+ align:start position:0%
+with transaction costs transaction costs
+create monopsony power MIT does not have
+
+ align:start position:0%
+create monopsony power MIT does not have
+ 
+
+ align:start position:0%
+create monopsony power MIT does not have
+to pay me the market
+
+ align:start position:0%
+to pay me the market
+ 
+
+ align:start position:0%
+to pay me the market
+wage because of these transaction costs
+
+ align:start position:0%
+wage because of these transaction costs
+ 
+
+ align:start position:0%
+wage because of these transaction costs
+and because of information
+
+ align:start position:0%
+and because of information
+ 
+
+ align:start position:0%
+and because of information
+limitations okay so it's not crazy to
+
+ align:start position:0%
+limitations okay so it's not crazy to
+ 
+
+ align:start position:0%
+limitations okay so it's not crazy to
+think indeed we now think that basically
+
+ align:start position:0%
+think indeed we now think that basically
+ 
+
+ align:start position:0%
+think indeed we now think that basically
+monopsony is a better description of
+
+ align:start position:0%
+monopsony is a better description of
+ 
+
+ align:start position:0%
+monopsony is a better description of
+almost all labor markets than is perfect
+
+ align:start position:0%
+almost all labor markets than is perfect
+ 
+
+ align:start position:0%
+almost all labor markets than is perfect
+competition this is a real SE change in
+
+ align:start position:0%
+competition this is a real SE change in
+ 
+
+ align:start position:0%
+competition this is a real SE change in
+the last 20 years is a real sort of
+
+ align:start position:0%
+the last 20 years is a real sort of
+ 
+
+ align:start position:0%
+the last 20 years is a real sort of
+takeover the monop city model in labor
+
+ align:start position:0%
+takeover the monop city model in labor
+ 
+
+ align:start position:0%
+takeover the monop city model in labor
+economics that we think it's probably
+
+ align:start position:0%
+economics that we think it's probably
+ 
+
+ align:start position:0%
+economics that we think it's probably
+much more likely if firms have monopsony
+
+ align:start position:0%
+much more likely if firms have monopsony
+ 
+
+ align:start position:0%
+much more likely if firms have monopsony
+power than that they're perfectly
+
+ align:start position:0%
+power than that they're perfectly
+ 
+
+ align:start position:0%
+power than that they're perfectly
+competitive okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah in the new higher market so that's
+
+ align:start position:0%
+yeah in the new higher market so that's
+ 
+
+ align:start position:0%
+yeah in the new higher market so that's
+a great Point there's still the
+
+ align:start position:0%
+a great Point there's still the
+ 
+
+ align:start position:0%
+a great Point there's still the
+information issue which is I'd have to
+
+ align:start position:0%
+information issue which is I'd have to
+ 
+
+ align:start position:0%
+information issue which is I'd have to
+go and collect a bunch of offers but
+
+ align:start position:0%
+go and collect a bunch of offers but
+ 
+
+ align:start position:0%
+go and collect a bunch of offers but
+other than that you're right you would
+
+ align:start position:0%
+other than that you're right you would
+ 
+
+ align:start position:0%
+other than that you're right you would
+think and indeed if you look at salaries
+
+ align:start position:0%
+think and indeed if you look at salaries
+ 
+
+ align:start position:0%
+think and indeed if you look at salaries
+of
+
+ align:start position:0%
+of
+ 
+
+ align:start position:0%
+of
+academics new higher salaries if you
+
+ align:start position:0%
+academics new higher salaries if you
+ 
+
+ align:start position:0%
+academics new higher salaries if you
+look at Sal academics you can basically
+
+ align:start position:0%
+look at Sal academics you can basically
+ 
+
+ align:start position:0%
+look at Sal academics you can basically
+predict them pretty well based on two
+
+ align:start position:0%
+predict them pretty well based on two
+ 
+
+ align:start position:0%
+predict them pretty well based on two
+based on essentially when do they get
+
+ align:start position:0%
+based on essentially when do they get
+ 
+
+ align:start position:0%
+based on essentially when do they get
+their last offer so new higher salaries
+
+ align:start position:0%
+their last offer so new higher salaries
+ 
+
+ align:start position:0%
+their last offer so new higher salaries
+are pretty flat and you'll get raises
+
+ align:start position:0%
+are pretty flat and you'll get raises
+ 
+
+ align:start position:0%
+are pretty flat and you'll get raises
+when they get an offer from another
+
+ align:start position:0%
+when they get an offer from another
+ 
+
+ align:start position:0%
+when they get an offer from another
+University so basically MIT will
+
+ align:start position:0%
+University so basically MIT will
+ 
+
+ align:start position:0%
+University so basically MIT will
+underpay you until you get an offer from
+
+ align:start position:0%
+underpay you until you get an offer from
+ 
+
+ align:start position:0%
+underpay you until you get an offer from
+another University and then they'll then
+
+ align:start position:0%
+another University and then they'll then
+ 
+
+ align:start position:0%
+another University and then they'll then
+they'll because that reveals information
+
+ align:start position:0%
+they'll because that reveals information
+ 
+
+ align:start position:0%
+they'll because that reveals information
+and then MIT can then can then do that
+
+ align:start position:0%
+and then MIT can then can then do that
+ 
+
+ align:start position:0%
+and then MIT can then can then do that
+okay good question all right now what
+
+ align:start position:0%
+okay good question all right now what
+ 
+
+ align:start position:0%
+okay good question all right now what
+does this mean for the government well
+
+ align:start position:0%
+does this mean for the government well
+ 
+
+ align:start position:0%
+does this mean for the government well
+this means that there is scope for gains
+
+ align:start position:0%
+this means that there is scope for gains
+ 
+
+ align:start position:0%
+this means that there is scope for gains
+from regulation because look this
+
+ align:start position:0%
+from regulation because look this
+ 
+
+ align:start position:0%
+from regulation because look this
+monopis has created a dead weight loss
+
+ align:start position:0%
+monopis has created a dead weight loss
+ 
+
+ align:start position:0%
+monopis has created a dead weight loss
+look at the we we off have 30 workers so
+
+ align:start position:0%
+look at the we we off have 30 workers so
+ 
+
+ align:start position:0%
+look at the we we off have 30 workers so
+a deadweight loss triangle from only
+
+ align:start position:0%
+a deadweight loss triangle from only
+ 
+
+ align:start position:0%
+a deadweight loss triangle from only
+hiring 20 workers that says their scope
+
+ align:start position:0%
+hiring 20 workers that says their scope
+ 
+
+ align:start position:0%
+hiring 20 workers that says their scope
+for optimal regulation just like the
+
+ align:start position:0%
+for optimal regulation just like the
+ 
+
+ align:start position:0%
+for optimal regulation just like the
+scope to Optimal regulation of monop of
+
+ align:start position:0%
+scope to Optimal regulation of monop of
+ 
+
+ align:start position:0%
+scope to Optimal regulation of monop of
+monopolis and what would optimal
+
+ align:start position:0%
+monopolis and what would optimal
+ 
+
+ align:start position:0%
+monopolis and what would optimal
+regulation look like well it could look
+
+ align:start position:0%
+regulation look like well it could look
+ 
+
+ align:start position:0%
+regulation look like well it could look
+like a minimum wage so imagine if figure
+
+ align:start position:0%
+like a minimum wage so imagine if figure
+ 
+
+ align:start position:0%
+like a minimum wage so imagine if figure
+165 we set a minimum wage equal to the
+
+ align:start position:0%
+165 we set a minimum wage equal to the
+ 
+
+ align:start position:0%
+165 we set a minimum wage equal to the
+market
+
+ align:start position:0%
+market
+ 
+
+ align:start position:0%
+market
+wage well now think about the firm's
+
+ align:start position:0%
+wage well now think about the firm's
+ 
+
+ align:start position:0%
+wage well now think about the firm's
+decision for any workers to the left of
+
+ align:start position:0%
+decision for any workers to the left of
+ 
+
+ align:start position:0%
+decision for any workers to the left of
+LM there's no poisoning effect because
+
+ align:start position:0%
+LM there's no poisoning effect because
+ 
+
+ align:start position:0%
+LM there's no poisoning effect because
+they can't lower the wage so they might
+
+ align:start position:0%
+they can't lower the wage so they might
+ 
+
+ align:start position:0%
+they can't lower the wage so they might
+as well higher the competitive level
+
+ align:start position:0%
+as well higher the competitive level
+ 
+
+ align:start position:0%
+as well higher the competitive level
+what has the minimum wage just done it
+
+ align:start position:0%
+what has the minimum wage just done it
+ 
+
+ align:start position:0%
+what has the minimum wage just done it
+has raised
+
+ align:start position:0%
+has raised
+ 
+
+ align:start position:0%
+has raised
+employment so this is how you can get
+
+ align:start position:0%
+employment so this is how you can get
+ 
+
+ align:start position:0%
+employment so this is how you can get
+this weird result that a minimum wage
+
+ align:start position:0%
+this weird result that a minimum wage
+ 
+
+ align:start position:0%
+this weird result that a minimum wage
+can raise employment because what the
+
+ align:start position:0%
+can raise employment because what the
+ 
+
+ align:start position:0%
+can raise employment because what the
+minimum wage has done has essentially
+
+ align:start position:0%
+minimum wage has done has essentially
+ 
+
+ align:start position:0%
+minimum wage has done has essentially
+eroded monopsony power or eroded the
+
+ align:start position:0%
+eroded monopsony power or eroded the
+ 
+
+ align:start position:0%
+eroded monopsony power or eroded the
+negative effects of monopsony by getting
+
+ align:start position:0%
+negative effects of monopsony by getting
+ 
+
+ align:start position:0%
+negative effects of monopsony by getting
+rid of this poisoning effect by saying
+
+ align:start position:0%
+rid of this poisoning effect by saying
+ 
+
+ align:start position:0%
+rid of this poisoning effect by saying
+well firms might as well hire Elm the
+
+ align:start position:0%
+well firms might as well hire Elm the
+ 
+
+ align:start position:0%
+well firms might as well hire Elm the
+reason they were hiring lower than El
+
+ align:start position:0%
+reason they were hiring lower than El
+ 
+
+ align:start position:0%
+reason they were hiring lower than El
+comp before was because they could lower
+
+ align:start position:0%
+comp before was because they could lower
+ 
+
+ align:start position:0%
+comp before was because they could lower
+the wage but now they
+
+ align:start position:0%
+the wage but now they
+ 
+
+ align:start position:0%
+the wage but now they
+can't so that is how a minimum wage can
+
+ align:start position:0%
+can't so that is how a minimum wage can
+ 
+
+ align:start position:0%
+can't so that is how a minimum wage can
+raise employment now of course so in
+
+ align:start position:0%
+raise employment now of course so in
+ 
+
+ align:start position:0%
+raise employment now of course so in
+subsets you can get a win-win government
+
+ align:start position:0%
+subsets you can get a win-win government
+ 
+
+ align:start position:0%
+subsets you can get a win-win government
+policy you can transfer Surplus to
+
+ align:start position:0%
+policy you can transfer Surplus to
+ 
+
+ align:start position:0%
+policy you can transfer Surplus to
+Consumers and raise employment everybody
+
+ align:start position:0%
+Consumers and raise employment everybody
+ 
+
+ align:start position:0%
+Consumers and raise employment everybody
+wins and that's how government policy
+
+ align:start position:0%
+wins and that's how government policy
+ 
+
+ align:start position:0%
+wins and that's how government policy
+can make things better in imperfect Mark
+
+ align:start position:0%
+can make things better in imperfect Mark
+ 
+
+ align:start position:0%
+can make things better in imperfect Mark
+with market
+
+ align:start position:0%
+with market
+ 
+
+ align:start position:0%
+with market
+failures now of course that isn't
+
+ align:start position:0%
+failures now of course that isn't
+ 
+
+ align:start position:0%
+failures now of course that isn't
+necessarily
+
+ align:start position:0%
+necessarily
+ 
+
+ align:start position:0%
+necessarily
+true what would happen if you set the
+
+ align:start position:0%
+true what would happen if you set the
+ 
+
+ align:start position:0%
+true what would happen if you set the
+minimum wage well let me ask first what
+
+ align:start position:0%
+minimum wage well let me ask first what
+ 
+
+ align:start position:0%
+minimum wage well let me ask first what
+happen if you set the minimum wage too
+
+ align:start position:0%
+happen if you set the minimum wage too
+ 
+
+ align:start position:0%
+happen if you set the minimum wage too
+low what if you set the minimum wage
+
+ align:start position:0%
+low what if you set the minimum wage
+ 
+
+ align:start position:0%
+low what if you set the minimum wage
+below
+
+ align:start position:0%
+below
+ 
+
+ align:start position:0%
+below
+W1 what would happen if the government
+
+ align:start position:0%
+W1 what would happen if the government
+ 
+
+ align:start position:0%
+W1 what would happen if the government
+put a minimum wage in was below
+
+ align:start position:0%
+put a minimum wage in was below
+ 
+
+ align:start position:0%
+put a minimum wage in was below
+W1 yeah no effect very important the
+
+ align:start position:0%
+W1 yeah no effect very important the
+ 
+
+ align:start position:0%
+W1 yeah no effect very important the
+private Market will always get around
+
+ align:start position:0%
+private Market will always get around
+ 
+
+ align:start position:0%
+private Market will always get around
+government regulations if it can a
+
+ align:start position:0%
+government regulations if it can a
+ 
+
+ align:start position:0%
+government regulations if it can a
+government regulation that doesn't bind
+
+ align:start position:0%
+government regulation that doesn't bind
+ 
+
+ align:start position:0%
+government regulation that doesn't bind
+is no government regulation at all it
+
+ align:start position:0%
+is no government regulation at all it
+ 
+
+ align:start position:0%
+is no government regulation at all it
+sounds obvious but it's not it's
+
+ align:start position:0%
+sounds obvious but it's not it's
+ 
+
+ align:start position:0%
+sounds obvious but it's not it's
+important to remember the first thing
+
+ align:start position:0%
+important to remember the first thing
+ 
+
+ align:start position:0%
+important to remember the first thing
+after to go regulations is do they
+
+ align:start position:0%
+after to go regulations is do they
+ 
+
+ align:start position:0%
+after to go regulations is do they
+matter okay then basically as you think
+
+ align:start position:0%
+matter okay then basically as you think
+ 
+
+ align:start position:0%
+matter okay then basically as you think
+about any minimum wage between
+
+ align:start position:0%
+about any minimum wage between
+ 
+
+ align:start position:0%
+about any minimum wage between
+W1 and even past W comp they will
+
+ align:start position:0%
+W1 and even past W comp they will
+ 
+
+ align:start position:0%
+W1 and even past W comp they will
+actually improve welfare but as it gets
+
+ align:start position:0%
+actually improve welfare but as it gets
+ 
+
+ align:start position:0%
+actually improve welfare but as it gets
+high enough the minimum wage could
+
+ align:start position:0%
+high enough the minimum wage could
+ 
+
+ align:start position:0%
+high enough the minimum wage could
+actually and cause firms once the
+
+ align:start position:0%
+actually and cause firms once the
+ 
+
+ align:start position:0%
+actually and cause firms once the
+minimum wage gets above
+
+ align:start position:0%
+minimum wage gets above
+ 
+
+ align:start position:0%
+minimum wage gets above
+um the level on the marginal revenue
+
+ align:start position:0%
+um the level on the marginal revenue
+ 
+
+ align:start position:0%
+um the level on the marginal revenue
+product curve that corresponds to L1 so
+
+ align:start position:0%
+product curve that corresponds to L1 so
+ 
+
+ align:start position:0%
+product curve that corresponds to L1 so
+you see where the L1 dash line hits the
+
+ align:start position:0%
+you see where the L1 dash line hits the
+ 
+
+ align:start position:0%
+you see where the L1 dash line hits the
+marginal revenue product curve once the
+
+ align:start position:0%
+marginal revenue product curve once the
+ 
+
+ align:start position:0%
+marginal revenue product curve once the
+wage gets above that level then you're
+
+ align:start position:0%
+wage gets above that level then you're
+ 
+
+ align:start position:0%
+wage gets above that level then you're
+making things worse you end up hiring
+
+ align:start position:0%
+making things worse you end up hiring
+ 
+
+ align:start position:0%
+making things worse you end up hiring
+fewer workers then the monopus would
+
+ align:start position:0%
+fewer workers then the monopus would
+ 
+
+ align:start position:0%
+fewer workers then the monopus would
+hire so once again the way to think
+
+ align:start position:0%
+hire so once again the way to think
+ 
+
+ align:start position:0%
+hire so once again the way to think
+government regulation once again come
+
+ align:start position:0%
+government regulation once again come
+ 
+
+ align:start position:0%
+government regulation once again come
+take 1441 we'll spend all semester on
+
+ align:start position:0%
+take 1441 we'll spend all semester on
+ 
+
+ align:start position:0%
+take 1441 we'll spend all semester on
+this the way to think about it is the
+
+ align:start position:0%
+this the way to think about it is the
+ 
+
+ align:start position:0%
+this the way to think about it is the
+market knows best unless there's a
+
+ align:start position:0%
+market knows best unless there's a
+ 
+
+ align:start position:0%
+market knows best unless there's a
+market failure the market failure raises
+
+ align:start position:0%
+market failure the market failure raises
+ 
+
+ align:start position:0%
+market failure the market failure raises
+the PO potential for the government to
+
+ align:start position:0%
+the PO potential for the government to
+ 
+
+ align:start position:0%
+the PO potential for the government to
+improve things but doesn't prove
+
+ align:start position:0%
+improve things but doesn't prove
+ 
+
+ align:start position:0%
+improve things but doesn't prove
+government will Pro improve things it
+
+ align:start position:0%
+government will Pro improve things it
+ 
+
+ align:start position:0%
+government will Pro improve things it
+does not prove government will improve
+
+ align:start position:0%
+does not prove government will improve
+ 
+
+ align:start position:0%
+does not prove government will improve
+things you need to actually study and
+
+ align:start position:0%
+things you need to actually study and
+ 
+
+ align:start position:0%
+things you need to actually study and
+examine the government policy to see if
+
+ align:start position:0%
+examine the government policy to see if
+ 
+
+ align:start position:0%
+examine the government policy to see if
+it makes it better or worse for minimum
+
+ align:start position:0%
+it makes it better or worse for minimum
+ 
+
+ align:start position:0%
+it makes it better or worse for minimum
+wages basically the consensus now is for
+
+ align:start position:0%
+wages basically the consensus now is for
+ 
+
+ align:start position:0%
+wages basically the consensus now is for
+minimum wages in the range that minimum
+
+ align:start position:0%
+minimum wages in the range that minimum
+ 
+
+ align:start position:0%
+minimum wages in the range that minimum
+wages are set in America which is being
+
+ align:start position:0%
+wages are set in America which is being
+ 
+
+ align:start position:0%
+wages are set in America which is being
+probably about $8 and12 an hour okay
+
+ align:start position:0%
+probably about $8 and12 an hour okay
+ 
+
+ align:start position:0%
+probably about $8 and12 an hour okay
+where most minimum wages are we the
+
+ align:start position:0%
+where most minimum wages are we the
+ 
+
+ align:start position:0%
+where most minimum wages are we the
+consensus seems to be that they are a
+
+ align:start position:0%
+consensus seems to be that they are a
+ 
+
+ align:start position:0%
+consensus seems to be that they are a
+good thing that basically they can cause
+
+ align:start position:0%
+good thing that basically they can cause
+ 
+
+ align:start position:0%
+good thing that basically they can cause
+benefits to workers without actually
+
+ align:start position:0%
+benefits to workers without actually
+ 
+
+ align:start position:0%
+benefits to workers without actually
+reducing employment once you get above
+
+ align:start position:0%
+reducing employment once you get above
+ 
+
+ align:start position:0%
+reducing employment once you get above
+12 the evidence gets more mixed so we
+
+ align:start position:0%
+12 the evidence gets more mixed so we
+ 
+
+ align:start position:0%
+12 the evidence gets more mixed so we
+now are seeing a series of 15-hour wage
+
+ align:start position:0%
+now are seeing a series of 15-hour wage
+ 
+
+ align:start position:0%
+now are seeing a series of 15-hour wage
+dollar minimum wage including
+
+ align:start position:0%
+dollar minimum wage including
+ 
+
+ align:start position:0%
+dollar minimum wage including
+Massachusetts the evidence on those is a
+
+ align:start position:0%
+Massachusetts the evidence on those is a
+ 
+
+ align:start position:0%
+Massachusetts the evidence on those is a
+little more mixed we need a little more
+
+ align:start position:0%
+little more mixed we need a little more
+ 
+
+ align:start position:0%
+little more mixed we need a little more
+time to study but there's some level at
+
+ align:start position:0%
+time to study but there's some level at
+ 
+
+ align:start position:0%
+time to study but there's some level at
+which a minimum wage definitionally is
+
+ align:start position:0%
+which a minimum wage definitionally is
+ 
+
+ align:start position:0%
+which a minimum wage definitionally is
+high enough it will cause unemployment
+
+ align:start position:0%
+high enough it will cause unemployment
+ 
+
+ align:start position:0%
+high enough it will cause unemployment
+that doesn't mean minum wage is bad it
+
+ align:start position:0%
+that doesn't mean minum wage is bad it
+ 
+
+ align:start position:0%
+that doesn't mean minum wage is bad it
+just means at that point there's a
+
+ align:start position:0%
+just means at that point there's a
+ 
+
+ align:start position:0%
+just means at that point there's a
+trade-off so if you go back to figure 16
+
+ align:start position:0%
+trade-off so if you go back to figure 16
+ 
+
+ align:start position:0%
+trade-off so if you go back to figure 16
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+two 162 does not imply we should not
+
+ align:start position:0%
+two 162 does not imply we should not
+ 
+
+ align:start position:0%
+two 162 does not imply we should not
+have minimum
+
+ align:start position:0%
+have minimum
+ 
+
+ align:start position:0%
+have minimum
+wage 162 just says there is a tradeoff
+
+ align:start position:0%
+wage 162 just says there is a tradeoff
+ 
+
+ align:start position:0%
+wage 162 just says there is a tradeoff
+you lose efficiency but you redistribute
+
+ align:start position:0%
+you lose efficiency but you redistribute
+ 
+
+ align:start position:0%
+you lose efficiency but you redistribute
+to
+
+ align:start position:0%
+to
+ 
+
+ align:start position:0%
+to
+workers okay in a standard model that's
+
+ align:start position:0%
+workers okay in a standard model that's
+ 
+
+ align:start position:0%
+workers okay in a standard model that's
+bad because we rate consumer and
+
+ align:start position:0%
+bad because we rate consumer and
+ 
+
+ align:start position:0%
+bad because we rate consumer and
+producer Surplus the same but in the
+
+ align:start position:0%
+producer Surplus the same but in the
+ 
+
+ align:start position:0%
+producer Surplus the same but in the
+real world it might not be we might
+
+ align:start position:0%
+real world it might not be we might
+ 
+
+ align:start position:0%
+real world it might not be we might
+value consumer surplus more than
+
+ align:start position:0%
+value consumer surplus more than
+ 
+
+ align:start position:0%
+value consumer surplus more than
+producer
+
+ align:start position:0%
+producer
+ 
+
+ align:start position:0%
+producer
+Surplus so the bottom line is the
+
+ align:start position:0%
+Surplus so the bottom line is the
+ 
+
+ align:start position:0%
+Surplus so the bottom line is the
+minimum wage isn't in no situation is it
+
+ align:start position:0%
+minimum wage isn't in no situation is it
+ 
+
+ align:start position:0%
+minimum wage isn't in no situation is it
+unambiguously bad it may actually be
+
+ align:start position:0%
+unambiguously bad it may actually be
+ 
+
+ align:start position:0%
+unambiguously bad it may actually be
+unambiguously good and depends on the
+
+ align:start position:0%
+unambiguously good and depends on the
+ 
+
+ align:start position:0%
+unambiguously good and depends on the
+structure of the labor
+
+ align:start position:0%
+structure of the labor
+ 
+
+ align:start position:0%
+structure of the labor
+market okay questions about
+
+ align:start position:0%
+market okay questions about
+ 
+
+ align:start position:0%
+market okay questions about
+that so once again the idea would be MIT
+
+ align:start position:0%
+that so once again the idea would be MIT
+ 
+
+ align:start position:0%
+that so once again the idea would be MIT
+is making excess money off me because I
+
+ align:start position:0%
+is making excess money off me because I
+ 
+
+ align:start position:0%
+is making excess money off me because I
+don't want to move if the government
+
+ align:start position:0%
+don't want to move if the government
+ 
+
+ align:start position:0%
+don't want to move if the government
+came in and raised my wages not too much
+
+ align:start position:0%
+came in and raised my wages not too much
+ 
+
+ align:start position:0%
+came in and raised my wages not too much
+that would make me better off and it
+
+ align:start position:0%
+that would make me better off and it
+ 
+
+ align:start position:0%
+that would make me better off and it
+would just come out of mit's profits it
+
+ align:start position:0%
+would just come out of mit's profits it
+ 
+
+ align:start position:0%
+would just come out of mit's profits it
+would just be a
+
+ align:start position:0%
+would just be a
+ 
+
+ align:start position:0%
+would just be a
+transfer but I'd be better off and they
+
+ align:start position:0%
+transfer but I'd be better off and they
+ 
+
+ align:start position:0%
+transfer but I'd be better off and they
+would they'd maybe because they pay
+
+ align:start position:0%
+would they'd maybe because they pay
+ 
+
+ align:start position:0%
+would they'd maybe because they pay
+higher wage they may hire another
+
+ align:start position:0%
+higher wage they may hire another
+ 
+
+ align:start position:0%
+higher wage they may hire another
+another professor okay and that would
+
+ align:start position:0%
+another professor okay and that would
+ 
+
+ align:start position:0%
+another professor okay and that would
+improve efficiency all right so with
+
+ align:start position:0%
+improve efficiency all right so with
+ 
+
+ align:start position:0%
+improve efficiency all right so with
+with monopsonist minimum wage is just
+
+ align:start position:0%
+with monopsonist minimum wage is just
+ 
+
+ align:start position:0%
+with monopsonist minimum wage is just
+induce efficient
+
+ align:start position:0%
+induce efficient
+ 
+
+ align:start position:0%
+induce efficient
+transfers now that's all I want to say
+
+ align:start position:0%
+transfers now that's all I want to say
+ 
+
+ align:start position:0%
+transfers now that's all I want to say
+about Labor markets I want to turn now
+
+ align:start position:0%
+about Labor markets I want to turn now
+ 
+
+ align:start position:0%
+about Labor markets I want to turn now
+to Capital markets which are a degree
+
+ align:start position:0%
+to Capital markets which are a degree
+ 
+
+ align:start position:0%
+to Capital markets which are a degree
+more complicated and therefore a degree
+
+ align:start position:0%
+more complicated and therefore a degree
+ 
+
+ align:start position:0%
+more complicated and therefore a degree
+more
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+interesting the main reason they're
+
+ align:start position:0%
+interesting the main reason they're
+ 
+
+ align:start position:0%
+interesting the main reason they're
+complicated is that
+
+ align:start position:0%
+complicated is that
+ 
+
+ align:start position:0%
+complicated is that
+capital is not tangible the way labor is
+
+ align:start position:0%
+capital is not tangible the way labor is
+ 
+
+ align:start position:0%
+capital is not tangible the way labor is
+labor you feel it you've done it it's an
+
+ align:start position:0%
+labor you feel it you've done it it's an
+ 
+
+ align:start position:0%
+labor you feel it you've done it it's an
+hour of work you know what work is
+
+ align:start position:0%
+hour of work you know what work is
+ 
+
+ align:start position:0%
+hour of work you know what work is
+capital what is it it's machines it's
+
+ align:start position:0%
+capital what is it it's machines it's
+ 
+
+ align:start position:0%
+capital what is it it's machines it's
+buildings it's vague
+
+ align:start position:0%
+buildings it's vague
+ 
+
+ align:start position:0%
+buildings it's vague
+thing so we're going to Now define
+
+ align:start position:0%
+thing so we're going to Now define
+ 
+
+ align:start position:0%
+thing so we're going to Now define
+capital more
+
+ align:start position:0%
+capital more
+ 
+
+ align:start position:0%
+capital more
+specifically by think about where
+
+ align:start position:0%
+specifically by think about where
+ 
+
+ align:start position:0%
+specifically by think about where
+Capital comes
+
+ align:start position:0%
+Capital comes
+ 
+
+ align:start position:0%
+Capital comes
+from where does the money come from to
+
+ align:start position:0%
+from where does the money come from to
+ 
+
+ align:start position:0%
+from where does the money come from to
+buy machines to finally to invest what
+
+ align:start position:0%
+buy machines to finally to invest what
+ 
+
+ align:start position:0%
+buy machines to finally to invest what
+goes all the way back to our farming
+
+ align:start position:0%
+goes all the way back to our farming
+ 
+
+ align:start position:0%
+goes all the way back to our farming
+agricultural
+
+ align:start position:0%
+agricultural
+ 
+
+ align:start position:0%
+agricultural
+economy farmers every year face a
+
+ align:start position:0%
+economy farmers every year face a
+ 
+
+ align:start position:0%
+economy farmers every year face a
+decision are they going to
+
+ align:start position:0%
+decision are they going to
+ 
+
+ align:start position:0%
+decision are they going to
+consume all of their crop or are they
+
+ align:start position:0%
+consume all of their crop or are they
+ 
+
+ align:start position:0%
+consume all of their crop or are they
+going to save some of the some of it to
+
+ align:start position:0%
+going to save some of the some of it to
+ 
+
+ align:start position:0%
+going to save some of the some of it to
+plant to create next year's
+
+ align:start position:0%
+plant to create next year's
+ 
+
+ align:start position:0%
+plant to create next year's
+crop so farmers face a decision of
+
+ align:start position:0%
+crop so farmers face a decision of
+ 
+
+ align:start position:0%
+crop so farmers face a decision of
+diverting today's consumption to
+
+ align:start position:0%
+diverting today's consumption to
+ 
+
+ align:start position:0%
+diverting today's consumption to
+tomorrow's consumption or next year's
+
+ align:start position:0%
+tomorrow's consumption or next year's
+ 
+
+ align:start position:0%
+tomorrow's consumption or next year's
+consumption how much of today's
+
+ align:start position:0%
+consumption how much of today's
+ 
+
+ align:start position:0%
+consumption how much of today's
+consumption they want to give up how
+
+ align:start position:0%
+consumption they want to give up how
+ 
+
+ align:start position:0%
+consumption they want to give up how
+much less they want to eat this year to
+
+ align:start position:0%
+much less they want to eat this year to
+ 
+
+ align:start position:0%
+much less they want to eat this year to
+have more to eat next year and that
+
+ align:start position:0%
+have more to eat next year and that
+ 
+
+ align:start position:0%
+have more to eat next year and that
+determines how many seeds they want to
+
+ align:start position:0%
+determines how many seeds they want to
+ 
+
+ align:start position:0%
+determines how many seeds they want to
+set
+
+ align:start position:0%
+set
+ 
+
+ align:start position:0%
+set
+aside that's what capital
+
+ align:start position:0%
+aside that's what capital
+ 
+
+ align:start position:0%
+aside that's what capital
+is capital is
+
+ align:start position:0%
+is capital is
+ 
+
+ align:start position:0%
+is capital is
+essentially what you take from
+
+ align:start position:0%
+essentially what you take from
+ 
+
+ align:start position:0%
+essentially what you take from
+today to have in the future when you buy
+
+ align:start position:0%
+today to have in the future when you buy
+ 
+
+ align:start position:0%
+today to have in the future when you buy
+a machine you are spending money today
+
+ align:start position:0%
+a machine you are spending money today
+ 
+
+ align:start position:0%
+a machine you are spending money today
+to get the machine so over the next few
+
+ align:start position:0%
+to get the machine so over the next few
+ 
+
+ align:start position:0%
+to get the machine so over the next few
+years it produces stuff that's no
+
+ align:start position:0%
+years it produces stuff that's no
+ 
+
+ align:start position:0%
+years it produces stuff that's no
+different than saving your
+
+ align:start position:0%
+different than saving your
+ 
+
+ align:start position:0%
+different than saving your
+seeds Okay that's what capital is is
+
+ align:start position:0%
+seeds Okay that's what capital is is
+ 
+
+ align:start position:0%
+seeds Okay that's what capital is is
+essentially the diversion of current
+
+ align:start position:0%
+essentially the diversion of current
+ 
+
+ align:start position:0%
+essentially the diversion of current
+consumption towards future
+
+ align:start position:0%
+consumption towards future
+ 
+
+ align:start position:0%
+consumption towards future
+consumption now unlike the
+
+ align:start position:0%
+consumption now unlike the
+ 
+
+ align:start position:0%
+consumption now unlike the
+farmer firms today don't get the money
+
+ align:start position:0%
+farmer firms today don't get the money
+ 
+
+ align:start position:0%
+farmer firms today don't get the money
+necessarily from themselves like the
+
+ align:start position:0%
+necessarily from themselves like the
+ 
+
+ align:start position:0%
+necessarily from themselves like the
+farmers did firms get their capital in
+
+ align:start position:0%
+farmers did firms get their capital in
+ 
+
+ align:start position:0%
+farmers did firms get their capital in
+what's called a capital Market well I
+
+ align:start position:0%
+what's called a capital Market well I
+ 
+
+ align:start position:0%
+what's called a capital Market well I
+just wrote that there firms get their
+
+ align:start position:0%
+just wrote that there firms get their
+ 
+
+ align:start position:0%
+just wrote that there firms get their
+capital in a capital Market what is the
+
+ align:start position:0%
+capital in a capital Market what is the
+ 
+
+ align:start position:0%
+capital in a capital Market what is the
+capital Market well that's a market with
+
+ align:start position:0%
+capital Market well that's a market with
+ 
+
+ align:start position:0%
+capital Market well that's a market with
+his demand for
+
+ align:start position:0%
+his demand for
+ 
+
+ align:start position:0%
+his demand for
+Capital which comes from how much which
+
+ align:start position:0%
+Capital which comes from how much which
+ 
+
+ align:start position:0%
+Capital which comes from how much which
+I'll derve in a few minutes comes from
+
+ align:start position:0%
+I'll derve in a few minutes comes from
+ 
+
+ align:start position:0%
+I'll derve in a few minutes comes from
+how much firms value the capital and a
+
+ align:start position:0%
+how much firms value the capital and a
+ 
+
+ align:start position:0%
+how much firms value the capital and a
+supply of capital well where does supply
+
+ align:start position:0%
+supply of capital well where does supply
+ 
+
+ align:start position:0%
+supply of capital well where does supply
+of capital come from what is capital
+
+ align:start position:0%
+of capital come from what is capital
+ 
+
+ align:start position:0%
+of capital come from what is capital
+it's basically the money you
+
+ align:start position:0%
+it's basically the money you
+ 
+
+ align:start position:0%
+it's basically the money you
+use to invest in the future where does
+
+ align:start position:0%
+use to invest in the future where does
+ 
+
+ align:start position:0%
+use to invest in the future where does
+it come from it comes from us the supply
+
+ align:start position:0%
+it come from it comes from us the supply
+ 
+
+ align:start position:0%
+it come from it comes from us the supply
+of capital is
+
+ align:start position:0%
+of capital is
+ 
+
+ align:start position:0%
+of capital is
+savings so the money firms use to buy
+
+ align:start position:0%
+savings so the money firms use to buy
+ 
+
+ align:start position:0%
+savings so the money firms use to buy
+their machines they borrow from
+
+ align:start position:0%
+their machines they borrow from
+ 
+
+ align:start position:0%
+their machines they borrow from
+people and that is how the Capital
+
+ align:start position:0%
+people and that is how the Capital
+ 
+
+ align:start position:0%
+people and that is how the Capital
+Market works so we talk about Capital we
+
+ align:start position:0%
+Market works so we talk about Capital we
+ 
+
+ align:start position:0%
+Market works so we talk about Capital we
+really think of it fundamentally as
+
+ align:start position:0%
+really think of it fundamentally as
+ 
+
+ align:start position:0%
+really think of it fundamentally as
+Financial Capital don't think of it
+
+ align:start position:0%
+Financial Capital don't think of it
+ 
+
+ align:start position:0%
+Financial Capital don't think of it
+anymore as machines and buildings think
+
+ align:start position:0%
+anymore as machines and buildings think
+ 
+
+ align:start position:0%
+anymore as machines and buildings think
+of it as Financial Capital the money you
+
+ align:start position:0%
+of it as Financial Capital the money you
+ 
+
+ align:start position:0%
+of it as Financial Capital the money you
+want to
+
+ align:start position:0%
+want to
+ 
+
+ align:start position:0%
+want to
+invest to divert today's consumption
+
+ align:start position:0%
+invest to divert today's consumption
+ 
+
+ align:start position:0%
+invest to divert today's consumption
+Mars consumption it comes from the
+
+ align:start position:0%
+Mars consumption it comes from the
+ 
+
+ align:start position:0%
+Mars consumption it comes from the
+savings that we do which is our decision
+
+ align:start position:0%
+savings that we do which is our decision
+ 
+
+ align:start position:0%
+savings that we do which is our decision
+to divert today's consumption to
+
+ align:start position:0%
+to divert today's consumption to
+ 
+
+ align:start position:0%
+to divert today's consumption to
+tomorrow's
+
+ align:start position:0%
+tomorrow's
+ 
+
+ align:start position:0%
+tomorrow's
+consumption okay so just
+
+ align:start position:0%
+consumption okay so just
+ 
+
+ align:start position:0%
+consumption okay so just
+as work just as workers decide how hard
+
+ align:start position:0%
+as work just as workers decide how hard
+ 
+
+ align:start position:0%
+as work just as workers decide how hard
+to work and that drives the supply of
+
+ align:start position:0%
+to work and that drives the supply of
+ 
+
+ align:start position:0%
+to work and that drives the supply of
+labor people decide how much to save and
+
+ align:start position:0%
+labor people decide how much to save and
+ 
+
+ align:start position:0%
+labor people decide how much to save and
+that drives the supply of capital so
+
+ align:start position:0%
+that drives the supply of capital so
+ 
+
+ align:start position:0%
+that drives the supply of capital so
+let's see that in figure
+
+ align:start position:0%
+let's see that in figure
+ 
+
+ align:start position:0%
+let's see that in figure
+166 figure 166 is the capital market
+
+ align:start position:0%
+166 figure 166 is the capital market
+ 
+
+ align:start position:0%
+166 figure 166 is the capital market
+equilibrium the demand for
+
+ align:start position:0%
+equilibrium the demand for
+ 
+
+ align:start position:0%
+equilibrium the demand for
+Capital comes from the marginal revenue
+
+ align:start position:0%
+Capital comes from the marginal revenue
+ 
+
+ align:start position:0%
+Capital comes from the marginal revenue
+product of
+
+ align:start position:0%
+product of
+ 
+
+ align:start position:0%
+product of
+capital just like the demand for labor
+
+ align:start position:0%
+capital just like the demand for labor
+ 
+
+ align:start position:0%
+capital just like the demand for labor
+comes the margin Revenue product of
+
+ align:start position:0%
+comes the margin Revenue product of
+ 
+
+ align:start position:0%
+comes the margin Revenue product of
+labor the demand for Capital comes the
+
+ align:start position:0%
+labor the demand for Capital comes the
+ 
+
+ align:start position:0%
+labor the demand for Capital comes the
+margin Revenue product of capital
+
+ align:start position:0%
+margin Revenue product of capital
+ 
+
+ align:start position:0%
+margin Revenue product of capital
+how much will the next unit of capital
+
+ align:start position:0%
+how much will the next unit of capital
+ 
+
+ align:start position:0%
+how much will the next unit of capital
+the next unit of financial investment
+
+ align:start position:0%
+the next unit of financial investment
+ 
+
+ align:start position:0%
+the next unit of financial investment
+what will it yield in terms of the value
+
+ align:start position:0%
+what will it yield in terms of the value
+ 
+
+ align:start position:0%
+what will it yield in terms of the value
+of what I'll
+
+ align:start position:0%
+of what I'll
+ 
+
+ align:start position:0%
+of what I'll
+produce how much will the next machine
+
+ align:start position:0%
+produce how much will the next machine
+ 
+
+ align:start position:0%
+produce how much will the next machine
+increase the quantity of goods and what
+
+ align:start position:0%
+increase the quantity of goods and what
+ 
+
+ align:start position:0%
+increase the quantity of goods and what
+can I sell those goods for so the same
+
+ align:start position:0%
+can I sell those goods for so the same
+ 
+
+ align:start position:0%
+can I sell those goods for so the same
+logic that applies to labor applies to
+
+ align:start position:0%
+logic that applies to labor applies to
+ 
+
+ align:start position:0%
+logic that applies to labor applies to
+Capital the supply of capital comes from
+
+ align:start position:0%
+Capital the supply of capital comes from
+ 
+
+ align:start position:0%
+Capital the supply of capital comes from
+workers
+
+ align:start position:0%
+workers
+ 
+
+ align:start position:0%
+workers
+saving why do workers save they save
+
+ align:start position:0%
+saving why do workers save they save
+ 
+
+ align:start position:0%
+saving why do workers save they save
+because they can get a return to that
+
+ align:start position:0%
+because they can get a return to that
+ 
+
+ align:start position:0%
+because they can get a return to that
+saving in the form of
+
+ align:start position:0%
+saving in the form of
+ 
+
+ align:start position:0%
+saving in the form of
+Interest I is the rate of interest
+
+ align:start position:0%
+Interest I is the rate of interest
+ 
+
+ align:start position:0%
+Interest I is the rate of interest
+that's the return that workers get on
+
+ align:start position:0%
+that's the return that workers get on
+ 
+
+ align:start position:0%
+that's the return that workers get on
+their savings so in other words you
+
+ align:start position:0%
+their savings so in other words you
+ 
+
+ align:start position:0%
+their savings so in other words you
+could think of I the technical defition
+
+ align:start position:0%
+could think of I the technical defition
+ 
+
+ align:start position:0%
+could think of I the technical defition
+of the interest rate is the rate that
+
+ align:start position:0%
+of the interest rate is the rate that
+ 
+
+ align:start position:0%
+of the interest rate is the rate that
+firms have to pay you to get your
+
+ align:start position:0%
+firms have to pay you to get your
+ 
+
+ align:start position:0%
+firms have to pay you to get your
+money I is the rate that firms have to
+
+ align:start position:0%
+money I is the rate that firms have to
+ 
+
+ align:start position:0%
+money I is the rate that firms have to
+pay Savers to get them to
+
+ align:start position:0%
+pay Savers to get them to
+ 
+
+ align:start position:0%
+pay Savers to get them to
+save okay so for example if the interest
+
+ align:start position:0%
+save okay so for example if the interest
+ 
+
+ align:start position:0%
+save okay so for example if the interest
+rate is 10%
+
+ align:start position:0%
+rate is 10%
+ 
+
+ align:start position:0%
+rate is 10%
+then if a house if I want to borrow a
+
+ align:start position:0%
+then if a house if I want to borrow a
+ 
+
+ align:start position:0%
+then if a house if I want to borrow a
+dollar from a household this period I
+
+ align:start position:0%
+dollar from a household this period I
+ 
+
+ align:start position:0%
+dollar from a household this period I
+have to pay them back a11 next
+
+ align:start position:0%
+have to pay them back a11 next
+ 
+
+ align:start position:0%
+have to pay them back a11 next
+period let me by the way one
+
+ align:start position:0%
+period let me by the way one
+ 
+
+ align:start position:0%
+period let me by the way one
+parenthetical comment time is a very
+
+ align:start position:0%
+parenthetical comment time is a very
+ 
+
+ align:start position:0%
+parenthetical comment time is a very
+elastic Concept in this class man don't
+
+ align:start position:0%
+elastic Concept in this class man don't
+ 
+
+ align:start position:0%
+elastic Concept in this class man don't
+be uptight in your thinking like the
+
+ align:start position:0%
+be uptight in your thinking like the
+ 
+
+ align:start position:0%
+be uptight in your thinking like the
+dude says okay basically time sometimes
+
+ align:start position:0%
+dude says okay basically time sometimes
+ 
+
+ align:start position:0%
+dude says okay basically time sometimes
+I'll say today tomorrow sometimes I'll
+
+ align:start position:0%
+I'll say today tomorrow sometimes I'll
+ 
+
+ align:start position:0%
+I'll say today tomorrow sometimes I'll
+say this year next year it's all the
+
+ align:start position:0%
+say this year next year it's all the
+ 
+
+ align:start position:0%
+say this year next year it's all the
+same man just means period one versus
+
+ align:start position:0%
+same man just means period one versus
+ 
+
+ align:start position:0%
+same man just means period one versus
+period two so don't get too caught up in
+
+ align:start position:0%
+period two so don't get too caught up in
+ 
+
+ align:start position:0%
+period two so don't get too caught up in
+the words I use just think of this as
+
+ align:start position:0%
+the words I use just think of this as
+ 
+
+ align:start position:0%
+the words I use just think of this as
+period one versus period two
+
+ align:start position:0%
+period one versus period two
+ 
+
+ align:start position:0%
+period one versus period two
+okay that's that's the key and I'll try
+
+ align:start position:0%
+okay that's that's the key and I'll try
+ 
+
+ align:start position:0%
+okay that's that's the key and I'll try
+to use as much as I can but I say today
+
+ align:start position:0%
+to use as much as I can but I say today
+ 
+
+ align:start position:0%
+to use as much as I can but I say today
+tomorrow this year next year it's all
+
+ align:start position:0%
+tomorrow this year next year it's all
+ 
+
+ align:start position:0%
+tomorrow this year next year it's all
+the same thing okay so don't do too
+
+ align:start position:0%
+the same thing okay so don't do too
+ 
+
+ align:start position:0%
+the same thing okay so don't do too
+caught up on the
+
+ align:start position:0%
+caught up on the
+ 
+
+ align:start position:0%
+caught up on the
+terminology now basically the idea is
+
+ align:start position:0%
+terminology now basically the idea is
+ 
+
+ align:start position:0%
+terminology now basically the idea is
+that the Su demand curve is downward
+
+ align:start position:0%
+that the Su demand curve is downward
+ 
+
+ align:start position:0%
+that the Su demand curve is downward
+sloping as the interest rate
+
+ align:start position:0%
+sloping as the interest rate
+ 
+
+ align:start position:0%
+sloping as the interest rate
+Rises firms want less
+
+ align:start position:0%
+Rises firms want less
+ 
+
+ align:start position:0%
+Rises firms want less
+Capital because why because interest
+
+ align:start position:0%
+Capital because why because interest
+ 
+
+ align:start position:0%
+Capital because why because interest
+rate Rising means that the opportunity
+
+ align:start position:0%
+rate Rising means that the opportunity
+ 
+
+ align:start position:0%
+rate Rising means that the opportunity
+cost employing machine has gone up
+
+ align:start position:0%
+cost employing machine has gone up
+ 
+
+ align:start position:0%
+cost employing machine has gone up
+because what can you do instead with
+
+ align:start position:0%
+because what can you do instead with
+ 
+
+ align:start position:0%
+because what can you do instead with
+your money hire a
+
+ align:start position:0%
+your money hire a
+ 
+
+ align:start position:0%
+your money hire a
+worker so an up a a downward sloping
+
+ align:start position:0%
+worker so an up a a downward sloping
+ 
+
+ align:start position:0%
+worker so an up a a downward sloping
+demand curve for capital is basically
+
+ align:start position:0%
+demand curve for capital is basically
+ 
+
+ align:start position:0%
+demand curve for capital is basically
+the rate at which firms are going to
+
+ align:start position:0%
+the rate at which firms are going to
+ 
+
+ align:start position:0%
+the rate at which firms are going to
+trade off capital for labor as interest
+
+ align:start position:0%
+trade off capital for labor as interest
+ 
+
+ align:start position:0%
+trade off capital for labor as interest
+State goes up they'll say fewer machines
+
+ align:start position:0%
+State goes up they'll say fewer machines
+ 
+
+ align:start position:0%
+State goes up they'll say fewer machines
+more labor and St goes down they'll say
+
+ align:start position:0%
+more labor and St goes down they'll say
+ 
+
+ align:start position:0%
+more labor and St goes down they'll say
+less labor more
+
+ align:start position:0%
+less labor more
+ 
+
+ align:start position:0%
+less labor more
+machines the supply curve slopes up
+
+ align:start position:0%
+machines the supply curve slopes up
+ 
+
+ align:start position:0%
+machines the supply curve slopes up
+because basically the more you pay
+
+ align:start position:0%
+because basically the more you pay
+ 
+
+ align:start position:0%
+because basically the more you pay
+people to save the more they'll
+
+ align:start position:0%
+people to save the more they'll
+ 
+
+ align:start position:0%
+people to save the more they'll
+save okay now let me pause for a second
+
+ align:start position:0%
+save okay now let me pause for a second
+ 
+
+ align:start position:0%
+save okay now let me pause for a second
+we are we have a whole series of courses
+
+ align:start position:0%
+we are we have a whole series of courses
+ 
+
+ align:start position:0%
+we are we have a whole series of courses
+in course 15 about the about Finance I'm
+
+ align:start position:0%
+in course 15 about the about Finance I'm
+ 
+
+ align:start position:0%
+in course 15 about the about Finance I'm
+doing Finance in like a lecture and a
+
+ align:start position:0%
+doing Finance in like a lecture and a
+ 
+
+ align:start position:0%
+doing Finance in like a lecture and a
+half here okay and if you find this
+
+ align:start position:0%
+half here okay and if you find this
+ 
+
+ align:start position:0%
+half here okay and if you find this
+interesting you take 1541 1542 the whole
+
+ align:start position:0%
+interesting you take 1541 1542 the whole
+ 
+
+ align:start position:0%
+interesting you take 1541 1542 the whole
+series of course you take course 15 by
+
+ align:start position:0%
+series of course you take course 15 by
+ 
+
+ align:start position:0%
+series of course you take course 15 by
+the way since all of you should really
+
+ align:start position:0%
+the way since all of you should really
+ 
+
+ align:start position:0%
+the way since all of you should really
+go be econ Majors you get economics
+
+ align:start position:0%
+go be econ Majors you get economics
+ 
+
+ align:start position:0%
+go be econ Majors you get economics
+elective credit for a couple of those
+
+ align:start position:0%
+elective credit for a couple of those
+ 
+
+ align:start position:0%
+elective credit for a couple of those
+courses you can Eon major and take some
+
+ align:start position:0%
+courses you can Eon major and take some
+ 
+
+ align:start position:0%
+courses you can Eon major and take some
+course 15 courses if you want to learn
+
+ align:start position:0%
+course 15 courses if you want to learn
+ 
+
+ align:start position:0%
+course 15 courses if you want to learn
+more more about Finance okay so
+
+ align:start position:0%
+more more about Finance okay so
+ 
+
+ align:start position:0%
+more more about Finance okay so
+basically um but let's just talk about
+
+ align:start position:0%
+basically um but let's just talk about
+ 
+
+ align:start position:0%
+basically um but let's just talk about
+this weird thing I'm talking about what
+
+ align:start position:0%
+this weird thing I'm talking about what
+ 
+
+ align:start position:0%
+this weird thing I'm talking about what
+does it mean that people loan money to a
+
+ align:start position:0%
+does it mean that people loan money to a
+ 
+
+ align:start position:0%
+does it mean that people loan money to a
+firm because we don't really necess loan
+
+ align:start position:0%
+firm because we don't really necess loan
+ 
+
+ align:start position:0%
+firm because we don't really necess loan
+money to a firm in fact firms get their
+
+ align:start position:0%
+money to a firm in fact firms get their
+ 
+
+ align:start position:0%
+money to a firm in fact firms get their
+money from people in three different
+
+ align:start position:0%
+money from people in three different
+ 
+
+ align:start position:0%
+money from people in three different
+ways there's three different ways we can
+
+ align:start position:0%
+ways there's three different ways we can
+ 
+
+ align:start position:0%
+ways there's three different ways we can
+essentially transfer our money to
+
+ align:start position:0%
+essentially transfer our money to
+ 
+
+ align:start position:0%
+essentially transfer our money to
+firms one
+
+ align:start position:0%
+firms one
+ 
+
+ align:start position:0%
+firms one
+way is we could put it in the
+
+ align:start position:0%
+way is we could put it in the
+ 
+
+ align:start position:0%
+way is we could put it in the
+bank okay you put your money in the bank
+
+ align:start position:0%
+bank okay you put your money in the bank
+ 
+
+ align:start position:0%
+bank okay you put your money in the bank
+the bank pays you an interest rate
+
+ align:start position:0%
+the bank pays you an interest rate
+ 
+
+ align:start position:0%
+the bank pays you an interest rate
+firms then go to the bank and borrow the
+
+ align:start position:0%
+firms then go to the bank and borrow the
+ 
+
+ align:start position:0%
+firms then go to the bank and borrow the
+money from the bank so we're not direct
+
+ align:start position:0%
+money from the bank so we're not direct
+ 
+
+ align:start position:0%
+money from the bank so we're not direct
+leaving the money to the firms we're
+
+ align:start position:0%
+leaving the money to the firms we're
+ 
+
+ align:start position:0%
+leaving the money to the firms we're
+doing it through an through a financial
+
+ align:start position:0%
+doing it through an through a financial
+ 
+
+ align:start position:0%
+doing it through an through a financial
+intermediary which is the bank so the
+
+ align:start position:0%
+intermediary which is the bank so the
+ 
+
+ align:start position:0%
+intermediary which is the bank so the
+most common way people get money to
+
+ align:start position:0%
+most common way people get money to
+ 
+
+ align:start position:0%
+most common way people get money to
+firms is by having money in the bank you
+
+ align:start position:0%
+firms is by having money in the bank you
+ 
+
+ align:start position:0%
+firms is by having money in the bank you
+don't know that you just think you're
+
+ align:start position:0%
+don't know that you just think you're
+ 
+
+ align:start position:0%
+don't know that you just think you're
+got a bank account yielding whatever but
+
+ align:start position:0%
+got a bank account yielding whatever but
+ 
+
+ align:start position:0%
+got a bank account yielding whatever but
+that's what you're doing you're just
+
+ align:start position:0%
+that's what you're doing you're just
+ 
+
+ align:start position:0%
+that's what you're doing you're just
+giving money to
+
+ align:start position:0%
+giving money to
+ 
+
+ align:start position:0%
+giving money to
+firms the second way you can do it is
+
+ align:start position:0%
+firms the second way you can do it is
+ 
+
+ align:start position:0%
+firms the second way you can do it is
+you can actually directly loan the money
+
+ align:start position:0%
+you can actually directly loan the money
+ 
+
+ align:start position:0%
+you can actually directly loan the money
+to the firm by buying corporate
+
+ align:start position:0%
+to the firm by buying corporate
+ 
+
+ align:start position:0%
+to the firm by buying corporate
+bonds okay a corporate bond is literally
+
+ align:start position:0%
+bonds okay a corporate bond is literally
+ 
+
+ align:start position:0%
+bonds okay a corporate bond is literally
+a loan to a firm now typically most of
+
+ align:start position:0%
+a loan to a firm now typically most of
+ 
+
+ align:start position:0%
+a loan to a firm now typically most of
+us who aren't Super Rich won't buy a
+
+ align:start position:0%
+us who aren't Super Rich won't buy a
+ 
+
+ align:start position:0%
+us who aren't Super Rich won't buy a
+corporate bond will buy a financial
+
+ align:start position:0%
+corporate bond will buy a financial
+ 
+
+ align:start position:0%
+corporate bond will buy a financial
+instrument that holds corporate bonds
+
+ align:start position:0%
+instrument that holds corporate bonds
+ 
+
+ align:start position:0%
+instrument that holds corporate bonds
+okay so I have a Vanguard bond fund
+
+ align:start position:0%
+okay so I have a Vanguard bond fund
+ 
+
+ align:start position:0%
+okay so I have a Vanguard bond fund
+Vanguard is a company that holds
+
+ align:start position:0%
+Vanguard is a company that holds
+ 
+
+ align:start position:0%
+Vanguard is a company that holds
+financial instruments so I own a little
+
+ align:start position:0%
+financial instruments so I own a little
+ 
+
+ align:start position:0%
+financial instruments so I own a little
+piece of a lot of bonds okay bonds are
+
+ align:start position:0%
+piece of a lot of bonds okay bonds are
+ 
+
+ align:start position:0%
+piece of a lot of bonds okay bonds are
+like millions of dollars I'm not gonna
+
+ align:start position:0%
+like millions of dollars I'm not gonna
+ 
+
+ align:start position:0%
+like millions of dollars I'm not gonna
+own a bond but I own a little piece of a
+
+ align:start position:0%
+own a bond but I own a little piece of a
+ 
+
+ align:start position:0%
+own a bond but I own a little piece of a
+bunch of them okay so I'm sort of that's
+
+ align:start position:0%
+bunch of them okay so I'm sort of that's
+ 
+
+ align:start position:0%
+bunch of them okay so I'm sort of that's
+the way you directly loan to a firm and
+
+ align:start position:0%
+the way you directly loan to a firm and
+ 
+
+ align:start position:0%
+the way you directly loan to a firm and
+then finally you can buy stocks which is
+
+ align:start position:0%
+then finally you can buy stocks which is
+ 
+
+ align:start position:0%
+then finally you can buy stocks which is
+another way directly probably the most
+
+ align:start position:0%
+another way directly probably the most
+ 
+
+ align:start position:0%
+another way directly probably the most
+direct way to give money to a firm you
+
+ align:start position:0%
+direct way to give money to a firm you
+ 
+
+ align:start position:0%
+direct way to give money to a firm you
+can only buy a share in a firm you can
+
+ align:start position:0%
+can only buy a share in a firm you can
+ 
+
+ align:start position:0%
+can only buy a share in a firm you can
+go out tomorrow you can buy a share in
+
+ align:start position:0%
+go out tomorrow you can buy a share in
+ 
+
+ align:start position:0%
+go out tomorrow you can buy a share in
+apple you get a piece of paper that says
+
+ align:start position:0%
+apple you get a piece of paper that says
+ 
+
+ align:start position:0%
+apple you get a piece of paper that says
+you own a share of Apple okay you've
+
+ align:start position:0%
+you own a share of Apple okay you've
+ 
+
+ align:start position:0%
+you own a share of Apple okay you've
+given Apple your money what are they
+
+ align:start position:0%
+given Apple your money what are they
+ 
+
+ align:start position:0%
+given Apple your money what are they
+giving you back they're giving you back
+
+ align:start position:0%
+giving you back they're giving you back
+ 
+
+ align:start position:0%
+giving you back they're giving you back
+two
+
+ align:start position:0%
+two
+ 
+
+ align:start position:0%
+two
+things the first is they're giving you
+
+ align:start position:0%
+things the first is they're giving you
+ 
+
+ align:start position:0%
+things the first is they're giving you
+back the promise that their price of
+
+ align:start position:0%
+back the promise that their price of
+ 
+
+ align:start position:0%
+back the promise that their price of
+that stock will go up that if you buy
+
+ align:start position:0%
+that stock will go up that if you buy
+ 
+
+ align:start position:0%
+that stock will go up that if you buy
+what Apple stock let's say Apple stock
+
+ align:start position:0%
+what Apple stock let's say Apple stock
+ 
+
+ align:start position:0%
+what Apple stock let's say Apple stock
+today selling at 100 I don't know what
+
+ align:start position:0%
+today selling at 100 I don't know what
+ 
+
+ align:start position:0%
+today selling at 100 I don't know what
+selling at okay it's probably much more
+
+ align:start position:0%
+selling at okay it's probably much more
+ 
+
+ align:start position:0%
+selling at okay it's probably much more
+than that selling at a 100 if I buy for
+
+ align:start position:0%
+than that selling at a 100 if I buy for
+ 
+
+ align:start position:0%
+than that selling at a 100 if I buy for
+100 then what that means I give Apple
+
+ align:start position:0%
+100 then what that means I give Apple
+ 
+
+ align:start position:0%
+100 then what that means I give Apple
+$100 they give me a share why do I do
+
+ align:start position:0%
+$100 they give me a share why do I do
+ 
+
+ align:start position:0%
+$100 they give me a share why do I do
+that because I think in five years Apple
+
+ align:start position:0%
+that because I think in five years Apple
+ 
+
+ align:start position:0%
+that because I think in five years Apple
+will be worth
+
+ align:start position:0%
+will be worth
+ 
+
+ align:start position:0%
+will be worth
+150 and then I could sell that share to
+
+ align:start position:0%
+150 and then I could sell that share to
+ 
+
+ align:start position:0%
+150 and then I could sell that share to
+someone else and get my
+
+ align:start position:0%
+someone else and get my
+ 
+
+ align:start position:0%
+someone else and get my
+$50 okay in addition some old style
+
+ align:start position:0%
+$50 okay in addition some old style
+ 
+
+ align:start position:0%
+$50 okay in addition some old style
+firms not the new firms old style firms
+
+ align:start position:0%
+firms not the new firms old style firms
+ 
+
+ align:start position:0%
+firms not the new firms old style firms
+also sometimes will just send regular
+
+ align:start position:0%
+also sometimes will just send regular
+ 
+
+ align:start position:0%
+also sometimes will just send regular
+checks to people on their stock called
+
+ align:start position:0%
+checks to people on their stock called
+ 
+
+ align:start position:0%
+checks to people on their stock called
+dividends that happens less and less but
+
+ align:start position:0%
+dividends that happens less and less but
+ 
+
+ align:start position:0%
+dividends that happens less and less but
+basically so I can put my money in the
+
+ align:start position:0%
+basically so I can put my money in the
+ 
+
+ align:start position:0%
+basically so I can put my money in the
+bank the bank pays me Interest the fir
+
+ align:start position:0%
+bank the bank pays me Interest the fir
+ 
+
+ align:start position:0%
+bank the bank pays me Interest the fir
+them borrow from the bank I can buy a
+
+ align:start position:0%
+them borrow from the bank I can buy a
+ 
+
+ align:start position:0%
+them borrow from the bank I can buy a
+corporate bond the bond pays me Interest
+
+ align:start position:0%
+corporate bond the bond pays me Interest
+ 
+
+ align:start position:0%
+corporate bond the bond pays me Interest
+okay it's a Rec direct loan or I can buy
+
+ align:start position:0%
+okay it's a Rec direct loan or I can buy
+ 
+
+ align:start position:0%
+okay it's a Rec direct loan or I can buy
+stock in which case I give the money to
+
+ align:start position:0%
+stock in which case I give the money to
+ 
+
+ align:start position:0%
+stock in which case I give the money to
+the firm and they pay me back by getting
+
+ align:start position:0%
+the firm and they pay me back by getting
+ 
+
+ align:start position:0%
+the firm and they pay me back by getting
+more valuable or paying me a dividend
+
+ align:start position:0%
+more valuable or paying me a dividend
+ 
+
+ align:start position:0%
+more valuable or paying me a dividend
+and that's essentially how I transfer
+
+ align:start position:0%
+and that's essentially how I transfer
+ 
+
+ align:start position:0%
+and that's essentially how I transfer
+money to firms okay questions about
+
+ align:start position:0%
+money to firms okay questions about
+ 
+
+ align:start position:0%
+money to firms okay questions about
+that
+
+ align:start position:0%
+that
+ 
+
+ align:start position:0%
+that
+yeah interest
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+rate you relate the interest rate to the
+
+ align:start position:0%
+rate you relate the interest rate to the
+ 
+
+ align:start position:0%
+rate you relate the interest rate to the
+slope I don't quite understand
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah yeah exactly there's a mathematical
+
+ align:start position:0%
+yeah yeah exactly there's a mathematical
+ 
+
+ align:start position:0%
+yeah yeah exactly there's a mathematical
+function uh essentially the demand curve
+
+ align:start position:0%
+function uh essentially the demand curve
+ 
+
+ align:start position:0%
+function uh essentially the demand curve
+will be a negative function of interest
+
+ align:start position:0%
+will be a negative function of interest
+ 
+
+ align:start position:0%
+will be a negative function of interest
+rates supply curve will be a positive
+
+ align:start position:0%
+rates supply curve will be a positive
+ 
+
+ align:start position:0%
+rates supply curve will be a positive
+function of interest rates there's a
+
+ align:start position:0%
+function of interest rates there's a
+ 
+
+ align:start position:0%
+function of interest rates there's a
+mathematical function just like other
+
+ align:start position:0%
+mathematical function just like other
+ 
+
+ align:start position:0%
+mathematical function just like other
+demand and Supply
+
+ align:start position:0%
+demand and Supply
+ 
+
+ align:start position:0%
+demand and Supply
+curves other
+
+ align:start position:0%
+curves other
+ 
+
+ align:start position:0%
+curves other
+questions okay so
+
+ align:start position:0%
+questions okay so
+ 
+
+ align:start position:0%
+questions okay so
+now let's come the demand part is sort
+
+ align:start position:0%
+now let's come the demand part is sort
+ 
+
+ align:start position:0%
+now let's come the demand part is sort
+of uninteresting we know how to drive
+
+ align:start position:0%
+of uninteresting we know how to drive
+ 
+
+ align:start position:0%
+of uninteresting we know how to drive
+this what you do is you take a
+
+ align:start position:0%
+this what you do is you take a
+ 
+
+ align:start position:0%
+this what you do is you take a
+production function you'd set up a you
+
+ align:start position:0%
+production function you'd set up a you
+ 
+
+ align:start position:0%
+production function you'd set up a you
+you would you would get a cost function
+
+ align:start position:0%
+you would you would get a cost function
+ 
+
+ align:start position:0%
+you would you would get a cost function
+you could solve for the marginal revenue
+
+ align:start position:0%
+you could solve for the marginal revenue
+ 
+
+ align:start position:0%
+you could solve for the marginal revenue
+product of capital okay you know how to
+
+ align:start position:0%
+product of capital okay you know how to
+ 
+
+ align:start position:0%
+product of capital okay you know how to
+do that the the supply side is more
+
+ align:start position:0%
+do that the the supply side is more
+ 
+
+ align:start position:0%
+do that the the supply side is more
+interesting and why is it more
+
+ align:start position:0%
+interesting and why is it more
+ 
+
+ align:start position:0%
+interesting and why is it more
+interesting because once again
+
+ align:start position:0%
+interesting because once again
+ 
+
+ align:start position:0%
+interesting because once again
+substitution income effects are going to
+
+ align:start position:0%
+substitution income effects are going to
+ 
+
+ align:start position:0%
+substitution income effects are going to
+mess things up just like they did for
+
+ align:start position:0%
+mess things up just like they did for
+ 
+
+ align:start position:0%
+mess things up just like they did for
+labor Supply they are going to do it for
+
+ align:start position:0%
+labor Supply they are going to do it for
+ 
+
+ align:start position:0%
+labor Supply they are going to do it for
+savings and they're going to do so in
+
+ align:start position:0%
+savings and they're going to do so in
+ 
+
+ align:start position:0%
+savings and they're going to do so in
+the framework of what we call
+
+ align:start position:0%
+the framework of what we call
+ 
+
+ align:start position:0%
+the framework of what we call
+intertemporal
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Choice which is your decision of how
+
+ align:start position:0%
+Choice which is your decision of how
+ 
+
+ align:start position:0%
+Choice which is your decision of how
+much do you consume and how much do you
+
+ align:start position:0%
+much do you consume and how much do you
+ 
+
+ align:start position:0%
+much do you consume and how much do you
+save so to do that let's go to figure
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+16 figure
+
+ align:start position:0%
+16 figure
+ 
+
+ align:start position:0%
+16 figure
+167 and this diagram describes the
+
+ align:start position:0%
+167 and this diagram describes the
+ 
+
+ align:start position:0%
+167 and this diagram describes the
+person's decision of how much to
+
+ align:start position:0%
+person's decision of how much to
+ 
+
+ align:start position:0%
+person's decision of how much to
+save okay I'm just G this graphically in
+
+ align:start position:0%
+save okay I'm just G this graphically in
+ 
+
+ align:start position:0%
+save okay I'm just G this graphically in
+section you're going to do the
+
+ align:start position:0%
+section you're going to do the
+ 
+
+ align:start position:0%
+section you're going to do the
+math okay
+
+ align:start position:0%
+math okay
+ 
+
+ align:start position:0%
+math okay
+individuals have a utility fun function
+
+ align:start position:0%
+individuals have a utility fun function
+ 
+
+ align:start position:0%
+individuals have a utility fun function
+we talked about youtility function we
+
+ align:start position:0%
+we talked about youtility function we
+ 
+
+ align:start position:0%
+we talked about youtility function we
+choose between two goods we always do
+
+ align:start position:0%
+choose between two goods we always do
+ 
+
+ align:start position:0%
+choose between two goods we always do
+two element utility function make the
+
+ align:start position:0%
+two element utility function make the
+ 
+
+ align:start position:0%
+two element utility function make the
+math easy talk about choos two goods we
+
+ align:start position:0%
+math easy talk about choos two goods we
+ 
+
+ align:start position:0%
+math easy talk about choos two goods we
+talked about choos between consumption
+
+ align:start position:0%
+talked about choos between consumption
+ 
+
+ align:start position:0%
+talked about choos between consumption
+and Leisure now we're talking about
+
+ align:start position:0%
+and Leisure now we're talking about
+ 
+
+ align:start position:0%
+and Leisure now we're talking about
+choosing between consumption in Period
+
+ align:start position:0%
+choosing between consumption in Period
+ 
+
+ align:start position:0%
+choosing between consumption in Period
+one and consumption in Period
+
+ align:start position:0%
+one and consumption in Period
+ 
+
+ align:start position:0%
+one and consumption in Period
+two now the
+
+ align:start position:0%
+two now the
+ 
+
+ align:start position:0%
+two now the
+tradeoff instead of being
+
+ align:start position:0%
+tradeoff instead of being
+ 
+
+ align:start position:0%
+tradeoff instead of being
+between pizza and
+
+ align:start position:0%
+between pizza and
+ 
+
+ align:start position:0%
+between pizza and
+cookies or being
+
+ align:start position:0%
+cookies or being
+ 
+
+ align:start position:0%
+cookies or being
+between or being between work Leisure
+
+ align:start position:0%
+between or being between work Leisure
+ 
+
+ align:start position:0%
+between or being between work Leisure
+and and consumption now between be
+
+ align:start position:0%
+and and consumption now between be
+ 
+
+ align:start position:0%
+and and consumption now between be
+consuming today versus consuming
+
+ align:start position:0%
+consuming today versus consuming
+ 
+
+ align:start position:0%
+consuming today versus consuming
+tomorrow and we understand the trade-off
+
+ align:start position:0%
+tomorrow and we understand the trade-off
+ 
+
+ align:start position:0%
+tomorrow and we understand the trade-off
+the trade-off is that basically people
+
+ align:start position:0%
+the trade-off is that basically people
+ 
+
+ align:start position:0%
+the trade-off is that basically people
+are by and large
+
+ align:start position:0%
+are by and large
+ 
+
+ align:start position:0%
+are by and large
+impatient if you ask them would you
+
+ align:start position:0%
+impatient if you ask them would you
+ 
+
+ align:start position:0%
+impatient if you ask them would you
+rather something today or tomorrow
+
+ align:start position:0%
+rather something today or tomorrow
+ 
+
+ align:start position:0%
+rather something today or tomorrow
+they'd rather have it today okay there's
+
+ align:start position:0%
+they'd rather have it today okay there's
+ 
+
+ align:start position:0%
+they'd rather have it today okay there's
+the famous marshmallow test they do on
+
+ align:start position:0%
+the famous marshmallow test they do on
+ 
+
+ align:start position:0%
+the famous marshmallow test they do on
+little kids where they see if they'll
+
+ align:start position:0%
+little kids where they see if they'll
+ 
+
+ align:start position:0%
+little kids where they see if they'll
+wait to get a marshmallow Okay most kids
+
+ align:start position:0%
+wait to get a marshmallow Okay most kids
+ 
+
+ align:start position:0%
+wait to get a marshmallow Okay most kids
+don't humans are impatient okay we'll
+
+ align:start position:0%
+don't humans are impatient okay we'll
+ 
+
+ align:start position:0%
+don't humans are impatient okay we'll
+come back to that in a few lectures talk
+
+ align:start position:0%
+come back to that in a few lectures talk
+ 
+
+ align:start position:0%
+come back to that in a few lectures talk
+about how you model that but for now
+
+ align:start position:0%
+about how you model that but for now
+ 
+
+ align:start position:0%
+about how you model that but for now
+let's just say humans are impatient on
+
+ align:start position:0%
+let's just say humans are impatient on
+ 
+
+ align:start position:0%
+let's just say humans are impatient on
+the on the other hand humans need money
+
+ align:start position:0%
+the on the other hand humans need money
+ 
+
+ align:start position:0%
+the on the other hand humans need money
+in both periods so let's do a simple
+
+ align:start position:0%
+in both periods so let's do a simple
+ 
+
+ align:start position:0%
+in both periods so let's do a simple
+example imagine my income is $80,000 a
+
+ align:start position:0%
+example imagine my income is $80,000 a
+ 
+
+ align:start position:0%
+example imagine my income is $80,000 a
+year okay and imagine I I can save that
+
+ align:start position:0%
+year okay and imagine I I can save that
+ 
+
+ align:start position:0%
+year okay and imagine I I can save that
+money at 10% so Y is 80,000 and let's
+
+ align:start position:0%
+money at 10% so Y is 80,000 and let's
+ 
+
+ align:start position:0%
+money at 10% so Y is 80,000 and let's
+imagine I only earn the income well okay
+
+ align:start position:0%
+imagine I only earn the income well okay
+ 
+
+ align:start position:0%
+imagine I only earn the income well okay
+management income is 8,000 I can save
+
+ align:start position:0%
+management income is 8,000 I can save
+ 
+
+ align:start position:0%
+management income is 8,000 I can save
+that at 10% and next year I want to stay
+
+ align:start position:0%
+that at 10% and next year I want to stay
+ 
+
+ align:start position:0%
+that at 10% and next year I want to stay
+home take care of my
+
+ align:start position:0%
+home take care of my
+ 
+
+ align:start position:0%
+home take care of my
+kids I don't want to
+
+ align:start position:0%
+kids I don't want to
+ 
+
+ align:start position:0%
+kids I don't want to
+work so what that means my my income imp
+
+ align:start position:0%
+work so what that means my my income imp
+ 
+
+ align:start position:0%
+work so what that means my my income imp
+Peri period one will be 80,000 but my
+
+ align:start position:0%
+Peri period one will be 80,000 but my
+ 
+
+ align:start position:0%
+Peri period one will be 80,000 but my
+income in Period two will be
+
+ align:start position:0%
+income in Period two will be
+ 
+
+ align:start position:0%
+income in Period two will be
+zero guess more complicate income in
+
+ align:start position:0%
+zero guess more complicate income in
+ 
+
+ align:start position:0%
+zero guess more complicate income in
+Period two you'll see that in the
+
+ align:start position:0%
+Period two you'll see that in the
+ 
+
+ align:start position:0%
+Period two you'll see that in the
+problem set okay my Inc in Period two
+
+ align:start position:0%
+problem set okay my Inc in Period two
+ 
+
+ align:start position:0%
+problem set okay my Inc in Period two
+would be zero okay now my question is
+
+ align:start position:0%
+would be zero okay now my question is
+ 
+
+ align:start position:0%
+would be zero okay now my question is
+what do I do well you could see that in
+
+ align:start position:0%
+what do I do well you could see that in
+ 
+
+ align:start position:0%
+what do I do well you could see that in
+figure
+
+ align:start position:0%
+figure
+ 
+
+ align:start position:0%
+figure
+167 one option is figure 167 has my
+
+ align:start position:0%
+167 one option is figure 167 has my
+ 
+
+ align:start position:0%
+167 one option is figure 167 has my
+first period consumption on the xaxis my
+
+ align:start position:0%
+first period consumption on the xaxis my
+ 
+
+ align:start position:0%
+first period consumption on the xaxis my
+secondary consumption the y axis one
+
+ align:start position:0%
+secondary consumption the y axis one
+ 
+
+ align:start position:0%
+secondary consumption the y axis one
+option would be to consume everything in
+
+ align:start position:0%
+option would be to consume everything in
+ 
+
+ align:start position:0%
+option would be to consume everything in
+Year One
+
+ align:start position:0%
+Year One
+ 
+
+ align:start position:0%
+Year One
+and nothing in year two that's not very
+
+ align:start position:0%
+and nothing in year two that's not very
+ 
+
+ align:start position:0%
+and nothing in year two that's not very
+attractive the other oper consume
+
+ align:start position:0%
+attractive the other oper consume
+ 
+
+ align:start position:0%
+attractive the other oper consume
+nothing in year one in which case I
+
+ align:start position:0%
+nothing in year one in which case I
+ 
+
+ align:start position:0%
+nothing in year one in which case I
+would have 88,000 in year two why
+
+ align:start position:0%
+would have 88,000 in year two why
+ 
+
+ align:start position:0%
+would have 88,000 in year two why
+because I would save 80,000 on a 10%
+
+ align:start position:0%
+because I would save 80,000 on a 10%
+ 
+
+ align:start position:0%
+because I would save 80,000 on a 10%
+interest so what's the tradeoff the
+
+ align:start position:0%
+interest so what's the tradeoff the
+ 
+
+ align:start position:0%
+interest so what's the tradeoff the
+tradeoff is the interest
+
+ align:start position:0%
+tradeoff is the interest
+ 
+
+ align:start position:0%
+tradeoff is the interest
+rate right or in other words what is the
+
+ align:start position:0%
+rate right or in other words what is the
+ 
+
+ align:start position:0%
+rate right or in other words what is the
+price of First Period
+
+ align:start position:0%
+price of First Period
+ 
+
+ align:start position:0%
+price of First Period
+consumption the price of First Period
+
+ align:start position:0%
+consumption the price of First Period
+ 
+
+ align:start position:0%
+consumption the price of First Period
+consumption okay is minus
+
+ align:start position:0%
+consumption okay is minus
+ 
+
+ align:start position:0%
+consumption okay is minus
+okay the price for consumption is minus
+
+ align:start position:0%
+okay the price for consumption is minus
+ 
+
+ align:start position:0%
+okay the price for consumption is minus
+1 plus
+
+ align:start position:0%
+1 plus
+ 
+
+ align:start position:0%
+1 plus
+I okay the price for once again I assume
+
+ align:start position:0%
+I okay the price for once again I assume
+ 
+
+ align:start position:0%
+I okay the price for once again I assume
+all Goods have a price of one when I
+
+ align:start position:0%
+all Goods have a price of one when I
+ 
+
+ align:start position:0%
+all Goods have a price of one when I
+came to price of goods this is what is
+
+ align:start position:0%
+came to price of goods this is what is
+ 
+
+ align:start position:0%
+came to price of goods this is what is
+the relative price of First Period
+
+ align:start position:0%
+the relative price of First Period
+ 
+
+ align:start position:0%
+the relative price of First Period
+consumption okay so assume the price of
+
+ align:start position:0%
+consumption okay so assume the price of
+ 
+
+ align:start position:0%
+consumption okay so assume the price of
+consumption in Period one is one the
+
+ align:start position:0%
+consumption in Period one is one the
+ 
+
+ align:start position:0%
+consumption in Period one is one the
+price of consumption in Period two is
+
+ align:start position:0%
+price of consumption in Period two is
+ 
+
+ align:start position:0%
+price of consumption in Period two is
+one we're normalizing everything to make
+
+ align:start position:0%
+one we're normalizing everything to make
+ 
+
+ align:start position:0%
+one we're normalizing everything to make
+our math easy throwing prices out okay
+
+ align:start position:0%
+our math easy throwing prices out okay
+ 
+
+ align:start position:0%
+our math easy throwing prices out okay
+every it's just it's just we're thinking
+
+ align:start position:0%
+every it's just it's just we're thinking
+ 
+
+ align:start position:0%
+every it's just it's just we're thinking
+in terms of goods effectively here so
+
+ align:start position:0%
+in terms of goods effectively here so
+ 
+
+ align:start position:0%
+in terms of goods effectively here so
+what is the relative price of consuming
+
+ align:start position:0%
+what is the relative price of consuming
+ 
+
+ align:start position:0%
+what is the relative price of consuming
+in Period one minus 1 plus I why is that
+
+ align:start position:0%
+in Period one minus 1 plus I why is that
+ 
+
+ align:start position:0%
+in Period one minus 1 plus I why is that
+because for every dollar I consume in
+
+ align:start position:0%
+because for every dollar I consume in
+ 
+
+ align:start position:0%
+because for every dollar I consume in
+Period one I give up one plus I dollars
+
+ align:start position:0%
+Period one I give up one plus I dollars
+ 
+
+ align:start position:0%
+Period one I give up one plus I dollars
+in Period
+
+ align:start position:0%
+in Period
+ 
+
+ align:start position:0%
+in Period
+two that is the opportunity cost of
+
+ align:start position:0%
+two that is the opportunity cost of
+ 
+
+ align:start position:0%
+two that is the opportunity cost of
+first period consumption is not having
+
+ align:start position:0%
+first period consumption is not having
+ 
+
+ align:start position:0%
+first period consumption is not having
+second period consumption once again
+
+ align:start position:0%
+second period consumption once again
+ 
+
+ align:start position:0%
+second period consumption once again
+dismal
+
+ align:start position:0%
+dismal
+ 
+
+ align:start position:0%
+dismal
+science every time you eat something
+
+ align:start position:0%
+science every time you eat something
+ 
+
+ align:start position:0%
+science every time you eat something
+you're giving up the possibility of
+
+ align:start position:0%
+you're giving up the possibility of
+ 
+
+ align:start position:0%
+you're giving up the possibility of
+saving that money eating more next year
+
+ align:start position:0%
+saving that money eating more next year
+ 
+
+ align:start position:0%
+saving that money eating more next year
+okay just like there's a the price of
+
+ align:start position:0%
+okay just like there's a the price of
+ 
+
+ align:start position:0%
+okay just like there's a the price of
+leisures the wage the price of First
+
+ align:start position:0%
+leisures the wage the price of First
+ 
+
+ align:start position:0%
+leisures the wage the price of First
+Period consumption is minus one plus I
+
+ align:start position:0%
+Period consumption is minus one plus I
+ 
+
+ align:start position:0%
+Period consumption is minus one plus I
+or the interest rate the amount of money
+
+ align:start position:0%
+or the interest rate the amount of money
+ 
+
+ align:start position:0%
+or the interest rate the amount of money
+you could have the next
+
+ align:start position:0%
+you could have the next
+ 
+
+ align:start position:0%
+you could have the next
+year okay so basically that is the
+
+ align:start position:0%
+year okay so basically that is the
+ 
+
+ align:start position:0%
+year okay so basically that is the
+tradeoff that is representing the
+
+ align:start position:0%
+tradeoff that is representing the
+ 
+
+ align:start position:0%
+tradeoff that is representing the
+interal Choice problem that's
+
+ align:start position:0%
+interal Choice problem that's
+ 
+
+ align:start position:0%
+interal Choice problem that's
+represented by the slope of this budget
+
+ align:start position:0%
+represented by the slope of this budget
+ 
+
+ align:start position:0%
+represented by the slope of this budget
+constraint which is minus1 plus I or
+
+ align:start position:0%
+constraint which is minus1 plus I or
+ 
+
+ align:start position:0%
+constraint which is minus1 plus I or
+minus 1.1 in our example the slope of
+
+ align:start position:0%
+minus 1.1 in our example the slope of
+ 
+
+ align:start position:0%
+minus 1.1 in our example the slope of
+the budget create represents the
+
+ align:start position:0%
+the budget create represents the
+ 
+
+ align:start position:0%
+the budget create represents the
+opportunity cost of first period
+
+ align:start position:0%
+opportunity cost of first period
+ 
+
+ align:start position:0%
+opportunity cost of first period
+consumption in terms of second period
+
+ align:start position:0%
+consumption in terms of second period
+ 
+
+ align:start position:0%
+consumption in terms of second period
+consumption okay okay likewise I have
+
+ align:start position:0%
+consumption okay okay likewise I have
+ 
+
+ align:start position:0%
+consumption okay okay likewise I have
+some indifference curve I have some
+
+ align:start position:0%
+some indifference curve I have some
+ 
+
+ align:start position:0%
+some indifference curve I have some
+indifference curve which represents my
+
+ align:start position:0%
+indifference curve which represents my
+ 
+
+ align:start position:0%
+indifference curve which represents my
+preferences over first and second period
+
+ align:start position:0%
+preferences over first and second period
+ 
+
+ align:start position:0%
+preferences over first and second period
+consumption how impatient I am basically
+
+ align:start position:0%
+consumption how impatient I am basically
+ 
+
+ align:start position:0%
+consumption how impatient I am basically
+okay so think of the Indi curve
+
+ align:start position:0%
+okay so think of the Indi curve
+ 
+
+ align:start position:0%
+okay so think of the Indi curve
+basically being how impatient I am so
+
+ align:start position:0%
+basically being how impatient I am so
+ 
+
+ align:start position:0%
+basically being how impatient I am so
+like with all these optimization
+
+ align:start position:0%
+like with all these optimization
+ 
+
+ align:start position:0%
+like with all these optimization
+problems I know what to
+
+ align:start position:0%
+problems I know what to
+ 
+
+ align:start position:0%
+problems I know what to
+do okay I find the tangency between the
+
+ align:start position:0%
+do okay I find the tangency between the
+ 
+
+ align:start position:0%
+do okay I find the tangency between the
+indifference curve which is essentially
+
+ align:start position:0%
+indifference curve which is essentially
+ 
+
+ align:start position:0%
+indifference curve which is essentially
+my impatience period one and two and the
+
+ align:start position:0%
+my impatience period one and two and the
+ 
+
+ align:start position:0%
+my impatience period one and two and the
+budget constraint which is the market
+
+ align:start position:0%
+budget constraint which is the market
+ 
+
+ align:start position:0%
+budget constraint which is the market
+rate at which I can trade off
+
+ align:start position:0%
+rate at which I can trade off
+ 
+
+ align:start position:0%
+rate at which I can trade off
+consumption period one period two
+
+ align:start position:0%
+consumption period one period two
+ 
+
+ align:start position:0%
+consumption period one period two
+remember going all the way back to
+
+ align:start position:0%
+remember going all the way back to
+ 
+
+ align:start position:0%
+remember going all the way back to
+lecture one the idea of opportunity cost
+
+ align:start position:0%
+lecture one the idea of opportunity cost
+ 
+
+ align:start position:0%
+lecture one the idea of opportunity cost
+is kind of like the concept of
+
+ align:start position:0%
+is kind of like the concept of
+ 
+
+ align:start position:0%
+is kind of like the concept of
+alchemy where I'm not literally turning
+
+ align:start position:0%
+alchemy where I'm not literally turning
+ 
+
+ align:start position:0%
+alchemy where I'm not literally turning
+period one consumption into period two
+
+ align:start position:0%
+period one consumption into period two
+ 
+
+ align:start position:0%
+period one consumption into period two
+consumption physically but I'm
+
+ align:start position:0%
+consumption physically but I'm
+ 
+
+ align:start position:0%
+consumption physically but I'm
+effectively doing it through opportunity
+
+ align:start position:0%
+effectively doing it through opportunity
+ 
+
+ align:start position:0%
+effectively doing it through opportunity
+cost by not consuming in Period one you
+
+ align:start position:0%
+cost by not consuming in Period one you
+ 
+
+ align:start position:0%
+cost by not consuming in Period one you
+get more in Period two so it's
+
+ align:start position:0%
+get more in Period two so it's
+ 
+
+ align:start position:0%
+get more in Period two so it's
+essentially alchemy that happens through
+
+ align:start position:0%
+essentially alchemy that happens through
+ 
+
+ align:start position:0%
+essentially alchemy that happens through
+the concept of opportunity cost in this
+
+ align:start position:0%
+the concept of opportunity cost in this
+ 
+
+ align:start position:0%
+the concept of opportunity cost in this
+case it happens through saving in the
+
+ align:start position:0%
+case it happens through saving in the
+ 
+
+ align:start position:0%
+case it happens through saving in the
+bank by Saving in the bank I turn a
+
+ align:start position:0%
+bank by Saving in the bank I turn a
+ 
+
+ align:start position:0%
+bank by Saving in the bank I turn a
+dollar today into a1ar 10 tomorrow
+
+ align:start position:0%
+dollar today into a1ar 10 tomorrow
+ 
+
+ align:start position:0%
+dollar today into a1ar 10 tomorrow
+dollar period one into a dollar 10 in
+
+ align:start position:0%
+dollar period one into a dollar 10 in
+ 
+
+ align:start position:0%
+dollar period one into a dollar 10 in
+Period
+
+ align:start position:0%
+Period
+ 
+
+ align:start position:0%
+Period
+two okay and that's what's happening
+
+ align:start position:0%
+two okay and that's what's happening
+ 
+
+ align:start position:0%
+two okay and that's what's happening
+here so my optimal consumption in this
+
+ align:start position:0%
+here so my optimal consumption in this
+ 
+
+ align:start position:0%
+here so my optimal consumption in this
+case is C1 in Period one so what do I do
+
+ align:start position:0%
+case is C1 in Period one so what do I do
+ 
+
+ align:start position:0%
+case is C1 in Period one so what do I do
+I say well look given my impatience
+
+ align:start position:0%
+I say well look given my impatience
+ 
+
+ align:start position:0%
+I say well look given my impatience
+level I want to consume C1 in Period one
+
+ align:start position:0%
+level I want to consume C1 in Period one
+ 
+
+ align:start position:0%
+level I want to consume C1 in Period one
+in figure
+
+ align:start position:0%
+in figure
+ 
+
+ align:start position:0%
+in figure
+167 what that means I'm going to save
+
+ align:start position:0%
+167 what that means I'm going to save
+ 
+
+ align:start position:0%
+167 what that means I'm going to save
+80,000 minus
+
+ align:start position:0%
+80,000 minus
+ 
+
+ align:start position:0%
+80,000 minus
+C1 what does that mean my period two
+
+ align:start position:0%
+C1 what does that mean my period two
+ 
+
+ align:start position:0%
+C1 what does that mean my period two
+consumption is it means my period two
+
+ align:start position:0%
+consumption is it means my period two
+ 
+
+ align:start position:0%
+consumption is it means my period two
+consumption is going to be the amount I
+
+ align:start position:0%
+consumption is going to be the amount I
+ 
+
+ align:start position:0%
+consumption is going to be the amount I
+saved times one plus the interest
+
+ align:start position:0%
+saved times one plus the interest
+ 
+
+ align:start position:0%
+saved times one plus the interest
+rate so it's going to be 1 plus I times
+
+ align:start position:0%
+rate so it's going to be 1 plus I times
+ 
+
+ align:start position:0%
+rate so it's going to be 1 plus I times
+80,000 minus
+
+ align:start position:0%
+80,000 minus
+ 
+
+ align:start position:0%
+80,000 minus
+C
+
+ align:start position:0%
+C
+ 
+
+ align:start position:0%
+C
+C1 now once again let's remember the
+
+ align:start position:0%
+C1 now once again let's remember the
+ 
+
+ align:start position:0%
+C1 now once again let's remember the
+trick I've done here without mentioning
+
+ align:start position:0%
+trick I've done here without mentioning
+ 
+
+ align:start position:0%
+trick I've done here without mentioning
+it this lecture is supposed to be about
+
+ align:start position:0%
+it this lecture is supposed to be about
+ 
+
+ align:start position:0%
+it this lecture is supposed to be about
+savings that's the first time I've
+
+ align:start position:0%
+savings that's the first time I've
+ 
+
+ align:start position:0%
+savings that's the first time I've
+mentioned
+
+ align:start position:0%
+mentioned
+ 
+
+ align:start position:0%
+mentioned
+savings why because savings is a
+
+ align:start position:0%
+savings why because savings is a
+ 
+
+ align:start position:0%
+savings why because savings is a
+bad savings is something you just have
+
+ align:start position:0%
+bad savings is something you just have
+ 
+
+ align:start position:0%
+bad savings is something you just have
+to do to get consumption period too no
+
+ align:start position:0%
+to do to get consumption period too no
+ 
+
+ align:start position:0%
+to do to get consumption period too no
+one wants to save this one's even a
+
+ align:start position:0%
+one wants to save this one's even a
+ 
+
+ align:start position:0%
+one wants to save this one's even a
+little more realistic for you guys
+
+ align:start position:0%
+little more realistic for you guys
+ 
+
+ align:start position:0%
+little more realistic for you guys
+although you're probably probably still
+
+ align:start position:0%
+although you're probably probably still
+ 
+
+ align:start position:0%
+although you're probably probably still
+frugal people but basically the idea
+
+ align:start position:0%
+frugal people but basically the idea
+ 
+
+ align:start position:0%
+frugal people but basically the idea
+savings is not a good thing we don't
+
+ align:start position:0%
+savings is not a good thing we don't
+ 
+
+ align:start position:0%
+savings is not a good thing we don't
+have a model where people it's not a
+
+ align:start position:0%
+have a model where people it's not a
+ 
+
+ align:start position:0%
+have a model where people it's not a
+Scrooge McDuck model where people want
+
+ align:start position:0%
+Scrooge McDuck model where people want
+ 
+
+ align:start position:0%
+Scrooge McDuck model where people want
+to swim in their money okay savings is
+
+ align:start position:0%
+to swim in their money okay savings is
+ 
+
+ align:start position:0%
+to swim in their money okay savings is
+not a good thing savings is a is a
+
+ align:start position:0%
+not a good thing savings is a is a
+ 
+
+ align:start position:0%
+not a good thing savings is a is a
+necessary tool to get consumption from
+
+ align:start position:0%
+necessary tool to get consumption from
+ 
+
+ align:start position:0%
+necessary tool to get consumption from
+period one to period two it's a bad we
+
+ align:start position:0%
+period one to period two it's a bad we
+ 
+
+ align:start position:0%
+period one to period two it's a bad we
+don't model bads we model Goods so we
+
+ align:start position:0%
+don't model bads we model Goods so we
+ 
+
+ align:start position:0%
+don't model bads we model Goods so we
+don't model savings we model consumption
+
+ align:start position:0%
+don't model savings we model consumption
+ 
+
+ align:start position:0%
+don't model savings we model consumption
+and then we get savings as a residual
+
+ align:start position:0%
+and then we get savings as a residual
+ 
+
+ align:start position:0%
+and then we get savings as a residual
+so when you want to solve for savings
+
+ align:start position:0%
+so when you want to solve for savings
+ 
+
+ align:start position:0%
+so when you want to solve for savings
+you model consumption and you get
+
+ align:start position:0%
+you model consumption and you get
+ 
+
+ align:start position:0%
+you model consumption and you get
+savings as the residual just like when
+
+ align:start position:0%
+savings as the residual just like when
+ 
+
+ align:start position:0%
+savings as the residual just like when
+you want to model work you solve for
+
+ align:start position:0%
+you want to model work you solve for
+ 
+
+ align:start position:0%
+you want to model work you solve for
+leisure and get work as the
+
+ align:start position:0%
+leisure and get work as the
+ 
+
+ align:start position:0%
+leisure and get work as the
+residual now let's ask what happens when
+
+ align:start position:0%
+residual now let's ask what happens when
+ 
+
+ align:start position:0%
+residual now let's ask what happens when
+the interest rate goes up okay once
+
+ align:start position:0%
+the interest rate goes up okay once
+ 
+
+ align:start position:0%
+the interest rate goes up okay once
+again I'm sorry I don't have time for
+
+ align:start position:0%
+again I'm sorry I don't have time for
+ 
+
+ align:start position:0%
+again I'm sorry I don't have time for
+the math here but we'll do it in section
+
+ align:start position:0%
+the math here but we'll do it in section
+ 
+
+ align:start position:0%
+the math here but we'll do it in section
+on Friday let's ask what happens when
+
+ align:start position:0%
+on Friday let's ask what happens when
+ 
+
+ align:start position:0%
+on Friday let's ask what happens when
+the interest rate goes up will we move
+
+ align:start position:0%
+the interest rate goes up will we move
+ 
+
+ align:start position:0%
+the interest rate goes up will we move
+from bc1 to
+
+ align:start position:0%
+from bc1 to
+ 
+
+ align:start position:0%
+from bc1 to
+bc2 that has guess what two
+
+ align:start position:0%
+bc2 that has guess what two
+ 
+
+ align:start position:0%
+bc2 that has guess what two
+effects on the one hand you get the
+
+ align:start position:0%
+effects on the one hand you get the
+ 
+
+ align:start position:0%
+effects on the one hand you get the
+substitution
+
+ align:start position:0%
+substitution
+ 
+
+ align:start position:0%
+substitution
+effect the substitution effect is the
+
+ align:start position:0%
+effect the substitution effect is the
+ 
+
+ align:start position:0%
+effect the substitution effect is the
+price of First Period consumption has
+
+ align:start position:0%
+price of First Period consumption has
+ 
+
+ align:start position:0%
+price of First Period consumption has
+gone up so you want to do less of it
+
+ align:start position:0%
+gone up so you want to do less of it
+ 
+
+ align:start position:0%
+gone up so you want to do less of it
+focus on that remember I'm not talking
+
+ align:start position:0%
+focus on that remember I'm not talking
+ 
+
+ align:start position:0%
+focus on that remember I'm not talking
+about savings I'm not talking about
+
+ align:start position:0%
+about savings I'm not talking about
+ 
+
+ align:start position:0%
+about savings I'm not talking about
+second period consumption the subsid
+
+ align:start position:0%
+second period consumption the subsid
+ 
+
+ align:start position:0%
+second period consumption the subsid
+income effects are purely in terms of
+
+ align:start position:0%
+income effects are purely in terms of
+ 
+
+ align:start position:0%
+income effects are purely in terms of
+first period consumption C1 is what
+
+ align:start position:0%
+first period consumption C1 is what
+ 
+
+ align:start position:0%
+first period consumption C1 is what
+you're maximizing over here the price of
+
+ align:start position:0%
+you're maximizing over here the price of
+ 
+
+ align:start position:0%
+you're maximizing over here the price of
+First Period consumption is gone up why
+
+ align:start position:0%
+First Period consumption is gone up why
+ 
+
+ align:start position:0%
+First Period consumption is gone up why
+is it gone up because the opportunity
+
+ align:start position:0%
+is it gone up because the opportunity
+ 
+
+ align:start position:0%
+is it gone up because the opportunity
+cost's gone up you can have more in
+
+ align:start position:0%
+cost's gone up you can have more in
+ 
+
+ align:start position:0%
+cost's gone up you can have more in
+Period two by Saving more so the
+
+ align:start position:0%
+Period two by Saving more so the
+ 
+
+ align:start position:0%
+Period two by Saving more so the
+substitution effect necessarily says you
+
+ align:start position:0%
+substitution effect necessarily says you
+ 
+
+ align:start position:0%
+substitution effect necessarily says you
+have less period one
+
+ align:start position:0%
+have less period one
+ 
+
+ align:start position:0%
+have less period one
+consumption but what about the income
+
+ align:start position:0%
+consumption but what about the income
+ 
+
+ align:start position:0%
+consumption but what about the income
+effect well consumption in Period two is
+
+ align:start position:0%
+effect well consumption in Period two is
+ 
+
+ align:start position:0%
+effect well consumption in Period two is
+a normal
+
+ align:start position:0%
+a normal
+ 
+
+ align:start position:0%
+a normal
+good I'm sorry consumption sorry
+
+ align:start position:0%
+good I'm sorry consumption sorry
+ 
+
+ align:start position:0%
+good I'm sorry consumption sorry
+consumption period one is a normal good
+
+ align:start position:0%
+consumption period one is a normal good
+ 
+
+ align:start position:0%
+consumption period one is a normal good
+cons period one is a normal good and are
+
+ align:start position:0%
+cons period one is a normal good and are
+ 
+
+ align:start position:0%
+cons period one is a normal good and are
+you richer or
+
+ align:start position:0%
+you richer or
+ 
+
+ align:start position:0%
+you richer or
+poor if the rate goes
+
+ align:start position:0%
+poor if the rate goes
+ 
+
+ align:start position:0%
+poor if the rate goes
+up are you effectively richer or poor
+
+ align:start position:0%
+up are you effectively richer or poor
+ 
+
+ align:start position:0%
+up are you effectively richer or poor
+effectively go ahead you know richer
+
+ align:start position:0%
+effectively go ahead you know richer
+ 
+
+ align:start position:0%
+effectively go ahead you know richer
+you're effectively richer because every
+
+ align:start position:0%
+you're effectively richer because every
+ 
+
+ align:start position:0%
+you're effectively richer because every
+dollar of savings yields more
+
+ align:start position:0%
+dollar of savings yields more
+ 
+
+ align:start position:0%
+dollar of savings yields more
+money so the income effect says since
+
+ align:start position:0%
+money so the income effect says since
+ 
+
+ align:start position:0%
+money so the income effect says since
+you're richer you want more of
+
+ align:start position:0%
+you're richer you want more of
+ 
+
+ align:start position:0%
+you're richer you want more of
+everything what's one of the things you
+
+ align:start position:0%
+everything what's one of the things you
+ 
+
+ align:start position:0%
+everything what's one of the things you
+want more of
+
+ align:start position:0%
+want more of
+ 
+
+ align:start position:0%
+want more of
+C1 so the income effect goes the other
+
+ align:start position:0%
+C1 so the income effect goes the other
+ 
+
+ align:start position:0%
+C1 so the income effect goes the other
+way you get the same sort of GIF and
+
+ align:start position:0%
+way you get the same sort of GIF and
+ 
+
+ align:start position:0%
+way you get the same sort of GIF and
+good effects without
+
+ align:start position:0%
+good effects without
+ 
+
+ align:start position:0%
+good effects without
+weirdness so actually whether a higher
+
+ align:start position:0%
+weirdness so actually whether a higher
+ 
+
+ align:start position:0%
+weirdness so actually whether a higher
+interest rate raised or low and saving
+
+ align:start position:0%
+interest rate raised or low and saving
+ 
+
+ align:start position:0%
+interest rate raised or low and saving
+is ambiguous once again think of the
+
+ align:start position:0%
+is ambiguous once again think of the
+ 
+
+ align:start position:0%
+is ambiguous once again think of the
+intuition it's even easier intuition
+
+ align:start position:0%
+intuition it's even easier intuition
+ 
+
+ align:start position:0%
+intuition it's even easier intuition
+here you're a kid you want a bike the
+
+ align:start position:0%
+here you're a kid you want a bike the
+ 
+
+ align:start position:0%
+here you're a kid you want a bike the
+bike's going to cost 200 bucks you can
+
+ align:start position:0%
+bike's going to cost 200 bucks you can
+ 
+
+ align:start position:0%
+bike's going to cost 200 bucks you can
+earn 10 bucks an hour so you work 20
+
+ align:start position:0%
+earn 10 bucks an hour so you work 20
+ 
+
+ align:start position:0%
+earn 10 bucks an hour so you work 20
+hours to get the bike then you quit well
+
+ align:start position:0%
+hours to get the bike then you quit well
+ 
+
+ align:start position:0%
+hours to get the bike then you quit well
+if you earn 15 bucks an hour you work
+
+ align:start position:0%
+if you earn 15 bucks an hour you work
+ 
+
+ align:start position:0%
+if you earn 15 bucks an hour you work
+few hours because all you want is the
+
+ align:start position:0%
+few hours because all you want is the
+ 
+
+ align:start position:0%
+few hours because all you want is the
+bike that would be a that would be a
+
+ align:start position:0%
+bike that would be a that would be a
+ 
+
+ align:start position:0%
+bike that would be a that would be a
+downward sloping supply curve in that
+
+ align:start position:0%
+downward sloping supply curve in that
+ 
+
+ align:start position:0%
+downward sloping supply curve in that
+case the interest rate rise would cause
+
+ align:start position:0%
+case the interest rate rise would cause
+ 
+
+ align:start position:0%
+case the interest rate rise would cause
+you I'm not working I'm sorry let me
+
+ align:start position:0%
+you I'm not working I'm sorry let me
+ 
+
+ align:start position:0%
+you I'm not working I'm sorry let me
+back up I did working going too fast
+
+ align:start position:0%
+back up I did working going too fast
+ 
+
+ align:start position:0%
+back up I did working going too fast
+here you want a bike it's 200 bucks so
+
+ align:start position:0%
+here you want a bike it's 200 bucks so
+ 
+
+ align:start position:0%
+here you want a bike it's 200 bucks so
+you got to save
+
+ align:start position:0%
+you got to save
+ 
+
+ align:start position:0%
+you got to save
+$200 um you got to save $200 so if the
+
+ align:start position:0%
+$200 um you got to save $200 so if the
+ 
+
+ align:start position:0%
+$200 um you got to save $200 so if the
+interest rate is
+
+ align:start position:0%
+interest rate is
+ 
+
+ align:start position:0%
+interest rate is
+% then you have to save say you know one
+
+ align:start position:0%
+% then you have to save say you know one
+ 
+
+ align:start position:0%
+% then you have to save say you know one
+you know uh you know 180 roughly this
+
+ align:start position:0%
+you know uh you know 180 roughly this
+ 
+
+ align:start position:0%
+you know uh you know 180 roughly this
+year okay to get the bike next year this
+
+ align:start position:0%
+year okay to get the bike next year this
+ 
+
+ align:start position:0%
+year okay to get the bike next year this
+rate 20% you'll have to save about 160
+
+ align:start position:0%
+rate 20% you'll have to save about 160
+ 
+
+ align:start position:0%
+rate 20% you'll have to save about 160
+this year to get the bike next year okay
+
+ align:start position:0%
+this year to get the bike next year okay
+ 
+
+ align:start position:0%
+this year to get the bike next year okay
+that's a b forget my old example I was
+
+ align:start position:0%
+that's a b forget my old example I was
+ 
+
+ align:start position:0%
+that's a b forget my old example I was
+on labor so if you want the bike next
+
+ align:start position:0%
+on labor so if you want the bike next
+ 
+
+ align:start position:0%
+on labor so if you want the bike next
+year for 200 bucks and this rates 10%
+
+ align:start position:0%
+year for 200 bucks and this rates 10%
+ 
+
+ align:start position:0%
+year for 200 bucks and this rates 10%
+you got to save 180 but 20% you got to
+
+ align:start position:0%
+you got to save 180 but 20% you got to
+ 
+
+ align:start position:0%
+you got to save 180 but 20% you got to
+save 160 so you're actually savings goes
+
+ align:start position:0%
+save 160 so you're actually savings goes
+ 
+
+ align:start position:0%
+save 160 so you're actually savings goes
+down a higher interest rate causes
+
+ align:start position:0%
+down a higher interest rate causes
+ 
+
+ align:start position:0%
+down a higher interest rate causes
+savings to go down that would be a
+
+ align:start position:0%
+savings to go down that would be a
+ 
+
+ align:start position:0%
+savings to go down that would be a
+downward sloping supply curve so just
+
+ align:start position:0%
+downward sloping supply curve so just
+ 
+
+ align:start position:0%
+downward sloping supply curve so just
+like labor Supply we don't know which
+
+ align:start position:0%
+like labor Supply we don't know which
+ 
+
+ align:start position:0%
+like labor Supply we don't know which
+way the capital supply curve goes and
+
+ align:start position:0%
+way the capital supply curve goes and
+ 
+
+ align:start position:0%
+way the capital supply curve goes and
+here unfortunately like unfortunately
+
+ align:start position:0%
+here unfortunately like unfortunately
+ 
+
+ align:start position:0%
+here unfortunately like unfortunately
+unlike labor Supply we don't even have
+
+ align:start position:0%
+unlike labor Supply we don't even have
+ 
+
+ align:start position:0%
+unlike labor Supply we don't even have
+good evidence we pretty much know that
+
+ align:start position:0%
+good evidence we pretty much know that
+ 
+
+ align:start position:0%
+good evidence we pretty much know that
+labor Supply curves slope up but are
+
+ align:start position:0%
+labor Supply curves slope up but are
+ 
+
+ align:start position:0%
+labor Supply curves slope up but are
+almost
+
+ align:start position:0%
+almost
+ 
+
+ align:start position:0%
+almost
+vertical with with capital Supply curves
+
+ align:start position:0%
+vertical with with capital Supply curves
+ 
+
+ align:start position:0%
+vertical with with capital Supply curves
+we actually don't
+
+ align:start position:0%
+we actually don't
+ 
+
+ align:start position:0%
+we actually don't
+know it's a real empirical weakness in
+
+ align:start position:0%
+know it's a real empirical weakness in
+ 
+
+ align:start position:0%
+know it's a real empirical weakness in
+economics so we are going to go ahead
+
+ align:start position:0%
+economics so we are going to go ahead
+ 
+
+ align:start position:0%
+economics so we are going to go ahead
+and assume substitution effects Dominate
+
+ align:start position:0%
+and assume substitution effects Dominate
+ 
+
+ align:start position:0%
+and assume substitution effects Dominate
+and generally draw upward slope opening
+
+ align:start position:0%
+and generally draw upward slope opening
+ 
+
+ align:start position:0%
+and generally draw upward slope opening
+Capital Supply Curves in this course but
+
+ align:start position:0%
+Capital Supply Curves in this course but
+ 
+
+ align:start position:0%
+Capital Supply Curves in this course but
+unfortunately we don't really know what
+
+ align:start position:0%
+unfortunately we don't really know what
+ 
+
+ align:start position:0%
+unfortunately we don't really know what
+the capital supply curve looks like okay
+
+ align:start position:0%
+the capital supply curve looks like okay
+ 
+
+ align:start position:0%
+the capital supply curve looks like okay
+I will stop there and we'll come back uh
+
+ align:start position:0%
+I will stop there and we'll come back uh
+ 
+
+ align:start position:0%
+I will stop there and we'll come back uh
+next time and just continue discussing
+
+ align:start position:0%
+next time and just continue discussing
+ 
+
+ align:start position:0%
+next time and just continue discussing
+we'll discuss how you should invest your
+
+ align:start position:0%
+we'll discuss how you should invest your
+ 
+
+ align:start position:0%
+we'll discuss how you should invest your
+money so come back next time and learn
+
+ align:start position:0%
+money so come back next time and learn
+ 
+
+ align:start position:0%
+money so come back next time and learn
+how you should invest your money
\ No newline at end of file
diff --git a/_WwudFI6YRs.txt b/_WwudFI6YRs.txt
new file mode 100644
index 0000000000000000000000000000000000000000..1381a9bfd92eeebbadf800f208658ef3c66e2c25
--- /dev/null
+++ b/_WwudFI6YRs.txt
@@ -0,0 +1,1547 @@
+align:start position:0%
+ 
+so I want to give to demystify a little
+
+ align:start position:0%
+so I want to give to demystify a little
+ 
+
+ align:start position:0%
+so I want to give to demystify a little
+this equations we sometimes use the
+
+ align:start position:0%
+this equations we sometimes use the
+ 
+
+ align:start position:0%
+this equations we sometimes use the
+basis to show everything that is
+
+ align:start position:0%
+basis to show everything that is
+ 
+
+ align:start position:0%
+basis to show everything that is
+happening so we have a good basis so
+
+ align:start position:0%
+happening so we have a good basis so
+ 
+
+ align:start position:0%
+happening so we have a good basis so
+let's look at it so how does it all look
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+thus this look in an orthonormal basis
+
+ align:start position:0%
+thus this look in an orthonormal basis
+ 
+
+ align:start position:0%
+thus this look in an orthonormal basis
+so which basis well you have one h0 was
+
+ align:start position:0%
+so which basis well you have one h0 was
+ 
+
+ align:start position:0%
+so which basis well you have one h0 was
+supposed to be down so we'll call these
+
+ align:start position:0%
+supposed to be down so we'll call these
+ 
+
+ align:start position:0%
+supposed to be down so we'll call these
+states and these are the eigenstates of
+
+ align:start position:0%
+states and these are the eigenstates of
+ 
+
+ align:start position:0%
+states and these are the eigenstates of
+h0 will have e n we could put a 0 we
+
+ align:start position:0%
+h0 will have e n we could put a 0 we
+ 
+
+ align:start position:0%
+h0 will have e n we could put a 0 we
+used to have that 0 there but since
+
+ align:start position:0%
+used to have that 0 there but since
+ 
+
+ align:start position:0%
+used to have that 0 there but since
+we're never gonna try to solve this
+
+ align:start position:0%
+we're never gonna try to solve this
+ 
+
+ align:start position:0%
+we're never gonna try to solve this
+equation in a different way as time goes
+
+ align:start position:0%
+equation in a different way as time goes
+ 
+
+ align:start position:0%
+equation in a different way as time goes
+on we're not the time-dependent system I
+
+ align:start position:0%
+on we're not the time-dependent system I
+ 
+
+ align:start position:0%
+on we're not the time-dependent system I
+said you doesn't have energy eigenstates
+
+ align:start position:0%
+said you doesn't have energy eigenstates
+ 
+
+ align:start position:0%
+said you doesn't have energy eigenstates
+so a perturbation theory is not gonna be
+
+ align:start position:0%
+so a perturbation theory is not gonna be
+ 
+
+ align:start position:0%
+so a perturbation theory is not gonna be
+about perturbing this energy so I will
+
+ align:start position:0%
+about perturbing this energy so I will
+ 
+
+ align:start position:0%
+about perturbing this energy so I will
+erase it
+
+ align:start position:0%
+erase it
+ 
+
+ align:start position:0%
+erase it
+E and there will be no confusion that's
+
+ align:start position:0%
+E and there will be no confusion that's
+ 
+
+ align:start position:0%
+E and there will be no confusion that's
+never gonna change now I'm gonna write
+
+ align:start position:0%
+never gonna change now I'm gonna write
+ 
+
+ align:start position:0%
+never gonna change now I'm gonna write
+an equation that may seem a little
+
+ align:start position:0%
+an equation that may seem a little
+ 
+
+ align:start position:0%
+an equation that may seem a little
+strange we want to solve for this potato
+
+ align:start position:0%
+strange we want to solve for this potato
+ 
+
+ align:start position:0%
+strange we want to solve for this potato
+so let's write an answer for this side
+
+ align:start position:0%
+so let's write an answer for this side
+ 
+
+ align:start position:0%
+so let's write an answer for this side
+tilde of T is gonna be the following sum
+
+ align:start position:0%
+tilde of T is gonna be the following sum
+ 
+
+ align:start position:0%
+tilde of T is gonna be the following sum
+over n CN and
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+if CNS are constant this is definitely
+
+ align:start position:0%
+if CNS are constant this is definitely
+ 
+
+ align:start position:0%
+if CNS are constant this is definitely
+not right these states must have some
+
+ align:start position:0%
+not right these states must have some
+ 
+
+ align:start position:0%
+not right these states must have some
+time dependence so at least I should put
+
+ align:start position:0%
+time dependence so at least I should put
+ 
+
+ align:start position:0%
+time dependence so at least I should put
+the time dependence here
+
+ align:start position:0%
+the time dependence here
+ 
+
+ align:start position:0%
+the time dependence here
+but even that this sounds a little wrong
+
+ align:start position:0%
+but even that this sounds a little wrong
+ 
+
+ align:start position:0%
+but even that this sounds a little wrong
+a priori you knew that in time
+
+ align:start position:0%
+a priori you knew that in time
+ 
+
+ align:start position:0%
+a priori you knew that in time
+independent problems you can always
+
+ align:start position:0%
+independent problems you can always
+ 
+
+ align:start position:0%
+independent problems you can always
+write a state as a superposition of your
+
+ align:start position:0%
+write a state as a superposition of your
+ 
+
+ align:start position:0%
+write a state as a superposition of your
+energy eigenstates so now this is the
+
+ align:start position:0%
+energy eigenstates so now this is the
+ 
+
+ align:start position:0%
+energy eigenstates so now this is the
+interacting picture we have not any more
+
+ align:start position:0%
+interacting picture we have not any more
+ 
+
+ align:start position:0%
+interacting picture we have not any more
+energy eigenstates in any sense
+
+ align:start position:0%
+energy eigenstates in any sense
+ 
+
+ align:start position:0%
+energy eigenstates in any sense
+can I write this does this make sense
+
+ align:start position:0%
+can I write this does this make sense
+ 
+
+ align:start position:0%
+can I write this does this make sense
+still well the answer is yes you can and
+
+ align:start position:0%
+still well the answer is yes you can and
+ 
+
+ align:start position:0%
+still well the answer is yes you can and
+the reason is that whatever you can say
+
+ align:start position:0%
+the reason is that whatever you can say
+ 
+
+ align:start position:0%
+the reason is that whatever you can say
+about this energy eigenstate they apply
+
+ align:start position:0%
+about this energy eigenstate they apply
+ 
+
+ align:start position:0%
+about this energy eigenstate they apply
+for early times they apply for late
+
+ align:start position:0%
+for early times they apply for late
+ 
+
+ align:start position:0%
+for early times they apply for late
+times they anyway exist there are a
+
+ align:start position:0%
+times they anyway exist there are a
+ 
+
+ align:start position:0%
+times they anyway exist there are a
+basis and what I said they are a basis
+
+ align:start position:0%
+basis and what I said they are a basis
+ 
+
+ align:start position:0%
+basis and what I said they are a basis
+so any wave function can be written in
+
+ align:start position:0%
+so any wave function can be written in
+ 
+
+ align:start position:0%
+so any wave function can be written in
+terms of them so if I look at side tilde
+
+ align:start position:0%
+terms of them so if I look at side tilde
+ 
+
+ align:start position:0%
+terms of them so if I look at side tilde
+time one second I should be able to find
+
+ align:start position:0%
+time one second I should be able to find
+ 
+
+ align:start position:0%
+time one second I should be able to find
+numbers that make this possible and if I
+
+ align:start position:0%
+numbers that make this possible and if I
+ 
+
+ align:start position:0%
+numbers that make this possible and if I
+look at it at two seconds I will find
+
+ align:start position:0%
+look at it at two seconds I will find
+ 
+
+ align:start position:0%
+look at it at two seconds I will find
+another set of numbers and make it
+
+ align:start position:0%
+another set of numbers and make it
+ 
+
+ align:start position:0%
+another set of numbers and make it
+possible so by the fact that I've
+
+ align:start position:0%
+possible so by the fact that I've
+ 
+
+ align:start position:0%
+possible so by the fact that I've
+included here a time dependence for the
+
+ align:start position:0%
+included here a time dependence for the
+ 
+
+ align:start position:0%
+included here a time dependence for the
+coefficients it is possible to write
+
+ align:start position:0%
+coefficients it is possible to write
+ 
+
+ align:start position:0%
+coefficients it is possible to write
+this these coefficients change in time
+
+ align:start position:0%
+this these coefficients change in time
+ 
+
+ align:start position:0%
+this these coefficients change in time
+in strange ways but that's our unknown
+
+ align:start position:0%
+in strange ways but that's our unknown
+ 
+
+ align:start position:0%
+in strange ways but that's our unknown
+if the if I knew how they change in time
+
+ align:start position:0%
+if the if I knew how they change in time
+ 
+
+ align:start position:0%
+if the if I knew how they change in time
+I would have solved the problem I don't
+
+ align:start position:0%
+I would have solved the problem I don't
+ 
+
+ align:start position:0%
+I would have solved the problem I don't
+know how they change in time but in
+
+ align:start position:0%
+know how they change in time but in
+ 
+
+ align:start position:0%
+know how they change in time but in
+general we will try to find for this
+
+ align:start position:0%
+general we will try to find for this
+ 
+
+ align:start position:0%
+general we will try to find for this
+coefficient so if you have side till
+
+ align:start position:0%
+coefficient so if you have side till
+ 
+
+ align:start position:0%
+coefficient so if you have side till
+that you know at the end of the day your
+
+ align:start position:0%
+that you know at the end of the day your
+ 
+
+ align:start position:0%
+that you know at the end of the day your
+goal is Phi of T so what is Phi of T
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+sigh of tea from this blackboard is the
+
+ align:start position:0%
+sigh of tea from this blackboard is the
+ 
+
+ align:start position:0%
+sigh of tea from this blackboard is the
+action of this operator on-site ilda
+
+ align:start position:0%
+action of this operator on-site ilda
+ 
+
+ align:start position:0%
+action of this operator on-site ilda
+that operator moves through the
+
+ align:start position:0%
+that operator moves through the
+ 
+
+ align:start position:0%
+that operator moves through the
+constants and through the sum and with
+
+ align:start position:0%
+constants and through the sum and with
+ 
+
+ align:start position:0%
+constants and through the sum and with
+the n states eigenstates of H 0 this
+
+ align:start position:0%
+the n states eigenstates of H 0 this
+ 
+
+ align:start position:0%
+the n states eigenstates of H 0 this
+just gives me minus AI e n T over H bar
+
+ align:start position:0%
+just gives me minus AI e n T over H bar
+ 
+
+ align:start position:0%
+just gives me minus AI e n T over H bar
+and and this expansion should make you
+
+ align:start position:0%
+and and this expansion should make you
+ 
+
+ align:start position:0%
+and and this expansion should make you
+feel good you say ok here it is these
+
+ align:start position:0%
+feel good you say ok here it is these
+ 
+
+ align:start position:0%
+feel good you say ok here it is these
+are my states my state in the my
+
+ align:start position:0%
+are my states my state in the my
+ 
+
+ align:start position:0%
+are my states my state in the my
+time-dependent wave function let's say
+
+ align:start position:0%
+time-dependent wave function let's say
+ 
+
+ align:start position:0%
+time-dependent wave function let's say
+and it's given by this formula if I
+
+ align:start position:0%
+and it's given by this formula if I
+ 
+
+ align:start position:0%
+and it's given by this formula if I
+didn't have a delta H we know that
+
+ align:start position:0%
+didn't have a delta H we know that
+ 
+
+ align:start position:0%
+didn't have a delta H we know that
+without a delta h sy tilde is constant
+
+ align:start position:0%
+without a delta h sy tilde is constant
+ 
+
+ align:start position:0%
+without a delta h sy tilde is constant
+so the c ends would be constant if
+
+ align:start position:0%
+so the c ends would be constant if
+ 
+
+ align:start position:0%
+so the c ends would be constant if
+there's no Delta H and if the C ends are
+
+ align:start position:0%
+there's no Delta H and if the C ends are
+ 
+
+ align:start position:0%
+there's no Delta H and if the C ends are
+continent there's no Delta H that's
+
+ align:start position:0%
+continent there's no Delta H that's
+ 
+
+ align:start position:0%
+continent there's no Delta H that's
+exactly how energy eigenstates evolve in
+
+ align:start position:0%
+exactly how energy eigenstates evolve in
+ 
+
+ align:start position:0%
+exactly how energy eigenstates evolve in
+time they are evolving with the
+
+ align:start position:0%
+time they are evolving with the
+ 
+
+ align:start position:0%
+time they are evolving with the
+Exponential's of the action of H 0 so
+
+ align:start position:0%
+Exponential's of the action of H 0 so
+ 
+
+ align:start position:0%
+Exponential's of the action of H 0 so
+this is consistent with all you know if
+
+ align:start position:0%
+this is consistent with all you know if
+ 
+
+ align:start position:0%
+this is consistent with all you know if
+Delta H turns on the C ends are gonna
+
+ align:start position:0%
+Delta H turns on the C ends are gonna
+ 
+
+ align:start position:0%
+Delta H turns on the C ends are gonna
+choir time dependence and we will know
+
+ align:start position:0%
+choir time dependence and we will know
+ 
+
+ align:start position:0%
+choir time dependence and we will know
+what the state is doing so this is good
+
+ align:start position:0%
+what the state is doing so this is good
+ 
+
+ align:start position:0%
+what the state is doing so this is good
+so let's plug into the new Schrodinger
+
+ align:start position:0%
+so let's plug into the new Schrodinger
+ 
+
+ align:start position:0%
+so let's plug into the new Schrodinger
+equation this expansion and this is our
+
+ align:start position:0%
+equation this expansion and this is our
+ 
+
+ align:start position:0%
+equation this expansion and this is our
+new sir in your equation so what do we
+
+ align:start position:0%
+new sir in your equation so what do we
+ 
+
+ align:start position:0%
+new sir in your equation so what do we
+get I get IH bar D DT of this I'll write
+
+ align:start position:0%
+get I get IH bar D DT of this I'll write
+ 
+
+ align:start position:0%
+get I get IH bar D DT of this I'll write
+it here with a sum I'll change to letter
+
+ align:start position:0%
+it here with a sum I'll change to letter
+ 
+
+ align:start position:0%
+it here with a sum I'll change to letter
+m bc m
+
+ align:start position:0%
+m bc m
+ 
+
+ align:start position:0%
+m bc m
+are these dots C M of T dot for time
+
+ align:start position:0%
+are these dots C M of T dot for time
+ 
+
+ align:start position:0%
+are these dots C M of T dot for time
+derivative many time use dot so I'm
+
+ align:start position:0%
+derivative many time use dot so I'm
+ 
+
+ align:start position:0%
+derivative many time use dot so I'm
+taking the time derivative of tried
+
+ align:start position:0%
+taking the time derivative of tried
+ 
+
+ align:start position:0%
+taking the time derivative of tried
+tilde as in the Schrodinger equation I
+
+ align:start position:0%
+tilde as in the Schrodinger equation I
+ 
+
+ align:start position:0%
+tilde as in the Schrodinger equation I
+go here CM m and this is supposed to be
+
+ align:start position:0%
+go here CM m and this is supposed to be
+ 
+
+ align:start position:0%
+go here CM m and this is supposed to be
+equal to Delta H tilde times this same
+
+ align:start position:0%
+equal to Delta H tilde times this same
+ 
+
+ align:start position:0%
+equal to Delta H tilde times this same
+state so it's going to be sum over and C
+
+ align:start position:0%
+state so it's going to be sum over and C
+ 
+
+ align:start position:0%
+state so it's going to be sum over and C
+n of T Delta H tilde n so this is the
+
+ align:start position:0%
+n of T Delta H tilde n so this is the
+ 
+
+ align:start position:0%
+n of T Delta H tilde n so this is the
+Schrodinger equation for this state I'm
+
+ align:start position:0%
+Schrodinger equation for this state I'm
+ 
+
+ align:start position:0%
+Schrodinger equation for this state I'm
+we're now looking at the Schrodinger
+
+ align:start position:0%
+we're now looking at the Schrodinger
+ 
+
+ align:start position:0%
+we're now looking at the Schrodinger
+equation in a basis because that may be
+
+ align:start position:0%
+equation in a basis because that may be
+ 
+
+ align:start position:0%
+equation in a basis because that may be
+a good way to solve it
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+well one way to solve it is to do in the
+
+ align:start position:0%
+well one way to solve it is to do in the
+ 
+
+ align:start position:0%
+well one way to solve it is to do in the
+right hand side a complete set introduce
+
+ align:start position:0%
+right hand side a complete set introduce
+ 
+
+ align:start position:0%
+right hand side a complete set introduce
+a complete sets of states so I'll put
+
+ align:start position:0%
+a complete sets of states so I'll put
+ 
+
+ align:start position:0%
+a complete sets of states so I'll put
+the sum over m m m and this whole sum
+
+ align:start position:0%
+the sum over m m m and this whole sum
+ 
+
+ align:start position:0%
+the sum over m m m and this whole sum
+over n C and of P Delta H and so this
+
+ align:start position:0%
+over n C and of P Delta H and so this
+ 
+
+ align:start position:0%
+over n C and of P Delta H and so this
+will be equal to sum over m the M is
+
+ align:start position:0%
+will be equal to sum over m the M is
+ 
+
+ align:start position:0%
+will be equal to sum over m the M is
+here and sum over n the bra can go all
+
+ align:start position:0%
+here and sum over n the bra can go all
+ 
+
+ align:start position:0%
+here and sum over n the bra can go all
+the way in and you write C n of T M
+
+ align:start position:0%
+the way in and you write C n of T M
+ 
+
+ align:start position:0%
+the way in and you write C n of T M
+Delta H
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+so this is our Schrodinger equation
+
+ align:start position:0%
+so this is our Schrodinger equation
+ 
+
+ align:start position:0%
+so this is our Schrodinger equation
+still and now it's kind of in a nice way
+
+ align:start position:0%
+still and now it's kind of in a nice way
+ 
+
+ align:start position:0%
+still and now it's kind of in a nice way
+in which we have similar letters on both
+
+ align:start position:0%
+in which we have similar letters on both
+ 
+
+ align:start position:0%
+in which we have similar letters on both
+sides a little bit of notation of I'll
+
+ align:start position:0%
+sides a little bit of notation of I'll
+ 
+
+ align:start position:0%
+sides a little bit of notation of I'll
+call this Delta H tilde M and we've done
+
+ align:start position:0%
+call this Delta H tilde M and we've done
+ 
+
+ align:start position:0%
+call this Delta H tilde M and we've done
+that in perturbation theory many many
+
+ align:start position:0%
+that in perturbation theory many many
+ 
+
+ align:start position:0%
+that in perturbation theory many many
+times so what is our equation well
+
+ align:start position:0%
+times so what is our equation well
+ 
+
+ align:start position:0%
+times so what is our equation well
+compare terms with equal value of the
+
+ align:start position:0%
+compare terms with equal value of the
+ 
+
+ align:start position:0%
+compare terms with equal value of the
+function in front of the state M so we
+
+ align:start position:0%
+function in front of the state M so we
+ 
+
+ align:start position:0%
+function in front of the state M so we
+get IH bar C m dot of T is equal to the
+
+ align:start position:0%
+get IH bar C m dot of T is equal to the
+ 
+
+ align:start position:0%
+get IH bar C m dot of T is equal to the
+sum over n CN or Delta H MN c n of t
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that's it it's a nice-looking equation
+
+ align:start position:0%
+that's it it's a nice-looking equation
+ 
+
+ align:start position:0%
+that's it it's a nice-looking equation
+it's a couple set of differential
+
+ align:start position:0%
+it's a couple set of differential
+ 
+
+ align:start position:0%
+it's a couple set of differential
+equations for an infinite set of
+
+ align:start position:0%
+equations for an infinite set of
+ 
+
+ align:start position:0%
+equations for an infinite set of
+functions in which the derivatives are
+
+ align:start position:0%
+functions in which the derivatives are
+ 
+
+ align:start position:0%
+functions in which the derivatives are
+obtained in terms of the Hamiltonian
+
+ align:start position:0%
+obtained in terms of the Hamiltonian
+ 
+
+ align:start position:0%
+obtained in terms of the Hamiltonian
+matrix elements for the transition
+
+ align:start position:0%
+matrix elements for the transition
+ 
+
+ align:start position:0%
+matrix elements for the transition
+Hamiltonian for the perturbation times
+
+ align:start position:0%
+Hamiltonian for the perturbation times
+ 
+
+ align:start position:0%
+Hamiltonian for the perturbation times
+these functions they're a little more
+
+ align:start position:0%
+these functions they're a little more
+ 
+
+ align:start position:0%
+these functions they're a little more
+notation here in in the sense of just
+
+ align:start position:0%
+notation here in in the sense of just
+ 
+
+ align:start position:0%
+notation here in in the sense of just
+understanding the structure of that
+
+ align:start position:0%
+understanding the structure of that
+ 
+
+ align:start position:0%
+understanding the structure of that
+matrix element that's useful because in
+
+ align:start position:0%
+matrix element that's useful because in
+ 
+
+ align:start position:0%
+matrix element that's useful because in
+practice all the tilde things at the end
+
+ align:start position:0%
+practice all the tilde things at the end
+ 
+
+ align:start position:0%
+practice all the tilde things at the end
+of the day groups we don't want them we
+
+ align:start position:0%
+of the day groups we don't want them we
+ 
+
+ align:start position:0%
+of the day groups we don't want them we
+want the original ones things without
+
+ align:start position:0%
+want the original ones things without
+ 
+
+ align:start position:0%
+want the original ones things without
+tilde and we always look for them so
+
+ align:start position:0%
+tilde and we always look for them so
+ 
+
+ align:start position:0%
+tilde and we always look for them so
+what is this matrix element Delta H m
+
+ align:start position:0%
+what is this matrix element Delta H m
+ 
+
+ align:start position:0%
+what is this matrix element Delta H m
+and tilde is M Delta H tilde and but
+
+ align:start position:0%
+and tilde is M Delta H tilde and but
+ 
+
+ align:start position:0%
+and tilde is M Delta H tilde and but
+remember what Delta H tilde was you have
+
+ align:start position:0%
+remember what Delta H tilde was you have
+ 
+
+ align:start position:0%
+remember what Delta H tilde was you have
+it here so we have m e to the IH 0 T
+
+ align:start position:0%
+it here so we have m e to the IH 0 T
+ 
+
+ align:start position:0%
+it here so we have m e to the IH 0 T
+over H bar Delta H e to the minus I h 0
+
+ align:start position:0%
+over H bar Delta H e to the minus I h 0
+ 
+
+ align:start position:0%
+over H bar Delta H e to the minus I h 0
+T over H bar and that's no problem
+
+ align:start position:0%
+T over H bar and that's no problem
+ 
+
+ align:start position:0%
+T over H bar and that's no problem
+everything is good here because those
+
+ align:start position:0%
+everything is good here because those
+ 
+
+ align:start position:0%
+everything is good here because those
+are eigenstates so we know how much you
+
+ align:start position:0%
+are eigenstates so we know how much you
+ 
+
+ align:start position:0%
+are eigenstates so we know how much you
+get by letting this act on that state
+
+ align:start position:0%
+get by letting this act on that state
+ 
+
+ align:start position:0%
+get by letting this act on that state
+and that other exponential act on the
+
+ align:start position:0%
+and that other exponential act on the
+ 
+
+ align:start position:0%
+and that other exponential act on the
+state on the right so what do we get e
+
+ align:start position:0%
+state on the right so what do we get e
+ 
+
+ align:start position:0%
+state on the right so what do we get e
+to the i e
+
+ align:start position:0%
+to the i e
+ 
+
+ align:start position:0%
+to the i e
+em T over H bar and from the other one
+
+ align:start position:0%
+em T over H bar and from the other one
+ 
+
+ align:start position:0%
+em T over H bar and from the other one
+e n P over H bar like this the two
+
+ align:start position:0%
+e n P over H bar like this the two
+ 
+
+ align:start position:0%
+e n P over H bar like this the two
+Exponential's give you that and then you
+
+ align:start position:0%
+Exponential's give you that and then you
+ 
+
+ align:start position:0%
+Exponential's give you that and then you
+have just Delta H your original
+
+ align:start position:0%
+have just Delta H your original
+ 
+
+ align:start position:0%
+have just Delta H your original
+perturbation between states of the
+
+ align:start position:0%
+perturbation between states of the
+ 
+
+ align:start position:0%
+perturbation between states of the
+Hamiltonian so you have here and M I'll
+
+ align:start position:0%
+Hamiltonian so you have here and M I'll
+ 
+
+ align:start position:0%
+Hamiltonian so you have here and M I'll
+write it this way Delta H and and just
+
+ align:start position:0%
+write it this way Delta H and and just
+ 
+
+ align:start position:0%
+write it this way Delta H and and just
+without the tilde which is M Delta H
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+most people call this the frequency m
+
+ align:start position:0%
+most people call this the frequency m
+ 
+
+ align:start position:0%
+most people call this the frequency m
+and e over H bar is a frequency so
+
+ align:start position:0%
+and e over H bar is a frequency so
+ 
+
+ align:start position:0%
+and e over H bar is a frequency so
+harmonic oscillator reminds of you of
+
+ align:start position:0%
+harmonic oscillator reminds of you of
+ 
+
+ align:start position:0%
+harmonic oscillator reminds of you of
+that a equal H bar Omega and for easier
+
+ align:start position:0%
+that a equal H bar Omega and for easier
+ 
+
+ align:start position:0%
+that a equal H bar Omega and for easier
+writing you write an Omega M n so this
+
+ align:start position:0%
+writing you write an Omega M n so this
+ 
+
+ align:start position:0%
+writing you write an Omega M n so this
+becomes e to the I Omega m and T times
+
+ align:start position:0%
+becomes e to the I Omega m and T times
+ 
+
+ align:start position:0%
+becomes e to the I Omega m and T times
+Delta H M so this is kind of nice
+
+ align:start position:0%
+Delta H M so this is kind of nice
+ 
+
+ align:start position:0%
+Delta H M so this is kind of nice
+notation so this matrix elements there
+
+ align:start position:0%
+notation so this matrix elements there
+ 
+
+ align:start position:0%
+notation so this matrix elements there
+of not well I'll write again the
+
+ align:start position:0%
+of not well I'll write again the
+ 
+
+ align:start position:0%
+of not well I'll write again the
+equation I h-bar C m dot of T would be
+
+ align:start position:0%
+equation I h-bar C m dot of T would be
+ 
+
+ align:start position:0%
+equation I h-bar C m dot of T would be
+the sum over n of e to the I Omega m and
+
+ align:start position:0%
+the sum over n of e to the I Omega m and
+ 
+
+ align:start position:0%
+the sum over n of e to the I Omega m and
+T Delta H M and C n of K
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that same equation has been rewritten in
+
+ align:start position:0%
+that same equation has been rewritten in
+ 
+
+ align:start position:0%
+that same equation has been rewritten in
+the viewpoint of this where we simplify
+
+ align:start position:0%
+the viewpoint of this where we simplify
+ 
+
+ align:start position:0%
+the viewpoint of this where we simplify
+the tilde and we can refer everything to
+
+ align:start position:0%
+the tilde and we can refer everything to
+ 
+
+ align:start position:0%
+the tilde and we can refer everything to
+our original basis so in a sense of I
+
+ align:start position:0%
+our original basis so in a sense of I
+ 
+
+ align:start position:0%
+our original basis so in a sense of I
+think this should be mystify things
+
+ align:start position:0%
+think this should be mystify things
+ 
+
+ align:start position:0%
+think this should be mystify things
+what's the situation
+
+ align:start position:0%
+what's the situation
+ 
+
+ align:start position:0%
+what's the situation
+what has happened is that if you have a
+
+ align:start position:0%
+what has happened is that if you have a
+ 
+
+ align:start position:0%
+what has happened is that if you have a
+basis you write an answer for the wave
+
+ align:start position:0%
+basis you write an answer for the wave
+ 
+
+ align:start position:0%
+basis you write an answer for the wave
+function of this form and the
+
+ align:start position:0%
+function of this form and the
+ 
+
+ align:start position:0%
+function of this form and the
+coefficients are solutions of those
+
+ align:start position:0%
+coefficients are solutions of those
+ 
+
+ align:start position:0%
+coefficients are solutions of those
+differential equations so we've
+
+ align:start position:0%
+differential equations so we've
+ 
+
+ align:start position:0%
+differential equations so we've
+translated the problem to something
+
+ align:start position:0%
+translated the problem to something
+ 
+
+ align:start position:0%
+translated the problem to something
+doable if you have lots of resources a
+
+ align:start position:0%
+doable if you have lots of resources a
+ 
+
+ align:start position:0%
+doable if you have lots of resources a
+computer and you solve coupled
+
+ align:start position:0%
+computer and you solve coupled
+ 
+
+ align:start position:0%
+computer and you solve coupled
+time-dependent differential equations
+
+ align:start position:0%
+time-dependent differential equations
+ 
+
+ align:start position:0%
+time-dependent differential equations
+first order these are not partic well it
+
+ align:start position:0%
+first order these are not partic well it
+ 
+
+ align:start position:0%
+first order these are not partic well it
+all depends how difficult is the time
+
+ align:start position:0%
+all depends how difficult is the time
+ 
+
+ align:start position:0%
+all depends how difficult is the time
+dependence here the exponential is not
+
+ align:start position:0%
+dependence here the exponential is not
+ 
+
+ align:start position:0%
+dependence here the exponential is not
+bad this well it all depends but this
+
+ align:start position:0%
+bad this well it all depends but this
+ 
+
+ align:start position:0%
+bad this well it all depends but this
+can be solved numerically can be solved
+
+ align:start position:0%
+can be solved numerically can be solved
+ 
+
+ align:start position:0%
+can be solved numerically can be solved
+with many methods this has made the
+
+ align:start position:0%
+with many methods this has made the
+ 
+
+ align:start position:0%
+with many methods this has made the
+problem concrete and we're going to try
+
+ align:start position:0%
+problem concrete and we're going to try
+ 
+
+ align:start position:0%
+problem concrete and we're going to try
+to understand how to solve it in cases
+
+ align:start position:0%
+to understand how to solve it in cases
+ 
+
+ align:start position:0%
+to understand how to solve it in cases
+of interest
\ No newline at end of file
diff --git a/_uNWqE3LS1E.txt b/_uNWqE3LS1E.txt
new file mode 100644
index 0000000000000000000000000000000000000000..4fae8deef63d6f2e018984bb244db1d3aa95fd41
--- /dev/null
+++ b/_uNWqE3LS1E.txt
@@ -0,0 +1,8131 @@
+align:start position:0%
+ 
+so in this final lecture I want to think
+
+ align:start position:0%
+so in this final lecture I want to think
+ 
+
+ align:start position:0%
+so in this final lecture I want to think
+on a bit uh sort of
+
+ align:start position:0%
+on a bit uh sort of
+ 
+
+ align:start position:0%
+on a bit uh sort of
+with an eye towards thinking about how
+
+ align:start position:0%
+with an eye towards thinking about how
+ 
+
+ align:start position:0%
+with an eye towards thinking about how
+one might actually make measurements
+
+ align:start position:0%
+one might actually make measurements
+ 
+
+ align:start position:0%
+one might actually make measurements
+that probe the nature of the black hole
+
+ align:start position:0%
+that probe the nature of the black hole
+ 
+
+ align:start position:0%
+that probe the nature of the black hole
+space times I discussed in the previous
+
+ align:start position:0%
+space times I discussed in the previous
+ 
+
+ align:start position:0%
+space times I discussed in the previous
+lecture I'm going to discuss motion in a
+
+ align:start position:0%
+lecture I'm going to discuss motion in a
+ 
+
+ align:start position:0%
+lecture I'm going to discuss motion in a
+black hole space-time we touched this we
+
+ align:start position:0%
+black hole space-time we touched this we
+ 
+
+ align:start position:0%
+black hole space-time we touched this we
+touched on this a little bit in the
+
+ align:start position:0%
+touched on this a little bit in the
+ 
+
+ align:start position:0%
+touched on this a little bit in the
+previous lecture where we discussed the
+
+ align:start position:0%
+previous lecture where we discussed the
+ 
+
+ align:start position:0%
+previous lecture where we discussed the
+motion of radial light rays okay we in
+
+ align:start position:0%
+motion of radial light rays okay we in
+ 
+
+ align:start position:0%
+motion of radial light rays okay we in
+fact used radial light rays as a as a
+
+ align:start position:0%
+fact used radial light rays as a as a
+ 
+
+ align:start position:0%
+fact used radial light rays as a as a
+critical tool for describing the
+
+ align:start position:0%
+critical tool for describing the
+ 
+
+ align:start position:0%
+critical tool for describing the
+property to the space-time we use that
+
+ align:start position:0%
+property to the space-time we use that
+ 
+
+ align:start position:0%
+property to the space-time we use that
+to help us understand the location of
+
+ align:start position:0%
+to help us understand the location of
+ 
+
+ align:start position:0%
+to help us understand the location of
+event horizons but I want to think a
+
+ align:start position:0%
+event horizons but I want to think a
+ 
+
+ align:start position:0%
+event horizons but I want to think a
+little bit more generally what it might
+
+ align:start position:0%
+little bit more generally what it might
+ 
+
+ align:start position:0%
+little bit more generally what it might
+look like if I have material orbiting in
+
+ align:start position:0%
+look like if I have material orbiting in
+ 
+
+ align:start position:0%
+look like if I have material orbiting in
+them in the vicinity of one of these
+
+ align:start position:0%
+them in the vicinity of one of these
+ 
+
+ align:start position:0%
+them in the vicinity of one of these
+black holes what if it's not light what
+
+ align:start position:0%
+black holes what if it's not light what
+ 
+
+ align:start position:0%
+black holes what if it's not light what
+if it's made out of matter and so what
+
+ align:start position:0%
+if it's made out of matter and so what
+ 
+
+ align:start position:0%
+if it's made out of matter and so what
+this is going to boil down to is
+
+ align:start position:0%
+this is going to boil down to is
+ 
+
+ align:start position:0%
+this is going to boil down to is
+understanding the behavior of judy's X
+
+ align:start position:0%
+understanding the behavior of judy's X
+ 
+
+ align:start position:0%
+understanding the behavior of judy's X
+in a black hole space-time and the naive
+
+ align:start position:0%
+in a black hole space-time and the naive
+ 
+
+ align:start position:0%
+in a black hole space-time and the naive
+approach to doing this is not wrong but
+
+ align:start position:0%
+approach to doing this is not wrong but
+ 
+
+ align:start position:0%
+approach to doing this is not wrong but
+naive what you do is you would just take
+
+ align:start position:0%
+naive what you do is you would just take
+ 
+
+ align:start position:0%
+naive what you do is you would just take
+the space-time okay take your Schwarz
+
+ align:start position:0%
+the space-time okay take your Schwarz
+ 
+
+ align:start position:0%
+the space-time okay take your Schwarz
+shield or take your Kerr space-time and
+
+ align:start position:0%
+shield or take your Kerr space-time and
+ 
+
+ align:start position:0%
+shield or take your Kerr space-time and
+turn a very large crank grind out all of
+
+ align:start position:0%
+turn a very large crank grind out all of
+ 
+
+ align:start position:0%
+turn a very large crank grind out all of
+the connection coefficients evaluate the
+
+ align:start position:0%
+the connection coefficients evaluate the
+ 
+
+ align:start position:0%
+the connection coefficients evaluate the
+judie tzuke equation integrate it up
+
+ align:start position:0%
+judie tzuke equation integrate it up
+ 
+
+ align:start position:0%
+judie tzuke equation integrate it up
+solve for the geodesics boom got
+
+ align:start position:0%
+solve for the geodesics boom got
+ 
+
+ align:start position:0%
+solve for the geodesics boom got
+yourself your motion okay and that is
+
+ align:start position:0%
+yourself your motion okay and that is
+ 
+
+ align:start position:0%
+yourself your motion okay and that is
+absolutely correct you can do that using
+
+ align:start position:0%
+absolutely correct you can do that using
+ 
+
+ align:start position:0%
+absolutely correct you can do that using
+your cur space-time or your
+
+ align:start position:0%
+your cur space-time or your
+ 
+
+ align:start position:0%
+your cur space-time or your
+Schwarzschild space-time in fact if you
+
+ align:start position:0%
+Schwarzschild space-time in fact if you
+ 
+
+ align:start position:0%
+Schwarzschild space-time in fact if you
+do that for you can get the connection
+
+ align:start position:0%
+do that for you can get the connection
+ 
+
+ align:start position:0%
+do that for you can get the connection
+coefficients describing this you know
+
+ align:start position:0%
+coefficients describing this you know
+ 
+
+ align:start position:0%
+coefficients describing this you know
+those are relatively easy to work out I
+
+ align:start position:0%
+those are relatively easy to work out I
+ 
+
+ align:start position:0%
+those are relatively easy to work out I
+think they are listed in Carroll and
+
+ align:start position:0%
+think they are listed in Carroll and
+ 
+
+ align:start position:0%
+think they are listed in Carroll and
+equation five point five three according
+
+ align:start position:0%
+equation five point five three according
+ 
+
+ align:start position:0%
+equation five point five three according
+to my notes that may just be for
+
+ align:start position:0%
+to my notes that may just be for
+ 
+
+ align:start position:0%
+to my notes that may just be for
+Schwartz Hill betting right they're all
+
+ align:start position:0%
+Schwartz Hill betting right they're all
+ 
+
+ align:start position:0%
+Schwartz Hill betting right they're all
+listed there and
+
+ align:start position:0%
+listed there and
+ 
+
+ align:start position:0%
+listed there and
+have a blast this approach is not wrong
+
+ align:start position:0%
+have a blast this approach is not wrong
+ 
+
+ align:start position:0%
+have a blast this approach is not wrong
+but my notes say but is not useful
+
+ align:start position:0%
+but my notes say but is not useful
+ 
+
+ align:start position:0%
+but my notes say but is not useful
+that's not really true I'll just say
+
+ align:start position:0%
+that's not really true I'll just say
+ 
+
+ align:start position:0%
+that's not really true I'll just say
+that there is a more useful approach to
+
+ align:start position:0%
+that there is a more useful approach to
+ 
+
+ align:start position:0%
+that there is a more useful approach to
+this a more fruitful approach is to
+
+ align:start position:0%
+this a more fruitful approach is to
+ 
+
+ align:start position:0%
+this a more fruitful approach is to
+exploit the fact that these are highly
+
+ align:start position:0%
+exploit the fact that these are highly
+ 
+
+ align:start position:0%
+exploit the fact that these are highly
+symmetric space times exploit the
+
+ align:start position:0%
+symmetric space times exploit the
+ 
+
+ align:start position:0%
+symmetric space times exploit the
+symmetries and the killing vectors and
+
+ align:start position:0%
+symmetries and the killing vectors and
+ 
+
+ align:start position:0%
+symmetries and the killing vectors and
+see how they can be used to reduce the
+
+ align:start position:0%
+see how they can be used to reduce the
+ 
+
+ align:start position:0%
+see how they can be used to reduce the
+number of degrees of freedom that you
+
+ align:start position:0%
+number of degrees of freedom that you
+ 
+
+ align:start position:0%
+number of degrees of freedom that you
+need to describe in this lecture I'm
+
+ align:start position:0%
+need to describe in this lecture I'm
+ 
+
+ align:start position:0%
+need to describe in this lecture I'm
+going to go through this in quite a bit
+
+ align:start position:0%
+going to go through this in quite a bit
+ 
+
+ align:start position:0%
+going to go through this in quite a bit
+of detail for Swart shield the concepts
+
+ align:start position:0%
+of detail for Swart shield the concepts
+ 
+
+ align:start position:0%
+of detail for Swart shield the concepts
+that I'm going to apply work for cur and
+
+ align:start position:0%
+that I'm going to apply work for cur and
+ 
+
+ align:start position:0%
+that I'm going to apply work for cur and
+for current Neuman as well okay
+
+ align:start position:0%
+for current Neuman as well okay
+ 
+
+ align:start position:0%
+for current Neuman as well okay
+Schwartz Hill is just a little easier to
+
+ align:start position:0%
+Schwartz Hill is just a little easier to
+ 
+
+ align:start position:0%
+Schwartz Hill is just a little easier to
+work with it's something that I can fit
+
+ align:start position:0%
+work with it's something that I can fit
+ 
+
+ align:start position:0%
+work with it's something that I can fit
+into a single lecture in particular one
+
+ align:start position:0%
+into a single lecture in particular one
+ 
+
+ align:start position:0%
+into a single lecture in particular one
+of the nice things about Schwartz Shield
+
+ align:start position:0%
+of the nice things about Schwartz Shield
+ 
+
+ align:start position:0%
+of the nice things about Schwartz Shield
+so let's go ahead and write down that
+
+ align:start position:0%
+so let's go ahead and write down that
+ 
+
+ align:start position:0%
+so let's go ahead and write down that
+space-time
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so one of the nice things about Schwartz
+
+ align:start position:0%
+so one of the nice things about Schwartz
+ 
+
+ align:start position:0%
+so one of the nice things about Schwartz
+Shield is it is spherically symmetric
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this means I can always rotate
+
+ align:start position:0%
+this means I can always rotate
+ 
+
+ align:start position:0%
+this means I can always rotate
+coordinates such that well let me think
+
+ align:start position:0%
+coordinates such that well let me think
+ 
+
+ align:start position:0%
+coordinates such that well let me think
+about which let's back up for a second
+
+ align:start position:0%
+about which let's back up for a second
+ 
+
+ align:start position:0%
+about which let's back up for a second
+imagine that I have some kind of a body
+
+ align:start position:0%
+imagine that I have some kind of a body
+ 
+
+ align:start position:0%
+imagine that I have some kind of a body
+orbiting a short shield black hole
+
+ align:start position:0%
+orbiting a short shield black hole
+ 
+
+ align:start position:0%
+orbiting a short shield black hole
+spherical symmetry tells me that there
+
+ align:start position:0%
+spherical symmetry tells me that there
+ 
+
+ align:start position:0%
+spherical symmetry tells me that there
+must be some notion of a conserved
+
+ align:start position:0%
+must be some notion of a conserved
+ 
+
+ align:start position:0%
+must be some notion of a conserved
+angular momentum such that that orbit
+
+ align:start position:0%
+angular momentum such that that orbit
+ 
+
+ align:start position:0%
+angular momentum such that that orbit
+always lies within a given plane put it
+
+ align:start position:0%
+always lies within a given plane put it
+ 
+
+ align:start position:0%
+always lies within a given plane put it
+another way because it is spherically
+
+ align:start position:0%
+another way because it is spherically
+ 
+
+ align:start position:0%
+another way because it is spherically
+symmetric there cannot exist a torque
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the black hole cannot exert a torque
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that changes the orientation of the
+
+ align:start position:0%
+that changes the orientation of the
+ 
+
+ align:start position:0%
+that changes the orientation of the
+orbital plane in particular because it
+
+ align:start position:0%
+orbital plane in particular because it
+ 
+
+ align:start position:0%
+orbital plane in particular because it
+is fairly symmetric there is no unique
+
+ align:start position:0%
+is fairly symmetric there is no unique
+ 
+
+ align:start position:0%
+is fairly symmetric there is no unique
+notion of an equator to this object and
+
+ align:start position:0%
+notion of an equator to this object and
+ 
+
+ align:start position:0%
+notion of an equator to this object and
+so you might as well define any orbits
+
+ align:start position:0%
+so you might as well define any orbits
+ 
+
+ align:start position:0%
+so you might as well define any orbits
+to live in the theta equals PI over 2
+
+ align:start position:0%
+to live in the theta equals PI over 2
+ 
+
+ align:start position:0%
+to live in the theta equals PI over 2
+plane you can always rotate your
+
+ align:start position:0%
+plane you can always rotate your
+ 
+
+ align:start position:0%
+plane you can always rotate your
+coordinates
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+to put any orbit in the state it equals
+
+ align:start position:0%
+to put any orbit in the state it equals
+ 
+
+ align:start position:0%
+to put any orbit in the state it equals
+PI over two plane it's actually a pretty
+
+ align:start position:0%
+PI over two plane it's actually a pretty
+ 
+
+ align:start position:0%
+PI over two plane it's actually a pretty
+simple exercise I won't do this but if
+
+ align:start position:0%
+simple exercise I won't do this but if
+ 
+
+ align:start position:0%
+simple exercise I won't do this but if
+you start with an orbit that is in the
+
+ align:start position:0%
+you start with an orbit that is in the
+ 
+
+ align:start position:0%
+you start with an orbit that is in the
+theta equals PI over two plane and it is
+
+ align:start position:0%
+theta equals PI over two plane and it is
+ 
+
+ align:start position:0%
+theta equals PI over two plane and it is
+moving such that its initial velocity
+
+ align:start position:0%
+moving such that its initial velocity
+ 
+
+ align:start position:0%
+moving such that its initial velocity
+would keep it in the state equals PI
+
+ align:start position:0%
+would keep it in the state equals PI
+ 
+
+ align:start position:0%
+would keep it in the state equals PI
+over two plane it's a very simple
+
+ align:start position:0%
+over two plane it's a very simple
+ 
+
+ align:start position:0%
+over two plane it's a very simple
+exercise using the judy's equation to
+
+ align:start position:0%
+exercise using the judy's equation to
+ 
+
+ align:start position:0%
+exercise using the judy's equation to
+show that it will always be in the Fit
+
+ align:start position:0%
+show that it will always be in the Fit
+ 
+
+ align:start position:0%
+show that it will always be in the Fit
+equals PI over two plane so spherical
+
+ align:start position:0%
+equals PI over two plane so spherical
+ 
+
+ align:start position:0%
+equals PI over two plane so spherical
+symmetry says you know what let's just
+
+ align:start position:0%
+symmetry says you know what let's just
+ 
+
+ align:start position:0%
+symmetry says you know what let's just
+forget about the theta degree of freedom
+
+ align:start position:0%
+forget about the theta degree of freedom
+ 
+
+ align:start position:0%
+forget about the theta degree of freedom
+I can always define my coordinates in
+
+ align:start position:0%
+I can always define my coordinates in
+ 
+
+ align:start position:0%
+I can always define my coordinates in
+such a way that it lives in the theta
+
+ align:start position:0%
+such a way that it lives in the theta
+ 
+
+ align:start position:0%
+such a way that it lives in the theta
+equals PI over two plane boom I have
+
+ align:start position:0%
+equals PI over two plane boom I have
+ 
+
+ align:start position:0%
+equals PI over two plane boom I have
+reduced my motion from in general being
+
+ align:start position:0%
+reduced my motion from in general being
+ 
+
+ align:start position:0%
+reduced my motion from in general being
+three spatial dimensions to two spatial
+
+ align:start position:0%
+three spatial dimensions to two spatial
+ 
+
+ align:start position:0%
+three spatial dimensions to two spatial
+dimensions that's another one the
+
+ align:start position:0%
+dimensions that's another one the
+ 
+
+ align:start position:0%
+dimensions that's another one the
+reasons why for pedagogical purposes
+
+ align:start position:0%
+reasons why for pedagogical purposes
+ 
+
+ align:start position:0%
+reasons why for pedagogical purposes
+it's nice to start with Schwartz shield
+
+ align:start position:0%
+it's nice to start with Schwartz shield
+ 
+
+ align:start position:0%
+it's nice to start with Schwartz shield
+for ker this is not the case okay Kerr
+
+ align:start position:0%
+for ker this is not the case okay Kerr
+ 
+
+ align:start position:0%
+for ker this is not the case okay Kerr
+is a little bit more complicated you
+
+ align:start position:0%
+is a little bit more complicated you
+ 
+
+ align:start position:0%
+is a little bit more complicated you
+have to treat the theta motion
+
+ align:start position:0%
+have to treat the theta motion
+ 
+
+ align:start position:0%
+have to treat the theta motion
+separately
+
+ align:start position:0%
+separately
+ 
+
+ align:start position:0%
+separately
+you cannot it's not symmetric and so you
+
+ align:start position:0%
+you cannot it's not symmetric and so you
+ 
+
+ align:start position:0%
+you cannot it's not symmetric and so you
+can't do that I have actually spent a
+
+ align:start position:0%
+can't do that I have actually spent a
+ 
+
+ align:start position:0%
+can't do that I have actually spent a
+tremendous amount of my career studying
+
+ align:start position:0%
+tremendous amount of my career studying
+ 
+
+ align:start position:0%
+tremendous amount of my career studying
+the orbits of objects around Kerr black
+
+ align:start position:0%
+the orbits of objects around Kerr black
+ 
+
+ align:start position:0%
+the orbits of objects around Kerr black
+holes and I do have to say that the
+
+ align:start position:0%
+holes and I do have to say that the
+ 
+
+ align:start position:0%
+holes and I do have to say that the
+additional complications that arise from
+
+ align:start position:0%
+additional complications that arise from
+ 
+
+ align:start position:0%
+additional complications that arise from
+this lack of cerissa T they're really
+
+ align:start position:0%
+this lack of cerissa T they're really
+ 
+
+ align:start position:0%
+this lack of cerissa T they're really
+beautiful okay there's an amazing amount
+
+ align:start position:0%
+beautiful okay there's an amazing amount
+ 
+
+ align:start position:0%
+beautiful okay there's an amazing amount
+of fun stuff you can do with it
+
+ align:start position:0%
+of fun stuff you can do with it
+ 
+
+ align:start position:0%
+of fun stuff you can do with it
+you know I mean it's it's there's a
+
+ align:start position:0%
+you know I mean it's it's there's a
+ 
+
+ align:start position:0%
+you know I mean it's it's there's a
+reason why I just keep coming back to
+
+ align:start position:0%
+reason why I just keep coming back to
+ 
+
+ align:start position:0%
+reason why I just keep coming back to
+this research problem and part of it is
+
+ align:start position:0%
+this research problem and part of it is
+ 
+
+ align:start position:0%
+this research problem and part of it is
+it's just bloody fun but if you're
+
+ align:start position:0%
+it's just bloody fun but if you're
+ 
+
+ align:start position:0%
+it's just bloody fun but if you're
+teaching this stuff for the first time
+
+ align:start position:0%
+teaching this stuff for the first time
+ 
+
+ align:start position:0%
+teaching this stuff for the first time
+it's not where you want to begin all
+
+ align:start position:0%
+it's not where you want to begin all
+ 
+
+ align:start position:0%
+it's not where you want to begin all
+right so Swart shield allows us to
+
+ align:start position:0%
+right so Swart shield allows us to
+ 
+
+ align:start position:0%
+right so Swart shield allows us to
+reduce it from a three-dimensional
+
+ align:start position:0%
+reduce it from a three-dimensional
+ 
+
+ align:start position:0%
+reduce it from a three-dimensional
+problem to a two-dimensional problem and
+
+ align:start position:0%
+problem to a two-dimensional problem and
+ 
+
+ align:start position:0%
+problem to a two-dimensional problem and
+Schwartz shield also has to killing
+
+ align:start position:0%
+Schwartz shield also has to killing
+ 
+
+ align:start position:0%
+Schwartz shield also has to killing
+vectors the time derivative of every
+
+ align:start position:0%
+vectors the time derivative of every
+ 
+
+ align:start position:0%
+vectors the time derivative of every
+metric component is equal to zero that
+
+ align:start position:0%
+metric component is equal to zero that
+ 
+
+ align:start position:0%
+metric component is equal to zero that
+means P downstairs T is constant
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so there is a time like killing vector
+
+ align:start position:0%
+so there is a time like killing vector
+ 
+
+ align:start position:0%
+so there is a time like killing vector
+so P downstairs T is constant everywhere
+
+ align:start position:0%
+so P downstairs T is constant everywhere
+ 
+
+ align:start position:0%
+so P downstairs T is constant everywhere
+along the orbit it means there exists a
+
+ align:start position:0%
+along the orbit it means there exists a
+ 
+
+ align:start position:0%
+along the orbit it means there exists a
+time like killing vector and so what we
+
+ align:start position:0%
+time like killing vector and so what we
+ 
+
+ align:start position:0%
+time like killing vector and so what we
+do is we associate this with the energy
+
+ align:start position:0%
+do is we associate this with the energy
+ 
+
+ align:start position:0%
+do is we associate this with the energy
+of the orbit we call this up to a minus
+
+ align:start position:0%
+of the orbit we call this up to a minus
+ 
+
+ align:start position:0%
+of the orbit we call this up to a minus
+sign and we choose that minus sign
+
+ align:start position:0%
+sign and we choose that minus sign
+ 
+
+ align:start position:0%
+sign and we choose that minus sign
+because if we imagine orbits a very very
+
+ align:start position:0%
+because if we imagine orbits a very very
+ 
+
+ align:start position:0%
+because if we imagine orbits a very very
+large radius the space time it's nearly
+
+ align:start position:0%
+large radius the space time it's nearly
+ 
+
+ align:start position:0%
+large radius the space time it's nearly
+flat and we want to sort of clear out
+
+ align:start position:0%
+flat and we want to sort of clear out
+ 
+
+ align:start position:0%
+flat and we want to sort of clear out
+the minus sign associates lowering our
+
+ align:start position:0%
+the minus sign associates lowering our
+ 
+
+ align:start position:0%
+the minus sign associates lowering our
+index here we're gonna call that
+
+ align:start position:0%
+index here we're gonna call that
+ 
+
+ align:start position:0%
+index here we're gonna call that
+constant negative of the energy of the
+
+ align:start position:0%
+constant negative of the energy of the
+ 
+
+ align:start position:0%
+constant negative of the energy of the
+orbit the space time is also independent
+
+ align:start position:0%
+orbit the space time is also independent
+ 
+
+ align:start position:0%
+orbit the space time is also independent
+of the angle Phi and so piece of Phi is
+
+ align:start position:0%
+of the angle Phi and so piece of Phi is
+ 
+
+ align:start position:0%
+of the angle Phi and so piece of Phi is
+a constant this means that the
+
+ align:start position:0%
+a constant this means that the
+ 
+
+ align:start position:0%
+a constant this means that the
+space-time has an axial killing factor
+
+ align:start position:0%
+space-time has an axial killing factor
+ 
+
+ align:start position:0%
+space-time has an axial killing factor
+something Associates motions around a
+
+ align:start position:0%
+something Associates motions around a
+ 
+
+ align:start position:0%
+something Associates motions around a
+symmetry axis so I'm gonna call this L
+
+ align:start position:0%
+symmetry axis so I'm gonna call this L
+ 
+
+ align:start position:0%
+symmetry axis so I'm gonna call this L
+well actually I will tend to call it L
+
+ align:start position:0%
+well actually I will tend to call it L
+ 
+
+ align:start position:0%
+well actually I will tend to call it L
+sub Z you can kind of think of this as
+
+ align:start position:0%
+sub Z you can kind of think of this as
+ 
+
+ align:start position:0%
+sub Z you can kind of think of this as
+after I have put everything in the state
+
+ align:start position:0%
+after I have put everything in the state
+ 
+
+ align:start position:0%
+after I have put everything in the state
+equals PI over 2 plane this is like an
+
+ align:start position:0%
+equals PI over 2 plane this is like an
+ 
+
+ align:start position:0%
+equals PI over 2 plane this is like an
+annual angular momentum on the angular
+
+ align:start position:0%
+annual angular momentum on the angular
+ 
+
+ align:start position:0%
+annual angular momentum on the angular
+momentum parallel to the axis normal to
+
+ align:start position:0%
+momentum parallel to the axis normal to
+ 
+
+ align:start position:0%
+momentum parallel to the axis normal to
+that plane I'm going to call that the
+
+ align:start position:0%
+that plane I'm going to call that the
+ 
+
+ align:start position:0%
+that plane I'm going to call that the
+z-axis
+
+ align:start position:0%
+z-axis
+ 
+
+ align:start position:0%
+z-axis
+it's worth noting that all three of
+
+ align:start position:0%
+it's worth noting that all three of
+ 
+
+ align:start position:0%
+it's worth noting that all three of
+these things are also true for Rison or
+
+ align:start position:0%
+these things are also true for Rison or
+ 
+
+ align:start position:0%
+these things are also true for Rison or
+Nordstrom black holes this one is not
+
+ align:start position:0%
+Nordstrom black holes this one is not
+ 
+
+ align:start position:0%
+Nordstrom black holes this one is not
+true for ker but these two are ok so
+
+ align:start position:0%
+true for ker but these two are ok so
+ 
+
+ align:start position:0%
+true for ker but these two are ok so
+although the details change many of the
+
+ align:start position:0%
+although the details change many of the
+ 
+
+ align:start position:0%
+although the details change many of the
+concepts will carry over when you look
+
+ align:start position:0%
+concepts will carry over when you look
+ 
+
+ align:start position:0%
+concepts will carry over when you look
+at different more complicated classes of
+
+ align:start position:0%
+at different more complicated classes of
+ 
+
+ align:start position:0%
+at different more complicated classes of
+black holes let's now think about the
+
+ align:start position:0%
+black holes let's now think about the
+ 
+
+ align:start position:0%
+black holes let's now think about the
+four momentum of the body moving in a
+
+ align:start position:0%
+four momentum of the body moving in a
+ 
+
+ align:start position:0%
+four momentum of the body moving in a
+swirl of space-time
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so let's say it's got a rest mass M then
+
+ align:start position:0%
+so let's say it's got a rest mass M then
+ 
+
+ align:start position:0%
+so let's say it's got a rest mass M then
+it will have three components remember I
+
+ align:start position:0%
+it will have three components remember I
+ 
+
+ align:start position:0%
+it will have three components remember I
+have put this thing in a plane where
+
+ align:start position:0%
+have put this thing in a plane where
+ 
+
+ align:start position:0%
+have put this thing in a plane where
+there is no theta motion it'll have
+
+ align:start position:0%
+there is no theta motion it'll have
+ 
+
+ align:start position:0%
+there is no theta motion it'll have
+three fate emotions describing its
+
+ align:start position:0%
+three fate emotions describing its
+ 
+
+ align:start position:0%
+three fate emotions describing its
+motion with respect to the time
+
+ align:start position:0%
+motion with respect to the time
+ 
+
+ align:start position:0%
+motion with respect to the time
+coordinate the radial coordinate and the
+
+ align:start position:0%
+coordinate the radial coordinate and the
+ 
+
+ align:start position:0%
+coordinate the radial coordinate and the
+actual coordinate Phi okay so before I
+
+ align:start position:0%
+actual coordinate Phi okay so before I
+ 
+
+ align:start position:0%
+actual coordinate Phi okay so before I
+do anything with this let's take
+
+ align:start position:0%
+do anything with this let's take
+ 
+
+ align:start position:0%
+do anything with this let's take
+advantage of the fact that we have these
+
+ align:start position:0%
+advantage of the fact that we have these
+ 
+
+ align:start position:0%
+advantage of the fact that we have these
+quantities that are constants so using
+
+ align:start position:0%
+quantities that are constants so using
+ 
+
+ align:start position:0%
+quantities that are constants so using
+the fact that P downstairs mu is what I
+
+ align:start position:0%
+the fact that P downstairs mu is what I
+ 
+
+ align:start position:0%
+the fact that P downstairs mu is what I
+get when I hit this guy that should be a
+
+ align:start position:0%
+get when I hit this guy that should be a
+ 
+
+ align:start position:0%
+get when I hit this guy that should be a
+new me this is what I get when I hit
+
+ align:start position:0%
+new me this is what I get when I hit
+ 
+
+ align:start position:0%
+new me this is what I get when I hit
+this guy with the metric I can write out
+
+ align:start position:0%
+this guy with the metric I can write out
+ 
+
+ align:start position:0%
+this guy with the metric I can write out
+P sub T and P sub Phi
+
+ align:start position:0%
+P sub T and P sub Phi
+ 
+
+ align:start position:0%
+P sub T and P sub Phi
+let's do that on another board well
+
+ align:start position:0%
+let's do that on another board well
+ 
+
+ align:start position:0%
+let's do that on another board well
+let's do piece of tea first
+
+ align:start position:0%
+let's do piece of tea first
+ 
+
+ align:start position:0%
+let's do piece of tea first
+so P sub T is going to be G tt piece of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay this is - there's an M from that
+
+ align:start position:0%
+okay this is - there's an M from that
+ 
+
+ align:start position:0%
+okay this is - there's an M from that
+minus sign from my metric okay and this
+
+ align:start position:0%
+minus sign from my metric okay and this
+ 
+
+ align:start position:0%
+minus sign from my metric okay and this
+whole thing I define as the negative
+
+ align:start position:0%
+whole thing I define as the negative
+ 
+
+ align:start position:0%
+whole thing I define as the negative
+energy E okay so that combination okay
+
+ align:start position:0%
+energy E okay so that combination okay
+ 
+
+ align:start position:0%
+energy E okay so that combination okay
+we're gonna we'll do something at the
+
+ align:start position:0%
+we're gonna we'll do something at the
+ 
+
+ align:start position:0%
+we're gonna we'll do something at the
+rest mass in just a moment
+
+ align:start position:0%
+rest mass in just a moment
+ 
+
+ align:start position:0%
+rest mass in just a moment
+but you should basically say that as
+
+ align:start position:0%
+but you should basically say that as
+ 
+
+ align:start position:0%
+but you should basically say that as
+look at this is saying that DT D tau
+
+ align:start position:0%
+look at this is saying that DT D tau
+ 
+
+ align:start position:0%
+look at this is saying that DT D tau
+which tells me about how the body moves
+
+ align:start position:0%
+which tells me about how the body moves
+ 
+
+ align:start position:0%
+which tells me about how the body moves
+the respects to the Schwarzschild time
+
+ align:start position:0%
+the respects to the Schwarzschild time
+ 
+
+ align:start position:0%
+the respects to the Schwarzschild time
+coordinate that component of four
+
+ align:start position:0%
+coordinate that component of four
+ 
+
+ align:start position:0%
+coordinate that component of four
+velocity times 1 minus 2 GM over R is a
+
+ align:start position:0%
+velocity times 1 minus 2 GM over R is a
+ 
+
+ align:start position:0%
+velocity times 1 minus 2 GM over R is a
+constant let's look at P downstairs so
+
+ align:start position:0%
+constant let's look at P downstairs so
+ 
+
+ align:start position:0%
+constant let's look at P downstairs so
+this is M R squared sine squared theta
+
+ align:start position:0%
+this is M R squared sine squared theta
+ 
+
+ align:start position:0%
+this is M R squared sine squared theta
+ah we've chosen our orbital plane 1
+
+ align:start position:0%
+ah we've chosen our orbital plane 1
+ 
+
+ align:start position:0%
+ah we've chosen our orbital plane 1
+times D Phi D tau this is equal to the
+
+ align:start position:0%
+times D Phi D tau this is equal to the
+ 
+
+ align:start position:0%
+times D Phi D tau this is equal to the
+angular mentum L sub Z in my notes I
+
+ align:start position:0%
+angular mentum L sub Z in my notes I
+ 
+
+ align:start position:0%
+angular mentum L sub Z in my notes I
+might flip around a little bit between L
+
+ align:start position:0%
+might flip around a little bit between L
+ 
+
+ align:start position:0%
+might flip around a little bit between L
+sub Z and L so let's massage these a
+
+ align:start position:0%
+sub Z and L so let's massage these a
+ 
+
+ align:start position:0%
+sub Z and L so let's massage these a
+little bit more so I can take these two
+
+ align:start position:0%
+little bit more so I can take these two
+ 
+
+ align:start position:0%
+little bit more so I can take these two
+expressions and I can use them to write
+
+ align:start position:0%
+expressions and I can use them to write
+ 
+
+ align:start position:0%
+expressions and I can use them to write
+DT D tau and D Phi D tau in terms of
+
+ align:start position:0%
+DT D tau and D Phi D tau in terms of
+ 
+
+ align:start position:0%
+DT D tau and D Phi D tau in terms of
+these conserved quantities so DT D tau
+
+ align:start position:0%
+these conserved quantities so DT D tau
+ 
+
+ align:start position:0%
+these conserved quantities so DT D tau
+is equal to I'm gonna call it e hat
+
+ align:start position:0%
+is equal to I'm gonna call it e hat
+ 
+
+ align:start position:0%
+is equal to I'm gonna call it e hat
+divided by 1 minus 2 GM over R
+
+ align:start position:0%
+divided by 1 minus 2 GM over R
+ 
+
+ align:start position:0%
+divided by 1 minus 2 GM over R
+if I D tau it's going to be L Z hat over
+
+ align:start position:0%
+if I D tau it's going to be L Z hat over
+ 
+
+ align:start position:0%
+if I D tau it's going to be L Z hat over
+R squared and so these quantities with a
+
+ align:start position:0%
+R squared and so these quantities with a
+ 
+
+ align:start position:0%
+R squared and so these quantities with a
+hat are just the conserved values
+
+ align:start position:0%
+hat are just the conserved values
+ 
+
+ align:start position:0%
+hat are just the conserved values
+normalized to the rest mass okay
+
+ align:start position:0%
+normalized to the rest mass okay
+ 
+
+ align:start position:0%
+normalized to the rest mass okay
+they all are proportional to rest mass
+
+ align:start position:0%
+they all are proportional to rest mass
+ 
+
+ align:start position:0%
+they all are proportional to rest mass
+but it's actually if you want to know
+
+ align:start position:0%
+but it's actually if you want to know
+ 
+
+ align:start position:0%
+but it's actually if you want to know
+what the this is essentially telling me
+
+ align:start position:0%
+what the this is essentially telling me
+ 
+
+ align:start position:0%
+what the this is essentially telling me
+about how clocks on the orbit tick
+
+ align:start position:0%
+about how clocks on the orbit tick
+ 
+
+ align:start position:0%
+about how clocks on the orbit tick
+relative to Talk clocks that are
+
+ align:start position:0%
+relative to Talk clocks that are
+ 
+
+ align:start position:0%
+relative to Talk clocks that are
+infinitely far away and that can't
+
+ align:start position:0%
+infinitely far away and that can't
+ 
+
+ align:start position:0%
+infinitely far away and that can't
+depend on the mass of the orbiting
+
+ align:start position:0%
+depend on the mass of the orbiting
+ 
+
+ align:start position:0%
+depend on the mass of the orbiting
+object this is telling me about how this
+
+ align:start position:0%
+object this is telling me about how this
+ 
+
+ align:start position:0%
+object this is telling me about how this
+small body is moving according to the
+
+ align:start position:0%
+small body is moving according to the
+ 
+
+ align:start position:0%
+small body is moving according to the
+clock of the orbiting observer and again
+
+ align:start position:0%
+clock of the orbiting observer and again
+ 
+
+ align:start position:0%
+clock of the orbiting observer and again
+that can't depend on the mass of the
+
+ align:start position:0%
+that can't depend on the mass of the
+ 
+
+ align:start position:0%
+that can't depend on the mass of the
+object okay
+
+ align:start position:0%
+object okay
+ 
+
+ align:start position:0%
+object okay
+so that's kind of cool so I've now
+
+ align:start position:0%
+so that's kind of cool so I've now
+ 
+
+ align:start position:0%
+so that's kind of cool so I've now
+managed to relate three to be two of the
+
+ align:start position:0%
+managed to relate three to be two of the
+ 
+
+ align:start position:0%
+managed to relate three to be two of the
+three components of the four momentum
+
+ align:start position:0%
+three components of the four momentum
+ 
+
+ align:start position:0%
+three components of the four momentum
+two functions of our and quantities that
+
+ align:start position:0%
+two functions of our and quantities that
+ 
+
+ align:start position:0%
+two functions of our and quantities that
+are known to be constant that's good
+
+ align:start position:0%
+are known to be constant that's good
+ 
+
+ align:start position:0%
+are known to be constant that's good
+we have one more overall constraint we
+
+ align:start position:0%
+we have one more overall constraint we
+ 
+
+ align:start position:0%
+we have one more overall constraint we
+know that if I take P dot P I get
+
+ align:start position:0%
+know that if I take P dot P I get
+ 
+
+ align:start position:0%
+know that if I take P dot P I get
+negative of the rest mass squared so
+
+ align:start position:0%
+negative of the rest mass squared so
+ 
+
+ align:start position:0%
+negative of the rest mass squared so
+this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay notice every single term is
+
+ align:start position:0%
+okay notice every single term is
+ 
+
+ align:start position:0%
+okay notice every single term is
+proportional to M Squared so I can
+
+ align:start position:0%
+proportional to M Squared so I can
+ 
+
+ align:start position:0%
+proportional to M Squared so I can
+divide that out I can insert DT D tau I
+
+ align:start position:0%
+divide that out I can insert DT D tau I
+ 
+
+ align:start position:0%
+divide that out I can insert DT D tau I
+can replace for this e divided by this
+
+ align:start position:0%
+can replace for this e divided by this
+ 
+
+ align:start position:0%
+can replace for this e divided by this
+guy I can replace D Phi D tau by my LZ
+
+ align:start position:0%
+guy I can replace D Phi D tau by my LZ
+ 
+
+ align:start position:0%
+guy I can replace D Phi D tau by my LZ
+hat divided by R squared doing so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+manipulating a little bit I get
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+get something like this and let me
+
+ align:start position:0%
+get something like this and let me
+ 
+
+ align:start position:0%
+get something like this and let me
+rearrange this a tiny bit
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+alright I have managed to reduce this to
+
+ align:start position:0%
+alright I have managed to reduce this to
+ 
+
+ align:start position:0%
+alright I have managed to reduce this to
+a one-dimensional problem okay so going
+
+ align:start position:0%
+a one-dimensional problem okay so going
+ 
+
+ align:start position:0%
+a one-dimensional problem okay so going
+from that line over there basically all
+
+ align:start position:0%
+from that line over there basically all
+ 
+
+ align:start position:0%
+from that line over there basically all
+I did was insert the relationship
+
+ align:start position:0%
+I did was insert the relationship
+ 
+
+ align:start position:0%
+I did was insert the relationship
+between DT D TV talent II the Phoebe
+
+ align:start position:0%
+between DT D TV talent II the Phoebe
+ 
+
+ align:start position:0%
+between DT D TV talent II the Phoebe
+towel and L cleared out some overall
+
+ align:start position:0%
+towel and L cleared out some overall
+ 
+
+ align:start position:0%
+towel and L cleared out some overall
+factors of things like 1 minus 2 GM over
+
+ align:start position:0%
+factors of things like 1 minus 2 GM over
+ 
+
+ align:start position:0%
+factors of things like 1 minus 2 GM over
+R manipulate manipulate manipulate and
+
+ align:start position:0%
+R manipulate manipulate manipulate and
+ 
+
+ align:start position:0%
+R manipulate manipulate manipulate and
+what you finally get is this lovely
+
+ align:start position:0%
+what you finally get is this lovely
+ 
+
+ align:start position:0%
+what you finally get is this lovely
+equation here that tells you how the
+
+ align:start position:0%
+equation here that tells you how the
+ 
+
+ align:start position:0%
+equation here that tells you how the
+radial velocity the radial velocity
+
+ align:start position:0%
+radial velocity the radial velocity
+ 
+
+ align:start position:0%
+radial velocity the radial velocity
+respect to proper time how it depends as
+
+ align:start position:0%
+respect to proper time how it depends as
+ 
+
+ align:start position:0%
+respect to proper time how it depends as
+a function of R given the energy and the
+
+ align:start position:0%
+a function of R given the energy and the
+ 
+
+ align:start position:0%
+a function of R given the energy and the
+angular momentum I have written it in
+
+ align:start position:0%
+angular momentum I have written it in
+ 
+
+ align:start position:0%
+angular momentum I have written it in
+this form because the problem is very
+
+ align:start position:0%
+this form because the problem is very
+ 
+
+ align:start position:0%
+this form because the problem is very
+strikingly reminiscent to the Newtonian
+
+ align:start position:0%
+strikingly reminiscent to the Newtonian
+ 
+
+ align:start position:0%
+strikingly reminiscent to the Newtonian
+problem of understanding the motion of a
+
+ align:start position:0%
+problem of understanding the motion of a
+ 
+
+ align:start position:0%
+problem of understanding the motion of a
+particle in a 1 over R potential which
+
+ align:start position:0%
+particle in a 1 over R potential which
+ 
+
+ align:start position:0%
+particle in a 1 over R potential which
+we often described as having an
+
+ align:start position:0%
+we often described as having an
+ 
+
+ align:start position:0%
+we often described as having an
+effective potential that has a
+
+ align:start position:0%
+effective potential that has a
+ 
+
+ align:start position:0%
+effective potential that has a
+gravitational term Newton's gravity or
+
+ align:start position:0%
+gravitational term Newton's gravity or
+ 
+
+ align:start position:0%
+gravitational term Newton's gravity or
+if you're doing things like quantum
+
+ align:start position:0%
+if you're doing things like quantum
+ 
+
+ align:start position:0%
+if you're doing things like quantum
+mechanics the Coulomb potential and a
+
+ align:start position:0%
+mechanics the Coulomb potential and a
+ 
+
+ align:start position:0%
+mechanics the Coulomb potential and a
+Coulomb barrier associated with the
+
+ align:start position:0%
+Coulomb barrier associated with the
+ 
+
+ align:start position:0%
+Coulomb barrier associated with the
+angular momentum of an orbit so one way
+
+ align:start position:0%
+angular momentum of an orbit so one way
+ 
+
+ align:start position:0%
+angular momentum of an orbit so one way
+to approach what we've got now ok one
+
+ align:start position:0%
+to approach what we've got now ok one
+ 
+
+ align:start position:0%
+to approach what we've got now ok one
+thing that we could do is essentially
+
+ align:start position:0%
+thing that we could do is essentially
+ 
+
+ align:start position:0%
+thing that we could do is essentially
+just pick your energy and your LZ pick
+
+ align:start position:0%
+just pick your energy and your LZ pick
+ 
+
+ align:start position:0%
+just pick your energy and your LZ pick
+your energy in your angular momentum
+
+ align:start position:0%
+your energy in your angular momentum
+ 
+
+ align:start position:0%
+your energy in your angular momentum
+pick an initial position
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+imagine you synchronize the clocks at T
+
+ align:start position:0%
+imagine you synchronize the clocks at T
+ 
+
+ align:start position:0%
+imagine you synchronize the clocks at T
+equals zero and then just integrate
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+you've got your DRD tau given here don't
+
+ align:start position:0%
+you've got your DRD tau given here don't
+ 
+
+ align:start position:0%
+you've got your DRD tau given here don't
+forget you also have D Phi D tau and DT
+
+ align:start position:0%
+forget you also have D Phi D tau and DT
+ 
+
+ align:start position:0%
+forget you also have D Phi D tau and DT
+D tau related to the energy and like so
+
+ align:start position:0%
+D tau related to the energy and like so
+ 
+
+ align:start position:0%
+D tau related to the energy and like so
+boom to closed system you can always do
+
+ align:start position:0%
+boom to closed system you can always do
+ 
+
+ align:start position:0%
+boom to closed system you can always do
+just sort of a little numerical
+
+ align:start position:0%
+just sort of a little numerical
+ 
+
+ align:start position:0%
+just sort of a little numerical
+integration of this in a certain sense
+
+ align:start position:0%
+integration of this in a certain sense
+ 
+
+ align:start position:0%
+integration of this in a certain sense
+this completely specifies the problem
+
+ align:start position:0%
+this completely specifies the problem
+ 
+
+ align:start position:0%
+this completely specifies the problem
+there's so much more we can do in
+
+ align:start position:0%
+there's so much more we can do in
+ 
+
+ align:start position:0%
+there's so much more we can do in
+particular what we see is that all of
+
+ align:start position:0%
+particular what we see is that all of
+ 
+
+ align:start position:0%
+particular what we see is that all of
+the interesting behavior associate with
+
+ align:start position:0%
+the interesting behavior associate with
+ 
+
+ align:start position:0%
+the interesting behavior associate with
+this orbit is bound up in this function
+
+ align:start position:0%
+this orbit is bound up in this function
+ 
+
+ align:start position:0%
+this orbit is bound up in this function
+V effective so something that's really
+
+ align:start position:0%
+V effective so something that's really
+ 
+
+ align:start position:0%
+V effective so something that's really
+useful for us to do is to take a look at
+
+ align:start position:0%
+useful for us to do is to take a look at
+ 
+
+ align:start position:0%
+useful for us to do is to take a look at
+what this V effective looks like okay so
+
+ align:start position:0%
+what this V effective looks like okay so
+ 
+
+ align:start position:0%
+what this V effective looks like okay so
+suppose you are given a particular value
+
+ align:start position:0%
+suppose you are given a particular value
+ 
+
+ align:start position:0%
+suppose you are given a particular value
+for e hat and LZ hat and you plot V
+
+ align:start position:0%
+for e hat and LZ hat and you plot V
+ 
+
+ align:start position:0%
+for e hat and LZ hat and you plot V
+effective versus R
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+well what you typically find is that
+
+ align:start position:0%
+well what you typically find is that
+ 
+
+ align:start position:0%
+well what you typically find is that
+it's got a behavior that looks kind of
+
+ align:start position:0%
+it's got a behavior that looks kind of
+ 
+
+ align:start position:0%
+it's got a behavior that looks kind of
+like this where this value right here is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the effect of equal to one okay notice
+
+ align:start position:0%
+the effect of equal to one okay notice
+ 
+
+ align:start position:0%
+the effect of equal to one okay notice
+as R goes to infinity you get 1 times 1
+
+ align:start position:0%
+as R goes to infinity you get 1 times 1
+ 
+
+ align:start position:0%
+as R goes to infinity you get 1 times 1
+so this asymptotes to 1 notice a hat
+
+ align:start position:0%
+so this asymptotes to 1 notice a hat
+ 
+
+ align:start position:0%
+so this asymptotes to 1 notice a hat
+squared has the same dimensions as V
+
+ align:start position:0%
+squared has the same dimensions as V
+ 
+
+ align:start position:0%
+squared has the same dimensions as V
+effective in fact in the unit choices
+
+ align:start position:0%
+effective in fact in the unit choices
+ 
+
+ align:start position:0%
+effective in fact in the unit choices
+I've used here they are both
+
+ align:start position:0%
+I've used here they are both
+ 
+
+ align:start position:0%
+I've used here they are both
+dimensionless so what we can do is plot
+
+ align:start position:0%
+dimensionless so what we can do is plot
+ 
+
+ align:start position:0%
+dimensionless so what we can do is plot
+let's imagine that we have what I'm
+
+ align:start position:0%
+let's imagine that we have what I'm
+ 
+
+ align:start position:0%
+let's imagine that we have what I'm
+gonna want to sketch this on a different
+
+ align:start position:0%
+gonna want to sketch this on a different
+ 
+
+ align:start position:0%
+gonna want to sketch this on a different
+board let me go over here so I'm gonna
+
+ align:start position:0%
+board let me go over here so I'm gonna
+ 
+
+ align:start position:0%
+board let me go over here so I'm gonna
+want to look at a couple of different
+
+ align:start position:0%
+want to look at a couple of different
+ 
+
+ align:start position:0%
+want to look at a couple of different
+values of the effective give me a couple
+
+ align:start position:0%
+values of the effective give me a couple
+ 
+
+ align:start position:0%
+values of the effective give me a couple
+of different values of e hat
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so here's an example this guy's
+
+ align:start position:0%
+okay so here's an example this guy's
+ 
+
+ align:start position:0%
+okay so here's an example this guy's
+putting up one so since he hat as I said
+
+ align:start position:0%
+putting up one so since he hat as I said
+ 
+
+ align:start position:0%
+putting up one so since he hat as I said
+has the same units as V effective let's
+
+ align:start position:0%
+has the same units as V effective let's
+ 
+
+ align:start position:0%
+has the same units as V effective let's
+plot them together so example one
+
+ align:start position:0%
+plot them together so example one
+ 
+
+ align:start position:0%
+plot them together so example one
+imagine if Yi hat lies right here okay
+
+ align:start position:0%
+imagine if Yi hat lies right here okay
+ 
+
+ align:start position:0%
+imagine if Yi hat lies right here okay
+let's call this P Hat 1 so this is some
+
+ align:start position:0%
+let's call this P Hat 1 so this is some
+ 
+
+ align:start position:0%
+let's call this P Hat 1 so this is some
+value that is greater than one what is
+
+ align:start position:0%
+value that is greater than one what is
+ 
+
+ align:start position:0%
+value that is greater than one what is
+the point of doing this well notice I'm
+
+ align:start position:0%
+the point of doing this well notice I'm
+ 
+
+ align:start position:0%
+the point of doing this well notice I'm
+gonna flip back and forth between these
+
+ align:start position:0%
+gonna flip back and forth between these
+ 
+
+ align:start position:0%
+gonna flip back and forth between these
+two middle boards here let's look at the
+
+ align:start position:0%
+two middle boards here let's look at the
+ 
+
+ align:start position:0%
+two middle boards here let's look at the
+equation that governs the radial motion
+
+ align:start position:0%
+equation that governs the radial motion
+ 
+
+ align:start position:0%
+equation that governs the radial motion
+of this body
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+DRD Tao has to be a real number this has
+
+ align:start position:0%
+DRD Tao has to be a real number this has
+ 
+
+ align:start position:0%
+DRD Tao has to be a real number this has
+to be a real number so we have to have a
+
+ align:start position:0%
+to be a real number so we have to have a
+ 
+
+ align:start position:0%
+to be a real number so we have to have a
+hat squared greater than or equal to V
+
+ align:start position:0%
+hat squared greater than or equal to V
+ 
+
+ align:start position:0%
+hat squared greater than or equal to V
+effective in order for dr D tau to have
+
+ align:start position:0%
+effective in order for dr D tau to have
+ 
+
+ align:start position:0%
+effective in order for dr D tau to have
+a meaningful solution so let's look at
+
+ align:start position:0%
+a meaningful solution so let's look at
+ 
+
+ align:start position:0%
+a meaningful solution so let's look at
+my example here we have one t hat one is
+
+ align:start position:0%
+my example here we have one t hat one is
+ 
+
+ align:start position:0%
+my example here we have one t hat one is
+greater than my effective potential
+
+ align:start position:0%
+greater than my effective potential
+ 
+
+ align:start position:0%
+greater than my effective potential
+everywhere at all radii until I get down
+
+ align:start position:0%
+everywhere at all radii until I get down
+ 
+
+ align:start position:0%
+everywhere at all radii until I get down
+to here it's called that r1 so in this
+
+ align:start position:0%
+to here it's called that r1 so in this
+ 
+
+ align:start position:0%
+to here it's called that r1 so in this
+case DRD tell if I think about this
+
+ align:start position:0%
+case DRD tell if I think about this
+ 
+
+ align:start position:0%
+case DRD tell if I think about this
+thing so note that's a finds DRD tau
+
+ align:start position:0%
+thing so note that's a finds DRD tau
+ 
+
+ align:start position:0%
+thing so note that's a finds DRD tau
+squared right let's suppose we take the
+
+ align:start position:0%
+squared right let's suppose we take the
+ 
+
+ align:start position:0%
+squared right let's suppose we take the
+negative square root
+
+ align:start position:0%
+negative square root
+ 
+
+ align:start position:0%
+negative square root
+the our D tau is positive and inward
+
+ align:start position:0%
+the our D tau is positive and inward
+ 
+
+ align:start position:0%
+the our D tau is positive and inward
+it's negative negative and real negative
+
+ align:start position:0%
+it's negative negative and real negative
+ 
+
+ align:start position:0%
+it's negative negative and real negative
+and real negative and real negative and
+
+ align:start position:0%
+and real negative and real negative and
+ 
+
+ align:start position:0%
+and real negative and real negative and
+real negative in real boom it's zero can
+
+ align:start position:0%
+real negative in real boom it's zero can
+ 
+
+ align:start position:0%
+real negative in real boom it's zero can
+it go into here nu cannot go into there
+
+ align:start position:0%
+it go into here nu cannot go into there
+ 
+
+ align:start position:0%
+it go into here nu cannot go into there
+because their a hat squared is less
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+sorry human squared inside here a hat
+
+ align:start position:0%
+sorry human squared inside here a hat
+ 
+
+ align:start position:0%
+sorry human squared inside here a hat
+squared is less than the effect of
+
+ align:start position:0%
+squared is less than the effect of
+ 
+
+ align:start position:0%
+squared is less than the effect of
+potential DRD tau is imaginary that
+
+ align:start position:0%
+potential DRD tau is imaginary that
+ 
+
+ align:start position:0%
+potential DRD tau is imaginary that
+doesn't make any sense the only option
+
+ align:start position:0%
+doesn't make any sense the only option
+ 
+
+ align:start position:0%
+doesn't make any sense the only option
+is for this guy to change sign and
+
+ align:start position:0%
+is for this guy to change sign and
+ 
+
+ align:start position:0%
+is for this guy to change sign and
+trundle right back out so e hat greater
+
+ align:start position:0%
+trundle right back out so e hat greater
+ 
+
+ align:start position:0%
+trundle right back out so e hat greater
+than one corresponds to a body that
+
+ align:start position:0%
+than one corresponds to a body that
+ 
+
+ align:start position:0%
+than one corresponds to a body that
+comes in
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+from large radius turns around at the
+
+ align:start position:0%
+from large radius turns around at the
+ 
+
+ align:start position:0%
+from large radius turns around at the
+particular radius where he hat is the
+
+ align:start position:0%
+particular radius where he hat is the
+ 
+
+ align:start position:0%
+particular radius where he hat is the
+square root of the effect potential and
+
+ align:start position:0%
+square root of the effect potential and
+ 
+
+ align:start position:0%
+square root of the effect potential and
+then goes back out to infinity or back
+
+ align:start position:0%
+then goes back out to infinity or back
+ 
+
+ align:start position:0%
+then goes back out to infinity or back
+out to let's not say infinity goes back
+
+ align:start position:0%
+out to let's not say infinity goes back
+ 
+
+ align:start position:0%
+out to let's not say infinity goes back
+out to large radius okay
+
+ align:start position:0%
+out to large radius okay
+ 
+
+ align:start position:0%
+out to large radius okay
+in Newtonian gravity we would call this
+
+ align:start position:0%
+in Newtonian gravity we would call this
+ 
+
+ align:start position:0%
+in Newtonian gravity we would call this
+a hyperbolic orbit okay this corresponds
+
+ align:start position:0%
+a hyperbolic orbit okay this corresponds
+ 
+
+ align:start position:0%
+a hyperbolic orbit okay this corresponds
+to so remember when I did this I have
+
+ align:start position:0%
+to so remember when I did this I have
+ 
+
+ align:start position:0%
+to so remember when I did this I have
+not I'm not actually I'm only computing
+
+ align:start position:0%
+not I'm not actually I'm only computing
+ 
+
+ align:start position:0%
+not I'm not actually I'm only computing
+the radial motion I'm not looking at the
+
+ align:start position:0%
+the radial motion I'm not looking at the
+ 
+
+ align:start position:0%
+the radial motion I'm not looking at the
+fine motion so this actually when you
+
+ align:start position:0%
+fine motion so this actually when you
+ 
+
+ align:start position:0%
+fine motion so this actually when you
+when you look at both the radial motion
+
+ align:start position:0%
+when you look at both the radial motion
+ 
+
+ align:start position:0%
+when you look at both the radial motion
+in the Phi motion what you see is that
+
+ align:start position:0%
+in the Phi motion what you see is that
+ 
+
+ align:start position:0%
+in the Phi motion what you see is that
+this is a body that comes in and then
+
+ align:start position:0%
+this is a body that comes in and then
+ 
+
+ align:start position:0%
+this is a body that comes in and then
+sort of whips around that small radius
+
+ align:start position:0%
+sort of whips around that small radius
+ 
+
+ align:start position:0%
+sort of whips around that small radius
+and goes right back out let's look at
+
+ align:start position:0%
+and goes right back out let's look at
+ 
+
+ align:start position:0%
+and goes right back out let's look at
+example another example let's call this
+
+ align:start position:0%
+example another example let's call this
+ 
+
+ align:start position:0%
+example another example let's call this
+e to some value that is less than 1 okay
+
+ align:start position:0%
+e to some value that is less than 1 okay
+ 
+
+ align:start position:0%
+e to some value that is less than 1 okay
+well for a hat - it's a potential
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+potential is underneath he had to
+
+ align:start position:0%
+potential is underneath he had to
+ 
+
+ align:start position:0%
+potential is underneath he had to
+squared only between these two radii
+
+ align:start position:0%
+squared only between these two radii
+ 
+
+ align:start position:0%
+squared only between these two radii
+which I will call R sub P in R sub a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+what we expect in this case is motion of
+
+ align:start position:0%
+what we expect in this case is motion of
+ 
+
+ align:start position:0%
+what we expect in this case is motion of
+this body essentially going back and
+
+ align:start position:0%
+this body essentially going back and
+ 
+
+ align:start position:0%
+this body essentially going back and
+forth and turning around at periastron
+
+ align:start position:0%
+forth and turning around at periastron
+ 
+
+ align:start position:0%
+forth and turning around at periastron
+and appo astron this is a relativistic
+
+ align:start position:0%
+and appo astron this is a relativistic
+ 
+
+ align:start position:0%
+and appo astron this is a relativistic
+generation relativistic generalization
+
+ align:start position:0%
+generation relativistic generalization
+ 
+
+ align:start position:0%
+generation relativistic generalization
+of an elliptical orbit okay in general
+
+ align:start position:0%
+of an elliptical orbit okay in general
+ 
+
+ align:start position:0%
+of an elliptical orbit okay in general
+activity they turn out generally not to
+
+ align:start position:0%
+activity they turn out generally not to
+ 
+
+ align:start position:0%
+activity they turn out generally not to
+be ellipses so we call this an eccentric
+
+ align:start position:0%
+be ellipses so we call this an eccentric
+ 
+
+ align:start position:0%
+be ellipses so we call this an eccentric
+orbit in the weak field limit if you
+
+ align:start position:0%
+orbit in the weak field limit if you
+ 
+
+ align:start position:0%
+orbit in the weak field limit if you
+imagine are being very very large it's
+
+ align:start position:0%
+imagine are being very very large it's
+ 
+
+ align:start position:0%
+imagine are being very very large it's
+not hard to show that the motion is
+
+ align:start position:0%
+not hard to show that the motion is
+ 
+
+ align:start position:0%
+not hard to show that the motion is
+nearly an ellipse but it's an ellipse
+
+ align:start position:0%
+nearly an ellipse but it's an ellipse
+ 
+
+ align:start position:0%
+nearly an ellipse but it's an ellipse
+whose long axis is slowly processing
+
+ align:start position:0%
+whose long axis is slowly processing
+ 
+
+ align:start position:0%
+whose long axis is slowly processing
+this actually leads to the famous
+
+ align:start position:0%
+this actually leads to the famous
+ 
+
+ align:start position:0%
+this actually leads to the famous
+perihelion precession of mercury that
+
+ align:start position:0%
+perihelion precession of mercury that
+ 
+
+ align:start position:0%
+perihelion precession of mercury that
+Einstein first calculated and this is an
+
+ align:start position:0%
+Einstein first calculated and this is an
+ 
+
+ align:start position:0%
+Einstein first calculated and this is an
+exercise that I am asking you to do on
+
+ align:start position:0%
+exercise that I am asking you to do on
+ 
+
+ align:start position:0%
+exercise that I am asking you to do on
+one of the final piece sets of this
+
+ align:start position:0%
+one of the final piece sets of this
+ 
+
+ align:start position:0%
+one of the final piece sets of this
+course using what I have set up here
+
+ align:start position:0%
+course using what I have set up here
+ 
+
+ align:start position:0%
+course using what I have set up here
+it's really not that difficult to do let
+
+ align:start position:0%
+it's really not that difficult to do let
+ 
+
+ align:start position:0%
+it's really not that difficult to do let
+me go to another board and note that one
+
+ align:start position:0%
+me go to another board and note that one
+ 
+
+ align:start position:0%
+me go to another board and note that one
+could imagine in energy such that the Rd
+
+ align:start position:0%
+could imagine in energy such that the Rd
+ 
+
+ align:start position:0%
+could imagine in energy such that the Rd
+tau is exactly zero
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so if you choose your energy so that you
+
+ align:start position:0%
+so if you choose your energy so that you
+ 
+
+ align:start position:0%
+so if you choose your energy so that you
+sit right here at the minimum of the
+
+ align:start position:0%
+sit right here at the minimum of the
+ 
+
+ align:start position:0%
+sit right here at the minimum of the
+potential I will label this as point s
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the energy that corresponds to exactly
+
+ align:start position:0%
+the energy that corresponds to exactly
+ 
+
+ align:start position:0%
+the energy that corresponds to exactly
+that point is what would be a that is
+
+ align:start position:0%
+that point is what would be a that is
+ 
+
+ align:start position:0%
+that point is what would be a that is
+there is a single point at which DRD tau
+
+ align:start position:0%
+there is a single point at which DRD tau
+ 
+
+ align:start position:0%
+there is a single point at which DRD tau
+equals zero anywhere away from that dr
+
+ align:start position:0%
+equals zero anywhere away from that dr
+ 
+
+ align:start position:0%
+equals zero anywhere away from that dr
+detail would be imaginary so that's not
+
+ align:start position:0%
+detail would be imaginary so that's not
+ 
+
+ align:start position:0%
+detail would be imaginary so that's not
+going to work
+
+ align:start position:0%
+going to work
+ 
+
+ align:start position:0%
+going to work
+but right at that point dr d tau equals
+
+ align:start position:0%
+but right at that point dr d tau equals
+ 
+
+ align:start position:0%
+but right at that point dr d tau equals
+zero and you get a circular orbit notice
+
+ align:start position:0%
+zero and you get a circular orbit notice
+ 
+
+ align:start position:0%
+zero and you get a circular orbit notice
+there's a second point in which that can
+
+ align:start position:0%
+there's a second point in which that can
+ 
+
+ align:start position:0%
+there's a second point in which that can
+happen let's call this point u perhaps
+
+ align:start position:0%
+happen let's call this point u perhaps
+ 
+
+ align:start position:0%
+happen let's call this point u perhaps
+you can guess why i called these points
+
+ align:start position:0%
+you can guess why i called these points
+ 
+
+ align:start position:0%
+you can guess why i called these points
+s and u if you imagine that you know you
+
+ align:start position:0%
+s and u if you imagine that you know you
+ 
+
+ align:start position:0%
+s and u if you imagine that you know you
+add a tiny amount of energy right here
+
+ align:start position:0%
+add a tiny amount of energy right here
+ 
+
+ align:start position:0%
+add a tiny amount of energy right here
+well it'll do is they'll execute small
+
+ align:start position:0%
+well it'll do is they'll execute small
+ 
+
+ align:start position:0%
+well it'll do is they'll execute small
+oscillations around the point s it'll
+
+ align:start position:0%
+oscillations around the point s it'll
+ 
+
+ align:start position:0%
+oscillations around the point s it'll
+sort of move it up to something that's
+
+ align:start position:0%
+sort of move it up to something that's
+ 
+
+ align:start position:0%
+sort of move it up to something that's
+similar to what I drew up there as e to
+
+ align:start position:0%
+similar to what I drew up there as e to
+ 
+
+ align:start position:0%
+similar to what I drew up there as e to
+but was a very small eccentricity so if
+
+ align:start position:0%
+but was a very small eccentricity so if
+ 
+
+ align:start position:0%
+but was a very small eccentricity so if
+I slightly disturb a circular orbit down
+
+ align:start position:0%
+I slightly disturb a circular orbit down
+ 
+
+ align:start position:0%
+I slightly disturb a circular orbit down
+here at s I essentially just oscillate
+
+ align:start position:0%
+here at s I essentially just oscillate
+ 
+
+ align:start position:0%
+here at s I essentially just oscillate
+in the vicinity of that circular orbit S
+
+ align:start position:0%
+in the vicinity of that circular orbit S
+ 
+
+ align:start position:0%
+in the vicinity of that circular orbit S
+stands for stable if I have an orbit up
+
+ align:start position:0%
+stands for stable if I have an orbit up
+ 
+
+ align:start position:0%
+stands for stable if I have an orbit up
+here at U and I very slightly perturb it
+
+ align:start position:0%
+here at U and I very slightly perturb it
+ 
+
+ align:start position:0%
+here at U and I very slightly perturb it
+well it'll either go in and eventually
+
+ align:start position:0%
+well it'll either go in and eventually
+ 
+
+ align:start position:0%
+well it'll either go in and eventually
+reach R equals 0 or it'll go out and
+
+ align:start position:0%
+reach R equals 0 or it'll go out and
+ 
+
+ align:start position:0%
+reach R equals 0 or it'll go out and
+then it's completely unbound and they'll
+
+ align:start position:0%
+then it's completely unbound and they'll
+ 
+
+ align:start position:0%
+then it's completely unbound and they'll
+just keep trundling all the way out
+
+ align:start position:0%
+just keep trundling all the way out
+ 
+
+ align:start position:0%
+just keep trundling all the way out
+essentially forever
+
+ align:start position:0%
+essentially forever
+ 
+
+ align:start position:0%
+essentially forever
+this guy is unstable stable orbits are
+
+ align:start position:0%
+this guy is unstable stable orbits are
+ 
+
+ align:start position:0%
+this guy is unstable stable orbits are
+particularly interesting and important
+
+ align:start position:0%
+particularly interesting and important
+ 
+
+ align:start position:0%
+particularly interesting and important
+so let's look at these look at these
+
+ align:start position:0%
+so let's look at these look at these
+ 
+
+ align:start position:0%
+so let's look at these look at these
+orbits and a little bit more care
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so the very definition of a circular
+
+ align:start position:0%
+so the very definition of a circular
+ 
+
+ align:start position:0%
+so the very definition of a circular
+orbit is that DRD tau equal to zero its
+
+ align:start position:0%
+orbit is that DRD tau equal to zero its
+ 
+
+ align:start position:0%
+orbit is that DRD tau equal to zero its
+radius does not change if DRD tau equals
+
+ align:start position:0%
+radius does not change if DRD tau equals
+ 
+
+ align:start position:0%
+radius does not change if DRD tau equals
+zero then it must have a hat equal the
+
+ align:start position:0%
+zero then it must have a hat equal the
+ 
+
+ align:start position:0%
+zero then it must have a hat equal the
+square root of the effective okay
+
+ align:start position:0%
+square root of the effective okay
+ 
+
+ align:start position:0%
+square root of the effective okay
+both of these orbits happen to live at
+
+ align:start position:0%
+both of these orbits happen to live at
+ 
+
+ align:start position:0%
+both of these orbits happen to live at
+either a minimum or a maximum of this
+
+ align:start position:0%
+either a minimum or a maximum of this
+ 
+
+ align:start position:0%
+either a minimum or a maximum of this
+potential curve so I'm going to require
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that the partial derivative of that
+
+ align:start position:0%
+that the partial derivative of that
+ 
+
+ align:start position:0%
+that the partial derivative of that
+potential with respect to R be equal to
+
+ align:start position:0%
+potential with respect to R be equal to
+ 
+
+ align:start position:0%
+potential with respect to R be equal to
+zero so let's take a look at this
+
+ align:start position:0%
+zero so let's take a look at this
+ 
+
+ align:start position:0%
+zero so let's take a look at this
+condition my effective potential is
+
+ align:start position:0%
+condition my effective potential is
+ 
+
+ align:start position:0%
+condition my effective potential is
+given up here do a little bit of algebra
+
+ align:start position:0%
+given up here do a little bit of algebra
+ 
+
+ align:start position:0%
+given up here do a little bit of algebra
+with this set this guy equal to zero
+
+ align:start position:0%
+with this set this guy equal to zero
+ 
+
+ align:start position:0%
+with this set this guy equal to zero
+what you'll find after your algebraic
+
+ align:start position:0%
+what you'll find after your algebraic
+ 
+
+ align:start position:0%
+what you'll find after your algebraic
+smoke clears is that you get this
+
+ align:start position:0%
+smoke clears is that you get this
+ 
+
+ align:start position:0%
+smoke clears is that you get this
+condition on the angular momentum
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+notice as our gets really large oh shoot
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+try that again
+
+ align:start position:0%
+try that again
+ 
+
+ align:start position:0%
+try that again
+notice as R gets really large that this
+
+ align:start position:0%
+notice as R gets really large that this
+ 
+
+ align:start position:0%
+notice as R gets really large that this
+asymptotes to plus or minus the square
+
+ align:start position:0%
+asymptotes to plus or minus the square
+ 
+
+ align:start position:0%
+asymptotes to plus or minus the square
+root of GM R that is indeed exactly what
+
+ align:start position:0%
+root of GM R that is indeed exactly what
+ 
+
+ align:start position:0%
+root of GM R that is indeed exactly what
+you get for the angular momentum of a
+
+ align:start position:0%
+you get for the angular momentum of a
+ 
+
+ align:start position:0%
+you get for the angular momentum of a
+circular Newtonian orbit okay so it's a
+
+ align:start position:0%
+circular Newtonian orbit okay so it's a
+ 
+
+ align:start position:0%
+circular Newtonian orbit okay so it's a
+nice sanity check it appears to be
+
+ align:start position:0%
+nice sanity check it appears to be
+ 
+
+ align:start position:0%
+nice sanity check it appears to be
+somewhat pathological and as R
+
+ align:start position:0%
+somewhat pathological and as R
+ 
+
+ align:start position:0%
+somewhat pathological and as R
+approaches 3 GM though hold that thought
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so now let's take that value of L
+
+ align:start position:0%
+okay so now let's take that value of L
+ 
+
+ align:start position:0%
+okay so now let's take that value of L
+plug it back into the potential and set
+
+ align:start position:0%
+plug it back into the potential and set
+ 
+
+ align:start position:0%
+plug it back into the potential and set
+e equal to the square root of that okay
+
+ align:start position:0%
+e equal to the square root of that okay
+ 
+
+ align:start position:0%
+e equal to the square root of that okay
+a little bit of algebra ensues and what
+
+ align:start position:0%
+a little bit of algebra ensues and what
+ 
+
+ align:start position:0%
+a little bit of algebra ensues and what
+you find set this equals 1 minus 2 GM
+
+ align:start position:0%
+you find set this equals 1 minus 2 GM
+ 
+
+ align:start position:0%
+you find set this equals 1 minus 2 GM
+over R over again that factor under a
+
+ align:start position:0%
+over R over again that factor under a
+ 
+
+ align:start position:0%
+over R over again that factor under a
+square root of 1 minus 3 GM over R again
+
+ align:start position:0%
+square root of 1 minus 3 GM over R again
+ 
+
+ align:start position:0%
+square root of 1 minus 3 GM over R again
+we sort of see something a little bit
+
+ align:start position:0%
+we sort of see something a little bit
+ 
+
+ align:start position:0%
+we sort of see something a little bit
+pathological happening as R goes to 3 GM
+
+ align:start position:0%
+pathological happening as R goes to 3 GM
+ 
+
+ align:start position:0%
+pathological happening as R goes to 3 GM
+let me make two comments about this so
+
+ align:start position:0%
+let me make two comments about this so
+ 
+
+ align:start position:0%
+let me make two comments about this so
+first of all notice that this energy it
+
+ align:start position:0%
+first of all notice that this energy it
+ 
+
+ align:start position:0%
+first of all notice that this energy it
+is smaller than what I can intuitively
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+you can sort of imagine remember a hat
+
+ align:start position:0%
+you can sort of imagine remember a hat
+ 
+
+ align:start position:0%
+you can sort of imagine remember a hat
+is the energy per unit rest mass you can
+
+ align:start position:0%
+is the energy per unit rest mass you can
+ 
+
+ align:start position:0%
+is the energy per unit rest mass you can
+think of this as something like total
+
+ align:start position:0%
+think of this as something like total
+ 
+
+ align:start position:0%
+think of this as something like total
+energy over m so the or energy associate
+
+ align:start position:0%
+energy over m so the or energy associate
+ 
+
+ align:start position:0%
+energy over m so the or energy associate
+the orbiting body it's got a rest energy
+
+ align:start position:0%
+the orbiting body it's got a rest energy
+ 
+
+ align:start position:0%
+the orbiting body it's got a rest energy
+a kinetic energy and a potential energy
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+divided by M swarn orbit to be bound
+
+ align:start position:0%
+divided by M swarn orbit to be bound
+ 
+
+ align:start position:0%
+divided by M swarn orbit to be bound
+it's a potential energy which is- must
+
+ align:start position:0%
+it's a potential energy which is- must
+ 
+
+ align:start position:0%
+it's a potential energy which is- must
+have larger magnitude than the kinetic
+
+ align:start position:0%
+have larger magnitude than the kinetic
+ 
+
+ align:start position:0%
+have larger magnitude than the kinetic
+energy okay so for a bound orbit a
+
+ align:start position:0%
+energy okay so for a bound orbit a
+ 
+
+ align:start position:0%
+energy okay so for a bound orbit a
+kinetic plus potential will be a
+
+ align:start position:0%
+kinetic plus potential will be a
+ 
+
+ align:start position:0%
+kinetic plus potential will be a
+negative quantity so the numerator is
+
+ align:start position:0%
+negative quantity so the numerator is
+ 
+
+ align:start position:0%
+negative quantity so the numerator is
+going to be something that when
+
+ align:start position:0%
+going to be something that when
+ 
+
+ align:start position:0%
+going to be something that when
+normalized to M is less than 1 so this
+
+ align:start position:0%
+normalized to M is less than 1 so this
+ 
+
+ align:start position:0%
+normalized to M is less than 1 so this
+is exactly what we expect student or
+
+ align:start position:0%
+is exactly what we expect student or
+ 
+
+ align:start position:0%
+is exactly what we expect student or
+'but notice also so if you take this
+
+ align:start position:0%
+'but notice also so if you take this
+ 
+
+ align:start position:0%
+'but notice also so if you take this
+formula and look at
+
+ align:start position:0%
+formula and look at
+ 
+
+ align:start position:0%
+formula and look at
+and the large our limit it goes to 1
+
+ align:start position:0%
+and the large our limit it goes to 1
+ 
+
+ align:start position:0%
+and the large our limit it goes to 1
+minus GM over 2r this is in fact exactly
+
+ align:start position:0%
+minus GM over 2r this is in fact exactly
+ 
+
+ align:start position:0%
+minus GM over 2r this is in fact exactly
+what you get when you look at the energy
+
+ align:start position:0%
+what you get when you look at the energy
+ 
+
+ align:start position:0%
+what you get when you look at the energy
+per unit mass throwing in you know just
+
+ align:start position:0%
+per unit mass throwing in you know just
+ 
+
+ align:start position:0%
+per unit mass throwing in you know just
+sort of by hand a rest mass the minus GM
+
+ align:start position:0%
+sort of by hand a rest mass the minus GM
+ 
+
+ align:start position:0%
+sort of by hand a rest mass the minus GM
+over 2r exactly corresponds to kinetic
+
+ align:start position:0%
+over 2r exactly corresponds to kinetic
+ 
+
+ align:start position:0%
+over 2r exactly corresponds to kinetic
+plus potential for a Newtonian circular
+
+ align:start position:0%
+plus potential for a Newtonian circular
+ 
+
+ align:start position:0%
+plus potential for a Newtonian circular
+orbit so lots of stuff is hanging
+
+ align:start position:0%
+orbit so lots of stuff is hanging
+ 
+
+ align:start position:0%
+orbit so lots of stuff is hanging
+together nicely so we've just learned
+
+ align:start position:0%
+together nicely so we've just learned
+ 
+
+ align:start position:0%
+together nicely so we've just learned
+that we can characterize the energy and
+
+ align:start position:0%
+that we can characterize the energy and
+ 
+
+ align:start position:0%
+that we can characterize the energy and
+annual angular momentum of circular
+
+ align:start position:0%
+annual angular momentum of circular
+ 
+
+ align:start position:0%
+annual angular momentum of circular
+orbits around my black hole let's look
+
+ align:start position:0%
+orbits around my black hole let's look
+ 
+
+ align:start position:0%
+orbits around my black hole let's look
+at a couple other things associated this
+
+ align:start position:0%
+at a couple other things associated this
+ 
+
+ align:start position:0%
+at a couple other things associated this
+so these plots where I look at the
+
+ align:start position:0%
+so these plots where I look at the
+ 
+
+ align:start position:0%
+so these plots where I look at the
+radial motion in this effective
+
+ align:start position:0%
+radial motion in this effective
+ 
+
+ align:start position:0%
+radial motion in this effective
+potential as I mentioned a few moments
+
+ align:start position:0%
+potential as I mentioned a few moments
+ 
+
+ align:start position:0%
+potential as I mentioned a few moments
+ago there's additional sort of degrees
+
+ align:start position:0%
+ago there's additional sort of degrees
+ 
+
+ align:start position:0%
+ago there's additional sort of degrees
+of freedom in the motion that are being
+
+ align:start position:0%
+of freedom in the motion that are being
+ 
+
+ align:start position:0%
+of freedom in the motion that are being
+suppressed here right so this thing is
+
+ align:start position:0%
+suppressed here right so this thing is
+ 
+
+ align:start position:0%
+suppressed here right so this thing is
+also moving in in that plane it's
+
+ align:start position:0%
+also moving in in that plane it's
+ 
+
+ align:start position:0%
+also moving in in that plane it's
+whirling around with respect to Phi
+
+ align:start position:0%
+whirling around with respect to Phi
+ 
+
+ align:start position:0%
+whirling around with respect to Phi
+we've lost that information in the way
+
+ align:start position:0%
+we've lost that information in the way
+ 
+
+ align:start position:0%
+we've lost that information in the way
+we've drawn this here let's define Omega
+
+ align:start position:0%
+we've drawn this here let's define Omega
+ 
+
+ align:start position:0%
+we've drawn this here let's define Omega
+to be the angular velocity of this orbit
+
+ align:start position:0%
+to be the angular velocity of this orbit
+ 
+
+ align:start position:0%
+to be the angular velocity of this orbit
+as seen by a distant observer
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay why am i doing it as seen by a
+
+ align:start position:0%
+okay why am i doing it as seen by a
+ 
+
+ align:start position:0%
+okay why am i doing it as seen by a
+distant observer well when things orbit
+
+ align:start position:0%
+distant observer well when things orbit
+ 
+
+ align:start position:0%
+distant observer well when things orbit
+there tends to be periodicity 'z that
+
+ align:start position:0%
+there tends to be periodicity 'z that
+ 
+
+ align:start position:0%
+there tends to be periodicity 'z that
+imprint themselves on observables it
+
+ align:start position:0%
+imprint themselves on observables it
+ 
+
+ align:start position:0%
+imprint themselves on observables it
+could be the period associate with the
+
+ align:start position:0%
+could be the period associate with the
+ 
+
+ align:start position:0%
+could be the period associate with the
+gravitational wave that rises out of
+
+ align:start position:0%
+gravitational wave that rises out of
+ 
+
+ align:start position:0%
+gravitational wave that rises out of
+this it could be the period associated
+
+ align:start position:0%
+this it could be the period associated
+ 
+
+ align:start position:0%
+this it could be the period associated
+with peaks and a light curve if this is
+
+ align:start position:0%
+with peaks and a light curve if this is
+ 
+
+ align:start position:0%
+with peaks and a light curve if this is
+a star orbiting around a black hole it
+
+ align:start position:0%
+a star orbiting around a black hole it
+ 
+
+ align:start position:0%
+a star orbiting around a black hole it
+could be oscillations in the x-ray flux
+
+ align:start position:0%
+could be oscillations in the x-ray flux
+ 
+
+ align:start position:0%
+could be oscillations in the x-ray flux
+if this is some kind of a lump in an
+
+ align:start position:0%
+if this is some kind of a lump in an
+ 
+
+ align:start position:0%
+if this is some kind of a lump in an
+accretion disk of material orbiting a
+
+ align:start position:0%
+accretion disk of material orbiting a
+ 
+
+ align:start position:0%
+accretion disk of material orbiting a
+black hole so if this is the angular
+
+ align:start position:0%
+black hole so if this is the angular
+ 
+
+ align:start position:0%
+black hole so if this is the angular
+velocity is seen by distant observers
+
+ align:start position:0%
+velocity is seen by distant observers
+ 
+
+ align:start position:0%
+velocity is seen by distant observers
+remember the time that distant observers
+
+ align:start position:0%
+remember the time that distant observers
+ 
+
+ align:start position:0%
+remember the time that distant observers
+use to the time in which the dissin
+
+ align:start position:0%
+use to the time in which the dissin
+ 
+
+ align:start position:0%
+use to the time in which the dissin
+observers clocks run is the Swart shield
+
+ align:start position:0%
+observers clocks run is the Swart shield
+ 
+
+ align:start position:0%
+observers clocks run is the Swart shield
+time T so this will be D Phi DT which I
+
+ align:start position:0%
+time T so this will be D Phi DT which I
+ 
+
+ align:start position:0%
+time T so this will be D Phi DT which I
+can write as D Phi D tau this is the
+
+ align:start position:0%
+can write as D Phi D tau this is the
+ 
+
+ align:start position:0%
+can write as D Phi D tau this is the
+angular velocity according to the orbit
+
+ align:start position:0%
+angular velocity according to the orbit
+ 
+
+ align:start position:0%
+angular velocity according to the orbit
+itself normalized to DT D tau now these
+
+ align:start position:0%
+itself normalized to DT D tau now these
+ 
+
+ align:start position:0%
+itself normalized to DT D tau now these
+are both quantities that are simply
+
+ align:start position:0%
+are both quantities that are simply
+ 
+
+ align:start position:0%
+are both quantities that are simply
+related to constants of the motion
+
+ align:start position:0%
+related to constants of the motion
+ 
+
+ align:start position:0%
+related to constants of the motion
+what I've got in the numerator here is L
+
+ align:start position:0%
+what I've got in the numerator here is L
+ 
+
+ align:start position:0%
+what I've got in the numerator here is L
+hat over R squared and what I've got in
+
+ align:start position:0%
+hat over R squared and what I've got in
+ 
+
+ align:start position:0%
+hat over R squared and what I've got in
+the denominator here is P hat over 1 - I
+
+ align:start position:0%
+the denominator here is P hat over 1 - I
+ 
+
+ align:start position:0%
+the denominator here is P hat over 1 - I
+dropped my G 1 - 2 GM over R so let's go
+
+ align:start position:0%
+dropped my G 1 - 2 GM over R so let's go
+ 
+
+ align:start position:0%
+dropped my G 1 - 2 GM over R so let's go
+ahead and take our solution here my hat
+
+ align:start position:0%
+ahead and take our solution here my hat
+ 
+
+ align:start position:0%
+ahead and take our solution here my hat
+is 1 - 2 GM over R divided by a square
+
+ align:start position:0%
+is 1 - 2 GM over R divided by a square
+ 
+
+ align:start position:0%
+is 1 - 2 GM over R divided by a square
+root of blah blah blah
+
+ align:start position:0%
+root of blah blah blah
+ 
+
+ align:start position:0%
+root of blah blah blah
+the 1 - 2 GM over R cancels my L hat is
+
+ align:start position:0%
+the 1 - 2 GM over R cancels my L hat is
+ 
+
+ align:start position:0%
+the 1 - 2 GM over R cancels my L hat is
+square root GM R divided by again that
+
+ align:start position:0%
+square root GM R divided by again that
+ 
+
+ align:start position:0%
+square root GM R divided by again that
+square root 1 - 3 GM over R notice the
+
+ align:start position:0%
+square root 1 - 3 GM over R notice the
+ 
+
+ align:start position:0%
+square root 1 - 3 GM over R notice the
+square root 1 - 3 GM over R factors all
+
+ align:start position:0%
+square root 1 - 3 GM over R factors all
+ 
+
+ align:start position:0%
+square root 1 - 3 GM over R factors all
+cancel so this becomes plus or minus
+
+ align:start position:0%
+cancel so this becomes plus or minus
+ 
+
+ align:start position:0%
+cancel so this becomes plus or minus
+one over R squared square root GMR looks
+
+ align:start position:0%
+one over R squared square root GMR looks
+ 
+
+ align:start position:0%
+one over R squared square root GMR looks
+like this plus and minus basically just
+
+ align:start position:0%
+like this plus and minus basically just
+ 
+
+ align:start position:0%
+like this plus and minus basically just
+cha respond to whether this motion sort
+
+ align:start position:0%
+cha respond to whether this motion sort
+ 
+
+ align:start position:0%
+cha respond to whether this motion sort
+of is going in the same sense as your
+
+ align:start position:0%
+of is going in the same sense as your
+ 
+
+ align:start position:0%
+of is going in the same sense as your
+Phi coordinate or in the opposite sense
+
+ align:start position:0%
+Phi coordinate or in the opposite sense
+ 
+
+ align:start position:0%
+Phi coordinate or in the opposite sense
+okay there's really no physics than that
+
+ align:start position:0%
+okay there's really no physics than that
+ 
+
+ align:start position:0%
+okay there's really no physics than that
+it's just comes along for the ride that
+
+ align:start position:0%
+it's just comes along for the ride that
+ 
+
+ align:start position:0%
+it's just comes along for the ride that
+both behave the same if you guys get
+
+ align:start position:0%
+both behave the same if you guys get
+ 
+
+ align:start position:0%
+both behave the same if you guys get
+interested in this and you do a similar
+
+ align:start position:0%
+interested in this and you do a similar
+ 
+
+ align:start position:0%
+interested in this and you do a similar
+calculation around a car black hole
+
+ align:start position:0%
+calculation around a car black hole
+ 
+
+ align:start position:0%
+calculation around a car black hole
+you'll find that your pro-grade solution
+
+ align:start position:0%
+you'll find that your pro-grade solution
+ 
+
+ align:start position:0%
+you'll find that your pro-grade solution
+gives you a different frequency than
+
+ align:start position:0%
+gives you a different frequency than
+ 
+
+ align:start position:0%
+gives you a different frequency than
+your a retrograde solution because of
+
+ align:start position:0%
+your a retrograde solution because of
+ 
+
+ align:start position:0%
+your a retrograde solution because of
+the fact that the dragging of inertial
+
+ align:start position:0%
+the fact that the dragging of inertial
+ 
+
+ align:start position:0%
+the fact that the dragging of inertial
+frames due to the spin of the black hole
+
+ align:start position:0%
+frames due to the spin of the black hole
+ 
+
+ align:start position:0%
+frames due to the spin of the black hole
+kind of breaks that symmetry so any
+
+ align:start position:0%
+kind of breaks that symmetry so any
+ 
+
+ align:start position:0%
+kind of breaks that symmetry so any
+which is interesting and well I'll make
+
+ align:start position:0%
+which is interesting and well I'll make
+ 
+
+ align:start position:0%
+which is interesting and well I'll make
+a comment about this in just a second
+
+ align:start position:0%
+a comment about this in just a second
+ 
+
+ align:start position:0%
+a comment about this in just a second
+which is kind of interesting and here's
+
+ align:start position:0%
+which is kind of interesting and here's
+ 
+
+ align:start position:0%
+which is kind of interesting and here's
+what I'll say sometimes people think
+
+ align:start position:0%
+what I'll say sometimes people think
+ 
+
+ align:start position:0%
+what I'll say sometimes people think
+this is more profound than it should be
+
+ align:start position:0%
+this is more profound than it should be
+ 
+
+ align:start position:0%
+this is more profound than it should be
+is this is in fact exactly the same
+
+ align:start position:0%
+is this is in fact exactly the same
+ 
+
+ align:start position:0%
+is this is in fact exactly the same
+frequency law that you get using
+
+ align:start position:0%
+frequency law that you get using
+ 
+
+ align:start position:0%
+frequency law that you get using
+Newtonian gravity this is actually
+
+ align:start position:0%
+Newtonian gravity this is actually
+ 
+
+ align:start position:0%
+Newtonian gravity this is actually
+exactly the same as Kepler's law
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that seems really really cool and it is
+
+ align:start position:0%
+that seems really really cool and it is
+ 
+
+ align:start position:0%
+that seems really really cool and it is
+it's actually really useful it makes it
+
+ align:start position:0%
+it's actually really useful it makes it
+ 
+
+ align:start position:0%
+it's actually really useful it makes it
+very easy to remember this ah but don't
+
+ align:start position:0%
+very easy to remember this ah but don't
+ 
+
+ align:start position:0%
+very easy to remember this ah but don't
+read too much into it okay it is more
+
+ align:start position:0%
+read too much into it okay it is more
+ 
+
+ align:start position:0%
+read too much into it okay it is more
+than anything it is a statement about a
+
+ align:start position:0%
+than anything it is a statement about a
+ 
+
+ align:start position:0%
+than anything it is a statement about a
+particular quality of this radial
+
+ align:start position:0%
+particular quality of this radial
+ 
+
+ align:start position:0%
+particular quality of this radial
+coordinate so remember and Newtonian
+
+ align:start position:0%
+coordinate so remember and Newtonian
+ 
+
+ align:start position:0%
+coordinate so remember and Newtonian
+gravity are tells me the distance
+
+ align:start position:0%
+gravity are tells me the distance
+ 
+
+ align:start position:0%
+gravity are tells me the distance
+between if I have an orbit at r1 and an
+
+ align:start position:0%
+between if I have an orbit at r1 and an
+ 
+
+ align:start position:0%
+between if I have an orbit at r1 and an
+orbit at r2 then I know that the
+
+ align:start position:0%
+orbit at r2 then I know that the
+ 
+
+ align:start position:0%
+orbit at r2 then I know that the
+distance between them is R two minus R
+
+ align:start position:0%
+distance between them is R two minus R
+ 
+
+ align:start position:0%
+distance between them is R two minus R
+one in the Schwarzschild space-time the
+
+ align:start position:0%
+one in the Schwarzschild space-time the
+ 
+
+ align:start position:0%
+one in the Schwarzschild space-time the
+distance between these two orbits is not
+
+ align:start position:0%
+distance between these two orbits is not
+ 
+
+ align:start position:0%
+distance between these two orbits is not
+r2 minus r1 however our two labels a
+
+ align:start position:0%
+r2 minus r1 however our two labels a
+ 
+
+ align:start position:0%
+r2 minus r1 however our two labels a
+sphere of surface area for pie r2
+
+ align:start position:0%
+sphere of surface area for pie r2
+ 
+
+ align:start position:0%
+sphere of surface area for pie r2
+squared + r1 labels a sphere of surface
+
+ align:start position:0%
+squared + r1 labels a sphere of surface
+ 
+
+ align:start position:0%
+squared + r1 labels a sphere of surface
+area for pie r1 squared it's easy to
+
+ align:start position:0%
+area for pie r1 squared it's easy to
+ 
+
+ align:start position:0%
+area for pie r1 squared it's easy to
+also show that the circumference of the
+
+ align:start position:0%
+also show that the circumference of the
+ 
+
+ align:start position:0%
+also show that the circumference of the
+orbit at r2 is 2 PI R 2 the
+
+ align:start position:0%
+orbit at r2 is 2 PI R 2 the
+ 
+
+ align:start position:0%
+orbit at r2 is 2 PI R 2 the
+circumference of the orbit at r1 is 2 pi
+
+ align:start position:0%
+circumference of the orbit at r1 is 2 pi
+ 
+
+ align:start position:0%
+circumference of the orbit at r1 is 2 pi
+r1 that more than anything is why we end
+
+ align:start position:0%
+r1 that more than anything is why we end
+ 
+
+ align:start position:0%
+r1 that more than anything is why we end
+up reproducing Kepler's law here is that
+
+ align:start position:0%
+up reproducing Kepler's law here is that
+ 
+
+ align:start position:0%
+up reproducing Kepler's law here is that
+this aerial coordinate is nicely
+
+ align:start position:0%
+this aerial coordinate is nicely
+ 
+
+ align:start position:0%
+this aerial coordinate is nicely
+amenable to this interpretation so is
+
+ align:start position:0%
+amenable to this interpretation so is
+ 
+
+ align:start position:0%
+amenable to this interpretation so is
+this orbit so I described over here an
+
+ align:start position:0%
+this orbit so I described over here an
+ 
+
+ align:start position:0%
+this orbit so I described over here an
+orbit that is unstable in an orbit that
+
+ align:start position:0%
+orbit that is unstable in an orbit that
+ 
+
+ align:start position:0%
+orbit that is unstable in an orbit that
+is stable I have described how to
+
+ align:start position:0%
+is stable I have described how to
+ 
+
+ align:start position:0%
+is stable I have described how to
+compute if I want to find a circular
+
+ align:start position:0%
+compute if I want to find a circular
+ 
+
+ align:start position:0%
+compute if I want to find a circular
+orbit at a given radius those formulas
+
+ align:start position:0%
+orbit at a given radius those formulas
+ 
+
+ align:start position:0%
+orbit at a given radius those formulas
+that I derived over there on the right
+
+ align:start position:0%
+that I derived over there on the right
+ 
+
+ align:start position:0%
+that I derived over there on the right
+most blackboards they tell me what the
+
+ align:start position:0%
+most blackboards they tell me what the
+ 
+
+ align:start position:0%
+most blackboards they tell me what the
+energy and the annual annual momentum
+
+ align:start position:0%
+energy and the annual annual momentum
+ 
+
+ align:start position:0%
+energy and the annual annual momentum
+needs to be as a function of R is that
+
+ align:start position:0%
+needs to be as a function of R is that
+ 
+
+ align:start position:0%
+needs to be as a function of R is that
+orbit stable well if it is I can check
+
+ align:start position:0%
+orbit stable well if it is I can check
+ 
+
+ align:start position:0%
+orbit stable well if it is I can check
+that by computing the second derivative
+
+ align:start position:0%
+that by computing the second derivative
+ 
+
+ align:start position:0%
+that by computing the second derivative
+of my effective potential
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so my orbits are stable if the second
+
+ align:start position:0%
+so my orbits are stable if the second
+ 
+
+ align:start position:0%
+so my orbits are stable if the second
+derivative with respect to R is greater
+
+ align:start position:0%
+derivative with respect to R is greater
+ 
+
+ align:start position:0%
+derivative with respect to R is greater
+than zero unstable if this turns out to
+
+ align:start position:0%
+than zero unstable if this turns out to
+ 
+
+ align:start position:0%
+than zero unstable if this turns out to
+be negative let's look at the crossover
+
+ align:start position:0%
+be negative let's look at the crossover
+ 
+
+ align:start position:0%
+be negative let's look at the crossover
+point from one to the other what if
+
+ align:start position:0%
+point from one to the other what if
+ 
+
+ align:start position:0%
+point from one to the other what if
+there is a radius where in fact the
+
+ align:start position:0%
+there is a radius where in fact the
+ 
+
+ align:start position:0%
+there is a radius where in fact the
+stable and the unstable orbits coincide
+
+ align:start position:0%
+stable and the unstable orbits coincide
+ 
+
+ align:start position:0%
+stable and the unstable orbits coincide
+in fact what winds finds if you look at
+
+ align:start position:0%
+in fact what winds finds if you look at
+ 
+
+ align:start position:0%
+in fact what winds finds if you look at
+the effective potential you imagine just
+
+ align:start position:0%
+the effective potential you imagine just
+ 
+
+ align:start position:0%
+the effective potential you imagine just
+sort of playing with L sub Z okay so
+
+ align:start position:0%
+sort of playing with L sub Z okay so
+ 
+
+ align:start position:0%
+sort of playing with L sub Z okay so
+let's say we take that L sub C and we
+
+ align:start position:0%
+let's say we take that L sub C and we
+ 
+
+ align:start position:0%
+let's say we take that L sub C and we
+just explore it for lots of different
+
+ align:start position:0%
+just explore it for lots of different
+ 
+
+ align:start position:0%
+just explore it for lots of different
+radii of the orbits you find that as the
+
+ align:start position:0%
+radii of the orbits you find that as the
+ 
+
+ align:start position:0%
+radii of the orbits you find that as the
+orbits radius gets smaller and smaller
+
+ align:start position:0%
+orbits radius gets smaller and smaller
+ 
+
+ align:start position:0%
+orbits radius gets smaller and smaller
+your stable orbit tends to go up and
+
+ align:start position:0%
+your stable orbit tends to go up and
+ 
+
+ align:start position:0%
+your stable orbit tends to go up and
+this minimum sort of becomes flatter and
+
+ align:start position:0%
+this minimum sort of becomes flatter and
+ 
+
+ align:start position:0%
+this minimum sort of becomes flatter and
+your unstable orbits on it comes down
+
+ align:start position:0%
+your unstable orbits on it comes down
+ 
+
+ align:start position:0%
+your unstable orbits on it comes down
+they sort of approach one another there
+
+ align:start position:0%
+they sort of approach one another there
+ 
+
+ align:start position:0%
+they sort of approach one another there
+is a point just when they coincide they
+
+ align:start position:0%
+is a point just when they coincide they
+ 
+
+ align:start position:0%
+is a point just when they coincide they
+should have an effective on it my
+
+ align:start position:0%
+should have an effective on it my
+ 
+
+ align:start position:0%
+should have an effective on it my
+apologies
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+right when they coincide this defines
+
+ align:start position:0%
+right when they coincide this defines
+ 
+
+ align:start position:0%
+right when they coincide this defines
+what we call the marginally stable orbit
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay I may have put this on a problem
+
+ align:start position:0%
+okay I may have put this on a problem
+ 
+
+ align:start position:0%
+okay I may have put this on a problem
+set but it might be one of the ones I
+
+ align:start position:0%
+set but it might be one of the ones I
+ 
+
+ align:start position:0%
+set but it might be one of the ones I
+say to drop so I'm just gonna go ahead
+
+ align:start position:0%
+say to drop so I'm just gonna go ahead
+ 
+
+ align:start position:0%
+say to drop so I'm just gonna go ahead
+and do the analysis when you compute
+
+ align:start position:0%
+and do the analysis when you compute
+ 
+
+ align:start position:0%
+and do the analysis when you compute
+this bearing in mind that your angular
+
+ align:start position:0%
+this bearing in mind that your angular
+ 
+
+ align:start position:0%
+this bearing in mind that your angular
+momentum is a constant so take this
+
+ align:start position:0%
+momentum is a constant so take this
+ 
+
+ align:start position:0%
+momentum is a constant so take this
+substitute in now your solution for L
+
+ align:start position:0%
+substitute in now your solution for L
+ 
+
+ align:start position:0%
+substitute in now your solution for L
+sub Z which I've written down over there
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+what you find is that the marginally
+
+ align:start position:0%
+what you find is that the marginally
+ 
+
+ align:start position:0%
+what you find is that the marginally
+stable orbit let's call it R sub M s it
+
+ align:start position:0%
+stable orbit let's call it R sub M s it
+ 
+
+ align:start position:0%
+stable orbit let's call it R sub M s it
+is located at a radius of 6 GM this is a
+
+ align:start position:0%
+is located at a radius of 6 GM this is a
+ 
+
+ align:start position:0%
+is located at a radius of 6 GM this is a
+profoundly new behavior that doesn't
+
+ align:start position:0%
+profoundly new behavior that doesn't
+ 
+
+ align:start position:0%
+profoundly new behavior that doesn't
+even come close to existing in Newtonian
+
+ align:start position:0%
+even come close to existing in Newtonian
+ 
+
+ align:start position:0%
+even come close to existing in Newtonian
+space lines doesn't come close to
+
+ align:start position:0%
+space lines doesn't come close to
+ 
+
+ align:start position:0%
+space lines doesn't come close to
+existing in Newtonian gravity excuse me
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the message I want you to understand is
+
+ align:start position:0%
+the message I want you to understand is
+ 
+
+ align:start position:0%
+the message I want you to understand is
+that what this tells us is that no
+
+ align:start position:0%
+that what this tells us is that no
+ 
+
+ align:start position:0%
+that what this tells us is that no
+stable circular orbits exists inside our
+
+ align:start position:0%
+stable circular orbits exists inside our
+ 
+
+ align:start position:0%
+stable circular orbits exists inside our
+equals
+
+ align:start position:0%
+equals
+ 
+
+ align:start position:0%
+equals
+6g so this is very very different
+
+ align:start position:0%
+6g so this is very very different
+ 
+
+ align:start position:0%
+6g so this is very very different
+behavior okay if I have and let's just
+
+ align:start position:0%
+behavior okay if I have and let's just
+ 
+
+ align:start position:0%
+behavior okay if I have and let's just
+say I have a very compact body but
+
+ align:start position:0%
+say I have a very compact body but
+ 
+
+ align:start position:0%
+say I have a very compact body but
+Newtonian gravity rules I can make
+
+ align:start position:0%
+Newtonian gravity rules I can make
+ 
+
+ align:start position:0%
+Newtonian gravity rules I can make
+circular orbits around it's basically go
+
+ align:start position:0%
+circular orbits around it's basically go
+ 
+
+ align:start position:0%
+circular orbits around it's basically go
+all the way down until they essentially
+
+ align:start position:0%
+all the way down until they essentially
+ 
+
+ align:start position:0%
+all the way down until they essentially
+touch the surface of that body and you
+
+ align:start position:0%
+touch the surface of that body and you
+ 
+
+ align:start position:0%
+touch the surface of that body and you
+might think based on this that you would
+
+ align:start position:0%
+might think based on this that you would
+ 
+
+ align:start position:0%
+might think based on this that you would
+want to make orbits that basically go
+
+ align:start position:0%
+want to make orbits that basically go
+ 
+
+ align:start position:0%
+want to make orbits that basically go
+all the way down that sort of kiss the
+
+ align:start position:0%
+all the way down that sort of kiss the
+ 
+
+ align:start position:0%
+all the way down that sort of kiss the
+edge of our equals to G M well this is
+
+ align:start position:0%
+edge of our equals to G M well this is
+ 
+
+ align:start position:0%
+edge of our equals to G M well this is
+telling you you can't do that when you
+
+ align:start position:0%
+telling you you can't do that when you
+ 
+
+ align:start position:0%
+telling you you can't do that when you
+get when you start trying to make orbits
+
+ align:start position:0%
+get when you start trying to make orbits
+ 
+
+ align:start position:0%
+get when you start trying to make orbits
+that go inside at least circulars that
+
+ align:start position:0%
+that go inside at least circulars that
+ 
+
+ align:start position:0%
+that go inside at least circulars that
+go inside 6gm they're not stable
+
+ align:start position:0%
+go inside 6gm they're not stable
+ 
+
+ align:start position:0%
+go inside 6gm they're not stable
+if someone sneezes on them they either
+
+ align:start position:0%
+if someone sneezes on them they either
+ 
+
+ align:start position:0%
+if someone sneezes on them they either
+are sort of blown out to infinity or
+
+ align:start position:0%
+are sort of blown out to infinity or
+ 
+
+ align:start position:0%
+are sort of blown out to infinity or
+they fall into the event horizon and in
+
+ align:start position:0%
+they fall into the event horizon and in
+ 
+
+ align:start position:0%
+they fall into the event horizon and in
+fact one of the consequences of this is
+
+ align:start position:0%
+fact one of the consequences of this is
+ 
+
+ align:start position:0%
+fact one of the consequences of this is
+that in Astrophysical systems we
+
+ align:start position:0%
+that in Astrophysical systems we
+ 
+
+ align:start position:0%
+that in Astrophysical systems we
+generically expect there to be kind of
+
+ align:start position:0%
+generically expect there to be kind of
+ 
+
+ align:start position:0%
+generically expect there to be kind of
+if you imagine material falling into a
+
+ align:start position:0%
+if you imagine material falling into a
+ 
+
+ align:start position:0%
+if you imagine material falling into a
+black hole imagine that there's like a
+
+ align:start position:0%
+black hole imagine that there's like a
+ 
+
+ align:start position:0%
+black hole imagine that there's like a
+star or something dumping gas into orbit
+
+ align:start position:0%
+star or something dumping gas into orbit
+ 
+
+ align:start position:0%
+star or something dumping gas into orbit
+around the black hole well it will tend
+
+ align:start position:0%
+around the black hole well it will tend
+ 
+
+ align:start position:0%
+around the black hole well it will tend
+to form a disk that orbits around this
+
+ align:start position:0%
+to form a disk that orbits around this
+ 
+
+ align:start position:0%
+to form a disk that orbits around this
+thing and the elements of the disk are
+
+ align:start position:0%
+thing and the elements of the disk are
+ 
+
+ align:start position:0%
+thing and the elements of the disk are
+always rubbing against each other and
+
+ align:start position:0%
+always rubbing against each other and
+ 
+
+ align:start position:0%
+always rubbing against each other and
+radiating that makes them get hot they
+
+ align:start position:0%
+radiating that makes them get hot they
+ 
+
+ align:start position:0%
+radiating that makes them get hot they
+lose energy because of this radiation
+
+ align:start position:0%
+lose energy because of this radiation
+ 
+
+ align:start position:0%
+lose energy because of this radiation
+and so they will very slowly sort of
+
+ align:start position:0%
+and so they will very slowly sort of
+ 
+
+ align:start position:0%
+and so they will very slowly sort of
+fall in but they make this kind of it's
+
+ align:start position:0%
+fall in but they make this kind of it's
+ 
+
+ align:start position:0%
+fall in but they make this kind of it's
+thought that in most cases that will
+
+ align:start position:0%
+thought that in most cases that will
+ 
+
+ align:start position:0%
+thought that in most cases that will
+make this kind of thick desk that fills
+
+ align:start position:0%
+make this kind of thick desk that fills
+ 
+
+ align:start position:0%
+make this kind of thick desk that fills
+much of the space-time surrounding the
+
+ align:start position:0%
+much of the space-time surrounding the
+ 
+
+ align:start position:0%
+much of the space-time surrounding the
+black hole but there'll be a hole in the
+
+ align:start position:0%
+black hole but there'll be a hole in the
+ 
+
+ align:start position:0%
+black hole but there'll be a hole in the
+center not just because the thing is a
+
+ align:start position:0%
+center not just because the thing is a
+ 
+
+ align:start position:0%
+center not just because the thing is a
+black hole okay I don't mean that kind
+
+ align:start position:0%
+black hole okay I don't mean that kind
+ 
+
+ align:start position:0%
+black hole okay I don't mean that kind
+of a hole though actually be something
+
+ align:start position:0%
+of a hole though actually be something
+ 
+
+ align:start position:0%
+of a hole though actually be something
+surrounding the black hole's event
+
+ align:start position:0%
+surrounding the black hole's event
+ 
+
+ align:start position:0%
+surrounding the black hole's event
+horizon because there are no stable
+
+ align:start position:0%
+horizon because there are no stable
+ 
+
+ align:start position:0%
+horizon because there are no stable
+circular orbits once the material comes
+
+ align:start position:0%
+circular orbits once the material comes
+ 
+
+ align:start position:0%
+circular orbits once the material comes
+in and hits this this particular radius
+
+ align:start position:0%
+in and hits this this particular radius
+ 
+
+ align:start position:0%
+in and hits this this particular radius
+6gm in the short Shield case it very
+
+ align:start position:0%
+6gm in the short Shield case it very
+ 
+
+ align:start position:0%
+6gm in the short Shield case it very
+rapidly falls in reach
+
+ align:start position:0%
+rapidly falls in reach
+ 
+
+ align:start position:0%
+rapidly falls in reach
+is the density of that material
+
+ align:start position:0%
+is the density of that material
+ 
+
+ align:start position:0%
+is the density of that material
+tremendously and you get this much
+
+ align:start position:0%
+tremendously and you get this much
+ 
+
+ align:start position:0%
+tremendously and you get this much
+thinner region of the disk where
+
+ align:start position:0%
+thinner region of the disk where
+ 
+
+ align:start position:0%
+thinner region of the disk where
+essentially things fall in practically
+
+ align:start position:0%
+essentially things fall in practically
+ 
+
+ align:start position:0%
+essentially things fall in practically
+instantly it shouldn't be noted that
+
+ align:start position:0%
+instantly it shouldn't be noted that
+ 
+
+ align:start position:0%
+instantly it shouldn't be noted that
+this 6gm is of course only four Schwartz
+
+ align:start position:0%
+this 6gm is of course only four Schwartz
+ 
+
+ align:start position:0%
+this 6gm is of course only four Schwartz
+yield if you talk about kur you actually
+
+ align:start position:0%
+yield if you talk about kur you actually
+ 
+
+ align:start position:0%
+yield if you talk about kur you actually
+have two different radii corresponding
+
+ align:start position:0%
+have two different radii corresponding
+ 
+
+ align:start position:0%
+have two different radii corresponding
+to material that goes around parallel to
+
+ align:start position:0%
+to material that goes around parallel to
+ 
+
+ align:start position:0%
+to material that goes around parallel to
+the black hole's spin a material that
+
+ align:start position:0%
+the black hole's spin a material that
+ 
+
+ align:start position:0%
+the black hole's spin a material that
+goes anti parallel to the black hole
+
+ align:start position:0%
+goes anti parallel to the black hole
+ 
+
+ align:start position:0%
+goes anti parallel to the black hole
+spin
+
+ align:start position:0%
+spin
+ 
+
+ align:start position:0%
+spin
+okay and it complicates things somewhat
+
+ align:start position:0%
+okay and it complicates things somewhat
+ 
+
+ align:start position:0%
+okay and it complicates things somewhat
+there's two different radii there the
+
+ align:start position:0%
+there's two different radii there the
+ 
+
+ align:start position:0%
+there's two different radii there the
+one that goes parallel tends to get a
+
+ align:start position:0%
+one that goes parallel tends to get a
+ 
+
+ align:start position:0%
+one that goes parallel tends to get a
+little bit closer
+
+ align:start position:0%
+little bit closer
+ 
+
+ align:start position:0%
+little bit closer
+well it's anti parallel tends to go out
+
+ align:start position:0%
+well it's anti parallel tends to go out
+ 
+
+ align:start position:0%
+well it's anti parallel tends to go out
+a little bit farther but the general
+
+ align:start position:0%
+a little bit farther but the general
+ 
+
+ align:start position:0%
+a little bit farther but the general
+prediction that there's an innermost
+
+ align:start position:0%
+prediction that there's an innermost
+ 
+
+ align:start position:0%
+prediction that there's an innermost
+orbit beyond which stable orbits do not
+
+ align:start position:0%
+orbit beyond which stable orbits do not
+ 
+
+ align:start position:0%
+orbit beyond which stable orbits do not
+exist that's robust and holds across the
+
+ align:start position:0%
+exist that's robust and holds across the
+ 
+
+ align:start position:0%
+exist that's robust and holds across the
+domain of black holes so let me conclude
+
+ align:start position:0%
+domain of black holes so let me conclude
+ 
+
+ align:start position:0%
+domain of black holes so let me conclude
+by talking about one final category of
+
+ align:start position:0%
+by talking about one final category of
+ 
+
+ align:start position:0%
+by talking about one final category of
+orbits photonic orbits
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so let's recall that when we were
+
+ align:start position:0%
+so let's recall that when we were
+ 
+
+ align:start position:0%
+so let's recall that when we were
+talking about null geodesics we
+
+ align:start position:0%
+talking about null geodesics we
+ 
+
+ align:start position:0%
+talking about null geodesics we
+parameterize them in such a way that D
+
+ align:start position:0%
+parameterize them in such a way that D
+ 
+
+ align:start position:0%
+parameterize them in such a way that D
+sort of the tangent to the world line
+
+ align:start position:0%
+sort of the tangent to the world line
+ 
+
+ align:start position:0%
+sort of the tangent to the world line
+has an affine parameter attached to it
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+such that we can write P equals DX D
+
+ align:start position:0%
+such that we can write P equals DX D
+ 
+
+ align:start position:0%
+such that we can write P equals DX D
+lambda okay these guys are null so P key
+
+ align:start position:0%
+lambda okay these guys are null so P key
+ 
+
+ align:start position:0%
+lambda okay these guys are null so P key
+equals zero for the case of orbiting
+
+ align:start position:0%
+equals zero for the case of orbiting
+ 
+
+ align:start position:0%
+equals zero for the case of orbiting
+bodies that was equal to minus mass
+
+ align:start position:0%
+bodies that was equal to minus mass
+ 
+
+ align:start position:0%
+bodies that was equal to minus mass
+squared mass is zero here so we're gonna
+
+ align:start position:0%
+squared mass is zero here so we're gonna
+ 
+
+ align:start position:0%
+squared mass is zero here so we're gonna
+follow a very similar procedure okay the
+
+ align:start position:0%
+follow a very similar procedure okay the
+ 
+
+ align:start position:0%
+follow a very similar procedure okay the
+space-time is still time independent so
+
+ align:start position:0%
+space-time is still time independent so
+ 
+
+ align:start position:0%
+space-time is still time independent so
+there is still a notion of a conserved
+
+ align:start position:0%
+there is still a notion of a conserved
+ 
+
+ align:start position:0%
+there is still a notion of a conserved
+energy it is still actually symmetric so
+
+ align:start position:0%
+energy it is still actually symmetric so
+ 
+
+ align:start position:0%
+energy it is still actually symmetric so
+there is still a notion of axial angular
+
+ align:start position:0%
+there is still a notion of axial angular
+ 
+
+ align:start position:0%
+there is still a notion of axial angular
+momentum but because P dot P is zero now
+
+ align:start position:0%
+momentum but because P dot P is zero now
+ 
+
+ align:start position:0%
+momentum but because P dot P is zero now
+rather than minus M Squared when we go
+
+ align:start position:0%
+rather than minus M Squared when we go
+ 
+
+ align:start position:0%
+rather than minus M Squared when we go
+through the exercise of that sort of
+
+ align:start position:0%
+through the exercise of that sort of
+ 
+
+ align:start position:0%
+through the exercise of that sort of
+parallels what we did for our massive
+
+ align:start position:0%
+parallels what we did for our massive
+ 
+
+ align:start position:0%
+parallels what we did for our massive
+particle we're going to derive a
+
+ align:start position:0%
+particle we're going to derive a
+ 
+
+ align:start position:0%
+particle we're going to derive a
+different potential so let's go ahead
+
+ align:start position:0%
+different potential so let's go ahead
+ 
+
+ align:start position:0%
+different potential so let's go ahead
+and evaluate this guy again I get zero
+
+ align:start position:0%
+and evaluate this guy again I get zero
+ 
+
+ align:start position:0%
+and evaluate this guy again I get zero
+equals minus 1 minus 2 GM over R DT D
+
+ align:start position:0%
+equals minus 1 minus 2 GM over R DT D
+ 
+
+ align:start position:0%
+equals minus 1 minus 2 GM over R DT D
+lambda squared plus 1 minus 2 GM over r
+
+ align:start position:0%
+lambda squared plus 1 minus 2 GM over r
+ 
+
+ align:start position:0%
+lambda squared plus 1 minus 2 GM over r
+dr d lambda squared I'm still going to
+
+ align:start position:0%
+dr d lambda squared I'm still going to
+ 
+
+ align:start position:0%
+dr d lambda squared I'm still going to
+require this thing to be in the theta
+
+ align:start position:0%
+require this thing to be in the theta
+ 
+
+ align:start position:0%
+require this thing to be in the theta
+equals PI over 2 plane so let me know
+
+ align:start position:0%
+equals PI over 2 plane so let me know
+ 
+
+ align:start position:0%
+equals PI over 2 plane so let me know
+seda term and I've set Santa to PI over
+
+ align:start position:0%
+seda term and I've set Santa to PI over
+ 
+
+ align:start position:0%
+seda term and I've set Santa to PI over
+2 so my sine squared theta is just 1
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+do I get this I'll remind you that I can
+
+ align:start position:0%
+do I get this I'll remind you that I can
+ 
+
+ align:start position:0%
+do I get this I'll remind you that I can
+relate so that the the relationship
+
+ align:start position:0%
+relate so that the the relationship
+ 
+
+ align:start position:0%
+relate so that the the relationship
+between the time light complan of
+
+ align:start position:0%
+between the time light complan of
+ 
+
+ align:start position:0%
+between the time light complan of
+momentum and energy the actual component
+
+ align:start position:0%
+momentum and energy the actual component
+ 
+
+ align:start position:0%
+momentum and energy the actual component
+of momentum and yang momentum it's
+
+ align:start position:0%
+of momentum and yang momentum it's
+ 
+
+ align:start position:0%
+of momentum and yang momentum it's
+exactly the same as before there's no
+
+ align:start position:0%
+exactly the same as before there's no
+ 
+
+ align:start position:0%
+exactly the same as before there's no
+rest mass appearing and so now I find so
+
+ align:start position:0%
+rest mass appearing and so now I find so
+ 
+
+ align:start position:0%
+rest mass appearing and so now I find so
+my energy I don't put a hat on it it's
+
+ align:start position:0%
+my energy I don't put a hat on it it's
+ 
+
+ align:start position:0%
+my energy I don't put a hat on it it's
+not energy bringing it mass cuz there is
+
+ align:start position:0%
+not energy bringing it mass cuz there is
+ 
+
+ align:start position:0%
+not energy bringing it mass cuz there is
+no mass that looks like so and my L
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+[Applause]
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+using them I can now derive an equation
+
+ align:start position:0%
+using them I can now derive an equation
+ 
+
+ align:start position:0%
+using them I can now derive an equation
+governing the radial motion of my light
+
+ align:start position:0%
+governing the radial motion of my light
+ 
+
+ align:start position:0%
+governing the radial motion of my light
+ray and sparing you the line or two of
+
+ align:start position:0%
+ray and sparing you the line or two of
+ 
+
+ align:start position:0%
+ray and sparing you the line or two of
+algebra it looks like this okay so kind
+
+ align:start position:0%
+algebra it looks like this okay so kind
+ 
+
+ align:start position:0%
+algebra it looks like this okay so kind
+of similar to what we had before if you
+
+ align:start position:0%
+of similar to what we had before if you
+ 
+
+ align:start position:0%
+of similar to what we had before if you
+look at it you'll see the term involving
+
+ align:start position:0%
+look at it you'll see the term involving
+ 
+
+ align:start position:0%
+look at it you'll see the term involving
+the angular momentum is a little bit
+
+ align:start position:0%
+the angular momentum is a little bit
+ 
+
+ align:start position:0%
+the angular momentum is a little bit
+different as you stare at this for a
+
+ align:start position:0%
+different as you stare at this for a
+ 
+
+ align:start position:0%
+different as you stare at this for a
+moment something should be disturbing
+
+ align:start position:0%
+moment something should be disturbing
+ 
+
+ align:start position:0%
+moment something should be disturbing
+you notice that the equation of motion
+
+ align:start position:0%
+you notice that the equation of motion
+ 
+
+ align:start position:0%
+you notice that the equation of motion
+appears to depend on the energy okay
+
+ align:start position:0%
+appears to depend on the energy okay
+ 
+
+ align:start position:0%
+appears to depend on the energy okay
+that should really bug you
+
+ align:start position:0%
+that should really bug you
+ 
+
+ align:start position:0%
+that should really bug you
+why should gamma rays and infrared
+
+ align:start position:0%
+why should gamma rays and infrared
+ 
+
+ align:start position:0%
+why should gamma rays and infrared
+radiation follow different trajectories
+
+ align:start position:0%
+radiation follow different trajectories
+ 
+
+ align:start position:0%
+radiation follow different trajectories
+okay as long as I am truly in a
+
+ align:start position:0%
+okay as long as I am truly in a
+ 
+
+ align:start position:0%
+okay as long as I am truly in a
+geometric optics limit
+
+ align:start position:0%
+geometric optics limit
+ 
+
+ align:start position:0%
+geometric optics limit
+I shouldn't okay now it is true that if
+
+ align:start position:0%
+I shouldn't okay now it is true that if
+ 
+
+ align:start position:0%
+I shouldn't okay now it is true that if
+you consider very long wavelength
+
+ align:start position:0%
+you consider very long wavelength
+ 
+
+ align:start position:0%
+you consider very long wavelength
+radiation you might need to worry about
+
+ align:start position:0%
+radiation you might need to worry about
+ 
+
+ align:start position:0%
+radiation you might need to worry about
+things you might need to solve the wave
+
+ align:start position:0%
+things you might need to solve the wave
+ 
+
+ align:start position:0%
+things you might need to solve the wave
+equation in the space-time but as long
+
+ align:start position:0%
+equation in the space-time but as long
+ 
+
+ align:start position:0%
+equation in the space-time but as long
+as the wave nature of this radiation is
+
+ align:start position:0%
+as the wave nature of this radiation is
+ 
+
+ align:start position:0%
+as the wave nature of this radiation is
+if the wavelength is small enough that
+
+ align:start position:0%
+if the wavelength is small enough that
+ 
+
+ align:start position:0%
+if the wavelength is small enough that
+it's negligible compared to to GM I
+
+ align:start position:0%
+it's negligible compared to to GM I
+ 
+
+ align:start position:0%
+it's negligible compared to to GM I
+shouldn't care what the energy is energy
+
+ align:start position:0%
+shouldn't care what the energy is energy
+ 
+
+ align:start position:0%
+shouldn't care what the energy is energy
+should not be influencing this okay and
+
+ align:start position:0%
+should not be influencing this okay and
+ 
+
+ align:start position:0%
+should not be influencing this okay and
+so what's going on is I need to repr
+
+ align:start position:0%
+so what's going on is I need to repr
+ 
+
+ align:start position:0%
+so what's going on is I need to repr
+amateur eyes this a little bit what I'm
+
+ align:start position:0%
+amateur eyes this a little bit what I'm
+ 
+
+ align:start position:0%
+amateur eyes this a little bit what I'm
+going to do to wash away my dependence
+
+ align:start position:0%
+going to do to wash away my dependence
+ 
+
+ align:start position:0%
+going to do to wash away my dependence
+on wash away my apparent dependence on
+
+ align:start position:0%
+on wash away my apparent dependence on
+ 
+
+ align:start position:0%
+on wash away my apparent dependence on
+the energy here is I'm going to redefine
+
+ align:start position:0%
+the energy here is I'm going to redefine
+ 
+
+ align:start position:0%
+the energy here is I'm going to redefine
+my affine parameter
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so let's take lambda 2 L divided by
+
+ align:start position:0%
+so let's take lambda 2 L divided by
+ 
+
+ align:start position:0%
+so let's take lambda 2 L divided by
+lambda and I am going to define B to be
+
+ align:start position:0%
+lambda and I am going to define B to be
+ 
+
+ align:start position:0%
+lambda and I am going to define B to be
+L divided by e this is a quantity that I
+
+ align:start position:0%
+L divided by e this is a quantity that I
+ 
+
+ align:start position:0%
+L divided by e this is a quantity that I
+will call the impact parameter and I'll
+
+ align:start position:0%
+will call the impact parameter and I'll
+ 
+
+ align:start position:0%
+will call the impact parameter and I'll
+describe why I'm calling it that in just
+
+ align:start position:0%
+describe why I'm calling it that in just
+ 
+
+ align:start position:0%
+describe why I'm calling it that in just
+a few minutes so I'm going to take this
+
+ align:start position:0%
+a few minutes so I'm going to take this
+ 
+
+ align:start position:0%
+a few minutes so I'm going to take this
+entire equation divide both sides by l
+
+ align:start position:0%
+entire equation divide both sides by l
+ 
+
+ align:start position:0%
+entire equation divide both sides by l
+squared and I get something that looks
+
+ align:start position:0%
+squared and I get something that looks
+ 
+
+ align:start position:0%
+squared and I get something that looks
+like this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+what I'm gonna do is say that the impact
+
+ align:start position:0%
+what I'm gonna do is say that the impact
+ 
+
+ align:start position:0%
+what I'm gonna do is say that the impact
+parameter B is what I can control
+
+ align:start position:0%
+parameter B is what I can control
+ 
+
+ align:start position:0%
+parameter B is what I can control
+it's the parameter that I like and
+
+ align:start position:0%
+it's the parameter that I like and
+ 
+
+ align:start position:0%
+it's the parameter that I like and
+control that defines the photon that I
+
+ align:start position:0%
+control that defines the photon that I
+ 
+
+ align:start position:0%
+control that defines the photon that I
+am studying here and everything after
+
+ align:start position:0%
+am studying here and everything after
+ 
+
+ align:start position:0%
+am studying here and everything after
+this this is my photon potential notice
+
+ align:start position:0%
+this this is my photon potential notice
+ 
+
+ align:start position:0%
+this this is my photon potential notice
+that the photon potential the photon
+
+ align:start position:0%
+that the photon potential the photon
+ 
+
+ align:start position:0%
+that the photon potential the photon
+potential has no free parameters in it
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+if I plot this guy as a function of our
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+kind it just looks like this okay
+
+ align:start position:0%
+kind it just looks like this okay
+ 
+
+ align:start position:0%
+kind it just looks like this okay
+two aspects of it are worth calling out
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this peak occurs at R equals three R
+
+ align:start position:0%
+this peak occurs at R equals three R
+ 
+
+ align:start position:0%
+this peak occurs at R equals three R
+equals 3 GM remember the way in which
+
+ align:start position:0%
+equals 3 GM remember the way in which
+ 
+
+ align:start position:0%
+equals 3 GM remember the way in which
+our energy still happen on the board
+
+ align:start position:0%
+our energy still happen on the board
+ 
+
+ align:start position:0%
+our energy still happen on the board
+here stings like the energy per unit
+
+ align:start position:0%
+here stings like the energy per unit
+ 
+
+ align:start position:0%
+here stings like the energy per unit
+mass and the angular mentum per unit
+
+ align:start position:0%
+mass and the angular mentum per unit
+ 
+
+ align:start position:0%
+mass and the angular mentum per unit
+mass all blew up when R equaled 3 GM 3
+
+ align:start position:0%
+mass all blew up when R equaled 3 GM 3
+ 
+
+ align:start position:0%
+mass all blew up when R equaled 3 GM 3
+GM is showing up now when I look at the
+
+ align:start position:0%
+GM is showing up now when I look at the
+ 
+
+ align:start position:0%
+GM is showing up now when I look at the
+motion of radiation ok look at massless
+
+ align:start position:0%
+motion of radiation ok look at massless
+ 
+
+ align:start position:0%
+motion of radiation ok look at massless
+radiation corresponding to a massless
+
+ align:start position:0%
+radiation corresponding to a massless
+ 
+
+ align:start position:0%
+radiation corresponding to a massless
+particle so to speak if I look at the
+
+ align:start position:0%
+particle so to speak if I look at the
+ 
+
+ align:start position:0%
+particle so to speak if I look at the
+energy per unit mass and the mass goes
+
+ align:start position:0%
+energy per unit mass and the mass goes
+ 
+
+ align:start position:0%
+energy per unit mass and the mass goes
+to 0 I get infinity so the fact that I
+
+ align:start position:0%
+to 0 I get infinity so the fact that I
+ 
+
+ align:start position:0%
+to 0 I get infinity so the fact that I
+was actually seeing sort of things
+
+ align:start position:0%
+was actually seeing sort of things
+ 
+
+ align:start position:0%
+was actually seeing sort of things
+blowing up as R goes to 3 GM was kind of
+
+ align:start position:0%
+blowing up as R goes to 3 GM was kind of
+ 
+
+ align:start position:0%
+blowing up as R goes to 3 GM was kind of
+like the equations hinting to me in
+
+ align:start position:0%
+like the equations hinting to me in
+ 
+
+ align:start position:0%
+like the equations hinting to me in
+advance that there was a hidden solution
+
+ align:start position:0%
+advance that there was a hidden solution
+ 
+
+ align:start position:0%
+advance that there was a hidden solution
+correspond to radiation that could be
+
+ align:start position:0%
+correspond to radiation that could be
+ 
+
+ align:start position:0%
+correspond to radiation that could be
+regarded as a particular limit that they
+
+ align:start position:0%
+regarded as a particular limit that they
+ 
+
+ align:start position:0%
+regarded as a particular limit that they
+were sort of struggling to communicate
+
+ align:start position:0%
+were sort of struggling to communicate
+ 
+
+ align:start position:0%
+were sort of struggling to communicate
+to me the earth in which I want to note
+
+ align:start position:0%
+to me the earth in which I want to note
+ 
+
+ align:start position:0%
+to me the earth in which I want to note
+is that the potential the height of the
+
+ align:start position:0%
+is that the potential the height of the
+ 
+
+ align:start position:0%
+is that the potential the height of the
+potential right here
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+it has a peak value of 1 over 27 G
+
+ align:start position:0%
+it has a peak value of 1 over 27 G
+ 
+
+ align:start position:0%
+it has a peak value of 1 over 27 G
+squared M Squared okay hold that thought
+
+ align:start position:0%
+squared M Squared okay hold that thought
+ 
+
+ align:start position:0%
+squared M Squared okay hold that thought
+for just a moment actually let me write
+
+ align:start position:0%
+for just a moment actually let me write
+ 
+
+ align:start position:0%
+for just a moment actually let me write
+it in a slightly different way this
+
+ align:start position:0%
+it in a slightly different way this
+ 
+
+ align:start position:0%
+it in a slightly different way this
+equals 1 over 3 root 3 G M squared so
+
+ align:start position:0%
+equals 1 over 3 root 3 G M squared so
+ 
+
+ align:start position:0%
+equals 1 over 3 root 3 G M squared so
+now to wrap this up I need to tell you
+
+ align:start position:0%
+now to wrap this up I need to tell you
+ 
+
+ align:start position:0%
+now to wrap this up I need to tell you
+what is really meant by this impact
+
+ align:start position:0%
+what is really meant by this impact
+ 
+
+ align:start position:0%
+what is really meant by this impact
+parameter
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so go back to freshman mechanics and
+
+ align:start position:0%
+so go back to freshman mechanics and
+ 
+
+ align:start position:0%
+so go back to freshman mechanics and
+impact parameter there is like let's say
+
+ align:start position:0%
+impact parameter there is like let's say
+ 
+
+ align:start position:0%
+impact parameter there is like let's say
+I have a problem where I am looking at I
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+am looking at an object that is on an in
+
+ align:start position:0%
+am looking at an object that is on an in
+ 
+
+ align:start position:0%
+am looking at an object that is on an in
+fall trajectory there's a momentum P
+
+ align:start position:0%
+fall trajectory there's a momentum P
+ 
+
+ align:start position:0%
+fall trajectory there's a momentum P
+that is describing this and it's moving
+
+ align:start position:0%
+that is describing this and it's moving
+ 
+
+ align:start position:0%
+that is describing this and it's moving
+in such a way it's not moving on a
+
+ align:start position:0%
+in such a way it's not moving on a
+ 
+
+ align:start position:0%
+in such a way it's not moving on a
+radial trajectory all right it's
+
+ align:start position:0%
+radial trajectory all right it's
+ 
+
+ align:start position:0%
+radial trajectory all right it's
+actually moving in a sense that is a
+
+ align:start position:0%
+actually moving in a sense that is a
+ 
+
+ align:start position:0%
+actually moving in a sense that is a
+little bit off of true to the radial
+
+ align:start position:0%
+little bit off of true to the radial
+ 
+
+ align:start position:0%
+little bit off of true to the radial
+direction okay this guy actually has an
+
+ align:start position:0%
+direction okay this guy actually has an
+ 
+
+ align:start position:0%
+direction okay this guy actually has an
+angular momentum that is given by let's
+
+ align:start position:0%
+angular momentum that is given by let's
+ 
+
+ align:start position:0%
+angular momentum that is given by let's
+say that this is equal to PX this is be
+
+ align:start position:0%
+say that this is equal to PX this is be
+ 
+
+ align:start position:0%
+say that this is equal to PX this is be
+Y hat this guy's got an angular momentum
+
+ align:start position:0%
+Y hat this guy's got an angular momentum
+ 
+
+ align:start position:0%
+Y hat this guy's got an angular momentum
+a B cross P okay that's the impact
+
+ align:start position:0%
+a B cross P okay that's the impact
+ 
+
+ align:start position:0%
+a B cross P okay that's the impact
+parameter associated with this thing it
+
+ align:start position:0%
+parameter associated with this thing it
+ 
+
+ align:start position:0%
+parameter associated with this thing it
+sort of tells me about this the the
+
+ align:start position:0%
+sort of tells me about this the the
+ 
+
+ align:start position:0%
+sort of tells me about this the the
+offset of this momentum from being
+
+ align:start position:0%
+offset of this momentum from being
+ 
+
+ align:start position:0%
+offset of this momentum from being
+directly radial towards the center of
+
+ align:start position:0%
+directly radial towards the center of
+ 
+
+ align:start position:0%
+directly radial towards the center of
+this object
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+well I'm going to use a similar notion
+
+ align:start position:0%
+well I'm going to use a similar notion
+ 
+
+ align:start position:0%
+well I'm going to use a similar notion
+to give me a geometric sense of what
+
+ align:start position:0%
+to give me a geometric sense of what
+ 
+
+ align:start position:0%
+to give me a geometric sense of what
+this impact parameter here means suppose
+
+ align:start position:0%
+this impact parameter here means suppose
+ 
+
+ align:start position:0%
+this impact parameter here means suppose
+here is my black hole this is a little
+
+ align:start position:0%
+here is my black hole this is a little
+ 
+
+ align:start position:0%
+here is my black hole this is a little
+circle of radius 2 g-m and I'm sitting
+
+ align:start position:0%
+circle of radius 2 g-m and I'm sitting
+ 
+
+ align:start position:0%
+circle of radius 2 g-m and I'm sitting
+where the heck out here safely far away
+
+ align:start position:0%
+where the heck out here safely far away
+ 
+
+ align:start position:0%
+where the heck out here safely far away
+from this thing
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and what I'm going to do is shoot light
+
+ align:start position:0%
+and what I'm going to do is shoot light
+ 
+
+ align:start position:0%
+and what I'm going to do is shoot light
+not quite radial what I'm going to do is
+
+ align:start position:0%
+not quite radial what I'm going to do is
+ 
+
+ align:start position:0%
+not quite radial what I'm going to do is
+I'm gonna have sort of an array of laser
+
+ align:start position:0%
+I'm gonna have sort of an array of laser
+ 
+
+ align:start position:0%
+I'm gonna have sort of an array of laser
+beams that kind of come up here and an
+
+ align:start position:0%
+beams that kind of come up here and an
+ 
+
+ align:start position:0%
+beams that kind of come up here and an
+array of laser beams and I'm gonna shoot
+
+ align:start position:0%
+array of laser beams and I'm gonna shoot
+ 
+
+ align:start position:0%
+array of laser beams and I'm gonna shoot
+them towards this this black hole okay
+
+ align:start position:0%
+them towards this this black hole okay
+ 
+
+ align:start position:0%
+them towards this this black hole okay
+and what I'm gonna do is I'm gonna
+
+ align:start position:0%
+and what I'm gonna do is I'm gonna
+ 
+
+ align:start position:0%
+and what I'm gonna do is I'm gonna
+offset the laser beams by a distance B
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and I'm gonna fire it straight towards
+
+ align:start position:0%
+and I'm gonna fire it straight towards
+ 
+
+ align:start position:0%
+and I'm gonna fire it straight towards
+this thing okay go through sort of a
+
+ align:start position:0%
+this thing okay go through sort of a
+ 
+
+ align:start position:0%
+this thing okay go through sort of a
+careful definition of what angular
+
+ align:start position:0%
+careful definition of what angular
+ 
+
+ align:start position:0%
+careful definition of what angular
+momentum means and you'll see that that
+
+ align:start position:0%
+momentum means and you'll see that that
+ 
+
+ align:start position:0%
+momentum means and you'll see that that
+definition of of impact parameter gives
+
+ align:start position:0%
+definition of of impact parameter gives
+ 
+
+ align:start position:0%
+definition of of impact parameter gives
+you a very nice sense of the energy
+
+ align:start position:0%
+you a very nice sense of the energy
+ 
+
+ align:start position:0%
+you a very nice sense of the energy
+associate with the trajectory of this
+
+ align:start position:0%
+associate with the trajectory of this
+ 
+
+ align:start position:0%
+associate with the trajectory of this
+beam and a notion of angular momentum
+
+ align:start position:0%
+beam and a notion of angular momentum
+ 
+
+ align:start position:0%
+beam and a notion of angular momentum
+associate with this okay so let's flip
+
+ align:start position:0%
+associate with this okay so let's flip
+ 
+
+ align:start position:0%
+associate with this okay so let's flip
+back and forth between a couple of
+
+ align:start position:0%
+back and forth between a couple of
+ 
+
+ align:start position:0%
+back and forth between a couple of
+different boards here there are three
+
+ align:start position:0%
+different boards here there are three
+ 
+
+ align:start position:0%
+different boards here there are three
+cases that are interesting
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+suppose B is small particular suppose I
+
+ align:start position:0%
+suppose B is small particular suppose I
+ 
+
+ align:start position:0%
+suppose B is small particular suppose I
+have B less than three root three G M
+
+ align:start position:0%
+have B less than three root three G M
+ 
+
+ align:start position:0%
+have B less than three root three G M
+okay so I start over here let's take the
+
+ align:start position:0%
+okay so I start over here let's take the
+ 
+
+ align:start position:0%
+okay so I start over here let's take the
+limit would it be equal zero
+
+ align:start position:0%
+limit would it be equal zero
+ 
+
+ align:start position:0%
+limit would it be equal zero
+well if B equals zero this guy just goes
+
+ align:start position:0%
+well if B equals zero this guy just goes
+ 
+
+ align:start position:0%
+well if B equals zero this guy just goes
+zoom straight into the black hole as
+
+ align:start position:0%
+zoom straight into the black hole as
+ 
+
+ align:start position:0%
+zoom straight into the black hole as
+long as it is anything less than three
+
+ align:start position:0%
+long as it is anything less than three
+ 
+
+ align:start position:0%
+long as it is anything less than three
+root three GM what will happen is when I
+
+ align:start position:0%
+root three GM what will happen is when I
+ 
+
+ align:start position:0%
+root three GM what will happen is when I
+shoot this thing in it goes in and it
+
+ align:start position:0%
+shoot this thing in it goes in and it
+ 
+
+ align:start position:0%
+shoot this thing in it goes in and it
+bends perhaps but it ends up going into
+
+ align:start position:0%
+bends perhaps but it ends up going into
+ 
+
+ align:start position:0%
+bends perhaps but it ends up going into
+the black hole let's look at this in the
+
+ align:start position:0%
+the black hole let's look at this in the
+ 
+
+ align:start position:0%
+the black hole let's look at this in the
+context of the equation of motion the
+
+ align:start position:0%
+context of the equation of motion the
+ 
+
+ align:start position:0%
+context of the equation of motion the
+potential and the impact parameter if B
+
+ align:start position:0%
+potential and the impact parameter if B
+ 
+
+ align:start position:0%
+potential and the impact parameter if B
+is less than one over three root three
+
+ align:start position:0%
+is less than one over three root three
+ 
+
+ align:start position:0%
+is less than one over three root three
+GM then 1 over B squared will be higher
+
+ align:start position:0%
+GM then 1 over B squared will be higher
+ 
+
+ align:start position:0%
+GM then 1 over B squared will be higher
+than this peak and this thing is just
+
+ align:start position:0%
+than this peak and this thing is just
+ 
+
+ align:start position:0%
+than this peak and this thing is just
+gonna be it's gonna go right over the
+
+ align:start position:0%
+gonna be it's gonna go right over the
+ 
+
+ align:start position:0%
+gonna be it's gonna go right over the
+top of the peak and it shoots into small
+
+ align:start position:0%
+top of the peak and it shoots into small
+ 
+
+ align:start position:0%
+top of the peak and it shoots into small
+radius okay remember L and D are
+
+ align:start position:0%
+radius okay remember L and D are
+ 
+
+ align:start position:0%
+radius okay remember L and D are
+constants of the motion so that B is a
+
+ align:start position:0%
+constants of the motion so that B is a
+ 
+
+ align:start position:0%
+constants of the motion so that B is a
+parameter that defines this this light
+
+ align:start position:0%
+parameter that defines this this light
+ 
+
+ align:start position:0%
+parameter that defines this this light
+for the entire trajectory 1 over B
+
+ align:start position:0%
+for the entire trajectory 1 over B
+ 
+
+ align:start position:0%
+for the entire trajectory 1 over B
+squared it's less than V Foat everywhere
+
+ align:start position:0%
+squared it's less than V Foat everywhere
+ 
+
+ align:start position:0%
+squared it's less than V Foat everywhere
+sue B greater than beef V fo everywhere
+
+ align:start position:0%
+sue B greater than beef V fo everywhere
+ 
+
+ align:start position:0%
+sue B greater than beef V fo everywhere
+to run a crucial typo and as such it
+
+ align:start position:0%
+to run a crucial typo and as such it
+ 
+
+ align:start position:0%
+to run a crucial typo and as such it
+shoots the light rain goes right over
+
+ align:start position:0%
+shoots the light rain goes right over
+ 
+
+ align:start position:0%
+shoots the light rain goes right over
+the peak
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+into the black hole eventually grinds up
+
+ align:start position:0%
+into the black hole eventually grinds up
+ 
+
+ align:start position:0%
+into the black hole eventually grinds up
+at R equals zero if B is greater than
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+three root three GM then one over B
+
+ align:start position:0%
+three root three GM then one over B
+ 
+
+ align:start position:0%
+three root three GM then one over B
+squared is less than V float at the peak
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this corresponds in this drawing to a
+
+ align:start position:0%
+this corresponds in this drawing to a
+ 
+
+ align:start position:0%
+this corresponds in this drawing to a
+beam of light that follows a trajectory
+
+ align:start position:0%
+beam of light that follows a trajectory
+ 
+
+ align:start position:0%
+beam of light that follows a trajectory
+that kind of comes in here at this point
+
+ align:start position:0%
+that kind of comes in here at this point
+ 
+
+ align:start position:0%
+that kind of comes in here at this point
+DRD tau if we were to continue going to
+
+ align:start position:0%
+DRD tau if we were to continue going to
+ 
+
+ align:start position:0%
+DRD tau if we were to continue going to
+smaller radii it would become imaginary
+
+ align:start position:0%
+smaller radii it would become imaginary
+ 
+
+ align:start position:0%
+smaller radii it would become imaginary
+that's not allowed so it switches
+
+ align:start position:0%
+that's not allowed so it switches
+ 
+
+ align:start position:0%
+that's not allowed so it switches
+direction and work trundles right back
+
+ align:start position:0%
+direction and work trundles right back
+ 
+
+ align:start position:0%
+direction and work trundles right back
+out to infinity on this diagram that
+
+ align:start position:0%
+out to infinity on this diagram that
+ 
+
+ align:start position:0%
+out to infinity on this diagram that
+corresponds to a light ray that's
+
+ align:start position:0%
+corresponds to a light ray that's
+ 
+
+ align:start position:0%
+corresponds to a light ray that's
+perhaps out here and this guy comes in
+
+ align:start position:0%
+perhaps out here and this guy comes in
+ 
+
+ align:start position:0%
+perhaps out here and this guy comes in
+maybe gets bent by the gravity a little
+
+ align:start position:0%
+maybe gets bent by the gravity a little
+ 
+
+ align:start position:0%
+maybe gets bent by the gravity a little
+bit and then just you shoots back off to
+
+ align:start position:0%
+bit and then just you shoots back off to
+ 
+
+ align:start position:0%
+bit and then just you shoots back off to
+infinity
+
+ align:start position:0%
+infinity
+ 
+
+ align:start position:0%
+infinity
+the critical point B equals 3 GM right
+
+ align:start position:0%
+the critical point B equals 3 GM right
+ 
+
+ align:start position:0%
+the critical point B equals 3 GM right
+where the impact parameter hits the peak
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so what happens in this plot is this guy
+
+ align:start position:0%
+so what happens in this plot is this guy
+ 
+
+ align:start position:0%
+so what happens in this plot is this guy
+comes in
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+hits the peak and just sits there
+
+ align:start position:0%
+hits the peak and just sits there
+ 
+
+ align:start position:0%
+hits the peak and just sits there
+forever
+
+ align:start position:0%
+forever
+ 
+
+ align:start position:0%
+forever
+[Applause]
+
+ align:start position:0%
+[Applause]
+ 
+
+ align:start position:0%
+[Applause]
+you get a little bit more of a physical
+
+ align:start position:0%
+you get a little bit more of a physical
+ 
+
+ align:start position:0%
+you get a little bit more of a physical
+sense as to what's going on by thinking
+
+ align:start position:0%
+sense as to what's going on by thinking
+ 
+
+ align:start position:0%
+sense as to what's going on by thinking
+about it here this guy comes in pitch
+
+ align:start position:0%
+about it here this guy comes in pitch
+ 
+
+ align:start position:0%
+about it here this guy comes in pitch
+this and then just whirls around and
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+lies on what we call the photon orbit
+
+ align:start position:0%
+lies on what we call the photon orbit
+ 
+
+ align:start position:0%
+lies on what we call the photon orbit
+what's the rate of that photon orbit R
+
+ align:start position:0%
+what's the rate of that photon orbit R
+ 
+
+ align:start position:0%
+what's the rate of that photon orbit R
+equals 3 GM now astrophysically a more
+
+ align:start position:0%
+equals 3 GM now astrophysically a more
+ 
+
+ align:start position:0%
+equals 3 GM now astrophysically a more
+interesting situation is imagine you had
+
+ align:start position:0%
+interesting situation is imagine you had
+ 
+
+ align:start position:0%
+interesting situation is imagine you had
+some source of light that dumps a lot of
+
+ align:start position:0%
+some source of light that dumps a lot of
+ 
+
+ align:start position:0%
+some source of light that dumps a lot of
+photons in the vicinity of a black hole
+
+ align:start position:0%
+photons in the vicinity of a black hole
+ 
+
+ align:start position:0%
+photons in the vicinity of a black hole
+some of those photons are going to tend
+
+ align:start position:0%
+some of those photons are going to tend
+ 
+
+ align:start position:0%
+some of those photons are going to tend
+to you know some of them are gonna go
+
+ align:start position:0%
+to you know some of them are gonna go
+ 
+
+ align:start position:0%
+to you know some of them are gonna go
+into the black hole some are gonna
+
+ align:start position:0%
+into the black hole some are gonna
+ 
+
+ align:start position:0%
+into the black hole some are gonna
+scatter a little bit and shoot off to
+
+ align:start position:0%
+scatter a little bit and shoot off to
+ 
+
+ align:start position:0%
+scatter a little bit and shoot off to
+infinity but if you imagine that there
+
+ align:start position:0%
+infinity but if you imagine that there
+ 
+
+ align:start position:0%
+infinity but if you imagine that there
+will be some population of them that
+
+ align:start position:0%
+will be some population of them that
+ 
+
+ align:start position:0%
+will be some population of them that
+gets stuck right on the R equals 3 GM
+
+ align:start position:0%
+gets stuck right on the R equals 3 GM
+ 
+
+ align:start position:0%
+gets stuck right on the R equals 3 GM
+orbit now that is an unstable orbit and
+
+ align:start position:0%
+orbit now that is an unstable orbit and
+ 
+
+ align:start position:0%
+orbit now that is an unstable orbit and
+in fact if you look at it what you find
+
+ align:start position:0%
+in fact if you look at it what you find
+ 
+
+ align:start position:0%
+in fact if you look at it what you find
+is that your typical typical photon is
+
+ align:start position:0%
+is that your typical typical photon is
+ 
+
+ align:start position:0%
+is that your typical typical photon is
+likely to whirl around a bunch of times
+
+ align:start position:0%
+likely to whirl around a bunch of times
+ 
+
+ align:start position:0%
+likely to whirl around a bunch of times
+and then you know if it's not precisely
+
+ align:start position:0%
+and then you know if it's not precisely
+ 
+
+ align:start position:0%
+and then you know if it's not precisely
+at 3 GM but it's 3.0 ooo-ooo-ooo-ooo 1
+
+ align:start position:0%
+at 3 GM but it's 3.0 ooo-ooo-ooo-ooo 1
+ 
+
+ align:start position:0%
+at 3 GM but it's 3.0 ooo-ooo-ooo-ooo 1
+GM in a whirl around maybe 10 or 15
+
+ align:start position:0%
+GM in a whirl around maybe 10 or 15
+ 
+
+ align:start position:0%
+GM in a whirl around maybe 10 or 15
+times and then it'll go off to infinity
+
+ align:start position:0%
+times and then it'll go off to infinity
+ 
+
+ align:start position:0%
+times and then it'll go off to infinity
+so we actually expect is if we have an
+
+ align:start position:0%
+so we actually expect is if we have an
+ 
+
+ align:start position:0%
+so we actually expect is if we have an
+object that is illuminated like this
+
+ align:start position:0%
+object that is illuminated like this
+ 
+
+ align:start position:0%
+object that is illuminated like this
+then we will actually see these things
+
+ align:start position:0%
+then we will actually see these things
+ 
+
+ align:start position:0%
+then we will actually see these things
+come out here and we will see it so bear
+
+ align:start position:0%
+come out here and we will see it so bear
+ 
+
+ align:start position:0%
+come out here and we will see it so bear
+in mind this is circularly this is
+
+ align:start position:0%
+in mind this is circularly this is
+ 
+
+ align:start position:0%
+in mind this is circularly this is
+symmetric so take this and rotate around
+
+ align:start position:0%
+symmetric so take this and rotate around
+ 
+
+ align:start position:0%
+symmetric so take this and rotate around
+a symmetry axis we expect to see a ring
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+whose radius is twice the critical
+
+ align:start position:0%
+whose radius is twice the critical
+ 
+
+ align:start position:0%
+whose radius is twice the critical
+impact parameter so it would have a
+
+ align:start position:0%
+impact parameter so it would have a
+ 
+
+ align:start position:0%
+impact parameter so it would have a
+diameter
+
+ align:start position:0%
+diameter
+ 
+
+ align:start position:0%
+diameter
+of 6 root 3 GM it would be essentially a
+
+ align:start position:0%
+of 6 root 3 GM it would be essentially a
+ 
+
+ align:start position:0%
+of 6 root 3 GM it would be essentially a
+ring or a circle of radius 3 root 3 GM
+
+ align:start position:0%
+ring or a circle of radius 3 root 3 GM
+ 
+
+ align:start position:0%
+ring or a circle of radius 3 root 3 GM
+this is in fact what the event horizon
+
+ align:start position:0%
+this is in fact what the event horizon
+ 
+
+ align:start position:0%
+this is in fact what the event horizon
+telescope measured so last year when I
+
+ align:start position:0%
+telescope measured so last year when I
+ 
+
+ align:start position:0%
+telescope measured so last year when I
+was lecturing this class this was
+
+ align:start position:0%
+was lecturing this class this was
+ 
+
+ align:start position:0%
+was lecturing this class this was
+announced almost I mean they they timed
+
+ align:start position:0%
+announced almost I mean they they timed
+ 
+
+ align:start position:0%
+announced almost I mean they they timed
+it well they put a secrete time that to
+
+ align:start position:0%
+it well they put a secrete time that to
+ 
+
+ align:start position:0%
+it well they put a secrete time that to
+about 2 or 3 lectures before I I
+
+ align:start position:0%
+about 2 or 3 lectures before I I
+ 
+
+ align:start position:0%
+about 2 or 3 lectures before I I
+discussed this this aspect of black
+
+ align:start position:0%
+discussed this this aspect of black
+ 
+
+ align:start position:0%
+discussed this this aspect of black
+holes so that was thank you event
+
+ align:start position:0%
+holes so that was thank you event
+ 
+
+ align:start position:0%
+holes so that was thank you event
+horizon telescope that was very nice of
+
+ align:start position:0%
+horizon telescope that was very nice of
+ 
+
+ align:start position:0%
+horizon telescope that was very nice of
+them and you know of course we don't
+
+ align:start position:0%
+them and you know of course we don't
+ 
+
+ align:start position:0%
+them and you know of course we don't
+expect so Schwarzschild black holes are
+
+ align:start position:0%
+expect so Schwarzschild black holes are
+ 
+
+ align:start position:0%
+expect so Schwarzschild black holes are
+probably a mathematical curiosity
+
+ align:start position:0%
+probably a mathematical curiosity
+ 
+
+ align:start position:0%
+probably a mathematical curiosity
+objects in the real universe all rotate
+
+ align:start position:0%
+objects in the real universe all rotate
+ 
+
+ align:start position:0%
+objects in the real universe all rotate
+we expect curve to be the generic
+
+ align:start position:0%
+we expect curve to be the generic
+ 
+
+ align:start position:0%
+we expect curve to be the generic
+solution and so there's a fair amount of
+
+ align:start position:0%
+solution and so there's a fair amount of
+ 
+
+ align:start position:0%
+solution and so there's a fair amount of
+work that goes into how do you correct
+
+ align:start position:0%
+work that goes into how do you correct
+ 
+
+ align:start position:0%
+work that goes into how do you correct
+this to do so doing this for Schwartz
+
+ align:start position:0%
+this to do so doing this for Schwartz
+ 
+
+ align:start position:0%
+this to do so doing this for Schwartz
+shield is because of spherical symmetry
+
+ align:start position:0%
+shield is because of spherical symmetry
+ 
+
+ align:start position:0%
+shield is because of spherical symmetry
+it's beautiful and it's simple occurs a
+
+ align:start position:0%
+it's beautiful and it's simple occurs a
+ 
+
+ align:start position:0%
+it's beautiful and it's simple occurs a
+little bit more complicated but you know
+
+ align:start position:0%
+little bit more complicated but you know
+ 
+
+ align:start position:0%
+little bit more complicated but you know
+it's a problem that can be solved and a
+
+ align:start position:0%
+it's a problem that can be solved and a
+ 
+
+ align:start position:0%
+it's a problem that can be solved and a
+lot of very smart people spend a lot of
+
+ align:start position:0%
+lot of very smart people spend a lot of
+ 
+
+ align:start position:0%
+lot of very smart people spend a lot of
+time doing this to sort of map out what
+
+ align:start position:0%
+time doing this to sort of map out what
+ 
+
+ align:start position:0%
+time doing this to sort of map out what
+the shadow of the black hole looks like
+
+ align:start position:0%
+the shadow of the black hole looks like
+ 
+
+ align:start position:0%
+the shadow of the black hole looks like
+what this ring would look like in the
+
+ align:start position:0%
+what this ring would look like in the
+ 
+
+ align:start position:0%
+what this ring would look like in the
+case of light coming off of a of a
+
+ align:start position:0%
+case of light coming off of a of a
+ 
+
+ align:start position:0%
+case of light coming off of a of a
+spinning black hole so that's it this is
+
+ align:start position:0%
+spinning black hole so that's it this is
+ 
+
+ align:start position:0%
+spinning black hole so that's it this is
+all that I'm going to present for 8 962
+
+ align:start position:0%
+all that I'm going to present for 8 962
+ 
+
+ align:start position:0%
+all that I'm going to present for 8 962
+in the spring of 2020 semester so to
+
+ align:start position:0%
+in the spring of 2020 semester so to
+ 
+
+ align:start position:0%
+in the spring of 2020 semester so to
+everyone as you are scattered around the
+
+ align:start position:0%
+everyone as you are scattered around the
+ 
+
+ align:start position:0%
+everyone as you are scattered around the
+world attempting to sort of stay
+
+ align:start position:0%
+world attempting to sort of stay
+ 
+
+ align:start position:0%
+world attempting to sort of stay
+connected to physics and your friends
+
+ align:start position:0%
+connected to physics and your friends
+ 
+
+ align:start position:0%
+connected to physics and your friends
+and your classwork I wish you good
+
+ align:start position:0%
+and your classwork I wish you good
+ 
+
+ align:start position:0%
+and your classwork I wish you good
+health
+
+ align:start position:0%
+health
+ 
+
+ align:start position:0%
+health
+and I hope to see you again at a time
+
+ align:start position:0%
+and I hope to see you again at a time
+ 
+
+ align:start position:0%
+and I hope to see you again at a time
+when the world is a little less crazy in
+
+ align:start position:0%
+when the world is a little less crazy in
+ 
+
+ align:start position:0%
+when the world is a little less crazy in
+the meantime enjoy a little beautiful
+
+ align:start position:0%
+the meantime enjoy a little beautiful
+ 
+
+ align:start position:0%
+the meantime enjoy a little beautiful
+black holes
\ No newline at end of file
diff --git a/aYg2je06Cpg.txt b/aYg2je06Cpg.txt
new file mode 100644
index 0000000000000000000000000000000000000000..8ade99e70980570dcef6748d0670c6f7ac2ccb95
--- /dev/null
+++ b/aYg2je06Cpg.txt
@@ -0,0 +1,1131 @@
+align:start position:0%
+ 
+let us now discuss in some more detail
+
+ align:start position:0%
+let us now discuss in some more detail
+ 
+
+ align:start position:0%
+let us now discuss in some more detail
+what it takes to carry out Bayesian
+
+ align:start position:0%
+what it takes to carry out Bayesian
+ 
+
+ align:start position:0%
+what it takes to carry out Bayesian
+inference when both random variables are
+
+ align:start position:0%
+inference when both random variables are
+ 
+
+ align:start position:0%
+inference when both random variables are
+discrete the unknown parameter theta is
+
+ align:start position:0%
+discrete the unknown parameter theta is
+ 
+
+ align:start position:0%
+discrete the unknown parameter theta is
+a random variable that takes values in a
+
+ align:start position:0%
+a random variable that takes values in a
+ 
+
+ align:start position:0%
+a random variable that takes values in a
+discrete set and we can think of these
+
+ align:start position:0%
+discrete set and we can think of these
+ 
+
+ align:start position:0%
+discrete set and we can think of these
+values as alternative hypothesis in this
+
+ align:start position:0%
+values as alternative hypothesis in this
+ 
+
+ align:start position:0%
+values as alternative hypothesis in this
+case we know how to do inference we have
+
+ align:start position:0%
+case we know how to do inference we have
+ 
+
+ align:start position:0%
+case we know how to do inference we have
+in our hands the Bayes rule and we have
+
+ align:start position:0%
+in our hands the Bayes rule and we have
+ 
+
+ align:start position:0%
+in our hands the Bayes rule and we have
+seen plenty of examples so instead of
+
+ align:start position:0%
+seen plenty of examples so instead of
+ 
+
+ align:start position:0%
+seen plenty of examples so instead of
+going through one more example in detail
+
+ align:start position:0%
+going through one more example in detail
+ 
+
+ align:start position:0%
+going through one more example in detail
+let us assume that we have a model that
+
+ align:start position:0%
+let us assume that we have a model that
+ 
+
+ align:start position:0%
+let us assume that we have a model that
+we have observed the value of x and that
+
+ align:start position:0%
+we have observed the value of x and that
+ 
+
+ align:start position:0%
+we have observed the value of x and that
+we have already determined the
+
+ align:start position:0%
+we have already determined the
+ 
+
+ align:start position:0%
+we have already determined the
+conditional pmf of the random variable
+
+ align:start position:0%
+conditional pmf of the random variable
+ 
+
+ align:start position:0%
+conditional pmf of the random variable
+theta as a concrete example suppose that
+
+ align:start position:0%
+theta as a concrete example suppose that
+ 
+
+ align:start position:0%
+theta as a concrete example suppose that
+theta can take values 1 2 or 3 we have
+
+ align:start position:0%
+theta can take values 1 2 or 3 we have
+ 
+
+ align:start position:0%
+theta can take values 1 2 or 3 we have
+obtained our observation and the
+
+ align:start position:0%
+obtained our observation and the
+ 
+
+ align:start position:0%
+obtained our observation and the
+conditional pmf takes this form we could
+
+ align:start position:0%
+conditional pmf takes this form we could
+ 
+
+ align:start position:0%
+conditional pmf takes this form we could
+stop at this point or we could continue
+
+ align:start position:0%
+stop at this point or we could continue
+ 
+
+ align:start position:0%
+stop at this point or we could continue
+by asking for a specific estimate of
+
+ align:start position:0%
+by asking for a specific estimate of
+ 
+
+ align:start position:0%
+by asking for a specific estimate of
+theta our best guess as what theta is
+
+ align:start position:0%
+theta our best guess as what theta is
+ 
+
+ align:start position:0%
+theta our best guess as what theta is
+one way of coming up with an estimate is
+
+ align:start position:0%
+one way of coming up with an estimate is
+ 
+
+ align:start position:0%
+one way of coming up with an estimate is
+to use the maximum a posteriori
+
+ align:start position:0%
+to use the maximum a posteriori
+ 
+
+ align:start position:0%
+to use the maximum a posteriori
+probability rule which looks for that
+
+ align:start position:0%
+probability rule which looks for that
+ 
+
+ align:start position:0%
+probability rule which looks for that
+value of theta that has the largest
+
+ align:start position:0%
+value of theta that has the largest
+ 
+
+ align:start position:0%
+value of theta that has the largest
+posterior or conditional probability in
+
+ align:start position:0%
+posterior or conditional probability in
+ 
+
+ align:start position:0%
+posterior or conditional probability in
+this example it is this value so our
+
+ align:start position:0%
+this example it is this value so our
+ 
+
+ align:start position:0%
+this example it is this value so our
+estimate is going to be equal to 2 an
+
+ align:start position:0%
+estimate is going to be equal to 2 an
+ 
+
+ align:start position:0%
+estimate is going to be equal to 2 an
+alternative way of coming up with an
+
+ align:start position:0%
+alternative way of coming up with an
+ 
+
+ align:start position:0%
+alternative way of coming up with an
+estimate could be the LMS rule which
+
+ align:start position:0%
+estimate could be the LMS rule which
+ 
+
+ align:start position:0%
+estimate could be the LMS rule which
+calculates an estimate equal to the
+
+ align:start position:0%
+calculates an estimate equal to the
+ 
+
+ align:start position:0%
+calculates an estimate equal to the
+conditional expectation of the unknown
+
+ align:start position:0%
+conditional expectation of the unknown
+ 
+
+ align:start position:0%
+conditional expectation of the unknown
+parameter given the observation that we
+
+ align:start position:0%
+parameter given the observation that we
+ 
+
+ align:start position:0%
+parameter given the observation that we
+have made this is just the mean of this
+
+ align:start position:0%
+have made this is just the mean of this
+ 
+
+ align:start position:0%
+have made this is just the mean of this
+conditional distribution in this example
+
+ align:start position:0%
+conditional distribution in this example
+ 
+
+ align:start position:0%
+conditional distribution in this example
+it would fall somewhere around here and
+
+ align:start position:0%
+it would fall somewhere around here and
+ 
+
+ align:start position:0%
+it would fall somewhere around here and
+the numerical value as you can check is
+
+ align:start position:0%
+the numerical value as you can check is
+ 
+
+ align:start position:0%
+the numerical value as you can check is
+equal to 2 point 2 next we may be
+
+ align:start position:0%
+equal to 2 point 2 next we may be
+ 
+
+ align:start position:0%
+equal to 2 point 2 next we may be
+interested in how good a certain
+
+ align:start position:0%
+interested in how good a certain
+ 
+
+ align:start position:0%
+interested in how good a certain
+estimate is and for the case where we
+
+ align:start position:0%
+estimate is and for the case where we
+ 
+
+ align:start position:0%
+estimate is and for the case where we
+interpret the values of theta as
+
+ align:start position:0%
+interpret the values of theta as
+ 
+
+ align:start position:0%
+interpret the values of theta as
+hypotheses a relevant criterion is the
+
+ align:start position:0%
+hypotheses a relevant criterion is the
+ 
+
+ align:start position:0%
+hypotheses a relevant criterion is the
+probability of error in this case
+
+ align:start position:0%
+probability of error in this case
+ 
+
+ align:start position:0%
+probability of error in this case
+because we already have some data
+
+ align:start position:0%
+because we already have some data
+ 
+
+ align:start position:0%
+because we already have some data
+available in our
+
+ align:start position:0%
+available in our
+ 
+
+ align:start position:0%
+available in our
+and were called to make an estimate what
+
+ align:start position:0%
+and were called to make an estimate what
+ 
+
+ align:start position:0%
+and were called to make an estimate what
+we care about is the conditional
+
+ align:start position:0%
+we care about is the conditional
+ 
+
+ align:start position:0%
+we care about is the conditional
+probability given the information that
+
+ align:start position:0%
+probability given the information that
+ 
+
+ align:start position:0%
+probability given the information that
+we have that we're making an error
+
+ align:start position:0%
+we have that we're making an error
+ 
+
+ align:start position:0%
+we have that we're making an error
+making an error means the following we
+
+ align:start position:0%
+making an error means the following we
+ 
+
+ align:start position:0%
+making an error means the following we
+have the observation the value of the
+
+ align:start position:0%
+have the observation the value of the
+ 
+
+ align:start position:0%
+have the observation the value of the
+estimate has been determined it is now a
+
+ align:start position:0%
+estimate has been determined it is now a
+ 
+
+ align:start position:0%
+estimate has been determined it is now a
+number and that's why we write it with a
+
+ align:start position:0%
+number and that's why we write it with a
+ 
+
+ align:start position:0%
+number and that's why we write it with a
+lowercase theta hat but the parameter is
+
+ align:start position:0%
+lowercase theta hat but the parameter is
+ 
+
+ align:start position:0%
+lowercase theta hat but the parameter is
+still unknown we don't know what it is
+
+ align:start position:0%
+still unknown we don't know what it is
+ 
+
+ align:start position:0%
+still unknown we don't know what it is
+it is described by this distribution and
+
+ align:start position:0%
+it is described by this distribution and
+ 
+
+ align:start position:0%
+it is described by this distribution and
+there is a probability that it's going
+
+ align:start position:0%
+there is a probability that it's going
+ 
+
+ align:start position:0%
+there is a probability that it's going
+to be different from our estimate what
+
+ align:start position:0%
+to be different from our estimate what
+ 
+
+ align:start position:0%
+to be different from our estimate what
+is this probability it depends on how we
+
+ align:start position:0%
+is this probability it depends on how we
+ 
+
+ align:start position:0%
+is this probability it depends on how we
+construct the estimates if in this
+
+ align:start position:0%
+construct the estimates if in this
+ 
+
+ align:start position:0%
+construct the estimates if in this
+example we use the map rule and we make
+
+ align:start position:0%
+example we use the map rule and we make
+ 
+
+ align:start position:0%
+example we use the map rule and we make
+an estimate of to the risk probability
+
+ align:start position:0%
+an estimate of to the risk probability
+ 
+
+ align:start position:0%
+an estimate of to the risk probability
+point six that the true value of theta
+
+ align:start position:0%
+point six that the true value of theta
+ 
+
+ align:start position:0%
+point six that the true value of theta
+is also equal to 2 and we are fine but
+
+ align:start position:0%
+is also equal to 2 and we are fine but
+ 
+
+ align:start position:0%
+is also equal to 2 and we are fine but
+there is a remaining probability of 0.4
+
+ align:start position:0%
+there is a remaining probability of 0.4
+ 
+
+ align:start position:0%
+there is a remaining probability of 0.4
+that the true value of theta is
+
+ align:start position:0%
+that the true value of theta is
+ 
+
+ align:start position:0%
+that the true value of theta is
+different than our estimate so there's
+
+ align:start position:0%
+different than our estimate so there's
+ 
+
+ align:start position:0%
+different than our estimate so there's
+probability point 4 of having made a
+
+ align:start position:0%
+probability point 4 of having made a
+ 
+
+ align:start position:0%
+probability point 4 of having made a
+mistake if instead of an estimate equal
+
+ align:start position:0%
+mistake if instead of an estimate equal
+ 
+
+ align:start position:0%
+mistake if instead of an estimate equal
+to 2 we had chosen an estimate equal to
+
+ align:start position:0%
+to 2 we had chosen an estimate equal to
+ 
+
+ align:start position:0%
+to 2 we had chosen an estimate equal to
+3 then the true parameter would be equal
+
+ align:start position:0%
+3 then the true parameter would be equal
+ 
+
+ align:start position:0%
+3 then the true parameter would be equal
+to our estimate with probability point 3
+
+ align:start position:0%
+to our estimate with probability point 3
+ 
+
+ align:start position:0%
+to our estimate with probability point 3
+but we would have made an error with
+
+ align:start position:0%
+but we would have made an error with
+ 
+
+ align:start position:0%
+but we would have made an error with
+probability point 7 which would be a
+
+ align:start position:0%
+probability point 7 which would be a
+ 
+
+ align:start position:0%
+probability point 7 which would be a
+bigger probability of error more
+
+ align:start position:0%
+bigger probability of error more
+ 
+
+ align:start position:0%
+bigger probability of error more
+generally the probability of error of a
+
+ align:start position:0%
+generally the probability of error of a
+ 
+
+ align:start position:0%
+generally the probability of error of a
+particular estimate is the sum of the
+
+ align:start position:0%
+particular estimate is the sum of the
+ 
+
+ align:start position:0%
+particular estimate is the sum of the
+probabilities of the other values of
+
+ align:start position:0%
+probabilities of the other values of
+ 
+
+ align:start position:0%
+probabilities of the other values of
+theta and if we want to keep the
+
+ align:start position:0%
+theta and if we want to keep the
+ 
+
+ align:start position:0%
+theta and if we want to keep the
+probability of error small we want to
+
+ align:start position:0%
+probability of error small we want to
+ 
+
+ align:start position:0%
+probability of error small we want to
+keep the sum of the probabilities of the
+
+ align:start position:0%
+keep the sum of the probabilities of the
+ 
+
+ align:start position:0%
+keep the sum of the probabilities of the
+other values small which means we want
+
+ align:start position:0%
+other values small which means we want
+ 
+
+ align:start position:0%
+other values small which means we want
+to pick an estimate for which its own
+
+ align:start position:0%
+to pick an estimate for which its own
+ 
+
+ align:start position:0%
+to pick an estimate for which its own
+probability is large and so by that
+
+ align:start position:0%
+probability is large and so by that
+ 
+
+ align:start position:0%
+probability is large and so by that
+argument we see that the way to achieve
+
+ align:start position:0%
+argument we see that the way to achieve
+ 
+
+ align:start position:0%
+argument we see that the way to achieve
+the smallest possible probability of
+
+ align:start position:0%
+the smallest possible probability of
+ 
+
+ align:start position:0%
+the smallest possible probability of
+error is to employ the map rule and this
+
+ align:start position:0%
+error is to employ the map rule and this
+ 
+
+ align:start position:0%
+error is to employ the map rule and this
+is a very important property of the map
+
+ align:start position:0%
+is a very important property of the map
+ 
+
+ align:start position:0%
+is a very important property of the map
+rule now this is the conditional
+
+ align:start position:0%
+rule now this is the conditional
+ 
+
+ align:start position:0%
+rule now this is the conditional
+probability of error given that we
+
+ align:start position:0%
+probability of error given that we
+ 
+
+ align:start position:0%
+probability of error given that we
+already have data in our hands but more
+
+ align:start position:0%
+already have data in our hands but more
+ 
+
+ align:start position:0%
+already have data in our hands but more
+generally we may want to compare
+
+ align:start position:0%
+generally we may want to compare
+ 
+
+ align:start position:0%
+generally we may want to compare
+estimators or talk about their
+
+ align:start position:0%
+estimators or talk about their
+ 
+
+ align:start position:0%
+estimators or talk about their
+performance
+
+ align:start position:0%
+performance
+ 
+
+ align:start position:0%
+performance
+in terms of their overall probability of
+
+ align:start position:0%
+in terms of their overall probability of
+ 
+
+ align:start position:0%
+in terms of their overall probability of
+terror we're designing a decision-making
+
+ align:start position:0%
+terror we're designing a decision-making
+ 
+
+ align:start position:0%
+terror we're designing a decision-making
+system that's going to process data and
+
+ align:start position:0%
+system that's going to process data and
+ 
+
+ align:start position:0%
+system that's going to process data and
+making decisions in order to say how
+
+ align:start position:0%
+making decisions in order to say how
+ 
+
+ align:start position:0%
+making decisions in order to say how
+good our system is we want to say that
+
+ align:start position:0%
+good our system is we want to say that
+ 
+
+ align:start position:0%
+good our system is we want to say that
+overall whenever you use the system
+
+ align:start position:0%
+overall whenever you use the system
+ 
+
+ align:start position:0%
+overall whenever you use the system
+there's going to be some random
+
+ align:start position:0%
+there's going to be some random
+ 
+
+ align:start position:0%
+there's going to be some random
+parameter there's going to be some value
+
+ align:start position:0%
+parameter there's going to be some value
+ 
+
+ align:start position:0%
+parameter there's going to be some value
+of the estimate and we want to know
+
+ align:start position:0%
+of the estimate and we want to know
+ 
+
+ align:start position:0%
+of the estimate and we want to know
+what's the probability that these two
+
+ align:start position:0%
+what's the probability that these two
+ 
+
+ align:start position:0%
+what's the probability that these two
+will be different we can calculate this
+
+ align:start position:0%
+will be different we can calculate this
+ 
+
+ align:start position:0%
+will be different we can calculate this
+overall probability of error by using
+
+ align:start position:0%
+overall probability of error by using
+ 
+
+ align:start position:0%
+overall probability of error by using
+the total probability theorem and the
+
+ align:start position:0%
+the total probability theorem and the
+ 
+
+ align:start position:0%
+the total probability theorem and the
+conditional probabilities of error as
+
+ align:start position:0%
+conditional probabilities of error as
+ 
+
+ align:start position:0%
+conditional probabilities of error as
+follows we condition on the value of x
+
+ align:start position:0%
+follows we condition on the value of x
+ 
+
+ align:start position:0%
+follows we condition on the value of x
+for any possible value of x we have a
+
+ align:start position:0%
+for any possible value of x we have a
+ 
+
+ align:start position:0%
+for any possible value of x we have a
+conditional probability of Terror and
+
+ align:start position:0%
+conditional probability of Terror and
+ 
+
+ align:start position:0%
+conditional probability of Terror and
+then we take a weighted average of these
+
+ align:start position:0%
+then we take a weighted average of these
+ 
+
+ align:start position:0%
+then we take a weighted average of these
+conditional probabilities of error there
+
+ align:start position:0%
+conditional probabilities of error there
+ 
+
+ align:start position:0%
+conditional probabilities of error there
+is also an alternative way of using the
+
+ align:start position:0%
+is also an alternative way of using the
+ 
+
+ align:start position:0%
+is also an alternative way of using the
+total probability theorem which would be
+
+ align:start position:0%
+total probability theorem which would be
+ 
+
+ align:start position:0%
+total probability theorem which would be
+to first condition on theta and
+
+ align:start position:0%
+to first condition on theta and
+ 
+
+ align:start position:0%
+to first condition on theta and
+calculate the conditional probability of
+
+ align:start position:0%
+calculate the conditional probability of
+ 
+
+ align:start position:0%
+calculate the conditional probability of
+error for a given choice of this unknown
+
+ align:start position:0%
+error for a given choice of this unknown
+ 
+
+ align:start position:0%
+error for a given choice of this unknown
+parameter and both of these formulas can
+
+ align:start position:0%
+parameter and both of these formulas can
+ 
+
+ align:start position:0%
+parameter and both of these formulas can
+be used which one of the two is more
+
+ align:start position:0%
+be used which one of the two is more
+ 
+
+ align:start position:0%
+be used which one of the two is more
+convenient really depends on the
+
+ align:start position:0%
+convenient really depends on the
+ 
+
+ align:start position:0%
+convenient really depends on the
+specifics of the problem finally we
+
+ align:start position:0%
+specifics of the problem finally we
+ 
+
+ align:start position:0%
+specifics of the problem finally we
+would like to make an important
+
+ align:start position:0%
+would like to make an important
+ 
+
+ align:start position:0%
+would like to make an important
+observation we argued that for any
+
+ align:start position:0%
+observation we argued that for any
+ 
+
+ align:start position:0%
+observation we argued that for any
+particular choice of an observation the
+
+ align:start position:0%
+particular choice of an observation the
+ 
+
+ align:start position:0%
+particular choice of an observation the
+map rule achieves the smallest possible
+
+ align:start position:0%
+map rule achieves the smallest possible
+ 
+
+ align:start position:0%
+map rule achieves the smallest possible
+probability of error so under the map
+
+ align:start position:0%
+probability of error so under the map
+ 
+
+ align:start position:0%
+probability of error so under the map
+rule this term is as small as possible
+
+ align:start position:0%
+rule this term is as small as possible
+ 
+
+ align:start position:0%
+rule this term is as small as possible
+for any given value of the random
+
+ align:start position:0%
+for any given value of the random
+ 
+
+ align:start position:0%
+for any given value of the random
+variable capital X since each term of
+
+ align:start position:0%
+variable capital X since each term of
+ 
+
+ align:start position:0%
+variable capital X since each term of
+this sum is as small as possible under
+
+ align:start position:0%
+this sum is as small as possible under
+ 
+
+ align:start position:0%
+this sum is as small as possible under
+the map rule it means that the overall
+
+ align:start position:0%
+the map rule it means that the overall
+ 
+
+ align:start position:0%
+the map rule it means that the overall
+sum will also be as small as possible
+
+ align:start position:0%
+sum will also be as small as possible
+ 
+
+ align:start position:0%
+sum will also be as small as possible
+and this means that the overall
+
+ align:start position:0%
+and this means that the overall
+ 
+
+ align:start position:0%
+and this means that the overall
+probability of error is also smallest
+
+ align:start position:0%
+probability of error is also smallest
+ 
+
+ align:start position:0%
+probability of error is also smallest
+under the map
+
+ align:start position:0%
+under the map
+ 
+
+ align:start position:0%
+under the map
+in this sense the map rule is the
+
+ align:start position:0%
+in this sense the map rule is the
+ 
+
+ align:start position:0%
+in this sense the map rule is the
+optimal way of coming up with estimates
+
+ align:start position:0%
+optimal way of coming up with estimates
+ 
+
+ align:start position:0%
+optimal way of coming up with estimates
+in the hypothesis testing context where
+
+ align:start position:0%
+in the hypothesis testing context where
+ 
+
+ align:start position:0%
+in the hypothesis testing context where
+we want to minimize the probability of
+
+ align:start position:0%
+we want to minimize the probability of
+ 
+
+ align:start position:0%
+we want to minimize the probability of
+error
\ No newline at end of file
diff --git a/b7SDngGtNDs.txt b/b7SDngGtNDs.txt
new file mode 100644
index 0000000000000000000000000000000000000000..378f9eee2db33dcb300504ab01cdfa82a4366ad2
--- /dev/null
+++ b/b7SDngGtNDs.txt
@@ -0,0 +1,521 @@
+The following content is
+provided under a Creative
+
+Commons license.
+
+Your support will help MIT
+OpenCourseWare continue to
+
+offer high-quality educational
+resources for free.
+
+To make a donation or view
+additional materials from
+
+hundreds of MIT courses, visit
+MIT OpenCourseWare at
+
+ocw.mit.edu.
+
+Hi I'm Jocelyn and we're going
+to go over fall 2009, the
+
+final exam, problem number 6.
+
+It says, the dipeptide shown
+below is derived from alanine
+
+and serine.
+
+And I'll write up that
+structure here.
+
+And we know it's a dipeptide
+because we
+
+see that it has two--
+
+what look like--
+
+amine groups and two kind
+of carboxyl groups.
+
+So that's an indicator that
+we're dealing with a dipeptide
+
+not just one amino acid.
+
+Something to notice right off
+the bat is that we're given
+
+the zwitterion form.
+
+We have the amine group at the
+end here is protonated and the
+
+carboxylic group on the other
+end is deprotonated.
+
+So moving to part 1.
+
+It asked us to indicate the
+position of the peptide bond.
+
+Hopefully this is a pretty
+straightforward task.
+
+We realize that the
+dipeptide bond is
+
+what makes the dipeptide.
+
+It's the bond between the amine
+group of one amino acid
+
+and the carboxyl group
+of another.
+
+Right there.
+
+So circling that carbon nitrogen
+bond would get you
+
+full credit on that part.
+
+Moving to part 2.
+
+We are asked to draw the
+skeletal structure of each
+
+constituent amino acid as it
+would be present in an aqueous
+
+solution of an extreme
+basicity, i.e. pH
+
+greater than 12.
+
+So before even starting to write
+we want to think about
+
+what extreme basicity means.
+
+Well it means that both our
+amine group and our carboxylic
+
+acid group are going
+to be deprotonated.
+
+So let's start with
+alanine first. We
+
+have the central carbon.
+
+The amine group.
+
+And the carboxylic acid group.
+
+Now I just drew that
+totally protonated.
+
+However we want to draw it
+totally deprotonated because
+
+it's in basic solution.
+
+So I'm just going to erase
+the extra hydrogens.
+
+And we have a deprotonated amine
+group and a deprotonated
+
+carboxyl group.
+
+And that is what it would look
+like in basic solution.
+
+Now serine is a little different
+because you have a
+
+side group with functionality.
+
+It has not just carbon
+and hydrogen.
+
+First drawing up the backbone
+here, we have a central
+
+carbon, which has a methyl
+alcohol group off of it.
+
+And attach the carboxylic
+acid.
+
+And amine group on
+the left here.
+
+So this one I drew as the
+zwitterion, which would be in
+
+moderately or kind of neutral.
+
+It depends upon the
+amino acid.
+
+But again we want to deprotonate
+our amine group
+
+here because pH greater than 12
+will not have a protonated
+
+amine group.
+
+Now the question is,
+what do we do with
+
+the side chain here?
+
+It has an H attached
+to an oxygen.
+
+Does that come off in super
+basic solution or not?
+
+A lot of students got
+tripped up on this.
+
+An alcohol actually has
+a pKa of about 16.
+
+And so it won't be deprotonated
+
+in an aqueous solution.
+
+Therefore we want to keep
+this hydrogen on.
+
+It will not be--
+
+this will not be a charged
+oxygen in the basic solution
+
+that we were asked about.
+
+So now we are going to
+move on to the second
+
+part of this problem.
+
+The second part asks us about
+the tertiary structure of the
+
+length of protein
+that is shown.
+
+I am not going to draw the whole
+length of protein but
+
+we're going to--
+
+at the four specified
+locations--
+
+we're going to indicate what
+we would call the tertiary
+
+structure; or what functionality
+is causing the
+
+tertiary structure.
+
+So looking at that
+protein chain.
+
+Professor Sadoway has indicated
+four different
+
+distinct parts of the chain.
+
+And the question is asking us,
+at each of the four numbered
+
+positions name one chemical
+change to the environment of
+
+the protein that would
+destabilize the associated
+
+feature in the tertiary
+structure.
+
+Explain the relevant chemistry
+so it's asking us to say what
+
+can we do to disrupt that
+tertiary structure?
+
+And the first thing we need to
+do is figure out what the
+
+tertiary structure is.
+
+So if we look at number 1, we
+see that it has two sulphur
+
+atoms connected together.
+
+So we call that a
+disulfide bond.
+
+The second part, we see that we
+have a phenyl group, so it
+
+has a very electron-deficient
+hydrogen interacting with a
+
+deprotonated carboxyl
+oxygen anion.
+
+And so we have a hydrogen bond
+there and that's what's
+
+causing those amino acids
+to be pulled together.
+
+So let's just say
+hydrogen bond.
+
+At the third number we see
+that we had a deprotonate
+
+carboxyl group and a protonated
+amine group
+
+interacting.
+
+And that's not quite a hydrogen
+bond but it's a
+
+negatively charged part of the
+molecule interacting with the
+
+positively charged part of
+a different molecule.
+
+And so we call that
+electrostatic interaction.
+
+It's similar to a hydrogen
+bond in that it's a
+
+intermolecular interaction
+that's causing these molecules
+
+to move closer, preference
+to be closer together.
+
+And now we come to
+the fourth part.
+
+Which is hydrophobic
+interactions.
+
+So we see that there
+are a lot of just
+
+carbon hydrogen chains.
+
+No oxygen is around, no
+amine groups around.
+
+Purely carbon and hydrogen.
+
+And because this is an aqueous
+solution, those hydrophobic
+
+parts of the molecules will
+preferentially go together and
+
+kind of make a little--
+
+almost like an-- oil
+droplet in water.
+
+They're trying to decrease the
+amount that they experience
+
+the polarity of the water.
+
+And so the interactions
+are hydrophobic.
+
+So now that we know what the
+functionality at each of these
+
+points in the DNA structure are,
+we can go back to what
+
+the question is actually asking
+us, which is, how can
+
+we actually disrupt
+these features.
+
+So the first one is the
+disulfide bond.
+
+And in class Professor Sadoway
+talked about how to disrupt
+
+the disulfide bond.
+
+And one of the ways
+is to put extreme
+
+heat on to the protein.
+
+And that breaks the disulfide
+bond and you can straighten
+
+out that portion of the DNA.
+
+This is how you straighten your
+hair if it's curly or
+
+other types of things with
+the disulfide bond.
+
+So heating the disulfide bond to
+extreme heat will cause it
+
+to break and thus the protein
+will lose that, that folding
+
+or whatever the disulfide bond
+imparted to that portion of
+
+the protein.
+
+Now going on to number 2.
+
+We have hydrogen bonding.
+
+And we see that it's between a
+alcohol group on a ring there
+
+and a carboxyl group.
+
+So one way to disrupt that
+hydrogen bond is to make the
+
+carboxyl group no longer
+deprotonated.
+
+So if we put back on the
+hydrogen to that oxygen it
+
+will become less partially
+negative.
+
+It will have a lower
+
+interaction with that hydrogen.
+
+And so we can say, to protonate
+that carboxyl we
+
+want to make the solution
+more acidic.
+
+So we can add acid.
+
+So the disulfide we're going
+to heat, the hydrogen bond
+
+we're going to add acid.
+
+Looking at number 3 we
+see that we have a
+
+electrostatic reaction.
+
+And so we want to not have that
+electrostatic reaction.
+
+And one way to do that is to
+make one of those entities not
+
+have a charge.
+
+So one way to do that would be
+to reprotonate the carboxylic
+
+acid, just as we did in
+the previous step.
+
+Or we could deprotonate
+the amine group.
+
+And that would cause it to lose
+its charge and thus the
+
+electrostatic interaction
+would be weaker or gone.
+
+So to deprotonate the amine
+group we should know that we
+
+want to add base.
+
+And the final part is, the
+portion with hydrophilic
+
+interactions.
+
+And here we want to figure
+out a way to make those
+
+hydrophobic portions of the
+amino acids not hold as
+
+tightly together.
+
+And one thing we learned
+about in class is
+
+something like soap.
+
+Something that has a hydrophobic
+side and a
+
+hydrophilic side.
+
+And so if we put soap in with
+this protein it can kind of
+
+stabilize the hydrophobic part
+and make it stretch out a
+
+little bit more, not
+ball up so tightly.
+
+So soap or detergent would be
+a good answer for this one.
+
+And so for this question, as
+long as you indicated the
+
+relevant chemistry, which is
+specified what tertiary
+
+structure you were looking
+at and how your suggested
+
+procedure would disrupt that
+tertiary structure, that's
+
+what Professor Sadoway was
+looking for and that would
+
+mean that you answered the
+question completely.
\ No newline at end of file
diff --git a/cRsptYEK1G4.txt b/cRsptYEK1G4.txt
new file mode 100644
index 0000000000000000000000000000000000000000..1cbd85bdeb57af351167e6a2b36f260a5981e952
--- /dev/null
+++ b/cRsptYEK1G4.txt
@@ -0,0 +1,1068 @@
+PROFESSOR: OK, earlier lecture
+introduced the logarithm as
+
+the inverse function
+to the exponential.
+
+And now it's time to do
+calculus, find its derivative.
+
+And we spoke about other inverse
+functions, and here is
+
+an important one: the inverse
+sine function, or sometimes
+
+called the arc sine.
+
+We'll find its derivative,
+too.
+
+OK, so what we're doing really
+is sort of completing the list
+
+of important rules
+for derivatives.
+
+We know about the derivative
+of a sum.
+
+Just add the derivatives.
+
+f minus g, just subtract
+the derivatives.
+
+We know the product rule and the
+quotient rule, so that's
+
+add, subtract, multiply,
+divide functions.
+
+And then very, very important is
+the chain of functions, the
+
+chain rule.
+
+This is never to be mixed
+up with that.
+
+You wouldn't do such a thing.
+
+And now we're adding
+one more f inverse.
+
+That's today, the derivative
+of the inverse.
+
+That will really complete
+the rules.
+
+Out of simple functions like
+exponential, sine and cosine,
+
+powers of x, this creates all
+the rest of the functions that
+
+we typically use.
+
+OK, so let's start with the most
+important of all: the f
+
+of x is e to the x.
+
+And then the inverse
+function, we
+
+named the natural logarithm.
+
+And notice, remember how
+I reversed the letters.
+
+Here, x is the input and y
+is the output from the
+
+exponential function.
+
+So for the inverse function,
+y is the input.
+
+I go backwards to x, and the
+thing to remember, the one
+
+thing to remember, just tell
+yourself x is the exponent.
+
+The logarithm is the exponent.
+
+OK, so a chain of functions
+is coming here, and it's a
+
+perfectly terrific chain.
+
+This is the rule for
+inverse functions.
+
+If I start with an x and I do
+f of x, that gets me to y.
+
+And now I do the inverse
+function, and it
+
+brings me back to x.
+
+So I really have a chain
+of functions.
+
+The chain has a very
+special result.
+
+And our situation is if we
+know how to take the
+
+derivative of f, this ought to
+tell us-- the chain rule--
+
+how to take the derivative
+of the
+
+inverse function, f inverse.
+
+Let me try it with this
+all-important example.
+
+So which--
+
+and notice also, chain
+goes the other way.
+
+If I start with y, do the
+inverse function, then
+
+I've reached x.
+
+Then f of x is y.
+
+Maybe before I take e to the
+x, let me take the function
+
+that always is the
+starting point.
+
+So practice is--
+
+I'll call this example of--
+
+just to remember how inverse
+functions work--
+
+linear functions.
+
+y equals ax plus b.
+
+That's f of x there.
+
+Linear.
+
+What's the inverse of that?
+
+Now the point about inverses
+is I want to solve for x in
+
+terms of y.
+
+I want to get x by itself.
+
+So I move b to the
+opposite side.
+
+So in the end, I want to
+get x equals something.
+
+And how do I do that?
+
+I move b to the opposite side,
+and then I still have ax, so I
+
+divide by a.
+
+Then I've got x by itself.
+
+This is the inverse.
+
+This is f inverse of y.
+
+Notice something about inverse
+functions, that here we did--
+
+this function f of x was
+created in two steps.
+
+it was sort of a chain
+in itself.
+
+The first step was
+multiply by a.
+
+We multiply and then we add.
+
+What's inverse function do?
+
+The inverse function takes y.
+
+Subtracts b.
+
+So it does subtract first
+to get y minus
+
+b, and then it divides.
+
+What's my point?
+
+My point is that if a function
+is built in two steps,
+
+multiply and then add in this
+nice case, the inverse
+
+function does the
+inverse steps.
+
+Instead of multiplying
+it divides.
+
+Instead of add, it subtracts.
+
+What it does though is
+the opposite order.
+
+Notice the multiply was done
+first, then the divide is
+
+last. The add was done second,
+the subtract was done first.
+
+When you invert things, the
+order-- well, you know it.
+
+It has to be that way.
+
+It's that way in life, right?
+
+If we're standing on the beach
+and we walk to the water and
+
+then we swim to the dock, so
+that's our function f of x
+
+from where we were to the dock,
+then how do we get back?
+
+Well, wise to swim
+first, right?
+
+You don't want to walk first.
+From the dock, you swim back.
+
+So you swam one way at the
+end, and then in the
+
+inverse, you swim--
+
+oh, you get it.
+
+OK, so now I'm ready
+for the real thing.
+
+I'll take one of those chains
+and take its derivative.
+
+Let me take the first one.
+
+So the first one says that the
+log of e to the x is x.
+
+That's--
+
+The logarithm was defined
+that way.
+
+That's what the log is.
+
+Let's take the derivative of
+that equation, the derivative
+
+of both sides.
+
+We will be learning what's the
+derivative of the log.
+
+That's what we don't know.
+
+So if I take the derivative,
+well, on the right-hand side,
+
+I certainly get 1.
+
+On the left-hand side, this
+is where it's interesting.
+
+So it's the chain rule.
+
+The log of something, so I
+should take the derivative--
+
+oh, I need a little more
+space here, over here.
+
+The derivative of log
+y, y is e to the x.
+
+Everybody's got that, right?
+
+So this is log y, and I'm taking
+its derivative with
+
+respect to y.
+
+But then I have to, as the chain
+rule tells me, take the
+
+derivative of what's inside.
+
+What's inside is e to the
+x, so I have dy dx.
+
+So I put dy dx.
+
+And the derivative on the
+right-hand side, the neat
+
+point here is that the
+x-derivative of that is 1.
+
+OK, now I'm going to learn what
+this is because I know
+
+what this is: the derivative
+of dy dx, the derivative of
+
+the exponential.
+
+Well, now comes the most
+important property that we use
+
+to construct this exponential.
+
+dy dx is e to the x.
+
+No problem, OK?
+
+And now, I'm going to divide
+by it to get what I want--
+
+almost. Almost, I say.
+
+Well, I've got the derivative
+of log y here.
+
+Correct, but there's a
+step to take still.
+
+I have to write--
+
+I want a function of y.
+
+The log is a function of y.
+
+It's derivative is--
+
+the answer is a function of y.
+
+So I have to go back
+from x to y.
+
+But that's simple.
+
+e to the x is y.
+
+Oh!
+
+Look at this fantastic answer.
+
+The derivative of the log, the
+thing we wanted, is 1 over y.
+
+Why do I say fantastic?
+
+Because out of the blue almost,
+we've discovered the
+
+function log y, which has that
+derivative 1 over y.
+
+And the point is this is
+the minus 1 power.
+
+It's the only power that we
+didn't produce earlier as a
+
+derivative.
+
+I have to make that point.
+
+You remember the very first
+derivatives we knew were the
+
+derivatives of x to the
+n-th, powers of x.
+
+Everybody knows that that's n
+times x to the n minus 1.
+
+The derivative of every power
+is one power below.
+
+With one exception.
+
+With one exception.
+
+If n is 0, so I have to
+put except n equals 0.
+
+Well, it's true when n is 0,
+so I don't mean the formula
+
+doesn't fail.
+
+What fails is when n is 0, this
+right-hand side is 0, and
+
+I don't get the minus 1 power.
+
+No power of x produces the minus
+1 power when I take the
+
+derivative.
+
+So that was like an open hole
+in the list of derivatives.
+
+Nobody was giving the derivative
+to be the minus 1
+
+power when we were looking
+at the powers of x.
+
+Well, here it showed up.
+
+Now, you'll say the
+letter y's there.
+
+OK, that's the 25th letter
+of the alphabet.
+
+I'm perfectly happy if you
+prefer the 26th letter.
+
+You can write d log z dz equals
+1/z if you want to.
+
+You can write, as you might
+like to, d by dx.
+
+Use the 24th letter
+of log x is 1/x.
+
+I'm perfectly OK for you to do
+that, to write the x there,
+
+now after we got the formula.
+
+Up to this point, I really had
+to keep x and y straight
+
+because I was beginning
+from y is e to the x.
+
+That was my starting point.
+
+OK, so that keeping them
+straight got me the derivative
+
+of log y as 1/y.
+
+End.
+
+Now, I'm totally happy if you
+use any other letter.
+
+Use t if you have
+things growing.
+
+And remember about the
+logarithm now.
+
+We can see why it
+grows so slowly.
+
+Because its slope is 1/y.
+
+Or let's look at this one,
+because we're used to thinking
+
+of graphs with x
+along the axis.
+
+And this is telling us that the
+slope of the log curve--
+
+the log curve is increasing, but
+the slope is decreasing,
+
+getting smaller and smaller.
+
+As x gets very small, it's
+just barely increasing.
+
+It does keep going on
+up to infinity,
+
+but very, very slowly.
+
+And why is that?
+
+That's because the exponential
+is going very, very quickly.
+
+And you remember that the one
+graph is just the flip of the
+
+other graph, so if one is
+climbing like mad, the other
+
+one is growing slowly.
+
+OK, that's the main facts, the
+most important formula of
+
+today's lecture.
+
+I could--
+
+do you feel like practice to
+take the chain in the opposite
+
+direction just to see
+what would happen?
+
+So what's the opposite
+direction?
+
+I guess the opposite direction
+is to start with--
+
+which did I start with?
+
+I started with log of
+e to the x is x.
+
+The opposite direction would be
+to start with e to the log
+
+y is y, right?
+
+That's the same chain.
+
+That's the f inverse coming
+before the f.
+
+What do I do?
+
+Take derivatives.
+
+Take the derivative
+of everything, OK?
+
+So take the derivative,
+the y-derivative.
+
+I get the nice thing.
+
+I mean, that's the fun part,
+taking the derivative on the
+
+right-hand side.
+
+On the left side, a little more
+work, but I know how to
+
+take the derivative of
+e to the something.
+
+It's the chain rule.
+
+Of course it's the chain rule.
+
+We got a chain here.
+
+So the derivative of e to the
+something, now you remember
+
+with the chain rule, is e to
+that same something times the
+
+derivative of what's inside.
+
+The derivative and what's
+inside is this guy: the
+
+derivative of log y dy.
+
+This is what we want to know,
+the one we know, and what is e
+
+to the log y?
+
+It's sitting up there
+on the line before.
+
+e to the log y is y.
+
+So this parenthesis is
+just containing y.
+
+Bring it down.
+
+Set it under there, and
+you have it again.
+
+The derivative of log y
+dy is 1 over e to the
+
+log y, which is y.
+
+OK, we sort of have done more
+about inverse functions than
+
+typical lectures might, but I
+did it really because they're
+
+kind of not so simple.
+
+And yet, they're crucially
+important in this situation of
+
+connecting exponential
+with log.
+
+And by the way, I prefer to
+start with exponential.
+
+The logic goes also just fine.
+
+In fact, some steps are a little
+smoother if you start
+
+with a logarithm function,
+define that somehow, and then
+
+take its inverse, which will
+be the exponential.
+
+But for me, the exponential
+is so all important.
+
+The logarithm is important, but
+it's not in the league of
+
+e to the x.
+
+So I prefer to do it this
+way to know e to the x.
+
+Now if you bear with me,
+I'll do the other
+
+derivative for today.
+
+The other derivative
+is this one.
+
+Can we do that?
+
+OK, so I want the derivative
+of this arc sine
+
+function, all right?
+
+So I'm going to--
+
+let me bring that.
+
+This side of the board is now
+going to be x is the inverse
+
+sine of y, or it's often called
+the arc sine of y.
+
+OK, good.
+
+All right.
+
+So again, I have a chain.
+
+I start with x.
+
+I create y.
+
+So y is sine x.
+
+So y is the sine of x, but
+x is the arc sine of y.
+
+That's the chain.
+
+Start with a y.
+
+Do f inverse.
+
+Do f, and you got y
+again, all right?
+
+Now, I'm interested in the
+derivative, the derivative of
+
+this arc sine of y.
+
+I want the y-derivative.
+
+I'm just going to copy this
+plan, but instead of e, I've
+
+got sines here.
+
+So take the y-derivative of both
+sides, the y-derivative
+
+of both sides.
+
+Well, I always like that one.
+
+The y-derivative of this
+is the chain rule.
+
+So I have the sine of some
+inside function.
+
+So the derivative is the cosine
+of that inside function
+
+times the derivative of the
+inside function, which is the
+
+guy we want.
+
+OK, so I have to figure
+out that thing.
+
+In other words, I guess I've
+got to think a little bit
+
+about these inverse
+trig functions.
+
+OK, so what's the story with
+the inverse trig functions?
+
+The point will be this
+is an angle.
+
+Ha!
+
+That's an angle.
+
+Let me draw the triangle.
+
+Here is my angle theta.
+
+Here is my sine theta.
+
+Here is my cos theta, and
+everybody knows that now the
+
+hypotenuse is 1.
+
+So here is theta.
+
+OK, whoa!
+
+Wait a minute.
+
+I would love theta to
+be the angle whose--
+
+oh, maybe it is.
+
+This is the angle whose sine--
+
+theta should be the angle
+whose sine is y, right?
+
+OK, theta is the angle
+whose sine is y.
+
+OK, let me make that happen.
+
+And now, tell me the other side
+because I got to get a
+
+cosine in here somewhere.
+
+What is this side?
+
+Back to Pythagoras, the
+most important fact
+
+about a right triangle.
+
+This side will be the
+square root of--
+
+this squared plus this squared
+is 1, so this is the square
+
+root of 1 minus y squared.
+
+And that's the cosine.
+
+The cosine of this angle theta
+is this guy divided by 1.
+
+We're there, and all I've used
+pretty quickly was I popped up
+
+a triangle there.
+
+I named an angle theta.
+
+I took its sine to be y, and
+I figured out what its
+
+cosine had to be.
+
+OK, so there's the theta.
+
+Its cosine has to be this,
+and now I'm ready to
+
+write out the answer.
+
+I'm ready to write down
+the answer there.
+
+That has a 1 equals--
+
+the cosine of theta, that's this
+times the derivative of
+
+the inverse sine.
+
+You see, I had to get this
+expression into something--
+
+I had to solve it for y.
+
+I had to figure out what
+that quantity is as
+
+a function of y.
+
+And now I just put
+this down below.
+
+So if I cross this out
+and put it down here,
+
+I've got the answer.
+
+There is the derivative of the
+arc sine function: 1 over the
+
+square root of 1 minus
+y squared.
+
+OK, it's not as beautiful as
+1/y, but it shows up in a lot
+
+of problems. As we said earlier,
+sines and cosines are
+
+involved with repeated motion,
+going around a circle, going
+
+up and down, going across
+and back, in and out.
+
+And it will turn out that this
+quantity, which is really
+
+coming from the Pythagoras, is
+going to turn up, and we'll
+
+need to know that it's the
+derivative of the arc sine.
+
+And may I just write down what's
+the derivative of the
+
+arc cosine as long
+as we're at it?
+
+And then I'm done.
+
+The derivative of the
+arc cosine, well,
+
+you remember what--
+
+what's the difference between
+sines and cosines when we take
+
+derivatives?
+
+The cosine has a minus.
+
+So there'll be a minus 1
+over the square root
+
+of 1 minus y squared.
+
+That's sort of unexpected.
+
+This function has
+this derivative.
+
+This function has the
+same derivative but
+
+with a minus sign.
+
+That suggests that somehow if I
+add those, yeah, let's just
+
+think about that for the
+last minute here.
+
+That says that if I add sine
+inverse y to cosine inverse y,
+
+their derivatives will cancel.
+
+So the derivative of that
+sum of this one--
+
+can I do a giant plus
+sign there?--
+
+is 0.
+
+The derivative of that plus the
+derivative of that is a
+
+plus thing and a minus
+thing, giving 0.
+
+So how could that be?
+
+Have you ever thought
+about what functions
+
+have derivative 0?
+
+Well, actually, you have.
+You know what
+
+functions have no slope.
+
+Constant functions.
+
+So I'm saying that it must
+happen that the arc sine
+
+function plus the arc cosine
+function is a constant.
+
+Then its derivative
+is 0, and we are
+
+happy with our formulas.
+
+And actually, that's true.
+
+The arc sine function
+gives me this angle.
+
+The arc cosine function
+would give me--
+
+shall I give that angle another
+name like alpha?
+
+This one would be the theta.
+
+That one would be the alpha.
+
+And do you believe that in that
+triangle theta plus alpha
+
+is a constant and therefore
+has derivative 0?
+
+In fact, yes, you
+know what it is.
+
+Theta plus alpha in a right
+triangle, if I add that angle
+
+and that angle, I
+get 90 degrees.
+
+A constant.
+
+Well, 90 degrees, but I
+shouldn't allow myself to
+
+write that.
+
+I must write it in radians.
+
+A constant.
+
+OK, don't forget the great
+result from today.
+
+We filled in the one power that
+was missing, and we're
+
+ready to go.
+
+Thank you.
+
+NARRATOR: This has been
+a production of MIT
+
+OpenCourseWare and
+Gilbert Strang.
+
+Funding for this video was
+provided by the Lord
+
+Foundation.
+
+To help OCW continue to provide
+free and open access
+
+to MIT courses, please
+make a donation at
+
+ocw.mit.edu/donate.
\ No newline at end of file
diff --git a/caonmXHGB60.txt b/caonmXHGB60.txt
new file mode 100644
index 0000000000000000000000000000000000000000..d9c4a2954ec3324f66359b7d0ac6327d3240dca3
--- /dev/null
+++ b/caonmXHGB60.txt
@@ -0,0 +1,8267 @@
+align:start position:0%
+ 
+the following content is provided under
+
+ align:start position:0%
+the following content is provided under
+ 
+
+ align:start position:0%
+the following content is provided under
+a Creative Commons license your support
+
+ align:start position:0%
+a Creative Commons license your support
+ 
+
+ align:start position:0%
+a Creative Commons license your support
+will help MIT open courseware continue
+
+ align:start position:0%
+will help MIT open courseware continue
+ 
+
+ align:start position:0%
+will help MIT open courseware continue
+to offer highquality educational
+
+ align:start position:0%
+to offer highquality educational
+ 
+
+ align:start position:0%
+to offer highquality educational
+resources for free to make a donation or
+
+ align:start position:0%
+resources for free to make a donation or
+ 
+
+ align:start position:0%
+resources for free to make a donation or
+to view additional materials from
+
+ align:start position:0%
+to view additional materials from
+ 
+
+ align:start position:0%
+to view additional materials from
+hundreds of MIT courses visit MIT open
+
+ align:start position:0%
+hundreds of MIT courses visit MIT open
+ 
+
+ align:start position:0%
+hundreds of MIT courses visit MIT open
+courseware at
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+ocw.mit.edu there were five types of
+
+ align:start position:0%
+ocw.mit.edu there were five types of
+ 
+
+ align:start position:0%
+ocw.mit.edu there were five types of
+problems we just did two
+
+ align:start position:0%
+problems we just did two
+ 
+
+ align:start position:0%
+problems we just did two
+and now I'm going to convince you that
+
+ align:start position:0%
+and now I'm going to convince you that
+ 
+
+ align:start position:0%
+and now I'm going to convince you that
+salt and water problems are in fact the
+
+ align:start position:0%
+salt and water problems are in fact the
+ 
+
+ align:start position:0%
+salt and water problems are in fact the
+same as weak acid weak based
+
+ align:start position:0%
+same as weak acid weak based
+ 
+
+ align:start position:0%
+same as weak acid weak based
+problems so we're going to move now to
+
+ align:start position:0%
+problems so we're going to move now to
+ 
+
+ align:start position:0%
+problems so we're going to move now to
+today's
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+handout so the pH of a salt
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+solution is determined by what made that
+
+ align:start position:0%
+solution is determined by what made that
+ 
+
+ align:start position:0%
+solution is determined by what made that
+salt so a salt is formed when you
+
+ align:start position:0%
+salt so a salt is formed when you
+ 
+
+ align:start position:0%
+salt so a salt is formed when you
+neutralize an acid with a base or a base
+
+ align:start position:0%
+neutralize an acid with a base or a base
+ 
+
+ align:start position:0%
+neutralize an acid with a base or a base
+with an
+
+ align:start position:0%
+with an
+ 
+
+ align:start position:0%
+with an
+acid and so depending on what acid and
+
+ align:start position:0%
+acid and so depending on what acid and
+ 
+
+ align:start position:0%
+acid and so depending on what acid and
+which base were used and mixed together
+
+ align:start position:0%
+which base were used and mixed together
+ 
+
+ align:start position:0%
+which base were used and mixed together
+the salt might have different a
+
+ align:start position:0%
+the salt might have different a
+ 
+
+ align:start position:0%
+the salt might have different a
+different pH so an example here if we
+
+ align:start position:0%
+different pH so an example here if we
+ 
+
+ align:start position:0%
+different pH so an example here if we
+had
+
+ align:start position:0%
+had
+ 
+
+ align:start position:0%
+had
+HCL and NaOH that's going to give our
+
+ align:start position:0%
+HCL and NaOH that's going to give our
+ 
+
+ align:start position:0%
+HCL and NaOH that's going to give our
+friend table salt NAC and
+
+ align:start position:0%
+friend table salt NAC and
+ 
+
+ align:start position:0%
+friend table salt NAC and
+water the pH of the salt in water is not
+
+ align:start position:0%
+water the pH of the salt in water is not
+ 
+
+ align:start position:0%
+water the pH of the salt in water is not
+always neutral in this case it would be
+
+ align:start position:0%
+always neutral in this case it would be
+ 
+
+ align:start position:0%
+always neutral in this case it would be
+but it's not always neutral it depends
+
+ align:start position:0%
+but it's not always neutral it depends
+ 
+
+ align:start position:0%
+but it's not always neutral it depends
+on the nature of the acid and the nature
+
+ align:start position:0%
+on the nature of the acid and the nature
+ 
+
+ align:start position:0%
+on the nature of the acid and the nature
+of the base that we're mixed together to
+
+ align:start position:0%
+of the base that we're mixed together to
+ 
+
+ align:start position:0%
+of the base that we're mixed together to
+form that salt so there's some
+
+ align:start position:0%
+form that salt so there's some
+ 
+
+ align:start position:0%
+form that salt so there's some
+rules to help you figure out whether
+
+ align:start position:0%
+rules to help you figure out whether
+ 
+
+ align:start position:0%
+rules to help you figure out whether
+something's going to be acidic or
+
+ align:start position:0%
+something's going to be acidic or
+ 
+
+ align:start position:0%
+something's going to be acidic or
+basic and if you have a salt that
+
+ align:start position:0%
+basic and if you have a salt that
+ 
+
+ align:start position:0%
+basic and if you have a salt that
+contains conjugate acids in ba conjugate
+
+ align:start position:0%
+contains conjugate acids in ba conjugate
+ 
+
+ align:start position:0%
+contains conjugate acids in ba conjugate
+acid of a weak base so it has a
+
+ align:start position:0%
+acid of a weak base so it has a
+ 
+
+ align:start position:0%
+acid of a weak base so it has a
+conjugate acid in it will produce an
+
+ align:start position:0%
+conjugate acid in it will produce an
+ 
+
+ align:start position:0%
+conjugate acid in it will produce an
+acidic
+
+ align:start position:0%
+acidic
+ 
+
+ align:start position:0%
+acidic
+solution and if you have a salt that has
+
+ align:start position:0%
+solution and if you have a salt that has
+ 
+
+ align:start position:0%
+solution and if you have a salt that has
+small highly charged metal cats like
+
+ align:start position:0%
+small highly charged metal cats like
+ 
+
+ align:start position:0%
+small highly charged metal cats like
+iron plus three that will also be
+
+ align:start position:0%
+iron plus three that will also be
+ 
+
+ align:start position:0%
+iron plus three that will also be
+acidic so we saw last time I had the
+
+ align:start position:0%
+acidic so we saw last time I had the
+ 
+
+ align:start position:0%
+acidic so we saw last time I had the
+medicine from prescription medicine for
+
+ align:start position:0%
+medicine from prescription medicine for
+ 
+
+ align:start position:0%
+medicine from prescription medicine for
+my daughter which was iron sulfate was
+
+ align:start position:0%
+my daughter which was iron sulfate was
+ 
+
+ align:start position:0%
+my daughter which was iron sulfate was
+highly
+
+ align:start position:0%
+highly
+ 
+
+ align:start position:0%
+highly
+acidic so note that periodic table group
+
+ align:start position:0%
+acidic so note that periodic table group
+ 
+
+ align:start position:0%
+acidic so note that periodic table group
+one and group two ions lithium plus 1
+
+ align:start position:0%
+one and group two ions lithium plus 1
+ 
+
+ align:start position:0%
+one and group two ions lithium plus 1
+calcium plus two sodium + one um any
+
+ align:start position:0%
+calcium plus two sodium + one um any
+ 
+
+ align:start position:0%
+calcium plus two sodium + one um any
+these are all going to be
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+neutral and in fact anything plus one
+
+ align:start position:0%
+neutral and in fact anything plus one
+ 
+
+ align:start position:0%
+neutral and in fact anything plus one
+neutral and then salts that can take
+
+ align:start position:0%
+neutral and then salts that can take
+ 
+
+ align:start position:0%
+neutral and then salts that can take
+conjugate bases of weak acids will
+
+ align:start position:0%
+conjugate bases of weak acids will
+ 
+
+ align:start position:0%
+conjugate bases of weak acids will
+produce basic solution so you're going
+
+ align:start position:0%
+produce basic solution so you're going
+ 
+
+ align:start position:0%
+produce basic solution so you're going
+to be asking yourself does this solution
+
+ align:start position:0%
+to be asking yourself does this solution
+ 
+
+ align:start position:0%
+to be asking yourself does this solution
+have a conjugate acid of a weak base
+
+ align:start position:0%
+have a conjugate acid of a weak base
+ 
+
+ align:start position:0%
+have a conjugate acid of a weak base
+does it have a conjugate base of a weak
+
+ align:start position:0%
+does it have a conjugate base of a weak
+ 
+
+ align:start position:0%
+does it have a conjugate base of a weak
+acid does it have have group one group
+
+ align:start position:0%
+acid does it have have group one group
+ 
+
+ align:start position:0%
+acid does it have have group one group
+two what's in there and then you can
+
+ align:start position:0%
+two what's in there and then you can
+ 
+
+ align:start position:0%
+two what's in there and then you can
+think about whether it's going to be
+
+ align:start position:0%
+think about whether it's going to be
+ 
+
+ align:start position:0%
+think about whether it's going to be
+acidic neutral or basic so let's look at
+
+ align:start position:0%
+acidic neutral or basic so let's look at
+ 
+
+ align:start position:0%
+acidic neutral or basic so let's look at
+some
+
+ align:start position:0%
+some
+ 
+
+ align:start position:0%
+some
+examples so we have a salt nh4 CL and we
+
+ align:start position:0%
+examples so we have a salt nh4 CL and we
+ 
+
+ align:start position:0%
+examples so we have a salt nh4 CL and we
+want to figure out is this going to
+
+ align:start position:0%
+want to figure out is this going to
+ 
+
+ align:start position:0%
+want to figure out is this going to
+produce an acidic solution a neutral
+
+ align:start position:0%
+produce an acidic solution a neutral
+ 
+
+ align:start position:0%
+produce an acidic solution a neutral
+solution or a basic solution so we need
+
+ align:start position:0%
+solution or a basic solution so we need
+ 
+
+ align:start position:0%
+solution or a basic solution so we need
+to think about what went into making
+
+ align:start position:0%
+to think about what went into making
+ 
+
+ align:start position:0%
+to think about what went into making
+this salt and we're going to break apart
+
+ align:start position:0%
+this salt and we're going to break apart
+ 
+
+ align:start position:0%
+this salt and we're going to break apart
+the salt and we're going to think about
+
+ align:start position:0%
+the salt and we're going to think about
+ 
+
+ align:start position:0%
+the salt and we're going to think about
+nh4 Plus and we're going to think about
+
+ align:start position:0%
+nh4 Plus and we're going to think about
+ 
+
+ align:start position:0%
+nh4 Plus and we're going to think about
+CL
+
+ align:start position:0%
+CL
+ 
+
+ align:start position:0%
+CL
+minus so let's think about
+
+ align:start position:0%
+minus so let's think about
+ 
+
+ align:start position:0%
+minus so let's think about
+nh4+ first and we're going to ask the
+
+ align:start position:0%
+nh4+ first and we're going to ask the
+ 
+
+ align:start position:0%
+nh4+ first and we're going to ask the
+question is nh4+ a conjugate acid of a
+
+ align:start position:0%
+question is nh4+ a conjugate acid of a
+ 
+
+ align:start position:0%
+question is nh4+ a conjugate acid of a
+weak base and therefore a weak acid
+
+ align:start position:0%
+weak base and therefore a weak acid
+ 
+
+ align:start position:0%
+weak base and therefore a weak acid
+itself one way to answer this question
+
+ align:start position:0%
+itself one way to answer this question
+ 
+
+ align:start position:0%
+itself one way to answer this question
+is to look up the KA for
+
+ align:start position:0%
+is to look up the KA for
+ 
+
+ align:start position:0%
+is to look up the KA for
+nh4+ which happens to be 5.6 * 10us 10
+
+ align:start position:0%
+nh4+ which happens to be 5.6 * 10us 10
+ 
+
+ align:start position:0%
+nh4+ which happens to be 5.6 * 10us 10
+you could also ask about the weak base
+
+ align:start position:0%
+you could also ask about the weak base
+ 
+
+ align:start position:0%
+you could also ask about the weak base
+that it came from the weak base in this
+
+ align:start position:0%
+that it came from the weak base in this
+ 
+
+ align:start position:0%
+that it came from the weak base in this
+case its conjugate base is NH3 and ask
+
+ align:start position:0%
+case its conjugate base is NH3 and ask
+ 
+
+ align:start position:0%
+case its conjugate base is NH3 and ask
+if that's a weak base so if you have
+
+ align:start position:0%
+if that's a weak base so if you have
+ 
+
+ align:start position:0%
+if that's a weak base so if you have
+something that is a con is an acid here
+
+ align:start position:0%
+something that is a con is an acid here
+ 
+
+ align:start position:0%
+something that is a con is an acid here
+you can think about what the base would
+
+ align:start position:0%
+you can think about what the base would
+ 
+
+ align:start position:0%
+you can think about what the base would
+be by removing H+ if you remove H+ from
+
+ align:start position:0%
+be by removing H+ if you remove H+ from
+ 
+
+ align:start position:0%
+be by removing H+ if you remove H+ from
+nh4+ you get NH3 and you can say is NH3
+
+ align:start position:0%
+nh4+ you get NH3 and you can say is NH3
+ 
+
+ align:start position:0%
+nh4+ you get NH3 and you can say is NH3
+a weak base and look up a KB in this
+
+ align:start position:0%
+a weak base and look up a KB in this
+ 
+
+ align:start position:0%
+a weak base and look up a KB in this
+case it's 1.8 * * 10us 5 so what do you
+
+ align:start position:0%
+case it's 1.8 * * 10us 5 so what do you
+ 
+
+ align:start position:0%
+case it's 1.8 * * 10us 5 so what do you
+do you think is this a is this a weak
+
+ align:start position:0%
+do you think is this a is this a weak
+ 
+
+ align:start position:0%
+do you think is this a is this a weak
+base and this a weak acid with those
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+numbers what do you think is that a weak
+
+ align:start position:0%
+numbers what do you think is that a weak
+ 
+
+ align:start position:0%
+numbers what do you think is that a weak
+weak acid is that a strong acid no so
+
+ align:start position:0%
+weak acid is that a strong acid no so
+ 
+
+ align:start position:0%
+weak acid is that a strong acid no so
+it's a weak acid is this a weak base
+
+ align:start position:0%
+it's a weak acid is this a weak base
+ 
+
+ align:start position:0%
+it's a weak acid is this a weak base
+yeah so we can look also in this uh this
+
+ align:start position:0%
+yeah so we can look also in this uh this
+ 
+
+ align:start position:0%
+yeah so we can look also in this uh this
+chart down here and so NH3 is a
+
+ align:start position:0%
+chart down here and so NH3 is a
+ 
+
+ align:start position:0%
+chart down here and so NH3 is a
+moderately weak base and nh4 plus is a
+
+ align:start position:0%
+moderately weak base and nh4 plus is a
+ 
+
+ align:start position:0%
+moderately weak base and nh4 plus is a
+very weak base but it is I mean weak a
+
+ align:start position:0%
+very weak base but it is I mean weak a
+ 
+
+ align:start position:0%
+very weak base but it is I mean weak a
+very weak acid but it is a weak acid so
+
+ align:start position:0%
+very weak acid but it is a weak acid so
+ 
+
+ align:start position:0%
+very weak acid but it is a weak acid so
+we do have a conjugate acid of a weak
+
+ align:start position:0%
+we do have a conjugate acid of a weak
+ 
+
+ align:start position:0%
+we do have a conjugate acid of a weak
+base so it is acidic not super acidic
+
+ align:start position:0%
+base so it is acidic not super acidic
+ 
+
+ align:start position:0%
+base so it is acidic not super acidic
+but it is acidic and NH3 is a weak base
+
+ align:start position:0%
+but it is acidic and NH3 is a weak base
+ 
+
+ align:start position:0%
+but it is acidic and NH3 is a weak base
+and so we probably had NH3 as our base
+
+ align:start position:0%
+and so we probably had NH3 as our base
+ 
+
+ align:start position:0%
+and so we probably had NH3 as our base
+that was being added and it formed the
+
+ align:start position:0%
+that was being added and it formed the
+ 
+
+ align:start position:0%
+that was being added and it formed the
+conjugate acid in this so then this
+
+ align:start position:0%
+conjugate acid in this so then this
+ 
+
+ align:start position:0%
+conjugate acid in this so then this
+would produce an acidic solution because
+
+ align:start position:0%
+would produce an acidic solution because
+ 
+
+ align:start position:0%
+would produce an acidic solution because
+we have this conjugate acid that's
+
+ align:start position:0%
+we have this conjugate acid that's
+ 
+
+ align:start position:0%
+we have this conjugate acid that's
+formed so from this part just from the
+
+ align:start position:0%
+formed so from this part just from the
+ 
+
+ align:start position:0%
+formed so from this part just from the
+nh4+ it should be
+
+ align:start position:0%
+nh4+ it should be
+ 
+
+ align:start position:0%
+nh4+ it should be
+acidic and now we can consider CL minus
+
+ align:start position:0%
+acidic and now we can consider CL minus
+ 
+
+ align:start position:0%
+acidic and now we can consider CL minus
+so here we're asking the question is CL
+
+ align:start position:0%
+so here we're asking the question is CL
+ 
+
+ align:start position:0%
+so here we're asking the question is CL
+minus a conjugate base of a weak acid
+
+ align:start position:0%
+minus a conjugate base of a weak acid
+ 
+
+ align:start position:0%
+minus a conjugate base of a weak acid
+and therefore itself a weak base and if
+
+ align:start position:0%
+and therefore itself a weak base and if
+ 
+
+ align:start position:0%
+and therefore itself a weak base and if
+you tried to look up the KB of Cl minus
+
+ align:start position:0%
+you tried to look up the KB of Cl minus
+ 
+
+ align:start position:0%
+you tried to look up the KB of Cl minus
+you would not find it in any table but
+
+ align:start position:0%
+you would not find it in any table but
+ 
+
+ align:start position:0%
+you would not find it in any table but
+you could find in a table it's conjugate
+
+ align:start position:0%
+you could find in a table it's conjugate
+ 
+
+ align:start position:0%
+you could find in a table it's conjugate
+acid so if you add H+ to CL minus you
+
+ align:start position:0%
+acid so if you add H+ to CL minus you
+ 
+
+ align:start position:0%
+acid so if you add H+ to CL minus you
+get HCL and so you could look up a KA
+
+ align:start position:0%
+get HCL and so you could look up a KA
+ 
+
+ align:start position:0%
+get HCL and so you could look up a KA
+for that in a table and it's time 10 7
+
+ align:start position:0%
+for that in a table and it's time 10 7
+ 
+
+ align:start position:0%
+for that in a table and it's time 10 7
+so is this a weak acid no it's a strong
+
+ align:start position:0%
+so is this a weak acid no it's a strong
+ 
+
+ align:start position:0%
+so is this a weak acid no it's a strong
+acid so it's not a weak acid it's a
+
+ align:start position:0%
+acid so it's not a weak acid it's a
+ 
+
+ align:start position:0%
+acid so it's not a weak acid it's a
+strong acid so is CL minus going to be
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+basic no so it is not it is not going to
+
+ align:start position:0%
+basic no so it is not it is not going to
+ 
+
+ align:start position:0%
+basic no so it is not it is not going to
+be a um a basic solution if we look over
+
+ align:start position:0%
+be a um a basic solution if we look over
+ 
+
+ align:start position:0%
+be a um a basic solution if we look over
+here we see HCL is a strong acid and so
+
+ align:start position:0%
+here we see HCL is a strong acid and so
+ 
+
+ align:start position:0%
+here we see HCL is a strong acid and so
+its conjugate base is ineffective at its
+
+ align:start position:0%
+its conjugate base is ineffective at its
+ 
+
+ align:start position:0%
+its conjugate base is ineffective at its
+base it just doesn't work as a base at
+
+ align:start position:0%
+base it just doesn't work as a base at
+ 
+
+ align:start position:0%
+base it just doesn't work as a base at
+all so with a number of 10 to the 7th it
+
+ align:start position:0%
+all so with a number of 10 to the 7th it
+ 
+
+ align:start position:0%
+all so with a number of 10 to the 7th it
+really goes to completion it's a strong
+
+ align:start position:0%
+really goes to completion it's a strong
+ 
+
+ align:start position:0%
+really goes to completion it's a strong
+acid by our definition and so CL minus
+
+ align:start position:0%
+acid by our definition and so CL minus
+ 
+
+ align:start position:0%
+acid by our definition and so CL minus
+is not going to do anything to the
+
+ align:start position:0%
+is not going to do anything to the
+ 
+
+ align:start position:0%
+is not going to do anything to the
+solution it's not going to be useful as
+
+ align:start position:0%
+solution it's not going to be useful as
+ 
+
+ align:start position:0%
+solution it's not going to be useful as
+a weak base so this solution is going to
+
+ align:start position:0%
+a weak base so this solution is going to
+ 
+
+ align:start position:0%
+a weak base so this solution is going to
+be neutral or this the part of the
+
+ align:start position:0%
+be neutral or this the part of the
+ 
+
+ align:start position:0%
+be neutral or this the part of the
+solution due to CL minus will be neutral
+
+ align:start position:0%
+solution due to CL minus will be neutral
+ 
+
+ align:start position:0%
+solution due to CL minus will be neutral
+so here we have something that is acidic
+
+ align:start position:0%
+so here we have something that is acidic
+ 
+
+ align:start position:0%
+so here we have something that is acidic
+and something that's neutral and so
+
+ align:start position:0%
+and something that's neutral and so
+ 
+
+ align:start position:0%
+and something that's neutral and so
+overall the solution is
+
+ align:start position:0%
+overall the solution is
+ 
+
+ align:start position:0%
+overall the solution is
+acidic so you need to break down the two
+
+ align:start position:0%
+acidic so you need to break down the two
+ 
+
+ align:start position:0%
+acidic so you need to break down the two
+parts you had an acid and a base being
+
+ align:start position:0%
+parts you had an acid and a base being
+ 
+
+ align:start position:0%
+parts you had an acid and a base being
+mixed here we had HCL um mixed with um
+
+ align:start position:0%
+mixed here we had HCL um mixed with um
+ 
+
+ align:start position:0%
+mixed here we had HCL um mixed with um
+NH3 and formed this nh4 um CL salt and
+
+ align:start position:0%
+NH3 and formed this nh4 um CL salt and
+ 
+
+ align:start position:0%
+NH3 and formed this nh4 um CL salt and
+that's going to be acidic because HCL
+
+ align:start position:0%
+that's going to be acidic because HCL
+ 
+
+ align:start position:0%
+that's going to be acidic because HCL
+was a weak acid its conjugate is
+
+ align:start position:0%
+was a weak acid its conjugate is
+ 
+
+ align:start position:0%
+was a weak acid its conjugate is
+ineffective whereas NH3 was a weak base
+
+ align:start position:0%
+ineffective whereas NH3 was a weak base
+ 
+
+ align:start position:0%
+ineffective whereas NH3 was a weak base
+so it has a conjugate acid that's a weak
+
+ align:start position:0%
+so it has a conjugate acid that's a weak
+ 
+
+ align:start position:0%
+so it has a conjugate acid that's a weak
+acid a very weak acid but still a weak
+
+ align:start position:0%
+acid a very weak acid but still a weak
+ 
+
+ align:start position:0%
+acid a very weak acid but still a weak
+acid all right so that's how you think
+
+ align:start position:0%
+acid all right so that's how you think
+ 
+
+ align:start position:0%
+acid all right so that's how you think
+about these salt problems so they really
+
+ align:start position:0%
+about these salt problems so they really
+ 
+
+ align:start position:0%
+about these salt problems so they really
+break down to weak acid and weak base
+
+ align:start position:0%
+break down to weak acid and weak base
+ 
+
+ align:start position:0%
+break down to weak acid and weak base
+problems so why don't you give this one
+
+ align:start position:0%
+problems so why don't you give this one
+ 
+
+ align:start position:0%
+problems so why don't you give this one
+a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+try all right all right let's just do 10
+
+ align:start position:0%
+try all right all right let's just do 10
+ 
+
+ align:start position:0%
+try all right all right let's just do 10
+more
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+seconds that is correct all right let's
+
+ align:start position:0%
+seconds that is correct all right let's
+ 
+
+ align:start position:0%
+seconds that is correct all right let's
+look at why that's
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+correct so it will produce a basic
+
+ align:start position:0%
+correct so it will produce a basic
+ 
+
+ align:start position:0%
+correct so it will produce a basic
+solution so we're going to break it down
+
+ align:start position:0%
+solution so we're going to break it down
+ 
+
+ align:start position:0%
+solution so we're going to break it down
+to to na+ that's one of the things in
+
+ align:start position:0%
+to to na+ that's one of the things in
+ 
+
+ align:start position:0%
+to to na+ that's one of the things in
+there and we ask is na+ a conjugate acid
+
+ align:start position:0%
+there and we ask is na+ a conjugate acid
+ 
+
+ align:start position:0%
+there and we ask is na+ a conjugate acid
+of a weak base is it going to be neutral
+
+ align:start position:0%
+of a weak base is it going to be neutral
+ 
+
+ align:start position:0%
+of a weak base is it going to be neutral
+acidic or basic and what's it going to
+
+ align:start position:0%
+acidic or basic and what's it going to
+ 
+
+ align:start position:0%
+acidic or basic and what's it going to
+be it's going to be neutral it is not a
+
+ align:start position:0%
+be it's going to be neutral it is not a
+ 
+
+ align:start position:0%
+be it's going to be neutral it is not a
+conjugate acid of a weak base it's group
+
+ align:start position:0%
+conjugate acid of a weak base it's group
+ 
+
+ align:start position:0%
+conjugate acid of a weak base it's group
+one it'll be
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+neutral so this is not contributing to
+
+ align:start position:0%
+neutral so this is not contributing to
+ 
+
+ align:start position:0%
+neutral so this is not contributing to
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+pH so let's look at the second part and
+
+ align:start position:0%
+pH so let's look at the second part and
+ 
+
+ align:start position:0%
+pH so let's look at the second part and
+look at ch3 Co minus so we have this can
+
+ align:start position:0%
+look at ch3 Co minus so we have this can
+ 
+
+ align:start position:0%
+look at ch3 Co minus so we have this can
+be divided into na+ and
+
+ align:start position:0%
+be divided into na+ and
+ 
+
+ align:start position:0%
+be divided into na+ and
+h3c minus and then we ask is this a
+
+ align:start position:0%
+h3c minus and then we ask is this a
+ 
+
+ align:start position:0%
+h3c minus and then we ask is this a
+conjugate base of a weak acid or we
+
+ align:start position:0%
+conjugate base of a weak acid or we
+ 
+
+ align:start position:0%
+conjugate base of a weak acid or we
+could ask the other question is this
+
+ align:start position:0%
+could ask the other question is this
+ 
+
+ align:start position:0%
+could ask the other question is this
+over here a weak acid and the KA for
+
+ align:start position:0%
+over here a weak acid and the KA for
+ 
+
+ align:start position:0%
+over here a weak acid and the KA for
+that was given so is that a weak acid or
+
+ align:start position:0%
+that was given so is that a weak acid or
+ 
+
+ align:start position:0%
+that was given so is that a weak acid or
+a strong acid is it
+
+ align:start position:0%
+a strong acid is it
+ 
+
+ align:start position:0%
+a strong acid is it
+weak or strong weak yes so the answer is
+
+ align:start position:0%
+weak or strong weak yes so the answer is
+ 
+
+ align:start position:0%
+weak or strong weak yes so the answer is
+yes it's weak and so its conjugate base
+
+ align:start position:0%
+yes it's weak and so its conjugate base
+ 
+
+ align:start position:0%
+yes it's weak and so its conjugate base
+would also be a weak
+
+ align:start position:0%
+would also be a weak
+ 
+
+ align:start position:0%
+would also be a weak
+base and so therefore this will be
+
+ align:start position:0%
+base and so therefore this will be
+ 
+
+ align:start position:0%
+base and so therefore this will be
+acidic so sometimes you'll be given Ka
+
+ align:start position:0%
+acidic so sometimes you'll be given Ka
+ 
+
+ align:start position:0%
+acidic so sometimes you'll be given Ka
+sometimes you'll be given KBS if you're
+
+ align:start position:0%
+sometimes you'll be given KBS if you're
+ 
+
+ align:start position:0%
+sometimes you'll be given KBS if you're
+given either one of them you can answer
+
+ align:start position:0%
+given either one of them you can answer
+ 
+
+ align:start position:0%
+given either one of them you can answer
+the question if you want you can convert
+
+ align:start position:0%
+the question if you want you can convert
+ 
+
+ align:start position:0%
+the question if you want you can convert
+your Ka to your KB what would you use to
+
+ align:start position:0%
+your Ka to your KB what would you use to
+ 
+
+ align:start position:0%
+your Ka to your KB what would you use to
+convert Ka to
+
+ align:start position:0%
+convert Ka to
+ 
+
+ align:start position:0%
+convert Ka to
+KB KW right but just with one of these
+
+ align:start position:0%
+KB KW right but just with one of these
+ 
+
+ align:start position:0%
+KB KW right but just with one of these
+pieces of information you should be able
+
+ align:start position:0%
+pieces of information you should be able
+ 
+
+ align:start position:0%
+pieces of information you should be able
+to answer this
+
+ align:start position:0%
+to answer this
+ 
+
+ align:start position:0%
+to answer this
+question so let's just look at the
+
+ align:start position:0%
+question so let's just look at the
+ 
+
+ align:start position:0%
+question so let's just look at the
+general rule now you have a compound
+
+ align:start position:0%
+general rule now you have a compound
+ 
+
+ align:start position:0%
+general rule now you have a compound
+XY that can be broken up into
+
+ align:start position:0%
+XY that can be broken up into
+ 
+
+ align:start position:0%
+XY that can be broken up into
+X+ and you'll ask yourself is X+ a
+
+ align:start position:0%
+X+ and you'll ask yourself is X+ a
+ 
+
+ align:start position:0%
+X+ and you'll ask yourself is X+ a
+conjugate acid of a weak base if yes
+
+ align:start position:0%
+conjugate acid of a weak base if yes
+ 
+
+ align:start position:0%
+conjugate acid of a weak base if yes
+then the solution will be acidic if no
+
+ align:start position:0%
+then the solution will be acidic if no
+ 
+
+ align:start position:0%
+then the solution will be acidic if no
+it'll be
+
+ align:start position:0%
+it'll be
+ 
+
+ align:start position:0%
+it'll be
+neutral for y you have y minus is y
+
+ align:start position:0%
+neutral for y you have y minus is y
+ 
+
+ align:start position:0%
+neutral for y you have y minus is y
+minus a conjugate base of a weak acid if
+
+ align:start position:0%
+minus a conjugate base of a weak acid if
+ 
+
+ align:start position:0%
+minus a conjugate base of a weak acid if
+yes then it's going to be add some basic
+
+ align:start position:0%
+yes then it's going to be add some basic
+ 
+
+ align:start position:0%
+yes then it's going to be add some basic
+uh nature to this if no neutral and then
+
+ align:start position:0%
+uh nature to this if no neutral and then
+ 
+
+ align:start position:0%
+uh nature to this if no neutral and then
+overall you say if it's acidic plus
+
+ align:start position:0%
+overall you say if it's acidic plus
+ 
+
+ align:start position:0%
+overall you say if it's acidic plus
+neutral that's acidic basic plus neutral
+
+ align:start position:0%
+neutral that's acidic basic plus neutral
+ 
+
+ align:start position:0%
+neutral that's acidic basic plus neutral
+basic neutral plus neutral neutral and
+
+ align:start position:0%
+basic neutral plus neutral neutral and
+ 
+
+ align:start position:0%
+basic neutral plus neutral neutral and
+if I give you a question of something
+
+ align:start position:0%
+if I give you a question of something
+ 
+
+ align:start position:0%
+if I give you a question of something
+that is acidic and basic you can answer
+
+ align:start position:0%
+that is acidic and basic you can answer
+ 
+
+ align:start position:0%
+that is acidic and basic you can answer
+the question without doing math because
+
+ align:start position:0%
+the question without doing math because
+ 
+
+ align:start position:0%
+the question without doing math because
+it'll depend on the KA of one thing and
+
+ align:start position:0%
+it'll depend on the KA of one thing and
+ 
+
+ align:start position:0%
+it'll depend on the KA of one thing and
+the KB of the other thing and you'll
+
+ align:start position:0%
+the KB of the other thing and you'll
+ 
+
+ align:start position:0%
+the KB of the other thing and you'll
+have to see which ones a stronger acid
+
+ align:start position:0%
+have to see which ones a stronger acid
+ 
+
+ align:start position:0%
+have to see which ones a stronger acid
+and which one
+
+ align:start position:0%
+and which one
+ 
+
+ align:start position:0%
+and which one
+or a stronger base and so you can't just
+
+ align:start position:0%
+or a stronger base and so you can't just
+ 
+
+ align:start position:0%
+or a stronger base and so you can't just
+simply answer the question now you may
+
+ align:start position:0%
+simply answer the question now you may
+ 
+
+ align:start position:0%
+simply answer the question now you may
+note that I did mention that problem set
+
+ align:start position:0%
+note that I did mention that problem set
+ 
+
+ align:start position:0%
+note that I did mention that problem set
+7even is long it takes a long time to do
+
+ align:start position:0%
+7even is long it takes a long time to do
+ 
+
+ align:start position:0%
+7even is long it takes a long time to do
+these problems and so an exam writing a
+
+ align:start position:0%
+these problems and so an exam writing a
+ 
+
+ align:start position:0%
+these problems and so an exam writing a
+fair exam when the problems take a long
+
+ align:start position:0%
+fair exam when the problems take a long
+ 
+
+ align:start position:0%
+fair exam when the problems take a long
+time to do is hard but these are short
+
+ align:start position:0%
+time to do is hard but these are short
+ 
+
+ align:start position:0%
+time to do is hard but these are short
+little things I could ask you to predict
+
+ align:start position:0%
+little things I could ask you to predict
+ 
+
+ align:start position:0%
+little things I could ask you to predict
+the pH of salt by just thinking about
+
+ align:start position:0%
+the pH of salt by just thinking about
+ 
+
+ align:start position:0%
+the pH of salt by just thinking about
+things and looking up some KBS and some
+
+ align:start position:0%
+things and looking up some KBS and some
+ 
+
+ align:start position:0%
+things and looking up some KBS and some
+Ka so these are good short questions on
+
+ align:start position:0%
+Ka so these are good short questions on
+ 
+
+ align:start position:0%
+Ka so these are good short questions on
+the exam so I'm probably not going to
+
+ align:start position:0%
+the exam so I'm probably not going to
+ 
+
+ align:start position:0%
+the exam so I'm probably not going to
+give you one if it's supposed to be a
+
+ align:start position:0%
+give you one if it's supposed to be a
+ 
+
+ align:start position:0%
+give you one if it's supposed to be a
+short question that is an acid and a
+
+ align:start position:0%
+short question that is an acid and a
+ 
+
+ align:start position:0%
+short question that is an acid and a
+base mixed uh mixed together because
+
+ align:start position:0%
+base mixed uh mixed together because
+ 
+
+ align:start position:0%
+base mixed uh mixed together because
+then you'd have to do some math so uh
+
+ align:start position:0%
+then you'd have to do some math so uh
+ 
+
+ align:start position:0%
+then you'd have to do some math so uh
+keep that keep that in mind all right so
+
+ align:start position:0%
+keep that keep that in mind all right so
+ 
+
+ align:start position:0%
+keep that keep that in mind all right so
+salts salt and water problems are really
+
+ align:start position:0%
+salts salt and water problems are really
+ 
+
+ align:start position:0%
+salts salt and water problems are really
+just weak acid in water or weak base in
+
+ align:start position:0%
+just weak acid in water or weak base in
+ 
+
+ align:start position:0%
+just weak acid in water or weak base in
+water problems which you already know
+
+ align:start position:0%
+water problems which you already know
+ 
+
+ align:start position:0%
+water problems which you already know
+how to do so we're going to move on now
+
+ align:start position:0%
+how to do so we're going to move on now
+ 
+
+ align:start position:0%
+how to do so we're going to move on now
+to
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+buffers
+
+ align:start position:0%
+buffers
+ 
+
+ align:start position:0%
+buffers
+buffers so a buffer is a solution that
+
+ align:start position:0%
+buffers so a buffer is a solution that
+ 
+
+ align:start position:0%
+buffers so a buffer is a solution that
+maintains
+
+ align:start position:0%
+maintains
+ 
+
+ align:start position:0%
+maintains
+approximately a constant pH there'll be
+
+ align:start position:0%
+approximately a constant pH there'll be
+ 
+
+ align:start position:0%
+approximately a constant pH there'll be
+a little range of pH that can change but
+
+ align:start position:0%
+a little range of pH that can change but
+ 
+
+ align:start position:0%
+a little range of pH that can change but
+the buffer tries to keep the pH constant
+
+ align:start position:0%
+the buffer tries to keep the pH constant
+ 
+
+ align:start position:0%
+the buffer tries to keep the pH constant
+you use a buffer to keep pH constant why
+
+ align:start position:0%
+you use a buffer to keep pH constant why
+ 
+
+ align:start position:0%
+you use a buffer to keep pH constant why
+is this important well buffers are are
+
+ align:start position:0%
+is this important well buffers are are
+ 
+
+ align:start position:0%
+is this important well buffers are are
+very important in biology we all work at
+
+ align:start position:0%
+very important in biology we all work at
+ 
+
+ align:start position:0%
+very important in biology we all work at
+a constant pH living things need to be
+
+ align:start position:0%
+a constant pH living things need to be
+ 
+
+ align:start position:0%
+a constant pH living things need to be
+at a constant pH but a lot of times
+
+ align:start position:0%
+at a constant pH but a lot of times
+ 
+
+ align:start position:0%
+at a constant pH but a lot of times
+chemical processes also need to be at a
+
+ align:start position:0%
+chemical processes also need to be at a
+ 
+
+ align:start position:0%
+chemical processes also need to be at a
+constant pH and here's just uh one
+
+ align:start position:0%
+constant pH and here's just uh one
+ 
+
+ align:start position:0%
+constant pH and here's just uh one
+example of why buffers are important um
+
+ align:start position:0%
+example of why buffers are important um
+ 
+
+ align:start position:0%
+example of why buffers are important um
+we're looking for alternative energy
+
+ align:start position:0%
+we're looking for alternative energy
+ 
+
+ align:start position:0%
+we're looking for alternative energy
+we're trying to develop Alternative
+
+ align:start position:0%
+we're trying to develop Alternative
+ 
+
+ align:start position:0%
+we're trying to develop Alternative
+Energy there's this idea of creating
+
+ align:start position:0%
+Energy there's this idea of creating
+ 
+
+ align:start position:0%
+Energy there's this idea of creating
+fuel cells that employ microbes these
+
+ align:start position:0%
+fuel cells that employ microbes these
+ 
+
+ align:start position:0%
+fuel cells that employ microbes these
+little uh red circles or microbes here
+
+ align:start position:0%
+little uh red circles or microbes here
+ 
+
+ align:start position:0%
+little uh red circles or microbes here
+there are microbes like um
+
+ align:start position:0%
+there are microbes like um
+ 
+
+ align:start position:0%
+there are microbes like um
+shanella that will live adhere to
+
+ align:start position:0%
+shanella that will live adhere to
+ 
+
+ align:start position:0%
+shanella that will live adhere to
+electrodes will live on a surfaces of
+
+ align:start position:0%
+electrodes will live on a surfaces of
+ 
+
+ align:start position:0%
+electrodes will live on a surfaces of
+electrodes metal electrodes and they
+
+ align:start position:0%
+electrodes metal electrodes and they
+ 
+
+ align:start position:0%
+electrodes metal electrodes and they
+will eat things like sugar and Organics
+
+ align:start position:0%
+will eat things like sugar and Organics
+ 
+
+ align:start position:0%
+will eat things like sugar and Organics
+and they will U respirate electrons into
+
+ align:start position:0%
+and they will U respirate electrons into
+ 
+
+ align:start position:0%
+and they will U respirate electrons into
+the metal electrodes so the electrons go
+
+ align:start position:0%
+the metal electrodes so the electrons go
+ 
+
+ align:start position:0%
+the metal electrodes so the electrons go
+in and you create an electric current
+
+ align:start position:0%
+in and you create an electric current
+ 
+
+ align:start position:0%
+in and you create an electric current
+and you can do uh have a fuel cell so
+
+ align:start position:0%
+and you can do uh have a fuel cell so
+ 
+
+ align:start position:0%
+and you can do uh have a fuel cell so
+it's a way of generating an electric
+
+ align:start position:0%
+it's a way of generating an electric
+ 
+
+ align:start position:0%
+it's a way of generating an electric
+current and then people have other ideas
+
+ align:start position:0%
+current and then people have other ideas
+ 
+
+ align:start position:0%
+current and then people have other ideas
+that some some microbes live in
+
+ align:start position:0%
+that some some microbes live in
+ 
+
+ align:start position:0%
+that some some microbes live in
+electrodes other microbes like moral
+
+ align:start position:0%
+electrodes other microbes like moral
+ 
+
+ align:start position:0%
+electrodes other microbes like moral
+thos um they live on carbon dioxide
+
+ align:start position:0%
+thos um they live on carbon dioxide
+ 
+
+ align:start position:0%
+thos um they live on carbon dioxide
+they convert carbon dioxide to things
+
+ align:start position:0%
+they convert carbon dioxide to things
+ 
+
+ align:start position:0%
+they convert carbon dioxide to things
+like acetyl COA which is a fuel so you
+
+ align:start position:0%
+like acetyl COA which is a fuel so you
+ 
+
+ align:start position:0%
+like acetyl COA which is a fuel so you
+throw those in there and then you like
+
+ align:start position:0%
+throw those in there and then you like
+ 
+
+ align:start position:0%
+throw those in there and then you like
+pump in CO2 and you make uh electric
+
+ align:start position:0%
+pump in CO2 and you make uh electric
+ 
+
+ align:start position:0%
+pump in CO2 and you make uh electric
+currents so there's a lot of great ideas
+
+ align:start position:0%
+currents so there's a lot of great ideas
+ 
+
+ align:start position:0%
+currents so there's a lot of great ideas
+of using microbes so some of my research
+
+ align:start position:0%
+of using microbes so some of my research
+ 
+
+ align:start position:0%
+of using microbes so some of my research
+relates to understanding the
+
+ align:start position:0%
+relates to understanding the
+ 
+
+ align:start position:0%
+relates to understanding the
+fundamentals of these Pathways and every
+
+ align:start position:0%
+fundamentals of these Pathways and every
+ 
+
+ align:start position:0%
+fundamentals of these Pathways and every
+once in a while I venture to hear one of
+
+ align:start position:0%
+once in a while I venture to hear one of
+ 
+
+ align:start position:0%
+once in a while I venture to hear one of
+these kind of um big energy talks about
+
+ align:start position:0%
+these kind of um big energy talks about
+ 
+
+ align:start position:0%
+these kind of um big energy talks about
+you know how is the development coming
+
+ align:start position:0%
+you know how is the development coming
+ 
+
+ align:start position:0%
+you know how is the development coming
+of these ideas and so I heard one talk
+
+ align:start position:0%
+of these ideas and so I heard one talk
+ 
+
+ align:start position:0%
+of these ideas and so I heard one talk
+and I I um was listening you I was I
+
+ align:start position:0%
+and I I um was listening you I was I
+ 
+
+ align:start position:0%
+and I I um was listening you I was I
+want you know you know is this really
+
+ align:start position:0%
+want you know you know is this really
+ 
+
+ align:start position:0%
+want you know you know is this really
+working are people getting this to work
+
+ align:start position:0%
+working are people getting this to work
+ 
+
+ align:start position:0%
+working are people getting this to work
+what's sort of the status and they
+
+ align:start position:0%
+what's sort of the status and they
+ 
+
+ align:start position:0%
+what's sort of the status and they
+talked about a lot of technical
+
+ align:start position:0%
+talked about a lot of technical
+ 
+
+ align:start position:0%
+talked about a lot of technical
+difficulties of getting it to work but
+
+ align:start position:0%
+difficulties of getting it to work but
+ 
+
+ align:start position:0%
+difficulties of getting it to work but
+they had discovered something amazing
+
+ align:start position:0%
+they had discovered something amazing
+ 
+
+ align:start position:0%
+they had discovered something amazing
+something that might really change the
+
+ align:start position:0%
+something that might really change the
+ 
+
+ align:start position:0%
+something that might really change the
+ability to do this and it turned out
+
+ align:start position:0%
+ability to do this and it turned out
+ 
+
+ align:start position:0%
+ability to do this and it turned out
+that when you're generating all this
+
+ align:start position:0%
+that when you're generating all this
+ 
+
+ align:start position:0%
+that when you're generating all this
+negative charge you need to have
+
+ align:start position:0%
+negative charge you need to have
+ 
+
+ align:start position:0%
+negative charge you need to have
+positive charge around like H+ for
+
+ align:start position:0%
+positive charge around like H+ for
+ 
+
+ align:start position:0%
+positive charge around like H+ for
+example and so you need to have protons
+
+ align:start position:0%
+example and so you need to have protons
+ 
+
+ align:start position:0%
+example and so you need to have protons
+but it mattered the concentration of
+
+ align:start position:0%
+but it mattered the concentration of
+ 
+
+ align:start position:0%
+but it mattered the concentration of
+those protons and they kind of had to be
+
+ align:start position:0%
+those protons and they kind of had to be
+ 
+
+ align:start position:0%
+those protons and they kind of had to be
+kept
+
+ align:start position:0%
+kept
+ 
+
+ align:start position:0%
+kept
+constant and they
+
+ align:start position:0%
+constant and they
+ 
+
+ align:start position:0%
+constant and they
+discovered buff
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+ERS 50 minutes of my life this was a
+
+ align:start position:0%
+ERS 50 minutes of my life this was a
+ 
+
+ align:start position:0%
+ERS 50 minutes of my life this was a
+talk at MIT the person discovered
+
+ align:start position:0%
+talk at MIT the person discovered
+ 
+
+ align:start position:0%
+talk at MIT the person discovered
+buffers I just felt like writing a
+
+ align:start position:0%
+buffers I just felt like writing a
+ 
+
+ align:start position:0%
+buffers I just felt like writing a
+letter to Washington saying can I have
+
+ align:start position:0%
+letter to Washington saying can I have
+ 
+
+ align:start position:0%
+letter to Washington saying can I have
+their research dollars because I already
+
+ align:start position:0%
+their research dollars because I already
+ 
+
+ align:start position:0%
+their research dollars because I already
+know about buffers I don't need to do a
+
+ align:start position:0%
+know about buffers I don't need to do a
+ 
+
+ align:start position:0%
+know about buffers I don't need to do a
+big research project to discover that
+
+ align:start position:0%
+big research project to discover that
+ 
+
+ align:start position:0%
+big research project to discover that
+buffers keep things a constant pH and
+
+ align:start position:0%
+buffers keep things a constant pH and
+ 
+
+ align:start position:0%
+buffers keep things a constant pH and
+that when you're using living organisms
+
+ align:start position:0%
+that when you're using living organisms
+ 
+
+ align:start position:0%
+that when you're using living organisms
+and doing experiments and doing
+
+ align:start position:0%
+and doing experiments and doing
+ 
+
+ align:start position:0%
+and doing experiments and doing
+reactions pH matters I already knew that
+
+ align:start position:0%
+reactions pH matters I already knew that
+ 
+
+ align:start position:0%
+reactions pH matters I already knew that
+everyone who takes 5111 already knows
+
+ align:start position:0%
+everyone who takes 5111 already knows
+ 
+
+ align:start position:0%
+everyone who takes 5111 already knows
+that and so this is part of the reason
+
+ align:start position:0%
+that and so this is part of the reason
+ 
+
+ align:start position:0%
+that and so this is part of the reason
+I'm teaching you this because you're
+
+ align:start position:0%
+I'm teaching you this because you're
+ 
+
+ align:start position:0%
+I'm teaching you this because you're
+some of you will not go on and study
+
+ align:start position:0%
+some of you will not go on and study
+ 
+
+ align:start position:0%
+some of you will not go on and study
+chemistry you'll be doing engineering
+
+ align:start position:0%
+chemistry you'll be doing engineering
+ 
+
+ align:start position:0%
+chemistry you'll be doing engineering
+you'll be doing Alternative Energy
+
+ align:start position:0%
+you'll be doing Alternative Energy
+ 
+
+ align:start position:0%
+you'll be doing Alternative Energy
+you'll doing all sorts of things and you
+
+ align:start position:0%
+you'll doing all sorts of things and you
+ 
+
+ align:start position:0%
+you'll doing all sorts of things and you
+can be the person in the room that
+
+ align:start position:0%
+can be the person in the room that
+ 
+
+ align:start position:0%
+can be the person in the room that
+raises your hand and go it's called a
+
+ align:start position:0%
+raises your hand and go it's called a
+ 
+
+ align:start position:0%
+raises your hand and go it's called a
+buffer and that is going to change the
+
+ align:start position:0%
+buffer and that is going to change the
+ 
+
+ align:start position:0%
+buffer and that is going to change the
+speed of that research they're just like
+
+ align:start position:0%
+speed of that research they're just like
+ 
+
+ align:start position:0%
+speed of that research they're just like
+right away they're going to be using
+
+ align:start position:0%
+right away they're going to be using
+ 
+
+ align:start position:0%
+right away they're going to be using
+buffers and when you do problem set
+
+ align:start position:0%
+buffers and when you do problem set
+ 
+
+ align:start position:0%
+buffers and when you do problem set
+7even you're going to know how to make a
+
+ align:start position:0%
+7even you're going to know how to make a
+ 
+
+ align:start position:0%
+7even you're going to know how to make a
+buffer so you can not only raise your
+
+ align:start position:0%
+buffer so you can not only raise your
+ 
+
+ align:start position:0%
+buffer so you can not only raise your
+hand and say it's called a buffer you
+
+ align:start position:0%
+hand and say it's called a buffer you
+ 
+
+ align:start position:0%
+hand and say it's called a buffer you
+could tell people how to make a buffer
+
+ align:start position:0%
+could tell people how to make a buffer
+ 
+
+ align:start position:0%
+could tell people how to make a buffer
+to use in their experiments so this is
+
+ align:start position:0%
+to use in their experiments so this is
+ 
+
+ align:start position:0%
+to use in their experiments so this is
+why the material I'm teaching you is
+
+ align:start position:0%
+why the material I'm teaching you is
+ 
+
+ align:start position:0%
+why the material I'm teaching you is
+really important I go out there and I
+
+ align:start position:0%
+really important I go out there and I
+ 
+
+ align:start position:0%
+really important I go out there and I
+hear these talks of people who are
+
+ align:start position:0%
+hear these talks of people who are
+ 
+
+ align:start position:0%
+hear these talks of people who are
+trying to do these Innovative things but
+
+ align:start position:0%
+trying to do these Innovative things but
+ 
+
+ align:start position:0%
+trying to do these Innovative things but
+they're lacking fundamental chemistry
+
+ align:start position:0%
+they're lacking fundamental chemistry
+ 
+
+ align:start position:0%
+they're lacking fundamental chemistry
+knowledge that's hindering their ability
+
+ align:start position:0%
+knowledge that's hindering their ability
+ 
+
+ align:start position:0%
+knowledge that's hindering their ability
+to do it so I want all of you to have
+
+ align:start position:0%
+to do it so I want all of you to have
+ 
+
+ align:start position:0%
+to do it so I want all of you to have
+this knowledge whether you study
+
+ align:start position:0%
+this knowledge whether you study
+ 
+
+ align:start position:0%
+this knowledge whether you study
+chemistry anymore or not so that you can
+
+ align:start position:0%
+chemistry anymore or not so that you can
+ 
+
+ align:start position:0%
+chemistry anymore or not so that you can
+be the person who brings the basic
+
+ align:start position:0%
+be the person who brings the basic
+ 
+
+ align:start position:0%
+be the person who brings the basic
+chemical principles into the design
+
+ align:start position:0%
+chemical principles into the design
+ 
+
+ align:start position:0%
+chemical principles into the design
+process and I care a lot about
+
+ align:start position:0%
+process and I care a lot about
+ 
+
+ align:start position:0%
+process and I care a lot about
+Alternative Energy it's going to be
+
+ align:start position:0%
+Alternative Energy it's going to be
+ 
+
+ align:start position:0%
+Alternative Energy it's going to be
+super important in the future I care
+
+ align:start position:0%
+super important in the future I care
+ 
+
+ align:start position:0%
+super important in the future I care
+that we don't destroy our planet going
+
+ align:start position:0%
+that we don't destroy our planet going
+ 
+
+ align:start position:0%
+that we don't destroy our planet going
+after some forms of energy and these
+
+ align:start position:0%
+after some forms of energy and these
+ 
+
+ align:start position:0%
+after some forms of energy and these
+idea of using microbes is a great one
+
+ align:start position:0%
+idea of using microbes is a great one
+ 
+
+ align:start position:0%
+idea of using microbes is a great one
+but we just need people who know how to
+
+ align:start position:0%
+but we just need people who know how to
+ 
+
+ align:start position:0%
+but we just need people who know how to
+work with them to get it to to to go
+
+ align:start position:0%
+work with them to get it to to to go
+ 
+
+ align:start position:0%
+work with them to get it to to to go
+right all right so
+
+ align:start position:0%
+right all right so
+ 
+
+ align:start position:0%
+right all right so
+buffers what are buffers you got to know
+
+ align:start position:0%
+buffers what are buffers you got to know
+ 
+
+ align:start position:0%
+buffers what are buffers you got to know
+about
+
+ align:start position:0%
+about
+ 
+
+ align:start position:0%
+about
+buffers a buffer consists an acid buffer
+
+ align:start position:0%
+buffers a buffer consists an acid buffer
+ 
+
+ align:start position:0%
+buffers a buffer consists an acid buffer
+consists of a weak acid and its
+
+ align:start position:0%
+consists of a weak acid and its
+ 
+
+ align:start position:0%
+consists of a weak acid and its
+conjugate base they're often supplied as
+
+ align:start position:0%
+conjugate base they're often supplied as
+ 
+
+ align:start position:0%
+conjugate base they're often supplied as
+a salt which means you have a counter
+
+ align:start position:0%
+a salt which means you have a counter
+ 
+
+ align:start position:0%
+a salt which means you have a counter
+ion that comes with it like sodium Plus
+
+ align:start position:0%
+ion that comes with it like sodium Plus
+ 
+
+ align:start position:0%
+ion that comes with it like sodium Plus
+or CL minus and it buffers on the acidic
+
+ align:start position:0%
+or CL minus and it buffers on the acidic
+ 
+
+ align:start position:0%
+or CL minus and it buffers on the acidic
+side of
+
+ align:start position:0%
+side of
+ 
+
+ align:start position:0%
+side of
+neutral a base buffer or a basic buffer
+
+ align:start position:0%
+neutral a base buffer or a basic buffer
+ 
+
+ align:start position:0%
+neutral a base buffer or a basic buffer
+has a weak base and it's conjugate acid
+
+ align:start position:0%
+has a weak base and it's conjugate acid
+ 
+
+ align:start position:0%
+has a weak base and it's conjugate acid
+often supplied as a salt and it buffers
+
+ align:start position:0%
+often supplied as a salt and it buffers
+ 
+
+ align:start position:0%
+often supplied as a salt and it buffers
+on the basic side of neutral so the key
+
+ align:start position:0%
+on the basic side of neutral so the key
+ 
+
+ align:start position:0%
+on the basic side of neutral so the key
+to a buffer is that that it has a
+
+ align:start position:0%
+to a buffer is that that it has a
+ 
+
+ align:start position:0%
+to a buffer is that that it has a
+conjugate acid it has an ha but it also
+
+ align:start position:0%
+conjugate acid it has an ha but it also
+ 
+
+ align:start position:0%
+conjugate acid it has an ha but it also
+has the conjugate base it has a minus if
+
+ align:start position:0%
+has the conjugate base it has a minus if
+ 
+
+ align:start position:0%
+has the conjugate base it has a minus if
+it just has a ha it's a weak acid that's
+
+ align:start position:0%
+it just has a ha it's a weak acid that's
+ 
+
+ align:start position:0%
+it just has a ha it's a weak acid that's
+not a buffer that's a weak acid if you
+
+ align:start position:0%
+not a buffer that's a weak acid if you
+ 
+
+ align:start position:0%
+not a buffer that's a weak acid if you
+just have a
+
+ align:start position:0%
+just have a
+ 
+
+ align:start position:0%
+just have a
+minus you just have your base that's not
+
+ align:start position:0%
+minus you just have your base that's not
+ 
+
+ align:start position:0%
+minus you just have your base that's not
+a buffer you need to be both an acid and
+
+ align:start position:0%
+a buffer you need to be both an acid and
+ 
+
+ align:start position:0%
+a buffer you need to be both an acid and
+a base a base and an acid an acid and a
+
+ align:start position:0%
+a base a base and an acid an acid and a
+ 
+
+ align:start position:0%
+a base a base and an acid an acid and a
+base on exam people do buffer problems
+
+ align:start position:0%
+base on exam people do buffer problems
+ 
+
+ align:start position:0%
+base on exam people do buffer problems
+and they just have one they don't have
+
+ align:start position:0%
+and they just have one they don't have
+ 
+
+ align:start position:0%
+and they just have one they don't have
+the other that's not a buffer and I'm
+
+ align:start position:0%
+the other that's not a buffer and I'm
+ 
+
+ align:start position:0%
+the other that's not a buffer and I'm
+going to write on your little exam
+
+ align:start position:0%
+going to write on your little exam
+ 
+
+ align:start position:0%
+going to write on your little exam
+remember me twirling around the room it
+
+ align:start position:0%
+remember me twirling around the room it
+ 
+
+ align:start position:0%
+remember me twirling around the room it
+was an acid and a base I don't think you
+
+ align:start position:0%
+was an acid and a base I don't think you
+ 
+
+ align:start position:0%
+was an acid and a base I don't think you
+can never forget this this will be in
+
+ align:start position:0%
+can never forget this this will be in
+ 
+
+ align:start position:0%
+can never forget this this will be in
+your brain
+
+ align:start position:0%
+your brain
+ 
+
+ align:start position:0%
+your brain
+forever buffer has an acid and a
+
+ align:start position:0%
+forever buffer has an acid and a
+ 
+
+ align:start position:0%
+forever buffer has an acid and a
+conjugate base a conjugate base and a
+
+ align:start position:0%
+conjugate base a conjugate base and a
+ 
+
+ align:start position:0%
+conjugate base a conjugate base and a
+conjugate acid okay let's look at some
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+examples so if you mix acetic
+
+ align:start position:0%
+examples so if you mix acetic
+ 
+
+ align:start position:0%
+examples so if you mix acetic
+acid and acetate salt it's conjugate
+
+ align:start position:0%
+acid and acetate salt it's conjugate
+ 
+
+ align:start position:0%
+acid and acetate salt it's conjugate
+buff conjugate base supplied in the form
+
+ align:start position:0%
+buff conjugate base supplied in the form
+ 
+
+ align:start position:0%
+buff conjugate base supplied in the form
+of a salt so here we have the acetic
+
+ align:start position:0%
+of a salt so here we have the acetic
+ 
+
+ align:start position:0%
+of a salt so here we have the acetic
+acid here we have the acetate the
+
+ align:start position:0%
+acid here we have the acetate the
+ 
+
+ align:start position:0%
+acid here we have the acetate the
+conjugate base often will be supplied
+
+ align:start position:0%
+conjugate base often will be supplied
+ 
+
+ align:start position:0%
+conjugate base often will be supplied
+there's probably going to be some na+
+
+ align:start position:0%
+there's probably going to be some na+
+ 
+
+ align:start position:0%
+there's probably going to be some na+
+around and you get this dynamic
+
+ align:start position:0%
+around and you get this dynamic
+ 
+
+ align:start position:0%
+around and you get this dynamic
+equilibrium it goes forward it goes back
+
+ align:start position:0%
+equilibrium it goes forward it goes back
+ 
+
+ align:start position:0%
+equilibrium it goes forward it goes back
+it goes forward it goes
+
+ align:start position:0%
+it goes forward it goes
+ 
+
+ align:start position:0%
+it goes forward it goes
+back so when you have this if you added
+
+ align:start position:0%
+back so when you have this if you added
+ 
+
+ align:start position:0%
+back so when you have this if you added
+a strong acid to this solution you put
+
+ align:start position:0%
+a strong acid to this solution you put
+ 
+
+ align:start position:0%
+a strong acid to this solution you put
+in more acid into
+
+ align:start position:0%
+in more acid into
+ 
+
+ align:start position:0%
+in more acid into
+this and you had equal amounts of this
+
+ align:start position:0%
+this and you had equal amounts of this
+ 
+
+ align:start position:0%
+this and you had equal amounts of this
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+this then your conjugate base is going
+
+ align:start position:0%
+this then your conjugate base is going
+ 
+
+ align:start position:0%
+this then your conjugate base is going
+to react with the strong
+
+ align:start position:0%
+to react with the strong
+ 
+
+ align:start position:0%
+to react with the strong
+acid and you're going to go in the back
+
+ align:start position:0%
+acid and you're going to go in the back
+ 
+
+ align:start position:0%
+acid and you're going to go in the back
+Direction and you're going to neutralize
+
+ align:start position:0%
+Direction and you're going to neutralize
+ 
+
+ align:start position:0%
+Direction and you're going to neutralize
+that acid that was added and the pH
+
+ align:start position:0%
+that acid that was added and the pH
+ 
+
+ align:start position:0%
+that acid that was added and the pH
+should stay more or less the same if you
+
+ align:start position:0%
+should stay more or less the same if you
+ 
+
+ align:start position:0%
+should stay more or less the same if you
+did a good job making your buffer
+
+ align:start position:0%
+did a good job making your buffer
+ 
+
+ align:start position:0%
+did a good job making your buffer
+so the buffer can respond to the changes
+
+ align:start position:0%
+so the buffer can respond to the changes
+ 
+
+ align:start position:0%
+so the buffer can respond to the changes
+in PH by shifts in different directions
+
+ align:start position:0%
+in PH by shifts in different directions
+ 
+
+ align:start position:0%
+in PH by shifts in different directions
+to use up the extra added acid or the
+
+ align:start position:0%
+to use up the extra added acid or the
+ 
+
+ align:start position:0%
+to use up the extra added acid or the
+other way the extra added base so in
+
+ align:start position:0%
+other way the extra added base so in
+ 
+
+ align:start position:0%
+other way the extra added base so in
+this case the acid that's added is
+
+ align:start position:0%
+this case the acid that's added is
+ 
+
+ align:start position:0%
+this case the acid that's added is
+effectively removed and the pH stays the
+
+ align:start position:0%
+effectively removed and the pH stays the
+ 
+
+ align:start position:0%
+effectively removed and the pH stays the
+same so a buffer can respond to added
+
+ align:start position:0%
+same so a buffer can respond to added
+ 
+
+ align:start position:0%
+same so a buffer can respond to added
+acid a buffer can also respond to added
+
+ align:start position:0%
+acid a buffer can also respond to added
+ 
+
+ align:start position:0%
+acid a buffer can also respond to added
+base if you add a base a strong base or
+
+ align:start position:0%
+base if you add a base a strong base or
+ 
+
+ align:start position:0%
+base if you add a base a strong base or
+any kind of
+
+ align:start position:0%
+any kind of
+ 
+
+ align:start position:0%
+any kind of
+base and in this case hydroxide ion
+
+ align:start position:0%
+base and in this case hydroxide ion
+ 
+
+ align:start position:0%
+base and in this case hydroxide ion
+would then remove a proton from the weak
+
+ align:start position:0%
+would then remove a proton from the weak
+ 
+
+ align:start position:0%
+would then remove a proton from the weak
+acid from the acetic acid forming water
+
+ align:start position:0%
+acid from the acetic acid forming water
+ 
+
+ align:start position:0%
+acid from the acetic acid forming water
+and some more of the conjugate
+
+ align:start position:0%
+and some more of the conjugate
+ 
+
+ align:start position:0%
+and some more of the conjugate
+base and it's effectively removed as
+
+ align:start position:0%
+base and it's effectively removed as
+ 
+
+ align:start position:0%
+base and it's effectively removed as
+well and those o ions are effectively
+
+ align:start position:0%
+well and those o ions are effectively
+ 
+
+ align:start position:0%
+well and those o ions are effectively
+removed and again if you did a good job
+
+ align:start position:0%
+removed and again if you did a good job
+ 
+
+ align:start position:0%
+removed and again if you did a good job
+designing this buffer the pH should stay
+
+ align:start position:0%
+designing this buffer the pH should stay
+ 
+
+ align:start position:0%
+designing this buffer the pH should stay
+constant
+
+ align:start position:0%
+constant
+ 
+
+ align:start position:0%
+constant
+so that's why you need the conjugate
+
+ align:start position:0%
+so that's why you need the conjugate
+ 
+
+ align:start position:0%
+so that's why you need the conjugate
+acid and the conjugate base you need the
+
+ align:start position:0%
+acid and the conjugate base you need the
+ 
+
+ align:start position:0%
+acid and the conjugate base you need the
+acid to react with the base that's added
+
+ align:start position:0%
+acid to react with the base that's added
+ 
+
+ align:start position:0%
+acid to react with the base that's added
+and keep the pH constant you need the
+
+ align:start position:0%
+and keep the pH constant you need the
+ 
+
+ align:start position:0%
+and keep the pH constant you need the
+base to react with the acid that's added
+
+ align:start position:0%
+base to react with the acid that's added
+ 
+
+ align:start position:0%
+base to react with the acid that's added
+and keep the pH constant if you just
+
+ align:start position:0%
+and keep the pH constant if you just
+ 
+
+ align:start position:0%
+and keep the pH constant if you just
+have one it's not going to be a
+
+ align:start position:0%
+have one it's not going to be a
+ 
+
+ align:start position:0%
+have one it's not going to be a
+buffer all right so buffer action again
+
+ align:start position:0%
+buffer all right so buffer action again
+ 
+
+ align:start position:0%
+buffer all right so buffer action again
+weak acid transfers its protons it's H+
+
+ align:start position:0%
+weak acid transfers its protons it's H+
+ 
+
+ align:start position:0%
+weak acid transfers its protons it's H+
+to O supplied by the base so here we
+
+ align:start position:0%
+to O supplied by the base so here we
+ 
+
+ align:start position:0%
+to O supplied by the base so here we
+have added we have added base and it's
+
+ align:start position:0%
+have added we have added base and it's
+ 
+
+ align:start position:0%
+have added we have added base and it's
+going to be reacted with the acid to be
+
+ align:start position:0%
+going to be reacted with the acid to be
+ 
+
+ align:start position:0%
+going to be reacted with the acid to be
+neutralized a conjugate um the conjugate
+
+ align:start position:0%
+neutralized a conjugate um the conjugate
+ 
+
+ align:start position:0%
+neutralized a conjugate um the conjugate
+base a minus can accept protons from an
+
+ align:start position:0%
+base a minus can accept protons from an
+ 
+
+ align:start position:0%
+base a minus can accept protons from an
+supplied acid if you add an acid it will
+
+ align:start position:0%
+supplied acid if you add an acid it will
+ 
+
+ align:start position:0%
+supplied acid if you add an acid it will
+take those and will neutralize the acid
+
+ align:start position:0%
+take those and will neutralize the acid
+ 
+
+ align:start position:0%
+take those and will neutralize the acid
+that's
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+added so let's think about what type of
+
+ align:start position:0%
+added so let's think about what type of
+ 
+
+ align:start position:0%
+added so let's think about what type of
+acids and conjugate bases are going to
+
+ align:start position:0%
+acids and conjugate bases are going to
+ 
+
+ align:start position:0%
+acids and conjugate bases are going to
+work to make a good buffer a strong acid
+
+ align:start position:0%
+work to make a good buffer a strong acid
+ 
+
+ align:start position:0%
+work to make a good buffer a strong acid
+in its conjugate base Cas does not make
+
+ align:start position:0%
+in its conjugate base Cas does not make
+ 
+
+ align:start position:0%
+in its conjugate base Cas does not make
+a good buffer why don't you tell me why
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yep so
+
+ align:start position:0%
+yep so
+ 
+
+ align:start position:0%
+yep so
+67% so it's really about the fact that
+
+ align:start position:0%
+67% so it's really about the fact that
+ 
+
+ align:start position:0%
+67% so it's really about the fact that
+the conjugate base of a strong acid is
+
+ align:start position:0%
+the conjugate base of a strong acid is
+ 
+
+ align:start position:0%
+the conjugate base of a strong acid is
+really not a base at all it's
+
+ align:start position:0%
+really not a base at all it's
+ 
+
+ align:start position:0%
+really not a base at all it's
+ineffective as a base and that's why
+
+ align:start position:0%
+ineffective as a base and that's why
+ 
+
+ align:start position:0%
+ineffective as a base and that's why
+it's not going to work buffer solution
+
+ align:start position:0%
+it's not going to work buffer solution
+ 
+
+ align:start position:0%
+it's not going to work buffer solution
+has to be in a dynamic equilibrium you
+
+ align:start position:0%
+has to be in a dynamic equilibrium you
+ 
+
+ align:start position:0%
+has to be in a dynamic equilibrium you
+have to be able to push it both ways
+
+ align:start position:0%
+have to be able to push it both ways
+ 
+
+ align:start position:0%
+have to be able to push it both ways
+otherwise it's not going to work so a
+
+ align:start position:0%
+otherwise it's not going to work so a
+ 
+
+ align:start position:0%
+otherwise it's not going to work so a
+conjugate base of a strong acid is
+
+ align:start position:0%
+conjugate base of a strong acid is
+ 
+
+ align:start position:0%
+conjugate base of a strong acid is
+ineffective as a base and so if you add
+
+ align:start position:0%
+ineffective as a base and so if you add
+ 
+
+ align:start position:0%
+ineffective as a base and so if you add
+an acid it won't be neutralized and the
+
+ align:start position:0%
+an acid it won't be neutralized and the
+ 
+
+ align:start position:0%
+an acid it won't be neutralized and the
+pH will change so you need to have that
+
+ align:start position:0%
+pH will change so you need to have that
+ 
+
+ align:start position:0%
+pH will change so you need to have that
+conj something that works as a conjugate
+
+ align:start position:0%
+conj something that works as a conjugate
+ 
+
+ align:start position:0%
+conj something that works as a conjugate
+base something that's able to interact
+
+ align:start position:0%
+base something that's able to interact
+ 
+
+ align:start position:0%
+base something that's able to interact
+with the hydronium ion or the acid
+
+ align:start position:0%
+with the hydronium ion or the acid
+ 
+
+ align:start position:0%
+with the hydronium ion or the acid
+that's added and take its proton to
+
+ align:start position:0%
+that's added and take its proton to
+ 
+
+ align:start position:0%
+that's added and take its proton to
+neutralize it if this doesn't happen the
+
+ align:start position:0%
+neutralize it if this doesn't happen the
+ 
+
+ align:start position:0%
+neutralize it if this doesn't happen the
+pH will be affected so you need to have
+
+ align:start position:0%
+pH will be affected so you need to have
+ 
+
+ align:start position:0%
+pH will be affected so you need to have
+weak acids and weak bases in your
+
+ align:start position:0%
+weak acids and weak bases in your
+ 
+
+ align:start position:0%
+weak acids and weak bases in your
+buffers they could be moderately weak or
+
+ align:start position:0%
+buffers they could be moderately weak or
+ 
+
+ align:start position:0%
+buffers they could be moderately weak or
+very weak or whatever but they H you
+
+ align:start position:0%
+very weak or whatever but they H you
+ 
+
+ align:start position:0%
+very weak or whatever but they H you
+have to have a conjugate set that's
+
+ align:start position:0%
+have to have a conjugate set that's
+ 
+
+ align:start position:0%
+have to have a conjugate set that's
+going to be able to push push both
+
+ align:start position:0%
+going to be able to push push both
+ 
+
+ align:start position:0%
+going to be able to push push both
+directions where the acid can interact
+
+ align:start position:0%
+directions where the acid can interact
+ 
+
+ align:start position:0%
+directions where the acid can interact
+with the added base and the base can
+
+ align:start position:0%
+with the added base and the base can
+ 
+
+ align:start position:0%
+with the added base and the base can
+interact with the added acid all right
+
+ align:start position:0%
+interact with the added acid all right
+ 
+
+ align:start position:0%
+interact with the added acid all right
+so all of this is really the same for a
+
+ align:start position:0%
+so all of this is really the same for a
+ 
+
+ align:start position:0%
+so all of this is really the same for a
+basic um buffer so we can look at an
+
+ align:start position:0%
+basic um buffer so we can look at an
+ 
+
+ align:start position:0%
+basic um buffer so we can look at an
+example here of ammonia plus water going
+
+ align:start position:0%
+example here of ammonia plus water going
+ 
+
+ align:start position:0%
+example here of ammonia plus water going
+to ammonium ion and hydroxide ion and we
+
+ align:start position:0%
+to ammonium ion and hydroxide ion and we
+ 
+
+ align:start position:0%
+to ammonium ion and hydroxide ion and we
+can think about the same things when you
+
+ align:start position:0%
+can think about the same things when you
+ 
+
+ align:start position:0%
+can think about the same things when you
+add a strong acid the base will accept
+
+ align:start position:0%
+add a strong acid the base will accept
+ 
+
+ align:start position:0%
+add a strong acid the base will accept
+the protons and make more of your
+
+ align:start position:0%
+the protons and make more of your
+ 
+
+ align:start position:0%
+the protons and make more of your
+conjugate acid when a strong base is
+
+ align:start position:0%
+conjugate acid when a strong base is
+ 
+
+ align:start position:0%
+conjugate acid when a strong base is
+added the conjugate acid will donate its
+
+ align:start position:0%
+added the conjugate acid will donate its
+ 
+
+ align:start position:0%
+added the conjugate acid will donate its
+proton and it will form NH3 again that
+
+ align:start position:0%
+proton and it will form NH3 again that
+ 
+
+ align:start position:0%
+proton and it will form NH3 again that
+conjugate base and water and the pH will
+
+ align:start position:0%
+conjugate base and water and the pH will
+ 
+
+ align:start position:0%
+conjugate base and water and the pH will
+stay the same so it's a same idea the
+
+ align:start position:0%
+stay the same so it's a same idea the
+ 
+
+ align:start position:0%
+stay the same so it's a same idea the
+only real difference between an acidic
+
+ align:start position:0%
+only real difference between an acidic
+ 
+
+ align:start position:0%
+only real difference between an acidic
+buffer and a basic buffer is whether it
+
+ align:start position:0%
+buffer and a basic buffer is whether it
+ 
+
+ align:start position:0%
+buffer and a basic buffer is whether it
+phes in the acidic range or in the basic
+
+ align:start position:0%
+phes in the acidic range or in the basic
+ 
+
+ align:start position:0%
+phes in the acidic range or in the basic
+range but the buffers work the same way
+
+ align:start position:0%
+range but the buffers work the same way
+ 
+
+ align:start position:0%
+range but the buffers work the same way
+so I can redraw this picture
+
+ align:start position:0%
+so I can redraw this picture
+ 
+
+ align:start position:0%
+so I can redraw this picture
+um to have our different symbols on it
+
+ align:start position:0%
+um to have our different symbols on it
+ 
+
+ align:start position:0%
+um to have our different symbols on it
+but the idea is the same the weak base
+
+ align:start position:0%
+but the idea is the same the weak base
+ 
+
+ align:start position:0%
+but the idea is the same the weak base
+um will take the proton supplied by the
+
+ align:start position:0%
+um will take the proton supplied by the
+ 
+
+ align:start position:0%
+um will take the proton supplied by the
+acid and the conjugate acid
+
+ align:start position:0%
+acid and the conjugate acid
+ 
+
+ align:start position:0%
+acid and the conjugate acid
+bh+ is going to uh protonate the O minus
+
+ align:start position:0%
+bh+ is going to uh protonate the O minus
+ 
+
+ align:start position:0%
+bh+ is going to uh protonate the O minus
+and again keep the pH constant so the
+
+ align:start position:0%
+and again keep the pH constant so the
+ 
+
+ align:start position:0%
+and again keep the pH constant so the
+idea again of the buffer then is that a
+
+ align:start position:0%
+idea again of the buffer then is that a
+ 
+
+ align:start position:0%
+idea again of the buffer then is that a
+buffer is a mixture of weak conjugate
+
+ align:start position:0%
+buffer is a mixture of weak conjugate
+ 
+
+ align:start position:0%
+buffer is a mixture of weak conjugate
+acids and bases again they're weak
+
+ align:start position:0%
+acids and bases again they're weak
+ 
+
+ align:start position:0%
+acids and bases again they're weak
+because its partner needs to be
+
+ align:start position:0%
+because its partner needs to be
+ 
+
+ align:start position:0%
+because its partner needs to be
+effective as an acid or a base it can't
+
+ align:start position:0%
+effective as an acid or a base it can't
+ 
+
+ align:start position:0%
+effective as an acid or a base it can't
+be ineffective weak acidbase mixtures
+
+ align:start position:0%
+be ineffective weak acidbase mixtures
+ 
+
+ align:start position:0%
+be ineffective weak acidbase mixtures
+that stabilize pH by providing a source
+
+ align:start position:0%
+that stabilize pH by providing a source
+ 
+
+ align:start position:0%
+that stabilize pH by providing a source
+or a sync for protons it either adds
+
+ align:start position:0%
+or a sync for protons it either adds
+ 
+
+ align:start position:0%
+or a sync for protons it either adds
+protons or takes protons away it can
+
+ align:start position:0%
+protons or takes protons away it can
+ 
+
+ align:start position:0%
+protons or takes protons away it can
+respond to added acid it can respond to
+
+ align:start position:0%
+respond to added acid it can respond to
+ 
+
+ align:start position:0%
+respond to added acid it can respond to
+added
+
+ align:start position:0%
+added
+ 
+
+ align:start position:0%
+added
+base so again pH is important and
+
+ align:start position:0%
+base so again pH is important and
+ 
+
+ align:start position:0%
+base so again pH is important and
+buffering is
+
+ align:start position:0%
+buffering is
+ 
+
+ align:start position:0%
+buffering is
+important our body has its own buffer
+
+ align:start position:0%
+important our body has its own buffer
+ 
+
+ align:start position:0%
+important our body has its own buffer
+buffing system so we have carbonic acid
+
+ align:start position:0%
+buffing system so we have carbonic acid
+ 
+
+ align:start position:0%
+buffing system so we have carbonic acid
+and bicarbonate buffering agents in our
+
+ align:start position:0%
+and bicarbonate buffering agents in our
+ 
+
+ align:start position:0%
+and bicarbonate buffering agents in our
+blood and our blood has to be kept in
+
+ align:start position:0%
+blood and our blood has to be kept in
+ 
+
+ align:start position:0%
+blood and our blood has to be kept in
+this sort of neutral range over here if
+
+ align:start position:0%
+this sort of neutral range over here if
+ 
+
+ align:start position:0%
+this sort of neutral range over here if
+it gets to acidic um that is very
+
+ align:start position:0%
+it gets to acidic um that is very
+ 
+
+ align:start position:0%
+it gets to acidic um that is very
+unhealthy for us leading to some pretty
+
+ align:start position:0%
+unhealthy for us leading to some pretty
+ 
+
+ align:start position:0%
+unhealthy for us leading to some pretty
+severe symptoms um and too much leads to
+
+ align:start position:0%
+severe symptoms um and too much leads to
+ 
+
+ align:start position:0%
+severe symptoms um and too much leads to
+death if it's too basic that's really
+
+ align:start position:0%
+death if it's too basic that's really
+ 
+
+ align:start position:0%
+death if it's too basic that's really
+bad also we have death and notice these
+
+ align:start position:0%
+bad also we have death and notice these
+ 
+
+ align:start position:0%
+bad also we have death and notice these
+are not all that far away there are a
+
+ align:start position:0%
+are not all that far away there are a
+ 
+
+ align:start position:0%
+are not all that far away there are a
+number of different medical conditions
+
+ align:start position:0%
+number of different medical conditions
+ 
+
+ align:start position:0%
+number of different medical conditions
+that can affect the pH diabetes their
+
+ align:start position:0%
+that can affect the pH diabetes their
+ 
+
+ align:start position:0%
+that can affect the pH diabetes their
+metabolic diseases something else that
+
+ align:start position:0%
+metabolic diseases something else that
+ 
+
+ align:start position:0%
+metabolic diseases something else that
+is under your
+
+ align:start position:0%
+is under your
+ 
+
+ align:start position:0%
+is under your
+control hydration you need to drink
+
+ align:start position:0%
+control hydration you need to drink
+ 
+
+ align:start position:0%
+control hydration you need to drink
+enough water and as the weather gets
+
+ align:start position:0%
+enough water and as the weather gets
+ 
+
+ align:start position:0%
+enough water and as the weather gets
+colder in Boston people often stop
+
+ align:start position:0%
+colder in Boston people often stop
+ 
+
+ align:start position:0%
+colder in Boston people often stop
+drinking as much water or start drinking
+
+ align:start position:0%
+drinking as much water or start drinking
+ 
+
+ align:start position:0%
+drinking as much water or start drinking
+like hot beverages which don't hydrate
+
+ align:start position:0%
+like hot beverages which don't hydrate
+ 
+
+ align:start position:0%
+like hot beverages which don't hydrate
+as well so keep hydrated if you're not
+
+ align:start position:0%
+as well so keep hydrated if you're not
+ 
+
+ align:start position:0%
+as well so keep hydrated if you're not
+hydrated you can if it's gets really bad
+
+ align:start position:0%
+hydrated you can if it's gets really bad
+ 
+
+ align:start position:0%
+hydrated you can if it's gets really bad
+it can start affecting the pH of your
+
+ align:start position:0%
+it can start affecting the pH of your
+ 
+
+ align:start position:0%
+it can start affecting the pH of your
+blood which is really not good so
+
+ align:start position:0%
+blood which is really not good so
+ 
+
+ align:start position:0%
+blood which is really not good so
+buffering very
+
+ align:start position:0%
+buffering very
+ 
+
+ align:start position:0%
+buffering very
+important all right so let's do a sample
+
+ align:start position:0%
+important all right so let's do a sample
+ 
+
+ align:start position:0%
+important all right so let's do a sample
+buffer
+
+ align:start position:0%
+buffer
+ 
+
+ align:start position:0%
+buffer
+problem so sample buffer problem and
+
+ align:start position:0%
+problem so sample buffer problem and
+ 
+
+ align:start position:0%
+problem so sample buffer problem and
+this is important I actually know of at
+
+ align:start position:0%
+this is important I actually know of at
+ 
+
+ align:start position:0%
+this is important I actually know of at
+least one Professor that if you want to
+
+ align:start position:0%
+least one Professor that if you want to
+ 
+
+ align:start position:0%
+least one Professor that if you want to
+do a europ with them they'll come to
+
+ align:start position:0%
+do a europ with them they'll come to
+ 
+
+ align:start position:0%
+do a europ with them they'll come to
+their office and they're going to say
+
+ align:start position:0%
+their office and they're going to say
+ 
+
+ align:start position:0%
+their office and they're going to say
+all right write down how you would
+
+ align:start position:0%
+all right write down how you would
+ 
+
+ align:start position:0%
+all right write down how you would
+design a buffer for me and do those
+
+ align:start position:0%
+design a buffer for me and do those
+ 
+
+ align:start position:0%
+design a buffer for me and do those
+calculations so I can tell you later who
+
+ align:start position:0%
+calculations so I can tell you later who
+ 
+
+ align:start position:0%
+calculations so I can tell you later who
+that is maybe I won't I don't know but
+
+ align:start position:0%
+that is maybe I won't I don't know but
+ 
+
+ align:start position:0%
+that is maybe I won't I don't know but
+this is one of the tests that someone
+
+ align:start position:0%
+this is one of the tests that someone
+ 
+
+ align:start position:0%
+this is one of the tests that someone
+uses to see if they want you as a EUR
+
+ align:start position:0%
+uses to see if they want you as a EUR
+ 
+
+ align:start position:0%
+uses to see if they want you as a EUR
+up okay so here we have one mole of
+
+ align:start position:0%
+up okay so here we have one mole of
+ 
+
+ align:start position:0%
+up okay so here we have one mole of
+formic acid and 0.5 moles of the
+
+ align:start position:0%
+formic acid and 0.5 moles of the
+ 
+
+ align:start position:0%
+formic acid and 0.5 moles of the
+conjugate base supplied in the form of a
+
+ align:start position:0%
+conjugate base supplied in the form of a
+ 
+
+ align:start position:0%
+conjugate base supplied in the form of a
+salt with sodium ions and those are
+
+ align:start position:0%
+salt with sodium ions and those are
+ 
+
+ align:start position:0%
+salt with sodium ions and those are
+added to water and diluted to a total
+
+ align:start position:0%
+added to water and diluted to a total
+ 
+
+ align:start position:0%
+added to water and diluted to a total
+final concentration of one liter and
+
+ align:start position:0%
+final concentration of one liter and
+ 
+
+ align:start position:0%
+final concentration of one liter and
+you're given the uh Ka and told to
+
+ align:start position:0%
+you're given the uh Ka and told to
+ 
+
+ align:start position:0%
+you're given the uh Ka and told to
+calculate the pH so the first step is to
+
+ align:start position:0%
+calculate the pH so the first step is to
+ 
+
+ align:start position:0%
+calculate the pH so the first step is to
+write out the equation so we have um an
+
+ align:start position:0%
+write out the equation so we have um an
+ 
+
+ align:start position:0%
+write out the equation so we have um an
+acid in water going to hydronium ions
+
+ align:start position:0%
+acid in water going to hydronium ions
+ 
+
+ align:start position:0%
+acid in water going to hydronium ions
+and a conjugate base over here and we
+
+ align:start position:0%
+and a conjugate base over here and we
+ 
+
+ align:start position:0%
+and a conjugate base over here and we
+want to think about what's there now
+
+ align:start position:0%
+want to think about what's there now
+ 
+
+ align:start position:0%
+want to think about what's there now
+what's it and what's at
+
+ align:start position:0%
+what's it and what's at
+ 
+
+ align:start position:0%
+what's it and what's at
+equilibrium so initial marity change in
+
+ align:start position:0%
+equilibrium so initial marity change in
+ 
+
+ align:start position:0%
+equilibrium so initial marity change in
+marity and your equilibrium marity so
+
+ align:start position:0%
+marity and your equilibrium marity so
+ 
+
+ align:start position:0%
+marity and your equilibrium marity so
+it's important this word marity don't
+
+ align:start position:0%
+it's important this word marity don't
+ 
+
+ align:start position:0%
+it's important this word marity don't
+put put moles in here put marity in here
+
+ align:start position:0%
+put put moles in here put marity in here
+ 
+
+ align:start position:0%
+put put moles in here put marity in here
+but I made it really easy for you
+
+ align:start position:0%
+but I made it really easy for you
+ 
+
+ align:start position:0%
+but I made it really easy for you
+because we have one mole in one liter so
+
+ align:start position:0%
+because we have one mole in one liter so
+ 
+
+ align:start position:0%
+because we have one mole in one liter so
+the marity is one 0.5 moles in one liter
+
+ align:start position:0%
+the marity is one 0.5 moles in one liter
+ 
+
+ align:start position:0%
+the marity is one 0.5 moles in one liter
+the marity is
+
+ align:start position:0%
+the marity is
+ 
+
+ align:start position:0%
+the marity is
+0.5 and this is also really important
+
+ align:start position:0%
+0.5 and this is also really important
+ 
+
+ align:start position:0%
+0.5 and this is also really important
+you're so used to only putting things
+
+ align:start position:0%
+you're so used to only putting things
+ 
+
+ align:start position:0%
+you're so used to only putting things
+here when it's a buffer problem you got
+
+ align:start position:0%
+here when it's a buffer problem you got
+ 
+
+ align:start position:0%
+here when it's a buffer problem you got
+to put something here too so you're
+
+ align:start position:0%
+to put something here too so you're
+ 
+
+ align:start position:0%
+to put something here too so you're
+adding the acid with the conjugate base
+
+ align:start position:0%
+adding the acid with the conjugate base
+ 
+
+ align:start position:0%
+adding the acid with the conjugate base
+at the same time this is not zero
+
+ align:start position:0%
+at the same time this is not zero
+ 
+
+ align:start position:0%
+at the same time this is not zero
+this is
+
+ align:start position:0%
+this is
+ 
+
+ align:start position:0%
+this is
+0.5 so now as this dynamic equilibrium
+
+ align:start position:0%
+0.5 so now as this dynamic equilibrium
+ 
+
+ align:start position:0%
+0.5 so now as this dynamic equilibrium
+goes you're losing some of this and
+
+ align:start position:0%
+goes you're losing some of this and
+ 
+
+ align:start position:0%
+goes you're losing some of this and
+gaining some of
+
+ align:start position:0%
+gaining some of
+ 
+
+ align:start position:0%
+gaining some of
+these so at equilibrium we have 1 molar
+
+ align:start position:0%
+these so at equilibrium we have 1 molar
+ 
+
+ align:start position:0%
+these so at equilibrium we have 1 molar
+minus x x is our hydronium ion
+
+ align:start position:0%
+minus x x is our hydronium ion
+ 
+
+ align:start position:0%
+minus x x is our hydronium ion
+concentration which is what we want to
+
+ align:start position:0%
+concentration which is what we want to
+ 
+
+ align:start position:0%
+concentration which is what we want to
+know to calculate pH and our conjugate
+
+ align:start position:0%
+know to calculate pH and our conjugate
+ 
+
+ align:start position:0%
+know to calculate pH and our conjugate
+base our formate formate ion is .5 plus
+
+ align:start position:0%
+base our formate formate ion is .5 plus
+ 
+
+ align:start position:0%
+base our formate formate ion is .5 plus
+X we're given a k a and we've written
+
+ align:start position:0%
+X we're given a k a and we've written
+ 
+
+ align:start position:0%
+X we're given a k a and we've written
+this expression as a acid in water so we
+
+ align:start position:0%
+this expression as a acid in water so we
+ 
+
+ align:start position:0%
+this expression as a acid in water so we
+can use Ka the equilibrium constant is
+
+ align:start position:0%
+can use Ka the equilibrium constant is
+ 
+
+ align:start position:0%
+can use Ka the equilibrium constant is
+for the expression as written so we can
+
+ align:start position:0%
+for the expression as written so we can
+ 
+
+ align:start position:0%
+for the expression as written so we can
+put that in and we can uh
+
+ align:start position:0%
+put that in and we can uh
+ 
+
+ align:start position:0%
+put that in and we can uh
+Supply um the uh fill the rest out we
+
+ align:start position:0%
+Supply um the uh fill the rest out we
+ 
+
+ align:start position:0%
+Supply um the uh fill the rest out we
+have our products we have the
+
+ align:start position:0%
+have our products we have the
+ 
+
+ align:start position:0%
+have our products we have the
+concentration of hydronium ion times the
+
+ align:start position:0%
+concentration of hydronium ion times the
+ 
+
+ align:start position:0%
+concentration of hydronium ion times the
+concentration of formate ion the
+
+ align:start position:0%
+concentration of formate ion the
+ 
+
+ align:start position:0%
+concentration of formate ion the
+conjugate base over the concentration of
+
+ align:start position:0%
+conjugate base over the concentration of
+ 
+
+ align:start position:0%
+conjugate base over the concentration of
+our formic acid and again again water
+
+ align:start position:0%
+our formic acid and again again water
+ 
+
+ align:start position:0%
+our formic acid and again again water
+does not appear in the expression
+
+ align:start position:0%
+does not appear in the expression
+ 
+
+ align:start position:0%
+does not appear in the expression
+because it's the solvent hydronium ion
+
+ align:start position:0%
+because it's the solvent hydronium ion
+ 
+
+ align:start position:0%
+because it's the solvent hydronium ion
+concentration is X the conjugate base
+
+ align:start position:0%
+concentration is X the conjugate base
+ 
+
+ align:start position:0%
+concentration is X the conjugate base
+concentration is05 + x and the conjugate
+
+ align:start position:0%
+concentration is05 + x and the conjugate
+ 
+
+ align:start position:0%
+concentration is05 + x and the conjugate
+acid concentration is 1 -
+
+ align:start position:0%
+acid concentration is 1 -
+ 
+
+ align:start position:0%
+acid concentration is 1 -
+x so we can now try that assumption that
+
+ align:start position:0%
+x so we can now try that assumption that
+ 
+
+ align:start position:0%
+x so we can now try that assumption that
+X is small or we can use the quadratic
+
+ align:start position:0%
+X is small or we can use the quadratic
+ 
+
+ align:start position:0%
+X is small or we can use the quadratic
+equation but why don't you just uh try
+
+ align:start position:0%
+equation but why don't you just uh try
+ 
+
+ align:start position:0%
+equation but why don't you just uh try
+that assumption I'm going to take this
+
+ align:start position:0%
+that assumption I'm going to take this
+ 
+
+ align:start position:0%
+that assumption I'm going to take this
+expression if you haven't written it all
+
+ align:start position:0%
+expression if you haven't written it all
+ 
+
+ align:start position:0%
+expression if you haven't written it all
+down yet put it right up here and now
+
+ align:start position:0%
+down yet put it right up here and now
+ 
+
+ align:start position:0%
+down yet put it right up here and now
+with a clicker why don't you tell me if
+
+ align:start position:0%
+with a clicker why don't you tell me if
+ 
+
+ align:start position:0%
+with a clicker why don't you tell me if
+we use the approximation that X is small
+
+ align:start position:0%
+we use the approximation that X is small
+ 
+
+ align:start position:0%
+we use the approximation that X is small
+compared to 1 in 0.5 what does this
+
+ align:start position:0%
+compared to 1 in 0.5 what does this
+ 
+
+ align:start position:0%
+compared to 1 in 0.5 what does this
+simplify
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+to all right 10 more seconds
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+all right so 70 uh something percent yep
+
+ align:start position:0%
+all right so 70 uh something percent yep
+ 
+
+ align:start position:0%
+all right so 70 uh something percent yep
+so let's take a look at
+
+ align:start position:0%
+so let's take a look at
+ 
+
+ align:start position:0%
+so let's take a look at
+that so here we're making the assumption
+
+ align:start position:0%
+that so here we're making the assumption
+ 
+
+ align:start position:0%
+that so here we're making the assumption
+that X is small compared to 0.5 and
+
+ align:start position:0%
+that X is small compared to 0.5 and
+ 
+
+ align:start position:0%
+that X is small compared to 0.5 and
+compared to one so that means that we
+
+ align:start position:0%
+compared to one so that means that we
+ 
+
+ align:start position:0%
+compared to one so that means that we
+draw drop the plus X from the 0.5 term
+
+ align:start position:0%
+draw drop the plus X from the 0.5 term
+ 
+
+ align:start position:0%
+draw drop the plus X from the 0.5 term
+and drop the minus X from the one term
+
+ align:start position:0%
+and drop the minus X from the one term
+ 
+
+ align:start position:0%
+and drop the minus X from the one term
+so we're saying that these are going to
+
+ align:start position:0%
+so we're saying that these are going to
+ 
+
+ align:start position:0%
+so we're saying that these are going to
+be small enough that it's still going to
+
+ align:start position:0%
+be small enough that it's still going to
+ 
+
+ align:start position:0%
+be small enough that it's still going to
+be pretty much 05 and one and then we
+
+ align:start position:0%
+be pretty much 05 and one and then we
+ 
+
+ align:start position:0%
+be pretty much 05 and one and then we
+have to test that in a minute so if we
+
+ align:start position:0%
+have to test that in a minute so if we
+ 
+
+ align:start position:0%
+have to test that in a minute so if we
+use this we can calculate X and it comes
+
+ align:start position:0%
+use this we can calculate X and it comes
+ 
+
+ align:start position:0%
+use this we can calculate X and it comes
+out to 3.54 *
+
+ align:start position:0%
+out to 3.54 *
+ 
+
+ align:start position:0%
+out to 3.54 *
+10-4 and then we can check the
+
+ align:start position:0%
+10-4 and then we can check the
+ 
+
+ align:start position:0%
+10-4 and then we can check the
+Assumption and before you told me how to
+
+ align:start position:0%
+Assumption and before you told me how to
+ 
+
+ align:start position:0%
+Assumption and before you told me how to
+check assumptions um um and that was I
+
+ align:start position:0%
+check assumptions um um and that was I
+ 
+
+ align:start position:0%
+check assumptions um um and that was I
+take X and I'll divide it by 0.5 which
+
+ align:start position:0%
+take X and I'll divide it by 0.5 which
+ 
+
+ align:start position:0%
+take X and I'll divide it by 0.5 which
+is the smaller of these two um and Times
+
+ align:start position:0%
+is the smaller of these two um and Times
+ 
+
+ align:start position:0%
+is the smaller of these two um and Times
+by 100% And we get
+
+ align:start position:0%
+by 100% And we get
+ 
+
+ align:start position:0%
+by 100% And we get
+0.69% Which is less than 5% so the
+
+ align:start position:0%
+0.69% Which is less than 5% so the
+ 
+
+ align:start position:0%
+0.69% Which is less than 5% so the
+assumption is okay um and we don't have
+
+ align:start position:0%
+assumption is okay um and we don't have
+ 
+
+ align:start position:0%
+assumption is okay um and we don't have
+to check it against one because if the
+
+ align:start position:0%
+to check it against one because if the
+ 
+
+ align:start position:0%
+to check it against one because if the
+Assumption X is small compared to the
+
+ align:start position:0%
+Assumption X is small compared to the
+ 
+
+ align:start position:0%
+Assumption X is small compared to the
+smaller number is valid it'll also be
+
+ align:start position:0%
+smaller number is valid it'll also be
+ 
+
+ align:start position:0%
+smaller number is valid it'll also be
+valid for the bigger number so you only
+
+ align:start position:0%
+valid for the bigger number so you only
+ 
+
+ align:start position:0%
+valid for the bigger number so you only
+check it for the smaller number and then
+
+ align:start position:0%
+check it for the smaller number and then
+ 
+
+ align:start position:0%
+check it for the smaller number and then
+we can
+
+ align:start position:0%
+we can
+ 
+
+ align:start position:0%
+we can
+um solve so we have to think about we
+
+ align:start position:0%
+um solve so we have to think about we
+ 
+
+ align:start position:0%
+um solve so we have to think about we
+solve for x we're happy with X our
+
+ align:start position:0%
+solve for x we're happy with X our
+ 
+
+ align:start position:0%
+solve for x we're happy with X our
+assumption was okay but then we have to
+
+ align:start position:0%
+assumption was okay but then we have to
+ 
+
+ align:start position:0%
+assumption was okay but then we have to
+remember what x is and X is the
+
+ align:start position:0%
+remember what x is and X is the
+ 
+
+ align:start position:0%
+remember what x is and X is the
+hydronium ion
+
+ align:start position:0%
+hydronium ion
+ 
+
+ align:start position:0%
+hydronium ion
+concentration and you always want to
+
+ align:start position:0%
+concentration and you always want to
+ 
+
+ align:start position:0%
+concentration and you always want to
+make sure to think about this because if
+
+ align:start position:0%
+make sure to think about this because if
+ 
+
+ align:start position:0%
+make sure to think about this because if
+it's hydroxide ion that's different so
+
+ align:start position:0%
+it's hydroxide ion that's different so
+ 
+
+ align:start position:0%
+it's hydroxide ion that's different so
+we can calculate pH pH is minus log of
+
+ align:start position:0%
+we can calculate pH pH is minus log of
+ 
+
+ align:start position:0%
+we can calculate pH pH is minus log of
+3.54 * 10- 4 which is equal to pH of
+
+ align:start position:0%
+3.54 * 10- 4 which is equal to pH of
+ 
+
+ align:start position:0%
+3.54 * 10- 4 which is equal to pH of
+3.45
+
+ align:start position:0%
+3.45
+ 
+
+ align:start position:0%
+3.45
+five and here we have two significant
+
+ align:start position:0%
+five and here we have two significant
+ 
+
+ align:start position:0%
+five and here we have two significant
+figures after the decimal point because
+
+ align:start position:0%
+figures after the decimal point because
+ 
+
+ align:start position:0%
+figures after the decimal point because
+the volume we had before only had two
+
+ align:start position:0%
+the volume we had before only had two
+ 
+
+ align:start position:0%
+the volume we had before only had two
+significant figures everything else had
+
+ align:start position:0%
+significant figures everything else had
+ 
+
+ align:start position:0%
+significant figures everything else had
+three but the volume was just 1.0 so
+
+ align:start position:0%
+three but the volume was just 1.0 so
+ 
+
+ align:start position:0%
+three but the volume was just 1.0 so
+that is our answer there all right so
+
+ align:start position:0%
+that is our answer there all right so
+ 
+
+ align:start position:0%
+that is our answer there all right so
+I'm going to um just briefly um start
+
+ align:start position:0%
+I'm going to um just briefly um start
+ 
+
+ align:start position:0%
+I'm going to um just briefly um start
+what happens well actually we'll do
+
+ align:start position:0%
+what happens well actually we'll do
+ 
+
+ align:start position:0%
+what happens well actually we'll do
+we'll do next this is how you would
+
+ align:start position:0%
+we'll do next this is how you would
+ 
+
+ align:start position:0%
+we'll do next this is how you would
+design the buffer for this next time
+
+ align:start position:0%
+design the buffer for this next time
+ 
+
+ align:start position:0%
+design the buffer for this next time
+we'll see what happens if we stress the
+
+ align:start position:0%
+we'll see what happens if we stress the
+ 
+
+ align:start position:0%
+we'll see what happens if we stress the
+buffer we designed
+
+ align:start position:0%
+buffer we designed
+ 
+
+ align:start position:0%
+buffer we designed
+by adding acid to it and see what the
+
+ align:start position:0%
+by adding acid to it and see what the
+ 
+
+ align:start position:0%
+by adding acid to it and see what the
+new result
+
+ align:start position:0%
+new result
+ 
+
+ align:start position:0%
+new result
+is all right so today we're going to
+
+ align:start position:0%
+is all right so today we're going to
+ 
+
+ align:start position:0%
+is all right so today we're going to
+finish uh lecture 22 so take out those
+
+ align:start position:0%
+finish uh lecture 22 so take out those
+ 
+
+ align:start position:0%
+finish uh lecture 22 so take out those
+lecture notes and uh on acids and bases
+
+ align:start position:0%
+lecture notes and uh on acids and bases
+ 
+
+ align:start position:0%
+lecture notes and uh on acids and bases
+and when we're done with that we'll just
+
+ align:start position:0%
+and when we're done with that we'll just
+ 
+
+ align:start position:0%
+and when we're done with that we'll just
+continue with acids and bases and we're
+
+ align:start position:0%
+continue with acids and bases and we're
+ 
+
+ align:start position:0%
+continue with acids and bases and we're
+going to continue with some acids and
+
+ align:start position:0%
+going to continue with some acids and
+ 
+
+ align:start position:0%
+going to continue with some acids and
+bases on Wednesday but we should finish
+
+ align:start position:0%
+bases on Wednesday but we should finish
+ 
+
+ align:start position:0%
+bases on Wednesday but we should finish
+on Wednesday and move on to oxidation
+
+ align:start position:0%
+on Wednesday and move on to oxidation
+ 
+
+ align:start position:0%
+on Wednesday and move on to oxidation
+reduction um and that will end exam 3
+
+ align:start position:0%
+reduction um and that will end exam 3
+ 
+
+ align:start position:0%
+reduction um and that will end exam 3
+material so uh exam 3 is sneaking up on
+
+ align:start position:0%
+material so uh exam 3 is sneaking up on
+ 
+
+ align:start position:0%
+material so uh exam 3 is sneaking up on
+us and it'll have thermodynamics
+
+ align:start position:0%
+us and it'll have thermodynamics
+ 
+
+ align:start position:0%
+us and it'll have thermodynamics
+chemical equilibrium solubility and acid
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+base all right so you should have
+
+ align:start position:0%
+base all right so you should have
+ 
+
+ align:start position:0%
+base all right so you should have
+already filled in your handout with all
+
+ align:start position:0%
+already filled in your handout with all
+ 
+
+ align:start position:0%
+already filled in your handout with all
+the information the parts that you uh
+
+ align:start position:0%
+the information the parts that you uh
+ 
+
+ align:start position:0%
+the information the parts that you uh
+we're filling in are uh in in bold here
+
+ align:start position:0%
+we're filling in are uh in in bold here
+ 
+
+ align:start position:0%
+we're filling in are uh in in bold here
+but I just want to remind you of what we
+
+ align:start position:0%
+but I just want to remind you of what we
+ 
+
+ align:start position:0%
+but I just want to remind you of what we
+were talking about so we had a sample
+
+ align:start position:0%
+were talking about so we had a sample
+ 
+
+ align:start position:0%
+were talking about so we had a sample
+buffer problem we had one mole of a
+
+ align:start position:0%
+buffer problem we had one mole of a
+ 
+
+ align:start position:0%
+buffer problem we had one mole of a
+conjugate acid and a half a mole of a
+
+ align:start position:0%
+conjugate acid and a half a mole of a
+ 
+
+ align:start position:0%
+conjugate acid and a half a mole of a
+con of its conjugate base supplied in
+
+ align:start position:0%
+con of its conjugate base supplied in
+ 
+
+ align:start position:0%
+con of its conjugate base supplied in
+the form of a salt were put in water and
+
+ align:start position:0%
+the form of a salt were put in water and
+ 
+
+ align:start position:0%
+the form of a salt were put in water and
+diluted to one to one liter so we
+
+ align:start position:0%
+diluted to one to one liter so we
+ 
+
+ align:start position:0%
+diluted to one to one liter so we
+calculated what um the hydronium ion
+
+ align:start position:0%
+calculated what um the hydronium ion
+ 
+
+ align:start position:0%
+calculated what um the hydronium ion
+concentration would be and therefore the
+
+ align:start position:0%
+concentration would be and therefore the
+ 
+
+ align:start position:0%
+concentration would be and therefore the
+pH using information that was given to
+
+ align:start position:0%
+pH using information that was given to
+ 
+
+ align:start position:0%
+pH using information that was given to
+us about the KA the acid ionization
+
+ align:start position:0%
+us about the KA the acid ionization
+ 
+
+ align:start position:0%
+us about the KA the acid ionization
+constant so um we got a pH of
+
+ align:start position:0%
+constant so um we got a pH of
+ 
+
+ align:start position:0%
+constant so um we got a pH of
+3.45 um someone asked me after class but
+
+ align:start position:0%
+3.45 um someone asked me after class but
+ 
+
+ align:start position:0%
+3.45 um someone asked me after class but
+isn't this conjugate base also reacting
+
+ align:start position:0%
+isn't this conjugate base also reacting
+ 
+
+ align:start position:0%
+isn't this conjugate base also reacting
+with water and forming some of this uh
+
+ align:start position:0%
+with water and forming some of this uh
+ 
+
+ align:start position:0%
+with water and forming some of this uh
+weak acid and the answer is yes um that
+
+ align:start position:0%
+weak acid and the answer is yes um that
+ 
+
+ align:start position:0%
+weak acid and the answer is yes um that
+we are writing this as a problem of acid
+
+ align:start position:0%
+we are writing this as a problem of acid
+ 
+
+ align:start position:0%
+we are writing this as a problem of acid
+in water because we can use the KA but
+
+ align:start position:0%
+in water because we can use the KA but
+ 
+
+ align:start position:0%
+in water because we can use the KA but
+we could have also written it the other
+
+ align:start position:0%
+we could have also written it the other
+ 
+
+ align:start position:0%
+we could have also written it the other
+way and written it and this is not in
+
+ align:start position:0%
+way and written it and this is not in
+ 
+
+ align:start position:0%
+way and written it and this is not in
+your notes but I just want to let you
+
+ align:start position:0%
+your notes but I just want to let you
+ 
+
+ align:start position:0%
+your notes but I just want to let you
+know um that the weak base in water
+
+ align:start position:0%
+know um that the weak base in water
+ 
+
+ align:start position:0%
+know um that the weak base in water
+could be written that way forming a
+
+ align:start position:0%
+could be written that way forming a
+ 
+
+ align:start position:0%
+could be written that way forming a
+conjugate acid and um hydroxide ions and
+
+ align:start position:0%
+conjugate acid and um hydroxide ions and
+ 
+
+ align:start position:0%
+conjugate acid and um hydroxide ions and
+so then it would be5 Min - x and 1 + x
+
+ align:start position:0%
+so then it would be5 Min - x and 1 + x
+ 
+
+ align:start position:0%
+so then it would be5 Min - x and 1 + x
+and x use KB then because it's a base in
+
+ align:start position:0%
+and x use KB then because it's a base in
+ 
+
+ align:start position:0%
+and x use KB then because it's a base in
+water to solve for x and calculate pH
+
+ align:start position:0%
+water to solve for x and calculate pH
+ 
+
+ align:start position:0%
+water to solve for x and calculate pH
+from p and if you try it you get
+
+ align:start position:0%
+from p and if you try it you get
+ 
+
+ align:start position:0%
+from p and if you try it you get
+3.45 so you can do these problems either
+
+ align:start position:0%
+3.45 so you can do these problems either
+ 
+
+ align:start position:0%
+3.45 so you can do these problems either
+way you can think about them as a weak
+
+ align:start position:0%
+way you can think about them as a weak
+ 
+
+ align:start position:0%
+way you can think about them as a weak
+base problem or a weak acid problem you
+
+ align:start position:0%
+base problem or a weak acid problem you
+ 
+
+ align:start position:0%
+base problem or a weak acid problem you
+just have to remember that there's if
+
+ align:start position:0%
+just have to remember that there's if
+ 
+
+ align:start position:0%
+just have to remember that there's if
+this is not zero when you start the uh
+
+ align:start position:0%
+this is not zero when you start the uh
+ 
+
+ align:start position:0%
+this is not zero when you start the uh
+the conjugate has some amount that's
+
+ align:start position:0%
+the conjugate has some amount that's
+ 
+
+ align:start position:0%
+the conjugate has some amount that's
+what makes it a good buffer so this can
+
+ align:start position:0%
+what makes it a good buffer so this can
+ 
+
+ align:start position:0%
+what makes it a good buffer so this can
+work either way but you also want to
+
+ align:start position:0%
+work either way but you also want to
+ 
+
+ align:start position:0%
+work either way but you also want to
+remember if you write it as an acid in
+
+ align:start position:0%
+remember if you write it as an acid in
+ 
+
+ align:start position:0%
+remember if you write it as an acid in
+water use Ka if you write it as a base
+
+ align:start position:0%
+water use Ka if you write it as a base
+ 
+
+ align:start position:0%
+water use Ka if you write it as a base
+in water use KB because those
+
+ align:start position:0%
+in water use KB because those
+ 
+
+ align:start position:0%
+in water use KB because those
+equilibrium constants are telling you
+
+ align:start position:0%
+equilibrium constants are telling you
+ 
+
+ align:start position:0%
+equilibrium constants are telling you
+about those ratios of the conjugate acid
+
+ align:start position:0%
+about those ratios of the conjugate acid
+ 
+
+ align:start position:0%
+about those ratios of the conjugate acid
+and the conjugate base at equilibrium So
+
+ align:start position:0%
+and the conjugate base at equilibrium So
+ 
+
+ align:start position:0%
+and the conjugate base at equilibrium So
+within the KA and the KB is information
+
+ align:start position:0%
+within the KA and the KB is information
+ 
+
+ align:start position:0%
+within the KA and the KB is information
+that you need about this Dynamic
+
+ align:start position:0%
+that you need about this Dynamic
+ 
+
+ align:start position:0%
+that you need about this Dynamic
+chemical equilibrium so both of these
+
+ align:start position:0%
+chemical equilibrium so both of these
+ 
+
+ align:start position:0%
+chemical equilibrium so both of these
+Ways work and by the end of sort of
+
+ align:start position:0%
+Ways work and by the end of sort of
+ 
+
+ align:start position:0%
+Ways work and by the end of sort of
+halfway through today's lecture you'll
+
+ align:start position:0%
+halfway through today's lecture you'll
+ 
+
+ align:start position:0%
+halfway through today's lecture you'll
+see yet another way to solve buffer
+
+ align:start position:0%
+see yet another way to solve buffer
+ 
+
+ align:start position:0%
+see yet another way to solve buffer
+problems and probably will be for most
+
+ align:start position:0%
+problems and probably will be for most
+ 
+
+ align:start position:0%
+problems and probably will be for most
+of you the preferred way to do it so
+
+ align:start position:0%
+of you the preferred way to do it so
+ 
+
+ align:start position:0%
+of you the preferred way to do it so
+there's a number of different ways which
+
+ align:start position:0%
+there's a number of different ways which
+ 
+
+ align:start position:0%
+there's a number of different ways which
+makes grading the exam lots of fun um
+
+ align:start position:0%
+makes grading the exam lots of fun um
+ 
+
+ align:start position:0%
+makes grading the exam lots of fun um
+and we have option one option two option
+
+ align:start position:0%
+and we have option one option two option
+ 
+
+ align:start position:0%
+and we have option one option two option
+three um to make sure that uh that that
+
+ align:start position:0%
+three um to make sure that uh that that
+ 
+
+ align:start position:0%
+three um to make sure that uh that that
+all the options are are possibly
+
+ align:start position:0%
+all the options are are possibly
+ 
+
+ align:start position:0%
+all the options are are possibly
+accounted for all right so the purpose
+
+ align:start position:0%
+accounted for all right so the purpose
+ 
+
+ align:start position:0%
+accounted for all right so the purpose
+of a buffer is to keep the pH pretty
+
+ align:start position:0%
+of a buffer is to keep the pH pretty
+ 
+
+ align:start position:0%
+of a buffer is to keep the pH pretty
+much constant so you can add a strong
+
+ align:start position:0%
+much constant so you can add a strong
+ 
+
+ align:start position:0%
+much constant so you can add a strong
+acid to it and the acid will be
+
+ align:start position:0%
+acid to it and the acid will be
+ 
+
+ align:start position:0%
+acid to it and the acid will be
+neutralized um keeping the pH const you
+
+ align:start position:0%
+neutralized um keeping the pH const you
+ 
+
+ align:start position:0%
+neutralized um keeping the pH const you
+can add a strong base to it and the base
+
+ align:start position:0%
+can add a strong base to it and the base
+ 
+
+ align:start position:0%
+can add a strong base to it and the base
+will be neutralized keeping the pH
+
+ align:start position:0%
+will be neutralized keeping the pH
+ 
+
+ align:start position:0%
+will be neutralized keeping the pH
+pretty constant so what you want in a
+
+ align:start position:0%
+pretty constant so what you want in a
+ 
+
+ align:start position:0%
+pretty constant so what you want in a
+buffer is to have a weak acid conjugate
+
+ align:start position:0%
+buffer is to have a weak acid conjugate
+ 
+
+ align:start position:0%
+buffer is to have a weak acid conjugate
+base pairing that allows it to be a
+
+ align:start position:0%
+base pairing that allows it to be a
+ 
+
+ align:start position:0%
+base pairing that allows it to be a
+source or sync for a strong acid or a
+
+ align:start position:0%
+source or sync for a strong acid or a
+ 
+
+ align:start position:0%
+source or sync for a strong acid or a
+strong base to keep the pH constant so
+
+ align:start position:0%
+strong base to keep the pH constant so
+ 
+
+ align:start position:0%
+strong base to keep the pH constant so
+now in this problem we're asked to
+
+ align:start position:0%
+now in this problem we're asked to
+ 
+
+ align:start position:0%
+now in this problem we're asked to
+calculate what would happen to the pH if
+
+ align:start position:0%
+calculate what would happen to the pH if
+ 
+
+ align:start position:0%
+calculate what would happen to the pH if
+0.1 moles of a strong acid had been
+
+ align:start position:0%
+0.1 moles of a strong acid had been
+ 
+
+ align:start position:0%
+0.1 moles of a strong acid had been
+included in our one um liter
+
+ align:start position:0%
+included in our one um liter
+ 
+
+ align:start position:0%
+included in our one um liter
+solution and and because 0.1 moles of
+
+ align:start position:0%
+solution and and because 0.1 moles of
+ 
+
+ align:start position:0%
+solution and and because 0.1 moles of
+our strong acid would react with equal
+
+ align:start position:0%
+our strong acid would react with equal
+ 
+
+ align:start position:0%
+our strong acid would react with equal
+number of moles of that conjugate base
+
+ align:start position:0%
+number of moles of that conjugate base
+ 
+
+ align:start position:0%
+number of moles of that conjugate base
+that's what the conjugate base does in a
+
+ align:start position:0%
+that's what the conjugate base does in a
+ 
+
+ align:start position:0%
+that's what the conjugate base does in a
+buffer it reacts with a strong acid that
+
+ align:start position:0%
+buffer it reacts with a strong acid that
+ 
+
+ align:start position:0%
+buffer it reacts with a strong acid that
+is supplied and it will form equal moles
+
+ align:start position:0%
+is supplied and it will form equal moles
+ 
+
+ align:start position:0%
+is supplied and it will form equal moles
+then of the uh the conjugate its
+
+ align:start position:0%
+then of the uh the conjugate its
+ 
+
+ align:start position:0%
+then of the uh the conjugate its
+conjugate acid so we have to do some
+
+ align:start position:0%
+conjugate acid so we have to do some
+ 
+
+ align:start position:0%
+conjugate acid so we have to do some
+subtraction so for the conjugate acid we
+
+ align:start position:0%
+subtraction so for the conjugate acid we
+ 
+
+ align:start position:0%
+subtraction so for the conjugate acid we
+had .5 moles and um and or sorry for the
+
+ align:start position:0%
+had .5 moles and um and or sorry for the
+ 
+
+ align:start position:0%
+had .5 moles and um and or sorry for the
+for the conjugate base we had 0. five
+
+ align:start position:0%
+for the conjugate base we had 0. five
+ 
+
+ align:start position:0%
+for the conjugate base we had 0. five
+moles we used up one of that 0 one of
+
+ align:start position:0%
+moles we used up one of that 0 one of
+ 
+
+ align:start position:0%
+moles we used up one of that 0 one of
+that reacting with a strong acid and we
+
+ align:start position:0%
+that reacting with a strong acid and we
+ 
+
+ align:start position:0%
+that reacting with a strong acid and we
+have 04 left so we have a new
+
+ align:start position:0%
+have 04 left so we have a new
+ 
+
+ align:start position:0%
+have 04 left so we have a new
+concentration for our conjugate
+
+ align:start position:0%
+concentration for our conjugate
+ 
+
+ align:start position:0%
+concentration for our conjugate
+base4 / 1 keep the mass
+
+ align:start position:0%
+base4 / 1 keep the mass
+ 
+
+ align:start position:0%
+base4 / 1 keep the mass
+simple4
+
+ align:start position:0%
+simple4
+ 
+
+ align:start position:0%
+simple4
+molar so for our conjugate acid we had
+
+ align:start position:0%
+molar so for our conjugate acid we had
+ 
+
+ align:start position:0%
+molar so for our conjugate acid we had
+one mole to begin with but we formed 0.1
+
+ align:start position:0%
+one mole to begin with but we formed 0.1
+ 
+
+ align:start position:0%
+one mole to begin with but we formed 0.1
+more
+
+ align:start position:0%
+more
+ 
+
+ align:start position:0%
+more
+when that strong acid was added so now
+
+ align:start position:0%
+when that strong acid was added so now
+ 
+
+ align:start position:0%
+when that strong acid was added so now
+we have 1.1 moles and a new
+
+ align:start position:0%
+we have 1.1 moles and a new
+ 
+
+ align:start position:0%
+we have 1.1 moles and a new
+marity so now we have to go back and we
+
+ align:start position:0%
+marity so now we have to go back and we
+ 
+
+ align:start position:0%
+marity so now we have to go back and we
+can use this expression again and
+
+ align:start position:0%
+can use this expression again and
+ 
+
+ align:start position:0%
+can use this expression again and
+determine what x is now what the
+
+ align:start position:0%
+determine what x is now what the
+ 
+
+ align:start position:0%
+determine what x is now what the
+hydronium ion concentration is now using
+
+ align:start position:0%
+hydronium ion concentration is now using
+ 
+
+ align:start position:0%
+hydronium ion concentration is now using
+Ka so why don't you tell me how um I
+
+ align:start position:0%
+Ka so why don't you tell me how um I
+ 
+
+ align:start position:0%
+Ka so why don't you tell me how um I
+would solve this what is the correct
+
+ align:start position:0%
+would solve this what is the correct
+ 
+
+ align:start position:0%
+would solve this what is the correct
+expression for KA and you can fill in
+
+ align:start position:0%
+expression for KA and you can fill in
+ 
+
+ align:start position:0%
+expression for KA and you can fill in
+your little table as you do it
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+all right let's just do 10 more
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+seconds all right so so let's just uh
+
+ align:start position:0%
+seconds all right so so let's just uh
+ 
+
+ align:start position:0%
+seconds all right so so let's just uh
+fill in that table if you haven't
+
+ align:start position:0%
+fill in that table if you haven't
+ 
+
+ align:start position:0%
+fill in that table if you haven't
+already so here now we can write this as
+
+ align:start position:0%
+already so here now we can write this as
+ 
+
+ align:start position:0%
+already so here now we can write this as
+an acid and water problem again again
+
+ align:start position:0%
+an acid and water problem again again
+ 
+
+ align:start position:0%
+an acid and water problem again again
+you could have done the base and water
+
+ align:start position:0%
+you could have done the base and water
+ 
+
+ align:start position:0%
+you could have done the base and water
+and use KB um but we'll just do it the
+
+ align:start position:0%
+and use KB um but we'll just do it the
+ 
+
+ align:start position:0%
+and use KB um but we'll just do it the
+same way we did before so we have our
+
+ align:start position:0%
+same way we did before so we have our
+ 
+
+ align:start position:0%
+same way we did before so we have our
+acid
+
+ align:start position:0%
+acid
+ 
+
+ align:start position:0%
+acid
+1.1 molar now remember this is marity so
+
+ align:start position:0%
+1.1 molar now remember this is marity so
+ 
+
+ align:start position:0%
+1.1 molar now remember this is marity so
+you don't want to put moles in here you
+
+ align:start position:0%
+you don't want to put moles in here you
+ 
+
+ align:start position:0%
+you don't want to put moles in here you
+want to put a concentration and some of
+
+ align:start position:0%
+want to put a concentration and some of
+ 
+
+ align:start position:0%
+want to put a concentration and some of
+that will be minus X then we have our
+
+ align:start position:0%
+that will be minus X then we have our
+ 
+
+ align:start position:0%
+that will be minus X then we have our
+044 plus X we can fill out the KA the KA
+
+ align:start position:0%
+044 plus X we can fill out the KA the KA
+ 
+
+ align:start position:0%
+044 plus X we can fill out the KA the KA
+again weak acid and water problem we
+
+ align:start position:0%
+again weak acid and water problem we
+ 
+
+ align:start position:0%
+again weak acid and water problem we
+have products hydronium ion over our our
+
+ align:start position:0%
+have products hydronium ion over our our
+ 
+
+ align:start position:0%
+have products hydronium ion over our our
+times our conjugate base over our
+
+ align:start position:0%
+times our conjugate base over our
+ 
+
+ align:start position:0%
+times our conjugate base over our
+conjugate acid equals 4 + x * X these
+
+ align:start position:0%
+conjugate acid equals 4 + x * X these
+ 
+
+ align:start position:0%
+conjugate acid equals 4 + x * X these
+two and 1.1 minus X on the
+
+ align:start position:0%
+two and 1.1 minus X on the
+ 
+
+ align:start position:0%
+two and 1.1 minus X on the
+bottom so you can always solve then for
+
+ align:start position:0%
+bottom so you can always solve then for
+ 
+
+ align:start position:0%
+bottom so you can always solve then for
+X which will tell you about the pH by
+
+ align:start position:0%
+X which will tell you about the pH by
+ 
+
+ align:start position:0%
+X which will tell you about the pH by
+using the KA and you just have to
+
+ align:start position:0%
+using the KA and you just have to
+ 
+
+ align:start position:0%
+using the KA and you just have to
+remember marity and remember these are
+
+ align:start position:0%
+remember marity and remember these are
+ 
+
+ align:start position:0%
+remember marity and remember these are
+the new marity after the reaction has
+
+ align:start position:0%
+the new marity after the reaction has
+ 
+
+ align:start position:0%
+the new marity after the reaction has
+occurred all right so we can use the um
+
+ align:start position:0%
+occurred all right so we can use the um
+ 
+
+ align:start position:0%
+occurred all right so we can use the um
+the approximation that X is small
+
+ align:start position:0%
+the approximation that X is small
+ 
+
+ align:start position:0%
+the approximation that X is small
+compared to 1.1 and4 to simplify this or
+
+ align:start position:0%
+compared to 1.1 and4 to simplify this or
+ 
+
+ align:start position:0%
+compared to 1.1 and4 to simplify this or
+we could use the quadratic equation if
+
+ align:start position:0%
+we could use the quadratic equation if
+ 
+
+ align:start position:0%
+we could use the quadratic equation if
+we simplify it we calculate X as 4.87 *
+
+ align:start position:0%
+we simplify it we calculate X as 4.87 *
+ 
+
+ align:start position:0%
+we simplify it we calculate X as 4.87 *
+10-4 and remember again that the
+
+ align:start position:0%
+10-4 and remember again that the
+ 
+
+ align:start position:0%
+10-4 and remember again that the
+approximation is you get rid of the plus
+
+ align:start position:0%
+approximation is you get rid of the plus
+ 
+
+ align:start position:0%
+approximation is you get rid of the plus
+X and Theus X
+
+ align:start position:0%
+X and Theus X
+ 
+
+ align:start position:0%
+X and Theus X
+here and then you have to check it with
+
+ align:start position:0%
+here and then you have to check it with
+ 
+
+ align:start position:0%
+here and then you have to check it with
+the 5% rule if you did that if you use
+
+ align:start position:0%
+the 5% rule if you did that if you use
+ 
+
+ align:start position:0%
+the 5% rule if you did that if you use
+the quadratic you don't have to check
+
+ align:start position:0%
+the quadratic you don't have to check
+ 
+
+ align:start position:0%
+the quadratic you don't have to check
+but if you use the 5% rule then you're
+
+ align:start position:0%
+but if you use the 5% rule then you're
+ 
+
+ align:start position:0%
+but if you use the 5% rule then you're
+asking is this number 4.87 * 10us 4 um
+
+ align:start position:0%
+asking is this number 4.87 * 10us 4 um
+ 
+
+ align:start position:0%
+asking is this number 4.87 * 10us 4 um
+within 5% of the smaller value which is
+
+ align:start position:0%
+within 5% of the smaller value which is
+ 
+
+ align:start position:0%
+within 5% of the smaller value which is
+04 and it is here it's
+
+ align:start position:0%
+04 and it is here it's
+ 
+
+ align:start position:0%
+04 and it is here it's
+0.12% so the assumption is okay that's
+
+ align:start position:0%
+0.12% so the assumption is okay that's
+ 
+
+ align:start position:0%
+0.12% so the assumption is okay that's
+less than 5% X is small and then we can
+
+ align:start position:0%
+less than 5% X is small and then we can
+ 
+
+ align:start position:0%
+less than 5% X is small and then we can
+solve um for for the pH so pH is minus
+
+ align:start position:0%
+solve um for for the pH so pH is minus
+ 
+
+ align:start position:0%
+solve um for for the pH so pH is minus
+log of the hydronium ion concentration
+
+ align:start position:0%
+log of the hydronium ion concentration
+ 
+
+ align:start position:0%
+log of the hydronium ion concentration
+which here is
+
+ align:start position:0%
+which here is
+ 
+
+ align:start position:0%
+which here is
+3.31 this only is two significant
+
+ align:start position:0%
+3.31 this only is two significant
+ 
+
+ align:start position:0%
+3.31 this only is two significant
+figures after the decimal because if you
+
+ align:start position:0%
+figures after the decimal because if you
+ 
+
+ align:start position:0%
+figures after the decimal because if you
+remember back on the other page the
+
+ align:start position:0%
+remember back on the other page the
+ 
+
+ align:start position:0%
+remember back on the other page the
+volume only had two so actually all
+
+ align:start position:0%
+volume only had two so actually all
+ 
+
+ align:start position:0%
+volume only had two so actually all
+these numbers here really just have two
+
+ align:start position:0%
+these numbers here really just have two
+ 
+
+ align:start position:0%
+these numbers here really just have two
+significant figures um we carried an
+
+ align:start position:0%
+significant figures um we carried an
+ 
+
+ align:start position:0%
+significant figures um we carried an
+extra um but it really just had two all
+
+ align:start position:0%
+extra um but it really just had two all
+ 
+
+ align:start position:0%
+extra um but it really just had two all
+right so our buffer was pretty good so
+
+ align:start position:0%
+right so our buffer was pretty good so
+ 
+
+ align:start position:0%
+right so our buffer was pretty good so
+we added 0.1 moles of a very strong acid
+
+ align:start position:0%
+we added 0.1 moles of a very strong acid
+ 
+
+ align:start position:0%
+we added 0.1 moles of a very strong acid
+and we only changed the pH we only
+
+ align:start position:0%
+and we only changed the pH we only
+ 
+
+ align:start position:0%
+and we only changed the pH we only
+lowered it from 3.45 to
+
+ align:start position:0%
+lowered it from 3.45 to
+ 
+
+ align:start position:0%
+lowered it from 3.45 to
+3.31 so that was a pretty good buffer
+
+ align:start position:0%
+3.31 so that was a pretty good buffer
+ 
+
+ align:start position:0%
+3.31 so that was a pretty good buffer
+that we had that we had uh designed
+
+ align:start position:0%
+that we had that we had uh designed
+ 
+
+ align:start position:0%
+that we had that we had uh designed
+there all right so that is how you do um
+
+ align:start position:0%
+there all right so that is how you do um
+ 
+
+ align:start position:0%
+there all right so that is how you do um
+a buffer problem and there are other
+
+ align:start position:0%
+a buffer problem and there are other
+ 
+
+ align:start position:0%
+a buffer problem and there are other
+kindes of things that you can be asked
+
+ align:start position:0%
+kindes of things that you can be asked
+ 
+
+ align:start position:0%
+kindes of things that you can be asked
+about with buffers um in particular you
+
+ align:start position:0%
+about with buffers um in particular you
+ 
+
+ align:start position:0%
+about with buffers um in particular you
+can also often be asked uh to design a
+
+ align:start position:0%
+can also often be asked uh to design a
+ 
+
+ align:start position:0%
+can also often be asked uh to design a
+buffer and when you design a buffer you
+
+ align:start position:0%
+buffer and when you design a buffer you
+ 
+
+ align:start position:0%
+buffer and when you design a buffer you
+must consider the following things the
+
+ align:start position:0%
+must consider the following things the
+ 
+
+ align:start position:0%
+must consider the following things the
+ratio of your conjugate acidbase pair
+
+ align:start position:0%
+ratio of your conjugate acidbase pair
+ 
+
+ align:start position:0%
+ratio of your conjugate acidbase pair
+and that they should also be weak
+
+ align:start position:0%
+and that they should also be weak
+ 
+
+ align:start position:0%
+and that they should also be weak
+conjugate acid based pairs the
+
+ align:start position:0%
+conjugate acid based pairs the
+ 
+
+ align:start position:0%
+conjugate acid based pairs the
+pka and the pH okay so here comes a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+derivation so here is our expression
+
+ align:start position:0%
+derivation so here is our expression
+ 
+
+ align:start position:0%
+derivation so here is our expression
+that should be familiar to you at this
+
+ align:start position:0%
+that should be familiar to you at this
+ 
+
+ align:start position:0%
+that should be familiar to you at this
+point for a weak acid ha in water going
+
+ align:start position:0%
+point for a weak acid ha in water going
+ 
+
+ align:start position:0%
+point for a weak acid ha in water going
+to hydronium ions and our conjugate base
+
+ align:start position:0%
+to hydronium ions and our conjugate base
+ 
+
+ align:start position:0%
+to hydronium ions and our conjugate base
+A minus it should also be familiar to
+
+ align:start position:0%
+A minus it should also be familiar to
+ 
+
+ align:start position:0%
+A minus it should also be familiar to
+you that you can write the um
+
+ align:start position:0%
+you that you can write the um
+ 
+
+ align:start position:0%
+you that you can write the um
+equilibrium expression for this acid in
+
+ align:start position:0%
+equilibrium expression for this acid in
+ 
+
+ align:start position:0%
+equilibrium expression for this acid in
+water as hydronium ion concentration
+
+ align:start position:0%
+water as hydronium ion concentration
+ 
+
+ align:start position:0%
+water as hydronium ion concentration
+times the concentration of the conjugate
+
+ align:start position:0%
+times the concentration of the conjugate
+ 
+
+ align:start position:0%
+times the concentration of the conjugate
+base over the concentration of the
+
+ align:start position:0%
+base over the concentration of the
+ 
+
+ align:start position:0%
+base over the concentration of the
+conjugate acid water which is our
+
+ align:start position:0%
+conjugate acid water which is our
+ 
+
+ align:start position:0%
+conjugate acid water which is our
+solvent doesn't appear in the
+
+ align:start position:0%
+solvent doesn't appear in the
+ 
+
+ align:start position:0%
+solvent doesn't appear in the
+expression we can rearrange this
+
+ align:start position:0%
+expression we can rearrange this
+ 
+
+ align:start position:0%
+expression we can rearrange this
+expression now and solve for hydronium
+
+ align:start position:0%
+expression now and solve for hydronium
+ 
+
+ align:start position:0%
+expression now and solve for hydronium
+ion
+
+ align:start position:0%
+ion
+ 
+
+ align:start position:0%
+ion
+concentrations we can take the log of
+
+ align:start position:0%
+concentrations we can take the log of
+ 
+
+ align:start position:0%
+concentrations we can take the log of
+both sides and get this log of hydronium
+
+ align:start position:0%
+both sides and get this log of hydronium
+ 
+
+ align:start position:0%
+both sides and get this log of hydronium
+concentration log of Ka plus log of ha
+
+ align:start position:0%
+concentration log of Ka plus log of ha
+ 
+
+ align:start position:0%
+concentration log of Ka plus log of ha
+over a minus multiply by negative to get
+
+ align:start position:0%
+over a minus multiply by negative to get
+ 
+
+ align:start position:0%
+over a minus multiply by negative to get
+this and so we have minus minus minus
+
+ align:start position:0%
+this and so we have minus minus minus
+ 
+
+ align:start position:0%
+this and so we have minus minus minus
+and minus the log of the hydronium ion
+
+ align:start position:0%
+and minus the log of the hydronium ion
+ 
+
+ align:start position:0%
+and minus the log of the hydronium ion
+concentration is what PH minus log of Ka
+
+ align:start position:0%
+concentration is what PH minus log of Ka
+ 
+
+ align:start position:0%
+concentration is what PH minus log of Ka
+is PKA and this is the same as that so
+
+ align:start position:0%
+is PKA and this is the same as that so
+ 
+
+ align:start position:0%
+is PKA and this is the same as that so
+that gives us this expression that pH
+
+ align:start position:0%
+that gives us this expression that pH
+ 
+
+ align:start position:0%
+that gives us this expression that pH
+equals PKA minus
+
+ align:start position:0%
+equals PKA minus
+ 
+
+ align:start position:0%
+equals PKA minus
+um the log of ha over a minus now it's
+
+ align:start position:0%
+um the log of ha over a minus now it's
+ 
+
+ align:start position:0%
+um the log of ha over a minus now it's
+important to point out that these are
+
+ align:start position:0%
+important to point out that these are
+ 
+
+ align:start position:0%
+important to point out that these are
+equilibrium concentrations of ha and a
+
+ align:start position:0%
+equilibrium concentrations of ha and a
+ 
+
+ align:start position:0%
+equilibrium concentrations of ha and a
+minus because we derived this expression
+
+ align:start position:0%
+minus because we derived this expression
+ 
+
+ align:start position:0%
+minus because we derived this expression
+from Ka and that's an equilibrium
+
+ align:start position:0%
+from Ka and that's an equilibrium
+ 
+
+ align:start position:0%
+from Ka and that's an equilibrium
+constant so these are equilibrium
+
+ align:start position:0%
+constant so these are equilibrium
+ 
+
+ align:start position:0%
+constant so these are equilibrium
+expressions and that makes this
+
+ align:start position:0%
+expressions and that makes this
+ 
+
+ align:start position:0%
+expressions and that makes this
+particular expression slightly less
+
+ align:start position:0%
+particular expression slightly less
+ 
+
+ align:start position:0%
+particular expression slightly less
+useful because we often don't want to
+
+ align:start position:0%
+useful because we often don't want to
+ 
+
+ align:start position:0%
+useful because we often don't want to
+have to calculate the equilibrium
+
+ align:start position:0%
+have to calculate the equilibrium
+ 
+
+ align:start position:0%
+have to calculate the equilibrium
+concentration we know how much we added
+
+ align:start position:0%
+concentration we know how much we added
+ 
+
+ align:start position:0%
+concentration we know how much we added
+and so we often want to use initial
+
+ align:start position:0%
+and so we often want to use initial
+ 
+
+ align:start position:0%
+and so we often want to use initial
+concentrations but we can consider
+
+ align:start position:0%
+concentrations but we can consider
+ 
+
+ align:start position:0%
+concentrations but we can consider
+whether the initial concentrations are
+
+ align:start position:0%
+whether the initial concentrations are
+ 
+
+ align:start position:0%
+whether the initial concentrations are
+actually pretty similar to the
+
+ align:start position:0%
+actually pretty similar to the
+ 
+
+ align:start position:0%
+actually pretty similar to the
+equilibrium concentrations I.E that X is
+
+ align:start position:0%
+equilibrium concentrations I.E that X is
+ 
+
+ align:start position:0%
+equilibrium concentrations I.E that X is
+small less than 5% so we know that a
+
+ align:start position:0%
+small less than 5% so we know that a
+ 
+
+ align:start position:0%
+small less than 5% so we know that a
+weak acid typically only loses a
+
+ align:start position:0%
+weak acid typically only loses a
+ 
+
+ align:start position:0%
+weak acid typically only loses a
+fraction of its protons hence the
+
+ align:start position:0%
+fraction of its protons hence the
+ 
+
+ align:start position:0%
+fraction of its protons hence the
+definition of weak acid weak acid in
+
+ align:start position:0%
+definition of weak acid weak acid in
+ 
+
+ align:start position:0%
+definition of weak acid weak acid in
+water doesn't ionize that much and a
+
+ align:start position:0%
+water doesn't ionize that much and a
+ 
+
+ align:start position:0%
+water doesn't ionize that much and a
+weak base typically only accepts a
+
+ align:start position:0%
+weak base typically only accepts a
+ 
+
+ align:start position:0%
+weak base typically only accepts a
+fraction of the protons that it could if
+
+ align:start position:0%
+fraction of the protons that it could if
+ 
+
+ align:start position:0%
+fraction of the protons that it could if
+it's a weak base so the initial
+
+ align:start position:0%
+it's a weak base so the initial
+ 
+
+ align:start position:0%
+it's a weak base so the initial
+concentration is often approximately
+
+ align:start position:0%
+concentration is often approximately
+ 
+
+ align:start position:0%
+concentration is often approximately
+equal to the equilibrium concentration
+
+ align:start position:0%
+equal to the equilibrium concentration
+ 
+
+ align:start position:0%
+equal to the equilibrium concentration
+and that's what we've been finding in a
+
+ align:start position:0%
+and that's what we've been finding in a
+ 
+
+ align:start position:0%
+and that's what we've been finding in a
+lot of these problems we find that the
+
+ align:start position:0%
+lot of these problems we find that the
+ 
+
+ align:start position:0%
+lot of these problems we find that the
+5% rule works pretty well it's usually
+
+ align:start position:0%
+5% rule works pretty well it's usually
+ 
+
+ align:start position:0%
+5% rule works pretty well it's usually
+less than 5% X is usually less than 5%
+
+ align:start position:0%
+less than 5% X is usually less than 5%
+ 
+
+ align:start position:0%
+less than 5% X is usually less than 5%
+of the initial concentration we had of
+
+ align:start position:0%
+of the initial concentration we had of
+ 
+
+ align:start position:0%
+of the initial concentration we had of
+ha or a minus and so therefore we can
+
+ align:start position:0%
+ha or a minus and so therefore we can
+ 
+
+ align:start position:0%
+ha or a minus and so therefore we can
+say that the pH is in fact approximately
+
+ align:start position:0%
+say that the pH is in fact approximately
+ 
+
+ align:start position:0%
+say that the pH is in fact approximately
+equal to the pka minus the log of the
+
+ align:start position:0%
+equal to the pka minus the log of the
+ 
+
+ align:start position:0%
+equal to the pka minus the log of the
+initial concentration of your ha over
+
+ align:start position:0%
+initial concentration of your ha over
+ 
+
+ align:start position:0%
+initial concentration of your ha over
+your initial concentration of a minus
+
+ align:start position:0%
+your initial concentration of a minus
+ 
+
+ align:start position:0%
+your initial concentration of a minus
+and this expression is known as the
+
+ align:start position:0%
+and this expression is known as the
+ 
+
+ align:start position:0%
+and this expression is known as the
+Henderson hosbach um equation and so
+
+ align:start position:0%
+Henderson hosbach um equation and so
+ 
+
+ align:start position:0%
+Henderson hosbach um equation and so
+this equation is only valid
+
+ align:start position:0%
+this equation is only valid
+ 
+
+ align:start position:0%
+this equation is only valid
+when your hydronium ion concentration is
+
+ align:start position:0%
+when your hydronium ion concentration is
+ 
+
+ align:start position:0%
+when your hydronium ion concentration is
+small compared to ha and a minus I.E
+
+ align:start position:0%
+small compared to ha and a minus I.E
+ 
+
+ align:start position:0%
+small compared to ha and a minus I.E
+less than 5% so this 5% rule
+
+ align:start position:0%
+less than 5% so this 5% rule
+ 
+
+ align:start position:0%
+less than 5% so this 5% rule
+must apply to use the Henderson hosbach
+
+ align:start position:0%
+must apply to use the Henderson hosbach
+ 
+
+ align:start position:0%
+must apply to use the Henderson hosbach
+equation the Henderson hosbach equation
+
+ align:start position:0%
+equation the Henderson hosbach equation
+ 
+
+ align:start position:0%
+equation the Henderson hosbach equation
+is a great equation to use for buffer
+
+ align:start position:0%
+is a great equation to use for buffer
+ 
+
+ align:start position:0%
+is a great equation to use for buffer
+problems and so we've showed you a
+
+ align:start position:0%
+problems and so we've showed you a
+ 
+
+ align:start position:0%
+problems and so we've showed you a
+couple different ways of doing buffer
+
+ align:start position:0%
+couple different ways of doing buffer
+ 
+
+ align:start position:0%
+couple different ways of doing buffer
+problems this is the final way I'm going
+
+ align:start position:0%
+problems this is the final way I'm going
+ 
+
+ align:start position:0%
+problems this is the final way I'm going
+to show you using the Henderson hoselock
+
+ align:start position:0%
+to show you using the Henderson hoselock
+ 
+
+ align:start position:0%
+to show you using the Henderson hoselock
+equation but you can only use it if x is
+
+ align:start position:0%
+equation but you can only use it if x is
+ 
+
+ align:start position:0%
+equation but you can only use it if x is
+small but most of the time x is going to
+
+ align:start position:0%
+small but most of the time x is going to
+ 
+
+ align:start position:0%
+small but most of the time x is going to
+be small because buffers are only
+
+ align:start position:0%
+be small because buffers are only
+ 
+
+ align:start position:0%
+be small because buffers are only
+buffers when you have a weak acid with a
+
+ align:start position:0%
+buffers when you have a weak acid with a
+ 
+
+ align:start position:0%
+buffers when you have a weak acid with a
+conjugate weak base
+
+ align:start position:0%
+conjugate weak base
+ 
+
+ align:start position:0%
+conjugate weak base
+and when you're talking about weak acids
+
+ align:start position:0%
+and when you're talking about weak acids
+ 
+
+ align:start position:0%
+and when you're talking about weak acids
+and bases X is small they don't ionize
+
+ align:start position:0%
+and bases X is small they don't ionize
+ 
+
+ align:start position:0%
+and bases X is small they don't ionize
+that much and importantly and I'll
+
+ align:start position:0%
+that much and importantly and I'll
+ 
+
+ align:start position:0%
+that much and importantly and I'll
+emphasize this this equation only works
+
+ align:start position:0%
+emphasize this this equation only works
+ 
+
+ align:start position:0%
+emphasize this this equation only works
+for buffers don't apply it for a just a
+
+ align:start position:0%
+for buffers don't apply it for a just a
+ 
+
+ align:start position:0%
+for buffers don't apply it for a just a
+regular weak acid in water or a weak
+
+ align:start position:0%
+regular weak acid in water or a weak
+ 
+
+ align:start position:0%
+regular weak acid in water or a weak
+base in water a strong acid in water a
+
+ align:start position:0%
+base in water a strong acid in water a
+ 
+
+ align:start position:0%
+base in water a strong acid in water a
+strong base in water it only applies for
+
+ align:start position:0%
+strong base in water it only applies for
+ 
+
+ align:start position:0%
+strong base in water it only applies for
+buffers buffers
+
+ align:start position:0%
+buffers buffers
+ 
+
+ align:start position:0%
+buffers buffers
+buffers now I know that MIT students
+
+ align:start position:0%
+buffers now I know that MIT students
+ 
+
+ align:start position:0%
+buffers now I know that MIT students
+love equations and they love doing math
+
+ align:start position:0%
+love equations and they love doing math
+ 
+
+ align:start position:0%
+love equations and they love doing math
+and so they try to apply this equation
+
+ align:start position:0%
+and so they try to apply this equation
+ 
+
+ align:start position:0%
+and so they try to apply this equation
+to every type of acidbase problem don't
+
+ align:start position:0%
+to every type of acidbase problem don't
+ 
+
+ align:start position:0%
+to every type of acidbase problem don't
+do it buffers
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+buffers you'll remember that now
+
+ align:start position:0%
+buffers you'll remember that now
+ 
+
+ align:start position:0%
+buffers you'll remember that now
+right because I'll I'll make noises
+
+ align:start position:0%
+right because I'll I'll make noises
+ 
+
+ align:start position:0%
+right because I'll I'll make noises
+again if you don't you'll remember that
+
+ align:start position:0%
+again if you don't you'll remember that
+ 
+
+ align:start position:0%
+again if you don't you'll remember that
+now
+
+ align:start position:0%
+now
+ 
+
+ align:start position:0%
+now
+right all right so let's use the
+
+ align:start position:0%
+right all right so let's use the
+ 
+
+ align:start position:0%
+right all right so let's use the
+Henderson hasselbach uh to design a
+
+ align:start position:0%
+Henderson hasselbach uh to design a
+ 
+
+ align:start position:0%
+Henderson hasselbach uh to design a
+buffer then so say we want to design a
+
+ align:start position:0%
+buffer then so say we want to design a
+ 
+
+ align:start position:0%
+buffer then so say we want to design a
+buffer at pH 6 uh 4.6 say you're
+
+ align:start position:0%
+buffer at pH 6 uh 4.6 say you're
+ 
+
+ align:start position:0%
+buffer at pH 6 uh 4.6 say you're
+interviewing for a europ position and uh
+
+ align:start position:0%
+interviewing for a europ position and uh
+ 
+
+ align:start position:0%
+interviewing for a europ position and uh
+the europ uh supervisor the the PI says
+
+ align:start position:0%
+the europ uh supervisor the the PI says
+ 
+
+ align:start position:0%
+the europ uh supervisor the the PI says
+uh tell me how you would design a buffer
+
+ align:start position:0%
+uh tell me how you would design a buffer
+ 
+
+ align:start position:0%
+uh tell me how you would design a buffer
+um pH 4.6 and you might uh go to the
+
+ align:start position:0%
+um pH 4.6 and you might uh go to the
+ 
+
+ align:start position:0%
+um pH 4.6 and you might uh go to the
+shelf and see what was available and
+
+ align:start position:0%
+shelf and see what was available and
+ 
+
+ align:start position:0%
+shelf and see what was available and
+then look up what uh the KA and PKA are
+
+ align:start position:0%
+then look up what uh the KA and PKA are
+ 
+
+ align:start position:0%
+then look up what uh the KA and PKA are
+because a buffer solution is most most
+
+ align:start position:0%
+because a buffer solution is most most
+ 
+
+ align:start position:0%
+because a buffer solution is most most
+effective in the range of the pka plus
+
+ align:start position:0%
+effective in the range of the pka plus
+ 
+
+ align:start position:0%
+effective in the range of the pka plus
+or minus one in fact the closer the pH
+
+ align:start position:0%
+or minus one in fact the closer the pH
+ 
+
+ align:start position:0%
+or minus one in fact the closer the pH
+that you want is to the pka the better
+
+ align:start position:0%
+that you want is to the pka the better
+ 
+
+ align:start position:0%
+that you want is to the pka the better
+the buffer it's going to be so we can
+
+ align:start position:0%
+the buffer it's going to be so we can
+ 
+
+ align:start position:0%
+the buffer it's going to be so we can
+look and see what's in the range there's
+
+ align:start position:0%
+look and see what's in the range there's
+ 
+
+ align:start position:0%
+look and see what's in the range there's
+several that are close to 4.6 that we
+
+ align:start position:0%
+several that are close to 4.6 that we
+ 
+
+ align:start position:0%
+several that are close to 4.6 that we
+can choose from and probably would end
+
+ align:start position:0%
+can choose from and probably would end
+ 
+
+ align:start position:0%
+can choose from and probably would end
+up choosing acetic acid because that
+
+ align:start position:0%
+up choosing acetic acid because that
+ 
+
+ align:start position:0%
+up choosing acetic acid because that
+would be on the Shelf whereas some of
+
+ align:start position:0%
+would be on the Shelf whereas some of
+ 
+
+ align:start position:0%
+would be on the Shelf whereas some of
+the others of these would not be there
+
+ align:start position:0%
+the others of these would not be there
+ 
+
+ align:start position:0%
+the others of these would not be there
+all right so acetate is going to work
+
+ align:start position:0%
+all right so acetate is going to work
+ 
+
+ align:start position:0%
+all right so acetate is going to work
+it's a pretty common buffer um so we can
+
+ align:start position:0%
+it's a pretty common buffer um so we can
+ 
+
+ align:start position:0%
+it's a pretty common buffer um so we can
+use acetic acid with a suitable pka of
+
+ align:start position:0%
+use acetic acid with a suitable pka of
+ 
+
+ align:start position:0%
+use acetic acid with a suitable pka of
+4.75 then we can use the Henderson
+
+ align:start position:0%
+4.75 then we can use the Henderson
+ 
+
+ align:start position:0%
+4.75 then we can use the Henderson
+hoselock equation because we're
+
+ align:start position:0%
+hoselock equation because we're
+ 
+
+ align:start position:0%
+hoselock equation because we're
+designing a buffer so we can use that
+
+ align:start position:0%
+designing a buffer so we can use that
+ 
+
+ align:start position:0%
+designing a buffer so we can use that
+equation and figure out what the ratio
+
+ align:start position:0%
+equation and figure out what the ratio
+ 
+
+ align:start position:0%
+equation and figure out what the ratio
+of acetic acid to its conjugate base
+
+ align:start position:0%
+of acetic acid to its conjugate base
+ 
+
+ align:start position:0%
+of acetic acid to its conjugate base
+should
+
+ align:start position:0%
+should
+ 
+
+ align:start position:0%
+should
+be so we can rearrange this expression
+
+ align:start position:0%
+be so we can rearrange this expression
+ 
+
+ align:start position:0%
+be so we can rearrange this expression
+we know the pka and we know the pH that
+
+ align:start position:0%
+we know the pka and we know the pH that
+ 
+
+ align:start position:0%
+we know the pka and we know the pH that
+we want and so we can subtract those and
+
+ align:start position:0%
+we want and so we can subtract those and
+ 
+
+ align:start position:0%
+we want and so we can subtract those and
+we get that the log of the ratio should
+
+ align:start position:0%
+we get that the log of the ratio should
+ 
+
+ align:start position:0%
+we get that the log of the ratio should
+be
+
+ align:start position:0%
+be
+ 
+
+ align:start position:0%
+be
+.15 and then inverse log will tell us
+
+ align:start position:0%
+.15 and then inverse log will tell us
+ 
+
+ align:start position:0%
+.15 and then inverse log will tell us
+that the ratio then of the acid to the
+
+ align:start position:0%
+that the ratio then of the acid to the
+ 
+
+ align:start position:0%
+that the ratio then of the acid to the
+conjugate base should be
+
+ align:start position:0%
+conjugate base should be
+ 
+
+ align:start position:0%
+conjugate base should be
+1.4 so you should use things with that
+
+ align:start position:0%
+1.4 so you should use things with that
+ 
+
+ align:start position:0%
+1.4 so you should use things with that
+ratio so for example you could use 1.4
+
+ align:start position:0%
+ratio so for example you could use 1.4
+ 
+
+ align:start position:0%
+ratio so for example you could use 1.4
+molar of the acid to one molar of the
+
+ align:start position:0%
+molar of the acid to one molar of the
+ 
+
+ align:start position:0%
+molar of the acid to one molar of the
+conjugate base and
+
+ align:start position:0%
+conjugate base and
+ 
+
+ align:start position:0%
+conjugate base and
+the the uh the total amounts are often
+
+ align:start position:0%
+the the uh the total amounts are often
+ 
+
+ align:start position:0%
+the the uh the total amounts are often
+less important than the ratio the ratio
+
+ align:start position:0%
+less important than the ratio the ratio
+ 
+
+ align:start position:0%
+less important than the ratio the ratio
+is very important but if you go too low
+
+ align:start position:0%
+is very important but if you go too low
+ 
+
+ align:start position:0%
+is very important but if you go too low
+in
+
+ align:start position:0%
+in
+ 
+
+ align:start position:0%
+in
+concentrations then that'll affect
+
+ align:start position:0%
+concentrations then that'll affect
+ 
+
+ align:start position:0%
+concentrations then that'll affect
+what's known as the buffering capacity
+
+ align:start position:0%
+what's known as the buffering capacity
+ 
+
+ align:start position:0%
+what's known as the buffering capacity
+which is the ability of the buffer to
+
+ align:start position:0%
+which is the ability of the buffer to
+ 
+
+ align:start position:0%
+which is the ability of the buffer to
+resist changes so if it's too dilute and
+
+ align:start position:0%
+resist changes so if it's too dilute and
+ 
+
+ align:start position:0%
+resist changes so if it's too dilute and
+a lot of strong acid or a lot of strong
+
+ align:start position:0%
+a lot of strong acid or a lot of strong
+ 
+
+ align:start position:0%
+a lot of strong acid or a lot of strong
+bases added then it won't be a good
+
+ align:start position:0%
+bases added then it won't be a good
+ 
+
+ align:start position:0%
+bases added then it won't be a good
+buffer anymore so the ratio is very
+
+ align:start position:0%
+buffer anymore so the ratio is very
+ 
+
+ align:start position:0%
+buffer anymore so the ratio is very
+important the amounts are important such
+
+ align:start position:0%
+important the amounts are important such
+ 
+
+ align:start position:0%
+important the amounts are important such
+that you have some resistance to change
+
+ align:start position:0%
+that you have some resistance to change
+ 
+
+ align:start position:0%
+that you have some resistance to change
+so the higher
+
+ align:start position:0%
+so the higher
+ 
+
+ align:start position:0%
+so the higher
+concentrations the more resistant to
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+change and if you Lo also if you use too
+
+ align:start position:0%
+change and if you Lo also if you use too
+ 
+
+ align:start position:0%
+change and if you Lo also if you use too
+low a concentration the Henderson
+
+ align:start position:0%
+low a concentration the Henderson
+ 
+
+ align:start position:0%
+low a concentration the Henderson
+hoselock equation is no longer valid so
+
+ align:start position:0%
+hoselock equation is no longer valid so
+ 
+
+ align:start position:0%
+hoselock equation is no longer valid so
+you can be asked to calculate sort of
+
+ align:start position:0%
+you can be asked to calculate sort of
+ 
+
+ align:start position:0%
+you can be asked to calculate sort of
+what the minimum concentration is that
+
+ align:start position:0%
+what the minimum concentration is that
+ 
+
+ align:start position:0%
+what the minimum concentration is that
+you would need to use and so for H 6 uh
+
+ align:start position:0%
+you would need to use and so for H 6 uh
+ 
+
+ align:start position:0%
+you would need to use and so for H 6 uh
+4.60 you can back calculate what the
+
+ align:start position:0%
+4.60 you can back calculate what the
+ 
+
+ align:start position:0%
+4.60 you can back calculate what the
+hydronium ion concentration is and it's
+
+ align:start position:0%
+hydronium ion concentration is and it's
+ 
+
+ align:start position:0%
+hydronium ion concentration is and it's
+2.5 * 10us 5 so for our 5% assumption to
+
+ align:start position:0%
+2.5 * 10us 5 so for our 5% assumption to
+ 
+
+ align:start position:0%
+2.5 * 10us 5 so for our 5% assumption to
+hold or to be valid that this number the
+
+ align:start position:0%
+hold or to be valid that this number the
+ 
+
+ align:start position:0%
+hold or to be valid that this number the
+hydronium ion concentration is less than
+
+ align:start position:0%
+hydronium ion concentration is less than
+ 
+
+ align:start position:0%
+hydronium ion concentration is less than
+5% of either one of these the
+
+ align:start position:0%
+5% of either one of these the
+ 
+
+ align:start position:0%
+5% of either one of these the
+concentrations here would have to be
+
+ align:start position:0%
+concentrations here would have to be
+ 
+
+ align:start position:0%
+concentrations here would have to be
+greater than 5 * 10us 4 so if if we use
+
+ align:start position:0%
+greater than 5 * 10us 4 so if if we use
+ 
+
+ align:start position:0%
+greater than 5 * 10us 4 so if if we use
+one Moler or something that's way above
+
+ align:start position:0%
+one Moler or something that's way above
+ 
+
+ align:start position:0%
+one Moler or something that's way above
+this but that would be the minimum if
+
+ align:start position:0%
+this but that would be the minimum if
+ 
+
+ align:start position:0%
+this but that would be the minimum if
+it's less than that that 5% doesn't
+
+ align:start position:0%
+it's less than that that 5% doesn't
+ 
+
+ align:start position:0%
+it's less than that that 5% doesn't
+really hold and you would not have a
+
+ align:start position:0%
+really hold and you would not have a
+ 
+
+ align:start position:0%
+really hold and you would not have a
+very good buffer in that case it
+
+ align:start position:0%
+very good buffer in that case it
+ 
+
+ align:start position:0%
+very good buffer in that case it
+wouldn't be very resistance to change X
+
+ align:start position:0%
+wouldn't be very resistance to change X
+ 
+
+ align:start position:0%
+wouldn't be very resistance to change X
+would be big compared to those numbers
+
+ align:start position:0%
+would be big compared to those numbers
+ 
+
+ align:start position:0%
+would be big compared to those numbers
+so that's how you go about designing a
+
+ align:start position:0%
+so that's how you go about designing a
+ 
+
+ align:start position:0%
+so that's how you go about designing a
+buffer and in that there were two things
+
+ align:start position:0%
+buffer and in that there were two things
+ 
+
+ align:start position:0%
+buffer and in that there were two things
+that are really common mistakes when I'm
+
+ align:start position:0%
+that are really common mistakes when I'm
+ 
+
+ align:start position:0%
+that are really common mistakes when I'm
+reviewing a paper for publication two of
+
+ align:start position:0%
+reviewing a paper for publication two of
+ 
+
+ align:start position:0%
+reviewing a paper for publication two of
+the things that I see the most often is
+
+ align:start position:0%
+the things that I see the most often is
+ 
+
+ align:start position:0%
+the things that I see the most often is
+that people one do not use the right
+
+ align:start position:0%
+that people one do not use the right
+ 
+
+ align:start position:0%
+that people one do not use the right
+buffer for their experiment they say oh
+
+ align:start position:0%
+buffer for their experiment they say oh
+ 
+
+ align:start position:0%
+buffer for their experiment they say oh
+I'm at P you know ph8 and they'll use a
+
+ align:start position:0%
+I'm at P you know ph8 and they'll use a
+ 
+
+ align:start position:0%
+I'm at P you know ph8 and they'll use a
+buffer that is in fact not a good buffer
+
+ align:start position:0%
+buffer that is in fact not a good buffer
+ 
+
+ align:start position:0%
+buffer that is in fact not a good buffer
+at ph8 so who knows what their data is
+
+ align:start position:0%
+at ph8 so who knows what their data is
+ 
+
+ align:start position:0%
+at ph8 so who knows what their data is
+telling us and the other thing that
+
+ align:start position:0%
+telling us and the other thing that
+ 
+
+ align:start position:0%
+telling us and the other thing that
+people will do is that they'll say oh
+
+ align:start position:0%
+people will do is that they'll say oh
+ 
+
+ align:start position:0%
+people will do is that they'll say oh
+yes it was buffered and the pka might be
+
+ align:start position:0%
+yes it was buffered and the pka might be
+ 
+
+ align:start position:0%
+yes it was buffered and the pka might be
+right but the concentration of the
+
+ align:start position:0%
+right but the concentration of the
+ 
+
+ align:start position:0%
+right but the concentration of the
+buffer is so low that you don't really
+
+ align:start position:0%
+buffer is so low that you don't really
+ 
+
+ align:start position:0%
+buffer is so low that you don't really
+imagine the buffer is doing anything so
+
+ align:start position:0%
+imagine the buffer is doing anything so
+ 
+
+ align:start position:0%
+imagine the buffer is doing anything so
+now you know how to avoid both of those
+
+ align:start position:0%
+now you know how to avoid both of those
+ 
+
+ align:start position:0%
+now you know how to avoid both of those
+pitfalls
\ No newline at end of file
diff --git a/crMyNv2fdkc.txt b/crMyNv2fdkc.txt
new file mode 100644
index 0000000000000000000000000000000000000000..400fe7d64f82726e8ffbb4b453f06f1cd23160bf
--- /dev/null
+++ b/crMyNv2fdkc.txt
@@ -0,0 +1,947 @@
+align:start position:0%
+ 
+the probabilistic method in
+
+ align:start position:0%
+the probabilistic method in
+ 
+
+ align:start position:0%
+the probabilistic method in
+combinatorics is a powerful method that
+
+ align:start position:0%
+combinatorics is a powerful method that
+ 
+
+ align:start position:0%
+combinatorics is a powerful method that
+can be used to demonstrate the existence
+
+ align:start position:0%
+can be used to demonstrate the existence
+ 
+
+ align:start position:0%
+can be used to demonstrate the existence
+of some object by introducing
+
+ align:start position:0%
+of some object by introducing
+ 
+
+ align:start position:0%
+of some object by introducing
+Randomness in this video we'll look at a
+
+ align:start position:0%
+Randomness in this video we'll look at a
+ 
+
+ align:start position:0%
+Randomness in this video we'll look at a
+basic example illustrating an
+
+ align:start position:0%
+basic example illustrating an
+ 
+
+ align:start position:0%
+basic example illustrating an
+application of the probabilistic method
+
+ align:start position:0%
+application of the probabilistic method
+ 
+
+ align:start position:0%
+application of the probabilistic method
+we'll show this theorem over here which
+
+ align:start position:0%
+we'll show this theorem over here which
+ 
+
+ align:start position:0%
+we'll show this theorem over here which
+says that if G is a graph with M edges
+
+ align:start position:0%
+says that if G is a graph with M edges
+ 
+
+ align:start position:0%
+says that if G is a graph with M edges
+then G has a bipartite subgraph with at
+
+ align:start position:0%
+then G has a bipartite subgraph with at
+ 
+
+ align:start position:0%
+then G has a bipartite subgraph with at
+least M over two edges so let me remind
+
+ align:start position:0%
+least M over two edges so let me remind
+ 
+
+ align:start position:0%
+least M over two edges so let me remind
+you the definition of a bipar graph is
+
+ align:start position:0%
+you the definition of a bipar graph is
+ 
+
+ align:start position:0%
+you the definition of a bipar graph is
+one where I can partition the vertices
+
+ align:start position:0%
+one where I can partition the vertices
+ 
+
+ align:start position:0%
+one where I can partition the vertices
+into two halves or two sets of vertices
+
+ align:start position:0%
+into two halves or two sets of vertices
+ 
+
+ align:start position:0%
+into two halves or two sets of vertices
+and all the
+
+ align:start position:0%
+and all the
+ 
+
+ align:start position:0%
+and all the
+edges go from one side to the other so
+
+ align:start position:0%
+edges go from one side to the other so
+ 
+
+ align:start position:0%
+edges go from one side to the other so
+that's an example of a bipartite graph
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and what this theorem is saying is that
+
+ align:start position:0%
+and what this theorem is saying is that
+ 
+
+ align:start position:0%
+and what this theorem is saying is that
+if we start with any graph G
+
+ align:start position:0%
+if we start with any graph G
+ 
+
+ align:start position:0%
+if we start with any graph G
+with some number of edges in this case
+
+ align:start position:0%
+with some number of edges in this case
+ 
+
+ align:start position:0%
+with some number of edges in this case
+five
+
+ align:start position:0%
+five
+ 
+
+ align:start position:0%
+five
+edges I can find a pretty large subgraph
+
+ align:start position:0%
+edges I can find a pretty large subgraph
+ 
+
+ align:start position:0%
+edges I can find a pretty large subgraph
+by keeping at least half of the edges of
+
+ align:start position:0%
+by keeping at least half of the edges of
+ 
+
+ align:start position:0%
+by keeping at least half of the edges of
+G for example we can do this keeping
+
+ align:start position:0%
+G for example we can do this keeping
+ 
+
+ align:start position:0%
+G for example we can do this keeping
+four of the five edges to get this
+
+ align:start position:0%
+four of the five edges to get this
+ 
+
+ align:start position:0%
+four of the five edges to get this
+subgraph G Prime and this graph G Prime
+
+ align:start position:0%
+subgraph G Prime and this graph G Prime
+ 
+
+ align:start position:0%
+subgraph G Prime and this graph G Prime
+is now bipart
+
+ align:start position:0%
+is now bipart
+ 
+
+ align:start position:0%
+is now bipart
+because I
+
+ align:start position:0%
+because I
+ 
+
+ align:start position:0%
+because I
+can put these two vertices on one
+
+ align:start position:0%
+can put these two vertices on one
+ 
+
+ align:start position:0%
+can put these two vertices on one
+side and these two vertices on the other
+
+ align:start position:0%
+side and these two vertices on the other
+ 
+
+ align:start position:0%
+side and these two vertices on the other
+side so that you see all the edges go
+
+ align:start position:0%
+side so that you see all the edges go
+ 
+
+ align:start position:0%
+side so that you see all the edges go
+from the red or the pink vertices to the
+
+ align:start position:0%
+from the red or the pink vertices to the
+ 
+
+ align:start position:0%
+from the red or the pink vertices to the
+green vertices and none between the pink
+
+ align:start position:0%
+green vertices and none between the pink
+ 
+
+ align:start position:0%
+green vertices and none between the pink
+and none between the
+
+ align:start position:0%
+and none between the
+ 
+
+ align:start position:0%
+and none between the
+greens so this is an example of um
+
+ align:start position:0%
+greens so this is an example of um
+ 
+
+ align:start position:0%
+greens so this is an example of um
+finding a large bipar subgraph in a
+
+ align:start position:0%
+finding a large bipar subgraph in a
+ 
+
+ align:start position:0%
+finding a large bipar subgraph in a
+graph G now let me prove this theorem
+
+ align:start position:0%
+graph G now let me prove this theorem
+ 
+
+ align:start position:0%
+graph G now let me prove this theorem
+illustrating the probabilistic
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+method so we're given this graph G and
+
+ align:start position:0%
+method so we're given this graph G and
+ 
+
+ align:start position:0%
+method so we're given this graph G and
+what we'll do is
+
+ align:start position:0%
+what we'll do is
+ 
+
+ align:start position:0%
+what we'll do is
+assign
+
+ align:start position:0%
+assign
+ 
+
+ align:start position:0%
+assign
+a
+
+ align:start position:0%
+a
+ 
+
+ align:start position:0%
+a
+color which will be either black or
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+white
+
+ align:start position:0%
+white
+ 
+
+ align:start position:0%
+white
+uniformly and independently at random
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+to each
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+vertex of the graph
+
+ align:start position:0%
+vertex of the graph
+ 
+
+ align:start position:0%
+vertex of the graph
+G so imagine flipping a coin for each
+
+ align:start position:0%
+G so imagine flipping a coin for each
+ 
+
+ align:start position:0%
+G so imagine flipping a coin for each
+vertex and coloring each vertex black or
+
+ align:start position:0%
+vertex and coloring each vertex black or
+ 
+
+ align:start position:0%
+vertex and coloring each vertex black or
+white after doing this we can put all
+
+ align:start position:0%
+white after doing this we can put all
+ 
+
+ align:start position:0%
+white after doing this we can put all
+the white vertices of G on one side and
+
+ align:start position:0%
+the white vertices of G on one side and
+ 
+
+ align:start position:0%
+the white vertices of G on one side and
+all the black vertices of G on the other
+
+ align:start position:0%
+all the black vertices of G on the other
+ 
+
+ align:start position:0%
+all the black vertices of G on the other
+side okay so now G has some number of
+
+ align:start position:0%
+side okay so now G has some number of
+ 
+
+ align:start position:0%
+side okay so now G has some number of
+vertices and there will be some edges
+
+ align:start position:0%
+vertices and there will be some edges
+ 
+
+ align:start position:0%
+vertices and there will be some edges
+going across from white to black some
+
+ align:start position:0%
+going across from white to black some
+ 
+
+ align:start position:0%
+going across from white to black some
+edges within white and some edges within
+
+ align:start position:0%
+edges within white and some edges within
+ 
+
+ align:start position:0%
+edges within white and some edges within
+black there could be a lot more edges
+
+ align:start position:0%
+black there could be a lot more edges
+ 
+
+ align:start position:0%
+black there could be a lot more edges
+but that's an example of what this graph
+
+ align:start position:0%
+but that's an example of what this graph
+ 
+
+ align:start position:0%
+but that's an example of what this graph
+might look
+
+ align:start position:0%
+might look
+ 
+
+ align:start position:0%
+might look
+like and now let me take G Prime to be
+
+ align:start position:0%
+like and now let me take G Prime to be
+ 
+
+ align:start position:0%
+like and now let me take G Prime to be
+the subgraph
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+consisting of
+
+ align:start position:0%
+consisting of
+ 
+
+ align:start position:0%
+consisting of
+edges with white on one end and black on
+
+ align:start position:0%
+edges with white on one end and black on
+ 
+
+ align:start position:0%
+edges with white on one end and black on
+the other end so two different colors on
+
+ align:start position:0%
+the other end so two different colors on
+ 
+
+ align:start position:0%
+the other end so two different colors on
+the two edges two end points of this
+
+ align:start position:0%
+the two edges two end points of this
+ 
+
+ align:start position:0%
+the two edges two end points of this
+Edge this is a subgraph it's a subset of
+
+ align:start position:0%
+Edge this is a subgraph it's a subset of
+ 
+
+ align:start position:0%
+Edge this is a subgraph it's a subset of
+the edges of
+
+ align:start position:0%
+the edges of
+ 
+
+ align:start position:0%
+the edges of
+G and note
+
+ align:start position:0%
+G and note
+ 
+
+ align:start position:0%
+G and note
+that
+
+ align:start position:0%
+that
+ 
+
+ align:start position:0%
+that
+every
+
+ align:start position:0%
+every
+ 
+
+ align:start position:0%
+every
+edge of G
+
+ align:start position:0%
+edge of G
+ 
+
+ align:start position:0%
+edge of G
+has
+
+ align:start position:0%
+has
+ 
+
+ align:start position:0%
+has
+probability 1 half of
+
+ align:start position:0%
+probability 1 half of
+ 
+
+ align:start position:0%
+probability 1 half of
+Being in G Prime because for this Edge
+
+ align:start position:0%
+Being in G Prime because for this Edge
+ 
+
+ align:start position:0%
+Being in G Prime because for this Edge
+there are four different
+
+ align:start position:0%
+there are four different
+ 
+
+ align:start position:0%
+there are four different
+possibilities for what the endpoint
+
+ align:start position:0%
+possibilities for what the endpoint
+ 
+
+ align:start position:0%
+possibilities for what the endpoint
+colors might look like and these four
+
+ align:start position:0%
+colors might look like and these four
+ 
+
+ align:start position:0%
+colors might look like and these four
+possibilities are equally likely and
+
+ align:start position:0%
+possibilities are equally likely and
+ 
+
+ align:start position:0%
+possibilities are equally likely and
+exactly two of them will create an edge
+
+ align:start position:0%
+exactly two of them will create an edge
+ 
+
+ align:start position:0%
+exactly two of them will create an edge
+that falls in G
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Prime now knowing this by linearity of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+expectations the number of
+
+ align:start position:0%
+expectations the number of
+ 
+
+ align:start position:0%
+expectations the number of
+edges
+
+ align:start position:0%
+edges
+ 
+
+ align:start position:0%
+edges
+of G
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Prime here G Prime is a random subgraph
+
+ align:start position:0%
+Prime here G Prime is a random subgraph
+ 
+
+ align:start position:0%
+Prime here G Prime is a random subgraph
+right where G is given G Prime depends
+
+ align:start position:0%
+right where G is given G Prime depends
+ 
+
+ align:start position:0%
+right where G is given G Prime depends
+on the coin flips that we made to assign
+
+ align:start position:0%
+on the coin flips that we made to assign
+ 
+
+ align:start position:0%
+on the coin flips that we made to assign
+colors so it's a random subgraph so the
+
+ align:start position:0%
+colors so it's a random subgraph so the
+ 
+
+ align:start position:0%
+colors so it's a random subgraph so the
+number of edges of G Prime is a random
+
+ align:start position:0%
+number of edges of G Prime is a random
+ 
+
+ align:start position:0%
+number of edges of G Prime is a random
+variable but this random variable has an
+
+ align:start position:0%
+variable but this random variable has an
+ 
+
+ align:start position:0%
+variable but this random variable has an
+expectation and we can compute this
+
+ align:start position:0%
+expectation and we can compute this
+ 
+
+ align:start position:0%
+expectation and we can compute this
+expectation using linear of expectations
+
+ align:start position:0%
+expectation using linear of expectations
+ 
+
+ align:start position:0%
+expectation using linear of expectations
+because each Edge Falls in G Prime with
+
+ align:start position:0%
+because each Edge Falls in G Prime with
+ 
+
+ align:start position:0%
+because each Edge Falls in G Prime with
+probability 1/2 and therefore the total
+
+ align:start position:0%
+probability 1/2 and therefore the total
+ 
+
+ align:start position:0%
+probability 1/2 and therefore the total
+expected number of edges in gpre is
+
+ align:start position:0%
+expected number of edges in gpre is
+ 
+
+ align:start position:0%
+expected number of edges in gpre is
+m/2 this is the expectation this is what
+
+ align:start position:0%
+m/2 this is the expectation this is what
+ 
+
+ align:start position:0%
+m/2 this is the expectation this is what
+happens on
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+average
+
+ align:start position:0%
+average
+ 
+
+ align:start position:0%
+average
+does some instance
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+of G
+
+ align:start position:0%
+of G
+ 
+
+ align:start position:0%
+of G
+Prime
+
+ align:start position:0%
+Prime
+ 
+
+ align:start position:0%
+Prime
+has at least m/2
+
+ align:start position:0%
+has at least m/2
+ 
+
+ align:start position:0%
+has at least m/2
+edges right if on average we get M over2
+
+ align:start position:0%
+edges right if on average we get M over2
+ 
+
+ align:start position:0%
+edges right if on average we get M over2
+edges then there must be some instance
+
+ align:start position:0%
+edges then there must be some instance
+ 
+
+ align:start position:0%
+edges then there must be some instance
+with at least M over2 edges and this G
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Prime is what we're looking
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+for it has at least M over two edges and
+
+ align:start position:0%
+for it has at least M over two edges and
+ 
+
+ align:start position:0%
+for it has at least M over two edges and
+it is bipartite because we've kept all
+
+ align:start position:0%
+it is bipartite because we've kept all
+ 
+
+ align:start position:0%
+it is bipartite because we've kept all
+the edges from the black side to the
+
+ align:start position:0%
+the edges from the black side to the
+ 
+
+ align:start position:0%
+the edges from the black side to the
+white side and so this G Prime is
+
+ align:start position:0%
+white side and so this G Prime is
+ 
+
+ align:start position:0%
+white side and so this G Prime is
+bipartite this finishes the proof of the
+
+ align:start position:0%
+bipartite this finishes the proof of the
+ 
+
+ align:start position:0%
+bipartite this finishes the proof of the
+theorem and you see that by introducing
+
+ align:start position:0%
+theorem and you see that by introducing
+ 
+
+ align:start position:0%
+theorem and you see that by introducing
+Randomness we can prove something about
+
+ align:start position:0%
+Randomness we can prove something about
+ 
+
+ align:start position:0%
+Randomness we can prove something about
+the existence of a structure with
+
+ align:start position:0%
+the existence of a structure with
+ 
+
+ align:start position:0%
+the existence of a structure with
+desired properties and it's a hmark of
+
+ align:start position:0%
+desired properties and it's a hmark of
+ 
+
+ align:start position:0%
+desired properties and it's a hmark of
+the probabilistic method and it's an
+
+ align:start position:0%
+the probabilistic method and it's an
+ 
+
+ align:start position:0%
+the probabilistic method and it's an
+important meth me that has lot of
+
+ align:start position:0%
+important meth me that has lot of
+ 
+
+ align:start position:0%
+important meth me that has lot of
+applications and this is one of the
+
+ align:start position:0%
+applications and this is one of the
+ 
+
+ align:start position:0%
+applications and this is one of the
+simplest examples of its applications
\ No newline at end of file
diff --git a/dfsPKoHv_F4.txt b/dfsPKoHv_F4.txt
new file mode 100644
index 0000000000000000000000000000000000000000..d593edd22efa0e5568c06ee59ad3b7083c3edaf6
--- /dev/null
+++ b/dfsPKoHv_F4.txt
@@ -0,0 +1,15739 @@
+align:start position:0%
+ 
+the following content is provided under
+
+ align:start position:0%
+the following content is provided under
+ 
+
+ align:start position:0%
+the following content is provided under
+a Creative Commons license your support
+
+ align:start position:0%
+a Creative Commons license your support
+ 
+
+ align:start position:0%
+a Creative Commons license your support
+will help MIT OpenCourseWare continue to
+
+ align:start position:0%
+will help MIT OpenCourseWare continue to
+ 
+
+ align:start position:0%
+will help MIT OpenCourseWare continue to
+offer high quality educational resources
+
+ align:start position:0%
+offer high quality educational resources
+ 
+
+ align:start position:0%
+offer high quality educational resources
+for free
+
+ align:start position:0%
+for free
+ 
+
+ align:start position:0%
+for free
+to make a donation or view additional
+
+ align:start position:0%
+to make a donation or view additional
+ 
+
+ align:start position:0%
+to make a donation or view additional
+materials from hundreds of MIT courses
+
+ align:start position:0%
+materials from hundreds of MIT courses
+ 
+
+ align:start position:0%
+materials from hundreds of MIT courses
+visit MIT opencourseware at ocw.mit.edu
+
+ align:start position:0%
+visit MIT opencourseware at ocw.mit.edu
+ 
+
+ align:start position:0%
+visit MIT opencourseware at ocw.mit.edu
+so where we left off was you know again
+
+ align:start position:0%
+so where we left off was you know again
+ 
+
+ align:start position:0%
+so where we left off was you know again
+I was telling you a story both
+
+ align:start position:0%
+I was telling you a story both
+ 
+
+ align:start position:0%
+I was telling you a story both
+conceptual and motivational and a little
+
+ align:start position:0%
+conceptual and motivational and a little
+ 
+
+ align:start position:0%
+conceptual and motivational and a little
+bit technical about how we got to the
+
+ align:start position:0%
+bit technical about how we got to the
+ 
+
+ align:start position:0%
+bit technical about how we got to the
+things we're trying to do now as part of
+
+ align:start position:0%
+things we're trying to do now as part of
+ 
+
+ align:start position:0%
+things we're trying to do now as part of
+the center and it involves again both
+
+ align:start position:0%
+the center and it involves again both
+ 
+
+ align:start position:0%
+the center and it involves again both
+the problems we want to solve we want to
+
+ align:start position:0%
+the problems we want to solve we want to
+ 
+
+ align:start position:0%
+the problems we want to solve we want to
+understand what is this common-sense
+
+ align:start position:0%
+understand what is this common-sense
+ 
+
+ align:start position:0%
+understand what is this common-sense
+knowledge about the physical world and
+
+ align:start position:0%
+knowledge about the physical world and
+ 
+
+ align:start position:0%
+knowledge about the physical world and
+the psychological world that's you can
+
+ align:start position:0%
+the psychological world that's you can
+ 
+
+ align:start position:0%
+the psychological world that's you can
+see in some form even in young infants
+
+ align:start position:0%
+see in some form even in young infants
+ 
+
+ align:start position:0%
+see in some form even in young infants
+and what are the learning mechanisms
+
+ align:start position:0%
+and what are the learning mechanisms
+ 
+
+ align:start position:0%
+and what are the learning mechanisms
+that build it and grow it and then
+
+ align:start position:0%
+that build it and grow it and then
+ 
+
+ align:start position:0%
+that build it and grow it and then
+what's the kind of technical ideas that
+
+ align:start position:0%
+what's the kind of technical ideas that
+ 
+
+ align:start position:0%
+what's the kind of technical ideas that
+are going to be also hopefully useful
+
+ align:start position:0%
+are going to be also hopefully useful
+ 
+
+ align:start position:0%
+are going to be also hopefully useful
+for building intelligent robots or other
+
+ align:start position:0%
+for building intelligent robots or other
+ 
+
+ align:start position:0%
+for building intelligent robots or other
+AI systems that can explain on the
+
+ align:start position:0%
+AI systems that can explain on the
+ 
+
+ align:start position:0%
+AI systems that can explain on the
+scientific side how this stuff works all
+
+ align:start position:0%
+scientific side how this stuff works all
+ 
+
+ align:start position:0%
+scientific side how this stuff works all
+right so that was all this business and
+
+ align:start position:0%
+right so that was all this business and
+ 
+
+ align:start position:0%
+right so that was all this business and
+what I was suggesting or I'll start to
+
+ align:start position:0%
+what I was suggesting or I'll start to
+ 
+
+ align:start position:0%
+what I was suggesting or I'll start to
+suggest here now is that it goes back to
+
+ align:start position:0%
+suggest here now is that it goes back to
+ 
+
+ align:start position:0%
+suggest here now is that it goes back to
+that quote I gave at the beginning from
+
+ align:start position:0%
+that quote I gave at the beginning from
+ 
+
+ align:start position:0%
+that quote I gave at the beginning from
+Craik right the guy who in 1943 wrote
+
+ align:start position:0%
+Craik right the guy who in 1943 wrote
+ 
+
+ align:start position:0%
+Craik right the guy who in 1943 wrote
+this book called the nature of
+
+ align:start position:0%
+this book called the nature of
+ 
+
+ align:start position:0%
+this book called the nature of
+explanation and he was saying that's the
+
+ align:start position:0%
+explanation and he was saying that's the
+ 
+
+ align:start position:0%
+explanation and he was saying that's the
+essence of intelligence is this ability
+
+ align:start position:0%
+essence of intelligence is this ability
+ 
+
+ align:start position:0%
+essence of intelligence is this ability
+to build models that allow you to
+
+ align:start position:0%
+to build models that allow you to
+ 
+
+ align:start position:0%
+to build models that allow you to
+explain the world
+
+ align:start position:0%
+explain the world
+ 
+
+ align:start position:0%
+explain the world
+- then reason simulate plan and so on
+
+ align:start position:0%
+- then reason simulate plan and so on
+ 
+
+ align:start position:0%
+- then reason simulate plan and so on
+right and I think we need tools for
+
+ align:start position:0%
+right and I think we need tools for
+ 
+
+ align:start position:0%
+right and I think we need tools for
+understanding how the brain is a
+
+ align:start position:0%
+understanding how the brain is a
+ 
+
+ align:start position:0%
+understanding how the brain is a
+modeling engine or you know an
+
+ align:start position:0%
+modeling engine or you know an
+ 
+
+ align:start position:0%
+modeling engine or you know an
+explaining engine or should we get a
+
+ align:start position:0%
+explaining engine or should we get a
+ 
+
+ align:start position:0%
+explaining engine or should we get a
+little bit recursive about it since what
+
+ align:start position:0%
+little bit recursive about it since what
+ 
+
+ align:start position:0%
+little bit recursive about it since what
+we're doing in science is also an
+
+ align:start position:0%
+we're doing in science is also an
+ 
+
+ align:start position:0%
+we're doing in science is also an
+explanatory activity we need modeling
+
+ align:start position:0%
+explanatory activity we need modeling
+ 
+
+ align:start position:0%
+explanatory activity we need modeling
+engines which in which we can build
+
+ align:start position:0%
+engines which in which we can build
+ 
+
+ align:start position:0%
+engines which in which we can build
+models of the brain as a modeling engine
+
+ align:start position:0%
+models of the brain as a modeling engine
+ 
+
+ align:start position:0%
+models of the brain as a modeling engine
+and that's where the probabilistic
+
+ align:start position:0%
+and that's where the probabilistic
+ 
+
+ align:start position:0%
+and that's where the probabilistic
+programs are gonna come so part of why I
+
+ align:start position:0%
+programs are gonna come so part of why I
+ 
+
+ align:start position:0%
+programs are gonna come so part of why I
+spent a while at the in the morning
+
+ align:start position:0%
+spent a while at the in the morning
+ 
+
+ align:start position:0%
+spent a while at the in the morning
+talking about these graphical models and
+
+ align:start position:0%
+talking about these graphical models and
+ 
+
+ align:start position:0%
+talking about these graphical models and
+the ways that we tried and I think may
+
+ align:start position:0%
+the ways that we tried and I think may
+ 
+
+ align:start position:0%
+the ways that we tried and I think may
+progress on but ultimately we're
+
+ align:start position:0%
+progress on but ultimately we're
+ 
+
+ align:start position:0%
+progress on but ultimately we're
+dissatisfied with talking about how
+
+ align:start position:0%
+dissatisfied with talking about how
+ 
+
+ align:start position:0%
+dissatisfied with talking about how
+we're modeling various aspects of
+
+ align:start position:0%
+we're modeling various aspects of
+ 
+
+ align:start position:0%
+we're modeling various aspects of
+cognition with these kinds of graphical
+
+ align:start position:0%
+cognition with these kinds of graphical
+ 
+
+ align:start position:0%
+cognition with these kinds of graphical
+models right I put up it didn't say too
+
+ align:start position:0%
+models right I put up it didn't say too
+ 
+
+ align:start position:0%
+models right I put up it didn't say too
+much about the technical details that's
+
+ align:start position:0%
+much about the technical details that's
+ 
+
+ align:start position:0%
+much about the technical details that's
+fine you can read a lot about it or not
+
+ align:start position:0%
+fine you can read a lot about it or not
+ 
+
+ align:start position:0%
+fine you can read a lot about it or not
+but these ways of using graphs mostly
+
+ align:start position:0%
+but these ways of using graphs mostly
+ 
+
+ align:start position:0%
+but these ways of using graphs mostly
+directed graphs to capture something
+
+ align:start position:0%
+directed graphs to capture something
+ 
+
+ align:start position:0%
+directed graphs to capture something
+about the structure of the world and
+
+ align:start position:0%
+about the structure of the world and
+ 
+
+ align:start position:0%
+about the structure of the world and
+then you put probabilities on it in some
+
+ align:start position:0%
+then you put probabilities on it in some
+ 
+
+ align:start position:0%
+then you put probabilities on it in some
+way like a diffusion process or a noisy
+
+ align:start position:0%
+way like a diffusion process or a noisy
+ 
+
+ align:start position:0%
+way like a diffusion process or a noisy
+transmission process for a food web
+
+ align:start position:0%
+transmission process for a food web
+ 
+
+ align:start position:0%
+transmission process for a food web
+that's a style of reasoning that is
+
+ align:start position:0%
+that's a style of reasoning that is
+ 
+
+ align:start position:0%
+that's a style of reasoning that is
+sometimes goes by the name of Bayesian
+
+ align:start position:0%
+sometimes goes by the name of Bayesian
+ 
+
+ align:start position:0%
+sometimes goes by the name of Bayesian
+networks for causal graphical models
+
+ align:start position:0%
+networks for causal graphical models
+ 
+
+ align:start position:0%
+networks for causal graphical models
+it's been it's been hugely influential
+
+ align:start position:0%
+it's been it's been hugely influential
+ 
+
+ align:start position:0%
+it's been it's been hugely influential
+in computer science many different
+
+ align:start position:0%
+in computer science many different
+ 
+
+ align:start position:0%
+in computer science many different
+fields not just AI and many fields
+
+ align:start position:0%
+fields not just AI and many fields
+ 
+
+ align:start position:0%
+fields not just AI and many fields
+outside of computer science not just
+
+ align:start position:0%
+outside of computer science not just
+ 
+
+ align:start position:0%
+outside of computer science not just
+cognitive science neuroscience in many
+
+ align:start position:0%
+cognitive science neuroscience in many
+ 
+
+ align:start position:0%
+cognitive science neuroscience in many
+areas of science and engineering here
+
+ align:start position:0%
+areas of science and engineering here
+ 
+
+ align:start position:0%
+areas of science and engineering here
+are just a few examples of some Bayesian
+
+ align:start position:0%
+are just a few examples of some Bayesian
+ 
+
+ align:start position:0%
+are just a few examples of some Bayesian
+networks you get if you search on Google
+
+ align:start position:0%
+networks you get if you search on Google
+ 
+
+ align:start position:0%
+networks you get if you search on Google
+image for Bayesian networks right and if
+
+ align:start position:0%
+image for Bayesian networks right and if
+ 
+
+ align:start position:0%
+image for Bayesian networks right and if
+you look carefully you'll see they come
+
+ align:start position:0%
+you look carefully you'll see they come
+ 
+
+ align:start position:0%
+you look carefully you'll see they come
+from biology economics many at chemical
+
+ align:start position:0%
+from biology economics many at chemical
+ 
+
+ align:start position:0%
+from biology economics many at chemical
+engineering whatever they're due to many
+
+ align:start position:0%
+engineering whatever they're due to many
+ 
+
+ align:start position:0%
+engineering whatever they're due to many
+people maybe more than anyone the person
+
+ align:start position:0%
+people maybe more than anyone the person
+ 
+
+ align:start position:0%
+people maybe more than anyone the person
+who's most associated with this idea and
+
+ align:start position:0%
+who's most associated with this idea and
+ 
+
+ align:start position:0%
+who's most associated with this idea and
+with the name Bayesian networks is Judea
+
+ align:start position:0%
+with the name Bayesian networks is Judea
+ 
+
+ align:start position:0%
+with the name Bayesian networks is Judea
+pearl he received the Turing award which
+
+ align:start position:0%
+pearl he received the Turing award which
+ 
+
+ align:start position:0%
+pearl he received the Turing award which
+is like the highest award in computer
+
+ align:start position:0%
+is like the highest award in computer
+ 
+
+ align:start position:0%
+is like the highest award in computer
+science you know this is a language that
+
+ align:start position:0%
+science you know this is a language that
+ 
+
+ align:start position:0%
+science you know this is a language that
+we were using and all the prelate of
+
+ align:start position:0%
+we were using and all the prelate of
+ 
+
+ align:start position:0%
+we were using and all the prelate of
+projects you saw up until now in some
+
+ align:start position:0%
+projects you saw up until now in some
+ 
+
+ align:start position:0%
+projects you saw up until now in some
+form that we and many others used
+
+ align:start position:0%
+form that we and many others used
+ 
+
+ align:start position:0%
+form that we and many others used
+because they provide a powerful set of
+
+ align:start position:0%
+because they provide a powerful set of
+ 
+
+ align:start position:0%
+because they provide a powerful set of
+tools for the general purpose tools
+
+ align:start position:0%
+tools for the general purpose tools
+ 
+
+ align:start position:0%
+tools for the general purpose tools
+right it goes back to this dream of
+
+ align:start position:0%
+right it goes back to this dream of
+ 
+
+ align:start position:0%
+right it goes back to this dream of
+building general-purpose systems for
+
+ align:start position:0%
+building general-purpose systems for
+ 
+
+ align:start position:0%
+building general-purpose systems for
+understanding the world
+
+ align:start position:0%
+understanding the world
+ 
+
+ align:start position:0%
+understanding the world
+so these provide general-purpose
+
+ align:start position:0%
+so these provide general-purpose
+ 
+
+ align:start position:0%
+so these provide general-purpose
+languages for representing causal
+
+ align:start position:0%
+languages for representing causal
+ 
+
+ align:start position:0%
+languages for representing causal
+structure debate you know I'll say a
+
+ align:start position:0%
+structure debate you know I'll say a
+ 
+
+ align:start position:0%
+structure debate you know I'll say a
+little bit more about that and
+
+ align:start position:0%
+little bit more about that and
+ 
+
+ align:start position:0%
+little bit more about that and
+general-purpose algorithms for doing the
+
+ align:start position:0%
+general-purpose algorithms for doing the
+ 
+
+ align:start position:0%
+general-purpose algorithms for doing the
+probabilistic inference on this so we
+
+ align:start position:0%
+probabilistic inference on this so we
+ 
+
+ align:start position:0%
+probabilistic inference on this so we
+talked about ways of combining
+
+ align:start position:0%
+talked about ways of combining
+ 
+
+ align:start position:0%
+talked about ways of combining
+sophisticated statistical inference with
+
+ align:start position:0%
+sophisticated statistical inference with
+ 
+
+ align:start position:0%
+sophisticated statistical inference with
+knowledge representation that's causal
+
+ align:start position:0%
+knowledge representation that's causal
+ 
+
+ align:start position:0%
+knowledge representation that's causal
+and compositional these models I'll just
+
+ align:start position:0%
+and compositional these models I'll just
+ 
+
+ align:start position:0%
+and compositional these models I'll just
+tell you a little bit about the one in
+
+ align:start position:0%
+tell you a little bit about the one in
+ 
+
+ align:start position:0%
+tell you a little bit about the one in
+the upper left up there that thing that
+
+ align:start position:0%
+the upper left up there that thing that
+ 
+
+ align:start position:0%
+the upper left up there that thing that
+says diseases and symptoms it is causal
+
+ align:start position:0%
+says diseases and symptoms it is causal
+ 
+
+ align:start position:0%
+says diseases and symptoms it is causal
+it is compositional it does support
+
+ align:start position:0%
+it is compositional it does support
+ 
+
+ align:start position:0%
+it is compositional it does support
+probabilistic inference and it was the
+
+ align:start position:0%
+probabilistic inference and it was the
+ 
+
+ align:start position:0%
+probabilistic inference and it was the
+heart of why we were doing what we were
+
+ align:start position:0%
+heart of why we were doing what we were
+ 
+
+ align:start position:0%
+heart of why we were doing what we were
+doing and showing you how different
+
+ align:start position:0%
+doing and showing you how different
+ 
+
+ align:start position:0%
+doing and showing you how different
+kinds of causal graphical models
+
+ align:start position:0%
+kinds of causal graphical models
+ 
+
+ align:start position:0%
+kinds of causal graphical models
+basically could capture different modes
+
+ align:start position:0%
+basically could capture different modes
+ 
+
+ align:start position:0%
+basically could capture different modes
+of people's reasoning and the idea that
+
+ align:start position:0%
+of people's reasoning and the idea that
+ 
+
+ align:start position:0%
+of people's reasoning and the idea that
+maybe learning about different domains
+
+ align:start position:0%
+maybe learning about different domains
+ 
+
+ align:start position:0%
+maybe learning about different domains
+was learning those different kinds of
+
+ align:start position:0%
+was learning those different kinds of
+ 
+
+ align:start position:0%
+was learning those different kinds of
+graph structures so let me say a little
+
+ align:start position:0%
+graph structures so let me say a little
+ 
+
+ align:start position:0%
+graph structures so let me say a little
+bit of how it works and then why it's
+
+ align:start position:0%
+bit of how it works and then why it's
+ 
+
+ align:start position:0%
+bit of how it works and then why it's
+not enough cuz it really isn't enough I
+
+ align:start position:0%
+not enough cuz it really isn't enough I
+ 
+
+ align:start position:0%
+not enough cuz it really isn't enough I
+mean it's it's it's the right start it's
+
+ align:start position:0%
+mean it's it's it's the right start it's
+ 
+
+ align:start position:0%
+mean it's it's it's the right start it's
+definitely in the right direction but we
+
+ align:start position:0%
+definitely in the right direction but we
+ 
+
+ align:start position:0%
+definitely in the right direction but we
+need to go beyond it that's where the
+
+ align:start position:0%
+need to go beyond it that's where the
+ 
+
+ align:start position:0%
+need to go beyond it that's where the
+probable stick programs come in so look
+
+ align:start position:0%
+probable stick programs come in so look
+ 
+
+ align:start position:0%
+probable stick programs come in so look
+at that network up there on the upper
+
+ align:start position:0%
+at that network up there on the upper
+ 
+
+ align:start position:0%
+at that network up there on the upper
+left it's some it's a what's one of the
+
+ align:start position:0%
+left it's some it's a what's one of the
+ 
+
+ align:start position:0%
+left it's some it's a what's one of the
+most famous Bayesian networks it's a
+
+ align:start position:0%
+most famous Bayesian networks it's a
+ 
+
+ align:start position:0%
+most famous Bayesian networks it's a
+textbook example it was one of the first
+
+ align:start position:0%
+textbook example it was one of the first
+ 
+
+ align:start position:0%
+textbook example it was one of the first
+actually implemented pay I systems was
+
+ align:start position:0%
+actually implemented pay I systems was
+ 
+
+ align:start position:0%
+actually implemented pay I systems was
+based on this for a system for medical
+
+ align:start position:0%
+based on this for a system for medical
+ 
+
+ align:start position:0%
+based on this for a system for medical
+diagnosis sort of a simple approximation
+
+ align:start position:0%
+diagnosis sort of a simple approximation
+ 
+
+ align:start position:0%
+diagnosis sort of a simple approximation
+to what a general practitioner might be
+
+ align:start position:0%
+to what a general practitioner might be
+ 
+
+ align:start position:0%
+to what a general practitioner might be
+doing if a patient comes in and reports
+
+ align:start position:0%
+doing if a patient comes in and reports
+ 
+
+ align:start position:0%
+doing if a patient comes in and reports
+some pattern of symptoms and they want
+
+ align:start position:0%
+some pattern of symptoms and they want
+ 
+
+ align:start position:0%
+some pattern of symptoms and they want
+to figure out what's wrong
+
+ align:start position:0%
+to figure out what's wrong
+ 
+
+ align:start position:0%
+to figure out what's wrong
+right so diagnosis of a disease to
+
+ align:start position:0%
+right so diagnosis of a disease to
+ 
+
+ align:start position:0%
+right so diagnosis of a disease to
+explain the symptoms the the the graph
+
+ align:start position:0%
+explain the symptoms the the the graph
+ 
+
+ align:start position:0%
+explain the symptoms the the the graph
+is a bipartite graph so two sets of
+
+ align:start position:0%
+is a bipartite graph so two sets of
+ 
+
+ align:start position:0%
+is a bipartite graph so two sets of
+nodes with the arrows again going down
+
+ align:start position:0%
+nodes with the arrows again going down
+ 
+
+ align:start position:0%
+nodes with the arrows again going down
+in the causal direction the the bottom
+
+ align:start position:0%
+in the causal direction the the bottom
+ 
+
+ align:start position:0%
+in the causal direction the the bottom
+layer the symptoms are the things that
+
+ align:start position:0%
+layer the symptoms are the things that
+ 
+
+ align:start position:0%
+layer the symptoms are the things that
+you can nominally observe right a
+
+ align:start position:0%
+you can nominally observe right a
+ 
+
+ align:start position:0%
+you can nominally observe right a
+patient comes in reporting some symptoms
+
+ align:start position:0%
+patient comes in reporting some symptoms
+ 
+
+ align:start position:0%
+patient comes in reporting some symptoms
+not all are observed but others maybe
+
+ align:start position:0%
+not all are observed but others maybe
+ 
+
+ align:start position:0%
+not all are observed but others maybe
+are things that you could test like a
+
+ align:start position:0%
+are things that you could test like a
+ 
+
+ align:start position:0%
+are things that you could test like a
+medical test results and then there's
+
+ align:start position:0%
+medical test results and then there's
+ 
+
+ align:start position:0%
+medical test results and then there's
+the top level is this level of latent
+
+ align:start position:0%
+the top level is this level of latent
+ 
+
+ align:start position:0%
+the top level is this level of latent
+structure the causes the things that
+
+ align:start position:0%
+structure the causes the things that
+ 
+
+ align:start position:0%
+structure the causes the things that
+cause the symptoms the arrows represent
+
+ align:start position:0%
+cause the symptoms the arrows represent
+ 
+
+ align:start position:0%
+cause the symptoms the arrows represent
+basically which diseases caused which
+
+ align:start position:0%
+basically which diseases caused which
+ 
+
+ align:start position:0%
+basically which diseases caused which
+symptoms in this model there's roughly
+
+ align:start position:0%
+symptoms in this model there's roughly
+ 
+
+ align:start position:0%
+symptoms in this model there's roughly
+five hundred six hundred diseases you
+
+ align:start position:0%
+five hundred six hundred diseases you
+ 
+
+ align:start position:0%
+five hundred six hundred diseases you
+know the common ish ones not all that
+
+ align:start position:0%
+know the common ish ones not all that
+ 
+
+ align:start position:0%
+know the common ish ones not all that
+common and four thousand symptoms so
+
+ align:start position:0%
+common and four thousand symptoms so
+ 
+
+ align:start position:0%
+common and four thousand symptoms so
+it's a big model and in some sense you
+
+ align:start position:0%
+it's a big model and in some sense you
+ 
+
+ align:start position:0%
+it's a big model and in some sense you
+can think of it as a big probability
+
+ align:start position:0%
+can think of it as a big probability
+ 
+
+ align:start position:0%
+can think of it as a big probability
+model right it's a way of specifying a
+
+ align:start position:0%
+model right it's a way of specifying a
+ 
+
+ align:start position:0%
+model right it's a way of specifying a
+joint distribution on this you know for
+
+ align:start position:0%
+joint distribution on this you know for
+ 
+
+ align:start position:0%
+joint distribution on this you know for
+4600 dimensional space but it's a very
+
+ align:start position:0%
+4600 dimensional space but it's a very
+ 
+
+ align:start position:0%
+4600 dimensional space but it's a very
+particular one that's causally
+
+ align:start position:0%
+particular one that's causally
+ 
+
+ align:start position:0%
+particular one that's causally
+structured it represents only the
+
+ align:start position:0%
+structured it represents only the
+ 
+
+ align:start position:0%
+structured it represents only the
+minimal causal dependencies and really
+
+ align:start position:0%
+minimal causal dependencies and really
+ 
+
+ align:start position:0%
+minimal causal dependencies and really
+the only the minimal probabilistic
+
+ align:start position:0%
+the only the minimal probabilistic
+ 
+
+ align:start position:0%
+the only the minimal probabilistic
+dependencies that sparsity is really
+
+ align:start position:0%
+dependencies that sparsity is really
+ 
+
+ align:start position:0%
+dependencies that sparsity is really
+important for how you use it whether
+
+ align:start position:0%
+important for how you use it whether
+ 
+
+ align:start position:0%
+important for how you use it whether
+you're talking about inference or
+
+ align:start position:0%
+you're talking about inference or
+ 
+
+ align:start position:0%
+you're talking about inference or
+learning so inference means observing
+
+ align:start position:0%
+learning so inference means observing
+ 
+
+ align:start position:0%
+learning so inference means observing
+patterns of symptoms or just observing
+
+ align:start position:0%
+patterns of symptoms or just observing
+ 
+
+ align:start position:0%
+patterns of symptoms or just observing
+the values of some of those variables
+
+ align:start position:0%
+the values of some of those variables
+ 
+
+ align:start position:0%
+the values of some of those variables
+and making guesses about the others like
+
+ align:start position:0%
+and making guesses about the others like
+ 
+
+ align:start position:0%
+and making guesses about the others like
+observing some symptoms and making
+
+ align:start position:0%
+observing some symptoms and making
+ 
+
+ align:start position:0%
+observing some symptoms and making
+guesses about the diseases that are most
+
+ align:start position:0%
+guesses about the diseases that are most
+ 
+
+ align:start position:0%
+guesses about the diseases that are most
+likely to have explained to those or you
+
+ align:start position:0%
+likely to have explained to those or you
+ 
+
+ align:start position:0%
+likely to have explained to those or you
+might make a prediction about other
+
+ align:start position:0%
+might make a prediction about other
+ 
+
+ align:start position:0%
+might make a prediction about other
+symptoms you could observe so you could
+
+ align:start position:0%
+symptoms you could observe so you could
+ 
+
+ align:start position:0%
+symptoms you could observe so you could
+kind of go up and then back down you
+
+ align:start position:0%
+kind of go up and then back down you
+ 
+
+ align:start position:0%
+kind of go up and then back down you
+could say well from these symptoms I
+
+ align:start position:0%
+could say well from these symptoms I
+ 
+
+ align:start position:0%
+could say well from these symptoms I
+think the patient might have one of
+
+ align:start position:0%
+think the patient might have one of
+ 
+
+ align:start position:0%
+think the patient might have one of
+these two rare diseases I don't know
+
+ align:start position:0%
+these two rare diseases I don't know
+ 
+
+ align:start position:0%
+these two rare diseases I don't know
+which one I better go in whatever but if
+
+ align:start position:0%
+which one I better go in whatever but if
+ 
+
+ align:start position:0%
+which one I better go in whatever but if
+it was this disease then it would
+
+ align:start position:0%
+it was this disease then it would
+ 
+
+ align:start position:0%
+it was this disease then it would
+predict that symptom or that test maybe
+
+ align:start position:0%
+predict that symptom or that test maybe
+ 
+
+ align:start position:0%
+predict that symptom or that test maybe
+but this disease wouldn't so then that
+
+ align:start position:0%
+but this disease wouldn't so then that
+ 
+
+ align:start position:0%
+but this disease wouldn't so then that
+suggests a way to plan an action you
+
+ align:start position:0%
+suggests a way to plan an action you
+ 
+
+ align:start position:0%
+suggests a way to plan an action you
+could take to figure things out and then
+
+ align:start position:0%
+could take to figure things out and then
+ 
+
+ align:start position:0%
+could take to figure things out and then
+I could go test for that symptom and
+
+ align:start position:0%
+I could go test for that symptom and
+ 
+
+ align:start position:0%
+I could go test for that symptom and
+that would tell me which of these
+
+ align:start position:0%
+that would tell me which of these
+ 
+
+ align:start position:0%
+that would tell me which of these
+diseases the patient has they're also
+
+ align:start position:0%
+diseases the patient has they're also
+ 
+
+ align:start position:0%
+diseases the patient has they're also
+useful in planning other kinds of you
+
+ align:start position:0%
+useful in planning other kinds of you
+ 
+
+ align:start position:0%
+useful in planning other kinds of you
+know treatments interventions like if
+
+ align:start position:0%
+know treatments interventions like if
+ 
+
+ align:start position:0%
+know treatments interventions like if
+you want to cure someone again we all
+
+ align:start position:0%
+you want to cure someone again we all
+ 
+
+ align:start position:0%
+you want to cure someone again we all
+know this intuitively you should try to
+
+ align:start position:0%
+know this intuitively you should try to
+ 
+
+ align:start position:0%
+know this intuitively you should try to
+cure the disease not the symptom right
+
+ align:start position:0%
+cure the disease not the symptom right
+ 
+
+ align:start position:0%
+cure the disease not the symptom right
+if you know if you have some way to act
+
+ align:start position:0%
+if you know if you have some way to act
+ 
+
+ align:start position:0%
+if you know if you have some way to act
+it to change the state of one of those
+
+ align:start position:0%
+it to change the state of one of those
+ 
+
+ align:start position:0%
+it to change the state of one of those
+disease variables to kind of turn it off
+
+ align:start position:0%
+disease variables to kind of turn it off
+ 
+
+ align:start position:0%
+disease variables to kind of turn it off
+it's you hopefully that reasonably that
+
+ align:start position:0%
+it's you hopefully that reasonably that
+ 
+
+ align:start position:0%
+it's you hopefully that reasonably that
+should relieve the symptoms if that
+
+ align:start position:0%
+should relieve the symptoms if that
+ 
+
+ align:start position:0%
+should relieve the symptoms if that
+disease gets turned off these symptoms
+
+ align:start position:0%
+disease gets turned off these symptoms
+ 
+
+ align:start position:0%
+disease gets turned off these symptoms
+are turned off whereas just treating the
+
+ align:start position:0%
+are turned off whereas just treating the
+ 
+
+ align:start position:0%
+are turned off whereas just treating the
+symptom like taking Advil for a headache
+
+ align:start position:0%
+symptom like taking Advil for a headache
+ 
+
+ align:start position:0%
+symptom like taking Advil for a headache
+is fine if that's all the problem is but
+
+ align:start position:0%
+is fine if that's all the problem is but
+ 
+
+ align:start position:0%
+is fine if that's all the problem is but
+if you if it's being caused by something
+
+ align:start position:0%
+if you if it's being caused by something
+ 
+
+ align:start position:0%
+if you if it's being caused by something
+you know god forbid like a brain tumor
+
+ align:start position:0%
+you know god forbid like a brain tumor
+ 
+
+ align:start position:0%
+you know god forbid like a brain tumor
+it's not going to help okay it's not
+
+ align:start position:0%
+it's not going to help okay it's not
+ 
+
+ align:start position:0%
+it's not going to help okay it's not
+gonna cure the problem in the long term
+
+ align:start position:0%
+gonna cure the problem in the long term
+ 
+
+ align:start position:0%
+gonna cure the problem in the long term
+okay so all those patterns of causal
+
+ align:start position:0%
+okay so all those patterns of causal
+ 
+
+ align:start position:0%
+okay so all those patterns of causal
+inference reasoning prediction action
+
+ align:start position:0%
+inference reasoning prediction action
+ 
+
+ align:start position:0%
+inference reasoning prediction action
+planning excavation is a beautiful
+
+ align:start position:0%
+planning excavation is a beautiful
+ 
+
+ align:start position:0%
+planning excavation is a beautiful
+language for capturing all of those you
+
+ align:start position:0%
+language for capturing all of those you
+ 
+
+ align:start position:0%
+language for capturing all of those you
+can automate all those inferences why
+
+ align:start position:0%
+can automate all those inferences why
+ 
+
+ align:start position:0%
+can automate all those inferences why
+isn't it enough then for for capturing
+
+ align:start position:0%
+isn't it enough then for for capturing
+ 
+
+ align:start position:0%
+isn't it enough then for for capturing
+common sense reasoning or this approach
+
+ align:start position:0%
+common sense reasoning or this approach
+ 
+
+ align:start position:0%
+common sense reasoning or this approach
+to cognition which I'm calling the kind
+
+ align:start position:0%
+to cognition which I'm calling the kind
+ 
+
+ align:start position:0%
+to cognition which I'm calling the kind
+of model building explaining part as
+
+ align:start position:0%
+of model building explaining part as
+ 
+
+ align:start position:0%
+of model building explaining part as
+opposed to the the pattern recognition
+
+ align:start position:0%
+opposed to the the pattern recognition
+ 
+
+ align:start position:0%
+opposed to the the pattern recognition
+part I mean again I don't want to get
+
+ align:start position:0%
+part I mean again I don't want to get
+ 
+
+ align:start position:0%
+part I mean again I don't want to get
+too far behind and talking about this
+
+ align:start position:0%
+too far behind and talking about this
+ 
+
+ align:start position:0%
+too far behind and talking about this
+but that example is so rich like if you
+
+ align:start position:0%
+but that example is so rich like if you
+ 
+
+ align:start position:0%
+but that example is so rich like if you
+you can build a neural network you could
+
+ align:start position:0%
+you can build a neural network you could
+ 
+
+ align:start position:0%
+you can build a neural network you could
+just turn the arrows around to learn a
+
+ align:start position:0%
+just turn the arrows around to learn a
+ 
+
+ align:start position:0%
+just turn the arrows around to learn a
+mapping from symptoms to diseases and
+
+ align:start position:0%
+mapping from symptoms to diseases and
+ 
+
+ align:start position:0%
+mapping from symptoms to diseases and
+that would be a pattern classifier right
+
+ align:start position:0%
+that would be a pattern classifier right
+ 
+
+ align:start position:0%
+that would be a pattern classifier right
+so these these two different paradigms
+
+ align:start position:0%
+so these these two different paradigms
+ 
+
+ align:start position:0%
+so these these two different paradigms
+for intelligence as some of the
+
+ align:start position:0%
+for intelligence as some of the
+ 
+
+ align:start position:0%
+for intelligence as some of the
+questions we're getting at and as I will
+
+ align:start position:0%
+questions we're getting at and as I will
+ 
+
+ align:start position:0%
+questions we're getting at and as I will
+show versions of that with some more
+
+ align:start position:0%
+show versions of that with some more
+ 
+
+ align:start position:0%
+show versions of that with some more
+interesting examples in a little bit
+
+ align:start position:0%
+interesting examples in a little bit
+ 
+
+ align:start position:0%
+interesting examples in a little bit
+right there often it's hard it's very
+
+ align:start position:0%
+right there often it's hard it's very
+ 
+
+ align:start position:0%
+right there often it's hard it's very
+subtle and the relations between them
+
+ align:start position:0%
+subtle and the relations between them
+ 
+
+ align:start position:0%
+subtle and the relations between them
+are are quite valuable so one way to
+
+ align:start position:0%
+are are quite valuable so one way to
+ 
+
+ align:start position:0%
+are are quite valuable so one way to
+work with such a model for example or
+
+ align:start position:0%
+work with such a model for example or
+ 
+
+ align:start position:0%
+work with such a model for example or
+one nice way I mean I mentioned a lot of
+
+ align:start position:0%
+one nice way I mean I mentioned a lot of
+ 
+
+ align:start position:0%
+one nice way I mean I mentioned a lot of
+people want to know and I'll keep
+
+ align:start position:0%
+people want to know and I'll keep
+ 
+
+ align:start position:0%
+people want to know and I'll keep
+talking about this for the rest of the
+
+ align:start position:0%
+talking about this for the rest of the
+ 
+
+ align:start position:0%
+talking about this for the rest of the
+hour that you can productive ways to
+
+ align:start position:0%
+hour that you can productive ways to
+ 
+
+ align:start position:0%
+hour that you can productive ways to
+combine these causal generative models
+
+ align:start position:0%
+combine these causal generative models
+ 
+
+ align:start position:0%
+combine these causal generative models
+with more you know pattern recognition
+
+ align:start position:0%
+with more you know pattern recognition
+ 
+
+ align:start position:0%
+with more you know pattern recognition
+approaches in some for some classes of
+
+ align:start position:0%
+approaches in some for some classes of
+ 
+
+ align:start position:0%
+approaches in some for some classes of
+this model it's it's but there are there
+
+ align:start position:0%
+this model it's it's but there are there
+ 
+
+ align:start position:0%
+this model it's it's but there are there
+are always general-purpose algorithms
+
+ align:start position:0%
+are always general-purpose algorithms
+ 
+
+ align:start position:0%
+are always general-purpose algorithms
+that can support these inferences that
+
+ align:start position:0%
+that can support these inferences that
+ 
+
+ align:start position:0%
+that can support these inferences that
+can tell you what diseases you're likely
+
+ align:start position:0%
+can tell you what diseases you're likely
+ 
+
+ align:start position:0%
+can tell you what diseases you're likely
+to have given what symptoms but in some
+
+ align:start position:0%
+to have given what symptoms but in some
+ 
+
+ align:start position:0%
+to have given what symptoms but in some
+cases they could be very fast in other
+
+ align:start position:0%
+cases they could be very fast in other
+ 
+
+ align:start position:0%
+cases they could be very fast in other
+cases they could be very slow whereas if
+
+ align:start position:0%
+cases they could be very slow whereas if
+ 
+
+ align:start position:0%
+cases they could be very slow whereas if
+you could imagine trying to learn a
+
+ align:start position:0%
+you could imagine trying to learn a
+ 
+
+ align:start position:0%
+you could imagine trying to learn a
+network that looks just like that only
+
+ align:start position:0%
+network that looks just like that only
+ 
+
+ align:start position:0%
+network that looks just like that only
+the arrows go up so they implement a
+
+ align:start position:0%
+the arrows go up so they implement a
+ 
+
+ align:start position:0%
+the arrows go up so they implement a
+mapping from data to diseases that could
+
+ align:start position:0%
+mapping from data to diseases that could
+ 
+
+ align:start position:0%
+mapping from data to diseases that could
+help to do to do much faster inference
+
+ align:start position:0%
+help to do to do much faster inference
+ 
+
+ align:start position:0%
+help to do to do much faster inference
+in the cases where that's possible so
+
+ align:start position:0%
+in the cases where that's possible so
+ 
+
+ align:start position:0%
+in the cases where that's possible so
+that's just one example of where you
+
+ align:start position:0%
+that's just one example of where you
+ 
+
+ align:start position:0%
+that's just one example of where you
+know a pair of a model which might be
+
+ align:start position:0%
+know a pair of a model which might be
+ 
+
+ align:start position:0%
+know a pair of a model which might be
+not a crazy way to think about for
+
+ align:start position:0%
+not a crazy way to think about for
+ 
+
+ align:start position:0%
+not a crazy way to think about for
+example more generally the way top-down
+
+ align:start position:0%
+example more generally the way top-down
+ 
+
+ align:start position:0%
+example more generally the way top-down
+and bottom-up connections work in the
+
+ align:start position:0%
+and bottom-up connections work in the
+ 
+
+ align:start position:0%
+and bottom-up connections work in the
+brain I'll I'll take that a little bit
+
+ align:start position:0%
+brain I'll I'll take that a little bit
+ 
+
+ align:start position:0%
+brain I'll I'll take that a little bit
+more literally in a vision example in a
+
+ align:start position:0%
+more literally in a vision example in a
+ 
+
+ align:start position:0%
+more literally in a vision example in a
+second but so there's a lot you can get
+
+ align:start position:0%
+second but so there's a lot you can get
+ 
+
+ align:start position:0%
+second but so there's a lot you can get
+from studying these causal graphical
+
+ align:start position:0%
+from studying these causal graphical
+ 
+
+ align:start position:0%
+from studying these causal graphical
+models including some version of what it
+
+ align:start position:0%
+models including some version of what it
+ 
+
+ align:start position:0%
+models including some version of what it
+is for the mind to explain the world and
+
+ align:start position:0%
+is for the mind to explain the world and
+ 
+
+ align:start position:0%
+is for the mind to explain the world and
+how that explanation and pattern
+
+ align:start position:0%
+how that explanation and pattern
+ 
+
+ align:start position:0%
+how that explanation and pattern
+recognition approach can work together
+
+ align:start position:0%
+recognition approach can work together
+ 
+
+ align:start position:0%
+recognition approach can work together
+but it's not enough to really get at the
+
+ align:start position:0%
+but it's not enough to really get at the
+ 
+
+ align:start position:0%
+but it's not enough to really get at the
+at the heart of common-sense the the
+
+ align:start position:0%
+at the heart of common-sense the the
+ 
+
+ align:start position:0%
+at the heart of common-sense the the
+mental generative models we build are
+
+ align:start position:0%
+mental generative models we build are
+ 
+
+ align:start position:0%
+mental generative models we build are
+more richly structured they're more like
+
+ align:start position:0%
+more richly structured they're more like
+ 
+
+ align:start position:0%
+more richly structured they're more like
+programs what do I mean by that well
+
+ align:start position:0%
+programs what do I mean by that well
+ 
+
+ align:start position:0%
+programs what do I mean by that well
+here I'm giving a bunch of examples of
+
+ align:start position:0%
+here I'm giving a bunch of examples of
+ 
+
+ align:start position:0%
+here I'm giving a bunch of examples of
+scientific theories or models not
+
+ align:start position:0%
+scientific theories or models not
+ 
+
+ align:start position:0%
+scientific theories or models not
+common-sense ones but I think the same
+
+ align:start position:0%
+common-sense ones but I think the same
+ 
+
+ align:start position:0%
+common-sense ones but I think the same
+idea applies Wiis of again explaining
+
+ align:start position:0%
+idea applies Wiis of again explaining
+ 
+
+ align:start position:0%
+idea applies Wiis of again explaining
+the world not just describing the
+
+ align:start position:0%
+the world not just describing the
+ 
+
+ align:start position:0%
+the world not just describing the
+pattern so we went at the beginning
+
+ align:start position:0%
+pattern so we went at the beginning
+ 
+
+ align:start position:0%
+pattern so we went at the beginning
+through Newton's laws versus Kepler's
+
+ align:start position:0%
+through Newton's laws versus Kepler's
+ 
+
+ align:start position:0%
+through Newton's laws versus Kepler's
+laws that's just one example and you
+
+ align:start position:0%
+laws that's just one example and you
+ 
+
+ align:start position:0%
+laws that's just one example and you
+might not a flood of those laws as a
+
+ align:start position:0%
+might not a flood of those laws as a
+ 
+
+ align:start position:0%
+might not a flood of those laws as a
+program but there's certainly not a
+
+ align:start position:0%
+program but there's certainly not a
+ 
+
+ align:start position:0%
+program but there's certainly not a
+graph right on the on the first slide
+
+ align:start position:0%
+graph right on the on the first slide
+ 
+
+ align:start position:0%
+graph right on the on the first slide
+when I showed Newton's laws there was a
+
+ align:start position:0%
+when I showed Newton's laws there was a
+ 
+
+ align:start position:0%
+when I showed Newton's laws there was a
+combination there was a bunch of symbols
+
+ align:start position:0%
+combination there was a bunch of symbols
+ 
+
+ align:start position:0%
+combination there was a bunch of symbols
+statements in English some math right
+
+ align:start position:0%
+statements in English some math right
+ 
+
+ align:start position:0%
+statements in English some math right
+but what it comes down to is basically a
+
+ align:start position:0%
+but what it comes down to is basically a
+ 
+
+ align:start position:0%
+but what it comes down to is basically a
+set of pieces of code that you could run
+
+ align:start position:0%
+set of pieces of code that you could run
+ 
+
+ align:start position:0%
+set of pieces of code that you could run
+to generate the orbits right it doesn't
+
+ align:start position:0%
+to generate the orbits right it doesn't
+ 
+
+ align:start position:0%
+to generate the orbits right it doesn't
+describe the sheep or the the velocities
+
+ align:start position:0%
+describe the sheep or the the velocities
+ 
+
+ align:start position:0%
+describe the sheep or the the velocities
+but it's a machine that you plug in some
+
+ align:start position:0%
+but it's a machine that you plug in some
+ 
+
+ align:start position:0%
+but it's a machine that you plug in some
+things you plug in some masses some
+
+ align:start position:0%
+things you plug in some masses some
+ 
+
+ align:start position:0%
+things you plug in some masses some
+objects some initial conditions and you
+
+ align:start position:0%
+objects some initial conditions and you
+ 
+
+ align:start position:0%
+objects some initial conditions and you
+press run and it generates the orbits
+
+ align:start position:0%
+press run and it generates the orbits
+ 
+
+ align:start position:0%
+press run and it generates the orbits
+just like what you're seeing there
+
+ align:start position:0%
+just like what you're seeing there
+ 
+
+ align:start position:0%
+just like what you're seeing there
+although those probably weren't
+
+ align:start position:0%
+although those probably weren't
+ 
+
+ align:start position:0%
+although those probably weren't
+generated that's a justice oh okay
+
+ align:start position:0%
+generated that's a justice oh okay
+ 
+
+ align:start position:0%
+generated that's a justice oh okay
+that's more like Kepler or Ptolemy but
+
+ align:start position:0%
+that's more like Kepler or Ptolemy but
+ 
+
+ align:start position:0%
+that's more like Kepler or Ptolemy but
+anyway but you know it's a powerful
+
+ align:start position:0%
+anyway but you know it's a powerful
+ 
+
+ align:start position:0%
+anyway but you know it's a powerful
+machine it's a machine which if you put
+
+ align:start position:0%
+machine it's a machine which if you put
+ 
+
+ align:start position:0%
+machine it's a machine which if you put
+down the right masses in the right
+
+ align:start position:0%
+down the right masses in the right
+ 
+
+ align:start position:0%
+down the right masses in the right
+position they don't just all go around
+
+ align:start position:0%
+position they don't just all go around
+ 
+
+ align:start position:0%
+position they don't just all go around
+in ellipses some of them are like moons
+
+ align:start position:0%
+in ellipses some of them are like moons
+ 
+
+ align:start position:0%
+in ellipses some of them are like moons
+and they will go around the things that
+
+ align:start position:0%
+and they will go around the things that
+ 
+
+ align:start position:0%
+and they will go around the things that
+will go around the others right and some
+
+ align:start position:0%
+will go around the others right and some
+ 
+
+ align:start position:0%
+will go around the others right and some
+of them will be like apples on the earth
+
+ align:start position:0%
+of them will be like apples on the earth
+ 
+
+ align:start position:0%
+of them will be like apples on the earth
+and they won't go around anything
+
+ align:start position:0%
+and they won't go around anything
+ 
+
+ align:start position:0%
+and they won't go around anything
+they'll just fall down right so that's
+
+ align:start position:0%
+they'll just fall down right so that's
+ 
+
+ align:start position:0%
+they'll just fall down right so that's
+the powerful machine and in the really
+
+ align:start position:0%
+the powerful machine and in the really
+ 
+
+ align:start position:0%
+the powerful machine and in the really
+simplest cases that machine those
+
+ align:start position:0%
+simplest cases that machine those
+ 
+
+ align:start position:0%
+simplest cases that machine those
+equations can be solved analytically
+
+ align:start position:0%
+equations can be solved analytically
+ 
+
+ align:start position:0%
+equations can be solved analytically
+right you can use calculus or other
+
+ align:start position:0%
+right you can use calculus or other
+ 
+
+ align:start position:0%
+right you can use calculus or other
+methods of analysis like Newton did he
+
+ align:start position:0%
+methods of analysis like Newton did he
+ 
+
+ align:start position:0%
+methods of analysis like Newton did he
+didn't have a computer and you can show
+
+ align:start position:0%
+didn't have a computer and you can show
+ 
+
+ align:start position:0%
+didn't have a computer and you can show
+that for two a two-body system one
+
+ align:start position:0%
+that for two a two-body system one
+ 
+
+ align:start position:0%
+that for two a two-body system one
+planet and one Sun you can solve those
+
+ align:start position:0%
+planet and one Sun you can solve those
+ 
+
+ align:start position:0%
+planet and one Sun you can solve those
+equations to show that you get Kepler's
+
+ align:start position:0%
+equations to show that you get Kepler's
+ 
+
+ align:start position:0%
+equations to show that you get Kepler's
+law amazing and if you if two under the
+
+ align:start position:0%
+law amazing and if you if two under the
+ 
+
+ align:start position:0%
+law amazing and if you if two under the
+approximation that you ignore that only
+
+ align:start position:0%
+approximation that you ignore that only
+ 
+
+ align:start position:0%
+approximation that you ignore that only
+the Sun is you know for every other
+
+ align:start position:0%
+the Sun is you know for every other
+ 
+
+ align:start position:0%
+the Sun is you know for every other
+planet it's only the Sun that's exerting
+
+ align:start position:0%
+planet it's only the Sun that's exerting
+ 
+
+ align:start position:0%
+planet it's only the Sun that's exerting
+a significant influence you can describe
+
+ align:start position:0%
+a significant influence you can describe
+ 
+
+ align:start position:0%
+a significant influence you can describe
+all of Kepler's laws this way but once
+
+ align:start position:0%
+all of Kepler's laws this way but once
+ 
+
+ align:start position:0%
+all of Kepler's laws this way but once
+you have more than two bodies
+
+ align:start position:0%
+you have more than two bodies
+ 
+
+ align:start position:0%
+you have more than two bodies
+interacting in some complex way like
+
+ align:start position:0%
+interacting in some complex way like
+ 
+
+ align:start position:0%
+interacting in some complex way like
+three masses similar in size near each
+
+ align:start position:0%
+three masses similar in size near each
+ 
+
+ align:start position:0%
+three masses similar in size near each
+other you can't solve the equations
+
+ align:start position:0%
+other you can't solve the equations
+ 
+
+ align:start position:0%
+other you can't solve the equations
+analytically anymore you basically just
+
+ align:start position:0%
+analytically anymore you basically just
+ 
+
+ align:start position:0%
+analytically anymore you basically just
+have to run a simulation for the most
+
+ align:start position:0%
+have to run a simulation for the most
+ 
+
+ align:start position:0%
+have to run a simulation for the most
+part the world is complicated and our
+
+ align:start position:0%
+part the world is complicated and our
+ 
+
+ align:start position:0%
+part the world is complicated and our
+models have to be run you here's a model
+
+ align:start position:0%
+models have to be run you here's a model
+ 
+
+ align:start position:0%
+models have to be run you here's a model
+of riverbed formation or these are
+
+ align:start position:0%
+of riverbed formation or these are
+ 
+
+ align:start position:0%
+of riverbed formation or these are
+snapshots of a model of galaxy collision
+
+ align:start position:0%
+snapshots of a model of galaxy collision
+ 
+
+ align:start position:0%
+snapshots of a model of galaxy collision
+or
+
+ align:start position:0%
+or
+ 
+
+ align:start position:0%
+or
+in climate modeling or aerodynamics so
+
+ align:start position:0%
+in climate modeling or aerodynamics so
+ 
+
+ align:start position:0%
+in climate modeling or aerodynamics so
+what a lot of you know basically what
+
+ align:start position:0%
+what a lot of you know basically what
+ 
+
+ align:start position:0%
+what a lot of you know basically what
+most modern science is is you write down
+
+ align:start position:0%
+most modern science is is you write down
+ 
+
+ align:start position:0%
+most modern science is is you write down
+descriptions of the causal processes
+
+ align:start position:0%
+descriptions of the causal processes
+ 
+
+ align:start position:0%
+descriptions of the causal processes
+something going on in the world and you
+
+ align:start position:0%
+something going on in the world and you
+ 
+
+ align:start position:0%
+something going on in the world and you
+study that through some combination of
+
+ align:start position:0%
+study that through some combination of
+ 
+
+ align:start position:0%
+study that through some combination of
+analysis and simulation to prety what
+
+ align:start position:0%
+analysis and simulation to prety what
+ 
+
+ align:start position:0%
+analysis and simulation to prety what
+would happen if you want to estimate
+
+ align:start position:0%
+would happen if you want to estimate
+ 
+
+ align:start position:0%
+would happen if you want to estimate
+parameters you try out some guesses of
+
+ align:start position:0%
+parameters you try out some guesses of
+ 
+
+ align:start position:0%
+parameters you try out some guesses of
+the parameters and you run this thing
+
+ align:start position:0%
+the parameters and you run this thing
+ 
+
+ align:start position:0%
+the parameters and you run this thing
+and you see if it's behavior looks like
+
+ align:start position:0%
+and you see if it's behavior looks like
+ 
+
+ align:start position:0%
+and you see if it's behavior looks like
+the data you observe if you are trying
+
+ align:start position:0%
+the data you observe if you are trying
+ 
+
+ align:start position:0%
+the data you observe if you are trying
+to decide between two different models
+
+ align:start position:0%
+to decide between two different models
+ 
+
+ align:start position:0%
+to decide between two different models
+you simulate each of them and you see
+
+ align:start position:0%
+you simulate each of them and you see
+ 
+
+ align:start position:0%
+you simulate each of them and you see
+which one looks more like the data you
+
+ align:start position:0%
+which one looks more like the data you
+ 
+
+ align:start position:0%
+which one looks more like the data you
+observe
+
+ align:start position:0%
+observe
+ 
+
+ align:start position:0%
+observe
+if you think there's something wrong
+
+ align:start position:0%
+if you think there's something wrong
+ 
+
+ align:start position:0%
+if you think there's something wrong
+with your model it doesn't quite look
+
+ align:start position:0%
+with your model it doesn't quite look
+ 
+
+ align:start position:0%
+with your model it doesn't quite look
+like the data you observe you think how
+
+ align:start position:0%
+like the data you observe you think how
+ 
+
+ align:start position:0%
+like the data you observe you think how
+can I change my model which basically if
+
+ align:start position:0%
+can I change my model which basically if
+ 
+
+ align:start position:0%
+can I change my model which basically if
+I run it it'll look more like the data I
+
+ align:start position:0%
+I run it it'll look more like the data I
+ 
+
+ align:start position:0%
+I run it it'll look more like the data I
+observe in some important way those are
+
+ align:start position:0%
+observe in some important way those are
+ 
+
+ align:start position:0%
+observe in some important way those are
+those activities of science those are
+
+ align:start position:0%
+those activities of science those are
+ 
+
+ align:start position:0%
+those activities of science those are
+what though those are in some form I'm
+
+ align:start position:0%
+what though those are in some form I'm
+ 
+
+ align:start position:0%
+what though those are in some form I'm
+arguing the activities of common sense
+
+ align:start position:0%
+arguing the activities of common sense
+ 
+
+ align:start position:0%
+arguing the activities of common sense
+explanation so when I'm talking about
+
+ align:start position:0%
+explanation so when I'm talking about
+ 
+
+ align:start position:0%
+explanation so when I'm talking about
+you know the child is scientist that's
+
+ align:start position:0%
+you know the child is scientist that's
+ 
+
+ align:start position:0%
+you know the child is scientist that's
+what I'm basically talking about it's
+
+ align:start position:0%
+what I'm basically talking about it's
+ 
+
+ align:start position:0%
+what I'm basically talking about it's
+some version of that and so that
+
+ align:start position:0%
+some version of that and so that
+ 
+
+ align:start position:0%
+some version of that and so that
+includes both using describing the
+
+ align:start position:0%
+includes both using describing the
+ 
+
+ align:start position:0%
+includes both using describing the
+causal processes with a program that you
+
+ align:start position:0%
+causal processes with a program that you
+ 
+
+ align:start position:0%
+causal processes with a program that you
+run or if you want to talk about
+
+ align:start position:0%
+run or if you want to talk about
+ 
+
+ align:start position:0%
+run or if you want to talk about
+learning right look the scientific
+
+ align:start position:0%
+learning right look the scientific
+ 
+
+ align:start position:0%
+learning right look the scientific
+analog is building one of these theories
+
+ align:start position:0%
+analog is building one of these theories
+ 
+
+ align:start position:0%
+analog is building one of these theories
+you don't build a what a theory of
+
+ align:start position:0%
+you don't build a what a theory of
+ 
+
+ align:start position:0%
+you don't build a what a theory of
+whether it's Newton's laws or Mendel's
+
+ align:start position:0%
+whether it's Newton's laws or Mendel's
+ 
+
+ align:start position:0%
+whether it's Newton's laws or Mendel's
+laws or any of these things by just
+
+ align:start position:0%
+laws or any of these things by just
+ 
+
+ align:start position:0%
+laws or any of these things by just
+finding patterns and data you do
+
+ align:start position:0%
+finding patterns and data you do
+ 
+
+ align:start position:0%
+finding patterns and data you do
+something like this this program thing
+
+ align:start position:0%
+something like this this program thing
+ 
+
+ align:start position:0%
+something like this this program thing
+but kind of recursively you mean you
+
+ align:start position:0%
+but kind of recursively you mean you
+ 
+
+ align:start position:0%
+but kind of recursively you mean you
+think you think of you having some kind
+
+ align:start position:0%
+think you think of you having some kind
+ 
+
+ align:start position:0%
+think you think of you having some kind
+of paradigm some program that generates
+
+ align:start position:0%
+of paradigm some program that generates
+ 
+
+ align:start position:0%
+of paradigm some program that generates
+programs and you use it to try to
+
+ align:start position:0%
+programs and you use it to try to
+ 
+
+ align:start position:0%
+programs and you use it to try to
+somehow search the space of programs to
+
+ align:start position:0%
+somehow search the space of programs to
+ 
+
+ align:start position:0%
+somehow search the space of programs to
+come up with a program that fits your
+
+ align:start position:0%
+come up with a program that fits your
+ 
+
+ align:start position:0%
+come up with a program that fits your
+data well okay so that's again kind of
+
+ align:start position:0%
+data well okay so that's again kind of
+ 
+
+ align:start position:0%
+data well okay so that's again kind of
+the big picture and now let's talk about
+
+ align:start position:0%
+the big picture and now let's talk about
+ 
+
+ align:start position:0%
+the big picture and now let's talk about
+how we can actually do something with
+
+ align:start position:0%
+how we can actually do something with
+ 
+
+ align:start position:0%
+how we can actually do something with
+this idea use these programs and all and
+
+ align:start position:0%
+this idea use these programs and all and
+ 
+
+ align:start position:0%
+this idea use these programs and all and
+you might be wondering okay maybe I
+
+ align:start position:0%
+you might be wondering okay maybe I
+ 
+
+ align:start position:0%
+you might be wondering okay maybe I
+maybe I understand well okay I want you
+
+ align:start position:0%
+maybe I understand well okay I want you
+ 
+
+ align:start position:0%
+maybe I understand well okay I want you
+to I'm realizing I didn't say the main
+
+ align:start position:0%
+to I'm realizing I didn't say the main
+ 
+
+ align:start position:0%
+to I'm realizing I didn't say the main
+thing I want you to understand the main
+
+ align:start position:0%
+thing I want you to understand the main
+ 
+
+ align:start position:0%
+thing I want you to understand the main
+thing I want you to get from this is how
+
+ align:start position:0%
+thing I want you to get from this is how
+ 
+
+ align:start position:0%
+thing I want you to get from this is how
+programs go beyond graphs right so none
+
+ align:start position:0%
+programs go beyond graphs right so none
+ 
+
+ align:start position:0%
+programs go beyond graphs right so none
+of these processes here can be nicely
+
+ align:start position:0%
+of these processes here can be nicely
+ 
+
+ align:start position:0%
+of these processes here can be nicely
+described with a graph right the way we
+
+ align:start position:0%
+described with a graph right the way we
+ 
+
+ align:start position:0%
+described with a graph right the way we
+have in the language of graphical models
+
+ align:start position:0%
+have in the language of graphical models
+ 
+
+ align:start position:0%
+have in the language of graphical models
+so that that the interesting causality I
+
+ align:start position:0%
+so that that the interesting causality I
+ 
+
+ align:start position:0%
+so that that the interesting causality I
+mean in some sense there's kind of a
+
+ align:start position:0%
+mean in some sense there's kind of a
+ 
+
+ align:start position:0%
+mean in some sense there's kind of a
+graph you can talk about the state of
+
+ align:start position:0%
+graph you can talk about the state of
+ 
+
+ align:start position:0%
+graph you can talk about the state of
+the world at time T and I'll show you
+
+ align:start position:0%
+the world at time T and I'll show you
+ 
+
+ align:start position:0%
+the world at time T and I'll show you
+graphs like this
+
+ align:start position:0%
+graphs like this
+ 
+
+ align:start position:0%
+graphs like this
+second the state of the world at time t
+
+ align:start position:0%
+second the state of the world at time t
+ 
+
+ align:start position:0%
+second the state of the world at time t
+plus one in an arrow forward in time but
+
+ align:start position:0%
+plus one in an arrow forward in time but
+ 
+
+ align:start position:0%
+plus one in an arrow forward in time but
+all the interesting stuff that science
+
+ align:start position:0%
+all the interesting stuff that science
+ 
+
+ align:start position:0%
+all the interesting stuff that science
+really gains power from are the much
+
+ align:start position:0%
+really gains power from are the much
+ 
+
+ align:start position:0%
+really gains power from are the much
+more fine grain structure captured in
+
+ align:start position:0%
+more fine grain structure captured in
+ 
+
+ align:start position:0%
+more fine grain structure captured in
+equations or functions that describe
+
+ align:start position:0%
+equations or functions that describe
+ 
+
+ align:start position:0%
+equations or functions that describe
+exactly how all this stuff works right
+
+ align:start position:0%
+exactly how all this stuff works right
+ 
+
+ align:start position:0%
+exactly how all this stuff works right
+and it needs languages like math or C++
+
+ align:start position:0%
+and it needs languages like math or C++
+ 
+
+ align:start position:0%
+and it needs languages like math or C++
+or Lisp it needs a symbolic language of
+
+ align:start position:0%
+or Lisp it needs a symbolic language of
+ 
+
+ align:start position:0%
+or Lisp it needs a symbolic language of
+processes to really do justice to the
+
+ align:start position:0%
+processes to really do justice to the
+ 
+
+ align:start position:0%
+processes to really do justice to the
+second thing I want to get which will
+
+ align:start position:0%
+second thing I want to get which will
+ 
+
+ align:start position:0%
+second thing I want to get which will
+take a minute to get but let's put it
+
+ align:start position:0%
+take a minute to get but let's put it
+ 
+
+ align:start position:0%
+take a minute to get but let's put it
+out there is yes okay maybe you get the
+
+ align:start position:0%
+out there is yes okay maybe you get the
+ 
+
+ align:start position:0%
+out there is yes okay maybe you get the
+idea that programs can be used to
+
+ align:start position:0%
+idea that programs can be used to
+ 
+
+ align:start position:0%
+idea that programs can be used to
+describe causal processes in interesting
+
+ align:start position:0%
+describe causal processes in interesting
+ 
+
+ align:start position:0%
+describe causal processes in interesting
+ways but where does the probability part
+
+ align:start position:0%
+ways but where does the probability part
+ 
+
+ align:start position:0%
+ways but where does the probability part
+come in right so it's it the same thing
+
+ align:start position:0%
+come in right so it's it the same thing
+ 
+
+ align:start position:0%
+come in right so it's it the same thing
+is actually true in graphical models if
+
+ align:start position:0%
+is actually true in graphical models if
+ 
+
+ align:start position:0%
+is actually true in graphical models if
+you go in how many people have read
+
+ align:start position:0%
+you go in how many people have read
+ 
+
+ align:start position:0%
+you go in how many people have read
+judea pearls 2000 book called causality
+
+ align:start position:0%
+judea pearls 2000 book called causality
+ 
+
+ align:start position:0%
+judea pearls 2000 book called causality
+how people have read his 88th book or
+
+ align:start position:0%
+how people have read his 88th book or
+ 
+
+ align:start position:0%
+how people have read his 88th book or
+nobody's read anything but okay so what
+
+ align:start position:0%
+nobody's read anything but okay so what
+ 
+
+ align:start position:0%
+nobody's read anything but okay so what
+pearl is most famous for I mean when we
+
+ align:start position:0%
+pearl is most famous for I mean when we
+ 
+
+ align:start position:0%
+pearl is most famous for I mean when we
+say pearls famous for inventing Bayesian
+
+ align:start position:0%
+say pearls famous for inventing Bayesian
+ 
+
+ align:start position:0%
+say pearls famous for inventing Bayesian
+networks that's based on work he did in
+
+ align:start position:0%
+networks that's based on work he did in
+ 
+
+ align:start position:0%
+networks that's based on work he did in
+the 80s which in which yes they were all
+
+ align:start position:0%
+the 80s which in which yes they were all
+ 
+
+ align:start position:0%
+the 80s which in which yes they were all
+probability models but then he came to
+
+ align:start position:0%
+probability models but then he came to
+ 
+
+ align:start position:0%
+probability models but then he came to
+it what he calls and I would call to a
+
+ align:start position:0%
+it what he calls and I would call to a
+ 
+
+ align:start position:0%
+it what he calls and I would call to a
+deeper view in which it was really about
+
+ align:start position:0%
+deeper view in which it was really about
+ 
+
+ align:start position:0%
+deeper view in which it was really about
+basically deterministic calls relations
+
+ align:start position:0%
+basically deterministic calls relations
+ 
+
+ align:start position:0%
+basically deterministic calls relations
+basically it was a graphical language
+
+ align:start position:0%
+basically it was a graphical language
+ 
+
+ align:start position:0%
+basically it was a graphical language
+for four equations certain classes of
+
+ align:start position:0%
+for four equations certain classes of
+ 
+
+ align:start position:0%
+for four equations certain classes of
+equations like structural equations if
+
+ align:start position:0%
+equations like structural equations if
+ 
+
+ align:start position:0%
+equations like structural equations if
+you know about linear structural
+
+ align:start position:0%
+you know about linear structural
+ 
+
+ align:start position:0%
+you know about linear structural
+equations but sort of like nonlinear
+
+ align:start position:0%
+equations but sort of like nonlinear
+ 
+
+ align:start position:0%
+equations but sort of like nonlinear
+structural equations and then
+
+ align:start position:0%
+structural equations and then
+ 
+
+ align:start position:0%
+structural equations and then
+probabilities are these things you put
+
+ align:start position:0%
+probabilities are these things you put
+ 
+
+ align:start position:0%
+probabilities are these things you put
+on just on top of it to capture the
+
+ align:start position:0%
+on just on top of it to capture the
+ 
+
+ align:start position:0%
+on just on top of it to capture the
+things you don't know that you're
+
+ align:start position:0%
+things you don't know that you're
+ 
+
+ align:start position:0%
+things you don't know that you're
+uncertain about and I think he was he
+
+ align:start position:0%
+uncertain about and I think he was he
+ 
+
+ align:start position:0%
+uncertain about and I think he was he
+was getting at the fact that two
+
+ align:start position:0%
+was getting at the fact that two
+ 
+
+ align:start position:0%
+was getting at the fact that two
+scientists and also two people there's
+
+ align:start position:0%
+scientists and also two people there's
+ 
+
+ align:start position:0%
+scientists and also two people there's
+some very nice work by Laura Schultz and
+
+ align:start position:0%
+some very nice work by Laura Schultz and
+ 
+
+ align:start position:0%
+some very nice work by Laura Schultz and
+Jessica Somerville both of whom will be
+
+ align:start position:0%
+Jessica Somerville both of whom will be
+ 
+
+ align:start position:0%
+Jessica Somerville both of whom will be
+here next week actually on how
+
+ align:start position:0%
+here next week actually on how
+ 
+
+ align:start position:0%
+here next week actually on how
+children's concepts of causality are
+
+ align:start position:0%
+children's concepts of causality are
+ 
+
+ align:start position:0%
+children's concepts of causality are
+basically deterministic at the core and
+
+ align:start position:0%
+basically deterministic at the core and
+ 
+
+ align:start position:0%
+basically deterministic at the core and
+where the probabilities come in is on
+
+ align:start position:0%
+where the probabilities come in is on
+ 
+
+ align:start position:0%
+where the probabilities come in is on
+the things that we don't observe or the
+
+ align:start position:0%
+the things that we don't observe or the
+ 
+
+ align:start position:0%
+the things that we don't observe or the
+things we don't know the the uncertainty
+
+ align:start position:0%
+things we don't know the the uncertainty
+ 
+
+ align:start position:0%
+things we don't know the the uncertainty
+not it's not that the world is noisy
+
+ align:start position:0%
+not it's not that the world is noisy
+ 
+
+ align:start position:0%
+not it's not that the world is noisy
+it's that we believe at least except for
+
+ align:start position:0%
+it's that we believe at least except for
+ 
+
+ align:start position:0%
+it's that we believe at least except for
+quantum mechanics but our intuitive
+
+ align:start position:0%
+quantum mechanics but our intuitive
+ 
+
+ align:start position:0%
+quantum mechanics but our intuitive
+notions are that the world is basically
+
+ align:start position:0%
+notions are that the world is basically
+ 
+
+ align:start position:0%
+notions are that the world is basically
+deterministic but with a lot of stuff we
+
+ align:start position:0%
+deterministic but with a lot of stuff we
+ 
+
+ align:start position:0%
+deterministic but with a lot of stuff we
+don't know this was for example
+
+ align:start position:0%
+don't know this was for example
+ 
+
+ align:start position:0%
+don't know this was for example
+Laplace's view in philosophy of science
+
+ align:start position:0%
+Laplace's view in philosophy of science
+ 
+
+ align:start position:0%
+Laplace's view in philosophy of science
+and really until quantum mechanics it
+
+ align:start position:0%
+and really until quantum mechanics it
+ 
+
+ align:start position:0%
+and really until quantum mechanics it
+was broadly the enlightenment science
+
+ align:start position:0%
+was broadly the enlightenment science
+ 
+
+ align:start position:0%
+was broadly the enlightenment science
+view right that the world is full of all
+
+ align:start position:0%
+view right that the world is full of all
+ 
+
+ align:start position:0%
+view right that the world is full of all
+these complicated deterministic machines
+
+ align:start position:0%
+these complicated deterministic machines
+ 
+
+ align:start position:0%
+these complicated deterministic machines
+and where uncertainty comes from the
+
+ align:start position:0%
+and where uncertainty comes from the
+ 
+
+ align:start position:0%
+and where uncertainty comes from the
+things that we can't observe or that we
+
+ align:start position:0%
+things that we can't observe or that we
+ 
+
+ align:start position:0%
+things that we can't observe or that we
+can't measure finely enough or they're
+
+ align:start position:0%
+can't measure finely enough or they're
+ 
+
+ align:start position:0%
+can't measure finely enough or they're
+just in some form current unknowable
+
+ align:start position:0%
+just in some form current unknowable
+ 
+
+ align:start position:0%
+just in some form current unknowable
+unknown or unknowable to us
+
+ align:start position:0%
+unknown or unknowable to us
+ 
+
+ align:start position:0%
+unknown or unknowable to us
+does that make sense so so the I mean
+
+ align:start position:0%
+does that make sense so so the I mean
+ 
+
+ align:start position:0%
+does that make sense so so the I mean
+you'll see more of this in a second but
+
+ align:start position:0%
+you'll see more of this in a second but
+ 
+
+ align:start position:0%
+you'll see more of this in a second but
+where the probabilities are going to
+
+ align:start position:0%
+where the probabilities are going to
+ 
+
+ align:start position:0%
+where the probabilities are going to
+come from is basically if there are
+
+ align:start position:0%
+come from is basically if there are
+ 
+
+ align:start position:0%
+come from is basically if there are
+inputs to the program that we don't know
+
+ align:start position:0%
+inputs to the program that we don't know
+ 
+
+ align:start position:0%
+inputs to the program that we don't know
+or parameters we don't know then in
+
+ align:start position:0%
+or parameters we don't know then in
+ 
+
+ align:start position:0%
+or parameters we don't know then in
+order to simulate them are gonna have to
+
+ align:start position:0%
+order to simulate them are gonna have to
+ 
+
+ align:start position:0%
+order to simulate them are gonna have to
+put distributions on those and make some
+
+ align:start position:0%
+put distributions on those and make some
+ 
+
+ align:start position:0%
+put distributions on those and make some
+guesses and then see what happens for
+
+ align:start position:0%
+guesses and then see what happens for
+ 
+
+ align:start position:0%
+guesses and then see what happens for
+different guesses does that make sense
+
+ align:start position:0%
+different guesses does that make sense
+ 
+
+ align:start position:0%
+different guesses does that make sense
+okay um good so that's again that's most
+
+ align:start position:0%
+okay um good so that's again that's most
+ 
+
+ align:start position:0%
+okay um good so that's again that's most
+of the technical stuff I need to say and
+
+ align:start position:0%
+of the technical stuff I need to say and
+ 
+
+ align:start position:0%
+of the technical stuff I need to say and
+you'll you'll learn about how to how
+
+ align:start position:0%
+you'll you'll learn about how to how
+ 
+
+ align:start position:0%
+you'll you'll learn about how to how
+this works in much more concrete details
+
+ align:start position:0%
+this works in much more concrete details
+ 
+
+ align:start position:0%
+this works in much more concrete details
+if you go to the tutorial afterwards
+
+ align:start position:0%
+if you go to the tutorial afterwards
+ 
+
+ align:start position:0%
+if you go to the tutorial afterwards
+that Tomer is gonna run what you'll see
+
+ align:start position:0%
+that Tomer is gonna run what you'll see
+ 
+
+ align:start position:0%
+that Tomer is gonna run what you'll see
+there is this so here are just a few
+
+ align:start position:0%
+there is this so here are just a few
+ 
+
+ align:start position:0%
+there is this so here are just a few
+examples many of you hopefully already
+
+ align:start position:0%
+examples many of you hopefully already
+ 
+
+ align:start position:0%
+examples many of you hopefully already
+looked at these the web pages from this
+
+ align:start position:0%
+looked at these the web pages from this
+ 
+
+ align:start position:0%
+looked at these the web pages from this
+problem on storage thing and what you
+
+ align:start position:0%
+problem on storage thing and what you
+ 
+
+ align:start position:0%
+problem on storage thing and what you
+see here is basically each of these
+
+ align:start position:0%
+see here is basically each of these
+ 
+
+ align:start position:0%
+see here is basically each of these
+boxes is a probabilistic program model
+
+ align:start position:0%
+boxes is a probabilistic program model
+ 
+
+ align:start position:0%
+boxes is a probabilistic program model
+it most of it is a bunch of defined
+
+ align:start position:0%
+it most of it is a bunch of defined
+ 
+
+ align:start position:0%
+it most of it is a bunch of defined
+statements so if you look here you'll
+
+ align:start position:0%
+statements so if you look here you'll
+ 
+
+ align:start position:0%
+statements so if you look here you'll
+see these define statements those are
+
+ align:start position:0%
+see these define statements those are
+ 
+
+ align:start position:0%
+see these define statements those are
+just defining functions they name the
+
+ align:start position:0%
+just defining functions they name the
+ 
+
+ align:start position:0%
+just defining functions they name the
+function they take some inputs which
+
+ align:start position:0%
+function they take some inputs which
+ 
+
+ align:start position:0%
+function they take some inputs which
+call other functions and then they maybe
+
+ align:start position:0%
+call other functions and then they maybe
+ 
+
+ align:start position:0%
+call other functions and then they maybe
+do something they have some output that
+
+ align:start position:0%
+do something they have some output that
+ 
+
+ align:start position:0%
+do something they have some output that
+might be a an object it might itself be
+
+ align:start position:0%
+might be a an object it might itself be
+ 
+
+ align:start position:0%
+might be a an object it might itself be
+a function you know this is these can be
+
+ align:start position:0%
+a function you know this is these can be
+ 
+
+ align:start position:0%
+a function you know this is these can be
+functions that generate other functions
+
+ align:start position:0%
+functions that generate other functions
+ 
+
+ align:start position:0%
+functions that generate other functions
+and in some sense oh and and and where
+
+ align:start position:0%
+and in some sense oh and and and where
+ 
+
+ align:start position:0%
+and in some sense oh and and and where
+the probabilities come in is that
+
+ align:start position:0%
+the probabilities come in is that
+ 
+
+ align:start position:0%
+the probabilities come in is that
+sometimes these functions call random
+
+ align:start position:0%
+sometimes these functions call random
+ 
+
+ align:start position:0%
+sometimes these functions call random
+number generators basically if you look
+
+ align:start position:0%
+number generators basically if you look
+ 
+
+ align:start position:0%
+number generators basically if you look
+carefully you'll see things like D relay
+
+ align:start position:0%
+carefully you'll see things like D relay
+ 
+
+ align:start position:0%
+carefully you'll see things like D relay
+or uniform draw or Gaussian or flip
+
+ align:start position:0%
+or uniform draw or Gaussian or flip
+ 
+
+ align:start position:0%
+or uniform draw or Gaussian or flip
+right those are primitive random
+
+ align:start position:0%
+right those are primitive random
+ 
+
+ align:start position:0%
+right those are primitive random
+functions that flip a coin or roll a die
+
+ align:start position:0%
+functions that flip a coin or roll a die
+ 
+
+ align:start position:0%
+functions that flip a coin or roll a die
+or draw from a Gaussian and those
+
+ align:start position:0%
+or draw from a Gaussian and those
+ 
+
+ align:start position:0%
+or draw from a Gaussian and those
+capture things that that are currently
+
+ align:start position:0%
+capture things that that are currently
+ 
+
+ align:start position:0%
+capture things that that are currently
+unknown right in a very important sense
+
+ align:start position:0%
+unknown right in a very important sense
+ 
+
+ align:start position:0%
+unknown right in a very important sense
+the particular language church that
+
+ align:start position:0%
+the particular language church that
+ 
+
+ align:start position:0%
+the particular language church that
+you're gonna learn here with it's sort
+
+ align:start position:0%
+you're gonna learn here with it's sort
+ 
+
+ align:start position:0%
+you're gonna learn here with it's sort
+of stochastic lists basically just
+
+ align:start position:0%
+of stochastic lists basically just
+ 
+
+ align:start position:0%
+of stochastic lists basically just
+functions that call other functions and
+
+ align:start position:0%
+functions that call other functions and
+ 
+
+ align:start position:0%
+functions that call other functions and
+maybe add in some randomness to that is
+
+ align:start position:0%
+maybe add in some randomness to that is
+ 
+
+ align:start position:0%
+maybe add in some randomness to that is
+very much analogous to the directed
+
+ align:start position:0%
+very much analogous to the directed
+ 
+
+ align:start position:0%
+very much analogous to the directed
+graph of a Bayesian network in a
+
+ align:start position:0%
+graph of a Bayesian network in a
+ 
+
+ align:start position:0%
+graph of a Bayesian network in a
+Bayesian network you have nodes and
+
+ align:start position:0%
+Bayesian network you have nodes and
+ 
+
+ align:start position:0%
+Bayesian network you have nodes and
+arrows and the parents of a node the
+
+ align:start position:0%
+arrows and the parents of a node the
+ 
+
+ align:start position:0%
+arrows and the parents of a node the
+ones that send arrows to it are the
+
+ align:start position:0%
+ones that send arrows to it are the
+ 
+
+ align:start position:0%
+ones that send arrows to it are the
+basically the minimal set of variables
+
+ align:start position:0%
+basically the minimal set of variables
+ 
+
+ align:start position:0%
+basically the minimal set of variables
+that if you were going to sample from
+
+ align:start position:0%
+that if you were going to sample from
+ 
+
+ align:start position:0%
+that if you were going to sample from
+this model you'd have to sample first in
+
+ align:start position:0%
+this model you'd have to sample first in
+ 
+
+ align:start position:0%
+this model you'd have to sample first in
+order to then sample the child variable
+
+ align:start position:0%
+order to then sample the child variable
+ 
+
+ align:start position:0%
+order to then sample the child variable
+cuz it's those are the key things it
+
+ align:start position:0%
+cuz it's those are the key things it
+ 
+
+ align:start position:0%
+cuz it's those are the key things it
+depends on and you can have a
+
+ align:start position:0%
+depends on and you can have a
+ 
+
+ align:start position:0%
+depends on and you can have a
+multi-layered Bayesian network that if
+
+ align:start position:0%
+multi-layered Bayesian network that if
+ 
+
+ align:start position:0%
+multi-layered Bayesian network that if
+you were going to sample from it is just
+
+ align:start position:0%
+you were going to sample from it is just
+ 
+
+ align:start position:0%
+you were going to sample from it is just
+you start at the top and you sort of go
+
+ align:start position:0%
+you start at the top and you sort of go
+ 
+
+ align:start position:0%
+you start at the top and you sort of go
+down that's exactly the same thing you
+
+ align:start position:0%
+down that's exactly the same thing you
+ 
+
+ align:start position:0%
+down that's exactly the same thing you
+have in these probabilistic programs
+
+ align:start position:0%
+have in these probabilistic programs
+ 
+
+ align:start position:0%
+have in these probabilistic programs
+where the defined statements are
+
+ align:start position:0%
+where the defined statements are
+ 
+
+ align:start position:0%
+where the defined statements are
+basically defining a function and said
+
+ align:start position:0%
+basically defining a function and said
+ 
+
+ align:start position:0%
+basically defining a function and said
+the func that the functions are the
+
+ align:start position:0%
+the func that the functions are the
+ 
+
+ align:start position:0%
+the func that the functions are the
+nodes
+
+ align:start position:0%
+nodes
+ 
+
+ align:start position:0%
+nodes
+and the other functions that they call
+
+ align:start position:0%
+and the other functions that they call
+ 
+
+ align:start position:0%
+and the other functions that they call
+as part of the statement are the things
+
+ align:start position:0%
+as part of the statement are the things
+ 
+
+ align:start position:0%
+as part of the statement are the things
+that are the nodes that send arrows
+
+ align:start position:0%
+that are the nodes that send arrows
+ 
+
+ align:start position:0%
+that are the nodes that send arrows
+there but the key is as you can imagine
+
+ align:start position:0%
+there but the key is as you can imagine
+ 
+
+ align:start position:0%
+there but the key is as you can imagine
+if you've ever I mean all of you written
+
+ align:start position:0%
+if you've ever I mean all of you written
+ 
+
+ align:start position:0%
+if you've ever I mean all of you written
+computer programs is that it's only very
+
+ align:start position:0%
+computer programs is that it's only very
+ 
+
+ align:start position:0%
+computer programs is that it's only very
+simple programs look like directed
+
+ align:start position:0%
+simple programs look like directed
+ 
+
+ align:start position:0%
+simple programs look like directed
+acyclic graphs and that's what a
+
+ align:start position:0%
+acyclic graphs and that's what a
+ 
+
+ align:start position:0%
+acyclic graphs and that's what a
+Bayesian network is it's very easy and
+
+ align:start position:0%
+Bayesian network is it's very easy and
+ 
+
+ align:start position:0%
+Bayesian network is it's very easy and
+often necessary to write a program to
+
+ align:start position:0%
+often necessary to write a program to
+ 
+
+ align:start position:0%
+often necessary to write a program to
+really capture something causally
+
+ align:start position:0%
+really capture something causally
+ 
+
+ align:start position:0%
+really capture something causally
+interesting in the world where it's not
+
+ align:start position:0%
+interesting in the world where it's not
+ 
+
+ align:start position:0%
+interesting in the world where it's not
+a directed a solute there's all sorts of
+
+ align:start position:0%
+a directed a solute there's all sorts of
+ 
+
+ align:start position:0%
+a directed a solute there's all sorts of
+cycles there's recursion one thing that
+
+ align:start position:0%
+cycles there's recursion one thing that
+ 
+
+ align:start position:0%
+cycles there's recursion one thing that
+a function can do is make a whole other
+
+ align:start position:0%
+a function can do is make a whole other
+ 
+
+ align:start position:0%
+a function can do is make a whole other
+graph right or often it's it might be
+
+ align:start position:0%
+graph right or often it's it might be
+ 
+
+ align:start position:0%
+graph right or often it's it might be
+directed in a cyclic but all the
+
+ align:start position:0%
+directed in a cyclic but all the
+ 
+
+ align:start position:0%
+directed in a cyclic but all the
+interesting stuff is kind of going on
+
+ align:start position:0%
+interesting stuff is kind of going on
+ 
+
+ align:start position:0%
+interesting stuff is kind of going on
+inside what happens when you evaluate
+
+ align:start position:0%
+inside what happens when you evaluate
+ 
+
+ align:start position:0%
+inside what happens when you evaluate
+one function so if you were to draw it
+
+ align:start position:0%
+one function so if you were to draw it
+ 
+
+ align:start position:0%
+one function so if you were to draw it
+as a graph it might look like you could
+
+ align:start position:0%
+as a graph it might look like you could
+ 
+
+ align:start position:0%
+as a graph it might look like you could
+draw a directed acyclic graph but all
+
+ align:start position:0%
+draw a directed acyclic graph but all
+ 
+
+ align:start position:0%
+draw a directed acyclic graph but all
+the interesting stuff will be going on
+
+ align:start position:0%
+the interesting stuff will be going on
+ 
+
+ align:start position:0%
+the interesting stuff will be going on
+inside one ERA or what one node or one
+
+ align:start position:0%
+inside one ERA or what one node or one
+ 
+
+ align:start position:0%
+inside one ERA or what one node or one
+arrow so let me get more specific about
+
+ align:start position:0%
+arrow so let me get more specific about
+ 
+
+ align:start position:0%
+arrow so let me get more specific about
+the particular kind of programs that
+
+ align:start position:0%
+the particular kind of programs that
+ 
+
+ align:start position:0%
+the particular kind of programs that
+we're going to be talking about in the
+
+ align:start position:0%
+we're going to be talking about in the
+ 
+
+ align:start position:0%
+we're going to be talking about in the
+language in a probabilistic programming
+
+ align:start position:0%
+language in a probabilistic programming
+ 
+
+ align:start position:0%
+language in a probabilistic programming
+language like church or in general in
+
+ align:start position:0%
+language like church or in general in
+ 
+
+ align:start position:0%
+language like church or in general in
+this view of the mind we're interested
+
+ align:start position:0%
+this view of the mind we're interested
+ 
+
+ align:start position:0%
+this view of the mind we're interested
+in being able to build really any I mean
+
+ align:start position:0%
+in being able to build really any I mean
+ 
+
+ align:start position:0%
+in being able to build really any I mean
+kind of thing again there's there's lots
+
+ align:start position:0%
+kind of thing again there's there's lots
+ 
+
+ align:start position:0%
+kind of thing again there's there's lots
+of big dreams here like I was saying
+
+ align:start position:0%
+of big dreams here like I was saying
+ 
+
+ align:start position:0%
+of big dreams here like I was saying
+before we had I felt like we had to give
+
+ align:start position:0%
+before we had I felt like we had to give
+ 
+
+ align:start position:0%
+before we had I felt like we had to give
+up on some dreams but we've replaced it
+
+ align:start position:0%
+up on some dreams but we've replaced it
+ 
+
+ align:start position:0%
+up on some dreams but we've replaced it
+with even grander ones like
+
+ align:start position:0%
+with even grander ones like
+ 
+
+ align:start position:0%
+with even grander ones like
+probabilistic modeling engines that can
+
+ align:start position:0%
+probabilistic modeling engines that can
+ 
+
+ align:start position:0%
+probabilistic modeling engines that can
+do any computable model but in the
+
+ align:start position:0%
+do any computable model but in the
+ 
+
+ align:start position:0%
+do any computable model but in the
+spirit of trying to scale up from
+
+ align:start position:0%
+spirit of trying to scale up from
+ 
+
+ align:start position:0%
+spirit of trying to scale up from
+something that we can get traction on
+
+ align:start position:0%
+something that we can get traction on
+ 
+
+ align:start position:0%
+something that we can get traction on
+right what I've been focusing on in a
+
+ align:start position:0%
+right what I've been focusing on in a
+ 
+
+ align:start position:0%
+right what I've been focusing on in a
+lot of my work recently and what we've
+
+ align:start position:0%
+lot of my work recently and what we've
+ 
+
+ align:start position:0%
+lot of my work recently and what we've
+been doing part of as part of the center
+
+ align:start position:0%
+been doing part of as part of the center
+ 
+
+ align:start position:0%
+been doing part of as part of the center
+our particular probabilistic programs
+
+ align:start position:0%
+our particular probabilistic programs
+ 
+
+ align:start position:0%
+our particular probabilistic programs
+that we think can capture this very
+
+ align:start position:0%
+that we think can capture this very
+ 
+
+ align:start position:0%
+that we think can capture this very
+early core of common sense intuitive
+
+ align:start position:0%
+early core of common sense intuitive
+ 
+
+ align:start position:0%
+early core of common sense intuitive
+physics and intuitive psychology in
+
+ align:start position:0%
+physics and intuitive psychology in
+ 
+
+ align:start position:0%
+physics and intuitive psychology in
+young kids it's what I called and I
+
+ align:start position:0%
+young kids it's what I called and I
+ 
+
+ align:start position:0%
+young kids it's what I called and I
+remember I mentioned this in the first
+
+ align:start position:0%
+remember I mentioned this in the first
+ 
+
+ align:start position:0%
+remember I mentioned this in the first
+lecture this game engine in your head
+
+ align:start position:0%
+lecture this game engine in your head
+ 
+
+ align:start position:0%
+lecture this game engine in your head
+right so it's programs for graphics
+
+ align:start position:0%
+right so it's programs for graphics
+ 
+
+ align:start position:0%
+right so it's programs for graphics
+engines physics engines planning engines
+
+ align:start position:0%
+engines physics engines planning engines
+ 
+
+ align:start position:0%
+engines physics engines planning engines
+the basic kinds of things you might use
+
+ align:start position:0%
+the basic kinds of things you might use
+ 
+
+ align:start position:0%
+the basic kinds of things you might use
+to build one of these immersive video
+
+ align:start position:0%
+to build one of these immersive video
+ 
+
+ align:start position:0%
+to build one of these immersive video
+games and we think if you wrap those
+
+ align:start position:0%
+games and we think if you wrap those
+ 
+
+ align:start position:0%
+games and we think if you wrap those
+inside this framework for probabilistic
+
+ align:start position:0%
+inside this framework for probabilistic
+ 
+
+ align:start position:0%
+inside this framework for probabilistic
+inference then that's a powerful way to
+
+ align:start position:0%
+inference then that's a powerful way to
+ 
+
+ align:start position:0%
+inference then that's a powerful way to
+do the kind of common-sense scene
+
+ align:start position:0%
+do the kind of common-sense scene
+ 
+
+ align:start position:0%
+do the kind of common-sense scene
+understanding whether it in these adult
+
+ align:start position:0%
+understanding whether it in these adult
+ 
+
+ align:start position:0%
+understanding whether it in these adult
+versions Ori or in the young kid
+
+ align:start position:0%
+versions Ori or in the young kid
+ 
+
+ align:start position:0%
+versions Ori or in the young kid
+versions now there's that this I mean to
+
+ align:start position:0%
+versions now there's that this I mean to
+ 
+
+ align:start position:0%
+versions now there's that this I mean to
+specify this probablistic programs view
+
+ align:start position:0%
+specify this probablistic programs view
+ 
+
+ align:start position:0%
+specify this probablistic programs view
+just like with Bayesian networks or
+
+ align:start position:0%
+just like with Bayesian networks or
+ 
+
+ align:start position:0%
+just like with Bayesian networks or
+these graphical models we wanted general
+
+ align:start position:0%
+these graphical models we wanted general
+ 
+
+ align:start position:0%
+these graphical models we wanted general
+purpose
+
+ align:start position:0%
+purpose
+ 
+
+ align:start position:0%
+purpose
+tools for representing interesting
+
+ align:start position:0%
+tools for representing interesting
+ 
+
+ align:start position:0%
+tools for representing interesting
+things in the world and for computing
+
+ align:start position:0%
+things in the world and for computing
+ 
+
+ align:start position:0%
+things in the world and for computing
+the inferences that were that we want
+
+ align:start position:0%
+the inferences that were that we want
+ 
+
+ align:start position:0%
+the inferences that were that we want
+which again which means basically
+
+ align:start position:0%
+which again which means basically
+ 
+
+ align:start position:0%
+which again which means basically
+observing say just like you observe the
+
+ align:start position:0%
+observing say just like you observe the
+ 
+
+ align:start position:0%
+observing say just like you observe the
+some of the symptoms and you want to
+
+ align:start position:0%
+some of the symptoms and you want to
+ 
+
+ align:start position:0%
+some of the symptoms and you want to
+compute the likely diseases that best
+
+ align:start position:0%
+compute the likely diseases that best
+ 
+
+ align:start position:0%
+compute the likely diseases that best
+explain the observed symptoms here we
+
+ align:start position:0%
+explain the observed symptoms here we
+ 
+
+ align:start position:0%
+explain the observed symptoms here we
+talk about observing the outputs of some
+
+ align:start position:0%
+talk about observing the outputs of some
+ 
+
+ align:start position:0%
+talk about observing the outputs of some
+of these programs these like the image
+
+ align:start position:0%
+of these programs these like the image
+ 
+
+ align:start position:0%
+of these programs these like the image
+that's the output of a graphics program
+
+ align:start position:0%
+that's the output of a graphics program
+ 
+
+ align:start position:0%
+that's the output of a graphics program
+and we want to work backwards and make a
+
+ align:start position:0%
+and we want to work backwards and make a
+ 
+
+ align:start position:0%
+and we want to work backwards and make a
+guess at the world state the input to
+
+ align:start position:0%
+guess at the world state the input to
+ 
+
+ align:start position:0%
+guess at the world state the input to
+the graphics engine that's most likely
+
+ align:start position:0%
+the graphics engine that's most likely
+ 
+
+ align:start position:0%
+the graphics engine that's most likely
+to have produced the image that's the
+
+ align:start position:0%
+to have produced the image that's the
+ 
+
+ align:start position:0%
+to have produced the image that's the
+analog of getting diseases from symptoms
+
+ align:start position:0%
+analog of getting diseases from symptoms
+ 
+
+ align:start position:0%
+analog of getting diseases from symptoms
+or that's again it's that's our
+
+ align:start position:0%
+or that's again it's that's our
+ 
+
+ align:start position:0%
+or that's again it's that's our
+explanation right there and there are
+
+ align:start position:0%
+explanation right there and there are
+ 
+
+ align:start position:0%
+explanation right there and there are
+lots of different algorithms for doing
+
+ align:start position:0%
+lots of different algorithms for doing
+ 
+
+ align:start position:0%
+lots of different algorithms for doing
+this I'm not going to say too much about
+
+ align:start position:0%
+this I'm not going to say too much about
+ 
+
+ align:start position:0%
+this I'm not going to say too much about
+them
+
+ align:start position:0%
+them
+ 
+
+ align:start position:0%
+them
+Tomer we'll say a little bit more in the
+
+ align:start position:0%
+Tomer we'll say a little bit more in the
+ 
+
+ align:start position:0%
+Tomer we'll say a little bit more in the
+afternoon the main thing I will do is I
+
+ align:start position:0%
+afternoon the main thing I will do is I
+ 
+
+ align:start position:0%
+afternoon the main thing I will do is I
+will say that that the main
+
+ align:start position:0%
+will say that that the main
+ 
+
+ align:start position:0%
+will say that that the main
+general-purpose algorithms for infants
+
+ align:start position:0%
+general-purpose algorithms for infants
+ 
+
+ align:start position:0%
+general-purpose algorithms for infants
+and probably sick programming language
+
+ align:start position:0%
+and probably sick programming language
+ 
+
+ align:start position:0%
+and probably sick programming language
+are in the category of slow and slower
+
+ align:start position:0%
+are in the category of slow and slower
+ 
+
+ align:start position:0%
+are in the category of slow and slower
+and really really slow and you know
+
+ align:start position:0%
+and really really slow and you know
+ 
+
+ align:start position:0%
+and really really slow and you know
+there's no this is one of the many ways
+
+ align:start position:0%
+there's no this is one of the many ways
+ 
+
+ align:start position:0%
+there's no this is one of the many ways
+in which there's no magic or no free
+
+ align:start position:0%
+in which there's no magic or no free
+ 
+
+ align:start position:0%
+in which there's no magic or no free
+lunch if you across all of AI in
+
+ align:start position:0%
+lunch if you across all of AI in
+ 
+
+ align:start position:0%
+lunch if you across all of AI in
+cognitive science when you build very
+
+ align:start position:0%
+cognitive science when you build very
+ 
+
+ align:start position:0%
+cognitive science when you build very
+powerful representations doing inference
+
+ align:start position:0%
+powerful representations doing inference
+ 
+
+ align:start position:0%
+powerful representations doing inference
+with them becomes very hard it's part of
+
+ align:start position:0%
+with them becomes very hard it's part of
+ 
+
+ align:start position:0%
+with them becomes very hard it's part of
+why people often like things like neural
+
+ align:start position:0%
+why people often like things like neural
+ 
+
+ align:start position:0%
+why people often like things like neural
+networks they're much weaker
+
+ align:start position:0%
+networks they're much weaker
+ 
+
+ align:start position:0%
+networks they're much weaker
+representations but inference can be
+
+ align:start position:0%
+representations but inference can be
+ 
+
+ align:start position:0%
+representations but inference can be
+much faster and at the moment the only
+
+ align:start position:0%
+much faster and at the moment the only
+ 
+
+ align:start position:0%
+much faster and at the moment the only
+totally general-purpose algorithms for
+
+ align:start position:0%
+totally general-purpose algorithms for
+ 
+
+ align:start position:0%
+totally general-purpose algorithms for
+doing inference with policy programs are
+
+ align:start position:0%
+doing inference with policy programs are
+ 
+
+ align:start position:0%
+doing inference with policy programs are
+slow but first of all they're getting
+
+ align:start position:0%
+slow but first of all they're getting
+ 
+
+ align:start position:0%
+slow but first of all they're getting
+faster people are coming up with and I
+
+ align:start position:0%
+faster people are coming up with and I
+ 
+
+ align:start position:0%
+faster people are coming up with and I
+can talk about this offline where that's
+
+ align:start position:0%
+can talk about this offline where that's
+ 
+
+ align:start position:0%
+can talk about this offline where that's
+going but also and this is where what
+
+ align:start position:0%
+going but also and this is where what
+ 
+
+ align:start position:0%
+going but also and this is where what
+I'll talk about in a more sharper way in
+
+ align:start position:0%
+I'll talk about in a more sharper way in
+ 
+
+ align:start position:0%
+I'll talk about in a more sharper way in
+a second um there are particular classes
+
+ align:start position:0%
+a second um there are particular classes
+ 
+
+ align:start position:0%
+a second um there are particular classes
+of problems big programs in particular
+
+ align:start position:0%
+of problems big programs in particular
+ 
+
+ align:start position:0%
+of problems big programs in particular
+the ones in the game engine in your head
+
+ align:start position:0%
+the ones in the game engine in your head
+ 
+
+ align:start position:0%
+the ones in the game engine in your head
+like for vision is inverse graphics and
+
+ align:start position:0%
+like for vision is inverse graphics and
+ 
+
+ align:start position:0%
+like for vision is inverse graphics and
+maybe some things about physics and
+
+ align:start position:0%
+maybe some things about physics and
+ 
+
+ align:start position:0%
+maybe some things about physics and
+psychology too but that's there's a lot
+
+ align:start position:0%
+psychology too but that's there's a lot
+ 
+
+ align:start position:0%
+psychology too but that's there's a lot
+that's that's just this I mean again I'm
+
+ align:start position:0%
+that's that's just this I mean again I'm
+ 
+
+ align:start position:0%
+that's that's just this I mean again I'm
+just thinking of the stuff of like
+
+ align:start position:0%
+just thinking of the stuff of like
+ 
+
+ align:start position:0%
+just thinking of the stuff of like
+what's going on with it when a kid is
+
+ align:start position:0%
+what's going on with it when a kid is
+ 
+
+ align:start position:0%
+what's going on with it when a kid is
+playing with some objects around them
+
+ align:start position:0%
+playing with some objects around them
+ 
+
+ align:start position:0%
+playing with some objects around them
+and thinking about what other people
+
+ align:start position:0%
+and thinking about what other people
+ 
+
+ align:start position:0%
+and thinking about what other people
+might think about those things it's just
+
+ align:start position:0%
+might think about those things it's just
+ 
+
+ align:start position:0%
+might think about those things it's just
+that setting where we think that you can
+
+ align:start position:0%
+that setting where we think that you can
+ 
+
+ align:start position:0%
+that setting where we think that you can
+build sort of in some sense special
+
+ align:start position:0%
+build sort of in some sense special
+ 
+
+ align:start position:0%
+build sort of in some sense special
+purpose I mean they're still pretty
+
+ align:start position:0%
+purpose I mean they're still pretty
+ 
+
+ align:start position:0%
+purpose I mean they're still pretty
+general but inference algorithms for
+
+ align:start position:0%
+general but inference algorithms for
+ 
+
+ align:start position:0%
+general but inference algorithms for
+doing inference in public programs for
+
+ align:start position:0%
+doing inference in public programs for
+ 
+
+ align:start position:0%
+doing inference in public programs for
+doing getting the causes from the
+
+ align:start position:0%
+doing getting the causes from the
+ 
+
+ align:start position:0%
+doing getting the causes from the
+effects that are much much faster than
+
+ align:start position:0%
+effects that are much much faster than
+ 
+
+ align:start position:0%
+effects that are much much faster than
+things that could work on just arbitrary
+
+ align:start position:0%
+things that could work on just arbitrary
+ 
+
+ align:start position:0%
+things that could work on just arbitrary
+probabilistic programs
+
+ align:start position:0%
+probabilistic programs
+ 
+
+ align:start position:0%
+probabilistic programs
+and that actually often look a lot like
+
+ align:start position:0%
+and that actually often look a lot like
+ 
+
+ align:start position:0%
+and that actually often look a lot like
+neural networks and in particular we can
+
+ align:start position:0%
+neural networks and in particular we can
+ 
+
+ align:start position:0%
+neural networks and in particular we can
+directly use say for example deep
+
+ align:start position:0%
+directly use say for example deep
+ 
+
+ align:start position:0%
+directly use say for example deep
+convolutional neural networks to build
+
+ align:start position:0%
+convolutional neural networks to build
+ 
+
+ align:start position:0%
+convolutional neural networks to build
+these recognition programs or you know
+
+ align:start position:0%
+these recognition programs or you know
+ 
+
+ align:start position:0%
+these recognition programs or you know
+especially basically inference programs
+
+ align:start position:0%
+especially basically inference programs
+ 
+
+ align:start position:0%
+especially basically inference programs
+that work by a pattern recognition in
+
+ align:start position:0%
+that work by a pattern recognition in
+ 
+
+ align:start position:0%
+that work by a pattern recognition in
+for example an inverse graphics approach
+
+ align:start position:0%
+for example an inverse graphics approach
+ 
+
+ align:start position:0%
+for example an inverse graphics approach
+division so that's what I'll show you
+
+ align:start position:0%
+division so that's what I'll show you
+ 
+
+ align:start position:0%
+division so that's what I'll show you
+basically now I'm gonna start off by
+
+ align:start position:0%
+basically now I'm gonna start off by
+ 
+
+ align:start position:0%
+basically now I'm gonna start off by
+just working through a couple of these
+
+ align:start position:0%
+just working through a couple of these
+ 
+
+ align:start position:0%
+just working through a couple of these
+arrows I'm gonna first talk about this
+
+ align:start position:0%
+arrows I'm gonna first talk about this
+ 
+
+ align:start position:0%
+arrows I'm gonna first talk about this
+sort of approach we've done to tackle
+
+ align:start position:0%
+sort of approach we've done to tackle
+ 
+
+ align:start position:0%
+sort of approach we've done to tackle
+both vision is inverse graphics and some
+
+ align:start position:0%
+both vision is inverse graphics and some
+ 
+
+ align:start position:0%
+both vision is inverse graphics and some
+intuitive physics on on the scene
+
+ align:start position:0%
+intuitive physics on on the scene
+ 
+
+ align:start position:0%
+intuitive physics on on the scene
+recovered and then say a little bit
+
+ align:start position:0%
+recovered and then say a little bit
+ 
+
+ align:start position:0%
+recovered and then say a little bit
+about the intuitive psychology side um
+
+ align:start position:0%
+about the intuitive psychology side um
+ 
+
+ align:start position:0%
+about the intuitive psychology side um
+the here's an example of the kind of
+
+ align:start position:0%
+the here's an example of the kind of
+ 
+
+ align:start position:0%
+the here's an example of the kind of
+specific domain we've studied it's like
+
+ align:start position:0%
+specific domain we've studied it's like
+ 
+
+ align:start position:0%
+specific domain we've studied it's like
+our Atari setting it's a kind of video
+
+ align:start position:0%
+our Atari setting it's a kind of video
+ 
+
+ align:start position:0%
+our Atari setting it's a kind of video
+game inspired by the real game Jenga
+
+ align:start position:0%
+game inspired by the real game Jenga
+ 
+
+ align:start position:0%
+game inspired by the real game Jenga
+Jenga is this cool game you played with
+
+ align:start position:0%
+Jenga is this cool game you played with
+ 
+
+ align:start position:0%
+Jenga is this cool game you played with
+wooden blocks you start off with a
+
+ align:start position:0%
+wooden blocks you start off with a
+ 
+
+ align:start position:0%
+wooden blocks you start off with a
+nicely very very very nicely stacked up
+
+ align:start position:0%
+nicely very very very nicely stacked up
+ 
+
+ align:start position:0%
+nicely very very very nicely stacked up
+thing and you take turns removing the
+
+ align:start position:0%
+thing and you take turns removing the
+ 
+
+ align:start position:0%
+thing and you take turns removing the
+blocks and the player who removes the
+
+ align:start position:0%
+blocks and the player who removes the
+ 
+
+ align:start position:0%
+blocks and the player who removes the
+block that makes the whole thing fall
+
+ align:start position:0%
+block that makes the whole thing fall
+ 
+
+ align:start position:0%
+block that makes the whole thing fall
+over as the one who loses and it really
+
+ align:start position:0%
+over as the one who loses and it really
+ 
+
+ align:start position:0%
+over as the one who loses and it really
+exercises this part of your brain that
+
+ align:start position:0%
+exercises this part of your brain that
+ 
+
+ align:start position:0%
+exercises this part of your brain that
+we've been studying here which is an
+
+ align:start position:0%
+we've been studying here which is an
+ 
+
+ align:start position:0%
+we've been studying here which is an
+ability to reason about stability and
+
+ align:start position:0%
+ability to reason about stability and
+ 
+
+ align:start position:0%
+ability to reason about stability and
+support which I very briefly went over
+
+ align:start position:0%
+support which I very briefly went over
+ 
+
+ align:start position:0%
+support which I very briefly went over
+this but this is something that it's one
+
+ align:start position:0%
+this but this is something that it's one
+ 
+
+ align:start position:0%
+this but this is something that it's one
+of the classic case studies of infant
+
+ align:start position:0%
+of the classic case studies of infant
+ 
+
+ align:start position:0%
+of the classic case studies of infant
+object knowledge looking at how
+
+ align:start position:0%
+object knowledge looking at how
+ 
+
+ align:start position:0%
+object knowledge looking at how
+basically these concepts develop in some
+
+ align:start position:0%
+basically these concepts develop in some
+ 
+
+ align:start position:0%
+basically these concepts develop in some
+really interesting ways over the first
+
+ align:start position:0%
+really interesting ways over the first
+ 
+
+ align:start position:0%
+really interesting ways over the first
+year of life though what we're doing
+
+ align:start position:0%
+year of life though what we're doing
+ 
+
+ align:start position:0%
+year of life though what we're doing
+here is building models and testing them
+
+ align:start position:0%
+here is building models and testing them
+ 
+
+ align:start position:0%
+here is building models and testing them
+primarily with adults it is part of what
+
+ align:start position:0%
+primarily with adults it is part of what
+ 
+
+ align:start position:0%
+primarily with adults it is part of what
+we're trying to do in our brains minds
+
+ align:start position:0%
+we're trying to do in our brains minds
+ 
+
+ align:start position:0%
+we're trying to do in our brains minds
+and machines research program here is
+
+ align:start position:0%
+and machines research program here is
+ 
+
+ align:start position:0%
+and machines research program here is
+which collaboration with Liz and others
+
+ align:start position:0%
+which collaboration with Liz and others
+ 
+
+ align:start position:0%
+which collaboration with Liz and others
+to actually test these ideas in
+
+ align:start position:0%
+to actually test these ideas in
+ 
+
+ align:start position:0%
+to actually test these ideas in
+experiments with infants but what I'll
+
+ align:start position:0%
+experiments with infants but what I'll
+ 
+
+ align:start position:0%
+experiments with infants but what I'll
+show you is just kind of think of it as
+
+ align:start position:0%
+show you is just kind of think of it as
+ 
+
+ align:start position:0%
+show you is just kind of think of it as
+like infant inspired adult intuitive
+
+ align:start position:0%
+like infant inspired adult intuitive
+ 
+
+ align:start position:0%
+like infant inspired adult intuitive
+physics that where we build and test the
+
+ align:start position:0%
+physics that where we build and test the
+ 
+
+ align:start position:0%
+physics that where we build and test the
+models in an easier way and then we're
+
+ align:start position:0%
+models in an easier way and then we're
+ 
+
+ align:start position:0%
+models in an easier way and then we're
+taking it down to kids going forward so
+
+ align:start position:0%
+taking it down to kids going forward so
+ 
+
+ align:start position:0%
+taking it down to kids going forward so
+the kind of experiment we can do with
+
+ align:start position:0%
+the kind of experiment we can do with
+ 
+
+ align:start position:0%
+the kind of experiment we can do with
+adults is show them these configurations
+
+ align:start position:0%
+adults is show them these configurations
+ 
+
+ align:start position:0%
+adults is show them these configurations
+of blocks and say for example how stable
+
+ align:start position:0%
+of blocks and say for example how stable
+ 
+
+ align:start position:0%
+of blocks and say for example how stable
+under gravity are is one of these
+
+ align:start position:0%
+under gravity are is one of these
+ 
+
+ align:start position:0%
+under gravity are is one of these
+guitars or configurations so you know
+
+ align:start position:0%
+guitars or configurations so you know
+ 
+
+ align:start position:0%
+guitars or configurations so you know
+like everything else you can make a
+
+ align:start position:0%
+like everything else you can make a
+ 
+
+ align:start position:0%
+like everything else you can make a
+judgment on a scale of 0 to 10 or 1 to 7
+
+ align:start position:0%
+judgment on a scale of 0 to 10 or 1 to 7
+ 
+
+ align:start position:0%
+judgment on a scale of 0 to 10 or 1 to 7
+and probably most people would agree
+
+ align:start position:0%
+and probably most people would agree
+ 
+
+ align:start position:0%
+and probably most people would agree
+that the ones in the upper left are
+
+ align:start position:0%
+that the ones in the upper left are
+ 
+
+ align:start position:0%
+that the ones in the upper left are
+relatively stable meaning if you just
+
+ align:start position:0%
+relatively stable meaning if you just
+ 
+
+ align:start position:0%
+relatively stable meaning if you just
+sort of run gravity on it it's not gonna
+
+ align:start position:0%
+sort of run gravity on it it's not gonna
+ 
+
+ align:start position:0%
+sort of run gravity on it it's not gonna
+fall over whereas the ones in the lower
+
+ align:start position:0%
+fall over whereas the ones in the lower
+ 
+
+ align:start position:0%
+fall over whereas the ones in the lower
+right are much more likely to fall under
+
+ align:start position:0%
+right are much more likely to fall under
+ 
+
+ align:start position:0%
+right are much more likely to fall under
+gravity fair enough that's what people
+
+ align:start position:0%
+gravity fair enough that's what people
+ 
+
+ align:start position:0%
+gravity fair enough that's what people
+say ok
+
+ align:start position:0%
+say ok
+ 
+
+ align:start position:0%
+say ok
+so that's the kind of thing we'd like to
+
+ align:start position:0%
+so that's the kind of thing we'd like to
+ 
+
+ align:start position:0%
+so that's the kind of thing we'd like to
+be able to explain as well as many other
+
+ align:start position:0%
+be able to explain as well as many other
+ 
+
+ align:start position:0%
+be able to explain as well as many other
+judgments you could make about this
+
+ align:start position:0%
+judgments you could make about this
+ 
+
+ align:start position:0%
+judgments you could make about this
+simple but not that simple world of
+
+ align:start position:0%
+simple but not that simple world of
+ 
+
+ align:start position:0%
+simple but not that simple world of
+objects and again you can see how in
+
+ align:start position:0%
+objects and again you can see how in
+ 
+
+ align:start position:0%
+objects and again you can see how in
+principle this could very nice the
+
+ align:start position:0%
+principle this could very nice the
+ 
+
+ align:start position:0%
+principle this could very nice the
+interface with what Denis was talking
+
+ align:start position:0%
+interface with what Denis was talking
+ 
+
+ align:start position:0%
+interface with what Denis was talking
+about he talked about their ambition to
+
+ align:start position:0%
+about he talked about their ambition to
+ 
+
+ align:start position:0%
+about he talked about their ambition to
+do the Shirley task which was this
+
+ align:start position:0%
+do the Shirley task which was this
+ 
+
+ align:start position:0%
+do the Shirley task which was this
+ability to basically take have a system
+
+ align:start position:0%
+ability to basically take have a system
+ 
+
+ align:start position:0%
+ability to basically take have a system
+that can take in instructions in
+
+ align:start position:0%
+that can take in instructions in
+ 
+
+ align:start position:0%
+that can take in instructions in
+language and manipulate objects in
+
+ align:start position:0%
+language and manipulate objects in
+ 
+
+ align:start position:0%
+language and manipulate objects in
+blocks world they are very far from that
+
+ align:start position:0%
+blocks world they are very far from that
+ 
+
+ align:start position:0%
+blocks world they are very far from that
+everybody's really far from having a
+
+ align:start position:0%
+everybody's really far from having a
+ 
+
+ align:start position:0%
+everybody's really far from having a
+general-purpose system that can do that
+
+ align:start position:0%
+general-purpose system that can do that
+ 
+
+ align:start position:0%
+general-purpose system that can do that
+in any way like a human does but we
+
+ align:start position:0%
+in any way like a human does but we
+ 
+
+ align:start position:0%
+in any way like a human does but we
+think we're building some of the common
+
+ align:start position:0%
+think we're building some of the common
+ 
+
+ align:start position:0%
+think we're building some of the common
+sense knowledge about the physical world
+
+ align:start position:0%
+sense knowledge about the physical world
+ 
+
+ align:start position:0%
+sense knowledge about the physical world
+that would be necessary to get something
+
+ align:start position:0%
+that would be necessary to get something
+ 
+
+ align:start position:0%
+that would be necessary to get something
+like that to work or to explain how kids
+
+ align:start position:0%
+like that to work or to explain how kids
+ 
+
+ align:start position:0%
+like that to work or to explain how kids
+play with blocks play with each other
+
+ align:start position:0%
+play with blocks play with each other
+ 
+
+ align:start position:0%
+play with blocks play with each other
+talk to each other while they're playing
+
+ align:start position:0%
+talk to each other while they're playing
+ 
+
+ align:start position:0%
+talk to each other while they're playing
+with blocks and so on so the first step
+
+ align:start position:0%
+with blocks and so on so the first step
+ 
+
+ align:start position:0%
+with blocks and so on so the first step
+is the vision part right in this picture
+
+ align:start position:0%
+is the vision part right in this picture
+ 
+
+ align:start position:0%
+is the vision part right in this picture
+here it's that blue graphics arrow
+
+ align:start position:0%
+here it's that blue graphics arrow
+ 
+
+ align:start position:0%
+here it's that blue graphics arrow
+here's another way into it we take we
+
+ align:start position:0%
+here's another way into it we take we
+ 
+
+ align:start position:0%
+here's another way into it we take we
+want to be able to take a 2d image and
+
+ align:start position:0%
+want to be able to take a 2d image and
+ 
+
+ align:start position:0%
+want to be able to take a 2d image and
+work backwards to the world state the
+
+ align:start position:0%
+work backwards to the world state the
+ 
+
+ align:start position:0%
+work backwards to the world state the
+kind of world egg that can support
+
+ align:start position:0%
+kind of world egg that can support
+ 
+
+ align:start position:0%
+kind of world egg that can support
+physical reasoning again when I remember
+
+ align:start position:0%
+physical reasoning again when I remember
+ 
+
+ align:start position:0%
+physical reasoning again when I remember
+these buzzwords call explaining the mind
+
+ align:start position:0%
+these buzzwords call explaining the mind
+ 
+
+ align:start position:0%
+these buzzwords call explaining the mind
+with the generative models that are
+
+ align:start position:0%
+with the generative models that are
+ 
+
+ align:start position:0%
+with the generative models that are
+causal and compositional we want a
+
+ align:start position:0%
+causal and compositional we want a
+ 
+
+ align:start position:0%
+causal and compositional we want a
+description of the world which supports
+
+ align:start position:0%
+description of the world which supports
+ 
+
+ align:start position:0%
+description of the world which supports
+causal reasoning of the sort that
+
+ align:start position:0%
+causal reasoning of the sort that
+ 
+
+ align:start position:0%
+causal reasoning of the sort that
+physics is doing like forces interacting
+
+ align:start position:0%
+physics is doing like forces interacting
+ 
+
+ align:start position:0%
+physics is doing like forces interacting
+with each other so it's got to have
+
+ align:start position:0%
+with each other so it's got to have
+ 
+
+ align:start position:0%
+with each other so it's got to have
+things that can exert force and can
+
+ align:start position:0%
+things that can exert force and can
+ 
+
+ align:start position:0%
+things that can exert force and can
+suffer forces got to have mass in some
+
+ align:start position:0%
+suffer forces got to have mass in some
+ 
+
+ align:start position:0%
+suffer forces got to have mass in some
+form it's got to be compositional
+
+ align:start position:0%
+form it's got to be compositional
+ 
+
+ align:start position:0%
+form it's got to be compositional
+because you got to be able to pick up a
+
+ align:start position:0%
+because you got to be able to pick up a
+ 
+
+ align:start position:0%
+because you got to be able to pick up a
+block and take it away or you know if I
+
+ align:start position:0%
+block and take it away or you know if I
+ 
+
+ align:start position:0%
+block and take it away or you know if I
+have these blocks over here and these
+
+ align:start position:0%
+have these blocks over here and these
+ 
+
+ align:start position:0%
+have these blocks over here and these
+blocks over here and I want to put these
+
+ align:start position:0%
+blocks over here and I want to put these
+ 
+
+ align:start position:0%
+blocks over here and I want to put these
+ones on top of there the world state has
+
+ align:start position:0%
+ones on top of there the world state has
+ 
+
+ align:start position:0%
+ones on top of there the world state has
+to be able to support any number of
+
+ align:start position:0%
+to be able to support any number of
+ 
+
+ align:start position:0%
+to be able to support any number of
+objects in any configuration and to
+
+ align:start position:0%
+objects in any configuration and to
+ 
+
+ align:start position:0%
+objects in any configuration and to
+literally compose a representation of a
+
+ align:start position:0%
+literally compose a representation of a
+ 
+
+ align:start position:0%
+literally compose a representation of a
+world of objects that are composed
+
+ align:start position:0%
+world of objects that are composed
+ 
+
+ align:start position:0%
+world of objects that are composed
+together to make a bigger things so
+
+ align:start position:0%
+together to make a bigger things so
+ 
+
+ align:start position:0%
+together to make a bigger things so
+really the only way we know how to do
+
+ align:start position:0%
+really the only way we know how to do
+ 
+
+ align:start position:0%
+really the only way we know how to do
+that is something like what sometimes in
+
+ align:start position:0%
+that is something like what sometimes in
+ 
+
+ align:start position:0%
+that is something like what sometimes in
+engineering called a CAD model or
+
+ align:start position:0%
+engineering called a CAD model or
+ 
+
+ align:start position:0%
+engineering called a CAD model or
+computer-aided design but it's basically
+
+ align:start position:0%
+computer-aided design but it's basically
+ 
+
+ align:start position:0%
+computer-aided design but it's basically
+a representation of three-dimensional
+
+ align:start position:0%
+a representation of three-dimensional
+ 
+
+ align:start position:0%
+a representation of three-dimensional
+objects often with something like a MASH
+
+ align:start position:0%
+objects often with something like a MASH
+ 
+
+ align:start position:0%
+objects often with something like a MASH
+or a grid of key points with their
+
+ align:start position:0%
+or a grid of key points with their
+ 
+
+ align:start position:0%
+or a grid of key points with their
+masses and Springs for stiffness
+
+ align:start position:0%
+masses and Springs for stiffness
+ 
+
+ align:start position:0%
+masses and Springs for stiffness
+something like that here my only picture
+
+ align:start position:0%
+something like that here my only picture
+ 
+
+ align:start position:0%
+something like that here my only picture
+of the world state looks an awful lot
+
+ align:start position:0%
+of the world state looks an awful lot
+ 
+
+ align:start position:0%
+of the world state looks an awful lot
+like the image only it's in black and
+
+ align:start position:0%
+like the image only it's in black and
+ 
+
+ align:start position:0%
+like the image only it's in black and
+white as head of color but the
+
+ align:start position:0%
+white as head of color but the
+ 
+
+ align:start position:0%
+white as head of color but the
+difference is that the thing on the
+
+ align:start position:0%
+difference is that the thing on the
+ 
+
+ align:start position:0%
+difference is that the thing on the
+bottom is actually an image whereas the
+
+ align:start position:0%
+bottom is actually an image whereas the
+ 
+
+ align:start position:0%
+bottom is actually an image whereas the
+thing on the top is just a 2d projection
+
+ align:start position:0%
+thing on the top is just a 2d projection
+ 
+
+ align:start position:0%
+thing on the top is just a 2d projection
+of a 3d model I'll show you that one
+
+ align:start position:0%
+of a 3d model I'll show you that one
+ 
+
+ align:start position:0%
+of a 3d model I'll show you that one
+I'll show you here's a few others so
+
+ align:start position:0%
+I'll show you here's a few others so
+ 
+
+ align:start position:0%
+I'll show you here's a few others so
+I'll go back and forth between these
+
+ align:start position:0%
+I'll go back and forth between these
+ 
+
+ align:start position:0%
+I'll go back and forth between these
+notice how it kind of looks like the
+
+ align:start position:0%
+notice how it kind of looks like the
+ 
+
+ align:start position:0%
+notice how it kind of looks like the
+blocks are moving around so what's
+
+ align:start position:0%
+blocks are moving around so what's
+ 
+
+ align:start position:0%
+blocks are moving around so what's
+actually going on is these are Sam
+
+ align:start position:0%
+actually going on is these are Sam
+ 
+
+ align:start position:0%
+actually going on is these are Sam
+from the Bayesian posterior in an
+
+ align:start position:0%
+from the Bayesian posterior in an
+ 
+
+ align:start position:0%
+from the Bayesian posterior in an
+inverse graphic system we put a prior on
+
+ align:start position:0%
+inverse graphic system we put a prior on
+ 
+
+ align:start position:0%
+inverse graphic system we put a prior on
+world stage which is basically a prior
+
+ align:start position:0%
+world stage which is basically a prior
+ 
+
+ align:start position:0%
+world stage which is basically a prior
+on what we think the world is made out
+
+ align:start position:0%
+on what we think the world is made out
+ 
+
+ align:start position:0%
+on what we think the world is made out
+of we think there's these Jenga blocks
+
+ align:start position:0%
+of we think there's these Jenga blocks
+ 
+
+ align:start position:0%
+of we think there's these Jenga blocks
+basically um and then the likelihood
+
+ align:start position:0%
+basically um and then the likelihood
+ 
+
+ align:start position:0%
+basically um and then the likelihood
+which is that that forward model it's
+
+ align:start position:0%
+which is that that forward model it's
+ 
+
+ align:start position:0%
+which is that that forward model it's
+the it's the probability of seeing a
+
+ align:start position:0%
+the it's the probability of seeing a
+ 
+
+ align:start position:0%
+the it's the probability of seeing a
+particular 2d image given a 3d
+
+ align:start position:0%
+particular 2d image given a 3d
+ 
+
+ align:start position:0%
+particular 2d image given a 3d
+configuration of blocks and going back
+
+ align:start position:0%
+configuration of blocks and going back
+ 
+
+ align:start position:0%
+configuration of blocks and going back
+to the thing you said it's basically
+
+ align:start position:0%
+to the thing you said it's basically
+ 
+
+ align:start position:0%
+to the thing you said it's basically
+deterministic with a little bit of noise
+
+ align:start position:0%
+deterministic with a little bit of noise
+ 
+
+ align:start position:0%
+deterministic with a little bit of noise
+it's deterministic it just follows the
+
+ align:start position:0%
+it's deterministic it just follows the
+ 
+
+ align:start position:0%
+it's deterministic it just follows the
+rules of OpenGL graphics basically says
+
+ align:start position:0%
+rules of OpenGL graphics basically says
+ 
+
+ align:start position:0%
+rules of OpenGL graphics basically says
+you know objects have surfaces they're
+
+ align:start position:0%
+you know objects have surfaces they're
+ 
+
+ align:start position:0%
+you know objects have surfaces they're
+not transparent you can't see through
+
+ align:start position:0%
+not transparent you can't see through
+ 
+
+ align:start position:0%
+not transparent you can't see through
+them that's an extra complication if you
+
+ align:start position:0%
+them that's an extra complication if you
+ 
+
+ align:start position:0%
+them that's an extra complication if you
+wanted to have that and and basically
+
+ align:start position:0%
+wanted to have that and and basically
+ 
+
+ align:start position:0%
+wanted to have that and and basically
+the image is formed by taking the
+
+ align:start position:0%
+the image is formed by taking the
+ 
+
+ align:start position:0%
+the image is formed by taking the
+closest surface of the closest object
+
+ align:start position:0%
+closest surface of the closest object
+ 
+
+ align:start position:0%
+closest surface of the closest object
+and bouncing a ray of light off of it
+
+ align:start position:0%
+and bouncing a ray of light off of it
+ 
+
+ align:start position:0%
+and bouncing a ray of light off of it
+which really just means taking its color
+
+ align:start position:0%
+which really just means taking its color
+ 
+
+ align:start position:0%
+which really just means taking its color
+and scaling it by intensity it's a very
+
+ align:start position:0%
+and scaling it by intensity it's a very
+ 
+
+ align:start position:0%
+and scaling it by intensity it's a very
+simple shadow model so that's the causal
+
+ align:start position:0%
+simple shadow model so that's the causal
+ 
+
+ align:start position:0%
+simple shadow model so that's the causal
+model and then we can add a little bit
+
+ align:start position:0%
+model and then we can add a little bit
+ 
+
+ align:start position:0%
+model and then we can add a little bit
+of uncertainty like for example maybe we
+
+ align:start position:0%
+of uncertainty like for example maybe we
+ 
+
+ align:start position:0%
+of uncertainty like for example maybe we
+can't you know there's a little bit of
+
+ align:start position:0%
+can't you know there's a little bit of
+ 
+
+ align:start position:0%
+can't you know there's a little bit of
+noise in the sensor data so you can you
+
+ align:start position:0%
+noise in the sensor data so you can you
+ 
+
+ align:start position:0%
+noise in the sensor data so you can you
+know you can be uncertain about exactly
+
+ align:start position:0%
+know you can be uncertain about exactly
+ 
+
+ align:start position:0%
+know you can be uncertain about exactly
+the low-level image features and then
+
+ align:start position:0%
+the low-level image features and then
+ 
+
+ align:start position:0%
+the low-level image features and then
+when you run one of these promising
+
+ align:start position:0%
+when you run one of these promising
+ 
+
+ align:start position:0%
+when you run one of these promising
+programs in Reverse to make a guess of
+
+ align:start position:0%
+programs in Reverse to make a guess of
+ 
+
+ align:start position:0%
+programs in Reverse to make a guess of
+what configuration of locks is most
+
+ align:start position:0%
+what configuration of locks is most
+ 
+
+ align:start position:0%
+what configuration of locks is most
+likely to have produced that image
+
+ align:start position:0%
+likely to have produced that image
+ 
+
+ align:start position:0%
+likely to have produced that image
+there's a little bit of posterior
+
+ align:start position:0%
+there's a little bit of posterior
+ 
+
+ align:start position:0%
+there's a little bit of posterior
+uncertainty that inherits from the fact
+
+ align:start position:0%
+uncertainty that inherits from the fact
+ 
+
+ align:start position:0%
+uncertainty that inherits from the fact
+that you just you know yeah or you can't
+
+ align:start position:0%
+that you just you know yeah or you can't
+ 
+
+ align:start position:0%
+that you just you know yeah or you can't
+exactly localize those objects in the
+
+ align:start position:0%
+exactly localize those objects in the
+ 
+
+ align:start position:0%
+exactly localize those objects in the
+world so again what you see here are
+
+ align:start position:0%
+world so again what you see here are
+ 
+
+ align:start position:0%
+world so again what you see here are
+three or four samples from the posterior
+
+ align:start position:0%
+three or four samples from the posterior
+ 
+
+ align:start position:0%
+three or four samples from the posterior
+the distribution over best guesses of
+
+ align:start position:0%
+the distribution over best guesses of
+ 
+
+ align:start position:0%
+the distribution over best guesses of
+the world state of 3d objects that were
+
+ align:start position:0%
+the world state of 3d objects that were
+ 
+
+ align:start position:0%
+the world state of 3d objects that were
+most likely to have rendered into that
+
+ align:start position:0%
+most likely to have rendered into that
+ 
+
+ align:start position:0%
+most likely to have rendered into that
+2d image and any one of those is now an
+
+ align:start position:0%
+2d image and any one of those is now an
+ 
+
+ align:start position:0%
+2d image and any one of those is now an
+actionable representation for physical
+
+ align:start position:0%
+actionable representation for physical
+ 
+
+ align:start position:0%
+actionable representation for physical
+manipulation or reasoning okay and how
+
+ align:start position:0%
+manipulation or reasoning okay and how
+ 
+
+ align:start position:0%
+manipulation or reasoning okay and how
+we actually compute that again I'm not
+
+ align:start position:0%
+we actually compute that again I'm not
+ 
+
+ align:start position:0%
+we actually compute that again I'm not
+going to go into right now I'll go into
+
+ align:start position:0%
+going to go into right now I'll go into
+ 
+
+ align:start position:0%
+going to go into right now I'll go into
+something something like it in a minute
+
+ align:start position:0%
+something something like it in a minute
+ 
+
+ align:start position:0%
+something something like it in a minute
+but at least in its most basic form it
+
+ align:start position:0%
+but at least in its most basic form it
+ 
+
+ align:start position:0%
+but at least in its most basic form it
+involves some rather unfortunately slow
+
+ align:start position:0%
+involves some rather unfortunately slow
+ 
+
+ align:start position:0%
+involves some rather unfortunately slow
+random search process through the space
+
+ align:start position:0%
+random search process through the space
+ 
+
+ align:start position:0%
+random search process through the space
+of blocks models okay here's another
+
+ align:start position:0%
+of blocks models okay here's another
+ 
+
+ align:start position:0%
+of blocks models okay here's another
+example this is another configuration
+
+ align:start position:0%
+example this is another configuration
+ 
+
+ align:start position:0%
+example this is another configuration
+there or another image and here is a few
+
+ align:start position:0%
+there or another image and here is a few
+ 
+
+ align:start position:0%
+there or another image and here is a few
+samples again from the posterior and
+
+ align:start position:0%
+samples again from the posterior and
+ 
+
+ align:start position:0%
+samples again from the posterior and
+hopefully when you see these things
+
+ align:start position:0%
+hopefully when you see these things
+ 
+
+ align:start position:0%
+hopefully when you see these things
+moving around whether it's this one or
+
+ align:start position:0%
+moving around whether it's this one or
+ 
+
+ align:start position:0%
+moving around whether it's this one or
+the one before you see them move a
+
+ align:start position:0%
+the one before you see them move a
+ 
+
+ align:start position:0%
+the one before you see them move a
+little bit but most of them look very
+
+ align:start position:0%
+little bit but most of them look very
+ 
+
+ align:start position:0%
+little bit but most of them look very
+similar right like you'd be hard-pressed
+
+ align:start position:0%
+similar right like you'd be hard-pressed
+ 
+
+ align:start position:0%
+similar right like you'd be hard-pressed
+to tell the difference if you looked
+
+ align:start position:0%
+to tell the difference if you looked
+ 
+
+ align:start position:0%
+to tell the difference if you looked
+away for a second between any one of
+
+ align:start position:0%
+away for a second between any one of
+ 
+
+ align:start position:0%
+away for a second between any one of
+those like what
+
+ align:start position:0%
+those like what
+ 
+
+ align:start position:0%
+those like what
+one of my are you actually seeing and
+
+ align:start position:0%
+one of my are you actually seeing and
+ 
+
+ align:start position:0%
+one of my are you actually seeing and
+that's exactly the point the the
+
+ align:start position:0%
+that's exactly the point the the
+ 
+
+ align:start position:0%
+that's exactly the point the the
+uncertainty you see there is meant to
+
+ align:start position:0%
+uncertainty you see there is meant to
+ 
+
+ align:start position:0%
+uncertainty you see there is meant to
+capture basically the uncertainty you
+
+ align:start position:0%
+capture basically the uncertainty you
+ 
+
+ align:start position:0%
+capture basically the uncertainty you
+have which in a single glance at an
+
+ align:start position:0%
+have which in a single glance at an
+ 
+
+ align:start position:0%
+have which in a single glance at an
+image like that
+
+ align:start position:0%
+image like that
+ 
+
+ align:start position:0%
+image like that
+you can't perfectly tell where the
+
+ align:start position:0%
+you can't perfectly tell where the
+ 
+
+ align:start position:0%
+you can't perfectly tell where the
+blocks are so basically any one of these
+
+ align:start position:0%
+blocks are so basically any one of these
+ 
+
+ align:start position:0%
+blocks are so basically any one of these
+can fit any one of these configurations
+
+ align:start position:0%
+can fit any one of these configurations
+ 
+
+ align:start position:0%
+can fit any one of these configurations
+up here is about equally good and we
+
+ align:start position:0%
+up here is about equally good and we
+ 
+
+ align:start position:0%
+up here is about equally good and we
+think your intuitive physics your sort
+
+ align:start position:0%
+think your intuitive physics your sort
+ 
+
+ align:start position:0%
+think your intuitive physics your sort
+of common sense core intuitive physics
+
+ align:start position:0%
+of common sense core intuitive physics
+ 
+
+ align:start position:0%
+of common sense core intuitive physics
+that even babies have is operating over
+
+ align:start position:0%
+that even babies have is operating over
+ 
+
+ align:start position:0%
+that even babies have is operating over
+one or a few samples like that now in
+
+ align:start position:0%
+one or a few samples like that now in
+ 
+
+ align:start position:0%
+one or a few samples like that now in
+separate work that is not really I don't
+
+ align:start position:0%
+separate work that is not really I don't
+ 
+
+ align:start position:0%
+separate work that is not really I don't
+think of it as really about common sense
+
+ align:start position:0%
+think of it as really about common sense
+ 
+
+ align:start position:0%
+think of it as really about common sense
+but it's one of the things we've been
+
+ align:start position:0%
+but it's one of the things we've been
+ 
+
+ align:start position:0%
+but it's one of the things we've been
+doing in our group and in CBMM where
+
+ align:start position:0%
+doing in our group and in CBMM where
+ 
+
+ align:start position:0%
+doing in our group and in CBMM where
+these ideas best make contact with the
+
+ align:start position:0%
+these ideas best make contact with the
+ 
+
+ align:start position:0%
+these ideas best make contact with the
+rest of what people are doing here and
+
+ align:start position:0%
+rest of what people are doing here and
+ 
+
+ align:start position:0%
+rest of what people are doing here and
+where we can really test you know
+
+ align:start position:0%
+where we can really test you know
+ 
+
+ align:start position:0%
+where we can really test you know
+interesting neural hypotheses
+
+ align:start position:0%
+interesting neural hypotheses
+ 
+
+ align:start position:0%
+interesting neural hypotheses
+potentially and understand the interplay
+
+ align:start position:0%
+potentially and understand the interplay
+ 
+
+ align:start position:0%
+potentially and understand the interplay
+between these generative models for
+
+ align:start position:0%
+between these generative models for
+ 
+
+ align:start position:0%
+between these generative models for
+explanation and the more sort of neural
+
+ align:start position:0%
+explanation and the more sort of neural
+ 
+
+ align:start position:0%
+explanation and the more sort of neural
+network type models for pattern
+
+ align:start position:0%
+network type models for pattern
+ 
+
+ align:start position:0%
+network type models for pattern
+recognition we've been we've been really
+
+ align:start position:0%
+recognition we've been we've been really
+ 
+
+ align:start position:0%
+recognition we've been we've been really
+pushing on this idea of vision is
+
+ align:start position:0%
+pushing on this idea of vision is
+ 
+
+ align:start position:0%
+pushing on this idea of vision is
+inverse graphics so I'll tell you a
+
+ align:start position:0%
+inverse graphics so I'll tell you a
+ 
+
+ align:start position:0%
+inverse graphics so I'll tell you a
+little bit about that because it's it's
+
+ align:start position:0%
+little bit about that because it's it's
+ 
+
+ align:start position:0%
+little bit about that because it's it's
+quite interesting for CMMI but I want to
+
+ align:start position:0%
+quite interesting for CMMI but I want to
+ 
+
+ align:start position:0%
+quite interesting for CMMI but I want to
+make sure to save I'll only do this for
+
+ align:start position:0%
+make sure to save I'll only do this for
+ 
+
+ align:start position:0%
+make sure to save I'll only do this for
+about five minutes and then go back to
+
+ align:start position:0%
+about five minutes and then go back to
+ 
+
+ align:start position:0%
+about five minutes and then go back to
+the how this gets used for more the
+
+ align:start position:0%
+the how this gets used for more the
+ 
+
+ align:start position:0%
+the how this gets used for more the
+intuitive physics and planning stuff so
+
+ align:start position:0%
+intuitive physics and planning stuff so
+ 
+
+ align:start position:0%
+intuitive physics and planning stuff so
+this is this is example an example from
+
+ align:start position:0%
+this is this is example an example from
+ 
+
+ align:start position:0%
+this is this is example an example from
+a paper by Tejas Kulkarni who's one of
+
+ align:start position:0%
+a paper by Tejas Kulkarni who's one of
+ 
+
+ align:start position:0%
+a paper by Tejas Kulkarni who's one of
+our grad students and it's joint work
+
+ align:start position:0%
+our grad students and it's joint work
+ 
+
+ align:start position:0%
+our grad students and it's joint work
+with a few other really smart people
+
+ align:start position:0%
+with a few other really smart people
+ 
+
+ align:start position:0%
+with a few other really smart people
+such as Vikash man Singha who's a
+
+ align:start position:0%
+such as Vikash man Singha who's a
+ 
+
+ align:start position:0%
+such as Vikash man Singha who's a
+research scientist at MIT and pushed me
+
+ align:start position:0%
+research scientist at MIT and pushed me
+ 
+
+ align:start position:0%
+research scientist at MIT and pushed me
+coley who's at Microsoft Research and it
+
+ align:start position:0%
+coley who's at Microsoft Research and it
+ 
+
+ align:start position:0%
+coley who's at Microsoft Research and it
+was a computer vision paper pure
+
+ align:start position:0%
+was a computer vision paper pure
+ 
+
+ align:start position:0%
+was a computer vision paper pure
+computer vision paper from the summer
+
+ align:start position:0%
+computer vision paper from the summer
+ 
+
+ align:start position:0%
+computer vision paper from the summer
+where he was developing a general or it
+
+ align:start position:0%
+where he was developing a general or it
+ 
+
+ align:start position:0%
+where he was developing a general or it
+was a specific kind of problems like
+
+ align:start position:0%
+was a specific kind of problems like
+ 
+
+ align:start position:0%
+was a specific kind of problems like
+programming language but a general one
+
+ align:start position:0%
+programming language but a general one
+ 
+
+ align:start position:0%
+programming language but a general one
+for doing this kind of vision as inverse
+
+ align:start position:0%
+for doing this kind of vision as inverse
+ 
+
+ align:start position:0%
+for doing this kind of vision as inverse
+graphics where you would you could give
+
+ align:start position:0%
+graphics where you would you could give
+ 
+
+ align:start position:0%
+graphics where you would you could give
+a number of different models here I'll
+
+ align:start position:0%
+a number of different models here I'll
+ 
+
+ align:start position:0%
+a number of different models here I'll
+show you one for faces and other one for
+
+ align:start position:0%
+show you one for faces and other one for
+ 
+
+ align:start position:0%
+show you one for faces and other one for
+bodies and other one for generic objects
+
+ align:start position:0%
+bodies and other one for generic objects
+ 
+
+ align:start position:0%
+bodies and other one for generic objects
+but basically you you can pretty easily
+
+ align:start position:0%
+but basically you you can pretty easily
+ 
+
+ align:start position:0%
+but basically you you can pretty easily
+specify a graphics model that when you
+
+ align:start position:0%
+specify a graphics model that when you
+ 
+
+ align:start position:0%
+specify a graphics model that when you
+run it in the forward Direction
+
+ align:start position:0%
+run it in the forward Direction
+ 
+
+ align:start position:0%
+run it in the forward Direction
+generates random images of objects in a
+
+ align:start position:0%
+generates random images of objects in a
+ 
+
+ align:start position:0%
+generates random images of objects in a
+certain class and then you can run it in
+
+ align:start position:0%
+certain class and then you can run it in
+ 
+
+ align:start position:0%
+certain class and then you can run it in
+the reverse direction to do scene
+
+ align:start position:0%
+the reverse direction to do scene
+ 
+
+ align:start position:0%
+the reverse direction to do scene
+parsing to go from the image to the
+
+ align:start position:0%
+parsing to go from the image to the
+ 
+
+ align:start position:0%
+parsing to go from the image to the
+observe or to the underlying scene so
+
+ align:start position:0%
+observe or to the underlying scene so
+ 
+
+ align:start position:0%
+observe or to the underlying scene so
+here's an example of this in phases
+
+ align:start position:0%
+here's an example of this in phases
+ 
+
+ align:start position:0%
+here's an example of this in phases
+where the graphics model it's it's it's
+
+ align:start position:0%
+where the graphics model it's it's it's
+ 
+
+ align:start position:0%
+where the graphics model it's it's it's
+really very directly based on work that
+
+ align:start position:0%
+really very directly based on work that
+ 
+
+ align:start position:0%
+really very directly based on work that
+Thomas Vetter who was a former a student
+
+ align:start position:0%
+Thomas Vetter who was a former a student
+ 
+
+ align:start position:0%
+Thomas Vetter who was a former a student
+or a postdoc of Tommy's actually so kind
+
+ align:start position:0%
+or a postdoc of Tommy's actually so kind
+ 
+
+ align:start position:0%
+or a postdoc of Tommy's actually so kind
+of a early ancestor of CBMM built and
+
+ align:start position:0%
+of a early ancestor of CBMM built and
+ 
+
+ align:start position:0%
+of a early ancestor of CBMM built and
+his group in Basel Switzerland
+
+ align:start position:0%
+his group in Basel Switzerland
+ 
+
+ align:start position:0%
+his group in Basel Switzerland
+where it's it's a simple but still
+
+ align:start position:0%
+where it's it's a simple but still
+ 
+
+ align:start position:0%
+where it's it's a simple but still
+pretty nice graphics model for making
+
+ align:start position:0%
+pretty nice graphics model for making
+ 
+
+ align:start position:0%
+pretty nice graphics model for making
+face images there's a model of the shape
+
+ align:start position:0%
+face images there's a model of the shape
+ 
+
+ align:start position:0%
+face images there's a model of the shape
+of the face which again it's like a CAD
+
+ align:start position:0%
+of the face which again it's like a CAD
+ 
+
+ align:start position:0%
+of the face which again it's like a CAD
+model it's a it's a mesh surface
+
+ align:start position:0%
+model it's a it's a mesh surface
+ 
+
+ align:start position:0%
+model it's a it's a mesh surface
+description pretty fine grained
+
+ align:start position:0%
+description pretty fine grained
+ 
+
+ align:start position:0%
+description pretty fine grained
+structure of the 2d but surface of a
+
+ align:start position:0%
+structure of the 2d but surface of a
+ 
+
+ align:start position:0%
+structure of the 2d but surface of a
+face in 3d and there's about 400
+
+ align:start position:0%
+face in 3d and there's about 400
+ 
+
+ align:start position:0%
+face in 3d and there's about 400
+dimensions to characterize the possible
+
+ align:start position:0%
+dimensions to characterize the possible
+ 
+
+ align:start position:0%
+dimensions to characterize the possible
+shapes of faces and there's another four
+
+ align:start position:0%
+shapes of faces and there's another four
+ 
+
+ align:start position:0%
+shapes of faces and there's another four
+in two dimensions to characterize the
+
+ align:start position:0%
+in two dimensions to characterize the
+ 
+
+ align:start position:0%
+in two dimensions to characterize the
+texture which is like the skin the beard
+
+ align:start position:0%
+texture which is like the skin the beard
+ 
+
+ align:start position:0%
+texture which is like the skin the beard
+the eyes you know the color and surface
+
+ align:start position:0%
+the eyes you know the color and surface
+ 
+
+ align:start position:0%
+the eyes you know the color and surface
+properties that get mapped on top of the
+
+ align:start position:0%
+properties that get mapped on top of the
+ 
+
+ align:start position:0%
+properties that get mapped on top of the
+mesh and then there's a little bit more
+
+ align:start position:0%
+mesh and then there's a little bit more
+ 
+
+ align:start position:0%
+mesh and then there's a little bit more
+graphic stuff which is generic not
+
+ align:start position:0%
+graphic stuff which is generic not
+ 
+
+ align:start position:0%
+graphic stuff which is generic not
+specific to faces that stuff is all
+
+ align:start position:0%
+specific to faces that stuff is all
+ 
+
+ align:start position:0%
+specific to faces that stuff is all
+specific to faces but then there's a
+
+ align:start position:0%
+specific to faces but then there's a
+ 
+
+ align:start position:0%
+specific to faces but then there's a
+simple lighting model so you basically
+
+ align:start position:0%
+simple lighting model so you basically
+ 
+
+ align:start position:0%
+simple lighting model so you basically
+have a point light source somewhere out
+
+ align:start position:0%
+have a point light source somewhere out
+ 
+
+ align:start position:0%
+have a point light source somewhere out
+there and you shine the light on the
+
+ align:start position:0%
+there and you shine the light on the
+ 
+
+ align:start position:0%
+there and you shine the light on the
+face it can produce shadows of course
+
+ align:start position:0%
+face it can produce shadows of course
+ 
+
+ align:start position:0%
+face it can produce shadows of course
+but not very complicated ones and then
+
+ align:start position:0%
+but not very complicated ones and then
+ 
+
+ align:start position:0%
+but not very complicated ones and then
+there's a viewpoint camera thing so you
+
+ align:start position:0%
+there's a viewpoint camera thing so you
+ 
+
+ align:start position:0%
+there's a viewpoint camera thing so you
+put the light source somewhere and you
+
+ align:start position:0%
+put the light source somewhere and you
+ 
+
+ align:start position:0%
+put the light source somewhere and you
+put a camera somewhere specifying the
+
+ align:start position:0%
+put a camera somewhere specifying the
+ 
+
+ align:start position:0%
+put a camera somewhere specifying the
+viewpoint and the combination of these
+
+ align:start position:0%
+viewpoint and the combination of these
+ 
+
+ align:start position:0%
+viewpoint and the combination of these
+shape texture lighting and camera give
+
+ align:start position:0%
+shape texture lighting and camera give
+ 
+
+ align:start position:0%
+shape texture lighting and camera give
+you a complete graphic specification it
+
+ align:start position:0%
+you a complete graphic specification it
+ 
+
+ align:start position:0%
+you a complete graphic specification it
+produces an image of a particular face
+
+ align:start position:0%
+produces an image of a particular face
+ 
+
+ align:start position:0%
+produces an image of a particular face
+lit from a particular direction and
+
+ align:start position:0%
+lit from a particular direction and
+ 
+
+ align:start position:0%
+lit from a particular direction and
+viewed from some particular viewpoint
+
+ align:start position:0%
+viewed from some particular viewpoint
+ 
+
+ align:start position:0%
+viewed from some particular viewpoint
+and distance and what you see on the
+
+ align:start position:0%
+and distance and what you see on the
+ 
+
+ align:start position:0%
+and distance and what you see on the
+right are random samples from this
+
+ align:start position:0%
+right are random samples from this
+ 
+
+ align:start position:0%
+right are random samples from this
+probabilistic program this generative
+
+ align:start position:0%
+probabilistic program this generative
+ 
+
+ align:start position:0%
+probabilistic program this generative
+model so you can just write this program
+
+ align:start position:0%
+model so you can just write this program
+ 
+
+ align:start position:0%
+model so you can just write this program
+and press go go-go-go-go and every time
+
+ align:start position:0%
+and press go go-go-go-go and every time
+ 
+
+ align:start position:0%
+and press go go-go-go-go and every time
+you run it you get a new face viewed
+
+ align:start position:0%
+you run it you get a new face viewed
+ 
+
+ align:start position:0%
+you run it you get a new face viewed
+from a new direction and lighting
+
+ align:start position:0%
+from a new direction and lighting
+ 
+
+ align:start position:0%
+from a new direction and lighting
+condition so that's the prior now what
+
+ align:start position:0%
+condition so that's the prior now what
+ 
+
+ align:start position:0%
+condition so that's the prior now what
+about inference well the idea of vision
+
+ align:start position:0%
+about inference well the idea of vision
+ 
+
+ align:start position:0%
+about inference well the idea of vision
+is inverse graphics is to say take a
+
+ align:start position:0%
+is inverse graphics is to say take a
+ 
+
+ align:start position:0%
+is inverse graphics is to say take a
+real image of a face like that one and
+
+ align:start position:0%
+real image of a face like that one and
+ 
+
+ align:start position:0%
+real image of a face like that one and
+see if you can produce from your
+
+ align:start position:0%
+see if you can produce from your
+ 
+
+ align:start position:0%
+see if you can produce from your
+graphics model something that looks like
+
+ align:start position:0%
+graphics model something that looks like
+ 
+
+ align:start position:0%
+graphics model something that looks like
+that so for example here in the lower
+
+ align:start position:0%
+that so for example here in the lower
+ 
+
+ align:start position:0%
+that so for example here in the lower
+left is an example of a face that was
+
+ align:start position:0%
+left is an example of a face that was
+ 
+
+ align:start position:0%
+left is an example of a face that was
+produced from the graphics model but
+
+ align:start position:0%
+produced from the graphics model but
+ 
+
+ align:start position:0%
+produced from the graphics model but
+hopefully most agree looks kind of like
+
+ align:start position:0%
+hopefully most agree looks kind of like
+ 
+
+ align:start position:0%
+hopefully most agree looks kind of like
+that not maybe not exactly the same but
+
+ align:start position:0%
+that not maybe not exactly the same but
+ 
+
+ align:start position:0%
+that not maybe not exactly the same but
+kind of enough and in building this
+
+ align:start position:0%
+kind of enough and in building this
+ 
+
+ align:start position:0%
+kind of enough and in building this
+system this pic this system by the way
+
+ align:start position:0%
+system this pic this system by the way
+ 
+
+ align:start position:0%
+system this pic this system by the way
+is called picture that's the first word
+
+ align:start position:0%
+is called picture that's the first word
+ 
+
+ align:start position:0%
+is called picture that's the first word
+of the paper title to the Kulkarni a
+
+ align:start position:0%
+of the paper title to the Kulkarni a
+ 
+
+ align:start position:0%
+of the paper title to the Kulkarni a
+tall paper um there were a few neat
+
+ align:start position:0%
+tall paper um there were a few neat
+ 
+
+ align:start position:0%
+tall paper um there were a few neat
+things that had to be done one of the
+
+ align:start position:0%
+things that had to be done one of the
+ 
+
+ align:start position:0%
+things that had to be done one of the
+things that had to be done was to come
+
+ align:start position:0%
+things that had to be done was to come
+ 
+
+ align:start position:0%
+things that had to be done was to come
+up with various ways to compare to to
+
+ align:start position:0%
+up with various ways to compare to to
+ 
+
+ align:start position:0%
+up with various ways to compare to to
+say what does it mean for the output of
+
+ align:start position:0%
+say what does it mean for the output of
+ 
+
+ align:start position:0%
+say what does it mean for the output of
+the graphics engine to look like the
+
+ align:start position:0%
+the graphics engine to look like the
+ 
+
+ align:start position:0%
+the graphics engine to look like the
+image in the case of faces actually
+
+ align:start position:0%
+image in the case of faces actually
+ 
+
+ align:start position:0%
+image in the case of faces actually
+matching at pixels is not completely
+
+ align:start position:0%
+matching at pixels is not completely
+ 
+
+ align:start position:0%
+matching at pixels is not completely
+crazy but for many most vision problems
+
+ align:start position:0%
+crazy but for many most vision problems
+ 
+
+ align:start position:0%
+crazy but for many most vision problems
+you're it's going to be unrealistic and
+
+ align:start position:0%
+you're it's going to be unrealistic and
+ 
+
+ align:start position:0%
+you're it's going to be unrealistic and
+not unnecessary to build a graphics
+
+ align:start position:0%
+not unnecessary to build a graphics
+ 
+
+ align:start position:0%
+not unnecessary to build a graphics
+engine that's pixel level realistic and
+
+ align:start position:0%
+engine that's pixel level realistic and
+ 
+
+ align:start position:0%
+engine that's pixel level realistic and
+so you might frig
+
+ align:start position:0%
+so you might frig
+ 
+
+ align:start position:0%
+so you might frig
+people want to have something where the
+
+ align:start position:0%
+people want to have something where the
+ 
+
+ align:start position:0%
+people want to have something where the
+graphics engine hypothesis is matched to
+
+ align:start position:0%
+graphics engine hypothesis is matched to
+ 
+
+ align:start position:0%
+graphics engine hypothesis is matched to
+the image with something like some kind
+
+ align:start position:0%
+the image with something like some kind
+ 
+
+ align:start position:0%
+the image with something like some kind
+of features like could be convolutional
+
+ align:start position:0%
+of features like could be convolutional
+ 
+
+ align:start position:0%
+of features like could be convolutional
+neural network features that's one way
+
+ align:start position:0%
+neural network features that's one way
+ 
+
+ align:start position:0%
+neural network features that's one way
+to use for example neural networks to
+
+ align:start position:0%
+to use for example neural networks to
+ 
+
+ align:start position:0%
+to use for example neural networks to
+make something like this work well and
+
+ align:start position:0%
+make something like this work well and
+ 
+
+ align:start position:0%
+make something like this work well and
+John John just showed me a paper by some
+
+ align:start position:0%
+John John just showed me a paper by some
+ 
+
+ align:start position:0%
+John John just showed me a paper by some
+other folks from Darmstadt which is
+
+ align:start position:0%
+other folks from Darmstadt which is
+ 
+
+ align:start position:0%
+other folks from Darmstadt which is
+doing what looks like a very interesting
+
+ align:start position:0%
+doing what looks like a very interesting
+ 
+
+ align:start position:0%
+doing what looks like a very interesting
+similar kind of thing
+
+ align:start position:0%
+similar kind of thing
+ 
+
+ align:start position:0%
+similar kind of thing
+let me let me show what what inference
+
+ align:start position:0%
+let me let me show what what inference
+ 
+
+ align:start position:0%
+let me let me show what what inference
+looks like in this model and then say
+
+ align:start position:0%
+looks like in this model and then say
+ 
+
+ align:start position:0%
+looks like in this model and then say
+what I think is an even more interesting
+
+ align:start position:0%
+what I think is an even more interesting
+ 
+
+ align:start position:0%
+what I think is an even more interesting
+way to use convolutional nets from
+
+ align:start position:0%
+way to use convolutional nets from
+ 
+
+ align:start position:0%
+way to use convolutional nets from
+another recent paper we've been looking
+
+ align:start position:0%
+another recent paper we've been looking
+ 
+
+ align:start position:0%
+another recent paper we've been looking
+at so here's um you just watch this this
+
+ align:start position:0%
+at so here's um you just watch this this
+ 
+
+ align:start position:0%
+at so here's um you just watch this this
+is one observed face and what you're
+
+ align:start position:0%
+is one observed face and what you're
+ 
+
+ align:start position:0%
+is one observed face and what you're
+seeing over here is just a trace of the
+
+ align:start position:0%
+seeing over here is just a trace of the
+ 
+
+ align:start position:0%
+seeing over here is just a trace of the
+system kind of do searching through the
+
+ align:start position:0%
+system kind of do searching through the
+ 
+
+ align:start position:0%
+system kind of do searching through the
+space of traces of the graphics program
+
+ align:start position:0%
+space of traces of the graphics program
+ 
+
+ align:start position:0%
+space of traces of the graphics program
+like basically trying out random faces
+
+ align:start position:0%
+like basically trying out random faces
+ 
+
+ align:start position:0%
+like basically trying out random faces
+that might look like that face there
+
+ align:start position:0%
+that might look like that face there
+ 
+
+ align:start position:0%
+that might look like that face there
+it's using a kind of MCMC inference very
+
+ align:start position:0%
+it's using a kind of MCMC inference very
+ 
+
+ align:start position:0%
+it's using a kind of MCMC inference very
+similar to what you're going to see from
+
+ align:start position:0%
+similar to what you're going to see from
+ 
+
+ align:start position:0%
+similar to what you're going to see from
+Tomer in the tutorial um it basically
+
+ align:start position:0%
+Tomer in the tutorial um it basically
+ 
+
+ align:start position:0%
+Tomer in the tutorial um it basically
+starts off with a random face and takes
+
+ align:start position:0%
+starts off with a random face and takes
+ 
+
+ align:start position:0%
+starts off with a random face and takes
+a bunch of small random steps that are
+
+ align:start position:0%
+a bunch of small random steps that are
+ 
+
+ align:start position:0%
+a bunch of small random steps that are
+biased towards getting making the image
+
+ align:start position:0%
+biased towards getting making the image
+ 
+
+ align:start position:0%
+biased towards getting making the image
+look more and more like the actual
+
+ align:start position:0%
+look more and more like the actual
+ 
+
+ align:start position:0%
+look more and more like the actual
+observed image right and at the end you
+
+ align:start position:0%
+observed image right and at the end you
+ 
+
+ align:start position:0%
+observed image right and at the end you
+have something which looks almost
+
+ align:start position:0%
+have something which looks almost
+ 
+
+ align:start position:0%
+have something which looks almost
+identical to the observed face right but
+
+ align:start position:0%
+identical to the observed face right but
+ 
+
+ align:start position:0%
+identical to the observed face right but
+key right oh is that though the observed
+
+ align:start position:0%
+key right oh is that though the observed
+ 
+
+ align:start position:0%
+key right oh is that though the observed
+face is literally just a 2d image the
+
+ align:start position:0%
+face is literally just a 2d image the
+ 
+
+ align:start position:0%
+face is literally just a 2d image the
+thing you're seeing on the right is a
+
+ align:start position:0%
+thing you're seeing on the right is a
+ 
+
+ align:start position:0%
+thing you're seeing on the right is a
+projection of a 3d model of a face and
+
+ align:start position:0%
+projection of a 3d model of a face and
+ 
+
+ align:start position:0%
+projection of a 3d model of a face and
+it's one that supports a lot of causal
+
+ align:start position:0%
+it's one that supports a lot of causal
+ 
+
+ align:start position:0%
+it's one that supports a lot of causal
+action right so here just to show you on
+
+ align:start position:0%
+action right so here just to show you on
+ 
+
+ align:start position:0%
+action right so here just to show you on
+a more interesting sort of higher
+
+ align:start position:0%
+a more interesting sort of higher
+ 
+
+ align:start position:0%
+a more interesting sort of higher
+resolution set of face images the ones
+
+ align:start position:0%
+resolution set of face images the ones
+ 
+
+ align:start position:0%
+resolution set of face images the ones
+on the left are observed images and then
+
+ align:start position:0%
+on the left are observed images and then
+ 
+
+ align:start position:0%
+on the left are observed images and then
+we do this we fit this model and then we
+
+ align:start position:0%
+we do this we fit this model and then we
+ 
+
+ align:start position:0%
+we do this we fit this model and then we
+can rotate it around and change the
+
+ align:start position:0%
+can rotate it around and change the
+ 
+
+ align:start position:0%
+can rotate it around and change the
+lighting if we had parameters that
+
+ align:start position:0%
+lighting if we had parameters that
+ 
+
+ align:start position:0%
+lighting if we had parameters that
+controlled expression there's no real
+
+ align:start position:0%
+controlled expression there's no real
+ 
+
+ align:start position:0%
+controlled expression there's no real
+expression parameters here that wouldn't
+
+ align:start position:0%
+expression parameters here that wouldn't
+ 
+
+ align:start position:0%
+expression parameters here that wouldn't
+be too hard to put in you can make the
+
+ align:start position:0%
+be too hard to put in you can make the
+ 
+
+ align:start position:0%
+be too hard to put in you can make the
+face happy or sad but you can see that
+
+ align:start position:0%
+face happy or sad but you can see that
+ 
+
+ align:start position:0%
+face happy or sad but you can see that
+that hopefully what you can see is that
+
+ align:start position:0%
+that hopefully what you can see is that
+ 
+
+ align:start position:0%
+that hopefully what you can see is that
+the recovered model supports fairly
+
+ align:start position:0%
+the recovered model supports fairly
+ 
+
+ align:start position:0%
+the recovered model supports fairly
+reasonable generalization to other
+
+ align:start position:0%
+reasonable generalization to other
+ 
+
+ align:start position:0%
+reasonable generalization to other
+viewpoints and lighting conditions it's
+
+ align:start position:0%
+viewpoints and lighting conditions it's
+ 
+
+ align:start position:0%
+viewpoints and lighting conditions it's
+the sort of thing that should make for
+
+ align:start position:0%
+the sort of thing that should make for
+ 
+
+ align:start position:0%
+the sort of thing that should make for
+more robust face recognition although
+
+ align:start position:0%
+more robust face recognition although
+ 
+
+ align:start position:0%
+more robust face recognition although
+that's not the main focus of what we're
+
+ align:start position:0%
+that's not the main focus of what we're
+ 
+
+ align:start position:0%
+that's not the main focus of what we're
+trying to use it here I just want to
+
+ align:start position:0%
+trying to use it here I just want to
+ 
+
+ align:start position:0%
+trying to use it here I just want to
+emphasize there's all sorts of things
+
+ align:start position:0%
+emphasize there's all sorts of things
+ 
+
+ align:start position:0%
+emphasize there's all sorts of things
+that would be useful if you had an
+
+ align:start position:0%
+that would be useful if you had an
+ 
+
+ align:start position:0%
+that would be useful if you had an
+actual 3d model of the face you could
+
+ align:start position:0%
+actual 3d model of the face you could
+ 
+
+ align:start position:0%
+actual 3d model of the face you could
+get from a single image or here's the
+
+ align:start position:0%
+get from a single image or here's the
+ 
+
+ align:start position:0%
+get from a single image or here's the
+same kind of idea now for a body pose
+
+ align:start position:0%
+same kind of idea now for a body pose
+ 
+
+ align:start position:0%
+same kind of idea now for a body pose
+system so now the image we're going to
+
+ align:start position:0%
+system so now the image we're going to
+ 
+
+ align:start position:0%
+system so now the image we're going to
+assume has a
+
+ align:start position:0%
+assume has a
+ 
+
+ align:start position:0%
+assume has a
+in it somewhere doing something remember
+
+ align:start position:0%
+in it somewhere doing something remember
+ 
+
+ align:start position:0%
+in it somewhere doing something remember
+back to that challenge I gave at the
+
+ align:start position:0%
+back to that challenge I gave at the
+ 
+
+ align:start position:0%
+back to that challenge I gave at the
+beginning about finding the bodies in a
+
+ align:start position:0%
+beginning about finding the bodies in a
+ 
+
+ align:start position:0%
+beginning about finding the bodies in a
+complex scene like the airplane full of
+
+ align:start position:0%
+complex scene like the airplane full of
+ 
+
+ align:start position:0%
+complex scene like the airplane full of
+computer vision researchers um and and
+
+ align:start position:0%
+computer vision researchers um and and
+ 
+
+ align:start position:0%
+computer vision researchers um and and
+whereas you know you found the right
+
+ align:start position:0%
+whereas you know you found the right
+ 
+
+ align:start position:0%
+whereas you know you found the right
+hand or the left toe right so we think
+
+ align:start position:0%
+hand or the left toe right so we think
+ 
+
+ align:start position:0%
+hand or the left toe right so we think
+that in order to do that you know you
+
+ align:start position:0%
+that in order to do that you know you
+ 
+
+ align:start position:0%
+that in order to do that you know you
+think you have to have something like an
+
+ align:start position:0%
+think you have to have something like an
+ 
+
+ align:start position:0%
+think you have to have something like an
+actual 3d model of a body what you see
+
+ align:start position:0%
+actual 3d model of a body what you see
+ 
+
+ align:start position:0%
+actual 3d model of a body what you see
+on the lower left is a bunch of samples
+
+ align:start position:0%
+on the lower left is a bunch of samples
+ 
+
+ align:start position:0%
+on the lower left is a bunch of samples
+from this so we basically just took a
+
+ align:start position:0%
+from this so we basically just took a
+ 
+
+ align:start position:0%
+from this so we basically just took a
+kind of an interesting 3d stick figure
+
+ align:start position:0%
+kind of an interesting 3d stick figure
+ 
+
+ align:start position:0%
+kind of an interesting 3d stick figure
+skeleton model and just put some some
+
+ align:start position:0%
+skeleton model and just put some some
+ 
+
+ align:start position:0%
+skeleton model and just put some some
+knobs on it you can tweak it around you
+
+ align:start position:0%
+knobs on it you can tweak it around you
+ 
+
+ align:start position:0%
+knobs on it you can tweak it around you
+can put some simple probability models
+
+ align:start position:0%
+can put some simple probability models
+ 
+
+ align:start position:0%
+can put some simple probability models
+to get a prior and these are just random
+
+ align:start position:0%
+to get a prior and these are just random
+ 
+
+ align:start position:0%
+to get a prior and these are just random
+samples of random body positions and the
+
+ align:start position:0%
+samples of random body positions and the
+ 
+
+ align:start position:0%
+samples of random body positions and the
+idea of the system is to kind of search
+
+ align:start position:0%
+idea of the system is to kind of search
+ 
+
+ align:start position:0%
+idea of the system is to kind of search
+through that space of body positions
+
+ align:start position:0%
+through that space of body positions
+ 
+
+ align:start position:0%
+through that space of body positions
+until you find one that which then when
+
+ align:start position:0%
+until you find one that which then when
+ 
+
+ align:start position:0%
+until you find one that which then when
+you project it from a certain camera
+
+ align:start position:0%
+you project it from a certain camera
+ 
+
+ align:start position:0%
+you project it from a certain camera
+angle looks like the body you're seeing
+
+ align:start position:0%
+angle looks like the body you're seeing
+ 
+
+ align:start position:0%
+angle looks like the body you're seeing
+so here's an example of this in action
+
+ align:start position:0%
+so here's an example of this in action
+ 
+
+ align:start position:0%
+so here's an example of this in action
+this is some guy I guess Usain Bolt so
+
+ align:start position:0%
+this is some guy I guess Usain Bolt so
+ 
+
+ align:start position:0%
+this is some guy I guess Usain Bolt so
+I'm kind of interesting slightly unusual
+
+ align:start position:0%
+I'm kind of interesting slightly unusual
+ 
+
+ align:start position:0%
+I'm kind of interesting slightly unusual
+pose as he's about to break the finish
+
+ align:start position:0%
+pose as he's about to break the finish
+ 
+
+ align:start position:0%
+pose as he's about to break the finish
+line maybe and here's the system in
+
+ align:start position:0%
+line maybe and here's the system in
+ 
+
+ align:start position:0%
+line maybe and here's the system in
+action so it starts off from a random
+
+ align:start position:0%
+action so it starts off from a random
+ 
+
+ align:start position:0%
+action so it starts off from a random
+position and again sort of takes some
+
+ align:start position:0%
+position and again sort of takes some
+ 
+
+ align:start position:0%
+position and again sort of takes some
+sticks a bunch of random steps in moving
+
+ align:start position:0%
+sticks a bunch of random steps in moving
+ 
+
+ align:start position:0%
+sticks a bunch of random steps in moving
+around in 3d space until it finds a
+
+ align:start position:0%
+around in 3d space until it finds a
+ 
+
+ align:start position:0%
+around in 3d space until it finds a
+configuration which when you project it
+
+ align:start position:0%
+configuration which when you project it
+ 
+
+ align:start position:0%
+configuration which when you project it
+into the image looks like what you see
+
+ align:start position:0%
+into the image looks like what you see
+ 
+
+ align:start position:0%
+into the image looks like what you see
+there now just wants a notice a key
+
+ align:start position:0%
+there now just wants a notice a key
+ 
+
+ align:start position:0%
+there now just wants a notice a key
+difference when I say looks like it
+
+ align:start position:0%
+difference when I say looks like it
+ 
+
+ align:start position:0%
+difference when I say looks like it
+doesn't look like it at the pixel level
+
+ align:start position:0%
+doesn't look like it at the pixel level
+ 
+
+ align:start position:0%
+doesn't look like it at the pixel level
+like the face did right it's only
+
+ align:start position:0%
+like the face did right it's only
+ 
+
+ align:start position:0%
+like the face did right it's only
+matching at the level of these basically
+
+ align:start position:0%
+matching at the level of these basically
+ 
+
+ align:start position:0%
+matching at the level of these basically
+enhanced edge statistics which you see
+
+ align:start position:0%
+enhanced edge statistics which you see
+ 
+
+ align:start position:0%
+enhanced edge statistics which you see
+here so this is an example of building a
+
+ align:start position:0%
+here so this is an example of building a
+ 
+
+ align:start position:0%
+here so this is an example of building a
+model it's not a photorealistic render
+
+ align:start position:0%
+model it's not a photorealistic render
+ 
+
+ align:start position:0%
+model it's not a photorealistic render
+it's this is this is the graphics model
+
+ align:start position:0%
+it's this is this is the graphics model
+ 
+
+ align:start position:0%
+it's this is this is the graphics model
+is all is not trying to match the image
+
+ align:start position:0%
+is all is not trying to match the image
+ 
+
+ align:start position:0%
+is all is not trying to match the image
+it's trying to match this or it could be
+
+ align:start position:0%
+it's trying to match this or it could be
+ 
+
+ align:start position:0%
+it's trying to match this or it could be
+for example some intermediate level of
+
+ align:start position:0%
+for example some intermediate level of
+ 
+
+ align:start position:0%
+for example some intermediate level of
+continent features and we think this is
+
+ align:start position:0%
+continent features and we think this is
+ 
+
+ align:start position:0%
+continent features and we think this is
+very powerful because more generally
+
+ align:start position:0%
+very powerful because more generally
+ 
+
+ align:start position:0%
+very powerful because more generally
+while we might have a really detailed
+
+ align:start position:0%
+while we might have a really detailed
+ 
+
+ align:start position:0%
+while we might have a really detailed
+model of facial appearance you know for
+
+ align:start position:0%
+model of facial appearance you know for
+ 
+
+ align:start position:0%
+model of facial appearance you know for
+bodies we don't have a good clothing
+
+ align:start position:0%
+bodies we don't have a good clothing
+ 
+
+ align:start position:0%
+bodies we don't have a good clothing
+model we're not trying to model the skin
+
+ align:start position:0%
+model we're not trying to model the skin
+ 
+
+ align:start position:0%
+model we're not trying to model the skin
+it's you know it's it's we're just
+
+ align:start position:0%
+it's you know it's it's we're just
+ 
+
+ align:start position:0%
+it's you know it's it's we're just
+trying to model just enough to solve the
+
+ align:start position:0%
+trying to model just enough to solve the
+ 
+
+ align:start position:0%
+trying to model just enough to solve the
+problem were interested in and again
+
+ align:start position:0%
+problem were interested in and again
+ 
+
+ align:start position:0%
+problem were interested in and again
+this is reflective of a much more broad
+
+ align:start position:0%
+this is reflective of a much more broad
+ 
+
+ align:start position:0%
+this is reflective of a much more broad
+theme and this idea of intelligence as
+
+ align:start position:0%
+theme and this idea of intelligence as
+ 
+
+ align:start position:0%
+theme and this idea of intelligence as
+explanation called you know modeling the
+
+ align:start position:0%
+explanation called you know modeling the
+ 
+
+ align:start position:0%
+explanation called you know modeling the
+causal structure of the world we don't
+
+ align:start position:0%
+causal structure of the world we don't
+ 
+
+ align:start position:0%
+causal structure of the world we don't
+expect even in science but certainly not
+
+ align:start position:0%
+expect even in science but certainly not
+ 
+
+ align:start position:0%
+expect even in science but certainly not
+in our intuitive theories to model the
+
+ align:start position:0%
+in our intuitive theories to model the
+ 
+
+ align:start position:0%
+in our intuitive theories to model the
+causal structure of the world at full
+
+ align:start position:0%
+causal structure of the world at full
+ 
+
+ align:start position:0%
+causal structure of the world at full
+detail and a way that either I am always
+
+ align:start position:0%
+detail and a way that either I am always
+ 
+
+ align:start position:0%
+detail and a way that either I am always
+misunderstood or always fail to
+
+ align:start position:0%
+misunderstood or always fail to
+ 
+
+ align:start position:0%
+misunderstood or always fail to
+communicate it's my fault really
+
+ align:start position:0%
+communicate it's my fault really
+ 
+
+ align:start position:0%
+communicate it's my fault really
+as I say oh we have these rich models of
+
+ align:start position:0%
+as I say oh we have these rich models of
+ 
+
+ align:start position:0%
+as I say oh we have these rich models of
+the world people often think that means
+
+ align:start position:0%
+the world people often think that means
+ 
+
+ align:start position:0%
+the world people often think that means
+that somehow the complete thing like if
+
+ align:start position:0%
+that somehow the complete thing like if
+ 
+
+ align:start position:0%
+that somehow the complete thing like if
+I say we have a physics engine in our
+
+ align:start position:0%
+I say we have a physics engine in our
+ 
+
+ align:start position:0%
+I say we have a physics engine in our
+head it means we have all of physics or
+
+ align:start position:0%
+head it means we have all of physics or
+ 
+
+ align:start position:0%
+head it means we have all of physics or
+if I say we have a graphics engine and
+
+ align:start position:0%
+if I say we have a graphics engine and
+ 
+
+ align:start position:0%
+if I say we have a graphics engine and
+we have all of every possible thing you
+
+ align:start position:0%
+we have all of every possible thing you
+ 
+
+ align:start position:0%
+we have all of every possible thing you
+know this isn't Pixar okay we're not
+
+ align:start position:0%
+know this isn't Pixar okay we're not
+ 
+
+ align:start position:0%
+know this isn't Pixar okay we're not
+trying to make a beautiful movie except
+
+ align:start position:0%
+trying to make a beautiful movie except
+ 
+
+ align:start position:0%
+trying to make a beautiful movie except
+maybe four faces right we're just trying
+
+ align:start position:0%
+maybe four faces right we're just trying
+ 
+
+ align:start position:0%
+maybe four faces right we're just trying
+to capture just the key parts just the
+
+ align:start position:0%
+to capture just the key parts just the
+ 
+
+ align:start position:0%
+to capture just the key parts just the
+key calls all parts of the way things
+
+ align:start position:0%
+key calls all parts of the way things
+ 
+
+ align:start position:0%
+key calls all parts of the way things
+move in the world as physical objects
+
+ align:start position:0%
+move in the world as physical objects
+ 
+
+ align:start position:0%
+move in the world as physical objects
+and the way images are formed that at
+
+ align:start position:0%
+and the way images are formed that at
+ 
+
+ align:start position:0%
+and the way images are formed that at
+the right level of abstraction that
+
+ align:start position:0%
+the right level of abstraction that
+ 
+
+ align:start position:0%
+the right level of abstraction that
+matters for us allows us to to do what
+
+ align:start position:0%
+matters for us allows us to to do what
+ 
+
+ align:start position:0%
+matters for us allows us to to do what
+we need to do this is just an example of
+
+ align:start position:0%
+we need to do this is just an example of
+ 
+
+ align:start position:0%
+we need to do this is just an example of
+our system doing solving some pretty
+
+ align:start position:0%
+our system doing solving some pretty
+ 
+
+ align:start position:0%
+our system doing solving some pretty
+challenging body pose recognition
+
+ align:start position:0%
+challenging body pose recognition
+ 
+
+ align:start position:0%
+challenging body pose recognition
+problems in 3d which cases which pose
+
+ align:start position:0%
+problems in 3d which cases which pose
+ 
+
+ align:start position:0%
+problems in 3d which cases which pose
+which are problematic even for the best
+
+ align:start position:0%
+which are problematic even for the best
+ 
+
+ align:start position:0%
+which are problematic even for the best
+of standard computer vision systems a
+
+ align:start position:0%
+of standard computer vision systems a
+ 
+
+ align:start position:0%
+of standard computer vision systems a
+bit either because it's a weird pose
+
+ align:start position:0%
+bit either because it's a weird pose
+ 
+
+ align:start position:0%
+bit either because it's a weird pose
+like these weird sports figures or
+
+ align:start position:0%
+like these weird sports figures or
+ 
+
+ align:start position:0%
+like these weird sports figures or
+because the body is heavily occluded and
+
+ align:start position:0%
+because the body is heavily occluded and
+ 
+
+ align:start position:0%
+because the body is heavily occluded and
+but I think again these are problems
+
+ align:start position:0%
+but I think again these are problems
+ 
+
+ align:start position:0%
+but I think again these are problems
+which people solve effortlessly and I
+
+ align:start position:0%
+which people solve effortlessly and I
+ 
+
+ align:start position:0%
+which people solve effortlessly and I
+think something like this is on the
+
+ align:start position:0%
+think something like this is on the
+ 
+
+ align:start position:0%
+think something like this is on the
+track of what we want to do you can
+
+ align:start position:0%
+track of what we want to do you can
+ 
+
+ align:start position:0%
+track of what we want to do you can
+apply the same kind of thing to more
+
+ align:start position:0%
+apply the same kind of thing to more
+ 
+
+ align:start position:0%
+apply the same kind of thing to more
+generic objects like this but I'm not
+
+ align:start position:0%
+generic objects like this but I'm not
+ 
+
+ align:start position:0%
+generic objects like this but I'm not
+gonna go into the details the last thing
+
+ align:start position:0%
+gonna go into the details the last thing
+ 
+
+ align:start position:0%
+gonna go into the details the last thing
+I want to say about vision before
+
+ align:start position:0%
+I want to say about vision before
+ 
+
+ align:start position:0%
+I want to say about vision before
+getting back to common sense for a few
+
+ align:start position:0%
+getting back to common sense for a few
+ 
+
+ align:start position:0%
+getting back to common sense for a few
+minutes is um this is and in some sense
+
+ align:start position:0%
+minutes is um this is and in some sense
+ 
+
+ align:start position:0%
+minutes is um this is and in some sense
+maybe this is the most important slide
+
+ align:start position:0%
+maybe this is the most important slide
+ 
+
+ align:start position:0%
+maybe this is the most important slide
+for the broader CBMM brains minds
+
+ align:start position:0%
+for the broader CBMM brains minds
+ 
+
+ align:start position:0%
+for the broader CBMM brains minds
+machines and cuz this is this is the the
+
+ align:start position:0%
+machines and cuz this is this is the the
+ 
+
+ align:start position:0%
+machines and cuz this is this is the the
+clearest thing I can point to to the
+
+ align:start position:0%
+clearest thing I can point to to the
+ 
+
+ align:start position:0%
+clearest thing I can point to to the
+thing I've been saying all along since
+
+ align:start position:0%
+thing I've been saying all along since
+ 
+
+ align:start position:0%
+thing I've been saying all along since
+the beginning of the morning about how
+
+ align:start position:0%
+the beginning of the morning about how
+ 
+
+ align:start position:0%
+the beginning of the morning about how
+we want to look for ways to combine the
+
+ align:start position:0%
+we want to look for ways to combine the
+ 
+
+ align:start position:0%
+we want to look for ways to combine the
+generative model view and the pattern
+
+ align:start position:0%
+generative model view and the pattern
+ 
+
+ align:start position:0%
+generative model view and the pattern
+recognition view right so the generative
+
+ align:start position:0%
+recognition view right so the generative
+ 
+
+ align:start position:0%
+recognition view right so the generative
+model is what you see on the left here
+
+ align:start position:0%
+model is what you see on the left here
+ 
+
+ align:start position:0%
+model is what you see on the left here
+it's the arrows going down it's exactly
+
+ align:start position:0%
+it's the arrows going down it's exactly
+ 
+
+ align:start position:0%
+it's the arrows going down it's exactly
+just the face graphics engine the same
+
+ align:start position:0%
+just the face graphics engine the same
+ 
+
+ align:start position:0%
+just the face graphics engine the same
+thing I showed you okay um the thing on
+
+ align:start position:0%
+thing I showed you okay um the thing on
+ 
+
+ align:start position:0%
+thing I showed you okay um the thing on
+the right is a with the arrows going up
+
+ align:start position:0%
+the right is a with the arrows going up
+ 
+
+ align:start position:0%
+the right is a with the arrows going up
+is a continent basically it's a
+
+ align:start position:0%
+is a continent basically it's a
+ 
+
+ align:start position:0%
+is a continent basically it's a
+out-of-the-box café style convolutional
+
+ align:start position:0%
+out-of-the-box café style convolutional
+ 
+
+ align:start position:0%
+out-of-the-box café style convolutional
+neural net with some fully connected
+
+ align:start position:0%
+neural net with some fully connected
+ 
+
+ align:start position:0%
+neural net with some fully connected
+layers on the top and then there's a few
+
+ align:start position:0%
+layers on the top and then there's a few
+ 
+
+ align:start position:0%
+layers on the top and then there's a few
+other - arrows which represent linear
+
+ align:start position:0%
+other - arrows which represent linear
+ 
+
+ align:start position:0%
+other - arrows which represent linear
+decoders from layers of that model to
+
+ align:start position:0%
+decoders from layers of that model to
+ 
+
+ align:start position:0%
+decoders from layers of that model to
+other things which are basically parts
+
+ align:start position:0%
+other things which are basically parts
+ 
+
+ align:start position:0%
+other things which are basically parts
+of the generative model and the idea
+
+ align:start position:0%
+of the generative model and the idea
+ 
+
+ align:start position:0%
+of the generative model and the idea
+here this is work due to ill kirill
+
+ align:start position:0%
+here this is work due to ill kirill
+ 
+
+ align:start position:0%
+here this is work due to ill kirill
+durum who some of you might have met he
+
+ align:start position:0%
+durum who some of you might have met he
+ 
+
+ align:start position:0%
+durum who some of you might have met he
+was here the other day
+
+ align:start position:0%
+was here the other day
+ 
+
+ align:start position:0%
+was here the other day
+he's one of our CBMM postdocs but also
+
+ align:start position:0%
+he's one of our CBMM postdocs but also
+ 
+
+ align:start position:0%
+he's one of our CBMM postdocs but also
+joint with Tejas em with vendrick who
+
+ align:start position:0%
+joint with Tejas em with vendrick who
+ 
+
+ align:start position:0%
+joint with Tejas em with vendrick who
+you saw before
+
+ align:start position:0%
+you saw before
+ 
+
+ align:start position:0%
+you saw before
+is to try to in a sense in several
+
+ align:start position:0%
+is to try to in a sense in several
+ 
+
+ align:start position:0%
+is to try to in a sense in several
+senses combine the best of these
+
+ align:start position:0%
+senses combine the best of these
+ 
+
+ align:start position:0%
+senses combine the best of these
+perspectives to say look if we want to
+
+ align:start position:0%
+perspectives to say look if we want to
+ 
+
+ align:start position:0%
+perspectives to say look if we want to
+recognize anything or you know perceive
+
+ align:start position:0%
+recognize anything or you know perceive
+ 
+
+ align:start position:0%
+recognize anything or you know perceive
+the structure of the world richly I
+
+ align:start position:0%
+the structure of the world richly I
+ 
+
+ align:start position:0%
+the structure of the world richly I
+think it needs to be something like it
+
+ align:start position:0%
+think it needs to be something like it
+ 
+
+ align:start position:0%
+think it needs to be something like it
+this inverse graphics are inverting a
+
+ align:start position:0%
+this inverse graphics are inverting a
+ 
+
+ align:start position:0%
+this inverse graphics are inverting a
+graphics program but you saw how slow it
+
+ align:start position:0%
+graphics program but you saw how slow it
+ 
+
+ align:start position:0%
+graphics program but you saw how slow it
+was you saw how it took a couple of
+
+ align:start position:0%
+was you saw how it took a couple of
+ 
+
+ align:start position:0%
+was you saw how it took a couple of
+seconds at least on our computer just
+
+ align:start position:0%
+seconds at least on our computer just
+ 
+
+ align:start position:0%
+seconds at least on our computer just
+for faces to search for the space of
+
+ align:start position:0%
+for faces to search for the space of
+ 
+
+ align:start position:0%
+for faces to search for the space of
+faces to Club with the convincing
+
+ align:start position:0%
+faces to Club with the convincing
+ 
+
+ align:start position:0%
+faces to Club with the convincing
+hypothesis that's way too slow it
+
+ align:start position:0%
+hypothesis that's way too slow it
+ 
+
+ align:start position:0%
+hypothesis that's way too slow it
+doesn't take you that long right we know
+
+ align:start position:0%
+doesn't take you that long right we know
+ 
+
+ align:start position:0%
+doesn't take you that long right we know
+a lot about exactly how long it takes
+
+ align:start position:0%
+a lot about exactly how long it takes
+ 
+
+ align:start position:0%
+a lot about exactly how long it takes
+you from VIN Rick and Nancy's and many
+
+ align:start position:0%
+you from VIN Rick and Nancy's and many
+ 
+
+ align:start position:0%
+you from VIN Rick and Nancy's and many
+other people's work so how can we how
+
+ align:start position:0%
+other people's work so how can we how
+ 
+
+ align:start position:0%
+other people's work so how can we how
+can visually much more generally be so
+
+ align:start position:0%
+can visually much more generally be so
+ 
+
+ align:start position:0%
+can visually much more generally be so
+rich in terms of the model it builds yet
+
+ align:start position:0%
+rich in terms of the model it builds yet
+ 
+
+ align:start position:0%
+rich in terms of the model it builds yet
+so fast well here's the proposal which
+
+ align:start position:0%
+so fast well here's the proposal which
+ 
+
+ align:start position:0%
+so fast well here's the proposal which
+is to take the fast the things that are
+
+ align:start position:0%
+is to take the fast the things that are
+ 
+
+ align:start position:0%
+is to take the fast the things that are
+good at being fast like the pattern
+
+ align:start position:0%
+good at being fast like the pattern
+ 
+
+ align:start position:0%
+good at being fast like the pattern
+recognizers the deep ones and train them
+
+ align:start position:0%
+recognizers the deep ones and train them
+ 
+
+ align:start position:0%
+recognizers the deep ones and train them
+to solve the hard inference problem or
+
+ align:start position:0%
+to solve the hard inference problem or
+ 
+
+ align:start position:0%
+to solve the hard inference problem or
+at least to do most of the work it's an
+
+ align:start position:0%
+at least to do most of the work it's an
+ 
+
+ align:start position:0%
+at least to do most of the work it's an
+idea which is very heavily inspired by
+
+ align:start position:0%
+idea which is very heavily inspired by
+ 
+
+ align:start position:0%
+idea which is very heavily inspired by
+an older idea of Jeff Hinton's sometimes
+
+ align:start position:0%
+an older idea of Jeff Hinton's sometimes
+ 
+
+ align:start position:0%
+an older idea of Jeff Hinton's sometimes
+called the Helmholtz machine here the
+
+ align:start position:0%
+called the Helmholtz machine here the
+ 
+
+ align:start position:0%
+called the Helmholtz machine here the
+idea in common with Hinton is to have a
+
+ align:start position:0%
+idea in common with Hinton is to have a
+ 
+
+ align:start position:0%
+idea in common with Hinton is to have a
+generative model and a recognition model
+
+ align:start position:0%
+generative model and a recognition model
+ 
+
+ align:start position:0%
+generative model and a recognition model
+where the recognition model is a neural
+
+ align:start position:0%
+where the recognition model is a neural
+ 
+
+ align:start position:0%
+where the recognition model is a neural
+network and it's trained to invert the
+
+ align:start position:0%
+network and it's trained to invert the
+ 
+
+ align:start position:0%
+network and it's trained to invert the
+generative model namely it's trained to
+
+ align:start position:0%
+generative model namely it's trained to
+ 
+
+ align:start position:0%
+generative model namely it's trained to
+map from not from sense data to task
+
+ align:start position:0%
+map from not from sense data to task
+ 
+
+ align:start position:0%
+map from not from sense data to task
+output but from sense data to the hidden
+
+ align:start position:0%
+output but from sense data to the hidden
+ 
+
+ align:start position:0%
+output but from sense data to the hidden
+deep causes of the generative model
+
+ align:start position:0%
+deep causes of the generative model
+ 
+
+ align:start position:0%
+deep causes of the generative model
+which then when you want to use this to
+
+ align:start position:0%
+which then when you want to use this to
+ 
+
+ align:start position:0%
+which then when you want to use this to
+act right like to plan what you're going
+
+ align:start position:0%
+act right like to plan what you're going
+ 
+
+ align:start position:0%
+act right like to plan what you're going
+to do you plan on the model to make an
+
+ align:start position:0%
+to do you plan on the model to make an
+ 
+
+ align:start position:0%
+to do you plan on the model to make an
+analogy to say the deep mind video game
+
+ align:start position:0%
+analogy to say the deep mind video game
+ 
+
+ align:start position:0%
+analogy to say the deep mind video game
+player this would be like having a
+
+ align:start position:0%
+player this would be like having a
+ 
+
+ align:start position:0%
+player this would be like having a
+system which in contrast to the deep Q
+
+ align:start position:0%
+system which in contrast to the deep Q
+ 
+
+ align:start position:0%
+system which in contrast to the deep Q
+network which maps from pixel images to
+
+ align:start position:0%
+network which maps from pixel images to
+ 
+
+ align:start position:0%
+network which maps from pixel images to
+joystick commands this would be like
+
+ align:start position:0%
+joystick commands this would be like
+ 
+
+ align:start position:0%
+joystick commands this would be like
+learning a network that maps from pixel
+
+ align:start position:0%
+learning a network that maps from pixel
+ 
+
+ align:start position:0%
+learning a network that maps from pixel
+images to the game state to the objects
+
+ align:start position:0%
+images to the game state to the objects
+ 
+
+ align:start position:0%
+images to the game state to the objects
+the sprites that are moving around the
+
+ align:start position:0%
+the sprites that are moving around the
+ 
+
+ align:start position:0%
+the sprites that are moving around the
+score and so on and then plans on that
+
+ align:start position:0%
+score and so on and then plans on that
+ 
+
+ align:start position:0%
+score and so on and then plans on that
+and I think that's much more like what
+
+ align:start position:0%
+and I think that's much more like what
+ 
+
+ align:start position:0%
+and I think that's much more like what
+people do is it is that here just in the
+
+ align:start position:0%
+people do is it is that here just in the
+ 
+
+ align:start position:0%
+people do is it is that here just in the
+limited case of faces what are we doing
+
+ align:start position:0%
+limited case of faces what are we doing
+ 
+
+ align:start position:0%
+limited case of faces what are we doing
+right so um what we what we've got here
+
+ align:start position:0%
+right so um what we what we've got here
+ 
+
+ align:start position:0%
+right so um what we what we've got here
+is we take this convolutional neural
+
+ align:start position:0%
+is we take this convolutional neural
+ 
+
+ align:start position:0%
+is we take this convolutional neural
+network we train it in ways that you can
+
+ align:start position:0%
+network we train it in ways that you can
+ 
+
+ align:start position:0%
+network we train it in ways that you can
+read about in the paper it's very easy
+
+ align:start position:0%
+read about in the paper it's very easy
+ 
+
+ align:start position:0%
+read about in the paper it's very easy
+kind of training to basically make
+
+ align:start position:0%
+kind of training to basically make
+ 
+
+ align:start position:0%
+kind of training to basically make
+predictions to make guesses about all
+
+ align:start position:0%
+predictions to make guesses about all
+ 
+
+ align:start position:0%
+predictions to make guesses about all
+the latent variables the shape the
+
+ align:start position:0%
+the latent variables the shape the
+ 
+
+ align:start position:0%
+the latent variables the shape the
+texture the lighting that the camera
+
+ align:start position:0%
+texture the lighting that the camera
+ 
+
+ align:start position:0%
+texture the lighting that the camera
+angle and then you take those guesses
+
+ align:start position:0%
+angle and then you take those guesses
+ 
+
+ align:start position:0%
+angle and then you take those guesses
+and they're there they start off that
+
+ align:start position:0%
+and they're there they start off that
+ 
+
+ align:start position:0%
+and they're there they start off that
+Markov chains once
+
+ align:start position:0%
+Markov chains once
+ 
+
+ align:start position:0%
+Markov chains once
+of starting off at a random graphics
+
+ align:start position:0%
+of starting off at a random graphics
+ 
+
+ align:start position:0%
+of starting off at a random graphics
+hypothesis you start off at a pretty
+
+ align:start position:0%
+hypothesis you start off at a pretty
+ 
+
+ align:start position:0%
+hypothesis you start off at a pretty
+good one and then refine it a little bit
+
+ align:start position:0%
+good one and then refine it a little bit
+ 
+
+ align:start position:0%
+good one and then refine it a little bit
+what you can see here in these blue and
+
+ align:start position:0%
+what you can see here in these blue and
+ 
+
+ align:start position:0%
+what you can see here in these blue and
+red curves is the blue curve is the the
+
+ align:start position:0%
+red curves is the blue curve is the the
+ 
+
+ align:start position:0%
+red curves is the blue curve is the the
+the dinette that the course of inference
+
+ align:start position:0%
+the dinette that the course of inference
+ 
+
+ align:start position:0%
+the dinette that the course of inference
+for the model I showed you before where
+
+ align:start position:0%
+for the model I showed you before where
+ 
+
+ align:start position:0%
+for the model I showed you before where
+you start off at a random guess and you
+
+ align:start position:0%
+you start off at a random guess and you
+ 
+
+ align:start position:0%
+you start off at a random guess and you
+know after I don't know 100 iterations
+
+ align:start position:0%
+know after I don't know 100 iterations
+ 
+
+ align:start position:0%
+know after I don't know 100 iterations
+of MCMC you you improve and you kind of
+
+ align:start position:0%
+of MCMC you you improve and you kind of
+ 
+
+ align:start position:0%
+of MCMC you you improve and you kind of
+get there whereas the red curve is what
+
+ align:start position:0%
+get there whereas the red curve is what
+ 
+
+ align:start position:0%
+get there whereas the red curve is what
+you see if you start off with the guess
+
+ align:start position:0%
+you see if you start off with the guess
+ 
+
+ align:start position:0%
+you see if you start off with the guess
+of this recognition model and you can
+
+ align:start position:0%
+of this recognition model and you can
+ 
+
+ align:start position:0%
+of this recognition model and you can
+see that you start off sort of in some
+
+ align:start position:0%
+see that you start off sort of in some
+ 
+
+ align:start position:0%
+see that you start off sort of in some
+sense almost as good as you're ever
+
+ align:start position:0%
+sense almost as good as you're ever
+ 
+
+ align:start position:0%
+sense almost as good as you're ever
+going to get and then you refine it well
+
+ align:start position:0%
+going to get and then you refine it well
+ 
+
+ align:start position:0%
+going to get and then you refine it well
+it might look like you were just
+
+ align:start position:0%
+it might look like you were just
+ 
+
+ align:start position:0%
+it might look like you were just
+refining it a little bit but this is a
+
+ align:start position:0%
+refining it a little bit but this is a
+ 
+
+ align:start position:0%
+refining it a little bit but this is a
+kind of a EE log scale it's a log plot
+
+ align:start position:0%
+kind of a EE log scale it's a log plot
+ 
+
+ align:start position:0%
+kind of a EE log scale it's a log plot
+of log probability so what looks like a
+
+ align:start position:0%
+of log probability so what looks like a
+ 
+
+ align:start position:0%
+of log probability so what looks like a
+little bit there on the red curve is
+
+ align:start position:0%
+little bit there on the red curve is
+ 
+
+ align:start position:0%
+little bit there on the red curve is
+actually a lot I mean perceptually you
+
+ align:start position:0%
+actually a lot I mean perceptually you
+ 
+
+ align:start position:0%
+actually a lot I mean perceptually you
+can see it here where if you take on the
+
+ align:start position:0%
+can see it here where if you take on the
+ 
+
+ align:start position:0%
+can see it here where if you take on the
+top I'm showing observed input faces on
+
+ align:start position:0%
+top I'm showing observed input faces on
+ 
+
+ align:start position:0%
+top I'm showing observed input faces on
+the bottom I'm showing the results of
+
+ align:start position:0%
+the bottom I'm showing the results of
+ 
+
+ align:start position:0%
+the bottom I'm showing the results of
+this full inverse graphics thing and
+
+ align:start position:0%
+this full inverse graphics thing and
+ 
+
+ align:start position:0%
+this full inverse graphics thing and
+they should look almost identical so if
+
+ align:start position:0%
+they should look almost identical so if
+ 
+
+ align:start position:0%
+they should look almost identical so if
+you if you the full model is able to
+
+ align:start position:0%
+you if you the full model is able to
+ 
+
+ align:start position:0%
+you if you the full model is able to
+basically perfectly invert this and come
+
+ align:start position:0%
+basically perfectly invert this and come
+ 
+
+ align:start position:0%
+basically perfectly invert this and come
+up with a face that really does look
+
+ align:start position:0%
+up with a face that really does look
+ 
+
+ align:start position:0%
+up with a face that really does look
+like on the top the ones in the middle
+
+ align:start position:0%
+like on the top the ones in the middle
+ 
+
+ align:start position:0%
+like on the top the ones in the middle
+are the best guess you get from this
+
+ align:start position:0%
+are the best guess you get from this
+ 
+
+ align:start position:0%
+are the best guess you get from this
+neural network that's been trained to
+
+ align:start position:0%
+neural network that's been trained to
+ 
+
+ align:start position:0%
+neural network that's been trained to
+approximately invert the generative
+
+ align:start position:0%
+approximately invert the generative
+ 
+
+ align:start position:0%
+approximately invert the generative
+model and what you can see is on first
+
+ align:start position:0%
+model and what you can see is on first
+ 
+
+ align:start position:0%
+model and what you can see is on first
+glance it should look pretty good but if
+
+ align:start position:0%
+glance it should look pretty good but if
+ 
+
+ align:start position:0%
+glance it should look pretty good but if
+you if you pay a little bit of attention
+
+ align:start position:0%
+you if you pay a little bit of attention
+ 
+
+ align:start position:0%
+you if you pay a little bit of attention
+you can see differences right like
+
+ align:start position:0%
+you can see differences right like
+ 
+
+ align:start position:0%
+you can see differences right like
+hopefully you can see this person is not
+
+ align:start position:0%
+hopefully you can see this person is not
+ 
+
+ align:start position:0%
+hopefully you can see this person is not
+actually that person in a way that this
+
+ align:start position:0%
+actually that person in a way that this
+ 
+
+ align:start position:0%
+actually that person in a way that this
+is much more convincingly or you know
+
+ align:start position:0%
+is much more convincingly or you know
+ 
+
+ align:start position:0%
+is much more convincingly or you know
+this person this one's pretty good but I
+
+ align:start position:0%
+this person this one's pretty good but I
+ 
+
+ align:start position:0%
+this person this one's pretty good but I
+think this one I think it's it's pretty
+
+ align:start position:0%
+think this one I think it's it's pretty
+ 
+
+ align:start position:0%
+think this one I think it's it's pretty
+easy to see yeah this isn't quite the
+
+ align:start position:0%
+easy to see yeah this isn't quite the
+ 
+
+ align:start position:0%
+easy to see yeah this isn't quite the
+same person as that one you guys agree
+
+ align:start position:0%
+same person as that one you guys agree
+ 
+
+ align:start position:0%
+same person as that one you guys agree
+we've we've done some experiments to
+
+ align:start position:0%
+we've we've done some experiments to
+ 
+
+ align:start position:0%
+we've we've done some experiments to
+verify this but hopefully it should look
+
+ align:start position:0%
+verify this but hopefully it should look
+ 
+
+ align:start position:0%
+verify this but hopefully it should look
+pretty similar that's the point right
+
+ align:start position:0%
+pretty similar that's the point right
+ 
+
+ align:start position:0%
+pretty similar that's the point right
+that that this that you you know how do
+
+ align:start position:0%
+that that this that you you know how do
+ 
+
+ align:start position:0%
+that that this that you you know how do
+you combine the best of these
+
+ align:start position:0%
+you combine the best of these
+ 
+
+ align:start position:0%
+you combine the best of these
+computational paradigms how can
+
+ align:start position:0%
+computational paradigms how can
+ 
+
+ align:start position:0%
+computational paradigms how can
+perception more generally be so rich it
+
+ align:start position:0%
+perception more generally be so rich it
+ 
+
+ align:start position:0%
+perception more generally be so rich it
+so fast well quite possibly like this it
+
+ align:start position:0%
+so fast well quite possibly like this it
+ 
+
+ align:start position:0%
+so fast well quite possibly like this it
+even actually might provide some some
+
+ align:start position:0%
+even actually might provide some some
+ 
+
+ align:start position:0%
+even actually might provide some some
+insight into the neural circuitry that
+
+ align:start position:0%
+insight into the neural circuitry that
+ 
+
+ align:start position:0%
+insight into the neural circuitry that
+Vin Rick and Dora saw and others have
+
+ align:start position:0%
+Vin Rick and Dora saw and others have
+ 
+
+ align:start position:0%
+Vin Rick and Dora saw and others have
+mapped out we think that this
+
+ align:start position:0%
+mapped out we think that this
+ 
+
+ align:start position:0%
+mapped out we think that this
+recognition model that's trained to
+
+ align:start position:0%
+recognition model that's trained to
+ 
+
+ align:start position:0%
+recognition model that's trained to
+invert the graphics model can provide a
+
+ align:start position:0%
+invert the graphics model can provide a
+ 
+
+ align:start position:0%
+invert the graphics model can provide a
+really nice account of some of vinner X
+
+ align:start position:0%
+really nice account of some of vinner X
+ 
+
+ align:start position:0%
+really nice account of some of vinner X
+data like you saw before but I will not
+
+ align:start position:0%
+data like you saw before but I will not
+ 
+
+ align:start position:0%
+data like you saw before but I will not
+go into the details because in maybe
+
+ align:start position:0%
+go into the details because in maybe
+ 
+
+ align:start position:0%
+go into the details because in maybe
+five to ten minutes I want to get back
+
+ align:start position:0%
+five to ten minutes I want to get back
+ 
+
+ align:start position:0%
+five to ten minutes I want to get back
+to physics and psychology okay
+
+ align:start position:0%
+to physics and psychology okay
+ 
+
+ align:start position:0%
+to physics and psychology okay
+so physics and and and there won't be
+
+ align:start position:0%
+so physics and and and there won't be
+ 
+
+ align:start position:0%
+so physics and and and there won't be
+any more neural networks because that's
+
+ align:start position:0%
+any more neural networks because that's
+ 
+
+ align:start position:0%
+any more neural networks because that's
+about as I mean I
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+I think we'd like to take that those
+
+ align:start position:0%
+I think we'd like to take that those
+ 
+
+ align:start position:0%
+I think we'd like to take that those
+ways of integrating the best of these
+
+ align:start position:0%
+ways of integrating the best of these
+ 
+
+ align:start position:0%
+ways of integrating the best of these
+approaches and apply them to these more
+
+ align:start position:0%
+approaches and apply them to these more
+ 
+
+ align:start position:0%
+approaches and apply them to these more
+general cases but that's about as far as
+
+ align:start position:0%
+general cases but that's about as far as
+ 
+
+ align:start position:0%
+general cases but that's about as far as
+we can get here what I want to just give
+
+ align:start position:0%
+we can get here what I want to just give
+ 
+
+ align:start position:0%
+we can get here what I want to just give
+you a taste of at least is how we're
+
+ align:start position:0%
+you a taste of at least is how we're
+ 
+
+ align:start position:0%
+you a taste of at least is how we're
+using ideas just purely from
+
+ align:start position:0%
+using ideas just purely from
+ 
+
+ align:start position:0%
+using ideas just purely from
+probablistic programs to capture more of
+
+ align:start position:0%
+probablistic programs to capture more of
+ 
+
+ align:start position:0%
+probablistic programs to capture more of
+this common-sense physics in psychology
+
+ align:start position:0%
+this common-sense physics in psychology
+ 
+
+ align:start position:0%
+this common-sense physics in psychology
+so let's say we can solve this problem
+
+ align:start position:0%
+so let's say we can solve this problem
+ 
+
+ align:start position:0%
+so let's say we can solve this problem
+by making a good guess of the 3d world
+
+ align:start position:0%
+by making a good guess of the 3d world
+ 
+
+ align:start position:0%
+by making a good guess of the 3d world
+state from the unit very quickly
+
+ align:start position:0%
+state from the unit very quickly
+ 
+
+ align:start position:0%
+state from the unit very quickly
+inverting this graphics engine now we
+
+ align:start position:0%
+inverting this graphics engine now we
+ 
+
+ align:start position:0%
+inverting this graphics engine now we
+can start to do some physical reasoning
+
+ align:start position:0%
+can start to do some physical reasoning
+ 
+
+ align:start position:0%
+can start to do some physical reasoning
+a la crakes you know mental model of the
+
+ align:start position:0%
+a la crakes you know mental model of the
+ 
+
+ align:start position:0%
+a la crakes you know mental model of the
+in the head of the physical world
+
+ align:start position:0%
+in the head of the physical world
+ 
+
+ align:start position:0%
+in the head of the physical world
+where we now take a physics engine which
+
+ align:start position:0%
+where we now take a physics engine which
+ 
+
+ align:start position:0%
+where we now take a physics engine which
+is a you know here again we're using the
+
+ align:start position:0%
+is a you know here again we're using the
+ 
+
+ align:start position:0%
+is a you know here again we're using the
+kind of physics engines that game
+
+ align:start position:0%
+kind of physics engines that game
+ 
+
+ align:start position:0%
+kind of physics engines that game
+physics like very simple I don't have
+
+ align:start position:0%
+physics like very simple I don't have
+ 
+
+ align:start position:0%
+physics like very simple I don't have
+time to go into the details
+
+ align:start position:0%
+time to go into the details
+ 
+
+ align:start position:0%
+time to go into the details
+although homers written a very nice
+
+ align:start position:0%
+although homers written a very nice
+ 
+
+ align:start position:0%
+although homers written a very nice
+paper with well with himself but he's
+
+ align:start position:0%
+paper with well with himself but he's
+ 
+
+ align:start position:0%
+paper with well with himself but he's
+nicely put my name and Liz's on it about
+
+ align:start position:0%
+nicely put my name and Liz's on it about
+ 
+
+ align:start position:0%
+nicely put my name and Liz's on it about
+sort of trying to introduce some of the
+
+ align:start position:0%
+sort of trying to introduce some of the
+ 
+
+ align:start position:0%
+sort of trying to introduce some of the
+basic game engine concepts to cognitive
+
+ align:start position:0%
+basic game engine concepts to cognitive
+ 
+
+ align:start position:0%
+basic game engine concepts to cognitive
+scientists so hopefully we'll be able to
+
+ align:start position:0%
+scientists so hopefully we'll be able to
+ 
+
+ align:start position:0%
+scientists so hopefully we'll be able to
+show you that soon too or you can read
+
+ align:start position:0%
+show you that soon too or you can read
+ 
+
+ align:start position:0%
+show you that soon too or you can read
+about that basically is that these
+
+ align:start position:0%
+about that basically is that these
+ 
+
+ align:start position:0%
+about that basically is that these
+physics engines are just doing again a
+
+ align:start position:0%
+physics engines are just doing again a
+ 
+
+ align:start position:0%
+physics engines are just doing again a
+very quick fast approximate
+
+ align:start position:0%
+very quick fast approximate
+ 
+
+ align:start position:0%
+very quick fast approximate
+implementation of certain aspects of
+
+ align:start position:0%
+implementation of certain aspects of
+ 
+
+ align:start position:0%
+implementation of certain aspects of
+Newtonian mechanics sufficient that if
+
+ align:start position:0%
+Newtonian mechanics sufficient that if
+ 
+
+ align:start position:0%
+Newtonian mechanics sufficient that if
+you run it a few time steps with a
+
+ align:start position:0%
+you run it a few time steps with a
+ 
+
+ align:start position:0%
+you run it a few time steps with a
+configuration of objects like that you
+
+ align:start position:0%
+configuration of objects like that you
+ 
+
+ align:start position:0%
+configuration of objects like that you
+might get something like what you see
+
+ align:start position:0%
+might get something like what you see
+ 
+
+ align:start position:0%
+might get something like what you see
+over there on the right that's an
+
+ align:start position:0%
+over there on the right that's an
+ 
+
+ align:start position:0%
+over there on the right that's an
+example of running this this approximate
+
+ align:start position:0%
+example of running this this approximate
+ 
+
+ align:start position:0%
+example of running this this approximate
+Newtonian physics forward a few time
+
+ align:start position:0%
+Newtonian physics forward a few time
+ 
+
+ align:start position:0%
+Newtonian physics forward a few time
+steps here's another sample from this
+
+ align:start position:0%
+steps here's another sample from this
+ 
+
+ align:start position:0%
+steps here's another sample from this
+model another kind of mental simulation
+
+ align:start position:0%
+model another kind of mental simulation
+ 
+
+ align:start position:0%
+model another kind of mental simulation
+we take a different slightly different
+
+ align:start position:0%
+we take a different slightly different
+ 
+
+ align:start position:0%
+we take a different slightly different
+guess of the world state naught and we
+
+ align:start position:0%
+guess of the world state naught and we
+ 
+
+ align:start position:0%
+guess of the world state naught and we
+run that forward a few time steps and
+
+ align:start position:0%
+run that forward a few time steps and
+ 
+
+ align:start position:0%
+run that forward a few time steps and
+you see something else happens right
+
+ align:start position:0%
+you see something else happens right
+ 
+
+ align:start position:0%
+you see something else happens right
+nothing here is claimed to be accurate
+
+ align:start position:0%
+nothing here is claimed to be accurate
+ 
+
+ align:start position:0%
+nothing here is claimed to be accurate
+in the ground truth way right neither
+
+ align:start position:0%
+in the ground truth way right neither
+ 
+
+ align:start position:0%
+in the ground truth way right neither
+one of these is exactly the right
+
+ align:start position:0%
+one of these is exactly the right
+ 
+
+ align:start position:0%
+one of these is exactly the right
+configuration of blocks and you run this
+
+ align:start position:0%
+configuration of blocks and you run this
+ 
+
+ align:start position:0%
+configuration of blocks and you run this
+thing forward and it only approximately
+
+ align:start position:0%
+thing forward and it only approximately
+ 
+
+ align:start position:0%
+thing forward and it only approximately
+captures the way blocks really bounce
+
+ align:start position:0%
+captures the way blocks really bounce
+ 
+
+ align:start position:0%
+captures the way blocks really bounce
+off each other it's a hard problem to
+
+ align:start position:0%
+off each other it's a hard problem to
+ 
+
+ align:start position:0%
+off each other it's a hard problem to
+actually totally realistically simulate
+
+ align:start position:0%
+actually totally realistically simulate
+ 
+
+ align:start position:0%
+actually totally realistically simulate
+but our point is that you don't really
+
+ align:start position:0%
+but our point is that you don't really
+ 
+
+ align:start position:0%
+but our point is that you don't really
+have to you just have to make a
+
+ align:start position:0%
+have to you just have to make a
+ 
+
+ align:start position:0%
+have to you just have to make a
+reasonable guess of the position of the
+
+ align:start position:0%
+reasonable guess of the position of the
+ 
+
+ align:start position:0%
+reasonable guess of the position of the
+blocks and a reasonable guess of what's
+
+ align:start position:0%
+blocks and a reasonable guess of what's
+ 
+
+ align:start position:0%
+blocks and a reasonable guess of what's
+going to happen a few time steps in the
+
+ align:start position:0%
+going to happen a few time steps in the
+ 
+
+ align:start position:0%
+going to happen a few time steps in the
+future to predict what you need to know
+
+ align:start position:0%
+future to predict what you need to know
+ 
+
+ align:start position:0%
+future to predict what you need to know
+in common sense which is that wow that's
+
+ align:start position:0%
+in common sense which is that wow that's
+ 
+
+ align:start position:0%
+in common sense which is that wow that's
+gonna fall over I better do something
+
+ align:start position:0%
+gonna fall over I better do something
+ 
+
+ align:start position:0%
+gonna fall over I better do something
+about it right and that's what our
+
+ align:start position:0%
+about it right and that's what our
+ 
+
+ align:start position:0%
+about it right and that's what our
+experiment taps into we give people a
+
+ align:start position:0%
+experiment taps into we give people a
+ 
+
+ align:start position:0%
+experiment taps into we give people a
+whole bunch of stimuli like the ones I
+
+ align:start position:0%
+whole bunch of stimuli like the ones I
+ 
+
+ align:start position:0%
+whole bunch of stimuli like the ones I
+showed you and ask them you know
+
+ align:start position:0%
+showed you and ask them you know
+ 
+
+ align:start position:0%
+showed you and ask them you know
+underground some graded scale how likely
+
+ align:start position:0%
+underground some graded scale how likely
+ 
+
+ align:start position:0%
+underground some graded scale how likely
+do you think it is to fall over and what
+
+ align:start position:0%
+do you think it is to fall over and what
+ 
+
+ align:start position:0%
+do you think it is to fall over and what
+you see here this is again one of those
+
+ align:start position:0%
+you see here this is again one of those
+ 
+
+ align:start position:0%
+you see here this is again one of those
+plots that always are
+
+ align:start position:0%
+plots that always are
+ 
+
+ align:start position:0%
+plots that always are
+the same where on the y-axis are the
+
+ align:start position:0%
+the same where on the y-axis are the
+ 
+
+ align:start position:0%
+the same where on the y-axis are the
+average human judgments now of it's an
+
+ align:start position:0%
+average human judgments now of it's an
+ 
+
+ align:start position:0%
+average human judgments now of it's an
+estimate of how unstable the tower is
+
+ align:start position:0%
+estimate of how unstable the tower is
+ 
+
+ align:start position:0%
+estimate of how unstable the tower is
+it's both the probability that it will
+
+ align:start position:0%
+it's both the probability that it will
+ 
+
+ align:start position:0%
+it's both the probability that it will
+fall but also how much of the tower will
+
+ align:start position:0%
+fall but also how much of the tower will
+ 
+
+ align:start position:0%
+fall but also how much of the tower will
+fall so it's like the expected
+
+ align:start position:0%
+fall so it's like the expected
+ 
+
+ align:start position:0%
+fall so it's like the expected
+proportion of the tower that's gonna
+
+ align:start position:0%
+proportion of the tower that's gonna
+ 
+
+ align:start position:0%
+proportion of the tower that's gonna
+fall over under gravity and along the
+
+ align:start position:0%
+fall over under gravity and along the
+ 
+
+ align:start position:0%
+fall over under gravity and along the
+x-axis is the model prediction which is
+
+ align:start position:0%
+x-axis is the model prediction which is
+ 
+
+ align:start position:0%
+x-axis is the model prediction which is
+just the average of a few samples from
+
+ align:start position:0%
+just the average of a few samples from
+ 
+
+ align:start position:0%
+just the average of a few samples from
+what I showed you you just take a few
+
+ align:start position:0%
+what I showed you you just take a few
+ 
+
+ align:start position:0%
+what I showed you you just take a few
+guesses of the world state run it
+
+ align:start position:0%
+guesses of the world state run it
+ 
+
+ align:start position:0%
+guesses of the world state run it
+forward a few time steps count up the
+
+ align:start position:0%
+forward a few time steps count up the
+ 
+
+ align:start position:0%
+forward a few time steps count up the
+proportion of blocks that fell and
+
+ align:start position:0%
+proportion of blocks that fell and
+ 
+
+ align:start position:0%
+proportion of blocks that fell and
+that's in that an average that and what
+
+ align:start position:0%
+that's in that an average that and what
+ 
+
+ align:start position:0%
+that's in that an average that and what
+you can see is that does a really nice
+
+ align:start position:0%
+you can see is that does a really nice
+ 
+
+ align:start position:0%
+you can see is that does a really nice
+job of predicting people's stability
+
+ align:start position:0%
+job of predicting people's stability
+ 
+
+ align:start position:0%
+job of predicting people's stability
+intuitions um i-i'll just point to what
+
+ align:start position:0%
+intuitions um i-i'll just point to what
+ 
+
+ align:start position:0%
+intuitions um i-i'll just point to what
+an interesting comparison because it
+
+ align:start position:0%
+an interesting comparison because it
+ 
+
+ align:start position:0%
+an interesting comparison because it
+does come in too weird where does the
+
+ align:start position:0%
+does come in too weird where does the
+ 
+
+ align:start position:0%
+does come in too weird where does the
+probability come in into these public
+
+ align:start position:0%
+probability come in into these public
+ 
+
+ align:start position:0%
+probability come in into these public
+programs well here's one very noticeable
+
+ align:start position:0%
+programs well here's one very noticeable
+ 
+
+ align:start position:0%
+programs well here's one very noticeable
+way so if you look down there on the
+
+ align:start position:0%
+way so if you look down there on the
+ 
+
+ align:start position:0%
+way so if you look down there on the
+lower right you'll see a smaller version
+
+ align:start position:0%
+lower right you'll see a smaller version
+ 
+
+ align:start position:0%
+lower right you'll see a smaller version
+of a similar plot which is um it's
+
+ align:start position:0%
+of a similar plot which is um it's
+ 
+
+ align:start position:0%
+of a similar plot which is um it's
+plotting now the results of it says
+
+ align:start position:0%
+plotting now the results of it says
+ 
+
+ align:start position:0%
+plotting now the results of it says
+ground truth physics but that's a little
+
+ align:start position:0%
+ground truth physics but that's a little
+ 
+
+ align:start position:0%
+ground truth physics but that's a little
+misleading maybe it's just a noiseless
+
+ align:start position:0%
+misleading maybe it's just a noiseless
+ 
+
+ align:start position:0%
+misleading maybe it's just a noiseless
+extension so we take the same physics
+
+ align:start position:0%
+extension so we take the same physics
+ 
+
+ align:start position:0%
+extension so we take the same physics
+model but we get rid of any of the state
+
+ align:start position:0%
+model but we get rid of any of the state
+ 
+
+ align:start position:0%
+model but we get rid of any of the state
+uncertainty so we tell it the exact the
+
+ align:start position:0%
+uncertainty so we tell it the exact the
+ 
+
+ align:start position:0%
+uncertainty so we tell it the exact the
+true position of the blocks and we give
+
+ align:start position:0%
+true position of the blocks and we give
+ 
+
+ align:start position:0%
+true position of the blocks and we give
+it the true physics whereas this our
+
+ align:start position:0%
+it the true physics whereas this our
+ 
+
+ align:start position:0%
+it the true physics whereas this our
+published stick physics engine allows
+
+ align:start position:0%
+published stick physics engine allows
+ 
+
+ align:start position:0%
+published stick physics engine allows
+for some uncertainty and exactly which
+
+ align:start position:0%
+for some uncertainty and exactly which
+ 
+
+ align:start position:0%
+for some uncertainty and exactly which
+forces are doing what but here we say
+
+ align:start position:0%
+forces are doing what but here we say
+ 
+
+ align:start position:0%
+forces are doing what but here we say
+we're just going to model gravity
+
+ align:start position:0%
+we're just going to model gravity
+ 
+
+ align:start position:0%
+we're just going to model gravity
+friction collisions as best we can and
+
+ align:start position:0%
+friction collisions as best we can and
+ 
+
+ align:start position:0%
+friction collisions as best we can and
+we're gonna get the state of the blocks
+
+ align:start position:0%
+we're gonna get the state of the blocks
+ 
+
+ align:start position:0%
+we're gonna get the state of the blocks
+perfectly and because it's noiseless you
+
+ align:start position:0%
+perfectly and because it's noiseless you
+ 
+
+ align:start position:0%
+perfectly and because it's noiseless you
+notice that so those those crosses over
+
+ align:start position:0%
+notice that so those those crosses over
+ 
+
+ align:start position:0%
+notice that so those those crosses over
+there are crosses because their error
+
+ align:start position:0%
+there are crosses because their error
+ 
+
+ align:start position:0%
+there are crosses because their error
+bar is both across people and model
+
+ align:start position:0%
+bar is both across people and model
+ 
+
+ align:start position:0%
+bar is both across people and model
+simulations now they're just vertical
+
+ align:start position:0%
+simulations now they're just vertical
+ 
+
+ align:start position:0%
+simulations now they're just vertical
+lines there's no error bars in the model
+
+ align:start position:0%
+lines there's no error bars in the model
+ 
+
+ align:start position:0%
+lines there's no error bars in the model
+simulation because it's deterministic
+
+ align:start position:0%
+simulation because it's deterministic
+ 
+
+ align:start position:0%
+simulation because it's deterministic
+its graded because of there's the
+
+ align:start position:0%
+its graded because of there's the
+ 
+
+ align:start position:0%
+its graded because of there's the
+proportion of the tower that falls over
+
+ align:start position:0%
+proportion of the tower that falls over
+ 
+
+ align:start position:0%
+proportion of the tower that falls over
+but what you see is the models a lot
+
+ align:start position:0%
+but what you see is the models a lot
+ 
+
+ align:start position:0%
+but what you see is the models a lot
+worse right it scatters much more the
+
+ align:start position:0%
+worse right it scatters much more the
+ 
+
+ align:start position:0%
+worse right it scatters much more the
+correlation drops from around point nine
+
+ align:start position:0%
+correlation drops from around point nine
+ 
+
+ align:start position:0%
+correlation drops from around point nine
+to around point six in terms of
+
+ align:start position:0%
+to around point six in terms of
+ 
+
+ align:start position:0%
+to around point six in terms of
+correlation of model with people's
+
+ align:start position:0%
+correlation of model with people's
+ 
+
+ align:start position:0%
+correlation of model with people's
+judgments and you have some cases like
+
+ align:start position:0%
+judgments and you have some cases like
+ 
+
+ align:start position:0%
+judgments and you have some cases like
+this red dot here that corresponds to
+
+ align:start position:0%
+this red dot here that corresponds to
+ 
+
+ align:start position:0%
+this red dot here that corresponds to
+this stimulus which goes from being a
+
+ align:start position:0%
+this stimulus which goes from being a
+ 
+
+ align:start position:0%
+this stimulus which goes from being a
+really nice model fit this is one which
+
+ align:start position:0%
+really nice model fit this is one which
+ 
+
+ align:start position:0%
+really nice model fit this is one which
+people judged to be very unstable and so
+
+ align:start position:0%
+people judged to be very unstable and so
+ 
+
+ align:start position:0%
+people judged to be very unstable and so
+does the probabilistic physics engine
+
+ align:start position:0%
+does the probabilistic physics engine
+ 
+
+ align:start position:0%
+does the probabilistic physics engine
+but actually it's not state it's not
+
+ align:start position:0%
+but actually it's not state it's not
+ 
+
+ align:start position:0%
+but actually it's not state it's not
+unstable at all it's actually perfectly
+
+ align:start position:0%
+unstable at all it's actually perfectly
+ 
+
+ align:start position:0%
+unstable at all it's actually perfectly
+stable the blocks are actually just
+
+ align:start position:0%
+stable the blocks are actually just
+ 
+
+ align:start position:0%
+stable the blocks are actually just
+perfectly balanced so that it doesn't
+
+ align:start position:0%
+perfectly balanced so that it doesn't
+ 
+
+ align:start position:0%
+perfectly balanced so that it doesn't
+fall although I'm sure everybody looks
+
+ align:start position:0%
+fall although I'm sure everybody looks
+ 
+
+ align:start position:0%
+fall although I'm sure everybody looks
+at that and finds that hard to believe
+
+ align:start position:0%
+at that and finds that hard to believe
+ 
+
+ align:start position:0%
+at that and finds that hard to believe
+right okay so this is nice this is a
+
+ align:start position:0%
+right okay so this is nice this is a
+ 
+
+ align:start position:0%
+right okay so this is nice this is a
+kind of physics illusion there are
+
+ align:start position:0%
+kind of physics illusion there are
+ 
+
+ align:start position:0%
+kind of physics illusion there are
+real-world versions of this out on the
+
+ align:start position:0%
+real-world versions of this out on the
+ 
+
+ align:start position:0%
+real-world versions of this out on the
+beaches not too far from here people
+
+ align:start position:0%
+beaches not too far from here people
+ 
+
+ align:start position:0%
+beaches not too far from here people
+like it's a fun thing to do to stock up
+
+ align:start position:0%
+like it's a fun thing to do to stock up
+ 
+
+ align:start position:0%
+like it's a fun thing to do to stock up
+in ways that are surprisingly stable we
+
+ align:start position:0%
+in ways that are surprisingly stable we
+ 
+
+ align:start position:0%
+in ways that are surprisingly stable we
+would say their surprise surprise
+
+ align:start position:0%
+would say their surprise surprise
+ 
+
+ align:start position:0%
+would say their surprise surprise
+because your intuitive physics has
+
+ align:start position:0%
+because your intuitive physics has
+ 
+
+ align:start position:0%
+because your intuitive physics has
+certain irreducible noise you can't
+
+ align:start position:0%
+certain irreducible noise you can't
+ 
+
+ align:start position:0%
+certain irreducible noise you can't
+we're suggesting here is that your
+
+ align:start position:0%
+we're suggesting here is that your
+ 
+
+ align:start position:0%
+we're suggesting here is that your
+physical intuitions you just you you
+
+ align:start position:0%
+physical intuitions you just you you
+ 
+
+ align:start position:0%
+physical intuitions you just you you
+you're always in some sense making a
+
+ align:start position:0%
+you're always in some sense making a
+ 
+
+ align:start position:0%
+you're always in some sense making a
+guess that's sensitive to the to the
+
+ align:start position:0%
+guess that's sensitive to the to the
+ 
+
+ align:start position:0%
+guess that's sensitive to the to the
+uncertainty about where things might be
+
+ align:start position:0%
+uncertainty about where things might be
+ 
+
+ align:start position:0%
+uncertainty about where things might be
+and what forces might be active on the
+
+ align:start position:0%
+and what forces might be active on the
+ 
+
+ align:start position:0%
+and what forces might be active on the
+world and it's very hard to see these as
+
+ align:start position:0%
+world and it's very hard to see these as
+ 
+
+ align:start position:0%
+world and it's very hard to see these as
+deterministic physics even when you know
+
+ align:start position:0%
+deterministic physics even when you know
+ 
+
+ align:start position:0%
+deterministic physics even when you know
+that that's exactly what's going on in
+
+ align:start position:0%
+that that's exactly what's going on in
+ 
+
+ align:start position:0%
+that that's exactly what's going on in
+that it is stable let me say just a
+
+ align:start position:0%
+that it is stable let me say just a
+ 
+
+ align:start position:0%
+that it is stable let me say just a
+little bit about planning right so how
+
+ align:start position:0%
+little bit about planning right so how
+ 
+
+ align:start position:0%
+little bit about planning right so how
+might you use this kind of model to
+
+ align:start position:0%
+might you use this kind of model to
+ 
+
+ align:start position:0%
+might you use this kind of model to
+build some model of you know this
+
+ align:start position:0%
+build some model of you know this
+ 
+
+ align:start position:0%
+build some model of you know this
+intuitive core intuitive psychology and
+
+ align:start position:0%
+intuitive core intuitive psychology and
+ 
+
+ align:start position:0%
+intuitive core intuitive psychology and
+I don't mean here all of theory of mind
+
+ align:start position:0%
+I don't mean here all of theory of mind
+ 
+
+ align:start position:0%
+I don't mean here all of theory of mind
+well here next week will hear a lot more
+
+ align:start position:0%
+well here next week will hear a lot more
+ 
+
+ align:start position:0%
+well here next week will hear a lot more
+like Rebecca Saxe will be down here
+
+ align:start position:0%
+like Rebecca Saxe will be down here
+ 
+
+ align:start position:0%
+like Rebecca Saxe will be down here
+we'll hear a lot more about much richer
+
+ align:start position:0%
+we'll hear a lot more about much richer
+ 
+
+ align:start position:0%
+we'll hear a lot more about much richer
+kinds of reasoning about other people's
+
+ align:start position:0%
+kinds of reasoning about other people's
+ 
+
+ align:start position:0%
+kinds of reasoning about other people's
+mental states that adults and older
+
+ align:start position:0%
+mental states that adults and older
+ 
+
+ align:start position:0%
+mental states that adults and older
+children can do but here we're talking
+
+ align:start position:0%
+children can do but here we're talking
+ 
+
+ align:start position:0%
+children can do but here we're talking
+about just as just as we were talking
+
+ align:start position:0%
+about just as just as we were talking
+ 
+
+ align:start position:0%
+about just as just as we were talking
+about what I was calling core intuitive
+
+ align:start position:0%
+about what I was calling core intuitive
+ 
+
+ align:start position:0%
+about what I was calling core intuitive
+physics again inspired by Liz's work of
+
+ align:start position:0%
+physics again inspired by Liz's work of
+ 
+
+ align:start position:0%
+physics again inspired by Liz's work of
+just you know what one objects do right
+
+ align:start position:0%
+just you know what one objects do right
+ 
+
+ align:start position:0%
+just you know what one objects do right
+here on the tabletop around us over
+
+ align:start position:0%
+here on the tabletop around us over
+ 
+
+ align:start position:0%
+here on the tabletop around us over
+short timescales the kind of core theory
+
+ align:start position:0%
+short timescales the kind of core theory
+ 
+
+ align:start position:0%
+short timescales the kind of core theory
+of mind something that even very young
+
+ align:start position:0%
+of mind something that even very young
+ 
+
+ align:start position:0%
+of mind something that even very young
+babies can do in some form or at least
+
+ align:start position:0%
+babies can do in some form or at least
+ 
+
+ align:start position:0%
+babies can do in some form or at least
+young children is controversy over
+
+ align:start position:0%
+young children is controversy over
+ 
+
+ align:start position:0%
+young children is controversy over
+exactly what age kids be able to do this
+
+ align:start position:0%
+exactly what age kids be able to do this
+ 
+
+ align:start position:0%
+exactly what age kids be able to do this
+can be able to do this sort of thing but
+
+ align:start position:0%
+can be able to do this sort of thing but
+ 
+
+ align:start position:0%
+can be able to do this sort of thing but
+you know in some form I think before
+
+ align:start position:0%
+you know in some form I think before
+ 
+
+ align:start position:0%
+you know in some form I think before
+certain before language it's the kind of
+
+ align:start position:0%
+certain before language it's the kind of
+ 
+
+ align:start position:0%
+certain before language it's the kind of
+thing that when you're starting to learn
+
+ align:start position:0%
+thing that when you're starting to learn
+ 
+
+ align:start position:0%
+thing that when you're starting to learn
+verbs the earliest language is kind of
+
+ align:start position:0%
+verbs the earliest language is kind of
+ 
+
+ align:start position:0%
+verbs the earliest language is kind of
+mentalistic and builds on this knowledge
+
+ align:start position:0%
+mentalistic and builds on this knowledge
+ 
+
+ align:start position:0%
+mentalistic and builds on this knowledge
+and and you know the intake the the red
+
+ align:start position:0%
+and and you know the intake the the red
+ 
+
+ align:start position:0%
+and and you know the intake the the red
+and blue ball chasing scene that you saw
+
+ align:start position:0%
+and blue ball chasing scene that you saw
+ 
+
+ align:start position:0%
+and blue ball chasing scene that you saw
+remember from Tomer that was 13 month
+
+ align:start position:0%
+remember from Tomer that was 13 month
+ 
+
+ align:start position:0%
+remember from Tomer that was 13 month
+old so there's definitely some form of
+
+ align:start position:0%
+old so there's definitely some form of
+ 
+
+ align:start position:0%
+old so there's definitely some form of
+kind of interpretation of beliefs and
+
+ align:start position:0%
+kind of interpretation of beliefs and
+ 
+
+ align:start position:0%
+kind of interpretation of beliefs and
+desires in some proto form that you can
+
+ align:start position:0%
+desires in some proto form that you can
+ 
+
+ align:start position:0%
+desires in some proto form that you can
+see even in in infants of around one
+
+ align:start position:0%
+see even in in infants of around one
+ 
+
+ align:start position:0%
+see even in in infants of around one
+year of age and it's it's exactly that
+
+ align:start position:0%
+year of age and it's it's exactly that
+ 
+
+ align:start position:0%
+year of age and it's it's exactly that
+kind of thing also remember that if you
+
+ align:start position:0%
+kind of thing also remember that if you
+ 
+
+ align:start position:0%
+kind of thing also remember that if you
+saw John Leonard's talk yesterday he was
+
+ align:start position:0%
+saw John Leonard's talk yesterday he was
+ 
+
+ align:start position:0%
+saw John Leonard's talk yesterday he was
+the robotics guy who talked about
+
+ align:start position:0%
+the robotics guy who talked about
+ 
+
+ align:start position:0%
+the robotics guy who talked about
+self-driving cars and how you know
+
+ align:start position:0%
+self-driving cars and how you know
+ 
+
+ align:start position:0%
+self-driving cars and how you know
+there's certain gaps in what they can do
+
+ align:start position:0%
+there's certain gaps in what they can do
+ 
+
+ align:start position:0%
+there's certain gaps in what they can do
+despite that all the publicity like they
+
+ align:start position:0%
+despite that all the publicity like they
+ 
+
+ align:start position:0%
+despite that all the publicity like they
+can't turn left basically I'm in an
+
+ align:start position:0%
+can't turn left basically I'm in an
+ 
+
+ align:start position:0%
+can't turn left basically I'm in an
+unrestricted intersection because
+
+ align:start position:0%
+unrestricted intersection because
+ 
+
+ align:start position:0%
+unrestricted intersection because
+there's a certain kind of theory of mine
+
+ align:start position:0%
+there's a certain kind of theory of mine
+ 
+
+ align:start position:0%
+there's a certain kind of theory of mine
+in street scenes when when cars could be
+
+ align:start position:0%
+in street scenes when when cars could be
+ 
+
+ align:start position:0%
+in street scenes when when cars could be
+coming and people could be crossing or
+
+ align:start position:0%
+coming and people could be crossing or
+ 
+
+ align:start position:0%
+coming and people could be crossing or
+all those things about the police
+
+ align:start position:0%
+all those things about the police
+ 
+
+ align:start position:0%
+all those things about the police
+officers like this part of why this is
+
+ align:start position:0%
+officers like this part of why this is
+ 
+
+ align:start position:0%
+officers like this part of why this is
+so exciting to me and why I love that
+
+ align:start position:0%
+so exciting to me and why I love that
+ 
+
+ align:start position:0%
+so exciting to me and why I love that
+talk is because it's this is I think the
+
+ align:start position:0%
+talk is because it's this is I think the
+ 
+
+ align:start position:0%
+talk is because it's this is I think the
+same common common sense knowledge that
+
+ align:start position:0%
+same common common sense knowledge that
+ 
+
+ align:start position:0%
+same common common sense knowledge that
+if we can really figure out how to
+
+ align:start position:0%
+if we can really figure out how to
+ 
+
+ align:start position:0%
+if we can really figure out how to
+sure this reasoning about beliefs and
+
+ align:start position:0%
+sure this reasoning about beliefs and
+ 
+
+ align:start position:0%
+sure this reasoning about beliefs and
+desires in the limited context where
+
+ align:start position:0%
+desires in the limited context where
+ 
+
+ align:start position:0%
+desires in the limited context where
+desires are people moving around in
+
+ align:start position:0%
+desires are people moving around in
+ 
+
+ align:start position:0%
+desires are people moving around in
+space around us and the beliefs or who
+
+ align:start position:0%
+space around us and the beliefs or who
+ 
+
+ align:start position:0%
+space around us and the beliefs or who
+can see who right and a man who can see
+
+ align:start position:0%
+can see who right and a man who can see
+ 
+
+ align:start position:0%
+can see who right and a man who can see
+who can see who right a lot of in
+
+ align:start position:0%
+who can see who right a lot of in
+ 
+
+ align:start position:0%
+who can see who right a lot of in
+driving the art of making eye contact
+
+ align:start position:0%
+driving the art of making eye contact
+ 
+
+ align:start position:0%
+driving the art of making eye contact
+with other drivers or pedestrians is
+
+ align:start position:0%
+with other drivers or pedestrians is
+ 
+
+ align:start position:0%
+with other drivers or pedestrians is
+seeing that they can see you or that
+
+ align:start position:0%
+seeing that they can see you or that
+ 
+
+ align:start position:0%
+seeing that they can see you or that
+they can see what you can see and they
+
+ align:start position:0%
+they can see what you can see and they
+ 
+
+ align:start position:0%
+they can see what you can see and they
+can see you seeing them it doesn't have
+
+ align:start position:0%
+can see you seeing them it doesn't have
+ 
+
+ align:start position:0%
+can see you seeing them it doesn't have
+to be super deeply recursive but it's a
+
+ align:start position:0%
+to be super deeply recursive but it's a
+ 
+
+ align:start position:0%
+to be super deeply recursive but it's a
+couple of layers deep we don't have to
+
+ align:start position:0%
+couple of layers deep we don't have to
+ 
+
+ align:start position:0%
+couple of layers deep we don't have to
+think about it consciously but we have
+
+ align:start position:0%
+think about it consciously but we have
+ 
+
+ align:start position:0%
+think about it consciously but we have
+to be able to do it so that's the kind
+
+ align:start position:0%
+to be able to do it so that's the kind
+ 
+
+ align:start position:0%
+to be able to do it so that's the kind
+of core belief desire theory of mind
+
+ align:start position:0%
+of core belief desire theory of mind
+ 
+
+ align:start position:0%
+of core belief desire theory of mind
+reasoning and here's how we've tried to
+
+ align:start position:0%
+reasoning and here's how we've tried to
+ 
+
+ align:start position:0%
+reasoning and here's how we've tried to
+capture this this with probabilistic
+
+ align:start position:0%
+capture this this with probabilistic
+ 
+
+ align:start position:0%
+capture this this with probabilistic
+programs this is work that Chris Baker
+
+ align:start position:0%
+programs this is work that Chris Baker
+ 
+
+ align:start position:0%
+programs this is work that Chris Baker
+started doing a few years ago we've and
+
+ align:start position:0%
+started doing a few years ago we've and
+ 
+
+ align:start position:0%
+started doing a few years ago we've and
+a lot of it joint with Rebecca Saxe and
+
+ align:start position:0%
+a lot of it joint with Rebecca Saxe and
+ 
+
+ align:start position:0%
+a lot of it joint with Rebecca Saxe and
+also with some of it with Julian Hara
+
+ align:start position:0%
+also with some of it with Julian Hara
+ 
+
+ align:start position:0%
+also with some of it with Julian Hara
+Edinger and some of it with Tomer so
+
+ align:start position:0%
+Edinger and some of it with Tomer so
+ 
+
+ align:start position:0%
+Edinger and some of it with Tomer so
+there's a whole bunch of us who've been
+
+ align:start position:0%
+there's a whole bunch of us who've been
+ 
+
+ align:start position:0%
+there's a whole bunch of us who've been
+working on versions of this but I'll
+
+ align:start position:0%
+working on versions of this but I'll
+ 
+
+ align:start position:0%
+working on versions of this but I'll
+just show you one or two examples it's
+
+ align:start position:0%
+just show you one or two examples it's
+ 
+
+ align:start position:0%
+just show you one or two examples it's
+again here the the key the key programs
+
+ align:start position:0%
+again here the the key the key programs
+ 
+
+ align:start position:0%
+again here the the key the key programs
+here are not graphics or physics engines
+
+ align:start position:0%
+here are not graphics or physics engines
+ 
+
+ align:start position:0%
+here are not graphics or physics engines
+but planning engines and perception
+
+ align:start position:0%
+but planning engines and perception
+ 
+
+ align:start position:0%
+but planning engines and perception
+engines so very simple kinds of robotics
+
+ align:start position:0%
+engines so very simple kinds of robotics
+ 
+
+ align:start position:0%
+engines so very simple kinds of robotics
+programs far too simple in this forum to
+
+ align:start position:0%
+programs far too simple in this forum to
+ 
+
+ align:start position:0%
+programs far too simple in this forum to
+build a self-driving car or a humanoid
+
+ align:start position:0%
+build a self-driving car or a humanoid
+ 
+
+ align:start position:0%
+build a self-driving car or a humanoid
+robot but maybe the kind of thing that
+
+ align:start position:0%
+robot but maybe the kind of thing that
+ 
+
+ align:start position:0%
+robot but maybe the kind of thing that
+in game game robots like the zombie or
+
+ align:start position:0%
+in game game robots like the zombie or
+ 
+
+ align:start position:0%
+in game game robots like the zombie or
+the security guard in quake or something
+
+ align:start position:0%
+the security guard in quake or something
+ 
+
+ align:start position:0%
+the security guard in quake or something
+might do something like this um so
+
+ align:start position:0%
+might do something like this um so
+ 
+
+ align:start position:0%
+might do something like this um so
+planning basically just means it's a
+
+ align:start position:0%
+planning basically just means it's a
+ 
+
+ align:start position:0%
+planning basically just means it's a
+little bit more than on it sort of
+
+ align:start position:0%
+little bit more than on it sort of
+ 
+
+ align:start position:0%
+little bit more than on it sort of
+shortest path planning but it's
+
+ align:start position:0%
+shortest path planning but it's
+ 
+
+ align:start position:0%
+shortest path planning but it's
+basically like find a sequence of
+
+ align:start position:0%
+basically like find a sequence of
+ 
+
+ align:start position:0%
+basically like find a sequence of
+actions in in a simple world like moving
+
+ align:start position:0%
+actions in in a simple world like moving
+ 
+
+ align:start position:0%
+actions in in a simple world like moving
+around a 2d environment that maximizes
+
+ align:start position:0%
+around a 2d environment that maximizes
+ 
+
+ align:start position:0%
+around a 2d environment that maximizes
+your long run expected reward so there's
+
+ align:start position:0%
+your long run expected reward so there's
+ 
+
+ align:start position:0%
+your long run expected reward so there's
+a kind of utility theory or what Laura
+
+ align:start position:0%
+a kind of utility theory or what Laura
+ 
+
+ align:start position:0%
+a kind of utility theory or what Laura
+Schultz calls a naive utility calculus
+
+ align:start position:0%
+Schultz calls a naive utility calculus
+ 
+
+ align:start position:0%
+Schultz calls a naive utility calculus
+here a calculation of costs and benefits
+
+ align:start position:0%
+here a calculation of costs and benefits
+ 
+
+ align:start position:0%
+here a calculation of costs and benefits
+where in a sense you get a big reward a
+
+ align:start position:0%
+where in a sense you get a big reward a
+ 
+
+ align:start position:0%
+where in a sense you get a big reward a
+good positive utility for getting to
+
+ align:start position:0%
+good positive utility for getting to
+ 
+
+ align:start position:0%
+good positive utility for getting to
+your goal and a small cost for each
+
+ align:start position:0%
+your goal and a small cost for each
+ 
+
+ align:start position:0%
+your goal and a small cost for each
+action you take and if you and under the
+
+ align:start position:0%
+action you take and if you and under the
+ 
+
+ align:start position:0%
+action you take and if you and under the
+under that view then in some sense and
+
+ align:start position:0%
+under that view then in some sense and
+ 
+
+ align:start position:0%
+under that view then in some sense and
+some actions might be costlier than
+
+ align:start position:0%
+some actions might be costlier than
+ 
+
+ align:start position:0%
+some actions might be costlier than
+others something that Homer is looking
+
+ align:start position:0%
+others something that Homer is looking
+ 
+
+ align:start position:0%
+others something that Homer is looking
+at in infants and something the Julian
+
+ align:start position:0%
+at in infants and something the Julian
+ 
+
+ align:start position:0%
+at in infants and something the Julian
+higher ed and jurors looked at in older
+
+ align:start position:0%
+higher ed and jurors looked at in older
+ 
+
+ align:start position:0%
+higher ed and jurors looked at in older
+kids this understanding of that but this
+
+ align:start position:0%
+kids this understanding of that but this
+ 
+
+ align:start position:0%
+kids this understanding of that but this
+this sort of basic cost benefit
+
+ align:start position:0%
+this sort of basic cost benefit
+ 
+
+ align:start position:0%
+this sort of basic cost benefit
+trade-off that is going on whenever you
+
+ align:start position:0%
+trade-off that is going on whenever you
+ 
+
+ align:start position:0%
+trade-off that is going on whenever you
+move around in environment and decide
+
+ align:start position:0%
+move around in environment and decide
+ 
+
+ align:start position:0%
+move around in environment and decide
+well is it worthwhile to go all the way
+
+ align:start position:0%
+well is it worthwhile to go all the way
+ 
+
+ align:start position:0%
+well is it worthwhile to go all the way
+there or you know well I know I like the
+
+ align:start position:0%
+there or you know well I know I like the
+ 
+
+ align:start position:0%
+there or you know well I know I like the
+coffee up at pie-in-the-sky better than
+
+ align:start position:0%
+coffee up at pie-in-the-sky better than
+ 
+
+ align:start position:0%
+coffee up at pie-in-the-sky better than
+the coffee and the dining-hall here at
+
+ align:start position:0%
+the coffee and the dining-hall here at
+ 
+
+ align:start position:0%
+the coffee and the dining-hall here at
+Swope but you know to think about am I
+
+ align:start position:0%
+Swope but you know to think about am I
+ 
+
+ align:start position:0%
+Swope but you know to think about am I
+gonna be late to my lecture am I gonna
+
+ align:start position:0%
+gonna be late to my lecture am I gonna
+ 
+
+ align:start position:0%
+gonna be late to my lecture am I gonna
+be late to Nancy's lecture those are
+
+ align:start position:0%
+be late to Nancy's lecture those are
+ 
+
+ align:start position:0%
+be late to Nancy's lecture those are
+different costs both costs it's that
+
+ align:start position:0%
+different costs both costs it's that
+ 
+
+ align:start position:0%
+different costs both costs it's that
+kind of calculation okay so here let me
+
+ align:start position:0%
+kind of calculation okay so here let me
+ 
+
+ align:start position:0%
+kind of calculation okay so here let me
+get more concrete so here's an example
+
+ align:start position:0%
+get more concrete so here's an example
+ 
+
+ align:start position:0%
+get more concrete so here's an example
+of a experiment that Chris did a few
+
+ align:start position:0%
+of a experiment that Chris did a few
+ 
+
+ align:start position:0%
+of a experiment that Chris did a few
+years ago we're again it's like what you
+
+ align:start position:0%
+years ago we're again it's like what you
+ 
+
+ align:start position:0%
+years ago we're again it's like what you
+saw with the Heider and Simmel the
+
+ align:start position:0%
+saw with the Heider and Simmel the
+ 
+
+ align:start position:0%
+saw with the Heider and Simmel the
+squares and Trump and the triangles and
+
+ align:start position:0%
+squares and Trump and the triangles and
+ 
+
+ align:start position:0%
+squares and Trump and the triangles and
+circles or the south gain and chipra the
+
+ align:start position:0%
+circles or the south gain and chipra the
+ 
+
+ align:start position:0%
+circles or the south gain and chipra the
+red and blue balls chasing each other
+
+ align:start position:0%
+red and blue balls chasing each other
+ 
+
+ align:start position:0%
+red and blue balls chasing each other
+very simple stuff here you see an agent
+
+ align:start position:0%
+very simple stuff here you see an agent
+ 
+
+ align:start position:0%
+very simple stuff here you see an agent
+it's like an overhead view of a room 2d
+
+ align:start position:0%
+it's like an overhead view of a room 2d
+ 
+
+ align:start position:0%
+it's like an overhead view of a room 2d
+environment from the top the agents
+
+ align:start position:0%
+environment from the top the agents
+ 
+
+ align:start position:0%
+environment from the top the agents
+moving along some path there are three
+
+ align:start position:0%
+moving along some path there are three
+ 
+
+ align:start position:0%
+moving along some path there are three
+possible goals a B or C and then there's
+
+ align:start position:0%
+possible goals a B or C and then there's
+ 
+
+ align:start position:0%
+possible goals a B or C and then there's
+maybe some obstacles or constraints like
+
+ align:start position:0%
+maybe some obstacles or constraints like
+ 
+
+ align:start position:0%
+maybe some obstacles or constraints like
+a wall like like you saw in those movies
+
+ align:start position:0%
+a wall like like you saw in those movies
+ 
+
+ align:start position:0%
+a wall like like you saw in those movies
+maybe the wall has a hole that he can
+
+ align:start position:0%
+maybe the wall has a hole that he can
+ 
+
+ align:start position:0%
+maybe the wall has a hole that he can
+pass through maybe it doesn't and across
+
+ align:start position:0%
+pass through maybe it doesn't and across
+ 
+
+ align:start position:0%
+pass through maybe it doesn't and across
+different trials of the experiment just
+
+ align:start position:0%
+different trials of the experiment just
+ 
+
+ align:start position:0%
+different trials of the experiment just
+like in the physics stuff we vary all
+
+ align:start position:0%
+like in the physics stuff we vary all
+ 
+
+ align:start position:0%
+like in the physics stuff we vary all
+the block configurations and so on here
+
+ align:start position:0%
+the block configurations and so on here
+ 
+
+ align:start position:0%
+the block configurations and so on here
+we vary where the goals are we vary
+
+ align:start position:0%
+we vary where the goals are we vary
+ 
+
+ align:start position:0%
+we vary where the goals are we vary
+whether the wall has a hole or not we
+
+ align:start position:0%
+whether the wall has a hole or not we
+ 
+
+ align:start position:0%
+whether the wall has a hole or not we
+vary the agents paths on different
+
+ align:start position:0%
+vary the agents paths on different
+ 
+
+ align:start position:0%
+vary the agents paths on different
+trials we also stop it at different
+
+ align:start position:0%
+trials we also stop it at different
+ 
+
+ align:start position:0%
+trials we also stop it at different
+points because we're trying to see as
+
+ align:start position:0%
+points because we're trying to see as
+ 
+
+ align:start position:0%
+points because we're trying to see as
+you watch this agent move around action
+
+ align:start position:0%
+you watch this agent move around action
+ 
+
+ align:start position:0%
+you watch this agent move around action
+unfolds over time
+
+ align:start position:0%
+unfolds over time
+ 
+
+ align:start position:0%
+unfolds over time
+how do your guesses about his goal
+
+ align:start position:0%
+how do your guesses about his goal
+ 
+
+ align:start position:0%
+how do your guesses about his goal
+change over time and what you see that
+
+ align:start position:0%
+change over time and what you see that
+ 
+
+ align:start position:0%
+change over time and what you see that
+so these are just examples of a few of
+
+ align:start position:0%
+so these are just examples of a few of
+ 
+
+ align:start position:0%
+so these are just examples of a few of
+the few of the scenes and here what you
+
+ align:start position:0%
+the few of the scenes and here what you
+ 
+
+ align:start position:0%
+the few of the scenes and here what you
+see our examples of the data again this
+
+ align:start position:0%
+see our examples of the data again this
+ 
+
+ align:start position:0%
+see our examples of the data again this
+is the y-axis is the average human
+
+ align:start position:0%
+is the y-axis is the average human
+ 
+
+ align:start position:0%
+is the y-axis is the average human
+judgment red blue and green is
+
+ align:start position:0%
+judgment red blue and green is
+ 
+
+ align:start position:0%
+judgment red blue and green is
+color-coded to the goal they're just
+
+ align:start position:0%
+color-coded to the goal they're just
+ 
+
+ align:start position:0%
+color-coded to the goal they're just
+asked how likely do you think each of
+
+ align:start position:0%
+asked how likely do you think each of
+ 
+
+ align:start position:0%
+asked how likely do you think each of
+those three things is his goal and then
+
+ align:start position:0%
+those three things is his goal and then
+ 
+
+ align:start position:0%
+those three things is his goal and then
+here the x-axis is time so these are
+
+ align:start position:0%
+here the x-axis is time so these are
+ 
+
+ align:start position:0%
+here the x-axis is time so these are
+time steps that we that we ask at
+
+ align:start position:0%
+time steps that we that we ask at
+ 
+
+ align:start position:0%
+time steps that we that we ask at
+different points along the trajectory
+
+ align:start position:0%
+different points along the trajectory
+ 
+
+ align:start position:0%
+different points along the trajectory
+and what you can see is that people are
+
+ align:start position:0%
+and what you can see is that people are
+ 
+
+ align:start position:0%
+and what you can see is that people are
+making various systemic kinds of
+
+ align:start position:0%
+making various systemic kinds of
+ 
+
+ align:start position:0%
+making various systemic kinds of
+judgments sometimes they're not sure
+
+ align:start position:0%
+judgments sometimes they're not sure
+ 
+
+ align:start position:0%
+judgments sometimes they're not sure
+whether his goal is a or b but they know
+
+ align:start position:0%
+whether his goal is a or b but they know
+ 
+
+ align:start position:0%
+whether his goal is a or b but they know
+it's not C and then after a little while
+
+ align:start position:0%
+it's not C and then after a little while
+ 
+
+ align:start position:0%
+it's not C and then after a little while
+there's some some Keese that happens and
+
+ align:start position:0%
+there's some some Keese that happens and
+ 
+
+ align:start position:0%
+there's some some Keese that happens and
+now they're quite sure it's a and not B
+
+ align:start position:0%
+now they're quite sure it's a and not B
+ 
+
+ align:start position:0%
+now they're quite sure it's a and not B
+or they could change their mind you know
+
+ align:start position:0%
+or they could change their mind you know
+ 
+
+ align:start position:0%
+or they could change their mind you know
+here people were pretty sure it was
+
+ align:start position:0%
+here people were pretty sure it was
+ 
+
+ align:start position:0%
+here people were pretty sure it was
+either green or red but not blue and
+
+ align:start position:0%
+either green or red but not blue and
+ 
+
+ align:start position:0%
+either green or red but not blue and
+then there comes a point where it's
+
+ align:start position:0%
+then there comes a point where it's
+ 
+
+ align:start position:0%
+then there comes a point where it's
+surely not green but it might be blue or
+
+ align:start position:0%
+surely not green but it might be blue or
+ 
+
+ align:start position:0%
+surely not green but it might be blue or
+red oh no then it's red here they were
+
+ align:start position:0%
+red oh no then it's red here they were
+ 
+
+ align:start position:0%
+red oh no then it's red here they were
+pretty sure it was green then nope
+
+ align:start position:0%
+pretty sure it was green then nope
+ 
+
+ align:start position:0%
+pretty sure it was green then nope
+definitely not green and now I think
+
+ align:start position:0%
+definitely not green and now I think
+ 
+
+ align:start position:0%
+definitely not green and now I think
+it's red it was probably never blue okay
+
+ align:start position:0%
+it's red it was probably never blue okay
+ 
+
+ align:start position:0%
+it's red it was probably never blue okay
+and this really striking thing to us is
+
+ align:start position:0%
+and this really striking thing to us is
+ 
+
+ align:start position:0%
+and this really striking thing to us is
+how closely you can match
+
+ align:start position:0%
+how closely you can match
+ 
+
+ align:start position:0%
+how closely you can match
+those judgments with this very simple
+
+ align:start position:0%
+those judgments with this very simple
+ 
+
+ align:start position:0%
+those judgments with this very simple
+probabilistic planning program run in
+
+ align:start position:0%
+probabilistic planning program run in
+ 
+
+ align:start position:0%
+probabilistic planning program run in
+Reverse so we take again this simple
+
+ align:start position:0%
+Reverse so we take again this simple
+ 
+
+ align:start position:0%
+Reverse so we take again this simple
+planning program that just says
+
+ align:start position:0%
+planning program that just says
+ 
+
+ align:start position:0%
+planning program that just says
+basically try to just just kind of get
+
+ align:start position:0%
+basically try to just just kind of get
+ 
+
+ align:start position:0%
+basically try to just just kind of get
+as efficiently as possible to your goal
+
+ align:start position:0%
+as efficiently as possible to your goal
+ 
+
+ align:start position:0%
+as efficiently as possible to your goal
+I don't know if your goal is though I
+
+ align:start position:0%
+I don't know if your goal is though I
+ 
+
+ align:start position:0%
+I don't know if your goal is though I
+observe your actions that result from an
+
+ align:start position:0%
+observe your actions that result from an
+ 
+
+ align:start position:0%
+observe your actions that result from an
+efficient plan and I want to work
+
+ align:start position:0%
+efficient plan and I want to work
+ 
+
+ align:start position:0%
+efficient plan and I want to work
+backwards to say what do I think your
+
+ align:start position:0%
+backwards to say what do I think your
+ 
+
+ align:start position:0%
+backwards to say what do I think your
+goal is your desire the rewarding state
+
+ align:start position:0%
+goal is your desire the rewarding state
+ 
+
+ align:start position:0%
+goal is your desire the rewarding state
+and just doing that just basically
+
+ align:start position:0%
+and just doing that just basically
+ 
+
+ align:start position:0%
+and just doing that just basically
+perfectly predicts people's data I mean
+
+ align:start position:0%
+perfectly predicts people's data I mean
+ 
+
+ align:start position:0%
+perfectly predicts people's data I mean
+this is of all the mathematical models
+
+ align:start position:0%
+this is of all the mathematical models
+ 
+
+ align:start position:0%
+this is of all the mathematical models
+of behavior I've ever had a hand in
+
+ align:start position:0%
+of behavior I've ever had a hand in
+ 
+
+ align:start position:0%
+of behavior I've ever had a hand in
+building this one works the best
+
+ align:start position:0%
+building this one works the best
+ 
+
+ align:start position:0%
+building this one works the best
+it's really quite striking to me it was
+
+ align:start position:0%
+it's really quite striking to me it was
+ 
+
+ align:start position:0%
+it's really quite striking to me it was
+striking because I was I came in
+
+ align:start position:0%
+striking because I was I came in
+ 
+
+ align:start position:0%
+striking because I was I came in
+thinking this would be a high level very
+
+ align:start position:0%
+thinking this would be a high level very
+ 
+
+ align:start position:0%
+thinking this would be a high level very
+high level weird flaky hard to model
+
+ align:start position:0%
+high level weird flaky hard to model
+ 
+
+ align:start position:0%
+high level weird flaky hard to model
+thing um here's just one more example of
+
+ align:start position:0%
+thing um here's just one more example of
+ 
+
+ align:start position:0%
+thing um here's just one more example of
+one of these things which actually puts
+
+ align:start position:0%
+one of these things which actually puts
+ 
+
+ align:start position:0%
+one of these things which actually puts
+beliefs in there and not just desire so
+
+ align:start position:0%
+beliefs in there and not just desire so
+ 
+
+ align:start position:0%
+beliefs in there and not just desire so
+it's a key part of intuitive psychology
+
+ align:start position:0%
+it's a key part of intuitive psychology
+ 
+
+ align:start position:0%
+it's a key part of intuitive psychology
+that we do joint inference over beliefs
+
+ align:start position:0%
+that we do joint inference over beliefs
+ 
+
+ align:start position:0%
+that we do joint inference over beliefs
+and desires in this one here we assume
+
+ align:start position:0%
+and desires in this one here we assume
+ 
+
+ align:start position:0%
+and desires in this one here we assume
+that you the subject the agent who's
+
+ align:start position:0%
+that you the subject the agent who's
+ 
+
+ align:start position:0%
+that you the subject the agent who's
+moving around all of us have shared full
+
+ align:start position:0%
+moving around all of us have shared full
+ 
+
+ align:start position:0%
+moving around all of us have shared full
+knowledge of the world so we know where
+
+ align:start position:0%
+knowledge of the world so we know where
+ 
+
+ align:start position:0%
+knowledge of the world so we know where
+the objects are we know where the holes
+
+ align:start position:0%
+the objects are we know where the holes
+ 
+
+ align:start position:0%
+the objects are we know where the holes
+are there's none of this false belief
+
+ align:start position:0%
+are there's none of this false belief
+ 
+
+ align:start position:0%
+are there's none of this false belief
+like you think something is there when
+
+ align:start position:0%
+like you think something is there when
+ 
+
+ align:start position:0%
+like you think something is there when
+it isn't now here's some later work that
+
+ align:start position:0%
+it isn't now here's some later work that
+ 
+
+ align:start position:0%
+it isn't now here's some later work that
+Chris did where I'm what we call the
+
+ align:start position:0%
+Chris did where I'm what we call the
+ 
+
+ align:start position:0%
+Chris did where I'm what we call the
+food truck studies where here we add in
+
+ align:start position:0%
+food truck studies where here we add in
+ 
+
+ align:start position:0%
+food truck studies where here we add in
+some uncertainty about beliefs in
+
+ align:start position:0%
+some uncertainty about beliefs in
+ 
+
+ align:start position:0%
+some uncertainty about beliefs in
+addition to desires and it's easiest
+
+ align:start position:0%
+addition to desires and it's easiest
+ 
+
+ align:start position:0%
+addition to desires and it's easiest
+just to explain what this one example up
+
+ align:start position:0%
+just to explain what this one example up
+ 
+
+ align:start position:0%
+just to explain what this one example up
+there in the upper left so here and this
+
+ align:start position:0%
+there in the upper left so here and this
+ 
+
+ align:start position:0%
+there in the upper left so here and this
+like a lot of university campuses lunch
+
+ align:start position:0%
+like a lot of university campuses lunch
+ 
+
+ align:start position:0%
+like a lot of university campuses lunch
+is best found at food trucks which can
+
+ align:start position:0%
+is best found at food trucks which can
+ 
+
+ align:start position:0%
+is best found at food trucks which can
+park in different spots around campus
+
+ align:start position:0%
+park in different spots around campus
+ 
+
+ align:start position:0%
+park in different spots around campus
+here the yellow the two yellow squares
+
+ align:start position:0%
+here the yellow the two yellow squares
+ 
+
+ align:start position:0%
+here the yellow the two yellow squares
+show the two parking spots on this part
+
+ align:start position:0%
+show the two parking spots on this part
+ 
+
+ align:start position:0%
+show the two parking spots on this part
+of campus and there are several
+
+ align:start position:0%
+of campus and there are several
+ 
+
+ align:start position:0%
+of campus and there are several
+different trucks that can common park in
+
+ align:start position:0%
+different trucks that can common park in
+ 
+
+ align:start position:0%
+different trucks that can common park in
+different places on different days
+
+ align:start position:0%
+different places on different days
+ 
+
+ align:start position:0%
+different places on different days
+there's a Korean truck that's K there's
+
+ align:start position:0%
+there's a Korean truck that's K there's
+ 
+
+ align:start position:0%
+there's a Korean truck that's K there's
+a Lebanese truck that's L there's also
+
+ align:start position:0%
+a Lebanese truck that's L there's also
+ 
+
+ align:start position:0%
+a Lebanese truck that's L there's also
+other trucks like a Mexican truck but
+
+ align:start position:0%
+other trucks like a Mexican truck but
+ 
+
+ align:start position:0%
+other trucks like a Mexican truck but
+there's only two spots so if the Korean
+
+ align:start position:0%
+there's only two spots so if the Korean
+ 
+
+ align:start position:0%
+there's only two spots so if the Korean
+one parts there on the Lebanese one
+
+ align:start position:0%
+one parts there on the Lebanese one
+ 
+
+ align:start position:0%
+one parts there on the Lebanese one
+parts there the Mexican has to have go
+
+ align:start position:0%
+parts there the Mexican has to have go
+ 
+
+ align:start position:0%
+parts there the Mexican has to have go
+somewhere else or can't come there today
+
+ align:start position:0%
+somewhere else or can't come there today
+ 
+
+ align:start position:0%
+somewhere else or can't come there today
+and on some days the trucks park in
+
+ align:start position:0%
+and on some days the trucks park in
+ 
+
+ align:start position:0%
+and on some days the trucks park in
+different places and some or a spot
+
+ align:start position:0%
+different places and some or a spot
+ 
+
+ align:start position:0%
+different places and some or a spot
+could also be unoccupied the trucks
+
+ align:start position:0%
+could also be unoccupied the trucks
+ 
+
+ align:start position:0%
+could also be unoccupied the trucks
+could be elsewhere so look at what
+
+ align:start position:0%
+could be elsewhere so look at what
+ 
+
+ align:start position:0%
+could be elsewhere so look at what
+happens on this day our friendly grad
+
+ align:start position:0%
+happens on this day our friendly grad
+ 
+
+ align:start position:0%
+happens on this day our friendly grad
+student Harold
+
+ align:start position:0%
+student Harold
+ 
+
+ align:start position:0%
+student Harold
+comes out from his office here and
+
+ align:start position:0%
+comes out from his office here and
+ 
+
+ align:start position:0%
+comes out from his office here and
+importantly the way we model interesting
+
+ align:start position:0%
+importantly the way we model interesting
+ 
+
+ align:start position:0%
+importantly the way we model interesting
+notions of evolving belief is that now
+
+ align:start position:0%
+notions of evolving belief is that now
+ 
+
+ align:start position:0%
+notions of evolving belief is that now
+we've got that perception and inference
+
+ align:start position:0%
+we've got that perception and inference
+ 
+
+ align:start position:0%
+we've got that perception and inference
+arrow there so Harold forms his belief
+
+ align:start position:0%
+arrow there so Harold forms his belief
+ 
+
+ align:start position:0%
+arrow there so Harold forms his belief
+about what's where based on what he can
+
+ align:start position:0%
+about what's where based on what he can
+ 
+
+ align:start position:0%
+about what's where based on what he can
+see and it's just the simplest
+
+ align:start position:0%
+see and it's just the simplest
+ 
+
+ align:start position:0%
+see and it's just the simplest
+perception model just line-of-sight
+
+ align:start position:0%
+perception model just line-of-sight
+ 
+
+ align:start position:0%
+perception model just line-of-sight
+access
+
+ align:start position:0%
+access
+ 
+
+ align:start position:0%
+access
+we assume he can kind of see anything
+
+ align:start position:0%
+we assume he can kind of see anything
+ 
+
+ align:start position:0%
+we assume he can kind of see anything
+that's unobstructed in his line of sight
+
+ align:start position:0%
+that's unobstructed in his line of sight
+ 
+
+ align:start position:0%
+that's unobstructed in his line of sight
+so that means that when he comes out
+
+ align:start position:0%
+so that means that when he comes out
+ 
+
+ align:start position:0%
+so that means that when he comes out
+here he can see that there was the
+
+ align:start position:0%
+here he can see that there was the
+ 
+
+ align:start position:0%
+here he can see that there was the
+Korean truck here but he can't see this
+
+ align:start position:0%
+Korean truck here but he can't see this
+ 
+
+ align:start position:0%
+Korean truck here but he can't see this
+is a wall or a building he can't see
+
+ align:start position:0%
+is a wall or a building he can't see
+ 
+
+ align:start position:0%
+is a wall or a building he can't see
+what's on the other side of that okay so
+
+ align:start position:0%
+what's on the other side of that okay so
+ 
+
+ align:start position:0%
+what's on the other side of that okay so
+what does he do well he walks down here
+
+ align:start position:0%
+what does he do well he walks down here
+ 
+
+ align:start position:0%
+what does he do well he walks down here
+he goes past the Korean truck goes
+
+ align:start position:0%
+he goes past the Korean truck goes
+ 
+
+ align:start position:0%
+he goes past the Korean truck goes
+around the other side of the building
+
+ align:start position:0%
+around the other side of the building
+ 
+
+ align:start position:0%
+around the other side of the building
+now at this point his line of sight can
+
+ align:start position:0%
+now at this point his line of sight can
+ 
+
+ align:start position:0%
+now at this point his line of sight can
+gives him he can see that there's the
+
+ align:start position:0%
+gives him he can see that there's the
+ 
+
+ align:start position:0%
+gives him he can see that there's the
+Lebanese truck there he turns around and
+
+ align:start position:0%
+Lebanese truck there he turns around and
+ 
+
+ align:start position:0%
+Lebanese truck there he turns around and
+he goes back to the Korean truck so the
+
+ align:start position:0%
+he goes back to the Korean truck so the
+ 
+
+ align:start position:0%
+he goes back to the Korean truck so the
+question for you is what is his favorite
+
+ align:start position:0%
+question for you is what is his favorite
+ 
+
+ align:start position:0%
+question for you is what is his favorite
+truck is it Korean Lebanese or Mexican
+
+ align:start position:0%
+truck is it Korean Lebanese or Mexican
+ 
+
+ align:start position:0%
+truck is it Korean Lebanese or Mexican
+Mexican yeah it doesn't sound very hard
+
+ align:start position:0%
+Mexican yeah it doesn't sound very hard
+ 
+
+ align:start position:0%
+Mexican yeah it doesn't sound very hard
+to figure that out but it's quite
+
+ align:start position:0%
+to figure that out but it's quite
+ 
+
+ align:start position:0%
+to figure that out but it's quite
+interesting because the Mexican one
+
+ align:start position:0%
+interesting because the Mexican one
+ 
+
+ align:start position:0%
+interesting because the Mexican one
+isn't even in the scene right the most
+
+ align:start position:0%
+isn't even in the scene right the most
+ 
+
+ align:start position:0%
+isn't even in the scene right the most
+basic kind of goal goal recognition and
+
+ align:start position:0%
+basic kind of goal goal recognition and
+ 
+
+ align:start position:0%
+basic kind of goal goal recognition and
+this again cuts right to the heart of
+
+ align:start position:0%
+this again cuts right to the heart of
+ 
+
+ align:start position:0%
+this again cuts right to the heart of
+the differencing recognition and
+
+ align:start position:0%
+the differencing recognition and
+ 
+
+ align:start position:0%
+the differencing recognition and
+explanation right there's been a lot of
+
+ align:start position:0%
+explanation right there's been a lot of
+ 
+
+ align:start position:0%
+explanation right there's been a lot of
+progress in machine vision systems for
+
+ align:start position:0%
+progress in machine vision systems for
+ 
+
+ align:start position:0%
+progress in machine vision systems for
+action understanding action recognition
+
+ align:start position:0%
+action understanding action recognition
+ 
+
+ align:start position:0%
+action understanding action recognition
+and so on and they do things like you
+
+ align:start position:0%
+and so on and they do things like you
+ 
+
+ align:start position:0%
+and so on and they do things like you
+know for example they take video and the
+
+ align:start position:0%
+know for example they take video and the
+ 
+
+ align:start position:0%
+know for example they take video and the
+best cue that somebody wants something
+
+ align:start position:0%
+best cue that somebody wants something
+ 
+
+ align:start position:0%
+best cue that somebody wants something
+is if they reach for it or move towards
+
+ align:start position:0%
+is if they reach for it or move towards
+ 
+
+ align:start position:0%
+is if they reach for it or move towards
+it and that's certainly what was going
+
+ align:start position:0%
+it and that's certainly what was going
+ 
+
+ align:start position:0%
+it and that's certainly what was going
+on here right in all of these scenes
+
+ align:start position:0%
+on here right in all of these scenes
+ 
+
+ align:start position:0%
+on here right in all of these scenes
+your best inference about what the guy's
+
+ align:start position:0%
+your best inference about what the guy's
+ 
+
+ align:start position:0%
+your best inference about what the guy's
+goal is is which thing is he moving
+
+ align:start position:0%
+goal is is which thing is he moving
+ 
+
+ align:start position:0%
+goal is is which thing is he moving
+towards and it's just it's just subtle
+
+ align:start position:0%
+towards and it's just it's just subtle
+ 
+
+ align:start position:0%
+towards and it's just it's just subtle
+to parse out the relative degrees of
+
+ align:start position:0%
+to parse out the relative degrees of
+ 
+
+ align:start position:0%
+to parse out the relative degrees of
+confidence when there's a complex
+
+ align:start position:0%
+confidence when there's a complex
+ 
+
+ align:start position:0%
+confidence when there's a complex
+environment with constraints but in
+
+ align:start position:0%
+environment with constraints but in
+ 
+
+ align:start position:0%
+environment with constraints but in
+every case by the end it's clear he's
+
+ align:start position:0%
+every case by the end it's clear he's
+ 
+
+ align:start position:0%
+every case by the end it's clear he's
+going for one thing and the thing he is
+
+ align:start position:0%
+going for one thing and the thing he is
+ 
+
+ align:start position:0%
+going for one thing and the thing he is
+moving towards is the thing he wants but
+
+ align:start position:0%
+moving towards is the thing he wants but
+ 
+
+ align:start position:0%
+moving towards is the thing he wants but
+here you have no trouble realizing that
+
+ align:start position:0%
+here you have no trouble realizing that
+ 
+
+ align:start position:0%
+here you have no trouble realizing that
+his goal is something that isn't even
+
+ align:start position:0%
+his goal is something that isn't even
+ 
+
+ align:start position:0%
+his goal is something that isn't even
+present in the scene yet he's still
+
+ align:start position:0%
+present in the scene yet he's still
+ 
+
+ align:start position:0%
+present in the scene yet he's still
+moving towards it in a sense he's moving
+
+ align:start position:0%
+moving towards it in a sense he's moving
+ 
+
+ align:start position:0%
+moving towards it in a sense he's moving
+towards his mental representation of it
+
+ align:start position:0%
+towards his mental representation of it
+ 
+
+ align:start position:0%
+towards his mental representation of it
+right he's moving towards the Mexican
+
+ align:start position:0%
+right he's moving towards the Mexican
+ 
+
+ align:start position:0%
+right he's moving towards the Mexican
+truck in his mind's model and that's him
+
+ align:start position:0%
+truck in his mind's model and that's him
+ 
+
+ align:start position:0%
+truck in his mind's model and that's him
+explaining the data he sees right for
+
+ align:start position:0%
+explaining the data he sees right for
+ 
+
+ align:start position:0%
+explaining the data he sees right for
+some reason he must have had maybe a
+
+ align:start position:0%
+some reason he must have had maybe a
+ 
+
+ align:start position:0%
+some reason he must have had maybe a
+prior belief that the Mexican truck
+
+ align:start position:0%
+prior belief that the Mexican truck
+ 
+
+ align:start position:0%
+prior belief that the Mexican truck
+would be there so he formed a plan to go
+
+ align:start position:0%
+would be there so he formed a plan to go
+ 
+
+ align:start position:0%
+would be there so he formed a plan to go
+there and in fact we can ask people not
+
+ align:start position:0%
+there and in fact we can ask people not
+ 
+
+ align:start position:0%
+there and in fact we can ask people not
+only which truck does he like this is
+
+ align:start position:0%
+only which truck does he like this is
+ 
+
+ align:start position:0%
+only which truck does he like this is
+Mexican truck that's what people say and
+
+ align:start position:0%
+Mexican truck that's what people say and
+ 
+
+ align:start position:0%
+Mexican truck that's what people say and
+here's the model but we also asked them
+
+ align:start position:0%
+here's the model but we also asked them
+ 
+
+ align:start position:0%
+here's the model but we also asked them
+a belief inference we say I'm prior to
+
+ align:start position:0%
+a belief inference we say I'm prior to
+ 
+
+ align:start position:0%
+a belief inference we say I'm prior to
+setting out what did Harold think was on
+
+ align:start position:0%
+setting out what did Harold think was on
+ 
+
+ align:start position:0%
+setting out what did Harold think was on
+the other side did he what was parked on
+
+ align:start position:0%
+the other side did he what was parked on
+ 
+
+ align:start position:0%
+the other side did he what was parked on
+the other spot that he couldn't see did
+
+ align:start position:0%
+the other spot that he couldn't see did
+ 
+
+ align:start position:0%
+the other spot that he couldn't see did
+he think it was Lebanese Mexican or a
+
+ align:start position:0%
+he think it was Lebanese Mexican or a
+ 
+
+ align:start position:0%
+he think it was Lebanese Mexican or a
+neither and we asked a degree of belief
+
+ align:start position:0%
+neither and we asked a degree of belief
+ 
+
+ align:start position:0%
+neither and we asked a degree of belief
+so you could say he had no idea but
+
+ align:start position:0%
+so you could say he had no idea but
+ 
+
+ align:start position:0%
+so you could say he had no idea but
+interestingly people say he probably
+
+ align:start position:0%
+interestingly people say he probably
+ 
+
+ align:start position:0%
+interestingly people say he probably
+thought it was Mexican
+
+ align:start position:0%
+thought it was Mexican
+ 
+
+ align:start position:0%
+thought it was Mexican
+because how else could you explain what
+
+ align:start position:0%
+because how else could you explain what
+ 
+
+ align:start position:0%
+because how else could you explain what
+he's doing right so I mean I think this
+
+ align:start position:0%
+he's doing right so I mean I think this
+ 
+
+ align:start position:0%
+he's doing right so I mean I think this
+is if I had to point to just one example
+
+ align:start position:0%
+is if I had to point to just one example
+ 
+
+ align:start position:0%
+is if I had to point to just one example
+of cognition as explanation it's this
+
+ align:start position:0%
+of cognition as explanation it's this
+ 
+
+ align:start position:0%
+of cognition as explanation it's this
+right he's the only sensible way and
+
+ align:start position:0%
+right he's the only sensible way and
+ 
+
+ align:start position:0%
+right he's the only sensible way and
+it's a very intuitive and compelling way
+
+ align:start position:0%
+it's a very intuitive and compelling way
+ 
+
+ align:start position:0%
+it's a very intuitive and compelling way
+to explain why did he go the way he did
+
+ align:start position:0%
+to explain why did he go the way he did
+ 
+
+ align:start position:0%
+to explain why did he go the way he did
+and then turn around just when he did
+
+ align:start position:0%
+and then turn around just when he did
+ 
+
+ align:start position:0%
+and then turn around just when he did
+and wind up just where he did is this
+
+ align:start position:0%
+and wind up just where he did is this
+ 
+
+ align:start position:0%
+and wind up just where he did is this
+set of six inferences basically that his
+
+ align:start position:0%
+set of six inferences basically that his
+ 
+
+ align:start position:0%
+set of six inferences basically that his
+favorite is Mexican his second favorite
+
+ align:start position:0%
+favorite is Mexican his second favorite
+ 
+
+ align:start position:0%
+favorite is Mexican his second favorite
+is Korea and that's also important his
+
+ align:start position:0%
+is Korea and that's also important his
+ 
+
+ align:start position:0%
+is Korea and that's also important his
+least favorite is Lebanese and he
+
+ align:start position:0%
+least favorite is Lebanese and he
+ 
+
+ align:start position:0%
+least favorite is Lebanese and he
+thought that Mexican was there which is
+
+ align:start position:0%
+thought that Mexican was there which is
+ 
+
+ align:start position:0%
+thought that Mexican was there which is
+why it was worthwhile to go and check at
+
+ align:start position:0%
+why it was worthwhile to go and check at
+ 
+
+ align:start position:0%
+why it was worthwhile to go and check at
+least he thought it was likely he wasn't
+
+ align:start position:0%
+least he thought it was likely he wasn't
+ 
+
+ align:start position:0%
+least he thought it was likely he wasn't
+sure it's right notice it's not very
+
+ align:start position:0%
+sure it's right notice it's not very
+ 
+
+ align:start position:0%
+sure it's right notice it's not very
+high but it was more likely than the
+
+ align:start position:0%
+high but it was more likely than the
+ 
+
+ align:start position:0%
+high but it was more likely than the
+other possibilities because of course if
+
+ align:start position:0%
+other possibilities because of course if
+ 
+
+ align:start position:0%
+other possibilities because of course if
+he thought if he was quite sure it was
+
+ align:start position:0%
+he thought if he was quite sure it was
+ 
+
+ align:start position:0%
+he thought if he was quite sure it was
+Lebanese well he wouldn't have bothered
+
+ align:start position:0%
+Lebanese well he wouldn't have bothered
+ 
+
+ align:start position:0%
+Lebanese well he wouldn't have bothered
+to go around there and in fact you do
+
+ align:start position:0%
+to go around there and in fact you do
+ 
+
+ align:start position:0%
+to go around there and in fact you do
+see that so you have ones I guess I
+
+ align:start position:0%
+see that so you have ones I guess I
+ 
+
+ align:start position:0%
+see that so you have ones I guess I
+don't have them here but there are
+
+ align:start position:0%
+don't have them here but there are
+ 
+
+ align:start position:0%
+don't have them here but there are
+scenes where he just goes straight here
+
+ align:start position:0%
+scenes where he just goes straight here
+ 
+
+ align:start position:0%
+scenes where he just goes straight here
+and then you know that's consistent with
+
+ align:start position:0%
+and then you know that's consistent with
+ 
+
+ align:start position:0%
+and then you know that's consistent with
+him thinking Kausalya was Lebanese and
+
+ align:start position:0%
+him thinking Kausalya was Lebanese and
+ 
+
+ align:start position:0%
+him thinking Kausalya was Lebanese and
+if he thought nothing was there well
+
+ align:start position:0%
+if he thought nothing was there well
+ 
+
+ align:start position:0%
+if he thought nothing was there well
+again he wouldn't have gone to check all
+
+ align:start position:0%
+again he wouldn't have gone to check all
+ 
+
+ align:start position:0%
+again he wouldn't have gone to check all
+right and again this model is extremely
+
+ align:start position:0%
+right and again this model is extremely
+ 
+
+ align:start position:0%
+right and again this model is extremely
+quantitatively predictive of people's
+
+ align:start position:0%
+quantitatively predictive of people's
+ 
+
+ align:start position:0%
+quantitatively predictive of people's
+judgments about both desires and beliefs
+
+ align:start position:0%
+judgments about both desires and beliefs
+ 
+
+ align:start position:0%
+judgments about both desires and beliefs
+you can read in some of Battaglia's
+
+ align:start position:0%
+you can read in some of Battaglia's
+ 
+
+ align:start position:0%
+you can read in some of Battaglia's
+papers ways in which you take the very
+
+ align:start position:0%
+papers ways in which you take the very
+ 
+
+ align:start position:0%
+papers ways in which you take the very
+same physics engine and use it for all
+
+ align:start position:0%
+same physics engine and use it for all
+ 
+
+ align:start position:0%
+same physics engine and use it for all
+these different tasks including sort of
+
+ align:start position:0%
+these different tasks including sort of
+ 
+
+ align:start position:0%
+these different tasks including sort of
+slightly weird ones like these tasks if
+
+ align:start position:0%
+slightly weird ones like these tasks if
+ 
+
+ align:start position:0%
+slightly weird ones like these tasks if
+if you know if you bump the table are
+
+ align:start position:0%
+if you know if you bump the table are
+ 
+
+ align:start position:0%
+if you know if you bump the table are
+you more likely to knock off red blocks
+
+ align:start position:0%
+you more likely to knock off red blocks
+ 
+
+ align:start position:0%
+you more likely to knock off red blocks
+or yellow blocks you know not a task you
+
+ align:start position:0%
+or yellow blocks you know not a task you
+ 
+
+ align:start position:0%
+or yellow blocks you know not a task you
+have you ever got in the end-to-end
+
+ align:start position:0%
+have you ever got in the end-to-end
+ 
+
+ align:start position:0%
+have you ever got in the end-to-end
+training on right but an example of the
+
+ align:start position:0%
+training on right but an example of the
+ 
+
+ align:start position:0%
+training on right but an example of the
+the compositionality of your model and
+
+ align:start position:0%
+the compositionality of your model and
+ 
+
+ align:start position:0%
+the compositionality of your model and
+your task right somebody asked me this
+
+ align:start position:0%
+your task right somebody asked me this
+ 
+
+ align:start position:0%
+your task right somebody asked me this
+during lunch and I think it is a key
+
+ align:start position:0%
+during lunch and I think it is a key
+ 
+
+ align:start position:0%
+during lunch and I think it is a key
+point to make about compositionality one
+
+ align:start position:0%
+point to make about compositionality one
+ 
+
+ align:start position:0%
+point to make about compositionality one
+of the key ways in which composite
+
+ align:start position:0%
+of the key ways in which composite
+ 
+
+ align:start position:0%
+of the key ways in which composite
+compositionality works in this view of
+
+ align:start position:0%
+compositionality works in this view of
+ 
+
+ align:start position:0%
+compositionality works in this view of
+the mind as opposed to the
+
+ align:start position:0%
+the mind as opposed to the
+ 
+
+ align:start position:0%
+the mind as opposed to the
+pattern-recognition view or the way
+
+ align:start position:0%
+pattern-recognition view or the way
+ 
+
+ align:start position:0%
+pattern-recognition view or the way
+let's say like a deep Q Network works
+
+ align:start position:0%
+let's say like a deep Q Network works
+ 
+
+ align:start position:0%
+let's say like a deep Q Network works
+I'm just ways of getting a very flexible
+
+ align:start position:0%
+I'm just ways of getting a very flexible
+ 
+
+ align:start position:0%
+I'm just ways of getting a very flexible
+repertoire of inferences from composing
+
+ align:start position:0%
+repertoire of inferences from composing
+ 
+
+ align:start position:0%
+repertoire of inferences from composing
+pieces without having to train
+
+ align:start position:0%
+pieces without having to train
+ 
+
+ align:start position:0%
+pieces without having to train
+specifically for it right is that if you
+
+ align:start position:0%
+specifically for it right is that if you
+ 
+
+ align:start position:0%
+specifically for it right is that if you
+if you have a physics engine you can
+
+ align:start position:0%
+if you have a physics engine you can
+ 
+
+ align:start position:0%
+if you have a physics engine you can
+simulate the physical world you can you
+
+ align:start position:0%
+simulate the physical world you can you
+ 
+
+ align:start position:0%
+simulate the physical world you can you
+can answer questions that you've never
+
+ align:start position:0%
+can answer questions that you've never
+ 
+
+ align:start position:0%
+can answer questions that you've never
+gotten any training at all to solve so
+
+ align:start position:0%
+gotten any training at all to solve so
+ 
+
+ align:start position:0%
+gotten any training at all to solve so
+in this experiment here we ask people if
+
+ align:start position:0%
+in this experiment here we ask people if
+ 
+
+ align:start position:0%
+in this experiment here we ask people if
+you bump the table hard enough to knock
+
+ align:start position:0%
+you bump the table hard enough to knock
+ 
+
+ align:start position:0%
+you bump the table hard enough to knock
+some of the blocks onto the floor is it
+
+ align:start position:0%
+some of the blocks onto the floor is it
+ 
+
+ align:start position:0%
+some of the blocks onto the floor is it
+more likely to be red or yellow blocks
+
+ align:start position:0%
+more likely to be red or yellow blocks
+ 
+
+ align:start position:0%
+more likely to be red or yellow blocks
+questions of will this tower fall over
+
+ align:start position:0%
+questions of will this tower fall over
+ 
+
+ align:start position:0%
+questions of will this tower fall over
+which we've made a lot of judgments
+
+ align:start position:0%
+which we've made a lot of judgments
+ 
+
+ align:start position:0%
+which we've made a lot of judgments
+that's or you've never made that kind of
+
+ align:start position:0%
+that's or you've never made that kind of
+ 
+
+ align:start position:0%
+that's or you've never made that kind of
+judgment or it's a slightly weird one
+
+ align:start position:0%
+judgment or it's a slightly weird one
+ 
+
+ align:start position:0%
+judgment or it's a slightly weird one
+right but you have no trouble making it
+
+ align:start position:0%
+right but you have no trouble making it
+ 
+
+ align:start position:0%
+right but you have no trouble making it
+and for many different configurations of
+
+ align:start position:0%
+and for many different configurations of
+ 
+
+ align:start position:0%
+and for many different configurations of
+blocks
+
+ align:start position:0%
+blocks
+ 
+
+ align:start position:0%
+blocks
+you make various create a different and
+
+ align:start position:0%
+you make various create a different and
+ 
+
+ align:start position:0%
+you make various create a different and
+the model catches it perfectly with no
+
+ align:start position:0%
+the model catches it perfectly with no
+ 
+
+ align:start position:0%
+the model catches it perfectly with no
+extra stuff put in you just you just
+
+ align:start position:0%
+extra stuff put in you just you just
+ 
+
+ align:start position:0%
+extra stuff put in you just you just
+take the same model and you ask it a
+
+ align:start position:0%
+take the same model and you ask it a
+ 
+
+ align:start position:0%
+take the same model and you ask it a
+different question
+
+ align:start position:0%
+different question
+ 
+
+ align:start position:0%
+different question
+so if our dream is to build a I can
+
+ align:start position:0%
+so if our dream is to build a I can
+ 
+
+ align:start position:0%
+so if our dream is to build a I can
+answer questions for example which a lot
+
+ align:start position:0%
+answer questions for example which a lot
+ 
+
+ align:start position:0%
+answer questions for example which a lot
+of people's dream is I think there's
+
+ align:start position:0%
+of people's dream is I think there's
+ 
+
+ align:start position:0%
+of people's dream is I think there's
+really no compelling alternative to
+
+ align:start position:0%
+really no compelling alternative to
+ 
+
+ align:start position:0%
+really no compelling alternative to
+something like this that you build a
+
+ align:start position:0%
+something like this that you build a
+ 
+
+ align:start position:0%
+something like this that you build a
+model that you can ask all the questions
+
+ align:start position:0%
+model that you can ask all the questions
+ 
+
+ align:start position:0%
+model that you can ask all the questions
+of that you'd want to ask and in this
+
+ align:start position:0%
+of that you'd want to ask and in this
+ 
+
+ align:start position:0%
+of that you'd want to ask and in this
+limited domain again it's just our Atari
+
+ align:start position:0%
+limited domain again it's just our Atari
+ 
+
+ align:start position:0%
+limited domain again it's just our Atari
+right in this limited omein of reasoning
+
+ align:start position:0%
+right in this limited omein of reasoning
+ 
+
+ align:start position:0%
+right in this limited omein of reasoning
+about the physics of blocks it's really
+
+ align:start position:0%
+about the physics of blocks it's really
+ 
+
+ align:start position:0%
+about the physics of blocks it's really
+critical what this physics engine is
+
+ align:start position:0%
+critical what this physics engine is
+ 
+
+ align:start position:0%
+critical what this physics engine is
+able to do ends of questions it can
+
+ align:start position:0%
+able to do ends of questions it can
+ 
+
+ align:start position:0%
+able to do ends of questions it can
+reason about things with different
+
+ align:start position:0%
+reason about things with different
+ 
+
+ align:start position:0%
+reason about things with different
+masses it can make guesses about the
+
+ align:start position:0%
+masses it can make guesses about the
+ 
+
+ align:start position:0%
+masses it can make guesses about the
+masses you can make some of the objects
+
+ align:start position:0%
+masses you can make some of the objects
+ 
+
+ align:start position:0%
+masses you can make some of the objects
+bigger or smaller you can add attached
+
+ align:start position:0%
+bigger or smaller you can add attached
+ 
+
+ align:start position:0%
+bigger or smaller you can add attached
+constraints like fences to the table and
+
+ align:start position:0%
+constraints like fences to the table and
+ 
+
+ align:start position:0%
+constraints like fences to the table and
+the same model without any fundamental
+
+ align:start position:0%
+the same model without any fundamental
+ 
+
+ align:start position:0%
+the same model without any fundamental
+change can answer all these questions so
+
+ align:start position:0%
+change can answer all these questions so
+ 
+
+ align:start position:0%
+change can answer all these questions so
+it doesn't have to be retrained because
+
+ align:start position:0%
+it doesn't have to be retrained because
+ 
+
+ align:start position:0%
+it doesn't have to be retrained because
+there's basically no training right it's
+
+ align:start position:0%
+there's basically no training right it's
+ 
+
+ align:start position:0%
+there's basically no training right it's
+just reasoning but if we want to
+
+ align:start position:0%
+just reasoning but if we want to
+ 
+
+ align:start position:0%
+just reasoning but if we want to
+understand how learning works we first
+
+ align:start position:0%
+understand how learning works we first
+ 
+
+ align:start position:0%
+understand how learning works we first
+have to understand what's learned I
+
+ align:start position:0%
+have to understand what's learned I
+ 
+
+ align:start position:0%
+have to understand what's learned I
+think right now we're only at the point
+
+ align:start position:0%
+think right now we're only at the point
+ 
+
+ align:start position:0%
+think right now we're only at the point
+where we're starting to really have a
+
+ align:start position:0%
+where we're starting to really have a
+ 
+
+ align:start position:0%
+where we're starting to really have a
+sense of what are these mental models of
+
+ align:start position:0%
+sense of what are these mental models of
+ 
+
+ align:start position:0%
+sense of what are these mental models of
+the physical physical world and
+
+ align:start position:0%
+the physical physical world and
+ 
+
+ align:start position:0%
+the physical physical world and
+intentional action these public programs
+
+ align:start position:0%
+intentional action these public programs
+ 
+
+ align:start position:0%
+intentional action these public programs
+that even young children are are using
+
+ align:start position:0%
+that even young children are are using
+ 
+
+ align:start position:0%
+that even young children are are using
+to reason about the world and then it's
+
+ align:start position:0%
+to reason about the world and then it's
+ 
+
+ align:start position:0%
+to reason about the world and then it's
+a separate question how those are built
+
+ align:start position:0%
+a separate question how those are built
+ 
+
+ align:start position:0%
+a separate question how those are built
+up right through some combination of you
+
+ align:start position:0%
+up right through some combination of you
+ 
+
+ align:start position:0%
+up right through some combination of you
+know scientific discovery sorts of
+
+ align:start position:0%
+know scientific discovery sorts of
+ 
+
+ align:start position:0%
+know scientific discovery sorts of
+processes and and the evolution so
+
+ align:start position:0%
+processes and and the evolution so
+ 
+
+ align:start position:0%
+processes and and the evolution so
+here's the story and I most of what I
+
+ align:start position:0%
+here's the story and I most of what I
+ 
+
+ align:start position:0%
+here's the story and I most of what I
+want to tell you but the rest you'll get
+
+ align:start position:0%
+want to tell you but the rest you'll get
+ 
+
+ align:start position:0%
+want to tell you but the rest you'll get
+to hear some of it you'll get to hear
+
+ align:start position:0%
+to hear some of it you'll get to hear
+ 
+
+ align:start position:0%
+to hear some of it you'll get to hear
+next week from both our developmental
+
+ align:start position:0%
+next week from both our developmental
+ 
+
+ align:start position:0%
+next week from both our developmental
+colleagues and from me and Tomer on more
+
+ align:start position:0%
+colleagues and from me and Tomer on more
+ 
+
+ align:start position:0%
+colleagues and from me and Tomer on more
+on the computational side but actually
+
+ align:start position:0%
+on the computational side but actually
+ 
+
+ align:start position:0%
+on the computational side but actually
+the most interesting part we just don't
+
+ align:start position:0%
+the most interesting part we just don't
+ 
+
+ align:start position:0%
+the most interesting part we just don't
+know yet so we hope you will actually
+
+ align:start position:0%
+know yet so we hope you will actually
+ 
+
+ align:start position:0%
+know yet so we hope you will actually
+write that next chapter of the story but
+
+ align:start position:0%
+write that next chapter of the story but
+ 
+
+ align:start position:0%
+write that next chapter of the story but
+here's the here's the outlines of we're
+
+ align:start position:0%
+here's the here's the outlines of we're
+ 
+
+ align:start position:0%
+here's the here's the outlines of we're
+just currently see things right we think
+
+ align:start position:0%
+just currently see things right we think
+ 
+
+ align:start position:0%
+just currently see things right we think
+that we have a good target for what is
+
+ align:start position:0%
+that we have a good target for what is
+ 
+
+ align:start position:0%
+that we have a good target for what is
+really the core of human intelligence
+
+ align:start position:0%
+really the core of human intelligence
+ 
+
+ align:start position:0%
+really the core of human intelligence
+what makes us so smart in terms of these
+
+ align:start position:0%
+what makes us so smart in terms of these
+ 
+
+ align:start position:0%
+what makes us so smart in terms of these
+ideas of both what we start with look
+
+ align:start position:0%
+ideas of both what we start with look
+ 
+
+ align:start position:0%
+ideas of both what we start with look
+this common sense core physics and
+
+ align:start position:0%
+this common sense core physics and
+ 
+
+ align:start position:0%
+this common sense core physics and
+psychology and how those things grow
+
+ align:start position:0%
+psychology and how those things grow
+ 
+
+ align:start position:0%
+psychology and how those things grow
+these are how you know what are the that
+
+ align:start position:0%
+these are how you know what are the that
+ 
+
+ align:start position:0%
+these are how you know what are the that
+the learning mechanisms that I've just
+
+ align:start position:0%
+the learning mechanisms that I've just
+ 
+
+ align:start position:0%
+the learning mechanisms that I've just
+just again more next week on the sort of
+
+ align:start position:0%
+just again more next week on the sort of
+ 
+
+ align:start position:0%
+just again more next week on the sort of
+science like mechanisms of hypothesis
+
+ align:start position:0%
+science like mechanisms of hypothesis
+ 
+
+ align:start position:0%
+science like mechanisms of hypothesis
+formation experiment testing plague
+
+ align:start position:0%
+formation experiment testing plague
+ 
+
+ align:start position:0%
+formation experiment testing plague
+exploration that you can use to build
+
+ align:start position:0%
+exploration that you can use to build
+ 
+
+ align:start position:0%
+exploration that you can use to build
+these intuitive theories much like
+
+ align:start position:0%
+these intuitive theories much like
+ 
+
+ align:start position:0%
+these intuitive theories much like
+scientists build their
+
+ align:start position:0%
+scientists build their
+ 
+
+ align:start position:0%
+scientists build their
+theories and that we're starting on the
+
+ align:start position:0%
+theories and that we're starting on the
+ 
+
+ align:start position:0%
+theories and that we're starting on the
+engineering side to have tools to
+
+ align:start position:0%
+engineering side to have tools to
+ 
+
+ align:start position:0%
+engineering side to have tools to
+capture this both to capture the
+
+ align:start position:0%
+capture this both to capture the
+ 
+
+ align:start position:0%
+capture this both to capture the
+knowledge and how it might grow use of
+
+ align:start position:0%
+knowledge and how it might grow use of
+ 
+
+ align:start position:0%
+knowledge and how it might grow use of
+probabilistic programs and things that
+
+ align:start position:0%
+probabilistic programs and things that
+ 
+
+ align:start position:0%
+probabilistic programs and things that
+sometimes go by the name of program
+
+ align:start position:0%
+sometimes go by the name of program
+ 
+
+ align:start position:0%
+sometimes go by the name of program
+induction or program synthesis or if you
+
+ align:start position:0%
+induction or program synthesis or if you
+ 
+
+ align:start position:0%
+induction or program synthesis or if you
+like hierarchical Bayes on programs that
+
+ align:start position:0%
+like hierarchical Bayes on programs that
+ 
+
+ align:start position:0%
+like hierarchical Bayes on programs that
+generate other programs where the search
+
+ align:start position:0%
+generate other programs where the search
+ 
+
+ align:start position:0%
+generate other programs where the search
+through for a good program is like the
+
+ align:start position:0%
+through for a good program is like the
+ 
+
+ align:start position:0%
+through for a good program is like the
+inference of a program that best
+
+ align:start position:0%
+inference of a program that best
+ 
+
+ align:start position:0%
+inference of a program that best
+explains the data as generated from a
+
+ align:start position:0%
+explains the data as generated from a
+ 
+
+ align:start position:0%
+explains the data as generated from a
+prior that's a higher level program if
+
+ align:start position:0%
+prior that's a higher level program if
+ 
+
+ align:start position:0%
+prior that's a higher level program if
+you go to the tutorial from Tomer you'll
+
+ align:start position:0%
+you go to the tutorial from Tomer you'll
+ 
+
+ align:start position:0%
+you go to the tutorial from Tomer you'll
+actually see building blocks like you
+
+ align:start position:0%
+actually see building blocks like you
+ 
+
+ align:start position:0%
+actually see building blocks like you
+can write church programs that will do
+
+ align:start position:0%
+can write church programs that will do
+ 
+
+ align:start position:0%
+can write church programs that will do
+something like that and you will see
+
+ align:start position:0%
+something like that and you will see
+ 
+
+ align:start position:0%
+something like that and you will see
+more of that next time but the key is
+
+ align:start position:0%
+more of that next time but the key is
+ 
+
+ align:start position:0%
+more of that next time but the key is
+that we have a language now which which
+
+ align:start position:0%
+that we have a language now which which
+ 
+
+ align:start position:0%
+that we have a language now which which
+keep you know keeps building the
+
+ align:start position:0%
+keep you know keeps building the
+ 
+
+ align:start position:0%
+keep you know keeps building the
+different ingredients that we think we
+
+ align:start position:0%
+different ingredients that we think we
+ 
+
+ align:start position:0%
+different ingredients that we think we
+need on the one hand we've gone from
+
+ align:start position:0%
+need on the one hand we've gone from
+ 
+
+ align:start position:0%
+need on the one hand we've gone from
+thinking that we need something like
+
+ align:start position:0%
+thinking that we need something like
+ 
+
+ align:start position:0%
+thinking that we need something like
+probablistic generative models which
+
+ align:start position:0%
+probablistic generative models which
+ 
+
+ align:start position:0%
+probablistic generative models which
+many people will agree with to recognize
+
+ align:start position:0%
+many people will agree with to recognize
+ 
+
+ align:start position:0%
+many people will agree with to recognize
+that not only do they have to be
+
+ align:start position:0%
+that not only do they have to be
+ 
+
+ align:start position:0%
+that not only do they have to be
+generative they have to be causal and
+
+ align:start position:0%
+generative they have to be causal and
+ 
+
+ align:start position:0%
+generative they have to be causal and
+compositional and they have to have this
+
+ align:start position:0%
+compositional and they have to have this
+ 
+
+ align:start position:0%
+compositional and they have to have this
+fine-grained compositional structure
+
+ align:start position:0%
+fine-grained compositional structure
+ 
+
+ align:start position:0%
+fine-grained compositional structure
+needed to capture the real stuff of the
+
+ align:start position:0%
+needed to capture the real stuff of the
+ 
+
+ align:start position:0%
+needed to capture the real stuff of the
+world not graphs but something more like
+
+ align:start position:0%
+world not graphs but something more like
+ 
+
+ align:start position:0%
+world not graphs but something more like
+equations that capture graphics or
+
+ align:start position:0%
+equations that capture graphics or
+ 
+
+ align:start position:0%
+equations that capture graphics or
+physics or planning of course that's not
+
+ align:start position:0%
+physics or planning of course that's not
+ 
+
+ align:start position:0%
+physics or planning of course that's not
+all right I mean as I tried to gesture
+
+ align:start position:0%
+all right I mean as I tried to gesture
+ 
+
+ align:start position:0%
+all right I mean as I tried to gesture
+at we need also ways to make these
+
+ align:start position:0%
+at we need also ways to make these
+ 
+
+ align:start position:0%
+at we need also ways to make these
+things work very very well that's the
+
+ align:start position:0%
+things work very very well that's the
+ 
+
+ align:start position:0%
+things work very very well that's the
+you know there might be a place in this
+
+ align:start position:0%
+you know there might be a place in this
+ 
+
+ align:start position:0%
+you know there might be a place in this
+picture for something like neural
+
+ align:start position:0%
+picture for something like neural
+ 
+
+ align:start position:0%
+picture for something like neural
+networks or some kind of you know
+
+ align:start position:0%
+networks or some kind of you know
+ 
+
+ align:start position:0%
+networks or some kind of you know
+alternative pros and con approach based
+
+ align:start position:0%
+alternative pros and con approach based
+ 
+
+ align:start position:0%
+alternative pros and con approach based
+on pattern recognition but these are
+
+ align:start position:0%
+on pattern recognition but these are
+ 
+
+ align:start position:0%
+on pattern recognition but these are
+just a number of the ways which I think
+
+ align:start position:0%
+just a number of the ways which I think
+ 
+
+ align:start position:0%
+just a number of the ways which I think
+we need to think about going forward we
+
+ align:start position:0%
+we need to think about going forward we
+ 
+
+ align:start position:0%
+we need to think about going forward we
+need to take the idea of both at the
+
+ align:start position:0%
+need to take the idea of both at the
+ 
+
+ align:start position:0%
+need to take the idea of both at the
+brain as a pattern recognition engine
+
+ align:start position:0%
+brain as a pattern recognition engine
+ 
+
+ align:start position:0%
+brain as a pattern recognition engine
+seriously and the idea of the brain as a
+
+ align:start position:0%
+seriously and the idea of the brain as a
+ 
+
+ align:start position:0%
+seriously and the idea of the brain as a
+modeling or explanation engine seriously
+
+ align:start position:0%
+modeling or explanation engine seriously
+ 
+
+ align:start position:0%
+modeling or explanation engine seriously
+we're excited because we now have tools
+
+ align:start position:0%
+we're excited because we now have tools
+ 
+
+ align:start position:0%
+we're excited because we now have tools
+to model modeling engines and maybe to
+
+ align:start position:0%
+to model modeling engines and maybe to
+ 
+
+ align:start position:0%
+to model modeling engines and maybe to
+model how pattern recognition engines
+
+ align:start position:0%
+model how pattern recognition engines
+ 
+
+ align:start position:0%
+model how pattern recognition engines
+and modeling engines might interact but
+
+ align:start position:0%
+and modeling engines might interact but
+ 
+
+ align:start position:0%
+and modeling engines might interact but
+really again the great challenges here
+
+ align:start position:0%
+really again the great challenges here
+ 
+
+ align:start position:0%
+really again the great challenges here
+are really very much in our future not
+
+ align:start position:0%
+are really very much in our future not
+ 
+
+ align:start position:0%
+are really very much in our future not
+the unforeseeable future but the
+
+ align:start position:0%
+the unforeseeable future but the
+ 
+
+ align:start position:0%
+the unforeseeable future but the
+foreseeable ones so help us work on it
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+you
\ No newline at end of file
diff --git a/eJqreNZPS64.txt b/eJqreNZPS64.txt
new file mode 100644
index 0000000000000000000000000000000000000000..c317b3655b3db79ce8733b4eb7ca5fc7ec5f3c68
--- /dev/null
+++ b/eJqreNZPS64.txt
@@ -0,0 +1,955 @@
+align:start position:0%
+ 
+hi and welcome today we're going to do a
+
+ align:start position:0%
+hi and welcome today we're going to do a
+ 
+
+ align:start position:0%
+hi and welcome today we're going to do a
+problem about
+
+ align:start position:0%
+problem about
+ 
+
+ align:start position:0%
+problem about
+where's approximations here's the
+
+ align:start position:0%
+where's approximations here's the
+ 
+
+ align:start position:0%
+where's approximations here's the
+question find the quadratic equation
+
+ align:start position:0%
+question find the quadratic equation
+ 
+
+ align:start position:0%
+question find the quadratic equation
+through the origin
+
+ align:start position:0%
+through the origin
+ 
+
+ align:start position:0%
+through the origin
+that is a best fit for these three
+
+ align:start position:0%
+that is a best fit for these three
+ 
+
+ align:start position:0%
+that is a best fit for these three
+points 1 1 2 5 and negative 1 negative 2
+
+ align:start position:0%
+points 1 1 2 5 and negative 1 negative 2
+ 
+
+ align:start position:0%
+points 1 1 2 5 and negative 1 negative 2
+I'll give you a minute to work that out
+
+ align:start position:0%
+I'll give you a minute to work that out
+ 
+
+ align:start position:0%
+I'll give you a minute to work that out
+on your own uh you can hit the pause
+
+ align:start position:0%
+on your own uh you can hit the pause
+ 
+
+ align:start position:0%
+on your own uh you can hit the pause
+button now and uh we'll be back in a
+
+ align:start position:0%
+button now and uh we'll be back in a
+ 
+
+ align:start position:0%
+button now and uh we'll be back in a
+minute to work the problem out together
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay and were we're back so what's the
+
+ align:start position:0%
+okay and were we're back so what's the
+ 
+
+ align:start position:0%
+okay and were we're back so what's the
+first step in a problem like this the
+
+ align:start position:0%
+first step in a problem like this the
+ 
+
+ align:start position:0%
+first step in a problem like this the
+first step is figuring out what our
+
+ align:start position:0%
+first step is figuring out what our
+ 
+
+ align:start position:0%
+first step is figuring out what our
+equation looks like the one that we're
+
+ align:start position:0%
+equation looks like the one that we're
+ 
+
+ align:start position:0%
+equation looks like the one that we're
+going to affine so our equation is going
+
+ align:start position:0%
+going to affine so our equation is going
+ 
+
+ align:start position:0%
+going to affine so our equation is going
+to look like C T plus DT squared equals
+
+ align:start position:0%
+to look like C T plus DT squared equals
+ 
+
+ align:start position:0%
+to look like C T plus DT squared equals
+y so that's what we're looking for we're
+
+ align:start position:0%
+y so that's what we're looking for we're
+ 
+
+ align:start position:0%
+y so that's what we're looking for we're
+looking for a quadratic equation through
+
+ align:start position:0%
+looking for a quadratic equation through
+ 
+
+ align:start position:0%
+looking for a quadratic equation through
+the origin now if it were just any
+
+ align:start position:0%
+the origin now if it were just any
+ 
+
+ align:start position:0%
+the origin now if it were just any
+quadratic equation then we would have a
+
+ align:start position:0%
+quadratic equation then we would have a
+ 
+
+ align:start position:0%
+quadratic equation then we would have a
+constant term but through the origin
+
+ align:start position:0%
+constant term but through the origin
+ 
+
+ align:start position:0%
+constant term but through the origin
+just means that the constant term is
+
+ align:start position:0%
+just means that the constant term is
+ 
+
+ align:start position:0%
+just means that the constant term is
+zero okay now what's the next step next
+
+ align:start position:0%
+zero okay now what's the next step next
+ 
+
+ align:start position:0%
+zero okay now what's the next step next
+we need to set up a matrix equation so
+
+ align:start position:0%
+we need to set up a matrix equation so
+ 
+
+ align:start position:0%
+we need to set up a matrix equation so
+we need an a a matrix a oops and which
+
+ align:start position:0%
+we need an a a matrix a oops and which
+ 
+
+ align:start position:0%
+we need an a a matrix a oops and which
+which matrix is that going to a B well
+
+ align:start position:0%
+which matrix is that going to a B well
+ 
+
+ align:start position:0%
+which matrix is that going to a B well
+let me start with the first coordinate
+
+ align:start position:0%
+let me start with the first coordinate
+ 
+
+ align:start position:0%
+let me start with the first coordinate
+of these three points and I'm going to
+
+ align:start position:0%
+of these three points and I'm going to
+ 
+
+ align:start position:0%
+of these three points and I'm going to
+put them in the first column of this
+
+ align:start position:0%
+put them in the first column of this
+ 
+
+ align:start position:0%
+put them in the first column of this
+matrix 1 2 negative 1 and then my second
+
+ align:start position:0%
+matrix 1 2 negative 1 and then my second
+ 
+
+ align:start position:0%
+matrix 1 2 negative 1 and then my second
+column is going to be the squares of
+
+ align:start position:0%
+column is going to be the squares of
+ 
+
+ align:start position:0%
+column is going to be the squares of
+these first coordinates 1 4 and 1 and my
+
+ align:start position:0%
+these first coordinates 1 4 and 1 and my
+ 
+
+ align:start position:0%
+these first coordinates 1 4 and 1 and my
+x hat
+
+ align:start position:0%
+x hat
+ 
+
+ align:start position:0%
+x hat
+that's just C and D and my B this is
+
+ align:start position:0%
+that's just C and D and my B this is
+ 
+
+ align:start position:0%
+that's just C and D and my B this is
+going to be the second coordinates 1 5
+
+ align:start position:0%
+going to be the second coordinates 1 5
+ 
+
+ align:start position:0%
+going to be the second coordinates 1 5
+and negative 2
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay why did I set this problem up like
+
+ align:start position:0%
+okay why did I set this problem up like
+ 
+
+ align:start position:0%
+okay why did I set this problem up like
+that well multiply a times X hat okay
+
+ align:start position:0%
+that well multiply a times X hat okay
+ 
+
+ align:start position:0%
+that well multiply a times X hat okay
+the first coordinate of a times X hat is
+
+ align:start position:0%
+the first coordinate of a times X hat is
+ 
+
+ align:start position:0%
+the first coordinate of a times X hat is
+1 times C plus 1 times D it's just the
+
+ align:start position:0%
+1 times C plus 1 times D it's just the
+ 
+
+ align:start position:0%
+1 times C plus 1 times D it's just the
+same as plugging in this first point
+
+ align:start position:0%
+same as plugging in this first point
+ 
+
+ align:start position:0%
+same as plugging in this first point
+into the left-hand side of this equation
+
+ align:start position:0%
+into the left-hand side of this equation
+ 
+
+ align:start position:0%
+into the left-hand side of this equation
+okay and similarly if I took the second
+
+ align:start position:0%
+okay and similarly if I took the second
+ 
+
+ align:start position:0%
+okay and similarly if I took the second
+point and plugged it in here I would
+
+ align:start position:0%
+point and plugged it in here I would
+ 
+
+ align:start position:0%
+point and plugged it in here I would
+just get 2 times C plus 4 times D which
+
+ align:start position:0%
+just get 2 times C plus 4 times D which
+ 
+
+ align:start position:0%
+just get 2 times C plus 4 times D which
+is just the same as the second
+
+ align:start position:0%
+is just the same as the second
+ 
+
+ align:start position:0%
+is just the same as the second
+coordinate in
+
+ align:start position:0%
+coordinate in
+ 
+
+ align:start position:0%
+coordinate in
+multiplication a times X had 2 times C
+
+ align:start position:0%
+multiplication a times X had 2 times C
+ 
+
+ align:start position:0%
+multiplication a times X had 2 times C
+plus 4 times D ok and where did the B
+
+ align:start position:0%
+plus 4 times D ok and where did the B
+ 
+
+ align:start position:0%
+plus 4 times D ok and where did the B
+come from well via B came from plugging
+
+ align:start position:0%
+come from well via B came from plugging
+ 
+
+ align:start position:0%
+come from well via B came from plugging
+in these points to the right hand side
+
+ align:start position:0%
+in these points to the right hand side
+ 
+
+ align:start position:0%
+in these points to the right hand side
+so 1 5 and negative 2 are just the Y
+
+ align:start position:0%
+so 1 5 and negative 2 are just the Y
+ 
+
+ align:start position:0%
+so 1 5 and negative 2 are just the Y
+coordinates of these three points good
+
+ align:start position:0%
+coordinates of these three points good
+ 
+
+ align:start position:0%
+coordinates of these three points good
+so what it would be great if if we get
+
+ align:start position:0%
+so what it would be great if if we get
+ 
+
+ align:start position:0%
+so what it would be great if if we get
+solved ax hat equals B but we can't
+
+ align:start position:0%
+solved ax hat equals B but we can't
+ 
+
+ align:start position:0%
+solved ax hat equals B but we can't
+solve ax hat equals B because there
+
+ align:start position:0%
+solve ax hat equals B because there
+ 
+
+ align:start position:0%
+solve ax hat equals B because there
+isn't a quadratic equation through the
+
+ align:start position:0%
+isn't a quadratic equation through the
+ 
+
+ align:start position:0%
+isn't a quadratic equation through the
+origin that contains these 3 points but
+
+ align:start position:0%
+origin that contains these 3 points but
+ 
+
+ align:start position:0%
+origin that contains these 3 points but
+we need to find the best approximation
+
+ align:start position:0%
+we need to find the best approximation
+ 
+
+ align:start position:0%
+we need to find the best approximation
+to that so that's the same as solving ax
+
+ align:start position:0%
+to that so that's the same as solving ax
+ 
+
+ align:start position:0%
+to that so that's the same as solving ax
+hat equals the projection of B onto the
+
+ align:start position:0%
+hat equals the projection of B onto the
+ 
+
+ align:start position:0%
+hat equals the projection of B onto the
+column space of a because we only have a
+
+ align:start position:0%
+column space of a because we only have a
+ 
+
+ align:start position:0%
+column space of a because we only have a
+chance of solving ax hat equals
+
+ align:start position:0%
+chance of solving ax hat equals
+ 
+
+ align:start position:0%
+chance of solving ax hat equals
+something if it's in the column space of
+
+ align:start position:0%
+something if it's in the column space of
+ 
+
+ align:start position:0%
+something if it's in the column space of
+a and remember from our projections part
+
+ align:start position:0%
+a and remember from our projections part
+ 
+
+ align:start position:0%
+a and remember from our projections part
+of the class that this is the same as
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+solving a transpose a X hat equals a
+
+ align:start position:0%
+solving a transpose a X hat equals a
+ 
+
+ align:start position:0%
+solving a transpose a X hat equals a
+transpose B good so that's what we're
+
+ align:start position:0%
+transpose B good so that's what we're
+ 
+
+ align:start position:0%
+transpose B good so that's what we're
+really going to adieu we're really going
+
+ align:start position:0%
+really going to adieu we're really going
+ 
+
+ align:start position:0%
+really going to adieu we're really going
+to solve a transpose ax hat equals a
+
+ align:start position:0%
+to solve a transpose ax hat equals a
+ 
+
+ align:start position:0%
+to solve a transpose ax hat equals a
+transpose B and now all we have to do is
+
+ align:start position:0%
+transpose B and now all we have to do is
+ 
+
+ align:start position:0%
+transpose B and now all we have to do is
+just a computation so let's do it so
+
+ align:start position:0%
+just a computation so let's do it so
+ 
+
+ align:start position:0%
+just a computation so let's do it so
+what is a transpose a going to do this
+
+ align:start position:0%
+what is a transpose a going to do this
+ 
+
+ align:start position:0%
+what is a transpose a going to do this
+kind of quickly because you should be
+
+ align:start position:0%
+kind of quickly because you should be
+ 
+
+ align:start position:0%
+kind of quickly because you should be
+good at multiplying matrices by now
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah sorry oh this I have the negative
+
+ align:start position:0%
+yeah sorry oh this I have the negative
+ 
+
+ align:start position:0%
+yeah sorry oh this I have the negative
+in the wrong place thank you thanks for
+
+ align:start position:0%
+in the wrong place thank you thanks for
+ 
+
+ align:start position:0%
+in the wrong place thank you thanks for
+that correction I have the negative
+
+ align:start position:0%
+that correction I have the negative
+ 
+
+ align:start position:0%
+that correction I have the negative
+backwards they're good okay and what do
+
+ align:start position:0%
+backwards they're good okay and what do
+ 
+
+ align:start position:0%
+backwards they're good okay and what do
+I get when I multiply these I'll let you
+
+ align:start position:0%
+I get when I multiply these I'll let you
+ 
+
+ align:start position:0%
+I get when I multiply these I'll let you
+check this is six eight eight and a ten
+
+ align:start position:0%
+check this is six eight eight and a ten
+ 
+
+ align:start position:0%
+check this is six eight eight and a ten
+okay and what is a transpose B well if
+
+ align:start position:0%
+okay and what is a transpose B well if
+ 
+
+ align:start position:0%
+okay and what is a transpose B well if
+you multiply this out all let you check
+
+ align:start position:0%
+you multiply this out all let you check
+ 
+
+ align:start position:0%
+you multiply this out all let you check
+that you get 13 and a 19 good so this is
+
+ align:start position:0%
+that you get 13 and a 19 good so this is
+ 
+
+ align:start position:0%
+that you get 13 and a 19 good so this is
+this is just some computation and so
+
+ align:start position:0%
+this is just some computation and so
+ 
+
+ align:start position:0%
+this is just some computation and so
+what we're solving here is 6 8 8 10
+
+ align:start position:0%
+what we're solving here is 6 8 8 10
+ 
+
+ align:start position:0%
+what we're solving here is 6 8 8 10
+times X hat equals 13 19 and we remember
+
+ align:start position:0%
+times X hat equals 13 19 and we remember
+ 
+
+ align:start position:0%
+times X hat equals 13 19 and we remember
+how to do this just by using elimination
+
+ align:start position:0%
+how to do this just by using elimination
+ 
+
+ align:start position:0%
+how to do this just by using elimination
+we replace the second row by 3 times the
+
+ align:start position:0%
+we replace the second row by 3 times the
+ 
+
+ align:start position:0%
+we replace the second row by 3 times the
+second row minus 4 times the first row
+
+ align:start position:0%
+second row minus 4 times the first row
+ 
+
+ align:start position:0%
+second row minus 4 times the first row
+again I'm going to do this quickly
+
+ align:start position:0%
+again I'm going to do this quickly
+ 
+
+ align:start position:0%
+again I'm going to do this quickly
+because you know this from other parts
+
+ align:start position:0%
+because you know this from other parts
+ 
+
+ align:start position:0%
+because you know this from other parts
+of the class you similarly change the B
+
+ align:start position:0%
+of the class you similarly change the B
+ 
+
+ align:start position:0%
+of the class you similarly change the B
+vector and we back solve to get D is
+
+ align:start position:0%
+vector and we back solve to get D is
+ 
+
+ align:start position:0%
+vector and we back solve to get D is
+negative five-halves and C equals let's
+
+ align:start position:0%
+negative five-halves and C equals let's
+ 
+
+ align:start position:0%
+negative five-halves and C equals let's
+plug that and then C I think you're
+
+ align:start position:0%
+plug that and then C I think you're
+ 
+
+ align:start position:0%
+plug that and then C I think you're
+going to get 11 over 2 so what's our
+
+ align:start position:0%
+going to get 11 over 2 so what's our
+ 
+
+ align:start position:0%
+going to get 11 over 2 so what's our
+final equation our final equation is y
+
+ align:start position:0%
+final equation our final equation is y
+ 
+
+ align:start position:0%
+final equation our final equation is y
+equals 11 halves t minus 5 halves T
+
+ align:start position:0%
+equals 11 halves t minus 5 halves T
+ 
+
+ align:start position:0%
+equals 11 halves t minus 5 halves T
+squared
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+good okay so this is our best fit
+
+ align:start position:0%
+good okay so this is our best fit
+ 
+
+ align:start position:0%
+good okay so this is our best fit
+quadratic equation through the origin
+
+ align:start position:0%
+quadratic equation through the origin
+ 
+
+ align:start position:0%
+quadratic equation through the origin
+now before I end let me do a couple
+
+ align:start position:0%
+now before I end let me do a couple
+ 
+
+ align:start position:0%
+now before I end let me do a couple
+things first let me go back and review
+
+ align:start position:0%
+things first let me go back and review
+ 
+
+ align:start position:0%
+things first let me go back and review
+what the key steps were whenever you're
+
+ align:start position:0%
+what the key steps were whenever you're
+ 
+
+ align:start position:0%
+what the key steps were whenever you're
+faced with such a best-fit equation
+
+ align:start position:0%
+faced with such a best-fit equation
+ 
+
+ align:start position:0%
+faced with such a best-fit equation
+first you want to see what the general
+
+ align:start position:0%
+first you want to see what the general
+ 
+
+ align:start position:0%
+first you want to see what the general
+form of the equation is next you want to
+
+ align:start position:0%
+form of the equation is next you want to
+ 
+
+ align:start position:0%
+form of the equation is next you want to
+write it in terms of matrices write down
+
+ align:start position:0%
+write it in terms of matrices write down
+ 
+
+ align:start position:0%
+write it in terms of matrices write down
+your your matrix a and your vector B and
+
+ align:start position:0%
+your your matrix a and your vector B and
+ 
+
+ align:start position:0%
+your your matrix a and your vector B and
+lastly you set up your projection
+
+ align:start position:0%
+lastly you set up your projection
+ 
+
+ align:start position:0%
+lastly you set up your projection
+equation and then all you have to do is
+
+ align:start position:0%
+equation and then all you have to do is
+ 
+
+ align:start position:0%
+equation and then all you have to do is
+just a computation good it might also be
+
+ align:start position:0%
+just a computation good it might also be
+ 
+
+ align:start position:0%
+just a computation good it might also be
+worth noting that um these three points
+
+ align:start position:0%
+worth noting that um these three points
+ 
+
+ align:start position:0%
+worth noting that um these three points
+certainly aren't on this quadratic
+
+ align:start position:0%
+certainly aren't on this quadratic
+ 
+
+ align:start position:0%
+certainly aren't on this quadratic
+equation for instance if I plug in one
+
+ align:start position:0%
+equation for instance if I plug in one
+ 
+
+ align:start position:0%
+equation for instance if I plug in one
+here I don't get one one I get one three
+
+ align:start position:0%
+here I don't get one one I get one three
+ 
+
+ align:start position:0%
+here I don't get one one I get one three
+but that's that's okay this is as close
+
+ align:start position:0%
+but that's that's okay this is as close
+ 
+
+ align:start position:0%
+but that's that's okay this is as close
+as we can do thanks
\ No newline at end of file
diff --git a/ejZtBwLUE3Y.txt b/ejZtBwLUE3Y.txt
new file mode 100644
index 0000000000000000000000000000000000000000..71dc962d1d75d8e0ab321941b4ea108e24480766
--- /dev/null
+++ b/ejZtBwLUE3Y.txt
@@ -0,0 +1,2840 @@
+The following content is
+provided under a Creative
+
+Commons license.
+
+Your support will help MIT
+OpenCourseWare continue to
+
+offer high quality educational
+resources for free.
+
+To make a donation, or view
+additional materials from
+
+hundreds of MIT courses, visit
+MIT OpenCourseWare at
+
+ocw.mit.edu.
+
+PROFESSOR: Ladies and gentlemen,
+welcome to
+
+lecture number 12.
+
+In this lecture, I would like
+to discuss with you solution
+
+methods for eigenproblems.
+
+This is a very large field,
+and all I can do really in
+
+this lecture is to give you or
+discuss this you a few of the
+
+solution methods that
+we are using in
+
+finite element analysis.
+
+So it will be a very brief
+introduction, a brief survey
+
+of the methods of solution that
+we're using for finite
+
+element eigenvalue problems.
+
+The generalized eigenvalue
+problem, K phi equals lambda M
+
+phi, is a problem that we
+encountered in the multiple
+
+position analysis.
+
+Please recognize that I'm
+calling lambda here, the
+
+eigenvalue, which was our omega
+
+squared in the last lecture.
+
+This is really the eigenproblems
+that we are
+
+primarily addressing ourselves
+to finite element analysis.
+
+The standard eigenproblems
+problem here, EVP stands for
+
+eigenproblem, has M equal
+to the identity matrix.
+
+So when we're talking about
+solution methods of this
+
+problem, we're really also talk
+about solution methods of
+
+this problem.
+
+If we have, in a [? multiple ?]
+position
+
+analysis, non-proportional
+damping, then we would have to
+
+solve this eigenproblem, which
+is a quadratic eigenproblem.
+
+I will not address myself to the
+solution of this problem,
+
+so in what follow, we are
+talking about a solution of
+
+this problem, and of course, the
+solution of this problem
+
+also, when M is equal to
+the identity matrix.
+
+In particular, we are interested
+in the solution of
+
+large eigenvalue problems when
+N, is say, greater than 500.
+
+N, of course, being the order of
+K and M, and with the half
+
+bandwidth, I should say,
+being greater than 60.
+
+The number of eigenvalues that
+we will be looking for, that
+
+we want to calculate, are say,
+1 to 1/3 of N. 1/3 of N is
+
+already large number
+of eigenvalues.
+
+Generally, we are talking about
+1 to and at most, 100
+
+for large eigenproblems.
+
+When we have a small eigenvalue
+problem, in other
+
+words, N being small, say 50
+or 100, there are a large
+
+number of different techniques
+that can be used to solve this
+
+eigenvalue problem, and it
+really does not make that much
+
+difference which technique
+you are using.
+
+The cost can still be quite
+significant, but certainly,
+
+when we're talking about very
+large eigenproblems, N being
+
+even larger than a 1,000 or
+2,000, then it is of up most
+
+concern to select a technique
+that is very effective.
+
+And I want to address myself
+really now towards those
+
+techniques that we feel are
+very effectively used in
+
+finite element analysis.
+
+In dynamic analysis, of course,
+with proportional
+
+damping, this was the eigenvalue
+problem that we
+
+wanted to solve.
+
+Now, if they are 0 frequencies
+present, in other words, when
+
+we have rigid body modes in the
+system, then we can use
+
+the following procedure to
+basically getting rid of these
+
+0 frequencies.
+
+We simply add, on the left hand
+side, a mu M phi, and on
+
+the right hand side,
+a mu M phi.
+
+And taking these two together,
+we are getting this
+
+coefficient matrix, and
+a new lambda value.
+
+That lambda value now is omega
+squared plus mu, where omega
+
+squared is equal to
+lambda minus mu.
+
+What we have been doing here,
+is basically, we have been
+
+applying a shift.
+
+In other words, if we were to
+plot the characteristic
+
+polynomial, giving us
+the eigenvalues, the
+
+characteristic polynomial of
+course, being p of lambda
+
+being determined K bar minus
+lambda M, where K bar is equal
+
+to K plus mu M.
+
+If we plug this characteristic
+polynomial, we will see this
+
+curve here, schematically drawn,
+of course, where the
+
+omega squared values would start
+here, in other words,
+
+the lowest omega squared
+value is, in fact, 0.
+
+Whereas our lambda value
+now starts right here.
+
+This is the shift that
+we [? imposed. ?]
+
+So, basically, we now recognize
+that we have all
+
+eigenvalues being greater than
+0, because this is our new
+
+starting value.
+
+All eigenvalues measured from
+here are greater than 0, the
+
+smallest one being mu,
+namely when omega
+
+squared is equal to 0.
+
+And the larger ones
+being here.
+
+It is effective to perform such
+a shift when we have 0
+
+eigenvalues, in other words, to
+operate on this eigenvalue,
+
+rather than on that one, because
+our techniques then
+
+are very stable and effective,
+and this shift here is, in
+
+general, therefore performed.
+
+So all we have to address
+ourselves to then from now on,
+
+is really, the solution of
+eigenvalues and eigenvectors,
+
+when all of the eigenvalues
+are greater than 0.
+
+If we start off with a problem
+where we have a 0 frequency,
+
+we apply the shift so that the
+eigenvalues now of this
+
+problem here are all
+greater than 0.
+
+In buckling analysis, we
+have this eigenproblem.
+
+We really did not talk about--
+
+we did not really at all about
+buckling analysis in the set
+
+of lectures, but you might just
+be interested in finding
+
+out how would we solve for
+these eigenvalues.
+
+Well, here is the characteristic
+polynomial.
+
+The smallest lambda value, of
+course, gives now a critical
+
+load, that is the one e would
+be interested in.
+
+It is effective here,
+to rewrite this
+
+problem in this form.
+
+All we do, is we are taking
+the lambda value onto the
+
+other side.
+
+In other words, we
+are dividing this
+
+equation here by a lambda.
+
+So that one of the lambda stands
+on this side, and KG
+
+phi on that side.
+
+The resulting problem is this
+one, where kappa is 1 over
+
+lambda and we have now
+here, is a K matrix.
+
+K is positive definite, and now
+it is more effective to
+
+operate on this equation.
+
+How do we obtain now
+the largest kappa?
+
+Because the largest kappa is the
+one that we are interested
+
+in, which corresponds to the
+smallest lambda, the smallest
+
+buckling load.
+
+Well, we would now perform
+a shift to the right,
+
+subtracting mu K from this side,
+from this side, and from
+
+that side, to obtain this
+eigenvalue problem.
+
+That means we are really
+shifting from here up to
+
+there, and now we are interested
+in solving kappa N
+
+by operating on this
+eigenproblems problem.
+
+It is this eigenvalue problem
+that we can operate on
+
+directly, using the techniques
+that I would be discussing
+
+later, to determine search
+method and the subspace
+
+iteration method.
+
+But before we get into those
+techniques, I would like to
+
+discuss with you some
+preliminary considerations
+
+that are important
+when we look at
+
+an eigenvalue solution.
+
+The important first point that
+I want to make is that there
+
+is a traditional approach
+for the solution of this
+
+eigenvalue problem here.
+
+Let's look at this eigenvalue
+problem.
+
+Where of course, when we're
+talking about a buckling
+
+analysis, we would have
+different matrices here, but
+
+basically, we still solve
+this eigenvalue problem.
+
+The traditional approach lies
+in factorizing the M matrix
+
+into Cholesky factors.
+
+We talked about the Cholesky
+factor when we talked about
+
+solution of equations.
+
+So here it comes up again.
+
+We would factorize the M matrix
+into Cholesky factors,
+
+as shown here.
+
+We define now a new eigenvector,
+phi curl being
+
+equal as shown here, L curl
+transpose times 5.
+
+We substitute from here into
+there, and we directly obtain
+
+this eigenvalue problem here.
+
+Now we have the standard
+eigenproblem.
+
+Now once we have a standard
+eigenproblem, there are a
+
+large number of techniques
+that can be used.
+
+For example, the QR method,
+the standard
+
+Jacobi method, et cetera.
+
+So this is, what
+we might call.
+
+a traditional approach to
+solve the generalized
+
+eigenproblem, this is the one
+here that we are really
+
+interested in.
+
+But it involves this
+transformation, and this
+
+transformation here can involve
+a very significant
+
+cost, because we have to find
+these Cholesky factors and
+
+then, of course, we have to
+calculate this K curl.
+
+Another way of performing
+a transformation of the
+
+generalized item problem to a
+standard form would be to
+
+solve the eigenproblem
+of M first.
+
+W here and W transpose
+[? store ?]
+
+the eigenvectors of the M
+matrix, and D squared is a
+
+diagonal matrix of the
+eigenvalues of M. And then
+
+having factored M in this form,
+an equation similar to
+
+this one here can be written.
+
+Where now, the transformation,
+of course, involves the
+
+eigenvectors, W.
+
+Well, this approach is
+sometimes still quite
+
+effective, but in general, it
+cannot be recommended because
+
+there's too much cost involved
+in the factorizing of the M
+
+matrix, and then particular,
+in the transformation here,
+
+and the solution of this problem
+and the, of course, to
+
+get from this problem, the phi
+vector, we have to go back to
+
+this equation.
+
+A direct solution of the
+generalized eigenvalue problem
+
+that we want to solve is
+really more effective.
+
+And now, we are ordering the
+lambdas as shown here.
+
+Remember, our smallest lambda
+now is greater than 0, the
+
+eigonvectors are stored as shown
+here, and for most of a
+
+position analysis, we are really
+interested in solving
+
+only for a certain number of
+eigen pairs, i equals 1 to p,
+
+as discussed in the last
+lecture, or i equals r to s.
+
+If we have a vibration
+excitation problem, we really
+
+only want to solve for specific
+frequencies and
+
+corresponding mode shapes
+in a certain
+
+interval, as shown here.
+
+The solution procedures on this
+generalized eigenvalue
+
+problem can be categorized
+into the following forms.
+
+The first solution procedure,
+or a whole class of solution
+
+procedures, that I should really
+say, which we might
+
+call the vector iteration
+techniques.
+
+The idea is the following--
+
+if we want to solve this
+problem, then why not solve it
+
+in the following way?
+
+Start off with a vector on this
+side, that we assume,
+
+calculate a new vector on this
+side, then take that new
+
+vector, plug it back on the
+right hand side, and cycle
+
+through this way.
+
+This is indeed inverse
+iteration.
+
+What do we do here?
+
+We are putting a vector on the
+right hand side, x1, when K is
+
+equal to 1, that vector
+we have to assume.
+
+Then we are multiplying out
+the right hand side.
+
+Now we have a set of
+simultaneous equations that we
+
+would solve just in the same way
+as we solve the equations
+
+in static analysis.
+
+We can think of this
+as a load vector.
+
+We are calculating this
+displacement vector, and then
+
+having got this displacement
+vector, and not taking care of
+
+this lambda, or having,
+basically, taken this lambda
+
+out of this equation.
+
+Which means that this vector
+will grow in lengths, or
+
+collapse in lengths.
+
+Therefore, want to scale this
+vector down to a good length--
+
+a length that does not hit
+overflow, so to say, or
+
+underflow in the machine.
+
+And that scaling is achieved
+as shown here.
+
+So, the final result then, this
+is just a scalar here, as
+
+you can see, is a vector here,
+which we can put on to the
+
+right hand side and keep
+on iterating around.
+
+In fact, we find as that
+iteration procedure converges
+
+to the lowest eigenvector,
+provided the starting vector
+
+is not orthogonal, is not
+M orthogonal to phi 1.
+
+This is one first iteration
+technique.
+
+Maybe I should put
+a side note down.
+
+A side note that many of you
+might have in your mind.
+
+Many of you might have the
+following question in your
+
+mind-- why he iterate, why does
+he not solve directly for
+
+the eigenvalues?
+
+Just like we saw a set of
+simultaneous equations.
+
+Well, there's one very important
+point, and this is
+
+the point--
+
+if we are solving an eigenvalue
+problem, and shown
+
+here, then really that
+means the following--
+
+we are saying that determinant,
+K minus lambda M
+
+shall be equal to 0.
+
+Why?
+
+Because if we write
+this equation in
+
+the following form--
+
+K minus lambda M times phi
+equals 0, then we have here a
+
+set of simultaneous equations
+with a 0 vector on
+
+the right hand side.
+
+And there is an important
+theorem in linear algebra that
+
+says, only a solution to this
+set of equations when this
+
+coefficient matrix
+is singular.
+
+Which means that the
+determinant of this
+
+coefficient matrix must be 0.
+
+So, what do we want?
+
+We really want to solve p of
+lambda determinant, K minus
+
+lambda M. We want to solve for
+the 0's of this polynomial.
+
+That's really what we want.
+
+Now, if we want to solve for
+the 0's of this polynomial,
+
+then we also have to understand
+that when k is of
+
+order 4, there will
+be four 0's.
+
+The polynomial itself
+will be of order 4.
+
+If K is of order, N, then
+there will be N 0's.
+
+So the polynomial is order N.
+However, if we want to find
+
+the solution of a polynomial,
+or order N, then we very
+
+quickly find that, in fact, we
+can only look up the solution
+
+to such polynomials if they are
+of low enough order, lower
+
+than say, 4.
+
+Above for larger order
+polynomials, there's no way
+
+you can look up the solution.
+
+You have to iterate to obtain
+the solution of the 0's of
+
+this polynomial.
+
+However, since this problem
+here, is completely equivalent
+
+to this problem.
+
+To solve this problem,
+you have to iterate.
+
+And this is the important
+conclusion.
+
+It is of up most importance that
+you understand that to
+
+solve an eigenvalue problem of
+order larger than say, 4, you
+
+will have to iterate.
+
+Because you're solving for the
+0's of a polynomial of order
+
+larger than 4.
+
+Only for very small order
+polynomials, we can look up
+
+the solutions in handbooks.
+
+So having grasped the fact that
+we have to iterate to
+
+solve for the 0's of this
+polynomial, to solve for the
+
+eigenvalues of this problem, we
+are stuck with iteration,
+
+and since we're stuck with
+iteration, we now want to come
+
+up with techniques to iterate.
+
+And the first technique to
+iterate is this vector
+
+iteration technique.
+
+And the basic idea, once more,
+is if you want to solve this
+
+equation, well, then why not
+iterate in the following way?
+
+Put some starting value in here,
+this number is just a
+
+scalar, let's neglect that
+effect for the moment.
+
+And having put a starting value
+in here, calculate this
+
+one and keep on cycling
+around this way.
+
+And that's what we call
+inverse iteration.
+
+Inverse iteration here, a vector
+inverse iteration,
+
+because we have to solve a set
+of equations here, with K as
+
+the coefficient matrix.
+
+There are other iteration
+techniques.
+
+There's also forward
+iteration.
+
+And basically, what we're
+saying there is--
+
+well if we are starting off here
+and going around in this
+
+circle, why not start off here
+and go around in that circle,
+
+the red line.
+
+And that, in fact, gives
+us forward iteration.
+
+One can prove that that forward
+iteration converges to
+
+the largest eigenvalue.
+
+We are usually interested in the
+smallest frequencies, the
+
+smallest eigenvalues, and
+therefore, we are using
+
+inverse iteration
+quite commonly.
+
+Then there is Rayleigh
+Quotient iteration.
+
+The Rayleigh Quotient iteration
+is again, an inverse
+
+iteration, however, with an
+acceleration scheme in it, a
+
+very effective acceleration
+scheme.
+
+This Rayleigh Quotient iteration
+can be employed to
+
+calculate one eigenvalue and
+vector, and then, of course,
+
+we have to deflate afterwards
+the matrix, the coefficient
+
+matrix for the eigenvector
+that we have calculated
+
+already, and we then could go on
+towards the calculation of
+
+additional eigenvalues
+and vectors.
+
+The same deflation also would
+be used in inverse iteration
+
+alone, and in forward
+iteration alone.
+
+In a Rayleigh Quotient
+iteration, we converge to an
+
+eigen pair, but which one
+is not guaranteed.
+
+So this is a class of
+techniques, iteration methods
+
+that we are using.
+
+Another class of techniques,
+again iteration methods, we
+
+are stuck with iteration, as
+I mentioned earlier, is the
+
+polynomial iteration methods.
+
+Here, we are saying that this
+problem is equivalent to that,
+
+we want to solve
+for these 0's.
+
+Therefore, for the 0's of this
+polynomial, sketched out here,
+
+and one way is to use
+Newton iteration.
+
+Here we have p, here
+we have p prime.
+
+Well, of course, if we have
+p here, we have to also
+
+recognize we should have
+the coefficients here.
+
+Well, these coefficients are
+given here, A0 to a n.
+
+And we could rewrite this
+polynomial in this form, once
+
+we know the zeroes.
+
+Now, if we don't know the
+zeroes, of course, we would be
+
+stuck on iterating on this
+matrix, where we would have to
+
+calculate these coefficients.
+
+However, there are now really,
+two different techniques.
+
+The first technique is explicit
+polynomial iteration.
+
+In the explicit polynomial
+iteration, we expand the
+
+polynomial and iterate for the
+0's, by that I mean, we
+
+actually expand this
+polynomial.
+
+However, this technique is not
+suitable for larger problems
+
+because first of all, there's
+much work to obtain the ai's,
+
+and then it's an unstable
+process.
+
+Unstable because small errors
+in these coefficients here,
+
+give large errors
+in the zeroes.
+
+So this is not a suitable
+technique, and we are better
+
+off using implicit polynomial
+iteration.
+
+In the implicit polynomial
+iteration, we evaluate the
+
+determinant all this
+matrix here.
+
+In others, p at mu i, via the L
+D L transpose factorization,
+
+which we discussed in the Gauss
+elimination solution,
+
+when we talked about Gauss
+elimination solution.
+
+To obtain the determinant of
+this matrix here then, we need
+
+simply to multiply all the
+diagonal elements.
+
+This technique is accurate,
+provided we do not encounter
+
+large multipliers L matrix.
+
+And if we do, we have to
+shift away, we have to
+
+change our mu i.
+
+Also we directly solve for
+lambda 1 and so on.
+
+And for the more we can use
+effectively a secant
+
+iteration, instead of
+calculating, in other words,
+
+the p prime at mu.
+
+This is here approximately equal
+to p prime, at mu i.
+
+Instead of calculating this
+derivative, we are putting
+
+this value here, which gives
+us an approximation to that
+
+derivative, this is what we
+call the secant iteration.
+
+Once we have calculated one
+eigenvalue, of course, we will
+
+have to deflate to calculate the
+next eigenvalue, and this
+
+is the process that
+he would pursue.
+
+Pictorially, we have here,
+our p lambda, this is the
+
+polynomial.
+
+Let me show it to you here.
+
+Here, we have the polynomial,
+here we have lambda 1, here we
+
+have lambda 2.
+
+In the secant iteration, we
+start off with the value of mu
+
+i minus 1 here, mu i, these
+two values are given.
+
+Usually, in a practical
+analysis, mu 0 would be this
+
+value here, and mu 1 would be
+a lower bound on lambda 1.
+
+And plugging these two values
+in, we get mu i plus 1, and
+
+you can see that this process
+would then converge to this
+
+eigenvalue.
+
+Once we have lambda 1, we can
+repeat the iteration.
+
+However, working now on p
+lambda divided by lambda
+
+minus lambda 1.
+
+And that means we are operating
+on this polynomial
+
+here, and polynomial then gives
+us the iteration on that
+
+polynomial then gives us
+the second eigenvalue.
+
+So we are deflating the actual p
+lambda by the lambda 1 value
+
+in order to obtain
+a convergence
+
+to the second value.
+
+Well, this is the one
+class of methods.
+
+Another class of methods, the
+third one, are the Sturm
+
+sequence methods.
+
+And here, the basic idea
+is the following--
+
+if we look at this eigenproblem,
+and I use a 4x4
+
+matrix here, then if we take a
+shift on this eigenproblem, mu
+
+S, and this is the shift here.
+
+Then if we factorize K minus
+mu S M, equal to L D L
+
+transpose, again, we're using
+our Gauss elimination
+
+procedures basically.
+
+Then the number of negative
+elements in D is equal to the
+
+number eigenvalues smaller
+than mu S, a
+
+very important point.
+
+Let us look at this example
+here of the 4x4 matrix.
+
+Here we have plotted
+characteristic polynomials.
+
+The characteristic polynomial of
+this 4x4 matrix, with that
+
+M matrix, of course, is drawn
+along here, four eigenvalues.
+
+And I have put mu S here
+as the red line.
+
+What this theorem says is if I
+factorize K minus mu S, M,
+
+this being the K matrix, the
+total K matrix, and the 4x4 M
+
+matrix goes in here.
+
+Then there would be one negative
+element in D. One
+
+only because mu S is large
+than lambda 1.
+
+If mu S were on this side
+here, there would be two
+
+negative elements in D. If mu
+S were on this side, there
+
+would be three negative
+elements in D--
+
+very important point because qw
+can use this procedure to
+
+directly calculate eigenvalues
+the way I will be discussing
+
+it just now.
+
+However, let us look a little
+bit more at why
+
+this hole is here.
+
+Well, it derives from the
+associated constraint problems
+
+with the original
+eigenproblem.
+
+The original eigenproblem
+corresponds to this beam
+
+problem, which we considered
+earlier already in the
+
+discussion of Gauss
+elimination.
+
+If I constrain this degree of
+freedom here, I get a new
+
+polynomial corresponding to
+this problem, and the
+
+important point is that the
+lowest root, the lowest value
+
+of this problem here lies in
+between these two-- lambda 1
+
+and lambda 2.
+
+The second one here, lies
+between lambda 2 and lambda 3,
+
+and the third one here lies
+between lambda 3 and lambda 4.
+
+The second associated constraint
+problem has two
+
+eigenvalues, and this one lies
+between these two, this one
+
+lies between these two.
+
+And the final eigenvalue
+problem here, the third
+
+associate constraint problem
+obtained by knocking out these
+
+degrees of freedom here, has one
+eigenvalue, and that one
+
+lies in between these
+two values here.
+
+It's this important fact
+that is used to
+
+derive this final result.
+
+Now, we have not time to go
+through the actual details,
+
+but this is the important
+fact here.
+
+In other words, that the
+[? i's ?] eigenvalue of this
+
+associated constraint problem,
+for example, the second
+
+eigenvalue of this associated
+constraint problem here,
+
+bisects or lies in between,
+not bisect--
+
+lies in between lambda 2 and
+lambda 3 of this eigenproblem
+
+here, and so on.
+
+That result is used to derive
+this final result, which we
+
+use effectively then in
+the eigen solution.
+
+And the class of techniques then
+that we are referring to
+
+using this fact are the Sturm
+sequence methods.
+
+So basically, what we are saying
+is the following--
+
+take this coefficient matrix,
+now I make the mu x available.
+
+We factorize that coefficient
+matrix into L D L transposed,
+
+and the number of negative
+elements in D is equal to the
+
+number of eigenvalues smaller
+than mu S, I. How
+
+do we use this fact?
+
+Well, if this is here, the
+polynomial, we could start off
+
+by putting mu S 1 into this
+point here, and we would find
+
+out the number of eigenvalues
+smaller than mu S 1.
+
+Then we are taking, mu S 2, and
+we find out the number of
+
+eigenvalues smaller
+than mu S 2.
+
+Of course, we would find that
+they are one more eigenvalue
+
+smaller than mu S 2.
+
+Then mu S 1, namely this one.
+
+So we know there's one
+eigenvalue in between mu S 1
+
+and mu S 2.
+
+Now we could bisect this
+interval, and we would find
+
+that, in fact, there is still
+one more eigenvalue smaller
+
+than mu S 3, then there was
+smaller than mu S 1.
+
+Because this eigenvalue
+still lies on the left
+
+side of mu S 3.
+
+So we bisect again,
+we get mu S 4.
+
+Notice this distance here, is
+equal to that distance here.
+
+And now, we would find that the
+eigenvalue still lies in
+
+between these two lines, between
+mu S 3 and mu S 4.
+
+And like that. we could
+continue bisecting the
+
+interval until we finally find a
+very small interval in which
+
+this eigenvalue must lie.
+
+We, of course, have to take care
+in the L D L transpose
+
+factorization, because we are
+not working on a positive
+
+definite matrix.
+
+The multipliers must be small,
+the L, I, J elements must
+
+remain small in the
+factorization.
+
+But provided that is the case,
+the round of errors are small,
+
+and the procedure
+is very stable.
+
+However, convergence can be very
+slow, can be extremely
+
+slow because you have to cut
+down the intervals further and
+
+further until you finally get
+a very small interval, in
+
+which you now know the
+eigenvalue does lie.
+
+Of course, at some point, you
+might want to switch to
+
+another iteration scheme.
+
+Once you know there is an
+eigenvalue in between say mu S
+
+3 and mu S 4, you might want
+to switch to a iteration
+
+scheme that converges to this
+particular value much faster.
+
+Finally, a whole class of
+methods that I would like to
+
+briefly mention to you are the
+methods of transformations,
+
+where we are operating on
+this eigenvalue problem,
+
+recognizing that phi transpose
+K phi is equal to lambda.
+
+And phi transpose M phi is
+equal to I. Where phi is
+
+defined as shown here, lambda
+is defined as shown here.
+
+This fact, of course, we use
+already earlier in the
+
+[? multiple ?]
+
+position analysis.
+
+Now how can we get
+phi and lambda?
+
+That is our objective.
+
+Well, if we know that this
+matrix diagonalizes the K
+
+matrix, and it also diagonalizes
+the M matrix,
+
+then why not try to construct
+it by iteration?
+
+And this is the basic idea in
+the transformation methods.
+
+What we do is the following-- we
+take the original K matrix,
+
+we are operating with
+P1 transpose K P1.
+
+On K, and on M, such as to make
+this resultant matrix
+
+here closer to a
+diagonal form.
+
+Ultimately, we want to get
+a diagonal matrix.
+
+Well, one step in the iteration
+is to make this P1
+
+transpose K P1 matrix, and P1
+transpose M P1 matrix, both of
+
+these matrices a little closer
+to diagonal form.
+
+Then K and M were
+by themselves.
+
+So this is the first step.
+
+Now, we have here, let's call
+this a K2 matrix, and this
+
+here an M2 matrix.
+
+Now, we are operating with P2
+transpose on K2, and also
+
+there's a P2 here.
+
+So let me take a different color
+to show that now we are
+
+operating with this part here,
+and that part there.
+
+And this, of course, we are
+doing in such a way as to have
+
+that P2 transposed, K2, P2
+is a little bit closer to
+
+diagonal form than was K2.
+
+I hope you can see these
+lines-- let me put
+
+them in once more.
+
+What I'm saying is we have K2
+after having applied P1
+
+transpose on P1, on K,
+and similar for M.
+
+And now we want to make K2 still
+a little bit closer to
+
+diagonal form.
+
+Well, we are now applying P2
+transposed on K2 and the P2 on
+
+K2, this one here has been
+replaced by K2, this one here
+
+has been replaced by M2.
+
+And what we're saying is that
+this final result, in this
+
+final result should be closer
+to diagonal form.
+
+In fact, this should be closer
+to I matrix, and this should
+
+be closer to the lambda
+matrix, ideally.
+
+Well, this is the basic process
+that is used in the
+
+generalized Jacobi method.
+
+We can show that if
+we choose specific
+
+matrices, P I matrices.
+
+That zero always one [? of ?]
+diagonal element.
+
+In other words, the P I matrix,
+zeroes a particular
+
+off diagonal element in this
+current coefficient matrix,
+
+similarly for the M2, for the
+current M coefficient matrix.
+
+Then we know in the generalized
+Jacobi method that
+
+the process finally converges.
+
+It converges and we get a
+diagonal matrix here.
+
+With proper scaling, it will
+be the identity matrix.
+
+And here, we are getting also a
+diagonal matrix, and if this
+
+is an identity matrix, this will
+actually be the matrix
+
+storing the eigenvalues.
+
+Well, this is the generalized
+Jacobi method here.
+
+They are other techniques that
+can also be used, of course,
+
+this is a very common approach
+taken when we have M being
+
+equal to the identity matrix.
+
+However, the disadvantage of
+this approach is that we are
+
+calculating all eigen pairs
+simultaneously.
+
+In finite element analysis,
+we are only interested in
+
+specific eigenvalues, so lowest
+P, or a certain number
+
+of eigenvalues in an interval.
+
+Here, we have to calculate all
+of the eigenvalues stored in
+
+the lambda matrix, and all
+of the eigenvectors.
+
+And the eigenvectors here, would
+be these vectors here.
+
+These are the the matrix phi,
+which is P1 times P2, up to P
+
+K, after K steps of iteration.
+
+This gives us the matrix
+phi, storing all of the
+
+eigenvectors.
+
+So the disadvantage is that we
+are calculating all of that
+
+eigenvectors, which in finite
+element analysis is hardly
+
+ever required.
+
+All we want is the total number
+of eigenvalues and
+
+eigenvectors.
+
+Remember, also if K
+is of [? order ?]
+
+1,000, this would be a
+tremendous amount of work
+
+involved and, in fact, it would
+be beyond the current
+
+state of computing capabilities
+to use a
+
+generalized Jacobi method on a
+K matrix 1,000x1,000 and an M
+
+matrix 1,000x1,000.
+
+You will certainly stretch the
+current computing capabilities
+
+tremendously by using the
+generalized Jacobi method on
+
+large eigenproblems.
+
+For large eigenproblems, it is
+really best to combine the
+
+basic approaches that
+I just mentioned.
+
+Let's recall the basic
+approaches.
+
+There were iteration methods,
+vector iteration methods,
+
+there were Sturm sequence
+methods, there was the
+
+transformation method.
+
+And then, of course, there were
+
+polynomial iteration methods.
+
+So really, four classes
+of methods that
+
+we are talking about.
+
+Each of them, we find,
+have some advantages.
+
+Well, as engineer, surely we
+want to now combine the
+
+advantages of each of these
+methods to come up with
+
+optimum techniques for our
+specific problems.
+
+Well, there are a number
+of thoughts
+
+that we would go through.
+
+First of all, a determinant
+search, a polynomial iteration
+
+method would be effective
+to get near a root.
+
+Vector iteration then could
+be used to calculate an
+
+eigenvalue and an eigenvector.
+
+The transformation method would
+be good to orthogonalize
+
+the current iteration vectors
+if we iterate with more than
+
+just one vector.
+
+And the Sturm sequence method
+is extremely powerful to
+
+assure that we have actually
+calculated the required
+
+eigenvalues and eigenvectors.
+
+Well, the first method then that
+I would like to discuss
+
+with you is the determinant
+search method.
+
+In this method, we have
+combined some of these
+
+techniques that I pointed
+out to you earlier
+
+in an optimum way.
+
+Here, we have the polynomial P
+lambda, we want to, of course,
+
+solve for the roots of
+that polynomial--
+
+that is our objective.
+
+Here is lambda 1, there
+is lambda 2.
+
+I also show a point,
+A, because I will
+
+refer to it just now.
+
+The basic scheme in the
+determinant search method is
+
+to look for the zeroes of
+the determinant, of the
+
+determinant K minus mu I M. Of
+course, these zeroes give us R
+
+equal to the eigenvalues.
+
+That's what we're interested
+in calculating.
+
+Well, we are calculating
+the determinant by the
+
+factorization of this matrix
+into L D L transpose, and we
+
+notice that this determinant is
+simply the product of the
+
+[? D I I's, ?] as I
+mentioned earlier.
+
+Now, having a certain starting
+value, mu 0, say, and mu 1.
+
+We can directly use the secant
+iteration, that I mentioned to
+
+you earlier to get close
+to an eigenvalue.
+
+Now, I also slipped in here
+an acceleration factor.
+
+This acceleration factor would
+be equal to 1 in the normal
+
+secant iteration that I showed
+to you earlier already.
+
+However, since we want to use
+this polynomial iteration
+
+technique only to get close to
+an eigenvalue, and we might
+
+actually obtain with eta equal
+to 1, sometimes slow
+
+convergence.
+
+What we do is we simply
+set it larger to
+
+accelerate the process.
+
+And this is what we're
+doing here.
+
+If we do jump beyond an
+eigenvalue because we have
+
+accelerated the secant
+iteration.
+
+In other words, if we do a jump
+across here, then since
+
+we are factorizing the matrix
+here, we can also look at the
+
+number of negative elements
+in the D matrix.
+
+These would tell us that we, in
+fact, have jumped across an
+
+unknown eigenvalue.
+
+So, in this particular case, of
+course, there would be one
+
+negative element in
+the D matrix.
+
+And we would know now we
+have jumped across.
+
+The jumping across an unknown
+eigenvalue is not possible
+
+when eta is equal to 1.
+
+However, it is possible when
+eta is greater than 1.
+
+And however, that jumping
+does not hurt us.
+
+In fact, all we will find is
+that the Sturm sequence count
+
+will tell us that we have jumped
+across an eigenvalue,
+
+and then, of course, we have to
+go to another strategy of
+
+solving for the eigenvalue
+more accurately.
+
+But the important point is that
+all we want to do via
+
+this procedure is to get into
+the vicinity of the
+
+eigenvalue.
+
+We do not want to calculate it
+accurately, all we want to do
+
+is get into the vicinity of
+an unknown eigenvalue.
+
+First, of course, lambda 1,
+then lambda 2, and so on.
+
+There's also a concern, of
+course, that we do not want to
+
+jump beyond A, because if we, in
+our process of looking for
+
+lambda 1, we are jumping too
+close to lambda 2, then via
+
+the other solution techniques
+that we are using later on
+
+then to calculate the eigenvalue
+more accurately, we
+
+would actually converge
+to lambda 2.
+
+And, of course, that we
+don't want, we want to
+
+calculate lambda 1.
+
+So, the process is then to start
+off with eta equal to 1,
+
+iterate, see how we are
+progressing towards an unknown
+
+eigenvalue.
+
+If that progressing is
+very slow, we are
+
+choosing eta larger.
+
+There are specific strategies
+that we're using to choose the
+
+right amount all eta.
+
+And until we find that we are
+close to an eigenvalue, either
+
+from the left or we have jumped
+across it already, but
+
+you should never
+jumped to far.
+
+And we are making sure that we
+never jump beyond that point
+
+A. and having jumped, we find
+that the Sturm sequence count
+
+tells us about it.
+
+And now, we are going on to
+another strategy, and that
+
+strategy is the vector
+iteration, vector inverse
+
+iteration method that I
+discussed with you earlier.
+
+What we are doing now, is we
+have a new coefficient matrix,
+
+that's the one.
+
+We are sitting here, say, and
+now I have assumed that we
+
+have, in fact, jumped.
+
+It's not necessary.
+
+We might have also approached
+from this side and come very
+
+close to lambda J. And now, we
+are using vector iteration to
+
+get this eigenvalue
+accurately.
+
+This coefficient here,
+or this value here
+
+corresponds to that length.
+
+And if you are adding this value
+here to this shift, we
+
+are getting an approximation
+to lambda J. And that, of
+
+course, is our objective.
+
+Once we have lambda J, we have
+calculated this eigenvalue--
+
+the eigenvector comes out, in x
+k plus 1 as k increases, so
+
+we have calculated this eigen
+pair, and now, of course, we
+
+would use deflation method, just
+the way I showed it to
+
+your earlier, for the polynomial
+iteration method.
+
+To deflate the polynomial of
+this value, implicitly--
+
+implicitly, that's important--
+
+and we would continue our
+iteration process towards that
+
+eigenvalue next.
+
+In this process, we also want
+to make sure that the
+
+iteration vector is deflated
+of the previously
+
+eigenvectors, for example,
+Gram-Schmidt
+
+orthogonalization.
+
+If the convergence is slow in
+this particular iteration
+
+here, we're using also the
+really Rayleigh-quotient
+
+iteration to speed up
+iteration itself.
+
+The advantage of the method--
+well, it calculates only the
+
+eigen pairs that are actually
+required., there's no prior
+
+transformation of the
+eigenprobelm necessary.
+
+The disadvantage of the method
+is that we have to perform
+
+many triangular factorizations.
+
+Therefore, the method is really
+only effective for
+
+small banded systems.
+
+If we want to calculate
+eigenvalues of large banded
+
+systems, we really need
+an algorithm with less
+
+factorizations, and more
+vector iterations.
+
+And that is the subspace
+iteration method.
+
+In fact, we have now extended
+the subspace iteration method
+
+to be also most effective for
+small banded systems.
+
+And I will just refer to
+it very briefly later.
+
+The basic steps of the subspace
+iteration method are
+
+the following.
+
+Here, we have the first
+equation used.
+
+We have on the right
+hand side, the
+
+current iteration vectors.
+
+Now, notice that in this
+particular case, we're
+
+iterating with q vectors,
+where q ip larger than p
+
+simultaneously.
+
+This gives us here, q right
+hand side vector.
+
+We are solving for
+q vectors here.
+
+This is an inverse iteration
+step on q vector
+
+simultaneously.
+
+Then we are calculating the
+projections of these k and m
+
+matrices on these vectors.
+
+Notice that this pat here,
+of course, is equal to
+
+this right hand side.
+
+So we would not calculate
+this here.
+
+We simply use the right hand
+side, which we have evaluated
+
+already and plug it
+right in there.
+
+But having calculated these two
+matrices, which are now of
+
+order q by q, we are solving
+eigenvalue problem all of
+
+these q by q matrices.
+
+And the solution of
+that eigenvalue
+
+problem is shown here.
+
+Notice this matrix here
+is a q by q matrix.
+
+We're using q vectors.
+
+This is a q by q matrix storing
+the eigenvectors of
+
+this eigen problem here, of the
+eigenproblem corresponding
+
+to these matrices.
+
+This here is the diagonal matrix
+listing the eigenvalues
+
+of the eigenproblem
+
+corresponding to these matrices.
+
+Having calculated these matrices
+here, and of course,
+
+that one too, we are performing
+this operation to
+
+get a new set of iteration
+vectors, which then are
+
+plugged back into here.
+
+Notice that the solution of
+this eigenproblem, q by q,
+
+might be a 50x50 matrix here,
+100x100 matrix, maybe a
+
+200x200, but that already would
+be a large number of
+
+vectors if we're using--
+
+a very large number
+of vectors.
+
+This solution of this
+eigenproblem can be
+
+effectively achieved via the
+generalized Jacobi method,
+
+which I referred to
+briefly earlier.
+
+Of course here, we are using
+our solution algorithm for
+
+static analysis.
+
+There's L D L transpose
+factorization involved here.
+
+And here, this is a simple
+matrix multiplication that has
+
+to be carried out.
+
+This part here, is the
+eigenproblem solution, and
+
+there's another vector
+
+multiplication carried out here.
+
+Now, under specific conditions,
+this eigensolution
+
+algorithm converges and the
+vectors stored in x k plus 1,
+
+they are q vectors now here,
+with appropriate ordering,
+
+converge to the phi matrix.
+
+This is now an n by q matrix,
+storing the lowest
+
+eigenvectorr, or I should
+say, the q eigenvectors
+
+corresponding to the
+lowest eigenvalues.
+
+And here, we have it written
+out, and of course, this is a
+
+diagonal matrix.
+
+The condition that we have to
+satisfy here is that the
+
+starting subspace spanned by
+these vectors here must not be
+
+orthogonal to the subspace
+spanned by the p eigenvectors
+
+that we are interested in.
+
+Of course, here, I'm talking
+about q eigenvectors.
+
+I really am only interested in
+p eigenvectors, in the lowest
+
+p eigenvectors.
+
+So in general, what happens is
+that I will only be interested
+
+in these eigenvectors here, and
+the lowest eigenvalues.
+
+One comes out here, I'm not
+too much concerned about.
+
+In fact, we are carrying these
+along only to accelerate the
+
+iteration scheme.
+
+And I will show you just know
+what the convergence rate is,
+
+and why we are carrying
+them along.
+
+So since we only interested in
+the lowest p eigenvalues and
+
+corresponding eigenvectors,
+we want to get convergence
+
+towards those, and what that
+means is that our starting
+
+vectors in here must not be m
+orthogonal to the eigenvectors
+
+that we want to calculate,
+phi 1 to phi p.
+
+If that condition is satisfied,
+one can show,
+
+theoretically, and of course,
+we see it in practice also,
+
+that this iteration scheme will
+always converge to the
+
+lowest eigenvectors and
+corresponding eigenvalues.
+
+One important point here, once
+we have calculated, say, a
+
+certain number of iteration
+vectors, and we have tested
+
+for convergence, we are saying
+that convergence is reached,
+
+say, when the current iterates
+on the eigenvalues don't
+
+change very much anymore.
+
+This tol might be 10 to the
+minus 6, as an example.
+
+Then once this condition is
+satisfied, we stop the
+
+iteration, and we really want
+to make then sure that we
+
+really converge to the
+eigenvalues of interest.
+
+And how is that accomplished?
+
+Well, if these are the
+p eigenvalues, we are
+
+calculating error bounds on
+these eigenvalues, indicated
+
+here by the blue lines here.
+
+And then just to the right
+of the error bound.
+
+Or we can really use that error
+bound, we apply a Sturm
+
+sequence shift, mu S. What this
+then says that k minus mu
+
+S factorize into L
+D L transpose.
+
+And we must now have in the D
+matrix, p negative elements.
+
+And only p, not more, not less,
+just p negative elements
+
+must be occurring
+in the D matrix.
+
+This check is absolutely sure.
+
+If this check a satisfied, we
+can be absolutely sure that we
+
+have calculated the eigenvalues
+of interest, the
+
+lowest p eigenvalues, in
+this particular case.
+
+So I repeat, after we have
+satisfied this convergence
+
+rate, or this conversions
+limit, I should say--
+
+typically 10 to the minus
+6, or 10 to the minus 8,
+
+depending on what accuracy
+you want.
+
+We calculating eigenvalue
+bounds, as shown here.
+
+We are putting a mu S Sturm
+sequence shift just to the
+
+right of the last eigenvalue
+bound, and if this is the p's
+
+eigenvalue, we must have
+here, exactly p
+
+negative elements indeed.
+
+The convergence rate of the
+iteration, we find is given by
+
+lambda i divided by
+lambda q plus 1.
+
+And the convergence rate to the
+eigenvalues of interest
+
+are just this value squared.
+
+Notice that we have
+here, q plus 1.
+
+So if we are interested in the
+p's eigenvalue,== the black
+
+pen doesn't work too well, let
+me take the blue one here--
+
+if you're interested in the p's
+eigenvalue as the largest
+
+eigenvalue, notice that the
+convergence rate is that
+
+lambda p plus-- lambda p divided
+by lambda q plus 1.
+
+That is the worst convergence
+rate that we are reaching
+
+because the other eigenvalues
+below lambda p are smaller,
+
+giving us better convergence
+rate.
+
+So this is the worst that we
+can reach, if we are only
+
+interested in p eigenvalues
+and corresponding
+
+eigenvectors.
+
+Notice however, that lambda
+q plus 1 must be
+
+greater than lambda p.
+
+If lambda q plus 1 is
+equal to lambda p,
+
+we would never converge.
+
+So this is the reason why we
+are choosing q to be larger
+
+than p, substantially
+large than p.
+
+For example, we might choose
+q to be typically, as an
+
+example, q being the maximum
+of 2p and p plus 8.
+
+This is a formula that
+we have used with
+
+quite a lot of success.
+
+In other words, when p is equal
+to 4, we would use--
+
+no, sorry, I should say
+the minimum here.
+
+the In other words, when
+p is equal to 4, we
+
+would have 8 here.
+
+When p is equal to
+8, it's the same.
+
+Because these two values
+give us the same.
+
+And when p is equal to 100,
+then we just have 8 more.
+
+Q is equal to 108.
+
+This 8 here is a safeguard, so
+that this cannot be equal to 1
+
+in practice.
+
+It would only be equal to 1 if
+we would have, basically.
+
+9 time the same root, and of
+course, that is a case which
+
+we would hardly encounter
+in practice.
+
+Now, regarding the choice
+of the starting values.
+
+For the vectors, there
+are two choices.
+
+x1 is simply a vector
+with 1 only.
+
+xj would be a vector with zeroes
+everywhere, but with a
+
+1 somewhere.
+
+And that one is in
+the j's entry--
+
+sorry, the k's entry.
+
+The k's entry for ek, ek has
+in the case, entry of 1.
+
+And otherwise, everywhere
+zeroes.
+
+This would be the second to
+the q minus first vector.
+
+And the last vector, we
+take a random vector.
+
+That is one choice of
+starting vectors.
+
+The Lanczos method can also be
+used to generate starting
+
+vectors very effectively.
+
+Once we have selected the
+starting vector, we go through
+
+the iteration schemes the way
+I have been displaying it.
+
+And there, it is important, once
+again, to perform after
+
+the convergence- the Sturm
+system sequence check, and
+
+also we might want to calculate
+error bounds on the
+
+eigenvalues and eigenvectors.
+
+These error bounds would be
+calculated by simply saying,
+
+well, if we want to satisfy--
+
+or if we want to solve for
+lambdas and phis that
+
+satisfies this equation,
+then why not see how
+
+close we will satisfy.
+
+Make that a minus and put here
+an error, say, R, on
+
+the right hand side.
+
+Substituting then the last
+values for lambda and phi that
+
+we just kind calculated, the
+last iterative values, we get
+
+this top line here.
+
+We're taking a norm
+the way I've been
+
+talking about earlier.
+
+And we are also taking a norm
+at the bottom to get,
+
+basically, a relative value,
+top to bottom.
+
+And then relative value
+gives us epsilon i.
+
+So epsilon i should be of order,
+10 to the minus 3, if
+
+we want to have three-digit
+accuracy in the eigenvalues
+
+and eigenvectors.
+
+In fact, the eigenvalues will
+generally be more accurate
+
+than the eigenvectors.
+
+That is, of course, a
+very low accuracy.
+
+Ideally, we have much
+more accuracy after
+
+the iteration schemes.
+
+We would have to tighten the
+tolerance, the tol value that
+
+I referred to earlier
+sufficiently to make epsilon i
+
+small enough.
+
+Now, I like to refer, very
+briefly also, to an
+
+accelerated subspace iteration
+method that we have been
+
+developing during the last
+years, which is a very
+
+substantial extension of this
+subspace iteration method.
+
+The idea here is, basically,
+that we wanted to combine the
+
+sum of the effective techniques
+that we are using
+
+in the polynomial iteration
+method, with the standard
+
+subspace iteration method
+that I have
+
+discussed with you here.
+
+Basically, in the accelerated
+subspace iteration method, we
+
+are not keeping a constant
+coefficient matrix, as
+
+we have done here.
+
+The k matrix never changed.
+
+Here, we are shifting the
+coefficient matrix, we are
+
+shifting through the spectrum.
+
+Much in the same way as we are
+pursuing it in the determined
+
+search method.
+
+And that is number one.
+
+And number two-- we are also
+not iterating with vectors
+
+that are always larger than
+the number of eigenvectors
+
+that we want to calculated.
+
+In fact, if we want to
+calculate, say, 100
+
+eigenvalues, we might just use
+four iteration vectors at a
+
+time, and shift through the
+spectrum, always with four
+
+iteration vectors, capturing
+the eigenvalues values and
+
+eigenvectors that we are really
+
+interested in, in bundles.
+
+So this is a way how we have
+very substantially accelerated
+
+the standard subspace iteration
+method that I have
+
+been talking to you
+about just now.
+
+If you are interested in seeing
+some solution times,
+
+please we look at
+this reference.
+
+Ladies and gentlemen, this
+then brings me to the
+
+conclusion of this lecture.
+
+And in fact, it also brings us
+to the conclusion of the whole
+
+set of lectures that I have
+been presenting to you.
+
+These set up lectures have been
+brief and very compact.
+
+They've been a survey
+introduction to the finite
+
+element method--
+
+a very brief and compact
+introduction and survey.
+
+Brief because there are
+only 12 lectures.
+
+Compact because I wanted to
+present to you as much as
+
+possible in these 12 lectures.
+
+And there is, of course, a lot
+of information that we could
+
+have talked about.
+
+However, I hope that the
+information that I had given
+
+in the lectures has been of
+interest to you, and it will
+
+also be valuable to you in your
+work and general decision
+
+making process of whether you
+want to use a finite element
+
+method, how you want to
+use it, and so on.
+
+I like to take the opportunity
+at this point to thank the
+
+Center of Advanced Engineering
+Studies for the terrific
+
+effort they've made in
+preparing the tapes.
+
+I'm very happy that they have
+been cooperative with me in
+
+the way they did, in the
+preparation of the tapes.
+
+I also would like to thank you
+as listeners for your patience
+
+of listening to the tapes and,
+once again, I hope you found
+
+the tapes interesting and
+have obtained some value
+
+information on them.
+
+Best of luck in your further
+studies of the
+
+finite element method.
\ No newline at end of file
diff --git a/exav1FKMfbw.txt b/exav1FKMfbw.txt
new file mode 100644
index 0000000000000000000000000000000000000000..82a6dc44d8bfecd358ea4d2ece1e876b62c8063a
--- /dev/null
+++ b/exav1FKMfbw.txt
@@ -0,0 +1,699 @@
+align:start position:0%
+ 
+let's go ahead and start our the first
+
+ align:start position:0%
+let's go ahead and start our the first
+ 
+
+ align:start position:0%
+let's go ahead and start our the first
+thing you'll see in the our console is
+
+ align:start position:0%
+thing you'll see in the our console is
+ 
+
+ align:start position:0%
+thing you'll see in the our console is
+the version of our you are using in
+
+ align:start position:0%
+the version of our you are using in
+ 
+
+ align:start position:0%
+the version of our you are using in
+other basic information related to
+
+ align:start position:0%
+other basic information related to
+ 
+
+ align:start position:0%
+other basic information related to
+licensing citations and demos to clear
+
+ align:start position:0%
+licensing citations and demos to clear
+ 
+
+ align:start position:0%
+licensing citations and demos to clear
+the console you can simply go to edit
+
+ align:start position:0%
+the console you can simply go to edit
+ 
+
+ align:start position:0%
+the console you can simply go to edit
+and select clear console we'll start by
+
+ align:start position:0%
+and select clear console we'll start by
+ 
+
+ align:start position:0%
+and select clear console we'll start by
+reading in our data set
+
+ align:start position:0%
+reading in our data set
+ 
+
+ align:start position:0%
+reading in our data set
+USDA dot CSV which contains all foods in
+
+ align:start position:0%
+USDA dot CSV which contains all foods in
+ 
+
+ align:start position:0%
+USDA dot CSV which contains all foods in
+the USDA database in 100 gram amounts
+
+ align:start position:0%
+the USDA database in 100 gram amounts
+ 
+
+ align:start position:0%
+the USDA database in 100 gram amounts
+you should have already downloaded the
+
+ align:start position:0%
+you should have already downloaded the
+ 
+
+ align:start position:0%
+you should have already downloaded the
+data set to your computer to be able to
+
+ align:start position:0%
+data set to your computer to be able to
+ 
+
+ align:start position:0%
+data set to your computer to be able to
+read the data set in our we first need
+
+ align:start position:0%
+read the data set in our we first need
+ 
+
+ align:start position:0%
+read the data set in our we first need
+to navigate to the directory in our
+
+ align:start position:0%
+to navigate to the directory in our
+ 
+
+ align:start position:0%
+to navigate to the directory in our
+computer where the data file USDA dot
+
+ align:start position:0%
+computer where the data file USDA dot
+ 
+
+ align:start position:0%
+computer where the data file USDA dot
+CSV is saved to do so if you are on a
+
+ align:start position:0%
+CSV is saved to do so if you are on a
+ 
+
+ align:start position:0%
+CSV is saved to do so if you are on a
+Mac go to the miscellaneous menu and
+
+ align:start position:0%
+Mac go to the miscellaneous menu and
+ 
+
+ align:start position:0%
+Mac go to the miscellaneous menu and
+select change working directory if you
+
+ align:start position:0%
+select change working directory if you
+ 
+
+ align:start position:0%
+select change working directory if you
+are on a PC go to the file menu select
+
+ align:start position:0%
+are on a PC go to the file menu select
+ 
+
+ align:start position:0%
+are on a PC go to the file menu select
+change directory and then navigate to
+
+ align:start position:0%
+change directory and then navigate to
+ 
+
+ align:start position:0%
+change directory and then navigate to
+the folder where you save the CSV file
+
+ align:start position:0%
+the folder where you save the CSV file
+ 
+
+ align:start position:0%
+the folder where you save the CSV file
+then press ok nothing has happened in
+
+ align:start position:0%
+then press ok nothing has happened in
+ 
+
+ align:start position:0%
+then press ok nothing has happened in
+our until now except changing the
+
+ align:start position:0%
+our until now except changing the
+ 
+
+ align:start position:0%
+our until now except changing the
+working directory to double check that
+
+ align:start position:0%
+working directory to double check that
+ 
+
+ align:start position:0%
+working directory to double check that
+we are in the right working directory we
+
+ align:start position:0%
+we are in the right working directory we
+ 
+
+ align:start position:0%
+we are in the right working directory we
+can type get WD which stands for get
+
+ align:start position:0%
+can type get WD which stands for get
+ 
+
+ align:start position:0%
+can type get WD which stands for get
+working directory and then our gives us
+
+ align:start position:0%
+working directory and then our gives us
+ 
+
+ align:start position:0%
+working directory and then our gives us
+the path to the folder we just selected
+
+ align:start position:0%
+the path to the folder we just selected
+ 
+
+ align:start position:0%
+the path to the folder we just selected
+now we should be ready to read in our
+
+ align:start position:0%
+now we should be ready to read in our
+ 
+
+ align:start position:0%
+now we should be ready to read in our
+data set we will use the function read
+
+ align:start position:0%
+data set we will use the function read
+ 
+
+ align:start position:0%
+data set we will use the function read
+CSV since the data set was given to us
+
+ align:start position:0%
+CSV since the data set was given to us
+ 
+
+ align:start position:0%
+CSV since the data set was given to us
+in a CSV format and let's save the
+
+ align:start position:0%
+in a CSV format and let's save the
+ 
+
+ align:start position:0%
+in a CSV format and let's save the
+output to a data frame and call it USDA
+
+ align:start position:0%
+output to a data frame and call it USDA
+ 
+
+ align:start position:0%
+output to a data frame and call it USDA
+and this is equal to read CSV and this
+
+ align:start position:0%
+and this is equal to read CSV and this
+ 
+
+ align:start position:0%
+and this is equal to read CSV and this
+takes has an input the name of the CSV
+
+ align:start position:0%
+takes has an input the name of the CSV
+ 
+
+ align:start position:0%
+takes has an input the name of the CSV
+file which is USDA dot CSV and don't
+
+ align:start position:0%
+file which is USDA dot CSV and don't
+ 
+
+ align:start position:0%
+file which is USDA dot CSV and don't
+forget the quotation marks around the
+
+ align:start position:0%
+forget the quotation marks around the
+ 
+
+ align:start position:0%
+forget the quotation marks around the
+name of the CSV file pressing enter are
+
+ align:start position:0%
+name of the CSV file pressing enter are
+ 
+
+ align:start position:0%
+name of the CSV file pressing enter are
+now read the information from the data
+
+ align:start position:0%
+now read the information from the data
+ 
+
+ align:start position:0%
+now read the information from the data
+set and saved it to the data frame USDA
+
+ align:start position:0%
+set and saved it to the data frame USDA
+ 
+
+ align:start position:0%
+set and saved it to the data frame USDA
+now it's time to learn about our data we
+
+ align:start position:0%
+now it's time to learn about our data we
+ 
+
+ align:start position:0%
+now it's time to learn about our data we
+can use the structure function or STR
+
+ align:start position:0%
+can use the structure function or STR
+ 
+
+ align:start position:0%
+can use the structure function or STR
+and R and give it the input USDA this
+
+ align:start position:0%
+and R and give it the input USDA this
+ 
+
+ align:start position:0%
+and R and give it the input USDA this
+gives us the following information we
+
+ align:start position:0%
+gives us the following information we
+ 
+
+ align:start position:0%
+gives us the following information we
+have 7000 58 observations or Foods in
+
+ align:start position:0%
+have 7000 58 observations or Foods in
+ 
+
+ align:start position:0%
+have 7000 58 observations or Foods in
+our data set along with 16 different
+
+ align:start position:0%
+our data set along with 16 different
+ 
+
+ align:start position:0%
+our data set along with 16 different
+variables the first bear
+
+ align:start position:0%
+variables the first bear
+ 
+
+ align:start position:0%
+variables the first bear
+gives a unique identification number for
+
+ align:start position:0%
+gives a unique identification number for
+ 
+
+ align:start position:0%
+gives a unique identification number for
+each of the food starting with the
+
+ align:start position:0%
+each of the food starting with the
+ 
+
+ align:start position:0%
+each of the food starting with the
+number 1001 the second variable gives a
+
+ align:start position:0%
+number 1001 the second variable gives a
+ 
+
+ align:start position:0%
+number 1001 the second variable gives a
+text description of each of the foods
+
+ align:start position:0%
+text description of each of the foods
+ 
+
+ align:start position:0%
+text description of each of the foods
+the third variable is the amount of
+
+ align:start position:0%
+the third variable is the amount of
+ 
+
+ align:start position:0%
+the third variable is the amount of
+calories and 100 grams of these foods
+
+ align:start position:0%
+calories and 100 grams of these foods
+ 
+
+ align:start position:0%
+calories and 100 grams of these foods
+and it's given to us in kilocalories
+
+ align:start position:0%
+and it's given to us in kilocalories
+ 
+
+ align:start position:0%
+and it's given to us in kilocalories
+then we also have information about the
+
+ align:start position:0%
+then we also have information about the
+ 
+
+ align:start position:0%
+then we also have information about the
+protein total fat carbohydrate saturated
+
+ align:start position:0%
+protein total fat carbohydrate saturated
+ 
+
+ align:start position:0%
+protein total fat carbohydrate saturated
+fat and sugar levels in grams as well as
+
+ align:start position:0%
+fat and sugar levels in grams as well as
+ 
+
+ align:start position:0%
+fat and sugar levels in grams as well as
+the sodium cholesterol calcium iron
+
+ align:start position:0%
+the sodium cholesterol calcium iron
+ 
+
+ align:start position:0%
+the sodium cholesterol calcium iron
+potassium and vitamin C levels in
+
+ align:start position:0%
+potassium and vitamin C levels in
+ 
+
+ align:start position:0%
+potassium and vitamin C levels in
+milligrams and finally the amount of
+
+ align:start position:0%
+milligrams and finally the amount of
+ 
+
+ align:start position:0%
+milligrams and finally the amount of
+vitamin E and vitamin D in what is known
+
+ align:start position:0%
+vitamin E and vitamin D in what is known
+ 
+
+ align:start position:0%
+vitamin E and vitamin D in what is known
+as international units and this is a
+
+ align:start position:0%
+as international units and this is a
+ 
+
+ align:start position:0%
+as international units and this is a
+standard measurement for drugs in
+
+ align:start position:0%
+standard measurement for drugs in
+ 
+
+ align:start position:0%
+standard measurement for drugs in
+vitamins now to obtain high level
+
+ align:start position:0%
+vitamins now to obtain high level
+ 
+
+ align:start position:0%
+vitamins now to obtain high level
+statistical information about our
+
+ align:start position:0%
+statistical information about our
+ 
+
+ align:start position:0%
+statistical information about our
+dataset we can use the summary function
+
+ align:start position:0%
+dataset we can use the summary function
+ 
+
+ align:start position:0%
+dataset we can use the summary function
+and give it as an input the USDA data
+
+ align:start position:0%
+and give it as an input the USDA data
+ 
+
+ align:start position:0%
+and give it as an input the USDA data
+frame the summary function gives us
+
+ align:start position:0%
+frame the summary function gives us
+ 
+
+ align:start position:0%
+frame the summary function gives us
+information such as the minimum the
+
+ align:start position:0%
+information such as the minimum the
+ 
+
+ align:start position:0%
+information such as the minimum the
+maximum and the mean values across all
+
+ align:start position:0%
+maximum and the mean values across all
+ 
+
+ align:start position:0%
+maximum and the mean values across all
+seven thousand and fifty-eight foods for
+
+ align:start position:0%
+seven thousand and fifty-eight foods for
+ 
+
+ align:start position:0%
+seven thousand and fifty-eight foods for
+each of the 16 different variables for
+
+ align:start position:0%
+each of the 16 different variables for
+ 
+
+ align:start position:0%
+each of the 16 different variables for
+instance the maximum amount of
+
+ align:start position:0%
+instance the maximum amount of
+ 
+
+ align:start position:0%
+instance the maximum amount of
+cholesterol is 3100 milligrams
+
+ align:start position:0%
+cholesterol is 3100 milligrams
+ 
+
+ align:start position:0%
+cholesterol is 3100 milligrams
+whereas the mean is only 41 point 55
+
+ align:start position:0%
+whereas the mean is only 41 point 55
+ 
+
+ align:start position:0%
+whereas the mean is only 41 point 55
+milligrams we also have information
+
+ align:start position:0%
+milligrams we also have information
+ 
+
+ align:start position:0%
+milligrams we also have information
+about the number of non-available
+
+ align:start position:0%
+about the number of non-available
+ 
+
+ align:start position:0%
+about the number of non-available
+entries for instance we have 1910 foods
+
+ align:start position:0%
+entries for instance we have 1910 foods
+ 
+
+ align:start position:0%
+entries for instance we have 1910 foods
+that are missing entries for their sugar
+
+ align:start position:0%
+that are missing entries for their sugar
+ 
+
+ align:start position:0%
+that are missing entries for their sugar
+levels now scrolling through this
+
+ align:start position:0%
+levels now scrolling through this
+ 
+
+ align:start position:0%
+levels now scrolling through this
+information a startling observation is
+
+ align:start position:0%
+information a startling observation is
+ 
+
+ align:start position:0%
+information a startling observation is
+the maximum level of sodium which is 38
+
+ align:start position:0%
+the maximum level of sodium which is 38
+ 
+
+ align:start position:0%
+the maximum level of sodium which is 38
+thousand seven hundred and fifty eight
+
+ align:start position:0%
+thousand seven hundred and fifty eight
+ 
+
+ align:start position:0%
+thousand seven hundred and fifty eight
+milligrams this number is huge given
+
+ align:start position:0%
+milligrams this number is huge given
+ 
+
+ align:start position:0%
+milligrams this number is huge given
+that the daily recommended maximum is
+
+ align:start position:0%
+that the daily recommended maximum is
+ 
+
+ align:start position:0%
+that the daily recommended maximum is
+only 2300 milligrams let's investigate
+
+ align:start position:0%
+only 2300 milligrams let's investigate
+ 
+
+ align:start position:0%
+only 2300 milligrams let's investigate
+this variable further in our next video
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+you
\ No newline at end of file
diff --git a/fFg4uXMpnV0.txt b/fFg4uXMpnV0.txt
new file mode 100644
index 0000000000000000000000000000000000000000..105766df918b2b578914f21d11dfb292c99c8c3b
--- /dev/null
+++ b/fFg4uXMpnV0.txt
@@ -0,0 +1,2356 @@
+The following content is
+provided under a Creative
+
+Commons License.
+
+Your support will help MIT
+OpenCourseWare continue to
+
+offer high-quality educational
+resources for free.
+
+To make a donation, or view
+additional materials from
+
+hundreds of MIT courses, visit
+MIT OpenCourseWare at
+
+ocw.mit.edu.
+
+PROFESSOR: OK, OK,
+Settle down.
+
+Settle down.
+
+It's 11:05.
+
+It's time to learn.
+
+All right.
+
+Last day we were looking at the
+emissions spectrum of the
+
+target in the x-ray tube.
+
+The target is the anode, and
+it's being a bombarded by
+
+electrons that have been
+accelerated across a potential
+
+difference of some tens of
+thousands of volts, and this
+
+was what we saw as the output,
+intensity versus wavelength.
+
+We see this whale shaped curve
+which we have attributed to
+
+bremsstrahlung, which is
+the breaking radiation.
+
+And then if the voltage
+is high enough, high
+
+enough to do what?
+
+High enough to eject inner shell
+electrons, we will get
+
+the cascade, and the cascade
+will give rise to specific
+
+values of wavelength associated
+with transitions
+
+within the target atom.
+
+There's too much talking.
+
+I want it absolutely silent or
+else somebody is going to
+
+leave. That's the only
+way it works here.
+
+I talk.
+
+You listen.
+
+And if you have a problem with
+that, there's a door here.
+
+There's a door there.
+
+And there's a door
+at the back.
+
+So let's get it straight
+right now.
+
+It's the only way
+it works here.
+
+Now what happens is that these
+characteristic lines are
+
+calculable in part.
+
+The K alpha line, the L alpha
+line we saw from Moseley's
+
+law, which is up here
+on the slide.
+
+and the leading edge of the
+whale shape curve, the
+
+bremsstrahlung is calculable
+by the Duane-Hunt Law.
+
+The rest of this is
+not calculable.
+
+So there it is.
+
+What I want to do today is
+harness this radiation.
+
+The reason we were studying
+x-rays in first place was that
+
+we said they had a length scale
+that was comparable to
+
+that of atomic dimensions.
+
+And so now we want to close
+the circle here and probe
+
+atomic arrangement by
+x-ray diffraction.
+
+And it goes by this
+three-letter
+
+initialization XRD.
+
+And in order to use x-ray
+diffraction to probe atomic
+
+structure, we're going to
+make another model.
+
+And this model is going
+to be simple.
+
+And it's going to be inaccurate,
+but it's going to
+
+be good enough to explain
+the phenomena that
+
+we're going to study.
+
+So the first thing I want to
+do in constructing a model
+
+that will allow to use x-ray
+diffraction, is to model the
+
+atoms as mirrors.
+
+That's the first assumption
+that we make.
+
+We model the atoms as mirrors.
+
+And when we model the atoms as
+mirrors, this means that we
+
+will invoke the laws of
+specular reflection.
+
+So if this table top is a plane
+of atoms, and I have a
+
+beam coming down at an angle,
+the laws of specular
+
+reflection say that the angle
+of incidence will equal the
+
+angle of reflection.
+
+So that's all we're doing by
+modeling the atoms as mirrors.
+
+Laws of speculative
+reflection apply.
+
+So that simply means that the
+angle of incidence, theta
+
+incidence equals theta
+reflection.
+
+And you'll see how that comes
+into play in a minute.
+
+And then the second thing we're
+going to do in order to
+
+get intensities is to use the
+concept of constructive and
+
+destructive interference.
+
+OK.
+
+So we apply interference
+criteria.
+
+And I will explain what
+that means in a
+
+second with a diagram.
+
+But in dense text, it simply
+means that in phase rays--
+
+it sounds like this rain in
+Spain falls mainly in the
+
+plain-- in-phase rays amplify.
+
+And out-of-phase rays dampen.
+
+So at some point, you'll study
+this in physics, but we need
+
+it right now, so I'll give you a
+little bit of foreshadowing,
+
+and then you'll be ahead
+of the game when you
+
+meet this in physics.
+
+So what I'm going to do is I'm
+going to show you two rays,
+
+and they both have the
+same wavelength.
+
+And I want to show
+you in phase.
+
+And so I want to illustrate this
+concept here, in-phase
+
+rays amplify.
+
+So let's give one ray here.
+
+I'm going to depict it as
+a wave. All right, so
+
+that's ray number 1.
+
+And beneath it, is
+ray number 2.
+
+It's got the same wavelength.
+
+So that means crest-to-crest
+distance is the same, and if
+
+it's in phase, in phase means
+that crest lines up with
+
+crest, trough lines
+up with trough.
+
+So I'm going to make another
+one seemingly identical.
+
+It's supposed to be identical
+to the capacity of
+
+my ability to draw.
+
+And so what this means is
+that these will amplify.
+
+So 1 plus 2, 1 plus 2 will
+give me something
+
+that looks like this.
+
+I'm going to line it up again.
+
+Only now the amplitude is double
+the amplitude of a
+
+single ray.
+
+That's what I'm trying
+to depict here.
+
+OK.
+
+So this is amplification.
+
+Now over here, I want to
+do the same thing.
+
+Only I'm going to have
+two rays, same
+
+wavelength, but out of phase.
+
+OK, so in phase is here, out
+of phase is to the right.
+
+So we'll have ray number
+3, which does this.
+
+And ray number 4, I'm going to
+line up with the crest of ray
+
+number 3, the trough of ray
+number 4, but it's going to be
+
+the same wavelength.
+
+So the distance between
+successive crests is the same.
+
+Only they're going to be
+offset by exactly half
+
+wavelength.
+
+So the crest here of wave
+3 lines up with the
+
+trough of wave 4.
+
+The trough of wave 3 lines up
+with the crest of wave 4, and
+
+so on, and so on, and so on.
+
+And if I drew this thing
+accurately, it would be
+
+obvious to you.
+
+But since I can't draw very
+well, then we're going
+
+to take 3 plus 4.
+
+And the sum of the crest
+and the trough is 0.
+
+The sum of the trough
+and the crest is 0.
+
+And so the sum here is 0.
+
+All right this is total
+destruction.
+
+This is cancellation.
+
+So in the extreme, you can have
+destructive interference
+
+that dampens to the point
+of obliteration.
+
+OK, so that's the two extremes,
+full amplification
+
+and complete cancellation.
+
+So now, I want to take this
+concept of planes as mirrors
+
+and rules of interference
+criteria, and now what I want
+
+to do is illuminate.
+
+And I want to use the
+full board here.
+
+So here's what we're
+going to do.
+
+We're going to take in
+phase, coherent--
+
+that's what coherent means.
+
+Coherent means that the
+radiation is in phase and
+
+monochromatic.
+
+What's that mean?
+
+Monochromatic means one color,
+which means single wavelength.
+
+So I have something of a single
+wavelength in phase.
+
+Coherent, monochromatic,
+incident radiation, so I've
+
+got a plurality of rays.
+
+I have this thing flooded
+by a beam.
+
+So what I'm going to
+do, is I'm going to
+
+draw some atoms here.
+
+And I'll put a second
+batch on top.
+
+And now I'm going to model
+these as mirrors.
+
+So I'm going to have the
+incident beam come in like so.
+
+The incident beam comes in like
+so at an angle theta.
+
+So this is theta incident.
+
+This is the angle
+of incidence.
+
+And according to our model, the
+beam is reflected at the
+
+same angle.
+
+So this is theta, reflection
+of theta.
+
+Reflection equals
+theta incidence.
+
+So that's the first
+thing that we do.
+
+And then the second thing we
+do, is we use the laws of
+
+interference.
+
+So I'm going to take a second
+beam, and it's going to go
+
+down to this atom here.
+
+So I'm going to bring
+it down like so.
+
+And it's going to come
+in at the same angle.
+
+And it's going to leave
+at the same angle.
+
+And if you'll excuse
+the drawing, these
+
+lines should be parallel.
+
+They should be coming in
+parallel, and they should be
+
+leaving parallel where these
+angles theta i and
+
+theta r are the same.
+
+Now how do we invoke the
+interference criteria?
+
+Well what I'm going to do
+is put a marker here.
+
+I'll put a marker.
+
+And I'll call the first one ray
+number 1, and the second
+
+one ray number 2.
+
+And what I'm going to show is if
+I start from ray number 1--
+
+maybe it's time for
+colored chalk--
+
+so if I start from ray number 1,
+to show that it's in phase
+
+with ray number 2, I'm going to
+draw this little waveform,
+
+and they're both lined up.
+
+So you can see crest lines up
+with crest. Trough lines up
+
+with trough, and they both
+have the same wavelength.
+
+So that makes the point
+coherent, monochromatic.
+
+But now things get interesting,
+because you can
+
+see that ray number 1 travels
+a shorter distance than ray
+
+number 2, and we can put on some
+coordinates here and mark
+
+the geometry, so we can say that
+the point at which the
+
+ray number 2 has to start
+traveling a longer distance,
+
+I'll drop a normal down,
+and I'm going to
+
+call this point A.
+
+This is point A.
+
+The bottom here is point B.
+
+And then up here where it
+catches up with ray number 1,
+
+the reflected ray number
+1, I'm going to
+
+call this point C.
+
+So you can you can see that
+ray number 2 has to travel
+
+this extra distance,
+AB plus BC.
+
+And now, if I want to get out
+to here where I'm now in the
+
+reflected zone, and I want ray
+number 1 reflected and ray
+
+number 2 reflected to continue
+to be in phase, there's a
+
+geometric constraint on
+the dimension of AB
+
+plus BC, isn't there?
+
+That length, AB plus BC must
+be a whole number of
+
+wavelengths.
+
+It must be an integer number
+of wavelengths of whatever
+
+this thing is, otherwise,
+these two will
+
+not being in phase.
+
+So that's the interference
+criterion.
+
+And n can equal 1, 2, 3, and so
+on, so this is called the
+
+order of reflection.
+
+And then we can go through
+the trigonometry.
+
+I'm not going to
+do it in class.
+
+It's just a waste of time.
+
+It'll bore everybody to tears.
+
+But if you want to do that at
+home at some point when you've
+
+got nothing to do, you
+can go through.
+
+You've got all the
+numbers here.
+
+You know the value of lambda.
+
+You know the distance AB,
+and you know what
+
+this distance is.
+
+This distance between successive
+planes is your
+
+dhkl, isn't it?
+
+So if you go through all of this
+analysis, you will show
+
+that n lambda is equal to 2
+times the d of the hkl spacing
+
+times the sign of theta.
+
+And this is called
+Bragg's Law.
+
+And Bragg's Law governs the
+reflection of incident
+
+radiation by a crystal.
+
+Now you'll notice I didn't
+put an apostrophe here.
+
+Some people put the apostrophe
+here, because the
+
+man's name was Bragg.
+
+Some people put the apostrophe
+here because, in fact, it was
+
+father and son.
+
+And they both together won
+the Nobel Prize in 1915.
+
+Now there have been people who
+lived to see, as Nobel Prize
+
+winners, one of their children
+win the Nobel Prize. but this
+
+is the only time in history a
+father and son team together
+
+won the Nobel Prize
+for the same work.
+
+And there are undoubtedly people
+sitting in this room
+
+who think the fact that the
+father and son could work
+
+together in physics for an
+extended period of time alone
+
+is deserving of the
+Nobel Prize.
+
+Now in 3.091, I'm going to keep
+it simple, always choose
+
+first order reflection, always
+n equals 1 in Bragg's Law.
+
+So therefore, we will write
+Bragg's Law as lambda equals
+
+2d sin theta.
+
+And to make the point, the d
+is specific to a particular
+
+set of planes.
+
+So it's a d spacing
+of the hkl planes.
+
+And it's the theta associated
+with the correct reflection of
+
+the hkl planes.
+
+Now how does destructive
+interference come into play?
+
+Destructive interference comes
+into play should there be a
+
+situation where I have
+a third ray.
+
+I'm going to bring a third
+ray in also at the
+
+same angle of incidence.
+
+And that ray is halfway between
+these two rays.
+
+And what situation
+could that be?
+
+That could be a situation in
+which the crystal structure
+
+has in a plane out from the
+board, an atom that sits
+
+halfway between these
+other two atoms.
+
+And if that happens,
+you can see.
+
+We can go through
+the derivation.
+
+But there's going to be a path
+length difference that's
+
+exactly 1/2 wavelength
+different.
+
+That's bad.
+
+It's not just there's going to
+be some measure of reduction.
+
+It's going to be total
+cancellation.
+
+And so by going through the set
+of crystal structures and
+
+recognizing that when you have
+1/2 wavelength difference, you
+
+get destructive interference.
+
+And therefore, you
+will see no line.
+
+The incident radiation will come
+in at this angle, and at
+
+the reflection angle for that
+particular plane, there will
+
+be nothing detected.
+
+So you can say that you have a
+combination of selection rules
+
+that involve the integral of
+both the rules of interference
+
+and interaction with the
+crystal structure.
+
+So let's generalize this and
+say if we take interference
+
+criteria plus the crystal
+structure, that is to say, the
+
+instant relationship of atom
+positions for a particular
+
+specimen, the combination of
+that will give rise to the set
+
+of expected reflections.
+
+So only when you satisfy the
+Bragg criterion do you get
+
+reflection.
+
+So you move the specimen.
+
+And only at that special angle
+will you get the reflections,
+
+will you get constructive
+interference.
+
+So this, in fact, is
+a fingerprint.
+
+This is a fingerprint
+of the crystal.
+
+In this case, we're not getting
+the chemical identity.
+
+We're getting the structural
+identity.
+
+So we can determine
+if something is
+
+BCC, FCC, and so on.
+
+So for example in BCC, that's
+exactly the case that I just
+
+illustrated.
+
+So in BCC we have atoms
+at the eight corners.
+
+And we have an atom
+dead center.
+
+There's a central atom.
+
+And the central atom lies in
+0 0 2 plane, doesn't it?
+
+The base of this is 0 0 1.
+
+And the top is an 0 0 1.
+
+But the central atom
+is an 0 0 2.
+
+And 0 0 2 is halfway between
+successive 0 0 1.
+
+So can you see that light
+that comes in?
+
+And it's going to be
+constructively reinforced.
+
+Off of 0 0 1 is going to be
+destructively reinforced off
+
+of 0 0 2, and the result is
+that in BCC, no 0 0 1
+
+reflection observed.
+
+The same thing happens in face
+centered cubic, right?
+
+What's the face of face centered
+cubic look like?
+
+It looks like this,
+doesn't it?
+
+So there's an 0 0 1.
+
+Here's an 0 0 1.
+
+What about this space
+centered atom?
+
+Where is it?
+
+That's an 0 0 2.
+
+It's halfway between 0 0 1.
+
+So at the angle where you
+would've expected, if you use
+
+the Bragg Law and calculate the
+angle at which for your
+
+particular crystal, because
+you know the d spacing.
+
+You fix the wavelength
+of your x-radiation
+
+coming out of the generator.
+
+At the angle where you would
+expect to see reflection off
+
+of 0 0 1, you will see nothing,
+because 0 0 2 is
+
+canceling 0 0 1.
+
+So you don't have to worry
+about all this.
+
+This has all been tabulated
+for you.
+
+Somebody has gone through
+and done all of this.
+
+Well, this is just
+making the point.
+
+See, there's a simple cubic.
+
+All the planes are reflecting.
+
+There's body-centered cubic.
+
+That's a/2.
+
+There's face-centered
+cubic a/2.
+
+0 0 2 is going to
+cancel 0 0 1.
+
+You're not going to see
+anything there.
+
+So people have gone through.
+
+And they've made this set
+of rules for reflection.
+
+So simple cubic, you
+get reflection
+
+from all the planes.
+
+Body-centered cubic, you just
+get these planes here.
+
+And it turns out that there's
+a simple rule that compactly
+
+represents which planes are
+going to reflect in
+
+body-centered cubic.
+
+And in BCC, the hkl, it's the
+planes for which h plus k plus
+
+l is an even number.
+
+h plus k plus l is even.
+
+And 0 was counted as even.
+
+So for example, 0 0 1 h
+plus k plus l is 1.
+
+It doesn't reflect.
+
+0 0 2, 0 plus 0 plus 2 is 2.
+
+It does reflect.
+
+And so on.
+
+You just go down
+the whole line.
+
+And so these are in ascending
+order of h squared plus k
+
+squared plus l squared, because
+that's a nice way of
+
+deciding how to add them up.
+
+And now in FCC the
+selection rule is
+
+a little bit different.
+
+In FCC you get reflection from
+planes when you write the HKL
+
+such that h, k, and l must be
+either all even numbers, or
+
+all odd numbers, or some people
+like to say unmixed.
+
+Some crystallographers say
+unmixed, meaning you can't
+
+have a combination of even
+numbers and odd number.
+
+So for example, 0 0 1 won't
+work because 0 is a zero.
+
+That's even.
+
+1 is odd.
+
+But 0 0 2, h plus k plus l all
+even or all odd, there you go
+
+all even or all odd unmixed.
+
+So this will work.
+
+And then so on.
+
+So you can go through and
+see which ones work.
+
+All right.
+
+So the next one here
+is in the sequence.
+
+This sums to 1.
+
+And what would sum to 2?
+
+It would be 0 1 1.
+
+And 0 1 1 doesn't work either
+because zero is even.
+
+And 1 is odd.
+
+The next one of the
+sequence is 1 1 1.
+
+These are all odd.
+
+So that one reflects.
+
+So in FCC, you don't
+see 0 0 1, 0 1 1.
+
+But 1 1 1 does reflect.
+
+And then 0 0 2, which is the
+next one, because 0 squared
+
+plus 0 squared plus
+2 squared is 4.
+
+This is even even.
+
+So that one works.
+
+So there's the sequence.
+
+And so now what we can do is use
+this technique in order to
+
+make measurements.
+
+But before we do so, I want to
+show you the experimental
+
+measurement, one way.
+
+There's several ways of
+conducting the measurement.
+
+And so the first way I'm going
+to show you is called
+
+diffractometry.
+
+And you can do this over
+in Building 13.
+
+If you get yourself a UROP, you
+might be assigned to make
+
+some measurements.
+
+So diffractometry is a form
+of x-ray diffraction.
+
+It's one of the techniques.
+
+And the way it works is you fix
+the wavelength and vary
+
+the angle of incidence,
+you don't
+
+rotate the x-ray generator.
+
+You rotate specimen and present
+continually varying
+
+angles to the thing.
+
+So this shows the technique
+in operation.
+
+So you have a specimen
+sitting here.
+
+The specimen can either be
+a thin film, or in other
+
+instances, we have a finely
+ground powder.
+
+So each of the powder grains
+presents a different angle.
+
+And coming out of the
+collimator is the
+
+monochromatic.
+
+We want a single wavelength.
+
+So this collimator means it's
+monochromatic and coherent.
+
+So that beam comes and
+strikes the specimen.
+
+And for historical reasons,
+instead of calling this the
+
+angle of incidence, and this the
+angle of reflection, they
+
+call the angle that goes to
+the detector 2 theta.
+
+In other words, the projection
+of the beam, this is theta
+
+incident equals theta r.
+
+So this is really 2
+theta incident, or
+
+it's 2 theta reflected.
+
+It's the same thing.
+
+So you'll see x-ray data
+usually reported
+
+in units of 2 theta.
+
+And here's the detector.
+
+And then all you do is you
+rotate the specimen.
+
+And by rotating the specimen
+with a detector, you're able
+
+to get the entire set
+of reflections.
+
+And whenever you move through
+an angle that satisfies the
+
+Bragg Law, you get a
+peak in intensity.
+
+And here's what the output
+would look like.
+
+So you're plotting intensity
+as a function of 2 theta.
+
+So somewhere along here at
+around, it looks like about 38
+
+degrees, you have satisfied the
+Bragg angle, and you get
+
+constructive interference.
+
+When you move off of 38
+degrees, destructive
+
+interference reigns supreme,
+and you get almost no
+
+reflection.
+
+Then you get to the right
+angle for 2 0 0, you get
+
+reflection.
+
+Well, all you get
+is these lines.
+
+You don't get these numbers.
+
+These numbers you don't
+get for free.
+
+So here's the experiment
+that we're going to do.
+
+We're going to run our
+x-ray generator
+
+with a copper target.
+
+Why do I tell you the
+copper target?
+
+Because you're going to
+fix the wavelength.
+
+And you fix the wavelength
+by choosing the target.
+
+So we've got copper target in
+our x-ray generator, OK?
+
+So remember, the sample
+is not the target.
+
+The sample is what is
+being irradiated.
+
+This is being bombed by the
+electrons in the tube, copper
+
+target in x-ray tube, and that
+means that the lambda of the
+
+radiation is lambda copper.
+
+And I'm going to use lambda
+copper K alpha because I know
+
+it's wavelength to five
+significant figures.
+
+It's 1.5418 angstroms.
+
+And here's the data set.
+
+I looked this up in
+the literature.
+
+Here's the data set from
+the experiment.
+
+And that's all you get,
+a set of 2 thetas.
+
+So here's my challenge to you.
+
+I'm telling you you've got an
+unknown sample that's cubic,
+
+and there's your data set.
+
+The task for you is determine
+two parts to the question.
+
+And we're going to
+do it together.
+
+First part, determine the
+crystal structure.
+
+So it's either FCC, BCC,
+or simple cubic.
+
+And the second part is
+determine the lattice
+
+constant, the value of
+the lattice constant.
+
+So you can get quantitative
+measurements.
+
+So I'm going to show
+you how to do it.
+
+So how are we going to do it?
+
+We're going to use
+this technique.
+
+This is my self-help
+book for you.
+
+And here's the key.
+
+Here's how I came
+up with this.
+
+There's a way to unravel this.
+
+And the way you unravel this
+is to take these two
+
+relationships.
+
+You have lambda equals
+2d sin theta is 1.
+
+And you also know that d--
+
+in fact, I'm going to keep
+writing hkl subscripts here--
+
+you know the dhkl
+is equal to a.
+
+That's this lattice constant.
+
+Be sure this is lattice
+constant.
+
+This is the cube edge
+measurement lattice constant
+
+divided by the square root
+of h squared plus k
+
+squared plus l squared.
+
+So what I do is I
+combine the two.
+
+If you combine these two,
+you can end up with this
+
+relationship.
+
+If you combine the two, you
+get lambda squared over 4a
+
+squared equals sin squared theta
+over h squared plus k
+
+squared plus l squared.
+
+And this is the key.
+
+Why is it the key?
+
+The value of lambda
+is set by you.
+
+You chose the target.
+
+The value of a is set
+by the sample.
+
+That's the lattice constant.
+
+So the ratio of two constants
+is a constant.
+
+Agreed?
+
+So this is a constant.
+
+So if the left side of the
+equation is a constant, the
+
+right side of the equation
+must be a constant.
+
+But h, k, and l vary.
+
+And theta varies.
+
+But the ratio of the variation,
+when mapped into
+
+sin square theta over h squared
+plus k squared plus l
+
+squared, this must
+be a constant.
+
+And that's going to be the
+way I work through
+
+this delightful problem.
+
+So let's see.
+
+Start with 2 theta values, and
+generate a set of sin squared
+
+theta values.
+
+That's what Sadoway says first.
+So I took 2 theta.
+
+And all I did was make 1 theta,
+and then took the sin
+
+of it, and then took
+the square the sin.
+
+So this is the data set
+transmogrified into sin
+
+squared theta.
+
+All right, what's the
+next thing he says?
+
+Normalize by dividing through
+with the first value.
+
+So I'm just going to take
+this whole series and
+
+divide it by 0.143.
+
+And now I end up, instead
+of 0.143, 0.191.
+
+I have 1, 1.34, and so on.
+
+That's what I mean
+by normalize.
+
+Normalize to the first entry.
+
+OK, What's next thing he says?
+
+Clear fractions.
+
+Clear fractions from the
+normalized column.
+
+So I'm going to multiply this
+by a common number.
+
+Because 1.34, remember this
+is experimental data.
+
+It's noisy.
+
+1.34 looks like 4/3.
+
+Doesn't it?
+
+It's fuzzy logic.
+
+And 2.67 looks like 2
+and 2/3, 3 and 2/3.
+
+That's roughly 4.
+
+5 and 1/3.
+
+The 3 looks like
+a magic number.
+
+So if a multiply this column by
+3, I get 3, 4, 8, 11, 12.
+
+What does it say next?
+
+Speculate on the h, k, l values,
+that if expressed as h
+
+squared plus k squared plus l
+squared would generate the
+
+sequence of the clear
+fractions column.
+
+And then that's going to take
+me to the selection rule.
+
+So I say, well how do I get 3?
+
+It's 1 plus 1 plus 1.
+
+4 is 2 squared plus 0 squared
+plus zero squared.
+
+8 is 2 squared plus 2 squared
+plus 0 squared.
+
+So I'm generating this thing.
+
+And now it's pretty
+obvious, right?
+
+Because now I've got
+to use these.
+
+And what do I see here?
+
+Well, 1 1 1 are all odd.
+
+2 0 0, all even.
+
+2 2 0, all even.
+
+Gee, this looks like it conforms
+to the selection
+
+rules for Bragg reflection
+from an FCC crystal
+
+And then to make sure that
+I'm on to something,
+
+what I do is this.
+
+Compute for each theta the value
+of sin square theta over
+
+h squared plus k squared plus
+l squared on the basis of
+
+those assumed values.
+
+What I'm doing is I'm saying if
+my hunch is right, whatever
+
+I choose for the theta and the
+assumed value h squared plus k
+
+squared plus l squared, that
+should be a constant that
+
+doesn't change.
+
+So let's test it.
+
+And sure enough, look.
+
+0.0477, 0.0478, so it looks
+like I'm on to something.
+
+And furthermore, I know
+what this is.
+
+That 0.0477 is this.
+
+This is 0.0477.
+
+And I know my lambda.
+
+That's 1.5418.
+
+So now I can calculate my a.
+
+So now I've determined
+that it's FCC.
+
+Plus if I go ahead and I
+calculate the a value, I get
+
+3.53 angstroms. And if it's FCC
+and it's 3.53 angstroms, I
+
+bet it's nickel.
+
+So that's how you index
+this stuff.
+
+So there we are.
+
+There are the selection rules.
+
+Now here's a little trick.
+
+Let me show you.
+
+Because when I go to index this,
+the first thing I do is
+
+I go for low hanging fruit.
+
+If you start looking for whether
+it's simple cubic,
+
+face-centered cubic, or
+body-centered cubic, let's
+
+look at the sum.
+
+So I've got simple cubic,
+body-centered cubic, and
+
+face-centered cubic.
+
+So the first plane on simple
+cubic, it's going to give me
+
+everything.
+
+It's going to give me
+1, 2, 3, 4, 5, 6.
+
+And FCC, what does it give us?
+
+If you start looking down
+there, it gives you
+
+3, 4, 8, 11, 12.
+
+Well, this is so different.
+
+3, 4, 8, 11 is so different
+from 1, 2, 3, 4.
+
+What does BCC give you?
+
+It gives you 2, 4,
+6, 8, 10, 12.
+
+Can you see you have
+a problem here?
+
+It's pretty easy to
+pull out FCC.
+
+But look at these two.
+
+Since you don't know, you're
+just normalizing.
+
+You can't tell.
+
+If I give you a number sequence
+that is in the order
+
+2, 4, 6, 8, 10, how do you know
+that that couldn't be 1,
+
+2, 3, 4, 5?
+
+There's a hook here, though.
+
+Look at the sequence of h
+plus h squared plus k
+
+squared plus l squared.
+
+Do you notice that there's no
+combination of h squared plus
+
+k squared plus l squared
+that gives you 7?
+
+You get 6.
+
+And then the next one is 8.
+
+But there is a sequence
+that gives you 14.
+
+So if you have a seventh line,
+if the seventh line to the
+
+first line, the ratio of h
+squared plus k squared plus l
+
+squared for angle number
+7 to h squared plus k
+
+squared plus l squared.
+
+For angle number 1, if
+it's equal to 7--
+
+and point of fact it's
+not 7:1, it's 14:2--
+
+and if it's equal to 8 for
+the seventh angle--
+
+then it must be simple cubic.
+
+And now you've sorted
+it all out.
+
+So you're an expert now.
+
+Now you can do it.
+
+OK, so you're going to get some
+practice on homework.
+
+So you can index crystals.
+
+You can determine a
+crystal structure.
+
+All right, a couple of other
+things we can do.
+
+There is a second technique.
+
+And it's called Laue diffraction
+after von Laue,
+
+who got the Nobel
+Prize in 1914.
+
+He beat the Braggs by one
+year for this technique.
+
+So he shines.
+
+In this case for Laue, it's a
+slightly different technique.
+
+What Laue does, is he
+uses light x-rays.
+
+That means variable lambda.
+
+So how would you get a fixed
+value of lambda?
+
+Well, you would pick off one of
+those lines, like maybe the
+
+K alpha line because it's
+a nice, singular line.
+
+And repress the bremsstrahlung
+and so on.
+
+But if I want a variable lambda,
+where do I go for
+
+variable lambda?
+
+I repress the lines.
+
+And I go for the
+bremsstrahlung.
+
+So now I've got lines varying
+all across the x
+
+region of the spectrum.
+
+So I use variable lambda.
+
+And I fixed the angle of
+incidence, whereas with
+
+diffractometry, I use a single
+value of lambda and vary.
+
+So here's the cartoon which
+shows what's going on.
+
+I'll do it one more time.
+
+So this is called
+camera obscura,
+
+which is darkened room.
+
+That's all this means
+is dark room.
+
+So let's say I've got the
+specimen on the back wall of
+
+this thing, and what I've got
+is white x-rays coming in.
+
+So the white x-ray enters
+through the face.
+
+I've got the plate here, and
+I've got the specimen sitting
+
+somewhere in between.
+
+And what happens is I
+get a spot pattern.
+
+I get a spot pattern.
+
+And the spot pattern is
+imitative of the symmetry of
+
+atomic arrangement.
+
+So I have to say a little bit
+about symmetry so we know what
+
+that means.
+
+So let's take a look
+at symmetry.
+
+So I'm going to talk a little
+bit about rotational
+
+symmetries.
+
+So let's look at that.
+
+So first one I'm going to look
+at is an 0 0 1 plane.
+
+So if I just take a projection
+of an 0 0 1 plane,
+
+it looks like this.
+
+Doesn't it?
+
+It's just the cube edge,
+or the cube bottom.
+
+So it's got a and
+a as the edge.
+
+And now, the rotational
+axis, it's about a
+
+normal rotational axis.
+
+A normal rotational axis.
+
+So what I'm going to ask is how
+many degrees do I have to
+
+go through before I get
+this same image back.
+
+You can see that you go 90
+degrees, it'll come back.
+
+If I stop at 45 degrees, it's
+going to look like this.
+
+You're going to say I know
+he moved the specimen.
+
+If I go 90 degrees, you
+can't tell it apart.
+
+So we define fold.
+
+The fold is equal to
+360 divided by the
+
+basic angle of rotation.
+
+So we would say that this plane
+here exhibits 4-fold
+
+symmetry, OK?
+
+Let's do a second one.
+
+The second one is 0 1 1.
+
+So if I look at 0 1 1,
+0 1 1 at this plane.
+
+0 1 1 goes across
+the diagonal.
+
+So I'm going to take the
+diagonal here and
+
+plot it like so.
+
+So it's going to have
+an edge of a.
+
+And it's going to have the
+diagonal, which is
+
+root 2 times a.
+
+And if I put a rotational axis
+in the center of that, clearly
+
+if I go only 90 degrees, I'm
+going to tell that the thing
+
+is rotated.
+
+I have to go 180 degrees before
+I can't tell that
+
+there's been any disturbance.
+
+So this one here has
+2-fold symmetry.
+
+We'll do one more.
+
+Because there's only three
+major ones that we
+
+have to deal with.
+
+And that is going to
+be the 1 1 1 plane.
+
+And the 1 1 1 plane.
+
+And the 1 1 1 plane, I think
+I've got an image of it here.
+
+You can see the 1 1 1 plane
+drawn in this cube.
+
+So what's the face of
+1 1 1 look like?
+
+The face of 1 1 1
+looks like this.
+
+That's face of 1 1 1.
+
+And if you go through this
+analysis, this is root 3a
+
+because it's a diagonal of
+a difference persuasion.
+
+So this is 3-fold symmetry.
+
+This has 3-fold rotational
+symmetry.
+
+And that means if I take
+a crystal such
+
+as this, for example.
+
+I've told you before, this is
+my silicon wafer, and this
+
+silicon wafer has been cut
+from a single crystal.
+
+So I'm looking at the edge
+of an atomic plane.
+
+The question is, which
+one is it?
+
+The crystal didn't come with
+a label on the side.
+
+I don't know what the crystal
+growth axis was.
+
+I started with a single crystal,
+and I dipped it into
+
+molten silicon.
+
+And just like rock mountain
+candy, I drop the heating
+
+coils and cause the
+liquid to solidify
+
+around the seed crystal.
+
+And I grow this salami that's
+about 8 inches in diameter,
+
+about 2 meters long.
+
+So now I go and I cut these
+things with the diamond wheel.
+
+So I'm cutting them normal to
+the growth axis, but I still
+
+don't know what plane
+I'm looking at.
+
+So if I use the Laue technique
+and put the crystal like so,
+
+bombard it with white
+x-rays, and I
+
+look at the spot pattern.
+
+The spot pattern is going
+to give me one of those
+
+symmetries.
+
+And if I get a 3-fold
+symmetry, I know I'm
+
+looking at 1 1 1.
+
+I mean, it's not going to
+be some wacko plane.
+
+It's going to be either face,
+edge, or diagonal.
+
+And on the basis of the symmetry
+in the Laue pattern,
+
+I can tell which plane
+I'm looking at.
+
+They use this stuff.
+
+They use it to make the devices
+that are in your cell
+
+phone and your computer.
+
+I'm not just telling
+you a story.
+
+All right.
+
+So let's look at some others.
+
+We'll go back to the
+Escher prints.
+
+Everything has symmetry.
+
+OK, so what's this one?
+
+See this?
+
+What's the symmetry?
+
+4-fold.
+
+How about this one?
+
+What do you think?
+
+3-fold.
+
+I even went into Photoshop
+just to show you
+
+how dedicated I am.
+
+So I took this image.
+
+And I told Photoshop to give
+me 120 degrees rotation.
+
+And I got this.
+
+You can even see the fold
+in the book there.
+
+So I'm really doing it.
+
+It's coming back.
+
+It's 120 degrees rotation.
+
+How about this one?
+
+That's 3.
+
+Now these are real
+Laue patterns.
+
+This is 4-fold.
+
+This is obviously 3-fold.
+
+This one is hard to see.
+
+But it turns out it's 2-fold.
+
+The one axis is just
+a little bit longer
+
+than the other axis.
+
+What about this one?
+
+That's our simple cubic puppy.
+
+Yes, 1-fold.
+
+Translational symmetry without
+rotational symmetry.
+
+You can make this by just
+moving them sideways.
+
+But you have to go all
+the way around.
+
+So that's 1-fold symmetry
+translation.
+
+Look at this one?
+
+What's going on here?
+
+Is that one of the
+Bravais lattices?
+
+This is called Penrose tile,
+again rotational symmetry
+
+without translational
+symmetry.
+
+You can take a patch of this
+and move it rotationally.
+
+But you can't take and
+cover a wall with it.
+
+So that's rotational without
+translational.
+
+See?
+
+You can go around this way.
+
+1, 2, 3, 4, 5, 6, 7, 8, 9,
+10, and reproduce this.
+
+But you can't use this as a unit
+cell and keep it hopping
+
+laterally and tile
+a wall with it.
+
+Here's another one, not
+a Bravais lattice.
+
+All right.
+
+So I told you at the beginning
+of this unit that there are
+
+ordered solids and disordered
+solids.
+
+We've been focusing
+on ordered solids.
+
+They have a unit cell.
+
+They're periodic.
+
+And we call them crystals.
+
+And next week we're going
+to start looking
+
+at disordered solid.
+
+So they have no building block,
+no long range order.
+
+And we call them glasses.
+
+For a long time, people thought
+that solis have to
+
+fall into one box or
+the other box.
+
+And then the best thing
+that can happen in
+
+science is not, oh, yeah.
+
+That's exactly what
+I expected.
+
+It's, I wonder what
+that means.
+
+And there was one of these
+moments in 1982.
+
+In 1982, a man by the name of
+Danny Shechtman from Technion
+
+in Israel, was over here in the
+United States working at
+
+the National Institute of
+Standards and Technology,
+
+which used to be National Bureau
+of Standards down in
+
+Gaithersburg, Maryland.
+
+And he was looking at a set of
+aluminum-manganese alloys.
+
+So aluminum is a metal.
+
+Manganese is a metal.
+
+You can make a solid solution
+which we call an alloy.
+
+And these are highly ordered.
+
+And what he found in his Laue
+measurements, were rotational
+
+symmetries that are impossible
+in a crystal.
+
+He was getting 5-fold
+symmetry.
+
+You can't get 5-fold symmetry.
+
+There is no set of planes
+here that will give
+
+you a 5-fold symmetry.
+
+They lack translational
+symmetry.
+
+They were called aperiodic.
+
+And the popular name for
+them was quasicrystals.
+
+So here's the Laue pattern of
+one of Danny Shechtman's
+
+aluminum-manganese specimens.
+
+I think this is 25%
+manganese and
+
+aluminum if I'm not mistaken.
+
+So let's count, 1, 2, 3,
+4, 5, 6, 7, 8, 9, 10.
+
+You can't have 10 or 5.
+
+Atoms don't work that way.
+
+But he got it.
+
+He got it, 5- fold,
+72 degrees.
+
+Now this is really,
+really exciting.
+
+This is a shot of
+his lab book.
+
+You're looking over
+his shoulder.
+
+These are the specimen
+numbers.
+
+And this is aluminum 25%
+manganese, April 8, 1982.
+
+So it's just another
+day at work.
+
+You could be doing this.
+
+And he can't believe
+what he's getting.
+
+He's wondering what's
+going on.
+
+You can't contribute this to
+a calibration error on the
+
+instrument.
+
+This thing is on unassailably
+5-fold symmetry.
+
+The joke is that this is not
+far from the Pentagon.
+
+Only within shouting distance
+of the Pentagon would you
+
+discover 5-fold symmetry.
+
+So there it is.
+
+So where have we come
+with all of this?
+
+We've come with the ability to
+start with some very simple
+
+ideas about x-ray generation.
+
+And we've come to the point
+where we can characterize
+
+crystals, get quantitative
+measurements of their lattice
+
+constants, and by using Laue
+
+techniques, investigate symmetry.
+
+OK.
+
+Let's adjourn.
+
+We'll see you on Friday.
\ No newline at end of file
diff --git a/fQm97XdYErA.txt b/fQm97XdYErA.txt
new file mode 100644
index 0000000000000000000000000000000000000000..bdb997c1da26f5a9e958527f626e0dbbe2702f76
--- /dev/null
+++ b/fQm97XdYErA.txt
@@ -0,0 +1,7955 @@
+align:start position:0%
+ 
+foreign
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+welcome to another lecture in my series
+
+ align:start position:0%
+welcome to another lecture in my series
+ 
+
+ align:start position:0%
+welcome to another lecture in my series
+on Urban Energy Systems and policy my
+
+ align:start position:0%
+on Urban Energy Systems and policy my
+ 
+
+ align:start position:0%
+on Urban Energy Systems and policy my
+name is David Sue I'm a professor in the
+
+ align:start position:0%
+name is David Sue I'm a professor in the
+ 
+
+ align:start position:0%
+name is David Sue I'm a professor in the
+department of urban studies and planning
+
+ align:start position:0%
+department of urban studies and planning
+ 
+
+ align:start position:0%
+department of urban studies and planning
+MIT
+
+ align:start position:0%
+MIT
+ 
+
+ align:start position:0%
+MIT
+and today I want to talk about studies
+
+ align:start position:0%
+and today I want to talk about studies
+ 
+
+ align:start position:0%
+and today I want to talk about studies
+and future possible fuel use carbon
+
+ align:start position:0%
+and future possible fuel use carbon
+ 
+
+ align:start position:0%
+and future possible fuel use carbon
+capture utilization storage and nuclear
+
+ align:start position:0%
+capture utilization storage and nuclear
+ 
+
+ align:start position:0%
+capture utilization storage and nuclear
+power
+
+ align:start position:0%
+power
+ 
+
+ align:start position:0%
+power
+in short this is kind of a grab bag of
+
+ align:start position:0%
+in short this is kind of a grab bag of
+ 
+
+ align:start position:0%
+in short this is kind of a grab bag of
+topics thinking about how cities exist
+
+ align:start position:0%
+topics thinking about how cities exist
+ 
+
+ align:start position:0%
+topics thinking about how cities exist
+in the larger Energy System
+
+ align:start position:0%
+in the larger Energy System
+ 
+
+ align:start position:0%
+in the larger Energy System
+the readings for today are all in the
+
+ align:start position:0%
+the readings for today are all in the
+ 
+
+ align:start position:0%
+the readings for today are all in the
+syllabus you can also see them by
+
+ align:start position:0%
+syllabus you can also see them by
+ 
+
+ align:start position:0%
+syllabus you can also see them by
+clicking on the purple links in the PDF
+
+ align:start position:0%
+clicking on the purple links in the PDF
+ 
+
+ align:start position:0%
+clicking on the purple links in the PDF
+and again
+
+ align:start position:0%
+and again
+ 
+
+ align:start position:0%
+and again
+that kind of have a more
+
+ align:start position:0%
+that kind of have a more
+ 
+
+ align:start position:0%
+that kind of have a more
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+philosophical discussion are really
+
+ align:start position:0%
+philosophical discussion are really
+ 
+
+ align:start position:0%
+philosophical discussion are really
+about really about how cities exist
+
+ align:start position:0%
+about really about how cities exist
+ 
+
+ align:start position:0%
+about really about how cities exist
+within a much larger Energy System and
+
+ align:start position:0%
+within a much larger Energy System and
+ 
+
+ align:start position:0%
+within a much larger Energy System and
+the reason why we could talk about these
+
+ align:start position:0%
+the reason why we could talk about these
+ 
+
+ align:start position:0%
+the reason why we could talk about these
+scenarios for future energy use is that
+
+ align:start position:0%
+scenarios for future energy use is that
+ 
+
+ align:start position:0%
+scenarios for future energy use is that
+the context is going to decide what we
+
+ align:start position:0%
+the context is going to decide what we
+ 
+
+ align:start position:0%
+the context is going to decide what we
+provide to pursue in cities
+
+ align:start position:0%
+provide to pursue in cities
+ 
+
+ align:start position:0%
+provide to pursue in cities
+so just to kind of take a large picture
+
+ align:start position:0%
+so just to kind of take a large picture
+ 
+
+ align:start position:0%
+so just to kind of take a large picture
+view of what we're trying to do to
+
+ align:start position:0%
+view of what we're trying to do to
+ 
+
+ align:start position:0%
+view of what we're trying to do to
+decarbonation this is from 2019 the
+
+ align:start position:0%
+decarbonation this is from 2019 the
+ 
+
+ align:start position:0%
+decarbonation this is from 2019 the
+global carbon project and their headline
+
+ align:start position:0%
+global carbon project and their headline
+ 
+
+ align:start position:0%
+global carbon project and their headline
+in 2019 was that CO2 emissions grow a
+
+ align:start position:0%
+in 2019 was that CO2 emissions grow a
+ 
+
+ align:start position:0%
+in 2019 was that CO2 emissions grow a
+bit slowly emerging climate policies but
+
+ align:start position:0%
+bit slowly emerging climate policies but
+ 
+
+ align:start position:0%
+bit slowly emerging climate policies but
+it's important to note that even before
+
+ align:start position:0%
+it's important to note that even before
+ 
+
+ align:start position:0%
+it's important to note that even before
+covid fossil fossil fuel CO2 emissions
+
+ align:start position:0%
+covid fossil fossil fuel CO2 emissions
+ 
+
+ align:start position:0%
+covid fossil fossil fuel CO2 emissions
+were growing more slowly but did not yet
+
+ align:start position:0%
+were growing more slowly but did not yet
+ 
+
+ align:start position:0%
+were growing more slowly but did not yet
+Decline and of course as we know in this
+
+ align:start position:0%
+Decline and of course as we know in this
+ 
+
+ align:start position:0%
+Decline and of course as we know in this
+red circle reinforces deal with
+
+ align:start position:0%
+red circle reinforces deal with
+ 
+
+ align:start position:0%
+red circle reinforces deal with
+commissions have to decline to Net Zero
+
+ align:start position:0%
+commissions have to decline to Net Zero
+ 
+
+ align:start position:0%
+commissions have to decline to Net Zero
+by around mid-century to meet our Paris
+
+ align:start position:0%
+by around mid-century to meet our Paris
+ 
+
+ align:start position:0%
+by around mid-century to meet our Paris
+climate agreement goals which is to keep
+
+ align:start position:0%
+climate agreement goals which is to keep
+ 
+
+ align:start position:0%
+climate agreement goals which is to keep
+our global temperatures less than 1.5
+
+ align:start position:0%
+our global temperatures less than 1.5
+ 
+
+ align:start position:0%
+our global temperatures less than 1.5
+degrees Celsius above
+
+ align:start position:0%
+degrees Celsius above
+ 
+
+ align:start position:0%
+degrees Celsius above
+um the previous averages which would
+
+ align:start position:0%
+um the previous averages which would
+ 
+
+ align:start position:0%
+um the previous averages which would
+avoid the most catastrophic effects of
+
+ align:start position:0%
+avoid the most catastrophic effects of
+ 
+
+ align:start position:0%
+avoid the most catastrophic effects of
+climate change and so this graph points
+
+ align:start position:0%
+climate change and so this graph points
+ 
+
+ align:start position:0%
+climate change and so this graph points
+out that in the last 10 years the growth
+
+ align:start position:0%
+out that in the last 10 years the growth
+ 
+
+ align:start position:0%
+out that in the last 10 years the growth
+of whole was slower relatively slower
+
+ align:start position:0%
+of whole was slower relatively slower
+ 
+
+ align:start position:0%
+of whole was slower relatively slower
+growth in the eight years up till covid
+
+ align:start position:0%
+growth in the eight years up till covid
+ 
+
+ align:start position:0%
+growth in the eight years up till covid
+in the 2019 projection was a slower
+
+ align:start position:0%
+in the 2019 projection was a slower
+ 
+
+ align:start position:0%
+in the 2019 projection was a slower
+decline still but not a slower growth
+
+ align:start position:0%
+decline still but not a slower growth
+ 
+
+ align:start position:0%
+decline still but not a slower growth
+still but did not yet decline
+
+ align:start position:0%
+still but did not yet decline
+ 
+
+ align:start position:0%
+still but did not yet decline
+if we look at the sources of global
+
+ align:start position:0%
+if we look at the sources of global
+ 
+
+ align:start position:0%
+if we look at the sources of global
+carbon emissions natural gas and oil are
+
+ align:start position:0%
+carbon emissions natural gas and oil are
+ 
+
+ align:start position:0%
+carbon emissions natural gas and oil are
+now the main drivers of global emissions
+
+ align:start position:0%
+now the main drivers of global emissions
+ 
+
+ align:start position:0%
+now the main drivers of global emissions
+growth you have gas growing about 2.6
+
+ align:start position:0%
+growth you have gas growing about 2.6
+ 
+
+ align:start position:0%
+growth you have gas growing about 2.6
+percent per year oil growing 0.9 sorry
+
+ align:start position:0%
+percent per year oil growing 0.9 sorry
+ 
+
+ align:start position:0%
+percent per year oil growing 0.9 sorry
+in 2019 alone and coal actually
+
+ align:start position:0%
+in 2019 alone and coal actually
+ 
+
+ align:start position:0%
+in 2019 alone and coal actually
+declining in 2019 with lower projection
+
+ align:start position:0%
+declining in 2019 with lower projection
+ 
+
+ align:start position:0%
+declining in 2019 with lower projection
+uh land carbon emissions also slightly
+
+ align:start position:0%
+uh land carbon emissions also slightly
+ 
+
+ align:start position:0%
+uh land carbon emissions also slightly
+increased driving up emissions in 2019.
+
+ align:start position:0%
+increased driving up emissions in 2019.
+ 
+
+ align:start position:0%
+increased driving up emissions in 2019.
+now this brings us back to the
+
+ align:start position:0%
+now this brings us back to the
+ 
+
+ align:start position:0%
+now this brings us back to the
+decarbonization pathways we've talked
+
+ align:start position:0%
+decarbonization pathways we've talked
+ 
+
+ align:start position:0%
+decarbonization pathways we've talked
+about in one of the first lectures this
+
+ align:start position:0%
+about in one of the first lectures this
+ 
+
+ align:start position:0%
+about in one of the first lectures this
+is the reference case this is
+
+ align:start position:0%
+is the reference case this is
+ 
+
+ align:start position:0%
+is the reference case this is
+essentially how much energy the U.S
+
+ align:start position:0%
+essentially how much energy the U.S
+ 
+
+ align:start position:0%
+essentially how much energy the U.S
+economy currently uses in 2020
+
+ align:start position:0%
+economy currently uses in 2020
+ 
+
+ align:start position:0%
+economy currently uses in 2020
+we've talked a lot about the scenario
+
+ align:start position:0%
+we've talked a lot about the scenario
+ 
+
+ align:start position:0%
+we've talked a lot about the scenario
+trying to achieve 100 renewable energy
+
+ align:start position:0%
+trying to achieve 100 renewable energy
+ 
+
+ align:start position:0%
+trying to achieve 100 renewable energy
+you can see that all the fossil fuel
+
+ align:start position:0%
+you can see that all the fossil fuel
+ 
+
+ align:start position:0%
+you can see that all the fossil fuel
+resources and resources have been
+
+ align:start position:0%
+resources and resources have been
+ 
+
+ align:start position:0%
+resources and resources have been
+replaced by renewable energy resources
+
+ align:start position:0%
+replaced by renewable energy resources
+ 
+
+ align:start position:0%
+replaced by renewable energy resources
+and of course of the third scenario
+
+ align:start position:0%
+and of course of the third scenario
+ 
+
+ align:start position:0%
+and of course of the third scenario
+which is the extentral low fuel price
+
+ align:start position:0%
+which is the extentral low fuel price
+ 
+
+ align:start position:0%
+which is the extentral low fuel price
+this is the central scenario where it's
+
+ align:start position:0%
+this is the central scenario where it's
+ 
+
+ align:start position:0%
+this is the central scenario where it's
+the lowest cost or least cost Pathway to
+
+ align:start position:0%
+the lowest cost or least cost Pathway to
+ 
+
+ align:start position:0%
+the lowest cost or least cost Pathway to
+decarbonization and this occurs in the
+
+ align:start position:0%
+decarbonization and this occurs in the
+ 
+
+ align:start position:0%
+decarbonization and this occurs in the
+scenario of a low fuel price meaning
+
+ align:start position:0%
+scenario of a low fuel price meaning
+ 
+
+ align:start position:0%
+scenario of a low fuel price meaning
+that fossil fuels remain relatively
+
+ align:start position:0%
+that fossil fuels remain relatively
+ 
+
+ align:start position:0%
+that fossil fuels remain relatively
+cheap so there are still some fossil
+
+ align:start position:0%
+cheap so there are still some fossil
+ 
+
+ align:start position:0%
+cheap so there are still some fossil
+fuel like natural gas and petroleum in
+
+ align:start position:0%
+fuel like natural gas and petroleum in
+ 
+
+ align:start position:0%
+fuel like natural gas and petroleum in
+this decarbonization pathway and we
+
+ align:start position:0%
+this decarbonization pathway and we
+ 
+
+ align:start position:0%
+this decarbonization pathway and we
+should know two things about the
+
+ align:start position:0%
+should know two things about the
+ 
+
+ align:start position:0%
+should know two things about the
+scenario
+
+ align:start position:0%
+scenario
+ 
+
+ align:start position:0%
+scenario
+first because it's the central at least
+
+ align:start position:0%
+first because it's the central at least
+ 
+
+ align:start position:0%
+first because it's the central at least
+cost pathway and its low fuel price
+
+ align:start position:0%
+cost pathway and its low fuel price
+ 
+
+ align:start position:0%
+cost pathway and its low fuel price
+scenario this is essentially a scenario
+
+ align:start position:0%
+scenario this is essentially a scenario
+ 
+
+ align:start position:0%
+scenario this is essentially a scenario
+they consider this paper if they have
+
+ align:start position:0%
+they consider this paper if they have
+ 
+
+ align:start position:0%
+they consider this paper if they have
+the maximum amount of fossil fuels that
+
+ align:start position:0%
+the maximum amount of fossil fuels that
+ 
+
+ align:start position:0%
+the maximum amount of fossil fuels that
+could be used you could still achieve
+
+ align:start position:0%
+could be used you could still achieve
+ 
+
+ align:start position:0%
+could be used you could still achieve
+decaronization and even in this scenario
+
+ align:start position:0%
+decaronization and even in this scenario
+ 
+
+ align:start position:0%
+decaronization and even in this scenario
+if we flip back a couple slides you can
+
+ align:start position:0%
+if we flip back a couple slides you can
+ 
+
+ align:start position:0%
+if we flip back a couple slides you can
+see that we currently have coal natural
+
+ align:start position:0%
+see that we currently have coal natural
+ 
+
+ align:start position:0%
+see that we currently have coal natural
+gaps petroleum around 31 exahjoules of
+
+ align:start position:0%
+gaps petroleum around 31 exahjoules of
+ 
+
+ align:start position:0%
+gaps petroleum around 31 exahjoules of
+natural gas and 39 exodules petroleum
+
+ align:start position:0%
+natural gas and 39 exodules petroleum
+ 
+
+ align:start position:0%
+natural gas and 39 exodules petroleum
+to go back to our Central low fuel price
+
+ align:start position:0%
+to go back to our Central low fuel price
+ 
+
+ align:start position:0%
+to go back to our Central low fuel price
+scenario you can see we only have about
+
+ align:start position:0%
+scenario you can see we only have about
+ 
+
+ align:start position:0%
+scenario you can see we only have about
+7.4 X volt of natural gas 512 exit
+
+ align:start position:0%
+7.4 X volt of natural gas 512 exit
+ 
+
+ align:start position:0%
+7.4 X volt of natural gas 512 exit
+joules of petroleum in both cases at
+
+ align:start position:0%
+joules of petroleum in both cases at
+ 
+
+ align:start position:0%
+joules of petroleum in both cases at
+about a 75 percent decline in how much
+
+ align:start position:0%
+about a 75 percent decline in how much
+ 
+
+ align:start position:0%
+about a 75 percent decline in how much
+energy we have to use from those two
+
+ align:start position:0%
+energy we have to use from those two
+ 
+
+ align:start position:0%
+energy we have to use from those two
+resources and still achieve
+
+ align:start position:0%
+resources and still achieve
+ 
+
+ align:start position:0%
+resources and still achieve
+decarbonization
+
+ align:start position:0%
+decarbonization
+ 
+
+ align:start position:0%
+decarbonization
+so the question is how do we go from
+
+ align:start position:0%
+so the question is how do we go from
+ 
+
+ align:start position:0%
+so the question is how do we go from
+reference case to a carbon neutral
+
+ align:start position:0%
+reference case to a carbon neutral
+ 
+
+ align:start position:0%
+reference case to a carbon neutral
+pathway that still has its fossil fuels
+
+ align:start position:0%
+pathway that still has its fossil fuels
+ 
+
+ align:start position:0%
+pathway that still has its fossil fuels
+we need to do four things this paper
+
+ align:start position:0%
+we need to do four things this paper
+ 
+
+ align:start position:0%
+we need to do four things this paper
+argues we have to lower our final energy
+
+ align:start position:0%
+argues we have to lower our final energy
+ 
+
+ align:start position:0%
+argues we have to lower our final energy
+use you can tell on the left hand side
+
+ align:start position:0%
+use you can tell on the left hand side
+ 
+
+ align:start position:0%
+use you can tell on the left hand side
+of all the same key diagrams there's
+
+ align:start position:0%
+of all the same key diagrams there's
+ 
+
+ align:start position:0%
+of all the same key diagrams there's
+less energy use going in in terms of
+
+ align:start position:0%
+less energy use going in in terms of
+ 
+
+ align:start position:0%
+less energy use going in in terms of
+primary energy
+
+ align:start position:0%
+primary energy
+ 
+
+ align:start position:0%
+primary energy
+decarbonize our electricity sources we
+
+ align:start position:0%
+decarbonize our electricity sources we
+ 
+
+ align:start position:0%
+decarbonize our electricity sources we
+can switch for follicle fuels good
+
+ align:start position:0%
+can switch for follicle fuels good
+ 
+
+ align:start position:0%
+can switch for follicle fuels good
+electricity in a lot of our energy
+
+ align:start position:0%
+electricity in a lot of our energy
+ 
+
+ align:start position:0%
+electricity in a lot of our energy
+technology or conversion Technologies
+
+ align:start position:0%
+technology or conversion Technologies
+ 
+
+ align:start position:0%
+technology or conversion Technologies
+and we need to do carbon capture
+
+ align:start position:0%
+and we need to do carbon capture
+ 
+
+ align:start position:0%
+and we need to do carbon capture
+utilization and storage that's what I
+
+ align:start position:0%
+utilization and storage that's what I
+ 
+
+ align:start position:0%
+utilization and storage that's what I
+want to talk about more now
+
+ align:start position:0%
+want to talk about more now
+ 
+
+ align:start position:0%
+want to talk about more now
+carbon capture utilization of storage
+
+ align:start position:0%
+carbon capture utilization of storage
+ 
+
+ align:start position:0%
+carbon capture utilization of storage
+why is this important
+
+ align:start position:0%
+why is this important
+ 
+
+ align:start position:0%
+why is this important
+well there's certain number of cons that
+
+ align:start position:0%
+well there's certain number of cons that
+ 
+
+ align:start position:0%
+well there's certain number of cons that
+people argue around ccufs one of the
+
+ align:start position:0%
+people argue around ccufs one of the
+ 
+
+ align:start position:0%
+people argue around ccufs one of the
+first cons is that it's been pushed by
+
+ align:start position:0%
+first cons is that it's been pushed by
+ 
+
+ align:start position:0%
+first cons is that it's been pushed by
+fossil fuel interest as a way to
+
+ align:start position:0%
+fossil fuel interest as a way to
+ 
+
+ align:start position:0%
+fossil fuel interest as a way to
+continue emissions if you look quite
+
+ align:start position:0%
+continue emissions if you look quite
+ 
+
+ align:start position:0%
+continue emissions if you look quite
+often on social media or quite often on
+
+ align:start position:0%
+often on social media or quite often on
+ 
+
+ align:start position:0%
+often on social media or quite often on
+the web if you have energy interests you
+
+ align:start position:0%
+the web if you have energy interests you
+ 
+
+ align:start position:0%
+the web if you have energy interests you
+may have been targeted by fossil fuel
+
+ align:start position:0%
+may have been targeted by fossil fuel
+ 
+
+ align:start position:0%
+may have been targeted by fossil fuel
+ads from Shell Exxon Chevron and other
+
+ align:start position:0%
+ads from Shell Exxon Chevron and other
+ 
+
+ align:start position:0%
+ads from Shell Exxon Chevron and other
+fossil fuel companies that argue that
+
+ align:start position:0%
+fossil fuel companies that argue that
+ 
+
+ align:start position:0%
+fossil fuel companies that argue that
+they're investing in carbon capture
+
+ align:start position:0%
+they're investing in carbon capture
+ 
+
+ align:start position:0%
+they're investing in carbon capture
+utilization and storage they're spending
+
+ align:start position:0%
+utilization and storage they're spending
+ 
+
+ align:start position:0%
+utilization and storage they're spending
+on these Technologies is a small
+
+ align:start position:0%
+on these Technologies is a small
+ 
+
+ align:start position:0%
+on these Technologies is a small
+fraction of what they're spending on
+
+ align:start position:0%
+fraction of what they're spending on
+ 
+
+ align:start position:0%
+fraction of what they're spending on
+their current extraction or new
+
+ align:start position:0%
+their current extraction or new
+ 
+
+ align:start position:0%
+their current extraction or new
+exploration operations to extract more
+
+ align:start position:0%
+exploration operations to extract more
+ 
+
+ align:start position:0%
+exploration operations to extract more
+fossil fuels so it's hard to argue that
+
+ align:start position:0%
+fossil fuels so it's hard to argue that
+ 
+
+ align:start position:0%
+fossil fuels so it's hard to argue that
+carbon capture utilization storage by
+
+ align:start position:0%
+carbon capture utilization storage by
+ 
+
+ align:start position:0%
+carbon capture utilization storage by
+fossil fuel companies May necessarily be
+
+ align:start position:0%
+fossil fuel companies May necessarily be
+ 
+
+ align:start position:0%
+fossil fuel companies May necessarily be
+in good faith
+
+ align:start position:0%
+in good faith
+ 
+
+ align:start position:0%
+in good faith
+another con with carbon Capital
+
+ align:start position:0%
+another con with carbon Capital
+ 
+
+ align:start position:0%
+another con with carbon Capital
+utilization storage or CC us support is
+
+ align:start position:0%
+utilization storage or CC us support is
+ 
+
+ align:start position:0%
+utilization storage or CC us support is
+that it's not economically competitive
+
+ align:start position:0%
+that it's not economically competitive
+ 
+
+ align:start position:0%
+that it's not economically competitive
+it's simply a higher cost of existing
+
+ align:start position:0%
+it's simply a higher cost of existing
+ 
+
+ align:start position:0%
+it's simply a higher cost of existing
+renewable alternatives
+
+ align:start position:0%
+renewable alternatives
+ 
+
+ align:start position:0%
+renewable alternatives
+another argument is that there's simply
+
+ align:start position:0%
+another argument is that there's simply
+ 
+
+ align:start position:0%
+another argument is that there's simply
+no fundamental economic value to scoring
+
+ align:start position:0%
+no fundamental economic value to scoring
+ 
+
+ align:start position:0%
+no fundamental economic value to scoring
+pardon except for avoiding the
+
+ align:start position:0%
+pardon except for avoiding the
+ 
+
+ align:start position:0%
+pardon except for avoiding the
+externalities of climate change in other
+
+ align:start position:0%
+externalities of climate change in other
+ 
+
+ align:start position:0%
+externalities of climate change in other
+words we should put Arvin we should
+
+ align:start position:0%
+words we should put Arvin we should
+ 
+
+ align:start position:0%
+words we should put Arvin we should
+store it if possible
+
+ align:start position:0%
+store it if possible
+ 
+
+ align:start position:0%
+store it if possible
+at the same time there's no fundamental
+
+ align:start position:0%
+at the same time there's no fundamental
+ 
+
+ align:start position:0%
+at the same time there's no fundamental
+use to get out of it unless we simply
+
+ align:start position:0%
+use to get out of it unless we simply
+ 
+
+ align:start position:0%
+use to get out of it unless we simply
+bit of a use to be avoiding the worst
+
+ align:start position:0%
+bit of a use to be avoiding the worst
+ 
+
+ align:start position:0%
+bit of a use to be avoiding the worst
+effects of climate change
+
+ align:start position:0%
+effects of climate change
+ 
+
+ align:start position:0%
+effects of climate change
+and because the only way that we could
+
+ align:start position:0%
+and because the only way that we could
+ 
+
+ align:start position:0%
+and because the only way that we could
+price actionality is through a carbon
+
+ align:start position:0%
+price actionality is through a carbon
+ 
+
+ align:start position:0%
+price actionality is through a carbon
+tax for Price these have not necessarily
+
+ align:start position:0%
+tax for Price these have not necessarily
+ 
+
+ align:start position:0%
+tax for Price these have not necessarily
+been proven to be politically viable in
+
+ align:start position:0%
+been proven to be politically viable in
+ 
+
+ align:start position:0%
+been proven to be politically viable in
+many cases so far you will notice that
+
+ align:start position:0%
+many cases so far you will notice that
+ 
+
+ align:start position:0%
+many cases so far you will notice that
+the new inflation reduction act does not
+
+ align:start position:0%
+the new inflation reduction act does not
+ 
+
+ align:start position:0%
+the new inflation reduction act does not
+include carbon products though there are
+
+ align:start position:0%
+include carbon products though there are
+ 
+
+ align:start position:0%
+include carbon products though there are
+still a number of politicians and policy
+
+ align:start position:0%
+still a number of politicians and policy
+ 
+
+ align:start position:0%
+still a number of politicians and policy
+makers who are still pushing for it
+
+ align:start position:0%
+makers who are still pushing for it
+ 
+
+ align:start position:0%
+makers who are still pushing for it
+of course one of the pros of carbon
+
+ align:start position:0%
+of course one of the pros of carbon
+ 
+
+ align:start position:0%
+of course one of the pros of carbon
+capture utilization storage is that in
+
+ align:start position:0%
+capture utilization storage is that in
+ 
+
+ align:start position:0%
+capture utilization storage is that in
+the short term we use still a lot of
+
+ align:start position:0%
+the short term we use still a lot of
+ 
+
+ align:start position:0%
+the short term we use still a lot of
+fossil fuels we also have relatively
+
+ align:start position:0%
+fossil fuels we also have relatively
+ 
+
+ align:start position:0%
+fossil fuels we also have relatively
+High possible fuel prices and so if we
+
+ align:start position:0%
+High possible fuel prices and so if we
+ 
+
+ align:start position:0%
+High possible fuel prices and so if we
+need to continue producing fossil fuels
+
+ align:start position:0%
+need to continue producing fossil fuels
+ 
+
+ align:start position:0%
+need to continue producing fossil fuels
+to avoid the worst short-term effects we
+
+ align:start position:0%
+to avoid the worst short-term effects we
+ 
+
+ align:start position:0%
+to avoid the worst short-term effects we
+are going to hopefully have carbon
+
+ align:start position:0%
+are going to hopefully have carbon
+ 
+
+ align:start position:0%
+are going to hopefully have carbon
+capture utilization storage to store or
+
+ align:start position:0%
+capture utilization storage to store or
+ 
+
+ align:start position:0%
+capture utilization storage to store or
+pronounce Gap emissions in the short
+
+ align:start position:0%
+pronounce Gap emissions in the short
+ 
+
+ align:start position:0%
+pronounce Gap emissions in the short
+term and in the future
+
+ align:start position:0%
+term and in the future
+ 
+
+ align:start position:0%
+term and in the future
+and one of the pros I guess for the idea
+
+ align:start position:0%
+and one of the pros I guess for the idea
+ 
+
+ align:start position:0%
+and one of the pros I guess for the idea
+of CC Us in the long term is that we
+
+ align:start position:0%
+of CC Us in the long term is that we
+ 
+
+ align:start position:0%
+of CC Us in the long term is that we
+simply need to reduce carbon
+
+ align:start position:0%
+simply need to reduce carbon
+ 
+
+ align:start position:0%
+simply need to reduce carbon
+concentration in the atmosphere the
+
+ align:start position:0%
+concentration in the atmosphere the
+ 
+
+ align:start position:0%
+concentration in the atmosphere the
+current levels are 415 parts per million
+
+ align:start position:0%
+current levels are 415 parts per million
+ 
+
+ align:start position:0%
+current levels are 415 parts per million
+if you simply stop reduce using
+
+ align:start position:0%
+if you simply stop reduce using
+ 
+
+ align:start position:0%
+if you simply stop reduce using
+pronounced apps or rather stop using
+
+ align:start position:0%
+pronounced apps or rather stop using
+ 
+
+ align:start position:0%
+pronounced apps or rather stop using
+volatile fuels tomorrow we'd still have
+
+ align:start position:0%
+volatile fuels tomorrow we'd still have
+ 
+
+ align:start position:0%
+volatile fuels tomorrow we'd still have
+to have a way to reduce our carbon
+
+ align:start position:0%
+to have a way to reduce our carbon
+ 
+
+ align:start position:0%
+to have a way to reduce our carbon
+concentration atmosphere to safe levels
+
+ align:start position:0%
+concentration atmosphere to safe levels
+ 
+
+ align:start position:0%
+concentration atmosphere to safe levels
+and so the latest ipct report
+
+ align:start position:0%
+and so the latest ipct report
+ 
+
+ align:start position:0%
+and so the latest ipct report
+recognizes that we need some kind of
+
+ align:start position:0%
+recognizes that we need some kind of
+ 
+
+ align:start position:0%
+recognizes that we need some kind of
+carbon dioxide removal or some kind of
+
+ align:start position:0%
+carbon dioxide removal or some kind of
+ 
+
+ align:start position:0%
+carbon dioxide removal or some kind of
+carbon capture utilization storage
+
+ align:start position:0%
+carbon capture utilization storage
+ 
+
+ align:start position:0%
+carbon capture utilization storage
+techniques to be developed
+
+ align:start position:0%
+techniques to be developed
+ 
+
+ align:start position:0%
+techniques to be developed
+and so this is actually uh to bring it
+
+ align:start position:0%
+and so this is actually uh to bring it
+ 
+
+ align:start position:0%
+and so this is actually uh to bring it
+back to what cities can or cannot do on
+
+ align:start position:0%
+back to what cities can or cannot do on
+ 
+
+ align:start position:0%
+back to what cities can or cannot do on
+one hand do you have the cities that are
+
+ align:start position:0%
+one hand do you have the cities that are
+ 
+
+ align:start position:0%
+one hand do you have the cities that are
+highlighted in blue Washington
+
+ align:start position:0%
+highlighted in blue Washington
+ 
+
+ align:start position:0%
+highlighted in blue Washington
+California and States like New York
+
+ align:start position:0%
+California and States like New York
+ 
+
+ align:start position:0%
+California and States like New York
+Vermont Massachusetts and
+
+ align:start position:0%
+Vermont Massachusetts and
+ 
+
+ align:start position:0%
+Vermont Massachusetts and
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+New York are all considering natural gas
+
+ align:start position:0%
+New York are all considering natural gas
+ 
+
+ align:start position:0%
+New York are all considering natural gas
+stems because simply we know that
+
+ align:start position:0%
+stems because simply we know that
+ 
+
+ align:start position:0%
+stems because simply we know that
+greenhouse gas emissions and car
+
+ align:start position:0%
+greenhouse gas emissions and car
+ 
+
+ align:start position:0%
+greenhouse gas emissions and car
+emissions and methane emissions
+
+ align:start position:0%
+emissions and methane emissions
+ 
+
+ align:start position:0%
+emissions and methane emissions
+especially are driving greenhouse gas
+
+ align:start position:0%
+especially are driving greenhouse gas
+ 
+
+ align:start position:0%
+especially are driving greenhouse gas
+Greenhouse climate change very quickly
+
+ align:start position:0%
+Greenhouse climate change very quickly
+ 
+
+ align:start position:0%
+Greenhouse climate change very quickly
+and so you have a number of cities and
+
+ align:start position:0%
+and so you have a number of cities and
+ 
+
+ align:start position:0%
+and so you have a number of cities and
+states all considering trying to pass
+
+ align:start position:0%
+states all considering trying to pass
+ 
+
+ align:start position:0%
+states all considering trying to pass
+the natural gas bans such as Berkeley
+
+ align:start position:0%
+the natural gas bans such as Berkeley
+ 
+
+ align:start position:0%
+the natural gas bans such as Berkeley
+California Seattle Washington I think
+
+ align:start position:0%
+California Seattle Washington I think
+ 
+
+ align:start position:0%
+California Seattle Washington I think
+San Jose also considered it and about 10
+
+ align:start position:0%
+San Jose also considered it and about 10
+ 
+
+ align:start position:0%
+San Jose also considered it and about 10
+or 15 pounds in Massachusetts have also
+
+ align:start position:0%
+or 15 pounds in Massachusetts have also
+ 
+
+ align:start position:0%
+or 15 pounds in Massachusetts have also
+proposed it at the latest Massachusetts
+
+ align:start position:0%
+proposed it at the latest Massachusetts
+ 
+
+ align:start position:0%
+proposed it at the latest Massachusetts
+climate legislation allows 10 City to
+
+ align:start position:0%
+climate legislation allows 10 City to
+ 
+
+ align:start position:0%
+climate legislation allows 10 City to
+experimentally fish
+
+ align:start position:0%
+experimentally fish
+ 
+
+ align:start position:0%
+experimentally fish
+at the same time just to consider what
+
+ align:start position:0%
+at the same time just to consider what
+ 
+
+ align:start position:0%
+at the same time just to consider what
+cities can't do necessarily look at all
+
+ align:start position:0%
+cities can't do necessarily look at all
+ 
+
+ align:start position:0%
+cities can't do necessarily look at all
+the states here in red these are all
+
+ align:start position:0%
+the states here in red these are all
+ 
+
+ align:start position:0%
+the states here in red these are all
+states that have passed legislation that
+
+ align:start position:0%
+states that have passed legislation that
+ 
+
+ align:start position:0%
+states that have passed legislation that
+prohibit local governments from
+
+ align:start position:0%
+prohibit local governments from
+ 
+
+ align:start position:0%
+prohibit local governments from
+restricting natural gas utility service
+
+ align:start position:0%
+restricting natural gas utility service
+ 
+
+ align:start position:0%
+restricting natural gas utility service
+in other words the states are family
+
+ align:start position:0%
+in other words the states are family
+ 
+
+ align:start position:0%
+in other words the states are family
+what cities can do and so the reason why
+
+ align:start position:0%
+what cities can do and so the reason why
+ 
+
+ align:start position:0%
+what cities can do and so the reason why
+we're considering our Alternatives or
+
+ align:start position:0%
+we're considering our Alternatives or
+ 
+
+ align:start position:0%
+we're considering our Alternatives or
+with the possibility of how much fossil
+
+ align:start position:0%
+with the possibility of how much fossil
+ 
+
+ align:start position:0%
+with the possibility of how much fossil
+fuels we're going to use in the future
+
+ align:start position:0%
+fuels we're going to use in the future
+ 
+
+ align:start position:0%
+fuels we're going to use in the future
+it's because these two kinds of States
+
+ align:start position:0%
+it's because these two kinds of States
+ 
+
+ align:start position:0%
+it's because these two kinds of States
+frankly blue States and red states have
+
+ align:start position:0%
+frankly blue States and red states have
+ 
+
+ align:start position:0%
+frankly blue States and red states have
+fundamentally different views on what
+
+ align:start position:0%
+fundamentally different views on what
+ 
+
+ align:start position:0%
+fundamentally different views on what
+the future use of fossil fuels could be
+
+ align:start position:0%
+the future use of fossil fuels could be
+ 
+
+ align:start position:0%
+the future use of fossil fuels could be
+both consider how we might try to
+
+ align:start position:0%
+both consider how we might try to
+ 
+
+ align:start position:0%
+both consider how we might try to
+achieve decarbonization and whether
+
+ align:start position:0%
+achieve decarbonization and whether
+ 
+
+ align:start position:0%
+achieve decarbonization and whether
+navigants can consider to use fossil
+
+ align:start position:0%
+navigants can consider to use fossil
+ 
+
+ align:start position:0%
+navigants can consider to use fossil
+fuels whether we can continue to use
+
+ align:start position:0%
+fuels whether we can continue to use
+ 
+
+ align:start position:0%
+fuels whether we can continue to use
+fossil fuels this is going to drive what
+
+ align:start position:0%
+fossil fuels this is going to drive what
+ 
+
+ align:start position:0%
+fossil fuels this is going to drive what
+we do in cities in policy
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so there's a couple of different ways to
+
+ align:start position:0%
+so there's a couple of different ways to
+ 
+
+ align:start position:0%
+so there's a couple of different ways to
+do carbon capture and storage in the
+
+ align:start position:0%
+do carbon capture and storage in the
+ 
+
+ align:start position:0%
+do carbon capture and storage in the
+lithosphere or geosphere essentially
+
+ align:start position:0%
+lithosphere or geosphere essentially
+ 
+
+ align:start position:0%
+lithosphere or geosphere essentially
+into the Earth's mantle and this is a
+
+ align:start position:0%
+into the Earth's mantle and this is a
+ 
+
+ align:start position:0%
+into the Earth's mantle and this is a
+diagram for the wristman paper we read
+
+ align:start position:0%
+diagram for the wristman paper we read
+ 
+
+ align:start position:0%
+diagram for the wristman paper we read
+uh on Tuesday and this shows different
+
+ align:start position:0%
+uh on Tuesday and this shows different
+ 
+
+ align:start position:0%
+uh on Tuesday and this shows different
+ways of taking you can basically uh have
+
+ align:start position:0%
+ways of taking you can basically uh have
+ 
+
+ align:start position:0%
+ways of taking you can basically uh have
+a pipeline up to 500 kilometers that
+
+ align:start position:0%
+a pipeline up to 500 kilometers that
+ 
+
+ align:start position:0%
+a pipeline up to 500 kilometers that
+takes uh carbon dioxide or Advanced gas
+
+ align:start position:0%
+takes uh carbon dioxide or Advanced gas
+ 
+
+ align:start position:0%
+takes uh carbon dioxide or Advanced gas
+emissions from a power plant and brings
+
+ align:start position:0%
+emissions from a power plant and brings
+ 
+
+ align:start position:0%
+emissions from a power plant and brings
+it to a CCS storage facility so you have
+
+ align:start position:0%
+it to a CCS storage facility so you have
+ 
+
+ align:start position:0%
+it to a CCS storage facility so you have
+some flexibility in disaggregating where
+
+ align:start position:0%
+some flexibility in disaggregating where
+ 
+
+ align:start position:0%
+some flexibility in disaggregating where
+the power plant is and when the CCS
+
+ align:start position:0%
+the power plant is and when the CCS
+ 
+
+ align:start position:0%
+the power plant is and when the CCS
+storage facility is you can bring in
+
+ align:start position:0%
+storage facility is you can bring in
+ 
+
+ align:start position:0%
+storage facility is you can bring in
+this pipeline you might be able to bring
+
+ align:start position:0%
+this pipeline you might be able to bring
+ 
+
+ align:start position:0%
+this pipeline you might be able to bring
+it by ship you can inject CO2 and store
+
+ align:start position:0%
+it by ship you can inject CO2 and store
+ 
+
+ align:start position:0%
+it by ship you can inject CO2 and store
+on the ground and this shows all the
+
+ align:start position:0%
+on the ground and this shows all the
+ 
+
+ align:start position:0%
+on the ground and this shows all the
+different ways you can start in the
+
+ align:start position:0%
+different ways you can start in the
+ 
+
+ align:start position:0%
+different ways you can start in the
+ground you have this impermeable cap
+
+ align:start position:0%
+ground you have this impermeable cap
+ 
+
+ align:start position:0%
+ground you have this impermeable cap
+rock that keeps the CO2 underground you
+
+ align:start position:0%
+rock that keeps the CO2 underground you
+ 
+
+ align:start position:0%
+rock that keeps the CO2 underground you
+pump it to about 1.5 kilometers deep or
+
+ align:start position:0%
+pump it to about 1.5 kilometers deep or
+ 
+
+ align:start position:0%
+pump it to about 1.5 kilometers deep or
+more you can put the CO2 into a complete
+
+ align:start position:0%
+more you can put the CO2 into a complete
+ 
+
+ align:start position:0%
+more you can put the CO2 into a complete
+the oil or gas Reservoir you can put it
+
+ align:start position:0%
+the oil or gas Reservoir you can put it
+ 
+
+ align:start position:0%
+the oil or gas Reservoir you can put it
+into the natural saline aquifer and as
+
+ align:start position:0%
+into the natural saline aquifer and as
+ 
+
+ align:start position:0%
+into the natural saline aquifer and as
+this little inset shows this carbon
+
+ align:start position:0%
+this little inset shows this carbon
+ 
+
+ align:start position:0%
+this little inset shows this carbon
+dioxide becomes stabilized within the
+
+ align:start position:0%
+dioxide becomes stabilized within the
+ 
+
+ align:start position:0%
+dioxide becomes stabilized within the
+porous rock forms natural compound
+
+ align:start position:0%
+porous rock forms natural compound
+ 
+
+ align:start position:0%
+porous rock forms natural compound
+within the surprise surrounding Brine
+
+ align:start position:0%
+within the surprise surrounding Brine
+ 
+
+ align:start position:0%
+within the surprise surrounding Brine
+and minerals
+
+ align:start position:0%
+and minerals
+ 
+
+ align:start position:0%
+and minerals
+of course this brings us to other
+
+ align:start position:0%
+of course this brings us to other
+ 
+
+ align:start position:0%
+of course this brings us to other
+possible ways to do carbon Capital
+
+ align:start position:0%
+possible ways to do carbon Capital
+ 
+
+ align:start position:0%
+possible ways to do carbon Capital
+utilization storage you might remember
+
+ align:start position:0%
+utilization storage you might remember
+ 
+
+ align:start position:0%
+utilization storage you might remember
+this figure from the tumulty report we
+
+ align:start position:0%
+this figure from the tumulty report we
+ 
+
+ align:start position:0%
+this figure from the tumulty report we
+read maybe I think the second or third
+
+ align:start position:0%
+read maybe I think the second or third
+ 
+
+ align:start position:0%
+read maybe I think the second or third
+week of class this shows Ontario's Green
+
+ align:start position:0%
+week of class this shows Ontario's Green
+ 
+
+ align:start position:0%
+week of class this shows Ontario's Green
+Belt we discussed the implications of
+
+ align:start position:0%
+Belt we discussed the implications of
+ 
+
+ align:start position:0%
+Belt we discussed the implications of
+land use not only for urban growth but
+
+ align:start position:0%
+land use not only for urban growth but
+ 
+
+ align:start position:0%
+land use not only for urban growth but
+for possible carbon capture and Storage
+
+ align:start position:0%
+for possible carbon capture and Storage
+ 
+
+ align:start position:0%
+for possible carbon capture and Storage
+so about two summers ago I spent quite a
+
+ align:start position:0%
+so about two summers ago I spent quite a
+ 
+
+ align:start position:0%
+so about two summers ago I spent quite a
+bit of time talking to my MIT colleagues
+
+ align:start position:0%
+bit of time talking to my MIT colleagues
+ 
+
+ align:start position:0%
+bit of time talking to my MIT colleagues
+uh we worked on this planet Grand
+
+ align:start position:0%
+uh we worked on this planet Grand
+ 
+
+ align:start position:0%
+uh we worked on this planet Grand
+Challenge project and correct called
+
+ align:start position:0%
+Challenge project and correct called
+ 
+
+ align:start position:0%
+Challenge project and correct called
+carbon and we produced from it out of
+
+ align:start position:0%
+carbon and we produced from it out of
+ 
+
+ align:start position:0%
+carbon and we produced from it out of
+the series of Graphics showing different
+
+ align:start position:0%
+the series of Graphics showing different
+ 
+
+ align:start position:0%
+the series of Graphics showing different
+ways that you might be able to express
+
+ align:start position:0%
+ways that you might be able to express
+ 
+
+ align:start position:0%
+ways that you might be able to express
+your apartment into direct field uh or
+
+ align:start position:0%
+your apartment into direct field uh or
+ 
+
+ align:start position:0%
+your apartment into direct field uh or
+into the biosphere
+
+ align:start position:0%
+into the biosphere
+ 
+
+ align:start position:0%
+into the biosphere
+so and one possibility is that you take
+
+ align:start position:0%
+so and one possibility is that you take
+ 
+
+ align:start position:0%
+so and one possibility is that you take
+carbon and you sequester into the soil
+
+ align:start position:0%
+carbon and you sequester into the soil
+ 
+
+ align:start position:0%
+carbon and you sequester into the soil
+microbiome the major medical engineer as
+
+ align:start position:0%
+microbiome the major medical engineer as
+ 
+
+ align:start position:0%
+microbiome the major medical engineer as
+the soil microbiome to uptake more
+
+ align:start position:0%
+the soil microbiome to uptake more
+ 
+
+ align:start position:0%
+the soil microbiome to uptake more
+carbon
+
+ align:start position:0%
+carbon
+ 
+
+ align:start position:0%
+carbon
+another possibility is perennial crops
+
+ align:start position:0%
+another possibility is perennial crops
+ 
+
+ align:start position:0%
+another possibility is perennial crops
+parental crops unlike annual crops are
+
+ align:start position:0%
+parental crops unlike annual crops are
+ 
+
+ align:start position:0%
+parental crops unlike annual crops are
+agricultural crops that actually can be
+
+ align:start position:0%
+agricultural crops that actually can be
+ 
+
+ align:start position:0%
+agricultural crops that actually can be
+harvested every year if they don't
+
+ align:start position:0%
+harvested every year if they don't
+ 
+
+ align:start position:0%
+harvested every year if they don't
+require replanting their root systems
+
+ align:start position:0%
+require replanting their root systems
+ 
+
+ align:start position:0%
+require replanting their root systems
+typically grow much deeper than typical
+
+ align:start position:0%
+typically grow much deeper than typical
+ 
+
+ align:start position:0%
+typically grow much deeper than typical
+annual crops the things we currently
+
+ align:start position:0%
+annual crops the things we currently
+ 
+
+ align:start position:0%
+annual crops the things we currently
+plant in a harvest every year Cornell
+
+ align:start position:0%
+plant in a harvest every year Cornell
+ 
+
+ align:start position:0%
+plant in a harvest every year Cornell
+crops because the root systems go down
+
+ align:start position:0%
+crops because the root systems go down
+ 
+
+ align:start position:0%
+crops because the root systems go down
+much deeper and they store more carbon
+
+ align:start position:0%
+much deeper and they store more carbon
+ 
+
+ align:start position:0%
+much deeper and they store more carbon
+into the soil
+
+ align:start position:0%
+into the soil
+ 
+
+ align:start position:0%
+into the soil
+another possibility is for crypto carbon
+
+ align:start position:0%
+another possibility is for crypto carbon
+ 
+
+ align:start position:0%
+another possibility is for crypto carbon
+in agricultural soils is abandoned
+
+ align:start position:0%
+in agricultural soils is abandoned
+ 
+
+ align:start position:0%
+in agricultural soils is abandoned
+croplands if abandoned croplands are no
+
+ align:start position:0%
+croplands if abandoned croplands are no
+ 
+
+ align:start position:0%
+croplands if abandoned croplands are no
+longer need to be harvested then we
+
+ align:start position:0%
+longer need to be harvested then we
+ 
+
+ align:start position:0%
+longer need to be harvested then we
+could store carbon into the soil and
+
+ align:start position:0%
+could store carbon into the soil and
+ 
+
+ align:start position:0%
+could store carbon into the soil and
+Abandoned cropland and leave it there
+
+ align:start position:0%
+Abandoned cropland and leave it there
+ 
+
+ align:start position:0%
+Abandoned cropland and leave it there
+these are all possibilities for
+
+ align:start position:0%
+these are all possibilities for
+ 
+
+ align:start position:0%
+these are all possibilities for
+agricultural soils
+
+ align:start position:0%
+agricultural soils
+ 
+
+ align:start position:0%
+agricultural soils
+another possibility for carbon capture
+
+ align:start position:0%
+another possibility for carbon capture
+ 
+
+ align:start position:0%
+another possibility for carbon capture
+its utilization of storage is forward
+
+ align:start position:0%
+its utilization of storage is forward
+ 
+
+ align:start position:0%
+its utilization of storage is forward
+sequestration
+
+ align:start position:0%
+sequestration
+ 
+
+ align:start position:0%
+sequestration
+in many cases you have natural carbon
+
+ align:start position:0%
+in many cases you have natural carbon
+ 
+
+ align:start position:0%
+in many cases you have natural carbon
+dioxide emissions from say a volcano you
+
+ align:start position:0%
+dioxide emissions from say a volcano you
+ 
+
+ align:start position:0%
+dioxide emissions from say a volcano you
+get Forest fertilization this is a
+
+ align:start position:0%
+get Forest fertilization this is a
+ 
+
+ align:start position:0%
+get Forest fertilization this is a
+ecosystem cycle that happens to my
+
+ align:start position:0%
+ecosystem cycle that happens to my
+ 
+
+ align:start position:0%
+ecosystem cycle that happens to my
+colleagues study you can see the CO2 is
+
+ align:start position:0%
+colleagues study you can see the CO2 is
+ 
+
+ align:start position:0%
+colleagues study you can see the CO2 is
+being prepared into a forest another
+
+ align:start position:0%
+being prepared into a forest another
+ 
+
+ align:start position:0%
+being prepared into a forest another
+possibility is terabetta this is
+
+ align:start position:0%
+possibility is terabetta this is
+ 
+
+ align:start position:0%
+possibility is terabetta this is
+something that Tyler Parham has studied
+
+ align:start position:0%
+something that Tyler Parham has studied
+ 
+
+ align:start position:0%
+something that Tyler Parham has studied
+in heaps uh how actually ancient
+
+ align:start position:0%
+in heaps uh how actually ancient
+ 
+
+ align:start position:0%
+in heaps uh how actually ancient
+cultures actually use charcoal and waste
+
+ align:start position:0%
+cultures actually use charcoal and waste
+ 
+
+ align:start position:0%
+cultures actually use charcoal and waste
+processes to actually create fairly rich
+
+ align:start position:0%
+processes to actually create fairly rich
+ 
+
+ align:start position:0%
+processes to actually create fairly rich
+soil called the Amazon apparently it
+
+ align:start position:0%
+soil called the Amazon apparently it
+ 
+
+ align:start position:0%
+soil called the Amazon apparently it
+results resulting in much more fertile
+
+ align:start position:0%
+results resulting in much more fertile
+ 
+
+ align:start position:0%
+results resulting in much more fertile
+soil for the Amazon lab today and one
+
+ align:start position:0%
+soil for the Amazon lab today and one
+ 
+
+ align:start position:0%
+soil for the Amazon lab today and one
+simple way to sequester carbon into soil
+
+ align:start position:0%
+simple way to sequester carbon into soil
+ 
+
+ align:start position:0%
+simple way to sequester carbon into soil
+is to avoid illegal logging and
+
+ align:start position:0%
+is to avoid illegal logging and
+ 
+
+ align:start position:0%
+is to avoid illegal logging and
+deforestation we know that quite a bit
+
+ align:start position:0%
+deforestation we know that quite a bit
+ 
+
+ align:start position:0%
+deforestation we know that quite a bit
+of carbon is sequestered in the Amazon
+
+ align:start position:0%
+of carbon is sequestered in the Amazon
+ 
+
+ align:start position:0%
+of carbon is sequestered in the Amazon
+rainforest we want to avoid illegal
+
+ align:start position:0%
+rainforest we want to avoid illegal
+ 
+
+ align:start position:0%
+rainforest we want to avoid illegal
+logging and deforestation in places like
+
+ align:start position:0%
+logging and deforestation in places like
+ 
+
+ align:start position:0%
+logging and deforestation in places like
+the Amazon if it's like Indonesia we can
+
+ align:start position:0%
+the Amazon if it's like Indonesia we can
+ 
+
+ align:start position:0%
+the Amazon if it's like Indonesia we can
+avoid that legal logging deforestation
+
+ align:start position:0%
+avoid that legal logging deforestation
+ 
+
+ align:start position:0%
+avoid that legal logging deforestation
+where essentially saving carbon dioxide
+
+ align:start position:0%
+where essentially saving carbon dioxide
+ 
+
+ align:start position:0%
+where essentially saving carbon dioxide
+from being released to the atmosphere
+
+ align:start position:0%
+from being released to the atmosphere
+ 
+
+ align:start position:0%
+from being released to the atmosphere
+another possibility of for storing
+
+ align:start position:0%
+another possibility of for storing
+ 
+
+ align:start position:0%
+another possibility of for storing
+carbon is in the hydrosphere this is
+
+ align:start position:0%
+carbon is in the hydrosphere this is
+ 
+
+ align:start position:0%
+carbon is in the hydrosphere this is
+something that hiding net and others
+
+ align:start position:0%
+something that hiding net and others
+ 
+
+ align:start position:0%
+something that hiding net and others
+have studied uh Charles Harvey in civil
+
+ align:start position:0%
+have studied uh Charles Harvey in civil
+ 
+
+ align:start position:0%
+have studied uh Charles Harvey in civil
+engineering studies how much carbon the
+
+ align:start position:0%
+engineering studies how much carbon the
+ 
+
+ align:start position:0%
+engineering studies how much carbon the
+sequester currently impede lands
+
+ align:start position:0%
+sequester currently impede lands
+ 
+
+ align:start position:0%
+sequester currently impede lands
+peatlands are essentially a decaying of
+
+ align:start position:0%
+peatlands are essentially a decaying of
+ 
+
+ align:start position:0%
+peatlands are essentially a decaying of
+vegetation from many centuries before
+
+ align:start position:0%
+vegetation from many centuries before
+ 
+
+ align:start position:0%
+vegetation from many centuries before
+they actually sequester quite a bit of
+
+ align:start position:0%
+they actually sequester quite a bit of
+ 
+
+ align:start position:0%
+they actually sequester quite a bit of
+carbon permafrost currently stores a lot
+
+ align:start position:0%
+carbon permafrost currently stores a lot
+ 
+
+ align:start position:0%
+carbon permafrost currently stores a lot
+of carbon in places like Siberia this is
+
+ align:start position:0%
+of carbon in places like Siberia this is
+ 
+
+ align:start position:0%
+of carbon in places like Siberia this is
+something we want to avoid warming the
+
+ align:start position:0%
+something we want to avoid warming the
+ 
+
+ align:start position:0%
+something we want to avoid warming the
+Earth because if we do have warming no
+
+ align:start position:0%
+Earth because if we do have warming no
+ 
+
+ align:start position:0%
+Earth because if we do have warming no
+release carbon dioxide and methane into
+
+ align:start position:0%
+release carbon dioxide and methane into
+ 
+
+ align:start position:0%
+release carbon dioxide and methane into
+the atmosphere
+
+ align:start position:0%
+the atmosphere
+ 
+
+ align:start position:0%
+the atmosphere
+Heidi NEP and others in MIT have studied
+
+ align:start position:0%
+Heidi NEP and others in MIT have studied
+ 
+
+ align:start position:0%
+Heidi NEP and others in MIT have studied
+uh postal hydrosphere or Postal
+
+ align:start position:0%
+uh postal hydrosphere or Postal
+ 
+
+ align:start position:0%
+uh postal hydrosphere or Postal
+sequestration of carbon I think blue um
+
+ align:start position:0%
+sequestration of carbon I think blue um
+ 
+
+ align:start position:0%
+sequestration of carbon I think blue um
+blue carbon is what they call it where
+
+ align:start position:0%
+blue carbon is what they call it where
+ 
+
+ align:start position:0%
+blue carbon is what they call it where
+you star store carbon dioxide in
+
+ align:start position:0%
+you star store carbon dioxide in
+ 
+
+ align:start position:0%
+you star store carbon dioxide in
+mangroves and salt marshes and
+
+ align:start position:0%
+mangroves and salt marshes and
+ 
+
+ align:start position:0%
+mangroves and salt marshes and
+seagrasses
+
+ align:start position:0%
+seagrasses
+ 
+
+ align:start position:0%
+seagrasses
+so these are all possibilities for
+
+ align:start position:0%
+so these are all possibilities for
+ 
+
+ align:start position:0%
+so these are all possibilities for
+carbon after utilization storage
+
+ align:start position:0%
+carbon after utilization storage
+ 
+
+ align:start position:0%
+carbon after utilization storage
+uh if we think about the utilization
+
+ align:start position:0%
+uh if we think about the utilization
+ 
+
+ align:start position:0%
+uh if we think about the utilization
+part of it what we might use carbon for
+
+ align:start position:0%
+part of it what we might use carbon for
+ 
+
+ align:start position:0%
+part of it what we might use carbon for
+this is and again I show you a McKinsey
+
+ align:start position:0%
+this is and again I show you a McKinsey
+ 
+
+ align:start position:0%
+this is and again I show you a McKinsey
+graph because this is the marginal
+
+ align:start position:0%
+graph because this is the marginal
+ 
+
+ align:start position:0%
+graph because this is the marginal
+Bateman plus curve that we've been
+
+ align:start position:0%
+Bateman plus curve that we've been
+ 
+
+ align:start position:0%
+Bateman plus curve that we've been
+talking about in previous classes on the
+
+ align:start position:0%
+talking about in previous classes on the
+ 
+
+ align:start position:0%
+talking about in previous classes on the
+vertical axis is the willingness to pay
+
+ align:start position:0%
+vertical axis is the willingness to pay
+ 
+
+ align:start position:0%
+vertical axis is the willingness to pay
+for manufacturers for CO2 in other words
+
+ align:start position:0%
+for manufacturers for CO2 in other words
+ 
+
+ align:start position:0%
+for manufacturers for CO2 in other words
+lots of Manufacturers have to need CO2
+
+ align:start position:0%
+lots of Manufacturers have to need CO2
+ 
+
+ align:start position:0%
+lots of Manufacturers have to need CO2
+as feedstock it's on the positive side
+
+ align:start position:0%
+as feedstock it's on the positive side
+ 
+
+ align:start position:0%
+as feedstock it's on the positive side
+manufacturers are willing to pay for
+
+ align:start position:0%
+manufacturers are willing to pay for
+ 
+
+ align:start position:0%
+manufacturers are willing to pay for
+carbon dioxide on the negative side
+
+ align:start position:0%
+carbon dioxide on the negative side
+ 
+
+ align:start position:0%
+carbon dioxide on the negative side
+they're willing to pay to get rid of CO2
+
+ align:start position:0%
+they're willing to pay to get rid of CO2
+ 
+
+ align:start position:0%
+they're willing to pay to get rid of CO2
+or they'd actually have to spend more
+
+ align:start position:0%
+or they'd actually have to spend more
+ 
+
+ align:start position:0%
+or they'd actually have to spend more
+money to take up CO2 so if you look at
+
+ align:start position:0%
+money to take up CO2 so if you look at
+ 
+
+ align:start position:0%
+money to take up CO2 so if you look at
+it right now there's this blue bar this
+
+ align:start position:0%
+it right now there's this blue bar this
+ 
+
+ align:start position:0%
+it right now there's this blue bar this
+is the expected cost for direct capture
+
+ align:start position:0%
+is the expected cost for direct capture
+ 
+
+ align:start position:0%
+is the expected cost for direct capture
+by 2030 and this is a typical cost of
+
+ align:start position:0%
+by 2030 and this is a typical cost of
+ 
+
+ align:start position:0%
+by 2030 and this is a typical cost of
+CO2 capture for high security Point
+
+ align:start position:0%
+CO2 capture for high security Point
+ 
+
+ align:start position:0%
+CO2 capture for high security Point
+sources so right now we can typically
+
+ align:start position:0%
+sources so right now we can typically
+ 
+
+ align:start position:0%
+sources so right now we can typically
+capture CO2 for high Purity Point
+
+ align:start position:0%
+capture CO2 for high Purity Point
+ 
+
+ align:start position:0%
+capture CO2 for high Purity Point
+sources and the economic uses of that
+
+ align:start position:0%
+sources and the economic uses of that
+ 
+
+ align:start position:0%
+sources and the economic uses of that
+are in things like biochar or carbon
+
+ align:start position:0%
+are in things like biochar or carbon
+ 
+
+ align:start position:0%
+are in things like biochar or carbon
+making compartment fiber in greenhouses
+
+ align:start position:0%
+making compartment fiber in greenhouses
+ 
+
+ align:start position:0%
+making compartment fiber in greenhouses
+and food and beverages right now we
+
+ align:start position:0%
+and food and beverages right now we
+ 
+
+ align:start position:0%
+and food and beverages right now we
+can't capture CO2 at economically viable
+
+ align:start position:0%
+can't capture CO2 at economically viable
+ 
+
+ align:start position:0%
+can't capture CO2 at economically viable
+price to use in applications like cement
+
+ align:start position:0%
+price to use in applications like cement
+ 
+
+ align:start position:0%
+price to use in applications like cement
+cement can actually made Stronger by
+
+ align:start position:0%
+cement can actually made Stronger by
+ 
+
+ align:start position:0%
+cement can actually made Stronger by
+adding carbon dioxide to it you can use
+
+ align:start position:0%
+adding carbon dioxide to it you can use
+ 
+
+ align:start position:0%
+adding carbon dioxide to it you can use
+it to do enhanced oil recovery you can
+
+ align:start position:0%
+it to do enhanced oil recovery you can
+ 
+
+ align:start position:0%
+it to do enhanced oil recovery you can
+actually pump CO2 into an oil reservoir
+
+ align:start position:0%
+actually pump CO2 into an oil reservoir
+ 
+
+ align:start position:0%
+actually pump CO2 into an oil reservoir
+and drive out more oil that way but
+
+ align:start position:0%
+and drive out more oil that way but
+ 
+
+ align:start position:0%
+and drive out more oil that way but
+right now it's not necessarily cost
+
+ align:start position:0%
+right now it's not necessarily cost
+ 
+
+ align:start position:0%
+right now it's not necessarily cost
+effective in many cases Aggregates
+
+ align:start position:0%
+effective in many cases Aggregates
+ 
+
+ align:start position:0%
+effective in many cases Aggregates
+storage these are all things that aren't
+
+ align:start position:0%
+storage these are all things that aren't
+ 
+
+ align:start position:0%
+storage these are all things that aren't
+necessarily possible to use with high
+
+ align:start position:0%
+necessarily possible to use with high
+ 
+
+ align:start position:0%
+necessarily possible to use with high
+Purity Point sources right now McKenzie
+
+ align:start position:0%
+Purity Point sources right now McKenzie
+ 
+
+ align:start position:0%
+Purity Point sources right now McKenzie
+report was interesting and then they
+
+ align:start position:0%
+report was interesting and then they
+ 
+
+ align:start position:0%
+report was interesting and then they
+look at what the viable Marketplace is
+
+ align:start position:0%
+look at what the viable Marketplace is
+ 
+
+ align:start position:0%
+look at what the viable Marketplace is
+for cc us now
+
+ align:start position:0%
+for cc us now
+ 
+
+ align:start position:0%
+for cc us now
+and they also do this I think useful
+
+ align:start position:0%
+and they also do this I think useful
+ 
+
+ align:start position:0%
+and they also do this I think useful
+graphic just showing potential
+
+ align:start position:0%
+graphic just showing potential
+ 
+
+ align:start position:0%
+graphic just showing potential
+industrial sources for carbon capture
+
+ align:start position:0%
+industrial sources for carbon capture
+ 
+
+ align:start position:0%
+industrial sources for carbon capture
+use in storage there's many plentiful uh
+
+ align:start position:0%
+use in storage there's many plentiful uh
+ 
+
+ align:start position:0%
+use in storage there's many plentiful uh
+sources you can see they have the sector
+
+ align:start position:0%
+sources you can see they have the sector
+ 
+
+ align:start position:0%
+sources you can see they have the sector
+here our heavy Industries High Purity
+
+ align:start position:0%
+here our heavy Industries High Purity
+ 
+
+ align:start position:0%
+here our heavy Industries High Purity
+industrial Point sources and diffuse and
+
+ align:start position:0%
+industrial Point sources and diffuse and
+ 
+
+ align:start position:0%
+industrial Point sources and diffuse and
+mobile emissions and they have a number
+
+ align:start position:0%
+mobile emissions and they have a number
+ 
+
+ align:start position:0%
+mobile emissions and they have a number
+of sites here so we actually have
+
+ align:start position:0%
+of sites here so we actually have
+ 
+
+ align:start position:0%
+of sites here so we actually have
+1400 sites for power those are
+
+ align:start position:0%
+1400 sites for power those are
+ 
+
+ align:start position:0%
+1400 sites for power those are
+essentially power plants average
+
+ align:start position:0%
+essentially power plants average
+ 
+
+ align:start position:0%
+essentially power plants average
+emissions per site in terms of the mega
+
+ align:start position:0%
+emissions per site in terms of the mega
+ 
+
+ align:start position:0%
+emissions per site in terms of the mega
+tons of CO2 are 1.3 it's very hard to
+
+ align:start position:0%
+tons of CO2 are 1.3 it's very hard to
+ 
+
+ align:start position:0%
+tons of CO2 are 1.3 it's very hard to
+capture a CO2 from heavy industry and
+
+ align:start position:0%
+capture a CO2 from heavy industry and
+ 
+
+ align:start position:0%
+capture a CO2 from heavy industry and
+from high Purity in-depthal Point
+
+ align:start position:0%
+from high Purity in-depthal Point
+ 
+
+ align:start position:0%
+from high Purity in-depthal Point
+sources because their emissions per site
+
+ align:start position:0%
+sources because their emissions per site
+ 
+
+ align:start position:0%
+sources because their emissions per site
+is quite low so you have to build all
+
+ align:start position:0%
+is quite low so you have to build all
+ 
+
+ align:start position:0%
+is quite low so you have to build all
+the same infrastructure or it may not be
+
+ align:start position:0%
+the same infrastructure or it may not be
+ 
+
+ align:start position:0%
+the same infrastructure or it may not be
+worth building infrastructure just to
+
+ align:start position:0%
+worth building infrastructure just to
+ 
+
+ align:start position:0%
+worth building infrastructure just to
+capture the low vision per site of
+
+ align:start position:0%
+capture the low vision per site of
+ 
+
+ align:start position:0%
+capture the low vision per site of
+course it's very hard to capture CO2
+
+ align:start position:0%
+course it's very hard to capture CO2
+ 
+
+ align:start position:0%
+course it's very hard to capture CO2
+from diffuse or mobile emissions
+
+ align:start position:0%
+from diffuse or mobile emissions
+ 
+
+ align:start position:0%
+from diffuse or mobile emissions
+if we look at the work of David Keith a
+
+ align:start position:0%
+if we look at the work of David Keith a
+ 
+
+ align:start position:0%
+if we look at the work of David Keith a
+professor both of biophysics and policy
+
+ align:start position:0%
+professor both of biophysics and policy
+ 
+
+ align:start position:0%
+professor both of biophysics and policy
+at Harvard he has a firm with many
+
+ align:start position:0%
+at Harvard he has a firm with many
+ 
+
+ align:start position:0%
+at Harvard he has a firm with many
+people working for department of
+
+ align:start position:0%
+people working for department of
+ 
+
+ align:start position:0%
+people working for department of
+engineering and this is what the subject
+
+ align:start position:0%
+engineering and this is what the subject
+ 
+
+ align:start position:0%
+engineering and this is what the subject
+of the David Roberts article was which
+
+ align:start position:0%
+of the David Roberts article was which
+ 
+
+ align:start position:0%
+of the David Roberts article was which
+is what the viable uses of direct air
+
+ align:start position:0%
+is what the viable uses of direct air
+ 
+
+ align:start position:0%
+is what the viable uses of direct air
+capture might be as he points out in
+
+ align:start position:0%
+capture might be as he points out in
+ 
+
+ align:start position:0%
+capture might be as he points out in
+this article it may not necessarily
+
+ align:start position:0%
+this article it may not necessarily
+ 
+
+ align:start position:0%
+this article it may not necessarily
+solve climate change it's not a silver
+
+ align:start position:0%
+solve climate change it's not a silver
+ 
+
+ align:start position:0%
+solve climate change it's not a silver
+bullet but there are interesting use
+
+ align:start position:0%
+bullet but there are interesting use
+ 
+
+ align:start position:0%
+bullet but there are interesting use
+cases that are actually promising
+
+ align:start position:0%
+cases that are actually promising
+ 
+
+ align:start position:0%
+cases that are actually promising
+developments
+
+ align:start position:0%
+developments
+ 
+
+ align:start position:0%
+developments
+so one particular case now this is just
+
+ align:start position:0%
+so one particular case now this is just
+ 
+
+ align:start position:0%
+so one particular case now this is just
+my carbon engineering website you can
+
+ align:start position:0%
+my carbon engineering website you can
+ 
+
+ align:start position:0%
+my carbon engineering website you can
+see that they have the solution called
+
+ align:start position:0%
+see that they have the solution called
+ 
+
+ align:start position:0%
+see that they have the solution called
+air to Fuels and that their carbon
+
+ align:start position:0%
+air to Fuels and that their carbon
+ 
+
+ align:start position:0%
+air to Fuels and that their carbon
+Engineering Process and direct air
+
+ align:start position:0%
+Engineering Process and direct air
+ 
+
+ align:start position:0%
+Engineering Process and direct air
+capture is a way of delivering synthetic
+
+ align:start position:0%
+capture is a way of delivering synthetic
+ 
+
+ align:start position:0%
+capture is a way of delivering synthetic
+Ultra load private fuels such as
+
+ align:start position:0%
+Ultra load private fuels such as
+ 
+
+ align:start position:0%
+Ultra load private fuels such as
+gasoline Diesel and Jet Jet fuels out of
+
+ align:start position:0%
+gasoline Diesel and Jet Jet fuels out of
+ 
+
+ align:start position:0%
+gasoline Diesel and Jet Jet fuels out of
+air I'm sorry jet a grade fuel uh fuel
+
+ align:start position:0%
+air I'm sorry jet a grade fuel uh fuel
+ 
+
+ align:start position:0%
+air I'm sorry jet a grade fuel uh fuel
+out of air water and renewable
+
+ align:start position:0%
+out of air water and renewable
+ 
+
+ align:start position:0%
+out of air water and renewable
+electricity this is the air to fuel
+
+ align:start position:0%
+electricity this is the air to fuel
+ 
+
+ align:start position:0%
+electricity this is the air to fuel
+solution that Roberts talks about in his
+
+ align:start position:0%
+solution that Roberts talks about in his
+ 
+
+ align:start position:0%
+solution that Roberts talks about in his
+article
+
+ align:start position:0%
+article
+ 
+
+ align:start position:0%
+article
+uh if you look at how this works we have
+
+ align:start position:0%
+uh if you look at how this works we have
+ 
+
+ align:start position:0%
+uh if you look at how this works we have
+CO2 in the atmosphere we capture it
+
+ align:start position:0%
+CO2 in the atmosphere we capture it
+ 
+
+ align:start position:0%
+CO2 in the atmosphere we capture it
+through direct air capture we take the
+
+ align:start position:0%
+through direct air capture we take the
+ 
+
+ align:start position:0%
+through direct air capture we take the
+atmospheric CO2 put into a fuel
+
+ align:start position:0%
+atmospheric CO2 put into a fuel
+ 
+
+ align:start position:0%
+atmospheric CO2 put into a fuel
+synthesis and we put in electricity a
+
+ align:start position:0%
+synthesis and we put in electricity a
+ 
+
+ align:start position:0%
+synthesis and we put in electricity a
+renewable electricity and water and we
+
+ align:start position:0%
+renewable electricity and water and we
+ 
+
+ align:start position:0%
+renewable electricity and water and we
+get Ultra load carbon fuels out of it so
+
+ align:start position:0%
+get Ultra load carbon fuels out of it so
+ 
+
+ align:start position:0%
+get Ultra load carbon fuels out of it so
+this is if this is not necessarily a
+
+ align:start position:0%
+this is if this is not necessarily a
+ 
+
+ align:start position:0%
+this is if this is not necessarily a
+carbon negative process it is at least
+
+ align:start position:0%
+carbon negative process it is at least
+ 
+
+ align:start position:0%
+carbon negative process it is at least
+at best a compartment neutral process or
+
+ align:start position:0%
+at best a compartment neutral process or
+ 
+
+ align:start position:0%
+at best a compartment neutral process or
+a way of providing ultra low carbon
+
+ align:start position:0%
+a way of providing ultra low carbon
+ 
+
+ align:start position:0%
+a way of providing ultra low carbon
+fuels and as the Roberts article points
+
+ align:start position:0%
+fuels and as the Roberts article points
+ 
+
+ align:start position:0%
+fuels and as the Roberts article points
+out there are states or there are policy
+
+ align:start position:0%
+out there are states or there are policy
+ 
+
+ align:start position:0%
+out there are states or there are policy
+situations like California's ultra low
+
+ align:start position:0%
+situations like California's ultra low
+ 
+
+ align:start position:0%
+situations like California's ultra low
+fuel standard where this may make this
+
+ align:start position:0%
+fuel standard where this may make this
+ 
+
+ align:start position:0%
+fuel standard where this may make this
+economically viable to produce this hard
+
+ align:start position:0%
+economically viable to produce this hard
+ 
+
+ align:start position:0%
+economically viable to produce this hard
+fuel in this way and it may make
+
+ align:start position:0%
+fuel in this way and it may make
+ 
+
+ align:start position:0%
+fuel in this way and it may make
+economically viable for one large actor
+
+ align:start position:0%
+economically viable for one large actor
+ 
+
+ align:start position:0%
+economically viable for one large actor
+to sign a power purchase agreement to
+
+ align:start position:0%
+to sign a power purchase agreement to
+ 
+
+ align:start position:0%
+to sign a power purchase agreement to
+buy a set amount of ultra low carbon
+
+ align:start position:0%
+buy a set amount of ultra low carbon
+ 
+
+ align:start position:0%
+buy a set amount of ultra low carbon
+fuels
+
+ align:start position:0%
+fuels
+ 
+
+ align:start position:0%
+fuels
+are there possibilities for the direct
+
+ align:start position:0%
+are there possibilities for the direct
+ 
+
+ align:start position:0%
+are there possibilities for the direct
+aircraft to technology that carbon
+
+ align:start position:0%
+aircraft to technology that carbon
+ 
+
+ align:start position:0%
+aircraft to technology that carbon
+engineering is developing is sucking
+
+ align:start position:0%
+engineering is developing is sucking
+ 
+
+ align:start position:0%
+engineering is developing is sucking
+carbonate out of the atmosphere directly
+
+ align:start position:0%
+carbonate out of the atmosphere directly
+ 
+
+ align:start position:0%
+carbonate out of the atmosphere directly
+to correct air factor I think it's
+
+ align:start position:0%
+to correct air factor I think it's
+ 
+
+ align:start position:0%
+to correct air factor I think it's
+permanent geological storage instead of
+
+ align:start position:0%
+permanent geological storage instead of
+ 
+
+ align:start position:0%
+permanent geological storage instead of
+the pipeline I showed you in the
+
+ align:start position:0%
+the pipeline I showed you in the
+ 
+
+ align:start position:0%
+the pipeline I showed you in the
+previous diagram it would just be the
+
+ align:start position:0%
+previous diagram it would just be the
+ 
+
+ align:start position:0%
+previous diagram it would just be the
+direct air capture technology instead of
+
+ align:start position:0%
+direct air capture technology instead of
+ 
+
+ align:start position:0%
+direct air capture technology instead of
+apparently piloting I think in British
+
+ align:start position:0%
+apparently piloting I think in British
+ 
+
+ align:start position:0%
+apparently piloting I think in British
+Columbia
+
+ align:start position:0%
+Columbia
+ 
+
+ align:start position:0%
+Columbia
+another possibility is what I mentioned
+
+ align:start position:0%
+another possibility is what I mentioned
+ 
+
+ align:start position:0%
+another possibility is what I mentioned
+before enhanced oil recovery you take
+
+ align:start position:0%
+before enhanced oil recovery you take
+ 
+
+ align:start position:0%
+before enhanced oil recovery you take
+atmospheric CO2 capture from direct air
+
+ align:start position:0%
+atmospheric CO2 capture from direct air
+ 
+
+ align:start position:0%
+atmospheric CO2 capture from direct air
+capture you can permanently store this
+
+ align:start position:0%
+capture you can permanently store this
+ 
+
+ align:start position:0%
+capture you can permanently store this
+in oil reservoir of the current oil
+
+ align:start position:0%
+in oil reservoir of the current oil
+ 
+
+ align:start position:0%
+in oil reservoir of the current oil
+production this is one situation that
+
+ align:start position:0%
+production this is one situation that
+ 
+
+ align:start position:0%
+production this is one situation that
+I've always been a little skeptical of
+
+ align:start position:0%
+I've always been a little skeptical of
+ 
+
+ align:start position:0%
+I've always been a little skeptical of
+that you know you can basically drive so
+
+ align:start position:0%
+that you know you can basically drive so
+ 
+
+ align:start position:0%
+that you know you can basically drive so
+much CO2 into the oil reservoir you can
+
+ align:start position:0%
+much CO2 into the oil reservoir you can
+ 
+
+ align:start position:0%
+much CO2 into the oil reservoir you can
+pump out the oil and somehow that still
+
+ align:start position:0%
+pump out the oil and somehow that still
+ 
+
+ align:start position:0%
+pump out the oil and somehow that still
+result in a low carbon fuel standard but
+
+ align:start position:0%
+result in a low carbon fuel standard but
+ 
+
+ align:start position:0%
+result in a low carbon fuel standard but
+you know if it had sold out if the
+
+ align:start position:0%
+you know if it had sold out if the
+ 
+
+ align:start position:0%
+you know if it had sold out if the
+calculations work out there's been more
+
+ align:start position:0%
+calculations work out there's been more
+ 
+
+ align:start position:0%
+calculations work out there's been more
+than one or two startups trying to do
+
+ align:start position:0%
+than one or two startups trying to do
+ 
+
+ align:start position:0%
+than one or two startups trying to do
+enhanced oil recovery using CO2 or
+
+ align:start position:0%
+enhanced oil recovery using CO2 or
+ 
+
+ align:start position:0%
+enhanced oil recovery using CO2 or
+trying to show that it could be a carbon
+
+ align:start position:0%
+trying to show that it could be a carbon
+ 
+
+ align:start position:0%
+trying to show that it could be a carbon
+neutral or carbon negative process
+
+ align:start position:0%
+neutral or carbon negative process
+ 
+
+ align:start position:0%
+neutral or carbon negative process
+and so we just destroy the diagram for
+
+ align:start position:0%
+and so we just destroy the diagram for
+ 
+
+ align:start position:0%
+and so we just destroy the diagram for
+the cover engineering website in this
+
+ align:start position:0%
+the cover engineering website in this
+ 
+
+ align:start position:0%
+the cover engineering website in this
+situation we have CO2 in the atmosphere
+
+ align:start position:0%
+situation we have CO2 in the atmosphere
+ 
+
+ align:start position:0%
+situation we have CO2 in the atmosphere
+we capture the director capture we
+
+ align:start position:0%
+we capture the director capture we
+ 
+
+ align:start position:0%
+we capture the director capture we
+inject it into a oil reservoir we
+
+ align:start position:0%
+inject it into a oil reservoir we
+ 
+
+ align:start position:0%
+inject it into a oil reservoir we
+actually get more crude oil out we
+
+ align:start position:0%
+actually get more crude oil out we
+ 
+
+ align:start position:0%
+actually get more crude oil out we
+refine it and we get fossil fuels put it
+
+ align:start position:0%
+refine it and we get fossil fuels put it
+ 
+
+ align:start position:0%
+refine it and we get fossil fuels put it
+into our existing infrastructure this is
+
+ align:start position:0%
+into our existing infrastructure this is
+ 
+
+ align:start position:0%
+into our existing infrastructure this is
+also meant to try to meet from the ultra
+
+ align:start position:0%
+also meant to try to meet from the ultra
+ 
+
+ align:start position:0%
+also meant to try to meet from the ultra
+low carbon fuel standards
+
+ align:start position:0%
+low carbon fuel standards
+ 
+
+ align:start position:0%
+low carbon fuel standards
+this brings me to Sprite to negative
+
+ align:start position:0%
+this brings me to Sprite to negative
+ 
+
+ align:start position:0%
+this brings me to Sprite to negative
+emissions commitment this is a project
+
+ align:start position:0%
+emissions commitment this is a project
+ 
+
+ align:start position:0%
+emissions commitment this is a project
+I've been following for a couple years
+
+ align:start position:0%
+I've been following for a couple years
+ 
+
+ align:start position:0%
+I've been following for a couple years
+and many people have been following
+
+ align:start position:0%
+and many people have been following
+ 
+
+ align:start position:0%
+and many people have been following
+stripe as you may know is an online
+
+ align:start position:0%
+stripe as you may know is an online
+ 
+
+ align:start position:0%
+stripe as you may know is an online
+payments company but in 2020 or 2019 I
+
+ align:start position:0%
+payments company but in 2020 or 2019 I
+ 
+
+ align:start position:0%
+payments company but in 2020 or 2019 I
+think they announced their negative
+
+ align:start position:0%
+think they announced their negative
+ 
+
+ align:start position:0%
+think they announced their negative
+admissions commitment which is when they
+
+ align:start position:0%
+admissions commitment which is when they
+ 
+
+ align:start position:0%
+admissions commitment which is when they
+pledge to pay one million dollars per
+
+ align:start position:0%
+pledge to pay one million dollars per
+ 
+
+ align:start position:0%
+pledge to pay one million dollars per
+year at any price the direct removal of
+
+ align:start position:0%
+year at any price the direct removal of
+ 
+
+ align:start position:0%
+year at any price the direct removal of
+carbon dioxide in the atmosphere and
+
+ align:start position:0%
+carbon dioxide in the atmosphere and
+ 
+
+ align:start position:0%
+carbon dioxide in the atmosphere and
+sequestration and long-term storage they
+
+ align:start position:0%
+sequestration and long-term storage they
+ 
+
+ align:start position:0%
+sequestration and long-term storage they
+built up a small team to evaluate
+
+ align:start position:0%
+built up a small team to evaluate
+ 
+
+ align:start position:0%
+built up a small team to evaluate
+different carbon removal Technologies
+
+ align:start position:0%
+different carbon removal Technologies
+ 
+
+ align:start position:0%
+different carbon removal Technologies
+and in 2020 they announced their first
+
+ align:start position:0%
+and in 2020 they announced their first
+ 
+
+ align:start position:0%
+and in 2020 they announced their first
+carbon removal purchases this was
+
+ align:start position:0%
+carbon removal purchases this was
+ 
+
+ align:start position:0%
+carbon removal purchases this was
+essentially a commitment the company
+
+ align:start position:0%
+essentially a commitment the company
+ 
+
+ align:start position:0%
+essentially a commitment the company
+made to try to pay money to start to
+
+ align:start position:0%
+made to try to pay money to start to
+ 
+
+ align:start position:0%
+made to try to pay money to start to
+Foster or start to build the market for
+
+ align:start position:0%
+Foster or start to build the market for
+ 
+
+ align:start position:0%
+Foster or start to build the market for
+negative emissions or perform removal
+
+ align:start position:0%
+negative emissions or perform removal
+ 
+
+ align:start position:0%
+negative emissions or perform removal
+and so I think this is a project I've
+
+ align:start position:0%
+and so I think this is a project I've
+ 
+
+ align:start position:0%
+and so I think this is a project I've
+been very interested in because they're
+
+ align:start position:0%
+been very interested in because they're
+ 
+
+ align:start position:0%
+been very interested in because they're
+very transparent on the criteria are and
+
+ align:start position:0%
+very transparent on the criteria are and
+ 
+
+ align:start position:0%
+very transparent on the criteria are and
+they're very transparent about the
+
+ align:start position:0%
+they're very transparent about the
+ 
+
+ align:start position:0%
+they're very transparent about the
+technology they're trying to Foster and
+
+ align:start position:0%
+technology they're trying to Foster and
+ 
+
+ align:start position:0%
+technology they're trying to Foster and
+if you look at their website you can
+
+ align:start position:0%
+if you look at their website you can
+ 
+
+ align:start position:0%
+if you look at their website you can
+click on the purple link up here to see
+
+ align:start position:0%
+click on the purple link up here to see
+ 
+
+ align:start position:0%
+click on the purple link up here to see
+their website you will see that they
+
+ align:start position:0%
+their website you will see that they
+ 
+
+ align:start position:0%
+their website you will see that they
+actually have almost all of these
+
+ align:start position:0%
+actually have almost all of these
+ 
+
+ align:start position:0%
+actually have almost all of these
+submissions and they show exactly how
+
+ align:start position:0%
+submissions and they show exactly how
+ 
+
+ align:start position:0%
+submissions and they show exactly how
+they evaluated submissions and why
+
+ align:start position:0%
+they evaluated submissions and why
+ 
+
+ align:start position:0%
+they evaluated submissions and why
+they've picked a certain portfolio
+
+ align:start position:0%
+they've picked a certain portfolio
+ 
+
+ align:start position:0%
+they've picked a certain portfolio
+Technologies
+
+ align:start position:0%
+Technologies
+ 
+
+ align:start position:0%
+Technologies
+so uh their criteria I think are very
+
+ align:start position:0%
+so uh their criteria I think are very
+ 
+
+ align:start position:0%
+so uh their criteria I think are very
+clear they show what their criteria are
+
+ align:start position:0%
+clear they show what their criteria are
+ 
+
+ align:start position:0%
+clear they show what their criteria are
+whether or not it's possible today the
+
+ align:start position:0%
+whether or not it's possible today the
+ 
+
+ align:start position:0%
+whether or not it's possible today the
+target is by 2040. so they're very clear
+
+ align:start position:0%
+target is by 2040. so they're very clear
+ 
+
+ align:start position:0%
+target is by 2040. so they're very clear
+that vrx making these purchases could
+
+ align:start position:0%
+that vrx making these purchases could
+ 
+
+ align:start position:0%
+that vrx making these purchases could
+try to Foster these Technologies so the
+
+ align:start position:0%
+try to Foster these Technologies so the
+ 
+
+ align:start position:0%
+try to Foster these Technologies so the
+criteria are they want everything to be
+
+ align:start position:0%
+criteria are they want everything to be
+ 
+
+ align:start position:0%
+criteria are they want everything to be
+sequestered beyond the biosphere this
+
+ align:start position:0%
+sequestered beyond the biosphere this
+ 
+
+ align:start position:0%
+sequestered beyond the biosphere this
+fundamentally shows a very different
+
+ align:start position:0%
+fundamentally shows a very different
+ 
+
+ align:start position:0%
+fundamentally shows a very different
+approach than the peripheral uh carbon
+
+ align:start position:0%
+approach than the peripheral uh carbon
+ 
+
+ align:start position:0%
+approach than the peripheral uh carbon
+product brand challenge team from MIT
+
+ align:start position:0%
+product brand challenge team from MIT
+ 
+
+ align:start position:0%
+product brand challenge team from MIT
+and that stripe doesn't actually believe
+
+ align:start position:0%
+and that stripe doesn't actually believe
+ 
+
+ align:start position:0%
+and that stripe doesn't actually believe
+that sequestering uh uh carbon in the
+
+ align:start position:0%
+that sequestering uh uh carbon in the
+ 
+
+ align:start position:0%
+that sequestering uh uh carbon in the
+biosphere is going to be effective this
+
+ align:start position:0%
+biosphere is going to be effective this
+ 
+
+ align:start position:0%
+biosphere is going to be effective this
+is because if you store things in the
+
+ align:start position:0%
+is because if you store things in the
+ 
+
+ align:start position:0%
+is because if you store things in the
+biosphere it may actually lead to you
+
+ align:start position:0%
+biosphere it may actually lead to you
+ 
+
+ align:start position:0%
+biosphere it may actually lead to you
+might have wildfires in the future and
+
+ align:start position:0%
+might have wildfires in the future and
+ 
+
+ align:start position:0%
+might have wildfires in the future and
+now I simply get rid of or obvious the
+
+ align:start position:0%
+now I simply get rid of or obvious the
+ 
+
+ align:start position:0%
+now I simply get rid of or obvious the
+effects of these carbon capture as sort
+
+ align:start position:0%
+effects of these carbon capture as sort
+ 
+
+ align:start position:0%
+effects of these carbon capture as sort
+of signature they also typically add
+
+ align:start position:0%
+of signature they also typically add
+ 
+
+ align:start position:0%
+of signature they also typically add
+very Silicon Valley Way evaluate whether
+
+ align:start position:0%
+very Silicon Valley Way evaluate whether
+ 
+
+ align:start position:0%
+very Silicon Valley Way evaluate whether
+or not this technology has a path to be
+
+ align:start position:0%
+or not this technology has a path to be
+ 
+
+ align:start position:0%
+or not this technology has a path to be
+a meaningful part of the carbon removal
+
+ align:start position:0%
+a meaningful part of the carbon removal
+ 
+
+ align:start position:0%
+a meaningful part of the carbon removal
+solution portfolio where that you can
+
+ align:start position:0%
+solution portfolio where that you can
+ 
+
+ align:start position:0%
+solution portfolio where that you can
+achieve sufficient volume
+
+ align:start position:0%
+achieve sufficient volume
+ 
+
+ align:start position:0%
+achieve sufficient volume
+it has to have a path to achieving uh
+
+ align:start position:0%
+it has to have a path to achieving uh
+ 
+
+ align:start position:0%
+it has to have a path to achieving uh
+being affordable at scale it has to
+
+ align:start position:0%
+being affordable at scale it has to
+ 
+
+ align:start position:0%
+being affordable at scale it has to
+achieve permanent storage of carbon
+
+ align:start position:0%
+achieve permanent storage of carbon
+ 
+
+ align:start position:0%
+achieve permanent storage of carbon
+currently we can store for greater than
+
+ align:start position:0%
+currently we can store for greater than
+ 
+
+ align:start position:0%
+currently we can store for greater than
+a thousand years as they that's their
+
+ align:start position:0%
+a thousand years as they that's their
+ 
+
+ align:start position:0%
+a thousand years as they that's their
+Target in 2040 their target or cost is
+
+ align:start position:0%
+Target in 2040 their target or cost is
+ 
+
+ align:start position:0%
+Target in 2040 their target or cost is
+less than a hundred dollars on their
+
+ align:start position:0%
+less than a hundred dollars on their
+ 
+
+ align:start position:0%
+less than a hundred dollars on their
+volume has to be a minimum of 0.5 bigot
+
+ align:start position:0%
+volume has to be a minimum of 0.5 bigot
+ 
+
+ align:start position:0%
+volume has to be a minimum of 0.5 bigot
+tons per year
+
+ align:start position:0%
+tons per year
+ 
+
+ align:start position:0%
+tons per year
+and the criteria are that the carbon
+
+ align:start position:0%
+and the criteria are that the carbon
+ 
+
+ align:start position:0%
+and the criteria are that the carbon
+sequestration have to be scientifically
+
+ align:start position:0%
+sequestration have to be scientifically
+ 
+
+ align:start position:0%
+sequestration have to be scientifically
+rigorous and transparent for
+
+ align:start position:0%
+rigorous and transparent for
+ 
+
+ align:start position:0%
+rigorous and transparent for
+verifiability
+
+ align:start position:0%
+verifiability
+ 
+
+ align:start position:0%
+verifiability
+it has to meet standards for quality and
+
+ align:start position:0%
+it has to meet standards for quality and
+ 
+
+ align:start position:0%
+it has to meet standards for quality and
+safety and be globally responsible and
+
+ align:start position:0%
+safety and be globally responsible and
+ 
+
+ align:start position:0%
+safety and be globally responsible and
+it has to have a net negative life cycle
+
+ align:start position:0%
+it has to have a net negative life cycle
+ 
+
+ align:start position:0%
+it has to have a net negative life cycle
+So currently we have a negativity ratio
+
+ align:start position:0%
+So currently we have a negativity ratio
+ 
+
+ align:start position:0%
+So currently we have a negativity ratio
+like this is reducing net atmospheric
+
+ align:start position:0%
+like this is reducing net atmospheric
+ 
+
+ align:start position:0%
+like this is reducing net atmospheric
+CO2
+
+ align:start position:0%
+CO2
+ 
+
+ align:start position:0%
+CO2
+expresses a ratio subject to appropriate
+
+ align:start position:0%
+expresses a ratio subject to appropriate
+ 
+
+ align:start position:0%
+expresses a ratio subject to appropriate
+boundary conditions this is currently a
+
+ align:start position:0%
+boundary conditions this is currently a
+ 
+
+ align:start position:0%
+boundary conditions this is currently a
+negativity ratio of less than or equal
+
+ align:start position:0%
+negativity ratio of less than or equal
+ 
+
+ align:start position:0%
+negativity ratio of less than or equal
+to one and of course in the future they
+
+ align:start position:0%
+to one and of course in the future they
+ 
+
+ align:start position:0%
+to one and of course in the future they
+want negativity ratio of less than one
+
+ align:start position:0%
+want negativity ratio of less than one
+ 
+
+ align:start position:0%
+want negativity ratio of less than one
+they want to get a net negative life
+
+ align:start position:0%
+they want to get a net negative life
+ 
+
+ align:start position:0%
+they want to get a net negative life
+cycle or the showing that we have net
+
+ align:start position:0%
+cycle or the showing that we have net
+ 
+
+ align:start position:0%
+cycle or the showing that we have net
+atmospheric carbon removed so this is
+
+ align:start position:0%
+atmospheric carbon removed so this is
+ 
+
+ align:start position:0%
+atmospheric carbon removed so this is
+what you know stripe is paying for in
+
+ align:start position:0%
+what you know stripe is paying for in
+ 
+
+ align:start position:0%
+what you know stripe is paying for in
+the first year they picked four
+
+ align:start position:0%
+the first year they picked four
+ 
+
+ align:start position:0%
+the first year they picked four
+Technologies I think ranging about 16
+
+ align:start position:0%
+Technologies I think ranging about 16
+ 
+
+ align:start position:0%
+Technologies I think ranging about 16
+per kind about six hundred dollars per
+
+ align:start position:0%
+per kind about six hundred dollars per
+ 
+
+ align:start position:0%
+per kind about six hundred dollars per
+ton simply because they had a portfolio
+
+ align:start position:0%
+ton simply because they had a portfolio
+ 
+
+ align:start position:0%
+ton simply because they had a portfolio
+they're trying to venture capital way
+
+ align:start position:0%
+they're trying to venture capital way
+ 
+
+ align:start position:0%
+they're trying to venture capital way
+they're into new technologies to for
+
+ align:start position:0%
+they're into new technologies to for
+ 
+
+ align:start position:0%
+they're into new technologies to for
+negative emissions
+
+ align:start position:0%
+negative emissions
+ 
+
+ align:start position:0%
+negative emissions
+and I I just to encourage you all to
+
+ align:start position:0%
+and I I just to encourage you all to
+ 
+
+ align:start position:0%
+and I I just to encourage you all to
+consider this to make context of your
+
+ align:start position:0%
+consider this to make context of your
+ 
+
+ align:start position:0%
+consider this to make context of your
+future careers they say it's a call to
+
+ align:start position:0%
+future careers they say it's a call to
+ 
+
+ align:start position:0%
+future careers they say it's a call to
+action the goal is not only to remove
+
+ align:start position:0%
+action the goal is not only to remove
+ 
+
+ align:start position:0%
+action the goal is not only to remove
+carbon from the atmosphere but to create
+
+ align:start position:0%
+carbon from the atmosphere but to create
+ 
+
+ align:start position:0%
+carbon from the atmosphere but to create
+a ecosystem of funders and Founders that
+
+ align:start position:0%
+a ecosystem of funders and Founders that
+ 
+
+ align:start position:0%
+a ecosystem of funders and Founders that
+will invent ways to solve the world's
+
+ align:start position:0%
+will invent ways to solve the world's
+ 
+
+ align:start position:0%
+will invent ways to solve the world's
+largest action problem or continue to
+
+ align:start position:0%
+largest action problem or continue to
+ 
+
+ align:start position:0%
+largest action problem or continue to
+search for Creative projects and experts
+
+ align:start position:0%
+search for Creative projects and experts
+ 
+
+ align:start position:0%
+search for Creative projects and experts
+reach out to us to work together on this
+
+ align:start position:0%
+reach out to us to work together on this
+ 
+
+ align:start position:0%
+reach out to us to work together on this
+effort or give any feedback and if
+
+ align:start position:0%
+effort or give any feedback and if
+ 
+
+ align:start position:0%
+effort or give any feedback and if
+you're an engineer or designer who cares
+
+ align:start position:0%
+you're an engineer or designer who cares
+ 
+
+ align:start position:0%
+you're an engineer or designer who cares
+about climate impact consider joining
+
+ align:start position:0%
+about climate impact consider joining
+ 
+
+ align:start position:0%
+about climate impact consider joining
+their team
+
+ align:start position:0%
+their team
+ 
+
+ align:start position:0%
+their team
+this has in the last two years Advanced
+
+ align:start position:0%
+this has in the last two years Advanced
+ 
+
+ align:start position:0%
+this has in the last two years Advanced
+even further you see this new uh
+
+ align:start position:0%
+even further you see this new uh
+ 
+
+ align:start position:0%
+even further you see this new uh
+commitment pulse Frontier led by stripe
+
+ align:start position:0%
+commitment pulse Frontier led by stripe
+ 
+
+ align:start position:0%
+commitment pulse Frontier led by stripe
+but joined by alphabet Shopify meta and
+
+ align:start position:0%
+but joined by alphabet Shopify meta and
+ 
+
+ align:start position:0%
+but joined by alphabet Shopify meta and
+McKinsey company these are not small
+
+ align:start position:0%
+McKinsey company these are not small
+ 
+
+ align:start position:0%
+McKinsey company these are not small
+companies this is essentially taking
+
+ align:start position:0%
+companies this is essentially taking
+ 
+
+ align:start position:0%
+companies this is essentially taking
+Stripes negative emissions commitment
+
+ align:start position:0%
+Stripes negative emissions commitment
+ 
+
+ align:start position:0%
+Stripes negative emissions commitment
+and expanding it even further what they
+
+ align:start position:0%
+and expanding it even further what they
+ 
+
+ align:start position:0%
+and expanding it even further what they
+call what they have said this basically
+
+ align:start position:0%
+call what they have said this basically
+ 
+
+ align:start position:0%
+call what they have said this basically
+a negative emissions commitment is is
+
+ align:start position:0%
+a negative emissions commitment is is
+ 
+
+ align:start position:0%
+a negative emissions commitment is is
+called an advanced Market commitment to
+
+ align:start position:0%
+called an advanced Market commitment to
+ 
+
+ align:start position:0%
+called an advanced Market commitment to
+accelerate carbon removal it's an
+
+ align:start position:0%
+accelerate carbon removal it's an
+ 
+
+ align:start position:0%
+accelerate carbon removal it's an
+advanced Market commitment because
+
+ align:start position:0%
+advanced Market commitment because
+ 
+
+ align:start position:0%
+advanced Market commitment because
+you're making the market by pledging
+
+ align:start position:0%
+you're making the market by pledging
+ 
+
+ align:start position:0%
+you're making the market by pledging
+money going forward by pledging the
+
+ align:start position:0%
+money going forward by pledging the
+ 
+
+ align:start position:0%
+money going forward by pledging the
+money is what's going to get people to
+
+ align:start position:0%
+money is what's going to get people to
+ 
+
+ align:start position:0%
+money is what's going to get people to
+enter the market with a long-term
+
+ align:start position:0%
+enter the market with a long-term
+ 
+
+ align:start position:0%
+enter the market with a long-term
+commitment to develop new technologies
+
+ align:start position:0%
+commitment to develop new technologies
+ 
+
+ align:start position:0%
+commitment to develop new technologies
+so scaling up from scribe's original one
+
+ align:start position:0%
+so scaling up from scribe's original one
+ 
+
+ align:start position:0%
+so scaling up from scribe's original one
+million dollar purchase in 2020 Frontier
+
+ align:start position:0%
+million dollar purchase in 2020 Frontier
+ 
+
+ align:start position:0%
+million dollar purchase in 2020 Frontier
+is an alliance to pay all this company
+
+ align:start position:0%
+is an alliance to pay all this company
+ 
+
+ align:start position:0%
+is an alliance to pay all this company
+is led by stripe which is Advanced
+
+ align:start position:0%
+is led by stripe which is Advanced
+ 
+
+ align:start position:0%
+is led by stripe which is Advanced
+Market committed to buy initial 925
+
+ align:start position:0%
+Market committed to buy initial 925
+ 
+
+ align:start position:0%
+Market committed to buy initial 925
+million dollars of primary carpet
+
+ align:start position:0%
+million dollars of primary carpet
+ 
+
+ align:start position:0%
+million dollars of primary carpet
+removal between 2022 and 2030. tens of
+
+ align:start position:0%
+removal between 2022 and 2030. tens of
+ 
+
+ align:start position:0%
+removal between 2022 and 2030. tens of
+thousands of businesses have joined
+
+ align:start position:0%
+thousands of businesses have joined
+ 
+
+ align:start position:0%
+thousands of businesses have joined
+stripe because stripe re quickly
+
+ align:start position:0%
+stripe because stripe re quickly
+ 
+
+ align:start position:0%
+stripe because stripe re quickly
+realized they're building a platform for
+
+ align:start position:0%
+realized they're building a platform for
+ 
+
+ align:start position:0%
+realized they're building a platform for
+negative emissions commitment and other
+
+ align:start position:0%
+negative emissions commitment and other
+ 
+
+ align:start position:0%
+negative emissions commitment and other
+companies wanted an easy way to try to
+
+ align:start position:0%
+companies wanted an easy way to try to
+ 
+
+ align:start position:0%
+companies wanted an easy way to try to
+do negative missions in a way that was
+
+ align:start position:0%
+do negative missions in a way that was
+ 
+
+ align:start position:0%
+do negative missions in a way that was
+verifiable perhaps more verifiable than
+
+ align:start position:0%
+verifiable perhaps more verifiable than
+ 
+
+ align:start position:0%
+verifiable perhaps more verifiable than
+a lot of our discussion around offsets
+
+ align:start position:0%
+a lot of our discussion around offsets
+ 
+
+ align:start position:0%
+a lot of our discussion around offsets
+so this brings us to another uh
+
+ align:start position:0%
+so this brings us to another uh
+ 
+
+ align:start position:0%
+so this brings us to another uh
+alternative feature for energy is this
+
+ align:start position:0%
+alternative feature for energy is this
+ 
+
+ align:start position:0%
+alternative feature for energy is this
+kind of question of nuclear and there's
+
+ align:start position:0%
+kind of question of nuclear and there's
+ 
+
+ align:start position:0%
+kind of question of nuclear and there's
+this uh I think silly question and I
+
+ align:start position:0%
+this uh I think silly question and I
+ 
+
+ align:start position:0%
+this uh I think silly question and I
+think
+
+ align:start position:0%
+think
+ 
+
+ align:start position:0%
+think
+um it was discussed recently in a
+
+ align:start position:0%
+um it was discussed recently in a
+ 
+
+ align:start position:0%
+um it was discussed recently in a
+podcast by David Roberts and others
+
+ align:start position:0%
+podcast by David Roberts and others
+ 
+
+ align:start position:0%
+podcast by David Roberts and others
+which is are you Pro or anti-nuclear is
+
+ align:start position:0%
+which is are you Pro or anti-nuclear is
+ 
+
+ align:start position:0%
+which is are you Pro or anti-nuclear is
+essentially a silly question you can
+
+ align:start position:0%
+essentially a silly question you can
+ 
+
+ align:start position:0%
+essentially a silly question you can
+make Pro or anti-arguments and we'll
+
+ align:start position:0%
+make Pro or anti-arguments and we'll
+ 
+
+ align:start position:0%
+make Pro or anti-arguments and we'll
+talk about those uh but there's maybe
+
+ align:start position:0%
+talk about those uh but there's maybe
+ 
+
+ align:start position:0%
+talk about those uh but there's maybe
+other ways we should think about it on
+
+ align:start position:0%
+other ways we should think about it on
+ 
+
+ align:start position:0%
+other ways we should think about it on
+the pro side the support team the point
+
+ align:start position:0%
+the pro side the support team the point
+ 
+
+ align:start position:0%
+the pro side the support team the point
+at all 2018 paper that I assigned for
+
+ align:start position:0%
+at all 2018 paper that I assigned for
+ 
+
+ align:start position:0%
+at all 2018 paper that I assigned for
+today makes convincing argument that
+
+ align:start position:0%
+today makes convincing argument that
+ 
+
+ align:start position:0%
+today makes convincing argument that
+it'll be more expensive to achieve
+
+ align:start position:0%
+it'll be more expensive to achieve
+ 
+
+ align:start position:0%
+it'll be more expensive to achieve
+decarbonization without firm resources
+
+ align:start position:0%
+decarbonization without firm resources
+ 
+
+ align:start position:0%
+decarbonization without firm resources
+and just to add another uh reason why
+
+ align:start position:0%
+and just to add another uh reason why
+ 
+
+ align:start position:0%
+and just to add another uh reason why
+they don't they don't consider this
+
+ align:start position:0%
+they don't they don't consider this
+ 
+
+ align:start position:0%
+they don't they don't consider this
+paper land use we know that solar and
+
+ align:start position:0%
+paper land use we know that solar and
+ 
+
+ align:start position:0%
+paper land use we know that solar and
+wind are less energy dense we'll talk
+
+ align:start position:0%
+wind are less energy dense we'll talk
+ 
+
+ align:start position:0%
+wind are less energy dense we'll talk
+about that next week and we know land
+
+ align:start position:0%
+about that next week and we know land
+ 
+
+ align:start position:0%
+about that next week and we know land
+use and permitting may be a serious
+
+ align:start position:0%
+use and permitting may be a serious
+ 
+
+ align:start position:0%
+use and permitting may be a serious
+problem for Renewables having said that
+
+ align:start position:0%
+problem for Renewables having said that
+ 
+
+ align:start position:0%
+problem for Renewables having said that
+land use may also be a problem for new
+
+ align:start position:0%
+land use may also be a problem for new
+ 
+
+ align:start position:0%
+land use may also be a problem for new
+nuclear power plants
+
+ align:start position:0%
+nuclear power plants
+ 
+
+ align:start position:0%
+nuclear power plants
+but on arguments against nuclear are
+
+ align:start position:0%
+but on arguments against nuclear are
+ 
+
+ align:start position:0%
+but on arguments against nuclear are
+will nuclear power ever get cheaper and
+
+ align:start position:0%
+will nuclear power ever get cheaper and
+ 
+
+ align:start position:0%
+will nuclear power ever get cheaper and
+we'll go into that argument in a little
+
+ align:start position:0%
+we'll go into that argument in a little
+ 
+
+ align:start position:0%
+we'll go into that argument in a little
+bit and of course there's other reasons
+
+ align:start position:0%
+bit and of course there's other reasons
+ 
+
+ align:start position:0%
+bit and of course there's other reasons
+why we might not want to use nuclear
+
+ align:start position:0%
+why we might not want to use nuclear
+ 
+
+ align:start position:0%
+why we might not want to use nuclear
+power nuclear waste proliferation of
+
+ align:start position:0%
+power nuclear waste proliferation of
+ 
+
+ align:start position:0%
+power nuclear waste proliferation of
+nuclear technology our concerns or have
+
+ align:start position:0%
+nuclear technology our concerns or have
+ 
+
+ align:start position:0%
+nuclear technology our concerns or have
+always been concerned writing the
+
+ align:start position:0%
+always been concerned writing the
+ 
+
+ align:start position:0%
+always been concerned writing the
+technology
+
+ align:start position:0%
+technology
+ 
+
+ align:start position:0%
+technology
+the reason why I guess
+
+ align:start position:0%
+the reason why I guess
+ 
+
+ align:start position:0%
+the reason why I guess
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+we can argue that this Pro or
+
+ align:start position:0%
+we can argue that this Pro or
+ 
+
+ align:start position:0%
+we can argue that this Pro or
+anti-nuclear stance may be silly it's
+
+ align:start position:0%
+anti-nuclear stance may be silly it's
+ 
+
+ align:start position:0%
+anti-nuclear stance may be silly it's
+because there's a more useful way to
+
+ align:start position:0%
+because there's a more useful way to
+ 
+
+ align:start position:0%
+because there's a more useful way to
+think about some of our problems with
+
+ align:start position:0%
+think about some of our problems with
+ 
+
+ align:start position:0%
+think about some of our problems with
+nuclear power and whatnot is a viable
+
+ align:start position:0%
+nuclear power and whatnot is a viable
+ 
+
+ align:start position:0%
+nuclear power and whatnot is a viable
+alternative going forward first there's
+
+ align:start position:0%
+alternative going forward first there's
+ 
+
+ align:start position:0%
+alternative going forward first there's
+the problem of operating and maintaining
+
+ align:start position:0%
+the problem of operating and maintaining
+ 
+
+ align:start position:0%
+the problem of operating and maintaining
+the existing nuclear Fleet alignment
+
+ align:start position:0%
+the existing nuclear Fleet alignment
+ 
+
+ align:start position:0%
+the existing nuclear Fleet alignment
+2012 article about Diablo Canyon Hot
+
+ align:start position:0%
+2012 article about Diablo Canyon Hot
+ 
+
+ align:start position:0%
+2012 article about Diablo Canyon Hot
+thoughts on the problems with keeping
+
+ align:start position:0%
+thoughts on the problems with keeping
+ 
+
+ align:start position:0%
+thoughts on the problems with keeping
+that Diablo Canyon open having said that
+
+ align:start position:0%
+that Diablo Canyon open having said that
+ 
+
+ align:start position:0%
+that Diablo Canyon open having said that
+the state of California and the
+
+ align:start position:0%
+the state of California and the
+ 
+
+ align:start position:0%
+the state of California and the
+governors just recently
+
+ align:start position:0%
+governors just recently
+ 
+
+ align:start position:0%
+governors just recently
+reversed his position on trying to close
+
+ align:start position:0%
+reversed his position on trying to close
+ 
+
+ align:start position:0%
+reversed his position on trying to close
+the album Canyon because Diablo Canyon
+
+ align:start position:0%
+the album Canyon because Diablo Canyon
+ 
+
+ align:start position:0%
+the album Canyon because Diablo Canyon
+has to stay open to essentially provide
+
+ align:start position:0%
+has to stay open to essentially provide
+ 
+
+ align:start position:0%
+has to stay open to essentially provide
+a large Department of the state's
+
+ align:start position:0%
+a large Department of the state's
+ 
+
+ align:start position:0%
+a large Department of the state's
+renewable energy or clean energy and
+
+ align:start position:0%
+renewable energy or clean energy and
+ 
+
+ align:start position:0%
+renewable energy or clean energy and
+resources to meet their low carbon goals
+
+ align:start position:0%
+resources to meet their low carbon goals
+ 
+
+ align:start position:0%
+resources to meet their low carbon goals
+so we know we can operate maintain the
+
+ align:start position:0%
+so we know we can operate maintain the
+ 
+
+ align:start position:0%
+so we know we can operate maintain the
+existing new group that we have with
+
+ align:start position:0%
+existing new group that we have with
+ 
+
+ align:start position:0%
+existing new group that we have with
+some modification we know there's an
+
+ align:start position:0%
+some modification we know there's an
+ 
+
+ align:start position:0%
+some modification we know there's an
+existing risks but more recently a lot
+
+ align:start position:0%
+existing risks but more recently a lot
+ 
+
+ align:start position:0%
+existing risks but more recently a lot
+of environmentalists and policy analysts
+
+ align:start position:0%
+of environmentalists and policy analysts
+ 
+
+ align:start position:0%
+of environmentalists and policy analysts
+have come around to the idea of trying
+
+ align:start position:0%
+have come around to the idea of trying
+ 
+
+ align:start position:0%
+have come around to the idea of trying
+to operating and maintaining the
+
+ align:start position:0%
+to operating and maintaining the
+ 
+
+ align:start position:0%
+to operating and maintaining the
+existing particular Fleet
+
+ align:start position:0%
+existing particular Fleet
+ 
+
+ align:start position:0%
+existing particular Fleet
+here's the question of should we try to
+
+ align:start position:0%
+here's the question of should we try to
+ 
+
+ align:start position:0%
+here's the question of should we try to
+build new nuclear power plants with our
+
+ align:start position:0%
+build new nuclear power plants with our
+ 
+
+ align:start position:0%
+build new nuclear power plants with our
+existing technology and
+
+ align:start position:0%
+existing technology and
+ 
+
+ align:start position:0%
+existing technology and
+um mechanisms we have two new nuclear
+
+ align:start position:0%
+um mechanisms we have two new nuclear
+ 
+
+ align:start position:0%
+um mechanisms we have two new nuclear
+power plants in North constructing the
+
+ align:start position:0%
+power plants in North constructing the
+ 
+
+ align:start position:0%
+power plants in North constructing the
+us both in the south
+
+ align:start position:0%
+us both in the south
+ 
+
+ align:start position:0%
+us both in the south
+currently I think one is nine billion
+
+ align:start position:0%
+currently I think one is nine billion
+ 
+
+ align:start position:0%
+currently I think one is nine billion
+dollars over budget I'm not sure how
+
+ align:start position:0%
+dollars over budget I'm not sure how
+ 
+
+ align:start position:0%
+dollars over budget I'm not sure how
+much the other one is over budget
+
+ align:start position:0%
+much the other one is over budget
+ 
+
+ align:start position:0%
+much the other one is over budget
+there's the Vogel power plant and
+
+ align:start position:0%
+there's the Vogel power plant and
+ 
+
+ align:start position:0%
+there's the Vogel power plant and
+there's one in South Carolina also
+
+ align:start position:0%
+there's one in South Carolina also
+ 
+
+ align:start position:0%
+there's one in South Carolina also
+that's also considerably over budget the
+
+ align:start position:0%
+that's also considerably over budget the
+ 
+
+ align:start position:0%
+that's also considerably over budget the
+absolutely of nuclear power plants are
+
+ align:start position:0%
+absolutely of nuclear power plants are
+ 
+
+ align:start position:0%
+absolutely of nuclear power plants are
+the path of building nuclear power
+
+ align:start position:0%
+the path of building nuclear power
+ 
+
+ align:start position:0%
+the path of building nuclear power
+plants under budget or at least within
+
+ align:start position:0%
+plants under budget or at least within
+ 
+
+ align:start position:0%
+plants under budget or at least within
+budget has been terrible with our
+
+ align:start position:0%
+budget has been terrible with our
+ 
+
+ align:start position:0%
+budget has been terrible with our
+existing technology
+
+ align:start position:0%
+existing technology
+ 
+
+ align:start position:0%
+existing technology
+of course a third possibility is to
+
+ align:start position:0%
+of course a third possibility is to
+ 
+
+ align:start position:0%
+of course a third possibility is to
+build new nuclear with new technology
+
+ align:start position:0%
+build new nuclear with new technology
+ 
+
+ align:start position:0%
+build new nuclear with new technology
+and this is the alternative of small
+
+ align:start position:0%
+and this is the alternative of small
+ 
+
+ align:start position:0%
+and this is the alternative of small
+modular reactors that are quite quite
+
+ align:start position:0%
+modular reactors that are quite quite
+ 
+
+ align:start position:0%
+modular reactors that are quite quite
+often counted by nuclear enthusiasts
+
+ align:start position:0%
+often counted by nuclear enthusiasts
+ 
+
+ align:start position:0%
+often counted by nuclear enthusiasts
+this is something that needs to be
+
+ align:start position:0%
+this is something that needs to be
+ 
+
+ align:start position:0%
+this is something that needs to be
+researched it needs to be proven out
+
+ align:start position:0%
+researched it needs to be proven out
+ 
+
+ align:start position:0%
+researched it needs to be proven out
+these are all different problems we need
+
+ align:start position:0%
+these are all different problems we need
+ 
+
+ align:start position:0%
+these are all different problems we need
+to solve with nuclear power they're all
+
+ align:start position:0%
+to solve with nuclear power they're all
+ 
+
+ align:start position:0%
+to solve with nuclear power they're all
+possible solutions
+
+ align:start position:0%
+possible solutions
+ 
+
+ align:start position:0%
+possible solutions
+some uh for example the first one is
+
+ align:start position:0%
+some uh for example the first one is
+ 
+
+ align:start position:0%
+some uh for example the first one is
+probably the easiest to achieve the
+
+ align:start position:0%
+probably the easiest to achieve the
+ 
+
+ align:start position:0%
+probably the easiest to achieve the
+second one we have a terrible history
+
+ align:start position:0%
+second one we have a terrible history
+ 
+
+ align:start position:0%
+second one we have a terrible history
+with the third we would probably need to
+
+ align:start position:0%
+with the third we would probably need to
+ 
+
+ align:start position:0%
+with the third we would probably need to
+research the seeds I think possible to
+
+ align:start position:0%
+research the seeds I think possible to
+ 
+
+ align:start position:0%
+research the seeds I think possible to
+build many nuclear power plants with new
+
+ align:start position:0%
+build many nuclear power plants with new
+ 
+
+ align:start position:0%
+build many nuclear power plants with new
+technology in a more cost effective way
+
+ align:start position:0%
+technology in a more cost effective way
+ 
+
+ align:start position:0%
+technology in a more cost effective way
+but to give you a sense of some of my
+
+ align:start position:0%
+but to give you a sense of some of my
+ 
+
+ align:start position:0%
+but to give you a sense of some of my
+skepticism about nuclear I'm open to the
+
+ align:start position:0%
+skepticism about nuclear I'm open to the
+ 
+
+ align:start position:0%
+skepticism about nuclear I'm open to the
+idea but skeptical because of the past
+
+ align:start position:0%
+idea but skeptical because of the past
+ 
+
+ align:start position:0%
+idea but skeptical because of the past
+history we have in nuclear empowerment
+
+ align:start position:0%
+history we have in nuclear empowerment
+ 
+
+ align:start position:0%
+history we have in nuclear empowerment
+so let me show you some of the problems
+
+ align:start position:0%
+so let me show you some of the problems
+ 
+
+ align:start position:0%
+so let me show you some of the problems
+we've had nuclear power plants and why
+
+ align:start position:0%
+we've had nuclear power plants and why
+ 
+
+ align:start position:0%
+we've had nuclear power plants and why
+they may be out competed by new
+
+ align:start position:0%
+they may be out competed by new
+ 
+
+ align:start position:0%
+they may be out competed by new
+renewable resources
+
+ align:start position:0%
+renewable resources
+ 
+
+ align:start position:0%
+renewable resources
+if you look at this is a a fairly nice
+
+ align:start position:0%
+if you look at this is a a fairly nice
+ 
+
+ align:start position:0%
+if you look at this is a a fairly nice
+set of graphs from our world in data it
+
+ align:start position:0%
+set of graphs from our world in data it
+ 
+
+ align:start position:0%
+set of graphs from our world in data it
+shows the price electricity from new
+
+ align:start position:0%
+shows the price electricity from new
+ 
+
+ align:start position:0%
+shows the price electricity from new
+power plants this is expressed in terms
+
+ align:start position:0%
+power plants this is expressed in terms
+ 
+
+ align:start position:0%
+power plants this is expressed in terms
+of the levelized costs and energy
+
+ align:start position:0%
+of the levelized costs and energy
+ 
+
+ align:start position:0%
+of the levelized costs and energy
+something we'll talk about in a few
+
+ align:start position:0%
+something we'll talk about in a few
+ 
+
+ align:start position:0%
+something we'll talk about in a few
+lectures from now and it shows in 2009
+
+ align:start position:0%
+lectures from now and it shows in 2009
+ 
+
+ align:start position:0%
+lectures from now and it shows in 2009
+on a per unit basis gas peaking plants
+
+ align:start position:0%
+on a per unit basis gas peaking plants
+ 
+
+ align:start position:0%
+on a per unit basis gas peaking plants
+declined from 275 dollars to 175 dollars
+
+ align:start position:0%
+declined from 275 dollars to 175 dollars
+ 
+
+ align:start position:0%
+declined from 275 dollars to 175 dollars
+uh gas combined cycle plants if you
+
+ align:start position:0%
+uh gas combined cycle plants if you
+ 
+
+ align:start position:0%
+uh gas combined cycle plants if you
+climb from 83 dollars to fifty six
+
+ align:start position:0%
+climb from 83 dollars to fifty six
+ 
+
+ align:start position:0%
+climb from 83 dollars to fifty six
+dollars the problem is coal-fired power
+
+ align:start position:0%
+dollars the problem is coal-fired power
+ 
+
+ align:start position:0%
+dollars the problem is coal-fired power
+plants essentially stayed stable in
+
+ align:start position:0%
+plants essentially stayed stable in
+ 
+
+ align:start position:0%
+plants essentially stayed stable in
+terms of costs over this decade and
+
+ align:start position:0%
+terms of costs over this decade and
+ 
+
+ align:start position:0%
+terms of costs over this decade and
+nuclear power plants actually increased
+
+ align:start position:0%
+nuclear power plants actually increased
+ 
+
+ align:start position:0%
+nuclear power plants actually increased
+by 26 from 123 per unit of power 155
+
+ align:start position:0%
+by 26 from 123 per unit of power 155
+ 
+
+ align:start position:0%
+by 26 from 123 per unit of power 155
+which is to say that basically these two
+
+ align:start position:0%
+which is to say that basically these two
+ 
+
+ align:start position:0%
+which is to say that basically these two
+natural gas based Technologies got
+
+ align:start position:0%
+natural gas based Technologies got
+ 
+
+ align:start position:0%
+natural gas based Technologies got
+cheaper all stayed the same and you
+
+ align:start position:0%
+cheaper all stayed the same and you
+ 
+
+ align:start position:0%
+cheaper all stayed the same and you
+could have got more expensive over the
+
+ align:start position:0%
+could have got more expensive over the
+ 
+
+ align:start position:0%
+could have got more expensive over the
+last decade obviously not making nuclear
+
+ align:start position:0%
+last decade obviously not making nuclear
+ 
+
+ align:start position:0%
+last decade obviously not making nuclear
+power nearly as competitive as before
+
+ align:start position:0%
+power nearly as competitive as before
+ 
+
+ align:start position:0%
+power nearly as competitive as before
+even though nuclear power is cleaner in
+
+ align:start position:0%
+even though nuclear power is cleaner in
+ 
+
+ align:start position:0%
+even though nuclear power is cleaner in
+many ways than not the gas
+
+ align:start position:0%
+many ways than not the gas
+ 
+
+ align:start position:0%
+many ways than not the gas
+what the article about is about mostudo
+
+ align:start position:0%
+what the article about is about mostudo
+ 
+
+ align:start position:0%
+what the article about is about mostudo
+is the fact the price of Solar modules
+
+ align:start position:0%
+is the fact the price of Solar modules
+ 
+
+ align:start position:0%
+is the fact the price of Solar modules
+has decreased by 99.6 since 1976. this
+
+ align:start position:0%
+has decreased by 99.6 since 1976. this
+ 
+
+ align:start position:0%
+has decreased by 99.6 since 1976. this
+essentially shows a steady March you
+
+ align:start position:0%
+essentially shows a steady March you
+ 
+
+ align:start position:0%
+essentially shows a steady March you
+might notice the vertical axis and the
+
+ align:start position:0%
+might notice the vertical axis and the
+ 
+
+ align:start position:0%
+might notice the vertical axis and the
+horizontal axes are both logarithmic
+
+ align:start position:0%
+horizontal axes are both logarithmic
+ 
+
+ align:start position:0%
+horizontal axes are both logarithmic
+scales so every time you go down one of
+
+ align:start position:0%
+scales so every time you go down one of
+ 
+
+ align:start position:0%
+scales so every time you go down one of
+these blocks it's basically having in
+
+ align:start position:0%
+these blocks it's basically having in
+ 
+
+ align:start position:0%
+these blocks it's basically having in
+place and as this graph points out with
+
+ align:start position:0%
+place and as this graph points out with
+ 
+
+ align:start position:0%
+place and as this graph points out with
+each doubling of capacity along the
+
+ align:start position:0%
+each doubling of capacity along the
+ 
+
+ align:start position:0%
+each doubling of capacity along the
+horizontal axis the price of Solar
+
+ align:start position:0%
+horizontal axis the price of Solar
+ 
+
+ align:start position:0%
+horizontal axis the price of Solar
+module dropped on average by 20 this is
+
+ align:start position:0%
+module dropped on average by 20 this is
+ 
+
+ align:start position:0%
+module dropped on average by 20 this is
+called The Learning rate or learning
+
+ align:start position:0%
+called The Learning rate or learning
+ 
+
+ align:start position:0%
+called The Learning rate or learning
+curve so the learning curve is
+
+ align:start position:0%
+curve so the learning curve is
+ 
+
+ align:start position:0%
+curve so the learning curve is
+essentially every time you double how
+
+ align:start position:0%
+essentially every time you double how
+ 
+
+ align:start position:0%
+essentially every time you double how
+much you make of it the price go down
+
+ align:start position:0%
+much you make of it the price go down
+ 
+
+ align:start position:0%
+much you make of it the price go down
+this is also referred to as rights law
+
+ align:start position:0%
+this is also referred to as rights law
+ 
+
+ align:start position:0%
+this is also referred to as rights law
+which has been studied quite a bit by
+
+ align:start position:0%
+which has been studied quite a bit by
+ 
+
+ align:start position:0%
+which has been studied quite a bit by
+Jessica transck especially my MIT
+
+ align:start position:0%
+Jessica transck especially my MIT
+ 
+
+ align:start position:0%
+Jessica transck especially my MIT
+colleague and idss
+
+ align:start position:0%
+colleague and idss
+ 
+
+ align:start position:0%
+colleague and idss
+and some of the theory around why this
+
+ align:start position:0%
+and some of the theory around why this
+ 
+
+ align:start position:0%
+and some of the theory around why this
+occurs is that as we have more
+
+ align:start position:0%
+occurs is that as we have more
+ 
+
+ align:start position:0%
+occurs is that as we have more
+deployment more and more competition or
+
+ align:start position:0%
+deployment more and more competition or
+ 
+
+ align:start position:0%
+deployment more and more competition or
+there's prices fall because there's more
+
+ align:start position:0%
+there's prices fall because there's more
+ 
+
+ align:start position:0%
+there's prices fall because there's more
+deployment it becomes competitive and
+
+ align:start position:0%
+deployment it becomes competitive and
+ 
+
+ align:start position:0%
+deployment it becomes competitive and
+you markets that increases demand and
+
+ align:start position:0%
+you markets that increases demand and
+ 
+
+ align:start position:0%
+you markets that increases demand and
+overcomes a virtuous circle where more
+
+ align:start position:0%
+overcomes a virtuous circle where more
+ 
+
+ align:start position:0%
+overcomes a virtuous circle where more
+deployment makes things cheaper on a per
+
+ align:start position:0%
+deployment makes things cheaper on a per
+ 
+
+ align:start position:0%
+deployment makes things cheaper on a per
+unit basis the more you make the cheaper
+
+ align:start position:0%
+unit basis the more you make the cheaper
+ 
+
+ align:start position:0%
+unit basis the more you make the cheaper
+it gets and Jessica Transit has written
+
+ align:start position:0%
+it gets and Jessica Transit has written
+ 
+
+ align:start position:0%
+it gets and Jessica Transit has written
+another paper about why the modularity
+
+ align:start position:0%
+another paper about why the modularity
+ 
+
+ align:start position:0%
+another paper about why the modularity
+of these systems across not only the
+
+ align:start position:0%
+of these systems across not only the
+ 
+
+ align:start position:0%
+of these systems across not only the
+solar cells the balances system has made
+
+ align:start position:0%
+solar cells the balances system has made
+ 
+
+ align:start position:0%
+solar cells the balances system has made
+these things get cheaper and she
+
+ align:start position:0%
+these things get cheaper and she
+ 
+
+ align:start position:0%
+these things get cheaper and she
+analyzes the different policy drivers
+
+ align:start position:0%
+analyzes the different policy drivers
+ 
+
+ align:start position:0%
+analyzes the different policy drivers
+ranging from German feed Insurance to
+
+ align:start position:0%
+ranging from German feed Insurance to
+ 
+
+ align:start position:0%
+ranging from German feed Insurance to
+Chinese investment in large portable TIG
+
+ align:start position:0%
+Chinese investment in large portable TIG
+ 
+
+ align:start position:0%
+Chinese investment in large portable TIG
+cell factories and policy drivers from
+
+ align:start position:0%
+cell factories and policy drivers from
+ 
+
+ align:start position:0%
+cell factories and policy drivers from
+the US Spain and other countries
+
+ align:start position:0%
+the US Spain and other countries
+ 
+
+ align:start position:0%
+the US Spain and other countries
+but the important point to take home
+
+ align:start position:0%
+but the important point to take home
+ 
+
+ align:start position:0%
+but the important point to take home
+from this is that you know we have a
+
+ align:start position:0%
+from this is that you know we have a
+ 
+
+ align:start position:0%
+from this is that you know we have a
+learning rate of about 36 percent here
+
+ align:start position:0%
+learning rate of about 36 percent here
+ 
+
+ align:start position:0%
+learning rate of about 36 percent here
+in this graph for solar PV
+
+ align:start position:0%
+in this graph for solar PV
+ 
+
+ align:start position:0%
+in this graph for solar PV
+we have a aggressively not as fast
+
+ align:start position:0%
+we have a aggressively not as fast
+ 
+
+ align:start position:0%
+we have a aggressively not as fast
+learning rate for offshore wind with
+
+ align:start position:0%
+learning rate for offshore wind with
+ 
+
+ align:start position:0%
+learning rate for offshore wind with
+steady decreases in the cost of optical
+
+ align:start position:0%
+steady decreases in the cost of optical
+ 
+
+ align:start position:0%
+steady decreases in the cost of optical
+wind you can see we're currently at low
+
+ align:start position:0%
+wind you can see we're currently at low
+ 
+
+ align:start position:0%
+wind you can see we're currently at low
+levels of deployment above throw in
+
+ align:start position:0%
+levels of deployment above throw in
+ 
+
+ align:start position:0%
+levels of deployment above throw in
+compared to new technologies onshore
+
+ align:start position:0%
+compared to new technologies onshore
+ 
+
+ align:start position:0%
+compared to new technologies onshore
+wind is much larger at deployment and
+
+ align:start position:0%
+wind is much larger at deployment and
+ 
+
+ align:start position:0%
+wind is much larger at deployment and
+much cheaper than off-pro wind that
+
+ align:start position:0%
+much cheaper than off-pro wind that
+ 
+
+ align:start position:0%
+much cheaper than off-pro wind that
+learning rate has also been comparable
+
+ align:start position:0%
+learning rate has also been comparable
+ 
+
+ align:start position:0%
+learning rate has also been comparable
+or in the same ballpark as solar PV
+
+ align:start position:0%
+or in the same ballpark as solar PV
+ 
+
+ align:start position:0%
+or in the same ballpark as solar PV
+look hole has no learning rate whole has
+
+ align:start position:0%
+look hole has no learning rate whole has
+ 
+
+ align:start position:0%
+look hole has no learning rate whole has
+not gotten significantly cheaper over
+
+ align:start position:0%
+not gotten significantly cheaper over
+ 
+
+ align:start position:0%
+not gotten significantly cheaper over
+the last decade and as we pointed out in
+
+ align:start position:0%
+the last decade and as we pointed out in
+ 
+
+ align:start position:0%
+the last decade and as we pointed out in
+previous graph Newport Powers actually
+
+ align:start position:0%
+previous graph Newport Powers actually
+ 
+
+ align:start position:0%
+previous graph Newport Powers actually
+gotten more expensive over time and so
+
+ align:start position:0%
+gotten more expensive over time and so
+ 
+
+ align:start position:0%
+gotten more expensive over time and so
+what I want to encourage you to think
+
+ align:start position:0%
+what I want to encourage you to think
+ 
+
+ align:start position:0%
+what I want to encourage you to think
+about is this in a competitive market
+
+ align:start position:0%
+about is this in a competitive market
+ 
+
+ align:start position:0%
+about is this in a competitive market
+which is to say that nuclear power is
+
+ align:start position:0%
+which is to say that nuclear power is
+ 
+
+ align:start position:0%
+which is to say that nuclear power is
+getting more expensive and everything
+
+ align:start position:0%
+getting more expensive and everything
+ 
+
+ align:start position:0%
+getting more expensive and everything
+else in solar and wind are getting
+
+ align:start position:0%
+else in solar and wind are getting
+ 
+
+ align:start position:0%
+else in solar and wind are getting
+cheaper faster the new carbon for
+
+ align:start position:0%
+cheaper faster the new carbon for
+ 
+
+ align:start position:0%
+cheaper faster the new carbon for
+nuclear is no longer simply declining it
+
+ align:start position:0%
+nuclear is no longer simply declining it
+ 
+
+ align:start position:0%
+nuclear is no longer simply declining it
+actually has to be behind at a rate at a
+
+ align:start position:0%
+actually has to be behind at a rate at a
+ 
+
+ align:start position:0%
+actually has to be behind at a rate at a
+comparable price that compete with solar
+
+ align:start position:0%
+comparable price that compete with solar
+ 
+
+ align:start position:0%
+comparable price that compete with solar
+wind and so so the Sepulveda L 2018
+
+ align:start position:0%
+wind and so so the Sepulveda L 2018
+ 
+
+ align:start position:0%
+wind and so so the Sepulveda L 2018
+paper argues the cost of the system will
+
+ align:start position:0%
+paper argues the cost of the system will
+ 
+
+ align:start position:0%
+paper argues the cost of the system will
+be much higher if we don't have Fern
+
+ align:start position:0%
+be much higher if we don't have Fern
+ 
+
+ align:start position:0%
+be much higher if we don't have Fern
+green resources such as nuclear energy
+
+ align:start position:0%
+green resources such as nuclear energy
+ 
+
+ align:start position:0%
+green resources such as nuclear energy
+or natural gas power plants that include
+
+ align:start position:0%
+or natural gas power plants that include
+ 
+
+ align:start position:0%
+or natural gas power plants that include
+carbon Capital storage or a large fiber
+
+ align:start position:0%
+carbon Capital storage or a large fiber
+ 
+
+ align:start position:0%
+carbon Capital storage or a large fiber
+resources but you know this picture is
+
+ align:start position:0%
+resources but you know this picture is
+ 
+
+ align:start position:0%
+resources but you know this picture is
+going to change over time and they do a
+
+ align:start position:0%
+going to change over time and they do a
+ 
+
+ align:start position:0%
+going to change over time and they do a
+lot of modeling this paper to show that
+
+ align:start position:0%
+lot of modeling this paper to show that
+ 
+
+ align:start position:0%
+lot of modeling this paper to show that
+we need nuclear energy to keep the cost
+
+ align:start position:0%
+we need nuclear energy to keep the cost
+ 
+
+ align:start position:0%
+we need nuclear energy to keep the cost
+of decompartmentation low anywhere
+
+ align:start position:0%
+of decompartmentation low anywhere
+ 
+
+ align:start position:0%
+of decompartmentation low anywhere
+anywhere from 10 to 60 percent lower
+
+ align:start position:0%
+anywhere from 10 to 60 percent lower
+ 
+
+ align:start position:0%
+anywhere from 10 to 60 percent lower
+having said that there's also other
+
+ align:start position:0%
+having said that there's also other
+ 
+
+ align:start position:0%
+having said that there's also other
+reports and other analysts looking at
+
+ align:start position:0%
+reports and other analysts looking at
+ 
+
+ align:start position:0%
+reports and other analysts looking at
+the idea that solar may get so cheap so
+
+ align:start position:0%
+the idea that solar may get so cheap so
+ 
+
+ align:start position:0%
+the idea that solar may get so cheap so
+quickly that we simply need to build
+
+ align:start position:0%
+quickly that we simply need to build
+ 
+
+ align:start position:0%
+quickly that we simply need to build
+twice as much of the uh to twice as much
+
+ align:start position:0%
+twice as much of the uh to twice as much
+ 
+
+ align:start position:0%
+twice as much of the uh to twice as much
+capacity as we need in other words for
+
+ align:start position:0%
+capacity as we need in other words for
+ 
+
+ align:start position:0%
+capacity as we need in other words for
+the times of year we don't have that
+
+ align:start position:0%
+the times of year we don't have that
+ 
+
+ align:start position:0%
+the times of year we don't have that
+much sun we simply build twice as many
+
+ align:start position:0%
+much sun we simply build twice as many
+ 
+
+ align:start position:0%
+much sun we simply build twice as many
+solar panels in order to try to meet
+
+ align:start position:0%
+solar panels in order to try to meet
+ 
+
+ align:start position:0%
+solar panels in order to try to meet
+that winter load or winter demand
+
+ align:start position:0%
+that winter load or winter demand
+ 
+
+ align:start position:0%
+that winter load or winter demand
+there's different possibilities there'll
+
+ align:start position:0%
+there's different possibilities there'll
+ 
+
+ align:start position:0%
+there's different possibilities there'll
+be different forecasts going forward but
+
+ align:start position:0%
+be different forecasts going forward but
+ 
+
+ align:start position:0%
+be different forecasts going forward but
+for nuclear energy it's a moving Target
+
+ align:start position:0%
+for nuclear energy it's a moving Target
+ 
+
+ align:start position:0%
+for nuclear energy it's a moving Target
+not only does the price of nuclear
+
+ align:start position:0%
+not only does the price of nuclear
+ 
+
+ align:start position:0%
+not only does the price of nuclear
+energy have to come down it has to meet
+
+ align:start position:0%
+energy have to come down it has to meet
+ 
+
+ align:start position:0%
+energy have to come down it has to meet
+targets of offshore wind and solar
+
+ align:start position:0%
+targets of offshore wind and solar
+ 
+
+ align:start position:0%
+targets of offshore wind and solar
+they're getting cheaper all the time
+
+ align:start position:0%
+they're getting cheaper all the time
+ 
+
+ align:start position:0%
+they're getting cheaper all the time
+batteries are also getting cheaper
+
+ align:start position:0%
+batteries are also getting cheaper
+ 
+
+ align:start position:0%
+batteries are also getting cheaper
+electrolyzers which is the technology by
+
+ align:start position:0%
+electrolyzers which is the technology by
+ 
+
+ align:start position:0%
+electrolyzers which is the technology by
+which we take electricity and create
+
+ align:start position:0%
+which we take electricity and create
+ 
+
+ align:start position:0%
+which we take electricity and create
+hydrogen is also getting cheaper so
+
+ align:start position:0%
+hydrogen is also getting cheaper so
+ 
+
+ align:start position:0%
+hydrogen is also getting cheaper so
+these are all kind of fluid Technologies
+
+ align:start position:0%
+these are all kind of fluid Technologies
+ 
+
+ align:start position:0%
+these are all kind of fluid Technologies
+and this is why we need the
+
+ align:start position:0%
+and this is why we need the
+ 
+
+ align:start position:0%
+and this is why we need the
+technological forecasting to show us how
+
+ align:start position:0%
+technological forecasting to show us how
+ 
+
+ align:start position:0%
+technological forecasting to show us how
+much more expensive it may be having
+
+ align:start position:0%
+much more expensive it may be having
+ 
+
+ align:start position:0%
+much more expensive it may be having
+said that because we know there's other
+
+ align:start position:0%
+said that because we know there's other
+ 
+
+ align:start position:0%
+said that because we know there's other
+ancillary effects we have land use
+
+ align:start position:0%
+ancillary effects we have land use
+ 
+
+ align:start position:0%
+ancillary effects we have land use
+obstacles we have rate of
+
+ align:start position:0%
+obstacles we have rate of
+ 
+
+ align:start position:0%
+obstacles we have rate of
+electrification of some of our
+
+ align:start position:0%
+electrification of some of our
+ 
+
+ align:start position:0%
+electrification of some of our
+Technologies we know we have policy
+
+ align:start position:0%
+Technologies we know we have policy
+ 
+
+ align:start position:0%
+Technologies we know we have policy
+barriers it's not clear necessarily if
+
+ align:start position:0%
+barriers it's not clear necessarily if
+ 
+
+ align:start position:0%
+barriers it's not clear necessarily if
+Austin is simply going to win out for
+
+ align:start position:0%
+Austin is simply going to win out for
+ 
+
+ align:start position:0%
+Austin is simply going to win out for
+some technologies over others but we
+
+ align:start position:0%
+some technologies over others but we
+ 
+
+ align:start position:0%
+some technologies over others but we
+know that the technologies that are
+
+ align:start position:0%
+know that the technologies that are
+ 
+
+ align:start position:0%
+know that the technologies that are
+getting more expensive over time are
+
+ align:start position:0%
+getting more expensive over time are
+ 
+
+ align:start position:0%
+getting more expensive over time are
+going to have a hard time competing for
+
+ align:start position:0%
+going to have a hard time competing for
+ 
+
+ align:start position:0%
+going to have a hard time competing for
+the Technologies getting cheaper over
+
+ align:start position:0%
+the Technologies getting cheaper over
+ 
+
+ align:start position:0%
+the Technologies getting cheaper over
+time
+
+ align:start position:0%
+time
+ 
+
+ align:start position:0%
+time
+uh so just to reinforce the point of
+
+ align:start position:0%
+uh so just to reinforce the point of
+ 
+
+ align:start position:0%
+uh so just to reinforce the point of
+electrification the price and Market
+
+ align:start position:0%
+electrification the price and Market
+ 
+
+ align:start position:0%
+electrification the price and Market
+size lithium ion battery since 1992 also
+
+ align:start position:0%
+size lithium ion battery since 1992 also
+ 
+
+ align:start position:0%
+size lithium ion battery since 1992 also
+exhibits a very fast learning rate the
+
+ align:start position:0%
+exhibits a very fast learning rate the
+ 
+
+ align:start position:0%
+exhibits a very fast learning rate the
+prices have declined by an average of
+
+ align:start position:0%
+prices have declined by an average of
+ 
+
+ align:start position:0%
+prices have declined by an average of
+18.9 for every doubling and capacity of
+
+ align:start position:0%
+18.9 for every doubling and capacity of
+ 
+
+ align:start position:0%
+18.9 for every doubling and capacity of
+batteries this shows you the steady
+
+ align:start position:0%
+batteries this shows you the steady
+ 
+
+ align:start position:0%
+batteries this shows you the steady
+March of battery prices going down which
+
+ align:start position:0%
+March of battery prices going down which
+ 
+
+ align:start position:0%
+March of battery prices going down which
+is why we're getting successively
+
+ align:start position:0%
+is why we're getting successively
+ 
+
+ align:start position:0%
+is why we're getting successively
+cheaper Generations electric cars and
+
+ align:start position:0%
+cheaper Generations electric cars and
+ 
+
+ align:start position:0%
+cheaper Generations electric cars and
+pretty much Lithium-ion batteries and
+
+ align:start position:0%
+pretty much Lithium-ion batteries and
+ 
+
+ align:start position:0%
+pretty much Lithium-ion batteries and
+everything uh you may we all know that
+
+ align:start position:0%
+everything uh you may we all know that
+ 
+
+ align:start position:0%
+everything uh you may we all know that
+our phones have gotten more powerful but
+
+ align:start position:0%
+our phones have gotten more powerful but
+ 
+
+ align:start position:0%
+our phones have gotten more powerful but
+now you can buy Power Banks Flags blades
+
+ align:start position:0%
+now you can buy Power Banks Flags blades
+ 
+
+ align:start position:0%
+now you can buy Power Banks Flags blades
+pretty much everything has an Olympia on
+
+ align:start position:0%
+pretty much everything has an Olympia on
+ 
+
+ align:start position:0%
+pretty much everything has an Olympia on
+battery that can replace a small
+
+ align:start position:0%
+battery that can replace a small
+ 
+
+ align:start position:0%
+battery that can replace a small
+combustion engine like leaf blowers very
+
+ align:start position:0%
+combustion engine like leaf blowers very
+ 
+
+ align:start position:0%
+combustion engine like leaf blowers very
+easily or electrical appliances very
+
+ align:start position:0%
+easily or electrical appliances very
+ 
+
+ align:start position:0%
+easily or electrical appliances very
+easily
+
+ align:start position:0%
+easily
+ 
+
+ align:start position:0%
+easily
+uh bringing us back to just the idea of
+
+ align:start position:0%
+uh bringing us back to just the idea of
+ 
+
+ align:start position:0%
+uh bringing us back to just the idea of
+costs and nuclear this is a paper
+
+ align:start position:0%
+costs and nuclear this is a paper
+ 
+
+ align:start position:0%
+costs and nuclear this is a paper
+written at MIT also in 2020 it's about
+
+ align:start position:0%
+written at MIT also in 2020 it's about
+ 
+
+ align:start position:0%
+written at MIT also in 2020 it's about
+sources of costs overrun in the nuclear
+
+ align:start position:0%
+sources of costs overrun in the nuclear
+ 
+
+ align:start position:0%
+sources of costs overrun in the nuclear
+power plant construction all spread New
+
+ align:start position:0%
+power plant construction all spread New
+ 
+
+ align:start position:0%
+power plant construction all spread New
+York Bridge engineering design and this
+
+ align:start position:0%
+York Bridge engineering design and this
+ 
+
+ align:start position:0%
+York Bridge engineering design and this
+is written by a student I had in this
+
+ align:start position:0%
+is written by a student I had in this
+ 
+
+ align:start position:0%
+is written by a student I had in this
+class at Philip eastgates and regulated
+
+ align:start position:0%
+class at Philip eastgates and regulated
+ 
+
+ align:start position:0%
+class at Philip eastgates and regulated
+Clement who is also a postdoc and grad
+
+ align:start position:0%
+Clement who is also a postdoc and grad
+ 
+
+ align:start position:0%
+Clement who is also a postdoc and grad
+student at MIT and all from Jessica
+
+ align:start position:0%
+student at MIT and all from Jessica
+ 
+
+ align:start position:0%
+student at MIT and all from Jessica
+working with James McNerney Jacob
+
+ align:start position:0%
+working with James McNerney Jacob
+ 
+
+ align:start position:0%
+working with James McNerney Jacob
+buongiorno and Jessica Transit here at
+
+ align:start position:0%
+buongiorno and Jessica Transit here at
+ 
+
+ align:start position:0%
+buongiorno and Jessica Transit here at
+IIT
+
+ align:start position:0%
+IIT
+ 
+
+ align:start position:0%
+IIT
+this paper essentially studied why
+
+ align:start position:0%
+this paper essentially studied why
+ 
+
+ align:start position:0%
+this paper essentially studied why
+office overruns have been occurring in
+
+ align:start position:0%
+office overruns have been occurring in
+ 
+
+ align:start position:0%
+office overruns have been occurring in
+nuclear power plants it finds that it
+
+ align:start position:0%
+nuclear power plants it finds that it
+ 
+
+ align:start position:0%
+nuclear power plants it finds that it
+has a negative learning rate nuclear
+
+ align:start position:0%
+has a negative learning rate nuclear
+ 
+
+ align:start position:0%
+has a negative learning rate nuclear
+Construction in the US has gotten
+
+ align:start position:0%
+Construction in the US has gotten
+ 
+
+ align:start position:0%
+Construction in the US has gotten
+steadily more expensive over time as the
+
+ align:start position:0%
+steadily more expensive over time as the
+ 
+
+ align:start position:0%
+steadily more expensive over time as the
+capacity has gone up this is a negative
+
+ align:start position:0%
+capacity has gone up this is a negative
+ 
+
+ align:start position:0%
+capacity has gone up this is a negative
+learning rate it shows for all these
+
+ align:start position:0%
+learning rate it shows for all these
+ 
+
+ align:start position:0%
+learning rate it shows for all these
+different technology types the override
+
+ align:start position:0%
+different technology types the override
+ 
+
+ align:start position:0%
+different technology types the override
+construction deposits steadily increased
+
+ align:start position:0%
+construction deposits steadily increased
+ 
+
+ align:start position:0%
+construction deposits steadily increased
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+analysis of why these prices have
+
+ align:start position:0%
+analysis of why these prices have
+ 
+
+ align:start position:0%
+analysis of why these prices have
+increased space they showed someone's
+
+ align:start position:0%
+increased space they showed someone's
+ 
+
+ align:start position:0%
+increased space they showed someone's
+across the board increase and all the
+
+ align:start position:0%
+across the board increase and all the
+ 
+
+ align:start position:0%
+across the board increase and all the
+different components of a nuclear power
+
+ align:start position:0%
+different components of a nuclear power
+ 
+
+ align:start position:0%
+different components of a nuclear power
+plant the blue bars are the direct cost
+
+ align:start position:0%
+plant the blue bars are the direct cost
+ 
+
+ align:start position:0%
+plant the blue bars are the direct cost
+of let's say the nuclear steam Supply
+
+ align:start position:0%
+of let's say the nuclear steam Supply
+ 
+
+ align:start position:0%
+of let's say the nuclear steam Supply
+system but the indirect cost is the
+
+ align:start position:0%
+system but the indirect cost is the
+ 
+
+ align:start position:0%
+system but the indirect cost is the
+essentially the soft possible the labor
+
+ align:start position:0%
+essentially the soft possible the labor
+ 
+
+ align:start position:0%
+essentially the soft possible the labor
+intensive components around building
+
+ align:start position:0%
+intensive components around building
+ 
+
+ align:start position:0%
+intensive components around building
+these Technologies you can see that this
+
+ align:start position:0%
+these Technologies you can see that this
+ 
+
+ align:start position:0%
+these Technologies you can see that this
+is a pretty much a steady increase
+
+ align:start position:0%
+is a pretty much a steady increase
+ 
+
+ align:start position:0%
+is a pretty much a steady increase
+across the board everything costs more
+
+ align:start position:0%
+across the board everything costs more
+ 
+
+ align:start position:0%
+across the board everything costs more
+hardly everything costs more because of
+
+ align:start position:0%
+hardly everything costs more because of
+ 
+
+ align:start position:0%
+hardly everything costs more because of
+these indirect costs or soft costs it is
+
+ align:start position:0%
+these indirect costs or soft costs it is
+ 
+
+ align:start position:0%
+these indirect costs or soft costs it is
+not clearly necessarily again if our
+
+ align:start position:0%
+not clearly necessarily again if our
+ 
+
+ align:start position:0%
+not clearly necessarily again if our
+current way way of delivering nuclear
+
+ align:start position:0%
+current way way of delivering nuclear
+ 
+
+ align:start position:0%
+current way way of delivering nuclear
+power plants is going to be effective we
+
+ align:start position:0%
+power plants is going to be effective we
+ 
+
+ align:start position:0%
+power plants is going to be effective we
+obviously need to rethink how we deliver
+
+ align:start position:0%
+obviously need to rethink how we deliver
+ 
+
+ align:start position:0%
+obviously need to rethink how we deliver
+nuclear power plants and this is another
+
+ align:start position:0%
+nuclear power plants and this is another
+ 
+
+ align:start position:0%
+nuclear power plants and this is another
+paper by Arnold grubler a fairly famous
+
+ align:start position:0%
+paper by Arnold grubler a fairly famous
+ 
+
+ align:start position:0%
+paper by Arnold grubler a fairly famous
+analyst this is written about 10 or 12
+
+ align:start position:0%
+analyst this is written about 10 or 12
+ 
+
+ align:start position:0%
+analyst this is written about 10 or 12
+years ago but this takes the French
+
+ align:start position:0%
+years ago but this takes the French
+ 
+
+ align:start position:0%
+years ago but this takes the French
+nuclear industry which is basically been
+
+ align:start position:0%
+nuclear industry which is basically been
+ 
+
+ align:start position:0%
+nuclear industry which is basically been
+always touted as the most successful
+
+ align:start position:0%
+always touted as the most successful
+ 
+
+ align:start position:0%
+always touted as the most successful
+nuclear energy in the world and again
+
+ align:start position:0%
+nuclear energy in the world and again
+ 
+
+ align:start position:0%
+nuclear energy in the world and again
+essentially looks at data from this
+
+ align:start position:0%
+essentially looks at data from this
+ 
+
+ align:start position:0%
+essentially looks at data from this
+program and finds negative learning by
+
+ align:start position:0%
+program and finds negative learning by
+ 
+
+ align:start position:0%
+program and finds negative learning by
+doing it reviews the history and
+
+ align:start position:0%
+doing it reviews the history and
+ 
+
+ align:start position:0%
+doing it reviews the history and
+economics of the French pwr program
+
+ align:start position:0%
+economics of the French pwr program
+ 
+
+ align:start position:0%
+economics of the French pwr program
+which is considered the most successful
+
+ align:start position:0%
+which is considered the most successful
+ 
+
+ align:start position:0%
+which is considered the most successful
+nuclear skill of experience in that
+
+ align:start position:0%
+nuclear skill of experience in that
+ 
+
+ align:start position:0%
+nuclear skill of experience in that
+country
+
+ align:start position:0%
+country
+ 
+
+ align:start position:0%
+country
+but drawing on largely unknown public
+
+ align:start position:0%
+but drawing on largely unknown public
+ 
+
+ align:start position:0%
+but drawing on largely unknown public
+records the paper reveals for the first
+
+ align:start position:0%
+records the paper reveals for the first
+ 
+
+ align:start position:0%
+records the paper reveals for the first
+time both absolute as well as yearly and
+
+ align:start position:0%
+time both absolute as well as yearly and
+ 
+
+ align:start position:0%
+time both absolute as well as yearly and
+specific reactive costs and evolution
+
+ align:start position:0%
+specific reactive costs and evolution
+ 
+
+ align:start position:0%
+specific reactive costs and evolution
+over time the most significant finding
+
+ align:start position:0%
+over time the most significant finding
+ 
+
+ align:start position:0%
+over time the most significant finding
+is that even in the most successful
+
+ align:start position:0%
+is that even in the most successful
+ 
+
+ align:start position:0%
+is that even in the most successful
+nuclear scale up is characterized by
+
+ align:start position:0%
+nuclear scale up is characterized by
+ 
+
+ align:start position:0%
+nuclear scale up is characterized by
+substantial escalation of real-time
+
+ align:start position:0%
+substantial escalation of real-time
+ 
+
+ align:start position:0%
+substantial escalation of real-time
+construction costs in other words we
+
+ align:start position:0%
+construction costs in other words we
+ 
+
+ align:start position:0%
+construction costs in other words we
+still don't have very much evidence over
+
+ align:start position:0%
+still don't have very much evidence over
+ 
+
+ align:start position:0%
+still don't have very much evidence over
+the last 40 or 50 years that nuclear
+
+ align:start position:0%
+the last 40 or 50 years that nuclear
+ 
+
+ align:start position:0%
+the last 40 or 50 years that nuclear
+power plants get cheaper over time they
+
+ align:start position:0%
+power plants get cheaper over time they
+ 
+
+ align:start position:0%
+power plants get cheaper over time they
+seem to get more expensive over time so
+
+ align:start position:0%
+seem to get more expensive over time so
+ 
+
+ align:start position:0%
+seem to get more expensive over time so
+again while I'm open to the idea of
+
+ align:start position:0%
+again while I'm open to the idea of
+ 
+
+ align:start position:0%
+again while I'm open to the idea of
+nuclear I would like to see it become
+
+ align:start position:0%
+nuclear I would like to see it become
+ 
+
+ align:start position:0%
+nuclear I would like to see it become
+cheaper before we actually think that
+
+ align:start position:0%
+cheaper before we actually think that
+ 
+
+ align:start position:0%
+cheaper before we actually think that
+it's going to be a viable uh part of our
+
+ align:start position:0%
+it's going to be a viable uh part of our
+ 
+
+ align:start position:0%
+it's going to be a viable uh part of our
+future energy system that means we
+
+ align:start position:0%
+future energy system that means we
+ 
+
+ align:start position:0%
+future energy system that means we
+should research it it does mean we
+
+ align:start position:0%
+should research it it does mean we
+ 
+
+ align:start position:0%
+should research it it does mean we
+should subsidize Research into it to try
+
+ align:start position:0%
+should subsidize Research into it to try
+ 
+
+ align:start position:0%
+should subsidize Research into it to try
+to bring it into a more cost competitive
+
+ align:start position:0%
+to bring it into a more cost competitive
+ 
+
+ align:start position:0%
+to bring it into a more cost competitive
+stance versus alternative or existing
+
+ align:start position:0%
+stance versus alternative or existing
+ 
+
+ align:start position:0%
+stance versus alternative or existing
+alternative and renewable energy
+
+ align:start position:0%
+alternative and renewable energy
+ 
+
+ align:start position:0%
+alternative and renewable energy
+resources but again we should recognize
+
+ align:start position:0%
+resources but again we should recognize
+ 
+
+ align:start position:0%
+resources but again we should recognize
+that our current costs don't make it
+
+ align:start position:0%
+that our current costs don't make it
+ 
+
+ align:start position:0%
+that our current costs don't make it
+economically viable to use nuclear power
+
+ align:start position:0%
+economically viable to use nuclear power
+ 
+
+ align:start position:0%
+economically viable to use nuclear power
+plants for the things that it's been
+
+ align:start position:0%
+plants for the things that it's been
+ 
+
+ align:start position:0%
+plants for the things that it's been
+touted for
+
+ align:start position:0%
+touted for
+ 
+
+ align:start position:0%
+touted for
+so thank you very much I look forward to
+
+ align:start position:0%
+so thank you very much I look forward to
+ 
+
+ align:start position:0%
+so thank you very much I look forward to
+our discussion in class on some of these
+
+ align:start position:0%
+our discussion in class on some of these
+ 
+
+ align:start position:0%
+our discussion in class on some of these
+themes
\ No newline at end of file
diff --git a/f_sNWn7zujU.txt b/f_sNWn7zujU.txt
new file mode 100644
index 0000000000000000000000000000000000000000..1634144a5520a087b66131e21a7b35846fd7bd1e
--- /dev/null
+++ b/f_sNWn7zujU.txt
@@ -0,0 +1,12673 @@
+align:start position:0%
+ 
+so last time
+
+ align:start position:0%
+so last time
+ 
+
+ align:start position:0%
+so last time
+we finished by proving
+
+ align:start position:0%
+we finished by proving
+ 
+
+ align:start position:0%
+we finished by proving
+bolzano's intermediate value theorem
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+which states that a continuous function
+
+ align:start position:0%
+which states that a continuous function
+ 
+
+ align:start position:0%
+which states that a continuous function
+achieves all values in between
+
+ align:start position:0%
+achieves all values in between
+ 
+
+ align:start position:0%
+achieves all values in between
+the function evaluated at the endpoints
+
+ align:start position:0%
+the function evaluated at the endpoints
+ 
+
+ align:start position:0%
+the function evaluated at the endpoints
+so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+if i have a continuous function
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and either
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+i take a value y between f of a and f of
+
+ align:start position:0%
+i take a value y between f of a and f of
+ 
+
+ align:start position:0%
+i take a value y between f of a and f of
+b so either f of a is less than f of b
+
+ align:start position:0%
+b so either f of a is less than f of b
+ 
+
+ align:start position:0%
+b so either f of a is less than f of b
+and y's in between
+
+ align:start position:0%
+and y's in between
+ 
+
+ align:start position:0%
+and y's in between
+is bigger than f of a and less than f of
+
+ align:start position:0%
+is bigger than f of a and less than f of
+ 
+
+ align:start position:0%
+is bigger than f of a and less than f of
+b
+
+ align:start position:0%
+b
+ 
+
+ align:start position:0%
+b
+or
+
+ align:start position:0%
+or
+ 
+
+ align:start position:0%
+or
+f of a is bigger than f of b but
+
+ align:start position:0%
+f of a is bigger than f of b but
+ 
+
+ align:start position:0%
+f of a is bigger than f of b but
+y is still in between them
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+then there exists
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+c in the interval a b
+
+ align:start position:0%
+c in the interval a b
+ 
+
+ align:start position:0%
+c in the interval a b
+so that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+f c equals y alright so every value in
+
+ align:start position:0%
+f c equals y alright so every value in
+ 
+
+ align:start position:0%
+f c equals y alright so every value in
+between f
+
+ align:start position:0%
+between f
+ 
+
+ align:start position:0%
+between f
+evaluated at the endpoints
+
+ align:start position:0%
+evaluated at the endpoints
+ 
+
+ align:start position:0%
+evaluated at the endpoints
+is achieved i drew the picture then
+
+ align:start position:0%
+is achieved i drew the picture then
+ 
+
+ align:start position:0%
+is achieved i drew the picture then
+along with this
+
+ align:start position:0%
+along with this
+ 
+
+ align:start position:0%
+along with this
+a b
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+f a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+f b
+
+ align:start position:0%
+f b
+ 
+
+ align:start position:0%
+f b
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+that could be
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the function and if we take anything
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+in between
+
+ align:start position:0%
+in between
+ 
+
+ align:start position:0%
+in between
+then there has to be
+
+ align:start position:0%
+then there has to be
+ 
+
+ align:start position:0%
+then there has to be
+some c
+
+ align:start position:0%
+some c
+ 
+
+ align:start position:0%
+some c
+so that f of c
+
+ align:start position:0%
+so that f of c
+ 
+
+ align:start position:0%
+so that f of c
+equals y okay at least in the picture
+
+ align:start position:0%
+equals y okay at least in the picture
+ 
+
+ align:start position:0%
+equals y okay at least in the picture
+i've drawn there's three different guys
+
+ align:start position:0%
+i've drawn there's three different guys
+ 
+
+ align:start position:0%
+i've drawn there's three different guys
+but there's always at least one
+
+ align:start position:0%
+but there's always at least one
+ 
+
+ align:start position:0%
+but there's always at least one
+okay and then um
+
+ align:start position:0%
+okay and then um
+ 
+
+ align:start position:0%
+okay and then um
+the last uh thing we talked about at the
+
+ align:start position:0%
+the last uh thing we talked about at the
+ 
+
+ align:start position:0%
+the last uh thing we talked about at the
+end of last lecture was that
+
+ align:start position:0%
+end of last lecture was that
+ 
+
+ align:start position:0%
+end of last lecture was that
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+image of
+
+ align:start position:0%
+image of
+ 
+
+ align:start position:0%
+image of
+a bounded closed and bounded interval by
+
+ align:start position:0%
+a bounded closed and bounded interval by
+ 
+
+ align:start position:0%
+a bounded closed and bounded interval by
+a continuous function
+
+ align:start position:0%
+a continuous function
+ 
+
+ align:start position:0%
+a continuous function
+is again
+
+ align:start position:0%
+is again
+ 
+
+ align:start position:0%
+is again
+a closed and bounded interval
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+where e corresponds to
+
+ align:start position:0%
+where e corresponds to
+ 
+
+ align:start position:0%
+where e corresponds to
+the absolute max of f and f corresponds
+
+ align:start position:0%
+the absolute max of f and f corresponds
+ 
+
+ align:start position:0%
+the absolute max of f and f corresponds
+so that i shouldn't call this f since we
+
+ align:start position:0%
+so that i shouldn't call this f since we
+ 
+
+ align:start position:0%
+so that i shouldn't call this f since we
+already have f being used
+
+ align:start position:0%
+already have f being used
+ 
+
+ align:start position:0%
+already have f being used
+and g
+
+ align:start position:0%
+and g
+ 
+
+ align:start position:0%
+and g
+corresponds to
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+let's make it d
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+corresponds to the absolute min of f
+
+ align:start position:0%
+corresponds to the absolute min of f
+ 
+
+ align:start position:0%
+corresponds to the absolute min of f
+okay so this uh
+
+ align:start position:0%
+okay so this uh
+ 
+
+ align:start position:0%
+okay so this uh
+is what we proved uh
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+last time is that f of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+if f is continuous then
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+there exists
+
+ align:start position:0%
+there exists
+ 
+
+ align:start position:0%
+there exists
+e d
+
+ align:start position:0%
+e d
+ 
+
+ align:start position:0%
+e d
+and r
+
+ align:start position:0%
+and r
+ 
+
+ align:start position:0%
+and r
+such that the range
+
+ align:start position:0%
+such that the range
+ 
+
+ align:start position:0%
+such that the range
+of this closed and bounded interval is
+
+ align:start position:0%
+of this closed and bounded interval is
+ 
+
+ align:start position:0%
+of this closed and bounded interval is
+again
+
+ align:start position:0%
+again
+ 
+
+ align:start position:0%
+again
+a closed and bounded interval okay so f
+
+ align:start position:0%
+a closed and bounded interval okay so f
+ 
+
+ align:start position:0%
+a closed and bounded interval okay so f
+is very well behaved
+
+ align:start position:0%
+is very well behaved
+ 
+
+ align:start position:0%
+is very well behaved
+on closed and bounded intervals
+
+ align:start position:0%
+on closed and bounded intervals
+ 
+
+ align:start position:0%
+on closed and bounded intervals
+and we'll see another way in which
+
+ align:start position:0%
+and we'll see another way in which
+ 
+
+ align:start position:0%
+and we'll see another way in which
+continuous functions are well behaved on
+
+ align:start position:0%
+continuous functions are well behaved on
+ 
+
+ align:start position:0%
+continuous functions are well behaved on
+a closed and bounded interval in just a
+
+ align:start position:0%
+a closed and bounded interval in just a
+ 
+
+ align:start position:0%
+a closed and bounded interval in just a
+second
+
+ align:start position:0%
+second
+ 
+
+ align:start position:0%
+second
+um now
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+you know a simple application of
+
+ align:start position:0%
+you know a simple application of
+ 
+
+ align:start position:0%
+you know a simple application of
+the balzano immediate value intermediate
+
+ align:start position:0%
+the balzano immediate value intermediate
+ 
+
+ align:start position:0%
+the balzano immediate value intermediate
+value theorem
+
+ align:start position:0%
+value theorem
+ 
+
+ align:start position:0%
+value theorem
+is um the following
+
+ align:start position:0%
+is um the following
+ 
+
+ align:start position:0%
+is um the following
+really it's an application of that
+
+ align:start position:0%
+really it's an application of that
+ 
+
+ align:start position:0%
+really it's an application of that
+theorem that i labeled the bisection
+
+ align:start position:0%
+theorem that i labeled the bisection
+ 
+
+ align:start position:0%
+theorem that i labeled the bisection
+method but uh
+
+ align:start position:0%
+method but uh
+ 
+
+ align:start position:0%
+method but uh
+let's uh
+
+ align:start position:0%
+let's uh
+ 
+
+ align:start position:0%
+let's uh
+you know chalk that up to the bolzando
+
+ align:start position:0%
+you know chalk that up to the bolzando
+ 
+
+ align:start position:0%
+you know chalk that up to the bolzando
+intermediate value theorem
+
+ align:start position:0%
+intermediate value theorem
+ 
+
+ align:start position:0%
+intermediate value theorem
+which is the following that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+if f of x
+
+ align:start position:0%
+if f of x
+ 
+
+ align:start position:0%
+if f of x
+is
+
+ align:start position:0%
+is
+ 
+
+ align:start position:0%
+is
+any odd
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+polynomial
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+then
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+f has
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+at least one
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+real root
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+so any odd polynomial has at least one
+
+ align:start position:0%
+so any odd polynomial has at least one
+ 
+
+ align:start position:0%
+so any odd polynomial has at least one
+real root so by the fundamental theorem
+
+ align:start position:0%
+real root so by the fundamental theorem
+ 
+
+ align:start position:0%
+real root so by the fundamental theorem
+of algebra every polynomial has exactly
+
+ align:start position:0%
+of algebra every polynomial has exactly
+ 
+
+ align:start position:0%
+of algebra every polynomial has exactly
+n roots n corresponding to the degree of
+
+ align:start position:0%
+n roots n corresponding to the degree of
+ 
+
+ align:start position:0%
+n roots n corresponding to the degree of
+the polynomial but these roots can be
+
+ align:start position:0%
+the polynomial but these roots can be
+ 
+
+ align:start position:0%
+the polynomial but these roots can be
+complex valued okay
+
+ align:start position:0%
+complex valued okay
+ 
+
+ align:start position:0%
+complex valued okay
+uh but for odd polynomials there must be
+
+ align:start position:0%
+uh but for odd polynomials there must be
+ 
+
+ align:start position:0%
+uh but for odd polynomials there must be
+at least one real root and this is a
+
+ align:start position:0%
+at least one real root and this is a
+ 
+
+ align:start position:0%
+at least one real root and this is a
+consequence of the bolzano interview
+
+ align:start position:0%
+consequence of the bolzano interview
+ 
+
+ align:start position:0%
+consequence of the bolzano interview
+intermediate value theorem but instead
+
+ align:start position:0%
+intermediate value theorem but instead
+ 
+
+ align:start position:0%
+intermediate value theorem but instead
+of proving this theorem in its full
+
+ align:start position:0%
+of proving this theorem in its full
+ 
+
+ align:start position:0%
+of proving this theorem in its full
+generality let me just give you kind of
+
+ align:start position:0%
+generality let me just give you kind of
+ 
+
+ align:start position:0%
+generality let me just give you kind of
+a representative example
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so let's take
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+f of x equals x to the
+
+ align:start position:0%
+f of x equals x to the
+ 
+
+ align:start position:0%
+f of x equals x to the
+
+ align:start position:0%
+ 
+
+ align:start position:0%
+
+ align:start position:0%
+ 
+
+ align:start position:0%
+[Music]
+
+ align:start position:0%
+[Music]
+ 
+
+ align:start position:0%
+[Music]
+minus x to the
+
+ align:start position:0%
+minus x to the
+ 
+
+ align:start position:0%
+minus x to the
+20 20
+
+ align:start position:0%
+20 20
+ 
+
+ align:start position:0%
+20 20
+plus
+
+ align:start position:0%
+plus
+ 
+
+ align:start position:0%
+plus
+i don't know what's today
+
+ align:start position:0%
+i don't know what's today
+ 
+
+ align:start position:0%
+i don't know what's today
+i think the 25th or 24th i don't know 10
+
+ align:start position:0%
+i think the 25th or 24th i don't know 10
+ 
+
+ align:start position:0%
+i think the 25th or 24th i don't know 10
+
+ align:start position:0%
+ 
+
+ align:start position:0%
+x
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+minus
+
+ align:start position:0%
+minus
+ 
+
+ align:start position:0%
+minus
+300.
+
+ align:start position:0%
+300.
+ 
+
+ align:start position:0%
+300.
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+so what's the point
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+as long as i plug in a big enough x
+
+ align:start position:0%
+as long as i plug in a big enough x
+ 
+
+ align:start position:0%
+as long as i plug in a big enough x
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+i will
+
+ align:start position:0%
+i will
+ 
+
+ align:start position:0%
+i will
+this will swamp everything
+
+ align:start position:0%
+this will swamp everything
+ 
+
+ align:start position:0%
+this will swamp everything
+here
+
+ align:start position:0%
+here
+ 
+
+ align:start position:0%
+here
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+so for example if i stick in
+
+ align:start position:0%
+so for example if i stick in
+ 
+
+ align:start position:0%
+so for example if i stick in
+f of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+you know 100 000
+
+ align:start position:0%
+you know 100 000
+ 
+
+ align:start position:0%
+you know 100 000
+i leave it to you to check that this is
+
+ align:start position:0%
+i leave it to you to check that this is
+ 
+
+ align:start position:0%
+i leave it to you to check that this is
+positive right because
+
+ align:start position:0%
+positive right because
+ 
+
+ align:start position:0%
+positive right because
+this will be a hundred thousand to the
+
+ align:start position:0%
+this will be a hundred thousand to the
+ 
+
+ align:start position:0%
+this will be a hundred thousand to the
+2020 minus a hundred thousand to the
+
+ align:start position:0%
+2020 minus a hundred thousand to the
+ 
+
+ align:start position:0%
+2020 minus a hundred thousand to the
+
+ align:start position:0%
+ 
+
+ align:start position:0%
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+or 20 21
+
+ align:start position:0%
+or 20 21
+ 
+
+ align:start position:0%
+or 20 21
+and then plus this which will be
+
+ align:start position:0%
+and then plus this which will be
+ 
+
+ align:start position:0%
+and then plus this which will be
+positive minus 300 this doesn't matter
+
+ align:start position:0%
+positive minus 300 this doesn't matter
+ 
+
+ align:start position:0%
+positive minus 300 this doesn't matter
+so what really matters is this big guy
+
+ align:start position:0%
+so what really matters is this big guy
+ 
+
+ align:start position:0%
+so what really matters is this big guy
+or this guy with the largest
+
+ align:start position:0%
+or this guy with the largest
+ 
+
+ align:start position:0%
+or this guy with the largest
+power will
+
+ align:start position:0%
+power will
+ 
+
+ align:start position:0%
+power will
+swamp all the other ones and eventually
+
+ align:start position:0%
+swamp all the other ones and eventually
+ 
+
+ align:start position:0%
+swamp all the other ones and eventually
+be positive if i stick in a large enough
+
+ align:start position:0%
+be positive if i stick in a large enough
+ 
+
+ align:start position:0%
+be positive if i stick in a large enough
+positive value
+
+ align:start position:0%
+positive value
+ 
+
+ align:start position:0%
+positive value
+and likewise
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+in fact for this guy
+
+ align:start position:0%
+in fact for this guy
+ 
+
+ align:start position:0%
+in fact for this guy
+if i stick in a negative
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+value
+
+ align:start position:0%
+value
+ 
+
+ align:start position:0%
+value
+then i get something very big but now
+
+ align:start position:0%
+then i get something very big but now
+ 
+
+ align:start position:0%
+then i get something very big but now
+with the minus sign which will again
+
+ align:start position:0%
+with the minus sign which will again
+ 
+
+ align:start position:0%
+with the minus sign which will again
+swamp all these earlier guys in fact i
+
+ align:start position:0%
+swamp all these earlier guys in fact i
+ 
+
+ align:start position:0%
+swamp all these earlier guys in fact i
+don't have to choose minus a hundred
+
+ align:start position:0%
+don't have to choose minus a hundred
+ 
+
+ align:start position:0%
+don't have to choose minus a hundred
+thousand if i just stick in zero i will
+
+ align:start position:0%
+thousand if i just stick in zero i will
+ 
+
+ align:start position:0%
+thousand if i just stick in zero i will
+get minus 300 which will be negative but
+
+ align:start position:0%
+get minus 300 which will be negative but
+ 
+
+ align:start position:0%
+get minus 300 which will be negative but
+you can check that if i stick in minus
+
+ align:start position:0%
+you can check that if i stick in minus
+ 
+
+ align:start position:0%
+you can check that if i stick in minus
+100 000 this will still be negative
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+thus by the intermediate value theorem
+
+ align:start position:0%
+thus by the intermediate value theorem
+ 
+
+ align:start position:0%
+thus by the intermediate value theorem
+there exists a c in
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+100 000
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+100 000
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+f of c equals 0 right because 0 is
+
+ align:start position:0%
+f of c equals 0 right because 0 is
+ 
+
+ align:start position:0%
+f of c equals 0 right because 0 is
+something in between
+
+ align:start position:0%
+something in between
+ 
+
+ align:start position:0%
+something in between
+f evaluated at these two endpoints
+
+ align:start position:0%
+f evaluated at these two endpoints
+ 
+
+ align:start position:0%
+f evaluated at these two endpoints
+all right
+
+ align:start position:0%
+all right
+ 
+
+ align:start position:0%
+all right
+but again
+
+ align:start position:0%
+but again
+ 
+
+ align:start position:0%
+but again
+you
+
+ align:start position:0%
+you
+ 
+
+ align:start position:0%
+you
+can prove this and the idea is the same
+
+ align:start position:0%
+can prove this and the idea is the same
+ 
+
+ align:start position:0%
+can prove this and the idea is the same
+is that as long as you go far enough uh
+
+ align:start position:0%
+is that as long as you go far enough uh
+ 
+
+ align:start position:0%
+is that as long as you go far enough uh
+out and positive then the polynomial
+
+ align:start position:0%
+out and positive then the polynomial
+ 
+
+ align:start position:0%
+out and positive then the polynomial
+will be
+
+ align:start position:0%
+will be
+ 
+
+ align:start position:0%
+will be
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+positive if the coefficient out of front
+
+ align:start position:0%
+positive if the coefficient out of front
+ 
+
+ align:start position:0%
+positive if the coefficient out of front
+is positive
+
+ align:start position:0%
+is positive
+ 
+
+ align:start position:0%
+is positive
+and if you go far enough out negative
+
+ align:start position:0%
+and if you go far enough out negative
+ 
+
+ align:start position:0%
+and if you go far enough out negative
+then
+
+ align:start position:0%
+then
+ 
+
+ align:start position:0%
+then
+um you'll get something that's uh
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that's negative and then you apply the
+
+ align:start position:0%
+that's negative and then you apply the
+ 
+
+ align:start position:0%
+that's negative and then you apply the
+intermediate value theorem to to be able
+
+ align:start position:0%
+intermediate value theorem to to be able
+ 
+
+ align:start position:0%
+intermediate value theorem to to be able
+to
+
+ align:start position:0%
+to
+ 
+
+ align:start position:0%
+to
+find a root
+
+ align:start position:0%
+find a root
+ 
+
+ align:start position:0%
+find a root
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+now of course uh one other thing we did
+
+ align:start position:0%
+now of course uh one other thing we did
+ 
+
+ align:start position:0%
+now of course uh one other thing we did
+with the statement of the mid max
+
+ align:start position:0%
+with the statement of the mid max
+ 
+
+ align:start position:0%
+with the statement of the mid max
+theorem was
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+you know can we
+
+ align:start position:0%
+you know can we
+ 
+
+ align:start position:0%
+you know can we
+drop
+
+ align:start position:0%
+drop
+ 
+
+ align:start position:0%
+drop
+um any of the assumptions on
+
+ align:start position:0%
+um any of the assumptions on
+ 
+
+ align:start position:0%
+um any of the assumptions on
+you know this theorem
+
+ align:start position:0%
+you know this theorem
+ 
+
+ align:start position:0%
+you know this theorem
+and you know you can see that the
+
+ align:start position:0%
+and you know you can see that the
+ 
+
+ align:start position:0%
+and you know you can see that the
+example is no
+
+ align:start position:0%
+example is no
+ 
+
+ align:start position:0%
+example is no
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+the question is if f
+
+ align:start position:0%
+the question is if f
+ 
+
+ align:start position:0%
+the question is if f
+from a closed and bounded interval
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+is not
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+continuous
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and let's say
+
+ align:start position:0%
+and let's say
+ 
+
+ align:start position:0%
+and let's say
+f of 0 is less than 0 f of a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+if b is bigger than 0 then
+
+ align:start position:0%
+if b is bigger than 0 then
+ 
+
+ align:start position:0%
+if b is bigger than 0 then
+does there exist
+
+ align:start position:0%
+does there exist
+ 
+
+ align:start position:0%
+does there exist
+c
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+a b such that
+
+ align:start position:0%
+a b such that
+ 
+
+ align:start position:0%
+a b such that
+f c equals zero
+
+ align:start position:0%
+f c equals zero
+ 
+
+ align:start position:0%
+f c equals zero
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+let me put that question mark at the end
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+all right
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and it's easy to come up with an example
+
+ align:start position:0%
+and it's easy to come up with an example
+ 
+
+ align:start position:0%
+and it's easy to come up with an example
+of a function
+
+ align:start position:0%
+of a function
+ 
+
+ align:start position:0%
+of a function
+that is not continuous that satisfies
+
+ align:start position:0%
+that is not continuous that satisfies
+ 
+
+ align:start position:0%
+that is not continuous that satisfies
+these conclusions and there does not
+
+ align:start position:0%
+these conclusions and there does not
+ 
+
+ align:start position:0%
+these conclusions and there does not
+exist a point in between so that f of c
+
+ align:start position:0%
+exist a point in between so that f of c
+ 
+
+ align:start position:0%
+exist a point in between so that f of c
+equals zero simplest being
+
+ align:start position:0%
+equals zero simplest being
+ 
+
+ align:start position:0%
+equals zero simplest being
+i'll just draw
+
+ align:start position:0%
+i'll just draw
+ 
+
+ align:start position:0%
+i'll just draw
+a picture let's go from
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+minus one
+
+ align:start position:0%
+minus one
+ 
+
+ align:start position:0%
+minus one
+one
+
+ align:start position:0%
+one
+ 
+
+ align:start position:0%
+one
+two okay
+
+ align:start position:0%
+two okay
+ 
+
+ align:start position:0%
+two okay
+so then the function
+
+ align:start position:0%
+so then the function
+ 
+
+ align:start position:0%
+so then the function
+is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+f of x equals
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+x minus 1 and
+
+ align:start position:0%
+x minus 1 and
+ 
+
+ align:start position:0%
+x minus 1 and
+this is for x not equal to
+
+ align:start position:0%
+this is for x not equal to
+ 
+
+ align:start position:0%
+this is for x not equal to
+uh one and
+
+ align:start position:0%
+uh one and
+ 
+
+ align:start position:0%
+uh one and
+you know let's make it uh let's make it
+
+ align:start position:0%
+you know let's make it uh let's make it
+ 
+
+ align:start position:0%
+you know let's make it uh let's make it
+a half there
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so this function looks like
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+half
+
+ align:start position:0%
+half
+ 
+
+ align:start position:0%
+half
+there
+
+ align:start position:0%
+there
+ 
+
+ align:start position:0%
+there
+okay so there's no value there's no c in
+
+ align:start position:0%
+okay so there's no value there's no c in
+ 
+
+ align:start position:0%
+okay so there's no value there's no c in
+between
+
+ align:start position:0%
+between
+ 
+
+ align:start position:0%
+between
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+x is between 0 and 2. so you see f of 0
+
+ align:start position:0%
+x is between 0 and 2. so you see f of 0
+ 
+
+ align:start position:0%
+x is between 0 and 2. so you see f of 0
+is equal to -1 that's negative f of 2 is
+
+ align:start position:0%
+is equal to -1 that's negative f of 2 is
+ 
+
+ align:start position:0%
+is equal to -1 that's negative f of 2 is
+equal to 1 it's positive but there
+
+ align:start position:0%
+equal to 1 it's positive but there
+ 
+
+ align:start position:0%
+equal to 1 it's positive but there
+exists no c in between
+
+ align:start position:0%
+exists no c in between
+ 
+
+ align:start position:0%
+exists no c in between
+so that f of c equals 0. okay
+
+ align:start position:0%
+so that f of c equals 0. okay
+ 
+
+ align:start position:0%
+so that f of c equals 0. okay
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+what's the point i'm making
+
+ align:start position:0%
+what's the point i'm making
+ 
+
+ align:start position:0%
+what's the point i'm making
+we really do need this hypothesis
+
+ align:start position:0%
+we really do need this hypothesis
+ 
+
+ align:start position:0%
+we really do need this hypothesis
+that the function is continuous for this
+
+ align:start position:0%
+that the function is continuous for this
+ 
+
+ align:start position:0%
+that the function is continuous for this
+theorem to be true
+
+ align:start position:0%
+theorem to be true
+ 
+
+ align:start position:0%
+theorem to be true
+okay if you drop that hypothesis then
+
+ align:start position:0%
+okay if you drop that hypothesis then
+ 
+
+ align:start position:0%
+okay if you drop that hypothesis then
+the theorem is no longer true
+
+ align:start position:0%
+the theorem is no longer true
+ 
+
+ align:start position:0%
+the theorem is no longer true
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so um
+
+ align:start position:0%
+okay so um
+ 
+
+ align:start position:0%
+okay so um
+now we're going to move on to a new
+
+ align:start position:0%
+now we're going to move on to a new
+ 
+
+ align:start position:0%
+now we're going to move on to a new
+concept
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+called uniform continuity
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and before i do this i'm going to bring
+
+ align:start position:0%
+and before i do this i'm going to bring
+ 
+
+ align:start position:0%
+and before i do this i'm going to bring
+up or i'm going to rewrite
+
+ align:start position:0%
+up or i'm going to rewrite
+ 
+
+ align:start position:0%
+up or i'm going to rewrite
+the definition of continuity
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+this is a old definition but i want to
+
+ align:start position:0%
+this is a old definition but i want to
+ 
+
+ align:start position:0%
+this is a old definition but i want to
+highlight a specific
+
+ align:start position:0%
+highlight a specific
+ 
+
+ align:start position:0%
+highlight a specific
+aspect of it so this is uh me writing
+
+ align:start position:0%
+aspect of it so this is uh me writing
+ 
+
+ align:start position:0%
+aspect of it so this is uh me writing
+the definition of a continuous function
+
+ align:start position:0%
+the definition of a continuous function
+ 
+
+ align:start position:0%
+the definition of a continuous function
+again
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+a function f
+
+ align:start position:0%
+a function f
+ 
+
+ align:start position:0%
+a function f
+from a set s to r
+
+ align:start position:0%
+from a set s to r
+ 
+
+ align:start position:0%
+from a set s to r
+is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+continuous
+
+ align:start position:0%
+continuous
+ 
+
+ align:start position:0%
+continuous
+so we said that means it's continuous at
+
+ align:start position:0%
+so we said that means it's continuous at
+ 
+
+ align:start position:0%
+so we said that means it's continuous at
+every point
+
+ align:start position:0%
+every point
+ 
+
+ align:start position:0%
+every point
+meaning
+
+ align:start position:0%
+meaning
+ 
+
+ align:start position:0%
+meaning
+if
+
+ align:start position:0%
+if
+ 
+
+ align:start position:0%
+if
+for all c and s
+
+ align:start position:0%
+for all c and s
+ 
+
+ align:start position:0%
+for all c and s
+it's continuous at c which means for all
+
+ align:start position:0%
+it's continuous at c which means for all
+ 
+
+ align:start position:0%
+it's continuous at c which means for all
+epsilon positive there exists a delta
+
+ align:start position:0%
+epsilon positive there exists a delta
+ 
+
+ align:start position:0%
+epsilon positive there exists a delta
+now this delta
+
+ align:start position:0%
+now this delta
+ 
+
+ align:start position:0%
+now this delta
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+you know we saw this in examples uh
+
+ align:start position:0%
+you know we saw this in examples uh
+ 
+
+ align:start position:0%
+you know we saw this in examples uh
+that we did proving continuity
+
+ align:start position:0%
+that we did proving continuity
+ 
+
+ align:start position:0%
+that we did proving continuity
+this usually depends on
+
+ align:start position:0%
+this usually depends on
+ 
+
+ align:start position:0%
+this usually depends on
+epsilon and c the point
+
+ align:start position:0%
+epsilon and c the point
+ 
+
+ align:start position:0%
+epsilon and c the point
+where i'm looking at
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+such that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+for all x and s
+
+ align:start position:0%
+for all x and s
+ 
+
+ align:start position:0%
+for all x and s
+x minus c less than delta implies that
+
+ align:start position:0%
+x minus c less than delta implies that
+ 
+
+ align:start position:0%
+x minus c less than delta implies that
+f of x minus f of c
+
+ align:start position:0%
+f of x minus f of c
+ 
+
+ align:start position:0%
+f of x minus f of c
+is less than epsilon
+
+ align:start position:0%
+is less than epsilon
+ 
+
+ align:start position:0%
+is less than epsilon
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+just to
+
+ align:start position:0%
+just to
+ 
+
+ align:start position:0%
+just to
+so this is again a bit of review but i
+
+ align:start position:0%
+so this is again a bit of review but i
+ 
+
+ align:start position:0%
+so this is again a bit of review but i
+just want to show you that in general
+
+ align:start position:0%
+just want to show you that in general
+ 
+
+ align:start position:0%
+just want to show you that in general
+you know when we
+
+ align:start position:0%
+you know when we
+ 
+
+ align:start position:0%
+you know when we
+verify that a function is continuous on
+
+ align:start position:0%
+verify that a function is continuous on
+ 
+
+ align:start position:0%
+verify that a function is continuous on
+a set we have to show it's continuous at
+
+ align:start position:0%
+a set we have to show it's continuous at
+ 
+
+ align:start position:0%
+a set we have to show it's continuous at
+every point in the set and that means
+
+ align:start position:0%
+every point in the set and that means
+ 
+
+ align:start position:0%
+every point in the set and that means
+for every epsilon there exists a delta
+
+ align:start position:0%
+for every epsilon there exists a delta
+ 
+
+ align:start position:0%
+for every epsilon there exists a delta
+but this delta can depend on usually it
+
+ align:start position:0%
+but this delta can depend on usually it
+ 
+
+ align:start position:0%
+but this delta can depend on usually it
+depends on epsilon but it can also
+
+ align:start position:0%
+depends on epsilon but it can also
+ 
+
+ align:start position:0%
+depends on epsilon but it can also
+depend on the point c which is where
+
+ align:start position:0%
+depend on the point c which is where
+ 
+
+ align:start position:0%
+depend on the point c which is where
+we're checking continuity at okay
+
+ align:start position:0%
+we're checking continuity at okay
+ 
+
+ align:start position:0%
+we're checking continuity at okay
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+for simple example let's take
+
+ align:start position:0%
+for simple example let's take
+ 
+
+ align:start position:0%
+for simple example let's take
+f of x equals 1 over x
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+on the interval 0 1 open interval 0 1.
+
+ align:start position:0%
+on the interval 0 1 open interval 0 1.
+ 
+
+ align:start position:0%
+on the interval 0 1 open interval 0 1.
+okay so i claim
+
+ align:start position:0%
+okay so i claim
+ 
+
+ align:start position:0%
+okay so i claim
+f of x
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+equals 1 over x is continuous
+
+ align:start position:0%
+equals 1 over x is continuous
+ 
+
+ align:start position:0%
+equals 1 over x is continuous
+so proof
+
+ align:start position:0%
+so proof
+ 
+
+ align:start position:0%
+so proof
+we have to show that for every c
+
+ align:start position:0%
+we have to show that for every c
+ 
+
+ align:start position:0%
+we have to show that for every c
+in 0 1 for all epsilon there exists that
+
+ align:start position:0%
+in 0 1 for all epsilon there exists that
+ 
+
+ align:start position:0%
+in 0 1 for all epsilon there exists that
+so let's see
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+b and 0 1.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+let
+
+ align:start position:0%
+let
+ 
+
+ align:start position:0%
+let
+epsilon be positive
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+now choose
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+again i mean i'm not since this is kind
+
+ align:start position:0%
+again i mean i'm not since this is kind
+ 
+
+ align:start position:0%
+again i mean i'm not since this is kind
+of review i'm not going to go through
+
+ align:start position:0%
+of review i'm not going to go through
+ 
+
+ align:start position:0%
+of review i'm not going to go through
+the process of of really the thinking
+
+ align:start position:0%
+the process of of really the thinking
+ 
+
+ align:start position:0%
+the process of of really the thinking
+behind choosing this
+
+ align:start position:0%
+behind choosing this
+ 
+
+ align:start position:0%
+behind choosing this
+this delta i mean there's you know
+
+ align:start position:0%
+this delta i mean there's you know
+ 
+
+ align:start position:0%
+this delta i mean there's you know
+calculations you do off to the side to
+
+ align:start position:0%
+calculations you do off to the side to
+ 
+
+ align:start position:0%
+calculations you do off to the side to
+try and get this delta but let's choose
+
+ align:start position:0%
+try and get this delta but let's choose
+ 
+
+ align:start position:0%
+try and get this delta but let's choose
+delta to be
+
+ align:start position:0%
+delta to be
+ 
+
+ align:start position:0%
+delta to be
+the minimum of
+
+ align:start position:0%
+the minimum of
+ 
+
+ align:start position:0%
+the minimum of
+c over 2
+
+ align:start position:0%
+c over 2
+ 
+
+ align:start position:0%
+c over 2
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+c squared over 2
+
+ align:start position:0%
+c squared over 2
+ 
+
+ align:start position:0%
+c squared over 2
+times epsilon
+
+ align:start position:0%
+times epsilon
+ 
+
+ align:start position:0%
+times epsilon
+so what you notice
+
+ align:start position:0%
+so what you notice
+ 
+
+ align:start position:0%
+so what you notice
+what i want to again emphasize is this
+
+ align:start position:0%
+what i want to again emphasize is this
+ 
+
+ align:start position:0%
+what i want to again emphasize is this
+delta depends on c the point we're
+
+ align:start position:0%
+delta depends on c the point we're
+ 
+
+ align:start position:0%
+delta depends on c the point we're
+looking at and epsilon okay
+
+ align:start position:0%
+looking at and epsilon okay
+ 
+
+ align:start position:0%
+looking at and epsilon okay
+so i claim this delta works
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+suppose x is in
+
+ align:start position:0%
+suppose x is in
+ 
+
+ align:start position:0%
+suppose x is in
+0 1 and x minus c
+
+ align:start position:0%
+0 1 and x minus c
+ 
+
+ align:start position:0%
+0 1 and x minus c
+is less than delta
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+then
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+absolute value of x this is equal to the
+
+ align:start position:0%
+absolute value of x this is equal to the
+ 
+
+ align:start position:0%
+absolute value of x this is equal to the
+f
+
+ align:start position:0%
+f
+ 
+
+ align:start position:0%
+f
+this is
+
+ align:start position:0%
+this is
+ 
+
+ align:start position:0%
+this is
+by the triangle inequality
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so let me write it this way
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+c
+
+ align:start position:0%
+c
+ 
+
+ align:start position:0%
+c
+absolute value
+
+ align:start position:0%
+absolute value
+ 
+
+ align:start position:0%
+absolute value
+is equal to
+
+ align:start position:0%
+is equal to
+ 
+
+ align:start position:0%
+is equal to
+c minus x plus x which is less than or
+
+ align:start position:0%
+c minus x plus x which is less than or
+ 
+
+ align:start position:0%
+c minus x plus x which is less than or
+equal to
+
+ align:start position:0%
+equal to
+ 
+
+ align:start position:0%
+equal to
+c minus x
+
+ align:start position:0%
+c minus x
+ 
+
+ align:start position:0%
+c minus x
+plus x
+
+ align:start position:0%
+plus x
+ 
+
+ align:start position:0%
+plus x
+which is less than delta
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+which is less than or equal to the
+
+ align:start position:0%
+which is less than or equal to the
+ 
+
+ align:start position:0%
+which is less than or equal to the
+minimum of these two so it's certainly
+
+ align:start position:0%
+minimum of these two so it's certainly
+ 
+
+ align:start position:0%
+minimum of these two so it's certainly
+mess less than or equal to c over two
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+plus x and now you know c and uh
+
+ align:start position:0%
+plus x and now you know c and uh
+ 
+
+ align:start position:0%
+plus x and now you know c and uh
+x these are in zero one so they're all
+
+ align:start position:0%
+x these are in zero one so they're all
+ 
+
+ align:start position:0%
+x these are in zero one so they're all
+positive
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and therefore i get that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+let's go to the next board
+
+ align:start position:0%
+let's go to the next board
+ 
+
+ align:start position:0%
+let's go to the next board
+[Applause]
+
+ align:start position:0%
+[Applause]
+ 
+
+ align:start position:0%
+[Applause]
+so if i subtract the c over to the other
+
+ align:start position:0%
+so if i subtract the c over to the other
+ 
+
+ align:start position:0%
+so if i subtract the c over to the other
+the c over 2 over to the other side i
+
+ align:start position:0%
+the c over 2 over to the other side i
+ 
+
+ align:start position:0%
+the c over 2 over to the other side i
+get that
+
+ align:start position:0%
+get that
+ 
+
+ align:start position:0%
+get that
+c over 2 is less than
+
+ align:start position:0%
+c over 2 is less than
+ 
+
+ align:start position:0%
+c over 2 is less than
+x all right so this is as long as x is
+
+ align:start position:0%
+x all right so this is as long as x is
+ 
+
+ align:start position:0%
+x all right so this is as long as x is
+in 0 1 and x minus c is less than delta
+
+ align:start position:0%
+in 0 1 and x minus c is less than delta
+ 
+
+ align:start position:0%
+in 0 1 and x minus c is less than delta
+okay this should not be a shock all
+
+ align:start position:0%
+okay this should not be a shock all
+ 
+
+ align:start position:0%
+okay this should not be a shock all
+right
+
+ align:start position:0%
+right
+ 
+
+ align:start position:0%
+right
+here's 0
+
+ align:start position:0%
+here's 0
+ 
+
+ align:start position:0%
+here's 0
+
+ align:start position:0%
+ 
+
+ align:start position:0%
+c
+
+ align:start position:0%
+c
+ 
+
+ align:start position:0%
+c
+c over 2
+
+ align:start position:0%
+c over 2
+ 
+
+ align:start position:0%
+c over 2
+3 c over 2.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+and so if x is in this interval it's
+
+ align:start position:0%
+and so if x is in this interval it's
+ 
+
+ align:start position:0%
+and so if x is in this interval it's
+certainly bounded away by c over two
+
+ align:start position:0%
+certainly bounded away by c over two
+ 
+
+ align:start position:0%
+certainly bounded away by c over two
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+um or if x is in here then x is
+
+ align:start position:0%
+um or if x is in here then x is
+ 
+
+ align:start position:0%
+um or if x is in here then x is
+certainly bigger than c over two
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+all right and now we look at
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+f of x minus f of c
+
+ align:start position:0%
+f of x minus f of c
+ 
+
+ align:start position:0%
+f of x minus f of c
+this is equal to 1 over x minus 1 over c
+
+ align:start position:0%
+this is equal to 1 over x minus 1 over c
+ 
+
+ align:start position:0%
+this is equal to 1 over x minus 1 over c
+equals
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+c minus x over x times c
+
+ align:start position:0%
+c minus x over x times c
+ 
+
+ align:start position:0%
+c minus x over x times c
+which is less than delta over x times c
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+because this is a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+and now x is less than x is bigger than
+
+ align:start position:0%
+and now x is less than x is bigger than
+ 
+
+ align:start position:0%
+and now x is less than x is bigger than
+c over 2 so if i take 1 over that
+
+ align:start position:0%
+c over 2 so if i take 1 over that
+ 
+
+ align:start position:0%
+c over 2 so if i take 1 over that
+i get
+
+ align:start position:0%
+i get
+ 
+
+ align:start position:0%
+i get
+1 over x is less than 2 over c so this
+
+ align:start position:0%
+1 over x is less than 2 over c so this
+ 
+
+ align:start position:0%
+1 over x is less than 2 over c so this
+is less than or equal to 2 delta
+
+ align:start position:0%
+is less than or equal to 2 delta
+ 
+
+ align:start position:0%
+is less than or equal to 2 delta
+over c squared and delta is the minimum
+
+ align:start position:0%
+over c squared and delta is the minimum
+ 
+
+ align:start position:0%
+over c squared and delta is the minimum
+of now c over 2 and c squared over 2
+
+ align:start position:0%
+of now c over 2 and c squared over 2
+ 
+
+ align:start position:0%
+of now c over 2 and c squared over 2
+times epsilon
+
+ align:start position:0%
+times epsilon
+ 
+
+ align:start position:0%
+times epsilon
+so this is less than or equal to 2 over
+
+ align:start position:0%
+so this is less than or equal to 2 over
+ 
+
+ align:start position:0%
+so this is less than or equal to 2 over
+c squared times c squared over two
+
+ align:start position:0%
+c squared times c squared over two
+ 
+
+ align:start position:0%
+c squared times c squared over two
+epsilon equals epsilon okay
+
+ align:start position:0%
+epsilon equals epsilon okay
+ 
+
+ align:start position:0%
+epsilon equals epsilon okay
+so i just went through the proof of
+
+ align:start position:0%
+so i just went through the proof of
+ 
+
+ align:start position:0%
+so i just went through the proof of
+continuity for one over x which uh
+
+ align:start position:0%
+continuity for one over x which uh
+ 
+
+ align:start position:0%
+continuity for one over x which uh
+you know using
+
+ align:start position:0%
+you know using
+ 
+
+ align:start position:0%
+you know using
+better machinery we could have proven
+
+ align:start position:0%
+better machinery we could have proven
+ 
+
+ align:start position:0%
+better machinery we could have proven
+but uh
+
+ align:start position:0%
+but uh
+ 
+
+ align:start position:0%
+but uh
+i did this to to highlight this point
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that's showing
+
+ align:start position:0%
+that's showing
+ 
+
+ align:start position:0%
+that's showing
+continuity of one over x on zero one
+
+ align:start position:0%
+continuity of one over x on zero one
+ 
+
+ align:start position:0%
+continuity of one over x on zero one
+that in showing that you know
+
+ align:start position:0%
+that in showing that you know
+ 
+
+ align:start position:0%
+that in showing that you know
+this delta that you are choosing depends
+
+ align:start position:0%
+this delta that you are choosing depends
+ 
+
+ align:start position:0%
+this delta that you are choosing depends
+kind of on the point you're looking at
+
+ align:start position:0%
+kind of on the point you're looking at
+ 
+
+ align:start position:0%
+kind of on the point you're looking at
+all right so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+now i want to make a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so you know what the definition of
+
+ align:start position:0%
+so you know what the definition of
+ 
+
+ align:start position:0%
+so you know what the definition of
+continuity says is for all c
+
+ align:start position:0%
+continuity says is for all c
+ 
+
+ align:start position:0%
+continuity says is for all c
+for all epsilon you can find a delta
+
+ align:start position:0%
+for all epsilon you can find a delta
+ 
+
+ align:start position:0%
+for all epsilon you can find a delta
+uh depending on epsilon and c
+
+ align:start position:0%
+uh depending on epsilon and c
+ 
+
+ align:start position:0%
+uh depending on epsilon and c
+now uniform continuity
+
+ align:start position:0%
+now uniform continuity
+ 
+
+ align:start position:0%
+now uniform continuity
+removes that necessity of delta
+
+ align:start position:0%
+removes that necessity of delta
+ 
+
+ align:start position:0%
+removes that necessity of delta
+depending on c
+
+ align:start position:0%
+depending on c
+ 
+
+ align:start position:0%
+depending on c
+okay and i'm going to make a
+
+ align:start position:0%
+okay and i'm going to make a
+ 
+
+ align:start position:0%
+okay and i'm going to make a
+possibly bad analogy in just a minute
+
+ align:start position:0%
+possibly bad analogy in just a minute
+ 
+
+ align:start position:0%
+possibly bad analogy in just a minute
+but first let me write down the
+
+ align:start position:0%
+but first let me write down the
+ 
+
+ align:start position:0%
+but first let me write down the
+definition of uniform continuity
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+let s be a subset of r
+
+ align:start position:0%
+let s be a subset of r
+ 
+
+ align:start position:0%
+let s be a subset of r
+f going from s to r
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+we say f
+
+ align:start position:0%
+we say f
+ 
+
+ align:start position:0%
+we say f
+is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uniformly
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+continuous
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+on s
+
+ align:start position:0%
+on s
+ 
+
+ align:start position:0%
+on s
+if
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+we're all epsilon positive
+
+ align:start position:0%
+we're all epsilon positive
+ 
+
+ align:start position:0%
+we're all epsilon positive
+there exists a delta depending only on
+
+ align:start position:0%
+there exists a delta depending only on
+ 
+
+ align:start position:0%
+there exists a delta depending only on
+epsilon
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+such that
+
+ align:start position:0%
+such that
+ 
+
+ align:start position:0%
+such that
+for all xc and s
+
+ align:start position:0%
+for all xc and s
+ 
+
+ align:start position:0%
+for all xc and s
+with x minus c less than delta
+
+ align:start position:0%
+with x minus c less than delta
+ 
+
+ align:start position:0%
+with x minus c less than delta
+we get that f of x
+
+ align:start position:0%
+we get that f of x
+ 
+
+ align:start position:0%
+we get that f of x
+minus f of c
+
+ align:start position:0%
+minus f of c
+ 
+
+ align:start position:0%
+minus f of c
+is less than epsilon
+
+ align:start position:0%
+is less than epsilon
+ 
+
+ align:start position:0%
+is less than epsilon
+okay so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+you know a function being continuous
+
+ align:start position:0%
+you know a function being continuous
+ 
+
+ align:start position:0%
+you know a function being continuous
+means that for all epsilon you can find
+
+ align:start position:0%
+means that for all epsilon you can find
+ 
+
+ align:start position:0%
+means that for all epsilon you can find
+a delta depending on one of these points
+
+ align:start position:0%
+a delta depending on one of these points
+ 
+
+ align:start position:0%
+a delta depending on one of these points
+depending on c so that if i have this
+
+ align:start position:0%
+depending on c so that if i have this
+ 
+
+ align:start position:0%
+depending on c so that if i have this
+then i have this
+
+ align:start position:0%
+then i have this
+ 
+
+ align:start position:0%
+then i have this
+uniform continuity says you can find a
+
+ align:start position:0%
+uniform continuity says you can find a
+ 
+
+ align:start position:0%
+uniform continuity says you can find a
+delta
+
+ align:start position:0%
+delta
+ 
+
+ align:start position:0%
+delta
+that works across the board okay um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so i'm gonna make a try and make a an
+
+ align:start position:0%
+so i'm gonna make a try and make a an
+ 
+
+ align:start position:0%
+so i'm gonna make a try and make a an
+analogy that hopefully i don't have to
+
+ align:start position:0%
+analogy that hopefully i don't have to
+ 
+
+ align:start position:0%
+analogy that hopefully i don't have to
+cut out of this lecture
+
+ align:start position:0%
+cut out of this lecture
+ 
+
+ align:start position:0%
+cut out of this lecture
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+but it's a bit like this
+
+ align:start position:0%
+but it's a bit like this
+ 
+
+ align:start position:0%
+but it's a bit like this
+let's take a trip down memory lane
+
+ align:start position:0%
+let's take a trip down memory lane
+ 
+
+ align:start position:0%
+let's take a trip down memory lane
+and imagine being at a party
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so you know everybody's in a party and
+
+ align:start position:0%
+so you know everybody's in a party and
+ 
+
+ align:start position:0%
+so you know everybody's in a party and
+let's
+
+ align:start position:0%
+let's
+ 
+
+ align:start position:0%
+let's
+say that everybody can hear
+
+ align:start position:0%
+say that everybody can hear
+ 
+
+ align:start position:0%
+say that everybody can hear
+their ears work just about the same
+
+ align:start position:0%
+their ears work just about the same
+ 
+
+ align:start position:0%
+their ears work just about the same
+and the goal is you know to try and
+
+ align:start position:0%
+and the goal is you know to try and
+ 
+
+ align:start position:0%
+and the goal is you know to try and
+understand each other's conversations
+
+ align:start position:0%
+understand each other's conversations
+ 
+
+ align:start position:0%
+understand each other's conversations
+try try and hear each other's
+
+ align:start position:0%
+try try and hear each other's
+ 
+
+ align:start position:0%
+try try and hear each other's
+conversations
+
+ align:start position:0%
+conversations
+ 
+
+ align:start position:0%
+conversations
+now in order for
+
+ align:start position:0%
+now in order for
+ 
+
+ align:start position:0%
+now in order for
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+you know
+
+ align:start position:0%
+you know
+ 
+
+ align:start position:0%
+you know
+me to hear this person's conversation
+
+ align:start position:0%
+me to hear this person's conversation
+ 
+
+ align:start position:0%
+me to hear this person's conversation
+depending on how loud they talk i have
+
+ align:start position:0%
+depending on how loud they talk i have
+ 
+
+ align:start position:0%
+depending on how loud they talk i have
+to be
+
+ align:start position:0%
+to be
+ 
+
+ align:start position:0%
+to be
+close enough to be able to hear them
+
+ align:start position:0%
+close enough to be able to hear them
+ 
+
+ align:start position:0%
+close enough to be able to hear them
+you know and this changes from person to
+
+ align:start position:0%
+you know and this changes from person to
+ 
+
+ align:start position:0%
+you know and this changes from person to
+person in the room maybe i have to i can
+
+ align:start position:0%
+person in the room maybe i have to i can
+ 
+
+ align:start position:0%
+person in the room maybe i have to i can
+stand a foot away from
+
+ align:start position:0%
+stand a foot away from
+ 
+
+ align:start position:0%
+stand a foot away from
+this person over here maybe this person
+
+ align:start position:0%
+this person over here maybe this person
+ 
+
+ align:start position:0%
+this person over here maybe this person
+over here is a
+
+ align:start position:0%
+over here is a
+ 
+
+ align:start position:0%
+over here is a
+low talker and i have to be almost up in
+
+ align:start position:0%
+low talker and i have to be almost up in
+ 
+
+ align:start position:0%
+low talker and i have to be almost up in
+their face to be able to hear them maybe
+
+ align:start position:0%
+their face to be able to hear them maybe
+ 
+
+ align:start position:0%
+their face to be able to hear them maybe
+that person just whispers and i have to
+
+ align:start position:0%
+that person just whispers and i have to
+ 
+
+ align:start position:0%
+that person just whispers and i have to
+be almost nose to nose to be able to
+
+ align:start position:0%
+be almost nose to nose to be able to
+ 
+
+ align:start position:0%
+be almost nose to nose to be able to
+hear them you know that's a bit like a
+
+ align:start position:0%
+hear them you know that's a bit like a
+ 
+
+ align:start position:0%
+hear them you know that's a bit like a
+function being
+
+ align:start position:0%
+function being
+ 
+
+ align:start position:0%
+function being
+continuous okay
+
+ align:start position:0%
+continuous okay
+ 
+
+ align:start position:0%
+continuous okay
+you know
+
+ align:start position:0%
+you know
+ 
+
+ align:start position:0%
+you know
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+threshold of hearing
+
+ align:start position:0%
+threshold of hearing
+ 
+
+ align:start position:0%
+threshold of hearing
+what they're saying is the epsilon and i
+
+ align:start position:0%
+what they're saying is the epsilon and i
+ 
+
+ align:start position:0%
+what they're saying is the epsilon and i
+have to change my delta depending on
+
+ align:start position:0%
+have to change my delta depending on
+ 
+
+ align:start position:0%
+have to change my delta depending on
+what point i'm at so that i can hear
+
+ align:start position:0%
+what point i'm at so that i can hear
+ 
+
+ align:start position:0%
+what point i'm at so that i can hear
+them
+
+ align:start position:0%
+them
+ 
+
+ align:start position:0%
+them
+now uniform continuity
+
+ align:start position:0%
+now uniform continuity
+ 
+
+ align:start position:0%
+now uniform continuity
+is kind of like
+
+ align:start position:0%
+is kind of like
+ 
+
+ align:start position:0%
+is kind of like
+everybody's um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+more or less speaking around the same uh
+
+ align:start position:0%
+more or less speaking around the same uh
+ 
+
+ align:start position:0%
+more or less speaking around the same uh
+level
+
+ align:start position:0%
+level
+ 
+
+ align:start position:0%
+level
+speaking at the same loudness all right
+
+ align:start position:0%
+speaking at the same loudness all right
+ 
+
+ align:start position:0%
+speaking at the same loudness all right
+so i just can be within say one foot of
+
+ align:start position:0%
+so i just can be within say one foot of
+ 
+
+ align:start position:0%
+so i just can be within say one foot of
+everybody and be able to understand them
+
+ align:start position:0%
+everybody and be able to understand them
+ 
+
+ align:start position:0%
+everybody and be able to understand them
+i go to this person if i'm within one
+
+ align:start position:0%
+i go to this person if i'm within one
+ 
+
+ align:start position:0%
+i go to this person if i'm within one
+foot i can hear them well
+
+ align:start position:0%
+foot i can hear them well
+ 
+
+ align:start position:0%
+foot i can hear them well
+if i go to this person i hear and
+
+ align:start position:0%
+if i go to this person i hear and
+ 
+
+ align:start position:0%
+if i go to this person i hear and
+within one foot i can hear them well and
+
+ align:start position:0%
+within one foot i can hear them well and
+ 
+
+ align:start position:0%
+within one foot i can hear them well and
+and so on all right so that's
+
+ align:start position:0%
+and so on all right so that's
+ 
+
+ align:start position:0%
+and so on all right so that's
+kind of the difference between you know
+
+ align:start position:0%
+kind of the difference between you know
+ 
+
+ align:start position:0%
+kind of the difference between you know
+or at least a loose analogy of the
+
+ align:start position:0%
+or at least a loose analogy of the
+ 
+
+ align:start position:0%
+or at least a loose analogy of the
+difference between continuity and
+
+ align:start position:0%
+difference between continuity and
+ 
+
+ align:start position:0%
+difference between continuity and
+uniform continuity
+
+ align:start position:0%
+uniform continuity
+ 
+
+ align:start position:0%
+uniform continuity
+all right um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so this is a
+
+ align:start position:0%
+so this is a
+ 
+
+ align:start position:0%
+so this is a
+you know
+
+ align:start position:0%
+you know
+ 
+
+ align:start position:0%
+you know
+reasonably interesting definition so we
+
+ align:start position:0%
+reasonably interesting definition so we
+ 
+
+ align:start position:0%
+reasonably interesting definition so we
+should see examples and negate it
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um first off
+
+ align:start position:0%
+um first off
+ 
+
+ align:start position:0%
+um first off
+you know i
+
+ align:start position:0%
+you know i
+ 
+
+ align:start position:0%
+you know i
+you should be able to convince yourself
+
+ align:start position:0%
+you should be able to convince yourself
+ 
+
+ align:start position:0%
+you should be able to convince yourself
+that a function that's uniformly
+
+ align:start position:0%
+that a function that's uniformly
+ 
+
+ align:start position:0%
+that a function that's uniformly
+continuous is actually continuous i'm
+
+ align:start position:0%
+continuous is actually continuous i'm
+ 
+
+ align:start position:0%
+continuous is actually continuous i'm
+not going to write that the proof of
+
+ align:start position:0%
+not going to write that the proof of
+ 
+
+ align:start position:0%
+not going to write that the proof of
+that down it follows essentially
+
+ align:start position:0%
+that down it follows essentially
+ 
+
+ align:start position:0%
+that down it follows essentially
+straight from the definition
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+but let's look at uh
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+let's look at a function which is
+
+ align:start position:0%
+let's look at a function which is
+ 
+
+ align:start position:0%
+let's look at a function which is
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+uniformly consent continuous so
+
+ align:start position:0%
+uniformly consent continuous so
+ 
+
+ align:start position:0%
+uniformly consent continuous so
+the function f of x
+
+ align:start position:0%
+the function f of x
+ 
+
+ align:start position:0%
+the function f of x
+equals x squared
+
+ align:start position:0%
+equals x squared
+ 
+
+ align:start position:0%
+equals x squared
+on the interval 0 1.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+is uniformly continuous
+
+ align:start position:0%
+is uniformly continuous
+ 
+
+ align:start position:0%
+is uniformly continuous
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+so what's the proof
+
+ align:start position:0%
+so what's the proof
+ 
+
+ align:start position:0%
+so what's the proof
+i want you to notice i'm going to use
+
+ align:start position:0%
+i want you to notice i'm going to use
+ 
+
+ align:start position:0%
+i want you to notice i'm going to use
+kind of in a
+
+ align:start position:0%
+kind of in a
+ 
+
+ align:start position:0%
+kind of in a
+very
+
+ align:start position:0%
+very
+ 
+
+ align:start position:0%
+very
+essential way that we're on this closed
+
+ align:start position:0%
+essential way that we're on this closed
+ 
+
+ align:start position:0%
+essential way that we're on this closed
+and bounded interval
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so we need to show that for every
+
+ align:start position:0%
+so we need to show that for every
+ 
+
+ align:start position:0%
+so we need to show that for every
+epsilon there exists a delta
+
+ align:start position:0%
+epsilon there exists a delta
+ 
+
+ align:start position:0%
+epsilon there exists a delta
+so that no matter what two points
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so if you'd like here's a picture that
+
+ align:start position:0%
+so if you'd like here's a picture that
+ 
+
+ align:start position:0%
+so if you'd like here's a picture that
+goes
+
+ align:start position:0%
+goes
+ 
+
+ align:start position:0%
+goes
+along with this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so that if i look at
+
+ align:start position:0%
+so that if i look at
+ 
+
+ align:start position:0%
+so that if i look at
+any two points that are close to each
+
+ align:start position:0%
+any two points that are close to each
+ 
+
+ align:start position:0%
+any two points that are close to each
+other less than delta
+
+ align:start position:0%
+other less than delta
+ 
+
+ align:start position:0%
+other less than delta
+their
+
+ align:start position:0%
+their
+ 
+
+ align:start position:0%
+their
+function's value
+
+ align:start position:0%
+function's value
+ 
+
+ align:start position:0%
+function's value
+is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+within epsilon and so let's say i'm on
+
+ align:start position:0%
+within epsilon and so let's say i'm on
+ 
+
+ align:start position:0%
+within epsilon and so let's say i'm on
+interval a b but not just this point i
+
+ align:start position:0%
+interval a b but not just this point i
+ 
+
+ align:start position:0%
+interval a b but not just this point i
+could go over here to two other
+
+ align:start position:0%
+could go over here to two other
+ 
+
+ align:start position:0%
+could go over here to two other
+points that are within delta of each
+
+ align:start position:0%
+points that are within delta of each
+ 
+
+ align:start position:0%
+points that are within delta of each
+other and if i look at
+
+ align:start position:0%
+other and if i look at
+ 
+
+ align:start position:0%
+other and if i look at
+the function evaluated
+
+ align:start position:0%
+the function evaluated
+ 
+
+ align:start position:0%
+the function evaluated
+at the two points
+
+ align:start position:0%
+at the two points
+ 
+
+ align:start position:0%
+at the two points
+and
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+then the difference between these two
+
+ align:start position:0%
+then the difference between these two
+ 
+
+ align:start position:0%
+then the difference between these two
+guys is also less than epsilon
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+so i can move
+
+ align:start position:0%
+so i can move
+ 
+
+ align:start position:0%
+so i can move
+through the party and as long as i'm
+
+ align:start position:0%
+through the party and as long as i'm
+ 
+
+ align:start position:0%
+through the party and as long as i'm
+close enough
+
+ align:start position:0%
+close enough
+ 
+
+ align:start position:0%
+close enough
+within you know a uniform distance to
+
+ align:start position:0%
+within you know a uniform distance to
+ 
+
+ align:start position:0%
+within you know a uniform distance to
+somebody i can i can hear them just fine
+
+ align:start position:0%
+somebody i can i can hear them just fine
+ 
+
+ align:start position:0%
+somebody i can i can hear them just fine
+all right so
+
+ align:start position:0%
+all right so
+ 
+
+ align:start position:0%
+all right so
+[Applause]
+
+ align:start position:0%
+[Applause]
+ 
+
+ align:start position:0%
+[Applause]
+what a nice trip down memory lane when
+
+ align:start position:0%
+what a nice trip down memory lane when
+ 
+
+ align:start position:0%
+what a nice trip down memory lane when
+we could be around other people um
+
+ align:start position:0%
+we could be around other people um
+ 
+
+ align:start position:0%
+we could be around other people um
+so let's show this function is uniformly
+
+ align:start position:0%
+so let's show this function is uniformly
+ 
+
+ align:start position:0%
+so let's show this function is uniformly
+continuous let epsilon be positive
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+choose delta to be
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+epsilon over 2.
+
+ align:start position:0%
+epsilon over 2.
+ 
+
+ align:start position:0%
+epsilon over 2.
+now you see this delta just depends on
+
+ align:start position:0%
+now you see this delta just depends on
+ 
+
+ align:start position:0%
+now you see this delta just depends on
+epsilon
+
+ align:start position:0%
+epsilon
+ 
+
+ align:start position:0%
+epsilon
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+then if
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+x and c are in 0 1
+
+ align:start position:0%
+x and c are in 0 1
+ 
+
+ align:start position:0%
+x and c are in 0 1
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+x minus c is less than delta
+
+ align:start position:0%
+x minus c is less than delta
+ 
+
+ align:start position:0%
+x minus c is less than delta
+then
+
+ align:start position:0%
+then
+ 
+
+ align:start position:0%
+then
+if i compute
+
+ align:start position:0%
+if i compute
+ 
+
+ align:start position:0%
+if i compute
+the difference x squared minus c squared
+
+ align:start position:0%
+the difference x squared minus c squared
+ 
+
+ align:start position:0%
+the difference x squared minus c squared
+this is
+
+ align:start position:0%
+this is
+ 
+
+ align:start position:0%
+this is
+i can write as x plus c times x minus c
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and now i use the triangle inequality
+
+ align:start position:0%
+and now i use the triangle inequality
+ 
+
+ align:start position:0%
+and now i use the triangle inequality
+this is less than or equal to
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+x minus c
+
+ align:start position:0%
+x minus c
+ 
+
+ align:start position:0%
+x minus c
+now these guys are in zero one so their
+
+ align:start position:0%
+now these guys are in zero one so their
+ 
+
+ align:start position:0%
+now these guys are in zero one so their
+absolute value is always bounded by one
+
+ align:start position:0%
+absolute value is always bounded by one
+ 
+
+ align:start position:0%
+absolute value is always bounded by one
+so this is less than or equal to one
+
+ align:start position:0%
+so this is less than or equal to one
+ 
+
+ align:start position:0%
+so this is less than or equal to one
+plus one
+
+ align:start position:0%
+plus one
+ 
+
+ align:start position:0%
+plus one
+and then x minus c is bounded by delta
+
+ align:start position:0%
+and then x minus c is bounded by delta
+ 
+
+ align:start position:0%
+and then x minus c is bounded by delta
+which equals two times delta and delta
+
+ align:start position:0%
+which equals two times delta and delta
+ 
+
+ align:start position:0%
+which equals two times delta and delta
+is chosen to be epsilon over two so i
+
+ align:start position:0%
+is chosen to be epsilon over two so i
+ 
+
+ align:start position:0%
+is chosen to be epsilon over two so i
+get epsilon
+
+ align:start position:0%
+get epsilon
+ 
+
+ align:start position:0%
+get epsilon
+all right now again how would you choose
+
+ align:start position:0%
+all right now again how would you choose
+ 
+
+ align:start position:0%
+all right now again how would you choose
+delta so it looks like i just chose this
+
+ align:start position:0%
+delta so it looks like i just chose this
+ 
+
+ align:start position:0%
+delta so it looks like i just chose this
+delta out of nowhere in practice how do
+
+ align:start position:0%
+delta out of nowhere in practice how do
+ 
+
+ align:start position:0%
+delta out of nowhere in practice how do
+you choose delta
+
+ align:start position:0%
+you choose delta
+ 
+
+ align:start position:0%
+you choose delta
+this is the computation you do you take
+
+ align:start position:0%
+this is the computation you do you take
+ 
+
+ align:start position:0%
+this is the computation you do you take
+x squared minus c squared split it
+
+ align:start position:0%
+x squared minus c squared split it
+ 
+
+ align:start position:0%
+x squared minus c squared split it
+you have this
+
+ align:start position:0%
+you have this
+ 
+
+ align:start position:0%
+you have this
+you can estimate with what you know
+
+ align:start position:0%
+you can estimate with what you know
+ 
+
+ align:start position:0%
+you can estimate with what you know
+above by
+
+ align:start position:0%
+above by
+ 
+
+ align:start position:0%
+above by
+2 here times delta
+
+ align:start position:0%
+2 here times delta
+ 
+
+ align:start position:0%
+2 here times delta
+so how do you choose delta so that two
+
+ align:start position:0%
+so how do you choose delta so that two
+ 
+
+ align:start position:0%
+so how do you choose delta so that two
+times delta is
+
+ align:start position:0%
+times delta is
+ 
+
+ align:start position:0%
+times delta is
+say equal to epsilon you choose delta to
+
+ align:start position:0%
+say equal to epsilon you choose delta to
+ 
+
+ align:start position:0%
+say equal to epsilon you choose delta to
+be epsilon over two
+
+ align:start position:0%
+be epsilon over two
+ 
+
+ align:start position:0%
+be epsilon over two
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+all right so um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+let's negate this definition and then
+
+ align:start position:0%
+let's negate this definition and then
+ 
+
+ align:start position:0%
+let's negate this definition and then
+look at one over x once again
+
+ align:start position:0%
+look at one over x once again
+ 
+
+ align:start position:0%
+look at one over x once again
+and check to see if it's uniformly
+
+ align:start position:0%
+and check to see if it's uniformly
+ 
+
+ align:start position:0%
+and check to see if it's uniformly
+continuous we'll show it's not
+
+ align:start position:0%
+continuous we'll show it's not
+ 
+
+ align:start position:0%
+continuous we'll show it's not
+so the negation
+
+ align:start position:0%
+so the negation
+ 
+
+ align:start position:0%
+so the negation
+f from s to r
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+is not uniformly
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+continuous
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+i saw a little bit of the new borat
+
+ align:start position:0%
+i saw a little bit of the new borat
+ 
+
+ align:start position:0%
+i saw a little bit of the new borat
+movie that came out so i almost wanted
+
+ align:start position:0%
+movie that came out so i almost wanted
+ 
+
+ align:start position:0%
+movie that came out so i almost wanted
+to say
+
+ align:start position:0%
+to say
+ 
+
+ align:start position:0%
+to say
+f is uniformly continuous not but i
+
+ align:start position:0%
+f is uniformly continuous not but i
+ 
+
+ align:start position:0%
+f is uniformly continuous not but i
+didn't
+
+ align:start position:0%
+didn't
+ 
+
+ align:start position:0%
+didn't
+it's not uniformly continuous
+
+ align:start position:0%
+it's not uniformly continuous
+ 
+
+ align:start position:0%
+it's not uniformly continuous
+if and now you negate the rest of the
+
+ align:start position:0%
+if and now you negate the rest of the
+ 
+
+ align:start position:0%
+if and now you negate the rest of the
+definition
+
+ align:start position:0%
+definition
+ 
+
+ align:start position:0%
+definition
+if there exists some bad epsilon
+
+ align:start position:0%
+if there exists some bad epsilon
+ 
+
+ align:start position:0%
+if there exists some bad epsilon
+such that no matter what delta you
+
+ align:start position:0%
+such that no matter what delta you
+ 
+
+ align:start position:0%
+such that no matter what delta you
+choose
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+there exists some bad x and c
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and s
+
+ align:start position:0%
+and s
+ 
+
+ align:start position:0%
+and s
+such that
+
+ align:start position:0%
+such that
+ 
+
+ align:start position:0%
+such that
+they're close to each other
+
+ align:start position:0%
+they're close to each other
+ 
+
+ align:start position:0%
+they're close to each other
+but the values are not
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+bigger than or equal to
+
+ align:start position:0%
+bigger than or equal to
+ 
+
+ align:start position:0%
+bigger than or equal to
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+let's
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+revisit one over x
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this is not
+
+ align:start position:0%
+this is not
+ 
+
+ align:start position:0%
+this is not
+uniformly continuous
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+on
+
+ align:start position:0%
+on
+ 
+
+ align:start position:0%
+on
+the open interval 0 1. so you see that
+
+ align:start position:0%
+the open interval 0 1. so you see that
+ 
+
+ align:start position:0%
+the open interval 0 1. so you see that
+this function is continuous but it's not
+
+ align:start position:0%
+this function is continuous but it's not
+ 
+
+ align:start position:0%
+this function is continuous but it's not
+uniformly continuous all right
+
+ align:start position:0%
+uniformly continuous all right
+ 
+
+ align:start position:0%
+uniformly continuous all right
+so we just proved that a minute ago that
+
+ align:start position:0%
+so we just proved that a minute ago that
+ 
+
+ align:start position:0%
+so we just proved that a minute ago that
+it's continuous so let me now
+
+ align:start position:0%
+it's continuous so let me now
+ 
+
+ align:start position:0%
+it's continuous so let me now
+give you the proof that this function is
+
+ align:start position:0%
+give you the proof that this function is
+ 
+
+ align:start position:0%
+give you the proof that this function is
+not uniformly continuous and what's the
+
+ align:start position:0%
+not uniformly continuous and what's the
+ 
+
+ align:start position:0%
+not uniformly continuous and what's the
+idea
+
+ align:start position:0%
+idea
+ 
+
+ align:start position:0%
+idea
+behind this
+
+ align:start position:0%
+behind this
+ 
+
+ align:start position:0%
+behind this
+here's one
+
+ align:start position:0%
+here's one
+ 
+
+ align:start position:0%
+here's one
+okay this is not to scale but there's
+
+ align:start position:0%
+okay this is not to scale but there's
+ 
+
+ align:start position:0%
+okay this is not to scale but there's
+one
+
+ align:start position:0%
+one
+ 
+
+ align:start position:0%
+one
+as well and
+
+ align:start position:0%
+as well and
+ 
+
+ align:start position:0%
+as well and
+one over x
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+you know
+
+ align:start position:0%
+you know
+ 
+
+ align:start position:0%
+you know
+shoots up to plus infinity as x
+
+ align:start position:0%
+shoots up to plus infinity as x
+ 
+
+ align:start position:0%
+shoots up to plus infinity as x
+approaches zero
+
+ align:start position:0%
+approaches zero
+ 
+
+ align:start position:0%
+approaches zero
+right
+
+ align:start position:0%
+right
+ 
+
+ align:start position:0%
+right
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+so what uniform continuity says is that
+
+ align:start position:0%
+so what uniform continuity says is that
+ 
+
+ align:start position:0%
+so what uniform continuity says is that
+if i take any two points in the interval
+
+ align:start position:0%
+if i take any two points in the interval
+ 
+
+ align:start position:0%
+if i take any two points in the interval
+that are close to each other then the
+
+ align:start position:0%
+that are close to each other then the
+ 
+
+ align:start position:0%
+that are close to each other then the
+outputs have to be close to each other
+
+ align:start position:0%
+outputs have to be close to each other
+ 
+
+ align:start position:0%
+outputs have to be close to each other
+all right
+
+ align:start position:0%
+all right
+ 
+
+ align:start position:0%
+all right
+continuity remember says if i fix a
+
+ align:start position:0%
+continuity remember says if i fix a
+ 
+
+ align:start position:0%
+continuity remember says if i fix a
+point
+
+ align:start position:0%
+point
+ 
+
+ align:start position:0%
+point
+then as long as i'm close to that point
+
+ align:start position:0%
+then as long as i'm close to that point
+ 
+
+ align:start position:0%
+then as long as i'm close to that point
+the outputs will be close to each other
+
+ align:start position:0%
+the outputs will be close to each other
+ 
+
+ align:start position:0%
+the outputs will be close to each other
+uniform says no matter what two points
+
+ align:start position:0%
+uniform says no matter what two points
+ 
+
+ align:start position:0%
+uniform says no matter what two points
+you choose as long as they're close
+
+ align:start position:0%
+you choose as long as they're close
+ 
+
+ align:start position:0%
+you choose as long as they're close
+together
+
+ align:start position:0%
+together
+ 
+
+ align:start position:0%
+together
+the outputs will be close together in a
+
+ align:start position:0%
+the outputs will be close together in a
+ 
+
+ align:start position:0%
+the outputs will be close together in a
+controlled way now if i take
+
+ align:start position:0%
+controlled way now if i take
+ 
+
+ align:start position:0%
+controlled way now if i take
+two points
+
+ align:start position:0%
+two points
+ 
+
+ align:start position:0%
+two points
+very close to each other here very close
+
+ align:start position:0%
+very close to each other here very close
+ 
+
+ align:start position:0%
+very close to each other here very close
+to zero
+
+ align:start position:0%
+to zero
+ 
+
+ align:start position:0%
+to zero
+they can be you know pretty close to
+
+ align:start position:0%
+they can be you know pretty close to
+ 
+
+ align:start position:0%
+they can be you know pretty close to
+each other
+
+ align:start position:0%
+each other
+ 
+
+ align:start position:0%
+each other
+but their differences
+
+ align:start position:0%
+but their differences
+ 
+
+ align:start position:0%
+but their differences
+i mean their values
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+can be
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+quite large
+
+ align:start position:0%
+quite large
+ 
+
+ align:start position:0%
+quite large
+even though
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the difference between the
+
+ align:start position:0%
+the difference between the
+ 
+
+ align:start position:0%
+the difference between the
+arguments are small the values can be
+
+ align:start position:0%
+arguments are small the values can be
+ 
+
+ align:start position:0%
+arguments are small the values can be
+quite large just because 1 over x
+
+ align:start position:0%
+quite large just because 1 over x
+ 
+
+ align:start position:0%
+quite large just because 1 over x
+shoots up so
+
+ align:start position:0%
+shoots up so
+ 
+
+ align:start position:0%
+shoots up so
+let's quantify this i have to tell you
+
+ align:start position:0%
+let's quantify this i have to tell you
+ 
+
+ align:start position:0%
+let's quantify this i have to tell you
+what the bad epsilon knot is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+choose epsilon not equals 2. now any
+
+ align:start position:0%
+choose epsilon not equals 2. now any
+ 
+
+ align:start position:0%
+choose epsilon not equals 2. now any
+epsilon naught
+
+ align:start position:0%
+epsilon naught
+ 
+
+ align:start position:0%
+epsilon naught
+will work just fine
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+let uh
+
+ align:start position:0%
+let uh
+ 
+
+ align:start position:0%
+let uh
+delta be positive so now we have to find
+
+ align:start position:0%
+delta be positive so now we have to find
+ 
+
+ align:start position:0%
+delta be positive so now we have to find
+x and c
+
+ align:start position:0%
+x and c
+ 
+
+ align:start position:0%
+x and c
+n s uh within distance delta to each
+
+ align:start position:0%
+n s uh within distance delta to each
+ 
+
+ align:start position:0%
+n s uh within distance delta to each
+other
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that
+
+ align:start position:0%
+that
+ 
+
+ align:start position:0%
+that
+whose values different differ very uh by
+
+ align:start position:0%
+whose values different differ very uh by
+ 
+
+ align:start position:0%
+whose values different differ very uh by
+at least two
+
+ align:start position:0%
+at least two
+ 
+
+ align:start position:0%
+at least two
+so let's choose
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+c to be
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the minimum of
+
+ align:start position:0%
+the minimum of
+ 
+
+ align:start position:0%
+the minimum of
+delta and a half
+
+ align:start position:0%
+delta and a half
+ 
+
+ align:start position:0%
+delta and a half
+and i'm going to choose x to be
+
+ align:start position:0%
+and i'm going to choose x to be
+ 
+
+ align:start position:0%
+and i'm going to choose x to be
+c over 2.
+
+ align:start position:0%
+c over 2.
+ 
+
+ align:start position:0%
+c over 2.
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so just ignoring this half for a minute
+
+ align:start position:0%
+so just ignoring this half for a minute
+ 
+
+ align:start position:0%
+so just ignoring this half for a minute
+c is equal to delta x is equal to delta
+
+ align:start position:0%
+c is equal to delta x is equal to delta
+ 
+
+ align:start position:0%
+c is equal to delta x is equal to delta
+over 2
+
+ align:start position:0%
+over 2
+ 
+
+ align:start position:0%
+over 2
+and then 1 over c minus one over x is
+
+ align:start position:0%
+and then 1 over c minus one over x is
+ 
+
+ align:start position:0%
+and then 1 over c minus one over x is
+going to be two over delta and if delta
+
+ align:start position:0%
+going to be two over delta and if delta
+ 
+
+ align:start position:0%
+going to be two over delta and if delta
+is very small that's certainly bigger
+
+ align:start position:0%
+is very small that's certainly bigger
+ 
+
+ align:start position:0%
+is very small that's certainly bigger
+than or equal to two but i had to throw
+
+ align:start position:0%
+than or equal to two but i had to throw
+ 
+
+ align:start position:0%
+than or equal to two but i had to throw
+in this one half here because i chose
+
+ align:start position:0%
+in this one half here because i chose
+ 
+
+ align:start position:0%
+in this one half here because i chose
+epsilon not to be two
+
+ align:start position:0%
+epsilon not to be two
+ 
+
+ align:start position:0%
+epsilon not to be two
+all right and delta's arbitrary
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+then we see that x minus c
+
+ align:start position:0%
+then we see that x minus c
+ 
+
+ align:start position:0%
+then we see that x minus c
+this equals c over two
+
+ align:start position:0%
+this equals c over two
+ 
+
+ align:start position:0%
+this equals c over two
+which is certainly less than or equal to
+
+ align:start position:0%
+which is certainly less than or equal to
+ 
+
+ align:start position:0%
+which is certainly less than or equal to
+since c is the minimum of delta and one
+
+ align:start position:0%
+since c is the minimum of delta and one
+ 
+
+ align:start position:0%
+since c is the minimum of delta and one
+over half is less than delta over two
+
+ align:start position:0%
+over half is less than delta over two
+ 
+
+ align:start position:0%
+over half is less than delta over two
+which is less than delta
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and if we compute
+
+ align:start position:0%
+and if we compute
+ 
+
+ align:start position:0%
+and if we compute
+one over x minus one over c
+
+ align:start position:0%
+one over x minus one over c
+ 
+
+ align:start position:0%
+one over x minus one over c
+this is uh
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+remember x is c over two so this one
+
+ align:start position:0%
+remember x is c over two so this one
+ 
+
+ align:start position:0%
+remember x is c over two so this one
+over x is two over c
+
+ align:start position:0%
+over x is two over c
+ 
+
+ align:start position:0%
+over x is two over c
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+1 over c
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+right
+
+ align:start position:0%
+right
+ 
+
+ align:start position:0%
+right
+and now
+
+ align:start position:0%
+and now
+ 
+
+ align:start position:0%
+and now
+from c
+
+ align:start position:0%
+from c
+ 
+
+ align:start position:0%
+from c
+being less than or equal to
+
+ align:start position:0%
+being less than or equal to
+ 
+
+ align:start position:0%
+being less than or equal to
+1 over half i get that 1 over c is going
+
+ align:start position:0%
+1 over half i get that 1 over c is going
+ 
+
+ align:start position:0%
+1 over half i get that 1 over c is going
+to be bigger than or equal to 2.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+all right
+
+ align:start position:0%
+all right
+ 
+
+ align:start position:0%
+all right
+and that's the end of the proof
+
+ align:start position:0%
+and that's the end of the proof
+ 
+
+ align:start position:0%
+and that's the end of the proof
+right so we see that even though
+
+ align:start position:0%
+right so we see that even though
+ 
+
+ align:start position:0%
+right so we see that even though
+these two uh
+
+ align:start position:0%
+these two uh
+ 
+
+ align:start position:0%
+these two uh
+these two arguments are very close to
+
+ align:start position:0%
+these two arguments are very close to
+ 
+
+ align:start position:0%
+these two arguments are very close to
+each other the outputs are in fact you
+
+ align:start position:0%
+each other the outputs are in fact you
+ 
+
+ align:start position:0%
+each other the outputs are in fact you
+know
+
+ align:start position:0%
+know
+ 
+
+ align:start position:0%
+know
+separated
+
+ align:start position:0%
+separated
+ 
+
+ align:start position:0%
+separated
+by some fixed distance
+
+ align:start position:0%
+by some fixed distance
+ 
+
+ align:start position:0%
+by some fixed distance
+at least two
+
+ align:start position:0%
+at least two
+ 
+
+ align:start position:0%
+at least two
+but we could actually make it you know
+
+ align:start position:0%
+but we could actually make it you know
+ 
+
+ align:start position:0%
+but we could actually make it you know
+bigger than three bigger than four
+
+ align:start position:0%
+bigger than three bigger than four
+ 
+
+ align:start position:0%
+bigger than three bigger than four
+whatever you like all right
+
+ align:start position:0%
+whatever you like all right
+ 
+
+ align:start position:0%
+whatever you like all right
+[Applause]
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+and i'm not going to go over this
+
+ align:start position:0%
+and i'm not going to go over this
+ 
+
+ align:start position:0%
+and i'm not going to go over this
+example
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+but in fact
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+i'll leave it to you or maybe i'll put
+
+ align:start position:0%
+i'll leave it to you or maybe i'll put
+ 
+
+ align:start position:0%
+i'll leave it to you or maybe i'll put
+it on the assignment f of x equals x
+
+ align:start position:0%
+it on the assignment f of x equals x
+ 
+
+ align:start position:0%
+it on the assignment f of x equals x
+squared
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+is not
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uniformly continuous on
+
+ align:start position:0%
+uniformly continuous on
+ 
+
+ align:start position:0%
+uniformly continuous on
+r so we should we saw that it's
+
+ align:start position:0%
+r so we should we saw that it's
+ 
+
+ align:start position:0%
+r so we should we saw that it's
+uniformly continuous on the closed
+
+ align:start position:0%
+uniformly continuous on the closed
+ 
+
+ align:start position:0%
+uniformly continuous on the closed
+interval 0 1
+
+ align:start position:0%
+interval 0 1
+ 
+
+ align:start position:0%
+interval 0 1
+but it's not uniformly continuous on
+
+ align:start position:0%
+but it's not uniformly continuous on
+ 
+
+ align:start position:0%
+but it's not uniformly continuous on
+all of r okay
+
+ align:start position:0%
+all of r okay
+ 
+
+ align:start position:0%
+all of r okay
+the reason being again kind of because
+
+ align:start position:0%
+the reason being again kind of because
+ 
+
+ align:start position:0%
+the reason being again kind of because
+you know x squared is starting to get
+
+ align:start position:0%
+you know x squared is starting to get
+ 
+
+ align:start position:0%
+you know x squared is starting to get
+big so i can take two things close to
+
+ align:start position:0%
+big so i can take two things close to
+ 
+
+ align:start position:0%
+big so i can take two things close to
+each other stick it into x squared and
+
+ align:start position:0%
+each other stick it into x squared and
+ 
+
+ align:start position:0%
+each other stick it into x squared and
+their outputs could be you know very
+
+ align:start position:0%
+their outputs could be you know very
+ 
+
+ align:start position:0%
+their outputs could be you know very
+different from each other
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+i didn't write out the proof of this one
+
+ align:start position:0%
+i didn't write out the proof of this one
+ 
+
+ align:start position:0%
+i didn't write out the proof of this one
+so we're going to go a little bit by
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+a little bit by the seat of our pants
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so we want to show this is not uniformly
+
+ align:start position:0%
+so we want to show this is not uniformly
+ 
+
+ align:start position:0%
+so we want to show this is not uniformly
+continuous so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+i think epsilon 0 equals 1 is going to
+
+ align:start position:0%
+i think epsilon 0 equals 1 is going to
+ 
+
+ align:start position:0%
+i think epsilon 0 equals 1 is going to
+work just fine
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that delta b positive
+
+ align:start position:0%
+that delta b positive
+ 
+
+ align:start position:0%
+that delta b positive
+and the idea
+
+ align:start position:0%
+and the idea
+ 
+
+ align:start position:0%
+and the idea
+is we want to choose
+
+ align:start position:0%
+is we want to choose
+ 
+
+ align:start position:0%
+is we want to choose
+x to be
+
+ align:start position:0%
+x to be
+ 
+
+ align:start position:0%
+x to be
+some number
+
+ align:start position:0%
+some number
+ 
+
+ align:start position:0%
+some number
+let's call it a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+plus
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+well
+
+ align:start position:0%
+well
+ 
+
+ align:start position:0%
+well
+c will be some number
+
+ align:start position:0%
+c will be some number
+ 
+
+ align:start position:0%
+c will be some number
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+c equals
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+some number
+
+ align:start position:0%
+some number
+ 
+
+ align:start position:0%
+some number
+x equals c
+
+ align:start position:0%
+x equals c
+ 
+
+ align:start position:0%
+x equals c
+plus
+
+ align:start position:0%
+plus
+ 
+
+ align:start position:0%
+plus
+delta over two okay so this is kind of
+
+ align:start position:0%
+delta over two okay so this is kind of
+ 
+
+ align:start position:0%
+delta over two okay so this is kind of
+scratch work off to the side and let's
+
+ align:start position:0%
+scratch work off to the side and let's
+ 
+
+ align:start position:0%
+scratch work off to the side and let's
+see if we can somehow choose c
+
+ align:start position:0%
+see if we can somehow choose c
+ 
+
+ align:start position:0%
+see if we can somehow choose c
+so that um so first off
+
+ align:start position:0%
+so that um so first off
+ 
+
+ align:start position:0%
+so that um so first off
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+you know x minus c
+
+ align:start position:0%
+you know x minus c
+ 
+
+ align:start position:0%
+you know x minus c
+will be c over 2
+
+ align:start position:0%
+will be c over 2
+ 
+
+ align:start position:0%
+will be c over 2
+will be delta over 2 which is less than
+
+ align:start position:0%
+will be delta over 2 which is less than
+ 
+
+ align:start position:0%
+will be delta over 2 which is less than
+delta
+
+ align:start position:0%
+delta
+ 
+
+ align:start position:0%
+delta
+and now let's see
+
+ align:start position:0%
+and now let's see
+ 
+
+ align:start position:0%
+and now let's see
+if we can
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+choose c
+
+ align:start position:0%
+choose c
+ 
+
+ align:start position:0%
+choose c
+so that
+
+ align:start position:0%
+so that
+ 
+
+ align:start position:0%
+so that
+x squared minus c squared
+
+ align:start position:0%
+x squared minus c squared
+ 
+
+ align:start position:0%
+x squared minus c squared
+is
+
+ align:start position:0%
+is
+ 
+
+ align:start position:0%
+is
+bigger than or equal to one
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+c is is
+
+ align:start position:0%
+c is is
+ 
+
+ align:start position:0%
+c is is
+kind of the thing that we get to play
+
+ align:start position:0%
+kind of the thing that we get to play
+ 
+
+ align:start position:0%
+kind of the thing that we get to play
+with here
+
+ align:start position:0%
+with here
+ 
+
+ align:start position:0%
+with here
+i mean this is how it actually goes
+
+ align:start position:0%
+i mean this is how it actually goes
+ 
+
+ align:start position:0%
+i mean this is how it actually goes
+uh if you're one to you know figure out
+
+ align:start position:0%
+uh if you're one to you know figure out
+ 
+
+ align:start position:0%
+uh if you're one to you know figure out
+the proof before you write it down you
+
+ align:start position:0%
+the proof before you write it down you
+ 
+
+ align:start position:0%
+the proof before you write it down you
+know the scratch work to the side
+
+ align:start position:0%
+know the scratch work to the side
+ 
+
+ align:start position:0%
+know the scratch work to the side
+all right so
+
+ align:start position:0%
+all right so
+ 
+
+ align:start position:0%
+all right so
+choose c so that this now
+
+ align:start position:0%
+choose c so that this now
+ 
+
+ align:start position:0%
+choose c so that this now
+let's start off with
+
+ align:start position:0%
+let's start off with
+ 
+
+ align:start position:0%
+let's start off with
+the thing that we're trying to bound
+
+ align:start position:0%
+the thing that we're trying to bound
+ 
+
+ align:start position:0%
+the thing that we're trying to bound
+from below and start computing some
+
+ align:start position:0%
+from below and start computing some
+ 
+
+ align:start position:0%
+from below and start computing some
+stuff
+
+ align:start position:0%
+stuff
+ 
+
+ align:start position:0%
+stuff
+this is equal to x plus c and c will be
+
+ align:start position:0%
+this is equal to x plus c and c will be
+ 
+
+ align:start position:0%
+this is equal to x plus c and c will be
+positive okay so
+
+ align:start position:0%
+positive okay so
+ 
+
+ align:start position:0%
+positive okay so
+um this will be
+
+ align:start position:0%
+um this will be
+ 
+
+ align:start position:0%
+um this will be
+c and x will be positive so x plus c
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+times x minus c
+
+ align:start position:0%
+times x minus c
+ 
+
+ align:start position:0%
+times x minus c
+now x plus c
+
+ align:start position:0%
+now x plus c
+ 
+
+ align:start position:0%
+now x plus c
+will be
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+2c plus
+
+ align:start position:0%
+2c plus
+ 
+
+ align:start position:0%
+2c plus
+delta over two
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+x minus c will be
+
+ align:start position:0%
+x minus c will be
+ 
+
+ align:start position:0%
+x minus c will be
+delta over two
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so so far all of these things are
+
+ align:start position:0%
+so so far all of these things are
+ 
+
+ align:start position:0%
+so so far all of these things are
+equality
+
+ align:start position:0%
+equality
+ 
+
+ align:start position:0%
+equality
+and we get this is equal to
+
+ align:start position:0%
+and we get this is equal to
+ 
+
+ align:start position:0%
+and we get this is equal to
+2c
+
+ align:start position:0%
+2c
+ 
+
+ align:start position:0%
+2c
+plus
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+delta
+
+ align:start position:0%
+delta
+ 
+
+ align:start position:0%
+delta
+is 2c plus delta squared over two
+
+ align:start position:0%
+is 2c plus delta squared over two
+ 
+
+ align:start position:0%
+is 2c plus delta squared over two
+and here we're going to choose c
+
+ align:start position:0%
+and here we're going to choose c
+ 
+
+ align:start position:0%
+and here we're going to choose c
+positive right so we're trying to show
+
+ align:start position:0%
+positive right so we're trying to show
+ 
+
+ align:start position:0%
+positive right so we're trying to show
+it's not uniformly continuous on r
+
+ align:start position:0%
+it's not uniformly continuous on r
+ 
+
+ align:start position:0%
+it's not uniformly continuous on r
+so we just need to find a value of c and
+
+ align:start position:0%
+so we just need to find a value of c and
+ 
+
+ align:start position:0%
+so we just need to find a value of c and
+a value of x
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so that they're within delta distance to
+
+ align:start position:0%
+so that they're within delta distance to
+ 
+
+ align:start position:0%
+so that they're within delta distance to
+each other but their outputs are bigger
+
+ align:start position:0%
+each other but their outputs are bigger
+ 
+
+ align:start position:0%
+each other but their outputs are bigger
+than or equal to one
+
+ align:start position:0%
+than or equal to one
+ 
+
+ align:start position:0%
+than or equal to one
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+so far if c is just something positive x
+
+ align:start position:0%
+so far if c is just something positive x
+ 
+
+ align:start position:0%
+so far if c is just something positive x
+is c plus delta over two then they're
+
+ align:start position:0%
+is c plus delta over two then they're
+ 
+
+ align:start position:0%
+is c plus delta over two then they're
+close
+
+ align:start position:0%
+close
+ 
+
+ align:start position:0%
+close
+their difference however is going to be
+
+ align:start position:0%
+their difference however is going to be
+ 
+
+ align:start position:0%
+their difference however is going to be
+just by this computation
+
+ align:start position:0%
+just by this computation
+ 
+
+ align:start position:0%
+just by this computation
+equal to
+
+ align:start position:0%
+equal to
+ 
+
+ align:start position:0%
+equal to
+2c plus delta over 2 times delta over 2
+
+ align:start position:0%
+2c plus delta over 2 times delta over 2
+ 
+
+ align:start position:0%
+2c plus delta over 2 times delta over 2
+squared
+
+ align:start position:0%
+squared
+ 
+
+ align:start position:0%
+squared
+now delta squared over 2 is always
+
+ align:start position:0%
+now delta squared over 2 is always
+ 
+
+ align:start position:0%
+now delta squared over 2 is always
+non-negative so it's certainly bigger
+
+ align:start position:0%
+non-negative so it's certainly bigger
+ 
+
+ align:start position:0%
+non-negative so it's certainly bigger
+than or equal to delta times c
+
+ align:start position:0%
+than or equal to delta times c
+ 
+
+ align:start position:0%
+than or equal to delta times c
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+now remember we wanted this thing to be
+
+ align:start position:0%
+now remember we wanted this thing to be
+ 
+
+ align:start position:0%
+now remember we wanted this thing to be
+bigger than or equal to one right now we
+
+ align:start position:0%
+bigger than or equal to one right now we
+ 
+
+ align:start position:0%
+bigger than or equal to one right now we
+have it's bigger than or equal to delta
+
+ align:start position:0%
+have it's bigger than or equal to delta
+ 
+
+ align:start position:0%
+have it's bigger than or equal to delta
+c
+
+ align:start position:0%
+c
+ 
+
+ align:start position:0%
+c
+so let's choose c to be
+
+ align:start position:0%
+so let's choose c to be
+ 
+
+ align:start position:0%
+so let's choose c to be
+one over delta
+
+ align:start position:0%
+one over delta
+ 
+
+ align:start position:0%
+one over delta
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+let's see that that works
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+choose
+
+ align:start position:0%
+choose
+ 
+
+ align:start position:0%
+choose
+c to be 1 over delta
+
+ align:start position:0%
+c to be 1 over delta
+ 
+
+ align:start position:0%
+c to be 1 over delta
+x to be
+
+ align:start position:0%
+x to be
+ 
+
+ align:start position:0%
+x to be
+1 over delta so c plus
+
+ align:start position:0%
+1 over delta so c plus
+ 
+
+ align:start position:0%
+1 over delta so c plus
+delta over 2.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+then these two values are close
+
+ align:start position:0%
+then these two values are close
+ 
+
+ align:start position:0%
+then these two values are close
+x minus c equals
+
+ align:start position:0%
+x minus c equals
+ 
+
+ align:start position:0%
+x minus c equals
+delta over 2
+
+ align:start position:0%
+delta over 2
+ 
+
+ align:start position:0%
+delta over 2
+is less than delta
+
+ align:start position:0%
+is less than delta
+ 
+
+ align:start position:0%
+is less than delta
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+x squared minus c squared
+
+ align:start position:0%
+x squared minus c squared
+ 
+
+ align:start position:0%
+x squared minus c squared
+equals x plus c
+
+ align:start position:0%
+equals x plus c
+ 
+
+ align:start position:0%
+equals x plus c
+times x
+
+ align:start position:0%
+times x
+ 
+
+ align:start position:0%
+times x
+minus c
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+x plus c as we did a minute ago is going
+
+ align:start position:0%
+x plus c as we did a minute ago is going
+ 
+
+ align:start position:0%
+x plus c as we did a minute ago is going
+to be
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+2 over delta plus delta over 2 that's x
+
+ align:start position:0%
+2 over delta plus delta over 2 that's x
+ 
+
+ align:start position:0%
+2 over delta plus delta over 2 that's x
+plus c
+
+ align:start position:0%
+plus c
+ 
+
+ align:start position:0%
+plus c
+x minus c is equal to delta over 2.
+
+ align:start position:0%
+x minus c is equal to delta over 2.
+ 
+
+ align:start position:0%
+x minus c is equal to delta over 2.
+which equals 1 plus
+
+ align:start position:0%
+which equals 1 plus
+ 
+
+ align:start position:0%
+which equals 1 plus
+delta squared over 4 which is bigger
+
+ align:start position:0%
+delta squared over 4 which is bigger
+ 
+
+ align:start position:0%
+delta squared over 4 which is bigger
+than or equal to 1
+
+ align:start position:0%
+than or equal to 1
+ 
+
+ align:start position:0%
+than or equal to 1
+our bad epsilon okay so
+
+ align:start position:0%
+our bad epsilon okay so
+ 
+
+ align:start position:0%
+our bad epsilon okay so
+f of x equals x squared is not uniformly
+
+ align:start position:0%
+f of x equals x squared is not uniformly
+ 
+
+ align:start position:0%
+f of x equals x squared is not uniformly
+continuous on r
+
+ align:start position:0%
+continuous on r
+ 
+
+ align:start position:0%
+continuous on r
+even though it is uniformly continuous
+
+ align:start position:0%
+even though it is uniformly continuous
+ 
+
+ align:start position:0%
+even though it is uniformly continuous
+on this closed and bounded interval
+
+ align:start position:0%
+on this closed and bounded interval
+ 
+
+ align:start position:0%
+on this closed and bounded interval
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+you know uniform continuity is really a
+
+ align:start position:0%
+you know uniform continuity is really a
+ 
+
+ align:start position:0%
+you know uniform continuity is really a
+relationship between a function
+
+ align:start position:0%
+relationship between a function
+ 
+
+ align:start position:0%
+relationship between a function
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+you know the the domain on which it's
+
+ align:start position:0%
+you know the the domain on which it's
+ 
+
+ align:start position:0%
+you know the the domain on which it's
+defined
+
+ align:start position:0%
+defined
+ 
+
+ align:start position:0%
+defined
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+but okay so this is uh kind of to wrap
+
+ align:start position:0%
+but okay so this is uh kind of to wrap
+ 
+
+ align:start position:0%
+but okay so this is uh kind of to wrap
+up
+
+ align:start position:0%
+up
+ 
+
+ align:start position:0%
+up
+our theme of
+
+ align:start position:0%
+our theme of
+ 
+
+ align:start position:0%
+our theme of
+continuous functions
+
+ align:start position:0%
+continuous functions
+ 
+
+ align:start position:0%
+continuous functions
+and how they're behaved on closed and
+
+ align:start position:0%
+and how they're behaved on closed and
+ 
+
+ align:start position:0%
+and how they're behaved on closed and
+bounded intervals and we see here that
+
+ align:start position:0%
+bounded intervals and we see here that
+ 
+
+ align:start position:0%
+bounded intervals and we see here that
+you know uniform continuity is a much
+
+ align:start position:0%
+you know uniform continuity is a much
+ 
+
+ align:start position:0%
+you know uniform continuity is a much
+stronger notion than
+
+ align:start position:0%
+stronger notion than
+ 
+
+ align:start position:0%
+stronger notion than
+continuity as i've said i mean you can
+
+ align:start position:0%
+continuity as i've said i mean you can
+ 
+
+ align:start position:0%
+continuity as i've said i mean you can
+easily prove from the definition that if
+
+ align:start position:0%
+easily prove from the definition that if
+ 
+
+ align:start position:0%
+easily prove from the definition that if
+a function is uniformly continuous on s
+
+ align:start position:0%
+a function is uniformly continuous on s
+ 
+
+ align:start position:0%
+a function is uniformly continuous on s
+then it's continuous on s
+
+ align:start position:0%
+then it's continuous on s
+ 
+
+ align:start position:0%
+then it's continuous on s
+all right
+
+ align:start position:0%
+all right
+ 
+
+ align:start position:0%
+all right
+now
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and we've seen that in general
+
+ align:start position:0%
+and we've seen that in general
+ 
+
+ align:start position:0%
+and we've seen that in general
+the reverse inclusion does not hold so
+
+ align:start position:0%
+the reverse inclusion does not hold so
+ 
+
+ align:start position:0%
+the reverse inclusion does not hold so
+let me just write this up
+
+ align:start position:0%
+let me just write this up
+ 
+
+ align:start position:0%
+let me just write this up
+as a remark
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+in general
+
+ align:start position:0%
+in general
+ 
+
+ align:start position:0%
+in general
+f
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uniformly continuous
+
+ align:start position:0%
+uniformly continuous
+ 
+
+ align:start position:0%
+uniformly continuous
+implies that
+
+ align:start position:0%
+implies that
+ 
+
+ align:start position:0%
+implies that
+f is
+
+ align:start position:0%
+f is
+ 
+
+ align:start position:0%
+f is
+continuous this just follows from the
+
+ align:start position:0%
+continuous this just follows from the
+ 
+
+ align:start position:0%
+continuous this just follows from the
+definition okay this is not difficult to
+
+ align:start position:0%
+definition okay this is not difficult to
+ 
+
+ align:start position:0%
+definition okay this is not difficult to
+show
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+but
+
+ align:start position:0%
+but
+ 
+
+ align:start position:0%
+but
+the converse does not hold
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+as we've just seen right we have two
+
+ align:start position:0%
+as we've just seen right we have two
+ 
+
+ align:start position:0%
+as we've just seen right we have two
+examples here f of x equals one over x
+
+ align:start position:0%
+examples here f of x equals one over x
+ 
+
+ align:start position:0%
+examples here f of x equals one over x
+on the open interval zero one which is
+
+ align:start position:0%
+on the open interval zero one which is
+ 
+
+ align:start position:0%
+on the open interval zero one which is
+continuous but it's not uniformly
+
+ align:start position:0%
+continuous but it's not uniformly
+ 
+
+ align:start position:0%
+continuous but it's not uniformly
+continuous and then we have the function
+
+ align:start position:0%
+continuous and then we have the function
+ 
+
+ align:start position:0%
+continuous and then we have the function
+f of x equals x squared which is
+
+ align:start position:0%
+f of x equals x squared which is
+ 
+
+ align:start position:0%
+f of x equals x squared which is
+not uniformly continuous on r but in
+
+ align:start position:0%
+not uniformly continuous on r but in
+ 
+
+ align:start position:0%
+not uniformly continuous on r but in
+fact it is uniformly continuous on this
+
+ align:start position:0%
+fact it is uniformly continuous on this
+ 
+
+ align:start position:0%
+fact it is uniformly continuous on this
+closed and bounded interval zero one
+
+ align:start position:0%
+closed and bounded interval zero one
+ 
+
+ align:start position:0%
+closed and bounded interval zero one
+this example here though is in fact the
+
+ align:start position:0%
+this example here though is in fact the
+ 
+
+ align:start position:0%
+this example here though is in fact the
+rule
+
+ align:start position:0%
+rule
+ 
+
+ align:start position:0%
+rule
+that if i'm looking at
+
+ align:start position:0%
+that if i'm looking at
+ 
+
+ align:start position:0%
+that if i'm looking at
+a continuous function
+
+ align:start position:0%
+a continuous function
+ 
+
+ align:start position:0%
+a continuous function
+or a function on my closed and bounded
+
+ align:start position:0%
+or a function on my closed and bounded
+ 
+
+ align:start position:0%
+or a function on my closed and bounded
+interval then in fact
+
+ align:start position:0%
+interval then in fact
+ 
+
+ align:start position:0%
+interval then in fact
+these two notions are equivalent so
+
+ align:start position:0%
+these two notions are equivalent so
+ 
+
+ align:start position:0%
+these two notions are equivalent so
+that's the the following theorem
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+let f
+
+ align:start position:0%
+let f
+ 
+
+ align:start position:0%
+let f
+be a function from
+
+ align:start position:0%
+be a function from
+ 
+
+ align:start position:0%
+be a function from
+a to b to r
+
+ align:start position:0%
+a to b to r
+ 
+
+ align:start position:0%
+a to b to r
+so a closed and bounded interval now not
+
+ align:start position:0%
+so a closed and bounded interval now not
+ 
+
+ align:start position:0%
+so a closed and bounded interval now not
+just an arbitrary set
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+then
+
+ align:start position:0%
+then
+ 
+
+ align:start position:0%
+then
+f is
+
+ align:start position:0%
+f is
+ 
+
+ align:start position:0%
+f is
+continuous
+
+ align:start position:0%
+continuous
+ 
+
+ align:start position:0%
+continuous
+on a b meaning it's continuous at every
+
+ align:start position:0%
+on a b meaning it's continuous at every
+ 
+
+ align:start position:0%
+on a b meaning it's continuous at every
+point
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+if and only if
+
+ align:start position:0%
+if and only if
+ 
+
+ align:start position:0%
+if and only if
+f is
+
+ align:start position:0%
+f is
+ 
+
+ align:start position:0%
+f is
+uniformly continuous
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+on a b okay
+
+ align:start position:0%
+on a b okay
+ 
+
+ align:start position:0%
+on a b okay
+and the necessity of being working on a
+
+ align:start position:0%
+and the necessity of being working on a
+ 
+
+ align:start position:0%
+and the necessity of being working on a
+closed and bounded interval
+
+ align:start position:0%
+closed and bounded interval
+ 
+
+ align:start position:0%
+closed and bounded interval
+um is seen again by these uh examples we
+
+ align:start position:0%
+um is seen again by these uh examples we
+ 
+
+ align:start position:0%
+um is seen again by these uh examples we
+by this example we had here of f of x
+
+ align:start position:0%
+by this example we had here of f of x
+ 
+
+ align:start position:0%
+by this example we had here of f of x
+equals one over x and f of x equals x
+
+ align:start position:0%
+equals one over x and f of x equals x
+ 
+
+ align:start position:0%
+equals one over x and f of x equals x
+squared on r and zero one okay
+
+ align:start position:0%
+squared on r and zero one okay
+ 
+
+ align:start position:0%
+squared on r and zero one okay
+but as long as we're looking on a closed
+
+ align:start position:0%
+but as long as we're looking on a closed
+ 
+
+ align:start position:0%
+but as long as we're looking on a closed
+and bounded interval
+
+ align:start position:0%
+and bounded interval
+ 
+
+ align:start position:0%
+and bounded interval
+uh continuous is equivalent to uniform
+
+ align:start position:0%
+uh continuous is equivalent to uniform
+ 
+
+ align:start position:0%
+uh continuous is equivalent to uniform
+continuity
+
+ align:start position:0%
+continuity
+ 
+
+ align:start position:0%
+continuity
+all right now this is also not the
+
+ align:start position:0%
+all right now this is also not the
+ 
+
+ align:start position:0%
+all right now this is also not the
+sharpest thing you can say
+
+ align:start position:0%
+sharpest thing you can say
+ 
+
+ align:start position:0%
+sharpest thing you can say
+um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+in fact
+
+ align:start position:0%
+in fact
+ 
+
+ align:start position:0%
+in fact
+what you can say is that if i replace
+
+ align:start position:0%
+what you can say is that if i replace
+ 
+
+ align:start position:0%
+what you can say is that if i replace
+this with what's called a compact set uh
+
+ align:start position:0%
+this with what's called a compact set uh
+ 
+
+ align:start position:0%
+this with what's called a compact set uh
+which i may put in the assignment i may
+
+ align:start position:0%
+which i may put in the assignment i may
+ 
+
+ align:start position:0%
+which i may put in the assignment i may
+not then this statement is still true
+
+ align:start position:0%
+not then this statement is still true
+ 
+
+ align:start position:0%
+not then this statement is still true
+and that's in some sense the sharpest uh
+
+ align:start position:0%
+and that's in some sense the sharpest uh
+ 
+
+ align:start position:0%
+and that's in some sense the sharpest uh
+statement but
+
+ align:start position:0%
+statement but
+ 
+
+ align:start position:0%
+statement but
+i think this is interesting enough
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+to just work on a closed and bounded
+
+ align:start position:0%
+to just work on a closed and bounded
+ 
+
+ align:start position:0%
+to just work on a closed and bounded
+interval
+
+ align:start position:0%
+interval
+ 
+
+ align:start position:0%
+interval
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+let's prove this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so again this direction
+
+ align:start position:0%
+so again this direction
+ 
+
+ align:start position:0%
+so again this direction
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+i should say
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+i leave this to you as an exercise
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uniform continuity implying uh
+
+ align:start position:0%
+uniform continuity implying uh
+ 
+
+ align:start position:0%
+uniform continuity implying uh
+continuity and leave it to you
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and i will do
+
+ align:start position:0%
+and i will do
+ 
+
+ align:start position:0%
+and i will do
+more difficult one
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and we'll use use kind of a
+
+ align:start position:0%
+and we'll use use kind of a
+ 
+
+ align:start position:0%
+and we'll use use kind of a
+you know philosophy like we did
+
+ align:start position:0%
+you know philosophy like we did
+ 
+
+ align:start position:0%
+you know philosophy like we did
+in the previous lecture where we used
+
+ align:start position:0%
+in the previous lecture where we used
+ 
+
+ align:start position:0%
+in the previous lecture where we used
+the definition of continuity or this
+
+ align:start position:0%
+the definition of continuity or this
+ 
+
+ align:start position:0%
+the definition of continuity or this
+theorem about
+
+ align:start position:0%
+theorem about
+ 
+
+ align:start position:0%
+theorem about
+uh continuity in terms of sequences and
+
+ align:start position:0%
+uh continuity in terms of sequences and
+ 
+
+ align:start position:0%
+uh continuity in terms of sequences and
+also the bolzano virus cross
+
+ align:start position:0%
+also the bolzano virus cross
+ 
+
+ align:start position:0%
+also the bolzano virus cross
+here
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay good we still have the negation of
+
+ align:start position:0%
+okay good we still have the negation of
+ 
+
+ align:start position:0%
+okay good we still have the negation of
+the definition of uniform continuity
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and that's what we'll need
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+all right so we're going to prove
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+f continuous implies uniformly
+
+ align:start position:0%
+f continuous implies uniformly
+ 
+
+ align:start position:0%
+f continuous implies uniformly
+continuous and we're going to do this by
+
+ align:start position:0%
+continuous and we're going to do this by
+ 
+
+ align:start position:0%
+continuous and we're going to do this by
+contradiction so
+
+ align:start position:0%
+contradiction so
+ 
+
+ align:start position:0%
+contradiction so
+suppose f
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+is continuous on a b but not uniformly
+
+ align:start position:0%
+is continuous on a b but not uniformly
+ 
+
+ align:start position:0%
+is continuous on a b but not uniformly
+continuous
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+all right and then we're gonna
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+break the universe
+
+ align:start position:0%
+break the universe
+ 
+
+ align:start position:0%
+break the universe
+some way
+
+ align:start position:0%
+some way
+ 
+
+ align:start position:0%
+some way
+all right
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+which shows that our assumption that f
+
+ align:start position:0%
+which shows that our assumption that f
+ 
+
+ align:start position:0%
+which shows that our assumption that f
+is not uniformly continuous
+
+ align:start position:0%
+is not uniformly continuous
+ 
+
+ align:start position:0%
+is not uniformly continuous
+does not hold
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so we use
+
+ align:start position:0%
+so we use
+ 
+
+ align:start position:0%
+so we use
+this negation of the definition of
+
+ align:start position:0%
+this negation of the definition of
+ 
+
+ align:start position:0%
+this negation of the definition of
+uniform continuity
+
+ align:start position:0%
+uniform continuity
+ 
+
+ align:start position:0%
+uniform continuity
+which says for
+
+ align:start position:0%
+which says for
+ 
+
+ align:start position:0%
+which says for
+that there exists a delta zero so let me
+
+ align:start position:0%
+that there exists a delta zero so let me
+ 
+
+ align:start position:0%
+that there exists a delta zero so let me
+write this out
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+i'm just going to rewrite this here then
+
+ align:start position:0%
+i'm just going to rewrite this here then
+ 
+
+ align:start position:0%
+i'm just going to rewrite this here then
+there exists a delta 0 such that for all
+
+ align:start position:0%
+there exists a delta 0 such that for all
+ 
+
+ align:start position:0%
+there exists a delta 0 such that for all
+delta positive there exists x
+
+ align:start position:0%
+delta positive there exists x
+ 
+
+ align:start position:0%
+delta positive there exists x
+c
+
+ align:start position:0%
+c
+ 
+
+ align:start position:0%
+c
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+a b
+
+ align:start position:0%
+a b
+ 
+
+ align:start position:0%
+a b
+which depend on delta
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+such that x minus c is less than delta
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+f of x minus f of c
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+it's greater than or equal to epsilon
+
+ align:start position:0%
+it's greater than or equal to epsilon
+ 
+
+ align:start position:0%
+it's greater than or equal to epsilon
+not
+
+ align:start position:0%
+not
+ 
+
+ align:start position:0%
+not
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+now
+
+ align:start position:0%
+now
+ 
+
+ align:start position:0%
+now
+this holds for
+
+ align:start position:0%
+this holds for
+ 
+
+ align:start position:0%
+this holds for
+every delta you can find the x and c so
+
+ align:start position:0%
+every delta you can find the x and c so
+ 
+
+ align:start position:0%
+every delta you can find the x and c so
+that x minus c is less than delta so f
+
+ align:start position:0%
+that x minus c is less than delta so f
+ 
+
+ align:start position:0%
+that x minus c is less than delta so f
+of x minus and f of x minus f of c is
+
+ align:start position:0%
+of x minus and f of x minus f of c is
+ 
+
+ align:start position:0%
+of x minus and f of x minus f of c is
+greater than or equal to epsilon naught
+
+ align:start position:0%
+greater than or equal to epsilon naught
+ 
+
+ align:start position:0%
+greater than or equal to epsilon naught
+so let's choose delta to be one over n
+
+ align:start position:0%
+so let's choose delta to be one over n
+ 
+
+ align:start position:0%
+so let's choose delta to be one over n
+for each natural number n
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and for all natural numbers n
+
+ align:start position:0%
+and for all natural numbers n
+ 
+
+ align:start position:0%
+and for all natural numbers n
+there exists
+
+ align:start position:0%
+there exists
+ 
+
+ align:start position:0%
+there exists
+xn
+
+ align:start position:0%
+xn
+ 
+
+ align:start position:0%
+xn
+cn and a b
+
+ align:start position:0%
+cn and a b
+ 
+
+ align:start position:0%
+cn and a b
+such that so this is a statement now
+
+ align:start position:0%
+such that so this is a statement now
+ 
+
+ align:start position:0%
+such that so this is a statement now
+with delta equals one over n
+
+ align:start position:0%
+with delta equals one over n
+ 
+
+ align:start position:0%
+with delta equals one over n
+x n minus c n is less than one over n
+
+ align:start position:0%
+x n minus c n is less than one over n
+ 
+
+ align:start position:0%
+x n minus c n is less than one over n
+and
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+f of x sub n
+
+ align:start position:0%
+f of x sub n
+ 
+
+ align:start position:0%
+f of x sub n
+minus f of
+
+ align:start position:0%
+minus f of
+ 
+
+ align:start position:0%
+minus f of
+c sub n
+
+ align:start position:0%
+c sub n
+ 
+
+ align:start position:0%
+c sub n
+is bigger than or equal to epsilon zero
+
+ align:start position:0%
+is bigger than or equal to epsilon zero
+ 
+
+ align:start position:0%
+is bigger than or equal to epsilon zero
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+now
+
+ align:start position:0%
+now
+ 
+
+ align:start position:0%
+now
+i have two sequences um
+
+ align:start position:0%
+i have two sequences um
+ 
+
+ align:start position:0%
+i have two sequences um
+here
+
+ align:start position:0%
+here
+ 
+
+ align:start position:0%
+here
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+they're bounded because they're in this
+
+ align:start position:0%
+they're bounded because they're in this
+ 
+
+ align:start position:0%
+they're bounded because they're in this
+closed and bounded interval
+
+ align:start position:0%
+closed and bounded interval
+ 
+
+ align:start position:0%
+closed and bounded interval
+so i can pass to a subsequence of one of
+
+ align:start position:0%
+so i can pass to a subsequence of one of
+ 
+
+ align:start position:0%
+so i can pass to a subsequence of one of
+them to start
+
+ align:start position:0%
+them to start
+ 
+
+ align:start position:0%
+them to start
+by
+
+ align:start position:0%
+by
+ 
+
+ align:start position:0%
+by
+the bolzano virustras theorem
+
+ align:start position:0%
+the bolzano virustras theorem
+ 
+
+ align:start position:0%
+the bolzano virustras theorem
+not bc horizontal virus truss i think
+
+ align:start position:0%
+not bc horizontal virus truss i think
+ 
+
+ align:start position:0%
+not bc horizontal virus truss i think
+that's
+
+ align:start position:0%
+that's
+ 
+
+ align:start position:0%
+that's
+probably somewhere else in the lecture
+
+ align:start position:0%
+probably somewhere else in the lecture
+ 
+
+ align:start position:0%
+probably somewhere else in the lecture
+or the previous i wrote bz but i meant
+
+ align:start position:0%
+or the previous i wrote bz but i meant
+ 
+
+ align:start position:0%
+or the previous i wrote bz but i meant
+bw
+
+ align:start position:0%
+bw
+ 
+
+ align:start position:0%
+bw
+by bolzano virustras
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+there exists
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+a subsequence
+
+ align:start position:0%
+a subsequence
+ 
+
+ align:start position:0%
+a subsequence
+x n sub k
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+of x sub n
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+x
+
+ align:start position:0%
+x
+ 
+
+ align:start position:0%
+x
+and a b
+
+ align:start position:0%
+and a b
+ 
+
+ align:start position:0%
+and a b
+such that
+
+ align:start position:0%
+such that
+ 
+
+ align:start position:0%
+such that
+limit as k goes to infinity of x of n
+
+ align:start position:0%
+limit as k goes to infinity of x of n
+ 
+
+ align:start position:0%
+limit as k goes to infinity of x of n
+sub k
+
+ align:start position:0%
+sub k
+ 
+
+ align:start position:0%
+sub k
+equals uh
+
+ align:start position:0%
+equals uh
+ 
+
+ align:start position:0%
+equals uh
+x so
+
+ align:start position:0%
+x so
+ 
+
+ align:start position:0%
+x so
+my balzona virustras from any bounded
+
+ align:start position:0%
+my balzona virustras from any bounded
+ 
+
+ align:start position:0%
+my balzona virustras from any bounded
+sequence we can find a convergent
+
+ align:start position:0%
+sequence we can find a convergent
+ 
+
+ align:start position:0%
+sequence we can find a convergent
+subsequence and because this subsequence
+
+ align:start position:0%
+subsequence and because this subsequence
+ 
+
+ align:start position:0%
+subsequence and because this subsequence
+is always between a and b
+
+ align:start position:0%
+is always between a and b
+ 
+
+ align:start position:0%
+is always between a and b
+the limit x will be between a and b all
+
+ align:start position:0%
+the limit x will be between a and b all
+ 
+
+ align:start position:0%
+the limit x will be between a and b all
+right
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+now
+
+ align:start position:0%
+now
+ 
+
+ align:start position:0%
+now
+if i look at
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+since
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the subsequence c in sub k is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+bounded between
+
+ align:start position:0%
+bounded between
+ 
+
+ align:start position:0%
+bounded between
+a and
+
+ align:start position:0%
+a and
+ 
+
+ align:start position:0%
+a and
+b
+
+ align:start position:0%
+b
+ 
+
+ align:start position:0%
+b
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+i have a subsequence of x of n sub k and
+
+ align:start position:0%
+i have a subsequence of x of n sub k and
+ 
+
+ align:start position:0%
+i have a subsequence of x of n sub k and
+i then obtain a subsequence of the c sub
+
+ align:start position:0%
+i then obtain a subsequence of the c sub
+ 
+
+ align:start position:0%
+i then obtain a subsequence of the c sub
+n's okay by just picking these integers
+
+ align:start position:0%
+n's okay by just picking these integers
+ 
+
+ align:start position:0%
+n's okay by just picking these integers
+to be the same
+
+ align:start position:0%
+to be the same
+ 
+
+ align:start position:0%
+to be the same
+all right
+
+ align:start position:0%
+all right
+ 
+
+ align:start position:0%
+all right
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+so now that subsequence is
+
+ align:start position:0%
+so now that subsequence is
+ 
+
+ align:start position:0%
+so now that subsequence is
+of the c sub n that's still uh you know
+
+ align:start position:0%
+of the c sub n that's still uh you know
+ 
+
+ align:start position:0%
+of the c sub n that's still uh you know
+they're all coming from a b so that's
+
+ align:start position:0%
+they're all coming from a b so that's
+ 
+
+ align:start position:0%
+they're all coming from a b so that's
+bounded by a b
+
+ align:start position:0%
+bounded by a b
+ 
+
+ align:start position:0%
+bounded by a b
+so it's bounded so by
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+bolzano virustras applied now to this
+
+ align:start position:0%
+bolzano virustras applied now to this
+ 
+
+ align:start position:0%
+bolzano virustras applied now to this
+subsequence
+
+ align:start position:0%
+subsequence
+ 
+
+ align:start position:0%
+subsequence
+there exists
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+a subsequence
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+c sub n sub k sub j
+
+ align:start position:0%
+c sub n sub k sub j
+ 
+
+ align:start position:0%
+c sub n sub k sub j
+j of
+
+ align:start position:0%
+j of
+ 
+
+ align:start position:0%
+j of
+c sub n sub k
+
+ align:start position:0%
+c sub n sub k
+ 
+
+ align:start position:0%
+c sub n sub k
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+an element c in a b
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+such that the limit as
+
+ align:start position:0%
+such that the limit as
+ 
+
+ align:start position:0%
+such that the limit as
+j goes to infinity of c sub n sub k sub
+
+ align:start position:0%
+j goes to infinity of c sub n sub k sub
+ 
+
+ align:start position:0%
+j goes to infinity of c sub n sub k sub
+j
+
+ align:start position:0%
+j
+ 
+
+ align:start position:0%
+j
+equals c okay so
+
+ align:start position:0%
+equals c okay so
+ 
+
+ align:start position:0%
+equals c okay so
+you know i found a subsequence of the x
+
+ align:start position:0%
+you know i found a subsequence of the x
+ 
+
+ align:start position:0%
+you know i found a subsequence of the x
+of n's
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+now i look at kind of a corresponding
+
+ align:start position:0%
+now i look at kind of a corresponding
+ 
+
+ align:start position:0%
+now i look at kind of a corresponding
+subsequence of the c sub n's where now
+
+ align:start position:0%
+subsequence of the c sub n's where now
+ 
+
+ align:start position:0%
+subsequence of the c sub n's where now
+this subsequence the n sub k's
+
+ align:start position:0%
+this subsequence the n sub k's
+ 
+
+ align:start position:0%
+this subsequence the n sub k's
+are
+
+ align:start position:0%
+are
+ 
+
+ align:start position:0%
+are
+coming from the n sub k is chosen for
+
+ align:start position:0%
+coming from the n sub k is chosen for
+ 
+
+ align:start position:0%
+coming from the n sub k is chosen for
+this subsequence
+
+ align:start position:0%
+this subsequence
+ 
+
+ align:start position:0%
+this subsequence
+that's still a bounded sequence so by
+
+ align:start position:0%
+that's still a bounded sequence so by
+ 
+
+ align:start position:0%
+that's still a bounded sequence so by
+bolzano virustrals i can take a
+
+ align:start position:0%
+bolzano virustrals i can take a
+ 
+
+ align:start position:0%
+bolzano virustrals i can take a
+subsequence of that
+
+ align:start position:0%
+subsequence of that
+ 
+
+ align:start position:0%
+subsequence of that
+and an element c
+
+ align:start position:0%
+and an element c
+ 
+
+ align:start position:0%
+and an element c
+so that i have convergence
+
+ align:start position:0%
+so that i have convergence
+ 
+
+ align:start position:0%
+so that i have convergence
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+all right
+
+ align:start position:0%
+all right
+ 
+
+ align:start position:0%
+all right
+so now
+
+ align:start position:0%
+so now
+ 
+
+ align:start position:0%
+so now
+let me just uh summarize
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+in summary
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+let's call these
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so in summary
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the sequence is
+
+ align:start position:0%
+the sequence is
+ 
+
+ align:start position:0%
+the sequence is
+x sub n sub k sub j so now this is even
+
+ align:start position:0%
+x sub n sub k sub j so now this is even
+ 
+
+ align:start position:0%
+x sub n sub k sub j so now this is even
+a subsequence of x of n sub k
+
+ align:start position:0%
+a subsequence of x of n sub k
+ 
+
+ align:start position:0%
+a subsequence of x of n sub k
+and c sub n sub k sub j
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+these are
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+subsequences of
+
+ align:start position:0%
+subsequences of
+ 
+
+ align:start position:0%
+subsequences of
+the original sequences x of n
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and c sub n
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+there's this x and c
+
+ align:start position:0%
+there's this x and c
+ 
+
+ align:start position:0%
+there's this x and c
+a b
+
+ align:start position:0%
+a b
+ 
+
+ align:start position:0%
+a b
+such that
+
+ align:start position:0%
+such that
+ 
+
+ align:start position:0%
+such that
+the limit
+
+ align:start position:0%
+the limit
+ 
+
+ align:start position:0%
+the limit
+as
+
+ align:start position:0%
+as
+ 
+
+ align:start position:0%
+as
+j goes to infinity of x of n sub j
+
+ align:start position:0%
+j goes to infinity of x of n sub j
+ 
+
+ align:start position:0%
+j goes to infinity of x of n sub j
+equals x
+
+ align:start position:0%
+equals x
+ 
+
+ align:start position:0%
+equals x
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+limit as j goes to infinity of c sub n
+
+ align:start position:0%
+limit as j goes to infinity of c sub n
+ 
+
+ align:start position:0%
+limit as j goes to infinity of c sub n
+sub
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+k j
+
+ align:start position:0%
+k j
+ 
+
+ align:start position:0%
+k j
+h j equals c
+
+ align:start position:0%
+h j equals c
+ 
+
+ align:start position:0%
+h j equals c
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+now i claim x equals c
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+now
+
+ align:start position:0%
+now
+ 
+
+ align:start position:0%
+now
+um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+0 is certainly bigger than or equal to x
+
+ align:start position:0%
+0 is certainly bigger than or equal to x
+ 
+
+ align:start position:0%
+0 is certainly bigger than or equal to x
+of n sub k sub j minus
+
+ align:start position:0%
+of n sub k sub j minus
+ 
+
+ align:start position:0%
+of n sub k sub j minus
+c sub n sub k sub j
+
+ align:start position:0%
+c sub n sub k sub j
+ 
+
+ align:start position:0%
+c sub n sub k sub j
+which is less than or equal to by
+
+ align:start position:0%
+which is less than or equal to by
+ 
+
+ align:start position:0%
+which is less than or equal to by
+how we've defined these sequences
+
+ align:start position:0%
+how we've defined these sequences
+ 
+
+ align:start position:0%
+how we've defined these sequences
+is less than or equal to one over n sub
+
+ align:start position:0%
+is less than or equal to one over n sub
+ 
+
+ align:start position:0%
+is less than or equal to one over n sub
+k sub j
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+all right
+
+ align:start position:0%
+all right
+ 
+
+ align:start position:0%
+all right
+and as j goes to infinity so first off
+
+ align:start position:0%
+and as j goes to infinity so first off
+ 
+
+ align:start position:0%
+and as j goes to infinity so first off
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+by
+
+ align:start position:0%
+by
+ 
+
+ align:start position:0%
+by
+the definition of uh subsequences
+
+ align:start position:0%
+the definition of uh subsequences
+ 
+
+ align:start position:0%
+the definition of uh subsequences
+um j is always bigger than or equal to n
+
+ align:start position:0%
+um j is always bigger than or equal to n
+ 
+
+ align:start position:0%
+um j is always bigger than or equal to n
+sub case or n sub k sub j is always
+
+ align:start position:0%
+sub case or n sub k sub j is always
+ 
+
+ align:start position:0%
+sub case or n sub k sub j is always
+bigger than or equal to j so this is
+
+ align:start position:0%
+bigger than or equal to j so this is
+ 
+
+ align:start position:0%
+bigger than or equal to j so this is
+always less than or equal to one over j
+
+ align:start position:0%
+always less than or equal to one over j
+ 
+
+ align:start position:0%
+always less than or equal to one over j
+this is just a consequence of how
+
+ align:start position:0%
+this is just a consequence of how
+ 
+
+ align:start position:0%
+this is just a consequence of how
+subsequences are defined okay you always
+
+ align:start position:0%
+subsequences are defined okay you always
+ 
+
+ align:start position:0%
+subsequences are defined okay you always
+have to move to the right after you've
+
+ align:start position:0%
+have to move to the right after you've
+ 
+
+ align:start position:0%
+have to move to the right after you've
+made a choice of
+
+ align:start position:0%
+made a choice of
+ 
+
+ align:start position:0%
+made a choice of
+a
+
+ align:start position:0%
+a
+ 
+
+ align:start position:0%
+a
+entry in the sequence that you're going
+
+ align:start position:0%
+entry in the sequence that you're going
+ 
+
+ align:start position:0%
+entry in the sequence that you're going
+to take as an element of your
+
+ align:start position:0%
+to take as an element of your
+ 
+
+ align:start position:0%
+to take as an element of your
+subsequence
+
+ align:start position:0%
+subsequence
+ 
+
+ align:start position:0%
+subsequence
+so 0 is bounded
+
+ align:start position:0%
+so 0 is bounded
+ 
+
+ align:start position:0%
+so 0 is bounded
+bounds this from below
+
+ align:start position:0%
+bounds this from below
+ 
+
+ align:start position:0%
+bounds this from below
+and it's bounded above by 1 over j which
+
+ align:start position:0%
+and it's bounded above by 1 over j which
+ 
+
+ align:start position:0%
+and it's bounded above by 1 over j which
+converges to 0. so
+
+ align:start position:0%
+converges to 0. so
+ 
+
+ align:start position:0%
+converges to 0. so
+the middle thing has to converge to zero
+
+ align:start position:0%
+the middle thing has to converge to zero
+ 
+
+ align:start position:0%
+the middle thing has to converge to zero
+by the squeeze theorem
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+but these two things that converges to x
+
+ align:start position:0%
+but these two things that converges to x
+ 
+
+ align:start position:0%
+but these two things that converges to x
+this converges to c
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and so
+
+ align:start position:0%
+and so
+ 
+
+ align:start position:0%
+and so
+the absolute value of x minus c equals 0
+
+ align:start position:0%
+the absolute value of x minus c equals 0
+ 
+
+ align:start position:0%
+the absolute value of x minus c equals 0
+and therefore
+
+ align:start position:0%
+and therefore
+ 
+
+ align:start position:0%
+and therefore
+x equals c
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+now we're almost home free
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+thus limit
+
+ align:start position:0%
+thus limit
+ 
+
+ align:start position:0%
+thus limit
+as j goes to infinity of x sub n sub k
+
+ align:start position:0%
+as j goes to infinity of x sub n sub k
+ 
+
+ align:start position:0%
+as j goes to infinity of x sub n sub k
+sub j
+
+ align:start position:0%
+sub j
+ 
+
+ align:start position:0%
+sub j
+equals c
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and limit as
+
+ align:start position:0%
+and limit as
+ 
+
+ align:start position:0%
+and limit as
+j goes to infinity
+
+ align:start position:0%
+j goes to infinity
+ 
+
+ align:start position:0%
+j goes to infinity
+c sub n sub k sub j
+
+ align:start position:0%
+c sub n sub k sub j
+ 
+
+ align:start position:0%
+c sub n sub k sub j
+equals
+
+ align:start position:0%
+equals
+ 
+
+ align:start position:0%
+equals
+c
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+[Applause]
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+all right now where's uh where's the
+
+ align:start position:0%
+all right now where's uh where's the
+ 
+
+ align:start position:0%
+all right now where's uh where's the
+kicker
+
+ align:start position:0%
+kicker
+ 
+
+ align:start position:0%
+kicker
+[Applause]
+
+ align:start position:0%
+[Applause]
+ 
+
+ align:start position:0%
+[Applause]
+this
+
+ align:start position:0%
+this
+ 
+
+ align:start position:0%
+this
+so these are subsequences of x sub n and
+
+ align:start position:0%
+so these are subsequences of x sub n and
+ 
+
+ align:start position:0%
+so these are subsequences of x sub n and
+c sub n
+
+ align:start position:0%
+c sub n
+ 
+
+ align:start position:0%
+c sub n
+[Applause]
+
+ align:start position:0%
+[Applause]
+ 
+
+ align:start position:0%
+[Applause]
+but each of those sequences is
+
+ align:start position:0%
+but each of those sequences is
+ 
+
+ align:start position:0%
+but each of those sequences is
+converging to a number c so by the
+
+ align:start position:0%
+converging to a number c so by the
+ 
+
+ align:start position:0%
+converging to a number c so by the
+theorem about continuity
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+since f is
+
+ align:start position:0%
+since f is
+ 
+
+ align:start position:0%
+since f is
+continuous
+
+ align:start position:0%
+continuous
+ 
+
+ align:start position:0%
+continuous
+at c this implies that 0
+
+ align:start position:0%
+at c this implies that 0
+ 
+
+ align:start position:0%
+at c this implies that 0
+equals the limit as j goes to infinity
+
+ align:start position:0%
+equals the limit as j goes to infinity
+ 
+
+ align:start position:0%
+equals the limit as j goes to infinity
+of
+
+ align:start position:0%
+of
+ 
+
+ align:start position:0%
+of
+f of x sub n sub
+
+ align:start position:0%
+f of x sub n sub
+ 
+
+ align:start position:0%
+f of x sub n sub
+so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+write it this way f of c minus f of c
+
+ align:start position:0%
+write it this way f of c minus f of c
+ 
+
+ align:start position:0%
+write it this way f of c minus f of c
+equals
+
+ align:start position:0%
+equals
+ 
+
+ align:start position:0%
+equals
+limit j goes to infinity of
+
+ align:start position:0%
+limit j goes to infinity of
+ 
+
+ align:start position:0%
+limit j goes to infinity of
+f of n sub
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+n sub
+
+ align:start position:0%
+n sub
+ 
+
+ align:start position:0%
+n sub
+c sub n sub k sub j
+
+ align:start position:0%
+c sub n sub k sub j
+ 
+
+ align:start position:0%
+c sub n sub k sub j
+which is bigger than or equal to epsilon
+
+ align:start position:0%
+which is bigger than or equal to epsilon
+ 
+
+ align:start position:0%
+which is bigger than or equal to epsilon
+zero right all of these are supposed to
+
+ align:start position:0%
+zero right all of these are supposed to
+ 
+
+ align:start position:0%
+zero right all of these are supposed to
+be bigger than or equal to some fixed
+
+ align:start position:0%
+be bigger than or equal to some fixed
+ 
+
+ align:start position:0%
+be bigger than or equal to some fixed
+epsilon zero which is positive
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and but we've just shown it's equal to
+
+ align:start position:0%
+and but we've just shown it's equal to
+ 
+
+ align:start position:0%
+and but we've just shown it's equal to
+zero
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and that's the contradiction
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+plus f is
+
+ align:start position:0%
+plus f is
+ 
+
+ align:start position:0%
+plus f is
+uniformly continuous
+
+ align:start position:0%
+uniformly continuous
+ 
+
+ align:start position:0%
+uniformly continuous
+on
+
+ align:start position:0%
+on
+ 
+
+ align:start position:0%
+on
+a b
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+all right so that concludes um
+
+ align:start position:0%
+all right so that concludes um
+ 
+
+ align:start position:0%
+all right so that concludes um
+you know what we'll say about continuity
+
+ align:start position:0%
+you know what we'll say about continuity
+ 
+
+ align:start position:0%
+you know what we'll say about continuity
+and as you'll note kind of going forward
+
+ align:start position:0%
+and as you'll note kind of going forward
+ 
+
+ align:start position:0%
+and as you'll note kind of going forward
+we're going to cover topics faster
+
+ align:start position:0%
+we're going to cover topics faster
+ 
+
+ align:start position:0%
+we're going to cover topics faster
+that's just because we have more
+
+ align:start position:0%
+that's just because we have more
+ 
+
+ align:start position:0%
+that's just because we have more
+machinery to to work with you know at
+
+ align:start position:0%
+machinery to to work with you know at
+ 
+
+ align:start position:0%
+machinery to to work with you know at
+the start it was very slow going just
+
+ align:start position:0%
+the start it was very slow going just
+ 
+
+ align:start position:0%
+the start it was very slow going just
+because
+
+ align:start position:0%
+because
+ 
+
+ align:start position:0%
+because
+one
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+it's the start of your first proof-based
+
+ align:start position:0%
+it's the start of your first proof-based
+ 
+
+ align:start position:0%
+it's the start of your first proof-based
+class so i'm going to go slow
+
+ align:start position:0%
+class so i'm going to go slow
+ 
+
+ align:start position:0%
+class so i'm going to go slow
+and two we didn't have much to work with
+
+ align:start position:0%
+and two we didn't have much to work with
+ 
+
+ align:start position:0%
+and two we didn't have much to work with
+we just had the real numbers are
+
+ align:start position:0%
+we just had the real numbers are
+ 
+
+ align:start position:0%
+we just had the real numbers are
+an ordered field with the least upper
+
+ align:start position:0%
+an ordered field with the least upper
+ 
+
+ align:start position:0%
+an ordered field with the least upper
+bound property but now we've covered
+
+ align:start position:0%
+bound property but now we've covered
+ 
+
+ align:start position:0%
+bound property but now we've covered
+sequences
+
+ align:start position:0%
+sequences
+ 
+
+ align:start position:0%
+sequences
+continuity we know more and it'll be
+
+ align:start position:0%
+continuity we know more and it'll be
+ 
+
+ align:start position:0%
+continuity we know more and it'll be
+easier to to
+
+ align:start position:0%
+easier to to
+ 
+
+ align:start position:0%
+easier to to
+prove new things and also
+
+ align:start position:0%
+prove new things and also
+ 
+
+ align:start position:0%
+prove new things and also
+you know hopefully familiarity with
+
+ align:start position:0%
+you know hopefully familiarity with
+ 
+
+ align:start position:0%
+you know hopefully familiarity with
+proof is getting with proofs
+
+ align:start position:0%
+proof is getting with proofs
+ 
+
+ align:start position:0%
+proof is getting with proofs
+is getting better so that
+
+ align:start position:0%
+is getting better so that
+ 
+
+ align:start position:0%
+is getting better so that
+my arguments can be a little bit shorter
+
+ align:start position:0%
+my arguments can be a little bit shorter
+ 
+
+ align:start position:0%
+my arguments can be a little bit shorter
+and not so
+
+ align:start position:0%
+and not so
+ 
+
+ align:start position:0%
+and not so
+so involved
+
+ align:start position:0%
+so involved
+ 
+
+ align:start position:0%
+so involved
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+we're moving on to something now
+
+ align:start position:0%
+we're moving on to something now
+ 
+
+ align:start position:0%
+we're moving on to something now
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+this is supposed to be about calculus
+
+ align:start position:0%
+this is supposed to be about calculus
+ 
+
+ align:start position:0%
+this is supposed to be about calculus
+we've covered limits uh continuity the
+
+ align:start position:0%
+we've covered limits uh continuity the
+ 
+
+ align:start position:0%
+we've covered limits uh continuity the
+next uh
+
+ align:start position:0%
+next uh
+ 
+
+ align:start position:0%
+next uh
+big topic
+
+ align:start position:0%
+big topic
+ 
+
+ align:start position:0%
+big topic
+has to be differentiability so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this is a new chapter
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+about the derivative
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so let's um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+let me first
+
+ align:start position:0%
+let me first
+ 
+
+ align:start position:0%
+let me first
+give you the precise definition so
+
+ align:start position:0%
+give you the precise definition so
+ 
+
+ align:start position:0%
+give you the precise definition so
+um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+first off
+
+ align:start position:0%
+first off
+ 
+
+ align:start position:0%
+first off
+i'll be saying uh
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+let i be
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+an interval
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+f goes from i to r
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and c an element of i
+
+ align:start position:0%
+and c an element of i
+ 
+
+ align:start position:0%
+and c an element of i
+now when i say an interval i don't mean
+
+ align:start position:0%
+now when i say an interval i don't mean
+ 
+
+ align:start position:0%
+now when i say an interval i don't mean
+it has to be closed and bounded like
+
+ align:start position:0%
+it has to be closed and bounded like
+ 
+
+ align:start position:0%
+it has to be closed and bounded like
+ones we've been working on i don't mean
+
+ align:start position:0%
+ones we've been working on i don't mean
+ 
+
+ align:start position:0%
+ones we've been working on i don't mean
+it has to be open you know it doesn't
+
+ align:start position:0%
+it has to be open you know it doesn't
+ 
+
+ align:start position:0%
+it has to be open you know it doesn't
+have to be a bounded interval like from
+
+ align:start position:0%
+have to be a bounded interval like from
+ 
+
+ align:start position:0%
+have to be a bounded interval like from
+zero to one it could be zero to infinity
+
+ align:start position:0%
+zero to one it could be zero to infinity
+ 
+
+ align:start position:0%
+zero to one it could be zero to infinity
+uh it can include the endpoints except
+
+ align:start position:0%
+uh it can include the endpoints except
+ 
+
+ align:start position:0%
+uh it can include the endpoints except
+of course infinity
+
+ align:start position:0%
+of course infinity
+ 
+
+ align:start position:0%
+of course infinity
+but i think you know what i mean and i
+
+ align:start position:0%
+but i think you know what i mean and i
+ 
+
+ align:start position:0%
+but i think you know what i mean and i
+don't have to write all this out for for
+
+ align:start position:0%
+don't have to write all this out for for
+ 
+
+ align:start position:0%
+don't have to write all this out for for
+what exactly an interval is so let i be
+
+ align:start position:0%
+what exactly an interval is so let i be
+ 
+
+ align:start position:0%
+what exactly an interval is so let i be
+an interval and f be a function from i
+
+ align:start position:0%
+an interval and f be a function from i
+ 
+
+ align:start position:0%
+an interval and f be a function from i
+to r
+
+ align:start position:0%
+to r
+ 
+
+ align:start position:0%
+to r
+and c uh a point of i
+
+ align:start position:0%
+and c uh a point of i
+ 
+
+ align:start position:0%
+and c uh a point of i
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+first off
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+you know convince yourselves of this but
+
+ align:start position:0%
+you know convince yourselves of this but
+ 
+
+ align:start position:0%
+you know convince yourselves of this but
+i think this should be pretty clear
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+for an interval
+
+ align:start position:0%
+for an interval
+ 
+
+ align:start position:0%
+for an interval
+every point in the interval is a cluster
+
+ align:start position:0%
+every point in the interval is a cluster
+ 
+
+ align:start position:0%
+every point in the interval is a cluster
+point of the interval
+
+ align:start position:0%
+point of the interval
+ 
+
+ align:start position:0%
+point of the interval
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+this is not
+
+ align:start position:0%
+this is not
+ 
+
+ align:start position:0%
+this is not
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+you know too difficult to prove but uh
+
+ align:start position:0%
+you know too difficult to prove but uh
+ 
+
+ align:start position:0%
+you know too difficult to prove but uh
+and i will not require you to prove it
+
+ align:start position:0%
+and i will not require you to prove it
+ 
+
+ align:start position:0%
+and i will not require you to prove it
+but i'm just saying this because i'm
+
+ align:start position:0%
+but i'm just saying this because i'm
+ 
+
+ align:start position:0%
+but i'm just saying this because i'm
+about to define a limit at c so
+
+ align:start position:0%
+about to define a limit at c so
+ 
+
+ align:start position:0%
+about to define a limit at c so
+uh it had better be a cluster point of
+
+ align:start position:0%
+uh it had better be a cluster point of
+ 
+
+ align:start position:0%
+uh it had better be a cluster point of
+of um you know a set
+
+ align:start position:0%
+of um you know a set
+ 
+
+ align:start position:0%
+of um you know a set
+containing um
+
+ align:start position:0%
+containing um
+ 
+
+ align:start position:0%
+containing um
+of a set
+
+ align:start position:0%
+of a set
+ 
+
+ align:start position:0%
+of a set
+that this limit is defined using so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+of i
+
+ align:start position:0%
+of i
+ 
+
+ align:start position:0%
+of i
+take away c
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and if you don't like this statement
+
+ align:start position:0%
+and if you don't like this statement
+ 
+
+ align:start position:0%
+and if you don't like this statement
+just forget i even wrote you know wrote
+
+ align:start position:0%
+just forget i even wrote you know wrote
+ 
+
+ align:start position:0%
+just forget i even wrote you know wrote
+it and we'll continue on
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+you say f
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+is differentiable
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+at c
+
+ align:start position:0%
+at c
+ 
+
+ align:start position:0%
+at c
+so this is the new
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+bit of terminology
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+if the limit
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+limit x goes to c
+
+ align:start position:0%
+limit x goes to c
+ 
+
+ align:start position:0%
+limit x goes to c
+f of x minus
+
+ align:start position:0%
+f of x minus
+ 
+
+ align:start position:0%
+f of x minus
+f of c over x minus c
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+exists
+
+ align:start position:0%
+exists
+ 
+
+ align:start position:0%
+exists
+okay if this limit exists we say the
+
+ align:start position:0%
+okay if this limit exists we say the
+ 
+
+ align:start position:0%
+okay if this limit exists we say the
+function's differentiable at z
+
+ align:start position:0%
+function's differentiable at z
+ 
+
+ align:start position:0%
+function's differentiable at z
+and
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+we write
+
+ align:start position:0%
+we write
+ 
+
+ align:start position:0%
+we write
+we use a notation
+
+ align:start position:0%
+we use a notation
+ 
+
+ align:start position:0%
+we use a notation
+f prime f apostrophe c
+
+ align:start position:0%
+f prime f apostrophe c
+ 
+
+ align:start position:0%
+f prime f apostrophe c
+for this limit
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+f is differentiable
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+every point
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+of the interval i we get a new function
+
+ align:start position:0%
+of the interval i we get a new function
+ 
+
+ align:start position:0%
+of the interval i we get a new function
+this function f prime of c which we
+
+ align:start position:0%
+this function f prime of c which we
+ 
+
+ align:start position:0%
+this function f prime of c which we
+denote by
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+we denote
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+function that's the derivative of f as f
+
+ align:start position:0%
+function that's the derivative of f as f
+ 
+
+ align:start position:0%
+function that's the derivative of f as f
+prime or df dx
+
+ align:start position:0%
+prime or df dx
+ 
+
+ align:start position:0%
+prime or df dx
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so the simplest guys that are
+
+ align:start position:0%
+okay so the simplest guys that are
+ 
+
+ align:start position:0%
+okay so the simplest guys that are
+differentiable are of course polynomials
+
+ align:start position:0%
+differentiable are of course polynomials
+ 
+
+ align:start position:0%
+differentiable are of course polynomials
+i think this is one of the first things
+
+ align:start position:0%
+i think this is one of the first things
+ 
+
+ align:start position:0%
+i think this is one of the first things
+you learned back in calculus um
+
+ align:start position:0%
+you learned back in calculus um
+ 
+
+ align:start position:0%
+you learned back in calculus um
+and
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+you know
+
+ align:start position:0%
+you know
+ 
+
+ align:start position:0%
+you know
+i'm not going to go through what this is
+
+ align:start position:0%
+i'm not going to go through what this is
+ 
+
+ align:start position:0%
+i'm not going to go through what this is
+supposed to represent you know this from
+
+ align:start position:0%
+supposed to represent you know this from
+ 
+
+ align:start position:0%
+supposed to represent you know this from
+calculus
+
+ align:start position:0%
+calculus
+ 
+
+ align:start position:0%
+calculus
+the best way to say what this number
+
+ align:start position:0%
+the best way to say what this number
+ 
+
+ align:start position:0%
+the best way to say what this number
+represents is the instantaneous rate of
+
+ align:start position:0%
+represents is the instantaneous rate of
+ 
+
+ align:start position:0%
+represents is the instantaneous rate of
+change of the function f at this point
+
+ align:start position:0%
+change of the function f at this point
+ 
+
+ align:start position:0%
+change of the function f at this point
+how is f
+
+ align:start position:0%
+how is f
+ 
+
+ align:start position:0%
+how is f
+changing at that point
+
+ align:start position:0%
+changing at that point
+ 
+
+ align:start position:0%
+changing at that point
+in the sense of increasing decreasing
+
+ align:start position:0%
+in the sense of increasing decreasing
+ 
+
+ align:start position:0%
+in the sense of increasing decreasing
+and so on
+
+ align:start position:0%
+and so on
+ 
+
+ align:start position:0%
+and so on
+all right
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+or you if you like you interpret this as
+
+ align:start position:0%
+or you if you like you interpret this as
+ 
+
+ align:start position:0%
+or you if you like you interpret this as
+being the slope of the line that is
+
+ align:start position:0%
+being the slope of the line that is
+ 
+
+ align:start position:0%
+being the slope of the line that is
+perfectly tangent to the curve
+
+ align:start position:0%
+perfectly tangent to the curve
+ 
+
+ align:start position:0%
+perfectly tangent to the curve
+uh to the graph of the function f but uh
+
+ align:start position:0%
+uh to the graph of the function f but uh
+ 
+
+ align:start position:0%
+uh to the graph of the function f but uh
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+you know what does that mean to be
+
+ align:start position:0%
+you know what does that mean to be
+ 
+
+ align:start position:0%
+you know what does that mean to be
+tangent to the graph of a function you
+
+ align:start position:0%
+tangent to the graph of a function you
+ 
+
+ align:start position:0%
+tangent to the graph of a function you
+know so that takes a bit of explaining
+
+ align:start position:0%
+know so that takes a bit of explaining
+ 
+
+ align:start position:0%
+know so that takes a bit of explaining
+so i'm not going to get into what the
+
+ align:start position:0%
+so i'm not going to get into what the
+ 
+
+ align:start position:0%
+so i'm not going to get into what the
+actual
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+interpretation of this number is
+
+ align:start position:0%
+interpretation of this number is
+ 
+
+ align:start position:0%
+interpretation of this number is
+i think you have a pretty good idea of
+
+ align:start position:0%
+i think you have a pretty good idea of
+ 
+
+ align:start position:0%
+i think you have a pretty good idea of
+what that is we're just going to start
+
+ align:start position:0%
+what that is we're just going to start
+ 
+
+ align:start position:0%
+what that is we're just going to start
+proving some properties of it
+
+ align:start position:0%
+proving some properties of it
+ 
+
+ align:start position:0%
+proving some properties of it
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+the simplest example of a function which
+
+ align:start position:0%
+the simplest example of a function which
+ 
+
+ align:start position:0%
+the simplest example of a function which
+is differentiable
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+is that of a monomial
+
+ align:start position:0%
+is that of a monomial
+ 
+
+ align:start position:0%
+is that of a monomial
+so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+f of x equals
+
+ align:start position:0%
+f of x equals
+ 
+
+ align:start position:0%
+f of x equals
+x to the n
+
+ align:start position:0%
+x to the n
+ 
+
+ align:start position:0%
+x to the n
+let's put let's put even a number in
+
+ align:start position:0%
+let's put let's put even a number in
+ 
+
+ align:start position:0%
+let's put let's put even a number in
+there
+
+ align:start position:0%
+there
+ 
+
+ align:start position:0%
+there
+so let uh
+
+ align:start position:0%
+so let uh
+ 
+
+ align:start position:0%
+so let uh
+let's write it this way
+
+ align:start position:0%
+let's write it this way
+ 
+
+ align:start position:0%
+let's write it this way
+but alpha being r
+
+ align:start position:0%
+but alpha being r
+ 
+
+ align:start position:0%
+but alpha being r
+and b a natural number
+
+ align:start position:0%
+and b a natural number
+ 
+
+ align:start position:0%
+and b a natural number
+zero
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+then
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+function f of x equals alpha times x to
+
+ align:start position:0%
+function f of x equals alpha times x to
+ 
+
+ align:start position:0%
+function f of x equals alpha times x to
+the n
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+is
+
+ align:start position:0%
+is
+ 
+
+ align:start position:0%
+is
+differentiable um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so i should have said here as well if a
+
+ align:start position:0%
+so i should have said here as well if a
+ 
+
+ align:start position:0%
+so i should have said here as well if a
+function is differentiable at every
+
+ align:start position:0%
+function is differentiable at every
+ 
+
+ align:start position:0%
+function is differentiable at every
+point where it's defined
+
+ align:start position:0%
+point where it's defined
+ 
+
+ align:start position:0%
+point where it's defined
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+or if a function is differentiable at
+
+ align:start position:0%
+or if a function is differentiable at
+ 
+
+ align:start position:0%
+or if a function is differentiable at
+every point in its domain i then we just
+
+ align:start position:0%
+every point in its domain i then we just
+ 
+
+ align:start position:0%
+every point in its domain i then we just
+say the function's differentiable
+
+ align:start position:0%
+say the function's differentiable
+ 
+
+ align:start position:0%
+say the function's differentiable
+so then this function this monomial is
+
+ align:start position:0%
+so then this function this monomial is
+ 
+
+ align:start position:0%
+so then this function this monomial is
+differentiable and
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+for all c f prime of c equals
+
+ align:start position:0%
+for all c f prime of c equals
+ 
+
+ align:start position:0%
+for all c f prime of c equals
+n times alpha x the n minus 1.
+
+ align:start position:0%
+n times alpha x the n minus 1.
+ 
+
+ align:start position:0%
+n times alpha x the n minus 1.
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+c
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+so let's give a proof of that
+
+ align:start position:0%
+so let's give a proof of that
+ 
+
+ align:start position:0%
+so let's give a proof of that
+and we'll use
+
+ align:start position:0%
+and we'll use
+ 
+
+ align:start position:0%
+and we'll use
+this
+
+ align:start position:0%
+this
+ 
+
+ align:start position:0%
+this
+kind of simple formula
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so let's take a look at
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+x minus c times this kind of
+
+ align:start position:0%
+x minus c times this kind of
+ 
+
+ align:start position:0%
+x minus c times this kind of
+weird looking sum to
+
+ align:start position:0%
+weird looking sum to
+ 
+
+ align:start position:0%
+weird looking sum to
+x
+
+ align:start position:0%
+x
+ 
+
+ align:start position:0%
+x
+n minus 1 minus j
+
+ align:start position:0%
+n minus 1 minus j
+ 
+
+ align:start position:0%
+n minus 1 minus j
+c to the
+
+ align:start position:0%
+c to the
+ 
+
+ align:start position:0%
+c to the
+j
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so this is equal to
+
+ align:start position:0%
+so this is equal to
+ 
+
+ align:start position:0%
+so this is equal to
+multiply the x through i get sum from
+
+ align:start position:0%
+multiply the x through i get sum from
+ 
+
+ align:start position:0%
+multiply the x through i get sum from
+j equals 0 to
+
+ align:start position:0%
+j equals 0 to
+ 
+
+ align:start position:0%
+j equals 0 to
+n minus 1
+
+ align:start position:0%
+n minus 1
+ 
+
+ align:start position:0%
+n minus 1
+x to the
+
+ align:start position:0%
+x to the
+ 
+
+ align:start position:0%
+x to the
+n minus j
+
+ align:start position:0%
+n minus j
+ 
+
+ align:start position:0%
+n minus j
+c to the j minus
+
+ align:start position:0%
+c to the j minus
+ 
+
+ align:start position:0%
+c to the j minus
+and i'm not going to use j again in the
+
+ align:start position:0%
+and i'm not going to use j again in the
+ 
+
+ align:start position:0%
+and i'm not going to use j again in the
+sum when i carry this c through i'm
+
+ align:start position:0%
+sum when i carry this c through i'm
+ 
+
+ align:start position:0%
+sum when i carry this c through i'm
+going to use l
+
+ align:start position:0%
+going to use l
+ 
+
+ align:start position:0%
+going to use l
+sum from l equals 0
+
+ align:start position:0%
+sum from l equals 0
+ 
+
+ align:start position:0%
+sum from l equals 0
+to
+
+ align:start position:0%
+to
+ 
+
+ align:start position:0%
+to
+n minus 1
+
+ align:start position:0%
+n minus 1
+ 
+
+ align:start position:0%
+n minus 1
+x to the
+
+ align:start position:0%
+x to the
+ 
+
+ align:start position:0%
+x to the
+n minus i'll put it this way j plus 1
+
+ align:start position:0%
+n minus i'll put it this way j plus 1
+ 
+
+ align:start position:0%
+n minus i'll put it this way j plus 1
+c to the j plus 1
+
+ align:start position:0%
+c to the j plus 1
+ 
+
+ align:start position:0%
+c to the j plus 1
+or
+
+ align:start position:0%
+or
+ 
+
+ align:start position:0%
+or
+l
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+and now i'm going to make a change of
+
+ align:start position:0%
+and now i'm going to make a change of
+ 
+
+ align:start position:0%
+and now i'm going to make a change of
+variables in the second sum
+
+ align:start position:0%
+variables in the second sum
+ 
+
+ align:start position:0%
+variables in the second sum
+and let j equals l plus 1.
+
+ align:start position:0%
+and let j equals l plus 1.
+ 
+
+ align:start position:0%
+and let j equals l plus 1.
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so in that case when l equals 0 j starts
+
+ align:start position:0%
+so in that case when l equals 0 j starts
+ 
+
+ align:start position:0%
+so in that case when l equals 0 j starts
+at 1
+
+ align:start position:0%
+at 1
+ 
+
+ align:start position:0%
+at 1
+when l hits n minus 1 j equals n so this
+
+ align:start position:0%
+when l hits n minus 1 j equals n so this
+ 
+
+ align:start position:0%
+when l hits n minus 1 j equals n so this
+equals the sum from j equals 0
+
+ align:start position:0%
+equals the sum from j equals 0
+ 
+
+ align:start position:0%
+equals the sum from j equals 0
+n minus 1 x n minus j c to the j minus
+
+ align:start position:0%
+n minus 1 x n minus j c to the j minus
+ 
+
+ align:start position:0%
+n minus 1 x n minus j c to the j minus
+sum
+
+ align:start position:0%
+sum
+ 
+
+ align:start position:0%
+sum
+j equals
+
+ align:start position:0%
+j equals
+ 
+
+ align:start position:0%
+j equals
+
+ align:start position:0%
+ 
+
+ align:start position:0%
+to n
+
+ align:start position:0%
+to n
+ 
+
+ align:start position:0%
+to n
+x
+
+ align:start position:0%
+x
+ 
+
+ align:start position:0%
+x
+n minus j c to the j
+
+ align:start position:0%
+n minus j c to the j
+ 
+
+ align:start position:0%
+n minus j c to the j
+so it's the same
+
+ align:start position:0%
+so it's the same
+ 
+
+ align:start position:0%
+so it's the same
+terms in the sum except starting at
+
+ align:start position:0%
+terms in the sum except starting at
+ 
+
+ align:start position:0%
+terms in the sum except starting at
+different places so what doesn't get
+
+ align:start position:0%
+different places so what doesn't get
+ 
+
+ align:start position:0%
+different places so what doesn't get
+killed here is the j equals 0 term
+
+ align:start position:0%
+killed here is the j equals 0 term
+ 
+
+ align:start position:0%
+killed here is the j equals 0 term
+because this one starts at j equals 1
+
+ align:start position:0%
+because this one starts at j equals 1
+ 
+
+ align:start position:0%
+because this one starts at j equals 1
+this one ends at n
+
+ align:start position:0%
+this one ends at n
+ 
+
+ align:start position:0%
+this one ends at n
+and so it kills the n minus 1 term so
+
+ align:start position:0%
+and so it kills the n minus 1 term so
+ 
+
+ align:start position:0%
+and so it kills the n minus 1 term so
+the only thing that survives from this
+
+ align:start position:0%
+the only thing that survives from this
+ 
+
+ align:start position:0%
+the only thing that survives from this
+sum is the j equals 0 term x to the n
+
+ align:start position:0%
+sum is the j equals 0 term x to the n
+ 
+
+ align:start position:0%
+sum is the j equals 0 term x to the n
+minus 0 c to the 0 minus
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and now from here
+
+ align:start position:0%
+and now from here
+ 
+
+ align:start position:0%
+and now from here
+everything gets killed except the n term
+
+ align:start position:0%
+everything gets killed except the n term
+ 
+
+ align:start position:0%
+everything gets killed except the n term
+so x to the n minus n c to the n
+
+ align:start position:0%
+so x to the n minus n c to the n
+ 
+
+ align:start position:0%
+so x to the n minus n c to the n
+equals x to the n minus c to the
+
+ align:start position:0%
+equals x to the n minus c to the
+ 
+
+ align:start position:0%
+equals x to the n minus c to the
+right so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this
+
+ align:start position:0%
+this
+ 
+
+ align:start position:0%
+this
+is therefore equal to
+
+ align:start position:0%
+is therefore equal to
+ 
+
+ align:start position:0%
+is therefore equal to
+this okay
+
+ align:start position:0%
+this okay
+ 
+
+ align:start position:0%
+this okay
+so we use this to compute this limit
+
+ align:start position:0%
+so we use this to compute this limit
+ 
+
+ align:start position:0%
+so we use this to compute this limit
+so then
+
+ align:start position:0%
+so then
+ 
+
+ align:start position:0%
+so then
+f prime of c is equal to the limit
+
+ align:start position:0%
+f prime of c is equal to the limit
+ 
+
+ align:start position:0%
+f prime of c is equal to the limit
+as x goes to c
+
+ align:start position:0%
+as x goes to c
+ 
+
+ align:start position:0%
+as x goes to c
+of x to the n
+
+ align:start position:0%
+of x to the n
+ 
+
+ align:start position:0%
+of x to the n
+alpha times x to the n times alpha times
+
+ align:start position:0%
+alpha times x to the n times alpha times
+ 
+
+ align:start position:0%
+alpha times x to the n times alpha times
+c to the n
+
+ align:start position:0%
+c to the n
+ 
+
+ align:start position:0%
+c to the n
+where x minus c now alpha is just a
+
+ align:start position:0%
+where x minus c now alpha is just a
+ 
+
+ align:start position:0%
+where x minus c now alpha is just a
+number it can pop out
+
+ align:start position:0%
+number it can pop out
+ 
+
+ align:start position:0%
+number it can pop out
+x to the n minus c to the n divided by x
+
+ align:start position:0%
+x to the n minus c to the n divided by x
+ 
+
+ align:start position:0%
+x to the n minus c to the n divided by x
+minus c is this thing divided by x minus
+
+ align:start position:0%
+minus c is this thing divided by x minus
+ 
+
+ align:start position:0%
+minus c is this thing divided by x minus
+c so this is equal to alpha
+
+ align:start position:0%
+c so this is equal to alpha
+ 
+
+ align:start position:0%
+c so this is equal to alpha
+times the limit as x goes to c
+
+ align:start position:0%
+times the limit as x goes to c
+ 
+
+ align:start position:0%
+times the limit as x goes to c
+of sum from
+
+ align:start position:0%
+of sum from
+ 
+
+ align:start position:0%
+of sum from
+j equals 0
+
+ align:start position:0%
+j equals 0
+ 
+
+ align:start position:0%
+j equals 0
+to n minus 1
+
+ align:start position:0%
+to n minus 1
+ 
+
+ align:start position:0%
+to n minus 1
+x to the n minus 1 minus j
+
+ align:start position:0%
+x to the n minus 1 minus j
+ 
+
+ align:start position:0%
+x to the n minus 1 minus j
+c to the j
+
+ align:start position:0%
+c to the j
+ 
+
+ align:start position:0%
+c to the j
+now this is just a polynomial in x
+
+ align:start position:0%
+now this is just a polynomial in x
+ 
+
+ align:start position:0%
+now this is just a polynomial in x
+okay polynomials are continuous
+
+ align:start position:0%
+okay polynomials are continuous
+ 
+
+ align:start position:0%
+okay polynomials are continuous
+functions so the limit as x goes to c is
+
+ align:start position:0%
+functions so the limit as x goes to c is
+ 
+
+ align:start position:0%
+functions so the limit as x goes to c is
+just you plug in c to x and so this
+
+ align:start position:0%
+just you plug in c to x and so this
+ 
+
+ align:start position:0%
+just you plug in c to x and so this
+equals alpha
+
+ align:start position:0%
+equals alpha
+ 
+
+ align:start position:0%
+equals alpha
+times sum from j equals 0 to n minus 1.
+
+ align:start position:0%
+times sum from j equals 0 to n minus 1.
+ 
+
+ align:start position:0%
+times sum from j equals 0 to n minus 1.
+c to the n minus 1
+
+ align:start position:0%
+c to the n minus 1
+ 
+
+ align:start position:0%
+c to the n minus 1
+minus j times j equals
+
+ align:start position:0%
+minus j times j equals
+ 
+
+ align:start position:0%
+minus j times j equals
+so c to the n minus 1 minus j times c to
+
+ align:start position:0%
+so c to the n minus 1 minus j times c to
+ 
+
+ align:start position:0%
+so c to the n minus 1 minus j times c to
+the j gives me c to the n minus 1.
+
+ align:start position:0%
+the j gives me c to the n minus 1.
+ 
+
+ align:start position:0%
+the j gives me c to the n minus 1.
+i'm summing in j
+
+ align:start position:0%
+i'm summing in j
+ 
+
+ align:start position:0%
+i'm summing in j
+there's no j here so that just pops out
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+times the sum
+
+ align:start position:0%
+times the sum
+ 
+
+ align:start position:0%
+times the sum
+j equals 0
+
+ align:start position:0%
+j equals 0
+ 
+
+ align:start position:0%
+j equals 0
+n minus 1
+
+ align:start position:0%
+n minus 1
+ 
+
+ align:start position:0%
+n minus 1
+and that's just there's n of d
+
+ align:start position:0%
+and that's just there's n of d
+ 
+
+ align:start position:0%
+and that's just there's n of d
+times 1 so this is just n
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and that's the proof
+
+ align:start position:0%
+and that's the proof
+ 
+
+ align:start position:0%
+and that's the proof
+okay so i'm sure you saw that at some
+
+ align:start position:0%
+okay so i'm sure you saw that at some
+ 
+
+ align:start position:0%
+okay so i'm sure you saw that at some
+point
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+next time we'll continue with
+
+ align:start position:0%
+next time we'll continue with
+ 
+
+ align:start position:0%
+next time we'll continue with
+we'll give an example of a function
+
+ align:start position:0%
+we'll give an example of a function
+ 
+
+ align:start position:0%
+we'll give an example of a function
+which is not differentiable at a point
+
+ align:start position:0%
+which is not differentiable at a point
+ 
+
+ align:start position:0%
+which is not differentiable at a point
+of course
+
+ align:start position:0%
+of course
+ 
+
+ align:start position:0%
+of course
+i think you probably already know this f
+
+ align:start position:0%
+i think you probably already know this f
+ 
+
+ align:start position:0%
+i think you probably already know this f
+of x equals the absolute value of x
+
+ align:start position:0%
+of x equals the absolute value of x
+ 
+
+ align:start position:0%
+of x equals the absolute value of x
+if there's time at some point
+
+ align:start position:0%
+if there's time at some point
+ 
+
+ align:start position:0%
+if there's time at some point
+i'll go over an example of a function
+
+ align:start position:0%
+i'll go over an example of a function
+ 
+
+ align:start position:0%
+i'll go over an example of a function
+which
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+was very surprising to people at one
+
+ align:start position:0%
+was very surprising to people at one
+ 
+
+ align:start position:0%
+was very surprising to people at one
+point so now that we have
+
+ align:start position:0%
+point so now that we have
+ 
+
+ align:start position:0%
+point so now that we have
+differentiability and continuity on the
+
+ align:start position:0%
+differentiability and continuity on the
+ 
+
+ align:start position:0%
+differentiability and continuity on the
+board
+
+ align:start position:0%
+board
+ 
+
+ align:start position:0%
+board
+for a long time
+
+ align:start position:0%
+for a long time
+ 
+
+ align:start position:0%
+for a long time
+some long since dead people
+
+ align:start position:0%
+some long since dead people
+ 
+
+ align:start position:0%
+some long since dead people
+believed that if you have a continuous
+
+ align:start position:0%
+believed that if you have a continuous
+ 
+
+ align:start position:0%
+believed that if you have a continuous
+function
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+any continuous function then there has
+
+ align:start position:0%
+any continuous function then there has
+ 
+
+ align:start position:0%
+any continuous function then there has
+to be at least one point where it's
+
+ align:start position:0%
+to be at least one point where it's
+ 
+
+ align:start position:0%
+to be at least one point where it's
+differentiable
+
+ align:start position:0%
+differentiable
+ 
+
+ align:start position:0%
+differentiable
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+there must be at least one point where
+
+ align:start position:0%
+there must be at least one point where
+ 
+
+ align:start position:0%
+there must be at least one point where
+it's differentiable
+
+ align:start position:0%
+it's differentiable
+ 
+
+ align:start position:0%
+it's differentiable
+and people tried to prove that for a
+
+ align:start position:0%
+and people tried to prove that for a
+ 
+
+ align:start position:0%
+and people tried to prove that for a
+long time and they couldn't because it's
+
+ align:start position:0%
+long time and they couldn't because it's
+ 
+
+ align:start position:0%
+long time and they couldn't because it's
+false
+
+ align:start position:0%
+false
+ 
+
+ align:start position:0%
+false
+virus ross who is again kind of the
+
+ align:start position:0%
+virus ross who is again kind of the
+ 
+
+ align:start position:0%
+virus ross who is again kind of the
+godfather of everything we're doing
+
+ align:start position:0%
+godfather of everything we're doing
+ 
+
+ align:start position:0%
+godfather of everything we're doing
+came up with a
+
+ align:start position:0%
+came up with a
+ 
+
+ align:start position:0%
+came up with a
+whole class of examples of functions
+
+ align:start position:0%
+whole class of examples of functions
+ 
+
+ align:start position:0%
+whole class of examples of functions
+that are continuous
+
+ align:start position:0%
+that are continuous
+ 
+
+ align:start position:0%
+that are continuous
+but are differentiable nowhere okay
+
+ align:start position:0%
+but are differentiable nowhere okay
+ 
+
+ align:start position:0%
+but are differentiable nowhere okay
+they're not differentiable at a single
+
+ align:start position:0%
+they're not differentiable at a single
+ 
+
+ align:start position:0%
+they're not differentiable at a single
+point
+
+ align:start position:0%
+point
+ 
+
+ align:start position:0%
+point
+all right
+
+ align:start position:0%
+all right
+ 
+
+ align:start position:0%
+all right
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+perhaps depending on time
+
+ align:start position:0%
+perhaps depending on time
+ 
+
+ align:start position:0%
+perhaps depending on time
+uh we'll go over this example
+
+ align:start position:0%
+uh we'll go over this example
+ 
+
+ align:start position:0%
+uh we'll go over this example
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+i think i'll stop there
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+you
\ No newline at end of file
diff --git a/fmx5Yj95sgQ.txt b/fmx5Yj95sgQ.txt
new file mode 100644
index 0000000000000000000000000000000000000000..4882bf8927bdf7cc8101550de08e695c165e8414
--- /dev/null
+++ b/fmx5Yj95sgQ.txt
@@ -0,0 +1,5651 @@
+align:start position:0%
+ 
+the following content is provided under
+
+ align:start position:0%
+the following content is provided under
+ 
+
+ align:start position:0%
+the following content is provided under
+a Creative Commons license your support
+
+ align:start position:0%
+a Creative Commons license your support
+ 
+
+ align:start position:0%
+a Creative Commons license your support
+will help MIT OpenCourseWare continue to
+
+ align:start position:0%
+will help MIT OpenCourseWare continue to
+ 
+
+ align:start position:0%
+will help MIT OpenCourseWare continue to
+offer high quality educational resources
+
+ align:start position:0%
+offer high quality educational resources
+ 
+
+ align:start position:0%
+offer high quality educational resources
+for free
+
+ align:start position:0%
+for free
+ 
+
+ align:start position:0%
+for free
+to make a donation or view additional
+
+ align:start position:0%
+to make a donation or view additional
+ 
+
+ align:start position:0%
+to make a donation or view additional
+materials from hundreds of MIT courses
+
+ align:start position:0%
+materials from hundreds of MIT courses
+ 
+
+ align:start position:0%
+materials from hundreds of MIT courses
+visit MIT opencourseware at ocw.mit.edu
+
+ align:start position:0%
+visit MIT opencourseware at ocw.mit.edu
+ 
+
+ align:start position:0%
+visit MIT opencourseware at ocw.mit.edu
+now why are we interested in sleep so we
+
+ align:start position:0%
+now why are we interested in sleep so we
+ 
+
+ align:start position:0%
+now why are we interested in sleep so we
+kind of think about this two modes
+
+ align:start position:0%
+kind of think about this two modes
+ 
+
+ align:start position:0%
+kind of think about this two modes
+online mode and offline mode the online
+
+ align:start position:0%
+online mode and offline mode the online
+ 
+
+ align:start position:0%
+online mode and offline mode the online
+mode you're taking information in the
+
+ align:start position:0%
+mode you're taking information in the
+ 
+
+ align:start position:0%
+mode you're taking information in the
+offline mode you're going back and
+
+ align:start position:0%
+offline mode you're going back and
+ 
+
+ align:start position:0%
+offline mode you're going back and
+evaluating information what's the
+
+ align:start position:0%
+evaluating information what's the
+ 
+
+ align:start position:0%
+evaluating information what's the
+purpose of evaluating information that
+
+ align:start position:0%
+purpose of evaluating information that
+ 
+
+ align:start position:0%
+purpose of evaluating information that
+you've taken in well if we think about
+
+ align:start position:0%
+you've taken in well if we think about
+ 
+
+ align:start position:0%
+you've taken in well if we think about
+the general problem that's being solved
+
+ align:start position:0%
+the general problem that's being solved
+ 
+
+ align:start position:0%
+the general problem that's being solved
+the problem of intelligence problem of
+
+ align:start position:0%
+the problem of intelligence problem of
+ 
+
+ align:start position:0%
+the problem of intelligence problem of
+intelligence is trying to is trying to
+
+ align:start position:0%
+intelligence is trying to is trying to
+ 
+
+ align:start position:0%
+intelligence is trying to is trying to
+understand and infer these sort of deep
+
+ align:start position:0%
+understand and infer these sort of deep
+ 
+
+ align:start position:0%
+understand and infer these sort of deep
+generalizable relationships rules you're
+
+ align:start position:0%
+generalizable relationships rules you're
+ 
+
+ align:start position:0%
+generalizable relationships rules you're
+trying to expect rules from instances
+
+ align:start position:0%
+trying to expect rules from instances
+ 
+
+ align:start position:0%
+trying to expect rules from instances
+and you'd like those rules to be Jenna's
+
+ align:start position:0%
+and you'd like those rules to be Jenna's
+ 
+
+ align:start position:0%
+and you'd like those rules to be Jenna's
+generally applicable as possible and in
+
+ align:start position:0%
+generally applicable as possible and in
+ 
+
+ align:start position:0%
+generally applicable as possible and in
+order to do that presumably one has to
+
+ align:start position:0%
+order to do that presumably one has to
+ 
+
+ align:start position:0%
+order to do that presumably one has to
+go back and evaluate the many individual
+
+ align:start position:0%
+go back and evaluate the many individual
+ 
+
+ align:start position:0%
+go back and evaluate the many individual
+instances to try to extract some kind of
+
+ align:start position:0%
+instances to try to extract some kind of
+ 
+
+ align:start position:0%
+instances to try to extract some kind of
+statistical regularity and then perhaps
+
+ align:start position:0%
+statistical regularity and then perhaps
+ 
+
+ align:start position:0%
+statistical regularity and then perhaps
+evaluate models that you have
+
+ align:start position:0%
+evaluate models that you have
+ 
+
+ align:start position:0%
+evaluate models that you have
+constructed in terms of their
+
+ align:start position:0%
+constructed in terms of their
+ 
+
+ align:start position:0%
+constructed in terms of their
+consistency with individual instances
+
+ align:start position:0%
+consistency with individual instances
+ 
+
+ align:start position:0%
+consistency with individual instances
+that you've already collected or perhaps
+
+ align:start position:0%
+that you've already collected or perhaps
+ 
+
+ align:start position:0%
+that you've already collected or perhaps
+future instances that that haven't yet
+
+ align:start position:0%
+future instances that that haven't yet
+ 
+
+ align:start position:0%
+future instances that that haven't yet
+play so you've got you get the you have
+
+ align:start position:0%
+play so you've got you get the you have
+ 
+
+ align:start position:0%
+play so you've got you get the you have
+the some of the raw material you bit a
+
+ align:start position:0%
+the some of the raw material you bit a
+ 
+
+ align:start position:0%
+the some of the raw material you bit a
+little model and then you continually
+
+ align:start position:0%
+little model and then you continually
+ 
+
+ align:start position:0%
+little model and then you continually
+test that model against new information
+
+ align:start position:0%
+test that model against new information
+ 
+
+ align:start position:0%
+test that model against new information
+that comes in and the question is when
+
+ align:start position:0%
+that comes in and the question is when
+ 
+
+ align:start position:0%
+that comes in and the question is when
+can you do that now you could do that
+
+ align:start position:0%
+can you do that now you could do that
+ 
+
+ align:start position:0%
+can you do that now you could do that
+when you're out and about in the world
+
+ align:start position:0%
+when you're out and about in the world
+ 
+
+ align:start position:0%
+when you're out and about in the world
+and well as as you as you saw and read
+
+ align:start position:0%
+and well as as you as you saw and read
+ 
+
+ align:start position:0%
+and well as as you as you saw and read
+in that paper when animals are sitting
+
+ align:start position:0%
+in that paper when animals are sitting
+ 
+
+ align:start position:0%
+in that paper when animals are sitting
+quietly they very quickly can switch
+
+ align:start position:0%
+quietly they very quickly can switch
+ 
+
+ align:start position:0%
+quietly they very quickly can switch
+into this kind of offline mode that
+
+ align:start position:0%
+into this kind of offline mode that
+ 
+
+ align:start position:0%
+into this kind of offline mode that
+looks a lot like sleep in fact electro
+
+ align:start position:0%
+looks a lot like sleep in fact electro
+ 
+
+ align:start position:0%
+looks a lot like sleep in fact electro
+physiologically sleep and quiet
+
+ align:start position:0%
+physiologically sleep and quiet
+ 
+
+ align:start position:0%
+physiologically sleep and quiet
+wakefulness and the hippocampus are
+
+ align:start position:0%
+wakefulness and the hippocampus are
+ 
+
+ align:start position:0%
+wakefulness and the hippocampus are
+nearly indistinguishable it's the same
+
+ align:start position:0%
+nearly indistinguishable it's the same
+ 
+
+ align:start position:0%
+nearly indistinguishable it's the same
+kind of offline mode it says ok when
+
+ align:start position:0%
+kind of offline mode it says ok when
+ 
+
+ align:start position:0%
+kind of offline mode it says ok when
+you're not and you know I'm not using
+
+ align:start position:0%
+you're not and you know I'm not using
+ 
+
+ align:start position:0%
+you're not and you know I'm not using
+this if the camp is not being used
+
+ align:start position:0%
+this if the camp is not being used
+ 
+
+ align:start position:0%
+this if the camp is not being used
+taking new information is in I quickly
+
+ align:start position:0%
+taking new information is in I quickly
+ 
+
+ align:start position:0%
+taking new information is in I quickly
+switch into this offline evaluation road
+
+ align:start position:0%
+switch into this offline evaluation road
+ 
+
+ align:start position:0%
+switch into this offline evaluation road
+but during sleep I no longer have the
+
+ align:start position:0%
+but during sleep I no longer have the
+ 
+
+ align:start position:0%
+but during sleep I no longer have the
+constraint of having to direct behavior
+
+ align:start position:0%
+constraint of having to direct behavior
+ 
+
+ align:start position:0%
+constraint of having to direct behavior
+behavior shut off inputs are shut off
+
+ align:start position:0%
+behavior shut off inputs are shut off
+ 
+
+ align:start position:0%
+behavior shut off inputs are shut off
+and now I can switch into this purely
+
+ align:start position:0%
+and now I can switch into this purely
+ 
+
+ align:start position:0%
+and now I can switch into this purely
+interest but internal introspective mode
+
+ align:start position:0%
+interest but internal introspective mode
+ 
+
+ align:start position:0%
+interest but internal introspective mode
+so what goes on during sleep
+
+ align:start position:0%
+so what goes on during sleep
+ 
+
+ align:start position:0%
+so what goes on during sleep
+in the simple experiment and we'll just
+
+ align:start position:0%
+in the simple experiment and we'll just
+ 
+
+ align:start position:0%
+in the simple experiment and we'll just
+we look at the activity when the animal
+
+ align:start position:0%
+we look at the activity when the animal
+ 
+
+ align:start position:0%
+we look at the activity when the animal
+is performing behavioral tasks and then
+
+ align:start position:0%
+is performing behavioral tasks and then
+ 
+
+ align:start position:0%
+is performing behavioral tasks and then
+we examine activity during sleep both
+
+ align:start position:0%
+we examine activity during sleep both
+ 
+
+ align:start position:0%
+we examine activity during sleep both
+before and after and ask is there
+
+ align:start position:0%
+before and after and ask is there
+ 
+
+ align:start position:0%
+before and after and ask is there
+anything about behavioral experience
+
+ align:start position:0%
+anything about behavioral experience
+ 
+
+ align:start position:0%
+anything about behavioral experience
+that changes activity during sleep and
+
+ align:start position:0%
+that changes activity during sleep and
+ 
+
+ align:start position:0%
+that changes activity during sleep and
+what we found was that if you look at
+
+ align:start position:0%
+what we found was that if you look at
+ 
+
+ align:start position:0%
+what we found was that if you look at
+activity during behavior and what you
+
+ align:start position:0%
+activity during behavior and what you
+ 
+
+ align:start position:0%
+activity during behavior and what you
+think about these spatial sequences
+
+ align:start position:0%
+think about these spatial sequences
+ 
+
+ align:start position:0%
+think about these spatial sequences
+being expressed and you look during
+
+ align:start position:0%
+being expressed and you look during
+ 
+
+ align:start position:0%
+being expressed and you look during
+sleep afterward you find that the
+
+ align:start position:0%
+sleep afterward you find that the
+ 
+
+ align:start position:0%
+sleep afterward you find that the
+spatial sequences are expressed again so
+
+ align:start position:0%
+spatial sequences are expressed again so
+ 
+
+ align:start position:0%
+spatial sequences are expressed again so
+the hippocampus replays the firing of
+
+ align:start position:0%
+the hippocampus replays the firing of
+ 
+
+ align:start position:0%
+the hippocampus replays the firing of
+these cell sequences but if but it
+
+ align:start position:0%
+these cell sequences but if but it
+ 
+
+ align:start position:0%
+these cell sequences but if but it
+replays the firing of these cell
+
+ align:start position:0%
+replays the firing of these cell
+ 
+
+ align:start position:0%
+replays the firing of these cell
+sequences at a timescale that appears to
+
+ align:start position:0%
+sequences at a timescale that appears to
+ 
+
+ align:start position:0%
+sequences at a timescale that appears to
+be compressed relative to the behavioral
+
+ align:start position:0%
+be compressed relative to the behavioral
+ 
+
+ align:start position:0%
+be compressed relative to the behavioral
+timescale so these are 8 play cells
+
+ align:start position:0%
+timescale so these are 8 play cells
+ 
+
+ align:start position:0%
+timescale so these are 8 play cells
+animals were walking from left to right
+
+ align:start position:0%
+animals were walking from left to right
+ 
+
+ align:start position:0%
+animals were walking from left to right
+the ticks indicate that's the location
+
+ align:start position:0%
+the ticks indicate that's the location
+ 
+
+ align:start position:0%
+the ticks indicate that's the location
+of the peak so these play cells will
+
+ align:start position:0%
+of the peak so these play cells will
+ 
+
+ align:start position:0%
+of the peak so these play cells will
+fire 1 1 through 8 as the animal moves
+
+ align:start position:0%
+fire 1 1 through 8 as the animal moves
+ 
+
+ align:start position:0%
+fire 1 1 through 8 as the animal moves
+along the track over about 5 seconds
+
+ align:start position:0%
+along the track over about 5 seconds
+ 
+
+ align:start position:0%
+along the track over about 5 seconds
+that's how long it takes animal walk
+
+ align:start position:0%
+that's how long it takes animal walk
+ 
+
+ align:start position:0%
+that's how long it takes animal walk
+from left to right the same sequence of
+
+ align:start position:0%
+from left to right the same sequence of
+ 
+
+ align:start position:0%
+from left to right the same sequence of
+1 2 3 4 5 6 7 8
+
+ align:start position:0%
+1 2 3 4 5 6 7 8
+ 
+
+ align:start position:0%
+1 2 3 4 5 6 7 8
+gets replayed during sleep but now over
+
+ align:start position:0%
+gets replayed during sleep but now over
+ 
+
+ align:start position:0%
+gets replayed during sleep but now over
+about 150 milliseconds same sequence so
+
+ align:start position:0%
+about 150 milliseconds same sequence so
+ 
+
+ align:start position:0%
+about 150 milliseconds same sequence so
+it's you're preserving time order not
+
+ align:start position:0%
+it's you're preserving time order not
+ 
+
+ align:start position:0%
+it's you're preserving time order not
+absolute time and that when you ask when
+
+ align:start position:0%
+absolute time and that when you ask when
+ 
+
+ align:start position:0%
+absolute time and that when you ask when
+these sequences are expressed what's
+
+ align:start position:0%
+these sequences are expressed what's
+ 
+
+ align:start position:0%
+these sequences are expressed what's
+going on in the local field potential
+
+ align:start position:0%
+going on in the local field potential
+ 
+
+ align:start position:0%
+going on in the local field potential
+these oscillations and this is where you
+
+ align:start position:0%
+these oscillations and this is where you
+ 
+
+ align:start position:0%
+these oscillations and this is where you
+find these sharp wave ripple events this
+
+ align:start position:0%
+find these sharp wave ripple events this
+ 
+
+ align:start position:0%
+find these sharp wave ripple events this
+is this ripple this is this ripple like
+
+ align:start position:0%
+is this ripple this is this ripple like
+ 
+
+ align:start position:0%
+is this ripple this is this ripple like
+event that I was describing to you so
+
+ align:start position:0%
+event that I was describing to you so
+ 
+
+ align:start position:0%
+event that I was describing to you so
+these sharp wave ripples are when these
+
+ align:start position:0%
+these sharp wave ripples are when these
+ 
+
+ align:start position:0%
+these sharp wave ripples are when these
+apparently compressed sequences are
+
+ align:start position:0%
+apparently compressed sequences are
+ 
+
+ align:start position:0%
+apparently compressed sequences are
+being expressed I can point out that a
+
+ align:start position:0%
+being expressed I can point out that a
+ 
+
+ align:start position:0%
+being expressed I can point out that a
+simple model for these sharp wave ripple
+
+ align:start position:0%
+simple model for these sharp wave ripple
+ 
+
+ align:start position:0%
+simple model for these sharp wave ripple
+reactivated sequences is the same model
+
+ align:start position:0%
+reactivated sequences is the same model
+ 
+
+ align:start position:0%
+reactivated sequences is the same model
+that's used that I like to use to
+
+ align:start position:0%
+that's used that I like to use to
+ 
+
+ align:start position:0%
+that's used that I like to use to
+explain phase procession during the fête
+
+ align:start position:0%
+explain phase procession during the fête
+ 
+
+ align:start position:0%
+explain phase procession during the fête
+oscillation that is I give it an input I
+
+ align:start position:0%
+oscillation that is I give it an input I
+ 
+
+ align:start position:0%
+oscillation that is I give it an input I
+sweep inhibition from high to low such
+
+ align:start position:0%
+sweep inhibition from high to low such
+ 
+
+ align:start position:0%
+sweep inhibition from high to low such
+that cells that again the strongest
+
+ align:start position:0%
+that cells that again the strongest
+ 
+
+ align:start position:0%
+that cells that again the strongest
+input fire earlier and this will
+
+ align:start position:0%
+input fire earlier and this will
+ 
+
+ align:start position:0%
+input fire earlier and this will
+reactivate a sequence so the difference
+
+ align:start position:0%
+reactivate a sequence so the difference
+ 
+
+ align:start position:0%
+reactivate a sequence so the difference
+between a theta sequence and a
+
+ align:start position:0%
+between a theta sequence and a
+ 
+
+ align:start position:0%
+between a theta sequence and a
+reactivated sequence is really just
+
+ align:start position:0%
+reactivated sequence is really just
+ 
+
+ align:start position:0%
+reactivated sequence is really just
+where's the input coming from if the
+
+ align:start position:0%
+where's the input coming from if the
+ 
+
+ align:start position:0%
+where's the input coming from if the
+inputs coming from what I'm actually
+
+ align:start position:0%
+inputs coming from what I'm actually
+ 
+
+ align:start position:0%
+inputs coming from what I'm actually
+experiencing right now now it's a theta
+
+ align:start position:0%
+experiencing right now now it's a theta
+ 
+
+ align:start position:0%
+experiencing right now now it's a theta
+sequence
+
+ align:start position:0%
+sequence
+ 
+
+ align:start position:0%
+sequence
+and as I move the input changes
+
+ align:start position:0%
+and as I move the input changes
+ 
+
+ align:start position:0%
+and as I move the input changes
+systematically and so again it looks
+
+ align:start position:0%
+systematically and so again it looks
+ 
+
+ align:start position:0%
+systematically and so again it looks
+like it's encoding information about
+
+ align:start position:0%
+like it's encoding information about
+ 
+
+ align:start position:0%
+like it's encoding information about
+space if I'm now offline and this
+
+ align:start position:0%
+space if I'm now offline and this
+ 
+
+ align:start position:0%
+space if I'm now offline and this
+information is being delivered to the
+
+ align:start position:0%
+information is being delivered to the
+ 
+
+ align:start position:0%
+information is being delivered to the
+hippocampus from some other source you
+
+ align:start position:0%
+hippocampus from some other source you
+ 
+
+ align:start position:0%
+hippocampus from some other source you
+can apply exactly the same operation get
+
+ align:start position:0%
+can apply exactly the same operation get
+ 
+
+ align:start position:0%
+can apply exactly the same operation get
+the same kind of sequence it's just now
+
+ align:start position:0%
+the same kind of sequence it's just now
+ 
+
+ align:start position:0%
+the same kind of sequence it's just now
+it's on information that is not tied to
+
+ align:start position:0%
+it's on information that is not tied to
+ 
+
+ align:start position:0%
+it's on information that is not tied to
+be sort of your you know immediate
+
+ align:start position:0%
+be sort of your you know immediate
+ 
+
+ align:start position:0%
+be sort of your you know immediate
+context or location so that's the only
+
+ align:start position:0%
+context or location so that's the only
+ 
+
+ align:start position:0%
+context or location so that's the only
+difference
+
+ align:start position:0%
+difference
+ 
+
+ align:start position:0%
+difference
+where is the input coming from now
+
+ align:start position:0%
+where is the input coming from now
+ 
+
+ align:start position:0%
+where is the input coming from now
+further if you think about this model
+
+ align:start position:0%
+further if you think about this model
+ 
+
+ align:start position:0%
+further if you think about this model
+you can imagine well thats of the depth
+
+ align:start position:0%
+you can imagine well thats of the depth
+ 
+
+ align:start position:0%
+you can imagine well thats of the depth
+of disinhibition could actually affect
+
+ align:start position:0%
+of disinhibition could actually affect
+ 
+
+ align:start position:0%
+of disinhibition could actually affect
+the length of the sequence but that's
+
+ align:start position:0%
+the length of the sequence but that's
+ 
+
+ align:start position:0%
+the length of the sequence but that's
+just sort of a mechanistic thing and if
+
+ align:start position:0%
+just sort of a mechanistic thing and if
+ 
+
+ align:start position:0%
+just sort of a mechanistic thing and if
+you actually look at the mechanisms that
+
+ align:start position:0%
+you actually look at the mechanisms that
+ 
+
+ align:start position:0%
+you actually look at the mechanisms that
+regulate sharp wave ripples in the theta
+
+ align:start position:0%
+regulate sharp wave ripples in the theta
+ 
+
+ align:start position:0%
+regulate sharp wave ripples in the theta
+oscillation it s it basically comes from
+
+ align:start position:0%
+oscillation it s it basically comes from
+ 
+
+ align:start position:0%
+oscillation it s it basically comes from
+the same structure it's a structure that
+
+ align:start position:0%
+the same structure it's a structure that
+ 
+
+ align:start position:0%
+the same structure it's a structure that
+regulates acetylcholine and that's a
+
+ align:start position:0%
+regulates acetylcholine and that's a
+ 
+
+ align:start position:0%
+regulates acetylcholine and that's a
+it's a neuromodulator that's associated
+
+ align:start position:0%
+it's a neuromodulator that's associated
+ 
+
+ align:start position:0%
+it's a neuromodulator that's associated
+with attention in memory and the
+
+ align:start position:0%
+with attention in memory and the
+ 
+
+ align:start position:0%
+with attention in memory and the
+structure called the medial septum so
+
+ align:start position:0%
+structure called the medial septum so
+ 
+
+ align:start position:0%
+structure called the medial septum so
+the medial septum provides the drive the
+
+ align:start position:0%
+the medial septum provides the drive the
+ 
+
+ align:start position:0%
+the medial septum provides the drive the
+cholinergic drive of the hippocampus
+
+ align:start position:0%
+cholinergic drive of the hippocampus
+ 
+
+ align:start position:0%
+cholinergic drive of the hippocampus
+damage the medial septum loss of
+
+ align:start position:0%
+damage the medial septum loss of
+ 
+
+ align:start position:0%
+damage the medial septum loss of
+cholinergic tone was one of the dominant
+
+ align:start position:0%
+cholinergic tone was one of the dominant
+ 
+
+ align:start position:0%
+cholinergic tone was one of the dominant
+models of nerd nerd degenerative
+
+ align:start position:0%
+models of nerd nerd degenerative
+ 
+
+ align:start position:0%
+models of nerd nerd degenerative
+cognitive and memory loss in Alzheimer's
+
+ align:start position:0%
+cognitive and memory loss in Alzheimer's
+ 
+
+ align:start position:0%
+cognitive and memory loss in Alzheimer's
+disease so what you find is one of the
+
+ align:start position:0%
+disease so what you find is one of the
+ 
+
+ align:start position:0%
+disease so what you find is one of the
+earliest indications of
+
+ align:start position:0%
+earliest indications of
+ 
+
+ align:start position:0%
+earliest indications of
+neurodegenerative damage in Alzheimer's
+
+ align:start position:0%
+neurodegenerative damage in Alzheimer's
+ 
+
+ align:start position:0%
+neurodegenerative damage in Alzheimer's
+is the loss of cholinergic tone and the
+
+ align:start position:0%
+is the loss of cholinergic tone and the
+ 
+
+ align:start position:0%
+is the loss of cholinergic tone and the
+systems that begin to break down are the
+
+ align:start position:0%
+systems that begin to break down are the
+ 
+
+ align:start position:0%
+systems that begin to break down are the
+systems that actually fall along this
+
+ align:start position:0%
+systems that actually fall along this
+ 
+
+ align:start position:0%
+systems that actually fall along this
+limbic pathway starting with hippocampus
+
+ align:start position:0%
+limbic pathway starting with hippocampus
+ 
+
+ align:start position:0%
+limbic pathway starting with hippocampus
+central cortex so as though the
+
+ align:start position:0%
+central cortex so as though the
+ 
+
+ align:start position:0%
+central cortex so as though the
+cholinergic system that regulates the
+
+ align:start position:0%
+cholinergic system that regulates the
+ 
+
+ align:start position:0%
+cholinergic system that regulates the
+expression of this oscillation in the
+
+ align:start position:0%
+expression of this oscillation in the
+ 
+
+ align:start position:0%
+expression of this oscillation in the
+hippocampus when it breaks down it leads
+
+ align:start position:0%
+hippocampus when it breaks down it leads
+ 
+
+ align:start position:0%
+hippocampus when it breaks down it leads
+to general memory loss in you know
+
+ align:start position:0%
+to general memory loss in you know
+ 
+
+ align:start position:0%
+to general memory loss in you know
+disruption and turns out the medial
+
+ align:start position:0%
+disruption and turns out the medial
+ 
+
+ align:start position:0%
+disruption and turns out the medial
+septum is also involved in regulating
+
+ align:start position:0%
+septum is also involved in regulating
+ 
+
+ align:start position:0%
+septum is also involved in regulating
+the expression of these sharp wave
+
+ align:start position:0%
+the expression of these sharp wave
+ 
+
+ align:start position:0%
+the expression of these sharp wave
+ripples so same system different modes
+
+ align:start position:0%
+ripples so same system different modes
+ 
+
+ align:start position:0%
+ripples so same system different modes
+one you know quiet one sort of active
+
+ align:start position:0%
+one you know quiet one sort of active
+ 
+
+ align:start position:0%
+one you know quiet one sort of active
+online when inactive
+
+ align:start position:0%
+online when inactive
+ 
+
+ align:start position:0%
+online when inactive
+offline same kind of modulation of
+
+ align:start position:0%
+offline same kind of modulation of
+ 
+
+ align:start position:0%
+offline same kind of modulation of
+excitability through an addition but
+
+ align:start position:0%
+excitability through an addition but
+ 
+
+ align:start position:0%
+excitability through an addition but
+that's the idea simple model sweep
+
+ align:start position:0%
+that's the idea simple model sweep
+ 
+
+ align:start position:0%
+that's the idea simple model sweep
+inhibition that gives you the sequences
+
+ align:start position:0%
+inhibition that gives you the sequences
+ 
+
+ align:start position:0%
+inhibition that gives you the sequences
+and then control the input you control
+
+ align:start position:0%
+and then control the input you control
+ 
+
+ align:start position:0%
+and then control the input you control
+the input to control the content you
+
+ align:start position:0%
+the input to control the content you
+ 
+
+ align:start position:0%
+the input to control the content you
+control the inhibition to control the
+
+ align:start position:0%
+control the inhibition to control the
+ 
+
+ align:start position:0%
+control the inhibition to control the
+structure of the timing those are the
+
+ align:start position:0%
+structure of the timing those are the
+ 
+
+ align:start position:0%
+structure of the timing those are the
+two things so the question is how could
+
+ align:start position:0%
+two things so the question is how could
+ 
+
+ align:start position:0%
+two things so the question is how could
+you control the input when we kind of
+
+ align:start position:0%
+you control the input when we kind of
+ 
+
+ align:start position:0%
+you control the input when we kind of
+thinking about what is the input into
+
+ align:start position:0%
+thinking about what is the input into
+ 
+
+ align:start position:0%
+thinking about what is the input into
+the hippocampus under these two
+
+ align:start position:0%
+the hippocampus under these two
+ 
+
+ align:start position:0%
+the hippocampus under these two
+conditions and as I mentioned
+
+ align:start position:0%
+conditions and as I mentioned
+ 
+
+ align:start position:0%
+conditions and as I mentioned
+hippocampus
+
+ align:start position:0%
+hippocampus
+ 
+
+ align:start position:0%
+hippocampus
+you've got the internal cortex Central
+
+ align:start position:0%
+you've got the internal cortex Central
+ 
+
+ align:start position:0%
+you've got the internal cortex Central
+cortex gets information across the brain
+
+ align:start position:0%
+cortex gets information across the brain
+ 
+
+ align:start position:0%
+cortex gets information across the brain
+is sort of the sensory Association our
+
+ align:start position:0%
+is sort of the sensory Association our
+ 
+
+ align:start position:0%
+is sort of the sensory Association our
+visual cortex auditory for this there
+
+ align:start position:0%
+visual cortex auditory for this there
+ 
+
+ align:start position:0%
+visual cortex auditory for this there
+all this information about the world
+
+ align:start position:0%
+all this information about the world
+ 
+
+ align:start position:0%
+all this information about the world
+converging on the hippocampus and then
+
+ align:start position:0%
+converging on the hippocampus and then
+ 
+
+ align:start position:0%
+converging on the hippocampus and then
+getting modulated and so you can think
+
+ align:start position:0%
+getting modulated and so you can think
+ 
+
+ align:start position:0%
+getting modulated and so you can think
+about let's look in for instance visual
+
+ align:start position:0%
+about let's look in for instance visual
+ 
+
+ align:start position:0%
+about let's look in for instance visual
+cortex so if we simultaneous recording
+
+ align:start position:0%
+cortex so if we simultaneous recording
+ 
+
+ align:start position:0%
+cortex so if we simultaneous recording
+video cortex and hippocampus we could
+
+ align:start position:0%
+video cortex and hippocampus we could
+ 
+
+ align:start position:0%
+video cortex and hippocampus we could
+see how these two structures communicate
+
+ align:start position:0%
+see how these two structures communicate
+ 
+
+ align:start position:0%
+see how these two structures communicate
+and when we do this in a simple task is
+
+ align:start position:0%
+and when we do this in a simple task is
+ 
+
+ align:start position:0%
+and when we do this in a simple task is
+like little figure eight tasks and I
+
+ align:start position:0%
+like little figure eight tasks and I
+ 
+
+ align:start position:0%
+like little figure eight tasks and I
+won't go into a lot of the details but
+
+ align:start position:0%
+won't go into a lot of the details but
+ 
+
+ align:start position:0%
+won't go into a lot of the details but
+one interesting thing that came out from
+
+ align:start position:0%
+one interesting thing that came out from
+ 
+
+ align:start position:0%
+one interesting thing that came out from
+doing this experiment recording visual
+
+ align:start position:0%
+doing this experiment recording visual
+ 
+
+ align:start position:0%
+doing this experiment recording visual
+cortex and hippocampus is that recording
+
+ align:start position:0%
+cortex and hippocampus is that recording
+ 
+
+ align:start position:0%
+cortex and hippocampus is that recording
+in the visual cortex when an animal is
+
+ align:start position:0%
+in the visual cortex when an animal is
+ 
+
+ align:start position:0%
+in the visual cortex when an animal is
+moving in space what you find is cells
+
+ align:start position:0%
+moving in space what you find is cells
+ 
+
+ align:start position:0%
+moving in space what you find is cells
+and the visual cortex have spatial like
+
+ align:start position:0%
+and the visual cortex have spatial like
+ 
+
+ align:start position:0%
+and the visual cortex have spatial like
+receptive fields similar to the
+
+ align:start position:0%
+receptive fields similar to the
+ 
+
+ align:start position:0%
+receptive fields similar to the
+hippocampus they're not a spatially
+
+ align:start position:0%
+hippocampus they're not a spatially
+ 
+
+ align:start position:0%
+hippocampus they're not a spatially
+tuned but here for instance r88 visual
+
+ align:start position:0%
+tuned but here for instance r88 visual
+ 
+
+ align:start position:0%
+tuned but here for instance r88 visual
+cortical cells and you can see that they
+
+ align:start position:0%
+cortical cells and you can see that they
+ 
+
+ align:start position:0%
+cortical cells and you can see that they
+fire they fire in a sequence they'll
+
+ align:start position:0%
+fire they fire in a sequence they'll
+ 
+
+ align:start position:0%
+fire they fire in a sequence they'll
+have different spatial receptive fields
+
+ align:start position:0%
+have different spatial receptive fields
+ 
+
+ align:start position:0%
+have different spatial receptive fields
+this shows where the where this one
+
+ align:start position:0%
+this shows where the where this one
+ 
+
+ align:start position:0%
+this shows where the where this one
+visual cortical cell likes to fire
+
+ align:start position:0%
+visual cortical cell likes to fire
+ 
+
+ align:start position:0%
+visual cortical cell likes to fire
+different visual cortical cells will
+
+ align:start position:0%
+different visual cortical cells will
+ 
+
+ align:start position:0%
+different visual cortical cells will
+fire at different locations so you when
+
+ align:start position:0%
+fire at different locations so you when
+ 
+
+ align:start position:0%
+fire at different locations so you when
+animals are moving in space you actually
+
+ align:start position:0%
+animals are moving in space you actually
+ 
+
+ align:start position:0%
+animals are moving in space you actually
+see sequential activation of these
+
+ align:start position:0%
+see sequential activation of these
+ 
+
+ align:start position:0%
+see sequential activation of these
+visual cortical responses and so if you
+
+ align:start position:0%
+visual cortical responses and so if you
+ 
+
+ align:start position:0%
+visual cortical responses and so if you
+have visual sequences visual perceptual
+
+ align:start position:0%
+have visual sequences visual perceptual
+ 
+
+ align:start position:0%
+have visual sequences visual perceptual
+sequences in hippocampal spatial
+
+ align:start position:0%
+sequences in hippocampal spatial
+ 
+
+ align:start position:0%
+sequences in hippocampal spatial
+sequences one question is how do those
+
+ align:start position:0%
+sequences one question is how do those
+ 
+
+ align:start position:0%
+sequences one question is how do those
+sequences how do those sequences relate
+
+ align:start position:0%
+sequences how do those sequences relate
+ 
+
+ align:start position:0%
+sequences how do those sequences relate
+offline when they annal for instance
+
+ align:start position:0%
+offline when they annal for instance
+ 
+
+ align:start position:0%
+offline when they annal for instance
+during sleep so you have sequences
+
+ align:start position:0%
+during sleep so you have sequences
+ 
+
+ align:start position:0%
+during sleep so you have sequences
+during sleep and the hippocampus
+
+ align:start position:0%
+during sleep and the hippocampus
+ 
+
+ align:start position:0%
+during sleep and the hippocampus
+sequence is varying sleep in the visual
+
+ align:start position:0%
+sequence is varying sleep in the visual
+ 
+
+ align:start position:0%
+sequence is varying sleep in the visual
+cortex and it turns out that those two
+
+ align:start position:0%
+cortex and it turns out that those two
+ 
+
+ align:start position:0%
+cortex and it turns out that those two
+things are actually they're correlated
+
+ align:start position:0%
+things are actually they're correlated
+ 
+
+ align:start position:0%
+things are actually they're correlated
+so in hippocampus
+
+ align:start position:0%
+so in hippocampus
+ 
+
+ align:start position:0%
+so in hippocampus
+plays out a spatial sequence the visual
+
+ align:start position:0%
+plays out a spatial sequence the visual
+ 
+
+ align:start position:0%
+plays out a spatial sequence the visual
+cortex plays out a visual sequence that
+
+ align:start position:0%
+cortex plays out a visual sequence that
+ 
+
+ align:start position:0%
+cortex plays out a visual sequence that
+corresponds to the visual responses at
+
+ align:start position:0%
+corresponds to the visual responses at
+ 
+
+ align:start position:0%
+corresponds to the visual responses at
+those locations so hippocampus plays out
+
+ align:start position:0%
+those locations so hippocampus plays out
+ 
+
+ align:start position:0%
+those locations so hippocampus plays out
+sequence of where it was visual cortex
+
+ align:start position:0%
+sequence of where it was visual cortex
+ 
+
+ align:start position:0%
+sequence of where it was visual cortex
+expresses the visual visual stimuli that
+
+ align:start position:0%
+expresses the visual visual stimuli that
+ 
+
+ align:start position:0%
+expresses the visual visual stimuli that
+were present along that sequence one
+
+ align:start position:0%
+were present along that sequence one
+ 
+
+ align:start position:0%
+were present along that sequence one
+thing about these sequences when we're
+
+ align:start position:0%
+thing about these sequences when we're
+ 
+
+ align:start position:0%
+thing about these sequences when we're
+looking when we were looking at
+
+ align:start position:0%
+looking when we were looking at
+ 
+
+ align:start position:0%
+looking when we were looking at
+hippocampal neocortical interactions is
+
+ align:start position:0%
+hippocampal neocortical interactions is
+ 
+
+ align:start position:0%
+hippocampal neocortical interactions is
+that the sequences are now at a much
+
+ align:start position:0%
+that the sequences are now at a much
+ 
+
+ align:start position:0%
+that the sequences are now at a much
+longer time scale and in fact this time
+
+ align:start position:0%
+longer time scale and in fact this time
+ 
+
+ align:start position:0%
+longer time scale and in fact this time
+scale which here is about on the order
+
+ align:start position:0%
+scale which here is about on the order
+ 
+
+ align:start position:0%
+scale which here is about on the order
+of about half a second to a second
+
+ align:start position:0%
+of about half a second to a second
+ 
+
+ align:start position:0%
+of about half a second to a second
+corresponds to another oscillation that
+
+ align:start position:0%
+corresponds to another oscillation that
+ 
+
+ align:start position:0%
+corresponds to another oscillation that
+is characteristic of sleep known as the
+
+ align:start position:0%
+is characteristic of sleep known as the
+ 
+
+ align:start position:0%
+is characteristic of sleep known as the
+slow oscillation so when you go to sleep
+
+ align:start position:0%
+slow oscillation so when you go to sleep
+ 
+
+ align:start position:0%
+slow oscillation so when you go to sleep
+brain rhythm the oscillations the
+
+ align:start position:0%
+brain rhythm the oscillations the
+ 
+
+ align:start position:0%
+brain rhythm the oscillations the
+dominant frequency start to slow down
+
+ align:start position:0%
+dominant frequency start to slow down
+ 
+
+ align:start position:0%
+dominant frequency start to slow down
+and you'll get this oscillation in this
+
+ align:start position:0%
+and you'll get this oscillation in this
+ 
+
+ align:start position:0%
+and you'll get this oscillation in this
+one Hertz or so frequency range that
+
+ align:start position:0%
+one Hertz or so frequency range that
+ 
+
+ align:start position:0%
+one Hertz or so frequency range that
+looks like if you record activity from a
+
+ align:start position:0%
+looks like if you record activity from a
+ 
+
+ align:start position:0%
+looks like if you record activity from a
+bunch of cells it looks like this this
+
+ align:start position:0%
+bunch of cells it looks like this this
+ 
+
+ align:start position:0%
+bunch of cells it looks like this this
+is the activity of a whole bunch of
+
+ align:start position:0%
+is the activity of a whole bunch of
+ 
+
+ align:start position:0%
+is the activity of a whole bunch of
+cells in the visual cortex in the
+
+ align:start position:0%
+cells in the visual cortex in the
+ 
+
+ align:start position:0%
+cells in the visual cortex in the
+hippocampus and you see that the
+
+ align:start position:0%
+hippocampus and you see that the
+ 
+
+ align:start position:0%
+hippocampus and you see that the
+activity is flipping between lots of
+
+ align:start position:0%
+activity is flipping between lots of
+ 
+
+ align:start position:0%
+activity is flipping between lots of
+cells active no cells active these are
+
+ align:start position:0%
+cells active no cells active these are
+ 
+
+ align:start position:0%
+cells active no cells active these are
+the so-called up-and-down states of
+
+ align:start position:0%
+the so-called up-and-down states of
+ 
+
+ align:start position:0%
+the so-called up-and-down states of
+cells during sleep that every half a
+
+ align:start position:0%
+cells during sleep that every half a
+ 
+
+ align:start position:0%
+cells during sleep that every half a
+second to a second or so many cells will
+
+ align:start position:0%
+second to a second or so many cells will
+ 
+
+ align:start position:0%
+second to a second or so many cells will
+become active then they'll all be shut
+
+ align:start position:0%
+become active then they'll all be shut
+ 
+
+ align:start position:0%
+become active then they'll all be shut
+off they'll become active again so
+
+ align:start position:0%
+off they'll become active again so
+ 
+
+ align:start position:0%
+off they'll become active again so
+you're flipping between is up and down
+
+ align:start position:0%
+you're flipping between is up and down
+ 
+
+ align:start position:0%
+you're flipping between is up and down
+like States and if you look at these up
+
+ align:start position:0%
+like States and if you look at these up
+ 
+
+ align:start position:0%
+like States and if you look at these up
+and down states in the visual cortex and
+
+ align:start position:0%
+and down states in the visual cortex and
+ 
+
+ align:start position:0%
+and down states in the visual cortex and
+you look at similar activity in the
+
+ align:start position:0%
+you look at similar activity in the
+ 
+
+ align:start position:0%
+you look at similar activity in the
+hippocampus you see these up and down
+
+ align:start position:0%
+hippocampus you see these up and down
+ 
+
+ align:start position:0%
+hippocampus you see these up and down
+like states in the hippocampus as well
+
+ align:start position:0%
+like states in the hippocampus as well
+ 
+
+ align:start position:0%
+like states in the hippocampus as well
+but you'll notice that the up state in
+
+ align:start position:0%
+but you'll notice that the up state in
+ 
+
+ align:start position:0%
+but you'll notice that the up state in
+the neocortex leads up state in the
+
+ align:start position:0%
+the neocortex leads up state in the
+ 
+
+ align:start position:0%
+the neocortex leads up state in the
+hippocampus so a neocortex first then
+
+ align:start position:0%
+hippocampus so a neocortex first then
+ 
+
+ align:start position:0%
+hippocampus so a neocortex first then
+hippocampus in your cortex tippecanoe
+
+ align:start position:0%
+hippocampus in your cortex tippecanoe
+ 
+
+ align:start position:0%
+hippocampus in your cortex tippecanoe
+clue neocortex seems to lead so again
+
+ align:start position:0%
+clue neocortex seems to lead so again
+ 
+
+ align:start position:0%
+clue neocortex seems to lead so again
+this question of who is providing the
+
+ align:start position:0%
+this question of who is providing the
+ 
+
+ align:start position:0%
+this question of who is providing the
+input you know that simple model or I'm
+
+ align:start position:0%
+input you know that simple model or I'm
+ 
+
+ align:start position:0%
+input you know that simple model or I'm
+sweeping inhibition during during the
+
+ align:start position:0%
+sweeping inhibition during during the
+ 
+
+ align:start position:0%
+sweeping inhibition during during the
+theta during active behavior that
+
+ align:start position:0%
+theta during active behavior that
+ 
+
+ align:start position:0%
+theta during active behavior that
+information is coming in from
+
+ align:start position:0%
+information is coming in from
+ 
+
+ align:start position:0%
+information is coming in from
+perceptions what I'm actually during
+
+ align:start position:0%
+perceptions what I'm actually during
+ 
+
+ align:start position:0%
+perceptions what I'm actually during
+sleep crisis where is that information
+
+ align:start position:0%
+sleep crisis where is that information
+ 
+
+ align:start position:0%
+sleep crisis where is that information
+coming from well this would say this is
+
+ align:start position:0%
+coming from well this would say this is
+ 
+
+ align:start position:0%
+coming from well this would say this is
+where it's coming from it's coming from
+
+ align:start position:0%
+where it's coming from it's coming from
+ 
+
+ align:start position:0%
+where it's coming from it's coming from
+these cortical areas let's say sensory
+
+ align:start position:0%
+these cortical areas let's say sensory
+ 
+
+ align:start position:0%
+these cortical areas let's say sensory
+visual cortical areas turn on they
+
+ align:start position:0%
+visual cortical areas turn on they
+ 
+
+ align:start position:0%
+visual cortical areas turn on they
+provide the information that the campus
+
+ align:start position:0%
+provide the information that the campus
+ 
+
+ align:start position:0%
+provide the information that the campus
+now the hippocampus turns on
+
+ align:start position:0%
+now the hippocampus turns on
+ 
+
+ align:start position:0%
+now the hippocampus turns on
+the campus responding to input coming in
+
+ align:start position:0%
+the campus responding to input coming in
+ 
+
+ align:start position:0%
+the campus responding to input coming in
+from sensory cortex if that's the case
+
+ align:start position:0%
+from sensory cortex if that's the case
+ 
+
+ align:start position:0%
+from sensory cortex if that's the case
+could we manipulate hippocampal activity
+
+ align:start position:0%
+could we manipulate hippocampal activity
+ 
+
+ align:start position:0%
+could we manipulate hippocampal activity
+by manipulating sensory cortex so this
+
+ align:start position:0%
+by manipulating sensory cortex so this
+ 
+
+ align:start position:0%
+by manipulating sensory cortex so this
+experiment simple experiment answer was
+
+ align:start position:0%
+experiment simple experiment answer was
+ 
+
+ align:start position:0%
+experiment simple experiment answer was
+yes need in this case we used the
+
+ align:start position:0%
+yes need in this case we used the
+ 
+
+ align:start position:0%
+yes need in this case we used the
+auditory system one of the reason for
+
+ align:start position:0%
+auditory system one of the reason for
+ 
+
+ align:start position:0%
+auditory system one of the reason for
+use the auditory system is unlike the
+
+ align:start position:0%
+use the auditory system is unlike the
+ 
+
+ align:start position:0%
+use the auditory system is unlike the
+visual system auditory system remains in
+
+ align:start position:0%
+visual system auditory system remains in
+ 
+
+ align:start position:0%
+visual system auditory system remains in
+a state of persistent and vigilance even
+
+ align:start position:0%
+a state of persistent and vigilance even
+ 
+
+ align:start position:0%
+a state of persistent and vigilance even
+during sleep auditory cortical responses
+
+ align:start position:0%
+during sleep auditory cortical responses
+ 
+
+ align:start position:0%
+during sleep auditory cortical responses
+even animal goes to sleep measure to
+
+ align:start position:0%
+even animal goes to sleep measure to
+ 
+
+ align:start position:0%
+even animal goes to sleep measure to
+measure auditory cortical response the
+
+ align:start position:0%
+measure auditory cortical response the
+ 
+
+ align:start position:0%
+measure auditory cortical response the
+same as when it's awake so essentially
+
+ align:start position:0%
+same as when it's awake so essentially
+ 
+
+ align:start position:0%
+same as when it's awake so essentially
+the auditory cortex stays vigilant
+
+ align:start position:0%
+the auditory cortex stays vigilant
+ 
+
+ align:start position:0%
+the auditory cortex stays vigilant
+during sleep which has clear
+
+ align:start position:0%
+during sleep which has clear
+ 
+
+ align:start position:0%
+during sleep which has clear
+evolutionary value so sleep you know
+
+ align:start position:0%
+evolutionary value so sleep you know
+ 
+
+ align:start position:0%
+evolutionary value so sleep you know
+it's trying to minimise arousal by you
+
+ align:start position:0%
+it's trying to minimise arousal by you
+ 
+
+ align:start position:0%
+it's trying to minimise arousal by you
+know sort of shutting off a visual input
+
+ align:start position:0%
+know sort of shutting off a visual input
+ 
+
+ align:start position:0%
+know sort of shutting off a visual input
+which may be of limited value anyway
+
+ align:start position:0%
+which may be of limited value anyway
+ 
+
+ align:start position:0%
+which may be of limited value anyway
+given you know of sort of the circadian
+
+ align:start position:0%
+given you know of sort of the circadian
+ 
+
+ align:start position:0%
+given you know of sort of the circadian
+nocturnal nature of you know of sort of
+
+ align:start position:0%
+nocturnal nature of you know of sort of
+ 
+
+ align:start position:0%
+nocturnal nature of you know of sort of
+visual stimuli so you can't see anything
+
+ align:start position:0%
+visual stimuli so you can't see anything
+ 
+
+ align:start position:0%
+visual stimuli so you can't see anything
+might as well actually close your eyes
+
+ align:start position:0%
+might as well actually close your eyes
+ 
+
+ align:start position:0%
+might as well actually close your eyes
+but you can still hear things
+
+ align:start position:0%
+but you can still hear things
+ 
+
+ align:start position:0%
+but you can still hear things
+so you and other animals are still
+
+ align:start position:0%
+so you and other animals are still
+ 
+
+ align:start position:0%
+so you and other animals are still
+listening if you hear you know pickup
+
+ align:start position:0%
+listening if you hear you know pickup
+ 
+
+ align:start position:0%
+listening if you hear you know pickup
+threats that might require that they
+
+ align:start position:0%
+threats that might require that they
+ 
+
+ align:start position:0%
+threats that might require that they
+actually work up so anyway taking
+
+ align:start position:0%
+actually work up so anyway taking
+ 
+
+ align:start position:0%
+actually work up so anyway taking
+advantage of that auditory system on so
+
+ align:start position:0%
+advantage of that auditory system on so
+ 
+
+ align:start position:0%
+advantage of that auditory system on so
+training animal on task where it learns
+
+ align:start position:0%
+training animal on task where it learns
+ 
+
+ align:start position:0%
+training animal on task where it learns
+to associate auditory cues with
+
+ align:start position:0%
+to associate auditory cues with
+ 
+
+ align:start position:0%
+to associate auditory cues with
+locations one sound right sound means go
+
+ align:start position:0%
+locations one sound right sound means go
+ 
+
+ align:start position:0%
+locations one sound right sound means go
+over here to get food left sound means
+
+ align:start position:0%
+over here to get food left sound means
+ 
+
+ align:start position:0%
+over here to get food left sound means
+go over there to get food very simple
+
+ align:start position:0%
+go over there to get food very simple
+ 
+
+ align:start position:0%
+go over there to get food very simple
+task then animal goes to sleep and you
+
+ align:start position:0%
+task then animal goes to sleep and you
+ 
+
+ align:start position:0%
+task then animal goes to sleep and you
+just continue to play the sounds so it's
+
+ align:start position:0%
+just continue to play the sounds so it's
+ 
+
+ align:start position:0%
+just continue to play the sounds so it's
+learned something and now you try to
+
+ align:start position:0%
+learned something and now you try to
+ 
+
+ align:start position:0%
+learned something and now you try to
+bias cortical activity during sleep and
+
+ align:start position:0%
+bias cortical activity during sleep and
+ 
+
+ align:start position:0%
+bias cortical activity during sleep and
+ask what does that do so this is the
+
+ align:start position:0%
+ask what does that do so this is the
+ 
+
+ align:start position:0%
+ask what does that do so this is the
+idea when the animal is actually running
+
+ align:start position:0%
+idea when the animal is actually running
+ 
+
+ align:start position:0%
+idea when the animal is actually running
+we can decode hippocampal activity so we
+
+ align:start position:0%
+we can decode hippocampal activity so we
+ 
+
+ align:start position:0%
+we can decode hippocampal activity so we
+can tell oh here's a hippocampal pattern
+
+ align:start position:0%
+can tell oh here's a hippocampal pattern
+ 
+
+ align:start position:0%
+can tell oh here's a hippocampal pattern
+that corresponds to the left side or the
+
+ align:start position:0%
+that corresponds to the left side or the
+ 
+
+ align:start position:0%
+that corresponds to the left side or the
+right side and in this case when the
+
+ align:start position:0%
+right side and in this case when the
+ 
+
+ align:start position:0%
+right side and in this case when the
+animal is performing the task play the
+
+ align:start position:0%
+animal is performing the task play the
+ 
+
+ align:start position:0%
+animal is performing the task play the
+right hand sound animal goes to the
+
+ align:start position:0%
+right hand sound animal goes to the
+ 
+
+ align:start position:0%
+right hand sound animal goes to the
+right hand side see this in the
+
+ align:start position:0%
+right hand side see this in the
+ 
+
+ align:start position:0%
+right hand side see this in the
+hippocampal response play left hand
+
+ align:start position:0%
+hippocampal response play left hand
+ 
+
+ align:start position:0%
+hippocampal response play left hand
+sound and I'll go to the left hand side
+
+ align:start position:0%
+sound and I'll go to the left hand side
+ 
+
+ align:start position:0%
+sound and I'll go to the left hand side
+again left hand plays fields and they
+
+ align:start position:0%
+again left hand plays fields and they
+ 
+
+ align:start position:0%
+again left hand plays fields and they
+don't was on the left right hand plays
+
+ align:start position:0%
+don't was on the left right hand plays
+ 
+
+ align:start position:0%
+don't was on the left right hand plays
+fields on it so this is this is what the
+
+ align:start position:0%
+fields on it so this is this is what the
+ 
+
+ align:start position:0%
+fields on it so this is this is what the
+experiment and the behavior looks like
+
+ align:start position:0%
+experiment and the behavior looks like
+ 
+
+ align:start position:0%
+experiment and the behavior looks like
+from the standpoint of the hippocampus
+
+ align:start position:0%
+from the standpoint of the hippocampus
+ 
+
+ align:start position:0%
+from the standpoint of the hippocampus
+very clear right right right sound right
+
+ align:start position:0%
+very clear right right right sound right
+ 
+
+ align:start position:0%
+very clear right right right sound right
+hippocampus right play cells left sound
+
+ align:start position:0%
+hippocampus right play cells left sound
+ 
+
+ align:start position:0%
+hippocampus right play cells left sound
+left play cells but now the animals
+
+ align:start position:0%
+left play cells but now the animals
+ 
+
+ align:start position:0%
+left play cells but now the animals
+going to go to sleep
+
+ align:start position:0%
+going to go to sleep
+ 
+
+ align:start position:0%
+going to go to sleep
+and we're gonna do the same thing
+
+ align:start position:0%
+and we're gonna do the same thing
+ 
+
+ align:start position:0%
+and we're gonna do the same thing
+continue to play the right sounds and
+
+ align:start position:0%
+continue to play the right sounds and
+ 
+
+ align:start position:0%
+continue to play the right sounds and
+the left sounds it's just that now the
+
+ align:start position:0%
+the left sounds it's just that now the
+ 
+
+ align:start position:0%
+the left sounds it's just that now the
+animal is not actually moving on the
+
+ align:start position:0%
+animal is not actually moving on the
+ 
+
+ align:start position:0%
+animal is not actually moving on the
+track and so we ask does that
+
+ align:start position:0%
+track and so we ask does that
+ 
+
+ align:start position:0%
+track and so we ask does that
+can we buy us the reactivated sequences
+
+ align:start position:0%
+can we buy us the reactivated sequences
+ 
+
+ align:start position:0%
+can we buy us the reactivated sequences
+that you get so there's the same thing
+
+ align:start position:0%
+that you get so there's the same thing
+ 
+
+ align:start position:0%
+that you get so there's the same thing
+now animals awake but now it's going to
+
+ align:start position:0%
+now animals awake but now it's going to
+ 
+
+ align:start position:0%
+now animals awake but now it's going to
+go to sleep and we just keep playing the
+
+ align:start position:0%
+go to sleep and we just keep playing the
+ 
+
+ align:start position:0%
+go to sleep and we just keep playing the
+sounds a little ticks there indicate the
+
+ align:start position:0%
+sounds a little ticks there indicate the
+ 
+
+ align:start position:0%
+sounds a little ticks there indicate the
+delivery of sounds every 10 seconds or
+
+ align:start position:0%
+delivery of sounds every 10 seconds or
+ 
+
+ align:start position:0%
+delivery of sounds every 10 seconds or
+so so we play a sound and now we look at
+
+ align:start position:0%
+so so we play a sound and now we look at
+ 
+
+ align:start position:0%
+so so we play a sound and now we look at
+the response the difference here is that
+
+ align:start position:0%
+the response the difference here is that
+ 
+
+ align:start position:0%
+the response the difference here is that
+animals not it's not running it's not
+
+ align:start position:0%
+animals not it's not running it's not
+ 
+
+ align:start position:0%
+animals not it's not running it's not
+behaving sound response now will decode
+
+ align:start position:0%
+behaving sound response now will decode
+ 
+
+ align:start position:0%
+behaving sound response now will decode
+the activity so here for instance we
+
+ align:start position:0%
+the activity so here for instance we
+ 
+
+ align:start position:0%
+the activity so here for instance we
+take a little short window here about
+
+ align:start position:0%
+take a little short window here about
+ 
+
+ align:start position:0%
+take a little short window here about
+half a second and what you see is this
+
+ align:start position:0%
+half a second and what you see is this
+ 
+
+ align:start position:0%
+half a second and what you see is this
+is this up like state multi-unit
+
+ align:start position:0%
+is this up like state multi-unit
+ 
+
+ align:start position:0%
+is this up like state multi-unit
+activity lots of cells firing decode
+
+ align:start position:0%
+activity lots of cells firing decode
+ 
+
+ align:start position:0%
+activity lots of cells firing decode
+activity and ask when you play the left
+
+ align:start position:0%
+activity and ask when you play the left
+ 
+
+ align:start position:0%
+activity and ask when you play the left
+sound
+
+ align:start position:0%
+sound
+ 
+
+ align:start position:0%
+sound
+what does activity decode to and here
+
+ align:start position:0%
+what does activity decode to and here
+ 
+
+ align:start position:0%
+what does activity decode to and here
+you see okay it's gonna decode into the
+
+ align:start position:0%
+you see okay it's gonna decode into the
+ 
+
+ align:start position:0%
+you see okay it's gonna decode into the
+left hand side so that's the basic basic
+
+ align:start position:0%
+left hand side so that's the basic basic
+ 
+
+ align:start position:0%
+left hand side so that's the basic basic
+hypothesis play left sound you get the
+
+ align:start position:0%
+hypothesis play left sound you get the
+ 
+
+ align:start position:0%
+hypothesis play left sound you get the
+replay of the left side of the of the
+
+ align:start position:0%
+replay of the left side of the of the
+ 
+
+ align:start position:0%
+replay of the left side of the of the
+track you play the right side you get
+
+ align:start position:0%
+track you play the right side you get
+ 
+
+ align:start position:0%
+track you play the right side you get
+reactivation of the right side of the
+
+ align:start position:0%
+reactivation of the right side of the
+ 
+
+ align:start position:0%
+reactivation of the right side of the
+track and that's that's what you get so
+
+ align:start position:0%
+track and that's that's what you get so
+ 
+
+ align:start position:0%
+track and that's that's what you get so
+when you play the left hand sound left
+
+ align:start position:0%
+when you play the left hand sound left
+ 
+
+ align:start position:0%
+when you play the left hand sound left
+sound bias activates cell play cells on
+
+ align:start position:0%
+sound bias activates cell play cells on
+ 
+
+ align:start position:0%
+sound bias activates cell play cells on
+the left side right side bias biases
+
+ align:start position:0%
+the left side right side bias biases
+ 
+
+ align:start position:0%
+the left side right side bias biases
+place also on the right and you can do
+
+ align:start position:0%
+place also on the right and you can do
+ 
+
+ align:start position:0%
+place also on the right and you can do
+the same kind of psychophysical
+
+ align:start position:0%
+the same kind of psychophysical
+ 
+
+ align:start position:0%
+the same kind of psychophysical
+experiments which has been done in
+
+ align:start position:0%
+experiments which has been done in
+ 
+
+ align:start position:0%
+experiments which has been done in
+humans either with with different mode
+
+ align:start position:0%
+humans either with with different mode
+ 
+
+ align:start position:0%
+humans either with with different mode
+different sensory modalities it's been
+
+ align:start position:0%
+different sensory modalities it's been
+ 
+
+ align:start position:0%
+different sensory modalities it's been
+done on olfaction it's also been done in
+
+ align:start position:0%
+done on olfaction it's also been done in
+ 
+
+ align:start position:0%
+done on olfaction it's also been done in
+audition so the equivalent experiment
+
+ align:start position:0%
+audition so the equivalent experiment
+ 
+
+ align:start position:0%
+audition so the equivalent experiment
+using auditory cueing in humans where
+
+ align:start position:0%
+using auditory cueing in humans where
+ 
+
+ align:start position:0%
+using auditory cueing in humans where
+you have people learn the simple task
+
+ align:start position:0%
+you have people learn the simple task
+ 
+
+ align:start position:0%
+you have people learn the simple task
+this was done in Ken Taylor's lab or
+
+ align:start position:0%
+this was done in Ken Taylor's lab or
+ 
+
+ align:start position:0%
+this was done in Ken Taylor's lab or
+they do the simple spatial matching game
+
+ align:start position:0%
+they do the simple spatial matching game
+ 
+
+ align:start position:0%
+they do the simple spatial matching game
+it's like you know where's the cat card
+
+ align:start position:0%
+it's like you know where's the cat card
+ 
+
+ align:start position:0%
+it's like you know where's the cat card
+where's the teapot card the variant here
+
+ align:start position:0%
+where's the teapot card the variant here
+ 
+
+ align:start position:0%
+where's the teapot card the variant here
+was when they flipped over the cat card
+
+ align:start position:0%
+was when they flipped over the cat card
+ 
+
+ align:start position:0%
+was when they flipped over the cat card
+they would play the cat sound meow they
+
+ align:start position:0%
+they would play the cat sound meow they
+ 
+
+ align:start position:0%
+they would play the cat sound meow they
+flip over the teapot sound they play a
+
+ align:start position:0%
+flip over the teapot sound they play a
+ 
+
+ align:start position:0%
+flip over the teapot sound they play a
+little you know associated an auditory
+
+ align:start position:0%
+little you know associated an auditory
+ 
+
+ align:start position:0%
+little you know associated an auditory
+cue teapot whistle and then people go to
+
+ align:start position:0%
+cue teapot whistle and then people go to
+ 
+
+ align:start position:0%
+cue teapot whistle and then people go to
+sleep and during sleep they would play
+
+ align:start position:0%
+sleep and during sleep they would play
+ 
+
+ align:start position:0%
+sleep and during sleep they would play
+either like the cat sound or the teapot
+
+ align:start position:0%
+either like the cat sound or the teapot
+ 
+
+ align:start position:0%
+either like the cat sound or the teapot
+sound and they found out when they would
+
+ align:start position:0%
+sound and they found out when they would
+ 
+
+ align:start position:0%
+sound and they found out when they would
+wake up and now they do the task they're
+
+ align:start position:0%
+wake up and now they do the task they're
+ 
+
+ align:start position:0%
+wake up and now they do the task they're
+better at if they played the cat sound
+
+ align:start position:0%
+better at if they played the cat sound
+ 
+
+ align:start position:0%
+better at if they played the cat sound
+during sleep they were better at
+
+ align:start position:0%
+during sleep they were better at
+ 
+
+ align:start position:0%
+during sleep they were better at
+remembering locations of cats then than
+
+ align:start position:0%
+remembering locations of cats then than
+ 
+
+ align:start position:0%
+remembering locations of cats then than
+the whistle so this says not only to
+
+ align:start position:0%
+the whistle so this says not only to
+ 
+
+ align:start position:0%
+the whistle so this says not only to
+sleep actually contribute to memory but
+
+ align:start position:0%
+sleep actually contribute to memory but
+ 
+
+ align:start position:0%
+sleep actually contribute to memory but
+it's selective and it not only is
+
+ align:start position:0%
+it's selective and it not only is
+ 
+
+ align:start position:0%
+it's selective and it not only is
+selective but it can be influenced it
+
+ align:start position:0%
+selective but it can be influenced it
+ 
+
+ align:start position:0%
+selective but it can be influenced it
+can be biased you can direct the nature
+
+ align:start position:0%
+can be biased you can direct the nature
+ 
+
+ align:start position:0%
+can be biased you can direct the nature
+of memory processing and then our
+
+ align:start position:0%
+of memory processing and then our
+ 
+
+ align:start position:0%
+of memory processing and then our
+experiments suggest that well one of the
+
+ align:start position:0%
+experiments suggest that well one of the
+ 
+
+ align:start position:0%
+experiments suggest that well one of the
+one of the consequences of this kind of
+
+ align:start position:0%
+one of the consequences of this kind of
+ 
+
+ align:start position:0%
+one of the consequences of this kind of
+sleep manipulation would be bias the
+
+ align:start position:0%
+sleep manipulation would be bias the
+ 
+
+ align:start position:0%
+sleep manipulation would be bias the
+memory reactivation in the hippocampus
+
+ align:start position:0%
+memory reactivation in the hippocampus
+ 
+
+ align:start position:0%
+memory reactivation in the hippocampus
+and so the idea is simple and that is
+
+ align:start position:0%
+and so the idea is simple and that is
+ 
+
+ align:start position:0%
+and so the idea is simple and that is
+that cortex bias is the state that the
+
+ align:start position:0%
+that cortex bias is the state that the
+ 
+
+ align:start position:0%
+that cortex bias is the state that the
+hippocampus gets and then the
+
+ align:start position:0%
+hippocampus gets and then the
+ 
+
+ align:start position:0%
+hippocampus gets and then the
+hippocampus takes that state sweeps
+
+ align:start position:0%
+hippocampus takes that state sweeps
+ 
+
+ align:start position:0%
+hippocampus takes that state sweeps
+inhibition replays a sequence and that
+
+ align:start position:0%
+inhibition replays a sequence and that
+ 
+
+ align:start position:0%
+inhibition replays a sequence and that
+sequence thing gets played back to the
+
+ align:start position:0%
+sequence thing gets played back to the
+ 
+
+ align:start position:0%
+sequence thing gets played back to the
+cortex so you know the cortex it sort of
+
+ align:start position:0%
+cortex so you know the cortex it sort of
+ 
+
+ align:start position:0%
+cortex so you know the cortex it sort of
+knows you know if it has these sort of
+
+ align:start position:0%
+knows you know if it has these sort of
+ 
+
+ align:start position:0%
+knows you know if it has these sort of
+discrete states but doesn't necessarily
+
+ align:start position:0%
+discrete states but doesn't necessarily
+ 
+
+ align:start position:0%
+discrete states but doesn't necessarily
+know what the cause of correlations
+
+ align:start position:0%
+know what the cause of correlations
+ 
+
+ align:start position:0%
+know what the cause of correlations
+might be what happens next
+
+ align:start position:0%
+might be what happens next
+ 
+
+ align:start position:0%
+might be what happens next
+it doesn't necessarily know what happens
+
+ align:start position:0%
+it doesn't necessarily know what happens
+ 
+
+ align:start position:0%
+it doesn't necessarily know what happens
+next it knows what happened hippocampus
+
+ align:start position:0%
+next it knows what happened hippocampus
+ 
+
+ align:start position:0%
+next it knows what happened hippocampus
+knows what happened next it has lots of
+
+ align:start position:0%
+knows what happened next it has lots of
+ 
+
+ align:start position:0%
+knows what happened next it has lots of
+instances of that though well I saw you
+
+ align:start position:0%
+instances of that though well I saw you
+ 
+
+ align:start position:0%
+instances of that though well I saw you
+know you know I saw red light what
+
+ align:start position:0%
+know you know I saw red light what
+ 
+
+ align:start position:0%
+know you know I saw red light what
+happens next
+
+ align:start position:0%
+happens next
+ 
+
+ align:start position:0%
+happens next
+oh yeah you know I saw red light and all
+
+ align:start position:0%
+oh yeah you know I saw red light and all
+ 
+
+ align:start position:0%
+oh yeah you know I saw red light and all
+the cars stopped okay that's great
+
+ align:start position:0%
+the cars stopped okay that's great
+ 
+
+ align:start position:0%
+the cars stopped okay that's great
+you know if I'm just the cortex that's
+
+ align:start position:0%
+you know if I'm just the cortex that's
+ 
+
+ align:start position:0%
+you know if I'm just the cortex that's
+what I learned all the cars stop if I'm
+
+ align:start position:0%
+what I learned all the cars stop if I'm
+ 
+
+ align:start position:0%
+what I learned all the cars stop if I'm
+hippocampus I'm a little bit smarter
+
+ align:start position:0%
+hippocampus I'm a little bit smarter
+ 
+
+ align:start position:0%
+hippocampus I'm a little bit smarter
+than that you know you know last Tuesday
+
+ align:start position:0%
+than that you know you know last Tuesday
+ 
+
+ align:start position:0%
+than that you know you know last Tuesday
+I was there there's a red light and all
+
+ align:start position:0%
+I was there there's a red light and all
+ 
+
+ align:start position:0%
+I was there there's a red light and all
+the cars except for these cyclists man
+
+ align:start position:0%
+the cars except for these cyclists man
+ 
+
+ align:start position:0%
+the cars except for these cyclists man
+they didn't stop they just kept on going
+
+ align:start position:0%
+they didn't stop they just kept on going
+ 
+
+ align:start position:0%
+they didn't stop they just kept on going
+so wait a minute so this there's a rule
+
+ align:start position:0%
+so wait a minute so this there's a rule
+ 
+
+ align:start position:0%
+so wait a minute so this there's a rule
+you know red light cars stop bicycles
+
+ align:start position:0%
+you know red light cars stop bicycles
+ 
+
+ align:start position:0%
+you know red light cars stop bicycles
+don't stop so you were fine right you
+
+ align:start position:0%
+don't stop so you were fine right you
+ 
+
+ align:start position:0%
+don't stop so you were fine right you
+have to refine these various what appear
+
+ align:start position:0%
+have to refine these various what appear
+ 
+
+ align:start position:0%
+have to refine these various what appear
+to be simple rules prefrontal cortex
+
+ align:start position:0%
+to be simple rules prefrontal cortex
+ 
+
+ align:start position:0%
+to be simple rules prefrontal cortex
+often that's actually used in an example
+
+ align:start position:0%
+often that's actually used in an example
+ 
+
+ align:start position:0%
+often that's actually used in an example
+how do you use the prefrontal cortex Oh
+
+ align:start position:0%
+how do you use the prefrontal cortex Oh
+ 
+
+ align:start position:0%
+how do you use the prefrontal cortex Oh
+red light means stop green light means
+
+ align:start position:0%
+red light means stop green light means
+ 
+
+ align:start position:0%
+red light means stop green light means
+go that's great except in the real world
+
+ align:start position:0%
+go that's great except in the real world
+ 
+
+ align:start position:0%
+go that's great except in the real world
+that rule is too simple it has to be
+
+ align:start position:0%
+that rule is too simple it has to be
+ 
+
+ align:start position:0%
+that rule is too simple it has to be
+refined has to be refined based on your
+
+ align:start position:0%
+refined has to be refined based on your
+ 
+
+ align:start position:0%
+refined has to be refined based on your
+particular experience in fact if you're
+
+ align:start position:0%
+particular experience in fact if you're
+ 
+
+ align:start position:0%
+particular experience in fact if you're
+really sophisticated red light means
+
+ align:start position:0%
+really sophisticated red light means
+ 
+
+ align:start position:0%
+really sophisticated red light means
+cars except for cabbies will stop right
+
+ align:start position:0%
+cars except for cabbies will stop right
+ 
+
+ align:start position:0%
+cars except for cabbies will stop right
+if I see a cabbie guarantee that guy's
+
+ align:start position:0%
+if I see a cabbie guarantee that guy's
+ 
+
+ align:start position:0%
+if I see a cabbie guarantee that guy's
+not gonna stop using an accelerator
+
+ align:start position:0%
+not gonna stop using an accelerator
+ 
+
+ align:start position:0%
+not gonna stop using an accelerator
+right it's a
+
+ align:start position:0%
+right it's a
+ 
+
+ align:start position:0%
+right it's a
+and that's kind of information that's
+
+ align:start position:0%
+and that's kind of information that's
+ 
+
+ align:start position:0%
+and that's kind of information that's
+what the hippocampus has and so you
+
+ align:start position:0%
+what the hippocampus has and so you
+ 
+
+ align:start position:0%
+what the hippocampus has and so you
+imagine that's what's going on neocortex
+
+ align:start position:0%
+imagine that's what's going on neocortex
+ 
+
+ align:start position:0%
+imagine that's what's going on neocortex
+in each one of these slow oscillations
+
+ align:start position:0%
+in each one of these slow oscillations
+ 
+
+ align:start position:0%
+in each one of these slow oscillations
+saying red light and they pick Amba says
+
+ align:start position:0%
+saying red light and they pick Amba says
+ 
+
+ align:start position:0%
+saying red light and they pick Amba says
+oh yeah okay cars stop red light again
+
+ align:start position:0%
+oh yeah okay cars stop red light again
+ 
+
+ align:start position:0%
+oh yeah okay cars stop red light again
+oh there was a bicycle thing bicycles
+
+ align:start position:0%
+oh there was a bicycle thing bicycles
+ 
+
+ align:start position:0%
+oh there was a bicycle thing bicycles
+continue to go red light and that was
+
+ align:start position:0%
+continue to go red light and that was
+ 
+
+ align:start position:0%
+continue to go red light and that was
+the cabbie incident so now you have all
+
+ align:start position:0%
+the cabbie incident so now you have all
+ 
+
+ align:start position:0%
+the cabbie incident so now you have all
+these different these sort of causal
+
+ align:start position:0%
+these different these sort of causal
+ 
+
+ align:start position:0%
+these different these sort of causal
+sequences that are being expressed back
+
+ align:start position:0%
+sequences that are being expressed back
+ 
+
+ align:start position:0%
+sequences that are being expressed back
+to the neocortex presumably in order to
+
+ align:start position:0%
+to the neocortex presumably in order to
+ 
+
+ align:start position:0%
+to the neocortex presumably in order to
+establish this this more comprehensive
+
+ align:start position:0%
+establish this this more comprehensive
+ 
+
+ align:start position:0%
+establish this this more comprehensive
+consolidated model of real-world traffic
+
+ align:start position:0%
+consolidated model of real-world traffic
+ 
+
+ align:start position:0%
+consolidated model of real-world traffic
+lights rather than the cartoon traffic
+
+ align:start position:0%
+lights rather than the cartoon traffic
+ 
+
+ align:start position:0%
+lights rather than the cartoon traffic
+lights and so that would be the idea
+
+ align:start position:0%
+lights and so that would be the idea
+ 
+
+ align:start position:0%
+lights and so that would be the idea
+what's going on during asleep now during
+
+ align:start position:0%
+what's going on during asleep now during
+ 
+
+ align:start position:0%
+what's going on during asleep now during
+quiet wakefulness you can think of the
+
+ align:start position:0%
+quiet wakefulness you can think of the
+ 
+
+ align:start position:0%
+quiet wakefulness you can think of the
+same sort of idea and that is that
+
+ align:start position:0%
+same sort of idea and that is that
+ 
+
+ align:start position:0%
+same sort of idea and that is that
+you're kind of evaluating evaluating
+
+ align:start position:0%
+you're kind of evaluating evaluating
+ 
+
+ align:start position:0%
+you're kind of evaluating evaluating
+multiple calls of contingencies each of
+
+ align:start position:0%
+multiple calls of contingencies each of
+ 
+
+ align:start position:0%
+multiple calls of contingencies each of
+which might be expressible as a simple
+
+ align:start position:0%
+which might be expressible as a simple
+ 
+
+ align:start position:0%
+which might be expressible as a simple
+rule but might also be experienced as
+
+ align:start position:0%
+rule but might also be experienced as
+ 
+
+ align:start position:0%
+rule but might also be experienced as
+distinct variations of that rule and the
+
+ align:start position:0%
+distinct variations of that rule and the
+ 
+
+ align:start position:0%
+distinct variations of that rule and the
+ideas okay do we use the rule or do we
+
+ align:start position:0%
+ideas okay do we use the rule or do we
+ 
+
+ align:start position:0%
+ideas okay do we use the rule or do we
+use the exceptions or how do we actually
+
+ align:start position:0%
+use the exceptions or how do we actually
+ 
+
+ align:start position:0%
+use the exceptions or how do we actually
+you know how do we refine the rule based
+
+ align:start position:0%
+you know how do we refine the rule based
+ 
+
+ align:start position:0%
+you know how do we refine the rule based
+upon these different instances or
+
+ align:start position:0%
+upon these different instances or
+ 
+
+ align:start position:0%
+upon these different instances or
+exceptions so you can think about that
+
+ align:start position:0%
+exceptions so you can think about that
+ 
+
+ align:start position:0%
+exceptions so you can think about that
+is refining the rule that's like the
+
+ align:start position:0%
+is refining the rule that's like the
+ 
+
+ align:start position:0%
+is refining the rule that's like the
+learning sign applying the rule that's
+
+ align:start position:0%
+learning sign applying the rule that's
+ 
+
+ align:start position:0%
+learning sign applying the rule that's
+the sort of a memory of decision-making
+
+ align:start position:0%
+the sort of a memory of decision-making
+ 
+
+ align:start position:0%
+the sort of a memory of decision-making
+aside so you can think about during
+
+ align:start position:0%
+aside so you can think about during
+ 
+
+ align:start position:0%
+aside so you can think about during
+quiet wakefulness this reactivation
+
+ align:start position:0%
+quiet wakefulness this reactivation
+ 
+
+ align:start position:0%
+quiet wakefulness this reactivation
+being used in the service of actual
+
+ align:start position:0%
+being used in the service of actual
+ 
+
+ align:start position:0%
+being used in the service of actual
+learning or in decision-making and so
+
+ align:start position:0%
+learning or in decision-making and so
+ 
+
+ align:start position:0%
+learning or in decision-making and so
+again you're at the paper and one of the
+
+ align:start position:0%
+again you're at the paper and one of the
+ 
+
+ align:start position:0%
+again you're at the paper and one of the
+things that we had discovered in
+
+ align:start position:0%
+things that we had discovered in
+ 
+
+ align:start position:0%
+things that we had discovered in
+interesting about reactivation during
+
+ align:start position:0%
+interesting about reactivation during
+ 
+
+ align:start position:0%
+interesting about reactivation during
+quiet wakefulness was that when animals
+
+ align:start position:0%
+quiet wakefulness was that when animals
+ 
+
+ align:start position:0%
+quiet wakefulness was that when animals
+stop after running on a track they do
+
+ align:start position:0%
+stop after running on a track they do
+ 
+
+ align:start position:0%
+stop after running on a track they do
+reactivate sequences this is raw data
+
+ align:start position:0%
+reactivate sequences this is raw data
+ 
+
+ align:start position:0%
+reactivate sequences this is raw data
+animal running from left to right and
+
+ align:start position:0%
+animal running from left to right and
+ 
+
+ align:start position:0%
+animal running from left to right and
+then stopping for a long period of time
+
+ align:start position:0%
+then stopping for a long period of time
+ 
+
+ align:start position:0%
+then stopping for a long period of time
+and you can see activity there these
+
+ align:start position:0%
+and you can see activity there these
+ 
+
+ align:start position:0%
+and you can see activity there these
+bursts of activity you blow things
+
+ align:start position:0%
+bursts of activity you blow things
+ 
+
+ align:start position:0%
+bursts of activity you blow things
+things up these these sharp wave ripples
+
+ align:start position:0%
+things up these these sharp wave ripples
+ 
+
+ align:start position:0%
+things up these these sharp wave ripples
+last about half a second or so so you
+
+ align:start position:0%
+last about half a second or so so you
+ 
+
+ align:start position:0%
+last about half a second or so so you
+see a burst of activity you see these
+
+ align:start position:0%
+see a burst of activity you see these
+ 
+
+ align:start position:0%
+see a burst of activity you see these
+place cell sequences in this case the
+
+ align:start position:0%
+place cell sequences in this case the
+ 
+
+ align:start position:0%
+place cell sequences in this case the
+sequence actually runs in time reversed
+
+ align:start position:0%
+sequence actually runs in time reversed
+ 
+
+ align:start position:0%
+sequence actually runs in time reversed
+fashion so in this case you know time
+
+ align:start position:0%
+fashion so in this case you know time
+ 
+
+ align:start position:0%
+fashion so in this case you know time
+reverse fashion just doesn't this
+
+ align:start position:0%
+reverse fashion just doesn't this
+ 
+
+ align:start position:0%
+reverse fashion just doesn't this
+seemed like planning or decision-making
+
+ align:start position:0%
+seemed like planning or decision-making
+ 
+
+ align:start position:0%
+seemed like planning or decision-making
+it may be a valuation of temporal
+
+ align:start position:0%
+it may be a valuation of temporal
+ 
+
+ align:start position:0%
+it may be a valuation of temporal
+correlations that might be relevant to
+
+ align:start position:0%
+correlations that might be relevant to
+ 
+
+ align:start position:0%
+correlations that might be relevant to
+behavior and learning but what would a
+
+ align:start position:0%
+behavior and learning but what would a
+ 
+
+ align:start position:0%
+behavior and learning but what would a
+reverse sequence actually have to do
+
+ align:start position:0%
+reverse sequence actually have to do
+ 
+
+ align:start position:0%
+reverse sequence actually have to do
+with with you know spatial learning and
+
+ align:start position:0%
+with with you know spatial learning and
+ 
+
+ align:start position:0%
+with with you know spatial learning and
+memory well that actually came from the
+
+ align:start position:0%
+memory well that actually came from the
+ 
+
+ align:start position:0%
+memory well that actually came from the
+insight into how this might be used came
+
+ align:start position:0%
+insight into how this might be used came
+ 
+
+ align:start position:0%
+insight into how this might be used came
+from computational models in fact
+
+ align:start position:0%
+from computational models in fact
+ 
+
+ align:start position:0%
+from computational models in fact
+computational models that the postdoc in
+
+ align:start position:0%
+computational models that the postdoc in
+ 
+
+ align:start position:0%
+computational models that the postdoc in
+this case Dave foster who made this
+
+ align:start position:0%
+this case Dave foster who made this
+ 
+
+ align:start position:0%
+this case Dave foster who made this
+discovery had used in his doctoral work
+
+ align:start position:0%
+discovery had used in his doctoral work
+ 
+
+ align:start position:0%
+discovery had used in his doctoral work
+where he was actually building model
+
+ align:start position:0%
+where he was actually building model
+ 
+
+ align:start position:0%
+where he was actually building model
+reinforcement learning models with
+
+ align:start position:0%
+reinforcement learning models with
+ 
+
+ align:start position:0%
+reinforcement learning models with
+spatial navigation and one of the
+
+ align:start position:0%
+spatial navigation and one of the
+ 
+
+ align:start position:0%
+spatial navigation and one of the
+problems in reinforcement learning is
+
+ align:start position:0%
+problems in reinforcement learning is
+ 
+
+ align:start position:0%
+problems in reinforcement learning is
+that reinforcement often comes after
+
+ align:start position:0%
+that reinforcement often comes after
+ 
+
+ align:start position:0%
+that reinforcement often comes after
+you've actually carried out the steps
+
+ align:start position:0%
+you've actually carried out the steps
+ 
+
+ align:start position:0%
+you've actually carried out the steps
+that lead up to it in other words you
+
+ align:start position:0%
+that lead up to it in other words you
+ 
+
+ align:start position:0%
+that lead up to it in other words you
+walk from left to right you get rewarded
+
+ align:start position:0%
+walk from left to right you get rewarded
+ 
+
+ align:start position:0%
+walk from left to right you get rewarded
+when you get here what you want to know
+
+ align:start position:0%
+when you get here what you want to know
+ 
+
+ align:start position:0%
+when you get here what you want to know
+is not just this is where the reward is
+
+ align:start position:0%
+is not just this is where the reward is
+ 
+
+ align:start position:0%
+is not just this is where the reward is
+what you really want to know is what
+
+ align:start position:0%
+what you really want to know is what
+ 
+
+ align:start position:0%
+what you really want to know is what
+were the what are the things that
+
+ align:start position:0%
+were the what are the things that
+ 
+
+ align:start position:0%
+were the what are the things that
+actually led up to that notice I want to
+
+ align:start position:0%
+actually led up to that notice I want to
+ 
+
+ align:start position:0%
+actually led up to that notice I want to
+take credit reward value and I want to
+
+ align:start position:0%
+take credit reward value and I want to
+ 
+
+ align:start position:0%
+take credit reward value and I want to
+spread it backward in time to place
+
+ align:start position:0%
+spread it backward in time to place
+ 
+
+ align:start position:0%
+spread it backward in time to place
+value on the things that predict or led
+
+ align:start position:0%
+value on the things that predict or led
+ 
+
+ align:start position:0%
+value on the things that predict or led
+up to reward the so called temporal
+
+ align:start position:0%
+up to reward the so called temporal
+ 
+
+ align:start position:0%
+up to reward the so called temporal
+credit assignment problem how do I give
+
+ align:start position:0%
+credit assignment problem how do I give
+ 
+
+ align:start position:0%
+credit assignment problem how do I give
+credit to things that actually lead up
+
+ align:start position:0%
+credit to things that actually lead up
+ 
+
+ align:start position:0%
+credit to things that actually lead up
+to a predict reward and thinking about
+
+ align:start position:0%
+to a predict reward and thinking about
+ 
+
+ align:start position:0%
+to a predict reward and thinking about
+how you might solve the temporal credit
+
+ align:start position:0%
+how you might solve the temporal credit
+ 
+
+ align:start position:0%
+how you might solve the temporal credit
+assignment problem this reverse
+
+ align:start position:0%
+assignment problem this reverse
+ 
+
+ align:start position:0%
+assignment problem this reverse
+reactivation actually has the capacity
+
+ align:start position:0%
+reactivation actually has the capacity
+ 
+
+ align:start position:0%
+reactivation actually has the capacity
+to to solve that problem in one step
+
+ align:start position:0%
+to to solve that problem in one step
+ 
+
+ align:start position:0%
+to to solve that problem in one step
+if you imagine when animal gets to the
+
+ align:start position:0%
+if you imagine when animal gets to the
+ 
+
+ align:start position:0%
+if you imagine when animal gets to the
+end gets some reward and if now at that
+
+ align:start position:0%
+end gets some reward and if now at that
+ 
+
+ align:start position:0%
+end gets some reward and if now at that
+point I pair the delivery of a rewards
+
+ align:start position:0%
+point I pair the delivery of a rewards
+ 
+
+ align:start position:0%
+point I pair the delivery of a rewards
+signal which I will indicate here is
+
+ align:start position:0%
+signal which I will indicate here is
+ 
+
+ align:start position:0%
+signal which I will indicate here is
+this is a cartoon suggesting this is
+
+ align:start position:0%
+this is a cartoon suggesting this is
+ 
+
+ align:start position:0%
+this is a cartoon suggesting this is
+dopamine or reward signal and I'm gonna
+
+ align:start position:0%
+dopamine or reward signal and I'm gonna
+ 
+
+ align:start position:0%
+dopamine or reward signal and I'm gonna
+pair that with the reverse sequence and
+
+ align:start position:0%
+pair that with the reverse sequence and
+ 
+
+ align:start position:0%
+pair that with the reverse sequence and
+now you can think of the Association
+
+ align:start position:0%
+now you can think of the Association
+ 
+
+ align:start position:0%
+now you can think of the Association
+this is my current location this is way
+
+ align:start position:0%
+this is my current location this is way
+ 
+
+ align:start position:0%
+this is my current location this is way
+back where I started from
+
+ align:start position:0%
+back where I started from
+ 
+
+ align:start position:0%
+back where I started from
+current location gets paired with strong
+
+ align:start position:0%
+current location gets paired with strong
+ 
+
+ align:start position:0%
+current location gets paired with strong
+reward remote location gets paired with
+
+ align:start position:0%
+reward remote location gets paired with
+ 
+
+ align:start position:0%
+reward remote location gets paired with
+low reward so this association will
+
+ align:start position:0%
+low reward so this association will
+ 
+
+ align:start position:0%
+low reward so this association will
+essentially solve will convolve this
+
+ align:start position:0%
+essentially solve will convolve this
+ 
+
+ align:start position:0%
+essentially solve will convolve this
+sort of this reward discrete reward
+
+ align:start position:0%
+sort of this reward discrete reward
+ 
+
+ align:start position:0%
+sort of this reward discrete reward
+impulse function will turn it into this
+
+ align:start position:0%
+impulse function will turn it into this
+ 
+
+ align:start position:0%
+impulse function will turn it into this
+continuous graded
+
+ align:start position:0%
+continuous graded
+ 
+
+ align:start position:0%
+continuous graded
+sort of monotonic reward gradient
+
+ align:start position:0%
+sort of monotonic reward gradient
+ 
+
+ align:start position:0%
+sort of monotonic reward gradient
+function translating this into this
+
+ align:start position:0%
+function translating this into this
+ 
+
+ align:start position:0%
+function translating this into this
+essentially in one step so the thinking
+
+ align:start position:0%
+essentially in one step so the thinking
+ 
+
+ align:start position:0%
+essentially in one step so the thinking
+is hey animals are actually using this
+
+ align:start position:0%
+is hey animals are actually using this
+ 
+
+ align:start position:0%
+is hey animals are actually using this
+to learn and they're using it to solve
+
+ align:start position:0%
+to learn and they're using it to solve
+ 
+
+ align:start position:0%
+to learn and they're using it to solve
+the temporal credit assignment problem
+
+ align:start position:0%
+the temporal credit assignment problem
+ 
+
+ align:start position:0%
+the temporal credit assignment problem
+in a way that would be that would be
+
+ align:start position:0%
+in a way that would be that would be
+ 
+
+ align:start position:0%
+in a way that would be that would be
+important for general reinforcement
+
+ align:start position:0%
+important for general reinforcement
+ 
+
+ align:start position:0%
+important for general reinforcement
+learning now I won't go into so we
+
+ align:start position:0%
+learning now I won't go into so we
+ 
+
+ align:start position:0%
+learning now I won't go into so we
+actually did this experiment recorded
+
+ align:start position:0%
+actually did this experiment recorded
+ 
+
+ align:start position:0%
+actually did this experiment recorded
+from the reward area the VTA
+
+ align:start position:0%
+from the reward area the VTA
+ 
+
+ align:start position:0%
+from the reward area the VTA
+and the hippocampus and indeed during
+
+ align:start position:0%
+and the hippocampus and indeed during
+ 
+
+ align:start position:0%
+and the hippocampus and indeed during
+these reactivation events you see the
+
+ align:start position:0%
+these reactivation events you see the
+ 
+
+ align:start position:0%
+these reactivation events you see the
+pairing of this reward signalling and
+
+ align:start position:0%
+pairing of this reward signalling and
+ 
+
+ align:start position:0%
+pairing of this reward signalling and
+it's not only do you see the pairing of
+
+ align:start position:0%
+it's not only do you see the pairing of
+ 
+
+ align:start position:0%
+it's not only do you see the pairing of
+the reward signaling but you find
+
+ align:start position:0%
+the reward signaling but you find
+ 
+
+ align:start position:0%
+the reward signaling but you find
+pairing of the reward signaling in which
+
+ align:start position:0%
+pairing of the reward signaling in which
+ 
+
+ align:start position:0%
+pairing of the reward signaling in which
+the precise firing of reward of source
+
+ align:start position:0%
+the precise firing of reward of source
+ 
+
+ align:start position:0%
+the precise firing of reward of source
+signals map on to the delivery of
+
+ align:start position:0%
+signals map on to the delivery of
+ 
+
+ align:start position:0%
+signals map on to the delivery of
+rewards at goal locations so it's not
+
+ align:start position:0%
+rewards at goal locations so it's not
+ 
+
+ align:start position:0%
+rewards at goal locations so it's not
+just certain sequences are good others
+
+ align:start position:0%
+just certain sequences are good others
+ 
+
+ align:start position:0%
+just certain sequences are good others
+are bad it's that there are certain
+
+ align:start position:0%
+are bad it's that there are certain
+ 
+
+ align:start position:0%
+are bad it's that there are certain
+locations along the sequence that have
+
+ align:start position:0%
+locations along the sequence that have
+ 
+
+ align:start position:0%
+locations along the sequence that have
+differential reward value so there's a
+
+ align:start position:0%
+differential reward value so there's a
+ 
+
+ align:start position:0%
+differential reward value so there's a
+mapping of relative reward to location
+
+ align:start position:0%
+mapping of relative reward to location
+ 
+
+ align:start position:0%
+mapping of relative reward to location
+and that if you look at this while
+
+ align:start position:0%
+and that if you look at this while
+ 
+
+ align:start position:0%
+and that if you look at this while
+animals are actually performing a task
+
+ align:start position:0%
+animals are actually performing a task
+ 
+
+ align:start position:0%
+animals are actually performing a task
+you can see biases in these sequences
+
+ align:start position:0%
+you can see biases in these sequences
+ 
+
+ align:start position:0%
+you can see biases in these sequences
+that correspond to planning so both of
+
+ align:start position:0%
+that correspond to planning so both of
+ 
+
+ align:start position:0%
+that correspond to planning so both of
+these elements of sequence reactivation
+
+ align:start position:0%
+these elements of sequence reactivation
+ 
+
+ align:start position:0%
+these elements of sequence reactivation
+this was some work by Dave Foster or he
+
+ align:start position:0%
+this was some work by Dave Foster or he
+ 
+
+ align:start position:0%
+this was some work by Dave Foster or he
+looked at an animal that has to just
+
+ align:start position:0%
+looked at an animal that has to just
+ 
+
+ align:start position:0%
+looked at an animal that has to just
+forge and find a location space when
+
+ align:start position:0%
+forge and find a location space when
+ 
+
+ align:start position:0%
+forge and find a location space when
+animals are searching for a location and
+
+ align:start position:0%
+animals are searching for a location and
+ 
+
+ align:start position:0%
+animals are searching for a location and
+you look at these reactivated sequences
+
+ align:start position:0%
+you look at these reactivated sequences
+ 
+
+ align:start position:0%
+you look at these reactivated sequences
+it turns out that reactivated sequences
+
+ align:start position:0%
+it turns out that reactivated sequences
+ 
+
+ align:start position:0%
+it turns out that reactivated sequences
+tend to be directed toward the locations
+
+ align:start position:0%
+tend to be directed toward the locations
+ 
+
+ align:start position:0%
+tend to be directed toward the locations
+where the animal thinks the goal might
+
+ align:start position:0%
+where the animal thinks the goal might
+ 
+
+ align:start position:0%
+where the animal thinks the goal might
+be so it's sort of thinking about things
+
+ align:start position:0%
+be so it's sort of thinking about things
+ 
+
+ align:start position:0%
+be so it's sort of thinking about things
+that would lead to reward so both sides
+
+ align:start position:0%
+that would lead to reward so both sides
+ 
+
+ align:start position:0%
+that would lead to reward so both sides
+of this kind of sequential computation
+
+ align:start position:0%
+of this kind of sequential computation
+ 
+
+ align:start position:0%
+of this kind of sequential computation
+seem to be expressed in the hippocampus
+
+ align:start position:0%
+seem to be expressed in the hippocampus
+ 
+
+ align:start position:0%
+seem to be expressed in the hippocampus
+Co expressional with reward during
+
+ align:start position:0%
+Co expressional with reward during
+ 
+
+ align:start position:0%
+Co expressional with reward during
+evaluation or learning the expression
+
+ align:start position:0%
+evaluation or learning the expression
+ 
+
+ align:start position:0%
+evaluation or learning the expression
+during reward directed behavior in the
+
+ align:start position:0%
+during reward directed behavior in the
+ 
+
+ align:start position:0%
+during reward directed behavior in the
+service of planning a decision-making
+
+ align:start position:0%
+service of planning a decision-making
+ 
+
+ align:start position:0%
+service of planning a decision-making
+and then finally round was done this is
+
+ align:start position:0%
+and then finally round was done this is
+ 
+
+ align:start position:0%
+and then finally round was done this is
+the paper that we had that we had that
+
+ align:start position:0%
+the paper that we had that we had that
+ 
+
+ align:start position:0%
+the paper that we had that we had that
+you had read is just looking at the
+
+ align:start position:0%
+you had read is just looking at the
+ 
+
+ align:start position:0%
+you had read is just looking at the
+structure of these reward sequences on
+
+ align:start position:0%
+structure of these reward sequences on
+ 
+
+ align:start position:0%
+structure of these reward sequences on
+long tracks and the thing the sort of
+
+ align:start position:0%
+long tracks and the thing the sort of
+ 
+
+ align:start position:0%
+long tracks and the thing the sort of
+the most salient point that came out of
+
+ align:start position:0%
+the most salient point that came out of
+ 
+
+ align:start position:0%
+the most salient point that came out of
+this
+
+ align:start position:0%
+this
+ 
+
+ align:start position:0%
+this
+paper is that this shirt this the
+
+ align:start position:0%
+paper is that this shirt this the
+ 
+
+ align:start position:0%
+paper is that this shirt this the
+phenomena of sharp wave ripple
+
+ align:start position:0%
+phenomena of sharp wave ripple
+ 
+
+ align:start position:0%
+phenomena of sharp wave ripple
+sequential activation that corresponds
+
+ align:start position:0%
+sequential activation that corresponds
+ 
+
+ align:start position:0%
+sequential activation that corresponds
+to these theta sequences when animals
+
+ align:start position:0%
+to these theta sequences when animals
+ 
+
+ align:start position:0%
+to these theta sequences when animals
+are sitting quietly over the course of
+
+ align:start position:0%
+are sitting quietly over the course of
+ 
+
+ align:start position:0%
+are sitting quietly over the course of
+these longer upstate like events takes
+
+ align:start position:0%
+these longer upstate like events takes
+ 
+
+ align:start position:0%
+these longer upstate like events takes
+the form of bursts of sharp wave ripples
+
+ align:start position:0%
+the form of bursts of sharp wave ripples
+ 
+
+ align:start position:0%
+the form of bursts of sharp wave ripples
+or sequences of these short sequences so
+
+ align:start position:0%
+or sequences of these short sequences so
+ 
+
+ align:start position:0%
+or sequences of these short sequences so
+there's this compositional notion that
+
+ align:start position:0%
+there's this compositional notion that
+ 
+
+ align:start position:0%
+there's this compositional notion that
+you form long sequences out of little
+
+ align:start position:0%
+you form long sequences out of little
+ 
+
+ align:start position:0%
+you form long sequences out of little
+short sequences and there the question
+
+ align:start position:0%
+short sequences and there the question
+ 
+
+ align:start position:0%
+short sequences and there the question
+is how do you actually put these short
+
+ align:start position:0%
+is how do you actually put these short
+ 
+
+ align:start position:0%
+is how do you actually put these short
+sequences together and why would you
+
+ align:start position:0%
+sequences together and why would you
+ 
+
+ align:start position:0%
+sequences together and why would you
+actually have a why would you have a
+
+ align:start position:0%
+actually have a why would you have a
+ 
+
+ align:start position:0%
+actually have a why would you have a
+representation that has this kind of
+
+ align:start position:0%
+representation that has this kind of
+ 
+
+ align:start position:0%
+representation that has this kind of
+compositional structure or you can it's
+
+ align:start position:0%
+compositional structure or you can it's
+ 
+
+ align:start position:0%
+compositional structure or you can it's
+the Lego block kind of idea where I can
+
+ align:start position:0%
+the Lego block kind of idea where I can
+ 
+
+ align:start position:0%
+the Lego block kind of idea where I can
+put together sequences from these
+
+ align:start position:0%
+put together sequences from these
+ 
+
+ align:start position:0%
+put together sequences from these
+fundamental ease more sort of elemental
+
+ align:start position:0%
+fundamental ease more sort of elemental
+ 
+
+ align:start position:0%
+fundamental ease more sort of elemental
+sequential units and this is just I
+
+ align:start position:0%
+sequential units and this is just I
+ 
+
+ align:start position:0%
+sequential units and this is just I
+don't show the movie but if I actually
+
+ align:start position:0%
+don't show the movie but if I actually
+ 
+
+ align:start position:0%
+don't show the movie but if I actually
+zoom in on one of those sequences that
+
+ align:start position:0%
+zoom in on one of those sequences that
+ 
+
+ align:start position:0%
+zoom in on one of those sequences that
+in that particular instance with animal
+
+ align:start position:0%
+in that particular instance with animal
+ 
+
+ align:start position:0%
+in that particular instance with animal
+stop you can see that longer there's a
+
+ align:start position:0%
+stop you can see that longer there's a
+ 
+
+ align:start position:0%
+stop you can see that longer there's a
+longer reactivated sequence that
+
+ align:start position:0%
+longer reactivated sequence that
+ 
+
+ align:start position:0%
+longer reactivated sequence that
+actually takes the form of for shorter
+
+ align:start position:0%
+actually takes the form of for shorter
+ 
+
+ align:start position:0%
+actually takes the form of for shorter
+sequences that's how that's how long
+
+ align:start position:0%
+sequences that's how that's how long
+ 
+
+ align:start position:0%
+sequences that's how that's how long
+sequences are being evaluated and I
+
+ align:start position:0%
+sequences are being evaluated and I
+ 
+
+ align:start position:0%
+sequences are being evaluated and I
+can't show that and one interesting
+
+ align:start position:0%
+can't show that and one interesting
+ 
+
+ align:start position:0%
+can't show that and one interesting
+thing about this was that if you look at
+
+ align:start position:0%
+thing about this was that if you look at
+ 
+
+ align:start position:0%
+thing about this was that if you look at
+these different sequences at different
+
+ align:start position:0%
+these different sequences at different
+ 
+
+ align:start position:0%
+these different sequences at different
+lengths different lengths shorter
+
+ align:start position:0%
+lengths different lengths shorter
+ 
+
+ align:start position:0%
+lengths different lengths shorter
+sequence longer sequences they all seem
+
+ align:start position:0%
+sequence longer sequences they all seem
+ 
+
+ align:start position:0%
+sequence longer sequences they all seem
+to have a fixed velocity and that is
+
+ align:start position:0%
+to have a fixed velocity and that is
+ 
+
+ align:start position:0%
+to have a fixed velocity and that is
+this is kind of a fixed where it is the
+
+ align:start position:0%
+this is kind of a fixed where it is the
+ 
+
+ align:start position:0%
+this is kind of a fixed where it is the
+speed of thought so that there is some
+
+ align:start position:0%
+speed of thought so that there is some
+ 
+
+ align:start position:0%
+speed of thought so that there is some
+fixed constraint that that that
+
+ align:start position:0%
+fixed constraint that that that
+ 
+
+ align:start position:0%
+fixed constraint that that that
+evaluating you know further out and the
+
+ align:start position:0%
+evaluating you know further out and the
+ 
+
+ align:start position:0%
+evaluating you know further out and the
+future simply takes more time and so
+
+ align:start position:0%
+future simply takes more time and so
+ 
+
+ align:start position:0%
+future simply takes more time and so
+that suggests that there's an
+
+ align:start position:0%
+that suggests that there's an
+ 
+
+ align:start position:0%
+that suggests that there's an
+interesting
+
+ align:start position:0%
+interesting
+ 
+
+ align:start position:0%
+interesting
+there's an interesting constraining
+
+ align:start position:0%
+there's an interesting constraining
+ 
+
+ align:start position:0%
+there's an interesting constraining
+capacity for extended evaluation that
+
+ align:start position:0%
+capacity for extended evaluation that
+ 
+
+ align:start position:0%
+capacity for extended evaluation that
+comes in the form of these like these
+
+ align:start position:0%
+comes in the form of these like these
+ 
+
+ align:start position:0%
+comes in the form of these like these
+these oscillatory modes or the slow
+
+ align:start position:0%
+these oscillatory modes or the slow
+ 
+
+ align:start position:0%
+these oscillatory modes or the slow
+oscillation longer or slower frequencies
+
+ align:start position:0%
+oscillation longer or slower frequencies
+ 
+
+ align:start position:0%
+oscillation longer or slower frequencies
+give you essentially more time longer
+
+ align:start position:0%
+give you essentially more time longer
+ 
+
+ align:start position:0%
+give you essentially more time longer
+sequences and that potentially if you
+
+ align:start position:0%
+sequences and that potentially if you
+ 
+
+ align:start position:0%
+sequences and that potentially if you
+want to go even longer you might
+
+ align:start position:0%
+want to go even longer you might
+ 
+
+ align:start position:0%
+want to go even longer you might
+actually even link sequences across
+
+ align:start position:0%
+actually even link sequences across
+ 
+
+ align:start position:0%
+actually even link sequences across
+subsequent cycles just as you as you
+
+ align:start position:0%
+subsequent cycles just as you as you
+ 
+
+ align:start position:0%
+subsequent cycles just as you as you
+could do across successive sharp wave
+
+ align:start position:0%
+could do across successive sharp wave
+ 
+
+ align:start position:0%
+could do across successive sharp wave
+ripples you might be able to do across
+
+ align:start position:0%
+ripples you might be able to do across
+ 
+
+ align:start position:0%
+ripples you might be able to do across
+successive slow ways so the idea that
+
+ align:start position:0%
+successive slow ways so the idea that
+ 
+
+ align:start position:0%
+successive slow ways so the idea that
+you have these oscillations that you can
+
+ align:start position:0%
+you have these oscillations that you can
+ 
+
+ align:start position:0%
+you have these oscillations that you can
+link or couple sequences across
+
+ align:start position:0%
+link or couple sequences across
+ 
+
+ align:start position:0%
+link or couple sequences across
+different cycles of these oscillations
+
+ align:start position:0%
+different cycles of these oscillations
+ 
+
+ align:start position:0%
+different cycles of these oscillations
+that you have oscillation of different
+
+ align:start position:0%
+that you have oscillation of different
+ 
+
+ align:start position:0%
+that you have oscillation of different
+frequencies suggests that that's the
+
+ align:start position:0%
+frequencies suggests that that's the
+ 
+
+ align:start position:0%
+frequencies suggests that that's the
+moat that this is the mechanism it's a
+
+ align:start position:0%
+moat that this is the mechanism it's a
+ 
+
+ align:start position:0%
+moat that this is the mechanism it's a
+cop
+
+ align:start position:0%
+cop
+ 
+
+ align:start position:0%
+cop
+no mechanism for sequences that are
+
+ align:start position:0%
+no mechanism for sequences that are
+ 
+
+ align:start position:0%
+no mechanism for sequences that are
+nested within oscillations by combining
+
+ align:start position:0%
+nested within oscillations by combining
+ 
+
+ align:start position:0%
+nested within oscillations by combining
+these oscillations you can construct
+
+ align:start position:0%
+these oscillations you can construct
+ 
+
+ align:start position:0%
+these oscillations you can construct
+these sequences in ways that presumably
+
+ align:start position:0%
+these sequences in ways that presumably
+ 
+
+ align:start position:0%
+these sequences in ways that presumably
+contribute to cognition but we don't so
+
+ align:start position:0%
+contribute to cognition but we don't so
+ 
+
+ align:start position:0%
+contribute to cognition but we don't so
+we now kind of see how things are
+
+ align:start position:0%
+we now kind of see how things are
+ 
+
+ align:start position:0%
+we now kind of see how things are
+structured and now the question is can
+
+ align:start position:0%
+structured and now the question is can
+ 
+
+ align:start position:0%
+structured and now the question is can
+we actually manipulate it so that would
+
+ align:start position:0%
+we actually manipulate it so that would
+ 
+
+ align:start position:0%
+we actually manipulate it so that would
+real that's really the challenge seeing
+
+ align:start position:0%
+real that's really the challenge seeing
+ 
+
+ align:start position:0%
+real that's really the challenge seeing
+the compositional structure having so
+
+ align:start position:0%
+the compositional structure having so
+ 
+
+ align:start position:0%
+the compositional structure having so
+demonstrated potential access the
+
+ align:start position:0%
+demonstrated potential access the
+ 
+
+ align:start position:0%
+demonstrated potential access the
+ability to bias content to core to bias
+
+ align:start position:0%
+ability to bias content to core to bias
+ 
+
+ align:start position:0%
+ability to bias content to core to bias
+the you know the structure when things
+
+ align:start position:0%
+the you know the structure when things
+ 
+
+ align:start position:0%
+the you know the structure when things
+occur what actually occurs now I think
+
+ align:start position:0%
+occur what actually occurs now I think
+ 
+
+ align:start position:0%
+occur what actually occurs now I think
+the capacity exists to essentially
+
+ align:start position:0%
+the capacity exists to essentially
+ 
+
+ align:start position:0%
+the capacity exists to essentially
+engineer the sequences themselves and
+
+ align:start position:0%
+engineer the sequences themselves and
+ 
+
+ align:start position:0%
+engineer the sequences themselves and
+that is that during the sleeper quiet
+
+ align:start position:0%
+that is that during the sleeper quiet
+ 
+
+ align:start position:0%
+that is that during the sleeper quiet
+wakeful States get animals to think
+
+ align:start position:0%
+wakeful States get animals to think
+ 
+
+ align:start position:0%
+wakeful States get animals to think
+about things that they have not actually
+
+ align:start position:0%
+about things that they have not actually
+ 
+
+ align:start position:0%
+about things that they have not actually
+experienced and test the hypothesis this
+
+ align:start position:0%
+experienced and test the hypothesis this
+ 
+
+ align:start position:0%
+experienced and test the hypothesis this
+is what actually this is what animals
+
+ align:start position:0%
+is what actually this is what animals
+ 
+
+ align:start position:0%
+is what actually this is what animals
+are using to construct these models to
+
+ align:start position:0%
+are using to construct these models to
+ 
+
+ align:start position:0%
+are using to construct these models to
+essentially tinker with the blocks of
+
+ align:start position:0%
+essentially tinker with the blocks of
+ 
+
+ align:start position:0%
+essentially tinker with the blocks of
+memory and cognition and then finally
+
+ align:start position:0%
+memory and cognition and then finally
+ 
+
+ align:start position:0%
+memory and cognition and then finally
+just pointing out its interested these
+
+ align:start position:0%
+just pointing out its interested these
+ 
+
+ align:start position:0%
+just pointing out its interested these
+ripple sequences same space and time
+
+ align:start position:0%
+ripple sequences same space and time
+ 
+
+ align:start position:0%
+ripple sequences same space and time
+scales theta sequences so again it's
+
+ align:start position:0%
+scales theta sequences so again it's
+ 
+
+ align:start position:0%
+scales theta sequences so again it's
+suggesting this is the fundamental unit
+
+ align:start position:0%
+suggesting this is the fundamental unit
+ 
+
+ align:start position:0%
+suggesting this is the fundamental unit
+it's not unique to the hippocampus
+
+ align:start position:0%
+it's not unique to the hippocampus
+ 
+
+ align:start position:0%
+it's not unique to the hippocampus
+essentially any brain system could
+
+ align:start position:0%
+essentially any brain system could
+ 
+
+ align:start position:0%
+essentially any brain system could
+express this kind of structure using
+
+ align:start position:0%
+express this kind of structure using
+ 
+
+ align:start position:0%
+express this kind of structure using
+that simple model where you see ramps
+
+ align:start position:0%
+that simple model where you see ramps
+ 
+
+ align:start position:0%
+that simple model where you see ramps
+and you see oscillations you're gonna
+
+ align:start position:0%
+and you see oscillations you're gonna
+ 
+
+ align:start position:0%
+and you see oscillations you're gonna
+get sequences and this capacity is
+
+ align:start position:0%
+get sequences and this capacity is
+ 
+
+ align:start position:0%
+get sequences and this capacity is
+something that probably is broadly
+
+ align:start position:0%
+something that probably is broadly
+ 
+
+ align:start position:0%
+something that probably is broadly
+expressed and enjoyed by different brain
+
+ align:start position:0%
+expressed and enjoyed by different brain
+ 
+
+ align:start position:0%
+expressed and enjoyed by different brain
+areas so there you go
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+you
\ No newline at end of file
diff --git a/gF4Mkkhyz1Q.txt b/gF4Mkkhyz1Q.txt
new file mode 100644
index 0000000000000000000000000000000000000000..18af013756bd823d593e5054cdf084589abc1e04
--- /dev/null
+++ b/gF4Mkkhyz1Q.txt
@@ -0,0 +1,13635 @@
+align:start position:0%
+ 
+the following content is provided under
+
+ align:start position:0%
+the following content is provided under
+ 
+
+ align:start position:0%
+the following content is provided under
+a Creative Commons license your support
+
+ align:start position:0%
+a Creative Commons license your support
+ 
+
+ align:start position:0%
+a Creative Commons license your support
+will help MIT OpenCourseWare continue to
+
+ align:start position:0%
+will help MIT OpenCourseWare continue to
+ 
+
+ align:start position:0%
+will help MIT OpenCourseWare continue to
+offer high quality educational resources
+
+ align:start position:0%
+offer high quality educational resources
+ 
+
+ align:start position:0%
+offer high quality educational resources
+for free
+
+ align:start position:0%
+for free
+ 
+
+ align:start position:0%
+for free
+to make a donation or to view additional
+
+ align:start position:0%
+to make a donation or to view additional
+ 
+
+ align:start position:0%
+to make a donation or to view additional
+materials from hundreds of MIT courses
+
+ align:start position:0%
+materials from hundreds of MIT courses
+ 
+
+ align:start position:0%
+materials from hundreds of MIT courses
+visit MIT opencourseware at ocw.mit.edu
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so today I'm going to talk about
+
+ align:start position:0%
+okay so today I'm going to talk about
+ 
+
+ align:start position:0%
+okay so today I'm going to talk about
+mast taproot and graft route and these
+
+ align:start position:0%
+mast taproot and graft route and these
+ 
+
+ align:start position:0%
+mast taproot and graft route and these
+are pretty cool new ideas in Bitcoin
+
+ align:start position:0%
+are pretty cool new ideas in Bitcoin
+ 
+
+ align:start position:0%
+are pretty cool new ideas in Bitcoin
+they're not really production-ready
+
+ align:start position:0%
+they're not really production-ready
+ 
+
+ align:start position:0%
+they're not really production-ready
+they're still sort of ideas but it's
+
+ align:start position:0%
+they're still sort of ideas but it's
+ 
+
+ align:start position:0%
+they're still sort of ideas but it's
+kind of neat to look at the future
+
+ align:start position:0%
+kind of neat to look at the future
+ 
+
+ align:start position:0%
+kind of neat to look at the future
+directions of how people are thinking
+
+ align:start position:0%
+directions of how people are thinking
+ 
+
+ align:start position:0%
+directions of how people are thinking
+about improving these protocols so we're
+
+ align:start position:0%
+about improving these protocols so we're
+ 
+
+ align:start position:0%
+about improving these protocols so we're
+going to talk about new types of scripts
+
+ align:start position:0%
+going to talk about new types of scripts
+ 
+
+ align:start position:0%
+going to talk about new types of scripts
+mast taproot and graft route and all the
+
+ align:start position:0%
+mast taproot and graft route and all the
+ 
+
+ align:start position:0%
+mast taproot and graft route and all the
+sort of interactions between these three
+
+ align:start position:0%
+sort of interactions between these three
+ 
+
+ align:start position:0%
+sort of interactions between these three
+things I will define these of course
+
+ align:start position:0%
+things I will define these of course
+ 
+
+ align:start position:0%
+things I will define these of course
+okay so so far we've talked about
+
+ align:start position:0%
+okay so so far we've talked about
+ 
+
+ align:start position:0%
+okay so so far we've talked about
+scripts and you've got op codes you've
+
+ align:start position:0%
+scripts and you've got op codes you've
+ 
+
+ align:start position:0%
+scripts and you've got op codes you've
+got a stack I think with the homework
+
+ align:start position:0%
+got a stack I think with the homework
+ 
+
+ align:start position:0%
+got a stack I think with the homework
+people sort of got the idea of okay I
+
+ align:start position:0%
+people sort of got the idea of okay I
+ 
+
+ align:start position:0%
+people sort of got the idea of okay I
+can do off return I can do op check sig
+
+ align:start position:0%
+can do off return I can do op check sig
+ 
+
+ align:start position:0%
+can do off return I can do op check sig
+you know and the basic idea of how it
+
+ align:start position:0%
+you know and the basic idea of how it
+ 
+
+ align:start position:0%
+you know and the basic idea of how it
+works so right now in Bitcoin it's
+
+ align:start position:0%
+works so right now in Bitcoin it's
+ 
+
+ align:start position:0%
+works so right now in Bitcoin it's
+mostly pay to pub key hash so most of
+
+ align:start position:0%
+mostly pay to pub key hash so most of
+ 
+
+ align:start position:0%
+mostly pay to pub key hash so most of
+the scripts that you'll see most of the
+
+ align:start position:0%
+the scripts that you'll see most of the
+ 
+
+ align:start position:0%
+the scripts that you'll see most of the
+output scripts and then in an output
+
+ align:start position:0%
+output scripts and then in an output
+ 
+
+ align:start position:0%
+output scripts and then in an output
+look like this right op dupe up flash
+
+ align:start position:0%
+look like this right op dupe up flash
+ 
+
+ align:start position:0%
+look like this right op dupe up flash
+160 some pub key hash people verify up
+
+ align:start position:0%
+160 some pub key hash people verify up
+ 
+
+ align:start position:0%
+160 some pub key hash people verify up
+check sake and then when you want to
+
+ align:start position:0%
+check sake and then when you want to
+ 
+
+ align:start position:0%
+check sake and then when you want to
+execute this script you put a pub key
+
+ align:start position:0%
+execute this script you put a pub key
+ 
+
+ align:start position:0%
+execute this script you put a pub key
+and a signature as your input it
+
+ align:start position:0%
+and a signature as your input it
+ 
+
+ align:start position:0%
+and a signature as your input it
+duplicates the pub key hashes it pushes
+
+ align:start position:0%
+duplicates the pub key hashes it pushes
+ 
+
+ align:start position:0%
+duplicates the pub key hashes it pushes
+this hash on to it checks that those two
+
+ align:start position:0%
+this hash on to it checks that those two
+ 
+
+ align:start position:0%
+this hash on to it checks that those two
+things are equal and this also removes
+
+ align:start position:0%
+things are equal and this also removes
+ 
+
+ align:start position:0%
+things are equal and this also removes
+those two things leaving only the
+
+ align:start position:0%
+those two things leaving only the
+ 
+
+ align:start position:0%
+those two things leaving only the
+signature and then checks the signature
+
+ align:start position:0%
+signature and then checks the signature
+ 
+
+ align:start position:0%
+signature and then checks the signature
+so if they're not equal if you try to
+
+ align:start position:0%
+so if they're not equal if you try to
+ 
+
+ align:start position:0%
+so if they're not equal if you try to
+sign with a different pub key than the
+
+ align:start position:0%
+sign with a different pub key than the
+ 
+
+ align:start position:0%
+sign with a different pub key than the
+one that is committed to in this bump
+
+ align:start position:0%
+one that is committed to in this bump
+ 
+
+ align:start position:0%
+one that is committed to in this bump
+key it'll fail at this point and if you
+
+ align:start position:0%
+key it'll fail at this point and if you
+ 
+
+ align:start position:0%
+key it'll fail at this point and if you
+put the right pump key but the wrong
+
+ align:start position:0%
+put the right pump key but the wrong
+ 
+
+ align:start position:0%
+put the right pump key but the wrong
+signature it'll fail at this point right
+
+ align:start position:0%
+signature it'll fail at this point right
+ 
+
+ align:start position:0%
+signature it'll fail at this point right
+so the well it'll fail the check sig
+
+ align:start position:0%
+so the well it'll fail the check sig
+ 
+
+ align:start position:0%
+so the well it'll fail the check sig
+will fail put a zero on the stack and
+
+ align:start position:0%
+will fail put a zero on the stack and
+ 
+
+ align:start position:0%
+will fail put a zero on the stack and
+then the stack will have a zero on it
+
+ align:start position:0%
+then the stack will have a zero on it
+ 
+
+ align:start position:0%
+then the stack will have a zero on it
+and that'll fail verify means
+
+ align:start position:0%
+and that'll fail verify means
+ 
+
+ align:start position:0%
+and that'll fail verify means
+immediately fail if these things are not
+
+ align:start position:0%
+immediately fail if these things are not
+ 
+
+ align:start position:0%
+immediately fail if these things are not
+equal okay and then in seg what we sort
+
+ align:start position:0%
+equal okay and then in seg what we sort
+ 
+
+ align:start position:0%
+equal okay and then in seg what we sort
+of a template in it so really this
+
+ align:start position:0%
+of a template in it so really this
+ 
+
+ align:start position:0%
+of a template in it so really this
+entire script became op 0 pub key ash
+
+ align:start position:0%
+entire script became op 0 pub key ash
+ 
+
+ align:start position:0%
+entire script became op 0 pub key ash
+which is confusing
+
+ align:start position:0%
+which is confusing
+ 
+
+ align:start position:0%
+which is confusing
+if you don't know what that means wait
+
+ align:start position:0%
+if you don't know what that means wait
+ 
+
+ align:start position:0%
+if you don't know what that means wait
+op 0 means just put a 0 on the stack and
+
+ align:start position:0%
+op 0 means just put a 0 on the stack and
+ 
+
+ align:start position:0%
+op 0 means just put a 0 on the stack and
+then put a pub key hash on the stack and
+
+ align:start position:0%
+then put a pub key hash on the stack and
+ 
+
+ align:start position:0%
+then put a pub key hash on the stack and
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+one can spend this but the idea in
+
+ align:start position:0%
+one can spend this but the idea in
+ 
+
+ align:start position:0%
+one can spend this but the idea in
+segments is yes software that is not
+
+ align:start position:0%
+segments is yes software that is not
+ 
+
+ align:start position:0%
+segments is yes software that is not
+aware of segue will see this as
+
+ align:start position:0%
+aware of segue will see this as
+ 
+
+ align:start position:0%
+aware of segue will see this as
+spendable by anyone without a signature
+
+ align:start position:0%
+spendable by anyone without a signature
+ 
+
+ align:start position:0%
+spendable by anyone without a signature
+software that is aware of segue knows
+
+ align:start position:0%
+software that is aware of segue knows
+ 
+
+ align:start position:0%
+software that is aware of segue knows
+that these two things are the same so
+
+ align:start position:0%
+that these two things are the same so
+ 
+
+ align:start position:0%
+that these two things are the same so
+essentially if you see this turn it into
+
+ align:start position:0%
+essentially if you see this turn it into
+ 
+
+ align:start position:0%
+essentially if you see this turn it into
+this right
+
+ align:start position:0%
+this right
+ 
+
+ align:start position:0%
+this right
+take the pub key hash and fill in these
+
+ align:start position:0%
+take the pub key hash and fill in these
+ 
+
+ align:start position:0%
+take the pub key hash and fill in these
+op codes and that's actually what the
+
+ align:start position:0%
+op codes and that's actually what the
+ 
+
+ align:start position:0%
+op codes and that's actually what the
+code does for the script interpreter
+
+ align:start position:0%
+code does for the script interpreter
+ 
+
+ align:start position:0%
+code does for the script interpreter
+it'll say oh it matches this template
+
+ align:start position:0%
+it'll say oh it matches this template
+ 
+
+ align:start position:0%
+it'll say oh it matches this template
+it's op 0 and a 20-byte piece of data
+
+ align:start position:0%
+it's op 0 and a 20-byte piece of data
+ 
+
+ align:start position:0%
+it's op 0 and a 20-byte piece of data
+turn it into this and then execute it so
+
+ align:start position:0%
+turn it into this and then execute it so
+ 
+
+ align:start position:0%
+turn it into this and then execute it so
+in this way segue it saves 3 bytes right
+
+ align:start position:0%
+in this way segue it saves 3 bytes right
+ 
+
+ align:start position:0%
+in this way segue it saves 3 bytes right
+because now you have one byte there
+
+ align:start position:0%
+because now you have one byte there
+ 
+
+ align:start position:0%
+because now you have one byte there
+instead of one two three four you lose a
+
+ align:start position:0%
+instead of one two three four you lose a
+ 
+
+ align:start position:0%
+instead of one two three four you lose a
+couple more bites elsewhere and sangwich
+
+ align:start position:0%
+couple more bites elsewhere and sangwich
+ 
+
+ align:start position:0%
+couple more bites elsewhere and sangwich
+so it actually tends to lose it a couple
+
+ align:start position:0%
+so it actually tends to lose it a couple
+ 
+
+ align:start position:0%
+so it actually tends to lose it a couple
+bites but whatever okay so this this
+
+ align:start position:0%
+bites but whatever okay so this this
+ 
+
+ align:start position:0%
+bites but whatever okay so this this
+works this makes sense any questions
+
+ align:start position:0%
+works this makes sense any questions
+ 
+
+ align:start position:0%
+works this makes sense any questions
+about beta punky hash works okay okay
+
+ align:start position:0%
+about beta punky hash works okay okay
+ 
+
+ align:start position:0%
+about beta punky hash works okay okay
+and there's also pay to script hash this
+
+ align:start position:0%
+and there's also pay to script hash this
+ 
+
+ align:start position:0%
+and there's also pay to script hash this
+is the other thing you'll see quite a
+
+ align:start position:0%
+is the other thing you'll see quite a
+ 
+
+ align:start position:0%
+is the other thing you'll see quite a
+bit of in Bitcoin today I don't know
+
+ align:start position:0%
+bit of in Bitcoin today I don't know
+ 
+
+ align:start position:0%
+bit of in Bitcoin today I don't know
+what the ratios are 80% paid a pumpkin
+
+ align:start position:0%
+what the ratios are 80% paid a pumpkin
+ 
+
+ align:start position:0%
+what the ratios are 80% paid a pumpkin
+has 20% of beta script - something like
+
+ align:start position:0%
+has 20% of beta script - something like
+ 
+
+ align:start position:0%
+has 20% of beta script - something like
+that
+
+ align:start position:0%
+that
+ 
+
+ align:start position:0%
+that
+so minority but significant and for paid
+
+ align:start position:0%
+so minority but significant and for paid
+ 
+
+ align:start position:0%
+so minority but significant and for paid
+a script ash it looks like this also
+
+ align:start position:0%
+a script ash it looks like this also
+ 
+
+ align:start position:0%
+a script ash it looks like this also
+sort of template right up hash 160 a
+
+ align:start position:0%
+sort of template right up hash 160 a
+ 
+
+ align:start position:0%
+sort of template right up hash 160 a
+script hash top equal that's it
+
+ align:start position:0%
+script hash top equal that's it
+ 
+
+ align:start position:0%
+script hash top equal that's it
+this also seems like wait all I have to
+
+ align:start position:0%
+this also seems like wait all I have to
+ 
+
+ align:start position:0%
+this also seems like wait all I have to
+do is provide a pre image of this and
+
+ align:start position:0%
+do is provide a pre image of this and
+ 
+
+ align:start position:0%
+do is provide a pre image of this and
+then I'll be able to spend the coins but
+
+ align:start position:0%
+then I'll be able to spend the coins but
+ 
+
+ align:start position:0%
+then I'll be able to spend the coins but
+the script interpreter knows no actually
+
+ align:start position:0%
+the script interpreter knows no actually
+ 
+
+ align:start position:0%
+the script interpreter knows no actually
+what this means if you see this template
+
+ align:start position:0%
+what this means if you see this template
+ 
+
+ align:start position:0%
+what this means if you see this template
+if you see this format verify that this
+
+ align:start position:0%
+if you see this format verify that this
+ 
+
+ align:start position:0%
+if you see this format verify that this
+is equal and then execute whatever the
+
+ align:start position:0%
+is equal and then execute whatever the
+ 
+
+ align:start position:0%
+is equal and then execute whatever the
+pre image was as a script so actually
+
+ align:start position:0%
+pre image was as a script so actually
+ 
+
+ align:start position:0%
+pre image was as a script so actually
+the first time I started programming
+
+ align:start position:0%
+the first time I started programming
+ 
+
+ align:start position:0%
+the first time I started programming
+Bitcoin stuff I did not know about paid
+
+ align:start position:0%
+Bitcoin stuff I did not know about paid
+ 
+
+ align:start position:0%
+Bitcoin stuff I did not know about paid
+a script hash and I was just trying to
+
+ align:start position:0%
+a script hash and I was just trying to
+ 
+
+ align:start position:0%
+a script hash and I was just trying to
+make my own transactions and I used this
+
+ align:start position:0%
+make my own transactions and I used this
+ 
+
+ align:start position:0%
+make my own transactions and I used this
+I just said well I want to see that I
+
+ align:start position:0%
+I just said well I want to see that I
+ 
+
+ align:start position:0%
+I just said well I want to see that I
+can you know get the script to execute
+
+ align:start position:0%
+can you know get the script to execute
+ 
+
+ align:start position:0%
+can you know get the script to execute
+right I'll just take a random number
+
+ align:start position:0%
+right I'll just take a random number
+ 
+
+ align:start position:0%
+right I'll just take a random number
+hash it put it into this thing and try
+
+ align:start position:0%
+hash it put it into this thing and try
+ 
+
+ align:start position:0%
+hash it put it into this thing and try
+to spend it and it never worked and I
+
+ align:start position:0%
+to spend it and it never worked and I
+ 
+
+ align:start position:0%
+to spend it and it never worked and I
+didn't know why and then a few days
+
+ align:start position:0%
+didn't know why and then a few days
+ 
+
+ align:start position:0%
+didn't know why and then a few days
+later I read about pay to script and I
+
+ align:start position:0%
+later I read about pay to script and I
+ 
+
+ align:start position:0%
+later I read about pay to script and I
+was like oh no wait it wasn't days later
+
+ align:start position:0%
+was like oh no wait it wasn't days later
+ 
+
+ align:start position:0%
+was like oh no wait it wasn't days later
+I just put an OP I put an op no op op
+
+ align:start position:0%
+I just put an OP I put an op no op op
+ 
+
+ align:start position:0%
+I just put an OP I put an op no op op
+one-sixty script pêche up equal and then
+
+ align:start position:0%
+one-sixty script pêche up equal and then
+ 
+
+ align:start position:0%
+one-sixty script pêche up equal and then
+it worked and I was like okay I don't
+
+ align:start position:0%
+it worked and I was like okay I don't
+ 
+
+ align:start position:0%
+it worked and I was like okay I don't
+know how Bitcoin works this doesn't make
+
+ align:start position:0%
+know how Bitcoin works this doesn't make
+ 
+
+ align:start position:0%
+know how Bitcoin works this doesn't make
+any sense I put a no op and then it
+
+ align:start position:0%
+any sense I put a no op and then it
+ 
+
+ align:start position:0%
+any sense I put a no op and then it
+starts working and then a few days later
+
+ align:start position:0%
+starts working and then a few days later
+ 
+
+ align:start position:0%
+starts working and then a few days later
+I read about paid a script cash and it
+
+ align:start position:0%
+I read about paid a script cash and it
+ 
+
+ align:start position:0%
+I read about paid a script cash and it
+was oh this actually has a special
+
+ align:start position:0%
+was oh this actually has a special
+ 
+
+ align:start position:0%
+was oh this actually has a special
+meaning this is a template where if you
+
+ align:start position:0%
+meaning this is a template where if you
+ 
+
+ align:start position:0%
+meaning this is a template where if you
+have - 60 a bunch of data and not equal
+
+ align:start position:0%
+have - 60 a bunch of data and not equal
+ 
+
+ align:start position:0%
+have - 60 a bunch of data and not equal
+then it interprets the preimage as a
+
+ align:start position:0%
+then it interprets the preimage as a
+ 
+
+ align:start position:0%
+then it interprets the preimage as a
+script does it have to be 20 bytes
+
+ align:start position:0%
+script does it have to be 20 bytes
+ 
+
+ align:start position:0%
+script does it have to be 20 bytes
+probably yeah I don't know there's
+
+ align:start position:0%
+probably yeah I don't know there's
+ 
+
+ align:start position:0%
+probably yeah I don't know there's
+actually a vulnerability here that the
+
+ align:start position:0%
+actually a vulnerability here that the
+ 
+
+ align:start position:0%
+actually a vulnerability here that the
+how pay to script hash got introduced is
+
+ align:start position:0%
+how pay to script hash got introduced is
+ 
+
+ align:start position:0%
+how pay to script hash got introduced is
+sort of an interesting debate there was
+
+ align:start position:0%
+sort of an interesting debate there was
+ 
+
+ align:start position:0%
+sort of an interesting debate there was
+like op eval paid a script hash a bunch
+
+ align:start position:0%
+like op eval paid a script hash a bunch
+ 
+
+ align:start position:0%
+like op eval paid a script hash a bunch
+of argument about it and this was in
+
+ align:start position:0%
+of argument about it and this was in
+ 
+
+ align:start position:0%
+of argument about it and this was in
+2012 I think or 11 or 12 and it it was
+
+ align:start position:0%
+2012 I think or 11 or 12 and it it was
+ 
+
+ align:start position:0%
+2012 I think or 11 or 12 and it it was
+sort of contentious and people argue
+
+ align:start position:0%
+sort of contentious and people argue
+ 
+
+ align:start position:0%
+sort of contentious and people argue
+about it and and in retrospect this is
+
+ align:start position:0%
+about it and and in retrospect this is
+ 
+
+ align:start position:0%
+about it and and in retrospect this is
+actually insecure because you're using
+
+ align:start position:0%
+actually insecure because you're using
+ 
+
+ align:start position:0%
+actually insecure because you're using
+hop hash 160 which is 160 bytes hash
+
+ align:start position:0%
+hop hash 160 which is 160 bytes hash
+ 
+
+ align:start position:0%
+hop hash 160 which is 160 bytes hash
+function it's basically sha 256 followed
+
+ align:start position:0%
+function it's basically sha 256 followed
+ 
+
+ align:start position:0%
+function it's basically sha 256 followed
+by ripe MD 160 this is not big enough
+
+ align:start position:0%
+by ripe MD 160 this is not big enough
+ 
+
+ align:start position:0%
+by ripe MD 160 this is not big enough
+right you have you're committing to a
+
+ align:start position:0%
+right you have you're committing to a
+ 
+
+ align:start position:0%
+right you have you're committing to a
+script cache which is 20 bytes
+
+ align:start position:0%
+script cache which is 20 bytes
+ 
+
+ align:start position:0%
+script cache which is 20 bytes
+however cool so normally you're like
+
+ align:start position:0%
+however cool so normally you're like
+ 
+
+ align:start position:0%
+however cool so normally you're like
+yeah whatever 160 bits is plenty you can
+
+ align:start position:0%
+yeah whatever 160 bits is plenty you can
+ 
+
+ align:start position:0%
+yeah whatever 160 bits is plenty you can
+have collision attacks where if you're
+
+ align:start position:0%
+have collision attacks where if you're
+ 
+
+ align:start position:0%
+have collision attacks where if you're
+doing multi-sig with someone else they
+
+ align:start position:0%
+doing multi-sig with someone else they
+ 
+
+ align:start position:0%
+doing multi-sig with someone else they
+may be able to calculate different pub
+
+ align:start position:0%
+may be able to calculate different pub
+ 
+
+ align:start position:0%
+may be able to calculate different pub
+keys so that your pump key you know they
+
+ align:start position:0%
+keys so that your pump key you know they
+ 
+
+ align:start position:0%
+keys so that your pump key you know they
+have a collision where two different 20
+
+ align:start position:0%
+have a collision where two different 20
+ 
+
+ align:start position:0%
+have a collision where two different 20
+bite scripts hash to the same thing
+
+ align:start position:0%
+bite scripts hash to the same thing
+ 
+
+ align:start position:0%
+bite scripts hash to the same thing
+there's sorry two different scripts hash
+
+ align:start position:0%
+there's sorry two different scripts hash
+ 
+
+ align:start position:0%
+there's sorry two different scripts hash
+to the same 20 bytes this is possible
+
+ align:start position:0%
+to the same 20 bytes this is possible
+ 
+
+ align:start position:0%
+to the same 20 bytes this is possible
+because that's only two to the 80 work
+
+ align:start position:0%
+because that's only two to the 80 work
+ 
+
+ align:start position:0%
+because that's only two to the 80 work
+which is still a lot and used to be
+
+ align:start position:0%
+which is still a lot and used to be
+ 
+
+ align:start position:0%
+which is still a lot and used to be
+considered like no one can do it to the
+
+ align:start position:0%
+considered like no one can do it to the
+ 
+
+ align:start position:0%
+considered like no one can do it to the
+80 is like beyond any human endeavor but
+
+ align:start position:0%
+80 is like beyond any human endeavor but
+ 
+
+ align:start position:0%
+80 is like beyond any human endeavor but
+Bitcoin does - to the 80 work every day
+
+ align:start position:0%
+Bitcoin does - to the 80 work every day
+ 
+
+ align:start position:0%
+Bitcoin does - to the 80 work every day
+hour
+
+ align:start position:0%
+hour
+ 
+
+ align:start position:0%
+hour
+I don't know something fairly reasonable
+
+ align:start position:0%
+I don't know something fairly reasonable
+ 
+
+ align:start position:0%
+I don't know something fairly reasonable
+so so now it's like wait - of the 80 is
+
+ align:start position:0%
+so so now it's like wait - of the 80 is
+ 
+
+ align:start position:0%
+so so now it's like wait - of the 80 is
+not enough we need you reach for the
+
+ align:start position:0%
+not enough we need you reach for the
+ 
+
+ align:start position:0%
+not enough we need you reach for the
+same security as Bitcoin which is
+
+ align:start position:0%
+same security as Bitcoin which is
+ 
+
+ align:start position:0%
+same security as Bitcoin which is
+generally a two to the 128 security
+
+ align:start position:0%
+generally a two to the 128 security
+ 
+
+ align:start position:0%
+generally a two to the 128 security
+parameter we would need this to be 256
+
+ align:start position:0%
+parameter we would need this to be 256
+ 
+
+ align:start position:0%
+parameter we would need this to be 256
+bits instead of 160 so when they
+
+ align:start position:0%
+bits instead of 160 so when they
+ 
+
+ align:start position:0%
+bits instead of 160 so when they
+upgraded the segment paid a witness
+
+ align:start position:0%
+upgraded the segment paid a witness
+ 
+
+ align:start position:0%
+upgraded the segment paid a witness
+script hash
+
+ align:start position:0%
+script hash
+ 
+
+ align:start position:0%
+script hash
+this has to be 32 bytes to eliminate any
+
+ align:start position:0%
+this has to be 32 bytes to eliminate any
+ 
+
+ align:start position:0%
+this has to be 32 bytes to eliminate any
+of those collisions of ulnar abilities
+
+ align:start position:0%
+of those collisions of ulnar abilities
+ 
+
+ align:start position:0%
+of those collisions of ulnar abilities
+so yeah so that's what distinguishes it
+
+ align:start position:0%
+so yeah so that's what distinguishes it
+ 
+
+ align:start position:0%
+so yeah so that's what distinguishes it
+so they look the same right
+
+ align:start position:0%
+so they look the same right
+ 
+
+ align:start position:0%
+so they look the same right
+it's just op 0 piece of data obsolete
+
+ align:start position:0%
+it's just op 0 piece of data obsolete
+ 
+
+ align:start position:0%
+it's just op 0 piece of data obsolete
+but they do completely different things
+
+ align:start position:0%
+but they do completely different things
+ 
+
+ align:start position:0%
+but they do completely different things
+based on how long the state is okay so
+
+ align:start position:0%
+based on how long the state is okay so
+ 
+
+ align:start position:0%
+based on how long the state is okay so
+that's pay descript hash any questions
+
+ align:start position:0%
+that's pay descript hash any questions
+ 
+
+ align:start position:0%
+that's pay descript hash any questions
+about the basic construction good ok I
+
+ align:start position:0%
+about the basic construction good ok I
+ 
+
+ align:start position:0%
+about the basic construction good ok I
+want to these free keys must sign in
+
+ align:start position:0%
+want to these free keys must sign in
+ 
+
+ align:start position:0%
+want to these free keys must sign in
+order to spend the coins so I say up to
+
+ align:start position:0%
+order to spend the coins so I say up to
+ 
+
+ align:start position:0%
+order to spend the coins so I say up to
+push three public keys onto the you know
+
+ align:start position:0%
+push three public keys onto the you know
+ 
+
+ align:start position:0%
+push three public keys onto the you know
+three public keys up three up check
+
+ align:start position:0%
+three public keys up three up check
+ 
+
+ align:start position:0%
+three public keys up three up check
+models you say so the idea is two of
+
+ align:start position:0%
+models you say so the idea is two of
+ 
+
+ align:start position:0%
+models you say so the idea is two of
+these three must sign so you can put off
+
+ align:start position:0%
+these three must sign so you can put off
+ 
+
+ align:start position:0%
+these three must sign so you can put off
+lon
+
+ align:start position:0%
+lon
+ 
+
+ align:start position:0%
+lon
+this OP three you can put up three this
+
+ align:start position:0%
+this OP three you can put up three this
+ 
+
+ align:start position:0%
+this OP three you can put up three this
+up three if you put up four three keys
+
+ align:start position:0%
+up three if you put up four three keys
+ 
+
+ align:start position:0%
+up three if you put up four three keys
+and then up three it probably will never
+
+ align:start position:0%
+and then up three it probably will never
+ 
+
+ align:start position:0%
+and then up three it probably will never
+be spendable and just never work I'm
+
+ align:start position:0%
+be spendable and just never work I'm
+ 
+
+ align:start position:0%
+be spendable and just never work I'm
+pretty sure you have to put the
+
+ align:start position:0%
+pretty sure you have to put the
+ 
+
+ align:start position:0%
+pretty sure you have to put the
+signatures in the correct order so when
+
+ align:start position:0%
+signatures in the correct order so when
+ 
+
+ align:start position:0%
+signatures in the correct order so when
+you spend you say op zero sig a 6e and
+
+ align:start position:0%
+you spend you say op zero sig a 6e and
+ 
+
+ align:start position:0%
+you spend you say op zero sig a 6e and
+then it's a see if you put sig see sig a
+
+ align:start position:0%
+then it's a see if you put sig see sig a
+ 
+
+ align:start position:0%
+then it's a see if you put sig see sig a
+it fails right okay this is a fun little
+
+ align:start position:0%
+it fails right okay this is a fun little
+ 
+
+ align:start position:0%
+it fails right okay this is a fun little
+part where you have to put in a zero
+
+ align:start position:0%
+part where you have to put in a zero
+ 
+
+ align:start position:0%
+part where you have to put in a zero
+byte before the signature is when you
+
+ align:start position:0%
+byte before the signature is when you
+ 
+
+ align:start position:0%
+byte before the signature is when you
+want to spend I'm not a hundred percent
+
+ align:start position:0%
+want to spend I'm not a hundred percent
+ 
+
+ align:start position:0%
+want to spend I'm not a hundred percent
+sure how that got in it was the screw up
+
+ align:start position:0%
+sure how that got in it was the screw up
+ 
+
+ align:start position:0%
+sure how that got in it was the screw up
+and we're just we just live with it
+
+ align:start position:0%
+and we're just we just live with it
+ 
+
+ align:start position:0%
+and we're just we just live with it
+forever you don't put the OP 0 it
+
+ align:start position:0%
+forever you don't put the OP 0 it
+ 
+
+ align:start position:0%
+forever you don't put the OP 0 it
+doesn't work and it's somewhat confusing
+
+ align:start position:0%
+doesn't work and it's somewhat confusing
+ 
+
+ align:start position:0%
+doesn't work and it's somewhat confusing
+it wastes the byte which is not a huge
+
+ align:start position:0%
+it wastes the byte which is not a huge
+ 
+
+ align:start position:0%
+it wastes the byte which is not a huge
+deal but it's just like what and they
+
+ align:start position:0%
+deal but it's just like what and they
+ 
+
+ align:start position:0%
+deal but it's just like what and they
+didn't fix that in segue right yeah we
+
+ align:start position:0%
+didn't fix that in segue right yeah we
+ 
+
+ align:start position:0%
+didn't fix that in segue right yeah we
+just stays in there who knows if it'll
+
+ align:start position:0%
+just stays in there who knows if it'll
+ 
+
+ align:start position:0%
+just stays in there who knows if it'll
+ever get out
+
+ align:start position:0%
+ever get out
+ 
+
+ align:start position:0%
+ever get out
+so saying it was an opportunity to fix
+
+ align:start position:0%
+so saying it was an opportunity to fix
+ 
+
+ align:start position:0%
+so saying it was an opportunity to fix
+it but yes
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+hard work so you put this in and you
+
+ align:start position:0%
+hard work so you put this in and you
+ 
+
+ align:start position:0%
+hard work so you put this in and you
+could say wait
+
+ align:start position:0%
+could say wait
+ 
+
+ align:start position:0%
+could say wait
+that's stupid wait you need a zero in
+
+ align:start position:0%
+that's stupid wait you need a zero in
+ 
+
+ align:start position:0%
+that's stupid wait you need a zero in
+front when you put the signors let's get
+
+ align:start position:0%
+front when you put the signors let's get
+ 
+
+ align:start position:0%
+front when you put the signors let's get
+rid of that so so now the old software
+
+ align:start position:0%
+rid of that so so now the old software
+ 
+
+ align:start position:0%
+rid of that so so now the old software
+says no I need a zero here and then if
+
+ align:start position:0%
+says no I need a zero here and then if
+ 
+
+ align:start position:0%
+says no I need a zero here and then if
+you if you don't put the zero and you
+
+ align:start position:0%
+you if you don't put the zero and you
+ 
+
+ align:start position:0%
+you if you don't put the zero and you
+just put the two signatures I fail this
+
+ align:start position:0%
+just put the two signatures I fail this
+ 
+
+ align:start position:0%
+just put the two signatures I fail this
+script and then it could just be any
+
+ align:start position:0%
+script and then it could just be any
+ 
+
+ align:start position:0%
+script and then it could just be any
+note any data and it was like any data
+
+ align:start position:0%
+note any data and it was like any data
+ 
+
+ align:start position:0%
+note any data and it was like any data
+any data on the stack would get it would
+
+ align:start position:0%
+any data on the stack would get it would
+ 
+
+ align:start position:0%
+any data on the stack would get it would
+get popped off right yeah and then the
+
+ align:start position:0%
+get popped off right yeah and then the
+ 
+
+ align:start position:0%
+get popped off right yeah and then the
+two signatures so if you said let's
+
+ align:start position:0%
+two signatures so if you said let's
+ 
+
+ align:start position:0%
+two signatures so if you said let's
+eliminate that requirement that would
+
+ align:start position:0%
+eliminate that requirement that would
+ 
+
+ align:start position:0%
+eliminate that requirement that would
+actually be a hard fork because it would
+
+ align:start position:0%
+actually be a hard fork because it would
+ 
+
+ align:start position:0%
+actually be a hard fork because it would
+be allowing scripts that were previously
+
+ align:start position:0%
+be allowing scripts that were previously
+ 
+
+ align:start position:0%
+be allowing scripts that were previously
+invalid to now become valid and that's a
+
+ align:start position:0%
+invalid to now become valid and that's a
+ 
+
+ align:start position:0%
+invalid to now become valid and that's a
+huge undertaking that has sort of only
+
+ align:start position:0%
+huge undertaking that has sort of only
+ 
+
+ align:start position:0%
+huge undertaking that has sort of only
+happened once in Bitcoin and that wasn't
+
+ align:start position:0%
+happened once in Bitcoin and that wasn't
+ 
+
+ align:start position:0%
+happened once in Bitcoin and that wasn't
+even planned and so it's just like
+
+ align:start position:0%
+even planned and so it's just like
+ 
+
+ align:start position:0%
+even planned and so it's just like
+whatever leave it they did soft work it
+
+ align:start position:0%
+whatever leave it they did soft work it
+ 
+
+ align:start position:0%
+whatever leave it they did soft work it
+then wait is it software or policy okay
+
+ align:start position:0%
+then wait is it software or policy okay
+ 
+
+ align:start position:0%
+then wait is it software or policy okay
+so they didn't sophomore could say it
+
+ align:start position:0%
+so they didn't sophomore could say it
+ 
+
+ align:start position:0%
+so they didn't sophomore could say it
+needs to be a zero so it could be
+
+ align:start position:0%
+needs to be a zero so it could be
+ 
+
+ align:start position:0%
+needs to be a zero so it could be
+non-standard or it could be an actual
+
+ align:start position:0%
+non-standard or it could be an actual
+ 
+
+ align:start position:0%
+non-standard or it could be an actual
+consensus rule that that has to be a
+
+ align:start position:0%
+consensus rule that that has to be a
+ 
+
+ align:start position:0%
+consensus rule that that has to be a
+zero it used to be anything and now it's
+
+ align:start position:0%
+zero it used to be anything and now it's
+ 
+
+ align:start position:0%
+zero it used to be anything and now it's
+it should be a zero put a zero and then
+
+ align:start position:0%
+it should be a zero put a zero and then
+ 
+
+ align:start position:0%
+it should be a zero put a zero and then
+it'll work
+
+ align:start position:0%
+it'll work
+ 
+
+ align:start position:0%
+it'll work
+but that that remains in segments as
+
+ align:start position:0%
+but that that remains in segments as
+ 
+
+ align:start position:0%
+but that that remains in segments as
+well with multi-sig they could have
+
+ align:start position:0%
+well with multi-sig they could have
+ 
+
+ align:start position:0%
+well with multi-sig they could have
+fixed it they didn't want to touch it it
+
+ align:start position:0%
+fixed it they didn't want to touch it it
+ 
+
+ align:start position:0%
+fixed it they didn't want to touch it it
+was just like whatever let you know when
+
+ align:start position:0%
+was just like whatever let you know when
+ 
+
+ align:start position:0%
+was just like whatever let you know when
+you see a when you see one of these turn
+
+ align:start position:0%
+you see a when you see one of these turn
+ 
+
+ align:start position:0%
+you see a when you see one of these turn
+it into one of these and just do the
+
+ align:start position:0%
+it into one of these and just do the
+ 
+
+ align:start position:0%
+it into one of these and just do the
+exact same thing you used to be doing
+
+ align:start position:0%
+exact same thing you used to be doing
+ 
+
+ align:start position:0%
+exact same thing you used to be doing
+that's a lot simpler and easier okay so
+
+ align:start position:0%
+that's a lot simpler and easier okay so
+ 
+
+ align:start position:0%
+that's a lot simpler and easier okay so
+kind of weird but this works right
+
+ align:start position:0%
+kind of weird but this works right
+ 
+
+ align:start position:0%
+kind of weird but this works right
+people use this a lot especially
+
+ align:start position:0%
+people use this a lot especially
+ 
+
+ align:start position:0%
+people use this a lot especially
+exchanges exchanges almost I very very
+
+ align:start position:0%
+exchanges exchanges almost I very very
+ 
+
+ align:start position:0%
+exchanges exchanges almost I very very
+often use this kind of construction
+
+ align:start position:0%
+often use this kind of construction
+ 
+
+ align:start position:0%
+often use this kind of construction
+because it helps people manage keys if
+
+ align:start position:0%
+because it helps people manage keys if
+ 
+
+ align:start position:0%
+because it helps people manage keys if
+one key gets compromised you don't lose
+
+ align:start position:0%
+one key gets compromised you don't lose
+ 
+
+ align:start position:0%
+one key gets compromised you don't lose
+all your money usually two of three
+
+ align:start position:0%
+all your money usually two of three
+ 
+
+ align:start position:0%
+all your money usually two of three
+sometimes three or four three of three
+
+ align:start position:0%
+sometimes three or four three of three
+ 
+
+ align:start position:0%
+sometimes three or four three of three
+two of to all sorts of constructions
+
+ align:start position:0%
+two of to all sorts of constructions
+ 
+
+ align:start position:0%
+two of to all sorts of constructions
+where this is extremely useful and
+
+ align:start position:0%
+where this is extremely useful and
+ 
+
+ align:start position:0%
+where this is extremely useful and
+actually I'll be talking about more
+
+ align:start position:0%
+actually I'll be talking about more
+ 
+
+ align:start position:0%
+actually I'll be talking about more
+powerful signature aggregation and
+
+ align:start position:0%
+powerful signature aggregation and
+ 
+
+ align:start position:0%
+powerful signature aggregation and
+multi-sig on Wednesday but for now this
+
+ align:start position:0%
+multi-sig on Wednesday but for now this
+ 
+
+ align:start position:0%
+multi-sig on Wednesday but for now this
+is what we use and how can
+
+ align:start position:0%
+is what we use and how can
+ 
+
+ align:start position:0%
+is what we use and how can
+we make this better so one interesting
+
+ align:start position:0%
+we make this better so one interesting
+ 
+
+ align:start position:0%
+we make this better so one interesting
+thing pay to pub key which is not really
+
+ align:start position:0%
+thing pay to pub key which is not really
+ 
+
+ align:start position:0%
+thing pay to pub key which is not really
+used anymore but used to be mused more
+
+ align:start position:0%
+used anymore but used to be mused more
+ 
+
+ align:start position:0%
+used anymore but used to be mused more
+frequently like in the early days like
+
+ align:start position:0%
+frequently like in the early days like
+ 
+
+ align:start position:0%
+frequently like in the early days like
+if you look at transactions in 2009-2010
+
+ align:start position:0%
+if you look at transactions in 2009-2010
+ 
+
+ align:start position:0%
+if you look at transactions in 2009-2010
+this is predominant I think and like all
+
+ align:start position:0%
+this is predominant I think and like all
+ 
+
+ align:start position:0%
+this is predominant I think and like all
+the mining outputs from a long time ago
+
+ align:start position:0%
+the mining outputs from a long time ago
+ 
+
+ align:start position:0%
+the mining outputs from a long time ago
+looked like this and the script the
+
+ align:start position:0%
+looked like this and the script the
+ 
+
+ align:start position:0%
+looked like this and the script the
+output script was just pump key objects
+
+ align:start position:0%
+output script was just pump key objects
+ 
+
+ align:start position:0%
+output script was just pump key objects
+ache which is really simple and then the
+
+ align:start position:0%
+ache which is really simple and then the
+ 
+
+ align:start position:0%
+ache which is really simple and then the
+idea is when you want to spend it you
+
+ align:start position:0%
+idea is when you want to spend it you
+ 
+
+ align:start position:0%
+idea is when you want to spend it you
+just push a signature on to the stack
+
+ align:start position:0%
+just push a signature on to the stack
+ 
+
+ align:start position:0%
+just push a signature on to the stack
+then you have signature pub key op check
+
+ align:start position:0%
+then you have signature pub key op check
+ 
+
+ align:start position:0%
+then you have signature pub key op check
+sig that's it it's really simple and it
+
+ align:start position:0%
+sig that's it it's really simple and it
+ 
+
+ align:start position:0%
+sig that's it it's really simple and it
+actually saves space right your pub key
+
+ align:start position:0%
+actually saves space right your pub key
+ 
+
+ align:start position:0%
+actually saves space right your pub key
+is 33 bytes whereas your pub key hash
+
+ align:start position:0%
+is 33 bytes whereas your pub key hash
+ 
+
+ align:start position:0%
+is 33 bytes whereas your pub key hash
+script the the pub key hash is 20 bytes
+
+ align:start position:0%
+script the the pub key hash is 20 bytes
+ 
+
+ align:start position:0%
+script the the pub key hash is 20 bytes
+so yeah the pub key hash is 12 bytes
+
+ align:start position:0%
+so yeah the pub key hash is 12 bytes
+ 
+
+ align:start position:0%
+so yeah the pub key hash is 12 bytes
+smaller plus the extra op codes makes it
+
+ align:start position:0%
+smaller plus the extra op codes makes it
+ 
+
+ align:start position:0%
+smaller plus the extra op codes makes it
+10 bytes savings for the output script
+
+ align:start position:0%
+10 bytes savings for the output script
+ 
+
+ align:start position:0%
+10 bytes savings for the output script
+right however when you spend with pay to
+
+ align:start position:0%
+right however when you spend with pay to
+ 
+
+ align:start position:0%
+right however when you spend with pay to
+pump key hash you need to put the pump
+
+ align:start position:0%
+pump key hash you need to put the pump
+ 
+
+ align:start position:0%
+pump key hash you need to put the pump
+key itself and the signature so you're
+
+ align:start position:0%
+key itself and the signature so you're
+ 
+
+ align:start position:0%
+key itself and the signature so you're
+putting that you're putting the pub key
+
+ align:start position:0%
+putting that you're putting the pub key
+ 
+
+ align:start position:0%
+putting that you're putting the pub key
+into the network either way eventually
+
+ align:start position:0%
+into the network either way eventually
+ 
+
+ align:start position:0%
+into the network either way eventually
+so this is actually overall more space
+
+ align:start position:0%
+so this is actually overall more space
+ 
+
+ align:start position:0%
+so this is actually overall more space
+efficient in that you're saving 23 bytes
+
+ align:start position:0%
+efficient in that you're saving 23 bytes
+ 
+
+ align:start position:0%
+efficient in that you're saving 23 bytes
+over the life cycle of it right when you
+
+ align:start position:0%
+over the life cycle of it right when you
+ 
+
+ align:start position:0%
+over the life cycle of it right when you
+the output is a little bit bigger but
+
+ align:start position:0%
+the output is a little bit bigger but
+ 
+
+ align:start position:0%
+the output is a little bit bigger but
+the input is significantly smaller so
+
+ align:start position:0%
+the input is significantly smaller so
+ 
+
+ align:start position:0%
+the input is significantly smaller so
+you end up saving why why do we always
+
+ align:start position:0%
+you end up saving why why do we always
+ 
+
+ align:start position:0%
+you end up saving why why do we always
+use pub key hashes instead of pump keys
+
+ align:start position:0%
+use pub key hashes instead of pump keys
+ 
+
+ align:start position:0%
+use pub key hashes instead of pump keys
+then does anyone there's a lot of
+
+ align:start position:0%
+then does anyone there's a lot of
+ 
+
+ align:start position:0%
+then does anyone there's a lot of
+different opinions on it and there's no
+
+ align:start position:0%
+different opinions on it and there's no
+ 
+
+ align:start position:0%
+different opinions on it and there's no
+you know it's a Bitcoin there's no like
+
+ align:start position:0%
+you know it's a Bitcoin there's no like
+ 
+
+ align:start position:0%
+you know it's a Bitcoin there's no like
+answer people have different ideas of
+
+ align:start position:0%
+answer people have different ideas of
+ 
+
+ align:start position:0%
+answer people have different ideas of
+why these are better any it is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah that's a that's a really probably
+
+ align:start position:0%
+yeah that's a that's a really probably
+ 
+
+ align:start position:0%
+yeah that's a that's a really probably
+the predominant one and that's gonna be
+
+ align:start position:0%
+the predominant one and that's gonna be
+ 
+
+ align:start position:0%
+the predominant one and that's gonna be
+a tricky one to try to convince people
+
+ align:start position:0%
+a tricky one to try to convince people
+ 
+
+ align:start position:0%
+a tricky one to try to convince people
+is not the case because I'll get to that
+
+ align:start position:0%
+is not the case because I'll get to that
+ 
+
+ align:start position:0%
+is not the case because I'll get to that
+but we people started arguing about like
+
+ align:start position:0%
+but we people started arguing about like
+ 
+
+ align:start position:0%
+but we people started arguing about like
+funky Asha won when when someone posted
+
+ align:start position:0%
+funky Asha won when when someone posted
+ 
+
+ align:start position:0%
+funky Asha won when when someone posted
+about grassroot everyone the discussion
+
+ align:start position:0%
+about grassroot everyone the discussion
+ 
+
+ align:start position:0%
+about grassroot everyone the discussion
+devolved into a wait I don't want my pub
+
+ align:start position:0%
+devolved into a wait I don't want my pub
+ 
+
+ align:start position:0%
+devolved into a wait I don't want my pub
+key on the network and and there's some
+
+ align:start position:0%
+key on the network and and there's some
+ 
+
+ align:start position:0%
+key on the network and and there's some
+arguments why you'd want a pub key hash
+
+ align:start position:0%
+arguments why you'd want a pub key hash
+ 
+
+ align:start position:0%
+arguments why you'd want a pub key hash
+and it's more secure but there's a lot
+
+ align:start position:0%
+and it's more secure but there's a lot
+ 
+
+ align:start position:0%
+and it's more secure but there's a lot
+of arguments that it doesn't actually
+
+ align:start position:0%
+of arguments that it doesn't actually
+ 
+
+ align:start position:0%
+of arguments that it doesn't actually
+provide any extra security so that's a
+
+ align:start position:0%
+provide any extra security so that's a
+ 
+
+ align:start position:0%
+provide any extra security so that's a
+tricky one but that is one that is
+
+ align:start position:0%
+tricky one but that is one that is
+ 
+
+ align:start position:0%
+tricky one but that is one that is
+probably a big one people like other
+
+ align:start position:0%
+probably a big one people like other
+ 
+
+ align:start position:0%
+probably a big one people like other
+ideas why do use punky hashes instead of
+
+ align:start position:0%
+ideas why do use punky hashes instead of
+ 
+
+ align:start position:0%
+ideas why do use punky hashes instead of
+pub keys themselves okay so sighs you
+
+ align:start position:0%
+pub keys themselves okay so sighs you
+ 
+
+ align:start position:0%
+pub keys themselves okay so sighs you
+want the outputs to be small also I'm
+
+ align:start position:0%
+want the outputs to be small also I'm
+ 
+
+ align:start position:0%
+want the outputs to be small also I'm
+pretty sure when Satoshi wrote all this
+
+ align:start position:0%
+pretty sure when Satoshi wrote all this
+ 
+
+ align:start position:0%
+pretty sure when Satoshi wrote all this
+he did not know about compressed public
+
+ align:start position:0%
+he did not know about compressed public
+ 
+
+ align:start position:0%
+he did not know about compressed public
+keys because that stuff was not in there
+
+ align:start position:0%
+keys because that stuff was not in there
+ 
+
+ align:start position:0%
+keys because that stuff was not in there
+for a while so I think I think I
+
+ align:start position:0%
+for a while so I think I think I
+ 
+
+ align:start position:0%
+for a while so I think I think I
+mentioned this before right did I
+
+ align:start position:0%
+mentioned this before right did I
+ 
+
+ align:start position:0%
+mentioned this before right did I
+mention compressed versus uncompressed
+
+ align:start position:0%
+mention compressed versus uncompressed
+ 
+
+ align:start position:0%
+mention compressed versus uncompressed
+web keys yeah probably
+
+ align:start position:0%
+web keys yeah probably
+ 
+
+ align:start position:0%
+web keys yeah probably
+okay so review the idea is you've got
+
+ align:start position:0%
+okay so review the idea is you've got
+ 
+
+ align:start position:0%
+okay so review the idea is you've got
+this whole curve kind of deal kind of
+
+ align:start position:0%
+this whole curve kind of deal kind of
+ 
+
+ align:start position:0%
+this whole curve kind of deal kind of
+thing and your your public key is a
+
+ align:start position:0%
+thing and your your public key is a
+ 
+
+ align:start position:0%
+thing and your your public key is a
+point on the curve you need an x and
+
+ align:start position:0%
+point on the curve you need an x and
+ 
+
+ align:start position:0%
+point on the curve you need an x and
+y-coordinate to represent the point
+
+ align:start position:0%
+y-coordinate to represent the point
+ 
+
+ align:start position:0%
+y-coordinate to represent the point
+however because it's symmetric you can
+
+ align:start position:0%
+however because it's symmetric you can
+ 
+
+ align:start position:0%
+however because it's symmetric you can
+just say well I'll tell you the x
+
+ align:start position:0%
+just say well I'll tell you the x
+ 
+
+ align:start position:0%
+just say well I'll tell you the x
+coordinate you know x equals seven I'm
+
+ align:start position:0%
+coordinate you know x equals seven I'm
+ 
+
+ align:start position:0%
+coordinate you know x equals seven I'm
+not going to tell you the y coordinate
+
+ align:start position:0%
+not going to tell you the y coordinate
+ 
+
+ align:start position:0%
+not going to tell you the y coordinate
+I'll just say y equals plus so Y you
+
+ align:start position:0%
+I'll just say y equals plus so Y you
+ 
+
+ align:start position:0%
+I'll just say y equals plus so Y you
+know go up or go down that way I can do
+
+ align:start position:0%
+know go up or go down that way I can do
+ 
+
+ align:start position:0%
+know go up or go down that way I can do
+32 bytes for this and one bit for that
+
+ align:start position:0%
+32 bytes for this and one bit for that
+ 
+
+ align:start position:0%
+32 bytes for this and one bit for that
+had the cost of a little bit of extra
+
+ align:start position:0%
+had the cost of a little bit of extra
+ 
+
+ align:start position:0%
+had the cost of a little bit of extra
+computation because then when I when I
+
+ align:start position:0%
+computation because then when I when I
+ 
+
+ align:start position:0%
+computation because then when I when I
+see you know so I could say maybe Y is
+
+ align:start position:0%
+see you know so I could say maybe Y is
+ 
+
+ align:start position:0%
+see you know so I could say maybe Y is
+actually five or something so if I say x
+
+ align:start position:0%
+actually five or something so if I say x
+ 
+
+ align:start position:0%
+actually five or something so if I say x
+equals seven y equals five that's quick
+
+ align:start position:0%
+equals seven y equals five that's quick
+ 
+
+ align:start position:0%
+equals seven y equals five that's quick
+but it takes more space if I say x
+
+ align:start position:0%
+but it takes more space if I say x
+ 
+
+ align:start position:0%
+but it takes more space if I say x
+equals seven y equals plus I not have to
+
+ align:start position:0%
+equals seven y equals plus I not have to
+ 
+
+ align:start position:0%
+equals seven y equals plus I not have to
+compute what Y is when I see this which
+
+ align:start position:0%
+compute what Y is when I see this which
+ 
+
+ align:start position:0%
+compute what Y is when I see this which
+is pretty quick
+
+ align:start position:0%
+is pretty quick
+ 
+
+ align:start position:0%
+is pretty quick
+what takes some time but it's good
+
+ align:start position:0%
+what takes some time but it's good
+ 
+
+ align:start position:0%
+what takes some time but it's good
+trade-off anyway I don't think Satoshi
+
+ align:start position:0%
+trade-off anyway I don't think Satoshi
+ 
+
+ align:start position:0%
+trade-off anyway I don't think Satoshi
+knew about this idea
+
+ align:start position:0%
+knew about this idea
+ 
+
+ align:start position:0%
+knew about this idea
+or it may be thought of it never put it
+
+ align:start position:0%
+or it may be thought of it never put it
+ 
+
+ align:start position:0%
+or it may be thought of it never put it
+in so the public keys were actually 65
+
+ align:start position:0%
+in so the public keys were actually 65
+ 
+
+ align:start position:0%
+in so the public keys were actually 65
+flights you want to keep the outputs
+
+ align:start position:0%
+flights you want to keep the outputs
+ 
+
+ align:start position:0%
+flights you want to keep the outputs
+small because they're in the UT Exocet
+
+ align:start position:0%
+small because they're in the UT Exocet
+ 
+
+ align:start position:0%
+small because they're in the UT Exocet
+they're in the database and you need to
+
+ align:start position:0%
+they're in the database and you need to
+ 
+
+ align:start position:0%
+they're in the database and you need to
+be alone through this and read it
+
+ align:start position:0%
+be alone through this and read it
+ 
+
+ align:start position:0%
+be alone through this and read it
+randomly like you don't know when it's
+
+ align:start position:0%
+randomly like you don't know when it's
+ 
+
+ align:start position:0%
+randomly like you don't know when it's
+gonna get spent so you don't know what
+
+ align:start position:0%
+gonna get spent so you don't know what
+ 
+
+ align:start position:0%
+gonna get spent so you don't know what
+transaction is going to query this so
+
+ align:start position:0%
+transaction is going to query this so
+ 
+
+ align:start position:0%
+transaction is going to query this so
+this has to go in like an actual
+
+ align:start position:0%
+this has to go in like an actual
+ 
+
+ align:start position:0%
+this has to go in like an actual
+database key value store kind of thing
+
+ align:start position:0%
+database key value store kind of thing
+ 
+
+ align:start position:0%
+database key value store kind of thing
+the signatures are don't have to be in
+
+ align:start position:0%
+the signatures are don't have to be in
+ 
+
+ align:start position:0%
+the signatures are don't have to be in
+any database they're just in these old
+
+ align:start position:0%
+any database they're just in these old
+ 
+
+ align:start position:0%
+any database they're just in these old
+blocks and you read from them linearly
+
+ align:start position:0%
+blocks and you read from them linearly
+ 
+
+ align:start position:0%
+blocks and you read from them linearly
+you basically read for the whole block
+
+ align:start position:0%
+you basically read for the whole block
+ 
+
+ align:start position:0%
+you basically read for the whole block
+at a time and high latency is fine
+
+ align:start position:0%
+at a time and high latency is fine
+ 
+
+ align:start position:0%
+at a time and high latency is fine
+there's never any timing critical reads
+
+ align:start position:0%
+there's never any timing critical reads
+ 
+
+ align:start position:0%
+there's never any timing critical reads
+for this so basically you can just you
+
+ align:start position:0%
+for this so basically you can just you
+ 
+
+ align:start position:0%
+for this so basically you can just you
+could store the blocks as just files on
+
+ align:start position:0%
+could store the blocks as just files on
+ 
+
+ align:start position:0%
+could store the blocks as just files on
+your hard drive you know block block 1
+
+ align:start position:0%
+your hard drive you know block block 1
+ 
+
+ align:start position:0%
+your hard drive you know block block 1
+dot dat or whatever block 2 dot that and
+
+ align:start position:0%
+dot dat or whatever block 2 dot that and
+ 
+
+ align:start position:0%
+dot dat or whatever block 2 dot that and
+have 500,000 files because you basically
+
+ align:start position:0%
+have 500,000 files because you basically
+ 
+
+ align:start position:0%
+have 500,000 files because you basically
+always read them a block at a time
+
+ align:start position:0%
+always read them a block at a time
+ 
+
+ align:start position:0%
+always read them a block at a time
+and you and you only have to read them
+
+ align:start position:0%
+and you and you only have to read them
+ 
+
+ align:start position:0%
+and you and you only have to read them
+when peep other people are doing IBD
+
+ align:start position:0%
+when peep other people are doing IBD
+ 
+
+ align:start position:0%
+when peep other people are doing IBD
+initial block download and you're
+
+ align:start position:0%
+initial block download and you're
+ 
+
+ align:start position:0%
+initial block download and you're
+serving them to them so you can prune
+
+ align:start position:0%
+serving them to them so you can prune
+ 
+
+ align:start position:0%
+serving them to them so you can prune
+these if you run a Bitcoin core with
+
+ align:start position:0%
+these if you run a Bitcoin core with
+ 
+
+ align:start position:0%
+these if you run a Bitcoin core with
+pruning anyway so that the main set idea
+
+ align:start position:0%
+pruning anyway so that the main set idea
+ 
+
+ align:start position:0%
+pruning anyway so that the main set idea
+is ok even if it overall increases the
+
+ align:start position:0%
+is ok even if it overall increases the
+ 
+
+ align:start position:0%
+is ok even if it overall increases the
+size of transactions it does reduce the
+
+ align:start position:0%
+size of transactions it does reduce the
+ 
+
+ align:start position:0%
+size of transactions it does reduce the
+size of the outputs which is the thing
+
+ align:start position:0%
+size of the outputs which is the thing
+ 
+
+ align:start position:0%
+size of the outputs which is the thing
+we really want to minimize for keeping
+
+ align:start position:0%
+we really want to minimize for keeping
+ 
+
+ align:start position:0%
+we really want to minimize for keeping
+the speed up ok questions about that
+
+ align:start position:0%
+the speed up ok questions about that
+ 
+
+ align:start position:0%
+the speed up ok questions about that
+cool ok so similarly same thing with
+
+ align:start position:0%
+cool ok so similarly same thing with
+ 
+
+ align:start position:0%
+cool ok so similarly same thing with
+beta punky hash and you know versus pay
+
+ align:start position:0%
+beta punky hash and you know versus pay
+ 
+
+ align:start position:0%
+beta punky hash and you know versus pay
+to punky instead of paid a script hash
+
+ align:start position:0%
+to punky instead of paid a script hash
+ 
+
+ align:start position:0%
+to punky instead of paid a script hash
+you could put the whole script in an
+
+ align:start position:0%
+you could put the whole script in an
+ 
+
+ align:start position:0%
+you could put the whole script in an
+output like a multi-city you could just
+
+ align:start position:0%
+output like a multi-city you could just
+ 
+
+ align:start position:0%
+output like a multi-city you could just
+have all three of your keys in your
+
+ align:start position:0%
+have all three of your keys in your
+ 
+
+ align:start position:0%
+have all three of your keys in your
+output script and that would save space
+
+ align:start position:0%
+output script and that would save space
+ 
+
+ align:start position:0%
+output script and that would save space
+over all your output is 20 bytes and
+
+ align:start position:0%
+over all your output is 20 bytes and
+ 
+
+ align:start position:0%
+over all your output is 20 bytes and
+then you reveal your whole hundred byte
+
+ align:start position:0%
+then you reveal your whole hundred byte
+ 
+
+ align:start position:0%
+then you reveal your whole hundred byte
+script so you save those 20 bytes same
+
+ align:start position:0%
+script so you save those 20 bytes same
+ 
+
+ align:start position:0%
+script so you save those 20 bytes same
+same amount but proportionally less time
+
+ align:start position:0%
+same amount but proportionally less time
+ 
+
+ align:start position:0%
+same amount but proportionally less time
+but it's you know it is some space
+
+ align:start position:0%
+but it's you know it is some space
+ 
+
+ align:start position:0%
+but it's you know it is some space
+savings overall but it's better to keep
+
+ align:start position:0%
+savings overall but it's better to keep
+ 
+
+ align:start position:0%
+savings overall but it's better to keep
+the output spot size small for you is if
+
+ align:start position:0%
+the output spot size small for you is if
+ 
+
+ align:start position:0%
+the output spot size small for you is if
+you do this does it actually work so it
+
+ align:start position:0%
+you do this does it actually work so it
+ 
+
+ align:start position:0%
+you do this does it actually work so it
+might not properly
+
+ align:start position:0%
+might not properly
+ 
+
+ align:start position:0%
+might not properly
+yeah so so it don't I wouldn't recommend
+
+ align:start position:0%
+yeah so so it don't I wouldn't recommend
+ 
+
+ align:start position:0%
+yeah so so it don't I wouldn't recommend
+this it probably will not really work
+
+ align:start position:0%
+this it probably will not really work
+ 
+
+ align:start position:0%
+this it probably will not really work
+maybe eventually it'll get confirmed if
+
+ align:start position:0%
+maybe eventually it'll get confirmed if
+ 
+
+ align:start position:0%
+maybe eventually it'll get confirmed if
+you find people to confirm it for you
+
+ align:start position:0%
+you find people to confirm it for you
+ 
+
+ align:start position:0%
+you find people to confirm it for you
+but most nodes will ignore these kinds
+
+ align:start position:0%
+but most nodes will ignore these kinds
+ 
+
+ align:start position:0%
+but most nodes will ignore these kinds
+of things okay so the question for today
+
+ align:start position:0%
+of things okay so the question for today
+ 
+
+ align:start position:0%
+of things okay so the question for today
+what if we want really really big
+
+ align:start position:0%
+what if we want really really big
+ 
+
+ align:start position:0%
+what if we want really really big
+scripts so two and three multi-sig is
+
+ align:start position:0%
+scripts so two and three multi-sig is
+ 
+
+ align:start position:0%
+scripts so two and three multi-sig is
+cool we can just show all three keys and
+
+ align:start position:0%
+cool we can just show all three keys and
+ 
+
+ align:start position:0%
+cool we can just show all three keys and
+there's 33 bytes of data that don't
+
+ align:start position:0%
+there's 33 bytes of data that don't
+ 
+
+ align:start position:0%
+there's 33 bytes of data that don't
+really get used right if you're signing
+
+ align:start position:0%
+really get used right if you're signing
+ 
+
+ align:start position:0%
+really get used right if you're signing
+with two of the three keys well that
+
+ align:start position:0%
+with two of the three keys well that
+ 
+
+ align:start position:0%
+with two of the three keys well that
+means one of the keys never got used it
+
+ align:start position:0%
+means one of the keys never got used it
+ 
+
+ align:start position:0%
+means one of the keys never got used it
+was sort of there and pointless for
+
+ align:start position:0%
+was sort of there and pointless for
+ 
+
+ align:start position:0%
+was sort of there and pointless for
+whatever it's 33 bytes so what if you
+
+ align:start position:0%
+whatever it's 33 bytes so what if you
+ 
+
+ align:start position:0%
+whatever it's 33 bytes so what if you
+want to do like 2 of 50 multi-sig so
+
+ align:start position:0%
+want to do like 2 of 50 multi-sig so
+ 
+
+ align:start position:0%
+want to do like 2 of 50 multi-sig so
+here's 50 different keys any two of
+
+ align:start position:0%
+here's 50 different keys any two of
+ 
+
+ align:start position:0%
+here's 50 different keys any two of
+these people can sign maybe you're in a
+
+ align:start position:0%
+these people can sign maybe you're in a
+ 
+
+ align:start position:0%
+these people can sign maybe you're in a
+company there's 50 employees and the
+
+ align:start position:0%
+company there's 50 employees and the
+ 
+
+ align:start position:0%
+company there's 50 employees and the
+policy is that okay any of these two
+
+ align:start position:0%
+policy is that okay any of these two
+ 
+
+ align:start position:0%
+policy is that okay any of these two
+people can use the coins for this like
+
+ align:start position:0%
+people can use the coins for this like
+ 
+
+ align:start position:0%
+people can use the coins for this like
+you know spending to buy lunch or
+
+ align:start position:0%
+you know spending to buy lunch or
+ 
+
+ align:start position:0%
+you know spending to buy lunch or
+whatever so how would you do to a 50
+
+ align:start position:0%
+whatever so how would you do to a 50
+ 
+
+ align:start position:0%
+whatever so how would you do to a 50
+moles sake
+
+ align:start position:0%
+moles sake
+ 
+
+ align:start position:0%
+moles sake
+any ideas okay you commit and only
+
+ align:start position:0%
+any ideas okay you commit and only
+ 
+
+ align:start position:0%
+any ideas okay you commit and only
+reveal part of a commitment so the cause
+
+ align:start position:0%
+reveal part of a commitment so the cause
+ 
+
+ align:start position:0%
+reveal part of a commitment so the cause
+of in solution to all of luck change
+
+ align:start position:0%
+of in solution to all of luck change
+ 
+
+ align:start position:0%
+of in solution to all of luck change
+problems Merkel trees right that's sort
+
+ align:start position:0%
+problems Merkel trees right that's sort
+ 
+
+ align:start position:0%
+problems Merkel trees right that's sort
+of the solution for all throw a Merkel
+
+ align:start position:0%
+of the solution for all throw a Merkel
+ 
+
+ align:start position:0%
+of the solution for all throw a Merkel
+tree on it which is sort of actually
+
+ align:start position:0%
+tree on it which is sort of actually
+ 
+
+ align:start position:0%
+tree on it which is sort of actually
+what I'm working on now for another
+
+ align:start position:0%
+what I'm working on now for another
+ 
+
+ align:start position:0%
+what I'm working on now for another
+things so yeah you commit to some kind
+
+ align:start position:0%
+things so yeah you commit to some kind
+ 
+
+ align:start position:0%
+things so yeah you commit to some kind
+of route and then you reveal only part
+
+ align:start position:0%
+of route and then you reveal only part
+ 
+
+ align:start position:0%
+of route and then you reveal only part
+of what you've committed to so the idea
+
+ align:start position:0%
+of what you've committed to so the idea
+ 
+
+ align:start position:0%
+of what you've committed to so the idea
+which is from some there's debate about
+
+ align:start position:0%
+which is from some there's debate about
+ 
+
+ align:start position:0%
+which is from some there's debate about
+who came up with this stuff right masked
+
+ align:start position:0%
+who came up with this stuff right masked
+ 
+
+ align:start position:0%
+who came up with this stuff right masked
+like Peter wool was into it but then
+
+ align:start position:0%
+like Peter wool was into it but then
+ 
+
+ align:start position:0%
+like Peter wool was into it but then
+someone else said they wrote a paper
+
+ align:start position:0%
+someone else said they wrote a paper
+ 
+
+ align:start position:0%
+someone else said they wrote a paper
+about it I don't know it was like 2013
+
+ align:start position:0%
+about it I don't know it was like 2013
+ 
+
+ align:start position:0%
+about it I don't know it was like 2013
+2014 the idea the original idea was make
+
+ align:start position:0%
+2014 the idea the original idea was make
+ 
+
+ align:start position:0%
+2014 the idea the original idea was make
+a Merck alized
+
+ align:start position:0%
+a Merck alized
+ 
+
+ align:start position:0%
+a Merck alized
+abstract abstract syntax tree so if you
+
+ align:start position:0%
+abstract abstract syntax tree so if you
+ 
+
+ align:start position:0%
+abstract abstract syntax tree so if you
+have done any like programming language
+
+ align:start position:0%
+have done any like programming language
+ 
+
+ align:start position:0%
+have done any like programming language
+courses
+
+ align:start position:0%
+courses
+ 
+
+ align:start position:0%
+courses
+you probably recognize the term Maps the
+
+ align:start position:0%
+you probably recognize the term Maps the
+ 
+
+ align:start position:0%
+you probably recognize the term Maps the
+abstract syntax tree asked which is sort
+
+ align:start position:0%
+abstract syntax tree asked which is sort
+ 
+
+ align:start position:0%
+abstract syntax tree asked which is sort
+of how compilers work they make this
+
+ align:start position:0%
+of how compilers work they make this
+ 
+
+ align:start position:0%
+of how compilers work they make this
+tree so the idea is okay we'll make
+
+ align:start position:0%
+tree so the idea is okay we'll make
+ 
+
+ align:start position:0%
+tree so the idea is okay we'll make
+every node in that tree like a merkel
+
+ align:start position:0%
+every node in that tree like a merkel
+ 
+
+ align:start position:0%
+every node in that tree like a merkel
+root so every single opcode can be
+
+ align:start position:0%
+root so every single opcode can be
+ 
+
+ align:start position:0%
+root so every single opcode can be
+revealed and be like swapped out and
+
+ align:start position:0%
+revealed and be like swapped out and
+ 
+
+ align:start position:0%
+revealed and be like swapped out and
+it's like super crazy that's
+
+ align:start position:0%
+it's like super crazy that's
+ 
+
+ align:start position:0%
+it's like super crazy that's
+sort of overkill so that was part of the
+
+ align:start position:0%
+sort of overkill so that was part of the
+ 
+
+ align:start position:0%
+sort of overkill so that was part of the
+initial idea and paper but a much
+
+ align:start position:0%
+initial idea and paper but a much
+ 
+
+ align:start position:0%
+initial idea and paper but a much
+simpler way the reason about it and
+
+ align:start position:0%
+simpler way the reason about it and
+ 
+
+ align:start position:0%
+simpler way the reason about it and
+program it would just be okay something
+
+ align:start position:0%
+program it would just be okay something
+ 
+
+ align:start position:0%
+program it would just be okay something
+like pay to script Merkel Ruth where I
+
+ align:start position:0%
+like pay to script Merkel Ruth where I
+ 
+
+ align:start position:0%
+like pay to script Merkel Ruth where I
+in my output script I have a route and
+
+ align:start position:0%
+in my output script I have a route and
+ 
+
+ align:start position:0%
+in my output script I have a route and
+then I reveal that there is a script
+
+ align:start position:0%
+then I reveal that there is a script
+ 
+
+ align:start position:0%
+then I reveal that there is a script
+that goes into that route and then I
+
+ align:start position:0%
+that goes into that route and then I
+ 
+
+ align:start position:0%
+that goes into that route and then I
+execute that script so for example I
+
+ align:start position:0%
+execute that script so for example I
+ 
+
+ align:start position:0%
+execute that script so for example I
+make four different scripts so this
+
+ align:start position:0%
+make four different scripts so this
+ 
+
+ align:start position:0%
+make four different scripts so this
+would be say - wait no anyway it's just
+
+ align:start position:0%
+would be say - wait no anyway it's just
+ 
+
+ align:start position:0%
+would be say - wait no anyway it's just
+for staff a different scripts there's no
+
+ align:start position:0%
+for staff a different scripts there's no
+ 
+
+ align:start position:0%
+for staff a different scripts there's no
+to choose and that results in four right
+
+ align:start position:0%
+to choose and that results in four right
+ 
+
+ align:start position:0%
+to choose and that results in four right
+but you know this is Allison Bob this is
+
+ align:start position:0%
+but you know this is Allison Bob this is
+ 
+
+ align:start position:0%
+but you know this is Allison Bob this is
+Bob Carol this is Carolyn Dave this is
+
+ align:start position:0%
+Bob Carol this is Carolyn Dave this is
+ 
+
+ align:start position:0%
+Bob Carol this is Carolyn Dave this is
+David or something and any of these any
+
+ align:start position:0%
+David or something and any of these any
+ 
+
+ align:start position:0%
+David or something and any of these any
+of these two people but you know four
+
+ align:start position:0%
+of these two people but you know four
+ 
+
+ align:start position:0%
+of these two people but you know four
+different groups can sign and then this
+
+ align:start position:0%
+different groups can sign and then this
+ 
+
+ align:start position:0%
+different groups can sign and then this
+is what you actually put in your output
+
+ align:start position:0%
+is what you actually put in your output
+ 
+
+ align:start position:0%
+is what you actually put in your output
+script and then when you want to spend
+
+ align:start position:0%
+script and then when you want to spend
+ 
+
+ align:start position:0%
+script and then when you want to spend
+you say okay I'm going to provide a
+
+ align:start position:0%
+you say okay I'm going to provide a
+ 
+
+ align:start position:0%
+you say okay I'm going to provide a
+proof so to spend reveal which I'm
+
+ align:start position:0%
+proof so to spend reveal which I'm
+ 
+
+ align:start position:0%
+proof so to spend reveal which I'm
+spending so for example I'm spending
+
+ align:start position:0%
+spending so for example I'm spending
+ 
+
+ align:start position:0%
+spending so for example I'm spending
+using script three and then I reveal a
+
+ align:start position:0%
+using script three and then I reveal a
+ 
+
+ align:start position:0%
+using script three and then I reveal a
+path to the route which would be I
+
+ align:start position:0%
+path to the route which would be I
+ 
+
+ align:start position:0%
+path to the route which would be I
+reveal four and this and then you
+
+ align:start position:0%
+reveal four and this and then you
+ 
+
+ align:start position:0%
+reveal four and this and then you
+compute you say okay hash to these two
+
+ align:start position:0%
+compute you say okay hash to these two
+ 
+
+ align:start position:0%
+compute you say okay hash to these two
+things together get that hash these two
+
+ align:start position:0%
+things together get that hash these two
+ 
+
+ align:start position:0%
+things together get that hash these two
+things together you get that and confirm
+
+ align:start position:0%
+things together you get that and confirm
+ 
+
+ align:start position:0%
+things together you get that and confirm
+that the result is equal to what was in
+
+ align:start position:0%
+that the result is equal to what was in
+ 
+
+ align:start position:0%
+that the result is equal to what was in
+the output script and if it is okay
+
+ align:start position:0%
+the output script and if it is okay
+ 
+
+ align:start position:0%
+the output script and if it is okay
+you've provided a valid proof a valid
+
+ align:start position:0%
+you've provided a valid proof a valid
+ 
+
+ align:start position:0%
+you've provided a valid proof a valid
+inclusion proof that script three was
+
+ align:start position:0%
+inclusion proof that script three was
+ 
+
+ align:start position:0%
+inclusion proof that script three was
+inside this root what's kind of cool in
+
+ align:start position:0%
+inside this root what's kind of cool in
+ 
+
+ align:start position:0%
+inside this root what's kind of cool in
+this case you do not need the binary
+
+ align:start position:0%
+this case you do not need the binary
+ 
+
+ align:start position:0%
+this case you do not need the binary
+tree to be perfect you can have
+
+ align:start position:0%
+tree to be perfect you can have
+ 
+
+ align:start position:0%
+tree to be perfect you can have
+different heights because you're not
+
+ align:start position:0%
+different heights because you're not
+ 
+
+ align:start position:0%
+different heights because you're not
+committing to the height of the tree
+
+ align:start position:0%
+committing to the height of the tree
+ 
+
+ align:start position:0%
+committing to the height of the tree
+when you're sending to it so you could
+
+ align:start position:0%
+when you're sending to it so you could
+ 
+
+ align:start position:0%
+when you're sending to it so you could
+have the you know the default case could
+
+ align:start position:0%
+have the you know the default case could
+ 
+
+ align:start position:0%
+have the you know the default case could
+be here and then a really big tree that
+
+ align:start position:0%
+be here and then a really big tree that
+ 
+
+ align:start position:0%
+be here and then a really big tree that
+goes down a lot over here so these in
+
+ align:start position:0%
+goes down a lot over here so these in
+ 
+
+ align:start position:0%
+goes down a lot over here so these in
+most cases yeah well most cases it's
+
+ align:start position:0%
+most cases yeah well most cases it's
+ 
+
+ align:start position:0%
+most cases yeah well most cases it's
+gonna be Alice and Bob signing and then
+
+ align:start position:0%
+gonna be Alice and Bob signing and then
+ 
+
+ align:start position:0%
+gonna be Alice and Bob signing and then
+Carol and Dave and Edna and whatever are
+
+ align:start position:0%
+Carol and Dave and Edna and whatever are
+ 
+
+ align:start position:0%
+Carol and Dave and Edna and whatever are
+unlikely so I'm gonna put it I'm gonna
+
+ align:start position:0%
+unlikely so I'm gonna put it I'm gonna
+ 
+
+ align:start position:0%
+unlikely so I'm gonna put it I'm gonna
+put Allison Bob here
+
+ align:start position:0%
+put Allison Bob here
+ 
+
+ align:start position:0%
+put Allison Bob here
+and then have the tree sort of
+
+ align:start position:0%
+and then have the tree sort of
+ 
+
+ align:start position:0%
+and then have the tree sort of
+asymmetrically getting longer over here
+
+ align:start position:0%
+asymmetrically getting longer over here
+ 
+
+ align:start position:0%
+asymmetrically getting longer over here
+so that when Alice and Bob sign they can
+
+ align:start position:0%
+so that when Alice and Bob sign they can
+ 
+
+ align:start position:0%
+so that when Alice and Bob sign they can
+just reveal this and then when the other
+
+ align:start position:0%
+just reveal this and then when the other
+ 
+
+ align:start position:0%
+just reveal this and then when the other
+people sign they're gonna have to reveal
+
+ align:start position:0%
+people sign they're gonna have to reveal
+ 
+
+ align:start position:0%
+people sign they're gonna have to reveal
+this and this and then i optimize my
+
+ align:start position:0%
+this and this and then i optimize my
+ 
+
+ align:start position:0%
+this and this and then i optimize my
+myspace for the most likely case so
+
+ align:start position:0%
+myspace for the most likely case so
+ 
+
+ align:start position:0%
+myspace for the most likely case so
+that's kind of cool what else so yeah
+
+ align:start position:0%
+that's kind of cool what else so yeah
+ 
+
+ align:start position:0%
+that's kind of cool what else so yeah
+however there are a probable game
+
+ align:start position:0%
+however there are a probable game
+ 
+
+ align:start position:0%
+however there are a probable game
+there's a bunch of problems one okay two
+
+ align:start position:0%
+there's a bunch of problems one okay two
+ 
+
+ align:start position:0%
+there's a bunch of problems one okay two
+of fifty is cool but what about so in
+
+ align:start position:0%
+of fifty is cool but what about so in
+ 
+
+ align:start position:0%
+of fifty is cool but what about so in
+the case of two of fifty let's just look
+
+ align:start position:0%
+the case of two of fifty let's just look
+ 
+
+ align:start position:0%
+the case of two of fifty let's just look
+through it you know fifty choose two I
+
+ align:start position:0%
+through it you know fifty choose two I
+ 
+
+ align:start position:0%
+through it you know fifty choose two I
+couldn't make the little numbers and
+
+ align:start position:0%
+couldn't make the little numbers and
+ 
+
+ align:start position:0%
+couldn't make the little numbers and
+parentheses the right way so that's a
+
+ align:start position:0%
+parentheses the right way so that's a
+ 
+
+ align:start position:0%
+parentheses the right way so that's a
+thousand two hundred twenty five
+
+ align:start position:0%
+thousand two hundred twenty five
+ 
+
+ align:start position:0%
+thousand two hundred twenty five
+different scripts and that would result
+
+ align:start position:0%
+different scripts and that would result
+ 
+
+ align:start position:0%
+different scripts and that would result
+in it if you do a regular whatever
+
+ align:start position:0%
+in it if you do a regular whatever
+ 
+
+ align:start position:0%
+in it if you do a regular whatever
+regular binary tree balanced I don't I
+
+ align:start position:0%
+regular binary tree balanced I don't I
+ 
+
+ align:start position:0%
+regular binary tree balanced I don't I
+forget all the words you get a tree
+
+ align:start position:0%
+forget all the words you get a tree
+ 
+
+ align:start position:0%
+forget all the words you get a tree
+height of 11 which is like actually kind
+
+ align:start position:0%
+height of 11 which is like actually kind
+ 
+
+ align:start position:0%
+height of 11 which is like actually kind
+of it's like ah so close right if it was
+
+ align:start position:0%
+of it's like ah so close right if it was
+ 
+
+ align:start position:0%
+of it's like ah so close right if it was
+1024 of you ten but a little over and
+
+ align:start position:0%
+1024 of you ten but a little over and
+ 
+
+ align:start position:0%
+1024 of you ten but a little over and
+actually since it doesn't have to be
+
+ align:start position:0%
+actually since it doesn't have to be
+ 
+
+ align:start position:0%
+actually since it doesn't have to be
+symmetric you can get like three high
+
+ align:start position:0%
+symmetric you can get like three high
+ 
+
+ align:start position:0%
+symmetric you can get like three high
+ten for most leaves and then eleven for
+
+ align:start position:0%
+ten for most leaves and then eleven for
+ 
+
+ align:start position:0%
+ten for most leaves and then eleven for
+some of them anyway so your proof size
+
+ align:start position:0%
+some of them anyway so your proof size
+ 
+
+ align:start position:0%
+some of them anyway so your proof size
+is gonna be 352 bytes which is you know
+
+ align:start position:0%
+is gonna be 352 bytes which is you know
+ 
+
+ align:start position:0%
+is gonna be 352 bytes which is you know
+okay and if you didn't use math you can
+
+ align:start position:0%
+okay and if you didn't use math you can
+ 
+
+ align:start position:0%
+okay and if you didn't use math you can
+say well I'm just gonna have a pay to
+
+ align:start position:0%
+say well I'm just gonna have a pay to
+ 
+
+ align:start position:0%
+say well I'm just gonna have a pay to
+script hash and the script is just gonna
+
+ align:start position:0%
+script hash and the script is just gonna
+ 
+
+ align:start position:0%
+script hash and the script is just gonna
+show all 50 keys and have you know opt
+
+ align:start position:0%
+show all 50 keys and have you know opt
+ 
+
+ align:start position:0%
+show all 50 keys and have you know opt
+to all 50 keys op three and that would
+
+ align:start position:0%
+to all 50 keys op three and that would
+ 
+
+ align:start position:0%
+to all 50 keys op three and that would
+be about well plus three or something
+
+ align:start position:0%
+be about well plus three or something
+ 
+
+ align:start position:0%
+be about well plus three or something
+but 1650 bytes so masked is an
+
+ align:start position:0%
+but 1650 bytes so masked is an
+ 
+
+ align:start position:0%
+but 1650 bytes so masked is an
+improvement and it's sort of like hey
+
+ align:start position:0%
+improvement and it's sort of like hey
+ 
+
+ align:start position:0%
+improvement and it's sort of like hey
+I'm doing log n write for all the
+
+ align:start position:0%
+I'm doing log n write for all the
+ 
+
+ align:start position:0%
+I'm doing log n write for all the
+different scripts I have log in if I
+
+ align:start position:0%
+different scripts I have log in if I
+ 
+
+ align:start position:0%
+different scripts I have log in if I
+actually committed to all the thousand
+
+ align:start position:0%
+actually committed to all the thousand
+ 
+
+ align:start position:0%
+actually committed to all the thousand
+two hundred twenty-five scripts with
+
+ align:start position:0%
+two hundred twenty-five scripts with
+ 
+
+ align:start position:0%
+two hundred twenty-five scripts with
+each of the two keys it'd be much bigger
+
+ align:start position:0%
+each of the two keys it'd be much bigger
+ 
+
+ align:start position:0%
+each of the two keys it'd be much bigger
+but I don't actually have to because
+
+ align:start position:0%
+but I don't actually have to because
+ 
+
+ align:start position:0%
+but I don't actually have to because
+I've got this whole 50 choose two in
+
+ align:start position:0%
+I've got this whole 50 choose two in
+ 
+
+ align:start position:0%
+I've got this whole 50 choose two in
+here so I've got two things right I've
+
+ align:start position:0%
+here so I've got two things right I've
+ 
+
+ align:start position:0%
+here so I've got two things right I've
+got this combinatorial thing and then
+
+ align:start position:0%
+got this combinatorial thing and then
+ 
+
+ align:start position:0%
+got this combinatorial thing and then
+this log thing and in balance it's like
+
+ align:start position:0%
+this log thing and in balance it's like
+ 
+
+ align:start position:0%
+this log thing and in balance it's like
+okay man like better but not actually
+
+ align:start position:0%
+okay man like better but not actually
+ 
+
+ align:start position:0%
+okay man like better but not actually
+that awesome right you're going from
+
+ align:start position:0%
+that awesome right you're going from
+ 
+
+ align:start position:0%
+that awesome right you're going from
+thousand 1.6 K to 350 bytes it gets
+
+ align:start position:0%
+thousand 1.6 K to 350 bytes it gets
+ 
+
+ align:start position:0%
+thousand 1.6 K to 350 bytes it gets
+worse let's say I want to do 25 of 50
+
+ align:start position:0%
+worse let's say I want to do 25 of 50
+ 
+
+ align:start position:0%
+worse let's say I want to do 25 of 50
+well that's 50 choose 25 which is around
+
+ align:start position:0%
+well that's 50 choose 25 which is around
+ 
+
+ align:start position:0%
+well that's 50 choose 25 which is around
+100 trillion different combinations the
+
+ align:start position:0%
+100 trillion different combinations the
+ 
+
+ align:start position:0%
+100 trillion different combinations the
+the tree height would not be 47 the
+
+ align:start position:0%
+the tree height would not be 47 the
+ 
+
+ align:start position:0%
+the tree height would not be 47 the
+proof size is gonna be wait did
+
+ align:start position:0%
+proof size is gonna be wait did
+ 
+
+ align:start position:0%
+proof size is gonna be wait did
+do that wrong hold on I think I'm I was
+
+ align:start position:0%
+do that wrong hold on I think I'm I was
+ 
+
+ align:start position:0%
+do that wrong hold on I think I'm I was
+47 by 32 is one 504 okay sorry I just
+
+ align:start position:0%
+47 by 32 is one 504 okay sorry I just
+ 
+
+ align:start position:0%
+47 by 32 is one 504 okay sorry I just
+put 20 I love for some reason I had 22
+
+ align:start position:0%
+put 20 I love for some reason I had 22
+ 
+
+ align:start position:0%
+put 20 I love for some reason I had 22
+there sorry I'll fix that but that is
+
+ align:start position:0%
+there sorry I'll fix that but that is
+ 
+
+ align:start position:0%
+there sorry I'll fix that but that is
+correct yeah one 504 so 1.5 K whereas
+
+ align:start position:0%
+correct yeah one 504 so 1.5 K whereas
+ 
+
+ align:start position:0%
+correct yeah one 504 so 1.5 K whereas
+the raw would still be 1,650 these are
+
+ align:start position:0%
+the raw would still be 1,650 these are
+ 
+
+ align:start position:0%
+the raw would still be 1,650 these are
+about the same this is not a great space
+
+ align:start position:0%
+about the same this is not a great space
+ 
+
+ align:start position:0%
+about the same this is not a great space
+savings right your your proofs are huge
+
+ align:start position:0%
+savings right your your proofs are huge
+ 
+
+ align:start position:0%
+savings right your your proofs are huge
+in fact I would say it's not only not
+
+ align:start position:0%
+in fact I would say it's not only not
+ 
+
+ align:start position:0%
+in fact I would say it's not only not
+much better it's worse right you're
+
+ align:start position:0%
+much better it's worse right you're
+ 
+
+ align:start position:0%
+much better it's worse right you're
+gonna have to compute two hundred
+
+ align:start position:0%
+gonna have to compute two hundred
+ 
+
+ align:start position:0%
+gonna have to compute two hundred
+trillion hashes in order to compute that
+
+ align:start position:0%
+trillion hashes in order to compute that
+ 
+
+ align:start position:0%
+trillion hashes in order to compute that
+root as the person creating the output
+
+ align:start position:0%
+root as the person creating the output
+ 
+
+ align:start position:0%
+root as the person creating the output
+script to verify inclusion you have to
+
+ align:start position:0%
+script to verify inclusion you have to
+ 
+
+ align:start position:0%
+script to verify inclusion you have to
+compute 47 hashes which is fine but 200
+
+ align:start position:0%
+compute 47 hashes which is fine but 200
+ 
+
+ align:start position:0%
+compute 47 hashes which is fine but 200
+rolling hashes is doable but that's
+
+ align:start position:0%
+rolling hashes is doable but that's
+ 
+
+ align:start position:0%
+rolling hashes is doable but that's
+gonna take a while and that's annoying
+
+ align:start position:0%
+gonna take a while and that's annoying
+ 
+
+ align:start position:0%
+gonna take a while and that's annoying
+and yeah how long hours days I don't
+
+ align:start position:0%
+and yeah how long hours days I don't
+ 
+
+ align:start position:0%
+and yeah how long hours days I don't
+know doable but not fun so mass doesn't
+
+ align:start position:0%
+know doable but not fun so mass doesn't
+ 
+
+ align:start position:0%
+know doable but not fun so mass doesn't
+really get you necessarily what you want
+
+ align:start position:0%
+really get you necessarily what you want
+ 
+
+ align:start position:0%
+really get you necessarily what you want
+here although this is kind of a silly
+
+ align:start position:0%
+here although this is kind of a silly
+ 
+
+ align:start position:0%
+here although this is kind of a silly
+case but none of the things really get
+
+ align:start position:0%
+case but none of the things really get
+ 
+
+ align:start position:0%
+case but none of the things really get
+you what you want here because of these
+
+ align:start position:0%
+you what you want here because of these
+ 
+
+ align:start position:0%
+you what you want here because of these
+sort of combinatorial problems okay any
+
+ align:start position:0%
+sort of combinatorial problems okay any
+ 
+
+ align:start position:0%
+sort of combinatorial problems okay any
+questions about or or questions or
+
+ align:start position:0%
+questions about or or questions or
+ 
+
+ align:start position:0%
+questions about or or questions or
+opposition's if I have screwed up some
+
+ align:start position:0%
+opposition's if I have screwed up some
+ 
+
+ align:start position:0%
+opposition's if I have screwed up some
+mess part of it is when you so compare
+
+ align:start position:0%
+mess part of it is when you so compare
+ 
+
+ align:start position:0%
+mess part of it is when you so compare
+these two if I show a tree height of 10
+
+ align:start position:0%
+these two if I show a tree height of 10
+ 
+
+ align:start position:0%
+these two if I show a tree height of 10
+or 11 huh that's weird there's like
+
+ align:start position:0%
+or 11 huh that's weird there's like
+ 
+
+ align:start position:0%
+or 11 huh that's weird there's like
+thousand different scripts around in
+
+ align:start position:0%
+thousand different scripts around in
+ 
+
+ align:start position:0%
+thousand different scripts around in
+this tree if I show a tree height of
+
+ align:start position:0%
+this tree if I show a tree height of
+ 
+
+ align:start position:0%
+this tree if I show a tree height of
+forty seven that's really weird someone
+
+ align:start position:0%
+forty seven that's really weird someone
+ 
+
+ align:start position:0%
+forty seven that's really weird someone
+either was just joking around and made
+
+ align:start position:0%
+either was just joking around and made
+ 
+
+ align:start position:0%
+either was just joking around and made
+this weird sparse tree with all these
+
+ align:start position:0%
+this weird sparse tree with all these
+ 
+
+ align:start position:0%
+this weird sparse tree with all these
+branches to just screw around and have a
+
+ align:start position:0%
+branches to just screw around and have a
+ 
+
+ align:start position:0%
+branches to just screw around and have a
+height of 47 or there's 200 trillion
+
+ align:start position:0%
+height of 47 or there's 200 trillion
+ 
+
+ align:start position:0%
+height of 47 or there's 200 trillion
+possible spending you know outcomes so
+
+ align:start position:0%
+possible spending you know outcomes so
+ 
+
+ align:start position:0%
+possible spending you know outcomes so
+it reveals information about the things
+
+ align:start position:0%
+it reveals information about the things
+ 
+
+ align:start position:0%
+it reveals information about the things
+that were not spent even though it
+
+ align:start position:0%
+that were not spent even though it
+ 
+
+ align:start position:0%
+that were not spent even though it
+doesn't reveal what the scripts were it
+
+ align:start position:0%
+doesn't reveal what the scripts were it
+ 
+
+ align:start position:0%
+doesn't reveal what the scripts were it
+to some extent reveals how many there
+
+ align:start position:0%
+to some extent reveals how many there
+ 
+
+ align:start position:0%
+to some extent reveals how many there
+were okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so even okay but still it is kind of
+
+ align:start position:0%
+so even okay but still it is kind of
+ 
+
+ align:start position:0%
+so even okay but still it is kind of
+useful right in the - of 50k
+
+ align:start position:0%
+useful right in the - of 50k
+ 
+
+ align:start position:0%
+useful right in the - of 50k
+yes this is better you know you have to
+
+ align:start position:0%
+yes this is better you know you have to
+ 
+
+ align:start position:0%
+yes this is better you know you have to
+compute a couple thousand something
+
+ align:start position:0%
+compute a couple thousand something
+ 
+
+ align:start position:0%
+compute a couple thousand something
+hashes no big deal
+
+ align:start position:0%
+hashes no big deal
+ 
+
+ align:start position:0%
+hashes no big deal
+you you reduce your size from one point
+
+ align:start position:0%
+you you reduce your size from one point
+ 
+
+ align:start position:0%
+you you reduce your size from one point
+6 K to 3 and 52 bytes that's a good deal
+
+ align:start position:0%
+6 K to 3 and 52 bytes that's a good deal
+ 
+
+ align:start position:0%
+6 K to 3 and 52 bytes that's a good deal
+here kind of not but this is also sort
+
+ align:start position:0%
+here kind of not but this is also sort
+ 
+
+ align:start position:0%
+here kind of not but this is also sort
+of a crazy there's other ways to address
+
+ align:start position:0%
+of a crazy there's other ways to address
+ 
+
+ align:start position:0%
+of a crazy there's other ways to address
+this but anyway it's pretty good there's
+
+ align:start position:0%
+this but anyway it's pretty good there's
+ 
+
+ align:start position:0%
+this but anyway it's pretty good there's
+there's sort of two or more than two
+
+ align:start position:0%
+there's sort of two or more than two
+ 
+
+ align:start position:0%
+there's sort of two or more than two
+different ways to implement this you
+
+ align:start position:0%
+different ways to implement this you
+ 
+
+ align:start position:0%
+different ways to implement this you
+could just say okay we're gonna have pay
+
+ align:start position:0%
+could just say okay we're gonna have pay
+ 
+
+ align:start position:0%
+could just say okay we're gonna have pay
+the script Merkel route where you have a
+
+ align:start position:0%
+the script Merkel route where you have a
+ 
+
+ align:start position:0%
+the script Merkel route where you have a
+template where it's like op op two or op
+
+ align:start position:0%
+template where it's like op op two or op
+ 
+
+ align:start position:0%
+template where it's like op op two or op
+of three or something and then some data
+
+ align:start position:0%
+of three or something and then some data
+ 
+
+ align:start position:0%
+of three or something and then some data
+and the idea is when you spend it you
+
+ align:start position:0%
+and the idea is when you spend it you
+ 
+
+ align:start position:0%
+and the idea is when you spend it you
+have to provide a proof and then the
+
+ align:start position:0%
+have to provide a proof and then the
+ 
+
+ align:start position:0%
+have to provide a proof and then the
+script itself and then you execute the
+
+ align:start position:0%
+script itself and then you execute the
+ 
+
+ align:start position:0%
+script itself and then you execute the
+script another way which is kind of cool
+
+ align:start position:0%
+script another way which is kind of cool
+ 
+
+ align:start position:0%
+script another way which is kind of cool
+and people were talking about it
+
+ align:start position:0%
+and people were talking about it
+ 
+
+ align:start position:0%
+and people were talking about it
+recently you have this called tail call
+
+ align:start position:0%
+recently you have this called tail call
+ 
+
+ align:start position:0%
+recently you have this called tail call
+recursion looking thing where the idea
+
+ align:start position:0%
+recursion looking thing where the idea
+ 
+
+ align:start position:0%
+recursion looking thing where the idea
+is if you evaluate your script and then
+
+ align:start position:0%
+is if you evaluate your script and then
+ 
+
+ align:start position:0%
+is if you evaluate your script and then
+there's two items left on the stack at
+
+ align:start position:0%
+there's two items left on the stack at
+ 
+
+ align:start position:0%
+there's two items left on the stack at
+the end what you say is okay the
+
+ align:start position:0%
+the end what you say is okay the
+ 
+
+ align:start position:0%
+the end what you say is okay the
+whichever is bottom or top one of these
+
+ align:start position:0%
+whichever is bottom or top one of these
+ 
+
+ align:start position:0%
+whichever is bottom or top one of these
+items the bottom one is a you know
+
+ align:start position:0%
+items the bottom one is a you know
+ 
+
+ align:start position:0%
+items the bottom one is a you know
+merkel root and then the other odd item
+
+ align:start position:0%
+merkel root and then the other odd item
+ 
+
+ align:start position:0%
+merkel root and then the other odd item
+on the stack is the proof and arguments
+
+ align:start position:0%
+on the stack is the proof and arguments
+ 
+
+ align:start position:0%
+on the stack is the proof and arguments
+you know another script so you can sort
+
+ align:start position:0%
+you know another script so you can sort
+ 
+
+ align:start position:0%
+you know another script so you can sort
+of recursively say okay well i went down
+
+ align:start position:0%
+of recursively say okay well i went down
+ 
+
+ align:start position:0%
+of recursively say okay well i went down
+into this script with this proof and
+
+ align:start position:0%
+into this script with this proof and
+ 
+
+ align:start position:0%
+into this script with this proof and
+then executed it and then things were
+
+ align:start position:0%
+then executed it and then things were
+ 
+
+ align:start position:0%
+then executed it and then things were
+left on the stack and it was another
+
+ align:start position:0%
+left on the stack and it was another
+ 
+
+ align:start position:0%
+left on the stack and it was another
+proof for another merkel root um so
+
+ align:start position:0%
+proof for another merkel root um so
+ 
+
+ align:start position:0%
+proof for another merkel root um so
+that's kind of cool
+
+ align:start position:0%
+that's kind of cool
+ 
+
+ align:start position:0%
+that's kind of cool
+you can make all sorts of crazy things
+
+ align:start position:0%
+you can make all sorts of crazy things
+ 
+
+ align:start position:0%
+you can make all sorts of crazy things
+with that i don't know how useful
+
+ align:start position:0%
+with that i don't know how useful
+ 
+
+ align:start position:0%
+with that i don't know how useful
+recursion recursion is in this case but
+
+ align:start position:0%
+recursion recursion is in this case but
+ 
+
+ align:start position:0%
+recursion recursion is in this case but
+there could be cases you're already in a
+
+ align:start position:0%
+there could be cases you're already in a
+ 
+
+ align:start position:0%
+there could be cases you're already in a
+binary tree so my personal thing is like
+
+ align:start position:0%
+binary tree so my personal thing is like
+ 
+
+ align:start position:0%
+binary tree so my personal thing is like
+why not just keep it simple and pay to a
+
+ align:start position:0%
+why not just keep it simple and pay to a
+ 
+
+ align:start position:0%
+why not just keep it simple and pay to a
+script merkel root but there's people
+
+ align:start position:0%
+script merkel root but there's people
+ 
+
+ align:start position:0%
+script merkel root but there's people
+who they think like no this should be
+
+ align:start position:0%
+who they think like no this should be
+ 
+
+ align:start position:0%
+who they think like no this should be
+more expressive like programming
+
+ align:start position:0%
+more expressive like programming
+ 
+
+ align:start position:0%
+more expressive like programming
+language e wise anyway so that's their
+
+ align:start position:0%
+language e wise anyway so that's their
+ 
+
+ align:start position:0%
+language e wise anyway so that's their
+state of mess mast has code there's a
+
+ align:start position:0%
+state of mess mast has code there's a
+ 
+
+ align:start position:0%
+state of mess mast has code there's a
+pull request and bit right yeah so
+
+ align:start position:0%
+pull request and bit right yeah so
+ 
+
+ align:start position:0%
+pull request and bit right yeah so
+there's some people who are really in
+
+ align:start position:0%
+there's some people who are really in
+ 
+
+ align:start position:0%
+there's some people who are really in
+the mast and like Bitcoin let's make a
+
+ align:start position:0%
+the mast and like Bitcoin let's make a
+ 
+
+ align:start position:0%
+the mast and like Bitcoin let's make a
+soft work and there's also people we're
+
+ align:start position:0%
+soft work and there's also people we're
+ 
+
+ align:start position:0%
+soft work and there's also people we're
+not as enthusiastic and so it's like no
+
+ align:start position:0%
+not as enthusiastic and so it's like no
+ 
+
+ align:start position:0%
+not as enthusiastic and so it's like no
+one's like opposed to it like this is a
+
+ align:start position:0%
+one's like opposed to it like this is a
+ 
+
+ align:start position:0%
+one's like opposed to it like this is a
+bad idea this will break Bitcoin but
+
+ align:start position:0%
+bad idea this will break Bitcoin but
+ 
+
+ align:start position:0%
+bad idea this will break Bitcoin but
+there's dead
+
+ align:start position:0%
+there's dead
+ 
+
+ align:start position:0%
+there's dead
+varying levels of like let's let's get
+
+ align:start position:0%
+varying levels of like let's let's get
+ 
+
+ align:start position:0%
+varying levels of like let's let's get
+this in you can do all these cool things
+
+ align:start position:0%
+this in you can do all these cool things
+ 
+
+ align:start position:0%
+this in you can do all these cool things
+versus and like is this really a
+
+ align:start position:0%
+versus and like is this really a
+ 
+
+ align:start position:0%
+versus and like is this really a
+priority is what are we gonna use with
+
+ align:start position:0%
+priority is what are we gonna use with
+ 
+
+ align:start position:0%
+priority is what are we gonna use with
+it kind of thing okay any questions
+
+ align:start position:0%
+it kind of thing okay any questions
+ 
+
+ align:start position:0%
+it kind of thing okay any questions
+about this I think we have yes
+
+ align:start position:0%
+about this I think we have yes
+ 
+
+ align:start position:0%
+about this I think we have yes
+quick break and then I'll do good off
+
+ align:start position:0%
+quick break and then I'll do good off
+ 
+
+ align:start position:0%
+quick break and then I'll do good off
+return which seems unconnected but I
+
+ align:start position:0%
+return which seems unconnected but I
+ 
+
+ align:start position:0%
+return which seems unconnected but I
+will show you how this connects to these
+
+ align:start position:0%
+will show you how this connects to these
+ 
+
+ align:start position:0%
+will show you how this connects to these
+issues we have
+
+ align:start position:0%
+issues we have
+ 
+
+ align:start position:0%
+issues we have
+okay so I've returned it was in the
+
+ align:start position:0%
+okay so I've returned it was in the
+ 
+
+ align:start position:0%
+okay so I've returned it was in the
+problem set you basically put this
+
+ align:start position:0%
+problem set you basically put this
+ 
+
+ align:start position:0%
+problem set you basically put this
+opcode in the front of your script and
+
+ align:start position:0%
+opcode in the front of your script and
+ 
+
+ align:start position:0%
+opcode in the front of your script and
+that Flags it as forever unspent able as
+
+ align:start position:0%
+that Flags it as forever unspent able as
+ 
+
+ align:start position:0%
+that Flags it as forever unspent able as
+an output so you put shouldn't put much
+
+ align:start position:0%
+an output so you put shouldn't put much
+ 
+
+ align:start position:0%
+an output so you put shouldn't put much
+money into these outputs because they
+
+ align:start position:0%
+money into these outputs because they
+ 
+
+ align:start position:0%
+money into these outputs because they
+are basically destroyed opera turn means
+
+ align:start position:0%
+are basically destroyed opera turn means
+ 
+
+ align:start position:0%
+are basically destroyed opera turn means
+you you know immediately returned from
+
+ align:start position:0%
+you you know immediately returned from
+ 
+
+ align:start position:0%
+you you know immediately returned from
+the the script evaluation and you return
+
+ align:start position:0%
+the the script evaluation and you return
+ 
+
+ align:start position:0%
+the the script evaluation and you return
+a false I think it used to be return
+
+ align:start position:0%
+a false I think it used to be return
+ 
+
+ align:start position:0%
+a false I think it used to be return
+whatever is on the top of the stack
+
+ align:start position:0%
+whatever is on the top of the stack
+ 
+
+ align:start position:0%
+whatever is on the top of the stack
+right which meant you could just spend
+
+ align:start position:0%
+right which meant you could just spend
+ 
+
+ align:start position:0%
+right which meant you could just spend
+anyone's money by using opportunity so
+
+ align:start position:0%
+anyone's money by using opportunity so
+ 
+
+ align:start position:0%
+anyone's money by using opportunity so
+they they they saw fork that to say no
+
+ align:start position:0%
+they they they saw fork that to say no
+ 
+
+ align:start position:0%
+they they they saw fork that to say no
+opera turn always fails instead of opera
+
+ align:start position:0%
+opera turn always fails instead of opera
+ 
+
+ align:start position:0%
+opera turn always fails instead of opera
+turn always tribute Lee succeeds which
+
+ align:start position:0%
+turn always tribute Lee succeeds which
+ 
+
+ align:start position:0%
+turn always tribute Lee succeeds which
+means you just put them up or turn to
+
+ align:start position:0%
+means you just put them up or turn to
+ 
+
+ align:start position:0%
+means you just put them up or turn to
+take anyways money so they figured that
+
+ align:start position:0%
+take anyways money so they figured that
+ 
+
+ align:start position:0%
+take anyways money so they figured that
+one out pretty quick so people use off
+
+ align:start position:0%
+one out pretty quick so people use off
+ 
+
+ align:start position:0%
+one out pretty quick so people use off
+return to put data into the blockchain
+
+ align:start position:0%
+return to put data into the blockchain
+ 
+
+ align:start position:0%
+return to put data into the blockchain
+why do people do this so it doesn't you
+
+ align:start position:0%
+why do people do this so it doesn't you
+ 
+
+ align:start position:0%
+why do people do this so it doesn't you
+know you can't spend it you can't do
+
+ align:start position:0%
+know you can't spend it you can't do
+ 
+
+ align:start position:0%
+know you can't spend it you can't do
+anything with this data but why do
+
+ align:start position:0%
+anything with this data but why do
+ 
+
+ align:start position:0%
+anything with this data but why do
+people do this
+
+ align:start position:0%
+people do this
+ 
+
+ align:start position:0%
+people do this
+it's kind of cool right to prove it's
+
+ align:start position:0%
+it's kind of cool right to prove it's
+ 
+
+ align:start position:0%
+it's kind of cool right to prove it's
+there right they just you want to put
+
+ align:start position:0%
+there right they just you want to put
+ 
+
+ align:start position:0%
+there right they just you want to put
+some data in and you just want to say
+
+ align:start position:0%
+some data in and you just want to say
+ 
+
+ align:start position:0%
+some data in and you just want to say
+hey I thought of this first I'm making a
+
+ align:start position:0%
+hey I thought of this first I'm making a
+ 
+
+ align:start position:0%
+hey I thought of this first I'm making a
+patent or I whatever you put data people
+
+ align:start position:0%
+patent or I whatever you put data people
+ 
+
+ align:start position:0%
+patent or I whatever you put data people
+people use a lot of opera turn people
+
+ align:start position:0%
+people use a lot of opera turn people
+ 
+
+ align:start position:0%
+people use a lot of opera turn people
+what was it like 10 percent yeah so
+
+ align:start position:0%
+what was it like 10 percent yeah so
+ 
+
+ align:start position:0%
+what was it like 10 percent yeah so
+that's
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+[Music]
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so that's a lot of data people using it
+
+ align:start position:0%
+so that's a lot of data people using it
+ 
+
+ align:start position:0%
+so that's a lot of data people using it
+um there's a better way okay so what if
+
+ align:start position:0%
+um there's a better way okay so what if
+ 
+
+ align:start position:0%
+um there's a better way okay so what if
+you wanted to do a zero byte opera turn
+
+ align:start position:0%
+you wanted to do a zero byte opera turn
+ 
+
+ align:start position:0%
+you wanted to do a zero byte opera turn
+it's not quite the same right because an
+
+ align:start position:0%
+it's not quite the same right because an
+ 
+
+ align:start position:0%
+it's not quite the same right because an
+opera turn everyone can see it and in
+
+ align:start position:0%
+opera turn everyone can see it and in
+ 
+
+ align:start position:0%
+opera turn everyone can see it and in
+some cases you might want that you might
+
+ align:start position:0%
+some cases you might want that you might
+ 
+
+ align:start position:0%
+some cases you might want that you might
+want to put an offer turn so that it's
+
+ align:start position:0%
+want to put an offer turn so that it's
+ 
+
+ align:start position:0%
+want to put an offer turn so that it's
+publicly visible but in a lot of cases
+
+ align:start position:0%
+publicly visible but in a lot of cases
+ 
+
+ align:start position:0%
+publicly visible but in a lot of cases
+in most cases I don't care about
+
+ align:start position:0%
+in most cases I don't care about
+ 
+
+ align:start position:0%
+in most cases I don't care about
+someone's random opera turn usually what
+
+ align:start position:0%
+someone's random opera turn usually what
+ 
+
+ align:start position:0%
+someone's random opera turn usually what
+you're putting into opera terms are like
+
+ align:start position:0%
+you're putting into opera terms are like
+ 
+
+ align:start position:0%
+you're putting into opera terms are like
+hashes right because you don't have much
+
+ align:start position:0%
+hashes right because you don't have much
+ 
+
+ align:start position:0%
+hashes right because you don't have much
+space anyway you have like 40 bytes or
+
+ align:start position:0%
+space anyway you have like 40 bytes or
+ 
+
+ align:start position:0%
+space anyway you have like 40 bytes or
+something so usually your space
+
+ align:start position:0%
+something so usually your space
+ 
+
+ align:start position:0%
+something so usually your space
+constrained so you put the hash of some
+
+ align:start position:0%
+constrained so you put the hash of some
+ 
+
+ align:start position:0%
+constrained so you put the hash of some
+document and then someone can prove no
+
+ align:start position:0%
+document and then someone can prove no
+ 
+
+ align:start position:0%
+document and then someone can prove no
+look I put the document on the
+
+ align:start position:0%
+look I put the document on the
+ 
+
+ align:start position:0%
+look I put the document on the
+blockchain by putting the hash of it
+
+ align:start position:0%
+blockchain by putting the hash of it
+ 
+
+ align:start position:0%
+blockchain by putting the hash of it
+that's a commitment to that document
+
+ align:start position:0%
+that's a commitment to that document
+ 
+
+ align:start position:0%
+that's a commitment to that document
+itself so I show that I had this data at
+
+ align:start position:0%
+itself so I show that I had this data at
+ 
+
+ align:start position:0%
+itself so I show that I had this data at
+some time before this block came out
+
+ align:start position:0%
+some time before this block came out
+ 
+
+ align:start position:0%
+some time before this block came out
+right that's essentially what you're
+
+ align:start position:0%
+right that's essentially what you're
+ 
+
+ align:start position:0%
+right that's essentially what you're
+proving you're proving you knew it
+
+ align:start position:0%
+proving you're proving you knew it
+ 
+
+ align:start position:0%
+proving you're proving you knew it
+before a certain time which is it in
+
+ align:start position:0%
+before a certain time which is it in
+ 
+
+ align:start position:0%
+before a certain time which is it in
+many cases really useful I mean that's
+
+ align:start position:0%
+many cases really useful I mean that's
+ 
+
+ align:start position:0%
+many cases really useful I mean that's
+sort of the whole point of the
+
+ align:start position:0%
+sort of the whole point of the
+ 
+
+ align:start position:0%
+sort of the whole point of the
+blockchain to prove that you knew about
+
+ align:start position:0%
+blockchain to prove that you knew about
+ 
+
+ align:start position:0%
+blockchain to prove that you knew about
+this transaction before a future
+
+ align:start position:0%
+this transaction before a future
+ 
+
+ align:start position:0%
+this transaction before a future
+transaction tries to double spend it you
+
+ align:start position:0%
+transaction tries to double spend it you
+ 
+
+ align:start position:0%
+transaction tries to double spend it you
+want to file a patent and hey had this
+
+ align:start position:0%
+want to file a patent and hey had this
+ 
+
+ align:start position:0%
+want to file a patent and hey had this
+idea first or you know prove these
+
+ align:start position:0%
+idea first or you know prove these
+ 
+
+ align:start position:0%
+idea first or you know prove these
+things okay how can we do this with zero
+
+ align:start position:0%
+things okay how can we do this with zero
+ 
+
+ align:start position:0%
+things okay how can we do this with zero
+bytes overhead okay you put it in the
+
+ align:start position:0%
+bytes overhead okay you put it in the
+ 
+
+ align:start position:0%
+bytes overhead okay you put it in the
+signature and this was not obvious and
+
+ align:start position:0%
+signature and this was not obvious and
+ 
+
+ align:start position:0%
+signature and this was not obvious and
+like no one thought of this until a year
+
+ align:start position:0%
+like no one thought of this until a year
+ 
+
+ align:start position:0%
+like no one thought of this until a year
+or two ago I think it was an upholsterer
+
+ align:start position:0%
+or two ago I think it was an upholsterer
+ 
+
+ align:start position:0%
+or two ago I think it was an upholsterer
+but I could be wrong but I just
+
+ align:start position:0%
+but I could be wrong but I just
+ 
+
+ align:start position:0%
+but I could be wrong but I just
+associate it with him because he worked
+
+ align:start position:0%
+associate it with him because he worked
+ 
+
+ align:start position:0%
+associate it with him because he worked
+on it but I'm not a hundred percent sure
+
+ align:start position:0%
+on it but I'm not a hundred percent sure
+ 
+
+ align:start position:0%
+on it but I'm not a hundred percent sure
+and he called it pay to contract hash
+
+ align:start position:0%
+and he called it pay to contract hash
+ 
+
+ align:start position:0%
+and he called it pay to contract hash
+which is confusing it's not a it's not
+
+ align:start position:0%
+which is confusing it's not a it's not
+ 
+
+ align:start position:0%
+which is confusing it's not a it's not
+at all the same as fada script hash it's
+
+ align:start position:0%
+at all the same as fada script hash it's
+ 
+
+ align:start position:0%
+at all the same as fada script hash it's
+not at all the same as paid a puppy ash
+
+ align:start position:0%
+not at all the same as paid a puppy ash
+ 
+
+ align:start position:0%
+not at all the same as paid a puppy ash
+but it's called paid a contract hash
+
+ align:start position:0%
+but it's called paid a contract hash
+ 
+
+ align:start position:0%
+but it's called paid a contract hash
+which makes it really confusing Bitcoin
+
+ align:start position:0%
+which makes it really confusing Bitcoin
+ 
+
+ align:start position:0%
+which makes it really confusing Bitcoin
+has really confusing names right like
+
+ align:start position:0%
+has really confusing names right like
+ 
+
+ align:start position:0%
+has really confusing names right like
+scripts it or pub key script wait script
+
+ align:start position:0%
+scripts it or pub key script wait script
+ 
+
+ align:start position:0%
+scripts it or pub key script wait script
+pub key script pub key does not have to
+
+ align:start position:0%
+pub key script pub key does not have to
+ 
+
+ align:start position:0%
+pub key script pub key does not have to
+have a pub key in it in most cases it
+
+ align:start position:0%
+have a pub key in it in most cases it
+ 
+
+ align:start position:0%
+have a pub key in it in most cases it
+doesn't it has a funky hash or a script
+
+ align:start position:0%
+doesn't it has a funky hash or a script
+ 
+
+ align:start position:0%
+doesn't it has a funky hash or a script
+hash it doesn't have to have anything in
+
+ align:start position:0%
+hash it doesn't have to have anything in
+ 
+
+ align:start position:0%
+hash it doesn't have to have anything in
+it but it's called screw
+
+ align:start position:0%
+it but it's called screw
+ 
+
+ align:start position:0%
+it but it's called screw
+Punkie and then script sig usually has
+
+ align:start position:0%
+Punkie and then script sig usually has
+ 
+
+ align:start position:0%
+Punkie and then script sig usually has
+signatures but again not always and
+
+ align:start position:0%
+signatures but again not always and
+ 
+
+ align:start position:0%
+signatures but again not always and
+there's all sorts of confusing names
+
+ align:start position:0%
+there's all sorts of confusing names
+ 
+
+ align:start position:0%
+there's all sorts of confusing names
+anyway here's our new contribution to
+
+ align:start position:0%
+anyway here's our new contribution to
+ 
+
+ align:start position:0%
+anyway here's our new contribution to
+confusing names kay to contract hash
+
+ align:start position:0%
+confusing names kay to contract hash
+ 
+
+ align:start position:0%
+confusing names kay to contract hash
+which is not really paying to anything
+
+ align:start position:0%
+which is not really paying to anything
+ 
+
+ align:start position:0%
+which is not really paying to anything
+there doesn't have to be a contract
+
+ align:start position:0%
+there doesn't have to be a contract
+ 
+
+ align:start position:0%
+there doesn't have to be a contract
+there is a hash involved but yeah okay
+
+ align:start position:0%
+there is a hash involved but yeah okay
+ 
+
+ align:start position:0%
+there is a hash involved but yeah okay
+so it's a weird name as you can't
+
+ align:start position:0%
+so it's a weird name as you can't
+ 
+
+ align:start position:0%
+so it's a weird name as you can't
+actually detect the contract you know
+
+ align:start position:0%
+actually detect the contract you know
+ 
+
+ align:start position:0%
+actually detect the contract you know
+paying to it but okay to review a
+
+ align:start position:0%
+paying to it but okay to review a
+ 
+
+ align:start position:0%
+paying to it but okay to review a
+snorrison I'm gonna use snore signatures
+
+ align:start position:0%
+snorrison I'm gonna use snore signatures
+ 
+
+ align:start position:0%
+snorrison I'm gonna use snore signatures
+this still works in ECDSA but you see
+
+ align:start position:0%
+this still works in ECDSA but you see
+ 
+
+ align:start position:0%
+this still works in ECDSA but you see
+the SA is weird annoying and it also
+
+ align:start position:0%
+the SA is weird annoying and it also
+ 
+
+ align:start position:0%
+the SA is weird annoying and it also
+makes more sense than Schnoor signatures
+
+ align:start position:0%
+makes more sense than Schnoor signatures
+ 
+
+ align:start position:0%
+makes more sense than Schnoor signatures
+so I'll explain that but but it totally
+
+ align:start position:0%
+so I'll explain that but but it totally
+ 
+
+ align:start position:0%
+so I'll explain that but but it totally
+works in EC it is DSA today so the idea
+
+ align:start position:0%
+works in EC it is DSA today so the idea
+ 
+
+ align:start position:0%
+works in EC it is DSA today so the idea
+of the short signature is okay this is
+
+ align:start position:0%
+of the short signature is okay this is
+ 
+
+ align:start position:0%
+of the short signature is okay this is
+my private key this is the message I
+
+ align:start position:0%
+my private key this is the message I
+ 
+
+ align:start position:0%
+my private key this is the message I
+want to sign this is a random sort of
+
+ align:start position:0%
+want to sign this is a random sort of
+ 
+
+ align:start position:0%
+want to sign this is a random sort of
+temporary private key I come up with and
+
+ align:start position:0%
+temporary private key I come up with and
+ 
+
+ align:start position:0%
+temporary private key I come up with and
+then this is that temporary private key
+
+ align:start position:0%
+then this is that temporary private key
+ 
+
+ align:start position:0%
+then this is that temporary private key
+turned into a public key write x Gina
+
+ align:start position:0%
+turned into a public key write x Gina
+ 
+
+ align:start position:0%
+turned into a public key write x Gina
+gets the public key version and then two
+
+ align:start position:0%
+gets the public key version and then two
+ 
+
+ align:start position:0%
+gets the public key version and then two
+to evaluate two to verify the signature
+
+ align:start position:0%
+to evaluate two to verify the signature
+ 
+
+ align:start position:0%
+to evaluate two to verify the signature
+you just multiply both sides by G so you
+
+ align:start position:0%
+you just multiply both sides by G so you
+ 
+
+ align:start position:0%
+you just multiply both sides by G so you
+get s times G K turns into our little a
+
+ align:start position:0%
+get s times G K turns into our little a
+ 
+
+ align:start position:0%
+get s times G K turns into our little a
+turns into big a this is just the hash
+
+ align:start position:0%
+turns into big a this is just the hash
+ 
+
+ align:start position:0%
+turns into big a this is just the hash
+32-byte hash so it's it stays the same
+
+ align:start position:0%
+32-byte hash so it's it stays the same
+ 
+
+ align:start position:0%
+32-byte hash so it's it stays the same
+so the signature is R and s the sorry
+
+ align:start position:0%
+so the signature is R and s the sorry
+ 
+
+ align:start position:0%
+so the signature is R and s the sorry
+the R and s so the signature and the
+
+ align:start position:0%
+the R and s so the signature and the
+ 
+
+ align:start position:0%
+the R and s so the signature and the
+pump key is a and the message is out
+
+ align:start position:0%
+pump key is a and the message is out
+ 
+
+ align:start position:0%
+pump key is a and the message is out
+okay so that's the signing or close
+
+ align:start position:0%
+okay so that's the signing or close
+ 
+
+ align:start position:0%
+okay so that's the signing or close
+enough to the signing that's using
+
+ align:start position:0%
+enough to the signing that's using
+ 
+
+ align:start position:0%
+enough to the signing that's using
+Bitcoin so pay to pub paid to contract
+
+ align:start position:0%
+Bitcoin so pay to pub paid to contract
+ 
+
+ align:start position:0%
+Bitcoin so pay to pub paid to contract
+hash says okay I want to put our betray
+
+ align:start position:0%
+hash says okay I want to put our betray
+ 
+
+ align:start position:0%
+hash says okay I want to put our betray
+data into my signature in a way that I
+
+ align:start position:0%
+data into my signature in a way that I
+ 
+
+ align:start position:0%
+data into my signature in a way that I
+can prove it was there so here's the
+
+ align:start position:0%
+can prove it was there so here's the
+ 
+
+ align:start position:0%
+can prove it was there so here's the
+normal equation now what if I redefined
+
+ align:start position:0%
+normal equation now what if I redefined
+ 
+
+ align:start position:0%
+normal equation now what if I redefined
+K normally K is just a random number but
+
+ align:start position:0%
+K normally K is just a random number but
+ 
+
+ align:start position:0%
+K normally K is just a random number but
+now I'm gonna redefine k k is now J so J
+
+ align:start position:0%
+now I'm gonna redefine k k is now J so J
+ 
+
+ align:start position:0%
+now I'm gonna redefine k k is now J so J
+is my new real random number and then
+
+ align:start position:0%
+is my new real random number and then
+ 
+
+ align:start position:0%
+is my new real random number and then
+I'm going to add the Hat no there's no G
+
+ align:start position:0%
+I'm going to add the Hat no there's no G
+ 
+
+ align:start position:0%
+I'm going to add the Hat no there's no G
+there shoot anyway G you should not be
+
+ align:start position:0%
+there shoot anyway G you should not be
+ 
+
+ align:start position:0%
+there shoot anyway G you should not be
+there but it should be there sorry okay
+
+ align:start position:0%
+there but it should be there sorry okay
+ 
+
+ align:start position:0%
+there but it should be there sorry okay
+they so I redefined K as J which is an
+
+ align:start position:0%
+they so I redefined K as J which is an
+ 
+
+ align:start position:0%
+they so I redefined K as J which is an
+actual random number
+
+ align:start position:0%
+actual random number
+ 
+
+ align:start position:0%
+actual random number
+plus the hash of the data I want to
+
+ align:start position:0%
+plus the hash of the data I want to
+ 
+
+ align:start position:0%
+plus the hash of the data I want to
+commit to and J times G I think yeah
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah anyway and then the signature it's
+
+ align:start position:0%
+yeah anyway and then the signature it's
+ 
+
+ align:start position:0%
+yeah anyway and then the signature it's
+still the same equation right I'm just
+
+ align:start position:0%
+still the same equation right I'm just
+ 
+
+ align:start position:0%
+still the same equation right I'm just
+saying okay it's this new K minus this
+
+ align:start position:0%
+saying okay it's this new K minus this
+ 
+
+ align:start position:0%
+saying okay it's this new K minus this
+thing and so nobody necessarily knows
+
+ align:start position:0%
+thing and so nobody necessarily knows
+ 
+
+ align:start position:0%
+thing and so nobody necessarily knows
+that I'm doing this right if I just tell
+
+ align:start position:0%
+that I'm doing this right if I just tell
+ 
+
+ align:start position:0%
+that I'm doing this right if I just tell
+you okay you know if I just tell you R
+
+ align:start position:0%
+you okay you know if I just tell you R
+ 
+
+ align:start position:0%
+you okay you know if I just tell you R
+and s the equation still holds
+
+ align:start position:0%
+and s the equation still holds
+ 
+
+ align:start position:0%
+and s the equation still holds
+it's just that K is a little special
+
+ align:start position:0%
+it's just that K is a little special
+ 
+
+ align:start position:0%
+it's just that K is a little special
+right i-44 anyone else it looks like a
+
+ align:start position:0%
+right i-44 anyone else it looks like a
+ 
+
+ align:start position:0%
+right i-44 anyone else it looks like a
+random number right it's a random number
+
+ align:start position:0%
+random number right it's a random number
+ 
+
+ align:start position:0%
+random number right it's a random number
+plus this other hash not times G so it's
+
+ align:start position:0%
+plus this other hash not times G so it's
+ 
+
+ align:start position:0%
+plus this other hash not times G so it's
+a random number plus a hash which hashes
+
+ align:start position:0%
+a random number plus a hash which hashes
+ 
+
+ align:start position:0%
+a random number plus a hash which hashes
+look pretty random so it's a random
+
+ align:start position:0%
+look pretty random so it's a random
+ 
+
+ align:start position:0%
+look pretty random so it's a random
+number plus some other random number
+
+ align:start position:0%
+number plus some other random number
+ 
+
+ align:start position:0%
+number plus some other random number
+no one's gonna sell that anything's
+
+ align:start position:0%
+no one's gonna sell that anything's
+ 
+
+ align:start position:0%
+no one's gonna sell that anything's
+weird about this however it is unique in
+
+ align:start position:0%
+weird about this however it is unique in
+ 
+
+ align:start position:0%
+weird about this however it is unique in
+that I've got this random number plus
+
+ align:start position:0%
+that I've got this random number plus
+ 
+
+ align:start position:0%
+that I've got this random number plus
+the hash of that random number times G
+
+ align:start position:0%
+the hash of that random number times G
+ 
+
+ align:start position:0%
+the hash of that random number times G
+in it and this extra data I put in okay
+
+ align:start position:0%
+in it and this extra data I put in okay
+ 
+
+ align:start position:0%
+in it and this extra data I put in okay
+so to verify if I don't tell you about
+
+ align:start position:0%
+so to verify if I don't tell you about
+ 
+
+ align:start position:0%
+so to verify if I don't tell you about
+this verification looks the same
+
+ align:start position:0%
+this verification looks the same
+ 
+
+ align:start position:0%
+this verification looks the same
+what if I do tell you about it though so
+
+ align:start position:0%
+what if I do tell you about it though so
+ 
+
+ align:start position:0%
+what if I do tell you about it though so
+normally this thing RS pump use a
+
+ align:start position:0%
+normally this thing RS pump use a
+ 
+
+ align:start position:0%
+normally this thing RS pump use a
+message exam but the signer can prove
+
+ align:start position:0%
+message exam but the signer can prove
+ 
+
+ align:start position:0%
+message exam but the signer can prove
+that r is not kg that there's this other
+
+ align:start position:0%
+that r is not kg that there's this other
+ 
+
+ align:start position:0%
+that r is not kg that there's this other
+K and you know that well it's K but
+
+ align:start position:0%
+K and you know that well it's K but
+ 
+
+ align:start position:0%
+K and you know that well it's K but
+there's something else in our I can
+
+ align:start position:0%
+there's something else in our I can
+ 
+
+ align:start position:0%
+there's something else in our I can
+prove that r is special after the fact
+
+ align:start position:0%
+prove that r is special after the fact
+ 
+
+ align:start position:0%
+prove that r is special after the fact
+right everyone knows what R is but I can
+
+ align:start position:0%
+right everyone knows what R is but I can
+ 
+
+ align:start position:0%
+right everyone knows what R is but I can
+then prove that something was in are
+
+ align:start position:0%
+then prove that something was in are
+ 
+
+ align:start position:0%
+then prove that something was in are
+also never reveal K even after the fact
+
+ align:start position:0%
+also never reveal K even after the fact
+ 
+
+ align:start position:0%
+also never reveal K even after the fact
+that'll let you figure out the person's
+
+ align:start position:0%
+that'll let you figure out the person's
+ 
+
+ align:start position:0%
+that'll let you figure out the person's
+private key so the idea is I can prove
+
+ align:start position:0%
+private key so the idea is I can prove
+ 
+
+ align:start position:0%
+private key so the idea is I can prove
+that R equals j plus the hash of the
+
+ align:start position:0%
+that R equals j plus the hash of the
+ 
+
+ align:start position:0%
+that R equals j plus the hash of the
+data and j times G here's where it's a
+
+ align:start position:0%
+data and j times G here's where it's a
+ 
+
+ align:start position:0%
+data and j times G here's where it's a
+little confusing right because this is
+
+ align:start position:0%
+little confusing right because this is
+ 
+
+ align:start position:0%
+little confusing right because this is
+this is already pub key and you're
+
+ align:start position:0%
+this is already pub key and you're
+ 
+
+ align:start position:0%
+this is already pub key and you're
+multiplying by G again right so that's
+
+ align:start position:0%
+multiplying by G again right so that's
+ 
+
+ align:start position:0%
+multiplying by G again right so that's
+where this is you know anyone can
+
+ align:start position:0%
+where this is you know anyone can
+ 
+
+ align:start position:0%
+where this is you know anyone can
+compute this right because I can say hey
+
+ align:start position:0%
+compute this right because I can say hey
+ 
+
+ align:start position:0%
+compute this right because I can say hey
+here's you already know our I can give
+
+ align:start position:0%
+here's you already know our I can give
+ 
+
+ align:start position:0%
+here's you already know our I can give
+you a J and some data such that J plus
+
+ align:start position:0%
+you a J and some data such that J plus
+ 
+
+ align:start position:0%
+you a J and some data such that J plus
+the hash of this data and J itself times
+
+ align:start position:0%
+the hash of this data and J itself times
+ 
+
+ align:start position:0%
+the hash of this data and J itself times
+G equals R
+
+ align:start position:0%
+G equals R
+ 
+
+ align:start position:0%
+G equals R
+I can't Forge this right if I try to
+
+ align:start position:0%
+I can't Forge this right if I try to
+ 
+
+ align:start position:0%
+I can't Forge this right if I try to
+forge this I say after the fact I want
+
+ align:start position:0%
+forge this I say after the fact I want
+ 
+
+ align:start position:0%
+forge this I say after the fact I want
+to come up with I just made our randomly
+
+ align:start position:0%
+to come up with I just made our randomly
+ 
+
+ align:start position:0%
+to come up with I just made our randomly
+right I didn't have any actual data and
+
+ align:start position:0%
+right I didn't have any actual data and
+ 
+
+ align:start position:0%
+right I didn't have any actual data and
+then after the fact I want to come up
+
+ align:start position:0%
+then after the fact I want to come up
+ 
+
+ align:start position:0%
+then after the fact I want to come up
+and then lie and say ya know I put this
+
+ align:start position:0%
+and then lie and say ya know I put this
+ 
+
+ align:start position:0%
+and then lie and say ya know I put this
+data in to this are okay now we need to
+
+ align:start position:0%
+data in to this are okay now we need to
+ 
+
+ align:start position:0%
+data in to this are okay now we need to
+solve for J right because my proof is
+
+ align:start position:0%
+solve for J right because my proof is
+ 
+
+ align:start position:0%
+solve for J right because my proof is
+gonna be J in this data so I've got the
+
+ align:start position:0%
+gonna be J in this data so I've got the
+ 
+
+ align:start position:0%
+gonna be J in this data so I've got the
+data I want and I want to figure out
+
+ align:start position:0%
+data I want and I want to figure out
+ 
+
+ align:start position:0%
+data I want and I want to figure out
+what J's so J is the hash of this data
+
+ align:start position:0%
+what J's so J is the hash of this data
+ 
+
+ align:start position:0%
+what J's so J is the hash of this data
+and J times G minus R oh shoot right
+
+ align:start position:0%
+and J times G minus R oh shoot right
+ 
+
+ align:start position:0%
+and J times G minus R oh shoot right
+that would be the equation I have to
+
+ align:start position:0%
+that would be the equation I have to
+ 
+
+ align:start position:0%
+that would be the equation I have to
+solve if I want to falsely prove that
+
+ align:start position:0%
+solve if I want to falsely prove that
+ 
+
+ align:start position:0%
+solve if I want to falsely prove that
+this data went into it the problem is
+
+ align:start position:0%
+this data went into it the problem is
+ 
+
+ align:start position:0%
+this data went into it the problem is
+I've got this thing where it's like J is
+
+ align:start position:0%
+I've got this thing where it's like J is
+ 
+
+ align:start position:0%
+I've got this thing where it's like J is
+defined in terms of the hash of J I
+
+ align:start position:0%
+defined in terms of the hash of J I
+ 
+
+ align:start position:0%
+defined in terms of the hash of J I
+don't I don't that's that's gonna be
+
+ align:start position:0%
+don't I don't that's that's gonna be
+ 
+
+ align:start position:0%
+don't I don't that's that's gonna be
+hard right if I'm defining J in terms of
+
+ align:start position:0%
+hard right if I'm defining J in terms of
+ 
+
+ align:start position:0%
+hard right if I'm defining J in terms of
+the hash of J I'm stuck because that's
+
+ align:start position:0%
+the hash of J I'm stuck because that's
+ 
+
+ align:start position:0%
+the hash of J I'm stuck because that's
+not how hash functions don't let me do
+
+ align:start position:0%
+not how hash functions don't let me do
+ 
+
+ align:start position:0%
+not how hash functions don't let me do
+that so this is actually kind of cool
+
+ align:start position:0%
+that so this is actually kind of cool
+ 
+
+ align:start position:0%
+that so this is actually kind of cool
+because it's a proof that there was some
+
+ align:start position:0%
+because it's a proof that there was some
+ 
+
+ align:start position:0%
+because it's a proof that there was some
+extra data that went in to the random R
+
+ align:start position:0%
+extra data that went in to the random R
+ 
+
+ align:start position:0%
+extra data that went in to the random R
+point before the signing happened right
+
+ align:start position:0%
+point before the signing happened right
+ 
+
+ align:start position:0%
+point before the signing happened right
+or well it's yeah it had to be before
+
+ align:start position:0%
+or well it's yeah it had to be before
+ 
+
+ align:start position:0%
+or well it's yeah it had to be before
+the signing happened because the
+
+ align:start position:0%
+the signing happened because the
+ 
+
+ align:start position:0%
+the signing happened because the
+signature has are in it and s is a
+
+ align:start position:0%
+signature has are in it and s is a
+ 
+
+ align:start position:0%
+signature has are in it and s is a
+function of r and this is cool because
+
+ align:start position:0%
+function of r and this is cool because
+ 
+
+ align:start position:0%
+function of r and this is cool because
+if you don't know about it it just looks
+
+ align:start position:0%
+if you don't know about it it just looks
+ 
+
+ align:start position:0%
+if you don't know about it it just looks
+like a regular signature with a like
+
+ align:start position:0%
+like a regular signature with a like
+ 
+
+ align:start position:0%
+like a regular signature with a like
+regular R value but if I tell you about
+
+ align:start position:0%
+regular R value but if I tell you about
+ 
+
+ align:start position:0%
+regular R value but if I tell you about
+it I was like yeah when I sign that I
+
+ align:start position:0%
+it I was like yeah when I sign that I
+ 
+
+ align:start position:0%
+it I was like yeah when I sign that I
+actually put some extra data into here
+
+ align:start position:0%
+actually put some extra data into here
+ 
+
+ align:start position:0%
+actually put some extra data into here
+so that's kind of better than off return
+
+ align:start position:0%
+so that's kind of better than off return
+ 
+
+ align:start position:0%
+so that's kind of better than off return
+right there's zero bytes overhead you're
+
+ align:start position:0%
+right there's zero bytes overhead you're
+ 
+
+ align:start position:0%
+right there's zero bytes overhead you're
+gonna sign anyway so you can put data
+
+ align:start position:0%
+gonna sign anyway so you can put data
+ 
+
+ align:start position:0%
+gonna sign anyway so you can put data
+inside a signatures are point you can
+
+ align:start position:0%
+inside a signatures are point you can
+ 
+
+ align:start position:0%
+inside a signatures are point you can
+even do it with other people's
+
+ align:start position:0%
+even do it with other people's
+ 
+
+ align:start position:0%
+even do it with other people's
+signatures there's no real private
+
+ align:start position:0%
+signatures there's no real private
+ 
+
+ align:start position:0%
+signatures there's no real private
+information here if I just can use some
+
+ align:start position:0%
+information here if I just can use some
+ 
+
+ align:start position:0%
+information here if I just can use some
+data it's totally safe right hey here's
+
+ align:start position:0%
+data it's totally safe right hey here's
+ 
+
+ align:start position:0%
+data it's totally safe right hey here's
+some data okay here's the J point that
+
+ align:start position:0%
+some data okay here's the J point that
+ 
+
+ align:start position:0%
+some data okay here's the J point that
+goes in that you know constructs this
+
+ align:start position:0%
+goes in that you know constructs this
+ 
+
+ align:start position:0%
+goes in that you know constructs this
+and they are like okay sounds good
+
+ align:start position:0%
+and they are like okay sounds good
+ 
+
+ align:start position:0%
+and they are like okay sounds good
+I can put someone else's data into this
+
+ align:start position:0%
+I can put someone else's data into this
+ 
+
+ align:start position:0%
+I can put someone else's data into this
+you just handle the data they give you
+
+ align:start position:0%
+you just handle the data they give you
+ 
+
+ align:start position:0%
+you just handle the data they give you
+the proof which in that case is just J
+
+ align:start position:0%
+the proof which in that case is just J
+ 
+
+ align:start position:0%
+the proof which in that case is just J
+so it's upper turn with zero byte
+
+ align:start position:0%
+so it's upper turn with zero byte
+ 
+
+ align:start position:0%
+so it's upper turn with zero byte
+overhead this is really cool I believe
+
+ align:start position:0%
+overhead this is really cool I believe
+ 
+
+ align:start position:0%
+overhead this is really cool I believe
+this is being used for like open
+
+ align:start position:0%
+this is being used for like open
+ 
+
+ align:start position:0%
+this is being used for like open
+timestamps now as of a few I think right
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+but but it's also nice it's not like a
+
+ align:start position:0%
+but but it's also nice it's not like a
+ 
+
+ align:start position:0%
+but but it's also nice it's not like a
+soft pork or anything this is just a fun
+
+ align:start position:0%
+soft pork or anything this is just a fun
+ 
+
+ align:start position:0%
+soft pork or anything this is just a fun
+trick you can do with your signatures so
+
+ align:start position:0%
+trick you can do with your signatures so
+ 
+
+ align:start position:0%
+trick you can do with your signatures so
+you can do this today if you want it and
+
+ align:start position:0%
+you can do this today if you want it and
+ 
+
+ align:start position:0%
+you can do this today if you want it and
+then prove to people later like hey I
+
+ align:start position:0%
+then prove to people later like hey I
+ 
+
+ align:start position:0%
+then prove to people later like hey I
+put my name into my signature direct
+
+ align:start position:0%
+put my name into my signature direct
+ 
+
+ align:start position:0%
+put my name into my signature direct
+replacement for the operator you you
+
+ align:start position:0%
+replacement for the operator you you
+ 
+
+ align:start position:0%
+replacement for the operator you you
+commit to the route right see so in
+
+ align:start position:0%
+commit to the route right see so in
+ 
+
+ align:start position:0%
+commit to the route right see so in
+their case this data is the Merkel route
+
+ align:start position:0%
+their case this data is the Merkel route
+ 
+
+ align:start position:0%
+their case this data is the Merkel route
+and then you can then prove so you can
+
+ align:start position:0%
+and then you can then prove so you can
+ 
+
+ align:start position:0%
+and then you can then prove so you can
+you know put a Merkel route here and
+
+ align:start position:0%
+you know put a Merkel route here and
+ 
+
+ align:start position:0%
+you know put a Merkel route here and
+then I prove that there's a Merkel route
+
+ align:start position:0%
+then I prove that there's a Merkel route
+ 
+
+ align:start position:0%
+then I prove that there's a Merkel route
+inside my signature and then I also
+
+ align:start position:0%
+inside my signature and then I also
+ 
+
+ align:start position:0%
+inside my signature and then I also
+prove a branch so that the data is in
+
+ align:start position:0%
+prove a branch so that the data is in
+ 
+
+ align:start position:0%
+prove a branch so that the data is in
+the Merkel route which is then in the
+
+ align:start position:0%
+the Merkel route which is then in the
+ 
+
+ align:start position:0%
+the Merkel route which is then in the
+our point which is in the signature
+
+ align:start position:0%
+our point which is in the signature
+ 
+
+ align:start position:0%
+our point which is in the signature
+which is in the blocks Merkel tree which
+
+ align:start position:0%
+which is in the blocks Merkel tree which
+ 
+
+ align:start position:0%
+which is in the blocks Merkel tree which
+is in the blockchain so you've got like
+
+ align:start position:0%
+is in the blockchain so you've got like
+ 
+
+ align:start position:0%
+is in the blockchain so you've got like
+four or five different proofs going on
+
+ align:start position:0%
+four or five different proofs going on
+ 
+
+ align:start position:0%
+four or five different proofs going on
+but they should all be working okay so
+
+ align:start position:0%
+but they should all be working okay so
+ 
+
+ align:start position:0%
+but they should all be working okay so
+this is this is kind of cool any idea
+
+ align:start position:0%
+this is this is kind of cool any idea
+ 
+
+ align:start position:0%
+this is this is kind of cool any idea
+why I was explaining all this in terms
+
+ align:start position:0%
+why I was explaining all this in terms
+ 
+
+ align:start position:0%
+why I was explaining all this in terms
+of like mast and multi-sig like these
+
+ align:start position:0%
+of like mast and multi-sig like these
+ 
+
+ align:start position:0%
+of like mast and multi-sig like these
+seem totally unconnected right any idea
+
+ align:start position:0%
+seem totally unconnected right any idea
+ 
+
+ align:start position:0%
+seem totally unconnected right any idea
+so yeah it took Bitcoin people like well
+
+ align:start position:0%
+so yeah it took Bitcoin people like well
+ 
+
+ align:start position:0%
+so yeah it took Bitcoin people like well
+over a year to see the after the you
+
+ align:start position:0%
+over a year to see the after the you
+ 
+
+ align:start position:0%
+over a year to see the after the you
+know in retrospect really obvious
+
+ align:start position:0%
+know in retrospect really obvious
+ 
+
+ align:start position:0%
+know in retrospect really obvious
+connection and thing to do with this
+
+ align:start position:0%
+connection and thing to do with this
+ 
+
+ align:start position:0%
+connection and thing to do with this
+but it took a year or two and then
+
+ align:start position:0%
+but it took a year or two and then
+ 
+
+ align:start position:0%
+but it took a year or two and then
+someone Greg posted on the mailing list
+
+ align:start position:0%
+someone Greg posted on the mailing list
+ 
+
+ align:start position:0%
+someone Greg posted on the mailing list
+in January like hey wait you can use
+
+ align:start position:0%
+in January like hey wait you can use
+ 
+
+ align:start position:0%
+in January like hey wait you can use
+this for something else and then it was
+
+ align:start position:0%
+this for something else and then it was
+ 
+
+ align:start position:0%
+this for something else and then it was
+like oh shoot like how did no one think
+
+ align:start position:0%
+like oh shoot like how did no one think
+ 
+
+ align:start position:0%
+like oh shoot like how did no one think
+of that
+
+ align:start position:0%
+of that
+ 
+
+ align:start position:0%
+of that
+so it's called tap root and I don't know
+
+ align:start position:0%
+so it's called tap root and I don't know
+ 
+
+ align:start position:0%
+so it's called tap root and I don't know
+why Greg called it that Greg Maxwell
+
+ align:start position:0%
+why Greg called it that Greg Maxwell
+ 
+
+ align:start position:0%
+why Greg called it that Greg Maxwell
+he's got was a big beard who works on
+
+ align:start position:0%
+he's got was a big beard who works on
+ 
+
+ align:start position:0%
+he's got was a big beard who works on
+Bitcoin he's super smart and stuff and
+
+ align:start position:0%
+Bitcoin he's super smart and stuff and
+ 
+
+ align:start position:0%
+Bitcoin he's super smart and stuff and
+it uses this pay to contract hash
+
+ align:start position:0%
+it uses this pay to contract hash
+ 
+
+ align:start position:0%
+it uses this pay to contract hash
+construction and it's the same equation
+
+ align:start position:0%
+construction and it's the same equation
+ 
+
+ align:start position:0%
+construction and it's the same equation
+but it took us a year or two to figure
+
+ align:start position:0%
+but it took us a year or two to figure
+ 
+
+ align:start position:0%
+but it took us a year or two to figure
+out that you can do this so the
+
+ align:start position:0%
+out that you can do this so the
+ 
+
+ align:start position:0%
+out that you can do this so the
+motivation here is paid a pub key hash
+
+ align:start position:0%
+motivation here is paid a pub key hash
+ 
+
+ align:start position:0%
+motivation here is paid a pub key hash
+and pay to script hash look different
+
+ align:start position:0%
+and pay to script hash look different
+ 
+
+ align:start position:0%
+and pay to script hash look different
+right you can tell just looking at the
+
+ align:start position:0%
+right you can tell just looking at the
+ 
+
+ align:start position:0%
+right you can tell just looking at the
+output these are totally different you
+
+ align:start position:0%
+output these are totally different you
+ 
+
+ align:start position:0%
+output these are totally different you
+know output scripts one of them's got a
+
+ align:start position:0%
+know output scripts one of them's got a
+ 
+
+ align:start position:0%
+know output scripts one of them's got a
+pub - one of them's got a script -
+
+ align:start position:0%
+pub - one of them's got a script -
+ 
+
+ align:start position:0%
+pub - one of them's got a script -
+different
+
+ align:start position:0%
+different
+ 
+
+ align:start position:0%
+different
+we don't want everything to look
+
+ align:start position:0%
+we don't want everything to look
+ 
+
+ align:start position:0%
+we don't want everything to look
+different then you can sort of sort
+
+ align:start position:0%
+different then you can sort of sort
+ 
+
+ align:start position:0%
+different then you can sort of sort
+things you can try to differentiate try
+
+ align:start position:0%
+things you can try to differentiate try
+ 
+
+ align:start position:0%
+things you can try to differentiate try
+to track people's coins things like that
+
+ align:start position:0%
+to track people's coins things like that
+ 
+
+ align:start position:0%
+to track people's coins things like that
+you want it to all look uniform to make
+
+ align:start position:0%
+you want it to all look uniform to make
+ 
+
+ align:start position:0%
+you want it to all look uniform to make
+it more anonymous so one thing you could
+
+ align:start position:0%
+it more anonymous so one thing you could
+ 
+
+ align:start position:0%
+it more anonymous so one thing you could
+do is just use pay to script - for
+
+ align:start position:0%
+do is just use pay to script - for
+ 
+
+ align:start position:0%
+do is just use pay to script - for
+everything you can put a pump key you
+
+ align:start position:0%
+everything you can put a pump key you
+ 
+
+ align:start position:0%
+everything you can put a pump key you
+know single essentially one of one
+
+ align:start position:0%
+know single essentially one of one
+ 
+
+ align:start position:0%
+know single essentially one of one
+multi-sig or just just the beta script
+
+ align:start position:0%
+multi-sig or just just the beta script
+ 
+
+ align:start position:0%
+multi-sig or just just the beta script
+hash pay to pub key hash script in paid
+
+ align:start position:0%
+hash pay to pub key hash script in paid
+ 
+
+ align:start position:0%
+hash pay to pub key hash script in paid
+a script hash you wouldn't do that you
+
+ align:start position:0%
+a script hash you wouldn't do that you
+ 
+
+ align:start position:0%
+a script hash you wouldn't do that you
+just have you'd have that you'd have the
+
+ align:start position:0%
+just have you'd have that you'd have the
+ 
+
+ align:start position:0%
+just have you'd have that you'd have the
+direct pay to pub key put into a script
+
+ align:start position:0%
+direct pay to pub key put into a script
+ 
+
+ align:start position:0%
+direct pay to pub key put into a script
+hash so that like it looks like a script
+
+ align:start position:0%
+hash so that like it looks like a script
+ 
+
+ align:start position:0%
+hash so that like it looks like a script
+- and then the script is public key up
+
+ align:start position:0%
+- and then the script is public key up
+ 
+
+ align:start position:0%
+- and then the script is public key up
+check sig it's actually not really any
+
+ align:start position:0%
+check sig it's actually not really any
+ 
+
+ align:start position:0%
+check sig it's actually not really any
+overhead I think you actually save a
+
+ align:start position:0%
+overhead I think you actually save a
+ 
+
+ align:start position:0%
+overhead I think you actually save a
+bite or two nobody does that
+
+ align:start position:0%
+bite or two nobody does that
+ 
+
+ align:start position:0%
+bite or two nobody does that
+you could that might solve like 80% of
+
+ align:start position:0%
+you could that might solve like 80% of
+ 
+
+ align:start position:0%
+you could that might solve like 80% of
+what this is trying to solve it's but
+
+ align:start position:0%
+what this is trying to solve it's but
+ 
+
+ align:start position:0%
+what this is trying to solve it's but
+it's kind of boring it doesn't use cool
+
+ align:start position:0%
+it's kind of boring it doesn't use cool
+ 
+
+ align:start position:0%
+it's kind of boring it doesn't use cool
+math so anyway okay the other the other
+
+ align:start position:0%
+math so anyway okay the other the other
+ 
+
+ align:start position:0%
+math so anyway okay the other the other
+the other observation is that in most
+
+ align:start position:0%
+the other observation is that in most
+ 
+
+ align:start position:0%
+the other observation is that in most
+cases scripts you have these sort of
+
+ align:start position:0%
+cases scripts you have these sort of
+ 
+
+ align:start position:0%
+cases scripts you have these sort of
+scripts and there's a hidden option
+
+ align:start position:0%
+scripts and there's a hidden option
+ 
+
+ align:start position:0%
+scripts and there's a hidden option
+which is or everyone signs so in the
+
+ align:start position:0%
+which is or everyone signs so in the
+ 
+
+ align:start position:0%
+which is or everyone signs so in the
+case of like two of 50 multi say well if
+
+ align:start position:0%
+case of like two of 50 multi say well if
+ 
+
+ align:start position:0%
+case of like two of 50 multi say well if
+all 50 people sign that's okay right
+
+ align:start position:0%
+all 50 people sign that's okay right
+ 
+
+ align:start position:0%
+all 50 people sign that's okay right
+that's no worse so if it's 25 of 50
+
+ align:start position:0%
+that's no worse so if it's 25 of 50
+ 
+
+ align:start position:0%
+that's no worse so if it's 25 of 50
+multi-sig if all 50 people happen to
+
+ align:start position:0%
+multi-sig if all 50 people happen to
+ 
+
+ align:start position:0%
+multi-sig if all 50 people happen to
+sign sure that's you know it's no loss
+
+ align:start position:0%
+sign sure that's you know it's no loss
+ 
+
+ align:start position:0%
+sign sure that's you know it's no loss
+of security so the idea is you use this
+
+ align:start position:0%
+of security so the idea is you use this
+ 
+
+ align:start position:0%
+of security so the idea is you use this
+pay to script paid a contract hashed
+
+ align:start position:0%
+pay to script paid a contract hashed
+ 
+
+ align:start position:0%
+pay to script paid a contract hashed
+instruction to merge Paytas pub key hash
+
+ align:start position:0%
+instruction to merge Paytas pub key hash
+ 
+
+ align:start position:0%
+instruction to merge Paytas pub key hash
+and pay to script a sh so that a single
+
+ align:start position:0%
+and pay to script a sh so that a single
+ 
+
+ align:start position:0%
+and pay to script a sh so that a single
+output can do both the ID as you make a
+
+ align:start position:0%
+output can do both the ID as you make a
+ 
+
+ align:start position:0%
+output can do both the ID as you make a
+key J and J is an actual key like you
+
+ align:start position:0%
+key J and J is an actual key like you
+ 
+
+ align:start position:0%
+key J and J is an actual key like you
+have the private key for it it's a
+
+ align:start position:0%
+have the private key for it it's a
+ 
+
+ align:start position:0%
+have the private key for it it's a
+regular old pump key and you have a
+
+ align:start position:0%
+regular old pump key and you have a
+ 
+
+ align:start position:0%
+regular old pump key and you have a
+script Z and instead of sending either
+
+ align:start position:0%
+script Z and instead of sending either
+ 
+
+ align:start position:0%
+script Z and instead of sending either
+to the script Z in a pane of script hash
+
+ align:start position:0%
+to the script Z in a pane of script hash
+ 
+
+ align:start position:0%
+to the script Z in a pane of script hash
+construction or to you know hash this
+
+ align:start position:0%
+construction or to you know hash this
+ 
+
+ align:start position:0%
+construction or to you know hash this
+key J and said to the pub key ash you
+
+ align:start position:0%
+key J and said to the pub key ash you
+ 
+
+ align:start position:0%
+key J and said to the pub key ash you
+say I'm gonna compute key C which is J
+
+ align:start position:0%
+say I'm gonna compute key C which is J
+ 
+
+ align:start position:0%
+say I'm gonna compute key C which is J
+plus the hash of my script concatenated
+
+ align:start position:0%
+plus the hash of my script concatenated
+ 
+
+ align:start position:0%
+plus the hash of my script concatenated
+with J times G so this is the same as
+
+ align:start position:0%
+with J times G so this is the same as
+ 
+
+ align:start position:0%
+with J times G so this is the same as
+the thing I just did with the operator
+
+ align:start position:0%
+the thing I just did with the operator
+ 
+
+ align:start position:0%
+the thing I just did with the operator
+mannan zero bytes right and then I send
+
+ align:start position:0%
+mannan zero bytes right and then I send
+ 
+
+ align:start position:0%
+mannan zero bytes right and then I send
+money to it
+
+ align:start position:0%
+money to it
+ 
+
+ align:start position:0%
+money to it
+and then what do I do I've sent money to
+
+ align:start position:0%
+and then what do I do I've sent money to
+ 
+
+ align:start position:0%
+and then what do I do I've sent money to
+this C point can I sign with C's private
+
+ align:start position:0%
+this C point can I sign with C's private
+ 
+
+ align:start position:0%
+this C point can I sign with C's private
+key right
+
+ align:start position:0%
+key right
+ 
+
+ align:start position:0%
+key right
+I know I know little J right that's a
+
+ align:start position:0%
+I know I know little J right that's a
+ 
+
+ align:start position:0%
+I know I know little J right that's a
+regular key can do I know little C sure
+
+ align:start position:0%
+regular key can do I know little C sure
+ 
+
+ align:start position:0%
+regular key can do I know little C sure
+right yeah I know that little C is just
+
+ align:start position:0%
+right yeah I know that little C is just
+ 
+
+ align:start position:0%
+right yeah I know that little C is just
+the J private key plus this hash so if I
+
+ align:start position:0%
+the J private key plus this hash so if I
+ 
+
+ align:start position:0%
+the J private key plus this hash so if I
+want to treat it as a pay to pub key
+
+ align:start position:0%
+want to treat it as a pay to pub key
+ 
+
+ align:start position:0%
+want to treat it as a pay to pub key
+hash I just signed with little C assign
+
+ align:start position:0%
+hash I just signed with little C assign
+ 
+
+ align:start position:0%
+hash I just signed with little C assign
+my transaction and I'm good
+
+ align:start position:0%
+my transaction and I'm good
+ 
+
+ align:start position:0%
+my transaction and I'm good
+nobody has to know that I did this
+
+ align:start position:0%
+nobody has to know that I did this
+ 
+
+ align:start position:0%
+nobody has to know that I did this
+however if I want to make it into a beta
+
+ align:start position:0%
+however if I want to make it into a beta
+ 
+
+ align:start position:0%
+however if I want to make it into a beta
+script a sh I reveal the script Z and
+
+ align:start position:0%
+script a sh I reveal the script Z and
+ 
+
+ align:start position:0%
+script a sh I reveal the script Z and
+the you know sub ki J and then I put
+
+ align:start position:0%
+the you know sub ki J and then I put
+ 
+
+ align:start position:0%
+the you know sub ki J and then I put
+some arguments on and then run the
+
+ align:start position:0%
+some arguments on and then run the
+ 
+
+ align:start position:0%
+some arguments on and then run the
+script so if I don't want to show that
+
+ align:start position:0%
+script so if I don't want to show that
+ 
+
+ align:start position:0%
+script so if I don't want to show that
+there was a script I don't have to write
+
+ align:start position:0%
+there was a script I don't have to write
+ 
+
+ align:start position:0%
+there was a script I don't have to write
+it just just sign with this the private
+
+ align:start position:0%
+it just just sign with this the private
+ 
+
+ align:start position:0%
+it just just sign with this the private
+keys that nobody knows that there was a
+
+ align:start position:0%
+keys that nobody knows that there was a
+ 
+
+ align:start position:0%
+keys that nobody knows that there was a
+script at all and it may so maybe 80
+
+ align:start position:0%
+script at all and it may so maybe 80
+ 
+
+ align:start position:0%
+script at all and it may so maybe 80
+maybe if everyone's using this 80% of
+
+ align:start position:0%
+maybe if everyone's using this 80% of
+ 
+
+ align:start position:0%
+maybe if everyone's using this 80% of
+the time that's what happens maybe there
+
+ align:start position:0%
+the time that's what happens maybe there
+ 
+
+ align:start position:0%
+the time that's what happens maybe there
+was a script in there maybe there wasn't
+
+ align:start position:0%
+was a script in there maybe there wasn't
+ 
+
+ align:start position:0%
+was a script in there maybe there wasn't
+can't tell right however if I want to
+
+ align:start position:0%
+can't tell right however if I want to
+ 
+
+ align:start position:0%
+can't tell right however if I want to
+reveal hey actually this time I'm using
+
+ align:start position:0%
+reveal hey actually this time I'm using
+ 
+
+ align:start position:0%
+reveal hey actually this time I'm using
+the script so I revealed J&Z everyone
+
+ align:start position:0%
+the script so I revealed J&Z everyone
+ 
+
+ align:start position:0%
+the script so I revealed J&Z everyone
+computes okay well if I add J to the
+
+ align:start position:0%
+computes okay well if I add J to the
+ 
+
+ align:start position:0%
+computes okay well if I add J to the
+hash of Z and J times G does that equal
+
+ align:start position:0%
+hash of Z and J times G does that equal
+ 
+
+ align:start position:0%
+hash of Z and J times G does that equal
+C the key that is in the output script
+
+ align:start position:0%
+C the key that is in the output script
+ 
+
+ align:start position:0%
+C the key that is in the output script
+itself and if it does cool that was a
+
+ align:start position:0%
+itself and if it does cool that was a
+ 
+
+ align:start position:0%
+itself and if it does cool that was a
+valid proof that you actually committed
+
+ align:start position:0%
+valid proof that you actually committed
+ 
+
+ align:start position:0%
+valid proof that you actually committed
+to Z and now I run the script to see any
+
+ align:start position:0%
+to Z and now I run the script to see any
+ 
+
+ align:start position:0%
+to Z and now I run the script to see any
+questions about this makes sense so it's
+
+ align:start position:0%
+questions about this makes sense so it's
+ 
+
+ align:start position:0%
+questions about this makes sense so it's
+actually pretty simple it follows
+
+ align:start position:0%
+actually pretty simple it follows
+ 
+
+ align:start position:0%
+actually pretty simple it follows
+directly from the proofs from the paid
+
+ align:start position:0%
+directly from the proofs from the paid
+ 
+
+ align:start position:0%
+directly from the proofs from the paid
+contract hash and it's really cool
+
+ align:start position:0%
+contract hash and it's really cool
+ 
+
+ align:start position:0%
+contract hash and it's really cool
+because Opie I thought it was doing
+
+ align:start position:0%
+because Opie I thought it was doing
+ 
+
+ align:start position:0%
+because Opie I thought it was doing
+anyway so what you can do is you can
+
+ align:start position:0%
+anyway so what you can do is you can
+ 
+
+ align:start position:0%
+anyway so what you can do is you can
+make the sum of everyone's keys and so
+
+ align:start position:0%
+make the sum of everyone's keys and so
+ 
+
+ align:start position:0%
+make the sum of everyone's keys and so
+in store signatures we can do this
+
+ align:start position:0%
+in store signatures we can do this
+ 
+
+ align:start position:0%
+in store signatures we can do this
+and we can sign without revealing each
+
+ align:start position:0%
+and we can sign without revealing each
+ 
+
+ align:start position:0%
+and we can sign without revealing each
+other's private keys so you can say okay
+
+ align:start position:0%
+other's private keys so you can say okay
+ 
+
+ align:start position:0%
+other's private keys so you can say okay
+in what I'm gonna do is J is the sum of
+
+ align:start position:0%
+in what I'm gonna do is J is the sum of
+ 
+
+ align:start position:0%
+in what I'm gonna do is J is the sum of
+like 50 different pub keys and then Z is
+
+ align:start position:0%
+like 50 different pub keys and then Z is
+ 
+
+ align:start position:0%
+like 50 different pub keys and then Z is
+that Merkel tree of two of 50 signatures
+
+ align:start position:0%
+that Merkel tree of two of 50 signatures
+ 
+
+ align:start position:0%
+that Merkel tree of two of 50 signatures
+so if I want to use two of 50 I have to
+
+ align:start position:0%
+so if I want to use two of 50 I have to
+ 
+
+ align:start position:0%
+so if I want to use two of 50 I have to
+reveal and then I have to do the proof
+
+ align:start position:0%
+reveal and then I have to do the proof
+ 
+
+ align:start position:0%
+reveal and then I have to do the proof
+but if I can get all 50 of 50 people to
+
+ align:start position:0%
+but if I can get all 50 of 50 people to
+ 
+
+ align:start position:0%
+but if I can get all 50 of 50 people to
+sign they can produce a signature with
+
+ align:start position:0%
+sign they can produce a signature with
+ 
+
+ align:start position:0%
+sign they can produce a signature with
+private key little C so when everyone's
+
+ align:start position:0%
+private key little C so when everyone's
+ 
+
+ align:start position:0%
+private key little C so when everyone's
+cooperating it it you don't even see
+
+ align:start position:0%
+cooperating it it you don't even see
+ 
+
+ align:start position:0%
+cooperating it it you don't even see
+that there was a script involved and you
+
+ align:start position:0%
+that there was a script involved and you
+ 
+
+ align:start position:0%
+that there was a script involved and you
+can do this with signatures you cannot
+
+ align:start position:0%
+can do this with signatures you cannot
+ 
+
+ align:start position:0%
+can do this with signatures you cannot
+do this with ECDSA so probably this
+
+ align:start position:0%
+do this with ECDSA so probably this
+ 
+
+ align:start position:0%
+do this with ECDSA so probably this
+would be you know put into Bitcoin
+
+ align:start position:0%
+would be you know put into Bitcoin
+ 
+
+ align:start position:0%
+would be you know put into Bitcoin
+alongside ashen or signature kind of
+
+ align:start position:0%
+alongside ashen or signature kind of
+ 
+
+ align:start position:0%
+alongside ashen or signature kind of
+construction and this seems useful
+
+ align:start position:0%
+construction and this seems useful
+ 
+
+ align:start position:0%
+construction and this seems useful
+because in most cases most smart
+
+ align:start position:0%
+because in most cases most smart
+ 
+
+ align:start position:0%
+because in most cases most smart
+contracts most multi say does have sort
+
+ align:start position:0%
+contracts most multi say does have sort
+ 
+
+ align:start position:0%
+contracts most multi say does have sort
+of an all participants sign clause
+
+ align:start position:0%
+of an all participants sign clause
+ 
+
+ align:start position:0%
+of an all participants sign clause
+even if we don't code it in right now
+
+ align:start position:0%
+even if we don't code it in right now
+ 
+
+ align:start position:0%
+even if we don't code it in right now
+it's generally the case like you know
+
+ align:start position:0%
+it's generally the case like you know
+ 
+
+ align:start position:0%
+it's generally the case like you know
+two of three will be saying well three
+
+ align:start position:0%
+two of three will be saying well three
+ 
+
+ align:start position:0%
+two of three will be saying well three
+of three is good and if you do three of
+
+ align:start position:0%
+of three is good and if you do three of
+ 
+
+ align:start position:0%
+of three is good and if you do three of
+three
+
+ align:start position:0%
+three
+ 
+
+ align:start position:0%
+three
+hey you don't even see that there was
+
+ align:start position:0%
+hey you don't even see that there was
+ 
+
+ align:start position:0%
+hey you don't even see that there was
+two of three and so that preserves
+
+ align:start position:0%
+two of three and so that preserves
+ 
+
+ align:start position:0%
+two of three and so that preserves
+privacy it's safe space and most of the
+
+ align:start position:0%
+privacy it's safe space and most of the
+ 
+
+ align:start position:0%
+privacy it's safe space and most of the
+time all the participants can be online
+
+ align:start position:0%
+time all the participants can be online
+ 
+
+ align:start position:0%
+time all the participants can be online
+so that's the same that's the same basic
+
+ align:start position:0%
+so that's the same that's the same basic
+ 
+
+ align:start position:0%
+so that's the same that's the same basic
+ideas and lightning if everyone's
+
+ align:start position:0%
+ideas and lightning if everyone's
+ 
+
+ align:start position:0%
+ideas and lightning if everyone's
+cooperative you don't even see that
+
+ align:start position:0%
+cooperative you don't even see that
+ 
+
+ align:start position:0%
+cooperative you don't even see that
+there was a lightning Channel right you
+
+ align:start position:0%
+there was a lightning Channel right you
+ 
+
+ align:start position:0%
+there was a lightning Channel right you
+just you know together broadcast a
+
+ align:start position:0%
+just you know together broadcast a
+ 
+
+ align:start position:0%
+just you know together broadcast a
+transaction with just two of two
+
+ align:start position:0%
+transaction with just two of two
+ 
+
+ align:start position:0%
+transaction with just two of two
+multi-state but in lightning you do see
+
+ align:start position:0%
+multi-state but in lightning you do see
+ 
+
+ align:start position:0%
+multi-state but in lightning you do see
+that there was two of two multi sakes so
+
+ align:start position:0%
+that there was two of two multi sakes so
+ 
+
+ align:start position:0%
+that there was two of two multi sakes so
+you can sort of see oh it was either a
+
+ align:start position:0%
+you can sort of see oh it was either a
+ 
+
+ align:start position:0%
+you can sort of see oh it was either a
+channel or multi-sig but in this kind of
+
+ align:start position:0%
+channel or multi-sig but in this kind of
+ 
+
+ align:start position:0%
+channel or multi-sig but in this kind of
+construction
+
+ align:start position:0%
+construction
+ 
+
+ align:start position:0%
+construction
+you wouldn't even show that you say okay
+
+ align:start position:0%
+you wouldn't even show that you say okay
+ 
+
+ align:start position:0%
+you wouldn't even show that you say okay
+this is actually two of two multi-sig
+
+ align:start position:0%
+this is actually two of two multi-sig
+ 
+
+ align:start position:0%
+this is actually two of two multi-sig
+but we can merge them Oh
+
+ align:start position:0%
+but we can merge them Oh
+ 
+
+ align:start position:0%
+but we can merge them Oh
+other weird trick you can make a public
+
+ align:start position:0%
+other weird trick you can make a public
+ 
+
+ align:start position:0%
+other weird trick you can make a public
+key and prove that there is no known
+
+ align:start position:0%
+key and prove that there is no known
+ 
+
+ align:start position:0%
+key and prove that there is no known
+private key right so what if I only want
+
+ align:start position:0%
+private key right so what if I only want
+ 
+
+ align:start position:0%
+private key right so what if I only want
+this script Z and there is no set of
+
+ align:start position:0%
+this script Z and there is no set of
+ 
+
+ align:start position:0%
+this script Z and there is no set of
+everyone signing right I don't want that
+
+ align:start position:0%
+everyone signing right I don't want that
+ 
+
+ align:start position:0%
+everyone signing right I don't want that
+to be a requirement what if I only want
+
+ align:start position:0%
+to be a requirement what if I only want
+ 
+
+ align:start position:0%
+to be a requirement what if I only want
+this script hash I can do that so
+
+ align:start position:0%
+this script hash I can do that so
+ 
+
+ align:start position:0%
+this script hash I can do that so
+interactively I can use someone else's J
+
+ align:start position:0%
+interactively I can use someone else's J
+ 
+
+ align:start position:0%
+interactively I can use someone else's J
+if I if there's
+
+ align:start position:0%
+if I if there's
+ 
+
+ align:start position:0%
+if I if there's
+you know if I'm sending into a script
+
+ align:start position:0%
+you know if I'm sending into a script
+ 
+
+ align:start position:0%
+you know if I'm sending into a script
+that involves someone else they say hey
+
+ align:start position:0%
+that involves someone else they say hey
+ 
+
+ align:start position:0%
+that involves someone else they say hey
+can you come up with a key J I'm going
+
+ align:start position:0%
+can you come up with a key J I'm going
+ 
+
+ align:start position:0%
+can you come up with a key J I'm going
+to compute a key see that's J plus the
+
+ align:start position:0%
+to compute a key see that's J plus the
+ 
+
+ align:start position:0%
+to compute a key see that's J plus the
+hash of the script comma J times G and
+
+ align:start position:0%
+hash of the script comma J times G and
+ 
+
+ align:start position:0%
+hash of the script comma J times G and
+then I can prove that to you after the
+
+ align:start position:0%
+then I can prove that to you after the
+ 
+
+ align:start position:0%
+then I can prove that to you after the
+fact and you can say okay well I know
+
+ align:start position:0%
+fact and you can say okay well I know
+ 
+
+ align:start position:0%
+fact and you can say okay well I know
+it's my key so interactive I can show
+
+ align:start position:0%
+it's my key so interactive I can show
+ 
+
+ align:start position:0%
+it's my key so interactive I can show
+that it's someone else's key
+
+ align:start position:0%
+that it's someone else's key
+ 
+
+ align:start position:0%
+that it's someone else's key
+non-interactive I can just say look I
+
+ align:start position:0%
+non-interactive I can just say look I
+ 
+
+ align:start position:0%
+non-interactive I can just say look I
+know the preimage of the x-coordinate of
+
+ align:start position:0%
+know the preimage of the x-coordinate of
+ 
+
+ align:start position:0%
+know the preimage of the x-coordinate of
+J so basically I know I can prove to you
+
+ align:start position:0%
+J so basically I know I can prove to you
+ 
+
+ align:start position:0%
+J so basically I know I can prove to you
+that like there's no way I came up with
+
+ align:start position:0%
+that like there's no way I came up with
+ 
+
+ align:start position:0%
+that like there's no way I came up with
+this point on the curve in the normal
+
+ align:start position:0%
+this point on the curve in the normal
+ 
+
+ align:start position:0%
+this point on the curve in the normal
+like multiplied by G way right because
+
+ align:start position:0%
+like multiplied by G way right because
+ 
+
+ align:start position:0%
+like multiplied by G way right because
+if I know you know that sort of shows
+
+ align:start position:0%
+if I know you know that sort of shows
+ 
+
+ align:start position:0%
+if I know you know that sort of shows
+that I came up with the x-coordinate by
+
+ align:start position:0%
+that I came up with the x-coordinate by
+ 
+
+ align:start position:0%
+that I came up with the x-coordinate by
+just hashing a random number or non
+
+ align:start position:0%
+just hashing a random number or non
+ 
+
+ align:start position:0%
+just hashing a random number or non
+random number if it's the hash of zero
+
+ align:start position:0%
+random number if it's the hash of zero
+ 
+
+ align:start position:0%
+random number if it's the hash of zero
+or if the hash of you know some some
+
+ align:start position:0%
+or if the hash of you know some some
+ 
+
+ align:start position:0%
+or if the hash of you know some some
+anything the idea is I randomly picked
+
+ align:start position:0%
+anything the idea is I randomly picked
+ 
+
+ align:start position:0%
+anything the idea is I randomly picked
+an x-coordinate on this curve figured
+
+ align:start position:0%
+an x-coordinate on this curve figured
+ 
+
+ align:start position:0%
+an x-coordinate on this curve figured
+out what the y-coordinate was turn that
+
+ align:start position:0%
+out what the y-coordinate was turn that
+ 
+
+ align:start position:0%
+out what the y-coordinate was turn that
+into a point and then used it in this
+
+ align:start position:0%
+into a point and then used it in this
+ 
+
+ align:start position:0%
+into a point and then used it in this
+construction if I do that you can be
+
+ align:start position:0%
+construction if I do that you can be
+ 
+
+ align:start position:0%
+construction if I do that you can be
+pretty sure that I don't know the
+
+ align:start position:0%
+pretty sure that I don't know the
+ 
+
+ align:start position:0%
+pretty sure that I don't know the
+private key for J because I didn't
+
+ align:start position:0%
+private key for J because I didn't
+ 
+
+ align:start position:0%
+private key for J because I didn't
+compute it the right way does that make
+
+ align:start position:0%
+compute it the right way does that make
+ 
+
+ align:start position:0%
+compute it the right way does that make
+sense yeah so you can do that that's a
+
+ align:start position:0%
+sense yeah so you can do that that's a
+ 
+
+ align:start position:0%
+sense yeah so you can do that that's a
+way to then prove to other people like
+
+ align:start position:0%
+way to then prove to other people like
+ 
+
+ align:start position:0%
+way to then prove to other people like
+there is no J right it's a point on the
+
+ align:start position:0%
+there is no J right it's a point on the
+ 
+
+ align:start position:0%
+there is no J right it's a point on the
+curve but it's a random point on the
+
+ align:start position:0%
+curve but it's a random point on the
+ 
+
+ align:start position:0%
+curve but it's a random point on the
+curve so there's no way I can sign with
+
+ align:start position:0%
+curve so there's no way I can sign with
+ 
+
+ align:start position:0%
+curve so there's no way I can sign with
+C right the only way that this is gonna
+
+ align:start position:0%
+C right the only way that this is gonna
+ 
+
+ align:start position:0%
+C right the only way that this is gonna
+that this you know I sent a pub key C
+
+ align:start position:0%
+that this you know I sent a pub key C
+ 
+
+ align:start position:0%
+that this you know I sent a pub key C
+and I prove to you look C is not a key
+
+ align:start position:0%
+and I prove to you look C is not a key
+ 
+
+ align:start position:0%
+and I prove to you look C is not a key
+that anyone can sign with however there
+
+ align:start position:0%
+that anyone can sign with however there
+ 
+
+ align:start position:0%
+that anyone can sign with however there
+is a point J and there's a script Z and
+
+ align:start position:0%
+is a point J and there's a script Z and
+ 
+
+ align:start position:0%
+is a point J and there's a script Z and
+you can execute the script so that's
+
+ align:start position:0%
+you can execute the script so that's
+ 
+
+ align:start position:0%
+you can execute the script so that's
+that's useful in many cases where you
+
+ align:start position:0%
+that's useful in many cases where you
+ 
+
+ align:start position:0%
+that's useful in many cases where you
+want to prove to people that look there
+
+ align:start position:0%
+want to prove to people that look there
+ 
+
+ align:start position:0%
+want to prove to people that look there
+is no key here it's just a script and
+
+ align:start position:0%
+is no key here it's just a script and
+ 
+
+ align:start position:0%
+is no key here it's just a script and
+then you you know everyone will find out
+
+ align:start position:0%
+then you you know everyone will find out
+ 
+
+ align:start position:0%
+then you you know everyone will find out
+later when you spend it but they don't
+
+ align:start position:0%
+later when you spend it but they don't
+ 
+
+ align:start position:0%
+later when you spend it but they don't
+have to know that there was no key they
+
+ align:start position:0%
+have to know that there was no key they
+ 
+
+ align:start position:0%
+have to know that there was no key they
+just know that the script got executed
+
+ align:start position:0%
+just know that the script got executed
+ 
+
+ align:start position:0%
+just know that the script got executed
+so that that's a nice sort of hatch
+
+ align:start position:0%
+so that that's a nice sort of hatch
+ 
+
+ align:start position:0%
+so that that's a nice sort of hatch
+where you can you know default if
+
+ align:start position:0%
+where you can you know default if
+ 
+
+ align:start position:0%
+where you can you know default if
+there's any use cases where in the
+
+ align:start position:0%
+there's any use cases where in the
+ 
+
+ align:start position:0%
+there's any use cases where in the
+current script hash you want that exact
+
+ align:start position:0%
+current script hash you want that exact
+ 
+
+ align:start position:0%
+current script hash you want that exact
+same functionality and you don't want
+
+ align:start position:0%
+same functionality and you don't want
+ 
+
+ align:start position:0%
+same functionality and you don't want
+this new functionality you can sort of
+
+ align:start position:0%
+this new functionality you can sort of
+ 
+
+ align:start position:0%
+this new functionality you can sort of
+get rid of it this way
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay the idea however is that we were
+
+ align:start position:0%
+okay the idea however is that we were
+ 
+
+ align:start position:0%
+okay the idea however is that we were
+trying to make your special transaction
+
+ align:start position:0%
+trying to make your special transaction
+ 
+
+ align:start position:0%
+trying to make your special transaction
+scripts not stand out but it's more that
+
+ align:start position:0%
+scripts not stand out but it's more that
+ 
+
+ align:start position:0%
+scripts not stand out but it's more that
+you can say let's say I have my wallet
+
+ align:start position:0%
+you can say let's say I have my wallet
+ 
+
+ align:start position:0%
+you can say let's say I have my wallet
+software and it always uses p2w sa fee -
+
+ align:start position:0%
+software and it always uses p2w sa fee -
+ 
+
+ align:start position:0%
+software and it always uses p2w sa fee -
+SH or something then I can say oh I bet
+
+ align:start position:0%
+SH or something then I can say oh I bet
+ 
+
+ align:start position:0%
+SH or something then I can say oh I bet
+this is the same person I can try to
+
+ align:start position:0%
+this is the same person I can try to
+ 
+
+ align:start position:0%
+this is the same person I can try to
+track who's spending yeah probably a big
+
+ align:start position:0%
+track who's spending yeah probably a big
+ 
+
+ align:start position:0%
+track who's spending yeah probably a big
+part of it is privacy maybe they're you
+
+ align:start position:0%
+part of it is privacy maybe they're you
+ 
+
+ align:start position:0%
+part of it is privacy maybe they're you
+know discriminate against that Emma's
+
+ align:start position:0%
+know discriminate against that Emma's
+ 
+
+ align:start position:0%
+know discriminate against that Emma's
+like minors probably the minors don't
+
+ align:start position:0%
+like minors probably the minors don't
+ 
+
+ align:start position:0%
+like minors probably the minors don't
+care but it's more like if if everyone's
+
+ align:start position:0%
+care but it's more like if if everyone's
+ 
+
+ align:start position:0%
+care but it's more like if if everyone's
+using software that could create similar
+
+ align:start position:0%
+using software that could create similar
+ 
+
+ align:start position:0%
+using software that could create similar
+transactions then it becomes much harder
+
+ align:start position:0%
+transactions then it becomes much harder
+ 
+
+ align:start position:0%
+transactions then it becomes much harder
+to tell people apart and it has more
+
+ align:start position:0%
+to tell people apart and it has more
+ 
+
+ align:start position:0%
+to tell people apart and it has more
+privacy for the transactions they need
+
+ align:start position:0%
+privacy for the transactions they need
+ 
+
+ align:start position:0%
+privacy for the transactions they need
+to know they need to know the script and
+
+ align:start position:0%
+to know they need to know the script and
+ 
+
+ align:start position:0%
+to know they need to know the script and
+J which is not obvious from see right if
+
+ align:start position:0%
+J which is not obvious from see right if
+ 
+
+ align:start position:0%
+J which is not obvious from see right if
+you jetan c is the only thing you see on
+
+ align:start position:0%
+you jetan c is the only thing you see on
+ 
+
+ align:start position:0%
+you jetan c is the only thing you see on
+the blockchain in the output and so they
+
+ align:start position:0%
+the blockchain in the output and so they
+ 
+
+ align:start position:0%
+the blockchain in the output and so they
+just say it's a key
+
+ align:start position:0%
+just say it's a key
+ 
+
+ align:start position:0%
+just say it's a key
+probably someone knows the private key
+
+ align:start position:0%
+probably someone knows the private key
+ 
+
+ align:start position:0%
+probably someone knows the private key
+maybe there's some weird thing like this
+
+ align:start position:0%
+maybe there's some weird thing like this
+ 
+
+ align:start position:0%
+maybe there's some weird thing like this
+going on you don't have to use this
+
+ align:start position:0%
+going on you don't have to use this
+ 
+
+ align:start position:0%
+going on you don't have to use this
+right and then yeah so they won't know
+
+ align:start position:0%
+right and then yeah so they won't know
+ 
+
+ align:start position:0%
+right and then yeah so they won't know
+what J or Z are yeah yeah you can
+
+ align:start position:0%
+what J or Z are yeah yeah you can
+ 
+
+ align:start position:0%
+what J or Z are yeah yeah you can
+publish it you can publically publish it
+
+ align:start position:0%
+publish it you can publically publish it
+ 
+
+ align:start position:0%
+publish it you can publically publish it
+if you want and tell everyone in the
+
+ align:start position:0%
+if you want and tell everyone in the
+ 
+
+ align:start position:0%
+if you want and tell everyone in the
+world hey this C is actually this J Plus
+
+ align:start position:0%
+world hey this C is actually this J Plus
+ 
+
+ align:start position:0%
+world hey this C is actually this J Plus
+this script Z they still can't spend it
+
+ align:start position:0%
+this script Z they still can't spend it
+ 
+
+ align:start position:0%
+this script Z they still can't spend it
+right that's all that can be public even
+
+ align:start position:0%
+right that's all that can be public even
+ 
+
+ align:start position:0%
+right that's all that can be public even
+beforehand and then they can see oh
+
+ align:start position:0%
+beforehand and then they can see oh
+ 
+
+ align:start position:0%
+beforehand and then they can see oh
+there's a script and a key and you can
+
+ align:start position:0%
+there's a script and a key and you can
+ 
+
+ align:start position:0%
+there's a script and a key and you can
+also say sign something and prove that
+
+ align:start position:0%
+also say sign something and prove that
+ 
+
+ align:start position:0%
+also say sign something and prove that
+you know the private key for J so you
+
+ align:start position:0%
+you know the private key for J so you
+ 
+
+ align:start position:0%
+you know the private key for J so you
+can say I'm not you know I can prove
+
+ align:start position:0%
+can say I'm not you know I can prove
+ 
+
+ align:start position:0%
+can say I'm not you know I can prove
+that I'm not doing this
+
+ align:start position:0%
+that I'm not doing this
+ 
+
+ align:start position:0%
+that I'm not doing this
+there is no J kind of thing so you can
+
+ align:start position:0%
+there is no J kind of thing so you can
+ 
+
+ align:start position:0%
+there is no J kind of thing so you can
+prove all those things but you don't
+
+ align:start position:0%
+prove all those things but you don't
+ 
+
+ align:start position:0%
+prove all those things but you don't
+need to write if you for normal usage
+
+ align:start position:0%
+need to write if you for normal usage
+ 
+
+ align:start position:0%
+need to write if you for normal usage
+you just send a key C spend from key C
+
+ align:start position:0%
+you just send a key C spend from key C
+ 
+
+ align:start position:0%
+you just send a key C spend from key C
+you're done and if you want to
+
+ align:start position:0%
+you're done and if you want to
+ 
+
+ align:start position:0%
+you're done and if you want to
+to spend from the script to Z you just
+
+ align:start position:0%
+to spend from the script to Z you just
+ 
+
+ align:start position:0%
+to spend from the script to Z you just
+provide J the script Z and then execute
+
+ align:start position:0%
+provide J the script Z and then execute
+ 
+
+ align:start position:0%
+provide J the script Z and then execute
+the script so it's nice and that even
+
+ align:start position:0%
+the script so it's nice and that even
+ 
+
+ align:start position:0%
+the script so it's nice and that even
+you might have had a script and then you
+
+ align:start position:0%
+you might have had a script and then you
+ 
+
+ align:start position:0%
+you might have had a script and then you
+didn't use it so you didn't reveal that
+
+ align:start position:0%
+didn't use it so you didn't reveal that
+ 
+
+ align:start position:0%
+didn't use it so you didn't reveal that
+there was a script so it helps with
+
+ align:start position:0%
+there was a script so it helps with
+ 
+
+ align:start position:0%
+there was a script so it helps with
+privacy it helps with efficiency in many
+
+ align:start position:0%
+privacy it helps with efficiency in many
+ 
+
+ align:start position:0%
+privacy it helps with efficiency in many
+cases because if you don't need to use
+
+ align:start position:0%
+cases because if you don't need to use
+ 
+
+ align:start position:0%
+cases because if you don't need to use
+the script you don't have to so in a lot
+
+ align:start position:0%
+the script you don't have to so in a lot
+ 
+
+ align:start position:0%
+the script you don't have to so in a lot
+of cases you say all you know everyone's
+
+ align:start position:0%
+of cases you say all you know everyone's
+ 
+
+ align:start position:0%
+of cases you say all you know everyone's
+all three of the two of three multi
+
+ align:start position:0%
+all three of the two of three multi
+ 
+
+ align:start position:0%
+all three of the two of three multi
+SIG's are on board so let's you see
+
+ align:start position:0%
+SIG's are on board so let's you see
+ 
+
+ align:start position:0%
+SIG's are on board so let's you see
+instead of the script Z so it's pretty
+
+ align:start position:0%
+instead of the script Z so it's pretty
+ 
+
+ align:start position:0%
+instead of the script Z so it's pretty
+cool okay so questions about this go
+
+ align:start position:0%
+cool okay so questions about this go
+ 
+
+ align:start position:0%
+cool okay so questions about this go
+into the next crazy thing okay so yeah a
+
+ align:start position:0%
+into the next crazy thing okay so yeah a
+ 
+
+ align:start position:0%
+into the next crazy thing okay so yeah a
+little notes about taproot anyone can
+
+ align:start position:0%
+little notes about taproot anyone can
+ 
+
+ align:start position:0%
+little notes about taproot anyone can
+make a key and script and send to it
+
+ align:start position:0%
+make a key and script and send to it
+ 
+
+ align:start position:0%
+make a key and script and send to it
+only the pub keys are needed right so if
+
+ align:start position:0%
+only the pub keys are needed right so if
+ 
+
+ align:start position:0%
+only the pub keys are needed right so if
+I want to send to something that's you
+
+ align:start position:0%
+I want to send to something that's you
+ 
+
+ align:start position:0%
+I want to send to something that's you
+know three of three Alice Bob and Carol
+
+ align:start position:0%
+know three of three Alice Bob and Carol
+ 
+
+ align:start position:0%
+know three of three Alice Bob and Carol
+add it all together or two of the three
+
+ align:start position:0%
+add it all together or two of the three
+ 
+
+ align:start position:0%
+add it all together or two of the three
+of Alice and Bob and Carol I don't have
+
+ align:start position:0%
+of Alice and Bob and Carol I don't have
+ 
+
+ align:start position:0%
+of Alice and Bob and Carol I don't have
+to even ask Alice Bob and Carol if I
+
+ align:start position:0%
+to even ask Alice Bob and Carol if I
+ 
+
+ align:start position:0%
+to even ask Alice Bob and Carol if I
+know their public keys I can just
+
+ align:start position:0%
+know their public keys I can just
+ 
+
+ align:start position:0%
+know their public keys I can just
+compute all this myself and send the
+
+ align:start position:0%
+compute all this myself and send the
+ 
+
+ align:start position:0%
+compute all this myself and send the
+send money to their send that one right
+
+ align:start position:0%
+send money to their send that one right
+ 
+
+ align:start position:0%
+send money to their send that one right
+and I can compute any construction I
+
+ align:start position:0%
+and I can compute any construction I
+ 
+
+ align:start position:0%
+and I can compute any construction I
+want I can make it one of three right I
+
+ align:start position:0%
+want I can make it one of three right I
+ 
+
+ align:start position:0%
+want I can make it one of three right I
+know that there's Alice BA I know Alice
+
+ align:start position:0%
+know that there's Alice BA I know Alice
+ 
+
+ align:start position:0%
+know that there's Alice BA I know Alice
+Bob and Carols public keys and I can say
+
+ align:start position:0%
+Bob and Carols public keys and I can say
+ 
+
+ align:start position:0%
+Bob and Carols public keys and I can say
+hey Alice Bob and Carol I'm giving you
+
+ align:start position:0%
+hey Alice Bob and Carol I'm giving you
+ 
+
+ align:start position:0%
+hey Alice Bob and Carol I'm giving you
+all money and you can fight over it or
+
+ align:start position:0%
+all money and you can fight over it or
+ 
+
+ align:start position:0%
+all money and you can fight over it or
+you can cooperate like it's you know any
+
+ align:start position:0%
+you can cooperate like it's you know any
+ 
+
+ align:start position:0%
+you can cooperate like it's you know any
+of you get it and so the idea is one of
+
+ align:start position:0%
+of you get it and so the idea is one of
+ 
+
+ align:start position:0%
+of you get it and so the idea is one of
+three multi-sig script goes into here
+
+ align:start position:0%
+three multi-sig script goes into here
+ 
+
+ align:start position:0%
+three multi-sig script goes into here
+and then three of three is here so if
+
+ align:start position:0%
+and then three of three is here so if
+ 
+
+ align:start position:0%
+and then three of three is here so if
+you cooperate you save a little bit of
+
+ align:start position:0%
+you cooperate you save a little bit of
+ 
+
+ align:start position:0%
+you cooperate you save a little bit of
+space on them and the fees are smaller
+
+ align:start position:0%
+space on them and the fees are smaller
+ 
+
+ align:start position:0%
+space on them and the fees are smaller
+but if you don't cooperate any of you
+
+ align:start position:0%
+but if you don't cooperate any of you
+ 
+
+ align:start position:0%
+but if you don't cooperate any of you
+can grab it immediately I don't know how
+
+ align:start position:0%
+can grab it immediately I don't know how
+ 
+
+ align:start position:0%
+can grab it immediately I don't know how
+useful that is but you could do this
+
+ align:start position:0%
+useful that is but you could do this
+ 
+
+ align:start position:0%
+useful that is but you could do this
+right you you don't need knowledge of
+
+ align:start position:0%
+right you you don't need knowledge of
+ 
+
+ align:start position:0%
+right you you don't need knowledge of
+any private keys to construct see only
+
+ align:start position:0%
+any private keys to construct see only
+ 
+
+ align:start position:0%
+any private keys to construct see only
+the pub keys are needed that's actually
+
+ align:start position:0%
+the pub keys are needed that's actually
+ 
+
+ align:start position:0%
+the pub keys are needed that's actually
+really nice because you're creating so
+
+ align:start position:0%
+really nice because you're creating so
+ 
+
+ align:start position:0%
+really nice because you're creating so
+that's that's the same is currently the
+
+ align:start position:0%
+that's that's the same is currently the
+ 
+
+ align:start position:0%
+that's that's the same is currently the
+case in Bitcoin right if you're creating
+
+ align:start position:0%
+case in Bitcoin right if you're creating
+ 
+
+ align:start position:0%
+case in Bitcoin right if you're creating
+an output script like paid a pub key
+
+ align:start position:0%
+an output script like paid a pub key
+ 
+
+ align:start position:0%
+an output script like paid a pub key
+hash paid a script hash there's no
+
+ align:start position:0%
+hash paid a script hash there's no
+ 
+
+ align:start position:0%
+hash paid a script hash there's no
+private keys involved in that process
+
+ align:start position:0%
+private keys involved in that process
+ 
+
+ align:start position:0%
+private keys involved in that process
+right you just tell everyone okay which
+
+ align:start position:0%
+right you just tell everyone okay which
+ 
+
+ align:start position:0%
+right you just tell everyone okay which
+differs and is the important distinction
+
+ align:start position:0%
+differs and is the important distinction
+ 
+
+ align:start position:0%
+differs and is the important distinction
+between the next school thing
+
+ align:start position:0%
+between the next school thing
+ 
+
+ align:start position:0%
+between the next school thing
+which is craft route also Greg Maxwell
+
+ align:start position:0%
+which is craft route also Greg Maxwell
+ 
+
+ align:start position:0%
+which is craft route also Greg Maxwell
+like a week or two after taproot they're
+
+ align:start position:0%
+like a week or two after taproot they're
+ 
+
+ align:start position:0%
+like a week or two after taproot they're
+not actually that similar but it was
+
+ align:start position:0%
+not actually that similar but it was
+ 
+
+ align:start position:0%
+not actually that similar but it was
+like wait you know people are sort of
+
+ align:start position:0%
+like wait you know people are sort of
+ 
+
+ align:start position:0%
+like wait you know people are sort of
+talking about it so the idea is allow a
+
+ align:start position:0%
+talking about it so the idea is allow a
+ 
+
+ align:start position:0%
+talking about it so the idea is allow a
+lot of scripts with a proof that goes up
+
+ align:start position:0%
+lot of scripts with a proof that goes up
+ 
+
+ align:start position:0%
+lot of scripts with a proof that goes up
+in size with of one okay it doesn't go
+
+ align:start position:0%
+in size with of one okay it doesn't go
+ 
+
+ align:start position:0%
+in size with of one okay it doesn't go
+up in size so the Merkel proofs right
+
+ align:start position:0%
+up in size so the Merkel proofs right
+ 
+
+ align:start position:0%
+up in size so the Merkel proofs right
+mast grow in log n so if you've got a
+
+ align:start position:0%
+mast grow in log n so if you've got a
+ 
+
+ align:start position:0%
+mast grow in log n so if you've got a
+million different scripts you're gonna
+
+ align:start position:0%
+million different scripts you're gonna
+ 
+
+ align:start position:0%
+million different scripts you're gonna
+take twenty something like twenty hashes
+
+ align:start position:0%
+take twenty something like twenty hashes
+ 
+
+ align:start position:0%
+take twenty something like twenty hashes
+or whatever to prove that what's a proof
+
+ align:start position:0%
+or whatever to prove that what's a proof
+ 
+
+ align:start position:0%
+or whatever to prove that what's a proof
+that go grows in of one of the number of
+
+ align:start position:0%
+that go grows in of one of the number of
+ 
+
+ align:start position:0%
+that go grows in of one of the number of
+things being proven it's actually not
+
+ align:start position:0%
+things being proven it's actually not
+ 
+
+ align:start position:0%
+things being proven it's actually not
+it's kind of obvious like I want to
+
+ align:start position:0%
+it's kind of obvious like I want to
+ 
+
+ align:start position:0%
+it's kind of obvious like I want to
+prove I want to prove something
+
+ align:start position:0%
+prove I want to prove something
+ 
+
+ align:start position:0%
+prove I want to prove something
+and the proof size does not change
+
+ align:start position:0%
+and the proof size does not change
+ 
+
+ align:start position:0%
+and the proof size does not change
+regardless of how many things
+
+ align:start position:0%
+regardless of how many things
+ 
+
+ align:start position:0%
+regardless of how many things
+I'm proving well it's just a signature
+
+ align:start position:0%
+I'm proving well it's just a signature
+ 
+
+ align:start position:0%
+I'm proving well it's just a signature
+right if I make a million signatures
+
+ align:start position:0%
+right if I make a million signatures
+ 
+
+ align:start position:0%
+right if I make a million signatures
+they're all the same size so I could
+
+ align:start position:0%
+they're all the same size so I could
+ 
+
+ align:start position:0%
+they're all the same size so I could
+instead of making a Merkel root I just
+
+ align:start position:0%
+instead of making a Merkel root I just
+ 
+
+ align:start position:0%
+instead of making a Merkel root I just
+have all these little leaves and I just
+
+ align:start position:0%
+have all these little leaves and I just
+ 
+
+ align:start position:0%
+have all these little leaves and I just
+sign them all and a leaf with a
+
+ align:start position:0%
+sign them all and a leaf with a
+ 
+
+ align:start position:0%
+sign them all and a leaf with a
+signature it's just as good okay so the
+
+ align:start position:0%
+signature it's just as good okay so the
+ 
+
+ align:start position:0%
+signature it's just as good okay so the
+idea is this is called graft root it's
+
+ align:start position:0%
+idea is this is called graft root it's
+ 
+
+ align:start position:0%
+idea is this is called graft root it's
+similar to trap fruit in that it's got
+
+ align:start position:0%
+similar to trap fruit in that it's got
+ 
+
+ align:start position:0%
+similar to trap fruit in that it's got
+sort of two execution paths you send to
+
+ align:start position:0%
+sort of two execution paths you send to
+ 
+
+ align:start position:0%
+sort of two execution paths you send to
+a key see and there's two ways to spend
+
+ align:start position:0%
+a key see and there's two ways to spend
+ 
+
+ align:start position:0%
+a key see and there's two ways to spend
+from it so you can use the regular pay
+
+ align:start position:0%
+from it so you can use the regular pay
+ 
+
+ align:start position:0%
+from it so you can use the regular pay
+to pub key hash mode where you're just
+
+ align:start position:0%
+to pub key hash mode where you're just
+ 
+
+ align:start position:0%
+to pub key hash mode where you're just
+spending from C you just sign with key C
+
+ align:start position:0%
+spending from C you just sign with key C
+ 
+
+ align:start position:0%
+spending from C you just sign with key C
+your transaction same as in tap root
+
+ align:start position:0%
+your transaction same as in tap root
+ 
+
+ align:start position:0%
+your transaction same as in tap root
+same as in regular Bitcoin right now
+
+ align:start position:0%
+same as in regular Bitcoin right now
+ 
+
+ align:start position:0%
+same as in regular Bitcoin right now
+that's the easy one the script version
+
+ align:start position:0%
+that's the easy one the script version
+ 
+
+ align:start position:0%
+that's the easy one the script version
+is I show a script s and a signature
+
+ align:start position:0%
+is I show a script s and a signature
+ 
+
+ align:start position:0%
+is I show a script s and a signature
+from key C on the message s and then I
+
+ align:start position:0%
+from key C on the message s and then I
+ 
+
+ align:start position:0%
+from key C on the message s and then I
+execute that script so this is kind of
+
+ align:start position:0%
+execute that script so this is kind of
+ 
+
+ align:start position:0%
+execute that script so this is kind of
+cool right you say look I'm sending you
+
+ align:start position:0%
+cool right you say look I'm sending you
+ 
+
+ align:start position:0%
+cool right you say look I'm sending you
+a key and either that key itself signs
+
+ align:start position:0%
+a key and either that key itself signs
+ 
+
+ align:start position:0%
+a key and either that key itself signs
+or that key endorses a script to the to
+
+ align:start position:0%
+or that key endorses a script to the to
+ 
+
+ align:start position:0%
+or that key endorses a script to the to
+be executed and I can make as many of
+
+ align:start position:0%
+be executed and I can make as many of
+ 
+
+ align:start position:0%
+be executed and I can make as many of
+these as I want right so if I want a
+
+ align:start position:0%
+these as I want right so if I want a
+ 
+
+ align:start position:0%
+these as I want right so if I want a
+thousand different scripts it's not like
+
+ align:start position:0%
+thousand different scripts it's not like
+ 
+
+ align:start position:0%
+thousand different scripts it's not like
+I have to prove
+
+ align:start position:0%
+I have to prove
+ 
+
+ align:start position:0%
+I have to prove
+inclusion in three that's gonna be
+
+ align:start position:0%
+inclusion in three that's gonna be
+ 
+
+ align:start position:0%
+inclusion in three that's gonna be
+height 22 or height 12 or whatever I
+
+ align:start position:0%
+height 22 or height 12 or whatever I
+ 
+
+ align:start position:0%
+height 22 or height 12 or whatever I
+just have a signature saying okay kisi
+
+ align:start position:0%
+just have a signature saying okay kisi
+ 
+
+ align:start position:0%
+just have a signature saying okay kisi
+signed this to of fifty multi-sig kisi
+
+ align:start position:0%
+signed this to of fifty multi-sig kisi
+ 
+
+ align:start position:0%
+signed this to of fifty multi-sig kisi
+also signed this three of 52 of two
+
+ align:start position:0%
+also signed this three of 52 of two
+ 
+
+ align:start position:0%
+also signed this three of 52 of two
+other two of fifty multi Singh so the
+
+ align:start position:0%
+other two of fifty multi Singh so the
+ 
+
+ align:start position:0%
+other two of fifty multi Singh so the
+one that I'm actually using I just
+
+ align:start position:0%
+one that I'm actually using I just
+ 
+
+ align:start position:0%
+one that I'm actually using I just
+provide the proof that it's you know the
+
+ align:start position:0%
+provide the proof that it's you know the
+ 
+
+ align:start position:0%
+provide the proof that it's you know the
+proof of inclusion is just a signature
+
+ align:start position:0%
+proof of inclusion is just a signature
+ 
+
+ align:start position:0%
+proof of inclusion is just a signature
+questions about this makes sense kind of
+
+ align:start position:0%
+questions about this makes sense kind of
+ 
+
+ align:start position:0%
+questions about this makes sense kind of
+weird it works
+
+ align:start position:0%
+weird it works
+ 
+
+ align:start position:0%
+weird it works
+the problem is did I even well that's
+
+ align:start position:0%
+the problem is did I even well that's
+ 
+
+ align:start position:0%
+the problem is did I even well that's
+the real problem is there is this kisi
+
+ align:start position:0%
+the real problem is there is this kisi
+ 
+
+ align:start position:0%
+the real problem is there is this kisi
+right so there's this sort of root key
+
+ align:start position:0%
+right so there's this sort of root key
+ 
+
+ align:start position:0%
+right so there's this sort of root key
+that controls the whole thing right
+
+ align:start position:0%
+that controls the whole thing right
+ 
+
+ align:start position:0%
+that controls the whole thing right
+implicit like the idea is kisi can all
+
+ align:start position:0%
+implicit like the idea is kisi can all
+ 
+
+ align:start position:0%
+implicit like the idea is kisi can all
+you know endorses all the different
+
+ align:start position:0%
+you know endorses all the different
+ 
+
+ align:start position:0%
+you know endorses all the different
+leaves so then in the case of mast
+
+ align:start position:0%
+leaves so then in the case of mast
+ 
+
+ align:start position:0%
+leaves so then in the case of mast
+you've got let's say four different
+
+ align:start position:0%
+you've got let's say four different
+ 
+
+ align:start position:0%
+you've got let's say four different
+scripts that can execute all four of
+
+ align:start position:0%
+scripts that can execute all four of
+ 
+
+ align:start position:0%
+scripts that can execute all four of
+those are committed to by the Merkle
+
+ align:start position:0%
+those are committed to by the Merkle
+ 
+
+ align:start position:0%
+those are committed to by the Merkle
+root in the case of graft root let's say
+
+ align:start position:0%
+root in the case of graft root let's say
+ 
+
+ align:start position:0%
+root in the case of graft root let's say
+you have four different scripts see
+
+ align:start position:0%
+you have four different scripts see
+ 
+
+ align:start position:0%
+you have four different scripts see
+signs all four of those different
+
+ align:start position:0%
+signs all four of those different
+ 
+
+ align:start position:0%
+signs all four of those different
+scripts the thing is seek ensign 10
+
+ align:start position:0%
+scripts the thing is seek ensign 10
+ 
+
+ align:start position:0%
+scripts the thing is seek ensign 10
+scripts sees got total control over this
+
+ align:start position:0%
+scripts sees got total control over this
+ 
+
+ align:start position:0%
+scripts sees got total control over this
+output whereas before in the Merc the
+
+ align:start position:0%
+output whereas before in the Merc the
+ 
+
+ align:start position:0%
+output whereas before in the Merc the
+mast idea it can be different people
+
+ align:start position:0%
+mast idea it can be different people
+ 
+
+ align:start position:0%
+mast idea it can be different people
+right it could be Alison Bob Carol and
+
+ align:start position:0%
+right it could be Alison Bob Carol and
+ 
+
+ align:start position:0%
+right it could be Alison Bob Carol and
+Dave Edna and Gertrude I don't know and
+
+ align:start position:0%
+Dave Edna and Gertrude I don't know and
+ 
+
+ align:start position:0%
+Dave Edna and Gertrude I don't know and
+they might not be friends none no single
+
+ align:start position:0%
+they might not be friends none no single
+ 
+
+ align:start position:0%
+they might not be friends none no single
+entity there has full control so the
+
+ align:start position:0%
+entity there has full control so the
+ 
+
+ align:start position:0%
+entity there has full control so the
+idea of of this is well you can combine
+
+ align:start position:0%
+idea of of this is well you can combine
+ 
+
+ align:start position:0%
+idea of of this is well you can combine
+a whole bunch of people the key C is
+
+ align:start position:0%
+a whole bunch of people the key C is
+ 
+
+ align:start position:0%
+a whole bunch of people the key C is
+essentially everyone and they all have
+
+ align:start position:0%
+essentially everyone and they all have
+ 
+
+ align:start position:0%
+essentially everyone and they all have
+to sign off on all the different scripts
+
+ align:start position:0%
+to sign off on all the different scripts
+ 
+
+ align:start position:0%
+to sign off on all the different scripts
+that could happen and then distribute
+
+ align:start position:0%
+that could happen and then distribute
+ 
+
+ align:start position:0%
+that could happen and then distribute
+those signatures on those scripts which
+
+ align:start position:0%
+those signatures on those scripts which
+ 
+
+ align:start position:0%
+those signatures on those scripts which
+are groups so okay any basic idea makes
+
+ align:start position:0%
+are groups so okay any basic idea makes
+ 
+
+ align:start position:0%
+are groups so okay any basic idea makes
+sense this one's a little weirder I
+
+ align:start position:0%
+sense this one's a little weirder I
+ 
+
+ align:start position:0%
+sense this one's a little weirder I
+think I don't know if there's also a way
+
+ align:start position:0%
+think I don't know if there's also a way
+ 
+
+ align:start position:0%
+think I don't know if there's also a way
+in this so in this one there's a way to
+
+ align:start position:0%
+in this so in this one there's a way to
+ 
+
+ align:start position:0%
+in this so in this one there's a way to
+prove that there is no key C so let's
+
+ align:start position:0%
+prove that there is no key C so let's
+ 
+
+ align:start position:0%
+prove that there is no key C so let's
+sort of say look it's only gonna be this
+
+ align:start position:0%
+sort of say look it's only gonna be this
+ 
+
+ align:start position:0%
+sort of say look it's only gonna be this
+script and no one's gonna sign in the
+
+ align:start position:0%
+script and no one's gonna sign in the
+ 
+
+ align:start position:0%
+script and no one's gonna sign in the
+normal just the key signs
+
+ align:start position:0%
+normal just the key signs
+ 
+
+ align:start position:0%
+normal just the key signs
+that there's also a way to do that here
+
+ align:start position:0%
+that there's also a way to do that here
+ 
+
+ align:start position:0%
+that there's also a way to do that here
+it's much less useful though because
+
+ align:start position:0%
+it's much less useful though because
+ 
+
+ align:start position:0%
+it's much less useful though because
+what you essentially do is you you start
+
+ align:start position:0%
+what you essentially do is you you start
+ 
+
+ align:start position:0%
+what you essentially do is you you start
+with your script and then you compute a
+
+ align:start position:0%
+with your script and then you compute a
+ 
+
+ align:start position:0%
+with your script and then you compute a
+signature on it
+
+ align:start position:0%
+signature on it
+ 
+
+ align:start position:0%
+signature on it
+but you also prove that there was no
+
+ align:start position:0%
+but you also prove that there was no
+ 
+
+ align:start position:0%
+but you also prove that there was no
+private key that made the signature you
+
+ align:start position:0%
+private key that made the signature you
+ 
+
+ align:start position:0%
+private key that made the signature you
+have time it's actually really fun what
+
+ align:start position:0%
+have time it's actually really fun what
+ 
+
+ align:start position:0%
+have time it's actually really fun what
+you do is so normally you say like okay
+
+ align:start position:0%
+you do is so normally you say like okay
+ 
+
+ align:start position:0%
+you do is so normally you say like okay
+s equals K minus the hash of my message
+
+ align:start position:0%
+s equals K minus the hash of my message
+ 
+
+ align:start position:0%
+s equals K minus the hash of my message
+and R times 0.8 what if I want to prove
+
+ align:start position:0%
+and R times 0.8 what if I want to prove
+ 
+
+ align:start position:0%
+and R times 0.8 what if I want to prove
+to you that there is no a G equals R
+
+ align:start position:0%
+to you that there is no a G equals R
+ 
+
+ align:start position:0%
+to you that there is no a G equals R
+minus the hash of message oh hey I want
+
+ align:start position:0%
+minus the hash of message oh hey I want
+ 
+
+ align:start position:0%
+minus the hash of message oh hey I want
+to prove that like I do not know that
+
+ align:start position:0%
+to prove that like I do not know that
+ 
+
+ align:start position:0%
+to prove that like I do not know that
+private key and nobody knows it so what
+
+ align:start position:0%
+private key and nobody knows it so what
+ 
+
+ align:start position:0%
+private key and nobody knows it so what
+I do is I actually have to do it both I
+
+ align:start position:0%
+I do is I actually have to do it both I
+ 
+
+ align:start position:0%
+I do is I actually have to do it both I
+say okay I know the preimage of the
+
+ align:start position:0%
+say okay I know the preimage of the
+ 
+
+ align:start position:0%
+say okay I know the preimage of the
+x-coordinate same with our wait can I do
+
+ align:start position:0%
+x-coordinate same with our wait can I do
+ 
+
+ align:start position:0%
+x-coordinate same with our wait can I do
+this
+
+ align:start position:0%
+this
+ 
+
+ align:start position:0%
+this
+anyway well basically what I do is I
+
+ align:start position:0%
+anyway well basically what I do is I
+ 
+
+ align:start position:0%
+anyway well basically what I do is I
+compute a public key randomly or no I I
+
+ align:start position:0%
+compute a public key randomly or no I I
+ 
+
+ align:start position:0%
+compute a public key randomly or no I I
+first get the message I want to sign I
+
+ align:start position:0%
+first get the message I want to sign I
+ 
+
+ align:start position:0%
+first get the message I want to sign I
+make a random R yeah yeah I make a
+
+ align:start position:0%
+make a random R yeah yeah I make a
+ 
+
+ align:start position:0%
+make a random R yeah yeah I make a
+random R and I show that it's random
+
+ align:start position:0%
+random R and I show that it's random
+ 
+
+ align:start position:0%
+random R and I show that it's random
+right I know the preimage of its
+
+ align:start position:0%
+right I know the preimage of its
+ 
+
+ align:start position:0%
+right I know the preimage of its
+coordinates or something I can prove
+
+ align:start position:0%
+coordinates or something I can prove
+ 
+
+ align:start position:0%
+coordinates or something I can prove
+that I didn't construct this I don't
+
+ align:start position:0%
+that I didn't construct this I don't
+ 
+
+ align:start position:0%
+that I didn't construct this I don't
+know the private key and then I solve
+
+ align:start position:0%
+know the private key and then I solve
+ 
+
+ align:start position:0%
+know the private key and then I solve
+for a and s essentially so I can show
+
+ align:start position:0%
+for a and s essentially so I can show
+ 
+
+ align:start position:0%
+for a and s essentially so I can show
+look I've got a signature but I can
+
+ align:start position:0%
+look I've got a signature but I can
+ 
+
+ align:start position:0%
+look I've got a signature but I can
+prove that no one signed right because I
+
+ align:start position:0%
+prove that no one signed right because I
+ 
+
+ align:start position:0%
+prove that no one signed right because I
+came up with the I think I'd make a
+
+ align:start position:0%
+came up with the I think I'd make a
+ 
+
+ align:start position:0%
+came up with the I think I'd make a
+random ass and then I solve for a I
+
+ align:start position:0%
+random ass and then I solve for a I
+ 
+
+ align:start position:0%
+random ass and then I solve for a I
+solve for big a you know make a random s
+
+ align:start position:0%
+solve for big a you know make a random s
+ 
+
+ align:start position:0%
+solve for big a you know make a random s
+multiply it by G solve for it right so a
+
+ align:start position:0%
+multiply it by G solve for it right so a
+ 
+
+ align:start position:0%
+multiply it by G solve for it right so a
+divided by hash of our weight I can't do
+
+ align:start position:0%
+divided by hash of our weight I can't do
+ 
+
+ align:start position:0%
+divided by hash of our weight I can't do
+that can i yeah I can this is good
+
+ align:start position:0%
+that can i yeah I can this is good
+ 
+
+ align:start position:0%
+that can i yeah I can this is good
+equals
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+I know it's equals R - s G alright so I
+
+ align:start position:0%
+I know it's equals R - s G alright so I
+ 
+
+ align:start position:0%
+I know it's equals R - s G alright so I
+come up with a random R put it in here
+
+ align:start position:0%
+come up with a random R put it in here
+ 
+
+ align:start position:0%
+come up with a random R put it in here
+come up with a message I want to sign
+
+ align:start position:0%
+come up with a message I want to sign
+ 
+
+ align:start position:0%
+come up with a message I want to sign
+and then solve for a so I can do that
+
+ align:start position:0%
+and then solve for a so I can do that
+ 
+
+ align:start position:0%
+and then solve for a so I can do that
+and I can prove that there was you know
+
+ align:start position:0%
+and I can prove that there was you know
+ 
+
+ align:start position:0%
+and I can prove that there was you know
+I can prove that there was no real a
+
+ align:start position:0%
+I can prove that there was no real a
+ 
+
+ align:start position:0%
+I can prove that there was no real a
+because of the way I constructed it like
+
+ align:start position:0%
+because of the way I constructed it like
+ 
+
+ align:start position:0%
+because of the way I constructed it like
+I know weird things about RNA and so I
+
+ align:start position:0%
+I know weird things about RNA and so I
+ 
+
+ align:start position:0%
+I know weird things about RNA and so I
+can show that this is not a real
+
+ align:start position:0%
+can show that this is not a real
+ 
+
+ align:start position:0%
+can show that this is not a real
+signature however in this case it's not
+
+ align:start position:0%
+signature however in this case it's not
+ 
+
+ align:start position:0%
+signature however in this case it's not
+that useful in the case of taproot it's
+
+ align:start position:0%
+that useful in the case of taproot it's
+ 
+
+ align:start position:0%
+that useful in the case of taproot it's
+useful because I might want to prove to
+
+ align:start position:0%
+useful because I might want to prove to
+ 
+
+ align:start position:0%
+useful because I might want to prove to
+people look this is just a script there
+
+ align:start position:0%
+people look this is just a script there
+ 
+
+ align:start position:0%
+people look this is just a script there
+is no key in this case I can still do
+
+ align:start position:0%
+is no key in this case I can still do
+ 
+
+ align:start position:0%
+is no key in this case I can still do
+that I can say there's just a script
+
+ align:start position:0%
+that I can say there's just a script
+ 
+
+ align:start position:0%
+that I can say there's just a script
+there is no key but then I can only do
+
+ align:start position:0%
+there is no key but then I can only do
+ 
+
+ align:start position:0%
+there is no key but then I can only do
+it once right I can only have one thing
+
+ align:start position:0%
+it once right I can only have one thing
+ 
+
+ align:start position:0%
+it once right I can only have one thing
+the whole idea of graft root is I can
+
+ align:start position:0%
+the whole idea of graft root is I can
+ 
+
+ align:start position:0%
+the whole idea of graft root is I can
+have a million different scripts that
+
+ align:start position:0%
+have a million different scripts that
+ 
+
+ align:start position:0%
+have a million different scripts that
+are all going into one key okay so the
+
+ align:start position:0%
+are all going into one key okay so the
+ 
+
+ align:start position:0%
+are all going into one key okay so the
+problem is the root key must die in
+
+ align:start position:0%
+problem is the root key must die in
+ 
+
+ align:start position:0%
+problem is the root key must die in
+every script and now you need to use
+
+ align:start position:0%
+every script and now you need to use
+ 
+
+ align:start position:0%
+every script and now you need to use
+private keys to create an address that's
+
+ align:start position:0%
+private keys to create an address that's
+ 
+
+ align:start position:0%
+private keys to create an address that's
+not great right it's maybe okay but you
+
+ align:start position:0%
+not great right it's maybe okay but you
+ 
+
+ align:start position:0%
+not great right it's maybe okay but you
+haven't had to do that before so so now
+
+ align:start position:0%
+haven't had to do that before so so now
+ 
+
+ align:start position:0%
+haven't had to do that before so so now
+we have to sign off on every script that
+
+ align:start position:0%
+we have to sign off on every script that
+ 
+
+ align:start position:0%
+we have to sign off on every script that
+we're endorsing in order to compute an
+
+ align:start position:0%
+we're endorsing in order to compute an
+ 
+
+ align:start position:0%
+we're endorsing in order to compute an
+address you can do this after the fact
+
+ align:start position:0%
+address you can do this after the fact
+ 
+
+ align:start position:0%
+address you can do this after the fact
+though so that's kind of the interesting
+
+ align:start position:0%
+though so that's kind of the interesting
+ 
+
+ align:start position:0%
+though so that's kind of the interesting
+thing about this is you can say okay I'm
+
+ align:start position:0%
+thing about this is you can say okay I'm
+ 
+
+ align:start position:0%
+thing about this is you can say okay I'm
+sending the key C which is this root key
+
+ align:start position:0%
+sending the key C which is this root key
+ 
+
+ align:start position:0%
+sending the key C which is this root key
+that's all 50 participants and then
+
+ align:start position:0%
+that's all 50 participants and then
+ 
+
+ align:start position:0%
+that's all 50 participants and then
+after the fact after it's been confirmed
+
+ align:start position:0%
+after the fact after it's been confirmed
+ 
+
+ align:start position:0%
+after the fact after it's been confirmed
+in the blockchain those 50 participants
+
+ align:start position:0%
+in the blockchain those 50 participants
+ 
+
+ align:start position:0%
+in the blockchain those 50 participants
+can say actually you know what
+
+ align:start position:0%
+can say actually you know what
+ 
+
+ align:start position:0%
+can say actually you know what
+two of two of 50 is good we're not
+
+ align:start position:0%
+two of two of 50 is good we're not
+ 
+
+ align:start position:0%
+two of two of 50 is good we're not
+suspending the money right now but we're
+
+ align:start position:0%
+suspending the money right now but we're
+ 
+
+ align:start position:0%
+suspending the money right now but we're
+all agreeing that yeah any two of us can
+
+ align:start position:0%
+all agreeing that yeah any two of us can
+ 
+
+ align:start position:0%
+all agreeing that yeah any two of us can
+spend this money later and so they all
+
+ align:start position:0%
+spend this money later and so they all
+ 
+
+ align:start position:0%
+spend this money later and so they all
+get together and all 50 sign with the
+
+ align:start position:0%
+get together and all 50 sign with the
+ 
+
+ align:start position:0%
+get together and all 50 sign with the
+root key see all the different scripts
+
+ align:start position:0%
+root key see all the different scripts
+ 
+
+ align:start position:0%
+root key see all the different scripts
+those 1225 scripts and then hand those
+
+ align:start position:0%
+those 1225 scripts and then hand those
+ 
+
+ align:start position:0%
+those 1225 scripts and then hand those
+signatures out to the respective people
+
+ align:start position:0%
+signatures out to the respective people
+ 
+
+ align:start position:0%
+signatures out to the respective people
+who who would be interested in that
+
+ align:start position:0%
+who who would be interested in that
+ 
+
+ align:start position:0%
+who who would be interested in that
+signature right so Alice and Bob if you
+
+ align:start position:0%
+signature right so Alice and Bob if you
+ 
+
+ align:start position:0%
+signature right so Alice and Bob if you
+want to spend the money we all made a
+
+ align:start position:0%
+want to spend the money we all made a
+ 
+
+ align:start position:0%
+want to spend the money we all made a
+signature endorsing your - of - you know
+
+ align:start position:0%
+signature endorsing your - of - you know
+ 
+
+ align:start position:0%
+signature endorsing your - of - you know
+- of 50 your two keys and Bob and Carol
+
+ align:start position:0%
+- of 50 your two keys and Bob and Carol
+ 
+
+ align:start position:0%
+- of 50 your two keys and Bob and Carol
+if you two want to spend the money we've
+
+ align:start position:0%
+if you two want to spend the money we've
+ 
+
+ align:start position:0%
+if you two want to spend the money we've
+made a script
+
+ align:start position:0%
+made a script
+ 
+
+ align:start position:0%
+made a script
+that's a you know that's endorsed by us
+
+ align:start position:0%
+that's a you know that's endorsed by us
+ 
+
+ align:start position:0%
+that's a you know that's endorsed by us
+saying your two keys can spend it it's
+
+ align:start position:0%
+saying your two keys can spend it it's
+ 
+
+ align:start position:0%
+saying your two keys can spend it it's
+really cool the overhead is one
+
+ align:start position:0%
+really cool the overhead is one
+ 
+
+ align:start position:0%
+really cool the overhead is one
+signature so you can have that like
+
+ align:start position:0%
+signature so you can have that like
+ 
+
+ align:start position:0%
+signature so you can have that like
+hundred trillion different you know 2050
+
+ align:start position:0%
+hundred trillion different you know 2050
+ 
+
+ align:start position:0%
+hundred trillion different you know 2050
+choose 25 which is 100 trillion well you
+
+ align:start position:0%
+choose 25 which is 100 trillion well you
+ 
+
+ align:start position:0%
+choose 25 which is 100 trillion well you
+got a sign 100 trillion times but when
+
+ align:start position:0%
+got a sign 100 trillion times but when
+ 
+
+ align:start position:0%
+got a sign 100 trillion times but when
+you spend from it it's small it's an
+
+ align:start position:0%
+you spend from it it's small it's an
+ 
+
+ align:start position:0%
+you spend from it it's small it's an
+extra thirty three bytes of overhead
+
+ align:start position:0%
+extra thirty three bytes of overhead
+ 
+
+ align:start position:0%
+extra thirty three bytes of overhead
+yeah the overhead is just a signature
+
+ align:start position:0%
+yeah the overhead is just a signature
+ 
+
+ align:start position:0%
+yeah the overhead is just a signature
+right so you say okay here's key see
+
+ align:start position:0%
+right so you say okay here's key see
+ 
+
+ align:start position:0%
+right so you say okay here's key see
+here's a signature from it here's the
+
+ align:start position:0%
+here's a signature from it here's the
+ 
+
+ align:start position:0%
+here's a signature from it here's the
+script to endorse the script being
+
+ align:start position:0%
+script to endorse the script being
+ 
+
+ align:start position:0%
+script to endorse the script being
+executed it's not actually 64 bytes you
+
+ align:start position:0%
+executed it's not actually 64 bytes you
+ 
+
+ align:start position:0%
+executed it's not actually 64 bytes you
+can get the overhead in 233 bytes
+
+ align:start position:0%
+can get the overhead in 233 bytes
+ 
+
+ align:start position:0%
+can get the overhead in 233 bytes
+because you can aggregate the s values
+
+ align:start position:0%
+because you can aggregate the s values
+ 
+
+ align:start position:0%
+because you can aggregate the s values
+of the signature I'll talk about this on
+
+ align:start position:0%
+of the signature I'll talk about this on
+ 
+
+ align:start position:0%
+of the signature I'll talk about this on
+Wednesday I don't think I actually came
+
+ align:start position:0%
+Wednesday I don't think I actually came
+ 
+
+ align:start position:0%
+Wednesday I don't think I actually came
+up with this but Greg cites me on it and
+
+ align:start position:0%
+up with this but Greg cites me on it and
+ 
+
+ align:start position:0%
+up with this but Greg cites me on it and
+it's like a yes no one thought of this
+
+ align:start position:0%
+it's like a yes no one thought of this
+ 
+
+ align:start position:0%
+it's like a yes no one thought of this
+huh but there's like a non-interactive
+
+ align:start position:0%
+huh but there's like a non-interactive
+ 
+
+ align:start position:0%
+huh but there's like a non-interactive
+partial aggregation of these things
+
+ align:start position:0%
+partial aggregation of these things
+ 
+
+ align:start position:0%
+partial aggregation of these things
+which I was really hoping we'd get into
+
+ align:start position:0%
+which I was really hoping we'd get into
+ 
+
+ align:start position:0%
+which I was really hoping we'd get into
+Bitcoin itself but I think it's too slow
+
+ align:start position:0%
+Bitcoin itself but I think it's too slow
+ 
+
+ align:start position:0%
+Bitcoin itself but I think it's too slow
+but in this case it's not that slow so
+
+ align:start position:0%
+but in this case it's not that slow so
+ 
+
+ align:start position:0%
+but in this case it's not that slow so
+people like yeah we'll use it here okay
+
+ align:start position:0%
+people like yeah we'll use it here okay
+ 
+
+ align:start position:0%
+people like yeah we'll use it here okay
+so this is kind of cool because it's
+
+ align:start position:0%
+so this is kind of cool because it's
+ 
+
+ align:start position:0%
+so this is kind of cool because it's
+simple right it's just more scripts can
+
+ align:start position:0%
+simple right it's just more scripts can
+ 
+
+ align:start position:0%
+simple right it's just more scripts can
+be at at any time it's all one scaling
+
+ align:start position:0%
+be at at any time it's all one scaling
+ 
+
+ align:start position:0%
+be at at any time it's all one scaling
+so if you have a million different
+
+ align:start position:0%
+so if you have a million different
+ 
+
+ align:start position:0%
+so if you have a million different
+scripts proving one of them just takes
+
+ align:start position:0%
+scripts proving one of them just takes
+ 
+
+ align:start position:0%
+scripts proving one of them just takes
+32 bytes or 33 or something C can be a
+
+ align:start position:0%
+32 bytes or 33 or something C can be a
+ 
+
+ align:start position:0%
+32 bytes or 33 or something C can be a
+threshold signature of many different
+
+ align:start position:0%
+threshold signature of many different
+ 
+
+ align:start position:0%
+threshold signature of many different
+parties the signature can be aggregated
+
+ align:start position:0%
+parties the signature can be aggregated
+ 
+
+ align:start position:0%
+parties the signature can be aggregated
+within the transaction
+
+ align:start position:0%
+within the transaction
+ 
+
+ align:start position:0%
+within the transaction
+the downside is this interactive setup
+
+ align:start position:0%
+the downside is this interactive setup
+ 
+
+ align:start position:0%
+the downside is this interactive setup
+where you can't just take Alice and Bob
+
+ align:start position:0%
+where you can't just take Alice and Bob
+ 
+
+ align:start position:0%
+where you can't just take Alice and Bob
+and Carols key and send to a graph route
+
+ align:start position:0%
+and Carols key and send to a graph route
+ 
+
+ align:start position:0%
+and Carols key and send to a graph route
+to a three multi-sig right Alice and Bob
+
+ align:start position:0%
+to a three multi-sig right Alice and Bob
+ 
+
+ align:start position:0%
+to a three multi-sig right Alice and Bob
+and Carol need to sign something in some
+
+ align:start position:0%
+and Carol need to sign something in some
+ 
+
+ align:start position:0%
+and Carol need to sign something in some
+cases that's no big deal
+
+ align:start position:0%
+cases that's no big deal
+ 
+
+ align:start position:0%
+cases that's no big deal
+right in some cases your connect to them
+
+ align:start position:0%
+right in some cases your connect to them
+ 
+
+ align:start position:0%
+right in some cases your connect to them
+over the internet and all the
+
+ align:start position:0%
+over the internet and all the
+ 
+
+ align:start position:0%
+over the internet and all the
+participants are cooperating sure will
+
+ align:start position:0%
+participants are cooperating sure will
+ 
+
+ align:start position:0%
+participants are cooperating sure will
+sign will create addresses or will pre
+
+ align:start position:0%
+sign will create addresses or will pre
+ 
+
+ align:start position:0%
+sign will create addresses or will pre
+sign all sorts of different addresses
+
+ align:start position:0%
+sign all sorts of different addresses
+ 
+
+ align:start position:0%
+sign all sorts of different addresses
+beforehand doable but sometimes you
+
+ align:start position:0%
+beforehand doable but sometimes you
+ 
+
+ align:start position:0%
+beforehand doable but sometimes you
+don't want this interactive set up
+
+ align:start position:0%
+don't want this interactive set up
+ 
+
+ align:start position:0%
+don't want this interactive set up
+sometimes I want to be able to send to
+
+ align:start position:0%
+sometimes I want to be able to send to
+ 
+
+ align:start position:0%
+sometimes I want to be able to send to
+participants of my choosing without
+
+ align:start position:0%
+participants of my choosing without
+ 
+
+ align:start position:0%
+participants of my choosing without
+their cooperation usually for standing
+
+ align:start position:0%
+their cooperation usually for standing
+ 
+
+ align:start position:0%
+their cooperation usually for standing
+people money they're ok with it right
+
+ align:start position:0%
+people money they're ok with it right
+ 
+
+ align:start position:0%
+people money they're ok with it right
+but sometimes you don't want them to be
+
+ align:start position:0%
+but sometimes you don't want them to be
+ 
+
+ align:start position:0%
+but sometimes you don't want them to be
+online okay
+
+ align:start position:0%
+online okay
+ 
+
+ align:start position:0%
+online okay
+so put this all together the idea and
+
+ align:start position:0%
+so put this all together the idea and
+ 
+
+ align:start position:0%
+so put this all together the idea and
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+the goal for this and I think the way
+
+ align:start position:0%
+the goal for this and I think the way
+ 
+
+ align:start position:0%
+the goal for this and I think the way
+it's gonna work in Bitcoin but this is
+
+ align:start position:0%
+it's gonna work in Bitcoin but this is
+ 
+
+ align:start position:0%
+it's gonna work in Bitcoin but this is
+still you know research kind of you have
+
+ align:start position:0%
+still you know research kind of you have
+ 
+
+ align:start position:0%
+still you know research kind of you have
+a unified output script so let's say
+
+ align:start position:0%
+a unified output script so let's say
+ 
+
+ align:start position:0%
+a unified output script so let's say
+it's a templated with op v and you say
+
+ align:start position:0%
+it's a templated with op v and you say
+ 
+
+ align:start position:0%
+it's a templated with op v and you say
+okay op v pub key now when i want to
+
+ align:start position:0%
+okay op v pub key now when i want to
+ 
+
+ align:start position:0%
+okay op v pub key now when i want to
+spend to it i have a bunch of options to
+
+ align:start position:0%
+spend to it i have a bunch of options to
+ 
+
+ align:start position:0%
+spend to it i have a bunch of options to
+spend I can just put a signature on the
+
+ align:start position:0%
+spend I can just put a signature on the
+ 
+
+ align:start position:0%
+spend I can just put a signature on the
+stack and then the program says oh
+
+ align:start position:0%
+stack and then the program says oh
+ 
+
+ align:start position:0%
+stack and then the program says oh
+there's a signature let me check if the
+
+ align:start position:0%
+there's a signature let me check if the
+ 
+
+ align:start position:0%
+there's a signature let me check if the
+signature matches the public key
+
+ align:start position:0%
+signature matches the public key
+ 
+
+ align:start position:0%
+signature matches the public key
+you know this funky and if it does cool
+
+ align:start position:0%
+you know this funky and if it does cool
+ 
+
+ align:start position:0%
+you know this funky and if it does cool
+the move money moves
+
+ align:start position:0%
+the move money moves
+ 
+
+ align:start position:0%
+the move money moves
+that's pub pay to pub key hash mode
+
+ align:start position:0%
+that's pub pay to pub key hash mode
+ 
+
+ align:start position:0%
+that's pub pay to pub key hash mode
+except it's not a match
+
+ align:start position:0%
+except it's not a match
+ 
+
+ align:start position:0%
+except it's not a match
+another thing I can do is provide a
+
+ align:start position:0%
+another thing I can do is provide a
+ 
+
+ align:start position:0%
+another thing I can do is provide a
+point J a script and a series of
+
+ align:start position:0%
+point J a script and a series of
+ 
+
+ align:start position:0%
+point J a script and a series of
+arguments for the script and that's
+
+ align:start position:0%
+arguments for the script and that's
+ 
+
+ align:start position:0%
+arguments for the script and that's
+Tapper I verify that J plus the you know
+
+ align:start position:0%
+Tapper I verify that J plus the you know
+ 
+
+ align:start position:0%
+Tapper I verify that J plus the you know
+I verify that J plus the hash of J and
+
+ align:start position:0%
+I verify that J plus the hash of J and
+ 
+
+ align:start position:0%
+I verify that J plus the hash of J and
+the script times G is equal to that pump
+
+ align:start position:0%
+the script times G is equal to that pump
+ 
+
+ align:start position:0%
+the script times G is equal to that pump
+key and then I execute that script
+
+ align:start position:0%
+key and then I execute that script
+ 
+
+ align:start position:0%
+key and then I execute that script
+another way to do it is if I've got this
+
+ align:start position:0%
+another way to do it is if I've got this
+ 
+
+ align:start position:0%
+another way to do it is if I've got this
+I've got C which is also just a point
+
+ align:start position:0%
+I've got C which is also just a point
+ 
+
+ align:start position:0%
+I've got C which is also just a point
+and I signature on the script and then a
+
+ align:start position:0%
+and I signature on the script and then a
+ 
+
+ align:start position:0%
+and I signature on the script and then a
+script and a bunch of arguments then I
+
+ align:start position:0%
+script and a bunch of arguments then I
+ 
+
+ align:start position:0%
+script and a bunch of arguments then I
+say oh this is crafter I'll verify this
+
+ align:start position:0%
+say oh this is crafter I'll verify this
+ 
+
+ align:start position:0%
+say oh this is crafter I'll verify this
+script this signature on this script and
+
+ align:start position:0%
+script this signature on this script and
+ 
+
+ align:start position:0%
+script this signature on this script and
+then execute with these arguments so I
+
+ align:start position:0%
+then execute with these arguments so I
+ 
+
+ align:start position:0%
+then execute with these arguments so I
+was it would be cool if you could do it
+
+ align:start position:0%
+was it would be cool if you could do it
+ 
+
+ align:start position:0%
+was it would be cool if you could do it
+just based on the number of items pushed
+
+ align:start position:0%
+just based on the number of items pushed
+ 
+
+ align:start position:0%
+just based on the number of items pushed
+but you might want to put like a flag or
+
+ align:start position:0%
+but you might want to put like a flag or
+ 
+
+ align:start position:0%
+but you might want to put like a flag or
+something here to distinguish between
+
+ align:start position:0%
+something here to distinguish between
+ 
+
+ align:start position:0%
+something here to distinguish between
+these two if it's this if there's just
+
+ align:start position:0%
+these two if it's this if there's just
+ 
+
+ align:start position:0%
+these two if it's this if there's just
+one element you can just quickly say
+
+ align:start position:0%
+one element you can just quickly say
+ 
+
+ align:start position:0%
+one element you can just quickly say
+okay it's made of funky but to
+
+ align:start position:0%
+okay it's made of funky but to
+ 
+
+ align:start position:0%
+okay it's made of funky but to
+distinguish between these two there
+
+ align:start position:0%
+distinguish between these two there
+ 
+
+ align:start position:0%
+distinguish between these two there
+might be weird edge cases where it's
+
+ align:start position:0%
+might be weird edge cases where it's
+ 
+
+ align:start position:0%
+might be weird edge cases where it's
+like well one of the arguments could
+
+ align:start position:0%
+like well one of the arguments could
+ 
+
+ align:start position:0%
+like well one of the arguments could
+also look like a script and annoying
+
+ align:start position:0%
+also look like a script and annoying
+ 
+
+ align:start position:0%
+also look like a script and annoying
+thing so you might put some like flag
+
+ align:start position:0%
+thing so you might put some like flag
+ 
+
+ align:start position:0%
+thing so you might put some like flag
+bite but anyway it's kind of nice in
+
+ align:start position:0%
+bite but anyway it's kind of nice in
+ 
+
+ align:start position:0%
+bite but anyway it's kind of nice in
+that when you send to an output you send
+
+ align:start position:0%
+that when you send to an output you send
+ 
+
+ align:start position:0%
+that when you send to an output you send
+to an address all the addresses look the
+
+ align:start position:0%
+to an address all the addresses look the
+ 
+
+ align:start position:0%
+to an address all the addresses look the
+same they just look like public keys but
+
+ align:start position:0%
+same they just look like public keys but
+ 
+
+ align:start position:0%
+same they just look like public keys but
+they could be any of these things and
+
+ align:start position:0%
+they could be any of these things and
+ 
+
+ align:start position:0%
+they could be any of these things and
+you only find out after the fact
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+in not only that you could have the same
+
+ align:start position:0%
+in not only that you could have the same
+ 
+
+ align:start position:0%
+in not only that you could have the same
+key have a taproot and also have a
+
+ align:start position:0%
+key have a taproot and also have a
+ 
+
+ align:start position:0%
+key have a taproot and also have a
+grafter right you could you could have
+
+ align:start position:0%
+grafter right you could you could have
+ 
+
+ align:start position:0%
+grafter right you could you could have
+you know so they're clear
+
+ align:start position:0%
+you know so they're clear
+ 
+
+ align:start position:0%
+you know so they're clear
+in a dress and I've gotten my wallet
+
+ align:start position:0%
+in a dress and I've gotten my wallet
+ 
+
+ align:start position:0%
+in a dress and I've gotten my wallet
+well there's three different ways I can
+
+ align:start position:0%
+well there's three different ways I can
+ 
+
+ align:start position:0%
+well there's three different ways I can
+spend this I can spend this with
+
+ align:start position:0%
+spend this I can spend this with
+ 
+
+ align:start position:0%
+spend this I can spend this with
+everyone all 50 people signing or I can
+
+ align:start position:0%
+everyone all 50 people signing or I can
+ 
+
+ align:start position:0%
+everyone all 50 people signing or I can
+spend it with the like you know a single
+
+ align:start position:0%
+spend it with the like you know a single
+ 
+
+ align:start position:0%
+spend it with the like you know a single
+script that's been endorsed this way
+
+ align:start position:0%
+script that's been endorsed this way
+ 
+
+ align:start position:0%
+script that's been endorsed this way
+that's got like priority and then I can
+
+ align:start position:0%
+that's got like priority and then I can
+ 
+
+ align:start position:0%
+that's got like priority and then I can
+also spend it with one of the millions
+
+ align:start position:0%
+also spend it with one of the millions
+ 
+
+ align:start position:0%
+also spend it with one of the millions
+of scripts that have been endorsed this
+
+ align:start position:0%
+of scripts that have been endorsed this
+ 
+
+ align:start position:0%
+of scripts that have been endorsed this
+way so I can use all three this is a
+
+ align:start position:0%
+way so I can use all three this is a
+ 
+
+ align:start position:0%
+way so I can use all three this is a
+little bit more efficient right because
+
+ align:start position:0%
+little bit more efficient right because
+ 
+
+ align:start position:0%
+little bit more efficient right because
+you're just revealing the script and a
+
+ align:start position:0%
+you're just revealing the script and a
+ 
+
+ align:start position:0%
+you're just revealing the script and a
+point this one you have to reveal
+
+ align:start position:0%
+point this one you have to reveal
+ 
+
+ align:start position:0%
+point this one you have to reveal
+oh no wait sorry this is wrong there's
+
+ align:start position:0%
+oh no wait sorry this is wrong there's
+ 
+
+ align:start position:0%
+oh no wait sorry this is wrong there's
+no see you already know see it's it's
+
+ align:start position:0%
+no see you already know see it's it's
+ 
+
+ align:start position:0%
+no see you already know see it's it's
+still a little more efficient yeah
+
+ align:start position:0%
+still a little more efficient yeah
+ 
+
+ align:start position:0%
+still a little more efficient yeah
+there's no see there you already know
+
+ align:start position:0%
+there's no see there you already know
+ 
+
+ align:start position:0%
+there's no see there you already know
+see you just put the signature on the
+
+ align:start position:0%
+see you just put the signature on the
+ 
+
+ align:start position:0%
+see you just put the signature on the
+script yeah okay so this is graph root
+
+ align:start position:0%
+script yeah okay so this is graph root
+ 
+
+ align:start position:0%
+script yeah okay so this is graph root
+tap root and then also part of the
+
+ align:start position:0%
+tap root and then also part of the
+ 
+
+ align:start position:0%
+tap root and then also part of the
+script can be masked you can have a mask
+
+ align:start position:0%
+script can be masked you can have a mask
+ 
+
+ align:start position:0%
+script can be masked you can have a mask
+top code you can combine all these
+
+ align:start position:0%
+top code you can combine all these
+ 
+
+ align:start position:0%
+top code you can combine all these
+things in crazy ways and have like
+
+ align:start position:0%
+things in crazy ways and have like
+ 
+
+ align:start position:0%
+things in crazy ways and have like
+really powerful scripting that way okay
+
+ align:start position:0%
+really powerful scripting that way okay
+ 
+
+ align:start position:0%
+really powerful scripting that way okay
+so when this stuff was proposed the
+
+ align:start position:0%
+so when this stuff was proposed the
+ 
+
+ align:start position:0%
+so when this stuff was proposed the
+argument was hey I don't want to spend
+
+ align:start position:0%
+argument was hey I don't want to spend
+ 
+
+ align:start position:0%
+argument was hey I don't want to spend
+to a public key I want to spend to a
+
+ align:start position:0%
+to a public key I want to spend to a
+ 
+
+ align:start position:0%
+to a public key I want to spend to a
+public key hash because quantum
+
+ align:start position:0%
+public key hash because quantum
+ 
+
+ align:start position:0%
+public key hash because quantum
+computers are coming and when the
+
+ align:start position:0%
+computers are coming and when the
+ 
+
+ align:start position:0%
+computers are coming and when the
+quantum computers come if you know my
+
+ align:start position:0%
+quantum computers come if you know my
+ 
+
+ align:start position:0%
+quantum computers come if you know my
+pub key you can just calculate my
+
+ align:start position:0%
+pub key you can just calculate my
+ 
+
+ align:start position:0%
+pub key you can just calculate my
+private key and take all my money but if
+
+ align:start position:0%
+private key and take all my money but if
+ 
+
+ align:start position:0%
+private key and take all my money but if
+you only know my public key hash quantum
+
+ align:start position:0%
+you only know my public key hash quantum
+ 
+
+ align:start position:0%
+you only know my public key hash quantum
+computer doesn't help you there right
+
+ align:start position:0%
+computer doesn't help you there right
+ 
+
+ align:start position:0%
+computer doesn't help you there right
+you're not going to be able to compute
+
+ align:start position:0%
+you're not going to be able to compute
+ 
+
+ align:start position:0%
+you're not going to be able to compute
+the preimage of a hash with the quantum
+
+ align:start position:0%
+the preimage of a hash with the quantum
+ 
+
+ align:start position:0%
+the preimage of a hash with the quantum
+computer there's yeah that's true all of
+
+ align:start position:0%
+computer there's yeah that's true all of
+ 
+
+ align:start position:0%
+computer there's yeah that's true all of
+those statements are true except in
+
+ align:start position:0%
+those statements are true except in
+ 
+
+ align:start position:0%
+those statements are true except in
+practice it's it's dumb because if
+
+ align:start position:0%
+practice it's it's dumb because if
+ 
+
+ align:start position:0%
+practice it's it's dumb because if
+there's a quantum computer that can
+
+ align:start position:0%
+there's a quantum computer that can
+ 
+
+ align:start position:0%
+there's a quantum computer that can
+compute your private key from your
+
+ align:start position:0%
+compute your private key from your
+ 
+
+ align:start position:0%
+compute your private key from your
+public key
+
+ align:start position:0%
+public key
+ 
+
+ align:start position:0%
+public key
+the only time using Punky hashes will
+
+ align:start position:0%
+the only time using Punky hashes will
+ 
+
+ align:start position:0%
+the only time using Punky hashes will
+help you is if somehow that quantum
+
+ align:start position:0%
+help you is if somehow that quantum
+ 
+
+ align:start position:0%
+help you is if somehow that quantum
+computer takes a really long time to
+
+ align:start position:0%
+computer takes a really long time to
+ 
+
+ align:start position:0%
+computer takes a really long time to
+compute your private key right because
+
+ align:start position:0%
+compute your private key right because
+ 
+
+ align:start position:0%
+compute your private key right because
+if it only takes them a minute to
+
+ align:start position:0%
+if it only takes them a minute to
+ 
+
+ align:start position:0%
+if it only takes them a minute to
+compute it well you have to reveal your
+
+ align:start position:0%
+compute it well you have to reveal your
+ 
+
+ align:start position:0%
+compute it well you have to reveal your
+public key to spend your money and then
+
+ align:start position:0%
+public key to spend your money and then
+ 
+
+ align:start position:0%
+public key to spend your money and then
+the attacker who has this nifty quantum
+
+ align:start position:0%
+the attacker who has this nifty quantum
+ 
+
+ align:start position:0%
+the attacker who has this nifty quantum
+computer can just say oh that's his
+
+ align:start position:0%
+computer can just say oh that's his
+ 
+
+ align:start position:0%
+computer can just say oh that's his
+public key I just saw it right
+
+ align:start position:0%
+public key I just saw it right
+ 
+
+ align:start position:0%
+public key I just saw it right
+and he signed and using his bubble key I
+
+ align:start position:0%
+and he signed and using his bubble key I
+ 
+
+ align:start position:0%
+and he signed and using his bubble key I
+just computers private key sign a
+
+ align:start position:0%
+just computers private key sign a
+ 
+
+ align:start position:0%
+just computers private key sign a
+different message and broadcast it and
+
+ align:start position:0%
+different message and broadcast it and
+ 
+
+ align:start position:0%
+different message and broadcast it and
+maybe I attach a higher fee because I
+
+ align:start position:0%
+maybe I attach a higher fee because I
+ 
+
+ align:start position:0%
+maybe I attach a higher fee because I
+don't care it's not my money and the
+
+ align:start position:0%
+don't care it's not my money and the
+ 
+
+ align:start position:0%
+don't care it's not my money and the
+miners are like well there's two
+
+ align:start position:0%
+miners are like well there's two
+ 
+
+ align:start position:0%
+miners are like well there's two
+different transactions one sending over
+
+ align:start position:0%
+different transactions one sending over
+ 
+
+ align:start position:0%
+different transactions one sending over
+here one sending over here this one has
+
+ align:start position:0%
+here one sending over here this one has
+ 
+
+ align:start position:0%
+here one sending over here this one has
+a much higher fee I'll use this one and
+
+ align:start position:0%
+a much higher fee I'll use this one and
+ 
+
+ align:start position:0%
+a much higher fee I'll use this one and
+the attacker with the quantum computer
+
+ align:start position:0%
+the attacker with the quantum computer
+ 
+
+ align:start position:0%
+the attacker with the quantum computer
+still takes all your money they can't
+
+ align:start position:0%
+still takes all your money they can't
+ 
+
+ align:start position:0%
+still takes all your money they can't
+take it at rest they have to wait for
+
+ align:start position:0%
+take it at rest they have to wait for
+ 
+
+ align:start position:0%
+take it at rest they have to wait for
+you to try to spend it and take it but
+
+ align:start position:0%
+you to try to spend it and take it but
+ 
+
+ align:start position:0%
+you to try to spend it and take it but
+you could say okay well actually I'm
+
+ align:start position:0%
+you could say okay well actually I'm
+ 
+
+ align:start position:0%
+you could say okay well actually I'm
+moving up five paid Punky hash and then
+
+ align:start position:0%
+moving up five paid Punky hash and then
+ 
+
+ align:start position:0%
+moving up five paid Punky hash and then
+for this I have to reveal pumpking
+
+ align:start position:0%
+for this I have to reveal pumpking
+ 
+
+ align:start position:0%
+for this I have to reveal pumpking
+signature for this I reveal pub key J
+
+ align:start position:0%
+signature for this I reveal pub key J
+ 
+
+ align:start position:0%
+signature for this I reveal pub key J
+component of pump key script for this I
+
+ align:start position:0%
+component of pump key script for this I
+ 
+
+ align:start position:0%
+component of pump key script for this I
+revealed you know see you missing but
+
+ align:start position:0%
+revealed you know see you missing but
+ 
+
+ align:start position:0%
+revealed you know see you missing but
+it's like kind of ugly waste of space
+
+ align:start position:0%
+it's like kind of ugly waste of space
+ 
+
+ align:start position:0%
+it's like kind of ugly waste of space
+and in most cases doesn't provide a lot
+
+ align:start position:0%
+and in most cases doesn't provide a lot
+ 
+
+ align:start position:0%
+and in most cases doesn't provide a lot
+of protection
+
+ align:start position:0%
+of protection
+ 
+
+ align:start position:0%
+of protection
+so there's hopefully better ways to deal
+
+ align:start position:0%
+so there's hopefully better ways to deal
+ 
+
+ align:start position:0%
+so there's hopefully better ways to deal
+with this one thing that I have sort of
+
+ align:start position:0%
+with this one thing that I have sort of
+ 
+
+ align:start position:0%
+with this one thing that I have sort of
+been joking about but it would be kind
+
+ align:start position:0%
+been joking about but it would be kind
+ 
+
+ align:start position:0%
+been joking about but it would be kind
+of fun to put it into wallets you can
+
+ align:start position:0%
+of fun to put it into wallets you can
+ 
+
+ align:start position:0%
+of fun to put it into wallets you can
+actually use tap root to commit to a
+
+ align:start position:0%
+actually use tap root to commit to a
+ 
+
+ align:start position:0%
+actually use tap root to commit to a
+Lamport like hash based pub key so in
+
+ align:start position:0%
+Lamport like hash based pub key so in
+ 
+
+ align:start position:0%
+Lamport like hash based pub key so in
+tap root this is actually quantum secure
+
+ align:start position:0%
+tap root this is actually quantum secure
+ 
+
+ align:start position:0%
+tap root this is actually quantum secure
+I hesitate to advertise this but it is a
+
+ align:start position:0%
+I hesitate to advertise this but it is a
+ 
+
+ align:start position:0%
+I hesitate to advertise this but it is a
+commitment that is not that the quantum
+
+ align:start position:0%
+commitment that is not that the quantum
+ 
+
+ align:start position:0%
+commitment that is not that the quantum
+computer cannot Forge right the the the
+
+ align:start position:0%
+computer cannot Forge right the the the
+ 
+
+ align:start position:0%
+computer cannot Forge right the the the
+whole wait where does it where as I
+
+ align:start position:0%
+whole wait where does it where as I
+ 
+
+ align:start position:0%
+whole wait where does it where as I
+saying the J equals hash of yeah this
+
+ align:start position:0%
+saying the J equals hash of yeah this
+ 
+
+ align:start position:0%
+saying the J equals hash of yeah this
+thing is still a problem for a quantum
+
+ align:start position:0%
+thing is still a problem for a quantum
+ 
+
+ align:start position:0%
+thing is still a problem for a quantum
+computer right you got I want to compute
+
+ align:start position:0%
+computer right you got I want to compute
+ 
+
+ align:start position:0%
+computer right you got I want to compute
+a J such that J equals this hash times G
+
+ align:start position:0%
+a J such that J equals this hash times G
+ 
+
+ align:start position:0%
+a J such that J equals this hash times G
+minus R the Jim J is in there as well
+
+ align:start position:0%
+minus R the Jim J is in there as well
+ 
+
+ align:start position:0%
+minus R the Jim J is in there as well
+even with a quantum computer maybe I can
+
+ align:start position:0%
+even with a quantum computer maybe I can
+ 
+
+ align:start position:0%
+even with a quantum computer maybe I can
+compute an arbitrary J and find its
+
+ align:start position:0%
+compute an arbitrary J and find its
+ 
+
+ align:start position:0%
+compute an arbitrary J and find its
+discrete log you know find the private
+
+ align:start position:0%
+discrete log you know find the private
+ 
+
+ align:start position:0%
+discrete log you know find the private
+key but it's still not going to satisfy
+
+ align:start position:0%
+key but it's still not going to satisfy
+ 
+
+ align:start position:0%
+key but it's still not going to satisfy
+this equation so I can't find I can't
+
+ align:start position:0%
+this equation so I can't find I can't
+ 
+
+ align:start position:0%
+this equation so I can't find I can't
+after the fact find a script in a J to
+
+ align:start position:0%
+after the fact find a script in a J to
+ 
+
+ align:start position:0%
+after the fact find a script in a J to
+compute
+
+ align:start position:0%
+compute
+ 
+
+ align:start position:0%
+compute
+see so that is safe even if a quantum
+
+ align:start position:0%
+see so that is safe even if a quantum
+ 
+
+ align:start position:0%
+see so that is safe even if a quantum
+computer exists right because that's
+
+ align:start position:0%
+computer exists right because that's
+ 
+
+ align:start position:0%
+computer exists right because that's
+based on the security the hash function
+
+ align:start position:0%
+based on the security the hash function
+ 
+
+ align:start position:0%
+based on the security the hash function
+so that's kind of an interesting little
+
+ align:start position:0%
+so that's kind of an interesting little
+ 
+
+ align:start position:0%
+so that's kind of an interesting little
+tidbit like hey this is this taproot
+
+ align:start position:0%
+tidbit like hey this is this taproot
+ 
+
+ align:start position:0%
+tidbit like hey this is this taproot
+construction this is hash based quantum
+
+ align:start position:0%
+construction this is hash based quantum
+ 
+
+ align:start position:0%
+construction this is hash based quantum
+computer appears and we say look we no
+
+ align:start position:0%
+computer appears and we say look we no
+ 
+
+ align:start position:0%
+computer appears and we say look we no
+longer allow C we no longer allow the
+
+ align:start position:0%
+longer allow C we no longer allow the
+ 
+
+ align:start position:0%
+longer allow C we no longer allow the
+normal spend where you sign with key C
+
+ align:start position:0%
+normal spend where you sign with key C
+ 
+
+ align:start position:0%
+normal spend where you sign with key C
+because signature is all this elliptic
+
+ align:start position:0%
+because signature is all this elliptic
+ 
+
+ align:start position:0%
+because signature is all this elliptic
+curve stuff it's broken however we do
+
+ align:start position:0%
+curve stuff it's broken however we do
+ 
+
+ align:start position:0%
+curve stuff it's broken however we do
+allow you to prove that there was a
+
+ align:start position:0%
+allow you to prove that there was a
+ 
+
+ align:start position:0%
+allow you to prove that there was a
+script Z can you know can committed to
+
+ align:start position:0%
+script Z can you know can committed to
+ 
+
+ align:start position:0%
+script Z can you know can committed to
+in C and then maybe this script has like
+
+ align:start position:0%
+in C and then maybe this script has like
+ 
+
+ align:start position:0%
+in C and then maybe this script has like
+a quantum safe signature in it and then
+
+ align:start position:0%
+a quantum safe signature in it and then
+ 
+
+ align:start position:0%
+a quantum safe signature in it and then
+we can use that what's nice about that
+
+ align:start position:0%
+we can use that what's nice about that
+ 
+
+ align:start position:0%
+we can use that what's nice about that
+is you can start using it sooner and
+
+ align:start position:0%
+is you can start using it sooner and
+ 
+
+ align:start position:0%
+is you can start using it sooner and
+without the overhead of all the extra
+
+ align:start position:0%
+without the overhead of all the extra
+ 
+
+ align:start position:0%
+without the overhead of all the extra
+space taken by the quantum signature
+
+ align:start position:0%
+space taken by the quantum signature
+ 
+
+ align:start position:0%
+space taken by the quantum signature
+because it's sort of a back-up plan it's
+
+ align:start position:0%
+because it's sort of a back-up plan it's
+ 
+
+ align:start position:0%
+because it's sort of a back-up plan it's
+like well normally I'm just signing with
+
+ align:start position:0%
+like well normally I'm just signing with
+ 
+
+ align:start position:0%
+like well normally I'm just signing with
+C right because I know what you know
+
+ align:start position:0%
+C right because I know what you know
+ 
+
+ align:start position:0%
+C right because I know what you know
+this is just my regular key and I do
+
+ align:start position:0%
+this is just my regular key and I do
+ 
+
+ align:start position:0%
+this is just my regular key and I do
+this but worst case scenario if a
+
+ align:start position:0%
+this but worst case scenario if a
+ 
+
+ align:start position:0%
+this but worst case scenario if a
+quantum computer appears in ten years
+
+ align:start position:0%
+quantum computer appears in ten years
+ 
+
+ align:start position:0%
+quantum computer appears in ten years
+I've got my other backup key here so
+
+ align:start position:0%
+I've got my other backup key here so
+ 
+
+ align:start position:0%
+I've got my other backup key here so
+that's kind of a cool thing I don't know
+
+ align:start position:0%
+that's kind of a cool thing I don't know
+ 
+
+ align:start position:0%
+that's kind of a cool thing I don't know
+how useful it is in practice but okay so
+
+ align:start position:0%
+how useful it is in practice but okay so
+ 
+
+ align:start position:0%
+how useful it is in practice but okay so
+yeah you got all these three things the
+
+ align:start position:0%
+yeah you got all these three things the
+ 
+
+ align:start position:0%
+yeah you got all these three things the
+other thing about this is I don't know
+
+ align:start position:0%
+other thing about this is I don't know
+ 
+
+ align:start position:0%
+other thing about this is I don't know
+big multi-sig is one use case it seems
+
+ align:start position:0%
+big multi-sig is one use case it seems
+ 
+
+ align:start position:0%
+big multi-sig is one use case it seems
+really powerful and like hey I can make
+
+ align:start position:0%
+really powerful and like hey I can make
+ 
+
+ align:start position:0%
+really powerful and like hey I can make
+these you know millions of different
+
+ align:start position:0%
+these you know millions of different
+ 
+
+ align:start position:0%
+these you know millions of different
+scripts and like Merkle trees of
+
+ align:start position:0%
+scripts and like Merkle trees of
+ 
+
+ align:start position:0%
+scripts and like Merkle trees of
+different scripts and tappero and
+
+ align:start position:0%
+different scripts and tappero and
+ 
+
+ align:start position:0%
+different scripts and tappero and
+graphic not a ton of like really good
+
+ align:start position:0%
+graphic not a ton of like really good
+ 
+
+ align:start position:0%
+graphic not a ton of like really good
+real-world use cases though I think that
+
+ align:start position:0%
+real-world use cases though I think that
+ 
+
+ align:start position:0%
+real-world use cases though I think that
+would motivate it a lot more because a
+
+ align:start position:0%
+would motivate it a lot more because a
+ 
+
+ align:start position:0%
+would motivate it a lot more because a
+lot of it a lot of the hesitation from
+
+ align:start position:0%
+lot of it a lot of the hesitation from
+ 
+
+ align:start position:0%
+lot of it a lot of the hesitation from
+people working on Bitcoin it's like okay
+
+ align:start position:0%
+people working on Bitcoin it's like okay
+ 
+
+ align:start position:0%
+people working on Bitcoin it's like okay
+what this is really cool but like what
+
+ align:start position:0%
+what this is really cool but like what
+ 
+
+ align:start position:0%
+what this is really cool but like what
+are we gonna do with it
+
+ align:start position:0%
+are we gonna do with it
+ 
+
+ align:start position:0%
+are we gonna do with it
+and multi-sig is not as I'll talk about
+
+ align:start position:0%
+and multi-sig is not as I'll talk about
+ 
+
+ align:start position:0%
+and multi-sig is not as I'll talk about
+and Wednesday multi-sig itself is not
+
+ align:start position:0%
+and Wednesday multi-sig itself is not
+ 
+
+ align:start position:0%
+and Wednesday multi-sig itself is not
+the best motivation because once we have
+
+ align:start position:0%
+the best motivation because once we have
+ 
+
+ align:start position:0%
+the best motivation because once we have
+more signatures and aggregate signatures
+
+ align:start position:0%
+more signatures and aggregate signatures
+ 
+
+ align:start position:0%
+more signatures and aggregate signatures
+there's direct ways to do multi-sig that
+
+ align:start position:0%
+there's direct ways to do multi-sig that
+ 
+
+ align:start position:0%
+there's direct ways to do multi-sig that
+are actually more privacy-preserving
+
+ align:start position:0%
+are actually more privacy-preserving
+ 
+
+ align:start position:0%
+are actually more privacy-preserving
+more space preserving so we need use
+
+ align:start position:0%
+more space preserving so we need use
+ 
+
+ align:start position:0%
+more space preserving so we need use
+cases and that was that's one of the
+
+ align:start position:0%
+cases and that was that's one of the
+ 
+
+ align:start position:0%
+cases and that was that's one of the
+debates like okay what do we do with
+
+ align:start position:0%
+debates like okay what do we do with
+ 
+
+ align:start position:0%
+debates like okay what do we do with
+this this is kind of cool you can make
+
+ align:start position:0%
+this this is kind of cool you can make
+ 
+
+ align:start position:0%
+this this is kind of cool you can make
+all sorts of weird smart contracts but
+
+ align:start position:0%
+all sorts of weird smart contracts but
+ 
+
+ align:start position:0%
+all sorts of weird smart contracts but
+what are some
+
+ align:start position:0%
+what are some
+ 
+
+ align:start position:0%
+what are some
+world news cases there's also sort of
+
+ align:start position:0%
+world news cases there's also sort of
+ 
+
+ align:start position:0%
+world news cases there's also sort of
+argument okay mast versus graph route
+
+ align:start position:0%
+argument okay mast versus graph route
+ 
+
+ align:start position:0%
+argument okay mast versus graph route
+versus both well if you have graphed
+
+ align:start position:0%
+versus both well if you have graphed
+ 
+
+ align:start position:0%
+versus both well if you have graphed
+route do you really need mast anymore
+
+ align:start position:0%
+route do you really need mast anymore
+ 
+
+ align:start position:0%
+route do you really need mast anymore
+right instead of this big Merkel tree
+
+ align:start position:0%
+right instead of this big Merkel tree
+ 
+
+ align:start position:0%
+right instead of this big Merkel tree
+you just have the signatures endorsing
+
+ align:start position:0%
+you just have the signatures endorsing
+ 
+
+ align:start position:0%
+you just have the signatures endorsing
+the leaves so it sort of seems better
+
+ align:start position:0%
+the leaves so it sort of seems better
+ 
+
+ align:start position:0%
+the leaves so it sort of seems better
+scalability there but grassroots
+
+ align:start position:0%
+scalability there but grassroots
+ 
+
+ align:start position:0%
+scalability there but grassroots
+interactive so maybe you still want
+
+ align:start position:0%
+interactive so maybe you still want
+ 
+
+ align:start position:0%
+interactive so maybe you still want
+masked maybe have both there's all sorts
+
+ align:start position:0%
+masked maybe have both there's all sorts
+ 
+
+ align:start position:0%
+masked maybe have both there's all sorts
+of debate on this and so that in
+
+ align:start position:0%
+of debate on this and so that in
+ 
+
+ align:start position:0%
+of debate on this and so that in
+practice they that may mean that sense
+
+ align:start position:0%
+practice they that may mean that sense
+ 
+
+ align:start position:0%
+practice they that may mean that sense
+people are arguing next year the year
+
+ align:start position:0%
+people are arguing next year the year
+ 
+
+ align:start position:0%
+people are arguing next year the year
+after it's hard to get everyone on board
+
+ align:start position:0%
+after it's hard to get everyone on board
+ 
+
+ align:start position:0%
+after it's hard to get everyone on board
+to do stuff there is code though some
+
+ align:start position:0%
+to do stuff there is code though some
+ 
+
+ align:start position:0%
+to do stuff there is code though some
+things have code some of them are like a
+
+ align:start position:0%
+things have code some of them are like a
+ 
+
+ align:start position:0%
+things have code some of them are like a
+lot of it's sort of obvious enough
+
+ align:start position:0%
+lot of it's sort of obvious enough
+ 
+
+ align:start position:0%
+lot of it's sort of obvious enough
+they're like yeah craft room makes sense
+
+ align:start position:0%
+they're like yeah craft room makes sense
+ 
+
+ align:start position:0%
+they're like yeah craft room makes sense
+just have them sign the taproot
+
+ align:start position:0%
+just have them sign the taproot
+ 
+
+ align:start position:0%
+just have them sign the taproot
+construction there's code for but it's
+
+ align:start position:0%
+construction there's code for but it's
+ 
+
+ align:start position:0%
+construction there's code for but it's
+not all like put together there's no
+
+ align:start position:0%
+not all like put together there's no
+ 
+
+ align:start position:0%
+not all like put together there's no
+like spec for all these things so if
+
+ align:start position:0%
+like spec for all these things so if
+ 
+
+ align:start position:0%
+like spec for all these things so if
+people are interested in this stuff
+
+ align:start position:0%
+people are interested in this stuff
+ 
+
+ align:start position:0%
+people are interested in this stuff
+start coding it start trying it out come
+
+ align:start position:0%
+start coding it start trying it out come
+ 
+
+ align:start position:0%
+start coding it start trying it out come
+up with cool use cases and maybe push
+
+ align:start position:0%
+up with cool use cases and maybe push
+ 
+
+ align:start position:0%
+up with cool use cases and maybe push
+for one thing or another to get in
+
+ align:start position:0%
+for one thing or another to get in
+ 
+
+ align:start position:0%
+for one thing or another to get in
+there's there's a pull request open in
+
+ align:start position:0%
+there's there's a pull request open in
+ 
+
+ align:start position:0%
+there's there's a pull request open in
+Bitcoin right now foremast I don't know
+
+ align:start position:0%
+Bitcoin right now foremast I don't know
+ 
+
+ align:start position:0%
+Bitcoin right now foremast I don't know
+some people are really into it and other
+
+ align:start position:0%
+some people are really into it and other
+ 
+
+ align:start position:0%
+some people are really into it and other
+people are like I don't know also how to
+
+ align:start position:0%
+people are like I don't know also how to
+ 
+
+ align:start position:0%
+people are like I don't know also how to
+implement math exactly so this is you
+
+ align:start position:0%
+implement math exactly so this is you
+ 
+
+ align:start position:0%
+implement math exactly so this is you
+know still research kind of level but I
+
+ align:start position:0%
+know still research kind of level but I
+ 
+
+ align:start position:0%
+know still research kind of level but I
+it seems that they're usable and that
+
+ align:start position:0%
+it seems that they're usable and that
+ 
+
+ align:start position:0%
+it seems that they're usable and that
+may improve some our contract
+
+ align:start position:0%
+may improve some our contract
+ 
+
+ align:start position:0%
+may improve some our contract
+functionality so cool stuff here any
+
+ align:start position:0%
+functionality so cool stuff here any
+ 
+
+ align:start position:0%
+functionality so cool stuff here any
+questions about this alright cool
+
+ align:start position:0%
+questions about this alright cool
+ 
+
+ align:start position:0%
+questions about this alright cool
+okay well so I'll do office hours
+
+ align:start position:0%
+okay well so I'll do office hours
+ 
+
+ align:start position:0%
+okay well so I'll do office hours
+tomorrow at four we talk about projects
+
+ align:start position:0%
+tomorrow at four we talk about projects
+ 
+
+ align:start position:0%
+tomorrow at four we talk about projects
+and stuff and the next class on
+
+ align:start position:0%
+and stuff and the next class on
+ 
+
+ align:start position:0%
+and stuff and the next class on
+Wednesday will be even more crazy
+
+ align:start position:0%
+Wednesday will be even more crazy
+ 
+
+ align:start position:0%
+Wednesday will be even more crazy
+elliptic curve stuff about aggregate
+
+ align:start position:0%
+elliptic curve stuff about aggregate
+ 
+
+ align:start position:0%
+elliptic curve stuff about aggregate
+signatures for signatures multi
+
+ align:start position:0%
+signatures for signatures multi
+ 
+
+ align:start position:0%
+signatures for signatures multi
+signatures threshold signatures things
+
+ align:start position:0%
+signatures threshold signatures things
+ 
+
+ align:start position:0%
+signatures threshold signatures things
+like that weight and also privacy I
+
+ align:start position:0%
+like that weight and also privacy I
+ 
+
+ align:start position:0%
+like that weight and also privacy I
+don't know how much of I'm gonna focus
+
+ align:start position:0%
+don't know how much of I'm gonna focus
+ 
+
+ align:start position:0%
+don't know how much of I'm gonna focus
+on the signature part I also put like
+
+ align:start position:0%
+on the signature part I also put like
+ 
+
+ align:start position:0%
+on the signature part I also put like
+privacy and coin joint in there which is
+
+ align:start position:0%
+privacy and coin joint in there which is
+ 
+
+ align:start position:0%
+privacy and coin joint in there which is
+related but might be squished towards
+
+ align:start position:0%
+related but might be squished towards
+ 
+
+ align:start position:0%
+related but might be squished towards
+the end if I don't have a ton of time
\ No newline at end of file
diff --git a/hGBNi4P9OfA.txt b/hGBNi4P9OfA.txt
new file mode 100644
index 0000000000000000000000000000000000000000..42ed2ef726c1034ecdd498bac20617add1e0e518
--- /dev/null
+++ b/hGBNi4P9OfA.txt
@@ -0,0 +1,4942 @@
+The following content is
+provided under a Creative
+
+Commons license.
+
+Your support will help
+MIT OpenCourseWare
+
+continue to offer high quality
+educational resources for free.
+
+To make a donation or to
+view additional materials
+
+from hundreds of MIT courses,
+visit MIT OpenCourseWare
+
+at ocw.mit.edu.
+
+JANET RANKIN: A
+general comment is by
+
+and large, I thought you
+guys did a great job.
+
+Your learning outcomes
+were for the most part
+
+specific, measurable,
+and realistic.
+
+The biggest problem I think
+I had was with-- the biggest
+
+problem that you
+had on average was
+
+the idea of the
+learning outcomes
+
+really have to be measurable.
+
+So if you use a word
+like appreciate,
+
+it's not measurable.
+
+So that's something to remember.
+
+If you use words like discuss,
+it's potentially measurable.
+
+But you need to make sure that
+you set up a venue for students
+
+to discuss.
+
+You can't just say you'll be
+able to discuss that and assume
+
+that they'll be
+able to discuss it,
+
+That If that's in
+your learning outcome,
+
+you have to set up some
+venue for them to discuss
+
+and you to know what
+they're discussing.
+
+And then the two biggest
+things that come up,
+
+or the two most problematic
+words that come up--
+
+and I compliment you all,
+because you did a great job.
+
+Nobody used understand.
+
+So that was awesome.
+
+But the other
+thing, there's words
+
+like explain and describe,
+which are perfectly good words
+
+to use in a learning outcome.
+
+But you have to make
+sure that when you say,
+
+students will explain
+the ideal gas law.
+
+They'll be able to
+explain the ideal gas law.
+
+Well do you know that
+they're really explaining it
+
+in the true sense of that
+word that they actually
+
+internalized what it means, and
+they're really explaining it?
+
+Or are they just spitting it
+back, spitting back, maybe,
+
+what they read in a
+book, a definition
+
+that they read in the book?
+
+So you have to make
+sure that you've
+
+set up a situation wherein
+they really are explaining.
+
+And they're not
+just remembering.
+
+So it's a great word to use.
+
+But you have to
+make sure that we're
+
+using in the right context.
+
+Same thing for describe.
+
+You can imagine that
+has the same issues.
+
+Describe da, da da, da, da.
+
+Well are you sure they're
+doing the describing?
+
+Or are they just remembering
+somebody else's description
+
+and writing it down?
+
+One good way around
+that is to tweak
+
+the parameters a little bit.
+
+To say, in a world where
+there is no oxygen,
+
+what do you expect this
+organism to look like,
+
+given that it has to run
+really fast or something?
+
+So come up with
+alternate realities
+
+that that actually force
+students to transfer and then
+
+re-explain.
+
+That can be helpful.
+
+That can be really,
+really helpful.
+
+I remember once in
+a kinetics class,
+
+we had been deriving
+the critical nucleus
+
+size for growth.
+
+And it's all based on a
+radius, a critical radius.
+
+And then on the exam,
+the guy said OK,
+
+they don't grow as sphere's.
+
+They grow as rectangular boxes.
+
+So then all of a
+sudden, we had to look
+
+at the ratio of the length
+to the height of the box
+
+or something.
+
+So that really wasn't
+just we were just
+
+remembering a solution
+or remembering a method.
+
+We had to actually think
+about what it meant
+
+and then reapply it.
+
+So just think about how
+you can get students
+
+to really describe, explain,
+derive even, because you
+
+can memorize a derivation.
+
+But if you really want them to
+derive it, what does that mean?
+
+How are you going to test that?
+
+So those are generally
+the biggest problems
+
+people have with
+learning outcomes.
+
+But by and large, you
+all did a great job.
+
+If you came in late, I'll give
+you your learning outcomes
+
+at the end to class.
+
+If you looked at the Wiki--
+and this is a test to see who
+
+looked at the Wiki--
+
+I had suggested you bring a web
+enabled device if you had one.
+
+And that's because
+I wanted to set up
+
+something called Back
+Channel The topic today
+
+is on active learning.
+
+And so this is just one method
+that might help your students,
+
+especially if you
+have a big class.
+
+So we don't really
+need it in this class,
+
+but I just wanted to
+give you the opportunity
+
+to play with it a little bit.
+
+It was designed for
+conferences actually.
+
+But it works pretty well,
+I think, in classes.
+
+So if you login to
+here, this is the URL.
+
+If you go to our
+Wiki page bookmarked,
+
+there's a link on the
+Wiki page, if you just
+
+want to link to it that way.
+
+And then at any
+point in the class,
+
+you can type a question in.
+
+And if you're on
+the page, you can
+
+see other people's questions.
+
+You can upvote and
+downvote their questions.
+
+And I will take a break
+in the middle, when you're
+
+doing some other things, and
+read what people have posted
+
+and then get back to you.
+
+So it's an opportunity
+for students to interact
+
+who may be a little more
+shy, who may not want to.
+
+I don't think we need
+that in this class.
+
+I don't think that there's
+any one of you that
+
+isn't willing to share
+your ideas, which is great.
+
+But this may be something
+that's of interest to you.
+
+Before we jump into the
+topic today, active learning,
+
+there were a couple
+of mud card questions
+
+that I just wanted
+to talk about.
+
+One was sometimes students
+may nod off during class.
+
+And if it's a big
+class, there's probably
+
+not a lot you can do about it.
+
+If you do enough
+active learning,
+
+though, that will keep them--
+that will make them wake up.
+
+Especially pair
+activities or activities
+
+where they have to talk to
+one or two other people,
+
+or two or three other
+people, it's pretty hard
+
+to be asleep during those.
+
+And you'll see.
+
+We're going to do something
+called a lightning round later
+
+on.
+
+And it's virtually impossible
+to be asleep during that.
+
+So you want to make
+sure that it's worth
+
+the student's time to
+actually be in class
+
+and be awake for it.
+
+And active learning can
+play a huge role in that.
+
+Sometimes people are tired.
+
+They stayed up too late
+for whatever reason.
+
+And you can't control
+everybody in your class.
+
+But you want to make sure that
+you're doing everything you
+
+can do to keep them engaged.
+
+And if it's just one
+student every now and then,
+
+you probably don't want
+to take it personally.
+
+It's probably not you.
+
+If the whole class
+is falling asleep,
+
+then it's probably
+a good opportunity
+
+to rethink your strategies.
+
+Somebody asked if there
+were good times of day
+
+to have a lecture.
+
+And part of it is you.
+
+Part of is your schedule.
+
+Sometimes you're allowed.
+
+You can pick that.
+
+And sometimes you really don't
+have much control over when
+
+you choose to teach your class.
+
+People do say that
+students, undergrads,
+
+people between the
+ages of 18 and 21
+
+are not particularly interested
+in being up at 8:00 or 9:00
+
+in the morning.
+
+But again you may not have
+any control over that.
+
+Generally speaking, that's a
+pretty low time for people.
+
+So if you want to take that
+into consideration, you might.
+
+But it depends as much
+on you as the students.
+
+If you're going to be
+really tired at 4:00
+
+but they're just waking up,
+then don't teach it at 4:00.
+
+Maybe don't teach at 4:00.
+
+And the last one was
+guiding readings.
+
+If you just put a
+lot of readings up,
+
+students might not know where
+to focus their attention
+
+until after the class.
+
+So there are reading
+questions, reading guides
+
+that you can post.
+
+Read such and such
+and try and think
+
+about how you might explain
+this, that, or the other thing.
+
+And then there's also
+pre-class questions
+
+you can ask that
+they might derive,
+
+that they may have to pull
+from the readings to answer.
+
+So the concept of just in
+time teaching, the idea
+
+that students do
+a reading and then
+
+they actually have to answer
+questions on the reading
+
+before they come to class
+and submit their answers.
+
+So there's a whole
+procedure around that.
+
+It can be very, very effective.
+
+You can do it for a large class.
+
+There's strategies
+and techniques
+
+to streamline the amount
+of time you put into it.
+
+But it does force them
+to do the reading.
+
+And it does guide, at some
+level, what they read.
+
+And that's a great
+great approach.
+
+And I'm happy to talk more about
+that at another time or later
+
+or offline.
+
+I did go to the Teaching
+with Technology conference,
+
+the Teaching Professor
+Technology Conference.
+
+And they were giving out little
+ribbons to stack on your badge.
+
+And this was a prominent one.
+
+It's in the syllabus,
+which I thought
+
+was just crazy timely because
+a couple of weeks ago.
+
+So if you want one of
+these to stick somewhere.
+
+And then they all said when I
+tweet, which was sort of weird.
+
+But anyway I brought those back.
+
+Anybody want some.
+
+Sometimes my computer
+doesn't wake up.
+
+So let's pretend that instead
+of the class active learning
+
+today, I decided I was going
+to teach you how to juggle.
+
+And I said, here's the
+equation for how to juggle.
+
+And here's the variables,
+F, D, V N, and H,
+
+which are ball in the
+air, ball in an hand,
+
+time hand is vacant, number
+of balls, number of hands.
+
+And this is this
+handy dandy equation,
+
+which if you balance it out, it
+describes the juggling process.
+
+And for those of you
+that are visual learners,
+
+I have a graph here, a
+yellow ball, a blue ball,
+
+and a pink ball.
+
+And then you can see that just
+shows the path of the balls.
+
+If you remember from
+physics, there's
+
+the equations of motion in the
+x direction in the y direction.
+
+And so I think I probably did a
+pretty good job of teaching you
+
+how to juggle.
+
+No, did a terrible job of
+teaching you how to juggle.
+
+I didn't even come close to
+teaching you how to juggle.
+
+And if I were to
+give you a test,
+
+let's say, and I were to
+measure whether or not
+
+you could juggle, I
+guarantee that some of you
+
+would be able to juggle.
+
+And I could say, I did a great
+job teaching how to juggle.
+
+But I didn't.
+
+If you knew how to
+juggle coming in,
+
+presumably you still
+know how to juggle.
+
+I did no harm, I think.
+
+However if you didn't know
+how to juggle coming in,
+
+you don't know
+how to juggle now.
+
+So why is this here now?
+
+Why did I bother to
+do this stupid thought
+
+experiment right now?
+
+AUDIENCE: Because
+this is clearly
+
+how most classes are taught.
+
+Obviously it would be
+easier to have a ball
+
+and show us how to juggle,
+active learning as opposed
+
+to just showing the theory
+behind it and ending there.
+
+JANET RANKIN: And I
+think a lot of times
+
+we really do, in science and
+engineering classes, we really
+
+put up a lot of equations.
+
+And then it's not like
+we expect somebody
+
+to do something
+physically with them.
+
+But we expect them to be able
+to manipulate the equations,
+
+transfer the equations,
+apply the equations.
+
+And we never really
+talked about that.
+
+We talked about the equations.
+
+So it's a real call
+in my mind, for us
+
+to think about what
+it is we really
+
+want students to be able to do.
+
+And then make sure that
+they're doing stuff
+
+to teach them that helps
+them learn how to do that.
+
+And I know you all
+read the readings
+
+and that they talk a lot
+about active learning.
+
+There's a few things about
+techniques for active learning.
+
+There's a few things about
+the why's of active learning.
+
+There's some data for why
+active learning works.
+
+But I'm guessing that
+there's a range of buy in
+
+at this point from you guys.
+
+Eh, I don't think it's worth it.
+
+Or I don't really know.
+
+So for the first 20
+minutes, 25 minutes
+
+of class, what
+I'd like you to do
+
+is I'd like you to
+pretend that you
+
+were part of a department,
+the STEM department.
+
+Call it whatever field you want.
+
+And there is a proposal
+that your department
+
+should commit funds
+to train professors
+
+and develop resources,
+the resources
+
+necessary for the adoption and
+ongoing use of active learning
+
+techniques in all courses.
+
+And the target date is 2017.
+
+You've got a year to
+get all courses up
+
+to speed with active
+learning stuff introduced
+
+into these classes and with
+a plan for how to do that.
+
+So what I'm going to do is I'm
+going to just count off one,
+
+two, three, one, two, three.
+
+And I'm going to ask
+you to form a group.
+
+If you're a one, go
+with the one group.
+
+Two go with the two group.
+
+A three go with the three group.
+
+And you're going to
+have to physically move.
+
+So just remember your number.
+
+One.
+
+AUDIENCE: Two.
+
+AUDIENCE: Three.
+
+AUDIENCE: One.
+
+AUDIENCE: Two.
+
+AUDIENCE: Three.
+
+AUDIENCE: One.
+
+AUDIENCE: Two.
+
+AUDIENCE: Three.
+
+AUDIENCE: One.
+
+AUDIENCE: Two.
+
+AUDIENCE: Three.
+
+AUDIENCE: One.
+
+JANET RANKIN: It doesn't matter
+that they're not the same size.
+
+Can we get all the ones, let's
+say all the ones up here?
+
+All the twos here.
+
+And all the threes there.
+
+And I'll tell you what
+to do in just a sec.
+
+So if you're group
+number one, you
+
+have to adopt the
+position that you are pro.
+
+You are going to push for the
+adoption of this resolution.
+
+And you have to come up
+with a set of arguments
+
+and a set of reasons
+why it's a good thing.
+
+I don't care what
+you think personally.
+
+I don't care if you think
+active learning is the worst
+
+idea ever.
+
+For the purposes
+of this debate, you
+
+need to pretend you're
+totally into it.
+
+And you need to come up with
+some good arguments why.
+
+Two are against it.
+
+Again, I don't care how
+you feel personally.
+
+But come up with some
+good solid arguments
+
+why you should not do this.
+
+AUDIENCE: We are against it?
+
+JANET RANKIN: Against,
+you do you not want it.
+
+No.
+
+Group number three, you
+got a little bit of time.
+
+But get to know each other.
+
+And you're going to
+hear the arguments.
+
+You're going to hear a case
+presented by the pro people,
+
+the con people.
+
+And then you are going
+to deliberate and decide
+
+what's going to happen
+in your department.
+
+You guys are the deciders.
+
+It's an American political joke.
+
+But we'll let that go.
+
+And you guys get this
+lovely microphone.
+
+So I'm going to give
+you 10 minutes for this.
+
+So be ready to share your views.
+
+You've got about,
+maybe, two or three
+
+minutes of a spiel of proof.
+
+And then we'll do one
+exchange of debate.
+
+And then the
+deciders will decide.
+
+[SIDE CONVERSATIONS]
+
+JANET RANKIN: I'm going to ask
+someone from each of the groups
+
+to make a statement
+that puts forth the side
+
+that you're supposed to defend,
+if that is the side you're
+
+supposed to defend.
+
+So we'll start with the pros.
+
+So someone from your
+group ready to talk pros?
+
+All right, Michelle.
+
+AUDIENCE: So we are
+pro active learning.
+
+And part of the
+basis for thinking
+
+that active learning's
+important is
+
+that we believe that
+without active learning,
+
+the professor usually
+just resorts to lecturing.
+
+And we think that lectures
+are not effective.
+
+Students don't learn
+simply because the material
+
+is presented to them.
+
+Lecturing wastes
+resources, because you
+
+could be lecturing to 1,000.
+
+But only 15 students
+may be reached.
+
+And if you use active
+learning instead of lecturing,
+
+it can make sure the students
+are paying attention.
+
+You can check that
+they're understanding.
+
+You can know what
+they are getting
+
+and what they're not getting.
+
+We also feel that active
+learning is a life skill.
+
+And that if students learn
+to learn by do things
+
+and they learn by
+talking to each other
+
+and by going through a
+process and solving problems,
+
+that they can take this skill to
+outside of the classroom later
+
+in society.
+
+Then that the society
+that you have students
+
+who are used to
+being active learners
+
+and who know how to
+solve problems that way.
+
+And we also think that the
+end, the big point that we have
+
+is that you remember
+things that you use.
+
+If you learn something,
+if it goes in one ear
+
+and out the other, if you
+don't actually use it,
+
+you're not going to remember it.
+
+If you're not forced to
+actually work through a problem
+
+and really think about it
+and use it in a classroom,
+
+that you're much less
+likely to actually hold on
+
+to that information.
+
+So these are all
+reasons why we think
+
+that we should promote active
+learning in our department.
+
+JANET RANKIN: OK,
+thank you very much.
+
+The con, or I guess I
+should say the not whatever.
+
+Anyway, group two.
+
+AUDIENCE: Do you want to do it?
+
+AUDIENCE: OK.
+
+We start with a basic question.
+
+The question is, why do we
+want to change what is working?
+
+We are training our students.
+
+They are getting job.
+
+The professor are doing well.
+
+They are collecting grants.
+
+The original [INAUDIBLE] is OK.
+
+So why do you want to
+change what is working?
+
+So that is the first question.
+
+Now the first thing is that,
+if you want to go about this,
+
+it's going to consume
+a lot of money.
+
+It's going to take
+a lot of money.
+
+And then it cuts
+into your funds.
+
+The one funds for other
+such, want to buy equipment
+
+for the laboratory, want
+to go hire scientists,
+
+want to go hire post doc.
+
+So why do we want to change?
+
+Where do we get these funds?
+
+We divert funds for the
+training of professors.
+
+And they're going to be
+little bit of no funds for all
+
+this such work.
+
+And secondly, the efforts
+to train professors
+
+is likely to be very huge.
+
+Professors are used to
+this method of teaching.
+
+And as you saw, they
+will not want to change.
+
+There's going to be a lot
+of time changing them.
+
+And we're not even sure,
+if we try to change them,
+
+whether they're going to be able
+to do it at the end of the day.
+
+Thirdly, we are not sure that
+the stakeholder would be happy.
+
+What about the alumni
+that are very much
+
+used to the method of teaching?
+
+What about the parents?
+
+are they now going
+to go against us?
+
+Will they not see that
+the professor no longer,
+
+just come to the class, give
+them group work like this
+
+without teaching,
+without writing?
+
+Then the professor is
+no longer teaching.
+
+And they are just going
+to collect their salary.
+
+And then, there's
+not to be constrained
+
+on time to cover syllabus.
+
+When I saw I spend
+a lot of money
+
+being in group work,
+individual, or this and that.
+
+So how do you complete
+your syllabus?
+
+You have about 20 topics
+to cover this semester.
+
+And by the time you
+start active learning,
+
+how are going you cover
+about 50% of them?
+
+Then you push all of
+that up [INAUDIBLE].
+
+So it's not going to work.
+
+We should just drop the idea.
+
+What have we value
+very last class?
+
+You have your class of 500.
+
+How do you want active
+learning to be effective?
+
+How do you want to treat them?
+
+It's good here, because we are
+just about 15 or less than 20.
+
+By the time you have
+500 students in a class,
+
+it's going to be very
+difficult for you
+
+to have active learning,
+difficult for the professor
+
+to control classes,
+and of course,
+
+difficult for you to really
+get something concrete out
+
+of the whole thing.
+
+So my final guys and professors,
+I think it's not necessary.
+
+the.
+
+System is working.
+
+Let it continue
+to work this way.
+
+Thank you.
+
+JANET RANKIN: So now
+what I'm going to do
+
+is I'm going to
+let each group ask
+
+one question or a set
+of clustered questions
+
+to the other group.
+
+The other group can answer them.
+
+And then the deciders can
+ask a couple questions.
+
+And then we'll let
+them deliberate.
+
+So group number one, like to ask
+some questions to group number
+
+two or make some comments?
+
+Go ahead.
+
+AUDIENCE: Yeah, I
+listened to you speak.
+
+And I want to ask you.
+
+You are saying that
+the system is changing.
+
+It is changing because the
+status quo isn't delivering.
+
+So that is why we are
+adopting active learning.
+
+And this is proven from
+a research perspective.
+
+There is actually letting more
+students learn more materials
+
+faster and more effectively.
+
+So what do you think about that?
+
+AUDIENCE: I'll
+answer it by saying
+
+the different research shows us
+that the student that is good
+
+is good.
+
+[INAUDIBLE]
+
+So why can't we just concentrate
+on getting those students?
+
+And what your presentation
+didn't say about funds,
+
+was the whole idea is
+to fund the proposal.
+
+And if we divert funds
+to this new program,
+
+and that's a very big issue.
+
+You have to concentrate
+on the question that
+
+is the diversion of
+funds away from research.
+
+So if we can get the new
+students and they can learn
+
+by [INAUDIBLE], and
+it's working great--
+
+go ahead.
+
+AUDIENCE: So you
+want to throw away
+
+the baby with the bath water?
+
+If you have 20
+students in a class,
+
+and you have five
+active learners,
+
+and then you want to
+discover 15 that wouldn't.
+
+This program is geared towards
+each one of the students
+
+in the class to participate.
+
+And I think it's
+more cost effective.
+
+If you could get
+all the 20 students
+
+to learn and to
+learn actively, I
+
+think that would pay itself
+off at the end of the--
+
+AUDIENCE: No, the
+problem there is that you
+
+have to face the proposal.
+
+This is 2017.
+
+It's a lot of change
+in a very short time.
+
+The proposal itself
+is already against--
+
+AUDIENCE: Our department
+could be three people big.
+
+We don't know how much
+the department is.
+
+[INTERPOSING VOICES]
+
+AUDIENCE: But then
+the issue there
+
+is that you're going
+to retrain professors.
+
+Professors are really
+stuck in their ways.
+
+And you spend all this money.
+
+And it's very short time.
+
+There's lots of
+people from the labs,
+
+and money from the labs
+in this very short time
+
+to train them on
+something we don't
+
+know if they're
+ready to buy into it.
+
+AUDIENCE: So I think
+your assumption is that--
+
+you're like, we're deferring
+funds from labs and resort.
+
+But you never once said you're
+diverting funds from anything
+
+related to the students.
+
+You're thinking of it from
+the professor perspective.
+
+But really professors are
+here to teach their students.
+
+And you're like, oh,
+we're taking money away
+
+from the research,
+from the lab equipment,
+
+from all these
+different things that
+
+sound great to the professor
+but have literally nothing
+
+to do with the students
+learning experience
+
+or the student's
+experience on campus.
+
+And from the
+student's perspective,
+
+that's really frustrating, when
+that's all the professors care
+
+about.
+
+And that's what
+makes a difference
+
+between a good professor
+and a crap professor
+
+is one who cares.
+
+And I think, if you want
+a professor to care,
+
+oftentimes they're willing
+to make the effort that
+
+is needed to change
+their teaching style
+
+or do whatever it is
+that's necessary to have
+
+their kid interested and
+engaged in the same material
+
+that this professor loves.
+
+So you keep talking
+about diverting funds.
+
+But you never once mentioned
+diverting these funds
+
+away from this one
+teaching initiative
+
+to a different
+teaching initiative.
+
+So just keep that in mind .
+
+AUDIENCE: So the
+problem is that when
+
+we are looking at the proposal
+itself, the time, 2017, this
+
+is already the end of 2015.
+
+So that means you
+are going to do this,
+
+by 2017, that means you're
+going to do it by 2016.
+
+We're not against active
+learning in the [INAUDIBLE].
+
+[LAUGHTER]
+
+[INTERPOSING VOICES]
+
+AUDIENCE: --the proposal.
+
+We are against-- we
+need these two group
+
+and against this proposal.
+
+So for this proposal, we
+are against this proposal,
+
+because you know how
+much it's about the funds
+
+and the resources.
+
+And that is why we are
+against the proposal.
+
+And also you pick
+whatever [INAUDIBLE],
+
+we're not even sure that
+it is going to work.
+
+JANET RANKIN: I'm going to
+take, because you guys actually
+
+did ask a question, so I'm
+going to count that to you
+
+Did you have another
+separate one?
+
+AJ, you look like you
+might have some questions.
+
+AUDIENCE: Yeah actually
+I was just curious,
+
+so if this initiative
+is really great,
+
+it looks like a lot
+of this research
+
+has been done since '80s.
+
+Why isn't it adopted?
+
+Why are we having this
+conversation now in 2015?
+
+AUDIENCE: I think
+we should look back
+
+at this issue of the lecturing
+system that we are using now.
+
+It's static.
+
+When there was no
+printing, lecturers then,
+
+they get the material.
+
+They reach the students.
+
+So lecturing is a Latin
+word that means reading.
+
+Now since then, now
+we are printing.
+
+We have information
+readily available
+
+that people can get on at
+their home and their own
+
+and develop to something.
+
+Too So there is a need for
+us to change to a new system,
+
+because the old system that
+more facilitated lecturing has
+
+changed.
+
+So then we have to change.
+
+JANET RANKIN: I'm
+going to turn it over
+
+to the deciders who
+now have to discuss.
+
+They've been resting
+for many minutes.
+
+So now they have to.
+
+So you have questions
+for each of the groups?
+
+AUDIENCE: Yeah.
+
+AUDIENCE: Yeah, thank you.
+
+Great arguments on both sides.
+
+I found it interesting, when
+you talked about the larger
+
+classes, so my first
+question is for this group.
+
+So how would active learning
+apply to a large class?
+
+The proposal is that
+it's for all courses.
+
+And so are there courses where
+this doesn't lend itself to?
+
+AUDIENCE: Even in the classes
+with 700, 800 students here,
+
+they still do active learning
+for the freshmen, i.e.
+
+Clicker questions.
+
+Oftentimes professors have
+to talk to your partners.
+
+So they'll pose a question.
+
+Everyone will click
+on their answer.
+
+And then they'll be
+like, now go back
+
+and talk to the person
+sitting next to you.
+
+And then you'll vote
+again in two minutes.
+
+So I think that's just one
+example of how you can engage
+
+a class of a lot of students.
+
+AUDIENCE: And to add
+to that, actually it's
+
+also been found out that when
+peers speak to themselves,
+
+they even learn the
+material better than when
+
+the expert, who may have lost
+touch to what it could be
+
+like to learn from a
+student's perspective.
+
+So peers speak to themselves
+and teach themselves even faster
+
+than the expert who
+is in front of them.
+
+AUDIENCE: Yeah I have comment
+for the against group.
+
+You mentioned that you
+don't require to create
+
+or active learning, because
+some students are very smart.
+
+They get it right.
+
+But don't you think
+that education
+
+is a right of every child?
+
+And they deserve to
+have a good shot at it.
+
+So why do you want to pull
+one child out of here,
+
+because he's not smart enough?
+
+AUDIENCE: I just
+to answer, I think
+
+we are pushing for
+the best education.
+
+We believe that is
+the traditional way.
+
+We think that active
+learning can happen
+
+outside of the classroom.
+
+This is the way it's
+worked for 300 plus years
+
+over at Harvard, one of
+the best universities, MIT
+
+for 100 plus years.
+
+We think that
+essentially it's working.
+
+And the reason we're having
+this conversation right
+
+now is because it has worked.
+
+So we want to
+continue that legacy.
+
+We think that every system
+is going to have problems.
+
+And if you analyze any system,
+you're going to find issues.
+
+And there are certainly
+some smaller inefficiencies
+
+within the lecture.
+
+But by and large, it's trusted.
+
+And it works.
+
+AUDIENCE: I want to
+add on what adding.
+
+So I think we are not pushing
+those less smart kids away,
+
+because they can actually
+learn from each other outside
+
+of class.
+
+We just want to say
+that doing the lecture
+
+is more efficient if the
+professor lecturing at them,
+
+giving all the information.
+
+As a footnote to that-- sorry--
+
+if professors come to the
+class and just give theory
+
+and go away, and the
+smart kids get it,
+
+then how do you measure the
+professor's performance?
+
+How do you think
+about, say, something
+
+like students information
+on educational quality?
+
+How do you measure that?
+
+AUDIENCE: You don't
+really need the professor
+
+to be extremely active and do
+active teaching in the class.
+
+The full student can
+actually get what they need.
+
+You have a bunch of homeworks.
+
+You have a bunch of test
+questions, exam questions,
+
+that student, whether
+they like it or not,
+
+they will surely be forced
+to read those things.
+
+And by the time they come
+back, they come back learning.
+
+Lot of graduate from MIT,
+they are l really doing well.
+
+About 25% start up
+their own business.
+
+Probably like 70% get
+jobs when they finish.
+
+What are you talking about?
+
+The system is working.
+
+And That's what we're saying.
+
+And their value is a great.
+
+The evaluation is
+done on the type
+
+of textbook, the
+mode of lecture,
+
+the [INAUDIBLE] lecture.
+
+So these are the things
+that I try to evaluate
+
+in the evaluation process.
+
+And it has been great.
+
+And we want it to continue.
+
+AUDIENCE: So we addressed
+the measuring impact.
+
+And that goes for both.
+
+But for the active
+learning, how do we
+
+quantify how much
+active learning needs
+
+to go into these different
+classrooms in the department?
+
+So how will we ensure
+the appropriate amount
+
+has been implemented in
+different classrooms?
+
+Basically, how much
+active learning
+
+needs to go into a
+classroom to create change
+
+or to strengthen our
+student learning?
+
+AUDIENCE: How much
+has to go in or how
+
+you're going to make sure that
+the professors are doing it?
+
+AUDIENCE: Both, I
+guess, is the question.
+
+If there's a professor that's
+more on the lecture side
+
+that might throw one thing pair
+share in and call it a day.
+
+So how do we ensure the
+appropriate active learning
+
+techniques and the quantity
+are there for the classrooms?
+
+AUDIENCE: I think we'd have
+to go back to the research
+
+and see how much, whether
+it's 30% of the time needs
+
+to be spent on active
+learning activities,
+
+or to see what has been proven,
+because active learning has
+
+been proven to be effective.
+
+But we would have to
+go back and make sure
+
+that we set a standard that,
+if it is 30% of the time
+
+or 70% of the time.
+
+And I think oversight
+from the department
+
+would be important, in that the
+leadership in the department
+
+will have to sit in on classes.
+
+And as part of the
+training of the professors,
+
+there has to be training.
+
+But then there has to be someone
+to observe them in the class,
+
+give feedback.
+
+The training has to be ongoing.
+
+It's not just a three
+hour seminar on this
+
+is with active learning is.
+
+And this is what you should do.
+
+I think it's going
+to be a long term
+
+investment in the
+professor training
+
+that someone's going to have
+to check up and give them
+
+feedback.
+
+And then they can
+adjust from there.
+
+JANET RANKIN: I'm sure that
+we could [INAUDIBLE] all day.
+
+But I'm going to give the
+deciders two and a half
+
+minutes, three minutes,
+to talk to each other
+
+and come up with a decision.
+
+All right, the
+committee has met.
+
+And now they're going
+to determine your fate
+
+in this department.
+
+AUDIENCE: Does this mic work?
+
+Is this on?
+
+Do I need to use the mic.
+
+You can hear?
+
+Well thank you again
+for your arguments.
+
+Certainly the panel felt
+that the pro arguments
+
+in terms of the benefits of
+active learning are great.
+
+And we definitely support that.
+
+However, given the time
+frame, and this proposal
+
+is very aggressive, it would
+be extremely disruptive.
+
+Also the amount of
+funds that we think
+
+that it would take
+to implement this
+
+would be very high without any
+proven way to measure success.
+
+So what we are willing
+to do is commit funds
+
+to a pilot program,
+where we can then
+
+measure what the success
+will be and then make
+
+it a decision next year
+as to whether or not
+
+we invest for the rest
+of the departments.
+
+[INTERPOSING VOICES]
+
+JANET RANKIN: So I hope you
+found this exercise useful.
+
+I just want to debrief
+on the exercise itself,
+
+why we bothered to do it.
+
+It took probably 45
+minutes of time to do it.
+
+But I made a decision
+that would be useful.
+
+So what did we get
+out of this exercise?
+
+What was the point?
+
+AUDIENCE: Whether you think
+that's it's worth it or not,
+
+it's really important time.
+
+Also, it seems
+this confrontation
+
+is happening a lot in the
+department, especially
+
+[INAUDIBLE] as they go
+through the program.
+
+I assumed this test would
+be debated quite a bit,
+
+internally and externally.
+
+JANET RANKIN: Other
+reasons we engaged in this?
+
+AUDIENCE: I think
+it gives everybody
+
+the opportunity to think deeply
+about the subject matter.
+
+And it also, even if you are
+against or for something,
+
+you have to have
+a deeper knowledge
+
+to be able to bring out the
+good points, certain issues that
+
+might actually make
+see [INAUDIBLE].
+
+JANET RANKIN: [INAUDIBLE],
+you want to add to that?
+
+AUDIENCE: The topic
+is active learning.
+
+And what we just demonstrated
+is active learning in practice.
+
+JANET RANKIN: Yes, exactly.
+
+And the idea to
+Gordon's point, the idea
+
+that it can be very, very
+useful for you to have students
+
+take an arbitrary
+position and argue it,
+
+because they will
+learn things, they
+
+will think about things,
+that they would not
+
+have thought about otherwise.
+
+And it's usually not a good
+idea to say OK everybody that
+
+thinks this, go over here.
+
+Everybody that thinks
+this, go over here,
+
+because all that
+does is reinforce
+
+what people think already.
+
+And maybe it's not
+completely correct.
+
+So this is often a
+very good technique,
+
+when there's two clear
+viewpoints or two clear sides.
+
+And you want students to
+really engage with that.
+
+And exactly, we could
+have had a discussion.
+
+Or I could have had
+PowerPoint slides that
+
+said, here are the good things.
+
+Here are the pros with active
+learning, bum, bum, bum, bum,
+
+bum.
+
+Here are the cons of active
+learning, bum, bum, bum, bum,
+
+bum.
+
+And that would've taken--
+
+just to come out of my
+neutral position here--
+
+that would have taken
+probably four minutes.
+
+Instead we took 35
+or so, 40 minutes.
+
+But I think you probably
+engaged with some
+
+of the ideas and
+concepts a little bit
+
+deeper, because you had to
+come up with it yourself.
+
+So yes, all those reasons.
+
+And it does come up often.
+
+People are discussing it.
+
+And it's not so clear cut.
+
+There's not a right answer.
+
+And you're going to want to say,
+OK, well we'll do it by 2019.
+
+Or we'll do it.
+
+But we won't do that.
+
+There's going to be deals and
+all those kinds of things.
+
+And that's OK.
+
+It's OK that there's
+not a right answer.
+
+But that was the point
+of this exercise.
+
+So that served as our
+discussion for active learning.
+
+But you guys did it.
+
+I didn't do anything.
+
+AUDIENCE: And that
+buttresses the point
+
+that active learning
+is the way to go.
+
+JANET RANKIN: Thank you.
+
+Yes, this is very meta.
+
+This is very meta here.
+
+Yeah and I do have to
+feel a little bit bad
+
+when you're like, what?
+
+Then we're going
+to do all the work.
+
+And the lecturer's just going
+to sit back and not do anything.
+
+I took it personally.
+
+But no, no, it's OK.
+
+One thing I wanted
+to bring up is
+
+if you haven't read the
+Scott Freeman article,
+
+it's in the reading
+list for today.
+
+It shows-- let me
+just bump to it--
+
+it shows essentially
+these results.
+
+He did a meta analysis of 225
+studies on active learning
+
+or on classes that that
+used active learning.
+
+And they showed a 12%
+decrease in the failure rate
+
+in classes that used
+active learning.
+
+And so I was telling the
+pro group that what say
+
+in the paper is that if it had
+been a clinical drug trial,
+
+and 12% of the people on the
+drug were having a better
+
+outcome than the people on the
+placebo, they would have had--
+
+or the people on the control--
+
+they would have had
+to stop the trial
+
+and give everyone the drug.
+
+So in the sense of why
+we're still lecturing,
+
+that's to me one of the
+biggest compelling reasons
+
+for why we should be doing
+more active learning.
+
+12% of the students are going
+to pass the class, on average,
+
+normalized.
+
+And they actually considered
+both experienced lecturers, who
+
+were just lecturing,
+people that were considered
+
+to be good lecturers
+that were just lecturing,
+
+as well as graduate students
+who were first time teachers
+
+but were using active learning.
+
+So they looked at
+all sorts of-- they
+
+mixed up all sorts of outcomes.
+
+And active learning appears to,
+the data's pretty conclusive.
+
+And this isn't the only
+study that shows it.
+
+So there are definitely issues.
+
+There are definitely
+implementation issues.
+
+They're definitely
+sticking points.
+
+But it's something that
+I think we can't ignore.
+
+AUDIENCE: I just want
+to add that it's not
+
+only that we have 12%
+decrease in the failure rate.
+
+We also have big shifts in
+the letter grade students get.
+
+For instance, more people
+shift from grade C to grade B
+
+or from B to A. And B
+to see a test like that.
+
+So that's really
+significant also.
+
+JANET RANKIN: So I just want
+not have learning outcomes.
+
+But I did want to have the
+discussion before I even
+
+introduced them.
+
+So I think you'll
+be able to explain
+
+the impact of active learning
+exercises in the classroom.
+
+You've already
+started to do that.
+
+And then you'll be able
+to identify and develop
+
+active learning exercises
+that you'll want to use.
+
+And you'll be able to think
+about how you might use them.
+
+I think, pretty attainable
+learning outcomes.
+
+I'm going to show
+the slide a lot
+
+throughout the rest of the time.
+
+But remember, it's
+constructive alignment.
+
+We've seen this diagram before.
+
+But the beauty of some of these
+active learning techniques
+
+is that their
+formative assessments
+
+of students' understanding,
+of students' learning.
+
+And so they are
+actually activities
+
+that happen in the class.
+
+But they're also measures,
+informative, formative measures
+
+of whether students
+are learning or not.
+
+So if somebody had come up with
+a really terrible argument,
+
+or it was clear that nobody
+had read any of the papers
+
+on the active learning
+research, then I
+
+would know that
+from this debate.
+
+I know what you've read
+and what you haven't read,
+
+and what you're
+thinking about and what
+
+you're not thinking about.
+
+And I get a good sense for
+whether or not it you know it
+
+and how much and how
+well you know it.
+
+And so do you.
+
+And we'll see that
+a little bit more
+
+in these other situations,
+where if you get a clicker
+
+question wrong or you get a
+multiple choice question wrong
+
+or that you can't participate
+in the lightning round,
+
+then you know that you've
+got to step up to the plate.
+
+Or you need to try
+something different.
+
+Or you're not really getting it.
+
+So you get information.
+
+The learner gets information.
+
+And the teacher
+gets information.
+
+AUDIENCE: I just thought
+that was really powerful
+
+in the readings, as well.
+
+They mentioned that,
+that students who,
+
+when they get in
+the group sections,
+
+if it's clear they really are
+getting a lot of things wrong,
+
+they know they need to step up.
+
+And that's in a different way, I
+think, than getting a bad grade
+
+on a paper.
+
+And you know the average
+distribution or whatever.
+
+Or the professor
+says you're wrong.
+
+But when you know that the
+people sitting right next
+
+to you are getting it and you're
+not, that really, I think,
+
+will push the student
+forward to do something.
+
+JANET RANKIN: It's
+news you can use.
+
+It's information.
+
+And then you're not
+being penalized.
+
+You're not in trouble.
+
+It's not affecting
+your grade if you
+
+act on it, if you take the
+information and use it.
+
+So that's why, I think
+that's the beauty of it.
+
+There are many, many
+active learning techniques.
+
+And if you looked at the
+website from University
+
+of South Florida
+has just, I think,
+
+it's close to 200 techniques
+for what you might do.
+
+I'm doing a bit of a--
+
+I call it the foie gras method.
+
+You know how they
+make foie gras?
+
+They force feed the goose.
+
+So I'm going to give a lot.
+
+And we're going to do a lot
+of different active learning
+
+things in this session.
+
+It's a little bit comical.
+
+I know it's kind of
+funny how many we're
+
+trying to cram into two hours.
+
+But I'm going to try to do that.
+
+So we'll do some of these.
+
+And we can talk about any
+one of them in particular.
+
+But a nice one to get students
+in the frame of your class
+
+is to they come in.
+
+And they have five minutes
+before you do anything
+
+to write down what they thought
+was the most interesting part
+
+of the reading or answer
+a certain question related
+
+to the reading or solve a
+problem or whatever it is.
+
+You give them a prompt.
+
+You sit down.
+
+You focus them.
+
+And then they're off.
+
+I do want to just focus on the
+word active for just a second.
+
+It may help you to think
+about active and interactive
+
+learning.
+
+There's all sorts of
+ways to chop it up.
+
+And at some level,
+it's semantics.
+
+But at some level, it isn't.
+
+So students can be
+active if they're
+
+sitting by themselves
+thinking about something
+
+and writing something
+down or solving a problem.
+
+That is active learning.
+
+They don't have to be
+talking to each other.
+
+You can do active learning
+in a class of 3,000 people.
+
+Stop and think.
+
+Answer this question.
+
+That's active learning.
+
+That's way more than
+happens in a lot of classes.
+
+Interactive learning generally
+implies that students
+
+are talking to each other.
+
+That's the most general
+categorizations you can get,
+
+active, interactive.
+
+So we're going to
+do a bunch of stuff
+
+with clickers or
+plickers, these things.
+
+But there's some other
+techniques you can do.
+
+You can put up a
+graph or an image.
+
+And you could say,
+OK, somebody come up
+
+and show me the green
+boundary in this picture.
+
+Show me a triple junction.
+
+Show me where the building, the
+crack in the building started.
+
+Show me whatever.
+
+And you pass the pointer.
+
+And then you have
+the student who
+
+has the pointer come up
+with another question
+
+and pass it to somebody else.
+
+So that's another nice technique
+that takes the responsibility
+
+off of the teacher.
+
+And so you're not
+picking on students.
+
+We've been doing mud
+cards, think, pair, share.
+
+We're going to do
+a lightning round.
+
+I'll talk a little bit
+more about jigsaw later.
+
+And if time allows,
+I'll show you
+
+a demo I did on diffusion using
+the students as the atoms.
+
+Sometimes if you're trying
+to ease in active learning,
+
+slowly into your class-- you
+don't want to do too much--
+
+you want to think about
+the short time things that
+
+don't require huge disruptions.
+
+If you want to go back
+to your seats, you can.
+
+Maybe I should let
+you guys do that.
+
+So you know what we'll do?
+
+While they're
+taking a break, I'm
+
+going to demo the beach ball.
+
+So this is nice.
+
+This is the beach
+ball technique.
+
+So when you catch
+the ball, I'd like
+
+you to tell me if you've
+had any experiences
+
+with active learning in
+classes that you've taken.
+
+And you can't count this one.
+
+AUDIENCE: I had active learning
+in my electricity and magnetism
+
+class.
+
+And that was called TEAL.
+
+And it's very polarized.
+
+The people for and against
+it, especially the students.
+
+So they basically
+tables of nine.
+
+And then within that table,
+you had groups of three.
+
+And each of those would be
+a problem solving group.
+
+So you'd have four problems
+to solve per two hour class
+
+period.
+
+And that would be going
+up to the board look
+
+and doing it by themselves.
+
+And then the teacher at the
+end would reveal the answers
+
+and tell us how
+to go through it.
+
+And, for my group at
+least, there was always--
+
+or my table--
+
+there was always
+this one person who
+
+would write every single time--
+
+JANET RANKIN: 3,000 People.
+
+Stop and think.
+
+Answer this question.
+
+That's active learning.
+
+That's way more that
+happens in a lot of classes.
+
+Interactive learning generally
+implies that students
+
+are talking to each other.
+
+And that's the most
+general categorizations
+
+you can get active, interactive.
+
+So we're going to do a bunch
+of stuff with clickers,
+
+or plickers, these things.
+
+But there's some other
+techniques you can do.
+
+You can put up a
+graph or an image.
+
+And you could say,
+OK, somebody come up
+
+and show me the green
+boundary in this picture.
+
+Show me a triple junction.
+
+Show me where the building, the
+crack in the building started.
+
+Show me whatever.
+
+And you pass the pointer.
+
+And then you have
+the student who
+
+has the pointer come up
+with another question
+
+and pass it to somebody else.
+
+So that's another nice technique
+that takes the responsibility
+
+off of the teacher.
+
+And so you're not
+picking on students.
+
+We've been doing mud
+cards, think, pair, share.
+
+We're going to do
+a lightning round.
+
+I'll talk a little bit
+more about jigsaw later on.
+
+And if time allows,
+I'll show you
+
+a demo I did on diffusion using
+the students as the atoms.
+
+Sometimes if you're trying
+to ease in active learning,
+
+slowly into your class--
+
+you don't want to do too much--
+
+you want to think about
+the short time things that
+
+don't require huge disruptions.
+
+If you want to go back
+to your seats, you can.
+
+Maybe I should let
+you guys do that.
+
+So you know what we'll do?
+
+While they're
+taking a break, I'm
+
+going to demo the beach ball.
+
+So this is nice.
+
+This is the beach
+ball technique.
+
+So when you catch
+the ball, I'd like
+
+you to tell me if you've
+had any experiences
+
+with active learning in
+classes that you've taken.
+
+And you can't count this one.
+
+AUDIENCE: I had active learning
+in my electricity and magnetism
+
+class.
+
+And that was called TEAL.
+
+It's very polarized, the people
+for and against it, especially
+
+the students.
+
+So we basically
+had tables of nine.
+
+And then within that table,
+we had groups of three.
+
+And each of those would be
+a problem solving group.
+
+So you'd have four problems
+to solve per two hour class
+
+period.
+
+And that would be
+going up to the board
+
+and doing it by themselves.
+and then the teacher at the end
+
+would reveal the
+answer and telling us
+
+how to go through it.
+
+And for my group at least--
+
+or my table-- there
+was always this one who
+
+would write every single time.
+
+And I feel like that detracted
+from active learning.
+
+I think it worked
+better for other people.
+
+JANET RANKIN: It's
+definitely polarized.
+
+Students really are not--
+
+I think we talked a
+little bit about this
+
+when we did some of
+the learning theories--
+
+but students really are
+polarized about whether they
+
+like it or not.
+
+The data that there's been
+some pretty good analysis
+
+of learning, measuring
+how much students learn,
+
+and then how much they retain
+and all that kind of stuff.
+
+And when you go
+through that, students
+
+seem to learn more and retain
+more in the active learning
+
+format, even though they
+really at least half of them
+
+don't like it at all.
+
+So it's an
+interesting commentary
+
+That's a good great story.
+
+So why don't you
+give the ball a toss?
+
+There you go.
+
+No, you have to
+answer a question.
+
+Have you ever experienced
+active learning
+
+in a classroom
+besides this class?
+
+And how did it work or not work?
+
+AUDIENCE: I would
+say yes to that.
+
+It's definitely the traditional
+method, sitting in front,
+
+face to face lecture.
+
+JANET RANKIN: Fair enough.
+
+Give a toss, toss to anyone.
+
+Are we going to get the
+same answer from all of you?
+
+If it's just--
+
+AUDIENCE: Is it
+the same question?
+
+JANET RANKIN: Yeah,
+same question.
+
+AUDIENCE: Yeah, I have.
+
+Because I recently
+studied in Sweden.
+
+And that's the way, most
+of the time that way,
+
+they teach in Sweden.
+
+So for some classes, generally
+in higher level classes,
+
+according with d-level classes,
+they use active learning.
+
+JANET RANKIN: Great and
+students buy into it?
+
+They're OK with it?
+
+They work at it?
+
+AUDIENCE: Culturally,
+they tend to veer
+
+towards active learning.
+
+JANET RANKIN: And that's
+a very interesting point,
+
+the idea that it can
+be a cultural thing.
+
+If everybody else is doing
+it, or it's expected,
+
+then that's what you do right.
+
+So some of these changes,
+there's an incubation period
+
+before they actually take off
+and they're widely accepted.
+
+AUDIENCE: In fact
+in Denmark, I think
+
+that's the only way they each.
+
+JANET RANKIN: It's
+pretty active.
+
+I have a colleague
+who's in, or friend
+
+who works at the
+University of Copenhagen,
+
+and all new faculty have to take
+a yearlong course on teaching,
+
+no matter what department,
+physics, math, a year long,
+
+the faculty.
+
+And here you could never force
+the faculty to do anything.
+
+So it's pretty
+interesting that they've
+
+been doing it for so long.
+
+AUDIENCE: I have a
+question about that.
+
+Is it the way that professors,
+their role as actual teachers
+
+is viewed?
+
+[INAUDIBLE]
+
+But seriously,
+people [INAUDIBLE]
+
+or something, I think definitely
+trying to enforce a teaching
+
+class would be a
+lot more receptive
+
+than if you tried to enforce
+that here, where teaching
+
+isn't necessarily the focus.
+
+JANET RANKIN: But there, it's
+a good research university.
+
+But on the teaching
+side, that's the norm.
+
+That's the expectation.
+
+AUDIENCE: But what
+about requiring--
+
+I know it's hard when
+you have professors
+
+that have been
+doing what they're
+
+doing for 25, 30, 40 years.
+
+It's hard to get them
+to adopt new techniques.
+
+But I think that requiring
+things-- the faculty
+
+that you can require things
+of are the new faculty, who
+
+have no power yet.
+
+JANET RANKIN: Yes and no.
+
+If the tenured system, the
+requirements for tenure
+
+don't change, then asking
+them to take on new-- oh,
+
+you guys should try
+active learning.
+
+Revamp this course.
+
+And then they don't get tenure.
+
+So it really has to be
+a whole systemic change,
+
+where the department buys in.
+
+The school buys in.
+
+The university buys
+in and says, OK, these
+
+are the criteria for tenure.
+
+And in that is you have
+to use active learning.
+
+Or you have to--
+
+that's where it would
+have to get change.
+
+Otherwise you
+can't expect people
+
+that aren't tenured to do it.
+
+You shouldn't.
+
+Let's give the
+ball one more toss.
+
+AUDIENCE: So it's
+been a long time
+
+since I've been in a classroom.
+
+I would say, in a
+regular classroom,
+
+I don't that I've
+been in a class that
+
+does active learning.
+
+But I have taken courses
+that are largely lab courses,
+
+like a mouse embryology
+course, where
+
+you have 15 minutes of lecture.
+
+And then you go into
+the lab And you do it.
+
+And the professor will
+walk around and help you
+
+with the technique.
+
+You're actually
+there with the mice.
+
+And you're actually
+doing something.
+
+So does that count?
+
+JANET RANKIN: Lab courses
+can be their own genre.
+
+But there has been
+this movement to take
+
+that's a little bit of what TEAL
+does, at a more simple level.
+
+And there's a little
+bit of lecture.
+
+And then students are supposed
+to answer some questions
+
+or do something.
+
+And then they come
+back together.
+
+And Studio Labs at WPI
+has that same format,
+
+where the classrooms are
+built with lab benches.
+
+And students sit at lab
+benches and see a lecture.
+
+And then they do
+some experiments.
+
+They're mini experiments.
+
+It's not whole mouse dissection.
+
+But they do a mini experiment.
+
+And then they report back.
+
+And there's an
+interchange like that.
+
+So there are some
+blending of the two.
+
+Often what people do
+in labs is different.
+
+And usually a good
+lab is fabulous.
+
+A good lab is fabulous, which
+is another argument for why
+
+active learning is
+good, because everybody
+
+thinks back about, oh, that
+lab course was so great.
+
+I learned so much
+and did so much.
+
+And yet that's the lab course.
+
+And then we have the lecture.
+
+So it's an interesting comment.
+
+So that was the beach ball.
+
+And you see you
+guys got to throw
+
+the ball at other students.
+
+So I didn't have
+to pick on every--
+
+I didn't have to call on
+people or pick on people.
+
+I had a little demo here
+about why it's important,
+
+just if you ask a question
+or you ask students
+
+if there are any questions
+or what questions they have.
+
+And that's generally
+a better phrase.
+
+What questions do you have?
+
+It's more welcoming, opposed to
+saying OK, who's stupid enough.
+
+Who's not following me?
+
+Say, OK, what are the questions?
+
+It's a more welcoming phrase.
+
+But the idea of waiting.
+
+So here, if I click
+on this little guy,
+
+you should hear 30
+seconds of music.
+
+So imagine you ask a question,
+30 seconds for people
+
+to think about it and
+formulate an answer.
+
+This is what 30 seconds
+feels like of dead time.
+
+Well, there'll be music.
+
+[MUSIC PLAYING]
+
+That's not part of it.
+
+So did that feel
+like a long time?
+
+I know we had a
+little break there.
+
+But that feels like a lot.
+
+Especially when you're
+standing up here,
+
+it feels like a long time.
+
+But 30 seconds, give
+them 30 seconds.
+
+The point is, if you want
+to give students 30 seconds,
+
+you're going to have to time it.
+
+You totally have to time it,
+because you will not estimate
+
+30 seconds effectively.
+
+You will totally
+underestimate it.
+
+And then another
+technique that you
+
+can piggyback on that is
+saying, OK, take 30 seconds.
+
+I'm not going to take any
+answers for 30 seconds.
+
+So you may have an
+answer right away.
+
+But I don't want to
+hear it for 30 seconds,
+
+because there's always
+that guy in the front.
+
+I had this guy in my
+high school math class.
+
+And he used to sit on his--
+this little short guy--
+
+and he used to sit on
+his foot on the chair.
+
+He's on his chair.
+
+And he's sitting on his foot.
+
+And he had his hand like this.
+
+And he was in the front row.
+
+And whenever the teacher asked
+the question, he would go.
+
+And he would come up off of it.
+
+And so he was always the guy
+that answer the questions.
+
+But that left some of us
+who took a little more time
+
+not having the
+opportunity, kind of
+
+like having the one person write
+all the time in the TEAL group.
+
+So that's a good way
+to go about that.
+
+We talk a little bit about
+using clicker questions
+
+to solicit feedback.
+
+And we've used the
+plickers in this class.
+
+We'll use them again.
+
+You can get dedicated
+clickers, these dedicated punch
+
+in things.
+
+They use them for TEAL, I think.
+
+Students may have
+to purchase them.
+
+That may cost money.
+
+The department may
+have to purchase them.
+
+That's another source of money.
+
+AUDIENCE: They make
+us buy everything.
+
+JANET RANKIN: So when I
+was at Brown, actually,
+
+the department would buy them.
+
+And they'd leave
+them in the library.
+
+And then you could check them
+out with your student ID.
+
+And then you got that.
+
+So you got it for the semester.
+
+But it was linked to your ID.
+
+And if you didn't bring it
+back, they'd charge you for it.
+
+But that's another way to do
+it, a fairer way to do it.
+
+We'll look at something
+called Socrative later on.
+
+I'll use it later on.
+
+But it's a text.
+
+It's an online format.
+
+So students need a
+smartphone or a laptop.
+
+But they don't need
+a separate clicker.
+
+There are issues with that,
+because not everybody is
+
+going to have a smartphone.
+
+And are you biasing your class
+against people that don't
+
+happen to have the technology?
+
+This is why I like
+plickers, because you
+
+don't need to buy anything.
+
+I give you the card.
+
+And I need to have
+the smartphone.
+
+But you don't.
+
+And then you could
+always use index cards
+
+or do the whole,
+put one finger up
+
+if you think it's A and two
+if it's B and three if it's
+
+C. That gets a little
+tough in a bigger class,
+
+because it's hard to see.
+
+It's hard to count.
+
+I like the fact that
+the clickers, plickers,
+
+and the Socrative
+or Poll Everywhere
+
+give you a histogram.
+
+So you get a really quick
+idea about who's getting it
+
+and who isn't getting it.
+
+So we're going to do
+a couple of these.
+
+Remember-- this is from
+the label of the free body
+
+diagram-- that these
+misconceptions always
+
+linger in a lecture class.
+
+We talked about this free
+diagram the other day.
+
+So let's just try this one here,
+give you another little warm up
+
+on the picker's.
+
+So you have the card.
+
+And I'm just going to ask
+you to look at the question.
+
+And when you're ready to
+answer, just hold up your card.
+
+And if you can keep your
+finger away from the pattern,
+
+that would be great, because
+it makes it hard to read it.
+
+And then however you want to--
+
+AUDIENCE: Does this work
+for larger classrooms?
+
+JANET RANKIN: It does.
+
+I have a colleague
+who uses it at Brown.
+
+And he just started
+teaching this semester.
+
+And he showed me his--
+
+or a friend-- he
+showed me his plickers.
+
+And he printed them
+out on 8 by 10,
+
+like a sheet of
+paper, cardstock.
+
+And they're enormous.
+
+They're like this big.
+
+AUDIENCE: How do you
+not get [INAUDIBLE]?
+
+Well Well they have
+to hold them up.
+
+You have to.
+
+And you can walk
+around a little bit.
+
+But I'll show you this.
+
+So I have the histogram.
+
+And I measured everybody.
+
+So now I know what you
+think about this question.
+
+I know who's got it right.
+
+I don't know who's got it right.
+
+But I know that most of you
+have chosen the correct answer.
+
+But there were a
+few of you picked up
+
+one of the other answers.
+
+And so now I know that it's a
+non-trivial number of you that
+
+picked an incorrect answer.
+
+So now I know exactly
+what I need to do.
+
+It's given me incredibly
+good information
+
+that there is some
+out there that
+
+have a pretty strong
+misunderstanding
+
+of the literature.
+
+And that's that
+some of you picked
+
+A. There's a lot of data to
+support that active learning,
+
+active technique supports
+student learning.
+
+I call your attention
+to the Freeman paper
+
+that's in the reading for
+today, also to the [? Haik ?]
+
+article, which was referenced.
+
+So those are two of the
+more compelling readings.
+
+But if you go through, you'll
+see quite a few studies
+
+that unambiguously show that
+active learning has an impact.
+
+So the incorrect answer is that
+it always involves group work.
+
+That's not true.
+
+It doesn't always involve work.
+
+As we said, you could
+just ask students
+
+to sit and think and then do
+something with their thoughts.
+
+And that would be active.
+
+So Rachel, you're smiling.
+
+Is there a--
+
+OK.
+
+AUDIENCE: Sometimes my
+face just does that.
+
+JANET RANKIN: I didn't
+know whether it was a smirk
+
+or whatever.
+
+And did I show you
+what this looks like?
+
+So you can see with the
+histogram looks like.
+
+I did?
+
+[INTERPOSING VOICES]
+
+You weren't here,
+though, when I did.
+
+The time I used it before.
+
+I'll show you offline.
+
+So the histogram is
+really, really useful.
+
+So it really can ferret
+out some misunderstanding.
+
+We don't have to go
+through all these.
+
+But this is another way to
+check for misunderstanding.
+
+I can ask this kind of question.
+
+It's a concept question.
+
+It's a conceptual question.
+
+And then I can ask
+you to pick an answer.
+
+And then I can see where
+your misconceptions
+
+lie about this topic.
+
+So it can be very, very-- it
+should be very, very focused.
+
+It's not just a
+busywork question
+
+it's a focused question
+with focus distractors.
+
+The distractors are
+the incorrect answers.
+
+AUDIENCE: Can we do this?
+
+I want to see what the
+spread of answers is.
+
+JANET RANKIN: Sure.
+
+Let's do it.
+
+AUDIENCE: They asked
+this question--
+
+I laughed, because they
+asked a very similar question
+
+at Harvard graduation.
+
+JANET RANKIN: Exactly.
+
+What was it called,
+a world of their own?
+
+AUDIENCE: Yeah one of those.
+
+JANET RANKIN: Two times, check.
+
+I've got to clear my responses.
+
+Let's go.
+
+So I'm getting you folks in
+the back without a problem.
+
+I got one.
+
+I'm missing one of you.
+
+Wow.
+
+So there's any number
+of things I could ask.
+
+We're going to do
+another pair, share
+
+around this kind of thing.
+
+But maybe not for this one.
+
+But this is amazing.
+
+Basically it's A
+got three votes.
+
+B got three votes.
+
+C got four votes.
+
+And D got three votes.
+
+So it's pretty amazing.
+
+AUDIENCE: What is
+the right answer?
+
+JANET RANKIN: Biologists?
+
+AUDIENCE: B.
+
+JANET RANKIN: The answer
+is B. And it's the most--
+
+maybe not surprising--
+but the idea
+
+that it's taking in
+things from the air.
+
+They're taking in gases.
+
+But there's chemical reactions
+which manifest themselves
+
+in a weight gain.
+
+[INTERPOSING VOICES]
+
+It's not a biology
+class, which is why--
+
+so that's just super telling.
+
+That would be incredible.
+
+If this were a biology class
+and that was the spread,
+
+that would just be
+really, really informative
+
+for the instructor.
+
+AUDIENCE: Really worrying.
+
+JANET RANKIN: Well
+yeah, that too.
+
+But it's biology class.
+
+So don't worry.
+
+But you do want to think
+very, very carefully
+
+about the wrong
+answers, because you
+
+want the wrong
+answers to tell you
+
+something about what students
+understand or don't understand.
+
+Generally speaking in
+the adoption of clickers,
+
+plickers, whatever, takes
+a three step process.
+
+One is that people
+generally start
+
+with these simple
+fact questions,
+
+and then more challenging
+conceptual questions, which
+
+I would put the
+one we just did at.
+
+That students, they might--
+
+arguing with each
+other could be useful.
+
+And then the third
+is you've just
+
+totally revamped the lecture.
+
+And it's all centered
+around these questions.
+
+And depending on
+how students answer,
+
+that's how you navigate
+through the lecture
+
+or through the
+course, class period.
+
+I would never recommend that
+anybody start with this one.
+
+I think that we're all capable
+of starting with two actually.
+
+And I think starting with
+three may be a waste of time,
+
+unless you really just want
+to check and see if people
+
+did the reading or something.
+
+It's a big class.
+
+And you just want to see if
+they've done the reading.
+
+But in general, I would
+say put your energy
+
+into coming up with some
+really good questions.
+
+And maybe don't ask as many.
+
+And then as I keep
+saying, I hope
+
+you can start to see how
+that's really, really linked.
+
+It's a measure of
+whether they get it.
+
+But it's also an activity
+to help them get it.
+
+So I've been minoring
+the Back Channel.
+
+Nobody's saying anything
+except for Dave.
+
+And I answered him.
+
+And because I gave
+you a break before,
+
+I may scoot on, continue on.
+
+So if you want take a second
+and login, that's fine.
+
+But I may not--
+
+AUDIENCE: That's the
+link for last year's.
+
+AUDIENCE: I entered it, and I
+put entered into last year's.
+
+And I got really confused.
+
+JANET RANKIN: Uh oh.
+
+So the one for this
+year is back here.
+
+Hold on.
+
+AUDIENCE: It's like
+four something,
+
+4125 instead of 3969.
+
+JANET RANKIN: Oh OK, thank you.
+
+So while you're
+doing that, I'm going
+
+to set up something which
+is called lightning round.
+
+And we're doing these two.
+
+So I'm going to just,
+sitting in your seat,
+
+if you can think about this
+question, just the question
+
+on the left.
+
+Based on research
+at NASA, what was
+
+the approximate net global
+change in temperature
+
+between 1880 and 1975?
+
+It's not a plicker question.
+
+It's just a question.
+
+Try to think about what
+you think the answer is.
+
+AUDIENCE: What is
+Celsius to Fahrenheit?
+
+JANET RANKIN: To get from
+Celsius to Fahrenheit?
+
+So you have to--
+
+well I always just
+double it and add 30.
+
+So it's 8/5 plus 32.
+
+[INTERPOSING VOICES]
+
+8/56 plus 32 is
+the real equation.
+
+Is it 8/5 or 9/5?
+
+AUDIENCE: 9.
+
+JANET RANKIN: 9/5 That's
+why I just double it.
+
+Close enough.
+
+So what I'm going to ask
+is that-- let's see--
+
+David, Gordon, and Julie.
+
+And if you can move down,
+down, just to the end.
+
+And then if Adam, [INAUDIBLE],
+Dave can come around?
+
+Just keep going.
+
+Keep going.
+
+That's fine.
+
+One, two, three, four-- no, no.
+
+You have to stand up, guys.
+
+No relaxing.
+
+Yes, but that's not--
+
+I can tell a story.
+
+Please stand up and move over.
+
+Move over.
+
+And just keep coming around.
+
+Everybody's up.
+
+Everybody's doing this.
+
+Michelle, so I
+need six, Michelle
+
+come on over here
+next to [INAUDIBLE].
+
+That's fine.
+
+Now [INAUDIBLE],
+you come around here
+
+please, and go
+opposite David, please.
+
+And everybody else just file
+in and go opposite someone.
+
+Sarah, do you want
+to participate?
+
+So here's what happens.
+
+I'm going to tell you to go.
+
+And you have two minutes.
+
+The person in this line
+takes some amount of time
+
+and says what their answer
+is and why they chose it.
+
+And the person in that line
+can ask questions or whatever,
+
+and then say what they thought
+and say why they thought that.
+
+So you're going to have a
+really quick conversation
+
+about your choices.
+
+And after two minutes, I'm going
+to tell you to please stop.
+
+And then you have
+to get a new person.
+
+And I'll show you
+how to do that.
+
+Everybody understand
+what we're doing?
+
+You're having a two
+minute exchange of ideas.
+
+And it's going to be loud.
+
+Believe me.
+
+And it's the person
+opposite you.
+
+Are you ready?
+
+Everyone ready?
+
+On your mark, get set, go.
+
+[INTERPOSING VOICES]
+
+Let me ask a question.
+
+Did you encounter people that
+had different choices than you?
+
+AUDIENCE: Yes.
+
+JANET RANKIN: Yes.
+
+So that generally means
+it's a pretty good question,
+
+because you get to hear lots
+of different perspectives.
+
+Now if this were the central
+part of the class, this topic,
+
+you might let the pairings
+go even longer, even more
+
+pairings.
+
+So did anybody change
+their mind based on what
+
+they heard a partner say?
+
+OK, a couple of you.
+
+Generally, what
+happens then is you
+
+would want to have
+a de-brief, where
+
+we talk about why you
+picked the answer you picked
+
+and what you picked.
+
+And most of the
+time, the choices
+
+are a little been informative.
+
+If you found, as the instructor,
+that everybody picked
+
+a negative number, well you're
+in a very different place
+
+than if people are arguing
+over how much positive it is.
+
+So you're going to
+use that information
+
+to find out about where
+the misconceptions are.
+
+What's the advantage
+of this method?
+
+Gordon.
+
+AUDIENCE: It's very
+interesting, I thought.
+
+One I found out is that the
+students talk to each other.
+
+We never talk to each other.
+
+And it's easier for
+them as to [INAUDIBLE].
+
+So at the beginning, they
+are aware of conflicts.
+
+But as we rotated,
+there was a convergence.
+
+It was very interesting.
+
+JANET RANKIN: [INAUDIBLE]
+have your hand up.
+
+AUDIENCE: Yes, one time
+I was laughing just
+
+because it was very effective.
+
+There was so much [INAUDIBLE].
+
+And when we started,
+one resisted
+
+some passionated idea about
+this is how it should be.
+
+And by the time it
+went to all the people,
+
+people can get all the idea.
+
+You try to look for
+the superior idea.
+
+Then you decide,
+oh, this is better.
+
+When we try to switch again,
+you listen to a better argument.
+
+So from which one decides
+without [INAUDIBLE]
+
+the first one?
+
+JANET RANKIN: A
+couple of points.
+
+One is that it's impossible not
+to-- when you pair people up,
+
+it's pretty hard for
+somebody not to participate.
+
+So if you have somebody
+that's resistant,
+
+they might still be resistant.
+
+But it's virtually impossible
+for them not to participate.
+
+And also it's a
+little less scary.
+
+One person, it's really noisy.
+
+You know you only have to talk
+to them for a minute or two.
+
+So it's a little less scary.
+
+Everybody's doing it.
+
+The other thing is that
+you definitely want
+
+to have some sort of de-brief.
+
+You can't just stop and
+go, OK, let's go on.
+
+You're going to have to find
+out what people's answers are.
+
+And you're going to have to
+address it or at least reveal
+
+the right answer, because
+there's many places
+
+many, many places
+for misconception.
+
+And also, then, if
+you do it enough,
+
+you can maybe--
+students can find
+
+arguments or people's
+explanations that
+
+resonate with them.
+
+And then you get exposed to
+different kinds of arguments
+
+or different kinds of ways
+of explaining the problem.
+
+So in this case, the answer is
+actually positive 0.4 degrees.
+
+So B is the correct
+answer, just so you know.
+
+AUDIENCE: Yes, I
+just want to make
+
+a comment that sometimes this
+method could be confusing
+
+as well.
+
+For instance, if you listen
+to two superior arguments,
+
+one against.
+
+For instance, I talked to
+someone who was actually
+
+in support of negative.
+
+And she brought an argument
+and so forth like that.
+
+And somebody
+thought of positive.
+
+And there was a strong
+argument also for that.
+
+Sometimes if you just
+be sitting on the fence,
+
+I don't know where to get off.
+
+JANET RANKIN: Well I think it's
+OK to be confused for a while.
+
+That's fine.
+
+As I said, if this were a
+course on global warming,
+
+climate change, whatever it
+is, we would have to make sure
+
+that we heard all of
+those explanations
+
+or a sampling of those
+explanations and said,
+
+oh, well that's a good.
+
+I can see why you think that.
+
+But you've forgotten about this.
+
+Or I can see why, so
+that you can process it
+
+all so that people
+don't leave confused.
+
+But it's good to hear
+the wrong answer,
+
+to be convinced of the
+wrong answer, maybe,
+
+but then to see why it's wrong.
+
+That's an important
+learning activity.
+
+AUDIENCE: But this
+method is only
+
+applicable for where you have
+cases where you can debate.
+
+Because if you have very clear
+cases, for example, if I ask,
+
+what is the color of the sky?
+
+It's a definite.
+
+But when it's fuzzy,
+then this can be--
+
+JANET RANKIN: Yes, or
+when it's a concept
+
+you think people might
+have difficulty with.
+
+Yeah, it's not going to work
+if it's a real clear cut.
+
+I want to demo one more method.
+
+This is think, pair, share.
+
+And I know we've been
+doing those forever.
+
+But I'm going to couple it
+with a clicker question.
+
+And I think we can do
+it in seven minutes.
+
+So
+
+I have two blocks here, because
+this is just too fun, really.
+
+I have two blocks.
+
+They're the same
+width and the same.
+
+Length but they are
+different thickness.
+
+And I have this thing.
+
+And I'm going to tap
+on the thin block.
+
+Makes more or less--
+
+it's not really a note.
+
+But it's some sound.
+
+And I'm going to
+ask you, when I do
+
+the same thing, the same
+force, the same place
+
+on the thick block, will
+the note be higher, lower,
+
+or the same as the thin block?
+
+And this should be A, B, and
+C, not one two and three.
+
+So but if it's A,
+B, and C go ahead
+
+and vote with your plickers.
+
+Do you know that's what
+they auto correct to?
+
+That's what it, if you're
+typing and you write plickers,
+
+it autocorrects
+to pluckers, which
+
+can be pretty embarrassing.
+
+AUDIENCE: So high
+is for A. You've not
+
+clicked on the thicker one.
+
+JANET RANKIN: I know.
+
+That's why you have to tell
+me what you think it is.
+
+AUDIENCE: Is this a A, B, and C?
+
+JANET RANKIN: A B
+and C. So there's
+
+no D. There's a reason for this.
+
+If I told you the
+answer, then there
+
+wouldn't be much fun in voting.
+
+And I have everybody.
+
+So I have a distribution.
+
+I'm not going to tell
+you the distribution.
+
+I'm not going to share that
+with you I'd like you to take--
+
+just cluster.
+
+It could be groups of three or
+four, whenever you have nearby,
+
+and talk about why you
+picked the answer you picked.
+
+And then I'm going to give you
+the opportunity to vote again.
+
+So in the interest of time,
+two minutes to discuss this.
+
+[SIDE CONVERSATIONS]
+
+I wanted to just call attention
+to a couple things I did.
+
+I walked around and tried to
+eavesdrop on your conversations
+
+so that I could tell what
+you were thinking about,
+
+but without putting
+you on the spot,
+
+without asking you to say,
+in front of everybody,
+
+what you thought.
+
+So that's one thing to do.
+
+Now I have a sense for
+your mental models,
+
+how you're thinking
+about the problem.
+
+So I have some really
+good information
+
+about why you think
+the answers you think.
+
+What I'm going to do is I'm
+going to give you the chance
+
+to re-vote.
+
+If you want to change
+your vote, you may.
+
+Or you don't have to.
+
+Some of the clicker
+software actually
+
+lets you save
+consecutive histograms,
+
+which can be useful.
+
+You can compare
+if there's change.
+
+This doesn't let you do it.
+
+So I just have to--
+
+AUDIENCE: Voting twice there?
+
+AUDIENCE: I'm voting
+for [INAUDIBLE].
+
+He's not present, so--
+
+JANET RANKIN: Voting in
+Chicago, early and often.
+
+We have exactly the
+same distribution,
+
+which flies in the face
+of some other data I
+
+was going to show you.
+
+But that's OK.
+
+I'll just in the interest of--
+
+so one thing I could do
+is I could call on you.
+
+And I could say, OK, if you
+said it was lower, tell me
+
+why you thought it was lower.
+
+And I could get some
+arguments for why you thought
+
+it was lower on the board.
+
+So some people think of cellos
+make lower sounds than violins.
+
+And some people think that doors
+on mansions have a low sound.
+
+And other people talked about
+xylophones and the length
+
+and the wavelength
+of the xylophone,
+
+and the longer wavelengths
+for the longer pieces.
+
+So I know a lot about how you're
+thinking about this problem.
+
+The other thing I
+know is that I am not
+
+telling you the answer yet.
+
+So there's a little bit
+of suspense in here.
+
+There's a little bit to
+try to keep you interested
+
+and wanting to know, wanting
+to understand the answer.
+
+AUDIENCE: Janet?
+
+JANET RANKIN: Yes?
+
+AUDIENCE: So you said we
+had the same distribution.
+
+But can we have a show of
+hands for how many people
+
+changed their answer?
+
+JANET RANKIN: That's
+a great question.
+
+Yes.
+
+Raise your hand if you
+changed your answer.
+
+It could've been amazing.
+
+AUDIENCE: So sometimes we've
+done that in my physics class.
+
+When they ask, who
+changed their answer?
+
+And everyone raises their hand.
+
+It's the same
+exact distribution.
+
+Or everyone goes from
+A and B to C and D.
+
+And even C and D originally
+only had three people,
+
+you'll see the entire shift.
+
+And it turns out
+A and B was right.
+
+When we vote the second time,
+we all picked another answer.
+
+JANET RANKIN: That's very funny.
+
+That could have happened.
+
+Sometimes a nice
+follow up question
+
+is how confident are
+you in your answer.
+
+So then that's a really
+good-- because you
+
+may have 80% of the
+people h the right answer
+
+but if you say how confident
+and hardly anybody is
+
+very confident then, you do
+need to talk about it some more.
+
+So it gives you some really,
+really good information.
+
+So here we go.
+
+Here's this one.
+
+It's higher.
+
+Exact same material.
+
+AUDIENCE: So when you play
+the marimba and the xylophone,
+
+you have bigger bars.
+
+That they get really thin
+when they're on the bass.
+
+The bass notes are really thin.
+
+And the really small high notes,
+they're really, really thick.
+
+JANET RANKIN: So
+that's one thing.
+
+The other thing is
+that on a xylophone,
+
+it's a standing wave, because
+you fixed the endpoints.
+
+And the wave just vibrates
+based on the length
+
+of the pins, the separation
+of the pins or the mounts.
+
+So in this case, it's
+a free vibration.
+
+So that's another
+different misconception.
+
+And then if you think-- so the
+easiest way to think about it
+
+is a diving board.
+
+If you had a thin diving board,
+and you went and jumped on it,
+
+it would go way down
+and come back up again.
+
+That's a long wavelength.
+
+And that's a low note.
+
+And then if you think about
+a stiffer diving board
+
+that you'd be kind of like, mmm.
+
+That's a shorter wavelength.
+
+So it's different.
+
+You have different-- and
+then any kind of a cavity,
+
+like a cello or a door of a
+house, if it's a big cavity,
+
+it's a bigger standing wave.
+
+It's still a standing wave.
+
+So those are very different.
+
+They are different models.
+
+So this technique
+is really great,
+
+because it really gives you
+incredible insight into what
+
+students' misconceptions are.
+
+And then you can really
+make sure to address
+
+those misconceptions to deal
+with their faulty models.
+
+So for the post-class
+assignment,
+
+I've asked you to
+think about what active
+
+learning techniques you might
+adopt in your own teaching,
+
+in your own classes.
+
+And then think about how
+you would adapt them,
+
+anticipate any
+issues or whatever.
+
+So hopefully you've
+gotten a good smattering.
+
+And I'll post the
+slides, which have
+
+some links and things in there
+if you want to look at videos.
+
+And also check out that
+list from University
+
+of South Florida.
+
+That has some amazing techniques
+that you might find useful.
+
+I'm going to send everybody off.
+
+But if you'd like to
+comment on the mud cards--
+
+I know we're over time--
+
+I have them here, if you
+want to make a comment.
+
+But otherwise, I will
+see you next time.
+
+And I'd like the plickers back.
\ No newline at end of file
diff --git a/hJfqUAKMEdw.txt b/hJfqUAKMEdw.txt
new file mode 100644
index 0000000000000000000000000000000000000000..10d3f97450191ba00831fa42acba45a3400032b1
--- /dev/null
+++ b/hJfqUAKMEdw.txt
@@ -0,0 +1,1301 @@
+align:start position:0%
+ 
+the following content is provided under
+
+ align:start position:0%
+the following content is provided under
+ 
+
+ align:start position:0%
+the following content is provided under
+a Creative Commons license your support
+
+ align:start position:0%
+a Creative Commons license your support
+ 
+
+ align:start position:0%
+a Creative Commons license your support
+will help MIT open courseware continue
+
+ align:start position:0%
+will help MIT open courseware continue
+ 
+
+ align:start position:0%
+will help MIT open courseware continue
+to offer highquality educational
+
+ align:start position:0%
+to offer highquality educational
+ 
+
+ align:start position:0%
+to offer highquality educational
+resources for free to make a donation or
+
+ align:start position:0%
+resources for free to make a donation or
+ 
+
+ align:start position:0%
+resources for free to make a donation or
+view additional materials from hundreds
+
+ align:start position:0%
+view additional materials from hundreds
+ 
+
+ align:start position:0%
+view additional materials from hundreds
+of MIT courses visit MIT opencourseware
+
+ align:start position:0%
+of MIT courses visit MIT opencourseware
+ 
+
+ align:start position:0%
+of MIT courses visit MIT opencourseware
+at
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+ocw.mit.edu in this demonstration we're
+
+ align:start position:0%
+ocw.mit.edu in this demonstration we're
+ 
+
+ align:start position:0%
+ocw.mit.edu in this demonstration we're
+going to study the reflectivity of light
+
+ align:start position:0%
+going to study the reflectivity of light
+ 
+
+ align:start position:0%
+going to study the reflectivity of light
+at a dialectric interface or a piece of
+
+ align:start position:0%
+at a dialectric interface or a piece of
+ 
+
+ align:start position:0%
+at a dialectric interface or a piece of
+glass
+
+ align:start position:0%
+glass
+ 
+
+ align:start position:0%
+glass
+the setup is here we have a laser helium
+
+ align:start position:0%
+the setup is here we have a laser helium
+ 
+
+ align:start position:0%
+the setup is here we have a laser helium
+neon laser here's the beam from the
+
+ align:start position:0%
+neon laser here's the beam from the
+ 
+
+ align:start position:0%
+neon laser here's the beam from the
+laser be reflected by a
+
+ align:start position:0%
+laser be reflected by a
+ 
+
+ align:start position:0%
+laser be reflected by a
+mirror and then we pass it through a
+
+ align:start position:0%
+mirror and then we pass it through a
+ 
+
+ align:start position:0%
+mirror and then we pass it through a
+quarter wave plate so the light here is
+
+ align:start position:0%
+quarter wave plate so the light here is
+ 
+
+ align:start position:0%
+quarter wave plate so the light here is
+circularly
+
+ align:start position:0%
+circularly
+ 
+
+ align:start position:0%
+circularly
+polarized and then we passed the
+
+ align:start position:0%
+polarized and then we passed the
+ 
+
+ align:start position:0%
+polarized and then we passed the
+circular polarized light through this
+
+ align:start position:0%
+circular polarized light through this
+ 
+
+ align:start position:0%
+circular polarized light through this
+polarizer so that by varying the
+
+ align:start position:0%
+polarizer so that by varying the
+ 
+
+ align:start position:0%
+polarizer so that by varying the
+transmission AIS of the polarizer we can
+
+ align:start position:0%
+transmission AIS of the polarizer we can
+ 
+
+ align:start position:0%
+transmission AIS of the polarizer we can
+vary the state of polarization of the
+
+ align:start position:0%
+vary the state of polarization of the
+ 
+
+ align:start position:0%
+vary the state of polarization of the
+light coming through the polarizer and
+
+ align:start position:0%
+light coming through the polarizer and
+ 
+
+ align:start position:0%
+light coming through the polarizer and
+light goes onto a piece of glass here
+
+ align:start position:0%
+light goes onto a piece of glass here
+ 
+
+ align:start position:0%
+light goes onto a piece of glass here
+then we have the transmitted light which
+
+ align:start position:0%
+then we have the transmitted light which
+ 
+
+ align:start position:0%
+then we have the transmitted light which
+is here falling on this circular screen
+
+ align:start position:0%
+is here falling on this circular screen
+ 
+
+ align:start position:0%
+is here falling on this circular screen
+and the reflected light falls on the
+
+ align:start position:0%
+and the reflected light falls on the
+ 
+
+ align:start position:0%
+and the reflected light falls on the
+screen also so we can by varying the the
+
+ align:start position:0%
+screen also so we can by varying the the
+ 
+
+ align:start position:0%
+screen also so we can by varying the the
+angle of incidence here we can vary the
+
+ align:start position:0%
+angle of incidence here we can vary the
+ 
+
+ align:start position:0%
+angle of incidence here we can vary the
+spot on the
+
+ align:start position:0%
+spot on the
+ 
+
+ align:start position:0%
+spot on the
+on the screen
+
+ align:start position:0%
+on the screen
+ 
+
+ align:start position:0%
+on the screen
+so first we'll start with vertically
+
+ align:start position:0%
+so first we'll start with vertically
+ 
+
+ align:start position:0%
+so first we'll start with vertically
+polarized light or transverse
+
+ align:start position:0%
+polarized light or transverse
+ 
+
+ align:start position:0%
+polarized light or transverse
+electric by setting the polarizer
+
+ align:start position:0%
+electric by setting the polarizer
+ 
+
+ align:start position:0%
+electric by setting the polarizer
+here along the vertical axis and the
+
+ align:start position:0%
+here along the vertical axis and the
+ 
+
+ align:start position:0%
+here along the vertical axis and the
+arrow the white Arrow indicates uh
+
+ align:start position:0%
+arrow the white Arrow indicates uh
+ 
+
+ align:start position:0%
+arrow the white Arrow indicates uh
+vertical polarization so we'll start
+
+ align:start position:0%
+vertical polarization so we'll start
+ 
+
+ align:start position:0%
+vertical polarization so we'll start
+with a small angle of
+
+ align:start position:0%
+with a small angle of
+ 
+
+ align:start position:0%
+with a small angle of
+incidence close to zero and then we
+
+ align:start position:0%
+incidence close to zero and then we
+ 
+
+ align:start position:0%
+incidence close to zero and then we
+slowly work up and what you want to
+
+ align:start position:0%
+slowly work up and what you want to
+ 
+
+ align:start position:0%
+slowly work up and what you want to
+watch is here we go through
+
+ align:start position:0%
+watch is here we go through
+ 
+
+ align:start position:0%
+watch is here we go through
+20° 30° or so and what you see is that
+
+ align:start position:0%
+20° 30° or so and what you see is that
+ 
+
+ align:start position:0%
+20° 30° or so and what you see is that
+the intensity of the light
+
+ align:start position:0%
+the intensity of the light
+ 
+
+ align:start position:0%
+the intensity of the light
+increases as we
+
+ align:start position:0%
+increases as we
+ 
+
+ align:start position:0%
+increases as we
+approach 90° we're here 80 and then 90
+
+ align:start position:0%
+approach 90° we're here 80 and then 90
+ 
+
+ align:start position:0%
+approach 90° we're here 80 and then 90
+and you can see that the light gets
+
+ align:start position:0%
+and you can see that the light gets
+ 
+
+ align:start position:0%
+and you can see that the light gets
+pretty
+
+ align:start position:0%
+pretty
+ 
+
+ align:start position:0%
+pretty
+bright the uh now we go back again
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+here's
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+50°
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+40° and so on all the way down to to
+
+ align:start position:0%
+40° and so on all the way down to to
+ 
+
+ align:start position:0%
+40° and so on all the way down to to
+zero angle of
+
+ align:start position:0%
+zero angle of
+ 
+
+ align:start position:0%
+zero angle of
+incidence now what I'm going to do is
+
+ align:start position:0%
+incidence now what I'm going to do is
+ 
+
+ align:start position:0%
+incidence now what I'm going to do is
+change the state of polarization to the
+
+ align:start position:0%
+change the state of polarization to the
+ 
+
+ align:start position:0%
+change the state of polarization to the
+horizontal
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+one by
+
+ align:start position:0%
+one by
+ 
+
+ align:start position:0%
+one by
+changing the transmission axis of the of
+
+ align:start position:0%
+changing the transmission axis of the of
+ 
+
+ align:start position:0%
+changing the transmission axis of the of
+the polarizer
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and then now let's look at the
+
+ align:start position:0%
+and then now let's look at the
+ 
+
+ align:start position:0%
+and then now let's look at the
+reflectivity as a function of angle of
+
+ align:start position:0%
+reflectivity as a function of angle of
+ 
+
+ align:start position:0%
+reflectivity as a function of angle of
+incidence here again with polarization
+
+ align:start position:0%
+incidence here again with polarization
+ 
+
+ align:start position:0%
+incidence here again with polarization
+along the horizontal plane or P
+
+ align:start position:0%
+along the horizontal plane or P
+ 
+
+ align:start position:0%
+along the horizontal plane or P
+polarization let's see now what happens
+
+ align:start position:0%
+polarization let's see now what happens
+ 
+
+ align:start position:0%
+polarization let's see now what happens
+so we start again about 4% here's 10°
+
+ align:start position:0%
+so we start again about 4% here's 10°
+ 
+
+ align:start position:0%
+so we start again about 4% here's 10°
+marker
+
+ align:start position:0%
+marker
+ 
+
+ align:start position:0%
+marker
+20°
+
+ align:start position:0%
+20°
+ 
+
+ align:start position:0%
+20°
+
+ align:start position:0%
+ 
+
+ align:start position:0%
+40 and now you you can see that the
+
+ align:start position:0%
+40 and now you you can see that the
+ 
+
+ align:start position:0%
+40 and now you you can see that the
+light is getting dimmer and dimmer here
+
+ align:start position:0%
+light is getting dimmer and dimmer here
+ 
+
+ align:start position:0%
+light is getting dimmer and dimmer here
+is 50 and here we reach the Brewster
+
+ align:start position:0%
+is 50 and here we reach the Brewster
+ 
+
+ align:start position:0%
+is 50 and here we reach the Brewster
+angle where the intensity is zero and
+
+ align:start position:0%
+angle where the intensity is zero and
+ 
+
+ align:start position:0%
+angle where the intensity is zero and
+then here is
+
+ align:start position:0%
+then here is
+ 
+
+ align:start position:0%
+then here is
+60°
+
+ align:start position:0%
+60°
+ 
+
+ align:start position:0%
+60°
+70 80 and you can see the light
+
+ align:start position:0%
+70 80 and you can see the light
+ 
+
+ align:start position:0%
+70 80 and you can see the light
+intensity is getting bigger and bigger
+
+ align:start position:0%
+intensity is getting bigger and bigger
+ 
+
+ align:start position:0%
+intensity is getting bigger and bigger
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+bigger in order to look at it a little
+
+ align:start position:0%
+bigger in order to look at it a little
+ 
+
+ align:start position:0%
+bigger in order to look at it a little
+bit better let's dim the room lights and
+
+ align:start position:0%
+bit better let's dim the room lights and
+ 
+
+ align:start position:0%
+bit better let's dim the room lights and
+do the experiments again
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+we're going to start with vertical
+
+ align:start position:0%
+we're going to start with vertical
+ 
+
+ align:start position:0%
+we're going to start with vertical
+polarization
+
+ align:start position:0%
+polarization
+ 
+
+ align:start position:0%
+polarization
+or S polarization or if you wish
+
+ align:start position:0%
+or S polarization or if you wish
+ 
+
+ align:start position:0%
+or S polarization or if you wish
+transverse electric and then we'll start
+
+ align:start position:0%
+transverse electric and then we'll start
+ 
+
+ align:start position:0%
+transverse electric and then we'll start
+varying the angle of incidence from zero
+
+ align:start position:0%
+varying the angle of incidence from zero
+ 
+
+ align:start position:0%
+varying the angle of incidence from zero
+here is 10
+
+ align:start position:0%
+here is 10
+ 
+
+ align:start position:0%
+here is 10
+de 20 and you can see that the light
+
+ align:start position:0%
+de 20 and you can see that the light
+ 
+
+ align:start position:0%
+de 20 and you can see that the light
+intensity is increasing here's
+
+ align:start position:0%
+intensity is increasing here's
+ 
+
+ align:start position:0%
+intensity is increasing here's
+30 40 and you can see it's increasing
+
+ align:start position:0%
+30 40 and you can see it's increasing
+ 
+
+ align:start position:0%
+30 40 and you can see it's increasing
+nicely
+
+ align:start position:0%
+nicely
+ 
+
+ align:start position:0%
+nicely
+50° here is
+
+ align:start position:0%
+50° here is
+ 
+
+ align:start position:0%
+50° here is
+60 70 now it's really getting
+
+ align:start position:0%
+60 70 now it's really getting
+ 
+
+ align:start position:0%
+60 70 now it's really getting
+bright
+
+ align:start position:0%
+bright
+ 
+
+ align:start position:0%
+bright
+80 and then as we approach 90 you can
+
+ align:start position:0%
+80 and then as we approach 90 you can
+ 
+
+ align:start position:0%
+80 and then as we approach 90 you can
+see that the angle the reflected beam is
+
+ align:start position:0%
+see that the angle the reflected beam is
+ 
+
+ align:start position:0%
+see that the angle the reflected beam is
+more intense than the transmitted beam
+
+ align:start position:0%
+more intense than the transmitted beam
+ 
+
+ align:start position:0%
+more intense than the transmitted beam
+and here we are very close to 90 and
+
+ align:start position:0%
+and here we are very close to 90 and
+ 
+
+ align:start position:0%
+and here we are very close to 90 and
+then again you see the other spots due
+
+ align:start position:0%
+then again you see the other spots due
+ 
+
+ align:start position:0%
+then again you see the other spots due
+to multiple
+
+ align:start position:0%
+to multiple
+ 
+
+ align:start position:0%
+to multiple
+Reflections and let's go back
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+now here we are the Den is going
+
+ align:start position:0%
+now here we are the Den is going
+ 
+
+ align:start position:0%
+now here we are the Den is going
+down here's the 60°
+
+ align:start position:0%
+down here's the 60°
+ 
+
+ align:start position:0%
+down here's the 60°
+marker
+
+ align:start position:0%
+marker
+ 
+
+ align:start position:0%
+marker
+50°
+
+ align:start position:0%
+50°
+ 
+
+ align:start position:0%
+50°
+40 30 and so on all the way to to
+
+ align:start position:0%
+40 30 and so on all the way to to
+ 
+
+ align:start position:0%
+40 30 and so on all the way to to
+zero now what I'll do I'm going to
+
+ align:start position:0%
+zero now what I'll do I'm going to
+ 
+
+ align:start position:0%
+zero now what I'll do I'm going to
+change the
+
+ align:start position:0%
+change the
+ 
+
+ align:start position:0%
+change the
+polarization to horizontal
+
+ align:start position:0%
+polarization to horizontal
+ 
+
+ align:start position:0%
+polarization to horizontal
+polarization or p polariz
+
+ align:start position:0%
+polarization or p polariz
+ 
+
+ align:start position:0%
+polarization or p polariz
+ation but just to make sure I have it
+
+ align:start position:0%
+ation but just to make sure I have it
+ 
+
+ align:start position:0%
+ation but just to make sure I have it
+right I'm going to do a little
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+check on
+
+ align:start position:0%
+check on
+ 
+
+ align:start position:0%
+check on
+the on the Brewster angle and then and
+
+ align:start position:0%
+the on the Brewster angle and then and
+ 
+
+ align:start position:0%
+the on the Brewster angle and then and
+then we'll start again so here now
+
+ align:start position:0%
+then we'll start again so here now
+ 
+
+ align:start position:0%
+then we'll start again so here now
+with with this horizontal
+
+ align:start position:0%
+with with this horizontal
+ 
+
+ align:start position:0%
+with with this horizontal
+polarization I'm going to now vary the
+
+ align:start position:0%
+polarization I'm going to now vary the
+ 
+
+ align:start position:0%
+polarization I'm going to now vary the
+angle of incidence as we watch the spot
+
+ align:start position:0%
+angle of incidence as we watch the spot
+ 
+
+ align:start position:0%
+angle of incidence as we watch the spot
+on the screen
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+you can see the spots the intensity is
+
+ align:start position:0%
+you can see the spots the intensity is
+ 
+
+ align:start position:0%
+you can see the spots the intensity is
+going down here's a 20°
+
+ align:start position:0%
+going down here's a 20°
+ 
+
+ align:start position:0%
+going down here's a 20°
+marker
+
+ align:start position:0%
+marker
+ 
+
+ align:start position:0%
+marker
+30 40 and now the spot's getting
+
+ align:start position:0%
+30 40 and now the spot's getting
+ 
+
+ align:start position:0%
+30 40 and now the spot's getting
+dimmer even more
+
+ align:start position:0%
+dimmer even more
+ 
+
+ align:start position:0%
+dimmer even more
+50 and as we get close to the Brewster
+
+ align:start position:0%
+50 and as we get close to the Brewster
+ 
+
+ align:start position:0%
+50 and as we get close to the Brewster
+angle goes to zero
+
+ align:start position:0%
+angle goes to zero
+ 
+
+ align:start position:0%
+angle goes to zero
+56.5 then here at
+
+ align:start position:0%
+56.5 then here at
+ 
+
+ align:start position:0%
+56.5 then here at
+60°
+
+ align:start position:0%
+60°
+ 
+
+ align:start position:0%
+60°
+70° it's picking up intensity fast 80
+
+ align:start position:0%
+70° it's picking up intensity fast 80
+ 
+
+ align:start position:0%
+70° it's picking up intensity fast 80
+and as it gets close
+
+ align:start position:0%
+and as it gets close
+ 
+
+ align:start position:0%
+and as it gets close
+to 90° intensity heads towards 100% And
+
+ align:start position:0%
+to 90° intensity heads towards 100% And
+ 
+
+ align:start position:0%
+to 90° intensity heads towards 100% And
+certainly looks brighter than the
+
+ align:start position:0%
+certainly looks brighter than the
+ 
+
+ align:start position:0%
+certainly looks brighter than the
+transmitted intensity also of course you
+
+ align:start position:0%
+transmitted intensity also of course you
+ 
+
+ align:start position:0%
+transmitted intensity also of course you
+see the effective multiple Reflections
+
+ align:start position:0%
+see the effective multiple Reflections
+ 
+
+ align:start position:0%
+see the effective multiple Reflections
+so let's go
+
+ align:start position:0%
+so let's go
+ 
+
+ align:start position:0%
+so let's go
+back is
+
+ align:start position:0%
+back is
+ 
+
+ align:start position:0%
+back is
+
+ align:start position:0%
+ 
+
+ align:start position:0%
+70 60 getting nice and dim and at
+
+ align:start position:0%
+70 60 getting nice and dim and at
+ 
+
+ align:start position:0%
+70 60 getting nice and dim and at
+56.5 goes to zero and then picks up
+
+ align:start position:0%
+56.5 goes to zero and then picks up
+ 
+
+ align:start position:0%
+56.5 goes to zero and then picks up
+again at 50 so now let's go back to to
+
+ align:start position:0%
+again at 50 so now let's go back to to
+ 
+
+ align:start position:0%
+again at 50 so now let's go back to to
+the rooster angle where it's
+
+ align:start position:0%
+the rooster angle where it's
+ 
+
+ align:start position:0%
+the rooster angle where it's
+extinguished where the light is pretty
+
+ align:start position:0%
+extinguished where the light is pretty
+ 
+
+ align:start position:0%
+extinguished where the light is pretty
+close to zero and let me then change the
+
+ align:start position:0%
+close to zero and let me then change the
+ 
+
+ align:start position:0%
+close to zero and let me then change the
+polarization back to to ver to
+
+ align:start position:0%
+polarization back to to ver to
+ 
+
+ align:start position:0%
+polarization back to to ver to
+Vertical here we are go back to the
+
+ align:start position:0%
+Vertical here we are go back to the
+ 
+
+ align:start position:0%
+Vertical here we are go back to the
+vertical and we see that the
+
+ align:start position:0%
+vertical and we see that the
+ 
+
+ align:start position:0%
+vertical and we see that the
+spot gets brighter and
+
+ align:start position:0%
+spot gets brighter and
+ 
+
+ align:start position:0%
+spot gets brighter and
+brighter so here it it is with vertical
+
+ align:start position:0%
+brighter so here it it is with vertical
+ 
+
+ align:start position:0%
+brighter so here it it is with vertical
+polarization and here is the
+
+ align:start position:0%
+polarization and here is the
+ 
+
+ align:start position:0%
+polarization and here is the
+intensity with horizontal
+
+ align:start position:0%
+intensity with horizontal
+ 
+
+ align:start position:0%
+intensity with horizontal
+polarization in summary we have shown
+
+ align:start position:0%
+polarization in summary we have shown
+ 
+
+ align:start position:0%
+polarization in summary we have shown
+how light is reflected at a dialectric
+
+ align:start position:0%
+how light is reflected at a dialectric
+ 
+
+ align:start position:0%
+how light is reflected at a dialectric
+interface or a piece of
+
+ align:start position:0%
+interface or a piece of
+ 
+
+ align:start position:0%
+interface or a piece of
+glass we've shown that for polarization
+
+ align:start position:0%
+glass we've shown that for polarization
+ 
+
+ align:start position:0%
+glass we've shown that for polarization
+in the vertical plane or S polarization
+
+ align:start position:0%
+in the vertical plane or S polarization
+ 
+
+ align:start position:0%
+in the vertical plane or S polarization
+the reflectivity goes from about 4% for
+
+ align:start position:0%
+the reflectivity goes from about 4% for
+ 
+
+ align:start position:0%
+the reflectivity goes from about 4% for
+zero angle of incidence to 100% for
+
+ align:start position:0%
+zero angle of incidence to 100% for
+ 
+
+ align:start position:0%
+zero angle of incidence to 100% for
+90° angle of incidence in contrast for
+
+ align:start position:0%
+90° angle of incidence in contrast for
+ 
+
+ align:start position:0%
+90° angle of incidence in contrast for
+horizontal polarization or P
+
+ align:start position:0%
+horizontal polarization or P
+ 
+
+ align:start position:0%
+horizontal polarization or P
+polarization the reflectivity again
+
+ align:start position:0%
+polarization the reflectivity again
+ 
+
+ align:start position:0%
+polarization the reflectivity again
+starts at 4% but goes down to zero at
+
+ align:start position:0%
+starts at 4% but goes down to zero at
+ 
+
+ align:start position:0%
+starts at 4% but goes down to zero at
+the Brewster angle and in this case for
+
+ align:start position:0%
+the Brewster angle and in this case for
+ 
+
+ align:start position:0%
+the Brewster angle and in this case for
+glass it's 56.5 de and then goes rapidly
+
+ align:start position:0%
+glass it's 56.5 de and then goes rapidly
+ 
+
+ align:start position:0%
+glass it's 56.5 de and then goes rapidly
+up to 100%
+
+ align:start position:0%
+up to 100%
+ 
+
+ align:start position:0%
+up to 100%
+for 90° angle of incidence
\ No newline at end of file
diff --git a/i59JDQ9hk10.txt b/i59JDQ9hk10.txt
new file mode 100644
index 0000000000000000000000000000000000000000..129622cc547b038bd7a761c0c195cfef69e7bde8
--- /dev/null
+++ b/i59JDQ9hk10.txt
@@ -0,0 +1,4269 @@
+The following
+content is provided
+
+under a Creative
+Commons license.
+
+Your support will help MIT
+OpenCourseWare continue
+
+to offer high quality
+educational resources for free.
+
+To make a donation or
+view additional materials
+
+from hundreds of MIT courses,
+visit MIT OpenCourseWare
+
+at ocw.mit.edu.
+
+DOUG LAUFFENBURGER:
+So we shall start.
+
+I haven't had the pleasure
+of meeting most of you.
+
+I'm Doug Lauffenburger.
+
+I'm gratefully invited for
+a guest presentation here.
+
+So I'll definitely enjoy it.
+
+There should be plenty of time.
+
+I'm not racing through
+a lot of material,
+
+so feel free to interrupt
+me with questions.
+
+And of course I'll try
+to respond as best I can.
+
+OK.
+
+Who has looked at the
+background materials that
+
+were posted on the web a
+long time ago, last night?
+
+Who already will admit
+to having looked at it?
+
+Good.
+
+All right.
+
+I guess that means
+I should do this
+
+because otherwise if
+you've read it already then
+
+there'd be no point, right?
+
+OK.
+
+OK.
+
+Well, where we are
+in your semester--
+
+you're learning a lot of things
+across the whole spectrum
+
+of computational
+systems biology.
+
+I hope I'll add
+something in here.
+
+It's actually a
+very specific topic.
+
+We talk about modeling of
+cell signaling networks,
+
+and in particular, one approach
+is worth going through today
+
+and that's the logic
+modeling framework.
+
+So I'll give you a little bit
+of a conceptual background
+
+for the first 10 or 15 minutes.
+
+Then we'll launch into
+the particular example
+
+that was in the main paper.
+
+And a little side light
+with an application of it
+
+to a particular cancer problem.
+
+And then that should take
+us pretty much to the end.
+
+OK.
+
+OK.
+
+The biological topic here
+is cell signaling, primarily
+
+mammalian cells.
+
+Certainly applicable
+to microbial cells
+
+in a simpler sense.
+
+So just to place the context,
+in mammalian cell biology,
+
+I'm a bio-engineer and a cell
+biologist at the same time.
+
+We're very interested in what
+controls the cell behavior,
+
+their phenotypic response.
+
+We know that it's
+in fact controlled
+
+by what it sees in their
+environment, growth
+
+factors, hormones, extracellular
+matrix, mechanical forces,
+
+cell-cell contacts.
+
+A variety of queues
+in the environment
+
+and the way these govern
+phenotype or control phenotype
+
+is that they influence,
+they regulate
+
+what I would call the
+execution processes.
+
+The crucial execution processes
+such as gene expression,
+
+transcription, and
+translation are
+
+governed by
+extracellular factors.
+
+Metabolism, synthesis
+of new molecules,
+
+cytoskeleton, motors,
+forced generation.
+
+These things all
+carry out phenotype
+
+governed by the extracellular
+stimuli or cues.
+
+And it happens via these
+biochemical signaling
+
+pathways that are activated
+primarily by cell surface
+
+receptors in the plasmid
+membrane-- cascades
+
+of biochemical reactions,
+mostly enzymatic.
+
+Some protein-protein
+docking, mostly
+
+post-translational
+modifications.
+
+Kinase phosphate reactions
+adding and taking off
+
+phosphate groups that change
+protein activities at locations
+
+and so forth.
+
+It could be other types of
+post-translation modifications.
+
+It could be second messengers,
+calcium, ATP aces and so forth.
+
+So, the extracellular--
+now my battery's dead.
+
+That's not good.
+
+Oh, there we go.
+
+Extracellular stimuli,
+generate the signals.
+
+They regulate gene expression,
+metabolism, cytoskeleton.
+
+They carry out phenotype.
+
+OK.
+
+So we want to learn about cell
+signaling network operations.
+
+There's actually multiple
+pathways involved.
+
+We really need to
+study many of them
+
+in concert to understand
+what the cells are doing.
+
+And a big question is,
+what kind of information
+
+do we need to study this?
+
+And on the end, we'd
+be interested in how
+
+phenotypic behavior does arise
+from variations and mutations
+
+in the genomic content of cells.
+
+But that genomic content,
+of course, is not modified,
+
+but its effects are
+influenced by what's
+
+the environment to these
+extracellular cues,
+
+log ins and so forth.
+
+So they influence what
+message is expressed.
+
+From that message
+they influence what's
+
+actually translated
+into protein.
+
+From those proteins
+they influence
+
+the post-translational
+modifications
+
+and what the proteins
+are actually doing.
+
+And so, in the
+end, the phenotype
+
+is carried out by these
+protein operations.
+
+And the question
+is, what information
+
+level that we might
+want to study.
+
+And of course you would
+love to have the information
+
+content at all levels--
+genomic information,
+
+transcriptional information,
+translational information,
+
+post-translational information.
+
+So integrating all those
+different data levels
+
+can be extremely valuable.
+
+In terms of the models I'm
+going to talk about today,
+
+they've essentially
+been living at the level
+
+of protein activities in
+these signaling pathways.
+
+OK.
+
+That will be the
+kind of data sets
+
+you'll see that will be analyzed
+with respect to the models.
+
+Obviously, they arise from
+these underlying mechanisms
+
+that, as influenced by
+the environmental context,
+
+altering the signaling
+protein activities.
+
+OK.
+
+And what's very
+interesting and there's
+
+going to be more and more
+progress in the coming years
+
+is relating what's in the
+genomic information-- mutations
+
+and variations to what's
+happening at the protein level.
+
+And some of the other
+instructors in this class
+
+are really some of
+the world's experts
+
+in figuring out how to do this.
+
+I'd like to just
+show this example
+
+as a motivation for
+this kind of approach.
+
+And that is if you do gene
+sequencing of many patient
+
+tumors-- in this
+case, I believe this
+
+was a paper on
+pancreatic tumors.
+
+This has been shown for pretty
+much every other type of tumor
+
+since then.
+
+In any given patient tumor,
+each one of these bars,
+
+there's dozens of
+mutations in each tumor.
+
+And a variety of
+types-- deletions,
+
+amplifications mutations
+and by and large, they're
+
+all different.
+
+There's very few
+mutations themselves
+
+that really carry over to
+a substantial proportion
+
+of one patient's
+tumor to another.
+
+There's some special cases
+that are fairly pervasive,
+
+but the predominant of these
+dozens and dozens of mutations
+
+and variations are
+different from one patient
+
+to another, and even
+in the same patient.
+
+So what's emerging
+as a productive way
+
+to think about this-- How
+do all these different types
+
+of mutations and
+specific mutations
+
+actually lead to classes
+of similar pathologies?
+
+And that is they
+tend to reside in
+
+what can be identified
+as pathways-- circuits,
+
+machines, things that
+are actually carrying out
+
+function at the protein level.
+
+So for instance-- I'm
+losing this again.
+
+For these pancreatic
+cancers on this wheel
+
+are about a dozen different
+signaling pathways
+
+and self-cycle control
+pathways and apoptosis
+
+controlled pathways.
+
+And if you look at any
+individual patient tumors,
+
+like this green one or this red
+one-- two different patients.
+
+If you actually look at the
+mutations at the genomic level,
+
+they're entirely different
+in the green patient
+
+tumor versus the
+red patient tumor.
+
+So if you're just trying
+to match gene mutation
+
+to pancreatic cancer,
+these two patients
+
+would look entirely different.
+
+But, it turns out, that you
+can line up their mutations
+
+into the same
+pathways and say, OK,
+
+the red tumor and
+the green tumor
+
+both have mutations that
+affect the TGF beta pathway.
+
+They're different
+mutations, but they've just
+
+regulated that pathway.
+
+And similarly, you can
+do that with pretty much
+
+all of the other mutations.
+
+That these tumors
+have been dysregulated
+
+in terms of particular pathways.
+
+But patient to
+patient to patient,
+
+it's happened by different
+genomic gene sequence
+
+mutations.
+
+So that the ability to
+look at these protein
+
+level pathways is
+a way of making
+
+really good productive sense
+of the gene sequencing data.
+
+So there's lots of labs trying
+to go from gene sequence
+
+up to pathway modulation.
+
+In our case, we're not
+going to show you that here.
+
+We're going to say,
+this is a motivation
+
+for starting at
+the protein level.
+
+And I'd like to show
+this picture too.
+
+Number one because it's
+such an anachronism.
+
+This is a circuit board from
+decades and decades and decades
+
+ago that none of
+you would recognize.
+
+But, in the molecular biology
+world, this kind of a picture,
+
+and in its modern form is viewed
+as a very appealing metaphor
+
+for how to think
+about these signaling
+
+pathways and signaling networks
+that take the extracellular
+
+information and turn it into
+governance of transcription,
+
+metabolism, cytoskeleton,
+and phenotype.
+
+So, just this
+metaphor of circuitry,
+
+where in white, the
+extracellular ligands,
+
+growth factors are
+somehow wired to the blue.
+
+The cell surface receptors,
+or B for instance--
+
+they're wired too.
+
+Kinases and other
+signaling proteins--
+
+they're wired to transcription
+factors, self-cycle control
+
+regulators,
+apoptosis regulators.
+
+So these very famous folks
+in cancer biology say,
+
+what you've got to understand
+is, these signalling networks
+
+as circuitry.
+
+And if the circuitry is
+dysregulated somehow,
+
+the wiring is different,
+then that's what's
+
+underlying malignant behavior.
+
+So, this is really
+beautiful but it's
+
+pretty much useless, right.
+
+Because there's no prediction or
+calculation or even hypothesis
+
+generation one can do
+from a picture like this.
+
+Yes, it's circuitry, but
+what do I do with it?
+
+So, what I want
+to show you today
+
+are efforts to
+turn them into what
+
+I would call an actionable
+model, a computable model.
+
+Yes, it looks kind
+of like circuitry,
+
+but in fact you would know
+how to do a calculation that
+
+would fit it to data
+and predict new data.
+
+And then you have, in fact, a
+model rather than a metaphor.
+
+That's the idea.
+
+So, one question is, if
+you want to turn that
+
+into a formal mathematical
+framework for circuitry
+
+that you can calculate--
+what kind of mathematics
+
+might you use?
+
+And in this class
+you're learning
+
+a whole spectrum of things.
+
+And one can think
+about it on one hand,
+
+if we knew all of
+those components
+
+and how they interacted, and
+could estimate rate constance
+
+and so forth, we could
+write differential equations
+
+for maybe the dozens and dozens
+of components and interactions
+
+and predict how they would
+play out dynamically with time.
+
+For most systems with
+the complexity that's
+
+really controlling cell
+biology, at this point in time,
+
+this is almost impossible.
+
+There's only rare
+cases where enough
+
+is known about
+signaling biochemistry
+
+to really write
+down differential
+
+equations for what's going on.
+
+At the other extreme,
+of course, is the type
+
+of mathematics one gets out
+of very, very large data sets,
+
+sequencing data sets,
+transcriptional, and so forth.
+
+More informatics
+type of analysis,
+
+where it has to do
+with multivariate
+
+regression and clustering,
+mutual information.
+
+And what we've been working on
+is someplace up in the middle
+
+where you don't have enough
+mechanistic prior knowledge
+
+to write this formal
+of physics, and yet
+
+takes you someplace beyond
+statistical associations.
+
+And this is one
+of the areas that
+
+might be worth your
+learning in this class.
+
+OK, this is really the same
+set of computational methods,
+
+just like it's cast in a
+little bit different form that
+
+delineates competition
+modeling, really
+
+into two kinds of classes.
+
+What's traditionally appreciated
+in most fields of engineering
+
+and physics are
+differential equations
+
+that are very theory driven.
+
+You have a theory.
+
+You have prior knowledge
+for what's happening.
+
+You're writing down the
+components involved,
+
+you're writing down
+how they interact.
+
+And typically,
+algebraic equations
+
+for those differential
+equations describe your theory,
+
+describe your prior knowledge.
+
+And now it's formalized and
+you estimate rate constants
+
+and so forth.
+
+Another whole class
+of information
+
+is data driven, in
+which, you really
+
+don't have a good theory
+about what components matter
+
+and how they interact.
+
+And so you start with
+data sets and from it
+
+you do classification or
+typologies or associations
+
+with different types of
+mathematics that at least try
+
+to make sense and get hypotheses
+out of these large data
+
+sets, where you don't
+have any theory.
+
+One reason that logic
+modeling appeals to me,
+
+is that it actually
+can be applied
+
+in either the theory driven
+or the data driven mode.
+
+You can say, I know
+nothing about my system.
+
+I just generate large data sets
+of signaling network activities
+
+induced by different
+stimuli, but I'm
+
+going to try to fit a
+logic model to it that
+
+says how the different
+components influencing
+
+each other in a logic way.
+
+Or, you could say,
+well, I know something.
+
+I have some prior knowledge.
+
+I may have interact ohms the say
+what molecular components are
+
+present in signaling networks.
+
+And so in principle, I
+kind of know who's involved
+
+and who might be
+influencing whom.
+
+And I could write a logic model
+based on that prior knowledge.
+
+And then run calculations
+and see if it actually
+
+makes predictions about
+experimental data.
+
+So that's one nice thing.
+
+It's a mathematical
+formalism that
+
+can either be run in data driven
+mode or in theory driven mode
+
+and go back and forth.
+
+So that's one reason--
+given one lecture to offer,
+
+I've decided to offer
+it on this topic.
+
+All right, with me so far?
+
+Any questions?
+
+Philosophy?
+
+OK.
+
+So, what we're
+going to do today is
+
+almost take a
+hybrid of these two.
+
+We're going to say, what
+prior knowledge do we have,
+
+and then recognize that
+it's really not enough.
+
+And so how do we now integrate
+that with empirical data
+
+to now come up with
+logic modeling that,
+
+in fact, is actionable
+and computable?
+
+OK.
+
+So what kind of prior
+knowledge do we have?
+
+Let's say we wanted to have
+a logic model for what's
+
+in these signaling networks
+down stream of growth factor
+
+receptors, or hormone receptors,
+or things like that, that then
+
+govern gene expression,
+metabolism and so forth.
+
+What prior knowledge do we have?
+
+And you folks
+probably have already
+
+seen some of this in the class.
+
+There's all kinds of
+databases of stuff.
+
+What's in those databases
+that might be relevant here?
+
+AUDIENCE: [INAUDIBLE] that the
+protein-protein interactions--
+
+if you switch proteins, they
+interact with each other,
+
+but maybe not necessarily
+what pathways they're in.
+
+DOUG LAUFFENBURGER: OK, good.
+
+And have you seen
+databases like that?
+
+AUDIENCE: Several of
+them have come up.
+
+DOUG LAUFFENBURGER: OK.
+
+Are you the only
+one who's seen them?
+
+Or is there anybody
+else that kind
+
+of noticed them in passing too?
+
+OK, good.
+
+Second, third,
+fourth, all right.
+
+That's a critical mass
+if I ever saw one.
+
+OK.
+
+So, I'm just going
+to allude to those.
+
+So there are pathway databases.
+
+And this is actually an
+old slide of a few years
+
+ago, so I'm sure the
+numbers are all different.
+
+And, in fact, there's new ones.
+
+I just haven't taken
+to updating the slide.
+
+But we'll, based on literature,
+take certain numbers
+
+of gene products, a
+few hundred of them,
+
+and organize them into pathways
+based on biological knowledge.
+
+There's other databases that
+are more interactomes, usually
+
+based on other kinds of
+experimental data-- yeast II
+
+hybrid, mass spectrometry,
+literature curation,
+
+that also tries to say who's
+physically interacting.
+
+So these node-- these pathway
+databases don't necessarily
+
+say, somebody's
+physically interacting,
+
+they say somebody might
+be upstream and downstream
+
+and so forth.
+
+And then they
+interactome databases
+
+say, component a
+and component b,
+
+there's some evidence that they
+have a physical association
+
+someplace along the way.
+
+So these are two
+complementary types
+
+of databases that, in
+fact, can be put together.
+
+OK.
+
+So an interesting
+thing about these--
+
+there's a number
+of these databases.
+
+And so in principle
+you could say, well
+
+if I want then to start-- if
+I want to generate a logic
+
+model for signaling
+networks, all
+
+I have to do is take
+what's in the database
+
+and say what pathways
+are there and what's
+
+known with their
+interactions, and now I've
+
+got a starting point.
+
+You know, I can
+actually draw a graph
+
+with lots of molecular nodes and
+lots of molecular interactions.
+
+So, you can do that.
+
+And so you can choose
+one of these databases
+
+and say I'm going
+to draw a graph that
+
+has what's believed to be
+true about nodes and pathways
+
+and interactions and
+signaling networks.
+
+But then you choose a different
+database and another database.
+
+And you'll actually get
+different information.
+
+OK.
+
+We actually did a study
+on this-- I probably
+
+should have given you the
+citation of that-- that
+
+said if you look at six or
+seven of these databases,
+
+they are not coincident.
+
+They have a very
+small intersections.
+
+Most of their information
+is non-redundant.
+
+And so you could try
+to put it all together.
+
+And we did this,
+again, in this paper
+
+that I'm not giving
+you a citation for.
+
+And so here's a number of
+nodes and signaling pathways
+
+downstream of receptors.
+
+And all the colored
+nodes are those
+
+in which they appear in
+only one of these-- one, two
+
+three, four, five,
+six databases.
+
+So if something's colored
+green, it's only in GeneGo
+
+and it's not in
+any of the others.
+
+If something's
+colored purple, it's
+
+in PANTHER and
+none of the others.
+
+OK.
+
+If they're gray-- some
+of these gray ones,
+
+they're in at least two.
+
+But out of these six, there's
+an exceedingly small number
+
+of nodes interactions that
+are in all six databases.
+
+Which was a real surprise
+to us when we did this.
+
+So what this means
+is, if you want
+
+to start with some
+prior knowledge graph
+
+that you're now going to fit
+a logic model to by mapping it
+
+against data, you first
+even have the choice, well,
+
+what am I going to start with?
+
+What is my prior knowledge?
+
+There;s not really
+consensus prior knowledge.
+
+So you can start with six
+different interaction graphs.
+
+Or you could try to
+put them all together
+
+and get a consensus graph.
+
+So you have all these choices.
+
+And right now, it's
+not as if is there's
+
+detailed analysis of what
+the best choice would
+
+be for your starting point.
+
+But I want to stress that,
+with respect to our approach,
+
+this is a starting
+point because one
+
+of the issues with the
+database information
+
+is that it's typically
+very diverse with respect
+
+to contact.
+
+What cell type did this
+information come from?
+
+What treatment conditions
+did it come from?
+
+If there's different cell
+types, different species,
+
+different mutations.
+
+So if I see interactions or
+if I don't see interactions,
+
+are they in conflict?
+
+Or they're just-- this
+one was in a lymphocyte,
+
+this one was in a
+hypatocye, this one
+
+was in a cardiac myocyte, and
+they're actually different.
+
+OK, so if I had a cell
+type specific database,
+
+or pulled that information
+out, that would be good.
+
+It would be a smaller
+number of things.
+
+But then under what
+treatment conditions?
+
+Because remember I said starting
+with the genomic content, what
+
+you actually see in terms
+of molecular interactions
+
+will be very strongly
+affected by what
+
+matrix were the
+cells growing on?
+
+Or was this in vivo?
+
+Was this in a multicellular
+culture situation?
+
+So, that's why this
+is a starting point
+
+and can't really
+be used to describe
+
+any particular experimental
+situation with much confidence.
+
+The other thing--
+and this is what
+
+I've been trying to
+emphasize from the start-- is
+
+that there's no calculation
+you can do on this.
+
+There's a group of
+folks in this field who
+
+propose some ideas that I
+think are very intriguing,
+
+but which, at least
+to me personally,
+
+there's not that
+much evidence for.
+
+And that is, that there's
+topological characteristics
+
+of these graphs, that then
+tell you what's important.
+
+So if I have a
+node that's somehow
+
+connected to more
+other nodes, that
+
+is going to be a
+more important node,
+
+and might be associated with the
+disease, versus a node that's
+
+connected to fewer.
+
+OK.
+
+Some of these are very, very
+appealing ideas conceptually.
+
+If you actually look for
+the experimental evidence
+
+that they're valid
+notions, it's very thin.
+
+But, that's where some
+folks would claim,
+
+oh, you can do predictions
+on the hypotheses based
+
+on these graphs because
+there are these graph theory
+
+characteristics
+that somehow might
+
+be biologically meaningful.
+
+OK.
+
+But I'd say, jury's out on
+whether, in fact, any of that
+
+is true.
+
+So, our view is-- OK, this
+is a good starting point,
+
+but in fact, needs to be
+mapped to empirical data
+
+in order to gain confidence
+about calculations you can do.
+
+So that's the goal of
+this kind of approach,
+
+is to say, let's
+stipulate that we start
+
+with some prior
+knowledge scaffold.
+
+This particular one is from
+the Ingenuity database.
+
+You could get one from
+any other database.
+
+You could get a consensus one
+from three or four if you want.
+
+And so it has, up here,
+extracellular stimuli,
+
+growth factors, cytokines.
+
+They're connected in their
+interactome II receptors.
+
+They're connected to scaffolding
+proteins and signaling proteins
+
+and kinases and so forth.
+
+They're connected to
+transcription factors,
+
+metabolic enzymes.
+
+So you can draw this graph.
+
+Say this might be what's
+going on in my cell.
+
+And then what we'd like
+to do is to turn this
+
+into a formal logic
+framework that's
+
+capable of then fitting
+experimental data,
+
+predicting new
+experimental data,
+
+and giving you a chance
+at biological hypothesis
+
+and testing.
+
+All right, so
+conceptually you get it?
+
+Two aspects-- some kind of
+starting prior knowledge,
+
+that's kind of a scaffold,
+a graph, for your network.
+
+And now you're going to turn it
+into a computable logic model
+
+by mapping it against
+empirical data.
+
+So, merely what it takes is
+the kind of conceptual diagram
+
+you see in any cell biology
+paper, any signaling paper,
+
+that says, well, a and b
+both influence e positively,
+
+and b influences f negatively,
+and c influences f positively.
+
+Then there's a
+feedback from g to a.
+
+That's inhibitory.
+
+You can draw those.
+
+But now, how do you turn it
+into a computable algorithm?
+
+So, what I'm going to spend
+most of the day on is,
+
+just conversion of
+this to a Boolean logic
+
+model that any one of these
+interactions is and-- a and b
+
+being active makes e active.
+
+c being active, but
+b not being active,
+
+allows f to be
+active, and so forth.
+
+You turn these into
+formal logic statements
+
+that you can compute on.
+
+At the very end,
+if we have time,
+
+I'll show how to relax this from
+a Boolean framework that's just
+
+on off, to something that
+can be more quantitative.
+
+All right.
+
+So that's the notion.
+
+Now what I'm going to do
+for the rest of the time
+
+is go through the specific
+example paper that says, OK,
+
+how do we in fact do this?
+
+What is a way to
+accomplish this?
+
+So now let's go back
+to a biological problem
+
+where there's going to be
+empirical, experimental data
+
+that we're now going
+to map against one
+
+of these prior knowledge
+interactome graphs.
+
+This particular study-- this was
+done with Peter Sorger, who's
+
+now at Harvard Medical School--
+had to do with liver cells.
+
+Liver cancer-- you'll see
+some application of that
+
+at the end-- that says we
+have liver cell hepatocytes.
+
+And we want to know how they
+respond to different growth
+
+factors, in cytokines
+in their environment.
+
+How that'll change their
+proliferation or death?
+
+Or the inflammatory
+cytokines that they produce.
+
+And we'd like to take-- this is
+just a pictorial diagram that
+
+could be in any
+cell biology paper,
+
+and make this calculable.
+
+So we could say what's
+different from a primary normal
+
+hepatocyte liver cell
+that's not cancerous?
+
+It might have a signaling logic.
+
+But if then we compare
+the signaling logic
+
+to a liver tumor cell type, or
+four different liver tumor cell
+
+types, what's different?
+
+If we can find some logic that's
+different for the tumor cell
+
+lines versus the normal primary
+lines-- some logic from here
+
+to there or to there-- that now
+tells you biologically, where
+
+the differences
+might be that have
+
+arisen from the
+genetic mutations.
+
+And where good drug
+targets might be,
+
+or predictions if
+I intervene here,
+
+if there's no difference in
+that logic, between normal
+
+and tumor, well then that
+won't have any effect.
+
+I want to look for
+the places where
+
+there is a difference
+in the signaling logic.
+
+And that would be a
+better drug target.
+
+OK, so the measurements
+are made in
+
+across 17 of these different
+signaling molecules
+
+here, pretty much
+all by measurement
+
+of a phosphorylation state.
+
+So if you've done cell
+biology or biochemistry--
+
+in these signaling
+pathways, many
+
+of the activities in
+these kinds of pathways
+
+that regulate this
+kind of cell behavior
+
+are kinases that end up
+affecting transcription factor
+
+activities and so forth.
+
+And it's the
+phosphorylation state
+
+of any these proteins
+that matters.
+
+If a phosphate is on some
+particular amino acid,
+
+the enzyme might be active.
+
+If it's not there it might
+be inactive and so forth.
+
+So, just measurement of
+phosphorylation states
+
+of 17 different proteins
+in these pathways
+
+distributed across
+multiple pathways.
+
+I've made these measurements on
+five different cell types, four
+
+tumor cell types,
+and the primaries
+
+in order to try to see what's
+different between primary
+
+and tumor.
+
+And then what might be
+different, patient to patient.
+
+In response to seven different
+extracellular stimuli,
+
+some of them growth
+factors, some of them
+
+cytokines, some of them actually
+bacterial metabolic products.
+
+We all know about the effects
+of microbiome these days.
+
+And, to further
+populate a database that
+
+might be capable
+of helping validate
+
+a model, a number of seven,
+in fact-- intercellular
+
+inhibitors.
+
+A small molecule,
+these things in black.
+
+One that might
+inhibit this kinase.
+
+One might inhibit that kinase.
+
+One might inhibit that kinase.
+
+So now if you add all
+those inhibitors too,
+
+then you start to change
+the network activities
+
+and the downstream behavior.
+
+So that's how
+extensive the data is.
+
+And this is actually for a
+few different time points.
+
+So the data looks
+something like this.
+
+Let's focus on the
+one on the left.
+
+This is just the primary,
+normal, human cells.
+
+It came from a liver donor.
+
+OK.
+
+Each row is one of the
+17 different signals,
+
+essentially measurement
+of the phosphorylation
+
+state of Akt or CREB
+or P52 of staph 3.
+
+OK?
+
+So measurements of
+its phosphorylation
+
+state that has something to do
+with its signaling activity.
+
+Each of the big columns are the
+seven different treatments--
+
+the different growth factors
+and cytokines and so forth.
+
+And the control.
+
+No stimulation.
+
+And within each one
+of these treatments,
+
+in each one of these
+stimuli, then there's
+
+seven different
+inhibitors that were
+
+used for the different pathways.
+
+So seven stimuli by seven
+inhibitors plus controls.
+
+And then three
+different time points.
+
+Sort of zero, 30
+minutes, and three hours.
+
+So the data looks
+something like this.
+
+If there's really no change,
+due to the stimulation
+
+or the inhibitor, you'll
+see something in gray.
+
+So in these gray bars,
+there was already
+
+phosphorylation of this
+transcription factor
+
+[INAUDIBLE] and it didn't really
+change under most treatments.
+
+If it was yellow,
+what it meant was,
+
+whatever the treatment was,
+you got a quick activation
+
+of that signal and
+then it went away.
+
+If it's late-- purple, then it
+didn't happen in the first half
+
+hour, but it started to
+show up a few hours later.
+
+And if it's green it showed
+up in the first half hour
+
+and it stayed sustained.
+
+So that's what the color means.
+
+But this is the real
+experimental data.
+
+And over here on the right is
+one of the tumor cell lines.
+
+And you can just
+see by inspection,
+
+it's different, right.
+
+The colors here are different
+from the colors there.
+
+All the same treatments,
+stimuli inhibitors.
+
+The colors are very different.
+
+You know, therefore that
+the signaling activities
+
+are very different.
+
+OK.
+
+Just by visual inspection.
+
+OK.
+
+So what we're going to try
+to do is build a logic model
+
+for this.
+
+A logic model for this.
+
+Compare them and say, oh where
+are the key differences in how
+
+the signaling pathways
+are getting activated?
+
+Downstream of the same stimuli.
+
+So, we start with
+our prior knowledge.
+
+This is from the Ingenuity
+database, which actually
+
+happened to be missing,
+even basic information
+
+about insulin signaling.
+
+So we just added
+our own information
+
+about what the
+insulin receptor does.
+
+It's kind of hard to believe.
+
+This is a database that
+cost a lot of money
+
+and they didn't have
+really much information
+
+about insulin
+receptor signaling.
+
+Very strange.
+
+So, downstream of
+our seven stimuli,
+
+down to the transcription
+factors of interest,
+
+there are about 82 molecular
+nodes and a hundred some edges
+
+that you'd pull out of
+the Ingenuity database.
+
+So here's our starting guess
+at what this looks like.
+
+There's no logic in here, but
+this is just, potentially,
+
+the things that the
+logic might operate on,
+
+downstream of stimuli, and
+when inhibited, and so forth.
+
+All right.
+
+So here's the process.
+
+This was the actual
+algorithmic process
+
+that I'll walk you through.
+
+On the left-hand side
+is the computer part.
+
+It said, OK, from the
+Ingenuity database,
+
+we had this prior
+knowledge about who
+
+was upstream, downstream,
+who affected whom.
+
+We strip this down
+some, because in terms
+
+of the measurements
+on the perturbations,
+
+there are some of the nodes
+that you just would not
+
+be able to see any
+measurable difference.
+
+OK, there was no stimulus
+upstream, or no perturbation.
+
+And it was not
+measured so you really
+
+wouldn't be able to tell
+if it changed or not.
+
+So you just take those out.
+
+Of everything remaining, now
+you don't know the logic.
+
+You know the potential.
+
+And so you say, well, of all
+the nodes and interactions
+
+remaining, I could have AND
+gates, I could have OR gates,
+
+you could have NOTS.
+
+And you say, OK, in
+principle, I could have,
+
+then, many, many, many,
+many, many different logic
+
+models that could work.
+
+So how do I know which one?
+
+Well now you skip
+over to the other side
+
+and say, well, but we have
+all this experimental data.
+
+We have the data from
+all the different stimuli
+
+and all the different inhibitors
+for any given cell type.
+
+And so, we have that data under
+all these different conditions.
+
+And what we're
+going to do is just
+
+run hundreds or thousands of
+these potentially appropriate
+
+models.
+
+Compare them to the data of
+whether any given node is
+
+activated or not, activated
+under treatment conditions,
+
+stimuli inhibitors.
+
+And we'll calculate the air.
+
+How good was any
+one of those models
+
+at actually matching those data?
+
+Simple as that.
+
+And then it's a
+matter of finding
+
+what are the best fit ones
+from the best fit ones.
+
+Could you improve them and
+make them fit even better?
+
+And in the end, how did you go
+from an initial prior knowledge
+
+scaffold to something that, in
+fact, fit the data really well,
+
+from which you could
+make new predictions.
+
+OK.
+
+So you get the approach here?
+
+All right, good.
+
+Now, in terms of figuring
+out how well any given
+
+model matches the data and how
+to go through model selection,
+
+there's a myriad of
+different approaches to this.
+
+And I'm not claiming
+that what we did
+
+was the absolute best approach.
+
+There's alternatives to
+it that one could consider
+
+and then perhaps could
+work even better.
+
+If you read the paper,
+you'll read the reasons
+
+for these choices.
+
+OK.
+
+So I'll let you do that.
+
+The way the model
+quality was calculated
+
+was to have an
+objective function that
+
+said we want to minimize
+some number, theta.
+
+And how do we calculate theta?
+
+Well, first of all, for
+whatever that model is,
+
+we're going to fit-- whether
+the model says some nodes
+
+should be on or
+off, one or zero.
+
+And we're going to compare
+it to the experimental data.
+
+Now the experimental
+data, I need to emphasize,
+
+isn't one or zero,
+it's normalized
+
+to go between one and zero.
+
+But the actual measurement
+might be 0.7 or 0.25.
+
+OK, so you're going to have
+error against the Boolean model
+
+even if all the edges are
+absolutely correct you'll
+
+still going to get some
+quantitative error.
+
+So you calculate that.
+
+The Boolean model
+says zero or one.
+
+The experimental
+data says 0.250, 0.7.
+
+And you say, OK,
+I'll calculate that.
+
+But then you might
+think, all right, well,
+
+somehow I've got to penalize
+bigger models with more
+
+nodes and more edges because
+surely the more nodes and edges
+
+I put in, I could
+capture more of the data.
+
+And I don't want to make
+the model infinitely large
+
+just to get the best fit.
+
+So I need to penalize that.
+
+Turns out it's not true, but
+nonetheless it's worth doing.
+
+So, you take a parameter
+that's the size of the model.
+
+It's basically just
+the number of nodes.
+
+The more nodes in
+it, the more you
+
+would be suspicious of
+the model for just fitting
+
+because it has too
+many components.
+
+And you multiply that size by
+a penalty parameter, alpha.
+
+So you have a bad
+objective function
+
+if there's a lot of
+error with the data,
+
+or if your model's too big.
+
+A better model would be, better
+fit to the data and smaller.
+
+That's the calculation.
+
+OK.
+
+And in the end-- and I'm going
+to show you how we did this.
+
+And I think the field is
+now really believing this.
+
+That what you're not after
+is a single best fit model.
+
+That one single model that gives
+you the very smallest data.
+
+Because honestly,
+within the uncertainty
+
+of the experimental
+data-- OK, there's
+
+a substantial number
+of models that
+
+could fit the data
+within that noise.
+
+So if you demanded
+the single best one,
+
+you say, well, but
+these other 50 actually
+
+fit it almost as good and within
+the uncertainty of the data.
+
+How can you really reject them?
+
+And you can't.
+
+So in the end, what's
+being striven for in most
+
+of the field is a
+family of models.
+
+And then you see
+what the consensus
+
+is and the differences
+within that family.
+
+The particular algorithm
+for generating and running
+
+through different
+potential models--
+
+because you just
+can't exhaustively
+
+sample all of them.
+
+OK, these networks are so large,
+that you can't exhaustively
+
+test all possibilities of
+all their logic and so forth.
+
+It's really prohibitive.
+
+So there's many different
+ways you can go about it.
+
+This particular method
+maybe you've already
+
+learned this in class
+for other applications
+
+as a genetic algorithm.
+
+So you start with
+some population.
+
+You start with your
+Ingenuity scaffold
+
+and then you randomly remove
+or take edges and things
+
+like that.
+
+So that if you've
+got a whole family,
+
+that's slightly different.
+
+For each one of them you
+evaluate the objective function
+
+against the data.
+
+And you get some of those that
+then are the most attractive.
+
+They seem to be the best fit.
+
+But, by no means would you
+imagine they are yet optimal.
+
+So, now you create a next
+generation from this population
+
+by the analog of genetics.
+
+Some of the very best--
+you say, OK, they're
+
+going to survive so I'm just
+going to take them as is.
+
+Some I'm going to
+mutate, I'm going
+
+to have a probability of
+mutating an edge here or there.
+
+You can have crossover,
+actually mating
+
+between one model
+and another model,
+
+so that the daughter
+model gets some
+
+of the arcs from the mother
+model and some of the arcs
+
+from the father model.
+
+So you just generate an
+ex-population, do it again.
+
+And once you've
+reached a set of models
+
+that fit your data
+within the criteria
+
+that you want, then you say,
+this is now my population.
+
+And these are now
+my best-fit models.
+
+So it's not exhaustive.
+
+You can definitely find
+local minimum here.
+
+There's no question about that.
+
+Yeah?
+
+AUDIENCE: Do you always take the
+best model into the next round?
+
+Or do you--
+
+DOUG LAUFFENBURGER: Yeah,
+that's the elite survival.
+
+If you don't
+incorporate that, you
+
+might lose the best
+ones in any given round.
+
+But this ensures you
+take the best subset.
+
+Let them go for it.
+
+AUDIENCE: Is there
+a worry that you
+
+might get stuck in [INAUDIBLE]?
+
+DOUG LAUFFENBURGER: Yes.
+
+Yes, absolutely.
+
+So now you run this with a
+number of different starting
+
+populations.
+
+And you see if you get to
+similar consensus models.
+
+Yeah, because
+absolutely, this does not
+
+guarantee any kind
+of a global minimum.
+
+You will always get local.
+
+So you have to condition
+it on a different set
+
+of initial populations.
+
+OK.
+
+Once you do this-- I'm going
+to show you some results
+
+first and then dig into some
+other ways to think about it.
+
+So it's plotted here.
+
+This is one of the
+tumor cell lines.
+
+What's plotted here, is again,
+all the rows or all the signals
+
+that were measured.
+
+All the big columns or
+all the different stimuli,
+
+and all the little columns
+are the different inhibitors.
+
+And I should point out, this
+is only for the 30 minute data.
+
+OK.
+
+This isn't for the
+three hour or both,
+
+this is just the 30 minute data.
+
+And basically where
+there's green,
+
+the model and data
+fit was considered OK.
+
+Where it's red, it's not OK.
+
+Where it's pink it's less bad.
+
+So by the shaded.
+
+And the yellow
+actually, the model
+
+really couldn't
+make a prediction.
+
+Now, why that's the case
+is what's showing up here
+
+is just the initial
+Ingenuity scaffold.
+
+The very best one that
+didn't add or remove any
+
+arcs or nodes from the
+Ingenuity prior knowledge.
+
+It's that all we're
+going to do is just
+
+run the best fit Boolean
+logic model we can on that.
+
+And it wasn't very good.
+
+It was about 45% error.
+
+Almost half of the
+nodes it got wrong.
+
+So what that tells you if you
+just take a scaffold from one
+
+is interactive databases
+and without adulterating it,
+
+just fit the best logic
+model to some data--
+
+OK, at least in this case, and
+we've done a number of others,
+
+it actually doesn't
+fit very well.
+
+And the reasons being,
+you're trying to fit this now
+
+to a very specific
+biological context.
+
+Hepatocyte tumor
+cells under these
+
+grow factor and
+cytokine treatments.
+
+That network is
+likely very different
+
+from whatever aggregate you
+got from literature curation
+
+and so forth in a database.
+
+There's going to be a lot of
+stuff in the database that's
+
+not applicable, because it
+came from a different cell
+
+type, a different
+condition, or there just
+
+wasn't enough experiments in
+the literature for hypatocytes.
+
+Maybe it was never
+measured under treatment
+
+with interferon gamma.
+
+So there's data here
+that the database never
+
+had access to literature
+that it had explored.
+
+So lots of reasons.
+
+Now when you go through the
+processes we just talked about,
+
+and in the end,
+the best fit models
+
+give you something like
+less than 10% error.
+
+So less than 10% of these
+squares are red or pink.
+
+OK, so that's the
+kind of improvement
+
+that you can take by
+generating an improved model.
+
+By adding and subtracting
+arcs and nodes.
+
+So this is what the model looks
+like in the end for this tumor
+
+cell line.
+
+And this is a consensus model
+from the 20 or so best fit.
+
+And so the thickness
+of a line is
+
+how strong the consensus was.
+
+The strongest would
+be all 20 had it.
+
+And the point here being,
+you see some purple.
+
+And I wish my pen wasn't
+fading in and out.
+
+If anybody has a pointer
+I'll be happy to have it.
+
+Where you see purple,
+those were arcs that
+
+weren't in the
+Ingenuity database
+
+and had to be put in to get
+the data to fit this well.
+
+And it turns out,
+if you actually
+
+go back to the literature, you
+find that those purple arcs
+
+were already described
+in the literature.
+
+It's just that they weren't
+captured in that database.
+
+Well that's green and purple.
+
+Then you see some
+blue and they were
+
+in some of the other
+tumor cell types
+
+but now in this
+particular hep G2
+
+But you can generate a
+model that works very well.
+
+And see that it's consistent
+with much of literature.
+
+It's a more stripped down
+than what's in the databases.
+
+And there's some new
+things in it, that in fact,
+
+if you go back to the
+literature you can find,
+
+because they just were
+captured in the database.
+
+All right.
+
+A few insights
+about the analysis.
+
+So I want to show you, here
+is the objective function.
+
+How well the model
+fit and that's in red.
+
+OK.
+
+And in blue is the actual
+fit to the experimental data.
+
+And again, the hirer
+it is the worse it is.
+
+And the green gives you
+essentially the size.
+
+And this is plotted
+against the size penalty.
+
+And what's very interesting,
+is even for very small size
+
+penalties, almost negligible,
+that the size of the model that
+
+turns out to be best fit
+is substantially smaller
+
+than what was in the database.
+
+OK, so you actually generate
+a small model immediately.
+
+A smaller model immediately,
+even without any size penalty.
+
+So your intuition
+that a bigger model
+
+was going to be better actually
+turns out to be incorrect.
+
+That even without a size
+penalty, the model strips down.
+
+And why is that?
+
+Why is that?
+
+Let me make that
+question number two.
+
+Just to see who's still awake.
+
+Why, in fitting this
+hepatocyte data,
+
+would a model that leaves out
+a lot of stuff in the Ingenuity
+
+database that's presumably
+going on actually
+
+fit the data better?
+
+A smaller model fits better?
+
+Why is that?
+
+Yeah.
+
+AUDIENCE: This is a [INAUDIBLE].
+
+Maybe the strength
+of the attractions
+
+aren't really taken
+into account here?
+
+And so the moving things
+out, essentially means
+
+that you're not sealing
+everything in the [INAUDIBLE].
+
+You're just taking one.
+
+DOUG LAUFFENBURGER: Yeah.
+
+That's essentially it.
+
+I think you've casted it an
+almost quantitative term,
+
+but I think it's true
+even in qualitative terms.
+
+And one way to think
+about it is-- let's
+
+say I have an extra
+arc or extra node.
+
+OK.
+
+I might capture some
+more true positives.
+
+I might actually
+capture more of my data,
+
+but I could actually now, gain
+more complex with my data.
+
+Because now I've put
+in logic that, yes,
+
+it captures this
+measurement, but now maybe it
+
+messes up these other two
+or three measurements.
+
+So you actually can
+make your model worse
+
+trying to capture some small
+piece, that in fact, adversely
+
+influences the effects on
+the other measurements.
+
+So you get you get false
+positives, false negatives,
+
+along with anything
+and that's true.
+
+And it just so happens that
+in these kind of situations
+
+those can outweigh.
+
+Then of course, as you
+increase the size penalty
+
+you can drive your model to
+be even smaller, fewer arcs,
+
+and now that of course
+does come at the expense
+
+of not fitting the data better.
+
+OK.
+
+So where we decided that
+the size penalty best lived
+
+was where it was large enough
+to ensure stripping down
+
+of nonessential nodes and
+arcs, but not large enough
+
+to start compromising the
+actual experimental fit.
+
+OK.
+
+And so that lived
+someplace around there.
+
+OK.
+
+An important thing--
+and this goes back
+
+to the consensus model.
+
+If you think about, quote,
+model identification,
+
+can you uniquely specify
+one model a best fit model?
+
+You really can't.
+
+What's plotted here is
+for any of the arcs that
+
+would end up in a model.
+
+Let's say we let's say we
+numbered them from one to I
+
+think it was 113
+in the first place.
+
+One arc, another arc,
+another arc, another arc.
+
+And you say, how
+frequently did they
+
+end up in the best fit models?
+
+Basically, only a small
+proportion of them
+
+were in all the best fit models.
+
+Some of them were in
+some models and some not.
+
+Of course the higher
+the tolerance,
+
+the more air you
+allowed and now you
+
+started to get
+models that all fit
+
+to within whatever that criteria
+was in which most of their arcs
+
+weren't the same.
+
+You could have a lot of
+different network structures
+
+that give you that same fit.
+
+If you require a very, very
+tiny fit, compared to air,
+
+something like this, then
+more of the arcs in the models
+
+have to be in common.
+
+OK.
+
+So that makes some sense.
+
+But you can't really completely
+identify a unique model.
+
+That goes to what I said before.
+
+OK.
+
+I was talking before
+about trade-offs
+
+between false positives
+and false negatives.
+
+You must know, I'm sure from
+previous things in this class,
+
+the receiver operating
+characteristic curves,
+
+where for every of your
+model parameter choices,
+
+you say, what are
+my results in terms
+
+of false positives
+versus true positives?
+
+And you're trying to
+find the optimal location
+
+along this type of path.
+
+And so, what's shown here is
+that the best predictive model,
+
+in fact, is the one where
+we have the size penalty
+
+to be right on the edge of not
+making the experimental data
+
+fit worse, but still
+strips out the most arcs.
+
+So again, that demonstrates
+that the smaller model actually
+
+is in fact better, in terms
+of finding this type of--
+
+And this shows if we actually
+put in some more arcs that
+
+tried to capture some
+more data, yes we decrease
+
+the false negatives,
+but, in fact, we
+
+increase the false positives.
+
+We actually shift
+ourselves on this curve.
+
+And so you decide whether
+that's desirable or not.
+
+Where you'd like to live.
+
+So you can analyze what you
+like about your best fit class
+
+of models in this kind of way.
+
+OK, so now we have some
+confidence in this.
+
+What are you going
+to do with it?
+
+And one thing I'd like to do is
+just make a priori predictions.
+
+Say I now believe that on
+these hepatocytes or tumor
+
+cells stimulated with
+these kind of things,
+
+I can calculate what the
+experimental signaling
+
+activities should be.
+
+All right.
+
+Let's see if we
+do that a priori.
+
+So let's now use new inhibitors
+that hadn't been used before.
+
+Combination of inhibitors,
+especially in cancer.
+
+People are always interested
+in combinatorial drugs.
+
+Experimentally it's
+prohibitive to run
+
+through all possible
+combinations.
+
+So this is one thing in
+the pharmaceutical field
+
+people believe these kind of
+models are really useful for.
+
+Let's try all possible
+drug combinations
+
+and see which ones
+are most promising.
+
+And instead of just one
+ligand growth factor cytokine
+
+at a time, do
+different combinations.
+
+So this is all an
+entirely new data set.
+
+So different treatments that
+are different combinations,
+
+different inhibitors, different
+combinations of inhibitors.
+
+And now you just run the model--
+it's not trained on this.
+
+It was trained on
+the previous data.
+
+And now a priori
+predicts this data set.
+
+And now, again, you look for
+the model fit in the bottom.
+
+And again, you want the smallest
+number of red and pink boxes.
+
+In effect it predicted to
+within about 11% error.
+
+About 11% of the boxes didn't
+fit well, but 89% percent did.
+
+And that's, in fact
+pretty close to the 9%
+
+that was on the
+original training model.
+
+So in terms of this, in
+this realm of studies,
+
+these a priori treatment
+conditions-- drug combinations,
+
+growth factors,
+cytokine combinations--
+
+this is a pretty good validation
+that this model wasn't
+
+just kind of trained and fit.
+
+That it, in fact,
+could predict then
+
+what was happening
+in these pathways.
+
+And then of course, what
+it allows you to do,
+
+where all the red
+boxes are-- it say, OK,
+
+that's where we need
+more intensive study.
+
+Now maybe we go back to
+the literature and say,
+
+is there more known
+about those nodes that
+
+was captured in whatever
+our interactive database
+
+that we started with?
+
+Maybe we need to supplement the
+scaffold with more information.
+
+That's out in the literature
+where more and more dedicated
+
+experiments are done.
+
+So it narrows down where the
+next set of investigations
+
+need to be, whether from the
+literature or from yourself.
+
+OK.
+
+So this is just then
+some biological results.
+
+If you do this for the four
+different hepatocellular lines.
+
+Some of the signaling
+activities are the same,
+
+and some are different.
+
+I think I'll skip that.
+
+All right, let me show this.
+
+So this says, where are the
+similarities and differences
+
+between the normal hepatocytes
+versus the tumor lines.
+
+Because this is
+where you would want
+
+to get the ideas for where
+the right drugs would be.
+
+Where is the logic different,
+between a normal liver
+
+cell and one of these
+transformed types.
+
+So, this is the same
+kind of scaffold.
+
+It'll get us the
+consensus models
+
+and the thickness of
+the line is how strong--
+
+what proportion of the models
+did that arc show up in?
+
+Along the best.
+
+If it's black, the arc was
+in the primary hepatocytes
+
+and all the cell lines.
+
+So black is just sort
+of consensus core.
+
+This is just invariably there.
+
+The blue was in the models
+for the primary hepatocytes,
+
+but for some reason didn't
+exist in the tumor cell lines.
+
+So we're signaling logic
+that normal hepatocytes use,
+
+that the tumor cell
+lines have somehow lost.
+
+Red, are arcs that weren't
+in the primary cells,
+
+but showed up in the
+tumor cell lines.
+
+So was logic that the normal
+liver cells apparently
+
+didn't use, but now showed
+up in the tumor cell lines.
+
+And why would there
+be these differences?
+
+Well this is where it goes back
+to then the genetic mutations
+
+and variations.
+
+Because going from a primary
+to some tumor cell line,
+
+there's enough of the genetic
+mutations, that in this case
+
+said, OK, I've got some genetic
+mutation that interrupts
+
+the link between map
+three kinase and Ikk.
+
+There was some docking
+protein or something
+
+that's now missing, not
+expressed as highly.
+
+It's got a mutation
+of amino acids
+
+and no longer docks right.
+
+It has a lower
+enzymatic activity.
+
+So now you can go
+back and trace.
+
+Can I find some
+genetic mutation that
+
+has to do with the
+loss of that arc?
+
+Or if I've got a red
+arc that shows up--
+
+like I said because
+there was something
+
+in my genetic mutations that
+now adds an activity here
+
+that wasn't there.
+
+Maybe something is now
+constituently active.
+
+Maybe something is just
+expressed at a higher level.
+
+And all of a sudden that
+pathway comes into play.
+
+So that's the cool thing.
+
+You can trace what's actually
+in the genetic mutations
+
+if you have some
+methodology for that,
+
+to what's actually been
+altered in the network logic.
+
+Yeah?
+
+AUDIENCE: Are the primary
+lines considered healthy lines?
+
+Or are they--
+
+DOUG LAUFFENBURGER: Yes.
+
+AUDIENCE: OK, so the--
+
+DOUG LAUFFENBURGER: Yeah.
+
+So they're from
+donors but they're
+
+mainly like motorcycle accident
+donors that don't either
+
+liver anymore but
+the liver was fine.
+
+So, yeah, they're
+from healthy donors.
+
+AUDIENCE: [INAUDIBLE].
+
+DOUG LAUFFENBURGER: Yeah.
+
+Yeah.
+
+It was the lines at some
+point came from a tumor
+
+and have been propagated
+in a culture, yeah.
+
+OK.
+
+What do I want to-- got
+a little bit more time.
+
+Let me do this.
+
+OK.
+
+So here's another interesting
+thing that can happen.
+
+If you take these
+models seriously,
+
+it can tell you something
+about the biochemistry, perhaps
+
+of what's going on.
+
+So see there's this dashed line
+here that I want to emphasize
+
+and we'll emphasize it
+again on another slide.
+
+That was one that
+had to be added.
+
+It just wasn't in the
+Ingenuity pathway, scaffold.
+
+Actually couldn't find it
+in any literature anywhere.
+
+But nonetheless you needed
+it to fit some data.
+
+So we kind of kept
+our eye on that one.
+
+What the heck is going on here?
+
+This dashed line from I kappa
+kinase up to step three.
+
+No evidence for that signaling
+linkage in the literature
+
+anywhere.
+
+What could that tell you?
+
+All right.
+
+Well, you go back to the
+data now and you say,
+
+well what of the data set, of
+the experimental measurements
+
+that we made, caused
+that arc to have
+
+to be there to
+fit the data well?
+
+OK.
+
+You can now ask that
+kind of question.
+
+Well remember I said in the
+data set were inhibitors.
+
+Some small molecule
+inhibitors against this kinase
+
+or that kinase or that kinase
+that would perturb the network
+
+and then give us relationships
+at the logic model
+
+and had to account for.
+
+Well, this one had
+to be there, mainly
+
+to account for data that came
+from an inhibitor of Ikk.
+
+That one of the kinases
+that we had a small molecule
+
+inhibitor for,
+inhabited this kinase.
+
+And somehow there
+turned out to be
+
+an effect on staph
+3 phosphorylation.
+
+And so you needed
+that arc to be there.
+
+So either the explanation
+that either there's,
+
+in fact, some real
+mechanism going on here.
+
+It might have been
+transcriptional
+
+that somehow the
+activity of this kinase
+
+affects the levels of expression
+and the responsiveness
+
+of staph 3.
+
+Or you say, ah, maybe it's
+a problem with the drug?
+
+It's a problem
+with the inhibitor.
+
+That, in fact, what you thought
+was an inhibitor that just
+
+affected this kinase, has
+an off-target target effect
+
+on that kind of that kinase.
+
+And it's just an artifact.
+
+That's an alternative
+explanation.
+
+Right, so that's the sort
+of thing you can test.
+
+And we did test it.
+
+And here's the data here.
+
+At the bottom is the kinase that
+you wanted the inhibition 2.
+
+And in the blue was the
+inhibitor that was actually
+
+used in the study, both
+in vivo and en vitro
+
+and it inhibited that kinase.
+
+But then we looked at the
+potential off target effect
+
+on that other-- the
+JAK2 [? stat ?] 3
+
+and it also did have
+activity on that.
+
+So it meant that
+that inhibitor had
+
+an effect, not just on the Ikk,
+but also on the JAK [? stat ?]
+
+3.
+
+And so that's why that
+arc had to be there,
+
+is because, in fact,
+that inhibitor,
+
+inhibited this kinase as well.
+
+So if we took that into account
+in terms of the algorithm,
+
+then we wouldn't have to
+have that arc because it
+
+was spurious and came
+from the arc, in fact,
+
+of that inhibitor.
+
+But the interesting thing
+is that, by taking the model
+
+seriously, we can
+actually find that.
+
+Because it was not previously
+known that this inhibitor had
+
+an off-target effect
+on that kinase.
+
+In effect, the interesting
+thing, pharmacologically,
+
+was that this
+small molecule that
+
+was aimed to be an inhibitor
+against this kinase
+
+was the best by far in treating
+lung airway inflammation,
+
+compared against
+a whole other set
+
+of other types of inhibitors
+for the same kinase.
+
+So now the reason
+might be is, it's
+
+better because it's also
+hitting this other kinase.
+
+That this off-target
+effect actually
+
+is therapeutically
+efficacious and in fact
+
+a combination of drugs
+against this kinase
+
+and the other kinase
+is what's required
+
+for the therapeutic benefit.
+
+So that's something
+that could be explored.
+
+And that's the sort of
+thing this model leads to.
+
+OK.
+
+Let me end by digging into
+this difference a little bit.
+
+Because I said, you
+see these differences
+
+between primary hepatocytes
+and the tumor cell lines.
+
+And the model said, just
+from examining the data sets,
+
+that the logic is different.
+
+OK.
+
+Is there any
+validation for that?
+
+Well, so let's go back and
+look at those differences
+
+with respect to literature.
+
+So if you just blow up
+that part of the model,
+
+there's eight edges
+that are strongly
+
+disparate between the primary,
+normal cell types and the tumor
+
+cells and they're
+all enumerated here.
+
+One, two, three, four,
+five, six, seven, eight.
+
+And they're essentially in
+three different pathways.
+
+So what the model
+is telling you is
+
+that there's three different
+pathways that are substantially
+
+different between a normal liver
+cell and a liver tumor cell.
+
+OK.
+
+So is there any evidence
+that this is really true?
+
+So let's look at one.
+
+On to this pathway that
+I've got differences.
+
+And you see blue
+here and red here.
+
+It says that this particular
+signaling node in normal cells
+
+is activated by this pathway.
+
+In the tumors, that
+regulation is lost
+
+and that actually comes
+through another pathway.
+
+And it turns this is
+consistent with literature
+
+that, in fact, in
+the tumor cells,
+
+you get a higher activity
+of this downstream node.
+
+And now I've lost
+my light again.
+
+This HSP27.
+
+Even though it's
+over expressed, you
+
+get less activation because
+this pathway is less strongly
+
+activated in red than
+the blue pathway is.
+
+So if you went by
+gene expression,
+
+you'd think in the
+tumor cells, this
+
+is a higher activated pathway.
+
+Turns out the
+logic is different,
+
+and you actually get
+less activation of it
+
+because it's coming from
+a different pathway.
+
+So that turns out to be true
+in the liver tumor literature.
+
+Another one-- I find this
+one really interesting.
+
+That in normal liver cells,
+to activate this Ikk pathway--
+
+that's a very important
+kinase pathway,
+
+governing the transcription
+factor of NF Kappa b.
+
+In a primary cell, I
+need this combined logic
+
+between a pathway downstream
+of insulin receptor
+
+and a pathway downstream
+of a cytokine.
+
+Only if both of those pathways
+are on, do I now turn this on.
+
+In the tumor cells,
+that check is lost.
+
+Only one pathway is required.
+
+OK.
+
+If this one is
+activated, I'm going
+
+to get this transcription
+factor activated.
+
+I don't have to wait for
+simultaneous activation
+
+of this pathway.
+
+Where as a normal
+says I have to.
+
+OK.
+
+That turns out to be true
+that in the liver cells,
+
+the progression is
+associated with a looser
+
+regulation of this
+transcription factor.
+
+And one more.
+
+I won't go into too much
+detail, but again, you
+
+see reds and blues here.
+
+In the tumor cell
+lines, you've now
+
+got activities
+downstream of insulin.
+
+That's normally just
+a survival factor,
+
+that's just not found
+in the primary cells.
+
+And that, in fact, is shown
+in the literature too,
+
+that insulin signaling
+shifts from metabolism
+
+to proliferation.
+
+It's mainly metabolic, stimulus.
+
+In the normal cells it turns
+into a proliferative stimulus
+
+in the tumor cells.
+
+OK.
+
+So, what this says is,
+just by mapping this logic
+
+scaffold, the scaffold
+against empirical data,
+
+developing a logic
+model, you in fact
+
+can find loci of differences
+between the normal cell
+
+signaling logic and tumor
+cells signalling logic
+
+for which there's evidence in
+the literature, none of which
+
+was in the original databases.
+
+Finally, I'm going
+I'm just going
+
+to say that it turns out in
+another study, what you could
+
+show is those three pathways
+that the model predicts
+
+are the differences
+between the liver tumor
+
+cells and the normal cells.
+
+That in order to kill
+these liver tumor cells,
+
+you need inhibitors against all
+three pathways simultaneously.
+
+You actually need
+combination drugs
+
+of three different pathway
+inhibitors to kill these cells.
+
+And it's exactly
+the three pathways
+
+that the model predicted of the
+differences between the normals
+
+and the tumor cells.
+
+OK.
+
+All right, so I will
+end here and then see
+
+if there's any more questions.
+
+Something that
+comes up a lot is--
+
+there's discomfort with Boolean
+logic because of zero, one.
+
+It's off, on, and of
+course we know biology,
+
+biochemistry doesn't
+work that way.
+
+And so there can be
+so many artifacts,
+
+so many places that you
+can get things wrong,
+
+because you're trying to fit a
+model where the measurement is
+
+supposed to be
+either zero or one,
+
+and you're comparing it
+against a measurement that
+
+might be 0.6.
+
+Well, 0.6, is that closer
+to 1, is it closer to 0?
+
+Is there some normalization
+that would shift it
+
+from one to the other.
+
+And instead of being a correct
+fit, it's now an incorrect fit.
+
+So you can see the
+room for artifacts
+
+by mapping quantitative data
+against a qualitative model.
+
+So, one thing done more
+recently is to admit that
+
+and say, well, let's say
+just relax this a bit.
+
+And instead of having step
+functions from off to on,
+
+that they're more graded.
+
+It's like an analog
+transfer function.
+
+So what you've essentially
+done is add one more parameter
+
+to every node, to every gate.
+
+Because of Boolean
+logic, there's
+
+essentially one
+hidden parameter.
+
+That's where you shift
+from off to on, right?
+
+There's some location of
+the level of the signal
+
+that you've decided is 0 or 1.
+
+So there's some parameter
+that you shift from,
+
+saying it's off to on.
+
+Well here now in this
+formalism there's that,
+
+but there's also then the slope
+of shifting from off to on.
+
+Is it still fairly steep?
+
+Is it really mild?
+
+Is it someplace in between?
+
+OK?
+
+And this can go with
+AND and OR gates too.
+
+Now, instead of
+just one dimension,
+
+one component being
+off to on or on to off,
+
+now you got AND and OR gates
+that have these slopes as well.
+
+So what this means is
+you require more data
+
+to fit this-- we call it a
+constrained fuzzy logic model
+
+because you've got-- if I've
+got 50 nodes in my system,
+
+I've got 50 more
+parameters I've got to fit.
+
+OK, so that requires more data.
+
+What's the benefit of it, is
+that your predictions now,
+
+in fact, can be quantitative.
+
+So you can go into
+the model and say
+
+here's a transcription
+factor CREB.
+
+I'm going to predict its
+phosphorylation state
+
+and its transcriptional
+activity, perhaps,
+
+based on the activities
+of two upstream kinases.
+
+And so if I had had an inhibitor
+for one of these kinases
+
+or another, how much would
+I shift the phosphorylation
+
+of this transcription factor?
+
+And what you actually see is
+these gradual curves, that if I
+
+start to inhibit
+[INAUDIBLE], OK, it gradually
+
+changes the
+phosphorylation of CREB.
+
+Or if I inhibit the
+activity of P38,
+
+it even more gradually
+effects the activity of CREB.
+
+So you can turn these into
+quantitative predictions
+
+of strong effects, weak effects.
+
+And again, look at
+drug combinations.
+
+So that's the advantage of going
+to this more analog transfer
+
+function logic model.
+
+You can deal with
+quantification much better,
+
+but at the cost of
+requiring more data.
+
+OK, I think I'll leave it here.
+
+It's about 3:15
+and so if there's
+
+more questions we can take
+them about any aspect of this.
+
+Most of you have stayed awake,
+I think that's a good thing.
+
+OK.
+
+More questions?
+
+AUDIENCE: [INAUDIBLE].
+
+When you have the model for
+the template of the Ikk story.
+
+And then it seems
+like it may not
+
+be as easy to back out
+the original data that
+
+led to that specific mode.
+
+For example, you
+showed that one arc
+
+was from this one treatment.
+
+But because if you trained
+the model the same as that
+
+and it's not deterministic,
+then what-- could you just add--
+
+DOUG LAUFFENBURGER: I think
+that's a great question.
+
+So let's say there's
+new arcs that you add,
+
+that weren't in the
+original scaffold.
+
+I mean that's what you got
+the biggest questions from.
+
+If you delete one,
+you say, ah, it's
+
+easy to believe why
+you would delete one.
+
+Any arc that you add
+to get a best fit,
+
+I think you've got to
+ask questions about.
+
+So in all those
+cases where there
+
+are arcs that were added that
+led to a better fit model,
+
+the first thing we did
+was go to the literature.
+
+Say, OK, is there literature
+on some affect of this node
+
+to that node?
+
+And it's just that
+that literature
+
+wasn't curated
+into that database
+
+or something like that.
+
+And most of the time
+we could find it there.
+
+OK.
+
+So then there were the cases,
+and this was the most prominent
+
+one, where from some
+added arc, we just
+
+couldn't find it
+in the literature.
+
+In this particular
+case, it was very
+
+easy to trace it to
+this particular effect
+
+of this inhibitor.
+
+I would say there's no reason
+to believe that that's always
+
+going to be the case.
+
+I don't have another example to
+show you where it was harder.
+
+Everything else we actually
+found in the literature.
+
+But you could imagine, having
+some new arc that you really
+
+couldn't find in the
+literature and there's
+
+no artifactual
+explanation for it.
+
+And now, how you trace it
+back to what the data was
+
+that might give you
+a more nuanced hint.
+
+It's a great question.
+
+I don't really know
+how we'll do that.
+
+I think, we and other
+practitioners who use this,
+
+I'm sure we'll run
+into it at some point.
+
+That's a great challenge
+to be thinking about.
+
+Yeah?
+
+AUDIENCE: I might have
+missed this earlier,
+
+but I was wondering,
+is this model actually
+
+able to incorporate the
+heterogeneity of a tumor,
+
+for example?
+
+Or the population heterogeneity?
+
+DOUG LAUFFENBURGER: That's also
+a really interesting question.
+
+Let me try to show
+something here.
+
+Yeah.
+
+So two things.
+
+One is, what's shown here--
+this is the four different tumor
+
+cells that we did.
+
+And what's shown in color is
+the arcs for each one of them.
+
+So yellow, orange, brown, red.
+
+So some places you see all
+four of those colors there.
+
+In some places only two or one.
+
+It says if I had four
+different tumor types,
+
+there's some slight differences
+in logic among them.
+
+You could translate
+to that is, well
+
+I could imagine
+then having a tumor
+
+that's a mixture of sub types
+and how would I discern that?
+
+One possible idea that's
+attractive to me--
+
+although we didn't really
+explore this in any form of
+
+[INAUDIBLE].
+
+We didn't really have
+the means to make
+
+experimental
+measurements on the tumor
+
+heterogeneity at the time.
+
+It's when you get to a
+set of consensus models.
+
+Right.
+
+So let's say you get the 50
+best fit models and you say,
+
+some arc is in 80% of them,
+but it's not in 20% of them,
+
+is it possible that
+that represents
+
+some of heterogeneity
+because you're
+
+getting an average of
+different subtypes?
+
+I don't know.
+
+Sometimes that appeals to
+me as potentially valid.
+
+Sometimes I think there's
+a flaw in that reasoning.
+
+Just because you get an average
+that's not then as strong.
+
+Does that necessarily
+reflect a sub-population?
+
+I don't know.
+
+So what we do know is,
+we can see differences
+
+when there are differences.
+
+How you actually see
+them then, if all you
+
+have is averaged
+data, maybe it's
+
+reflected in the heterogeneity
+of the consensus models.
+
+Maybe not.
+
+It would be an
+interesting to explore.
+
+Anybody else?
+
+All right.
+
+All set.
+
+Thanks.
\ No newline at end of file
diff --git a/iMDKTNDBSxE.txt b/iMDKTNDBSxE.txt
new file mode 100644
index 0000000000000000000000000000000000000000..fb8d0638c6ead39b64facc8425966969abf57e43
--- /dev/null
+++ b/iMDKTNDBSxE.txt
@@ -0,0 +1,323 @@
+align:start position:0%
+ 
+a web-based program that will provide
+
+ align:start position:0%
+a web-based program that will provide
+ 
+
+ align:start position:0%
+a web-based program that will provide
+free access to primary materials for
+
+ align:start position:0%
+free access to primary materials for
+ 
+
+ align:start position:0%
+free access to primary materials for
+virtually every
+
+ align:start position:0%
+virtually every
+ 
+
+ align:start position:0%
+virtually every
+[Applause]
+
+ align:start position:0%
+[Applause]
+ 
+
+ align:start position:0%
+[Applause]
+[Music]
+
+ align:start position:0%
+[Music]
+ 
+
+ align:start position:0%
+[Music]
+course when we have some number of
+
+ align:start position:0%
+course when we have some number of
+ 
+
+ align:start position:0%
+course when we have some number of
+equations say n equations and N unknown
+
+ align:start position:0%
+equations say n equations and N unknown
+ 
+
+ align:start position:0%
+equations say n equations and N unknown
+the the placebo and people who got the
+
+ align:start position:0%
+the the placebo and people who got the
+ 
+
+ align:start position:0%
+the the placebo and people who got the
+pill if they were not any me
+
+ align:start position:0%
+pill if they were not any me
+ 
+
+ align:start position:0%
+pill if they were not any me
+before are some small what's a a natural
+
+ align:start position:0%
+before are some small what's a a natural
+ 
+
+ align:start position:0%
+before are some small what's a a natural
+um what's a what's a reasonable way of
+
+ align:start position:0%
+um what's a what's a reasonable way of
+ 
+
+ align:start position:0%
+um what's a what's a reasonable way of
+proceeding here right what's a
+
+ align:start position:0%
+proceeding here right what's a
+ 
+
+ align:start position:0%
+proceeding here right what's a
+reasonable
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+way I live in s Paulo Brazil where I go
+
+ align:start position:0%
+way I live in s Paulo Brazil where I go
+ 
+
+ align:start position:0%
+way I live in s Paulo Brazil where I go
+to medical school and I started using
+
+ align:start position:0%
+to medical school and I started using
+ 
+
+ align:start position:0%
+to medical school and I started using
+ocw when I was 15 I guess and I
+
+ align:start position:0%
+ocw when I was 15 I guess and I
+ 
+
+ align:start position:0%
+ocw when I was 15 I guess and I
+discovered ocw on YouTube about 5 years
+
+ align:start position:0%
+discovered ocw on YouTube about 5 years
+ 
+
+ align:start position:0%
+discovered ocw on YouTube about 5 years
+ago I absolutely love MIT open course it
+
+ align:start position:0%
+ago I absolutely love MIT open course it
+ 
+
+ align:start position:0%
+ago I absolutely love MIT open course it
+lowered the bar of entering a new
+
+ align:start position:0%
+lowered the bar of entering a new
+ 
+
+ align:start position:0%
+lowered the bar of entering a new
+learning territory for me and It
+
+ align:start position:0%
+learning territory for me and It
+ 
+
+ align:start position:0%
+learning territory for me and It
+ultimately allowed me to carve out a
+
+ align:start position:0%
+ultimately allowed me to carve out a
+ 
+
+ align:start position:0%
+ultimately allowed me to carve out a
+unique career pathway during the
+
+ align:start position:0%
+unique career pathway during the
+ 
+
+ align:start position:0%
+unique career pathway during the
+covid-19 pandemic I was unemployed I
+
+ align:start position:0%
+covid-19 pandemic I was unemployed I
+ 
+
+ align:start position:0%
+covid-19 pandemic I was unemployed I
+started as a poet and a painter and a
+
+ align:start position:0%
+started as a poet and a painter and a
+ 
+
+ align:start position:0%
+started as a poet and a painter and a
+sculptor I made the transition to
+
+ align:start position:0%
+sculptor I made the transition to
+ 
+
+ align:start position:0%
+sculptor I made the transition to
+working for a financial technology
+
+ align:start position:0%
+working for a financial technology
+ 
+
+ align:start position:0%
+working for a financial technology
+startup ocw allowed me to gain a more
+
+ align:start position:0%
+startup ocw allowed me to gain a more
+ 
+
+ align:start position:0%
+startup ocw allowed me to gain a more
+solid grasp on the basic Sciences it's
+
+ align:start position:0%
+solid grasp on the basic Sciences it's
+ 
+
+ align:start position:0%
+solid grasp on the basic Sciences it's
+helped me learn about the things I love
+
+ align:start position:0%
+helped me learn about the things I love
+ 
+
+ align:start position:0%
+helped me learn about the things I love
+learning about human Behavioral Sciences
+
+ align:start position:0%
+learning about human Behavioral Sciences
+ 
+
+ align:start position:0%
+learning about human Behavioral Sciences
+psychology programming and python
+
+ align:start position:0%
+psychology programming and python
+ 
+
+ align:start position:0%
+psychology programming and python
+thermodynamics just absolutely
+
+ align:start position:0%
+thermodynamics just absolutely
+ 
+
+ align:start position:0%
+thermodynamics just absolutely
+fascinating artificial intelligence then
+
+ align:start position:0%
+fascinating artificial intelligence then
+ 
+
+ align:start position:0%
+fascinating artificial intelligence then
+you should also start your Learning
+
+ align:start position:0%
+you should also start your Learning
+ 
+
+ align:start position:0%
+you should also start your Learning
+Journey with MIT open courseware and I
+
+ align:start position:0%
+Journey with MIT open courseware and I
+ 
+
+ align:start position:0%
+Journey with MIT open courseware and I
+think we probably should bring one more
+
+ align:start position:0%
+think we probably should bring one more
+ 
+
+ align:start position:0%
+think we probably should bring one more
+friend for the ride so we can reach 10
+
+ align:start position:0%
+friend for the ride so we can reach 10
+ 
+
+ align:start position:0%
+friend for the ride so we can reach 10
+million
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+soon
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+[Music]
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+[Music]
\ No newline at end of file
diff --git a/iPWIqjYkVns.txt b/iPWIqjYkVns.txt
new file mode 100644
index 0000000000000000000000000000000000000000..053dbf81b768397e8f217fd216f11da1b0a12112
--- /dev/null
+++ b/iPWIqjYkVns.txt
@@ -0,0 +1,12360 @@
+align:start position:0%
+ 
+the following content is provided under
+
+ align:start position:0%
+the following content is provided under
+ 
+
+ align:start position:0%
+the following content is provided under
+a Creative Commons license your support
+
+ align:start position:0%
+a Creative Commons license your support
+ 
+
+ align:start position:0%
+a Creative Commons license your support
+will help MIT open courseware continue
+
+ align:start position:0%
+will help MIT open courseware continue
+ 
+
+ align:start position:0%
+will help MIT open courseware continue
+to offer highquality educational
+
+ align:start position:0%
+to offer highquality educational
+ 
+
+ align:start position:0%
+to offer highquality educational
+resources for free to make a donation or
+
+ align:start position:0%
+resources for free to make a donation or
+ 
+
+ align:start position:0%
+resources for free to make a donation or
+to view additional materials from
+
+ align:start position:0%
+to view additional materials from
+ 
+
+ align:start position:0%
+to view additional materials from
+hundreds of MIT courses visit MIT open
+
+ align:start position:0%
+hundreds of MIT courses visit MIT open
+ 
+
+ align:start position:0%
+hundreds of MIT courses visit MIT open
+courseware at
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+ocw.mit.edu okay let us
+
+ align:start position:0%
+ocw.mit.edu okay let us
+ 
+
+ align:start position:0%
+ocw.mit.edu okay let us
+start so last
+
+ align:start position:0%
+start so last
+ 
+
+ align:start position:0%
+start so last
+time we finished uh
+
+ align:start position:0%
+time we finished uh
+ 
+
+ align:start position:0%
+time we finished uh
+discussing conation
+
+ align:start position:0%
+discussing conation
+ 
+
+ align:start position:0%
+discussing conation
+of closed
+
+ align:start position:0%
+of closed
+ 
+
+ align:start position:0%
+of closed
+string and open
+
+ align:start position:0%
+string and open
+ 
+
+ align:start position:0%
+string and open
+strings and we
+
+ align:start position:0%
+strings and we
+ 
+
+ align:start position:0%
+strings and we
+see we saw that
+
+ align:start position:0%
+see we saw that
+ 
+
+ align:start position:0%
+see we saw that
+um if you want to
+
+ align:start position:0%
+um if you want to
+ 
+
+ align:start position:0%
+um if you want to
+quantize
+
+ align:start position:0%
+quantize
+ 
+
+ align:start position:0%
+quantize
+Strings
+
+ align:start position:0%
+Strings
+ 
+
+ align:start position:0%
+Strings
+consistently in a minkovsky space
+
+ align:start position:0%
+consistently in a minkovsky space
+ 
+
+ align:start position:0%
+consistently in a minkovsky space
+time then you need 26
+
+ align:start position:0%
+time then you need 26
+ 
+
+ align:start position:0%
+time then you need 26
+Dimensions okay we also saw that when
+
+ align:start position:0%
+Dimensions okay we also saw that when
+ 
+
+ align:start position:0%
+Dimensions okay we also saw that when
+you quantize the photon oh when you
+
+ align:start position:0%
+you quantize the photon oh when you
+ 
+
+ align:start position:0%
+you quantize the photon oh when you
+contest open strings then you see a
+
+ align:start position:0%
+contest open strings then you see a
+ 
+
+ align:start position:0%
+contest open strings then you see a
+vector field a massless vector field in
+
+ align:start position:0%
+vector field a massless vector field in
+ 
+
+ align:start position:0%
+vector field a massless vector field in
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+Spectrum uh plus a infinite number of
+
+ align:start position:0%
+Spectrum uh plus a infinite number of
+ 
+
+ align:start position:0%
+Spectrum uh plus a infinite number of
+massive modes and when you quantize
+
+ align:start position:0%
+massive modes and when you quantize
+ 
+
+ align:start position:0%
+massive modes and when you quantize
+close strings then you see a mass spin
+
+ align:start position:0%
+close strings then you see a mass spin
+ 
+
+ align:start position:0%
+close strings then you see a mass spin
+two particles which is a
+
+ align:start position:0%
+two particles which is a
+ 
+
+ align:start position:0%
+two particles which is a
+graviton in your massive Spectrum plus
+
+ align:start position:0%
+graviton in your massive Spectrum plus
+ 
+
+ align:start position:0%
+graviton in your massive Spectrum plus
+infinite number of massive modes
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so that essentially uh is the
+
+ align:start position:0%
+okay so that essentially uh is the
+ 
+
+ align:start position:0%
+okay so that essentially uh is the
+essence of Str theory is that the stren
+
+ align:start position:0%
+essence of Str theory is that the stren
+ 
+
+ align:start position:0%
+essence of Str theory is that the stren
+series contains graviton in a quantum
+
+ align:start position:0%
+series contains graviton in a quantum
+ 
+
+ align:start position:0%
+series contains graviton in a quantum
+mechanical way um so should be
+
+ align:start position:0%
+mechanical way um so should be
+ 
+
+ align:start position:0%
+mechanical way um so should be
+consistent should be considered as a
+
+ align:start position:0%
+consistent should be considered as a
+ 
+
+ align:start position:0%
+consistent should be considered as a
+theory of quantum
+
+ align:start position:0%
+theory of quantum
+ 
+
+ align:start position:0%
+theory of quantum
+gravity so today we start talking about
+
+ align:start position:0%
+gravity so today we start talking about
+ 
+
+ align:start position:0%
+gravity so today we start talking about
+lot object in string theory it's called
+
+ align:start position:0%
+lot object in string theory it's called
+ 
+
+ align:start position:0%
+lot object in string theory it's called
+Uh a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+dein okay so we discussed open strings
+
+ align:start position:0%
+dein okay so we discussed open strings
+ 
+
+ align:start position:0%
+dein okay so we discussed open strings
+so let's go back to the open
+
+ align:start position:0%
+so let's go back to the open
+ 
+
+ align:start position:0%
+so let's go back to the open
+string for the open
+
+ align:start position:0%
+string for the open
+ 
+
+ align:start position:0%
+string for the open
+string say after we fixed the work sheet
+
+ align:start position:0%
+string say after we fixed the work sheet
+ 
+
+ align:start position:0%
+string say after we fixed the work sheet
+to be
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+flat then work sheet action can be
+
+ align:start position:0%
+flat then work sheet action can be
+ 
+
+ align:start position:0%
+flat then work sheet action can be
+written as the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+following
+
+ align:start position:0%
+following
+ 
+
+ align:start position:0%
+following
+okay so you can when you get the when
+
+ align:start position:0%
+okay so you can when you get the when
+ 
+
+ align:start position:0%
+okay so you can when you get the when
+you obtain the equation motion for
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+X say you
+
+ align:start position:0%
+X say you
+ 
+
+ align:start position:0%
+X say you
+will then have something like
+
+ align:start position:0%
+will then have something like
+ 
+
+ align:start position:0%
+will then have something like
+this so you need to do integration by
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+part plus a total derivative term okay
+
+ align:start position:0%
+part plus a total derivative term okay
+ 
+
+ align:start position:0%
+part plus a total derivative term okay
+plus a total derivative term and total
+
+ align:start position:0%
+plus a total derivative term and total
+ 
+
+ align:start position:0%
+plus a total derivative term and total
+dtive term we we induce a term on the
+
+ align:start position:0%
+dtive term we we induce a term on the
+ 
+
+ align:start position:0%
+dtive term we we induce a term on the
+boundary if you have open
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+string say at Sigma equal to Z and
+
+ align:start position:0%
+string say at Sigma equal to Z and
+ 
+
+ align:start position:0%
+string say at Sigma equal to Z and
+Pi
+
+ align:start position:0%
+Pi
+ 
+
+ align:start position:0%
+Pi
+okay so um
+
+ align:start position:0%
+okay so um
+ 
+
+ align:start position:0%
+okay so um
+so this is still
+
+ align:start position:0%
+so this is still
+ 
+
+ align:start position:0%
+so this is still
+detal and uh so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um so from this term you get the
+
+ align:start position:0%
+um so from this term you get the
+ 
+
+ align:start position:0%
+um so from this term you get the
+equation
+
+ align:start position:0%
+equation
+ 
+
+ align:start position:0%
+equation
+motion and then you induce a boundary
+
+ align:start position:0%
+motion and then you induce a boundary
+ 
+
+ align:start position:0%
+motion and then you induce a boundary
+term evaluate
+
+ align:start position:0%
+term evaluate
+ 
+
+ align:start position:0%
+term evaluate
+it because open string there two
+
+ align:start position:0%
+it because open string there two
+ 
+
+ align:start position:0%
+it because open string there two
+boundaries at zero and
+
+ align:start position:0%
+boundaries at zero and
+ 
+
+ align:start position:0%
+boundaries at zero and
+Pi then you do such a boundary term at
+
+ align:start position:0%
+Pi then you do such a boundary term at
+ 
+
+ align:start position:0%
+Pi then you do such a boundary term at
+the boundary we need to um also get rid
+
+ align:start position:0%
+the boundary we need to um also get rid
+ 
+
+ align:start position:0%
+the boundary we need to um also get rid
+of
+
+ align:start position:0%
+of
+ 
+
+ align:start position:0%
+of
+otherwise uh the equation motion is not
+
+ align:start position:0%
+otherwise uh the equation motion is not
+ 
+
+ align:start position:0%
+otherwise uh the equation motion is not
+satisfied and uh what we discuss is soal
+
+ align:start position:0%
+satisfied and uh what we discuss is soal
+ 
+
+ align:start position:0%
+satisfied and uh what we discuss is soal
+Luman boundary conditions is just take
+
+ align:start position:0%
+Luman boundary conditions is just take
+ 
+
+ align:start position:0%
+Luman boundary conditions is just take
+the partti of Sigma equal to zero P
+
+ align:start position:0%
+the partti of Sigma equal to zero P
+ 
+
+ align:start position:0%
+the partti of Sigma equal to zero P
+Sigma X mu to be zero but in general for
+
+ align:start position:0%
+Sigma X mu to be zero but in general for
+ 
+
+ align:start position:0%
+Sigma X mu to be zero but in general for
+any
+
+ align:start position:0%
+any
+ 
+
+ align:start position:0%
+any
+mu say for any
+
+ align:start position:0%
+mu say for any
+ 
+
+ align:start position:0%
+mu say for any
+mu you have a choice of four boundary
+
+ align:start position:0%
+mu you have a choice of four boundary
+ 
+
+ align:start position:0%
+mu you have a choice of four boundary
+conditions you can choose Del X mu equal
+
+ align:start position:0%
+conditions you can choose Del X mu equal
+ 
+
+ align:start position:0%
+conditions you can choose Del X mu equal
+to
+
+ align:start position:0%
+to
+ 
+
+ align:start position:0%
+to
+zero or how should see Sigma X mual
+
+ align:start position:0%
+zero or how should see Sigma X mual
+ 
+
+ align:start position:0%
+zero or how should see Sigma X mual
+to0
+
+ align:start position:0%
+to0
+ 
+
+ align:start position:0%
+to0
+say at Sigma equal
+
+ align:start position:0%
+say at Sigma equal
+ 
+
+ align:start position:0%
+say at Sigma equal
+to0 and you have the similar choices at
+
+ align:start position:0%
+to0 and you have the similar choices at
+ 
+
+ align:start position:0%
+to0 and you have the similar choices at
+Sigma equal to
+
+ align:start position:0%
+Sigma equal to
+ 
+
+ align:start position:0%
+Sigma equal to
+Pi so all together you have actually
+
+ align:start position:0%
+Pi so all together you have actually
+ 
+
+ align:start position:0%
+Pi so all together you have actually
+Four
+
+ align:start position:0%
+Four
+ 
+
+ align:start position:0%
+Four
+possible four possible boundary
+
+ align:start position:0%
+possible four possible boundary
+ 
+
+ align:start position:0%
+possible four possible boundary
+conditions for each Direction so for
+
+ align:start position:0%
+conditions for each Direction so for
+ 
+
+ align:start position:0%
+conditions for each Direction so for
+each Direction you have four possible
+
+ align:start position:0%
+each Direction you have four possible
+ 
+
+ align:start position:0%
+each Direction you have four possible
+boundary conditions if you can see the
+
+ align:start position:0%
+boundary conditions if you can see the
+ 
+
+ align:start position:0%
+boundary conditions if you can see the
+all possible directions there are many
+
+ align:start position:0%
+all possible directions there are many
+ 
+
+ align:start position:0%
+all possible directions there are many
+many different boundary conditions okay
+
+ align:start position:0%
+many different boundary conditions okay
+ 
+
+ align:start position:0%
+many different boundary conditions okay
+they in principle many many different
+
+ align:start position:0%
+they in principle many many different
+ 
+
+ align:start position:0%
+they in principle many many different
+boundary
+
+ align:start position:0%
+boundary
+ 
+
+ align:start position:0%
+boundary
+conditions so let's now look at what the
+
+ align:start position:0%
+conditions so let's now look at what the
+ 
+
+ align:start position:0%
+conditions so let's now look at what the
+other boundary conditions mean okay we
+
+ align:start position:0%
+other boundary conditions mean okay we
+ 
+
+ align:start position:0%
+other boundary conditions mean okay we
+look at the case which is the you just
+
+ align:start position:0%
+look at the case which is the you just
+ 
+
+ align:start position:0%
+look at the case which is the you just
+impose this
+
+ align:start position:0%
+impose this
+ 
+
+ align:start position:0%
+impose this
+everywhere at both Sigma equal to Z and
+
+ align:start position:0%
+everywhere at both Sigma equal to Z and
+ 
+
+ align:start position:0%
+everywhere at both Sigma equal to Z and
+sigma equal to Pi and for all directions
+
+ align:start position:0%
+sigma equal to Pi and for all directions
+ 
+
+ align:start position:0%
+sigma equal to Pi and for all directions
+but now let us explore uh this more
+
+ align:start position:0%
+but now let us explore uh this more
+ 
+
+ align:start position:0%
+but now let us explore uh this more
+General boundary
+
+ align:start position:0%
+General boundary
+ 
+
+ align:start position:0%
+General boundary
+conditions first
+
+ align:start position:0%
+conditions first
+ 
+
+ align:start position:0%
+conditions first
+let's just quickly look at what this B
+
+ align:start position:0%
+let's just quickly look at what this B
+ 
+
+ align:start position:0%
+let's just quickly look at what this B
+so so this is called the rich boundary
+
+ align:start position:0%
+so so this is called the rich boundary
+ 
+
+ align:start position:0%
+so so this is called the rich boundary
+condition this is called Lum so first
+
+ align:start position:0%
+condition this is called Lum so first
+ 
+
+ align:start position:0%
+condition this is called Lum so first
+let's look at what does this boundary
+
+ align:start position:0%
+let's look at what does this boundary
+ 
+
+ align:start position:0%
+let's look at what does this boundary
+condition mean
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so if we have say let's consider
+
+ align:start position:0%
+okay so if we have say let's consider
+ 
+
+ align:start position:0%
+okay so if we have say let's consider
+some direction
+
+ align:start position:0%
+some direction
+ 
+
+ align:start position:0%
+some direction
+I say Delta x i equal to
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+zero say at Sigma equal to zero
+
+ align:start position:0%
+zero say at Sigma equal to zero
+ 
+
+ align:start position:0%
+zero say at Sigma equal to zero
+say t equal to
+
+ align:start position:0%
+say t equal to
+ 
+
+ align:start position:0%
+say t equal to
+zero so this is the example of this say
+
+ align:start position:0%
+zero so this is the example of this say
+ 
+
+ align:start position:0%
+zero so this is the example of this say
+der boundary condition in I Direction
+
+ align:start position:0%
+der boundary condition in I Direction
+ 
+
+ align:start position:0%
+der boundary condition in I Direction
+so suppose at Sigma equal to zero you
+
+ align:start position:0%
+so suppose at Sigma equal to zero you
+ 
+
+ align:start position:0%
+so suppose at Sigma equal to zero you
+have you impose
+
+ align:start position:0%
+have you impose
+ 
+
+ align:start position:0%
+have you impose
+this so what this
+
+ align:start position:0%
+this so what this
+ 
+
+ align:start position:0%
+this so what this
+means is said the variation of x i at
+
+ align:start position:0%
+means is said the variation of x i at
+ 
+
+ align:start position:0%
+means is said the variation of x i at
+Sigma equal to zero at all time does not
+
+ align:start position:0%
+Sigma equal to zero at all time does not
+ 
+
+ align:start position:0%
+Sigma equal to zero at all time does not
+change so T is like parameterize your W
+
+ align:start position:0%
+change so T is like parameterize your W
+ 
+
+ align:start position:0%
+change so T is like parameterize your W
+sheet a Time the W sheet
+
+ align:start position:0%
+sheet a Time the W sheet
+ 
+
+ align:start position:0%
+sheet a Time the W sheet
+motion so this tells you that at all
+
+ align:start position:0%
+motion so this tells you that at all
+ 
+
+ align:start position:0%
+motion so this tells you that at all
+time the value of the X side does not
+
+ align:start position:0%
+time the value of the X side does not
+ 
+
+ align:start position:0%
+time the value of the X side does not
+change at the end point so what this
+
+ align:start position:0%
+change at the end point so what this
+ 
+
+ align:start position:0%
+change at the end point so what this
+means this directly translate into x
+
+ align:start position:0%
+means this directly translate into x
+ 
+
+ align:start position:0%
+means this directly translate into x
+i Sigma = to zero and T should be a
+
+ align:start position:0%
+i Sigma = to zero and T should be a
+ 
+
+ align:start position:0%
+i Sigma = to zero and T should be a
+constant okay should be a
+
+ align:start position:0%
+constant okay should be a
+ 
+
+ align:start position:0%
+constant okay should be a
+constant so this is the dtive
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+condition and so let's look at some
+
+ align:start position:0%
+condition and so let's look at some
+ 
+
+ align:start position:0%
+condition and so let's look at some
+examples to understand a little bit more
+
+ align:start position:0%
+examples to understand a little bit more
+ 
+
+ align:start position:0%
+examples to understand a little bit more
+explicitly what what this a kind of
+
+ align:start position:0%
+explicitly what what this a kind of
+ 
+
+ align:start position:0%
+explicitly what what this a kind of
+condition uh what this the condition
+
+ align:start position:0%
+condition uh what this the condition
+ 
+
+ align:start position:0%
+condition uh what this the condition
+means okay so let's first consider a
+
+ align:start position:0%
+means okay so let's first consider a
+ 
+
+ align:start position:0%
+means okay so let's first consider a
+example say
+
+ align:start position:0%
+example say
+ 
+
+ align:start position:0%
+example say
+suppose in all
+
+ align:start position:0%
+suppose in all
+ 
+
+ align:start position:0%
+suppose in all
+directions say from zero to D minus
+
+ align:start position:0%
+directions say from zero to D minus
+ 
+
+ align:start position:0%
+directions say from zero to D minus
+2 okay we
+
+ align:start position:0%
+2 okay we
+ 
+
+ align:start position:0%
+2 okay we
+use
+
+ align:start position:0%
+use
+ 
+
+ align:start position:0%
+use
+suppose uh uh uh
+
+ align:start position:0%
+suppose uh uh uh
+ 
+
+ align:start position:0%
+suppose uh uh uh
+use new boundary condition uh uh that's
+
+ align:start position:0%
+use new boundary condition uh uh that's
+ 
+
+ align:start position:0%
+use new boundary condition uh uh that's
+what we be for uh for
+
+ align:start position:0%
+what we be for uh for
+ 
+
+ align:start position:0%
+what we be for uh for
+both Sigma equal to zero and
+
+ align:start position:0%
+both Sigma equal to zero and
+ 
+
+ align:start position:0%
+both Sigma equal to zero and
+Pi but for the last
+
+ align:start position:0%
+Pi but for the last
+ 
+
+ align:start position:0%
+Pi but for the last
+coordinate so X D minus
+
+ align:start position:0%
+coordinate so X D minus
+ 
+
+ align:start position:0%
+coordinate so X D minus
+one okay so let's impose the uh the Der
+
+ align:start position:0%
+one okay so let's impose the uh the Der
+ 
+
+ align:start position:0%
+one okay so let's impose the uh the Der
+boundary condition say let's take it to
+
+ align:start position:0%
+boundary condition say let's take it to
+ 
+
+ align:start position:0%
+boundary condition say let's take it to
+be a at Sigma both Sigma and 0al to Pi
+
+ align:start position:0%
+be a at Sigma both Sigma and 0al to Pi
+ 
+
+ align:start position:0%
+be a at Sigma both Sigma and 0al to Pi
+okay so for the for the moment let's
+
+ align:start position:0%
+okay so for the for the moment let's
+ 
+
+ align:start position:0%
+okay so for the for the moment let's
+take the boundary to be same at both
+
+ align:start position:0%
+take the boundary to be same at both
+ 
+
+ align:start position:0%
+take the boundary to be same at both
+Sigma equal to 0 and
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Pi so let's look at what this condition
+
+ align:start position:0%
+Pi so let's look at what this condition
+ 
+
+ align:start position:0%
+Pi so let's look at what this condition
+means okay let's look at this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+example so what this condition
+
+ align:start position:0%
+example so what this condition
+ 
+
+ align:start position:0%
+example so what this condition
+means so let's draw a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+figure so I cannot draw many directions
+
+ align:start position:0%
+figure so I cannot draw many directions
+ 
+
+ align:start position:0%
+figure so I cannot draw many directions
+in particular cannot draw 626
+
+ align:start position:0%
+in particular cannot draw 626
+ 
+
+ align:start position:0%
+in particular cannot draw 626
+Dimensions so let me call the horizontal
+
+ align:start position:0%
+Dimensions so let me call the horizontal
+ 
+
+ align:start position:0%
+Dimensions so let me call the horizontal
+axis is all the the connection of all
+
+ align:start position:0%
+axis is all the the connection of all
+ 
+
+ align:start position:0%
+axis is all the the connection of all
+the dimensions up to D minus
+
+ align:start position:0%
+the dimensions up to D minus
+ 
+
+ align:start position:0%
+the dimensions up to D minus
+2 and and and this AIS SI is the D minus
+
+ align:start position:0%
+2 and and and this AIS SI is the D minus
+ 
+
+ align:start position:0%
+2 and and and this AIS SI is the D minus
+one
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay then the end point the XD minus y =
+
+ align:start position:0%
+okay then the end point the XD minus y =
+ 
+
+ align:start position:0%
+okay then the end point the XD minus y =
+to a at the end
+
+ align:start position:0%
+to a at the end
+ 
+
+ align:start position:0%
+to a at the end
+point so suppose this is the nine of x
+
+ align:start position:0%
+point so suppose this is the nine of x
+ 
+
+ align:start position:0%
+point so suppose this is the nine of x
+equal
+
+ align:start position:0%
+equal
+ 
+
+ align:start position:0%
+equal
+to a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so suppose this is the hypersurface
+
+ align:start position:0%
+okay so suppose this is the hypersurface
+ 
+
+ align:start position:0%
+okay so suppose this is the hypersurface
+uh for X XD minus y = to a then that
+
+ align:start position:0%
+uh for X XD minus y = to a then that
+ 
+
+ align:start position:0%
+uh for X XD minus y = to a then that
+boundary recogition tells
+
+ align:start position:0%
+boundary recogition tells
+ 
+
+ align:start position:0%
+boundary recogition tells
+you that whatever open string the
+
+ align:start position:0%
+you that whatever open string the
+ 
+
+ align:start position:0%
+you that whatever open string the
+motion the end point must be restricted
+
+ align:start position:0%
+motion the end point must be restricted
+ 
+
+ align:start position:0%
+motion the end point must be restricted
+to this hypers
+
+ align:start position:0%
+to this hypers
+ 
+
+ align:start position:0%
+to this hypers
+surface okay so that what this
+
+ align:start position:0%
+surface okay so that what this
+ 
+
+ align:start position:0%
+surface okay so that what this
+geometrically what this condition means
+
+ align:start position:0%
+geometrically what this condition means
+ 
+
+ align:start position:0%
+geometrically what this condition means
+it it just say let's consider XT minus 1
+
+ align:start position:0%
+it it just say let's consider XT minus 1
+ 
+
+ align:start position:0%
+it it just say let's consider XT minus 1
+= to a which is a hypers Surface in
+
+ align:start position:0%
+= to a which is a hypers Surface in
+ 
+
+ align:start position:0%
+= to a which is a hypers Surface in
+space time and then then the then this
+
+ align:start position:0%
+space time and then then the then this
+ 
+
+ align:start position:0%
+space time and then then the then this
+then this condition means that the Ender
+
+ align:start position:0%
+then this condition means that the Ender
+ 
+
+ align:start position:0%
+then this condition means that the Ender
+point of the
+
+ align:start position:0%
+point of the
+ 
+
+ align:start position:0%
+point of the
+string must be restricted to this
+
+ align:start position:0%
+string must be restricted to this
+ 
+
+ align:start position:0%
+string must be restricted to this
+surface the interior of the string can
+
+ align:start position:0%
+surface the interior of the string can
+ 
+
+ align:start position:0%
+surface the interior of the string can
+be any can be out have low restriction
+
+ align:start position:0%
+be any can be out have low restriction
+ 
+
+ align:start position:0%
+be any can be out have low restriction
+but end the point have to be on this
+
+ align:start position:0%
+but end the point have to be on this
+ 
+
+ align:start position:0%
+but end the point have to be on this
+surface okay is this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+clear okay so you can
+
+ align:start position:0%
+clear okay so you can
+ 
+
+ align:start position:0%
+clear okay so you can
+generalize so this is the first example
+
+ align:start position:0%
+generalize so this is the first example
+ 
+
+ align:start position:0%
+generalize so this is the first example
+you can generalize let's consider X from
+
+ align:start position:0%
+you can generalize let's consider X from
+ 
+
+ align:start position:0%
+you can generalize let's consider X from
+zero to some value
+
+ align:start position:0%
+zero to some value
+ 
+
+ align:start position:0%
+zero to some value
+P of course p is smaller than the total
+
+ align:start position:0%
+P of course p is smaller than the total
+ 
+
+ align:start position:0%
+P of course p is smaller than the total
+number Dimensions which is n for Sigma 0
+
+ align:start position:0%
+number Dimensions which is n for Sigma 0
+ 
+
+ align:start position:0%
+number Dimensions which is n for Sigma 0
+and the
+
+ align:start position:0%
+and the
+ 
+
+ align:start position:0%
+and the
+pi and
+
+ align:start position:0%
+pi and
+ 
+
+ align:start position:0%
+pi and
+then and then the rest say XP +
+
+ align:start position:0%
+then and then the rest say XP +
+ 
+
+ align:start position:0%
+then and then the rest say XP +
+1 XP +
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+2 to XT minus one this directions
+
+ align:start position:0%
+2 to XT minus one this directions
+ 
+
+ align:start position:0%
+2 to XT minus one this directions
+we impos the the boundary
+
+ align:start position:0%
+we impos the the boundary
+ 
+
+ align:start position:0%
+we impos the the boundary
+conditions uh and and let me call this a
+
+ align:start position:0%
+conditions uh and and let me call this a
+ 
+
+ align:start position:0%
+conditions uh and and let me call this a
+some Vector
+
+ align:start position:0%
+some Vector
+ 
+
+ align:start position:0%
+some Vector
+a some Vector a for both Sigma and sigma
+
+ align:start position:0%
+a some Vector a for both Sigma and sigma
+ 
+
+ align:start position:0%
+a some Vector a for both Sigma and sigma
+equal to zero and Pi okay so a just some
+
+ align:start position:0%
+equal to zero and Pi okay so a just some
+ 
+
+ align:start position:0%
+equal to zero and Pi okay so a just some
+constant Vector of the same Dimension as
+
+ align:start position:0%
+constant Vector of the same Dimension as
+ 
+
+ align:start position:0%
+constant Vector of the same Dimension as
+the number of X here okay the same as
+
+ align:start position:0%
+the number of X here okay the same as
+ 
+
+ align:start position:0%
+the number of X here okay the same as
+the number of X here and and this is
+
+ align:start position:0%
+the number of X here and and this is
+ 
+
+ align:start position:0%
+the number of X here and and this is
+just a more General way to impose this
+
+ align:start position:0%
+just a more General way to impose this
+ 
+
+ align:start position:0%
+just a more General way to impose this
+to more directions okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+is this notation
+
+ align:start position:0%
+is this notation
+ 
+
+ align:start position:0%
+is this notation
+clear yes it's why is there a repeated
+
+ align:start position:0%
+clear yes it's why is there a repeated
+ 
+
+ align:start position:0%
+clear yes it's why is there a repeated
+superscript oh sorry pus P plus
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+2 yes and maybe do we talk about like a
+
+ align:start position:0%
+2 yes and maybe do we talk about like a
+ 
+
+ align:start position:0%
+2 yes and maybe do we talk about like a
+different zero and Pi behaviors or is
+
+ align:start position:0%
+different zero and Pi behaviors or is
+ 
+
+ align:start position:0%
+different zero and Pi behaviors or is
+that not interesting no we will talk
+
+ align:start position:0%
+that not interesting no we will talk
+ 
+
+ align:start position:0%
+that not interesting no we will talk
+about that let's look at simple cage
+
+ align:start position:0%
+about that let's look at simple cage
+ 
+
+ align:start position:0%
+about that let's look at simple cage
+first yeah
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so is this notation
+
+ align:start position:0%
+so is this notation
+ 
+
+ align:start position:0%
+so is this notation
+clear so so again I can do this on the
+
+ align:start position:0%
+clear so so again I can do this on the
+ 
+
+ align:start position:0%
+clear so so again I can do this on the
+similar plot like
+
+ align:start position:0%
+similar plot like
+ 
+
+ align:start position:0%
+similar plot like
+this so now horizontal
+
+ align:start position:0%
+this so now horizontal
+ 
+
+ align:start position:0%
+this so now horizontal
+axis I do x0 to p and vertical axis I do
+
+ align:start position:0%
+axis I do x0 to p and vertical axis I do
+ 
+
+ align:start position:0%
+axis I do x0 to p and vertical axis I do
+p p + 1 all the way to D minus one so
+
+ align:start position:0%
+p p + 1 all the way to D minus one so
+ 
+
+ align:start position:0%
+p p + 1 all the way to D minus one so
+now both axis are multiple
+
+ align:start position:0%
+now both axis are multiple
+ 
+
+ align:start position:0%
+now both axis are multiple
+dimensional and then
+
+ align:start position:0%
+dimensional and then
+ 
+
+ align:start position:0%
+dimensional and then
+this this specifies
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so this
+
+ align:start position:0%
+so this
+ 
+
+ align:start position:0%
+so this
+a specifies a
+
+ align:start position:0%
+a specifies a
+ 
+
+ align:start position:0%
+a specifies a
+p plus one
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+dimensional hypersurface uh
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+surface right so
+
+ align:start position:0%
+surface right so
+ 
+
+ align:start position:0%
+surface right so
+this so so the value of those coordinate
+
+ align:start position:0%
+this so so the value of those coordinate
+ 
+
+ align:start position:0%
+this so so the value of those coordinate
+are
+
+ align:start position:0%
+are
+ 
+
+ align:start position:0%
+are
+fixed but the value of those coordinate
+
+ align:start position:0%
+fixed but the value of those coordinate
+ 
+
+ align:start position:0%
+fixed but the value of those coordinate
+can be arbitrary
+
+ align:start position:0%
+can be arbitrary
+ 
+
+ align:start position:0%
+can be arbitrary
+so so there's p+ one fre parameter here
+
+ align:start position:0%
+so so there's p+ one fre parameter here
+ 
+
+ align:start position:0%
+so so there's p+ one fre parameter here
+okay and so this is p+1 dimensional
+
+ align:start position:0%
+okay and so this is p+1 dimensional
+ 
+
+ align:start position:0%
+okay and so this is p+1 dimensional
+surface in the space time and this
+
+ align:start position:0%
+surface in the space time and this
+ 
+
+ align:start position:0%
+surface in the space time and this
+condition means that the end point of
+
+ align:start position:0%
+condition means that the end point of
+ 
+
+ align:start position:0%
+condition means that the end point of
+the whatever open string must be
+
+ align:start position:0%
+the whatever open string must be
+ 
+
+ align:start position:0%
+the whatever open string must be
+restricted to this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+surface okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+is the picture
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+clear yes
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+sorry yeah we are talking about the how
+
+ align:start position:0%
+sorry yeah we are talking about the how
+ 
+
+ align:start position:0%
+sorry yeah we are talking about the how
+to impose the uh uh what's the meaning
+
+ align:start position:0%
+to impose the uh uh what's the meaning
+ 
+
+ align:start position:0%
+to impose the uh uh what's the meaning
+of impose the dally boundary
+
+ align:start position:0%
+of impose the dally boundary
+ 
+
+ align:start position:0%
+of impose the dally boundary
+condition instead of Luman boundary
+
+ align:start position:0%
+condition instead of Luman boundary
+ 
+
+ align:start position:0%
+condition instead of Luman boundary
+condition so we now impose the dur
+
+ align:start position:0%
+condition so we now impose the dur
+ 
+
+ align:start position:0%
+condition so we now impose the dur
+boundary condition which corresponding
+
+ align:start position:0%
+boundary condition which corresponding
+ 
+
+ align:start position:0%
+boundary condition which corresponding
+to the evaluation of the end point
+
+ align:start position:0%
+to the evaluation of the end point
+ 
+
+ align:start position:0%
+to the evaluation of the end point
+should be
+
+ align:start position:0%
+should be
+ 
+
+ align:start position:0%
+should be
+zero and then this can be specified by
+
+ align:start position:0%
+zero and then this can be specified by
+ 
+
+ align:start position:0%
+zero and then this can be specified by
+the end point you take some constant
+
+ align:start position:0%
+the end point you take some constant
+ 
+
+ align:start position:0%
+the end point you take some constant
+value and so that's the
+
+ align:start position:0%
+value and so that's the
+ 
+
+ align:start position:0%
+value and so that's the
+geometric um way to think about this D
+
+ align:start position:0%
+geometric um way to think about this D
+ 
+
+ align:start position:0%
+geometric um way to think about this D
+different der boundary
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+conditions
+
+ align:start position:0%
+conditions
+ 
+
+ align:start position:0%
+conditions
+okay so if you look at this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+naivity so previously when we consider
+
+ align:start position:0%
+naivity so previously when we consider
+ 
+
+ align:start position:0%
+naivity so previously when we consider
+the num boundary condition condition for
+
+ align:start position:0%
+the num boundary condition condition for
+ 
+
+ align:start position:0%
+the num boundary condition condition for
+all
+
+ align:start position:0%
+all
+ 
+
+ align:start position:0%
+all
+directions then then string then there's
+
+ align:start position:0%
+directions then then string then there's
+ 
+
+ align:start position:0%
+directions then then string then there's
+no
+
+ align:start position:0%
+no
+ 
+
+ align:start position:0%
+no
+restriction to the string then the
+
+ align:start position:0%
+restriction to the string then the
+ 
+
+ align:start position:0%
+restriction to the string then the
+string can move anywhere okay so now
+
+ align:start position:0%
+string can move anywhere okay so now
+ 
+
+ align:start position:0%
+string can move anywhere okay so now
+when you when in some directions you
+
+ align:start position:0%
+when you when in some directions you
+ 
+
+ align:start position:0%
+when you when in some directions you
+impose the Der condition then we see
+
+ align:start position:0%
+impose the Der condition then we see
+ 
+
+ align:start position:0%
+impose the Der condition then we see
+that the the motion of the string get
+
+ align:start position:0%
+that the the motion of the string get
+ 
+
+ align:start position:0%
+that the the motion of the string get
+restricted and at this end point now
+
+ align:start position:0%
+restricted and at this end point now
+ 
+
+ align:start position:0%
+restricted and at this end point now
+have to some some sof dimension of the
+
+ align:start position:0%
+have to some some sof dimension of the
+ 
+
+ align:start position:0%
+have to some some sof dimension of the
+space
+
+ align:start position:0%
+space
+ 
+
+ align:start position:0%
+space
+time okay
+
+ align:start position:0%
+time okay
+ 
+
+ align:start position:0%
+time okay
+so at the first side this may seems to
+
+ align:start position:0%
+so at the first side this may seems to
+ 
+
+ align:start position:0%
+so at the first side this may seems to
+be a nonsensical thing to do just you
+
+ align:start position:0%
+be a nonsensical thing to do just you
+ 
+
+ align:start position:0%
+be a nonsensical thing to do just you
+say h you ask why somehow I have to
+
+ align:start position:0%
+say h you ask why somehow I have to
+ 
+
+ align:start position:0%
+say h you ask why somehow I have to
+restrict some open strings to some sub
+
+ align:start position:0%
+restrict some open strings to some sub
+ 
+
+ align:start position:0%
+restrict some open strings to some sub
+manifold in the space time okay so why
+
+ align:start position:0%
+manifold in the space time okay so why
+ 
+
+ align:start position:0%
+manifold in the space time okay so why
+should I do that in particular that
+
+ align:start position:0%
+should I do that in particular that
+ 
+
+ align:start position:0%
+should I do that in particular that
+breaks Len symmetry okay in particular
+
+ align:start position:0%
+breaks Len symmetry okay in particular
+ 
+
+ align:start position:0%
+breaks Len symmetry okay in particular
+that breaks Len so the last thing about
+
+ align:start position:0%
+that breaks Len so the last thing about
+ 
+
+ align:start position:0%
+that breaks Len so the last thing about
+the uh uh uh the new man bation we did
+
+ align:start position:0%
+the uh uh uh the new man bation we did
+ 
+
+ align:start position:0%
+the uh uh uh the new man bation we did
+before in all directions so that respect
+
+ align:start position:0%
+before in all directions so that respect
+ 
+
+ align:start position:0%
+before in all directions so that respect
+Len Symmetry and once you introduce some
+
+ align:start position:0%
+Len Symmetry and once you introduce some
+ 
+
+ align:start position:0%
+Len Symmetry and once you introduce some
+directions the D boundary condition you
+
+ align:start position:0%
+directions the D boundary condition you
+ 
+
+ align:start position:0%
+directions the D boundary condition you
+necessarily break Len symmetry because
+
+ align:start position:0%
+necessarily break Len symmetry because
+ 
+
+ align:start position:0%
+necessarily break Len symmetry because
+you because you select out some SP
+
+ align:start position:0%
+you because you select out some SP
+ 
+
+ align:start position:0%
+you because you select out some SP
+select out some directions versus some
+
+ align:start position:0%
+select out some directions versus some
+ 
+
+ align:start position:0%
+select out some directions versus some
+other okay and uh and so you necessarily
+
+ align:start position:0%
+other okay and uh and so you necessarily
+ 
+
+ align:start position:0%
+other okay and uh and so you necessarily
+break L symmetry you also break
+
+ align:start position:0%
+break L symmetry you also break
+ 
+
+ align:start position:0%
+break L symmetry you also break
+translation
+
+ align:start position:0%
+translation
+ 
+
+ align:start position:0%
+translation
+symmetry because the uh because the yeah
+
+ align:start position:0%
+symmetry because the uh because the yeah
+ 
+
+ align:start position:0%
+symmetry because the uh because the yeah
+you have to specify some sub manifold
+
+ align:start position:0%
+you have to specify some sub manifold
+ 
+
+ align:start position:0%
+you have to specify some sub manifold
+you also break the translations
+
+ align:start position:0%
+you also break the translations
+ 
+
+ align:start position:0%
+you also break the translations
+image so as side this seems to be a
+
+ align:start position:0%
+image so as side this seems to be a
+ 
+
+ align:start position:0%
+image so as side this seems to be a
+nonsensical thing to do so that's why
+
+ align:start position:0%
+nonsensical thing to do so that's why
+ 
+
+ align:start position:0%
+nonsensical thing to do so that's why
+for many years actually people did not
+
+ align:start position:0%
+for many years actually people did not
+ 
+
+ align:start position:0%
+for many years actually people did not
+look at this object even
+
+ align:start position:0%
+look at this object even
+ 
+
+ align:start position:0%
+look at this object even
+though even though for a person to to
+
+ align:start position:0%
+though even though for a person to to
+ 
+
+ align:start position:0%
+though even though for a person to to
+work out screen theory on the first
+
+ align:start position:0%
+work out screen theory on the first
+ 
+
+ align:start position:0%
+work out screen theory on the first
+day you you should already realize the
+
+ align:start position:0%
+day you you should already realize the
+ 
+
+ align:start position:0%
+day you you should already realize the
+boundary conditions okay but for many
+
+ align:start position:0%
+boundary conditions okay but for many
+ 
+
+ align:start position:0%
+boundary conditions okay but for many
+years people did not pay attention to
+
+ align:start position:0%
+years people did not pay attention to
+ 
+
+ align:start position:0%
+years people did not pay attention to
+this kind of bound
+
+ align:start position:0%
+this kind of bound
+ 
+
+ align:start position:0%
+this kind of bound
+Recs but in
+
+ align:start position:0%
+Recs but in
+ 
+
+ align:start position:0%
+Recs but in
+out those that's B recognitions plays a
+
+ align:start position:0%
+out those that's B recognitions plays a
+ 
+
+ align:start position:0%
+out those that's B recognitions plays a
+key role in stren
+
+ align:start position:0%
+key role in stren
+ 
+
+ align:start position:0%
+key role in stren
+theory and the
+
+ align:start position:0%
+theory and the
+ 
+
+ align:start position:0%
+theory and the
+key is to take a slight different
+
+ align:start position:0%
+key is to take a slight different
+ 
+
+ align:start position:0%
+key is to take a slight different
+perspective at those sub manifold
+
+ align:start position:0%
+perspective at those sub manifold
+ 
+
+ align:start position:0%
+perspective at those sub manifold
+okay so now what you should think about
+
+ align:start position:0%
+okay so now what you should think about
+ 
+
+ align:start position:0%
+okay so now what you should think about
+is
+
+ align:start position:0%
+is
+ 
+
+ align:start position:0%
+is
+now what you think about is the
+
+ align:start position:0%
+now what you think about is the
+ 
+
+ align:start position:0%
+now what you think about is the
+following so you think about maybe for
+
+ align:start position:0%
+following so you think about maybe for
+ 
+
+ align:start position:0%
+following so you think about maybe for
+the whole space
+
+ align:start position:0%
+the whole space
+ 
+
+ align:start position:0%
+the whole space
+time for the whole space time time only
+
+ align:start position:0%
+time for the whole space time time only
+ 
+
+ align:start position:0%
+time for the whole space time time only
+close string is the most natural object
+
+ align:start position:0%
+close string is the most natural object
+ 
+
+ align:start position:0%
+close string is the most natural object
+they can move
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+anywhere but then there are some special
+
+ align:start position:0%
+anywhere but then there are some special
+ 
+
+ align:start position:0%
+anywhere but then there are some special
+places in the in the space
+
+ align:start position:0%
+places in the in the space
+ 
+
+ align:start position:0%
+places in the in the space
+time some kind of
+
+ align:start position:0%
+time some kind of
+ 
+
+ align:start position:0%
+time some kind of
+defect and at those defect the closed
+
+ align:start position:0%
+defect and at those defect the closed
+ 
+
+ align:start position:0%
+defect and at those defect the closed
+string can break to become open
+
+ align:start position:0%
+string can break to become open
+ 
+
+ align:start position:0%
+string can break to become open
+string okay can become open stren and if
+
+ align:start position:0%
+string okay can become open stren and if
+ 
+
+ align:start position:0%
+string okay can become open stren and if
+you take that perspective then that give
+
+ align:start position:0%
+you take that perspective then that give
+ 
+
+ align:start position:0%
+you take that perspective then that give
+special meaning to such kind of special
+
+ align:start position:0%
+special meaning to such kind of special
+ 
+
+ align:start position:0%
+special meaning to such kind of special
+sub manifold which open string can end
+
+ align:start position:0%
+sub manifold which open string can end
+ 
+
+ align:start position:0%
+sub manifold which open string can end
+then then there's some kind of object
+
+ align:start position:0%
+then then there's some kind of object
+ 
+
+ align:start position:0%
+then then there's some kind of object
+there because the existence of certain
+
+ align:start position:0%
+there because the existence of certain
+ 
+
+ align:start position:0%
+there because the existence of certain
+object there then then the open the then
+
+ align:start position:0%
+object there then then the open the then
+ 
+
+ align:start position:0%
+object there then then the open the then
+then the open string can end there okay
+
+ align:start position:0%
+then the open string can end there okay
+ 
+
+ align:start position:0%
+then the open string can end there okay
+yes so indeed if you have that
+
+ align:start position:0%
+yes so indeed if you have that
+ 
+
+ align:start position:0%
+yes so indeed if you have that
+perspective then instead of having it
+
+ align:start position:0%
+perspective then instead of having it
+ 
+
+ align:start position:0%
+perspective then instead of having it
+lie along hyperplanes I mean is it more
+
+ align:start position:0%
+lie along hyperplanes I mean is it more
+ 
+
+ align:start position:0%
+lie along hyperplanes I mean is it more
+natural to have it just lie upon some
+
+ align:start position:0%
+natural to have it just lie upon some
+ 
+
+ align:start position:0%
+natural to have it just lie upon some
+other manifold oh you can yeah I'm just
+
+ align:start position:0%
+other manifold oh you can yeah I'm just
+ 
+
+ align:start position:0%
+other manifold oh you can yeah I'm just
+taking you I'm just sending you the simp
+
+ align:start position:0%
+taking you I'm just sending you the simp
+ 
+
+ align:start position:0%
+taking you I'm just sending you the simp
+example and and once you realize in this
+
+ align:start position:0%
+example and and once you realize in this
+ 
+
+ align:start position:0%
+example and and once you realize in this
+simple example then you can then you can
+
+ align:start position:0%
+simple example then you can then you can
+ 
+
+ align:start position:0%
+simple example then you can then you can
+generalize the OB complicated scenario
+
+ align:start position:0%
+generalize the OB complicated scenario
+ 
+
+ align:start position:0%
+generalize the OB complicated scenario
+you can imagine yeah now let's just
+
+ align:start position:0%
+you can imagine yeah now let's just
+ 
+
+ align:start position:0%
+you can imagine yeah now let's just
+think about in the simplest
+
+ align:start position:0%
+think about in the simplest
+ 
+
+ align:start position:0%
+think about in the simplest
+case imposing those boundary condition
+
+ align:start position:0%
+case imposing those boundary condition
+ 
+
+ align:start position:0%
+case imposing those boundary condition
+become
+
+ align:start position:0%
+become
+ 
+
+ align:start position:0%
+become
+natural if you think
+
+ align:start position:0%
+natural if you think
+ 
+
+ align:start position:0%
+natural if you think
+those those places in space time are
+
+ align:start position:0%
+those those places in space time are
+ 
+
+ align:start position:0%
+those those places in space time are
+special places which which something can
+
+ align:start position:0%
+special places which which something can
+ 
+
+ align:start position:0%
+special places which which something can
+happen is not the same as other places
+
+ align:start position:0%
+happen is not the same as other places
+ 
+
+ align:start position:0%
+happen is not the same as other places
+okay and and to say those spaces are
+
+ align:start position:0%
+okay and and to say those spaces are
+ 
+
+ align:start position:0%
+okay and and to say those spaces are
+happen so you give a
+
+ align:start position:0%
+happen so you give a
+ 
+
+ align:start position:0%
+happen so you give a
+l so so you
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+imagine so for example you can
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+imagine
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+some SpaceTime
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+defect so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+sitting at say this x p +
+
+ align:start position:0%
+sitting at say this x p +
+ 
+
+ align:start position:0%
+sitting at say this x p +
+
+ align:start position:0%
+ 
+
+ align:start position:0%
+x = to
+
+ align:start position:0%
+x = to
+ 
+
+ align:start position:0%
+x = to
+a okay sitting at that
+
+ align:start position:0%
+a okay sitting at that
+ 
+
+ align:start position:0%
+a okay sitting at that
+[Applause]
+
+ align:start position:0%
+[Applause]
+ 
+
+ align:start position:0%
+[Applause]
+location so where open string can end
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so such a defect we call it de
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+brain we give a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+[Applause]
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+lame
+
+ align:start position:0%
+lame
+ 
+
+ align:start position:0%
+lame
+okay so D is clear because it's a dally
+
+ align:start position:0%
+okay so D is clear because it's a dally
+ 
+
+ align:start position:0%
+okay so D is clear because it's a dally
+binary condition and the Brain because
+
+ align:start position:0%
+binary condition and the Brain because
+ 
+
+ align:start position:0%
+binary condition and the Brain because
+it's some extended surface
+
+ align:start position:0%
+it's some extended surface
+ 
+
+ align:start position:0%
+it's some extended surface
+[Applause]
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay and uh so we often use the rotation
+
+ align:start position:0%
+okay and uh so we often use the rotation
+ 
+
+ align:start position:0%
+okay and uh so we often use the rotation
+say DP
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+brain so P delot the L of spatial
+
+ align:start position:0%
+brain so P delot the L of spatial
+ 
+
+ align:start position:0%
+brain so P delot the L of spatial
+Dimensions along the brain okay so in
+
+ align:start position:0%
+Dimensions along the brain okay so in
+ 
+
+ align:start position:0%
+Dimensions along the brain okay so in
+this case there's a p spatial Dimensions
+
+ align:start position:0%
+this case there's a p spatial Dimensions
+ 
+
+ align:start position:0%
+this case there's a p spatial Dimensions
+along the plane along the plane along
+
+ align:start position:0%
+along the plane along the plane along
+ 
+
+ align:start position:0%
+along the plane along the plane along
+the uh uh this uh uh um uh brain so we
+
+ align:start position:0%
+the uh uh this uh uh um uh brain so we
+ 
+
+ align:start position:0%
+the uh uh this uh uh um uh brain so we
+call DP brain
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so right
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+now right now DP brain is merely just a
+
+ align:start position:0%
+now right now DP brain is merely just a
+ 
+
+ align:start position:0%
+now right now DP brain is merely just a
+place which you impose a boundary
+
+ align:start position:0%
+place which you impose a boundary
+ 
+
+ align:start position:0%
+place which you impose a boundary
+conditions which open string uh uh which
+
+ align:start position:0%
+conditions which open string uh uh which
+ 
+
+ align:start position:0%
+conditions which open string uh uh which
+open strings uh can can end but we will
+
+ align:start position:0%
+open strings uh can can end but we will
+ 
+
+ align:start position:0%
+open strings uh can can end but we will
+soon see that actually a DE is a dynamic
+
+ align:start position:0%
+soon see that actually a DE is a dynamic
+ 
+
+ align:start position:0%
+soon see that actually a DE is a dynamic
+object and it's actually a dynamic
+
+ align:start position:0%
+object and it's actually a dynamic
+ 
+
+ align:start position:0%
+object and it's actually a dynamic
+object and this actually can moves can
+
+ align:start position:0%
+object and this actually can moves can
+ 
+
+ align:start position:0%
+object and this actually can moves can
+can fluctuates can can jump around Etc
+
+ align:start position:0%
+can fluctuates can can jump around Etc
+ 
+
+ align:start position:0%
+can fluctuates can can jump around Etc
+okay and uh so also from this
+
+ align:start position:0%
+okay and uh so also from this
+ 
+
+ align:start position:0%
+okay and uh so also from this
+perspective our previous Newman boundary
+
+ align:start position:0%
+perspective our previous Newman boundary
+ 
+
+ align:start position:0%
+perspective our previous Newman boundary
+condition if we have
+
+ align:start position:0%
+condition if we have
+ 
+
+ align:start position:0%
+condition if we have
+Luman in all
+
+ align:start position:0%
+Luman in all
+ 
+
+ align:start position:0%
+Luman in all
+Direction so if we have Lan boundary
+
+ align:start position:0%
+Direction so if we have Lan boundary
+ 
+
+ align:start position:0%
+Direction so if we have Lan boundary
+condition in all directions
+
+ align:start position:0%
+condition in all directions
+ 
+
+ align:start position:0%
+condition in all directions
+[Applause]
+
+ align:start position:0%
+[Applause]
+ 
+
+ align:start position:0%
+[Applause]
+then in this
+
+ align:start position:0%
+then in this
+ 
+
+ align:start position:0%
+then in this
+case the open string can end
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+everywhere and
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+anywhere from this New
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Perspective from this New Perspective we
+
+ align:start position:0%
+Perspective from this New Perspective we
+ 
+
+ align:start position:0%
+Perspective from this New Perspective we
+call this a space fing
+
+ align:start position:0%
+call this a space fing
+ 
+
+ align:start position:0%
+call this a space fing
+brain we call that this
+
+ align:start position:0%
+brain we call that this
+ 
+
+ align:start position:0%
+brain we call that this
+a a space fing
+
+ align:start position:0%
+a a space fing
+ 
+
+ align:start position:0%
+a a space fing
+[Applause]
+
+ align:start position:0%
+[Applause]
+ 
+
+ align:start position:0%
+[Applause]
+brain
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so so the Der bound the Lum
+
+ align:start position:0%
+okay so so the Der bound the Lum
+ 
+
+ align:start position:0%
+okay so so the Der bound the Lum
+boundary condition we considered before
+
+ align:start position:0%
+boundary condition we considered before
+ 
+
+ align:start position:0%
+boundary condition we considered before
+uh should be considered as actually you
+
+ align:start position:0%
+uh should be considered as actually you
+ 
+
+ align:start position:0%
+uh should be considered as actually you
+feel the whole space time with such a
+
+ align:start position:0%
+feel the whole space time with such a
+ 
+
+ align:start position:0%
+feel the whole space time with such a
+brain and then uh then uh then the
+
+ align:start position:0%
+brain and then uh then uh then the
+ 
+
+ align:start position:0%
+brain and then uh then uh then the
+string can in principle move anywhere so
+
+ align:start position:0%
+string can in principle move anywhere so
+ 
+
+ align:start position:0%
+string can in principle move anywhere so
+for example in the bosonic string we
+
+ align:start position:0%
+for example in the bosonic string we
+ 
+
+ align:start position:0%
+for example in the bosonic string we
+talked about
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+before this group corresponding to a d25
+
+ align:start position:0%
+before this group corresponding to a d25
+ 
+
+ align:start position:0%
+before this group corresponding to a d25
+brain
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+say d25 brain because there's 25 spatial
+
+ align:start position:0%
+say d25 brain because there's 25 spatial
+ 
+
+ align:start position:0%
+say d25 brain because there's 25 spatial
+Dimensions
+
+ align:start position:0%
+Dimensions
+ 
+
+ align:start position:0%
+Dimensions
+okay such a brain when you impose the
+
+ align:start position:0%
+okay such a brain when you impose the
+ 
+
+ align:start position:0%
+okay such a brain when you impose the
+Aluma boundary condition all directions
+
+ align:start position:0%
+Aluma boundary condition all directions
+ 
+
+ align:start position:0%
+Aluma boundary condition all directions
+or if you are in the Super
+
+ align:start position:0%
+or if you are in the Super
+ 
+
+ align:start position:0%
+or if you are in the Super
+string which the total number of space
+
+ align:start position:0%
+string which the total number of space
+ 
+
+ align:start position:0%
+string which the total number of space
+time is 10 and then the spatial number
+
+ align:start position:0%
+time is 10 and then the spatial number
+ 
+
+ align:start position:0%
+time is 10 and then the spatial number
+spatial Dimension is nine then you have
+
+ align:start position:0%
+spatial Dimension is nine then you have
+ 
+
+ align:start position:0%
+spatial Dimension is nine then you have
+dine then these are the dine brains
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+any questions about
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this yes um these B
+
+ align:start position:0%
+this yes um these B
+ 
+
+ align:start position:0%
+this yes um these B
+conditions they're imposed like they're
+
+ align:start position:0%
+conditions they're imposed like they're
+ 
+
+ align:start position:0%
+conditions they're imposed like they're
+imposed at the quantum level right it's
+
+ align:start position:0%
+imposed at the quantum level right it's
+ 
+
+ align:start position:0%
+imposed at the quantum level right it's
+not just that the classical solution um
+
+ align:start position:0%
+not just that the classical solution um
+ 
+
+ align:start position:0%
+not just that the classical solution um
+has to have end points on the Ste but is
+
+ align:start position:0%
+has to have end points on the Ste but is
+ 
+
+ align:start position:0%
+has to have end points on the Ste but is
+the the fluctuations around the
+
+ align:start position:0%
+the the fluctuations around the
+ 
+
+ align:start position:0%
+the the fluctuations around the
+classical solution that we consider yeah
+
+ align:start position:0%
+classical solution that we consider yeah
+ 
+
+ align:start position:0%
+classical solution that we consider yeah
+we will talk about that uh we will talk
+
+ align:start position:0%
+we will talk about that uh we will talk
+ 
+
+ align:start position:0%
+we will talk about that uh we will talk
+about
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um any other
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+questions
+
+ align:start position:0%
+questions
+ 
+
+ align:start position:0%
+questions
+good so so let me make a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+load you can in principle impress the
+
+ align:start position:0%
+load you can in principle impress the
+ 
+
+ align:start position:0%
+load you can in principle impress the
+Der B condition in any direction you
+
+ align:start position:0%
+Der B condition in any direction you
+ 
+
+ align:start position:0%
+Der B condition in any direction you
+like except in the x0
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+direction okay it because x0 cannot be a
+
+ align:start position:0%
+direction okay it because x0 cannot be a
+ 
+
+ align:start position:0%
+direction okay it because x0 cannot be a
+constant x0 have so x0 is the time is
+
+ align:start position:0%
+constant x0 have so x0 is the time is
+ 
+
+ align:start position:0%
+constant x0 have so x0 is the time is
+our real time in the in the minkovsky
+
+ align:start position:0%
+our real time in the in the minkovsky
+ 
+
+ align:start position:0%
+our real time in the in the minkovsky
+space so the scream moves in this
+
+ align:start position:0%
+space so the scream moves in this
+ 
+
+ align:start position:0%
+space so the scream moves in this
+minkovski space time and this x0 is that
+
+ align:start position:0%
+minkovski space time and this x0 is that
+ 
+
+ align:start position:0%
+minkovski space time and this x0 is that
+time and the time cannot stand still
+
+ align:start position:0%
+time and the time cannot stand still
+ 
+
+ align:start position:0%
+time and the time cannot stand still
+okay in order to have this you need the
+
+ align:start position:0%
+okay in order to have this you need the
+ 
+
+ align:start position:0%
+okay in order to have this you need the
+you need that uh uh location to stand
+
+ align:start position:0%
+you need that uh uh location to stand
+ 
+
+ align:start position:0%
+you need that uh uh location to stand
+still and the uh the time cannot stand
+
+ align:start position:0%
+still and the uh the time cannot stand
+ 
+
+ align:start position:0%
+still and the uh the time cannot stand
+still so so so this cannot be a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+constant so
+
+ align:start position:0%
+constant so
+ 
+
+ align:start position:0%
+constant so
+um so you cannot imp
+
+ align:start position:0%
+um so you cannot imp
+ 
+
+ align:start position:0%
+um so you cannot imp
+uh the dtive boundary condition in the
+
+ align:start position:0%
+uh the dtive boundary condition in the
+ 
+
+ align:start position:0%
+uh the dtive boundary condition in the
+time
+
+ align:start position:0%
+time
+ 
+
+ align:start position:0%
+time
+Direction so the
+
+ align:start position:0%
+Direction so the
+ 
+
+ align:start position:0%
+Direction so the
+smallest in the minkovski space time the
+
+ align:start position:0%
+smallest in the minkovski space time the
+ 
+
+ align:start position:0%
+smallest in the minkovski space time the
+smallest will be a dzero
+
+ align:start position:0%
+smallest will be a dzero
+ 
+
+ align:start position:0%
+smallest will be a dzero
+brain which impose the D bound condition
+
+ align:start position:0%
+brain which impose the D bound condition
+ 
+
+ align:start position:0%
+brain which impose the D bound condition
+in all spal directions except in time in
+
+ align:start position:0%
+in all spal directions except in time in
+ 
+
+ align:start position:0%
+in all spal directions except in time in
+time you always impose the Lum then then
+
+ align:start position:0%
+time you always impose the Lum then then
+ 
+
+ align:start position:0%
+time you always impose the Lum then then
+the small a small situation would be
+
+ align:start position:0%
+the small a small situation would be
+ 
+
+ align:start position:0%
+the small a small situation would be
+called D zero
+
+ align:start position:0%
+called D zero
+ 
+
+ align:start position:0%
+called D zero
+brain which is a point and then the open
+
+ align:start position:0%
+brain which is a point and then the open
+ 
+
+ align:start position:0%
+brain which is a point and then the open
+string can end on this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+point
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+[Music]
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay yes so a question so this idea
+
+ align:start position:0%
+okay yes so a question so this idea
+ 
+
+ align:start position:0%
+okay yes so a question so this idea
+about calling um the the the noon or
+
+ align:start position:0%
+about calling um the the the noon or
+ 
+
+ align:start position:0%
+about calling um the the the noon or
+boundary conditions uh to like d25
+
+ align:start position:0%
+boundary conditions uh to like d25
+ 
+
+ align:start position:0%
+boundary conditions uh to like d25
+brains or D9 brains so this is a little
+
+ align:start position:0%
+brains or D9 brains so this is a little
+ 
+
+ align:start position:0%
+brains or D9 brains so this is a little
+bit perplexing because it seems like not
+
+ align:start position:0%
+bit perplexing because it seems like not
+ 
+
+ align:start position:0%
+bit perplexing because it seems like not
+imposing d clay boundary conditions this
+
+ align:start position:0%
+imposing d clay boundary conditions this
+ 
+
+ align:start position:0%
+imposing d clay boundary conditions this
+implies that not imposing d clay
+
+ align:start position:0%
+implies that not imposing d clay
+ 
+
+ align:start position:0%
+implies that not imposing d clay
+boundary conditions is equivalent to
+
+ align:start position:0%
+boundary conditions is equivalent to
+ 
+
+ align:start position:0%
+boundary conditions is equivalent to
+applying NOS which is not they're not
+
+ align:start position:0%
+applying NOS which is not they're not
+ 
+
+ align:start position:0%
+applying NOS which is not they're not
+like I mean they're like mutually
+
+ align:start position:0%
+like I mean they're like mutually
+ 
+
+ align:start position:0%
+like I mean they're like mutually
+exclusive it's not like so I mean I
+
+ align:start position:0%
+exclusive it's not like so I mean I
+ 
+
+ align:start position:0%
+exclusive it's not like so I mean I
+don't understand why it is that so so
+
+ align:start position:0%
+don't understand why it is that so so
+ 
+
+ align:start position:0%
+don't understand why it is that so so
+does this thing behave like a 24 brain
+
+ align:start position:0%
+does this thing behave like a 24 brain
+ 
+
+ align:start position:0%
+does this thing behave like a 24 brain
+like does it have the same properties as
+
+ align:start position:0%
+like does it have the same properties as
+ 
+
+ align:start position:0%
+like does it have the same properties as
+like a 24 brain or something like that
+
+ align:start position:0%
+like a 24 brain or something like that
+ 
+
+ align:start position:0%
+like a 24 brain or something like that
+which you mean 25 brain so what I'm
+
+ align:start position:0%
+which you mean 25 brain so what I'm
+ 
+
+ align:start position:0%
+which you mean 25 brain so what I'm
+saying is that it seems that the nomon
+
+ align:start position:0%
+saying is that it seems that the nomon
+ 
+
+ align:start position:0%
+saying is that it seems that the nomon
+boundary conditions have a different
+
+ align:start position:0%
+boundary conditions have a different
+ 
+
+ align:start position:0%
+boundary conditions have a different
+character than like a different flavor
+
+ align:start position:0%
+character than like a different flavor
+ 
+
+ align:start position:0%
+character than like a different flavor
+of how they work than the d clay
+
+ align:start position:0%
+of how they work than the d clay
+ 
+
+ align:start position:0%
+of how they work than the d clay
+boundary conditions so it just seems
+
+ align:start position:0%
+boundary conditions so it just seems
+ 
+
+ align:start position:0%
+boundary conditions so it just seems
+strange to me that you would still call
+
+ align:start position:0%
+strange to me that you would still call
+ 
+
+ align:start position:0%
+strange to me that you would still call
+it a brain like a d25 when um no um so
+
+ align:start position:0%
+it a brain like a d25 when um no um so
+ 
+
+ align:start position:0%
+it a brain like a d25 when um no um so
+so in those
+
+ align:start position:0%
+so in those
+ 
+
+ align:start position:0%
+so in those
+cases in those case for example in this
+
+ align:start position:0%
+cases in those case for example in this
+ 
+
+ align:start position:0%
+cases in those case for example in this
+case which we have L condition all the
+
+ align:start position:0%
+case which we have L condition all the
+ 
+
+ align:start position:0%
+case which we have L condition all the
+other directions except one then this is
+
+ align:start position:0%
+other directions except one then this is
+ 
+
+ align:start position:0%
+other directions except one then this is
+a 24 dimensional then this is a 25
+
+ align:start position:0%
+a 24 dimensional then this is a 25
+ 
+
+ align:start position:0%
+a 24 dimensional then this is a 25
+dimensional manifold which the string uh
+
+ align:start position:0%
+dimensional manifold which the string uh
+ 
+
+ align:start position:0%
+dimensional manifold which the string uh
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+on and uh I just oh I see course so
+
+ align:start position:0%
+on and uh I just oh I see course so
+ 
+
+ align:start position:0%
+on and uh I just oh I see course so
+right you have to apply the all the
+
+ align:start position:0%
+right you have to apply the all the
+ 
+
+ align:start position:0%
+right you have to apply the all the
+other okay I I understand yeah yeah yeah
+
+ align:start position:0%
+other okay I I understand yeah yeah yeah
+ 
+
+ align:start position:0%
+other okay I I understand yeah yeah yeah
+yeah so it's yeah any other
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+questions okay
+
+ align:start position:0%
+questions okay
+ 
+
+ align:start position:0%
+questions okay
+good so now let's consider more
+
+ align:start position:0%
+good so now let's consider more
+ 
+
+ align:start position:0%
+good so now let's consider more
+complicated slightly more complicated
+
+ align:start position:0%
+complicated slightly more complicated
+ 
+
+ align:start position:0%
+complicated slightly more complicated
+boundary conditions so by introducing
+
+ align:start position:0%
+boundary conditions so by introducing
+ 
+
+ align:start position:0%
+boundary conditions so by introducing
+this deep
+
+ align:start position:0%
+this deep
+ 
+
+ align:start position:0%
+this deep
+brain now you can actually you can have
+
+ align:start position:0%
+brain now you can actually you can have
+ 
+
+ align:start position:0%
+brain now you can actually you can have
+all different possible bound conditions
+
+ align:start position:0%
+all different possible bound conditions
+ 
+
+ align:start position:0%
+all different possible bound conditions
+as we said here there for each Direction
+
+ align:start position:0%
+as we said here there for each Direction
+ 
+
+ align:start position:0%
+as we said here there for each Direction
+you have can have in principle four
+
+ align:start position:0%
+you have can have in principle four
+ 
+
+ align:start position:0%
+you have can have in principle four
+possible choices and then if you have 20
+
+ align:start position:0%
+possible choices and then if you have 20
+ 
+
+ align:start position:0%
+possible choices and then if you have 20
+say so for time Direction you don't but
+
+ align:start position:0%
+say so for time Direction you don't but
+ 
+
+ align:start position:0%
+say so for time Direction you don't but
+for 25 dimensions 25 spatial dimensions
+
+ align:start position:0%
+for 25 dimensions 25 spatial dimensions
+ 
+
+ align:start position:0%
+for 25 dimensions 25 spatial dimensions
+and each Dimension you have a four
+
+ align:start position:0%
+and each Dimension you have a four
+ 
+
+ align:start position:0%
+and each Dimension you have a four
+choices then you have four to the^ 25
+
+ align:start position:0%
+choices then you have four to the^ 25
+ 
+
+ align:start position:0%
+choices then you have four to the^ 25
+possible choices of different boundary
+
+ align:start position:0%
+possible choices of different boundary
+ 
+
+ align:start position:0%
+possible choices of different boundary
+conditions so now let's talk about other
+
+ align:start position:0%
+conditions so now let's talk about other
+ 
+
+ align:start position:0%
+conditions so now let's talk about other
+boundary
+
+ align:start position:0%
+boundary
+ 
+
+ align:start position:0%
+boundary
+conditions
+
+ align:start position:0%
+conditions
+ 
+
+ align:start position:0%
+conditions
+so but but use the picture of deepend we
+
+ align:start position:0%
+so but but use the picture of deepend we
+ 
+
+ align:start position:0%
+so but but use the picture of deepend we
+can talk about them
+
+ align:start position:0%
+can talk about them
+ 
+
+ align:start position:0%
+can talk about them
+all we can talk about them
+
+ align:start position:0%
+all we can talk about them
+ 
+
+ align:start position:0%
+all we can talk about them
+[Applause]
+
+ align:start position:0%
+[Applause]
+ 
+
+ align:start position:0%
+[Applause]
+all
+
+ align:start position:0%
+all
+ 
+
+ align:start position:0%
+all
+so so let let
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+consider more than one brains
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so let's consider the
+
+ align:start position:0%
+okay so let's consider the
+ 
+
+ align:start position:0%
+okay so let's consider the
+situation we have two such DP
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+brain so the so this direction is still
+
+ align:start position:0%
+brain so the so this direction is still
+ 
+
+ align:start position:0%
+brain so the so this direction is still
+X1 x01 to
+
+ align:start position:0%
+X1 x01 to
+ 
+
+ align:start position:0%
+X1 x01 to
+p and then this is all the transverse
+
+ align:start position:0%
+p and then this is all the transverse
+ 
+
+ align:start position:0%
+p and then this is all the transverse
+all the all the other
+
+ align:start position:0%
+all the all the other
+ 
+
+ align:start position:0%
+all the all the other
+directions so suppose you have a brain
+
+ align:start position:0%
+directions so suppose you have a brain
+ 
+
+ align:start position:0%
+directions so suppose you have a brain
+at the at a
+
+ align:start position:0%
+at the at a
+ 
+
+ align:start position:0%
+at the at a
+and another brain at
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+B okay at the a vector specified by
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+B okay so now in this case we can have
+
+ align:start position:0%
+B okay so now in this case we can have
+ 
+
+ align:start position:0%
+B okay so now in this case we can have
+four type of open strings
+
+ align:start position:0%
+four type of open strings
+ 
+
+ align:start position:0%
+four type of open strings
+[Applause]
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+we can have four type of open strings
+
+ align:start position:0%
+we can have four type of open strings
+ 
+
+ align:start position:0%
+we can have four type of open strings
+for example I can have open string which
+
+ align:start position:0%
+for example I can have open string which
+ 
+
+ align:start position:0%
+for example I can have open string which
+end on
+
+ align:start position:0%
+end on
+ 
+
+ align:start position:0%
+end on
+B and I can have open string end on a
+
+ align:start position:0%
+B and I can have open string end on a
+ 
+
+ align:start position:0%
+B and I can have open string end on a
+but I can also have end open string
+
+ align:start position:0%
+but I can also have end open string
+ 
+
+ align:start position:0%
+but I can also have end open string
+which go from B to a and for o opening
+
+ align:start position:0%
+which go from B to a and for o opening
+ 
+
+ align:start position:0%
+which go from B to a and for o opening
+from A to
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+B
+
+ align:start position:0%
+B
+ 
+
+ align:start position:0%
+B
+okay so so in this case the boundary
+
+ align:start position:0%
+okay so so in this case the boundary
+ 
+
+ align:start position:0%
+okay so so in this case the boundary
+condition would be the
+
+ align:start position:0%
+condition would be the
+ 
+
+ align:start position:0%
+condition would be the
+x01 to P is still a lum boundary
+
+ align:start position:0%
+x01 to P is still a lum boundary
+ 
+
+ align:start position:0%
+x01 to P is still a lum boundary
+condition for
+
+ align:start position:0%
+condition for
+ 
+
+ align:start position:0%
+condition for
+both for both Sigma equal to Zer and
+
+ align:start position:0%
+both for both Sigma equal to Zer and
+ 
+
+ align:start position:0%
+both for both Sigma equal to Zer and
+sigma equal to
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Pi but for
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the other
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+directions okay you can have either your
+
+ align:start position:0%
+directions okay you can have either your
+ 
+
+ align:start position:0%
+directions okay you can have either your
+Sigma zero can either be in a or b
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+or Sigma equal to Pi can either be a or
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+b okay so that give you the four type of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+strings okay I give you four type of
+
+ align:start position:0%
+strings okay I give you four type of
+ 
+
+ align:start position:0%
+strings okay I give you four type of
+different
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+strings now you can also consider brains
+
+ align:start position:0%
+strings now you can also consider brains
+ 
+
+ align:start position:0%
+strings now you can also consider brains
+of different
+
+ align:start position:0%
+of different
+ 
+
+ align:start position:0%
+of different
+Dimensions so now you can consider
+
+ align:start position:0%
+Dimensions so now you can consider
+ 
+
+ align:start position:0%
+Dimensions so now you can consider
+brains of a different
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+dimensions say for
+
+ align:start position:0%
+dimensions say for
+ 
+
+ align:start position:0%
+dimensions say for
+example say suppose let's single out the
+
+ align:start position:0%
+example say suppose let's single out the
+ 
+
+ align:start position:0%
+example say suppose let's single out the
+two directions D- 2 and D-
+
+ align:start position:0%
+two directions D- 2 and D-
+ 
+
+ align:start position:0%
+two directions D- 2 and D-
+1 and let's suppose all the other
+
+ align:start position:0%
+1 and let's suppose all the other
+ 
+
+ align:start position:0%
+1 and let's suppose all the other
+directions are in the Newman
+
+ align:start position:0%
+directions are in the Newman
+ 
+
+ align:start position:0%
+directions are in the Newman
+Direction so let's consider two kind of
+
+ align:start position:0%
+Direction so let's consider two kind of
+ 
+
+ align:start position:0%
+Direction so let's consider two kind of
+brains one is that extended in the D
+
+ align:start position:0%
+brains one is that extended in the D
+ 
+
+ align:start position:0%
+brains one is that extended in the D
+minus 2 Direction say at some value of D
+
+ align:start position:0%
+minus 2 Direction say at some value of D
+ 
+
+ align:start position:0%
+minus 2 Direction say at some value of D
+minus
+
+ align:start position:0%
+minus
+ 
+
+ align:start position:0%
+minus
+one and let's consider another brain
+
+ align:start position:0%
+one and let's consider another brain
+ 
+
+ align:start position:0%
+one and let's consider another brain
+which is localized in both D minus one
+
+ align:start position:0%
+which is localized in both D minus one
+ 
+
+ align:start position:0%
+which is localized in both D minus one
+and D minus
+
+ align:start position:0%
+and D minus
+ 
+
+ align:start position:0%
+and D minus
+2 okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+then you can again have four type of
+
+ align:start position:0%
+then you can again have four type of
+ 
+
+ align:start position:0%
+then you can again have four type of
+strings end
+
+ align:start position:0%
+strings end
+ 
+
+ align:start position:0%
+strings end
+itself ending itself and then ending
+
+ align:start position:0%
+itself ending itself and then ending
+ 
+
+ align:start position:0%
+itself ending itself and then ending
+between these
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+two so again you can see the oriented
+
+ align:start position:0%
+two so again you can see the oriented
+ 
+
+ align:start position:0%
+two so again you can see the oriented
+stream because we can see the oriented
+
+ align:start position:0%
+stream because we can see the oriented
+ 
+
+ align:start position:0%
+stream because we can see the oriented
+string so you can again can see the
+
+ align:start position:0%
+string so you can again can see the
+ 
+
+ align:start position:0%
+string so you can again can see the
+stream like
+
+ align:start position:0%
+stream like
+ 
+
+ align:start position:0%
+stream like
+that so so so so let me call this brain
+
+ align:start position:0%
+that so so so so let me call this brain
+ 
+
+ align:start position:0%
+that so so so so let me call this brain
+one this brain
+
+ align:start position:0%
+one this brain
+ 
+
+ align:start position:0%
+one this brain
+two so let's consider the one two
+
+ align:start position:0%
+two so let's consider the one two
+ 
+
+ align:start position:0%
+two so let's consider the one two
+string it's from one to two then the one
+
+ align:start position:0%
+string it's from one to two then the one
+ 
+
+ align:start position:0%
+string it's from one to two then the one
+two
+
+ align:start position:0%
+two
+ 
+
+ align:start position:0%
+two
+stren with corresponding to the boundary
+
+ align:start position:0%
+stren with corresponding to the boundary
+ 
+
+ align:start position:0%
+stren with corresponding to the boundary
+condition say at D minus
+
+ align:start position:0%
+condition say at D minus
+ 
+
+ align:start position:0%
+condition say at D minus
+2 say at Sigma equal to
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+zero you
+
+ align:start position:0%
+zero you
+ 
+
+ align:start position:0%
+zero you
+impose you impose the um the new
+
+ align:start position:0%
+impose you impose the um the new
+ 
+
+ align:start position:0%
+impose you impose the um the new
+boundary
+
+ align:start position:0%
+boundary
+ 
+
+ align:start position:0%
+boundary
+condition okay because it can move
+
+ align:start position:0%
+condition okay because it can move
+ 
+
+ align:start position:0%
+condition okay because it can move
+freely in the in the in the D minus 2
+
+ align:start position:0%
+freely in the in the in the D minus 2
+ 
+
+ align:start position:0%
+freely in the in the in the D minus 2
+Direction and uh but in
+
+ align:start position:0%
+Direction and uh but in
+ 
+
+ align:start position:0%
+Direction and uh but in
+the at Sigma equal to
+
+ align:start position:0%
+the at Sigma equal to
+ 
+
+ align:start position:0%
+the at Sigma equal to
+Pi then then this should be fixed as
+
+ align:start position:0%
+Pi then then this should be fixed as
+ 
+
+ align:start position:0%
+Pi then then this should be fixed as
+some value so let's suppose say this is
+
+ align:start position:0%
+some value so let's suppose say this is
+ 
+
+ align:start position:0%
+some value so let's suppose say this is
+A1
+
+ align:start position:0%
+A1
+ 
+
+ align:start position:0%
+A1
+B1 then then add that we fixed at
+
+ align:start position:0%
+B1 then then add that we fixed at
+ 
+
+ align:start position:0%
+B1 then then add that we fixed at
+A1 Okay so so this is one two string
+
+ align:start position:0%
+A1 Okay so so this is one two string
+ 
+
+ align:start position:0%
+A1 Okay so so this is one two string
+then you can have one end which is a the
+
+ align:start position:0%
+then you can have one end which is a the
+ 
+
+ align:start position:0%
+then you can have one end which is a the
+new Bond new condition but the other end
+
+ align:start position:0%
+new Bond new condition but the other end
+ 
+
+ align:start position:0%
+new Bond new condition but the other end
+which is the bond new
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+condition okay is this clear to you and
+
+ align:start position:0%
+condition okay is this clear to you and
+ 
+
+ align:start position:0%
+condition okay is this clear to you and
+then for this two one string then we'll
+
+ align:start position:0%
+then for this two one string then we'll
+ 
+
+ align:start position:0%
+then for this two one string then we'll
+be
+
+ align:start position:0%
+be
+ 
+
+ align:start position:0%
+be
+opposite for the two w string for the D
+
+ align:start position:0%
+opposite for the two w string for the D
+ 
+
+ align:start position:0%
+opposite for the two w string for the D
+minus 2 Direction at Sigma equal to Z
+
+ align:start position:0%
+minus 2 Direction at Sigma equal to Z
+ 
+
+ align:start position:0%
+minus 2 Direction at Sigma equal to Z
+will be the D condition but that Sigma
+
+ align:start position:0%
+will be the D condition but that Sigma
+ 
+
+ align:start position:0%
+will be the D condition but that Sigma
+equal to Pi would be the new condition
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay any questions about
+
+ align:start position:0%
+okay any questions about
+ 
+
+ align:start position:0%
+okay any questions about
+this so these are pretty
+
+ align:start position:0%
+this so these are pretty
+ 
+
+ align:start position:0%
+this so these are pretty
+simple you just need to you just need to
+
+ align:start position:0%
+simple you just need to you just need to
+ 
+
+ align:start position:0%
+simple you just need to you just need to
+get used to it and spend a couple
+
+ align:start position:0%
+get used to it and spend a couple
+ 
+
+ align:start position:0%
+get used to it and spend a couple
+minutes draw a couple diagram then you
+
+ align:start position:0%
+minutes draw a couple diagram then you
+ 
+
+ align:start position:0%
+minutes draw a couple diagram then you
+will be an expert you'll be exper this
+
+ align:start position:0%
+will be an expert you'll be exper this
+ 
+
+ align:start position:0%
+will be an expert you'll be exper this
+is pretty
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Elementary so important remark
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+say a DP
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+brain as we said before it breaks
+
+ align:start position:0%
+brain as we said before it breaks
+ 
+
+ align:start position:0%
+brain as we said before it breaks
+translation
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+symmetry translational andent
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+symmetries
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay of the original minkovski space
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+time to a
+
+ align:start position:0%
+time to a
+ 
+
+ align:start position:0%
+time to a
+subgroup say the subgroup is that you
+
+ align:start position:0%
+subgroup say the subgroup is that you
+ 
+
+ align:start position:0%
+subgroup say the subgroup is that you
+have still have translation Symmetry and
+
+ align:start position:0%
+have still have translation Symmetry and
+ 
+
+ align:start position:0%
+have still have translation Symmetry and
+the lent symmetry along the brain
+
+ align:start position:0%
+the lent symmetry along the brain
+ 
+
+ align:start position:0%
+the lent symmetry along the brain
+Direction say along the brain Direction
+
+ align:start position:0%
+Direction say along the brain Direction
+ 
+
+ align:start position:0%
+Direction say along the brain Direction
+you still can translate the string can
+
+ align:start position:0%
+you still can translate the string can
+ 
+
+ align:start position:0%
+you still can translate the string can
+still translate in that direction and
+
+ align:start position:0%
+still translate in that direction and
+ 
+
+ align:start position:0%
+still translate in that direction and
+still there's no R IM in that direction
+
+ align:start position:0%
+still there's no R IM in that direction
+ 
+
+ align:start position:0%
+still there's no R IM in that direction
+so so there's still F symmetry in one p
+
+ align:start position:0%
+so so there's still F symmetry in one p
+ 
+
+ align:start position:0%
+so so there's still F symmetry in one p
+one comma P so in the time and P spatial
+
+ align:start position:0%
+one comma P so in the time and P spatial
+ 
+
+ align:start position:0%
+one comma P so in the time and P spatial
+Dimensions along the
+
+ align:start position:0%
+Dimensions along the
+ 
+
+ align:start position:0%
+Dimensions along the
+brain and then you you have rotational
+
+ align:start position:0%
+brain and then you you have rotational
+ 
+
+ align:start position:0%
+brain and then you you have rotational
+symmetries in the direction transverse
+
+ align:start position:0%
+symmetries in the direction transverse
+ 
+
+ align:start position:0%
+symmetries in the direction transverse
+to the brain so that's D minus oneus
+
+ align:start position:0%
+to the brain so that's D minus oneus
+ 
+
+ align:start position:0%
+to the brain so that's D minus oneus
+P okay so that's the so that's the
+
+ align:start position:0%
+P okay so that's the so that's the
+ 
+
+ align:start position:0%
+P okay so that's the so that's the
+rotation among those coordinates so you
+
+ align:start position:0%
+rotation among those coordinates so you
+ 
+
+ align:start position:0%
+rotation among those coordinates so you
+can have the lent symmetry along those
+
+ align:start position:0%
+can have the lent symmetry along those
+ 
+
+ align:start position:0%
+can have the lent symmetry along those
+directions then the rotational symmetry
+
+ align:start position:0%
+directions then the rotational symmetry
+ 
+
+ align:start position:0%
+directions then the rotational symmetry
+is along those directions okay so this
+
+ align:start position:0%
+is along those directions okay so this
+ 
+
+ align:start position:0%
+is along those directions okay so this
+is for TP brain so so the um so this is
+
+ align:start position:0%
+is for TP brain so so the um so this is
+ 
+
+ align:start position:0%
+is for TP brain so so the um so this is
+the remaining
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+symmetry so this is remaining symmetry
+
+ align:start position:0%
+symmetry so this is remaining symmetry
+ 
+
+ align:start position:0%
+symmetry so this is remaining symmetry
+uh uh uh say if you have a DP brain in
+
+ align:start position:0%
+uh uh uh say if you have a DP brain in
+ 
+
+ align:start position:0%
+uh uh uh say if you have a DP brain in
+the in the in the space time of course
+
+ align:start position:0%
+the in the in the space time of course
+ 
+
+ align:start position:0%
+the in the in the space time of course
+if you have multiple DP brain ex then
+
+ align:start position:0%
+if you have multiple DP brain ex then
+ 
+
+ align:start position:0%
+if you have multiple DP brain ex then
+then then it's broken even
+
+ align:start position:0%
+then then it's broken even
+ 
+
+ align:start position:0%
+then then it's broken even
+more yes why do we assume that brains
+
+ align:start position:0%
+more yes why do we assume that brains
+ 
+
+ align:start position:0%
+more yes why do we assume that brains
+are
+
+ align:start position:0%
+are
+ 
+
+ align:start position:0%
+are
+topologically open not compa oh yeah we
+
+ align:start position:0%
+topologically open not compa oh yeah we
+ 
+
+ align:start position:0%
+topologically open not compa oh yeah we
+can talk yeah here I'm just talking
+
+ align:start position:0%
+can talk yeah here I'm just talking
+ 
+
+ align:start position:0%
+can talk yeah here I'm just talking
+about the simplest situation I'm
+
+ align:start position:0%
+about the simplest situation I'm
+ 
+
+ align:start position:0%
+about the simplest situation I'm
+imposing the simplest boundary condition
+
+ align:start position:0%
+imposing the simplest boundary condition
+ 
+
+ align:start position:0%
+imposing the simplest boundary condition
+just like this kind of boundary
+
+ align:start position:0%
+just like this kind of boundary
+ 
+
+ align:start position:0%
+just like this kind of boundary
+conditions and then this kind of
+
+ align:start position:0%
+conditions and then this kind of
+ 
+
+ align:start position:0%
+conditions and then this kind of
+boundary conditions is applies to the
+
+ align:start position:0%
+boundary conditions is applies to the
+ 
+
+ align:start position:0%
+boundary conditions is applies to the
+infinite the um yeah you can once later
+
+ align:start position:0%
+infinite the um yeah you can once later
+ 
+
+ align:start position:0%
+infinite the um yeah you can once later
+we talk about the debr can be dynamical
+
+ align:start position:0%
+we talk about the debr can be dynamical
+ 
+
+ align:start position:0%
+we talk about the debr can be dynamical
+ex then you can consider complicated
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+configurations
+
+ align:start position:0%
+configurations
+ 
+
+ align:start position:0%
+configurations
+yes so so far we consider one boundary
+
+ align:start position:0%
+yes so so far we consider one boundary
+ 
+
+ align:start position:0%
+yes so so far we consider one boundary
+condition is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+zero yeah so how about condition when
+
+ align:start position:0%
+zero yeah so how about condition when
+ 
+
+ align:start position:0%
+zero yeah so how about condition when
+derivative is non
+
+ align:start position:0%
+derivative is non
+ 
+
+ align:start position:0%
+derivative is non
+zero and then so when Sigma X is non Z
+
+ align:start position:0%
+zero and then so when Sigma X is non Z
+ 
+
+ align:start position:0%
+zero and then so when Sigma X is non Z
+some Conant numberers
+
+ align:start position:0%
+some Conant numberers
+ 
+
+ align:start position:0%
+some Conant numberers
+and there was like X
+
+ align:start position:0%
+and there was like X
+ 
+
+ align:start position:0%
+and there was like X
+Plus ah you are saying something like
+
+ align:start position:0%
+Plus ah you are saying something like
+ 
+
+ align:start position:0%
+Plus ah you are saying something like
+this you're saying the some combination
+
+ align:start position:0%
+this you're saying the some combination
+ 
+
+ align:start position:0%
+this you're saying the some combination
+of
+
+ align:start position:0%
+of
+ 
+
+ align:start position:0%
+of
+this X Plus der yeah yeah yeah that can
+
+ align:start position:0%
+this X Plus der yeah yeah yeah that can
+ 
+
+ align:start position:0%
+this X Plus der yeah yeah yeah that can
+happen that does not happen in the
+
+ align:start position:0%
+happen that does not happen in the
+ 
+
+ align:start position:0%
+happen that does not happen in the
+straight minkovski space because in the
+
+ align:start position:0%
+straight minkovski space because in the
+ 
+
+ align:start position:0%
+straight minkovski space because in the
+straight movi space this is the uh the
+
+ align:start position:0%
+straight movi space this is the uh the
+ 
+
+ align:start position:0%
+straight movi space this is the uh the
+action so you can only have one or the
+
+ align:start position:0%
+action so you can only have one or the
+ 
+
+ align:start position:0%
+action so you can only have one or the
+other but if you say have vovi but you
+
+ align:start position:0%
+other but if you say have vovi but you
+ 
+
+ align:start position:0%
+other but if you say have vovi but you
+turn on some Electric
+
+ align:start position:0%
+turn on some Electric
+ 
+
+ align:start position:0%
+turn on some Electric
+fi then then you can actually have such
+
+ align:start position:0%
+fi then then you can actually have such
+ 
+
+ align:start position:0%
+fi then then you can actually have such
+kind of mix bound conditions yeah just
+
+ align:start position:0%
+kind of mix bound conditions yeah just
+ 
+
+ align:start position:0%
+kind of mix bound conditions yeah just
+there there exist such St it depend on
+
+ align:start position:0%
+there there exist such St it depend on
+ 
+
+ align:start position:0%
+there there exist such St it depend on
+the specific dynamical situation so this
+
+ align:start position:0%
+the specific dynamical situation so this
+ 
+
+ align:start position:0%
+the specific dynamical situation so this
+is a this is empty flat Movic space then
+
+ align:start position:0%
+is a this is empty flat Movic space then
+ 
+
+ align:start position:0%
+is a this is empty flat Movic space then
+you can only have those bound
+
+ align:start position:0%
+you can only have those bound
+ 
+
+ align:start position:0%
+you can only have those bound
+recognitions and when some con also can
+
+ align:start position:0%
+recognitions and when some con also can
+ 
+
+ align:start position:0%
+recognitions and when some con also can
+be
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+to sorry when
+
+ align:start position:0%
+to sorry when
+ 
+
+ align:start position:0%
+to sorry when
+X um that I'm not sure uh uh uh that is
+
+ align:start position:0%
+X um that I'm not sure uh uh uh that is
+ 
+
+ align:start position:0%
+X um that I'm not sure uh uh uh that is
+different uh um yeah because that does
+
+ align:start position:0%
+different uh um yeah because that does
+ 
+
+ align:start position:0%
+different uh um yeah because that does
+not satisfy that the uh does not satisfy
+
+ align:start position:0%
+not satisfy that the uh does not satisfy
+ 
+
+ align:start position:0%
+not satisfy that the uh does not satisfy
+that boundary condition and so so we
+
+ align:start position:0%
+that boundary condition and so so we
+ 
+
+ align:start position:0%
+that boundary condition and so so we
+have to look at specific
+
+ align:start position:0%
+have to look at specific
+ 
+
+ align:start position:0%
+have to look at specific
+situation we have to look at specific
+
+ align:start position:0%
+situation we have to look at specific
+ 
+
+ align:start position:0%
+situation we have to look at specific
+situation just for the flat minkovski
+
+ align:start position:0%
+situation just for the flat minkovski
+ 
+
+ align:start position:0%
+situation just for the flat minkovski
+space these are the only boundary
+
+ align:start position:0%
+space these are the only boundary
+ 
+
+ align:start position:0%
+space these are the only boundary
+condition you can have and uh and the we
+
+ align:start position:0%
+condition you can have and uh and the we
+ 
+
+ align:start position:0%
+condition you can have and uh and the we
+will not have uh we will not be able to
+
+ align:start position:0%
+will not have uh we will not be able to
+ 
+
+ align:start position:0%
+will not have uh we will not be able to
+do it in this course but you can
+
+ align:start position:0%
+do it in this course but you can
+ 
+
+ align:start position:0%
+do it in this course but you can
+consider the situation uh uh because the
+
+ align:start position:0%
+consider the situation uh uh because the
+ 
+
+ align:start position:0%
+consider the situation uh uh because the
+in open string you can have
+
+ align:start position:0%
+in open string you can have
+ 
+
+ align:start position:0%
+in open string you can have
+electromagnetic field you can have a
+
+ align:start position:0%
+electromagnetic field you can have a
+ 
+
+ align:start position:0%
+electromagnetic field you can have a
+photon so you can in principle t on
+
+ align:start position:0%
+photon so you can in principle t on
+ 
+
+ align:start position:0%
+photon so you can in principle t on
+electromagnetic field and then that will
+
+ align:start position:0%
+electromagnetic field and then that will
+ 
+
+ align:start position:0%
+electromagnetic field and then that will
+modify the boundary condition then you
+
+ align:start position:0%
+modify the boundary condition then you
+ 
+
+ align:start position:0%
+modify the boundary condition then you
+can have actually mixed boundary
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+conditions do people ever consider this
+
+ align:start position:0%
+conditions do people ever consider this
+ 
+
+ align:start position:0%
+conditions do people ever consider this
+string between two de brains as
+
+ align:start position:0%
+string between two de brains as
+ 
+
+ align:start position:0%
+string between two de brains as
+topological defect because it happening
+
+ align:start position:0%
+topological defect because it happening
+ 
+
+ align:start position:0%
+topological defect because it happening
+between you mean stream between
+
+ align:start position:0%
+between you mean stream between
+ 
+
+ align:start position:0%
+between you mean stream between
+different stream before between
+
+ align:start position:0%
+different stream before between
+ 
+
+ align:start position:0%
+different stream before between
+different de brains
+
+ align:start position:0%
+different de brains
+ 
+
+ align:start position:0%
+different de brains
+yes you can see that the de brain
+
+ align:start position:0%
+yes you can see that the de brain
+ 
+
+ align:start position:0%
+yes you can see that the de brain
+themselves as topological defect rather
+
+ align:start position:0%
+themselves as topological defect rather
+ 
+
+ align:start position:0%
+themselves as topological defect rather
+than the the the stream between them as
+
+ align:start position:0%
+than the the the stream between them as
+ 
+
+ align:start position:0%
+than the the the stream between them as
+topological defect the de themselves are
+
+ align:start position:0%
+topological defect the de themselves are
+ 
+
+ align:start position:0%
+topological defect the de themselves are
+defect strings are just yeah as we will
+
+ align:start position:0%
+defect strings are just yeah as we will
+ 
+
+ align:start position:0%
+defect strings are just yeah as we will
+talk about we will talk about it now uh
+
+ align:start position:0%
+talk about we will talk about it now uh
+ 
+
+ align:start position:0%
+talk about we will talk about it now uh
+uh the strings on the de brain they're
+
+ align:start position:0%
+uh the strings on the de brain they're
+ 
+
+ align:start position:0%
+uh the strings on the de brain they're
+just the excitations of the de
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+brains so now after talking about those
+
+ align:start position:0%
+brains so now after talking about those
+ 
+
+ align:start position:0%
+brains so now after talking about those
+boundary conditions then we can again go
+
+ align:start position:0%
+boundary conditions then we can again go
+ 
+
+ align:start position:0%
+boundary conditions then we can again go
+through the procedure of qu quaning open
+
+ align:start position:0%
+through the procedure of qu quaning open
+ 
+
+ align:start position:0%
+through the procedure of qu quaning open
+string with those boundary conditions
+
+ align:start position:0%
+string with those boundary conditions
+ 
+
+ align:start position:0%
+string with those boundary conditions
+okay then we see what do we
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+get now let's talk about the open stream
+
+ align:start position:0%
+get now let's talk about the open stream
+ 
+
+ align:start position:0%
+get now let's talk about the open stream
+Spectrum on the DP brain
+
+ align:start position:0%
+Spectrum on the DP brain
+ 
+
+ align:start position:0%
+Spectrum on the DP brain
+so so as you can see already from those
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+pictures because they restriction on
+
+ align:start position:0%
+pictures because they restriction on
+ 
+
+ align:start position:0%
+pictures because they restriction on
+their end point so essentially the those
+
+ align:start position:0%
+their end point so essentially the those
+ 
+
+ align:start position:0%
+their end point so essentially the those
+strings they can only move along the
+
+ align:start position:0%
+strings they can only move along the
+ 
+
+ align:start position:0%
+strings they can only move along the
+direction of the brain okay they can
+
+ align:start position:0%
+direction of the brain okay they can
+ 
+
+ align:start position:0%
+direction of the brain okay they can
+only move the direction along the brain
+
+ align:start position:0%
+only move the direction along the brain
+ 
+
+ align:start position:0%
+only move the direction along the brain
+so essentially they can be
+
+ align:start position:0%
+so essentially they can be
+ 
+
+ align:start position:0%
+so essentially they can be
+considered as leing on the brain okay so
+
+ align:start position:0%
+considered as leing on the brain okay so
+ 
+
+ align:start position:0%
+considered as leing on the brain okay so
+those open string are leing on those DP
+
+ align:start position:0%
+those open string are leing on those DP
+ 
+
+ align:start position:0%
+those open string are leing on those DP
+brains Okay so so when we quantize those
+
+ align:start position:0%
+brains Okay so so when we quantize those
+ 
+
+ align:start position:0%
+brains Okay so so when we quantize those
+open strings then we then we will get
+
+ align:start position:0%
+open strings then we then we will get
+ 
+
+ align:start position:0%
+open strings then we then we will get
+the excitations of those open string the
+
+ align:start position:0%
+the excitations of those open string the
+ 
+
+ align:start position:0%
+the excitations of those open string the
+state of those open strings then on the
+
+ align:start position:0%
+state of those open strings then on the
+ 
+
+ align:start position:0%
+state of those open strings then on the
+de brains
+
+ align:start position:0%
+de brains
+ 
+
+ align:start position:0%
+de brains
+okay so so let me first introduce some
+
+ align:start position:0%
+okay so so let me first introduce some
+ 
+
+ align:start position:0%
+okay so so let me first introduce some
+rotations previously we have the
+
+ align:start position:0%
+rotations previously we have the
+ 
+
+ align:start position:0%
+rotations previously we have the
+rotation mu refers to all directions so
+
+ align:start position:0%
+rotation mu refers to all directions so
+ 
+
+ align:start position:0%
+rotation mu refers to all directions so
+now I separate into Alpha and a and
+
+ align:start position:0%
+now I separate into Alpha and a and
+ 
+
+ align:start position:0%
+now I separate into Alpha and a and
+Alpha is the Newman boundary Newman
+
+ align:start position:0%
+Alpha is the Newman boundary Newman
+ 
+
+ align:start position:0%
+Alpha is the Newman boundary Newman
+directions from zero to
+
+ align:start position:0%
+directions from zero to
+ 
+
+ align:start position:0%
+directions from zero to
+p and a are the D uh directions from p +
+
+ align:start position:0%
+p and a are the D uh directions from p +
+ 
+
+ align:start position:0%
+p and a are the D uh directions from p +
+1 to D minus
+
+ align:start position:0%
+1 to D minus
+ 
+
+ align:start position:0%
+1 to D minus
+one okay so this D minus oneus P of them
+
+ align:start position:0%
+one okay so this D minus oneus P of them
+ 
+
+ align:start position:0%
+one okay so this D minus oneus P of them
+okay so D minus y minus P of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+them so for the new boundary condition
+
+ align:start position:0%
+them so for the new boundary condition
+ 
+
+ align:start position:0%
+them so for the new boundary condition
+is just identical to what we had
+
+ align:start position:0%
+is just identical to what we had
+ 
+
+ align:start position:0%
+is just identical to what we had
+before so let me just write it down to
+
+ align:start position:0%
+before so let me just write it down to
+ 
+
+ align:start position:0%
+before so let me just write it down to
+remind you
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so these are the say the most
+
+ align:start position:0%
+okay so these are the say the most
+ 
+
+ align:start position:0%
+okay so these are the say the most
+General
+
+ align:start position:0%
+General
+ 
+
+ align:start position:0%
+General
+solution so so so in this case in
+
+ align:start position:0%
+solution so so so in this case in
+ 
+
+ align:start position:0%
+solution so so so in this case in
+particular if you remember you have XL
+
+ align:start position:0%
+particular if you remember you have XL
+ 
+
+ align:start position:0%
+particular if you remember you have XL
+equal to XR so the left moving and Right
+
+ align:start position:0%
+equal to XR so the left moving and Right
+ 
+
+ align:start position:0%
+equal to XR so the left moving and Right
+Moving are the
+
+ align:start position:0%
+Moving are the
+ 
+
+ align:start position:0%
+Moving are the
+same controlled by the same function and
+
+ align:start position:0%
+same controlled by the same function and
+ 
+
+ align:start position:0%
+same controlled by the same function and
+so that's why you get this cosine coine
+
+ align:start position:0%
+so that's why you get this cosine coine
+ 
+
+ align:start position:0%
+so that's why you get this cosine coine
+and when you take the derivative of
+
+ align:start position:0%
+and when you take the derivative of
+ 
+
+ align:start position:0%
+and when you take the derivative of
+Sigma become s then vanishes at the end
+
+ align:start position:0%
+Sigma become s then vanishes at the end
+ 
+
+ align:start position:0%
+Sigma become s then vanishes at the end
+point
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so so this is story is just exactly
+
+ align:start position:0%
+okay so so this is story is just exactly
+ 
+
+ align:start position:0%
+okay so so this is story is just exactly
+identical as before now let's look at
+
+ align:start position:0%
+identical as before now let's look at
+ 
+
+ align:start position:0%
+identical as before now let's look at
+the Der uh
+
+ align:start position:0%
+the Der uh
+ 
+
+ align:start position:0%
+the Der uh
+conditions so the for the Der conditions
+
+ align:start position:0%
+conditions so the for the Der conditions
+ 
+
+ align:start position:0%
+conditions so the for the Der conditions
+Let's uh
+
+ align:start position:0%
+Let's uh
+ 
+
+ align:start position:0%
+Let's uh
+again write down the most
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+General possible boundary conditions for
+
+ align:start position:0%
+General possible boundary conditions for
+ 
+
+ align:start position:0%
+General possible boundary conditions for
+uh for the boundary uh yeah first write
+
+ align:start position:0%
+uh for the boundary uh yeah first write
+ 
+
+ align:start position:0%
+uh for the boundary uh yeah first write
+down the most General solution
+
+ align:start position:0%
+down the most General solution
+ 
+
+ align:start position:0%
+down the most General solution
+for for for such a field so you have x
+
+ align:start position:0%
+for for for such a field so you have x
+ 
+
+ align:start position:0%
+for for for such a field so you have x
+a then 2 I pa a
+
+ align:start position:0%
+a then 2 I pa a
+ 
+
+ align:start position:0%
+a then 2 I pa a
+t then you have
+
+ align:start position:0%
+t then you have
+ 
+
+ align:start position:0%
+t then you have
+R tus Sigma
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and L A Plus
+
+ align:start position:0%
+and L A Plus
+ 
+
+ align:start position:0%
+and L A Plus
+Sigma
+
+ align:start position:0%
+Sigma
+ 
+
+ align:start position:0%
+Sigma
+okay but now the boundary condition we
+
+ align:start position:0%
+okay but now the boundary condition we
+ 
+
+ align:start position:0%
+okay but now the boundary condition we
+need to
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+impose is X
+
+ align:start position:0%
+impose is X
+ 
+
+ align:start position:0%
+impose is X
+a and sigma equal to zero and
+
+ align:start position:0%
+a and sigma equal to zero and
+ 
+
+ align:start position:0%
+a and sigma equal to zero and
+Pi Sigma 0o T and the Sigma Pi t
+
+ align:start position:0%
+Pi Sigma 0o T and the Sigma Pi t
+ 
+
+ align:start position:0%
+Pi Sigma 0o T and the Sigma Pi t
+equal
+
+ align:start position:0%
+equal
+ 
+
+ align:start position:0%
+equal
+to ba so so here I call them a but let
+
+ align:start position:0%
+to ba so so here I call them a but let
+ 
+
+ align:start position:0%
+to ba so so here I call them a but let
+me call them B because it's AAL to write
+
+ align:start position:0%
+me call them B because it's AAL to write
+ 
+
+ align:start position:0%
+me call them B because it's AAL to write
+a to the a to the index a so let me just
+
+ align:start position:0%
+a to the a to the index a so let me just
+ 
+
+ align:start position:0%
+a to the a to the index a so let me just
+call them B the vector B
+
+ align:start position:0%
+call them B the vector B
+ 
+
+ align:start position:0%
+call them B the vector B
+okay so now we have to impose this
+
+ align:start position:0%
+okay so now we have to impose this
+ 
+
+ align:start position:0%
+okay so now we have to impose this
+boundary
+
+ align:start position:0%
+boundary
+ 
+
+ align:start position:0%
+boundary
+condition so you can immediately see
+
+ align:start position:0%
+condition so you can immediately see
+ 
+
+ align:start position:0%
+condition so you can immediately see
+that because of this this boundary
+
+ align:start position:0%
+that because of this this boundary
+ 
+
+ align:start position:0%
+that because of this this boundary
+condition XA have to be
+
+ align:start position:0%
+condition XA have to be
+ 
+
+ align:start position:0%
+condition XA have to be
+ba okay x a have to be ba and this PA
+
+ align:start position:0%
+ba okay x a have to be ba and this PA
+ 
+
+ align:start position:0%
+ba okay x a have to be ba and this PA
+have to be
+
+ align:start position:0%
+have to be
+ 
+
+ align:start position:0%
+have to be
+zero PA have to be zero otherwise you
+
+ align:start position:0%
+zero PA have to be zero otherwise you
+ 
+
+ align:start position:0%
+zero PA have to be zero otherwise you
+won't satisfy this because this change
+
+ align:start position:0%
+won't satisfy this because this change
+ 
+
+ align:start position:0%
+won't satisfy this because this change
+with
+
+ align:start position:0%
+with
+ 
+
+ align:start position:0%
+with
+time and then you want the sum of them
+
+ align:start position:0%
+time and then you want the sum of them
+ 
+
+ align:start position:0%
+time and then you want the sum of them
+to be zero at x equal to Z Sigma equal
+
+ align:start position:0%
+to be zero at x equal to Z Sigma equal
+ 
+
+ align:start position:0%
+to be zero at x equal to Z Sigma equal
+to zero so that gives you XL = to minus
+
+ align:start position:0%
+to zero so that gives you XL = to minus
+ 
+
+ align:start position:0%
+to zero so that gives you XL = to minus
+XR so this is from the boundary
+
+ align:start position:0%
+XR so this is from the boundary
+ 
+
+ align:start position:0%
+XR so this is from the boundary
+condition at Sigma equal to
+
+ align:start position:0%
+condition at Sigma equal to
+ 
+
+ align:start position:0%
+condition at Sigma equal to
+zero okay
+
+ align:start position:0%
+zero okay
+ 
+
+ align:start position:0%
+zero okay
+and then the boundary condition Sigma
+
+ align:start position:0%
+and then the boundary condition Sigma
+ 
+
+ align:start position:0%
+and then the boundary condition Sigma
+equal to
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Pi you deduce both of them a periodic
+
+ align:start position:0%
+Pi you deduce both of them a periodic
+ 
+
+ align:start position:0%
+Pi you deduce both of them a periodic
+bound recognitions the they periodic
+
+ align:start position:0%
+bound recognitions the they periodic
+ 
+
+ align:start position:0%
+bound recognitions the they periodic
+functions in 2
+
+ align:start position:0%
+functions in 2
+ 
+
+ align:start position:0%
+functions in 2
+pi
+
+ align:start position:0%
+pi
+ 
+
+ align:start position:0%
+pi
+okay the
+
+ align:start position:0%
+okay the
+ 
+
+ align:start position:0%
+okay the
+perod uh you can see it easily so at the
+
+ align:start position:0%
+perod uh you can see it easily so at the
+ 
+
+ align:start position:0%
+perod uh you can see it easily so at the
+to Sigma equal to zero you just have XR
+
+ align:start position:0%
+to Sigma equal to zero you just have XR
+ 
+
+ align:start position:0%
+to Sigma equal to zero you just have XR
+to plus XL t equal to yeah should be
+
+ align:start position:0%
+to plus XL t equal to yeah should be
+ 
+
+ align:start position:0%
+to plus XL t equal to yeah should be
+equal to zero so you should XL equal to
+
+ align:start position:0%
+equal to zero so you should XL equal to
+ 
+
+ align:start position:0%
+equal to zero so you should XL equal to
+minus
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+XR so so now you can just write down
+
+ align:start position:0%
+XR so so now you can just write down
+ 
+
+ align:start position:0%
+XR so so now you can just write down
+explicitly just still this is a periodic
+
+ align:start position:0%
+explicitly just still this is a periodic
+ 
+
+ align:start position:0%
+explicitly just still this is a periodic
+function in 2 pi so the expansion is
+
+ align:start position:0%
+function in 2 pi so the expansion is
+ 
+
+ align:start position:0%
+function in 2 pi so the expansion is
+essentially the same so the only
+
+ align:start position:0%
+essentially the same so the only
+ 
+
+ align:start position:0%
+essentially the same so the only
+difference for those
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+directions is that now you have B Alpha
+
+ align:start position:0%
+directions is that now you have B Alpha
+ 
+
+ align:start position:0%
+directions is that now you have B Alpha
+ba now you don't have this term because
+
+ align:start position:0%
+ba now you don't have this term because
+ 
+
+ align:start position:0%
+ba now you don't have this term because
+this term is zero and then
+
+ align:start position:0%
+this term is zero and then
+ 
+
+ align:start position:0%
+this term is zero and then
+not equal to zero alpha n
+
+ align:start position:0%
+not equal to zero alpha n
+ 
+
+ align:start position:0%
+not equal to zero alpha n
+a/ nus n t sign in
+
+ align:start position:0%
+a/ nus n t sign in
+ 
+
+ align:start position:0%
+a/ nus n t sign in
+Sigma okay there's some preactor here I
+
+ align:start position:0%
+Sigma okay there's some preactor here I
+ 
+
+ align:start position:0%
+Sigma okay there's some preactor here I
+forgot to write okay some Alpha Prime ex
+
+ align:start position:0%
+forgot to write okay some Alpha Prime ex
+ 
+
+ align:start position:0%
+forgot to write okay some Alpha Prime ex
+by convention let's not worry about
+
+ align:start position:0%
+by convention let's not worry about
+ 
+
+ align:start position:0%
+by convention let's not worry about
+those
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+things okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so now you do
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+quation so the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+quation in new boundary condition of
+
+ align:start position:0%
+quation in new boundary condition of
+ 
+
+ align:start position:0%
+quation in new boundary condition of
+course identical to
+
+ align:start position:0%
+course identical to
+ 
+
+ align:start position:0%
+course identical to
+before oh yeah first let me just explain
+
+ align:start position:0%
+before oh yeah first let me just explain
+ 
+
+ align:start position:0%
+before oh yeah first let me just explain
+the PA equal to zero just make R Mark so
+
+ align:start position:0%
+the PA equal to zero just make R Mark so
+ 
+
+ align:start position:0%
+the PA equal to zero just make R Mark so
+so this is of course expected
+
+ align:start position:0%
+so this is of course expected
+ 
+
+ align:start position:0%
+so this is of course expected
+because if the string is limited to
+
+ align:start position:0%
+because if the string is limited to
+ 
+
+ align:start position:0%
+because if the string is limited to
+moving on this plane then of course it
+
+ align:start position:0%
+moving on this plane then of course it
+ 
+
+ align:start position:0%
+moving on this plane then of course it
+cannot move in the perpendicular
+
+ align:start position:0%
+cannot move in the perpendicular
+ 
+
+ align:start position:0%
+cannot move in the perpendicular
+Direction so cannot have Center of mass
+
+ align:start position:0%
+Direction so cannot have Center of mass
+ 
+
+ align:start position:0%
+Direction so cannot have Center of mass
+momentum in the so cannot have cental
+
+ align:start position:0%
+momentum in the so cannot have cental
+ 
+
+ align:start position:0%
+momentum in the so cannot have cental
+mass momentum in the perpendicular
+
+ align:start position:0%
+mass momentum in the perpendicular
+ 
+
+ align:start position:0%
+mass momentum in the perpendicular
+Direction so so this is indeed what you
+
+ align:start position:0%
+Direction so so this is indeed what you
+ 
+
+ align:start position:0%
+Direction so so this is indeed what you
+intuitively expect okay uh uh the the
+
+ align:start position:0%
+intuitively expect okay uh uh the the
+ 
+
+ align:start position:0%
+intuitively expect okay uh uh the the
+center of mass momentum can only be in
+
+ align:start position:0%
+center of mass momentum can only be in
+ 
+
+ align:start position:0%
+center of mass momentum can only be in
+the One Direction can only be in the in
+
+ align:start position:0%
+the One Direction can only be in the in
+ 
+
+ align:start position:0%
+the One Direction can only be in the in
+the Newman
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+directions so so the quation of the new
+
+ align:start position:0%
+directions so so the quation of the new
+ 
+
+ align:start position:0%
+directions so so the quation of the new
+is exactly the same as before and
+
+ align:start position:0%
+is exactly the same as before and
+ 
+
+ align:start position:0%
+is exactly the same as before and
+actually conation in which
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+directions with this set up also the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+same also exactly the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+same because the only only change is
+
+ align:start position:0%
+same because the only only change is
+ 
+
+ align:start position:0%
+same because the only only change is
+coine Sigma go to S Sigma you can work
+
+ align:start position:0%
+coine Sigma go to S Sigma you can work
+ 
+
+ align:start position:0%
+coine Sigma go to S Sigma you can work
+through that procedure and and you find
+
+ align:start position:0%
+through that procedure and and you find
+ 
+
+ align:start position:0%
+through that procedure and and you find
+that uh nothing really changes so
+
+ align:start position:0%
+that uh nothing really changes so
+ 
+
+ align:start position:0%
+that uh nothing really changes so
+exactly the
+
+ align:start position:0%
+exactly the
+ 
+
+ align:start position:0%
+exactly the
+same as that of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+n
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay in
+
+ align:start position:0%
+okay in
+ 
+
+ align:start position:0%
+okay in
+particular in particular the commutation
+
+ align:start position:0%
+particular in particular the commutation
+ 
+
+ align:start position:0%
+particular in particular the commutation
+relations between all those
+
+ align:start position:0%
+relations between all those
+ 
+
+ align:start position:0%
+relations between all those
+modes does not change at all just are
+
+ align:start position:0%
+modes does not change at all just are
+ 
+
+ align:start position:0%
+modes does not change at all just are
+exact the same as what you would have in
+
+ align:start position:0%
+exact the same as what you would have in
+ 
+
+ align:start position:0%
+exact the same as what you would have in
+the in the um
+
+ align:start position:0%
+the in the um
+ 
+
+ align:start position:0%
+the in the um
+um in the uh um in the Luman case so
+
+ align:start position:0%
+um in the uh um in the Luman case so
+ 
+
+ align:start position:0%
+um in the uh um in the Luman case so
+this is also physically
+
+ align:start position:0%
+this is also physically
+ 
+
+ align:start position:0%
+this is also physically
+latal this is a physical
+
+ align:start position:0%
+latal this is a physical
+ 
+
+ align:start position:0%
+latal this is a physical
+Lal so imposing such boundary
+
+ align:start position:0%
+Lal so imposing such boundary
+ 
+
+ align:start position:0%
+Lal so imposing such boundary
+conditions essentially you only restrict
+
+ align:start position:0%
+conditions essentially you only restrict
+ 
+
+ align:start position:0%
+conditions essentially you only restrict
+to the center of mass motion so you can
+
+ align:start position:0%
+to the center of mass motion so you can
+ 
+
+ align:start position:0%
+to the center of mass motion so you can
+no longer move in the perpendicular
+
+ align:start position:0%
+no longer move in the perpendicular
+ 
+
+ align:start position:0%
+no longer move in the perpendicular
+directions but the string can oscillates
+
+ align:start position:0%
+directions but the string can oscillates
+ 
+
+ align:start position:0%
+directions but the string can oscillates
+but string can still oscillate in all 10
+
+ align:start position:0%
+but string can still oscillate in all 10
+ 
+
+ align:start position:0%
+but string can still oscillate in all 10
+Dimensions there's no difference in the
+
+ align:start position:0%
+Dimensions there's no difference in the
+ 
+
+ align:start position:0%
+Dimensions there's no difference in the
+way the string illat and uh so so stram
+
+ align:start position:0%
+way the string illat and uh so so stram
+ 
+
+ align:start position:0%
+way the string illat and uh so so stram
+still oscillates in 10 Dimensions so uh
+
+ align:start position:0%
+still oscillates in 10 Dimensions so uh
+ 
+
+ align:start position:0%
+still oscillates in 10 Dimensions so uh
+so everything is the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+same yeah a Str still oscillat in all
+
+ align:start position:0%
+same yeah a Str still oscillat in all
+ 
+
+ align:start position:0%
+same yeah a Str still oscillat in all
+the in all directions in
+
+ align:start position:0%
+the in all directions in
+ 
+
+ align:start position:0%
+the in all directions in
+particular the Z point energy is the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+same 0 point energy on the worldsheet is
+
+ align:start position:0%
+same 0 point energy on the worldsheet is
+ 
+
+ align:start position:0%
+same 0 point energy on the worldsheet is
+the same okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so this means that the mass formula we
+
+ align:start position:0%
+so this means that the mass formula we
+ 
+
+ align:start position:0%
+so this means that the mass formula we
+derived before for the Newman boundary
+
+ align:start position:0%
+derived before for the Newman boundary
+ 
+
+ align:start position:0%
+derived before for the Newman boundary
+condition we exactly applies without any
+
+ align:start position:0%
+condition we exactly applies without any
+ 
+
+ align:start position:0%
+condition we exactly applies without any
+change okay without any
+
+ align:start position:0%
+change okay without any
+ 
+
+ align:start position:0%
+change okay without any
+change in particular the Mass Spectrum
+
+ align:start position:0%
+change in particular the Mass Spectrum
+ 
+
+ align:start position:0%
+change in particular the Mass Spectrum
+will also be EXA essentially the
+
+ align:start position:0%
+will also be EXA essentially the
+ 
+
+ align:start position:0%
+will also be EXA essentially the
+massless or massive Spectrum will be
+
+ align:start position:0%
+massless or massive Spectrum will be
+ 
+
+ align:start position:0%
+massless or massive Spectrum will be
+also be essentially the exact the same
+
+ align:start position:0%
+also be essentially the exact the same
+ 
+
+ align:start position:0%
+also be essentially the exact the same
+as
+
+ align:start position:0%
+as
+ 
+
+ align:start position:0%
+as
+before uh uh uh uh one second
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so so let me just mention one
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+point that this is
+
+ align:start position:0%
+point that this is
+ 
+
+ align:start position:0%
+point that this is
+identical okay that this is
+
+ align:start position:0%
+identical okay that this is
+ 
+
+ align:start position:0%
+identical okay that this is
+identical is actually related to that
+
+ align:start position:0%
+identical is actually related to that
+ 
+
+ align:start position:0%
+identical is actually related to that
+for the for for the derory boundary
+
+ align:start position:0%
+for the for for the derory boundary
+ 
+
+ align:start position:0%
+for the for for the derory boundary
+condition on both sides uh this is still
+
+ align:start position:0%
+condition on both sides uh this is still
+ 
+
+ align:start position:0%
+condition on both sides uh this is still
+a periodic boundary periodic function to
+
+ align:start position:0%
+a periodic boundary periodic function to
+ 
+
+ align:start position:0%
+a periodic boundary periodic function to
+Pi and so uh and so you get this in such
+
+ align:start position:0%
+Pi and so uh and so you get this in such
+ 
+
+ align:start position:0%
+Pi and so uh and so you get this in such
+a case say if say if one end point is is
+
+ align:start position:0%
+a case say if say if one end point is is
+ 
+
+ align:start position:0%
+a case say if say if one end point is is
+the new bounding condition but the other
+
+ align:start position:0%
+the new bounding condition but the other
+ 
+
+ align:start position:0%
+the new bounding condition but the other
+point end point is the rich bounding
+
+ align:start position:0%
+point end point is the rich bounding
+ 
+
+ align:start position:0%
+point end point is the rich bounding
+condition then the story is a little bit
+
+ align:start position:0%
+condition then the story is a little bit
+ 
+
+ align:start position:0%
+condition then the story is a little bit
+more subtle okay and uh then you
+
+ align:start position:0%
+more subtle okay and uh then you
+ 
+
+ align:start position:0%
+more subtle okay and uh then you
+actually get the then the then the um
+
+ align:start position:0%
+actually get the then the then the um
+ 
+
+ align:start position:0%
+actually get the then the then the um
+then the frequency of each modes become
+
+ align:start position:0%
+then the frequency of each modes become
+ 
+
+ align:start position:0%
+then the frequency of each modes become
+half integer rather than integer and
+
+ align:start position:0%
+half integer rather than integer and
+ 
+
+ align:start position:0%
+half integer rather than integer and
+then you will get the different Zer
+
+ align:start position:0%
+then you will get the different Zer
+ 
+
+ align:start position:0%
+then you will get the different Zer
+Point Energy and there the Spectrum will
+
+ align:start position:0%
+Point Energy and there the Spectrum will
+ 
+
+ align:start position:0%
+Point Energy and there the Spectrum will
+change exact okay um uh so I will not do
+
+ align:start position:0%
+change exact okay um uh so I will not do
+ 
+
+ align:start position:0%
+change exact okay um uh so I will not do
+it
+
+ align:start position:0%
+it
+ 
+
+ align:start position:0%
+it
+now maybe put it in your next p set so
+
+ align:start position:0%
+now maybe put it in your next p set so
+ 
+
+ align:start position:0%
+now maybe put it in your next p set so
+that you can do it
+
+ align:start position:0%
+that you can do it
+ 
+
+ align:start position:0%
+that you can do it
+yourself yeah yeah you have a question I
+
+ align:start position:0%
+yourself yeah yeah you have a question I
+ 
+
+ align:start position:0%
+yourself yeah yeah you have a question I
+think you answer the question what
+
+ align:start position:0%
+think you answer the question what
+ 
+
+ align:start position:0%
+think you answer the question what
+happens p
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+z Oh yeah yeah for the p z yeah indeed
+
+ align:start position:0%
+z Oh yeah yeah for the p z yeah indeed
+ 
+
+ align:start position:0%
+z Oh yeah yeah for the p z yeah indeed
+it's a little bit tricky to do the light
+
+ align:start position:0%
+it's a little bit tricky to do the light
+ 
+
+ align:start position:0%
+it's a little bit tricky to do the light
+con gaug yeah um um yeah for p z It's
+
+ align:start position:0%
+con gaug yeah um um yeah for p z It's
+ 
+
+ align:start position:0%
+con gaug yeah um um yeah for p z It's
+tricky to do that con gaug but you can
+
+ align:start position:0%
+tricky to do that con gaug but you can
+ 
+
+ align:start position:0%
+tricky to do that con gaug but you can
+do using other quantisation procedure
+
+ align:start position:0%
+do using other quantisation procedure
+ 
+
+ align:start position:0%
+do using other quantisation procedure
+then you can do the same same thing yeah
+
+ align:start position:0%
+then you can do the same same thing yeah
+ 
+
+ align:start position:0%
+then you can do the same same thing yeah
+but the conclusion does not change
+
+ align:start position:0%
+but the conclusion does not change
+ 
+
+ align:start position:0%
+but the conclusion does not change
+between different
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+piece yes maybe I miss this but for for
+
+ align:start position:0%
+piece yes maybe I miss this but for for
+ 
+
+ align:start position:0%
+piece yes maybe I miss this but for for
+the two different brains if you have a
+
+ align:start position:0%
+the two different brains if you have a
+ 
+
+ align:start position:0%
+the two different brains if you have a
+string going from one brain to another
+
+ align:start position:0%
+string going from one brain to another
+ 
+
+ align:start position:0%
+string going from one brain to another
+yeah you said from a point to a brain
+
+ align:start position:0%
+yeah you said from a point to a brain
+ 
+
+ align:start position:0%
+yeah you said from a point to a brain
+the story changes what about like from
+
+ align:start position:0%
+the story changes what about like from
+ 
+
+ align:start position:0%
+the story changes what about like from
+one brain to another is it exactly the
+
+ align:start position:0%
+one brain to another is it exactly the
+ 
+
+ align:start position:0%
+one brain to another is it exactly the
+same as this or is it oh oh yeah yeah
+
+ align:start position:0%
+same as this or is it oh oh yeah yeah
+ 
+
+ align:start position:0%
+same as this or is it oh oh yeah yeah
+that's also a good question um which I
+
+ align:start position:0%
+that's also a good question um which I
+ 
+
+ align:start position:0%
+that's also a good question um which I
+made Might already have something like
+
+ align:start position:0%
+made Might already have something like
+ 
+
+ align:start position:0%
+made Might already have something like
+this in the current P set um and if not
+
+ align:start position:0%
+this in the current P set um and if not
+ 
+
+ align:start position:0%
+this in the current P set um and if not
+I will put in the next p set
+
+ align:start position:0%
+I will put in the next p set
+ 
+
+ align:start position:0%
+I will put in the next p set
+because you asked
+
+ align:start position:0%
+because you asked
+ 
+
+ align:start position:0%
+because you asked
+uh um yeah you see there's a distance
+
+ align:start position:0%
+uh um yeah you see there's a distance
+ 
+
+ align:start position:0%
+uh um yeah you see there's a distance
+between them so now you actually need to
+
+ align:start position:0%
+between them so now you actually need to
+ 
+
+ align:start position:0%
+between them so now you actually need to
+include the sigma
+
+ align:start position:0%
+include the sigma
+ 
+
+ align:start position:0%
+include the sigma
+term now you actually need to include
+
+ align:start position:0%
+term now you actually need to include
+ 
+
+ align:start position:0%
+term now you actually need to include
+the sigma term here and to count this
+
+ align:start position:0%
+the sigma term here and to count this
+ 
+
+ align:start position:0%
+the sigma term here and to count this
+difference because now the zero and the
+
+ align:start position:0%
+difference because now the zero and the
+ 
+
+ align:start position:0%
+difference because now the zero and the
+pi is no longer the same yeah the here I
+
+ align:start position:0%
+pi is no longer the same yeah the here I
+ 
+
+ align:start position:0%
+pi is no longer the same yeah the here I
+don't need to put in the sigma term
+
+ align:start position:0%
+don't need to put in the sigma term
+ 
+
+ align:start position:0%
+don't need to put in the sigma term
+because the zero and the pi are the same
+
+ align:start position:0%
+because the zero and the pi are the same
+ 
+
+ align:start position:0%
+because the zero and the pi are the same
+yeah so the0 Point Energy would change
+
+ align:start position:0%
+yeah so the0 Point Energy would change
+ 
+
+ align:start position:0%
+yeah so the0 Point Energy would change
+yeah they Point Energy will change and
+
+ align:start position:0%
+yeah they Point Energy will change and
+ 
+
+ align:start position:0%
+yeah they Point Energy will change and
+and essentially it's given by the mass
+
+ align:start position:0%
+and essentially it's given by the mass
+ 
+
+ align:start position:0%
+and essentially it's given by the mass
+of the string stretched between them
+
+ align:start position:0%
+of the string stretched between them
+ 
+
+ align:start position:0%
+of the string stretched between them
+yeah yeah so that will be yeah that's a
+
+ align:start position:0%
+yeah yeah so that will be yeah that's a
+ 
+
+ align:start position:0%
+yeah yeah so that will be yeah that's a
+very instructive exercise actually maybe
+
+ align:start position:0%
+very instructive exercise actually maybe
+ 
+
+ align:start position:0%
+very instructive exercise actually maybe
+I already put in the current piece I
+
+ align:start position:0%
+I already put in the current piece I
+ 
+
+ align:start position:0%
+I already put in the current piece I
+don't remember um
+
+ align:start position:0%
+don't remember um
+ 
+
+ align:start position:0%
+don't remember um
+anyway other
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+questions good so now now let's look at
+
+ align:start position:0%
+questions good so now now let's look at
+ 
+
+ align:start position:0%
+questions good so now now let's look at
+more explicit at the open stren Spectrum
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so again it's the same thing you just
+
+ align:start position:0%
+so again it's the same thing you just
+ 
+
+ align:start position:0%
+so again it's the same thing you just
+act Alpha minus
+
+ align:start position:0%
+act Alpha minus
+ 
+
+ align:start position:0%
+act Alpha minus
+N1
+
+ align:start position:0%
+N1
+ 
+
+ align:start position:0%
+N1
+mu1 you can act M1
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+times say
+
+ align:start position:0%
+times say
+ 
+
+ align:start position:0%
+times say
+NK mu
+
+ align:start position:0%
+NK mu
+ 
+
+ align:start position:0%
+NK mu
+k n k
+
+ align:start position:0%
+k n k
+ 
+
+ align:start position:0%
+k n k
+MK the only
+
+ align:start position:0%
+MK the only
+ 
+
+ align:start position:0%
+MK the only
+difference is now your vacuum state is
+
+ align:start position:0%
+difference is now your vacuum state is
+ 
+
+ align:start position:0%
+difference is now your vacuum state is
+only can only have momentum in the P
+
+ align:start position:0%
+only can only have momentum in the P
+ 
+
+ align:start position:0%
+only can only have momentum in the P
+Alpha Direction that's essentially the
+
+ align:start position:0%
+Alpha Direction that's essentially the
+ 
+
+ align:start position:0%
+Alpha Direction that's essentially the
+only difference okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and uh and again the mass square now is
+
+ align:start position:0%
+and uh and again the mass square now is
+ 
+
+ align:start position:0%
+and uh and again the mass square now is
+just minus P Alpha P Alpha okay only
+
+ align:start position:0%
+just minus P Alpha P Alpha okay only
+ 
+
+ align:start position:0%
+just minus P Alpha P Alpha okay only
+along the Alum
+
+ align:start position:0%
+along the Alum
+ 
+
+ align:start position:0%
+along the Alum
+directions so so this is
+
+ align:start position:0%
+directions so so this is
+ 
+
+ align:start position:0%
+directions so so this is
+really then each mod on the string each
+
+ align:start position:0%
+really then each mod on the string each
+ 
+
+ align:start position:0%
+really then each mod on the string each
+oscillation modes of the string now
+
+ align:start position:0%
+oscillation modes of the string now
+ 
+
+ align:start position:0%
+oscillation modes of the string now
+should really corresponding to a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+particle or fields in P plus one
+
+ align:start position:0%
+particle or fields in P plus one
+ 
+
+ align:start position:0%
+particle or fields in P plus one
+dimensional
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+what
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+volume of the DP
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+brain okay so we call this is the W
+
+ align:start position:0%
+brain okay so we call this is the W
+ 
+
+ align:start position:0%
+brain okay so we call this is the W
+volume we call the directions all these
+
+ align:start position:0%
+volume we call the directions all these
+ 
+
+ align:start position:0%
+volume we call the directions all these
+directions together is the W volume of
+
+ align:start position:0%
+directions together is the W volume of
+ 
+
+ align:start position:0%
+directions together is the W volume of
+the DP brain so so since that since the
+
+ align:start position:0%
+the DP brain so so since that since the
+ 
+
+ align:start position:0%
+the DP brain so so since that since the
+string can only move along the DP brain
+
+ align:start position:0%
+string can only move along the DP brain
+ 
+
+ align:start position:0%
+string can only move along the DP brain
+so so they can only corresponding to the
+
+ align:start position:0%
+so so they can only corresponding to the
+ 
+
+ align:start position:0%
+so so they can only corresponding to the
+field or particles within the DP brain
+
+ align:start position:0%
+field or particles within the DP brain
+ 
+
+ align:start position:0%
+field or particles within the DP brain
+they cannot move in the opposite
+
+ align:start position:0%
+they cannot move in the opposite
+ 
+
+ align:start position:0%
+they cannot move in the opposite
+direction they cannot move in the in the
+
+ align:start position:0%
+direction they cannot move in the in the
+ 
+
+ align:start position:0%
+direction they cannot move in the in the
+perpendicular
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Direction okay so so the really
+
+ align:start position:0%
+Direction okay so so the really
+ 
+
+ align:start position:0%
+Direction okay so so the really
+leaves on the brain
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay and uh in this then then all those
+
+ align:start position:0%
+okay and uh in this then then all those
+ 
+
+ align:start position:0%
+okay and uh in this then then all those
+things may be
+
+ align:start position:0%
+things may be
+ 
+
+ align:start position:0%
+things may be
+considered as the excitations of the
+
+ align:start position:0%
+considered as the excitations of the
+ 
+
+ align:start position:0%
+considered as the excitations of the
+brains okay
+
+ align:start position:0%
+brains okay
+ 
+
+ align:start position:0%
+brains okay
+what can be the string can be regarded
+
+ align:start position:0%
+what can be the string can be regarded
+ 
+
+ align:start position:0%
+what can be the string can be regarded
+as excitation yeah that's right yeah
+
+ align:start position:0%
+as excitation yeah that's right yeah
+ 
+
+ align:start position:0%
+as excitation yeah that's right yeah
+because you can excite certain strings
+
+ align:start position:0%
+because you can excite certain strings
+ 
+
+ align:start position:0%
+because you can excite certain strings
+and not excite strings excit and they're
+
+ align:start position:0%
+and not excite strings excit and they're
+ 
+
+ align:start position:0%
+and not excite strings excit and they're
+all moving along the
+
+ align:start position:0%
+all moving along the
+ 
+
+ align:start position:0%
+all moving along the
+brain
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah and the important thing is that the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+states should fall into
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+representations now of this symmetry
+
+ align:start position:0%
+representations now of this symmetry
+ 
+
+ align:start position:0%
+representations now of this symmetry
+because that's the only remaining
+
+ align:start position:0%
+because that's the only remaining
+ 
+
+ align:start position:0%
+because that's the only remaining
+symmetry
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+point one
+
+ align:start position:0%
+point one
+ 
+
+ align:start position:0%
+point one
+p and the rotation in the transverse
+
+ align:start position:0%
+p and the rotation in the transverse
+ 
+
+ align:start position:0%
+p and the rotation in the transverse
+directions
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay and again just by
+
+ align:start position:0%
+okay and again just by
+ 
+
+ align:start position:0%
+okay and again just by
+this you can show that you actually make
+
+ align:start position:0%
+this you can show that you actually make
+ 
+
+ align:start position:0%
+this you can show that you actually make
+sense only in the 26 Dimension okay
+
+ align:start position:0%
+sense only in the 26 Dimension okay
+ 
+
+ align:start position:0%
+sense only in the 26 Dimension okay
+again makes sense only in the 26
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Dimension so so now let's again look at
+
+ align:start position:0%
+Dimension so so now let's again look at
+ 
+
+ align:start position:0%
+Dimension so so now let's again look at
+the mass States so so as I mentioned
+
+ align:start position:0%
+the mass States so so as I mentioned
+ 
+
+ align:start position:0%
+the mass States so so as I mentioned
+before the mass formula is exactly the
+
+ align:start position:0%
+before the mass formula is exactly the
+ 
+
+ align:start position:0%
+before the mass formula is exactly the
+same as before because the oscillation
+
+ align:start position:0%
+same as before because the oscillation
+ 
+
+ align:start position:0%
+same as before because the oscillation
+mode behaves exactly the same so the
+
+ align:start position:0%
+mode behaves exactly the same so the
+ 
+
+ align:start position:0%
+mode behaves exactly the same so the
+mass formula exactly behaves the same as
+
+ align:start position:0%
+mass formula exactly behaves the same as
+ 
+
+ align:start position:0%
+mass formula exactly behaves the same as
+before so the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+massat then is the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+following yeah yeah when we see the
+
+ align:start position:0%
+following yeah yeah when we see the
+ 
+
+ align:start position:0%
+following yeah yeah when we see the
+particles in p+ one dimension World
+
+ align:start position:0%
+particles in p+ one dimension World
+ 
+
+ align:start position:0%
+particles in p+ one dimension World
+volume yeah but you know that inary the
+
+ align:start position:0%
+volume yeah but you know that inary the
+ 
+
+ align:start position:0%
+volume yeah but you know that inary the
+particles it's like a very local object
+
+ align:start position:0%
+particles it's like a very local object
+ 
+
+ align:start position:0%
+particles it's like a very local object
+but the open string can you know one end
+
+ align:start position:0%
+but the open string can you know one end
+ 
+
+ align:start position:0%
+but the open string can you know one end
+one one one end of open string located
+
+ align:start position:0%
+one one one end of open string located
+ 
+
+ align:start position:0%
+one one one end of open string located
+one point not the other one located very
+
+ align:start position:0%
+one point not the other one located very
+ 
+
+ align:start position:0%
+one point not the other one located very
+far away but is that picture same as no
+
+ align:start position:0%
+far away but is that picture same as no
+ 
+
+ align:start position:0%
+far away but is that picture same as no
+no
+
+ align:start position:0%
+no
+ 
+
+ align:start position:0%
+no
+it that's a good
+
+ align:start position:0%
+it that's a good
+ 
+
+ align:start position:0%
+it that's a good
+question so
+
+ align:start position:0%
+question so
+ 
+
+ align:start position:0%
+question so
+um when I say particles is I'm talking
+
+ align:start position:0%
+um when I say particles is I'm talking
+ 
+
+ align:start position:0%
+um when I say particles is I'm talking
+about the uh Center of mass motion okay
+
+ align:start position:0%
+about the uh Center of mass motion okay
+ 
+
+ align:start position:0%
+about the uh Center of mass motion okay
+okay uh uh yeah for each oscillation
+
+ align:start position:0%
+okay uh uh yeah for each oscillation
+ 
+
+ align:start position:0%
+okay uh uh yeah for each oscillation
+modes you see that's corresponding to
+
+ align:start position:0%
+modes you see that's corresponding to
+ 
+
+ align:start position:0%
+modes you see that's corresponding to
+yeah for
+
+ align:start position:0%
+yeah for
+ 
+
+ align:start position:0%
+yeah for
+particular for particular oscillation
+
+ align:start position:0%
+particular for particular oscillation
+ 
+
+ align:start position:0%
+particular for particular oscillation
+modes then the other than other than
+
+ align:start position:0%
+modes then the other than other than
+ 
+
+ align:start position:0%
+modes then the other than other than
+those quantum number yeah uh uh yeah let
+
+ align:start position:0%
+those quantum number yeah uh uh yeah let
+ 
+
+ align:start position:0%
+those quantum number yeah uh uh yeah let
+me finish this I will answer that
+
+ align:start position:0%
+me finish this I will answer that
+ 
+
+ align:start position:0%
+me finish this I will answer that
+question yeah yeah I will write this
+
+ align:start position:0%
+question yeah yeah I will write this
+ 
+
+ align:start position:0%
+question yeah yeah I will write this
+down then see explicitly so so let
+
+ align:start position:0%
+down then see explicitly so so let
+ 
+
+ align:start position:0%
+down then see explicitly so so let
+Master States so so
+
+ align:start position:0%
+Master States so so
+ 
+
+ align:start position:0%
+Master States so so
+again using the light com so again we
+
+ align:start position:0%
+again using the light com so again we
+ 
+
+ align:start position:0%
+again using the light com so again we
+use the light com you can separate the
+
+ align:start position:0%
+use the light com you can separate the
+ 
+
+ align:start position:0%
+use the light com you can separate the
+direction to plus
+
+ align:start position:0%
+direction to plus
+ 
+
+ align:start position:0%
+direction to plus
+minus and I in the in the Newman
+
+ align:start position:0%
+minus and I in the in the Newman
+ 
+
+ align:start position:0%
+minus and I in the in the Newman
+Direction and in the D direction again
+
+ align:start position:0%
+Direction and in the D direction again
+ 
+
+ align:start position:0%
+Direction and in the D direction again
+it's just the p+1 to D minus one
+
+ align:start position:0%
+it's just the p+1 to D minus one
+ 
+
+ align:start position:0%
+it's just the p+1 to D minus one
+okay and then the M mode would be the
+
+ align:start position:0%
+okay and then the M mode would be the
+ 
+
+ align:start position:0%
+okay and then the M mode would be the
+same as before you have Alpha minus one
+
+ align:start position:0%
+same as before you have Alpha minus one
+ 
+
+ align:start position:0%
+same as before you have Alpha minus one
+I acting on P
+
+ align:start position:0%
+I acting on P
+ 
+
+ align:start position:0%
+I acting on P
+Alpha and Alpha minus one a AC on P
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Alpha and
+
+ align:start position:0%
+Alpha and
+ 
+
+ align:start position:0%
+Alpha and
+plus plus infinite
+
+ align:start position:0%
+plus plus infinite
+ 
+
+ align:start position:0%
+plus plus infinite
+number plus the uh uh yeah plus infinite
+
+ align:start position:0%
+number plus the uh uh yeah plus infinite
+ 
+
+ align:start position:0%
+number plus the uh uh yeah plus infinite
+number of massive modes
+
+ align:start position:0%
+number of massive modes
+ 
+
+ align:start position:0%
+number of massive modes
+okay so let me just initiate this
+
+ align:start position:0%
+okay so let me just initiate this
+ 
+
+ align:start position:0%
+okay so let me just initiate this
+point so this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so the lighton
+
+ align:start position:0%
+so the lighton
+ 
+
+ align:start position:0%
+so the lighton
+S as before the lighton gauge further
+
+ align:start position:0%
+S as before the lighton gauge further
+ 
+
+ align:start position:0%
+S as before the lighton gauge further
+breaks this pite symmetry to only only a
+
+ align:start position:0%
+breaks this pite symmetry to only only a
+ 
+
+ align:start position:0%
+breaks this pite symmetry to only only a
+subg group but you can already see from
+
+ align:start position:0%
+subg group but you can already see from
+ 
+
+ align:start position:0%
+subg group but you can already see from
+here this must corresponding to a vector
+
+ align:start position:0%
+here this must corresponding to a vector
+ 
+
+ align:start position:0%
+here this must corresponding to a vector
+particle okay so uh so this is like a
+
+ align:start position:0%
+particle okay so uh so this is like a
+ 
+
+ align:start position:0%
+particle okay so uh so this is like a
+mess
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Vector M this vector
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah so uh uh so to answer your question
+
+ align:start position:0%
+yeah so uh uh so to answer your question
+ 
+
+ align:start position:0%
+yeah so uh uh so to answer your question
+so example for for typical modes like
+
+ align:start position:0%
+so example for for typical modes like
+ 
+
+ align:start position:0%
+so example for for typical modes like
+this the only quantum number you have is
+
+ align:start position:0%
+this the only quantum number you have is
+ 
+
+ align:start position:0%
+this the only quantum number you have is
+p
+
+ align:start position:0%
+p
+ 
+
+ align:start position:0%
+p
+Alpha and and this Vector
+
+ align:start position:0%
+Alpha and and this Vector
+ 
+
+ align:start position:0%
+Alpha and and this Vector
+indices this Vector index so so so from
+
+ align:start position:0%
+indices this Vector index so so so from
+ 
+
+ align:start position:0%
+indices this Vector index so so so from
+the perspective of the quantum number
+
+ align:start position:0%
+the perspective of the quantum number
+ 
+
+ align:start position:0%
+the perspective of the quantum number
+and this really is just like a vector
+
+ align:start position:0%
+and this really is just like a vector
+ 
+
+ align:start position:0%
+and this really is just like a vector
+particle yeah just like a vector
+
+ align:start position:0%
+particle yeah just like a vector
+ 
+
+ align:start position:0%
+particle yeah just like a vector
+particle um and and then you can
+
+ align:start position:0%
+particle um and and then you can
+ 
+
+ align:start position:0%
+particle um and and then you can
+describe it by by Vector field
+
+ align:start position:0%
+describe it by by Vector field
+ 
+
+ align:start position:0%
+describe it by by Vector field
+Etc it is a very good
+
+ align:start position:0%
+Etc it is a very good
+ 
+
+ align:start position:0%
+Etc it is a very good
+question say
+
+ align:start position:0%
+question say
+ 
+
+ align:start position:0%
+question say
+suppose in the situation which I have a
+
+ align:start position:0%
+suppose in the situation which I have a
+ 
+
+ align:start position:0%
+suppose in the situation which I have a
+string suppose the stren is really very
+
+ align:start position:0%
+string suppose the stren is really very
+ 
+
+ align:start position:0%
+string suppose the stren is really very
+long it's very big then I should be able
+
+ align:start position:0%
+long it's very big then I should be able
+ 
+
+ align:start position:0%
+long it's very big then I should be able
+to see this one dimensional structure
+
+ align:start position:0%
+to see this one dimensional structure
+ 
+
+ align:start position:0%
+to see this one dimensional structure
+indeed uh then that means that even
+
+ align:start position:0%
+indeed uh then that means that even
+ 
+
+ align:start position:0%
+indeed uh then that means that even
+though this correspond this this just
+
+ align:start position:0%
+though this correspond this this just
+ 
+
+ align:start position:0%
+though this correspond this this just
+corresponding to one particular mode of
+
+ align:start position:0%
+corresponding to one particular mode of
+ 
+
+ align:start position:0%
+corresponding to one particular mode of
+the string and and to see the string
+
+ align:start position:0%
+the string and and to see the string
+ 
+
+ align:start position:0%
+the string and and to see the string
+structure you have to be able to see you
+
+ align:start position:0%
+structure you have to be able to see you
+ 
+
+ align:start position:0%
+structure you have to be able to see you
+can excite this into other uh other
+
+ align:start position:0%
+can excite this into other uh other
+ 
+
+ align:start position:0%
+can excite this into other uh other
+different modes
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Etc let say if we just stretch the
+
+ align:start position:0%
+Etc let say if we just stretch the
+ 
+
+ align:start position:0%
+Etc let say if we just stretch the
+string yeah I mean yeah yeah stretch the
+
+ align:start position:0%
+string yeah I mean yeah yeah stretch the
+ 
+
+ align:start position:0%
+string yeah I mean yeah yeah stretch the
+string B to excite the string in a
+
+ align:start position:0%
+string B to excite the string in a
+ 
+
+ align:start position:0%
+string B to excite the string in a
+different way it means living this
+
+ align:start position:0%
+different way it means living this
+ 
+
+ align:start position:0%
+different way it means living this
+particular State oh I see yeah yeah just
+
+ align:start position:0%
+particular State oh I see yeah yeah just
+ 
+
+ align:start position:0%
+particular State oh I see yeah yeah just
+I'm talking about the interpretation of
+
+ align:start position:0%
+I'm talking about the interpretation of
+ 
+
+ align:start position:0%
+I'm talking about the interpretation of
+this particular state which is like A
+
+ align:start position:0%
+this particular state which is like A
+ 
+
+ align:start position:0%
+this particular state which is like A
+Spacetime
+
+ align:start position:0%
+Spacetime
+ 
+
+ align:start position:0%
+Spacetime
+particle okay actually this St uh
+
+ align:start position:0%
+particle okay actually this St uh
+ 
+
+ align:start position:0%
+particle okay actually this St uh
+conversity decided the all the
+
+ align:start position:0%
+conversity decided the all the
+ 
+
+ align:start position:0%
+conversity decided the all the
+configuration of the open SP yeah it
+
+ align:start position:0%
+configuration of the open SP yeah it
+ 
+
+ align:start position:0%
+configuration of the open SP yeah it
+determines all the configuration
+
+ align:start position:0%
+determines all the configuration
+ 
+
+ align:start position:0%
+determines all the configuration
+determin all the oscillation mode of the
+
+ align:start position:0%
+determin all the oscillation mode of the
+ 
+
+ align:start position:0%
+determin all the oscillation mode of the
+open string just the other oscillation
+
+ align:start position:0%
+open string just the other oscillation
+ 
+
+ align:start position:0%
+open string just the other oscillation
+modes they all lot excited okay but of
+
+ align:start position:0%
+modes they all lot excited okay but of
+ 
+
+ align:start position:0%
+modes they all lot excited okay but of
+course if if you can observe this one
+
+ align:start position:0%
+course if if you can observe this one
+ 
+
+ align:start position:0%
+course if if you can observe this one
+dimensional object then you can find the
+
+ align:start position:0%
+dimensional object then you can find the
+ 
+
+ align:start position:0%
+dimensional object then you can find the
+ways to excite them and and then you
+
+ align:start position:0%
+ways to excite them and and then you
+ 
+
+ align:start position:0%
+ways to excite them and and then you
+know this is not a particle it's one
+
+ align:start position:0%
+know this is not a particle it's one
+ 
+
+ align:start position:0%
+know this is not a particle it's one
+dimensional object
+
+ align:start position:0%
+dimensional object
+ 
+
+ align:start position:0%
+dimensional object
+ex yeah
+
+ align:start position:0%
+ex yeah
+ 
+
+ align:start position:0%
+ex yeah
+yeah but in order to see this one diens
+
+ align:start position:0%
+yeah but in order to see this one diens
+ 
+
+ align:start position:0%
+yeah but in order to see this one diens
+structure you have to Pro a final
+
+ align:start position:0%
+structure you have to Pro a final
+ 
+
+ align:start position:0%
+structure you have to Pro a final
+structure than just those quantum
+
+ align:start position:0%
+structure than just those quantum
+ 
+
+ align:start position:0%
+structure than just those quantum
+numbers yeah if if those are the only
+
+ align:start position:0%
+numbers yeah if if those are the only
+ 
+
+ align:start position:0%
+numbers yeah if if those are the only
+quantum number you can Pro then it's
+
+ align:start position:0%
+quantum number you can Pro then it's
+ 
+
+ align:start position:0%
+quantum number you can Pro then it's
+like
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+particle so so this is like M Vector but
+
+ align:start position:0%
+particle so so this is like M Vector but
+ 
+
+ align:start position:0%
+particle so so this is like M Vector but
+now those
+
+ align:start position:0%
+now those
+ 
+
+ align:start position:0%
+now those
+Skies they have index a which is not in
+
+ align:start position:0%
+Skies they have index a which is not in
+ 
+
+ align:start position:0%
+Skies they have index a which is not in
+the pite here so those are now scal
+
+ align:start position:0%
+the pite here so those are now scal
+ 
+
+ align:start position:0%
+the pite here so those are now scal
+field
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Fields okay those are Scala fields on
+
+ align:start position:0%
+Fields okay those are Scala fields on
+ 
+
+ align:start position:0%
+Fields okay those are Scala fields on
+the on the on the world volume of the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+difference okay so now we
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+find so previously when we consider the
+
+ align:start position:0%
+find so previously when we consider the
+ 
+
+ align:start position:0%
+find so previously when we consider the
+all human directions we only see a
+
+ align:start position:0%
+all human directions we only see a
+ 
+
+ align:start position:0%
+all human directions we only see a
+vector field they moving all 26
+
+ align:start position:0%
+vector field they moving all 26
+ 
+
+ align:start position:0%
+vector field they moving all 26
+Dimension but
+
+ align:start position:0%
+Dimension but
+ 
+
+ align:start position:0%
+Dimension but
+now so this so This masses modes they
+
+ align:start position:0%
+now so this so This masses modes they
+ 
+
+ align:start position:0%
+now so this so This masses modes they
+give
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+rise to a vector field the M Vector
+
+ align:start position:0%
+rise to a vector field the M Vector
+ 
+
+ align:start position:0%
+rise to a vector field the M Vector
+field a
+
+ align:start position:0%
+field a
+ 
+
+ align:start position:0%
+field a
+alpha and
+
+ align:start position:0%
+alpha and
+ 
+
+ align:start position:0%
+alpha and
+uh D minus P minus one scal of field
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+by a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so essentially when you introduce
+
+ align:start position:0%
+okay so essentially when you introduce
+ 
+
+ align:start position:0%
+okay so essentially when you introduce
+de brain compare to the space fing brain
+
+ align:start position:0%
+de brain compare to the space fing brain
+ 
+
+ align:start position:0%
+de brain compare to the space fing brain
+case which we considered before in the
+
+ align:start position:0%
+case which we considered before in the
+ 
+
+ align:start position:0%
+case which we considered before in the
+Luman
+
+ align:start position:0%
+Luman
+ 
+
+ align:start position:0%
+Luman
+Direction the some component of those
+
+ align:start position:0%
+Direction the some component of those
+ 
+
+ align:start position:0%
+Direction the some component of those
+gauge
+
+ align:start position:0%
+gauge
+ 
+
+ align:start position:0%
+gauge
+Fields now become the oscillation in the
+
+ align:start position:0%
+Fields now become the oscillation in the
+ 
+
+ align:start position:0%
+Fields now become the oscillation in the
+transverse Direction and now they just
+
+ align:start position:0%
+transverse Direction and now they just
+ 
+
+ align:start position:0%
+transverse Direction and now they just
+essentially become a a scaler Fields
+
+ align:start position:0%
+essentially become a a scaler Fields
+ 
+
+ align:start position:0%
+essentially become a a scaler Fields
+okay is this
+
+ align:start position:0%
+okay is this
+ 
+
+ align:start position:0%
+okay is this
+clear so so now instead you have a a
+
+ align:start position:0%
+clear so so now instead you have a a
+ 
+
+ align:start position:0%
+clear so so now instead you have a a
+smaller Vector field plus some plus a
+
+ align:start position:0%
+smaller Vector field plus some plus a
+ 
+
+ align:start position:0%
+smaller Vector field plus some plus a
+bunch of Scala
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Fields as we said before then the low
+
+ align:start position:0%
+Fields as we said before then the low
+ 
+
+ align:start position:0%
+Fields as we said before then the low
+energy effective
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+action so the low energy effective
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+action for such Master
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+modes must be have the
+
+ align:start position:0%
+modes must be have the
+ 
+
+ align:start position:0%
+modes must be have the
+structure say so this is in the p+ one
+
+ align:start position:0%
+structure say so this is in the p+ one
+ 
+
+ align:start position:0%
+structure say so this is in the p+ one
+dimensional World volume of the string
+
+ align:start position:0%
+dimensional World volume of the string
+ 
+
+ align:start position:0%
+dimensional World volume of the string
+say of a Max well
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the and uh and just uh as a uh say Mass
+
+ align:start position:0%
+the and uh and just uh as a uh say Mass
+ 
+
+ align:start position:0%
+the and uh and just uh as a uh say Mass
+scaler
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+field and then of course they
+
+ align:start position:0%
+field and then of course they
+ 
+
+ align:start position:0%
+field and then of course they
+are more complicated contributions just
+
+ align:start position:0%
+are more complicated contributions just
+ 
+
+ align:start position:0%
+are more complicated contributions just
+this is a low energy and L
+
+ align:start position:0%
+this is a low energy and L
+ 
+
+ align:start position:0%
+this is a low energy and L
+energy then then the structure of those
+
+ align:start position:0%
+energy then then the structure of those
+ 
+
+ align:start position:0%
+energy then then the structure of those
+excitations that must be described by
+
+ align:start position:0%
+excitations that must be described by
+ 
+
+ align:start position:0%
+excitations that must be described by
+this kind of low energy factive
+
+ align:start position:0%
+this kind of low energy factive
+ 
+
+ align:start position:0%
+this kind of low energy factive
+Theory okay and this is again just
+
+ align:start position:0%
+Theory okay and this is again just
+ 
+
+ align:start position:0%
+Theory okay and this is again just
+determined by the universality of a m
+
+ align:start position:0%
+determined by the universality of a m
+ 
+
+ align:start position:0%
+determined by the universality of a m
+modes
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+now now there's
+
+ align:start position:0%
+now now there's
+ 
+
+ align:start position:0%
+now now there's
+very so now let me first
+
+ align:start position:0%
+very so now let me first
+ 
+
+ align:start position:0%
+very so now let me first
+note let me emphasize the a
+
+ align:start position:0%
+note let me emphasize the a
+ 
+
+ align:start position:0%
+note let me emphasize the a
+point is said the
+
+ align:start position:0%
+point is said the
+ 
+
+ align:start position:0%
+point is said the
+number of Master mode M Scala
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+field so we have such a bunch of scalar
+
+ align:start position:0%
+field so we have such a bunch of scalar
+ 
+
+ align:start position:0%
+field so we have such a bunch of scalar
+Fields okay it's exactly the number of
+
+ align:start position:0%
+Fields okay it's exactly the number of
+ 
+
+ align:start position:0%
+Fields okay it's exactly the number of
+transvers
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+interactions to the deep
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+brain okay so essentially associated
+
+ align:start position:0%
+brain okay so essentially associated
+ 
+
+ align:start position:0%
+brain okay so essentially associated
+with each transverse Direction you have
+
+ align:start position:0%
+with each transverse Direction you have
+ 
+
+ align:start position:0%
+with each transverse Direction you have
+a scalar excitations you you have a mly
+
+ align:start position:0%
+a scalar excitations you you have a mly
+ 
+
+ align:start position:0%
+a scalar excitations you you have a mly
+scalar
+
+ align:start position:0%
+scalar
+ 
+
+ align:start position:0%
+scalar
+field okay
+
+ align:start position:0%
+field okay
+ 
+
+ align:start position:0%
+field okay
+so emphasize this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+point so those scal
+
+ align:start position:0%
+point so those scal
+ 
+
+ align:start position:0%
+point so those scal
+fields some of you may can already have
+
+ align:start position:0%
+fields some of you may can already have
+ 
+
+ align:start position:0%
+fields some of you may can already have
+guessed they have a very simple
+
+ align:start position:0%
+guessed they have a very simple
+ 
+
+ align:start position:0%
+guessed they have a very simple
+physical
+
+ align:start position:0%
+physical
+ 
+
+ align:start position:0%
+physical
+explanation they have very they have a
+
+ align:start position:0%
+explanation they have very they have a
+ 
+
+ align:start position:0%
+explanation they have very they have a
+very simple physical
+
+ align:start position:0%
+very simple physical
+ 
+
+ align:start position:0%
+very simple physical
+interpretation and those Scala field
+
+ align:start position:0%
+interpretation and those Scala field
+ 
+
+ align:start position:0%
+interpretation and those Scala field
+they can be considered as as describing
+
+ align:start position:0%
+they can be considered as as describing
+ 
+
+ align:start position:0%
+they can be considered as as describing
+the motions and the fluctuations of the
+
+ align:start position:0%
+the motions and the fluctuations of the
+ 
+
+ align:start position:0%
+the motions and the fluctuations of the
+de brain in the transverse
+
+ align:start position:0%
+de brain in the transverse
+ 
+
+ align:start position:0%
+de brain in the transverse
+directions
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so for each transverse Direction
+
+ align:start position:0%
+okay so for each transverse Direction
+ 
+
+ align:start position:0%
+okay so for each transverse Direction
+you have such a massive scalar
+
+ align:start position:0%
+you have such a massive scalar
+ 
+
+ align:start position:0%
+you have such a massive scalar
+field and each of scalar
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+field for
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so more precisely so more explicitly
+
+ align:start position:0%
+so more precisely so more explicitly
+ 
+
+ align:start position:0%
+so more precisely so more explicitly
+just as a as as a cartoon picture
+
+ align:start position:0%
+just as a as as a cartoon picture
+ 
+
+ align:start position:0%
+just as a as as a cartoon picture
+suppose let's consider say the P minus
+
+ align:start position:0%
+suppose let's consider say the P minus
+ 
+
+ align:start position:0%
+suppose let's consider say the P minus
+One
+
+ align:start position:0%
+One
+ 
+
+ align:start position:0%
+One
+Direction p+ One Direction this
+
+ align:start position:0%
+Direction p+ One Direction this
+ 
+
+ align:start position:0%
+Direction p+ One Direction this
+direction uh p+1
+
+ align:start position:0%
+direction uh p+1
+ 
+
+ align:start position:0%
+direction uh p+1
+Direction so suppose you have a dein
+
+ align:start position:0%
+Direction so suppose you have a dein
+ 
+
+ align:start position:0%
+Direction so suppose you have a dein
+sitting here at some value of
+
+ align:start position:0%
+sitting here at some value of
+ 
+
+ align:start position:0%
+sitting here at some value of
+a
+
+ align:start position:0%
+a
+ 
+
+ align:start position:0%
+a
+okay so when we impose the when we
+
+ align:start position:0%
+okay so when we impose the when we
+ 
+
+ align:start position:0%
+okay so when we impose the when we
+impose the D binary
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+condition yeah so uh uh uh so those are
+
+ align:start position:0%
+condition yeah so uh uh uh so those are
+ 
+
+ align:start position:0%
+condition yeah so uh uh uh so those are
+the X1 01 and P directions
+
+ align:start position:0%
+the X1 01 and P directions
+ 
+
+ align:start position:0%
+the X1 01 and P directions
+okay yeah yeah uh um yeah this is other
+
+ align:start position:0%
+okay yeah yeah uh um yeah this is other
+ 
+
+ align:start position:0%
+okay yeah yeah uh um yeah this is other
+uh uh x0 and the P directions uh you
+
+ align:start position:0%
+uh uh x0 and the P directions uh you
+ 
+
+ align:start position:0%
+uh uh x0 and the P directions uh you
+have a debring sitting here at some
+
+ align:start position:0%
+have a debring sitting here at some
+ 
+
+ align:start position:0%
+have a debring sitting here at some
+value of
+
+ align:start position:0%
+value of
+ 
+
+ align:start position:0%
+value of
+a so when we impulse the Der boundary
+
+ align:start position:0%
+a so when we impulse the Der boundary
+ 
+
+ align:start position:0%
+a so when we impulse the Der boundary
+conditions that boundary condition does
+
+ align:start position:0%
+conditions that boundary condition does
+ 
+
+ align:start position:0%
+conditions that boundary condition does
+not depend on the value of x0 and P so
+
+ align:start position:0%
+not depend on the value of x0 and P so
+ 
+
+ align:start position:0%
+not depend on the value of x0 and P so
+they are same everywhere so that's why I
+
+ align:start position:0%
+they are same everywhere so that's why I
+ 
+
+ align:start position:0%
+they are same everywhere so that's why I
+draw it
+
+ align:start position:0%
+draw it
+ 
+
+ align:start position:0%
+draw it
+flat exact
+
+ align:start position:0%
+flat exact
+ 
+
+ align:start position:0%
+flat exact
+flat but now if you have some
+
+ align:start position:0%
+flat but now if you have some
+ 
+
+ align:start position:0%
+flat but now if you have some
+excitations in the Five p+ One
+
+ align:start position:0%
+excitations in the Five p+ One
+ 
+
+ align:start position:0%
+excitations in the Five p+ One
+Direction so 5 p+ one is a field
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+in the world volume of the half can have
+
+ align:start position:0%
+in the world volume of the half can have
+ 
+
+ align:start position:0%
+in the world volume of the half can have
+P for
+
+ align:start position:0%
+P for
+ 
+
+ align:start position:0%
+P for
+momentum you can go to coordinate space
+
+ align:start position:0%
+momentum you can go to coordinate space
+ 
+
+ align:start position:0%
+momentum you can go to coordinate space
+then the F then their functions just X1
+
+ align:start position:0%
+then the F then their functions just X1
+ 
+
+ align:start position:0%
+then the F then their functions just X1
+XP okay X
+
+ align:start position:0%
+XP okay X
+ 
+
+ align:start position:0%
+XP okay X
+XP and then then the profile of this
+
+ align:start position:0%
+XP and then then the profile of this
+ 
+
+ align:start position:0%
+XP and then then the profile of this
+F essentially tells
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+you that the de brain
+
+ align:start position:0%
+you that the de brain
+ 
+
+ align:start position:0%
+you that the de brain
+so if you have a scal of field
+
+ align:start position:0%
+so if you have a scal of field
+ 
+
+ align:start position:0%
+so if you have a scal of field
+excitation like this then the shape of
+
+ align:start position:0%
+excitation like this then the shape of
+ 
+
+ align:start position:0%
+excitation like this then the shape of
+the de brain actually is no longer
+
+ align:start position:0%
+the de brain actually is no longer
+ 
+
+ align:start position:0%
+the de brain actually is no longer
+strictly flat actually have a profile
+
+ align:start position:0%
+strictly flat actually have a profile
+ 
+
+ align:start position:0%
+strictly flat actually have a profile
+given by this scaler field
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so I will not justify this precise
+
+ align:start position:0%
+okay so I will not justify this precise
+ 
+
+ align:start position:0%
+okay so I will not justify this precise
+uh so this can be justified
+
+ align:start position:0%
+uh so this can be justified
+ 
+
+ align:start position:0%
+uh so this can be justified
+mathematically to really show that this
+
+ align:start position:0%
+mathematically to really show that this
+ 
+
+ align:start position:0%
+mathematically to really show that this
+is the case okay and I will do that uh
+
+ align:start position:0%
+is the case okay and I will do that uh
+ 
+
+ align:start position:0%
+is the case okay and I will do that uh
+here but let me just
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+mention some support for this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+picture so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+okay so so you f first you can show at
+
+ align:start position:0%
+okay so so you f first you can show at
+ 
+
+ align:start position:0%
+okay so so you f first you can show at
+the worksheet
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+level having such excitations
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so so having such excitations so
+
+ align:start position:0%
+okay so so having such excitations so
+ 
+
+ align:start position:0%
+okay so so having such excitations so
+which I just call it fire
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+excitations so this is a picture in
+
+ align:start position:0%
+excitations so this is a picture in
+ 
+
+ align:start position:0%
+excitations so this is a picture in
+momentum
+
+ align:start position:0%
+momentum
+ 
+
+ align:start position:0%
+momentum
+space have five excitations
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+modifies the judicially boundary
+
+ align:start position:0%
+modifies the judicially boundary
+ 
+
+ align:start position:0%
+modifies the judicially boundary
+condition Okay so so this you can show
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+explicitly so this is first point which
+
+ align:start position:0%
+explicitly so this is first point which
+ 
+
+ align:start position:0%
+explicitly so this is first point which
+I we not going to
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+there and the second
+
+ align:start position:0%
+there and the second
+ 
+
+ align:start position:0%
+there and the second
+point is that you can actually work out
+
+ align:start position:0%
+point is that you can actually work out
+ 
+
+ align:start position:0%
+point is that you can actually work out
+the precise
+
+ align:start position:0%
+the precise
+ 
+
+ align:start position:0%
+the precise
+preactor there is a way Say by doing a
+
+ align:start position:0%
+preactor there is a way Say by doing a
+ 
+
+ align:start position:0%
+preactor there is a way Say by doing a
+string the um calculation uh Say by
+
+ align:start position:0%
+string the um calculation uh Say by
+ 
+
+ align:start position:0%
+string the um calculation uh Say by
+Computing the partition function this
+
+ align:start position:0%
+Computing the partition function this
+ 
+
+ align:start position:0%
+Computing the partition function this
+there's a way you can actually work out
+
+ align:start position:0%
+there's a way you can actually work out
+ 
+
+ align:start position:0%
+there's a way you can actually work out
+the prefactor precise
+
+ align:start position:0%
+the prefactor precise
+ 
+
+ align:start position:0%
+the prefactor precise
+preactor so let me call this the
+
+ align:start position:0%
+preactor so let me call this the
+ 
+
+ align:start position:0%
+preactor so let me call this the
+equation
+
+ align:start position:0%
+equation
+ 
+
+ align:start position:0%
+equation
+star so you can actually work out
+
+ align:start position:0%
+star so you can actually work out
+ 
+
+ align:start position:0%
+star so you can actually work out
+the so that was just by
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+General this is just by General
+
+ align:start position:0%
+General this is just by General
+ 
+
+ align:start position:0%
+General this is just by General
+principle say say if you have a Mass
+
+ align:start position:0%
+principle say say if you have a Mass
+ 
+
+ align:start position:0%
+principle say say if you have a Mass
+Spectrum then the L must behave like
+
+ align:start position:0%
+Spectrum then the L must behave like
+ 
+
+ align:start position:0%
+Spectrum then the L must behave like
+this and but but this prefa is not fixed
+
+ align:start position:0%
+this and but but this prefa is not fixed
+ 
+
+ align:start position:0%
+this and but but this prefa is not fixed
+okay and but you can
+
+ align:start position:0%
+okay and but you can
+ 
+
+ align:start position:0%
+okay and but you can
+actually with the interpretation F say
+
+ align:start position:0%
+actually with the interpretation F say
+ 
+
+ align:start position:0%
+actually with the interpretation F say
+as the fluctuations of this der boundary
+
+ align:start position:0%
+as the fluctuations of this der boundary
+ 
+
+ align:start position:0%
+as the fluctuations of this der boundary
+condition you can actually fix the
+
+ align:start position:0%
+condition you can actually fix the
+ 
+
+ align:start position:0%
+condition you can actually fix the
+precise the prefactor
+
+ align:start position:0%
+precise the prefactor
+ 
+
+ align:start position:0%
+precise the prefactor
+here so working out the uh working out
+
+ align:start position:0%
+here so working out the uh working out
+ 
+
+ align:start position:0%
+here so working out the uh working out
+the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+pre okay
+
+ align:start position:0%
+pre okay
+ 
+
+ align:start position:0%
+pre okay
+you can show that actually this action
+
+ align:start position:0%
+you can show that actually this action
+ 
+
+ align:start position:0%
+you can show that actually this action
+can be written as the
+
+ align:start position:0%
+can be written as the
+ 
+
+ align:start position:0%
+can be written as the
+following
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+TP again it's integrated only o over the
+
+ align:start position:0%
+TP again it's integrated only o over the
+ 
+
+ align:start position:0%
+TP again it's integrated only o over the
+water volume of the dein p+
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+one and you actually first we find
+
+ align:start position:0%
+one and you actually first we find
+ 
+
+ align:start position:0%
+one and you actually first we find
+actually there's a constant
+
+ align:start position:0%
+actually there's a constant
+ 
+
+ align:start position:0%
+actually there's a constant
+term when you work out that action
+
+ align:start position:0%
+term when you work out that action
+ 
+
+ align:start position:0%
+term when you work out that action
+precisely and then you have
+
+ align:start position:0%
+precisely and then you have
+ 
+
+ align:start position:0%
+precisely and then you have
+this F term
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and ex and this uh
+
+ align:start position:0%
+and ex and this uh
+ 
+
+ align:start position:0%
+and ex and this uh
+um let me yeah actually I should have
+
+ align:start position:0%
+um let me yeah actually I should have
+ 
+
+ align:start position:0%
+um let me yeah actually I should have
+done it
+
+ align:start position:0%
+done it
+ 
+
+ align:start position:0%
+done it
+there uh uh so there is a summation in a
+
+ align:start position:0%
+there uh uh so there is a summation in a
+ 
+
+ align:start position:0%
+there uh uh so there is a summation in a
+over here
+
+ align:start position:0%
+over here
+ 
+
+ align:start position:0%
+over here
+right so this TP this
+
+ align:start position:0%
+right so this TP this
+ 
+
+ align:start position:0%
+right so this TP this
+preactor is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+actually you can work out the pre SI
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+preactor and this
+
+ align:start position:0%
+preactor and this
+ 
+
+ align:start position:0%
+preactor and this
+preactor is given by the
+
+ align:start position:0%
+preactor is given by the
+ 
+
+ align:start position:0%
+preactor is given by the
+mass over DP
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Bri per unit
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+volume or in other words the brain
+
+ align:start position:0%
+volume or in other words the brain
+ 
+
+ align:start position:0%
+volume or in other words the brain
+tension so I will explain where does
+
+ align:start position:0%
+tension so I will explain where does
+ 
+
+ align:start position:0%
+tension so I will explain where does
+this come from where how do we Define a
+
+ align:start position:0%
+this come from where how do we Define a
+ 
+
+ align:start position:0%
+this come from where how do we Define a
+brain tension uh but for l let me just
+
+ align:start position:0%
+brain tension uh but for l let me just
+ 
+
+ align:start position:0%
+brain tension uh but for l let me just
+introduce this concept of brain
+
+ align:start position:0%
+introduce this concept of brain
+ 
+
+ align:start position:0%
+introduce this concept of brain
+tension so if you look out the prefa you
+
+ align:start position:0%
+tension so if you look out the prefa you
+ 
+
+ align:start position:0%
+tension so if you look out the prefa you
+find the prefa is
+
+ align:start position:0%
+find the prefa is
+ 
+
+ align:start position:0%
+find the prefa is
+precisely the brain uh tension okay
+
+ align:start position:0%
+precisely the brain uh tension okay
+ 
+
+ align:start position:0%
+precisely the brain uh tension okay
+brain tension so now if you look at this
+
+ align:start position:0%
+brain tension so now if you look at this
+ 
+
+ align:start position:0%
+brain tension so now if you look at this
+equation so then this
+
+ align:start position:0%
+equation so then this
+ 
+
+ align:start position:0%
+equation so then this
+one is just like a static
+
+ align:start position:0%
+one is just like a static
+ 
+
+ align:start position:0%
+one is just like a static
+mm okay this one is like a static mumm
+
+ align:start position:0%
+mm okay this one is like a static mumm
+ 
+
+ align:start position:0%
+mm okay this one is like a static mumm
+so so you also find this one in this a
+
+ align:start position:0%
+so so you also find this one in this a
+ 
+
+ align:start position:0%
+so so you also find this one in this a
+ler effective action
+
+ align:start position:0%
+ler effective action
+ 
+
+ align:start position:0%
+ler effective action
+but this one is very important because
+
+ align:start position:0%
+but this one is very important because
+ 
+
+ align:start position:0%
+but this one is very important because
+the so so this one is like static term
+
+ align:start position:0%
+the so so this one is like static term
+ 
+
+ align:start position:0%
+the so so this one is like static term
+and now if you look at this
+
+ align:start position:0%
+and now if you look at this
+ 
+
+ align:start position:0%
+and now if you look at this
+term so now if you
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+consider the situation which a alpha is
+
+ align:start position:0%
+consider the situation which a alpha is
+ 
+
+ align:start position:0%
+consider the situation which a alpha is
+equal to zero so you don't have any
+
+ align:start position:0%
+equal to zero so you don't have any
+ 
+
+ align:start position:0%
+equal to zero so you don't have any
+excitation of the vector field but F A
+
+ align:start position:0%
+excitation of the vector field but F A
+ 
+
+ align:start position:0%
+excitation of the vector field but F A
+only depend on T only depend on the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+time and then this effective action then
+
+ align:start position:0%
+time and then this effective action then
+ 
+
+ align:start position:0%
+time and then this effective action then
+will
+
+ align:start position:0%
+will
+ 
+
+ align:start position:0%
+will
+become TP then the volume of the
+
+ align:start position:0%
+become TP then the volume of the
+ 
+
+ align:start position:0%
+become TP then the volume of the
+P then DT 12 5 do a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+S
+
+ align:start position:0%
+S
+ 
+
+ align:start position:0%
+S
+okay and uh so VP is the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+volume of DP brain
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+volume of the DP brain and this tension
+
+ align:start position:0%
+volume of the DP brain and this tension
+ 
+
+ align:start position:0%
+volume of the DP brain and this tension
+times DP brain so this is just the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+mass so this is just the mass so uh so
+
+ align:start position:0%
+mass so this is just the mass so uh so
+ 
+
+ align:start position:0%
+mass so this is just the mass so uh so
+you can rewrite this just one
+
+ align:start position:0%
+you can rewrite this just one
+ 
+
+ align:start position:0%
+you can rewrite this just one
+half
+
+ align:start position:0%
+half
+ 
+
+ align:start position:0%
+half
+and D
+
+ align:start position:0%
+and D
+ 
+
+ align:start position:0%
+and D
+brain by dot
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Square
+
+ align:start position:0%
+Square
+ 
+
+ align:start position:0%
+Square
+okay and MD brain
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+TP times the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+volume so you see this is
+
+ align:start position:0%
+volume so you see this is
+ 
+
+ align:start position:0%
+volume so you see this is
+precisely like a
+
+ align:start position:0%
+precisely like a
+ 
+
+ align:start position:0%
+precisely like a
+particle like the whole brain
+
+ align:start position:0%
+particle like the whole brain
+ 
+
+ align:start position:0%
+particle like the whole brain
+moving the Lis motion moving of of some
+
+ align:start position:0%
+moving the Lis motion moving of of some
+ 
+
+ align:start position:0%
+moving the Lis motion moving of of some
+some
+
+ align:start position:0%
+some
+ 
+
+ align:start position:0%
+some
+object okay so again this give you the
+
+ align:start position:0%
+object okay so again this give you the
+ 
+
+ align:start position:0%
+object okay so again this give you the
+interpretation that the f
+
+ align:start position:0%
+interpretation that the f
+ 
+
+ align:start position:0%
+interpretation that the f
+can be interpreted uh as
+
+ align:start position:0%
+can be interpreted uh as
+ 
+
+ align:start position:0%
+can be interpreted uh as
+the as the degree Freedom which describe
+
+ align:start position:0%
+the as the degree Freedom which describe
+ 
+
+ align:start position:0%
+the as the degree Freedom which describe
+the motion of the
+
+ align:start position:0%
+the motion of the
+ 
+
+ align:start position:0%
+the motion of the
+brain
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay h
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+um so do you have any questions about
+
+ align:start position:0%
+um so do you have any questions about
+ 
+
+ align:start position:0%
+um so do you have any questions about
+this yes we introduce the Dynamics of
+
+ align:start position:0%
+this yes we introduce the Dynamics of
+ 
+
+ align:start position:0%
+this yes we introduce the Dynamics of
+brain from begin
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+with fact between term and D term change
+
+ align:start position:0%
+with fact between term and D term change
+ 
+
+ align:start position:0%
+with fact between term and D term change
+sorry if we introduce the Dynamics for
+
+ align:start position:0%
+sorry if we introduce the Dynamics for
+ 
+
+ align:start position:0%
+sorry if we introduce the Dynamics for
+brain from beginning then with the the
+
+ align:start position:0%
+brain from beginning then with the the
+ 
+
+ align:start position:0%
+brain from beginning then with the the
+pre factors of this Max
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+now now those prefa depend on your
+
+ align:start position:0%
+now now those prefa depend on your
+ 
+
+ align:start position:0%
+now now those prefa depend on your
+normalization and those prefa depend on
+
+ align:start position:0%
+normalization and those prefa depend on
+ 
+
+ align:start position:0%
+normalization and those prefa depend on
+normalization so you can normalize them
+
+ align:start position:0%
+normalization so you can normalize them
+ 
+
+ align:start position:0%
+normalization so you can normalize them
+in some particular
+
+ align:start position:0%
+in some particular
+ 
+
+ align:start position:0%
+in some particular
+way um you can normalize
+
+ align:start position:0%
+way um you can normalize
+ 
+
+ align:start position:0%
+way um you can normalize
+them yeah what here what I'm saying is
+
+ align:start position:0%
+them yeah what here what I'm saying is
+ 
+
+ align:start position:0%
+them yeah what here what I'm saying is
+that there is a specific larization
+
+ align:start position:0%
+that there is a specific larization
+ 
+
+ align:start position:0%
+that there is a specific larization
+which then the F can precisely be
+
+ align:start position:0%
+which then the F can precisely be
+ 
+
+ align:start position:0%
+which then the F can precisely be
+interpreted
+
+ align:start position:0%
+interpreted
+ 
+
+ align:start position:0%
+interpreted
+as the motion of the D
+
+ align:start position:0%
+as the motion of the D
+ 
+
+ align:start position:0%
+as the motion of the D
+brain yeah five always corresponding to
+
+ align:start position:0%
+brain yeah five always corresponding to
+ 
+
+ align:start position:0%
+brain yeah five always corresponding to
+the motion of D but this specific
+
+ align:start position:0%
+the motion of D but this specific
+ 
+
+ align:start position:0%
+the motion of D but this specific
+lonization then five can be really
+
+ align:start position:0%
+lonization then five can be really
+ 
+
+ align:start position:0%
+lonization then five can be really
+interpret as a dynamical version of this
+
+ align:start position:0%
+interpret as a dynamical version of this
+ 
+
+ align:start position:0%
+interpret as a dynamical version of this
+coordinate in the transverse Direction
+
+ align:start position:0%
+coordinate in the transverse Direction
+ 
+
+ align:start position:0%
+coordinate in the transverse Direction
+and with that normalization then you see
+
+ align:start position:0%
+and with that normalization then you see
+ 
+
+ align:start position:0%
+and with that normalization then you see
+that this n effective action is like the
+
+ align:start position:0%
+that this n effective action is like the
+ 
+
+ align:start position:0%
+that this n effective action is like the
+motion of a massive
+
+ align:start position:0%
+motion of a massive
+ 
+
+ align:start position:0%
+motion of a massive
+object okay it's like a the motion of a
+
+ align:start position:0%
+object okay it's like a the motion of a
+ 
+
+ align:start position:0%
+object okay it's like a the motion of a
+massive object and and this give you the
+
+ align:start position:0%
+massive object and and this give you the
+ 
+
+ align:start position:0%
+massive object and and this give you the
+confirmation that F indeed is the should
+
+ align:start position:0%
+confirmation that F indeed is the should
+ 
+
+ align:start position:0%
+confirmation that F indeed is the should
+be considered
+
+ align:start position:0%
+be considered
+ 
+
+ align:start position:0%
+be considered
+Freedom describe the motion of the deep
+
+ align:start position:0%
+Freedom describe the motion of the deep
+ 
+
+ align:start position:0%
+Freedom describe the motion of the deep
+brain
+
+ align:start position:0%
+brain
+ 
+
+ align:start position:0%
+brain
+yes that's I that is only in the low
+
+ align:start position:0%
+yes that's I that is only in the low
+ 
+
+ align:start position:0%
+yes that's I that is only in the low
+energy continue when you the
+
+ align:start position:0%
+energy continue when you the
+ 
+
+ align:start position:0%
+energy continue when you the
+higher of open Str yeah so yeah so
+
+ align:start position:0%
+higher of open Str yeah so yeah so
+ 
+
+ align:start position:0%
+higher of open Str yeah so yeah so
+that's a good question which I don't
+
+ align:start position:0%
+that's a good question which I don't
+ 
+
+ align:start position:0%
+that's a good question which I don't
+have time to to discuss now uh but I can
+
+ align:start position:0%
+have time to to discuss now uh but I can
+ 
+
+ align:start position:0%
+have time to to discuss now uh but I can
+but I will describe as the beginning of
+
+ align:start position:0%
+but I will describe as the beginning of
+ 
+
+ align:start position:0%
+but I will describe as the beginning of
+next lecture just so so this is a know
+
+ align:start position:0%
+next lecture just so so this is a know
+ 
+
+ align:start position:0%
+next lecture just so so this is a know
+enery story then you can actually
+
+ align:start position:0%
+enery story then you can actually
+ 
+
+ align:start position:0%
+enery story then you can actually
+include the subset of higher order terms
+
+ align:start position:0%
+include the subset of higher order terms
+ 
+
+ align:start position:0%
+include the subset of higher order terms
+then you find those this infinite number
+
+ align:start position:0%
+then you find those this infinite number
+ 
+
+ align:start position:0%
+then you find those this infinite number
+of higher order terms you can sum and
+
+ align:start position:0%
+of higher order terms you can sum and
+ 
+
+ align:start position:0%
+of higher order terms you can sum and
+then this precisely generalize to the
+
+ align:start position:0%
+then this precisely generalize to the
+ 
+
+ align:start position:0%
+then this precisely generalize to the
+motion of a relativistic object yeah
+
+ align:start position:0%
+motion of a relativistic object yeah
+ 
+
+ align:start position:0%
+motion of a relativistic object yeah
+because if you want to yeah because this
+
+ align:start position:0%
+because if you want to yeah because this
+ 
+
+ align:start position:0%
+because if you want to yeah because this
+is no energies have to be non
+
+ align:start position:0%
+is no energies have to be non
+ 
+
+ align:start position:0%
+is no energies have to be non
+relativistic but then you can generalize
+
+ align:start position:0%
+relativistic but then you can generalize
+ 
+
+ align:start position:0%
+relativistic but then you can generalize
+generally if you sum
+
+ align:start position:0%
+generally if you sum
+ 
+
+ align:start position:0%
+generally if you sum
+over infinite number of higher terms
+
+ align:start position:0%
+over infinite number of higher terms
+ 
+
+ align:start position:0%
+over infinite number of higher terms
+then this describe relativistic motion
+
+ align:start position:0%
+then this describe relativistic motion
+ 
+
+ align:start position:0%
+then this describe relativistic motion
+uh of object and again that's a lot of
+
+ align:start position:0%
+uh of object and again that's a lot of
+ 
+
+ align:start position:0%
+uh of object and again that's a lot of
+independent confirmation that this is
+
+ align:start position:0%
+independent confirmation that this is
+ 
+
+ align:start position:0%
+independent confirmation that this is
+the describe the motion of the deep
+
+ align:start position:0%
+the describe the motion of the deep
+ 
+
+ align:start position:0%
+the describe the motion of the deep
+brain yeah yes um so I'm kind of
+
+ align:start position:0%
+brain yeah yes um so I'm kind of
+ 
+
+ align:start position:0%
+brain yeah yes um so I'm kind of
+fundamentally uh confused about how so
+
+ align:start position:0%
+fundamentally uh confused about how so
+ 
+
+ align:start position:0%
+fundamentally uh confused about how so
+we started with a de brain which was a
+
+ align:start position:0%
+we started with a de brain which was a
+ 
+
+ align:start position:0%
+we started with a de brain which was a
+topological defect in our background
+
+ align:start position:0%
+topological defect in our background
+ 
+
+ align:start position:0%
+topological defect in our background
+manifold yeah so like a black brain or
+
+ align:start position:0%
+manifold yeah so like a black brain or
+ 
+
+ align:start position:0%
+manifold yeah so like a black brain or
+something right yeah and uh we are
+
+ align:start position:0%
+something right yeah and uh we are
+ 
+
+ align:start position:0%
+something right yeah and uh we are
+looking at motion of strings in this
+
+ align:start position:0%
+looking at motion of strings in this
+ 
+
+ align:start position:0%
+looking at motion of strings in this
+background manifold yeah and this is so
+
+ align:start position:0%
+background manifold yeah and this is so
+ 
+
+ align:start position:0%
+background manifold yeah and this is so
+why do we all of a sudden have the
+
+ align:start position:0%
+why do we all of a sudden have the
+ 
+
+ align:start position:0%
+why do we all of a sudden have the
+string motion affect the background like
+
+ align:start position:0%
+string motion affect the background like
+ 
+
+ align:start position:0%
+string motion affect the background like
+we never even introduce any couple into
+
+ align:start position:0%
+we never even introduce any couple into
+ 
+
+ align:start position:0%
+we never even introduce any couple into
+the back yeah yeah yeah so that's the
+
+ align:start position:0%
+the back yeah yeah yeah so that's the
+ 
+
+ align:start position:0%
+the back yeah yeah yeah so that's the
+that's
+
+ align:start position:0%
+that's
+ 
+
+ align:start position:0%
+that's
+precisely so this is a very good
+
+ align:start position:0%
+precisely so this is a very good
+ 
+
+ align:start position:0%
+precisely so this is a very good
+question this is
+
+ align:start position:0%
+question this is
+ 
+
+ align:start position:0%
+question this is
+precisely the remarkable thing about the
+
+ align:start position:0%
+precisely the remarkable thing about the
+ 
+
+ align:start position:0%
+precisely the remarkable thing about the
+stren
+
+ align:start position:0%
+stren
+ 
+
+ align:start position:0%
+stren
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+so yeah so uh I was going to say at the
+
+ align:start position:0%
+so yeah so uh I was going to say at the
+ 
+
+ align:start position:0%
+so yeah so uh I was going to say at the
+beginning of Le next but now let me say
+
+ align:start position:0%
+beginning of Le next but now let me say
+ 
+
+ align:start position:0%
+beginning of Le next but now let me say
+it so at the beginning you introduce the
+
+ align:start position:0%
+it so at the beginning you introduce the
+ 
+
+ align:start position:0%
+it so at the beginning you introduce the
+deep brain just by some rigid boundary
+
+ align:start position:0%
+deep brain just by some rigid boundary
+ 
+
+ align:start position:0%
+deep brain just by some rigid boundary
+conditions some rigid boundary
+
+ align:start position:0%
+conditions some rigid boundary
+ 
+
+ align:start position:0%
+conditions some rigid boundary
+conditions
+
+ align:start position:0%
+conditions
+ 
+
+ align:start position:0%
+conditions
+and uh looks like this is a non damic
+
+ align:start position:0%
+and uh looks like this is a non damic
+ 
+
+ align:start position:0%
+and uh looks like this is a non damic
+object because we are introducing some
+
+ align:start position:0%
+object because we are introducing some
+ 
+
+ align:start position:0%
+object because we are introducing some
+rigid boundary
+
+ align:start position:0%
+rigid boundary
+ 
+
+ align:start position:0%
+rigid boundary
+conditions but now when you quantize the
+
+ align:start position:0%
+conditions but now when you quantize the
+ 
+
+ align:start position:0%
+conditions but now when you quantize the
+strings on those deep
+
+ align:start position:0%
+strings on those deep
+ 
+
+ align:start position:0%
+strings on those deep
+brains and then you find the those
+
+ align:start position:0%
+brains and then you find the those
+ 
+
+ align:start position:0%
+brains and then you find the those
+strings now give the give the Deep
+
+ align:start position:0%
+strings now give the give the Deep
+ 
+
+ align:start position:0%
+strings now give the give the Deep
+braing itself
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+knife is it because there's a graviton
+
+ align:start position:0%
+knife is it because there's a graviton
+ 
+
+ align:start position:0%
+knife is it because there's a graviton
+no no no have nothing to do with
+
+ align:start position:0%
+no no no have nothing to do with
+ 
+
+ align:start position:0%
+no no no have nothing to do with
+graviton have nothing to do with
+
+ align:start position:0%
+graviton have nothing to do with
+ 
+
+ align:start position:0%
+graviton have nothing to do with
+graviton start with a rigid boundary
+
+ align:start position:0%
+graviton start with a rigid boundary
+ 
+
+ align:start position:0%
+graviton start with a rigid boundary
+conditions but now you find a b this
+
+ align:start position:0%
+conditions but now you find a b this
+ 
+
+ align:start position:0%
+conditions but now you find a b this
+boundary conditions then you can
+
+ align:start position:0%
+boundary conditions then you can
+ 
+
+ align:start position:0%
+boundary conditions then you can
+generate then you have some excitations
+
+ align:start position:0%
+generate then you have some excitations
+ 
+
+ align:start position:0%
+generate then you have some excitations
+then the coherent motion of this
+
+ align:start position:0%
+then the coherent motion of this
+ 
+
+ align:start position:0%
+then the coherent motion of this
+excitations now give this
+
+ align:start position:0%
+excitations now give this
+ 
+
+ align:start position:0%
+excitations now give this
+object a
+
+ align:start position:0%
+object a
+ 
+
+ align:start position:0%
+object a
+Dynamics so that's a precis remarkable
+
+ align:start position:0%
+Dynamics so that's a precis remarkable
+ 
+
+ align:start position:0%
+Dynamics so that's a precis remarkable
+thing about String Theory so what if you
+
+ align:start position:0%
+thing about String Theory so what if you
+ 
+
+ align:start position:0%
+thing about String Theory so what if you
+have two strings or both ending on the
+
+ align:start position:0%
+have two strings or both ending on the
+ 
+
+ align:start position:0%
+have two strings or both ending on the
+same brain no no no this including all
+
+ align:start position:0%
+same brain no no no this including all
+ 
+
+ align:start position:0%
+same brain no no no this including all
+the strings you can have as many strings
+
+ align:start position:0%
+the strings you can have as many strings
+ 
+
+ align:start position:0%
+the strings you can have as many strings
+as you want
+
+ align:start position:0%
+as you want
+ 
+
+ align:start position:0%
+as you want
+well we're quantizing one particular
+
+ align:start position:0%
+well we're quantizing one particular
+ 
+
+ align:start position:0%
+well we're quantizing one particular
+object and we're looking at a spectrum
+
+ align:start position:0%
+object and we're looking at a spectrum
+ 
+
+ align:start position:0%
+object and we're looking at a spectrum
+of a single string starting here yeah
+
+ align:start position:0%
+of a single string starting here yeah
+ 
+
+ align:start position:0%
+of a single string starting here yeah
+yeah each string have such excitations
+
+ align:start position:0%
+yeah each string have such excitations
+ 
+
+ align:start position:0%
+yeah each string have such excitations
+but then each different string will
+
+ align:start position:0%
+but then each different string will
+ 
+
+ align:start position:0%
+but then each different string will
+generate a different Dynamics for the no
+
+ align:start position:0%
+generate a different Dynamics for the no
+ 
+
+ align:start position:0%
+generate a different Dynamics for the no
+the same Dynamic you just have two
+
+ align:start position:0%
+the same Dynamic you just have two
+ 
+
+ align:start position:0%
+the same Dynamic you just have two
+particles it's just like you have one
+
+ align:start position:0%
+particles it's just like you have one
+ 
+
+ align:start position:0%
+particles it's just like you have one
+Photon here another Photon there it's
+
+ align:start position:0%
+Photon here another Photon there it's
+ 
+
+ align:start position:0%
+Photon here another Photon there it's
+the same
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+thing and this is the same
+
+ align:start position:0%
+thing and this is the same
+ 
+
+ align:start position:0%
+thing and this is the same
+thing about how stry regenerate
+
+ align:start position:0%
+thing about how stry regenerate
+ 
+
+ align:start position:0%
+thing about how stry regenerate
+gravity so let me just uh uh say a few
+
+ align:start position:0%
+gravity so let me just uh uh say a few
+ 
+
+ align:start position:0%
+gravity so let me just uh uh say a few
+words here
+
+ align:start position:0%
+words here
+ 
+
+ align:start position:0%
+words here
+so at the beginning when we quanti the
+
+ align:start position:0%
+so at the beginning when we quanti the
+ 
+
+ align:start position:0%
+so at the beginning when we quanti the
+close stream we consider a Clos stream
+
+ align:start position:0%
+close stream we consider a Clos stream
+ 
+
+ align:start position:0%
+close stream we consider a Clos stream
+moving in again in a rigid wi kovski
+
+ align:start position:0%
+moving in again in a rigid wi kovski
+ 
+
+ align:start position:0%
+moving in again in a rigid wi kovski
+space time yeah because that matric is
+
+ align:start position:0%
+space time yeah because that matric is
+ 
+
+ align:start position:0%
+space time yeah because that matric is
+rigid we just consider in the rigid wovi
+
+ align:start position:0%
+rigid we just consider in the rigid wovi
+ 
+
+ align:start position:0%
+rigid we just consider in the rigid wovi
+space time but now when you quantize
+
+ align:start position:0%
+space time but now when you quantize
+ 
+
+ align:start position:0%
+space time but now when you quantize
+that close string then you see that
+
+ align:start position:0%
+that close string then you see that
+ 
+
+ align:start position:0%
+that close string then you see that
+close string actually have been two
+
+ align:start position:0%
+close string actually have been two
+ 
+
+ align:start position:0%
+close string actually have been two
+excitations have spin two
+
+ align:start position:0%
+excitations have spin two
+ 
+
+ align:start position:0%
+excitations have spin two
+excitations that means that string
+
+ align:start position:0%
+excitations that means that string
+ 
+
+ align:start position:0%
+excitations that means that string
+actually has gravity ational effect and
+
+ align:start position:0%
+actually has gravity ational effect and
+ 
+
+ align:start position:0%
+actually has gravity ational effect and
+once you have spin two
+
+ align:start position:0%
+once you have spin two
+ 
+
+ align:start position:0%
+once you have spin two
+excitations then
+
+ align:start position:0%
+excitations then
+ 
+
+ align:start position:0%
+excitations then
+Einstein already from Einstein gravity
+
+ align:start position:0%
+Einstein already from Einstein gravity
+ 
+
+ align:start position:0%
+Einstein already from Einstein gravity
+tells us that the space time is no
+
+ align:start position:0%
+tells us that the space time is no
+ 
+
+ align:start position:0%
+tells us that the space time is no
+longer
+
+ align:start position:0%
+longer
+ 
+
+ align:start position:0%
+longer
+rigid that actually can deform the I
+
+ align:start position:0%
+rigid that actually can deform the I
+ 
+
+ align:start position:0%
+rigid that actually can deform the I
+deform the mop space time by by putting
+
+ align:start position:0%
+deform the mop space time by by putting
+ 
+
+ align:start position:0%
+deform the mop space time by by putting
+in those excitation this been two
+
+ align:start position:0%
+in those excitation this been two
+ 
+
+ align:start position:0%
+in those excitation this been two
+excitations and if you put enough of
+
+ align:start position:0%
+excitations and if you put enough of
+ 
+
+ align:start position:0%
+excitations and if you put enough of
+them then you deform the mov SP time to
+
+ align:start position:0%
+them then you deform the mov SP time to
+ 
+
+ align:start position:0%
+them then you deform the mov SP time to
+some other curve space time then you can
+
+ align:start position:0%
+some other curve space time then you can
+ 
+
+ align:start position:0%
+some other curve space time then you can
+actually describe
+
+ align:start position:0%
+actually describe
+ 
+
+ align:start position:0%
+actually describe
+generically the quantum gravitational
+
+ align:start position:0%
+generically the quantum gravitational
+ 
+
+ align:start position:0%
+generically the quantum gravitational
+dynamics of General curve space time so
+
+ align:start position:0%
+dynamics of General curve space time so
+ 
+
+ align:start position:0%
+dynamics of General curve space time so
+here is the same thing we start with a
+
+ align:start position:0%
+here is the same thing we start with a
+ 
+
+ align:start position:0%
+here is the same thing we start with a
+rid deep brain then we quantize the
+
+ align:start position:0%
+rid deep brain then we quantize the
+ 
+
+ align:start position:0%
+rid deep brain then we quantize the
+excitations on then we quantize the
+
+ align:start position:0%
+excitations on then we quantize the
+ 
+
+ align:start position:0%
+excitations on then we quantize the
+degre freedom on the D brain and then we
+
+ align:start position:0%
+degre freedom on the D brain and then we
+ 
+
+ align:start position:0%
+degre freedom on the D brain and then we
+find those degrees Freedom corresponding
+
+ align:start position:0%
+find those degrees Freedom corresponding
+ 
+
+ align:start position:0%
+find those degrees Freedom corresponding
+to the fluctuation of the D brain and if
+
+ align:start position:0%
+to the fluctuation of the D brain and if
+ 
+
+ align:start position:0%
+to the fluctuation of the D brain and if
+you have enough of them say if you have
+
+ align:start position:0%
+you have enough of them say if you have
+ 
+
+ align:start position:0%
+you have enough of them say if you have
+so have five only depend on T to be the
+
+ align:start position:0%
+so have five only depend on T to be the
+ 
+
+ align:start position:0%
+so have five only depend on T to be the
+same everywhere so that's some coherent
+
+ align:start position:0%
+same everywhere so that's some coherent
+ 
+
+ align:start position:0%
+same everywhere so that's some coherent
+motion for every point on this brain so
+
+ align:start position:0%
+motion for every point on this brain so
+ 
+
+ align:start position:0%
+motion for every point on this brain so
+then say if you build enough kind
+
+ align:start position:0%
+then say if you build enough kind
+ 
+
+ align:start position:0%
+then say if you build enough kind
+excitations then you can actually make
+
+ align:start position:0%
+excitations then you can actually make
+ 
+
+ align:start position:0%
+excitations then you can actually make
+the deep brain moves ET they become a
+
+ align:start position:0%
+the deep brain moves ET they become a
+ 
+
+ align:start position:0%
+the deep brain moves ET they become a
+fully Dynamic object yeah so that's
+
+ align:start position:0%
+fully Dynamic object yeah so that's
+ 
+
+ align:start position:0%
+fully Dynamic object yeah so that's
+precisely the remarkable thing about
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yes
+
+ align:start position:0%
+yes
+ 
+
+ align:start position:0%
+yes
+Dynamic just
+
+ align:start position:0%
+Dynamic just
+ 
+
+ align:start position:0%
+Dynamic just
+normalize or no we don't know how to
+
+ align:start position:0%
+normalize or no we don't know how to
+ 
+
+ align:start position:0%
+normalize or no we don't know how to
+describe dynamical brain from the
+
+ align:start position:0%
+describe dynamical brain from the
+ 
+
+ align:start position:0%
+describe dynamical brain from the
+beginning
+
+ align:start position:0%
+beginning
+ 
+
+ align:start position:0%
+beginning
+no that's how we do it we we first start
+
+ align:start position:0%
+no that's how we do it we we first start
+ 
+
+ align:start position:0%
+no that's how we do it we we first start
+with some uh uh so this is called the
+
+ align:start position:0%
+with some uh uh so this is called the
+ 
+
+ align:start position:0%
+with some uh uh so this is called the
+background dependent uh quantization you
+
+ align:start position:0%
+background dependent uh quantization you
+ 
+
+ align:start position:0%
+background dependent uh quantization you
+start with a specific
+
+ align:start position:0%
+start with a specific
+ 
+
+ align:start position:0%
+start with a specific
+solution you start with a specific
+
+ align:start position:0%
+solution you start with a specific
+ 
+
+ align:start position:0%
+solution you start with a specific
+configuration of the de brain which we
+
+ align:start position:0%
+configuration of the de brain which we
+ 
+
+ align:start position:0%
+configuration of the de brain which we
+you happen to be able to quantize then
+
+ align:start position:0%
+you happen to be able to quantize then
+ 
+
+ align:start position:0%
+you happen to be able to quantize then
+you can find all the excitations around
+
+ align:start position:0%
+you can find all the excitations around
+ 
+
+ align:start position:0%
+you can find all the excitations around
+that particular configuration and then
+
+ align:start position:0%
+that particular configuration and then
+ 
+
+ align:start position:0%
+that particular configuration and then
+you can turn on those excitation to move
+
+ align:start position:0%
+you can turn on those excitation to move
+ 
+
+ align:start position:0%
+you can turn on those excitation to move
+away from those
+
+ align:start position:0%
+away from those
+ 
+
+ align:start position:0%
+away from those
+points
+
+ align:start position:0%
+points
+ 
+
+ align:start position:0%
+points
+yeah yeah so that's essentially what
+
+ align:start position:0%
+yeah yeah so that's essentially what
+ 
+
+ align:start position:0%
+yeah yeah so that's essentially what
+we're doing here here right okay okay
+
+ align:start position:0%
+we're doing here here right okay okay
+ 
+
+ align:start position:0%
+we're doing here here right okay okay
+let's stop
\ No newline at end of file
diff --git a/iR6FUYCNi5A.txt b/iR6FUYCNi5A.txt
new file mode 100644
index 0000000000000000000000000000000000000000..5b3c69b31dcf28922292b9df178ab98cdc9854f8
--- /dev/null
+++ b/iR6FUYCNi5A.txt
@@ -0,0 +1,6203 @@
+align:start position:0%
+ 
+the following content is provided under
+
+ align:start position:0%
+the following content is provided under
+ 
+
+ align:start position:0%
+the following content is provided under
+a Creative Commons license your support
+
+ align:start position:0%
+a Creative Commons license your support
+ 
+
+ align:start position:0%
+a Creative Commons license your support
+will help MIT open courseware continue
+
+ align:start position:0%
+will help MIT open courseware continue
+ 
+
+ align:start position:0%
+will help MIT open courseware continue
+to offer highquality educational
+
+ align:start position:0%
+to offer highquality educational
+ 
+
+ align:start position:0%
+to offer highquality educational
+resources for free to make a donation or
+
+ align:start position:0%
+resources for free to make a donation or
+ 
+
+ align:start position:0%
+resources for free to make a donation or
+to view additional materials from
+
+ align:start position:0%
+to view additional materials from
+ 
+
+ align:start position:0%
+to view additional materials from
+hundreds of MIT courses visit MIT
+
+ align:start position:0%
+hundreds of MIT courses visit MIT
+ 
+
+ align:start position:0%
+hundreds of MIT courses visit MIT
+opencourseware at
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+ocw.mit.edu this is going to be really
+
+ align:start position:0%
+ocw.mit.edu this is going to be really
+ 
+
+ align:start position:0%
+ocw.mit.edu this is going to be really
+informal and you can try and follow
+
+ align:start position:0%
+informal and you can try and follow
+ 
+
+ align:start position:0%
+informal and you can try and follow
+along if you want um I'm just going to
+
+ align:start position:0%
+along if you want um I'm just going to
+ 
+
+ align:start position:0%
+along if you want um I'm just going to
+show you my basic workflow from
+
+ align:start position:0%
+show you my basic workflow from
+ 
+
+ align:start position:0%
+show you my basic workflow from
+illustrator to after effect to Premiere
+
+ align:start position:0%
+illustrator to after effect to Premiere
+ 
+
+ align:start position:0%
+illustrator to after effect to Premiere
+and like some important I guess like
+
+ align:start position:0%
+and like some important I guess like
+ 
+
+ align:start position:0%
+and like some important I guess like
+basic tools that you might
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+use Elizabeth okay I just started we
+
+ align:start position:0%
+use Elizabeth okay I just started we
+ 
+
+ align:start position:0%
+use Elizabeth okay I just started we
+finally got everything set
+
+ align:start position:0%
+finally got everything set
+ 
+
+ align:start position:0%
+finally got everything set
+up I don't know how
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+to a little make it any better okay I'll
+
+ align:start position:0%
+to a little make it any better okay I'll
+ 
+
+ align:start position:0%
+to a little make it any better okay I'll
+wait a little bit
+
+ align:start position:0%
+wait a little bit
+ 
+
+ align:start position:0%
+wait a little bit
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+um okay um so first thing is creating
+
+ align:start position:0%
+um okay um so first thing is creating
+ 
+
+ align:start position:0%
+um okay um so first thing is creating
+your canvas so if you open up
+
+ align:start position:0%
+your canvas so if you open up
+ 
+
+ align:start position:0%
+your canvas so if you open up
+illustrator it's just file
+
+ align:start position:0%
+illustrator it's just file
+ 
+
+ align:start position:0%
+illustrator it's just file
+new um you can name it whatever you
+
+ align:start position:0%
+new um you can name it whatever you
+ 
+
+ align:start position:0%
+new um you can name it whatever you
+want and then the profile is going to be
+
+ align:start position:0%
+want and then the profile is going to be
+ 
+
+ align:start position:0%
+want and then the profile is going to be
+automatically set to one of these
+
+ align:start position:0%
+automatically set to one of these
+ 
+
+ align:start position:0%
+automatically set to one of these
+options but I adjust the width and the
+
+ align:start position:0%
+options but I adjust the width and the
+ 
+
+ align:start position:0%
+options but I adjust the width and the
+height to match the screen size of the
+
+ align:start position:0%
+height to match the screen size of the
+ 
+
+ align:start position:0%
+height to match the screen size of the
+video that we capture um which is
+
+ align:start position:0%
+video that we capture um which is
+ 
+
+ align:start position:0%
+video that we capture um which is
+usually 1920 x 1080 pixels so you want
+
+ align:start position:0%
+usually 1920 x 1080 pixels so you want
+ 
+
+ align:start position:0%
+usually 1920 x 1080 pixels so you want
+to make sure the width is 1920 the
+
+ align:start position:0%
+to make sure the width is 1920 the
+ 
+
+ align:start position:0%
+to make sure the width is 1920 the
+height is 1080 and the units are
+
+ align:start position:0%
+height is 1080 and the units are
+ 
+
+ align:start position:0%
+height is 1080 and the units are
+pixels uh um and you can keep the color
+
+ align:start position:0%
+pixels uh um and you can keep the color
+ 
+
+ align:start position:0%
+pixels uh um and you can keep the color
+mode um and the pixel grid the same and
+
+ align:start position:0%
+mode um and the pixel grid the same and
+ 
+
+ align:start position:0%
+mode um and the pixel grid the same and
+you press okay and your screen should
+
+ align:start position:0%
+you press okay and your screen should
+ 
+
+ align:start position:0%
+you press okay and your screen should
+look something like this
+
+ align:start position:0%
+look something like this
+ 
+
+ align:start position:0%
+look something like this
+um and this is just the drawing surface
+
+ align:start position:0%
+um and this is just the drawing surface
+ 
+
+ align:start position:0%
+um and this is just the drawing surface
+on which you're going to
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+work
+
+ align:start position:0%
+work
+ 
+
+ align:start position:0%
+work
+um do you guys want to follow along or
+
+ align:start position:0%
+um do you guys want to follow along or
+ 
+
+ align:start position:0%
+um do you guys want to follow along or
+should I just keep
+
+ align:start position:0%
+should I just keep
+ 
+
+ align:start position:0%
+should I just keep
+going from
+
+ align:start position:0%
+going from
+ 
+
+ align:start position:0%
+going from
+here nod
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+how about um sorry can you go through
+
+ align:start position:0%
+how about um sorry can you go through
+ 
+
+ align:start position:0%
+how about um sorry can you go through
+just like drawing a single shape and
+
+ align:start position:0%
+just like drawing a single shape and
+ 
+
+ align:start position:0%
+just like drawing a single shape and
+then maybe like draw like a person's
+
+ align:start position:0%
+then maybe like draw like a person's
+ 
+
+ align:start position:0%
+then maybe like draw like a person's
+face and then export it out of an
+
+ align:start position:0%
+face and then export it out of an
+ 
+
+ align:start position:0%
+face and then export it out of an
+illustrator and then animate it in After
+
+ align:start position:0%
+illustrator and then animate it in After
+ 
+
+ align:start position:0%
+illustrator and then animate it in After
+Effects and the that's a yeah okay yeah
+
+ align:start position:0%
+Effects and the that's a yeah okay yeah
+ 
+
+ align:start position:0%
+Effects and the that's a yeah okay yeah
+oh is that what you g to do yeah yeah
+
+ align:start position:0%
+oh is that what you g to do yeah yeah
+ 
+
+ align:start position:0%
+oh is that what you g to do yeah yeah
+okay sorry go ahead yeah yeah no worries
+
+ align:start position:0%
+okay sorry go ahead yeah yeah no worries
+ 
+
+ align:start position:0%
+okay sorry go ahead yeah yeah no worries
+um so this is just going over some basic
+
+ align:start position:0%
+um so this is just going over some basic
+ 
+
+ align:start position:0%
+um so this is just going over some basic
+tools um I like expanding the right tool
+
+ align:start position:0%
+tools um I like expanding the right tool
+ 
+
+ align:start position:0%
+tools um I like expanding the right tool
+panel just so I can see everything um
+
+ align:start position:0%
+panel just so I can see everything um
+ 
+
+ align:start position:0%
+panel just so I can see everything um
+especially the layers that's um a tool I
+
+ align:start position:0%
+especially the layers that's um a tool I
+ 
+
+ align:start position:0%
+especially the layers that's um a tool I
+use a lot um basic things that you're
+
+ align:start position:0%
+use a lot um basic things that you're
+ 
+
+ align:start position:0%
+use a lot um basic things that you're
+going to use are the paintbrush this is
+
+ align:start position:0%
+going to use are the paintbrush this is
+ 
+
+ align:start position:0%
+going to use are the paintbrush this is
+how you mimic writing on your tablet so
+
+ align:start position:0%
+how you mimic writing on your tablet so
+ 
+
+ align:start position:0%
+how you mimic writing on your tablet so
+you
+
+ align:start position:0%
+you
+ 
+
+ align:start position:0%
+you
+can mimic your handwriting um you can
+
+ align:start position:0%
+can mimic your handwriting um you can
+ 
+
+ align:start position:0%
+can mimic your handwriting um you can
+draw basic shapes with this um but they
+
+ align:start position:0%
+draw basic shapes with this um but they
+ 
+
+ align:start position:0%
+draw basic shapes with this um but they
+appear
+
+ align:start position:0%
+appear
+ 
+
+ align:start position:0%
+appear
+as lines so everything in illustrator is
+
+ align:start position:0%
+as lines so everything in illustrator is
+ 
+
+ align:start position:0%
+as lines so everything in illustrator is
+a vector so this is a solid object um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah and then if you want to make
+
+ align:start position:0%
+yeah and then if you want to make
+ 
+
+ align:start position:0%
+yeah and then if you want to make
+shapes um there's a rectangle tool over
+
+ align:start position:0%
+shapes um there's a rectangle tool over
+ 
+
+ align:start position:0%
+shapes um there's a rectangle tool over
+here and you can hold down on it and
+
+ align:start position:0%
+here and you can hold down on it and
+ 
+
+ align:start position:0%
+here and you can hold down on it and
+find other shapes um and then you can
+
+ align:start position:0%
+find other shapes um and then you can
+ 
+
+ align:start position:0%
+find other shapes um and then you can
+just drag to place it um if you want to
+
+ align:start position:0%
+just drag to place it um if you want to
+ 
+
+ align:start position:0%
+just drag to place it um if you want to
+change the Border color or the color of
+
+ align:start position:0%
+change the Border color or the color of
+ 
+
+ align:start position:0%
+change the Border color or the color of
+an individual line you can click on this
+
+ align:start position:0%
+an individual line you can click on this
+ 
+
+ align:start position:0%
+an individual line you can click on this
+this is stroke color um double click and
+
+ align:start position:0%
+this is stroke color um double click and
+ 
+
+ align:start position:0%
+this is stroke color um double click and
+it'll just give you a fuller color
+
+ align:start position:0%
+it'll just give you a fuller color
+ 
+
+ align:start position:0%
+it'll just give you a fuller color
+spectrum
+
+ align:start position:0%
+spectrum
+ 
+
+ align:start position:0%
+spectrum
+you can select anything and if you want
+
+ align:start position:0%
+you can select anything and if you want
+ 
+
+ align:start position:0%
+you can select anything and if you want
+to change the fill right now the fill
+
+ align:start position:0%
+to change the fill right now the fill
+ 
+
+ align:start position:0%
+to change the fill right now the fill
+the white box with the red line through
+
+ align:start position:0%
+the white box with the red line through
+ 
+
+ align:start position:0%
+the white box with the red line through
+it means that it's transparent um but
+
+ align:start position:0%
+it means that it's transparent um but
+ 
+
+ align:start position:0%
+it means that it's transparent um but
+you can choose any color you want and
+
+ align:start position:0%
+you can choose any color you want and
+ 
+
+ align:start position:0%
+you can choose any color you want and
+it'll like change the shape um if you
+
+ align:start position:0%
+it'll like change the shape um if you
+ 
+
+ align:start position:0%
+it'll like change the shape um if you
+want to draw a free form shape the
+
+ align:start position:0%
+want to draw a free form shape the
+ 
+
+ align:start position:0%
+want to draw a free form shape the
+pencil tool will connect lines to make a
+
+ align:start position:0%
+pencil tool will connect lines to make a
+ 
+
+ align:start position:0%
+pencil tool will connect lines to make a
+a potentially solid object so if you
+
+ align:start position:0%
+a potentially solid object so if you
+ 
+
+ align:start position:0%
+a potentially solid object so if you
+want to make like an irregular polygon
+
+ align:start position:0%
+want to make like an irregular polygon
+ 
+
+ align:start position:0%
+want to make like an irregular polygon
+or
+
+ align:start position:0%
+or
+ 
+
+ align:start position:0%
+or
+some other shape the pencil tool
+
+ align:start position:0%
+some other shape the pencil tool
+ 
+
+ align:start position:0%
+some other shape the pencil tool
+automatically connects them even if you
+
+ align:start position:0%
+automatically connects them even if you
+ 
+
+ align:start position:0%
+automatically connects them even if you
+don't completely draw them together you
+
+ align:start position:0%
+don't completely draw them together you
+ 
+
+ align:start position:0%
+don't completely draw them together you
+can also redraw lines
+
+ align:start position:0%
+can also redraw lines
+ 
+
+ align:start position:0%
+can also redraw lines
+sometimes if you draw them in the same
+
+ align:start position:0%
+sometimes if you draw them in the same
+ 
+
+ align:start position:0%
+sometimes if you draw them in the same
+direction that you originally did so you
+
+ align:start position:0%
+direction that you originally did so you
+ 
+
+ align:start position:0%
+direction that you originally did so you
+can like
+
+ align:start position:0%
+can like
+ 
+
+ align:start position:0%
+can like
+adjust the border of a shape
+
+ align:start position:0%
+adjust the border of a shape
+ 
+
+ align:start position:0%
+adjust the border of a shape
+slightly
+
+ align:start position:0%
+slightly
+ 
+
+ align:start position:0%
+slightly
+um what else the black selection tool
+
+ align:start position:0%
+um what else the black selection tool
+ 
+
+ align:start position:0%
+um what else the black selection tool
+can help you select entire objects um
+
+ align:start position:0%
+can help you select entire objects um
+ 
+
+ align:start position:0%
+can help you select entire objects um
+you highlight
+
+ align:start position:0%
+you highlight
+ 
+
+ align:start position:0%
+you highlight
+I'm sorry no no
+
+ align:start position:0%
+I'm sorry no no
+ 
+
+ align:start position:0%
+I'm sorry no no
+worries is it not recording yeah it was
+
+ align:start position:0%
+worries is it not recording yeah it was
+ 
+
+ align:start position:0%
+worries is it not recording yeah it was
+not
+
+ align:start position:0%
+not
+ 
+
+ align:start position:0%
+not
+okay do you want me to do a quick time
+
+ align:start position:0%
+okay do you want me to do a quick time
+ 
+
+ align:start position:0%
+okay do you want me to do a quick time
+recording this backup as a backup
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah
+
+ align:start position:0%
+yeah
+ 
+
+ align:start position:0%
+yeah
+okay um okay so the black
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the black selection Arrow can help you
+
+ align:start position:0%
+the black selection Arrow can help you
+ 
+
+ align:start position:0%
+the black selection Arrow can help you
+select entire objects or you can drag to
+
+ align:start position:0%
+select entire objects or you can drag to
+ 
+
+ align:start position:0%
+select entire objects or you can drag to
+select groups of objects um the white
+
+ align:start position:0%
+select groups of objects um the white
+ 
+
+ align:start position:0%
+select groups of objects um the white
+selection Arrow you can select
+
+ align:start position:0%
+selection Arrow you can select
+ 
+
+ align:start position:0%
+selection Arrow you can select
+individual points on objects so you can
+
+ align:start position:0%
+individual points on objects so you can
+ 
+
+ align:start position:0%
+individual points on objects so you can
+um like select a point on the path and
+
+ align:start position:0%
+um like select a point on the path and
+ 
+
+ align:start position:0%
+um like select a point on the path and
+then move it around so you can warp a
+
+ align:start position:0%
+then move it around so you can warp a
+ 
+
+ align:start position:0%
+then move it around so you can warp a
+line that already
+
+ align:start position:0%
+line that already
+ 
+
+ align:start position:0%
+line that already
+exists um and like change its direction
+
+ align:start position:0%
+exists um and like change its direction
+ 
+
+ align:start position:0%
+exists um and like change its direction
+and things like that um let me think
+
+ align:start position:0%
+and things like that um let me think
+ 
+
+ align:start position:0%
+and things like that um let me think
+the ey dropper tool is useful if you
+
+ align:start position:0%
+the ey dropper tool is useful if you
+ 
+
+ align:start position:0%
+the ey dropper tool is useful if you
+let's say I
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+was um took a paintbrush and I had a
+
+ align:start position:0%
+was um took a paintbrush and I had a
+ 
+
+ align:start position:0%
+was um took a paintbrush and I had a
+specific stroke weight I had a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+specific color that I was using to draw
+
+ align:start position:0%
+specific color that I was using to draw
+ 
+
+ align:start position:0%
+specific color that I was using to draw
+I don't know a circle or
+
+ align:start position:0%
+I don't know a circle or
+ 
+
+ align:start position:0%
+I don't know a circle or
+spiral um and
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+then I reverted black back to like black
+
+ align:start position:0%
+then I reverted black back to like black
+ 
+
+ align:start position:0%
+then I reverted black back to like black
+and one point um but I want to go back
+
+ align:start position:0%
+and one point um but I want to go back
+ 
+
+ align:start position:0%
+and one point um but I want to go back
+to that
+
+ align:start position:0%
+to that
+ 
+
+ align:start position:0%
+to that
+size and color um the eye dropper tool
+
+ align:start position:0%
+size and color um the eye dropper tool
+ 
+
+ align:start position:0%
+size and color um the eye dropper tool
+will hold both those information so if I
+
+ align:start position:0%
+will hold both those information so if I
+ 
+
+ align:start position:0%
+will hold both those information so if I
+just ey dropper that then it'll turn
+
+ align:start position:0%
+just ey dropper that then it'll turn
+ 
+
+ align:start position:0%
+just ey dropper that then it'll turn
+blue and eight point brush but if I ey
+
+ align:start position:0%
+blue and eight point brush but if I ey
+ 
+
+ align:start position:0%
+blue and eight point brush but if I ey
+drop the black then it'll go back to one
+
+ align:start position:0%
+drop the black then it'll go back to one
+ 
+
+ align:start position:0%
+drop the black then it'll go back to one
+point in black um so it just saves you
+
+ align:start position:0%
+point in black um so it just saves you
+ 
+
+ align:start position:0%
+point in black um so it just saves you
+some time if you want to completely
+
+ align:start position:0%
+some time if you want to completely
+ 
+
+ align:start position:0%
+some time if you want to completely
+recreate something the last thing that's
+
+ align:start position:0%
+recreate something the last thing that's
+ 
+
+ align:start position:0%
+recreate something the last thing that's
+important in illustrator is
+
+ align:start position:0%
+important in illustrator is
+ 
+
+ align:start position:0%
+important in illustrator is
+layers um I usually divide up my
+
+ align:start position:0%
+layers um I usually divide up my
+ 
+
+ align:start position:0%
+layers um I usually divide up my
+Project based on like types of objects
+
+ align:start position:0%
+Project based on like types of objects
+ 
+
+ align:start position:0%
+Project based on like types of objects
+so if I was doing this from scratch I
+
+ align:start position:0%
+so if I was doing this from scratch I
+ 
+
+ align:start position:0%
+so if I was doing this from scratch I
+would probably put all the stuff I drew
+
+ align:start position:0%
+would probably put all the stuff I drew
+ 
+
+ align:start position:0%
+would probably put all the stuff I drew
+with a paintbrush on one layer um all
+
+ align:start position:0%
+with a paintbrush on one layer um all
+ 
+
+ align:start position:0%
+with a paintbrush on one layer um all
+the shapes on a separate layer um you
+
+ align:start position:0%
+the shapes on a separate layer um you
+ 
+
+ align:start position:0%
+the shapes on a separate layer um you
+create a new layer just by clicking this
+
+ align:start position:0%
+create a new layer just by clicking this
+ 
+
+ align:start position:0%
+create a new layer just by clicking this
+new little page here and it's basically
+
+ align:start position:0%
+new little page here and it's basically
+ 
+
+ align:start position:0%
+new little page here and it's basically
+just a way to group objects and
+
+ align:start position:0%
+just a way to group objects and
+ 
+
+ align:start position:0%
+just a way to group objects and
+manipulate them independently from each
+
+ align:start position:0%
+manipulate them independently from each
+ 
+
+ align:start position:0%
+manipulate them independently from each
+other
+
+ align:start position:0%
+other
+ 
+
+ align:start position:0%
+other
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+so for example I will move this square
+
+ align:start position:0%
+so for example I will move this square
+ 
+
+ align:start position:0%
+so for example I will move this square
+into Layer Two and I'll just animate
+
+ align:start position:0%
+into Layer Two and I'll just animate
+ 
+
+ align:start position:0%
+into Layer Two and I'll just animate
+using Layer Two
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um and you can
+
+ align:start position:0%
+um and you can
+ 
+
+ align:start position:0%
+um and you can
+toggle um a lock on each layer so if I
+
+ align:start position:0%
+toggle um a lock on each layer so if I
+ 
+
+ align:start position:0%
+toggle um a lock on each layer so if I
+put a lock on layer one that means I
+
+ align:start position:0%
+put a lock on layer one that means I
+ 
+
+ align:start position:0%
+put a lock on layer one that means I
+can't do anything to these objects like
+
+ align:start position:0%
+can't do anything to these objects like
+ 
+
+ align:start position:0%
+can't do anything to these objects like
+I can't manipulate them accidentally and
+
+ align:start position:0%
+I can't manipulate them accidentally and
+ 
+
+ align:start position:0%
+I can't manipulate them accidentally and
+the eyeball triggers whether you can see
+
+ align:start position:0%
+the eyeball triggers whether you can see
+ 
+
+ align:start position:0%
+the eyeball triggers whether you can see
+it or not so sometimes I you want to
+
+ align:start position:0%
+it or not so sometimes I you want to
+ 
+
+ align:start position:0%
+it or not so sometimes I you want to
+draw something in one layer and then you
+
+ align:start position:0%
+draw something in one layer and then you
+ 
+
+ align:start position:0%
+draw something in one layer and then you
+create a couple more on top of it um and
+
+ align:start position:0%
+create a couple more on top of it um and
+ 
+
+ align:start position:0%
+create a couple more on top of it um and
+you don't want to see the original one
+
+ align:start position:0%
+you don't want to see the original one
+ 
+
+ align:start position:0%
+you don't want to see the original one
+and I usually name my layer something to
+
+ align:start position:0%
+and I usually name my layer something to
+ 
+
+ align:start position:0%
+and I usually name my layer something to
+remind me what they are um for the
+
+ align:start position:0%
+remind me what they are um for the
+ 
+
+ align:start position:0%
+remind me what they are um for the
+purposes of After Effects just so um
+
+ align:start position:0%
+purposes of After Effects just so um
+ 
+
+ align:start position:0%
+purposes of After Effects just so um
+it's less confusing when I get there so
+
+ align:start position:0%
+it's less confusing when I get there so
+ 
+
+ align:start position:0%
+it's less confusing when I get there so
+this would be text and Layer Two will be
+
+ align:start position:0%
+this would be text and Layer Two will be
+ 
+
+ align:start position:0%
+this would be text and Layer Two will be
+rectangle if I can spell
+
+ align:start position:0%
+rectangle if I can spell
+ 
+
+ align:start position:0%
+rectangle if I can spell
+rectangle
+
+ align:start position:0%
+rectangle
+ 
+
+ align:start position:0%
+rectangle
+um that's pretty much all there is to
+
+ align:start position:0%
+um that's pretty much all there is to
+ 
+
+ align:start position:0%
+um that's pretty much all there is to
+know about illustrator you can save the
+
+ align:start position:0%
+know about illustrator you can save the
+ 
+
+ align:start position:0%
+know about illustrator you can save the
+files um it'll save as aai which is
+
+ align:start position:0%
+files um it'll save as aai which is
+ 
+
+ align:start position:0%
+files um it'll save as aai which is
+important when you animate something
+
+ align:start position:0%
+important when you animate something
+ 
+
+ align:start position:0%
+important when you animate something
+save it somewhere where you're going to
+
+ align:start position:0%
+save it somewhere where you're going to
+ 
+
+ align:start position:0%
+save it somewhere where you're going to
+remember where it
+
+ align:start position:0%
+remember where it
+ 
+
+ align:start position:0%
+remember where it
+is um and you can just keep the default
+
+ align:start position:0%
+is um and you can just keep the default
+ 
+
+ align:start position:0%
+is um and you can just keep the default
+settings if okay so here's where it's
+
+ align:start position:0%
+settings if okay so here's where it's
+ 
+
+ align:start position:0%
+settings if okay so here's where it's
+going to Branch off if you want a still
+
+ align:start position:0%
+going to Branch off if you want a still
+ 
+
+ align:start position:0%
+going to Branch off if you want a still
+transparent image over your video or an
+
+ align:start position:0%
+transparent image over your video or an
+ 
+
+ align:start position:0%
+transparent image over your video or an
+animation um if you just want a still
+
+ align:start position:0%
+animation um if you just want a still
+ 
+
+ align:start position:0%
+animation um if you just want a still
+transparent image you can draw it an
+
+ align:start position:0%
+transparent image you can draw it an
+ 
+
+ align:start position:0%
+transparent image you can draw it an
+illustrator like this um just click file
+
+ align:start position:0%
+illustrator like this um just click file
+ 
+
+ align:start position:0%
+illustrator like this um just click file
+export um and it'll automatically go to
+
+ align:start position:0%
+export um and it'll automatically go to
+ 
+
+ align:start position:0%
+export um and it'll automatically go to
+PNG um click use artboards because that
+
+ align:start position:0%
+PNG um click use artboards because that
+ 
+
+ align:start position:0%
+PNG um click use artboards because that
+preserves the screen dimensions that you
+
+ align:start position:0%
+preserves the screen dimensions that you
+ 
+
+ align:start position:0%
+preserves the screen dimensions that you
+specified in the
+
+ align:start position:0%
+specified in the
+ 
+
+ align:start position:0%
+specified in the
+beginning um and you click export and
+
+ align:start position:0%
+beginning um and you click export and
+ 
+
+ align:start position:0%
+beginning um and you click export and
+it'll give you this popup window and
+
+ align:start position:0%
+it'll give you this popup window and
+ 
+
+ align:start position:0%
+it'll give you this popup window and
+here is where you can choose whether you
+
+ align:start position:0%
+here is where you can choose whether you
+ 
+
+ align:start position:0%
+here is where you can choose whether you
+want like a white background a black
+
+ align:start position:0%
+want like a white background a black
+ 
+
+ align:start position:0%
+want like a white background a black
+background or a transparent um which is
+
+ align:start position:0%
+background or a transparent um which is
+ 
+
+ align:start position:0%
+background or a transparent um which is
+really nice if you just want like a text
+
+ align:start position:0%
+really nice if you just want like a text
+ 
+
+ align:start position:0%
+really nice if you just want like a text
+overlay on your video because you
+
+ align:start position:0%
+overlay on your video because you
+ 
+
+ align:start position:0%
+overlay on your video because you
+automatically have an image with Vector
+
+ align:start position:0%
+automatically have an image with Vector
+ 
+
+ align:start position:0%
+automatically have an image with Vector
+art in it or vector words and a
+
+ align:start position:0%
+art in it or vector words and a
+ 
+
+ align:start position:0%
+art in it or vector words and a
+transparent background um and you just
+
+ align:start position:0%
+transparent background um and you just
+ 
+
+ align:start position:0%
+transparent background um and you just
+click okay and then your image will be
+
+ align:start position:0%
+click okay and then your image will be
+ 
+
+ align:start position:0%
+click okay and then your image will be
+exported I think mine's in my downloads
+
+ align:start position:0%
+exported I think mine's in my downloads
+ 
+
+ align:start position:0%
+exported I think mine's in my downloads
+folder yeah just as like a PNG file
+
+ align:start position:0%
+folder yeah just as like a PNG file
+ 
+
+ align:start position:0%
+folder yeah just as like a PNG file
+which you can import into iMovie or
+
+ align:start position:0%
+which you can import into iMovie or
+ 
+
+ align:start position:0%
+which you can import into iMovie or
+Premiere or um Final Cut Pro and overlay
+
+ align:start position:0%
+Premiere or um Final Cut Pro and overlay
+ 
+
+ align:start position:0%
+Premiere or um Final Cut Pro and overlay
+it just like another video track or an
+
+ align:start position:0%
+it just like another video track or an
+ 
+
+ align:start position:0%
+it just like another video track or an
+image um okay that is everything for
+
+ align:start position:0%
+image um okay that is everything for
+ 
+
+ align:start position:0%
+image um okay that is everything for
+illustrator so I will close
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that now
+
+ align:start position:0%
+that now
+ 
+
+ align:start position:0%
+that now
+if you want to animate um animate in
+
+ align:start position:0%
+if you want to animate um animate in
+ 
+
+ align:start position:0%
+if you want to animate um animate in
+After
+
+ align:start position:0%
+After
+ 
+
+ align:start position:0%
+After
+Effects most likely um you can also
+
+ align:start position:0%
+Effects most likely um you can also
+ 
+
+ align:start position:0%
+Effects most likely um you can also
+learn flash animation but that's a
+
+ align:start position:0%
+learn flash animation but that's a
+ 
+
+ align:start position:0%
+learn flash animation but that's a
+different concept behind it
+
+ align:start position:0%
+different concept behind it
+ 
+
+ align:start position:0%
+different concept behind it
+um so the way you start a composition in
+
+ align:start position:0%
+um so the way you start a composition in
+ 
+
+ align:start position:0%
+um so the way you start a composition in
+After Effects and import your images
+
+ align:start position:0%
+After Effects and import your images
+ 
+
+ align:start position:0%
+After Effects and import your images
+that you started in illustrator um you
+
+ align:start position:0%
+that you started in illustrator um you
+ 
+
+ align:start position:0%
+that you started in illustrator um you
+exit out of the initial window when it
+
+ align:start position:0%
+exit out of the initial window when it
+ 
+
+ align:start position:0%
+exit out of the initial window when it
+asks you to create a new composition
+
+ align:start position:0%
+asks you to create a new composition
+ 
+
+ align:start position:0%
+asks you to create a new composition
+because we're going to just import our
+
+ align:start position:0%
+because we're going to just import our
+ 
+
+ align:start position:0%
+because we're going to just import our
+files from illustrator as a new
+
+ align:start position:0%
+files from illustrator as a new
+ 
+
+ align:start position:0%
+files from illustrator as a new
+composition so you just double click in
+
+ align:start position:0%
+composition so you just double click in
+ 
+
+ align:start position:0%
+composition so you just double click in
+the project window and it'll give you a
+
+ align:start position:0%
+the project window and it'll give you a
+ 
+
+ align:start position:0%
+the project window and it'll give you a
+popup window that says import file I'm
+
+ align:start position:0%
+popup window that says import file I'm
+ 
+
+ align:start position:0%
+popup window that says import file I'm
+sure there's another way to do this but
+
+ align:start position:0%
+sure there's another way to do this but
+ 
+
+ align:start position:0%
+sure there's another way to do this but
+this is just how I was taught um you can
+
+ align:start position:0%
+this is just how I was taught um you can
+ 
+
+ align:start position:0%
+this is just how I was taught um you can
+probably go file open or something like
+
+ align:start position:0%
+probably go file open or something like
+ 
+
+ align:start position:0%
+probably go file open or something like
+that um go to wherever you saved your
+
+ align:start position:0%
+that um go to wherever you saved your
+ 
+
+ align:start position:0%
+that um go to wherever you saved your
+illustrator file um enable all
+
+ align:start position:0%
+illustrator file um enable all
+ 
+
+ align:start position:0%
+illustrator file um enable all
+acceptable files and then import it as a
+
+ align:start position:0%
+acceptable files and then import it as a
+ 
+
+ align:start position:0%
+acceptable files and then import it as a
+composition um that just means it will
+
+ align:start position:0%
+composition um that just means it will
+ 
+
+ align:start position:0%
+composition um that just means it will
+process each layer in your illustrator
+
+ align:start position:0%
+process each layer in your illustrator
+ 
+
+ align:start position:0%
+process each layer in your illustrator
+file as a different layer in your
+
+ align:start position:0%
+file as a different layer in your
+ 
+
+ align:start position:0%
+file as a different layer in your
+composition which will be important when
+
+ align:start position:0%
+composition which will be important when
+ 
+
+ align:start position:0%
+composition which will be important when
+it comes to
+
+ align:start position:0%
+it comes to
+ 
+
+ align:start position:0%
+it comes to
+animating um and then from here you can
+
+ align:start position:0%
+animating um and then from here you can
+ 
+
+ align:start position:0%
+animating um and then from here you can
+alter your composition settings my
+
+ align:start position:0%
+alter your composition settings my
+ 
+
+ align:start position:0%
+alter your composition settings my
+tablet as side
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um and and you can name your composition
+
+ align:start position:0%
+um and and you can name your composition
+ 
+
+ align:start position:0%
+um and and you can name your composition
+um it'll automatically adopt the name
+
+ align:start position:0%
+um it'll automatically adopt the name
+ 
+
+ align:start position:0%
+um it'll automatically adopt the name
+that you named your illustrator file um
+
+ align:start position:0%
+that you named your illustrator file um
+ 
+
+ align:start position:0%
+that you named your illustrator file um
+you can customize the width and the
+
+ align:start position:0%
+you can customize the width and the
+ 
+
+ align:start position:0%
+you can customize the width and the
+height which should be the same
+
+ align:start position:0%
+height which should be the same
+ 
+
+ align:start position:0%
+height which should be the same
+dimensions that you specified before um
+
+ align:start position:0%
+dimensions that you specified before um
+ 
+
+ align:start position:0%
+dimensions that you specified before um
+you want it to be in square pixels
+
+ align:start position:0%
+you want it to be in square pixels
+ 
+
+ align:start position:0%
+you want it to be in square pixels
+sometimes it defaults
+
+ align:start position:0%
+sometimes it defaults
+ 
+
+ align:start position:0%
+sometimes it defaults
+to different size and I think
+
+ align:start position:0%
+to different size and I think
+ 
+
+ align:start position:0%
+to different size and I think
+rectangular pixels are silly and they
+
+ align:start position:0%
+rectangular pixels are silly and they
+ 
+
+ align:start position:0%
+rectangular pixels are silly and they
+mess up how your video is going to look
+
+ align:start position:0%
+mess up how your video is going to look
+ 
+
+ align:start position:0%
+mess up how your video is going to look
+eventually or how your animations relate
+
+ align:start position:0%
+eventually or how your animations relate
+ 
+
+ align:start position:0%
+eventually or how your animations relate
+to your video the frame rate is
+
+ align:start position:0%
+to your video the frame rate is
+ 
+
+ align:start position:0%
+to your video the frame rate is
+important because it allows you to match
+
+ align:start position:0%
+important because it allows you to match
+ 
+
+ align:start position:0%
+important because it allows you to match
+up your animation exactly to your video
+
+ align:start position:0%
+up your animation exactly to your video
+ 
+
+ align:start position:0%
+up your animation exactly to your video
+um in Adobe Premiere the frame rate is
+
+ align:start position:0%
+um in Adobe Premiere the frame rate is
+ 
+
+ align:start position:0%
+um in Adobe Premiere the frame rate is
+30 the default for After Effects is 25
+
+ align:start position:0%
+30 the default for After Effects is 25
+ 
+
+ align:start position:0%
+30 the default for After Effects is 25
+and that messed me up on my first
+
+ align:start position:0%
+and that messed me up on my first
+ 
+
+ align:start position:0%
+and that messed me up on my first
+project because I was trying to time
+
+ align:start position:0%
+project because I was trying to time
+ 
+
+ align:start position:0%
+project because I was trying to time
+everything and then it was off by
+
+ align:start position:0%
+everything and then it was off by
+ 
+
+ align:start position:0%
+everything and then it was off by
+um five frames per second which is
+
+ align:start position:0%
+um five frames per second which is
+ 
+
+ align:start position:0%
+um five frames per second which is
+really frustrating um I don't know what
+
+ align:start position:0%
+really frustrating um I don't know what
+ 
+
+ align:start position:0%
+really frustrating um I don't know what
+they are for imove your final cut but I
+
+ align:start position:0%
+they are for imove your final cut but I
+ 
+
+ align:start position:0%
+they are for imove your final cut but I
+would check um when you go in before you
+
+ align:start position:0%
+would check um when you go in before you
+ 
+
+ align:start position:0%
+would check um when you go in before you
+start your project
+
+ align:start position:0%
+start your project
+ 
+
+ align:start position:0%
+start your project
+um okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um I set the background color to white
+
+ align:start position:0%
+um I set the background color to white
+ 
+
+ align:start position:0%
+um I set the background color to white
+just so I can see everything um because
+
+ align:start position:0%
+just so I can see everything um because
+ 
+
+ align:start position:0%
+just so I can see everything um because
+I usually draw with a white background
+
+ align:start position:0%
+I usually draw with a white background
+ 
+
+ align:start position:0%
+I usually draw with a white background
+in illustrator if you want to set the
+
+ align:start position:0%
+in illustrator if you want to set the
+ 
+
+ align:start position:0%
+in illustrator if you want to set the
+default background in illustrator to
+
+ align:start position:0%
+default background in illustrator to
+ 
+
+ align:start position:0%
+default background in illustrator to
+Black and do white text and set that as
+
+ align:start position:0%
+Black and do white text and set that as
+ 
+
+ align:start position:0%
+Black and do white text and set that as
+transparent in front of your video um
+
+ align:start position:0%
+transparent in front of your video um
+ 
+
+ align:start position:0%
+transparent in front of your video um
+then a black background would make more
+
+ align:start position:0%
+then a black background would make more
+ 
+
+ align:start position:0%
+then a black background would make more
+sense this background color does not
+
+ align:start position:0%
+sense this background color does not
+ 
+
+ align:start position:0%
+sense this background color does not
+export with the video though so your
+
+ align:start position:0%
+export with the video though so your
+ 
+
+ align:start position:0%
+export with the video though so your
+animations are still transparent it's
+
+ align:start position:0%
+animations are still transparent it's
+ 
+
+ align:start position:0%
+animations are still transparent it's
+just so you can see things in After
+
+ align:start position:0%
+just so you can see things in After
+ 
+
+ align:start position:0%
+just so you can see things in After
+Effects um and usually what I do before
+
+ align:start position:0%
+Effects um and usually what I do before
+ 
+
+ align:start position:0%
+Effects um and usually what I do before
+I start an After Effects project is I
+
+ align:start position:0%
+I start an After Effects project is I
+ 
+
+ align:start position:0%
+I start an After Effects project is I
+look at how long the audio is for the
+
+ align:start position:0%
+look at how long the audio is for the
+ 
+
+ align:start position:0%
+look at how long the audio is for the
+portion that I want to animate so for
+
+ align:start position:0%
+portion that I want to animate so for
+ 
+
+ align:start position:0%
+portion that I want to animate so for
+example I was working with Andrea
+
+ align:start position:0%
+example I was working with Andrea
+ 
+
+ align:start position:0%
+example I was working with Andrea
+yesterday and she wanted a goat um
+
+ align:start position:0%
+yesterday and she wanted a goat um
+ 
+
+ align:start position:0%
+yesterday and she wanted a goat um
+during one of her lines when she says
+
+ align:start position:0%
+during one of her lines when she says
+ 
+
+ align:start position:0%
+during one of her lines when she says
+and the force of a mountain goat jumping
+
+ align:start position:0%
+and the force of a mountain goat jumping
+ 
+
+ align:start position:0%
+and the force of a mountain goat jumping
+on your teeth is some amount of Newtons
+
+ align:start position:0%
+on your teeth is some amount of Newtons
+ 
+
+ align:start position:0%
+on your teeth is some amount of Newtons
+or whatever the line is um and you look
+
+ align:start position:0%
+or whatever the line is um and you look
+ 
+
+ align:start position:0%
+or whatever the line is um and you look
+at the duration of how long it takes you
+
+ align:start position:0%
+at the duration of how long it takes you
+ 
+
+ align:start position:0%
+at the duration of how long it takes you
+to say that line in your editing
+
+ align:start position:0%
+to say that line in your editing
+ 
+
+ align:start position:0%
+to say that line in your editing
+software and that's how long I set my
+
+ align:start position:0%
+software and that's how long I set my
+ 
+
+ align:start position:0%
+software and that's how long I set my
+duration of my animation to be so it's
+
+ align:start position:0%
+duration of my animation to be so it's
+ 
+
+ align:start position:0%
+duration of my animation to be so it's
+really easy it's really like modular I'm
+
+ align:start position:0%
+really easy it's really like modular I'm
+ 
+
+ align:start position:0%
+really easy it's really like modular I'm
+animating for this part of the video and
+
+ align:start position:0%
+animating for this part of the video and
+ 
+
+ align:start position:0%
+animating for this part of the video and
+I have this much space to do it in um
+
+ align:start position:0%
+I have this much space to do it in um
+ 
+
+ align:start position:0%
+I have this much space to do it in um
+and because I don't have an audio track
+
+ align:start position:0%
+and because I don't have an audio track
+ 
+
+ align:start position:0%
+and because I don't have an audio track
+right now I'm just going to set it to 15
+
+ align:start position:0%
+right now I'm just going to set it to 15
+ 
+
+ align:start position:0%
+right now I'm just going to set it to 15
+seconds so that's good um then you can
+
+ align:start position:0%
+seconds so that's good um then you can
+ 
+
+ align:start position:0%
+seconds so that's good um then you can
+double click on your composition to open
+
+ align:start position:0%
+double click on your composition to open
+ 
+
+ align:start position:0%
+double click on your composition to open
+it and this is going to be your display
+
+ align:start position:0%
+it and this is going to be your display
+ 
+
+ align:start position:0%
+it and this is going to be your display
+window this is your timeline it's where
+
+ align:start position:0%
+window this is your timeline it's where
+ 
+
+ align:start position:0%
+window this is your timeline it's where
+I guess the animation is taking place
+
+ align:start position:0%
+I guess the animation is taking place
+ 
+
+ align:start position:0%
+I guess the animation is taking place
+and you can see different things
+
+ align:start position:0%
+and you can see different things
+ 
+
+ align:start position:0%
+and you can see different things
+um and here's where your you're going to
+
+ align:start position:0%
+um and here's where your you're going to
+ 
+
+ align:start position:0%
+um and here's where your you're going to
+be doing a lot of the animation stuff
+
+ align:start position:0%
+be doing a lot of the animation stuff
+ 
+
+ align:start position:0%
+be doing a lot of the animation stuff
+this little options window I guess um
+
+ align:start position:0%
+this little options window I guess um
+ 
+
+ align:start position:0%
+this little options window I guess um
+you can still toggle the visibility just
+
+ align:start position:0%
+you can still toggle the visibility just
+ 
+
+ align:start position:0%
+you can still toggle the visibility just
+like you did in
+
+ align:start position:0%
+like you did in
+ 
+
+ align:start position:0%
+like you did in
+illustrator and so H let's say um I'm
+
+ align:start position:0%
+illustrator and so H let's say um I'm
+ 
+
+ align:start position:0%
+illustrator and so H let's say um I'm
+just going to show you how to animate
+
+ align:start position:0%
+just going to show you how to animate
+ 
+
+ align:start position:0%
+just going to show you how to animate
+this rectangle for example um so the
+
+ align:start position:0%
+this rectangle for example um so the
+ 
+
+ align:start position:0%
+this rectangle for example um so the
+first thing you want to do is right
+
+ align:start position:0%
+first thing you want to do is right
+ 
+
+ align:start position:0%
+first thing you want to do is right
+click on it and create shapes from the
+
+ align:start position:0%
+click on it and create shapes from the
+ 
+
+ align:start position:0%
+click on it and create shapes from the
+vector layer basically this just allows
+
+ align:start position:0%
+vector layer basically this just allows
+ 
+
+ align:start position:0%
+vector layer basically this just allows
+um after effects to take the vector
+
+ align:start position:0%
+um after effects to take the vector
+ 
+
+ align:start position:0%
+um after effects to take the vector
+shapes or objects that you created an
+
+ align:start position:0%
+shapes or objects that you created an
+ 
+
+ align:start position:0%
+shapes or objects that you created an
+illustrator and translate it into a
+
+ align:start position:0%
+illustrator and translate it into a
+ 
+
+ align:start position:0%
+illustrator and translate it into a
+manipul
+
+ align:start position:0%
+manipul
+ 
+
+ align:start position:0%
+manipul
+manipulatable format um for After
+
+ align:start position:0%
+manipulatable format um for After
+ 
+
+ align:start position:0%
+manipulatable format um for After
+Effects um so then you have this new
+
+ align:start position:0%
+Effects um so then you have this new
+ 
+
+ align:start position:0%
+Effects um so then you have this new
+item object I don't know called
+
+ align:start position:0%
+item object I don't know called
+ 
+
+ align:start position:0%
+item object I don't know called
+rectangle outlines um and you can look
+
+ align:start position:0%
+rectangle outlines um and you can look
+ 
+
+ align:start position:0%
+rectangle outlines um and you can look
+inside and their contents if you had
+
+ align:start position:0%
+inside and their contents if you had
+ 
+
+ align:start position:0%
+inside and their contents if you had
+multiple objects in the same layer you'd
+
+ align:start position:0%
+multiple objects in the same layer you'd
+ 
+
+ align:start position:0%
+multiple objects in the same layer you'd
+have multiple groups but I just have the
+
+ align:start position:0%
+have multiple groups but I just have the
+ 
+
+ align:start position:0%
+have multiple groups but I just have the
+one rectangle so I only have group
+
+ align:start position:0%
+one rectangle so I only have group
+ 
+
+ align:start position:0%
+one rectangle so I only have group
+one um and so in order to move this what
+
+ align:start position:0%
+one um and so in order to move this what
+ 
+
+ align:start position:0%
+one um and so in order to move this what
+I'm going to do is open up group one and
+
+ align:start position:0%
+I'm going to do is open up group one and
+ 
+
+ align:start position:0%
+I'm going to do is open up group one and
+I
+
+ align:start position:0%
+I
+ 
+
+ align:start position:0%
+I
+have um different
+
+ align:start position:0%
+have um different
+ 
+
+ align:start position:0%
+have um different
+options and you guys are going to be
+
+ align:start position:0%
+options and you guys are going to be
+ 
+
+ align:start position:0%
+options and you guys are going to be
+doing a lot of transform animations um
+
+ align:start position:0%
+doing a lot of transform animations um
+ 
+
+ align:start position:0%
+doing a lot of transform animations um
+so these are things like if you want
+
+ align:start position:0%
+so these are things like if you want
+ 
+
+ align:start position:0%
+so these are things like if you want
+something to move around on the screen
+
+ align:start position:0%
+something to move around on the screen
+ 
+
+ align:start position:0%
+something to move around on the screen
+if you want something to change in size
+
+ align:start position:0%
+if you want something to change in size
+ 
+
+ align:start position:0%
+if you want something to change in size
+or rotate or things like that um so what
+
+ align:start position:0%
+or rotate or things like that um so what
+ 
+
+ align:start position:0%
+or rotate or things like that um so what
+you're going to do for if you wanted
+
+ align:start position:0%
+you're going to do for if you wanted
+ 
+
+ align:start position:0%
+you're going to do for if you wanted
+let's say I wanted this rectangle to
+
+ align:start position:0%
+let's say I wanted this rectangle to
+ 
+
+ align:start position:0%
+let's say I wanted this rectangle to
+move across the screen and grow
+
+ align:start position:0%
+move across the screen and grow
+ 
+
+ align:start position:0%
+move across the screen and grow
+bigger the things that I will and and in
+
+ align:start position:0%
+bigger the things that I will and and in
+ 
+
+ align:start position:0%
+bigger the things that I will and and in
+After Effects you want to think in key
+
+ align:start position:0%
+After Effects you want to think in key
+ 
+
+ align:start position:0%
+After Effects you want to think in key
+frames so what does it look like at one
+
+ align:start position:0%
+frames so what does it look like at one
+ 
+
+ align:start position:0%
+frames so what does it look like at one
+point in the animation and then what do
+
+ align:start position:0%
+point in the animation and then what do
+ 
+
+ align:start position:0%
+point in the animation and then what do
+you want it to look like in two
+
+ align:start position:0%
+you want it to look like in two
+ 
+
+ align:start position:0%
+you want it to look like in two
+seconds um so right now this is where I
+
+ align:start position:0%
+seconds um so right now this is where I
+ 
+
+ align:start position:0%
+seconds um so right now this is where I
+want it to start so I'll click a little
+
+ align:start position:0%
+want it to start so I'll click a little
+ 
+
+ align:start position:0%
+want it to start so I'll click a little
+stopwatch on position and scale and
+
+ align:start position:0%
+stopwatch on position and scale and
+ 
+
+ align:start position:0%
+stopwatch on position and scale and
+these will set key frames for both
+
+ align:start position:0%
+these will set key frames for both
+ 
+
+ align:start position:0%
+these will set key frames for both
+position and scale so now after effects
+
+ align:start position:0%
+position and scale so now after effects
+ 
+
+ align:start position:0%
+position and scale so now after effects
+remembers where the rectangle is at this
+
+ align:start position:0%
+remembers where the rectangle is at this
+ 
+
+ align:start position:0%
+remembers where the rectangle is at this
+point in time then I'll set it forward
+
+ align:start position:0%
+point in time then I'll set it forward
+ 
+
+ align:start position:0%
+point in time then I'll set it forward
+to let's say 2 seconds I want in 2
+
+ align:start position:0%
+to let's say 2 seconds I want in 2
+ 
+
+ align:start position:0%
+to let's say 2 seconds I want in 2
+seconds I want my rectangle to move and
+
+ align:start position:0%
+seconds I want my rectangle to move and
+ 
+
+ align:start position:0%
+seconds I want my rectangle to move and
+then it's as easy as dragging the
+
+ align:start position:0%
+then it's as easy as dragging the
+ 
+
+ align:start position:0%
+then it's as easy as dragging the
+rectangle to where you want it to be and
+
+ align:start position:0%
+rectangle to where you want it to be and
+ 
+
+ align:start position:0%
+rectangle to where you want it to be and
+then changing its size so let's say I
+
+ align:start position:0%
+then changing its size so let's say I
+ 
+
+ align:start position:0%
+then changing its size so let's say I
+want it to be really big like that and
+
+ align:start position:0%
+want it to be really big like that and
+ 
+
+ align:start position:0%
+want it to be really big like that and
+then once you make those changes after
+
+ align:start position:0%
+then once you make those changes after
+ 
+
+ align:start position:0%
+then once you make those changes after
+effects automatically sets another key
+
+ align:start position:0%
+effects automatically sets another key
+ 
+
+ align:start position:0%
+effects automatically sets another key
+frame for you in your
+
+ align:start position:0%
+frame for you in your
+ 
+
+ align:start position:0%
+frame for you in your
+timeline then you can review what you
+
+ align:start position:0%
+timeline then you can review what you
+ 
+
+ align:start position:0%
+timeline then you can review what you
+want the animation to do by dragging
+
+ align:start position:0%
+want the animation to do by dragging
+ 
+
+ align:start position:0%
+want the animation to do by dragging
+this back um and pushing space which is
+
+ align:start position:0%
+this back um and pushing space which is
+ 
+
+ align:start position:0%
+this back um and pushing space which is
+the same thing as play and then you can
+
+ align:start position:0%
+the same thing as play and then you can
+ 
+
+ align:start position:0%
+the same thing as play and then you can
+watch how over the two seconds it
+
+ align:start position:0%
+watch how over the two seconds it
+ 
+
+ align:start position:0%
+watch how over the two seconds it
+transitions from one point in space to
+
+ align:start position:0%
+transitions from one point in space to
+ 
+
+ align:start position:0%
+transitions from one point in space to
+another point in space and another one
+
+ align:start position:0%
+another point in space and another one
+ 
+
+ align:start position:0%
+another point in space and another one
+size to another size um you can edit and
+
+ align:start position:0%
+size to another size um you can edit and
+ 
+
+ align:start position:0%
+size to another size um you can edit and
+delete key frames you can add more in
+
+ align:start position:0%
+delete key frames you can add more in
+ 
+
+ align:start position:0%
+delete key frames you can add more in
+the middle let's say I wanted it to go
+
+ align:start position:0%
+the middle let's say I wanted it to go
+ 
+
+ align:start position:0%
+the middle let's say I wanted it to go
+up and left before I wanted it to go up
+
+ align:start position:0%
+up and left before I wanted it to go up
+ 
+
+ align:start position:0%
+up and left before I wanted it to go up
+and right um You can just set it to the
+
+ align:start position:0%
+and right um You can just set it to the
+ 
+
+ align:start position:0%
+and right um You can just set it to the
+middle of this animation and drag it up
+
+ align:start position:0%
+middle of this animation and drag it up
+ 
+
+ align:start position:0%
+middle of this animation and drag it up
+and left to where you would want it to
+
+ align:start position:0%
+and left to where you would want it to
+ 
+
+ align:start position:0%
+and left to where you would want it to
+be and then it'll keep scaling si uh the
+
+ align:start position:0%
+be and then it'll keep scaling si uh the
+ 
+
+ align:start position:0%
+be and then it'll keep scaling si uh the
+size at the same time but then it'll
+
+ align:start position:0%
+size at the same time but then it'll
+ 
+
+ align:start position:0%
+size at the same time but then it'll
+just adjust its position path in the new
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+animation
+
+ align:start position:0%
+animation
+ 
+
+ align:start position:0%
+animation
+um and that's the really The Bare Bones
+
+ align:start position:0%
+um and that's the really The Bare Bones
+ 
+
+ align:start position:0%
+um and that's the really The Bare Bones
+of Animation um the one other thing you
+
+ align:start position:0%
+of Animation um the one other thing you
+ 
+
+ align:start position:0%
+of Animation um the one other thing you
+guys might use is let's
+
+ align:start position:0%
+guys might use is let's
+ 
+
+ align:start position:0%
+guys might use is let's
+see um if you want to group multiple
+
+ align:start position:0%
+see um if you want to group multiple
+ 
+
+ align:start position:0%
+see um if you want to group multiple
+items um and have them move at the same
+
+ align:start position:0%
+items um and have them move at the same
+ 
+
+ align:start position:0%
+items um and have them move at the same
+time for
+
+ align:start position:0%
+time for
+ 
+
+ align:start position:0%
+time for
+example
+
+ align:start position:0%
+example
+ 
+
+ align:start position:0%
+example
+um let's see I'm going to take my text
+
+ align:start position:0%
+um let's see I'm going to take my text
+ 
+
+ align:start position:0%
+um let's see I'm going to take my text
+layer create shapes from vector layer
+
+ align:start position:0%
+layer create shapes from vector layer
+ 
+
+ align:start position:0%
+layer create shapes from vector layer
+and now I have another layer of
+
+ align:start position:0%
+and now I have another layer of
+ 
+
+ align:start position:0%
+and now I have another layer of
+objects um except this one has many
+
+ align:start position:0%
+objects um except this one has many
+ 
+
+ align:start position:0%
+objects um except this one has many
+contents many groups of things that I
+
+ align:start position:0%
+contents many groups of things that I
+ 
+
+ align:start position:0%
+contents many groups of things that I
+can manipulate so let's say I want both
+
+ align:start position:0%
+can manipulate so let's say I want both
+ 
+
+ align:start position:0%
+can manipulate so let's say I want both
+these spirals to move at the same time
+
+ align:start position:0%
+these spirals to move at the same time
+ 
+
+ align:start position:0%
+these spirals to move at the same time
+um I haven't found a better way to do
+
+ align:start position:0%
+um I haven't found a better way to do
+ 
+
+ align:start position:0%
+um I haven't found a better way to do
+this but um so I learned that the
+
+ align:start position:0%
+this but um so I learned that the
+ 
+
+ align:start position:0%
+this but um so I learned that the
+spirals are groups 2 and
+
+ align:start position:0%
+spirals are groups 2 and
+ 
+
+ align:start position:0%
+spirals are groups 2 and
+three I can click on contents just to
+
+ align:start position:0%
+three I can click on contents just to
+ 
+
+ align:start position:0%
+three I can click on contents just to
+highlight everything add a new empty
+
+ align:start position:0%
+highlight everything add a new empty
+ 
+
+ align:start position:0%
+highlight everything add a new empty
+group and it's just labeled whatever the
+
+ align:start position:0%
+group and it's just labeled whatever the
+ 
+
+ align:start position:0%
+group and it's just labeled whatever the
+highest number like the one after the
+
+ align:start position:0%
+highest number like the one after the
+ 
+
+ align:start position:0%
+highest number like the one after the
+highest number you can rename it to
+
+ align:start position:0%
+highest number you can rename it to
+ 
+
+ align:start position:0%
+highest number you can rename it to
+something like spirals so you remember
+
+ align:start position:0%
+something like spirals so you remember
+ 
+
+ align:start position:0%
+something like spirals so you remember
+it um you can highlight both of
+
+ align:start position:0%
+it um you can highlight both of
+ 
+
+ align:start position:0%
+it um you can highlight both of
+these and just drag it into the new
+
+ align:start position:0%
+these and just drag it into the new
+ 
+
+ align:start position:0%
+these and just drag it into the new
+group
+
+ align:start position:0%
+group
+ 
+
+ align:start position:0%
+group
+and that way you can transform spirals
+
+ align:start position:0%
+and that way you can transform spirals
+ 
+
+ align:start position:0%
+and that way you can transform spirals
+as a unit you can um say I wanted them
+
+ align:start position:0%
+as a unit you can um say I wanted them
+ 
+
+ align:start position:0%
+as a unit you can um say I wanted them
+to
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+rotate and so
+
+ align:start position:0%
+rotate and so
+ 
+
+ align:start position:0%
+rotate and so
+then oh God okay that's kind of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+rotating um and so it set the key frames
+
+ align:start position:0%
+rotating um and so it set the key frames
+ 
+
+ align:start position:0%
+rotating um and so it set the key frames
+for rotations but instead of just
+
+ align:start position:0%
+for rotations but instead of just
+ 
+
+ align:start position:0%
+for rotations but instead of just
+manipulating one spiral I have two
+
+ align:start position:0%
+manipulating one spiral I have two
+ 
+
+ align:start position:0%
+manipulating one spiral I have two
+grouped together and then the rectangle
+
+ align:start position:0%
+grouped together and then the rectangle
+ 
+
+ align:start position:0%
+grouped together and then the rectangle
+animation is still going
+
+ align:start position:0%
+animation is still going
+ 
+
+ align:start position:0%
+animation is still going
+um from
+
+ align:start position:0%
+um from
+ 
+
+ align:start position:0%
+um from
+before can you can you put to what do
+
+ align:start position:0%
+before can you can you put to what do
+ 
+
+ align:start position:0%
+before can you can you put to what do
+you mean put a point that on uh Pivot
+
+ align:start position:0%
+you mean put a point that on uh Pivot
+ 
+
+ align:start position:0%
+you mean put a point that on uh Pivot
+Point um I think so I don't usually
+
+ align:start position:0%
+Point um I think so I don't usually
+ 
+
+ align:start position:0%
+Point um I think so I don't usually
+rotate things in my animations I'm Pro
+
+ align:start position:0%
+rotate things in my animations I'm Pro
+ 
+
+ align:start position:0%
+rotate things in my animations I'm Pro
+let's see I think it's probably the
+
+ align:start position:0%
+let's see I think it's probably the
+ 
+
+ align:start position:0%
+let's see I think it's probably the
+Anchor
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Point CR
+
+ align:start position:0%
+Point CR
+ 
+
+ align:start position:0%
+Point CR
+yeah so that's the pivot point I don't
+
+ align:start position:0%
+yeah so that's the pivot point I don't
+ 
+
+ align:start position:0%
+yeah so that's the pivot point I don't
+know how to change that
+
+ align:start position:0%
+know how to change that
+ 
+
+ align:start position:0%
+know how to change that
+necessarily okay there you go you can
+
+ align:start position:0%
+necessarily okay there you go you can
+ 
+
+ align:start position:0%
+necessarily okay there you go you can
+just adjust it in relation to the Anchor
+
+ align:start position:0%
+just adjust it in relation to the Anchor
+ 
+
+ align:start position:0%
+just adjust it in relation to the Anchor
+Point so you can change this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+value yeah a lot of this is just playing
+
+ align:start position:0%
+value yeah a lot of this is just playing
+ 
+
+ align:start position:0%
+value yeah a lot of this is just playing
+around and seeing what you want to do
+
+ align:start position:0%
+around and seeing what you want to do
+ 
+
+ align:start position:0%
+around and seeing what you want to do
+you can ask me questions afterward and
+
+ align:start position:0%
+you can ask me questions afterward and
+ 
+
+ align:start position:0%
+you can ask me questions afterward and
+I'd be happy to like troubleshoot it
+
+ align:start position:0%
+I'd be happy to like troubleshoot it
+ 
+
+ align:start position:0%
+I'd be happy to like troubleshoot it
+with you
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um yeah so I guess that's how you pivot
+
+ align:start position:0%
+um yeah so I guess that's how you pivot
+ 
+
+ align:start position:0%
+um yeah so I guess that's how you pivot
+and so it'll maintain the rotation just
+
+ align:start position:0%
+and so it'll maintain the rotation just
+ 
+
+ align:start position:0%
+and so it'll maintain the rotation just
+around the smaller Anchor Point
+
+ align:start position:0%
+around the smaller Anchor Point
+ 
+
+ align:start position:0%
+around the smaller Anchor Point
+now
+
+ align:start position:0%
+now
+ 
+
+ align:start position:0%
+now
+um let's
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+see
+
+ align:start position:0%
+see
+ 
+
+ align:start position:0%
+see
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+if this is might be useful um so if you
+
+ align:start position:0%
+if this is might be useful um so if you
+ 
+
+ align:start position:0%
+if this is might be useful um so if you
+already go in and you have a lot of work
+
+ align:start position:0%
+already go in and you have a lot of work
+ 
+
+ align:start position:0%
+already go in and you have a lot of work
+um so for example in a different project
+
+ align:start position:0%
+um so for example in a different project
+ 
+
+ align:start position:0%
+um so for example in a different project
+what happened was I had the outline of a
+
+ align:start position:0%
+what happened was I had the outline of a
+ 
+
+ align:start position:0%
+what happened was I had the outline of a
+cell and I was showing contents of the
+
+ align:start position:0%
+cell and I was showing contents of the
+ 
+
+ align:start position:0%
+cell and I was showing contents of the
+nucleus and when I screened it to my
+
+ align:start position:0%
+nucleus and when I screened it to my
+ 
+
+ align:start position:0%
+nucleus and when I screened it to my
+project adviser she said it's great but
+
+ align:start position:0%
+project adviser she said it's great but
+ 
+
+ align:start position:0%
+project adviser she said it's great but
+we're not focusing on the nucleus of the
+
+ align:start position:0%
+we're not focusing on the nucleus of the
+ 
+
+ align:start position:0%
+we're not focusing on the nucleus of the
+cell and so I can't really see what's
+
+ align:start position:0%
+cell and so I can't really see what's
+ 
+
+ align:start position:0%
+cell and so I can't really see what's
+going on so I had already done all this
+
+ align:start position:0%
+going on so I had already done all this
+ 
+
+ align:start position:0%
+going on so I had already done all this
+animation with individual squiggles of
+
+ align:start position:0%
+animation with individual squiggles of
+ 
+
+ align:start position:0%
+animation with individual squiggles of
+DNA and proteins moving around in the
+
+ align:start position:0%
+DNA and proteins moving around in the
+ 
+
+ align:start position:0%
+DNA and proteins moving around in the
+nucleus and I wanted to preserve that
+
+ align:start position:0%
+nucleus and I wanted to preserve that
+ 
+
+ align:start position:0%
+nucleus and I wanted to preserve that
+animation but um I needed to just zoom
+
+ align:start position:0%
+animation but um I needed to just zoom
+ 
+
+ align:start position:0%
+animation but um I needed to just zoom
+in on everything and you can do this
+
+ align:start position:0%
+in on everything and you can do this
+ 
+
+ align:start position:0%
+in on everything and you can do this
+with a thing called a null
+
+ align:start position:0%
+with a thing called a null
+ 
+
+ align:start position:0%
+with a thing called a null
+object
+
+ align:start position:0%
+object
+ 
+
+ align:start position:0%
+object
+um see if I remember how to do this okay
+
+ align:start position:0%
+um see if I remember how to do this okay
+ 
+
+ align:start position:0%
+um see if I remember how to do this okay
+layer um new and then a null object and
+
+ align:start position:0%
+layer um new and then a null object and
+ 
+
+ align:start position:0%
+layer um new and then a null object and
+so it'll appear in here as just null one
+
+ align:start position:0%
+so it'll appear in here as just null one
+ 
+
+ align:start position:0%
+so it'll appear in here as just null one
+and basically it's a way to group
+
+ align:start position:0%
+and basically it's a way to group
+ 
+
+ align:start position:0%
+and basically it's a way to group
+multiple animations at the same time
+
+ align:start position:0%
+multiple animations at the same time
+ 
+
+ align:start position:0%
+multiple animations at the same time
+um you can just leave it named n one I
+
+ align:start position:0%
+um you can just leave it named n one I
+ 
+
+ align:start position:0%
+um you can just leave it named n one I
+guess but so let's say I want the spiral
+
+ align:start position:0%
+guess but so let's say I want the spiral
+ 
+
+ align:start position:0%
+guess but so let's say I want the spiral
+and the rectangle to both be smaller
+
+ align:start position:0%
+and the rectangle to both be smaller
+ 
+
+ align:start position:0%
+and the rectangle to both be smaller
+because they're both way too big um so
+
+ align:start position:0%
+because they're both way too big um so
+ 
+
+ align:start position:0%
+because they're both way too big um so
+then you can set these
+
+ align:start position:0%
+then you can set these
+ 
+
+ align:start position:0%
+then you can set these
+layers as um you can set the null object
+
+ align:start position:0%
+layers as um you can set the null object
+ 
+
+ align:start position:0%
+layers as um you can set the null object
+as the parent of these layers this is
+
+ align:start position:0%
+as the parent of these layers this is
+ 
+
+ align:start position:0%
+as the parent of these layers this is
+say parent and you can have a drop down
+
+ align:start position:0%
+say parent and you can have a drop down
+ 
+
+ align:start position:0%
+say parent and you can have a drop down
+menu and so you can set both these
+
+ align:start position:0%
+menu and so you can set both these
+ 
+
+ align:start position:0%
+menu and so you can set both these
+layers to have their parent as null one
+
+ align:start position:0%
+layers to have their parent as null one
+ 
+
+ align:start position:0%
+layers to have their parent as null one
+and then you can animate null one as
+
+ align:start position:0%
+and then you can animate null one as
+ 
+
+ align:start position:0%
+and then you can animate null one as
+though it were an independent object so
+
+ align:start position:0%
+though it were an independent object so
+ 
+
+ align:start position:0%
+though it were an independent object so
+let's
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+say I just want the scale of everything
+
+ align:start position:0%
+say I just want the scale of everything
+ 
+
+ align:start position:0%
+say I just want the scale of everything
+to go down so because those are both
+
+ align:start position:0%
+to go down so because those are both
+ 
+
+ align:start position:0%
+to go down so because those are both
+grouped under under the null layer then
+
+ align:start position:0%
+grouped under under the null layer then
+ 
+
+ align:start position:0%
+grouped under under the null layer then
+the scale goes down or or you can
+
+ align:start position:0%
+the scale goes down or or you can
+ 
+
+ align:start position:0%
+the scale goes down or or you can
+animate it independently so let's say I
+
+ align:start position:0%
+animate it independently so let's say I
+ 
+
+ align:start position:0%
+animate it independently so let's say I
+want the scale at 100% but as the
+
+ align:start position:0%
+want the scale at 100% but as the
+ 
+
+ align:start position:0%
+want the scale at 100% but as the
+rectangle grows I want everything to
+
+ align:start position:0%
+rectangle grows I want everything to
+ 
+
+ align:start position:0%
+rectangle grows I want everything to
+shrink because it got too big and so
+
+ align:start position:0%
+shrink because it got too big and so
+ 
+
+ align:start position:0%
+shrink because it got too big and so
+then you can turn the scale down of
+
+ align:start position:0%
+then you can turn the scale down of
+ 
+
+ align:start position:0%
+then you can turn the scale down of
+everything so when I run the animation
+
+ align:start position:0%
+everything so when I run the animation
+ 
+
+ align:start position:0%
+everything so when I run the animation
+the rectangle's going to grow the
+
+ align:start position:0%
+the rectangle's going to grow the
+ 
+
+ align:start position:0%
+the rectangle's going to grow the
+spirals are going to rotate but then
+
+ align:start position:0%
+spirals are going to rotate but then
+ 
+
+ align:start position:0%
+spirals are going to rotate but then
+everything because it's all grouped
+
+ align:start position:0%
+everything because it's all grouped
+ 
+
+ align:start position:0%
+everything because it's all grouped
+under the null layer is going to
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+shrink um so I guess those are the
+
+ align:start position:0%
+shrink um so I guess those are the
+ 
+
+ align:start position:0%
+shrink um so I guess those are the
+basics of it um once you have your After
+
+ align:start position:0%
+basics of it um once you have your After
+ 
+
+ align:start position:0%
+basics of it um once you have your After
+Effects file um you can I would save it
+
+ align:start position:0%
+Effects file um you can I would save it
+ 
+
+ align:start position:0%
+Effects file um you can I would save it
+as something just so you don't lose
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+anything
+
+ align:start position:0%
+anything
+ 
+
+ align:start position:0%
+anything
+um and then you can do one of two things
+
+ align:start position:0%
+um and then you can do one of two things
+ 
+
+ align:start position:0%
+um and then you can do one of two things
+um so if you want to um edit in
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Premiere you can
+
+ align:start position:0%
+Premiere you can
+ 
+
+ align:start position:0%
+Premiere you can
+start um Adobe products are really nice
+
+ align:start position:0%
+start um Adobe products are really nice
+ 
+
+ align:start position:0%
+start um Adobe products are really nice
+where where they auto update to each
+
+ align:start position:0%
+where where they auto update to each
+ 
+
+ align:start position:0%
+where where they auto update to each
+other so if you change the Illustrator
+
+ align:start position:0%
+other so if you change the Illustrator
+ 
+
+ align:start position:0%
+other so if you change the Illustrator
+files that um make up the composition
+
+ align:start position:0%
+files that um make up the composition
+ 
+
+ align:start position:0%
+files that um make up the composition
+and after effects then your After
+
+ align:start position:0%
+and after effects then your After
+ 
+
+ align:start position:0%
+and after effects then your After
+Effects will change to reflect those
+
+ align:start position:0%
+Effects will change to reflect those
+ 
+
+ align:start position:0%
+Effects will change to reflect those
+changes so like if you messed up drawing
+
+ align:start position:0%
+changes so like if you messed up drawing
+ 
+
+ align:start position:0%
+changes so like if you messed up drawing
+something or you want a shape to look a
+
+ align:start position:0%
+something or you want a shape to look a
+ 
+
+ align:start position:0%
+something or you want a shape to look a
+little bit different um you can up if
+
+ align:start position:0%
+little bit different um you can up if
+ 
+
+ align:start position:0%
+little bit different um you can up if
+you update the illustrator file your
+
+ align:start position:0%
+you update the illustrator file your
+ 
+
+ align:start position:0%
+you update the illustrator file your
+After Effects project will also update
+
+ align:start position:0%
+After Effects project will also update
+ 
+
+ align:start position:0%
+After Effects project will also update
+same thing with your After Effects
+
+ align:start position:0%
+same thing with your After Effects
+ 
+
+ align:start position:0%
+same thing with your After Effects
+project and premiere
+
+ align:start position:0%
+project and premiere
+ 
+
+ align:start position:0%
+project and premiere
+um so if I have a premier project I can
+
+ align:start position:0%
+um so if I have a premier project I can
+ 
+
+ align:start position:0%
+um so if I have a premier project I can
+just drag oh crap do this
+
+ align:start position:0%
+just drag oh crap do this
+ 
+
+ align:start position:0%
+just drag oh crap do this
+backwards you can drag your After
+
+ align:start position:0%
+backwards you can drag your After
+ 
+
+ align:start position:0%
+backwards you can drag your After
+Effects composition into Premiere just
+
+ align:start position:0%
+Effects composition into Premiere just
+ 
+
+ align:start position:0%
+Effects composition into Premiere just
+to import media and then I have my test
+
+ align:start position:0%
+to import media and then I have my test
+ 
+
+ align:start position:0%
+to import media and then I have my test
+animation and I can drop it here to
+
+ align:start position:0%
+animation and I can drop it here to
+ 
+
+ align:start position:0%
+animation and I can drop it here to
+create a sequence um and so right now
+
+ align:start position:0%
+create a sequence um and so right now
+ 
+
+ align:start position:0%
+create a sequence um and so right now
+because it's transparent um I can't see
+
+ align:start position:0%
+because it's transparent um I can't see
+ 
+
+ align:start position:0%
+because it's transparent um I can't see
+anything but if I were
+
+ align:start position:0%
+anything but if I were
+ 
+
+ align:start position:0%
+anything but if I were
+to add add a color
+
+ align:start position:0%
+to add add a color
+ 
+
+ align:start position:0%
+to add add a color
+match
+
+ align:start position:0%
+match
+ 
+
+ align:start position:0%
+match
+in light blue it's going to be really
+
+ align:start position:0%
+in light blue it's going to be really
+ 
+
+ align:start position:0%
+in light blue it's going to be really
+garish and add it on the video layer
+
+ align:start position:0%
+garish and add it on the video layer
+ 
+
+ align:start position:0%
+garish and add it on the video layer
+below the animation then it'll appear so
+
+ align:start position:0%
+below the animation then it'll appear so
+ 
+
+ align:start position:0%
+below the animation then it'll appear so
+like the animation itself is
+
+ align:start position:0%
+like the animation itself is
+ 
+
+ align:start position:0%
+like the animation itself is
+transparent if you don't want to edit um
+
+ align:start position:0%
+transparent if you don't want to edit um
+ 
+
+ align:start position:0%
+transparent if you don't want to edit um
+and so now if I make changes in After
+
+ align:start position:0%
+and so now if I make changes in After
+ 
+
+ align:start position:0%
+and so now if I make changes in After
+Effects it'll automatically update those
+
+ align:start position:0%
+Effects it'll automatically update those
+ 
+
+ align:start position:0%
+Effects it'll automatically update those
+changes in Premiere which I find really
+
+ align:start position:0%
+changes in Premiere which I find really
+ 
+
+ align:start position:0%
+changes in Premiere which I find really
+handy as I'm video editing and switching
+
+ align:start position:0%
+handy as I'm video editing and switching
+ 
+
+ align:start position:0%
+handy as I'm video editing and switching
+back and forth if you don't want to edit
+
+ align:start position:0%
+back and forth if you don't want to edit
+ 
+
+ align:start position:0%
+back and forth if you don't want to edit
+in Premiere that is totally
+
+ align:start position:0%
+in Premiere that is totally
+ 
+
+ align:start position:0%
+in Premiere that is totally
+fine um and you just need to export your
+
+ align:start position:0%
+fine um and you just need to export your
+ 
+
+ align:start position:0%
+fine um and you just need to export your
+composition um I was just playing around
+
+ align:start position:0%
+composition um I was just playing around
+ 
+
+ align:start position:0%
+composition um I was just playing around
+with this earlier usually I don't export
+
+ align:start position:0%
+with this earlier usually I don't export
+ 
+
+ align:start position:0%
+with this earlier usually I don't export
+so I don't necessarily have the ideal
+
+ align:start position:0%
+so I don't necessarily have the ideal
+ 
+
+ align:start position:0%
+so I don't necessarily have the ideal
+settings for it um but we can play
+
+ align:start position:0%
+settings for it um but we can play
+ 
+
+ align:start position:0%
+settings for it um but we can play
+around and see what works so file export
+
+ align:start position:0%
+around and see what works so file export
+ 
+
+ align:start position:0%
+around and see what works so file export
+to Adobe Media
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+encoder um and then it adds it
+
+ align:start position:0%
+encoder um and then it adds it
+ 
+
+ align:start position:0%
+encoder um and then it adds it
+automatically to the CU and you can
+
+ align:start position:0%
+automatically to the CU and you can
+ 
+
+ align:start position:0%
+automatically to the CU and you can
+choose um preset export settings over
+
+ align:start position:0%
+choose um preset export settings over
+ 
+
+ align:start position:0%
+choose um preset export settings over
+here um I created a preset for the edex
+
+ align:start position:0%
+here um I created a preset for the edex
+ 
+
+ align:start position:0%
+here um I created a preset for the edex
+videos that I'm working on and so I
+
+ align:start position:0%
+videos that I'm working on and so I
+ 
+
+ align:start position:0%
+videos that I'm working on and so I
+usually just select that um and then
+
+ align:start position:0%
+usually just select that um and then
+ 
+
+ align:start position:0%
+usually just select that um and then
+once
+
+ align:start position:0%
+once
+ 
+
+ align:start position:0%
+once
+you do all that then you can just push
+
+ align:start position:0%
+you do all that then you can just push
+ 
+
+ align:start position:0%
+you do all that then you can just push
+play um and then the media encoder does
+
+ align:start position:0%
+play um and then the media encoder does
+ 
+
+ align:start position:0%
+play um and then the media encoder does
+its thing I don't know exactly what it
+
+ align:start position:0%
+its thing I don't know exactly what it
+ 
+
+ align:start position:0%
+its thing I don't know exactly what it
+does I think it's like a combination of
+
+ align:start position:0%
+does I think it's like a combination of
+ 
+
+ align:start position:0%
+does I think it's like a combination of
+rendering and just making sure
+
+ align:start position:0%
+rendering and just making sure
+ 
+
+ align:start position:0%
+rendering and just making sure
+I don't know changing the file format
+
+ align:start position:0%
+I don't know changing the file format
+ 
+
+ align:start position:0%
+I don't know changing the file format
+from
+
+ align:start position:0%
+from
+ 
+
+ align:start position:0%
+from
+a uh After Effects project to in this
+
+ align:start position:0%
+a uh After Effects project to in this
+ 
+
+ align:start position:0%
+a uh After Effects project to in this
+case an mp4 file so for a lot of you
+
+ align:start position:0%
+case an mp4 file so for a lot of you
+ 
+
+ align:start position:0%
+case an mp4 file so for a lot of you
+guys I'm imagining you want to do
+
+ align:start position:0%
+guys I'm imagining you want to do
+ 
+
+ align:start position:0%
+guys I'm imagining you want to do
+animation overlay right so you can't do
+
+ align:start position:0%
+animation overlay right so you can't do
+ 
+
+ align:start position:0%
+animation overlay right so you can't do
+that in stuff like iMovie so what you
+
+ align:start position:0%
+that in stuff like iMovie so what you
+ 
+
+ align:start position:0%
+that in stuff like iMovie so what you
+will have to do which is like a super
+
+ align:start position:0%
+will have to do which is like a super
+ 
+
+ align:start position:0%
+will have to do which is like a super
+janky work EG is you create the
+
+ align:start position:0%
+janky work EG is you create the
+ 
+
+ align:start position:0%
+janky work EG is you create the
+animation and after effects you go in
+
+ align:start position:0%
+animation and after effects you go in
+ 
+
+ align:start position:0%
+animation and after effects you go in
+Premiere and that's where you overlay it
+
+ align:start position:0%
+Premiere and that's where you overlay it
+ 
+
+ align:start position:0%
+Premiere and that's where you overlay it
+on top of your liveaction footage and
+
+ align:start position:0%
+on top of your liveaction footage and
+ 
+
+ align:start position:0%
+on top of your liveaction footage and
+then you export that little chunk into
+
+ align:start position:0%
+then you export that little chunk into
+ 
+
+ align:start position:0%
+then you export that little chunk into
+your movie Project does that make sense
+
+ align:start position:0%
+your movie Project does that make sense
+ 
+
+ align:start position:0%
+your movie Project does that make sense
+to you guys so would you mind showing
+
+ align:start position:0%
+to you guys so would you mind showing
+ 
+
+ align:start position:0%
+to you guys so would you mind showing
+real quick how to do it in Premiere
+
+ align:start position:0%
+real quick how to do it in Premiere
+ 
+
+ align:start position:0%
+real quick how to do it in Premiere
+where you overlay or you overlay an
+
+ align:start position:0%
+where you overlay or you overlay an
+ 
+
+ align:start position:0%
+where you overlay or you overlay an
+animation on top of your live action
+
+ align:start position:0%
+animation on top of your live action
+ 
+
+ align:start position:0%
+animation on top of your live action
+footage
+
+ align:start position:0%
+footage
+ 
+
+ align:start position:0%
+footage
+sure
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um let's so it's basically just doing
+
+ align:start position:0%
+um let's so it's basically just doing
+ 
+
+ align:start position:0%
+um let's so it's basically just doing
+what I was doing besides um and just
+
+ align:start position:0%
+what I was doing besides um and just
+ 
+
+ align:start position:0%
+what I was doing besides um and just
+using something besides the color mat I
+
+ align:start position:0%
+using something besides the color mat I
+ 
+
+ align:start position:0%
+using something besides the color mat I
+will see if I have any movies on my
+
+ align:start position:0%
+will see if I have any movies on my
+ 
+
+ align:start position:0%
+will see if I have any movies on my
+computer I don't know if I do so if you
+
+ align:start position:0%
+computer I don't know if I do so if you
+ 
+
+ align:start position:0%
+computer I don't know if I do so if you
+are holding your hands out like this how
+
+ align:start position:0%
+are holding your hands out like this how
+ 
+
+ align:start position:0%
+are holding your hands out like this how
+do you um what's the best way to time
+
+ align:start position:0%
+do you um what's the best way to time
+ 
+
+ align:start position:0%
+do you um what's the best way to time
+and place the
+
+ align:start position:0%
+and place the
+ 
+
+ align:start position:0%
+and place the
+animations basically have to draw them
+
+ align:start position:0%
+animations basically have to draw them
+ 
+
+ align:start position:0%
+animations basically have to draw them
+without seeing a background in After
+
+ align:start position:0%
+without seeing a background in After
+ 
+
+ align:start position:0%
+without seeing a background in After
+Effects
+
+ align:start position:0%
+Effects
+ 
+
+ align:start position:0%
+Effects
+right yeah
+
+ align:start position:0%
+right yeah
+ 
+
+ align:start position:0%
+right yeah
+um so the
+
+ align:start position:0%
+um so the
+ 
+
+ align:start position:0%
+um so the
+way let's see okay I have a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+video um
+
+ align:start position:0%
+video um
+ 
+
+ align:start position:0%
+video um
+okay so the way I
+
+ align:start position:0%
+okay so the way I
+ 
+
+ align:start position:0%
+okay so the way I
+would animate an After Effects is my
+
+ align:start position:0%
+would animate an After Effects is my
+ 
+
+ align:start position:0%
+would animate an After Effects is my
+window still open okay
+
+ align:start position:0%
+window still open okay
+ 
+
+ align:start position:0%
+window still open okay
+cool is to use the time codes so
+
+ align:start position:0%
+cool is to use the time codes so
+ 
+
+ align:start position:0%
+cool is to use the time codes so
+Premiere has a Time code and it's right
+
+ align:start position:0%
+Premiere has a Time code and it's right
+ 
+
+ align:start position:0%
+Premiere has a Time code and it's right
+here and it um matches up with I'm turn
+
+ align:start position:0%
+here and it um matches up with I'm turn
+ 
+
+ align:start position:0%
+here and it um matches up with I'm turn
+off my volume
+
+ align:start position:0%
+off my volume
+ 
+
+ align:start position:0%
+off my volume
+where um the movie
+
+ align:start position:0%
+where um the movie
+ 
+
+ align:start position:0%
+where um the movie
+is so for example
+
+ align:start position:0%
+is so for example
+ 
+
+ align:start position:0%
+is so for example
+if drag this
+
+ align:start position:0%
+if drag this
+ 
+
+ align:start position:0%
+if drag this
+down so right now like the animation is
+
+ align:start position:0%
+down so right now like the animation is
+ 
+
+ align:start position:0%
+down so right now like the animation is
+overlaid for my movie and the formatting
+
+ align:start position:0%
+overlaid for my movie and the formatting
+ 
+
+ align:start position:0%
+overlaid for my movie and the formatting
+is weird cuz I didn't do the movie
+
+ align:start position:0%
+is weird cuz I didn't do the movie
+ 
+
+ align:start position:0%
+is weird cuz I didn't do the movie
+first let's
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+see okay um what I would do is let's say
+
+ align:start position:0%
+see okay um what I would do is let's say
+ 
+
+ align:start position:0%
+see okay um what I would do is let's say
+for
+
+ align:start position:0%
+for
+ 
+
+ align:start position:0%
+for
+example I wanted at four uh 5 Seconds
+
+ align:start position:0%
+example I wanted at four uh 5 Seconds
+ 
+
+ align:start position:0%
+example I wanted at four uh 5 Seconds
+something to happen like something to
+
+ align:start position:0%
+something to happen like something to
+ 
+
+ align:start position:0%
+something to happen like something to
+pop up above my hand then I would take
+
+ align:start position:0%
+pop up above my hand then I would take
+ 
+
+ align:start position:0%
+pop up above my hand then I would take
+note of the time code or whenever you
+
+ align:start position:0%
+note of the time code or whenever you
+ 
+
+ align:start position:0%
+note of the time code or whenever you
+raise your hand in the video so let's
+
+ align:start position:0%
+raise your hand in the video so let's
+ 
+
+ align:start position:0%
+raise your hand in the video so let's
+say it was at 11 seconds um
+
+ align:start position:0%
+say it was at 11 seconds um
+ 
+
+ align:start position:0%
+say it was at 11 seconds um
+and 24
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+frames um
+
+ align:start position:0%
+frames um
+ 
+
+ align:start position:0%
+frames um
+then you go back
+
+ align:start position:0%
+then you go back
+ 
+
+ align:start position:0%
+then you go back
+into Adobe um After Effects and you can
+
+ align:start position:0%
+into Adobe um After Effects and you can
+ 
+
+ align:start position:0%
+into Adobe um After Effects and you can
+scroll over to 11 frames and make sure
+
+ align:start position:0%
+scroll over to 11 frames and make sure
+ 
+
+ align:start position:0%
+scroll over to 11 frames and make sure
+the time code here is listed here um and
+
+ align:start position:0%
+the time code here is listed here um and
+ 
+
+ align:start position:0%
+the time code here is listed here um and
+so you just switch back and forth and
+
+ align:start position:0%
+so you just switch back and forth and
+ 
+
+ align:start position:0%
+so you just switch back and forth and
+adjust the time code of your animations
+
+ align:start position:0%
+adjust the time code of your animations
+ 
+
+ align:start position:0%
+adjust the time code of your animations
+to the time code where you want it to
+
+ align:start position:0%
+to the time code where you want it to
+ 
+
+ align:start position:0%
+to the time code where you want it to
+appear in the
+
+ align:start position:0%
+appear in the
+ 
+
+ align:start position:0%
+appear in the
+video
+
+ align:start position:0%
+video
+ 
+
+ align:start position:0%
+video
+um and you can drag key frames to adjust
+
+ align:start position:0%
+um and you can drag key frames to adjust
+ 
+
+ align:start position:0%
+um and you can drag key frames to adjust
+that so like if I say well the rectangle
+
+ align:start position:0%
+that so like if I say well the rectangle
+ 
+
+ align:start position:0%
+that so like if I say well the rectangle
+move too fast in this video um I
+
+ align:start position:0%
+move too fast in this video um I
+ 
+
+ align:start position:0%
+move too fast in this video um I
+actually want the animation to end at
+
+ align:start position:0%
+actually want the animation to end at
+ 
+
+ align:start position:0%
+actually want the animation to end at
+329 instead of 2 seconds I can drag my
+
+ align:start position:0%
+329 instead of 2 seconds I can drag my
+ 
+
+ align:start position:0%
+329 instead of 2 seconds I can drag my
+cursor to
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+3 29 and then just drag the key frame
+
+ align:start position:0%
+3 29 and then just drag the key frame
+ 
+
+ align:start position:0%
+3 29 and then just drag the key frame
+frame to match it that's usually how I
+
+ align:start position:0%
+frame to match it that's usually how I
+ 
+
+ align:start position:0%
+frame to match it that's usually how I
+do it just because it's a lot easier to
+
+ align:start position:0%
+do it just because it's a lot easier to
+ 
+
+ align:start position:0%
+do it just because it's a lot easier to
+visualize um and then it will
+
+ align:start position:0%
+visualize um and then it will
+ 
+
+ align:start position:0%
+visualize um and then it will
+automatically update in here and the
+
+ align:start position:0%
+automatically update in here and the
+ 
+
+ align:start position:0%
+automatically update in here and the
+animation just got a lot
+
+ align:start position:0%
+animation just got a lot
+ 
+
+ align:start position:0%
+animation just got a lot
+longer and so now when I push play
+
+ align:start position:0%
+longer and so now when I push play
+ 
+
+ align:start position:0%
+longer and so now when I push play
+instead of taking two seconds it's still
+
+ align:start position:0%
+instead of taking two seconds it's still
+ 
+
+ align:start position:0%
+instead of taking two seconds it's still
+going until
+
+ align:start position:0%
+going until
+ 
+
+ align:start position:0%
+going until
+3:29
+
+ align:start position:0%
+3:29
+ 
+
+ align:start position:0%
+3:29
+um yeah it's a lot of playing around I
+
+ align:start position:0%
+um yeah it's a lot of playing around I
+ 
+
+ align:start position:0%
+um yeah it's a lot of playing around I
+don't have uh like a really really
+
+ align:start position:0%
+don't have uh like a really really
+ 
+
+ align:start position:0%
+don't have uh like a really really
+concrete method of doing it and I'm
+
+ align:start position:0%
+concrete method of doing it and I'm
+ 
+
+ align:start position:0%
+concrete method of doing it and I'm
+still learning
+
+ align:start position:0%
+still learning
+ 
+
+ align:start position:0%
+still learning
+animation too so
+
+ align:start position:0%
+animation too so
+ 
+
+ align:start position:0%
+animation too so
+um yeah I don't have the perfect answer
+
+ align:start position:0%
+um yeah I don't have the perfect answer
+ 
+
+ align:start position:0%
+um yeah I don't have the perfect answer
+but usually it's a lot of switching
+
+ align:start position:0%
+but usually it's a lot of switching
+ 
+
+ align:start position:0%
+but usually it's a lot of switching
+between Windows which is why when you
+
+ align:start position:0%
+between Windows which is why when you
+ 
+
+ align:start position:0%
+between Windows which is why when you
+have two monitors it's really nice
+
+ align:start position:0%
+have two monitors it's really nice
+ 
+
+ align:start position:0%
+have two monitors it's really nice
+um but a lot of just like checking the
+
+ align:start position:0%
+um but a lot of just like checking the
+ 
+
+ align:start position:0%
+um but a lot of just like checking the
+time code exactly and making little
+
+ align:start position:0%
+time code exactly and making little
+ 
+
+ align:start position:0%
+time code exactly and making little
+adjustments at a time first you do it's
+
+ align:start position:0%
+adjustments at a time first you do it's
+ 
+
+ align:start position:0%
+adjustments at a time first you do it's
+kind of like how you edit a movie you
+
+ align:start position:0%
+kind of like how you edit a movie you
+ 
+
+ align:start position:0%
+kind of like how you edit a movie you
+start with a rough cut you start with a
+
+ align:start position:0%
+start with a rough cut you start with a
+ 
+
+ align:start position:0%
+start with a rough cut you start with a
+rough animation of what you want and
+
+ align:start position:0%
+rough animation of what you want and
+ 
+
+ align:start position:0%
+rough animation of what you want and
+then you can adjust the key frames to
+
+ align:start position:0%
+then you can adjust the key frames to
+ 
+
+ align:start position:0%
+then you can adjust the key frames to
+time it to the video that you're working
+
+ align:start position:0%
+time it to the video that you're working
+ 
+
+ align:start position:0%
+time it to the video that you're working
+with so I think the thing that'll be
+
+ align:start position:0%
+with so I think the thing that'll be
+ 
+
+ align:start position:0%
+with so I think the thing that'll be
+most productive for you guys is if you
+
+ align:start position:0%
+most productive for you guys is if you
+ 
+
+ align:start position:0%
+most productive for you guys is if you
+attempt to do your own animation and
+
+ align:start position:0%
+attempt to do your own animation and
+ 
+
+ align:start position:0%
+attempt to do your own animation and
+then if you run into problems email St
+
+ align:start position:0%
+then if you run into problems email St
+ 
+
+ align:start position:0%
+then if you run into problems email St
+um or you can email me we'll be around
+
+ align:start position:0%
+um or you can email me we'll be around
+ 
+
+ align:start position:0%
+um or you can email me we'll be around
+tomorrow if people are working and I'll
+
+ align:start position:0%
+tomorrow if people are working and I'll
+ 
+
+ align:start position:0%
+tomorrow if people are working and I'll
+be on campus tomorrow actually if you
+
+ align:start position:0%
+be on campus tomorrow actually if you
+ 
+
+ align:start position:0%
+be on campus tomorrow actually if you
+need help um but I think the most
+
+ align:start position:0%
+need help um but I think the most
+ 
+
+ align:start position:0%
+need help um but I think the most
+efficient route is if you try a little
+
+ align:start position:0%
+efficient route is if you try a little
+ 
+
+ align:start position:0%
+efficient route is if you try a little
+bit on your own first and then when
+
+ align:start position:0%
+bit on your own first and then when
+ 
+
+ align:start position:0%
+bit on your own first and then when
+specific questions pop up you
+
+ align:start position:0%
+specific questions pop up you
+ 
+
+ align:start position:0%
+specific questions pop up you
+can yeah and if you have anything
+
+ align:start position:0%
+can yeah and if you have anything
+ 
+
+ align:start position:0%
+can yeah and if you have anything
+specific in mind that you don't think
+
+ align:start position:0%
+specific in mind that you don't think
+ 
+
+ align:start position:0%
+specific in mind that you don't think
+you can accomplish with what I've taught
+
+ align:start position:0%
+you can accomplish with what I've taught
+ 
+
+ align:start position:0%
+you can accomplish with what I've taught
+you so far then you can definitely come
+
+ align:start position:0%
+you so far then you can definitely come
+ 
+
+ align:start position:0%
+you so far then you can definitely come
+talk to me or I can come over and talk
+
+ align:start position:0%
+talk to me or I can come over and talk
+ 
+
+ align:start position:0%
+talk to me or I can come over and talk
+to you and we can talk through what your
+
+ align:start position:0%
+to you and we can talk through what your
+ 
+
+ align:start position:0%
+to you and we can talk through what your
+picture was for animating something and
+
+ align:start position:0%
+picture was for animating something and
+ 
+
+ align:start position:0%
+picture was for animating something and
+how you can best do that either using
+
+ align:start position:0%
+how you can best do that either using
+ 
+
+ align:start position:0%
+how you can best do that either using
+the tools that I just taught you or
+
+ align:start position:0%
+the tools that I just taught you or
+ 
+
+ align:start position:0%
+the tools that I just taught you or
+using other things like I know how to
+
+ align:start position:0%
+using other things like I know how to
+ 
+
+ align:start position:0%
+using other things like I know how to
+mimic handwriting to write out a word
+
+ align:start position:0%
+mimic handwriting to write out a word
+ 
+
+ align:start position:0%
+mimic handwriting to write out a word
+and I don't know if that's necessary for
+
+ align:start position:0%
+and I don't know if that's necessary for
+ 
+
+ align:start position:0%
+and I don't know if that's necessary for
+any of you but like that's a thing that
+
+ align:start position:0%
+any of you but like that's a thing that
+ 
+
+ align:start position:0%
+any of you but like that's a thing that
+you can do in After Effects it's just a
+
+ align:start position:0%
+you can do in After Effects it's just a
+ 
+
+ align:start position:0%
+you can do in After Effects it's just a
+little more complicated than what I've
+
+ align:start position:0%
+little more complicated than what I've
+ 
+
+ align:start position:0%
+little more complicated than what I've
+shown you so far
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+I have two questions one of them is um
+
+ align:start position:0%
+I have two questions one of them is um
+ 
+
+ align:start position:0%
+I have two questions one of them is um
+I've used a premium Pro before but then
+
+ align:start position:0%
+I've used a premium Pro before but then
+ 
+
+ align:start position:0%
+I've used a premium Pro before but then
+the sizing because I'm not sure when I
+
+ align:start position:0%
+the sizing because I'm not sure when I
+ 
+
+ align:start position:0%
+the sizing because I'm not sure when I
+do in PR Pro it looks like the sizing is
+
+ align:start position:0%
+do in PR Pro it looks like the sizing is
+ 
+
+ align:start position:0%
+do in PR Pro it looks like the sizing is
+correct however when I exported it to
+
+ align:start position:0%
+correct however when I exported it to
+ 
+
+ align:start position:0%
+correct however when I exported it to
+external video the sizing was wrong so
+
+ align:start position:0%
+external video the sizing was wrong so
+ 
+
+ align:start position:0%
+external video the sizing was wrong so
+is that setting um for exporting from
+
+ align:start position:0%
+is that setting um for exporting from
+ 
+
+ align:start position:0%
+is that setting um for exporting from
+Premiere um let's see I mean like if I
+
+ align:start position:0%
+Premiere um let's see I mean like if I
+ 
+
+ align:start position:0%
+Premiere um let's see I mean like if I
+see if I see the screen like this yes I
+
+ align:start position:0%
+see if I see the screen like this yes I
+ 
+
+ align:start position:0%
+see if I see the screen like this yes I
+think that all this is is this
+
+ align:start position:0%
+think that all this is is this
+ 
+
+ align:start position:0%
+think that all this is is this
+everything that's in the screen that
+
+ align:start position:0%
+everything that's in the screen that
+ 
+
+ align:start position:0%
+everything that's in the screen that
+will be shown in the in the actual video
+
+ align:start position:0%
+will be shown in the in the actual video
+ 
+
+ align:start position:0%
+will be shown in the in the actual video
+yeah so right now because so what this
+
+ align:start position:0%
+yeah so right now because so what this
+ 
+
+ align:start position:0%
+yeah so right now because so what this
+is I recorded this movie on my camera on
+
+ align:start position:0%
+is I recorded this movie on my camera on
+ 
+
+ align:start position:0%
+is I recorded this movie on my camera on
+my computer which is lower quality than
+
+ align:start position:0%
+my computer which is lower quality than
+ 
+
+ align:start position:0%
+my computer which is lower quality than
+the camera than your camcorders which
+
+ align:start position:0%
+the camera than your camcorders which
+ 
+
+ align:start position:0%
+the camera than your camcorders which
+should record in 1920 by 1080 um so like
+
+ align:start position:0%
+should record in 1920 by 1080 um so like
+ 
+
+ align:start position:0%
+should record in 1920 by 1080 um so like
+right now this like this on this in the
+
+ align:start position:0%
+right now this like this on this in the
+ 
+
+ align:start position:0%
+right now this like this on this in the
+upper right hand corner is what's going
+
+ align:start position:0%
+upper right hand corner is what's going
+ 
+
+ align:start position:0%
+upper right hand corner is what's going
+to be exported so the if I exported it
+
+ align:start position:0%
+to be exported so the if I exported it
+ 
+
+ align:start position:0%
+to be exported so the if I exported it
+right now it would export with this
+
+ align:start position:0%
+right now it would export with this
+ 
+
+ align:start position:0%
+right now it would export with this
+weird black border
+
+ align:start position:0%
+weird black border
+ 
+
+ align:start position:0%
+weird black border
+because my video is smaller than this
+
+ align:start position:0%
+because my video is smaller than this
+ 
+
+ align:start position:0%
+because my video is smaller than this
+composition so it's preferable to expand
+
+ align:start position:0%
+composition so it's preferable to expand
+ 
+
+ align:start position:0%
+composition so it's preferable to expand
+the screen can we expand the video yeah
+
+ align:start position:0%
+the screen can we expand the video yeah
+ 
+
+ align:start position:0%
+the screen can we expand the video yeah
+you can you can individually so if I
+
+ align:start position:0%
+you can you can individually so if I
+ 
+
+ align:start position:0%
+you can you can individually so if I
+take out the you can double click and
+
+ align:start position:0%
+take out the you can double click and
+ 
+
+ align:start position:0%
+take out the you can double click and
+like this is how you digitally Zoom oh
+
+ align:start position:0%
+like this is how you digitally Zoom oh
+ 
+
+ align:start position:0%
+like this is how you digitally Zoom oh
+basically you can manipulate it just
+
+ align:start position:0%
+basically you can manipulate it just
+ 
+
+ align:start position:0%
+basically you can manipulate it just
+like any other object and make it bigger
+
+ align:start position:0%
+like any other object and make it bigger
+ 
+
+ align:start position:0%
+like any other object and make it bigger
+so it fills the
+
+ align:start position:0%
+so it fills the
+ 
+
+ align:start position:0%
+so it fills the
+screen this will be in what do you mean
+
+ align:start position:0%
+screen this will be in what do you mean
+ 
+
+ align:start position:0%
+screen this will be in what do you mean
+this will be so this ex screen will be
+
+ align:start position:0%
+this will be so this ex screen will be
+ 
+
+ align:start position:0%
+this will be so this ex screen will be
+the one that
+
+ align:start position:0%
+the one that
+ 
+
+ align:start position:0%
+the one that
+yeah so whatever you see in this preview
+
+ align:start position:0%
+yeah so whatever you see in this preview
+ 
+
+ align:start position:0%
+yeah so whatever you see in this preview
+screen is what's going to come out when
+
+ align:start position:0%
+screen is what's going to come out when
+ 
+
+ align:start position:0%
+screen is what's going to come out when
+you export it um and then you can change
+
+ align:start position:0%
+you export it um and then you can change
+ 
+
+ align:start position:0%
+you export it um and then you can change
+export settings file export media um and
+
+ align:start position:0%
+export settings file export media um and
+ 
+
+ align:start position:0%
+export settings file export media um and
+you can like change the file type that
+
+ align:start position:0%
+you can like change the file type that
+ 
+
+ align:start position:0%
+you can like change the file type that
+you want it to be and the video format
+
+ align:start position:0%
+you want it to be and the video format
+ 
+
+ align:start position:0%
+you want it to be and the video format
+um I use the settings thatx needs to
+
+ align:start position:0%
+um I use the settings thatx needs to
+ 
+
+ align:start position:0%
+um I use the settings thatx needs to
+upload usually just because that's it
+
+ align:start position:0%
+upload usually just because that's it
+ 
+
+ align:start position:0%
+upload usually just because that's it
+works and it produces a high enough
+
+ align:start position:0%
+works and it produces a high enough
+ 
+
+ align:start position:0%
+works and it produces a high enough
+quality video um but if you know things
+
+ align:start position:0%
+quality video um but if you know things
+ 
+
+ align:start position:0%
+quality video um but if you know things
+about audio and video and things like
+
+ align:start position:0%
+about audio and video and things like
+ 
+
+ align:start position:0%
+about audio and video and things like
+that you can
+
+ align:start position:0%
+that you can
+ 
+
+ align:start position:0%
+that you can
+add like a a copyright encoded into the
+
+ align:start position:0%
+add like a a copyright encoded into the
+ 
+
+ align:start position:0%
+add like a a copyright encoded into the
+video itself if you really want to
+
+ align:start position:0%
+video itself if you really want to
+ 
+
+ align:start position:0%
+video itself if you really want to
+protect it and things like that but less
+
+ align:start position:0%
+protect it and things like that but less
+ 
+
+ align:start position:0%
+protect it and things like that but less
+necessary can I check the camera were
+
+ align:start position:0%
+necessary can I check the camera were
+ 
+
+ align:start position:0%
+necessary can I check the camera were
+given is how many
+
+ align:start position:0%
+given is how many
+ 
+
+ align:start position:0%
+given is how many
+frames I think it's 30 uh I'll double
+
+ align:start position:0%
+frames I think it's 30 uh I'll double
+ 
+
+ align:start position:0%
+frames I think it's 30 uh I'll double
+check
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+it if I want to get a let's say I have a
+
+ align:start position:0%
+it if I want to get a let's say I have a
+ 
+
+ align:start position:0%
+it if I want to get a let's say I have a
+video I took a video yep but at the
+
+ align:start position:0%
+video I took a video yep but at the
+ 
+
+ align:start position:0%
+video I took a video yep but at the
+moment I want to cut that frame and
+
+ align:start position:0%
+moment I want to cut that frame and
+ 
+
+ align:start position:0%
+moment I want to cut that frame and
+extend that frame to make it like a
+
+ align:start position:0%
+extend that frame to make it like a
+ 
+
+ align:start position:0%
+extend that frame to make it like a
+picture because I want to explain the
+
+ align:start position:0%
+picture because I want to explain the
+ 
+
+ align:start position:0%
+picture because I want to explain the
+concept yeah so how do I do that um so
+
+ align:start position:0%
+concept yeah so how do I do that um so
+ 
+
+ align:start position:0%
+concept yeah so how do I do that um so
+this is something I can I don't know how
+
+ align:start position:0%
+this is something I can I don't know how
+ 
+
+ align:start position:0%
+this is something I can I don't know how
+to do it in Final Cut I know how to do
+
+ align:start position:0%
+to do it in Final Cut I know how to do
+ 
+
+ align:start position:0%
+to do it in Final Cut I know how to do
+it in Premiere so hypothetically in
+
+ align:start position:0%
+it in Premiere so hypothetically in
+ 
+
+ align:start position:0%
+it in Premiere so hypothetically in
+Premiere that's a bad frame to pause
+
+ align:start position:0%
+Premiere that's a bad frame to pause
+ 
+
+ align:start position:0%
+Premiere that's a bad frame to pause
+let's say I want to pause this Frame um
+
+ align:start position:0%
+let's say I want to pause this Frame um
+ 
+
+ align:start position:0%
+let's say I want to pause this Frame um
+you can do like there's a button here it
+
+ align:start position:0%
+you can do like there's a button here it
+ 
+
+ align:start position:0%
+you can do like there's a button here it
+just says export frame um I click it and
+
+ align:start position:0%
+just says export frame um I click it and
+ 
+
+ align:start position:0%
+just says export frame um I click it and
+then it's uh what do I want it to be
+
+ align:start position:0%
+then it's uh what do I want it to be
+ 
+
+ align:start position:0%
+then it's uh what do I want it to be
+it's
+
+ align:start position:0%
+it's
+ 
+
+ align:start position:0%
+it's
+like still face um and it's an I just
+
+ align:start position:0%
+like still face um and it's an I just
+ 
+
+ align:start position:0%
+like still face um and it's an I just
+wanted a JPEG I guess um and then this
+
+ align:start position:0%
+wanted a JPEG I guess um and then this
+ 
+
+ align:start position:0%
+wanted a JPEG I guess um and then this
+box just means uh you import it into the
+
+ align:start position:0%
+box just means uh you import it into the
+ 
+
+ align:start position:0%
+box just means uh you import it into the
+project automatically so no matter where
+
+ align:start position:0%
+project automatically so no matter where
+ 
+
+ align:start position:0%
+project automatically so no matter where
+it saves it in this case it's saving it
+
+ align:start position:0%
+it saves it in this case it's saving it
+ 
+
+ align:start position:0%
+it saves it in this case it's saving it
+in my premere folder and click okay and
+
+ align:start position:0%
+in my premere folder and click okay and
+ 
+
+ align:start position:0%
+in my premere folder and click okay and
+then it automatically appears as an
+
+ align:start position:0%
+then it automatically appears as an
+ 
+
+ align:start position:0%
+then it automatically appears as an
+image in your Media Browser area um and
+
+ align:start position:0%
+image in your Media Browser area um and
+ 
+
+ align:start position:0%
+image in your Media Browser area um and
+so then if you want to extend this Frame
+
+ align:start position:0%
+so then if you want to extend this Frame
+ 
+
+ align:start position:0%
+so then if you want to extend this Frame
+what I would personally do is use the
+
+ align:start position:0%
+what I would personally do is use the
+ 
+
+ align:start position:0%
+what I would personally do is use the
+razor tool
+
+ align:start position:0%
+razor tool
+ 
+
+ align:start position:0%
+razor tool
+cut the clip into two use the selection
+
+ align:start position:0%
+cut the clip into two use the selection
+ 
+
+ align:start position:0%
+cut the clip into two use the selection
+tool and drag this over so I have some
+
+ align:start position:0%
+tool and drag this over so I have some
+ 
+
+ align:start position:0%
+tool and drag this over so I have some
+space to include it and then include the
+
+ align:start position:0%
+space to include it and then include the
+ 
+
+ align:start position:0%
+space to include it and then include the
+still
+
+ align:start position:0%
+still
+ 
+
+ align:start position:0%
+still
+image and then just seal that Gap back
+
+ align:start position:0%
+image and then just seal that Gap back
+ 
+
+ align:start position:0%
+image and then just seal that Gap back
+up so now instead of just seeing me
+
+ align:start position:0%
+up so now instead of just seeing me
+ 
+
+ align:start position:0%
+up so now instead of just seeing me
+talk I should have brought it closer but
+
+ align:start position:0%
+talk I should have brought it closer but
+ 
+
+ align:start position:0%
+talk I should have brought it closer but
+then I'll talk I'll talk I'll talk and
+
+ align:start position:0%
+then I'll talk I'll talk I'll talk and
+ 
+
+ align:start position:0%
+then I'll talk I'll talk I'll talk and
+then the still frame will
+
+ align:start position:0%
+then the still frame will
+ 
+
+ align:start position:0%
+then the still frame will
+happen for like however many seconds you
+
+ align:start position:0%
+happen for like however many seconds you
+ 
+
+ align:start position:0%
+happen for like however many seconds you
+set it and you can adjust the size and
+
+ align:start position:0%
+set it and you can adjust the size and
+ 
+
+ align:start position:0%
+set it and you can adjust the size and
+timing of that and then the video will
+
+ align:start position:0%
+timing of that and then the video will
+ 
+
+ align:start position:0%
+timing of that and then the video will
+resume when you're ready for
+
+ align:start position:0%
+resume when you're ready for
+ 
+
+ align:start position:0%
+resume when you're ready for
+to um I don't exactly know what the FR
+
+ align:start position:0%
+to um I don't exactly know what the FR
+ 
+
+ align:start position:0%
+to um I don't exactly know what the FR
+rate of the Vixie is it records both in
+
+ align:start position:0%
+rate of the Vixie is it records both in
+ 
+
+ align:start position:0%
+rate of the Vixie is it records both in
+24 and 30 but if you open the video up
+
+ align:start position:0%
+24 and 30 but if you open the video up
+ 
+
+ align:start position:0%
+24 and 30 but if you open the video up
+in Qui time and you do command I it
+
+ align:start position:0%
+in Qui time and you do command I it
+ 
+
+ align:start position:0%
+in Qui time and you do command I it
+should tell you what it was recorded
+
+ align:start position:0%
+should tell you what it was recorded
+ 
+
+ align:start position:0%
+should tell you what it was recorded
+in and I just found that out by Googling
+
+ align:start position:0%
+in and I just found that out by Googling
+ 
+
+ align:start position:0%
+in and I just found that out by Googling
+it so yeah underestimate
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the are there any other questions about
+
+ align:start position:0%
+the are there any other questions about
+ 
+
+ align:start position:0%
+the are there any other questions about
+animating or editing or
+
+ align:start position:0%
+animating or editing or
+ 
+
+ align:start position:0%
+animating or editing or
+adobe I mean we're just going to stick
+
+ align:start position:0%
+adobe I mean we're just going to stick
+ 
+
+ align:start position:0%
+adobe I mean we're just going to stick
+around for the rest of today so if you
+
+ align:start position:0%
+around for the rest of today so if you
+ 
+
+ align:start position:0%
+around for the rest of today so if you
+just want to hang out here and work or
+
+ align:start position:0%
+just want to hang out here and work or
+ 
+
+ align:start position:0%
+just want to hang out here and work or
+you want to go back to the classroom and
+
+ align:start position:0%
+you want to go back to the classroom and
+ 
+
+ align:start position:0%
+you want to go back to the classroom and
+work we'll be
+
+ align:start position:0%
+work we'll be
+ 
+
+ align:start position:0%
+work we'll be
+around mhm
\ No newline at end of file
diff --git a/jMPc6-bcnH8.txt b/jMPc6-bcnH8.txt
new file mode 100644
index 0000000000000000000000000000000000000000..f69db8f68712e1dd980a7c1b5debbacc8d987abb
--- /dev/null
+++ b/jMPc6-bcnH8.txt
@@ -0,0 +1,1371 @@
+align:start position:0%
+ 
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+i recommended the process of how to
+
+ align:start position:0%
+i recommended the process of how to
+ 
+
+ align:start position:0%
+i recommended the process of how to
+approach there's a i've
+
+ align:start position:0%
+approach there's a i've
+ 
+
+ align:start position:0%
+approach there's a i've
+as a
+
+ align:start position:0%
+as a
+ 
+
+ align:start position:0%
+as a
+the five steps or one way to think about
+
+ align:start position:0%
+the five steps or one way to think about
+ 
+
+ align:start position:0%
+the five steps or one way to think about
+you could have six or seven
+
+ align:start position:0%
+you could have six or seven
+ 
+
+ align:start position:0%
+you could have six or seven
+in the text i we wrote some time ago i
+
+ align:start position:0%
+in the text i we wrote some time ago i
+ 
+
+ align:start position:0%
+in the text i we wrote some time ago i
+we had seven put out because we went to
+
+ align:start position:0%
+we had seven put out because we went to
+ 
+
+ align:start position:0%
+we had seven put out because we went to
+a more complexity but um
+
+ align:start position:0%
+a more complexity but um
+ 
+
+ align:start position:0%
+a more complexity but um
+i'm now going to talk about these
+
+ align:start position:0%
+i'm now going to talk about these
+ 
+
+ align:start position:0%
+i'm now going to talk about these
+central five uh but it's mostly to cover
+
+ align:start position:0%
+central five uh but it's mostly to cover
+ 
+
+ align:start position:0%
+central five uh but it's mostly to cover
+the bases there's this five is not the
+
+ align:start position:0%
+the bases there's this five is not the
+ 
+
+ align:start position:0%
+the bases there's this five is not the
+magic
+
+ align:start position:0%
+magic
+ 
+
+ align:start position:0%
+magic
+number so the first one we need a
+
+ align:start position:0%
+number so the first one we need a
+ 
+
+ align:start position:0%
+number so the first one we need a
+valuation model
+
+ align:start position:0%
+valuation model
+ 
+
+ align:start position:0%
+valuation model
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+uh for those of you who are filling out
+
+ align:start position:0%
+uh for those of you who are filling out
+ 
+
+ align:start position:0%
+uh for those of you who are filling out
+your initial project form a number of
+
+ align:start position:0%
+your initial project form a number of
+ 
+
+ align:start position:0%
+your initial project form a number of
+you
+
+ align:start position:0%
+you
+ 
+
+ align:start position:0%
+you
+uh weren't quite understood that i
+
+ align:start position:0%
+uh weren't quite understood that i
+ 
+
+ align:start position:0%
+uh weren't quite understood that i
+what was involved when i asked about
+
+ align:start position:0%
+what was involved when i asked about
+ 
+
+ align:start position:0%
+what was involved when i asked about
+having a
+
+ align:start position:0%
+having a
+ 
+
+ align:start position:0%
+having a
+model of your system but you mean to
+
+ align:start position:0%
+model of your system but you mean to
+ 
+
+ align:start position:0%
+model of your system but you mean to
+have you need to have some way of saying
+
+ align:start position:0%
+have you need to have some way of saying
+ 
+
+ align:start position:0%
+have you need to have some way of saying
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+if i design the model or i set up my
+
+ align:start position:0%
+if i design the model or i set up my
+ 
+
+ align:start position:0%
+if i design the model or i set up my
+model in my system in a particular place
+
+ align:start position:0%
+model in my system in a particular place
+ 
+
+ align:start position:0%
+model in my system in a particular place
+which is not only the machinery and the
+
+ align:start position:0%
+which is not only the machinery and the
+ 
+
+ align:start position:0%
+which is not only the machinery and the
+production of a process but also my my
+
+ align:start position:0%
+production of a process but also my my
+ 
+
+ align:start position:0%
+production of a process but also my my
+employees my marketing my sales my
+
+ align:start position:0%
+employees my marketing my sales my
+ 
+
+ align:start position:0%
+employees my marketing my sales my
+productivity and so forth you need to
+
+ align:start position:0%
+productivity and so forth you need to
+ 
+
+ align:start position:0%
+productivity and so forth you need to
+have a way of
+
+ align:start position:0%
+have a way of
+ 
+
+ align:start position:0%
+have a way of
+transforming those assets and your use
+
+ align:start position:0%
+transforming those assets and your use
+ 
+
+ align:start position:0%
+transforming those assets and your use
+into some kind of valuation it can be an
+
+ align:start position:0%
+into some kind of valuation it can be an
+ 
+
+ align:start position:0%
+into some kind of valuation it can be an
+economic valuation as in this particular
+
+ align:start position:0%
+economic valuation as in this particular
+ 
+
+ align:start position:0%
+economic valuation as in this particular
+case or it can be a performance
+
+ align:start position:0%
+case or it can be a performance
+ 
+
+ align:start position:0%
+case or it can be a performance
+evaluation i'm
+
+ align:start position:0%
+evaluation i'm
+ 
+
+ align:start position:0%
+evaluation i'm
+running an emergency
+
+ align:start position:0%
+running an emergency
+ 
+
+ align:start position:0%
+running an emergency
+medical effort to say come combat ebola
+
+ align:start position:0%
+medical effort to say come combat ebola
+ 
+
+ align:start position:0%
+medical effort to say come combat ebola
+uh how well do how quickly and how well
+
+ align:start position:0%
+uh how well do how quickly and how well
+ 
+
+ align:start position:0%
+uh how well do how quickly and how well
+do i contain the disease so it may be
+
+ align:start position:0%
+do i contain the disease so it may be
+ 
+
+ align:start position:0%
+do i contain the disease so it may be
+performance based rather than money
+
+ align:start position:0%
+performance based rather than money
+ 
+
+ align:start position:0%
+performance based rather than money
+based
+
+ align:start position:0%
+based
+ 
+
+ align:start position:0%
+based
+and in this case as from the garage i
+
+ align:start position:0%
+and in this case as from the garage i
+ 
+
+ align:start position:0%
+and in this case as from the garage i
+have things about the demand the
+
+ align:start position:0%
+have things about the demand the
+ 
+
+ align:start position:0%
+have things about the demand the
+capacity the revenues costs and so forth
+
+ align:start position:0%
+capacity the revenues costs and so forth
+ 
+
+ align:start position:0%
+capacity the revenues costs and so forth
+and i have a present value and so forth
+
+ align:start position:0%
+and i have a present value and so forth
+ 
+
+ align:start position:0%
+and i have a present value and so forth
+so i need a model which says
+
+ align:start position:0%
+so i need a model which says
+ 
+
+ align:start position:0%
+so i need a model which says
+if
+
+ align:start position:0%
+if
+ 
+
+ align:start position:0%
+if
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+following happen and you've made these
+
+ align:start position:0%
+following happen and you've made these
+ 
+
+ align:start position:0%
+following happen and you've made these
+design decisions here's what the
+
+ align:start position:0%
+design decisions here's what the
+ 
+
+ align:start position:0%
+design decisions here's what the
+performance is going to be
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+secondly you need to think about
+
+ align:start position:0%
+secondly you need to think about
+ 
+
+ align:start position:0%
+secondly you need to think about
+which of the most important
+
+ align:start position:0%
+which of the most important
+ 
+
+ align:start position:0%
+which of the most important
+uncertainties
+
+ align:start position:0%
+uncertainties
+ 
+
+ align:start position:0%
+uncertainties
+as uh you could imagine and then those
+
+ align:start position:0%
+as uh you could imagine and then those
+ 
+
+ align:start position:0%
+as uh you could imagine and then those
+who filled out the initial project
+
+ align:start position:0%
+who filled out the initial project
+ 
+
+ align:start position:0%
+who filled out the initial project
+report were
+
+ align:start position:0%
+report were
+ 
+
+ align:start position:0%
+report were
+doing
+
+ align:start position:0%
+doing
+ 
+
+ align:start position:0%
+doing
+you can list them and there are lots and
+
+ align:start position:0%
+you can list them and there are lots and
+ 
+
+ align:start position:0%
+you can list them and there are lots and
+lots of uncertainties all kinds of
+
+ align:start position:0%
+lots of uncertainties all kinds of
+ 
+
+ align:start position:0%
+lots of uncertainties all kinds of
+things can happen
+
+ align:start position:0%
+things can happen
+ 
+
+ align:start position:0%
+things can happen
+the question is what should you really
+
+ align:start position:0%
+the question is what should you really
+ 
+
+ align:start position:0%
+the question is what should you really
+pay attention to
+
+ align:start position:0%
+pay attention to
+ 
+
+ align:start position:0%
+pay attention to
+so you need to think about
+
+ align:start position:0%
+so you need to think about
+ 
+
+ align:start position:0%
+so you need to think about
+which are the
+
+ align:start position:0%
+which are the
+ 
+
+ align:start position:0%
+which are the
+issues the uncertainties that you want
+
+ align:start position:0%
+issues the uncertainties that you want
+ 
+
+ align:start position:0%
+issues the uncertainties that you want
+to focus on not that they all don't
+
+ align:start position:0%
+to focus on not that they all don't
+ 
+
+ align:start position:0%
+to focus on not that they all don't
+exist but some of them are second order
+
+ align:start position:0%
+exist but some of them are second order
+ 
+
+ align:start position:0%
+exist but some of them are second order
+effect so which are the first order
+
+ align:start position:0%
+effect so which are the first order
+ 
+
+ align:start position:0%
+effect so which are the first order
+effects
+
+ align:start position:0%
+effects
+ 
+
+ align:start position:0%
+effects
+one of the ways to do that is to use a
+
+ align:start position:0%
+one of the ways to do that is to use a
+ 
+
+ align:start position:0%
+one of the ways to do that is to use a
+tornado diagram which i will uh
+
+ align:start position:0%
+tornado diagram which i will uh
+ 
+
+ align:start position:0%
+tornado diagram which i will uh
+illustrate here but i'll describe in
+
+ align:start position:0%
+illustrate here but i'll describe in
+ 
+
+ align:start position:0%
+illustrate here but i'll describe in
+more detail later on in the course but
+
+ align:start position:0%
+more detail later on in the course but
+ 
+
+ align:start position:0%
+more detail later on in the course but
+you need to have some way of filtering
+
+ align:start position:0%
+you need to have some way of filtering
+ 
+
+ align:start position:0%
+you need to have some way of filtering
+out
+
+ align:start position:0%
+out
+ 
+
+ align:start position:0%
+out
+the important issues to focus on
+
+ align:start position:0%
+the important issues to focus on
+ 
+
+ align:start position:0%
+the important issues to focus on
+in the garage case it was the level of
+
+ align:start position:0%
+in the garage case it was the level of
+ 
+
+ align:start position:0%
+in the garage case it was the level of
+demand i
+
+ align:start position:0%
+demand i
+ 
+
+ align:start position:0%
+demand i
+sort of didn't talk about the strength
+
+ align:start position:0%
+sort of didn't talk about the strength
+ 
+
+ align:start position:0%
+sort of didn't talk about the strength
+of the concrete or parking registrations
+
+ align:start position:0%
+of the concrete or parking registrations
+ 
+
+ align:start position:0%
+of the concrete or parking registrations
+or things like that but uh focusing on
+
+ align:start position:0%
+or things like that but uh focusing on
+ 
+
+ align:start position:0%
+or things like that but uh focusing on
+the right
+
+ align:start position:0%
+the right
+ 
+
+ align:start position:0%
+the right
+issues
+
+ align:start position:0%
+issues
+ 
+
+ align:start position:0%
+issues
+and i say that in the context that
+
+ align:start position:0%
+and i say that in the context that
+ 
+
+ align:start position:0%
+and i say that in the context that
+here in the from the garage case you can
+
+ align:start position:0%
+here in the from the garage case you can
+ 
+
+ align:start position:0%
+here in the from the garage case you can
+have all kinds of uncertainties that are
+
+ align:start position:0%
+have all kinds of uncertainties that are
+ 
+
+ align:start position:0%
+have all kinds of uncertainties that are
+playing out and each of these will give
+
+ align:start position:0%
+playing out and each of these will give
+ 
+
+ align:start position:0%
+playing out and each of these will give
+you different results at the end so
+
+ align:start position:0%
+you different results at the end so
+ 
+
+ align:start position:0%
+you different results at the end so
+which ones am i really going to focus on
+
+ align:start position:0%
+which ones am i really going to focus on
+ 
+
+ align:start position:0%
+which ones am i really going to focus on
+i don't want to be swamped by everything
+
+ align:start position:0%
+i don't want to be swamped by everything
+ 
+
+ align:start position:0%
+i don't want to be swamped by everything
+else
+
+ align:start position:0%
+else
+ 
+
+ align:start position:0%
+else
+so one way to do it is a tornado diagram
+
+ align:start position:0%
+so one way to do it is a tornado diagram
+ 
+
+ align:start position:0%
+so one way to do it is a tornado diagram
+which the end result is that you have
+
+ align:start position:0%
+which the end result is that you have
+ 
+
+ align:start position:0%
+which the end result is that you have
+various uncertainties this is taken from
+
+ align:start position:0%
+various uncertainties this is taken from
+ 
+
+ align:start position:0%
+various uncertainties this is taken from
+somebody's project some years back
+
+ align:start position:0%
+somebody's project some years back
+ 
+
+ align:start position:0%
+somebody's project some years back
+the demand the revenues operating costs
+
+ align:start position:0%
+the demand the revenues operating costs
+ 
+
+ align:start position:0%
+the demand the revenues operating costs
+et cetera down here
+
+ align:start position:0%
+et cetera down here
+ 
+
+ align:start position:0%
+et cetera down here
+and from the base case that is a the
+
+ align:start position:0%
+and from the base case that is a the
+ 
+
+ align:start position:0%
+and from the base case that is a the
+median case if you want the forecast
+
+ align:start position:0%
+median case if you want the forecast
+ 
+
+ align:start position:0%
+median case if you want the forecast
+case
+
+ align:start position:0%
+case
+ 
+
+ align:start position:0%
+case
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+you have a performance and if the demand
+
+ align:start position:0%
+you have a performance and if the demand
+ 
+
+ align:start position:0%
+you have a performance and if the demand
+went up in one way or down it have this
+
+ align:start position:0%
+went up in one way or down it have this
+ 
+
+ align:start position:0%
+went up in one way or down it have this
+range of effects
+
+ align:start position:0%
+range of effects
+ 
+
+ align:start position:0%
+range of effects
+and it's called a tornado diagram
+
+ align:start position:0%
+and it's called a tornado diagram
+ 
+
+ align:start position:0%
+and it's called a tornado diagram
+because when you look at the sensitivity
+
+ align:start position:0%
+because when you look at the sensitivity
+ 
+
+ align:start position:0%
+because when you look at the sensitivity
+to each of these uncertainties
+
+ align:start position:0%
+to each of these uncertainties
+ 
+
+ align:start position:0%
+to each of these uncertainties
+uh you stack the results so the ones
+
+ align:start position:0%
+uh you stack the results so the ones
+ 
+
+ align:start position:0%
+uh you stack the results so the ones
+which are least incentive at the bottom
+
+ align:start position:0%
+which are least incentive at the bottom
+ 
+
+ align:start position:0%
+which are least incentive at the bottom
+the ones that are most sensitive are at
+
+ align:start position:0%
+the ones that are most sensitive are at
+ 
+
+ align:start position:0%
+the ones that are most sensitive are at
+the top and therefore it has this funnel
+
+ align:start position:0%
+the top and therefore it has this funnel
+ 
+
+ align:start position:0%
+the top and therefore it has this funnel
+shape and that's why it's called a
+
+ align:start position:0%
+shape and that's why it's called a
+ 
+
+ align:start position:0%
+shape and that's why it's called a
+tornado diagram because it is
+
+ align:start position:0%
+tornado diagram because it is
+ 
+
+ align:start position:0%
+tornado diagram because it is
+the way a tornado looks like uh
+
+ align:start position:0%
+the way a tornado looks like uh
+ 
+
+ align:start position:0%
+the way a tornado looks like uh
+prototypically
+
+ align:start position:0%
+prototypically
+ 
+
+ align:start position:0%
+prototypically
+so the the idea is basically you think
+
+ align:start position:0%
+so the the idea is basically you think
+ 
+
+ align:start position:0%
+so the the idea is basically you think
+about
+
+ align:start position:0%
+about
+ 
+
+ align:start position:0%
+about
+how much your uncertainties might vary
+
+ align:start position:0%
+how much your uncertainties might vary
+ 
+
+ align:start position:0%
+how much your uncertainties might vary
+within a standard deviation
+
+ align:start position:0%
+within a standard deviation
+ 
+
+ align:start position:0%
+within a standard deviation
+and or and if it's symmetric or not
+
+ align:start position:0%
+and or and if it's symmetric or not
+ 
+
+ align:start position:0%
+and or and if it's symmetric or not
+symmetric
+
+ align:start position:0%
+symmetric
+ 
+
+ align:start position:0%
+symmetric
+and you run the analysis with those
+
+ align:start position:0%
+and you run the analysis with those
+ 
+
+ align:start position:0%
+and you run the analysis with those
+extremes and you see which are the ones
+
+ align:start position:0%
+extremes and you see which are the ones
+ 
+
+ align:start position:0%
+extremes and you see which are the ones
+that have the most effect
+
+ align:start position:0%
+that have the most effect
+ 
+
+ align:start position:0%
+that have the most effect
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+in this case for example the demand is
+
+ align:start position:0%
+in this case for example the demand is
+ 
+
+ align:start position:0%
+in this case for example the demand is
+the most important one in this uh
+
+ align:start position:0%
+the most important one in this uh
+ 
+
+ align:start position:0%
+the most important one in this uh
+particular case and so this you can
+
+ align:start position:0%
+particular case and so this you can
+ 
+
+ align:start position:0%
+particular case and so this you can
+focus on the revenue maybe next but the
+
+ align:start position:0%
+focus on the revenue maybe next but the
+ 
+
+ align:start position:0%
+focus on the revenue maybe next but the
+other ones don't make that much
+
+ align:start position:0%
+other ones don't make that much
+ 
+
+ align:start position:0%
+other ones don't make that much
+difference so that at least for the
+
+ align:start position:0%
+difference so that at least for the
+ 
+
+ align:start position:0%
+difference so that at least for the
+beginning we focus on the top ones and
+
+ align:start position:0%
+beginning we focus on the top ones and
+ 
+
+ align:start position:0%
+beginning we focus on the top ones and
+proceed ahead so at some level once you
+
+ align:start position:0%
+proceed ahead so at some level once you
+ 
+
+ align:start position:0%
+proceed ahead so at some level once you
+consider that things can be uncertain
+
+ align:start position:0%
+consider that things can be uncertain
+ 
+
+ align:start position:0%
+consider that things can be uncertain
+you may be swamped by all the
+
+ align:start position:0%
+you may be swamped by all the
+ 
+
+ align:start position:0%
+you may be swamped by all the
+possibilities all the things that could
+
+ align:start position:0%
+possibilities all the things that could
+ 
+
+ align:start position:0%
+possibilities all the things that could
+happen and you don't want to do that you
+
+ align:start position:0%
+happen and you don't want to do that you
+ 
+
+ align:start position:0%
+happen and you don't want to do that you
+want to have some way of focusing your
+
+ align:start position:0%
+want to have some way of focusing your
+ 
+
+ align:start position:0%
+want to have some way of focusing your
+attention on the things that matter and
+
+ align:start position:0%
+attention on the things that matter and
+ 
+
+ align:start position:0%
+attention on the things that matter and
+a tornado diagram is one way to do it
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+you may also want to think about how
+
+ align:start position:0%
+you may also want to think about how
+ 
+
+ align:start position:0%
+you may also want to think about how
+things may change over time
+
+ align:start position:0%
+things may change over time
+ 
+
+ align:start position:0%
+things may change over time
+this was the
+
+ align:start position:0%
+this was the
+ 
+
+ align:start position:0%
+this was the
+basic forecast that we use for the
+
+ align:start position:0%
+basic forecast that we use for the
+ 
+
+ align:start position:0%
+basic forecast that we use for the
+garage case i'm not pretending it's the
+
+ align:start position:0%
+garage case i'm not pretending it's the
+ 
+
+ align:start position:0%
+garage case i'm not pretending it's the
+right one but i'm simply saying it's an
+
+ align:start position:0%
+right one but i'm simply saying it's an
+ 
+
+ align:start position:0%
+right one but i'm simply saying it's an
+illustration of the kind of issue that
+
+ align:start position:0%
+illustration of the kind of issue that
+ 
+
+ align:start position:0%
+illustration of the kind of issue that
+you have
+
+ align:start position:0%
+you have
+ 
+
+ align:start position:0%
+you have
+so you start at a particular level and
+
+ align:start position:0%
+so you start at a particular level and
+ 
+
+ align:start position:0%
+so you start at a particular level and
+you think it might grow particularly
+
+ align:start position:0%
+you think it might grow particularly
+ 
+
+ align:start position:0%
+you think it might grow particularly
+quickly at that time and it might level
+
+ align:start position:0%
+quickly at that time and it might level
+ 
+
+ align:start position:0%
+quickly at that time and it might level
+off
+
+ align:start position:0%
+off
+ 
+
+ align:start position:0%
+off
+and that one of the forecasts that we
+
+ align:start position:0%
+and that one of the forecasts that we
+ 
+
+ align:start position:0%
+and that one of the forecasts that we
+were looking at today which was a uh
+
+ align:start position:0%
+were looking at today which was a uh
+ 
+
+ align:start position:0%
+were looking at today which was a uh
+renewable energy uh by the energy
+
+ align:start position:0%
+renewable energy uh by the energy
+ 
+
+ align:start position:0%
+renewable energy uh by the energy
+production by renewables you saw that
+
+ align:start position:0%
+production by renewables you saw that
+ 
+
+ align:start position:0%
+production by renewables you saw that
+many forecasts had a growth and then
+
+ align:start position:0%
+many forecasts had a growth and then
+ 
+
+ align:start position:0%
+many forecasts had a growth and then
+leveled off so thinking that this may be
+
+ align:start position:0%
+leveled off so thinking that this may be
+ 
+
+ align:start position:0%
+leveled off so thinking that this may be
+appropriate for your problem uh is
+
+ align:start position:0%
+appropriate for your problem uh is
+ 
+
+ align:start position:0%
+appropriate for your problem uh is
+something you will do that is your
+
+ align:start position:0%
+something you will do that is your
+ 
+
+ align:start position:0%
+something you will do that is your
+forecast may have a certain uncertainty
+
+ align:start position:0%
+forecast may have a certain uncertainty
+ 
+
+ align:start position:0%
+forecast may have a certain uncertainty
+all along but it may be around a
+
+ align:start position:0%
+all along but it may be around a
+ 
+
+ align:start position:0%
+all along but it may be around a
+particular pattern of growth which might
+
+ align:start position:0%
+particular pattern of growth which might
+ 
+
+ align:start position:0%
+particular pattern of growth which might
+be an s-shaped pattern it might be
+
+ align:start position:0%
+be an s-shaped pattern it might be
+ 
+
+ align:start position:0%
+be an s-shaped pattern it might be
+this shape it might be a straight
+
+ align:start position:0%
+this shape it might be a straight
+ 
+
+ align:start position:0%
+this shape it might be a straight
+shape it might be exponential but you
+
+ align:start position:0%
+shape it might be exponential but you
+ 
+
+ align:start position:0%
+shape it might be exponential but you
+want to think about a distribution
+
+ align:start position:0%
+want to think about a distribution
+ 
+
+ align:start position:0%
+want to think about a distribution
+aspect over time not just at any one
+
+ align:start position:0%
+aspect over time not just at any one
+ 
+
+ align:start position:0%
+aspect over time not just at any one
+time
\ No newline at end of file
diff --git a/jwfeVqhqEB8.txt b/jwfeVqhqEB8.txt
new file mode 100644
index 0000000000000000000000000000000000000000..7c2820a2336c7e9d6957ded36f69bb0dddb97e82
--- /dev/null
+++ b/jwfeVqhqEB8.txt
@@ -0,0 +1,440 @@
+If you put water in the freezer, you'll end
+up with ice. If you leave ice on your countertop,
+
+you'll end up with liquid water. You've almost
+certainly seen these phase changes in your
+
+everyday experience. But there's more to freezing
+and melting than meets the eye, and we can
+
+use these seemingly simple phenomena to make
+buildings significantly more energy efficient.
+
+In this video, we'll explain the concept of
+"latent heat" and see how it can dramatically
+
+reduce heating and cooling costs in homes
+and skyscrapers alike.
+
+This video is part of the Conservation video
+series.
+
+In order to analyze or modify a system, it
+is important to understand how the laws of
+
+conservation place constraints on that system.
+
+Hi. My name is Stephen Ray and I am a graduate
+student in the Department of Mechanical Engineering
+
+at MIT. My research in the Building Technology
+Lab under the guidance of Professor Leon Glicksman
+
+focuses on energy efficient buildings.
+
+In order to understand the topic of this video,
+you should be familiar with the Law of Conservation
+
+of Energy. You should also be familiar with
+the effects of intermolecular forces on phase
+
+transitions.
+
+After watching this video, you should be able
+to describe the energy transformations that
+
+occur during a phase change and apply the
+law of conservation of energy to phase changes.
+
+Let's start with a demonstration.
+
+Here we have a container of water to which
+we are adding table salt.
+
+Quite a bit of table salt, actually.
+
+Let's stir that up.
+
+Next, we are going to crush up some ice to
+add to the salt water.
+
+Our goal is to lower the temperature of the
+ice bath.
+
+Let's add some more salt.
+
+Freezing point depression, yeah!
+
+Alright, minus 8 degrees Celcius. That's pretty
+good.
+
+Let's place a smaller container of liquid
+water into this ice bath. We've added green
+
+food coloring to the water so that it is easier
+for you to see.
+
+After a few minutes, we'll insert a thermometer
+and watch the temperature drop as the water
+
+is cooled by the ice bath.
+
+The temperature reads about -5 degrees Celsius.
+The green water is still a liquid even though
+
+the temperature is below the normal freezing
+point of water. This is called supercooling.
+
+In the next step of this demo, we are going
+to add a couple of small pieces of ice to
+
+the green water. The supercooled water will
+crystallize rapidly with the addition of the
+
+ice.
+
+When this happens, what do you predict will
+happen to the temperature on the thermometer?
+
+Will it increase, decrease, or stay the same?
+
+What reasoning supports your prediction? Pause
+the video here to discuss your ideas with
+
+the person beside you, then continue playing
+the video to see what happens.
+
+Okay, ready to see what happens? Be sure to
+keep your eye on the digital display.
+
+Now we'll drop a couple of small pieces of
+ice into the container of green water.
+
+Watch what's happening.
+
+The green water froze. There is still a little
+bit of liquid, but we can turn the container
+
+upside down and you can see that the ice remains
+inside.
+
+So, when the liquid froze, what happened to
+the temperature?
+
+The temperature went up! Is this what you
+predicted? How can we explain what happened?
+
+Well, let's think about what happens at a
+molecular level when water changes phase from
+
+a liquid to a solid. In the liquid state,
+water molecules are moving around a lot. As
+
+it gets colder, the water molecules slow down.
+
+Generally speaking, as the water cools and
+solidifies, there is an increase in hydrogen
+
+bonding, the dominant intermolecular force
+amongst the water molecules.
+
+With this hint, can you now explain why we
+observed a temperature increase when the water
+
+froze? Pause the video, take a moment to think
+about it on your own and then discuss your
+
+idea with a classmate. Then, continue playing
+the video for an explanation.
+
+As we said before, when water transitions
+from liquid to solid, there is an increase
+
+in the number of hydrogen bonds that are formed
+between water molecules. Does bond formation
+
+release energy or require energy?
+
+Bond formation releases energy.
+
+So then, is the process of ice forming exothermic
+or endothermic?
+
+Ice formation is exothermic.
+
+If we were to do an energy balance on the
+system and the surroundings, we would see
+
+that the energy that was released by the water
+freezing is equivalent to the thermal energy
+
+that caused the temperature to increase. This
+is the Law of Conservation of Energy.
+
+Generally speaking, when a substance transitions
+between phases, intermolecular forces between
+
+neighboring molecules are either formed or
+broken. When a substance transitions from
+
+a liquid to a solid, intermolecular forces,
+or bonds, are formed and energy is released
+
+to the surroundings. This is called the latent
+heat of fusion.
+
+Going in the other direction, when a substance
+transitions from a solid to a liquid, energy
+
+is required to overcome intermolecular forces,
+so this is an endothermic process. Energy
+
+is absorbed from the surroundings. This is
+called the latent heat of melting.
+
+The latent heat of melting is equivalent in
+magnitude to the latent heat of fusion, but
+
+opposite in sign.
+
+This phenomenon of latent heat is used in
+a variety of ways to heat and cool buildings.
+
+Using melting ice to absorb thermal energy
+from the surroundings saves some buildings
+
+thousands of dollars a year in cooling costs.
+
+Consider a large office building during the
+middle of a hot summer day. In order to keep
+
+the building comfortable, the air conditioning
+is running at full power, requiring a lot
+
+of electricity from the utility company. The
+utility companies can't easily shut down their
+
+power plants, so nearly the same amount of
+electricity is produced during the night as
+
+is during the day. However, nighttime demand
+for electricity is very low, so utility companies
+
+sell this electricity at a lower price. This
+is common practice by utility companies across
+
+the U.S.
+
+Engineers have thought of a way to buy the
+electricity during the night when it is very
+
+cheap, but use it during the day when they
+need to run the air conditioning. This strategy
+
+is called peak load shifting. Think about
+what you have learned so far. There are a
+
+variety of ways this can be done. How do you
+think they do this? Pause the video here,
+
+take a moment to think about it, and discuss
+your idea with the person next to you. Continue
+
+playing the video to hear about one way they
+do this.
+
+One way we can decrease the amount of electricity
+needed in the daytime to cool a building is
+
+to use the energy storage capacity of ice,
+or its latent heat of melting.
+
+Large tanks, such as these in the basement
+of the Bank of America Tower in New York,
+
+store water that is frozen over night using
+cheap electricity. During the day, the ice
+
+melts and absorbs energy from the cooling
+fluid running through the building's air conditioning
+
+system. Each of the tanks in the Bank of America
+building holds approximately 1600 gallons
+
+of water which translates to roughly 570 kilowatt
+hours of cooling capacity. Bank of America
+
+reports that these ice tanks supply 25% of
+their cooling energy annually.
+
+The desire to harness latent heat has led
+to the development of a class of materials
+
+called phase change materials. These materials
+have been specifically designed to change
+
+phase at desirable temperatures so that they
+can store and release energy in a way that
+
+is useful to consumers. This slide shows some
+examples of these materials. The materials
+
+on this slide fall into three classes of phase
+change materials: inorganic salt hydrates,
+
+paraffinic hydrocarbons, and organic fatty
+acids.
+
+Some ordinary building materials such as concrete,
+dry wall, or insulation have been specially
+
+engineered over the past 50 years to contain
+microscopic pellets of phase change materials.
+
+Cellulose insulation, shown here, is commonly
+used to insulate attics and walls. Researchers
+
+at the Oak Ridge National Laboratories in
+the United States have impregnated small paraffin
+
+pellets in this common type of insulation
+to increase its performance.
+
+Because these pellets are microscopic, the
+phase change insulation looks exactly like
+
+the ordinary insulation to our naked eye.
+However, under a Scanning Electron Microscopic,
+
+the clusters of paraffinic pellets are easy
+to spot.
+
+Now lets look at the measured performance
+of a similar type of phase change insulation
+
+that is installed in a typical residential
+roof. The chart here shows the heat transfer
+
+into a house on the vertical axis and time
+on the horizontal axis. The two large black
+
+peaks, which occur during two consecutive
+summer days, correspond to the large amount
+
+of heat transfer into a home that a conventional
+roof allows. The smaller green peaks show
+
+how changing the roof surface material and
+venting the attic significantly help lower
+
+the heat transfer into a home by approximately
+70%. This reduction in heat transfer leads
+
+to less energy required for cooling the home.
+The purple curve shows that if phase change
+
+insulation is used in addition to these roof
+modifications, we can reduce the required
+
+cooling energy by 90%!
+
+How does phase change insulation help save
+energy? Pause the video, take a moment to
+
+think about it, and share your thoughts with
+a classmate.
+
+Consider two homes with and without PCM roof
+insulation. Both homes are exposed to the
+
+same amount of solar energy from the sun.
+Although not all of that energy enters the
+
+home without PCM insulation, a significant
+portion is transferred through the roof into
+
+the house. The house with PCM insulation reduces
+this amount because some of the energy that
+
+would otherwise enter the house is used to
+melt the phase change material in the roof.
+
+In order for this effect to occur each day,
+the phase change material must solidify every
+
+night before it can melt again the next day.
+
+Let's take a look at this chart of example
+phase change materials again. What phase change
+
+material would you use in a home or building
+in Singapore? Why? What additional information
+
+might you need to know to help make your decision?
+Pause the video here and discuss your choice
+
+with the person beside you.
+
+On average, year-round temperatures in Singapore
+hover between 23 and 32 degrees Celcius. This
+
+is important when making our decision. Some
+of you may have selected the calcium chloride
+
+hydrate as a candidate phase change material
+because its melting temperature falls within
+
+the range of daytime high temperatures in
+Singapore. You may have selected octadecane
+
+for a similar reason. If you eliminated paraffin
+wax and palmitic acid, it was probably because
+
+their melting points are so much higher than
+the highest outdoor temperatures reached in
+
+the day. However, these phase change materials
+could be used on a conventional dark-colored
+
+roof where temperatures can exceed 70 C because
+of all the energy absorbed from the sun. Caprylic
+
+acid, on the other hand, has such a low melting
+temperature, that few, if any, building components
+
+would ever drop below this temperature.
+
+So, let's go back to calcium chloride hydrate
+and octadecane. Both would melt and solidify
+
+within the temperature range of the environment,
+but octadecane has a higher heat of fusion,
+
+which leads to greater potential energy savings.
+While it is beyond the scope of this video,
+
+we also need to think about the heat transfer
+properties of the other building materials
+
+used in the roof and the cost and stability
+of the phase change materials.
+
+Today, you learned about the concept of latent
+heat and how the energy transformations that
+
+occur during a phase change are a consequence
+of the law of conservation of energy. You
+
+also saw how engineers have used the concept
+of latent heat to design phase change materials
+
+that can allow us to cool and heat homes more
+efficiently. The incorporation of phase change
+
+materials in building materials is still an
+active area of research. There are still engineering
+
+challenges to address, perhaps by you, in
+order to make these technologies cost-effective
+
+and more widely used.
\ No newline at end of file
diff --git a/mc1y8m9-hOM.txt b/mc1y8m9-hOM.txt
new file mode 100644
index 0000000000000000000000000000000000000000..65045aa06604bbbc36fe3d031484522440db0f9c
--- /dev/null
+++ b/mc1y8m9-hOM.txt
@@ -0,0 +1,13523 @@
+align:start position:0%
+ 
+the following content is provided under
+
+ align:start position:0%
+the following content is provided under
+ 
+
+ align:start position:0%
+the following content is provided under
+a creative common license your support
+
+ align:start position:0%
+a creative common license your support
+ 
+
+ align:start position:0%
+a creative common license your support
+will help MIT open courseware continue
+
+ align:start position:0%
+will help MIT open courseware continue
+ 
+
+ align:start position:0%
+will help MIT open courseware continue
+to offer highquality educational
+
+ align:start position:0%
+to offer highquality educational
+ 
+
+ align:start position:0%
+to offer highquality educational
+resources for free to make a donation or
+
+ align:start position:0%
+resources for free to make a donation or
+ 
+
+ align:start position:0%
+resources for free to make a donation or
+to view additional materials from
+
+ align:start position:0%
+to view additional materials from
+ 
+
+ align:start position:0%
+to view additional materials from
+hundreds of MIT courses visit MIT
+
+ align:start position:0%
+hundreds of MIT courses visit MIT
+ 
+
+ align:start position:0%
+hundreds of MIT courses visit MIT
+opencourseware at
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+ocw.mit.edu we're talking about
+
+ align:start position:0%
+ocw.mit.edu we're talking about
+ 
+
+ align:start position:0%
+ocw.mit.edu we're talking about
+um generalized linear models and in
+
+ align:start position:0%
+um generalized linear models and in
+ 
+
+ align:start position:0%
+um generalized linear models and in
+generalized linear models we generalize
+
+ align:start position:0%
+generalized linear models we generalize
+ 
+
+ align:start position:0%
+generalized linear models we generalize
+uh linear models in two ways uh the
+
+ align:start position:0%
+uh linear models in two ways uh the
+ 
+
+ align:start position:0%
+uh linear models in two ways uh the
+first one is to allow for different
+
+ align:start position:0%
+first one is to allow for different
+ 
+
+ align:start position:0%
+first one is to allow for different
+distribution for the response variables
+
+ align:start position:0%
+distribution for the response variables
+ 
+
+ align:start position:0%
+distribution for the response variables
+and the distributions that we wanted was
+
+ align:start position:0%
+and the distributions that we wanted was
+ 
+
+ align:start position:0%
+and the distributions that we wanted was
+uh the exponential
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+family and uh this is a family that can
+
+ align:start position:0%
+family and uh this is a family that can
+ 
+
+ align:start position:0%
+family and uh this is a family that can
+be generalized over uh random variables
+
+ align:start position:0%
+be generalized over uh random variables
+ 
+
+ align:start position:0%
+be generalized over uh random variables
+that are defined on say RQ in general
+
+ align:start position:0%
+that are defined on say RQ in general
+ 
+
+ align:start position:0%
+that are defined on say RQ in general
+with parameters in RK but we're going to
+
+ align:start position:0%
+with parameters in RK but we're going to
+ 
+
+ align:start position:0%
+with parameters in RK but we're going to
+focus in a very specific case where uh
+
+ align:start position:0%
+focus in a very specific case where uh
+ 
+
+ align:start position:0%
+focus in a very specific case where uh
+this is when R is equal uh Y is a real
+
+ align:start position:0%
+this is when R is equal uh Y is a real
+ 
+
+ align:start position:0%
+this is when R is equal uh Y is a real
+valued resp resp variable which is the
+
+ align:start position:0%
+valued resp resp variable which is the
+ 
+
+ align:start position:0%
+valued resp resp variable which is the
+one you're used to when you're doing uh
+
+ align:start position:0%
+one you're used to when you're doing uh
+ 
+
+ align:start position:0%
+one you're used to when you're doing uh
+linear regression and the parameter
+
+ align:start position:0%
+linear regression and the parameter
+ 
+
+ align:start position:0%
+linear regression and the parameter
+Theta also uh lives in R and so we're
+
+ align:start position:0%
+Theta also uh lives in R and so we're
+ 
+
+ align:start position:0%
+Theta also uh lives in R and so we're
+going to talk about the canonical case
+
+ align:start position:0%
+going to talk about the canonical case
+ 
+
+ align:start position:0%
+going to talk about the canonical case
+so that's the
+
+ align:start position:0%
+so that's the
+ 
+
+ align:start position:0%
+so that's the
+canonical uh uh exponential family where
+
+ align:start position:0%
+canonical uh uh exponential family where
+ 
+
+ align:start position:0%
+canonical uh uh exponential family where
+you have a density F Theta of X which is
+
+ align:start position:0%
+you have a density F Theta of X which is
+ 
+
+ align:start position:0%
+you have a density F Theta of X which is
+of the form
+
+ align:start position:0%
+of the form
+ 
+
+ align:start position:0%
+of the form
+exponential uh minus uh sorry
+
+ align:start position:0%
+exponential uh minus uh sorry
+ 
+
+ align:start position:0%
+exponential uh minus uh sorry
+exponential plus and then we have Y
+
+ align:start position:0%
+exponential plus and then we have Y
+ 
+
+ align:start position:0%
+exponential plus and then we have Y
+which interact with Theta only by taking
+
+ align:start position:0%
+which interact with Theta only by taking
+ 
+
+ align:start position:0%
+which interact with Theta only by taking
+a product then there's a term that
+
+ align:start position:0%
+a product then there's a term that
+ 
+
+ align:start position:0%
+a product then there's a term that
+depends only on Theta uh some dispersion
+
+ align:start position:0%
+depends only on Theta uh some dispersion
+ 
+
+ align:start position:0%
+depends only on Theta uh some dispersion
+parameter fi and then we have some
+
+ align:start position:0%
+parameter fi and then we have some
+ 
+
+ align:start position:0%
+parameter fi and then we have some
+normalization Factor let's call it C of
+
+ align:start position:0%
+normalization Factor let's call it C of
+ 
+
+ align:start position:0%
+normalization Factor let's call it C of
+Y
+
+ align:start position:0%
+Y
+ 
+
+ align:start position:0%
+Y
+uh five so it only depends so I really
+
+ align:start position:0%
+uh five so it only depends so I really
+ 
+
+ align:start position:0%
+uh five so it only depends so I really
+should not matter too much so it's a c
+
+ align:start position:0%
+should not matter too much so it's a c
+ 
+
+ align:start position:0%
+should not matter too much so it's a c
+of yfi and that's really just a
+
+ align:start position:0%
+of yfi and that's really just a
+ 
+
+ align:start position:0%
+of yfi and that's really just a
+normalization factor and here we said
+
+ align:start position:0%
+normalization factor and here we said
+ 
+
+ align:start position:0%
+normalization factor and here we said
+that we're going to assume that fi is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+known okay I just I have no idea what I
+
+ align:start position:0%
+known okay I just I have no idea what I
+ 
+
+ align:start position:0%
+known okay I just I have no idea what I
+write I don't know if you guys canite
+
+ align:start position:0%
+write I don't know if you guys canite
+ 
+
+ align:start position:0%
+write I don't know if you guys canite
+read I don't know what chalk has been
+
+ align:start position:0%
+read I don't know what chalk has been
+ 
+
+ align:start position:0%
+read I don't know what chalk has been
+used today but I just can't see it um
+
+ align:start position:0%
+used today but I just can't see it um
+ 
+
+ align:start position:0%
+used today but I just can't see it um
+that's not my fault um all right so
+
+ align:start position:0%
+that's not my fault um all right so
+ 
+
+ align:start position:0%
+that's not my fault um all right so
+we're going to assume that fi is known
+
+ align:start position:0%
+we're going to assume that fi is known
+ 
+
+ align:start position:0%
+we're going to assume that fi is known
+and so we saw that you know several
+
+ align:start position:0%
+and so we saw that you know several
+ 
+
+ align:start position:0%
+and so we saw that you know several
+distributions that we know well
+
+ align:start position:0%
+distributions that we know well
+ 
+
+ align:start position:0%
+distributions that we know well
+including the gaon for example belong to
+
+ align:start position:0%
+including the gaon for example belong to
+ 
+
+ align:start position:0%
+including the gaon for example belong to
+this family and there's other ones such
+
+ align:start position:0%
+this family and there's other ones such
+ 
+
+ align:start position:0%
+this family and there's other ones such
+as
+
+ align:start position:0%
+as
+ 
+
+ align:start position:0%
+as
+P sorry p and Burnley so if the pmf has
+
+ align:start position:0%
+P sorry p and Burnley so if the pmf has
+ 
+
+ align:start position:0%
+P sorry p and Burnley so if the pmf has
+this form if you have a discrete random
+
+ align:start position:0%
+this form if you have a discrete random
+ 
+
+ align:start position:0%
+this form if you have a discrete random
+variable this is also valid and uh the
+
+ align:start position:0%
+variable this is also valid and uh the
+ 
+
+ align:start position:0%
+variable this is also valid and uh the
+reason why we introduced this family is
+
+ align:start position:0%
+reason why we introduced this family is
+ 
+
+ align:start position:0%
+reason why we introduced this family is
+because there're going to be some
+
+ align:start position:0%
+because there're going to be some
+ 
+
+ align:start position:0%
+because there're going to be some
+properties so we know that this thing
+
+ align:start position:0%
+properties so we know that this thing
+ 
+
+ align:start position:0%
+properties so we know that this thing
+here this function B of theta is
+
+ align:start position:0%
+here this function B of theta is
+ 
+
+ align:start position:0%
+here this function B of theta is
+essentially what completely
+
+ align:start position:0%
+essentially what completely
+ 
+
+ align:start position:0%
+essentially what completely
+characterizes your distribution right so
+
+ align:start position:0%
+characterizes your distribution right so
+ 
+
+ align:start position:0%
+characterizes your distribution right so
+if f is fixed we know that the
+
+ align:start position:0%
+if f is fixed we know that the
+ 
+
+ align:start position:0%
+if f is fixed we know that the
+interaction is the form this form and
+
+ align:start position:0%
+interaction is the form this form and
+ 
+
+ align:start position:0%
+interaction is the form this form and
+this really just comes from the fact
+
+ align:start position:0%
+this really just comes from the fact
+ 
+
+ align:start position:0%
+this really just comes from the fact
+that we want the function to integrate
+
+ align:start position:0%
+that we want the function to integrate
+ 
+
+ align:start position:0%
+that we want the function to integrate
+to one so this B here in the canonical
+
+ align:start position:0%
+to one so this B here in the canonical
+ 
+
+ align:start position:0%
+to one so this B here in the canonical
+form encodes everything we want to know
+
+ align:start position:0%
+form encodes everything we want to know
+ 
+
+ align:start position:0%
+form encodes everything we want to know
+if I tell you what B of theta is and of
+
+ align:start position:0%
+if I tell you what B of theta is and of
+ 
+
+ align:start position:0%
+if I tell you what B of theta is and of
+course I tell you what f is but let's
+
+ align:start position:0%
+course I tell you what f is but let's
+ 
+
+ align:start position:0%
+course I tell you what f is but let's
+say for a second that five is equal to
+
+ align:start position:0%
+say for a second that five is equal to
+ 
+
+ align:start position:0%
+say for a second that five is equal to
+one if I tell you this B of theta you
+
+ align:start position:0%
+one if I tell you this B of theta you
+ 
+
+ align:start position:0%
+one if I tell you this B of theta you
+know exactly what distribution I'm
+
+ align:start position:0%
+know exactly what distribution I'm
+ 
+
+ align:start position:0%
+know exactly what distribution I'm
+talking about
+
+ align:start position:0%
+talking about
+ 
+
+ align:start position:0%
+talking about
+so it should encode everything that's
+
+ align:start position:0%
+so it should encode everything that's
+ 
+
+ align:start position:0%
+so it should encode everything that's
+you know specific to this distribution
+
+ align:start position:0%
+you know specific to this distribution
+ 
+
+ align:start position:0%
+you know specific to this distribution
+such as mean variance all the moments
+
+ align:start position:0%
+such as mean variance all the moments
+ 
+
+ align:start position:0%
+such as mean variance all the moments
+that you would want and uh uh we'll see
+
+ align:start position:0%
+that you would want and uh uh we'll see
+ 
+
+ align:start position:0%
+that you would want and uh uh we'll see
+how we can compute from this thing uh uh
+
+ align:start position:0%
+how we can compute from this thing uh uh
+ 
+
+ align:start position:0%
+how we can compute from this thing uh uh
+the mean and the variance for example So
+
+ align:start position:0%
+the mean and the variance for example So
+ 
+
+ align:start position:0%
+the mean and the variance for example So
+today we're going to talk about
+
+ align:start position:0%
+today we're going to talk about
+ 
+
+ align:start position:0%
+today we're going to talk about
+likelihood and we're going to start with
+
+ align:start position:0%
+likelihood and we're going to start with
+ 
+
+ align:start position:0%
+likelihood and we're going to start with
+the likelihood function or the log
+
+ align:start position:0%
+the likelihood function or the log
+ 
+
+ align:start position:0%
+the likelihood function or the log
+likelihood for one observation from this
+
+ align:start position:0%
+likelihood for one observation from this
+ 
+
+ align:start position:0%
+likelihood for one observation from this
+we're going to do some computations and
+
+ align:start position:0%
+we're going to do some computations and
+ 
+
+ align:start position:0%
+we're going to do some computations and
+then we'll move on to the actual log
+
+ align:start position:0%
+then we'll move on to the actual log
+ 
+
+ align:start position:0%
+then we'll move on to the actual log
+likelihood based on N independent
+
+ align:start position:0%
+likelihood based on N independent
+ 
+
+ align:start position:0%
+likelihood based on N independent
+observations and here as we will see the
+
+ align:start position:0%
+observations and here as we will see the
+ 
+
+ align:start position:0%
+observations and here as we will see the
+observations are not going to be
+
+ align:start position:0%
+observations are not going to be
+ 
+
+ align:start position:0%
+observations are not going to be
+identically distributed because we're
+
+ align:start position:0%
+identically distributed because we're
+ 
+
+ align:start position:0%
+identically distributed because we're
+going to want each of them I mean
+
+ align:start position:0%
+going to want each of them I mean
+ 
+
+ align:start position:0%
+going to want each of them I mean
+conditionally on X to have a different
+
+ align:start position:0%
+conditionally on X to have a different
+ 
+
+ align:start position:0%
+conditionally on X to have a different
+to be a different function of X okay to
+
+ align:start position:0%
+to be a different function of X okay to
+ 
+
+ align:start position:0%
+to be a different function of X okay to
+where Theta is just a different function
+
+ align:start position:0%
+where Theta is just a different function
+ 
+
+ align:start position:0%
+where Theta is just a different function
+of X for each of the observations right
+
+ align:start position:0%
+of X for each of the observations right
+ 
+
+ align:start position:0%
+of X for each of the observations right
+so remember the log
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+likelihood and this is for one
+
+ align:start position:0%
+likelihood and this is for one
+ 
+
+ align:start position:0%
+likelihood and this is for one
+observation is just the log of the
+
+ align:start position:0%
+observation is just the log of the
+ 
+
+ align:start position:0%
+observation is just the log of the
+density
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+right and uh uh we have this identity
+
+ align:start position:0%
+right and uh uh we have this identity
+ 
+
+ align:start position:0%
+right and uh uh we have this identity
+that I mentioned uh uh at the end of the
+
+ align:start position:0%
+that I mentioned uh uh at the end of the
+ 
+
+ align:start position:0%
+that I mentioned uh uh at the end of the
+class on Tuesday and this identity is
+
+ align:start position:0%
+class on Tuesday and this identity is
+ 
+
+ align:start position:0%
+class on Tuesday and this identity is
+just that the expectation of the
+
+ align:start position:0%
+just that the expectation of the
+ 
+
+ align:start position:0%
+just that the expectation of the
+derivative of this guy with respect to
+
+ align:start position:0%
+derivative of this guy with respect to
+ 
+
+ align:start position:0%
+derivative of this guy with respect to
+Theta is equal to zero so let's see why
+
+ align:start position:0%
+Theta is equal to zero so let's see why
+ 
+
+ align:start position:0%
+Theta is equal to zero so let's see why
+so if I take the derivative with respect
+
+ align:start position:0%
+so if I take the derivative with respect
+ 
+
+ align:start position:0%
+so if I take the derivative with respect
+to Theta of log F Theta of X what I get
+
+ align:start position:0%
+to Theta of log F Theta of X what I get
+ 
+
+ align:start position:0%
+to Theta of log F Theta of X what I get
+is the derivative with respect to
+
+ align:start position:0%
+is the derivative with respect to
+ 
+
+ align:start position:0%
+is the derivative with respect to
+Theta of f Theta of x divided by F Theta
+
+ align:start position:0%
+Theta of f Theta of x divided by F Theta
+ 
+
+ align:start position:0%
+Theta of f Theta of x divided by F Theta
+of
+
+ align:start position:0%
+of
+ 
+
+ align:start position:0%
+of
+X right now if I take the expectation of
+
+ align:start position:0%
+X right now if I take the expectation of
+ 
+
+ align:start position:0%
+X right now if I take the expectation of
+this guy
+
+ align:start position:0%
+this guy
+ 
+
+ align:start position:0%
+this guy
+with respect to this steta as
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+well what I get is that this thing what
+
+ align:start position:0%
+well what I get is that this thing what
+ 
+
+ align:start position:0%
+well what I get is that this thing what
+is the expectation well it's just the
+
+ align:start position:0%
+is the expectation well it's just the
+ 
+
+ align:start position:0%
+is the expectation well it's just the
+integral against F Theta or if I'm in a
+
+ align:start position:0%
+integral against F Theta or if I'm in a
+ 
+
+ align:start position:0%
+integral against F Theta or if I'm in a
+discrete case I just have the sum
+
+ align:start position:0%
+discrete case I just have the sum
+ 
+
+ align:start position:0%
+discrete case I just have the sum
+against F Theta right if it's a pmf just
+
+ align:start position:0%
+against F Theta right if it's a pmf just
+ 
+
+ align:start position:0%
+against F Theta right if it's a pmf just
+the distribu the definition of right the
+
+ align:start position:0%
+the distribu the definition of right the
+ 
+
+ align:start position:0%
+the distribu the definition of right the
+expectation of X is either the integral
+
+ align:start position:0%
+expectation of X is either the integral
+ 
+
+ align:start position:0%
+expectation of X is either the integral
+well let's say of H of X is the integral
+
+ align:start position:0%
+well let's say of H of X is the integral
+ 
+
+ align:start position:0%
+well let's say of H of X is the integral
+of H ofx F Theta of x if this is
+
+ align:start position:0%
+of H ofx F Theta of x if this is
+ 
+
+ align:start position:0%
+of H ofx F Theta of x if this is
+discrete or it's just the sum of h ofx f
+
+ align:start position:0%
+discrete or it's just the sum of h ofx f
+ 
+
+ align:start position:0%
+discrete or it's just the sum of h ofx f
+Theta of
+
+ align:start position:0%
+Theta of
+ 
+
+ align:start position:0%
+Theta of
+x if x is discret uh so if it's
+
+ align:start position:0%
+x if x is discret uh so if it's
+ 
+
+ align:start position:0%
+x if x is discret uh so if it's
+continuous you put this uh you know
+
+ align:start position:0%
+continuous you put this uh you know
+ 
+
+ align:start position:0%
+continuous you put this uh you know
+sweet soft sum and if it's uh put the
+
+ align:start position:0%
+sweet soft sum and if it's uh put the
+ 
+
+ align:start position:0%
+sweet soft sum and if it's uh put the
+this guy it's the same thing right so
+
+ align:start position:0%
+this guy it's the same thing right so
+ 
+
+ align:start position:0%
+this guy it's the same thing right so
+I'm just going to illustrate the case
+
+ align:start position:0%
+I'm just going to illustrate the case
+ 
+
+ align:start position:0%
+I'm just going to illustrate the case
+when it's continuous so this is what
+
+ align:start position:0%
+when it's continuous so this is what
+ 
+
+ align:start position:0%
+when it's continuous so this is what
+well this is the integral of partial
+
+ align:start position:0%
+well this is the integral of partial
+ 
+
+ align:start position:0%
+well this is the integral of partial
+derivative with respect to Theta of f
+
+ align:start position:0%
+derivative with respect to Theta of f
+ 
+
+ align:start position:0%
+derivative with respect to Theta of f
+Theta of x / f Theta of X time F Theta
+
+ align:start position:0%
+Theta of x / f Theta of X time F Theta
+ 
+
+ align:start position:0%
+Theta of x / f Theta of X time F Theta
+of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+X DX and now this F Theta is cancel so
+
+ align:start position:0%
+X DX and now this F Theta is cancel so
+ 
+
+ align:start position:0%
+X DX and now this F Theta is cancel so
+I'm actually left with the integral of
+
+ align:start position:0%
+I'm actually left with the integral of
+ 
+
+ align:start position:0%
+I'm actually left with the integral of
+the derivative which I'm going to write
+
+ align:start position:0%
+the derivative which I'm going to write
+ 
+
+ align:start position:0%
+the derivative which I'm going to write
+as the derivative of the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+integral but F Theta
+
+ align:start position:0%
+integral but F Theta
+ 
+
+ align:start position:0%
+integral but F Theta
+being being a
+
+ align:start position:0%
+being being a
+ 
+
+ align:start position:0%
+being being a
+um uh sorry F Theta being a density for
+
+ align:start position:0%
+um uh sorry F Theta being a density for
+ 
+
+ align:start position:0%
+um uh sorry F Theta being a density for
+any value of theta that I can take this
+
+ align:start position:0%
+any value of theta that I can take this
+ 
+
+ align:start position:0%
+any value of theta that I can take this
+is the function as a function of theta
+
+ align:start position:0%
+is the function as a function of theta
+ 
+
+ align:start position:0%
+is the function as a function of theta
+well actually as a as a function of
+
+ align:start position:0%
+well actually as a as a function of
+ 
+
+ align:start position:0%
+well actually as a as a function of
+theta this function is constantly equal
+
+ align:start position:0%
+theta this function is constantly equal
+ 
+
+ align:start position:0%
+theta this function is constantly equal
+to
+
+ align:start position:0%
+to
+ 
+
+ align:start position:0%
+to
+one right for any Theta I take it takes
+
+ align:start position:0%
+one right for any Theta I take it takes
+ 
+
+ align:start position:0%
+one right for any Theta I take it takes
+value one so this is constantly equal to
+
+ align:start position:0%
+value one so this is constantly equal to
+ 
+
+ align:start position:0%
+value one so this is constantly equal to
+one I put three bars to say that for any
+
+ align:start position:0%
+one I put three bars to say that for any
+ 
+
+ align:start position:0%
+one I put three bars to say that for any
+value of theta this is one which
+
+ align:start position:0%
+value of theta this is one which
+ 
+
+ align:start position:0%
+value of theta this is one which
+actually tells me that the derivative is
+
+ align:start position:0%
+actually tells me that the derivative is
+ 
+
+ align:start position:0%
+actually tells me that the derivative is
+equal to
+
+ align:start position:0%
+equal to
+ 
+
+ align:start position:0%
+equal to
+zero okay yes
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that the that's the definition of the
+
+ align:start position:0%
+that the that's the definition of the
+ 
+
+ align:start position:0%
+that the that's the definition of the
+expectation oh sorry uh no that's just
+
+ align:start position:0%
+expectation oh sorry uh no that's just
+ 
+
+ align:start position:0%
+expectation oh sorry uh no that's just
+the the definition of the derivative of
+
+ align:start position:0%
+the the definition of the derivative of
+ 
+
+ align:start position:0%
+the the definition of the derivative of
+a log of a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+function log of f Prime is frime over F
+
+ align:start position:0%
+function log of f Prime is frime over F
+ 
+
+ align:start position:0%
+function log of f Prime is frime over F
+right that's a log
+
+ align:start position:0%
+right that's a log
+ 
+
+ align:start position:0%
+right that's a log
+yeah just by elimination
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+I'm
+
+ align:start position:0%
+I'm
+ 
+
+ align:start position:0%
+I'm
+sorry yeah and that and you do good
+
+ align:start position:0%
+sorry yeah and that and you do good
+ 
+
+ align:start position:0%
+sorry yeah and that and you do good
+because that's probably how my mind's
+
+ align:start position:0%
+because that's probably how my mind's
+ 
+
+ align:start position:0%
+because that's probably how my mind's
+processes and so I'm like yeah L here's
+
+ align:start position:0%
+processes and so I'm like yeah L here's
+ 
+
+ align:start position:0%
+processes and so I'm like yeah L here's
+enough
+
+ align:start position:0%
+enough
+ 
+
+ align:start position:0%
+enough
+information
+
+ align:start position:0%
+information
+ 
+
+ align:start position:0%
+information
+um okay everybody's good with this so
+
+ align:start position:0%
+um okay everybody's good with this so
+ 
+
+ align:start position:0%
+um okay everybody's good with this so
+you know that was convenient so it just
+
+ align:start position:0%
+you know that was convenient so it just
+ 
+
+ align:start position:0%
+you know that was convenient so it just
+said that the expectation of the
+
+ align:start position:0%
+said that the expectation of the
+ 
+
+ align:start position:0%
+said that the expectation of the
+derivative of the log likelihood is
+
+ align:start position:0%
+derivative of the log likelihood is
+ 
+
+ align:start position:0%
+derivative of the log likelihood is
+equal to zero that's going to be our
+
+ align:start position:0%
+equal to zero that's going to be our
+ 
+
+ align:start position:0%
+equal to zero that's going to be our
+first identity let's move move on to the
+
+ align:start position:0%
+first identity let's move move on to the
+ 
+
+ align:start position:0%
+first identity let's move move on to the
+second identity using exactly the same
+
+ align:start position:0%
+second identity using exactly the same
+ 
+
+ align:start position:0%
+second identity using exactly the same
+trick which is let's hope that at some
+
+ align:start position:0%
+trick which is let's hope that at some
+ 
+
+ align:start position:0%
+trick which is let's hope that at some
+point we have the integral of this
+
+ align:start position:0%
+point we have the integral of this
+ 
+
+ align:start position:0%
+point we have the integral of this
+function that's constantly equal to one
+
+ align:start position:0%
+function that's constantly equal to one
+ 
+
+ align:start position:0%
+function that's constantly equal to one
+as a function of theta and then should
+
+ align:start position:0%
+as a function of theta and then should
+ 
+
+ align:start position:0%
+as a function of theta and then should
+show that use the fact that its
+
+ align:start position:0%
+show that use the fact that its
+ 
+
+ align:start position:0%
+show that use the fact that its
+derivative is equal to zero so if I
+
+ align:start position:0%
+derivative is equal to zero so if I
+ 
+
+ align:start position:0%
+derivative is equal to zero so if I
+start taking the second derivative of
+
+ align:start position:0%
+start taking the second derivative of
+ 
+
+ align:start position:0%
+start taking the second derivative of
+the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+log uh of f of
+
+ align:start position:0%
+log uh of f of
+ 
+
+ align:start position:0%
+log uh of f of
+theta so what is this well it's the
+
+ align:start position:0%
+theta so what is this well it's the
+ 
+
+ align:start position:0%
+theta so what is this well it's the
+second derivative of it's the the
+
+ align:start position:0%
+second derivative of it's the the
+ 
+
+ align:start position:0%
+second derivative of it's the the
+derivative of this guy here so I'm going
+
+ align:start position:0%
+derivative of this guy here so I'm going
+ 
+
+ align:start position:0%
+derivative of this guy here so I'm going
+to go straight to it so it's second
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+derivative of f Theta of X time F Theta
+
+ align:start position:0%
+derivative of f Theta of X time F Theta
+ 
+
+ align:start position:0%
+derivative of f Theta of X time F Theta
+of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+x
+
+ align:start position:0%
+x
+ 
+
+ align:start position:0%
+x
+minus second derivative first derivative
+
+ align:start position:0%
+minus second derivative first derivative
+ 
+
+ align:start position:0%
+minus second derivative first derivative
+of f Theta of
+
+ align:start position:0%
+of f Theta of
+ 
+
+ align:start position:0%
+of f Theta of
+x times first derivative of f Theta of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+X here is some super important stuff
+
+ align:start position:0%
+X here is some super important stuff
+ 
+
+ align:start position:0%
+X here is some super important stuff
+no I'm kidding and uh so you can still
+
+ align:start position:0%
+no I'm kidding and uh so you can still
+ 
+
+ align:start position:0%
+no I'm kidding and uh so you can still
+see that guy over there all right so
+
+ align:start position:0%
+see that guy over there all right so
+ 
+
+ align:start position:0%
+see that guy over there all right so
+it's just the square and then I divide
+
+ align:start position:0%
+it's just the square and then I divide
+ 
+
+ align:start position:0%
+it's just the square and then I divide
+by F Theta of x
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+s
+
+ align:start position:0%
+s
+ 
+
+ align:start position:0%
+s
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+so here I have the second derivative
+
+ align:start position:0%
+so here I have the second derivative
+ 
+
+ align:start position:0%
+so here I have the second derivative
+times F itself and here I have the
+
+ align:start position:0%
+times F itself and here I have the
+ 
+
+ align:start position:0%
+times F itself and here I have the
+product of the first derivative itself
+
+ align:start position:0%
+product of the first derivative itself
+ 
+
+ align:start position:0%
+product of the first derivative itself
+with itself right so that's the square
+
+ align:start position:0%
+with itself right so that's the square
+ 
+
+ align:start position:0%
+with itself right so that's the square
+so now I'm going to integrate this guy
+
+ align:start position:0%
+so now I'm going to integrate this guy
+ 
+
+ align:start position:0%
+so now I'm going to integrate this guy
+so if I take the
+
+ align:start position:0%
+so if I take the
+ 
+
+ align:start position:0%
+so if I take the
+expectation of this thing here
+
+ align:start position:0%
+expectation of this thing here
+ 
+
+ align:start position:0%
+expectation of this thing here
+what I get is the integral so here the
+
+ align:start position:0%
+what I get is the integral so here the
+ 
+
+ align:start position:0%
+what I get is the integral so here the
+only thing that's going to happen when
+
+ align:start position:0%
+only thing that's going to happen when
+ 
+
+ align:start position:0%
+only thing that's going to happen when
+I'm going to take my integral is that
+
+ align:start position:0%
+I'm going to take my integral is that
+ 
+
+ align:start position:0%
+I'm going to take my integral is that
+this one of those squares is going to
+
+ align:start position:0%
+this one of those squares is going to
+ 
+
+ align:start position:0%
+this one of those squares is going to
+cancel against F Theta right so I'm
+
+ align:start position:0%
+cancel against F Theta right so I'm
+ 
+
+ align:start position:0%
+cancel against F Theta right so I'm
+going to get the second
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+derivative um minus the second
+
+ align:start position:0%
+derivative um minus the second
+ 
+
+ align:start position:0%
+derivative um minus the second
+derivative squared
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and then I'm divided by F
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Theta and I know that this thing is
+
+ align:start position:0%
+Theta and I know that this thing is
+ 
+
+ align:start position:0%
+Theta and I know that this thing is
+equal to
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+zero okay now one of this guy here uh
+
+ align:start position:0%
+zero okay now one of this guy here uh
+ 
+
+ align:start position:0%
+zero okay now one of this guy here uh
+sorry why do I have uh yeah so I have
+
+ align:start position:0%
+sorry why do I have uh yeah so I have
+ 
+
+ align:start position:0%
+sorry why do I have uh yeah so I have
+this guy here so this guy here is going
+
+ align:start position:0%
+this guy here so this guy here is going
+ 
+
+ align:start position:0%
+this guy here so this guy here is going
+to
+
+ align:start position:0%
+to
+ 
+
+ align:start position:0%
+to
+cancel right so this is what this is um
+
+ align:start position:0%
+cancel right so this is what this is um
+ 
+
+ align:start position:0%
+cancel right so this is what this is um
+uh equal
+
+ align:start position:0%
+uh equal
+ 
+
+ align:start position:0%
+uh equal
+to uh uh the
+
+ align:start position:0%
+to uh uh the
+ 
+
+ align:start position:0%
+to uh uh the
+integral of the
+
+ align:start position:0%
+integral of the
+ 
+
+ align:start position:0%
+integral of the
+partial so the second derivative of f
+
+ align:start position:0%
+partial so the second derivative of f
+ 
+
+ align:start position:0%
+partial so the second derivative of f
+Theta of
+
+ align:start position:0%
+Theta of
+ 
+
+ align:start position:0%
+Theta of
+X right because those two guys cancel
+
+ align:start position:0%
+X right because those two guys cancel
+ 
+
+ align:start position:0%
+X right because those two guys cancel
+minus the integral of the second
+
+ align:start position:0%
+minus the integral of the second
+ 
+
+ align:start position:0%
+minus the integral of the second
+[Music]
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+derivative
+
+ align:start position:0%
+derivative
+ 
+
+ align:start position:0%
+derivative
+okay and
+
+ align:start position:0%
+okay and
+ 
+
+ align:start position:0%
+okay and
+um this is telling me what it's telling
+
+ align:start position:0%
+um this is telling me what it's telling
+ 
+
+ align:start position:0%
+um this is telling me what it's telling
+me that
+
+ align:start position:0%
+me that
+ 
+
+ align:start position:0%
+me that
+[Music]
+
+ align:start position:0%
+[Music]
+ 
+
+ align:start position:0%
+[Music]
+um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh yeah I'm losing one because I have
+
+ align:start position:0%
+uh yeah I'm losing one because I have
+ 
+
+ align:start position:0%
+uh yeah I'm losing one because I have
+some weird consequences thank you uh
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so this is actually yeah okay
+
+ align:start position:0%
+okay so this is actually yeah okay
+ 
+
+ align:start position:0%
+okay so this is actually yeah okay
+because now this is not
+
+ align:start position:0%
+because now this is not
+ 
+
+ align:start position:0%
+because now this is not
+well uh this is still positive so I know
+
+ align:start position:0%
+well uh this is still positive so I know
+ 
+
+ align:start position:0%
+well uh this is still positive so I know
+this thing I want to say that this thing
+
+ align:start position:0%
+this thing I want to say that this thing
+ 
+
+ align:start position:0%
+this thing I want to say that this thing
+is actually equal to
+
+ align:start position:0%
+is actually equal to
+ 
+
+ align:start position:0%
+is actually equal to
+zero but then it gives me some weird
+
+ align:start position:0%
+zero but then it gives me some weird
+ 
+
+ align:start position:0%
+zero but then it gives me some weird
+things which are that
+
+ align:start position:0%
+things which are that
+ 
+
+ align:start position:0%
+things which are that
+um I have the integral of a positive
+
+ align:start position:0%
+um I have the integral of a positive
+ 
+
+ align:start position:0%
+um I have the integral of a positive
+function which is equal to zero
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah that's what I'm thinking of doing
+
+ align:start position:0%
+yeah that's what I'm thinking of doing
+ 
+
+ align:start position:0%
+yeah that's what I'm thinking of doing
+but I'm going to get zero for this
+
+ align:start position:0%
+but I'm going to get zero for this
+ 
+
+ align:start position:0%
+but I'm going to get zero for this
+entire integral which means that have
+
+ align:start position:0%
+entire integral which means that have
+ 
+
+ align:start position:0%
+entire integral which means that have
+the integral of a positive function
+
+ align:start position:0%
+the integral of a positive function
+ 
+
+ align:start position:0%
+the integral of a positive function
+which is equal to zero which means that
+
+ align:start position:0%
+which is equal to zero which means that
+ 
+
+ align:start position:0%
+which is equal to zero which means that
+this function is equal to zero which uh
+
+ align:start position:0%
+this function is equal to zero which uh
+ 
+
+ align:start position:0%
+this function is equal to zero which uh
+sounds a little bad basically tells me
+
+ align:start position:0%
+sounds a little bad basically tells me
+ 
+
+ align:start position:0%
+sounds a little bad basically tells me
+that this function f Theta is
+
+ align:start position:0%
+that this function f Theta is
+ 
+
+ align:start position:0%
+that this function f Theta is
+linear
+
+ align:start position:0%
+linear
+ 
+
+ align:start position:0%
+linear
+um so I I went a little too far I
+
+ align:start position:0%
+um so I I went a little too far I
+ 
+
+ align:start position:0%
+um so I I went a little too far I
+believe because I only want to prove
+
+ align:start position:0%
+believe because I only want to prove
+ 
+
+ align:start position:0%
+believe because I only want to prove
+that the expectation of the second
+
+ align:start position:0%
+that the expectation of the second
+ 
+
+ align:start position:0%
+that the expectation of the second
+derivative uh
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um I want to show that the expectation
+
+ align:start position:0%
+um I want to show that the expectation
+ 
+
+ align:start position:0%
+um I want to show that the expectation
+of the I mean is that true actually that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh um yeah so I want to pull this out
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and uh so let's see if I keep rolling
+
+ align:start position:0%
+and uh so let's see if I keep rolling
+ 
+
+ align:start position:0%
+and uh so let's see if I keep rolling
+with this I'm going to get that well no
+
+ align:start position:0%
+with this I'm going to get that well no
+ 
+
+ align:start position:0%
+with this I'm going to get that well no
+because the fact that it's divided by F
+
+ align:start position:0%
+because the fact that it's divided by F
+ 
+
+ align:start position:0%
+because the fact that it's divided by F
+Theta means that indeed the second
+
+ align:start position:0%
+Theta means that indeed the second
+ 
+
+ align:start position:0%
+Theta means that indeed the second
+derivative is equal to zero so I cannot
+
+ align:start position:0%
+derivative is equal to zero so I cannot
+ 
+
+ align:start position:0%
+derivative is equal to zero so I cannot
+do this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+here okay uh maybe
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+I that's
+
+ align:start position:0%
+I that's
+ 
+
+ align:start position:0%
+I that's
+correct um
+
+ align:start position:0%
+correct um
+ 
+
+ align:start position:0%
+correct um
+okay but um let's uh write it like this
+
+ align:start position:0%
+okay but um let's uh write it like this
+ 
+
+ align:start position:0%
+okay but um let's uh write it like this
+so you write so this is what this is the
+
+ align:start position:0%
+so you write so this is what this is the
+ 
+
+ align:start position:0%
+so you write so this is what this is the
+expectation of the uh the partial with
+
+ align:start position:0%
+expectation of the uh the partial with
+ 
+
+ align:start position:0%
+expectation of the uh the partial with
+respect to Theta of f Theta of x divided
+
+ align:start position:0%
+respect to Theta of f Theta of x divided
+ 
+
+ align:start position:0%
+respect to Theta of f Theta of x divided
+by F Theta of
+
+ align:start position:0%
+by F Theta of
+ 
+
+ align:start position:0%
+by F Theta of
+x squared right and this is the the
+
+ align:start position:0%
+x squared right and this is the the
+ 
+
+ align:start position:0%
+x squared right and this is the the
+exactly the derivative of f of the log
+
+ align:start position:0%
+exactly the derivative of f of the log
+ 
+
+ align:start position:0%
+exactly the derivative of f of the log
+right so that's indeed this thing is
+
+ align:start position:0%
+right so that's indeed this thing is
+ 
+
+ align:start position:0%
+right so that's indeed this thing is
+equal to the expectation with respect to
+
+ align:start position:0%
+equal to the expectation with respect to
+ 
+
+ align:start position:0%
+equal to the expectation with respect to
+theeta
+
+ align:start position:0%
+theeta
+ 
+
+ align:start position:0%
+theeta
+of the partial of
+
+ align:start position:0%
+of the partial of
+ 
+
+ align:start position:0%
+of the partial of
+L uh well of log of f
+
+ align:start position:0%
+L uh well of log of f
+ 
+
+ align:start position:0%
+L uh well of log of f
+Theta divided by partial
+
+ align:start position:0%
+Theta divided by partial
+ 
+
+ align:start position:0%
+Theta divided by partial
+Theta all right so this is one of the
+
+ align:start position:0%
+Theta all right so this is one of the
+ 
+
+ align:start position:0%
+Theta all right so this is one of the
+guys that I want squared so this is one
+
+ align:start position:0%
+guys that I want squared so this is one
+ 
+
+ align:start position:0%
+guys that I want squared so this is one
+of the guys that I
+
+ align:start position:0%
+of the guys that I
+ 
+
+ align:start position:0%
+of the guys that I
+want and uh this is actually equal so
+
+ align:start position:0%
+want and uh this is actually equal so
+ 
+
+ align:start position:0%
+want and uh this is actually equal so
+this will be equal to the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+expectation oh yeah right right right so
+
+ align:start position:0%
+expectation oh yeah right right right so
+ 
+
+ align:start position:0%
+expectation oh yeah right right right so
+this term should be equal to zero ABS
+
+ align:start position:0%
+this term should be equal to zero ABS
+ 
+
+ align:start position:0%
+this term should be equal to zero ABS
+yeah I wanted this was not zero you're
+
+ align:start position:0%
+yeah I wanted this was not zero you're
+ 
+
+ align:start position:0%
+yeah I wanted this was not zero you're
+absolutely right so at some point I got
+
+ align:start position:0%
+absolutely right so at some point I got
+ 
+
+ align:start position:0%
+absolutely right so at some point I got
+confused because I thought putting this
+
+ align:start position:0%
+confused because I thought putting this
+ 
+
+ align:start position:0%
+confused because I thought putting this
+equal to zero would mean that this is
+
+ align:start position:0%
+equal to zero would mean that this is
+ 
+
+ align:start position:0%
+equal to zero would mean that this is
+zero but this thing is not equal to zero
+
+ align:start position:0%
+zero but this thing is not equal to zero
+ 
+
+ align:start position:0%
+zero but this thing is not equal to zero
+so this thing you're right I take the
+
+ align:start position:0%
+so this thing you're right I take the
+ 
+
+ align:start position:0%
+so this thing you're right I take the
+same trick as before and this is
+
+ align:start position:0%
+same trick as before and this is
+ 
+
+ align:start position:0%
+same trick as before and this is
+actually equal to zero which means that
+
+ align:start position:0%
+actually equal to zero which means that
+ 
+
+ align:start position:0%
+actually equal to zero which means that
+now I have what's on the left hand side
+
+ align:start position:0%
+now I have what's on the left hand side
+ 
+
+ align:start position:0%
+now I have what's on the left hand side
+which is equal to what's on the right
+
+ align:start position:0%
+which is equal to what's on the right
+ 
+
+ align:start position:0%
+which is equal to what's on the right
+hand side and if I recap I get that e
+
+ align:start position:0%
+hand side and if I recap I get that e
+ 
+
+ align:start position:0%
+hand side and if I recap I get that e
+Theta of uh the second
+
+ align:start position:0%
+Theta of uh the second
+ 
+
+ align:start position:0%
+Theta of uh the second
+derivative of the log of f
+
+ align:start position:0%
+derivative of the log of f
+ 
+
+ align:start position:0%
+derivative of the log of f
+Theta is equal to minus because I had a
+
+ align:start position:0%
+Theta is equal to minus because I had a
+ 
+
+ align:start position:0%
+Theta is equal to minus because I had a
+minus sign here to the expectation with
+
+ align:start position:0%
+minus sign here to the expectation with
+ 
+
+ align:start position:0%
+minus sign here to the expectation with
+respect to Theta of log of f Theta
+
+ align:start position:0%
+respect to Theta of log of f Theta
+ 
+
+ align:start position:0%
+respect to Theta of log of f Theta
+divided by
+
+ align:start position:0%
+divided by
+ 
+
+ align:start position:0%
+divided by
+Theta squared okay thank you for uh
+
+ align:start position:0%
+Theta squared okay thank you for uh
+ 
+
+ align:start position:0%
+Theta squared okay thank you for uh
+being on on watch when I'm falling apart
+
+ align:start position:0%
+being on on watch when I'm falling apart
+ 
+
+ align:start position:0%
+being on on watch when I'm falling apart
+all right so this is exactly what you
+
+ align:start position:0%
+all right so this is exactly what you
+ 
+
+ align:start position:0%
+all right so this is exactly what you
+have here except that both terms have
+
+ align:start position:0%
+have here except that both terms have
+ 
+
+ align:start position:0%
+have here except that both terms have
+been put on the same side all right so
+
+ align:start position:0%
+been put on the same side all right so
+ 
+
+ align:start position:0%
+been put on the same side all right so
+those things are going to be useful to
+
+ align:start position:0%
+those things are going to be useful to
+ 
+
+ align:start position:0%
+those things are going to be useful to
+us so maybe we should write them
+
+ align:start position:0%
+us so maybe we should write them
+ 
+
+ align:start position:0%
+us so maybe we should write them
+somewhere uh
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+here and then we have that the
+
+ align:start position:0%
+here and then we have that the
+ 
+
+ align:start position:0%
+here and then we have that the
+expectation of the uh second derivative
+
+ align:start position:0%
+expectation of the uh second derivative
+ 
+
+ align:start position:0%
+expectation of the uh second derivative
+of the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+log is equal to
+
+ align:start position:0%
+log is equal to
+ 
+
+ align:start position:0%
+log is equal to
+minus uh
+
+ align:start position:0%
+minus uh
+ 
+
+ align:start position:0%
+minus uh
+expectation of the square of the first
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+derivative okay and this is indeed my
+
+ align:start position:0%
+derivative okay and this is indeed my
+ 
+
+ align:start position:0%
+derivative okay and this is indeed my
+fisser information this is just telling
+
+ align:start position:0%
+fisser information this is just telling
+ 
+
+ align:start position:0%
+fisser information this is just telling
+me what is the second derivative of uh
+
+ align:start position:0%
+me what is the second derivative of uh
+ 
+
+ align:start position:0%
+me what is the second derivative of uh
+my log likelihood at Theta right so
+
+ align:start position:0%
+my log likelihood at Theta right so
+ 
+
+ align:start position:0%
+my log likelihood at Theta right so
+everything is with respect to Theta when
+
+ align:start position:0%
+everything is with respect to Theta when
+ 
+
+ align:start position:0%
+everything is with respect to Theta when
+I take these expectations and so it
+
+ align:start position:0%
+I take these expectations and so it
+ 
+
+ align:start position:0%
+I take these expectations and so it
+tells me that the expectation of the log
+
+ align:start position:0%
+tells me that the expectation of the log
+ 
+
+ align:start position:0%
+tells me that the expectation of the log
+likely of the of the uh second
+
+ align:start position:0%
+likely of the of the uh second
+ 
+
+ align:start position:0%
+likely of the of the uh second
+derivative at least first of all what
+
+ align:start position:0%
+derivative at least first of all what
+ 
+
+ align:start position:0%
+derivative at least first of all what
+it's telling me is that it's concave
+
+ align:start position:0%
+it's telling me is that it's concave
+ 
+
+ align:start position:0%
+it's telling me is that it's concave
+right because the second derivative of
+
+ align:start position:0%
+right because the second derivative of
+ 
+
+ align:start position:0%
+right because the second derivative of
+this thing which is the second
+
+ align:start position:0%
+this thing which is the second
+ 
+
+ align:start position:0%
+this thing which is the second
+derivative of the K Divergence is
+
+ align:start position:0%
+derivative of the K Divergence is
+ 
+
+ align:start position:0%
+derivative of the K Divergence is
+actually minus something which is must
+
+ align:start position:0%
+actually minus something which is must
+ 
+
+ align:start position:0%
+actually minus something which is must
+be non- negative and so it's telling me
+
+ align:start position:0%
+be non- negative and so it's telling me
+ 
+
+ align:start position:0%
+be non- negative and so it's telling me
+that it's concave here at this
+
+ align:start position:0%
+that it's concave here at this
+ 
+
+ align:start position:0%
+that it's concave here at this
+maximum okay and in particular it's also
+
+ align:start position:0%
+maximum okay and in particular it's also
+ 
+
+ align:start position:0%
+maximum okay and in particular it's also
+telling me that it has to be strictly
+
+ align:start position:0%
+telling me that it has to be strictly
+ 
+
+ align:start position:0%
+telling me that it has to be strictly
+positive unless the derivative of f is
+
+ align:start position:0%
+positive unless the derivative of f is
+ 
+
+ align:start position:0%
+positive unless the derivative of f is
+equal to zero so if unless f is constant
+
+ align:start position:0%
+equal to zero so if unless f is constant
+ 
+
+ align:start position:0%
+equal to zero so if unless f is constant
+then uh I don't have a I'm not it's not
+
+ align:start position:0%
+then uh I don't have a I'm not it's not
+ 
+
+ align:start position:0%
+then uh I don't have a I'm not it's not
+going to
+
+ align:start position:0%
+going to
+ 
+
+ align:start position:0%
+going to
+change all right
+
+ align:start position:0%
+change all right
+ 
+
+ align:start position:0%
+change all right
+do you have a
+
+ align:start position:0%
+do you have a
+ 
+
+ align:start position:0%
+do you have a
+question so now let's use
+
+ align:start position:0%
+question so now let's use
+ 
+
+ align:start position:0%
+question so now let's use
+this so what does my log likelihood look
+
+ align:start position:0%
+this so what does my log likelihood look
+ 
+
+ align:start position:0%
+this so what does my log likelihood look
+like when I actually comput it for this
+
+ align:start position:0%
+like when I actually comput it for this
+ 
+
+ align:start position:0%
+like when I actually comput it for this
+canonical exponential family right I
+
+ align:start position:0%
+canonical exponential family right I
+ 
+
+ align:start position:0%
+canonical exponential family right I
+mean we have this exponential function
+
+ align:start position:0%
+mean we have this exponential function
+ 
+
+ align:start position:0%
+mean we have this exponential function
+so taking the log should make my life
+
+ align:start position:0%
+so taking the log should make my life
+ 
+
+ align:start position:0%
+so taking the log should make my life
+much easier and indeed it does so if I
+
+ align:start position:0%
+much easier and indeed it does so if I
+ 
+
+ align:start position:0%
+much easier and indeed it does so if I
+look at the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+canonical what I have is that the log of
+
+ align:start position:0%
+canonical what I have is that the log of
+ 
+
+ align:start position:0%
+canonical what I have is that the log of
+f
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Theta of
+
+ align:start position:0%
+Theta of
+ 
+
+ align:start position:0%
+Theta of
+X well it's equal simply to Y Theta
+
+ align:start position:0%
+X well it's equal simply to Y Theta
+ 
+
+ align:start position:0%
+X well it's equal simply to Y Theta
+minus B of
+
+ align:start position:0%
+minus B of
+ 
+
+ align:start position:0%
+minus B of
+theta divided five plus this function
+
+ align:start position:0%
+theta divided five plus this function
+ 
+
+ align:start position:0%
+theta divided five plus this function
+that only depends that does not depend
+
+ align:start position:0%
+that only depends that does not depend
+ 
+
+ align:start position:0%
+that only depends that does not depend
+on
+
+ align:start position:0%
+on
+ 
+
+ align:start position:0%
+on
+Theta
+
+ align:start position:0%
+Theta
+ 
+
+ align:start position:0%
+Theta
+okay so let's see what this tells me
+
+ align:start position:0%
+okay so let's see what this tells me
+ 
+
+ align:start position:0%
+okay so let's see what this tells me
+what do let's just plug in those
+
+ align:start position:0%
+what do let's just plug in those
+ 
+
+ align:start position:0%
+what do let's just plug in those
+equalities in there right I mean I can
+
+ align:start position:0%
+equalities in there right I mean I can
+ 
+
+ align:start position:0%
+equalities in there right I mean I can
+take the derivative of the right hand
+
+ align:start position:0%
+take the derivative of the right hand
+ 
+
+ align:start position:0%
+take the derivative of the right hand
+side and just say that in expectation is
+
+ align:start position:0%
+side and just say that in expectation is
+ 
+
+ align:start position:0%
+side and just say that in expectation is
+equal to zero so if I start looking at
+
+ align:start position:0%
+equal to zero so if I start looking at
+ 
+
+ align:start position:0%
+equal to zero so if I start looking at
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+derivative this is equal to what well
+
+ align:start position:0%
+derivative this is equal to what well
+ 
+
+ align:start position:0%
+derivative this is equal to what well
+here I'm going to pick up only uh y
+
+ align:start position:0%
+here I'm going to pick up only uh y
+ 
+
+ align:start position:0%
+here I'm going to pick up only uh y
+sorry this is a function of
+
+ align:start position:0%
+sorry this is a function of
+ 
+
+ align:start position:0%
+sorry this is a function of
+Y uh I'm going to pick only
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh all right I was talking about
+
+ align:start position:0%
+uh all right I was talking about
+ 
+
+ align:start position:0%
+uh all right I was talking about
+likelihood so I actually need to put the
+
+ align:start position:0%
+likelihood so I actually need to put the
+ 
+
+ align:start position:0%
+likelihood so I actually need to put the
+random variable here uh so I get y minus
+
+ align:start position:0%
+random variable here uh so I get y minus
+ 
+
+ align:start position:0%
+random variable here uh so I get y minus
+the derivative of B of theta since it's
+
+ align:start position:0%
+the derivative of B of theta since it's
+ 
+
+ align:start position:0%
+the derivative of B of theta since it's
+only a function of theta I'm just going
+
+ align:start position:0%
+only a function of theta I'm just going
+ 
+
+ align:start position:0%
+only a function of theta I'm just going
+to write B Prime is that okay rather
+
+ align:start position:0%
+to write B Prime is that okay rather
+ 
+
+ align:start position:0%
+to write B Prime is that okay rather
+than having the partial with respect to
+
+ align:start position:0%
+than having the partial with respect to
+ 
+
+ align:start position:0%
+than having the partial with respect to
+Theta then this is a constant this does
+
+ align:start position:0%
+Theta then this is a constant this does
+ 
+
+ align:start position:0%
+Theta then this is a constant this does
+not depend on Theta so it goes
+
+ align:start position:0%
+not depend on Theta so it goes
+ 
+
+ align:start position:0%
+not depend on Theta so it goes
+away
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so if I start taking the
+
+ align:start position:0%
+okay so if I start taking the
+ 
+
+ align:start position:0%
+okay so if I start taking the
+expectation of this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+guy I get the expectation of this
+
+ align:start position:0%
+guy I get the expectation of this
+ 
+
+ align:start position:0%
+guy I get the expectation of this
+guy which is the expectation of
+
+ align:start position:0%
+guy which is the expectation of
+ 
+
+ align:start position:0%
+guy which is the expectation of
+Y minus well this does not depend on y
+
+ align:start position:0%
+Y minus well this does not depend on y
+ 
+
+ align:start position:0%
+Y minus well this does not depend on y
+so it's just itself B Prime of theta and
+
+ align:start position:0%
+so it's just itself B Prime of theta and
+ 
+
+ align:start position:0%
+so it's just itself B Prime of theta and
+the whole thing is divided by five but
+
+ align:start position:0%
+the whole thing is divided by five but
+ 
+
+ align:start position:0%
+the whole thing is divided by five but
+from my first equality over there I know
+
+ align:start position:0%
+from my first equality over there I know
+ 
+
+ align:start position:0%
+from my first equality over there I know
+that this thing is actually equal to
+
+ align:start position:0%
+that this thing is actually equal to
+ 
+
+ align:start position:0%
+that this thing is actually equal to
+zero right we just proved that so in
+
+ align:start position:0%
+zero right we just proved that so in
+ 
+
+ align:start position:0%
+zero right we just proved that so in
+particular it means that since f is non
+
+ align:start position:0%
+particular it means that since f is non
+ 
+
+ align:start position:0%
+particular it means that since f is non
+zero it means that this guy must be
+
+ align:start position:0%
+zero it means that this guy must be
+ 
+
+ align:start position:0%
+zero it means that this guy must be
+equal to this guy or F is not Infinity
+
+ align:start position:0%
+equal to this guy or F is not Infinity
+ 
+
+ align:start position:0%
+equal to this guy or F is not Infinity
+say and so that
+
+ align:start position:0%
+say and so that
+ 
+
+ align:start position:0%
+say and so that
+implies that the expectation with
+
+ align:start position:0%
+implies that the expectation with
+ 
+
+ align:start position:0%
+implies that the expectation with
+respect to Theta of
+
+ align:start position:0%
+respect to Theta of
+ 
+
+ align:start position:0%
+respect to Theta of
+Y is equal to B Prime of theta
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+I'm sorry you're not registered in this
+
+ align:start position:0%
+I'm sorry you're not registered in this
+ 
+
+ align:start position:0%
+I'm sorry you're not registered in this
+class I'm going to have to ask you to
+
+ align:start position:0%
+class I'm going to have to ask you to
+ 
+
+ align:start position:0%
+class I'm going to have to ask you to
+leave I'm not
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+kidding you are I've never seen you here
+
+ align:start position:0%
+kidding you are I've never seen you here
+ 
+
+ align:start position:0%
+kidding you are I've never seen you here
+I mean I saw you for the first
+
+ align:start position:0%
+I mean I saw you for the first
+ 
+
+ align:start position:0%
+I mean I saw you for the first
+Lector
+
+ align:start position:0%
+Lector
+ 
+
+ align:start position:0%
+Lector
+okay um all right so e Theta of Y is
+
+ align:start position:0%
+okay um all right so e Theta of Y is
+ 
+
+ align:start position:0%
+okay um all right so e Theta of Y is
+equal to B Prime of theta everybody
+
+ align:start position:0%
+equal to B Prime of theta everybody
+ 
+
+ align:start position:0%
+equal to B Prime of theta everybody
+agrees with
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that so this is actually nice because if
+
+ align:start position:0%
+that so this is actually nice because if
+ 
+
+ align:start position:0%
+that so this is actually nice because if
+I tell you okay I told you if I give you
+
+ align:start position:0%
+I tell you okay I told you if I give you
+ 
+
+ align:start position:0%
+I tell you okay I told you if I give you
+a an exponential family the only thing I
+
+ align:start position:0%
+a an exponential family the only thing I
+ 
+
+ align:start position:0%
+a an exponential family the only thing I
+really need to tell you is what B Theta
+
+ align:start position:0%
+really need to tell you is what B Theta
+ 
+
+ align:start position:0%
+really need to tell you is what B Theta
+is and if I give you B of theta then you
+
+ align:start position:0%
+is and if I give you B of theta then you
+ 
+
+ align:start position:0%
+is and if I give you B of theta then you
+know Computing a derivative is actually
+
+ align:start position:0%
+know Computing a derivative is actually
+ 
+
+ align:start position:0%
+know Computing a derivative is actually
+much easier than having to integrate y
+
+ align:start position:0%
+much easier than having to integrate y
+ 
+
+ align:start position:0%
+much easier than having to integrate y
+against the density itself I mean you
+
+ align:start position:0%
+against the density itself I mean you
+ 
+
+ align:start position:0%
+against the density itself I mean you
+could really have fun and try to compute
+
+ align:start position:0%
+could really have fun and try to compute
+ 
+
+ align:start position:0%
+could really have fun and try to compute
+this which you would be able to do
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+right and then there's the plus C of Y
+
+ align:start position:0%
+right and then there's the plus C of Y
+ 
+
+ align:start position:0%
+right and then there's the plus C of Y
+five blah blah blah Dy and that's the
+
+ align:start position:0%
+five blah blah blah Dy and that's the
+ 
+
+ align:start position:0%
+five blah blah blah Dy and that's the
+way you would actually compute this
+
+ align:start position:0%
+way you would actually compute this
+ 
+
+ align:start position:0%
+way you would actually compute this
+thing but that would be uh that would be
+
+ align:start position:0%
+thing but that would be uh that would be
+ 
+
+ align:start position:0%
+thing but that would be uh that would be
+really sorry this this guy is here that
+
+ align:start position:0%
+really sorry this this guy is here that
+ 
+
+ align:start position:0%
+really sorry this this guy is here that
+would be painful right I don't know what
+
+ align:start position:0%
+would be painful right I don't know what
+ 
+
+ align:start position:0%
+would be painful right I don't know what
+this normalization looks like so I would
+
+ align:start position:0%
+this normalization looks like so I would
+ 
+
+ align:start position:0%
+this normalization looks like so I would
+have to also explicit that so I can
+
+ align:start position:0%
+have to also explicit that so I can
+ 
+
+ align:start position:0%
+have to also explicit that so I can
+actually compute this thing and you know
+
+ align:start position:0%
+actually compute this thing and you know
+ 
+
+ align:start position:0%
+actually compute this thing and you know
+just the same way if you want to compute
+
+ align:start position:0%
+just the same way if you want to compute
+ 
+
+ align:start position:0%
+just the same way if you want to compute
+the expectation of a
+
+ align:start position:0%
+the expectation of a
+ 
+
+ align:start position:0%
+the expectation of a
+gaan well okay the expectation of a gaan
+
+ align:start position:0%
+gaan well okay the expectation of a gaan
+ 
+
+ align:start position:0%
+gaan well okay the expectation of a gaan
+is not the most difficult one but you
+
+ align:start position:0%
+is not the most difficult one but you
+ 
+
+ align:start position:0%
+is not the most difficult one but you
+know even if you compute the expectation
+
+ align:start position:0%
+know even if you compute the expectation
+ 
+
+ align:start position:0%
+know even if you compute the expectation
+of a Pon you start to have to work a
+
+ align:start position:0%
+of a Pon you start to have to work a
+ 
+
+ align:start position:0%
+of a Pon you start to have to work a
+little bit there's a few things that you
+
+ align:start position:0%
+little bit there's a few things that you
+ 
+
+ align:start position:0%
+little bit there's a few things that you
+have to work through here I'm just
+
+ align:start position:0%
+have to work through here I'm just
+ 
+
+ align:start position:0%
+have to work through here I'm just
+telling you all you have to know is what
+
+ align:start position:0%
+telling you all you have to know is what
+ 
+
+ align:start position:0%
+telling you all you have to know is what
+B of theta is and then you can just take
+
+ align:start position:0%
+B of theta is and then you can just take
+ 
+
+ align:start position:0%
+B of theta is and then you can just take
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+derivative let's see what the second
+
+ align:start position:0%
+derivative let's see what the second
+ 
+
+ align:start position:0%
+derivative let's see what the second
+equality is going to give
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+us okay so what is the second equality
+
+ align:start position:0%
+us okay so what is the second equality
+ 
+
+ align:start position:0%
+us okay so what is the second equality
+quity uh it's telling me that if I look
+
+ align:start position:0%
+quity uh it's telling me that if I look
+ 
+
+ align:start position:0%
+quity uh it's telling me that if I look
+at the second derivative and then I took
+
+ align:start position:0%
+at the second derivative and then I took
+ 
+
+ align:start position:0%
+at the second derivative and then I took
+it I take its expectation uh I'm gonna
+
+ align:start position:0%
+it I take its expectation uh I'm gonna
+ 
+
+ align:start position:0%
+it I take its expectation uh I'm gonna
+have something which is equal to
+
+ align:start position:0%
+have something which is equal to
+ 
+
+ align:start position:0%
+have something which is equal to
+negative uh this guy squared we've
+
+ align:start position:0%
+negative uh this guy squared we've
+ 
+
+ align:start position:0%
+negative uh this guy squared we've
+already comp uh sorry that that was the
+
+ align:start position:0%
+already comp uh sorry that that was the
+ 
+
+ align:start position:0%
+already comp uh sorry that that was the
+log
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+right we've already computed this uh
+
+ align:start position:0%
+right we've already computed this uh
+ 
+
+ align:start position:0%
+right we've already computed this uh
+this first derivative of the likelihood
+
+ align:start position:0%
+this first derivative of the likelihood
+ 
+
+ align:start position:0%
+this first derivative of the likelihood
+right it's just the expectation of the
+
+ align:start position:0%
+right it's just the expectation of the
+ 
+
+ align:start position:0%
+right it's just the expectation of the
+square of this thing here
+
+ align:start position:0%
+square of this thing here
+ 
+
+ align:start position:0%
+square of this thing here
+right so
+
+ align:start position:0%
+right so
+ 
+
+ align:start position:0%
+right so
+expectation of the derivative with
+
+ align:start position:0%
+expectation of the derivative with
+ 
+
+ align:start position:0%
+expectation of the derivative with
+respect to Theta of log F Theta of x
+
+ align:start position:0%
+respect to Theta of log F Theta of x
+ 
+
+ align:start position:0%
+respect to Theta of log F Theta of x
+divided partial
+
+ align:start position:0%
+divided partial
+ 
+
+ align:start position:0%
+divided partial
+Theta
+
+ align:start position:0%
+Theta
+ 
+
+ align:start position:0%
+Theta
+Square uh this is equal to the
+
+ align:start position:0%
+Square uh this is equal to the
+ 
+
+ align:start position:0%
+Square uh this is equal to the
+expectation of the square of Y minus B
+
+ align:start position:0%
+expectation of the square of Y minus B
+ 
+
+ align:start position:0%
+expectation of the square of Y minus B
+Theta ID
+
+ align:start position:0%
+Theta ID
+ 
+
+ align:start position:0%
+Theta ID
+5^
+
+ align:start position:0%
+5^
+ 
+
+ align:start position:0%
+5^
+squar right B Prime Theta
+
+ align:start position:0%
+squar right B Prime Theta
+ 
+
+ align:start position:0%
+squar right B Prime Theta
+square and uh
+
+ align:start position:0%
+square and uh
+ 
+
+ align:start position:0%
+square and uh
+uh okay sorry I'm actually going to move
+
+ align:start position:0%
+uh okay sorry I'm actually going to move
+ 
+
+ align:start position:0%
+uh okay sorry I'm actually going to move
+on with
+
+ align:start position:0%
+on with
+ 
+
+ align:start position:0%
+on with
+the okay and uh so if I start Computing
+
+ align:start position:0%
+the okay and uh so if I start Computing
+ 
+
+ align:start position:0%
+the okay and uh so if I start Computing
+what is this thing well this we just
+
+ align:start position:0%
+what is this thing well this we just
+ 
+
+ align:start position:0%
+what is this thing well this we just
+agreed that this was
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+what the expectation of theta
+
+ align:start position:0%
+what the expectation of theta
+ 
+
+ align:start position:0%
+what the expectation of theta
+right so that's just the expectation
+
+ align:start position:0%
+right so that's just the expectation
+ 
+
+ align:start position:0%
+right so that's just the expectation
+sorry the expectation of Y we just
+
+ align:start position:0%
+sorry the expectation of Y we just
+ 
+
+ align:start position:0%
+sorry the expectation of Y we just
+computed here
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah that's B Prime there's a derivative
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+here
+
+ align:start position:0%
+here
+ 
+
+ align:start position:0%
+here
+okay so now uh this is what how this is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+simply anyone
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+I'm sorry variance of Y but there's the
+
+ align:start position:0%
+I'm sorry variance of Y but there's the
+ 
+
+ align:start position:0%
+I'm sorry variance of Y but there's the
+scaling by five square
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+right okay so that's so this is negative
+
+ align:start position:0%
+right okay so that's so this is negative
+ 
+
+ align:start position:0%
+right okay so that's so this is negative
+of the right hand side of our inequality
+
+ align:start position:0%
+of the right hand side of our inequality
+ 
+
+ align:start position:0%
+of the right hand side of our inequality
+and now I just have to take one more
+
+ align:start position:0%
+and now I just have to take one more
+ 
+
+ align:start position:0%
+and now I just have to take one more
+derivative uh to this guy right so if
+
+ align:start position:0%
+derivative uh to this guy right so if
+ 
+
+ align:start position:0%
+derivative uh to this guy right so if
+now if I look at and if I look at the
+
+ align:start position:0%
+now if I look at and if I look at the
+ 
+
+ align:start position:0%
+now if I look at and if I look at the
+left hand side now I have that the
+
+ align:start position:0%
+left hand side now I have that the
+ 
+
+ align:start position:0%
+left hand side now I have that the
+partial itive the second derivative of
+
+ align:start position:0%
+partial itive the second derivative of
+ 
+
+ align:start position:0%
+partial itive the second derivative of
+log of f Theta of Y divid partial of
+
+ align:start position:0%
+log of f Theta of Y divid partial of
+ 
+
+ align:start position:0%
+log of f Theta of Y divid partial of
+theta
+
+ align:start position:0%
+theta
+ 
+
+ align:start position:0%
+theta
+squared so this thing is equal to well
+
+ align:start position:0%
+squared so this thing is equal to well
+ 
+
+ align:start position:0%
+squared so this thing is equal to well
+now I'm not left with much the Y part is
+
+ align:start position:0%
+now I'm not left with much the Y part is
+ 
+
+ align:start position:0%
+now I'm not left with much the Y part is
+going to go away and I'm left only with
+
+ align:start position:0%
+going to go away and I'm left only with
+ 
+
+ align:start position:0%
+going to go away and I'm left only with
+the second derivative of theta minus the
+
+ align:start position:0%
+the second derivative of theta minus the
+ 
+
+ align:start position:0%
+the second derivative of theta minus the
+second derivative of theta divid
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+five okay
+
+ align:start position:0%
+five okay
+ 
+
+ align:start position:0%
+five okay
+so if I take
+
+ align:start position:0%
+so if I take
+ 
+
+ align:start position:0%
+so if I take
+expectation well it just doesn't
+
+ align:start position:0%
+expectation well it just doesn't
+ 
+
+ align:start position:0%
+expectation well it just doesn't
+change this is deterministic so now what
+
+ align:start position:0%
+change this is deterministic so now what
+ 
+
+ align:start position:0%
+change this is deterministic so now what
+I've established is that this guy is
+
+ align:start position:0%
+I've established is that this guy is
+ 
+
+ align:start position:0%
+I've established is that this guy is
+equal to negative this guy so those two
+
+ align:start position:0%
+equal to negative this guy so those two
+ 
+
+ align:start position:0%
+equal to negative this guy so those two
+things are the signs are going to go
+
+ align:start position:0%
+things are the signs are going to go
+ 
+
+ align:start position:0%
+things are the signs are going to go
+away and so this implies that the
+
+ align:start position:0%
+away and so this implies that the
+ 
+
+ align:start position:0%
+away and so this implies that the
+variance of Y is equal to B prime prime
+
+ align:start position:0%
+variance of Y is equal to B prime prime
+ 
+
+ align:start position:0%
+variance of Y is equal to B prime prime
+Theta and then I have a 5 Square in
+
+ align:start position:0%
+Theta and then I have a 5 Square in
+ 
+
+ align:start position:0%
+Theta and then I have a 5 Square in
+denominator that cancels only one the
+
+ align:start position:0%
+denominator that cancels only one the
+ 
+
+ align:start position:0%
+denominator that cancels only one the
+five in the denominator that cancels
+
+ align:start position:0%
+five in the denominator that cancels
+ 
+
+ align:start position:0%
+five in the denominator that cancels
+only one of the five squares so it's
+
+ align:start position:0%
+only one of the five squares so it's
+ 
+
+ align:start position:0%
+only one of the five squares so it's
+time
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+five so now I have that my second
+
+ align:start position:0%
+five so now I have that my second
+ 
+
+ align:start position:0%
+five so now I have that my second
+derivative since I know f is completely
+
+ align:start position:0%
+derivative since I know f is completely
+ 
+
+ align:start position:0%
+derivative since I know f is completely
+determined determining the
+
+ align:start position:0%
+determined determining the
+ 
+
+ align:start position:0%
+determined determining the
+variance all right and so basically
+
+ align:start position:0%
+variance all right and so basically
+ 
+
+ align:start position:0%
+variance all right and so basically
+that's what B that's why B is called the
+
+ align:start position:0%
+that's what B that's why B is called the
+ 
+
+ align:start position:0%
+that's what B that's why B is called the
+cumulant generating function is not
+
+ align:start position:0%
+cumulant generating function is not
+ 
+
+ align:start position:0%
+cumulant generating function is not
+generating moments but cumulants but
+
+ align:start position:0%
+generating moments but cumulants but
+ 
+
+ align:start position:0%
+generating moments but cumulants but
+cumulants in this case correct respond
+
+ align:start position:0%
+cumulants in this case correct respond
+ 
+
+ align:start position:0%
+cumulants in this case correct respond
+basically to the moments at least for
+
+ align:start position:0%
+basically to the moments at least for
+ 
+
+ align:start position:0%
+basically to the moments at least for
+the first two if I start going F farther
+
+ align:start position:0%
+the first two if I start going F farther
+ 
+
+ align:start position:0%
+the first two if I start going F farther
+I'm not going to have I'm going to have
+
+ align:start position:0%
+I'm not going to have I'm going to have
+ 
+
+ align:start position:0%
+I'm not going to have I'm going to have
+more combinations of the expectation of
+
+ align:start position:0%
+more combinations of the expectation of
+ 
+
+ align:start position:0%
+more combinations of the expectation of
+Y3 Y 2 and why itself
+
+ align:start position:0%
+Y3 Y 2 and why itself
+ 
+
+ align:start position:0%
+Y3 Y 2 and why itself
+okay so but you know as we know those
+
+ align:start position:0%
+okay so but you know as we know those
+ 
+
+ align:start position:0%
+okay so but you know as we know those
+are the ones that are usually the most
+
+ align:start position:0%
+are the ones that are usually the most
+ 
+
+ align:start position:0%
+are the ones that are usually the most
+useful at least if we're interested in a
+
+ align:start position:0%
+useful at least if we're interested in a
+ 
+
+ align:start position:0%
+useful at least if we're interested in a
+SYM totic performance the central limit
+
+ align:start position:0%
+SYM totic performance the central limit
+ 
+
+ align:start position:0%
+SYM totic performance the central limit
+theorem tells us that all that matters
+
+ align:start position:0%
+theorem tells us that all that matters
+ 
+
+ align:start position:0%
+theorem tells us that all that matters
+are the first two moments and then the
+
+ align:start position:0%
+are the first two moments and then the
+ 
+
+ align:start position:0%
+are the first two moments and then the
+rest is just going to go and say well it
+
+ align:start position:0%
+rest is just going to go and say well it
+ 
+
+ align:start position:0%
+rest is just going to go and say well it
+doesn't matter it's all going to a
+
+ align:start position:0%
+doesn't matter it's all going to a
+ 
+
+ align:start position:0%
+doesn't matter it's all going to a
+normal anyway
+
+ align:start position:0%
+normal anyway
+ 
+
+ align:start position:0%
+normal anyway
+so let's go to a Pon for example right
+
+ align:start position:0%
+so let's go to a Pon for example right
+ 
+
+ align:start position:0%
+so let's go to a Pon for example right
+so if I had a Pon
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+distribution all right so this is a
+
+ align:start position:0%
+distribution all right so this is a
+ 
+
+ align:start position:0%
+distribution all right so this is a
+discrete
+
+ align:start position:0%
+discrete
+ 
+
+ align:start position:0%
+discrete
+distribution and uh what I know is that
+
+ align:start position:0%
+distribution and uh what I know is that
+ 
+
+ align:start position:0%
+distribution and uh what I know is that
+uh so F uh let me call uh mu the
+
+ align:start position:0%
+uh so F uh let me call uh mu the
+ 
+
+ align:start position:0%
+uh so F uh let me call uh mu the
+parameter of Y this is
+
+ align:start position:0%
+parameter of Y this is
+ 
+
+ align:start position:0%
+parameter of Y this is
+uh well okay so it's mu to the Y divided
+
+ align:start position:0%
+uh well okay so it's mu to the Y divided
+ 
+
+ align:start position:0%
+uh well okay so it's mu to the Y divided
+by y factorial exponential minus mu okay
+
+ align:start position:0%
+by y factorial exponential minus mu okay
+ 
+
+ align:start position:0%
+by y factorial exponential minus mu okay
+so mu is usually called Lambda and Y is
+
+ align:start position:0%
+so mu is usually called Lambda and Y is
+ 
+
+ align:start position:0%
+so mu is usually called Lambda and Y is
+usually called X that's why it takes me
+
+ align:start position:0%
+usually called X that's why it takes me
+ 
+
+ align:start position:0%
+usually called X that's why it takes me
+a little bit of time but usually it's
+
+ align:start position:0%
+a little bit of time but usually it's
+ 
+
+ align:start position:0%
+a little bit of time but usually it's
+Lambda to the X over factorial X
+
+ align:start position:0%
+Lambda to the X over factorial X
+ 
+
+ align:start position:0%
+Lambda to the X over factorial X
+exponential minus Lambda this thing
+
+ align:start position:0%
+exponential minus Lambda this thing
+ 
+
+ align:start position:0%
+exponential minus Lambda this thing
+clearly since this is just the series
+
+ align:start position:0%
+clearly since this is just the series
+ 
+
+ align:start position:0%
+clearly since this is just the series
+expansion of the exponential when I sum
+
+ align:start position:0%
+expansion of the exponential when I sum
+ 
+
+ align:start position:0%
+expansion of the exponential when I sum
+those things from zero to Infinity this
+
+ align:start position:0%
+those things from zero to Infinity this
+ 
+
+ align:start position:0%
+those things from zero to Infinity this
+thing sums to one but then if I wanted
+
+ align:start position:0%
+thing sums to one but then if I wanted
+ 
+
+ align:start position:0%
+thing sums to one but then if I wanted
+to start understanding what the
+
+ align:start position:0%
+to start understanding what the
+ 
+
+ align:start position:0%
+to start understanding what the
+expectation of this thing is uh right so
+
+ align:start position:0%
+expectation of this thing is uh right so
+ 
+
+ align:start position:0%
+expectation of this thing is uh right so
+if I want to understand the expectations
+
+ align:start position:0%
+if I want to understand the expectations
+ 
+
+ align:start position:0%
+if I want to understand the expectations
+with respect to mu of uh
+
+ align:start position:0%
+with respect to mu of uh
+ 
+
+ align:start position:0%
+with respect to mu of uh
+y then I would have to compute the sum
+
+ align:start position:0%
+y then I would have to compute the sum
+ 
+
+ align:start position:0%
+y then I would have to compute the sum
+from k equal 0 or let's say yeah from k
+
+ align:start position:0%
+from k equal 0 or let's say yeah from k
+ 
+
+ align:start position:0%
+from k equal 0 or let's say yeah from k
+equals z to Infinity of um y times mu
+
+ align:start position:0%
+equals z to Infinity of um y times mu
+ 
+
+ align:start position:0%
+equals z to Infinity of um y times mu
+sorry of K * mu to the K Over factorial
+
+ align:start position:0%
+sorry of K * mu to the K Over factorial
+ 
+
+ align:start position:0%
+sorry of K * mu to the K Over factorial
+K exponential minus mu which means that
+
+ align:start position:0%
+K exponential minus mu which means that
+ 
+
+ align:start position:0%
+K exponential minus mu which means that
+I would essentially have to
+
+ align:start position:0%
+I would essentially have to
+ 
+
+ align:start position:0%
+I would essentially have to
+take the derivative
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay um that I would have to take the
+
+ align:start position:0%
+okay um that I would have to take the
+ 
+
+ align:start position:0%
+okay um that I would have to take the
+derivative of my um uh series uh in the
+
+ align:start position:0%
+derivative of my um uh series uh in the
+ 
+
+ align:start position:0%
+derivative of my um uh series uh in the
+end so you know I can do this this is a
+
+ align:start position:0%
+end so you know I can do this this is a
+ 
+
+ align:start position:0%
+end so you know I can do this this is a
+standard exercise you've probably done
+
+ align:start position:0%
+standard exercise you've probably done
+ 
+
+ align:start position:0%
+standard exercise you've probably done
+it when you took probability but let's
+
+ align:start position:0%
+it when you took probability but let's
+ 
+
+ align:start position:0%
+it when you took probability but let's
+see if we can actually just Ser it off
+
+ align:start position:0%
+see if we can actually just Ser it off
+ 
+
+ align:start position:0%
+see if we can actually just Ser it off
+from the first derivative of B so to do
+
+ align:start position:0%
+from the first derivative of B so to do
+ 
+
+ align:start position:0%
+from the first derivative of B so to do
+that we need to write this in the form
+
+ align:start position:0%
+that we need to write this in the form
+ 
+
+ align:start position:0%
+that we need to write this in the form
+of an exponential where there's one
+
+ align:start position:0%
+of an exponential where there's one
+ 
+
+ align:start position:0%
+of an exponential where there's one
+parameter that captures mu that
+
+ align:start position:0%
+parameter that captures mu that
+ 
+
+ align:start position:0%
+parameter that captures mu that
+interacts with Y just doing this
+
+ align:start position:0%
+interacts with Y just doing this
+ 
+
+ align:start position:0%
+interacts with Y just doing this
+parameter times Y and then something
+
+ align:start position:0%
+parameter times Y and then something
+ 
+
+ align:start position:0%
+parameter times Y and then something
+that depends only on Y and then
+
+ align:start position:0%
+that depends only on Y and then
+ 
+
+ align:start position:0%
+that depends only on Y and then
+something that depends only on uh sorry
+
+ align:start position:0%
+something that depends only on uh sorry
+ 
+
+ align:start position:0%
+something that depends only on uh sorry
+something depends only on on me that's
+
+ align:start position:0%
+something depends only on on me that's
+ 
+
+ align:start position:0%
+something depends only on on me that's
+the important one that's going to be our
+
+ align:start position:0%
+the important one that's going to be our
+ 
+
+ align:start position:0%
+the important one that's going to be our
+B and then there's going to be something
+
+ align:start position:0%
+B and then there's going to be something
+ 
+
+ align:start position:0%
+B and then there's going to be something
+that depends only on uh y okay so let's
+
+ align:start position:0%
+that depends only on uh y okay so let's
+ 
+
+ align:start position:0%
+that depends only on uh y okay so let's
+write this and check that this F mu
+
+ align:start position:0%
+write this and check that this F mu
+ 
+
+ align:start position:0%
+write this and check that this F mu
+indeed belongs to this canonical
+
+ align:start position:0%
+indeed belongs to this canonical
+ 
+
+ align:start position:0%
+indeed belongs to this canonical
+exponential family so I definitely have
+
+ align:start position:0%
+exponential family so I definitely have
+ 
+
+ align:start position:0%
+exponential family so I definitely have
+an exponential that comes from this guy
+
+ align:start position:0%
+an exponential that comes from this guy
+ 
+
+ align:start position:0%
+an exponential that comes from this guy
+so I have minus mu and then this thing
+
+ align:start position:0%
+so I have minus mu and then this thing
+ 
+
+ align:start position:0%
+so I have minus mu and then this thing
+is going to give me what it's going to
+
+ align:start position:0%
+is going to give me what it's going to
+ 
+
+ align:start position:0%
+is going to give me what it's going to
+give me plus y log mu
+
+ align:start position:0%
+give me plus y log mu
+ 
+
+ align:start position:0%
+give me plus y log mu
+and then I'm going to have minus log of
+
+ align:start position:0%
+and then I'm going to have minus log of
+ 
+
+ align:start position:0%
+and then I'm going to have minus log of
+Y factorial
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+right okay so clearly I have a term that
+
+ align:start position:0%
+right okay so clearly I have a term that
+ 
+
+ align:start position:0%
+right okay so clearly I have a term that
+depends only on mu a terms that depend
+
+ align:start position:0%
+depends only on mu a terms that depend
+ 
+
+ align:start position:0%
+depends only on mu a terms that depend
+only on Y and I have a product of Y and
+
+ align:start position:0%
+only on Y and I have a product of Y and
+ 
+
+ align:start position:0%
+only on Y and I have a product of Y and
+something that depends on me if I want
+
+ align:start position:0%
+something that depends on me if I want
+ 
+
+ align:start position:0%
+something that depends on me if I want
+to be canonical I must have this to be
+
+ align:start position:0%
+to be canonical I must have this to be
+ 
+
+ align:start position:0%
+to be canonical I must have this to be
+exactly the parameter Theta
+
+ align:start position:0%
+exactly the parameter Theta
+ 
+
+ align:start position:0%
+exactly the parameter Theta
+itself okay so I'm going to call this
+
+ align:start position:0%
+itself okay so I'm going to call this
+ 
+
+ align:start position:0%
+itself okay so I'm going to call this
+guy
+
+ align:start position:0%
+guy
+ 
+
+ align:start position:0%
+guy
+Theta okay so Theta is log mu which
+
+ align:start position:0%
+Theta okay so Theta is log mu which
+ 
+
+ align:start position:0%
+Theta okay so Theta is log mu which
+means that mu is equal to e to the Theta
+
+ align:start position:0%
+means that mu is equal to e to the Theta
+ 
+
+ align:start position:0%
+means that mu is equal to e to the Theta
+and so wherever I see mu I'm going to
+
+ align:start position:0%
+and so wherever I see mu I'm going to
+ 
+
+ align:start position:0%
+and so wherever I see mu I'm going to
+replace it by U to the Theta because my
+
+ align:start position:0%
+replace it by U to the Theta because my
+ 
+
+ align:start position:0%
+replace it by U to the Theta because my
+new parameter now is Theta so this is
+
+ align:start position:0%
+new parameter now is Theta so this is
+ 
+
+ align:start position:0%
+new parameter now is Theta so this is
+what this is equal to
+
+ align:start position:0%
+what this is equal to
+ 
+
+ align:start position:0%
+what this is equal to
+exponential y * Theta and then I'm going
+
+ align:start position:0%
+exponential y * Theta and then I'm going
+ 
+
+ align:start position:0%
+exponential y * Theta and then I'm going
+to have minus E of
+
+ align:start position:0%
+to have minus E of
+ 
+
+ align:start position:0%
+to have minus E of
+theta and then who cares something that
+
+ align:start position:0%
+theta and then who cares something that
+ 
+
+ align:start position:0%
+theta and then who cares something that
+depends only on on you so this is my C
+
+ align:start position:0%
+depends only on on you so this is my C
+ 
+
+ align:start position:0%
+depends only on on you so this is my C
+of Y and F is equal to one in this case
+
+ align:start position:0%
+of Y and F is equal to one in this case
+ 
+
+ align:start position:0%
+of Y and F is equal to one in this case
+uh uh so that's all I care about so let
+
+ align:start position:0%
+uh uh so that's all I care about so let
+ 
+
+ align:start position:0%
+uh uh so that's all I care about so let
+me I mean let's let's use it
+
+ align:start position:0%
+me I mean let's let's use it
+ 
+
+ align:start position:0%
+me I mean let's let's use it
+right okay so this is my canonical
+
+ align:start position:0%
+right okay so this is my canonical
+ 
+
+ align:start position:0%
+right okay so this is my canonical
+exponential
+
+ align:start position:0%
+exponential
+ 
+
+ align:start position:0%
+exponential
+Family Y interact with Theta exactly
+
+ align:start position:0%
+Family Y interact with Theta exactly
+ 
+
+ align:start position:0%
+Family Y interact with Theta exactly
+like this and then I have this function
+
+ align:start position:0%
+like this and then I have this function
+ 
+
+ align:start position:0%
+like this and then I have this function
+so this function here must
+
+ align:start position:0%
+so this function here must
+ 
+
+ align:start position:0%
+so this function here must
+be B of
+
+ align:start position:0%
+be B of
+ 
+
+ align:start position:0%
+be B of
+theta right so from this function
+
+ align:start position:0%
+theta right so from this function
+ 
+
+ align:start position:0%
+theta right so from this function
+exponential Theta I'm supposed to be
+
+ align:start position:0%
+exponential Theta I'm supposed to be
+ 
+
+ align:start position:0%
+exponential Theta I'm supposed to be
+able to read what the mean is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+because since in this course I always
+
+ align:start position:0%
+because since in this course I always
+ 
+
+ align:start position:0%
+because since in this course I always
+know what the dispersion is I can
+
+ align:start position:0%
+know what the dispersion is I can
+ 
+
+ align:start position:0%
+know what the dispersion is I can
+actually always absorb it into Theta for
+
+ align:start position:0%
+actually always absorb it into Theta for
+ 
+
+ align:start position:0%
+actually always absorb it into Theta for
+one but here it's really of the form y
+
+ align:start position:0%
+one but here it's really of the form y
+ 
+
+ align:start position:0%
+one but here it's really of the form y
+times something divided by one right
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+I mean I could have if it was like log
+
+ align:start position:0%
+I mean I could have if it was like log
+ 
+
+ align:start position:0%
+I mean I could have if it was like log
+of mu divided by five it would be the
+
+ align:start position:0%
+of mu divided by five it would be the
+ 
+
+ align:start position:0%
+of mu divided by five it would be the
+question of whether I want to call
+
+ align:start position:0%
+question of whether I want to call
+ 
+
+ align:start position:0%
+question of whether I want to call
+five five my dispersion or if I want to
+
+ align:start position:0%
+five five my dispersion or if I want to
+ 
+
+ align:start position:0%
+five five my dispersion or if I want to
+just like have it in there but if I know
+
+ align:start position:0%
+just like have it in there but if I know
+ 
+
+ align:start position:0%
+just like have it in there but if I know
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+usually so okay this makes no difference
+
+ align:start position:0%
+usually so okay this makes no difference
+ 
+
+ align:start position:0%
+usually so okay this makes no difference
+in practice but the real thing is when
+
+ align:start position:0%
+in practice but the real thing is when
+ 
+
+ align:start position:0%
+in practice but the real thing is when
+you it's never going to happen that this
+
+ align:start position:0%
+you it's never going to happen that this
+ 
+
+ align:start position:0%
+you it's never going to happen that this
+thing this dispersion is going to be an
+
+ align:start position:0%
+thing this dispersion is going to be an
+ 
+
+ align:start position:0%
+thing this dispersion is going to be an
+exact number if it's an actual numerical
+
+ align:start position:0%
+exact number if it's an actual numerical
+ 
+
+ align:start position:0%
+exact number if it's an actual numerical
+number this just means that this number
+
+ align:start position:0%
+number this just means that this number
+ 
+
+ align:start position:0%
+number this just means that this number
+should be absorb in the uh in the
+
+ align:start position:0%
+should be absorb in the uh in the
+ 
+
+ align:start position:0%
+should be absorb in the uh in the
+definition of theta but if it's
+
+ align:start position:0%
+definition of theta but if it's
+ 
+
+ align:start position:0%
+definition of theta but if it's
+something that is called Sigma say and I
+
+ align:start position:0%
+something that is called Sigma say and I
+ 
+
+ align:start position:0%
+something that is called Sigma say and I
+say and I will assume that Sigma is
+
+ align:start position:0%
+say and I will assume that Sigma is
+ 
+
+ align:start position:0%
+say and I will assume that Sigma is
+known then it's probably uh preferable
+
+ align:start position:0%
+known then it's probably uh preferable
+ 
+
+ align:start position:0%
+known then it's probably uh preferable
+to keep it in the dispersion so you can
+
+ align:start position:0%
+to keep it in the dispersion so you can
+ 
+
+ align:start position:0%
+to keep it in the dispersion so you can
+see that there's this parameter here
+
+ align:start position:0%
+see that there's this parameter here
+ 
+
+ align:start position:0%
+see that there's this parameter here
+that you can essentially play with okay
+
+ align:start position:0%
+that you can essentially play with okay
+ 
+
+ align:start position:0%
+that you can essentially play with okay
+that it doesn't make any difference when
+
+ align:start position:0%
+that it doesn't make any difference when
+ 
+
+ align:start position:0%
+that it doesn't make any difference when
+you know
+
+ align:start position:0%
+you know
+ 
+
+ align:start position:0%
+you know
+five okay so now uh what I have so okay
+
+ align:start position:0%
+five okay so now uh what I have so okay
+ 
+
+ align:start position:0%
+five okay so now uh what I have so okay
+so if I look at the
+
+ align:start position:0%
+so if I look at the
+ 
+
+ align:start position:0%
+so if I look at the
+expectation of some y so now I'm going
+
+ align:start position:0%
+expectation of some y so now I'm going
+ 
+
+ align:start position:0%
+expectation of some y so now I'm going
+to have Y which follows my P
+
+ align:start position:0%
+to have Y which follows my P
+ 
+
+ align:start position:0%
+to have Y which follows my P
+mu I'm going to take I'm going to look
+
+ align:start position:0%
+mu I'm going to take I'm going to look
+ 
+
+ align:start position:0%
+mu I'm going to take I'm going to look
+at the expectation and I know that the
+
+ align:start position:0%
+at the expectation and I know that the
+ 
+
+ align:start position:0%
+at the expectation and I know that the
+expectation is B
+
+ align:start position:0%
+expectation is B
+ 
+
+ align:start position:0%
+expectation is B
+Prime of theta
+
+ align:start position:0%
+Prime of theta
+ 
+
+ align:start position:0%
+Prime of theta
+right agreed that's what I just
+
+ align:start position:0%
+right agreed that's what I just
+ 
+
+ align:start position:0%
+right agreed that's what I just
+erased I
+
+ align:start position:0%
+erased I
+ 
+
+ align:start position:0%
+erased I
+think agreed with this the derivative
+
+ align:start position:0%
+think agreed with this the derivative
+ 
+
+ align:start position:0%
+think agreed with this the derivative
+all right so what is this well it's the
+
+ align:start position:0%
+all right so what is this well it's the
+ 
+
+ align:start position:0%
+all right so what is this well it's the
+derivative of e to the Theta which is e
+
+ align:start position:0%
+derivative of e to the Theta which is e
+ 
+
+ align:start position:0%
+derivative of e to the Theta which is e
+to the Theta which is
+
+ align:start position:0%
+to the Theta which is
+ 
+
+ align:start position:0%
+to the Theta which is
+Mu so my is parameterized by its mean I
+
+ align:start position:0%
+Mu so my is parameterized by its mean I
+ 
+
+ align:start position:0%
+Mu so my is parameterized by its mean I
+can also compute the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+variance which is equal to minus the
+
+ align:start position:0%
+variance which is equal to minus the
+ 
+
+ align:start position:0%
+variance which is equal to minus the
+second derivative of uh is it uh yeah no
+
+ align:start position:0%
+second derivative of uh is it uh yeah no
+ 
+
+ align:start position:0%
+second derivative of uh is it uh yeah no
+it's equal to the second derivative of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+B dispersion is equal to one again if I
+
+ align:start position:0%
+B dispersion is equal to one again if I
+ 
+
+ align:start position:0%
+B dispersion is equal to one again if I
+took uh fi elsewhere I would see it uh I
+
+ align:start position:0%
+took uh fi elsewhere I would see it uh I
+ 
+
+ align:start position:0%
+took uh fi elsewhere I would see it uh I
+would see it here as well right so if I
+
+ align:start position:0%
+would see it here as well right so if I
+ 
+
+ align:start position:0%
+would see it here as well right so if I
+just absorb five here I would see it
+
+ align:start position:0%
+just absorb five here I would see it
+ 
+
+ align:start position:0%
+just absorb five here I would see it
+divided here it would not make any
+
+ align:start position:0%
+divided here it would not make any
+ 
+
+ align:start position:0%
+divided here it would not make any
+difference and what is the second
+
+ align:start position:0%
+difference and what is the second
+ 
+
+ align:start position:0%
+difference and what is the second
+derivative of the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+exponential it's still the
+
+ align:start position:0%
+exponential it's still the
+ 
+
+ align:start position:0%
+exponential it's still the
+exponential so it's still equal to
+
+ align:start position:0%
+exponential so it's still equal to
+ 
+
+ align:start position:0%
+exponential so it's still equal to
+me
+
+ align:start position:0%
+me
+ 
+
+ align:start position:0%
+me
+okay so that certainly makes our uh life
+
+ align:start position:0%
+okay so that certainly makes our uh life
+ 
+
+ align:start position:0%
+okay so that certainly makes our uh life
+uh easier just uh one quick remark
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+here's here's the B function I I giving
+
+ align:start position:0%
+here's here's the B function I I giving
+ 
+
+ align:start position:0%
+here's here's the B function I I giving
+you a problem can the B function of some
+
+ align:start position:0%
+you a problem can the B function of some
+ 
+
+ align:start position:0%
+you a problem can the B function of some
+uh this this function B can it ever be
+
+ align:start position:0%
+uh this this function B can it ever be
+ 
+
+ align:start position:0%
+uh this this function B can it ever be
+equal
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+to log of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+theta who says yes
+
+ align:start position:0%
+theta who says yes
+ 
+
+ align:start position:0%
+theta who says yes
+who says
+
+ align:start position:0%
+who says
+ 
+
+ align:start position:0%
+who says
+no
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+why yeah all right
+
+ align:start position:0%
+why yeah all right
+ 
+
+ align:start position:0%
+why yeah all right
+so what I've learned from this sort of
+
+ align:start position:0%
+so what I've learned from this sort of
+ 
+
+ align:start position:0%
+so what I've learned from this sort of
+completely analytic right so we just
+
+ align:start position:0%
+completely analytic right so we just
+ 
+
+ align:start position:0%
+completely analytic right so we just
+took derivatives and this thing just
+
+ align:start position:0%
+took derivatives and this thing just
+ 
+
+ align:start position:0%
+took derivatives and this thing just
+happened right this thing actually
+
+ align:start position:0%
+happened right this thing actually
+ 
+
+ align:start position:0%
+happened right this thing actually
+allowed us to relate the second
+
+ align:start position:0%
+allowed us to relate the second
+ 
+
+ align:start position:0%
+allowed us to relate the second
+derivative of B to the variance and one
+
+ align:start position:0%
+derivative of B to the variance and one
+ 
+
+ align:start position:0%
+derivative of B to the variance and one
+thing that we know about a variance is
+
+ align:start position:0%
+thing that we know about a variance is
+ 
+
+ align:start position:0%
+thing that we know about a variance is
+that this is non- negative and in
+
+ align:start position:0%
+that this is non- negative and in
+ 
+
+ align:start position:0%
+that this is non- negative and in
+particular it's always positive right I
+
+ align:start position:0%
+particular it's always positive right I
+ 
+
+ align:start position:0%
+particular it's always positive right I
+mean if I give you an expon a canonical
+
+ align:start position:0%
+mean if I give you an expon a canonical
+ 
+
+ align:start position:0%
+mean if I give you an expon a canonical
+exponential family that has zero
+
+ align:start position:0%
+exponential family that has zero
+ 
+
+ align:start position:0%
+exponential family that has zero
+variance trust me you will see it right
+
+ align:start position:0%
+variance trust me you will see it right
+ 
+
+ align:start position:0%
+variance trust me you will see it right
+I mean that means that this thing is not
+
+ align:start position:0%
+I mean that means that this thing is not
+ 
+
+ align:start position:0%
+I mean that means that this thing is not
+going to look like something that's
+
+ align:start position:0%
+going to look like something that's
+ 
+
+ align:start position:0%
+going to look like something that's
+finite it means it's going to have a
+
+ align:start position:0%
+finite it means it's going to have a
+ 
+
+ align:start position:0%
+finite it means it's going to have a
+point mass is going to take value
+
+ align:start position:0%
+point mass is going to take value
+ 
+
+ align:start position:0%
+point mass is going to take value
+Infinity at one point so this will
+
+ align:start position:0%
+Infinity at one point so this will
+ 
+
+ align:start position:0%
+Infinity at one point so this will
+basically never happen this thing is
+
+ align:start position:0%
+basically never happen this thing is
+ 
+
+ align:start position:0%
+basically never happen this thing is
+actually strictly positive which means
+
+ align:start position:0%
+actually strictly positive which means
+ 
+
+ align:start position:0%
+actually strictly positive which means
+that this thing is always like strictly
+
+ align:start position:0%
+that this thing is always like strictly
+ 
+
+ align:start position:0%
+that this thing is always like strictly
+concave it means that the second
+
+ align:start position:0%
+concave it means that the second
+ 
+
+ align:start position:0%
+concave it means that the second
+derivative of this function B has to be
+
+ align:start position:0%
+derivative of this function B has to be
+ 
+
+ align:start position:0%
+derivative of this function B has to be
+strictly uh positive and so that the
+
+ align:start position:0%
+strictly uh positive and so that the
+ 
+
+ align:start position:0%
+strictly uh positive and so that the
+function is convex okay so this is
+
+ align:start position:0%
+function is convex okay so this is
+ 
+
+ align:start position:0%
+function is convex okay so this is
+concave so this is definitely not
+
+ align:start position:0%
+concave so this is definitely not
+ 
+
+ align:start position:0%
+concave so this is definitely not
+working I need to have something that
+
+ align:start position:0%
+working I need to have something that
+ 
+
+ align:start position:0%
+working I need to have something that
+looks like this when I talk about my
+
+ align:start position:0%
+looks like this when I talk about my
+ 
+
+ align:start position:0%
+looks like this when I talk about my
+be okay so Theta squared uh we'll see a
+
+ align:start position:0%
+be okay so Theta squared uh we'll see a
+ 
+
+ align:start position:0%
+be okay so Theta squared uh we'll see a
+bunch exponential Theta you know there's
+
+ align:start position:0%
+bunch exponential Theta you know there's
+ 
+
+ align:start position:0%
+bunch exponential Theta you know there's
+a bunch of them but if you start writing
+
+ align:start position:0%
+a bunch of them but if you start writing
+ 
+
+ align:start position:0%
+a bunch of them but if you start writing
+something and you find B you know try to
+
+ align:start position:0%
+something and you find B you know try to
+ 
+
+ align:start position:0%
+something and you find B you know try to
+think of the plot of B in your mind and
+
+ align:start position:0%
+think of the plot of B in your mind and
+ 
+
+ align:start position:0%
+think of the plot of B in your mind and
+you find that b looks like it's going to
+
+ align:start position:0%
+you find that b looks like it's going to
+ 
+
+ align:start position:0%
+you find that b looks like it's going to
+be concave you've been you've made a
+
+ align:start position:0%
+be concave you've been you've made a
+ 
+
+ align:start position:0%
+be concave you've been you've made a
+sign mistake somewhere
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+all right so we've done a pretty big
+
+ align:start position:0%
+all right so we've done a pretty big
+ 
+
+ align:start position:0%
+all right so we've done a pretty big
+parenthesis to try to characterize what
+
+ align:start position:0%
+parenthesis to try to characterize what
+ 
+
+ align:start position:0%
+parenthesis to try to characterize what
+the distribution of Y was going to be
+
+ align:start position:0%
+the distribution of Y was going to be
+ 
+
+ align:start position:0%
+the distribution of Y was going to be
+right we wanted to extend from say gaan
+
+ align:start position:0%
+right we wanted to extend from say gaan
+ 
+
+ align:start position:0%
+right we wanted to extend from say gaan
+to something else and uh but when we're
+
+ align:start position:0%
+to something else and uh but when we're
+ 
+
+ align:start position:0%
+to something else and uh but when we're
+doing regression which means the
+
+ align:start position:0%
+doing regression which means the
+ 
+
+ align:start position:0%
+doing regression which means the
+generalized linear models we are not
+
+ align:start position:0%
+generalized linear models we are not
+ 
+
+ align:start position:0%
+generalized linear models we are not
+interested in the distribution of Y but
+
+ align:start position:0%
+interested in the distribution of Y but
+ 
+
+ align:start position:0%
+interested in the distribution of Y but
+really the conditional distribution of Y
+
+ align:start position:0%
+really the conditional distribution of Y
+ 
+
+ align:start position:0%
+really the conditional distribution of Y
+given X so I need now to sort of couple
+
+ align:start position:0%
+given X so I need now to sort of couple
+ 
+
+ align:start position:0%
+given X so I need now to sort of couple
+those back together all right so what I
+
+ align:start position:0%
+those back together all right so what I
+ 
+
+ align:start position:0%
+those back together all right so what I
+know is that
+
+ align:start position:0%
+know is that
+ 
+
+ align:start position:0%
+know is that
+this say mu in this case which is the
+
+ align:start position:0%
+this say mu in this case which is the
+ 
+
+ align:start position:0%
+this say mu in this case which is the
+expectation what I want to say is that
+
+ align:start position:0%
+expectation what I want to say is that
+ 
+
+ align:start position:0%
+expectation what I want to say is that
+the conditional expectation of Y uh uh
+
+ align:start position:0%
+the conditional expectation of Y uh uh
+ 
+
+ align:start position:0%
+the conditional expectation of Y uh uh
+given mu sorry the conditional
+
+ align:start position:0%
+given mu sorry the conditional
+ 
+
+ align:start position:0%
+given mu sorry the conditional
+expectation of Y given
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+X this is some mu of X right and when we
+
+ align:start position:0%
+X this is some mu of X right and when we
+ 
+
+ align:start position:0%
+X this is some mu of X right and when we
+did linear models we said well this
+
+ align:start position:0%
+did linear models we said well this
+ 
+
+ align:start position:0%
+did linear models we said well this
+thing was some X transpose beta for
+
+ align:start position:0%
+thing was some X transpose beta for
+ 
+
+ align:start position:0%
+thing was some X transpose beta for
+linear
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+models and the whole premise of this
+
+ align:start position:0%
+models and the whole premise of this
+ 
+
+ align:start position:0%
+models and the whole premise of this
+chapter is to say well this might make
+
+ align:start position:0%
+chapter is to say well this might make
+ 
+
+ align:start position:0%
+chapter is to say well this might make
+no sense because X transpose beta can
+
+ align:start position:0%
+no sense because X transpose beta can
+ 
+
+ align:start position:0%
+no sense because X transpose beta can
+take the entire range of real values
+
+ align:start position:0%
+take the entire range of real values
+ 
+
+ align:start position:0%
+take the entire range of real values
+whereas this mu can take only a partial
+
+ align:start position:0%
+whereas this mu can take only a partial
+ 
+
+ align:start position:0%
+whereas this mu can take only a partial
+range so even if you actually focus on
+
+ align:start position:0%
+range so even if you actually focus on
+ 
+
+ align:start position:0%
+range so even if you actually focus on
+the uh on the pon for example we know
+
+ align:start position:0%
+the uh on the pon for example we know
+ 
+
+ align:start position:0%
+the uh on the pon for example we know
+that the expectation of a Pon has to be
+
+ align:start position:0%
+that the expectation of a Pon has to be
+ 
+
+ align:start position:0%
+that the expectation of a Pon has to be
+a non- negative number actually positive
+
+ align:start position:0%
+a non- negative number actually positive
+ 
+
+ align:start position:0%
+a non- negative number actually positive
+number as soon as you have a little bit
+
+ align:start position:0%
+number as soon as you have a little bit
+ 
+
+ align:start position:0%
+number as soon as you have a little bit
+of variance right it's mu itself mu is a
+
+ align:start position:0%
+of variance right it's mu itself mu is a
+ 
+
+ align:start position:0%
+of variance right it's mu itself mu is a
+positive number and so it's not going to
+
+ align:start position:0%
+positive number and so it's not going to
+ 
+
+ align:start position:0%
+positive number and so it's not going to
+make any sense to assume that mu of X is
+
+ align:start position:0%
+make any sense to assume that mu of X is
+ 
+
+ align:start position:0%
+make any sense to assume that mu of X is
+equal to X transpose beta because you
+
+ align:start position:0%
+equal to X transpose beta because you
+ 
+
+ align:start position:0%
+equal to X transpose beta because you
+might find some x's for which this value
+
+ align:start position:0%
+might find some x's for which this value
+ 
+
+ align:start position:0%
+might find some x's for which this value
+ends up being negative and so we're
+
+ align:start position:0%
+ends up being negative and so we're
+ 
+
+ align:start position:0%
+ends up being negative and so we're
+going to need what we call the link
+
+ align:start position:0%
+going to need what we call the link
+ 
+
+ align:start position:0%
+going to need what we call the link
+function that relates that transforms mu
+
+ align:start position:0%
+function that relates that transforms mu
+ 
+
+ align:start position:0%
+function that relates that transforms mu
+Maps it onto the real line so that you
+
+ align:start position:0%
+Maps it onto the real line so that you
+ 
+
+ align:start position:0%
+Maps it onto the real line so that you
+can now express it of the form X
+
+ align:start position:0%
+can now express it of the form X
+ 
+
+ align:start position:0%
+can now express it of the form X
+transpose beta all right so we're going
+
+ align:start position:0%
+transpose beta all right so we're going
+ 
+
+ align:start position:0%
+transpose beta all right so we're going
+to take um not this but we're going to
+
+ align:start position:0%
+to take um not this but we're going to
+ 
+
+ align:start position:0%
+to take um not this but we're going to
+assume that g of mu of
+
+ align:start position:0%
+assume that g of mu of
+ 
+
+ align:start position:0%
+assume that g of mu of
+X is now equal to Xpose beta and that's
+
+ align:start position:0%
+X is now equal to Xpose beta and that's
+ 
+
+ align:start position:0%
+X is now equal to Xpose beta and that's
+the generalized linear models right
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so as I
+
+ align:start position:0%
+okay so as I
+ 
+
+ align:start position:0%
+okay so as I
+said it's kind of weird to
+
+ align:start position:0%
+said it's kind of weird to
+ 
+
+ align:start position:0%
+said it's kind of weird to
+transform X transpose beta a mu to make
+
+ align:start position:0%
+transform X transpose beta a mu to make
+ 
+
+ align:start position:0%
+transform X transpose beta a mu to make
+it take the real line it feels like at
+
+ align:start position:0%
+it take the real line it feels like at
+ 
+
+ align:start position:0%
+it take the real line it feels like at
+least to me it feels a bit more natural
+
+ align:start position:0%
+least to me it feels a bit more natural
+ 
+
+ align:start position:0%
+least to me it feels a bit more natural
+to take X transpose beta and make it fit
+
+ align:start position:0%
+to take X transpose beta and make it fit
+ 
+
+ align:start position:0%
+to take X transpose beta and make it fit
+to the particular distribution that I
+
+ align:start position:0%
+to the particular distribution that I
+ 
+
+ align:start position:0%
+to the particular distribution that I
+want and so I'm goingon to want to talk
+
+ align:start position:0%
+want and so I'm goingon to want to talk
+ 
+
+ align:start position:0%
+want and so I'm goingon to want to talk
+about G and G inverse at the same time
+
+ align:start position:0%
+about G and G inverse at the same time
+ 
+
+ align:start position:0%
+about G and G inverse at the same time
+so I'm gonna actually take always G so G
+
+ align:start position:0%
+so I'm gonna actually take always G so G
+ 
+
+ align:start position:0%
+so I'm gonna actually take always G so G
+is my link
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+function and I'm going to want G to be
+
+ align:start position:0%
+function and I'm going to want G to be
+ 
+
+ align:start position:0%
+function and I'm going to want G to be
+uh continuously
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+differentiable okay let's say that it
+
+ align:start position:0%
+differentiable okay let's say that it
+ 
+
+ align:start position:0%
+differentiable okay let's say that it
+has a derivative and its derivative is
+
+ align:start position:0%
+has a derivative and its derivative is
+ 
+
+ align:start position:0%
+has a derivative and its derivative is
+uh is continuous and I'm going to want
+
+ align:start position:0%
+uh is continuous and I'm going to want
+ 
+
+ align:start position:0%
+uh is continuous and I'm going to want
+uh uh G to be strictly increased
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay and that actually implies that g
+
+ align:start position:0%
+okay and that actually implies that g
+ 
+
+ align:start position:0%
+okay and that actually implies that g
+inverse exists actually that's not true
+
+ align:start position:0%
+inverse exists actually that's not true
+ 
+
+ align:start position:0%
+inverse exists actually that's not true
+um what I'm also going to
+
+ align:start position:0%
+um what I'm also going to
+ 
+
+ align:start position:0%
+um what I'm also going to
+want is
+
+ align:start position:0%
+want is
+ 
+
+ align:start position:0%
+want is
+that
+
+ align:start position:0%
+that
+ 
+
+ align:start position:0%
+that
+g of
+
+ align:start position:0%
+g of
+ 
+
+ align:start position:0%
+g of
+mu uh
+
+ align:start position:0%
+mu uh
+ 
+
+ align:start position:0%
+mu uh
+spans uh okay how do I do this um uh
+
+ align:start position:0%
+spans uh okay how do I do this um uh
+ 
+
+ align:start position:0%
+spans uh okay how do I do this um uh
+well
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so I want that g as I range for all
+
+ align:start position:0%
+okay so I want that g as I range for all
+ 
+
+ align:start position:0%
+okay so I want that g as I range for all
+possible values of mu whether they're
+
+ align:start position:0%
+possible values of mu whether they're
+ 
+
+ align:start position:0%
+possible values of mu whether they're
+all positive values or whether they're
+
+ align:start position:0%
+all positive values or whether they're
+ 
+
+ align:start position:0%
+all positive values or whether they're
+values that are limited between the
+
+ align:start position:0%
+values that are limited between the
+ 
+
+ align:start position:0%
+values that are limited between the
+interval Z one I want those to span the
+
+ align:start position:0%
+interval Z one I want those to span the
+ 
+
+ align:start position:0%
+interval Z one I want those to span the
+entire real line so that when I want to
+
+ align:start position:0%
+entire real line so that when I want to
+ 
+
+ align:start position:0%
+entire real line so that when I want to
+talk about G inverse is defin over the
+
+ align:start position:0%
+talk about G inverse is defin over the
+ 
+
+ align:start position:0%
+talk about G inverse is defin over the
+entire real line I know where I started
+
+ align:start position:0%
+entire real line I know where I started
+ 
+
+ align:start position:0%
+entire real line I know where I started
+okay so uh uh uh this implies that g
+
+ align:start position:0%
+okay so uh uh uh this implies that g
+ 
+
+ align:start position:0%
+okay so uh uh uh this implies that g
+inverse exists
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+what else does it imply about G
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+inverse so for a function to be
+
+ align:start position:0%
+inverse so for a function to be
+ 
+
+ align:start position:0%
+inverse so for a function to be
+invertible only I only need for it to be
+
+ align:start position:0%
+invertible only I only need for it to be
+ 
+
+ align:start position:0%
+invertible only I only need for it to be
+strictly monotone right I don't need it
+
+ align:start position:0%
+strictly monotone right I don't need it
+ 
+
+ align:start position:0%
+strictly monotone right I don't need it
+to be strictly increasing so in
+
+ align:start position:0%
+to be strictly increasing so in
+ 
+
+ align:start position:0%
+to be strictly increasing so in
+particular the fact that I picked
+
+ align:start position:0%
+particular the fact that I picked
+ 
+
+ align:start position:0%
+particular the fact that I picked
+increasing implies that this guy is
+
+ align:start position:0%
+increasing implies that this guy is
+ 
+
+ align:start position:0%
+increasing implies that this guy is
+actually
+
+ align:start position:0%
+actually
+ 
+
+ align:start position:0%
+actually
+increasing
+
+ align:start position:0%
+increasing
+ 
+
+ align:start position:0%
+increasing
+okay uh that's the image
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so this is my uh link function and
+
+ align:start position:0%
+okay so this is my uh link function and
+ 
+
+ align:start position:0%
+okay so this is my uh link function and
+this slide is just telling me I want my
+
+ align:start position:0%
+this slide is just telling me I want my
+ 
+
+ align:start position:0%
+this slide is just telling me I want my
+function to be invertible so I can talk
+
+ align:start position:0%
+function to be invertible so I can talk
+ 
+
+ align:start position:0%
+function to be invertible so I can talk
+about G inverse I'm going to switch
+
+ align:start position:0%
+about G inverse I'm going to switch
+ 
+
+ align:start position:0%
+about G inverse I'm going to switch
+between the two so what link functions
+
+ align:start position:0%
+between the two so what link functions
+ 
+
+ align:start position:0%
+between the two so what link functions
+am I going to get right so for linear
+
+ align:start position:0%
+am I going to get right so for linear
+ 
+
+ align:start position:0%
+am I going to get right so for linear
+models we just said there's no link
+
+ align:start position:0%
+models we just said there's no link
+ 
+
+ align:start position:0%
+models we just said there's no link
+function which is the same as saying
+
+ align:start position:0%
+function which is the same as saying
+ 
+
+ align:start position:0%
+function which is the same as saying
+that the link function is identity which
+
+ align:start position:0%
+that the link function is identity which
+ 
+
+ align:start position:0%
+that the link function is identity which
+certainly satisfies all these conditions
+
+ align:start position:0%
+certainly satisfies all these conditions
+ 
+
+ align:start position:0%
+certainly satisfies all these conditions
+it's invertible it has all these nice
+
+ align:start position:0%
+it's invertible it has all these nice
+ 
+
+ align:start position:0%
+it's invertible it has all these nice
+properties but you know might as well
+
+ align:start position:0%
+properties but you know might as well
+ 
+
+ align:start position:0%
+properties but you know might as well
+not talk about it for Pon data when we
+
+ align:start position:0%
+not talk about it for Pon data when we
+ 
+
+ align:start position:0%
+not talk about it for Pon data when we
+assume that the conditional distribution
+
+ align:start position:0%
+assume that the conditional distribution
+ 
+
+ align:start position:0%
+assume that the conditional distribution
+of Y given X is
+
+ align:start position:0%
+of Y given X is
+ 
+
+ align:start position:0%
+of Y given X is
+Pon then mu as I just said is required
+
+ align:start position:0%
+Pon then mu as I just said is required
+ 
+
+ align:start position:0%
+Pon then mu as I just said is required
+to be positive so I need a g that goes
+
+ align:start position:0%
+to be positive so I need a g that goes
+ 
+
+ align:start position:0%
+to be positive so I need a g that goes
+from the
+
+ align:start position:0%
+from the
+ 
+
+ align:start position:0%
+from the
+interval zero Infinity to the entire
+
+ align:start position:0%
+interval zero Infinity to the entire
+ 
+
+ align:start position:0%
+interval zero Infinity to the entire
+real line I need a function that starts
+
+ align:start position:0%
+real line I need a function that starts
+ 
+
+ align:start position:0%
+real line I need a function that starts
+from one end and just you know takes not
+
+ align:start position:0%
+from one end and just you know takes not
+ 
+
+ align:start position:0%
+from one end and just you know takes not
+only the the positive values are split
+
+ align:start position:0%
+only the the positive values are split
+ 
+
+ align:start position:0%
+only the the positive values are split
+between positive and negative values and
+
+ align:start position:0%
+between positive and negative values and
+ 
+
+ align:start position:0%
+between positive and negative values and
+here for example I could take the log
+
+ align:start position:0%
+here for example I could take the log
+ 
+
+ align:start position:0%
+here for example I could take the log
+link right so the log
+
+ align:start position:0%
+link right so the log
+ 
+
+ align:start position:0%
+link right so the log
+is defined on this entire
+
+ align:start position:0%
+is defined on this entire
+ 
+
+ align:start position:0%
+is defined on this entire
+interval and as I range from zero to
+
+ align:start position:0%
+interval and as I range from zero to
+ 
+
+ align:start position:0%
+interval and as I range from zero to
+plus infinity the log is ranging from
+
+ align:start position:0%
+plus infinity the log is ranging from
+ 
+
+ align:start position:0%
+plus infinity the log is ranging from
+negative Infinity to plus infinity
+
+ align:start position:0%
+negative Infinity to plus infinity
+ 
+
+ align:start position:0%
+negative Infinity to plus infinity
+right so you know you can probably think
+
+ align:start position:0%
+right so you know you can probably think
+ 
+
+ align:start position:0%
+right so you know you can probably think
+of other functions that do that like two
+
+ align:start position:0%
+of other functions that do that like two
+ 
+
+ align:start position:0%
+of other functions that do that like two
+times log that's another one right but
+
+ align:start position:0%
+times log that's another one right but
+ 
+
+ align:start position:0%
+times log that's another one right but
+there's many other you can think of and
+
+ align:start position:0%
+there's many other you can think of and
+ 
+
+ align:start position:0%
+there's many other you can think of and
+uh but let's say the log is one of them
+
+ align:start position:0%
+uh but let's say the log is one of them
+ 
+
+ align:start position:0%
+uh but let's say the log is one of them
+that you might want to think
+
+ align:start position:0%
+that you might want to think
+ 
+
+ align:start position:0%
+that you might want to think
+about
+
+ align:start position:0%
+about
+ 
+
+ align:start position:0%
+about
+um then um
+
+ align:start position:0%
+um then um
+ 
+
+ align:start position:0%
+um then um
+there's uh um and we'll see that this is
+
+ align:start position:0%
+there's uh um and we'll see that this is
+ 
+
+ align:start position:0%
+there's uh um and we'll see that this is
+actually I mean it is a natural one in
+
+ align:start position:0%
+actually I mean it is a natural one in
+ 
+
+ align:start position:0%
+actually I mean it is a natural one in
+the sense that it's one of the first
+
+ align:start position:0%
+the sense that it's one of the first
+ 
+
+ align:start position:0%
+the sense that it's one of the first
+function we can think of it we'll see
+
+ align:start position:0%
+function we can think of it we'll see
+ 
+
+ align:start position:0%
+function we can think of it we'll see
+also that it has another canonical
+
+ align:start position:0%
+also that it has another canonical
+ 
+
+ align:start position:0%
+also that it has another canonical
+property that makes it a Natural Choice
+
+ align:start position:0%
+property that makes it a Natural Choice
+ 
+
+ align:start position:0%
+property that makes it a Natural Choice
+uh the other one is uh the other example
+
+ align:start position:0%
+uh the other one is uh the other example
+ 
+
+ align:start position:0%
+uh the other one is uh the other example
+where we had a even stronger condition
+
+ align:start position:0%
+where we had a even stronger condition
+ 
+
+ align:start position:0%
+where we had a even stronger condition
+on what mu could be mu could only be a
+
+ align:start position:0%
+on what mu could be mu could only be a
+ 
+
+ align:start position:0%
+on what mu could be mu could only be a
+number between zero and one that was the
+
+ align:start position:0%
+number between zero and one that was the
+ 
+
+ align:start position:0%
+number between zero and one that was the
+probability of success of a coin flip
+
+ align:start position:0%
+probability of success of a coin flip
+ 
+
+ align:start position:0%
+probability of success of a coin flip
+right the probability of success of a
+
+ align:start position:0%
+right the probability of success of a
+ 
+
+ align:start position:0%
+right the probability of success of a
+burnly random variable and now I need G
+
+ align:start position:0%
+burnly random variable and now I need G
+ 
+
+ align:start position:0%
+burnly random variable and now I need G
+to map zero one to the entire real line
+
+ align:start position:0%
+to map zero one to the entire real line
+ 
+
+ align:start position:0%
+to map zero one to the entire real line
+and so here are a bunch of uh of things
+
+ align:start position:0%
+and so here are a bunch of uh of things
+ 
+
+ align:start position:0%
+and so here are a bunch of uh of things
+that you can come up with because you
+
+ align:start position:0%
+that you can come up with because you
+ 
+
+ align:start position:0%
+that you can come up with because you
+know now you start to have maybe I mean
+
+ align:start position:0%
+know now you start to have maybe I mean
+ 
+
+ align:start position:0%
+know now you start to have maybe I mean
+you know I claim I will soon claim that
+
+ align:start position:0%
+you know I claim I will soon claim that
+ 
+
+ align:start position:0%
+you know I claim I will soon claim that
+this one log of mu divided by one minus
+
+ align:start position:0%
+this one log of mu divided by one minus
+ 
+
+ align:start position:0%
+this one log of mu divided by one minus
+mu is the most natural one but maybe you
+
+ align:start position:0%
+mu is the most natural one but maybe you
+ 
+
+ align:start position:0%
+mu is the most natural one but maybe you
+know if you had never thought of this
+
+ align:start position:0%
+know if you had never thought of this
+ 
+
+ align:start position:0%
+know if you had never thought of this
+that might not be the most the first
+
+ align:start position:0%
+that might not be the most the first
+ 
+
+ align:start position:0%
+that might not be the most the first
+function you would come up with right uh
+
+ align:start position:0%
+function you would come up with right uh
+ 
+
+ align:start position:0%
+function you would come up with right uh
+you mentioned trigonometric functions
+
+ align:start position:0%
+you mentioned trigonometric functions
+ 
+
+ align:start position:0%
+you mentioned trigonometric functions
+for example uh so you know maybe you can
+
+ align:start position:0%
+for example uh so you know maybe you can
+ 
+
+ align:start position:0%
+for example uh so you know maybe you can
+come up with something that like you
+
+ align:start position:0%
+come up with something that like you
+ 
+
+ align:start position:0%
+come up with something that like you
+know comes from I don't know hyper um uh
+
+ align:start position:0%
+know comes from I don't know hyper um uh
+ 
+
+ align:start position:0%
+know comes from I don't know hyper um uh
+hyperbolic trigonometry or something so
+
+ align:start position:0%
+hyperbolic trigonometry or something so
+ 
+
+ align:start position:0%
+hyperbolic trigonometry or something so
+what does this function do well we'll
+
+ align:start position:0%
+what does this function do well we'll
+ 
+
+ align:start position:0%
+what does this function do well we'll
+see a picture but this function does map
+
+ align:start position:0%
+see a picture but this function does map
+ 
+
+ align:start position:0%
+see a picture but this function does map
+the interval 01 to the entire real line
+
+ align:start position:0%
+the interval 01 to the entire real line
+ 
+
+ align:start position:0%
+the interval 01 to the entire real line
+we also discussed the fact that if we
+
+ align:start position:0%
+we also discussed the fact that if we
+ 
+
+ align:start position:0%
+we also discussed the fact that if we
+think
+
+ align:start position:0%
+think
+ 
+
+ align:start position:0%
+think
+reciprocally uh well a function uh what
+
+ align:start position:0%
+reciprocally uh well a function uh what
+ 
+
+ align:start position:0%
+reciprocally uh well a function uh what
+I want if I want to think about G
+
+ align:start position:0%
+I want if I want to think about G
+ 
+
+ align:start position:0%
+I want if I want to think about G
+inverse I want a function that Maps the
+
+ align:start position:0%
+inverse I want a function that Maps the
+ 
+
+ align:start position:0%
+inverse I want a function that Maps the
+entire real line into the unit interval
+
+ align:start position:0%
+entire real line into the unit interval
+ 
+
+ align:start position:0%
+entire real line into the unit interval
+and as we said if I'm not a very
+
+ align:start position:0%
+and as we said if I'm not a very
+ 
+
+ align:start position:0%
+and as we said if I'm not a very
+creative statistici or problemist I can
+
+ align:start position:0%
+creative statistici or problemist I can
+ 
+
+ align:start position:0%
+creative statistici or problemist I can
+just pick my favorites continuous
+
+ align:start position:0%
+just pick my favorites continuous
+ 
+
+ align:start position:0%
+just pick my favorites continuous
+strictly increasing uh cumulative
+
+ align:start position:0%
+strictly increasing uh cumulative
+ 
+
+ align:start position:0%
+strictly increasing uh cumulative
+distribution function which as we know
+
+ align:start position:0%
+distribution function which as we know
+ 
+
+ align:start position:0%
+distribution function which as we know
+will arise as soon as I have a density
+
+ align:start position:0%
+will arise as soon as I have a density
+ 
+
+ align:start position:0%
+will arise as soon as I have a density
+that has support on the entire real line
+
+ align:start position:0%
+that has support on the entire real line
+ 
+
+ align:start position:0%
+that has support on the entire real line
+right if I have support everywhere then
+
+ align:start position:0%
+right if I have support everywhere then
+ 
+
+ align:start position:0%
+right if I have support everywhere then
+it means that my um
+
+ align:start position:0%
+it means that my um
+ 
+
+ align:start position:0%
+it means that my um
+uh by meaning that the fun the density
+
+ align:start position:0%
+uh by meaning that the fun the density
+ 
+
+ align:start position:0%
+uh by meaning that the fun the density
+is strictly positive everywhere then it
+
+ align:start position:0%
+is strictly positive everywhere then it
+ 
+
+ align:start position:0%
+is strictly positive everywhere then it
+means that my uh uh communative
+
+ align:start position:0%
+means that my uh uh communative
+ 
+
+ align:start position:0%
+means that my uh uh communative
+distribution function has to be strictly
+
+ align:start position:0%
+distribution function has to be strictly
+ 
+
+ align:start position:0%
+distribution function has to be strictly
+increasing and of course it has to go
+
+ align:start position:0%
+increasing and of course it has to go
+ 
+
+ align:start position:0%
+increasing and of course it has to go
+from zero to one because that's just
+
+ align:start position:0%
+from zero to one because that's just
+ 
+
+ align:start position:0%
+from zero to one because that's just
+nature of those things and so for
+
+ align:start position:0%
+nature of those things and so for
+ 
+
+ align:start position:0%
+nature of those things and so for
+example I can take the gussan that's one
+
+ align:start position:0%
+example I can take the gussan that's one
+ 
+
+ align:start position:0%
+example I can take the gussan that's one
+such function but I could also take you
+
+ align:start position:0%
+such function but I could also take you
+ 
+
+ align:start position:0%
+such function but I could also take you
+know the double exponential that looks
+
+ align:start position:0%
+know the double exponential that looks
+ 
+
+ align:start position:0%
+know the double exponential that looks
+like an exponential on one end and an
+
+ align:start position:0%
+like an exponential on one end and an
+ 
+
+ align:start position:0%
+like an exponential on one end and an
+exponential on the other end and uh uh
+
+ align:start position:0%
+exponential on the other end and uh uh
+ 
+
+ align:start position:0%
+exponential on the other end and uh uh
+uh basically if you take uh something
+
+ align:start position:0%
+uh basically if you take uh something
+ 
+
+ align:start position:0%
+uh basically if you take uh something
+which is called uh which if you take
+
+ align:start position:0%
+which is called uh which if you take
+ 
+
+ align:start position:0%
+which is called uh which if you take
+capital F which is the um gaussian
+
+ align:start position:0%
+capital F which is the um gaussian
+ 
+
+ align:start position:0%
+capital F which is the um gaussian
+standard gaussian Cula distribution
+
+ align:start position:0%
+standard gaussian Cula distribution
+ 
+
+ align:start position:0%
+standard gaussian Cula distribution
+function it does work for you and you
+
+ align:start position:0%
+function it does work for you and you
+ 
+
+ align:start position:0%
+function it does work for you and you
+can take its inverse and in this case we
+
+ align:start position:0%
+can take its inverse and in this case we
+ 
+
+ align:start position:0%
+can take its inverse and in this case we
+don't talk about so this guy is called
+
+ align:start position:0%
+don't talk about so this guy is called
+ 
+
+ align:start position:0%
+don't talk about so this guy is called
+logit or logit and this guy is called
+
+ align:start position:0%
+logit or logit and this guy is called
+ 
+
+ align:start position:0%
+logit or logit and this guy is called
+proit and you see it usually every time
+
+ align:start position:0%
+proit and you see it usually every time
+ 
+
+ align:start position:0%
+proit and you see it usually every time
+you have a package on uh a Iz in your
+
+ align:start position:0%
+you have a package on uh a Iz in your
+ 
+
+ align:start position:0%
+you have a package on uh a Iz in your
+models uh you're trying to implement you
+
+ align:start position:0%
+models uh you're trying to implement you
+ 
+
+ align:start position:0%
+models uh you're trying to implement you
+have this choice and for what's called
+
+ align:start position:0%
+have this choice and for what's called
+ 
+
+ align:start position:0%
+have this choice and for what's called
+logistic regression so it's kind of
+
+ align:start position:0%
+logistic regression so it's kind of
+ 
+
+ align:start position:0%
+logistic regression so it's kind of
+funny that it's called logistic
+
+ align:start position:0%
+funny that it's called logistic
+ 
+
+ align:start position:0%
+funny that it's called logistic
+regression but you can actually use the
+
+ align:start position:0%
+regression but you can actually use the
+ 
+
+ align:start position:0%
+regression but you can actually use the
+proit link which in this case is get I
+
+ align:start position:0%
+proit link which in this case is get I
+ 
+
+ align:start position:0%
+proit link which in this case is get I
+guess is called proit regression but
+
+ align:start position:0%
+guess is called proit regression but
+ 
+
+ align:start position:0%
+guess is called proit regression but
+those things are essentially equivalent
+
+ align:start position:0%
+those things are essentially equivalent
+ 
+
+ align:start position:0%
+those things are essentially equivalent
+and it's really a matter of taste okay
+
+ align:start position:0%
+and it's really a matter of taste okay
+ 
+
+ align:start position:0%
+and it's really a matter of taste okay
+maybe of community some communities
+
+ align:start position:0%
+maybe of community some communities
+ 
+
+ align:start position:0%
+maybe of community some communities
+might prefer one or the other we'll see
+
+ align:start position:0%
+might prefer one or the other we'll see
+ 
+
+ align:start position:0%
+might prefer one or the other we'll see
+that again as I claimed before the
+
+ align:start position:0%
+that again as I claimed before the
+ 
+
+ align:start position:0%
+that again as I claimed before the
+logistic one the lit one uh is uh has a
+
+ align:start position:0%
+logistic one the lit one uh is uh has a
+ 
+
+ align:start position:0%
+logistic one the lit one uh is uh has a
+slightly more compelling argument for
+
+ align:start position:0%
+slightly more compelling argument for
+ 
+
+ align:start position:0%
+slightly more compelling argument for
+its reason to exist I guess this one the
+
+ align:start position:0%
+its reason to exist I guess this one the
+ 
+
+ align:start position:0%
+its reason to exist I guess this one the
+compelling argument is that is involved
+
+ align:start position:0%
+compelling argument is that is involved
+ 
+
+ align:start position:0%
+compelling argument is that is involved
+the central uh the standard gaussian
+
+ align:start position:0%
+the central uh the standard gaussian
+ 
+
+ align:start position:0%
+the central uh the standard gaussian
+which of course is something that should
+
+ align:start position:0%
+which of course is something that should
+ 
+
+ align:start position:0%
+which of course is something that should
+show up everywhere and then you can
+
+ align:start position:0%
+show up everywhere and then you can
+ 
+
+ align:start position:0%
+show up everywhere and then you can
+think about crazy stuff okay something
+
+ align:start position:0%
+think about crazy stuff okay something
+ 
+
+ align:start position:0%
+think about crazy stuff okay something
+that even even crazy gets a name uh
+
+ align:start position:0%
+that even even crazy gets a name uh
+ 
+
+ align:start position:0%
+that even even crazy gets a name uh
+complimentary log log which is the log
+
+ align:start position:0%
+complimentary log log which is the log
+ 
+
+ align:start position:0%
+complimentary log log which is the log
+of minus log one minus okay you know why
+
+ align:start position:0%
+of minus log one minus okay you know why
+ 
+
+ align:start position:0%
+of minus log one minus okay you know why
+not
+
+ align:start position:0%
+not
+ 
+
+ align:start position:0%
+not
+um so I guess you can iterate that thing
+
+ align:start position:0%
+um so I guess you can iterate that thing
+ 
+
+ align:start position:0%
+um so I guess you can iterate that thing
+right you can just do put a One log one
+
+ align:start position:0%
+right you can just do put a One log one
+ 
+
+ align:start position:0%
+right you can just do put a One log one
+minus in front of this thing it's still
+
+ align:start position:0%
+minus in front of this thing it's still
+ 
+
+ align:start position:0%
+minus in front of this thing it's still
+going to go all right so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um that's not true I have to put a minus
+
+ align:start position:0%
+um that's not true I have to put a minus
+ 
+
+ align:start position:0%
+um that's not true I have to put a minus
+and take another
+
+ align:start position:0%
+and take another
+ 
+
+ align:start position:0%
+and take another
+another no that's not true okay so um
+
+ align:start position:0%
+another no that's not true okay so um
+ 
+
+ align:start position:0%
+another no that's not true okay so um
+okay so you can think of whatever you
+
+ align:start position:0%
+okay so you can think of whatever you
+ 
+
+ align:start position:0%
+okay so you can think of whatever you
+want but now um uh you can actually so I
+
+ align:start position:0%
+want but now um uh you can actually so I
+ 
+
+ align:start position:0%
+want but now um uh you can actually so I
+I'll show so I claim that the lit link
+
+ align:start position:0%
+I'll show so I claim that the lit link
+ 
+
+ align:start position:0%
+I'll show so I claim that the lit link
+is the Natural Choice so here's a
+
+ align:start position:0%
+is the Natural Choice so here's a
+ 
+
+ align:start position:0%
+is the Natural Choice so here's a
+picture I should have actually plotted
+
+ align:start position:0%
+picture I should have actually plotted
+ 
+
+ align:start position:0%
+picture I should have actually plotted
+the other one uh so we can actually
+
+ align:start position:0%
+the other one uh so we can actually
+ 
+
+ align:start position:0%
+the other one uh so we can actually
+compare it uh to be fair I don't even
+
+ align:start position:0%
+compare it uh to be fair I don't even
+ 
+
+ align:start position:0%
+compare it uh to be fair I don't even
+remember how it would actually fit in
+
+ align:start position:0%
+remember how it would actually fit in
+ 
+
+ align:start position:0%
+remember how it would actually fit in
+those uh in those two functions so the
+
+ align:start position:0%
+those uh in those two functions so the
+ 
+
+ align:start position:0%
+those uh in those two functions so the
+blue one which is this one for those of
+
+ align:start position:0%
+blue one which is this one for those of
+ 
+
+ align:start position:0%
+blue one which is this one for those of
+you who don't see the difference between
+
+ align:start position:0%
+you who don't see the difference between
+ 
+
+ align:start position:0%
+you who don't see the difference between
+blue and red sorry about that uh so this
+
+ align:start position:0%
+blue and red sorry about that uh so this
+ 
+
+ align:start position:0%
+blue and red sorry about that uh so this
+is the so the blue one is the uh
+
+ align:start position:0%
+is the so the blue one is the uh
+ 
+
+ align:start position:0%
+is the so the blue one is the uh
+logistic one so that's okay so this guy
+
+ align:start position:0%
+logistic one so that's okay so this guy
+ 
+
+ align:start position:0%
+logistic one so that's okay so this guy
+is the function that does e todx over 1
+
+ align:start position:0%
+is the function that does e todx over 1
+ 
+
+ align:start position:0%
+is the function that does e todx over 1
+plus e todx as you can see this is a
+
+ align:start position:0%
+plus e todx as you can see this is a
+ 
+
+ align:start position:0%
+plus e todx as you can see this is a
+function that's supposed to map the
+
+ align:start position:0%
+function that's supposed to map the
+ 
+
+ align:start position:0%
+function that's supposed to map the
+entire real line into the interval 01
+
+ align:start position:0%
+entire real line into the interval 01
+ 
+
+ align:start position:0%
+entire real line into the interval 01
+okay so that's supposed to be the in
+
+ align:start position:0%
+okay so that's supposed to be the in
+ 
+
+ align:start position:0%
+okay so that's supposed to be the in
+inverse of your function and I claim
+
+ align:start position:0%
+inverse of your function and I claim
+ 
+
+ align:start position:0%
+inverse of your function and I claim
+that this is the inverse of the logistic
+
+ align:start position:0%
+that this is the inverse of the logistic
+ 
+
+ align:start position:0%
+that this is the inverse of the logistic
+of the late function and the blue one
+
+ align:start position:0%
+of the late function and the blue one
+ 
+
+ align:start position:0%
+of the late function and the blue one
+well this is the gon CDF so you know
+
+ align:start position:0%
+well this is the gon CDF so you know
+ 
+
+ align:start position:0%
+well this is the gon CDF so you know
+it's clearly the inverse of the inverse
+
+ align:start position:0%
+it's clearly the inverse of the inverse
+ 
+
+ align:start position:0%
+it's clearly the inverse of the inverse
+of the ga and CDF and that's the red one
+
+ align:start position:0%
+of the ga and CDF and that's the red one
+ 
+
+ align:start position:0%
+of the ga and CDF and that's the red one
+that's the one that goes here so one of
+
+ align:start position:0%
+that's the one that goes here so one of
+ 
+
+ align:start position:0%
+that's the one that goes here so one of
+the thing uh that I would guess that the
+
+ align:start position:0%
+the thing uh that I would guess that the
+ 
+
+ align:start position:0%
+the thing uh that I would guess that the
+complementary log log is something
+
+ align:start position:0%
+complementary log log is something
+ 
+
+ align:start position:0%
+complementary log log is something
+that's probably going above here and for
+
+ align:start position:0%
+that's probably going above here and for
+ 
+
+ align:start position:0%
+that's probably going above here and for
+which the slope is actually even a
+
+ align:start position:0%
+which the slope is actually even a
+ 
+
+ align:start position:0%
+which the slope is actually even a
+little flatter as you cross uh zero okay
+
+ align:start position:0%
+little flatter as you cross uh zero okay
+ 
+
+ align:start position:0%
+little flatter as you cross uh zero okay
+um so okay so of course this is not our
+
+ align:start position:0%
+um so okay so of course this is not our
+ 
+
+ align:start position:0%
+um so okay so of course this is not our
+link functions these are the inverse of
+
+ align:start position:0%
+link functions these are the inverse of
+ 
+
+ align:start position:0%
+link functions these are the inverse of
+our link function so what do they look
+
+ align:start position:0%
+our link function so what do they look
+ 
+
+ align:start position:0%
+our link function so what do they look
+like when I actually basically flip my
+
+ align:start position:0%
+like when I actually basically flip my
+ 
+
+ align:start position:0%
+like when I actually basically flip my
+uh my thing like this so this is what I
+
+ align:start position:0%
+uh my thing like this so this is what I
+ 
+
+ align:start position:0%
+uh my thing like this so this is what I
+see okay and so I can see that in blue
+
+ align:start position:0%
+see okay and so I can see that in blue
+ 
+
+ align:start position:0%
+see okay and so I can see that in blue
+this is my logistic link so I have it
+
+ align:start position:0%
+this is my logistic link so I have it
+ 
+
+ align:start position:0%
+this is my logistic link so I have it
+crosses zero with a slightly faster rate
+
+ align:start position:0%
+crosses zero with a slightly faster rate
+ 
+
+ align:start position:0%
+crosses zero with a slightly faster rate
+remember our hope if we could use the
+
+ align:start position:0%
+remember our hope if we could use the
+ 
+
+ align:start position:0%
+remember our hope if we could use the
+identity that would be very nice to us
+
+ align:start position:0%
+identity that would be very nice to us
+ 
+
+ align:start position:0%
+identity that would be very nice to us
+right we would just want to take the
+
+ align:start position:0%
+right we would just want to take the
+ 
+
+ align:start position:0%
+right we would just want to take the
+identity the problem is that if I start
+
+ align:start position:0%
+identity the problem is that if I start
+ 
+
+ align:start position:0%
+identity the problem is that if I start
+you know having the identity that goes
+
+ align:start position:0%
+you know having the identity that goes
+ 
+
+ align:start position:0%
+you know having the identity that goes
+here it's GNA start being a problem and
+
+ align:start position:0%
+here it's GNA start being a problem and
+ 
+
+ align:start position:0%
+here it's GNA start being a problem and
+this is the um um uh the the provit link
+
+ align:start position:0%
+this is the um um uh the the provit link
+ 
+
+ align:start position:0%
+this is the um um uh the the provit link
+the F inverse that you see here it's a
+
+ align:start position:0%
+the F inverse that you see here it's a
+ 
+
+ align:start position:0%
+the F inverse that you see here it's a
+little flatter uh I mean you can check
+
+ align:start position:0%
+little flatter uh I mean you can check
+ 
+
+ align:start position:0%
+little flatter uh I mean you can check
+right what uh you can compute the
+
+ align:start position:0%
+right what uh you can compute the
+ 
+
+ align:start position:0%
+right what uh you can compute the
+derivative uh at zero of those guys and
+
+ align:start position:0%
+derivative uh at zero of those guys and
+ 
+
+ align:start position:0%
+derivative uh at zero of those guys and
+you will see that the what is the
+
+ align:start position:0%
+you will see that the what is the
+ 
+
+ align:start position:0%
+you will see that the what is the
+derivative of
+
+ align:start position:0%
+derivative of
+ 
+
+ align:start position:0%
+derivative of
+the so log so I'm taking the derivative
+
+ align:start position:0%
+the so log so I'm taking the derivative
+ 
+
+ align:start position:0%
+the so log so I'm taking the derivative
+of log of x over 1 - x so it's uh 1 /x
+
+ align:start position:0%
+of log of x over 1 - x so it's uh 1 /x
+ 
+
+ align:start position:0%
+of log of x over 1 - x so it's uh 1 /x
+uh Min - one overx no uh minus one over
+
+ align:start position:0%
+uh Min - one overx no uh minus one over
+ 
+
+ align:start position:0%
+uh Min - one overx no uh minus one over
+1 -
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+x okay so if I look at 0.5 actually
+
+ align:start position:0%
+x okay so if I look at 0.5 actually
+ 
+
+ align:start position:0%
+x okay so if I look at 0.5 actually
+sorry this is the interval 01 so I'm
+
+ align:start position:0%
+sorry this is the interval 01 so I'm
+ 
+
+ align:start position:0%
+sorry this is the interval 01 so I'm
+interested in the slope at 0.5
+
+ align:start position:0%
+interested in the slope at 0.5
+ 
+
+ align:start position:0%
+interested in the slope at 0.5
+so no
+
+ align:start position:0%
+so no
+ 
+
+ align:start position:0%
+so no
+uh yes Plus thank you so at 0.5 what I
+
+ align:start position:0%
+uh yes Plus thank you so at 0.5 what I
+ 
+
+ align:start position:0%
+uh yes Plus thank you so at 0.5 what I
+get is uh 2 + two
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah okay so
+
+ align:start position:0%
+yeah okay so
+ 
+
+ align:start position:0%
+yeah okay so
+that's okay so that's the slope that we
+
+ align:start position:0%
+that's okay so that's the slope that we
+ 
+
+ align:start position:0%
+that's okay so that's the slope that we
+get and if you compute for uh
+
+ align:start position:0%
+get and if you compute for uh
+ 
+
+ align:start position:0%
+get and if you compute for uh
+derivative what is the derivative of f
+
+ align:start position:0%
+derivative what is the derivative of f
+ 
+
+ align:start position:0%
+derivative what is the derivative of f
+inverse well it's a little fi of x
+
+ align:start position:0%
+inverse well it's a little fi of x
+ 
+
+ align:start position:0%
+inverse well it's a little fi of x
+divided by little fi of capital F
+
+ align:start position:0%
+divided by little fi of capital F
+ 
+
+ align:start position:0%
+divided by little fi of capital F
+inverse of
+
+ align:start position:0%
+inverse of
+ 
+
+ align:start position:0%
+inverse of
+X so little fi
+
+ align:start position:0%
+X so little fi
+ 
+
+ align:start position:0%
+X so little fi
+at at one2 I don't
+
+ align:start position:0%
+at at one2 I don't
+ 
+
+ align:start position:0%
+at at one2 I don't
+know uh
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah I guess I can probably compute the
+
+ align:start position:0%
+yeah I guess I can probably compute the
+ 
+
+ align:start position:0%
+yeah I guess I can probably compute the
+derivative of capital fi at zero which
+
+ align:start position:0%
+derivative of capital fi at zero which
+ 
+
+ align:start position:0%
+derivative of capital fi at zero which
+is going to be just one over square2 pi
+
+ align:start position:0%
+is going to be just one over square2 pi
+ 
+
+ align:start position:0%
+is going to be just one over square2 pi
+and then just say well the slope has to
+
+ align:start position:0%
+and then just say well the slope has to
+ 
+
+ align:start position:0%
+and then just say well the slope has to
+be you know one over
+
+ align:start position:0%
+be you know one over
+ 
+
+ align:start position:0%
+be you know one over
+that um okay so you know S 2 pi
+
+ align:start position:0%
+that um okay so you know S 2 pi
+ 
+
+ align:start position:0%
+that um okay so you know S 2 pi
+um okay so that's just a comparison but
+
+ align:start position:0%
+um okay so that's just a comparison but
+ 
+
+ align:start position:0%
+um okay so that's just a comparison but
+again so far we do not have any reason
+
+ align:start position:0%
+again so far we do not have any reason
+ 
+
+ align:start position:0%
+again so far we do not have any reason
+to prefer one to the other and so now
+
+ align:start position:0%
+to prefer one to the other and so now
+ 
+
+ align:start position:0%
+to prefer one to the other and so now
+I'm going to start giving you some
+
+ align:start position:0%
+I'm going to start giving you some
+ 
+
+ align:start position:0%
+I'm going to start giving you some
+reasons to prefer one one to the other
+
+ align:start position:0%
+reasons to prefer one one to the other
+ 
+
+ align:start position:0%
+reasons to prefer one one to the other
+and uh one of those two and actually for
+
+ align:start position:0%
+and uh one of those two and actually for
+ 
+
+ align:start position:0%
+and uh one of those two and actually for
+each canonical family there is something
+
+ align:start position:0%
+each canonical family there is something
+ 
+
+ align:start position:0%
+each canonical family there is something
+which is called the canonical link and
+
+ align:start position:0%
+which is called the canonical link and
+ 
+
+ align:start position:0%
+which is called the canonical link and
+when you don't have any other reasons to
+
+ align:start position:0%
+when you don't have any other reasons to
+ 
+
+ align:start position:0%
+when you don't have any other reasons to
+choose anything else why not choose the
+
+ align:start position:0%
+choose anything else why not choose the
+ 
+
+ align:start position:0%
+choose anything else why not choose the
+canonical one and the canonical link is
+
+ align:start position:0%
+canonical one and the canonical link is
+ 
+
+ align:start position:0%
+canonical one and the canonical link is
+the one that says okay what I want is g
+
+ align:start position:0%
+the one that says okay what I want is g
+ 
+
+ align:start position:0%
+the one that says okay what I want is g
+to map me onto the real line
+
+ align:start position:0%
+to map me onto the real line
+ 
+
+ align:start position:0%
+to map me onto the real line
+right
+
+ align:start position:0%
+right
+ 
+
+ align:start position:0%
+right
+and but me is not the parameter of my
+
+ align:start position:0%
+and but me is not the parameter of my
+ 
+
+ align:start position:0%
+and but me is not the parameter of my
+canonical family right I mean it's just
+
+ align:start position:0%
+canonical family right I mean it's just
+ 
+
+ align:start position:0%
+canonical family right I mean it's just
+so here for example mu is e of theta but
+
+ align:start position:0%
+so here for example mu is e of theta but
+ 
+
+ align:start position:0%
+so here for example mu is e of theta but
+the canonical parameter is
+
+ align:start position:0%
+the canonical parameter is
+ 
+
+ align:start position:0%
+the canonical parameter is
+Theta and uh but the the parameter of a
+
+ align:start position:0%
+Theta and uh but the the parameter of a
+ 
+
+ align:start position:0%
+Theta and uh but the the parameter of a
+canonical exponential family is
+
+ align:start position:0%
+canonical exponential family is
+ 
+
+ align:start position:0%
+canonical exponential family is
+something that lives in the entire real
+
+ align:start position:0%
+something that lives in the entire real
+ 
+
+ align:start position:0%
+something that lives in the entire real
+line right it was defined for all
+
+ align:start position:0%
+line right it was defined for all
+ 
+
+ align:start position:0%
+line right it was defined for all
+thetas and so in particular I can just
+
+ align:start position:0%
+thetas and so in particular I can just
+ 
+
+ align:start position:0%
+thetas and so in particular I can just
+assume I can just take Theta to be the
+
+ align:start position:0%
+assume I can just take Theta to be the
+ 
+
+ align:start position:0%
+assume I can just take Theta to be the
+one that's X transposed Beta And so in
+
+ align:start position:0%
+one that's X transposed Beta And so in
+ 
+
+ align:start position:0%
+one that's X transposed Beta And so in
+particular I'm just going to try to find
+
+ align:start position:0%
+particular I'm just going to try to find
+ 
+
+ align:start position:0%
+particular I'm just going to try to find
+the link that just says okay okay when I
+
+ align:start position:0%
+the link that just says okay okay when I
+ 
+
+ align:start position:0%
+the link that just says okay okay when I
+take G of
+
+ align:start position:0%
+take G of
+ 
+
+ align:start position:0%
+take G of
+mu I'm going to map so that's what's
+
+ align:start position:0%
+mu I'm going to map so that's what's
+ 
+
+ align:start position:0%
+mu I'm going to map so that's what's
+going to be right so I know that g of mu
+
+ align:start position:0%
+going to be right so I know that g of mu
+ 
+
+ align:start position:0%
+going to be right so I know that g of mu
+is going to be equal to X beta and now
+
+ align:start position:0%
+is going to be equal to X beta and now
+ 
+
+ align:start position:0%
+is going to be equal to X beta and now
+what I'm going to say is say okay let's
+
+ align:start position:0%
+what I'm going to say is say okay let's
+ 
+
+ align:start position:0%
+what I'm going to say is say okay let's
+just take the G that makes this guy
+
+ align:start position:0%
+just take the G that makes this guy
+ 
+
+ align:start position:0%
+just take the G that makes this guy
+equal to Theta so that this is Theta
+
+ align:start position:0%
+equal to Theta so that this is Theta
+ 
+
+ align:start position:0%
+equal to Theta so that this is Theta
+that actually model like X transpose
+
+ align:start position:0%
+that actually model like X transpose
+ 
+
+ align:start position:0%
+that actually model like X transpose
+beta feels pretty
+
+ align:start position:0%
+beta feels pretty
+ 
+
+ align:start position:0%
+beta feels pretty
+canonical right I mean what
+
+ align:start position:0%
+canonical right I mean what
+ 
+
+ align:start position:0%
+canonical right I mean what
+else what other Central easy choice
+
+ align:start position:0%
+else what other Central easy choice
+ 
+
+ align:start position:0%
+else what other Central easy choice
+would you take this was pretty easy
+
+ align:start position:0%
+would you take this was pretty easy
+ 
+
+ align:start position:0%
+would you take this was pretty easy
+there's is a natural parameter for this
+
+ align:start position:0%
+there's is a natural parameter for this
+ 
+
+ align:start position:0%
+there's is a natural parameter for this
+canonical uh family and it takes value
+
+ align:start position:0%
+canonical uh family and it takes value
+ 
+
+ align:start position:0%
+canonical uh family and it takes value
+on the entire real line I have a
+
+ align:start position:0%
+on the entire real line I have a
+ 
+
+ align:start position:0%
+on the entire real line I have a
+function that Maps mu onto the entire
+
+ align:start position:0%
+function that Maps mu onto the entire
+ 
+
+ align:start position:0%
+function that Maps mu onto the entire
+real line so let's just map it to the
+
+ align:start position:0%
+real line so let's just map it to the
+ 
+
+ align:start position:0%
+real line so let's just map it to the
+actual
+
+ align:start position:0%
+actual
+ 
+
+ align:start position:0%
+actual
+parameter okay so now uh what I claim uh
+
+ align:start position:0%
+parameter okay so now uh what I claim uh
+ 
+
+ align:start position:0%
+parameter okay so now uh what I claim uh
+okay why do I have this well we've
+
+ align:start position:0%
+okay why do I have this well we've
+ 
+
+ align:start position:0%
+okay why do I have this well we've
+already figured that out the canonical
+
+ align:start position:0%
+already figured that out the canonical
+ 
+
+ align:start position:0%
+already figured that out the canonical
+link function is strictly increasing
+
+ align:start position:0%
+link function is strictly increasing
+ 
+
+ align:start position:0%
+link function is strictly increasing
+okay sorry so I said that so now I want
+
+ align:start position:0%
+okay sorry so I said that so now I want
+ 
+
+ align:start position:0%
+okay sorry so I said that so now I want
+this
+
+ align:start position:0%
+this
+ 
+
+ align:start position:0%
+this
+guy so I want
+
+ align:start position:0%
+guy so I want
+ 
+
+ align:start position:0%
+guy so I want
+mu G of
+
+ align:start position:0%
+mu G of
+ 
+
+ align:start position:0%
+mu G of
+mu to be equal to Theta
+
+ align:start position:0%
+mu to be equal to Theta
+ 
+
+ align:start position:0%
+mu to be equal to Theta
+which is equivalent to saying that I
+
+ align:start position:0%
+which is equivalent to saying that I
+ 
+
+ align:start position:0%
+which is equivalent to saying that I
+want mu to be equal to G inverse of
+
+ align:start position:0%
+want mu to be equal to G inverse of
+ 
+
+ align:start position:0%
+want mu to be equal to G inverse of
+theta but we know that mu is
+
+ align:start position:0%
+theta but we know that mu is
+ 
+
+ align:start position:0%
+theta but we know that mu is
+what B Prime of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+theta so that means that b Prime is the
+
+ align:start position:0%
+theta so that means that b Prime is the
+ 
+
+ align:start position:0%
+theta so that means that b Prime is the
+same function as G
+
+ align:start position:0%
+same function as G
+ 
+
+ align:start position:0%
+same function as G
+inverse and I claim that this is
+
+ align:start position:0%
+inverse and I claim that this is
+ 
+
+ align:start position:0%
+inverse and I claim that this is
+actually giving me indeed a function
+
+ align:start position:0%
+actually giving me indeed a function
+ 
+
+ align:start position:0%
+actually giving me indeed a function
+that has uh the properties that I want
+
+ align:start position:0%
+that has uh the properties that I want
+ 
+
+ align:start position:0%
+that has uh the properties that I want
+because before I said just pick any
+
+ align:start position:0%
+because before I said just pick any
+ 
+
+ align:start position:0%
+because before I said just pick any
+function that has these properties and
+
+ align:start position:0%
+function that has these properties and
+ 
+
+ align:start position:0%
+function that has these properties and
+now I'm giving you a very hard rule to
+
+ align:start position:0%
+now I'm giving you a very hard rule to
+ 
+
+ align:start position:0%
+now I'm giving you a very hard rule to
+pick this though you need still to check
+
+ align:start position:0%
+pick this though you need still to check
+ 
+
+ align:start position:0%
+pick this though you need still to check
+that it satisfies those condition in
+
+ align:start position:0%
+that it satisfies those condition in
+ 
+
+ align:start position:0%
+that it satisfies those condition in
+particular that it's increasing and
+
+ align:start position:0%
+particular that it's increasing and
+ 
+
+ align:start position:0%
+particular that it's increasing and
+invertible and so for this to be
+
+ align:start position:0%
+invertible and so for this to be
+ 
+
+ align:start position:0%
+invertible and so for this to be
+increasing and invertible strictly
+
+ align:start position:0%
+increasing and invertible strictly
+ 
+
+ align:start position:0%
+increasing and invertible strictly
+increasing and invertible really what I
+
+ align:start position:0%
+increasing and invertible really what I
+ 
+
+ align:start position:0%
+increasing and invertible really what I
+need is that the inverse is strictly
+
+ align:start position:0%
+need is that the inverse is strictly
+ 
+
+ align:start position:0%
+need is that the inverse is strictly
+increasing and invertible which is the
+
+ align:start position:0%
+increasing and invertible which is the
+ 
+
+ align:start position:0%
+increasing and invertible which is the
+case here because uh uh B Prime as we
+
+ align:start position:0%
+case here because uh uh B Prime as we
+ 
+
+ align:start position:0%
+case here because uh uh B Prime as we
+said well B Prime is the derivative of a
+
+ align:start position:0%
+said well B Prime is the derivative of a
+ 
+
+ align:start position:0%
+said well B Prime is the derivative of a
+strictly convex function a strictly
+
+ align:start position:0%
+strictly convex function a strictly
+ 
+
+ align:start position:0%
+strictly convex function a strictly
+convex function has a second derivative
+
+ align:start position:0%
+convex function has a second derivative
+ 
+
+ align:start position:0%
+convex function has a second derivative
+that's strictly positive we just figured
+
+ align:start position:0%
+that's strictly positive we just figured
+ 
+
+ align:start position:0%
+that's strictly positive we just figured
+it out using the fact that the variance
+
+ align:start position:0%
+it out using the fact that the variance
+ 
+
+ align:start position:0%
+it out using the fact that the variance
+was strictly positive and if f is
+
+ align:start position:0%
+was strictly positive and if f is
+ 
+
+ align:start position:0%
+was strictly positive and if f is
+strictly positive then uh this thing has
+
+ align:start position:0%
+strictly positive then uh this thing has
+ 
+
+ align:start position:0%
+strictly positive then uh this thing has
+to be uh strictly positive so if B prime
+
+ align:start position:0%
+to be uh strictly positive so if B prime
+ 
+
+ align:start position:0%
+to be uh strictly positive so if B prime
+prime is strictly positive this is the
+
+ align:start position:0%
+prime is strictly positive this is the
+ 
+
+ align:start position:0%
+prime is strictly positive this is the
+derivative of a function called B Prime
+
+ align:start position:0%
+derivative of a function called B Prime
+ 
+
+ align:start position:0%
+derivative of a function called B Prime
+if your derivative is strictly positive
+
+ align:start position:0%
+if your derivative is strictly positive
+ 
+
+ align:start position:0%
+if your derivative is strictly positive
+you are strictly
+
+ align:start position:0%
+you are strictly
+ 
+
+ align:start position:0%
+you are strictly
+increasing and so we know that b Prime
+
+ align:start position:0%
+increasing and so we know that b Prime
+ 
+
+ align:start position:0%
+increasing and so we know that b Prime
+is indeed strictly
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+increasing and uh what I need also to
+
+ align:start position:0%
+increasing and uh what I need also to
+ 
+
+ align:start position:0%
+increasing and uh what I need also to
+check well I guess uh this is already
+
+ align:start position:0%
+check well I guess uh this is already
+ 
+
+ align:start position:0%
+check well I guess uh this is already
+checked in its own because B Prime is
+
+ align:start position:0%
+checked in its own because B Prime is
+ 
+
+ align:start position:0%
+checked in its own because B Prime is
+actually um mapping all of R into uh the
+
+ align:start position:0%
+actually um mapping all of R into uh the
+ 
+
+ align:start position:0%
+actually um mapping all of R into uh the
+the possible values I mean when Theta
+
+ align:start position:0%
+the possible values I mean when Theta
+ 
+
+ align:start position:0%
+the possible values I mean when Theta
+ranges on the entire real line then B
+
+ align:start position:0%
+ranges on the entire real line then B
+ 
+
+ align:start position:0%
+ranges on the entire real line then B
+Prime ranges in the entire interval of
+
+ align:start position:0%
+Prime ranges in the entire interval of
+ 
+
+ align:start position:0%
+Prime ranges in the entire interval of
+the the mean values that it can take
+
+ align:start position:0%
+the the mean values that it can take
+ 
+
+ align:start position:0%
+the the mean values that it can take
+right and so now I have this thing
+
+ align:start position:0%
+right and so now I have this thing
+ 
+
+ align:start position:0%
+right and so now I have this thing
+that's completely defined B Prime
+
+ align:start position:0%
+that's completely defined B Prime
+ 
+
+ align:start position:0%
+that's completely defined B Prime
+inverse is a valid
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+link and it's called the canonical
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+link okay so again if I give you an
+
+ align:start position:0%
+link okay so again if I give you an
+ 
+
+ align:start position:0%
+link okay so again if I give you an
+exponential family which is another way
+
+ align:start position:0%
+exponential family which is another way
+ 
+
+ align:start position:0%
+exponential family which is another way
+of saying you I give you a convex
+
+ align:start position:0%
+of saying you I give you a convex
+ 
+
+ align:start position:0%
+of saying you I give you a convex
+function B which you know gives you some
+
+ align:start position:0%
+function B which you know gives you some
+ 
+
+ align:start position:0%
+function B which you know gives you some
+exponential family then if you just take
+
+ align:start position:0%
+exponential family then if you just take
+ 
+
+ align:start position:0%
+exponential family then if you just take
+B Prime inverse this gives you the
+
+ align:start position:0%
+B Prime inverse this gives you the
+ 
+
+ align:start position:0%
+B Prime inverse this gives you the
+associated canonical link for this
+
+ align:start position:0%
+associated canonical link for this
+ 
+
+ align:start position:0%
+associated canonical link for this
+canonical exponential family all
+
+ align:start position:0%
+canonical exponential family all
+ 
+
+ align:start position:0%
+canonical exponential family all
+right so let's see why so okay clearly
+
+ align:start position:0%
+right so let's see why so okay clearly
+ 
+
+ align:start position:0%
+right so let's see why so okay clearly
+there's an advantage of doing this which
+
+ align:start position:0%
+there's an advantage of doing this which
+ 
+
+ align:start position:0%
+there's an advantage of doing this which
+is is I don't have to actually think
+
+ align:start position:0%
+is is I don't have to actually think
+ 
+
+ align:start position:0%
+is is I don't have to actually think
+about which one to pick if I don't want
+
+ align:start position:0%
+about which one to pick if I don't want
+ 
+
+ align:start position:0%
+about which one to pick if I don't want
+to think about it but uh uh there's
+
+ align:start position:0%
+to think about it but uh uh there's
+ 
+
+ align:start position:0%
+to think about it but uh uh there's
+other advantages that come to it and
+
+ align:start position:0%
+other advantages that come to it and
+ 
+
+ align:start position:0%
+other advantages that come to it and
+we'll see that in the representation
+
+ align:start position:0%
+we'll see that in the representation
+ 
+
+ align:start position:0%
+we'll see that in the representation
+there's basically going to be some life
+
+ align:start position:0%
+there's basically going to be some life
+ 
+
+ align:start position:0%
+there's basically going to be some life
+cancellations that show up so before we
+
+ align:start position:0%
+cancellations that show up so before we
+ 
+
+ align:start position:0%
+cancellations that show up so before we
+go there let's just compute the
+
+ align:start position:0%
+go there let's just compute the
+ 
+
+ align:start position:0%
+go there let's just compute the
+canonical link for the burnly
+
+ align:start position:0%
+canonical link for the burnly
+ 
+
+ align:start position:0%
+canonical link for the burnly
+distribution all right so remember the
+
+ align:start position:0%
+distribution all right so remember the
+ 
+
+ align:start position:0%
+distribution all right so remember the
+burnly distribution has a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+pmf which is part of the canonical
+
+ align:start position:0%
+pmf which is part of the canonical
+ 
+
+ align:start position:0%
+pmf which is part of the canonical
+exponential family all right so the pmf
+
+ align:start position:0%
+exponential family all right so the pmf
+ 
+
+ align:start position:0%
+exponential family all right so the pmf
+of the burnly is um uh F Theta of
+
+ align:start position:0%
+of the burnly is um uh F Theta of
+ 
+
+ align:start position:0%
+of the burnly is um uh F Theta of
+X is
+
+ align:start position:0%
+X is
+ 
+
+ align:start position:0%
+X is
+uh okay
+
+ align:start position:0%
+uh okay
+ 
+
+ align:start position:0%
+uh okay
+so let me just write it like this so
+
+ align:start position:0%
+so let me just write it like this so
+ 
+
+ align:start position:0%
+so let me just write it like this so
+it's p to the x one so P to the Y let's
+
+ align:start position:0%
+it's p to the x one so P to the Y let's
+ 
+
+ align:start position:0%
+it's p to the x one so P to the Y let's
+say one minus P to the 1 minus
+
+ align:start position:0%
+say one minus P to the 1 minus
+ 
+
+ align:start position:0%
+say one minus P to the 1 minus
+y which I will write as
+
+ align:start position:0%
+y which I will write as
+ 
+
+ align:start position:0%
+y which I will write as
+exponential y log
+
+ align:start position:0%
+exponential y log
+ 
+
+ align:start position:0%
+exponential y log
+P plus uh oneus
+
+ align:start position:0%
+P plus uh oneus
+ 
+
+ align:start position:0%
+P plus uh oneus
+y log 1 minus
+
+ align:start position:0%
+y log 1 minus
+ 
+
+ align:start position:0%
+y log 1 minus
+P okay we've done that last time now I'm
+
+ align:start position:0%
+P okay we've done that last time now I'm
+ 
+
+ align:start position:0%
+P okay we've done that last time now I'm
+going to group my terms in y to see how
+
+ align:start position:0%
+going to group my terms in y to see how
+ 
+
+ align:start position:0%
+going to group my terms in y to see how
+y interacts with this parameter
+
+ align:start position:0%
+y interacts with this parameter
+ 
+
+ align:start position:0%
+y interacts with this parameter
+p and what I'm getting is Y which is
+
+ align:start position:0%
+p and what I'm getting is Y which is
+ 
+
+ align:start position:0%
+p and what I'm getting is Y which is
+time log P / 1 minus p and then the only
+
+ align:start position:0%
+time log P / 1 minus p and then the only
+ 
+
+ align:start position:0%
+time log P / 1 minus p and then the only
+term that remains is log 1 minus
+
+ align:start position:0%
+term that remains is log 1 minus
+ 
+
+ align:start position:0%
+term that remains is log 1 minus
+P
+
+ align:start position:0%
+P
+ 
+
+ align:start position:0%
+P
+okay now I want this to be a canonical
+
+ align:start position:0%
+okay now I want this to be a canonical
+ 
+
+ align:start position:0%
+okay now I want this to be a canonical
+exponential family which means that I
+
+ align:start position:0%
+exponential family which means that I
+ 
+
+ align:start position:0%
+exponential family which means that I
+just need to call this guy so it is part
+
+ align:start position:0%
+just need to call this guy so it is part
+ 
+
+ align:start position:0%
+just need to call this guy so it is part
+of the exponential family I can read
+
+ align:start position:0%
+of the exponential family I can read
+ 
+
+ align:start position:0%
+of the exponential family I can read
+that if I want it to be canonical this
+
+ align:start position:0%
+that if I want it to be canonical this
+ 
+
+ align:start position:0%
+that if I want it to be canonical this
+guy must be Theta
+
+ align:start position:0%
+guy must be Theta
+ 
+
+ align:start position:0%
+guy must be Theta
+itself okay so I have that Theta is
+
+ align:start position:0%
+itself okay so I have that Theta is
+ 
+
+ align:start position:0%
+itself okay so I have that Theta is
+equal to log P 1 minus P if I invert
+
+ align:start position:0%
+equal to log P 1 minus P if I invert
+ 
+
+ align:start position:0%
+equal to log P 1 minus P if I invert
+this thing it tells me that P is e to
+
+ align:start position:0%
+this thing it tells me that P is e to
+ 
+
+ align:start position:0%
+this thing it tells me that P is e to
+the Theta / 1 + e to the Theta right
+
+ align:start position:0%
+the Theta / 1 + e to the Theta right
+ 
+
+ align:start position:0%
+the Theta / 1 + e to the Theta right
+it's just inverting this
+
+ align:start position:0%
+it's just inverting this
+ 
+
+ align:start position:0%
+it's just inverting this
+function and so that means that this
+
+ align:start position:0%
+function and so that means that this
+ 
+
+ align:start position:0%
+function and so that means that this
+thing is actually so in particular it
+
+ align:start position:0%
+thing is actually so in particular it
+ 
+
+ align:start position:0%
+thing is actually so in particular it
+means that
+
+ align:start position:0%
+means that
+ 
+
+ align:start position:0%
+means that
+log 1 - p is equal to log 1 minus this
+
+ align:start position:0%
+log 1 - p is equal to log 1 minus this
+ 
+
+ align:start position:0%
+log 1 - p is equal to log 1 minus this
+thing so the exponential thetas go away
+
+ align:start position:0%
+thing so the exponential thetas go away
+ 
+
+ align:start position:0%
+thing so the exponential thetas go away
+so in the numerator so this is what I
+
+ align:start position:0%
+so in the numerator so this is what I
+ 
+
+ align:start position:0%
+so in the numerator so this is what I
+get right that's the log one minus this
+
+ align:start position:0%
+get right that's the log one minus this
+ 
+
+ align:start position:0%
+get right that's the log one minus this
+guy which is equal to minus log 1 + e to
+
+ align:start position:0%
+guy which is equal to minus log 1 + e to
+ 
+
+ align:start position:0%
+guy which is equal to minus log 1 + e to
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+Theta
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so I'm going a bit fast but these
+
+ align:start position:0%
+okay so I'm going a bit fast but these
+ 
+
+ align:start position:0%
+okay so I'm going a bit fast but these
+are very Elementary
+
+ align:start position:0%
+are very Elementary
+ 
+
+ align:start position:0%
+are very Elementary
+manipulations Maybe it requires one more
+
+ align:start position:0%
+manipulations Maybe it requires one more
+ 
+
+ align:start position:0%
+manipulations Maybe it requires one more
+line to convince yourself but
+
+ align:start position:0%
+line to convince yourself but
+ 
+
+ align:start position:0%
+line to convince yourself but
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+just do it in the comfort of your room
+
+ align:start position:0%
+just do it in the comfort of your room
+ 
+
+ align:start position:0%
+just do it in the comfort of your room
+and then what you have is the
+
+ align:start position:0%
+and then what you have is the
+ 
+
+ align:start position:0%
+and then what you have is the
+exponential of y * Theta and then I have
+
+ align:start position:0%
+exponential of y * Theta and then I have
+ 
+
+ align:start position:0%
+exponential of y * Theta and then I have
+minus log 1 + e
+
+ align:start position:0%
+minus log 1 + e
+ 
+
+ align:start position:0%
+minus log 1 + e
+Theta okay so this is the representation
+
+ align:start position:0%
+Theta okay so this is the representation
+ 
+
+ align:start position:0%
+Theta okay so this is the representation
+of the pmf of a burnly distribution as
+
+ align:start position:0%
+of the pmf of a burnly distribution as
+ 
+
+ align:start position:0%
+of the pmf of a burnly distribution as
+part of a member of the canonical
+
+ align:start position:0%
+part of a member of the canonical
+ 
+
+ align:start position:0%
+part of a member of the canonical
+exponential family and it tells me that
+
+ align:start position:0%
+exponential family and it tells me that
+ 
+
+ align:start position:0%
+exponential family and it tells me that
+b of theta is
+
+ align:start position:0%
+b of theta is
+ 
+
+ align:start position:0%
+b of theta is
+equal to log 1 plus e of
+
+ align:start position:0%
+equal to log 1 plus e of
+ 
+
+ align:start position:0%
+equal to log 1 plus e of
+theta that's what I have there from
+
+ align:start position:0%
+theta that's what I have there from
+ 
+
+ align:start position:0%
+theta that's what I have there from
+there I can compute the expectation
+
+ align:start position:0%
+there I can compute the expectation
+ 
+
+ align:start position:0%
+there I can compute the expectation
+which you know hopefully I'm going to
+
+ align:start position:0%
+which you know hopefully I'm going to
+ 
+
+ align:start position:0%
+which you know hopefully I'm going to
+get p as the mean and P * 1 minus p as
+
+ align:start position:0%
+get p as the mean and P * 1 minus p as
+ 
+
+ align:start position:0%
+get p as the mean and P * 1 minus p as
+the variance otherwise that would be
+
+ align:start position:0%
+the variance otherwise that would be
+ 
+
+ align:start position:0%
+the variance otherwise that would be
+weird
+
+ align:start position:0%
+weird
+ 
+
+ align:start position:0%
+weird
+um so let's just do
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this B
+
+ align:start position:0%
+this B
+ 
+
+ align:start position:0%
+this B
+Prime of theta should give me the mean
+
+ align:start position:0%
+Prime of theta should give me the mean
+ 
+
+ align:start position:0%
+Prime of theta should give me the mean
+and indeed B Prime of theta is e to the
+
+ align:start position:0%
+and indeed B Prime of theta is e to the
+ 
+
+ align:start position:0%
+and indeed B Prime of theta is e to the
+Theta divided by 1+ e to the Theta which
+
+ align:start position:0%
+Theta divided by 1+ e to the Theta which
+ 
+
+ align:start position:0%
+Theta divided by 1+ e to the Theta which
+is exactly this spe that I had
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+there okay just for fun uh let's uh well
+
+ align:start position:0%
+there okay just for fun uh let's uh well
+ 
+
+ align:start position:0%
+there okay just for fun uh let's uh well
+I don't know maybe that's not part of it
+
+ align:start position:0%
+I don't know maybe that's not part of it
+ 
+
+ align:start position:0%
+I don't know maybe that's not part of it
+yeah let's not compute the second
+
+ align:start position:0%
+yeah let's not compute the second
+ 
+
+ align:start position:0%
+yeah let's not compute the second
+derivative it's probably going to be on
+
+ align:start position:0%
+derivative it's probably going to be on
+ 
+
+ align:start position:0%
+derivative it's probably going to be on
+your homework at some point um if not on
+
+ align:start position:0%
+your homework at some point um if not on
+ 
+
+ align:start position:0%
+your homework at some point um if not on
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+final uh all right
+
+ align:start position:0%
+final uh all right
+ 
+
+ align:start position:0%
+final uh all right
+so B Prime now we know oh I erased it of
+
+ align:start position:0%
+so B Prime now we know oh I erased it of
+ 
+
+ align:start position:0%
+so B Prime now we know oh I erased it of
+course um G the canonical link is B
+
+ align:start position:0%
+course um G the canonical link is B
+ 
+
+ align:start position:0%
+course um G the canonical link is B
+Prime
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+inverse and I claim that this is going
+
+ align:start position:0%
+inverse and I claim that this is going
+ 
+
+ align:start position:0%
+inverse and I claim that this is going
+to give me the legit function log of mu
+
+ align:start position:0%
+to give me the legit function log of mu
+ 
+
+ align:start position:0%
+to give me the legit function log of mu
+over 1 minus mu so let's check that so B
+
+ align:start position:0%
+over 1 minus mu so let's check that so B
+ 
+
+ align:start position:0%
+over 1 minus mu so let's check that so B
+Prime is this thing uh so now I want to
+
+ align:start position:0%
+Prime is this thing uh so now I want to
+ 
+
+ align:start position:0%
+Prime is this thing uh so now I want to
+find the inverse
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+well I should really call my inverse of
+
+ align:start position:0%
+well I should really call my inverse of
+ 
+
+ align:start position:0%
+well I should really call my inverse of
+function of p and I've done it before
+
+ align:start position:0%
+function of p and I've done it before
+ 
+
+ align:start position:0%
+function of p and I've done it before
+right all I have to do is to solve this
+
+ align:start position:0%
+right all I have to do is to solve this
+ 
+
+ align:start position:0%
+right all I have to do is to solve this
+equation which I've actually just done
+
+ align:start position:0%
+equation which I've actually just done
+ 
+
+ align:start position:0%
+equation which I've actually just done
+it that's where I'm actually coming from
+
+ align:start position:0%
+it that's where I'm actually coming from
+ 
+
+ align:start position:0%
+it that's where I'm actually coming from
+so it's actually telling me that the
+
+ align:start position:0%
+so it's actually telling me that the
+ 
+
+ align:start position:0%
+so it's actually telling me that the
+solution of this thing is uh equal to
+
+ align:start position:0%
+solution of this thing is uh equal to
+ 
+
+ align:start position:0%
+solution of this thing is uh equal to
+log of p over 1 minus
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+P
+
+ align:start position:0%
+P
+ 
+
+ align:start position:0%
+P
+okay we just solve this thing both ways
+
+ align:start position:0%
+okay we just solve this thing both ways
+ 
+
+ align:start position:0%
+okay we just solve this thing both ways
+and this is
+
+ align:start position:0%
+and this is
+ 
+
+ align:start position:0%
+and this is
+indeed
+
+ align:start position:0%
+indeed
+ 
+
+ align:start position:0%
+indeed
+logit of P by definition of
+
+ align:start position:0%
+logit of P by definition of
+ 
+
+ align:start position:0%
+logit of P by definition of
+logit so B Prime inverse this function
+
+ align:start position:0%
+logit so B Prime inverse this function
+ 
+
+ align:start position:0%
+logit so B Prime inverse this function
+that seemed to come out of nowhere is
+
+ align:start position:0%
+that seemed to come out of nowhere is
+ 
+
+ align:start position:0%
+that seemed to come out of nowhere is
+really just the inverse of B Prime which
+
+ align:start position:0%
+really just the inverse of B Prime which
+ 
+
+ align:start position:0%
+really just the inverse of B Prime which
+we know is the canonical link and
+
+ align:start position:0%
+we know is the canonical link and
+ 
+
+ align:start position:0%
+we know is the canonical link and
+canonical is some sort of ad hoc choices
+
+ align:start position:0%
+canonical is some sort of ad hoc choices
+ 
+
+ align:start position:0%
+canonical is some sort of ad hoc choices
+that we've made by saying let's just
+
+ align:start position:0%
+that we've made by saying let's just
+ 
+
+ align:start position:0%
+that we've made by saying let's just
+take the link such that D of mu is
+
+ align:start position:0%
+take the link such that D of mu is
+ 
+
+ align:start position:0%
+take the link such that D of mu is
+giving me the actual canonical parameter
+
+ align:start position:0%
+giving me the actual canonical parameter
+ 
+
+ align:start position:0%
+giving me the actual canonical parameter
+f
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah yeah you're
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+right um now of course I'm going through
+
+ align:start position:0%
+right um now of course I'm going through
+ 
+
+ align:start position:0%
+right um now of course I'm going through
+all this trouble but you could see it
+
+ align:start position:0%
+all this trouble but you could see it
+ 
+
+ align:start position:0%
+all this trouble but you could see it
+immediately I know this is going to be
+
+ align:start position:0%
+immediately I know this is going to be
+ 
+
+ align:start position:0%
+immediately I know this is going to be
+Theta we also have FR knowledge
+
+ align:start position:0%
+Theta we also have FR knowledge
+ 
+
+ align:start position:0%
+Theta we also have FR knowledge
+hopefully that the expectation of a
+
+ align:start position:0%
+hopefully that the expectation of a
+ 
+
+ align:start position:0%
+hopefully that the expectation of a
+burnly is p itself so right at this step
+
+ align:start position:0%
+burnly is p itself so right at this step
+ 
+
+ align:start position:0%
+burnly is p itself so right at this step
+when I say that I'm going going to take
+
+ align:start position:0%
+when I say that I'm going going to take
+ 
+
+ align:start position:0%
+when I say that I'm going going to take
+Theta to be this guy already knew that
+
+ align:start position:0%
+Theta to be this guy already knew that
+ 
+
+ align:start position:0%
+Theta to be this guy already knew that
+the canonical link was the late
+
+ align:start position:0%
+the canonical link was the late
+ 
+
+ align:start position:0%
+the canonical link was the late
+link because I just say oh here is Theta
+
+ align:start position:0%
+link because I just say oh here is Theta
+ 
+
+ align:start position:0%
+link because I just say oh here is Theta
+and it's just this function of me
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+B okay so you can do that for a bunch of
+
+ align:start position:0%
+B okay so you can do that for a bunch of
+ 
+
+ align:start position:0%
+B okay so you can do that for a bunch of
+examples and this is what they're going
+
+ align:start position:0%
+examples and this is what they're going
+ 
+
+ align:start position:0%
+examples and this is what they're going
+to give you so in the gaussian case b of
+
+ align:start position:0%
+to give you so in the gaussian case b of
+ 
+
+ align:start position:0%
+to give you so in the gaussian case b of
+theta we've actually computed it
+
+ align:start position:0%
+theta we've actually computed it
+ 
+
+ align:start position:0%
+theta we've actually computed it
+actually once this is Theta Square over
+
+ align:start position:0%
+actually once this is Theta Square over
+ 
+
+ align:start position:0%
+actually once this is Theta Square over
+two so the derivative of this thing is
+
+ align:start position:0%
+two so the derivative of this thing is
+ 
+
+ align:start position:0%
+two so the derivative of this thing is
+really just Theta which means that g or
+
+ align:start position:0%
+really just Theta which means that g or
+ 
+
+ align:start position:0%
+really just Theta which means that g or
+G inverse is actually equal to the
+
+ align:start position:0%
+G inverse is actually equal to the
+ 
+
+ align:start position:0%
+G inverse is actually equal to the
+identity okay and again sort of you know
+
+ align:start position:0%
+identity okay and again sort of you know
+ 
+
+ align:start position:0%
+identity okay and again sort of you know
+sanity check when I'm in the gaon case
+
+ align:start position:0%
+sanity check when I'm in the gaon case
+ 
+
+ align:start position:0%
+sanity check when I'm in the gaon case
+there's nothing General about General
+
+ align:start position:0%
+there's nothing General about General
+ 
+
+ align:start position:0%
+there's nothing General about General
+linear models they don't have a link the
+
+ align:start position:0%
+linear models they don't have a link the
+ 
+
+ align:start position:0%
+linear models they don't have a link the
+pon case uh you can actually check uh
+
+ align:start position:0%
+pon case uh you can actually check uh
+ 
+
+ align:start position:0%
+pon case uh you can actually check uh
+did we do this actually yes we did it
+
+ align:start position:0%
+did we do this actually yes we did it
+ 
+
+ align:start position:0%
+did we do this actually yes we did it
+right so that's when we had this e of
+
+ align:start position:0%
+right so that's when we had this e of
+ 
+
+ align:start position:0%
+right so that's when we had this e of
+theta and so B is e of theta which means
+
+ align:start position:0%
+theta and so B is e of theta which means
+ 
+
+ align:start position:0%
+theta and so B is e of theta which means
+that the natural link is the E inverse
+
+ align:start position:0%
+that the natural link is the E inverse
+ 
+
+ align:start position:0%
+that the natural link is the E inverse
+which is log uh which is the inverse of
+
+ align:start position:0%
+which is log uh which is the inverse of
+ 
+
+ align:start position:0%
+which is log uh which is the inverse of
+exponential and so that's the log
+
+ align:start position:0%
+exponential and so that's the log
+ 
+
+ align:start position:0%
+exponential and so that's the log
+logarithm link which as I said you know
+
+ align:start position:0%
+logarithm link which as I said you know
+ 
+
+ align:start position:0%
+logarithm link which as I said you know
+I I use the word natural but you can
+
+ align:start position:0%
+I I use the word natural but you can
+ 
+
+ align:start position:0%
+I I use the word natural but you can
+also use the word canonical if you want
+
+ align:start position:0%
+also use the word canonical if you want
+ 
+
+ align:start position:0%
+also use the word canonical if you want
+to describe this function as being the
+
+ align:start position:0%
+to describe this function as being the
+ 
+
+ align:start position:0%
+to describe this function as being the
+right function to map the positive real
+
+ align:start position:0%
+right function to map the positive real
+ 
+
+ align:start position:0%
+right function to map the positive real
+line to the entire real line the burnly
+
+ align:start position:0%
+line to the entire real line the burnly
+ 
+
+ align:start position:0%
+line to the entire real line the burnly
+would just did it so B the cumulative
+
+ align:start position:0%
+would just did it so B the cumulative
+ 
+
+ align:start position:0%
+would just did it so B the cumulative
+cumul during function is log of 1 plus e
+
+ align:start position:0%
+cumul during function is log of 1 plus e
+ 
+
+ align:start position:0%
+cumul during function is log of 1 plus e
+of theta which is log of uh mu over 1us
+
+ align:start position:0%
+of theta which is log of uh mu over 1us
+ 
+
+ align:start position:0%
+of theta which is log of uh mu over 1us
+mu and uh and Gamma fun function where
+
+ align:start position:0%
+mu and uh and Gamma fun function where
+ 
+
+ align:start position:0%
+mu and uh and Gamma fun function where
+you have the thing you're going to see
+
+ align:start position:0%
+you have the thing you're going to see
+ 
+
+ align:start position:0%
+you have the thing you're going to see
+is log minus log of minus denta you've
+
+ align:start position:0%
+is log minus log of minus denta you've
+ 
+
+ align:start position:0%
+is log minus log of minus denta you've
+see this this the reciprocal link is the
+
+ align:start position:0%
+see this this the reciprocal link is the
+ 
+
+ align:start position:0%
+see this this the reciprocal link is the
+link that actually shows up so uh minus
+
+ align:start position:0%
+link that actually shows up so uh minus
+ 
+
+ align:start position:0%
+link that actually shows up so uh minus
+one over mu okay that Maps this is
+
+ align:start position:0%
+one over mu okay that Maps this is
+ 
+
+ align:start position:0%
+one over mu okay that Maps this is
+another uh link sorry this is um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+uh yeah okay that's the
+
+ align:start position:0%
+uh yeah okay that's the
+ 
+
+ align:start position:0%
+uh yeah okay that's the
+one okay so um are there any questions
+
+ align:start position:0%
+one okay so um are there any questions
+ 
+
+ align:start position:0%
+one okay so um are there any questions
+about canonical links canonical
+
+ align:start position:0%
+about canonical links canonical
+ 
+
+ align:start position:0%
+about canonical links canonical
+families I use the word canonical a lot
+
+ align:start position:0%
+families I use the word canonical a lot
+ 
+
+ align:start position:0%
+families I use the word canonical a lot
+uh but uh is everything fitting together
+
+ align:start position:0%
+uh but uh is everything fitting together
+ 
+
+ align:start position:0%
+uh but uh is everything fitting together
+right now right so we have this function
+
+ align:start position:0%
+right now right so we have this function
+ 
+
+ align:start position:0%
+right now right so we have this function
+we have the canonical exponential family
+
+ align:start position:0%
+we have the canonical exponential family
+ 
+
+ align:start position:0%
+we have the canonical exponential family
+by assumption it has a function B which
+
+ align:start position:0%
+by assumption it has a function B which
+ 
+
+ align:start position:0%
+by assumption it has a function B which
+contains every information we want we
+
+ align:start position:0%
+contains every information we want we
+ 
+
+ align:start position:0%
+contains every information we want we
+just at the beginning of the lecture we
+
+ align:start position:0%
+just at the beginning of the lecture we
+ 
+
+ align:start position:0%
+just at the beginning of the lecture we
+established that it has information
+
+ align:start position:0%
+established that it has information
+ 
+
+ align:start position:0%
+established that it has information
+about the mean in the first derivative
+
+ align:start position:0%
+about the mean in the first derivative
+ 
+
+ align:start position:0%
+about the mean in the first derivative
+about the variance in the second
+
+ align:start position:0%
+about the variance in the second
+ 
+
+ align:start position:0%
+about the variance in the second
+derivative and it's also giving us the
+
+ align:start position:0%
+derivative and it's also giving us the
+ 
+
+ align:start position:0%
+derivative and it's also giving us the
+canonical link all right so just cherish
+
+ align:start position:0%
+canonical link all right so just cherish
+ 
+
+ align:start position:0%
+canonical link all right so just cherish
+this B once you found it because it's
+
+ align:start position:0%
+this B once you found it because it's
+ 
+
+ align:start position:0%
+this B once you found it because it's
+everything you need
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah uh I don't know um political
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+preference um you know uh I don't know
+
+ align:start position:0%
+preference um you know uh I don't know
+ 
+
+ align:start position:0%
+preference um you know uh I don't know
+honestly
+
+ align:start position:0%
+honestly
+ 
+
+ align:start position:0%
+honestly
+if I were you know a serious
+
+ align:start position:0%
+if I were you know a serious
+ 
+
+ align:start position:0%
+if I were you know a serious
+practitioner I probably would have a
+
+ align:start position:0%
+practitioner I probably would have a
+ 
+
+ align:start position:0%
+practitioner I probably would have a
+better answer for you at this point I
+
+ align:start position:0%
+better answer for you at this point I
+ 
+
+ align:start position:0%
+better answer for you at this point I
+just don't I think it's a matter of
+
+ align:start position:0%
+just don't I think it's a matter of
+ 
+
+ align:start position:0%
+just don't I think it's a matter of
+practice and and and actual preferences
+
+ align:start position:0%
+practice and and and actual preferences
+ 
+
+ align:start position:0%
+practice and and and actual preferences
+you can also try both we didn't mention
+
+ align:start position:0%
+you can also try both we didn't mention
+ 
+
+ align:start position:0%
+you can also try both we didn't mention
+that you know there's this idea of crow
+
+ align:start position:0%
+that you know there's this idea of crow
+ 
+
+ align:start position:0%
+that you know there's this idea of crow
+validation well we mentioned it without
+
+ align:start position:0%
+validation well we mentioned it without
+ 
+
+ align:start position:0%
+validation well we mentioned it without
+going too much into details but you know
+
+ align:start position:0%
+going too much into details but you know
+ 
+
+ align:start position:0%
+going too much into details but you know
+you could try both and see which one
+
+ align:start position:0%
+you could try both and see which one
+ 
+
+ align:start position:0%
+you could try both and see which one
+performs best on a yet data set in terms
+
+ align:start position:0%
+performs best on a yet data set in terms
+ 
+
+ align:start position:0%
+performs best on a yet data set in terms
+of prediction and just say I prefer this
+
+ align:start position:0%
+of prediction and just say I prefer this
+ 
+
+ align:start position:0%
+of prediction and just say I prefer this
+one of the two because this actually
+
+ align:start position:0%
+one of the two because this actually
+ 
+
+ align:start position:0%
+one of the two because this actually
+comes as part of your modeling
+
+ align:start position:0%
+comes as part of your modeling
+ 
+
+ align:start position:0%
+comes as part of your modeling
+assumption right you modeled not only
+
+ align:start position:0%
+assumption right you modeled not only
+ 
+
+ align:start position:0%
+assumption right you modeled not only
+did you decide to model the image of me
+
+ align:start position:0%
+did you decide to model the image of me
+ 
+
+ align:start position:0%
+did you decide to model the image of me
+through the link function as a linear
+
+ align:start position:0%
+through the link function as a linear
+ 
+
+ align:start position:0%
+through the link function as a linear
+model but you really really what you're
+
+ align:start position:0%
+model but you really really what you're
+ 
+
+ align:start position:0%
+model but you really really what you're
+saying right your model is saying well
+
+ align:start position:0%
+saying right your model is saying well
+ 
+
+ align:start position:0%
+saying right your model is saying well
+so you have two pieces of M the
+
+ align:start position:0%
+so you have two pieces of M the
+ 
+
+ align:start position:0%
+so you have two pieces of M the
+distribution of Y but you also have the
+
+ align:start position:0%
+distribution of Y but you also have the
+ 
+
+ align:start position:0%
+distribution of Y but you also have the
+fact that mu is modeled as G inverse of
+
+ align:start position:0%
+fact that mu is modeled as G inverse of
+ 
+
+ align:start position:0%
+fact that mu is modeled as G inverse of
+X transpose beta and for different G's
+
+ align:start position:0%
+X transpose beta and for different G's
+ 
+
+ align:start position:0%
+X transpose beta and for different G's
+this is just different modeling
+
+ align:start position:0%
+this is just different modeling
+ 
+
+ align:start position:0%
+this is just different modeling
+assumptions right
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so you know why should this be be linear
+
+ align:start position:0%
+so you know why should this be be linear
+ 
+
+ align:start position:0%
+so you know why should this be be linear
+this thing be linear I don't know my my
+
+ align:start position:0%
+this thing be linear I don't know my my
+ 
+
+ align:start position:0%
+this thing be linear I don't know my my
+you know my authority uh as a person
+
+ align:start position:0%
+you know my authority uh as a person
+ 
+
+ align:start position:0%
+you know my authority uh as a person
+who's not examined the tal and data sets
+
+ align:start position:0%
+who's not examined the tal and data sets
+ 
+
+ align:start position:0%
+who's not examined the tal and data sets
+uh for both things would be that the
+
+ align:start position:0%
+uh for both things would be that the
+ 
+
+ align:start position:0%
+uh for both things would be that the
+changes are fairly
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+minor okay so this was all for one
+
+ align:start position:0%
+minor okay so this was all for one
+ 
+
+ align:start position:0%
+minor okay so this was all for one
+observation we just you know basically
+
+ align:start position:0%
+observation we just you know basically
+ 
+
+ align:start position:0%
+observation we just you know basically
+did probility right we describe some
+
+ align:start position:0%
+did probility right we describe some
+ 
+
+ align:start position:0%
+did probility right we describe some
+densities some properties of the
+
+ align:start position:0%
+densities some properties of the
+ 
+
+ align:start position:0%
+densities some properties of the
+densities how to compute expectations
+
+ align:start position:0%
+densities how to compute expectations
+ 
+
+ align:start position:0%
+densities how to compute expectations
+that was really just probability there
+
+ align:start position:0%
+that was really just probability there
+ 
+
+ align:start position:0%
+that was really just probability there
+was no dat invol evolved at any point we
+
+ align:start position:0%
+was no dat invol evolved at any point we
+ 
+
+ align:start position:0%
+was no dat invol evolved at any point we
+did a bit of modeling it was all for one
+
+ align:start position:0%
+did a bit of modeling it was all for one
+ 
+
+ align:start position:0%
+did a bit of modeling it was all for one
+observation what we're going to try to
+
+ align:start position:0%
+observation what we're going to try to
+ 
+
+ align:start position:0%
+observation what we're going to try to
+do now is given do the you know the
+
+ align:start position:0%
+do now is given do the you know the
+ 
+
+ align:start position:0%
+do now is given do the you know the
+reverse engineering to probability that
+
+ align:start position:0%
+reverse engineering to probability that
+ 
+
+ align:start position:0%
+reverse engineering to probability that
+is statistics given data what can I
+
+ align:start position:0%
+is statistics given data what can I
+ 
+
+ align:start position:0%
+is statistics given data what can I
+infer about my model now remember
+
+ align:start position:0%
+infer about my model now remember
+ 
+
+ align:start position:0%
+infer about my model now remember
+there's three parameters that are sort
+
+ align:start position:0%
+there's three parameters that are sort
+ 
+
+ align:start position:0%
+there's three parameters that are sort
+of floating around in this model right
+
+ align:start position:0%
+of floating around in this model right
+ 
+
+ align:start position:0%
+of floating around in this model right
+there one that was
+
+ align:start position:0%
+there one that was
+ 
+
+ align:start position:0%
+there one that was
+Theta there one that was mu and there
+
+ align:start position:0%
+Theta there one that was mu and there
+ 
+
+ align:start position:0%
+Theta there one that was mu and there
+one that is beta okay so those are the
+
+ align:start position:0%
+one that is beta okay so those are the
+ 
+
+ align:start position:0%
+one that is beta okay so those are the
+three parameters that are floating
+
+ align:start position:0%
+three parameters that are floating
+ 
+
+ align:start position:0%
+three parameters that are floating
+around what we wanted to say what we
+
+ align:start position:0%
+around what we wanted to say what we
+ 
+
+ align:start position:0%
+around what we wanted to say what we
+said is that the
+
+ align:start position:0%
+said is that the
+ 
+
+ align:start position:0%
+said is that the
+expectation of Y given X is Mu of
+
+ align:start position:0%
+expectation of Y given X is Mu of
+ 
+
+ align:start position:0%
+expectation of Y given X is Mu of
+X okay so if I estimate mu I know the
+
+ align:start position:0%
+X okay so if I estimate mu I know the
+ 
+
+ align:start position:0%
+X okay so if I estimate mu I know the
+conditional expectation of Y given X
+
+ align:start position:0%
+conditional expectation of Y given X
+ 
+
+ align:start position:0%
+conditional expectation of Y given X
+which definitely gives
+
+ align:start position:0%
+which definitely gives
+ 
+
+ align:start position:0%
+which definitely gives
+me Theta of X right how do I go from U
+
+ align:start position:0%
+me Theta of X right how do I go from U
+ 
+
+ align:start position:0%
+me Theta of X right how do I go from U
+of x to Theta of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+X
+
+ align:start position:0%
+X
+ 
+
+ align:start position:0%
+X
+yeah the inverse of what
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+of the
+
+ align:start position:0%
+of the
+ 
+
+ align:start position:0%
+of the
+arrow yeah sure but how do I uh how do I
+
+ align:start position:0%
+arrow yeah sure but how do I uh how do I
+ 
+
+ align:start position:0%
+arrow yeah sure but how do I uh how do I
+go from this guy to this
+
+ align:start position:0%
+go from this guy to this
+ 
+
+ align:start position:0%
+go from this guy to this
+guy so Theta is a function of mu
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+is yeah right so we just computed that
+
+ align:start position:0%
+is yeah right so we just computed that
+ 
+
+ align:start position:0%
+is yeah right so we just computed that
+mu was B Prime of theta so it means that
+
+ align:start position:0%
+mu was B Prime of theta so it means that
+ 
+
+ align:start position:0%
+mu was B Prime of theta so it means that
+Theta is just B Prime inverse of mu okay
+
+ align:start position:0%
+Theta is just B Prime inverse of mu okay
+ 
+
+ align:start position:0%
+Theta is just B Prime inverse of mu okay
+so those two things are the same as far
+
+ align:start position:0%
+so those two things are the same as far
+ 
+
+ align:start position:0%
+so those two things are the same as far
+as we're concerned because because we
+
+ align:start position:0%
+as we're concerned because because we
+ 
+
+ align:start position:0%
+as we're concerned because because we
+know that b Prime is strictly increasing
+
+ align:start position:0%
+know that b Prime is strictly increasing
+ 
+
+ align:start position:0%
+know that b Prime is strictly increasing
+it's invertible so it's just a matter of
+
+ align:start position:0%
+it's invertible so it's just a matter of
+ 
+
+ align:start position:0%
+it's invertible so it's just a matter of
+reparameterization and we just can
+
+ align:start position:0%
+reparameterization and we just can
+ 
+
+ align:start position:0%
+reparameterization and we just can
+switch from one to the other whenever we
+
+ align:start position:0%
+switch from one to the other whenever we
+ 
+
+ align:start position:0%
+switch from one to the other whenever we
+want but why we go through me because
+
+ align:start position:0%
+want but why we go through me because
+ 
+
+ align:start position:0%
+want but why we go through me because
+you know so far for the entire semester
+
+ align:start position:0%
+you know so far for the entire semester
+ 
+
+ align:start position:0%
+you know so far for the entire semester
+I told you there's one parameter that's
+
+ align:start position:0%
+I told you there's one parameter that's
+ 
+
+ align:start position:0%
+I told you there's one parameter that's
+Theta does not have to be the mean and
+
+ align:start position:0%
+Theta does not have to be the mean and
+ 
+
+ align:start position:0%
+Theta does not have to be the mean and
+that's the parameter that we care about
+
+ align:start position:0%
+that's the parameter that we care about
+ 
+
+ align:start position:0%
+that's the parameter that we care about
+that's the one on which we want to do
+
+ align:start position:0%
+that's the one on which we want to do
+ 
+
+ align:start position:0%
+that's the one on which we want to do
+interference that's the one for which
+
+ align:start position:0%
+interference that's the one for which
+ 
+
+ align:start position:0%
+interference that's the one for which
+we're going to compute the Fisher
+
+ align:start position:0%
+we're going to compute the Fisher
+ 
+
+ align:start position:0%
+we're going to compute the Fisher
+information this was the parameter that
+
+ align:start position:0%
+information this was the parameter that
+ 
+
+ align:start position:0%
+information this was the parameter that
+was you know our object of worship and
+
+ align:start position:0%
+was you know our object of worship and
+ 
+
+ align:start position:0%
+was you know our object of worship and
+now I'm saying oh I'm going to have Mew
+
+ align:start position:0%
+now I'm saying oh I'm going to have Mew
+ 
+
+ align:start position:0%
+now I'm saying oh I'm going to have Mew
+that's like coming around and why we
+
+ align:start position:0%
+that's like coming around and why we
+ 
+
+ align:start position:0%
+that's like coming around and why we
+have me is because this is the Mew that
+
+ align:start position:0%
+have me is because this is the Mew that
+ 
+
+ align:start position:0%
+have me is because this is the Mew that
+we use to go to Beta all right so I can
+
+ align:start position:0%
+we use to go to Beta all right so I can
+ 
+
+ align:start position:0%
+we use to go to Beta all right so I can
+go freely from B Prime to uh uh from
+
+ align:start position:0%
+go freely from B Prime to uh uh from
+ 
+
+ align:start position:0%
+go freely from B Prime to uh uh from
+Theta to Mu using B prime or B Prime
+
+ align:start position:0%
+Theta to Mu using B prime or B Prime
+ 
+
+ align:start position:0%
+Theta to Mu using B prime or B Prime
+inverse and now I can go from me to uh
+
+ align:start position:0%
+inverse and now I can go from me to uh
+ 
+
+ align:start position:0%
+inverse and now I can go from me to uh
+beta because I have that g of mu of X is
+
+ align:start position:0%
+beta because I have that g of mu of X is
+ 
+
+ align:start position:0%
+beta because I have that g of mu of X is
+beta transpose
+
+ align:start position:0%
+beta transpose
+ 
+
+ align:start position:0%
+beta transpose
+X okay so in the end now this is going
+
+ align:start position:0%
+X okay so in the end now this is going
+ 
+
+ align:start position:0%
+X okay so in the end now this is going
+to be my object of worship this is going
+
+ align:start position:0%
+to be my object of worship this is going
+ 
+
+ align:start position:0%
+to be my object of worship this is going
+to be the parameter that matters because
+
+ align:start position:0%
+to be the parameter that matters because
+ 
+
+ align:start position:0%
+to be the parameter that matters because
+once I set beta I set everything else
+
+ align:start position:0%
+once I set beta I set everything else
+ 
+
+ align:start position:0%
+once I set beta I set everything else
+through this
+
+ align:start position:0%
+through this
+ 
+
+ align:start position:0%
+through this
+chain so the question is if I start
+
+ align:start position:0%
+chain so the question is if I start
+ 
+
+ align:start position:0%
+chain so the question is if I start
+stacking up this pile of parameters
+
+ align:start position:0%
+stacking up this pile of parameters
+ 
+
+ align:start position:0%
+stacking up this pile of parameters
+right so I start with my uh beta which
+
+ align:start position:0%
+right so I start with my uh beta which
+ 
+
+ align:start position:0%
+right so I start with my uh beta which
+in terms gives me a me which in terms
+
+ align:start position:0%
+in terms gives me a me which in terms
+ 
+
+ align:start position:0%
+in terms gives me a me which in terms
+gives me a Theta can I just have like a
+
+ align:start position:0%
+gives me a Theta can I just have like a
+ 
+
+ align:start position:0%
+gives me a Theta can I just have like a
+long
+
+ align:start position:0%
+long
+ 
+
+ align:start position:0%
+long
+streamlined uh uh can I what what what
+
+ align:start position:0%
+streamlined uh uh can I what what what
+ 
+
+ align:start position:0%
+streamlined uh uh can I what what what
+is the outcome when I actually start
+
+ align:start position:0%
+is the outcome when I actually start
+ 
+
+ align:start position:0%
+is the outcome when I actually start
+writing my likelihood not as a function
+
+ align:start position:0%
+writing my likelihood not as a function
+ 
+
+ align:start position:0%
+writing my likelihood not as a function
+of theta not as a function of mu but as
+
+ align:start position:0%
+of theta not as a function of mu but as
+ 
+
+ align:start position:0%
+of theta not as a function of mu but as
+a function of beta which is the one at
+
+ align:start position:0%
+a function of beta which is the one at
+ 
+
+ align:start position:0%
+a function of beta which is the one at
+the end of the chain okay and hopefully
+
+ align:start position:0%
+the end of the chain okay and hopefully
+ 
+
+ align:start position:0%
+the end of the chain okay and hopefully
+things are going to happen nicely and
+
+ align:start position:0%
+things are going to happen nicely and
+ 
+
+ align:start position:0%
+things are going to happen nicely and
+they might not
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah is G is G that's my link right G of
+
+ align:start position:0%
+yeah is G is G that's my link right G of
+ 
+
+ align:start position:0%
+yeah is G is G that's my link right G of
+mu of X now it's mu is a function of X
+
+ align:start position:0%
+mu of X now it's mu is a function of X
+ 
+
+ align:start position:0%
+mu of X now it's mu is a function of X
+because it's conditional on
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+X okay so this is really Theta of
+
+ align:start position:0%
+X okay so this is really Theta of
+ 
+
+ align:start position:0%
+X okay so this is really Theta of
+X mu of X but B is not a function of X
+
+ align:start position:0%
+X mu of X but B is not a function of X
+ 
+
+ align:start position:0%
+X mu of X but B is not a function of X
+because it's just a there just something
+
+ align:start position:0%
+because it's just a there just something
+ 
+
+ align:start position:0%
+because it's just a there just something
+that tells me what the function of X
+
+ align:start position:0%
+that tells me what the function of X
+ 
+
+ align:start position:0%
+that tells me what the function of X
+is m
+
+ align:start position:0%
+is m
+ 
+
+ align:start position:0%
+is m
+new is the conditional expectation of Y
+
+ align:start position:0%
+new is the conditional expectation of Y
+ 
+
+ align:start position:0%
+new is the conditional expectation of Y
+given X it has actually a fancy name in
+
+ align:start position:0%
+given X it has actually a fancy name in
+ 
+
+ align:start position:0%
+given X it has actually a fancy name in
+the statistics literature it's
+
+ align:start position:0%
+the statistics literature it's
+ 
+
+ align:start position:0%
+the statistics literature it's
+called anybody knows the name of this
+
+ align:start position:0%
+called anybody knows the name of this
+ 
+
+ align:start position:0%
+called anybody knows the name of this
+function U of X which is the conditional
+
+ align:start position:0%
+function U of X which is the conditional
+ 
+
+ align:start position:0%
+function U of X which is the conditional
+expectation of Y given
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+X that's the regression function that's
+
+ align:start position:0%
+X that's the regression function that's
+ 
+
+ align:start position:0%
+X that's the regression function that's
+actual definition if I tell you what is
+
+ align:start position:0%
+actual definition if I tell you what is
+ 
+
+ align:start position:0%
+actual definition if I tell you what is
+the definition of the regression
+
+ align:start position:0%
+the definition of the regression
+ 
+
+ align:start position:0%
+the definition of the regression
+function that's just the conditional
+
+ align:start position:0%
+function that's just the conditional
+ 
+
+ align:start position:0%
+function that's just the conditional
+expectation of y
+
+ align:start position:0%
+expectation of y
+ 
+
+ align:start position:0%
+expectation of y
+x and uh just you know I could look at
+
+ align:start position:0%
+x and uh just you know I could look at
+ 
+
+ align:start position:0%
+x and uh just you know I could look at
+any property of the conditional
+
+ align:start position:0%
+any property of the conditional
+ 
+
+ align:start position:0%
+any property of the conditional
+distribution of Y given X I could look
+
+ align:start position:0%
+distribution of Y given X I could look
+ 
+
+ align:start position:0%
+distribution of Y given X I could look
+at the conditional 95th percentile I
+
+ align:start position:0%
+at the conditional 95th percentile I
+ 
+
+ align:start position:0%
+at the conditional 95th percentile I
+could look at the conditional median I
+
+ align:start position:0%
+could look at the conditional median I
+ 
+
+ align:start position:0%
+could look at the conditional median I
+could look at the conditional inter
+
+ align:start position:0%
+could look at the conditional inter
+ 
+
+ align:start position:0%
+could look at the conditional inter
+profile range could look at the
+
+ align:start position:0%
+profile range could look at the
+ 
+
+ align:start position:0%
+profile range could look at the
+conditional variance but I decide to
+
+ align:start position:0%
+conditional variance but I decide to
+ 
+
+ align:start position:0%
+conditional variance but I decide to
+look at the conditional expectation
+
+ align:start position:0%
+look at the conditional expectation
+ 
+
+ align:start position:0%
+look at the conditional expectation
+which is uh called the regression
+
+ align:start position:0%
+which is uh called the regression
+ 
+
+ align:start position:0%
+which is uh called the regression
+function okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yes oh there's no transpose here uh
+
+ align:start position:0%
+yes oh there's no transpose here uh
+ 
+
+ align:start position:0%
+yes oh there's no transpose here uh
+actually only Victor Manuel uses Prime
+
+ align:start position:0%
+actually only Victor Manuel uses Prime
+ 
+
+ align:start position:0%
+actually only Victor Manuel uses Prime
+for transpose and I found it confusing
+
+ align:start position:0%
+for transpose and I found it confusing
+ 
+
+ align:start position:0%
+for transpose and I found it confusing
+with the derivatives so primes here is
+
+ align:start position:0%
+with the derivatives so primes here is
+ 
+
+ align:start position:0%
+with the derivatives so primes here is
+only a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+derivative oh yeah sorry beta transpose
+
+ align:start position:0%
+derivative oh yeah sorry beta transpose
+ 
+
+ align:start position:0%
+derivative oh yeah sorry beta transpose
+X sorry I thought you okay so you said
+
+ align:start position:0%
+X sorry I thought you okay so you said
+ 
+
+ align:start position:0%
+X sorry I thought you okay so you said
+what I said that g of mu of X is beta
+
+ align:start position:0%
+what I said that g of mu of X is beta
+ 
+
+ align:start position:0%
+what I said that g of mu of X is beta
+transpose
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+X isn't that the same
+
+ align:start position:0%
+X isn't that the same
+ 
+
+ align:start position:0%
+X isn't that the same
+thing those X is a vector here right so
+
+ align:start position:0%
+thing those X is a vector here right so
+ 
+
+ align:start position:0%
+thing those X is a vector here right so
+X trans beta and beta transpose X are
+
+ align:start position:0%
+X trans beta and beta transpose X are
+ 
+
+ align:start position:0%
+X trans beta and beta transpose X are
+the same
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+thing right so beta is looks like this x
+
+ align:start position:0%
+thing right so beta is looks like this x
+ 
+
+ align:start position:0%
+thing right so beta is looks like this x
+looks like this so it's just simple
+
+ align:start position:0%
+looks like this so it's just simple
+ 
+
+ align:start position:0%
+looks like this so it's just simple
+simple
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+number yeah you're right when I I'm
+
+ align:start position:0%
+number yeah you're right when I I'm
+ 
+
+ align:start position:0%
+number yeah you're right when I I'm
+going to start to look at matrices I'm
+
+ align:start position:0%
+going to start to look at matrices I'm
+ 
+
+ align:start position:0%
+going to start to look at matrices I'm
+going to have to be slightly more
+
+ align:start position:0%
+going to have to be slightly more
+ 
+
+ align:start position:0%
+going to have to be slightly more
+careful when I do
+
+ align:start position:0%
+careful when I do
+ 
+
+ align:start position:0%
+careful when I do
+this okay so let's do the reverse
+
+ align:start position:0%
+this okay so let's do the reverse
+ 
+
+ align:start position:0%
+this okay so let's do the reverse
+engineering I'm giving you data from
+
+ align:start position:0%
+engineering I'm giving you data from
+ 
+
+ align:start position:0%
+engineering I'm giving you data from
+this data hopefully you should be able
+
+ align:start position:0%
+this data hopefully you should be able
+ 
+
+ align:start position:0%
+this data hopefully you should be able
+to get what the conditional if I give
+
+ align:start position:0%
+to get what the conditional if I give
+ 
+
+ align:start position:0%
+to get what the conditional if I give
+you an infinite amount of data you would
+
+ align:start position:0%
+you an infinite amount of data you would
+ 
+
+ align:start position:0%
+you an infinite amount of data you would
+know exactly what the of pairs X Y you
+
+ align:start position:0%
+know exactly what the of pairs X Y you
+ 
+
+ align:start position:0%
+know exactly what the of pairs X Y you
+would know exactly what the conditional
+
+ align:start position:0%
+would know exactly what the conditional
+ 
+
+ align:start position:0%
+would know exactly what the conditional
+distribution of Y given X
+
+ align:start position:0%
+distribution of Y given X
+ 
+
+ align:start position:0%
+distribution of Y given X
+is and uh in particular you would know
+
+ align:start position:0%
+is and uh in particular you would know
+ 
+
+ align:start position:0%
+is and uh in particular you would know
+what the conditional expectation of Y
+
+ align:start position:0%
+what the conditional expectation of Y
+ 
+
+ align:start position:0%
+what the conditional expectation of Y
+given X is which means that you would
+
+ align:start position:0%
+given X is which means that you would
+ 
+
+ align:start position:0%
+given X is which means that you would
+know mu which means that you would know
+
+ align:start position:0%
+know mu which means that you would know
+ 
+
+ align:start position:0%
+know mu which means that you would know
+Theta which means that you would know
+
+ align:start position:0%
+Theta which means that you would know
+ 
+
+ align:start position:0%
+Theta which means that you would know
+beta okay now when I have a finite
+
+ align:start position:0%
+beta okay now when I have a finite
+ 
+
+ align:start position:0%
+beta okay now when I have a finite
+number of observations I'm going to try
+
+ align:start position:0%
+number of observations I'm going to try
+ 
+
+ align:start position:0%
+number of observations I'm going to try
+to estimate mu of X but really I'm going
+
+ align:start position:0%
+to estimate mu of X but really I'm going
+ 
+
+ align:start position:0%
+to estimate mu of X but really I'm going
+to go the other round way around because
+
+ align:start position:0%
+to go the other round way around because
+ 
+
+ align:start position:0%
+to go the other round way around because
+the fact that I assume specific that mu
+
+ align:start position:0%
+the fact that I assume specific that mu
+ 
+
+ align:start position:0%
+the fact that I assume specific that mu
+of X is of the form G of mu of X is X
+
+ align:start position:0%
+of X is of the form G of mu of X is X
+ 
+
+ align:start position:0%
+of X is of the form G of mu of X is X
+transpose beta then that means that I
+
+ align:start position:0%
+transpose beta then that means that I
+ 
+
+ align:start position:0%
+transpose beta then that means that I
+only have to estimate beta which is a
+
+ align:start position:0%
+only have to estimate beta which is a
+ 
+
+ align:start position:0%
+only have to estimate beta which is a
+much simpler object than the entire
+
+ align:start position:0%
+much simpler object than the entire
+ 
+
+ align:start position:0%
+much simpler object than the entire
+regression function okay and so that's
+
+ align:start position:0%
+regression function okay and so that's
+ 
+
+ align:start position:0%
+regression function okay and so that's
+what I'm going to go for I'm going to
+
+ align:start position:0%
+what I'm going to go for I'm going to
+ 
+
+ align:start position:0%
+what I'm going to go for I'm going to
+try to represent the likelihood the log
+
+ align:start position:0%
+try to represent the likelihood the log
+ 
+
+ align:start position:0%
+try to represent the likelihood the log
+likelihood of my data as a function not
+
+ align:start position:0%
+likelihood of my data as a function not
+ 
+
+ align:start position:0%
+likelihood of my data as a function not
+of theta not of mu but of beta and then
+
+ align:start position:0%
+of theta not of mu but of beta and then
+ 
+
+ align:start position:0%
+of theta not of mu but of beta and then
+maximize that guy all right so now
+
+ align:start position:0%
+maximize that guy all right so now
+ 
+
+ align:start position:0%
+maximize that guy all right so now
+rather than thinking of just one
+
+ align:start position:0%
+rather than thinking of just one
+ 
+
+ align:start position:0%
+rather than thinking of just one
+observation I'm going to have a bunch of
+
+ align:start position:0%
+observation I'm going to have a bunch of
+ 
+
+ align:start position:0%
+observation I'm going to have a bunch of
+observations and every time you see here
+
+ align:start position:0%
+observations and every time you see here
+ 
+
+ align:start position:0%
+observations and every time you see here
+so this might actually look a little
+
+ align:start position:0%
+so this might actually look a little
+ 
+
+ align:start position:0%
+so this might actually look a little
+confusing but uh let's just make sure
+
+ align:start position:0%
+confusing but uh let's just make sure
+ 
+
+ align:start position:0%
+confusing but uh let's just make sure
+that we understand each other before we
+
+ align:start position:0%
+that we understand each other before we
+ 
+
+ align:start position:0%
+that we understand each other before we
+go any further so I'm going to have
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+observations X1
+
+ align:start position:0%
+observations X1
+ 
+
+ align:start position:0%
+observations X1
+y1 all the way to xn YN just like in a
+
+ align:start position:0%
+y1 all the way to xn YN just like in a
+ 
+
+ align:start position:0%
+y1 all the way to xn YN just like in a
+natural regression problem except that
+
+ align:start position:0%
+natural regression problem except that
+ 
+
+ align:start position:0%
+natural regression problem except that
+here my y's might be zero1 valued they
+
+ align:start position:0%
+here my y's might be zero1 valued they
+ 
+
+ align:start position:0%
+here my y's might be zero1 valued they
+might be positive value they might be
+
+ align:start position:0%
+might be positive value they might be
+ 
+
+ align:start position:0%
+might be positive value they might be
+exponential they might be anything in
+
+ align:start position:0%
+exponential they might be anything in
+ 
+
+ align:start position:0%
+exponential they might be anything in
+the canonical exponential family and
+
+ align:start position:0%
+the canonical exponential family and
+ 
+
+ align:start position:0%
+the canonical exponential family and
+um okay so I have this uh I have this
+
+ align:start position:0%
+um okay so I have this uh I have this
+ 
+
+ align:start position:0%
+um okay so I have this uh I have this
+thing and now what I have is that so my
+
+ align:start position:0%
+thing and now what I have is that so my
+ 
+
+ align:start position:0%
+thing and now what I have is that so my
+observations are X1 y1 xn YN and what I
+
+ align:start position:0%
+observations are X1 y1 xn YN and what I
+ 
+
+ align:start position:0%
+observations are X1 y1 xn YN and what I
+want is that uh I'm going to talk about
+
+ align:start position:0%
+want is that uh I'm going to talk about
+ 
+
+ align:start position:0%
+want is that uh I'm going to talk about
+I'm going to assume that the conditional
+
+ align:start position:0%
+I'm going to assume that the conditional
+ 
+
+ align:start position:0%
+I'm going to assume that the conditional
+expectation of Yi given X
+
+ align:start position:0%
+expectation of Yi given X
+ 
+
+ align:start position:0%
+expectation of Yi given X
+sorry yeah the conditional the
+
+ align:start position:0%
+sorry yeah the conditional the
+ 
+
+ align:start position:0%
+sorry yeah the conditional the
+conditional distribution of Yi given XI
+
+ align:start position:0%
+conditional distribution of Yi given XI
+ 
+
+ align:start position:0%
+conditional distribution of Yi given XI
+is something that has density
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+did I put an eye on white
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah I'm not going to deal with the FI
+
+ align:start position:0%
+yeah I'm not going to deal with the FI
+ 
+
+ align:start position:0%
+yeah I'm not going to deal with the FI
+and the C now and what why do I have
+
+ align:start position:0%
+and the C now and what why do I have
+ 
+
+ align:start position:0%
+and the C now and what why do I have
+Theta I and not Theta is because Theta I
+
+ align:start position:0%
+Theta I and not Theta is because Theta I
+ 
+
+ align:start position:0%
+Theta I and not Theta is because Theta I
+is really a function of the of um uh
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+of x i right so it's really Theta I of x
+
+ align:start position:0%
+of x i right so it's really Theta I of x
+ 
+
+ align:start position:0%
+of x i right so it's really Theta I of x
+i but what do I know about Theta I of XI
+
+ align:start position:0%
+i but what do I know about Theta I of XI
+ 
+
+ align:start position:0%
+i but what do I know about Theta I of XI
+it's actually equal
+
+ align:start position:0%
+it's actually equal
+ 
+
+ align:start position:0%
+it's actually equal
+to um B I did this error twice B Prime
+
+ align:start position:0%
+to um B I did this error twice B Prime
+ 
+
+ align:start position:0%
+to um B I did this error twice B Prime
+inverse of mu of XI
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay and also know that this thing is
+
+ align:start position:0%
+okay and also know that this thing is
+ 
+
+ align:start position:0%
+okay and also know that this thing is
+actually I'm going to assume that this
+
+ align:start position:0%
+actually I'm going to assume that this
+ 
+
+ align:start position:0%
+actually I'm going to assume that this
+is of the form beta transpose XI okay
+
+ align:start position:0%
+is of the form beta transpose XI okay
+ 
+
+ align:start position:0%
+is of the form beta transpose XI okay
+and this is why I have a Theta I is
+
+ align:start position:0%
+and this is why I have a Theta I is
+ 
+
+ align:start position:0%
+and this is why I have a Theta I is
+because this Theta I is a function of XI
+
+ align:start position:0%
+because this Theta I is a function of XI
+ 
+
+ align:start position:0%
+because this Theta I is a function of XI
+and I'm going to assume a very simple
+
+ align:start position:0%
+and I'm going to assume a very simple
+ 
+
+ align:start position:0%
+and I'm going to assume a very simple
+form for this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+thing sorry sorry sorry sorry that's uh
+
+ align:start position:0%
+thing sorry sorry sorry sorry that's uh
+ 
+
+ align:start position:0%
+thing sorry sorry sorry sorry that's uh
+yeah sorry I should not write it like
+
+ align:start position:0%
+yeah sorry I should not write it like
+ 
+
+ align:start position:0%
+yeah sorry I should not write it like
+this this is only when I have the
+
+ align:start position:0%
+this this is only when I have the
+ 
+
+ align:start position:0%
+this this is only when I have the
+canonical length so this is actually
+
+ align:start position:0%
+canonical length so this is actually
+ 
+
+ align:start position:0%
+canonical length so this is actually
+equal to B Prime inverse of G of X I
+
+ align:start position:0%
+equal to B Prime inverse of G of X I
+ 
+
+ align:start position:0%
+equal to B Prime inverse of G of X I
+transpose
+
+ align:start position:0%
+transpose
+ 
+
+ align:start position:0%
+transpose
+Beta And when I have the canonical
+
+ align:start position:0%
+Beta And when I have the canonical
+ 
+
+ align:start position:0%
+Beta And when I have the canonical
+link sorry G inverse those two things
+
+ align:start position:0%
+link sorry G inverse those two things
+ 
+
+ align:start position:0%
+link sorry G inverse those two things
+are actually canceling each
+
+ align:start position:0%
+are actually canceling each
+ 
+
+ align:start position:0%
+are actually canceling each
+other
+
+ align:start position:0%
+other
+ 
+
+ align:start position:0%
+other
+okay so as before I'm going to stack
+
+ align:start position:0%
+okay so as before I'm going to stack
+ 
+
+ align:start position:0%
+okay so as before I'm going to stack
+everything into some uh well actually
+
+ align:start position:0%
+everything into some uh well actually
+ 
+
+ align:start position:0%
+everything into some uh well actually
+I'm not going to stack anything for the
+
+ align:start position:0%
+I'm not going to stack anything for the
+ 
+
+ align:start position:0%
+I'm not going to stack anything for the
+moment I'm just going to give you a peek
+
+ align:start position:0%
+moment I'm just going to give you a peek
+ 
+
+ align:start position:0%
+moment I'm just going to give you a peek
+at what's happening next week uh rather
+
+ align:start position:0%
+at what's happening next week uh rather
+ 
+
+ align:start position:0%
+at what's happening next week uh rather
+than just manipulating uh the data all
+
+ align:start position:0%
+than just manipulating uh the data all
+ 
+
+ align:start position:0%
+than just manipulating uh the data all
+right
+
+ align:start position:0%
+right
+ 
+
+ align:start position:0%
+right
+so here is how we're going to proceed at
+
+ align:start position:0%
+so here is how we're going to proceed at
+ 
+
+ align:start position:0%
+so here is how we're going to proceed at
+this
+
+ align:start position:0%
+this
+ 
+
+ align:start position:0%
+this
+point well now I'm going to want to
+
+ align:start position:0%
+point well now I'm going to want to
+ 
+
+ align:start position:0%
+point well now I'm going to want to
+write my likelihood function not as a
+
+ align:start position:0%
+write my likelihood function not as a
+ 
+
+ align:start position:0%
+write my likelihood function not as a
+function of theta but as a function of
+
+ align:start position:0%
+function of theta but as a function of
+ 
+
+ align:start position:0%
+function of theta but as a function of
+beta because that that's the parameter
+
+ align:start position:0%
+beta because that that's the parameter
+ 
+
+ align:start position:0%
+beta because that that's the parameter
+I'm actually trying to maximize
+
+ align:start position:0%
+I'm actually trying to maximize
+ 
+
+ align:start position:0%
+I'm actually trying to maximize
+right so if I have a link so this thing
+
+ align:start position:0%
+right so if I have a link so this thing
+ 
+
+ align:start position:0%
+right so if I have a link so this thing
+that matters here I'm going to call
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+H by definition this is going to be h of
+
+ align:start position:0%
+H by definition this is going to be h of
+ 
+
+ align:start position:0%
+H by definition this is going to be h of
+X I transpose beta Helena you have a
+
+ align:start position:0%
+X I transpose beta Helena you have a
+ 
+
+ align:start position:0%
+X I transpose beta Helena you have a
+question okay so right so this is just
+
+ align:start position:0%
+question okay so right so this is just
+ 
+
+ align:start position:0%
+question okay so right so this is just
+the all the things that we know right
+
+ align:start position:0%
+the all the things that we know right
+ 
+
+ align:start position:0%
+the all the things that we know right
+Theta is just the by definition of the
+
+ align:start position:0%
+Theta is just the by definition of the
+ 
+
+ align:start position:0%
+Theta is just the by definition of the
+fact that mu is B Prime of theta the
+
+ align:start position:0%
+fact that mu is B Prime of theta the
+ 
+
+ align:start position:0%
+fact that mu is B Prime of theta the
+mean is B Prime of theta it means that
+
+ align:start position:0%
+mean is B Prime of theta it means that
+ 
+
+ align:start position:0%
+mean is B Prime of theta it means that
+Theta is B Prime inverse of mu and then
+
+ align:start position:0%
+Theta is B Prime inverse of mu and then
+ 
+
+ align:start position:0%
+Theta is B Prime inverse of mu and then
+uh mu is modeled from the systematic
+
+ align:start position:0%
+uh mu is modeled from the systematic
+ 
+
+ align:start position:0%
+uh mu is modeled from the systematic
+component G of mu is X I transpose beta
+
+ align:start position:0%
+component G of mu is X I transpose beta
+ 
+
+ align:start position:0%
+component G of mu is X I transpose beta
+so this is G inverse of X I transpose
+
+ align:start position:0%
+so this is G inverse of X I transpose
+ 
+
+ align:start position:0%
+so this is G inverse of X I transpose
+beta so I want to have B Prime IND
+
+ align:start position:0%
+beta so I want to have B Prime IND
+ 
+
+ align:start position:0%
+beta so I want to have B Prime IND
+inverse of G Prime of G inverse this
+
+ align:start position:0%
+inverse of G Prime of G inverse this
+ 
+
+ align:start position:0%
+inverse of G Prime of G inverse this
+function is a bit annoying to say so I'm
+
+ align:start position:0%
+function is a bit annoying to say so I'm
+ 
+
+ align:start position:0%
+function is a bit annoying to say so I'm
+just going to call it
+
+ align:start position:0%
+just going to call it
+ 
+
+ align:start position:0%
+just going to call it
+h and when I do the composition of two
+
+ align:start position:0%
+h and when I do the composition of two
+ 
+
+ align:start position:0%
+h and when I do the composition of two
+inverse it's the inverse of the
+
+ align:start position:0%
+inverse it's the inverse of the
+ 
+
+ align:start position:0%
+inverse it's the inverse of the
+composition of those two things in the
+
+ align:start position:0%
+composition of those two things in the
+ 
+
+ align:start position:0%
+composition of those two things in the
+reverse order so H is really the inverse
+
+ align:start position:0%
+reverse order so H is really the inverse
+ 
+
+ align:start position:0%
+reverse order so H is really the inverse
+of G composed with B Prime G of B Prime
+
+ align:start position:0%
+of G composed with B Prime G of B Prime
+ 
+
+ align:start position:0%
+of G composed with B Prime G of B Prime
+inverse okay and now if I have the
+
+ align:start position:0%
+inverse okay and now if I have the
+ 
+
+ align:start position:0%
+inverse okay and now if I have the
+canonical length since I know that g is
+
+ align:start position:0%
+canonical length since I know that g is
+ 
+
+ align:start position:0%
+canonical length since I know that g is
+B Prime inverse this is really just the
+
+ align:start position:0%
+B Prime inverse this is really just the
+ 
+
+ align:start position:0%
+B Prime inverse this is really just the
+identity so as you can imagine
+
+ align:start position:0%
+identity so as you can imagine
+ 
+
+ align:start position:0%
+identity so as you can imagine
+this entire
+
+ align:start position:0%
+this entire
+ 
+
+ align:start position:0%
+this entire
+thing which is actually quite
+
+ align:start position:0%
+thing which is actually quite
+ 
+
+ align:start position:0%
+thing which is actually quite
+complicated would just say oh this thing
+
+ align:start position:0%
+complicated would just say oh this thing
+ 
+
+ align:start position:0%
+complicated would just say oh this thing
+actually does not show up when I have
+
+ align:start position:0%
+actually does not show up when I have
+ 
+
+ align:start position:0%
+actually does not show up when I have
+the canonical link I really just have
+
+ align:start position:0%
+the canonical link I really just have
+ 
+
+ align:start position:0%
+the canonical link I really just have
+that Theta I can be replaced by XI of
+
+ align:start position:0%
+that Theta I can be replaced by XI of
+ 
+
+ align:start position:0%
+that Theta I can be replaced by XI of
+beta so think about going back to this
+
+ align:start position:0%
+beta so think about going back to this
+ 
+
+ align:start position:0%
+beta so think about going back to this
+guy here now beta theta becomes only XI
+
+ align:start position:0%
+guy here now beta theta becomes only XI
+ 
+
+ align:start position:0%
+guy here now beta theta becomes only XI
+transpose
+
+ align:start position:0%
+transpose
+ 
+
+ align:start position:0%
+transpose
+beta that's going to be much more simple
+
+ align:start position:0%
+beta that's going to be much more simple
+ 
+
+ align:start position:0%
+beta that's going to be much more simple
+simple to optimize because remember when
+
+ align:start position:0%
+simple to optimize because remember when
+ 
+
+ align:start position:0%
+simple to optimize because remember when
+I'm going to do log likelihood this
+
+ align:start position:0%
+I'm going to do log likelihood this
+ 
+
+ align:start position:0%
+I'm going to do log likelihood this
+thing is going to go away I'm going to
+
+ align:start position:0%
+thing is going to go away I'm going to
+ 
+
+ align:start position:0%
+thing is going to go away I'm going to
+sum those guys and so what I'm going to
+
+ align:start position:0%
+sum those guys and so what I'm going to
+ 
+
+ align:start position:0%
+sum those guys and so what I'm going to
+have is something which is essentially
+
+ align:start position:0%
+have is something which is essentially
+ 
+
+ align:start position:0%
+have is something which is essentially
+linear in beta and then I'm going to
+
+ align:start position:0%
+linear in beta and then I'm going to
+ 
+
+ align:start position:0%
+linear in beta and then I'm going to
+have this minus B which is just minus
+
+ align:start position:0%
+have this minus B which is just minus
+ 
+
+ align:start position:0%
+have this minus B which is just minus
+the sum of convex functions of beta so
+
+ align:start position:0%
+the sum of convex functions of beta so
+ 
+
+ align:start position:0%
+the sum of convex functions of beta so
+I'm going to have to bring in the tools
+
+ align:start position:0%
+I'm going to have to bring in the tools
+ 
+
+ align:start position:0%
+I'm going to have to bring in the tools
+of convex optimization now it's not just
+
+ align:start position:0%
+of convex optimization now it's not just
+ 
+
+ align:start position:0%
+of convex optimization now it's not just
+going to be take the gradient set it to
+
+ align:start position:0%
+going to be take the gradient set it to
+ 
+
+ align:start position:0%
+going to be take the gradient set it to
+zero it's going to be more complicated
+
+ align:start position:0%
+zero it's going to be more complicated
+ 
+
+ align:start position:0%
+zero it's going to be more complicated
+to do that I'm going to have to do that
+
+ align:start position:0%
+to do that I'm going to have to do that
+ 
+
+ align:start position:0%
+to do that I'm going to have to do that
+in an iterative fashion and so that's
+
+ align:start position:0%
+in an iterative fashion and so that's
+ 
+
+ align:start position:0%
+in an iterative fashion and so that's
+what I'm telling you when you look at
+
+ align:start position:0%
+what I'm telling you when you look at
+ 
+
+ align:start position:0%
+what I'm telling you when you look at
+your log likelihood for all those
+
+ align:start position:0%
+your log likelihood for all those
+ 
+
+ align:start position:0%
+your log likelihood for all those
+functions you sum the exponential goes
+
+ align:start position:0%
+functions you sum the exponential goes
+ 
+
+ align:start position:0%
+functions you sum the exponential goes
+away because you had the log and then
+
+ align:start position:0%
+away because you had the log and then
+ 
+
+ align:start position:0%
+away because you had the log and then
+you have all these things here I kept
+
+ align:start position:0%
+you have all these things here I kept
+ 
+
+ align:start position:0%
+you have all these things here I kept
+the B I kept the H but if H is the
+
+ align:start position:0%
+the B I kept the H but if H is the
+ 
+
+ align:start position:0%
+the B I kept the H but if H is the
+identity this is the linear function the
+
+ align:start position:0%
+identity this is the linear function the
+ 
+
+ align:start position:0%
+identity this is the linear function the
+linear part y i * X I transpose beta
+
+ align:start position:0%
+linear part y i * X I transpose beta
+ 
+
+ align:start position:0%
+linear part y i * X I transpose beta
+minus B of my Theta which is now only X
+
+ align:start position:0%
+minus B of my Theta which is now only X
+ 
+
+ align:start position:0%
+minus B of my Theta which is now only X
+I transpose beta and that's the function
+
+ align:start position:0%
+I transpose beta and that's the function
+ 
+
+ align:start position:0%
+I transpose beta and that's the function
+I want to maximize in
+
+ align:start position:0%
+I want to maximize in
+ 
+
+ align:start position:0%
+I want to maximize in
+beta
+
+ align:start position:0%
+beta
+ 
+
+ align:start position:0%
+beta
+okay that's a simple I mean it's a
+
+ align:start position:0%
+okay that's a simple I mean it's a
+ 
+
+ align:start position:0%
+okay that's a simple I mean it's a
+complex function when I know what B is I
+
+ align:start position:0%
+complex function when I know what B is I
+ 
+
+ align:start position:0%
+complex function when I know what B is I
+have an explicit formula formula for
+
+ align:start position:0%
+have an explicit formula formula for
+ 
+
+ align:start position:0%
+have an explicit formula formula for
+this and I want to just bring in some
+
+ align:start position:0%
+this and I want to just bring in some
+ 
+
+ align:start position:0%
+this and I want to just bring in some
+optimization and uh that's uh what we're
+
+ align:start position:0%
+optimization and uh that's uh what we're
+ 
+
+ align:start position:0%
+optimization and uh that's uh what we're
+going to do and we're going to see three
+
+ align:start position:0%
+going to do and we're going to see three
+ 
+
+ align:start position:0%
+going to do and we're going to see three
+different methods which are really
+
+ align:start position:0%
+different methods which are really
+ 
+
+ align:start position:0%
+different methods which are really
+basically the same method it's something
+
+ align:start position:0%
+basically the same method it's something
+ 
+
+ align:start position:0%
+basically the same method it's something
+which is B based on it's just a
+
+ align:start position:0%
+which is B based on it's just a
+ 
+
+ align:start position:0%
+which is B based on it's just a
+adaptation or specialization of the
+
+ align:start position:0%
+adaptation or specialization of the
+ 
+
+ align:start position:0%
+adaptation or specialization of the
+So-Cal Newton rapon method which is
+
+ align:start position:0%
+So-Cal Newton rapon method which is
+ 
+
+ align:start position:0%
+So-Cal Newton rapon method which is
+essentially telling you do iterative
+
+ align:start position:0%
+essentially telling you do iterative
+ 
+
+ align:start position:0%
+essentially telling you do iterative
+local quadratic approximation to your
+
+ align:start position:0%
+local quadratic approximation to your
+ 
+
+ align:start position:0%
+local quadratic approximation to your
+function so second order tiller
+
+ align:start position:0%
+function so second order tiller
+ 
+
+ align:start position:0%
+function so second order tiller
+expansion minimize this guy and then do
+
+ align:start position:0%
+expansion minimize this guy and then do
+ 
+
+ align:start position:0%
+expansion minimize this guy and then do
+it again from where you were okay and uh
+
+ align:start position:0%
+it again from where you were okay and uh
+ 
+
+ align:start position:0%
+it again from where you were okay and uh
+we'll see that this can be actually
+
+ align:start position:0%
+we'll see that this can be actually
+ 
+
+ align:start position:0%
+we'll see that this can be actually
+implemented using what's called
+
+ align:start position:0%
+implemented using what's called
+ 
+
+ align:start position:0%
+implemented using what's called
+iteratively reweighted Le squares which
+
+ align:start position:0%
+iteratively reweighted Le squares which
+ 
+
+ align:start position:0%
+iteratively reweighted Le squares which
+means that every step since it's just a
+
+ align:start position:0%
+means that every step since it's just a
+ 
+
+ align:start position:0%
+means that every step since it's just a
+quadratic it's going to be just squares
+
+ align:start position:0%
+quadratic it's going to be just squares
+ 
+
+ align:start position:0%
+quadratic it's going to be just squares
+in there every step can actually be
+
+ align:start position:0%
+in there every step can actually be
+ 
+
+ align:start position:0%
+in there every step can actually be
+solved by using awaited uh e squares
+
+ align:start position:0%
+solved by using awaited uh e squares
+ 
+
+ align:start position:0%
+solved by using awaited uh e squares
+version of the problem okay so uh I'm
+
+ align:start position:0%
+version of the problem okay so uh I'm
+ 
+
+ align:start position:0%
+version of the problem okay so uh I'm
+going to stop here for today so we'll
+
+ align:start position:0%
+going to stop here for today so we'll
+ 
+
+ align:start position:0%
+going to stop here for today so we'll
+continue and uh uh probably not finish
+
+ align:start position:0%
+continue and uh uh probably not finish
+ 
+
+ align:start position:0%
+continue and uh uh probably not finish
+this chapter but finish next week and uh
+
+ align:start position:0%
+this chapter but finish next week and uh
+ 
+
+ align:start position:0%
+this chapter but finish next week and uh
+and then I think there's only one
+
+ align:start position:0%
+and then I think there's only one
+ 
+
+ align:start position:0%
+and then I think there's only one
+lecture um actually for the last lecture
+
+ align:start position:0%
+lecture um actually for the last lecture
+ 
+
+ align:start position:0%
+lecture um actually for the last lecture
+what do you guys want to
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+do do you want to have donuts and cider
+
+ align:start position:0%
+do do you want to have donuts and cider
+ 
+
+ align:start position:0%
+do do you want to have donuts and cider
+do you wanna do you want to just have
+
+ align:start position:0%
+do you wanna do you want to just have
+ 
+
+ align:start position:0%
+do you wanna do you want to just have
+like some more like uh outlooking uh uh
+
+ align:start position:0%
+like some more like uh outlooking uh uh
+ 
+
+ align:start position:0%
+like some more like uh outlooking uh uh
+lecture on you know what's uh happening
+
+ align:start position:0%
+lecture on you know what's uh happening
+ 
+
+ align:start position:0%
+lecture on you know what's uh happening
+post 1975 in
+
+ align:start position:0%
+post 1975 in
+ 
+
+ align:start position:0%
+post 1975 in
+statistics uh do you want to have a a
+
+ align:start position:0%
+statistics uh do you want to have a a
+ 
+
+ align:start position:0%
+statistics uh do you want to have a a
+review for the final
+
+ align:start position:0%
+review for the final
+ 
+
+ align:start position:0%
+review for the final
+exam pragmatic people all
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+right you want to do interesting advanc
+
+ align:start position:0%
+right you want to do interesting advanc
+ 
+
+ align:start position:0%
+right you want to do interesting advanc
+for for the last lecture yeah so that's
+
+ align:start position:0%
+for for the last lecture yeah so that's
+ 
+
+ align:start position:0%
+for for the last lecture yeah so that's
+sort
+
+ align:start position:0%
+sort
+ 
+
+ align:start position:0%
+sort
+of yeah the thing is I think uh so this
+
+ align:start position:0%
+of yeah the thing is I think uh so this
+ 
+
+ align:start position:0%
+of yeah the thing is I think uh so this
+there's two that that's basically what
+
+ align:start position:0%
+there's two that that's basically what
+ 
+
+ align:start position:0%
+there's two that that's basically what
+I'm asking right interesting topics
+
+ align:start position:0%
+I'm asking right interesting topics
+ 
+
+ align:start position:0%
+I'm asking right interesting topics
+versus uh uh let's like ask me any
+
+ align:start position:0%
+versus uh uh let's like ask me any
+ 
+
+ align:start position:0%
+versus uh uh let's like ask me any
+question you want those questions can be
+
+ align:start position:0%
+question you want those questions can be
+ 
+
+ align:start position:0%
+question you want those questions can be
+about interesting Advanced topics though
+
+ align:start position:0%
+about interesting Advanced topics though
+ 
+
+ align:start position:0%
+about interesting Advanced topics though
+like what are interesting Advanced
+
+ align:start position:0%
+like what are interesting Advanced
+ 
+
+ align:start position:0%
+like what are interesting Advanced
+topics I'm
+
+ align:start position:0%
+topics I'm
+ 
+
+ align:start position:0%
+topics I'm
+sorry yeah yeah we can always do the
+
+ align:start position:0%
+sorry yeah yeah we can always do the
+ 
+
+ align:start position:0%
+sorry yeah yeah we can always do the
+donuts we can
+
+ align:start position:0%
+donuts we can
+ 
+
+ align:start position:0%
+donuts we can
+[Laughter]
+
+ align:start position:0%
+[Laughter]
+ 
+
+ align:start position:0%
+[Laughter]
+always all right we'll do that all right
+
+ align:start position:0%
+always all right we'll do that all right
+ 
+
+ align:start position:0%
+always all right we'll do that all right
+see you guys have a good weekend
\ No newline at end of file
diff --git a/mcwwXuYkBGY.txt b/mcwwXuYkBGY.txt
new file mode 100644
index 0000000000000000000000000000000000000000..f3f763e782241e9c284e906f37218b4c5061f63e
--- /dev/null
+++ b/mcwwXuYkBGY.txt
@@ -0,0 +1,9139 @@
+align:start position:0%
+ 
+the following content is provided under
+
+ align:start position:0%
+the following content is provided under
+ 
+
+ align:start position:0%
+the following content is provided under
+a Creative Commons license your support
+
+ align:start position:0%
+a Creative Commons license your support
+ 
+
+ align:start position:0%
+a Creative Commons license your support
+will help MIT open courseware continue
+
+ align:start position:0%
+will help MIT open courseware continue
+ 
+
+ align:start position:0%
+will help MIT open courseware continue
+to offer highquality educational
+
+ align:start position:0%
+to offer highquality educational
+ 
+
+ align:start position:0%
+to offer highquality educational
+resources for free to make a donation or
+
+ align:start position:0%
+resources for free to make a donation or
+ 
+
+ align:start position:0%
+resources for free to make a donation or
+to view additional materials from
+
+ align:start position:0%
+to view additional materials from
+ 
+
+ align:start position:0%
+to view additional materials from
+hundreds of MIT courses visit MIT open
+
+ align:start position:0%
+hundreds of MIT courses visit MIT open
+ 
+
+ align:start position:0%
+hundreds of MIT courses visit MIT open
+courseware at
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+ocw.mit.edu what I want to do today is
+
+ align:start position:0%
+ocw.mit.edu what I want to do today is
+ 
+
+ align:start position:0%
+ocw.mit.edu what I want to do today is
+uh finish uh second installment of phase
+
+ align:start position:0%
+uh finish uh second installment of phase
+ 
+
+ align:start position:0%
+uh finish uh second installment of phase
+diagrams last day we looked at un phase
+
+ align:start position:0%
+diagrams last day we looked at un phase
+ 
+
+ align:start position:0%
+diagrams last day we looked at un phase
+diagrams that is to say single component
+
+ align:start position:0%
+diagrams that is to say single component
+ 
+
+ align:start position:0%
+diagrams that is to say single component
+so that meant all we had to do was worry
+
+ align:start position:0%
+so that meant all we had to do was worry
+ 
+
+ align:start position:0%
+so that meant all we had to do was worry
+about uh pressure versus temperature
+
+ align:start position:0%
+about uh pressure versus temperature
+ 
+
+ align:start position:0%
+about uh pressure versus temperature
+because everything's of simple
+
+ align:start position:0%
+because everything's of simple
+ 
+
+ align:start position:0%
+because everything's of simple
+composition and uh I've got up here on
+
+ align:start position:0%
+composition and uh I've got up here on
+ 
+
+ align:start position:0%
+composition and uh I've got up here on
+the uh uh display uh phase diagram of
+
+ align:start position:0%
+the uh uh display uh phase diagram of
+ 
+
+ align:start position:0%
+the uh uh display uh phase diagram of
+water which we looked at last day and
+
+ align:start position:0%
+water which we looked at last day and
+ 
+
+ align:start position:0%
+water which we looked at last day and
+I've redrawn it here for uh convenience
+
+ align:start position:0%
+I've redrawn it here for uh convenience
+ 
+
+ align:start position:0%
+I've redrawn it here for uh convenience
+and I just wanted to draw your attention
+
+ align:start position:0%
+and I just wanted to draw your attention
+ 
+
+ align:start position:0%
+and I just wanted to draw your attention
+to several things we're looking at how
+
+ align:start position:0%
+to several things we're looking at how
+ 
+
+ align:start position:0%
+to several things we're looking at how
+the stability of the different phases of
+
+ align:start position:0%
+the stability of the different phases of
+ 
+
+ align:start position:0%
+the stability of the different phases of
+water varies with pressure and
+
+ align:start position:0%
+water varies with pressure and
+ 
+
+ align:start position:0%
+water varies with pressure and
+temperature I've drawn the solid region
+
+ align:start position:0%
+temperature I've drawn the solid region
+ 
+
+ align:start position:0%
+temperature I've drawn the solid region
+over here single phase liquid region up
+
+ align:start position:0%
+over here single phase liquid region up
+ 
+
+ align:start position:0%
+over here single phase liquid region up
+here single phase and Vapor region over
+
+ align:start position:0%
+here single phase and Vapor region over
+ 
+
+ align:start position:0%
+here single phase and Vapor region over
+here single phase and at some point we
+
+ align:start position:0%
+here single phase and at some point we
+ 
+
+ align:start position:0%
+here single phase and at some point we
+Transit from solid to liquid and it
+
+ align:start position:0%
+Transit from solid to liquid and it
+ 
+
+ align:start position:0%
+Transit from solid to liquid and it
+doesn't happen at a single point it
+
+ align:start position:0%
+doesn't happen at a single point it
+ 
+
+ align:start position:0%
+doesn't happen at a single point it
+happens over a range of temperatures and
+
+ align:start position:0%
+happens over a range of temperatures and
+ 
+
+ align:start position:0%
+happens over a range of temperatures and
+pressures along this line which is
+
+ align:start position:0%
+pressures along this line which is
+ 
+
+ align:start position:0%
+pressures along this line which is
+called the coexistence Curve so whenever
+
+ align:start position:0%
+called the coexistence Curve so whenever
+ 
+
+ align:start position:0%
+called the coexistence Curve so whenever
+you have two phases in equilibrium uh
+
+ align:start position:0%
+you have two phases in equilibrium uh
+ 
+
+ align:start position:0%
+you have two phases in equilibrium uh
+they Define a coexistence curve and so
+
+ align:start position:0%
+they Define a coexistence curve and so
+ 
+
+ align:start position:0%
+they Define a coexistence curve and so
+here's the solid liquid coexistence curv
+
+ align:start position:0%
+here's the solid liquid coexistence curv
+ 
+
+ align:start position:0%
+here's the solid liquid coexistence curv
+liquid vapor and solid Vapor um we saw
+
+ align:start position:0%
+liquid vapor and solid Vapor um we saw
+ 
+
+ align:start position:0%
+liquid vapor and solid Vapor um we saw
+what happens at our life which is the
+
+ align:start position:0%
+what happens at our life which is the
+ 
+
+ align:start position:0%
+what happens at our life which is the
+one atmosphere isobar this equilibrium
+
+ align:start position:0%
+one atmosphere isobar this equilibrium
+ 
+
+ align:start position:0%
+one atmosphere isobar this equilibrium
+solid liquid that's ice water is at 0
+
+ align:start position:0%
+solid liquid that's ice water is at 0
+ 
+
+ align:start position:0%
+solid liquid that's ice water is at 0
+degrees C and the normal boiling point
+
+ align:start position:0%
+degrees C and the normal boiling point
+ 
+
+ align:start position:0%
+degrees C and the normal boiling point
+that is to say one atmosphere applied
+
+ align:start position:0%
+that is to say one atmosphere applied
+ 
+
+ align:start position:0%
+that is to say one atmosphere applied
+pressure which is nominally sea level is
+
+ align:start position:0%
+pressure which is nominally sea level is
+ 
+
+ align:start position:0%
+pressure which is nominally sea level is
+uh 100° C
+
+ align:start position:0%
+uh 100° C
+ 
+
+ align:start position:0%
+uh 100° C
+and we saw how boiling point varies with
+
+ align:start position:0%
+and we saw how boiling point varies with
+ 
+
+ align:start position:0%
+and we saw how boiling point varies with
+applied pressure and that is defined
+
+ align:start position:0%
+applied pressure and that is defined
+ 
+
+ align:start position:0%
+applied pressure and that is defined
+along this coexistence curve um the
+
+ align:start position:0%
+along this coexistence curve um the
+ 
+
+ align:start position:0%
+along this coexistence curve um the
+other thing to note is when the three
+
+ align:start position:0%
+other thing to note is when the three
+ 
+
+ align:start position:0%
+other thing to note is when the three
+coexistence curves intersect we have
+
+ align:start position:0%
+coexistence curves intersect we have
+ 
+
+ align:start position:0%
+coexistence curves intersect we have
+this unique unique set of circumstances
+
+ align:start position:0%
+this unique unique set of circumstances
+ 
+
+ align:start position:0%
+this unique unique set of circumstances
+called the triple point where all three
+
+ align:start position:0%
+called the triple point where all three
+ 
+
+ align:start position:0%
+called the triple point where all three
+phases coexist and they coexist at only
+
+ align:start position:0%
+phases coexist and they coexist at only
+ 
+
+ align:start position:0%
+phases coexist and they coexist at only
+one point that is to say one temperature
+
+ align:start position:0%
+one point that is to say one temperature
+ 
+
+ align:start position:0%
+one point that is to say one temperature
+pressure combination which uh is uh very
+
+ align:start position:0%
+pressure combination which uh is uh very
+ 
+
+ align:start position:0%
+pressure combination which uh is uh very
+nearly identical to the uh
+
+ align:start position:0%
+nearly identical to the uh
+ 
+
+ align:start position:0%
+nearly identical to the uh
+solidification temperature this is not
+
+ align:start position:0%
+solidification temperature this is not
+ 
+
+ align:start position:0%
+solidification temperature this is not
+to scale so this is slightly higher than
+
+ align:start position:0%
+to scale so this is slightly higher than
+ 
+
+ align:start position:0%
+to scale so this is slightly higher than
+Z degrees C it's about 1/ 100th of a
+
+ align:start position:0%
+Z degrees C it's about 1/ 100th of a
+ 
+
+ align:start position:0%
+Z degrees C it's about 1/ 100th of a
+degrees of a degree uh above zero at a
+
+ align:start position:0%
+degrees of a degree uh above zero at a
+ 
+
+ align:start position:0%
+degrees of a degree uh above zero at a
+reduced pressure of 4.58 millimeters of
+
+ align:start position:0%
+reduced pressure of 4.58 millimeters of
+ 
+
+ align:start position:0%
+reduced pressure of 4.58 millimeters of
+mercury and at this point here the
+
+ align:start position:0%
+mercury and at this point here the
+ 
+
+ align:start position:0%
+mercury and at this point here the
+triple point you in fact have ice cubes
+
+ align:start position:0%
+triple point you in fact have ice cubes
+ 
+
+ align:start position:0%
+triple point you in fact have ice cubes
+floating in boiling water there's the
+
+ align:start position:0%
+floating in boiling water there's the
+ 
+
+ align:start position:0%
+floating in boiling water there's the
+triple point and then the last thing was
+
+ align:start position:0%
+triple point and then the last thing was
+ 
+
+ align:start position:0%
+triple point and then the last thing was
+I I talked about super critical fluids
+
+ align:start position:0%
+I I talked about super critical fluids
+ 
+
+ align:start position:0%
+I I talked about super critical fluids
+at the end of last lecture uh just for
+
+ align:start position:0%
+at the end of last lecture uh just for
+ 
+
+ align:start position:0%
+at the end of last lecture uh just for
+completeness in the case of water water
+
+ align:start position:0%
+completeness in the case of water water
+ 
+
+ align:start position:0%
+completeness in the case of water water
+turns into a supercritical fluid at the
+
+ align:start position:0%
+turns into a supercritical fluid at the
+ 
+
+ align:start position:0%
+turns into a supercritical fluid at the
+elevated uh temperature of 374 de C 218
+
+ align:start position:0%
+elevated uh temperature of 374 de C 218
+ 
+
+ align:start position:0%
+elevated uh temperature of 374 de C 218
+atmospheres above this pressure
+
+ align:start position:0%
+atmospheres above this pressure
+ 
+
+ align:start position:0%
+atmospheres above this pressure
+temperature pair we have something that
+
+ align:start position:0%
+temperature pair we have something that
+ 
+
+ align:start position:0%
+temperature pair we have something that
+is simply fluid it's neither a liquid
+
+ align:start position:0%
+is simply fluid it's neither a liquid
+ 
+
+ align:start position:0%
+is simply fluid it's neither a liquid
+nor a a vapor You could argue that it's
+
+ align:start position:0%
+nor a a vapor You could argue that it's
+ 
+
+ align:start position:0%
+nor a a vapor You could argue that it's
+a highly condensed vapor or highly
+
+ align:start position:0%
+a highly condensed vapor or highly
+ 
+
+ align:start position:0%
+a highly condensed vapor or highly
+rarified liquid but it uh it has a the
+
+ align:start position:0%
+rarified liquid but it uh it has a the
+ 
+
+ align:start position:0%
+rarified liquid but it uh it has a the
+properties of a of a super critical
+
+ align:start position:0%
+properties of a of a super critical
+ 
+
+ align:start position:0%
+properties of a of a super critical
+fluid so uh what I want to do today what
+
+ align:start position:0%
+fluid so uh what I want to do today what
+ 
+
+ align:start position:0%
+fluid so uh what I want to do today what
+I want to do today is to now uh look at
+
+ align:start position:0%
+I want to do today is to now uh look at
+ 
+
+ align:start position:0%
+I want to do today is to now uh look at
+um multicomponent systems and we want to
+
+ align:start position:0%
+um multicomponent systems and we want to
+ 
+
+ align:start position:0%
+um multicomponent systems and we want to
+start with a two component
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+systems two component
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+systems so we're not going to be talking
+
+ align:start position:0%
+systems so we're not going to be talking
+ 
+
+ align:start position:0%
+systems so we're not going to be talking
+about pure materials c will equal two so
+
+ align:start position:0%
+about pure materials c will equal two so
+ 
+
+ align:start position:0%
+about pure materials c will equal two so
+that means now we have to think about
+
+ align:start position:0%
+that means now we have to think about
+ 
+
+ align:start position:0%
+that means now we have to think about
+temperature pressure and composition
+
+ align:start position:0%
+temperature pressure and composition
+ 
+
+ align:start position:0%
+temperature pressure and composition
+because composition is a variable
+
+ align:start position:0%
+because composition is a variable
+ 
+
+ align:start position:0%
+because composition is a variable
+between the two components
+
+ align:start position:0%
+between the two components
+ 
+
+ align:start position:0%
+between the two components
+components and that gets to be messy
+
+ align:start position:0%
+components and that gets to be messy
+ 
+
+ align:start position:0%
+components and that gets to be messy
+because we already
+
+ align:start position:0%
+because we already
+ 
+
+ align:start position:0%
+because we already
+had uh pressure temperature diagram for
+
+ align:start position:0%
+had uh pressure temperature diagram for
+ 
+
+ align:start position:0%
+had uh pressure temperature diagram for
+let's say component a this is component
+
+ align:start position:0%
+let's say component a this is component
+ 
+
+ align:start position:0%
+let's say component a this is component
+a and over here I've got the pressure
+
+ align:start position:0%
+a and over here I've got the pressure
+ 
+
+ align:start position:0%
+a and over here I've got the pressure
+temperature variation of component B and
+
+ align:start position:0%
+temperature variation of component B and
+ 
+
+ align:start position:0%
+temperature variation of component B and
+here I've drawn the solid liquid
+
+ align:start position:0%
+here I've drawn the solid liquid
+ 
+
+ align:start position:0%
+here I've drawn the solid liquid
+coexistance curve as it normally is
+
+ align:start position:0%
+coexistance curve as it normally is
+ 
+
+ align:start position:0%
+coexistance curve as it normally is
+found in most materials which is to say
+
+ align:start position:0%
+found in most materials which is to say
+ 
+
+ align:start position:0%
+found in most materials which is to say
+positive because solids are generally
+
+ align:start position:0%
+positive because solids are generally
+ 
+
+ align:start position:0%
+positive because solids are generally
+denser than the uh than the liquids
+
+ align:start position:0%
+denser than the uh than the liquids
+ 
+
+ align:start position:0%
+denser than the uh than the liquids
+water is one of the exceptions so now
+
+ align:start position:0%
+water is one of the exceptions so now
+ 
+
+ align:start position:0%
+water is one of the exceptions so now
+the question is how do various
+
+ align:start position:0%
+the question is how do various
+ 
+
+ align:start position:0%
+the question is how do various
+properties change with composition so if
+
+ align:start position:0%
+properties change with composition so if
+ 
+
+ align:start position:0%
+properties change with composition so if
+I ask what's going on in between here so
+
+ align:start position:0%
+I ask what's going on in between here so
+ 
+
+ align:start position:0%
+I ask what's going on in between here so
+I can join these two so I I'm going to
+
+ align:start position:0%
+I can join these two so I I'm going to
+ 
+
+ align:start position:0%
+I can join these two so I I'm going to
+need a three-dimensional plot pressure
+
+ align:start position:0%
+need a three-dimensional plot pressure
+ 
+
+ align:start position:0%
+need a three-dimensional plot pressure
+temperature composition so I have an
+
+ align:start position:0%
+temperature composition so I have an
+ 
+
+ align:start position:0%
+temperature composition so I have an
+Infinity of uni phase diagrams all
+
+ align:start position:0%
+Infinity of uni phase diagrams all
+ 
+
+ align:start position:0%
+Infinity of uni phase diagrams all
+across here from Pure a all the way over
+
+ align:start position:0%
+across here from Pure a all the way over
+ 
+
+ align:start position:0%
+across here from Pure a all the way over
+to Pure B with all of the different
+
+ align:start position:0%
+to Pure B with all of the different
+ 
+
+ align:start position:0%
+to Pure B with all of the different
+composition ratios in between so for
+
+ align:start position:0%
+composition ratios in between so for
+ 
+
+ align:start position:0%
+composition ratios in between so for
+example I could look at here's the
+
+ align:start position:0%
+example I could look at here's the
+ 
+
+ align:start position:0%
+example I could look at here's the
+melting point this is the melting point
+
+ align:start position:0%
+melting point this is the melting point
+ 
+
+ align:start position:0%
+melting point this is the melting point
+of a and here's the melting point of B
+
+ align:start position:0%
+of a and here's the melting point of B
+ 
+
+ align:start position:0%
+of a and here's the melting point of B
+and I might ask how does the melting
+
+ align:start position:0%
+and I might ask how does the melting
+ 
+
+ align:start position:0%
+and I might ask how does the melting
+point vary with composition so is that a
+
+ align:start position:0%
+point vary with composition so is that a
+ 
+
+ align:start position:0%
+point vary with composition so is that a
+case of is it is a case of just connect
+
+ align:start position:0%
+case of is it is a case of just connect
+ 
+
+ align:start position:0%
+case of is it is a case of just connect
+the dots if I know the melting points of
+
+ align:start position:0%
+the dots if I know the melting points of
+ 
+
+ align:start position:0%
+the dots if I know the melting points of
+the two end members say copper and
+
+ align:start position:0%
+the two end members say copper and
+ 
+
+ align:start position:0%
+the two end members say copper and
+nickel and I want to know what's the
+
+ align:start position:0%
+nickel and I want to know what's the
+ 
+
+ align:start position:0%
+nickel and I want to know what's the
+melting point of a 50/50 copper nickel
+
+ align:start position:0%
+melting point of a 50/50 copper nickel
+ 
+
+ align:start position:0%
+melting point of a 50/50 copper nickel
+alloy is it just the halfway temperature
+
+ align:start position:0%
+alloy is it just the halfway temperature
+ 
+
+ align:start position:0%
+alloy is it just the halfway temperature
+between the two or does the temperature
+
+ align:start position:0%
+between the two or does the temperature
+ 
+
+ align:start position:0%
+between the two or does the temperature
+go through a local maximum or does it go
+
+ align:start position:0%
+go through a local maximum or does it go
+ 
+
+ align:start position:0%
+go through a local maximum or does it go
+through a local minimum or does the
+
+ align:start position:0%
+through a local minimum or does the
+ 
+
+ align:start position:0%
+through a local minimum or does the
+temperature go nuts I mean the question
+
+ align:start position:0%
+temperature go nuts I mean the question
+ 
+
+ align:start position:0%
+temperature go nuts I mean the question
+is how does temperature of some critical
+
+ align:start position:0%
+is how does temperature of some critical
+ 
+
+ align:start position:0%
+is how does temperature of some critical
+feature vary with composition so we need
+
+ align:start position:0%
+feature vary with composition so we need
+ 
+
+ align:start position:0%
+feature vary with composition so we need
+to look at three-dimensional stability
+
+ align:start position:0%
+to look at three-dimensional stability
+ 
+
+ align:start position:0%
+to look at three-dimensional stability
+maps and this is a pain in the neck
+
+ align:start position:0%
+maps and this is a pain in the neck
+ 
+
+ align:start position:0%
+maps and this is a pain in the neck
+because it's 3D and it's it's messy but
+
+ align:start position:0%
+because it's 3D and it's it's messy but
+ 
+
+ align:start position:0%
+because it's 3D and it's it's messy but
+fortunately this is
+
+ align:start position:0%
+fortunately this is
+ 
+
+ align:start position:0%
+fortunately this is
+3091 and 3091 is 3091 is concerned about
+
+ align:start position:0%
+3091 and 3091 is 3091 is concerned about
+ 
+
+ align:start position:0%
+3091 and 3091 is 3091 is concerned about
+sof Solid State chemistry so in 3091 we
+
+ align:start position:0%
+sof Solid State chemistry so in 3091 we
+ 
+
+ align:start position:0%
+sof Solid State chemistry so in 3091 we
+care more about liquid solid
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+equilibrium instead of liquid Vapor
+
+ align:start position:0%
+equilibrium instead of liquid Vapor
+ 
+
+ align:start position:0%
+equilibrium instead of liquid Vapor
+equilibrium because we don't process too
+
+ align:start position:0%
+equilibrium because we don't process too
+ 
+
+ align:start position:0%
+equilibrium because we don't process too
+many uh materials in the vapor State we
+
+ align:start position:0%
+many uh materials in the vapor State we
+ 
+
+ align:start position:0%
+many uh materials in the vapor State we
+don't use too many materials as Vapors
+
+ align:start position:0%
+don't use too many materials as Vapors
+ 
+
+ align:start position:0%
+don't use too many materials as Vapors
+this is the equilibrium that's most
+
+ align:start position:0%
+this is the equilibrium that's most
+ 
+
+ align:start position:0%
+this is the equilibrium that's most
+important so when we we know that
+
+ align:start position:0%
+important so when we we know that
+ 
+
+ align:start position:0%
+important so when we we know that
+equilibria equilibria depend upon
+
+ align:start position:0%
+equilibria equilibria depend upon
+ 
+
+ align:start position:0%
+equilibria equilibria depend upon
+depend upon temperature pressure and
+
+ align:start position:0%
+depend upon temperature pressure and
+ 
+
+ align:start position:0%
+depend upon temperature pressure and
+composition and it turns out that when
+
+ align:start position:0%
+composition and it turns out that when
+ 
+
+ align:start position:0%
+composition and it turns out that when
+it comes to the liquid solid equilibrium
+
+ align:start position:0%
+it comes to the liquid solid equilibrium
+ 
+
+ align:start position:0%
+it comes to the liquid solid equilibrium
+liquid solid equilibrium is strongly
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+dependent there's a strong dependence
+
+ align:start position:0%
+dependent there's a strong dependence
+ 
+
+ align:start position:0%
+dependent there's a strong dependence
+between the temperature of
+
+ align:start position:0%
+between the temperature of
+ 
+
+ align:start position:0%
+between the temperature of
+transformation and
+
+ align:start position:0%
+transformation and
+ 
+
+ align:start position:0%
+transformation and
+composition whereas the relationship
+
+ align:start position:0%
+composition whereas the relationship
+ 
+
+ align:start position:0%
+composition whereas the relationship
+between the temperature of the trans
+
+ align:start position:0%
+between the temperature of the trans
+ 
+
+ align:start position:0%
+between the temperature of the trans
+transformation and pressure is
+
+ align:start position:0%
+transformation and pressure is
+ 
+
+ align:start position:0%
+transformation and pressure is
+weakly weakly dependent there's a weak
+
+ align:start position:0%
+weakly weakly dependent there's a weak
+ 
+
+ align:start position:0%
+weakly weakly dependent there's a weak
+dependence between pressure and the
+
+ align:start position:0%
+dependence between pressure and the
+ 
+
+ align:start position:0%
+dependence between pressure and the
+temperature of the transformation and we
+
+ align:start position:0%
+temperature of the transformation and we
+ 
+
+ align:start position:0%
+temperature of the transformation and we
+saw that last day these are not to scale
+
+ align:start position:0%
+saw that last day these are not to scale
+ 
+
+ align:start position:0%
+saw that last day these are not to scale
+in other words these lines are nearly
+
+ align:start position:0%
+in other words these lines are nearly
+ 
+
+ align:start position:0%
+in other words these lines are nearly
+vertical for solid liquid you would have
+
+ align:start position:0%
+vertical for solid liquid you would have
+ 
+
+ align:start position:0%
+vertical for solid liquid you would have
+to apply geological pressures to alter
+
+ align:start position:0%
+to apply geological pressures to alter
+ 
+
+ align:start position:0%
+to apply geological pressures to alter
+the melting point of water substantially
+
+ align:start position:0%
+the melting point of water substantially
+ 
+
+ align:start position:0%
+the melting point of water substantially
+all right whereas we saw it doesn't take
+
+ align:start position:0%
+all right whereas we saw it doesn't take
+ 
+
+ align:start position:0%
+all right whereas we saw it doesn't take
+anything more than just a rise in
+
+ align:start position:0%
+anything more than just a rise in
+ 
+
+ align:start position:0%
+anything more than just a rise in
+elevation several thousand feet to move
+
+ align:start position:0%
+elevation several thousand feet to move
+ 
+
+ align:start position:0%
+elevation several thousand feet to move
+the boiling point a lot so that means
+
+ align:start position:0%
+the boiling point a lot so that means
+ 
+
+ align:start position:0%
+the boiling point a lot so that means
+that I can throw away the pressure
+
+ align:start position:0%
+that I can throw away the pressure
+ 
+
+ align:start position:0%
+that I can throw away the pressure
+dependence throw away the pressure
+
+ align:start position:0%
+dependence throw away the pressure
+ 
+
+ align:start position:0%
+dependence throw away the pressure
+dependence and just focus on the
+
+ align:start position:0%
+dependence and just focus on the
+ 
+
+ align:start position:0%
+dependence and just focus on the
+two-dimensional relationship between the
+
+ align:start position:0%
+two-dimensional relationship between the
+ 
+
+ align:start position:0%
+two-dimensional relationship between the
+temperature of a transformation and the
+
+ align:start position:0%
+temperature of a transformation and the
+ 
+
+ align:start position:0%
+temperature of a transformation and the
+composition so that's what we're going
+
+ align:start position:0%
+composition so that's what we're going
+ 
+
+ align:start position:0%
+composition so that's what we're going
+to do we're going to look at three
+
+ align:start position:0%
+to do we're going to look at three
+ 
+
+ align:start position:0%
+to do we're going to look at three
+different types of of binary systems and
+
+ align:start position:0%
+different types of of binary systems and
+ 
+
+ align:start position:0%
+different types of of binary systems and
+in each case we're going to assume that
+
+ align:start position:0%
+in each case we're going to assume that
+ 
+
+ align:start position:0%
+in each case we're going to assume that
+the pressure is one atmosphere and we
+
+ align:start position:0%
+the pressure is one atmosphere and we
+ 
+
+ align:start position:0%
+the pressure is one atmosphere and we
+know that the the dependence of the
+
+ align:start position:0%
+know that the the dependence of the
+ 
+
+ align:start position:0%
+know that the the dependence of the
+transer temperatures that we write is
+
+ align:start position:0%
+transer temperatures that we write is
+ 
+
+ align:start position:0%
+transer temperatures that we write is
+going to be negligible in terms of the
+
+ align:start position:0%
+going to be negligible in terms of the
+ 
+
+ align:start position:0%
+going to be negligible in terms of the
+impact that pressure might have on them
+
+ align:start position:0%
+impact that pressure might have on them
+ 
+
+ align:start position:0%
+impact that pressure might have on them
+so let's look at we're going to look at
+
+ align:start position:0%
+so let's look at we're going to look at
+ 
+
+ align:start position:0%
+so let's look at we're going to look at
+three different types of uh uh systems
+
+ align:start position:0%
+three different types of uh uh systems
+ 
+
+ align:start position:0%
+three different types of uh uh systems
+and they're all dependent upon the
+
+ align:start position:0%
+and they're all dependent upon the
+ 
+
+ align:start position:0%
+and they're all dependent upon the
+extent of solubility and I've given them
+
+ align:start position:0%
+extent of solubility and I've given them
+ 
+
+ align:start position:0%
+extent of solubility and I've given them
+the very um oh how what's the word very
+
+ align:start position:0%
+the very um oh how what's the word very
+ 
+
+ align:start position:0%
+the very um oh how what's the word very
+uh catchy very catchy uh distinctions of
+
+ align:start position:0%
+uh catchy very catchy uh distinctions of
+ 
+
+ align:start position:0%
+uh catchy very catchy uh distinctions of
+type one type two and type three all
+
+ align:start position:0%
+type one type two and type three all
+ 
+
+ align:start position:0%
+type one type two and type three all
+right so let's look at type one type one
+
+ align:start position:0%
+right so let's look at type one type one
+ 
+
+ align:start position:0%
+right so let's look at type one type one
+type binary system okay and type one
+
+ align:start position:0%
+type binary system okay and type one
+ 
+
+ align:start position:0%
+type binary system okay and type one
+binary system has
+
+ align:start position:0%
+binary system has
+ 
+
+ align:start position:0%
+binary system has
+complete complete
+
+ align:start position:0%
+complete complete
+ 
+
+ align:start position:0%
+complete complete
+solubility by this I mean complete
+
+ align:start position:0%
+solubility by this I mean complete
+ 
+
+ align:start position:0%
+solubility by this I mean complete
+solubility of the two components
+
+ align:start position:0%
+solubility of the two components
+ 
+
+ align:start position:0%
+solubility of the two components
+complete solubility in
+
+ align:start position:0%
+complete solubility in
+ 
+
+ align:start position:0%
+complete solubility in
+solid and liquid
+
+ align:start position:0%
+solid and liquid
+ 
+
+ align:start position:0%
+solid and liquid
+States so that is to say if I mix A and
+
+ align:start position:0%
+States so that is to say if I mix A and
+ 
+
+ align:start position:0%
+States so that is to say if I mix A and
+B they will mix in all proportions as
+
+ align:start position:0%
+B they will mix in all proportions as
+ 
+
+ align:start position:0%
+B they will mix in all proportions as
+solids and they'll mix in all
+
+ align:start position:0%
+solids and they'll mix in all
+ 
+
+ align:start position:0%
+solids and they'll mix in all
+proportions as liquids and the second
+
+ align:start position:0%
+proportions as liquids and the second
+ 
+
+ align:start position:0%
+proportions as liquids and the second
+thing is we're looking looking at change
+
+ align:start position:0%
+thing is we're looking looking at change
+ 
+
+ align:start position:0%
+thing is we're looking looking at change
+of
+
+ align:start position:0%
+of
+ 
+
+ align:start position:0%
+of
+state change of state so this diagram
+
+ align:start position:0%
+state change of state so this diagram
+ 
+
+ align:start position:0%
+state change of state so this diagram
+applies to a change of state and since
+
+ align:start position:0%
+applies to a change of state and since
+ 
+
+ align:start position:0%
+applies to a change of state and since
+we're talking
+
+ align:start position:0%
+we're talking
+ 
+
+ align:start position:0%
+we're talking
+about solid liquid that's the only one
+
+ align:start position:0%
+about solid liquid that's the only one
+ 
+
+ align:start position:0%
+about solid liquid that's the only one
+we need to uh document
+
+ align:start position:0%
+we need to uh document
+ 
+
+ align:start position:0%
+we need to uh document
+so and you know let's think about what's
+
+ align:start position:0%
+so and you know let's think about what's
+ 
+
+ align:start position:0%
+so and you know let's think about what's
+the relevant chemistry here I mean I've
+
+ align:start position:0%
+the relevant chemistry here I mean I've
+ 
+
+ align:start position:0%
+the relevant chemistry here I mean I've
+been telling you that phase diagrams are
+
+ align:start position:0%
+been telling you that phase diagrams are
+ 
+
+ align:start position:0%
+been telling you that phase diagrams are
+stability maps and you can just look at
+
+ align:start position:0%
+stability maps and you can just look at
+ 
+
+ align:start position:0%
+stability maps and you can just look at
+them and and consult them but there's
+
+ align:start position:0%
+them and and consult them but there's
+ 
+
+ align:start position:0%
+them and and consult them but there's
+always some basic chemistry embedded in
+
+ align:start position:0%
+always some basic chemistry embedded in
+ 
+
+ align:start position:0%
+always some basic chemistry embedded in
+these diagrams so for example if it were
+
+ align:start position:0%
+these diagrams so for example if it were
+ 
+
+ align:start position:0%
+these diagrams so for example if it were
+a metal system and I were to tell you
+
+ align:start position:0%
+a metal system and I were to tell you
+ 
+
+ align:start position:0%
+a metal system and I were to tell you
+that these two metals a and b mix in all
+
+ align:start position:0%
+that these two metals a and b mix in all
+ 
+
+ align:start position:0%
+that these two metals a and b mix in all
+proportions as solids and liquids what
+
+ align:start position:0%
+proportions as solids and liquids what
+ 
+
+ align:start position:0%
+proportions as solids and liquids what
+would have to be the characteristics of
+
+ align:start position:0%
+would have to be the characteristics of
+ 
+
+ align:start position:0%
+would have to be the characteristics of
+those two metals they would have to be
+
+ align:start position:0%
+those two metals they would have to be
+ 
+
+ align:start position:0%
+those two metals they would have to be
+either very nearly similar or maximally
+
+ align:start position:0%
+either very nearly similar or maximally
+ 
+
+ align:start position:0%
+either very nearly similar or maximally
+different they have to be very nearly
+
+ align:start position:0%
+different they have to be very nearly
+ 
+
+ align:start position:0%
+different they have to be very nearly
+similar and in fact that's it's the sort
+
+ align:start position:0%
+similar and in fact that's it's the sort
+ 
+
+ align:start position:0%
+similar and in fact that's it's the sort
+of a takeoff on like dissolves like so
+
+ align:start position:0%
+of a takeoff on like dissolves like so
+ 
+
+ align:start position:0%
+of a takeoff on like dissolves like so
+complete solid solubility in a liquid
+
+ align:start position:0%
+complete solid solubility in a liquid
+ 
+
+ align:start position:0%
+complete solid solubility in a liquid
+state with respect to metals when it
+
+ align:start position:0%
+state with respect to metals when it
+ 
+
+ align:start position:0%
+state with respect to metals when it
+comes to Metals there's a a set of rules
+
+ align:start position:0%
+comes to Metals there's a a set of rules
+ 
+
+ align:start position:0%
+comes to Metals there's a a set of rules
+called the Hume Ry
+
+ align:start position:0%
+called the Hume Ry
+ 
+
+ align:start position:0%
+called the Hume Ry
+rules Hume Ry was a a British uh
+
+ align:start position:0%
+rules Hume Ry was a a British uh
+ 
+
+ align:start position:0%
+rules Hume Ry was a a British uh
+metallurgist and he
+
+ align:start position:0%
+metallurgist and he
+ 
+
+ align:start position:0%
+metallurgist and he
+enunciated a set of rules for uh
+
+ align:start position:0%
+enunciated a set of rules for uh
+ 
+
+ align:start position:0%
+enunciated a set of rules for uh
+identifying candidate systems that will
+
+ align:start position:0%
+identifying candidate systems that will
+ 
+
+ align:start position:0%
+identifying candidate systems that will
+have this type of phase diagram and
+
+ align:start position:0%
+have this type of phase diagram and
+ 
+
+ align:start position:0%
+have this type of phase diagram and
+they're very simple anybody in 3091
+
+ align:start position:0%
+they're very simple anybody in 3091
+ 
+
+ align:start position:0%
+they're very simple anybody in 3091
+would have come up with these rules if
+
+ align:start position:0%
+would have come up with these rules if
+ 
+
+ align:start position:0%
+would have come up with these rules if
+you thought about it before Hume R but
+
+ align:start position:0%
+you thought about it before Hume R but
+ 
+
+ align:start position:0%
+you thought about it before Hume R but
+he beat you to it so you can't get the
+
+ align:start position:0%
+he beat you to it so you can't get the
+ 
+
+ align:start position:0%
+he beat you to it so you can't get the
+glory anymore but let's think about it
+
+ align:start position:0%
+glory anymore but let's think about it
+ 
+
+ align:start position:0%
+glory anymore but let's think about it
+what would have to be the situation if
+
+ align:start position:0%
+what would have to be the situation if
+ 
+
+ align:start position:0%
+what would have to be the situation if
+the two metals A and B are going to mix
+
+ align:start position:0%
+the two metals A and B are going to mix
+ 
+
+ align:start position:0%
+the two metals A and B are going to mix
+in all proportions then they must be
+
+ align:start position:0%
+in all proportions then they must be
+ 
+
+ align:start position:0%
+in all proportions then they must be
+very similar so they must have similar
+
+ align:start position:0%
+very similar so they must have similar
+ 
+
+ align:start position:0%
+very similar so they must have similar
+Crystal
+
+ align:start position:0%
+Crystal
+ 
+
+ align:start position:0%
+Crystal
+structures Crystal structures that way
+
+ align:start position:0%
+structures Crystal structures that way
+ 
+
+ align:start position:0%
+structures Crystal structures that way
+you get simple substitutional solid
+
+ align:start position:0%
+you get simple substitutional solid
+ 
+
+ align:start position:0%
+you get simple substitutional solid
+Solutions and furthermore if they're
+
+ align:start position:0%
+Solutions and furthermore if they're
+ 
+
+ align:start position:0%
+Solutions and furthermore if they're
+going to substitute solid for solid they
+
+ align:start position:0%
+going to substitute solid for solid they
+ 
+
+ align:start position:0%
+going to substitute solid for solid they
+should have similar Atomic Dimensions
+
+ align:start position:0%
+should have similar Atomic Dimensions
+ 
+
+ align:start position:0%
+should have similar Atomic Dimensions
+right it does no good to have two FCC
+
+ align:start position:0%
+right it does no good to have two FCC
+ 
+
+ align:start position:0%
+right it does no good to have two FCC
+Metals mixing where one has
+
+ align:start position:0%
+Metals mixing where one has
+ 
+
+ align:start position:0%
+Metals mixing where one has
+a atomic radius that is so large that it
+
+ align:start position:0%
+a atomic radius that is so large that it
+ 
+
+ align:start position:0%
+a atomic radius that is so large that it
+has to force fit into the lattice of the
+
+ align:start position:0%
+has to force fit into the lattice of the
+ 
+
+ align:start position:0%
+has to force fit into the lattice of the
+other similar Atomic
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+volumes similar Atomic volumes and
+
+ align:start position:0%
+volumes similar Atomic volumes and
+ 
+
+ align:start position:0%
+volumes similar Atomic volumes and
+lastly bring in some chemistry we want
+
+ align:start position:0%
+lastly bring in some chemistry we want
+ 
+
+ align:start position:0%
+lastly bring in some chemistry we want
+them to mix and not chemically react so
+
+ align:start position:0%
+them to mix and not chemically react so
+ 
+
+ align:start position:0%
+them to mix and not chemically react so
+they should have a
+
+ align:start position:0%
+they should have a
+ 
+
+ align:start position:0%
+they should have a
+small value in electro negativity
+
+ align:start position:0%
+small value in electro negativity
+ 
+
+ align:start position:0%
+small value in electro negativity
+difference if they're both the same size
+
+ align:start position:0%
+difference if they're both the same size
+ 
+
+ align:start position:0%
+difference if they're both the same size
+the both crystal structure but they have
+
+ align:start position:0%
+the both crystal structure but they have
+ 
+
+ align:start position:0%
+the both crystal structure but they have
+a high El negativity difference they're
+
+ align:start position:0%
+a high El negativity difference they're
+ 
+
+ align:start position:0%
+a high El negativity difference they're
+going to engage an electron transfer so
+
+ align:start position:0%
+going to engage an electron transfer so
+ 
+
+ align:start position:0%
+going to engage an electron transfer so
+that's no good but I I think this set of
+
+ align:start position:0%
+that's no good but I I think this set of
+ 
+
+ align:start position:0%
+that's no good but I I think this set of
+hum Ry rules is nice to reflect upon in
+
+ align:start position:0%
+hum Ry rules is nice to reflect upon in
+ 
+
+ align:start position:0%
+hum Ry rules is nice to reflect upon in
+the light of everything else we've
+
+ align:start position:0%
+the light of everything else we've
+ 
+
+ align:start position:0%
+the light of everything else we've
+learned 3091 because the phase diagrams
+
+ align:start position:0%
+learned 3091 because the phase diagrams
+ 
+
+ align:start position:0%
+learned 3091 because the phase diagrams
+have as I said earlier they have
+
+ align:start position:0%
+have as I said earlier they have
+ 
+
+ align:start position:0%
+have as I said earlier they have
+embedded in them a lot of basic
+
+ align:start position:0%
+embedded in them a lot of basic
+ 
+
+ align:start position:0%
+embedded in them a lot of basic
+chemistry which goes back to electronic
+
+ align:start position:0%
+chemistry which goes back to electronic
+ 
+
+ align:start position:0%
+chemistry which goes back to electronic
+structure of the constituents so let's
+
+ align:start position:0%
+structure of the constituents so let's
+ 
+
+ align:start position:0%
+structure of the constituents so let's
+draw a schematic of an AB diagram
+
+ align:start position:0%
+draw a schematic of an AB diagram
+ 
+
+ align:start position:0%
+draw a schematic of an AB diagram
+for one such system that I call type one
+
+ align:start position:0%
+for one such system that I call type one
+ 
+
+ align:start position:0%
+for one such system that I call type one
+so I'm plotting a versus B this is
+
+ align:start position:0%
+so I'm plotting a versus B this is
+ 
+
+ align:start position:0%
+so I'm plotting a versus B this is
+temperature on the vertical axis
+
+ align:start position:0%
+temperature on the vertical axis
+ 
+
+ align:start position:0%
+temperature on the vertical axis
+horizontal axis is composition so on the
+
+ align:start position:0%
+horizontal axis is composition so on the
+ 
+
+ align:start position:0%
+horizontal axis is composition so on the
+left side I have pure a the right side I
+
+ align:start position:0%
+left side I have pure a the right side I
+ 
+
+ align:start position:0%
+left side I have pure a the right side I
+have pure B and I'm looking at solid
+
+ align:start position:0%
+have pure B and I'm looking at solid
+ 
+
+ align:start position:0%
+have pure B and I'm looking at solid
+liquid equilibrium so at this extreme
+
+ align:start position:0%
+liquid equilibrium so at this extreme
+ 
+
+ align:start position:0%
+liquid equilibrium so at this extreme
+pure a this n member must be the melting
+
+ align:start position:0%
+pure a this n member must be the melting
+ 
+
+ align:start position:0%
+pure a this n member must be the melting
+point of pure
+
+ align:start position:0%
+point of pure
+ 
+
+ align:start position:0%
+point of pure
+a and the Other Extreme is pure B so
+
+ align:start position:0%
+a and the Other Extreme is pure B so
+ 
+
+ align:start position:0%
+a and the Other Extreme is pure B so
+this is the melting point of pure B and
+
+ align:start position:0%
+this is the melting point of pure B and
+ 
+
+ align:start position:0%
+this is the melting point of pure B and
+I've drawn it just arbitrarily where the
+
+ align:start position:0%
+I've drawn it just arbitrarily where the
+ 
+
+ align:start position:0%
+I've drawn it just arbitrarily where the
+melting point of B has happens to be
+
+ align:start position:0%
+melting point of B has happens to be
+ 
+
+ align:start position:0%
+melting point of B has happens to be
+higher than the melting point of a but
+
+ align:start position:0%
+higher than the melting point of a but
+ 
+
+ align:start position:0%
+higher than the melting point of a but
+it doesn't matter one has to be larger
+
+ align:start position:0%
+it doesn't matter one has to be larger
+ 
+
+ align:start position:0%
+it doesn't matter one has to be larger
+than the other and so now this is what
+
+ align:start position:0%
+than the other and so now this is what
+ 
+
+ align:start position:0%
+than the other and so now this is what
+the phase di this is going to answer the
+
+ align:start position:0%
+the phase di this is going to answer the
+ 
+
+ align:start position:0%
+the phase di this is going to answer the
+question how does melting point vary as
+
+ align:start position:0%
+question how does melting point vary as
+ 
+
+ align:start position:0%
+question how does melting point vary as
+a function of composition it varies like
+
+ align:start position:0%
+a function of composition it varies like
+ 
+
+ align:start position:0%
+a function of composition it varies like
+this it's not a straight line for two
+
+ align:start position:0%
+this it's not a straight line for two
+ 
+
+ align:start position:0%
+this it's not a straight line for two
+reasons the first one being that if when
+
+ align:start position:0%
+reasons the first one being that if when
+ 
+
+ align:start position:0%
+reasons the first one being that if when
+you take thermodynamics uh subsequently
+
+ align:start position:0%
+you take thermodynamics uh subsequently
+ 
+
+ align:start position:0%
+you take thermodynamics uh subsequently
+if you choose to do so you'll understand
+
+ align:start position:0%
+if you choose to do so you'll understand
+ 
+
+ align:start position:0%
+if you choose to do so you'll understand
+the the physical chemistry behind what
+
+ align:start position:0%
+the the physical chemistry behind what
+ 
+
+ align:start position:0%
+the the physical chemistry behind what
+I'm going to tell you let me just state
+
+ align:start position:0%
+I'm going to tell you let me just state
+ 
+
+ align:start position:0%
+I'm going to tell you let me just state
+it without proof that if C is greater
+
+ align:start position:0%
+it without proof that if C is greater
+ 
+
+ align:start position:0%
+it without proof that if C is greater
+than one in other words if you're not in
+
+ align:start position:0%
+than one in other words if you're not in
+ 
+
+ align:start position:0%
+than one in other words if you're not in
+a pure material if you're in a
+
+ align:start position:0%
+a pure material if you're in a
+ 
+
+ align:start position:0%
+a pure material if you're in a
+multicomponent system if C is greater
+
+ align:start position:0%
+multicomponent system if C is greater
+ 
+
+ align:start position:0%
+multicomponent system if C is greater
+than one it's impossible to go from
+
+ align:start position:0%
+than one it's impossible to go from
+ 
+
+ align:start position:0%
+than one it's impossible to go from
+phase
+
+ align:start position:0%
+phase
+ 
+
+ align:start position:0%
+phase
+one to phase
+
+ align:start position:0%
+one to phase
+ 
+
+ align:start position:0%
+one to phase
+two cannot go from phase one to phase
+
+ align:start position:0%
+two cannot go from phase one to phase
+ 
+
+ align:start position:0%
+two cannot go from phase one to phase
+two without a
+
+ align:start position:0%
+two without a
+ 
+
+ align:start position:0%
+two without a
+two-phase region in
+
+ align:start position:0%
+two-phase region in
+ 
+
+ align:start position:0%
+two-phase region in
+between so we can't go from all liquid
+
+ align:start position:0%
+between so we can't go from all liquid
+ 
+
+ align:start position:0%
+between so we can't go from all liquid
+to all solid remember we said these mix
+
+ align:start position:0%
+to all solid remember we said these mix
+ 
+
+ align:start position:0%
+to all solid remember we said these mix
+in all proportions down here so solids
+
+ align:start position:0%
+in all proportions down here so solids
+ 
+
+ align:start position:0%
+in all proportions down here so solids
+you can mix any mix any ratio of a and b
+
+ align:start position:0%
+you can mix any mix any ratio of a and b
+ 
+
+ align:start position:0%
+you can mix any mix any ratio of a and b
+as solids any mix of a and b as liquids
+
+ align:start position:0%
+as solids any mix of a and b as liquids
+ 
+
+ align:start position:0%
+as solids any mix of a and b as liquids
+but because we must go through a
+
+ align:start position:0%
+but because we must go through a
+ 
+
+ align:start position:0%
+but because we must go through a
+two-phase regime this opens
+
+ align:start position:0%
+two-phase regime this opens
+ 
+
+ align:start position:0%
+two-phase regime this opens
+up to give a two-phase regime so up here
+
+ align:start position:0%
+up to give a two-phase regime so up here
+ 
+
+ align:start position:0%
+up to give a two-phase regime so up here
+this is all liquid down here this is all
+
+ align:start position:0%
+this is all liquid down here this is all
+ 
+
+ align:start position:0%
+this is all liquid down here this is all
+solid and in between is a two-phase
+
+ align:start position:0%
+solid and in between is a two-phase
+ 
+
+ align:start position:0%
+solid and in between is a two-phase
+regime of liquid and solid we can call
+
+ align:start position:0%
+regime of liquid and solid we can call
+ 
+
+ align:start position:0%
+regime of liquid and solid we can call
+it
+
+ align:start position:0%
+it
+ 
+
+ align:start position:0%
+it
+slush slush we've seen slush before
+
+ align:start position:0%
+slush slush we've seen slush before
+ 
+
+ align:start position:0%
+slush slush we've seen slush before
+we've seen ice slush in water the
+
+ align:start position:0%
+we've seen ice slush in water the
+ 
+
+ align:start position:0%
+we've seen ice slush in water the
+two-phase equilibrium for a pure
+
+ align:start position:0%
+two-phase equilibrium for a pure
+ 
+
+ align:start position:0%
+two-phase equilibrium for a pure
+material this is now Liquid Plus solid
+
+ align:start position:0%
+material this is now Liquid Plus solid
+ 
+
+ align:start position:0%
+material this is now Liquid Plus solid
+in a uh multicomponent system so up here
+
+ align:start position:0%
+in a uh multicomponent system so up here
+ 
+
+ align:start position:0%
+in a uh multicomponent system so up here
+we have singlephase
+
+ align:start position:0%
+we have singlephase
+ 
+
+ align:start position:0%
+we have singlephase
+liquid because they're mixing in all
+
+ align:start position:0%
+liquid because they're mixing in all
+ 
+
+ align:start position:0%
+liquid because they're mixing in all
+proportions so this is a solution down
+
+ align:start position:0%
+proportions so this is a solution down
+ 
+
+ align:start position:0%
+proportions so this is a solution down
+here these are solid Solutions and in
+
+ align:start position:0%
+here these are solid Solutions and in
+ 
+
+ align:start position:0%
+here these are solid Solutions and in
+here we
+
+ align:start position:0%
+here we
+ 
+
+ align:start position:0%
+here we
+have a two-phase regime a liquid phase
+
+ align:start position:0%
+have a two-phase regime a liquid phase
+ 
+
+ align:start position:0%
+have a two-phase regime a liquid phase
+homogeneous a solid phase
+
+ align:start position:0%
+homogeneous a solid phase
+ 
+
+ align:start position:0%
+homogeneous a solid phase
+homogeneous and this these lines are now
+
+ align:start position:0%
+homogeneous and this these lines are now
+ 
+
+ align:start position:0%
+homogeneous and this these lines are now
+no longer called the melting line or the
+
+ align:start position:0%
+no longer called the melting line or the
+ 
+
+ align:start position:0%
+no longer called the melting line or the
+or the freezing line we have two
+
+ align:start position:0%
+or the freezing line we have two
+ 
+
+ align:start position:0%
+or the freezing line we have two
+different lines right the upper line
+
+ align:start position:0%
+different lines right the upper line
+ 
+
+ align:start position:0%
+different lines right the upper line
+defines the lowest temperature for any
+
+ align:start position:0%
+defines the lowest temperature for any
+ 
+
+ align:start position:0%
+defines the lowest temperature for any
+composition pick any composition you
+
+ align:start position:0%
+composition pick any composition you
+ 
+
+ align:start position:0%
+composition pick any composition you
+want this temperature is the lowest
+
+ align:start position:0%
+want this temperature is the lowest
+ 
+
+ align:start position:0%
+want this temperature is the lowest
+composition at which you have only
+
+ align:start position:0%
+composition at which you have only
+ 
+
+ align:start position:0%
+composition at which you have only
+liquid present change the composition
+
+ align:start position:0%
+liquid present change the composition
+ 
+
+ align:start position:0%
+liquid present change the composition
+and that temperature changes but below
+
+ align:start position:0%
+and that temperature changes but below
+ 
+
+ align:start position:0%
+and that temperature changes but below
+this temperature you start to see the
+
+ align:start position:0%
+this temperature you start to see the
+ 
+
+ align:start position:0%
+this temperature you start to see the
+emergence of solid so this line here is
+
+ align:start position:0%
+emergence of solid so this line here is
+ 
+
+ align:start position:0%
+emergence of solid so this line here is
+called the liquidous
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+liquidous liquidous
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+is is the line associated with this
+
+ align:start position:0%
+is is the line associated with this
+ 
+
+ align:start position:0%
+is is the line associated with this
+reaction singlephase liquid goes to
+
+ align:start position:0%
+reaction singlephase liquid goes to
+ 
+
+ align:start position:0%
+reaction singlephase liquid goes to
+Liquid Plus
+
+ align:start position:0%
+Liquid Plus
+ 
+
+ align:start position:0%
+Liquid Plus
+solid and the lower line is called
+
+ align:start position:0%
+solid and the lower line is called
+ 
+
+ align:start position:0%
+solid and the lower line is called
+solidus the lower line is called solidus
+
+ align:start position:0%
+solidus the lower line is called solidus
+ 
+
+ align:start position:0%
+solidus the lower line is called solidus
+and it represents the complimentary set
+
+ align:start position:0%
+and it represents the complimentary set
+ 
+
+ align:start position:0%
+and it represents the complimentary set
+the solidus is the highest temperature
+
+ align:start position:0%
+the solidus is the highest temperature
+ 
+
+ align:start position:0%
+the solidus is the highest temperature
+at any composition for which you have
+
+ align:start position:0%
+at any composition for which you have
+ 
+
+ align:start position:0%
+at any composition for which you have
+only solid present if you see at the
+
+ align:start position:0%
+only solid present if you see at the
+ 
+
+ align:start position:0%
+only solid present if you see at the
+line that I've
+
+ align:start position:0%
+line that I've
+ 
+
+ align:start position:0%
+line that I've
+drawn the solidest temperature is the
+
+ align:start position:0%
+drawn the solidest temperature is the
+ 
+
+ align:start position:0%
+drawn the solidest temperature is the
+highest temperature for which we have
+
+ align:start position:0%
+highest temperature for which we have
+ 
+
+ align:start position:0%
+highest temperature for which we have
+solid solution present if we raise the
+
+ align:start position:0%
+solid solution present if we raise the
+ 
+
+ align:start position:0%
+solid solution present if we raise the
+temperature anymore we go into a
+
+ align:start position:0%
+temperature anymore we go into a
+ 
+
+ align:start position:0%
+temperature anymore we go into a
+two-phase regime some liquid starts to
+
+ align:start position:0%
+two-phase regime some liquid starts to
+ 
+
+ align:start position:0%
+two-phase regime some liquid starts to
+emerge so the solidus represents the
+
+ align:start position:0%
+emerge so the solidus represents the
+ 
+
+ align:start position:0%
+emerge so the solidus represents the
+highest temperature for all solid and
+
+ align:start position:0%
+highest temperature for all solid and
+ 
+
+ align:start position:0%
+highest temperature for all solid and
+and it represents solid goes to Liquid
+
+ align:start position:0%
+and it represents solid goes to Liquid
+ 
+
+ align:start position:0%
+and it represents solid goes to Liquid
+Plus solid homogeneous solid all right
+
+ align:start position:0%
+Plus solid homogeneous solid all right
+ 
+
+ align:start position:0%
+Plus solid homogeneous solid all right
+so let's write it again this is the
+
+ align:start position:0%
+so let's write it again this is the
+ 
+
+ align:start position:0%
+so let's write it again this is the
+lowest temperature
+
+ align:start position:0%
+lowest temperature
+ 
+
+ align:start position:0%
+lowest temperature
+for only
+
+ align:start position:0%
+for only
+ 
+
+ align:start position:0%
+for only
+liquid and this is at any c at any
+
+ align:start position:0%
+liquid and this is at any c at any
+ 
+
+ align:start position:0%
+liquid and this is at any c at any
+composition any value of composition and
+
+ align:start position:0%
+composition any value of composition and
+ 
+
+ align:start position:0%
+composition any value of composition and
+the solidest is the highest is the
+
+ align:start position:0%
+the solidest is the highest is the
+ 
+
+ align:start position:0%
+the solidest is the highest is the
+highest temperature for only solid to be
+
+ align:start position:0%
+highest temperature for only solid to be
+ 
+
+ align:start position:0%
+highest temperature for only solid to be
+present at any
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+composition this only applies once you
+
+ align:start position:0%
+composition this only applies once you
+ 
+
+ align:start position:0%
+composition this only applies once you
+move off of Purity so in here this is
+
+ align:start position:0%
+move off of Purity so in here this is
+ 
+
+ align:start position:0%
+move off of Purity so in here this is
+showing you how things vary as a
+
+ align:start position:0%
+showing you how things vary as a
+ 
+
+ align:start position:0%
+showing you how things vary as a
+function of composition um and such a
+
+ align:start position:0%
+function of composition um and such a
+ 
+
+ align:start position:0%
+function of composition um and such a
+diagram that has such similarities
+
+ align:start position:0%
+diagram that has such similarities
+ 
+
+ align:start position:0%
+diagram that has such similarities
+because the N members must have common
+
+ align:start position:0%
+because the N members must have common
+ 
+
+ align:start position:0%
+because the N members must have common
+bonding common size and so on this type
+
+ align:start position:0%
+bonding common size and so on this type
+ 
+
+ align:start position:0%
+bonding common size and so on this type
+of a diagram is called
+
+ align:start position:0%
+of a diagram is called
+ 
+
+ align:start position:0%
+of a diagram is called
+isomorphous this is an isomorphous
+
+ align:start position:0%
+isomorphous this is an isomorphous
+ 
+
+ align:start position:0%
+isomorphous this is an isomorphous
+diagram and the shape looks like a lens
+
+ align:start position:0%
+diagram and the shape looks like a lens
+ 
+
+ align:start position:0%
+diagram and the shape looks like a lens
+doesn't it it looks like a lens it's a
+
+ align:start position:0%
+doesn't it it looks like a lens it's a
+ 
+
+ align:start position:0%
+doesn't it it looks like a lens it's a
+lens shaped diagram lens
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+shaped lens shape but if you want to get
+
+ align:start position:0%
+shaped lens shape but if you want to get
+ 
+
+ align:start position:0%
+shaped lens shape but if you want to get
+fancy we don't say lens shape we say
+
+ align:start position:0%
+fancy we don't say lens shape we say
+ 
+
+ align:start position:0%
+fancy we don't say lens shape we say
+lenticular from the Latin lens Len the
+
+ align:start position:0%
+lenticular from the Latin lens Len the
+ 
+
+ align:start position:0%
+lenticular from the Latin lens Len the
+genitive is lenus so lenticular it's a
+
+ align:start position:0%
+genitive is lenus so lenticular it's a
+ 
+
+ align:start position:0%
+genitive is lenus so lenticular it's a
+lenticular diagram okay
+
+ align:start position:0%
+lenticular diagram okay
+ 
+
+ align:start position:0%
+lenticular diagram okay
+so now we have it let's look at some
+
+ align:start position:0%
+so now we have it let's look at some
+ 
+
+ align:start position:0%
+so now we have it let's look at some
+example systems let's look at some
+
+ align:start position:0%
+example systems let's look at some
+ 
+
+ align:start position:0%
+example systems let's look at some
+example systems that exhibit this kind
+
+ align:start position:0%
+example systems that exhibit this kind
+ 
+
+ align:start position:0%
+example systems that exhibit this kind
+of Behavior Uh Oh you know what before
+
+ align:start position:0%
+of Behavior Uh Oh you know what before
+ 
+
+ align:start position:0%
+of Behavior Uh Oh you know what before
+we do that I I meant to show you this we
+
+ align:start position:0%
+we do that I I meant to show you this we
+ 
+
+ align:start position:0%
+we do that I I meant to show you this we
+talked about what happens at ultra high
+
+ align:start position:0%
+talked about what happens at ultra high
+ 
+
+ align:start position:0%
+talked about what happens at ultra high
+pressures this is water we're down in
+
+ align:start position:0%
+pressures this is water we're down in
+ 
+
+ align:start position:0%
+pressures this is water we're down in
+here see look at this is now kilobars
+
+ align:start position:0%
+here see look at this is now kilobars
+ 
+
+ align:start position:0%
+here see look at this is now kilobars
+thousands of atmospheres so this is the
+
+ align:start position:0%
+thousands of atmospheres so this is the
+ 
+
+ align:start position:0%
+thousands of atmospheres so this is the
+normal line that you see that's this
+
+ align:start position:0%
+normal line that you see that's this
+ 
+
+ align:start position:0%
+normal line that you see that's this
+line that I've shown you that's here
+
+ align:start position:0%
+line that I've shown you that's here
+ 
+
+ align:start position:0%
+line that I've shown you that's here
+okay so there's ice at a density about
+
+ align:start position:0%
+okay so there's ice at a density about
+ 
+
+ align:start position:0%
+okay so there's ice at a density about
+0.92 and normal water is about one so
+
+ align:start position:0%
+0.92 and normal water is about one so
+ 
+
+ align:start position:0%
+0.92 and normal water is about one so
+ice floats on water but if you keep
+
+ align:start position:0%
+ice floats on water but if you keep
+ 
+
+ align:start position:0%
+ice floats on water but if you keep
+pressing eventually you'll force that
+
+ align:start position:0%
+pressing eventually you'll force that
+ 
+
+ align:start position:0%
+pressing eventually you'll force that
+crystal structure to change and it'll
+
+ align:start position:0%
+crystal structure to change and it'll
+ 
+
+ align:start position:0%
+crystal structure to change and it'll
+become more close packed and now you see
+
+ align:start position:0%
+become more close packed and now you see
+ 
+
+ align:start position:0%
+become more close packed and now you see
+normal behavior so liquid goes to solid
+
+ align:start position:0%
+normal behavior so liquid goes to solid
+ 
+
+ align:start position:0%
+normal behavior so liquid goes to solid
+and all of these different Roman
+
+ align:start position:0%
+and all of these different Roman
+ 
+
+ align:start position:0%
+and all of these different Roman
+numerals represent different Crystal
+
+ align:start position:0%
+numerals represent different Crystal
+ 
+
+ align:start position:0%
+numerals represent different Crystal
+structures ice has at least nine
+
+ align:start position:0%
+structures ice has at least nine
+ 
+
+ align:start position:0%
+structures ice has at least nine
+different Crystal structures okay and
+
+ align:start position:0%
+different Crystal structures okay and
+ 
+
+ align:start position:0%
+different Crystal structures okay and
+some of these are really interesting
+
+ align:start position:0%
+some of these are really interesting
+ 
+
+ align:start position:0%
+some of these are really interesting
+look at this one this is these are all
+
+ align:start position:0%
+look at this one this is these are all
+ 
+
+ align:start position:0%
+look at this one this is these are all
+triple points right this is ice 3 ice
+
+ align:start position:0%
+triple points right this is ice 3 ice
+ 
+
+ align:start position:0%
+triple points right this is ice 3 ice
+one and liquid so in a in a single
+
+ align:start position:0%
+one and liquid so in a in a single
+ 
+
+ align:start position:0%
+one and liquid so in a in a single
+component system that's a triple point
+
+ align:start position:0%
+component system that's a triple point
+ 
+
+ align:start position:0%
+component system that's a triple point
+that's uniquely defined now look at what
+
+ align:start position:0%
+that's uniquely defined now look at what
+ 
+
+ align:start position:0%
+that's uniquely defined now look at what
+happens over here this is a triple point
+
+ align:start position:0%
+happens over here this is a triple point
+ 
+
+ align:start position:0%
+happens over here this is a triple point
+between ice 6 ice7 and liquid and it's
+
+ align:start position:0%
+between ice 6 ice7 and liquid and it's
+ 
+
+ align:start position:0%
+between ice 6 ice7 and liquid and it's
+at about 80° C way up there now look at
+
+ align:start position:0%
+at about 80° C way up there now look at
+ 
+
+ align:start position:0%
+at about 80° C way up there now look at
+this one this is i7 I'm right I'm in a
+
+ align:start position:0%
+this one this is i7 I'm right I'm in a
+ 
+
+ align:start position:0%
+this one this is i7 I'm right I'm in a
+singlephase regime ice 7 it's 100° C I
+
+ align:start position:0%
+singlephase regime ice 7 it's 100° C I
+ 
+
+ align:start position:0%
+singlephase regime ice 7 it's 100° C I
+have to go to 25 kilobar but you know we
+
+ align:start position:0%
+have to go to 25 kilobar but you know we
+ 
+
+ align:start position:0%
+have to go to 25 kilobar but you know we
+have Laboratories so it's 100° C and it
+
+ align:start position:0%
+have Laboratories so it's 100° C and it
+ 
+
+ align:start position:0%
+have Laboratories so it's 100° C and it
+it's not Vapor remember water boils
+
+ align:start position:0%
+it's not Vapor remember water boils
+ 
+
+ align:start position:0%
+it's not Vapor remember water boils
+normal boiling point is 100 degrees C
+
+ align:start position:0%
+normal boiling point is 100 degrees C
+ 
+
+ align:start position:0%
+normal boiling point is 100 degrees C
+but if I apply 25 kilobars I not only
+
+ align:start position:0%
+but if I apply 25 kilobars I not only
+ 
+
+ align:start position:0%
+but if I apply 25 kilobars I not only
+move through the liquid I go not only
+
+ align:start position:0%
+move through the liquid I go not only
+ 
+
+ align:start position:0%
+move through the liquid I go not only
+through liquid I go right across the
+
+ align:start position:0%
+through liquid I go right across the
+ 
+
+ align:start position:0%
+through liquid I go right across the
+solid so you saw I brought the dry ice
+
+ align:start position:0%
+solid so you saw I brought the dry ice
+ 
+
+ align:start position:0%
+solid so you saw I brought the dry ice
+into the classroom by the way I was here
+
+ align:start position:0%
+into the classroom by the way I was here
+ 
+
+ align:start position:0%
+into the classroom by the way I was here
+yesterday there was still half of the
+
+ align:start position:0%
+yesterday there was still half of the
+ 
+
+ align:start position:0%
+yesterday there was still half of the
+block was still sitting there cuz I left
+
+ align:start position:0%
+block was still sitting there cuz I left
+ 
+
+ align:start position:0%
+block was still sitting there cuz I left
+it in the box and it was was had this
+
+ align:start position:0%
+it in the box and it was was had this
+ 
+
+ align:start position:0%
+it in the box and it was was had this
+little comfort zone of CO2 Vapor around
+
+ align:start position:0%
+little comfort zone of CO2 Vapor around
+ 
+
+ align:start position:0%
+little comfort zone of CO2 Vapor around
+it was just naturally thinning in took a
+
+ align:start position:0%
+it was just naturally thinning in took a
+ 
+
+ align:start position:0%
+it was just naturally thinning in took a
+long time what's my point my point is
+
+ align:start position:0%
+long time what's my point my point is
+ 
+
+ align:start position:0%
+long time what's my point my point is
+when you make such a metastable state
+
+ align:start position:0%
+when you make such a metastable state
+ 
+
+ align:start position:0%
+when you make such a metastable state
+and bring it into some unnatural
+
+ align:start position:0%
+and bring it into some unnatural
+ 
+
+ align:start position:0%
+and bring it into some unnatural
+conditions it will it will last for a
+
+ align:start position:0%
+conditions it will it will last for a
+ 
+
+ align:start position:0%
+conditions it will it will last for a
+long long time the kinetics are quite
+
+ align:start position:0%
+long long time the kinetics are quite
+ 
+
+ align:start position:0%
+long long time the kinetics are quite
+slow so let's say we go into the lab we
+
+ align:start position:0%
+slow so let's say we go into the lab we
+ 
+
+ align:start position:0%
+slow so let's say we go into the lab we
+make ice 7 it's 100° C it's 25 KOB and
+
+ align:start position:0%
+make ice 7 it's 100° C it's 25 KOB and
+ 
+
+ align:start position:0%
+make ice 7 it's 100° C it's 25 KOB and
+there's a party going on down the hall
+
+ align:start position:0%
+there's a party going on down the hall
+ 
+
+ align:start position:0%
+there's a party going on down the hall
+so we come out and we've got some ice
+
+ align:start position:0%
+so we come out and we've got some ice
+ 
+
+ align:start position:0%
+so we come out and we've got some ice
+seven and it's going it's going to start
+
+ align:start position:0%
+seven and it's going it's going to start
+ 
+
+ align:start position:0%
+seven and it's going it's going to start
+to want to to to melt right cuz the
+
+ align:start position:0%
+to want to to to melt right cuz the
+ 
+
+ align:start position:0%
+to want to to to melt right cuz the
+temperature's falling and the
+
+ align:start position:0%
+temperature's falling and the
+ 
+
+ align:start position:0%
+temperature's falling and the
+temperature is going to fall so you're
+
+ align:start position:0%
+temperature is going to fall so you're
+ 
+
+ align:start position:0%
+temperature is going to fall so you're
+going to move this way and down but some
+
+ align:start position:0%
+going to move this way and down but some
+ 
+
+ align:start position:0%
+going to move this way and down but some
+of it's going to be left so now you go
+
+ align:start position:0%
+of it's going to be left so now you go
+ 
+
+ align:start position:0%
+of it's going to be left so now you go
+up to somebody you take some ice seven
+
+ align:start position:0%
+up to somebody you take some ice seven
+ 
+
+ align:start position:0%
+up to somebody you take some ice seven
+you drop it in the drink and the drink
+
+ align:start position:0%
+you drop it in the drink and the drink
+ 
+
+ align:start position:0%
+you drop it in the drink and the drink
+heats up and starts to boil and the ice
+
+ align:start position:0%
+heats up and starts to boil and the ice
+ 
+
+ align:start position:0%
+heats up and starts to boil and the ice
+sinks to the bottom of the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+glass that might get someone to rethink
+
+ align:start position:0%
+glass that might get someone to rethink
+ 
+
+ align:start position:0%
+glass that might get someone to rethink
+their drinking habits you see but this
+
+ align:start position:0%
+their drinking habits you see but this
+ 
+
+ align:start position:0%
+their drinking habits you see but this
+is this is the power of changing
+
+ align:start position:0%
+is this is the power of changing
+ 
+
+ align:start position:0%
+is this is the power of changing
+pressure and temperature all right by
+
+ align:start position:0%
+pressure and temperature all right by
+ 
+
+ align:start position:0%
+pressure and temperature all right by
+the way those of you who know Cat's
+
+ align:start position:0%
+the way those of you who know Cat's
+ 
+
+ align:start position:0%
+the way those of you who know Cat's
+Cradle by Kurt Vaga there's ice nine it
+
+ align:start position:0%
+Cradle by Kurt Vaga there's ice nine it
+ 
+
+ align:start position:0%
+Cradle by Kurt Vaga there's ice nine it
+exists all right it's been characterized
+
+ align:start position:0%
+exists all right it's been characterized
+ 
+
+ align:start position:0%
+exists all right it's been characterized
+so somebody actually measured this stuff
+
+ align:start position:0%
+so somebody actually measured this stuff
+ 
+
+ align:start position:0%
+so somebody actually measured this stuff
+and we're still here we didn't freeze
+
+ align:start position:0%
+and we're still here we didn't freeze
+ 
+
+ align:start position:0%
+and we're still here we didn't freeze
+the whole world so you can relax he he
+
+ align:start position:0%
+the whole world so you can relax he he
+ 
+
+ align:start position:0%
+the whole world so you can relax he he
+needs to rename that maybe ice 11 or
+
+ align:start position:0%
+needs to rename that maybe ice 11 or
+ 
+
+ align:start position:0%
+needs to rename that maybe ice 11 or
+something I don't know if there are any
+
+ align:start position:0%
+something I don't know if there are any
+ 
+
+ align:start position:0%
+something I don't know if there are any
+more phases here okay so here's a here's
+
+ align:start position:0%
+more phases here okay so here's a here's
+ 
+
+ align:start position:0%
+more phases here okay so here's a here's
+a phase diagram copper nickel that's a
+
+ align:start position:0%
+a phase diagram copper nickel that's a
+ 
+
+ align:start position:0%
+a phase diagram copper nickel that's a
+lenticular diagram copper and nickel
+
+ align:start position:0%
+lenticular diagram copper and nickel
+ 
+
+ align:start position:0%
+lenticular diagram copper and nickel
+both FCC metals very similar in atomic
+
+ align:start position:0%
+both FCC metals very similar in atomic
+ 
+
+ align:start position:0%
+both FCC metals very similar in atomic
+Dimension very small electro negativity
+
+ align:start position:0%
+Dimension very small electro negativity
+ 
+
+ align:start position:0%
+Dimension very small electro negativity
+difference so you have a lens-shaped
+
+ align:start position:0%
+difference so you have a lens-shaped
+ 
+
+ align:start position:0%
+difference so you have a lens-shaped
+diagram copper melts at 1085 Centigrade
+
+ align:start position:0%
+diagram copper melts at 1085 Centigrade
+ 
+
+ align:start position:0%
+diagram copper melts at 1085 Centigrade
+nickel melts at 1455 and there's the
+
+ align:start position:0%
+nickel melts at 1455 and there's the
+ 
+
+ align:start position:0%
+nickel melts at 1455 and there's the
+liquidous and the solidest and in
+
+ align:start position:0%
+liquidous and the solidest and in
+ 
+
+ align:start position:0%
+liquidous and the solidest and in
+between if you cool at any one of these
+
+ align:start position:0%
+between if you cool at any one of these
+ 
+
+ align:start position:0%
+between if you cool at any one of these
+uh concentrations you're going to go
+
+ align:start position:0%
+uh concentrations you're going to go
+ 
+
+ align:start position:0%
+uh concentrations you're going to go
+through this two-phase regime we're
+
+ align:start position:0%
+through this two-phase regime we're
+ 
+
+ align:start position:0%
+through this two-phase regime we're
+going to talk a little bit more about
+
+ align:start position:0%
+going to talk a little bit more about
+ 
+
+ align:start position:0%
+going to talk a little bit more about
+that in a second here's a ceramic system
+
+ align:start position:0%
+that in a second here's a ceramic system
+ 
+
+ align:start position:0%
+that in a second here's a ceramic system
+here's nickel ox oide magnesium oxide so
+
+ align:start position:0%
+here's nickel ox oide magnesium oxide so
+ 
+
+ align:start position:0%
+here's nickel ox oide magnesium oxide so
+this is an ionic solid right it's nickel
+
+ align:start position:0%
+this is an ionic solid right it's nickel
+ 
+
+ align:start position:0%
+this is an ionic solid right it's nickel
+cats magnesium cations I and oxide
+
+ align:start position:0%
+cats magnesium cations I and oxide
+ 
+
+ align:start position:0%
+cats magnesium cations I and oxide
+anions and the nickel and magnesium are
+
+ align:start position:0%
+anions and the nickel and magnesium are
+ 
+
+ align:start position:0%
+anions and the nickel and magnesium are
+roughly similar in size modest electro
+
+ align:start position:0%
+roughly similar in size modest electro
+ 
+
+ align:start position:0%
+roughly similar in size modest electro
+negativity difference and so this one
+
+ align:start position:0%
+negativity difference and so this one
+ 
+
+ align:start position:0%
+negativity difference and so this one
+starts at 20 uh 2,000 Centigrade goes up
+
+ align:start position:0%
+starts at 20 uh 2,000 Centigrade goes up
+ 
+
+ align:start position:0%
+starts at 20 uh 2,000 Centigrade goes up
+to 2800 Centigrade has a lens-shaped
+
+ align:start position:0%
+to 2800 Centigrade has a lens-shaped
+ 
+
+ align:start position:0%
+to 2800 Centigrade has a lens-shaped
+diagram here's one this is gold nickel
+
+ align:start position:0%
+diagram here's one this is gold nickel
+ 
+
+ align:start position:0%
+diagram here's one this is gold nickel
+it's almost lenticular look at the top
+
+ align:start position:0%
+it's almost lenticular look at the top
+ 
+
+ align:start position:0%
+it's almost lenticular look at the top
+part here there's the nickel melting
+
+ align:start position:0%
+part here there's the nickel melting
+ 
+
+ align:start position:0%
+part here there's the nickel melting
+point is up around
+
+ align:start position:0%
+point is up around
+ 
+
+ align:start position:0%
+point is up around
+1450 uh gold melts at 1063 it's almost
+
+ align:start position:0%
+1450 uh gold melts at 1063 it's almost
+ 
+
+ align:start position:0%
+1450 uh gold melts at 1063 it's almost
+perfectly lenticular with this little
+
+ align:start position:0%
+perfectly lenticular with this little
+ 
+
+ align:start position:0%
+perfectly lenticular with this little
+bit of a dip here sort of the liquid
+
+ align:start position:0%
+bit of a dip here sort of the liquid
+ 
+
+ align:start position:0%
+bit of a dip here sort of the liquid
+solid uh um analogy to an asot Trope but
+
+ align:start position:0%
+solid uh um analogy to an asot Trope but
+ 
+
+ align:start position:0%
+solid uh um analogy to an asot Trope but
+again you see they're both FCC Metals
+
+ align:start position:0%
+again you see they're both FCC Metals
+ 
+
+ align:start position:0%
+again you see they're both FCC Metals
+both FCC Metals but in this case the
+
+ align:start position:0%
+both FCC Metals but in this case the
+ 
+
+ align:start position:0%
+both FCC Metals but in this case the
+electr negativity difference is a little
+
+ align:start position:0%
+electr negativity difference is a little
+ 
+
+ align:start position:0%
+electr negativity difference is a little
+bit larger than you'd like and so you
+
+ align:start position:0%
+bit larger than you'd like and so you
+ 
+
+ align:start position:0%
+bit larger than you'd like and so you
+see a little bit of a freezing point
+
+ align:start position:0%
+see a little bit of a freezing point
+ 
+
+ align:start position:0%
+see a little bit of a freezing point
+depression here all right so now I want
+
+ align:start position:0%
+depression here all right so now I want
+ 
+
+ align:start position:0%
+depression here all right so now I want
+to go back and talk about what's going
+
+ align:start position:0%
+to go back and talk about what's going
+ 
+
+ align:start position:0%
+to go back and talk about what's going
+on inside that uh two-phase regime
+
+ align:start position:0%
+on inside that uh two-phase regime
+ 
+
+ align:start position:0%
+on inside that uh two-phase regime
+because that two-phase regime is is uh
+
+ align:start position:0%
+because that two-phase regime is is uh
+ 
+
+ align:start position:0%
+because that two-phase regime is is uh
+is peculiar it's peculiar so let's see
+
+ align:start position:0%
+is peculiar it's peculiar so let's see
+ 
+
+ align:start position:0%
+is peculiar it's peculiar so let's see
+what happens if we take something of a
+
+ align:start position:0%
+what happens if we take something of a
+ 
+
+ align:start position:0%
+what happens if we take something of a
+particular composition and cool it so
+
+ align:start position:0%
+particular composition and cool it so
+ 
+
+ align:start position:0%
+particular composition and cool it so
+here's what I'm doing I'm going to blow
+
+ align:start position:0%
+here's what I'm doing I'm going to blow
+ 
+
+ align:start position:0%
+here's what I'm doing I'm going to blow
+this up going to blow this up and what I
+
+ align:start position:0%
+this up going to blow this up and what I
+ 
+
+ align:start position:0%
+this up going to blow this up and what I
+want to do is take something that's
+
+ align:start position:0%
+want to do is take something that's
+ 
+
+ align:start position:0%
+want to do is take something that's
+about
+
+ align:start position:0%
+about
+ 
+
+ align:start position:0%
+about
+40% here's where we are we're looking at
+
+ align:start position:0%
+40% here's where we are we're looking at
+ 
+
+ align:start position:0%
+40% here's where we are we're looking at
+this is the liquidous
+
+ align:start position:0%
+this is the liquidous
+ 
+
+ align:start position:0%
+this is the liquidous
+here liquidous line and this is the
+
+ align:start position:0%
+here liquidous line and this is the
+ 
+
+ align:start position:0%
+here liquidous line and this is the
+solidest
+
+ align:start position:0%
+solidest
+ 
+
+ align:start position:0%
+solidest
+line so this is all solid this is single
+
+ align:start position:0%
+line so this is all solid this is single
+ 
+
+ align:start position:0%
+line so this is all solid this is single
+phase P equals 1 this is all
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+liquid single phase and this is Liquid
+
+ align:start position:0%
+liquid single phase and this is Liquid
+ 
+
+ align:start position:0%
+liquid single phase and this is Liquid
+Plus
+
+ align:start position:0%
+Plus
+ 
+
+ align:start position:0%
+Plus
+solid and let's say we drop the
+
+ align:start position:0%
+solid and let's say we drop the
+ 
+
+ align:start position:0%
+solid and let's say we drop the
+temperature down into the middle of this
+
+ align:start position:0%
+temperature down into the middle of this
+ 
+
+ align:start position:0%
+temperature down into the middle of this
+two-phase regime what's happening here
+
+ align:start position:0%
+two-phase regime what's happening here
+ 
+
+ align:start position:0%
+two-phase regime what's happening here
+this is a two-phase system and we we
+
+ align:start position:0%
+this is a two-phase system and we we
+ 
+
+ align:start position:0%
+this is a two-phase system and we we
+have a liquid and a solid and the phase
+
+ align:start position:0%
+have a liquid and a solid and the phase
+ 
+
+ align:start position:0%
+have a liquid and a solid and the phase
+diagram tells us the composition so
+
+ align:start position:0%
+diagram tells us the composition so
+ 
+
+ align:start position:0%
+diagram tells us the composition so
+here's the sequence here's let's look at
+
+ align:start position:0%
+here's the sequence here's let's look at
+ 
+
+ align:start position:0%
+here's the sequence here's let's look at
+say comp composition uh C2 there
+
+ align:start position:0%
+say comp composition uh C2 there
+ 
+
+ align:start position:0%
+say comp composition uh C2 there
+composition C2 is about
+
+ align:start position:0%
+composition C2 is about
+ 
+
+ align:start position:0%
+composition C2 is about
+40% uh Nickel in Copper so at 1300° C we
+
+ align:start position:0%
+40% uh Nickel in Copper so at 1300° C we
+ 
+
+ align:start position:0%
+40% uh Nickel in Copper so at 1300° C we
+have liquid homogeneous liquid and if we
+
+ align:start position:0%
+have liquid homogeneous liquid and if we
+ 
+
+ align:start position:0%
+have liquid homogeneous liquid and if we
+go down to 1200°
+
+ align:start position:0%
+go down to 1200°
+ 
+
+ align:start position:0%
+go down to 1200°
+C at 1200° C we have a homogeneous solid
+
+ align:start position:0%
+C at 1200° C we have a homogeneous solid
+ 
+
+ align:start position:0%
+C at 1200° C we have a homogeneous solid
+these are the different grains so this
+
+ align:start position:0%
+these are the different grains so this
+ 
+
+ align:start position:0%
+these are the different grains so this
+is liquid this is solid and it's poly
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+crystallin solid poly crystallin and the
+
+ align:start position:0%
+crystallin solid poly crystallin and the
+ 
+
+ align:start position:0%
+crystallin solid poly crystallin and the
+composition each of these grains is the
+
+ align:start position:0%
+composition each of these grains is the
+ 
+
+ align:start position:0%
+composition each of these grains is the
+same what's happening at
+
+ align:start position:0%
+same what's happening at
+ 
+
+ align:start position:0%
+same what's happening at
+1250 1250 this diagram says I should
+
+ align:start position:0%
+1250 1250 this diagram says I should
+ 
+
+ align:start position:0%
+1250 1250 this diagram says I should
+have solid and liquid solid and liquid
+
+ align:start position:0%
+have solid and liquid solid and liquid
+ 
+
+ align:start position:0%
+have solid and liquid solid and liquid
+but look the composition of that liquid
+
+ align:start position:0%
+but look the composition of that liquid
+ 
+
+ align:start position:0%
+but look the composition of that liquid
+is not
+
+ align:start position:0%
+is not
+ 
+
+ align:start position:0%
+is not
+40% Nickel in Copper the composition is
+
+ align:start position:0%
+40% Nickel in Copper the composition is
+ 
+
+ align:start position:0%
+40% Nickel in Copper the composition is
+way over here it's about
+
+ align:start position:0%
+way over here it's about
+ 
+
+ align:start position:0%
+way over here it's about
+32% and the composition of the solid is
+
+ align:start position:0%
+32% and the composition of the solid is
+ 
+
+ align:start position:0%
+32% and the composition of the solid is
+up here at about 45%
+
+ align:start position:0%
+up here at about 45%
+ 
+
+ align:start position:0%
+up here at about 45%
+% this is
+
+ align:start position:0%
+% this is
+ 
+
+ align:start position:0%
+% this is
+32% uh what am I looking at 32% nickel
+
+ align:start position:0%
+32% uh what am I looking at 32% nickel
+ 
+
+ align:start position:0%
+32% uh what am I looking at 32% nickel
+and this is 45%
+
+ align:start position:0%
+and this is 45%
+ 
+
+ align:start position:0%
+and this is 45%
+nickel so I have a nickel Rich solid and
+
+ align:start position:0%
+nickel so I have a nickel Rich solid and
+ 
+
+ align:start position:0%
+nickel so I have a nickel Rich solid and
+I have a copper Rich liquid there's a
+
+ align:start position:0%
+I have a copper Rich liquid there's a
+ 
+
+ align:start position:0%
+I have a copper Rich liquid there's a
+there's a a shift a
+
+ align:start position:0%
+there's a a shift a
+ 
+
+ align:start position:0%
+there's a a shift a
+shift and suppose I take something of a
+
+ align:start position:0%
+shift and suppose I take something of a
+ 
+
+ align:start position:0%
+shift and suppose I take something of a
+different composition so this is the C2
+
+ align:start position:0%
+different composition so this is the C2
+ 
+
+ align:start position:0%
+different composition so this is the C2
+that's on a diagram here's C1 I think it
+
+ align:start position:0%
+that's on a diagram here's C1 I think it
+ 
+
+ align:start position:0%
+that's on a diagram here's C1 I think it
+starts at around what does it start at
+
+ align:start position:0%
+starts at around what does it start at
+ 
+
+ align:start position:0%
+starts at around what does it start at
+it starts at around 35 5% nickel this
+
+ align:start position:0%
+it starts at around 35 5% nickel this
+ 
+
+ align:start position:0%
+it starts at around 35 5% nickel this
+started at 40% nickel C1 is 35% nickel I
+
+ align:start position:0%
+started at 40% nickel C1 is 35% nickel I
+ 
+
+ align:start position:0%
+started at 40% nickel C1 is 35% nickel I
+cool it down to the same temperature
+
+ align:start position:0%
+cool it down to the same temperature
+ 
+
+ align:start position:0%
+cool it down to the same temperature
+it's the same end members the liquid at
+
+ align:start position:0%
+it's the same end members the liquid at
+ 
+
+ align:start position:0%
+it's the same end members the liquid at
+this temperature has a unique value of
+
+ align:start position:0%
+this temperature has a unique value of
+ 
+
+ align:start position:0%
+this temperature has a unique value of
+nickel content so it doesn't matter what
+
+ align:start position:0%
+nickel content so it doesn't matter what
+ 
+
+ align:start position:0%
+nickel content so it doesn't matter what
+the composition is I will always end up
+
+ align:start position:0%
+the composition is I will always end up
+ 
+
+ align:start position:0%
+the composition is I will always end up
+with a liquid of one composition and a
+
+ align:start position:0%
+with a liquid of one composition and a
+ 
+
+ align:start position:0%
+with a liquid of one composition and a
+solid of the other composition well how
+
+ align:start position:0%
+solid of the other composition well how
+ 
+
+ align:start position:0%
+solid of the other composition well how
+can I start with two different this is
+
+ align:start position:0%
+can I start with two different this is
+ 
+
+ align:start position:0%
+can I start with two different this is
+40% and this is 35 5% nickel 40% nickel
+
+ align:start position:0%
+40% and this is 35 5% nickel 40% nickel
+ 
+
+ align:start position:0%
+40% and this is 35 5% nickel 40% nickel
+35% nickel these end members are the
+
+ align:start position:0%
+35% nickel these end members are the
+ 
+
+ align:start position:0%
+35% nickel these end members are the
+same there's only one variable left it's
+
+ align:start position:0%
+same there's only one variable left it's
+ 
+
+ align:start position:0%
+same there's only one variable left it's
+the relative amounts of these because I
+
+ align:start position:0%
+the relative amounts of these because I
+ 
+
+ align:start position:0%
+the relative amounts of these because I
+need conservation of mass because at the
+
+ align:start position:0%
+need conservation of mass because at the
+ 
+
+ align:start position:0%
+need conservation of mass because at the
+end of the day if I add up all the
+
+ align:start position:0%
+end of the day if I add up all the
+ 
+
+ align:start position:0%
+end of the day if I add up all the
+nickel in the liquid and all the nickel
+
+ align:start position:0%
+nickel in the liquid and all the nickel
+ 
+
+ align:start position:0%
+nickel in the liquid and all the nickel
+in the solid it still has to be net 40%
+
+ align:start position:0%
+in the solid it still has to be net 40%
+ 
+
+ align:start position:0%
+in the solid it still has to be net 40%
+nickel only in here it's 45% nickel up
+
+ align:start position:0%
+nickel only in here it's 45% nickel up
+ 
+
+ align:start position:0%
+nickel only in here it's 45% nickel up
+here it's 32% nickel so I've got a a
+
+ align:start position:0%
+here it's 32% nickel so I've got a a
+ 
+
+ align:start position:0%
+here it's 32% nickel so I've got a a
+verer scale scale I got a sliding scale
+
+ align:start position:0%
+verer scale scale I got a sliding scale
+ 
+
+ align:start position:0%
+verer scale scale I got a sliding scale
+that I can move so that if I have
+
+ align:start position:0%
+that I can move so that if I have
+ 
+
+ align:start position:0%
+that I can move so that if I have
+something that's 35% in other words it's
+
+ align:start position:0%
+something that's 35% in other words it's
+ 
+
+ align:start position:0%
+something that's 35% in other words it's
+got it it needs less of this phase so
+
+ align:start position:0%
+got it it needs less of this phase so
+ 
+
+ align:start position:0%
+got it it needs less of this phase so
+the 35% is going to end up doing this
+
+ align:start position:0%
+the 35% is going to end up doing this
+ 
+
+ align:start position:0%
+the 35% is going to end up doing this
+whereas the 40% is going to end up doing
+
+ align:start position:0%
+whereas the 40% is going to end up doing
+ 
+
+ align:start position:0%
+whereas the 40% is going to end up doing
+this it's the relative amounts this this
+
+ align:start position:0%
+this it's the relative amounts this this
+ 
+
+ align:start position:0%
+this it's the relative amounts this this
+line that tells me what the
+
+ align:start position:0%
+line that tells me what the
+ 
+
+ align:start position:0%
+line that tells me what the
+concentration of the solid and the
+
+ align:start position:0%
+concentration of the solid and the
+ 
+
+ align:start position:0%
+concentration of the solid and the
+liquid at any temperature is called the
+
+ align:start position:0%
+liquid at any temperature is called the
+ 
+
+ align:start position:0%
+liquid at any temperature is called the
+tie line so the ti line defines the
+
+ align:start position:0%
+tie line so the ti line defines the
+ 
+
+ align:start position:0%
+tie line so the ti line defines the
+composition and members the liquid and
+
+ align:start position:0%
+composition and members the liquid and
+ 
+
+ align:start position:0%
+composition and members the liquid and
+the solid in that two phase regime and
+
+ align:start position:0%
+the solid in that two phase regime and
+ 
+
+ align:start position:0%
+the solid in that two phase regime and
+we can take all of this that I've been
+
+ align:start position:0%
+we can take all of this that I've been
+ 
+
+ align:start position:0%
+we can take all of this that I've been
+talking about and we can we can codify
+
+ align:start position:0%
+talking about and we can we can codify
+ 
+
+ align:start position:0%
+talking about and we can we can codify
+it we can codify it in terms of a simple
+
+ align:start position:0%
+it we can codify it in terms of a simple
+ 
+
+ align:start position:0%
+it we can codify it in terms of a simple
+rule that captures the notion of phase
+
+ align:start position:0%
+rule that captures the notion of phase
+ 
+
+ align:start position:0%
+rule that captures the notion of phase
+separation and conservation of mass and
+
+ align:start position:0%
+separation and conservation of mass and
+ 
+
+ align:start position:0%
+separation and conservation of mass and
+that's called the lever
+
+ align:start position:0%
+that's called the lever
+ 
+
+ align:start position:0%
+that's called the lever
+rule the lever rule the lever rule
+
+ align:start position:0%
+rule the lever rule the lever rule
+ 
+
+ align:start position:0%
+rule the lever rule the lever rule
+answers the question how much of each
+
+ align:start position:0%
+answers the question how much of each
+ 
+
+ align:start position:0%
+answers the question how much of each
+phase is present the relative
+
+ align:start position:0%
+phase is present the relative
+ 
+
+ align:start position:0%
+phase is present the relative
+amount relative
+
+ align:start position:0%
+amount relative
+ 
+
+ align:start position:0%
+amount relative
+amount present
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+of each
+
+ align:start position:0%
+of each
+ 
+
+ align:start position:0%
+of each
+phase in the two-phase
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+regime in a two-phase
+
+ align:start position:0%
+regime in a two-phase
+ 
+
+ align:start position:0%
+regime in a two-phase
+region two-phase region so for example I
+
+ align:start position:0%
+region two-phase region so for example I
+ 
+
+ align:start position:0%
+region two-phase region so for example I
+think on the next one I've got this set
+
+ align:start position:0%
+think on the next one I've got this set
+ 
+
+ align:start position:0%
+think on the next one I've got this set
+up yeah here it is so here we are with
+
+ align:start position:0%
+up yeah here it is so here we are with
+ 
+
+ align:start position:0%
+up yeah here it is so here we are with
+the 40% nickel it's 40% Nickel in Copper
+
+ align:start position:0%
+the 40% nickel it's 40% Nickel in Copper
+ 
+
+ align:start position:0%
+the 40% nickel it's 40% Nickel in Copper
+we've dropped down into the two-phase
+
+ align:start position:0%
+we've dropped down into the two-phase
+ 
+
+ align:start position:0%
+we've dropped down into the two-phase
+regime draw the tie line and the tie
+
+ align:start position:0%
+regime draw the tie line and the tie
+ 
+
+ align:start position:0%
+regime draw the tie line and the tie
+line tells us that the liquid the liquid
+
+ align:start position:0%
+line tells us that the liquid the liquid
+ 
+
+ align:start position:0%
+line tells us that the liquid the liquid
+will the proportionate as follows so
+
+ align:start position:0%
+will the proportionate as follows so
+ 
+
+ align:start position:0%
+will the proportionate as follows so
+this is
+
+ align:start position:0%
+this is
+ 
+
+ align:start position:0%
+this is
+40% nickel at all
+
+ align:start position:0%
+40% nickel at all
+ 
+
+ align:start position:0%
+40% nickel at all
+liquid all right now we drop the
+
+ align:start position:0%
+liquid all right now we drop the
+ 
+
+ align:start position:0%
+liquid all right now we drop the
+temperature this is 1300 now we drop
+
+ align:start position:0%
+temperature this is 1300 now we drop
+ 
+
+ align:start position:0%
+temperature this is 1300 now we drop
+down to 1250 and we know according to
+
+ align:start position:0%
+down to 1250 and we know according to
+ 
+
+ align:start position:0%
+down to 1250 and we know according to
+the phase diagram we're going to end up
+
+ align:start position:0%
+the phase diagram we're going to end up
+ 
+
+ align:start position:0%
+the phase diagram we're going to end up
+with a liquid and a solid and
+
+ align:start position:0%
+with a liquid and a solid and
+ 
+
+ align:start position:0%
+with a liquid and a solid and
+furthermore from the tie line the tie
+
+ align:start position:0%
+furthermore from the tie line the tie
+ 
+
+ align:start position:0%
+furthermore from the tie line the tie
+line tells us that the solid is going to
+
+ align:start position:0%
+line tells us that the solid is going to
+ 
+
+ align:start position:0%
+line tells us that the solid is going to
+be
+
+ align:start position:0%
+be
+ 
+
+ align:start position:0%
+be
+45% nickel and the liquid is going to be
+
+ align:start position:0%
+45% nickel and the liquid is going to be
+ 
+
+ align:start position:0%
+45% nickel and the liquid is going to be
+32% nickel the question is what are the
+
+ align:start position:0%
+32% nickel the question is what are the
+ 
+
+ align:start position:0%
+32% nickel the question is what are the
+relative values and it just it's shown
+
+ align:start position:0%
+relative values and it just it's shown
+ 
+
+ align:start position:0%
+relative values and it just it's shown
+right up there on the on the uh
+
+ align:start position:0%
+right up there on the on the uh
+ 
+
+ align:start position:0%
+right up there on the on the uh
+transparency that the percent of the
+
+ align:start position:0%
+transparency that the percent of the
+ 
+
+ align:start position:0%
+transparency that the percent of the
+liquid is equal to the in this case the
+
+ align:start position:0%
+liquid is equal to the in this case the
+ 
+
+ align:start position:0%
+liquid is equal to the in this case the
+N member 45 minus the individual amount
+
+ align:start position:0%
+N member 45 minus the individual amount
+ 
+
+ align:start position:0%
+N member 45 minus the individual amount
+at the at the concentration of the bulk
+
+ align:start position:0%
+at the at the concentration of the bulk
+ 
+
+ align:start position:0%
+at the at the concentration of the bulk
+minus the divided by the N members of
+
+ align:start position:0%
+minus the divided by the N members of
+ 
+
+ align:start position:0%
+minus the divided by the N members of
+the tie line we'll multiply that by 100%
+
+ align:start position:0%
+the tie line we'll multiply that by 100%
+ 
+
+ align:start position:0%
+the tie line we'll multiply that by 100%
+And that gives us a value of
+
+ align:start position:0%
+And that gives us a value of
+ 
+
+ align:start position:0%
+And that gives us a value of
+38% present as liquid and why is it
+
+ align:start position:0%
+38% present as liquid and why is it
+ 
+
+ align:start position:0%
+38% present as liquid and why is it
+called the lever rule because if you
+
+ align:start position:0%
+called the lever rule because if you
+ 
+
+ align:start position:0%
+called the lever rule because if you
+look at the tie line here's where we are
+
+ align:start position:0%
+look at the tie line here's where we are
+ 
+
+ align:start position:0%
+look at the tie line here's where we are
+we're at this value which is shown in
+
+ align:start position:0%
+we're at this value which is shown in
+ 
+
+ align:start position:0%
+we're at this value which is shown in
+the phase diagram as uh Z this is our
+
+ align:start position:0%
+the phase diagram as uh Z this is our
+ 
+
+ align:start position:0%
+the phase diagram as uh Z this is our
+40% and the amount of the liquid is X
+
+ align:start position:0%
+40% and the amount of the liquid is X
+ 
+
+ align:start position:0%
+40% and the amount of the liquid is X
+and the amount of the solid is y and so
+
+ align:start position:0%
+and the amount of the solid is y and so
+ 
+
+ align:start position:0%
+and the amount of the solid is y and so
+when I'm asking how much liquid is
+
+ align:start position:0%
+when I'm asking how much liquid is
+ 
+
+ align:start position:0%
+when I'm asking how much liquid is
+present I choose the amount opposite as
+
+ align:start position:0%
+present I choose the amount opposite as
+ 
+
+ align:start position:0%
+present I choose the amount opposite as
+you do on on a on a seesaw or a teeter
+
+ align:start position:0%
+you do on on a on a seesaw or a teeter
+ 
+
+ align:start position:0%
+you do on on a on a seesaw or a teeter
+totter in other words to calculate what
+
+ align:start position:0%
+totter in other words to calculate what
+ 
+
+ align:start position:0%
+totter in other words to calculate what
+the force is here you take the amount
+
+ align:start position:0%
+the force is here you take the amount
+ 
+
+ align:start position:0%
+the force is here you take the amount
+between the fulcrum and the opposite
+
+ align:start position:0%
+between the fulcrum and the opposite
+ 
+
+ align:start position:0%
+between the fulcrum and the opposite
+side divided by the total length so this
+
+ align:start position:0%
+side divided by the total length so this
+ 
+
+ align:start position:0%
+side divided by the total length so this
+is really this is
+
+ align:start position:0%
+is really this is
+ 
+
+ align:start position:0%
+is really this is
+uh YZ over XY gives us liquid and then
+
+ align:start position:0%
+uh YZ over XY gives us liquid and then
+ 
+
+ align:start position:0%
+uh YZ over XY gives us liquid and then
+the complement gives us the amount for
+
+ align:start position:0%
+the complement gives us the amount for
+ 
+
+ align:start position:0%
+the complement gives us the amount for
+solid so you see that worked out for you
+
+ align:start position:0%
+solid so you see that worked out for you
+ 
+
+ align:start position:0%
+solid so you see that worked out for you
+at
+
+ align:start position:0%
+at
+ 
+
+ align:start position:0%
+at
+the on the transparency and this works
+
+ align:start position:0%
+the on the transparency and this works
+ 
+
+ align:start position:0%
+the on the transparency and this works
+for any two-phase regime so whenever
+
+ align:start position:0%
+for any two-phase regime so whenever
+ 
+
+ align:start position:0%
+for any two-phase regime so whenever
+something drops into a two-phase regime
+
+ align:start position:0%
+something drops into a two-phase regime
+ 
+
+ align:start position:0%
+something drops into a two-phase regime
+disproportionation has to occur and the
+
+ align:start position:0%
+disproportionation has to occur and the
+ 
+
+ align:start position:0%
+disproportionation has to occur and the
+lever rule will give you the relative
+
+ align:start position:0%
+lever rule will give you the relative
+ 
+
+ align:start position:0%
+lever rule will give you the relative
+amounts the ti line tells you the
+
+ align:start position:0%
+amounts the ti line tells you the
+ 
+
+ align:start position:0%
+amounts the ti line tells you the
+composition and the lever rule tells you
+
+ align:start position:0%
+composition and the lever rule tells you
+ 
+
+ align:start position:0%
+composition and the lever rule tells you
+the relative amounts two things I want
+
+ align:start position:0%
+the relative amounts two things I want
+ 
+
+ align:start position:0%
+the relative amounts two things I want
+this to be like your you know the that
+
+ align:start position:0%
+this to be like your you know the that
+ 
+
+ align:start position:0%
+this to be like your you know the that
+mansurian candidate you know this is
+
+ align:start position:0%
+mansurian candidate you know this is
+ 
+
+ align:start position:0%
+mansurian candidate you know this is
+your CU if if you from now on if you
+
+ align:start position:0%
+your CU if if you from now on if you
+ 
+
+ align:start position:0%
+your CU if if you from now on if you
+hear two phase you just go lever
+
+ align:start position:0%
+hear two phase you just go lever
+ 
+
+ align:start position:0%
+hear two phase you just go lever
+rule go lever rule lever rule what are
+
+ align:start position:0%
+rule go lever rule lever rule what are
+ 
+
+ align:start position:0%
+rule go lever rule lever rule what are
+the nend members TI line TI line lever
+
+ align:start position:0%
+the nend members TI line TI line lever
+ 
+
+ align:start position:0%
+the nend members TI line TI line lever
+rule TI line lever rule whenever you see
+
+ align:start position:0%
+rule TI line lever rule whenever you see
+ 
+
+ align:start position:0%
+rule TI line lever rule whenever you see
+two-phase
+
+ align:start position:0%
+two-phase
+ 
+
+ align:start position:0%
+two-phase
+regime and it'll keep you out of trouble
+
+ align:start position:0%
+regime and it'll keep you out of trouble
+ 
+
+ align:start position:0%
+regime and it'll keep you out of trouble
+keep you out of trouble I mean many
+
+ align:start position:0%
+keep you out of trouble I mean many
+ 
+
+ align:start position:0%
+keep you out of trouble I mean many
+times I get into trouble and I just
+
+ align:start position:0%
+times I get into trouble and I just
+ 
+
+ align:start position:0%
+times I get into trouble and I just
+think of the lever rule I'm out of
+
+ align:start position:0%
+think of the lever rule I'm out of
+ 
+
+ align:start position:0%
+think of the lever rule I'm out of
+trouble okay
+
+ align:start position:0%
+trouble okay
+ 
+
+ align:start position:0%
+trouble okay
+so now let's look at a second case
+
+ align:start position:0%
+so now let's look at a second case
+ 
+
+ align:start position:0%
+so now let's look at a second case
+second case is type
+
+ align:start position:0%
+second case is type
+ 
+
+ align:start position:0%
+second case is type
+two type two phase diagram type two
+
+ align:start position:0%
+two type two phase diagram type two
+ 
+
+ align:start position:0%
+two type two phase diagram type two
+phase diagram in contrast to complete
+
+ align:start position:0%
+phase diagram in contrast to complete
+ 
+
+ align:start position:0%
+phase diagram in contrast to complete
+solubility type two phas diagram is is
+
+ align:start position:0%
+solubility type two phas diagram is is
+ 
+
+ align:start position:0%
+solubility type two phas diagram is is
+characterized by system that has
+
+ align:start position:0%
+characterized by system that has
+ 
+
+ align:start position:0%
+characterized by system that has
+partial partial or
+
+ align:start position:0%
+partial partial or
+ 
+
+ align:start position:0%
+partial partial or
+limited or limited
+
+ align:start position:0%
+limited or limited
+ 
+
+ align:start position:0%
+limited or limited
+solubility so when you try to mix A and
+
+ align:start position:0%
+solubility so when you try to mix A and
+ 
+
+ align:start position:0%
+solubility so when you try to mix A and
+B they don't mix in all proportions they
+
+ align:start position:0%
+B they don't mix in all proportions they
+ 
+
+ align:start position:0%
+B they don't mix in all proportions they
+only mix up to a certain point so that's
+
+ align:start position:0%
+only mix up to a certain point so that's
+ 
+
+ align:start position:0%
+only mix up to a certain point so that's
+like a solubility limit or a missil
+
+ align:start position:0%
+like a solubility limit or a missil
+ 
+
+ align:start position:0%
+like a solubility limit or a missil
+missil or solubility synonymous this
+
+ align:start position:0%
+missil or solubility synonymous this
+ 
+
+ align:start position:0%
+missil or solubility synonymous this
+leads to a missil Gap a range of
+
+ align:start position:0%
+leads to a missil Gap a range of
+ 
+
+ align:start position:0%
+leads to a missil Gap a range of
+composition over which you can't mix the
+
+ align:start position:0%
+composition over which you can't mix the
+ 
+
+ align:start position:0%
+composition over which you can't mix the
+two of them and form a homogeneous
+
+ align:start position:0%
+two of them and form a homogeneous
+ 
+
+ align:start position:0%
+two of them and form a homogeneous
+solution and in this case there's no
+
+ align:start position:0%
+solution and in this case there's no
+ 
+
+ align:start position:0%
+solution and in this case there's no
+change of
+
+ align:start position:0%
+change of
+ 
+
+ align:start position:0%
+change of
+state no change of state so that's
+
+ align:start position:0%
+state no change of state so that's
+ 
+
+ align:start position:0%
+state no change of state so that's
+either always
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+liquid always liquid or always
+
+ align:start position:0%
+liquid always liquid or always
+ 
+
+ align:start position:0%
+liquid always liquid or always
+solid always
+
+ align:start position:0%
+solid always
+ 
+
+ align:start position:0%
+solid always
+solid so let's look at the phase diagram
+
+ align:start position:0%
+solid so let's look at the phase diagram
+ 
+
+ align:start position:0%
+solid so let's look at the phase diagram
+for one of these type of systems
+
+ align:start position:0%
+for one of these type of systems
+ 
+
+ align:start position:0%
+for one of these type of systems
+a b I'm plotting composition across the
+
+ align:start position:0%
+a b I'm plotting composition across the
+ 
+
+ align:start position:0%
+a b I'm plotting composition across the
+uh abscissa the ordinate is
+
+ align:start position:0%
+uh abscissa the ordinate is
+ 
+
+ align:start position:0%
+uh abscissa the ordinate is
+temperature and this gives us a
+
+ align:start position:0%
+temperature and this gives us a
+ 
+
+ align:start position:0%
+temperature and this gives us a
+synclinal phase diagram a synclinal
+
+ align:start position:0%
+synclinal phase diagram a synclinal
+ 
+
+ align:start position:0%
+synclinal phase diagram a synclinal
+phase diagram so above we have single
+
+ align:start position:0%
+phase diagram so above we have single
+ 
+
+ align:start position:0%
+phase diagram so above we have single
+phase so this is either want to just say
+
+ align:start position:0%
+phase so this is either want to just say
+ 
+
+ align:start position:0%
+phase so this is either want to just say
+single
+
+ align:start position:0%
+single
+ 
+
+ align:start position:0%
+single
+phase and this is dual
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+phase dual phase single phase dual phase
+
+ align:start position:0%
+phase dual phase single phase dual phase
+ 
+
+ align:start position:0%
+phase dual phase single phase dual phase
+so for example this could be a solid
+
+ align:start position:0%
+so for example this could be a solid
+ 
+
+ align:start position:0%
+so for example this could be a solid
+this could be all liquid and then in
+
+ align:start position:0%
+this could be all liquid and then in
+ 
+
+ align:start position:0%
+this could be all liquid and then in
+here we have two
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+liquids or it could be all solid and
+
+ align:start position:0%
+liquids or it could be all solid and
+ 
+
+ align:start position:0%
+liquids or it could be all solid and
+inside here we have two solids when it
+
+ align:start position:0%
+inside here we have two solids when it
+ 
+
+ align:start position:0%
+inside here we have two solids when it
+comes to solid Solutions people use
+
+ align:start position:0%
+comes to solid Solutions people use
+ 
+
+ align:start position:0%
+comes to solid Solutions people use
+Greek letters and call this Alpha and
+
+ align:start position:0%
+Greek letters and call this Alpha and
+ 
+
+ align:start position:0%
+Greek letters and call this Alpha and
+beta so this is the coexistence
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+curve or the solubility limit what's the
+
+ align:start position:0%
+curve or the solubility limit what's the
+ 
+
+ align:start position:0%
+curve or the solubility limit what's the
+coexistence curve the coexistence curve
+
+ align:start position:0%
+coexistence curve the coexistence curve
+ 
+
+ align:start position:0%
+coexistence curve the coexistence curve
+is liquid is an equilibrium with liquid
+
+ align:start position:0%
+is liquid is an equilibrium with liquid
+ 
+
+ align:start position:0%
+is liquid is an equilibrium with liquid
+one and liquid 2 in other words if you
+
+ align:start position:0%
+one and liquid 2 in other words if you
+ 
+
+ align:start position:0%
+one and liquid 2 in other words if you
+drop into this two-phase regime what
+
+ align:start position:0%
+drop into this two-phase regime what
+ 
+
+ align:start position:0%
+drop into this two-phase regime what
+happens as soon as you hear
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+two-phase TI line lever rule the ti line
+
+ align:start position:0%
+two-phase TI line lever rule the ti line
+ 
+
+ align:start position:0%
+two-phase TI line lever rule the ti line
+will give you the concentrations at the
+
+ align:start position:0%
+will give you the concentrations at the
+ 
+
+ align:start position:0%
+will give you the concentrations at the
+end or solid goes to Alpha plus beta
+
+ align:start position:0%
+end or solid goes to Alpha plus beta
+ 
+
+ align:start position:0%
+end or solid goes to Alpha plus beta
+both of these are solid
+
+ align:start position:0%
+both of these are solid
+ 
+
+ align:start position:0%
+both of these are solid
+Solutions let's take a look at at some
+
+ align:start position:0%
+Solutions let's take a look at at some
+ 
+
+ align:start position:0%
+Solutions let's take a look at at some
+of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+these this is gold nickel at low
+
+ align:start position:0%
+these this is gold nickel at low
+ 
+
+ align:start position:0%
+these this is gold nickel at low
+temperatures look what happens at low
+
+ align:start position:0%
+temperatures look what happens at low
+ 
+
+ align:start position:0%
+temperatures look what happens at low
+temperatures gold nickel will actually
+
+ align:start position:0%
+temperatures gold nickel will actually
+ 
+
+ align:start position:0%
+temperatures gold nickel will actually
+phase separate so if you take something
+
+ align:start position:0%
+phase separate so if you take something
+ 
+
+ align:start position:0%
+phase separate so if you take something
+like uh this one here which is 50 we%
+
+ align:start position:0%
+like uh this one here which is 50 we%
+ 
+
+ align:start position:0%
+like uh this one here which is 50 we%
+nickel drop at high temperatures they
+
+ align:start position:0%
+nickel drop at high temperatures they
+ 
+
+ align:start position:0%
+nickel drop at high temperatures they
+mix in all proportions drop into here we
+
+ align:start position:0%
+mix in all proportions drop into here we
+ 
+
+ align:start position:0%
+mix in all proportions drop into here we
+have a slush consisting of liquid and
+
+ align:start position:0%
+have a slush consisting of liquid and
+ 
+
+ align:start position:0%
+have a slush consisting of liquid and
+solid and they have different
+
+ align:start position:0%
+solid and they have different
+ 
+
+ align:start position:0%
+solid and they have different
+compositions given by the Tha line drop
+
+ align:start position:0%
+compositions given by the Tha line drop
+ 
+
+ align:start position:0%
+compositions given by the Tha line drop
+even lower in temperature and all of a
+
+ align:start position:0%
+even lower in temperature and all of a
+ 
+
+ align:start position:0%
+even lower in temperature and all of a
+sudden it's a single- face solid
+
+ align:start position:0%
+sudden it's a single- face solid
+ 
+
+ align:start position:0%
+sudden it's a single- face solid
+solution FCC lattice with golden nickel
+
+ align:start position:0%
+solution FCC lattice with golden nickel
+ 
+
+ align:start position:0%
+solution FCC lattice with golden nickel
+atoms 50/50 well in this case it's
+
+ align:start position:0%
+atoms 50/50 well in this case it's
+ 
+
+ align:start position:0%
+atoms 50/50 well in this case it's
+weight percent so it's not exactly on an
+
+ align:start position:0%
+weight percent so it's not exactly on an
+ 
+
+ align:start position:0%
+weight percent so it's not exactly on an
+atomic basis there it's about 75 and
+
+ align:start position:0%
+atomic basis there it's about 75 and
+ 
+
+ align:start position:0%
+atomic basis there it's about 75 and
+then we drop into lower temperatures and
+
+ align:start position:0%
+then we drop into lower temperatures and
+ 
+
+ align:start position:0%
+then we drop into lower temperatures and
+now they face separate so we end up it's
+
+ align:start position:0%
+now they face separate so we end up it's
+ 
+
+ align:start position:0%
+now they face separate so we end up it's
+for example at 600° let's get down to
+
+ align:start position:0%
+for example at 600° let's get down to
+ 
+
+ align:start position:0%
+for example at 600° let's get down to
+say room temperature this is uh 300° C
+
+ align:start position:0%
+say room temperature this is uh 300° C
+ 
+
+ align:start position:0%
+say room temperature this is uh 300° C
+but the lines are starting to get fairly
+
+ align:start position:0%
+but the lines are starting to get fairly
+ 
+
+ align:start position:0%
+but the lines are starting to get fairly
+steep what you find is that it'll phase
+
+ align:start position:0%
+steep what you find is that it'll phase
+ 
+
+ align:start position:0%
+steep what you find is that it'll phase
+separate so that you'll end up with
+
+ align:start position:0%
+separate so that you'll end up with
+ 
+
+ align:start position:0%
+separate so that you'll end up with
+zones that are nickel rich and zones
+
+ align:start position:0%
+zones that are nickel rich and zones
+ 
+
+ align:start position:0%
+zones that are nickel rich and zones
+that are gold rich and the ti line tells
+
+ align:start position:0%
+that are gold rich and the ti line tells
+ 
+
+ align:start position:0%
+that are gold rich and the ti line tells
+you the concentr the composition I of
+
+ align:start position:0%
+you the concentr the composition I of
+ 
+
+ align:start position:0%
+you the concentr the composition I of
+both of those and members here's one
+
+ align:start position:0%
+both of those and members here's one
+ 
+
+ align:start position:0%
+both of those and members here's one
+hexane
+
+ align:start position:0%
+hexane
+ 
+
+ align:start position:0%
+hexane
+nitrobenzene at high temperatures they
+
+ align:start position:0%
+nitrobenzene at high temperatures they
+ 
+
+ align:start position:0%
+nitrobenzene at high temperatures they
+mix in all proportions you drop the
+
+ align:start position:0%
+mix in all proportions you drop the
+ 
+
+ align:start position:0%
+mix in all proportions you drop the
+temperature and then they phase separate
+
+ align:start position:0%
+temperature and then they phase separate
+ 
+
+ align:start position:0%
+temperature and then they phase separate
+just as oil and water so down at this
+
+ align:start position:0%
+just as oil and water so down at this
+ 
+
+ align:start position:0%
+just as oil and water so down at this
+temperature you will have a hexane Rich
+
+ align:start position:0%
+temperature you will have a hexane Rich
+ 
+
+ align:start position:0%
+temperature you will have a hexane Rich
+phase and a Nitro Benzene Rich phase and
+
+ align:start position:0%
+phase and a Nitro Benzene Rich phase and
+ 
+
+ align:start position:0%
+phase and a Nitro Benzene Rich phase and
+the lower and lower you get in
+
+ align:start position:0%
+the lower and lower you get in
+ 
+
+ align:start position:0%
+the lower and lower you get in
+temperature the greater that separation
+
+ align:start position:0%
+temperature the greater that separation
+ 
+
+ align:start position:0%
+temperature the greater that separation
+think about it at this constant
+
+ align:start position:0%
+think about it at this constant
+ 
+
+ align:start position:0%
+think about it at this constant
+temperature what this is saying is that
+
+ align:start position:0%
+temperature what this is saying is that
+ 
+
+ align:start position:0%
+temperature what this is saying is that
+you can put a certain amount of nitro
+
+ align:start position:0%
+you can put a certain amount of nitro
+ 
+
+ align:start position:0%
+you can put a certain amount of nitro
+Benzene into hexane and that's the
+
+ align:start position:0%
+Benzene into hexane and that's the
+ 
+
+ align:start position:0%
+Benzene into hexane and that's the
+solubility limit if you try to put any
+
+ align:start position:0%
+solubility limit if you try to put any
+ 
+
+ align:start position:0%
+solubility limit if you try to put any
+more nitrobenzene into hexane it won't
+
+ align:start position:0%
+more nitrobenzene into hexane it won't
+ 
+
+ align:start position:0%
+more nitrobenzene into hexane it won't
+go in on the other side it says you can
+
+ align:start position:0%
+go in on the other side it says you can
+ 
+
+ align:start position:0%
+go in on the other side it says you can
+put a small amount of hexane and
+
+ align:start position:0%
+put a small amount of hexane and
+ 
+
+ align:start position:0%
+put a small amount of hexane and
+nitrobenzene if you try to put anymore
+
+ align:start position:0%
+nitrobenzene if you try to put anymore
+ 
+
+ align:start position:0%
+nitrobenzene if you try to put anymore
+it won't go in it'll just precipitate
+
+ align:start position:0%
+it won't go in it'll just precipitate
+ 
+
+ align:start position:0%
+it won't go in it'll just precipitate
+out and furthermore this makes sense to
+
+ align:start position:0%
+out and furthermore this makes sense to
+ 
+
+ align:start position:0%
+out and furthermore this makes sense to
+you doesn't it at this temperature I can
+
+ align:start position:0%
+you doesn't it at this temperature I can
+ 
+
+ align:start position:0%
+you doesn't it at this temperature I can
+put say 0.1 units of nitrobenzene if I
+
+ align:start position:0%
+put say 0.1 units of nitrobenzene if I
+ 
+
+ align:start position:0%
+put say 0.1 units of nitrobenzene if I
+raise the temperature the solubility
+
+ align:start position:0%
+raise the temperature the solubility
+ 
+
+ align:start position:0%
+raise the temperature the solubility
+goes up with temperature all of this is
+
+ align:start position:0%
+goes up with temperature all of this is
+ 
+
+ align:start position:0%
+goes up with temperature all of this is
+making sense and finally you get to a
+
+ align:start position:0%
+making sense and finally you get to a
+ 
+
+ align:start position:0%
+making sense and finally you get to a
+temperature here above which they mix in
+
+ align:start position:0%
+temperature here above which they mix in
+ 
+
+ align:start position:0%
+temperature here above which they mix in
+all proportions and this temperature is
+
+ align:start position:0%
+all proportions and this temperature is
+ 
+
+ align:start position:0%
+all proportions and this temperature is
+called the
+
+ align:start position:0%
+called the
+ 
+
+ align:start position:0%
+called the
+consolute consolute temperature above
+
+ align:start position:0%
+consolute consolute temperature above
+ 
+
+ align:start position:0%
+consolute consolute temperature above
+the consolute temperature even a system
+
+ align:start position:0%
+the consolute temperature even a system
+ 
+
+ align:start position:0%
+the consolute temperature even a system
+that has a propensity for limited
+
+ align:start position:0%
+that has a propensity for limited
+ 
+
+ align:start position:0%
+that has a propensity for limited
+solubility will mix in all proportions
+
+ align:start position:0%
+solubility will mix in all proportions
+ 
+
+ align:start position:0%
+solubility will mix in all proportions
+so you see this in uh different systems
+
+ align:start position:0%
+so you see this in uh different systems
+ 
+
+ align:start position:0%
+so you see this in uh different systems
+here's look this one's a surprise this
+
+ align:start position:0%
+here's look this one's a surprise this
+ 
+
+ align:start position:0%
+here's look this one's a surprise this
+is two Alkali halides sodium chloride
+
+ align:start position:0%
+is two Alkali halides sodium chloride
+ 
+
+ align:start position:0%
+is two Alkali halides sodium chloride
+and potassium chloride you'd expect
+
+ align:start position:0%
+and potassium chloride you'd expect
+ 
+
+ align:start position:0%
+and potassium chloride you'd expect
+those to just trade off with one another
+
+ align:start position:0%
+those to just trade off with one another
+ 
+
+ align:start position:0%
+those to just trade off with one another
+but there's a problem here the sodium
+
+ align:start position:0%
+but there's a problem here the sodium
+ 
+
+ align:start position:0%
+but there's a problem here the sodium
+ion and the potassium ion are different
+
+ align:start position:0%
+ion and the potassium ion are different
+ 
+
+ align:start position:0%
+ion and the potassium ion are different
+enough in atomic Dimension different
+
+ align:start position:0%
+enough in atomic Dimension different
+ 
+
+ align:start position:0%
+enough in atomic Dimension different
+enough in charge density that as you get
+
+ align:start position:0%
+enough in charge density that as you get
+ 
+
+ align:start position:0%
+enough in charge density that as you get
+to low temperatures they phas separate
+
+ align:start position:0%
+to low temperatures they phas separate
+ 
+
+ align:start position:0%
+to low temperatures they phas separate
+they face separate so instead of making
+
+ align:start position:0%
+they face separate so instead of making
+ 
+
+ align:start position:0%
+they face separate so instead of making
+a perfect solid solution at lower
+
+ align:start position:0%
+a perfect solid solution at lower
+ 
+
+ align:start position:0%
+a perfect solid solution at lower
+temperatures the single-phase solid
+
+ align:start position:0%
+temperatures the single-phase solid
+ 
+
+ align:start position:0%
+temperatures the single-phase solid
+solution breaks into a potassium rich
+
+ align:start position:0%
+solution breaks into a potassium rich
+ 
+
+ align:start position:0%
+solution breaks into a potassium rich
+solid solution and a sodium Rich solid
+
+ align:start position:0%
+solid solution and a sodium Rich solid
+ 
+
+ align:start position:0%
+solid solution and a sodium Rich solid
+solution here's from the polymer world
+
+ align:start position:0%
+solution here's from the polymer world
+ 
+
+ align:start position:0%
+solution here's from the polymer world
+this one is polystyrene polybutadiene
+
+ align:start position:0%
+this one is polystyrene polybutadiene
+ 
+
+ align:start position:0%
+this one is polystyrene polybutadiene
+at high temperatures you can mix them
+
+ align:start position:0%
+at high temperatures you can mix them
+ 
+
+ align:start position:0%
+at high temperatures you can mix them
+make a
+
+ align:start position:0%
+make a
+ 
+
+ align:start position:0%
+make a
+co-polymer a co- polymer mix in all
+
+ align:start position:0%
+co-polymer a co- polymer mix in all
+ 
+
+ align:start position:0%
+co-polymer a co- polymer mix in all
+proportions as you drop the temperature
+
+ align:start position:0%
+proportions as you drop the temperature
+ 
+
+ align:start position:0%
+proportions as you drop the temperature
+they will phase separate and you'll end
+
+ align:start position:0%
+they will phase separate and you'll end
+ 
+
+ align:start position:0%
+they will phase separate and you'll end
+up with something that is islands of a
+
+ align:start position:0%
+up with something that is islands of a
+ 
+
+ align:start position:0%
+up with something that is islands of a
+polystyrene Rich phase not pure
+
+ align:start position:0%
+polystyrene Rich phase not pure
+ 
+
+ align:start position:0%
+polystyrene Rich phase not pure
+polystyrene there's a certain amount of
+
+ align:start position:0%
+polystyrene there's a certain amount of
+ 
+
+ align:start position:0%
+polystyrene there's a certain amount of
+polybutene in it and then the other
+
+ align:start position:0%
+polybutene in it and then the other
+ 
+
+ align:start position:0%
+polybutene in it and then the other
+phase will be polyad with a certain
+
+ align:start position:0%
+phase will be polyad with a certain
+ 
+
+ align:start position:0%
+phase will be polyad with a certain
+amount of polystyrene they phase
+
+ align:start position:0%
+amount of polystyrene they phase
+ 
+
+ align:start position:0%
+amount of polystyrene they phase
+separate here's one certain systems
+
+ align:start position:0%
+separate here's one certain systems
+ 
+
+ align:start position:0%
+separate here's one certain systems
+instead of exhibiting a consolute
+
+ align:start position:0%
+instead of exhibiting a consolute
+ 
+
+ align:start position:0%
+instead of exhibiting a consolute
+temperature in this fashion for entropic
+
+ align:start position:0%
+temperature in this fashion for entropic
+ 
+
+ align:start position:0%
+temperature in this fashion for entropic
+reasons the system is flipped upside
+
+ align:start position:0%
+reasons the system is flipped upside
+ 
+
+ align:start position:0%
+reasons the system is flipped upside
+down so this is a lower critical
+
+ align:start position:0%
+down so this is a lower critical
+ 
+
+ align:start position:0%
+down so this is a lower critical
+temperature this is weird because
+
+ align:start position:0%
+temperature this is weird because
+ 
+
+ align:start position:0%
+temperature this is weird because
+normally you think as you raise
+
+ align:start position:0%
+normally you think as you raise
+ 
+
+ align:start position:0%
+normally you think as you raise
+temperature you increase solubility this
+
+ align:start position:0%
+temperature you increase solubility this
+ 
+
+ align:start position:0%
+temperature you increase solubility this
+one case where it does it goes the
+
+ align:start position:0%
+one case where it does it goes the
+ 
+
+ align:start position:0%
+one case where it does it goes the
+inverse so water triethylamine mixes in
+
+ align:start position:0%
+inverse so water triethylamine mixes in
+ 
+
+ align:start position:0%
+inverse so water triethylamine mixes in
+all proportions at low temperature at
+
+ align:start position:0%
+all proportions at low temperature at
+ 
+
+ align:start position:0%
+all proportions at low temperature at
+higher temperatures there's the so
+
+ align:start position:0%
+higher temperatures there's the so
+ 
+
+ align:start position:0%
+higher temperatures there's the so
+instead of being synclinal this is
+
+ align:start position:0%
+instead of being synclinal this is
+ 
+
+ align:start position:0%
+instead of being synclinal this is
+anticlinal It's a U-shaped curve so
+
+ align:start position:0%
+anticlinal It's a U-shaped curve so
+ 
+
+ align:start position:0%
+anticlinal It's a U-shaped curve so
+single phase out here down here they mix
+
+ align:start position:0%
+single phase out here down here they mix
+ 
+
+ align:start position:0%
+single phase out here down here they mix
+in all proportions up here you can put a
+
+ align:start position:0%
+in all proportions up here you can put a
+ 
+
+ align:start position:0%
+in all proportions up here you can put a
+certain amount of triethylamine in and
+
+ align:start position:0%
+certain amount of triethylamine in and
+ 
+
+ align:start position:0%
+certain amount of triethylamine in and
+then it stops then you get the second
+
+ align:start position:0%
+then it stops then you get the second
+ 
+
+ align:start position:0%
+then it stops then you get the second
+phase now here's the weirdest one of all
+
+ align:start position:0%
+phase now here's the weirdest one of all
+ 
+
+ align:start position:0%
+phase now here's the weirdest one of all
+this is nicotine and water it has an
+
+ align:start position:0%
+this is nicotine and water it has an
+ 
+
+ align:start position:0%
+this is nicotine and water it has an
+upper critical uh point and a lower
+
+ align:start position:0%
+upper critical uh point and a lower
+ 
+
+ align:start position:0%
+upper critical uh point and a lower
+critical point so at low temperatures
+
+ align:start position:0%
+critical point so at low temperatures
+ 
+
+ align:start position:0%
+critical point so at low temperatures
+you can mix nicotine and water in all
+
+ align:start position:0%
+you can mix nicotine and water in all
+ 
+
+ align:start position:0%
+you can mix nicotine and water in all
+proportions and at very high
+
+ align:start position:0%
+proportions and at very high
+ 
+
+ align:start position:0%
+proportions and at very high
+temperatures you can mix nicotine and
+
+ align:start position:0%
+temperatures you can mix nicotine and
+ 
+
+ align:start position:0%
+temperatures you can mix nicotine and
+water in all proportions and at
+
+ align:start position:0%
+water in all proportions and at
+ 
+
+ align:start position:0%
+water in all proportions and at
+intermediate temperatures they face
+
+ align:start position:0%
+intermediate temperatures they face
+ 
+
+ align:start position:0%
+intermediate temperatures they face
+separate there's the map that tells you
+
+ align:start position:0%
+separate there's the map that tells you
+ 
+
+ align:start position:0%
+separate there's the map that tells you
+how the system behaves as a function of
+
+ align:start position:0%
+how the system behaves as a function of
+ 
+
+ align:start position:0%
+how the system behaves as a function of
+temperature and composition so in here
+
+ align:start position:0%
+temperature and composition so in here
+ 
+
+ align:start position:0%
+temperature and composition so in here
+you can't get the you can't get a
+
+ align:start position:0%
+you can't get the you can't get a
+ 
+
+ align:start position:0%
+you can't get the you can't get a
+homogeneous solution if you try to make
+
+ align:start position:0%
+homogeneous solution if you try to make
+ 
+
+ align:start position:0%
+homogeneous solution if you try to make
+a 50/50 mix of water and nicotine and
+
+ align:start position:0%
+a 50/50 mix of water and nicotine and
+ 
+
+ align:start position:0%
+a 50/50 mix of water and nicotine and
+you heat that to 100° C it'll phas
+
+ align:start position:0%
+you heat that to 100° C it'll phas
+ 
+
+ align:start position:0%
+you heat that to 100° C it'll phas
+separate you will not even though you'll
+
+ align:start position:0%
+separate you will not even though you'll
+ 
+
+ align:start position:0%
+separate you will not even though you'll
+mix it at room temperature and it'll be
+
+ align:start position:0%
+mix it at room temperature and it'll be
+ 
+
+ align:start position:0%
+mix it at room temperature and it'll be
+homogeneous as you raise the temperature
+
+ align:start position:0%
+homogeneous as you raise the temperature
+ 
+
+ align:start position:0%
+homogeneous as you raise the temperature
+all of a sudden you'll see milkiness
+
+ align:start position:0%
+all of a sudden you'll see milkiness
+ 
+
+ align:start position:0%
+all of a sudden you'll see milkiness
+Globs of one forming in the other so
+
+ align:start position:0%
+Globs of one forming in the other so
+ 
+
+ align:start position:0%
+Globs of one forming in the other so
+what would happen if we were to take 60%
+
+ align:start position:0%
+what would happen if we were to take 60%
+ 
+
+ align:start position:0%
+what would happen if we were to take 60%
+sodium chloride and cool it down to say
+
+ align:start position:0%
+sodium chloride and cool it down to say
+ 
+
+ align:start position:0%
+sodium chloride and cool it down to say
+400 degrees C what happens bingo
+
+ align:start position:0%
+400 degrees C what happens bingo
+ 
+
+ align:start position:0%
+400 degrees C what happens bingo
+TI line P equals 2 so the homogeneous
+
+ align:start position:0%
+TI line P equals 2 so the homogeneous
+ 
+
+ align:start position:0%
+TI line P equals 2 so the homogeneous
+solid solution breaks into an alpha
+
+ align:start position:0%
+solid solution breaks into an alpha
+ 
+
+ align:start position:0%
+solid solution breaks into an alpha
+which is the designation for the
+
+ align:start position:0%
+which is the designation for the
+ 
+
+ align:start position:0%
+which is the designation for the
+potassium chloride Rich solid solution
+
+ align:start position:0%
+potassium chloride Rich solid solution
+ 
+
+ align:start position:0%
+potassium chloride Rich solid solution
+and beta which is the designation for
+
+ align:start position:0%
+and beta which is the designation for
+ 
+
+ align:start position:0%
+and beta which is the designation for
+the sodium chloride Rich solid solution
+
+ align:start position:0%
+the sodium chloride Rich solid solution
+ 
+
+ align:start position:0%
+the sodium chloride Rich solid solution
+and how do we figure out the relative
+
+ align:start position:0%
+and how do we figure out the relative
+ 
+
+ align:start position:0%
+and how do we figure out the relative
+amounts of Alpha and
+
+ align:start position:0%
+amounts of Alpha and
+ 
+
+ align:start position:0%
+amounts of Alpha and
+beta lever rule it's a two-phase regime
+
+ align:start position:0%
+beta lever rule it's a two-phase regime
+ 
+
+ align:start position:0%
+beta lever rule it's a two-phase regime
+lever rule that's it that's
+
+ align:start position:0%
+lever rule that's it that's
+ 
+
+ align:start position:0%
+lever rule that's it that's
+it so now what I want to I do a little
+
+ align:start position:0%
+it so now what I want to I do a little
+ 
+
+ align:start position:0%
+it so now what I want to I do a little
+experiment here show you how this works
+
+ align:start position:0%
+experiment here show you how this works
+ 
+
+ align:start position:0%
+experiment here show you how this works
+so I'm going to work with a simple
+
+ align:start position:0%
+so I'm going to work with a simple
+ 
+
+ align:start position:0%
+so I'm going to work with a simple
+system this is oo and water oo is a
+
+ align:start position:0%
+system this is oo and water oo is a
+ 
+
+ align:start position:0%
+system this is oo and water oo is a
+drink it's a lure from the absent family
+
+ align:start position:0%
+drink it's a lure from the absent family
+ 
+
+ align:start position:0%
+drink it's a lure from the absent family
+and the wormwood is the chief flavoring
+
+ align:start position:0%
+and the wormwood is the chief flavoring
+ 
+
+ align:start position:0%
+and the wormwood is the chief flavoring
+agent it contains licorice hop fennel
+
+ align:start position:0%
+agent it contains licorice hop fennel
+ 
+
+ align:start position:0%
+agent it contains licorice hop fennel
+Angelica root an AED so the thing is
+
+ align:start position:0%
+Angelica root an AED so the thing is
+ 
+
+ align:start position:0%
+Angelica root an AED so the thing is
+it's got a lot of oil in it it's very
+
+ align:start position:0%
+it's got a lot of oil in it it's very
+ 
+
+ align:start position:0%
+it's got a lot of oil in it it's very
+oily it's clear and colorless but it's
+
+ align:start position:0%
+oily it's clear and colorless but it's
+ 
+
+ align:start position:0%
+oily it's clear and colorless but it's
+very
+
+ align:start position:0%
+very
+ 
+
+ align:start position:0%
+very
+oily and then water of course you know
+
+ align:start position:0%
+oily and then water of course you know
+ 
+
+ align:start position:0%
+oily and then water of course you know
+what water is so let's have a look Tom
+
+ align:start position:0%
+what water is so let's have a look Tom
+ 
+
+ align:start position:0%
+what water is so let's have a look Tom
+can we cut to the document camera
+
+ align:start position:0%
+can we cut to the document camera
+ 
+
+ align:start position:0%
+can we cut to the document camera
+here so what I'm going to do what I'm
+
+ align:start position:0%
+here so what I'm going to do what I'm
+ 
+
+ align:start position:0%
+here so what I'm going to do what I'm
+I'm going to do is I'm going
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+to here's
+
+ align:start position:0%
+to here's
+ 
+
+ align:start position:0%
+to here's
+water and here's uzo and these are at
+
+ align:start position:0%
+water and here's uzo and these are at
+ 
+
+ align:start position:0%
+water and here's uzo and these are at
+room temperature and I'm assuming the
+
+ align:start position:0%
+room temperature and I'm assuming the
+ 
+
+ align:start position:0%
+room temperature and I'm assuming the
+phase diagram looks like this I can put
+
+ align:start position:0%
+phase diagram looks like this I can put
+ 
+
+ align:start position:0%
+phase diagram looks like this I can put
+a little bit of uzo into water and I can
+
+ align:start position:0%
+a little bit of uzo into water and I can
+ 
+
+ align:start position:0%
+a little bit of uzo into water and I can
+put a little bit of water into oo but if
+
+ align:start position:0%
+put a little bit of water into oo but if
+ 
+
+ align:start position:0%
+put a little bit of water into oo but if
+I exceed these solubility limits in here
+
+ align:start position:0%
+I exceed these solubility limits in here
+ 
+
+ align:start position:0%
+I exceed these solubility limits in here
+this is milky because it's two phase
+
+ align:start position:0%
+this is milky because it's two phase
+ 
+
+ align:start position:0%
+this is milky because it's two phase
+this is milky and this is clear why
+
+ align:start position:0%
+this is milky and this is clear why
+ 
+
+ align:start position:0%
+this is milky and this is clear why
+because this is single phase
+
+ align:start position:0%
+because this is single phase
+ 
+
+ align:start position:0%
+because this is single phase
+and this is p equal 2 so we're going to
+
+ align:start position:0%
+and this is p equal 2 so we're going to
+ 
+
+ align:start position:0%
+and this is p equal 2 so we're going to
+do an experiment here so what I'm going
+
+ align:start position:0%
+do an experiment here so what I'm going
+ 
+
+ align:start position:0%
+do an experiment here so what I'm going
+to do is I'm going to put just this is
+
+ align:start position:0%
+to do is I'm going to put just this is
+ 
+
+ align:start position:0%
+to do is I'm going to put just this is
+just pure water you know what pure water
+
+ align:start position:0%
+just pure water you know what pure water
+ 
+
+ align:start position:0%
+just pure water you know what pure water
+looks like so that's pure water
+
+ align:start position:0%
+looks like so that's pure water
+ 
+
+ align:start position:0%
+looks like so that's pure water
+distilled water and here's some
+
+ align:start position:0%
+distilled water and here's some
+ 
+
+ align:start position:0%
+distilled water and here's some
+oo and this is clear and colorless as
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+well clear and colorless okay so now
+
+ align:start position:0%
+well clear and colorless okay so now
+ 
+
+ align:start position:0%
+well clear and colorless okay so now
+what I'm going to do is I'm going to
+
+ align:start position:0%
+what I'm going to do is I'm going to
+ 
+
+ align:start position:0%
+what I'm going to do is I'm going to
+pour uh water
+
+ align:start position:0%
+pour uh water
+ 
+
+ align:start position:0%
+pour uh water
+into the oo
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+see if I pour a little bit in I can stir
+
+ align:start position:0%
+see if I pour a little bit in I can stir
+ 
+
+ align:start position:0%
+see if I pour a little bit in I can stir
+this and it will dissolve but if I pour
+
+ align:start position:0%
+this and it will dissolve but if I pour
+ 
+
+ align:start position:0%
+this and it will dissolve but if I pour
+so what I'm doing here is I'm pouring
+
+ align:start position:0%
+so what I'm doing here is I'm pouring
+ 
+
+ align:start position:0%
+so what I'm doing here is I'm pouring
+water into uzo and I'm coming across if
+
+ align:start position:0%
+water into uzo and I'm coming across if
+ 
+
+ align:start position:0%
+water into uzo and I'm coming across if
+I pour too much water in I'm going to
+
+ align:start position:0%
+I pour too much water in I'm going to
+ 
+
+ align:start position:0%
+I pour too much water in I'm going to
+hit this myability Gap and this will
+
+ align:start position:0%
+hit this myability Gap and this will
+ 
+
+ align:start position:0%
+hit this myability Gap and this will
+precipitate out and when it precipitates
+
+ align:start position:0%
+precipitate out and when it precipitates
+ 
+
+ align:start position:0%
+precipitate out and when it precipitates
+out it's got a different index it's
+
+ align:start position:0%
+out it's got a different index it's
+ 
+
+ align:start position:0%
+out it's got a different index it's
+going to look milky in fact I think I've
+
+ align:start position:0%
+going to look milky in fact I think I've
+ 
+
+ align:start position:0%
+going to look milky in fact I think I've
+already hit there look at
+
+ align:start position:0%
+already hit there look at
+ 
+
+ align:start position:0%
+already hit there look at
+this all right so I've crossed the Miss
+
+ align:start position:0%
+this all right so I've crossed the Miss
+ 
+
+ align:start position:0%
+this all right so I've crossed the Miss
+ability
+
+ align:start position:0%
+ability
+ 
+
+ align:start position:0%
+ability
+Gap now if if my hunch is correct I
+
+ align:start position:0%
+Gap now if if my hunch is correct I
+ 
+
+ align:start position:0%
+Gap now if if my hunch is correct I
+should be able to keep adding water and
+
+ align:start position:0%
+should be able to keep adding water and
+ 
+
+ align:start position:0%
+should be able to keep adding water and
+eventually emerge on this side so let's
+
+ align:start position:0%
+eventually emerge on this side so let's
+ 
+
+ align:start position:0%
+eventually emerge on this side so let's
+see what
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+happens so we'll dilute it so I'm going
+
+ align:start position:0%
+happens so we'll dilute it so I'm going
+ 
+
+ align:start position:0%
+happens so we'll dilute it so I'm going
+to pour this down to
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+almost tiny fraction now we'll pour in
+
+ align:start position:0%
+almost tiny fraction now we'll pour in
+ 
+
+ align:start position:0%
+almost tiny fraction now we'll pour in
+more there
+
+ align:start position:0%
+more there
+ 
+
+ align:start position:0%
+more there
+so I've crossed the Miss ability Gap
+
+ align:start position:0%
+so I've crossed the Miss ability Gap
+ 
+
+ align:start position:0%
+so I've crossed the Miss ability Gap
+right I can do it the other way let's
+
+ align:start position:0%
+right I can do it the other way let's
+ 
+
+ align:start position:0%
+right I can do it the other way let's
+start with uh water we can go across oh
+
+ align:start position:0%
+start with uh water we can go across oh
+ 
+
+ align:start position:0%
+start with uh water we can go across oh
+we can do the other it doesn't matter
+
+ align:start position:0%
+we can do the other it doesn't matter
+ 
+
+ align:start position:0%
+we can do the other it doesn't matter
+okay so now what's the what's the
+
+ align:start position:0%
+okay so now what's the what's the
+ 
+
+ align:start position:0%
+okay so now what's the what's the
+difference between this and absent absen
+
+ align:start position:0%
+difference between this and absent absen
+ 
+
+ align:start position:0%
+difference between this and absent absen
+is similar but it's
+
+ align:start position:0%
+is similar but it's
+ 
+
+ align:start position:0%
+is similar but it's
+uh it's got uh a little more color to
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+it AB santh is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+green and this the same kind of a
+
+ align:start position:0%
+green and this the same kind of a
+ 
+
+ align:start position:0%
+green and this the same kind of a
+and so when you add water to Aban you're
+
+ align:start position:0%
+and so when you add water to Aban you're
+ 
+
+ align:start position:0%
+and so when you add water to Aban you're
+supposed to add it five parts water and
+
+ align:start position:0%
+supposed to add it five parts water and
+ 
+
+ align:start position:0%
+supposed to add it five parts water and
+one
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+part cuz we're going to make the Louch
+
+ align:start position:0%
+part cuz we're going to make the Louch
+ 
+
+ align:start position:0%
+part cuz we're going to make the Louch
+which is the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Milky okay this is the way Aban would be
+
+ align:start position:0%
+Milky okay this is the way Aban would be
+ 
+
+ align:start position:0%
+Milky okay this is the way Aban would be
+drunk uh let's see pour this into here
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so you can see how milky this is now
+
+ align:start position:0%
+so you can see how milky this is now
+ 
+
+ align:start position:0%
+so you can see how milky this is now
+when tus lat Trek drank he called he
+
+ align:start position:0%
+when tus lat Trek drank he called he
+ 
+
+ align:start position:0%
+when tus lat Trek drank he called he
+made a drink called the earthquake what
+
+ align:start position:0%
+made a drink called the earthquake what
+ 
+
+ align:start position:0%
+made a drink called the earthquake what
+he did with the earthquake is he added
+
+ align:start position:0%
+he did with the earthquake is he added
+ 
+
+ align:start position:0%
+he did with the earthquake is he added
+cognac he added cognac to the absen
+
+ align:start position:0%
+cognac he added cognac to the absen
+ 
+
+ align:start position:0%
+cognac he added cognac to the absen
+Louch all right so what are we going to
+
+ align:start position:0%
+Louch all right so what are we going to
+ 
+
+ align:start position:0%
+Louch all right so what are we going to
+do here what's the chemistry the
+
+ align:start position:0%
+do here what's the chemistry the
+ 
+
+ align:start position:0%
+do here what's the chemistry the
+chemistry is the following I've got oil
+
+ align:start position:0%
+chemistry is the following I've got oil
+ 
+
+ align:start position:0%
+chemistry is the following I've got oil
+droplets here in water okay oil and then
+
+ align:start position:0%
+droplets here in water okay oil and then
+ 
+
+ align:start position:0%
+droplets here in water okay oil and then
+over here is
+
+ align:start position:0%
+over here is
+ 
+
+ align:start position:0%
+over here is
+water what I'm going to do is I'm going
+
+ align:start position:0%
+water what I'm going to do is I'm going
+ 
+
+ align:start position:0%
+water what I'm going to do is I'm going
+to put ethyl alcohol ch3
+
+ align:start position:0%
+to put ethyl alcohol ch3
+ 
+
+ align:start position:0%
+to put ethyl alcohol ch3
+ch2 and what does the O do the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+O makes a hydrogen
+
+ align:start position:0%
+O makes a hydrogen
+ 
+
+ align:start position:0%
+O makes a hydrogen
+bond so I've got a hydrophilic
+
+ align:start position:0%
+bond so I've got a hydrophilic
+ 
+
+ align:start position:0%
+bond so I've got a hydrophilic
+head got a hydrophilic
+
+ align:start position:0%
+head got a hydrophilic
+ 
+
+ align:start position:0%
+head got a hydrophilic
+head right ethyl alcohol is amphipathic
+
+ align:start position:0%
+head right ethyl alcohol is amphipathic
+ 
+
+ align:start position:0%
+head right ethyl alcohol is amphipathic
+and this is a hydrophobic
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+tail hydrophobic tail so the hydrophobic
+
+ align:start position:0%
+tail hydrophobic tail so the hydrophobic
+ 
+
+ align:start position:0%
+tail hydrophobic tail so the hydrophobic
+tail can stack the oily phase of the
+
+ align:start position:0%
+tail can stack the oily phase of the
+ 
+
+ align:start position:0%
+tail can stack the oily phase of the
+luch this is what you do in cooking you
+
+ align:start position:0%
+luch this is what you do in cooking you
+ 
+
+ align:start position:0%
+luch this is what you do in cooking you
+see how many recipes will ask you to add
+
+ align:start position:0%
+see how many recipes will ask you to add
+ 
+
+ align:start position:0%
+see how many recipes will ask you to add
+a little bit of alcohol and then
+
+ align:start position:0%
+a little bit of alcohol and then
+ 
+
+ align:start position:0%
+a little bit of alcohol and then
+subsequently ask you to to heat it and
+
+ align:start position:0%
+subsequently ask you to to heat it and
+ 
+
+ align:start position:0%
+subsequently ask you to to heat it and
+you say well wait a minute alcohol's
+
+ align:start position:0%
+you say well wait a minute alcohol's
+ 
+
+ align:start position:0%
+you say well wait a minute alcohol's
+going to evaporate what's going on
+
+ align:start position:0%
+going to evaporate what's going on
+ 
+
+ align:start position:0%
+going to evaporate what's going on
+whenever they're asking for alcohol
+
+ align:start position:0%
+whenever they're asking for alcohol
+ 
+
+ align:start position:0%
+whenever they're asking for alcohol
+chances are you're adding something
+
+ align:start position:0%
+chances are you're adding something
+ 
+
+ align:start position:0%
+chances are you're adding something
+fatty to an
+
+ align:start position:0%
+fatty to an
+ 
+
+ align:start position:0%
+fatty to an
+acous uh solution and it doesn't want to
+
+ align:start position:0%
+acous uh solution and it doesn't want to
+ 
+
+ align:start position:0%
+acous uh solution and it doesn't want to
+mix as soon as you add the alcohol co-
+
+ align:start position:0%
+mix as soon as you add the alcohol co-
+ 
+
+ align:start position:0%
+mix as soon as you add the alcohol co-
+solvates alcohol is magical for this a
+
+ align:start position:0%
+solvates alcohol is magical for this a
+ 
+
+ align:start position:0%
+solvates alcohol is magical for this a
+amphipathic character so let's make the
+
+ align:start position:0%
+amphipathic character so let's make the
+ 
+
+ align:start position:0%
+amphipathic character so let's make the
+earthquake the earthquake is with this
+
+ align:start position:0%
+earthquake the earthquake is with this
+ 
+
+ align:start position:0%
+earthquake the earthquake is with this
+we're going to add a little bit of
+
+ align:start position:0%
+we're going to add a little bit of
+ 
+
+ align:start position:0%
+we're going to add a little bit of
+this there it's clear it's it's a it's a
+
+ align:start position:0%
+this there it's clear it's it's a it's a
+ 
+
+ align:start position:0%
+this there it's clear it's it's a it's a
+beautiful green uh green gold color but
+
+ align:start position:0%
+beautiful green uh green gold color but
+ 
+
+ align:start position:0%
+beautiful green uh green gold color but
+it's clear because what's happened now
+
+ align:start position:0%
+it's clear because what's happened now
+ 
+
+ align:start position:0%
+it's clear because what's happened now
+I've put in a third component now I've
+
+ align:start position:0%
+I've put in a third component now I've
+ 
+
+ align:start position:0%
+I've put in a third component now I've
+got water oo alcohol and as I add
+
+ align:start position:0%
+got water oo alcohol and as I add
+ 
+
+ align:start position:0%
+got water oo alcohol and as I add
+alcohol I narrow the Mis ability
+
+ align:start position:0%
+alcohol I narrow the Mis ability
+ 
+
+ align:start position:0%
+alcohol I narrow the Mis ability
+Gap Miss ability Gap Narrows as a result
+
+ align:start position:0%
+Gap Miss ability Gap Narrows as a result
+ 
+
+ align:start position:0%
+Gap Miss ability Gap Narrows as a result
+of that it's
+
+ align:start position:0%
+of that it's
+ 
+
+ align:start position:0%
+of that it's
+fantastic okay Tomy we go back to the uh
+
+ align:start position:0%
+fantastic okay Tomy we go back to the uh
+ 
+
+ align:start position:0%
+fantastic okay Tomy we go back to the uh
+computer graphic please
+
+ align:start position:0%
+computer graphic please
+ 
+
+ align:start position:0%
+computer graphic please
+so this is where we were we were along
+
+ align:start position:0%
+so this is where we were we were along
+ 
+
+ align:start position:0%
+so this is where we were we were along
+This Ti line and I figured the Louch is
+
+ align:start position:0%
+This Ti line and I figured the Louch is
+ 
+
+ align:start position:0%
+This Ti line and I figured the Louch is
+here it's five parts water one part um
+
+ align:start position:0%
+here it's five parts water one part um
+ 
+
+ align:start position:0%
+here it's five parts water one part um
+absen and then away we go this is uh
+
+ align:start position:0%
+absen and then away we go this is uh
+ 
+
+ align:start position:0%
+absen and then away we go this is uh
+this is the late uh 1800s why did absen
+
+ align:start position:0%
+this is the late uh 1800s why did absen
+ 
+
+ align:start position:0%
+this is the late uh 1800s why did absen
+take over in in France because there was
+
+ align:start position:0%
+take over in in France because there was
+ 
+
+ align:start position:0%
+take over in in France because there was
+a a blight that wiped out The Vineyards
+
+ align:start position:0%
+a a blight that wiped out The Vineyards
+ 
+
+ align:start position:0%
+a a blight that wiped out The Vineyards
+and so the price of wine shot up and
+
+ align:start position:0%
+and so the price of wine shot up and
+ 
+
+ align:start position:0%
+and so the price of wine shot up and
+people started turning to absent so you
+
+ align:start position:0%
+people started turning to absent so you
+ 
+
+ align:start position:0%
+people started turning to absent so you
+hear he's making the loose he's pouring
+
+ align:start position:0%
+hear he's making the loose he's pouring
+ 
+
+ align:start position:0%
+hear he's making the loose he's pouring
+water through a SL oted spoon on which
+
+ align:start position:0%
+water through a SL oted spoon on which
+ 
+
+ align:start position:0%
+water through a SL oted spoon on which
+there's a sugar cube and here's a woman
+
+ align:start position:0%
+there's a sugar cube and here's a woman
+ 
+
+ align:start position:0%
+there's a sugar cube and here's a woman
+looking at him saying wow is he ever
+
+ align:start position:0%
+looking at him saying wow is he ever
+ 
+
+ align:start position:0%
+looking at him saying wow is he ever
+cool what a
+
+ align:start position:0%
+cool what a
+ 
+
+ align:start position:0%
+cool what a
+guy hey it's the 1800s all right this is
+
+ align:start position:0%
+guy hey it's the 1800s all right this is
+ 
+
+ align:start position:0%
+guy hey it's the 1800s all right this is
+object of art this is Van
+
+ align:start position:0%
+object of art this is Van
+ 
+
+ align:start position:0%
+object of art this is Van
+go this is Picasso this is the absen
+
+ align:start position:0%
+go this is Picasso this is the absen
+ 
+
+ align:start position:0%
+go this is Picasso this is the absen
+Drinker this is a Picasso after he I
+
+ align:start position:0%
+Drinker this is a Picasso after he I
+ 
+
+ align:start position:0%
+Drinker this is a Picasso after he I
+guess he'd had a lot of Aban this
+
+ align:start position:0%
+guess he'd had a lot of Aban this
+ 
+
+ align:start position:0%
+guess he'd had a lot of Aban this
+is the only thing I can recognize here
+
+ align:start position:0%
+is the only thing I can recognize here
+ 
+
+ align:start position:0%
+is the only thing I can recognize here
+is the slotted spoon with what appears
+
+ align:start position:0%
+is the slotted spoon with what appears
+ 
+
+ align:start position:0%
+is the slotted spoon with what appears
+to be a rather large sugar cube and this
+
+ align:start position:0%
+to be a rather large sugar cube and this
+ 
+
+ align:start position:0%
+to be a rather large sugar cube and this
+is somebody's mind after huge quantities
+
+ align:start position:0%
+is somebody's mind after huge quantities
+ 
+
+ align:start position:0%
+is somebody's mind after huge quantities
+of the thing about it is it had fuon in
+
+ align:start position:0%
+of the thing about it is it had fuon in
+ 
+
+ align:start position:0%
+of the thing about it is it had fuon in
+it which comes from the White Cedar and
+
+ align:start position:0%
+it which comes from the White Cedar and
+ 
+
+ align:start position:0%
+it which comes from the White Cedar and
+what this does is it um antagonizes The
+
+ align:start position:0%
+what this does is it um antagonizes The
+ 
+
+ align:start position:0%
+what this does is it um antagonizes The
+receptors that regulate neuron firing we
+
+ align:start position:0%
+receptors that regulate neuron firing we
+ 
+
+ align:start position:0%
+receptors that regulate neuron firing we
+could think much faster but you know we
+
+ align:start position:0%
+could think much faster but you know we
+ 
+
+ align:start position:0%
+could think much faster but you know we
+we kind of slow ourselves down so it's
+
+ align:start position:0%
+we kind of slow ourselves down so it's
+ 
+
+ align:start position:0%
+we kind of slow ourselves down so it's
+the gamma aminobutyric acid that that
+
+ align:start position:0%
+the gamma aminobutyric acid that that
+ 
+
+ align:start position:0%
+the gamma aminobutyric acid that that
+helps us stay in place and actually
+
+ align:start position:0%
+helps us stay in place and actually
+ 
+
+ align:start position:0%
+helps us stay in place and actually
+epileptics suffer from a lack of
+
+ align:start position:0%
+epileptics suffer from a lack of
+ 
+
+ align:start position:0%
+epileptics suffer from a lack of
+Regulation right but that's a motor
+
+ align:start position:0%
+Regulation right but that's a motor
+ 
+
+ align:start position:0%
+Regulation right but that's a motor
+regulation but in case of you know
+
+ align:start position:0%
+regulation but in case of you know
+ 
+
+ align:start position:0%
+regulation but in case of you know
+mental acuity so this is one of these
+
+ align:start position:0%
+mental acuity so this is one of these
+ 
+
+ align:start position:0%
+mental acuity so this is one of these
+cases where the alcohol tracks with the
+
+ align:start position:0%
+cases where the alcohol tracks with the
+ 
+
+ align:start position:0%
+cases where the alcohol tracks with the
+with the thujone and so instead of
+
+ align:start position:0%
+with the thujone and so instead of
+ 
+
+ align:start position:0%
+with the thujone and so instead of
+making you drunk and and stupid it makes
+
+ align:start position:0%
+making you drunk and and stupid it makes
+ 
+
+ align:start position:0%
+making you drunk and and stupid it makes
+you drunk and very very you know highly
+
+ align:start position:0%
+you drunk and very very you know highly
+ 
+
+ align:start position:0%
+you drunk and very very you know highly
+active and um uh but unfortunately large
+
+ align:start position:0%
+active and um uh but unfortunately large
+ 
+
+ align:start position:0%
+active and um uh but unfortunately large
+quantities of it also had other
+
+ align:start position:0%
+quantities of it also had other
+ 
+
+ align:start position:0%
+quantities of it also had other
+neurological disorders uh if you seen
+
+ align:start position:0%
+neurological disorders uh if you seen
+ 
+
+ align:start position:0%
+neurological disorders uh if you seen
+Mulan Rouge you'll see here this is It's
+
+ align:start position:0%
+Mulan Rouge you'll see here this is It's
+ 
+
+ align:start position:0%
+Mulan Rouge you'll see here this is It's
+All About absen in in that period so
+
+ align:start position:0%
+All About absen in in that period so
+ 
+
+ align:start position:0%
+All About absen in in that period so
+what happened was uh this absen took
+
+ align:start position:0%
+what happened was uh this absen took
+ 
+
+ align:start position:0%
+what happened was uh this absen took
+over I mean people drank huge quantities
+
+ align:start position:0%
+over I mean people drank huge quantities
+ 
+
+ align:start position:0%
+over I mean people drank huge quantities
+of this in place of wine eventually the
+
+ align:start position:0%
+of this in place of wine eventually the
+ 
+
+ align:start position:0%
+of this in place of wine eventually the
+wine uh was restored The Vineyards in
+
+ align:start position:0%
+wine uh was restored The Vineyards in
+ 
+
+ align:start position:0%
+wine uh was restored The Vineyards in
+France were restored by grafting onto
+
+ align:start position:0%
+France were restored by grafting onto
+ 
+
+ align:start position:0%
+France were restored by grafting onto
+American stocks so there are very few
+
+ align:start position:0%
+American stocks so there are very few
+ 
+
+ align:start position:0%
+American stocks so there are very few
+Wines in France that are not produced as
+
+ align:start position:0%
+Wines in France that are not produced as
+ 
+
+ align:start position:0%
+Wines in France that are not produced as
+hybrids on American stock so
+
+ align:start position:0%
+hybrids on American stock so
+ 
+
+ align:start position:0%
+hybrids on American stock so
+occasionally you'll see a bottle of wine
+
+ align:start position:0%
+occasionally you'll see a bottle of wine
+ 
+
+ align:start position:0%
+occasionally you'll see a bottle of wine
+says V Old Vine meaning that that was
+
+ align:start position:0%
+says V Old Vine meaning that that was
+ 
+
+ align:start position:0%
+says V Old Vine meaning that that was
+spared from the felox blight but by and
+
+ align:start position:0%
+spared from the felox blight but by and
+ 
+
+ align:start position:0%
+spared from the felox blight but by and
+large it's on American Vin so French
+
+ align:start position:0%
+large it's on American Vin so French
+ 
+
+ align:start position:0%
+large it's on American Vin so French
+wines are grown on American Roots just
+
+ align:start position:0%
+wines are grown on American Roots just
+ 
+
+ align:start position:0%
+wines are grown on American Roots just
+remember that okay so uh
+
+ align:start position:0%
+remember that okay so uh
+ 
+
+ align:start position:0%
+remember that okay so uh
+the um so now the the wine cooperatives
+
+ align:start position:0%
+the um so now the the wine cooperatives
+ 
+
+ align:start position:0%
+the um so now the the wine cooperatives
+wanted to get people to switch back to
+
+ align:start position:0%
+wanted to get people to switch back to
+ 
+
+ align:start position:0%
+wanted to get people to switch back to
+wine so there was this strange alliance
+
+ align:start position:0%
+wine so there was this strange alliance
+ 
+
+ align:start position:0%
+wine so there was this strange alliance
+between the wine cooperatives and the
+
+ align:start position:0%
+between the wine cooperatives and the
+ 
+
+ align:start position:0%
+between the wine cooperatives and the
+temperance movement to get people to
+
+ align:start position:0%
+temperance movement to get people to
+ 
+
+ align:start position:0%
+temperance movement to get people to
+stop drinking absent and so what
+
+ align:start position:0%
+stop drinking absent and so what
+ 
+
+ align:start position:0%
+stop drinking absent and so what
+happened was there were a number of
+
+ align:start position:0%
+happened was there were a number of
+ 
+
+ align:start position:0%
+happened was there were a number of
+murder trials in which uh somehow it was
+
+ align:start position:0%
+murder trials in which uh somehow it was
+ 
+
+ align:start position:0%
+murder trials in which uh somehow it was
+portrayed that Aban figured prominently
+
+ align:start position:0%
+portrayed that Aban figured prominently
+ 
+
+ align:start position:0%
+portrayed that Aban figured prominently
+and so little by little governments
+
+ align:start position:0%
+and so little by little governments
+ 
+
+ align:start position:0%
+and so little by little governments
+banned it and this is uh uh October 7th
+
+ align:start position:0%
+banned it and this is uh uh October 7th
+ 
+
+ align:start position:0%
+banned it and this is uh uh October 7th
+1910 where ABS santh is being banned in
+
+ align:start position:0%
+1910 where ABS santh is being banned in
+ 
+
+ align:start position:0%
+1910 where ABS santh is being banned in
+Switzerland so here it says gentlemen
+
+ align:start position:0%
+Switzerland so here it says gentlemen
+ 
+
+ align:start position:0%
+Switzerland so here it says gentlemen
+this is the hour and this is the uh uh
+
+ align:start position:0%
+this is the hour and this is the uh uh
+ 
+
+ align:start position:0%
+this is the hour and this is the uh uh
+symbol of absen Aban was known
+
+ align:start position:0%
+symbol of absen Aban was known
+ 
+
+ align:start position:0%
+symbol of absen Aban was known
+affectionately as the green fairy that's
+
+ align:start position:0%
+affectionately as the green fairy that's
+ 
+
+ align:start position:0%
+affectionately as the green fairy that's
+why in in Mulan Rouge you'll see this
+
+ align:start position:0%
+why in in Mulan Rouge you'll see this
+ 
+
+ align:start position:0%
+why in in Mulan Rouge you'll see this
+sort of Tinkerbell type figure uh Nicole
+
+ align:start position:0%
+sort of Tinkerbell type figure uh Nicole
+ 
+
+ align:start position:0%
+sort of Tinkerbell type figure uh Nicole
+Kidman playing this Tinkerbell figure in
+
+ align:start position:0%
+Kidman playing this Tinkerbell figure in
+ 
+
+ align:start position:0%
+Kidman playing this Tinkerbell figure in
+an animation well she's she's the green
+
+ align:start position:0%
+an animation well she's she's the green
+ 
+
+ align:start position:0%
+an animation well she's she's the green
+fairy and she has a wand made of opal
+
+ align:start position:0%
+fairy and she has a wand made of opal
+ 
+
+ align:start position:0%
+fairy and she has a wand made of opal
+because the beverage is opalescent
+
+ align:start position:0%
+because the beverage is opalescent
+ 
+
+ align:start position:0%
+because the beverage is opalescent
+because when when it when it shimmers
+
+ align:start position:0%
+because when when it when it shimmers
+ 
+
+ align:start position:0%
+because when when it when it shimmers
+you have great Radiance and index of
+
+ align:start position:0%
+you have great Radiance and index of
+ 
+
+ align:start position:0%
+you have great Radiance and index of
+refraction that give you that internal
+
+ align:start position:0%
+refraction that give you that internal
+ 
+
+ align:start position:0%
+refraction that give you that internal
+incipient surface so here's the green
+
+ align:start position:0%
+incipient surface so here's the green
+ 
+
+ align:start position:0%
+incipient surface so here's the green
+fairy slain by the temperance movement
+
+ align:start position:0%
+fairy slain by the temperance movement
+ 
+
+ align:start position:0%
+fairy slain by the temperance movement
+and uh and so
+
+ align:start position:0%
+and uh and so
+ 
+
+ align:start position:0%
+and uh and so
+on so uh the last thing I wanted to to
+
+ align:start position:0%
+on so uh the last thing I wanted to to
+ 
+
+ align:start position:0%
+on so uh the last thing I wanted to to
+comment on is how we use the two-phase
+
+ align:start position:0%
+comment on is how we use the two-phase
+ 
+
+ align:start position:0%
+comment on is how we use the two-phase
+regime in
+
+ align:start position:0%
+regime in
+ 
+
+ align:start position:0%
+regime in
+purification so much of what we know
+
+ align:start position:0%
+purification so much of what we know
+ 
+
+ align:start position:0%
+purification so much of what we know
+about uh purification requires that we
+
+ align:start position:0%
+about uh purification requires that we
+ 
+
+ align:start position:0%
+about uh purification requires that we
+go into a two-phase regime because the
+
+ align:start position:0%
+go into a two-phase regime because the
+ 
+
+ align:start position:0%
+go into a two-phase regime because the
+thing that happens in a two-phase regime
+
+ align:start position:0%
+thing that happens in a two-phase regime
+ 
+
+ align:start position:0%
+thing that happens in a two-phase regime
+is two-phase region implies
+
+ align:start position:0%
+is two-phase region implies
+ 
+
+ align:start position:0%
+is two-phase region implies
+compositional
+
+ align:start position:0%
+compositional
+ 
+
+ align:start position:0%
+compositional
+differentiation compositional
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+differentiation so for example let's
+
+ align:start position:0%
+differentiation so for example let's
+ 
+
+ align:start position:0%
+differentiation so for example let's
+look at here's the phase diagram for one
+
+ align:start position:0%
+look at here's the phase diagram for one
+ 
+
+ align:start position:0%
+look at here's the phase diagram for one
+time I'm going to go to uh liquid Vapor
+
+ align:start position:0%
+time I'm going to go to uh liquid Vapor
+ 
+
+ align:start position:0%
+time I'm going to go to uh liquid Vapor
+so this is the liquid Vapor phase
+
+ align:start position:0%
+so this is the liquid Vapor phase
+ 
+
+ align:start position:0%
+so this is the liquid Vapor phase
+diagram of
+
+ align:start position:0%
+diagram of
+ 
+
+ align:start position:0%
+diagram of
+ethyl alcohol and water so we know that
+
+ align:start position:0%
+ethyl alcohol and water so we know that
+ 
+
+ align:start position:0%
+ethyl alcohol and water so we know that
+water boils at 100° C this is normal
+
+ align:start position:0%
+water boils at 100° C this is normal
+ 
+
+ align:start position:0%
+water boils at 100° C this is normal
+boiling point and ethyl alcohol boils at
+
+ align:start position:0%
+boiling point and ethyl alcohol boils at
+ 
+
+ align:start position:0%
+boiling point and ethyl alcohol boils at
+78.5 degrees
+
+ align:start position:0%
+78.5 degrees
+ 
+
+ align:start position:0%
+78.5 degrees
+C and you know they're both polar
+
+ align:start position:0%
+C and you know they're both polar
+ 
+
+ align:start position:0%
+C and you know they're both polar
+liquids ethyl alcohol is a little bit uh
+
+ align:start position:0%
+liquids ethyl alcohol is a little bit uh
+ 
+
+ align:start position:0%
+liquids ethyl alcohol is a little bit uh
+more elongated than uh water so it's
+
+ align:start position:0%
+more elongated than uh water so it's
+ 
+
+ align:start position:0%
+more elongated than uh water so it's
+very nearly an isomorphous phase diagram
+
+ align:start position:0%
+very nearly an isomorphous phase diagram
+ 
+
+ align:start position:0%
+very nearly an isomorphous phase diagram
+there's a tiny little uh dip
+
+ align:start position:0%
+there's a tiny little uh dip
+ 
+
+ align:start position:0%
+there's a tiny little uh dip
+but by and large it's an isomorphous
+
+ align:start position:0%
+but by and large it's an isomorphous
+ 
+
+ align:start position:0%
+but by and large it's an isomorphous
+phase diagram okay so alcohol and water
+
+ align:start position:0%
+phase diagram okay so alcohol and water
+ 
+
+ align:start position:0%
+phase diagram okay so alcohol and water
+missable in all proportions in the vapor
+
+ align:start position:0%
+missable in all proportions in the vapor
+ 
+
+ align:start position:0%
+missable in all proportions in the vapor
+obviously and this is the liquid so this
+
+ align:start position:0%
+obviously and this is the liquid so this
+ 
+
+ align:start position:0%
+obviously and this is the liquid so this
+is the two-phase Liquid Plus Vapor
+
+ align:start position:0%
+is the two-phase Liquid Plus Vapor
+ 
+
+ align:start position:0%
+is the two-phase Liquid Plus Vapor
+regime so let's say you've got some wine
+
+ align:start position:0%
+regime so let's say you've got some wine
+ 
+
+ align:start position:0%
+regime so let's say you've got some wine
+and it's 10% alcohol so what do you do
+
+ align:start position:0%
+and it's 10% alcohol so what do you do
+ 
+
+ align:start position:0%
+and it's 10% alcohol so what do you do
+you heat the wine up to this two-phase
+
+ align:start position:0%
+you heat the wine up to this two-phase
+ 
+
+ align:start position:0%
+you heat the wine up to this two-phase
+regime and now in the two-phase regime
+
+ align:start position:0%
+regime and now in the two-phase regime
+ 
+
+ align:start position:0%
+regime and now in the two-phase regime
+TI line so what do you note you note
+
+ align:start position:0%
+TI line so what do you note you note
+ 
+
+ align:start position:0%
+TI line so what do you note you note
+that the alcohol content of the vapor is
+
+ align:start position:0%
+that the alcohol content of the vapor is
+ 
+
+ align:start position:0%
+that the alcohol content of the vapor is
+much higher than the alcohol content of
+
+ align:start position:0%
+much higher than the alcohol content of
+ 
+
+ align:start position:0%
+much higher than the alcohol content of
+the liquid so what we can do is we can
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+condense condense The
+
+ align:start position:0%
+condense condense The
+ 
+
+ align:start position:0%
+condense condense The
+Vapor which puts us down here and now
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+reheat condense reheat condense and by
+
+ align:start position:0%
+reheat condense reheat condense and by
+ 
+
+ align:start position:0%
+reheat condense reheat condense and by
+doing so we can raise the alcohol
+
+ align:start position:0%
+doing so we can raise the alcohol
+ 
+
+ align:start position:0%
+doing so we can raise the alcohol
+content or in some cases this could be
+
+ align:start position:0%
+content or in some cases this could be
+ 
+
+ align:start position:0%
+content or in some cases this could be
+the way you purify for the liquid it
+
+ align:start position:0%
+the way you purify for the liquid it
+ 
+
+ align:start position:0%
+the way you purify for the liquid it
+doesn't matter I mean you either want
+
+ align:start position:0%
+doesn't matter I mean you either want
+ 
+
+ align:start position:0%
+doesn't matter I mean you either want
+the condensate or you want what was uh
+
+ align:start position:0%
+the condensate or you want what was uh
+ 
+
+ align:start position:0%
+the condensate or you want what was uh
+the base from which you took the
+
+ align:start position:0%
+the base from which you took the
+ 
+
+ align:start position:0%
+the base from which you took the
+condensate and and this is used over and
+
+ align:start position:0%
+condensate and and this is used over and
+ 
+
+ align:start position:0%
+condensate and and this is used over and
+over again it's used in the solid state
+
+ align:start position:0%
+over again it's used in the solid state
+ 
+
+ align:start position:0%
+over again it's used in the solid state
+to purify Metals look up here on the on
+
+ align:start position:0%
+to purify Metals look up here on the on
+ 
+
+ align:start position:0%
+to purify Metals look up here on the on
+the uh slide suppose I have a a solution
+
+ align:start position:0%
+the uh slide suppose I have a a solution
+ 
+
+ align:start position:0%
+the uh slide suppose I have a a solution
+that consists of um uh over here say
+
+ align:start position:0%
+that consists of um uh over here say
+ 
+
+ align:start position:0%
+that consists of um uh over here say
+60%
+
+ align:start position:0%
+60%
+ 
+
+ align:start position:0%
+60%
+60% uh nickel it's all liquid drop down
+
+ align:start position:0%
+60% uh nickel it's all liquid drop down
+ 
+
+ align:start position:0%
+60% uh nickel it's all liquid drop down
+into this two-phase regime the solid
+
+ align:start position:0%
+into this two-phase regime the solid
+ 
+
+ align:start position:0%
+into this two-phase regime the solid
+that comes out has very much less gold
+
+ align:start position:0%
+that comes out has very much less gold
+ 
+
+ align:start position:0%
+that comes out has very much less gold
+in it that means that the liquid behind
+
+ align:start position:0%
+in it that means that the liquid behind
+ 
+
+ align:start position:0%
+in it that means that the liquid behind
+is go the last liquid to solidify is
+
+ align:start position:0%
+is go the last liquid to solidify is
+ 
+
+ align:start position:0%
+is go the last liquid to solidify is
+going to have more gold in it than the
+
+ align:start position:0%
+going to have more gold in it than the
+ 
+
+ align:start position:0%
+going to have more gold in it than the
+bulk that I started with so I can keep
+
+ align:start position:0%
+bulk that I started with so I can keep
+ 
+
+ align:start position:0%
+bulk that I started with so I can keep
+taking that fraction by moving into a
+
+ align:start position:0%
+taking that fraction by moving into a
+ 
+
+ align:start position:0%
+taking that fraction by moving into a
+regime where the composition splits and
+
+ align:start position:0%
+regime where the composition splits and
+ 
+
+ align:start position:0%
+regime where the composition splits and
+I either want the the high fraction or
+
+ align:start position:0%
+I either want the the high fraction or
+ 
+
+ align:start position:0%
+I either want the the high fraction or
+the low fraction so this is the
+
+ align:start position:0%
+the low fraction so this is the
+ 
+
+ align:start position:0%
+the low fraction so this is the
+principle by which in fact the computer
+
+ align:start position:0%
+principle by which in fact the computer
+ 
+
+ align:start position:0%
+principle by which in fact the computer
+grade silicon is made we start with
+
+ align:start position:0%
+grade silicon is made we start with
+ 
+
+ align:start position:0%
+grade silicon is made we start with
+beach sand we upgrade to something
+
+ align:start position:0%
+beach sand we upgrade to something
+ 
+
+ align:start position:0%
+beach sand we upgrade to something
+that's got to be about four or 59
+
+ align:start position:0%
+that's got to be about four or 59
+ 
+
+ align:start position:0%
+that's got to be about four or 59
+silicon for single crystal growth how do
+
+ align:start position:0%
+silicon for single crystal growth how do
+ 
+
+ align:start position:0%
+silicon for single crystal growth how do
+we go from something that's about 98%
+
+ align:start position:0%
+we go from something that's about 98%
+ 
+
+ align:start position:0%
+we go from something that's about 98%
+silicon 2% impurities to such a high
+
+ align:start position:0%
+silicon 2% impurities to such a high
+ 
+
+ align:start position:0%
+silicon 2% impurities to such a high
+degree of uh purification by dropping
+
+ align:start position:0%
+degree of uh purification by dropping
+ 
+
+ align:start position:0%
+degree of uh purification by dropping
+repeatedly into the two-phase regime and
+
+ align:start position:0%
+repeatedly into the two-phase regime and
+ 
+
+ align:start position:0%
+repeatedly into the two-phase regime and
+pulling out the P fraction so the the
+
+ align:start position:0%
+pulling out the P fraction so the the
+ 
+
+ align:start position:0%
+pulling out the P fraction so the the
+key here
+
+ align:start position:0%
+key here
+ 
+
+ align:start position:0%
+key here
+is compositional differentiation which
+
+ align:start position:0%
+is compositional differentiation which
+ 
+
+ align:start position:0%
+is compositional differentiation which
+then then allows you to distill so you
+
+ align:start position:0%
+then then allows you to distill so you
+ 
+
+ align:start position:0%
+then then allows you to distill so you
+start with 10% you end up 40% you go
+
+ align:start position:0%
+start with 10% you end up 40% you go
+ 
+
+ align:start position:0%
+start with 10% you end up 40% you go
+from wine you end up with brandy or
+
+ align:start position:0%
+from wine you end up with brandy or
+ 
+
+ align:start position:0%
+from wine you end up with brandy or
+cognac so there it is it's all back to
+
+ align:start position:0%
+cognac so there it is it's all back to
+ 
+
+ align:start position:0%
+cognac so there it is it's all back to
+chemistry chemistry chemistry okay we'll
+
+ align:start position:0%
+chemistry chemistry chemistry okay we'll
+ 
+
+ align:start position:0%
+chemistry chemistry chemistry okay we'll
+see you on Wednesday
\ No newline at end of file
diff --git a/n-NpJQgSLrk.txt b/n-NpJQgSLrk.txt
new file mode 100644
index 0000000000000000000000000000000000000000..582e68d7c259bdefc3bfaeda2783b04f8e6271c8
--- /dev/null
+++ b/n-NpJQgSLrk.txt
@@ -0,0 +1,3407 @@
+The following
+content is provided
+
+under a Creative
+Commons license.
+
+Your support will help MIT
+OpenCourseWare continue
+
+to offer high quality
+educational resources for free.
+
+To make a donation or to
+view additional materials
+
+from hundreds of MIT courses,
+visit MIT OpenCourseWare
+
+at ocw.mit.edu.
+
+PROFESSOR: All right,
+so now today, the topic
+
+we are going to discuss will
+be the ON and OFF channels
+
+in the retina.
+
+I will provide you
+with a brief overview
+
+again of what we have
+covered before about this,
+
+and then will go on and
+look at this in some depth.
+
+Now before I start
+on that, let me just
+
+very briefly mention again
+that the syllabus-- which
+
+all of you I presume have.
+
+If any of you doesn't have
+a syllabus-- any one of you
+
+doesn't have a syllabus,
+we can provide one for you.
+
+What I would like to
+encourage all of your
+
+again is that you do this
+so-called preparatory
+
+reading that appears
+for each session, which
+
+will make it easier
+for you to follow,
+
+and consequently, also
+memorize the basic facts
+
+that we are going
+to be dealing with.
+
+Alright, so therefore let me get
+started with the so-called ON
+
+and OFF channels.
+
+And what I would like
+to do first of all
+
+is to tell you what are the
+major questions we are going
+
+to pose in dealing with
+this very-- to me at least--
+
+very interesting question
+of the ON and OFF channels.
+
+The first prime question
+you're going to ask
+
+is why did the ON and
+OFF channels evolve?
+
+What is their function?
+
+As I've already
+indicated before,
+
+it is rather complicated to
+have created these two channels,
+
+and therefore there
+must have been
+
+a great deal of evolutionary
+pressures to accomplish this.
+
+So that's the prime
+question we're going to ask.
+
+Now more specifically
+we're going
+
+to ask how the
+rods and the cones
+
+are involved in the creation
+of the ON and OFF channels.
+
+And then you're going to
+ask how do the ON and OFF
+
+channels contribute
+to the center
+
+and surround organization
+of retinal ganglion cells,
+
+because this has been a big
+issue among many investigators
+
+over the past 20 or so years.
+
+Then you're going to ask what
+role do these channels play
+
+in giving rise to the
+transforms that we had discussed
+
+the last time in visual cortex.
+
+And lastly we're
+going to ask what
+
+are the consequences of
+blocking the ON channel
+
+on neuronal activity
+and on perception.
+
+And this last
+question then will be
+
+successful in answering
+several of the questions
+
+that we pose as to why we have
+these curious arrangement of ON
+
+and OFF channels in the retina.
+
+All right.
+
+So now let me first of all talk
+about the neuronal responses--
+
+sorry-- of the ON and OFF
+retinal ganglion cells.
+
+First of all, if you
+remember, I told you
+
+that back in the 19th
+century, Keffer Hartline
+
+was the first to record
+from single neurons
+
+by dissecting single
+fires in the optic nerve.
+
+And then what he did-- he
+shone light into the eye.
+
+And then subsequently--
+especially when
+
+I talked the last time
+about Hubel and Wiesel--
+
+what was done is to
+use reflected light.
+
+And most currently we
+using reflected light
+
+by presenting images on
+a computer monitor facing
+
+the animal or the
+human we are studying.
+
+Now when Keffer
+Hartline did this
+
+by shining light
+into the eye, he
+
+noticed that there are some
+says which are called ON cells,
+
+some cells that are OFF
+cells, and some cells which
+
+are both ON and OFF.
+
+Now his idea at that time
+was, using that method,
+
+that ON cells discharge
+when a stimulus came on
+
+in the visual
+field, and OFF cells
+
+signaled their termination.
+
+That was his idea,
+and that's why
+
+I call them ON and OFF cells.
+
+So subsequently, especially when
+reflected the light was used,
+
+a different view had
+emerged as to what
+
+might be the reason for
+having these kinds of cells.
+
+And this was further enhanced
+by the beautiful findings
+
+of Kuffler, when he
+noticed that there
+
+was center-surround
+organization in these cells
+
+at the so-called ON,
+OFF, and ON/OFF cells
+
+responded vigorously
+when a light was
+
+shown into the center,
+but responded less
+
+when the light shown
+into the surround.
+
+So then people began to do
+all kinds of experiments
+
+to try to study this in
+further detail, and one of them
+
+was to use reflected light,
+either by using a projector
+
+or by using a color monitor.
+
+And when they did that-- I'm
+going to show this to you
+
+schematically-- they
+found that if you
+
+had a certain lit background
+like we have here,
+
+you could present the
+stimulus either by virtue
+
+of light increment or by
+virtue of light decrement.
+
+And as I had mentioned
+to you before,
+
+the visual system
+is dramatically
+
+different from the other
+senses that we have in
+
+that we need to be able to see
+dark stimuli in a background,
+
+like letters on a page, as well
+as light incremental stimuli.
+
+And so this idea then,
+if it's selected that way
+
+schematically, looks like this.
+
+An ON cell will fire
+vigorously when a bright spot
+
+appears in the center, and
+will not fire to a dark spot.
+
+If anything, it'll be
+slightly inhibited.
+
+OK?
+
+By contrast, when you look at
+an OFF cell, you get inverse.
+
+It fires vigorously.
+
+If you would, it gets
+excited by a dark spot.
+
+It gets excited by the
+detriment in light illumination.
+
+Now if you did the same thing
+using a much larger spot
+
+of light-- that is shown
+here-- what you see here
+
+is that the
+center-surround antagonism
+
+that we talked
+about fully applies
+
+to this kind of stimulation
+conditions as well.
+
+Use a large spot, bright
+spot, or dark spot
+
+and you see that
+the over responses
+
+of the cells-- the responses
+are much more limited than when
+
+you confine the simulation
+to the center, only
+
+further emphasizing
+this important fact
+
+about center-surround
+antagonism--
+
+this incredible increasing
+complexity of the organization
+
+of neurons that you see
+already in the retina.
+
+OK, so now we are
+going to next look
+
+at the anatomy of the ON
+and OFF ganglion cells.
+
+And as we look at these various
+ways of studying the ON and OFF
+
+channels, we are gradually
+going to understand
+
+what these two systems
+are really for.
+
+So the first thing is to use
+this method that I had also
+
+already described, namely that
+you can record intracellularly
+
+from a cell, understand
+its functional responses,
+
+and then you can inject
+a label, and then
+
+you can process
+that anatomically
+
+to see what it looks like.
+
+So when this was done, a
+very interesting new finding
+
+had emerged, which
+is depicted here.
+
+Here we have the
+photoreceptors--
+
+just the tail end of
+them, if you will-- that
+
+connect to the bipolar cells.
+
+Two bipolar cells are shown.
+
+And then they project into the
+inner plexiform layer, which
+
+we often just refer
+to as IPL, which
+
+is subdivided into
+two parts-- A and B.
+
+And it was shown that
+the majority of cells
+
+arborize in either one or the
+other of these two sublamina
+
+in the inner plexiform layer.
+
+But there were also some
+cells, which is not shown here,
+
+that had arborization
+in both of these lamina,
+
+and that's to
+anticipate actually
+
+the property of those cells,
+which are called the ON/OFF
+
+cells.
+
+Now furthermore, it was found--
+because these cells were
+
+labeled after recording--
+that the cells that arborized
+
+in subliminal A, or the
+inner plexiform layer,
+
+were so-called OFF cells,
+and those that arborized
+
+in subliminal B,
+like this one here,
+
+and this one here, and this
+one here, were ON cells.
+
+OK?
+
+So there was a distinct
+spatial segregation
+
+into the lamina of those
+retinal ganglion cells that
+
+were ON and OFF, and
+also furthermore,
+
+those that were
+ON/OFF because they
+
+had arborization
+in both of them.
+
+So that was the basic finding.
+
+Now when that was
+discovered, people
+
+went on and asked
+the question, what
+
+is the spacial
+arrangement of these cells
+
+on the retinal
+surface, if you will.
+
+And so experiments were done
+in which cells were labeled,
+
+in most cases with
+the Golgi stain,
+
+and then the retina was looked
+at head on with a microscope.
+
+Now the interesting thing
+about a microscope is,
+
+which all of you
+I'm sure know, is
+
+that the higher
+the magnification
+
+that you use, the shorter
+the focus of the microscope.
+
+And in fact, what
+you can do here
+
+is when you look
+at his head I like
+
+that, if you can focus either
+in sublamina A or sublamina B,
+
+and if you do that, since
+we had gotten these results,
+
+you know that whatever focuses
+into sublamina A would be OFF
+
+cells, and whatever
+comes into focus
+
+and the [INAUDIBLE] is
+coming to focus in B,
+
+would be the ON cells.
+
+So then what was
+done by a fellow
+
+called Heinz Wesley is
+he asked a question, what
+
+is the spacial
+arrangement of these two?
+
+Do they respect
+each other, or what?
+
+And so when he did that,
+here is a good example
+
+of what that looks like.
+
+Here we have labeled both the
+ON and OFF cells using the two
+
+depth of [INAUDIBLE],
+and you can
+
+see they're kind
+of helter skelter.
+
+Then if he focus deeper, he
+focus only in the ON cells.
+
+It looks like a they're
+very, very nicely arranged,
+
+and that's also true
+for the OFF cells.
+
+And they respect each other.
+
+Looking at the dendritic
+arbors, there's
+
+a little overlap among
+the dendrites themselves
+
+of the cells.
+
+So what's this then said is that
+the ON cells respect each other
+
+but don't seem to give a
+damn about the OFF cells.
+
+And the reverse applied
+to the OFF cells.
+
+OK?
+
+So as if there were two
+independent entities.
+
+So that was a very
+interesting finding.
+
+And so that was one of
+the initial cues saying
+
+that these ON and OFF
+cells do different things,
+
+and each is a devoted
+entity to what it does.
+
+All right so now to understand
+this even better, let's go back
+
+and take a brief overview
+of the retinal connections
+
+so we can understand how
+these systems came about.
+
+And the first thing to do is
+to talk about the photoreceptor
+
+basics.
+
+And I told you many times--
+by now I'm sure all of you
+
+know that already-- that all
+photoreceptors hyperpolarize
+
+to light.
+
+Then I also told you when
+photoreceptors depolarize--
+
+that's when they release
+their neurotransmitter, which
+
+is glutamate.
+
+And that glutamate acts on
+both the horizontal cells
+
+and the bipolar cells.
+
+And then furthermore, just
+to look in the details--
+
+this you don't need to remember
+exactly in these words-- photon
+
+absorption by the photopigment
+results in isomerization
+
+of the chromophore from
+11-cis to all-trans.
+
+To all-trans this causes
+hyperpolarization, thereby
+
+reducing
+neurotransmitter release.
+
+But what you do need to
+remember is the next step,
+
+which says the same thing
+in much simpler words.
+
+It says that the two
+classes of bipolars,
+
+the ON and the OFF, synaptic
+junction of the OFF bipolars
+
+is sign conserving, and
+that of the ON bipolars
+
+is sign inverting.
+
+And so as I've told you the
+last time, as you hyperpolarize
+
+and depolarize
+the photoreceptor,
+
+an OFF bipolar cell does
+the same thing like this,
+
+but the ON bipolar
+does the opposite, OK?
+
+So you created a
+two-ended system--
+
+a double-ended system, if you
+will-- from a single-ended one
+
+that you have in
+the photoreceptors.
+
+Now, yet another fact that
+is important to remember
+
+is that the ON bipolar
+cell receptor is mGluR6.
+
+That is a specific molecule
+that exists in most animals,
+
+only in the retina, created
+anew in the course of evolution,
+
+indicating what
+considerable pressure there
+
+had to be able to
+have an ON system.
+
+And lastly I should add here
+also that the OFF bipolar
+
+receptors are mGlueR1 and 2
+and they follow, pretty much,
+
+the way the
+photoreceptors respond,
+
+which means that
+their activation leads
+
+to the opening of channels,
+causing depolarization.
+
+And of course you all know
+that-- I should restate maybe
+
+once more-- that when neurons
+in the retina that had greater
+
+potentials, when
+they depolarize,
+
+neurotransmitters released.
+
+When they hyperpolarize,
+they do not release them.
+
+In anything, they
+stop releasing them.
+
+OK.
+
+So now let's look at this wiring
+again in more graphic detail.
+
+Here we have a cone.
+
+And the fact is that
+in central retina,
+
+each cone connects with at
+least two bipolar cells.
+
+So in other words, in the
+retina there are many, many more
+
+bipolars than there
+are photoreceptors,
+
+which is amazing if you
+think about the numbers.
+
+I don't know if you
+remember the numbers.
+
+I told you there are more than
+50 million cones, and maybe
+
+150 million rods, in the retina.
+
+So the retina is an
+unbelievably complex structure
+
+with millions and millions
+and millions of cells.
+
+All right.
+
+So what happens then-- you
+create these ON and OFF bipolar
+
+cells.
+
+The OFF ones, by virtue are
+sign conserving synapse.
+
+The OFF, by virtue, are
+sign conserving synapse.
+
+And they connect with two basic
+classes of ganglion cells--
+
+the ON and the OFF.
+
+So the ON and OFF
+signals, in large part,
+
+then are sent
+separately, especially
+
+to the [INAUDIBLE] nucleus.
+
+But let's not forget
+that they also
+
+have the so-called ON/OFF cells.
+
+And many of them actually end
+up projecting the colliculus,
+
+as we'll talk about later on.
+
+So this is a very basic wiring.
+
+They can then add here,
+as I've already said.
+
+This is sign inverting synapse.
+
+This is sign-conserving
+sign conserving synapse.
+
+And then we can add
+the fact that we
+
+have horizontal cells that
+collect signals going sideways
+
+on the retinal surface,
+thereby creating--
+
+hypothetically speaking, at
+least-- the surround effect,
+
+although that we will look at
+in just a minute in more detail
+
+because some people had
+proposed-- many hypotheses had
+
+emerged why we have
+ON and OFF channels--
+
+and a lot of the
+hypotheses was to create
+
+this famous
+center-surround antagonism
+
+that you see in the
+retinal ganglion cells.
+
+I'll have a model
+for that in a minute.
+
+OK, so here we have
+the ON and OFF systems.
+
+And again I want
+to point out to you
+
+that they terminate in different
+sublamina, the inner plexiform
+
+layer-- the ON in sublamina
+B and the OFF in sublamina A,
+
+whereas the ON/OFF system
+looks something like this.
+
+It has dendritic arbors.
+
+They are ON/OFF ganglion
+cell in both layers,
+
+and connects to both the
+ON and the OFF like that.
+
+So that's how you
+create these three
+
+types of cells at the
+very simple level.
+
+Now the issue that I
+just to referred to
+
+is how is this surround
+mechanism created.
+
+One hypothesis is
+that it's created
+
+by virtue of the
+horizontal cells
+
+predominantly, as shown
+in this figure, which
+
+is pretty much what
+you had seen before.
+
+So the surround is created by
+the horizontal cell network.
+
+An alternative hypothesis
+that was for a while popular
+
+was that actually the reason
+we have ON or OFF channels
+
+is to create the surround
+antagonism in retinal ganglion
+
+cells by using this kind
+of wiring arrangement.
+
+I'm not going to go
+into details about this
+
+because to anticipate
+what I'm going
+
+to tell you is that this model
+does not seem to be correct,
+
+and that of course
+is often the case.
+
+We have many, many
+different models
+
+and then one of
+our tasks is to try
+
+to figure out which
+one is correct.
+
+And you know what
+often happens is
+
+that if three models
+are correct, well
+
+there's a fourth one you
+didn't even think about.
+
+So that sometimes
+happens, and especially
+
+when you study the brain.
+
+All right.
+
+So now we are going to move on.
+
+This is, unless you had read
+the preparatory material,
+
+is something that
+may puzzle you--
+
+the effects of APB
+on the responses
+
+of neurons in the visual system.
+
+So now I'm going to ask you guys
+as to how many of you actually
+
+know what APB is.
+
+Oh, I see all
+these hands raised.
+
+Oh my goodness.
+
+All right.
+
+So nobody knows what the APB is.
+
+That's good.
+
+So that way you are going to
+learn something brand new.
+
+But if you get a chance and
+read the preparatory material,
+
+then it will be easier for to
+remember these many, many facts
+
+that I'm going to try to impart
+on you with each lecture.
+
+All right, so APB.
+
+APB stands for an
+artificial molecule called
+
+2-amino-4-phosphonobutyric acid.
+
+And to show that to you in
+some detail, it is shown here--
+
+2-amino-4-phosphonobuterate .
+
+Butyrate-- "ate," as you
+know, stands for acid.
+
+OK?
+
+So this molecule, as I
+mentioned to you before,
+
+was invented, if you
+will, by Watkins and Evans
+
+in England, who are
+molecular biologists.
+
+And their game, as I mentioned,
+is to create new molecules--
+
+and many of which are either
+analogs or antagonists
+
+of neurotransmitters.
+
+Now this is a glutamate
+neurotransmitter
+
+that is discharged by many,
+many cells in the brain,
+
+including your photoreceptors.
+
+So this is a variant of that.
+
+Now once this molecule
+was invented, or created,
+
+I should say
+perhaps, people began
+
+to ask the question, well
+what is this variant?
+
+What can they do for us?
+
+And that was the basic
+game they all played.
+
+You create molecule after
+molecule after molecule,
+
+and then you test them to
+see whether they can tell you
+
+something useful in
+studying the brain.
+
+And it turns out that there's--
+I've mentioned before also--
+
+most of those molecules you
+can throw into the waste paper
+
+basket.
+
+But the few of them come out
+and become very, very useful.
+
+And this one here--
+that's the reason
+
+I'm mentioning it to
+you-- this APB turned out
+
+to be a magic bullet.
+
+First of all-- you
+should remember this--
+
+that this a
+neurotransmitter analog.
+
+So what happens is in a
+way it acts like glutamate,
+
+but it acts really specifically
+on the neurotransmitter
+
+sites of the ON bipolar cells.
+
+And what it does-- it
+fills the receptor site,
+
+which then makes those
+neurons insensitive
+
+to subsequent light stimulation.
+
+All right?
+
+So this then is a
+remarkable molecule.
+
+And consequently, people began
+to do all sorts of experiments.
+
+And it was discovered that
+when this substance was applied
+
+to the retina, indeed shining
+light into the receptor
+
+fields of cells failed
+to elicit a response.
+
+But by contrast, when
+as part of dark stimulus
+
+was present in the
+receptor field,
+
+the cells continued to fire.
+
+So that was a basic finding,
+and so a method was developed
+
+to study this in the monkey.
+
+And let me show you
+what the method is
+
+so you can get a
+sense of what it's
+
+like to do
+experiments like this.
+
+So the method was
+to put two tubes
+
+into the eye of an anesthetized,
+paralyzed animal, through one
+
+of which you could
+infuse a substance,
+
+and through the other which
+the substance could exit.
+
+Because if there were no exiting
+and you fuse something in here,
+
+the eye would swell
+up, so to speak,
+
+and it would kill
+the cells in the eye.
+
+So you got to circulate it.
+
+So what you have to do also
+is to take the vitreous humor
+
+and make sure that-- you know
+that's a jelly-like substance--
+
+to make it so that it was fluid
+enough to come out of this tube
+
+here, as well.
+
+So then you could present to
+the eye either a solution that
+
+had no effect on
+anything, because you made
+
+that solution with enough
+molecular substances
+
+similar to what's in
+the vitreous already.
+
+OK?
+
+And then what you
+could do is you
+
+could switch over using
+this same substance
+
+and add a little bit of APB.
+
+Now APB is a very
+powerful substance
+
+so you need only small amounts
+of it to have an effect.
+
+And then what you
+did is you recorded
+
+from either the lateral
+geniculate nucleus,
+
+in this case, or from
+the optic nerve fibers,
+
+or from the visual cortex.
+
+And so now you have
+this magic bullet,
+
+and first, however, you want
+to determine, is it true.
+
+What has been found originally
+in the mutt puppy-- is it also
+
+true in the monkey?
+
+If you inject this APB
+into the eye of a monkey,
+
+do you really stop the
+responses of ON-center cells
+
+to view light
+visual stimulation,
+
+light incremental stimulation.
+
+And the answer is lucky
+B-- because otherwise I
+
+wouldn't be telling
+you this, of course--
+
+is that the answer is yes.
+
+So here is an example
+of taking a response.
+
+These are cumulative
+histograms, OK?
+
+You've turned the light
+on, and then turned it off.
+
+And you can see here's an
+ON-center cell responds
+
+vigorously under
+normal conditions.
+
+You put APB into the eye,
+the cell stops responding.
+
+And then when the animal
+recovers from this,
+
+you wash it out, so to speak,
+then the response returns.
+
+By contrast, we
+do same experiment
+
+in an OFF-center cell,
+shown on the right.
+
+You see that the cell
+continues to respond
+
+when you put APB into the eye.
+
+So this is indeed
+a magic bullet,
+
+which selectively
+blocks the ON system,
+
+and has no significant
+effect on the OFF system.
+
+So this then opened
+the gates to study
+
+what happens when you do
+these kinds of experiments--
+
+in this case, in
+monkeys-- to determine
+
+what might be the function
+of these two systems.
+
+And so this then enabled one
+to test the various hypotheses,
+
+which I had mentioned
+to you briefly before.
+
+The first hypothesis
+you can ask,
+
+is it true-- as that model
+I've shown you the right--
+
+that it is interaction
+between the ON or OFF systems
+
+that gives rise to the
+center-surround antagonism
+
+of cells in the retina.
+
+That's one thing you could test.
+
+So to assess that,
+let me show you
+
+what the experimental
+procedure is.
+
+What you do here-- here is
+a receptive field of a cell.
+
+And in this case, this cell--
+the recording is taking place
+
+in the geniculate-- and
+this particular cell
+
+is one that is color selective.
+
+It responds best to
+a small red spot.
+
+And if you hit the surround
+with a different color,
+
+the cell is inhibited.
+
+So the way this is
+then done is you
+
+shine the light on
+the center, then
+
+you shine the light
+on the surround,
+
+and then you're
+in the OFF cycle--
+
+you just hit the surround alone.
+
+So this then shown to
+you here over time.
+
+Here's a center stimulation.
+
+Turn it on.
+
+Then you hit the surround.
+
+Then you turn it off.
+
+So because-- and
+the center stays on,
+
+and during the OFF cycle,
+you hit the surround.
+
+So this shows the
+exact manner in which
+
+you turn these on and off.
+
+All right.
+
+So now the big question is,
+how do ON- and OFF-center cells
+
+respond to this
+stimulus arrangement.
+
+So say you have an ON cell,
+which would discharge to this.
+
+Then the response
+should decrease
+
+because of the
+surround inhibition.
+
+And you'll see the
+normal response.
+
+And the question
+now-- what's going
+
+to happen if you put in the APB?
+
+Well there are a number
+of possibilities.
+
+One is that nothing's
+going to happen.
+
+That's unlikely because
+I already showed you
+
+that APB blocks the ON
+response of the center.
+
+The other possibility
+is that you
+
+lose the center-surround
+antagonism, which
+
+would prove that the ON and OFF
+systems play a significant role
+
+in creating
+center-surround antagonism.
+
+All right.
+
+So those are some of
+the possibilities.
+
+And of course a
+third possibility
+
+is that the OFF cells also
+lose their surround antagonism,
+
+although their responses to
+the center are unaffected.
+
+So let's take a look at that.
+
+And here are the data
+under normal conditions.
+
+This again is the stimulation
+arrangement lined up,
+
+but you can see here
+there's a huge response when
+
+you hit the center
+with a red spot,
+
+and then when you hit
+the surround there's
+
+a huge inhibition.
+
+When you remove that,
+the response returns.
+
+And then during the
+OFF cycle, there's
+
+some spontaneous activity, but
+the surround activation even
+
+stops that.
+
+So there's very strong
+center-surround antagonism.
+
+All right.
+
+So now I want you to
+guess for a minute.
+
+What do you think
+is going to happen
+
+when we inject APB into the eye?
+
+Think about it for a
+minute and I'll tell you.
+
+I listed some of
+the alternatives,
+
+and you can have a
+hypothesis of your own
+
+of what you think might happen.
+
+All right let me show you
+what really happened, OK?
+
+When this happened, actually,
+the experimenter thought,
+
+my god, we lost a cell
+while we were recording.
+
+But then, subsequently when
+the APB was washed out,
+
+you got the same
+response as before.
+
+And so the cell wasn't lost,
+but the APB was so effective
+
+that it stopped the
+response of the cell
+
+completely, both of the
+center and to the surround.
+
+And now let's ask the question,
+what happens when you do this,
+
+not to an ON-center cell,
+but an OFF-center cell.
+
+Think about it
+again for a minute
+
+and ask what do you
+think would happen then.
+
+OK, so here it is.
+
+Here is an OFF-center
+ganglion cell.
+
+And it shows here, using the
+same stimulus conditions, that
+
+in this case, because
+there's an OFF
+
+cell, adding the
+surround decreases
+
+the degree of inhibition
+turning OFF cycle.
+
+And here again the same
+thing is happening.
+
+But the same thing happens
+under both normal conditions
+
+and after APB had been injected.
+
+So what this experiment then
+shows-- and of course one
+
+does this with
+many, many cells--
+
+is to prove that the
+hypothesis, that the ON and OFF
+
+systems play a significant role
+in center-surround antagonism,
+
+is wrong.
+
+And because of that, that
+hypothesis has been eliminated.
+
+All right.
+
+So then we can move on
+and ask the next question.
+
+I mean, let me first
+draw this up again here.
+
+All right.
+
+Here we have the
+photoreceptors--
+
+the cone photoreceptors-- the
+horizontal cells, and the ON
+
+and OFF cells.
+
+So this alternative hypothesis,
+that the surround inhibition
+
+is due to horizontal
+cells, therefore,
+
+has gained much
+greater acceptance.
+
+OK.
+
+So now we are going
+to move upstairs
+
+and we're going to go to area V1
+where we can ask the question,
+
+well what were the transforms
+that we had seen in V1.
+
+I presume all of you remember.
+
+What are the three major
+transforms we talked about?
+
+Who remembers?
+
+Come on.
+
+Sure you remember that, don't
+you-- that we have cells--
+
+most of the cells are
+orientation specific, right?
+
+Most of the cells are
+direction selective.
+
+And most of the
+cells are selective
+
+for spatial frequency.
+
+So those are three of
+the major transforms.
+
+The other two we talked about is
+a convergence of the ON and OFF
+
+channels onto single
+cells in the cortex.
+
+And the other was that
+there was a binocular input
+
+to many of the cells.
+
+So those were the
+major transforms
+
+we talked about the last time.
+
+And again I want to emphasize
+the importance of this
+
+by telling you that
+Hubel received the Nobel
+
+Prize for those discoveries
+of how V1 operates.
+
+OK?
+
+And of course I mentioned
+before that Keffer Hartline,
+
+when he discovered the ON
+and OFF systems using light
+
+that he shown into the eye--
+he called them the ON and OFF
+
+cells-- he received the
+Nobel Prize as well.
+
+So those are truly, truly
+major, major discoveries
+
+and have triggered hundreds
+and hundreds of experiments
+
+trying to understand better.
+
+And certainly one of the
+questions that was raised
+
+is how does orientation,
+and direction cell activity,
+
+and special frequencies
+activity, for that matter,
+
+arise in area of V1.
+
+And one prominent
+hypotheses was indeed
+
+that the reason we have
+ON and OFF channels
+
+is to create these transforms
+in the visual cortex.
+
+So what we can then
+do, now that one
+
+has this magic
+bullet of the APB,
+
+that one can record
+from a cortical cell.
+
+See how it responds when
+you inject APB in contrast
+
+to before you injected
+it and after injected it.
+
+So that's the big question
+you're going to ask next.
+
+All right.
+
+So here is an example of what
+of cortical cell's response
+
+looks like using this kind of
+histogram when a bar of light,
+
+in this case, is moved
+across the receptive field.
+
+Now this is a complex cell.
+
+And you can see it gives
+a vigorous response when
+
+the light edge goes
+across, and then it
+
+gives a vigorous response when
+the dark edge goes across.
+
+I'm showing this only for
+one direction of motion.
+
+So that is a natural response.
+
+So now the question
+comes up, what
+
+happens when you inject
+APB into the eye.
+
+A number of possibilities exist.
+
+The most basic one I think
+most of you would buy
+
+is that the light edge response
+is produced predominantly
+
+by the ON channel,
+and the dark edge
+
+response by the OFF channel.
+
+And if that is the
+case, then this response
+
+should be eliminated by
+blocking it with APB in the eye.
+
+And if you do that, that's
+exactly what happens.
+
+You can see here under
+normal conditions,
+
+you get a vigorous response
+for both light and dark edges.
+
+After APB, only a dark
+edge response remains.
+
+So this then established
+that these responses
+
+to the different edges-- the
+light edges and dark edges--
+
+are a product of the input from
+the retina to the geniculate,
+
+and then to the cortex from the
+ON and the OFF channels, which
+
+then converge in
+many cortical cells,
+
+as is the case in this
+particular cortical cell.
+
+So that then establishes
+this very basic fact.
+
+Now the next
+question we can ask--
+
+what about those transforms
+you talked about?
+
+Let's first of all
+look at the transform
+
+of direction selectivity.
+
+So we can take a cell
+that is, in this case,
+
+directionally biased.
+
+And you can see what
+the response is before
+
+and after APB is injected.
+
+And what you see
+here-- we move the bar
+
+across in one direction, and
+then we move the bar back
+
+across the opposite direction.
+
+So the first half shows
+a downward movement--
+
+the second half,
+the upward movement.
+
+Now what you see here
+that the cell responds
+
+is much more vigorous.
+
+It's not 100%
+direction selective.
+
+I showed you some of
+those the last time.
+
+This one is a bias--
+about a four to one bias--
+
+much more response to
+the downward movement
+
+than the upward movement.
+
+But the cell responds both
+the light and the dark edge
+
+in both directions,
+and it lines up
+
+with the temporal
+arrangement here,
+
+proving indeed that
+this is a complex cell.
+
+Now then when you
+inject APB into the eye,
+
+look what happens.
+
+You eliminate the light
+edge response here and here,
+
+but the cell is still
+directionally biased.
+
+So direction specificity
+was maintained.
+
+And when this was
+studied in many,
+
+many, many cells--
+even cells that
+
+were 100% direction specific--
+blocking the ON channel
+
+did not eliminate
+directionality in the cortex.
+
+So that then indicates that
+the ON and OFF channels did not
+
+arise to bring about direction
+selectivity in the cortex.
+
+And so that brings us
+to the second transform,
+
+which is orientation
+specificity.
+
+So we can do that next.
+
+And here we have an example
+using a very similar procedure.
+
+Again, a complex cell
+when the APB is injected.
+
+The light edge
+response disappears.
+
+You move the bar across
+the different orientations
+
+and this is the orientation
+specificity you get.
+
+Now this is calculated here on
+the basis of only the dark edge
+
+response because you
+want to keep it the same
+
+as you're going to do here.
+
+Since the light edge
+response is eliminated,
+
+you can see that the cells
+orientation specificity is also
+
+unaffected, meaning
+that the orientation
+
+specificity of
+the cortical cells
+
+is not due to the interaction
+between the ON and OFF channel.
+
+Similar experiments were also
+done with spatial frequency
+
+selectivity, and again,
+no effect was found.
+
+So this then led
+to the conclusion
+
+that the ON and OFF
+channels did not
+
+arise for the purpose of
+creating the transforms that we
+
+had denoted in our last
+lecture about single cells
+
+in the visual cortex.
+
+All right.
+
+So now what we can do
+is here-- we can come up
+
+with a silly model, just
+to make it memorable,
+
+which is to say
+that the ON and OFF
+
+channels flow into the cortex.
+
+And these attributes we talked
+about-- orientation, direction,
+
+and spacial frequencies
+selectivity--
+
+are produced by
+cortical filters.
+
+What you have in
+the cortex are all
+
+kinds of inhibitory interneurons
+and the interactions
+
+among many, many neurons.
+
+And that kind of
+activity that you
+
+get there is the one that
+produces these attributes,
+
+not the interaction between
+the ON and OFF channels
+
+that flow into
+the visual cortex.
+
+All right.
+
+So now the next
+question we can ask,
+
+or what happens on APB under
+photopic viewing conditions.
+
+We'll talk about scotopic,
+as well as photopic, vision.
+
+To do this, and to answer how it
+affects our visual capacities,
+
+what we do is to turn to
+behavioral experiments.
+
+In behavioral experiments,
+what you can do
+
+is you can present
+various kinds of stimuli.
+
+You can train a
+monkey-- in this case,
+
+with monkeys-- to see how
+well they perceive a stimulus,
+
+and ask them to make an eye
+movement to that stimulus.
+
+So when you do
+this-- testing that
+
+hypothesis I've shown you
+earlier about light increment
+
+and light decrement--
+what we can do
+
+is to train a monkey
+to first fixate.
+
+And then after the
+monkey fixated,
+
+you can present either
+a light incremental spot
+
+or a light decremental spot.
+
+The monkey's task is to make
+a saccade to that target.
+
+And of course, those
+spots will appear randomly
+
+in several different
+locations in each trial,
+
+so the monkey doesn't know
+where he's going to appear.
+
+And if he makes a
+correct saccade to it,
+
+he will get a drop of
+apple juice for a reward.
+
+So that is the procedure.
+
+And so now the question
+then comes up--
+
+how well does the
+monkey do in being
+
+able to detect light
+increment and light decrement?
+
+So if you do that, luckily
+one gets a very clear cut
+
+and dramatic result.
+
+Here is the section
+that I will show
+
+you data for light
+increment, and here
+
+is a section showing
+data for light decrement.
+
+So here is an example.
+
+What you measure
+here are two things--
+
+you measure the monkey's
+percent correct performance,
+
+and you measure what the
+saccadic latencies are
+
+to make a saccade to the target.
+
+So it shows here that
+under normal conditions,
+
+the monkey's
+performances is over 90%,
+
+and that he has a
+very nice distribution
+
+of saccadic latencies
+with a mean of about two
+
+in 53 milliseconds.
+
+Then when you apply APB
+to the eye, what happens
+
+is that the monkey's
+performance drops dramatically.
+
+He is just a little
+bit above probability,
+
+and his latencies are very,
+very late-- very, very,
+
+very long-- 406 milliseconds.
+
+So in other words,
+the monkey can barely
+
+perceive a light
+incremental stimulus
+
+by virtue of having blocked
+the ON channel in the retina
+
+by APB.
+
+Now if you do the
+same experiment
+
+with light decrement,
+what you see here
+
+is the monkey's
+performance remains
+
+normal-- about 95% correct.
+
+And the latency
+distribution is also
+
+about the same-- two in 49,
+versus two in 51 milliseconds.
+
+So that then says that
+indeed the ability
+
+to detect light
+incremental stimuli
+
+has been devastated by
+the injection of APB,
+
+and therefore raised the
+idea that the ON and OFF
+
+channels are for the purpose
+of quickly and efficiently
+
+detecting light increment,
+as well as light decrement.
+
+So that then was
+the basic finding
+
+that was obtained with this
+behavioral experiment studying
+
+the monkey's
+performance on being
+
+able to process visual stimuli.
+
+Now we are going to get
+a bit more complicated,
+
+because what we
+talked about so far
+
+was under photopic
+conditions, meaning
+
+when your cones were
+fully functional.
+
+So the question is what happens
+under scotopic conditions,
+
+meaning what happens
+when you're dark adapted.
+
+Now we have talked
+about this before.
+
+It was pointed out,
+initially by Schultze,
+
+that we have two basic classes
+of photoreceptors-- the rods
+
+and the cones-- and that the
+rods are for night vision.
+
+So now the question is, what
+happens under night vision
+
+conditions.
+
+And when this was found-- this
+was truly, truly baffling.
+
+And I'm going to
+show you the data.
+
+It showed here under
+light adapted conditions
+
+with the same kind of
+data-- but shown only
+
+as histograms in this
+case-- the monkey
+
+does equally well
+for light and dark.
+
+And when you apply
+APB, the monkey
+
+has difficulty seeing the
+light incremental stimulus,
+
+but has little loss in the
+light decremental stimulus.
+
+OK?
+
+But when you do the same thing
+under dark adapted conditions,
+
+when only the rods
+are operative,
+
+a curious thing happens.
+
+The monkey doesn't see either
+light increment or light
+
+decrement.
+
+In other words, and the
+way to put it shortly,
+
+is to say that the monkey
+has become night blind.
+
+Now there are, among humans, a
+small population of individuals
+
+individuals who are
+night blind, and what's
+
+the situation with them?
+
+It's called "night
+blind" because they just
+
+see very poorly at night.
+
+And, in fact, when
+that is known,
+
+they only get a special kind
+of driver's license-- one
+
+saying you can drive
+in the daytime,
+
+but you can't drive at night.
+
+So now we have a
+monkey here with APB
+
+injected-- that
+he's night blind.
+
+And also you see the same data
+reflected in the latencies,
+
+just like before.
+
+And it shows that the
+monkey is devastated
+
+both for light increment
+and light decrement
+
+by having a tremendous
+increase-- more
+
+than a tripling of
+latencies for the few trials
+
+that he did carry out correctly.
+
+So now this being the case,
+it raises a big question--
+
+and I'm sorry that things
+are getting so complicated,
+
+but the brain is
+complicated-- as
+
+to just what is the nature
+and arrangement of the rods
+
+in the retina, and
+how does that relate
+
+to the arrangement of the cones?
+
+OK?
+
+So that brings me to
+an interesting point.
+
+Again, as so often
+happens, whenever
+
+you're confronted
+with a puzzle, you
+
+have all kinds of hypotheses.
+
+And then luckily if you do
+this instead of experiments,
+
+you come up with the
+right kinds of tools.
+
+You can eliminate most of them
+and come up with the right one.
+
+Now, so we can
+ask, first of all,
+
+without talking
+about APB at all now,
+
+simply ask a general
+question-- what
+
+happens to the receptive fields,
+or retinal ganglion cells,
+
+under dark adapted conditions?
+
+And what happens is that the
+receptive fields become larger.
+
+Now this initially-- discovered
+by Barlow in England--
+
+was negated by the other
+individuals saying,
+
+you just got scattering of
+light-- that's why it's larger.
+
+So it was kind of
+dismissed, but in the end
+
+it turned that he was
+right, as you shall see.
+
+The other thing that happened
+is that the color selectivity
+
+response disappears in the
+retinal ganglion cells.
+
+And not only that, but it
+disappears behaviorally.
+
+So when you have a
+red rose, and you
+
+look at a red rose at night when
+only your rods are functional,
+
+it looks like a black rose.
+
+The rods cannot process color.
+
+OK?
+
+They can only process light
+increment and decrement.
+
+OK, again just to reiterate--
+the receptive fields
+
+become larger.
+
+OK.
+
+So the big question is
+what on earth is happening,
+
+what kind of wiring
+is taking place,
+
+or what kind of
+connections are created
+
+to create these two things.
+
+Now the second one is the
+one that's the big puzzle.
+
+The first one we can
+understand because it's
+
+been shown that rods
+are only one type
+
+and that they don't
+carry color information.
+
+Now to study this further, way
+back when in the 1870s-- 1880s,
+
+Cajal did the large number
+of experiments of this sort.
+
+If you remember, I told you
+that Cajal played a central role
+
+in using the Golgi stain, and
+that he and Golgi received
+
+the Nobel Prize in 1906
+for their major discoveries
+
+about this.
+
+So now he argued that
+the way this happens
+
+is that rods and the
+cones connect differently
+
+with the ganglion cells.
+
+And so here is a
+picture of Cajal.
+
+He spent most of
+his life like this,
+
+looking through a
+microscope, endlessly looking
+
+at brain slices, and studying
+the individual cells--
+
+the shapes and drew them,
+as you can see his pencil.
+
+He is in the middle drawing,
+actually, a cell there.
+
+And so he speculated
+about this a great deal.
+
+And he was just a
+remarkable person.
+
+And he had written
+an autobiography.
+
+And the way he speaks in this--
+translated from Spanish--
+
+but he has an incredibly
+colorful way of talking--
+
+"had," I guess I should say.
+
+And I want to
+quote some of this,
+
+because I think you'll find
+it interesting and amusing.
+
+So he said, "Since this
+impression received by the rods
+
+is different from that
+taken by the cone,
+
+it is necessary from
+every point of view
+
+that each of these
+specific impressions
+
+should be conveyed through the
+retina by a separate channel."
+
+The translation leaves a lot
+to be desired, but that's OK.
+
+So then he went
+on and said, "When
+
+we reason with common sense
+and lift a war club determined
+
+upon vigorous action,
+nature ultimately hears us."
+
+Very picturesque, as if nature
+had heard anyone, right?
+
+"Knowing what I was
+looking for--" meaning he
+
+had a hypothetical bias, right--
+"I began to explore eagerly
+
+retina of fishes and mammals.
+
+Finally as a reward
+of my faith, there
+
+deigned to appear most clearly
+and brilliantly those two
+
+types of bipolar cells
+demanded by theory
+
+and guessed by reason."
+
+What he means by
+this is that there
+
+were two kinds of basic
+kinds of bipolar cells--
+
+and not the ON and OFF.
+
+But in this case, what
+he was talking about,
+
+he was talking about rod
+bipolars and cone bipolars.
+
+He said the rod photoreceptors
+connect with rod bipolars,
+
+and the cone photoreceptors
+with cone bipolars.
+
+So that's what [INAUDIBLE]
+then established,
+
+and that finding was
+basically correct.
+
+But then he went on to say that
+these two kinds of bipolars
+
+hook up with two types
+of ganglion cells,
+
+thereby forming separate
+channels to the brain.
+
+So that was an interesting
+conclusion, and for many years
+
+that was accepted.
+
+And interestingly enough,
+as it so often happens
+
+with hypotheses,
+this conclusion--
+
+even though you had
+the drawings looking
+
+through the microscope
+showing that there were
+
+these separate channels--
+turned out to be largely
+
+not one-- almost entirely wrong.
+
+Now what do we mean by that?
+
+Well people began
+to do all sorts
+
+of very careful intercellular
+recordings in the retina,
+
+and using much
+more sophisticated
+
+anatomical procedures
+than Cajal was
+
+able to use, thanks to the
+new developments in the field.
+
+And they discovered, first of
+all-- let me back up a second.
+
+This is sort of the model
+that he had proposed.
+
+He had the cone model
+and the rod model,
+
+not distinguishing
+between the ON and OFF.
+
+And so the model that
+then subsequently emerged
+
+was that ganglion cells
+in most of the retina
+
+actually receive a convergent
+input- except in the fovia,
+
+because you don't have rods
+there-- so that you don't have
+
+a doubling of ganglion
+cells-- some for rods
+
+and some for cones-- but
+both the rods and the cones,
+
+through separate pathways,
+feed into the ganglion cell.
+
+So then this was analyzed
+in much, much more detail.
+
+And now I'm going to point this
+out to you by providing you
+
+with an overview of the
+retinal connections.
+
+OK.
+
+So here we have the three
+basic classes of cones.
+
+All right?
+
+And we have the rods.
+
+All right?
+
+Then, if you look at
+the cones, each cone
+
+gives rise to at least two
+bipolar cell-- an ON and OFF
+
+bipolar cell.
+
+But the rods in
+most species only
+
+have a single kind
+of bipolar cell,
+
+and they can refer to that
+as an ON bipolar cell,
+
+because the synapses are all
+sign-inverting synapses using
+
+the mGluR6 neurotransmitter
+receptor site.
+
+So that's what we have there.
+
+Now if you look further down
+here at the ganglion cells--
+
+and what we have is of course,
+that we have the ON and OFF
+
+bipolar cells from
+the cones feed
+
+into the ON and
+OFF ganglion cells.
+
+So now the questions are what
+happens to the ON bipolar
+
+cells?
+
+How do they connect
+to these cells
+
+since they do not form
+a separate pathway?
+
+And this has been
+again-- things got
+
+very complicated in
+the course of evolution
+
+where it was very important
+to try to conserve things
+
+as much as possible,
+and that's why we do not
+
+have separate pathways
+for rods and cones.
+
+If we did we'd need
+a huge eye, and we'd
+
+need at least twice
+as many ganglion cells
+
+than we have at the present
+time, which is about a million
+
+in each eye.
+
+OK, so what really happened
+is-- dumb-founding almost--
+
+is that a so-called
+amacrine cell --
+
+I told you there are different
+classes of amacrine cells--
+
+one of them is a so-called
+A2 amacrine cell.
+
+That is a cell that
+receives a direct input
+
+from the ON bipolar cells.
+
+Now that amacrine cell
+connects to ganglion cells
+
+in two different ways.
+
+It makes a gap junction
+connection with the ON bipolar
+
+cells, and it makes a
+glycinergic synaptic connection
+
+with the OFF ganglion cell.
+
+So let's label this.
+
+What we have here-- this is
+inner plexiform layer again,
+
+and here is the outer
+plexiform layer.
+
+And what we have here--
+just to remind you,
+
+that already know-- we have
+a sign-inverting synapse
+
+for the ON, and sign-conserving
+for the OFF bipolars
+
+that connect with the cones.
+
+And now we have here-- let's
+proceed to the A2 amacrine
+
+cell that is feeding into
+these cells from the rods.
+
+And what we have here is a
+glycinergic synapse, so-called.
+
+That's a real synapse.
+
+It's inhibitory.
+
+And then here we have what
+is called a gap junction.
+
+I'm sure all of you know
+what these things are.
+
+Gap junction is what you
+call an electrical synapse.
+
+So they transform the signal
+without any neurotransmitters
+
+involved.
+
+So it directly activates-- in
+this case, this fiber here--
+
+and drives it.
+
+So what you create
+in the inner retina
+
+then here is a
+double ended system
+
+for the rods that is created in
+the outer retina for the cones.
+
+So you create [INAUDIBLE].
+
+Here are the OFF, and here are
+the ON inputs to the ON and OFF
+
+ganglion cells.
+
+Now because of this
+arrangement, what happens
+
+is that the size
+of the receptive
+
+fields under dark
+adaptive conditions
+
+is bigger because a bigger range
+of connections from the rods
+
+to the ganglion cells.
+
+So all this is nice
+wiring that finally,
+
+after many, many
+years of experiments,
+
+has been clarified.
+
+Sorry it is so complicated.
+
+That's just how it is.
+
+Explains then the claim that
+you have bigger receptive fields
+
+at night than in the daytime.
+
+And now that has been
+generally accepted.
+
+OK so now the central
+conclusions that we come to
+
+is that ON and OFF
+channels have emerged
+
+in the course of evolution
+to enable organisms
+
+to process light both
+incrementally and decrementally
+
+for being able to see
+things rapidly and quickly.
+
+All right?
+
+So that is the prime function.
+
+Nature has gone to
+incredible extent
+
+to modify the basic organization
+of the visual system
+
+and the retina to
+create a way to be
+
+able to process
+both light increment
+
+and decrement rapidly.
+
+Now that may provide you
+with a little cute mnemonic,
+
+if you will.
+
+Here we have a fish.
+
+Fish also, believe it or not,
+have ON and OFF channels.
+
+Now what happens is
+if below here there
+
+is a predator--
+a large fish that
+
+is trying to catch this fish--
+because of the sun shining
+
+on it, it reflects
+the light, and so
+
+this fish would see
+this particular predator
+
+by virtue of light increment.
+
+Got it?
+
+By contrast, if you
+have osprey up here
+
+that's trying to
+catch this fish,
+
+that osprey against the sky
+would be seen as a dark object.
+
+OK?
+
+And so now, since this fish
+has both ON and OFF cells
+
+in its retina, it's
+going to do this.
+
+You ready?
+
+He's going to escape, OK?
+
+So that then, in a
+nutshell, tells us
+
+why we have ON and OFF channels
+in the visual system-- namely
+
+to enable us to process both
+light increment and light
+
+decrement effectively.
+
+And as I've mentioned
+to you before,
+
+whenever you read or
+write, you see things
+
+mostly by virtue
+of your OFF system
+
+because you have dark print or a
+dark pen on a light background.
+
+But of course the
+obverse is also the case.
+
+So this was known
+for ages and ages.
+
+And that's why
+eventually, instead
+
+of having print
+in which you have
+
+a black page with
+white letters, you now
+
+a white page with black
+letters, because that's
+
+much more economical to achieve.
+
+And you can read both
+light incremental
+
+and light decremental
+letters equally well
+
+because we have these
+ON and OFF channels.
+
+OK.
+
+So on the basis of
+this then, we are
+
+ready to summarize why we
+have this remarkable duality
+
+in the retina, originating
+in the ON and OFF channels,
+
+whose circuits we
+by now, I presume,
+
+you understand pretty well.
+
+So just to reiterate for
+the umpteenth time, which
+
+is easy to remember by
+now, all photoreceptors
+
+hyperpolarize to light.
+
+Secondly, the cone driven
+ON and OFF channels
+
+originate at the level of
+the retinal bipolar cells.
+
+OK?
+
+For ON bipolars
+you have a system,
+
+which involves
+sign-inverting synapses.
+
+OK?
+
+The neuron transmitted by
+the way of the photoreceptors
+
+is glutamate.
+
+And you come to the receptor
+sites-- the mGluR6 receptor is
+
+the one that inverts the signal
+for the ON bipolar cells.
+
+And the mGluR1 and 2 is the
+neurotransmitter receptor site
+
+for the OFF bipolar cells.
+
+Now APB-- can
+important to remember
+
+this-- is that glutamate analog.
+
+A lot of people make a mistake
+and think it's an antagonist.
+
+It's a glutamate analog.
+
+So what happens is that
+it blocks the ON bipolar.
+
+Now let me say just a couple
+more words about this.
+
+We move our eyes about
+three times a second.
+
+Every time you move your eye
+some mechanisms in the retina
+
+wipe the slate
+clean, so to speak,
+
+because if it didn't,
+then the image that
+
+would fall on the retina
+after you moved your eye
+
+would interfere
+with the image that
+
+had fallen on the
+eye beforehand.
+
+So there's an
+incredibly rapid system
+
+that breaks down the
+molecular arrangement
+
+of glutamate and many other
+transmitters in the retina
+
+so that with each
+movement of the eye,
+
+you can see things clearly.
+
+Now there is an exception
+to that, of course,
+
+under extreme conditions.
+
+We have what is
+called "after images,"
+
+like when you look at
+the sun for a while.
+
+Then you will see an after
+image lingering on in your eye.
+
+But under normal
+illumination conditions,
+
+the slate is wiped clean
+with every shift in the eye.
+
+Quite amazing.
+
+All right.
+
+Then APB blocks the ON response
+of retinal ganglion cells.
+
+The OFF response and
+center-surround antagonism
+
+are unaffected.
+
+APB blocks lighted
+responses in the cortex,
+
+but has no effect on
+orientation, direction,
+
+and spatial frequency
+selectivity.
+
+APB reduces the sensitivity
+for light increment,
+
+and the ON and OFF channels for
+rods arise in the inner retina.
+
+And I should add
+here that there's
+
+only one kind of rod bipolar,
+which is the ON-type.
+
+There are no OFF-type
+rod biopolars.
+
+Then in most primates there
+are only ON rod bipolars.
+
+The rod ON and OFF
+channels are created
+
+in the inner retina
+by the amacrine cells,
+
+predominately by the
+so-called A2 amacrine cell,
+
+as I told you.
+
+Lastly, excitatory
+signals are generated
+
+for both light increment
+and for light decrement
+
+by virtue of the ON
+and OFF channels.
+
+So those are the
+major conclusions
+
+that we need to make about this
+remarkable achievement of how
+
+the visual system works,
+by virtue of having created
+
+the ON and the OFF channels,
+by virtue of having then
+
+done this, by virtue of creating
+from a single-ended system
+
+of the photoreceptors,
+a double-ended system
+
+at the level of
+the bipolar cells.
+
+So that then is--
+sorry how complicated
+
+it is-- the basic layout of
+the retina and the ON and OFF
+
+channels.
+
+Next time we are going to talk
+about yet another subdivision
+
+in retinal ganglion cells-- the
+so-called midget and parasol
+
+cells.
+
+I think I've mentioned
+to you before that we
+
+have several different classes
+of retinal ganglion cells--
+
+not just ON and OFF.
+
+And the so-called
+midget and parasol cells
+
+have ON and OFF subdivisions.
+
+And then there are
+several other cells
+
+that do all kinds
+of other things.
+
+We will talk about
+some of those.
+
+But the overwhelming, largest
+number of cells in the retina
+
+are the midget and the
+parasol, and so they
+
+deserve the greatest
+scrutiny as to why
+
+we have those two systems.
+
+And that's we are going
+to discuss the next time.
+
+So that pretty well finishes
+what I had to cover today,
+
+and so if any of you
+have any questions,
+
+I will be happy to try to answer
+them for you, as long as it
+
+pertains, of course, to
+the ON and OFF channels.
+
+Anybody not clear
+on the rules of how
+
+APB works-- that it's an analog,
+that it fills the receptor
+
+sites of the ON bipolar
+cells, rendering
+
+them insensitive to
+subsequent light stimulation?
+
+Now I should add maybe
+one more thing here
+
+is that unlike the glutamate,
+which is broken down
+
+in milliseconds, this
+artificial substance-- APB--
+
+there's no natural
+optic mechanism for it.
+
+And so it lingers on, and
+that's why it is so effective.
+
+And it has to be washed out
+of the eye-- you typically
+
+have to wait 10-- 15 minutes
+for the eye to return to normal
+
+because there's no rapid
+optic mechanism for the APB,
+
+in contrast to the glutamate.
+
+Well it sounds like I
+was reasonably clear.
+
+I hope you can absorb
+this and marvel
+
+at the inventiveness, if
+you will, of evolution
+
+to have created this
+incredible mechanisms that we
+
+see in the retina.
+
+It's just dumb-founding.
+
+Yes, it's just incredible.
+
+So that then is what we
+going to finish with today.
+
+And so I will see
+you Wednesday, and we
+
+talk about the midget and
+parasol systems, which
+
+is also very
+interesting, by the way.
+
+And I hope you've
+enjoyed hearing
+
+about what those
+two systems are for.
\ No newline at end of file
diff --git a/nSin1QDLUDs.txt b/nSin1QDLUDs.txt
new file mode 100644
index 0000000000000000000000000000000000000000..0750f77eb98a8d394ad5e8c75a0c1b8eef98f330
--- /dev/null
+++ b/nSin1QDLUDs.txt
@@ -0,0 +1,1219 @@
+align:start position:0%
+ 
+if you
+
+ align:start position:0%
+if you
+ 
+
+ align:start position:0%
+if you
+are wearing rings as i do it's a good
+
+ align:start position:0%
+are wearing rings as i do it's a good
+ 
+
+ align:start position:0%
+are wearing rings as i do it's a good
+idea to take them off
+
+ align:start position:0%
+idea to take them off
+ 
+
+ align:start position:0%
+idea to take them off
+because when you prepare the dough it's
+
+ align:start position:0%
+because when you prepare the dough it's
+ 
+
+ align:start position:0%
+because when you prepare the dough it's
+not great
+
+ align:start position:0%
+not great
+ 
+
+ align:start position:0%
+not great
+it's not very hydrating if you are
+
+ align:start position:0%
+it's not very hydrating if you are
+ 
+
+ align:start position:0%
+it's not very hydrating if you are
+wearing rings
+
+ align:start position:0%
+wearing rings
+ 
+
+ align:start position:0%
+wearing rings
+i once lost a stone
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+very safe either but you want to of
+
+ align:start position:0%
+very safe either but you want to of
+ 
+
+ align:start position:0%
+very safe either but you want to of
+course
+
+ align:start position:0%
+course
+ 
+
+ align:start position:0%
+course
+wash the vegetables okay the broccoli
+
+ align:start position:0%
+wash the vegetables okay the broccoli
+ 
+
+ align:start position:0%
+wash the vegetables okay the broccoli
+you can just
+
+ align:start position:0%
+you can just
+ 
+
+ align:start position:0%
+you can just
+cut them into small pieces and maybe you
+
+ align:start position:0%
+cut them into small pieces and maybe you
+ 
+
+ align:start position:0%
+cut them into small pieces and maybe you
+can make a small
+
+ align:start position:0%
+can make a small
+ 
+
+ align:start position:0%
+can make a small
+sofrito with the alga
+
+ align:start position:0%
+sofrito with the alga
+ 
+
+ align:start position:0%
+sofrito with the alga
+that's one option the
+
+ align:start position:0%
+that's one option the
+ 
+
+ align:start position:0%
+that's one option the
+spinach you can just use them as they
+
+ align:start position:0%
+spinach you can just use them as they
+ 
+
+ align:start position:0%
+spinach you can just use them as they
+are
+
+ align:start position:0%
+are
+ 
+
+ align:start position:0%
+are
+in the pepperoni you need to wash them
+
+ align:start position:0%
+in the pepperoni you need to wash them
+ 
+
+ align:start position:0%
+in the pepperoni you need to wash them
+cut them remove the seeds
+
+ align:start position:0%
+cut them remove the seeds
+ 
+
+ align:start position:0%
+cut them remove the seeds
+and then you can cut them in stripes for
+
+ align:start position:0%
+and then you can cut them in stripes for
+ 
+
+ align:start position:0%
+and then you can cut them in stripes for
+example
+
+ align:start position:0%
+example
+ 
+
+ align:start position:0%
+example
+that's a good thing and again you can
+
+ align:start position:0%
+that's a good thing and again you can
+ 
+
+ align:start position:0%
+that's a good thing and again you can
+put them in the
+
+ align:start position:0%
+put them in the
+ 
+
+ align:start position:0%
+put them in the
+pan so they roast a little bit
+
+ align:start position:0%
+pan so they roast a little bit
+ 
+
+ align:start position:0%
+pan so they roast a little bit
+a tiny bit of oil you can do the same
+
+ align:start position:0%
+a tiny bit of oil you can do the same
+ 
+
+ align:start position:0%
+a tiny bit of oil you can do the same
+thing
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+i like them cut longitudinally but if
+
+ align:start position:0%
+i like them cut longitudinally but if
+ 
+
+ align:start position:0%
+i like them cut longitudinally but if
+you want to cut them
+
+ align:start position:0%
+you want to cut them
+ 
+
+ align:start position:0%
+you want to cut them
+in disks that's fine and look
+
+ align:start position:0%
+in disks that's fine and look
+ 
+
+ align:start position:0%
+in disks that's fine and look
+for the melon it's a little bit more
+
+ align:start position:0%
+for the melon it's a little bit more
+ 
+
+ align:start position:0%
+for the melon it's a little bit more
+complex but not too much
+
+ align:start position:0%
+complex but not too much
+ 
+
+ align:start position:0%
+complex but not too much
+so you want to cut it in disks
+
+ align:start position:0%
+so you want to cut it in disks
+ 
+
+ align:start position:0%
+so you want to cut it in disks
+as see as thin as you can so it cooks
+
+ align:start position:0%
+as see as thin as you can so it cooks
+ 
+
+ align:start position:0%
+as see as thin as you can so it cooks
+fast yeah yes
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay we got it and then you first put it
+
+ align:start position:0%
+okay we got it and then you first put it
+ 
+
+ align:start position:0%
+okay we got it and then you first put it
+with a little bit of salt
+
+ align:start position:0%
+with a little bit of salt
+ 
+
+ align:start position:0%
+with a little bit of salt
+um in the sink because the idea is that
+
+ align:start position:0%
+um in the sink because the idea is that
+ 
+
+ align:start position:0%
+um in the sink because the idea is that
+you want
+
+ align:start position:0%
+you want
+ 
+
+ align:start position:0%
+you want
+the bitter to go away sometimes the
+
+ align:start position:0%
+the bitter to go away sometimes the
+ 
+
+ align:start position:0%
+the bitter to go away sometimes the
+eggplants can be a little bit bitter
+
+ align:start position:0%
+eggplants can be a little bit bitter
+ 
+
+ align:start position:0%
+eggplants can be a little bit bitter
+then you have to rinse it very well dry
+
+ align:start position:0%
+then you have to rinse it very well dry
+ 
+
+ align:start position:0%
+then you have to rinse it very well dry
+it
+
+ align:start position:0%
+it
+ 
+
+ align:start position:0%
+it
+and then just roast it on the pan high
+
+ align:start position:0%
+and then just roast it on the pan high
+ 
+
+ align:start position:0%
+and then just roast it on the pan high
+fire
+
+ align:start position:0%
+fire
+ 
+
+ align:start position:0%
+fire
+for short times that's it
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay we wash them
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+cut them in the shape that you prefer
+
+ align:start position:0%
+cut them in the shape that you prefer
+ 
+
+ align:start position:0%
+cut them in the shape that you prefer
+i recommend to do small slices
+
+ align:start position:0%
+i recommend to do small slices
+ 
+
+ align:start position:0%
+i recommend to do small slices
+because again they cook faster and if
+
+ align:start position:0%
+because again they cook faster and if
+ 
+
+ align:start position:0%
+because again they cook faster and if
+you want
+
+ align:start position:0%
+you want
+ 
+
+ align:start position:0%
+you want
+you can saute them for example with
+
+ align:start position:0%
+you can saute them for example with
+ 
+
+ align:start position:0%
+you can saute them for example with
+chipotle
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so this is the vegetable team
+
+ align:start position:0%
+so this is the vegetable team
+ 
+
+ align:start position:0%
+so this is the vegetable team
+the other team will
+
+ align:start position:0%
+the other team will
+ 
+
+ align:start position:0%
+the other team will
+start preparing pizza
+
+ align:start position:0%
+start preparing pizza
+ 
+
+ align:start position:0%
+start preparing pizza
+pizza you'll need
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+i will help you with this and then we
+
+ align:start position:0%
+i will help you with this and then we
+ 
+
+ align:start position:0%
+i will help you with this and then we
+will add
+
+ align:start position:0%
+will add
+ 
+
+ align:start position:0%
+will add
+some whatever
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so don't forget that i'm giving you very
+
+ align:start position:0%
+so don't forget that i'm giving you very
+ 
+
+ align:start position:0%
+so don't forget that i'm giving you very
+precise measurements but this is only
+
+ align:start position:0%
+precise measurements but this is only
+ 
+
+ align:start position:0%
+precise measurements but this is only
+because it's the first time that you're
+
+ align:start position:0%
+because it's the first time that you're
+ 
+
+ align:start position:0%
+because it's the first time that you're
+making pizza
+
+ align:start position:0%
+making pizza
+ 
+
+ align:start position:0%
+making pizza
+once you have done pizza if you're
+
+ align:start position:0%
+once you have done pizza if you're
+ 
+
+ align:start position:0%
+once you have done pizza if you're
+trying for a few times you won't need
+
+ align:start position:0%
+trying for a few times you won't need
+ 
+
+ align:start position:0%
+trying for a few times you won't need
+la bilancia the scale anymore you will
+
+ align:start position:0%
+la bilancia the scale anymore you will
+ 
+
+ align:start position:0%
+la bilancia the scale anymore you will
+do everything
+
+ align:start position:0%
+do everything
+ 
+
+ align:start position:0%
+do everything
+yes okay bye
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+i'm gonna put the two events at two
+
+ align:start position:0%
+i'm gonna put the two events at two
+ 
+
+ align:start position:0%
+i'm gonna put the two events at two
+different temperatures so they see the
+
+ align:start position:0%
+different temperatures so they see the
+ 
+
+ align:start position:0%
+different temperatures so they see the
+result
+
+ align:start position:0%
+result
+ 
+
+ align:start position:0%
+result
+cooking the pizza at 400 fahrenheit and
+
+ align:start position:0%
+cooking the pizza at 400 fahrenheit and
+ 
+
+ align:start position:0%
+cooking the pizza at 400 fahrenheit and
+500 paranoids
+
+ align:start position:0%
+500 paranoids
+ 
+
+ align:start position:0%
+500 paranoids
+you were
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+right so you want the dough
+
+ align:start position:0%
+right so you want the dough
+ 
+
+ align:start position:0%
+right so you want the dough
+to be to stick together but you don't
+
+ align:start position:0%
+to be to stick together but you don't
+ 
+
+ align:start position:0%
+to be to stick together but you don't
+want it to be sticky
+
+ align:start position:0%
+want it to be sticky
+ 
+
+ align:start position:0%
+want it to be sticky
+start with not too much then you don't
+
+ align:start position:0%
+start with not too much then you don't
+ 
+
+ align:start position:0%
+start with not too much then you don't
+have to worry
+
+ align:start position:0%
+have to worry
+ 
+
+ align:start position:0%
+have to worry
+if the dough becomes too sticky
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and then i was telling them you can take
+
+ align:start position:0%
+and then i was telling them you can take
+ 
+
+ align:start position:0%
+and then i was telling them you can take
+it out of
+
+ align:start position:0%
+it out of
+ 
+
+ align:start position:0%
+it out of
+the bowl that you're using the measuring
+
+ align:start position:0%
+the bowl that you're using the measuring
+ 
+
+ align:start position:0%
+the bowl that you're using the measuring
+cup
+
+ align:start position:0%
+cup
+ 
+
+ align:start position:0%
+cup
+and you can mix it on the counter
+
+ align:start position:0%
+and you can mix it on the counter
+ 
+
+ align:start position:0%
+and you can mix it on the counter
+you just put it on you wait
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+a little bit more water
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+don't worry you don't have to be
+
+ align:start position:0%
+don't worry you don't have to be
+ 
+
+ align:start position:0%
+don't worry you don't have to be
+delicate you can be
+
+ align:start position:0%
+delicate you can be
+ 
+
+ align:start position:0%
+delicate you can be
+strong with the pizza i'll show you now
+
+ align:start position:0%
+strong with the pizza i'll show you now
+ 
+
+ align:start position:0%
+strong with the pizza i'll show you now
+the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this isn't much dough you can
+
+ align:start position:0%
+this isn't much dough you can
+ 
+
+ align:start position:0%
+this isn't much dough you can
+you can either
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+mix it this way and then you can make
+
+ align:start position:0%
+mix it this way and then you can make
+ 
+
+ align:start position:0%
+mix it this way and then you can make
+the circle movement
+
+ align:start position:0%
+the circle movement
+ 
+
+ align:start position:0%
+the circle movement
+with your palm you see
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+good and yeah you can probably add
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and we make
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so that we can make large rectangles
+
+ align:start position:0%
+so that we can make large rectangles
+ 
+
+ align:start position:0%
+so that we can make large rectangles
+your fingers
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay in this way we are sure that there
+
+ align:start position:0%
+okay in this way we are sure that there
+ 
+
+ align:start position:0%
+okay in this way we are sure that there
+are no bubbles in the dough
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so we put the pasta
+
+ align:start position:0%
+so we put the pasta
+ 
+
+ align:start position:0%
+so we put the pasta
+and then you put mozzarella as much as
+
+ align:start position:0%
+and then you put mozzarella as much as
+ 
+
+ align:start position:0%
+and then you put mozzarella as much as
+little
+
+ align:start position:0%
+little
+ 
+
+ align:start position:0%
+little
+spice and you're gonna put the toppings
+
+ align:start position:0%
+spice and you're gonna put the toppings
+ 
+
+ align:start position:0%
+spice and you're gonna put the toppings
+your favorite toppings everything is
+
+ align:start position:0%
+your favorite toppings everything is
+ 
+
+ align:start position:0%
+your favorite toppings everything is
+allowed
+
+ align:start position:0%
+allowed
+ 
+
+ align:start position:0%
+allowed
+sprinkle them with oregano you put
+
+ align:start position:0%
+sprinkle them with oregano you put
+ 
+
+ align:start position:0%
+sprinkle them with oregano you put
+a couple of spoonful of olive oil on
+
+ align:start position:0%
+a couple of spoonful of olive oil on
+ 
+
+ align:start position:0%
+a couple of spoonful of olive oil on
+each
+
+ align:start position:0%
+each
+ 
+
+ align:start position:0%
+each
+pizza and a pinch of
+
+ align:start position:0%
+pizza and a pinch of
+ 
+
+ align:start position:0%
+pizza and a pinch of
+salad okay pasta
+
+ align:start position:0%
+salad okay pasta
+ 
+
+ align:start position:0%
+salad okay pasta
+also stopping we put it at the very
+
+ align:start position:0%
+also stopping we put it at the very
+ 
+
+ align:start position:0%
+also stopping we put it at the very
+end we don't put it the basilico
+
+ align:start position:0%
+end we don't put it the basilico
+ 
+
+ align:start position:0%
+end we don't put it the basilico
+it doesn't taste good look at troy look
+
+ align:start position:0%
+it doesn't taste good look at troy look
+ 
+
+ align:start position:0%
+it doesn't taste good look at troy look
+at troy
+
+ align:start position:0%
+at troy
+ 
+
+ align:start position:0%
+at troy
+okay oh we're not gonna make more yes
+
+ align:start position:0%
+okay oh we're not gonna make more yes
+ 
+
+ align:start position:0%
+okay oh we're not gonna make more yes
+we're gonna make smart
+
+ align:start position:0%
+we're gonna make smart
+ 
+
+ align:start position:0%
+we're gonna make smart
+no no no you guys and we'll help
+
+ align:start position:0%
+no no no you guys and we'll help
+ 
+
+ align:start position:0%
+no no no you guys and we'll help
+yourself could we add some colors
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+oh
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+they are very very tasty the taste is
+
+ align:start position:0%
+they are very very tasty the taste is
+ 
+
+ align:start position:0%
+they are very very tasty the taste is
+very intense so you don't
+
+ align:start position:0%
+very intense so you don't
+ 
+
+ align:start position:0%
+very intense so you don't
+need maybe if you want to put them you
+
+ align:start position:0%
+need maybe if you want to put them you
+ 
+
+ align:start position:0%
+need maybe if you want to put them you
+can also cut them
+
+ align:start position:0%
+can also cut them
+ 
+
+ align:start position:0%
+can also cut them
+and like little pieces in different
+
+ align:start position:0%
+and like little pieces in different
+ 
+
+ align:start position:0%
+and like little pieces in different
+locations because if you taste it if you
+
+ align:start position:0%
+locations because if you taste it if you
+ 
+
+ align:start position:0%
+locations because if you taste it if you
+take a whole lot
+
+ align:start position:0%
+take a whole lot
+ 
+
+ align:start position:0%
+take a whole lot
+it's good but not everybody like likes
+
+ align:start position:0%
+it's good but not everybody like likes
+ 
+
+ align:start position:0%
+it's good but not everybody like likes
+it because
+
+ align:start position:0%
+it because
+ 
+
+ align:start position:0%
+it because
+the taste is kind of intense if you want
+
+ align:start position:0%
+the taste is kind of intense if you want
+ 
+
+ align:start position:0%
+the taste is kind of intense if you want
+to use the prosciutto
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the top is like 400 fahrenheits and the
+
+ align:start position:0%
+the top is like 400 fahrenheits and the
+ 
+
+ align:start position:0%
+the top is like 400 fahrenheits and the
+bottom one at 500
+
+ align:start position:0%
+bottom one at 500
+ 
+
+ align:start position:0%
+bottom one at 500
+they will cook differently i made it on
+
+ align:start position:0%
+they will cook differently i made it on
+ 
+
+ align:start position:0%
+they will cook differently i made it on
+purpose so that you can
+
+ align:start position:0%
+purpose so that you can
+ 
+
+ align:start position:0%
+purpose so that you can
+decide like what you like best everybody
+
+ align:start position:0%
+decide like what you like best everybody
+ 
+
+ align:start position:0%
+decide like what you like best everybody
+has a different taste
+
+ align:start position:0%
+has a different taste
+ 
+
+ align:start position:0%
+has a different taste
+you can experiment you can make
+
+ align:start position:0%
+you can experiment you can make
+ 
+
+ align:start position:0%
+you can experiment you can make
+different thicknesses of the pizza
+
+ align:start position:0%
+different thicknesses of the pizza
+ 
+
+ align:start position:0%
+different thicknesses of the pizza
+and you can bake them at the different
+
+ align:start position:0%
+and you can bake them at the different
+ 
+
+ align:start position:0%
+and you can bake them at the different
+temperatures
+
+ align:start position:0%
+temperatures
+ 
+
+ align:start position:0%
+temperatures
+another small detail i give you the
+
+ align:start position:0%
+another small detail i give you the
+ 
+
+ align:start position:0%
+another small detail i give you the
+temperature in fahrenheit because
+
+ align:start position:0%
+temperature in fahrenheit because
+ 
+
+ align:start position:0%
+temperature in fahrenheit because
+that's what we have here in italy
+
+ align:start position:0%
+that's what we have here in italy
+ 
+
+ align:start position:0%
+that's what we have here in italy
+the temperatures are in gravity
+
+ align:start position:0%
+the temperatures are in gravity
+ 
+
+ align:start position:0%
+the temperatures are in gravity
+gradient
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+thank oh
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+bye
\ No newline at end of file
diff --git a/o84SekTsgPo.txt b/o84SekTsgPo.txt
new file mode 100644
index 0000000000000000000000000000000000000000..ce366df626957922589ee374b07b25833f7a4f66
--- /dev/null
+++ b/o84SekTsgPo.txt
@@ -0,0 +1,301 @@
+What do the growth of a plant and the rusting
+of a truck have in common? Both processes
+
+involve mass transfer. In this video, you'll
+learn how to apply the concept of a control
+
+volume and the law of conservation of mass
+to real-world scenarios.
+
+This video is part of the Conservation video
+series.
+
+In order to analyze or modify a system, it
+is important to understand how the laws of
+
+conservation place constraints on that system.
+
+Hi. My name is Mark Bathe and I am a professor
+in the Department of Biological Engineering
+
+at MIT.
+
+By watching this video, you will be able to
+apply the law of conservation of mass to real-world
+
+scenarios.
+
+Before watching this video, however; you should
+have had experience with basic reaction stoichiometry.
+
+In the 18th century, Antoine Lavoisier, a
+French scientist, showed that there is no
+
+overall change in mass when a reaction takes
+place in a sealed container.
+
+This observation is called the law of mass
+conservation.
+
+What would Lavoisier say about a plant's growth...
+...or a car rusting?
+
+Can conservation of mass be applied to these
+scenarios?
+
+Of course it can.
+
+By using a conceptual tool called a "control
+volume," we can more easily apply the law
+
+of mass conservation to these scenarios.
+
+What is a control volume? A control volume
+is a fictitious boundary that separates a
+
+system of interest from its surroundings.
+A control volume is NOT a tangible, solid
+
+boundary. Nor does the control volume have
+to be a specific shape or size. A control
+
+volume can transmit energy or mass. A control
+volume should be seen merely as a tool, and
+
+defining a control volume is a matter of convenience.
+Depending on the question being investigated
+
+some control volumes may be more convenient
+than others.
+
+Before we go back to the growing plant or
+the rusting car example, let's go through
+
+a more visual example to demonstrate the idea
+of a control volume.
+
+Here we have a sink filling with water.
+What if we wanted to know how much water is
+
+accumulating in the basin? What control volume
+might we choose to help us answer this question?
+
+Well, what if we were to define the faucet
+as our control volume? We could look at the
+
+flow into and out of the control volume. Would
+this give us enough information to figure
+
+out how much water is accumulating in our
+basin? No.
+
+What if we defined the whole bathroom as our
+control volume? We could look at the flow
+
+going through all of the plumbing in the bathroom.
+Would this give us enough information to figure
+
+out how much water is accumulating in our
+basin?
+
+Yes, but we'd also have a lot of information
+to deal with. This probably wouldn't be the
+
+most efficient way to solve the problem.
+
+What if instead we defined the basin itself
+as the control volume? Ah-ha. We could look
+
+at the flow going into and out of the control
+volume and figure out how much water is actually
+
+accumulating in our basin. We have enough
+information to figure out what we want to
+
+know, but not so much information that it
+is cumbersome to deal with.
+
+Now, we will see how we can use the concept
+of a control volume and general chemistry
+
+knowledge to better understand the application
+of the conservation of mass to the growing
+
+plant and rusting car scenarios.
+
+Back to the growing plant. Let's say that
+over some period of time, the plant grows
+
+and gains a mass of 25grams. Although the
+plant isn't living in a sealed container,
+
+we can still apply the law of mass conservation
+to the growing plant by specifying a control
+
+volume and accounting for the mass entering
+and exiting that control volume.
+
+Most plants make their food using photosynthesis.
+The overall reaction for photosynthesis is
+
+carbon dioxide plus water plus light energy
+yields glucose plus oxygen. We'll assume that
+
+the plant's mass comes from glucose and it's
+downstream products.
+
+Now please take a minute to think about what
+control volume we might specify to apply the
+
+law of mass conservation to the plant's growth.
+[short pause]
+
+If we think of the plant as our control volume,
+we can apply the law of conservation of mass
+
+to perform a mass balance on the system.
+Any mass that is accumulated in our system
+
+must equal any mass that entered the system
+minus any mass that left the system. This
+
+is the law of mass conservation.
+
+What mass is entering the control volume?
+Carbon dioxide and water.
+
+What mass is exiting the system? Oxygen.
+
+Drawing a diagram like this helps us keep
+track of the information that we know and
+
+the information that we don't know.
+
+Note that we ignored the light energy because
+we are performing a mass balance. We can substitute
+
+25 grams in for the accumulation term in the
+mass balance equation. Now please pause the
+
+video here and see if you can figure out how
+much carbon dioxide and water entered the
+
+system and how much oxygen exited the system.
+Please continue playing the video to see the
+
+worked solutions.
+
+Using basic stoichiometry, we can see that
+37 grams of carbon dioxide entered the system...
+
+15 grams of water also entered the system...
+
+And 27 grams of oxygen exited the system.
+
+We can compare these results to our mass balance
+and see that our inputs minus our output equals
+
+the mass gained by the plant.
+So, the law of mass conservation not only
+
+holds, but it gives us important insight into
+the process of a growing plant. Fantastic!
+
+Now, let's turn to our next example, that
+of a rusting car.
+
+The car has rusted, but the rust has fallen
+off of the car, resulting in a decrease in
+
+the mass of the car.
+
+Measurements show that the car has lost mass,
+but has mass really not been conserved?
+
+Let's think about this scenario a little more
+carefully. What is happening when a car rusts?
+
+Can we write an equation to explain what is
+happening chemically?
+
+Rusting happens by iron oxidation. This reaction
+can be written as 3O2 + 4Fe -> 2Fe2O3. Measurements
+
+show that the car lost 10g of mass.
+Now please take a minute to think about what
+
+control volume we might specify to apply the
+law of mass conservation to the rusting car.
+
+[short pause]
+
+If we define the car as our system or control
+volume, a concept that we introduced earlier,
+
+we can perform a mass balance on the car.
+Remember, any mass that is accumulated in
+
+our system should equal any mass that entered
+the system minus any mass that left the system.
+
+Our system, the car, lost 10g of mass. This
+is a negative accumulation.
+
+During the rusting process, did any mass enter
+our system? Yes, the mass due to the oxygen
+
+that reacted with the iron on the car's body.
+
+In our scenario, where a car has rusted and
+the rust fell off of the car, has any mass
+
+left our system? Yes. The mass of the rust,
+or iron oxide.
+
+Now please pause the video here and see if
+you can figure out how much oxygen entered
+
+the system and how much iron oxide exited
+the system. Please continue playing the video
+
+to see the worked solutions.
+
+Using basic stoichiometry, we can see that
+4.3 grams of oxygen entered the system...
+
+and 14.3 grams of iron oxide exited the system.
+
+We can compare this to our mass balance to
+see that our mass in minus our mass out equals
+
+the negative accumulation of mass of our car.
+
+Again, the law of conservation of mass has
+served as a useful tool to learn something
+
+important about our system.
+
+This video illustrated how the law of conservation
+of mass can be applied to real-world scenarios.
+
+Although real-world scenarios might seem overwhelming
+at first, we can use a problem-solving tool
+
+called a control volume to help narrow our
+focus. The law of conservation of mass allows
+
+us to perform a mass balance on the control
+volume. In other words, any mass that has
+
+accumulated in our system must equal any mass
+that entered the system minus any mass that
+
+exited the system.
+
+This simple idea will provide a basis for
+understanding systems throughout your time
+
+at SUTD and beyond.
+
+FAANTASTIC! (will have to "cut and paste"
+this audio from earlier)
\ No newline at end of file
diff --git a/pP7mt_Ie04Y.txt b/pP7mt_Ie04Y.txt
new file mode 100644
index 0000000000000000000000000000000000000000..11c9ef95f03bf4d83442c83e1cb01285cc427acd
--- /dev/null
+++ b/pP7mt_Ie04Y.txt
@@ -0,0 +1,923 @@
+align:start position:0%
+ 
+the following content is provided under
+
+ align:start position:0%
+the following content is provided under
+ 
+
+ align:start position:0%
+the following content is provided under
+a Creative Commons license your support
+
+ align:start position:0%
+a Creative Commons license your support
+ 
+
+ align:start position:0%
+a Creative Commons license your support
+will help MIT OpenCourseWare continue to
+
+ align:start position:0%
+will help MIT OpenCourseWare continue to
+ 
+
+ align:start position:0%
+will help MIT OpenCourseWare continue to
+offer high quality educational resources
+
+ align:start position:0%
+offer high quality educational resources
+ 
+
+ align:start position:0%
+offer high quality educational resources
+for free
+
+ align:start position:0%
+for free
+ 
+
+ align:start position:0%
+for free
+to make a donation or to view additional
+
+ align:start position:0%
+to make a donation or to view additional
+ 
+
+ align:start position:0%
+to make a donation or to view additional
+materials from hundreds of MIT courses
+
+ align:start position:0%
+materials from hundreds of MIT courses
+ 
+
+ align:start position:0%
+materials from hundreds of MIT courses
+visit MIT opencourseware at ocw.mit.edu
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+there's been any developments upon to
+
+ align:start position:0%
+there's been any developments upon to
+ 
+
+ align:start position:0%
+there's been any developments upon to
+see why has been helping the situation
+
+ align:start position:0%
+see why has been helping the situation
+ 
+
+ align:start position:0%
+see why has been helping the situation
+that are making the situation fit in
+
+ align:start position:0%
+that are making the situation fit in
+ 
+
+ align:start position:0%
+that are making the situation fit in
+anyway the recent areas what is it all
+
+ align:start position:0%
+anyway the recent areas what is it all
+ 
+
+ align:start position:0%
+anyway the recent areas what is it all
+claim down
+
+ align:start position:0%
+claim down
+ 
+
+ align:start position:0%
+claim down
+is there well I think it goes many
+
+ align:start position:0%
+is there well I think it goes many
+ 
+
+ align:start position:0%
+is there well I think it goes many
+directions so actually I think the most
+
+ align:start position:0%
+directions so actually I think the most
+ 
+
+ align:start position:0%
+directions so actually I think the most
+dramatic fact about the last election
+
+ align:start position:0%
+dramatic fact about the last election
+ 
+
+ align:start position:0%
+dramatic fact about the last election
+the 2016 election was not the election
+
+ align:start position:0%
+the 2016 election was not the election
+ 
+
+ align:start position:0%
+the 2016 election was not the election
+of Trump
+
+ align:start position:0%
+of Trump
+ 
+
+ align:start position:0%
+of Trump
+the most striking fact was the Sanders
+
+ align:start position:0%
+the most striking fact was the Sanders
+ 
+
+ align:start position:0%
+the most striking fact was the Sanders
+campaign I mean the fact that a
+
+ align:start position:0%
+campaign I mean the fact that a
+ 
+
+ align:start position:0%
+campaign I mean the fact that a
+billionaire was elected okay and it's
+
+ align:start position:0%
+billionaire was elected okay and it's
+ 
+
+ align:start position:0%
+billionaire was elected okay and it's
+not a big break from American history
+
+ align:start position:0%
+not a big break from American history
+ 
+
+ align:start position:0%
+not a big break from American history
+that goes on all the time but if the
+
+ align:start position:0%
+that goes on all the time but if the
+ 
+
+ align:start position:0%
+that goes on all the time but if the
+Sanders campaign broke sharply with over
+
+ align:start position:0%
+Sanders campaign broke sharply with over
+ 
+
+ align:start position:0%
+Sanders campaign broke sharply with over
+a hundred years of American political
+
+ align:start position:0%
+a hundred years of American political
+ 
+
+ align:start position:0%
+a hundred years of American political
+history I mean if we had you know media
+
+ align:start position:0%
+history I mean if we had you know media
+ 
+
+ align:start position:0%
+history I mean if we had you know media
+that we're talking about reality that
+
+ align:start position:0%
+that we're talking about reality that
+ 
+
+ align:start position:0%
+that we're talking about reality that
+would be the headline American elections
+
+ align:start position:0%
+would be the headline American elections
+ 
+
+ align:start position:0%
+would be the headline American elections
+are brought this plenty of substantial
+
+ align:start position:0%
+are brought this plenty of substantial
+ 
+
+ align:start position:0%
+are brought this plenty of substantial
+political mainstream political science
+
+ align:start position:0%
+political mainstream political science
+ 
+
+ align:start position:0%
+political mainstream political science
+research on this now if you look just at
+
+ align:start position:0%
+research on this now if you look just at
+ 
+
+ align:start position:0%
+research on this now if you look just at
+simple variables like say campaign
+
+ align:start position:0%
+simple variables like say campaign
+ 
+
+ align:start position:0%
+simple variables like say campaign
+funding something as simple as that
+
+ align:start position:0%
+funding something as simple as that
+ 
+
+ align:start position:0%
+funding something as simple as that
+the predictability of electability by
+
+ align:start position:0%
+the predictability of electability by
+ 
+
+ align:start position:0%
+the predictability of electability by
+campaign funding is literally almost a
+
+ align:start position:0%
+campaign funding is literally almost a
+ 
+
+ align:start position:0%
+campaign funding is literally almost a
+straight line there's a recent study by
+
+ align:start position:0%
+straight line there's a recent study by
+ 
+
+ align:start position:0%
+straight line there's a recent study by
+Tom Ferguson over to UMass one of the
+
+ align:start position:0%
+Tom Ferguson over to UMass one of the
+ 
+
+ align:start position:0%
+Tom Ferguson over to UMass one of the
+main scholars it works on this who
+
+ align:start position:0%
+main scholars it works on this who
+ 
+
+ align:start position:0%
+main scholars it works on this who
+studied congressional elected for
+
+ align:start position:0%
+studied congressional elected for
+ 
+
+ align:start position:0%
+studied congressional elected for
+presidential elections have been shown
+
+ align:start position:0%
+presidential elections have been shown
+ 
+
+ align:start position:0%
+presidential elections have been shown
+for a long time but there was the first
+
+ align:start position:0%
+for a long time but there was the first
+ 
+
+ align:start position:0%
+for a long time but there was the first
+main study of congressional elections
+
+ align:start position:0%
+main study of congressional elections
+ 
+
+ align:start position:0%
+main study of congressional elections
+they went from 1980 to the present all
+
+ align:start position:0%
+they went from 1980 to the present all
+ 
+
+ align:start position:0%
+they went from 1980 to the present all
+over the country simply asking what's
+
+ align:start position:0%
+over the country simply asking what's
+ 
+
+ align:start position:0%
+over the country simply asking what's
+the relation between campaign spending
+
+ align:start position:0%
+the relation between campaign spending
+ 
+
+ align:start position:0%
+the relation between campaign spending
+and elect
+
+ align:start position:0%
+and elect
+ 
+
+ align:start position:0%
+and elect
+ability and it is literally a straight
+
+ align:start position:0%
+ability and it is literally a straight
+ 
+
+ align:start position:0%
+ability and it is literally a straight
+line you just don't get results like
+
+ align:start position:0%
+line you just don't get results like
+ 
+
+ align:start position:0%
+line you just don't get results like
+that in the social sciences the more
+
+ align:start position:0%
+that in the social sciences the more
+ 
+
+ align:start position:0%
+that in the social sciences the more
+campaign spending the more you get
+
+ align:start position:0%
+campaign spending the more you get
+ 
+
+ align:start position:0%
+campaign spending the more you get
+elected and that goes back well it well
+
+ align:start position:0%
+elected and that goes back well it well
+ 
+
+ align:start position:0%
+elected and that goes back well it well
+into the late 19th century act is a
+
+ align:start position:0%
+into the late 19th century act is a
+ 
+
+ align:start position:0%
+into the late 19th century act is a
+famous campaign manager Mark Hannah the
+
+ align:start position:0%
+famous campaign manager Mark Hannah the
+ 
+
+ align:start position:0%
+famous campaign manager Mark Hannah the
+back 1890s he was asked once what do you
+
+ align:start position:0%
+back 1890s he was asked once what do you
+ 
+
+ align:start position:0%
+back 1890s he was asked once what do you
+have with the what's the secret for
+
+ align:start position:0%
+have with the what's the secret for
+ 
+
+ align:start position:0%
+have with the what's the secret for
+running a successful election campaign
+
+ align:start position:0%
+running a successful election campaign
+ 
+
+ align:start position:0%
+running a successful election campaign
+and he said you have to have two things
+
+ align:start position:0%
+and he said you have to have two things
+ 
+
+ align:start position:0%
+and he said you have to have two things
+the first one is money and I can't
+
+ align:start position:0%
+the first one is money and I can't
+ 
+
+ align:start position:0%
+the first one is money and I can't
+remember the second one that's American
+
+ align:start position:0%
+remember the second one that's American
+ 
+
+ align:start position:0%
+remember the second one that's American
+politics overwhelming near-certainty
+
+ align:start position:0%
+politics overwhelming near-certainty
+ 
+
+ align:start position:0%
+politics overwhelming near-certainty
+well all of a sudden you get a guy who's
+
+ align:start position:0%
+well all of a sudden you get a guy who's
+ 
+
+ align:start position:0%
+well all of a sudden you get a guy who's
+unknown has no support from any of the
+
+ align:start position:0%
+unknown has no support from any of the
+ 
+
+ align:start position:0%
+unknown has no support from any of the
+sources of wealth no support from the
+
+ align:start position:0%
+sources of wealth no support from the
+ 
+
+ align:start position:0%
+sources of wealth no support from the
+wealthy you know corporate support
+
+ align:start position:0%
+wealthy you know corporate support
+ 
+
+ align:start position:0%
+wealthy you know corporate support
+dismissed by the media's ridiculous very
+
+ align:start position:0%
+dismissed by the media's ridiculous very
+ 
+
+ align:start position:0%
+dismissed by the media's ridiculous very
+negative media campaign he was basically
+
+ align:start position:0%
+negative media campaign he was basically
+ 
+
+ align:start position:0%
+negative media campaign he was basically
+unknown even used the scare word
+
+ align:start position:0%
+unknown even used the scare word
+ 
+
+ align:start position:0%
+unknown even used the scare word
+socialist he would have won the
+
+ align:start position:0%
+socialist he would have won the
+ 
+
+ align:start position:0%
+socialist he would have won the
+Democratic Party nomination if it hadn't
+
+ align:start position:0%
+Democratic Party nomination if it hadn't
+ 
+
+ align:start position:0%
+Democratic Party nomination if it hadn't
+been for the Clinton Obama shenanigans
+
+ align:start position:0%
+been for the Clinton Obama shenanigans
+ 
+
+ align:start position:0%
+been for the Clinton Obama shenanigans
+to keep the party from reflecting its
+
+ align:start position:0%
+to keep the party from reflecting its
+ 
+
+ align:start position:0%
+to keep the party from reflecting its
+popular constituency that's an
+
+ align:start position:0%
+popular constituency that's an
+ 
+
+ align:start position:0%
+popular constituency that's an
+incredible break from history and right
+
+ align:start position:0%
+incredible break from history and right
+ 
+
+ align:start position:0%
+incredible break from history and right
+now incidentally he's by far the most
+
+ align:start position:0%
+now incidentally he's by far the most
+ 
+
+ align:start position:0%
+now incidentally he's by far the most
+popular political figure in the country
+
+ align:start position:0%
+popular political figure in the country
+ 
+
+ align:start position:0%
+popular political figure in the country
+way above anyone else well those are
+
+ align:start position:0%
+way above anyone else well those are
+ 
+
+ align:start position:0%
+way above anyone else well those are
+signs that other things are chained
+
+ align:start position:0%
+signs that other things are chained
+ 
+
+ align:start position:0%
+signs that other things are chained
+especially among young people is way out
+
+ align:start position:0%
+especially among young people is way out
+ 
+
+ align:start position:0%
+especially among young people is way out
+that's the future of electorate so these
+
+ align:start position:0%
+that's the future of electorate so these
+ 
+
+ align:start position:0%
+that's the future of electorate so these
+are things that are going off in the
+
+ align:start position:0%
+are things that are going off in the
+ 
+
+ align:start position:0%
+are things that are going off in the
+other direction there's plenty of
+
+ align:start position:0%
+other direction there's plenty of
+ 
+
+ align:start position:0%
+other direction there's plenty of
+opportunities if they're grasped and
+
+ align:start position:0%
+opportunities if they're grasped and
+ 
+
+ align:start position:0%
+opportunities if they're grasped and
+it's kind of easy to sink into sort of
+
+ align:start position:0%
+it's kind of easy to sink into sort of
+ 
+
+ align:start position:0%
+it's kind of easy to sink into sort of
+hopelessness what's the point no but
+
+ align:start position:0%
+hopelessness what's the point no but
+ 
+
+ align:start position:0%
+hopelessness what's the point no but
+it's just really bad
+
+ align:start position:0%
+it's just really bad
+ 
+
+ align:start position:0%
+it's just really bad
+mistake first of all the issues are
+
+ align:start position:0%
+mistake first of all the issues are
+ 
+
+ align:start position:0%
+mistake first of all the issues are
+extremely important done there's an
+
+ align:start position:0%
+extremely important done there's an
+ 
+
+ align:start position:0%
+extremely important done there's an
+awful lot can be done even in the kind
+
+ align:start position:0%
+awful lot can be done even in the kind
+ 
+
+ align:start position:0%
+awful lot can be done even in the kind
+of thing that Harley hoshide was doing
+
+ align:start position:0%
+of thing that Harley hoshide was doing
+ 
+
+ align:start position:0%
+of thing that Harley hoshide was doing
+reaching people who were deeply embedded
+
+ align:start position:0%
+reaching people who were deeply embedded
+ 
+
+ align:start position:0%
+reaching people who were deeply embedded
+in the the ultra red constituency a
+
+ align:start position:0%
+in the the ultra red constituency a
+ 
+
+ align:start position:0%
+in the the ultra red constituency a
+deeply religious conservative
+
+ align:start position:0%
+deeply religious conservative
+ 
+
+ align:start position:0%
+deeply religious conservative
+traditional a/d government for the
+
+ align:start position:0%
+traditional a/d government for the
+ 
+
+ align:start position:0%
+traditional a/d government for the
+reasons that they see which you can
+
+ align:start position:0%
+reasons that they see which you can
+ 
+
+ align:start position:0%
+reasons that they see which you can
+understand them be changed incidentally
+
+ align:start position:0%
+understand them be changed incidentally
+ 
+
+ align:start position:0%
+understand them be changed incidentally
+if you look back in the past these same
+
+ align:start position:0%
+if you look back in the past these same
+ 
+
+ align:start position:0%
+if you look back in the past these same
+sectors of the population where the most
+
+ align:start position:0%
+sectors of the population where the most
+ 
+
+ align:start position:0%
+sectors of the population where the most
+carried forward the most extreme radical
+
+ align:start position:0%
+carried forward the most extreme radical
+ 
+
+ align:start position:0%
+carried forward the most extreme radical
+Democratic programs in American history
+
+ align:start position:0%
+Democratic programs in American history
+ 
+
+ align:start position:0%
+Democratic programs in American history
+the term populism is thrown around now
+
+ align:start position:0%
+the term populism is thrown around now
+ 
+
+ align:start position:0%
+the term populism is thrown around now
+but it used to mean something and the
+
+ align:start position:0%
+but it used to mean something and the
+ 
+
+ align:start position:0%
+but it used to mean something and the
+populist movement in the United States
+
+ align:start position:0%
+populist movement in the United States
+ 
+
+ align:start position:0%
+populist movement in the United States
+which began with farmers and Texas and
+
+ align:start position:0%
+which began with farmers and Texas and
+ 
+
+ align:start position:0%
+which began with farmers and Texas and
+spread through the Midwest Kansas and
+
+ align:start position:0%
+spread through the Midwest Kansas and
+ 
+
+ align:start position:0%
+spread through the Midwest Kansas and
+places like that was a really powerful
+
+ align:start position:0%
+places like that was a really powerful
+ 
+
+ align:start position:0%
+places like that was a really powerful
+radical democratic movement
+
+ align:start position:0%
+radical democratic movement
+ 
+
+ align:start position:0%
+radical democratic movement
+all linked up with the Knights of Labor
+
+ align:start position:0%
+all linked up with the Knights of Labor
+ 
+
+ align:start position:0%
+all linked up with the Knights of Labor
+the main labor movement whose slogan was
+
+ align:start position:0%
+the main labor movement whose slogan was
+ 
+
+ align:start position:0%
+the main labor movement whose slogan was
+that working people or owned and run the
+
+ align:start position:0%
+that working people or owned and run the
+ 
+
+ align:start position:0%
+that working people or owned and run the
+factories I mean though it was smashed
+
+ align:start position:0%
+factories I mean though it was smashed
+ 
+
+ align:start position:0%
+factories I mean though it was smashed
+by force finally but this is by far the
+
+ align:start position:0%
+by force finally but this is by far the
+ 
+
+ align:start position:0%
+by force finally but this is by far the
+most real democratic movement in
+
+ align:start position:0%
+most real democratic movement in
+ 
+
+ align:start position:0%
+most real democratic movement in
+American history and maybe the world and
+
+ align:start position:0%
+American history and maybe the world and
+ 
+
+ align:start position:0%
+American history and maybe the world and
+it comes out of the Texas and Kansas
+
+ align:start position:0%
+it comes out of the Texas and Kansas
+ 
+
+ align:start position:0%
+it comes out of the Texas and Kansas
+farmers same people
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+you
\ No newline at end of file
diff --git a/ppxK4R8XWfU.txt b/ppxK4R8XWfU.txt
new file mode 100644
index 0000000000000000000000000000000000000000..fd333fbc9dca356c0c697be4653b1e0bd4a12e73
--- /dev/null
+++ b/ppxK4R8XWfU.txt
@@ -0,0 +1,17107 @@
+align:start position:0%
+ 
+so we're talking about navigation how
+
+ align:start position:0%
+so we're talking about navigation how
+ 
+
+ align:start position:0%
+so we're talking about navigation how
+you know where you are and how you can
+
+ align:start position:0%
+you know where you are and how you can
+ 
+
+ align:start position:0%
+you know where you are and how you can
+get from here to wherever else you want
+
+ align:start position:0%
+get from here to wherever else you want
+ 
+
+ align:start position:0%
+get from here to wherever else you want
+to go
+
+ align:start position:0%
+to go
+ 
+
+ align:start position:0%
+to go
+and last time we talked about just the
+
+ align:start position:0%
+and last time we talked about just the
+ 
+
+ align:start position:0%
+and last time we talked about just the
+general problems that arise in
+
+ align:start position:0%
+general problems that arise in
+ 
+
+ align:start position:0%
+general problems that arise in
+navigation and we talked about the para
+
+ align:start position:0%
+navigation and we talked about the para
+ 
+
+ align:start position:0%
+navigation and we talked about the para
+hippocampal place area
+
+ align:start position:0%
+hippocampal place area
+ 
+
+ align:start position:0%
+hippocampal place area
+and other
+
+ align:start position:0%
+and other
+ 
+
+ align:start position:0%
+and other
+parts of the brain that are involved in
+
+ align:start position:0%
+parts of the brain that are involved in
+ 
+
+ align:start position:0%
+parts of the brain that are involved in
+navigation so today we're going to
+
+ align:start position:0%
+navigation so today we're going to
+ 
+
+ align:start position:0%
+navigation so today we're going to
+continue that but we're going to talk
+
+ align:start position:0%
+continue that but we're going to talk
+ 
+
+ align:start position:0%
+continue that but we're going to talk
+more about the actual populations of
+
+ align:start position:0%
+more about the actual populations of
+ 
+
+ align:start position:0%
+more about the actual populations of
+neurons in your head that are involved
+
+ align:start position:0%
+neurons in your head that are involved
+ 
+
+ align:start position:0%
+neurons in your head that are involved
+in doing this and we'll talk about a
+
+ align:start position:0%
+in doing this and we'll talk about a
+ 
+
+ align:start position:0%
+in doing this and we'll talk about a
+particular aspect of the problem of
+
+ align:start position:0%
+particular aspect of the problem of
+ 
+
+ align:start position:0%
+particular aspect of the problem of
+navigation which is called reorientation
+
+ align:start position:0%
+navigation which is called reorientation
+ 
+
+ align:start position:0%
+navigation which is called reorientation
+that's what happens when you lose your
+
+ align:start position:0%
+that's what happens when you lose your
+ 
+
+ align:start position:0%
+that's what happens when you lose your
+bearings and you need to figure out
+
+ align:start position:0%
+bearings and you need to figure out
+ 
+
+ align:start position:0%
+bearings and you need to figure out
+where you are again reset your
+
+ align:start position:0%
+where you are again reset your
+ 
+
+ align:start position:0%
+where you are again reset your
+internal
+
+ align:start position:0%
+internal
+ 
+
+ align:start position:0%
+internal
+map of yours of where you are
+
+ align:start position:0%
+map of yours of where you are
+ 
+
+ align:start position:0%
+map of yours of where you are
+and then we'll talk about the idea that
+
+ align:start position:0%
+and then we'll talk about the idea that
+ 
+
+ align:start position:0%
+and then we'll talk about the idea that
+this whole system for navigation cool as
+
+ align:start position:0%
+this whole system for navigation cool as
+ 
+
+ align:start position:0%
+this whole system for navigation cool as
+it is and fascinating as navigation
+
+ align:start position:0%
+it is and fascinating as navigation
+ 
+
+ align:start position:0%
+it is and fascinating as navigation
+itself is is even more interesting
+
+ align:start position:0%
+itself is is even more interesting
+ 
+
+ align:start position:0%
+itself is is even more interesting
+because there's increasing evidence that
+
+ align:start position:0%
+because there's increasing evidence that
+ 
+
+ align:start position:0%
+because there's increasing evidence that
+we use that same system for lots of
+
+ align:start position:0%
+we use that same system for lots of
+ 
+
+ align:start position:0%
+we use that same system for lots of
+other aspects of high-level cognition
+
+ align:start position:0%
+other aspects of high-level cognition
+ 
+
+ align:start position:0%
+other aspects of high-level cognition
+that have nothing to do with space per
+
+ align:start position:0%
+that have nothing to do with space per
+ 
+
+ align:start position:0%
+that have nothing to do with space per
+se
+
+ align:start position:0%
+se
+ 
+
+ align:start position:0%
+se
+okay that's the and then we'll have a
+
+ align:start position:0%
+okay that's the and then we'll have a
+ 
+
+ align:start position:0%
+okay that's the and then we'll have a
+quiz short quiz
+
+ align:start position:0%
+quiz short quiz
+ 
+
+ align:start position:0%
+quiz short quiz
+that's the agenda here we go so the
+
+ align:start position:0%
+that's the agenda here we go so the
+ 
+
+ align:start position:0%
+that's the agenda here we go so the
+basic problems of navigation are one
+
+ align:start position:0%
+basic problems of navigation are one
+ 
+
+ align:start position:0%
+basic problems of navigation are one
+where am i
+
+ align:start position:0%
+where am i
+ 
+
+ align:start position:0%
+where am i
+and two how do i get from here to
+
+ align:start position:0%
+and two how do i get from here to
+ 
+
+ align:start position:0%
+and two how do i get from here to
+wherever else i want to go
+
+ align:start position:0%
+wherever else i want to go
+ 
+
+ align:start position:0%
+wherever else i want to go
+and as i mentioned last time we can
+
+ align:start position:0%
+and as i mentioned last time we can
+ 
+
+ align:start position:0%
+and as i mentioned last time we can
+break down each of these into a bunch of
+
+ align:start position:0%
+break down each of these into a bunch of
+ 
+
+ align:start position:0%
+break down each of these into a bunch of
+different components and facets of that
+
+ align:start position:0%
+different components and facets of that
+ 
+
+ align:start position:0%
+different components and facets of that
+question so when we want to know where
+
+ align:start position:0%
+question so when we want to know where
+ 
+
+ align:start position:0%
+question so when we want to know where
+we are
+
+ align:start position:0%
+we are
+ 
+
+ align:start position:0%
+we are
+that can that can involve recognizing a
+
+ align:start position:0%
+that can that can involve recognizing a
+ 
+
+ align:start position:0%
+that can that can involve recognizing a
+familiar location so if you see a
+
+ align:start position:0%
+familiar location so if you see a
+ 
+
+ align:start position:0%
+familiar location so if you see a
+photograph or you were plunked down
+
+ align:start position:0%
+photograph or you were plunked down
+ 
+
+ align:start position:0%
+photograph or you were plunked down
+spontaneously in an environment
+
+ align:start position:0%
+spontaneously in an environment
+ 
+
+ align:start position:0%
+spontaneously in an environment
+someplace you know you would visually
+
+ align:start position:0%
+someplace you know you would visually
+ 
+
+ align:start position:0%
+someplace you know you would visually
+recognize it and that would be one way
+
+ align:start position:0%
+recognize it and that would be one way
+ 
+
+ align:start position:0%
+recognize it and that would be one way
+to know where you were like this is my
+
+ align:start position:0%
+to know where you were like this is my
+ 
+
+ align:start position:0%
+to know where you were like this is my
+living room
+
+ align:start position:0%
+living room
+ 
+
+ align:start position:0%
+living room
+even if that location is unfamiliar and
+
+ align:start position:0%
+even if that location is unfamiliar and
+ 
+
+ align:start position:0%
+even if that location is unfamiliar and
+you're plunked down at random you still
+
+ align:start position:0%
+you're plunked down at random you still
+ 
+
+ align:start position:0%
+you're plunked down at random you still
+have some idea of what kind of a place
+
+ align:start position:0%
+have some idea of what kind of a place
+ 
+
+ align:start position:0%
+have some idea of what kind of a place
+this is am i in a natural environment an
+
+ align:start position:0%
+this is am i in a natural environment an
+ 
+
+ align:start position:0%
+this is am i in a natural environment an
+urban environment am i inside am i
+
+ align:start position:0%
+urban environment am i inside am i
+ 
+
+ align:start position:0%
+urban environment am i inside am i
+outside et cetera
+
+ align:start position:0%
+outside et cetera
+ 
+
+ align:start position:0%
+outside et cetera
+and finally you had you would have some
+
+ align:start position:0%
+and finally you had you would have some
+ 
+
+ align:start position:0%
+and finally you had you would have some
+sense of where you are with respect to
+
+ align:start position:0%
+sense of where you are with respect to
+ 
+
+ align:start position:0%
+sense of where you are with respect to
+the immediate bounding
+
+ align:start position:0%
+the immediate bounding
+ 
+
+ align:start position:0%
+the immediate bounding
+structures in your immediate environment
+
+ align:start position:0%
+structures in your immediate environment
+ 
+
+ align:start position:0%
+structures in your immediate environment
+like for example where you are in this
+
+ align:start position:0%
+like for example where you are in this
+ 
+
+ align:start position:0%
+like for example where you are in this
+room like as i'm talking to you right
+
+ align:start position:0%
+room like as i'm talking to you right
+ 
+
+ align:start position:0%
+room like as i'm talking to you right
+now i'm aware that there's a wall behind
+
+ align:start position:0%
+now i'm aware that there's a wall behind
+ 
+
+ align:start position:0%
+now i'm aware that there's a wall behind
+me right
+
+ align:start position:0%
+me right
+ 
+
+ align:start position:0%
+me right
+that kind of immediate
+
+ align:start position:0%
+that kind of immediate
+ 
+
+ align:start position:0%
+that kind of immediate
+spatial
+
+ align:start position:0%
+spatial
+ 
+
+ align:start position:0%
+spatial
+location
+
+ align:start position:0%
+location
+ 
+
+ align:start position:0%
+location
+in terms of questions that arise when we
+
+ align:start position:0%
+in terms of questions that arise when we
+ 
+
+ align:start position:0%
+in terms of questions that arise when we
+have to figure out how do we get from
+
+ align:start position:0%
+have to figure out how do we get from
+ 
+
+ align:start position:0%
+have to figure out how do we get from
+here to wherever else we want to go
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+if you can directly see or hear your
+
+ align:start position:0%
+if you can directly see or hear your
+ 
+
+ align:start position:0%
+if you can directly see or hear your
+destination then you have the simplest
+
+ align:start position:0%
+destination then you have the simplest
+ 
+
+ align:start position:0%
+destination then you have the simplest
+possible kind of navigation strategy you
+
+ align:start position:0%
+possible kind of navigation strategy you
+ 
+
+ align:start position:0%
+possible kind of navigation strategy you
+just go toward that thing okay that's
+
+ align:start position:0%
+just go toward that thing okay that's
+ 
+
+ align:start position:0%
+just go toward that thing okay that's
+called beaconing and it's like the
+
+ align:start position:0%
+called beaconing and it's like the
+ 
+
+ align:start position:0%
+called beaconing and it's like the
+minimalist case works great if you can
+
+ align:start position:0%
+minimalist case works great if you can
+ 
+
+ align:start position:0%
+minimalist case works great if you can
+see or hear your destination
+
+ align:start position:0%
+see or hear your destination
+ 
+
+ align:start position:0%
+see or hear your destination
+but when you can't
+
+ align:start position:0%
+but when you can't
+ 
+
+ align:start position:0%
+but when you can't
+you need to know
+
+ align:start position:0%
+you need to know
+ 
+
+ align:start position:0%
+you need to know
+where am i in this in my broader
+
+ align:start position:0%
+where am i in this in my broader
+ 
+
+ align:start position:0%
+where am i in this in my broader
+understanding of the layout of my
+
+ align:start position:0%
+understanding of the layout of my
+ 
+
+ align:start position:0%
+understanding of the layout of my
+environment and where is my goal and for
+
+ align:start position:0%
+environment and where is my goal and for
+ 
+
+ align:start position:0%
+environment and where is my goal and for
+that you need a mental map of your
+
+ align:start position:0%
+that you need a mental map of your
+ 
+
+ align:start position:0%
+that you need a mental map of your
+environment and we'll talk more about
+
+ align:start position:0%
+environment and we'll talk more about
+ 
+
+ align:start position:0%
+environment and we'll talk more about
+that today that's why it's in red
+
+ align:start position:0%
+that today that's why it's in red
+ 
+
+ align:start position:0%
+that today that's why it's in red
+you also need to know your current
+
+ align:start position:0%
+you also need to know your current
+ 
+
+ align:start position:0%
+you also need to know your current
+heading in that environment it's not
+
+ align:start position:0%
+heading in that environment it's not
+ 
+
+ align:start position:0%
+heading in that environment it's not
+enough to know in my map of the world i
+
+ align:start position:0%
+enough to know in my map of the world i
+ 
+
+ align:start position:0%
+enough to know in my map of the world i
+am here with a dot you need to know
+
+ align:start position:0%
+am here with a dot you need to know
+ 
+
+ align:start position:0%
+am here with a dot you need to know
+which way you're facing in that map of
+
+ align:start position:0%
+which way you're facing in that map of
+ 
+
+ align:start position:0%
+which way you're facing in that map of
+the world in order to plan your
+
+ align:start position:0%
+the world in order to plan your
+ 
+
+ align:start position:0%
+the world in order to plan your
+navigation we'll talk about that too
+
+ align:start position:0%
+navigation we'll talk about that too
+ 
+
+ align:start position:0%
+navigation we'll talk about that too
+we also need to know what routes are
+
+ align:start position:0%
+we also need to know what routes are
+ 
+
+ align:start position:0%
+we also need to know what routes are
+possible from here so i may want to go
+
+ align:start position:0%
+possible from here so i may want to go
+ 
+
+ align:start position:0%
+possible from here so i may want to go
+over to stata and get a cup of coffee
+
+ align:start position:0%
+over to stata and get a cup of coffee
+ 
+
+ align:start position:0%
+over to stata and get a cup of coffee
+but i can't go this way i got to go
+
+ align:start position:0%
+but i can't go this way i got to go
+ 
+
+ align:start position:0%
+but i can't go this way i got to go
+around because i can't go through that
+
+ align:start position:0%
+around because i can't go through that
+ 
+
+ align:start position:0%
+around because i can't go through that
+glass okay and so finally that this
+
+ align:start position:0%
+glass okay and so finally that this
+ 
+
+ align:start position:0%
+glass okay and so finally that this
+whole magnificent system that enables us
+
+ align:start position:0%
+whole magnificent system that enables us
+ 
+
+ align:start position:0%
+whole magnificent system that enables us
+to process all this stuff works pretty
+
+ align:start position:0%
+to process all this stuff works pretty
+ 
+
+ align:start position:0%
+to process all this stuff works pretty
+impressively but every once in a while
+
+ align:start position:0%
+impressively but every once in a while
+ 
+
+ align:start position:0%
+impressively but every once in a while
+something will go wrong and it will you
+
+ align:start position:0%
+something will go wrong and it will you
+ 
+
+ align:start position:0%
+something will go wrong and it will you
+know get the wrong signal and then we're
+
+ align:start position:0%
+know get the wrong signal and then we're
+ 
+
+ align:start position:0%
+know get the wrong signal and then we're
+lost and so then we need a way to regain
+
+ align:start position:0%
+lost and so then we need a way to regain
+ 
+
+ align:start position:0%
+lost and so then we need a way to regain
+our bearings and we'll talk about that
+
+ align:start position:0%
+our bearings and we'll talk about that
+ 
+
+ align:start position:0%
+our bearings and we'll talk about that
+too
+
+ align:start position:0%
+too
+ 
+
+ align:start position:0%
+too
+um so
+
+ align:start position:0%
+um so
+ 
+
+ align:start position:0%
+um so
+last time i talked about a bunch of
+
+ align:start position:0%
+last time i talked about a bunch of
+ 
+
+ align:start position:0%
+last time i talked about a bunch of
+brain regions that are implicated in
+
+ align:start position:0%
+brain regions that are implicated in
+ 
+
+ align:start position:0%
+brain regions that are implicated in
+perceiving scenes and in navigation
+
+ align:start position:0%
+perceiving scenes and in navigation
+ 
+
+ align:start position:0%
+perceiving scenes and in navigation
+we talked about the perihipic apple
+
+ align:start position:0%
+we talked about the perihipic apple
+ 
+
+ align:start position:0%
+we talked about the perihipic apple
+place area right here and this region
+
+ align:start position:0%
+place area right here and this region
+ 
+
+ align:start position:0%
+place area right here and this region
+over here formerly known as tos now
+
+ align:start position:0%
+over here formerly known as tos now
+ 
+
+ align:start position:0%
+over here formerly known as tos now
+known as opa you don't need to remember
+
+ align:start position:0%
+known as opa you don't need to remember
+ 
+
+ align:start position:0%
+known as opa you don't need to remember
+all that it's the bit that's out on the
+
+ align:start position:0%
+all that it's the bit that's out on the
+ 
+
+ align:start position:0%
+all that it's the bit that's out on the
+lateral surface that we can zap because
+
+ align:start position:0%
+lateral surface that we can zap because
+ 
+
+ align:start position:0%
+lateral surface that we can zap because
+it's out there
+
+ align:start position:0%
+it's out there
+ 
+
+ align:start position:0%
+it's out there
+and both of those regions seem to be
+
+ align:start position:0%
+and both of those regions seem to be
+ 
+
+ align:start position:0%
+and both of those regions seem to be
+involved broadly in perceiving the shape
+
+ align:start position:0%
+involved broadly in perceiving the shape
+ 
+
+ align:start position:0%
+involved broadly in perceiving the shape
+of space around you
+
+ align:start position:0%
+of space around you
+ 
+
+ align:start position:0%
+of space around you
+we also talked a bit about retrosplenial
+
+ align:start position:0%
+we also talked a bit about retrosplenial
+ 
+
+ align:start position:0%
+we also talked a bit about retrosplenial
+cortex that region that's hiding in the
+
+ align:start position:0%
+cortex that region that's hiding in the
+ 
+
+ align:start position:0%
+cortex that region that's hiding in the
+sulcus here that you can see better when
+
+ align:start position:0%
+sulcus here that you can see better when
+ 
+
+ align:start position:0%
+sulcus here that you can see better when
+you mathematically unfold the sulcus
+
+ align:start position:0%
+you mathematically unfold the sulcus
+ 
+
+ align:start position:0%
+you mathematically unfold the sulcus
+there it is responds more to scenes and
+
+ align:start position:0%
+there it is responds more to scenes and
+ 
+
+ align:start position:0%
+there it is responds more to scenes and
+objects and that region seems to be
+
+ align:start position:0%
+objects and that region seems to be
+ 
+
+ align:start position:0%
+objects and that region seems to be
+involved in something like getting your
+
+ align:start position:0%
+involved in something like getting your
+ 
+
+ align:start position:0%
+involved in something like getting your
+bearings that is the location and
+
+ align:start position:0%
+bearings that is the location and
+ 
+
+ align:start position:0%
+bearings that is the location and
+orientation of where you are
+
+ align:start position:0%
+orientation of where you are
+ 
+
+ align:start position:0%
+orientation of where you are
+with respect to your cognitive map and
+
+ align:start position:0%
+with respect to your cognitive map and
+ 
+
+ align:start position:0%
+with respect to your cognitive map and
+environment okay so to make that a
+
+ align:start position:0%
+environment okay so to make that a
+ 
+
+ align:start position:0%
+environment okay so to make that a
+little more vivid i gave you one
+
+ align:start position:0%
+little more vivid i gave you one
+ 
+
+ align:start position:0%
+little more vivid i gave you one
+description of a patient before but
+
+ align:start position:0%
+description of a patient before but
+ 
+
+ align:start position:0%
+description of a patient before but
+here's from another study
+
+ align:start position:0%
+here's from another study
+ 
+
+ align:start position:0%
+here's from another study
+patients with damage to retrosplenial
+
+ align:start position:0%
+patients with damage to retrosplenial
+ 
+
+ align:start position:0%
+patients with damage to retrosplenial
+cortex
+
+ align:start position:0%
+cortex
+ 
+
+ align:start position:0%
+cortex
+so here's from a recent article in every
+
+ align:start position:0%
+so here's from a recent article in every
+ 
+
+ align:start position:0%
+so here's from a recent article in every
+case the patient with this damage was
+
+ align:start position:0%
+case the patient with this damage was
+ 
+
+ align:start position:0%
+case the patient with this damage was
+able to recognize landmarks in their
+
+ align:start position:0%
+able to recognize landmarks in their
+ 
+
+ align:start position:0%
+able to recognize landmarks in their
+neighborhoods and retained a sense of
+
+ align:start position:0%
+neighborhoods and retained a sense of
+ 
+
+ align:start position:0%
+neighborhoods and retained a sense of
+familiarity i know that place that's the
+
+ align:start position:0%
+familiarity i know that place that's the
+ 
+
+ align:start position:0%
+familiarity i know that place that's the
+coffee shop five blocks from my house
+
+ align:start position:0%
+coffee shop five blocks from my house
+ 
+
+ align:start position:0%
+coffee shop five blocks from my house
+right but despite that
+
+ align:start position:0%
+right but despite that
+ 
+
+ align:start position:0%
+right but despite that
+none of those patients were able to find
+
+ align:start position:0%
+none of those patients were able to find
+ 
+
+ align:start position:0%
+none of those patients were able to find
+their way in familiar environments and
+
+ align:start position:0%
+their way in familiar environments and
+ 
+
+ align:start position:0%
+their way in familiar environments and
+all but one were unable to learn new
+
+ align:start position:0%
+all but one were unable to learn new
+ 
+
+ align:start position:0%
+all but one were unable to learn new
+routes so they can recognize visual the
+
+ align:start position:0%
+routes so they can recognize visual the
+ 
+
+ align:start position:0%
+routes so they can recognize visual the
+visual form of a particular place but
+
+ align:start position:0%
+visual form of a particular place but
+ 
+
+ align:start position:0%
+visual form of a particular place but
+they don't know how to relate that to
+
+ align:start position:0%
+they don't know how to relate that to
+ 
+
+ align:start position:0%
+they don't know how to relate that to
+their cognitive map of the world and
+
+ align:start position:0%
+their cognitive map of the world and
+ 
+
+ align:start position:0%
+their cognitive map of the world and
+their therefore plan a route from there
+
+ align:start position:0%
+their therefore plan a route from there
+ 
+
+ align:start position:0%
+their therefore plan a route from there
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+so um the part that i only alluded to at
+
+ align:start position:0%
+so um the part that i only alluded to at
+ 
+
+ align:start position:0%
+so um the part that i only alluded to at
+the end yes question
+
+ align:start position:0%
+the end yes question
+ 
+
+ align:start position:0%
+the end yes question
+okay is the
+
+ align:start position:0%
+okay is the
+ 
+
+ align:start position:0%
+okay is the
+retros cortex home to the clock on the
+
+ align:start position:0%
+retros cortex home to the clock on the
+ 
+
+ align:start position:0%
+retros cortex home to the clock on the
+cops or is it
+
+ align:start position:0%
+cops or is it
+ 
+
+ align:start position:0%
+cops or is it
+great question we don't exactly know the
+
+ align:start position:0%
+great question we don't exactly know the
+ 
+
+ align:start position:0%
+great question we don't exactly know the
+typical story is that the home of the
+
+ align:start position:0%
+typical story is that the home of the
+ 
+
+ align:start position:0%
+typical story is that the home of the
+cognitive map is the hippocampus which
+
+ align:start position:0%
+cognitive map is the hippocampus which
+ 
+
+ align:start position:0%
+cognitive map is the hippocampus which
+we're about to talk talk about next for
+
+ align:start position:0%
+we're about to talk talk about next for
+ 
+
+ align:start position:0%
+we're about to talk talk about next for
+reasons i will tell you but all of this
+
+ align:start position:0%
+reasons i will tell you but all of this
+ 
+
+ align:start position:0%
+reasons i will tell you but all of this
+is kind of this is a very active area of
+
+ align:start position:0%
+is kind of this is a very active area of
+ 
+
+ align:start position:0%
+is kind of this is a very active area of
+research it kills me every time i do
+
+ align:start position:0%
+research it kills me every time i do
+ 
+
+ align:start position:0%
+research it kills me every time i do
+these lectures i look at my old notes
+
+ align:start position:0%
+these lectures i look at my old notes
+ 
+
+ align:start position:0%
+these lectures i look at my old notes
+and i think here are these 10 other
+
+ align:start position:0%
+and i think here are these 10 other
+ 
+
+ align:start position:0%
+and i think here are these 10 other
+awesome studies and then i try to fit
+
+ align:start position:0%
+awesome studies and then i try to fit
+ 
+
+ align:start position:0%
+awesome studies and then i try to fit
+them in and then they just don't fit so
+
+ align:start position:0%
+them in and then they just don't fit so
+ 
+
+ align:start position:0%
+them in and then they just don't fit so
+actually one question i want to ask you
+
+ align:start position:0%
+actually one question i want to ask you
+ 
+
+ align:start position:0%
+actually one question i want to ask you
+guys after this lecture is should i in
+
+ align:start position:0%
+guys after this lecture is should i in
+ 
+
+ align:start position:0%
+guys after this lecture is should i in
+future either later in this course or in
+
+ align:start position:0%
+future either later in this course or in
+ 
+
+ align:start position:0%
+future either later in this course or in
+future courses allocate even more time
+
+ align:start position:0%
+future courses allocate even more time
+ 
+
+ align:start position:0%
+future courses allocate even more time
+or do you guys feel like okay enough
+
+ align:start position:0%
+or do you guys feel like okay enough
+ 
+
+ align:start position:0%
+or do you guys feel like okay enough
+already with navigation but i just think
+
+ align:start position:0%
+already with navigation but i just think
+ 
+
+ align:start position:0%
+already with navigation but i just think
+it's the coolest system so there's lots
+
+ align:start position:0%
+it's the coolest system so there's lots
+ 
+
+ align:start position:0%
+it's the coolest system so there's lots
+of work
+
+ align:start position:0%
+of work
+ 
+
+ align:start position:0%
+of work
+exactly trying to answer that kind of
+
+ align:start position:0%
+exactly trying to answer that kind of
+ 
+
+ align:start position:0%
+exactly trying to answer that kind of
+question and i'll give you
+
+ align:start position:0%
+question and i'll give you
+ 
+
+ align:start position:0%
+question and i'll give you
+a current snapshot of the approximate
+
+ align:start position:0%
+a current snapshot of the approximate
+ 
+
+ align:start position:0%
+a current snapshot of the approximate
+state but all of this is in flux and
+
+ align:start position:0%
+state but all of this is in flux and
+ 
+
+ align:start position:0%
+state but all of this is in flux and
+very much actively investigated
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+cognitive map what do we mean by that
+
+ align:start position:0%
+cognitive map what do we mean by that
+ 
+
+ align:start position:0%
+cognitive map what do we mean by that
+just to remind you of this classic study
+
+ align:start position:0%
+just to remind you of this classic study
+ 
+
+ align:start position:0%
+just to remind you of this classic study
+from the 1940s in rats where the rat
+
+ align:start position:0%
+from the 1940s in rats where the rat
+ 
+
+ align:start position:0%
+from the 1940s in rats where the rat
+when they learned this route and then
+
+ align:start position:0%
+when they learned this route and then
+ 
+
+ align:start position:0%
+when they learned this route and then
+went up here and found their gold block
+
+ align:start position:0%
+went up here and found their gold block
+ 
+
+ align:start position:0%
+went up here and found their gold block
+the rat immediately comes out and goes
+
+ align:start position:0%
+the rat immediately comes out and goes
+ 
+
+ align:start position:0%
+the rat immediately comes out and goes
+straight toward the goal telling you
+
+ align:start position:0%
+straight toward the goal telling you
+ 
+
+ align:start position:0%
+straight toward the goal telling you
+they've learned something much more
+
+ align:start position:0%
+they've learned something much more
+ 
+
+ align:start position:0%
+they've learned something much more
+interesting than the series of left and
+
+ align:start position:0%
+interesting than the series of left and
+ 
+
+ align:start position:0%
+interesting than the series of left and
+right turns to get to the goal they must
+
+ align:start position:0%
+right turns to get to the goal they must
+ 
+
+ align:start position:0%
+right turns to get to the goal they must
+have done something much more like
+
+ align:start position:0%
+have done something much more like
+ 
+
+ align:start position:0%
+have done something much more like
+actually learned the layout of space and
+
+ align:start position:0%
+actually learned the layout of space and
+ 
+
+ align:start position:0%
+actually learned the layout of space and
+the relative position of that goal so
+
+ align:start position:0%
+the relative position of that goal so
+ 
+
+ align:start position:0%
+the relative position of that goal so
+they could come up with a new vector to
+
+ align:start position:0%
+they could come up with a new vector to
+ 
+
+ align:start position:0%
+they could come up with a new vector to
+get there when the original route was
+
+ align:start position:0%
+get there when the original route was
+ 
+
+ align:start position:0%
+get there when the original route was
+blocked
+
+ align:start position:0%
+blocked
+ 
+
+ align:start position:0%
+blocked
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+and you guys can do this too right when
+
+ align:start position:0%
+and you guys can do this too right when
+ 
+
+ align:start position:0%
+and you guys can do this too right when
+your root is blocked you come up with a
+
+ align:start position:0%
+your root is blocked you come up with a
+ 
+
+ align:start position:0%
+your root is blocked you come up with a
+novel root right
+
+ align:start position:0%
+novel root right
+ 
+
+ align:start position:0%
+novel root right
+uh and you do that by having some
+
+ align:start position:0%
+uh and you do that by having some
+ 
+
+ align:start position:0%
+uh and you do that by having some
+knowledge of your environment something
+
+ align:start position:0%
+knowledge of your environment something
+ 
+
+ align:start position:0%
+knowledge of your environment something
+tantamount to that in your head
+
+ align:start position:0%
+tantamount to that in your head
+ 
+
+ align:start position:0%
+tantamount to that in your head
+some version of that
+
+ align:start position:0%
+some version of that
+ 
+
+ align:start position:0%
+some version of that
+and further you know where you are in
+
+ align:start position:0%
+and further you know where you are in
+ 
+
+ align:start position:0%
+and further you know where you are in
+that map like right now you know where
+
+ align:start position:0%
+that map like right now you know where
+ 
+
+ align:start position:0%
+that map like right now you know where
+you are
+
+ align:start position:0%
+you are
+ 
+
+ align:start position:0%
+you are
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+now here's the cool thing
+
+ align:start position:0%
+now here's the cool thing
+ 
+
+ align:start position:0%
+now here's the cool thing
+specific neurons in your hippocampus
+
+ align:start position:0%
+specific neurons in your hippocampus
+ 
+
+ align:start position:0%
+specific neurons in your hippocampus
+right now are firing telling you that
+
+ align:start position:0%
+right now are firing telling you that
+ 
+
+ align:start position:0%
+right now are firing telling you that
+you are right there
+
+ align:start position:0%
+you are right there
+ 
+
+ align:start position:0%
+you are right there
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+so these neurons are called place cells
+
+ align:start position:0%
+so these neurons are called place cells
+ 
+
+ align:start position:0%
+so these neurons are called place cells
+and this is what they do okay so i'll be
+
+ align:start position:0%
+and this is what they do okay so i'll be
+ 
+
+ align:start position:0%
+and this is what they do okay so i'll be
+a place cell or what rather what i'll do
+
+ align:start position:0%
+a place cell or what rather what i'll do
+ 
+
+ align:start position:0%
+a place cell or what rather what i'll do
+is i will act out the activity of a
+
+ align:start position:0%
+is i will act out the activity of a
+ 
+
+ align:start position:0%
+is i will act out the activity of a
+place cell by a series of clicks i will
+
+ align:start position:0%
+place cell by a series of clicks i will
+ 
+
+ align:start position:0%
+place cell by a series of clicks i will
+make as i walk around so imagine there's
+
+ align:start position:0%
+make as i walk around so imagine there's
+ 
+
+ align:start position:0%
+make as i walk around so imagine there's
+an electrode in my hippocampus and you
+
+ align:start position:0%
+an electrode in my hippocampus and you
+ 
+
+ align:start position:0%
+an electrode in my hippocampus and you
+are hearing the activity of a single
+
+ align:start position:0%
+are hearing the activity of a single
+ 
+
+ align:start position:0%
+are hearing the activity of a single
+neuron in my hippocampus as i walk
+
+ align:start position:0%
+neuron in my hippocampus as i walk
+ 
+
+ align:start position:0%
+neuron in my hippocampus as i walk
+around and here's what it would do
+
+ align:start position:0%
+around and here's what it would do
+ 
+
+ align:start position:0%
+around and here's what it would do
+you'd hear background firing so it's
+
+ align:start position:0%
+you'd hear background firing so it's
+ 
+
+ align:start position:0%
+you'd hear background firing so it's
+going to go click click
+
+ align:start position:0%
+going to go click click
+ 
+
+ align:start position:0%
+going to go click click
+click click click noisy background
+
+ align:start position:0%
+click click click noisy background
+ 
+
+ align:start position:0%
+click click click noisy background
+finding firing click click
+
+ align:start position:0%
+finding firing click click
+ 
+
+ align:start position:0%
+finding firing click click
+click click
+
+ align:start position:0%
+click click
+ 
+
+ align:start position:0%
+click click
+click click click click click
+
+ align:start position:0%
+click click click click click
+ 
+
+ align:start position:0%
+click click click click click
+click click click click click click
+
+ align:start position:0%
+click click click click click click
+ 
+
+ align:start position:0%
+click click click click click click
+click click click click click
+
+ align:start position:0%
+click click click click click
+ 
+
+ align:start position:0%
+click click click click click
+click
+
+ align:start position:0%
+click
+ 
+
+ align:start position:0%
+click
+click click okay i'm not going to go
+
+ align:start position:0%
+click click okay i'm not going to go
+ 
+
+ align:start position:0%
+click click okay i'm not going to go
+down there click click click click click
+
+ align:start position:0%
+down there click click click click click
+ 
+
+ align:start position:0%
+down there click click click click click
+click look click click click click click
+
+ align:start position:0%
+click look click click click click click
+ 
+
+ align:start position:0%
+click look click click click click click
+click click click
+
+ align:start position:0%
+click click click
+ 
+
+ align:start position:0%
+click click click
+click click click click
+
+ align:start position:0%
+click click click click
+ 
+
+ align:start position:0%
+click click click click
+click click click
+
+ align:start position:0%
+click click click
+ 
+
+ align:start position:0%
+click click click
+so that's one neuron that fires only
+
+ align:start position:0%
+so that's one neuron that fires only
+ 
+
+ align:start position:0%
+so that's one neuron that fires only
+when i'm right over there that place
+
+ align:start position:0%
+when i'm right over there that place
+ 
+
+ align:start position:0%
+when i'm right over there that place
+it's not where i'm facing over there
+
+ align:start position:0%
+it's not where i'm facing over there
+ 
+
+ align:start position:0%
+it's not where i'm facing over there
+it's not what i'm looking at
+
+ align:start position:0%
+it's not what i'm looking at
+ 
+
+ align:start position:0%
+it's not what i'm looking at
+particularly it's when i'm right there
+
+ align:start position:0%
+particularly it's when i'm right there
+ 
+
+ align:start position:0%
+particularly it's when i'm right there
+okay that's a place cell
+
+ align:start position:0%
+okay that's a place cell
+ 
+
+ align:start position:0%
+okay that's a place cell
+and so there's lots of place cells in
+
+ align:start position:0%
+and so there's lots of place cells in
+ 
+
+ align:start position:0%
+and so there's lots of place cells in
+your hippocampus
+
+ align:start position:0%
+your hippocampus
+ 
+
+ align:start position:0%
+your hippocampus
+that do that and they do it for
+
+ align:start position:0%
+that do that and they do it for
+ 
+
+ align:start position:0%
+that do that and they do it for
+different locations in your environment
+
+ align:start position:0%
+different locations in your environment
+ 
+
+ align:start position:0%
+different locations in your environment
+and all of this was first worked out of
+
+ align:start position:0%
+and all of this was first worked out of
+ 
+
+ align:start position:0%
+and all of this was first worked out of
+course in rodents who were running
+
+ align:start position:0%
+course in rodents who were running
+ 
+
+ align:start position:0%
+course in rodents who were running
+around who had electrodes in their
+
+ align:start position:0%
+around who had electrodes in their
+ 
+
+ align:start position:0%
+around who had electrodes in their
+hippocampus but where those electrodes
+
+ align:start position:0%
+hippocampus but where those electrodes
+ 
+
+ align:start position:0%
+hippocampus but where those electrodes
+were connected with a loose tether so
+
+ align:start position:0%
+were connected with a loose tether so
+ 
+
+ align:start position:0%
+were connected with a loose tether so
+that the rodent could move around in
+
+ align:start position:0%
+that the rodent could move around in
+ 
+
+ align:start position:0%
+that the rodent could move around in
+their environment while recording from
+
+ align:start position:0%
+their environment while recording from
+ 
+
+ align:start position:0%
+their environment while recording from
+individual neurons in the campus okay so
+
+ align:start position:0%
+individual neurons in the campus okay so
+ 
+
+ align:start position:0%
+individual neurons in the campus okay so
+that's the setup
+
+ align:start position:0%
+that's the setup
+ 
+
+ align:start position:0%
+that's the setup
+and so i'm going to show you a movie of
+
+ align:start position:0%
+and so i'm going to show you a movie of
+ 
+
+ align:start position:0%
+and so i'm going to show you a movie of
+an aerial view
+
+ align:start position:0%
+an aerial view
+ 
+
+ align:start position:0%
+an aerial view
+of a rodent
+
+ align:start position:0%
+of a rodent
+ 
+
+ align:start position:0%
+of a rodent
+moving around
+
+ align:start position:0%
+moving around
+ 
+
+ align:start position:0%
+moving around
+a rat moving around in its environment
+
+ align:start position:0%
+a rat moving around in its environment
+ 
+
+ align:start position:0%
+a rat moving around in its environment
+can you see the little rat there
+
+ align:start position:0%
+can you see the little rat there
+ 
+
+ align:start position:0%
+can you see the little rat there
+um and what's happening is this um video
+
+ align:start position:0%
+um and what's happening is this um video
+ 
+
+ align:start position:0%
+um and what's happening is this um video
+is tracing out the rat's path with the
+
+ align:start position:0%
+is tracing out the rat's path with the
+ 
+
+ align:start position:0%
+is tracing out the rat's path with the
+light gray and every time that it's
+
+ align:start position:0%
+light gray and every time that it's
+ 
+
+ align:start position:0%
+light gray and every time that it's
+recording from one neuron every time
+
+ align:start position:0%
+recording from one neuron every time
+ 
+
+ align:start position:0%
+recording from one neuron every time
+that neuron fires it makes a red dot and
+
+ align:start position:0%
+that neuron fires it makes a red dot and
+ 
+
+ align:start position:0%
+that neuron fires it makes a red dot and
+so this is obviously sped up but as the
+
+ align:start position:0%
+so this is obviously sped up but as the
+ 
+
+ align:start position:0%
+so this is obviously sped up but as the
+rat moves around in his environment you
+
+ align:start position:0%
+rat moves around in his environment you
+ 
+
+ align:start position:0%
+rat moves around in his environment you
+see an accumulation like more firing
+
+ align:start position:0%
+see an accumulation like more firing
+ 
+
+ align:start position:0%
+see an accumulation like more firing
+when the rat is right there
+
+ align:start position:0%
+when the rat is right there
+ 
+
+ align:start position:0%
+when the rat is right there
+it's not which direction the rat is
+
+ align:start position:0%
+it's not which direction the rat is
+ 
+
+ align:start position:0%
+it's not which direction the rat is
+going through when he goes there just
+
+ align:start position:0%
+going through when he goes there just
+ 
+
+ align:start position:0%
+going through when he goes there just
+basically whenever he passes through
+
+ align:start position:0%
+basically whenever he passes through
+ 
+
+ align:start position:0%
+basically whenever he passes through
+that in any direction
+
+ align:start position:0%
+that in any direction
+ 
+
+ align:start position:0%
+that in any direction
+neurons fire more than anywhere else and
+
+ align:start position:0%
+neurons fire more than anywhere else and
+ 
+
+ align:start position:0%
+neurons fire more than anywhere else and
+then if we take that and blur it as
+
+ align:start position:0%
+then if we take that and blur it as
+ 
+
+ align:start position:0%
+then if we take that and blur it as
+scientists like to do to make nice
+
+ align:start position:0%
+scientists like to do to make nice
+ 
+
+ align:start position:0%
+scientists like to do to make nice
+idealized pictures
+
+ align:start position:0%
+idealized pictures
+ 
+
+ align:start position:0%
+idealized pictures
+that is the place cell for that neuron
+
+ align:start position:0%
+that is the place cell for that neuron
+ 
+
+ align:start position:0%
+that is the place cell for that neuron
+that is the place in space
+
+ align:start position:0%
+that is the place in space
+ 
+
+ align:start position:0%
+that is the place in space
+that that animal has to be to make that
+
+ align:start position:0%
+that that animal has to be to make that
+ 
+
+ align:start position:0%
+that that animal has to be to make that
+neuron fire
+
+ align:start position:0%
+neuron fire
+ 
+
+ align:start position:0%
+neuron fire
+yeah question is it one dimension
+
+ align:start position:0%
+yeah question is it one dimension
+ 
+
+ align:start position:0%
+yeah question is it one dimension
+i mean can multiple cases be mapped to
+
+ align:start position:0%
+i mean can multiple cases be mapped to
+ 
+
+ align:start position:0%
+i mean can multiple cases be mapped to
+save your home um that's complicated
+
+ align:start position:0%
+save your home um that's complicated
+ 
+
+ align:start position:0%
+save your home um that's complicated
+in an immediate environment like this
+
+ align:start position:0%
+in an immediate environment like this
+ 
+
+ align:start position:0%
+in an immediate environment like this
+generally not okay i'll show you some
+
+ align:start position:0%
+generally not okay i'll show you some
+ 
+
+ align:start position:0%
+generally not okay i'll show you some
+examples in a moment
+
+ align:start position:0%
+examples in a moment
+ 
+
+ align:start position:0%
+examples in a moment
+it's more complicated if you follow that
+
+ align:start position:0%
+it's more complicated if you follow that
+ 
+
+ align:start position:0%
+it's more complicated if you follow that
+cell when the animal moves to new
+
+ align:start position:0%
+cell when the animal moves to new
+ 
+
+ align:start position:0%
+cell when the animal moves to new
+locations so let me say a few more
+
+ align:start position:0%
+locations so let me say a few more
+ 
+
+ align:start position:0%
+locations so let me say a few more
+things and then i'll then if it's not
+
+ align:start position:0%
+things and then i'll then if it's not
+ 
+
+ align:start position:0%
+things and then i'll then if it's not
+clear i'll take questions oops i'm going
+
+ align:start position:0%
+clear i'll take questions oops i'm going
+ 
+
+ align:start position:0%
+clear i'll take questions oops i'm going
+to see it again
+
+ align:start position:0%
+to see it again
+ 
+
+ align:start position:0%
+to see it again
+okay right so so in answer to josh's
+
+ align:start position:0%
+okay right so so in answer to josh's
+ 
+
+ align:start position:0%
+okay right so so in answer to josh's
+question here are a bunch of place cells
+
+ align:start position:0%
+question here are a bunch of place cells
+ 
+
+ align:start position:0%
+question here are a bunch of place cells
+from a rodent exploring the same
+
+ align:start position:0%
+from a rodent exploring the same
+ 
+
+ align:start position:0%
+from a rodent exploring the same
+environment so you might say well
+
+ align:start position:0%
+environment so you might say well
+ 
+
+ align:start position:0%
+environment so you might say well
+there's like a hot spot here and a
+
+ align:start position:0%
+there's like a hot spot here and a
+ 
+
+ align:start position:0%
+there's like a hot spot here and a
+little sub one there but in general most
+
+ align:start position:0%
+little sub one there but in general most
+ 
+
+ align:start position:0%
+little sub one there but in general most
+of these cells respond with a hot spot
+
+ align:start position:0%
+of these cells respond with a hot spot
+ 
+
+ align:start position:0%
+of these cells respond with a hot spot
+in a particular single location in this
+
+ align:start position:0%
+in a particular single location in this
+ 
+
+ align:start position:0%
+in a particular single location in this
+particular environment
+
+ align:start position:0%
+particular environment
+ 
+
+ align:start position:0%
+particular environment
+okay did you have a different question
+
+ align:start position:0%
+okay did you have a different question
+ 
+
+ align:start position:0%
+okay did you have a different question
+about that yes
+
+ align:start position:0%
+about that yes
+ 
+
+ align:start position:0%
+about that yes
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+that all depends on the wrath
+
+ align:start position:0%
+that all depends on the wrath
+ 
+
+ align:start position:0%
+that all depends on the wrath
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+the unconscious of the fact whether it's
+
+ align:start position:0%
+the unconscious of the fact whether it's
+ 
+
+ align:start position:0%
+the unconscious of the fact whether it's
+in that place
+
+ align:start position:0%
+in that place
+ 
+
+ align:start position:0%
+in that place
+if the rat was anesthetized or if he was
+
+ align:start position:0%
+if the rat was anesthetized or if he was
+ 
+
+ align:start position:0%
+if the rat was anesthetized or if he was
+you know blindfolded and you passively
+
+ align:start position:0%
+you know blindfolded and you passively
+ 
+
+ align:start position:0%
+you know blindfolded and you passively
+moved him around in that space and he
+
+ align:start position:0%
+moved him around in that space and he
+ 
+
+ align:start position:0%
+moved him around in that space and he
+had no idea no way to tell where he was
+
+ align:start position:0%
+had no idea no way to tell where he was
+ 
+
+ align:start position:0%
+had no idea no way to tell where he was
+that wouldn't work however if the rat
+
+ align:start position:0%
+that wouldn't work however if the rat
+ 
+
+ align:start position:0%
+that wouldn't work however if the rat
+knows the environment
+
+ align:start position:0%
+knows the environment
+ 
+
+ align:start position:0%
+knows the environment
+and then you do this in a darkened room
+
+ align:start position:0%
+and then you do this in a darkened room
+ 
+
+ align:start position:0%
+and then you do this in a darkened room
+where he's actively locomoting around
+
+ align:start position:0%
+where he's actively locomoting around
+ 
+
+ align:start position:0%
+where he's actively locomoting around
+these things will still work pretty well
+
+ align:start position:0%
+these things will still work pretty well
+ 
+
+ align:start position:0%
+these things will still work pretty well
+because rats are very good at keeping
+
+ align:start position:0%
+because rats are very good at keeping
+ 
+
+ align:start position:0%
+because rats are very good at keeping
+track of where they are
+
+ align:start position:0%
+track of where they are
+ 
+
+ align:start position:0%
+track of where they are
+even without visual cues if they know
+
+ align:start position:0%
+even without visual cues if they know
+ 
+
+ align:start position:0%
+even without visual cues if they know
+the environment they'll have other cues
+
+ align:start position:0%
+the environment they'll have other cues
+ 
+
+ align:start position:0%
+the environment they'll have other cues
+like tactile cues and like they will
+
+ align:start position:0%
+like tactile cues and like they will
+ 
+
+ align:start position:0%
+like tactile cues and like they will
+know how far they went in each direction
+
+ align:start position:0%
+know how far they went in each direction
+ 
+
+ align:start position:0%
+know how far they went in each direction
+remember i talked briefly about the
+
+ align:start position:0%
+remember i talked briefly about the
+ 
+
+ align:start position:0%
+remember i talked briefly about the
+tunisian ants doing dead reckoning
+
+ align:start position:0%
+tunisian ants doing dead reckoning
+ 
+
+ align:start position:0%
+tunisian ants doing dead reckoning
+right keeping track of their vector and
+
+ align:start position:0%
+right keeping track of their vector and
+ 
+
+ align:start position:0%
+right keeping track of their vector and
+speed at each moment and integrating the
+
+ align:start position:0%
+speed at each moment and integrating the
+ 
+
+ align:start position:0%
+speed at each moment and integrating the
+whole thing to know where they are
+
+ align:start position:0%
+whole thing to know where they are
+ 
+
+ align:start position:0%
+whole thing to know where they are
+that's called dead reckoning rats are
+
+ align:start position:0%
+that's called dead reckoning rats are
+ 
+
+ align:start position:0%
+that's called dead reckoning rats are
+pretty good at that too
+
+ align:start position:0%
+pretty good at that too
+ 
+
+ align:start position:0%
+pretty good at that too
+another question over here yeah
+
+ align:start position:0%
+another question over here yeah
+ 
+
+ align:start position:0%
+another question over here yeah
+um the police officers do they have like
+
+ align:start position:0%
+um the police officers do they have like
+ 
+
+ align:start position:0%
+um the police officers do they have like
+uh look at math as well like how like
+
+ align:start position:0%
+uh look at math as well like how like
+ 
+
+ align:start position:0%
+uh look at math as well like how like
+we'll get there great question we'll get
+
+ align:start position:0%
+we'll get there great question we'll get
+ 
+
+ align:start position:0%
+we'll get there great question we'll get
+there
+
+ align:start position:0%
+there
+ 
+
+ align:start position:0%
+there
+i'll just give you the answer no they
+
+ align:start position:0%
+i'll just give you the answer no they
+ 
+
+ align:start position:0%
+i'll just give you the answer no they
+don't it's too bad um
+
+ align:start position:0%
+don't it's too bad um
+ 
+
+ align:start position:0%
+don't it's too bad um
+they could have they could have been all
+
+ align:start position:0%
+they could have they could have been all
+ 
+
+ align:start position:0%
+they could have they could have been all
+organized but it's actually a little
+
+ align:start position:0%
+organized but it's actually a little
+ 
+
+ align:start position:0%
+organized but it's actually a little
+complicated how would you organize them
+
+ align:start position:0%
+complicated how would you organize them
+ 
+
+ align:start position:0%
+complicated how would you organize them
+then what if you like learned more stuff
+
+ align:start position:0%
+then what if you like learned more stuff
+ 
+
+ align:start position:0%
+then what if you like learned more stuff
+off of the edge of space well like i had
+
+ align:start position:0%
+off of the edge of space well like i had
+ 
+
+ align:start position:0%
+off of the edge of space well like i had
+a whole other piece of your hippocampus
+
+ align:start position:0%
+a whole other piece of your hippocampus
+ 
+
+ align:start position:0%
+a whole other piece of your hippocampus
+i would be inconvenienced so maybe
+
+ align:start position:0%
+i would be inconvenienced so maybe
+ 
+
+ align:start position:0%
+i would be inconvenienced so maybe
+that's why it doesn't work whereas with
+
+ align:start position:0%
+that's why it doesn't work whereas with
+ 
+
+ align:start position:0%
+that's why it doesn't work whereas with
+visual space
+
+ align:start position:0%
+visual space
+ 
+
+ align:start position:0%
+visual space
+you know you're your retina topic
+
+ align:start position:0%
+you know you're your retina topic
+ 
+
+ align:start position:0%
+you know you're your retina topic
+information always stays the same we
+
+ align:start position:0%
+information always stays the same we
+ 
+
+ align:start position:0%
+information always stays the same we
+don't have to suddenly add
+
+ align:start position:0%
+don't have to suddenly add
+ 
+
+ align:start position:0%
+don't have to suddenly add
+a whole new part of retinotopic space
+
+ align:start position:0%
+a whole new part of retinotopic space
+ 
+
+ align:start position:0%
+a whole new part of retinotopic space
+thereby screwing up our retina topic
+
+ align:start position:0%
+thereby screwing up our retina topic
+ 
+
+ align:start position:0%
+thereby screwing up our retina topic
+maps in the brain i'm just making that
+
+ align:start position:0%
+maps in the brain i'm just making that
+ 
+
+ align:start position:0%
+maps in the brain i'm just making that
+up as a possible reason i don't know if
+
+ align:start position:0%
+up as a possible reason i don't know if
+ 
+
+ align:start position:0%
+up as a possible reason i don't know if
+that's why yeah what's sorry behind you
+
+ align:start position:0%
+that's why yeah what's sorry behind you
+ 
+
+ align:start position:0%
+that's why yeah what's sorry behind you
+david who what's tell me your name
+
+ align:start position:0%
+david who what's tell me your name
+ 
+
+ align:start position:0%
+david who what's tell me your name
+justin yeah right hi um so i was
+
+ align:start position:0%
+justin yeah right hi um so i was
+ 
+
+ align:start position:0%
+justin yeah right hi um so i was
+wondering like if you're in a smaller
+
+ align:start position:0%
+wondering like if you're in a smaller
+ 
+
+ align:start position:0%
+wondering like if you're in a smaller
+space comparatively or like a bigger
+
+ align:start position:0%
+space comparatively or like a bigger
+ 
+
+ align:start position:0%
+space comparatively or like a bigger
+space right like
+
+ align:start position:0%
+space right like
+ 
+
+ align:start position:0%
+space right like
+more areas of these specific uh place
+
+ align:start position:0%
+more areas of these specific uh place
+ 
+
+ align:start position:0%
+more areas of these specific uh place
+cells that like what they're mapping to
+
+ align:start position:0%
+cells that like what they're mapping to
+ 
+
+ align:start position:0%
+cells that like what they're mapping to
+um will they also scale up right now
+
+ align:start position:0%
+um will they also scale up right now
+ 
+
+ align:start position:0%
+um will they also scale up right now
+it's a great question i don't know the
+
+ align:start position:0%
+it's a great question i don't know the
+ 
+
+ align:start position:0%
+it's a great question i don't know the
+answer my guess is they'll scale
+
+ align:start position:0%
+answer my guess is they'll scale
+ 
+
+ align:start position:0%
+answer my guess is they'll scale
+according to the space
+
+ align:start position:0%
+according to the space
+ 
+
+ align:start position:0%
+according to the space
+right like so if if i had if that if my
+
+ align:start position:0%
+right like so if if i had if that if my
+ 
+
+ align:start position:0%
+right like so if if i had if that if my
+place my fake place cell field that i
+
+ align:start position:0%
+place my fake place cell field that i
+ 
+
+ align:start position:0%
+place my fake place cell field that i
+just acted out over there is maybe five
+
+ align:start position:0%
+just acted out over there is maybe five
+ 
+
+ align:start position:0%
+just acted out over there is maybe five
+feet across if i was then confined to a
+
+ align:start position:0%
+feet across if i was then confined to a
+ 
+
+ align:start position:0%
+feet across if i was then confined to a
+little space you'd probably have smaller
+
+ align:start position:0%
+little space you'd probably have smaller
+ 
+
+ align:start position:0%
+little space you'd probably have smaller
+ones for that space but i don't know
+
+ align:start position:0%
+ones for that space but i don't know
+ 
+
+ align:start position:0%
+ones for that space but i don't know
+let me say a little bit more about this
+
+ align:start position:0%
+let me say a little bit more about this
+ 
+
+ align:start position:0%
+let me say a little bit more about this
+so so just to catch this out the place
+
+ align:start position:0%
+so so just to catch this out the place
+ 
+
+ align:start position:0%
+so so just to catch this out the place
+field is the location in space the
+
+ align:start position:0%
+field is the location in space the
+ 
+
+ align:start position:0%
+field is the location in space the
+animal has to be to make that
+
+ align:start position:0%
+animal has to be to make that
+ 
+
+ align:start position:0%
+animal has to be to make that
+hippocampal cell fire okay
+
+ align:start position:0%
+hippocampal cell fire okay
+ 
+
+ align:start position:0%
+hippocampal cell fire okay
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+let's distinguish that from a receptive
+
+ align:start position:0%
+let's distinguish that from a receptive
+ 
+
+ align:start position:0%
+let's distinguish that from a receptive
+field in visual cortex which is a
+
+ align:start position:0%
+field in visual cortex which is a
+ 
+
+ align:start position:0%
+field in visual cortex which is a
+similar idea but a different one a
+
+ align:start position:0%
+similar idea but a different one a
+ 
+
+ align:start position:0%
+similar idea but a different one a
+receptive field in visual cortex is the
+
+ align:start position:0%
+receptive field in visual cortex is the
+ 
+
+ align:start position:0%
+receptive field in visual cortex is the
+location in the visual field where a
+
+ align:start position:0%
+location in the visual field where a
+ 
+
+ align:start position:0%
+location in the visual field where a
+stimulus has to be to make a visual
+
+ align:start position:0%
+stimulus has to be to make a visual
+ 
+
+ align:start position:0%
+stimulus has to be to make a visual
+neuron fire
+
+ align:start position:0%
+neuron fire
+ 
+
+ align:start position:0%
+neuron fire
+not where the animal itself has to be
+
+ align:start position:0%
+not where the animal itself has to be
+ 
+
+ align:start position:0%
+not where the animal itself has to be
+where the stimulus has to be okay so
+
+ align:start position:0%
+where the stimulus has to be okay so
+ 
+
+ align:start position:0%
+where the stimulus has to be okay so
+keep those ideas separate they're
+
+ align:start position:0%
+keep those ideas separate they're
+ 
+
+ align:start position:0%
+keep those ideas separate they're
+related but different
+
+ align:start position:0%
+related but different
+ 
+
+ align:start position:0%
+related but different
+okay so what about you know we and
+
+ align:start position:0%
+okay so what about you know we and
+ 
+
+ align:start position:0%
+okay so what about you know we and
+rodents tend to go around mostly on a 2d
+
+ align:start position:0%
+rodents tend to go around mostly on a 2d
+ 
+
+ align:start position:0%
+rodents tend to go around mostly on a 2d
+plane
+
+ align:start position:0%
+plane
+ 
+
+ align:start position:0%
+plane
+that is we have buildings and trees and
+
+ align:start position:0%
+that is we have buildings and trees and
+ 
+
+ align:start position:0%
+that is we have buildings and trees and
+stuff we sometimes go up in the z-axis
+
+ align:start position:0%
+stuff we sometimes go up in the z-axis
+ 
+
+ align:start position:0%
+stuff we sometimes go up in the z-axis
+but most we live in a 2d plane
+
+ align:start position:0%
+but most we live in a 2d plane
+ 
+
+ align:start position:0%
+but most we live in a 2d plane
+but that's not true of all animals so
+
+ align:start position:0%
+but that's not true of all animals so
+ 
+
+ align:start position:0%
+but that's not true of all animals so
+recall the bat that i mentioned last
+
+ align:start position:0%
+recall the bat that i mentioned last
+ 
+
+ align:start position:0%
+recall the bat that i mentioned last
+time these amazing flyers and navigators
+
+ align:start position:0%
+time these amazing flyers and navigators
+ 
+
+ align:start position:0%
+time these amazing flyers and navigators
+who fly in 3d and complicated
+
+ align:start position:0%
+who fly in 3d and complicated
+ 
+
+ align:start position:0%
+who fly in 3d and complicated
+trajectories and yet have
+
+ align:start position:0%
+trajectories and yet have
+ 
+
+ align:start position:0%
+trajectories and yet have
+amazing abilities to keep track of where
+
+ align:start position:0%
+amazing abilities to keep track of where
+ 
+
+ align:start position:0%
+amazing abilities to keep track of where
+they are over 30 to 50 miles that they
+
+ align:start position:0%
+they are over 30 to 50 miles that they
+ 
+
+ align:start position:0%
+they are over 30 to 50 miles that they
+fly at night
+
+ align:start position:0%
+fly at night
+ 
+
+ align:start position:0%
+fly at night
+and even as they change their
+
+ align:start position:0%
+and even as they change their
+ 
+
+ align:start position:0%
+and even as they change their
+orientation
+
+ align:start position:0%
+orientation
+ 
+
+ align:start position:0%
+orientation
+well it turns out that in the
+
+ align:start position:0%
+well it turns out that in the
+ 
+
+ align:start position:0%
+well it turns out that in the
+hippocampus of bats there's a bunch of
+
+ align:start position:0%
+hippocampus of bats there's a bunch of
+ 
+
+ align:start position:0%
+hippocampus of bats there's a bunch of
+work where people have
+
+ align:start position:0%
+work where people have
+ 
+
+ align:start position:0%
+work where people have
+put
+
+ align:start position:0%
+put
+ 
+
+ align:start position:0%
+put
+um remote
+
+ align:start position:0%
+um remote
+ 
+
+ align:start position:0%
+um remote
+what do you call these things recording
+
+ align:start position:0%
+what do you call these things recording
+ 
+
+ align:start position:0%
+what do you call these things recording
+devices on bats where you can remotely
+
+ align:start position:0%
+devices on bats where you can remotely
+ 
+
+ align:start position:0%
+devices on bats where you can remotely
+record
+
+ align:start position:0%
+record
+ 
+
+ align:start position:0%
+record
+neural activity in the hippocampus as
+
+ align:start position:0%
+neural activity in the hippocampus as
+ 
+
+ align:start position:0%
+neural activity in the hippocampus as
+the bat flies around
+
+ align:start position:0%
+the bat flies around
+ 
+
+ align:start position:0%
+the bat flies around
+and turns out that bats have play cells
+
+ align:start position:0%
+and turns out that bats have play cells
+ 
+
+ align:start position:0%
+and turns out that bats have play cells
+too and their place cells
+
+ align:start position:0%
+too and their place cells
+ 
+
+ align:start position:0%
+too and their place cells
+as they they all also can do this in a
+
+ align:start position:0%
+as they they all also can do this in a
+ 
+
+ align:start position:0%
+as they they all also can do this in a
+lab environment where they're flying
+
+ align:start position:0%
+lab environment where they're flying
+ 
+
+ align:start position:0%
+lab environment where they're flying
+around and you keep track of their
+
+ align:start position:0%
+around and you keep track of their
+ 
+
+ align:start position:0%
+around and you keep track of their
+location uh with cameras so you know
+
+ align:start position:0%
+location uh with cameras so you know
+ 
+
+ align:start position:0%
+location uh with cameras so you know
+exactly where they are in 3d space
+
+ align:start position:0%
+exactly where they are in 3d space
+ 
+
+ align:start position:0%
+exactly where they are in 3d space
+and it turns out that place cells in
+
+ align:start position:0%
+and it turns out that place cells in
+ 
+
+ align:start position:0%
+and it turns out that place cells in
+bats are three-dimensional because bats
+
+ align:start position:0%
+bats are three-dimensional because bats
+ 
+
+ align:start position:0%
+bats are three-dimensional because bats
+live in a three-dimensional world
+
+ align:start position:0%
+live in a three-dimensional world
+ 
+
+ align:start position:0%
+live in a three-dimensional world
+so whereas rodent these would be a bunch
+
+ align:start position:0%
+so whereas rodent these would be a bunch
+ 
+
+ align:start position:0%
+so whereas rodent these would be a bunch
+of kind of schematized place cells
+
+ align:start position:0%
+of kind of schematized place cells
+ 
+
+ align:start position:0%
+of kind of schematized place cells
+for uh of different hippocampal cells in
+
+ align:start position:0%
+for uh of different hippocampal cells in
+ 
+
+ align:start position:0%
+for uh of different hippocampal cells in
+a rodent
+
+ align:start position:0%
+a rodent
+ 
+
+ align:start position:0%
+a rodent
+these are different place cells
+
+ align:start position:0%
+these are different place cells
+ 
+
+ align:start position:0%
+these are different place cells
+for different hippocampal cells and a
+
+ align:start position:0%
+for different hippocampal cells and a
+ 
+
+ align:start position:0%
+for different hippocampal cells and a
+bat
+
+ align:start position:0%
+bat
+ 
+
+ align:start position:0%
+bat
+makes sense bats need this they need to
+
+ align:start position:0%
+makes sense bats need this they need to
+ 
+
+ align:start position:0%
+makes sense bats need this they need to
+know not making sense okay so the bat is
+
+ align:start position:0%
+know not making sense okay so the bat is
+ 
+
+ align:start position:0%
+know not making sense okay so the bat is
+moving around in three dimensions its
+
+ align:start position:0%
+moving around in three dimensions its
+ 
+
+ align:start position:0%
+moving around in three dimensions its
+place field isn't just like the one i
+
+ align:start position:0%
+place field isn't just like the one i
+ 
+
+ align:start position:0%
+place field isn't just like the one i
+did there i can't act this out because i
+
+ align:start position:0%
+did there i can't act this out because i
+ 
+
+ align:start position:0%
+did there i can't act this out because i
+can't fly but that play cell might fire
+
+ align:start position:0%
+can't fly but that play cell might fire
+ 
+
+ align:start position:0%
+can't fly but that play cell might fire
+over in that location but then if the
+
+ align:start position:0%
+over in that location but then if the
+ 
+
+ align:start position:0%
+over in that location but then if the
+bat flew directly above it it wouldn't
+
+ align:start position:0%
+bat flew directly above it it wouldn't
+ 
+
+ align:start position:0%
+bat flew directly above it it wouldn't
+so it's got three dimensions okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um okay
+
+ align:start position:0%
+um okay
+ 
+
+ align:start position:0%
+um okay
+so i said before that i had one of those
+
+ align:start position:0%
+so i said before that i had one of those
+ 
+
+ align:start position:0%
+so i said before that i had one of those
+and i acted it out but what's the
+
+ align:start position:0%
+and i acted it out but what's the
+ 
+
+ align:start position:0%
+and i acted it out but what's the
+evidence for that
+
+ align:start position:0%
+evidence for that
+ 
+
+ align:start position:0%
+evidence for that
+that evidence in humans came way after
+
+ align:start position:0%
+that evidence in humans came way after
+ 
+
+ align:start position:0%
+that evidence in humans came way after
+the evidence in rodents
+
+ align:start position:0%
+the evidence in rodents
+ 
+
+ align:start position:0%
+the evidence in rodents
+um because as you can imagine it's
+
+ align:start position:0%
+um because as you can imagine it's
+ 
+
+ align:start position:0%
+um because as you can imagine it's
+harder to arrange to record from
+
+ align:start position:0%
+harder to arrange to record from
+ 
+
+ align:start position:0%
+harder to arrange to record from
+individual neurons in human
+
+ align:start position:0%
+individual neurons in human
+ 
+
+ align:start position:0%
+individual neurons in human
+hippocampuses
+
+ align:start position:0%
+hippocampuses
+ 
+
+ align:start position:0%
+hippocampuses
+nonetheless
+
+ align:start position:0%
+nonetheless
+ 
+
+ align:start position:0%
+nonetheless
+as i've mentioned a few times there are
+
+ align:start position:0%
+as i've mentioned a few times there are
+ 
+
+ align:start position:0%
+as i've mentioned a few times there are
+occasional opportunities where a
+
+ align:start position:0%
+occasional opportunities where a
+ 
+
+ align:start position:0%
+occasional opportunities where a
+neurosurgeon has stuck an electrode in
+
+ align:start position:0%
+neurosurgeon has stuck an electrode in
+ 
+
+ align:start position:0%
+neurosurgeon has stuck an electrode in
+an interesting part of the brain for
+
+ align:start position:0%
+an interesting part of the brain for
+ 
+
+ align:start position:0%
+an interesting part of the brain for
+clinical reasons and the patient and the
+
+ align:start position:0%
+clinical reasons and the patient and the
+ 
+
+ align:start position:0%
+clinical reasons and the patient and the
+neurosurgeon are nice enough
+
+ align:start position:0%
+neurosurgeon are nice enough
+ 
+
+ align:start position:0%
+neurosurgeon are nice enough
+to let scientists collect data
+
+ align:start position:0%
+to let scientists collect data
+ 
+
+ align:start position:0%
+to let scientists collect data
+so i'm going to show you a really gross
+
+ align:start position:0%
+so i'm going to show you a really gross
+ 
+
+ align:start position:0%
+so i'm going to show you a really gross
+bloody picture if that's going to bother
+
+ align:start position:0%
+bloody picture if that's going to bother
+ 
+
+ align:start position:0%
+bloody picture if that's going to bother
+you just look away okay
+
+ align:start position:0%
+you just look away okay
+ 
+
+ align:start position:0%
+you just look away okay
+so um this is neurosurgery you take the
+
+ align:start position:0%
+so um this is neurosurgery you take the
+ 
+
+ align:start position:0%
+so um this is neurosurgery you take the
+skull off you take the dura off that's
+
+ align:start position:0%
+skull off you take the dura off that's
+ 
+
+ align:start position:0%
+skull off you take the dura off that's
+the direct surface of the brain the
+
+ align:start position:0%
+the direct surface of the brain the
+ 
+
+ align:start position:0%
+the direct surface of the brain the
+neurosurgeons stick electrodes right on
+
+ align:start position:0%
+neurosurgeons stick electrodes right on
+ 
+
+ align:start position:0%
+neurosurgeons stick electrodes right on
+top of there and in this case they put
+
+ align:start position:0%
+top of there and in this case they put
+ 
+
+ align:start position:0%
+top of there and in this case they put
+them deep inside the brain okay the
+
+ align:start position:0%
+them deep inside the brain okay the
+ 
+
+ align:start position:0%
+them deep inside the brain okay the
+gross pictures are gone we have just a
+
+ align:start position:0%
+gross pictures are gone we have just a
+ 
+
+ align:start position:0%
+gross pictures are gone we have just a
+nice clean
+
+ align:start position:0%
+nice clean
+ 
+
+ align:start position:0%
+nice clean
+uh x-ray here um so in these cases these
+
+ align:start position:0%
+uh x-ray here um so in these cases these
+ 
+
+ align:start position:0%
+uh x-ray here um so in these cases these
+are um
+
+ align:start position:0%
+are um
+ 
+
+ align:start position:0%
+are um
+this is a patient who's got an electrode
+
+ align:start position:0%
+this is a patient who's got an electrode
+ 
+
+ align:start position:0%
+this is a patient who's got an electrode
+sticking straight into the brain from
+
+ align:start position:0%
+sticking straight into the brain from
+ 
+
+ align:start position:0%
+sticking straight into the brain from
+the surface straight down into the
+
+ align:start position:0%
+the surface straight down into the
+ 
+
+ align:start position:0%
+the surface straight down into the
+hippocampus
+
+ align:start position:0%
+hippocampus
+ 
+
+ align:start position:0%
+hippocampus
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+kind of horrifying but
+
+ align:start position:0%
+kind of horrifying but
+ 
+
+ align:start position:0%
+kind of horrifying but
+sometimes clinically called for seizures
+
+ align:start position:0%
+sometimes clinically called for seizures
+ 
+
+ align:start position:0%
+sometimes clinically called for seizures
+very often start in hippocampus so this
+
+ align:start position:0%
+very often start in hippocampus so this
+ 
+
+ align:start position:0%
+very often start in hippocampus so this
+is a common place for
+
+ align:start position:0%
+is a common place for
+ 
+
+ align:start position:0%
+is a common place for
+clinicians to put electrodes
+
+ align:start position:0%
+clinicians to put electrodes
+ 
+
+ align:start position:0%
+clinicians to put electrodes
+um and so uh what would you do if you
+
+ align:start position:0%
+um and so uh what would you do if you
+ 
+
+ align:start position:0%
+um and so uh what would you do if you
+had a patient who was willing to do your
+
+ align:start position:0%
+had a patient who was willing to do your
+ 
+
+ align:start position:0%
+had a patient who was willing to do your
+short experiment while hanging out in
+
+ align:start position:0%
+short experiment while hanging out in
+ 
+
+ align:start position:0%
+short experiment while hanging out in
+the hospital waiting to have a seizure
+
+ align:start position:0%
+the hospital waiting to have a seizure
+ 
+
+ align:start position:0%
+the hospital waiting to have a seizure
+with electrodes in their hippocampus
+
+ align:start position:0%
+with electrodes in their hippocampus
+ 
+
+ align:start position:0%
+with electrodes in their hippocampus
+well duh you'd have them play a little
+
+ align:start position:0%
+well duh you'd have them play a little
+ 
+
+ align:start position:0%
+well duh you'd have them play a little
+um a little game in a virtual space and
+
+ align:start position:0%
+um a little game in a virtual space and
+ 
+
+ align:start position:0%
+um a little game in a virtual space and
+some kind of you don't even need vr you
+
+ align:start position:0%
+some kind of you don't even need vr you
+ 
+
+ align:start position:0%
+some kind of you don't even need vr you
+can use a pretty
+
+ align:start position:0%
+can use a pretty
+ 
+
+ align:start position:0%
+can use a pretty
+cheesy little video game and i'm sure
+
+ align:start position:0%
+cheesy little video game and i'm sure
+ 
+
+ align:start position:0%
+cheesy little video game and i'm sure
+this one was quite cheesy this study was
+
+ align:start position:0%
+this one was quite cheesy this study was
+ 
+
+ align:start position:0%
+this one was quite cheesy this study was
+done back in 2003
+
+ align:start position:0%
+done back in 2003
+ 
+
+ align:start position:0%
+done back in 2003
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+they had patients navigate through a
+
+ align:start position:0%
+they had patients navigate through a
+ 
+
+ align:start position:0%
+they had patients navigate through a
+space this is an aerial view of the
+
+ align:start position:0%
+space this is an aerial view of the
+ 
+
+ align:start position:0%
+space this is an aerial view of the
+space the patients didn't see that they
+
+ align:start position:0%
+space the patients didn't see that they
+ 
+
+ align:start position:0%
+space the patients didn't see that they
+saw this kind of front view and they
+
+ align:start position:0%
+saw this kind of front view and they
+ 
+
+ align:start position:0%
+saw this kind of front view and they
+kind of navigated around with the
+
+ align:start position:0%
+kind of navigated around with the
+ 
+
+ align:start position:0%
+kind of navigated around with the
+joystick in that space and there were
+
+ align:start position:0%
+joystick in that space and there were
+ 
+
+ align:start position:0%
+joystick in that space and there were
+three
+
+ align:start position:0%
+three
+ 
+
+ align:start position:0%
+three
+kind of visually recognizable kind of
+
+ align:start position:0%
+kind of visually recognizable kind of
+ 
+
+ align:start position:0%
+kind of visually recognizable kind of
+locations in that space and they had to
+
+ align:start position:0%
+locations in that space and they had to
+ 
+
+ align:start position:0%
+locations in that space and they had to
+do things to go from one location to
+
+ align:start position:0%
+do things to go from one location to
+ 
+
+ align:start position:0%
+do things to go from one location to
+another
+
+ align:start position:0%
+another
+ 
+
+ align:start position:0%
+another
+okay details don't really matter
+
+ align:start position:0%
+okay details don't really matter
+ 
+
+ align:start position:0%
+okay details don't really matter
+so all the while um ekstrom and
+
+ align:start position:0%
+so all the while um ekstrom and
+ 
+
+ align:start position:0%
+so all the while um ekstrom and
+colleagues are recording from individual
+
+ align:start position:0%
+colleagues are recording from individual
+ 
+
+ align:start position:0%
+colleagues are recording from individual
+neurons in this patient's hippocampus
+
+ align:start position:0%
+neurons in this patient's hippocampus
+ 
+
+ align:start position:0%
+neurons in this patient's hippocampus
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+so here's an example of a place cell so
+
+ align:start position:0%
+so here's an example of a place cell so
+ 
+
+ align:start position:0%
+so here's an example of a place cell so
+this is a diagram of the space i just
+
+ align:start position:0%
+this is a diagram of the space i just
+ 
+
+ align:start position:0%
+this is a diagram of the space i just
+showed you right with those
+
+ align:start position:0%
+showed you right with those
+ 
+
+ align:start position:0%
+showed you right with those
+three recognizable locations and other
+
+ align:start position:0%
+three recognizable locations and other
+ 
+
+ align:start position:0%
+three recognizable locations and other
+locations that the patient could
+
+ align:start position:0%
+locations that the patient could
+ 
+
+ align:start position:0%
+locations that the patient could
+virtually navigate through with the
+
+ align:start position:0%
+virtually navigate through with the
+ 
+
+ align:start position:0%
+virtually navigate through with the
+joystick the red lines are the patient's
+
+ align:start position:0%
+joystick the red lines are the patient's
+ 
+
+ align:start position:0%
+joystick the red lines are the patient's
+trajectory as they moved around in that
+
+ align:start position:0%
+trajectory as they moved around in that
+ 
+
+ align:start position:0%
+trajectory as they moved around in that
+space
+
+ align:start position:0%
+space
+ 
+
+ align:start position:0%
+space
+and the colors within each square are
+
+ align:start position:0%
+and the colors within each square are
+ 
+
+ align:start position:0%
+and the colors within each square are
+the average firing rate
+
+ align:start position:0%
+the average firing rate
+ 
+
+ align:start position:0%
+the average firing rate
+when the patient navigated through that
+
+ align:start position:0%
+when the patient navigated through that
+ 
+
+ align:start position:0%
+when the patient navigated through that
+location
+
+ align:start position:0%
+location
+ 
+
+ align:start position:0%
+location
+and so this is the place field of that
+
+ align:start position:0%
+and so this is the place field of that
+ 
+
+ align:start position:0%
+and so this is the place field of that
+individual cell in this patient's brain
+
+ align:start position:0%
+individual cell in this patient's brain
+ 
+
+ align:start position:0%
+individual cell in this patient's brain
+as they went through this space because
+
+ align:start position:0%
+as they went through this space because
+ 
+
+ align:start position:0%
+as they went through this space because
+the firing rate there was around five
+
+ align:start position:0%
+the firing rate there was around five
+ 
+
+ align:start position:0%
+the firing rate there was around five
+hertz compared to you know three hertz
+
+ align:start position:0%
+hertz compared to you know three hertz
+ 
+
+ align:start position:0%
+hertz compared to you know three hertz
+for some other locations and mostly
+
+ align:start position:0%
+for some other locations and mostly
+ 
+
+ align:start position:0%
+for some other locations and mostly
+lower than that
+
+ align:start position:0%
+lower than that
+ 
+
+ align:start position:0%
+lower than that
+okay does that make sense so we're just
+
+ align:start position:0%
+okay does that make sense so we're just
+ 
+
+ align:start position:0%
+okay does that make sense so we're just
+just like the rodent experiment but it's
+
+ align:start position:0%
+just like the rodent experiment but it's
+ 
+
+ align:start position:0%
+just like the rodent experiment but it's
+a person with a joystick looking at this
+
+ align:start position:0%
+a person with a joystick looking at this
+ 
+
+ align:start position:0%
+a person with a joystick looking at this
+space as they go through this virtual
+
+ align:start position:0%
+space as they go through this virtual
+ 
+
+ align:start position:0%
+space as they go through this virtual
+environment and we're mapping out their
+
+ align:start position:0%
+environment and we're mapping out their
+ 
+
+ align:start position:0%
+environment and we're mapping out their
+place fields like that okay
+
+ align:start position:0%
+place fields like that okay
+ 
+
+ align:start position:0%
+place fields like that okay
+so that shows that humans have placed
+
+ align:start position:0%
+so that shows that humans have placed
+ 
+
+ align:start position:0%
+so that shows that humans have placed
+fields in their hippocampus just as
+
+ align:start position:0%
+fields in their hippocampus just as
+ 
+
+ align:start position:0%
+fields in their hippocampus just as
+rodents and bats do yeah
+
+ align:start position:0%
+rodents and bats do yeah
+ 
+
+ align:start position:0%
+rodents and bats do yeah
+all this is like independent of
+
+ align:start position:0%
+all this is like independent of
+ 
+
+ align:start position:0%
+all this is like independent of
+landmarks
+
+ align:start position:0%
+landmarks
+ 
+
+ align:start position:0%
+landmarks
+um that's a very complicated question
+
+ align:start position:0%
+um that's a very complicated question
+ 
+
+ align:start position:0%
+um that's a very complicated question
+this patient had access to landmarks
+
+ align:start position:0%
+this patient had access to landmarks
+ 
+
+ align:start position:0%
+this patient had access to landmarks
+they are seeing as they go through
+
+ align:start position:0%
+they are seeing as they go through
+ 
+
+ align:start position:0%
+they are seeing as they go through
+so one could ask for example if you did
+
+ align:start position:0%
+so one could ask for example if you did
+ 
+
+ align:start position:0%
+so one could ask for example if you did
+it with your eyes closed and you had to
+
+ align:start position:0%
+it with your eyes closed and you had to
+ 
+
+ align:start position:0%
+it with your eyes closed and you had to
+go by dead reckoning remembering the
+
+ align:start position:0%
+go by dead reckoning remembering the
+ 
+
+ align:start position:0%
+go by dead reckoning remembering the
+left and right turns you had in a
+
+ align:start position:0%
+left and right turns you had in a
+ 
+
+ align:start position:0%
+left and right turns you had in a
+familiar environment how well could
+
+ align:start position:0%
+familiar environment how well could
+ 
+
+ align:start position:0%
+familiar environment how well could
+these things go they would go for at
+
+ align:start position:0%
+these things go they would go for at
+ 
+
+ align:start position:0%
+these things go they would go for at
+least a while
+
+ align:start position:0%
+least a while
+ 
+
+ align:start position:0%
+least a while
+they'd probably go for longer in rodents
+
+ align:start position:0%
+they'd probably go for longer in rodents
+ 
+
+ align:start position:0%
+they'd probably go for longer in rodents
+because rodents
+
+ align:start position:0%
+because rodents
+ 
+
+ align:start position:0%
+because rodents
+are more accustomed to navigating in the
+
+ align:start position:0%
+are more accustomed to navigating in the
+ 
+
+ align:start position:0%
+are more accustomed to navigating in the
+dark and they rely less on visual cues
+
+ align:start position:0%
+dark and they rely less on visual cues
+ 
+
+ align:start position:0%
+dark and they rely less on visual cues
+and more on other cues
+
+ align:start position:0%
+and more on other cues
+ 
+
+ align:start position:0%
+and more on other cues
+but yeah these are not
+
+ align:start position:0%
+but yeah these are not
+ 
+
+ align:start position:0%
+but yeah these are not
+place cells aren't just visually
+
+ align:start position:0%
+place cells aren't just visually
+ 
+
+ align:start position:0%
+place cells aren't just visually
+responsive right so
+
+ align:start position:0%
+responsive right so
+ 
+
+ align:start position:0%
+responsive right so
+if we had like for example if we set up
+
+ align:start position:0%
+if we had like for example if we set up
+ 
+
+ align:start position:0%
+if we had like for example if we set up
+a a um a distinctive sound source in
+
+ align:start position:0%
+a a um a distinctive sound source in
+ 
+
+ align:start position:0%
+a a um a distinctive sound source in
+this corner of the room and a different
+
+ align:start position:0%
+this corner of the room and a different
+ 
+
+ align:start position:0%
+this corner of the room and a different
+you know like say somebody was singing
+
+ align:start position:0%
+you know like say somebody was singing
+ 
+
+ align:start position:0%
+you know like say somebody was singing
+quietly over here
+
+ align:start position:0%
+quietly over here
+ 
+
+ align:start position:0%
+quietly over here
+and we um
+
+ align:start position:0%
+and we um
+ 
+
+ align:start position:0%
+and we um
+tied a dog over there who was barking
+
+ align:start position:0%
+tied a dog over there who was barking
+ 
+
+ align:start position:0%
+tied a dog over there who was barking
+right and you you walked around in this
+
+ align:start position:0%
+right and you you walked around in this
+ 
+
+ align:start position:0%
+right and you you walked around in this
+room with your eyes closed you'd have a
+
+ align:start position:0%
+room with your eyes closed you'd have a
+ 
+
+ align:start position:0%
+room with your eyes closed you'd have a
+pretty you'd have a good way to keep
+
+ align:start position:0%
+pretty you'd have a good way to keep
+ 
+
+ align:start position:0%
+pretty you'd have a good way to keep
+track of your bearings as you moved
+
+ align:start position:0%
+track of your bearings as you moved
+ 
+
+ align:start position:0%
+track of your bearings as you moved
+around because you'd know that the
+
+ align:start position:0%
+around because you'd know that the
+ 
+
+ align:start position:0%
+around because you'd know that the
+singing was coming from here and the dog
+
+ align:start position:0%
+singing was coming from here and the dog
+ 
+
+ align:start position:0%
+singing was coming from here and the dog
+barking was coming from there you
+
+ align:start position:0%
+barking was coming from there you
+ 
+
+ align:start position:0%
+barking was coming from there you
+wouldn't be seeing anything your eyes
+
+ align:start position:0%
+wouldn't be seeing anything your eyes
+ 
+
+ align:start position:0%
+wouldn't be seeing anything your eyes
+would be closed but your place cells
+
+ align:start position:0%
+would be closed but your place cells
+ 
+
+ align:start position:0%
+would be closed but your place cells
+would work pretty well okay so whenever
+
+ align:start position:0%
+would work pretty well okay so whenever
+ 
+
+ align:start position:0%
+would work pretty well okay so whenever
+you have some basis for knowing where
+
+ align:start position:0%
+you have some basis for knowing where
+ 
+
+ align:start position:0%
+you have some basis for knowing where
+you are no matter what modality is
+
+ align:start position:0%
+you are no matter what modality is
+ 
+
+ align:start position:0%
+you are no matter what modality is
+telling you that
+
+ align:start position:0%
+telling you that
+ 
+
+ align:start position:0%
+telling you that
+usually it's many modalities those place
+
+ align:start position:0%
+usually it's many modalities those place
+ 
+
+ align:start position:0%
+usually it's many modalities those place
+cells will go
+
+ align:start position:0%
+cells will go
+ 
+
+ align:start position:0%
+cells will go
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+okay so humans have these things too so
+
+ align:start position:0%
+okay so humans have these things too so
+ 
+
+ align:start position:0%
+okay so humans have these things too so
+you can think of the place cell as the
+
+ align:start position:0%
+you can think of the place cell as the
+ 
+
+ align:start position:0%
+you can think of the place cell as the
+kind of you are here system right
+
+ align:start position:0%
+kind of you are here system right
+ 
+
+ align:start position:0%
+kind of you are here system right
+that is the whole set of place cells any
+
+ align:start position:0%
+that is the whole set of place cells any
+ 
+
+ align:start position:0%
+that is the whole set of place cells any
+one place will only tell you are you in
+
+ align:start position:0%
+one place will only tell you are you in
+ 
+
+ align:start position:0%
+one place will only tell you are you in
+this particular location or not but you
+
+ align:start position:0%
+this particular location or not but you
+ 
+
+ align:start position:0%
+this particular location or not but you
+have a whole array of them then
+
+ align:start position:0%
+have a whole array of them then
+ 
+
+ align:start position:0%
+have a whole array of them then
+collectively
+
+ align:start position:0%
+collectively
+ 
+
+ align:start position:0%
+collectively
+that that whole representation across
+
+ align:start position:0%
+that that whole representation across
+ 
+
+ align:start position:0%
+that that whole representation across
+all of those neurons can tell you where
+
+ align:start position:0%
+all of those neurons can tell you where
+ 
+
+ align:start position:0%
+all of those neurons can tell you where
+you are in your familiar environment
+
+ align:start position:0%
+you are in your familiar environment
+ 
+
+ align:start position:0%
+you are in your familiar environment
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+but if you want to not just know where
+
+ align:start position:0%
+but if you want to not just know where
+ 
+
+ align:start position:0%
+but if you want to not just know where
+you are but you want to go somewhere
+
+ align:start position:0%
+you are but you want to go somewhere
+ 
+
+ align:start position:0%
+you are but you want to go somewhere
+else like there
+
+ align:start position:0%
+else like there
+ 
+
+ align:start position:0%
+else like there
+you also need to know your current
+
+ align:start position:0%
+you also need to know your current
+ 
+
+ align:start position:0%
+you also need to know your current
+heading as we discussed last time okay
+
+ align:start position:0%
+heading as we discussed last time okay
+ 
+
+ align:start position:0%
+heading as we discussed last time okay
+so it turns out
+
+ align:start position:0%
+so it turns out
+ 
+
+ align:start position:0%
+so it turns out
+that there's a whole other batch of
+
+ align:start position:0%
+that there's a whole other batch of
+ 
+
+ align:start position:0%
+that there's a whole other batch of
+cells
+
+ align:start position:0%
+cells
+ 
+
+ align:start position:0%
+cells
+that tell you what way you're heading
+
+ align:start position:0%
+that tell you what way you're heading
+ 
+
+ align:start position:0%
+that tell you what way you're heading
+okay these are called head direction
+
+ align:start position:0%
+okay these are called head direction
+ 
+
+ align:start position:0%
+okay these are called head direction
+cells
+
+ align:start position:0%
+cells
+ 
+
+ align:start position:0%
+cells
+also first studied in rodents
+
+ align:start position:0%
+also first studied in rodents
+ 
+
+ align:start position:0%
+also first studied in rodents
+and each head direction cell responds
+
+ align:start position:0%
+and each head direction cell responds
+ 
+
+ align:start position:0%
+and each head direction cell responds
+when that rodent is heading in a
+
+ align:start position:0%
+when that rodent is heading in a
+ 
+
+ align:start position:0%
+when that rodent is heading in a
+particular direction
+
+ align:start position:0%
+particular direction
+ 
+
+ align:start position:0%
+particular direction
+not in another direction
+
+ align:start position:0%
+not in another direction
+ 
+
+ align:start position:0%
+not in another direction
+okay so for example
+
+ align:start position:0%
+okay so for example
+ 
+
+ align:start position:0%
+okay so for example
+you have you know
+
+ align:start position:0%
+you have you know
+ 
+
+ align:start position:0%
+you have you know
+if we're mapping along the x-axis
+
+ align:start position:0%
+if we're mapping along the x-axis
+ 
+
+ align:start position:0%
+if we're mapping along the x-axis
+different heading direction so the
+
+ align:start position:0%
+different heading direction so the
+ 
+
+ align:start position:0%
+different heading direction so the
+rodent is facing in different directions
+
+ align:start position:0%
+rodent is facing in different directions
+ 
+
+ align:start position:0%
+rodent is facing in different directions
+in his environment you map up the whole
+
+ align:start position:0%
+in his environment you map up the whole
+ 
+
+ align:start position:0%
+in his environment you map up the whole
+360 degrees
+
+ align:start position:0%
+360 degrees
+ 
+
+ align:start position:0%
+360 degrees
+this would be the response of one cell
+
+ align:start position:0%
+this would be the response of one cell
+ 
+
+ align:start position:0%
+this would be the response of one cell
+as that
+
+ align:start position:0%
+as that
+ 
+
+ align:start position:0%
+as that
+rodent moves around
+
+ align:start position:0%
+rodent moves around
+ 
+
+ align:start position:0%
+rodent moves around
+this one will be tuned to this
+
+ align:start position:0%
+this one will be tuned to this
+ 
+
+ align:start position:0%
+this one will be tuned to this
+particular direction it would fire only
+
+ align:start position:0%
+particular direction it would fire only
+ 
+
+ align:start position:0%
+particular direction it would fire only
+when the rodent was facing this way not
+
+ align:start position:0%
+when the rodent was facing this way not
+ 
+
+ align:start position:0%
+when the rodent was facing this way not
+when it was facing this way or this way
+
+ align:start position:0%
+when it was facing this way or this way
+ 
+
+ align:start position:0%
+when it was facing this way or this way
+or this way or this way
+
+ align:start position:0%
+or this way or this way
+ 
+
+ align:start position:0%
+or this way or this way
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+so everybody get how where you are in
+
+ align:start position:0%
+so everybody get how where you are in
+ 
+
+ align:start position:0%
+so everybody get how where you are in
+space is different that's not a very
+
+ align:start position:0%
+space is different that's not a very
+ 
+
+ align:start position:0%
+space is different that's not a very
+good way to show this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+where you are in space
+
+ align:start position:0%
+where you are in space
+ 
+
+ align:start position:0%
+where you are in space
+is different from where you're
+
+ align:start position:0%
+is different from where you're
+ 
+
+ align:start position:0%
+is different from where you're
+aimed and headed in that location okay
+
+ align:start position:0%
+aimed and headed in that location okay
+ 
+
+ align:start position:0%
+aimed and headed in that location okay
+two orthogonal axes of
+
+ align:start position:0%
+two orthogonal axes of
+ 
+
+ align:start position:0%
+two orthogonal axes of
+relevant to your location yeah
+
+ align:start position:0%
+relevant to your location yeah
+ 
+
+ align:start position:0%
+relevant to your location yeah
+so this isn't the angle of the head
+
+ align:start position:0%
+so this isn't the angle of the head
+ 
+
+ align:start position:0%
+so this isn't the angle of the head
+respect the body right it's the entire
+
+ align:start position:0%
+respect the body right it's the entire
+ 
+
+ align:start position:0%
+respect the body right it's the entire
+um i think
+
+ align:start position:0%
+um i think
+ 
+
+ align:start position:0%
+um i think
+i meant to look that up again because
+
+ align:start position:0%
+i meant to look that up again because
+ 
+
+ align:start position:0%
+i meant to look that up again because
+this question always arises um i think
+
+ align:start position:0%
+this question always arises um i think
+ 
+
+ align:start position:0%
+this question always arises um i think
+that there's some muck about that in the
+
+ align:start position:0%
+that there's some muck about that in the
+ 
+
+ align:start position:0%
+that there's some muck about that in the
+literature which is why i never remember
+
+ align:start position:0%
+literature which is why i never remember
+ 
+
+ align:start position:0%
+literature which is why i never remember
+a clear answer usually in a rodent
+
+ align:start position:0%
+a clear answer usually in a rodent
+ 
+
+ align:start position:0%
+a clear answer usually in a rodent
+especially they're the same
+
+ align:start position:0%
+especially they're the same
+ 
+
+ align:start position:0%
+especially they're the same
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+and whether you know because you know
+
+ align:start position:0%
+and whether you know because you know
+ 
+
+ align:start position:0%
+and whether you know because you know
+runs can turn their heads a little bit
+
+ align:start position:0%
+runs can turn their heads a little bit
+ 
+
+ align:start position:0%
+runs can turn their heads a little bit
+but you know mostly they're gonna
+
+ align:start position:0%
+but you know mostly they're gonna
+ 
+
+ align:start position:0%
+but you know mostly they're gonna
+keep it aimed the way they're moving
+
+ align:start position:0%
+keep it aimed the way they're moving
+ 
+
+ align:start position:0%
+keep it aimed the way they're moving
+um so i don't know this is a long
+
+ align:start position:0%
+um so i don't know this is a long
+ 
+
+ align:start position:0%
+um so i don't know this is a long
+complicated excuse that i forget what
+
+ align:start position:0%
+complicated excuse that i forget what
+ 
+
+ align:start position:0%
+complicated excuse that i forget what
+the answer to that is um but send me an
+
+ align:start position:0%
+the answer to that is um but send me an
+ 
+
+ align:start position:0%
+the answer to that is um but send me an
+email and i'll look it up i meant to
+
+ align:start position:0%
+email and i'll look it up i meant to
+ 
+
+ align:start position:0%
+email and i'll look it up i meant to
+before this lecture just ran out of time
+
+ align:start position:0%
+before this lecture just ran out of time
+ 
+
+ align:start position:0%
+before this lecture just ran out of time
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+most of the time they'll be the same i
+
+ align:start position:0%
+most of the time they'll be the same i
+ 
+
+ align:start position:0%
+most of the time they'll be the same i
+actually i'm i'm pretty sure it's which
+
+ align:start position:0%
+actually i'm i'm pretty sure it's which
+ 
+
+ align:start position:0%
+actually i'm i'm pretty sure it's which
+way your body's facing because if i turn
+
+ align:start position:0%
+way your body's facing because if i turn
+ 
+
+ align:start position:0%
+way your body's facing because if i turn
+like this well anyway i'm not going that
+
+ align:start position:0%
+like this well anyway i'm not going that
+ 
+
+ align:start position:0%
+like this well anyway i'm not going that
+way yeah and have you found at least 360
+
+ align:start position:0%
+way yeah and have you found at least 360
+ 
+
+ align:start position:0%
+way yeah and have you found at least 360
+cents for each sort of angle
+
+ align:start position:0%
+cents for each sort of angle
+ 
+
+ align:start position:0%
+cents for each sort of angle
+i mean are there cells for each yes yes
+
+ align:start position:0%
+i mean are there cells for each yes yes
+ 
+
+ align:start position:0%
+i mean are there cells for each yes yes
+they they pretty much evenly tile the
+
+ align:start position:0%
+they they pretty much evenly tile the
+ 
+
+ align:start position:0%
+they they pretty much evenly tile the
+360 degrees around the animal yeah so
+
+ align:start position:0%
+360 degrees around the animal yeah so
+ 
+
+ align:start position:0%
+360 degrees around the animal yeah so
+collectively that whole set of cells
+
+ align:start position:0%
+collectively that whole set of cells
+ 
+
+ align:start position:0%
+collectively that whole set of cells
+just as a collective set of place cells
+
+ align:start position:0%
+just as a collective set of place cells
+ 
+
+ align:start position:0%
+just as a collective set of place cells
+is sufficient to tell the animal where
+
+ align:start position:0%
+is sufficient to tell the animal where
+ 
+
+ align:start position:0%
+is sufficient to tell the animal where
+it is a collective set of head direction
+
+ align:start position:0%
+it is a collective set of head direction
+ 
+
+ align:start position:0%
+it is a collective set of head direction
+cells is sufficient to tell the animal
+
+ align:start position:0%
+cells is sufficient to tell the animal
+ 
+
+ align:start position:0%
+cells is sufficient to tell the animal
+which way it's oriented
+
+ align:start position:0%
+which way it's oriented
+ 
+
+ align:start position:0%
+which way it's oriented
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+okay i think we just said all these
+
+ align:start position:0%
+okay i think we just said all these
+ 
+
+ align:start position:0%
+okay i think we just said all these
+things are in a structure called the
+
+ align:start position:0%
+things are in a structure called the
+ 
+
+ align:start position:0%
+things are in a structure called the
+well first found in a structure called
+
+ align:start position:0%
+well first found in a structure called
+ 
+
+ align:start position:0%
+well first found in a structure called
+the subiculum which is part of the
+
+ align:start position:0%
+the subiculum which is part of the
+ 
+
+ align:start position:0%
+the subiculum which is part of the
+hippocampus but since then they've been
+
+ align:start position:0%
+hippocampus but since then they've been
+ 
+
+ align:start position:0%
+hippocampus but since then they've been
+found in lots of different regions you
+
+ align:start position:0%
+found in lots of different regions you
+ 
+
+ align:start position:0%
+found in lots of different regions you
+don't need to remember that
+
+ align:start position:0%
+don't need to remember that
+ 
+
+ align:start position:0%
+don't need to remember that
+um so they get input from lots of
+
+ align:start position:0%
+um so they get input from lots of
+ 
+
+ align:start position:0%
+um so they get input from lots of
+different information there's many
+
+ align:start position:0%
+different information there's many
+ 
+
+ align:start position:0%
+different information there's many
+different ways to know which way we're
+
+ align:start position:0%
+different ways to know which way we're
+ 
+
+ align:start position:0%
+different ways to know which way we're
+oriented
+
+ align:start position:0%
+oriented
+ 
+
+ align:start position:0%
+oriented
+for example too bad we don't have a
+
+ align:start position:0%
+for example too bad we don't have a
+ 
+
+ align:start position:0%
+for example too bad we don't have a
+rotating chair
+
+ align:start position:0%
+rotating chair
+ 
+
+ align:start position:0%
+rotating chair
+if we did i would have done the
+
+ align:start position:0%
+if we did i would have done the
+ 
+
+ align:start position:0%
+if we did i would have done the
+following ridiculous thing i would have
+
+ align:start position:0%
+following ridiculous thing i would have
+ 
+
+ align:start position:0%
+following ridiculous thing i would have
+sat one of you in it and told you to
+
+ align:start position:0%
+sat one of you in it and told you to
+ 
+
+ align:start position:0%
+sat one of you in it and told you to
+close your eyes and i would suddenly
+
+ align:start position:0%
+close your eyes and i would suddenly
+ 
+
+ align:start position:0%
+close your eyes and i would suddenly
+turn it
+
+ align:start position:0%
+turn it
+ 
+
+ align:start position:0%
+turn it
+and the person in the chair would notice
+
+ align:start position:0%
+and the person in the chair would notice
+ 
+
+ align:start position:0%
+and the person in the chair would notice
+that right that's your vestibular system
+
+ align:start position:0%
+that right that's your vestibular system
+ 
+
+ align:start position:0%
+that right that's your vestibular system
+that tells you if your body's being
+
+ align:start position:0%
+that tells you if your body's being
+ 
+
+ align:start position:0%
+that tells you if your body's being
+turned even if you yourself don't decide
+
+ align:start position:0%
+turned even if you yourself don't decide
+ 
+
+ align:start position:0%
+turned even if you yourself don't decide
+to turn it it will tell you if you get
+
+ align:start position:0%
+to turn it it will tell you if you get
+ 
+
+ align:start position:0%
+to turn it it will tell you if you get
+turned that's another cue that provides
+
+ align:start position:0%
+turned that's another cue that provides
+ 
+
+ align:start position:0%
+turned that's another cue that provides
+input to the head direction cells just
+
+ align:start position:0%
+input to the head direction cells just
+ 
+
+ align:start position:0%
+input to the head direction cells just
+as visual information does and
+
+ align:start position:0%
+as visual information does and
+ 
+
+ align:start position:0%
+as visual information does and
+potentially auditory information and
+
+ align:start position:0%
+potentially auditory information and
+ 
+
+ align:start position:0%
+potentially auditory information and
+lots of other kinds of information
+
+ align:start position:0%
+lots of other kinds of information
+ 
+
+ align:start position:0%
+lots of other kinds of information
+so many different sources of information
+
+ align:start position:0%
+so many different sources of information
+ 
+
+ align:start position:0%
+so many different sources of information
+feed in to inform these head direction
+
+ align:start position:0%
+feed in to inform these head direction
+ 
+
+ align:start position:0%
+feed in to inform these head direction
+cells about the orientation of the
+
+ align:start position:0%
+cells about the orientation of the
+ 
+
+ align:start position:0%
+cells about the orientation of the
+animal
+
+ align:start position:0%
+animal
+ 
+
+ align:start position:0%
+animal
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+all right so you can think of this as
+
+ align:start position:0%
+all right so you can think of this as
+ 
+
+ align:start position:0%
+all right so you can think of this as
+the brain's compass right
+
+ align:start position:0%
+the brain's compass right
+ 
+
+ align:start position:0%
+the brain's compass right
+telling the organism what way they're
+
+ align:start position:0%
+telling the organism what way they're
+ 
+
+ align:start position:0%
+telling the organism what way they're
+facing
+
+ align:start position:0%
+facing
+ 
+
+ align:start position:0%
+facing
+okay and
+
+ align:start position:0%
+okay and
+ 
+
+ align:start position:0%
+okay and
+lots of organisms have versions of this
+
+ align:start position:0%
+lots of organisms have versions of this
+ 
+
+ align:start position:0%
+lots of organisms have versions of this
+in the fly there's an amazing structure
+
+ align:start position:0%
+in the fly there's an amazing structure
+ 
+
+ align:start position:0%
+in the fly there's an amazing structure
+that was discovered just a couple years
+
+ align:start position:0%
+that was discovered just a couple years
+ 
+
+ align:start position:0%
+that was discovered just a couple years
+ago where the there's a whole kind of
+
+ align:start position:0%
+ago where the there's a whole kind of
+ 
+
+ align:start position:0%
+ago where the there's a whole kind of
+layout of this little neural structure i
+
+ align:start position:0%
+layout of this little neural structure i
+ 
+
+ align:start position:0%
+layout of this little neural structure i
+forget what it's called but actually
+
+ align:start position:0%
+forget what it's called but actually
+ 
+
+ align:start position:0%
+forget what it's called but actually
+spatially in that structure there's a
+
+ align:start position:0%
+spatially in that structure there's a
+ 
+
+ align:start position:0%
+spatially in that structure there's a
+little array
+
+ align:start position:0%
+little array
+ 
+
+ align:start position:0%
+little array
+of direction cells so actually you could
+
+ align:start position:0%
+of direction cells so actually you could
+ 
+
+ align:start position:0%
+of direction cells so actually you could
+see it in a little spatial map
+
+ align:start position:0%
+see it in a little spatial map
+ 
+
+ align:start position:0%
+see it in a little spatial map
+of direction
+
+ align:start position:0%
+of direction
+ 
+
+ align:start position:0%
+of direction
+in that little structure in the fly
+
+ align:start position:0%
+in that little structure in the fly
+ 
+
+ align:start position:0%
+in that little structure in the fly
+okay in humans and primates and rodents
+
+ align:start position:0%
+okay in humans and primates and rodents
+ 
+
+ align:start position:0%
+okay in humans and primates and rodents
+it's not organized spatially like a
+
+ align:start position:0%
+it's not organized spatially like a
+ 
+
+ align:start position:0%
+it's not organized spatially like a
+literal
+
+ align:start position:0%
+literal
+ 
+
+ align:start position:0%
+literal
+map of direction
+
+ align:start position:0%
+map of direction
+ 
+
+ align:start position:0%
+map of direction
+okay so now we have where you are and
+
+ align:start position:0%
+okay so now we have where you are and
+ 
+
+ align:start position:0%
+okay so now we have where you are and
+which way you're facing
+
+ align:start position:0%
+which way you're facing
+ 
+
+ align:start position:0%
+which way you're facing
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+you know one pool of cells place cells
+
+ align:start position:0%
+you know one pool of cells place cells
+ 
+
+ align:start position:0%
+you know one pool of cells place cells
+for where you are another pool of cells
+
+ align:start position:0%
+for where you are another pool of cells
+ 
+
+ align:start position:0%
+for where you are another pool of cells
+for which way you're heading
+
+ align:start position:0%
+for which way you're heading
+ 
+
+ align:start position:0%
+for which way you're heading
+but those are just we're just getting
+
+ align:start position:0%
+but those are just we're just getting
+ 
+
+ align:start position:0%
+but those are just we're just getting
+going here the coolest navigation
+
+ align:start position:0%
+going here the coolest navigation
+ 
+
+ align:start position:0%
+going here the coolest navigation
+related cells
+
+ align:start position:0%
+related cells
+ 
+
+ align:start position:0%
+related cells
+are grid cells in entering cortex okay
+
+ align:start position:0%
+are grid cells in entering cortex okay
+ 
+
+ align:start position:0%
+are grid cells in entering cortex okay
+so this is a slice of the brain like
+
+ align:start position:0%
+so this is a slice of the brain like
+ 
+
+ align:start position:0%
+so this is a slice of the brain like
+this
+
+ align:start position:0%
+this
+ 
+
+ align:start position:0%
+this
+showing the hippocampus this folded up
+
+ align:start position:0%
+showing the hippocampus this folded up
+ 
+
+ align:start position:0%
+showing the hippocampus this folded up
+thing right here
+
+ align:start position:0%
+thing right here
+ 
+
+ align:start position:0%
+thing right here
+an interrental cortex is just
+
+ align:start position:0%
+an interrental cortex is just
+ 
+
+ align:start position:0%
+an interrental cortex is just
+just
+
+ align:start position:0%
+just
+ 
+
+ align:start position:0%
+just
+right next door
+
+ align:start position:0%
+right next door
+ 
+
+ align:start position:0%
+right next door
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+so in internal cortex
+
+ align:start position:0%
+so in internal cortex
+ 
+
+ align:start position:0%
+so in internal cortex
+these things were discovered a little
+
+ align:start position:0%
+these things were discovered a little
+ 
+
+ align:start position:0%
+these things were discovered a little
+around a dozen years ago
+
+ align:start position:0%
+around a dozen years ago
+ 
+
+ align:start position:0%
+around a dozen years ago
+maybe 15 years ago and i'm going to show
+
+ align:start position:0%
+maybe 15 years ago and i'm going to show
+ 
+
+ align:start position:0%
+maybe 15 years ago and i'm going to show
+you a video of a rodent moving around
+
+ align:start position:0%
+you a video of a rodent moving around
+ 
+
+ align:start position:0%
+you a video of a rodent moving around
+his environment
+
+ align:start position:0%
+his environment
+ 
+
+ align:start position:0%
+his environment
+mapping out activity like we saw before
+
+ align:start position:0%
+mapping out activity like we saw before
+ 
+
+ align:start position:0%
+mapping out activity like we saw before
+but now we're in entering cortex and
+
+ align:start position:0%
+but now we're in entering cortex and
+ 
+
+ align:start position:0%
+but now we're in entering cortex and
+this neuron is going to be a grid cell
+
+ align:start position:0%
+this neuron is going to be a grid cell
+ 
+
+ align:start position:0%
+this neuron is going to be a grid cell
+and you'll see why as it moves around in
+
+ align:start position:0%
+and you'll see why as it moves around in
+ 
+
+ align:start position:0%
+and you'll see why as it moves around in
+its space
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+maybe
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+come on here we go
+
+ align:start position:0%
+come on here we go
+ 
+
+ align:start position:0%
+come on here we go
+okay so there's the rodent he's moving
+
+ align:start position:0%
+okay so there's the rodent he's moving
+ 
+
+ align:start position:0%
+okay so there's the rodent he's moving
+around that's the tether taking the
+
+ align:start position:0%
+around that's the tether taking the
+ 
+
+ align:start position:0%
+around that's the tether taking the
+neural activity the white dots are every
+
+ align:start position:0%
+neural activity the white dots are every
+ 
+
+ align:start position:0%
+neural activity the white dots are every
+time this one neuron fires we're
+
+ align:start position:0%
+time this one neuron fires we're
+ 
+
+ align:start position:0%
+time this one neuron fires we're
+following one neuron this whole time
+
+ align:start position:0%
+following one neuron this whole time
+ 
+
+ align:start position:0%
+following one neuron this whole time
+and the rodent is moving around sped up
+
+ align:start position:0%
+and the rodent is moving around sped up
+ 
+
+ align:start position:0%
+and the rodent is moving around sped up
+video so you can see this happening and
+
+ align:start position:0%
+video so you can see this happening and
+ 
+
+ align:start position:0%
+video so you can see this happening and
+at first it looks like completely random
+
+ align:start position:0%
+at first it looks like completely random
+ 
+
+ align:start position:0%
+at first it looks like completely random
+but as the rodent keeps migrating around
+
+ align:start position:0%
+but as the rodent keeps migrating around
+ 
+
+ align:start position:0%
+but as the rodent keeps migrating around
+in his space there you start to see that
+
+ align:start position:0%
+in his space there you start to see that
+ 
+
+ align:start position:0%
+in his space there you start to see that
+they're like blobs in there it's not
+
+ align:start position:0%
+they're like blobs in there it's not
+ 
+
+ align:start position:0%
+they're like blobs in there it's not
+totally random they're particular blobs
+
+ align:start position:0%
+totally random they're particular blobs
+ 
+
+ align:start position:0%
+totally random they're particular blobs
+that are clustered
+
+ align:start position:0%
+that are clustered
+ 
+
+ align:start position:0%
+that are clustered
+and oh my god those blobs are organized
+
+ align:start position:0%
+and oh my god those blobs are organized
+ 
+
+ align:start position:0%
+and oh my god those blobs are organized
+in a hexagonal grid
+
+ align:start position:0%
+in a hexagonal grid
+ 
+
+ align:start position:0%
+in a hexagonal grid
+it's a hexagon
+
+ align:start position:0%
+it's a hexagon
+ 
+
+ align:start position:0%
+it's a hexagon
+isn't that awesome that's a grid cell
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+oops there we go we don't need to see it
+
+ align:start position:0%
+oops there we go we don't need to see it
+ 
+
+ align:start position:0%
+oops there we go we don't need to see it
+again
+
+ align:start position:0%
+again
+ 
+
+ align:start position:0%
+again
+so this is a picture of what you just
+
+ align:start position:0%
+so this is a picture of what you just
+ 
+
+ align:start position:0%
+so this is a picture of what you just
+saw the trajectory of the animal and the
+
+ align:start position:0%
+saw the trajectory of the animal and the
+ 
+
+ align:start position:0%
+saw the trajectory of the animal and the
+hot spots uh in that array and here's a
+
+ align:start position:0%
+hot spots uh in that array and here's a
+ 
+
+ align:start position:0%
+hot spots uh in that array and here's a
+kind of smooth mathy version of where
+
+ align:start position:0%
+kind of smooth mathy version of where
+ 
+
+ align:start position:0%
+kind of smooth mathy version of where
+the firing is significant in that space
+
+ align:start position:0%
+the firing is significant in that space
+ 
+
+ align:start position:0%
+the firing is significant in that space
+both showing you hexagonal grid cells
+
+ align:start position:0%
+both showing you hexagonal grid cells
+ 
+
+ align:start position:0%
+both showing you hexagonal grid cells
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+this is at first glance a very weird
+
+ align:start position:0%
+this is at first glance a very weird
+ 
+
+ align:start position:0%
+this is at first glance a very weird
+thing why would it help to have a um
+
+ align:start position:0%
+thing why would it help to have a um
+ 
+
+ align:start position:0%
+thing why would it help to have a um
+a kind of plate essentially a place
+
+ align:start position:0%
+a kind of plate essentially a place
+ 
+
+ align:start position:0%
+a kind of plate essentially a place
+field that has multiple different places
+
+ align:start position:0%
+field that has multiple different places
+ 
+
+ align:start position:0%
+field that has multiple different places
+that make it fire okay and actually
+
+ align:start position:0%
+that make it fire okay and actually
+ 
+
+ align:start position:0%
+that make it fire okay and actually
+somebody asked before where their place
+
+ align:start position:0%
+somebody asked before where their place
+ 
+
+ align:start position:0%
+somebody asked before where their place
+cells have two hot spots place cells
+
+ align:start position:0%
+cells have two hot spots place cells
+ 
+
+ align:start position:0%
+cells have two hot spots place cells
+generally have one but grid cells as you
+
+ align:start position:0%
+generally have one but grid cells as you
+ 
+
+ align:start position:0%
+generally have one but grid cells as you
+see have many organized in this grid
+
+ align:start position:0%
+see have many organized in this grid
+ 
+
+ align:start position:0%
+see have many organized in this grid
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+the the kind of circuitry and math of
+
+ align:start position:0%
+the the kind of circuitry and math of
+ 
+
+ align:start position:0%
+the the kind of circuitry and math of
+this whole system is mind-blowing and
+
+ align:start position:0%
+this whole system is mind-blowing and
+ 
+
+ align:start position:0%
+this whole system is mind-blowing and
+super exciting and the talk that i
+
+ align:start position:0%
+super exciting and the talk that i
+ 
+
+ align:start position:0%
+super exciting and the talk that i
+mentioned yesterday uh was on this topic
+
+ align:start position:0%
+mentioned yesterday uh was on this topic
+ 
+
+ align:start position:0%
+mentioned yesterday uh was on this topic
+and many people are working on this and
+
+ align:start position:0%
+and many people are working on this and
+ 
+
+ align:start position:0%
+and many people are working on this and
+they're working out like really deep
+
+ align:start position:0%
+they're working out like really deep
+ 
+
+ align:start position:0%
+they're working out like really deep
+interesting math about how you can take
+
+ align:start position:0%
+interesting math about how you can take
+ 
+
+ align:start position:0%
+interesting math about how you can take
+these cells how they remain arranged
+
+ align:start position:0%
+these cells how they remain arranged
+ 
+
+ align:start position:0%
+these cells how they remain arranged
+spatially in the brain at multiple
+
+ align:start position:0%
+spatially in the brain at multiple
+ 
+
+ align:start position:0%
+spatially in the brain at multiple
+scales and how you can use them to
+
+ align:start position:0%
+scales and how you can use them to
+ 
+
+ align:start position:0%
+scales and how you can use them to
+do path integration and keep track of
+
+ align:start position:0%
+do path integration and keep track of
+ 
+
+ align:start position:0%
+do path integration and keep track of
+how far you an animal has gone along
+
+ align:start position:0%
+how far you an animal has gone along
+ 
+
+ align:start position:0%
+how far you an animal has gone along
+this trajectory it's a little bit much
+
+ align:start position:0%
+this trajectory it's a little bit much
+ 
+
+ align:start position:0%
+this trajectory it's a little bit much
+for this course but i'll just say the
+
+ align:start position:0%
+for this course but i'll just say the
+ 
+
+ align:start position:0%
+for this course but i'll just say the
+current thinking is
+
+ align:start position:0%
+current thinking is
+ 
+
+ align:start position:0%
+current thinking is
+what these
+
+ align:start position:0%
+what these
+ 
+
+ align:start position:0%
+what these
+what these cells enable us to do is to
+
+ align:start position:0%
+what these cells enable us to do is to
+ 
+
+ align:start position:0%
+what these cells enable us to do is to
+keep track of how far we've gone in each
+
+ align:start position:0%
+keep track of how far we've gone in each
+ 
+
+ align:start position:0%
+keep track of how far we've gone in each
+direction and that's really crucial in
+
+ align:start position:0%
+direction and that's really crucial in
+ 
+
+ align:start position:0%
+direction and that's really crucial in
+navigation we need to know uh where we
+
+ align:start position:0%
+navigation we need to know uh where we
+ 
+
+ align:start position:0%
+navigation we need to know uh where we
+are not just by the landmarks we see we
+
+ align:start position:0%
+are not just by the landmarks we see we
+ 
+
+ align:start position:0%
+are not just by the landmarks we see we
+need to know how far we've gone in a
+
+ align:start position:0%
+need to know how far we've gone in a
+ 
+
+ align:start position:0%
+need to know how far we've gone in a
+given direction and the thought is that
+
+ align:start position:0%
+given direction and the thought is that
+ 
+
+ align:start position:0%
+given direction and the thought is that
+that's the function that these grid
+
+ align:start position:0%
+that's the function that these grid
+ 
+
+ align:start position:0%
+that's the function that these grid
+cells primarily serve in navigation
+
+ align:start position:0%
+cells primarily serve in navigation
+ 
+
+ align:start position:0%
+cells primarily serve in navigation
+um and so that's
+
+ align:start position:0%
+um and so that's
+ 
+
+ align:start position:0%
+um and so that's
+especially important for dead reckoning
+
+ align:start position:0%
+especially important for dead reckoning
+ 
+
+ align:start position:0%
+especially important for dead reckoning
+like integrating you know where you've
+
+ align:start position:0%
+like integrating you know where you've
+ 
+
+ align:start position:0%
+like integrating you know where you've
+gone according to your trajectories okay
+
+ align:start position:0%
+gone according to your trajectories okay
+ 
+
+ align:start position:0%
+gone according to your trajectories okay
+so you also need head direction cells at
+
+ align:start position:0%
+so you also need head direction cells at
+ 
+
+ align:start position:0%
+so you also need head direction cells at
+each point so you can think of the head
+
+ align:start position:0%
+each point so you can think of the head
+ 
+
+ align:start position:0%
+each point so you can think of the head
+direction cells is telling you the
+
+ align:start position:0%
+direction cells is telling you the
+ 
+
+ align:start position:0%
+direction cells is telling you the
+orientation of your vector and the grid
+
+ align:start position:0%
+orientation of your vector and the grid
+ 
+
+ align:start position:0%
+orientation of your vector and the grid
+cells of telling you the magnitude of
+
+ align:start position:0%
+cells of telling you the magnitude of
+ 
+
+ align:start position:0%
+cells of telling you the magnitude of
+the vector of how far you went and you
+
+ align:start position:0%
+the vector of how far you went and you
+ 
+
+ align:start position:0%
+the vector of how far you went and you
+take a whole bunch of those and you
+
+ align:start position:0%
+take a whole bunch of those and you
+ 
+
+ align:start position:0%
+take a whole bunch of those and you
+integrate them and you know where you've
+
+ align:start position:0%
+integrate them and you know where you've
+ 
+
+ align:start position:0%
+integrate them and you know where you've
+gone from your starting point
+
+ align:start position:0%
+gone from your starting point
+ 
+
+ align:start position:0%
+gone from your starting point
+and lots of animals do all that math in
+
+ align:start position:0%
+and lots of animals do all that math in
+ 
+
+ align:start position:0%
+and lots of animals do all that math in
+their head like it's pretty complicated
+
+ align:start position:0%
+their head like it's pretty complicated
+ 
+
+ align:start position:0%
+their head like it's pretty complicated
+integrals right but they all do
+
+ align:start position:0%
+integrals right but they all do
+ 
+
+ align:start position:0%
+integrals right but they all do
+that um okay so this is super awesome
+
+ align:start position:0%
+that um okay so this is super awesome
+ 
+
+ align:start position:0%
+that um okay so this is super awesome
+work and uh fittingly the 2014 nobel
+
+ align:start position:0%
+work and uh fittingly the 2014 nobel
+ 
+
+ align:start position:0%
+work and uh fittingly the 2014 nobel
+prize was awarded to
+
+ align:start position:0%
+prize was awarded to
+ 
+
+ align:start position:0%
+prize was awarded to
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+the the mosers a husband then husband
+
+ align:start position:0%
+the the mosers a husband then husband
+ 
+
+ align:start position:0%
+the the mosers a husband then husband
+wife team
+
+ align:start position:0%
+wife team
+ 
+
+ align:start position:0%
+wife team
+who discovered the grid cells uh and for
+
+ align:start position:0%
+who discovered the grid cells uh and for
+ 
+
+ align:start position:0%
+who discovered the grid cells uh and for
+and also to john o'keefe who discovered
+
+ align:start position:0%
+and also to john o'keefe who discovered
+ 
+
+ align:start position:0%
+and also to john o'keefe who discovered
+place cells uh decades earlier
+
+ align:start position:0%
+place cells uh decades earlier
+ 
+
+ align:start position:0%
+place cells uh decades earlier
+um and it's um it's a super exciting
+
+ align:start position:0%
+um and it's um it's a super exciting
+ 
+
+ align:start position:0%
+um and it's um it's a super exciting
+line of work and continuing continuing
+
+ align:start position:0%
+line of work and continuing continuing
+ 
+
+ align:start position:0%
+line of work and continuing continuing
+to be very exciting one okay so so far
+
+ align:start position:0%
+to be very exciting one okay so so far
+ 
+
+ align:start position:0%
+to be very exciting one okay so so far
+we've talked about place cells in the
+
+ align:start position:0%
+we've talked about place cells in the
+ 
+
+ align:start position:0%
+we've talked about place cells in the
+hippocampus direction cells in the
+
+ align:start position:0%
+hippocampus direction cells in the
+ 
+
+ align:start position:0%
+hippocampus direction cells in the
+subiculum and lots of other places
+
+ align:start position:0%
+subiculum and lots of other places
+ 
+
+ align:start position:0%
+subiculum and lots of other places
+and end to rhino grid cells in enter
+
+ align:start position:0%
+and end to rhino grid cells in enter
+ 
+
+ align:start position:0%
+and end to rhino grid cells in enter
+rhino cortex and this is just a
+
+ align:start position:0%
+rhino cortex and this is just a
+ 
+
+ align:start position:0%
+rhino cortex and this is just a
+schematic diagram of where those
+
+ align:start position:0%
+schematic diagram of where those
+ 
+
+ align:start position:0%
+schematic diagram of where those
+locations are the anatomy is complicated
+
+ align:start position:0%
+locations are the anatomy is complicated
+ 
+
+ align:start position:0%
+locations are the anatomy is complicated
+and you don't need to know it no they're
+
+ align:start position:0%
+and you don't need to know it no they're
+ 
+
+ align:start position:0%
+and you don't need to know it no they're
+all sort of in the hippocampus and it's
+
+ align:start position:0%
+all sort of in the hippocampus and it's
+ 
+
+ align:start position:0%
+all sort of in the hippocampus and it's
+neighboring structures that's good
+
+ align:start position:0%
+neighboring structures that's good
+ 
+
+ align:start position:0%
+neighboring structures that's good
+enough for for here
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+well okay know that the grid cells are
+
+ align:start position:0%
+well okay know that the grid cells are
+ 
+
+ align:start position:0%
+well okay know that the grid cells are
+in internal cortex and the place cells
+
+ align:start position:0%
+in internal cortex and the place cells
+ 
+
+ align:start position:0%
+in internal cortex and the place cells
+are in hippocampus that's worth knowing
+
+ align:start position:0%
+are in hippocampus that's worth knowing
+ 
+
+ align:start position:0%
+are in hippocampus that's worth knowing
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+direction cells are kind of all over
+
+ align:start position:0%
+direction cells are kind of all over
+ 
+
+ align:start position:0%
+direction cells are kind of all over
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+that's cool but there's one more cool
+
+ align:start position:0%
+that's cool but there's one more cool
+ 
+
+ align:start position:0%
+that's cool but there's one more cool
+kind of cell actually there's several
+
+ align:start position:0%
+kind of cell actually there's several
+ 
+
+ align:start position:0%
+kind of cell actually there's several
+more the new one a new one i never heard
+
+ align:start position:0%
+more the new one a new one i never heard
+ 
+
+ align:start position:0%
+more the new one a new one i never heard
+of was reported in this job talk
+
+ align:start position:0%
+of was reported in this job talk
+ 
+
+ align:start position:0%
+of was reported in this job talk
+yesterday but we won't go there we'll
+
+ align:start position:0%
+yesterday but we won't go there we'll
+ 
+
+ align:start position:0%
+yesterday but we won't go there we'll
+try to keep it simple uh another well
+
+ align:start position:0%
+try to keep it simple uh another well
+ 
+
+ align:start position:0%
+try to keep it simple uh another well
+established one is called a border cell
+
+ align:start position:0%
+established one is called a border cell
+ 
+
+ align:start position:0%
+established one is called a border cell
+okay so this is the these are the place
+
+ align:start position:0%
+okay so this is the these are the place
+ 
+
+ align:start position:0%
+okay so this is the these are the place
+fields of three different neurons
+
+ align:start position:0%
+fields of three different neurons
+ 
+
+ align:start position:0%
+fields of three different neurons
+from an animal
+
+ align:start position:0%
+from an animal
+ 
+
+ align:start position:0%
+from an animal
+moving around in this space
+
+ align:start position:0%
+moving around in this space
+ 
+
+ align:start position:0%
+moving around in this space
+okay so you see how these are very
+
+ align:start position:0%
+okay so you see how these are very
+ 
+
+ align:start position:0%
+okay so you see how these are very
+interesting kind of place fields they're
+
+ align:start position:0%
+interesting kind of place fields they're
+ 
+
+ align:start position:0%
+interesting kind of place fields they're
+not just like a nice round blob they
+
+ align:start position:0%
+not just like a nice round blob they
+ 
+
+ align:start position:0%
+not just like a nice round blob they
+stretch around a whole border of the
+
+ align:start position:0%
+stretch around a whole border of the
+ 
+
+ align:start position:0%
+stretch around a whole border of the
+animal's environment
+
+ align:start position:0%
+animal's environment
+ 
+
+ align:start position:0%
+animal's environment
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+so does that make you think of anything
+
+ align:start position:0%
+so does that make you think of anything
+ 
+
+ align:start position:0%
+so does that make you think of anything
+does that ring any bells with other
+
+ align:start position:0%
+does that ring any bells with other
+ 
+
+ align:start position:0%
+does that ring any bells with other
+stuff we've talked about in here
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+right think we've talked a bunch about
+
+ align:start position:0%
+right think we've talked a bunch about
+ 
+
+ align:start position:0%
+right think we've talked a bunch about
+how the parahippocampal place area cares
+
+ align:start position:0%
+how the parahippocampal place area cares
+ 
+
+ align:start position:0%
+how the parahippocampal place area cares
+about the shape of space around you
+
+ align:start position:0%
+about the shape of space around you
+ 
+
+ align:start position:0%
+about the shape of space around you
+right well you might think that you'd
+
+ align:start position:0%
+right well you might think that you'd
+ 
+
+ align:start position:0%
+right well you might think that you'd
+really want to have awareness of where
+
+ align:start position:0%
+really want to have awareness of where
+ 
+
+ align:start position:0%
+really want to have awareness of where
+you are with respect to navigational
+
+ align:start position:0%
+you are with respect to navigational
+ 
+
+ align:start position:0%
+you are with respect to navigational
+barriers
+
+ align:start position:0%
+barriers
+ 
+
+ align:start position:0%
+barriers
+it turns out border cells respond not
+
+ align:start position:0%
+it turns out border cells respond not
+ 
+
+ align:start position:0%
+it turns out border cells respond not
+just to walls if you put a rodent in an
+
+ align:start position:0%
+just to walls if you put a rodent in an
+ 
+
+ align:start position:0%
+just to walls if you put a rodent in an
+environment where there's a cliff they
+
+ align:start position:0%
+environment where there's a cliff they
+ 
+
+ align:start position:0%
+environment where there's a cliff they
+can't go off the border cells also
+
+ align:start position:0%
+can't go off the border cells also
+ 
+
+ align:start position:0%
+can't go off the border cells also
+respond to the edge of that cliff okay
+
+ align:start position:0%
+respond to the edge of that cliff okay
+ 
+
+ align:start position:0%
+respond to the edge of that cliff okay
+so any navigational barrier basically
+
+ align:start position:0%
+so any navigational barrier basically
+ 
+
+ align:start position:0%
+so any navigational barrier basically
+telling you where you are with respect
+
+ align:start position:0%
+telling you where you are with respect
+ 
+
+ align:start position:0%
+telling you where you are with respect
+to navigational barriers
+
+ align:start position:0%
+to navigational barriers
+ 
+
+ align:start position:0%
+to navigational barriers
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+all right
+
+ align:start position:0%
+all right
+ 
+
+ align:start position:0%
+all right
+and blah blah blah okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+as i mentioned in the last lecture when
+
+ align:start position:0%
+as i mentioned in the last lecture when
+ 
+
+ align:start position:0%
+as i mentioned in the last lecture when
+we talked about the para hippocampal
+
+ align:start position:0%
+we talked about the para hippocampal
+ 
+
+ align:start position:0%
+we talked about the para hippocampal
+place area the shape of space around you
+
+ align:start position:0%
+place area the shape of space around you
+ 
+
+ align:start position:0%
+place area the shape of space around you
+has this kind of privileged role in many
+
+ align:start position:0%
+has this kind of privileged role in many
+ 
+
+ align:start position:0%
+has this kind of privileged role in many
+aspects of navigation
+
+ align:start position:0%
+aspects of navigation
+ 
+
+ align:start position:0%
+aspects of navigation
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+now we're going to talk about this
+
+ align:start position:0%
+now we're going to talk about this
+ 
+
+ align:start position:0%
+now we're going to talk about this
+problem of reorienting or regaining your
+
+ align:start position:0%
+problem of reorienting or regaining your
+ 
+
+ align:start position:0%
+problem of reorienting or regaining your
+um your sense of direction once you've
+
+ align:start position:0%
+um your sense of direction once you've
+ 
+
+ align:start position:0%
+um your sense of direction once you've
+been disoriented
+
+ align:start position:0%
+been disoriented
+ 
+
+ align:start position:0%
+been disoriented
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+and so
+
+ align:start position:0%
+and so
+ 
+
+ align:start position:0%
+and so
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+again i mentioned this before but just
+
+ align:start position:0%
+again i mentioned this before but just
+ 
+
+ align:start position:0%
+again i mentioned this before but just
+to give you in the give you the
+
+ align:start position:0%
+to give you in the give you the
+ 
+
+ align:start position:0%
+to give you in the give you the
+intuition of what we're talking about
+
+ align:start position:0%
+intuition of what we're talking about
+ 
+
+ align:start position:0%
+intuition of what we're talking about
+here
+
+ align:start position:0%
+here
+ 
+
+ align:start position:0%
+here
+you come up from the subway in manhattan
+
+ align:start position:0%
+you come up from the subway in manhattan
+ 
+
+ align:start position:0%
+you come up from the subway in manhattan
+or any other environment that you that's
+
+ align:start position:0%
+or any other environment that you that's
+ 
+
+ align:start position:0%
+or any other environment that you that's
+rectilinear that you know
+
+ align:start position:0%
+rectilinear that you know
+ 
+
+ align:start position:0%
+rectilinear that you know
+and you know which stop you're coming at
+
+ align:start position:0%
+and you know which stop you're coming at
+ 
+
+ align:start position:0%
+and you know which stop you're coming at
+up at so you kind of know where you are
+
+ align:start position:0%
+up at so you kind of know where you are
+ 
+
+ align:start position:0%
+up at so you kind of know where you are
+but you come out and you don't know
+
+ align:start position:0%
+but you come out and you don't know
+ 
+
+ align:start position:0%
+but you come out and you don't know
+which way to head right you don't know
+
+ align:start position:0%
+which way to head right you don't know
+ 
+
+ align:start position:0%
+which way to head right you don't know
+which way is which
+
+ align:start position:0%
+which way is which
+ 
+
+ align:start position:0%
+which way is which
+all right
+
+ align:start position:0%
+all right
+ 
+
+ align:start position:0%
+all right
+so that's a modern version of a classic
+
+ align:start position:0%
+so that's a modern version of a classic
+ 
+
+ align:start position:0%
+so that's a modern version of a classic
+problem that animals face in their
+
+ align:start position:0%
+problem that animals face in their
+ 
+
+ align:start position:0%
+problem that animals face in their
+environment they may know where they are
+
+ align:start position:0%
+environment they may know where they are
+ 
+
+ align:start position:0%
+environment they may know where they are
+but that doesn't tell them which way
+
+ align:start position:0%
+but that doesn't tell them which way
+ 
+
+ align:start position:0%
+but that doesn't tell them which way
+they're facing
+
+ align:start position:0%
+they're facing
+ 
+
+ align:start position:0%
+they're facing
+so just to be really concrete about this
+
+ align:start position:0%
+so just to be really concrete about this
+ 
+
+ align:start position:0%
+so just to be really concrete about this
+so here's an aerial view of a person
+
+ align:start position:0%
+so here's an aerial view of a person
+ 
+
+ align:start position:0%
+so here's an aerial view of a person
+you're standing here
+
+ align:start position:0%
+you're standing here
+ 
+
+ align:start position:0%
+you're standing here
+you have a cognitive map in your mind
+
+ align:start position:0%
+you have a cognitive map in your mind
+ 
+
+ align:start position:0%
+you have a cognitive map in your mind
+and your place cells are telling you
+
+ align:start position:0%
+and your place cells are telling you
+ 
+
+ align:start position:0%
+and your place cells are telling you
+your location in that map okay so you
+
+ align:start position:0%
+your location in that map okay so you
+ 
+
+ align:start position:0%
+your location in that map okay so you
+know where you are in that map
+
+ align:start position:0%
+know where you are in that map
+ 
+
+ align:start position:0%
+know where you are in that map
+but to you and you're looking down a
+
+ align:start position:0%
+but to you and you're looking down a
+ 
+
+ align:start position:0%
+but to you and you're looking down a
+street so you know that you're oriented
+
+ align:start position:0%
+street so you know that you're oriented
+ 
+
+ align:start position:0%
+street so you know that you're oriented
+with respect to some external
+
+ align:start position:0%
+with respect to some external
+ 
+
+ align:start position:0%
+with respect to some external
+axis like this
+
+ align:start position:0%
+axis like this
+ 
+
+ align:start position:0%
+axis like this
+but you don't know
+
+ align:start position:0%
+but you don't know
+ 
+
+ align:start position:0%
+but you don't know
+how your mental map should be aligned
+
+ align:start position:0%
+how your mental map should be aligned
+ 
+
+ align:start position:0%
+how your mental map should be aligned
+with that street
+
+ align:start position:0%
+with that street
+ 
+
+ align:start position:0%
+with that street
+are you facing
+
+ align:start position:0%
+are you facing
+ 
+
+ align:start position:0%
+are you facing
+like this facing north
+
+ align:start position:0%
+like this facing north
+ 
+
+ align:start position:0%
+like this facing north
+in manhattan
+
+ align:start position:0%
+in manhattan
+ 
+
+ align:start position:0%
+in manhattan
+or
+
+ align:start position:0%
+or
+ 
+
+ align:start position:0%
+or
+are you facing south
+
+ align:start position:0%
+are you facing south
+ 
+
+ align:start position:0%
+are you facing south
+right
+
+ align:start position:0%
+right
+ 
+
+ align:start position:0%
+right
+so that's the problem of reorientation
+
+ align:start position:0%
+so that's the problem of reorientation
+ 
+
+ align:start position:0%
+so that's the problem of reorientation
+is figuring out your particular
+
+ align:start position:0%
+is figuring out your particular
+ 
+
+ align:start position:0%
+is figuring out your particular
+orientation not just your location but
+
+ align:start position:0%
+orientation not just your location but
+ 
+
+ align:start position:0%
+orientation not just your location but
+which way you're facing in a known
+
+ align:start position:0%
+which way you're facing in a known
+ 
+
+ align:start position:0%
+which way you're facing in a known
+environment okay and we've all faced
+
+ align:start position:0%
+environment okay and we've all faced
+ 
+
+ align:start position:0%
+environment okay and we've all faced
+some version of this presumably at some
+
+ align:start position:0%
+some version of this presumably at some
+ 
+
+ align:start position:0%
+some version of this presumably at some
+point
+
+ align:start position:0%
+point
+ 
+
+ align:start position:0%
+point
+and it's annoying it takes a while to
+
+ align:start position:0%
+and it's annoying it takes a while to
+ 
+
+ align:start position:0%
+and it's annoying it takes a while to
+figure out and then i don't know if
+
+ align:start position:0%
+figure out and then i don't know if
+ 
+
+ align:start position:0%
+figure out and then i don't know if
+anybody's had this experience i've had
+
+ align:start position:0%
+anybody's had this experience i've had
+ 
+
+ align:start position:0%
+anybody's had this experience i've had
+it only in manhattan because that's
+
+ align:start position:0%
+it only in manhattan because that's
+ 
+
+ align:start position:0%
+it only in manhattan because that's
+where this arises for me but i'm sure
+
+ align:start position:0%
+where this arises for me but i'm sure
+ 
+
+ align:start position:0%
+where this arises for me but i'm sure
+there are other locations where you come
+
+ align:start position:0%
+there are other locations where you come
+ 
+
+ align:start position:0%
+there are other locations where you come
+up and you think you're going one way
+
+ align:start position:0%
+up and you think you're going one way
+ 
+
+ align:start position:0%
+up and you think you're going one way
+and then all of a sudden like your whole
+
+ align:start position:0%
+and then all of a sudden like your whole
+ 
+
+ align:start position:0%
+and then all of a sudden like your whole
+like it's like your whole mental map
+
+ align:start position:0%
+like it's like your whole mental map
+ 
+
+ align:start position:0%
+like it's like your whole mental map
+goes kaboom
+
+ align:start position:0%
+goes kaboom
+ 
+
+ align:start position:0%
+goes kaboom
+so how many people have had that
+
+ align:start position:0%
+so how many people have had that
+ 
+
+ align:start position:0%
+so how many people have had that
+experience like it's very sudden and
+
+ align:start position:0%
+experience like it's very sudden and
+ 
+
+ align:start position:0%
+experience like it's very sudden and
+punk date yeah
+
+ align:start position:0%
+punk date yeah
+ 
+
+ align:start position:0%
+punk date yeah
+turns out that when that happens all of
+
+ align:start position:0%
+turns out that when that happens all of
+ 
+
+ align:start position:0%
+turns out that when that happens all of
+your neurons flip together in unison
+
+ align:start position:0%
+your neurons flip together in unison
+ 
+
+ align:start position:0%
+your neurons flip together in unison
+like they're all in cahoots they have
+
+ align:start position:0%
+like they're all in cahoots they have
+ 
+
+ align:start position:0%
+like they're all in cahoots they have
+one version of this when you have that
+
+ align:start position:0%
+one version of this when you have that
+ 
+
+ align:start position:0%
+one version of this when you have that
+experience it's because they're all
+
+ align:start position:0%
+experience it's because they're all
+ 
+
+ align:start position:0%
+experience it's because they're all
+flipping together and i'll show you some
+
+ align:start position:0%
+flipping together and i'll show you some
+ 
+
+ align:start position:0%
+flipping together and i'll show you some
+data on that in a second
+
+ align:start position:0%
+data on that in a second
+ 
+
+ align:start position:0%
+data on that in a second
+okay all right
+
+ align:start position:0%
+okay all right
+ 
+
+ align:start position:0%
+okay all right
+so there's a very evolutionary old
+
+ align:start position:0%
+so there's a very evolutionary old
+ 
+
+ align:start position:0%
+so there's a very evolutionary old
+system for solving just this problem and
+
+ align:start position:0%
+system for solving just this problem and
+ 
+
+ align:start position:0%
+system for solving just this problem and
+it's a wonderful little kind of piece of
+
+ align:start position:0%
+it's a wonderful little kind of piece of
+ 
+
+ align:start position:0%
+it's a wonderful little kind of piece of
+the literature that i'm going to spend a
+
+ align:start position:0%
+the literature that i'm going to spend a
+ 
+
+ align:start position:0%
+the literature that i'm going to spend a
+couple minutes on because it's so
+
+ align:start position:0%
+couple minutes on because it's so
+ 
+
+ align:start position:0%
+couple minutes on because it's so
+classic
+
+ align:start position:0%
+classic
+ 
+
+ align:start position:0%
+classic
+and so cool
+
+ align:start position:0%
+and so cool
+ 
+
+ align:start position:0%
+and so cool
+and this started with work by randy
+
+ align:start position:0%
+and this started with work by randy
+ 
+
+ align:start position:0%
+and this started with work by randy
+gallistail in the 1980s and so what he
+
+ align:start position:0%
+gallistail in the 1980s and so what he
+ 
+
+ align:start position:0%
+gallistail in the 1980s and so what he
+did was he studied this problem of
+
+ align:start position:0%
+did was he studied this problem of
+ 
+
+ align:start position:0%
+did was he studied this problem of
+reorientation that is figuring out your
+
+ align:start position:0%
+reorientation that is figuring out your
+ 
+
+ align:start position:0%
+reorientation that is figuring out your
+orientation in a known environment once
+
+ align:start position:0%
+orientation in a known environment once
+ 
+
+ align:start position:0%
+orientation in a known environment once
+you've been disoriented okay it's a very
+
+ align:start position:0%
+you've been disoriented okay it's a very
+ 
+
+ align:start position:0%
+you've been disoriented okay it's a very
+particular aspect of the problem of
+
+ align:start position:0%
+particular aspect of the problem of
+ 
+
+ align:start position:0%
+particular aspect of the problem of
+navigation
+
+ align:start position:0%
+navigation
+ 
+
+ align:start position:0%
+navigation
+so he put rats in a rectangular
+
+ align:start position:0%
+so he put rats in a rectangular
+ 
+
+ align:start position:0%
+so he put rats in a rectangular
+environment and he had them explore the
+
+ align:start position:0%
+environment and he had them explore the
+ 
+
+ align:start position:0%
+environment and he had them explore the
+environment
+
+ align:start position:0%
+environment
+ 
+
+ align:start position:0%
+environment
+and then he hid some
+
+ align:start position:0%
+and then he hid some
+ 
+
+ align:start position:0%
+and then he hid some
+rat relevant thing like a little piece
+
+ align:start position:0%
+rat relevant thing like a little piece
+ 
+
+ align:start position:0%
+rat relevant thing like a little piece
+of food say a chocolate chip in that
+
+ align:start position:0%
+of food say a chocolate chip in that
+ 
+
+ align:start position:0%
+of food say a chocolate chip in that
+corner okay rat sees that happen rad is
+
+ align:start position:0%
+corner okay rat sees that happen rad is
+ 
+
+ align:start position:0%
+corner okay rat sees that happen rad is
+interested take rat out of box before
+
+ align:start position:0%
+interested take rat out of box before
+ 
+
+ align:start position:0%
+interested take rat out of box before
+they get to go take the the chocolate
+
+ align:start position:0%
+they get to go take the the chocolate
+ 
+
+ align:start position:0%
+they get to go take the the chocolate
+chip
+
+ align:start position:0%
+chip
+ 
+
+ align:start position:0%
+chip
+and then you disorient the rat you don't
+
+ align:start position:0%
+and then you disorient the rat you don't
+ 
+
+ align:start position:0%
+and then you disorient the rat you don't
+grab them by the tail and swing them
+
+ align:start position:0%
+grab them by the tail and swing them
+ 
+
+ align:start position:0%
+grab them by the tail and swing them
+around but you do some slower version
+
+ align:start position:0%
+around but you do some slower version
+ 
+
+ align:start position:0%
+around but you do some slower version
+you don't want to make them sick you do
+
+ align:start position:0%
+you don't want to make them sick you do
+ 
+
+ align:start position:0%
+you don't want to make them sick you do
+some slower version of that so they've
+
+ align:start position:0%
+some slower version of that so they've
+ 
+
+ align:start position:0%
+some slower version of that so they've
+lost track of which way they're facing
+
+ align:start position:0%
+lost track of which way they're facing
+ 
+
+ align:start position:0%
+lost track of which way they're facing
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+now you put them in a new box new box
+
+ align:start position:0%
+now you put them in a new box new box
+ 
+
+ align:start position:0%
+now you put them in a new box new box
+because you don't want the smell to
+
+ align:start position:0%
+because you don't want the smell to
+ 
+
+ align:start position:0%
+because you don't want the smell to
+still be there new box
+
+ align:start position:0%
+still be there new box
+ 
+
+ align:start position:0%
+still be there new box
+and you see which way the rat goes
+
+ align:start position:0%
+and you see which way the rat goes
+ 
+
+ align:start position:0%
+and you see which way the rat goes
+and you find that the rat goes 50 50 to
+
+ align:start position:0%
+and you find that the rat goes 50 50 to
+ 
+
+ align:start position:0%
+and you find that the rat goes 50 50 to
+those two corners
+
+ align:start position:0%
+those two corners
+ 
+
+ align:start position:0%
+those two corners
+what does that mean the rat has encoded
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+he doesn't go randomly to any corner
+
+ align:start position:0%
+he doesn't go randomly to any corner
+ 
+
+ align:start position:0%
+he doesn't go randomly to any corner
+he goes to corners you know it was in a
+
+ align:start position:0%
+he goes to corners you know it was in a
+ 
+
+ align:start position:0%
+he goes to corners you know it was in a
+corner he doesn't go randomly to any
+
+ align:start position:0%
+corner he doesn't go randomly to any
+ 
+
+ align:start position:0%
+corner he doesn't go randomly to any
+corner yeah
+
+ align:start position:0%
+corner yeah
+ 
+
+ align:start position:0%
+corner yeah
+i'm jack i'm sorry
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+like it's specifically in
+
+ align:start position:0%
+like it's specifically in
+ 
+
+ align:start position:0%
+like it's specifically in
+like one of these directions
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+you've got to say a little more than
+
+ align:start position:0%
+you've got to say a little more than
+ 
+
+ align:start position:0%
+you've got to say a little more than
+that what's to the left what's different
+
+ align:start position:0%
+that what's to the left what's different
+ 
+
+ align:start position:0%
+that what's to the left what's different
+about those two corners and the other
+
+ align:start position:0%
+about those two corners and the other
+ 
+
+ align:start position:0%
+about those two corners and the other
+two yeah isabel well he's looking at the
+
+ align:start position:0%
+two yeah isabel well he's looking at the
+ 
+
+ align:start position:0%
+two yeah isabel well he's looking at the
+shape of the room
+
+ align:start position:0%
+shape of the room
+ 
+
+ align:start position:0%
+shape of the room
+there's two longer walls and two
+
+ align:start position:0%
+there's two longer walls and two
+ 
+
+ align:start position:0%
+there's two longer walls and two
+shoulder walls he recognizes that he's
+
+ align:start position:0%
+shoulder walls he recognizes that he's
+ 
+
+ align:start position:0%
+shoulder walls he recognizes that he's
+basically involved he has to go to what
+
+ align:start position:0%
+basically involved he has to go to what
+ 
+
+ align:start position:0%
+basically involved he has to go to what
+looks like the right complaint
+
+ align:start position:0%
+looks like the right complaint
+ 
+
+ align:start position:0%
+looks like the right complaint
+exactly he has to have encoded the axis
+
+ align:start position:0%
+exactly he has to have encoded the axis
+ 
+
+ align:start position:0%
+exactly he has to have encoded the axis
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+the the orient the fact that the the
+
+ align:start position:0%
+the the orient the fact that the the
+ 
+
+ align:start position:0%
+the the orient the fact that the the
+room has a is longer on one axis than
+
+ align:start position:0%
+room has a is longer on one axis than
+ 
+
+ align:start position:0%
+room has a is longer on one axis than
+another
+
+ align:start position:0%
+another
+ 
+
+ align:start position:0%
+another
+and he's essentially encoded that
+
+ align:start position:0%
+and he's essentially encoded that
+ 
+
+ align:start position:0%
+and he's essentially encoded that
+chocolate chip was on the right side of
+
+ align:start position:0%
+chocolate chip was on the right side of
+ 
+
+ align:start position:0%
+chocolate chip was on the right side of
+the long wall or the left side of the
+
+ align:start position:0%
+the long wall or the left side of the
+ 
+
+ align:start position:0%
+the long wall or the left side of the
+short wall and both of those corners are
+
+ align:start position:0%
+short wall and both of those corners are
+ 
+
+ align:start position:0%
+short wall and both of those corners are
+consistent with that that's why he goes
+
+ align:start position:0%
+consistent with that that's why he goes
+ 
+
+ align:start position:0%
+consistent with that that's why he goes
+50 50 to them
+
+ align:start position:0%
+50 50 to them
+ 
+
+ align:start position:0%
+50 50 to them
+he can't go 100 of the time to the right
+
+ align:start position:0%
+he can't go 100 of the time to the right
+ 
+
+ align:start position:0%
+he can't go 100 of the time to the right
+corner because he has no information
+
+ align:start position:0%
+corner because he has no information
+ 
+
+ align:start position:0%
+corner because he has no information
+that would tell him that in this
+
+ align:start position:0%
+that would tell him that in this
+ 
+
+ align:start position:0%
+that would tell him that in this
+experiment okay everybody clear so it
+
+ align:start position:0%
+experiment okay everybody clear so it
+ 
+
+ align:start position:0%
+experiment okay everybody clear so it
+tells you he learned where the thing is
+
+ align:start position:0%
+tells you he learned where the thing is
+ 
+
+ align:start position:0%
+tells you he learned where the thing is
+with respect to the shape of the room
+
+ align:start position:0%
+with respect to the shape of the room
+ 
+
+ align:start position:0%
+with respect to the shape of the room
+and its particular aspect ratio okay
+
+ align:start position:0%
+and its particular aspect ratio okay
+ 
+
+ align:start position:0%
+and its particular aspect ratio okay
+so now the plot thickens
+
+ align:start position:0%
+so now the plot thickens
+ 
+
+ align:start position:0%
+so now the plot thickens
+and now they repeat the experiment but
+
+ align:start position:0%
+and now they repeat the experiment but
+ 
+
+ align:start position:0%
+and now they repeat the experiment but
+this time they make some very rat
+
+ align:start position:0%
+this time they make some very rat
+ 
+
+ align:start position:0%
+this time they make some very rat
+salient asymmetry over here you make a
+
+ align:start position:0%
+salient asymmetry over here you make a
+ 
+
+ align:start position:0%
+salient asymmetry over here you make a
+color and a texture
+
+ align:start position:0%
+color and a texture
+ 
+
+ align:start position:0%
+color and a texture
+and you make other things to make this
+
+ align:start position:0%
+and you make other things to make this
+ 
+
+ align:start position:0%
+and you make other things to make this
+wall very saliently different
+
+ align:start position:0%
+wall very saliently different
+ 
+
+ align:start position:0%
+wall very saliently different
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+so you would think the rat motivated to
+
+ align:start position:0%
+so you would think the rat motivated to
+ 
+
+ align:start position:0%
+so you would think the rat motivated to
+find the chocolate chip would now go 100
+
+ align:start position:0%
+find the chocolate chip would now go 100
+ 
+
+ align:start position:0%
+find the chocolate chip would now go 100
+to that corner when we put them in the
+
+ align:start position:0%
+to that corner when we put them in the
+ 
+
+ align:start position:0%
+to that corner when we put them in the
+new box with the same landmark queue
+
+ align:start position:0%
+new box with the same landmark queue
+ 
+
+ align:start position:0%
+new box with the same landmark queue
+over there
+
+ align:start position:0%
+over there
+ 
+
+ align:start position:0%
+over there
+but no the rat goes 50 50 to the same
+
+ align:start position:0%
+but no the rat goes 50 50 to the same
+ 
+
+ align:start position:0%
+but no the rat goes 50 50 to the same
+two corners
+
+ align:start position:0%
+two corners
+ 
+
+ align:start position:0%
+two corners
+and in control experiments many
+
+ align:start position:0%
+and in control experiments many
+ 
+
+ align:start position:0%
+and in control experiments many
+controlled conditions you can show and
+
+ align:start position:0%
+controlled conditions you can show and
+ 
+
+ align:start position:0%
+controlled conditions you can show and
+i'll show you one in a moment the rat
+
+ align:start position:0%
+i'll show you one in a moment the rat
+ 
+
+ align:start position:0%
+i'll show you one in a moment the rat
+absolutely knows about this wall he's
+
+ align:start position:0%
+absolutely knows about this wall he's
+ 
+
+ align:start position:0%
+absolutely knows about this wall he's
+encoded the presence of that asymmetric
+
+ align:start position:0%
+encoded the presence of that asymmetric
+ 
+
+ align:start position:0%
+encoded the presence of that asymmetric
+wall so he has the information that
+
+ align:start position:0%
+wall so he has the information that
+ 
+
+ align:start position:0%
+wall so he has the information that
+should enable him to break the symmetry
+
+ align:start position:0%
+should enable him to break the symmetry
+ 
+
+ align:start position:0%
+should enable him to break the symmetry
+but he doesn't use it
+
+ align:start position:0%
+but he doesn't use it
+ 
+
+ align:start position:0%
+but he doesn't use it
+that's weird you should be surprised
+
+ align:start position:0%
+that's weird you should be surprised
+ 
+
+ align:start position:0%
+that's weird you should be surprised
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+everybody get why that's weird he could
+
+ align:start position:0%
+everybody get why that's weird he could
+ 
+
+ align:start position:0%
+everybody get why that's weird he could
+have solved this one perfectly this time
+
+ align:start position:0%
+have solved this one perfectly this time
+ 
+
+ align:start position:0%
+have solved this one perfectly this time
+he has the information he's not using
+
+ align:start position:0%
+he has the information he's not using
+ 
+
+ align:start position:0%
+he has the information he's not using
+that information
+
+ align:start position:0%
+that information
+ 
+
+ align:start position:0%
+that information
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+that's weird
+
+ align:start position:0%
+that's weird
+ 
+
+ align:start position:0%
+that's weird
+but then liz spelke and her colleagues
+
+ align:start position:0%
+but then liz spelke and her colleagues
+ 
+
+ align:start position:0%
+but then liz spelke and her colleagues
+came along 10 years later and said let's
+
+ align:start position:0%
+came along 10 years later and said let's
+ 
+
+ align:start position:0%
+came along 10 years later and said let's
+try this with infants
+
+ align:start position:0%
+try this with infants
+ 
+
+ align:start position:0%
+try this with infants
+and so they did the infant version where
+
+ align:start position:0%
+and so they did the infant version where
+ 
+
+ align:start position:0%
+and so they did the infant version where
+you put the infant in a room with a
+
+ align:start position:0%
+you put the infant in a room with a
+ 
+
+ align:start position:0%
+you put the infant in a room with a
+symmetrical with a um
+
+ align:start position:0%
+symmetrical with a um
+ 
+
+ align:start position:0%
+symmetrical with a um
+in a rectangular room and you hide the
+
+ align:start position:0%
+in a rectangular room and you hide the
+ 
+
+ align:start position:0%
+in a rectangular room and you hide the
+doors so the infant doesn't have any uh
+
+ align:start position:0%
+doors so the infant doesn't have any uh
+ 
+
+ align:start position:0%
+doors so the infant doesn't have any uh
+cues other than the shape of the room
+
+ align:start position:0%
+cues other than the shape of the room
+ 
+
+ align:start position:0%
+cues other than the shape of the room
+um um 18 to 24 month old infants
+
+ align:start position:0%
+um um 18 to 24 month old infants
+ 
+
+ align:start position:0%
+um um 18 to 24 month old infants
+um and then uh you hide a toy in a
+
+ align:start position:0%
+um and then uh you hide a toy in a
+ 
+
+ align:start position:0%
+um and then uh you hide a toy in a
+corner and you see what the infant does
+
+ align:start position:0%
+corner and you see what the infant does
+ 
+
+ align:start position:0%
+corner and you see what the infant does
+and uh oh actually what you do with the
+
+ align:start position:0%
+and uh oh actually what you do with the
+ 
+
+ align:start position:0%
+and uh oh actually what you do with the
+infant is you make this wall really
+
+ align:start position:0%
+infant is you make this wall really
+ 
+
+ align:start position:0%
+infant is you make this wall really
+salient in all kinds of ways you in one
+
+ align:start position:0%
+salient in all kinds of ways you in one
+ 
+
+ align:start position:0%
+salient in all kinds of ways you in one
+case that was red velvet and they first
+
+ align:start position:0%
+case that was red velvet and they first
+ 
+
+ align:start position:0%
+case that was red velvet and they first
+showed the and these aren't like these
+
+ align:start position:0%
+showed the and these aren't like these
+ 
+
+ align:start position:0%
+showed the and these aren't like these
+are i guess toddlers right they first
+
+ align:start position:0%
+are i guess toddlers right they first
+ 
+
+ align:start position:0%
+are i guess toddlers right they first
+show them that when you knock on the red
+
+ align:start position:0%
+show them that when you knock on the red
+ 
+
+ align:start position:0%
+show them that when you knock on the red
+wall music happens
+
+ align:start position:0%
+wall music happens
+ 
+
+ align:start position:0%
+wall music happens
+totally cool riveting for a little kid
+
+ align:start position:0%
+totally cool riveting for a little kid
+ 
+
+ align:start position:0%
+totally cool riveting for a little kid
+they totally get it they know all about
+
+ align:start position:0%
+they totally get it they know all about
+ 
+
+ align:start position:0%
+they totally get it they know all about
+the music wall very salient to them
+
+ align:start position:0%
+the music wall very salient to them
+ 
+
+ align:start position:0%
+the music wall very salient to them
+nonetheless you put them in this
+
+ align:start position:0%
+nonetheless you put them in this
+ 
+
+ align:start position:0%
+nonetheless you put them in this
+experiment and they behave just like
+
+ align:start position:0%
+experiment and they behave just like
+ 
+
+ align:start position:0%
+experiment and they behave just like
+rodents they go 50 50 to the two corners
+
+ align:start position:0%
+rodents they go 50 50 to the two corners
+ 
+
+ align:start position:0%
+rodents they go 50 50 to the two corners
+even though they notice the red music
+
+ align:start position:0%
+even though they notice the red music
+ 
+
+ align:start position:0%
+even though they notice the red music
+wall and it could have solved the
+
+ align:start position:0%
+wall and it could have solved the
+ 
+
+ align:start position:0%
+wall and it could have solved the
+problem for them perfectly and they were
+
+ align:start position:0%
+problem for them perfectly and they were
+ 
+
+ align:start position:0%
+problem for them perfectly and they were
+motivated they didn't use the
+
+ align:start position:0%
+motivated they didn't use the
+ 
+
+ align:start position:0%
+motivated they didn't use the
+information
+
+ align:start position:0%
+information
+ 
+
+ align:start position:0%
+information
+everybody get why that's
+
+ align:start position:0%
+everybody get why that's
+ 
+
+ align:start position:0%
+everybody get why that's
+kind of interesting and kind of
+
+ align:start position:0%
+kind of interesting and kind of
+ 
+
+ align:start position:0%
+kind of interesting and kind of
+surprising
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+now you might say okay rodents infants
+
+ align:start position:0%
+now you might say okay rodents infants
+ 
+
+ align:start position:0%
+now you might say okay rodents infants
+they're dummies
+
+ align:start position:0%
+they're dummies
+ 
+
+ align:start position:0%
+they're dummies
+uh we wouldn't do that
+
+ align:start position:0%
+uh we wouldn't do that
+ 
+
+ align:start position:0%
+uh we wouldn't do that
+us smart adult humans would we
+
+ align:start position:0%
+us smart adult humans would we
+ 
+
+ align:start position:0%
+us smart adult humans would we
+but oh yes you would
+
+ align:start position:0%
+but oh yes you would
+ 
+
+ align:start position:0%
+but oh yes you would
+under certain circumstances
+
+ align:start position:0%
+under certain circumstances
+ 
+
+ align:start position:0%
+under certain circumstances
+if we tied up your language system
+
+ align:start position:0%
+if we tied up your language system
+ 
+
+ align:start position:0%
+if we tied up your language system
+and there's lots of ways of doing that
+
+ align:start position:0%
+and there's lots of ways of doing that
+ 
+
+ align:start position:0%
+and there's lots of ways of doing that
+one way is called shadowing so it's kind
+
+ align:start position:0%
+one way is called shadowing so it's kind
+ 
+
+ align:start position:0%
+one way is called shadowing so it's kind
+of like simultaneous translation but you
+
+ align:start position:0%
+of like simultaneous translation but you
+ 
+
+ align:start position:0%
+of like simultaneous translation but you
+don't translate try this sometime i do
+
+ align:start position:0%
+don't translate try this sometime i do
+ 
+
+ align:start position:0%
+don't translate try this sometime i do
+this occasionally when i'm bored in my
+
+ align:start position:0%
+this occasionally when i'm bored in my
+ 
+
+ align:start position:0%
+this occasionally when i'm bored in my
+car just because it's amusingly
+
+ align:start position:0%
+car just because it's amusingly
+ 
+
+ align:start position:0%
+car just because it's amusingly
+difficult turn on the radio listen to
+
+ align:start position:0%
+difficult turn on the radio listen to
+ 
+
+ align:start position:0%
+difficult turn on the radio listen to
+somebody talking and just repeat
+
+ align:start position:0%
+somebody talking and just repeat
+ 
+
+ align:start position:0%
+somebody talking and just repeat
+everything they say
+
+ align:start position:0%
+everything they say
+ 
+
+ align:start position:0%
+everything they say
+after they say it right
+
+ align:start position:0%
+after they say it right
+ 
+
+ align:start position:0%
+after they say it right
+i'm not even translating it's still
+
+ align:start position:0%
+i'm not even translating it's still
+ 
+
+ align:start position:0%
+i'm not even translating it's still
+demanding right so you have to you have
+
+ align:start position:0%
+demanding right so you have to you have
+ 
+
+ align:start position:0%
+demanding right so you have to you have
+to be listening and producing
+
+ align:start position:0%
+to be listening and producing
+ 
+
+ align:start position:0%
+to be listening and producing
+right okay a little running thing okay
+
+ align:start position:0%
+right okay a little running thing okay
+ 
+
+ align:start position:0%
+right okay a little running thing okay
+so that's called verbal shadowing and
+
+ align:start position:0%
+so that's called verbal shadowing and
+ 
+
+ align:start position:0%
+so that's called verbal shadowing and
+it's an established way to really like
+
+ align:start position:0%
+it's an established way to really like
+ 
+
+ align:start position:0%
+it's an established way to really like
+tie up your language system and kind of
+
+ align:start position:0%
+tie up your language system and kind of
+ 
+
+ align:start position:0%
+tie up your language system and kind of
+take it offline so you can't really use
+
+ align:start position:0%
+take it offline so you can't really use
+ 
+
+ align:start position:0%
+take it offline so you can't really use
+it
+
+ align:start position:0%
+it
+ 
+
+ align:start position:0%
+it
+when you do this experiment on human
+
+ align:start position:0%
+when you do this experiment on human
+ 
+
+ align:start position:0%
+when you do this experiment on human
+adults
+
+ align:start position:0%
+adults
+ 
+
+ align:start position:0%
+adults
+if they're verbally shadowing and their
+
+ align:start position:0%
+if they're verbally shadowing and their
+ 
+
+ align:start position:0%
+if they're verbally shadowing and their
+language system is tied up they behave
+
+ align:start position:0%
+language system is tied up they behave
+ 
+
+ align:start position:0%
+language system is tied up they behave
+just like rodents and infants that is
+
+ align:start position:0%
+just like rodents and infants that is
+ 
+
+ align:start position:0%
+just like rodents and infants that is
+they use the shape of the space
+
+ align:start position:0%
+they use the shape of the space
+ 
+
+ align:start position:0%
+they use the shape of the space
+but they don't use salient landmarks
+
+ align:start position:0%
+but they don't use salient landmarks
+ 
+
+ align:start position:0%
+but they don't use salient landmarks
+that could help them solve it perfectly
+
+ align:start position:0%
+that could help them solve it perfectly
+ 
+
+ align:start position:0%
+that could help them solve it perfectly
+they go 50 50 to the two corners
+
+ align:start position:0%
+they go 50 50 to the two corners
+ 
+
+ align:start position:0%
+they go 50 50 to the two corners
+they become rats and infants
+
+ align:start position:0%
+they become rats and infants
+ 
+
+ align:start position:0%
+they become rats and infants
+we become rats and infants
+
+ align:start position:0%
+we become rats and infants
+ 
+
+ align:start position:0%
+we become rats and infants
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+so liz spelke has spun a whole
+
+ align:start position:0%
+so liz spelke has spun a whole
+ 
+
+ align:start position:0%
+so liz spelke has spun a whole
+fascinating big
+
+ align:start position:0%
+fascinating big
+ 
+
+ align:start position:0%
+fascinating big
+theoretical story
+
+ align:start position:0%
+theoretical story
+ 
+
+ align:start position:0%
+theoretical story
+about how what this really means well
+
+ align:start position:0%
+about how what this really means well
+ 
+
+ align:start position:0%
+about how what this really means well
+let me just say a little bit more about
+
+ align:start position:0%
+let me just say a little bit more about
+ 
+
+ align:start position:0%
+let me just say a little bit more about
+about this first before i do her whole
+
+ align:start position:0%
+about this first before i do her whole
+ 
+
+ align:start position:0%
+about this first before i do her whole
+big story okay yeah so the idea is so
+
+ align:start position:0%
+big story okay yeah so the idea is so
+ 
+
+ align:start position:0%
+big story okay yeah so the idea is so
+first of all
+
+ align:start position:0%
+first of all
+ 
+
+ align:start position:0%
+first of all
+why would it make sense for rodents at
+
+ align:start position:0%
+why would it make sense for rodents at
+ 
+
+ align:start position:0%
+why would it make sense for rodents at
+least let's just consider the rats to
+
+ align:start position:0%
+least let's just consider the rats to
+ 
+
+ align:start position:0%
+least let's just consider the rats to
+use only the shape of space to reorient
+
+ align:start position:0%
+use only the shape of space to reorient
+ 
+
+ align:start position:0%
+use only the shape of space to reorient
+themselves when they're disoriented at
+
+ align:start position:0%
+themselves when they're disoriented at
+ 
+
+ align:start position:0%
+themselves when they're disoriented at
+first glance that seems really crazy
+
+ align:start position:0%
+first glance that seems really crazy
+ 
+
+ align:start position:0%
+first glance that seems really crazy
+but if you think about rodents in
+
+ align:start position:0%
+but if you think about rodents in
+ 
+
+ align:start position:0%
+but if you think about rodents in
+natural environments
+
+ align:start position:0%
+natural environments
+ 
+
+ align:start position:0%
+natural environments
+the idea is that like actually in
+
+ align:start position:0%
+the idea is that like actually in
+ 
+
+ align:start position:0%
+the idea is that like actually in
+natural environments features change
+
+ align:start position:0%
+natural environments features change
+ 
+
+ align:start position:0%
+natural environments features change
+snow comes and goes plants come and go
+
+ align:start position:0%
+snow comes and goes plants come and go
+ 
+
+ align:start position:0%
+snow comes and goes plants come and go
+odors change
+
+ align:start position:0%
+odors change
+ 
+
+ align:start position:0%
+odors change
+all those kinds of
+
+ align:start position:0%
+all those kinds of
+ 
+
+ align:start position:0%
+all those kinds of
+features of the environment can change
+
+ align:start position:0%
+features of the environment can change
+ 
+
+ align:start position:0%
+features of the environment can change
+but the
+
+ align:start position:0%
+but the
+ 
+
+ align:start position:0%
+but the
+shape of the environment like that
+
+ align:start position:0%
+shape of the environment like that
+ 
+
+ align:start position:0%
+shape of the environment like that
+there's a slope like this and a barrier
+
+ align:start position:0%
+there's a slope like this and a barrier
+ 
+
+ align:start position:0%
+there's a slope like this and a barrier
+here and a cliff there those are more
+
+ align:start position:0%
+here and a cliff there those are more
+ 
+
+ align:start position:0%
+here and a cliff there those are more
+stable features of the environment so it
+
+ align:start position:0%
+stable features of the environment so it
+ 
+
+ align:start position:0%
+stable features of the environment so it
+actually makes evolutionary sense for
+
+ align:start position:0%
+actually makes evolutionary sense for
+ 
+
+ align:start position:0%
+actually makes evolutionary sense for
+disoriented rodents at least to use the
+
+ align:start position:0%
+disoriented rodents at least to use the
+ 
+
+ align:start position:0%
+disoriented rodents at least to use the
+shape of space more than the features
+
+ align:start position:0%
+shape of space more than the features
+ 
+
+ align:start position:0%
+shape of space more than the features
+the colors and textures and odors of a
+
+ align:start position:0%
+the colors and textures and odors of a
+ 
+
+ align:start position:0%
+the colors and textures and odors of a
+space
+
+ align:start position:0%
+space
+ 
+
+ align:start position:0%
+space
+as landmarks to reorient themselves does
+
+ align:start position:0%
+as landmarks to reorient themselves does
+ 
+
+ align:start position:0%
+as landmarks to reorient themselves does
+that make sense
+
+ align:start position:0%
+that make sense
+ 
+
+ align:start position:0%
+that make sense
+and so the idea is that rodents have
+
+ align:start position:0%
+and so the idea is that rodents have
+ 
+
+ align:start position:0%
+and so the idea is that rodents have
+through evolution kind of evolved this
+
+ align:start position:0%
+through evolution kind of evolved this
+ 
+
+ align:start position:0%
+through evolution kind of evolved this
+system for reorienting themselves when
+
+ align:start position:0%
+system for reorienting themselves when
+ 
+
+ align:start position:0%
+system for reorienting themselves when
+they lose their bearings that relies
+
+ align:start position:0%
+they lose their bearings that relies
+ 
+
+ align:start position:0%
+they lose their bearings that relies
+only on the shape of space
+
+ align:start position:0%
+only on the shape of space
+ 
+
+ align:start position:0%
+only on the shape of space
+so restrictively that even if another
+
+ align:start position:0%
+so restrictively that even if another
+ 
+
+ align:start position:0%
+so restrictively that even if another
+cue becomes relevant and important they
+
+ align:start position:0%
+cue becomes relevant and important they
+ 
+
+ align:start position:0%
+cue becomes relevant and important they
+don't use it
+
+ align:start position:0%
+don't use it
+ 
+
+ align:start position:0%
+don't use it
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+the further idea is that we have some
+
+ align:start position:0%
+the further idea is that we have some
+ 
+
+ align:start position:0%
+the further idea is that we have some
+version of this system in our heads as
+
+ align:start position:0%
+version of this system in our heads as
+ 
+
+ align:start position:0%
+version of this system in our heads as
+well
+
+ align:start position:0%
+well
+ 
+
+ align:start position:0%
+well
+and as smart adult humans we learn all
+
+ align:start position:0%
+and as smart adult humans we learn all
+ 
+
+ align:start position:0%
+and as smart adult humans we learn all
+kinds of other strategies to get beyond
+
+ align:start position:0%
+kinds of other strategies to get beyond
+ 
+
+ align:start position:0%
+kinds of other strategies to get beyond
+this we're not trapped with only being
+
+ align:start position:0%
+this we're not trapped with only being
+ 
+
+ align:start position:0%
+this we're not trapped with only being
+able to use this one system to solve it
+
+ align:start position:0%
+able to use this one system to solve it
+ 
+
+ align:start position:0%
+able to use this one system to solve it
+we can use other systems
+
+ align:start position:0%
+we can use other systems
+ 
+
+ align:start position:0%
+we can use other systems
+possibly language to help us say things
+
+ align:start position:0%
+possibly language to help us say things
+ 
+
+ align:start position:0%
+possibly language to help us say things
+to ourselves like it's on the left side
+
+ align:start position:0%
+to ourselves like it's on the left side
+ 
+
+ align:start position:0%
+to ourselves like it's on the left side
+of the short wall
+
+ align:start position:0%
+of the short wall
+ 
+
+ align:start position:0%
+of the short wall
+right that's what spelkey thinks is
+
+ align:start position:0%
+right that's what spelkey thinks is
+ 
+
+ align:start position:0%
+right that's what spelkey thinks is
+there's some version in your head of
+
+ align:start position:0%
+there's some version in your head of
+ 
+
+ align:start position:0%
+there's some version in your head of
+it's on the left side of the short wall
+
+ align:start position:0%
+it's on the left side of the short wall
+ 
+
+ align:start position:0%
+it's on the left side of the short wall
+and that's why adults can do this
+
+ align:start position:0%
+and that's why adults can do this
+ 
+
+ align:start position:0%
+and that's why adults can do this
+when their language system isn't tied up
+
+ align:start position:0%
+when their language system isn't tied up
+ 
+
+ align:start position:0%
+when their language system isn't tied up
+i don't think that's exactly right but
+
+ align:start position:0%
+i don't think that's exactly right but
+ 
+
+ align:start position:0%
+i don't think that's exactly right but
+it's a beautiful story and there's some
+
+ align:start position:0%
+it's a beautiful story and there's some
+ 
+
+ align:start position:0%
+it's a beautiful story and there's some
+evidence for it okay
+
+ align:start position:0%
+evidence for it okay
+ 
+
+ align:start position:0%
+evidence for it okay
+anyway
+
+ align:start position:0%
+anyway
+ 
+
+ align:start position:0%
+anyway
+part of the reason i go through this
+
+ align:start position:0%
+part of the reason i go through this
+ 
+
+ align:start position:0%
+part of the reason i go through this
+whole thing well one i think these
+
+ align:start position:0%
+whole thing well one i think these
+ 
+
+ align:start position:0%
+whole thing well one i think these
+experiments are cool but it's also been
+
+ align:start position:0%
+experiments are cool but it's also been
+ 
+
+ align:start position:0%
+experiments are cool but it's also been
+the basis of a kind of core idea in
+
+ align:start position:0%
+the basis of a kind of core idea in
+ 
+
+ align:start position:0%
+the basis of a kind of core idea in
+cognitive science
+
+ align:start position:0%
+cognitive science
+ 
+
+ align:start position:0%
+cognitive science
+and that idea is called informational
+
+ align:start position:0%
+and that idea is called informational
+ 
+
+ align:start position:0%
+and that idea is called informational
+encapsulation
+
+ align:start position:0%
+encapsulation
+ 
+
+ align:start position:0%
+encapsulation
+so think about just lots of syllables
+
+ align:start position:0%
+so think about just lots of syllables
+ 
+
+ align:start position:0%
+so think about just lots of syllables
+for a pretty simple idea
+
+ align:start position:0%
+for a pretty simple idea
+ 
+
+ align:start position:0%
+for a pretty simple idea
+you have this system for reorientation
+
+ align:start position:0%
+you have this system for reorientation
+ 
+
+ align:start position:0%
+you have this system for reorientation
+and it is designed to use the shape of
+
+ align:start position:0%
+and it is designed to use the shape of
+ 
+
+ align:start position:0%
+and it is designed to use the shape of
+space around you as the cue that you use
+
+ align:start position:0%
+space around you as the cue that you use
+ 
+
+ align:start position:0%
+space around you as the cue that you use
+to reorient yourself when you're
+
+ align:start position:0%
+to reorient yourself when you're
+ 
+
+ align:start position:0%
+to reorient yourself when you're
+disoriented
+
+ align:start position:0%
+disoriented
+ 
+
+ align:start position:0%
+disoriented
+that system is kind of hardwired to do
+
+ align:start position:0%
+that system is kind of hardwired to do
+ 
+
+ align:start position:0%
+that system is kind of hardwired to do
+just that
+
+ align:start position:0%
+just that
+ 
+
+ align:start position:0%
+just that
+and if some other part of your brain has
+
+ align:start position:0%
+and if some other part of your brain has
+ 
+
+ align:start position:0%
+and if some other part of your brain has
+information that could solve the problem
+
+ align:start position:0%
+information that could solve the problem
+ 
+
+ align:start position:0%
+information that could solve the problem
+like the presence of a relevant feature
+
+ align:start position:0%
+like the presence of a relevant feature
+ 
+
+ align:start position:0%
+like the presence of a relevant feature
+that could you could use
+
+ align:start position:0%
+that could you could use
+ 
+
+ align:start position:0%
+that could you could use
+you don't have that's this your
+
+ align:start position:0%
+you don't have that's this your
+ 
+
+ align:start position:0%
+you don't have that's this your
+reorientation system doesn't have access
+
+ align:start position:0%
+reorientation system doesn't have access
+ 
+
+ align:start position:0%
+reorientation system doesn't have access
+to that information it's informationally
+
+ align:start position:0%
+to that information it's informationally
+ 
+
+ align:start position:0%
+to that information it's informationally
+encapsulated it only has access to the
+
+ align:start position:0%
+encapsulated it only has access to the
+ 
+
+ align:start position:0%
+encapsulated it only has access to the
+particular inputs that are kind of
+
+ align:start position:0%
+particular inputs that are kind of
+ 
+
+ align:start position:0%
+particular inputs that are kind of
+hardwired into it okay
+
+ align:start position:0%
+hardwired into it okay
+ 
+
+ align:start position:0%
+hardwired into it okay
+and so
+
+ align:start position:0%
+and so
+ 
+
+ align:start position:0%
+and so
+um 20 years ago a lot of people kind of
+
+ align:start position:0%
+um 20 years ago a lot of people kind of
+ 
+
+ align:start position:0%
+um 20 years ago a lot of people kind of
+went wild with us and said that all the
+
+ align:start position:0%
+went wild with us and said that all the
+ 
+
+ align:start position:0%
+went wild with us and said that all the
+you know brain regions that i've talked
+
+ align:start position:0%
+you know brain regions that i've talked
+ 
+
+ align:start position:0%
+you know brain regions that i've talked
+about and cognitive systems that we're
+
+ align:start position:0%
+about and cognitive systems that we're
+ 
+
+ align:start position:0%
+about and cognitive systems that we're
+considering this course are
+
+ align:start position:0%
+considering this course are
+ 
+
+ align:start position:0%
+considering this course are
+informationally encapsulated it's kind
+
+ align:start position:0%
+informationally encapsulated it's kind
+ 
+
+ align:start position:0%
+informationally encapsulated it's kind
+of an extreme idea that goes far beyond
+
+ align:start position:0%
+of an extreme idea that goes far beyond
+ 
+
+ align:start position:0%
+of an extreme idea that goes far beyond
+functional specificity to say like the
+
+ align:start position:0%
+functional specificity to say like the
+ 
+
+ align:start position:0%
+functional specificity to say like the
+inputs are extremely restricted to each
+
+ align:start position:0%
+inputs are extremely restricted to each
+ 
+
+ align:start position:0%
+inputs are extremely restricted to each
+region and that's probably not true
+
+ align:start position:0%
+region and that's probably not true
+ 
+
+ align:start position:0%
+region and that's probably not true
+but there's some
+
+ align:start position:0%
+but there's some
+ 
+
+ align:start position:0%
+but there's some
+limitations on the information that each
+
+ align:start position:0%
+limitations on the information that each
+ 
+
+ align:start position:0%
+limitations on the information that each
+of these processors we're considering in
+
+ align:start position:0%
+of these processors we're considering in
+ 
+
+ align:start position:0%
+of these processors we're considering in
+this course has access to and this is
+
+ align:start position:0%
+this course has access to and this is
+ 
+
+ align:start position:0%
+this course has access to and this is
+kind of the kind of classic evidence
+
+ align:start position:0%
+kind of the kind of classic evidence
+ 
+
+ align:start position:0%
+kind of the kind of classic evidence
+behavioral evidence that some of those
+
+ align:start position:0%
+behavioral evidence that some of those
+ 
+
+ align:start position:0%
+behavioral evidence that some of those
+systems have very restricted inputs does
+
+ align:start position:0%
+systems have very restricted inputs does
+ 
+
+ align:start position:0%
+systems have very restricted inputs does
+that make sense idea of informational
+
+ align:start position:0%
+that make sense idea of informational
+ 
+
+ align:start position:0%
+that make sense idea of informational
+encapsulation not is it you know
+
+ align:start position:0%
+encapsulation not is it you know
+ 
+
+ align:start position:0%
+encapsulation not is it you know
+absolute truth about the brain but as an
+
+ align:start position:0%
+absolute truth about the brain but as an
+ 
+
+ align:start position:0%
+absolute truth about the brain but as an
+idea that is
+
+ align:start position:0%
+idea that is
+ 
+
+ align:start position:0%
+idea that is
+interesting to consider
+
+ align:start position:0%
+interesting to consider
+ 
+
+ align:start position:0%
+interesting to consider
+individually for each of the systems we
+
+ align:start position:0%
+individually for each of the systems we
+ 
+
+ align:start position:0%
+individually for each of the systems we
+study
+
+ align:start position:0%
+study
+ 
+
+ align:start position:0%
+study
+there's been pushback about the
+
+ align:start position:0%
+there's been pushback about the
+ 
+
+ align:start position:0%
+there's been pushback about the
+extremeness of this claim that infants
+
+ align:start position:0%
+extremeness of this claim that infants
+ 
+
+ align:start position:0%
+extremeness of this claim that infants
+and rodents only use the shape of space
+
+ align:start position:0%
+and rodents only use the shape of space
+ 
+
+ align:start position:0%
+and rodents only use the shape of space
+there are circumstances where you can
+
+ align:start position:0%
+there are circumstances where you can
+ 
+
+ align:start position:0%
+there are circumstances where you can
+get them to use other information but
+
+ align:start position:0%
+get them to use other information but
+ 
+
+ align:start position:0%
+get them to use other information but
+it's definitely true that the shape of
+
+ align:start position:0%
+it's definitely true that the shape of
+ 
+
+ align:start position:0%
+it's definitely true that the shape of
+space is the dominant cue for
+
+ align:start position:0%
+space is the dominant cue for
+ 
+
+ align:start position:0%
+space is the dominant cue for
+reorienting
+
+ align:start position:0%
+reorienting
+ 
+
+ align:start position:0%
+reorienting
+in
+
+ align:start position:0%
+in
+ 
+
+ align:start position:0%
+in
+in rodents and infants
+
+ align:start position:0%
+in rodents and infants
+ 
+
+ align:start position:0%
+in rodents and infants
+all right
+
+ align:start position:0%
+all right
+ 
+
+ align:start position:0%
+all right
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+when you're lost as i've mentioned
+
+ align:start position:0%
+when you're lost as i've mentioned
+ 
+
+ align:start position:0%
+when you're lost as i've mentioned
+there's two questions you need to answer
+
+ align:start position:0%
+there's two questions you need to answer
+ 
+
+ align:start position:0%
+there's two questions you need to answer
+where are you and which way you're
+
+ align:start position:0%
+where are you and which way you're
+ 
+
+ align:start position:0%
+where are you and which way you're
+oriented right this last stuff we were
+
+ align:start position:0%
+oriented right this last stuff we were
+ 
+
+ align:start position:0%
+oriented right this last stuff we were
+talking about is about the which way
+
+ align:start position:0%
+talking about is about the which way
+ 
+
+ align:start position:0%
+talking about is about the which way
+you're oriented question
+
+ align:start position:0%
+you're oriented question
+ 
+
+ align:start position:0%
+you're oriented question
+okay and i just showed you some evidence
+
+ align:start position:0%
+okay and i just showed you some evidence
+ 
+
+ align:start position:0%
+okay and i just showed you some evidence
+for this general finding that the
+
+ align:start position:0%
+for this general finding that the
+ 
+
+ align:start position:0%
+for this general finding that the
+geometric cues the shape of space
+
+ align:start position:0%
+geometric cues the shape of space
+ 
+
+ align:start position:0%
+geometric cues the shape of space
+uh are the dominant cubes you use to
+
+ align:start position:0%
+uh are the dominant cubes you use to
+ 
+
+ align:start position:0%
+uh are the dominant cubes you use to
+reorient yourself to to get your heading
+
+ align:start position:0%
+reorient yourself to to get your heading
+ 
+
+ align:start position:0%
+reorient yourself to to get your heading
+back when you're disoriented okay
+
+ align:start position:0%
+back when you're disoriented okay
+ 
+
+ align:start position:0%
+back when you're disoriented okay
+um but
+
+ align:start position:0%
+um but
+ 
+
+ align:start position:0%
+um but
+do we really know that those cues are
+
+ align:start position:0%
+do we really know that those cues are
+ 
+
+ align:start position:0%
+do we really know that those cues are
+different for for place recognition and
+
+ align:start position:0%
+different for for place recognition and
+ 
+
+ align:start position:0%
+different for for place recognition and
+for heading direction right so i've sort
+
+ align:start position:0%
+for heading direction right so i've sort
+ 
+
+ align:start position:0%
+for heading direction right so i've sort
+of said here are two different parts of
+
+ align:start position:0%
+of said here are two different parts of
+ 
+
+ align:start position:0%
+of said here are two different parts of
+the problem but do they function
+
+ align:start position:0%
+the problem but do they function
+ 
+
+ align:start position:0%
+the problem but do they function
+differently
+
+ align:start position:0%
+differently
+ 
+
+ align:start position:0%
+differently
+do we really use different cues do we
+
+ align:start position:0%
+do we really use different cues do we
+ 
+
+ align:start position:0%
+do we really use different cues do we
+use the shape of space more for heading
+
+ align:start position:0%
+use the shape of space more for heading
+ 
+
+ align:start position:0%
+use the shape of space more for heading
+direction and maybe other cues for place
+
+ align:start position:0%
+direction and maybe other cues for place
+ 
+
+ align:start position:0%
+direction and maybe other cues for place
+recognition for knowing where we are
+
+ align:start position:0%
+recognition for knowing where we are
+ 
+
+ align:start position:0%
+recognition for knowing where we are
+okay so i'm going to show you a very
+
+ align:start position:0%
+okay so i'm going to show you a very
+ 
+
+ align:start position:0%
+okay so i'm going to show you a very
+elegant behavioral experiment in mice
+
+ align:start position:0%
+elegant behavioral experiment in mice
+ 
+
+ align:start position:0%
+elegant behavioral experiment in mice
+that does this all all at once in one
+
+ align:start position:0%
+that does this all all at once in one
+ 
+
+ align:start position:0%
+that does this all all at once in one
+experiment
+
+ align:start position:0%
+experiment
+ 
+
+ align:start position:0%
+experiment
+so this is josh julian a former lab tech
+
+ align:start position:0%
+so this is josh julian a former lab tech
+ 
+
+ align:start position:0%
+so this is josh julian a former lab tech
+in my lab i get no credit for this
+
+ align:start position:0%
+in my lab i get no credit for this
+ 
+
+ align:start position:0%
+in my lab i get no credit for this
+whatsoever i'm proud even though i
+
+ align:start position:0%
+whatsoever i'm proud even though i
+ 
+
+ align:start position:0%
+whatsoever i'm proud even though i
+shouldn't be proud he was just an
+
+ align:start position:0%
+shouldn't be proud he was just an
+ 
+
+ align:start position:0%
+shouldn't be proud he was just an
+endogenously smart guy who went on and
+
+ align:start position:0%
+endogenously smart guy who went on and
+ 
+
+ align:start position:0%
+endogenously smart guy who went on and
+did an awesome experiment after he left
+
+ align:start position:0%
+did an awesome experiment after he left
+ 
+
+ align:start position:0%
+did an awesome experiment after he left
+my lab and went off to grad school and
+
+ align:start position:0%
+my lab and went off to grad school and
+ 
+
+ align:start position:0%
+my lab and went off to grad school and
+here's his awesome experiment
+
+ align:start position:0%
+here's his awesome experiment
+ 
+
+ align:start position:0%
+here's his awesome experiment
+okay so he said let's get mice to do
+
+ align:start position:0%
+okay so he said let's get mice to do
+ 
+
+ align:start position:0%
+okay so he said let's get mice to do
+both of these tasks they have to know
+
+ align:start position:0%
+both of these tasks they have to know
+ 
+
+ align:start position:0%
+both of these tasks they have to know
+where they are and which way they're
+
+ align:start position:0%
+where they are and which way they're
+ 
+
+ align:start position:0%
+where they are and which way they're
+oriented
+
+ align:start position:0%
+oriented
+ 
+
+ align:start position:0%
+oriented
+okay we're gonna do the same
+
+ align:start position:0%
+okay we're gonna do the same
+ 
+
+ align:start position:0%
+okay we're gonna do the same
+disorientation thing take them out turn
+
+ align:start position:0%
+disorientation thing take them out turn
+ 
+
+ align:start position:0%
+disorientation thing take them out turn
+them around till they're disoriented but
+
+ align:start position:0%
+them around till they're disoriented but
+ 
+
+ align:start position:0%
+them around till they're disoriented but
+these mice have to learn two different
+
+ align:start position:0%
+these mice have to learn two different
+ 
+
+ align:start position:0%
+these mice have to learn two different
+environments okay one environment has
+
+ align:start position:0%
+environments okay one environment has
+ 
+
+ align:start position:0%
+environments okay one environment has
+the vertical stripes on the short wall
+
+ align:start position:0%
+the vertical stripes on the short wall
+ 
+
+ align:start position:0%
+the vertical stripes on the short wall
+on one of the short walls the other
+
+ align:start position:0%
+on one of the short walls the other
+ 
+
+ align:start position:0%
+on one of the short walls the other
+environment has horizontal stripes on
+
+ align:start position:0%
+environment has horizontal stripes on
+ 
+
+ align:start position:0%
+environment has horizontal stripes on
+the short wall
+
+ align:start position:0%
+the short wall
+ 
+
+ align:start position:0%
+the short wall
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+so you do the same experiment you bait
+
+ align:start position:0%
+so you do the same experiment you bait
+ 
+
+ align:start position:0%
+so you do the same experiment you bait
+one corner and you see where the rodent
+
+ align:start position:0%
+one corner and you see where the rodent
+ 
+
+ align:start position:0%
+one corner and you see where the rodent
+goes does he go to the two opposite
+
+ align:start position:0%
+goes does he go to the two opposite
+ 
+
+ align:start position:0%
+goes does he go to the two opposite
+corners
+
+ align:start position:0%
+corners
+ 
+
+ align:start position:0%
+corners
+exactly the same experiment but he has
+
+ align:start position:0%
+exactly the same experiment but he has
+ 
+
+ align:start position:0%
+exactly the same experiment but he has
+to remember which room is to solve the
+
+ align:start position:0%
+to remember which room is to solve the
+ 
+
+ align:start position:0%
+to remember which room is to solve the
+problem he has to know whether he's he
+
+ align:start position:0%
+problem he has to know whether he's he
+ 
+
+ align:start position:0%
+problem he has to know whether he's he
+has to discover rediscover the vertical
+
+ align:start position:0%
+has to discover rediscover the vertical
+ 
+
+ align:start position:0%
+has to discover rediscover the vertical
+stripes or the horizontal stripes and
+
+ align:start position:0%
+stripes or the horizontal stripes and
+ 
+
+ align:start position:0%
+stripes or the horizontal stripes and
+act accordingly because when he's in the
+
+ align:start position:0%
+act accordingly because when he's in the
+ 
+
+ align:start position:0%
+act accordingly because when he's in the
+vertical context the um the thing gets
+
+ align:start position:0%
+vertical context the um the thing gets
+ 
+
+ align:start position:0%
+vertical context the um the thing gets
+hit he does this over repeated trials
+
+ align:start position:0%
+hit he does this over repeated trials
+ 
+
+ align:start position:0%
+hit he does this over repeated trials
+the the the food gets hid
+
+ align:start position:0%
+the the the food gets hid
+ 
+
+ align:start position:0%
+the the the food gets hid
+um on the um
+
+ align:start position:0%
+um on the um
+ 
+
+ align:start position:0%
+um on the um
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+hey let me get this right long wall on
+
+ align:start position:0%
+hey let me get this right long wall on
+ 
+
+ align:start position:0%
+hey let me get this right long wall on
+the left
+
+ align:start position:0%
+the left
+ 
+
+ align:start position:0%
+the left
+yeah right um
+
+ align:start position:0%
+yeah right um
+ 
+
+ align:start position:0%
+yeah right um
+yeah so
+
+ align:start position:0%
+yeah so
+ 
+
+ align:start position:0%
+yeah so
+when the long wall is on the left of the
+
+ align:start position:0%
+when the long wall is on the left of the
+ 
+
+ align:start position:0%
+when the long wall is on the left of the
+rodent okay that corner the long wall is
+
+ align:start position:0%
+rodent okay that corner the long wall is
+ 
+
+ align:start position:0%
+rodent okay that corner the long wall is
+on the left everybody oriented whereas
+
+ align:start position:0%
+on the left everybody oriented whereas
+ 
+
+ align:start position:0%
+on the left everybody oriented whereas
+when he's in the in the blue context the
+
+ align:start position:0%
+when he's in the in the blue context the
+ 
+
+ align:start position:0%
+when he's in the in the blue context the
+reward here
+
+ align:start position:0%
+reward here
+ 
+
+ align:start position:0%
+reward here
+the long wall is on the right
+
+ align:start position:0%
+the long wall is on the right
+ 
+
+ align:start position:0%
+the long wall is on the right
+okay so you have to learn those two
+
+ align:start position:0%
+okay so you have to learn those two
+ 
+
+ align:start position:0%
+okay so you have to learn those two
+different environments and that the
+
+ align:start position:0%
+different environments and that the
+ 
+
+ align:start position:0%
+different environments and that the
+the relevant shape cues are opposite in
+
+ align:start position:0%
+the relevant shape cues are opposite in
+ 
+
+ align:start position:0%
+the relevant shape cues are opposite in
+each okay everybody got that
+
+ align:start position:0%
+each okay everybody got that
+ 
+
+ align:start position:0%
+each okay everybody got that
+okay now
+
+ align:start position:0%
+okay now
+ 
+
+ align:start position:0%
+okay now
+what you find is that the rodent can
+
+ align:start position:0%
+what you find is that the rodent can
+ 
+
+ align:start position:0%
+what you find is that the rodent can
+learn that just fine okay so this shows
+
+ align:start position:0%
+learn that just fine okay so this shows
+ 
+
+ align:start position:0%
+learn that just fine okay so this shows
+that when you put the rodent in the
+
+ align:start position:0%
+that when you put the rodent in the
+ 
+
+ align:start position:0%
+that when you put the rodent in the
+vertical context in a room like this
+
+ align:start position:0%
+vertical context in a room like this
+ 
+
+ align:start position:0%
+vertical context in a room like this
+um they go more
+
+ align:start position:0%
+um they go more
+ 
+
+ align:start position:0%
+um they go more
+to these two corners than those two
+
+ align:start position:0%
+to these two corners than those two
+ 
+
+ align:start position:0%
+to these two corners than those two
+corners
+
+ align:start position:0%
+corners
+ 
+
+ align:start position:0%
+corners
+whereas when you put him in a um in a
+
+ align:start position:0%
+whereas when you put him in a um in a
+ 
+
+ align:start position:0%
+whereas when you put him in a um in a
+horizontal context with horizontal
+
+ align:start position:0%
+horizontal context with horizontal
+ 
+
+ align:start position:0%
+horizontal context with horizontal
+stripes he goes more to those two
+
+ align:start position:0%
+stripes he goes more to those two
+ 
+
+ align:start position:0%
+stripes he goes more to those two
+corners than those two corners
+
+ align:start position:0%
+corners than those two corners
+ 
+
+ align:start position:0%
+corners than those two corners
+that tells you the rodent has used the
+
+ align:start position:0%
+that tells you the rodent has used the
+ 
+
+ align:start position:0%
+that tells you the rodent has used the
+orientation of the stripes to figure out
+
+ align:start position:0%
+orientation of the stripes to figure out
+ 
+
+ align:start position:0%
+orientation of the stripes to figure out
+which room he's in and hence which two
+
+ align:start position:0%
+which room he's in and hence which two
+ 
+
+ align:start position:0%
+which room he's in and hence which two
+corners are the right ones
+
+ align:start position:0%
+corners are the right ones
+ 
+
+ align:start position:0%
+corners are the right ones
+everybody got that
+
+ align:start position:0%
+everybody got that
+ 
+
+ align:start position:0%
+everybody got that
+but here's the amazing thing even though
+
+ align:start position:0%
+but here's the amazing thing even though
+ 
+
+ align:start position:0%
+but here's the amazing thing even though
+in this experiment the very same animals
+
+ align:start position:0%
+in this experiment the very same animals
+ 
+
+ align:start position:0%
+in this experiment the very same animals
+in the very same trials are using those
+
+ align:start position:0%
+in the very same trials are using those
+ 
+
+ align:start position:0%
+in the very same trials are using those
+stripes
+
+ align:start position:0%
+stripes
+ 
+
+ align:start position:0%
+stripes
+to figure out which room they're in
+
+ align:start position:0%
+to figure out which room they're in
+ 
+
+ align:start position:0%
+to figure out which room they're in
+they don't use those stripes at all
+
+ align:start position:0%
+they don't use those stripes at all
+ 
+
+ align:start position:0%
+they don't use those stripes at all
+to break the symmetry and to go only to
+
+ align:start position:0%
+to break the symmetry and to go only to
+ 
+
+ align:start position:0%
+to break the symmetry and to go only to
+the great corner
+
+ align:start position:0%
+the great corner
+ 
+
+ align:start position:0%
+the great corner
+which they could do
+
+ align:start position:0%
+which they could do
+ 
+
+ align:start position:0%
+which they could do
+but don't
+
+ align:start position:0%
+but don't
+ 
+
+ align:start position:0%
+but don't
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+once you've trained the rodents on these
+
+ align:start position:0%
+once you've trained the rodents on these
+ 
+
+ align:start position:0%
+once you've trained the rodents on these
+two things that the reward is here uh in
+
+ align:start position:0%
+two things that the reward is here uh in
+ 
+
+ align:start position:0%
+two things that the reward is here uh in
+um the ver the vertical context and
+
+ align:start position:0%
+um the ver the vertical context and
+ 
+
+ align:start position:0%
+um the ver the vertical context and
+they're in the horizontal context you
+
+ align:start position:0%
+they're in the horizontal context you
+ 
+
+ align:start position:0%
+they're in the horizontal context you
+disorient them you put them back in you
+
+ align:start position:0%
+disorient them you put them back in you
+ 
+
+ align:start position:0%
+disorient them you put them back in you
+find that when you have vertical stripes
+
+ align:start position:0%
+find that when you have vertical stripes
+ 
+
+ align:start position:0%
+find that when you have vertical stripes
+they go to these two corners i'm just
+
+ align:start position:0%
+they go to these two corners i'm just
+ 
+
+ align:start position:0%
+they go to these two corners i'm just
+repeating the data when there are
+
+ align:start position:0%
+repeating the data when there are
+ 
+
+ align:start position:0%
+repeating the data when there are
+horizontal stripes they go to those two
+
+ align:start position:0%
+horizontal stripes they go to those two
+ 
+
+ align:start position:0%
+horizontal stripes they go to those two
+corners okay they've learned that
+
+ align:start position:0%
+corners okay they've learned that
+ 
+
+ align:start position:0%
+corners okay they've learned that
+but why do they go to those two corners
+
+ align:start position:0%
+but why do they go to those two corners
+ 
+
+ align:start position:0%
+but why do they go to those two corners
+they learn the damn stripes they use
+
+ align:start position:0%
+they learn the damn stripes they use
+ 
+
+ align:start position:0%
+they learn the damn stripes they use
+them to know which room they're in but
+
+ align:start position:0%
+them to know which room they're in but
+ 
+
+ align:start position:0%
+them to know which room they're in but
+they don't use them to break the
+
+ align:start position:0%
+they don't use them to break the
+ 
+
+ align:start position:0%
+they don't use them to break the
+asymmetry and decide which is the
+
+ align:start position:0%
+asymmetry and decide which is the
+ 
+
+ align:start position:0%
+asymmetry and decide which is the
+correct corner
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so this is like a microcosm of
+
+ align:start position:0%
+okay so this is like a microcosm of
+ 
+
+ align:start position:0%
+okay so this is like a microcosm of
+everything i've been saying so far all
+
+ align:start position:0%
+everything i've been saying so far all
+ 
+
+ align:start position:0%
+everything i've been saying so far all
+in one experiment
+
+ align:start position:0%
+in one experiment
+ 
+
+ align:start position:0%
+in one experiment
+right the rodents are noticing those
+
+ align:start position:0%
+right the rodents are noticing those
+ 
+
+ align:start position:0%
+right the rodents are noticing those
+feature cues using them to figure out
+
+ align:start position:0%
+feature cues using them to figure out
+ 
+
+ align:start position:0%
+feature cues using them to figure out
+which room they're in where are they
+
+ align:start position:0%
+which room they're in where are they
+ 
+
+ align:start position:0%
+which room they're in where are they
+but failing to use those features the
+
+ align:start position:0%
+but failing to use those features the
+ 
+
+ align:start position:0%
+but failing to use those features the
+orientation of the stripes
+
+ align:start position:0%
+orientation of the stripes
+ 
+
+ align:start position:0%
+orientation of the stripes
+to figure out which of the two corners
+
+ align:start position:0%
+to figure out which of the two corners
+ 
+
+ align:start position:0%
+to figure out which of the two corners
+is the correct one
+
+ align:start position:0%
+is the correct one
+ 
+
+ align:start position:0%
+is the correct one
+they're not even encoding food is near
+
+ align:start position:0%
+they're not even encoding food is near
+ 
+
+ align:start position:0%
+they're not even encoding food is near
+stripes
+
+ align:start position:0%
+stripes
+ 
+
+ align:start position:0%
+stripes
+like duh that should have been easy
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+right so this is a beautiful i mean this
+
+ align:start position:0%
+right so this is a beautiful i mean this
+ 
+
+ align:start position:0%
+right so this is a beautiful i mean this
+is even more evidence for informational
+
+ align:start position:0%
+is even more evidence for informational
+ 
+
+ align:start position:0%
+is even more evidence for informational
+encapsulation of this system because it
+
+ align:start position:0%
+encapsulation of this system because it
+ 
+
+ align:start position:0%
+encapsulation of this system because it
+shows us on the very same trial they
+
+ align:start position:0%
+shows us on the very same trial they
+ 
+
+ align:start position:0%
+shows us on the very same trial they
+used the stripe information to know
+
+ align:start position:0%
+used the stripe information to know
+ 
+
+ align:start position:0%
+used the stripe information to know
+which room they were they failed to use
+
+ align:start position:0%
+which room they were they failed to use
+ 
+
+ align:start position:0%
+which room they were they failed to use
+it to figure out their orientation in
+
+ align:start position:0%
+it to figure out their orientation in
+ 
+
+ align:start position:0%
+it to figure out their orientation in
+that room
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this sort of making sense i realized
+
+ align:start position:0%
+this sort of making sense i realized
+ 
+
+ align:start position:0%
+this sort of making sense i realized
+kind of subtle it's sort of simple and
+
+ align:start position:0%
+kind of subtle it's sort of simple and
+ 
+
+ align:start position:0%
+kind of subtle it's sort of simple and
+subtle at the same time
+
+ align:start position:0%
+subtle at the same time
+ 
+
+ align:start position:0%
+subtle at the same time
+um yeah so now the themselves that you
+
+ align:start position:0%
+um yeah so now the themselves that you
+ 
+
+ align:start position:0%
+um yeah so now the themselves that you
+showed us on the very first
+
+ align:start position:0%
+showed us on the very first
+ 
+
+ align:start position:0%
+showed us on the very first
+maps
+
+ align:start position:0%
+maps
+ 
+
+ align:start position:0%
+maps
+what are they doing here yeah exactly
+
+ align:start position:0%
+what are they doing here yeah exactly
+ 
+
+ align:start position:0%
+what are they doing here yeah exactly
+great question let's look at that that's
+
+ align:start position:0%
+great question let's look at that that's
+ 
+
+ align:start position:0%
+great question let's look at that that's
+what we're doing next it's a great
+
+ align:start position:0%
+what we're doing next it's a great
+ 
+
+ align:start position:0%
+what we're doing next it's a great
+question what are the damn place cells
+
+ align:start position:0%
+question what are the damn place cells
+ 
+
+ align:start position:0%
+question what are the damn place cells
+doing here
+
+ align:start position:0%
+doing here
+ 
+
+ align:start position:0%
+doing here
+great question
+
+ align:start position:0%
+great question
+ 
+
+ align:start position:0%
+great question
+okay let's say a little bit more and
+
+ align:start position:0%
+okay let's say a little bit more and
+ 
+
+ align:start position:0%
+okay let's say a little bit more and
+then we'll think about what the play
+
+ align:start position:0%
+then we'll think about what the play
+ 
+
+ align:start position:0%
+then we'll think about what the play
+cells are doing
+
+ align:start position:0%
+cells are doing
+ 
+
+ align:start position:0%
+cells are doing
+okay so let me just like restate cash
+
+ align:start position:0%
+okay so let me just like restate cash
+ 
+
+ align:start position:0%
+okay so let me just like restate cash
+out the findings here
+
+ align:start position:0%
+out the findings here
+ 
+
+ align:start position:0%
+out the findings here
+the mice are using the features to
+
+ align:start position:0%
+the mice are using the features to
+ 
+
+ align:start position:0%
+the mice are using the features to
+figure out which place they're in are
+
+ align:start position:0%
+figure out which place they're in are
+ 
+
+ align:start position:0%
+figure out which place they're in are
+they in this one or that one but they
+
+ align:start position:0%
+they in this one or that one but they
+ 
+
+ align:start position:0%
+they in this one or that one but they
+are failing
+
+ align:start position:0%
+are failing
+ 
+
+ align:start position:0%
+are failing
+to use those features to figure out
+
+ align:start position:0%
+to use those features to figure out
+ 
+
+ align:start position:0%
+to use those features to figure out
+which is the correct corner they're
+
+ align:start position:0%
+which is the correct corner they're
+ 
+
+ align:start position:0%
+which is the correct corner they're
+still 50 50 for the two corners even
+
+ align:start position:0%
+still 50 50 for the two corners even
+ 
+
+ align:start position:0%
+still 50 50 for the two corners even
+though
+
+ align:start position:0%
+though
+ 
+
+ align:start position:0%
+though
+logically they have that information and
+
+ align:start position:0%
+logically they have that information and
+ 
+
+ align:start position:0%
+logically they have that information and
+they could use it and they should use it
+
+ align:start position:0%
+they could use it and they should use it
+ 
+
+ align:start position:0%
+they could use it and they should use it
+they don't
+
+ align:start position:0%
+they don't
+ 
+
+ align:start position:0%
+they don't
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+so that means the mice are using
+
+ align:start position:0%
+so that means the mice are using
+ 
+
+ align:start position:0%
+so that means the mice are using
+features in this case orientation for
+
+ align:start position:0%
+features in this case orientation for
+ 
+
+ align:start position:0%
+features in this case orientation for
+place recognition
+
+ align:start position:0%
+place recognition
+ 
+
+ align:start position:0%
+place recognition
+but not for um regaining their
+
+ align:start position:0%
+but not for um regaining their
+ 
+
+ align:start position:0%
+but not for um regaining their
+orientation within that place
+
+ align:start position:0%
+orientation within that place
+ 
+
+ align:start position:0%
+orientation within that place
+i've just i'm just repeating what i said
+
+ align:start position:0%
+i've just i'm just repeating what i said
+ 
+
+ align:start position:0%
+i've just i'm just repeating what i said
+before is that making sense
+
+ align:start position:0%
+before is that making sense
+ 
+
+ align:start position:0%
+before is that making sense
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+so now
+
+ align:start position:0%
+so now
+ 
+
+ align:start position:0%
+so now
+david's question what are the place
+
+ align:start position:0%
+david's question what are the place
+ 
+
+ align:start position:0%
+david's question what are the place
+cells doing here great question let's
+
+ align:start position:0%
+cells doing here great question let's
+ 
+
+ align:start position:0%
+cells doing here great question let's
+look it's mice so we can do that
+
+ align:start position:0%
+look it's mice so we can do that
+ 
+
+ align:start position:0%
+look it's mice so we can do that
+or k nathat all can do that and josh
+
+ align:start position:0%
+or k nathat all can do that and josh
+ 
+
+ align:start position:0%
+or k nathat all can do that and josh
+julian my amazing former lab tech so
+
+ align:start position:0%
+julian my amazing former lab tech so
+ 
+
+ align:start position:0%
+julian my amazing former lab tech so
+again i get no credit whatsoever
+
+ align:start position:0%
+again i get no credit whatsoever
+ 
+
+ align:start position:0%
+again i get no credit whatsoever
+okay so what do they do
+
+ align:start position:0%
+okay so what do they do
+ 
+
+ align:start position:0%
+okay so what do they do
+they allow the mice to forage for crumbs
+
+ align:start position:0%
+they allow the mice to forage for crumbs
+ 
+
+ align:start position:0%
+they allow the mice to forage for crumbs
+in a box like this okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+they disorient the mouse before each
+
+ align:start position:0%
+they disorient the mouse before each
+ 
+
+ align:start position:0%
+they disorient the mouse before each
+trial take him out turn him around so he
+
+ align:start position:0%
+trial take him out turn him around so he
+ 
+
+ align:start position:0%
+trial take him out turn him around so he
+doesn't know which way he's facing put
+
+ align:start position:0%
+doesn't know which way he's facing put
+ 
+
+ align:start position:0%
+doesn't know which way he's facing put
+him in the box
+
+ align:start position:0%
+him in the box
+ 
+
+ align:start position:0%
+him in the box
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+and they find that place cells have a
+
+ align:start position:0%
+and they find that place cells have a
+ 
+
+ align:start position:0%
+and they find that place cells have a
+particular location in that box not
+
+ align:start position:0%
+particular location in that box not
+ 
+
+ align:start position:0%
+particular location in that box not
+surprising that's what place cells do
+
+ align:start position:0%
+surprising that's what place cells do
+ 
+
+ align:start position:0%
+surprising that's what place cells do
+so here are two different trials two
+
+ align:start position:0%
+so here are two different trials two
+ 
+
+ align:start position:0%
+so here are two different trials two
+different cells that were mapped out in
+
+ align:start position:0%
+different cells that were mapped out in
+ 
+
+ align:start position:0%
+different cells that were mapped out in
+a rodent doing this this cell responds
+
+ align:start position:0%
+a rodent doing this this cell responds
+ 
+
+ align:start position:0%
+a rodent doing this this cell responds
+always in that corner
+
+ align:start position:0%
+always in that corner
+ 
+
+ align:start position:0%
+always in that corner
+another cell responds only in that
+
+ align:start position:0%
+another cell responds only in that
+ 
+
+ align:start position:0%
+another cell responds only in that
+corner okay these are just place cells
+
+ align:start position:0%
+corner okay these are just place cells
+ 
+
+ align:start position:0%
+corner okay these are just place cells
+like we described before doing what
+
+ align:start position:0%
+like we described before doing what
+ 
+
+ align:start position:0%
+like we described before doing what
+place cells do
+
+ align:start position:0%
+place cells do
+ 
+
+ align:start position:0%
+place cells do
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+but now
+
+ align:start position:0%
+but now
+ 
+
+ align:start position:0%
+but now
+sometimes those place cells are off by
+
+ align:start position:0%
+sometimes those place cells are off by
+ 
+
+ align:start position:0%
+sometimes those place cells are off by
+180 degrees
+
+ align:start position:0%
+180 degrees
+ 
+
+ align:start position:0%
+180 degrees
+even though the stripes should resolve
+
+ align:start position:0%
+even though the stripes should resolve
+ 
+
+ align:start position:0%
+even though the stripes should resolve
+the ambiguity
+
+ align:start position:0%
+the ambiguity
+ 
+
+ align:start position:0%
+the ambiguity
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+so those same cells
+
+ align:start position:0%
+so those same cells
+ 
+
+ align:start position:0%
+so those same cells
+on other trials
+
+ align:start position:0%
+on other trials
+ 
+
+ align:start position:0%
+on other trials
+respond to the opposite corner
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so the place cells
+
+ align:start position:0%
+so the place cells
+ 
+
+ align:start position:0%
+so the place cells
+are doing just what the rodent is doing
+
+ align:start position:0%
+are doing just what the rodent is doing
+ 
+
+ align:start position:0%
+are doing just what the rodent is doing
+the place cells are confused am i facing
+
+ align:start position:0%
+the place cells are confused am i facing
+ 
+
+ align:start position:0%
+the place cells are confused am i facing
+you know am i am i phase am i oriented
+
+ align:start position:0%
+you know am i am i phase am i oriented
+ 
+
+ align:start position:0%
+you know am i am i phase am i oriented
+like this or am i oriented like that the
+
+ align:start position:0%
+like this or am i oriented like that the
+ 
+
+ align:start position:0%
+like this or am i oriented like that the
+place cells don't know and the rodent
+
+ align:start position:0%
+place cells don't know and the rodent
+ 
+
+ align:start position:0%
+place cells don't know and the rodent
+doesn't know
+
+ align:start position:0%
+doesn't know
+ 
+
+ align:start position:0%
+doesn't know
+and the coolest thing about this
+
+ align:start position:0%
+and the coolest thing about this
+ 
+
+ align:start position:0%
+and the coolest thing about this
+experiment is that these things are
+
+ align:start position:0%
+experiment is that these things are
+ 
+
+ align:start position:0%
+experiment is that these things are
+linked on the trials where the rodent
+
+ align:start position:0%
+linked on the trials where the rodent
+ 
+
+ align:start position:0%
+linked on the trials where the rodent
+goes to the wrong corner the place cells
+
+ align:start position:0%
+goes to the wrong corner the place cells
+ 
+
+ align:start position:0%
+goes to the wrong corner the place cells
+are also in the wrong corner
+
+ align:start position:0%
+are also in the wrong corner
+ 
+
+ align:start position:0%
+are also in the wrong corner
+okay they systematically determine which
+
+ align:start position:0%
+okay they systematically determine which
+ 
+
+ align:start position:0%
+okay they systematically determine which
+way the animal will go
+
+ align:start position:0%
+way the animal will go
+ 
+
+ align:start position:0%
+way the animal will go
+okay so
+
+ align:start position:0%
+okay so
+ 
+
+ align:start position:0%
+okay so
+um oh and also as i mentioned before
+
+ align:start position:0%
+um oh and also as i mentioned before
+ 
+
+ align:start position:0%
+um oh and also as i mentioned before
+like all those cells are in cahoots
+
+ align:start position:0%
+like all those cells are in cahoots
+ 
+
+ align:start position:0%
+like all those cells are in cahoots
+they're all in sync going the same way
+
+ align:start position:0%
+they're all in sync going the same way
+ 
+
+ align:start position:0%
+they're all in sync going the same way
+so when one of the cells
+
+ align:start position:0%
+so when one of the cells
+ 
+
+ align:start position:0%
+so when one of the cells
+rotates to the opposite corner all the
+
+ align:start position:0%
+rotates to the opposite corner all the
+ 
+
+ align:start position:0%
+rotates to the opposite corner all the
+other ones rotate to the opposite corner
+
+ align:start position:0%
+other ones rotate to the opposite corner
+ 
+
+ align:start position:0%
+other ones rotate to the opposite corner
+so it's as though somehow on trial to
+
+ align:start position:0%
+so it's as though somehow on trial to
+ 
+
+ align:start position:0%
+so it's as though somehow on trial to
+trial
+
+ align:start position:0%
+trial
+ 
+
+ align:start position:0%
+trial
+the rodent
+
+ align:start position:0%
+the rodent
+ 
+
+ align:start position:0%
+the rodent
+thinks he's oriented in one way he's
+
+ align:start position:0%
+thinks he's oriented in one way he's
+ 
+
+ align:start position:0%
+thinks he's oriented in one way he's
+actually 50 50 which way he's oriented
+
+ align:start position:0%
+actually 50 50 which way he's oriented
+ 
+
+ align:start position:0%
+actually 50 50 which way he's oriented
+he's not using the feature cues
+
+ align:start position:0%
+he's not using the feature cues
+ 
+
+ align:start position:0%
+he's not using the feature cues
+and his behavior according to where he
+
+ align:start position:0%
+and his behavior according to where he
+ 
+
+ align:start position:0%
+and his behavior according to where he
+looks for the food
+
+ align:start position:0%
+looks for the food
+ 
+
+ align:start position:0%
+looks for the food
+exactly follows that way he's oriented
+
+ align:start position:0%
+exactly follows that way he's oriented
+ 
+
+ align:start position:0%
+exactly follows that way he's oriented
+and so do all of his place cells
+
+ align:start position:0%
+and so do all of his place cells
+ 
+
+ align:start position:0%
+and so do all of his place cells
+okay that's that whole system goes
+
+ align:start position:0%
+okay that's that whole system goes
+ 
+
+ align:start position:0%
+okay that's that whole system goes
+together
+
+ align:start position:0%
+together
+ 
+
+ align:start position:0%
+together
+that tells you that those place cells
+
+ align:start position:0%
+that tells you that those place cells
+ 
+
+ align:start position:0%
+that tells you that those place cells
+are relevant behaviorally they are the
+
+ align:start position:0%
+are relevant behaviorally they are the
+ 
+
+ align:start position:0%
+are relevant behaviorally they are the
+they are the system that either directly
+
+ align:start position:0%
+they are the system that either directly
+ 
+
+ align:start position:0%
+they are the system that either directly
+determines or is tightly linked to the
+
+ align:start position:0%
+determines or is tightly linked to the
+ 
+
+ align:start position:0%
+determines or is tightly linked to the
+system that determines
+
+ align:start position:0%
+system that determines
+ 
+
+ align:start position:0%
+system that determines
+which way the animal thinks he's facing
+
+ align:start position:0%
+which way the animal thinks he's facing
+ 
+
+ align:start position:0%
+which way the animal thinks he's facing
+okay i realize this is a little bit
+
+ align:start position:0%
+okay i realize this is a little bit
+ 
+
+ align:start position:0%
+okay i realize this is a little bit
+complicated
+
+ align:start position:0%
+complicated
+ 
+
+ align:start position:0%
+complicated
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+does it make sense to you that
+
+ align:start position:0%
+does it make sense to you that
+ 
+
+ align:start position:0%
+does it make sense to you that
+you know as we've been talking about
+
+ align:start position:0%
+you know as we've been talking about
+ 
+
+ align:start position:0%
+you know as we've been talking about
+with reorientation
+
+ align:start position:0%
+with reorientation
+ 
+
+ align:start position:0%
+with reorientation
+even though the animal should know from
+
+ align:start position:0%
+even though the animal should know from
+ 
+
+ align:start position:0%
+even though the animal should know from
+this stripe
+
+ align:start position:0%
+this stripe
+ 
+
+ align:start position:0%
+this stripe
+the difference between that corner and
+
+ align:start position:0%
+the difference between that corner and
+ 
+
+ align:start position:0%
+the difference between that corner and
+this corner he doesn't know behaviorally
+
+ align:start position:0%
+this corner he doesn't know behaviorally
+ 
+
+ align:start position:0%
+this corner he doesn't know behaviorally
+he's looking for food right there and
+
+ align:start position:0%
+he's looking for food right there and
+ 
+
+ align:start position:0%
+he's looking for food right there and
+yet he goes 50 50. weird and stupid
+
+ align:start position:0%
+yet he goes 50 50. weird and stupid
+ 
+
+ align:start position:0%
+yet he goes 50 50. weird and stupid
+right
+
+ align:start position:0%
+right
+ 
+
+ align:start position:0%
+right
+place cells do the same thing
+
+ align:start position:0%
+place cells do the same thing
+ 
+
+ align:start position:0%
+place cells do the same thing
+okay and further the place cells and the
+
+ align:start position:0%
+okay and further the place cells and the
+ 
+
+ align:start position:0%
+okay and further the place cells and the
+behavior go together
+
+ align:start position:0%
+behavior go together
+ 
+
+ align:start position:0%
+behavior go together
+yeah
+
+ align:start position:0%
+yeah
+ 
+
+ align:start position:0%
+yeah
+so if you're reading information off of
+
+ align:start position:0%
+so if you're reading information off of
+ 
+
+ align:start position:0%
+so if you're reading information off of
+play sales can you stop it can you
+
+ align:start position:0%
+play sales can you stop it can you
+ 
+
+ align:start position:0%
+play sales can you stop it can you
+provide ah
+
+ align:start position:0%
+provide ah
+ 
+
+ align:start position:0%
+provide ah
+wouldn't that be nice
+
+ align:start position:0%
+wouldn't that be nice
+ 
+
+ align:start position:0%
+wouldn't that be nice
+turns out you can't for the reason
+
+ align:start position:0%
+turns out you can't for the reason
+ 
+
+ align:start position:0%
+turns out you can't for the reason
+someone over here asked a long time ago
+
+ align:start position:0%
+someone over here asked a long time ago
+ 
+
+ align:start position:0%
+someone over here asked a long time ago
+you i think
+
+ align:start position:0%
+you i think
+ 
+
+ align:start position:0%
+you i think
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+and that's because they're all
+
+ align:start position:0%
+and that's because they're all
+ 
+
+ align:start position:0%
+and that's because they're all
+interleaved together
+
+ align:start position:0%
+interleaved together
+ 
+
+ align:start position:0%
+interleaved together
+and if you zap just one you're not going
+
+ align:start position:0%
+and if you zap just one you're not going
+ 
+
+ align:start position:0%
+and if you zap just one you're not going
+to one cell you're not going to have an
+
+ align:start position:0%
+to one cell you're not going to have an
+ 
+
+ align:start position:0%
+to one cell you're not going to have an
+effect and if you zap a whole region you
+
+ align:start position:0%
+effect and if you zap a whole region you
+ 
+
+ align:start position:0%
+effect and if you zap a whole region you
+get all of them and you get muck
+
+ align:start position:0%
+get all of them and you get muck
+ 
+
+ align:start position:0%
+get all of them and you get muck
+so you can't do that manipulation
+
+ align:start position:0%
+so you can't do that manipulation
+ 
+
+ align:start position:0%
+so you can't do that manipulation
+unfortunately you need some kind of
+
+ align:start position:0%
+unfortunately you need some kind of
+ 
+
+ align:start position:0%
+unfortunately you need some kind of
+topography to do the manipulation
+
+ align:start position:0%
+topography to do the manipulation
+ 
+
+ align:start position:0%
+topography to do the manipulation
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+okay so i just said how all this
+
+ align:start position:0%
+okay so i just said how all this
+ 
+
+ align:start position:0%
+okay so i just said how all this
+i got ahead of myself how it relates to
+
+ align:start position:0%
+i got ahead of myself how it relates to
+ 
+
+ align:start position:0%
+i got ahead of myself how it relates to
+behavior uh but just to go through that
+
+ align:start position:0%
+behavior uh but just to go through that
+ 
+
+ align:start position:0%
+behavior uh but just to go through that
+quickly so what we've done here is
+
+ align:start position:0%
+quickly so what we've done here is
+ 
+
+ align:start position:0%
+quickly so what we've done here is
+they've trained the mouse on this
+
+ align:start position:0%
+they've trained the mouse on this
+ 
+
+ align:start position:0%
+they've trained the mouse on this
+classic reorientation task they
+
+ align:start position:0%
+classic reorientation task they
+ 
+
+ align:start position:0%
+classic reorientation task they
+disorient the mouse before each trial
+
+ align:start position:0%
+disorient the mouse before each trial
+ 
+
+ align:start position:0%
+disorient the mouse before each trial
+while recording from hippocampal place
+
+ align:start position:0%
+while recording from hippocampal place
+ 
+
+ align:start position:0%
+while recording from hippocampal place
+cells
+
+ align:start position:0%
+cells
+ 
+
+ align:start position:0%
+cells
+as before given cell flips 180 degrees
+
+ align:start position:0%
+as before given cell flips 180 degrees
+ 
+
+ align:start position:0%
+as before given cell flips 180 degrees
+from trial to trial
+
+ align:start position:0%
+from trial to trial
+ 
+
+ align:start position:0%
+from trial to trial
+despite the fact that the stripes should
+
+ align:start position:0%
+despite the fact that the stripes should
+ 
+
+ align:start position:0%
+despite the fact that the stripes should
+disambiguate it and tell them which way
+
+ align:start position:0%
+disambiguate it and tell them which way
+ 
+
+ align:start position:0%
+disambiguate it and tell them which way
+is oriented
+
+ align:start position:0%
+is oriented
+ 
+
+ align:start position:0%
+is oriented
+and by the way the head direction cells
+
+ align:start position:0%
+and by the way the head direction cells
+ 
+
+ align:start position:0%
+and by the way the head direction cells
+and the grid cells also flip in the same
+
+ align:start position:0%
+and the grid cells also flip in the same
+ 
+
+ align:start position:0%
+and the grid cells also flip in the same
+way in cahoots with the head with the
+
+ align:start position:0%
+way in cahoots with the head with the
+ 
+
+ align:start position:0%
+way in cahoots with the head with the
+place cells
+
+ align:start position:0%
+place cells
+ 
+
+ align:start position:0%
+place cells
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+but you can tell which corner the animal
+
+ align:start position:0%
+but you can tell which corner the animal
+ 
+
+ align:start position:0%
+but you can tell which corner the animal
+will go to by looking at what the place
+
+ align:start position:0%
+will go to by looking at what the place
+ 
+
+ align:start position:0%
+will go to by looking at what the place
+cells respond right
+
+ align:start position:0%
+cells respond right
+ 
+
+ align:start position:0%
+cells respond right
+and so when the place sells
+
+ align:start position:0%
+and so when the place sells
+ 
+
+ align:start position:0%
+and so when the place sells
+when this place cell
+
+ align:start position:0%
+when this place cell
+ 
+
+ align:start position:0%
+when this place cell
+represents that location the animal
+
+ align:start position:0%
+represents that location the animal
+ 
+
+ align:start position:0%
+represents that location the animal
+searches first there and when it flips
+
+ align:start position:0%
+searches first there and when it flips
+ 
+
+ align:start position:0%
+searches first there and when it flips
+around they search in the opposite
+
+ align:start position:0%
+around they search in the opposite
+ 
+
+ align:start position:0%
+around they search in the opposite
+corner
+
+ align:start position:0%
+corner
+ 
+
+ align:start position:0%
+corner
+okay so all of that just shows this
+
+ align:start position:0%
+okay so all of that just shows this
+ 
+
+ align:start position:0%
+okay so all of that just shows this
+really strong link between the play
+
+ align:start position:0%
+really strong link between the play
+ 
+
+ align:start position:0%
+really strong link between the play
+cells and behavior
+
+ align:start position:0%
+cells and behavior
+ 
+
+ align:start position:0%
+cells and behavior
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+so to recap we've talked about four
+
+ align:start position:0%
+so to recap we've talked about four
+ 
+
+ align:start position:0%
+so to recap we've talked about four
+different kinds of cells involved in
+
+ align:start position:0%
+different kinds of cells involved in
+ 
+
+ align:start position:0%
+different kinds of cells involved in
+representing space and navigating around
+
+ align:start position:0%
+representing space and navigating around
+ 
+
+ align:start position:0%
+representing space and navigating around
+in it
+
+ align:start position:0%
+in it
+ 
+
+ align:start position:0%
+in it
+place cells that are like the you are
+
+ align:start position:0%
+place cells that are like the you are
+ 
+
+ align:start position:0%
+place cells that are like the you are
+here they respond when you're in a
+
+ align:start position:0%
+here they respond when you're in a
+ 
+
+ align:start position:0%
+here they respond when you're in a
+particular location direction cells that
+
+ align:start position:0%
+particular location direction cells that
+ 
+
+ align:start position:0%
+particular location direction cells that
+respond when you're heading in one
+
+ align:start position:0%
+respond when you're heading in one
+ 
+
+ align:start position:0%
+respond when you're heading in one
+direction not in another direction
+
+ align:start position:0%
+direction not in another direction
+ 
+
+ align:start position:0%
+direction not in another direction
+uh border cells that represent that that
+
+ align:start position:0%
+uh border cells that represent that that
+ 
+
+ align:start position:0%
+uh border cells that represent that that
+fire when you're near a particular
+
+ align:start position:0%
+fire when you're near a particular
+ 
+
+ align:start position:0%
+fire when you're near a particular
+border in the environment i have border
+
+ align:start position:0%
+border in the environment i have border
+ 
+
+ align:start position:0%
+border in the environment i have border
+cells going right now throughout this
+
+ align:start position:0%
+cells going right now throughout this
+ 
+
+ align:start position:0%
+cells going right now throughout this
+whole lecture i've got a batch of border
+
+ align:start position:0%
+whole lecture i've got a batch of border
+ 
+
+ align:start position:0%
+whole lecture i've got a batch of border
+cells right that are going
+
+ align:start position:0%
+cells right that are going
+ 
+
+ align:start position:0%
+cells right that are going
+grid cells that do this amazing thing of
+
+ align:start position:0%
+grid cells that do this amazing thing of
+ 
+
+ align:start position:0%
+grid cells that do this amazing thing of
+firing when the animal is in multiple
+
+ align:start position:0%
+firing when the animal is in multiple
+ 
+
+ align:start position:0%
+firing when the animal is in multiple
+different locations and those locations
+
+ align:start position:0%
+different locations and those locations
+ 
+
+ align:start position:0%
+different locations and those locations
+that make it fire are arranged in a
+
+ align:start position:0%
+that make it fire are arranged in a
+ 
+
+ align:start position:0%
+that make it fire are arranged in a
+hexagonal grid
+
+ align:start position:0%
+hexagonal grid
+ 
+
+ align:start position:0%
+hexagonal grid
+think of it as a kind of ruler telling
+
+ align:start position:0%
+think of it as a kind of ruler telling
+ 
+
+ align:start position:0%
+think of it as a kind of ruler telling
+the rodent how far he's gone in his
+
+ align:start position:0%
+the rodent how far he's gone in his
+ 
+
+ align:start position:0%
+the rodent how far he's gone in his
+space and those grid cells are like the
+
+ align:start position:0%
+space and those grid cells are like the
+ 
+
+ align:start position:0%
+space and those grid cells are like the
+rulers
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah right
+
+ align:start position:0%
+yeah right
+ 
+
+ align:start position:0%
+yeah right
+those are those are the four kind we've
+
+ align:start position:0%
+those are those are the four kind we've
+ 
+
+ align:start position:0%
+those are those are the four kind we've
+talked about okay
+
+ align:start position:0%
+talked about okay
+ 
+
+ align:start position:0%
+talked about okay
+so now
+
+ align:start position:0%
+so now
+ 
+
+ align:start position:0%
+so now
+here's the cool thing all this stuff
+
+ align:start position:0%
+here's the cool thing all this stuff
+ 
+
+ align:start position:0%
+here's the cool thing all this stuff
+navigation is awesome
+
+ align:start position:0%
+navigation is awesome
+ 
+
+ align:start position:0%
+navigation is awesome
+right we need it it's important all
+
+ align:start position:0%
+right we need it it's important all
+ 
+
+ align:start position:0%
+right we need it it's important all
+night you know all uh mobile animals
+
+ align:start position:0%
+night you know all uh mobile animals
+ 
+
+ align:start position:0%
+night you know all uh mobile animals
+need it for the reasons we've been
+
+ align:start position:0%
+need it for the reasons we've been
+ 
+
+ align:start position:0%
+need it for the reasons we've been
+talking about
+
+ align:start position:0%
+talking about
+ 
+
+ align:start position:0%
+talking about
+but you you can use this whole system
+
+ align:start position:0%
+but you you can use this whole system
+ 
+
+ align:start position:0%
+but you you can use this whole system
+for so much more than just navigation
+
+ align:start position:0%
+for so much more than just navigation
+ 
+
+ align:start position:0%
+for so much more than just navigation
+once you have this fancy system in your
+
+ align:start position:0%
+once you have this fancy system in your
+ 
+
+ align:start position:0%
+once you have this fancy system in your
+head to keep track of your location to
+
+ align:start position:0%
+head to keep track of your location to
+ 
+
+ align:start position:0%
+head to keep track of your location to
+keep track of your direction to keep
+
+ align:start position:0%
+keep track of your direction to keep
+ 
+
+ align:start position:0%
+keep track of your direction to keep
+track of where things are how you're
+
+ align:start position:0%
+track of where things are how you're
+ 
+
+ align:start position:0%
+track of where things are how you're
+moving through that space you can use
+
+ align:start position:0%
+moving through that space you can use
+ 
+
+ align:start position:0%
+moving through that space you can use
+that whole magnificent system in other
+
+ align:start position:0%
+that whole magnificent system in other
+ 
+
+ align:start position:0%
+that whole magnificent system in other
+ways and in the last three or four years
+
+ align:start position:0%
+ways and in the last three or four years
+ 
+
+ align:start position:0%
+ways and in the last three or four years
+there's just a huge number of studies
+
+ align:start position:0%
+there's just a huge number of studies
+ 
+
+ align:start position:0%
+there's just a huge number of studies
+that are really starting to take this
+
+ align:start position:0%
+that are really starting to take this
+ 
+
+ align:start position:0%
+that are really starting to take this
+very seriously particularly the grid
+
+ align:start position:0%
+very seriously particularly the grid
+ 
+
+ align:start position:0%
+very seriously particularly the grid
+cells and thinking about how the grid
+
+ align:start position:0%
+cells and thinking about how the grid
+ 
+
+ align:start position:0%
+cells and thinking about how the grid
+cells
+
+ align:start position:0%
+cells
+ 
+
+ align:start position:0%
+cells
+i mean probably the whole system but
+
+ align:start position:0%
+i mean probably the whole system but
+ 
+
+ align:start position:0%
+i mean probably the whole system but
+people have been focusing on the grid
+
+ align:start position:0%
+people have been focusing on the grid
+ 
+
+ align:start position:0%
+people have been focusing on the grid
+cells
+
+ align:start position:0%
+cells
+ 
+
+ align:start position:0%
+cells
+and how they're used in multiple
+
+ align:start position:0%
+and how they're used in multiple
+ 
+
+ align:start position:0%
+and how they're used in multiple
+different situations
+
+ align:start position:0%
+different situations
+ 
+
+ align:start position:0%
+different situations
+so here's one
+
+ align:start position:0%
+so here's one
+ 
+
+ align:start position:0%
+so here's one
+okay this is a cool study where what
+
+ align:start position:0%
+okay this is a cool study where what
+ 
+
+ align:start position:0%
+okay this is a cool study where what
+these guys did was they stuck a little
+
+ align:start position:0%
+these guys did was they stuck a little
+ 
+
+ align:start position:0%
+these guys did was they stuck a little
+device hanging around people's necks the
+
+ align:start position:0%
+device hanging around people's necks the
+ 
+
+ align:start position:0%
+device hanging around people's necks the
+subject's necks have little camera
+
+ align:start position:0%
+subject's necks have little camera
+ 
+
+ align:start position:0%
+subject's necks have little camera
+aiming forward it takes pictures at
+
+ align:start position:0%
+aiming forward it takes pictures at
+ 
+
+ align:start position:0%
+aiming forward it takes pictures at
+random intervals and records the
+
+ align:start position:0%
+random intervals and records the
+ 
+
+ align:start position:0%
+random intervals and records the
+person's gps location okay
+
+ align:start position:0%
+person's gps location okay
+ 
+
+ align:start position:0%
+person's gps location okay
+so you send them off for a few months
+
+ align:start position:0%
+so you send them off for a few months
+ 
+
+ align:start position:0%
+so you send them off for a few months
+with this little device and you do
+
+ align:start position:0%
+with this little device and you do
+ 
+
+ align:start position:0%
+with this little device and you do
+something to protect people's privacy i
+
+ align:start position:0%
+something to protect people's privacy i
+ 
+
+ align:start position:0%
+something to protect people's privacy i
+don't know exactly how they maneuver
+
+ align:start position:0%
+don't know exactly how they maneuver
+ 
+
+ align:start position:0%
+don't know exactly how they maneuver
+that but i'm sure they found a way
+
+ align:start position:0%
+that but i'm sure they found a way
+ 
+
+ align:start position:0%
+that but i'm sure they found a way
+uh and so then they get this set of
+
+ align:start position:0%
+uh and so then they get this set of
+ 
+
+ align:start position:0%
+uh and so then they get this set of
+photographs taken from this person's
+
+ align:start position:0%
+photographs taken from this person's
+ 
+
+ align:start position:0%
+photographs taken from this person's
+kind of front view of wherever they were
+
+ align:start position:0%
+kind of front view of wherever they were
+ 
+
+ align:start position:0%
+kind of front view of wherever they were
+over several months as they went
+
+ align:start position:0%
+over several months as they went
+ 
+
+ align:start position:0%
+over several months as they went
+wherever they went in their lives okay
+
+ align:start position:0%
+wherever they went in their lives okay
+ 
+
+ align:start position:0%
+wherever they went in their lives okay
+with a little gps tag for each
+
+ align:start position:0%
+with a little gps tag for each
+ 
+
+ align:start position:0%
+with a little gps tag for each
+photograph okay
+
+ align:start position:0%
+photograph okay
+ 
+
+ align:start position:0%
+photograph okay
+so then what they do is they bring the
+
+ align:start position:0%
+so then what they do is they bring the
+ 
+
+ align:start position:0%
+so then what they do is they bring the
+subjects in and pop them in the scanner
+
+ align:start position:0%
+subjects in and pop them in the scanner
+ 
+
+ align:start position:0%
+subjects in and pop them in the scanner
+and show them some of those pictures
+
+ align:start position:0%
+and show them some of those pictures
+ 
+
+ align:start position:0%
+and show them some of those pictures
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+and they asked people to relive the
+
+ align:start position:0%
+and they asked people to relive the
+ 
+
+ align:start position:0%
+and they asked people to relive the
+experience that they had when they were
+
+ align:start position:0%
+experience that they had when they were
+ 
+
+ align:start position:0%
+experience that they had when they were
+looking at that thing
+
+ align:start position:0%
+looking at that thing
+ 
+
+ align:start position:0%
+looking at that thing
+right if you put this on me it'd be my
+
+ align:start position:0%
+right if you put this on me it'd be my
+ 
+
+ align:start position:0%
+right if you put this on me it'd be my
+monitor like all the time and i wouldn't
+
+ align:start position:0%
+monitor like all the time and i wouldn't
+ 
+
+ align:start position:0%
+monitor like all the time and i wouldn't
+know which
+
+ align:start position:0%
+know which
+ 
+
+ align:start position:0%
+know which
+experience to relive but i guess these
+
+ align:start position:0%
+experience to relive but i guess these
+ 
+
+ align:start position:0%
+experience to relive but i guess these
+people had you know richer lives let's
+
+ align:start position:0%
+people had you know richer lives let's
+ 
+
+ align:start position:0%
+people had you know richer lives let's
+hope
+
+ align:start position:0%
+hope
+ 
+
+ align:start position:0%
+hope
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+so now what they do is they use multiple
+
+ align:start position:0%
+so now what they do is they use multiple
+ 
+
+ align:start position:0%
+so now what they do is they use multiple
+voxel pattern analysis
+
+ align:start position:0%
+voxel pattern analysis
+ 
+
+ align:start position:0%
+voxel pattern analysis
+in the hippocampus
+
+ align:start position:0%
+in the hippocampus
+ 
+
+ align:start position:0%
+in the hippocampus
+while people are reliving those
+
+ align:start position:0%
+while people are reliving those
+ 
+
+ align:start position:0%
+while people are reliving those
+experiences in the scanner by looking at
+
+ align:start position:0%
+experiences in the scanner by looking at
+ 
+
+ align:start position:0%
+experiences in the scanner by looking at
+those images taken from their
+
+ align:start position:0%
+those images taken from their
+ 
+
+ align:start position:0%
+those images taken from their
+front-facing cameras
+
+ align:start position:0%
+front-facing cameras
+ 
+
+ align:start position:0%
+front-facing cameras
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+um and then they asked is the pattern of
+
+ align:start position:0%
+um and then they asked is the pattern of
+ 
+
+ align:start position:0%
+um and then they asked is the pattern of
+response in the hippocampus like some
+
+ align:start position:0%
+response in the hippocampus like some
+ 
+
+ align:start position:0%
+response in the hippocampus like some
+bunch of voxels here's some pattern
+
+ align:start position:0%
+bunch of voxels here's some pattern
+ 
+
+ align:start position:0%
+bunch of voxels here's some pattern
+is it more similar for events the
+
+ align:start position:0%
+is it more similar for events the
+ 
+
+ align:start position:0%
+is it more similar for events the
+subject remembers that are near that
+
+ align:start position:0%
+subject remembers that are near that
+ 
+
+ align:start position:0%
+subject remembers that are near that
+were nearby in space okay
+
+ align:start position:0%
+were nearby in space okay
+ 
+
+ align:start position:0%
+were nearby in space okay
+so you do this for me it's like yes i
+
+ align:start position:0%
+so you do this for me it's like yes i
+ 
+
+ align:start position:0%
+so you do this for me it's like yes i
+occasionally go to the state of
+
+ align:start position:0%
+occasionally go to the state of
+ 
+
+ align:start position:0%
+occasionally go to the state of
+cafeteria and i you know occasionally go
+
+ align:start position:0%
+cafeteria and i you know occasionally go
+ 
+
+ align:start position:0%
+cafeteria and i you know occasionally go
+to the
+
+ align:start position:0%
+to the
+ 
+
+ align:start position:0%
+to the
+koch center cafeteria
+
+ align:start position:0%
+koch center cafeteria
+ 
+
+ align:start position:0%
+koch center cafeteria
+and i spend a lot of time at home and
+
+ align:start position:0%
+and i spend a lot of time at home and
+ 
+
+ align:start position:0%
+and i spend a lot of time at home and
+those two things are closer to each
+
+ align:start position:0%
+those two things are closer to each
+ 
+
+ align:start position:0%
+those two things are closer to each
+other than my home thing are the
+
+ align:start position:0%
+other than my home thing are the
+ 
+
+ align:start position:0%
+other than my home thing are the
+patterns more similar for nearby
+
+ align:start position:0%
+patterns more similar for nearby
+ 
+
+ align:start position:0%
+patterns more similar for nearby
+locations than for more distant
+
+ align:start position:0%
+locations than for more distant
+ 
+
+ align:start position:0%
+locations than for more distant
+locations okay
+
+ align:start position:0%
+locations okay
+ 
+
+ align:start position:0%
+locations okay
+and they were
+
+ align:start position:0%
+and they were
+ 
+
+ align:start position:0%
+and they were
+so this is the distance on a log scale
+
+ align:start position:0%
+so this is the distance on a log scale
+ 
+
+ align:start position:0%
+so this is the distance on a log scale
+between two patterns
+
+ align:start position:0%
+between two patterns
+ 
+
+ align:start position:0%
+between two patterns
+that result from the subject looking at
+
+ align:start position:0%
+that result from the subject looking at
+ 
+
+ align:start position:0%
+that result from the subject looking at
+two different images and this is the
+
+ align:start position:0%
+two different images and this is the
+ 
+
+ align:start position:0%
+two different images and this is the
+similarity
+
+ align:start position:0%
+similarity
+ 
+
+ align:start position:0%
+similarity
+of the pattern in the hippocampus
+
+ align:start position:0%
+of the pattern in the hippocampus
+ 
+
+ align:start position:0%
+of the pattern in the hippocampus
+now some of you might be wondering in
+
+ align:start position:0%
+now some of you might be wondering in
+ 
+
+ align:start position:0%
+now some of you might be wondering in
+fact i wonder this too i think this is a
+
+ align:start position:0%
+fact i wonder this too i think this is a
+ 
+
+ align:start position:0%
+fact i wonder this too i think this is a
+cool study so i'm presenting it but it
+
+ align:start position:0%
+cool study so i'm presenting it but it
+ 
+
+ align:start position:0%
+cool study so i'm presenting it but it
+sort of doesn't make sense to me because
+
+ align:start position:0%
+sort of doesn't make sense to me because
+ 
+
+ align:start position:0%
+sort of doesn't make sense to me because
+everything we know about the hippocampus
+
+ align:start position:0%
+everything we know about the hippocampus
+ 
+
+ align:start position:0%
+everything we know about the hippocampus
+is those place cells are pretty
+
+ align:start position:0%
+is those place cells are pretty
+ 
+
+ align:start position:0%
+is those place cells are pretty
+interleaved so how you manage to get a
+
+ align:start position:0%
+interleaved so how you manage to get a
+ 
+
+ align:start position:0%
+interleaved so how you manage to get a
+pattern
+
+ align:start position:0%
+pattern
+ 
+
+ align:start position:0%
+pattern
+response
+
+ align:start position:0%
+response
+ 
+
+ align:start position:0%
+response
+reading out a systematic location out of
+
+ align:start position:0%
+reading out a systematic location out of
+ 
+
+ align:start position:0%
+reading out a systematic location out of
+the hippocampus is a mystery to me so
+
+ align:start position:0%
+the hippocampus is a mystery to me so
+ 
+
+ align:start position:0%
+the hippocampus is a mystery to me so
+they can't be like fully there must be
+
+ align:start position:0%
+they can't be like fully there must be
+ 
+
+ align:start position:0%
+they can't be like fully there must be
+some kind of structure in there to the
+
+ align:start position:0%
+some kind of structure in there to the
+ 
+
+ align:start position:0%
+some kind of structure in there to the
+layout of those cells
+
+ align:start position:0%
+layout of those cells
+ 
+
+ align:start position:0%
+layout of those cells
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+to enable them to get this information
+
+ align:start position:0%
+to enable them to get this information
+ 
+
+ align:start position:0%
+to enable them to get this information
+okay so everybody get how
+
+ align:start position:0%
+okay so everybody get how
+ 
+
+ align:start position:0%
+okay so everybody get how
+it's telling you that hippocampus is is
+
+ align:start position:0%
+it's telling you that hippocampus is is
+ 
+
+ align:start position:0%
+it's telling you that hippocampus is is
+remembering and reliving
+
+ align:start position:0%
+remembering and reliving
+ 
+
+ align:start position:0%
+remembering and reliving
+some representation of the locations of
+
+ align:start position:0%
+some representation of the locations of
+ 
+
+ align:start position:0%
+some representation of the locations of
+those
+
+ align:start position:0%
+those
+ 
+
+ align:start position:0%
+those
+of where you had those experiences
+
+ align:start position:0%
+of where you had those experiences
+ 
+
+ align:start position:0%
+of where you had those experiences
+everybody get how this shows us
+
+ align:start position:0%
+everybody get how this shows us
+ 
+
+ align:start position:0%
+everybody get how this shows us
+but then they asked another interesting
+
+ align:start position:0%
+but then they asked another interesting
+ 
+
+ align:start position:0%
+but then they asked another interesting
+question and they said oh
+
+ align:start position:0%
+question and they said oh
+ 
+
+ align:start position:0%
+question and they said oh
+does it also represent time so we've
+
+ align:start position:0%
+does it also represent time so we've
+ 
+
+ align:start position:0%
+does it also represent time so we've
+been talking about space for the last
+
+ align:start position:0%
+been talking about space for the last
+ 
+
+ align:start position:0%
+been talking about space for the last
+two lectures but now we're like going
+
+ align:start position:0%
+two lectures but now we're like going
+ 
+
+ align:start position:0%
+two lectures but now we're like going
+straight off the deep end and our first
+
+ align:start position:0%
+straight off the deep end and our first
+ 
+
+ align:start position:0%
+straight off the deep end and our first
+step not even near the deep end yet is
+
+ align:start position:0%
+step not even near the deep end yet is
+ 
+
+ align:start position:0%
+step not even near the deep end yet is
+does it do not just space but time
+
+ align:start position:0%
+does it do not just space but time
+ 
+
+ align:start position:0%
+does it do not just space but time
+so they can take all those photographs
+
+ align:start position:0%
+so they can take all those photographs
+ 
+
+ align:start position:0%
+so they can take all those photographs
+and say okay how far apart in time were
+
+ align:start position:0%
+and say okay how far apart in time were
+ 
+
+ align:start position:0%
+and say okay how far apart in time were
+these two photographs taken
+
+ align:start position:0%
+these two photographs taken
+ 
+
+ align:start position:0%
+these two photographs taken
+and they can do the same graph
+
+ align:start position:0%
+and they can do the same graph
+ 
+
+ align:start position:0%
+and they can do the same graph
+and yes they get a relationship with
+
+ align:start position:0%
+and yes they get a relationship with
+ 
+
+ align:start position:0%
+and yes they get a relationship with
+time as well the farther apart in time
+
+ align:start position:0%
+time as well the farther apart in time
+ 
+
+ align:start position:0%
+time as well the farther apart in time
+people saw those two patterns the more
+
+ align:start position:0%
+people saw those two patterns the more
+ 
+
+ align:start position:0%
+people saw those two patterns the more
+different the patterns in the
+
+ align:start position:0%
+different the patterns in the
+ 
+
+ align:start position:0%
+different the patterns in the
+hippocampus
+
+ align:start position:0%
+hippocampus
+ 
+
+ align:start position:0%
+hippocampus
+isn't that cool
+
+ align:start position:0%
+isn't that cool
+ 
+
+ align:start position:0%
+isn't that cool
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+so that's one example showing that the
+
+ align:start position:0%
+so that's one example showing that the
+ 
+
+ align:start position:0%
+so that's one example showing that the
+hippocampus holds some kind of
+
+ align:start position:0%
+hippocampus holds some kind of
+ 
+
+ align:start position:0%
+hippocampus holds some kind of
+large scale of representation of not
+
+ align:start position:0%
+large scale of representation of not
+ 
+
+ align:start position:0%
+large scale of representation of not
+just space but also time
+
+ align:start position:0%
+just space but also time
+ 
+
+ align:start position:0%
+just space but also time
+and so there's a lot of work on how this
+
+ align:start position:0%
+and so there's a lot of work on how this
+ 
+
+ align:start position:0%
+and so there's a lot of work on how this
+gives structures to our memories for
+
+ align:start position:0%
+gives structures to our memories for
+ 
+
+ align:start position:0%
+gives structures to our memories for
+distances over the range of
+
+ align:start position:0%
+distances over the range of
+ 
+
+ align:start position:0%
+distances over the range of
+100 meters and times between you know 15
+
+ align:start position:0%
+100 meters and times between you know 15
+ 
+
+ align:start position:0%
+100 meters and times between you know 15
+hours
+
+ align:start position:0%
+hours
+ 
+
+ align:start position:0%
+hours
+and a month i'm going to run out of time
+
+ align:start position:0%
+and a month i'm going to run out of time
+ 
+
+ align:start position:0%
+and a month i'm going to run out of time
+so unless it's a clarification question
+
+ align:start position:0%
+so unless it's a clarification question
+ 
+
+ align:start position:0%
+so unless it's a clarification question
+i'm going to keep going
+
+ align:start position:0%
+i'm going to keep going
+ 
+
+ align:start position:0%
+i'm going to keep going
+yeah okay
+
+ align:start position:0%
+yeah okay
+ 
+
+ align:start position:0%
+yeah okay
+yeah
+
+ align:start position:0%
+yeah
+ 
+
+ align:start position:0%
+yeah
+yes if you just did it like that so you
+
+ align:start position:0%
+yes if you just did it like that so you
+ 
+
+ align:start position:0%
+yes if you just did it like that so you
+have to do something to pick out
+
+ align:start position:0%
+have to do something to pick out
+ 
+
+ align:start position:0%
+have to do something to pick out
+um time things that aren't confounded
+
+ align:start position:0%
+um time things that aren't confounded
+ 
+
+ align:start position:0%
+um time things that aren't confounded
+with space you could you have this big
+
+ align:start position:0%
+with space you could you have this big
+ 
+
+ align:start position:0%
+with space you could you have this big
+sample of pictures and you take a subset
+
+ align:start position:0%
+sample of pictures and you take a subset
+ 
+
+ align:start position:0%
+sample of pictures and you take a subset
+where you balance for it absolutely they
+
+ align:start position:0%
+where you balance for it absolutely they
+ 
+
+ align:start position:0%
+where you balance for it absolutely they
+would have to do that
+
+ align:start position:0%
+would have to do that
+ 
+
+ align:start position:0%
+would have to do that
+i can't actually remember but they must
+
+ align:start position:0%
+i can't actually remember but they must
+ 
+
+ align:start position:0%
+i can't actually remember but they must
+have done that you'd
+
+ align:start position:0%
+have done that you'd
+ 
+
+ align:start position:0%
+have done that you'd
+imperfect as peer review is you'd never
+
+ align:start position:0%
+imperfect as peer review is you'd never
+ 
+
+ align:start position:0%
+imperfect as peer review is you'd never
+get through peer review if you didn't
+
+ align:start position:0%
+get through peer review if you didn't
+ 
+
+ align:start position:0%
+get through peer review if you didn't
+take care of that problem
+
+ align:start position:0%
+take care of that problem
+ 
+
+ align:start position:0%
+take care of that problem
+okay okay so that's the first thing
+
+ align:start position:0%
+okay okay so that's the first thing
+ 
+
+ align:start position:0%
+okay okay so that's the first thing
+here's another even more radical example
+
+ align:start position:0%
+here's another even more radical example
+ 
+
+ align:start position:0%
+here's another even more radical example
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+so people have shown that grid-like
+
+ align:start position:0%
+so people have shown that grid-like
+ 
+
+ align:start position:0%
+so people have shown that grid-like
+representations and i'm skipping over
+
+ align:start position:0%
+representations and i'm skipping over
+ 
+
+ align:start position:0%
+representations and i'm skipping over
+most of the details here to give you the
+
+ align:start position:0%
+most of the details here to give you the
+ 
+
+ align:start position:0%
+most of the details here to give you the
+gist because actually the details are a
+
+ align:start position:0%
+gist because actually the details are a
+ 
+
+ align:start position:0%
+gist because actually the details are a
+bit complicated
+
+ align:start position:0%
+bit complicated
+ 
+
+ align:start position:0%
+bit complicated
+but they've shown that people seem to
+
+ align:start position:0%
+but they've shown that people seem to
+ 
+
+ align:start position:0%
+but they've shown that people seem to
+use their grid cell system
+
+ align:start position:0%
+use their grid cell system
+ 
+
+ align:start position:0%
+use their grid cell system
+when they are thinking about conceptual
+
+ align:start position:0%
+when they are thinking about conceptual
+ 
+
+ align:start position:0%
+when they are thinking about conceptual
+spaces
+
+ align:start position:0%
+spaces
+ 
+
+ align:start position:0%
+spaces
+not just physical spaces
+
+ align:start position:0%
+not just physical spaces
+ 
+
+ align:start position:0%
+not just physical spaces
+okay so there's one classic experiment
+
+ align:start position:0%
+okay so there's one classic experiment
+ 
+
+ align:start position:0%
+okay so there's one classic experiment
+in which these guys taught subjects a
+
+ align:start position:0%
+in which these guys taught subjects a
+ 
+
+ align:start position:0%
+in which these guys taught subjects a
+conceptual space they taught them about
+
+ align:start position:0%
+conceptual space they taught them about
+ 
+
+ align:start position:0%
+conceptual space they taught them about
+different kinds of birds
+
+ align:start position:0%
+different kinds of birds
+ 
+
+ align:start position:0%
+different kinds of birds
+okay and these birds differed on two
+
+ align:start position:0%
+okay and these birds differed on two
+ 
+
+ align:start position:0%
+okay and these birds differed on two
+dimensions
+
+ align:start position:0%
+dimensions
+ 
+
+ align:start position:0%
+dimensions
+they could vary in neck length or in leg
+
+ align:start position:0%
+they could vary in neck length or in leg
+ 
+
+ align:start position:0%
+they could vary in neck length or in leg
+length and these things were
+
+ align:start position:0%
+length and these things were
+ 
+
+ align:start position:0%
+length and these things were
+orthogonally varied so they made some
+
+ align:start position:0%
+orthogonally varied so they made some
+ 
+
+ align:start position:0%
+orthogonally varied so they made some
+artificial birds that kind of filled up
+
+ align:start position:0%
+artificial birds that kind of filled up
+ 
+
+ align:start position:0%
+artificial birds that kind of filled up
+that space
+
+ align:start position:0%
+that space
+ 
+
+ align:start position:0%
+that space
+okay so here are some of the birds this
+
+ align:start position:0%
+okay so here are some of the birds this
+ 
+
+ align:start position:0%
+okay so here are some of the birds this
+one has short legs and okay here's
+
+ align:start position:0%
+one has short legs and okay here's
+ 
+
+ align:start position:0%
+one has short legs and okay here's
+here's one with short legs and a long
+
+ align:start position:0%
+here's one with short legs and a long
+ 
+
+ align:start position:0%
+here's one with short legs and a long
+neck
+
+ align:start position:0%
+neck
+ 
+
+ align:start position:0%
+neck
+and um here's one with a longer neck and
+
+ align:start position:0%
+and um here's one with a longer neck and
+ 
+
+ align:start position:0%
+and um here's one with a longer neck and
+shorter leg uh wait let's see longer
+
+ align:start position:0%
+shorter leg uh wait let's see longer
+ 
+
+ align:start position:0%
+shorter leg uh wait let's see longer
+legs and shorter neck right there okay
+
+ align:start position:0%
+legs and shorter neck right there okay
+ 
+
+ align:start position:0%
+legs and shorter neck right there okay
+so you got every possible combination
+
+ align:start position:0%
+so you got every possible combination
+ 
+
+ align:start position:0%
+so you got every possible combination
+they didn't show people a space like
+
+ align:start position:0%
+they didn't show people a space like
+ 
+
+ align:start position:0%
+they didn't show people a space like
+that they just taught them um things
+
+ align:start position:0%
+that they just taught them um things
+ 
+
+ align:start position:0%
+that they just taught them um things
+about these different birds they had to
+
+ align:start position:0%
+about these different birds they had to
+ 
+
+ align:start position:0%
+about these different birds they had to
+remember their names and various facts
+
+ align:start position:0%
+remember their names and various facts
+ 
+
+ align:start position:0%
+remember their names and various facts
+about them
+
+ align:start position:0%
+about them
+ 
+
+ align:start position:0%
+about them
+and so the idea is that when people
+
+ align:start position:0%
+and so the idea is that when people
+ 
+
+ align:start position:0%
+and so the idea is that when people
+learn about those birds they
+
+ align:start position:0%
+learn about those birds they
+ 
+
+ align:start position:0%
+learn about those birds they
+mentally construct a 2d space because in
+
+ align:start position:0%
+mentally construct a 2d space because in
+ 
+
+ align:start position:0%
+mentally construct a 2d space because in
+fact those birds
+
+ align:start position:0%
+fact those birds
+ 
+
+ align:start position:0%
+fact those birds
+were generated from a 2d space varying
+
+ align:start position:0%
+were generated from a 2d space varying
+ 
+
+ align:start position:0%
+were generated from a 2d space varying
+neck length and leg length
+
+ align:start position:0%
+neck length and leg length
+ 
+
+ align:start position:0%
+neck length and leg length
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+and so then when they scan subjects
+
+ align:start position:0%
+and so then when they scan subjects
+ 
+
+ align:start position:0%
+and so then when they scan subjects
+they
+
+ align:start position:0%
+they
+ 
+
+ align:start position:0%
+they
+found essentially a neural signature of
+
+ align:start position:0%
+found essentially a neural signature of
+ 
+
+ align:start position:0%
+found essentially a neural signature of
+a grid system
+
+ align:start position:0%
+a grid system
+ 
+
+ align:start position:0%
+a grid system
+representing that 2d space
+
+ align:start position:0%
+representing that 2d space
+ 
+
+ align:start position:0%
+representing that 2d space
+so even though the grid system
+
+ align:start position:0%
+so even though the grid system
+ 
+
+ align:start position:0%
+so even though the grid system
+presumably evolved to enable us to
+
+ align:start position:0%
+presumably evolved to enable us to
+ 
+
+ align:start position:0%
+presumably evolved to enable us to
+navigate around in a 2d space and keep
+
+ align:start position:0%
+navigate around in a 2d space and keep
+ 
+
+ align:start position:0%
+navigate around in a 2d space and keep
+track of where we are in that 2d space
+
+ align:start position:0%
+track of where we are in that 2d space
+ 
+
+ align:start position:0%
+track of where we are in that 2d space
+it seems like it's now getting co-opted
+
+ align:start position:0%
+it seems like it's now getting co-opted
+ 
+
+ align:start position:0%
+it seems like it's now getting co-opted
+and being used for all kinds of
+
+ align:start position:0%
+and being used for all kinds of
+ 
+
+ align:start position:0%
+and being used for all kinds of
+representations of 2d spaces including
+
+ align:start position:0%
+representations of 2d spaces including
+ 
+
+ align:start position:0%
+representations of 2d spaces including
+extremely abstract artificial learned 2d
+
+ align:start position:0%
+extremely abstract artificial learned 2d
+ 
+
+ align:start position:0%
+extremely abstract artificial learned 2d
+spaces that you weren't even taught
+
+ align:start position:0%
+spaces that you weren't even taught
+ 
+
+ align:start position:0%
+spaces that you weren't even taught
+explicitly as a 2d space you were just
+
+ align:start position:0%
+explicitly as a 2d space you were just
+ 
+
+ align:start position:0%
+explicitly as a 2d space you were just
+taught these birds okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so that's pretty amazing
+
+ align:start position:0%
+so that's pretty amazing
+ 
+
+ align:start position:0%
+so that's pretty amazing
+in another recent study they had
+
+ align:start position:0%
+in another recent study they had
+ 
+
+ align:start position:0%
+in another recent study they had
+subjects
+
+ align:start position:0%
+subjects
+ 
+
+ align:start position:0%
+subjects
+play a do a role playing game
+
+ align:start position:0%
+play a do a role playing game
+ 
+
+ align:start position:0%
+play a do a role playing game
+while in the scanner in the role-playing
+
+ align:start position:0%
+while in the scanner in the role-playing
+ 
+
+ align:start position:0%
+while in the scanner in the role-playing
+game they're interacting with virtual
+
+ align:start position:0%
+game they're interacting with virtual
+ 
+
+ align:start position:0%
+game they're interacting with virtual
+characters
+
+ align:start position:0%
+characters
+ 
+
+ align:start position:0%
+characters
+and those virtual characters had um
+
+ align:start position:0%
+and those virtual characters had um
+ 
+
+ align:start position:0%
+and those virtual characters had um
+different kinds of social power and
+
+ align:start position:0%
+different kinds of social power and
+ 
+
+ align:start position:0%
+different kinds of social power and
+different affiliations with other
+
+ align:start position:0%
+different affiliations with other
+ 
+
+ align:start position:0%
+different affiliations with other
+individuals
+
+ align:start position:0%
+individuals
+ 
+
+ align:start position:0%
+individuals
+so here's another
+
+ align:start position:0%
+so here's another
+ 
+
+ align:start position:0%
+so here's another
+um kind of so the social space that was
+
+ align:start position:0%
+um kind of so the social space that was
+ 
+
+ align:start position:0%
+um kind of so the social space that was
+kind of invented by the experiment
+
+ align:start position:0%
+kind of invented by the experiment
+ 
+
+ align:start position:0%
+kind of invented by the experiment
+experimenters and the subjects are
+
+ align:start position:0%
+experimenters and the subjects are
+ 
+
+ align:start position:0%
+experimenters and the subjects are
+playing this game interacting with other
+
+ align:start position:0%
+playing this game interacting with other
+ 
+
+ align:start position:0%
+playing this game interacting with other
+virtual individuals who vary in social
+
+ align:start position:0%
+virtual individuals who vary in social
+ 
+
+ align:start position:0%
+virtual individuals who vary in social
+dominance and uh and their affiliation
+
+ align:start position:0%
+dominance and uh and their affiliation
+ 
+
+ align:start position:0%
+dominance and uh and their affiliation
+to to others
+
+ align:start position:0%
+to to others
+ 
+
+ align:start position:0%
+to to others
+and they find
+
+ align:start position:0%
+and they find
+ 
+
+ align:start position:0%
+and they find
+um place cell activity that seems to
+
+ align:start position:0%
+um place cell activity that seems to
+ 
+
+ align:start position:0%
+um place cell activity that seems to
+echo
+
+ align:start position:0%
+echo
+ 
+
+ align:start position:0%
+echo
+uh the position of another person
+
+ align:start position:0%
+uh the position of another person
+ 
+
+ align:start position:0%
+uh the position of another person
+in that social space and that's
+
+ align:start position:0%
+in that social space and that's
+ 
+
+ align:start position:0%
+in that social space and that's
+extremely abstract and yet again
+
+ align:start position:0%
+extremely abstract and yet again
+ 
+
+ align:start position:0%
+extremely abstract and yet again
+parts of the navigation spatial system
+
+ align:start position:0%
+parts of the navigation spatial system
+ 
+
+ align:start position:0%
+parts of the navigation spatial system
+are being co-opted to do this i'm not
+
+ align:start position:0%
+are being co-opted to do this i'm not
+ 
+
+ align:start position:0%
+are being co-opted to do this i'm not
+giving you the details on how all this
+
+ align:start position:0%
+giving you the details on how all this
+ 
+
+ align:start position:0%
+giving you the details on how all this
+is done i'm just telling you that this
+
+ align:start position:0%
+is done i'm just telling you that this
+ 
+
+ align:start position:0%
+is done i'm just telling you that this
+studies have shown that these systems
+
+ align:start position:0%
+studies have shown that these systems
+ 
+
+ align:start position:0%
+studies have shown that these systems
+are being co-opted for other uses
+
+ align:start position:0%
+are being co-opted for other uses
+ 
+
+ align:start position:0%
+are being co-opted for other uses
+here's another very charming
+
+ align:start position:0%
+here's another very charming
+ 
+
+ align:start position:0%
+here's another very charming
+non-spatial use well sort of spatial use
+
+ align:start position:0%
+non-spatial use well sort of spatial use
+ 
+
+ align:start position:0%
+non-spatial use well sort of spatial use
+of place cells so those bats turns out
+
+ align:start position:0%
+of place cells so those bats turns out
+ 
+
+ align:start position:0%
+of place cells so those bats turns out
+are extremely social organisms they have
+
+ align:start position:0%
+are extremely social organisms they have
+ 
+
+ align:start position:0%
+are extremely social organisms they have
+very sophisticated social structures and
+
+ align:start position:0%
+very sophisticated social structures and
+ 
+
+ align:start position:0%
+very sophisticated social structures and
+they care a lot about each other and
+
+ align:start position:0%
+they care a lot about each other and
+ 
+
+ align:start position:0%
+they care a lot about each other and
+who's related to whom and who's doing
+
+ align:start position:0%
+who's related to whom and who's doing
+ 
+
+ align:start position:0%
+who's related to whom and who's doing
+what to whom
+
+ align:start position:0%
+what to whom
+ 
+
+ align:start position:0%
+what to whom
+and it turns out that um there are
+
+ align:start position:0%
+and it turns out that um there are
+ 
+
+ align:start position:0%
+and it turns out that um there are
+social place cells in bats that is cells
+
+ align:start position:0%
+social place cells in bats that is cells
+ 
+
+ align:start position:0%
+social place cells in bats that is cells
+in this bats brain if i were a vat that
+
+ align:start position:0%
+in this bats brain if i were a vat that
+ 
+
+ align:start position:0%
+in this bats brain if i were a vat that
+would be representing your location jack
+
+ align:start position:0%
+would be representing your location jack
+ 
+
+ align:start position:0%
+would be representing your location jack
+okay so not the usual thing where my
+
+ align:start position:0%
+okay so not the usual thing where my
+ 
+
+ align:start position:0%
+okay so not the usual thing where my
+place cells are just saying where am i
+
+ align:start position:0%
+place cells are just saying where am i
+ 
+
+ align:start position:0%
+place cells are just saying where am i
+i'm watching you and my place starts out
+
+ align:start position:0%
+i'm watching you and my place starts out
+ 
+
+ align:start position:0%
+i'm watching you and my place starts out
+telling me where are you
+
+ align:start position:0%
+telling me where are you
+ 
+
+ align:start position:0%
+telling me where are you
+right something social organisms care a
+
+ align:start position:0%
+right something social organisms care a
+ 
+
+ align:start position:0%
+right something social organisms care a
+lot about including bats so they have
+
+ align:start position:0%
+lot about including bats so they have
+ 
+
+ align:start position:0%
+lot about including bats so they have
+an observer bat here hanging upside down
+
+ align:start position:0%
+an observer bat here hanging upside down
+ 
+
+ align:start position:0%
+an observer bat here hanging upside down
+and he's watching this bat fly over to
+
+ align:start position:0%
+and he's watching this bat fly over to
+ 
+
+ align:start position:0%
+and he's watching this bat fly over to
+there and back and then in this
+
+ align:start position:0%
+there and back and then in this
+ 
+
+ align:start position:0%
+there and back and then in this
+experiment he subsequently flies that
+
+ align:start position:0%
+experiment he subsequently flies that
+ 
+
+ align:start position:0%
+experiment he subsequently flies that
+same path that's how we know that he's
+
+ align:start position:0%
+same path that's how we know that he's
+ 
+
+ align:start position:0%
+same path that's how we know that he's
+watching that path because he has to
+
+ align:start position:0%
+watching that path because he has to
+ 
+
+ align:start position:0%
+watching that path because he has to
+mimic the bat's path that he just
+
+ align:start position:0%
+mimic the bat's path that he just
+ 
+
+ align:start position:0%
+mimic the bat's path that he just
+observed but while he's watching that
+
+ align:start position:0%
+observed but while he's watching that
+ 
+
+ align:start position:0%
+observed but while he's watching that
+bat
+
+ align:start position:0%
+bat
+ 
+
+ align:start position:0%
+bat
+fly on that path
+
+ align:start position:0%
+fly on that path
+ 
+
+ align:start position:0%
+fly on that path
+what you see is here's a cell right here
+
+ align:start position:0%
+what you see is here's a cell right here
+ 
+
+ align:start position:0%
+what you see is here's a cell right here
+here is um the path flown uh by the bat
+
+ align:start position:0%
+here is um the path flown uh by the bat
+ 
+
+ align:start position:0%
+here is um the path flown uh by the bat
+like out and back
+
+ align:start position:0%
+like out and back
+ 
+
+ align:start position:0%
+like out and back
+um and this is when the bat is flying
+
+ align:start position:0%
+um and this is when the bat is flying
+ 
+
+ align:start position:0%
+um and this is when the bat is flying
+out and back himself and this is when
+
+ align:start position:0%
+out and back himself and this is when
+ 
+
+ align:start position:0%
+out and back himself and this is when
+the other bat is flying out and back
+
+ align:start position:0%
+the other bat is flying out and back
+ 
+
+ align:start position:0%
+the other bat is flying out and back
+blurred a little bit here's here's the
+
+ align:start position:0%
+blurred a little bit here's here's the
+ 
+
+ align:start position:0%
+blurred a little bit here's here's the
+place field for self and the place field
+
+ align:start position:0%
+place field for self and the place field
+ 
+
+ align:start position:0%
+place field for self and the place field
+for other they're not the same a given
+
+ align:start position:0%
+for other they're not the same a given
+ 
+
+ align:start position:0%
+for other they're not the same a given
+cell doesn't represent the same location
+
+ align:start position:0%
+cell doesn't represent the same location
+ 
+
+ align:start position:0%
+cell doesn't represent the same location
+when it's me who's there and when it's
+
+ align:start position:0%
+when it's me who's there and when it's
+ 
+
+ align:start position:0%
+when it's me who's there and when it's
+the person or bad i'm watching who's
+
+ align:start position:0%
+the person or bad i'm watching who's
+ 
+
+ align:start position:0%
+the person or bad i'm watching who's
+there right
+
+ align:start position:0%
+there right
+ 
+
+ align:start position:0%
+there right
+but there are place fields in both cases
+
+ align:start position:0%
+but there are place fields in both cases
+ 
+
+ align:start position:0%
+but there are place fields in both cases
+right
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+social place cells
+
+ align:start position:0%
+social place cells
+ 
+
+ align:start position:0%
+social place cells
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+i'm going to keep going because
+
+ align:start position:0%
+i'm going to keep going because
+ 
+
+ align:start position:0%
+i'm going to keep going because
+otherwise i'm going to run out of time
+
+ align:start position:0%
+otherwise i'm going to run out of time
+ 
+
+ align:start position:0%
+otherwise i'm going to run out of time
+but i'll hang around after
+
+ align:start position:0%
+but i'll hang around after
+ 
+
+ align:start position:0%
+but i'll hang around after
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+place this this whole system is used uh
+
+ align:start position:0%
+place this this whole system is used uh
+ 
+
+ align:start position:0%
+place this this whole system is used uh
+not just for representing
+
+ align:start position:0%
+not just for representing
+ 
+
+ align:start position:0%
+not just for representing
+social status
+
+ align:start position:0%
+social status
+ 
+
+ align:start position:0%
+social status
+you know what kind of bird this is in
+
+ align:start position:0%
+you know what kind of bird this is in
+ 
+
+ align:start position:0%
+you know what kind of bird this is in
+this abstract bird space
+
+ align:start position:0%
+this abstract bird space
+ 
+
+ align:start position:0%
+this abstract bird space
+uh but actually for making decisions for
+
+ align:start position:0%
+uh but actually for making decisions for
+ 
+
+ align:start position:0%
+uh but actually for making decisions for
+thinking okay so
+
+ align:start position:0%
+thinking okay so
+ 
+
+ align:start position:0%
+thinking okay so
+as rats run in mazes
+
+ align:start position:0%
+as rats run in mazes
+ 
+
+ align:start position:0%
+as rats run in mazes
+you can you can record we've shown this
+
+ align:start position:0%
+you can you can record we've shown this
+ 
+
+ align:start position:0%
+you can you can record we've shown this
+already you can show multiple
+
+ align:start position:0%
+already you can show multiple
+ 
+
+ align:start position:0%
+already you can show multiple
+hippocampal place cells and can you guys
+
+ align:start position:0%
+hippocampal place cells and can you guys
+ 
+
+ align:start position:0%
+hippocampal place cells and can you guys
+imagine that if we were recording from
+
+ align:start position:0%
+imagine that if we were recording from
+ 
+
+ align:start position:0%
+imagine that if we were recording from
+several different hippocampal cells at
+
+ align:start position:0%
+several different hippocampal cells at
+ 
+
+ align:start position:0%
+several different hippocampal cells at
+the same time
+
+ align:start position:0%
+the same time
+ 
+
+ align:start position:0%
+the same time
+we could read out those cells and make a
+
+ align:start position:0%
+we could read out those cells and make a
+ 
+
+ align:start position:0%
+we could read out those cells and make a
+guess about where the rat is in its
+
+ align:start position:0%
+guess about where the rat is in its
+ 
+
+ align:start position:0%
+guess about where the rat is in its
+location right it's just like mvpa but
+
+ align:start position:0%
+location right it's just like mvpa but
+ 
+
+ align:start position:0%
+location right it's just like mvpa but
+done across neurons right so we have
+
+ align:start position:0%
+done across neurons right so we have
+ 
+
+ align:start position:0%
+done across neurons right so we have
+pretty good sense of where the where the
+
+ align:start position:0%
+pretty good sense of where the where the
+ 
+
+ align:start position:0%
+pretty good sense of where the where the
+rat is okay
+
+ align:start position:0%
+rat is okay
+ 
+
+ align:start position:0%
+rat is okay
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+now we have a rat navigating around in
+
+ align:start position:0%
+now we have a rat navigating around in
+ 
+
+ align:start position:0%
+now we have a rat navigating around in
+this maze and what i'm going to show you
+
+ align:start position:0%
+this maze and what i'm going to show you
+ 
+
+ align:start position:0%
+this maze and what i'm going to show you
+the white circle is where the rat
+
+ align:start position:0%
+the white circle is where the rat
+ 
+
+ align:start position:0%
+the white circle is where the rat
+actually is
+
+ align:start position:0%
+actually is
+ 
+
+ align:start position:0%
+actually is
+and the little color thing is telling
+
+ align:start position:0%
+and the little color thing is telling
+ 
+
+ align:start position:0%
+and the little color thing is telling
+you where the simultaneous readout from
+
+ align:start position:0%
+you where the simultaneous readout from
+ 
+
+ align:start position:0%
+you where the simultaneous readout from
+several place cells in that rat's
+
+ align:start position:0%
+several place cells in that rat's
+ 
+
+ align:start position:0%
+several place cells in that rat's
+hippocampus
+
+ align:start position:0%
+hippocampus
+ 
+
+ align:start position:0%
+hippocampus
+um would would predict where the rat is
+
+ align:start position:0%
+um would would predict where the rat is
+ 
+
+ align:start position:0%
+um would would predict where the rat is
+like can we tell where the rat is by
+
+ align:start position:0%
+like can we tell where the rat is by
+ 
+
+ align:start position:0%
+like can we tell where the rat is by
+looking at us place cells okay so right
+
+ align:start position:0%
+looking at us place cells okay so right
+ 
+
+ align:start position:0%
+looking at us place cells okay so right
+here they're in the same place it makes
+
+ align:start position:0%
+here they're in the same place it makes
+ 
+
+ align:start position:0%
+here they're in the same place it makes
+sense the rat is right there and we're
+
+ align:start position:0%
+sense the rat is right there and we're
+ 
+
+ align:start position:0%
+sense the rat is right there and we're
+reading it out
+
+ align:start position:0%
+reading it out
+ 
+
+ align:start position:0%
+reading it out
+okay so far so good
+
+ align:start position:0%
+okay so far so good
+ 
+
+ align:start position:0%
+okay so far so good
+but now what we're going to do
+
+ align:start position:0%
+but now what we're going to do
+ 
+
+ align:start position:0%
+but now what we're going to do
+is watch what that place cell location
+
+ align:start position:0%
+is watch what that place cell location
+ 
+
+ align:start position:0%
+is watch what that place cell location
+does as the rat moves around in his
+
+ align:start position:0%
+does as the rat moves around in his
+ 
+
+ align:start position:0%
+does as the rat moves around in his
+environment and makes decisions about
+
+ align:start position:0%
+environment and makes decisions about
+ 
+
+ align:start position:0%
+environment and makes decisions about
+where to go next
+
+ align:start position:0%
+where to go next
+ 
+
+ align:start position:0%
+where to go next
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+okay so what we're going to see is the
+
+ align:start position:0%
+okay so what we're going to see is the
+ 
+
+ align:start position:0%
+okay so what we're going to see is the
+rat is going to come up to an
+
+ align:start position:0%
+rat is going to come up to an
+ 
+
+ align:start position:0%
+rat is going to come up to an
+intersection of the maze i think it's
+
+ align:start position:0%
+intersection of the maze i think it's
+ 
+
+ align:start position:0%
+intersection of the maze i think it's
+that in that i think it's right here
+
+ align:start position:0%
+that in that i think it's right here
+ 
+
+ align:start position:0%
+that in that i think it's right here
+and he's going to decide am i going to
+
+ align:start position:0%
+and he's going to decide am i going to
+ 
+
+ align:start position:0%
+and he's going to decide am i going to
+go this way am i going to go that way
+
+ align:start position:0%
+go this way am i going to go that way
+ 
+
+ align:start position:0%
+go this way am i going to go that way
+and as the rat stays there deciding
+
+ align:start position:0%
+and as the rat stays there deciding
+ 
+
+ align:start position:0%
+and as the rat stays there deciding
+which way to go and the white dot stays
+
+ align:start position:0%
+which way to go and the white dot stays
+ 
+
+ align:start position:0%
+which way to go and the white dot stays
+there as he sits there thinking huh
+
+ align:start position:0%
+there as he sits there thinking huh
+ 
+
+ align:start position:0%
+there as he sits there thinking huh
+should i do this should i do that you
+
+ align:start position:0%
+should i do this should i do that you
+ 
+
+ align:start position:0%
+should i do this should i do that you
+could call it neural deliberation we
+
+ align:start position:0%
+could call it neural deliberation we
+ 
+
+ align:start position:0%
+could call it neural deliberation we
+will see what his place cell activity
+
+ align:start position:0%
+will see what his place cell activity
+ 
+
+ align:start position:0%
+will see what his place cell activity
+shows you
+
+ align:start position:0%
+shows you
+ 
+
+ align:start position:0%
+shows you
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+so here we go
+
+ align:start position:0%
+so here we go
+ 
+
+ align:start position:0%
+so here we go
+rat starts there whoops how do i play
+
+ align:start position:0%
+rat starts there whoops how do i play
+ 
+
+ align:start position:0%
+rat starts there whoops how do i play
+this here
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so rad is heading up there and so
+
+ align:start position:0%
+okay so rad is heading up there and so
+ 
+
+ align:start position:0%
+okay so rad is heading up there and so
+are his place cells he comes up to the
+
+ align:start position:0%
+are his place cells he comes up to the
+ 
+
+ align:start position:0%
+are his place cells he comes up to the
+intersection
+
+ align:start position:0%
+intersection
+ 
+
+ align:start position:0%
+intersection
+he stays in one place but look what his
+
+ align:start position:0%
+he stays in one place but look what his
+ 
+
+ align:start position:0%
+he stays in one place but look what his
+place cells are doing should i go over
+
+ align:start position:0%
+place cells are doing should i go over
+ 
+
+ align:start position:0%
+place cells are doing should i go over
+there
+
+ align:start position:0%
+there
+ 
+
+ align:start position:0%
+there
+i'm just interpreting what this means
+
+ align:start position:0%
+i'm just interpreting what this means
+ 
+
+ align:start position:0%
+i'm just interpreting what this means
+but it sure looks like neural
+
+ align:start position:0%
+but it sure looks like neural
+ 
+
+ align:start position:0%
+but it sure looks like neural
+deliberation to me
+
+ align:start position:0%
+deliberation to me
+ 
+
+ align:start position:0%
+deliberation to me
+and that's what he decided everybody get
+
+ align:start position:0%
+and that's what he decided everybody get
+ 
+
+ align:start position:0%
+and that's what he decided everybody get
+what we just saw
+
+ align:start position:0%
+what we just saw
+ 
+
+ align:start position:0%
+what we just saw
+he while he's standing there he's in one
+
+ align:start position:0%
+he while he's standing there he's in one
+ 
+
+ align:start position:0%
+he while he's standing there he's in one
+place but he's clearly deciding where to
+
+ align:start position:0%
+place but he's clearly deciding where to
+ 
+
+ align:start position:0%
+place but he's clearly deciding where to
+go next and while he's deciding those
+
+ align:start position:0%
+go next and while he's deciding those
+ 
+
+ align:start position:0%
+go next and while he's deciding those
+place cells are
+
+ align:start position:0%
+place cells are
+ 
+
+ align:start position:0%
+place cells are
+essentially apparently running
+
+ align:start position:0%
+essentially apparently running
+ 
+
+ align:start position:0%
+essentially apparently running
+simulations of where he might go next
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so we started with this big long
+
+ align:start position:0%
+okay so we started with this big long
+ 
+
+ align:start position:0%
+okay so we started with this big long
+list of things you need to know to
+
+ align:start position:0%
+list of things you need to know to
+ 
+
+ align:start position:0%
+list of things you need to know to
+navigate around in the world and the
+
+ align:start position:0%
+navigate around in the world and the
+ 
+
+ align:start position:0%
+navigate around in the world and the
+neural basis of all this is really not
+
+ align:start position:0%
+neural basis of all this is really not
+ 
+
+ align:start position:0%
+neural basis of all this is really not
+understood yet but i've shown you what i
+
+ align:start position:0%
+understood yet but i've shown you what i
+ 
+
+ align:start position:0%
+understood yet but i've shown you what i
+think are a bunch of
+
+ align:start position:0%
+think are a bunch of
+ 
+
+ align:start position:0%
+think are a bunch of
+tantalizing snippets
+
+ align:start position:0%
+tantalizing snippets
+ 
+
+ align:start position:0%
+tantalizing snippets
+um which lead to the idea that our best
+
+ align:start position:0%
+um which lead to the idea that our best
+ 
+
+ align:start position:0%
+um which lead to the idea that our best
+current guess about the kind of neural
+
+ align:start position:0%
+current guess about the kind of neural
+ 
+
+ align:start position:0%
+current guess about the kind of neural
+locus of these things which is very far
+
+ align:start position:0%
+locus of these things which is very far
+ 
+
+ align:start position:0%
+locus of these things which is very far
+from the actual understanding of how
+
+ align:start position:0%
+from the actual understanding of how
+ 
+
+ align:start position:0%
+from the actual understanding of how
+they work
+
+ align:start position:0%
+they work
+ 
+
+ align:start position:0%
+they work
+is that the perception of the layout of
+
+ align:start position:0%
+is that the perception of the layout of
+ 
+
+ align:start position:0%
+is that the perception of the layout of
+space around us the ppa and the
+
+ align:start position:0%
+space around us the ppa and the
+ 
+
+ align:start position:0%
+space around us the ppa and the
+occipital place area are very involved
+
+ align:start position:0%
+occipital place area are very involved
+ 
+
+ align:start position:0%
+occipital place area are very involved
+in that
+
+ align:start position:0%
+in that
+ 
+
+ align:start position:0%
+in that
+also
+
+ align:start position:0%
+also
+ 
+
+ align:start position:0%
+also
+in saying for an unfamiliar place what
+
+ align:start position:0%
+in saying for an unfamiliar place what
+ 
+
+ align:start position:0%
+in saying for an unfamiliar place what
+kind of place is this i didn't show you
+
+ align:start position:0%
+kind of place is this i didn't show you
+ 
+
+ align:start position:0%
+kind of place is this i didn't show you
+those data but you can in fact decode
+
+ align:start position:0%
+those data but you can in fact decode
+ 
+
+ align:start position:0%
+those data but you can in fact decode
+whether you're looking at a scene or a
+
+ align:start position:0%
+whether you're looking at a scene or a
+ 
+
+ align:start position:0%
+whether you're looking at a scene or a
+beach by looking at the pattern of
+
+ align:start position:0%
+beach by looking at the pattern of
+ 
+
+ align:start position:0%
+beach by looking at the pattern of
+response in the ppa
+
+ align:start position:0%
+response in the ppa
+ 
+
+ align:start position:0%
+response in the ppa
+we talked about the idea that the
+
+ align:start position:0%
+we talked about the idea that the
+ 
+
+ align:start position:0%
+we talked about the idea that the
+retrosplenial cortex may be involved in
+
+ align:start position:0%
+retrosplenial cortex may be involved in
+ 
+
+ align:start position:0%
+retrosplenial cortex may be involved in
+recognizing familiar locations that's a
+
+ align:start position:0%
+recognizing familiar locations that's a
+ 
+
+ align:start position:0%
+recognizing familiar locations that's a
+bit of a question mark
+
+ align:start position:0%
+bit of a question mark
+ 
+
+ align:start position:0%
+bit of a question mark
+that the idea that your map of the world
+
+ align:start position:0%
+that the idea that your map of the world
+ 
+
+ align:start position:0%
+that the idea that your map of the world
+is represented in your hippocampus by
+
+ align:start position:0%
+is represented in your hippocampus by
+ 
+
+ align:start position:0%
+is represented in your hippocampus by
+way of place cells which also say where
+
+ align:start position:0%
+way of place cells which also say where
+ 
+
+ align:start position:0%
+way of place cells which also say where
+you are in that world
+
+ align:start position:0%
+you are in that world
+ 
+
+ align:start position:0%
+you are in that world
+that you're heading direction in humans
+
+ align:start position:0%
+that you're heading direction in humans
+ 
+
+ align:start position:0%
+that you're heading direction in humans
+i didn't give you all the evidence for
+
+ align:start position:0%
+i didn't give you all the evidence for
+ 
+
+ align:start position:0%
+i didn't give you all the evidence for
+this but in humans there's quite a bit
+
+ align:start position:0%
+this but in humans there's quite a bit
+ 
+
+ align:start position:0%
+this but in humans there's quite a bit
+of evidence that retrosplenial cortex is
+
+ align:start position:0%
+of evidence that retrosplenial cortex is
+ 
+
+ align:start position:0%
+of evidence that retrosplenial cortex is
+very involved in heading direction i
+
+ align:start position:0%
+very involved in heading direction i
+ 
+
+ align:start position:0%
+very involved in heading direction i
+guess i did give you evidence patients
+
+ align:start position:0%
+guess i did give you evidence patients
+ 
+
+ align:start position:0%
+guess i did give you evidence patients
+who have had damage there and can
+
+ align:start position:0%
+who have had damage there and can
+ 
+
+ align:start position:0%
+who have had damage there and can
+recognize places but not know how
+
+ align:start position:0%
+recognize places but not know how
+ 
+
+ align:start position:0%
+recognize places but not know how
+they're oriented there
+
+ align:start position:0%
+they're oriented there
+ 
+
+ align:start position:0%
+they're oriented there
+that planning routes around boundaries
+
+ align:start position:0%
+that planning routes around boundaries
+ 
+
+ align:start position:0%
+that planning routes around boundaries
+in your environment uh involves the
+
+ align:start position:0%
+in your environment uh involves the
+ 
+
+ align:start position:0%
+in your environment uh involves the
+occipital place area and the peripheral
+
+ align:start position:0%
+occipital place area and the peripheral
+ 
+
+ align:start position:0%
+occipital place area and the peripheral
+campbell place area
+
+ align:start position:0%
+campbell place area
+ 
+
+ align:start position:0%
+campbell place area
+and that this business of reorientation
+
+ align:start position:0%
+and that this business of reorientation
+ 
+
+ align:start position:0%
+and that this business of reorientation
+seems to particularly involve
+
+ align:start position:0%
+seems to particularly involve
+ 
+
+ align:start position:0%
+seems to particularly involve
+heading direction cells in humans most
+
+ align:start position:0%
+heading direction cells in humans most
+ 
+
+ align:start position:0%
+heading direction cells in humans most
+likely in retrospective cortex
+
+ align:start position:0%
+likely in retrospective cortex
+ 
+
+ align:start position:0%
+likely in retrospective cortex
+so you don't need to memorize all that i
+
+ align:start position:0%
+so you don't need to memorize all that i
+ 
+
+ align:start position:0%
+so you don't need to memorize all that i
+mean you know i don't care that much
+
+ align:start position:0%
+mean you know i don't care that much
+ 
+
+ align:start position:0%
+mean you know i don't care that much
+about the locations what i want you guys
+
+ align:start position:0%
+about the locations what i want you guys
+ 
+
+ align:start position:0%
+about the locations what i want you guys
+to understand is what are these problems
+
+ align:start position:0%
+to understand is what are these problems
+ 
+
+ align:start position:0%
+to understand is what are these problems
+that are involved in navigation and what
+
+ align:start position:0%
+that are involved in navigation and what
+ 
+
+ align:start position:0%
+that are involved in navigation and what
+kinds of things can we learn with
+
+ align:start position:0%
+kinds of things can we learn with
+ 
+
+ align:start position:0%
+kinds of things can we learn with
+different kinds of behavioral and neural
+
+ align:start position:0%
+different kinds of behavioral and neural
+ 
+
+ align:start position:0%
+different kinds of behavioral and neural
+measures and you may have noticed in the
+
+ align:start position:0%
+measures and you may have noticed in the
+ 
+
+ align:start position:0%
+measures and you may have noticed in the
+last couple lectures that i presented
+
+ align:start position:0%
+last couple lectures that i presented
+ 
+
+ align:start position:0%
+last couple lectures that i presented
+lots of behavioral data because actually
+
+ align:start position:0%
+lots of behavioral data because actually
+ 
+
+ align:start position:0%
+lots of behavioral data because actually
+so far the richest insights about how
+
+ align:start position:0%
+so far the richest insights about how
+ 
+
+ align:start position:0%
+so far the richest insights about how
+the system actually works still come or
+
+ align:start position:0%
+the system actually works still come or
+ 
+
+ align:start position:0%
+the system actually works still come or
+many of the rich ones come from
+
+ align:start position:0%
+many of the rich ones come from
+ 
+
+ align:start position:0%
+many of the rich ones come from
+behavioral data okay quiz is in two
+
+ align:start position:0%
+behavioral data okay quiz is in two
+ 
+
+ align:start position:0%
+behavioral data okay quiz is in two
+minutes does anybody want to ask me a
+
+ align:start position:0%
+minutes does anybody want to ask me a
+ 
+
+ align:start position:0%
+minutes does anybody want to ask me a
+question before the quiz
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah so you have to do lots of controls
+
+ align:start position:0%
+yeah so you have to do lots of controls
+ 
+
+ align:start position:0%
+yeah so you have to do lots of controls
+to to work that out and i didn't show
+
+ align:start position:0%
+to to work that out and i didn't show
+ 
+
+ align:start position:0%
+to to work that out and i didn't show
+you any of the you know details of the
+
+ align:start position:0%
+you any of the you know details of the
+ 
+
+ align:start position:0%
+you any of the you know details of the
+data uh but yeah these guys are pretty
+
+ align:start position:0%
+data uh but yeah these guys are pretty
+ 
+
+ align:start position:0%
+data uh but yeah these guys are pretty
+careful and there are all these things
+
+ align:start position:0%
+careful and there are all these things
+ 
+
+ align:start position:0%
+careful and there are all these things
+there are many different ways in which
+
+ align:start position:0%
+there are many different ways in which
+ 
+
+ align:start position:0%
+there are many different ways in which
+people are watching
+
+ align:start position:0%
+people are watching
+ 
+
+ align:start position:0%
+people are watching
+neuro
+
+ align:start position:0%
+neuro
+ 
+
+ align:start position:0%
+neuro
+watching hippocampal neurons and
+
+ align:start position:0%
+watching hippocampal neurons and
+ 
+
+ align:start position:0%
+watching hippocampal neurons and
+decoding trajectories from hippocampal
+
+ align:start position:0%
+decoding trajectories from hippocampal
+ 
+
+ align:start position:0%
+decoding trajectories from hippocampal
+neurons
+
+ align:start position:0%
+neurons
+ 
+
+ align:start position:0%
+neurons
+you may have heard about replay which is
+
+ align:start position:0%
+you may have heard about replay which is
+ 
+
+ align:start position:0%
+you may have heard about replay which is
+like a big thing in this department
+
+ align:start position:0%
+like a big thing in this department
+ 
+
+ align:start position:0%
+like a big thing in this department
+tanagawa and wilson labs study this
+
+ align:start position:0%
+tanagawa and wilson labs study this
+ 
+
+ align:start position:0%
+tanagawa and wilson labs study this
+where you have a rodent moving around in
+
+ align:start position:0%
+where you have a rodent moving around in
+ 
+
+ align:start position:0%
+where you have a rodent moving around in
+one trajectory
+
+ align:start position:0%
+one trajectory
+ 
+
+ align:start position:0%
+one trajectory
+during the day and then you record from
+
+ align:start position:0%
+during the day and then you record from
+ 
+
+ align:start position:0%
+during the day and then you record from
+those neurons at night and you see
+
+ align:start position:0%
+those neurons at night and you see
+ 
+
+ align:start position:0%
+those neurons at night and you see
+replay of the trajectories that the
+
+ align:start position:0%
+replay of the trajectories that the
+ 
+
+ align:start position:0%
+replay of the trajectories that the
+rodent went through in the previous day
+
+ align:start position:0%
+rodent went through in the previous day
+ 
+
+ align:start position:0%
+rodent went through in the previous day
+and so there you have to be really
+
+ align:start position:0%
+and so there you have to be really
+ 
+
+ align:start position:0%
+and so there you have to be really
+careful to say okay there's a lot of
+
+ align:start position:0%
+careful to say okay there's a lot of
+ 
+
+ align:start position:0%
+careful to say okay there's a lot of
+data and a lot of noise and is this
+
+ align:start position:0%
+data and a lot of noise and is this
+ 
+
+ align:start position:0%
+data and a lot of noise and is this
+really more than the noise and it is but
+
+ align:start position:0%
+really more than the noise and it is but
+ 
+
+ align:start position:0%
+really more than the noise and it is but
+it takes a lot of statistical work to
+
+ align:start position:0%
+it takes a lot of statistical work to
+ 
+
+ align:start position:0%
+it takes a lot of statistical work to
+show that
+
+ align:start position:0%
+show that
+ 
+
+ align:start position:0%
+show that
+yeah
+
+ align:start position:0%
+yeah
+ 
+
+ align:start position:0%
+yeah
+scenario um say like a place that i know
+
+ align:start position:0%
+scenario um say like a place that i know
+ 
+
+ align:start position:0%
+scenario um say like a place that i know
+yeah uh with the nuance
+
+ align:start position:0%
+yeah uh with the nuance
+ 
+
+ align:start position:0%
+yeah uh with the nuance
+um the same neurons inspire if i go back
+
+ align:start position:0%
+um the same neurons inspire if i go back
+ 
+
+ align:start position:0%
+um the same neurons inspire if i go back
+to that environment i've assumed for
+
+ align:start position:0%
+to that environment i've assumed for
+ 
+
+ align:start position:0%
+to that environment i've assumed for
+like the truth yeah yeah
+
+ align:start position:0%
+like the truth yeah yeah
+ 
+
+ align:start position:0%
+like the truth yeah yeah
+but
+
+ align:start position:0%
+but
+ 
+
+ align:start position:0%
+but
+but then you can't really have that or
+
+ align:start position:0%
+but then you can't really have that or
+ 
+
+ align:start position:0%
+but then you can't really have that or
+like you can't be
+
+ align:start position:0%
+like you can't be
+ 
+
+ align:start position:0%
+like you can't be
+it's a good question how do we have
+
+ align:start position:0%
+it's a good question how do we have
+ 
+
+ align:start position:0%
+it's a good question how do we have
+enough neurons yeah especially for some
+
+ align:start position:0%
+enough neurons yeah especially for some
+ 
+
+ align:start position:0%
+enough neurons yeah especially for some
+place we go every six months are they
+
+ align:start position:0%
+place we go every six months are they
+ 
+
+ align:start position:0%
+place we go every six months are they
+sitting around waiting for us to go back
+
+ align:start position:0%
+sitting around waiting for us to go back
+ 
+
+ align:start position:0%
+sitting around waiting for us to go back
+there no there's some recycling of
+
+ align:start position:0%
+there no there's some recycling of
+ 
+
+ align:start position:0%
+there no there's some recycling of
+neurons across very different locations
+
+ align:start position:0%
+neurons across very different locations
+ 
+
+ align:start position:0%
+neurons across very different locations
+so within that location they'll be
+
+ align:start position:0%
+so within that location they'll be
+ 
+
+ align:start position:0%
+so within that location they'll be
+consistent but yes you do recycle so the
+
+ align:start position:0%
+consistent but yes you do recycle so the
+ 
+
+ align:start position:0%
+consistent but yes you do recycle so the
+same neuron will have one place cell in
+
+ align:start position:0%
+same neuron will have one place cell in
+ 
+
+ align:start position:0%
+same neuron will have one place cell in
+this environment and it may or may not
+
+ align:start position:0%
+this environment and it may or may not
+ 
+
+ align:start position:0%
+this environment and it may or may not
+have a place cell in another environment
+
+ align:start position:0%
+have a place cell in another environment
+ 
+
+ align:start position:0%
+have a place cell in another environment
+that's a good question
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+you
\ No newline at end of file
diff --git a/pqkYqU11ETA.txt b/pqkYqU11ETA.txt
new file mode 100644
index 0000000000000000000000000000000000000000..da511e0b096a5d039c2fca72fd3a31eca84cecbe
--- /dev/null
+++ b/pqkYqU11ETA.txt
@@ -0,0 +1,7211 @@
+align:start position:0%
+ 
+The following content is provided under
+
+ align:start position:0%
+The following content is provided under
+ 
+
+ align:start position:0%
+The following content is provided under
+a Creative Common License. Your support
+
+ align:start position:0%
+a Creative Common License. Your support
+ 
+
+ align:start position:0%
+a Creative Common License. Your support
+will help MIT Open Courseware continue
+
+ align:start position:0%
+will help MIT Open Courseware continue
+ 
+
+ align:start position:0%
+will help MIT Open Courseware continue
+to offer high-quality educational
+
+ align:start position:0%
+to offer high-quality educational
+ 
+
+ align:start position:0%
+to offer high-quality educational
+resources for free. To make a donation
+
+ align:start position:0%
+resources for free. To make a donation
+ 
+
+ align:start position:0%
+resources for free. To make a donation
+or view additional materials from
+
+ align:start position:0%
+or view additional materials from
+ 
+
+ align:start position:0%
+or view additional materials from
+hundreds of MIT courses, visit MIT Open
+
+ align:start position:0%
+hundreds of MIT courses, visit MIT Open
+ 
+
+ align:start position:0%
+hundreds of MIT courses, visit MIT Open
+Courseware at
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+ocw.mmit.edu. So today, what we've been
+
+ align:start position:0%
+ocw.mmit.edu. So today, what we've been
+ 
+
+ align:start position:0%
+ocw.mmit.edu. So today, what we've been
+doing, we've been looking at how there's
+
+ align:start position:0%
+doing, we've been looking at how there's
+ 
+
+ align:start position:0%
+doing, we've been looking at how there's
+a lot of different representations for
+
+ align:start position:0%
+a lot of different representations for
+ 
+
+ align:start position:0%
+a lot of different representations for
+CT systems. They look almost the same as
+
+ align:start position:0%
+CT systems. They look almost the same as
+ 
+
+ align:start position:0%
+CT systems. They look almost the same as
+a lot of representations for DT systems.
+
+ align:start position:0%
+a lot of representations for DT systems.
+ 
+
+ align:start position:0%
+a lot of representations for DT systems.
+And today I want to go one more step and
+
+ align:start position:0%
+And today I want to go one more step and
+ 
+
+ align:start position:0%
+And today I want to go one more step and
+show how there's actually a bunch of
+
+ align:start position:0%
+show how there's actually a bunch of
+ 
+
+ align:start position:0%
+show how there's actually a bunch of
+relationships between
+
+ align:start position:0%
+relationships between
+ 
+
+ align:start position:0%
+relationships between
+them. That's when things become very
+
+ align:start position:0%
+them. That's when things become very
+ 
+
+ align:start position:0%
+them. That's when things become very
+powerful. And so I want to do that by
+
+ align:start position:0%
+powerful. And so I want to do that by
+ 
+
+ align:start position:0%
+powerful. And so I want to do that by
+thinking about a very simple
+
+ align:start position:0%
+thinking about a very simple
+ 
+
+ align:start position:0%
+thinking about a very simple
+example. Thinking about a CT system and
+
+ align:start position:0%
+example. Thinking about a CT system and
+ 
+
+ align:start position:0%
+example. Thinking about a CT system and
+how you would convert that CT
+
+ align:start position:0%
+how you would convert that CT
+ 
+
+ align:start position:0%
+how you would convert that CT
+system into a DT representation.
+
+ align:start position:0%
+system into a DT representation.
+ 
+
+ align:start position:0%
+system into a DT representation.
+This is a problem we've worked on
+
+ align:start position:0%
+This is a problem we've worked on
+ 
+
+ align:start position:0%
+This is a problem we've worked on
+before, the leaky tank system. We've
+
+ align:start position:0%
+before, the leaky tank system. We've
+ 
+
+ align:start position:0%
+before, the leaky tank system. We've
+already seen a gazillion representations
+
+ align:start position:0%
+already seen a gazillion representations
+ 
+
+ align:start position:0%
+already seen a gazillion representations
+for
+
+ align:start position:0%
+for
+ 
+
+ align:start position:0%
+for
+it. We can think about the leaky ta tank
+
+ align:start position:0%
+it. We can think about the leaky ta tank
+ 
+
+ align:start position:0%
+it. We can think about the leaky ta tank
+system as a differential equation. We
+
+ align:start position:0%
+system as a differential equation. We
+ 
+
+ align:start position:0%
+system as a differential equation. We
+derived that in lecture
+
+ align:start position:0%
+derived that in lecture
+ 
+
+ align:start position:0%
+derived that in lecture
+one. We can think of it as a block
+
+ align:start position:0%
+one. We can think of it as a block
+ 
+
+ align:start position:0%
+one. We can think of it as a block
+diagram lecture one. We can think about
+
+ align:start position:0%
+diagram lecture one. We can think about
+ 
+
+ align:start position:0%
+diagram lecture one. We can think about
+it as a functional that was about two
+
+ align:start position:0%
+it as a functional that was about two
+ 
+
+ align:start position:0%
+it as a functional that was about two
+lectures ago as a system function that
+
+ align:start position:0%
+lectures ago as a system function that
+ 
+
+ align:start position:0%
+lectures ago as a system function that
+was lelass transforms that was about a
+
+ align:start position:0%
+was lelass transforms that was about a
+ 
+
+ align:start position:0%
+was lelass transforms that was about a
+week ago. We can think about an impulse
+
+ align:start position:0%
+week ago. We can think about an impulse
+ 
+
+ align:start position:0%
+week ago. We can think about an impulse
+response because the fundamental signal
+
+ align:start position:0%
+response because the fundamental signal
+ 
+
+ align:start position:0%
+response because the fundamental signal
+in CT, the thing that plays the same
+
+ align:start position:0%
+in CT, the thing that plays the same
+ 
+
+ align:start position:0%
+in CT, the thing that plays the same
+role as the unit sample in DT is the
+
+ align:start position:0%
+role as the unit sample in DT is the
+ 
+
+ align:start position:0%
+role as the unit sample in DT is the
+unit impulse. So we can think about the
+
+ align:start position:0%
+unit impulse. So we can think about the
+ 
+
+ align:start position:0%
+unit impulse. So we can think about the
+impulse response and there's a variety
+
+ align:start position:0%
+impulse response and there's a variety
+ 
+
+ align:start position:0%
+impulse response and there's a variety
+of connections between all of those.
+
+ align:start position:0%
+of connections between all of those.
+ 
+
+ align:start position:0%
+of connections between all of those.
+What I want to do today is compare the
+
+ align:start position:0%
+What I want to do today is compare the
+ 
+
+ align:start position:0%
+What I want to do today is compare the
+step response of the leaky tank system
+
+ align:start position:0%
+step response of the leaky tank system
+ 
+
+ align:start position:0%
+step response of the leaky tank system
+to the step
+
+ align:start position:0%
+to the step
+ 
+
+ align:start position:0%
+to the step
+response of a DT approximation to the
+
+ align:start position:0%
+response of a DT approximation to the
+ 
+
+ align:start position:0%
+response of a DT approximation to the
+leaky tank system.
+
+ align:start position:0%
+leaky tank system.
+ 
+
+ align:start position:0%
+leaky tank system.
+To get started then I want to figure out
+
+ align:start position:0%
+To get started then I want to figure out
+ 
+
+ align:start position:0%
+To get started then I want to figure out
+the step response of the leaky tank
+
+ align:start position:0%
+the step response of the leaky tank
+ 
+
+ align:start position:0%
+the step response of the leaky tank
+system for you. You should think about
+
+ align:start position:0%
+system for you. You should think about
+ 
+
+ align:start position:0%
+system for you. You should think about
+this as practice for the exam. You
+
+ align:start position:0%
+this as practice for the exam. You
+ 
+
+ align:start position:0%
+this as practice for the exam. You
+should be able to do this in 30
+
+ align:start position:0%
+should be able to do this in 30
+ 
+
+ align:start position:0%
+should be able to do this in 30
+seconds. So start compare your answers
+
+ align:start position:0%
+seconds. So start compare your answers
+ 
+
+ align:start position:0%
+seconds. So start compare your answers
+to your neighbor. Figure out uh what is
+
+ align:start position:0%
+to your neighbor. Figure out uh what is
+ 
+
+ align:start position:0%
+to your neighbor. Figure out uh what is
+the step response for the leaky tank
+
+ align:start position:0%
+the step response for the leaky tank
+ 
+
+ align:start position:0%
+the step response for the leaky tank
+system.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+No, no.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay, this question is too simple, so
+
+ align:start position:0%
+Okay, this question is too simple, so
+ 
+
+ align:start position:0%
+Okay, this question is too simple, so
+we're going to blast ahead. What's the
+
+ align:start position:0%
+we're going to blast ahead. What's the
+ 
+
+ align:start position:0%
+we're going to blast ahead. What's the
+answer? What's the step response for the
+
+ align:start position:0%
+answer? What's the step response for the
+ 
+
+ align:start position:0%
+answer? What's the step response for the
+leaky tank system? Everybody raise your
+
+ align:start position:0%
+leaky tank system? Everybody raise your
+ 
+
+ align:start position:0%
+leaky tank system? Everybody raise your
+hand. Let me see how many numbers. Okay,
+
+ align:start position:0%
+hand. Let me see how many numbers. Okay,
+ 
+
+ align:start position:0%
+hand. Let me see how many numbers. Okay,
+it's not quite as high a fraction as I
+
+ align:start position:0%
+it's not quite as high a fraction as I
+ 
+
+ align:start position:0%
+it's not quite as high a fraction as I
+would have liked. Uh, take another 15
+
+ align:start position:0%
+would have liked. Uh, take another 15
+ 
+
+ align:start position:0%
+would have liked. Uh, take another 15
+seconds or better yet, talk to your
+
+ align:start position:0%
+seconds or better yet, talk to your
+ 
+
+ align:start position:0%
+seconds or better yet, talk to your
+neighbor. Explain your answer to your
+
+ align:start position:0%
+neighbor. Explain your answer to your
+ 
+
+ align:start position:0%
+neighbor. Explain your answer to your
+neighbor and let your neighbor tell you
+
+ align:start position:0%
+neighbor and let your neighbor tell you
+ 
+
+ align:start position:0%
+neighbor and let your neighbor tell you
+why you're wrong.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay,
+
+ align:start position:0%
+Okay,
+ 
+
+ align:start position:0%
+Okay,
+revote. So, what's the step response of
+
+ align:start position:0%
+revote. So, what's the step response of
+ 
+
+ align:start position:0%
+revote. So, what's the step response of
+the leaky tank tank system?
+
+ align:start position:0%
+the leaky tank tank system?
+ 
+
+ align:start position:0%
+the leaky tank tank system?
+Better, better, better, better, better,
+
+ align:start position:0%
+Better, better, better, better, better,
+ 
+
+ align:start position:0%
+Better, better, better, better, better,
+better, better. Okay, almost 100%. Not
+
+ align:start position:0%
+better, better. Okay, almost 100%. Not
+ 
+
+ align:start position:0%
+better, better. Okay, almost 100%. Not
+quite. Another question. How many ways
+
+ align:start position:0%
+quite. Another question. How many ways
+ 
+
+ align:start position:0%
+quite. Another question. How many ways
+can you find the step response of the
+
+ align:start position:0%
+can you find the step response of the
+ 
+
+ align:start position:0%
+can you find the step response of the
+leaky tank system? One represents more
+
+ align:start position:0%
+leaky tank system? One represents more
+ 
+
+ align:start position:0%
+leaky tank system? One represents more
+than one. I'm not going to have a
+
+ align:start position:0%
+than one. I'm not going to have a
+ 
+
+ align:start position:0%
+than one. I'm not going to have a
+representation for zero, right? More
+
+ align:start position:0%
+representation for zero, right? More
+ 
+
+ align:start position:0%
+representation for zero, right? More
+than one, more than two, more than
+
+ align:start position:0%
+than one, more than two, more than
+ 
+
+ align:start position:0%
+than one, more than two, more than
+three, more than four, more than five.
+
+ align:start position:0%
+three, more than four, more than five.
+ 
+
+ align:start position:0%
+three, more than four, more than five.
+How many ways can you find
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that? Don't just stare at me with blank
+
+ align:start position:0%
+that? Don't just stare at me with blank
+ 
+
+ align:start position:0%
+that? Don't just stare at me with blank
+looks.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay. What's a good way to find the step
+
+ align:start position:0%
+Okay. What's a good way to find the step
+ 
+
+ align:start position:0%
+Okay. What's a good way to find the step
+response of the
+
+ align:start position:0%
+response of the
+ 
+
+ align:start position:0%
+response of the
+system? You can shout. That way, I won't
+
+ align:start position:0%
+system? You can shout. That way, I won't
+ 
+
+ align:start position:0%
+system? You can shout. That way, I won't
+be able to identify where you're coming
+
+ align:start position:0%
+be able to identify where you're coming
+ 
+
+ align:start position:0%
+be able to identify where you're coming
+from, and I won't be able to point to
+
+ align:start position:0%
+from, and I won't be able to point to
+ 
+
+ align:start position:0%
+from, and I won't be able to point to
+you. But you have to be quick because if
+
+ align:start position:0%
+you. But you have to be quick because if
+ 
+
+ align:start position:0%
+you. But you have to be quick because if
+I see your mouth move, then I'll know
+
+ align:start position:0%
+I see your mouth move, then I'll know
+ 
+
+ align:start position:0%
+I see your mouth move, then I'll know
+which one you are. So, when I look this
+
+ align:start position:0%
+which one you are. So, when I look this
+ 
+
+ align:start position:0%
+which one you are. So, when I look this
+way, you shout over here, right? There's
+
+ align:start position:0%
+way, you shout over here, right? There's
+ 
+
+ align:start position:0%
+way, you shout over here, right? There's
+simple ways to do this, right?
+
+ align:start position:0%
+simple ways to do this, right?
+ 
+
+ align:start position:0%
+simple ways to do this, right?
+What's a good way to find the step
+
+ align:start position:0%
+What's a good way to find the step
+ 
+
+ align:start position:0%
+What's a good way to find the step
+response of of the leaky tank system?
+
+ align:start position:0%
+response of of the leaky tank system?
+ 
+
+ align:start position:0%
+response of of the leaky tank system?
+You have the transfer function
+
+ align:start position:0%
+You have the transfer function
+ 
+
+ align:start position:0%
+You have the transfer function
+multiplied with 1x then we have the
+
+ align:start position:0%
+multiplied with 1x then we have the
+ 
+
+ align:start position:0%
+multiplied with 1x then we have the
+trans that's a relatively advanced way
+
+ align:start position:0%
+trans that's a relatively advanced way
+ 
+
+ align:start position:0%
+trans that's a relatively advanced way
+and in completely correct. Could
+
+ align:start position:0%
+and in completely correct. Could
+ 
+
+ align:start position:0%
+and in completely correct. Could
+somebody tell me an even simpler way?
+
+ align:start position:0%
+somebody tell me an even simpler way?
+ 
+
+ align:start position:0%
+somebody tell me an even simpler way?
+Yes. What's the behavior as t goes to
+
+ align:start position:0%
+Yes. What's the behavior as t goes to
+ 
+
+ align:start position:0%
+Yes. What's the behavior as t goes to
+infinity? Okay. What is it? If I'm if I
+
+ align:start position:0%
+infinity? Okay. What is it? If I'm if I
+ 
+
+ align:start position:0%
+infinity? Okay. What is it? If I'm if I
+let's do something easier. What's the
+
+ align:start position:0%
+let's do something easier. What's the
+ 
+
+ align:start position:0%
+let's do something easier. What's the
+input?
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Well, it's a unit step, right? So the
+
+ align:start position:0%
+Well, it's a unit step, right? So the
+ 
+
+ align:start position:0%
+Well, it's a unit step, right? So the
+input is some unit step thing, right? So
+
+ align:start position:0%
+input is some unit step thing, right? So
+ 
+
+ align:start position:0%
+input is some unit step thing, right? So
+my input, if I think about some input r
+
+ align:start position:0%
+my input, if I think about some input r
+ 
+
+ align:start position:0%
+my input, if I think about some input r
+of t, the input is something that looks
+
+ align:start position:0%
+of t, the input is something that looks
+ 
+
+ align:start position:0%
+of t, the input is something that looks
+like that, right? So if I look at like
+
+ align:start position:0%
+like that, right? So if I look at like
+ 
+
+ align:start position:0%
+like that, right? So if I look at like
+you suggested, if I look at what's going
+
+ align:start position:0%
+you suggested, if I look at what's going
+ 
+
+ align:start position:0%
+you suggested, if I look at what's going
+to happen for t goes to infinity, what's
+
+ align:start position:0%
+to happen for t goes to infinity, what's
+ 
+
+ align:start position:0%
+to happen for t goes to infinity, what's
+going to happen? Eventually, the rate at
+
+ align:start position:0%
+going to happen? Eventually, the rate at
+ 
+
+ align:start position:0%
+going to happen? Eventually, the rate at
+which water is going out is going to be
+
+ align:start position:0%
+which water is going out is going to be
+ 
+
+ align:start position:0%
+which water is going out is going to be
+the same as the rate that it's going in.
+
+ align:start position:0%
+the same as the rate that it's going in.
+ 
+
+ align:start position:0%
+the same as the rate that it's going in.
+So if
+
+ align:start position:0%
+So if
+ 
+
+ align:start position:0%
+So if
+so based on that, do I like this one,
+
+ align:start position:0%
+so based on that, do I like this one,
+ 
+
+ align:start position:0%
+so based on that, do I like this one,
+this one, this one, this one, or that
+
+ align:start position:0%
+this one, this one, this one, or that
+ 
+
+ align:start position:0%
+this one, this one, this one, or that
+one?
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Knocks out one and three because we're
+
+ align:start position:0%
+Knocks out one and three because we're
+ 
+
+ align:start position:0%
+Knocks out one and three because we're
+not expecting it go to zero because the
+
+ align:start position:0%
+not expecting it go to zero because the
+ 
+
+ align:start position:0%
+not expecting it go to zero because the
+input didn't go to zero. Good. Okay. So
+
+ align:start position:0%
+input didn't go to zero. Good. Okay. So
+ 
+
+ align:start position:0%
+input didn't go to zero. Good. Okay. So
+it's maybe this or this or
+
+ align:start position:0%
+it's maybe this or this or
+ 
+
+ align:start position:0%
+it's maybe this or this or
+that. What's a good
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+method? What's a good method? Yes. So
+
+ align:start position:0%
+method? What's a good method? Yes. So
+ 
+
+ align:start position:0%
+method? What's a good method? Yes. So
+confused me is that the original problem
+
+ align:start position:0%
+confused me is that the original problem
+ 
+
+ align:start position:0%
+confused me is that the original problem
+on the on the problem set we had it was
+
+ align:start position:0%
+on the on the problem set we had it was
+ 
+
+ align:start position:0%
+on the on the problem set we had it was
+a second order system but like this one
+
+ align:start position:0%
+a second order system but like this one
+ 
+
+ align:start position:0%
+a second order system but like this one
+was first order. This is first order.
+
+ align:start position:0%
+was first order. This is first order.
+ 
+
+ align:start position:0%
+was first order. This is first order.
+Yeah. So then you know that it's going
+
+ align:start position:0%
+Yeah. So then you know that it's going
+ 
+
+ align:start position:0%
+Yeah. So then you know that it's going
+to be it's going to look like something
+
+ align:start position:0%
+to be it's going to look like something
+ 
+
+ align:start position:0%
+to be it's going to look like something
+that's first order. Still looks like
+
+ align:start position:0%
+that's first order. Still looks like
+ 
+
+ align:start position:0%
+that's first order. Still looks like
+something that's first order. That's
+
+ align:start position:0%
+something that's first order. That's
+ 
+
+ align:start position:0%
+something that's first order. That's
+good.
+
+ align:start position:0%
+good.
+ 
+
+ align:start position:0%
+good.
+I asked the question here and I flicked
+
+ align:start position:0%
+I asked the question here and I flicked
+ 
+
+ align:start position:0%
+I asked the question here and I flicked
+back here. That was a clue.
+
+ align:start position:0%
+back here. That was a clue.
+ 
+
+ align:start position:0%
+back here. That was a clue.
+How many ways can you think of to do
+
+ align:start position:0%
+How many ways can you think of to do
+ 
+
+ align:start position:0%
+How many ways can you think of to do
+this problem?
+
+ align:start position:0%
+this problem?
+ 
+
+ align:start position:0%
+this problem?
+Five ways.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay, you could think about solving it
+
+ align:start position:0%
+Okay, you could think about solving it
+ 
+
+ align:start position:0%
+Okay, you could think about solving it
+by looking at the differential equation.
+
+ align:start position:0%
+by looking at the differential equation.
+ 
+
+ align:start position:0%
+by looking at the differential equation.
+How how many of you could do
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that? Okay, how many of you took 1803?
+
+ align:start position:0%
+that? Okay, how many of you took 1803?
+ 
+
+ align:start position:0%
+that? Okay, how many of you took 1803?
+Ah, good. Good. So, all of you could do
+
+ align:start position:0%
+Ah, good. Good. So, all of you could do
+ 
+
+ align:start position:0%
+Ah, good. Good. So, all of you could do
+it by doing the lower lefthand corner,
+
+ align:start position:0%
+it by doing the lower lefthand corner,
+ 
+
+ align:start position:0%
+it by doing the lower lefthand corner,
+right? Okay, you could all do it that
+
+ align:start position:0%
+right? Okay, you could all do it that
+ 
+
+ align:start position:0%
+right? Okay, you could all do it that
+way. Uh, you could all do it with block
+
+ align:start position:0%
+way. Uh, you could all do it with block
+ 
+
+ align:start position:0%
+way. Uh, you could all do it with block
+diagrams, right? I we went around we
+
+ align:start position:0%
+diagrams, right? I we went around we
+ 
+
+ align:start position:0%
+diagrams, right? I we went around we
+thought about how you put a signal into
+
+ align:start position:0%
+thought about how you put a signal into
+ 
+
+ align:start position:0%
+thought about how you put a signal into
+a block diagram and you can chase it
+
+ align:start position:0%
+a block diagram and you can chase it
+ 
+
+ align:start position:0%
+a block diagram and you can chase it
+around the 10, right? You could do it
+
+ align:start position:0%
+around the 10, right? You could do it
+ 
+
+ align:start position:0%
+around the 10, right? You could do it
+that way. You So there's at least five
+
+ align:start position:0%
+that way. You So there's at least five
+ 
+
+ align:start position:0%
+that way. You So there's at least five
+ways. Just as rehearsal, I'm showing two
+
+ align:start position:0%
+ways. Just as rehearsal, I'm showing two
+ 
+
+ align:start position:0%
+ways. Just as rehearsal, I'm showing two
+ways here that don't quite fall there.
+
+ align:start position:0%
+ways here that don't quite fall there.
+ 
+
+ align:start position:0%
+ways here that don't quite fall there.
+So my answer would have been at least
+
+ align:start position:0%
+So my answer would have been at least
+ 
+
+ align:start position:0%
+So my answer would have been at least
+seven ways that I can do this problem
+
+ align:start position:0%
+seven ways that I can do this problem
+ 
+
+ align:start position:0%
+seven ways that I can do this problem
+because I'm going to show you two new
+
+ align:start position:0%
+because I'm going to show you two new
+ 
+
+ align:start position:0%
+because I'm going to show you two new
+ones that don't appear directly. One way
+
+ align:start position:0%
+ones that don't appear directly. One way
+ 
+
+ align:start position:0%
+ones that don't appear directly. One way
+is to think about the diff differential
+
+ align:start position:0%
+is to think about the diff differential
+ 
+
+ align:start position:0%
+is to think about the diff differential
+equation.
+
+ align:start position:0%
+equation.
+ 
+
+ align:start position:0%
+equation.
+Solve it for t less than zero and t
+
+ align:start position:0%
+Solve it for t less than zero and t
+ 
+
+ align:start position:0%
+Solve it for t less than zero and t
+greater than
+
+ align:start position:0%
+greater than
+ 
+
+ align:start position:0%
+greater than
+zero. Paste the solutions
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+together with me so far. So solver for t
+
+ align:start position:0%
+together with me so far. So solver for t
+ 
+
+ align:start position:0%
+together with me so far. So solver for t
+less than zero. The answer is zero
+
+ align:start position:0%
+less than zero. The answer is zero
+ 
+
+ align:start position:0%
+less than zero. The answer is zero
+because there was no input. Started at
+
+ align:start position:0%
+because there was no input. Started at
+ 
+
+ align:start position:0%
+because there was no input. Started at
+rest. Solver for t bigger than zero.
+
+ align:start position:0%
+rest. Solver for t bigger than zero.
+ 
+
+ align:start position:0%
+rest. Solver for t bigger than zero.
+That means the input is
+
+ align:start position:0%
+That means the input is
+ 
+
+ align:start position:0%
+That means the input is
+one. So you can get some answer for t
+
+ align:start position:0%
+one. So you can get some answer for t
+ 
+
+ align:start position:0%
+one. So you can get some answer for t
+bigger than zero. Paste the two
+
+ align:start position:0%
+bigger than zero. Paste the two
+ 
+
+ align:start position:0%
+bigger than zero. Paste the two
+solutions together by using
+
+ align:start position:0%
+solutions together by using
+ 
+
+ align:start position:0%
+solutions together by using
+um unitstep functions.
+
+ align:start position:0%
+um unitstep functions.
+ 
+
+ align:start position:0%
+um unitstep functions.
+put the total answer back into the der
+
+ align:start position:0%
+put the total answer back into the der
+ 
+
+ align:start position:0%
+put the total answer back into the der
+into the differential
+
+ align:start position:0%
+into the differential
+ 
+
+ align:start position:0%
+into the differential
+equation. That total answer better have
+
+ align:start position:0%
+equation. That total answer better have
+ 
+
+ align:start position:0%
+equation. That total answer better have
+the property that it solves the
+
+ align:start position:0%
+the property that it solves the
+ 
+
+ align:start position:0%
+the property that it solves the
+differential equation for all
+
+ align:start position:0%
+differential equation for all
+ 
+
+ align:start position:0%
+differential equation for all
+time. Okay, nod your head yes. It'll
+
+ align:start position:0%
+time. Okay, nod your head yes. It'll
+ 
+
+ align:start position:0%
+time. Okay, nod your head yes. It'll
+make me feel like you're I'm doing a
+
+ align:start position:0%
+make me feel like you're I'm doing a
+ 
+
+ align:start position:0%
+make me feel like you're I'm doing a
+fantastic job. Right? So, uh and the
+
+ align:start position:0%
+fantastic job. Right? So, uh and the
+ 
+
+ align:start position:0%
+fantastic job. Right? So, uh and the
+only trick there is thinking about how
+
+ align:start position:0%
+only trick there is thinking about how
+ 
+
+ align:start position:0%
+only trick there is thinking about how
+do you do things like differentiate a
+
+ align:start position:0%
+do you do things like differentiate a
+ 
+
+ align:start position:0%
+do you do things like differentiate a
+unitep function. But the derivative of a
+
+ align:start position:0%
+unitep function. But the derivative of a
+ 
+
+ align:start position:0%
+unitep function. But the derivative of a
+unitep function is delta function.
+
+ align:start position:0%
+unitep function is delta function.
+ 
+
+ align:start position:0%
+unitep function is delta function.
+the derivative of one of these things
+
+ align:start position:0%
+the derivative of one of these things
+ 
+
+ align:start position:0%
+the derivative of one of these things
+which looks like a product of something
+
+ align:start position:0%
+which looks like a product of something
+ 
+
+ align:start position:0%
+which looks like a product of something
+that exists for all time and something
+
+ align:start position:0%
+that exists for all time and something
+ 
+
+ align:start position:0%
+that exists for all time and something
+that turns on at zero. It's just the
+
+ align:start position:0%
+that turns on at zero. It's just the
+ 
+
+ align:start position:0%
+that turns on at zero. It's just the
+product rule. Derivative of the first
+
+ align:start position:0%
+product rule. Derivative of the first
+ 
+
+ align:start position:0%
+product rule. Derivative of the first
+times the second plus second times the
+
+ align:start position:0%
+times the second plus second times the
+ 
+
+ align:start position:0%
+times the second plus second times the
+der of the first except I said the same
+
+ align:start position:0%
+der of the first except I said the same
+ 
+
+ align:start position:0%
+der of the first except I said the same
+thing twice. Um
+
+ align:start position:0%
+thing twice. Um
+ 
+
+ align:start position:0%
+thing twice. Um
+okay. And so if you do that you end up
+
+ align:start position:0%
+okay. And so if you do that you end up
+ 
+
+ align:start position:0%
+okay. And so if you do that you end up
+finding out that to match the delta
+
+ align:start position:0%
+finding out that to match the delta
+ 
+
+ align:start position:0%
+finding out that to match the delta
+functions and the u functions it places
+
+ align:start position:0%
+functions and the u functions it places
+ 
+
+ align:start position:0%
+functions and the u functions it places
+additional constraints on the constants.
+
+ align:start position:0%
+additional constraints on the constants.
+ 
+
+ align:start position:0%
+additional constraints on the constants.
+And the answer looks like this.
+
+ align:start position:0%
+And the answer looks like this.
+ 
+
+ align:start position:0%
+And the answer looks like this.
+Okay, everybody sort of sees what I'm
+
+ align:start position:0%
+Okay, everybody sort of sees what I'm
+ 
+
+ align:start position:0%
+Okay, everybody sort of sees what I'm
+saying? Here's a different way you could
+
+ align:start position:0%
+saying? Here's a different way you could
+ 
+
+ align:start position:0%
+saying? Here's a different way you could
+do it. You could think
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+systems. So on the chart, I told you
+
+ align:start position:0%
+systems. So on the chart, I told you
+ 
+
+ align:start position:0%
+systems. So on the chart, I told you
+what the unit uh impulse response was.
+
+ align:start position:0%
+what the unit uh impulse response was.
+ 
+
+ align:start position:0%
+what the unit uh impulse response was.
+It's one over to E the minus T over to U
+
+ align:start position:0%
+It's one over to E the minus T over to U
+ 
+
+ align:start position:0%
+It's one over to E the minus T over to U
+of TOA U of T. Uh so you could use that
+
+ align:start position:0%
+of TOA U of T. Uh so you could use that
+ 
+
+ align:start position:0%
+of TOA U of T. Uh so you could use that
+to figure out the
+
+ align:start position:0%
+to figure out the
+ 
+
+ align:start position:0%
+to figure out the
+response. If I know that delta goes into
+
+ align:start position:0%
+response. If I know that delta goes into
+ 
+
+ align:start position:0%
+response. If I know that delta goes into
+a system, it gives me the um unit
+
+ align:start position:0%
+a system, it gives me the um unit
+ 
+
+ align:start position:0%
+a system, it gives me the um unit
+impulse response h of
+
+ align:start position:0%
+impulse response h of
+ 
+
+ align:start position:0%
+impulse response h of
+t. And the question then is find the
+
+ align:start position:0%
+t. And the question then is find the
+ 
+
+ align:start position:0%
+t. And the question then is find the
+unitst step response. Well, there's an
+
+ align:start position:0%
+unitst step response. Well, there's an
+ 
+
+ align:start position:0%
+unitst step response. Well, there's an
+easy way to find the unit step. That's
+
+ align:start position:0%
+easy way to find the unit step. That's
+ 
+
+ align:start position:0%
+easy way to find the unit step. That's
+just the integral of the unit
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+impulse. So apparently the unit step
+
+ align:start position:0%
+impulse. So apparently the unit step
+ 
+
+ align:start position:0%
+impulse. So apparently the unit step
+response of this thing is the same as
+
+ align:start position:0%
+response of this thing is the same as
+ 
+
+ align:start position:0%
+response of this thing is the same as
+the unit impulse response of this
+
+ align:start position:0%
+the unit impulse response of this
+ 
+
+ align:start position:0%
+the unit impulse response of this
+combined system.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+But we know from our analysis of systems
+
+ align:start position:0%
+But we know from our analysis of systems
+ 
+
+ align:start position:0%
+But we know from our analysis of systems
+that you're allowed to commute things.
+
+ align:start position:0%
+that you're allowed to commute things.
+ 
+
+ align:start position:0%
+that you're allowed to commute things.
+So that means I can flip this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+order. Which means then that all I need
+
+ align:start position:0%
+order. Which means then that all I need
+ 
+
+ align:start position:0%
+order. Which means then that all I need
+to do is integrate the impulse response
+
+ align:start position:0%
+to do is integrate the impulse response
+ 
+
+ align:start position:0%
+to do is integrate the impulse response
+of this thing which I knew by
+
+ align:start position:0%
+of this thing which I knew by
+ 
+
+ align:start position:0%
+of this thing which I knew by
+assumption. So if I integrate the
+
+ align:start position:0%
+assumption. So if I integrate the
+ 
+
+ align:start position:0%
+assumption. So if I integrate the
+impulse response, I get the step
+
+ align:start position:0%
+impulse response, I get the step
+ 
+
+ align:start position:0%
+impulse response, I get the step
+response. That's another way of doing
+
+ align:start position:0%
+response. That's another way of doing
+ 
+
+ align:start position:0%
+response. That's another way of doing
+it. I could do it by lelass transforms.
+
+ align:start position:0%
+it. I could do it by lelass transforms.
+ 
+
+ align:start position:0%
+it. I could do it by lelass transforms.
+I could do it a gazillion ways, right?
+
+ align:start position:0%
+I could do it a gazillion ways, right?
+ 
+
+ align:start position:0%
+I could do it a gazillion ways, right?
+Easy. you should go home and make sure
+
+ align:start position:0%
+Easy. you should go home and make sure
+ 
+
+ align:start position:0%
+Easy. you should go home and make sure
+you can do all of
+
+ align:start position:0%
+you can do all of
+ 
+
+ align:start position:0%
+you can do all of
+those. Okay, so the answer then was
+
+ align:start position:0%
+those. Okay, so the answer then was
+ 
+
+ align:start position:0%
+those. Okay, so the answer then was
+number two. It's this thing. It's the
+
+ align:start position:0%
+number two. It's this thing. It's the
+ 
+
+ align:start position:0%
+number two. It's this thing. It's the
+first order response. Like was said, it
+
+ align:start position:0%
+first order response. Like was said, it
+ 
+
+ align:start position:0%
+first order response. Like was said, it
+has to go to a particular final value
+
+ align:start position:0%
+has to go to a particular final value
+ 
+
+ align:start position:0%
+has to go to a particular final value
+which is equal to the um uh final value
+
+ align:start position:0%
+which is equal to the um uh final value
+ 
+
+ align:start position:0%
+which is equal to the um uh final value
+of the input. There's a there's a
+
+ align:start position:0%
+of the input. There's a there's a
+ 
+
+ align:start position:0%
+of the input. There's a there's a
+variety of ways you could get that.
+
+ align:start position:0%
+variety of ways you could get that.
+ 
+
+ align:start position:0%
+variety of ways you could get that.
+Okay, the point of today then is to take
+
+ align:start position:0%
+Okay, the point of today then is to take
+ 
+
+ align:start position:0%
+Okay, the point of today then is to take
+that unit sample response that unit
+
+ align:start position:0%
+that unit sample response that unit
+ 
+
+ align:start position:0%
+that unit sample response that unit
+response and figure out ways to
+
+ align:start position:0%
+response and figure out ways to
+ 
+
+ align:start position:0%
+response and figure out ways to
+approximate it. What I want to do is
+
+ align:start position:0%
+approximate it. What I want to do is
+ 
+
+ align:start position:0%
+approximate it. What I want to do is
+think about how I would make a discrete
+
+ align:start position:0%
+think about how I would make a discrete
+ 
+
+ align:start position:0%
+think about how I would make a discrete
+representation for the CT system, the
+
+ align:start position:0%
+representation for the CT system, the
+ 
+
+ align:start position:0%
+representation for the CT system, the
+leaky tank
+
+ align:start position:0%
+leaky tank
+ 
+
+ align:start position:0%
+leaky tank
+system. You've done this in homework.
+
+ align:start position:0%
+system. You've done this in homework.
+ 
+
+ align:start position:0%
+system. You've done this in homework.
+This was homework
+
+ align:start position:0%
+This was homework
+ 
+
+ align:start position:0%
+This was homework
+one. What I'm trying to do is get some
+
+ align:start position:0%
+one. What I'm trying to do is get some
+ 
+
+ align:start position:0%
+one. What I'm trying to do is get some
+new perspective by thinking about all
+
+ align:start position:0%
+new perspective by thinking about all
+ 
+
+ align:start position:0%
+new perspective by thinking about all
+those representations that we have on
+
+ align:start position:0%
+those representations that we have on
+ 
+
+ align:start position:0%
+those representations that we have on
+the answer that you already derived in
+
+ align:start position:0%
+the answer that you already derived in
+ 
+
+ align:start position:0%
+the answer that you already derived in
+homework one.
+
+ align:start position:0%
+homework one.
+ 
+
+ align:start position:0%
+homework one.
+So if I wanted to represent this system,
+
+ align:start position:0%
+So if I wanted to represent this system,
+ 
+
+ align:start position:0%
+So if I wanted to represent this system,
+the leaky tank system by a difference
+
+ align:start position:0%
+the leaky tank system by a difference
+ 
+
+ align:start position:0%
+the leaky tank system by a difference
+equation, one way to get the difference
+
+ align:start position:0%
+equation, one way to get the difference
+ 
+
+ align:start position:0%
+equation, one way to get the difference
+equation is to make an approximation to
+
+ align:start position:0%
+equation is to make an approximation to
+ 
+
+ align:start position:0%
+equation is to make an approximation to
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+derivative based on
+
+ align:start position:0%
+derivative based on
+ 
+
+ align:start position:0%
+derivative based on
+differences. The easiest way to do that
+
+ align:start position:0%
+differences. The easiest way to do that
+ 
+
+ align:start position:0%
+differences. The easiest way to do that
+is something that we will call the
+
+ align:start position:0%
+is something that we will call the
+ 
+
+ align:start position:0%
+is something that we will call the
+forward oiler
+
+ align:start position:0%
+forward oiler
+ 
+
+ align:start position:0%
+forward oiler
+method. Uh in the forward oiler method,
+
+ align:start position:0%
+method. Uh in the forward oiler method,
+ 
+
+ align:start position:0%
+method. Uh in the forward oiler method,
+what we do is we think about all the
+
+ align:start position:0%
+what we do is we think about all the
+ 
+
+ align:start position:0%
+what we do is we think about all the
+functions of time. Say we have an x
+
+ align:start position:0%
+functions of time. Say we have an x
+ 
+
+ align:start position:0%
+functions of time. Say we have an x
+function of time and a y function of
+
+ align:start position:0%
+function of time and a y function of
+ 
+
+ align:start position:0%
+function of time and a y function of
+time, the input and the output.
+
+ align:start position:0%
+time, the input and the output.
+ 
+
+ align:start position:0%
+time, the input and the output.
+I've got the continuous version and the
+
+ align:start position:0%
+I've got the continuous version and the
+ 
+
+ align:start position:0%
+I've got the continuous version and the
+discrete version. That's the sub C and
+
+ align:start position:0%
+discrete version. That's the sub C and
+ 
+
+ align:start position:0%
+discrete version. That's the sub C and
+the sub
+
+ align:start position:0%
+the sub
+ 
+
+ align:start position:0%
+the sub
+D. The way I could make an association
+
+ align:start position:0%
+D. The way I could make an association
+ 
+
+ align:start position:0%
+D. The way I could make an association
+between discrete and continuous is by
+
+ align:start position:0%
+between discrete and continuous is by
+ 
+
+ align:start position:0%
+between discrete and continuous is by
+sampling the
+
+ align:start position:0%
+sampling the
+ 
+
+ align:start position:0%
+sampling the
+signals. So I could say that if I knew X
+
+ align:start position:0%
+signals. So I could say that if I knew X
+ 
+
+ align:start position:0%
+signals. So I could say that if I knew X
+subC of T, that's going to be some
+
+ align:start position:0%
+subC of T, that's going to be some
+ 
+
+ align:start position:0%
+subC of T, that's going to be some
+squirrely function. But I don't know the
+
+ align:start position:0%
+squirrely function. But I don't know the
+ 
+
+ align:start position:0%
+squirrely function. But I don't know the
+answer. I don't know what that is. But
+
+ align:start position:0%
+answer. I don't know what that is. But
+ 
+
+ align:start position:0%
+answer. I don't know what that is. But
+whatever it is, I will say that the
+
+ align:start position:0%
+whatever it is, I will say that the
+ 
+
+ align:start position:0%
+whatever it is, I will say that the
+discrete version at time
+
+ align:start position:0%
+discrete version at time
+ 
+
+ align:start position:0%
+discrete version at time
+n is the same as the continuous version
+
+ align:start position:0%
+n is the same as the continuous version
+ 
+
+ align:start position:0%
+n is the same as the continuous version
+at time n * t. t is a sampling
+
+ align:start position:0%
+at time n * t. t is a sampling
+ 
+
+ align:start position:0%
+at time n * t. t is a sampling
+interval. And the discrete version of
+
+ align:start position:0%
+interval. And the discrete version of
+ 
+
+ align:start position:0%
+interval. And the discrete version of
+this uh y function, this output function
+
+ align:start position:0%
+this uh y function, this output function
+ 
+
+ align:start position:0%
+this uh y function, this output function
+at time n +1 t is the n+1
+
+ align:start position:0%
+at time n +1 t is the n+1
+ 
+
+ align:start position:0%
+at time n +1 t is the n+1
+sample of the discretetized output
+
+ align:start position:0%
+sample of the discretetized output
+ 
+
+ align:start position:0%
+sample of the discretetized output
+signal. Then the trick to to um solving
+
+ align:start position:0%
+signal. Then the trick to to um solving
+ 
+
+ align:start position:0%
+signal. Then the trick to to um solving
+the differential equation remember the
+
+ align:start position:0%
+the differential equation remember the
+ 
+
+ align:start position:0%
+the differential equation remember the
+differential equation looked like
+
+ align:start position:0%
+differential equation looked like
+ 
+
+ align:start position:0%
+differential equation looked like
+to y dot of t is x of t uh minus y of t.
+
+ align:start position:0%
+to y dot of t is x of t uh minus y of t.
+ 
+
+ align:start position:0%
+to y dot of t is x of t uh minus y of t.
+I need to have a way of thinking about
+
+ align:start position:0%
+I need to have a way of thinking about
+ 
+
+ align:start position:0%
+I need to have a way of thinking about
+this y dot
+
+ align:start position:0%
+this y dot
+ 
+
+ align:start position:0%
+this y dot
+thing. A way of thinking about the y dot
+
+ align:start position:0%
+thing. A way of thinking about the y dot
+ 
+
+ align:start position:0%
+thing. A way of thinking about the y dot
+thing would be the slope of the line
+
+ align:start position:0%
+thing would be the slope of the line
+ 
+
+ align:start position:0%
+thing would be the slope of the line
+that connects this sample to the next
+
+ align:start position:0%
+that connects this sample to the next
+ 
+
+ align:start position:0%
+that connects this sample to the next
+sample. We call it forward order because
+
+ align:start position:0%
+sample. We call it forward order because
+ 
+
+ align:start position:0%
+sample. We call it forward order because
+at time n we we approximate the
+
+ align:start position:0%
+at time n we we approximate the
+ 
+
+ align:start position:0%
+at time n we we approximate the
+derivative at time n by looking
+
+ align:start position:0%
+derivative at time n by looking
+ 
+
+ align:start position:0%
+derivative at time n by looking
+forward. So we approximate the
+
+ align:start position:0%
+forward. So we approximate the
+ 
+
+ align:start position:0%
+forward. So we approximate the
+derivative of y continuous at time nt by
+
+ align:start position:0%
+derivative of y continuous at time nt by
+ 
+
+ align:start position:0%
+derivative of y continuous at time nt by
+looking forward. yd of n +1 minus yd of
+
+ align:start position:0%
+looking forward. yd of n +1 minus yd of
+ 
+
+ align:start position:0%
+looking forward. yd of n +1 minus yd of
+n
+
+ align:start position:0%
+n
+ 
+
+ align:start position:0%
+n
+/t. Then all we need to do is make that
+
+ align:start position:0%
+/t. Then all we need to do is make that
+ 
+
+ align:start position:0%
+/t. Then all we need to do is make that
+substitution into the differential
+
+ align:start position:0%
+substitution into the differential
+ 
+
+ align:start position:0%
+substitution into the differential
+equation.
+
+ align:start position:0%
+equation.
+ 
+
+ align:start position:0%
+equation.
+and it turns it into a difference
+
+ align:start position:0%
+and it turns it into a difference
+ 
+
+ align:start position:0%
+and it turns it into a difference
+equation. So if I make the substitution
+
+ align:start position:0%
+equation. So if I make the substitution
+ 
+
+ align:start position:0%
+equation. So if I make the substitution
+that y dot is given by this kind of an
+
+ align:start position:0%
+that y dot is given by this kind of an
+ 
+
+ align:start position:0%
+that y dot is given by this kind of an
+expression substitute into this
+
+ align:start position:0%
+expression substitute into this
+ 
+
+ align:start position:0%
+expression substitute into this
+expression I get a difference equation
+
+ align:start position:0%
+expression I get a difference equation
+ 
+
+ align:start position:0%
+expression I get a difference equation
+that is in some sense equivalent to the
+
+ align:start position:0%
+that is in some sense equivalent to the
+ 
+
+ align:start position:0%
+that is in some sense equivalent to the
+original differential
+
+ align:start position:0%
+original differential
+ 
+
+ align:start position:0%
+original differential
+equation. I can solve that difference
+
+ align:start position:0%
+equation. I can solve that difference
+ 
+
+ align:start position:0%
+equation. I can solve that difference
+equation and I get that bottom
+
+ align:start position:0%
+equation and I get that bottom
+ 
+
+ align:start position:0%
+equation and I get that bottom
+difference
+
+ align:start position:0%
+difference
+ 
+
+ align:start position:0%
+difference
+relationship. That's what you did in
+
+ align:start position:0%
+relationship. That's what you did in
+ 
+
+ align:start position:0%
+relationship. That's what you did in
+homework one. If you were to plot that
+
+ align:start position:0%
+homework one. If you were to plot that
+ 
+
+ align:start position:0%
+homework one. If you were to plot that
+answer, here's what you would
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+get. The blue curve represents the
+
+ align:start position:0%
+get. The blue curve represents the
+ 
+
+ align:start position:0%
+get. The blue curve represents the
+continuous the solution to the leaky
+
+ align:start position:0%
+continuous the solution to the leaky
+ 
+
+ align:start position:0%
+continuous the solution to the leaky
+tank problem. The continuous problem 1
+
+ align:start position:0%
+tank problem. The continuous problem 1
+ 
+
+ align:start position:0%
+tank problem. The continuous problem 1
+minus e to the minus t over towo
+
+ align:start position:0%
+minus e to the minus t over towo
+ 
+
+ align:start position:0%
+minus e to the minus t over towo
+quantity u of t. So that's the blue
+
+ align:start position:0%
+quantity u of t. So that's the blue
+ 
+
+ align:start position:0%
+quantity u of t. So that's the blue
+line. If you select the sampling
+
+ align:start position:0%
+line. If you select the sampling
+ 
+
+ align:start position:0%
+line. If you select the sampling
+interval to be small compared to tao,
+
+ align:start position:0%
+interval to be small compared to tao,
+ 
+
+ align:start position:0%
+interval to be small compared to tao,
+tao was the time constant for the CT
+
+ align:start position:0%
+tao was the time constant for the CT
+ 
+
+ align:start position:0%
+tao was the time constant for the CT
+system. If you select the sampling
+
+ align:start position:0%
+system. If you select the sampling
+ 
+
+ align:start position:0%
+system. If you select the sampling
+interval to be small 0.1, the samples
+
+ align:start position:0%
+interval to be small 0.1, the samples
+ 
+
+ align:start position:0%
+interval to be small 0.1, the samples
+that you calculate fall right on top of
+
+ align:start position:0%
+that you calculate fall right on top of
+ 
+
+ align:start position:0%
+that you calculate fall right on top of
+the line.
+
+ align:start position:0%
+the line.
+ 
+
+ align:start position:0%
+the line.
+Great. That's what we would want, right?
+
+ align:start position:0%
+Great. That's what we would want, right?
+ 
+
+ align:start position:0%
+Great. That's what we would want, right?
+We're trying to make a dt approximation.
+
+ align:start position:0%
+We're trying to make a dt approximation.
+ 
+
+ align:start position:0%
+We're trying to make a dt approximation.
+If the approximation work, the solution
+
+ align:start position:0%
+If the approximation work, the solution
+ 
+
+ align:start position:0%
+If the approximation work, the solution
+to the dt equations should be the same
+
+ align:start position:0%
+to the dt equations should be the same
+ 
+
+ align:start position:0%
+to the dt equations should be the same
+in some sense as the solution to the ct
+
+ align:start position:0%
+in some sense as the solution to the ct
+ 
+
+ align:start position:0%
+in some sense as the solution to the ct
+equations.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+But if you change capital t, you get
+
+ align:start position:0%
+But if you change capital t, you get
+ 
+
+ align:start position:0%
+But if you change capital t, you get
+something that looks decreasingly like
+
+ align:start position:0%
+something that looks decreasingly like
+ 
+
+ align:start position:0%
+something that looks decreasingly like
+the continuous version. If you make t uh
+
+ align:start position:0%
+the continuous version. If you make t uh
+ 
+
+ align:start position:0%
+the continuous version. If you make t uh
+step bigger and bigger per per time, t
+
+ align:start position:0%
+step bigger and bigger per per time, t
+ 
+
+ align:start position:0%
+step bigger and bigger per per time, t
+is the sampling interval. If I started
+
+ align:start position:0%
+is the sampling interval. If I started
+ 
+
+ align:start position:0%
+is the sampling interval. If I started
+with a small sampling interval, I got a
+
+ align:start position:0%
+with a small sampling interval, I got a
+ 
+
+ align:start position:0%
+with a small sampling interval, I got a
+good approximation. By the time I get
+
+ align:start position:0%
+good approximation. By the time I get
+ 
+
+ align:start position:0%
+good approximation. By the time I get
+the sampling interval up to 2T, it the
+
+ align:start position:0%
+the sampling interval up to 2T, it the
+ 
+
+ align:start position:0%
+the sampling interval up to 2T, it the
+solution to the DT problem looks nothing
+
+ align:start position:0%
+solution to the DT problem looks nothing
+ 
+
+ align:start position:0%
+solution to the DT problem looks nothing
+like the solution to the CT
+
+ align:start position:0%
+like the solution to the CT
+ 
+
+ align:start position:0%
+like the solution to the CT
+problem. Okay, that's a general problem
+
+ align:start position:0%
+problem. Okay, that's a general problem
+ 
+
+ align:start position:0%
+problem. Okay, that's a general problem
+in a numerical method. So, what we're
+
+ align:start position:0%
+in a numerical method. So, what we're
+ 
+
+ align:start position:0%
+in a numerical method. So, what we're
+really talking about is analysis of
+
+ align:start position:0%
+really talking about is analysis of
+ 
+
+ align:start position:0%
+really talking about is analysis of
+numerical methods. What went
+
+ align:start position:0%
+numerical methods. What went
+ 
+
+ align:start position:0%
+numerical methods. What went
+wrong? Why is it that the approximation
+
+ align:start position:0%
+wrong? Why is it that the approximation
+ 
+
+ align:start position:0%
+wrong? Why is it that the approximation
+worked well and didn't work well? I
+
+ align:start position:0%
+worked well and didn't work well? I
+ 
+
+ align:start position:0%
+worked well and didn't work well? I
+mean, it's intuitively clear that that's
+
+ align:start position:0%
+mean, it's intuitively clear that that's
+ 
+
+ align:start position:0%
+mean, it's intuitively clear that that's
+what you should have done, but we'd like
+
+ align:start position:0%
+what you should have done, but we'd like
+ 
+
+ align:start position:0%
+what you should have done, but we'd like
+to be a little more formal and we'd like
+
+ align:start position:0%
+to be a little more formal and we'd like
+ 
+
+ align:start position:0%
+to be a little more formal and we'd like
+to be a little more quantitative. What
+
+ align:start position:0%
+to be a little more quantitative. What
+ 
+
+ align:start position:0%
+to be a little more quantitative. What
+was it that went
+
+ align:start position:0%
+was it that went
+ 
+
+ align:start position:0%
+was it that went
+wrong? So, to get some insight, let's
+
+ align:start position:0%
+wrong? So, to get some insight, let's
+ 
+
+ align:start position:0%
+wrong? So, to get some insight, let's
+figure out the pole for the DT system.
+
+ align:start position:0%
+figure out the pole for the DT system.
+ 
+
+ align:start position:0%
+figure out the pole for the DT system.
+Where's the pole?
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay. Where's the pole? Where's the pole
+
+ align:start position:0%
+Okay. Where's the pole? Where's the pole
+ 
+
+ align:start position:0%
+Okay. Where's the pole? Where's the pole
+of the DT
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+system? Okay. not a large voter turnout
+
+ align:start position:0%
+system? Okay. not a large voter turnout
+ 
+
+ align:start position:0%
+system? Okay. not a large voter turnout
+but 100% among those who turned out. So
+
+ align:start position:0%
+but 100% among those who turned out. So
+ 
+
+ align:start position:0%
+but 100% among those who turned out. So
+the answer is uh number two. It's pretty
+
+ align:start position:0%
+the answer is uh number two. It's pretty
+ 
+
+ align:start position:0%
+the answer is uh number two. It's pretty
+simple to see how that would be the
+
+ align:start position:0%
+simple to see how that would be the
+ 
+
+ align:start position:0%
+simple to see how that would be the
+answer. If you start with the difference
+
+ align:start position:0%
+answer. If you start with the difference
+ 
+
+ align:start position:0%
+answer. If you start with the difference
+equation, it's very simple to write a z
+
+ align:start position:0%
+equation, it's very simple to write a z
+ 
+
+ align:start position:0%
+equation, it's very simple to write a z
+transform. This evaluate y at n + one is
+
+ align:start position:0%
+transform. This evaluate y at n + one is
+ 
+
+ align:start position:0%
+transform. This evaluate y at n + one is
+the reverse of a delay. It's an advance.
+
+ align:start position:0%
+the reverse of a delay. It's an advance.
+ 
+
+ align:start position:0%
+the reverse of a delay. It's an advance.
+Delay is multiplied by z minus one. So
+
+ align:start position:0%
+Delay is multiplied by z minus one. So
+ 
+
+ align:start position:0%
+Delay is multiplied by z minus one. So
+advanced is multiply by
+
+ align:start position:0%
+advanced is multiply by
+ 
+
+ align:start position:0%
+advanced is multiply by
+Z. So you can take the Z transform of
+
+ align:start position:0%
+Z. So you can take the Z transform of
+ 
+
+ align:start position:0%
+Z. So you can take the Z transform of
+the difference equation to to derive the
+
+ align:start position:0%
+the difference equation to to derive the
+ 
+
+ align:start position:0%
+the difference equation to to derive the
+Z
+
+ align:start position:0%
+Z
+ 
+
+ align:start position:0%
+Z
+transform of the system
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+function. And then clearly there's a
+
+ align:start position:0%
+function. And then clearly there's a
+ 
+
+ align:start position:0%
+function. And then clearly there's a
+pole here at Z = 1 - T over
+
+ align:start position:0%
+pole here at Z = 1 - T over
+ 
+
+ align:start position:0%
+pole here at Z = 1 - T over
+to so the answer was number two. And it
+
+ align:start position:0%
+to so the answer was number two. And it
+ 
+
+ align:start position:0%
+to so the answer was number two. And it
+gives us a way to think
+
+ align:start position:0%
+gives us a way to think
+ 
+
+ align:start position:0%
+gives us a way to think
+about why the difference
+
+ align:start position:0%
+about why the difference
+ 
+
+ align:start position:0%
+about why the difference
+solution didn't work. Well, what we can
+
+ align:start position:0%
+solution didn't work. Well, what we can
+ 
+
+ align:start position:0%
+solution didn't work. Well, what we can
+see is that even though you remember the
+
+ align:start position:0%
+see is that even though you remember the
+ 
+
+ align:start position:0%
+see is that even though you remember the
+the um what was the pole of the CT
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+system? What's the pole of the CT
+
+ align:start position:0%
+system? What's the pole of the CT
+ 
+
+ align:start position:0%
+system? What's the pole of the CT
+system?
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+How do you think about the pole of a CT
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+system? Close. What's the pole of the CT
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+system? Minus one over towal. So we
+
+ align:start position:0%
+system? Minus one over towal. So we
+ 
+
+ align:start position:0%
+system? Minus one over towal. So we
+would do the same sort of thing but now
+
+ align:start position:0%
+would do the same sort of thing but now
+ 
+
+ align:start position:0%
+would do the same sort of thing but now
+with with a lelass transform, right?
+
+ align:start position:0%
+with with a lelass transform, right?
+ 
+
+ align:start position:0%
+with with a lelass transform, right?
+So we would say that we could write the
+
+ align:start position:0%
+So we would say that we could write the
+ 
+
+ align:start position:0%
+So we would say that we could write the
+applause transform of this. This would
+
+ align:start position:0%
+applause transform of this. This would
+ 
+
+ align:start position:0%
+applause transform of this. This would
+be s to
+
+ align:start position:0%
+be s to
+ 
+
+ align:start position:0%
+be s to
+y is x minus
+
+ align:start position:0%
+y is x minus
+ 
+
+ align:start position:0%
+y is x minus
+y. And the uh pole is going to end up
+
+ align:start position:0%
+y. And the uh pole is going to end up
+ 
+
+ align:start position:0%
+y. And the uh pole is going to end up
+with the pole that we get in the s plane
+
+ align:start position:0%
+with the pole that we get in the s plane
+ 
+
+ align:start position:0%
+with the pole that we get in the s plane
+is going to be 1 over 1
+
+ align:start position:0%
+is going to be 1 over 1
+ 
+
+ align:start position:0%
+is going to be 1 over 1
+- 1 over
+
+ align:start position:0%
+- 1 over
+ 
+
+ align:start position:0%
+- 1 over
+to despite the fact that the pole in the
+
+ align:start position:0%
+to despite the fact that the pole in the
+ 
+
+ align:start position:0%
+to despite the fact that the pole in the
+s
+
+ align:start position:0%
+s
+ 
+
+ align:start position:0%
+s
+plane was the same for all the
+
+ align:start position:0%
+plane was the same for all the
+ 
+
+ align:start position:0%
+plane was the same for all the
+simulations. The simulations the
+
+ align:start position:0%
+simulations. The simulations the
+ 
+
+ align:start position:0%
+simulations. The simulations the
+discrete versions look different. And
+
+ align:start position:0%
+discrete versions look different. And
+ 
+
+ align:start position:0%
+discrete versions look different. And
+that's because the pole for the DT
+
+ align:start position:0%
+that's because the pole for the DT
+ 
+
+ align:start position:0%
+that's because the pole for the DT
+system is not the same. The pole for the
+
+ align:start position:0%
+system is not the same. The pole for the
+ 
+
+ align:start position:0%
+system is not the same. The pole for the
+DT system depended both on tow as did
+
+ align:start position:0%
+DT system depended both on tow as did
+ 
+
+ align:start position:0%
+DT system depended both on tow as did
+the pole for the CT
+
+ align:start position:0%
+the pole for the CT
+ 
+
+ align:start position:0%
+the pole for the CT
+system. But the DCT the DT system the
+
+ align:start position:0%
+system. But the DCT the DT system the
+ 
+
+ align:start position:0%
+system. But the DCT the DT system the
+pole depended also on capital
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+T. Right? So we said that the pole you
+
+ align:start position:0%
+T. Right? So we said that the pole you
+ 
+
+ align:start position:0%
+T. Right? So we said that the pole you
+remember the solution to the last
+
+ align:start position:0%
+remember the solution to the last
+ 
+
+ align:start position:0%
+remember the solution to the last
+problem the pole was at 1 minus t over
+
+ align:start position:0%
+problem the pole was at 1 minus t over
+ 
+
+ align:start position:0%
+problem the pole was at 1 minus t over
+tow. So if t over tow is 0.1 the pole is
+
+ align:start position:0%
+tow. So if t over tow is 0.1 the pole is
+ 
+
+ align:start position:0%
+tow. So if t over tow is 0.1 the pole is
+at
+
+ align:start position:0%
+at
+ 
+
+ align:start position:0%
+at
+0.9. If t over tow is 3 the pole is at
+
+ align:start position:0%
+0.9. If t over tow is 3 the pole is at
+ 
+
+ align:start position:0%
+0.9. If t over tow is 3 the pole is at
+7. If the pole is at 2 it's 1 - 2 is
+
+ align:start position:0%
+7. If the pole is at 2 it's 1 - 2 is
+ 
+
+ align:start position:0%
+7. If the pole is at 2 it's 1 - 2 is
+minus1.
+
+ align:start position:0%
+minus1.
+ 
+
+ align:start position:0%
+minus1.
+So the pole for the dt system depends on
+
+ align:start position:0%
+So the pole for the dt system depends on
+ 
+
+ align:start position:0%
+So the pole for the dt system depends on
+both t and
+
+ align:start position:0%
+both t and
+ 
+
+ align:start position:0%
+both t and
+toao and it's given formally by by this
+
+ align:start position:0%
+toao and it's given formally by by this
+ 
+
+ align:start position:0%
+toao and it's given formally by by this
+relationship that
+
+ align:start position:0%
+relationship that
+ 
+
+ align:start position:0%
+relationship that
+z the equivalent pole in the dt system
+
+ align:start position:0%
+z the equivalent pole in the dt system
+ 
+
+ align:start position:0%
+z the equivalent pole in the dt system
+is 1 minus t over
+
+ align:start position:0%
+is 1 minus t over
+ 
+
+ align:start position:0%
+is 1 minus t over
+tow. So the pole in the CT system was um
+
+ align:start position:0%
+tow. So the pole in the CT system was um
+ 
+
+ align:start position:0%
+tow. So the pole in the CT system was um
+minus one over to the pole in the dt
+
+ align:start position:0%
+minus one over to the pole in the dt
+ 
+
+ align:start position:0%
+minus one over to the pole in the dt
+system
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+moved. The amazing
+
+ align:start position:0%
+moved. The amazing
+ 
+
+ align:start position:0%
+moved. The amazing
+thing is that the correspondence between
+
+ align:start position:0%
+thing is that the correspondence between
+ 
+
+ align:start position:0%
+thing is that the correspondence between
+where the pole in the CT system
+
+ align:start position:0%
+where the pole in the CT system
+ 
+
+ align:start position:0%
+where the pole in the CT system
+was and where the pole in the DT system
+
+ align:start position:0%
+was and where the pole in the DT system
+ 
+
+ align:start position:0%
+was and where the pole in the DT system
+is is completely determined by the
+
+ align:start position:0%
+is is completely determined by the
+ 
+
+ align:start position:0%
+is is completely determined by the
+forward oiler method. It has nothing to
+
+ align:start position:0%
+forward oiler method. It has nothing to
+ 
+
+ align:start position:0%
+forward oiler method. It has nothing to
+do with the particular
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+problem. Okay. So we just did we just
+
+ align:start position:0%
+problem. Okay. So we just did we just
+ 
+
+ align:start position:0%
+problem. Okay. So we just did we just
+figured out the map between the pole in
+
+ align:start position:0%
+figured out the map between the pole in
+ 
+
+ align:start position:0%
+figured out the map between the pole in
+the S domain and the pole in the Z
+
+ align:start position:0%
+the S domain and the pole in the Z
+ 
+
+ align:start position:0%
+the S domain and the pole in the Z
+domain for a particular problem for the
+
+ align:start position:0%
+domain for a particular problem for the
+ 
+
+ align:start position:0%
+domain for a particular problem for the
+leaky tank. It turns out that that same
+
+ align:start position:0%
+leaky tank. It turns out that that same
+ 
+
+ align:start position:0%
+leaky tank. It turns out that that same
+map holds for every differential
+
+ align:start position:0%
+map holds for every differential
+ 
+
+ align:start position:0%
+map holds for every differential
+equation. So what I want to think about
+
+ align:start position:0%
+equation. So what I want to think about
+ 
+
+ align:start position:0%
+equation. So what I want to think about
+now is how you would prove such a
+
+ align:start position:0%
+now is how you would prove such a
+ 
+
+ align:start position:0%
+now is how you would prove such a
+statement.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+So think about regardless of the CT
+
+ align:start position:0%
+So think about regardless of the CT
+ 
+
+ align:start position:0%
+So think about regardless of the CT
+system that we're thinking
+
+ align:start position:0%
+system that we're thinking
+ 
+
+ align:start position:0%
+system that we're thinking
+about I can always write it in a block
+
+ align:start position:0%
+about I can always write it in a block
+ 
+
+ align:start position:0%
+about I can always write it in a block
+diagram form with adders integrators
+
+ align:start position:0%
+diagram form with adders integrators
+ 
+
+ align:start position:0%
+diagram form with adders integrators
+u is it adders integrators and
+
+ align:start position:0%
+u is it adders integrators and
+ 
+
+ align:start position:0%
+u is it adders integrators and
+gains so for the leaky tank system that
+
+ align:start position:0%
+gains so for the leaky tank system that
+ 
+
+ align:start position:0%
+gains so for the leaky tank system that
+was easy I my system looked like um
+
+ align:start position:0%
+was easy I my system looked like um
+ 
+
+ align:start position:0%
+was easy I my system looked like um
+let's see I had one over towo
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+integrate
+
+ align:start position:0%
+integrate
+ 
+
+ align:start position:0%
+integrate
+add. So my system for the leaky tank
+
+ align:start position:0%
+add. So my system for the leaky tank
+ 
+
+ align:start position:0%
+add. So my system for the leaky tank
+system looked like
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that. So the point is that there's an a
+
+ align:start position:0%
+that. So the point is that there's an a
+ 
+
+ align:start position:0%
+that. So the point is that there's an a
+there. The oiler forward relationship is
+
+ align:start position:0%
+there. The oiler forward relationship is
+ 
+
+ align:start position:0%
+there. The oiler forward relationship is
+telling me how I can figure
+
+ align:start position:0%
+telling me how I can figure
+ 
+
+ align:start position:0%
+telling me how I can figure
+out a dt representation for the a
+
+ align:start position:0%
+out a dt representation for the a
+ 
+
+ align:start position:0%
+out a dt representation for the a
+function. So let's think about what a
+
+ align:start position:0%
+function. So let's think about what a
+ 
+
+ align:start position:0%
+function. So let's think about what a
+is. a a is a thing that in
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+ct. If the output of a is y, what's the
+
+ align:start position:0%
+ct. If the output of a is y, what's the
+ 
+
+ align:start position:0%
+ct. If the output of a is y, what's the
+input to a?
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+The derivative. It's the derivative. So
+
+ align:start position:0%
+The derivative. It's the derivative. So
+ 
+
+ align:start position:0%
+The derivative. It's the derivative. So
+the input we would want to call y
+
+ align:start position:0%
+the input we would want to call y
+ 
+
+ align:start position:0%
+the input we would want to call y
+dot. So I might say that's
+
+ align:start position:0%
+dot. So I might say that's
+ 
+
+ align:start position:0%
+dot. So I might say that's
+x. So if the input is x, which is y dot,
+
+ align:start position:0%
+x. So if the input is x, which is y dot,
+ 
+
+ align:start position:0%
+x. So if the input is x, which is y dot,
+I put it through an a box and it comes
+
+ align:start position:0%
+I put it through an a box and it comes
+ 
+
+ align:start position:0%
+I put it through an a box and it comes
+out
+
+ align:start position:0%
+out
+ 
+
+ align:start position:0%
+out
+y. So what's the oiler forward rule
+
+ align:start position:0%
+y. So what's the oiler forward rule
+ 
+
+ align:start position:0%
+y. So what's the oiler forward rule
+say? So the oiler forward rule says that
+
+ align:start position:0%
+say? So the oiler forward rule says that
+ 
+
+ align:start position:0%
+say? So the oiler forward rule says that
+if I want to compute x of n, the nth
+
+ align:start position:0%
+if I want to compute x of n, the nth
+ 
+
+ align:start position:0%
+if I want to compute x of n, the nth
+sample of this thing, I should do y dot.
+
+ align:start position:0%
+sample of this thing, I should do y dot.
+ 
+
+ align:start position:0%
+sample of this thing, I should do y dot.
+But y dot I'm doing oiler forward. But I
+
+ align:start position:0%
+But y dot I'm doing oiler forward. But I
+ 
+
+ align:start position:0%
+But y dot I'm doing oiler forward. But I
+should look
+
+ align:start position:0%
+should look
+ 
+
+ align:start position:0%
+should look
+ahead. So I should compute y dot as y of
+
+ align:start position:0%
+ahead. So I should compute y dot as y of
+ 
+
+ align:start position:0%
+ahead. So I should compute y dot as y of
+n + 1 - y of n /
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+t.
+
+ align:start position:0%
+t.
+ 
+
+ align:start position:0%
+t.
+Okay. Now if I want to make a dt
+
+ align:start position:0%
+Okay. Now if I want to make a dt
+ 
+
+ align:start position:0%
+Okay. Now if I want to make a dt
+equivalent system, what I'd like to have
+
+ align:start position:0%
+equivalent system, what I'd like to have
+ 
+
+ align:start position:0%
+equivalent system, what I'd like to have
+is some kind of a box that I could put x
+
+ align:start position:0%
+is some kind of a box that I could put x
+ 
+
+ align:start position:0%
+is some kind of a box that I could put x
+of n in and get y of n out.
+
+ align:start position:0%
+of n in and get y of n out.
+ 
+
+ align:start position:0%
+of n in and get y of n out.
+If I had such a
+
+ align:start position:0%
+If I had such a
+ 
+
+ align:start position:0%
+If I had such a
+box, then I could replace every A in my
+
+ align:start position:0%
+box, then I could replace every A in my
+ 
+
+ align:start position:0%
+box, then I could replace every A in my
+CT block diagram with this new box that
+
+ align:start position:0%
+CT block diagram with this new box that
+ 
+
+ align:start position:0%
+CT block diagram with this new box that
+depends only on
+
+ align:start position:0%
+depends only on
+ 
+
+ align:start position:0%
+depends only on
+delays. So let's think about what would
+
+ align:start position:0%
+delays. So let's think about what would
+ 
+
+ align:start position:0%
+delays. So let's think about what would
+be in that box. If I wanted to make y of
+
+ align:start position:0%
+be in that box. If I wanted to make y of
+ 
+
+ align:start position:0%
+be in that box. If I wanted to make y of
+n out of x of n according to this rule,
+
+ align:start position:0%
+n out of x of n according to this rule,
+ 
+
+ align:start position:0%
+n out of x of n according to this rule,
+what would I
+
+ align:start position:0%
+what would I
+ 
+
+ align:start position:0%
+what would I
+do? Well, let's see. y of n +
+
+ align:start position:0%
+do? Well, let's see. y of n +
+ 
+
+ align:start position:0%
+do? Well, let's see. y of n +
+1 should be y of
+
+ align:start position:0%
+1 should be y of
+ 
+
+ align:start position:0%
+1 should be y of
+n added to tx of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+n. So if I want to compute y of n + 1,
+
+ align:start position:0%
+n. So if I want to compute y of n + 1,
+ 
+
+ align:start position:0%
+n. So if I want to compute y of n + 1,
+oh dear, what's y of n plus one? Where's
+
+ align:start position:0%
+oh dear, what's y of n plus one? Where's
+ 
+
+ align:start position:0%
+oh dear, what's y of n plus one? Where's
+how do I generate my my output? I want
+
+ align:start position:0%
+how do I generate my my output? I want
+ 
+
+ align:start position:0%
+how do I generate my my output? I want
+to be y I want to be y of n. Where's y
+
+ align:start position:0%
+to be y I want to be y of n. Where's y
+ 
+
+ align:start position:0%
+to be y I want to be y of n. Where's y
+of n plus one?
+
+ align:start position:0%
+of n plus one?
+ 
+
+ align:start position:0%
+of n plus one?
+If I knew y of n, how would I compute y
+
+ align:start position:0%
+If I knew y of n, how would I compute y
+ 
+
+ align:start position:0%
+If I knew y of n, how would I compute y
+of n plus one?
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+It would be back one.
+
+ align:start position:0%
+It would be back one.
+ 
+
+ align:start position:0%
+It would be back one.
+So if I had an r
+
+ align:start position:0%
+So if I had an r
+ 
+
+ align:start position:0%
+So if I had an r
+here, what would be the name of this
+
+ align:start position:0%
+here, what would be the name of this
+ 
+
+ align:start position:0%
+here, what would be the name of this
+guy? This would be y of n plus one,
+
+ align:start position:0%
+guy? This would be y of n plus one,
+ 
+
+ align:start position:0%
+guy? This would be y of n plus one,
+right? Delays have the property that
+
+ align:start position:0%
+right? Delays have the property that
+ 
+
+ align:start position:0%
+right? Delays have the property that
+their output is minus
+
+ align:start position:0%
+their output is minus
+ 
+
+ align:start position:0%
+their output is minus
+one. I need a signal that's plus one. So
+
+ align:start position:0%
+one. I need a signal that's plus one. So
+ 
+
+ align:start position:0%
+one. I need a signal that's plus one. So
+I need the reverse of a delay.
+
+ align:start position:0%
+I need the reverse of a delay.
+ 
+
+ align:start position:0%
+I need the reverse of a delay.
+which I can implement by having this y
+
+ align:start position:0%
+which I can implement by having this y
+ 
+
+ align:start position:0%
+which I can implement by having this y
+signal being generated by an
+
+ align:start position:0%
+signal being generated by an
+ 
+
+ align:start position:0%
+signal being generated by an
+r. Then this equation says that in order
+
+ align:start position:0%
+r. Then this equation says that in order
+ 
+
+ align:start position:0%
+r. Then this equation says that in order
+to compute y of n plus1 this thing, what
+
+ align:start position:0%
+to compute y of n plus1 this thing, what
+ 
+
+ align:start position:0%
+to compute y of n plus1 this thing, what
+I need to do is add this to
+
+ align:start position:0%
+I need to do is add this to
+ 
+
+ align:start position:0%
+I need to do is add this to
+that. So I need to
+
+ align:start position:0%
+that. So I need to
+ 
+
+ align:start position:0%
+that. So I need to
+add
+
+ align:start position:0%
+add
+ 
+
+ align:start position:0%
+add
+this
+
+ align:start position:0%
+this
+ 
+
+ align:start position:0%
+this
+to that.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay, the oiler forward rule says if I
+
+ align:start position:0%
+Okay, the oiler forward rule says if I
+ 
+
+ align:start position:0%
+Okay, the oiler forward rule says if I
+want to make a discrete approximation to
+
+ align:start position:0%
+want to make a discrete approximation to
+ 
+
+ align:start position:0%
+want to make a discrete approximation to
+the relationship between y at the output
+
+ align:start position:0%
+the relationship between y at the output
+ 
+
+ align:start position:0%
+the relationship between y at the output
+and its derivative at the input, I
+
+ align:start position:0%
+and its derivative at the input, I
+ 
+
+ align:start position:0%
+and its derivative at the input, I
+should do make one of those
+
+ align:start position:0%
+should do make one of those
+ 
+
+ align:start position:0%
+should do make one of those
+boxes. Okay, I have a rule now.
+
+ align:start position:0%
+boxes. Okay, I have a rule now.
+ 
+
+ align:start position:0%
+boxes. Okay, I have a rule now.
+Regardless of my CT
+
+ align:start position:0%
+Regardless of my CT
+ 
+
+ align:start position:0%
+Regardless of my CT
+system, I'll take every integrator and
+
+ align:start position:0%
+system, I'll take every integrator and
+ 
+
+ align:start position:0%
+system, I'll take every integrator and
+stick one of those in
+
+ align:start position:0%
+stick one of those in
+ 
+
+ align:start position:0%
+stick one of those in
+it. And what I'll have is a DT
+
+ align:start position:0%
+it. And what I'll have is a DT
+ 
+
+ align:start position:0%
+it. And what I'll have is a DT
+approximation to my CT system. that's
+
+ align:start position:0%
+approximation to my CT system. that's
+ 
+
+ align:start position:0%
+approximation to my CT system. that's
+everywhere based on the oiler forward
+
+ align:start position:0%
+everywhere based on the oiler forward
+ 
+
+ align:start position:0%
+everywhere based on the oiler forward
+rule. Is that
+
+ align:start position:0%
+rule. Is that
+ 
+
+ align:start position:0%
+rule. Is that
+clear? So now I have a rule for
+
+ align:start position:0%
+clear? So now I have a rule for
+ 
+
+ align:start position:0%
+clear? So now I have a rule for
+converting an arbitrary CT system into
+
+ align:start position:0%
+converting an arbitrary CT system into
+ 
+
+ align:start position:0%
+converting an arbitrary CT system into
+an equivalent DT system. Equivalent in
+
+ align:start position:0%
+an equivalent DT system. Equivalent in
+ 
+
+ align:start position:0%
+an equivalent DT system. Equivalent in
+the sense of oiler
+
+ align:start position:0%
+the sense of oiler
+ 
+
+ align:start position:0%
+the sense of oiler
+forward and I know that that
+
+ align:start position:0%
+forward and I know that that
+ 
+
+ align:start position:0%
+forward and I know that that
+transformation will hold. But it's even
+
+ align:start position:0%
+transformation will hold. But it's even
+ 
+
+ align:start position:0%
+transformation will hold. But it's even
+better than
+
+ align:start position:0%
+better than
+ 
+
+ align:start position:0%
+better than
+that because I can now say something
+
+ align:start position:0%
+that because I can now say something
+ 
+
+ align:start position:0%
+that because I can now say something
+about the relationship between the
+
+ align:start position:0%
+about the relationship between the
+ 
+
+ align:start position:0%
+about the relationship between the
+position of the pole in the CT
+
+ align:start position:0%
+position of the pole in the CT
+ 
+
+ align:start position:0%
+position of the pole in the CT
+system and the position of the pole in
+
+ align:start position:0%
+system and the position of the pole in
+ 
+
+ align:start position:0%
+system and the position of the pole in
+the dt system because I know this
+
+ align:start position:0%
+the dt system because I know this
+ 
+
+ align:start position:0%
+the dt system because I know this
+original system the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+a I'm going to think of a as being 1 / s
+
+ align:start position:0%
+a I'm going to think of a as being 1 / s
+ 
+
+ align:start position:0%
+a I'm going to think of a as being 1 / s
+that's the applause transform
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+transformation and I want that to be
+
+ align:start position:0%
+transformation and I want that to be
+ 
+
+ align:start position:0%
+transformation and I want that to be
+equivalent
+
+ align:start position:0%
+equivalent
+ 
+
+ align:start position:0%
+equivalent
+according to this map to some
+
+ align:start position:0%
+according to this map to some
+ 
+
+ align:start position:0%
+according to this map to some
+transformation in
+
+ align:start position:0%
+transformation in
+ 
+
+ align:start position:0%
+transformation in
+Z. Right? So I can look at this thing
+
+ align:start position:0%
+Z. Right? So I can look at this thing
+ 
+
+ align:start position:0%
+Z. Right? So I can look at this thing
+and I can see well that system function
+
+ align:start position:0%
+and I can see well that system function
+ 
+
+ align:start position:0%
+and I can see well that system function
+if I represent that whole block by a
+
+ align:start position:0%
+if I represent that whole block by a
+ 
+
+ align:start position:0%
+if I represent that whole block by a
+system function the system
+
+ align:start position:0%
+system function the system
+ 
+
+ align:start position:0%
+system function the system
+transformation is looks like
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that but ours that's the same as 1 /
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+z but that's the same as t over z minus
+
+ align:start position:0%
+z but that's the same as t over z minus
+ 
+
+ align:start position:0%
+z but that's the same as t over z minus
+one.
+
+ align:start position:0%
+one.
+ 
+
+ align:start position:0%
+one.
+Apparently, there's a relationship
+
+ align:start position:0%
+Apparently, there's a relationship
+ 
+
+ align:start position:0%
+Apparently, there's a relationship
+between S and
+
+ align:start position:0%
+between S and
+ 
+
+ align:start position:0%
+between S and
+Z. In fact, Z minus one is ST. Z is 1 +
+
+ align:start position:0%
+Z. In fact, Z minus one is ST. Z is 1 +
+ 
+
+ align:start position:0%
+Z. In fact, Z minus one is ST. Z is 1 +
+ST. Regardless of how of what CT system
+
+ align:start position:0%
+ST. Regardless of how of what CT system
+ 
+
+ align:start position:0%
+ST. Regardless of how of what CT system
+I started
+
+ align:start position:0%
+I started
+ 
+
+ align:start position:0%
+I started
+with, if I use the Oiler forward
+
+ align:start position:0%
+with, if I use the Oiler forward
+ 
+
+ align:start position:0%
+with, if I use the Oiler forward
+relationship to make a DT approximation
+
+ align:start position:0%
+relationship to make a DT approximation
+ 
+
+ align:start position:0%
+relationship to make a DT approximation
+of the integrator, the resulting
+
+ align:start position:0%
+of the integrator, the resulting
+ 
+
+ align:start position:0%
+of the integrator, the resulting
+transformation will always have that
+
+ align:start position:0%
+transformation will always have that
+ 
+
+ align:start position:0%
+transformation will always have that
+property.
+
+ align:start position:0%
+property.
+ 
+
+ align:start position:0%
+property.
+That's exactly what we saw over here.
+
+ align:start position:0%
+That's exactly what we saw over here.
+ 
+
+ align:start position:0%
+That's exactly what we saw over here.
+So we think about the A's in the
+
+ align:start position:0%
+So we think about the A's in the
+ 
+
+ align:start position:0%
+So we think about the A's in the
+original system being mapped to
+
+ align:start position:0%
+original system being mapped to
+ 
+
+ align:start position:0%
+original system being mapped to
+something uh that's a little bit more
+
+ align:start position:0%
+something uh that's a little bit more
+ 
+
+ align:start position:0%
+something uh that's a little bit more
+complicated showed
+
+ align:start position:0%
+complicated showed
+ 
+
+ align:start position:0%
+complicated showed
+here but it's a DT
+
+ align:start position:0%
+here but it's a DT
+ 
+
+ align:start position:0%
+here but it's a DT
+[Music]
+
+ align:start position:0%
+[Music]
+ 
+
+ align:start position:0%
+[Music]
+representation and that DT
+
+ align:start position:0%
+representation and that DT
+ 
+
+ align:start position:0%
+representation and that DT
+representation always has this property
+
+ align:start position:0%
+representation always has this property
+ 
+
+ align:start position:0%
+representation always has this property
+that wherever the poles were in S I can
+
+ align:start position:0%
+that wherever the poles were in S I can
+ 
+
+ align:start position:0%
+that wherever the poles were in S I can
+find where the poles were in Z by taking
+
+ align:start position:0%
+find where the poles were in Z by taking
+ 
+
+ align:start position:0%
+find where the poles were in Z by taking
+Z = 1 plus ST
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+t that's how we get from uh that's how
+
+ align:start position:0%
+t that's how we get from uh that's how
+ 
+
+ align:start position:0%
+t that's how we get from uh that's how
+we get the dependence on t if the
+
+ align:start position:0%
+we get the dependence on t if the
+ 
+
+ align:start position:0%
+we get the dependence on t if the
+original pole was like over here at
+
+ align:start position:0%
+original pole was like over here at
+ 
+
+ align:start position:0%
+original pole was like over here at
+minus1 over
+
+ align:start position:0%
+minus1 over
+ 
+
+ align:start position:0%
+minus1 over
+tow we just put u s = -1 / and we get
+
+ align:start position:0%
+tow we just put u s = -1 / and we get
+ 
+
+ align:start position:0%
+tow we just put u s = -1 / and we get
+precisely this relationship that we got
+
+ align:start position:0%
+precisely this relationship that we got
+ 
+
+ align:start position:0%
+precisely this relationship that we got
+before the 1 plus s t which is what I
+
+ align:start position:0%
+before the 1 plus s t which is what I
+ 
+
+ align:start position:0%
+before the 1 plus s t which is what I
+found here is the same as the 1 minus t
+
+ align:start position:0%
+found here is the same as the 1 minus t
+ 
+
+ align:start position:0%
+found here is the same as the 1 minus t
+over t tow that we found for the
+
+ align:start position:0%
+over t tow that we found for the
+ 
+
+ align:start position:0%
+over t tow that we found for the
+particular example of the leaky tank.
+
+ align:start position:0%
+particular example of the leaky tank.
+ 
+
+ align:start position:0%
+particular example of the leaky tank.
+Yes, I think you mentioned this earlier,
+
+ align:start position:0%
+Yes, I think you mentioned this earlier,
+ 
+
+ align:start position:0%
+Yes, I think you mentioned this earlier,
+but this is purely because of the
+
+ align:start position:0%
+but this is purely because of the
+ 
+
+ align:start position:0%
+but this is purely because of the
+mechanics of the forward oiler. Because
+
+ align:start position:0%
+mechanics of the forward oiler. Because
+ 
+
+ align:start position:0%
+mechanics of the forward oiler. Because
+of forward oiler, this is only true if I
+
+ align:start position:0%
+of forward oiler, this is only true if I
+ 
+
+ align:start position:0%
+of forward oiler, this is only true if I
+decide that all of my
+
+ align:start position:0%
+decide that all of my
+ 
+
+ align:start position:0%
+decide that all of my
+integrators are approximated using the
+
+ align:start position:0%
+integrators are approximated using the
+ 
+
+ align:start position:0%
+integrators are approximated using the
+forward oiler rule. It's absolutely
+
+ align:start position:0%
+forward oiler rule. It's absolutely
+ 
+
+ align:start position:0%
+forward oiler rule. It's absolutely
+true. Okay. And that's an interesting
+
+ align:start position:0%
+true. Okay. And that's an interesting
+ 
+
+ align:start position:0%
+true. Okay. And that's an interesting
+result. What it says is that if I think
+
+ align:start position:0%
+result. What it says is that if I think
+ 
+
+ align:start position:0%
+result. What it says is that if I think
+about how were the poles distributed in
+
+ align:start position:0%
+about how were the poles distributed in
+ 
+
+ align:start position:0%
+about how were the poles distributed in
+the splane, I just use that rule to
+
+ align:start position:0%
+the splane, I just use that rule to
+ 
+
+ align:start position:0%
+the splane, I just use that rule to
+figure out how they'll be distributed in
+
+ align:start position:0%
+figure out how they'll be distributed in
+ 
+
+ align:start position:0%
+figure out how they'll be distributed in
+the z
+
+ align:start position:0%
+the z
+ 
+
+ align:start position:0%
+the z
+plane. The rule says take the splane
+
+ align:start position:0%
+plane. The rule says take the splane
+ 
+
+ align:start position:0%
+plane. The rule says take the splane
+pole, scale it by capital t, and then
+
+ align:start position:0%
+pole, scale it by capital t, and then
+ 
+
+ align:start position:0%
+pole, scale it by capital t, and then
+shift the answer by one.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Well, that's pretty interesting because
+
+ align:start position:0%
+Well, that's pretty interesting because
+ 
+
+ align:start position:0%
+Well, that's pretty interesting because
+that means that there are S's over
+
+ align:start position:0%
+that means that there are S's over
+ 
+
+ align:start position:0%
+that means that there are S's over
+here that when I go through that map end
+
+ align:start position:0%
+here that when I go through that map end
+ 
+
+ align:start position:0%
+here that when I go through that map end
+up outside the unit circle. That's
+
+ align:start position:0%
+up outside the unit circle. That's
+ 
+
+ align:start position:0%
+up outside the unit circle. That's
+exactly what I
+
+ align:start position:0%
+exactly what I
+ 
+
+ align:start position:0%
+exactly what I
+found. That transformation has the
+
+ align:start position:0%
+found. That transformation has the
+ 
+
+ align:start position:0%
+found. That transformation has the
+property that it can map a
+
+ align:start position:0%
+property that it can map a
+ 
+
+ align:start position:0%
+property that it can map a
+stable CT system, a perfectly well-
+
+ align:start position:0%
+stable CT system, a perfectly well-
+ 
+
+ align:start position:0%
+stable CT system, a perfectly well-
+behaved CT system into an oscilly or
+
+ align:start position:0%
+behaved CT system into an oscilly or
+ 
+
+ align:start position:0%
+behaved CT system into an oscilly or
+even a growing divergent DT system. And
+
+ align:start position:0%
+even a growing divergent DT system. And
+ 
+
+ align:start position:0%
+even a growing divergent DT system. And
+you can see that simply because of the
+
+ align:start position:0%
+you can see that simply because of the
+ 
+
+ align:start position:0%
+you can see that simply because of the
+map between uh Z and S. Had S been some
+
+ align:start position:0%
+map between uh Z and S. Had S been some
+ 
+
+ align:start position:0%
+map between uh Z and S. Had S been some
+number over
+
+ align:start position:0%
+number over
+ 
+
+ align:start position:0%
+number over
+here, the the uh response the the um
+
+ align:start position:0%
+here, the the uh response the the um
+ 
+
+ align:start position:0%
+here, the the uh response the the um
+unit impulse response of the CT system
+
+ align:start position:0%
+unit impulse response of the CT system
+ 
+
+ align:start position:0%
+unit impulse response of the CT system
+would have been completely well behaved
+
+ align:start position:0%
+would have been completely well behaved
+ 
+
+ align:start position:0%
+would have been completely well behaved
+e to the minus
+
+ align:start position:0%
+e to the minus
+ 
+
+ align:start position:0%
+e to the minus
+ST but the response to the DT equivalent
+
+ align:start position:0%
+ST but the response to the DT equivalent
+ 
+
+ align:start position:0%
+ST but the response to the DT equivalent
+would be badly behaved because it would
+
+ align:start position:0%
+would be badly behaved because it would
+ 
+
+ align:start position:0%
+would be badly behaved because it would
+have mapped outside the unit
+
+ align:start position:0%
+have mapped outside the unit
+ 
+
+ align:start position:0%
+have mapped outside the unit
+circle. Okay. And as you motivated the
+
+ align:start position:0%
+circle. Okay. And as you motivated the
+ 
+
+ align:start position:0%
+circle. Okay. And as you motivated the
+that's only true because I did oiler
+
+ align:start position:0%
+that's only true because I did oiler
+ 
+
+ align:start position:0%
+that's only true because I did oiler
+forward. I can do precisely the same
+
+ align:start position:0%
+forward. I can do precisely the same
+ 
+
+ align:start position:0%
+forward. I can do precisely the same
+analysis for backward
+
+ align:start position:0%
+analysis for backward
+ 
+
+ align:start position:0%
+analysis for backward
+oiler. Instead of approximating
+
+ align:start position:0%
+oiler. Instead of approximating
+ 
+
+ align:start position:0%
+oiler. Instead of approximating
+derivatives by looking forward in time
+
+ align:start position:0%
+derivatives by looking forward in time
+ 
+
+ align:start position:0%
+derivatives by looking forward in time
+like I did before, I could instead look
+
+ align:start position:0%
+like I did before, I could instead look
+ 
+
+ align:start position:0%
+like I did before, I could instead look
+backward in
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+time. If I look backward in time, it
+
+ align:start position:0%
+time. If I look backward in time, it
+ 
+
+ align:start position:0%
+time. If I look backward in time, it
+looks almost the same. Now I say the
+
+ align:start position:0%
+looks almost the same. Now I say the
+ 
+
+ align:start position:0%
+looks almost the same. Now I say the
+derivative at the time n cap t is n
+
+ align:start position:0%
+derivative at the time n cap t is n
+ 
+
+ align:start position:0%
+derivative at the time n cap t is n
+minus n minus one. Look
+
+ align:start position:0%
+minus n minus one. Look
+ 
+
+ align:start position:0%
+minus n minus one. Look
+backwards. Seems like a trivial
+
+ align:start position:0%
+backwards. Seems like a trivial
+ 
+
+ align:start position:0%
+backwards. Seems like a trivial
+difference. But in fact the answer comes
+
+ align:start position:0%
+difference. But in fact the answer comes
+ 
+
+ align:start position:0%
+difference. But in fact the answer comes
+out completely different. If I look
+
+ align:start position:0%
+out completely different. If I look
+ 
+
+ align:start position:0%
+out completely different. If I look
+backwards in time instead let's see if I
+
+ align:start position:0%
+backwards in time instead let's see if I
+ 
+
+ align:start position:0%
+backwards in time instead let's see if I
+can. So if I look backwards in time
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+instead what I can think about now is
+
+ align:start position:0%
+instead what I can think about now is
+ 
+
+ align:start position:0%
+instead what I can think about now is
+replacing every one of these a operators
+
+ align:start position:0%
+replacing every one of these a operators
+ 
+
+ align:start position:0%
+replacing every one of these a operators
+again. So think about a. A was this
+
+ align:start position:0%
+again. So think about a. A was this
+ 
+
+ align:start position:0%
+again. So think about a. A was this
+thing that Y came out of and Y dot must
+
+ align:start position:0%
+thing that Y came out of and Y dot must
+ 
+
+ align:start position:0%
+thing that Y came out of and Y dot must
+have gone into which was
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+X and now I'm using oiler backward
+
+ align:start position:0%
+X and now I'm using oiler backward
+ 
+
+ align:start position:0%
+X and now I'm using oiler backward
+instead. So now I want um X of
+
+ align:start position:0%
+instead. So now I want um X of
+ 
+
+ align:start position:0%
+instead. So now I want um X of
+N should be look backwards in time. So I
+
+ align:start position:0%
+N should be look backwards in time. So I
+ 
+
+ align:start position:0%
+N should be look backwards in time. So I
+want y of n minus y of n minus
+
+ align:start position:0%
+want y of n minus y of n minus
+ 
+
+ align:start position:0%
+want y of n minus y of n minus
+one /
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+t. So
+
+ align:start position:0%
+t. So
+ 
+
+ align:start position:0%
+t. So
+uh what this says is that I want to take
+
+ align:start position:0%
+uh what this says is that I want to take
+ 
+
+ align:start position:0%
+uh what this says is that I want to take
+y of n should be y of n minus one added
+
+ align:start position:0%
+y of n should be y of n minus one added
+ 
+
+ align:start position:0%
+y of n should be y of n minus one added
+to t * x of
+
+ align:start position:0%
+to t * x of
+ 
+
+ align:start position:0%
+to t * x of
+n. So that's a system that if I started
+
+ align:start position:0%
+n. So that's a system that if I started
+ 
+
+ align:start position:0%
+n. So that's a system that if I started
+with x of n and I wanted to generate y
+
+ align:start position:0%
+with x of n and I wanted to generate y
+ 
+
+ align:start position:0%
+with x of n and I wanted to generate y
+of
+
+ align:start position:0%
+of
+ 
+
+ align:start position:0%
+of
+n, it's almost the same as the other one
+
+ align:start position:0%
+n, it's almost the same as the other one
+ 
+
+ align:start position:0%
+n, it's almost the same as the other one
+except now it says when I want to
+
+ align:start position:0%
+except now it says when I want to
+ 
+
+ align:start position:0%
+except now it says when I want to
+construct y of n, start with a delayed
+
+ align:start position:0%
+construct y of n, start with a delayed
+ 
+
+ align:start position:0%
+construct y of n, start with a delayed
+version of y. How do I get a delayed
+
+ align:start position:0%
+version of y. How do I get a delayed
+ 
+
+ align:start position:0%
+version of y. How do I get a delayed
+version of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+y? Delay it. So I take
+
+ align:start position:0%
+y? Delay it. So I take
+ 
+
+ align:start position:0%
+y? Delay it. So I take
+y and I delay
+
+ align:start position:0%
+y and I delay
+ 
+
+ align:start position:0%
+y and I delay
+it like
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that. What comes out here is y of n
+
+ align:start position:0%
+that. What comes out here is y of n
+ 
+
+ align:start position:0%
+that. What comes out here is y of n
+minus
+
+ align:start position:0%
+minus
+ 
+
+ align:start position:0%
+minus
+one and then y of n is y of n minus one
+
+ align:start position:0%
+one and then y of n is y of n minus one
+ 
+
+ align:start position:0%
+one and then y of n is y of n minus one
+added
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+to t * x
+
+ align:start position:0%
+to t * x
+ 
+
+ align:start position:0%
+to t * x
+ofn. So it's like
+
+ align:start position:0%
+ofn. So it's like
+ 
+
+ align:start position:0%
+ofn. So it's like
+that. It's almost the same, but the math
+
+ align:start position:0%
+that. It's almost the same, but the math
+ 
+
+ align:start position:0%
+that. It's almost the same, but the math
+is different, right? So now I'm
+
+ align:start position:0%
+is different, right? So now I'm
+ 
+
+ align:start position:0%
+is different, right? So now I'm
+replacing my A's, which are always 1 / s
+
+ align:start position:0%
+replacing my A's, which are always 1 / s
+ 
+
+ align:start position:0%
+replacing my A's, which are always 1 / s
+with a system that looks like t going
+
+ align:start position:0%
+with a system that looks like t going
+ 
+
+ align:start position:0%
+with a system that looks like t going
+forward divided by 1 - r in the
+
+ align:start position:0%
+forward divided by 1 - r in the
+ 
+
+ align:start position:0%
+forward divided by 1 - r in the
+bottom. So that's t over 1 - 1 /
+
+ align:start position:0%
+bottom. So that's t over 1 - 1 /
+ 
+
+ align:start position:0%
+bottom. So that's t over 1 - 1 /
+z. So that's zt over z minus
+
+ align:start position:0%
+z. So that's zt over z minus
+ 
+
+ align:start position:0%
+z. So that's zt over z minus
+one. So that means that z minus one
+
+ align:start position:0%
+one. So that means that z minus one
+ 
+
+ align:start position:0%
+one. So that means that z minus one
+now is s t
+
+ align:start position:0%
+now is s t
+ 
+
+ align:start position:0%
+now is s t
+z cross multiplying 1 - s t on z is 1.
+
+ align:start position:0%
+z cross multiplying 1 - s t on z is 1.
+ 
+
+ align:start position:0%
+z cross multiplying 1 - s t on z is 1.
+So z is 1 over 1 - s t. I got something
+
+ align:start position:0%
+So z is 1 over 1 - s t. I got something
+ 
+
+ align:start position:0%
+So z is 1 over 1 - s t. I got something
+that looks completely different. This is
+
+ align:start position:0%
+that looks completely different. This is
+ 
+
+ align:start position:0%
+that looks completely different. This is
+backward
+
+ align:start position:0%
+backward
+ 
+
+ align:start position:0%
+backward
+oiler. This is forward oiler. So the
+
+ align:start position:0%
+oiler. This is forward oiler. So the
+ 
+
+ align:start position:0%
+oiler. This is forward oiler. So the
+answer for forward oiler over here is 1
+
+ align:start position:0%
+answer for forward oiler over here is 1
+ 
+
+ align:start position:0%
+answer for forward oiler over here is 1
+plus
+
+ align:start position:0%
+plus
+ 
+
+ align:start position:0%
+plus
+st. The answer for backward oiler is one
+
+ align:start position:0%
+st. The answer for backward oiler is one
+ 
+
+ align:start position:0%
+st. The answer for backward oiler is one
+one over 1 minus
+
+ align:start position:0%
+one over 1 minus
+ 
+
+ align:start position:0%
+one over 1 minus
+s. Everybody with
+
+ align:start position:0%
+s. Everybody with
+ 
+
+ align:start position:0%
+s. Everybody with
+me? So now when I think about where do
+
+ align:start position:0%
+me? So now when I think about where do
+ 
+
+ align:start position:0%
+me? So now when I think about where do
+the poles
+
+ align:start position:0%
+the poles
+ 
+
+ align:start position:0%
+the poles
+land if I make the backwards oiler
+
+ align:start position:0%
+land if I make the backwards oiler
+ 
+
+ align:start position:0%
+land if I make the backwards oiler
+approximation they fall on this
+
+ align:start position:0%
+approximation they fall on this
+ 
+
+ align:start position:0%
+approximation they fall on this
+relationship instead of the
+
+ align:start position:0%
+relationship instead of the
+ 
+
+ align:start position:0%
+relationship instead of the
+previous. And the interesting thing
+
+ align:start position:0%
+previous. And the interesting thing
+ 
+
+ align:start position:0%
+previous. And the interesting thing
+about that relationship is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that if you think about the way this
+
+ align:start position:0%
+that if you think about the way this
+ 
+
+ align:start position:0%
+that if you think about the way this
+works, every point in the left half
+
+ align:start position:0%
+works, every point in the left half
+ 
+
+ align:start position:0%
+works, every point in the left half
+plane of
+
+ align:start position:0%
+plane of
+ 
+
+ align:start position:0%
+plane of
+S according to this
+
+ align:start position:0%
+S according to this
+ 
+
+ align:start position:0%
+S according to this
+map ends up inside a little circle in
+
+ align:start position:0%
+map ends up inside a little circle in
+ 
+
+ align:start position:0%
+map ends up inside a little circle in
+the Z domain.
+
+ align:start position:0%
+the Z domain.
+ 
+
+ align:start position:0%
+the Z domain.
+The entire left half
+
+ align:start position:0%
+The entire left half
+ 
+
+ align:start position:0%
+The entire left half
+plane maps into the circle that's shaded
+
+ align:start position:0%
+plane maps into the circle that's shaded
+ 
+
+ align:start position:0%
+plane maps into the circle that's shaded
+in the right. If you just make a
+
+ align:start position:0%
+in the right. If you just make a
+ 
+
+ align:start position:0%
+in the right. If you just make a
+picture, if you just think
+
+ align:start position:0%
+picture, if you just think
+ 
+
+ align:start position:0%
+picture, if you just think
+about plug in S= 1, where does Z happen?
+
+ align:start position:0%
+about plug in S= 1, where does Z happen?
+ 
+
+ align:start position:0%
+about plug in S= 1, where does Z happen?
+Plug in S= minus1, where's the new Z?
+
+ align:start position:0%
+Plug in S= minus1, where's the new Z?
+ 
+
+ align:start position:0%
+Plug in S= minus1, where's the new Z?
+You plug in S= 1 /T, where's the new Z?
+
+ align:start position:0%
+You plug in S= 1 /T, where's the new Z?
+ 
+
+ align:start position:0%
+You plug in S= 1 /T, where's the new Z?
+All of the values in the left half plane
+
+ align:start position:0%
+All of the values in the left half plane
+ 
+
+ align:start position:0%
+All of the values in the left half plane
+for S map inside a small
+
+ align:start position:0%
+for S map inside a small
+ 
+
+ align:start position:0%
+for S map inside a small
+circle in the Z
+
+ align:start position:0%
+circle in the Z
+ 
+
+ align:start position:0%
+circle in the Z
+plane. Which means
+
+ align:start position:0%
+plane. Which means
+ 
+
+ align:start position:0%
+plane. Which means
+that if the original system had a pole
+
+ align:start position:0%
+that if the original system had a pole
+ 
+
+ align:start position:0%
+that if the original system had a pole
+anywhere in the left half plane,
+
+ align:start position:0%
+anywhere in the left half plane,
+ 
+
+ align:start position:0%
+anywhere in the left half plane,
+remember left half planes, leftsided,
+
+ align:start position:0%
+remember left half planes, leftsided,
+ 
+
+ align:start position:0%
+remember left half planes, leftsided,
+we're thinking that those are the kinds
+
+ align:start position:0%
+we're thinking that those are the kinds
+ 
+
+ align:start position:0%
+we're thinking that those are the kinds
+of systems whose uh unit sample unit
+
+ align:start position:0%
+of systems whose uh unit sample unit
+ 
+
+ align:start position:0%
+of systems whose uh unit sample unit
+impulse responses converge toward zero.
+
+ align:start position:0%
+impulse responses converge toward zero.
+ 
+
+ align:start position:0%
+impulse responses converge toward zero.
+If you had a system who that had poles
+
+ align:start position:0%
+If you had a system who that had poles
+ 
+
+ align:start position:0%
+If you had a system who that had poles
+in the left half plane and you do the
+
+ align:start position:0%
+in the left half plane and you do the
+ 
+
+ align:start position:0%
+in the left half plane and you do the
+backwards oiler transformation, you're
+
+ align:start position:0%
+backwards oiler transformation, you're
+ 
+
+ align:start position:0%
+backwards oiler transformation, you're
+guaranteed to get a system that has
+
+ align:start position:0%
+guaranteed to get a system that has
+ 
+
+ align:start position:0%
+guaranteed to get a system that has
+poles inside the unit
+
+ align:start position:0%
+poles inside the unit
+ 
+
+ align:start position:0%
+poles inside the unit
+circle. In fact, they're in a smaller
+
+ align:start position:0%
+circle. In fact, they're in a smaller
+ 
+
+ align:start position:0%
+circle. In fact, they're in a smaller
+circle than the unit
+
+ align:start position:0%
+circle than the unit
+ 
+
+ align:start position:0%
+circle than the unit
+circle. Okay, everybody sort of know
+
+ align:start position:0%
+circle. Okay, everybody sort of know
+ 
+
+ align:start position:0%
+circle. Okay, everybody sort of know
+what I'm talking about?
+
+ align:start position:0%
+what I'm talking about?
+ 
+
+ align:start position:0%
+what I'm talking about?
+So this is the idea of thinking about
+
+ align:start position:0%
+So this is the idea of thinking about
+ 
+
+ align:start position:0%
+So this is the idea of thinking about
+not relationships among DT
+
+ align:start position:0%
+not relationships among DT
+ 
+
+ align:start position:0%
+not relationships among DT
+representations or representations among
+
+ align:start position:0%
+representations or representations among
+ 
+
+ align:start position:0%
+representations or representations among
+CT systems but relations between CT and
+
+ align:start position:0%
+CT systems but relations between CT and
+ 
+
+ align:start position:0%
+CT systems but relations between CT and
+DT. It's because we can cast each of
+
+ align:start position:0%
+DT. It's because we can cast each of
+ 
+
+ align:start position:0%
+DT. It's because we can cast each of
+those kinds of systems into a polomial
+
+ align:start position:0%
+those kinds of systems into a polomial
+ 
+
+ align:start position:0%
+those kinds of systems into a polomial
+representation that we can make a
+
+ align:start position:0%
+representation that we can make a
+ 
+
+ align:start position:0%
+representation that we can make a
+correspondence between the CT system and
+
+ align:start position:0%
+correspondence between the CT system and
+ 
+
+ align:start position:0%
+correspondence between the CT system and
+the DT approximation. I'll talk about
+
+ align:start position:0%
+the DT approximation. I'll talk about
+ 
+
+ align:start position:0%
+the DT approximation. I'll talk about
+just one more and that's the trapezoid
+
+ align:start position:0%
+just one more and that's the trapezoid
+ 
+
+ align:start position:0%
+just one more and that's the trapezoid
+rule which is what you did in homework
+
+ align:start position:0%
+rule which is what you did in homework
+ 
+
+ align:start position:0%
+rule which is what you did in homework
+two. You may remember homework two right
+
+ align:start position:0%
+two. You may remember homework two right
+ 
+
+ align:start position:0%
+two. You may remember homework two right
+since it was due like yesterday. Uh so
+
+ align:start position:0%
+since it was due like yesterday. Uh so
+ 
+
+ align:start position:0%
+since it was due like yesterday. Uh so
+the last problem in homework two had to
+
+ align:start position:0%
+the last problem in homework two had to
+ 
+
+ align:start position:0%
+the last problem in homework two had to
+do with finding a numerical
+
+ align:start position:0%
+do with finding a numerical
+ 
+
+ align:start position:0%
+do with finding a numerical
+approximation to the mass and spring
+
+ align:start position:0%
+approximation to the mass and spring
+ 
+
+ align:start position:0%
+approximation to the mass and spring
+system. And if you remember we did three
+
+ align:start position:0%
+system. And if you remember we did three
+ 
+
+ align:start position:0%
+system. And if you remember we did three
+of them. Those three were actually
+
+ align:start position:0%
+of them. Those three were actually
+ 
+
+ align:start position:0%
+of them. Those three were actually
+forward oiler, backward oiler and
+
+ align:start position:0%
+forward oiler, backward oiler and
+ 
+
+ align:start position:0%
+forward oiler, backward oiler and
+trapezoidal rule.
+
+ align:start position:0%
+trapezoidal rule.
+ 
+
+ align:start position:0%
+trapezoidal rule.
+trapezoidal rule says okay I didn't like
+
+ align:start position:0%
+trapezoidal rule says okay I didn't like
+ 
+
+ align:start position:0%
+trapezoidal rule says okay I didn't like
+this idea of looking
+
+ align:start position:0%
+this idea of looking
+ 
+
+ align:start position:0%
+this idea of looking
+forward that seems
+
+ align:start position:0%
+forward that seems
+ 
+
+ align:start position:0%
+forward that seems
+anti-ymmetric what's special about
+
+ align:start position:0%
+anti-ymmetric what's special about
+ 
+
+ align:start position:0%
+anti-ymmetric what's special about
+forwards or backwards that's also
+
+ align:start position:0%
+forwards or backwards that's also
+ 
+
+ align:start position:0%
+forwards or backwards that's also
+treating backwards special I want to
+
+ align:start position:0%
+treating backwards special I want to
+ 
+
+ align:start position:0%
+treating backwards special I want to
+treat it symmetric in time that's what
+
+ align:start position:0%
+treat it symmetric in time that's what
+ 
+
+ align:start position:0%
+treat it symmetric in time that's what
+the centered difference approximation
+
+ align:start position:0%
+the centered difference approximation
+ 
+
+ align:start position:0%
+the centered difference approximation
+did the center difference approximation
+
+ align:start position:0%
+did the center difference approximation
+ 
+
+ align:start position:0%
+did the center difference approximation
+in homework two was based on a
+
+ align:start position:0%
+in homework two was based on a
+ 
+
+ align:start position:0%
+in homework two was based on a
+trapezoidal rule the trapezoidal rule
+
+ align:start position:0%
+trapezoidal rule the trapezoidal rule
+ 
+
+ align:start position:0%
+trapezoidal rule the trapezoidal rule
+says okay let me approximate my DT
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+output. Let me let me think about a
+
+ align:start position:0%
+output. Let me let me think about a
+ 
+
+ align:start position:0%
+output. Let me let me think about a
+sequence of samples in a DT output. Y
+
+ align:start position:0%
+sequence of samples in a DT output. Y
+ 
+
+ align:start position:0%
+sequence of samples in a DT output. Y
+then let me force the differential
+
+ align:start position:0%
+then let me force the differential
+ 
+
+ align:start position:0%
+then let me force the differential
+equation to be true at every point
+
+ align:start position:0%
+equation to be true at every point
+ 
+
+ align:start position:0%
+equation to be true at every point
+between
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+samples in the forward oiler and the
+
+ align:start position:0%
+samples in the forward oiler and the
+ 
+
+ align:start position:0%
+samples in the forward oiler and the
+backward. We forced the differential
+
+ align:start position:0%
+backward. We forced the differential
+ 
+
+ align:start position:0%
+backward. We forced the differential
+equation to be true at integers n.
+
+ align:start position:0%
+equation to be true at integers n.
+ 
+
+ align:start position:0%
+equation to be true at integers n.
+that made us compute derivatives by
+
+ align:start position:0%
+that made us compute derivatives by
+ 
+
+ align:start position:0%
+that made us compute derivatives by
+looking forward or backwards. In a
+
+ align:start position:0%
+looking forward or backwards. In a
+ 
+
+ align:start position:0%
+looking forward or backwards. In a
+trapezoidal rule, we force the
+
+ align:start position:0%
+trapezoidal rule, we force the
+ 
+
+ align:start position:0%
+trapezoidal rule, we force the
+differential equation to be true between
+
+ align:start position:0%
+differential equation to be true between
+ 
+
+ align:start position:0%
+differential equation to be true between
+samples. Then we say okay the the signal
+
+ align:start position:0%
+samples. Then we say okay the the signal
+ 
+
+ align:start position:0%
+samples. Then we say okay the the signal
+yc should be the average of those
+
+ align:start position:0%
+yc should be the average of those
+ 
+
+ align:start position:0%
+yc should be the average of those
+samples and the derivative should be the
+
+ align:start position:0%
+samples and the derivative should be the
+ 
+
+ align:start position:0%
+samples and the derivative should be the
+difference of the two samples divided by
+
+ align:start position:0%
+difference of the two samples divided by
+ 
+
+ align:start position:0%
+difference of the two samples divided by
+t. So they're
+
+ align:start position:0%
+t. So they're
+ 
+
+ align:start position:0%
+t. So they're
+centered. Everybody see that? So, we're
+
+ align:start position:0%
+centered. Everybody see that? So, we're
+ 
+
+ align:start position:0%
+centered. Everybody see that? So, we're
+going to force the differential equation
+
+ align:start position:0%
+going to force the differential equation
+ 
+
+ align:start position:0%
+going to force the differential equation
+to be true at points between the samples
+
+ align:start position:0%
+to be true at points between the samples
+ 
+
+ align:start position:0%
+to be true at points between the samples
+of the difference
+
+ align:start position:0%
+of the difference
+ 
+
+ align:start position:0%
+of the difference
+equation. And that's going to give me a
+
+ align:start position:0%
+equation. And that's going to give me a
+ 
+
+ align:start position:0%
+equation. And that's going to give me a
+different kind of relationship that
+
+ align:start position:0%
+different kind of relationship that
+ 
+
+ align:start position:0%
+different kind of relationship that
+looks strikingly the same as these kinds
+
+ align:start position:0%
+looks strikingly the same as these kinds
+ 
+
+ align:start position:0%
+looks strikingly the same as these kinds
+of
+
+ align:start position:0%
+of
+ 
+
+ align:start position:0%
+of
+relationships. Okay. So now I'm going to
+
+ align:start position:0%
+relationships. Okay. So now I'm going to
+ 
+
+ align:start position:0%
+relationships. Okay. So now I'm going to
+say
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um that I would like to
+
+ align:start position:0%
+um that I would like to
+ 
+
+ align:start position:0%
+um that I would like to
+have a which maps y dot is
+
+ align:start position:0%
+have a which maps y dot is
+ 
+
+ align:start position:0%
+have a which maps y dot is
+x except now what I'm going to want to
+
+ align:start position:0%
+x except now what I'm going to want to
+ 
+
+ align:start position:0%
+x except now what I'm going to want to
+say is that
+
+ align:start position:0%
+say is that
+ 
+
+ align:start position:0%
+say is that
+uh x which I will represent as the
+
+ align:start position:0%
+uh x which I will represent as the
+ 
+
+ align:start position:0%
+uh x which I will represent as the
+average of the nth and n minus
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+one should be constrained to be the
+
+ align:start position:0%
+one should be constrained to be the
+ 
+
+ align:start position:0%
+one should be constrained to be the
+derivative of this guy which I will
+
+ align:start position:0%
+derivative of this guy which I will
+ 
+
+ align:start position:0%
+derivative of this guy which I will
+do by looking at the corresponding
+
+ align:start position:0%
+do by looking at the corresponding
+ 
+
+ align:start position:0%
+do by looking at the corresponding
+values of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+y.
+
+ align:start position:0%
+y.
+ 
+
+ align:start position:0%
+y.
+Okay. And so that gives me a different
+
+ align:start position:0%
+Okay. And so that gives me a different
+ 
+
+ align:start position:0%
+Okay. And so that gives me a different
+way of doing the approximation. I get y
+
+ align:start position:0%
+way of doing the approximation. I get y
+ 
+
+ align:start position:0%
+way of doing the approximation. I get y
+of n should be y of n minus one
+
+ align:start position:0%
+of n should be y of n minus one
+ 
+
+ align:start position:0%
+of n should be y of n minus one
+uh let's see plus t / 2 x of n + x of n
+
+ align:start position:0%
+uh let's see plus t / 2 x of n + x of n
+ 
+
+ align:start position:0%
+uh let's see plus t / 2 x of n + x of n
+minus
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+one. Just a different rule for how to do
+
+ align:start position:0%
+one. Just a different rule for how to do
+ 
+
+ align:start position:0%
+one. Just a different rule for how to do
+the derivative. That's all I've done.
+
+ align:start position:0%
+the derivative. That's all I've done.
+ 
+
+ align:start position:0%
+the derivative. That's all I've done.
+But it gives me a different kind of a
+
+ align:start position:0%
+But it gives me a different kind of a
+ 
+
+ align:start position:0%
+But it gives me a different kind of a
+system. Now I want to have x of n go
+
+ align:start position:0%
+system. Now I want to have x of n go
+ 
+
+ align:start position:0%
+system. Now I want to have x of n go
+into something that I will make my new a
+
+ align:start position:0%
+into something that I will make my new a
+ 
+
+ align:start position:0%
+into something that I will make my new a
+boxes. Uh to compute y of n I should
+
+ align:start position:0%
+boxes. Uh to compute y of n I should
+ 
+
+ align:start position:0%
+boxes. Uh to compute y of n I should
+have a delayed version. Well that's
+
+ align:start position:0%
+have a delayed version. Well that's
+ 
+
+ align:start position:0%
+have a delayed version. Well that's
+easy. I make one of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+those and y of n should be the sum of
+
+ align:start position:0%
+those and y of n should be the sum of
+ 
+
+ align:start position:0%
+those and y of n should be the sum of
+the delayed
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+version and t over
+
+ align:start position:0%
+version and t over
+ 
+
+ align:start position:0%
+version and t over
+two times a delayed version of x. So
+
+ align:start position:0%
+two times a delayed version of x. So
+ 
+
+ align:start position:0%
+two times a delayed version of x. So
+I'll have to do
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this. So now I have the sum of x and a
+
+ align:start position:0%
+this. So now I have the sum of x and a
+ 
+
+ align:start position:0%
+this. So now I have the sum of x and a
+delayed version of x and I put that
+
+ align:start position:0%
+delayed version of x and I put that
+ 
+
+ align:start position:0%
+delayed version of x and I put that
+through t
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+/2. So here's my new discrete
+
+ align:start position:0%
+/2. So here's my new discrete
+ 
+
+ align:start position:0%
+/2. So here's my new discrete
+approximation to the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+accumulator and I do just the same thing
+
+ align:start position:0%
+accumulator and I do just the same thing
+ 
+
+ align:start position:0%
+accumulator and I do just the same thing
+I did before. I say
+
+ align:start position:0%
+I did before. I say
+ 
+
+ align:start position:0%
+I did before. I say
+um what's the value of what's the
+
+ align:start position:0%
+um what's the value of what's the
+ 
+
+ align:start position:0%
+um what's the value of what's the
+relationship between S and Z.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+So my a which is the same as 1 / s now
+
+ align:start position:0%
+So my a which is the same as 1 / s now
+ 
+
+ align:start position:0%
+So my a which is the same as 1 / s now
+becomes that block diagram which looks
+
+ align:start position:0%
+becomes that block diagram which looks
+ 
+
+ align:start position:0%
+becomes that block diagram which looks
+like t over two uh looks like r +
+
+ align:start position:0%
+like t over two uh looks like r +
+ 
+
+ align:start position:0%
+like t over two uh looks like r +
+one see 1 plus r. Let's do it the other
+
+ align:start position:0%
+one see 1 plus r. Let's do it the other
+ 
+
+ align:start position:0%
+one see 1 plus r. Let's do it the other
+way. So t over 2 1 plus
+
+ align:start position:0%
+way. So t over 2 1 plus
+ 
+
+ align:start position:0%
+way. So t over 2 1 plus
+r 1 minus
+
+ align:start position:0%
+r 1 minus
+ 
+
+ align:start position:0%
+r 1 minus
+r. So t over two from here, 1 plus r
+
+ align:start position:0%
+r. So t over two from here, 1 plus r
+ 
+
+ align:start position:0%
+r. So t over two from here, 1 plus r
+from here, one over 1 minus r from
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+there. Uh which I can convert into z and
+
+ align:start position:0%
+there. Uh which I can convert into z and
+ 
+
+ align:start position:0%
+there. Uh which I can convert into z and
+I'll get t / 2 z + 1 / z minus
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+one. I don't think I made any mistakes
+
+ align:start position:0%
+one. I don't think I made any mistakes
+ 
+
+ align:start position:0%
+one. I don't think I made any mistakes
+yet.
+
+ align:start position:0%
+yet.
+ 
+
+ align:start position:0%
+yet.
+So then I get
+
+ align:start position:0%
+So then I get
+ 
+
+ align:start position:0%
+So then I get
+um so z + one uh z minus
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+one bring that over there bring that
+
+ align:start position:0%
+one bring that over there bring that
+ 
+
+ align:start position:0%
+one bring that over there bring that
+over there st over 2 z +
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+one and now bring the z's over here 1
+
+ align:start position:0%
+one and now bring the z's over here 1
+ 
+
+ align:start position:0%
+one and now bring the z's over here 1
+minus s t over 2 operates on z to give
+
+ align:start position:0%
+minus s t over 2 operates on z to give
+ 
+
+ align:start position:0%
+minus s t over 2 operates on z to give
+me
+
+ align:start position:0%
+me
+ 
+
+ align:start position:0%
+me
+1 + s t /
+
+ align:start position:0%
+1 + s t /
+ 
+
+ align:start position:0%
+1 + s t /
+2. So
+
+ align:start position:0%
+2. So
+ 
+
+ align:start position:0%
+2. So
+z is 1 + s t /2 over 1 - s t
+
+ align:start position:0%
+z is 1 + s t /2 over 1 - s t
+ 
+
+ align:start position:0%
+z is 1 + s t /2 over 1 - s t
+over2. So that's my new transformation
+
+ align:start position:0%
+over2. So that's my new transformation
+ 
+
+ align:start position:0%
+over2. So that's my new transformation
+based on the trapezoidal
+
+ align:start position:0%
+based on the trapezoidal
+ 
+
+ align:start position:0%
+based on the trapezoidal
+rule which is showed here. Hopefully
+
+ align:start position:0%
+rule which is showed here. Hopefully
+ 
+
+ align:start position:0%
+rule which is showed here. Hopefully
+they match. So z maps to 1 + s t /2 / 1
+
+ align:start position:0%
+they match. So z maps to 1 + s t /2 / 1
+ 
+
+ align:start position:0%
+they match. So z maps to 1 + s t /2 / 1
+- s t over2. And the interesting thing
+
+ align:start position:0%
+- s t over2. And the interesting thing
+ 
+
+ align:start position:0%
+- s t over2. And the interesting thing
+about that transformation is that it
+
+ align:start position:0%
+about that transformation is that it
+ 
+
+ align:start position:0%
+about that transformation is that it
+maps the entire left half plane of
+
+ align:start position:0%
+maps the entire left half plane of
+ 
+
+ align:start position:0%
+maps the entire left half plane of
+S precisely into the unit
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+circle. That was the reason that the
+
+ align:start position:0%
+circle. That was the reason that the
+ 
+
+ align:start position:0%
+circle. That was the reason that the
+trapezoidal rule worked so much better
+
+ align:start position:0%
+trapezoidal rule worked so much better
+ 
+
+ align:start position:0%
+trapezoidal rule worked so much better
+on the problems that you tried in
+
+ align:start position:0%
+on the problems that you tried in
+ 
+
+ align:start position:0%
+on the problems that you tried in
+homework two.
+
+ align:start position:0%
+homework two.
+ 
+
+ align:start position:0%
+homework two.
+So if the pole starts out being
+
+ align:start position:0%
+So if the pole starts out being
+ 
+
+ align:start position:0%
+So if the pole starts out being
+real so that it's someplace in the s
+
+ align:start position:0%
+real so that it's someplace in the s
+ 
+
+ align:start position:0%
+real so that it's someplace in the s
+plane on this red
+
+ align:start position:0%
+plane on this red
+ 
+
+ align:start position:0%
+plane on this red
+arrow, oiler forward gave us a pole in
+
+ align:start position:0%
+arrow, oiler forward gave us a pole in
+ 
+
+ align:start position:0%
+arrow, oiler forward gave us a pole in
+the z plane that could be if t is big
+
+ align:start position:0%
+the z plane that could be if t is big
+ 
+
+ align:start position:0%
+the z plane that could be if t is big
+enough outside the unit
+
+ align:start position:0%
+enough outside the unit
+ 
+
+ align:start position:0%
+enough outside the unit
+circle. In the oiler backwards method,
+
+ align:start position:0%
+circle. In the oiler backwards method,
+ 
+
+ align:start position:0%
+circle. In the oiler backwards method,
+it always lands someplace in the unit
+
+ align:start position:0%
+it always lands someplace in the unit
+ 
+
+ align:start position:0%
+it always lands someplace in the unit
+circle. In the trapezoidal rule, it
+
+ align:start position:0%
+circle. In the trapezoidal rule, it
+ 
+
+ align:start position:0%
+circle. In the trapezoidal rule, it
+lands someplace in the unit
+
+ align:start position:0%
+lands someplace in the unit
+ 
+
+ align:start position:0%
+lands someplace in the unit
+circle. But in the mass spring problem,
+
+ align:start position:0%
+circle. But in the mass spring problem,
+ 
+
+ align:start position:0%
+circle. But in the mass spring problem,
+the poles were on the imaginary
+
+ align:start position:0%
+the poles were on the imaginary
+ 
+
+ align:start position:0%
+the poles were on the imaginary
+axis, which means that in the oiler
+
+ align:start position:0%
+axis, which means that in the oiler
+ 
+
+ align:start position:0%
+axis, which means that in the oiler
+forward method, the poles went outside
+
+ align:start position:0%
+forward method, the poles went outside
+ 
+
+ align:start position:0%
+forward method, the poles went outside
+the unit circle. That's the reason the
+
+ align:start position:0%
+the unit circle. That's the reason the
+ 
+
+ align:start position:0%
+the unit circle. That's the reason the
+solution to the mass spring problem
+
+ align:start position:0%
+solution to the mass spring problem
+ 
+
+ align:start position:0%
+solution to the mass spring problem
+diverged.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+In the oiler backward method, the poles
+
+ align:start position:0%
+In the oiler backward method, the poles
+ 
+
+ align:start position:0%
+In the oiler backward method, the poles
+that were on the J omega axis mapped to
+
+ align:start position:0%
+that were on the J omega axis mapped to
+ 
+
+ align:start position:0%
+that were on the J omega axis mapped to
+the perimeter of this inside circle.
+
+ align:start position:0%
+the perimeter of this inside circle.
+ 
+
+ align:start position:0%
+the perimeter of this inside circle.
+That's why they converged even though
+
+ align:start position:0%
+That's why they converged even though
+ 
+
+ align:start position:0%
+That's why they converged even though
+the mass spring system should have
+
+ align:start position:0%
+the mass spring system should have
+ 
+
+ align:start position:0%
+the mass spring system should have
+oscillated
+
+ align:start position:0%
+oscillated
+ 
+
+ align:start position:0%
+oscillated
+forever in the solution that you did
+
+ align:start position:0%
+forever in the solution that you did
+ 
+
+ align:start position:0%
+forever in the solution that you did
+with oiler backwards. It converged and
+
+ align:start position:0%
+with oiler backwards. It converged and
+ 
+
+ align:start position:0%
+with oiler backwards. It converged and
+that's because it ma the method maps
+
+ align:start position:0%
+that's because it ma the method maps
+ 
+
+ align:start position:0%
+that's because it ma the method maps
+poles on the J omega axis inside the
+
+ align:start position:0%
+poles on the J omega axis inside the
+ 
+
+ align:start position:0%
+poles on the J omega axis inside the
+unit circle. That's not what we want.
+
+ align:start position:0%
+unit circle. That's not what we want.
+ 
+
+ align:start position:0%
+unit circle. That's not what we want.
+What we want for the mass spring system
+
+ align:start position:0%
+What we want for the mass spring system
+ 
+
+ align:start position:0%
+What we want for the mass spring system
+is to map the J omega poles directly
+
+ align:start position:0%
+is to map the J omega poles directly
+ 
+
+ align:start position:0%
+is to map the J omega poles directly
+onto the unit circle so that pure
+
+ align:start position:0%
+onto the unit circle so that pure
+ 
+
+ align:start position:0%
+onto the unit circle so that pure
+oscillations over here corresponds to
+
+ align:start position:0%
+oscillations over here corresponds to
+ 
+
+ align:start position:0%
+oscillations over here corresponds to
+pure oscillations over there and that's
+
+ align:start position:0%
+pure oscillations over there and that's
+ 
+
+ align:start position:0%
+pure oscillations over there and that's
+exactly what the trapezoidal rule
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+does. Okay. So the point then the and
+
+ align:start position:0%
+does. Okay. So the point then the and
+ 
+
+ align:start position:0%
+does. Okay. So the point then the and
+this was the solution to that homework
+
+ align:start position:0%
+this was the solution to that homework
+ 
+
+ align:start position:0%
+this was the solution to that homework
+problem.
+
+ align:start position:0%
+problem.
+ 
+
+ align:start position:0%
+problem.
+So the point is that not only are we
+
+ align:start position:0%
+So the point is that not only are we
+ 
+
+ align:start position:0%
+So the point is that not only are we
+interested in figuring out relationships
+
+ align:start position:0%
+interested in figuring out relationships
+ 
+
+ align:start position:0%
+interested in figuring out relationships
+among the different representations for
+
+ align:start position:0%
+among the different representations for
+ 
+
+ align:start position:0%
+among the different representations for
+CT systems and among the different
+
+ align:start position:0%
+CT systems and among the different
+ 
+
+ align:start position:0%
+CT systems and among the different
+representations for DT systems, there's
+
+ align:start position:0%
+representations for DT systems, there's
+ 
+
+ align:start position:0%
+representations for DT systems, there's
+a lot of insight that you can get,
+
+ align:start position:0%
+a lot of insight that you can get,
+ 
+
+ align:start position:0%
+a lot of insight that you can get,
+especially into things like numerical
+
+ align:start position:0%
+especially into things like numerical
+ 
+
+ align:start position:0%
+especially into things like numerical
+approximations by thinking about how the
+
+ align:start position:0%
+approximations by thinking about how the
+ 
+
+ align:start position:0%
+approximations by thinking about how the
+relationships in one domain map to the
\ No newline at end of file
diff --git a/qEBi0K5wfOs.txt b/qEBi0K5wfOs.txt
new file mode 100644
index 0000000000000000000000000000000000000000..839efdaf2536689d7c5a8780a5e51acc43cea8ee
--- /dev/null
+++ b/qEBi0K5wfOs.txt
@@ -0,0 +1,1715 @@
+align:start position:0%
+ 
+hello welcome back to recitation I'm
+
+ align:start position:0%
+hello welcome back to recitation I'm
+ 
+
+ align:start position:0%
+hello welcome back to recitation I'm
+sure you're becoming more and more
+
+ align:start position:0%
+sure you're becoming more and more
+ 
+
+ align:start position:0%
+sure you're becoming more and more
+familiar with the determinants of
+
+ align:start position:0%
+familiar with the determinants of
+ 
+
+ align:start position:0%
+familiar with the determinants of
+matrices in the lecture we also learned
+
+ align:start position:0%
+matrices in the lecture we also learned
+ 
+
+ align:start position:0%
+matrices in the lecture we also learned
+the geometric interpretation of the
+
+ align:start position:0%
+the geometric interpretation of the
+ 
+
+ align:start position:0%
+the geometric interpretation of the
+determinant the absolute value of the
+
+ align:start position:0%
+determinant the absolute value of the
+ 
+
+ align:start position:0%
+determinant the absolute value of the
+determinant of a matrix is simply equal
+
+ align:start position:0%
+determinant of a matrix is simply equal
+ 
+
+ align:start position:0%
+determinant of a matrix is simply equal
+to the volume of the parallelepiped
+
+ align:start position:0%
+to the volume of the parallelepiped
+ 
+
+ align:start position:0%
+to the volume of the parallelepiped
+spent by the row vectors of the matrix
+
+ align:start position:0%
+spent by the row vectors of the matrix
+ 
+
+ align:start position:0%
+spent by the row vectors of the matrix
+so today we're going to apply this fact
+
+ align:start position:0%
+so today we're going to apply this fact
+ 
+
+ align:start position:0%
+so today we're going to apply this fact
+to solve the following problem I have a
+
+ align:start position:0%
+to solve the following problem I have a
+ 
+
+ align:start position:0%
+to solve the following problem I have a
+tetrahedron T in this 3d space and the
+
+ align:start position:0%
+tetrahedron T in this 3d space and the
+ 
+
+ align:start position:0%
+tetrahedron T in this 3d space and the
+vertices of T are given by au which is
+
+ align:start position:0%
+vertices of T are given by au which is
+ 
+
+ align:start position:0%
+vertices of T are given by au which is
+the origin a 1 a 2 and a 3 so I have
+
+ align:start position:0%
+the origin a 1 a 2 and a 3 so I have
+ 
+
+ align:start position:0%
+the origin a 1 a 2 and a 3 so I have
+highlighted this tetrahedron using the
+
+ align:start position:0%
+highlighted this tetrahedron using the
+ 
+
+ align:start position:0%
+highlighted this tetrahedron using the
+blue chalk so this is T and our first
+
+ align:start position:0%
+blue chalk so this is T and our first
+ 
+
+ align:start position:0%
+blue chalk so this is T and our first
+goal is to compute the volume of T using
+
+ align:start position:0%
+goal is to compute the volume of T using
+ 
+
+ align:start position:0%
+goal is to compute the volume of T using
+the determinant and the second part is
+
+ align:start position:0%
+the determinant and the second part is
+ 
+
+ align:start position:0%
+the determinant and the second part is
+if I fix a 1 and a 2
+
+ align:start position:0%
+if I fix a 1 and a 2
+ 
+
+ align:start position:0%
+if I fix a 1 and a 2
+but moving a 3 to another point a 3
+
+ align:start position:0%
+but moving a 3 to another point a 3
+ 
+
+ align:start position:0%
+but moving a 3 to another point a 3
+prime which is given by this coordinate
+
+ align:start position:0%
+prime which is given by this coordinate
+ 
+
+ align:start position:0%
+prime which is given by this coordinate
+I ask you to compute the volume again ok
+
+ align:start position:0%
+I ask you to compute the volume again ok
+ 
+
+ align:start position:0%
+I ask you to compute the volume again ok
+so since we want to use the fact that
+
+ align:start position:0%
+so since we want to use the fact that
+ 
+
+ align:start position:0%
+so since we want to use the fact that
+the determinant is related to the volume
+
+ align:start position:0%
+the determinant is related to the volume
+ 
+
+ align:start position:0%
+the determinant is related to the volume
+we have to figure out that which volume
+
+ align:start position:0%
+we have to figure out that which volume
+ 
+
+ align:start position:0%
+we have to figure out that which volume
+we should be looking at we know that the
+
+ align:start position:0%
+we should be looking at we know that the
+ 
+
+ align:start position:0%
+we should be looking at we know that the
+determinant is related the volume of a
+
+ align:start position:0%
+determinant is related the volume of a
+ 
+
+ align:start position:0%
+determinant is related the volume of a
+parallelepiped but here we only have a
+
+ align:start position:0%
+parallelepiped but here we only have a
+ 
+
+ align:start position:0%
+parallelepiped but here we only have a
+tetrahedron so the first goal should be
+
+ align:start position:0%
+tetrahedron so the first goal should be
+ 
+
+ align:start position:0%
+tetrahedron so the first goal should be
+to find out which parapet you should be
+
+ align:start position:0%
+to find out which parapet you should be
+ 
+
+ align:start position:0%
+to find out which parapet you should be
+working with ok why don't she hit the
+
+ align:start position:0%
+working with ok why don't she hit the
+ 
+
+ align:start position:0%
+working with ok why don't she hit the
+pause try to work it out yourself you
+
+ align:start position:0%
+pause try to work it out yourself you
+ 
+
+ align:start position:0%
+pause try to work it out yourself you
+can sketch the parallelepiped on this
+
+ align:start position:0%
+can sketch the parallelepiped on this
+ 
+
+ align:start position:0%
+can sketch the parallelepiped on this
+picture and I will return in a while and
+
+ align:start position:0%
+picture and I will return in a while and
+ 
+
+ align:start position:0%
+picture and I will return in a while and
+continue working with you
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+all right how did your computation go
+
+ align:start position:0%
+all right how did your computation go
+ 
+
+ align:start position:0%
+all right how did your computation go
+now let's complete complete this picture
+
+ align:start position:0%
+now let's complete complete this picture
+ 
+
+ align:start position:0%
+now let's complete complete this picture
+together
+
+ align:start position:0%
+together
+ 
+
+ align:start position:0%
+together
+as we were saying we need a parallel
+
+ align:start position:0%
+as we were saying we need a parallel
+ 
+
+ align:start position:0%
+as we were saying we need a parallel
+pipette so that we can use the fact that
+
+ align:start position:0%
+pipette so that we can use the fact that
+ 
+
+ align:start position:0%
+pipette so that we can use the fact that
+the determinant is related to the volume
+
+ align:start position:0%
+the determinant is related to the volume
+ 
+
+ align:start position:0%
+the determinant is related to the volume
+here I have a tetrahedron and let's look
+
+ align:start position:0%
+here I have a tetrahedron and let's look
+ 
+
+ align:start position:0%
+here I have a tetrahedron and let's look
+at these three edges Oh a 1 Oh a 2 in Oh
+
+ align:start position:0%
+at these three edges Oh a 1 Oh a 2 in Oh
+ 
+
+ align:start position:0%
+at these three edges Oh a 1 Oh a 2 in Oh
+a 3 all of them meet at the origin so
+
+ align:start position:0%
+a 3 all of them meet at the origin so
+ 
+
+ align:start position:0%
+a 3 all of them meet at the origin so
+why don't we just consider the power
+
+ align:start position:0%
+why don't we just consider the power
+ 
+
+ align:start position:0%
+why don't we just consider the power
+pipette spent by the same three edges
+
+ align:start position:0%
+pipette spent by the same three edges
+ 
+
+ align:start position:0%
+pipette spent by the same three edges
+it's a natural choice because at least
+
+ align:start position:0%
+it's a natural choice because at least
+ 
+
+ align:start position:0%
+it's a natural choice because at least
+it shares three edges with T okay now
+
+ align:start position:0%
+it shares three edges with T okay now
+ 
+
+ align:start position:0%
+it shares three edges with T okay now
+let's move on to this picture here as
+
+ align:start position:0%
+let's move on to this picture here as
+ 
+
+ align:start position:0%
+let's move on to this picture here as
+you can see I have joined this prototype
+
+ align:start position:0%
+you can see I have joined this prototype
+ 
+
+ align:start position:0%
+you can see I have joined this prototype
+it in red chalk so the blue part is my
+
+ align:start position:0%
+it in red chalk so the blue part is my
+ 
+
+ align:start position:0%
+it in red chalk so the blue part is my
+original T in the red part let me call
+
+ align:start position:0%
+original T in the red part let me call
+ 
+
+ align:start position:0%
+original T in the red part let me call
+it P is the power pipette spent by edge
+
+ align:start position:0%
+it P is the power pipette spent by edge
+ 
+
+ align:start position:0%
+it P is the power pipette spent by edge
+Oh a 1 Oh a 2 and O is 3 so that's the
+
+ align:start position:0%
+Oh a 1 Oh a 2 and O is 3 so that's the
+ 
+
+ align:start position:0%
+Oh a 1 Oh a 2 and O is 3 so that's the
+parallel pipette then I'm going to work
+
+ align:start position:0%
+parallel pipette then I'm going to work
+ 
+
+ align:start position:0%
+parallel pipette then I'm going to work
+with now the next step is to relate the
+
+ align:start position:0%
+with now the next step is to relate the
+ 
+
+ align:start position:0%
+with now the next step is to relate the
+volume of T to the volume of P ok let's
+
+ align:start position:0%
+volume of T to the volume of P ok let's
+ 
+
+ align:start position:0%
+volume of T to the volume of P ok let's
+record together what is the volume of a
+
+ align:start position:0%
+record together what is the volume of a
+ 
+
+ align:start position:0%
+record together what is the volume of a
+tetrahedron we note that the volume of a
+
+ align:start position:0%
+tetrahedron we note that the volume of a
+ 
+
+ align:start position:0%
+tetrahedron we note that the volume of a
+tetrahedron is going to be equal to one
+
+ align:start position:0%
+tetrahedron is going to be equal to one
+ 
+
+ align:start position:0%
+tetrahedron is going to be equal to one
+third of the area of the base times the
+
+ align:start position:0%
+third of the area of the base times the
+ 
+
+ align:start position:0%
+third of the area of the base times the
+height right of course you can choose
+
+ align:start position:0%
+height right of course you can choose
+ 
+
+ align:start position:0%
+height right of course you can choose
+any side any phase to be the base but
+
+ align:start position:0%
+any side any phase to be the base but
+ 
+
+ align:start position:0%
+any side any phase to be the base but
+for convenience we're going to choose
+
+ align:start position:0%
+for convenience we're going to choose
+ 
+
+ align:start position:0%
+for convenience we're going to choose
+the triangle Oh a-one a-two to be the
+
+ align:start position:0%
+the triangle Oh a-one a-two to be the
+ 
+
+ align:start position:0%
+the triangle Oh a-one a-two to be the
+base of T so volume of T is going to be
+
+ align:start position:0%
+base of T so volume of T is going to be
+ 
+
+ align:start position:0%
+base of T so volume of T is going to be
+equal to 1/3 times the area of triangle
+
+ align:start position:0%
+equal to 1/3 times the area of triangle
+ 
+
+ align:start position:0%
+equal to 1/3 times the area of triangle
+Oh a 1 a 2 so I use this a to indicate
+
+ align:start position:0%
+Oh a 1 a 2 so I use this a to indicate
+ 
+
+ align:start position:0%
+Oh a 1 a 2 so I use this a to indicate
+the area then times the height well if I
+
+ align:start position:0%
+the area then times the height well if I
+ 
+
+ align:start position:0%
+the area then times the height well if I
+choose this to be my base then this a 3
+
+ align:start position:0%
+choose this to be my base then this a 3
+ 
+
+ align:start position:0%
+choose this to be my base then this a 3
+becomes the apex then the height is
+
+ align:start position:0%
+becomes the apex then the height is
+ 
+
+ align:start position:0%
+becomes the apex then the height is
+simply equal to the distance from a 3 to
+
+ align:start position:0%
+simply equal to the distance from a 3 to
+ 
+
+ align:start position:0%
+simply equal to the distance from a 3 to
+the triangle
+
+ align:start position:0%
+the triangle
+ 
+
+ align:start position:0%
+the triangle
+Oh a 1 a 2 let me use letter H to denote
+
+ align:start position:0%
+Oh a 1 a 2 let me use letter H to denote
+ 
+
+ align:start position:0%
+Oh a 1 a 2 let me use letter H to denote
+this quantity so that's the height and
+
+ align:start position:0%
+this quantity so that's the height and
+ 
+
+ align:start position:0%
+this quantity so that's the height and
+the volume of T is equal to 1/3 of the
+
+ align:start position:0%
+the volume of T is equal to 1/3 of the
+ 
+
+ align:start position:0%
+the volume of T is equal to 1/3 of the
+product of the area of the base times
+
+ align:start position:0%
+product of the area of the base times
+ 
+
+ align:start position:0%
+product of the area of the base times
+the height ok this is the volume of T
+
+ align:start position:0%
+the height ok this is the volume of T
+ 
+
+ align:start position:0%
+the height ok this is the volume of T
+now let's see what the volume of what
+
+ align:start position:0%
+now let's see what the volume of what
+ 
+
+ align:start position:0%
+now let's see what the volume of what
+the volume of P is so P is Apollo pipe
+
+ align:start position:0%
+the volume of P is so P is Apollo pipe
+ 
+
+ align:start position:0%
+the volume of P is so P is Apollo pipe
+it the volume of a power pipette is
+
+ align:start position:0%
+it the volume of a power pipette is
+ 
+
+ align:start position:0%
+it the volume of a power pipette is
+simply equal to the area of the base
+
+ align:start position:0%
+simply equal to the area of the base
+ 
+
+ align:start position:0%
+simply equal to the area of the base
+times its height this time which phase
+
+ align:start position:0%
+times its height this time which phase
+ 
+
+ align:start position:0%
+times its height this time which phase
+would you choose to be the base well of
+
+ align:start position:0%
+would you choose to be the base well of
+ 
+
+ align:start position:0%
+would you choose to be the base well of
+course you would like to choose this
+
+ align:start position:0%
+course you would like to choose this
+ 
+
+ align:start position:0%
+course you would like to choose this
+parallelogram to be the base because it
+
+ align:start position:0%
+parallelogram to be the base because it
+ 
+
+ align:start position:0%
+parallelogram to be the base because it
+contains the base of T if we do so so we
+
+ align:start position:0%
+contains the base of T if we do so so we
+ 
+
+ align:start position:0%
+contains the base of T if we do so so we
+want to choose this pelegrin to be the
+
+ align:start position:0%
+want to choose this pelegrin to be the
+ 
+
+ align:start position:0%
+want to choose this pelegrin to be the
+base then what is the area of this well
+
+ align:start position:0%
+base then what is the area of this well
+ 
+
+ align:start position:0%
+base then what is the area of this well
+it clearly contains two copies of the
+
+ align:start position:0%
+it clearly contains two copies of the
+ 
+
+ align:start position:0%
+it clearly contains two copies of the
+triangle Oh a 1 a 2
+
+ align:start position:0%
+triangle Oh a 1 a 2
+ 
+
+ align:start position:0%
+triangle Oh a 1 a 2
+so the area of the telegram is simply
+
+ align:start position:0%
+so the area of the telegram is simply
+ 
+
+ align:start position:0%
+so the area of the telegram is simply
+equal to twice the area of the triangle
+
+ align:start position:0%
+equal to twice the area of the triangle
+ 
+
+ align:start position:0%
+equal to twice the area of the triangle
+Oh a 1 a 2 then what is the height of of
+
+ align:start position:0%
+Oh a 1 a 2 then what is the height of of
+ 
+
+ align:start position:0%
+Oh a 1 a 2 then what is the height of of
+P again if you choose this face to be
+
+ align:start position:0%
+P again if you choose this face to be
+ 
+
+ align:start position:0%
+P again if you choose this face to be
+the base then a 3 becomes the apex again
+
+ align:start position:0%
+the base then a 3 becomes the apex again
+ 
+
+ align:start position:0%
+the base then a 3 becomes the apex again
+then the height of the parallelepiped is
+
+ align:start position:0%
+then the height of the parallelepiped is
+ 
+
+ align:start position:0%
+then the height of the parallelepiped is
+equal to the distance from a 3 to the
+
+ align:start position:0%
+equal to the distance from a 3 to the
+ 
+
+ align:start position:0%
+equal to the distance from a 3 to the
+base which is the same as the distance
+
+ align:start position:0%
+base which is the same as the distance
+ 
+
+ align:start position:0%
+base which is the same as the distance
+from a 3 to try and go Oh a 1 a 2 so
+
+ align:start position:0%
+from a 3 to try and go Oh a 1 a 2 so
+ 
+
+ align:start position:0%
+from a 3 to try and go Oh a 1 a 2 so
+here the height is also equal to H
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+now you can compare these two formula
+
+ align:start position:0%
+now you can compare these two formula
+ 
+
+ align:start position:0%
+now you can compare these two formula
+you see that volume of T is simply equal
+
+ align:start position:0%
+you see that volume of T is simply equal
+ 
+
+ align:start position:0%
+you see that volume of T is simply equal
+to one sector of volume of P that's the
+
+ align:start position:0%
+to one sector of volume of P that's the
+ 
+
+ align:start position:0%
+to one sector of volume of P that's the
+connection between the volume of the
+
+ align:start position:0%
+connection between the volume of the
+ 
+
+ align:start position:0%
+connection between the volume of the
+tetrahedron with the volume of the
+
+ align:start position:0%
+tetrahedron with the volume of the
+ 
+
+ align:start position:0%
+tetrahedron with the volume of the
+prototype it in order to compute volume
+
+ align:start position:0%
+prototype it in order to compute volume
+ 
+
+ align:start position:0%
+prototype it in order to compute volume
+of T we only need to compute the volume
+
+ align:start position:0%
+of T we only need to compute the volume
+ 
+
+ align:start position:0%
+of T we only need to compute the volume
+of P now let's compute the volume of
+
+ align:start position:0%
+of P now let's compute the volume of
+ 
+
+ align:start position:0%
+of P now let's compute the volume of
+this parallelepiped we know that it's
+
+ align:start position:0%
+this parallelepiped we know that it's
+ 
+
+ align:start position:0%
+this parallelepiped we know that it's
+related to the determinant of a matrix
+
+ align:start position:0%
+related to the determinant of a matrix
+ 
+
+ align:start position:0%
+related to the determinant of a matrix
+and the row vectors of that matrix are
+
+ align:start position:0%
+and the row vectors of that matrix are
+ 
+
+ align:start position:0%
+and the row vectors of that matrix are
+given by these three edges so because
+
+ align:start position:0%
+given by these three edges so because
+ 
+
+ align:start position:0%
+given by these three edges so because
+all of them start from zero we only need
+
+ align:start position:0%
+all of them start from zero we only need
+ 
+
+ align:start position:0%
+all of them start from zero we only need
+the coordinate of a1 a2 and a3 so here
+
+ align:start position:0%
+the coordinate of a1 a2 and a3 so here
+ 
+
+ align:start position:0%
+the coordinate of a1 a2 and a3 so here
+volume of P is equal to the absolute
+
+ align:start position:0%
+volume of P is equal to the absolute
+ 
+
+ align:start position:0%
+volume of P is equal to the absolute
+value so don't forget the absolute value
+
+ align:start position:0%
+value so don't forget the absolute value
+ 
+
+ align:start position:0%
+value so don't forget the absolute value
+sign absolute value of the determinant
+
+ align:start position:0%
+sign absolute value of the determinant
+ 
+
+ align:start position:0%
+sign absolute value of the determinant
+of a 3x3 matrix so we just need to copy
+
+ align:start position:0%
+of a 3x3 matrix so we just need to copy
+ 
+
+ align:start position:0%
+of a 3x3 matrix so we just need to copy
+the coordinates of the vertices down
+
+ align:start position:0%
+the coordinates of the vertices down
+ 
+
+ align:start position:0%
+the coordinates of the vertices down
+here the first one is 2 2 negative 1
+
+ align:start position:0%
+here the first one is 2 2 negative 1
+ 
+
+ align:start position:0%
+here the first one is 2 2 negative 1
+these two are two coasts next one and a2
+
+ align:start position:0%
+these two are two coasts next one and a2
+ 
+
+ align:start position:0%
+these two are two coasts next one and a2
+is 1 3 0 a 3 is negative 1 1 for the
+
+ align:start position:0%
+is 1 3 0 a 3 is negative 1 1 for the
+ 
+
+ align:start position:0%
+is 1 3 0 a 3 is negative 1 1 for the
+absolute value of this determinant and
+
+ align:start position:0%
+absolute value of this determinant and
+ 
+
+ align:start position:0%
+absolute value of this determinant and
+if you compute this this is a 3x3 matrix
+
+ align:start position:0%
+if you compute this this is a 3x3 matrix
+ 
+
+ align:start position:0%
+if you compute this this is a 3x3 matrix
+the determinant should be easy to
+
+ align:start position:0%
+the determinant should be easy to
+ 
+
+ align:start position:0%
+the determinant should be easy to
+compute and the result should be 12
+
+ align:start position:0%
+compute and the result should be 12
+ 
+
+ align:start position:0%
+compute and the result should be 12
+so that's the volume of P which means
+
+ align:start position:0%
+so that's the volume of P which means
+ 
+
+ align:start position:0%
+so that's the volume of P which means
+the volume of the tetrahedron T is equal
+
+ align:start position:0%
+the volume of the tetrahedron T is equal
+ 
+
+ align:start position:0%
+the volume of the tetrahedron T is equal
+to 12 over 6 which is 2 did you get the
+
+ align:start position:0%
+to 12 over 6 which is 2 did you get the
+ 
+
+ align:start position:0%
+to 12 over 6 which is 2 did you get the
+correct answer okay so in order to
+
+ align:start position:0%
+correct answer okay so in order to
+ 
+
+ align:start position:0%
+correct answer okay so in order to
+compute the volume of T we have related
+
+ align:start position:0%
+compute the volume of T we have related
+ 
+
+ align:start position:0%
+compute the volume of T we have related
+to attach a parallel pipe ap which
+
+ align:start position:0%
+to attach a parallel pipe ap which
+ 
+
+ align:start position:0%
+to attach a parallel pipe ap which
+contains T all right now let's look at
+
+ align:start position:0%
+contains T all right now let's look at
+ 
+
+ align:start position:0%
+contains T all right now let's look at
+the second part the second part says
+
+ align:start position:0%
+the second part the second part says
+ 
+
+ align:start position:0%
+the second part the second part says
+that if I keep a 1 and a 2 and changed
+
+ align:start position:0%
+that if I keep a 1 and a 2 and changed
+ 
+
+ align:start position:0%
+that if I keep a 1 and a 2 and changed
+but I move a 3 to a new point so a 3 is
+
+ align:start position:0%
+but I move a 3 to a new point so a 3 is
+ 
+
+ align:start position:0%
+but I move a 3 to a new point so a 3 is
+going to be moved to a point given by a
+
+ align:start position:0%
+going to be moved to a point given by a
+ 
+
+ align:start position:0%
+going to be moved to a point given by a
+3 Prime and the coordinate is negative
+
+ align:start position:0%
+3 Prime and the coordinate is negative
+ 
+
+ align:start position:0%
+3 Prime and the coordinate is negative
+201 negative 199 and 104 and I'm asking
+
+ align:start position:0%
+201 negative 199 and 104 and I'm asking
+ 
+
+ align:start position:0%
+201 negative 199 and 104 and I'm asking
+you to compute the volume of the new
+
+ align:start position:0%
+you to compute the volume of the new
+ 
+
+ align:start position:0%
+you to compute the volume of the new
+tetrahedron well as you can see this
+
+ align:start position:0%
+tetrahedron well as you can see this
+ 
+
+ align:start position:0%
+tetrahedron well as you can see this
+point seems to be far away from the
+
+ align:start position:0%
+point seems to be far away from the
+ 
+
+ align:start position:0%
+point seems to be far away from the
+origin I am NOT even able to draw this
+
+ align:start position:0%
+origin I am NOT even able to draw this
+ 
+
+ align:start position:0%
+origin I am NOT even able to draw this
+point here but you can imagine as this
+
+ align:start position:0%
+point here but you can imagine as this
+ 
+
+ align:start position:0%
+point here but you can imagine as this
+point goes far away from the origin this
+
+ align:start position:0%
+point goes far away from the origin this
+ 
+
+ align:start position:0%
+point goes far away from the origin this
+spike is going to become more and more
+
+ align:start position:0%
+spike is going to become more and more
+ 
+
+ align:start position:0%
+spike is going to become more and more
+pointy in other words the entire
+
+ align:start position:0%
+pointy in other words the entire
+ 
+
+ align:start position:0%
+pointy in other words the entire
+tetrahedron looks more and more like a
+
+ align:start position:0%
+tetrahedron looks more and more like a
+ 
+
+ align:start position:0%
+tetrahedron looks more and more like a
+needle but nonetheless we can use the
+
+ align:start position:0%
+needle but nonetheless we can use the
+ 
+
+ align:start position:0%
+needle but nonetheless we can use the
+same method to compute it at the volume
+
+ align:start position:0%
+same method to compute it at the volume
+ 
+
+ align:start position:0%
+same method to compute it at the volume
+so we follow the same idea the volume of
+
+ align:start position:0%
+so we follow the same idea the volume of
+ 
+
+ align:start position:0%
+so we follow the same idea the volume of
+T is going to be equal to 1/6 of the
+
+ align:start position:0%
+T is going to be equal to 1/6 of the
+ 
+
+ align:start position:0%
+T is going to be equal to 1/6 of the
+volume of P and in this case that's
+
+ align:start position:0%
+volume of P and in this case that's
+ 
+
+ align:start position:0%
+volume of P and in this case that's
+going to become the absolute value of
+
+ align:start position:0%
+going to become the absolute value of
+ 
+
+ align:start position:0%
+going to become the absolute value of
+the determinant of a 3x3 matrix whose
+
+ align:start position:0%
+the determinant of a 3x3 matrix whose
+ 
+
+ align:start position:0%
+the determinant of a 3x3 matrix whose
+robe actors are given by these three
+
+ align:start position:0%
+robe actors are given by these three
+ 
+
+ align:start position:0%
+robe actors are given by these three
+edges so in this case we again copy down
+
+ align:start position:0%
+edges so in this case we again copy down
+ 
+
+ align:start position:0%
+edges so in this case we again copy down
+the coordinates of three vertices the
+
+ align:start position:0%
+the coordinates of three vertices the
+ 
+
+ align:start position:0%
+the coordinates of three vertices the
+first one is 2 2 negative 1
+
+ align:start position:0%
+first one is 2 2 negative 1
+ 
+
+ align:start position:0%
+first one is 2 2 negative 1
+second one is 1 3 0 the third one should
+
+ align:start position:0%
+second one is 1 3 0 the third one should
+ 
+
+ align:start position:0%
+second one is 1 3 0 the third one should
+become this
+
+ align:start position:0%
+become this
+ 
+
+ align:start position:0%
+become this
+so negative 201 199 104 okay
+
+ align:start position:0%
+so negative 201 199 104 okay
+ 
+
+ align:start position:0%
+so negative 201 199 104 okay
+that should give me the volume of the
+
+ align:start position:0%
+that should give me the volume of the
+ 
+
+ align:start position:0%
+that should give me the volume of the
+neo tetrahedron let me call it t prime
+
+ align:start position:0%
+neo tetrahedron let me call it t prime
+ 
+
+ align:start position:0%
+neo tetrahedron let me call it t prime
+just to differentiate from the previous
+
+ align:start position:0%
+just to differentiate from the previous
+ 
+
+ align:start position:0%
+just to differentiate from the previous
+tetrahedron and of course you can
+
+ align:start position:0%
+tetrahedron and of course you can
+ 
+
+ align:start position:0%
+tetrahedron and of course you can
+compute this determinant explicitly if
+
+ align:start position:0%
+compute this determinant explicitly if
+ 
+
+ align:start position:0%
+compute this determinant explicitly if
+you do so you will see the answer should
+
+ align:start position:0%
+you do so you will see the answer should
+ 
+
+ align:start position:0%
+you do so you will see the answer should
+be 2 again but in fact there's a way
+
+ align:start position:0%
+be 2 again but in fact there's a way
+ 
+
+ align:start position:0%
+be 2 again but in fact there's a way
+that you can just write out the answer
+
+ align:start position:0%
+that you can just write out the answer
+ 
+
+ align:start position:0%
+that you can just write out the answer
+directly without any real computation
+
+ align:start position:0%
+directly without any real computation
+ 
+
+ align:start position:0%
+directly without any real computation
+let's pay attention to the last row in
+
+ align:start position:0%
+let's pay attention to the last row in
+ 
+
+ align:start position:0%
+let's pay attention to the last row in
+other words let's pay attention to this
+
+ align:start position:0%
+other words let's pay attention to this
+ 
+
+ align:start position:0%
+other words let's pay attention to this
+new a3 while a 3 prime what do you
+
+ align:start position:0%
+new a3 while a 3 prime what do you
+ 
+
+ align:start position:0%
+new a3 while a 3 prime what do you
+observe here a 3 prime if you consider
+
+ align:start position:0%
+observe here a 3 prime if you consider
+ 
+
+ align:start position:0%
+observe here a 3 prime if you consider
+the difference between a 3 and a 3 Prime
+
+ align:start position:0%
+the difference between a 3 and a 3 Prime
+ 
+
+ align:start position:0%
+the difference between a 3 and a 3 Prime
+in other words if you consider how much
+
+ align:start position:0%
+in other words if you consider how much
+ 
+
+ align:start position:0%
+in other words if you consider how much
+you have moved your apex you will see
+
+ align:start position:0%
+you have moved your apex you will see
+ 
+
+ align:start position:0%
+you have moved your apex you will see
+that's equal to negative 100 a 1 right
+
+ align:start position:0%
+that's equal to negative 100 a 1 right
+ 
+
+ align:start position:0%
+that's equal to negative 100 a 1 right
+so a 3 is negative 1 1 4 a 3 prime is
+
+ align:start position:0%
+so a 3 is negative 1 1 4 a 3 prime is
+ 
+
+ align:start position:0%
+so a 3 is negative 1 1 4 a 3 prime is
+this that's exactly equal to negative
+
+ align:start position:0%
+this that's exactly equal to negative
+ 
+
+ align:start position:0%
+this that's exactly equal to negative
+100 times a 1 what does that mean well
+
+ align:start position:0%
+100 times a 1 what does that mean well
+ 
+
+ align:start position:0%
+100 times a 1 what does that mean well
+from the point of view of matrix you are
+
+ align:start position:0%
+from the point of view of matrix you are
+ 
+
+ align:start position:0%
+from the point of view of matrix you are
+subtracting from the original 3rd row
+
+ align:start position:0%
+subtracting from the original 3rd row
+ 
+
+ align:start position:0%
+subtracting from the original 3rd row
+100 times the first row but this is this
+
+ align:start position:0%
+100 times the first row but this is this
+ 
+
+ align:start position:0%
+100 times the first row but this is this
+row operation does not change the
+
+ align:start position:0%
+row operation does not change the
+ 
+
+ align:start position:0%
+row operation does not change the
+determinant in other words you know that
+
+ align:start position:0%
+determinant in other words you know that
+ 
+
+ align:start position:0%
+determinant in other words you know that
+this determinant should be the same as
+
+ align:start position:0%
+this determinant should be the same as
+ 
+
+ align:start position:0%
+this determinant should be the same as
+the previous one so you can write out to
+
+ align:start position:0%
+the previous one so you can write out to
+ 
+
+ align:start position:0%
+the previous one so you can write out to
+directly from this picture we can also
+
+ align:start position:0%
+directly from this picture we can also
+ 
+
+ align:start position:0%
+directly from this picture we can also
+see that fact so from this picture we
+
+ align:start position:0%
+see that fact so from this picture we
+ 
+
+ align:start position:0%
+see that fact so from this picture we
+know that this section is saying that I
+
+ align:start position:0%
+know that this section is saying that I
+ 
+
+ align:start position:0%
+know that this section is saying that I
+need to move a 3 in the inverse
+
+ align:start position:0%
+need to move a 3 in the inverse
+ 
+
+ align:start position:0%
+need to move a 3 in the inverse
+direction of a 1 by 100 times a 1 so
+
+ align:start position:0%
+direction of a 1 by 100 times a 1 so
+ 
+
+ align:start position:0%
+direction of a 1 by 100 times a 1 so
+you're moving a 3
+
+ align:start position:0%
+you're moving a 3
+ 
+
+ align:start position:0%
+you're moving a 3
+prologue to a one but it doesn't matter
+
+ align:start position:0%
+prologue to a one but it doesn't matter
+ 
+
+ align:start position:0%
+prologue to a one but it doesn't matter
+how far you've moved your apex you're
+
+ align:start position:0%
+how far you've moved your apex you're
+ 
+
+ align:start position:0%
+how far you've moved your apex you're
+moving in a way that remains parallel to
+
+ align:start position:0%
+moving in a way that remains parallel to
+ 
+
+ align:start position:0%
+moving in a way that remains parallel to
+the base which is saying that this
+
+ align:start position:0%
+the base which is saying that this
+ 
+
+ align:start position:0%
+the base which is saying that this
+movement does not change the height
+
+ align:start position:0%
+movement does not change the height
+ 
+
+ align:start position:0%
+movement does not change the height
+since a1 a2 are fixed your base is fixed
+
+ align:start position:0%
+since a1 a2 are fixed your base is fixed
+ 
+
+ align:start position:0%
+since a1 a2 are fixed your base is fixed
+is fixed and you're not changing the
+
+ align:start position:0%
+is fixed and you're not changing the
+ 
+
+ align:start position:0%
+is fixed and you're not changing the
+height so of course the volume is not
+
+ align:start position:0%
+height so of course the volume is not
+ 
+
+ align:start position:0%
+height so of course the volume is not
+changing that's also a reason another
+
+ align:start position:0%
+changing that's also a reason another
+ 
+
+ align:start position:0%
+changing that's also a reason another
+way to see that the volume of T prime is
+
+ align:start position:0%
+way to see that the volume of T prime is
+ 
+
+ align:start position:0%
+way to see that the volume of T prime is
+simply equal to the volume of T okay
+
+ align:start position:0%
+simply equal to the volume of T okay
+ 
+
+ align:start position:0%
+simply equal to the volume of T okay
+this completes this problem I hope this
+
+ align:start position:0%
+this completes this problem I hope this
+ 
+
+ align:start position:0%
+this completes this problem I hope this
+example is helpful to you and we should
+
+ align:start position:0%
+example is helpful to you and we should
+ 
+
+ align:start position:0%
+example is helpful to you and we should
+keep in mind that the fact that the
+
+ align:start position:0%
+keep in mind that the fact that the
+ 
+
+ align:start position:0%
+keep in mind that the fact that the
+determinant is rated to volume sometimes
+
+ align:start position:0%
+determinant is rated to volume sometimes
+ 
+
+ align:start position:0%
+determinant is rated to volume sometimes
+can become very handy in computing the
+
+ align:start position:0%
+can become very handy in computing the
+ 
+
+ align:start position:0%
+can become very handy in computing the
+volume of certain geometric objects
+
+ align:start position:0%
+volume of certain geometric objects
+ 
+
+ align:start position:0%
+volume of certain geometric objects
+thank you for watching and I'm looking
+
+ align:start position:0%
+thank you for watching and I'm looking
+ 
+
+ align:start position:0%
+thank you for watching and I'm looking
+forward to seeing you soon
\ No newline at end of file
diff --git a/rzGmSWxhwM8.txt b/rzGmSWxhwM8.txt
new file mode 100644
index 0000000000000000000000000000000000000000..5f67767a6f813d957deca76027de15ef46765df2
--- /dev/null
+++ b/rzGmSWxhwM8.txt
@@ -0,0 +1,379 @@
+The following content is
+provided under a Creative
+
+Commons license.
+
+Your support will help MIT Open
+CourseWare continue to
+
+offer high-quality educational
+resources for free.
+
+To make a donation or view
+additional materials from
+
+hundreds of MIT courses, visit
+MIT OpenCourseWare at
+
+ocw.mit.edu.
+
+We, we are solid
+state devices.
+
+This is soft matter.
+
+My eyes are photo detectors.
+
+Band gap of about two
+electron volts.
+
+They're just not made
+of a compound
+
+semiconductor inorganic.
+
+And this motion is just
+conformational
+
+changes in a polymer.
+
+See it's all chemistry.
+
+The rest is stamp collecting.
+
+So the principles that apply to
+inanimate objects apply to
+
+animate objects.
+
+And the solid-state chemistry
+umbrella is very broad.
+
+If I say solid-state chemistry,
+people are apt to
+
+think of electronic devices,
+transistors, what have you.
+
+But that extends to
+the life sciences.
+
+I mean we, as human beings,
+are chemical machines.
+
+So this is the classical view.
+
+Electronic structuring informs
+bonding but then in 3.091
+
+bonding informs atomic
+arrangement, which tells you
+
+everything.
+
+The shape of all things, it's
+all electronic structure.
+
+There's nothing more.
+
+The difference is that the
+focus in the chemistry
+
+department, their focus
+is the molecule.
+
+Whereas in 3.091 I like to
+think of the focus being
+
+aggregates of molecules,
+namely solids.
+
+Because engineering systems
+are made of solids.
+
+If you're steeped in chemistry
+from high school, you've had
+
+the AP curriculum, again 3.091
+might be something that is a
+
+fresh look at chemistry from
+a slightly different
+
+perspective.
+
+What I wanted to play for you as
+you're leaving today is an
+
+old Beatles song, Lucy in
+the Sky with Diamonds.
+
+Being able to bring in subject
+matter, music, art,
+
+literature, into a chemistry
+class and make the connections
+
+to the world around us, I think
+is most important in the
+
+21st century, when problem
+solving even in the technical
+
+domain is going to require
+skills that build bridges to
+
+the humanities, arts and
+social sciences.
+
+And so I like to think of
+3.091 not as a chemistry
+
+class, but rather a
+chemistry-centered class.
+
+The majority of students taking
+3.091 at MIT may never
+
+take another chemistry class.
+
+So I ask myself what topics are
+critical for someone who
+
+might major in electrical
+engineering?
+
+Or for someone who might
+major in physics?
+
+Or what's the chemistry that's
+critical to an MIT student who
+
+might major in political
+science or economics?
+
+And that informs my
+choice of topics.
+
+And it turns out that that
+doesn't diminish from the
+
+education of the student who
+may choose to major in a
+
+chemically intensive discipline
+such as material
+
+science, chemical engineering,
+or even chemistry itself.
+
+I don't view the presentation
+of the subject matter as a
+
+linear track, where this
+is the beginning
+
+and this is the end.
+
+I view it more along the
+lines of a spiral.
+
+And so the first time you
+encounter a certain concept
+
+it's at a rather superficial
+introductory level.
+
+And then at some point later
+in the semester you spiral
+
+back and see it again.
+
+And then maybe there's a little
+more context and a
+
+little more intensity.
+
+Maybe there's a little
+more mathematics
+
+associated with it.
+
+And then you'll see it
+applied later again.
+
+And through that revisiting--
+
+repetition by design--
+
+I think that key concepts
+get driven home.
+
+Some people are shocked that
+I stand in front of a chalk
+
+board and I write on it and I
+believe that that's still a
+
+valid means of teaching.
+
+For the first-time learner
+I think it's important to
+
+activate all of the
+learning channels.
+
+The act of drawing
+and inspiring
+
+them to draw is important.
+
+And maybe the person at home
+ought to put themselves in a
+
+chair in the auditorium and be
+taking notes as though they
+
+are attending the lecture.
+
+Watching those videos,
+especially for someone that
+
+has had a fair bit of high
+school chemistry, you're going
+
+to hear a lot of the same things
+but maybe coming at you
+
+at a slightly elevated level.
+
+But not so elevated that
+you won't follow it.
+
+And I think that's good for a
+high school student to be
+
+talked to at a higher level.
+
+I think the videos also have
+utility for people that are
+
+interested in specific topics.
+
+I mean for example, if somebody
+needs to know
+
+something about x-rays, or the
+use of x-rays, dropping in to
+
+that three-lecture sequence on
+x-rays could be quite useful.
+
+I think it's possible to
+sample with a goal of
+
+mastering a particular
+concept.
+
+So clearly for the learner out
+in the World Wide Web, going
+
+to recitation and interacting
+with a recitation instructor
+
+is not practical.
+
+So in lieu of the recitation
+section OCW has created these
+
+help session videos.
+
+We actually hired some
+recitation instructors from
+
+the fall of 2009 and asked
+them to work through some
+
+sample problems and what you see
+in the help session video
+
+is essentially what would
+have happened in
+
+a recitation section.
+
+I issue the homework questions
+with model solutions at the
+
+beginning of the unit.
+
+So the homework becomes
+a study aid.
+
+And I recommend to students
+that they try the homework
+
+problems without referring to
+the answer key initially.
+
+And to turn to the answer key
+when they reach an impediment.
+
+What's the message of 3.091
+for the man on the street?
+
+An understanding of those
+relationships.
+
+Electronic structure
+to bonding.
+
+Bonding to atomic arrangement.
+
+Atomic arrangement
+to properties.
+
+Is the key to understanding
+the world around us.
+
+And in particular it's the
+key to fueling invention.
+
+And I believe in practice very
+much and in the application of
+
+science in service
+for humanity.
+
+Why do we worry about designing
+a car that's a
+
+zero-emission vehicle, as
+if to do no harm to the
+
+environment?
+
+Why don't we go even further and
+say, what about a car that
+
+purifies the air as it
+drives down the road?
+
+So that the air in the wake of
+the car is cleaner than the
+
+air in front of the car?
+
+And I'm finding that
+increasingly that's a message
+
+that resonates with
+the students.
+
+They want to take the tools
+of technical analytically
+
+centered education and
+put them to work to
+
+solve societal problems.
\ No newline at end of file
diff --git a/s98jdWi2kEs.txt b/s98jdWi2kEs.txt
new file mode 100644
index 0000000000000000000000000000000000000000..0ee9961e4bd66e4a7dbb756c902596be6025ea28
--- /dev/null
+++ b/s98jdWi2kEs.txt
@@ -0,0 +1,3931 @@
+The following content is
+provided under a Creative
+
+Commons license.
+
+Your support will help MIT
+OpenCourseWare continue to
+
+offer high-quality educational
+resources for free.
+
+To make a donation or view
+additional materials from
+
+hundreds of MIT courses, visit
+MIT OpenCourseWare at
+
+ocw.mit.edu.
+
+PROFESSOR: OK, so let's
+get started.
+
+I want to talk mostly about
+countable state Markov chains
+
+today, which is the new topic
+we started on Wednesday.
+
+I want to talk just a little bit
+about the strong law proof
+
+that was in the third
+problem of the quiz.
+
+I'm not doing that because
+none of you understood
+
+anything about it.
+
+I'm doing it because all of you
+understood more about it
+
+than I thought you would.
+
+And in fact, I've always avoided
+saying too much about
+
+this proof because I thought
+everybody was tuning them out.
+
+And for the class here, it looks
+like a lot of you have
+
+tried seriously to understand
+these things.
+
+So I thought I would explain
+that one part of the quiz in
+
+detail so that you'd see the
+parts you're missing, and so
+
+that [INAUDIBLE] all these other
+proofs that we have,
+
+talking about the strong law
+and the strong law for
+
+renewals, and putting them
+together and all of these
+
+things, all of them are
+essentially the same.
+
+And it's just a matter
+of figuring out
+
+how things fit together.
+
+So I wanted to talk about that
+because it's clear that most
+
+of you understand enough about
+it that it makes sense.
+
+The situation in the quiz, which
+is very close to the
+
+usual queuing situation and
+little theorem type things,
+
+there's a sequence
+of Y sub i's.
+
+They're IID.
+
+There's the service times for
+G/G infinity queue, and n of
+
+t, which is a renewal
+process for the
+
+arrivals to the process.
+
+We have arrivals coming in
+according to this renewal
+
+process, which means the
+[INAUDIBLE] arrival times, X
+
+sub i, were IID.
+
+And we want to put those
+two things together.
+
+And we want to find out
+what this limit is.
+
+If it's a limit, show
+that it's a limit.
+
+And hopefully show that it's
+a limit with probability 1.
+
+And I think a large number of
+you basically realize that
+
+this argument consisted
+of a bunch of steps.
+
+Some people with more
+detail than others.
+
+But the first step, which we do
+in all of these arguments,
+
+is to divide and multiply
+by n of t of omega.
+
+So we're starting out, looking
+at some particular sample
+
+path, and start out by
+multiplying and dividing by n
+
+of t of omega.
+
+The next thing is to claim that
+the limit of this times
+
+this is equal to the limit of
+this times the limit of this.
+
+Almost no one recognized that as
+a real problem, and that is
+
+a real problem.
+
+It's probably the least
+obvious thing
+
+in this whole problem.
+
+I'm not saying you shouldn't
+have done that, because I've
+
+been doing that in all
+the proofs I've been
+
+giving you all along.
+
+It is sort of obvious
+that that works.
+
+And when you're constructing a
+proof, especially in a quiz
+
+when you don't have much time,
+things which are almost
+
+obvious or which look obvious,
+you should just go ahead and
+
+assume them and come back later
+when you have time to
+
+see whether that really
+makes sense.
+
+That's the way you
+do research also.
+
+You don't do research by
+painstakingly establishing
+
+every point in some
+linear path.
+
+What you do is you carelessly
+as you can and with as much
+
+insight as you can, you jump
+all the way to the end, you
+
+see where you're trying to go,
+you see how to get there, and
+
+then you come back and you try
+to figure out what each
+
+of the steps are.
+
+So this is certainly a very
+reasonable way of solving this
+
+problem, because it looks like
+this limit should be equal to
+
+this limit times this limit.
+
+The next step in the argument is
+to claim that this sum, up
+
+to N of t of omega, over
+N of t of omega, as
+
+t approaches infinity--
+
+the argument is that t
+approaches infinity--
+
+this N of t of omega goes
+through, one by one, a
+
+sequence, 1, 2, 3, 4,
+5, and so forth.
+
+So this limit is equal
+to that limit.
+
+I've never been able to figure
+out whether that's obvious or
+
+not obvious.
+
+It is just on the borderline
+between what's obvious and not
+
+obvious, so I'm gonna
+prove it to you.
+
+And then the next step is to see
+that N of t of omega over
+
+t is equal to 1/X-bar
+with probability 1.
+
+And this limit is equal to
+Y-bar with probability 1.
+
+The first argument, this equal
+to 1/X-bar is because of the
+
+strong law with renewals.
+
+And this one over here is
+because of the strong law of
+
+large numbers.
+
+And most of you managed
+to get this.
+
+And the whole argument assumes
+that X-bar is less than
+
+infinity, and Y-bar is
+less than infinity.
+
+Now, how do you go back and
+actually see that this
+
+actually makes sense?
+
+And that's what I
+want to do next.
+
+And if you look at this, you
+can't do it by starting here
+
+and working your way down to
+there, because there's no way
+
+you're going to argue that this
+limit is equal to this
+
+product of limit unless you know
+something about this and
+
+you know something about this.
+
+So you really have to establish
+that these things
+
+have limits first before
+you can go back
+
+and establish this.
+
+In the same way, you have to
+know something about this
+
+before you can establish this.
+
+So what you have to do way after
+you've managed to have
+
+the insight to jump the whole
+way through this thing, is to
+
+go back and argue each of the
+points, but argue them in
+
+reverse order.
+
+And that's very often the way
+you do research, and it's
+
+certainly the way
+you do quizzes.
+
+So let's see where those
+arguments were.
+
+Start out by letting A1 be the
+set of omega for which this
+
+limit here, N of t of omega over
+t, is equal to 1/X-bar.
+
+By the strong law for renewal
+processes, the probability of
+
+A1 equals 1.
+
+This is stating this in a little
+cleaner way, I think,
+
+than we stated the strong law
+of renewals originally,
+
+because we started out by
+tumbling together this
+
+statement and this statement.
+
+I think it's cleaner to say,
+start out, there's a set of
+
+omega 1 for which this
+limit exists.
+
+And what the strong law says is
+that that set of omega has
+
+probability 1.
+
+And now we have some terminology
+for A1, what it
+
+actually means.
+
+It is the set of omega
+for which this works.
+
+You never have it working
+for all omega,
+
+only for some omega.
+
+Then the next step, let A2 be
+the set of omega for which the
+
+limit is n goes to infinity of
+1/n times the sum of Y sub i
+
+of omega, is equal to Y-bar.
+
+By the strong law of large
+numbers, the probability of A2
+
+is equal to 1.
+
+So now we've established there's
+an A1, there's an A2.
+
+Each of them have
+probability 1.
+
+On A1, one limit exists.
+
+On A2, the other limit exists.
+
+And we have two sets, both
+at probability 1.
+
+What's the probability of the
+intersection of them?
+
+It has to be 1 also.
+
+So with that, you know that
+equation three is equal to
+
+equation four for omega
+in the sets, A1, A2.
+
+And also, you know that
+the probability of A1,
+
+A2 is equal to 1.
+
+So we've established this part
+of the argument down here.
+
+Now we want to go up and
+establish this part of the
+
+argument, which as I said, I
+can't convince myself that
+
+it's necessary or
+not necessary.
+
+But since I can't convince
+myself, I thought, in trying
+
+to make up solutions for the
+quiz, I ought to actually
+
+write a proof of it.
+
+And I want to show you what the
+proof is so that, if it's
+
+not obvious to you, you'll know
+exactly how to do it.
+
+And if it is obvious, you can
+maybe sort out exactly why
+
+it's obvious.
+
+So this is an epsilon delta
+kind of argument.
+
+We assume that omega is in A2.
+
+That's the set for which
+the strong law of
+
+large numbers holds.
+
+There exists some integer, n,
+which is a function of both
+
+epsilon and omega.
+
+This is the funny thing
+about all of
+
+these strong law arguments.
+
+In almost all of them,
+you're dealing with
+
+individual sample paths.
+
+When you start saying something
+exists as a limit,
+
+you're not saying that it exists
+as a limit for the
+
+random variables.
+
+You're saying it exists
+as a limit for a
+
+set of sample paths.
+
+And therefore, this epsilon here
+that you're gonna choose,
+
+you need some integer there,
+such that this minus this is
+
+less than epsilon.
+
+I think I'm going to have
+to give up on this.
+
+These things run out of
+batteries too quickly.
+
+So we have that this difference
+here must be less
+
+than epsilon if n is bigger than
+that m of epsilon omega.
+
+That's simply what
+a limit means.
+
+That's the definition
+of a limit.
+
+The only way to define a limit
+sensibly is to say, for all
+
+epsilon greater than 0, no
+matter how small the epsilon
+
+is, you can always find an
+n big enough that this
+
+difference here is less
+than epsilon.
+
+Then if omega is also in A1, the
+limit of N of t of omega
+
+has to be equal to infinity.
+
+If you want to, you can just
+say, we proved in class that
+
+the limit of t of omega is
+equal to infinity with
+
+probability 1, and introduce
+another set, A3.
+
+You want to do a
+probability 1.
+
+But let's do it this way.
+
+And then there has to be a t,
+which is also a function of
+
+epsilon and omega, such
+that N of t and
+
+omega is greater than--
+
+that's an integer, by the way.
+
+That's greater than or equal to
+m of epsilon of omega for
+
+all t, which is greater
+than or equal to t
+
+of epsilon of omega.
+
+That says that this difference
+here is less than omega.
+
+And that's true for all epsilon
+greater than 0.
+
+And that says that, in fact,
+this limit has to exist.
+
+This limit over here is equal
+to Y-bar with probability 1.
+
+So that's what we were trying to
+prove here, that this limit
+
+is the same as this limit.
+
+So we found out what
+this limit is.
+
+We found out that it exists with
+probability 1, namely on
+
+the set A2.
+
+This is equal to this, not
+necessarily on A2,
+
+but on A1 and A2.
+
+So we got into there.
+
+Now how do we get the fact that
+this limit times this
+
+limit is equal to the limit
+of [? these. ?]
+
+Now we have a chance of
+proceeding, because we've
+
+actually shown that this limit
+exists on some set with
+
+probability 1, this limit
+exists on some set with
+
+probability 1.
+
+So we can look at that set and
+say, for omega in that set,
+
+this limit exists and
+this limit exists.
+
+Those limits are non-0 and
+they're non-infinite.
+
+The important thing is that
+they're non-infinite.
+
+And we move on from there,
+and to do that carefully.
+
+And again, I'm not suggesting
+that I expect any of you to do
+
+this on the quiz.
+
+I would have been amazed
+if you had.
+
+It took me quite a while to sort
+it out, because all these
+
+things are tangled together.
+
+Where am I?
+
+I want to be in the
+next slide.
+
+Ah, there we go.
+
+Finally, we can interchange the
+limit of a product of two
+
+functions--
+
+say, f of t, g of t--
+
+with the product
+of the limits.
+
+Can we do that?
+
+If the two functions each have
+finite limits, as the
+
+functions of interests do for
+omega in A1, A2, then the
+
+answer is yes.
+
+And if you look at any book
+on analysis, I'm sure that
+
+theorem is somewhere in the
+first couple of chapters.
+
+But anyway, if you're the kind
+of person like I am who would
+
+rather sort something out for
+yourself rather than look it
+
+up, there's a trick involved
+in doing it.
+
+It's this equality right here.
+
+f of t times g of t minus ab.
+
+What you want to do is somehow
+make that look like f of t
+
+minus a, which you have
+some control over, and
+
+g of t minus b.
+
+So the identity is this is equal
+to f of t minus a times
+
+g of t minus b--
+
+we have control over that--
+
+plus a times g of t minus b,
+plus b times f of t minus a.
+
+And you multiply and add all
+those things together and you
+
+see that that is just
+an identity.
+
+And therefore the magnitude of
+f of t times g of t minus ab
+
+is less than or equal to this.
+
+And then you go through all the
+epsilon delta stuff again.
+
+For any epsilon greater than
+0, you choose a t such that
+
+this is less than or equal
+to epsilon for t
+
+greater than the t epsilon.
+
+This is less than or equal to
+epsilon for t greater than or
+
+equal to t epsilon.
+
+And then this difference here
+is less than or equal to
+
+epsilon squared plus this.
+
+And with a little extra fiddling
+around, that shows
+
+you have that f of t, g of t
+minus ab approaches 0 as t
+
+gets large.
+
+So that's the whole thing.
+
+Now, let me reemphasize
+again, I did not
+
+expect you to do that.
+
+I did not expect you to know how
+to do analysis arguments
+
+like that, because
+analysis is not a
+
+prerequisite for the course.
+
+I do want to show you that the
+kinds of things we've been
+
+doing are not, in fact,
+impossible.
+
+If you trace them out from
+beginning to end and put in
+
+every little detail in them.
+
+If you have to go through
+these kinds of arguments
+
+again, you will in fact know
+how to make it precise and
+
+know how to put all
+those details in.
+
+Let's go back to countable
+state Markov chains.
+
+As we've said, two states are
+in the same class as they
+
+communicate.
+
+It's the same definition as
+for finite state chains.
+
+They communicate if there's some
+path by which you can get
+
+from i to j, and there's some
+path from which you can get
+
+from j to i.
+
+And you can't get there in one
+step only, but you can get
+
+there in some finite
+number of steps.
+
+So that's the definition of
+two states communicating.
+
+The theorem that we sort of
+proved last time is that all
+
+states in the same class are
+
+recurrent or all are transient.
+
+That's the same as the theorem
+we have for finite state
+
+Markov chains.
+
+It's just a little hard
+to establish here.
+
+The argument is that you assume
+that j is recurrent.
+
+If j is recurrent,
+then the sum has
+
+to be equal to infinity.
+
+How do you interpret
+that sum there?
+
+What is it?
+
+P sub jj, super n, is the
+probability that you will be
+
+in state j at time n given
+that you're in
+
+state j at time 0.
+
+So what we're doing is we're
+starting out in time 0.
+
+This quantity here is the
+probability that we'll be in
+
+state j at time n.
+
+Since you either are or you're
+not, since this is also equal
+
+to the expected value of state
+j at time n, given
+
+state j at time 0.
+
+So when you add all these up,
+you're adding expectations.
+
+So this quantity here is simply
+the expected number of
+
+recurrences to state j from time
+1 up to time infinity.
+
+And that number of recurrences
+is equal to infinity.
+
+You remember we argued last time
+that the probability of
+
+one recurrence had to be equal
+to 1 if it was recurrent.
+
+If you got back to j once in
+finite time, you're going to
+
+get back again in a
+finite time again.
+
+You're going to get back
+again in finite time.
+
+It might take a very, very long
+time, but it's finite,
+
+and you have an infinite number
+of returns as time goes
+
+to infinity.
+
+So that is the consequence
+of j being recurrent.
+
+For any i such that j and i
+communicate, there's some path
+
+at some length m such that the
+probability of going from
+
+state i to state j in m steps
+is greater than 0.
+
+That's by meaning
+of communicate.
+
+And there's some m and
+some pji of l.
+
+Oh, for [? some m. ?]
+
+And there's some way of getting
+back from j to i.
+
+So what you're doing is going
+from state i to state j, and
+
+there is some path
+for doing that.
+
+You're wobbling around,
+returning to state j,
+
+returning to state j,
+maybe returning to
+
+state i along the way.
+
+That's part of it.
+
+And eventually there's
+some path for going
+
+from j back to i again.
+
+So this sum here is greater
+than or equal.
+
+And now all I'm doing is summing
+up the paths which in
+
+m steps go from i to j, and
+those paths which in the final
+
+l steps go from j back to i.
+
+And they do whatever they
+want to in between.
+
+So I'm summing over the number
+of times they are in between.
+
+And this sum here is
+summing over pjjk.
+
+And that sum is infinite,
+so this sum is infinite.
+
+So that shows that if j is
+recurrent, then i is recurrent
+
+also for any i in
+the same class.
+
+And you can do the same thing
+reversing i and j, obviously.
+
+And if that's true for all
+classes that are very
+
+recurrent, all law classes that
+are transient have to be
+
+in the same class also, because
+a state is either
+
+transient or it's recurrent.
+
+If a state j is recurrent,
+then the
+
+recurrence time, T sub jj.
+
+When you read this chapter or
+read my notes, I apologize
+
+because there's a huge
+confusion here.
+
+And the confusion comes from
+the fact that there's an
+
+extraordinary amount
+of notation here.
+
+We're dealing with all the
+notation of finite-state
+
+Markov chains.
+
+We're dealing with all the
+notation of renewal processes.
+
+And we're jumping back and forth
+between theorems for one
+
+and theorems for the other.
+
+And then we're inventing
+a lot of new notation.
+
+And I have to rewrite
+that section.
+
+But anyway, the results are all
+correct as far as I know.
+
+I mean, all of you can remember
+notation much better
+
+than I can.
+
+So if I can remember this
+notation, you can also.
+
+Let me put it that way.
+
+So I can't feel too
+sorry for you.
+
+I want to rewrite it because I'm
+feeling sorry for myself
+
+after every year I go through
+this and try to re-understand
+
+it again, and I find it
+very hard to do it.
+
+So I'm going to rewrite
+it and get rid of
+
+some of that notation.
+
+We've already seen that if you
+have a chain like this, which
+
+is simply the Markov chain
+corresponding to Bernoulli
+
+trials, if it's Bernoulli trials
+with p equals 1/2, you
+
+move up a probability
+1/2, you move down
+
+with probability 1/2.
+
+As we said, you eventually
+disperse.
+
+And as you disperse, the
+probability of being in any
+
+one of these states goes to 0.
+
+And what that means is that the
+individual probabilities
+
+of the states is going to 0.
+
+You can also see, not so easily,
+that you're eventually
+
+going to return to each state
+with probability 1.
+
+And I'm sorry I didn't give
+that definition first.
+
+We gave it last time.
+
+If the expected value of the
+renewal time is less than
+
+infinity, then j is positive
+recurrent.
+
+If T sub jj, the recurrence
+time, is a random variable but
+
+it has infinite expectation,
+then j is not recurrent.
+
+And finally, if none of those
+things happen, j is transient.
+
+So that we went through
+last time.
+
+And for p equals 1/2, and in
+both of these situations, the
+
+probability of being in any
+state is going to 0.
+
+The expected time of returning
+is going to infinity.
+
+But with probability 1, you
+will return eventually.
+
+So in both of these cases, these
+are both examples of no
+
+recurrence.
+
+Let's say more about positive
+recurrence and no recurrence.
+
+Suppose, first, that i and j
+are both recurrent and they
+
+both communicate with
+each other.
+
+In other words, there's a path
+from i to j, there's a path
+
+from j to i.
+
+And I want to look at
+the renewal process
+
+of returns to j.
+
+You've sorted out by now, I
+think, that recurrence means
+
+exactly what you
+think it means.
+
+A recurrence means, starting
+from a state j, there's a
+
+recurrence to j if eventually
+you come back to j.
+
+And this random variable, the
+recurrence of random variable,
+
+is the amount of time it takes
+you to get back to j once
+
+you've been in j.
+
+That's a random variable.
+
+So let's look at the renewal
+process, starting in j, of
+
+returning to j eventually.
+
+This is one of the
+things that makes
+
+this whole study awkward.
+
+We have renewal processes when
+we start at j and we bob back
+
+to j at various periods
+of time.
+
+If we start in i and we're
+interested in returns to j,
+
+then we have something called
+a delayed renewal process.
+
+All the theorems about
+renewals apply there.
+
+It's a little harder to
+see what's going on.
+
+It's in the end of
+chapter four.
+
+You should have read it,
+at least quickly.
+
+But we're going to avoid those
+theorems and instead go
+
+directly using the theorems
+of renewal processes.
+
+But there's still places where
+the transitions are awkward.
+
+So I can warn you about that.
+
+But the renewal reward theorem,
+if I look at this
+
+renewal process, I get a
+renewal every time I
+
+return to state j.
+
+But in that renewal process of
+returns to state j, what I'm
+
+really interested in is returns
+to state i, because
+
+what I'm trying to do here is
+relate how often do you go to
+
+state i with how often
+do you go to state j?
+
+So we have a little bit of a
+symmetry in it, because we're
+
+starting in state j,
+because that gives
+
+us a renewal process.
+
+But now we have this renewal
+reward process, where we give
+
+ourselves a reward of 1 every
+time we hit state i.
+
+And we have a renewal every
+time we hit state j.
+
+So how does that renewal
+process work?
+
+Well, it's a renewal process
+just like every other one
+
+we've studied.
+
+It has this peculiar feature
+here that is a discrete time
+
+renewal process.
+
+And with discrete time renewal
+processes, as we've seen, you
+
+can save yourself a lot of
+aggravation by only looking at
+
+these discrete times.
+
+Namely, you only look
+at integer times.
+
+And now when you only look
+at integer times--
+
+well, whether you look at
+integer times or not--
+
+this is the fundamental theorem
+of renewal rewards.
+
+If you look at the limit as t
+goes to infinity, there's the
+
+integral of the rewards
+you pick up.
+
+For this discrete case, this
+is just a summation of the
+
+rewards that you get.
+
+This summation here by the
+theorem is equal to the
+
+expected number of rewards
+within one renewal period.
+
+Namely, this is the expected
+number of recurrences of state
+
+i per state j.
+
+So in between each occurrence
+of state j, what's the
+
+expected number of
+i's that I hit?
+
+And that's the number
+that it is.
+
+We don't know what that number
+is, but we could calculate it
+
+if we wanted to.
+
+It's not a limit of anything.
+
+Well, it's a sort of a limit,
+but not very much of a limit
+
+that's well defined.
+
+And the theorem says that this
+integral is equal to that
+
+expected value divided by
+the expected recurrence
+
+time of T sub jj.
+
+Now, we argue that this is,
+in fact, the number of
+
+occurrences of state i.
+
+So it's in the limit.
+
+It's 1 over the expected
+value of the recurrence
+
+time to state i.
+
+So what this says is the 1 over
+the recurrence time to
+
+state i is equal to the expected
+number of recurrences
+
+to state i per state j divided
+by the expected
+
+time in state j.
+
+If you think about that for a
+minute, it's something which
+
+is intuitively obvious.
+
+I mean, you look at this long
+sequences of things.
+
+You keep hitting j's every
+once in a while.
+
+And then what you do,
+is you count all of
+
+the i's that occur.
+
+So now looking at it this way,
+you're going to count the
+
+number of i's that occur
+in between each j.
+
+You can't have a simultaneous
+i and j.
+
+The state is o or j.
+
+So for each recurrence period,
+you count the number of i's
+
+that occur.
+
+And what this is then saying,
+is the expected time between
+
+i's is equal to the expected
+time between j's divided by--
+
+if I turn this equation upside
+down, the expected time
+
+between i's is equal to the
+expected time between j's
+
+divided by the expected
+number of i's per j.
+
+What else would you expect?
+
+It has to be that way, right?
+
+But this says that it
+indeed, is that way.
+
+Mathematics is sometimes
+confusing with countable-state
+
+chains as we've seen.
+
+OK, so the theorem then says for
+i and j recurrent, either
+
+both are positive-recurrent or
+both are null-recurrent.
+
+So this is adding to the
+theorem we had earlier.
+
+The theorem we had earlier says
+that all states within a
+
+class are either recurrent
+or they're transient.
+
+This now divides the ones that
+are recurrent into two
+
+subsets, those that are
+null-recurrent and those that
+
+are positive-recurrent.
+
+It says that for states within
+a class, either all of them
+
+are recurrent or all
+of them are--
+
+all of them are
+positive-recurrent or all of
+
+them are null-recurrent.
+
+And this theorem shows it
+because this theorem says
+
+there has to be an expected
+number of occurrences of state
+
+i between each occurrence
+of state j.
+
+Why is that?
+
+Because there has to be
+a path from i to j.
+
+And there has to be a path that
+doesn't go through i.
+
+Because if you have a path from
+i that goes back to i and
+
+then off to j, there's also
+this path from i to j.
+
+So there's a path from i to j.
+
+There's a path from j to i that
+does not go through i.
+
+That has positive probability
+because paths are only defined
+
+over transitions with positive
+probability.
+
+So this quantity is always
+positive if you're talking
+
+about two states in
+the same class.
+
+So what this relationship says,
+along with the fact that
+
+it's a very nice and convenient
+relationship--
+
+I almost put it in the
+quiz for finite
+
+state and Markov chains.
+
+And you cam be happy I didn't,
+because proving it takes a
+
+little more agility than
+what one might
+
+expect at this point.
+
+The theorem then says that if i
+and j are recurrent, either
+
+both are positive-recurrent or
+both are null-recurrent, what
+
+the overall theorem then says
+is that for every class of
+
+states, either all of them are
+transient, all of them are
+
+null-recurrent, or all of them
+are positive-recurrent.
+
+And that's sort of a convenient
+relationship.
+
+You can't have some states
+that you never get to.
+
+Or you only get to with an
+infinite recurrence time in a
+
+class and others that you keep
+coming back to all the time.
+
+If there's a path from one to
+the other, then they have to
+
+work the same way.
+
+This sort of makes it
+obvious why that is.
+
+And this is too sensitive.
+
+OK.
+
+OK , so now we want to look
+at steady state for
+
+positive-recurrent chain.
+
+Do you remember that when we
+looked at finite state in
+
+Markov chains, we did all this
+classification stuff, and then
+
+we went into all this
+matrix stuff?
+
+And the outcome of the matrix
+stuff, the most important
+
+things, were that there
+is a steady state.
+
+There's always a set of
+probabilities such that if you
+
+start the chain in those
+probabilities, the chain stays
+
+in those probabilities.
+
+There's always a set of pi sub
+i's, which are probabilities.
+
+They all sum to 1.
+
+They're all non-negative.
+
+And each of them satisfy the
+relationship, the probability
+
+that you're in state j at time
+t is equal to the probability
+
+that you're in state i at
+time t minus 1 times the
+
+probability of going
+from state i to j.
+
+This is completely familiar
+from finite-state chains.
+
+And this is exactly
+the same for
+
+countable-state and Markov chains.
+
+The only question is, it's now
+not at all sure that that
+
+equation has a solution
+anymore.
+
+And unfortunately, you can't
+use matrix theory to prove
+
+that it has a solution.
+
+So we have to find some
+other way of doing it.
+
+So we look in our toolbox,
+which we developed
+
+throughout the term.
+
+And there's only one obvious
+thing to try, and
+
+it's renewal theory.
+
+So we use renewal theory.
+
+We then want to have one other
+definition, which you'll see
+
+throughout the rest of the term
+and every time you start
+
+reading about Markov chains.
+
+When you read about Markov
+chains in queuing kinds of
+
+situations, which are the kinds
+of things that occur all
+
+over the place, almost all of
+those Markov chains are
+
+countable-state Markov chains.
+
+And therefore, you need a
+convenient word to talk about
+
+a class of states where all of
+the states in that class
+
+communicate with each other.
+
+And irreducible is the
+definition that we use.
+
+An irreducible Markov chain is
+a Markov chain in which all
+
+pairs of states communicate
+with each other.
+
+And before, when we were talking
+about finite-state
+
+Markov chains, if all states
+communicated with each other,
+
+then they were are recurrent.
+
+You had a recurrent Markov
+chain, end of story.
+
+Now we've seen that you can have
+a Markov chain where all
+
+the states communicate
+with each other.
+
+We just had these
+two examples--
+
+these two examples here
+where they all
+
+communicate with each other.
+
+But depending on what p and q
+are, they're either transition
+
+transient, or they're
+positive-recurrent, or they're
+
+null-recurrent.
+
+The first one can't even be
+positive-recurrent, but it can
+
+be recurrent.
+
+And the bottom one can also
+be positive-recurrent.
+
+So any Markov chain where all
+the states communicate with
+
+each other--
+
+there's a path from everything
+to everything else--
+
+which is the usual situation,
+is called an irreducible
+
+Markov chain.
+
+An irreducible can now be
+positive-recurrent,
+
+null-recurrent, or transient.
+
+All the states in an irreducible
+Markov chain have
+
+to be transient, or all
+of them have to be
+
+positive-recurrent, or all
+of them have to be
+
+null-recurrent.
+
+You can't share these
+qualities over
+
+an irreducible chain.
+
+That's what this last
+theorem just said.
+
+OK, so if a steady
+state exists--
+
+namely if the solution to those
+equations exist, and if
+
+the probability that X sub 0
+equals i is equal to pi i.
+
+And incidentally, in the version
+that got handed out,
+
+that equation there was
+a little bit garbled.
+
+That one.
+
+Said the probability that X sub
+0 was equal to pi i, which
+
+doesn't make any sense.
+
+If a steady-state exists
+and you start out in
+
+steady-state--
+
+namely, the starting state X
+sub 0 is in state i with
+
+probability pi sub i by for
+every i, this is the same
+
+trick we played for
+
+finite-state and Markov chains.
+
+As we go through this, I will
+try to explain what's the same
+
+and what's different.
+
+And this is completely
+the same.
+
+So there's nothing new here.
+
+Then, this situation of being in
+steady-state persists from
+
+one unit of time to the next.
+
+Namely, if you start out in
+steady-state, then the
+
+probability that X sub 1 is
+equal to j is equal to the sum
+
+over i of pi sub i.
+
+That's the probability that
+X sub 0 is equal to i.
+
+Times P sub i j, which by the
+steady-state equations, is
+
+equal to pi sub j.
+
+So you start out in
+steady-state.
+
+After one transition, you're
+in steady-state again.
+
+You're in steady-state
+at time 1.
+
+Guess what, you're
+in state time 2.
+
+You're in steady-state again.
+
+And you stay in steady-state
+forever.
+
+So when you iterate, the
+probability that you're in
+
+state j at time X sub n is
+equal to pi sub j also.
+
+This is assuming that you
+started out in steady-state.
+
+So again, we need some
+new notation here.
+
+Let's let N sub j of tilde be
+the number of visits to j in
+
+the period 0 to t starting
+in steady-state.
+
+Namely, if you start in state j,
+we get a renewal process to
+
+talk about the returns
+to state j.
+
+If we start in steady-state,
+then this first return to
+
+state j is going to have a
+different set of probabilities
+
+than all subsequent returns
+to state j.
+
+So N sub j of t, tilde is now
+not a renewal process, but a
+
+delayed renewal process.
+
+So we have to deal with it
+a little bit differently.
+
+But it's a very nice thing
+because for all t, the
+
+expected number of returns to
+state j over t transitions is
+
+equal to n times pi sub j.
+
+Pi sub j is the probability that
+you will be in state j at
+
+any time n.
+
+And it stays the same
+for every n.
+
+So if we look at the expected
+number of times we hit state
+
+j, it's exactly equal
+to n times pi sub j.
+
+And again, here's this
+awkward thing about
+
+renewals and Markov.
+
+Yes?
+
+AUDIENCE: So is that sort of
+like an ensemble average--
+
+PROFESSOR: Yes.
+
+AUDIENCE: Or is the time
+average [INAUDIBLE]?
+
+PROFESSOR: Well, it's an
+ensemble average and it's a
+
+time average.
+
+But the thing we're working
+with here is the
+
+fact there's a time--
+
+is the fact that it's an
+ensemble average, yes.
+
+But it's convenient
+because it's an
+
+exact ensemble average.
+
+Usually, with renewal processes,
+things are ugly
+
+until you start getting
+into the limit zone.
+
+Here, everything is nice
+and clean all the time.
+
+So we start out in steady-state
+and we get this
+
+beautiful result.
+
+It's starting in steady-state.
+
+The expected number of visit
+to state j by time n--
+
+oh, this is interesting.
+
+That t there should
+be n obviously.
+
+Well, since we have t's
+everywhere else, that n there
+
+should probably be t also.
+
+So you can fix it whichever
+way you want.
+
+n's and t's are the same.
+
+I mean, for the purposes of this
+lecture, let all t's be
+
+n's and let all n's be t's.
+
+This works for some things.
+
+This starts in steady state,
+stays in steady state.
+
+It doesn't work for renewals
+because it's a delayed renewal
+
+process, so you can't talk
+about a renewal process
+
+starting in state j, because you
+don't know that it starts
+
+in state j.
+
+So sometimes we want
+to deal with this.
+
+Sometimes we want to
+deal with this.
+
+This is the number of returns
+to t starting in state j.
+
+This is the number of returns
+to state j over 0 to t if we
+
+start in steady-state.
+
+Here's a useful hack, which you
+can use a lot of the time.
+
+Look at what N sub
+i j of t is.
+
+It's the number of times
+you hit state j
+
+starting in state i.
+
+So let's look at it as you go
+for while, you hit state j for
+
+the first time.
+
+After hitting state j for the
+first time, you then go
+
+through a number of repetitions
+of state j.
+
+But after that first time you
+hit state j, you have a
+
+renewal process starting then.
+
+In other words, you have a
+delayed renewal process up to
+
+the first renewal.
+
+After that, you have
+all the statistics
+
+of a renewal process.
+
+So the idea then is N
+sub i j of t is 1.
+
+Counts 1 for the first visit
+to j, if there are any.
+
+Plus, N sub i j of t minus
+1 for all the subsequent
+
+recurrences from j to j.
+
+Thus, when you look at the
+expected values of this, the
+
+expected value of N sub i j of
+t is less than or equal to 1
+
+for this first recurrence, for
+this first visit, plus the
+
+expected value of N sub j j of
+some number smaller than t.
+
+But N sub j j of
+t grows with t.
+
+It's a number of visits
+over some interval.
+
+And as the interval gets bigger
+and bigger, the number
+
+of visits can't shrink.
+
+So you just put the t there
+to make it an upper bound.
+
+And then, when you look at
+starting in steady-state, what
+
+you get is the sum overall
+starting states pi sub i of
+
+the expected value of
+N sub i j of t.
+
+And this is less than or equal
+to 1 plus the expected value
+
+of N sub j j of t also.
+
+So this says you can always get
+from N tilde of t to N sub
+
+j j of t, by just giving
+up this term 1
+
+here as an upper bound.
+
+If you don't like that proof--
+
+and it's not really a proof.
+
+If you try to make it a proof,
+it gets kind of ugly.
+
+It's part of the proof of
+theorem 4 in the text, which
+
+is even more ugly.
+
+Because it's mathematically
+clean with equations, but you
+
+don't get any idea of why it's
+true from looking at it.
+
+This you know why it's true from
+looking at it, but you're
+
+not quite sure that it satisfies
+the equations that
+
+you would like.
+
+I am trying to move you from
+being totally dependent on
+
+equations to being more
+dependent on ideas like this,
+
+where you can see
+what's going on.
+
+But I'm also urging you, after
+you see what's going on, to
+
+have a way to put the equations
+in to see that
+
+you're absolutely
+right with it.
+
+OK, now, we come to the major
+theorem of countable-state and
+
+Markov chains.
+
+It's sort of the crucial
+thing that everything
+
+else is based on.
+
+I mean, everything beyond
+what we've already done.
+
+For any irreducible
+Markov chain--
+
+in other words, for any Markov
+chain where all the states
+
+communicate with each other,
+the steady-state equations
+
+have a solution if and only
+if the states are
+
+positive-recurrent.
+
+Now, remember, either all the
+states are positive-recurrent
+
+or none of them are.
+
+So there's nothing
+confusing there.
+
+If all the states are
+positive-recurrent, then there
+
+is a steady-state solution.
+
+There is a solution to
+those equations.
+
+And if the set of states are
+transient, or null-recurrent,
+
+then there isn't a solution
+to all those equations.
+
+If a solution exists, then the
+probability, the steady-state
+
+probability is state i is 1 over
+the main recurrence time
+
+to state i.
+
+This is a relationship that we
+established by using renewal
+
+theory for finite-state
+and Markov chains.
+
+We're just coming
+back to it here.
+
+One thing which is important
+here is that pi sub i is
+
+greater than 0 for all i.
+
+This is a property we
+had for finite-state
+
+Markov chains also.
+
+But it's a good deal more
+surprising here.
+
+When you have a countable number
+of states, saying that
+
+every one of them has a positive
+probability is--
+
+I don't think it's entirely
+intuitive.
+
+If you think about it
+for a long time,
+
+it's sort of intuitive.
+
+But it's the kind of intuitive
+thing that really pushes your
+
+intuition into understanding
+what's going on.
+
+So let's give a Pf of this,
+of the only if part.
+
+And I will warn you
+about reading the
+
+proof in the notes.
+
+It's ugly because it just goes
+through a bunch of logical
+
+relationships and equations.
+
+You have no idea of where
+it's going or why.
+
+And finally, at the
+end it says, QED.
+
+I went through it.
+
+It's correct.
+
+But damned if I know why.
+
+And so, anyway, that has
+to be rewritten.
+
+But, anyway here's the Pf.
+
+Start out by assuming that the
+steady-state equations exist.
+
+We want to show
+positive-recurrence.
+
+Pick any j and any t.
+
+Pick any state and any time.
+
+pi sub j is equal to the
+expected value of N sub j
+
+tilde of t.
+
+That we chose for any
+Markov chain at all.
+
+If you start out in
+steady-state, you stay in
+
+steady-state.
+
+So under the assumption that
+we're in steady-state--
+
+under the assumption that we
+start out in steady-state, we
+
+stay in steady-state.
+
+This pi sub j times t has to be
+the expected value of the
+
+number of recurrences to state
+j over t time units.
+
+And what we showed on
+the last slide--
+
+you must have realized I was
+doing this for some reason.
+
+This is less than or equal to 1
+plus the expected recurrence
+
+time of state j.
+
+So pi sub j is less than or
+equal to 1 over t times this
+
+expected recurrence
+time for state j.
+
+And if we go to the limit as t
+goes to infinity, this 1 over
+
+t dribbles away to
+nothingness.
+
+So this is less than or equal to
+the limit of expected value
+
+of N sub j j of t over t.
+
+What is that?
+
+That's the expected number,
+long-term rate of
+
+visits to state j.
+
+It's what we've shown as equal
+to 1 over the expected renewal
+
+time of state j.
+
+Now, if the sum of the pi sub
+j's is equal to 1, remember
+
+what happens when you sum a
+countable set of numbers.
+
+If all of them are 0, then no
+matter how many of them you
+
+sum, you have 0.
+
+And when you go to the limit,
+you still have 0.
+
+So when you sum a set of
+countable set of non-negative
+
+numbers, you have
+to have a limit.
+
+Because it's non-decreasing.
+
+And that sum is equal to 1.
+
+Then somewhere along the line,
+you've got to find the
+
+positive probability.
+
+One of the [INAUDIBLE]
+
+has to be positive.
+
+I mean, this is almost an
+amusing proof because you work
+
+so hard to prove that one
+of them is positive.
+
+And then, almost for free, you
+get the fact that all of them
+
+have to be positive.
+
+So some pi j is greater
+than 0.
+
+If pi j is less than or equal
+to this, thus the limit as t
+
+approaches infinity of the
+expected value of N sub j j of
+
+t over t is greater than 0 for
+that j, which says j has to be
+
+positive-recurrent.
+
+Which says all the states have
+to be positive-recurrent
+
+because we've already
+shown that.
+
+So all the states are
+positive-recurrent.
+
+Then you still have to show that
+this inequality here is
+
+equality, and you've got to do
+that by playing around with
+
+summing up these things.
+
+Something has been left
+out, we have to sum
+
+those up over j.
+
+And that's another mess.
+
+I'm not going to do
+it here in class.
+
+But just sort of see
+why this happened.
+
+Yeah?
+
+AUDIENCE: [INAUDIBLE].
+
+Why do you have to show
+the equality?
+
+PROFESSOR: Why do I have
+to the equality?
+
+Because if I want to show that
+all of the pi sub i's are
+
+positive, how do I show that?
+
+All I've done is started
+out with an arbitrary--
+
+oh, I've started out with
+an arbitrary j and
+
+an arbitrary t.
+
+Because I got the fact that this
+was positive-recurrent by
+
+arguing that at least
+one of the pi sub
+
+j's had to be positive.
+
+From this I can argue
+that they're all
+
+positive-recurrent, which tells
+me that this number is
+
+greater than 0.
+
+But that doesn't show me that
+this number is greater than 0.
+
+But it is.
+
+I mean, it's all right.
+
+It all works out.
+
+But not quite in such a simple
+way as you would hope.
+
+OK, so now let's go back to
+what we called birth-death
+
+chains, but look at a slightly
+more general version of them.
+
+These are things that you--
+
+I mean, queuing theory is
+built on these things.
+
+Everything in queuing theory.
+
+Or not everything, but all the
+things that come from a
+
+Poisson kind of background.
+
+All of these somehow look at
+the birth-death chains.
+
+And the way a birth-death
+chain works is you have
+
+arbitrary self-loops.
+
+You have positive probabilities
+going from each
+
+state to the next state up.
+
+You have positive probabilities
+going from the
+
+higher state to the
+lower state.
+
+All transitions are
+limited from--
+
+i can only go to i plus 1,
+or i, for i minus 1.
+
+You can't make big jumps.
+
+You can only make jumps
+of one step.
+
+And other than that, it's
+completely general.
+
+OK, now we go through an
+interesting argument.
+
+We look at an arbitrary
+state i.
+
+And for this arbitrary state i,
+like i equals 2, we look at
+
+the number of transitions
+that go from 2 to 3.
+
+And the number transitions that
+go from 3 to 2 for any
+
+old sample path whatsoever.
+
+And for any sample path,
+the number of
+
+transitions that go up--
+
+if we start down there, before
+you can come back,
+
+you've got to go up.
+
+So if you're on that side, you
+have one more up transition
+
+than you have down transition.
+
+If you're on that side, you
+have the same number of up
+
+transitions and down
+transitions.
+
+So that as you look over a
+longer and longer time, the
+
+number of up transitions is
+effectively the same as the
+
+number of down transitions.
+
+If you have a steady-state, pi
+sub i is the fraction of time
+
+you're in state i.
+
+pi sub i times p sub i is the
+fraction of time you're going
+
+from state i to state
+i plus 1.
+
+And pi sub i by plus 1 times q
+sub i plus 1 is the fraction
+
+of time you're going
+from state i plus 1
+
+down to state i.
+
+What we've just argued by the
+fact that sample path averages
+
+and ensemble averages have to
+be equal is that pi sub i
+
+times p sub i is equal to
+pi sub i plus 1 times
+
+q sub i plus 1.
+
+In the next slide, I will
+talk about whether to
+
+believe that or not.
+
+For the moment, let's
+say we believe it.
+
+And from this equation, we
+see that the steady-state
+
+probability of i plus 1 is
+equal to the steady-state
+
+probability of i times p sub
+i over q sub i plus 1.
+
+It says that the steady-state
+probability of each pi is
+
+determined by the steady-state
+probability of the state
+
+underneath it.
+
+So you just go up.
+
+You can calculate the
+steady-state of each, the
+
+probability of each if you know
+the probability of the
+
+state below it.
+
+So if you recurse on this, pi
+sub i plus 1 is equal to pi
+
+sub i times this ratio is equal
+to pi sub i minus 1
+
+times this ratio times p sub i
+minus 1 over q sub i is equal
+
+to pi sub i minus 2 times
+this triple of things.
+
+It tells you that what you want
+to do is define row sub i
+
+as the difference of these two
+probabilities, namely rob i,
+
+for any state i, is the ratio
+of that probability to that
+
+probability.
+
+And this equation then turns
+into pi sub i plus 1 equals pi
+
+sub i times row sub i.
+
+If you put all those
+things together--
+
+if you just paste them one after
+the other, the way I was
+
+suggesting--
+
+what you get is pi sub i is
+equal to pi sub 0 times this
+
+product of terms.
+
+The product of terms looks
+a little ugly.
+
+Why don't I care about
+that very much?
+
+Well, because usually, when you
+have a chain like this,
+
+all the Ps are the same and
+all the Qs are the same--
+
+or all the Ps are the same for
+some point beyond someplace,
+
+they're are different
+before that.
+
+There's always some structure
+to make life easy for you.
+
+Oh, that's my computer.
+
+It's telling me what
+time it is.
+
+I'm sorry.
+
+OK.
+
+So pi sub i is this.
+
+We then have to calculate
+pi sub 0.
+
+Pi sub 0 is then 1 divided
+by the sum of all the
+
+probabilities is pi sub 0 times
+all those other things.
+
+It's 1 plus the sum here.
+
+And now if you don't believe
+what I did here, and I don't
+
+blame you for being a little
+bit skeptical.
+
+If you don't believe this, then
+you look at this and you
+
+say, OK, I can now go back and
+look at the steady state
+
+equations themselves and I can
+plug this into the steady
+
+state equations themselves.
+
+And you will immediately see
+that this solution satisfies
+
+the steady state equations.
+
+OK.
+
+Oh, damn.
+
+Excuse my language.
+
+OK.
+
+So we have our birth-death
+chain with all these
+
+transitions here.
+
+We have our solution to it.
+
+Note that the solution is only
+a function of these rows.
+
+It's only a function of the
+ratio of p sub i to
+
+Q sub i plus 1.
+
+It doesn't depend on those
+self loops at all.
+
+Isn't that peculiar?
+
+Completely independent of what
+those self loops are.
+
+Well, you'll see later that it's
+not totally independent
+
+of it, but it's essentially
+independent of it.
+
+And you think about that for a
+while and suddenly it's not
+
+that confusing because those
+equations have come from
+
+looking at up transitions
+and down transitions.
+
+By looking at an up transition
+and a down transition at one
+
+place here, it tells you
+something about the fraction
+
+of time you're over there and
+the fraction of time you're
+
+down there if you know what
+these steady state
+
+probabilities are.
+
+So if you think about it for a
+bit, you realize that these
+
+steady state probabilities
+cannot depend that strongly on
+
+what those self loops are.
+
+So this all sort
+of makes sense.
+
+The next thing is the expression
+for pi 0--
+
+namely this thing here--
+
+is a product of these terms.
+
+It converges and therefore the
+chain is positive recurrent
+
+because there is a solution to
+the steady state equation.
+
+It converges if the
+row sub i's are
+
+asymptotically less than 1.
+
+So for example, if
+the row sub i's--
+
+beyond i equals 100--
+
+are bounded by, say, 0.9, then
+these terms have to go to 0
+
+rapidly after i equals 100 and
+this product has to converge.
+
+I say essentially here of all
+these particular cases where
+
+the row sub i's are very close
+to 1, and they're converging
+
+very slowly to 1
+and who knows.
+
+But for most of the things we
+do, these row sub i's are
+
+strictly less than
+1 as you move up.
+
+And it says that you have
+to have steady state
+
+probabilities.
+
+So for most birth-death chains,
+it's almost immediate
+
+to establish whether it's
+recurrent, positive recurrent,
+
+or not positive recurrent.
+
+And we'll talk more about that
+when we get into Markov
+
+processes, but that's enough
+of it for now.
+
+Comment on methodology.
+
+We could check the renewal
+results carefully, because
+
+what we're doing here is
+assuming something rather
+
+peculiar about time averages
+and ensemble averages.
+
+And sometimes you have to worry
+about those things, but
+
+here, we don't have to worry
+about it because we have this
+
+major theorem which tells
+us if steady state
+
+probabilities exist--
+
+and they exist because they
+satisfy these equations--
+
+then you have positive
+recurrence.
+
+So it says the methodology to
+use is not to get involved in
+
+any deep theory, but just
+to see if these
+
+equations are satisfied.
+
+Again, good mathematicians
+are lazy--
+
+good engineers are
+even lazier.
+
+That's my motto of the day.
+
+And finally, birth-death
+chains are going to be
+
+particularly useful in queuing
+where the births are arrivals
+
+and the deaths are departures.
+
+OK.
+
+Now we come to reversibility.
+
+I'm glad we're coming to that
+towards the end of the lecture
+
+because reversibility is
+something which I don't think
+
+any of you guys even--
+
+and I think this is a
+pretty smart class--
+
+but I've never seen anybody who
+understands reversibility
+
+the first time they
+think about it.
+
+It's a very peculiar concept and
+the results coming from it
+
+are peculiar, and we will have
+to live with it for a while.
+
+But let's start out with
+the easy things--
+
+just with a definition of
+what a Markov chain is.
+
+This top equation here says
+that the probability of a
+
+whole bunch of states--
+
+X sub n plus k down to X sub n
+plus 1 given the stated time,
+
+n, down to the stated time 0.
+
+Because of the Markov condition,
+that has to be
+
+equal to the probability
+of these terms
+
+just given X sub n.
+
+Namely, if you know what X sub
+n is, for the future, you
+
+don't have to know what any of
+those previous states are.
+
+You get that directly from
+where we started with the
+
+Markov chains-- the probability
+of X sub n plus 1,
+
+given all this stuff, and
+then you just add the
+
+other things onto it.
+
+Now, if you define A plus as any
+event which is defined in
+
+terms of X sub n plus 1, X of n
+plus 2, and so forth up, and
+
+if you define A minus as
+anything which is a function
+
+of X sub n minus 1, X sub n
+minus 2, down to X sub 0, then
+
+what this equations
+says is that the
+
+probability of any A plus--
+
+given X sub n and A minus--
+
+is equal to the probability
+of A plus given X sub n.
+
+And this hasn't gotten
+hard yet.
+
+If you think this is
+hard, just wait.
+
+If we now multiply this by
+the probability of A
+
+minus given X sub n--
+
+and what I'm trying to get at
+is, how do you reason about
+
+the probabilities of
+earlier states
+
+given the present state?
+
+We're used to proceeding
+in time.
+
+We're used to looking at
+the past for telling
+
+what the future is.
+
+And every once and a while, you
+want to look at the future
+
+and predict what the
+past had to be.
+
+It's probably more important to
+talk about the future given
+
+the past, because sometimes
+you don't know
+
+what the future is.
+
+But mathematically, you
+have to sort that out.
+
+So if we multiply this equation
+by the probability of
+
+A minus, given X sub n,
+we don't know what
+
+that is, but it exists.
+
+It's a defined conditional
+probability.
+
+Then what we get is the
+probability of A plus and A
+
+minus, given X sub n, is equal
+to the probability of A plus,
+
+given X sub n, times the
+probability of A
+
+minus, given X sub n.
+
+So that the probability of the
+future and the past, given
+
+what's happening now, is equal
+to the probability of the
+
+future, given what's happening
+now, times the probability the
+
+past, given what's
+happening now.
+
+Which may be a more interesting
+way of looking at
+
+past and future and present
+than this totally
+
+asymmetric way here.
+
+This is a nice, symmetric
+way of looking at it.
+
+And as soon as you see that this
+has to be true, then you
+
+can turn around and write this
+the opposite way, and you see
+
+that the probability of A minus,
+given X sub n, and A
+
+plus is equal to the
+probability of A
+
+minus given X sub n.
+
+Which says that the probability
+of the past, given
+
+X sub n and the future, is equal
+to the probability of
+
+the past just given X sub n.
+
+You can go from past the future
+or you can go from
+
+future to past.
+
+And incidentally, if you people
+have trouble trying to
+
+think of the past and
+the future as
+
+being symmetric animals--
+
+and I do too--
+
+everything we do with time can
+also be done on a line going
+
+from left to right, or it
+can be done on a line
+
+going from bottom up.
+
+Going from bottom up, it's
+hard to say that this is
+
+symmetric to this.
+
+If you look at it on a line
+going from left to right, it's
+
+kind of easy to see that this
+is symmetric between left to
+
+right and right to left.
+
+So every time you get confused
+about these arguments, put
+
+them on a line and argue right
+to left and left to right
+
+instead of earlier and later.
+
+Because mathematically, it's
+the same thing, but it's
+
+easier to see these
+symmetries.
+
+And now, if you think of A minus
+as being X sub n minus
+
+1, and you think of A plus as
+being X sub n plus 1, X sub n
+
+plus 2 and so forth up, what
+this equation says is that the
+
+probability of the last state
+in the past, given the state
+
+now and everything in the
+future, is equal to the
+
+probability of the last state
+in the past given X sub n.
+
+Now, this isn't reversibility.
+
+I'm not saying that these
+are special process.
+
+This is true for any Markov
+chain in the world.
+
+These relationships
+are always true.
+
+This is one reason why many
+people view this as the real
+
+Markov condition, as opposed to
+any of these other things.
+
+They say that three events
+have a Markov condition
+
+between them if there's
+one of them which is
+
+in between the other.
+
+Where you can say that the
+probability of the left one,
+
+given the middle one, times
+the right one, given the
+
+middle one, is equal to the
+probability of the left and
+
+the right given the middle.
+
+It says that the past and the
+future, given the present, are
+
+independent of each other.
+
+It says that as soon as you
+know what the present is,
+
+everything down there
+is independent of
+
+everything up there.
+
+That's a pretty powerful
+condition.
+
+And you'll see that we can do an
+awful lot with it, so it's
+
+going to be important.
+
+OK.
+
+So let's go on with that.
+
+By Bayes rule--
+
+and incidentally, this is why
+Bayes got into so much trouble
+
+with the other statisticians
+in the world.
+
+Because the other statisticians
+in the world
+
+really got emotionally upset at
+the idea of talking about
+
+the past given the future.
+
+That was almost an attack on
+their religion as well as all
+
+the mathematics they knew and
+everything else they knew.
+
+It was really hitting them below
+the belt, so to speak.
+
+So they didn't like this.
+
+But now, we've recognized that
+Bayes' Law is just the
+
+consequence of the axioms of
+probability, and there's
+
+nothing strange about it.
+
+You write down these conditional
+probabilities and
+
+that's sitting there,
+facing you.
+
+But what it says here is that
+the probability of the state
+
+at time n minus 1, given the
+state of time n, is equal to
+
+the probability of the state
+of time n, given n minus 1,
+
+times the probability of X
+n minus 1 divided by the
+
+probability of X n.
+
+In other words, you put this
+over in this side, and it says
+
+the probability of X n times the
+probability of X n minus 1
+
+given X n is that probability
+up there.
+
+It says that the probability
+of A given B times the
+
+probability of B is equal to the
+probability of A times the
+
+probability of B given A. And
+that's just the definition of
+
+a conditional probability,
+nothing more.
+
+OK.
+
+If the forward chain is in
+a steady state, then the
+
+probability that X sub n minus
+1 equals j, given X sub n
+
+equals i, is pji times pi sub
+j divided by pi sub i.
+
+These probabilities become
+just probabilities which
+
+depend on i but not on n.
+
+Now what's going on here is
+when you look at this
+
+equation, it looks peculiar
+because normally with a Markov
+
+chain, we start out at time 0
+with some assumed probability
+
+distribution.
+
+And as soon as you start out
+with some assumed probability
+
+distribution at time 0 and you
+start talking about the past
+
+condition on the future,
+it gets very sticky.
+
+Because when you talk about
+the past condition on the
+
+future, you can only go back to
+time equals 0, and you know
+
+what's happening down there
+because you have some
+
+established probabilities
+at 0.
+
+So what it says is in this
+equation here, it says that
+
+the Markov chain, defined
+by this rule--
+
+I guess I ought to back
+and look at the
+
+previous slide for that.
+
+This is saying the probability
+of the state at time n minus
+
+1, conditional on the entire
+future, is equal to the
+
+probability of X sub n minus
+1 just given X sub n.
+
+This is the Markov condition,
+but it's the Markov condition
+
+turned around.
+
+Usually we talk about the next
+state given the previous state
+
+and everything before that.
+
+Here, we're talking about
+the previous state given
+
+everything after that.
+
+So this really is the Markov
+condition on what we might
+
+view as a backward chain.
+
+But to be a Markov chain, these
+transition probabilities
+
+have to be independent of n.
+
+The transition probabilities
+are not going to be
+
+independent of n if you have
+these arbitrary probabilities
+
+at time 0 lousing
+everything up.
+
+So you can get around
+this in two ways.
+
+One way to get around it is
+to say let's restrict our
+
+attention to positive recurrent
+processes which are
+
+starting out in a
+steady state.
+
+And if we start out in a steady
+state, then these
+
+probabilities here--
+
+looking at these probabilities
+here--
+
+if you go from here down to
+here, you'll find out that
+
+this does not depend on n.
+
+And if you have an initial state
+which is something other
+
+than steady state, then these
+will depend on it.
+
+Let me put this down in
+the next chain up.
+
+The probability of X sub n minus
+1 given X sub n is going
+
+to be independent of n if this
+is independent of n, which it
+
+is, because we have a
+homogeneous Markov chain.
+
+And this is independent of n and
+this is independent of n.
+
+Now, this will just be the
+probability of pi sub i if X
+
+sub n minus 1 is equal to i.
+
+And this will be pi sub i if
+probability of X sub n is
+
+equal to i.
+
+So this and this will be
+independent of n if in fact we
+
+start out in a steady state.
+
+In other words, it won't be.
+
+So what we're doing here is we
+normally think of a Markov
+
+chain starting out at time 0
+because how else can you get
+
+it started?
+
+And we think of it in forward
+time, and then we say, well,
+
+we want to make it homogeneous,
+because we want
+
+to make it always do the same
+thing in the future otherwise
+
+it doesn't really look much
+like the a Markov chain.
+
+So what we're saying is that
+this backward chain-- we have
+
+backward probabilities
+defined now--
+
+the backward probabilities are
+homogeneous if the forward
+
+probabilities start
+in a steady state.
+
+You could probably make a
+similar statement but say the
+
+forward probabilities are
+homogeneous if the backward
+
+probabilities start
+in a steady state.
+
+But I don't know when you're
+going to start.
+
+You're going to have to start it
+sometime in the future, and
+
+that gets too philosophical
+to understand.
+
+OK.
+
+If we think of the chain as
+starting in a steady state at
+
+time minus infinity, these are
+also the equations of the
+
+homogeneous Markov chain.
+
+We can start at time minus
+infinity wherever we want to--
+
+it doesn't make any
+difference--
+
+because by the time we get to
+state 0, we will be in steady
+
+state, and the whole range of
+where we want to look at
+
+things will be in
+steady state.
+
+OK.
+
+So aside from this issue about
+starting at 0 and steady state
+
+and things like that, what we've
+really shown here is
+
+that you can look at a Markov
+chain either going forward or
+
+going backward.
+
+Or look at it going rightward
+or going leftward.
+
+And that's really pretty
+important.
+
+OK.
+
+That still doesn't say anything
+about it being
+
+reversible.
+
+What reversibility is--
+
+it comes from looking at
+this equation here.
+
+This says what the transition
+probabilities are, going
+
+backwards, and this
+is the transition
+
+probabilities going forward.
+
+These are the steady state
+probabilities.
+
+And if we define P star of ji
+as a backward transition
+
+probabilities--
+
+namely, the probability that at
+this time or in stage A--
+
+given that in this next time,
+which to us, is the previous
+
+time, we're in state i, is the
+probability of going in a
+
+backward direction
+from j to i.
+
+This gets into whether this is
+P star of ij or P star of ij.
+
+But I did check it carefully,
+so it has to be right.
+
+So anyway, when you substitute
+this in for this, the
+
+conditions that you get is pi
+sub i times P star of ij is
+
+equal to pi j times P of ji.
+
+These are the same equations
+that we had for
+
+a birth-death chain.
+
+But now, we're not talking
+about birth-death chains.
+
+Now we're talking about
+any old chain.
+
+Yeah?
+
+AUDIENCE: Doesn't this only
+make sense for positive
+
+recurring chains?
+
+PROFESSOR: Yes.
+
+Sorry.
+
+I should keep emphasizing that,
+because it only makes
+
+sense when you can define the
+steady state probabilities.
+
+Yes.
+
+The steady state probabilities
+are necessary in order to even
+
+define this P star of ji.
+
+But once you have that steady
+state condition, and once you
+
+know what the steady state
+probabilities are, then you
+
+can calculate backward
+probabilities, you can
+
+calculate forward probabilities,
+and this is a
+
+very simple relationship
+that they satisfy.
+
+It makes sense because this
+is a normal form.
+
+You look at state transition
+probabilities and you look at
+
+the probability of being in
+one state and then the
+
+probability of going
+to the next state.
+
+And the question is the
+next state back there
+
+or is it over there?
+
+And if it's a star, then it
+means it's back there.
+
+And then we define a chain as
+being reversible if P star of
+
+ij is equal to P sub ij,
+for all i and all j.
+
+And what that means is that
+all birth-death chains are
+
+reversible.
+
+And now let me show you
+what that means.
+
+If we look at arrivals and
+departures for a birth-death
+
+change, sometimes you go in a
+self loop, so you don't go up
+
+and you don't go down.
+
+Other times you either
+go down or you go up.
+
+We have arrivals coming in.
+
+Arrivals correspond to upper
+transitions, departures
+
+correspond to downward
+transitions so that when you
+
+look at it in a normal way,
+you start out at time 0.
+
+You're in state 0.
+
+You have an arrival.
+
+Nothing happens for a while.
+
+You have another arrival, but
+this time, you have a
+
+departure, you have another
+departure, and you wind up in
+
+state 0 again.
+
+As far states are concerned,
+you go from
+
+state 0 to state 1.
+
+You stay in state 1.
+
+In other words, this is the
+difference between arrivals
+
+and departures.
+
+This is what the state is.
+
+You stay in state 1.
+
+Then you go up and you get
+another arrival, you get a
+
+departure, and then you
+get a departure,
+
+according to this chain.
+
+Now, let's look at it
+coming in this way.
+
+When we look at it
+coming backwards
+
+in time, what happens?
+
+We're going along here,
+we're in state 0,
+
+suddenly we move up.
+
+If we want to view this as a
+backward moving Markov chain,
+
+this corresponds to an
+arrival of something.
+
+This corresponds to
+another arrival.
+
+This corresponds
+to a departure.
+
+We go along here with nothing
+else happening, we get another
+
+departure, and there we are back
+in a steady state again.
+
+And for any birth-death
+chain, we can do this.
+
+Because any birth-death chain
+we can look at as an arrival
+
+and departure process.
+
+We have arrivals, we
+have departures--
+
+we might have states
+that go negative.
+
+That would be rather awkward,
+but we can have that.
+
+But now, if we know that these
+steady state probabilities
+
+govern the probability of
+arrivals and the probabilities
+
+of departures, if we know that
+we have reversibility, then
+
+these events here have the
+same probability as these
+
+events here.
+
+It means that when we look at
+things going from right back
+
+to left, it means that the
+things that we viewed as
+
+departures here look
+like arrivals.
+
+And what we're going to do next
+time is use that to prove
+
+Burke's Theorem, which says
+using this idea that if you
+
+look at the process of
+departures in a birth-death
+
+chain where arrivals are all
+with probability P and
+
+departures are all with
+probability Q, then you get
+
+this nice set of probabilities
+for arrivals and departures.
+
+Arrivals are independent
+of everything else--
+
+same probability at every
+unit of time.
+
+Departures are the same way.
+
+But when you're looking from
+left to right, you can only
+
+get departures when your state
+is greater than 0.
+
+When you're coming in looking
+this way, these things that
+
+looked like departures before
+are looking like arrivals.
+
+These arrivals form a Bernoulli
+Process, and the
+
+Bernoulli Process says that
+given the future, the
+
+probability of a departure,
+at any instant of time, is
+
+independent of everything
+in the future.
+
+Now, that is not intuitive.
+
+If you think it's intuitive,
+go back and think again.
+
+Because it's not.
+
+But anyway, I'm going
+to stop here.
+
+You have this to mull over.
+
+We will try to sort it out
+a little more next time.
+
+This is something that's going
+to take your cooperation to
+
+sort it out, also.
\ No newline at end of file
diff --git a/tEpU7QiRiUk.txt b/tEpU7QiRiUk.txt
new file mode 100644
index 0000000000000000000000000000000000000000..f15e16a7fd538f14261f84e8b54a2c298b4c9fc6
--- /dev/null
+++ b/tEpU7QiRiUk.txt
@@ -0,0 +1,20147 @@
+align:start position:0%
+ 
+Okay. So, this this little bit that I
+
+ align:start position:0%
+Okay. So, this this little bit that I
+ 
+
+ align:start position:0%
+Okay. So, this this little bit that I
+sent out to you that of course was
+
+ align:start position:0%
+sent out to you that of course was
+ 
+
+ align:start position:0%
+sent out to you that of course was
+unreadable, but this way you know at
+
+ align:start position:0%
+unreadable, but this way you know at
+ 
+
+ align:start position:0%
+unreadable, but this way you know at
+least that I was trying
+
+ align:start position:0%
+least that I was trying
+ 
+
+ align:start position:0%
+least that I was trying
+um I I I wanted you to
+
+ align:start position:0%
+um I I I wanted you to
+ 
+
+ align:start position:0%
+um I I I wanted you to
+have a brief sense of of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Tolken academic style which um you you
+
+ align:start position:0%
+Tolken academic style which um you you
+ 
+
+ align:start position:0%
+Tolken academic style which um you you
+will or would or have discovered um is
+
+ align:start position:0%
+will or would or have discovered um is
+ 
+
+ align:start position:0%
+will or would or have discovered um is
+not all that dissimilar from from his
+
+ align:start position:0%
+not all that dissimilar from from his
+ 
+
+ align:start position:0%
+not all that dissimilar from from his
+literary style. Actually, let's let's
+
+ align:start position:0%
+literary style. Actually, let's let's
+ 
+
+ align:start position:0%
+literary style. Actually, let's let's
+back up a moment. Um, how how much of
+
+ align:start position:0%
+back up a moment. Um, how how much of
+ 
+
+ align:start position:0%
+back up a moment. Um, how how much of
+this uh fantasy literature have you all
+
+ align:start position:0%
+this uh fantasy literature have you all
+ 
+
+ align:start position:0%
+this uh fantasy literature have you all
+read? Lewis, have you read all all seven
+
+ align:start position:0%
+read? Lewis, have you read all all seven
+ 
+
+ align:start position:0%
+read? Lewis, have you read all all seven
+Narnia books? Do you do you agree?
+
+ align:start position:0%
+Narnia books? Do you do you agree?
+ 
+
+ align:start position:0%
+Narnia books? Do you do you agree?
+Nothing. Okay. I don't remember most of
+
+ align:start position:0%
+Nothing. Okay. I don't remember most of
+ 
+
+ align:start position:0%
+Nothing. Okay. I don't remember most of
+it because I read it when I was like
+
+ align:start position:0%
+it because I read it when I was like
+ 
+
+ align:start position:0%
+it because I read it when I was like
+seven. Yeah. Yeah.
+
+ align:start position:0%
+seven. Yeah. Yeah.
+ 
+
+ align:start position:0%
+seven. Yeah. Yeah.
+I just recently read in the wardrobe.
+
+ align:start position:0%
+I just recently read in the wardrobe.
+ 
+
+ align:start position:0%
+I just recently read in the wardrobe.
+Uhhuh. I read the that and the the great
+
+ align:start position:0%
+Uhhuh. I read the that and the the great
+ 
+
+ align:start position:0%
+Uhhuh. I read the that and the the great
+divorce. And the great divorce. Any any
+
+ align:start position:0%
+divorce. And the great divorce. Any any
+ 
+
+ align:start position:0%
+divorce. And the great divorce. Any any
+of you read the screw tape letters? I
+
+ align:start position:0%
+of you read the screw tape letters? I
+ 
+
+ align:start position:0%
+of you read the screw tape letters? I
+keep meaning to. I have it.
+
+ align:start position:0%
+keep meaning to. I have it.
+ 
+
+ align:start position:0%
+keep meaning to. I have it.
+Yeah. Okay. Okay. Well, what what did
+
+ align:start position:0%
+Yeah. Okay. Okay. Well, what what did
+ 
+
+ align:start position:0%
+Yeah. Okay. Okay. Well, what what did
+you think about Caner's
+
+ align:start position:0%
+you think about Caner's
+ 
+
+ align:start position:0%
+you think about Caner's
+uh assessment of the Narnia series as
+
+ align:start position:0%
+uh assessment of the Narnia series as
+ 
+
+ align:start position:0%
+uh assessment of the Narnia series as
+uneven and very much for children, for
+
+ align:start position:0%
+uneven and very much for children, for
+ 
+
+ align:start position:0%
+uneven and very much for children, for
+school boys, right? Not just children. I
+
+ align:start position:0%
+school boys, right? Not just children. I
+ 
+
+ align:start position:0%
+school boys, right? Not just children. I
+was confused more about like I had been
+
+ align:start position:0%
+was confused more about like I had been
+ 
+
+ align:start position:0%
+was confused more about like I had been
+told and I learned of C. Louis more as a
+
+ align:start position:0%
+told and I learned of C. Louis more as a
+ 
+
+ align:start position:0%
+told and I learned of C. Louis more as a
+born again Christian, not as what they
+
+ align:start position:0%
+born again Christian, not as what they
+ 
+
+ align:start position:0%
+born again Christian, not as what they
+were talking about, which was, you know,
+
+ align:start position:0%
+were talking about, which was, you know,
+ 
+
+ align:start position:0%
+were talking about, which was, you know,
+the pessimistic and stuff like that and
+
+ align:start position:0%
+the pessimistic and stuff like that and
+ 
+
+ align:start position:0%
+the pessimistic and stuff like that and
+depressive religious stuff. And in fact,
+
+ align:start position:0%
+depressive religious stuff. And in fact,
+ 
+
+ align:start position:0%
+depressive religious stuff. And in fact,
+what I found always with the Narnia ones
+
+ align:start position:0%
+what I found always with the Narnia ones
+ 
+
+ align:start position:0%
+what I found always with the Narnia ones
+and especially with the great divorce
+
+ align:start position:0%
+and especially with the great divorce
+ 
+
+ align:start position:0%
+and especially with the great divorce
+was it was really really uplifting
+
+ align:start position:0%
+was it was really really uplifting
+ 
+
+ align:start position:0%
+was it was really really uplifting
+because unlike a lot of other Christian
+
+ align:start position:0%
+because unlike a lot of other Christian
+ 
+
+ align:start position:0%
+because unlike a lot of other Christian
+things where it was sort of pressing
+
+ align:start position:0%
+things where it was sort of pressing
+ 
+
+ align:start position:0%
+things where it was sort of pressing
+down on you that there was this good,
+
+ align:start position:0%
+down on you that there was this good,
+ 
+
+ align:start position:0%
+down on you that there was this good,
+you know, horrible evil and wonderful
+
+ align:start position:0%
+you know, horrible evil and wonderful
+ 
+
+ align:start position:0%
+you know, horrible evil and wonderful
+good, but it was the human choice of
+
+ align:start position:0%
+good, but it was the human choice of
+ 
+
+ align:start position:0%
+good, but it was the human choice of
+which one they wanted and they could
+
+ align:start position:0%
+which one they wanted and they could
+ 
+
+ align:start position:0%
+which one they wanted and they could
+choose and they could change their mind
+
+ align:start position:0%
+choose and they could change their mind
+ 
+
+ align:start position:0%
+choose and they could change their mind
+a few times and stuff like that. And
+
+ align:start position:0%
+a few times and stuff like that. And
+ 
+
+ align:start position:0%
+a few times and stuff like that. And
+that was what was so uplifting to it,
+
+ align:start position:0%
+that was what was so uplifting to it,
+ 
+
+ align:start position:0%
+that was what was so uplifting to it,
+which really confused me then. Like
+
+ align:start position:0%
+which really confused me then. Like
+ 
+
+ align:start position:0%
+which really confused me then. Like
+Caner, I mean, we're going to talk about
+
+ align:start position:0%
+Caner, I mean, we're going to talk about
+ 
+
+ align:start position:0%
+Caner, I mean, we're going to talk about
+this, but but Caner doesn't really like
+
+ align:start position:0%
+this, but but Caner doesn't really like
+ 
+
+ align:start position:0%
+this, but but Caner doesn't really like
+either of these characters, does he?
+
+ align:start position:0%
+either of these characters, does he?
+ 
+
+ align:start position:0%
+either of these characters, does he?
+Want to ring his neck? You wanted to
+
+ align:start position:0%
+Want to ring his neck? You wanted to
+ 
+
+ align:start position:0%
+Want to ring his neck? You wanted to
+ring Caner's neck? Oh, okay. Okay. All
+
+ align:start position:0%
+ring Caner's neck? Oh, okay. Okay. All
+ 
+
+ align:start position:0%
+ring Caner's neck? Oh, okay. Okay. All
+right. Well, you'll get your chance to
+
+ align:start position:0%
+right. Well, you'll get your chance to
+ 
+
+ align:start position:0%
+right. Well, you'll get your chance to
+ring Caner's neck. Um, so, okay. So,
+
+ align:start position:0%
+ring Caner's neck. Um, so, okay. So,
+ 
+
+ align:start position:0%
+ring Caner's neck. Um, so, okay. So,
+let's let's hold on to that. So, Lewis
+
+ align:start position:0%
+let's let's hold on to that. So, Lewis
+ 
+
+ align:start position:0%
+let's let's hold on to that. So, Lewis
+is fairly wellknown in at least the
+
+ align:start position:0%
+is fairly wellknown in at least the
+ 
+
+ align:start position:0%
+is fairly wellknown in at least the
+vaguest and general sense, except for
+
+ align:start position:0%
+vaguest and general sense, except for
+ 
+
+ align:start position:0%
+vaguest and general sense, except for
+Anarie, who didn't grow up in the United
+
+ align:start position:0%
+Anarie, who didn't grow up in the United
+ 
+
+ align:start position:0%
+Anarie, who didn't grow up in the United
+States, right? So I mean part part of
+
+ align:start position:0%
+States, right? So I mean part part of
+ 
+
+ align:start position:0%
+States, right? So I mean part part of
+the point that Caner is making here that
+
+ align:start position:0%
+the point that Caner is making here that
+ 
+
+ align:start position:0%
+the point that Caner is making here that
+I think is valid is that um that there's
+
+ align:start position:0%
+I think is valid is that um that there's
+ 
+
+ align:start position:0%
+I think is valid is that um that there's
+this particular kind of intellectual
+
+ align:start position:0%
+this particular kind of intellectual
+ 
+
+ align:start position:0%
+this particular kind of intellectual
+uh space which opens up in Britain
+
+ align:start position:0%
+uh space which opens up in Britain
+ 
+
+ align:start position:0%
+uh space which opens up in Britain
+between the wars and and into World War
+
+ align:start position:0%
+between the wars and and into World War
+ 
+
+ align:start position:0%
+between the wars and and into World War
+II that appeals for maybe some set of
+
+ align:start position:0%
+II that appeals for maybe some set of
+ 
+
+ align:start position:0%
+II that appeals for maybe some set of
+bizarre reasons. You want to sit
+
+ align:start position:0%
+bizarre reasons. You want to sit
+ 
+
+ align:start position:0%
+bizarre reasons. You want to sit
+probably down at that end um to
+
+ align:start position:0%
+probably down at that end um to
+ 
+
+ align:start position:0%
+probably down at that end um to
+Americans in particular. And so we can
+
+ align:start position:0%
+Americans in particular. And so we can
+ 
+
+ align:start position:0%
+Americans in particular. And so we can
+think about we can think about that too,
+
+ align:start position:0%
+think about we can think about that too,
+ 
+
+ align:start position:0%
+think about we can think about that too,
+right? What's going on with that? Okay,
+
+ align:start position:0%
+right? What's going on with that? Okay,
+ 
+
+ align:start position:0%
+right? What's going on with that? Okay,
+so what about
+
+ align:start position:0%
+so what about
+ 
+
+ align:start position:0%
+so what about
+Tolken? Uh, so okay, we've all we've all
+
+ align:start position:0%
+Tolken? Uh, so okay, we've all we've all
+ 
+
+ align:start position:0%
+Tolken? Uh, so okay, we've all we've all
+seen the movie recently. We we No. Yeah,
+
+ align:start position:0%
+seen the movie recently. We we No. Yeah,
+ 
+
+ align:start position:0%
+seen the movie recently. We we No. Yeah,
+I'm the odd one out. Never read the
+
+ align:start position:0%
+I'm the odd one out. Never read the
+ 
+
+ align:start position:0%
+I'm the odd one out. Never read the
+books, never seen the movies. Oh,
+
+ align:start position:0%
+books, never seen the movies. Oh,
+ 
+
+ align:start position:0%
+books, never seen the movies. Oh,
+really? I know nothing about
+
+ align:start position:0%
+really? I know nothing about
+ 
+
+ align:start position:0%
+really? I know nothing about
+Huh. Okay. Is that Is that right? Odd
+
+ align:start position:0%
+Huh. Okay. Is that Is that right? Odd
+ 
+
+ align:start position:0%
+Huh. Okay. Is that Is that right? Odd
+odd one out. The rest of you I'm pretty
+
+ align:start position:0%
+odd one out. The rest of you I'm pretty
+ 
+
+ align:start position:0%
+odd one out. The rest of you I'm pretty
+sure I'm the odd one out since I'm
+
+ align:start position:0%
+sure I'm the odd one out since I'm
+ 
+
+ align:start position:0%
+sure I'm the odd one out since I'm
+always the odd one out when I say that.
+
+ align:start position:0%
+always the odd one out when I say that.
+ 
+
+ align:start position:0%
+always the odd one out when I say that.
+So No, I know one other person.
+
+ align:start position:0%
+So No, I know one other person.
+ 
+
+ align:start position:0%
+So No, I know one other person.
+But you've all read the books in
+
+ align:start position:0%
+But you've all read the books in
+ 
+
+ align:start position:0%
+But you've all read the books in
+addition to
+
+ align:start position:0%
+addition to
+ 
+
+ align:start position:0%
+addition to
+Oh, everything.
+
+ align:start position:0%
+Oh, everything.
+ 
+
+ align:start position:0%
+Oh, everything.
+Okay. Okay. Right. The whole the whole
+
+ align:start position:0%
+Okay. Okay. Right. The whole the whole
+ 
+
+ align:start position:0%
+Okay. Okay. Right. The whole the whole
+nine yards and then some.
+
+ align:start position:0%
+nine yards and then some.
+ 
+
+ align:start position:0%
+nine yards and then some.
+Okay. Well, okay. Good. Good. So, so we
+
+ align:start position:0%
+Okay. Well, okay. Good. Good. So, so we
+ 
+
+ align:start position:0%
+Okay. Well, okay. Good. Good. So, so we
+we have a my assumption coming in was
+
+ align:start position:0%
+we have a my assumption coming in was
+ 
+
+ align:start position:0%
+we have a my assumption coming in was
+that we would be fairly mutually
+
+ align:start position:0%
+that we would be fairly mutually
+ 
+
+ align:start position:0%
+that we would be fairly mutually
+literate
+
+ align:start position:0%
+literate
+ 
+
+ align:start position:0%
+literate
+um in this respect.
+
+ align:start position:0%
+um in this respect.
+ 
+
+ align:start position:0%
+um in this respect.
+Let me start by taking us back to last
+
+ align:start position:0%
+Let me start by taking us back to last
+ 
+
+ align:start position:0%
+Let me start by taking us back to last
+week. As I was saying, when I was first
+
+ align:start position:0%
+week. As I was saying, when I was first
+ 
+
+ align:start position:0%
+week. As I was saying, when I was first
+handing back the discussion papers, it
+
+ align:start position:0%
+handing back the discussion papers, it
+ 
+
+ align:start position:0%
+handing back the discussion papers, it
+was clear not only from our
+
+ align:start position:0%
+was clear not only from our
+ 
+
+ align:start position:0%
+was clear not only from our
+conversation, but then going back and
+
+ align:start position:0%
+conversation, but then going back and
+ 
+
+ align:start position:0%
+conversation, but then going back and
+reading your discussion notes um after
+
+ align:start position:0%
+reading your discussion notes um after
+ 
+
+ align:start position:0%
+reading your discussion notes um after
+class that that um Binham's book was
+
+ align:start position:0%
+class that that um Binham's book was
+ 
+
+ align:start position:0%
+class that that um Binham's book was
+deeply disturbing.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Yes. Okay. And uh I I wish I wish Greg
+
+ align:start position:0%
+Yes. Okay. And uh I I wish I wish Greg
+ 
+
+ align:start position:0%
+Yes. Okay. And uh I I wish I wish Greg
+were here because in particular Greg had
+
+ align:start position:0%
+were here because in particular Greg had
+ 
+
+ align:start position:0%
+were here because in particular Greg had
+he said this in class but then he also
+
+ align:start position:0%
+he said this in class but then he also
+ 
+
+ align:start position:0%
+he said this in class but then he also
+again emphasized it in his in his
+
+ align:start position:0%
+again emphasized it in his in his
+ 
+
+ align:start position:0%
+again emphasized it in his in his
+discussion paper uh that that the book
+
+ align:start position:0%
+discussion paper uh that that the book
+ 
+
+ align:start position:0%
+discussion paper uh that that the book
+was so different. her argument, the
+
+ align:start position:0%
+was so different. her argument, the
+ 
+
+ align:start position:0%
+was so different. her argument, the
+things she was talking about were so
+
+ align:start position:0%
+things she was talking about were so
+ 
+
+ align:start position:0%
+things she was talking about were so
+different than than the
+
+ align:start position:0%
+different than than the
+ 
+
+ align:start position:0%
+different than than the
+Catholic institution that he understood
+
+ align:start position:0%
+Catholic institution that he understood
+ 
+
+ align:start position:0%
+Catholic institution that he understood
+from, you know, his childhood experience
+
+ align:start position:0%
+from, you know, his childhood experience
+ 
+
+ align:start position:0%
+from, you know, his childhood experience
+and and and whatever else. Um, and one
+
+ align:start position:0%
+and and and whatever else. Um, and one
+ 
+
+ align:start position:0%
+and and and whatever else. Um, and one
+of the things that we had talked about
+
+ align:start position:0%
+of the things that we had talked about
+ 
+
+ align:start position:0%
+of the things that we had talked about
+last week was at least the possibility
+
+ align:start position:0%
+last week was at least the possibility
+ 
+
+ align:start position:0%
+last week was at least the possibility
+that the piece of the medieval mental
+
+ align:start position:0%
+that the piece of the medieval mental
+ 
+
+ align:start position:0%
+that the piece of the medieval mental
+world that mine that Binham is exploring
+
+ align:start position:0%
+world that mine that Binham is exploring
+ 
+
+ align:start position:0%
+world that mine that Binham is exploring
+is one that has not particularly come
+
+ align:start position:0%
+is one that has not particularly come
+ 
+
+ align:start position:0%
+is one that has not particularly come
+forward to us. Although, right, we
+
+ align:start position:0%
+forward to us. Although, right, we
+ 
+
+ align:start position:0%
+forward to us. Although, right, we
+talked a little bit about um, uh, the
+
+ align:start position:0%
+talked a little bit about um, uh, the
+ 
+
+ align:start position:0%
+talked a little bit about um, uh, the
+fascination with this current um,
+
+ align:start position:0%
+fascination with this current um,
+ 
+
+ align:start position:0%
+fascination with this current um,
+Passion movie, right? and that that
+
+ align:start position:0%
+Passion movie, right? and that that
+ 
+
+ align:start position:0%
+Passion movie, right? and that that
+shares some of that um that particular
+
+ align:start position:0%
+shares some of that um that particular
+ 
+
+ align:start position:0%
+shares some of that um that particular
+kind of a medieval
+
+ align:start position:0%
+kind of a medieval
+ 
+
+ align:start position:0%
+kind of a medieval
+sensibility.
+
+ align:start position:0%
+sensibility.
+ 
+
+ align:start position:0%
+sensibility.
+Obviously Tolken and and maybe Lewis to
+
+ align:start position:0%
+Obviously Tolken and and maybe Lewis to
+ 
+
+ align:start position:0%
+Obviously Tolken and and maybe Lewis to
+a less obvious extent, but but Tolken in
+
+ align:start position:0%
+a less obvious extent, but but Tolken in
+ 
+
+ align:start position:0%
+a less obvious extent, but but Tolken in
+particular has very much reached into
+
+ align:start position:0%
+particular has very much reached into
+ 
+
+ align:start position:0%
+particular has very much reached into
+the present, right, with a with at least
+
+ align:start position:0%
+the present, right, with a with at least
+ 
+
+ align:start position:0%
+the present, right, with a with at least
+a medievalism, right? a kind of
+
+ align:start position:0%
+a medievalism, right? a kind of
+ 
+
+ align:start position:0%
+a medievalism, right? a kind of
+sensibility that is derived and we can
+
+ align:start position:0%
+sensibility that is derived and we can
+ 
+
+ align:start position:0%
+sensibility that is derived and we can
+talk about how medieval is it really uh
+
+ align:start position:0%
+talk about how medieval is it really uh
+ 
+
+ align:start position:0%
+talk about how medieval is it really uh
+but a sensibility that people understand
+
+ align:start position:0%
+but a sensibility that people understand
+ 
+
+ align:start position:0%
+but a sensibility that people understand
+to be medieval and and and which is
+
+ align:start position:0%
+to be medieval and and and which is
+ 
+
+ align:start position:0%
+to be medieval and and and which is
+totally
+
+ align:start position:0%
+totally
+ 
+
+ align:start position:0%
+totally
+appealing right mill billions and
+
+ align:start position:0%
+appealing right mill billions and
+ 
+
+ align:start position:0%
+appealing right mill billions and
+billions of dollars worth appealing.
+
+ align:start position:0%
+billions of dollars worth appealing.
+ 
+
+ align:start position:0%
+billions of dollars worth appealing.
+Um I mean aside from the fact that Caner
+
+ align:start position:0%
+Um I mean aside from the fact that Caner
+ 
+
+ align:start position:0%
+Um I mean aside from the fact that Caner
+doesn't like it very much although
+
+ align:start position:0%
+doesn't like it very much although
+ 
+
+ align:start position:0%
+doesn't like it very much although
+doesn't one suspect that he's just
+
+ align:start position:0%
+doesn't one suspect that he's just
+ 
+
+ align:start position:0%
+doesn't one suspect that he's just
+jealous. Yeah. Yeah. I mean there's that
+
+ align:start position:0%
+jealous. Yeah. Yeah. I mean there's that
+ 
+
+ align:start position:0%
+jealous. Yeah. Yeah. I mean there's that
+tone. I mean, he even talks about he he
+
+ align:start position:0%
+tone. I mean, he even talks about he he
+ 
+
+ align:start position:0%
+tone. I mean, he even talks about he he
+talks about the other Oxford Dons who
+
+ align:start position:0%
+talks about the other Oxford Dons who
+ 
+
+ align:start position:0%
+talks about the other Oxford Dons who
+were jealous and you could just tell he
+
+ align:start position:0%
+were jealous and you could just tell he
+ 
+
+ align:start position:0%
+were jealous and you could just tell he
+completely
+
+ align:start position:0%
+completely
+ 
+
+ align:start position:0%
+completely
+empathizes. Um, okay. So, we can we can
+
+ align:start position:0%
+empathizes. Um, okay. So, we can we can
+ 
+
+ align:start position:0%
+empathizes. Um, okay. So, we can we can
+we can write we can write down because
+
+ align:start position:0%
+we can write we can write down because
+ 
+
+ align:start position:0%
+we can write we can write down because
+he made money off of it, things like
+
+ align:start position:0%
+he made money off of it, things like
+ 
+
+ align:start position:0%
+he made money off of it, things like
+that. Anything that's popular and makes
+
+ align:start position:0%
+that. Anything that's popular and makes
+ 
+
+ align:start position:0%
+that. Anything that's popular and makes
+money is obviously not, you know, good
+
+ align:start position:0%
+money is obviously not, you know, good
+ 
+
+ align:start position:0%
+money is obviously not, you know, good
+enough quality for or something. Yeah, I
+
+ align:start position:0%
+enough quality for or something. Yeah, I
+ 
+
+ align:start position:0%
+enough quality for or something. Yeah, I
+think there's a piece of that. I mean
+
+ align:start position:0%
+think there's a piece of that. I mean
+ 
+
+ align:start position:0%
+think there's a piece of that. I mean
+there was a whole uh a
+
+ align:start position:0%
+there was a whole uh a
+ 
+
+ align:start position:0%
+there was a whole uh a
+Marxist school of thought in the really
+
+ align:start position:0%
+Marxist school of thought in the really
+ 
+
+ align:start position:0%
+Marxist school of thought in the really
+in the 70s I guess um coming out of the
+
+ align:start position:0%
+in the 70s I guess um coming out of the
+ 
+
+ align:start position:0%
+in the 70s I guess um coming out of the
+British public school system which is
+
+ align:start position:0%
+British public school system which is
+ 
+
+ align:start position:0%
+British public school system which is
+their private school system. So not to
+
+ align:start position:0%
+their private school system. So not to
+ 
+
+ align:start position:0%
+their private school system. So not to
+confuse you, uh that that was very anti-
+
+ align:start position:0%
+confuse you, uh that that was very anti-
+ 
+
+ align:start position:0%
+confuse you, uh that that was very anti-
+Tolken and and more or less the gist of
+
+ align:start position:0%
+Tolken and and more or less the gist of
+ 
+
+ align:start position:0%
+Tolken and and more or less the gist of
+it was this is so popular it's made so
+
+ align:start position:0%
+it was this is so popular it's made so
+ 
+
+ align:start position:0%
+it was this is so popular it's made so
+much money it it must be capitalism at
+
+ align:start position:0%
+much money it it must be capitalism at
+ 
+
+ align:start position:0%
+much money it it must be capitalism at
+its sort of rawest nakedest you know
+
+ align:start position:0%
+its sort of rawest nakedest you know
+ 
+
+ align:start position:0%
+its sort of rawest nakedest you know
+most vile manifestation which seems kind
+
+ align:start position:0%
+most vile manifestation which seems kind
+ 
+
+ align:start position:0%
+most vile manifestation which seems kind
+of ironic because I mean if there was
+
+ align:start position:0%
+of ironic because I mean if there was
+ 
+
+ align:start position:0%
+of ironic because I mean if there was
+ever a lite right it's our friend Tolken
+
+ align:start position:0%
+ever a lite right it's our friend Tolken
+ 
+
+ align:start position:0%
+ever a lite right it's our friend Tolken
+I mean he's not exactly you know um the
+
+ align:start position:0%
+I mean he's not exactly you know um the
+ 
+
+ align:start position:0%
+I mean he's not exactly you know um the
+entrepreneur u right on you know sort of
+
+ align:start position:0%
+entrepreneur u right on you know sort of
+ 
+
+ align:start position:0%
+entrepreneur u right on you know sort of
+right on the edge of his next million.
+
+ align:start position:0%
+right on the edge of his next million.
+ 
+
+ align:start position:0%
+right on the edge of his next million.
+Um but but anyway, uh that that
+
+ align:start position:0%
+Um but but anyway, uh that that
+ 
+
+ align:start position:0%
+Um but but anyway, uh that that
+accusation has been made, right? If if
+
+ align:start position:0%
+accusation has been made, right? If if
+ 
+
+ align:start position:0%
+accusation has been made, right? If if
+the masses appreciate it and pay for it,
+
+ align:start position:0%
+the masses appreciate it and pay for it,
+ 
+
+ align:start position:0%
+the masses appreciate it and pay for it,
+surely it can't be any
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+good. So, and we so and we'll we'll
+
+ align:start position:0%
+good. So, and we so and we'll we'll
+ 
+
+ align:start position:0%
+good. So, and we so and we'll we'll
+we'll come back to that. But before we
+
+ align:start position:0%
+we'll come back to that. But before we
+ 
+
+ align:start position:0%
+we'll come back to that. But before we
+do that, how do we square
+
+ align:start position:0%
+do that, how do we square
+ 
+
+ align:start position:0%
+do that, how do we square
+binum with
+
+ align:start position:0%
+binum with
+ 
+
+ align:start position:0%
+binum with
+this medieval sensibility that you've
+
+ align:start position:0%
+this medieval sensibility that you've
+ 
+
+ align:start position:0%
+this medieval sensibility that you've
+now uh been exposed to in sort of its
+
+ align:start position:0%
+now uh been exposed to in sort of its
+ 
+
+ align:start position:0%
+now uh been exposed to in sort of its
+scholarly version in Lewis's The
+
+ align:start position:0%
+scholarly version in Lewis's The
+ 
+
+ align:start position:0%
+scholarly version in Lewis's The
+Discarded Image? I mean, this model that
+
+ align:start position:0%
+Discarded Image? I mean, this model that
+ 
+
+ align:start position:0%
+Discarded Image? I mean, this model that
+Lewis says is out there that everybody
+
+ align:start position:0%
+Lewis says is out there that everybody
+ 
+
+ align:start position:0%
+Lewis says is out there that everybody
+more or less subscribes to. This is the
+
+ align:start position:0%
+more or less subscribes to. This is the
+ 
+
+ align:start position:0%
+more or less subscribes to. This is the
+world and how they understand it. How
+
+ align:start position:0%
+world and how they understand it. How
+ 
+
+ align:start position:0%
+world and how they understand it. How
+does that square or even or even
+
+ align:start position:0%
+does that square or even or even
+ 
+
+ align:start position:0%
+does that square or even or even
+Tolken's madeup world that is at least
+
+ align:start position:0%
+Tolken's madeup world that is at least
+ 
+
+ align:start position:0%
+Tolken's madeup world that is at least
+um uh based right on his understanding
+
+ align:start position:0%
+um uh based right on his understanding
+ 
+
+ align:start position:0%
+um uh based right on his understanding
+of of a real medieval world? How do we
+
+ align:start position:0%
+of of a real medieval world? How do we
+ 
+
+ align:start position:0%
+of of a real medieval world? How do we
+square that with binum? Yeah, go ahead.
+
+ align:start position:0%
+square that with binum? Yeah, go ahead.
+ 
+
+ align:start position:0%
+square that with binum? Yeah, go ahead.
+Go ahead. Lewis made the assertion that
+
+ align:start position:0%
+Go ahead. Lewis made the assertion that
+ 
+
+ align:start position:0%
+Go ahead. Lewis made the assertion that
+the people in medieval society kept this
+
+ align:start position:0%
+the people in medieval society kept this
+ 
+
+ align:start position:0%
+the people in medieval society kept this
+stuff, this model and their religion
+
+ align:start position:0%
+stuff, this model and their religion
+ 
+
+ align:start position:0%
+stuff, this model and their religion
+entirely separate. I that that they that
+
+ align:start position:0%
+entirely separate. I that that they that
+ 
+
+ align:start position:0%
+entirely separate. I that that they that
+they tried to, you know, that that they
+
+ align:start position:0%
+they tried to, you know, that that they
+ 
+
+ align:start position:0%
+they tried to, you know, that that they
+could could could they could reconcile
+
+ align:start position:0%
+could could could they could reconcile
+ 
+
+ align:start position:0%
+could could could they could reconcile
+they didn't even reconcile these things
+
+ align:start position:0%
+they didn't even reconcile these things
+ 
+
+ align:start position:0%
+they didn't even reconcile these things
+in their head that they just they
+
+ align:start position:0%
+in their head that they just they
+ 
+
+ align:start position:0%
+in their head that they just they
+weren't like the two were just complet
+
+ align:start position:0%
+weren't like the two were just complet
+ 
+
+ align:start position:0%
+weren't like the two were just complet
+wholly separate and they could have
+
+ align:start position:0%
+wholly separate and they could have
+ 
+
+ align:start position:0%
+wholly separate and they could have
+these these in many cases uh what we
+
+ align:start position:0%
+these these in many cases uh what we
+ 
+
+ align:start position:0%
+these these in many cases uh what we
+might call contradictory views now and
+
+ align:start position:0%
+might call contradictory views now and
+ 
+
+ align:start position:0%
+might call contradictory views now and
+just didn't you know that was the way it
+
+ align:start position:0%
+just didn't you know that was the way it
+ 
+
+ align:start position:0%
+just didn't you know that was the way it
+is by their Okay. Yeah. Go ahead.
+
+ align:start position:0%
+is by their Okay. Yeah. Go ahead.
+ 
+
+ align:start position:0%
+is by their Okay. Yeah. Go ahead.
+I think talking from the present
+
+ align:start position:0%
+I think talking from the present
+ 
+
+ align:start position:0%
+I think talking from the present
+perspective like Louiswis's model is
+
+ align:start position:0%
+perspective like Louiswis's model is
+ 
+
+ align:start position:0%
+perspective like Louiswis's model is
+very familiar. Like I don't know if it's
+
+ align:start position:0%
+very familiar. Like I don't know if it's
+ 
+
+ align:start position:0%
+very familiar. Like I don't know if it's
+just more wellknown nothing that in this
+
+ align:start position:0%
+just more wellknown nothing that in this
+ 
+
+ align:start position:0%
+just more wellknown nothing that in this
+book that I read was really new to me. I
+
+ align:start position:0%
+book that I read was really new to me. I
+ 
+
+ align:start position:0%
+book that I read was really new to me. I
+don't think I don't know if that's
+
+ align:start position:0%
+don't think I don't know if that's
+ 
+
+ align:start position:0%
+don't think I don't know if that's
+because I've been exposed to medieval
+
+ align:start position:0%
+because I've been exposed to medieval
+ 
+
+ align:start position:0%
+because I've been exposed to medieval
+literature before but it was it was
+
+ align:start position:0%
+literature before but it was it was
+ 
+
+ align:start position:0%
+literature before but it was it was
+fairly standard and ordinary whereas as
+
+ align:start position:0%
+fairly standard and ordinary whereas as
+ 
+
+ align:start position:0%
+fairly standard and ordinary whereas as
+Greg said the bin was just
+
+ align:start position:0%
+Greg said the bin was just
+ 
+
+ align:start position:0%
+Greg said the bin was just
+extraordinary. So is that true for all
+
+ align:start position:0%
+extraordinary. So is that true for all
+ 
+
+ align:start position:0%
+extraordinary. So is that true for all
+of you? Is this a model that is readily
+
+ align:start position:0%
+of you? Is this a model that is readily
+ 
+
+ align:start position:0%
+of you? Is this a model that is readily
+accessible to you floating around in
+
+ align:start position:0%
+accessible to you floating around in
+ 
+
+ align:start position:0%
+accessible to you floating around in
+your head?
+
+ align:start position:0%
+your head?
+ 
+
+ align:start position:0%
+your head?
+Someone says, "Oh, that man is so
+
+ align:start position:0%
+Someone says, "Oh, that man is so
+ 
+
+ align:start position:0%
+Someone says, "Oh, that man is so
+color." And you know instantly or they
+
+ align:start position:0%
+color." And you know instantly or they
+ 
+
+ align:start position:0%
+color." And you know instantly or they
+say by Jove and you know instantly what
+
+ align:start position:0%
+say by Jove and you know instantly what
+ 
+
+ align:start position:0%
+say by Jove and you know instantly what
+is being invoked or you know if I was to
+
+ align:start position:0%
+is being invoked or you know if I was to
+ 
+
+ align:start position:0%
+is being invoked or you know if I was to
+break up a fight in the hallway and say
+
+ align:start position:0%
+break up a fight in the hallway and say
+ 
+
+ align:start position:0%
+break up a fight in the hallway and say
+ah the influence of Mars at work again
+
+ align:start position:0%
+ah the influence of Mars at work again
+ 
+
+ align:start position:0%
+ah the influence of Mars at work again
+everybody around me would know me. Is
+
+ align:start position:0%
+everybody around me would know me. Is
+ 
+
+ align:start position:0%
+everybody around me would know me. Is
+that true?
+
+ align:start position:0%
+that true?
+ 
+
+ align:start position:0%
+that true?
+Depends what you got of those yet. Two
+
+ align:start position:0%
+Depends what you got of those yet. Two
+ 
+
+ align:start position:0%
+Depends what you got of those yet. Two
+are three. Okay. So besides the
+
+ align:start position:0%
+are three. Okay. So besides the
+ 
+
+ align:start position:0%
+are three. Okay. So besides the
+references to um I guess gods which I
+
+ align:start position:0%
+references to um I guess gods which I
+ 
+
+ align:start position:0%
+references to um I guess gods which I
+just kind of have acquired over the
+
+ align:start position:0%
+just kind of have acquired over the
+ 
+
+ align:start position:0%
+just kind of have acquired over the
+years the influence of Mars and the
+
+ align:start position:0%
+years the influence of Mars and the
+ 
+
+ align:start position:0%
+years the influence of Mars and the
+relation to the planets everything else
+
+ align:start position:0%
+relation to the planets everything else
+ 
+
+ align:start position:0%
+relation to the planets everything else
+he mentioned was new to me and that
+
+ align:start position:0%
+he mentioned was new to me and that
+ 
+
+ align:start position:0%
+he mentioned was new to me and that
+might be because I had never I mean
+
+ align:start position:0%
+might be because I had never I mean
+ 
+
+ align:start position:0%
+might be because I had never I mean
+besides the Canterbury Tales which isn't
+
+ align:start position:0%
+besides the Canterbury Tales which isn't
+ 
+
+ align:start position:0%
+besides the Canterbury Tales which isn't
+even really that medieval the only
+
+ align:start position:0%
+even really that medieval the only
+ 
+
+ align:start position:0%
+even really that medieval the only
+exposure I have to that literature. So
+
+ align:start position:0%
+exposure I have to that literature. So
+ 
+
+ align:start position:0%
+exposure I have to that literature. So
+if you're not exposed to it I don't
+
+ align:start position:0%
+if you're not exposed to it I don't
+ 
+
+ align:start position:0%
+if you're not exposed to it I don't
+think you really have a place to pick it
+
+ align:start position:0%
+think you really have a place to pick it
+ 
+
+ align:start position:0%
+think you really have a place to pick it
+up until this book was very I learned a
+
+ align:start position:0%
+up until this book was very I learned a
+ 
+
+ align:start position:0%
+up until this book was very I learned a
+lot from it because I had never been
+
+ align:start position:0%
+lot from it because I had never been
+ 
+
+ align:start position:0%
+lot from it because I had never been
+exposed to it before. Good useful
+
+ align:start position:0%
+exposed to it before. Good useful
+ 
+
+ align:start position:0%
+exposed to it before. Good useful
+cocktail party information.
+
+ align:start position:0%
+cocktail party information.
+ 
+
+ align:start position:0%
+cocktail party information.
+Um, perhaps something to me. Go ahead,
+
+ align:start position:0%
+Um, perhaps something to me. Go ahead,
+ 
+
+ align:start position:0%
+Um, perhaps something to me. Go ahead,
+Nick. Yeah, that's I mean that's what I
+
+ align:start position:0%
+Nick. Yeah, that's I mean that's what I
+ 
+
+ align:start position:0%
+Nick. Yeah, that's I mean that's what I
+wrote about is that I had a real hard
+
+ align:start position:0%
+wrote about is that I had a real hard
+ 
+
+ align:start position:0%
+wrote about is that I had a real hard
+time connecting with the first part
+
+ align:start position:0%
+time connecting with the first part
+ 
+
+ align:start position:0%
+time connecting with the first part
+because I've never read like, you know,
+
+ align:start position:0%
+because I've never read like, you know,
+ 
+
+ align:start position:0%
+because I've never read like, you know,
+Chower or Dante or any any of those guys
+
+ align:start position:0%
+Chower or Dante or any any of those guys
+ 
+
+ align:start position:0%
+Chower or Dante or any any of those guys
+and like he kept like quoting them and
+
+ align:start position:0%
+and like he kept like quoting them and
+ 
+
+ align:start position:0%
+and like he kept like quoting them and
+stuff and it was like yeah, I had the
+
+ align:start position:0%
+stuff and it was like yeah, I had the
+ 
+
+ align:start position:0%
+stuff and it was like yeah, I had the
+same issue that he kept putting in all
+
+ align:start position:0%
+same issue that he kept putting in all
+ 
+
+ align:start position:0%
+same issue that he kept putting in all
+this evidence and I couldn't put it into
+
+ align:start position:0%
+this evidence and I couldn't put it into
+ 
+
+ align:start position:0%
+this evidence and I couldn't put it into
+context of where this evidence came
+
+ align:start position:0%
+context of where this evidence came
+ 
+
+ align:start position:0%
+context of where this evidence came
+from. It was like I was like, "Yeah,
+
+ align:start position:0%
+from. It was like I was like, "Yeah,
+ 
+
+ align:start position:0%
+from. It was like I was like, "Yeah,
+that makes sense, but it would be a lot
+
+ align:start position:0%
+that makes sense, but it would be a lot
+ 
+
+ align:start position:0%
+that makes sense, but it would be a lot
+more rewarding if I knew exactly the
+
+ align:start position:0%
+more rewarding if I knew exactly the
+ 
+
+ align:start position:0%
+more rewarding if I knew exactly the
+context that that evidence came in."
+
+ align:start position:0%
+context that that evidence came in."
+ 
+
+ align:start position:0%
+context that that evidence came in."
+What were you going to say, Miranda? I
+
+ align:start position:0%
+What were you going to say, Miranda? I
+ 
+
+ align:start position:0%
+What were you going to say, Miranda? I
+guess I had a lot of it was more like I
+
+ align:start position:0%
+guess I had a lot of it was more like I
+ 
+
+ align:start position:0%
+guess I had a lot of it was more like I
+had sort of known some of these ideas
+
+ align:start position:0%
+had sort of known some of these ideas
+ 
+
+ align:start position:0%
+had sort of known some of these ideas
+like but I never really liked I'd read
+
+ align:start position:0%
+like but I never really liked I'd read
+ 
+
+ align:start position:0%
+like but I never really liked I'd read
+oh yeah they have you know they thought
+
+ align:start position:0%
+oh yeah they have you know they thought
+ 
+
+ align:start position:0%
+oh yeah they have you know they thought
+that the earth was the middle of the you
+
+ align:start position:0%
+that the earth was the middle of the you
+ 
+
+ align:start position:0%
+that the earth was the middle of the you
+know I'd never really thought about them
+
+ align:start position:0%
+know I'd never really thought about them
+ 
+
+ align:start position:0%
+know I'd never really thought about them
+and why you know I always thought of
+
+ align:start position:0%
+and why you know I always thought of
+ 
+
+ align:start position:0%
+and why you know I always thought of
+them as you know well we're more
+
+ align:start position:0%
+them as you know well we're more
+ 
+
+ align:start position:0%
+them as you know well we're more
+advanced than that we've gotten that
+
+ align:start position:0%
+advanced than that we've gotten that
+ 
+
+ align:start position:0%
+advanced than that we've gotten that
+idea but what I liked was that
+
+ align:start position:0%
+idea but what I liked was that
+ 
+
+ align:start position:0%
+idea but what I liked was that
+especially at the beginning of the
+
+ align:start position:0%
+especially at the beginning of the
+ 
+
+ align:start position:0%
+especially at the beginning of the
+heavens thing he sort of went you know
+
+ align:start position:0%
+heavens thing he sort of went you know
+ 
+
+ align:start position:0%
+heavens thing he sort of went you know
+well your idea you know the modern idea
+
+ align:start position:0%
+well your idea you know the modern idea
+ 
+
+ align:start position:0%
+well your idea you know the modern idea
+of how the laws of nature work are just
+
+ align:start position:0%
+of how the laws of nature work are just
+ 
+
+ align:start position:0%
+of how the laws of nature work are just
+as stupid as theirs you know no he
+
+ align:start position:0%
+as stupid as theirs you know no he
+ 
+
+ align:start position:0%
+as stupid as theirs you know no he
+doesn't say they're Or it's just it's
+
+ align:start position:0%
+doesn't say they're Or it's just it's
+ 
+
+ align:start position:0%
+doesn't say they're Or it's just it's
+not we're not you know it's not that the
+
+ align:start position:0%
+not we're not you know it's not that the
+ 
+
+ align:start position:0%
+not we're not you know it's not that the
+same way maybe it was that we're not
+
+ align:start position:0%
+same way maybe it was that we're not
+ 
+
+ align:start position:0%
+same way maybe it was that we're not
+like it sort of broke down that we are
+
+ align:start position:0%
+like it sort of broke down that we are
+ 
+
+ align:start position:0%
+like it sort of broke down that we are
+better than their ideas that you know
+
+ align:start position:0%
+better than their ideas that you know
+ 
+
+ align:start position:0%
+better than their ideas that you know
+why is it that our ideas that well you
+
+ align:start position:0%
+why is it that our ideas that well you
+ 
+
+ align:start position:0%
+why is it that our ideas that well you
+know these things are sentient beings
+
+ align:start position:0%
+know these things are sentient beings
+ 
+
+ align:start position:0%
+know these things are sentient beings
+that you know therefore can obey laws
+
+ align:start position:0%
+that you know therefore can obey laws
+ 
+
+ align:start position:0%
+that you know therefore can obey laws
+versus their ideas well they like each
+
+ align:start position:0%
+versus their ideas well they like each
+ 
+
+ align:start position:0%
+versus their ideas well they like each
+other and therefore they want to get to
+
+ align:start position:0%
+other and therefore they want to get to
+ 
+
+ align:start position:0%
+other and therefore they want to get to
+they want to get together right that's
+
+ align:start position:0%
+they want to get together right that's
+ 
+
+ align:start position:0%
+they want to get together right that's
+right you know okay so if I'm a stone
+
+ align:start position:0%
+right you know okay so if I'm a stone
+ 
+
+ align:start position:0%
+right you know okay so if I'm a stone
+I'm
+
+ align:start position:0%
+I'm
+ 
+
+ align:start position:0%
+I'm
+heavy and I desperately want to be where
+
+ align:start position:0%
+heavy and I desperately want to be where
+ 
+
+ align:start position:0%
+heavy and I desperately want to be where
+I belong long, which is on the earth.
+
+ align:start position:0%
+I belong long, which is on the earth.
+ 
+
+ align:start position:0%
+I belong long, which is on the earth.
+So, if somebody drops me off of a
+
+ align:start position:0%
+So, if somebody drops me off of a
+ 
+
+ align:start position:0%
+So, if somebody drops me off of a
+tower, I'm going to get as quickly as I
+
+ align:start position:0%
+tower, I'm going to get as quickly as I
+ 
+
+ align:start position:0%
+tower, I'm going to get as quickly as I
+possibly can back to Earth, which is
+
+ align:start position:0%
+possibly can back to Earth, which is
+ 
+
+ align:start position:0%
+possibly can back to Earth, which is
+down, right? Okay. And that's what I do
+
+ align:start position:0%
+down, right? Okay. And that's what I do
+ 
+
+ align:start position:0%
+down, right? Okay. And that's what I do
+if I'm a stone. Now, in our world, we
+
+ align:start position:0%
+if I'm a stone. Now, in our world, we
+ 
+
+ align:start position:0%
+if I'm a stone. Now, in our world, we
+have this thing called the law of
+
+ align:start position:0%
+have this thing called the law of
+ 
+
+ align:start position:0%
+have this thing called the law of
+gravity. And if I drop a stone off of a
+
+ align:start position:0%
+gravity. And if I drop a stone off of a
+ 
+
+ align:start position:0%
+gravity. And if I drop a stone off of a
+tower, the gravity police jump out,
+
+ align:start position:0%
+tower, the gravity police jump out,
+ 
+
+ align:start position:0%
+tower, the gravity police jump out,
+right? the way in the in the the
+
+ align:start position:0%
+right? the way in the in the the
+ 
+
+ align:start position:0%
+right? the way in the in the the
+metaphor that he uses, right? And you
+
+ align:start position:0%
+metaphor that he uses, right? And you
+ 
+
+ align:start position:0%
+metaphor that he uses, right? And you
+know, says, "Get thee down to that large
+
+ align:start position:0%
+know, says, "Get thee down to that large
+ 
+
+ align:start position:0%
+know, says, "Get thee down to that large
+mass," right? And off I go because I've
+
+ align:start position:0%
+mass," right? And off I go because I've
+ 
+
+ align:start position:0%
+mass," right? And off I go because I've
+been told that's what I'm supposed to
+
+ align:start position:0%
+been told that's what I'm supposed to
+ 
+
+ align:start position:0%
+been told that's what I'm supposed to
+do. I mean, the the passage is on 94.
+
+ align:start position:0%
+do. I mean, the the passage is on 94.
+ 
+
+ align:start position:0%
+do. I mean, the the passage is on 94.
+Um, but though neither statement can be
+
+ align:start position:0%
+Um, but though neither statement can be
+ 
+
+ align:start position:0%
+Um, but though neither statement can be
+taken literally, it does not follow that
+
+ align:start position:0%
+taken literally, it does not follow that
+ 
+
+ align:start position:0%
+taken literally, it does not follow that
+it makes no difference which is used. On
+
+ align:start position:0%
+it makes no difference which is used. On
+ 
+
+ align:start position:0%
+it makes no difference which is used. On
+the imaginative and emotional level, it
+
+ align:start position:0%
+the imaginative and emotional level, it
+ 
+
+ align:start position:0%
+the imaginative and emotional level, it
+makes a great difference whether with
+
+ align:start position:0%
+makes a great difference whether with
+ 
+
+ align:start position:0%
+makes a great difference whether with
+the medievalss we project upon the
+
+ align:start position:0%
+the medievalss we project upon the
+ 
+
+ align:start position:0%
+the medievalss we project upon the
+universe our strivings and desires or
+
+ align:start position:0%
+universe our strivings and desires or
+ 
+
+ align:start position:0%
+universe our strivings and desires or
+with the moderns, our police system and
+
+ align:start position:0%
+with the moderns, our police system and
+ 
+
+ align:start position:0%
+with the moderns, our police system and
+our traffic
+
+ align:start position:0%
+our traffic
+ 
+
+ align:start position:0%
+our traffic
+regulations. I mean, do you did you find
+
+ align:start position:0%
+regulations. I mean, do you did you find
+ 
+
+ align:start position:0%
+regulations. I mean, do you did you find
+that
+
+ align:start position:0%
+that
+ 
+
+ align:start position:0%
+that
+compelling? It's a kind of an upsetting
+
+ align:start position:0%
+compelling? It's a kind of an upsetting
+ 
+
+ align:start position:0%
+compelling? It's a kind of an upsetting
+way to think about gravity though, isn't
+
+ align:start position:0%
+way to think about gravity though, isn't
+ 
+
+ align:start position:0%
+way to think about gravity though, isn't
+it?
+
+ align:start position:0%
+it?
+ 
+
+ align:start position:0%
+it?
+Yes and no. But I mean I'm kind of torn
+
+ align:start position:0%
+Yes and no. But I mean I'm kind of torn
+ 
+
+ align:start position:0%
+Yes and no. But I mean I'm kind of torn
+as to whether or not
+
+ align:start position:0%
+as to whether or not
+ 
+
+ align:start position:0%
+as to whether or not
+to like initially I just think you know
+
+ align:start position:0%
+to like initially I just think you know
+ 
+
+ align:start position:0%
+to like initially I just think you know
+well that's kind of shallow assessment
+
+ align:start position:0%
+well that's kind of shallow assessment
+ 
+
+ align:start position:0%
+well that's kind of shallow assessment
+on his part of how we are looking at at
+
+ align:start position:0%
+on his part of how we are looking at at
+ 
+
+ align:start position:0%
+on his part of how we are looking at at
+something like that you know that well
+
+ align:start position:0%
+something like that you know that well
+ 
+
+ align:start position:0%
+something like that you know that well
+well you dummy you know that's not
+
+ align:start position:0%
+well you dummy you know that's not
+ 
+
+ align:start position:0%
+well you dummy you know that's not
+actually how we think about it
+
+ align:start position:0%
+actually how we think about it
+ 
+
+ align:start position:0%
+actually how we think about it
+but
+
+ align:start position:0%
+but
+ 
+
+ align:start position:0%
+but
+I I feel like if he'd made a case that
+
+ align:start position:0%
+I I feel like if he'd made a case that
+ 
+
+ align:start position:0%
+I I feel like if he'd made a case that
+you know because because a physicist
+
+ align:start position:0%
+you know because because a physicist
+ 
+
+ align:start position:0%
+you know because because a physicist
+doesn't really think that you know that
+
+ align:start position:0%
+doesn't really think that you know that
+ 
+
+ align:start position:0%
+doesn't really think that you know that
+that there's that something is obeying a
+
+ align:start position:0%
+that there's that something is obeying a
+ 
+
+ align:start position:0%
+that there's that something is obeying a
+law. It's that there is a set of
+
+ align:start position:0%
+law. It's that there is a set of
+ 
+
+ align:start position:0%
+law. It's that there is a set of
+mathematical equations which describe
+
+ align:start position:0%
+mathematical equations which describe
+ 
+
+ align:start position:0%
+mathematical equations which describe
+how something what something does what
+
+ align:start position:0%
+how something what something does what
+ 
+
+ align:start position:0%
+how something what something does what
+happens right not that it's but but then
+
+ align:start position:0%
+happens right not that it's but but then
+ 
+
+ align:start position:0%
+happens right not that it's but but then
+you know that's really you know people
+
+ align:start position:0%
+you know that's really you know people
+ 
+
+ align:start position:0%
+you know that's really you know people
+could have thought in in kind of similar
+
+ align:start position:0%
+could have thought in in kind of similar
+ 
+
+ align:start position:0%
+could have thought in in kind of similar
+there could have been more to what they
+
+ align:start position:0%
+there could have been more to what they
+ 
+
+ align:start position:0%
+there could have been more to what they
+were thinking in medieval times uh about
+
+ align:start position:0%
+were thinking in medieval times uh about
+ 
+
+ align:start position:0%
+were thinking in medieval times uh about
+the actions of things you know in in
+
+ align:start position:0%
+the actions of things you know in in
+ 
+
+ align:start position:0%
+the actions of things you know in in
+their their likes and dislikes they
+
+ align:start position:0%
+their their likes and dislikes they
+ 
+
+ align:start position:0%
+their their likes and dislikes they
+could have understood it and I he's kind
+
+ align:start position:0%
+could have understood it and I he's kind
+ 
+
+ align:start position:0%
+could have understood it and I he's kind
+of kind of alludes to the fact that they
+
+ align:start position:0%
+of kind of alludes to the fact that they
+ 
+
+ align:start position:0%
+of kind of alludes to the fact that they
+understood it better than that and just
+
+ align:start position:0%
+understood it better than that and just
+ 
+
+ align:start position:0%
+understood it better than that and just
+use that as allegory. Let me let me ask
+
+ align:start position:0%
+use that as allegory. Let me let me ask
+ 
+
+ align:start position:0%
+use that as allegory. Let me let me ask
+you a question about math. Mhm.
+
+ align:start position:0%
+you a question about math. Mhm.
+ 
+
+ align:start position:0%
+you a question about math. Mhm.
+Okay. And this is not this is not a
+
+ align:start position:0%
+Okay. And this is not this is not a
+ 
+
+ align:start position:0%
+Okay. And this is not this is not a
+question that that
+
+ align:start position:0%
+question that that
+ 
+
+ align:start position:0%
+question that that
+um the medieval man would ever have even
+
+ align:start position:0%
+um the medieval man would ever have even
+ 
+
+ align:start position:0%
+um the medieval man would ever have even
+had to have thought
+
+ align:start position:0%
+had to have thought
+ 
+
+ align:start position:0%
+had to have thought
+about. But I mean do you
+
+ align:start position:0%
+about. But I mean do you
+ 
+
+ align:start position:0%
+about. But I mean do you
+believe that math is
+
+ align:start position:0%
+believe that math is
+ 
+
+ align:start position:0%
+believe that math is
+true? Right? And by true I mean true
+
+ align:start position:0%
+true? Right? And by true I mean true
+ 
+
+ align:start position:0%
+true? Right? And by true I mean true
+with like a capital T.
+
+ align:start position:0%
+with like a capital T.
+ 
+
+ align:start position:0%
+with like a capital T.
+true for all time, for all place,
+
+ align:start position:0%
+true for all time, for all place,
+ 
+
+ align:start position:0%
+true for all time, for all place,
+because it's true and separate, right?
+
+ align:start position:0%
+because it's true and separate, right?
+ 
+
+ align:start position:0%
+because it's true and separate, right?
+Not true because I've figured it out and
+
+ align:start position:0%
+Not true because I've figured it out and
+ 
+
+ align:start position:0%
+Not true because I've figured it out and
+the formulas all line up together, okay?
+
+ align:start position:0%
+the formulas all line up together, okay?
+ 
+
+ align:start position:0%
+the formulas all line up together, okay?
+But true because it's really
+
+ align:start position:0%
+But true because it's really
+ 
+
+ align:start position:0%
+But true because it's really
+true. And
+
+ align:start position:0%
+true. And
+ 
+
+ align:start position:0%
+true. And
+therefore, when we figure out that
+
+ align:start position:0%
+therefore, when we figure out that
+ 
+
+ align:start position:0%
+therefore, when we figure out that
+gravity works in a certain way, and
+
+ align:start position:0%
+gravity works in a certain way, and
+ 
+
+ align:start position:0%
+gravity works in a certain way, and
+here's the mathematical formula, all
+
+ align:start position:0%
+here's the mathematical formula, all
+ 
+
+ align:start position:0%
+here's the mathematical formula, all
+we're doing is tapping into a truth
+
+ align:start position:0%
+we're doing is tapping into a truth
+ 
+
+ align:start position:0%
+we're doing is tapping into a truth
+that's already
+
+ align:start position:0%
+that's already
+ 
+
+ align:start position:0%
+that's already
+there. Do do you all believe that? Yeah,
+
+ align:start position:0%
+there. Do do you all believe that? Yeah,
+ 
+
+ align:start position:0%
+there. Do do you all believe that? Yeah,
+Peter. I mean, I view math more as a
+
+ align:start position:0%
+Peter. I mean, I view math more as a
+ 
+
+ align:start position:0%
+Peter. I mean, I view math more as a
+tool to create a model. I mean, I think
+
+ align:start position:0%
+tool to create a model. I mean, I think
+ 
+
+ align:start position:0%
+tool to create a model. I mean, I think
+I think Lewis makes the point somewhere
+
+ align:start position:0%
+I think Lewis makes the point somewhere
+ 
+
+ align:start position:0%
+I think Lewis makes the point somewhere
+that even, you know, up until the 1920s
+
+ align:start position:0%
+that even, you know, up until the 1920s
+ 
+
+ align:start position:0%
+that even, you know, up until the 1920s
+and 30s, we were still viewing a model
+
+ align:start position:0%
+and 30s, we were still viewing a model
+ 
+
+ align:start position:0%
+and 30s, we were still viewing a model
+we thought was true and then we started
+
+ align:start position:0%
+we thought was true and then we started
+ 
+
+ align:start position:0%
+we thought was true and then we started
+getting into quantum mechanics and that
+
+ align:start position:0%
+getting into quantum mechanics and that
+ 
+
+ align:start position:0%
+getting into quantum mechanics and that
+kind of changed our whole view of the
+
+ align:start position:0%
+kind of changed our whole view of the
+ 
+
+ align:start position:0%
+kind of changed our whole view of the
+earth. I mean, if you told someone in
+
+ align:start position:0%
+earth. I mean, if you told someone in
+ 
+
+ align:start position:0%
+earth. I mean, if you told someone in
+the 1900 that if you jump into a wall
+
+ align:start position:0%
+the 1900 that if you jump into a wall
+ 
+
+ align:start position:0%
+the 1900 that if you jump into a wall
+enough, you'd actually go through it at
+
+ align:start position:0%
+enough, you'd actually go through it at
+ 
+
+ align:start position:0%
+enough, you'd actually go through it at
+one point, you know, they wouldn't
+
+ align:start position:0%
+one point, you know, they wouldn't
+ 
+
+ align:start position:0%
+one point, you know, they wouldn't
+believe you. But it's I mean, it's just
+
+ align:start position:0%
+believe you. But it's I mean, it's just
+ 
+
+ align:start position:0%
+believe you. But it's I mean, it's just
+it's statistically possible to do
+
+ align:start position:0%
+it's statistically possible to do
+ 
+
+ align:start position:0%
+it's statistically possible to do
+something like that. But you can't
+
+ align:start position:0%
+something like that. But you can't
+ 
+
+ align:start position:0%
+something like that. But you can't
+really have a I mean the problem I have
+
+ align:start position:0%
+really have a I mean the problem I have
+ 
+
+ align:start position:0%
+really have a I mean the problem I have
+I mean in my in my experience that there
+
+ align:start position:0%
+I mean in my in my experience that there
+ 
+
+ align:start position:0%
+I mean in my in my experience that there
+is no model that will describe
+
+ align:start position:0%
+is no model that will describe
+ 
+
+ align:start position:0%
+is no model that will describe
+everything. There's just a whole bunch
+
+ align:start position:0%
+everything. There's just a whole bunch
+ 
+
+ align:start position:0%
+everything. There's just a whole bunch
+of tools that describe that thing. Kind
+
+ align:start position:0%
+of tools that describe that thing. Kind
+ 
+
+ align:start position:0%
+of tools that describe that thing. Kind
+of how Louis says that they had a whole
+
+ align:start position:0%
+of how Louis says that they had a whole
+ 
+
+ align:start position:0%
+of how Louis says that they had a whole
+bunch of observations and then they made
+
+ align:start position:0%
+bunch of observations and then they made
+ 
+
+ align:start position:0%
+bunch of observations and then they made
+a model that fit it and now we have a
+
+ align:start position:0%
+a model that fit it and now we have a
+ 
+
+ align:start position:0%
+a model that fit it and now we have a
+whole bunch of other rather bizarre you
+
+ align:start position:0%
+whole bunch of other rather bizarre you
+ 
+
+ align:start position:0%
+whole bunch of other rather bizarre you
+know things by classical physics
+
+ align:start position:0%
+know things by classical physics
+ 
+
+ align:start position:0%
+know things by classical physics
+standards that and you have to create a
+
+ align:start position:0%
+standards that and you have to create a
+ 
+
+ align:start position:0%
+standards that and you have to create a
+new model. So I don't think that there
+
+ align:start position:0%
+new model. So I don't think that there
+ 
+
+ align:start position:0%
+new model. So I don't think that there
+is any I don't think that math can be
+
+ align:start position:0%
+is any I don't think that math can be
+ 
+
+ align:start position:0%
+is any I don't think that math can be
+viewed as true. It's just a dummy. Okay.
+
+ align:start position:0%
+viewed as true. It's just a dummy. Okay.
+ 
+
+ align:start position:0%
+viewed as true. It's just a dummy. Okay.
+If you start from that position, then
+
+ align:start position:0%
+If you start from that position, then
+ 
+
+ align:start position:0%
+If you start from that position, then
+the medieval position is not hard to
+
+ align:start position:0%
+the medieval position is not hard to
+ 
+
+ align:start position:0%
+the medieval position is not hard to
+walk yourself into at all. Right? It's
+
+ align:start position:0%
+walk yourself into at all. Right? It's
+ 
+
+ align:start position:0%
+walk yourself into at all. Right? It's
+just working with a slightly different
+
+ align:start position:0%
+just working with a slightly different
+ 
+
+ align:start position:0%
+just working with a slightly different
+set of tools, a different set of
+
+ align:start position:0%
+set of tools, a different set of
+ 
+
+ align:start position:0%
+set of tools, a different set of
+authors, ancient authorities, etc.
+
+ align:start position:0%
+authors, ancient authorities, etc.
+ 
+
+ align:start position:0%
+authors, ancient authorities, etc.
+However, if you really believe that the
+
+ align:start position:0%
+However, if you really believe that the
+ 
+
+ align:start position:0%
+However, if you really believe that the
+math thing is true with a capital T,
+
+ align:start position:0%
+math thing is true with a capital T,
+ 
+
+ align:start position:0%
+math thing is true with a capital T,
+it's much harder to buy this, right?
+
+ align:start position:0%
+it's much harder to buy this, right?
+ 
+
+ align:start position:0%
+it's much harder to buy this, right?
+Then this then this is wrong in the
+
+ align:start position:0%
+Then this then this is wrong in the
+ 
+
+ align:start position:0%
+Then this then this is wrong in the
+capital W kind of a way, right? because
+
+ align:start position:0%
+capital W kind of a way, right? because
+ 
+
+ align:start position:0%
+capital W kind of a way, right? because
+the other thing is true and this isn't
+
+ align:start position:0%
+the other thing is true and this isn't
+ 
+
+ align:start position:0%
+the other thing is true and this isn't
+that and therefore it's a question of
+
+ align:start position:0%
+that and therefore it's a question of
+ 
+
+ align:start position:0%
+that and therefore it's a question of
+having missed the mark misunderstood the
+
+ align:start position:0%
+having missed the mark misunderstood the
+ 
+
+ align:start position:0%
+having missed the mark misunderstood the
+facts right not not tapped into um
+
+ align:start position:0%
+facts right not not tapped into um
+ 
+
+ align:start position:0%
+facts right not not tapped into um
+reality and and my guess is Peter that
+
+ align:start position:0%
+reality and and my guess is Peter that
+ 
+
+ align:start position:0%
+reality and and my guess is Peter that
+that your kind of ecumenical view on
+
+ align:start position:0%
+that your kind of ecumenical view on
+ 
+
+ align:start position:0%
+that your kind of ecumenical view on
+this is not widely shared around here um
+
+ align:start position:0%
+this is not widely shared around here um
+ 
+
+ align:start position:0%
+this is not widely shared around here um
+well at least in my well I'm not a
+
+ align:start position:0%
+well at least in my well I'm not a
+ 
+
+ align:start position:0%
+well at least in my well I'm not a
+physicist we kind of do fake physics in
+
+ align:start position:0%
+physicist we kind of do fake physics in
+ 
+
+ align:start position:0%
+physicist we kind of do fake physics in
+my department but you do fake physics
+
+ align:start position:0%
+my department but you do fake physics
+ 
+
+ align:start position:0%
+my department but you do fake physics
+you know, kind of priest. What were you
+
+ align:start position:0%
+you know, kind of priest. What were you
+ 
+
+ align:start position:0%
+you know, kind of priest. What were you
+going to say, Mon? I'm with him.
+
+ align:start position:0%
+going to say, Mon? I'm with him.
+ 
+
+ align:start position:0%
+going to say, Mon? I'm with him.
+I agree. I mean, math I mean, math is
+
+ align:start position:0%
+I agree. I mean, math I mean, math is
+ 
+
+ align:start position:0%
+I agree. I mean, math I mean, math is
+But there might be a reason you're all
+
+ align:start position:0%
+But there might be a reason you're all
+ 
+
+ align:start position:0%
+But there might be a reason you're all
+in this class.
+
+ align:start position:0%
+in this class.
+ 
+
+ align:start position:0%
+in this class.
+Yeah. Go ahead, Henry. And then Annie.
+
+ align:start position:0%
+Yeah. Go ahead, Henry. And then Annie.
+ 
+
+ align:start position:0%
+Yeah. Go ahead, Henry. And then Annie.
+No, I mean I'm a physicist and I don't
+
+ align:start position:0%
+No, I mean I'm a physicist and I don't
+ 
+
+ align:start position:0%
+No, I mean I'm a physicist and I don't
+think mathematics has an existence on
+
+ align:start position:0%
+think mathematics has an existence on
+ 
+
+ align:start position:0%
+think mathematics has an existence on
+its own. Okay. I don't I don't think
+
+ align:start position:0%
+its own. Okay. I don't I don't think
+ 
+
+ align:start position:0%
+its own. Okay. I don't I don't think
+it's like a being like you almost
+
+ align:start position:0%
+it's like a being like you almost
+ 
+
+ align:start position:0%
+it's like a being like you almost
+described it. Like it's not math doesn't
+
+ align:start position:0%
+described it. Like it's not math doesn't
+ 
+
+ align:start position:0%
+described it. Like it's not math doesn't
+exist without the models. Like I don't
+
+ align:start position:0%
+exist without the models. Like I don't
+ 
+
+ align:start position:0%
+exist without the models. Like I don't
+think I think actually most physicists
+
+ align:start position:0%
+think I think actually most physicists
+ 
+
+ align:start position:0%
+think I think actually most physicists
+now right if we could have caught them
+
+ align:start position:0%
+now right if we could have caught them
+ 
+
+ align:start position:0%
+now right if we could have caught them
+all what 25 years ago we would have
+
+ align:start position:0%
+all what 25 years ago we would have
+ 
+
+ align:start position:0%
+all what 25 years ago we would have
+gotten a slightly different
+
+ align:start position:0%
+gotten a slightly different
+ 
+
+ align:start position:0%
+gotten a slightly different
+answer right I I mean I think it's
+
+ align:start position:0%
+answer right I I mean I think it's
+ 
+
+ align:start position:0%
+answer right I I mean I think it's
+really
+
+ align:start position:0%
+really
+ 
+
+ align:start position:0%
+really
+changed people are a lot more
+
+ align:start position:0%
+changed people are a lot more
+ 
+
+ align:start position:0%
+changed people are a lot more
+comfortable with being less certain
+
+ align:start position:0%
+comfortable with being less certain
+ 
+
+ align:start position:0%
+comfortable with being less certain
+um but what were you going to say Annie
+
+ align:start position:0%
+um but what were you going to say Annie
+ 
+
+ align:start position:0%
+um but what were you going to say Annie
+well I don't know I guess I'm a freak of
+
+ align:start position:0%
+well I don't know I guess I'm a freak of
+ 
+
+ align:start position:0%
+well I don't know I guess I'm a freak of
+guru but I don't know I do sort of think
+
+ align:start position:0%
+guru but I don't know I do sort of think
+ 
+
+ align:start position:0%
+guru but I don't know I do sort of think
+math is true and that like one and one
+
+ align:start position:0%
+math is true and that like one and one
+ 
+
+ align:start position:0%
+math is true and that like one and one
+will always equal two. No matter what,
+
+ align:start position:0%
+will always equal two. No matter what,
+ 
+
+ align:start position:0%
+will always equal two. No matter what,
+no matter where you are, no matter what
+
+ align:start position:0%
+no matter where you are, no matter what
+ 
+
+ align:start position:0%
+no matter where you are, no matter what
+time you're in, one and one are always
+
+ align:start position:0%
+time you're in, one and one are always
+ 
+
+ align:start position:0%
+time you're in, one and one are always
+two. Never changes. And that like, yeah,
+
+ align:start position:0%
+two. Never changes. And that like, yeah,
+ 
+
+ align:start position:0%
+two. Never changes. And that like, yeah,
+our models change. Like, we're always
+
+ align:start position:0%
+our models change. Like, we're always
+ 
+
+ align:start position:0%
+our models change. Like, we're always
+learning new things, and we're always
+
+ align:start position:0%
+learning new things, and we're always
+ 
+
+ align:start position:0%
+learning new things, and we're always
+making better observations, coming up
+
+ align:start position:0%
+making better observations, coming up
+ 
+
+ align:start position:0%
+making better observations, coming up
+with new models, but presumably we're
+
+ align:start position:0%
+with new models, but presumably we're
+ 
+
+ align:start position:0%
+with new models, but presumably we're
+getting closer and closer to the truth,
+
+ align:start position:0%
+getting closer and closer to the truth,
+ 
+
+ align:start position:0%
+getting closer and closer to the truth,
+to the capital T. And so, I don't think
+
+ align:start position:0%
+to the capital T. And so, I don't think
+ 
+
+ align:start position:0%
+to the capital T. And so, I don't think
+I don't know. I don't think that the
+
+ align:start position:0%
+I don't know. I don't think that the
+ 
+
+ align:start position:0%
+I don't know. I don't think that the
+medieval way was necessarily wrong,
+
+ align:start position:0%
+medieval way was necessarily wrong,
+ 
+
+ align:start position:0%
+medieval way was necessarily wrong,
+right? because it was based on the
+
+ align:start position:0%
+right? because it was based on the
+ 
+
+ align:start position:0%
+right? because it was based on the
+observations they had like similar to
+
+ align:start position:0%
+observations they had like similar to
+ 
+
+ align:start position:0%
+observations they had like similar to
+what Peter thinks and now we have more
+
+ align:start position:0%
+what Peter thinks and now we have more
+ 
+
+ align:start position:0%
+what Peter thinks and now we have more
+observations and so we have a better
+
+ align:start position:0%
+observations and so we have a better
+ 
+
+ align:start position:0%
+observations and so we have a better
+model but you know who knows in 100
+
+ align:start position:0%
+model but you know who knows in 100
+ 
+
+ align:start position:0%
+model but you know who knows in 100
+years we probably have something
+
+ align:start position:0%
+years we probably have something
+ 
+
+ align:start position:0%
+years we probably have something
+completely different than what we think
+
+ align:start position:0%
+completely different than what we think
+ 
+
+ align:start position:0%
+completely different than what we think
+now and quantum mechanics will be crazy
+
+ align:start position:0%
+now and quantum mechanics will be crazy
+ 
+
+ align:start position:0%
+now and quantum mechanics will be crazy
+and you know whatever they'll think we
+
+ align:start position:0%
+and you know whatever they'll think we
+ 
+
+ align:start position:0%
+and you know whatever they'll think we
+were all like
+
+ align:start position:0%
+were all like
+ 
+
+ align:start position:0%
+were all like
+and you know there'll be all those
+
+ align:start position:0%
+and you know there'll be all those
+ 
+
+ align:start position:0%
+and you know there'll be all those
+stupid people in the 20th century that
+
+ align:start position:0%
+stupid people in the 20th century that
+ 
+
+ align:start position:0%
+stupid people in the 20th century that
+thought that but I feel like we're
+
+ align:start position:0%
+thought that but I feel like we're
+ 
+
+ align:start position:0%
+thought that but I feel like we're
+getting closer somehow
+
+ align:start position:0%
+getting closer somehow
+ 
+
+ align:start position:0%
+getting closer somehow
+what were you going to say mom
+
+ align:start position:0%
+what were you going to say mom
+ 
+
+ align:start position:0%
+what were you going to say mom
+I forgot Okay, I've always I have a
+
+ align:start position:0%
+I forgot Okay, I've always I have a
+ 
+
+ align:start position:0%
+I forgot Okay, I've always I have a
+problem with you who say 1 + 1 equals 1
+
+ align:start position:0%
+problem with you who say 1 + 1 equals 1
+ 
+
+ align:start position:0%
+problem with you who say 1 + 1 equals 1
+or 1 plus 1 equals 2 and in fact if you
+
+ align:start position:0%
+or 1 plus 1 equals 2 and in fact if you
+ 
+
+ align:start position:0%
+or 1 plus 1 equals 2 and in fact if you
+take a lot of people have been having
+
+ align:start position:0%
+take a lot of people have been having
+ 
+
+ align:start position:0%
+take a lot of people have been having
+sort of joking around if you take a lot
+
+ align:start position:0%
+sort of joking around if you take a lot
+ 
+
+ align:start position:0%
+sort of joking around if you take a lot
+of the mod you know the mathematical
+
+ align:start position:0%
+of the mod you know the mathematical
+ 
+
+ align:start position:0%
+of the mod you know the mathematical
+models you know x^2 x you know x= like
+
+ align:start position:0%
+models you know x^2 x you know x= like
+ 
+
+ align:start position:0%
+models you know x^2 x you know x= like
+you can you can prove things like 1
+
+ align:start position:0%
+you can you can prove things like 1
+ 
+
+ align:start position:0%
+you can you can prove things like 1
+equals 2 and problematic and it's sort
+
+ align:start position:0%
+equals 2 and problematic and it's sort
+ 
+
+ align:start position:0%
+equals 2 and problematic and it's sort
+of problematic because by you you know
+
+ align:start position:0%
+of problematic because by you you know
+ 
+
+ align:start position:0%
+of problematic because by you you know
+manipulating these little x's and
+
+ align:start position:0%
+manipulating these little x's and
+ 
+
+ align:start position:0%
+manipulating these little x's and
+squares and you know square roots and
+
+ align:start position:0%
+squares and you know square roots and
+ 
+
+ align:start position:0%
+squares and you know square roots and
+stuff you can make things equal other
+
+ align:start position:0%
+stuff you can make things equal other
+ 
+
+ align:start position:0%
+stuff you can make things equal other
+things you know in you one cup plus two
+
+ align:start position:0%
+things you know in you one cup plus two
+ 
+
+ align:start position:0%
+things you know in you one cup plus two
+cups doesn't really, you know, it
+
+ align:start position:0%
+cups doesn't really, you know, it
+ 
+
+ align:start position:0%
+cups doesn't really, you know, it
+doesn't actually always equal three type
+
+ align:start position:0%
+doesn't actually always equal three type
+ 
+
+ align:start position:0%
+doesn't actually always equal three type
+of thing. And it's really weird because
+
+ align:start position:0%
+of thing. And it's really weird because
+ 
+
+ align:start position:0%
+of thing. And it's really weird because
+sounds like a faulty proof to me.
+
+ align:start position:0%
+sounds like a faulty proof to me.
+ 
+
+ align:start position:0%
+sounds like a faulty proof to me.
+What happens when you start dividing by
+
+ align:start position:0%
+What happens when you start dividing by
+ 
+
+ align:start position:0%
+What happens when you start dividing by
+zero? Yeah, it's easy enough to like I
+
+ align:start position:0%
+zero? Yeah, it's easy enough to like I
+ 
+
+ align:start position:0%
+zero? Yeah, it's easy enough to like I
+think therefore you can't take it as
+
+ align:start position:0%
+think therefore you can't take it as
+ 
+
+ align:start position:0%
+think therefore you can't take it as
+absolute fact because it's just gotten
+
+ align:start position:0%
+absolute fact because it's just gotten
+ 
+
+ align:start position:0%
+absolute fact because it's just gotten
+so complicated that you can manipulate
+
+ align:start position:0%
+so complicated that you can manipulate
+ 
+
+ align:start position:0%
+so complicated that you can manipulate
+it into whatever facts you want. But I
+
+ align:start position:0%
+it into whatever facts you want. But I
+ 
+
+ align:start position:0%
+it into whatever facts you want. But I
+mean I I I think that's kind of just
+
+ align:start position:0%
+mean I I I think that's kind of just
+ 
+
+ align:start position:0%
+mean I I I think that's kind of just
+because you can manipulate it in a
+
+ align:start position:0%
+because you can manipulate it in a
+ 
+
+ align:start position:0%
+because you can manipulate it in a
+fashion that is against the rules. I
+
+ align:start position:0%
+fashion that is against the rules. I
+ 
+
+ align:start position:0%
+fashion that is against the rules. I
+mean, just because someone who doesn't
+
+ align:start position:0%
+mean, just because someone who doesn't
+ 
+
+ align:start position:0%
+mean, just because someone who doesn't
+necessarily know all the rules can can
+
+ align:start position:0%
+necessarily know all the rules can can
+ 
+
+ align:start position:0%
+necessarily know all the rules can can
+can misunderstand it, I don't think
+
+ align:start position:0%
+can misunderstand it, I don't think
+ 
+
+ align:start position:0%
+can misunderstand it, I don't think
+makes it necessarily valable. Jump in,
+
+ align:start position:0%
+makes it necessarily valable. Jump in,
+ 
+
+ align:start position:0%
+makes it necessarily valable. Jump in,
+Nick. Um, I mean, I kind of agree with
+
+ align:start position:0%
+Nick. Um, I mean, I kind of agree with
+ 
+
+ align:start position:0%
+Nick. Um, I mean, I kind of agree with
+Annie. Like, I think there's like
+
+ align:start position:0%
+Annie. Like, I think there's like
+ 
+
+ align:start position:0%
+Annie. Like, I think there's like
+especially arithmetic, like I think I'm
+
+ align:start position:0%
+especially arithmetic, like I think I'm
+ 
+
+ align:start position:0%
+especially arithmetic, like I think I'm
+kind of believer 1 plus one's always
+
+ align:start position:0%
+kind of believer 1 plus one's always
+ 
+
+ align:start position:0%
+kind of believer 1 plus one's always
+going to equal two. Like, I've seen some
+
+ align:start position:0%
+going to equal two. Like, I've seen some
+ 
+
+ align:start position:0%
+going to equal two. Like, I've seen some
+guys prove that it doesn't, but I don't.
+
+ align:start position:0%
+guys prove that it doesn't, but I don't.
+ 
+
+ align:start position:0%
+guys prove that it doesn't, but I don't.
+And, uh, like also I think geometry has
+
+ align:start position:0%
+And, uh, like also I think geometry has
+ 
+
+ align:start position:0%
+And, uh, like also I think geometry has
+some like innately true properties like
+
+ align:start position:0%
+some like innately true properties like
+ 
+
+ align:start position:0%
+some like innately true properties like
+circles and triangles. I think there's
+
+ align:start position:0%
+circles and triangles. I think there's
+ 
+
+ align:start position:0%
+circles and triangles. I think there's
+some things there that no matter where
+
+ align:start position:0%
+some things there that no matter where
+ 
+
+ align:start position:0%
+some things there that no matter where
+you find them, they'll always be the
+
+ align:start position:0%
+you find them, they'll always be the
+ 
+
+ align:start position:0%
+you find them, they'll always be the
+same. You know, like if an angle is an
+
+ align:start position:0%
+same. You know, like if an angle is an
+ 
+
+ align:start position:0%
+same. You know, like if an angle is an
+angle, stuff like that. Well, geometry
+
+ align:start position:0%
+angle, stuff like that. Well, geometry
+ 
+
+ align:start position:0%
+angle, stuff like that. Well, geometry
+is a problem. The Greeks can never tie
+
+ align:start position:0%
+is a problem. The Greeks can never tie
+ 
+
+ align:start position:0%
+is a problem. The Greeks can never tie
+an angle. I mean, they just couldn't. I
+
+ align:start position:0%
+an angle. I mean, they just couldn't. I
+ 
+
+ align:start position:0%
+an angle. I mean, they just couldn't. I
+mean, you could think that you could
+
+ align:start position:0%
+mean, you could think that you could
+ 
+
+ align:start position:0%
+mean, you could think that you could
+split an angle into three equal parts,
+
+ align:start position:0%
+split an angle into three equal parts,
+ 
+
+ align:start position:0%
+split an angle into three equal parts,
+but you can't. I mean, using geometric
+
+ align:start position:0%
+but you can't. I mean, using geometric
+ 
+
+ align:start position:0%
+but you can't. I mean, using geometric
+constructs is impossible. I mean,
+
+ align:start position:0%
+constructs is impossible. I mean,
+ 
+
+ align:start position:0%
+constructs is impossible. I mean,
+everything you do in math is based on a
+
+ align:start position:0%
+everything you do in math is based on a
+ 
+
+ align:start position:0%
+everything you do in math is based on a
+certain set of assumptions just like
+
+ align:start position:0%
+certain set of assumptions just like
+ 
+
+ align:start position:0%
+certain set of assumptions just like
+everything we do in physics. I mean, all
+
+ align:start position:0%
+everything we do in physics. I mean, all
+ 
+
+ align:start position:0%
+everything we do in physics. I mean, all
+quantum mechanics is based
+
+ align:start position:0%
+quantum mechanics is based
+ 
+
+ align:start position:0%
+quantum mechanics is based
+on some number of postulates. Mhm. Yeah.
+
+ align:start position:0%
+on some number of postulates. Mhm. Yeah.
+ 
+
+ align:start position:0%
+on some number of postulates. Mhm. Yeah.
+Yeah, I forgot the number. But I mean
+
+ align:start position:0%
+Yeah, I forgot the number. But I mean
+ 
+
+ align:start position:0%
+Yeah, I forgot the number. But I mean
+there's a whole I mean it's all based on
+
+ align:start position:0%
+there's a whole I mean it's all based on
+ 
+
+ align:start position:0%
+there's a whole I mean it's all based on
+what you think is true. You can do
+
+ align:start position:0%
+what you think is true. You can do
+ 
+
+ align:start position:0%
+what you think is true. You can do
+non-ucukitian geometry and just
+
+ align:start position:0%
+non-ucukitian geometry and just
+ 
+
+ align:start position:0%
+non-ucukitian geometry and just
+completely throw everything that you
+
+ align:start position:0%
+completely throw everything that you
+ 
+
+ align:start position:0%
+completely throw everything that you
+know about classical geometry out the
+
+ align:start position:0%
+know about classical geometry out the
+ 
+
+ align:start position:0%
+know about classical geometry out the
+window. And I mean if you know Uklid
+
+ align:start position:0%
+window. And I mean if you know Uklid
+ 
+
+ align:start position:0%
+window. And I mean if you know Uklid
+believed one thing based on his set of
+
+ align:start position:0%
+believed one thing based on his set of
+ 
+
+ align:start position:0%
+believed one thing based on his set of
+assumptions, but you know anti-uclid can
+
+ align:start position:0%
+assumptions, but you know anti-uclid can
+ 
+
+ align:start position:0%
+assumptions, but you know anti-uclid can
+you know get completely different
+
+ align:start position:0%
+you know get completely different
+ 
+
+ align:start position:0%
+you know get completely different
+results. Let me let me let me ask a a
+
+ align:start position:0%
+results. Let me let me let me ask a a
+ 
+
+ align:start position:0%
+results. Let me let me let me ask a a
+slightly different question but that I
+
+ align:start position:0%
+slightly different question but that I
+ 
+
+ align:start position:0%
+slightly different question but that I
+think will still keep us thinking about
+
+ align:start position:0%
+think will still keep us thinking about
+ 
+
+ align:start position:0%
+think will still keep us thinking about
+this set of problems. If Lewis is right
+
+ align:start position:0%
+this set of problems. If Lewis is right
+ 
+
+ align:start position:0%
+this set of problems. If Lewis is right
+and that what the and that we could
+
+ align:start position:0%
+and that what the and that we could
+ 
+
+ align:start position:0%
+and that what the and that we could
+characterize sort of the general
+
+ align:start position:0%
+characterize sort of the general
+ 
+
+ align:start position:0%
+characterize sort of the general
+medieval mindset as having a couple of
+
+ align:start position:0%
+medieval mindset as having a couple of
+ 
+
+ align:start position:0%
+medieval mindset as having a couple of
+characteristics. One, it's bookish,
+
+ align:start position:0%
+characteristics. One, it's bookish,
+ 
+
+ align:start position:0%
+characteristics. One, it's bookish,
+right? He claims that in no uncertain
+
+ align:start position:0%
+right? He claims that in no uncertain
+ 
+
+ align:start position:0%
+right? He claims that in no uncertain
+terms. It wants to believe everything,
+
+ align:start position:0%
+terms. It wants to believe everything,
+ 
+
+ align:start position:0%
+terms. It wants to believe everything,
+right, that's ever been written by an
+
+ align:start position:0%
+right, that's ever been written by an
+ 
+
+ align:start position:0%
+right, that's ever been written by an
+authority. It's
+
+ align:start position:0%
+authority. It's
+ 
+
+ align:start position:0%
+authority. It's
+systematic, right? it wants to take all
+
+ align:start position:0%
+systematic, right? it wants to take all
+ 
+
+ align:start position:0%
+systematic, right? it wants to take all
+of the different things that it's read
+
+ align:start position:0%
+of the different things that it's read
+ 
+
+ align:start position:0%
+of the different things that it's read
+and somehow make sense of them. So he
+
+ align:start position:0%
+and somehow make sense of them. So he
+ 
+
+ align:start position:0%
+and somehow make sense of them. So he
+says, right, if there was an invention
+
+ align:start position:0%
+says, right, if there was an invention
+ 
+
+ align:start position:0%
+says, right, if there was an invention
+they would have really appreciated, it
+
+ align:start position:0%
+they would have really appreciated, it
+ 
+
+ align:start position:0%
+they would have really appreciated, it
+was the card index. That's a really
+
+ align:start position:0%
+was the card index. That's a really
+ 
+
+ align:start position:0%
+was the card index. That's a really
+great line. Um that's a that's a
+
+ align:start position:0%
+great line. Um that's a that's a
+ 
+
+ align:start position:0%
+great line. Um that's a that's a
+wonderful line.
+
+ align:start position:0%
+wonderful line.
+ 
+
+ align:start position:0%
+wonderful line.
+uh if it is those
+
+ align:start position:0%
+uh if it is those
+ 
+
+ align:start position:0%
+uh if it is those
+things and we know that there's all of
+
+ align:start position:0%
+things and we know that there's all of
+ 
+
+ align:start position:0%
+things and we know that there's all of
+this sort of competing information
+
+ align:start position:0%
+this sort of competing information
+ 
+
+ align:start position:0%
+this sort of competing information
+that's out there. You we're struggling
+
+ align:start position:0%
+that's out there. You we're struggling
+ 
+
+ align:start position:0%
+that's out there. You we're struggling
+right now with some competing
+
+ align:start position:0%
+right now with some competing
+ 
+
+ align:start position:0%
+right now with some competing
+information right in our own um uh sort
+
+ align:start position:0%
+information right in our own um uh sort
+ 
+
+ align:start position:0%
+information right in our own um uh sort
+of niche of the cosmological project.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um where what where does that leave a
+
+ align:start position:0%
+um where what where does that leave a
+ 
+
+ align:start position:0%
+um where what where does that leave a
+medieval thinker right if they if Lewis
+
+ align:start position:0%
+medieval thinker right if they if Lewis
+ 
+
+ align:start position:0%
+medieval thinker right if they if Lewis
+is right and they're compelled right to
+
+ align:start position:0%
+is right and they're compelled right to
+ 
+
+ align:start position:0%
+is right and they're compelled right to
+be
+
+ align:start position:0%
+be
+ 
+
+ align:start position:0%
+be
+systematic and eclectic although they
+
+ align:start position:0%
+systematic and eclectic although they
+ 
+
+ align:start position:0%
+systematic and eclectic although they
+might not have seen it that way and to
+
+ align:start position:0%
+might not have seen it that way and to
+ 
+
+ align:start position:0%
+might not have seen it that way and to
+believe all authorities whether they're
+
+ align:start position:0%
+believe all authorities whether they're
+ 
+
+ align:start position:0%
+believe all authorities whether they're
+pagan or Christian or poetry or you know
+
+ align:start position:0%
+pagan or Christian or poetry or you know
+ 
+
+ align:start position:0%
+pagan or Christian or poetry or you know
+history or chronicle or whatever
+
+ align:start position:0%
+history or chronicle or whatever
+ 
+
+ align:start position:0%
+history or chronicle or whatever
+If I have to take all of this stuff and
+
+ align:start position:0%
+If I have to take all of this stuff and
+ 
+
+ align:start position:0%
+If I have to take all of this stuff and
+somehow make sense of it, where does
+
+ align:start position:0%
+somehow make sense of it, where does
+ 
+
+ align:start position:0%
+somehow make sense of it, where does
+that leave
+
+ align:start position:0%
+that leave
+ 
+
+ align:start position:0%
+that leave
+me? I mean, Lewis might just be
+
+ align:start position:0%
+me? I mean, Lewis might just be
+ 
+
+ align:start position:0%
+me? I mean, Lewis might just be
+wrong. That's one possibility.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Multiple personalities.
+
+ align:start position:0%
+Multiple personalities.
+ 
+
+ align:start position:0%
+Multiple personalities.
+[Laughter]
+
+ align:start position:0%
+[Laughter]
+ 
+
+ align:start position:0%
+[Laughter]
+Okay. A lot of demented individuals of
+
+ align:start position:0%
+Okay. A lot of demented individuals of
+ 
+
+ align:start position:0%
+Okay. A lot of demented individuals of
+which we read, you know, last week. I
+
+ align:start position:0%
+which we read, you know, last week. I
+ 
+
+ align:start position:0%
+which we read, you know, last week. I
+don't think that was why they were
+
+ align:start position:0%
+don't think that was why they were
+ 
+
+ align:start position:0%
+don't think that was why they were
+demented, though. Ian, I I think that
+
+ align:start position:0%
+demented, though. Ian, I I think that
+ 
+
+ align:start position:0%
+demented, though. Ian, I I think that
+the the kind of naive belief of anyone
+
+ align:start position:0%
+the the kind of naive belief of anyone
+ 
+
+ align:start position:0%
+the the kind of naive belief of anyone
+presuming to be in authority is is, you
+
+ align:start position:0%
+presuming to be in authority is is, you
+ 
+
+ align:start position:0%
+presuming to be in authority is is, you
+know, is just that is rather naive and
+
+ align:start position:0%
+know, is just that is rather naive and
+ 
+
+ align:start position:0%
+know, is just that is rather naive and
+and kind of results in I'd like to think
+
+ align:start position:0%
+and kind of results in I'd like to think
+ 
+
+ align:start position:0%
+and kind of results in I'd like to think
+that that if there's any one thing that
+
+ align:start position:0%
+that that if there's any one thing that
+ 
+
+ align:start position:0%
+that that if there's any one thing that
+we now do better than than they might
+
+ align:start position:0%
+we now do better than than they might
+ 
+
+ align:start position:0%
+we now do better than than they might
+have done, it's, you know,
+
+ align:start position:0%
+have done, it's, you know,
+ 
+
+ align:start position:0%
+have done, it's, you know,
+valuing certain authorities over others,
+
+ align:start position:0%
+valuing certain authorities over others,
+ 
+
+ align:start position:0%
+valuing certain authorities over others,
+you know, or or weighing the weighing
+
+ align:start position:0%
+you know, or or weighing the weighing
+ 
+
+ align:start position:0%
+you know, or or weighing the weighing
+the value of certain things over others,
+
+ align:start position:0%
+the value of certain things over others,
+ 
+
+ align:start position:0%
+the value of certain things over others,
+not just on the basis of how interesting
+
+ align:start position:0%
+not just on the basis of how interesting
+ 
+
+ align:start position:0%
+not just on the basis of how interesting
+it is or how compelling they wrote. Mhm.
+
+ align:start position:0%
+it is or how compelling they wrote. Mhm.
+ 
+
+ align:start position:0%
+it is or how compelling they wrote. Mhm.
+Uh but
+
+ align:start position:0%
+Uh but
+ 
+
+ align:start position:0%
+Uh but
+it's I don't know. I I I think that's
+
+ align:start position:0%
+it's I don't know. I I I think that's
+ 
+
+ align:start position:0%
+it's I don't know. I I I think that's
+the may
+
+ align:start position:0%
+the may
+ 
+
+ align:start position:0%
+the may
+maybe I guess I'm not really answering
+
+ align:start position:0%
+maybe I guess I'm not really answering
+ 
+
+ align:start position:0%
+maybe I guess I'm not really answering
+the question, but that was just my the
+
+ align:start position:0%
+the question, but that was just my the
+ 
+
+ align:start position:0%
+the question, but that was just my the
+one thing you made me think about was
+
+ align:start position:0%
+one thing you made me think about was
+ 
+
+ align:start position:0%
+one thing you made me think about was
+that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+they're I think they just they ended up
+
+ align:start position:0%
+they're I think they just they ended up
+ 
+
+ align:start position:0%
+they're I think they just they ended up
+getting muddling a lot of things
+
+ align:start position:0%
+getting muddling a lot of things
+ 
+
+ align:start position:0%
+getting muddling a lot of things
+together simply based on the fact that
+
+ align:start position:0%
+together simply based on the fact that
+ 
+
+ align:start position:0%
+together simply based on the fact that
+they're willing to take poets as
+
+ align:start position:0%
+they're willing to take poets as
+ 
+
+ align:start position:0%
+they're willing to take poets as
+scientific authorities, things like that
+
+ align:start position:0%
+scientific authorities, things like that
+ 
+
+ align:start position:0%
+scientific authorities, things like that
+that they Well, I mean, are they
+
+ align:start position:0%
+that they Well, I mean, are they
+ 
+
+ align:start position:0%
+that they Well, I mean, are they
+actually willing to take poets as
+
+ align:start position:0%
+actually willing to take poets as
+ 
+
+ align:start position:0%
+actually willing to take poets as
+scientific
+
+ align:start position:0%
+scientific
+ 
+
+ align:start position:0%
+scientific
+authorities? Is that or are they quote
+
+ align:start position:0%
+authorities? Is that or are they quote
+ 
+
+ align:start position:0%
+authorities? Is that or are they quote
+unquote scientific authority or is there
+
+ align:start position:0%
+unquote scientific authority or is there
+ 
+
+ align:start position:0%
+unquote scientific authority or is there
+a distinction? Well, I mean there was
+
+ align:start position:0%
+a distinction? Well, I mean there was
+ 
+
+ align:start position:0%
+a distinction? Well, I mean there was
+much less of I mean the poets wrote a
+
+ align:start position:0%
+much less of I mean the poets wrote a
+ 
+
+ align:start position:0%
+much less of I mean the poets wrote a
+lot about science whereas you don't see
+
+ align:start position:0%
+lot about science whereas you don't see
+ 
+
+ align:start position:0%
+lot about science whereas you don't see
+many poets writing about our model of
+
+ align:start position:0%
+many poets writing about our model of
+ 
+
+ align:start position:0%
+many poets writing about our model of
+the universe. I mean
+
+ align:start position:0%
+the universe. I mean
+ 
+
+ align:start position:0%
+the universe. I mean
+oh here I had to take this class with
+
+ align:start position:0%
+oh here I had to take this class with
+ 
+
+ align:start position:0%
+oh here I had to take this class with
+John Hilder and we read this book about
+
+ align:start position:0%
+John Hilder and we read this book about
+ 
+
+ align:start position:0%
+John Hilder and we read this book about
+astrophysical poetry. I thought I was
+
+ align:start position:0%
+astrophysical poetry. I thought I was
+ 
+
+ align:start position:0%
+astrophysical poetry. I thought I was
+going to a lot I clarified that with a
+
+ align:start position:0%
+going to a lot I clarified that with a
+ 
+
+ align:start position:0%
+going to a lot I clarified that with a
+lot of people. Yeah. People race sonnets
+
+ align:start position:0%
+lot of people. Yeah. People race sonnets
+ 
+
+ align:start position:0%
+lot of people. Yeah. People race sonnets
+and 3091. It's you know they're not very
+
+ align:start position:0%
+and 3091. It's you know they're not very
+ 
+
+ align:start position:0%
+and 3091. It's you know they're not very
+pretty. I think I think there's a wider
+
+ align:start position:0%
+pretty. I think I think there's a wider
+ 
+
+ align:start position:0%
+pretty. I think I think there's a wider
+divide. I mean, I think what he saying
+
+ align:start position:0%
+divide. I mean, I think what he saying
+ 
+
+ align:start position:0%
+divide. I mean, I think what he saying
+is probably just a wider divide now
+
+ align:start position:0%
+is probably just a wider divide now
+ 
+
+ align:start position:0%
+is probably just a wider divide now
+between the authorities than there was
+
+ align:start position:0%
+between the authorities than there was
+ 
+
+ align:start position:0%
+between the authorities than there was
+back then that poets had a better maybe
+
+ align:start position:0%
+back then that poets had a better maybe
+ 
+
+ align:start position:0%
+back then that poets had a better maybe
+they had a better understanding of their
+
+ align:start position:0%
+they had a better understanding of their
+ 
+
+ align:start position:0%
+they had a better understanding of their
+model or it was much more accessible to
+
+ align:start position:0%
+model or it was much more accessible to
+ 
+
+ align:start position:0%
+model or it was much more accessible to
+them than our model is today. So it's
+
+ align:start position:0%
+them than our model is today. So it's
+ 
+
+ align:start position:0%
+them than our model is today. So it's
+harder for but it's Lewis then being
+
+ align:start position:0%
+harder for but it's Lewis then being
+ 
+
+ align:start position:0%
+harder for but it's Lewis then being
+inconsistent when he tells us which he
+
+ align:start position:0%
+inconsistent when he tells us which he
+ 
+
+ align:start position:0%
+inconsistent when he tells us which he
+does in no uncertain terms that theology
+
+ align:start position:0%
+does in no uncertain terms that theology
+ 
+
+ align:start position:0%
+does in no uncertain terms that theology
+right spiritual advice all that stuff is
+
+ align:start position:0%
+right spiritual advice all that stuff is
+ 
+
+ align:start position:0%
+right spiritual advice all that stuff is
+in fact separate from the general
+
+ align:start position:0%
+in fact separate from the general
+ 
+
+ align:start position:0%
+in fact separate from the general
+cultural
+
+ align:start position:0%
+cultural
+ 
+
+ align:start position:0%
+cultural
+model. I mean how do we square that?
+
+ align:start position:0%
+model. I mean how do we square that?
+ 
+
+ align:start position:0%
+model. I mean how do we square that?
+Well kind of makes sense. I mean think
+
+ align:start position:0%
+Well kind of makes sense. I mean think
+ 
+
+ align:start position:0%
+Well kind of makes sense. I mean think
+about how many scientists are Christians
+
+ align:start position:0%
+about how many scientists are Christians
+ 
+
+ align:start position:0%
+about how many scientists are Christians
+right? like you know you're a scientist
+
+ align:start position:0%
+right? like you know you're a scientist
+ 
+
+ align:start position:0%
+right? like you know you're a scientist
+and you you know you go to church and
+
+ align:start position:0%
+and you you know you go to church and
+ 
+
+ align:start position:0%
+and you you know you go to church and
+one day and you believe that God created
+
+ align:start position:0%
+one day and you believe that God created
+ 
+
+ align:start position:0%
+one day and you believe that God created
+the world in seven days but then on
+
+ align:start position:0%
+the world in seven days but then on
+ 
+
+ align:start position:0%
+the world in seven days but then on
+Monday you go to like your work and you
+
+ align:start position:0%
+Monday you go to like your work and you
+ 
+
+ align:start position:0%
+Monday you go to like your work and you
+believe in evolution and but that's not
+
+ align:start position:0%
+believe in evolution and but that's not
+ 
+
+ align:start position:0%
+believe in evolution and but that's not
+the claim exactly that Lewis is making
+
+ align:start position:0%
+the claim exactly that Lewis is making
+ 
+
+ align:start position:0%
+the claim exactly that Lewis is making
+right I mean he says oh go ahead just in
+
+ align:start position:0%
+right I mean he says oh go ahead just in
+ 
+
+ align:start position:0%
+right I mean he says oh go ahead just in
+terms of religion it makes sense because
+
+ align:start position:0%
+terms of religion it makes sense because
+ 
+
+ align:start position:0%
+terms of religion it makes sense because
+all I mean before I mean when you're
+
+ align:start position:0%
+all I mean before I mean when you're
+ 
+
+ align:start position:0%
+all I mean before I mean when you're
+looking at the pagan religions it's a
+
+ align:start position:0%
+looking at the pagan religions it's a
+ 
+
+ align:start position:0%
+looking at the pagan religions it's a
+nature is a big part of the religion you
+
+ align:start position:0%
+nature is a big part of the religion you
+ 
+
+ align:start position:0%
+nature is a big part of the religion you
+can't it's very hard to separate the
+
+ align:start position:0%
+can't it's very hard to separate the
+ 
+
+ align:start position:0%
+can't it's very hard to separate the
+world that exists from the theology that
+
+ align:start position:0%
+world that exists from the theology that
+ 
+
+ align:start position:0%
+world that exists from the theology that
+exists. On the other hand, with
+
+ align:start position:0%
+exists. On the other hand, with
+ 
+
+ align:start position:0%
+exists. On the other hand, with
+religions like Christianity, they're
+
+ align:start position:0%
+religions like Christianity, they're
+ 
+
+ align:start position:0%
+religions like Christianity, they're
+they are removed from the natural world.
+
+ align:start position:0%
+they are removed from the natural world.
+ 
+
+ align:start position:0%
+they are removed from the natural world.
+So, it's easier to it's easier to see
+
+ align:start position:0%
+So, it's easier to it's easier to see
+ 
+
+ align:start position:0%
+So, it's easier to it's easier to see
+that there was that there could have
+
+ align:start position:0%
+that there was that there could have
+ 
+
+ align:start position:0%
+that there was that there could have
+that people who were both Christians
+
+ align:start position:0%
+that people who were both Christians
+ 
+
+ align:start position:0%
+that people who were both Christians
+could see both the natural world and the
+
+ align:start position:0%
+could see both the natural world and the
+ 
+
+ align:start position:0%
+could see both the natural world and the
+theological world as two separate things
+
+ align:start position:0%
+theological world as two separate things
+ 
+
+ align:start position:0%
+theological world as two separate things
+because they don't really interact that
+
+ align:start position:0%
+because they don't really interact that
+ 
+
+ align:start position:0%
+because they don't really interact that
+much.
+
+ align:start position:0%
+much.
+ 
+
+ align:start position:0%
+much.
+But I think we're talking more
+
+ align:start position:0%
+But I think we're talking more
+ 
+
+ align:start position:0%
+But I think we're talking more
+about almost like a psychological
+
+ align:start position:0%
+about almost like a psychological
+ 
+
+ align:start position:0%
+about almost like a psychological
+divide. I mean, there's it's almost as
+
+ align:start position:0%
+divide. I mean, there's it's almost as
+ 
+
+ align:start position:0%
+divide. I mean, there's it's almost as
+if when you're thinking about
+
+ align:start position:0%
+if when you're thinking about
+ 
+
+ align:start position:0%
+if when you're thinking about
+one, you're just completely ignoring the
+
+ align:start position:0%
+one, you're just completely ignoring the
+ 
+
+ align:start position:0%
+one, you're just completely ignoring the
+other, right? But is that like I mean I
+
+ align:start position:0%
+other, right? But is that like I mean I
+ 
+
+ align:start position:0%
+other, right? But is that like I mean I
+mean I'm very much non-religious person,
+
+ align:start position:0%
+mean I'm very much non-religious person,
+ 
+
+ align:start position:0%
+mean I'm very much non-religious person,
+but it sounds like a lot of it is very
+
+ align:start position:0%
+but it sounds like a lot of it is very
+ 
+
+ align:start position:0%
+but it sounds like a lot of it is very
+much of the Christianity stuff is that
+
+ align:start position:0%
+much of the Christianity stuff is that
+ 
+
+ align:start position:0%
+much of the Christianity stuff is that
+there's, you know, there's heaven and
+
+ align:start position:0%
+there's, you know, there's heaven and
+ 
+
+ align:start position:0%
+there's, you know, there's heaven and
+there's hell, but earth is just
+
+ align:start position:0%
+there's hell, but earth is just
+ 
+
+ align:start position:0%
+there's hell, but earth is just
+something you deal with while you're,
+
+ align:start position:0%
+something you deal with while you're,
+ 
+
+ align:start position:0%
+something you deal with while you're,
+you know, trying to work away your sins
+
+ align:start position:0%
+you know, trying to work away your sins
+ 
+
+ align:start position:0%
+you know, trying to work away your sins
+and to get to heaven. And so figuring
+
+ align:start position:0%
+and to get to heaven. And so figuring
+ 
+
+ align:start position:0%
+and to get to heaven. And so figuring
+out how earth works isn't really what
+
+ align:start position:0%
+out how earth works isn't really what
+ 
+
+ align:start position:0%
+out how earth works isn't really what
+you know something to do with religion.
+
+ align:start position:0%
+you know something to do with religion.
+ 
+
+ align:start position:0%
+you know something to do with religion.
+It's more your own moralistic stuff
+
+ align:start position:0%
+It's more your own moralistic stuff
+ 
+
+ align:start position:0%
+It's more your own moralistic stuff
+that's dealing with it and then dealing
+
+ align:start position:0%
+that's dealing with it and then dealing
+ 
+
+ align:start position:0%
+that's dealing with it and then dealing
+with then figuring that out is separate
+
+ align:start position:0%
+with then figuring that out is separate
+ 
+
+ align:start position:0%
+with then figuring that out is separate
+than that. Go ahead. But now I have to
+
+ align:start position:0%
+than that. Go ahead. But now I have to
+ 
+
+ align:start position:0%
+than that. Go ahead. But now I have to
+think of this one passage where they
+
+ align:start position:0%
+think of this one passage where they
+ 
+
+ align:start position:0%
+think of this one passage where they
+talk about being in a the earth being
+
+ align:start position:0%
+talk about being in a the earth being
+ 
+
+ align:start position:0%
+talk about being in a the earth being
+the center of the universe, right?
+
+ align:start position:0%
+the center of the universe, right?
+ 
+
+ align:start position:0%
+the center of the universe, right?
+Thinking of a Mhm. that but then on then
+
+ align:start position:0%
+Thinking of a Mhm. that but then on then
+ 
+
+ align:start position:0%
+Thinking of a Mhm. that but then on then
+there's this passage which states you're
+
+ align:start position:0%
+there's this passage which states you're
+ 
+
+ align:start position:0%
+there's this passage which states you're
+outside the city walls. Yes. So I think
+
+ align:start position:0%
+outside the city walls. Yes. So I think
+ 
+
+ align:start position:0%
+outside the city walls. Yes. So I think
+here we have this kind of fundamental
+
+ align:start position:0%
+here we have this kind of fundamental
+ 
+
+ align:start position:0%
+here we have this kind of fundamental
+justosition where these two conflict
+
+ align:start position:0%
+justosition where these two conflict
+ 
+
+ align:start position:0%
+justosition where these two conflict
+because in one way yes God is the center
+
+ align:start position:0%
+because in one way yes God is the center
+ 
+
+ align:start position:0%
+because in one way yes God is the center
+and is the light and in this other way
+
+ align:start position:0%
+and is the light and in this other way
+ 
+
+ align:start position:0%
+and is the light and in this other way
+which puts us at the periphery but in in
+
+ align:start position:0%
+which puts us at the periphery but in in
+ 
+
+ align:start position:0%
+which puts us at the periphery but in in
+the model we are at the center and so I
+
+ align:start position:0%
+the model we are at the center and so I
+ 
+
+ align:start position:0%
+the model we are at the center and so I
+mean there there has to be some exchange
+
+ align:start position:0%
+mean there there has to be some exchange
+ 
+
+ align:start position:0%
+mean there there has to be some exchange
+of then he does explain how they're
+
+ align:start position:0%
+of then he does explain how they're
+ 
+
+ align:start position:0%
+of then he does explain how they're
+trying to reconcile this that we're
+
+ align:start position:0%
+trying to reconcile this that we're
+ 
+
+ align:start position:0%
+trying to reconcile this that we're
+actually looking inward and therefore we
+
+ align:start position:0%
+actually looking inward and therefore we
+ 
+
+ align:start position:0%
+actually looking inward and therefore we
+are at the center but we really are not.
+
+ align:start position:0%
+are at the center but we really are not.
+ 
+
+ align:start position:0%
+are at the center but we really are not.
+So, I mean, I think there was conflict
+
+ align:start position:0%
+So, I mean, I think there was conflict
+ 
+
+ align:start position:0%
+So, I mean, I think there was conflict
+in people's minds that they were trying
+
+ align:start position:0%
+in people's minds that they were trying
+ 
+
+ align:start position:0%
+in people's minds that they were trying
+to to decide what what was right. They
+
+ align:start position:0%
+to to decide what what was right. They
+ 
+
+ align:start position:0%
+to to decide what what was right. They
+were not divorcing the two entirely.
+
+ align:start position:0%
+were not divorcing the two entirely.
+ 
+
+ align:start position:0%
+were not divorcing the two entirely.
+Well, he let's let's go back to Lewis's
+
+ align:start position:0%
+Well, he let's let's go back to Lewis's
+ 
+
+ align:start position:0%
+Well, he let's let's go back to Lewis's
+argument because it's a it is a
+
+ align:start position:0%
+argument because it's a it is a
+ 
+
+ align:start position:0%
+argument because it's a it is a
+complicated one. It starts I mean it
+
+ align:start position:0%
+complicated one. It starts I mean it
+ 
+
+ align:start position:0%
+complicated one. It starts I mean it
+goes through the whole book really,
+
+ align:start position:0%
+goes through the whole book really,
+ 
+
+ align:start position:0%
+goes through the whole book really,
+right? But it's he lays it out first um
+
+ align:start position:0%
+right? But it's he lays it out first um
+ 
+
+ align:start position:0%
+right? But it's he lays it out first um
+starting on page 18 and he says he he
+
+ align:start position:0%
+starting on page 18 and he says he he
+ 
+
+ align:start position:0%
+starting on page 18 and he says he he
+opens up a space for himself to be
+
+ align:start position:0%
+opens up a space for himself to be
+ 
+
+ align:start position:0%
+opens up a space for himself to be
+contradictory essentially by saying one
+
+ align:start position:0%
+contradictory essentially by saying one
+ 
+
+ align:start position:0%
+contradictory essentially by saying one
+particular class of experts the great
+
+ align:start position:0%
+particular class of experts the great
+ 
+
+ align:start position:0%
+particular class of experts the great
+spiritual writers ignore the model
+
+ align:start position:0%
+spiritual writers ignore the model
+ 
+
+ align:start position:0%
+spiritual writers ignore the model
+almost completely. We need to know
+
+ align:start position:0%
+almost completely. We need to know
+ 
+
+ align:start position:0%
+almost completely. We need to know
+something about the model if we're to
+
+ align:start position:0%
+something about the model if we're to
+ 
+
+ align:start position:0%
+something about the model if we're to
+read Chaucer but we can neglect it if
+
+ align:start position:0%
+read Chaucer but we can neglect it if
+ 
+
+ align:start position:0%
+read Chaucer but we can neglect it if
+we're going to read St. Bernard right or
+
+ align:start position:0%
+we're going to read St. Bernard right or
+ 
+
+ align:start position:0%
+we're going to read St. Bernard right or
+the imitation of Christ or blah blah
+
+ align:start position:0%
+the imitation of Christ or blah blah
+ 
+
+ align:start position:0%
+the imitation of Christ or blah blah
+blah. He gives all these possibilities.
+
+ align:start position:0%
+blah. He gives all these possibilities.
+ 
+
+ align:start position:0%
+blah. He gives all these possibilities.
+Um so that's one way of dealing with
+
+ align:start position:0%
+Um so that's one way of dealing with
+ 
+
+ align:start position:0%
+Um so that's one way of dealing with
+this is saying even though the model
+
+ align:start position:0%
+this is saying even though the model
+ 
+
+ align:start position:0%
+this is saying even though the model
+looks to be intensely religious right
+
+ align:start position:0%
+looks to be intensely religious right
+ 
+
+ align:start position:0%
+looks to be intensely religious right
+the spheres the intelligences
+
+ align:start position:0%
+the spheres the intelligences
+ 
+
+ align:start position:0%
+the spheres the intelligences
+um the inclining because of the love of
+
+ align:start position:0%
+um the inclining because of the love of
+ 
+
+ align:start position:0%
+um the inclining because of the love of
+God the primum mobile why is the primo
+
+ align:start position:0%
+God the primum mobile why is the primo
+ 
+
+ align:start position:0%
+God the primum mobile why is the primo
+mobile even moving well because it loves
+
+ align:start position:0%
+mobile even moving well because it loves
+ 
+
+ align:start position:0%
+mobile even moving well because it loves
+God so much right and because it loves
+
+ align:start position:0%
+God so much right and because it loves
+ 
+
+ align:start position:0%
+God so much right and because it loves
+God so much it has to move and in what
+
+ align:start position:0%
+God so much it has to move and in what
+ 
+
+ align:start position:0%
+God so much it has to move and in what
+direction does it move it's perfect love
+
+ align:start position:0%
+direction does it move it's perfect love
+ 
+
+ align:start position:0%
+direction does it move it's perfect love
+after all so it moves in a circle right
+
+ align:start position:0%
+after all so it moves in a circle right
+ 
+
+ align:start position:0%
+after all so it moves in a circle right
+isn't Isn't this obvious that this would
+
+ align:start position:0%
+isn't Isn't this obvious that this would
+ 
+
+ align:start position:0%
+isn't Isn't this obvious that this would
+be how it would work? I mean, all of
+
+ align:start position:0%
+be how it would work? I mean, all of
+ 
+
+ align:start position:0%
+be how it would work? I mean, all of
+that sounds to us kind of
+
+ align:start position:0%
+that sounds to us kind of
+ 
+
+ align:start position:0%
+that sounds to us kind of
+religious, right? If we if we had to
+
+ align:start position:0%
+religious, right? If we if we had to
+ 
+
+ align:start position:0%
+religious, right? If we if we had to
+just sort of read it casually and
+
+ align:start position:0%
+just sort of read it casually and
+ 
+
+ align:start position:0%
+just sort of read it casually and
+classify it now, we'd say, "Oh, wow.
+
+ align:start position:0%
+classify it now, we'd say, "Oh, wow.
+ 
+
+ align:start position:0%
+classify it now, we'd say, "Oh, wow.
+What a lot of religious superstition."
+
+ align:start position:0%
+What a lot of religious superstition."
+ 
+
+ align:start position:0%
+What a lot of religious superstition."
+And by the same token, it seems like a
+
+ align:start position:0%
+And by the same token, it seems like a
+ 
+
+ align:start position:0%
+And by the same token, it seems like a
+lot of the spirit the great spiritual
+
+ align:start position:0%
+lot of the spirit the great spiritual
+ 
+
+ align:start position:0%
+lot of the spirit the great spiritual
+writers he cites I mean I wouldn't be
+
+ align:start position:0%
+writers he cites I mean I wouldn't be
+ 
+
+ align:start position:0%
+writers he cites I mean I wouldn't be
+surprised if you know a generation later
+
+ align:start position:0%
+surprised if you know a generation later
+ 
+
+ align:start position:0%
+surprised if you know a generation later
+they were being quoted in in you know in
+
+ align:start position:0%
+they were being quoted in in you know in
+ 
+
+ align:start position:0%
+they were being quoted in in you know in
+research being done by medieval writers
+
+ align:start position:0%
+research being done by medieval writers
+ 
+
+ align:start position:0%
+research being done by medieval writers
+inations of their model right I mean it
+
+ align:start position:0%
+inations of their model right I mean it
+ 
+
+ align:start position:0%
+inations of their model right I mean it
+seems like the way he characterizes
+
+ align:start position:0%
+seems like the way he characterizes
+ 
+
+ align:start position:0%
+seems like the way he characterizes
+these authors that that's exactly what
+
+ align:start position:0%
+these authors that that's exactly what
+ 
+
+ align:start position:0%
+these authors that that's exactly what
+they would do. They do get used in the
+
+ align:start position:0%
+they would do. They do get used in the
+ 
+
+ align:start position:0%
+they would do. They do get used in the
+building of the model even though they
+
+ align:start position:0%
+building of the model even though they
+ 
+
+ align:start position:0%
+building of the model even though they
+don't rely on the model. Absolutely.
+
+ align:start position:0%
+don't rely on the model. Absolutely.
+ 
+
+ align:start position:0%
+don't rely on the model. Absolutely.
+Absolutely. Let let's go on just a
+
+ align:start position:0%
+Absolutely. Let let's go on just a
+ 
+
+ align:start position:0%
+Absolutely. Let let's go on just a
+little bit further in that passage
+
+ align:start position:0%
+little bit further in that passage
+ 
+
+ align:start position:0%
+little bit further in that passage
+there. That is the medievals, right?
+
+ align:start position:0%
+there. That is the medievals, right?
+ 
+
+ align:start position:0%
+there. That is the medievals, right?
+Their cosmology and their religion were
+
+ align:start position:0%
+Their cosmology and their religion were
+ 
+
+ align:start position:0%
+Their cosmology and their religion were
+not such easy bedfellows as might be
+
+ align:start position:0%
+not such easy bedfellows as might be
+ 
+
+ align:start position:0%
+not such easy bedfellows as might be
+supposed, right? That's the that's the
+
+ align:start position:0%
+supposed, right? That's the that's the
+ 
+
+ align:start position:0%
+supposed, right? That's the that's the
+irony here. And we at first may fail to
+
+ align:start position:0%
+irony here. And we at first may fail to
+ 
+
+ align:start position:0%
+irony here. And we at first may fail to
+notice this. For the cosmology appears
+
+ align:start position:0%
+notice this. For the cosmology appears
+ 
+
+ align:start position:0%
+notice this. For the cosmology appears
+to us in its firmly theistic basis and
+
+ align:start position:0%
+to us in its firmly theistic basis and
+ 
+
+ align:start position:0%
+to us in its firmly theistic basis and
+its ready welcome to the supernatural to
+
+ align:start position:0%
+its ready welcome to the supernatural to
+ 
+
+ align:start position:0%
+its ready welcome to the supernatural to
+be eminently religious. That's what I
+
+ align:start position:0%
+be eminently religious. That's what I
+ 
+
+ align:start position:0%
+be eminently religious. That's what I
+was just trying to say and paraphrase.
+
+ align:start position:0%
+was just trying to say and paraphrase.
+ 
+
+ align:start position:0%
+was just trying to say and paraphrase.
+Um but then he says it is not eminently
+
+ align:start position:0%
+Um but then he says it is not eminently
+ 
+
+ align:start position:0%
+Um but then he says it is not eminently
+Christian. So he has this long text in
+
+ align:start position:0%
+Christian. So he has this long text in
+ 
+
+ align:start position:0%
+Christian. So he has this long text in
+which everything is pulled together,
+
+ align:start position:0%
+which everything is pulled together,
+ 
+
+ align:start position:0%
+which everything is pulled together,
+everything is syncric, right? Everything
+
+ align:start position:0%
+everything is syncric, right? Everything
+ 
+
+ align:start position:0%
+everything is syncric, right? Everything
+is eclectic. We we work and work and
+
+ align:start position:0%
+is eclectic. We we work and work and
+ 
+
+ align:start position:0%
+is eclectic. We we work and work and
+work to save the appearances.
+
+ align:start position:0%
+work to save the appearances.
+ 
+
+ align:start position:0%
+work to save the appearances.
+Um and yet on this one fundamental issue
+
+ align:start position:0%
+Um and yet on this one fundamental issue
+ 
+
+ align:start position:0%
+Um and yet on this one fundamental issue
+we have this unbridgegable divide right
+
+ align:start position:0%
+we have this unbridgegable divide right
+ 
+
+ align:start position:0%
+we have this unbridgegable divide right
+which
+
+ align:start position:0%
+which
+ 
+
+ align:start position:0%
+which
+is Christian that is theology spiritual
+
+ align:start position:0%
+is Christian that is theology spiritual
+ 
+
+ align:start position:0%
+is Christian that is theology spiritual
+advice homalytics whatever and then kind
+
+ align:start position:0%
+advice homalytics whatever and then kind
+ 
+
+ align:start position:0%
+advice homalytics whatever and then kind
+of the way we think the world really
+
+ align:start position:0%
+of the way we think the world really
+ 
+
+ align:start position:0%
+of the way we think the world really
+works and the way we write poetry and
+
+ align:start position:0%
+works and the way we write poetry and
+ 
+
+ align:start position:0%
+works and the way we write poetry and
+the way we make illusions and metaphors
+
+ align:start position:0%
+the way we make illusions and metaphors
+ 
+
+ align:start position:0%
+the way we make illusions and metaphors
+and the allegorories we tell and the
+
+ align:start position:0%
+and the allegorories we tell and the
+ 
+
+ align:start position:0%
+and the allegorories we tell and the
+fiction we write and the way we write
+
+ align:start position:0%
+fiction we write and the way we write
+ 
+
+ align:start position:0%
+fiction we write and the way we write
+love poetry. and and right and
+
+ align:start position:0%
+love poetry. and and right and
+ 
+
+ align:start position:0%
+love poetry. and and right and
+everything else that's important in
+
+ align:start position:0%
+everything else that's important in
+ 
+
+ align:start position:0%
+everything else that's important in
+life.
+
+ align:start position:0%
+life.
+ 
+
+ align:start position:0%
+life.
+Um, if this is true, if if Lewis isn't
+
+ align:start position:0%
+Um, if this is true, if if Lewis isn't
+ 
+
+ align:start position:0%
+Um, if this is true, if if Lewis isn't
+just setting this up to help himself get
+
+ align:start position:0%
+just setting this up to help himself get
+ 
+
+ align:start position:0%
+just setting this up to help himself get
+out of a sticky wicket, right, which he
+
+ align:start position:0%
+out of a sticky wicket, right, which he
+ 
+
+ align:start position:0%
+out of a sticky wicket, right, which he
+might
+
+ align:start position:0%
+might
+ 
+
+ align:start position:0%
+might
+be, one way we can reconcile these
+
+ align:start position:0%
+be, one way we can reconcile these
+ 
+
+ align:start position:0%
+be, one way we can reconcile these
+medievalists, if you will, the medieval
+
+ align:start position:0%
+medievalists, if you will, the medieval
+ 
+
+ align:start position:0%
+medievalists, if you will, the medieval
+world that we feel so comfortable
+
+ align:start position:0%
+world that we feel so comfortable
+ 
+
+ align:start position:0%
+world that we feel so comfortable
+imagining and say
+
+ align:start position:0%
+imagining and say
+ 
+
+ align:start position:0%
+imagining and say
+Binham's medieval world, which is so
+
+ align:start position:0%
+Binham's medieval world, which is so
+ 
+
+ align:start position:0%
+Binham's medieval world, which is so
+bizarre to us, is we could
+
+ align:start position:0%
+bizarre to us, is we could
+ 
+
+ align:start position:0%
+bizarre to us, is we could
+say,
+
+ align:start position:0%
+say,
+ 
+
+ align:start position:0%
+say,
+well, you know,
+
+ align:start position:0%
+well, you know,
+ 
+
+ align:start position:0%
+well, you know,
+Middle Earth is comfortable because
+
+ align:start position:0%
+Middle Earth is comfortable because
+ 
+
+ align:start position:0%
+Middle Earth is comfortable because
+Middle Earth is clearly part of this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+model and Binham's saints are so
+
+ align:start position:0%
+model and Binham's saints are so
+ 
+
+ align:start position:0%
+model and Binham's saints are so
+uncomfortable to us because they're part
+
+ align:start position:0%
+uncomfortable to us because they're part
+ 
+
+ align:start position:0%
+uncomfortable to us because they're part
+of that thing that is eminently
+
+ align:start position:0%
+of that thing that is eminently
+ 
+
+ align:start position:0%
+of that thing that is eminently
+Christian, right? They're the real deal.
+
+ align:start position:0%
+Christian, right? They're the real deal.
+ 
+
+ align:start position:0%
+Christian, right? They're the real deal.
+Also, I mean, I haven't read the books
+
+ align:start position:0%
+Also, I mean, I haven't read the books
+ 
+
+ align:start position:0%
+Also, I mean, I haven't read the books
+for a very long time. the but I don't
+
+ align:start position:0%
+for a very long time. the but I don't
+ 
+
+ align:start position:0%
+for a very long time. the but I don't
+remember that much religious stuff in
+
+ align:start position:0%
+remember that much religious stuff in
+ 
+
+ align:start position:0%
+remember that much religious stuff in
+the general like prominent like you know
+
+ align:start position:0%
+the general like prominent like you know
+ 
+
+ align:start position:0%
+the general like prominent like you know
+a lot of books nowadays when a lot I
+
+ align:start position:0%
+a lot of books nowadays when a lot I
+ 
+
+ align:start position:0%
+a lot of books nowadays when a lot I
+mean a lot of books nowadays when they
+
+ align:start position:0%
+mean a lot of books nowadays when they
+ 
+
+ align:start position:0%
+mean a lot of books nowadays when they
+write a fantasy thing they set up the
+
+ align:start position:0%
+write a fantasy thing they set up the
+ 
+
+ align:start position:0%
+write a fantasy thing they set up the
+whole world with you know here is one
+
+ align:start position:0%
+whole world with you know here is one
+ 
+
+ align:start position:0%
+whole world with you know here is one
+land here's another land here's another
+
+ align:start position:0%
+land here's another land here's another
+ 
+
+ align:start position:0%
+land here's another land here's another
+land here is the governments of these
+
+ align:start position:0%
+land here is the governments of these
+ 
+
+ align:start position:0%
+land here is the governments of these
+places which both he did and here's the
+
+ align:start position:0%
+places which both he did and here's the
+ 
+
+ align:start position:0%
+places which both he did and here's the
+basic religion of the group that was
+
+ align:start position:0%
+basic religion of the group that was
+ 
+
+ align:start position:0%
+basic religion of the group that was
+that the film really was was entirely
+
+ align:start position:0%
+that the film really was was entirely
+ 
+
+ align:start position:0%
+that the film really was was entirely
+you know it starts from creation
+
+ align:start position:0%
+you know it starts from creation
+ 
+
+ align:start position:0%
+you know it starts from creation
+basically by god and who creates these
+
+ align:start position:0%
+basically by god and who creates these
+ 
+
+ align:start position:0%
+basically by god and who creates these
+things who sing and create the world and
+
+ align:start position:0%
+things who sing and create the world and
+ 
+
+ align:start position:0%
+things who sing and create the world and
+which is you know an eminently you know
+
+ align:start position:0%
+which is you know an eminently you know
+ 
+
+ align:start position:0%
+which is you know an eminently you know
+where that comes from the singing as
+
+ align:start position:0%
+where that comes from the singing as
+ 
+
+ align:start position:0%
+where that comes from the singing as
+part of music of anor it sounds like
+
+ align:start position:0%
+part of music of anor it sounds like
+ 
+
+ align:start position:0%
+part of music of anor it sounds like
+something that was mentioned in here
+
+ align:start position:0%
+something that was mentioned in here
+ 
+
+ align:start position:0%
+something that was mentioned in here
+yeah it's also in in in in Botheus the
+
+ align:start position:0%
+yeah it's also in in in in Botheus the
+ 
+
+ align:start position:0%
+yeah it's also in in in in Botheus the
+his consolation of philosophy
+
+ align:start position:0%
+his consolation of philosophy
+ 
+
+ align:start position:0%
+his consolation of philosophy
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+basically all all philosophy comes to us
+
+ align:start position:0%
+basically all all philosophy comes to us
+ 
+
+ align:start position:0%
+basically all all philosophy comes to us
+through the I guess I don't I don't
+
+ align:start position:0%
+through the I guess I don't I don't
+ 
+
+ align:start position:0%
+through the I guess I don't I don't
+quite want to say angelic but the you
+
+ align:start position:0%
+quite want to say angelic but the you
+ 
+
+ align:start position:0%
+quite want to say angelic but the you
+know the celestial voices in in song.
+
+ align:start position:0%
+know the celestial voices in in song.
+ 
+
+ align:start position:0%
+know the celestial voices in in song.
+It's an interesting idea.
+
+ align:start position:0%
+It's an interesting idea.
+ 
+
+ align:start position:0%
+It's an interesting idea.
+Um and and and I think it's not an
+
+ align:start position:0%
+Um and and and I think it's not an
+ 
+
+ align:start position:0%
+Um and and and I think it's not an
+accident that Tolken is so fond
+
+ align:start position:0%
+accident that Tolken is so fond
+ 
+
+ align:start position:0%
+accident that Tolken is so fond
+of the of lyric
+
+ align:start position:0%
+of the of lyric
+ 
+
+ align:start position:0%
+of the of lyric
+poetry, right? I mean, the book doesn't
+
+ align:start position:0%
+poetry, right? I mean, the book doesn't
+ 
+
+ align:start position:0%
+poetry, right? I mean, the book doesn't
+actually sing, but it practically does,
+
+ align:start position:0%
+actually sing, but it practically does,
+ 
+
+ align:start position:0%
+actually sing, but it practically does,
+right? If you read it out loud, it would
+
+ align:start position:0%
+right? If you read it out loud, it would
+ 
+
+ align:start position:0%
+right? If you read it out loud, it would
+be good if you knew what meter to put
+
+ align:start position:0%
+be good if you knew what meter to put
+ 
+
+ align:start position:0%
+be good if you knew what meter to put
+with all of those poems, wouldn't it?
+
+ align:start position:0%
+with all of those poems, wouldn't it?
+ 
+
+ align:start position:0%
+with all of those poems, wouldn't it?
+when you read it out loud, you're never
+
+ align:start position:0%
+when you read it out loud, you're never
+ 
+
+ align:start position:0%
+when you read it out loud, you're never
+quite sure what to do with those because
+
+ align:start position:0%
+quite sure what to do with those because
+ 
+
+ align:start position:0%
+quite sure what to do with those because
+you have this feeling that you should
+
+ align:start position:0%
+you have this feeling that you should
+ 
+
+ align:start position:0%
+you have this feeling that you should
+have heard them before you just read
+
+ align:start position:0%
+have heard them before you just read
+ 
+
+ align:start position:0%
+have heard them before you just read
+them. And the I mean the thing that the
+
+ align:start position:0%
+them. And the I mean the thing that the
+ 
+
+ align:start position:0%
+them. And the I mean the thing that the
+Sylmerelion is the Kent Sylmerelion and
+
+ align:start position:0%
+Sylmerelion is the Kent Sylmerelion and
+ 
+
+ align:start position:0%
+Sylmerelion is the Kent Sylmerelion and
+it's supposed to be a whole long poem
+
+ align:start position:0%
+it's supposed to be a whole long poem
+ 
+
+ align:start position:0%
+it's supposed to be a whole long poem
+and he's paraphrasing it right in
+
+ align:start position:0%
+and he's paraphrasing it right in
+ 
+
+ align:start position:0%
+and he's paraphrasing it right in
+summary for us and that you know
+
+ align:start position:0%
+summary for us and that you know
+ 
+
+ align:start position:0%
+summary for us and that you know
+sometimes he has excerpts of the real
+
+ align:start position:0%
+sometimes he has excerpts of the real
+ 
+
+ align:start position:0%
+sometimes he has excerpts of the real
+thing and he'll have you know and even
+
+ align:start position:0%
+thing and he'll have you know and even
+ 
+
+ align:start position:0%
+thing and he'll have you know and even
+everything else you know all the other
+
+ align:start position:0%
+everything else you know all the other
+ 
+
+ align:start position:0%
+everything else you know all the other
+little stories he tells he's like well
+
+ align:start position:0%
+little stories he tells he's like well
+ 
+
+ align:start position:0%
+little stories he tells he's like well
+I'm just paraphrasing the the songs and
+
+ align:start position:0%
+I'm just paraphrasing the the songs and
+ 
+
+ align:start position:0%
+I'm just paraphrasing the the songs and
+the the ballads and Right. Right. Well,
+
+ align:start position:0%
+the the ballads and Right. Right. Well,
+ 
+
+ align:start position:0%
+the the ballads and Right. Right. Well,
+I mean the the the line of confusion for
+
+ align:start position:0%
+I mean the the the line of confusion for
+ 
+
+ align:start position:0%
+I mean the the the line of confusion for
+him
+
+ align:start position:0%
+him
+ 
+
+ align:start position:0%
+him
+between storytelling that is writing
+
+ align:start position:0%
+between storytelling that is writing
+ 
+
+ align:start position:0%
+between storytelling that is writing
+fiction and chronicle writing that is
+
+ align:start position:0%
+fiction and chronicle writing that is
+ 
+
+ align:start position:0%
+fiction and chronicle writing that is
+being a historian
+
+ align:start position:0%
+being a historian
+ 
+
+ align:start position:0%
+being a historian
+um is very is very fine. And and one of
+
+ align:start position:0%
+um is very is very fine. And and one of
+ 
+
+ align:start position:0%
+um is very is very fine. And and one of
+the ways you know that is because at the
+
+ align:start position:0%
+the ways you know that is because at the
+ 
+
+ align:start position:0%
+the ways you know that is because at the
+end of at the end of the return of the
+
+ align:start position:0%
+end of at the end of the return of the
+ 
+
+ align:start position:0%
+end of at the end of the return of the
+king you get all those
+
+ align:start position:0%
+king you get all those
+ 
+
+ align:start position:0%
+king you get all those
+appendices right I mean how many works
+
+ align:start position:0%
+appendices right I mean how many works
+ 
+
+ align:start position:0%
+appendices right I mean how many works
+of fiction come with what six seven
+
+ align:start position:0%
+of fiction come with what six seven
+ 
+
+ align:start position:0%
+of fiction come with what six seven
+appendices and and some of the
+
+ align:start position:0%
+appendices and and some of the
+ 
+
+ align:start position:0%
+appendices and and some of the
+appendices are about language okay fine
+
+ align:start position:0%
+appendices are about language okay fine
+ 
+
+ align:start position:0%
+appendices are about language okay fine
+you know we don't all speak Elvish so we
+
+ align:start position:0%
+you know we don't all speak Elvish so we
+ 
+
+ align:start position:0%
+you know we don't all speak Elvish so we
+have to have that clarified for us but
+
+ align:start position:0%
+have to have that clarified for us but
+ 
+
+ align:start position:0%
+have to have that clarified for us but
+some of the appendices are exactly the
+
+ align:start position:0%
+some of the appendices are exactly the
+ 
+
+ align:start position:0%
+some of the appendices are exactly the
+kind kind of appendices a historian
+
+ align:start position:0%
+kind kind of appendices a historian
+ 
+
+ align:start position:0%
+kind kind of appendices a historian
+would write. Now, it turns out you
+
+ align:start position:0%
+would write. Now, it turns out you
+ 
+
+ align:start position:0%
+would write. Now, it turns out you
+actually need to know this prequel. You
+
+ align:start position:0%
+actually need to know this prequel. You
+ 
+
+ align:start position:0%
+actually need to know this prequel. You
+need to know this tale. You need to know
+
+ align:start position:0%
+need to know this tale. You need to know
+ 
+
+ align:start position:0%
+need to know this tale. You need to know
+how this happened. You need to know
+
+ align:start position:0%
+how this happened. You need to know
+ 
+
+ align:start position:0%
+how this happened. You need to know
+where these people came from, right?
+
+ align:start position:0%
+where these people came from, right?
+ 
+
+ align:start position:0%
+where these people came from, right?
+It's completely like a historical
+
+ align:start position:0%
+It's completely like a historical
+ 
+
+ align:start position:0%
+It's completely like a historical
+text, you know, right down to the
+
+ align:start position:0%
+text, you know, right down to the
+ 
+
+ align:start position:0%
+text, you know, right down to the
+footnotes and the appendices.
+
+ align:start position:0%
+footnotes and the appendices.
+ 
+
+ align:start position:0%
+footnotes and the appendices.
+Um, why, you know, if you're really
+
+ align:start position:0%
+Um, why, you know, if you're really
+ 
+
+ align:start position:0%
+Um, why, you know, if you're really
+writing
+
+ align:start position:0%
+writing
+ 
+
+ align:start position:0%
+writing
+fiction, why not just get that into the
+
+ align:start position:0%
+fiction, why not just get that into the
+ 
+
+ align:start position:0%
+fiction, why not just get that into the
+story? After all, you
+
+ align:start position:0%
+story? After all, you
+ 
+
+ align:start position:0%
+story? After all, you
+could, but it makes it makes it more
+
+ align:start position:0%
+could, but it makes it makes it more
+ 
+
+ align:start position:0%
+could, but it makes it makes it more
+more readable. Just like a historian
+
+ align:start position:0%
+more readable. Just like a historian
+ 
+
+ align:start position:0%
+more readable. Just like a historian
+who's, you know, trying to write
+
+ align:start position:0%
+who's, you know, trying to write
+ 
+
+ align:start position:0%
+who's, you know, trying to write
+something and make it make his his
+
+ align:start position:0%
+something and make it make his his
+ 
+
+ align:start position:0%
+something and make it make his his
+treatis readable rather than dry, you
+
+ align:start position:0%
+treatis readable rather than dry, you
+ 
+
+ align:start position:0%
+treatis readable rather than dry, you
+know, push push a lot of the stuff into
+
+ align:start position:0%
+know, push push a lot of the stuff into
+ 
+
+ align:start position:0%
+know, push push a lot of the stuff into
+the appendix. Okay. Well, maybe the
+
+ align:start position:0%
+the appendix. Okay. Well, maybe the
+ 
+
+ align:start position:0%
+the appendix. Okay. Well, maybe the
+grammar, right? The Elvish grammar is
+
+ align:start position:0%
+grammar, right? The Elvish grammar is
+ 
+
+ align:start position:0%
+grammar, right? The Elvish grammar is
+dry, but some of the story material
+
+ align:start position:0%
+dry, but some of the story material
+ 
+
+ align:start position:0%
+dry, but some of the story material
+there is good. Some of the story
+
+ align:start position:0%
+there is good. Some of the story
+ 
+
+ align:start position:0%
+there is good. Some of the story
+material there ended up in the movies
+
+ align:start position:0%
+material there ended up in the movies
+ 
+
+ align:start position:0%
+material there ended up in the movies
+after all,
+
+ align:start position:0%
+after all,
+ 
+
+ align:start position:0%
+after all,
+right? Get those chips going. Yeah. Go
+
+ align:start position:0%
+right? Get those chips going. Yeah. Go
+ 
+
+ align:start position:0%
+right? Get those chips going. Yeah. Go
+ahead, Amory. Well, I think that's
+
+ align:start position:0%
+ahead, Amory. Well, I think that's
+ 
+
+ align:start position:0%
+ahead, Amory. Well, I think that's
+exactly the point. Is he writing a story
+
+ align:start position:0%
+exactly the point. Is he writing a story
+ 
+
+ align:start position:0%
+exactly the point. Is he writing a story
+or is he writing history? And I think I
+
+ align:start position:0%
+or is he writing history? And I think I
+ 
+
+ align:start position:0%
+or is he writing history? And I think I
+mean essentially he's writing the
+
+ align:start position:0%
+mean essentially he's writing the
+ 
+
+ align:start position:0%
+mean essentially he's writing the
+history of of this tale, right, as it
+
+ align:start position:0%
+history of of this tale, right, as it
+ 
+
+ align:start position:0%
+history of of this tale, right, as it
+occurred to him in his mind. So I think
+
+ align:start position:0%
+occurred to him in his mind. So I think
+ 
+
+ align:start position:0%
+occurred to him in his mind. So I think
+it I think it's really hard to make this
+
+ align:start position:0%
+it I think it's really hard to make this
+ 
+
+ align:start position:0%
+it I think it's really hard to make this
+distinction. Obviously it's not real,
+
+ align:start position:0%
+distinction. Obviously it's not real,
+ 
+
+ align:start position:0%
+distinction. Obviously it's not real,
+right? So it's not medieval history that
+
+ align:start position:0%
+right? So it's not medieval history that
+ 
+
+ align:start position:0%
+right? So it's not medieval history that
+he's writing,
+
+ align:start position:0%
+he's writing,
+ 
+
+ align:start position:0%
+he's writing,
+but I think it's more it's more
+
+ align:start position:0%
+but I think it's more it's more
+ 
+
+ align:start position:0%
+but I think it's more it's more
+scholarly than just a work of fiction,
+
+ align:start position:0%
+scholarly than just a work of fiction,
+ 
+
+ align:start position:0%
+scholarly than just a work of fiction,
+you know? I don't know if you can and
+
+ align:start position:0%
+you know? I don't know if you can and
+ 
+
+ align:start position:0%
+you know? I don't know if you can and
+from that point of view, I think it
+
+ align:start position:0%
+from that point of view, I think it
+ 
+
+ align:start position:0%
+from that point of view, I think it
+makes sense to be writing it in this
+
+ align:start position:0%
+makes sense to be writing it in this
+ 
+
+ align:start position:0%
+makes sense to be writing it in this
+kind of
+
+ align:start position:0%
+kind of
+ 
+
+ align:start position:0%
+kind of
+quasi scholarly manner. I had a
+
+ align:start position:0%
+quasi scholarly manner. I had a
+ 
+
+ align:start position:0%
+quasi scholarly manner. I had a
+question. Did he publish The Hobbit
+
+ align:start position:0%
+question. Did he publish The Hobbit
+ 
+
+ align:start position:0%
+question. Did he publish The Hobbit
+before he wrote the Lord?
+
+ align:start position:0%
+before he wrote the Lord?
+ 
+
+ align:start position:0%
+before he wrote the Lord?
+Yeah. Long before um much to the
+
+ align:start position:0%
+Yeah. Long before um much to the
+ 
+
+ align:start position:0%
+Yeah. Long before um much to the
+ridicule of his colleagues as you can
+
+ align:start position:0%
+ridicule of his colleagues as you can
+ 
+
+ align:start position:0%
+ridicule of his colleagues as you can
+imagine. Well, I don't know maybe you
+
+ align:start position:0%
+imagine. Well, I don't know maybe you
+ 
+
+ align:start position:0%
+imagine. Well, I don't know maybe you
+can't imagine. I mean sort of you know
+
+ align:start position:0%
+can't imagine. I mean sort of you know
+ 
+
+ align:start position:0%
+can't imagine. I mean sort of you know
+take your average faculty member at MIT
+
+ align:start position:0%
+take your average faculty member at MIT
+ 
+
+ align:start position:0%
+take your average faculty member at MIT
+and then add another sort of you know 50
+
+ align:start position:0%
+and then add another sort of you know 50
+ 
+
+ align:start position:0%
+and then add another sort of you know 50
+times factor of
+
+ align:start position:0%
+times factor of
+ 
+
+ align:start position:0%
+times factor of
+stuffiness right and and then you've got
+
+ align:start position:0%
+stuffiness right and and then you've got
+ 
+
+ align:start position:0%
+stuffiness right and and then you've got
+you know your Oxford Dawn in the 20s30s
+
+ align:start position:0%
+you know your Oxford Dawn in the 20s30s
+ 
+
+ align:start position:0%
+you know your Oxford Dawn in the 20s30s
+or 40s. Um, I mean, his colleagues
+
+ align:start position:0%
+or 40s. Um, I mean, his colleagues
+ 
+
+ align:start position:0%
+or 40s. Um, I mean, his colleagues
+weren't just kind of beused. They were
+
+ align:start position:0%
+weren't just kind of beused. They were
+ 
+
+ align:start position:0%
+weren't just kind of beused. They were
+they were outraged. I mean, it was
+
+ align:start position:0%
+they were outraged. I mean, it was
+ 
+
+ align:start position:0%
+they were outraged. I mean, it was
+deeply embarrassing. It was like having
+
+ align:start position:0%
+deeply embarrassing. It was like having
+ 
+
+ align:start position:0%
+deeply embarrassing. It was like having
+a nutcase um on your
+
+ align:start position:0%
+a nutcase um on your
+ 
+
+ align:start position:0%
+a nutcase um on your
+faculty because I mean, and after all,
+
+ align:start position:0%
+faculty because I mean, and after all,
+ 
+
+ align:start position:0%
+faculty because I mean, and after all,
+The Hobbit is a very has a very
+
+ align:start position:0%
+The Hobbit is a very has a very
+ 
+
+ align:start position:0%
+The Hobbit is a very has a very
+different cast to it, right, than The
+
+ align:start position:0%
+different cast to it, right, than The
+ 
+
+ align:start position:0%
+different cast to it, right, than The
+Lord of the Rings, even though even
+
+ align:start position:0%
+Lord of the Rings, even though even
+ 
+
+ align:start position:0%
+Lord of the Rings, even though even
+though in some sense it's all one story,
+
+ align:start position:0%
+though in some sense it's all one story,
+ 
+
+ align:start position:0%
+though in some sense it's all one story,
+right? And often children who are old
+
+ align:start position:0%
+right? And often children who are old
+ 
+
+ align:start position:0%
+right? And often children who are old
+enough to read The Hobbit will discover
+
+ align:start position:0%
+enough to read The Hobbit will discover
+ 
+
+ align:start position:0%
+enough to read The Hobbit will discover
+much to their disappointment that
+
+ align:start position:0%
+much to their disappointment that
+ 
+
+ align:start position:0%
+much to their disappointment that
+they're not the least bit interested in
+
+ align:start position:0%
+they're not the least bit interested in
+ 
+
+ align:start position:0%
+they're not the least bit interested in
+The Lord of the Rings because you've got
+
+ align:start position:0%
+The Lord of the Rings because you've got
+ 
+
+ align:start position:0%
+The Lord of the Rings because you've got
+to get through that first what 60 pages
+
+ align:start position:0%
+to get through that first what 60 pages
+ 
+
+ align:start position:0%
+to get through that first what 60 pages
+before anything happens at all. Right.
+
+ align:start position:0%
+before anything happens at all. Right.
+ 
+
+ align:start position:0%
+before anything happens at all. Right.
+And that's not how you write a book for
+
+ align:start position:0%
+And that's not how you write a book for
+ 
+
+ align:start position:0%
+And that's not how you write a book for
+children. For sure. Yeah. Annie. No.
+
+ align:start position:0%
+children. For sure. Yeah. Annie. No.
+ 
+
+ align:start position:0%
+children. For sure. Yeah. Annie. No.
+Okay. I never got I started reading Lord
+
+ align:start position:0%
+Okay. I never got I started reading Lord
+ 
+
+ align:start position:0%
+Okay. I never got I started reading Lord
+of the Rings and I never got through it.
+
+ align:start position:0%
+of the Rings and I never got through it.
+ 
+
+ align:start position:0%
+of the Rings and I never got through it.
+I loved The Hobbit but couldn't deal
+
+ align:start position:0%
+I loved The Hobbit but couldn't deal
+ 
+
+ align:start position:0%
+I loved The Hobbit but couldn't deal
+with I just couldn't deal with the style
+
+ align:start position:0%
+with I just couldn't deal with the style
+ 
+
+ align:start position:0%
+with I just couldn't deal with the style
+of writing. Is that still true? Yeah.
+
+ align:start position:0%
+of writing. Is that still true? Yeah.
+ 
+
+ align:start position:0%
+of writing. Is that still true? Yeah.
+still. Uhhuh. It's what I love about
+
+ align:start position:0%
+still. Uhhuh. It's what I love about
+ 
+
+ align:start position:0%
+still. Uhhuh. It's what I love about
+also CS Lewis is just the way he writes.
+
+ align:start position:0%
+also CS Lewis is just the way he writes.
+ 
+
+ align:start position:0%
+also CS Lewis is just the way he writes.
+It just seems very marriageable. It's it
+
+ align:start position:0%
+It just seems very marriageable. It's it
+ 
+
+ align:start position:0%
+It just seems very marriageable. It's it
+seems very flowing while while J.R.
+
+ align:start position:0%
+seems very flowing while while J.R.
+ 
+
+ align:start position:0%
+seems very flowing while while J.R.
+Token sort of write like it to me it's
+
+ align:start position:0%
+Token sort of write like it to me it's
+ 
+
+ align:start position:0%
+Token sort of write like it to me it's
+even more like a history stuff because
+
+ align:start position:0%
+even more like a history stuff because
+ 
+
+ align:start position:0%
+even more like a history stuff because
+and in fact what he said in
+
+ align:start position:0%
+and in fact what he said in
+ 
+
+ align:start position:0%
+and in fact what he said in
+um how he wrote it, you know, pretending
+
+ align:start position:0%
+um how he wrote it, you know, pretending
+ 
+
+ align:start position:0%
+um how he wrote it, you know, pretending
+that this was something he was
+
+ align:start position:0%
+that this was something he was
+ 
+
+ align:start position:0%
+that this was something he was
+translating. I can see that a lot
+
+ align:start position:0%
+translating. I can see that a lot
+ 
+
+ align:start position:0%
+translating. I can see that a lot
+because therefore it sounds to me like
+
+ align:start position:0%
+because therefore it sounds to me like
+ 
+
+ align:start position:0%
+because therefore it sounds to me like
+he's trying to write a textbook almost.
+
+ align:start position:0%
+he's trying to write a textbook almost.
+ 
+
+ align:start position:0%
+he's trying to write a textbook almost.
+So it's very drag and very textbook like
+
+ align:start position:0%
+So it's very drag and very textbook like
+ 
+
+ align:start position:0%
+So it's very drag and very textbook like
+and more like writing a history than
+
+ align:start position:0%
+and more like writing a history than
+ 
+
+ align:start position:0%
+and more like writing a history than
+writing a story. Yeah. Go ahead, Ian.
+
+ align:start position:0%
+writing a story. Yeah. Go ahead, Ian.
+ 
+
+ align:start position:0%
+writing a story. Yeah. Go ahead, Ian.
+And I found I think just just as CS
+
+ align:start position:0%
+And I found I think just just as CS
+ 
+
+ align:start position:0%
+And I found I think just just as CS
+Lewis is saying and and kind of actually
+
+ align:start position:0%
+Lewis is saying and and kind of actually
+ 
+
+ align:start position:0%
+Lewis is saying and and kind of actually
+what I found about the discarded image
+
+ align:start position:0%
+what I found about the discarded image
+ 
+
+ align:start position:0%
+what I found about the discarded image
+as well is that he's it's interesting
+
+ align:start position:0%
+as well is that he's it's interesting
+ 
+
+ align:start position:0%
+as well is that he's it's interesting
+for its own merit and if it isn't then
+
+ align:start position:0%
+for its own merit and if it isn't then
+ 
+
+ align:start position:0%
+for its own merit and if it isn't then
+you're probably in trouble. And I mean I
+
+ align:start position:0%
+you're probably in trouble. And I mean I
+ 
+
+ align:start position:0%
+you're probably in trouble. And I mean I
+personally found it very interesting
+
+ align:start position:0%
+personally found it very interesting
+ 
+
+ align:start position:0%
+personally found it very interesting
+because of what it's talking about. The
+
+ align:start position:0%
+because of what it's talking about. The
+ 
+
+ align:start position:0%
+because of what it's talking about. The
+Lord of the Rings. The Lord of the
+
+ align:start position:0%
+Lord of the Rings. The Lord of the
+ 
+
+ align:start position:0%
+Lord of the Rings. The Lord of the
+Rings. just make sure as well as also a
+
+ align:start position:0%
+Rings. just make sure as well as also a
+ 
+
+ align:start position:0%
+Rings. just make sure as well as also a
+lot of discarded image I felt the same
+
+ align:start position:0%
+lot of discarded image I felt the same
+ 
+
+ align:start position:0%
+lot of discarded image I felt the same
+way he wrote in the like the very he
+
+ align:start position:0%
+way he wrote in the like the very he
+ 
+
+ align:start position:0%
+way he wrote in the like the very he
+didn't really you know he spent a lot of
+
+ align:start position:0%
+didn't really you know he spent a lot of
+ 
+
+ align:start position:0%
+didn't really you know he spent a lot of
+time talking about the examples and not
+
+ align:start position:0%
+time talking about the examples and not
+ 
+
+ align:start position:0%
+time talking about the examples and not
+you know and and there was analysis but
+
+ align:start position:0%
+you know and and there was analysis but
+ 
+
+ align:start position:0%
+you know and and there was analysis but
+it wasn't you know it was all it was all
+
+ align:start position:0%
+it wasn't you know it was all it was all
+ 
+
+ align:start position:0%
+it wasn't you know it was all it was all
+very entwined in the examples and if you
+
+ align:start position:0%
+very entwined in the examples and if you
+ 
+
+ align:start position:0%
+very entwined in the examples and if you
+if you didn't find and I was talking to
+
+ align:start position:0%
+if you didn't find and I was talking to
+ 
+
+ align:start position:0%
+if you didn't find and I was talking to
+Greg about this who didn't necessarily
+
+ align:start position:0%
+Greg about this who didn't necessarily
+ 
+
+ align:start position:0%
+Greg about this who didn't necessarily
+find some of the examples as compelling
+
+ align:start position:0%
+find some of the examples as compelling
+ 
+
+ align:start position:0%
+find some of the examples as compelling
+or as interesting as I did just because
+
+ align:start position:0%
+or as interesting as I did just because
+ 
+
+ align:start position:0%
+or as interesting as I did just because
+I'm interested in this kind of stuff and
+
+ align:start position:0%
+I'm interested in this kind of stuff and
+ 
+
+ align:start position:0%
+I'm interested in this kind of stuff and
+just you know it wasn't as interesting
+
+ align:start position:0%
+just you know it wasn't as interesting
+ 
+
+ align:start position:0%
+just you know it wasn't as interesting
+just like he's saying the medieval
+
+ align:start position:0%
+just like he's saying the medieval
+ 
+
+ align:start position:0%
+just like he's saying the medieval
+authors how they
+
+ align:start position:0%
+authors how they
+ 
+
+ align:start position:0%
+authors how they
+wrote I mean one one thing just to make
+
+ align:start position:0%
+wrote I mean one one thing just to make
+ 
+
+ align:start position:0%
+wrote I mean one one thing just to make
+a note of there's nothing per se that we
+
+ align:start position:0%
+a note of there's nothing per se that we
+ 
+
+ align:start position:0%
+a note of there's nothing per se that we
+can do about it but we don't
+
+ align:start position:0%
+can do about it but we don't
+ 
+
+ align:start position:0%
+can do about it but we don't
+share the vast wealth of sort of
+
+ align:start position:0%
+share the vast wealth of sort of
+ 
+
+ align:start position:0%
+share the vast wealth of sort of
+immediately recallable references that
+
+ align:start position:0%
+immediately recallable references that
+ 
+
+ align:start position:0%
+immediately recallable references that
+these guys are carrying around in their
+
+ align:start position:0%
+these guys are carrying around in their
+ 
+
+ align:start position:0%
+these guys are carrying around in their
+heads. I mean, these two individuals and
+
+ align:start position:0%
+heads. I mean, these two individuals and
+ 
+
+ align:start position:0%
+heads. I mean, these two individuals and
+and others of their of their time in
+
+ align:start position:0%
+and others of their of their time in
+ 
+
+ align:start position:0%
+and others of their of their time in
+particular, but but these two especially
+
+ align:start position:0%
+particular, but but these two especially
+ 
+
+ align:start position:0%
+particular, but but these two especially
+are living in some other
+
+ align:start position:0%
+are living in some other
+ 
+
+ align:start position:0%
+are living in some other
+place, right? I mean, they they just
+
+ align:start position:0%
+place, right? I mean, they they just
+ 
+
+ align:start position:0%
+place, right? I mean, they they just
+don't inhabit their everyday world all
+
+ align:start position:0%
+don't inhabit their everyday world all
+ 
+
+ align:start position:0%
+don't inhabit their everyday world all
+that much.
+
+ align:start position:0%
+that much.
+ 
+
+ align:start position:0%
+that much.
+uh for for Lewis it's clear that you
+
+ align:start position:0%
+uh for for Lewis it's clear that you
+ 
+
+ align:start position:0%
+uh for for Lewis it's clear that you
+know Dante is much more real than you
+
+ align:start position:0%
+know Dante is much more real than you
+ 
+
+ align:start position:0%
+know Dante is much more real than you
+know than the current government in
+
+ align:start position:0%
+know than the current government in
+ 
+
+ align:start position:0%
+know than the current government in
+Britain right at the time you know that
+
+ align:start position:0%
+Britain right at the time you know that
+ 
+
+ align:start position:0%
+Britain right at the time you know that
+that that's that's the set of references
+
+ align:start position:0%
+that that's that's the set of references
+ 
+
+ align:start position:0%
+that that's that's the set of references
+that inform his entire
+
+ align:start position:0%
+that inform his entire
+ 
+
+ align:start position:0%
+that inform his entire
+life and there and there are a set of
+
+ align:start position:0%
+life and there and there are a set of
+ 
+
+ align:start position:0%
+life and there and there are a set of
+references that for the most part we
+
+ align:start position:0%
+references that for the most part we
+ 
+
+ align:start position:0%
+references that for the most part we
+don't have anymore are um or if we do,
+
+ align:start position:0%
+don't have anymore are um or if we do,
+ 
+
+ align:start position:0%
+don't have anymore are um or if we do,
+we've just picked them up on the edges,
+
+ align:start position:0%
+we've just picked them up on the edges,
+ 
+
+ align:start position:0%
+we've just picked them up on the edges,
+right? We've read part of the Canterbury
+
+ align:start position:0%
+right? We've read part of the Canterbury
+ 
+
+ align:start position:0%
+right? We've read part of the Canterbury
+Tales, you know, in translation, right?
+
+ align:start position:0%
+Tales, you know, in translation, right?
+ 
+
+ align:start position:0%
+Tales, you know, in translation, right?
+We've read Dante, but in translation,
+
+ align:start position:0%
+We've read Dante, but in translation,
+ 
+
+ align:start position:0%
+We've read Dante, but in translation,
+we've read Beaowolf again, um in
+
+ align:start position:0%
+we've read Beaowolf again, um in
+ 
+
+ align:start position:0%
+we've read Beaowolf again, um in
+translation. And and maybe we haven't
+
+ align:start position:0%
+translation. And and maybe we haven't
+ 
+
+ align:start position:0%
+translation. And and maybe we haven't
+even read all of those. We've just read
+
+ align:start position:0%
+even read all of those. We've just read
+ 
+
+ align:start position:0%
+even read all of those. We've just read
+one, right? Or or a smattering of of
+
+ align:start position:0%
+one, right? Or or a smattering of of
+ 
+
+ align:start position:0%
+one, right? Or or a smattering of of
+one. And it's h it's hard to um to even
+
+ align:start position:0%
+one. And it's h it's hard to um to even
+ 
+
+ align:start position:0%
+one. And it's h it's hard to um to even
+put ourselves into their sort of
+
+ align:start position:0%
+put ourselves into their sort of
+ 
+
+ align:start position:0%
+put ourselves into their sort of
+creative mental space, right? Because
+
+ align:start position:0%
+creative mental space, right? Because
+ 
+
+ align:start position:0%
+creative mental space, right? Because
+the set of facts, the set of
+
+ align:start position:0%
+the set of facts, the set of
+ 
+
+ align:start position:0%
+the set of facts, the set of
+information, the set of ideas that we're
+
+ align:start position:0%
+information, the set of ideas that we're
+ 
+
+ align:start position:0%
+information, the set of ideas that we're
+carrying around are are not, you know,
+
+ align:start position:0%
+carrying around are are not, you know,
+ 
+
+ align:start position:0%
+carrying around are are not, you know,
+are not there set at all. But Annie, you
+
+ align:start position:0%
+are not there set at all. But Annie, you
+ 
+
+ align:start position:0%
+are not there set at all. But Annie, you
+were going to say something. Was it you?
+
+ align:start position:0%
+were going to say something. Was it you?
+ 
+
+ align:start position:0%
+were going to say something. Was it you?
+Was it Amarie? No. Okay. Let me change
+
+ align:start position:0%
+Was it Amarie? No. Okay. Let me change
+ 
+
+ align:start position:0%
+Was it Amarie? No. Okay. Let me change
+tax for a minute completely and I think
+
+ align:start position:0%
+tax for a minute completely and I think
+ 
+
+ align:start position:0%
+tax for a minute completely and I think
+we'll come we'll come back around to all
+
+ align:start position:0%
+we'll come we'll come back around to all
+ 
+
+ align:start position:0%
+we'll come we'll come back around to all
+of this. But let let me try another
+
+ align:start position:0%
+of this. But let let me try another
+ 
+
+ align:start position:0%
+of this. But let let me try another
+comparison with something we've already
+
+ align:start position:0%
+comparison with something we've already
+ 
+
+ align:start position:0%
+comparison with something we've already
+read. So
+
+ align:start position:0%
+read. So
+ 
+
+ align:start position:0%
+read. So
+Broadell, one of the things that we were
+
+ align:start position:0%
+Broadell, one of the things that we were
+ 
+
+ align:start position:0%
+Broadell, one of the things that we were
+thinking about with
+
+ align:start position:0%
+thinking about with
+ 
+
+ align:start position:0%
+thinking about with
+Broadell was the impact in his case of
+
+ align:start position:0%
+Broadell was the impact in his case of
+ 
+
+ align:start position:0%
+Broadell was the impact in his case of
+the German prisoner of war experience,
+
+ align:start position:0%
+the German prisoner of war experience,
+ 
+
+ align:start position:0%
+the German prisoner of war experience,
+right?
+
+ align:start position:0%
+right?
+ 
+
+ align:start position:0%
+right?
+And maybe not a rejection of all that
+
+ align:start position:0%
+And maybe not a rejection of all that
+ 
+
+ align:start position:0%
+And maybe not a rejection of all that
+was modern, but certainly a longing,
+
+ align:start position:0%
+was modern, but certainly a longing,
+ 
+
+ align:start position:0%
+was modern, but certainly a longing,
+right, for something that was not
+
+ align:start position:0%
+right, for something that was not
+ 
+
+ align:start position:0%
+right, for something that was not
+modern, in his case, early modern and a
+
+ align:start position:0%
+modern, in his case, early modern and a
+ 
+
+ align:start position:0%
+modern, in his case, early modern and a
+place, right, a strong strong attachment
+
+ align:start position:0%
+place, right, a strong strong attachment
+ 
+
+ align:start position:0%
+place, right, a strong strong attachment
+to place, which in his case was
+
+ align:start position:0%
+to place, which in his case was
+ 
+
+ align:start position:0%
+to place, which in his case was
+Mediterranean
+
+ align:start position:0%
+Mediterranean
+ 
+
+ align:start position:0%
+Mediterranean
+France, to the point where we even
+
+ align:start position:0%
+France, to the point where we even
+ 
+
+ align:start position:0%
+France, to the point where we even
+thought that we might want to classify
+
+ align:start position:0%
+thought that we might want to classify
+ 
+
+ align:start position:0%
+thought that we might want to classify
+by that book in one particular sense,
+
+ align:start position:0%
+by that book in one particular sense,
+ 
+
+ align:start position:0%
+by that book in one particular sense,
+right? As a love letter to that place
+
+ align:start position:0%
+right? As a love letter to that place
+ 
+
+ align:start position:0%
+right? As a love letter to that place
+and that
+
+ align:start position:0%
+and that
+ 
+
+ align:start position:0%
+and that
+time, would we want to make similar
+
+ align:start position:0%
+time, would we want to make similar
+ 
+
+ align:start position:0%
+time, would we want to make similar
+arguments with say Middle Earth or I
+
+ align:start position:0%
+arguments with say Middle Earth or I
+ 
+
+ align:start position:0%
+arguments with say Middle Earth or I
+should say the Lord of the Rings?
+
+ align:start position:0%
+should say the Lord of the Rings?
+ 
+
+ align:start position:0%
+should say the Lord of the Rings?
+Go ahead, Miranda. Especially from the
+
+ align:start position:0%
+Go ahead, Miranda. Especially from the
+ 
+
+ align:start position:0%
+Go ahead, Miranda. Especially from the
+article where they sounded a lot like
+
+ align:start position:0%
+article where they sounded a lot like
+ 
+
+ align:start position:0%
+article where they sounded a lot like
+him in sort of the well what they you
+
+ align:start position:0%
+him in sort of the well what they you
+ 
+
+ align:start position:0%
+him in sort of the well what they you
+know calling them sort of sort of
+
+ align:start position:0%
+know calling them sort of sort of
+ 
+
+ align:start position:0%
+know calling them sort of sort of
+dinosaurs for what they really wanted
+
+ align:start position:0%
+dinosaurs for what they really wanted
+ 
+
+ align:start position:0%
+dinosaurs for what they really wanted
+was to keep these old stories and old
+
+ align:start position:0%
+was to keep these old stories and old
+ 
+
+ align:start position:0%
+was to keep these old stories and old
+feelings and yet because they were
+
+ align:start position:0%
+feelings and yet because they were
+ 
+
+ align:start position:0%
+feelings and yet because they were
+trying to keep these thing alive.
+
+ align:start position:0%
+trying to keep these thing alive.
+ 
+
+ align:start position:0%
+trying to keep these thing alive.
+They're actually pioneers in a bunch of
+
+ align:start position:0%
+They're actually pioneers in a bunch of
+ 
+
+ align:start position:0%
+They're actually pioneers in a bunch of
+different ways like you know they're one
+
+ align:start position:0%
+different ways like you know they're one
+ 
+
+ align:start position:0%
+different ways like you know they're one
+like he says you know the first person
+
+ align:start position:0%
+like he says you know the first person
+ 
+
+ align:start position:0%
+like he says you know the first person
+to basically say well it's okay to talk
+
+ align:start position:0%
+to basically say well it's okay to talk
+ 
+
+ align:start position:0%
+to basically say well it's okay to talk
+about love as a historical thing and by
+
+ align:start position:0%
+about love as a historical thing and by
+ 
+
+ align:start position:0%
+about love as a historical thing and by
+for CS Lewis and some of the fantasy
+
+ align:start position:0%
+for CS Lewis and some of the fantasy
+ 
+
+ align:start position:0%
+for CS Lewis and some of the fantasy
+stuff it's okay to write you know write
+
+ align:start position:0%
+stuff it's okay to write you know write
+ 
+
+ align:start position:0%
+stuff it's okay to write you know write
+fantasies that for adult for adults and
+
+ align:start position:0%
+fantasies that for adult for adults and
+ 
+
+ align:start position:0%
+fantasies that for adult for adults and
+it's sort of I think the same thing
+
+ align:start position:0%
+it's sort of I think the same thing
+ 
+
+ align:start position:0%
+it's sort of I think the same thing
+happened with Rodella that you know
+
+ align:start position:0%
+happened with Rodella that you know
+ 
+
+ align:start position:0%
+happened with Rodella that you know
+because he sort of wanted to keep a hold
+
+ align:start position:0%
+because he sort of wanted to keep a hold
+ 
+
+ align:start position:0%
+because he sort of wanted to keep a hold
+of this old thing this oldfashioned
+
+ align:start position:0%
+of this old thing this oldfashioned
+ 
+
+ align:start position:0%
+of this old thing this oldfashioned
+feeling yet he was also this pioneer of
+
+ align:start position:0%
+feeling yet he was also this pioneer of
+ 
+
+ align:start position:0%
+feeling yet he was also this pioneer of
+what of the way to do such a thing,
+
+ align:start position:0%
+what of the way to do such a thing,
+ 
+
+ align:start position:0%
+what of the way to do such a thing,
+right? I mean, after all, um, the
+
+ align:start position:0%
+right? I mean, after all, um, the
+ 
+
+ align:start position:0%
+right? I mean, after all, um, the
+Mediterranean in the age of Philip II is
+
+ align:start position:0%
+Mediterranean in the age of Philip II is
+ 
+
+ align:start position:0%
+Mediterranean in the age of Philip II is
+clearly a history book,
+
+ align:start position:0%
+clearly a history book,
+ 
+
+ align:start position:0%
+clearly a history book,
+right? And The Lord of the Rings is
+
+ align:start position:0%
+right? And The Lord of the Rings is
+ 
+
+ align:start position:0%
+right? And The Lord of the Rings is
+clearly in the bookstore under
+
+ align:start position:0%
+clearly in the bookstore under
+ 
+
+ align:start position:0%
+clearly in the bookstore under
+fiction and there's no movie, right, for
+
+ align:start position:0%
+fiction and there's no movie, right, for
+ 
+
+ align:start position:0%
+fiction and there's no movie, right, for
+uh the Mediterranean in the age of
+
+ align:start position:0%
+uh the Mediterranean in the age of
+ 
+
+ align:start position:0%
+uh the Mediterranean in the age of
+Philip II. Can you imagine the movie?
+
+ align:start position:0%
+Philip II. Can you imagine the movie?
+ 
+
+ align:start position:0%
+Philip II. Can you imagine the movie?
+And it would most certainly not be
+
+ align:start position:0%
+And it would most certainly not be
+ 
+
+ align:start position:0%
+And it would most certainly not be
+filmed in New Zealand, right? Not a
+
+ align:start position:0%
+filmed in New Zealand, right? Not a
+ 
+
+ align:start position:0%
+filmed in New Zealand, right? Not a
+chance. Yeah. Go ahead, Peter. I mean,
+
+ align:start position:0%
+chance. Yeah. Go ahead, Peter. I mean,
+ 
+
+ align:start position:0%
+chance. Yeah. Go ahead, Peter. I mean,
+we made the comparison with Brell that
+
+ align:start position:0%
+we made the comparison with Brell that
+ 
+
+ align:start position:0%
+we made the comparison with Brell that
+he wasn't really living, you know, in
+
+ align:start position:0%
+he wasn't really living, you know, in
+ 
+
+ align:start position:0%
+he wasn't really living, you know, in
+his time frame. I mean, both Lewis and
+
+ align:start position:0%
+his time frame. I mean, both Lewis and
+ 
+
+ align:start position:0%
+his time frame. I mean, both Lewis and
+Tolken were World War I veterans, right?
+
+ align:start position:0%
+Tolken were World War I veterans, right?
+ 
+
+ align:start position:0%
+Tolken were World War I veterans, right?
+That's what I seem to remember. that I
+
+ align:start position:0%
+That's what I seem to remember. that I
+ 
+
+ align:start position:0%
+That's what I seem to remember. that I
+mean that's the only compar I mean I
+
+ align:start position:0%
+mean that's the only compar I mean I
+ 
+
+ align:start position:0%
+mean that's the only compar I mean I
+can't really speak from experience of
+
+ align:start position:0%
+can't really speak from experience of
+ 
+
+ align:start position:0%
+can't really speak from experience of
+reading the books by Louis and Tolken
+
+ align:start position:0%
+reading the books by Louis and Tolken
+ 
+
+ align:start position:0%
+reading the books by Louis and Tolken
+but it seems to me that the comparison
+
+ align:start position:0%
+but it seems to me that the comparison
+ 
+
+ align:start position:0%
+but it seems to me that the comparison
+between Bradell and Louis and Tolken
+
+ align:start position:0%
+between Bradell and Louis and Tolken
+ 
+
+ align:start position:0%
+between Bradell and Louis and Tolken
+would be that their experiences in war
+
+ align:start position:0%
+would be that their experiences in war
+ 
+
+ align:start position:0%
+would be that their experiences in war
+kind of make make them less willing to
+
+ align:start position:0%
+kind of make make them less willing to
+ 
+
+ align:start position:0%
+kind of make make them less willing to
+want to live in a contemporary their
+
+ align:start position:0%
+want to live in a contemporary their
+ 
+
+ align:start position:0%
+want to live in a contemporary their
+contemporary time period and they're
+
+ align:start position:0%
+contemporary time period and they're
+ 
+
+ align:start position:0%
+contemporary time period and they're
+much more comfortable living somewhere
+
+ align:start position:0%
+much more comfortable living somewhere
+ 
+
+ align:start position:0%
+much more comfortable living somewhere
+else where um you know they can control
+
+ align:start position:0%
+else where um you know they can control
+ 
+
+ align:start position:0%
+else where um you know they can control
+what's going on although I mean this
+
+ align:start position:0%
+what's going on although I mean this
+ 
+
+ align:start position:0%
+what's going on although I mean this
+isn't quite as much the case with
+
+ align:start position:0%
+isn't quite as much the case with
+ 
+
+ align:start position:0%
+isn't quite as much the case with
+Broadell but clearly with both Lewis and
+
+ align:start position:0%
+Broadell but clearly with both Lewis and
+ 
+
+ align:start position:0%
+Broadell but clearly with both Lewis and
+Tolken the mental world they're living
+
+ align:start position:0%
+Tolken the mental world they're living
+ 
+
+ align:start position:0%
+Tolken the mental world they're living
+in. It's full of
+
+ align:start position:0%
+in. It's full of
+ 
+
+ align:start position:0%
+in. It's full of
+war, right? I mean, it's, you know,
+
+ align:start position:0%
+war, right? I mean, it's, you know,
+ 
+
+ align:start position:0%
+war, right? I mean, it's, you know,
+presumably the horrors of the 20th
+
+ align:start position:0%
+presumably the horrors of the 20th
+ 
+
+ align:start position:0%
+presumably the horrors of the 20th
+century don't shock them given the given
+
+ align:start position:0%
+century don't shock them given the given
+ 
+
+ align:start position:0%
+century don't shock them given the given
+the me the the violence of the mental
+
+ align:start position:0%
+the me the the violence of the mental
+ 
+
+ align:start position:0%
+the me the the violence of the mental
+world um that that that they're
+
+ align:start position:0%
+world um that that that they're
+ 
+
+ align:start position:0%
+world um that that that they're
+inhabiting. Go ahead, Amarie.
+
+ align:start position:0%
+inhabiting. Go ahead, Amarie.
+ 
+
+ align:start position:0%
+inhabiting. Go ahead, Amarie.
+I think if you look at Lord of the Rings
+
+ align:start position:0%
+I think if you look at Lord of the Rings
+ 
+
+ align:start position:0%
+I think if you look at Lord of the Rings
+especially, you can see a lot of I think
+
+ align:start position:0%
+especially, you can see a lot of I think
+ 
+
+ align:start position:0%
+especially, you can see a lot of I think
+World War I influences in it. I think
+
+ align:start position:0%
+World War I influences in it. I think
+ 
+
+ align:start position:0%
+World War I influences in it. I think
+the book makes
+
+ align:start position:0%
+the book makes
+ 
+
+ align:start position:0%
+the book makes
+a the reference to it and I think I've
+
+ align:start position:0%
+a the reference to it and I think I've
+ 
+
+ align:start position:0%
+a the reference to it and I think I've
+heard other people talking about it as
+
+ align:start position:0%
+heard other people talking about it as
+ 
+
+ align:start position:0%
+heard other people talking about it as
+well. Like if you take the dead marshes
+
+ align:start position:0%
+well. Like if you take the dead marshes
+ 
+
+ align:start position:0%
+well. Like if you take the dead marshes
+with people lying on their backs looking
+
+ align:start position:0%
+with people lying on their backs looking
+ 
+
+ align:start position:0%
+with people lying on their backs looking
+up. I mean that's how you died when you
+
+ align:start position:0%
+up. I mean that's how you died when you
+ 
+
+ align:start position:0%
+up. I mean that's how you died when you
+were in a trench. And that's I think
+
+ align:start position:0%
+were in a trench. And that's I think
+ 
+
+ align:start position:0%
+were in a trench. And that's I think
+that's you can find other very similar
+
+ align:start position:0%
+that's you can find other very similar
+ 
+
+ align:start position:0%
+that's you can find other very similar
+analogies. So in a way yes I think we
+
+ align:start position:0%
+analogies. So in a way yes I think we
+ 
+
+ align:start position:0%
+analogies. So in a way yes I think we
+have them escaping to this world where
+
+ align:start position:0%
+have them escaping to this world where
+ 
+
+ align:start position:0%
+have them escaping to this world where
+they're in control but still that world
+
+ align:start position:0%
+they're in control but still that world
+ 
+
+ align:start position:0%
+they're in control but still that world
+is dominated by memories that they can't
+
+ align:start position:0%
+is dominated by memories that they can't
+ 
+
+ align:start position:0%
+is dominated by memories that they can't
+leave behind even though they're
+
+ align:start position:0%
+leave behind even though they're
+ 
+
+ align:start position:0%
+leave behind even though they're
+escaping. So, I think it's it's an
+
+ align:start position:0%
+escaping. So, I think it's it's an
+ 
+
+ align:start position:0%
+escaping. So, I think it's it's an
+interesting what were you saying, Lana?
+
+ align:start position:0%
+interesting what were you saying, Lana?
+ 
+
+ align:start position:0%
+interesting what were you saying, Lana?
+I was thinking it's an escape thing, but
+
+ align:start position:0%
+I was thinking it's an escape thing, but
+ 
+
+ align:start position:0%
+I was thinking it's an escape thing, but
+and they're creating this other world
+
+ align:start position:0%
+and they're creating this other world
+ 
+
+ align:start position:0%
+and they're creating this other world
+and it would still be very heavily
+
+ align:start position:0%
+and it would still be very heavily
+ 
+
+ align:start position:0%
+and it would still be very heavily
+influenced by their war experiences, but
+
+ align:start position:0%
+influenced by their war experiences, but
+ 
+
+ align:start position:0%
+influenced by their war experiences, but
+another way if since they keep on
+
+ align:start position:0%
+another way if since they keep on
+ 
+
+ align:start position:0%
+another way if since they keep on
+creating a past,
+
+ align:start position:0%
+creating a past,
+ 
+
+ align:start position:0%
+creating a past,
+World War I was really, really shocking
+
+ align:start position:0%
+World War I was really, really shocking
+ 
+
+ align:start position:0%
+World War I was really, really shocking
+in general. I mean, it was horrible. But
+
+ align:start position:0%
+in general. I mean, it was horrible. But
+ 
+
+ align:start position:0%
+in general. I mean, it was horrible. But
+imagine if instead of the world that
+
+ align:start position:0%
+imagine if instead of the world that
+ 
+
+ align:start position:0%
+imagine if instead of the world that
+instead of if if in the world that we
+
+ align:start position:0%
+instead of if if in the world that we
+ 
+
+ align:start position:0%
+instead of if if in the world that we
+had been living there had been all these
+
+ align:start position:0%
+had been living there had been all these
+ 
+
+ align:start position:0%
+had been living there had been all these
+big huge horrible wars before World War
+
+ align:start position:0%
+big huge horrible wars before World War
+ 
+
+ align:start position:0%
+big huge horrible wars before World War
+I wouldn't have been as bad.
+
+ align:start position:0%
+I wouldn't have been as bad.
+ 
+
+ align:start position:0%
+I wouldn't have been as bad.
+But there have been many horrible wars.
+
+ align:start position:0%
+But there have been many horrible wars.
+ 
+
+ align:start position:0%
+But there have been many horrible wars.
+There have been many horrible wars. Why?
+
+ align:start position:0%
+There have been many horrible wars. Why?
+ 
+
+ align:start position:0%
+There have been many horrible wars. Why?
+I mean an interesting question that that
+
+ align:start position:0%
+I mean an interesting question that that
+ 
+
+ align:start position:0%
+I mean an interesting question that that
+historians of the 20th century are you
+
+ align:start position:0%
+historians of the 20th century are you
+ 
+
+ align:start position:0%
+historians of the 20th century are you
+know sort of endlessly deeply fascinated
+
+ align:start position:0%
+know sort of endlessly deeply fascinated
+ 
+
+ align:start position:0%
+know sort of endlessly deeply fascinated
+by right is why why does World War I
+
+ align:start position:0%
+by right is why why does World War I
+ 
+
+ align:start position:0%
+by right is why why does World War I
+have this incredible cultural
+
+ align:start position:0%
+have this incredible cultural
+ 
+
+ align:start position:0%
+have this incredible cultural
+impact right why why is I mean
+
+ align:start position:0%
+impact right why why is I mean
+ 
+
+ align:start position:0%
+impact right why why is I mean
+that historical experience which you
+
+ align:start position:0%
+that historical experience which you
+ 
+
+ align:start position:0%
+that historical experience which you
+know after all if we knew a lot about um
+
+ align:start position:0%
+know after all if we knew a lot about um
+ 
+
+ align:start position:0%
+know after all if we knew a lot about um
+the 30 years war right if you grew up in
+
+ align:start position:0%
+the 30 years war right if you grew up in
+ 
+
+ align:start position:0%
+the 30 years war right if you grew up in
+as a school child in Germany
+
+ align:start position:0%
+as a school child in Germany
+ 
+
+ align:start position:0%
+as a school child in Germany
+you would have been steeped in the
+
+ align:start position:0%
+you would have been steeped in the
+ 
+
+ align:start position:0%
+you would have been steeped in the
+simplicimous literature. You know,
+
+ align:start position:0%
+simplicimous literature. You know,
+ 
+
+ align:start position:0%
+simplicimous literature. You know,
+that's a pretty miserable, awful book.
+
+ align:start position:0%
+that's a pretty miserable, awful book.
+ 
+
+ align:start position:0%
+that's a pretty miserable, awful book.
+Um, and to read it in German is triply
+
+ align:start position:0%
+Um, and to read it in German is triply
+ 
+
+ align:start position:0%
+Um, and to read it in German is triply
+miserable and awful. Uh, so I mean,
+
+ align:start position:0%
+miserable and awful. Uh, so I mean,
+ 
+
+ align:start position:0%
+miserable and awful. Uh, so I mean,
+Europeans had narratives for themselves
+
+ align:start position:0%
+Europeans had narratives for themselves
+ 
+
+ align:start position:0%
+Europeans had narratives for themselves
+of of other horrific moments that that,
+
+ align:start position:0%
+of of other horrific moments that that,
+ 
+
+ align:start position:0%
+of of other horrific moments that that,
+you know, that upset, if you will, the
+
+ align:start position:0%
+you know, that upset, if you will, the
+ 
+
+ align:start position:0%
+you know, that upset, if you will, the
+very foundations of culture. And yet,
+
+ align:start position:0%
+very foundations of culture. And yet,
+ 
+
+ align:start position:0%
+very foundations of culture. And yet,
+and yet World War I has played out, at
+
+ align:start position:0%
+and yet World War I has played out, at
+ 
+
+ align:start position:0%
+and yet World War I has played out, at
+least amongst the historians and the
+
+ align:start position:0%
+least amongst the historians and the
+ 
+
+ align:start position:0%
+least amongst the historians and the
+literary types, right, as this deeply
+
+ align:start position:0%
+literary types, right, as this deeply
+ 
+
+ align:start position:0%
+literary types, right, as this deeply
+um unsettling
+
+ align:start position:0%
+um unsettling
+ 
+
+ align:start position:0%
+um unsettling
+experience and and I think we're, you
+
+ align:start position:0%
+experience and and I think we're, you
+ 
+
+ align:start position:0%
+experience and and I think we're, you
+know, we're seeing it played out in
+
+ align:start position:0%
+know, we're seeing it played out in
+ 
+
+ align:start position:0%
+know, we're seeing it played out in
+these middle of the century historians.
+
+ align:start position:0%
+these middle of the century historians.
+ 
+
+ align:start position:0%
+these middle of the century historians.
+Yeah. Go ahead, Miranda. I mean, I'd
+
+ align:start position:0%
+Yeah. Go ahead, Miranda. I mean, I'd
+ 
+
+ align:start position:0%
+Yeah. Go ahead, Miranda. I mean, I'd
+always learned that one of the major
+
+ align:start position:0%
+always learned that one of the major
+ 
+
+ align:start position:0%
+always learned that one of the major
+reasons why it was so dramatic was
+
+ align:start position:0%
+reasons why it was so dramatic was
+ 
+
+ align:start position:0%
+reasons why it was so dramatic was
+because they were basically trying to
+
+ align:start position:0%
+because they were basically trying to
+ 
+
+ align:start position:0%
+because they were basically trying to
+keep with the oldfashioned warfare
+
+ align:start position:0%
+keep with the oldfashioned warfare
+ 
+
+ align:start position:0%
+keep with the oldfashioned warfare
+where, you know, you run at people from
+
+ align:start position:0%
+where, you know, you run at people from
+ 
+
+ align:start position:0%
+where, you know, you run at people from
+across the, you know, the land. And but
+
+ align:start position:0%
+across the, you know, the land. And but
+ 
+
+ align:start position:0%
+across the, you know, the land. And but
+this is a point when we were starting to
+
+ align:start position:0%
+this is a point when we were starting to
+ 
+
+ align:start position:0%
+this is a point when we were starting to
+get into machine guns and such like
+
+ align:start position:0%
+get into machine guns and such like
+ 
+
+ align:start position:0%
+get into machine guns and such like
+that. And so it was it was just this
+
+ align:start position:0%
+that. And so it was it was just this
+ 
+
+ align:start position:0%
+that. And so it was it was just this
+sort of absolute slaughter that was just
+
+ align:start position:0%
+sort of absolute slaughter that was just
+ 
+
+ align:start position:0%
+sort of absolute slaughter that was just
+pointless was the problem. Like before
+
+ align:start position:0%
+pointless was the problem. Like before
+ 
+
+ align:start position:0%
+pointless was the problem. Like before
+then, you know, war sort of it wasn't,
+
+ align:start position:0%
+then, you know, war sort of it wasn't,
+ 
+
+ align:start position:0%
+then, you know, war sort of it wasn't,
+you know, didn't have that much point,
+
+ align:start position:0%
+you know, didn't have that much point,
+ 
+
+ align:start position:0%
+you know, didn't have that much point,
+but just wasn't this. Yeah.
+
+ align:start position:0%
+but just wasn't this. Yeah.
+ 
+
+ align:start position:0%
+but just wasn't this. Yeah.
+And it wasn't this, you know, I've moved
+
+ align:start position:0%
+And it wasn't this, you know, I've moved
+ 
+
+ align:start position:0%
+And it wasn't this, you know, I've moved
+two inches and then I've died. You know,
+
+ align:start position:0%
+two inches and then I've died. You know,
+ 
+
+ align:start position:0%
+two inches and then I've died. You know,
+you move usually, you know, at least 3,
+
+ align:start position:0%
+you move usually, you know, at least 3,
+ 
+
+ align:start position:0%
+you move usually, you know, at least 3,
+four feet.
+
+ align:start position:0%
+four feet.
+ 
+
+ align:start position:0%
+four feet.
+So, was and it didn't just a subtle
+
+ align:start position:0%
+So, was and it didn't just a subtle
+ 
+
+ align:start position:0%
+So, was and it didn't just a subtle
+distinction and it just it like killed
+
+ align:start position:0%
+distinction and it just it like killed
+ 
+
+ align:start position:0%
+distinction and it just it like killed
+off basically like an entire generation
+
+ align:start position:0%
+off basically like an entire generation
+ 
+
+ align:start position:0%
+off basically like an entire generation
+of people versus, you know, other wars
+
+ align:start position:0%
+of people versus, you know, other wars
+ 
+
+ align:start position:0%
+of people versus, you know, other wars
+where they kill off a lot and lot of
+
+ align:start position:0%
+where they kill off a lot and lot of
+ 
+
+ align:start position:0%
+where they kill off a lot and lot of
+people, but it wasn't one specific, you
+
+ align:start position:0%
+people, but it wasn't one specific, you
+ 
+
+ align:start position:0%
+people, but it wasn't one specific, you
+know, upand cominging generation. That
+
+ align:start position:0%
+know, upand cominging generation. That
+ 
+
+ align:start position:0%
+know, upand cominging generation. That
+may be the key piece. But go but go
+
+ align:start position:0%
+may be the key piece. But go but go
+ 
+
+ align:start position:0%
+may be the key piece. But go but go
+ahead, Nick. Um I was thinking about two
+
+ align:start position:0%
+ahead, Nick. Um I was thinking about two
+ 
+
+ align:start position:0%
+ahead, Nick. Um I was thinking about two
+things in um in Tolken that like reflect
+
+ align:start position:0%
+things in um in Tolken that like reflect
+ 
+
+ align:start position:0%
+things in um in Tolken that like reflect
+on World War I. Like the first one
+
+ align:start position:0%
+on World War I. Like the first one
+ 
+
+ align:start position:0%
+on World War I. Like the first one
+that's was actually done in the movie
+
+ align:start position:0%
+that's was actually done in the movie
+ 
+
+ align:start position:0%
+that's was actually done in the movie
+and I don't remember it exactly from the
+
+ align:start position:0%
+and I don't remember it exactly from the
+ 
+
+ align:start position:0%
+and I don't remember it exactly from the
+book but it definitely hits on things is
+
+ align:start position:0%
+book but it definitely hits on things is
+ 
+
+ align:start position:0%
+book but it definitely hits on things is
+where like the Saron characters talking
+
+ align:start position:0%
+where like the Saron characters talking
+ 
+
+ align:start position:0%
+where like the Saron characters talking
+about how there's this new age and it's
+
+ align:start position:0%
+about how there's this new age and it's
+ 
+
+ align:start position:0%
+about how there's this new age and it's
+like the iron hand of the orc and you
+
+ align:start position:0%
+like the iron hand of the orc and you
+ 
+
+ align:start position:0%
+like the iron hand of the orc and you
+know machinery
+
+ align:start position:0%
+know machinery
+ 
+
+ align:start position:0%
+know machinery
+exactly like World War I. It's almost
+
+ align:start position:0%
+exactly like World War I. It's almost
+ 
+
+ align:start position:0%
+exactly like World War I. It's almost
+like I feel like he's contrasting like
+
+ align:start position:0%
+like I feel like he's contrasting like
+ 
+
+ align:start position:0%
+like I feel like he's contrasting like
+World War I being like the uh you know
+
+ align:start position:0%
+World War I being like the uh you know
+ 
+
+ align:start position:0%
+World War I being like the uh you know
+the darker armies versus the uh you know
+
+ align:start position:0%
+the darker armies versus the uh you know
+ 
+
+ align:start position:0%
+the darker armies versus the uh you know
+the guys on horses and stuff because
+
+ align:start position:0%
+the guys on horses and stuff because
+ 
+
+ align:start position:0%
+the guys on horses and stuff because
+like the thing you see with the guys and
+
+ align:start position:0%
+like the thing you see with the guys and
+ 
+
+ align:start position:0%
+like the thing you see with the guys and
+horses that there's heroes. There's like
+
+ align:start position:0%
+horses that there's heroes. There's like
+ 
+
+ align:start position:0%
+horses that there's heroes. There's like
+guys who you know individual achievement
+
+ align:start position:0%
+guys who you know individual achievement
+ 
+
+ align:start position:0%
+guys who you know individual achievement
+and that in World World War I is like
+
+ align:start position:0%
+and that in World World War I is like
+ 
+
+ align:start position:0%
+and that in World World War I is like
+the one war in history that like I know
+
+ align:start position:0%
+the one war in history that like I know
+ 
+
+ align:start position:0%
+the one war in history that like I know
+a bit about that I can't name a single
+
+ align:start position:0%
+a bit about that I can't name a single
+ 
+
+ align:start position:0%
+a bit about that I can't name a single
+hero from like I can't name a general.
+
+ align:start position:0%
+hero from like I can't name a general.
+ 
+
+ align:start position:0%
+hero from like I can't name a general.
+The red bars.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+I thought Snoopy was the hero. Come on.
+
+ align:start position:0%
+I thought Snoopy was the hero. Come on.
+ 
+
+ align:start position:0%
+I thought Snoopy was the hero. Come on.
+Doesn't Snoopy take him down? Yes. Yeah.
+
+ align:start position:0%
+Doesn't Snoopy take him down? Yes. Yeah.
+ 
+
+ align:start position:0%
+Doesn't Snoopy take him down? Yes. Yeah.
+Did you guys Do you guys was that song
+
+ align:start position:0%
+Did you guys Do you guys was that song
+ 
+
+ align:start position:0%
+Did you guys Do you guys was that song
+still? I don't know the song. Okay,
+
+ align:start position:0%
+still? I don't know the song. Okay,
+ 
+
+ align:start position:0%
+still? I don't know the song. Okay,
+we're not going to sing it though. Um
+
+ align:start position:0%
+we're not going to sing it though. Um
+ 
+
+ align:start position:0%
+we're not going to sing it though. Um
+later another class.
+
+ align:start position:0%
+later another class.
+ 
+
+ align:start position:0%
+later another class.
+Um, okay. So, let's think about heroes
+
+ align:start position:0%
+Um, okay. So, let's think about heroes
+ 
+
+ align:start position:0%
+Um, okay. So, let's think about heroes
+for a moment because I think that is a
+
+ align:start position:0%
+for a moment because I think that is a
+ 
+
+ align:start position:0%
+for a moment because I think that is a
+critical piece to this. Aside from the
+
+ align:start position:0%
+critical piece to this. Aside from the
+ 
+
+ align:start position:0%
+critical piece to this. Aside from the
+Red Baron, it may well have felt like
+
+ align:start position:0%
+Red Baron, it may well have felt like
+ 
+
+ align:start position:0%
+Red Baron, it may well have felt like
+there was nothing heroic about World War
+
+ align:start position:0%
+there was nothing heroic about World War
+ 
+
+ align:start position:0%
+there was nothing heroic about World War
+I. Ultimately, it was
+
+ align:start position:0%
+I. Ultimately, it was
+ 
+
+ align:start position:0%
+I. Ultimately, it was
+anti-heroic. Okay. Now, the heroic mode
+
+ align:start position:0%
+anti-heroic. Okay. Now, the heroic mode
+ 
+
+ align:start position:0%
+anti-heroic. Okay. Now, the heroic mode
+is one we recognize. Um that who I just
+
+ align:start position:0%
+is one we recognize. Um that who I just
+ 
+
+ align:start position:0%
+is one we recognize. Um that who I just
+happened to bring with me cuz I thought
+
+ align:start position:0%
+happened to bring with me cuz I thought
+ 
+
+ align:start position:0%
+happened to bring with me cuz I thought
+it might come in handy.
+
+ align:start position:0%
+it might come in handy.
+ 
+
+ align:start position:0%
+it might come in handy.
+Um if I can find love coincidentally.
+
+ align:start position:0%
+Um if I can find love coincidentally.
+ 
+
+ align:start position:0%
+Um if I can find love coincidentally.
+Yeah,
+
+ align:start position:0%
+Yeah,
+ 
+
+ align:start position:0%
+Yeah,
+coincidentally.
+
+ align:start position:0%
+coincidentally.
+ 
+
+ align:start position:0%
+coincidentally.
+Okay.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Um this is Beaolf with the dragon.
+
+ align:start position:0%
+Um this is Beaolf with the dragon.
+ 
+
+ align:start position:0%
+Um this is Beaolf with the dragon.
+That's the other thing, right? It's one
+
+ align:start position:0%
+That's the other thing, right? It's one
+ 
+
+ align:start position:0%
+That's the other thing, right? It's one
+thing to be to go down, right? slaying
+
+ align:start position:0%
+thing to be to go down, right? slaying
+ 
+
+ align:start position:0%
+thing to be to go down, right? slaying
+the dragon. And it's another thing to be
+
+ align:start position:0%
+the dragon. And it's another thing to be
+ 
+
+ align:start position:0%
+the dragon. And it's another thing to be
+gunned down by machine gun fire having
+
+ align:start position:0%
+gunned down by machine gun fire having
+ 
+
+ align:start position:0%
+gunned down by machine gun fire having
+gone only a few inches, right? And we
+
+ align:start position:0%
+gone only a few inches, right? And we
+ 
+
+ align:start position:0%
+gone only a few inches, right? And we
+can say, gosh, what difference does it
+
+ align:start position:0%
+can say, gosh, what difference does it
+ 
+
+ align:start position:0%
+can say, gosh, what difference does it
+make if you've gone 10 feet or a few
+
+ align:start position:0%
+make if you've gone 10 feet or a few
+ 
+
+ align:start position:0%
+make if you've gone 10 feet or a few
+inches? But maybe it does make a
+
+ align:start position:0%
+inches? But maybe it does make a
+ 
+
+ align:start position:0%
+inches? But maybe it does make a
+difference. Um, but I mean, another
+
+ align:start position:0%
+difference. Um, but I mean, another
+ 
+
+ align:start position:0%
+difference. Um, but I mean, another
+another piece of it is is is class. I
+
+ align:start position:0%
+another piece of it is is is class. I
+ 
+
+ align:start position:0%
+another piece of it is is is class. I
+think that I mean, World War I, the the
+
+ align:start position:0%
+think that I mean, World War I, the the
+ 
+
+ align:start position:0%
+think that I mean, World War I, the the
+boys from Oxford and Cambridge actually
+
+ align:start position:0%
+boys from Oxford and Cambridge actually
+ 
+
+ align:start position:0%
+boys from Oxford and Cambridge actually
+go and they don't come back. And that
+
+ align:start position:0%
+go and they don't come back. And that
+ 
+
+ align:start position:0%
+go and they don't come back. And that
+that's felt very deeply. But hang hang
+
+ align:start position:0%
+that's felt very deeply. But hang hang
+ 
+
+ align:start position:0%
+that's felt very deeply. But hang hang
+on a second, Nick. Okay, so here here is
+
+ align:start position:0%
+on a second, Nick. Okay, so here here is
+ 
+
+ align:start position:0%
+on a second, Nick. Okay, so here here is
+Beaolf getting ready to deliver the
+
+ align:start position:0%
+Beaolf getting ready to deliver the
+ 
+
+ align:start position:0%
+Beaolf getting ready to deliver the
+fatal wound. Once again, the king,
+
+ align:start position:0%
+fatal wound. Once again, the king,
+ 
+
+ align:start position:0%
+fatal wound. Once again, the king,
+that's Beaolf, gathered his strength and
+
+ align:start position:0%
+that's Beaolf, gathered his strength and
+ 
+
+ align:start position:0%
+that's Beaolf, gathered his strength and
+drew his stabbing knife he carried on
+
+ align:start position:0%
+drew his stabbing knife he carried on
+ 
+
+ align:start position:0%
+drew his stabbing knife he carried on
+his belt, sharpened for battle. He stuck
+
+ align:start position:0%
+his belt, sharpened for battle. He stuck
+ 
+
+ align:start position:0%
+his belt, sharpened for battle. He stuck
+it deep in the dragon's flank. Beowolf
+
+ align:start position:0%
+it deep in the dragon's flank. Beowolf
+ 
+
+ align:start position:0%
+it deep in the dragon's flank. Beowolf
+dealt it a deadly wound. They had killed
+
+ align:start position:0%
+dealt it a deadly wound. They had killed
+ 
+
+ align:start position:0%
+dealt it a deadly wound. They had killed
+the enemy. Courage quelled his life.
+
+ align:start position:0%
+the enemy. Courage quelled his life.
+ 
+
+ align:start position:0%
+the enemy. Courage quelled his life.
+That pair of kinsmen, partners and
+
+ align:start position:0%
+That pair of kinsmen, partners and
+ 
+
+ align:start position:0%
+That pair of kinsmen, partners and
+nobility, had destroyed the foe. So
+
+ align:start position:0%
+nobility, had destroyed the foe. So
+ 
+
+ align:start position:0%
+nobility, had destroyed the foe. So
+every man should act be at hand when
+
+ align:start position:0%
+every man should act be at hand when
+ 
+
+ align:start position:0%
+every man should act be at hand when
+needed. This is Wigloff who comes to
+
+ align:start position:0%
+needed. This is Wigloff who comes to
+ 
+
+ align:start position:0%
+needed. This is Wigloff who comes to
+Beaolf's aid and um at the last moment
+
+ align:start position:0%
+Beaolf's aid and um at the last moment
+ 
+
+ align:start position:0%
+Beaolf's aid and um at the last moment
+when he's been deserted by everyone
+
+ align:start position:0%
+when he's been deserted by everyone
+ 
+
+ align:start position:0%
+when he's been deserted by everyone
+else. Okay. So this so every man should
+
+ align:start position:0%
+else. Okay. So this so every man should
+ 
+
+ align:start position:0%
+else. Okay. So this so every man should
+act be at hand when needed. But now for
+
+ align:start position:0%
+act be at hand when needed. But now for
+ 
+
+ align:start position:0%
+act be at hand when needed. But now for
+the king this would be the last of his
+
+ align:start position:0%
+the king this would be the last of his
+ 
+
+ align:start position:0%
+the king this would be the last of his
+many labors and triumphs in the world.
+
+ align:start position:0%
+many labors and triumphs in the world.
+ 
+
+ align:start position:0%
+many labors and triumphs in the world.
+And then we have the wound starting to
+
+ align:start position:0%
+And then we have the wound starting to
+ 
+
+ align:start position:0%
+And then we have the wound starting to
+ooze and do all of the things. Um and
+
+ align:start position:0%
+ooze and do all of the things. Um and
+ 
+
+ align:start position:0%
+ooze and do all of the things. Um and
+then Bea Wolf has to have his dying
+
+ align:start position:0%
+then Bea Wolf has to have his dying
+ 
+
+ align:start position:0%
+then Bea Wolf has to have his dying
+speech, right? because heroes get to
+
+ align:start position:0%
+speech, right? because heroes get to
+ 
+
+ align:start position:0%
+speech, right? because heroes get to
+have dying speeches, but boys being
+
+ align:start position:0%
+have dying speeches, but boys being
+ 
+
+ align:start position:0%
+have dying speeches, but boys being
+killed by machine guns obviously don't
+
+ align:start position:0%
+killed by machine guns obviously don't
+ 
+
+ align:start position:0%
+killed by machine guns obviously don't
+get to have dying speeches. Uh, which is
+
+ align:start position:0%
+get to have dying speeches. Uh, which is
+ 
+
+ align:start position:0%
+get to have dying speeches. Uh, which is
+a problem. Now is the time when I would
+
+ align:start position:0%
+a problem. Now is the time when I would
+ 
+
+ align:start position:0%
+a problem. Now is the time when I would
+have wanted to bestow this armor on my
+
+ align:start position:0%
+have wanted to bestow this armor on my
+ 
+
+ align:start position:0%
+have wanted to bestow this armor on my
+own son. Had it been my fortune to have
+
+ align:start position:0%
+own son. Had it been my fortune to have
+ 
+
+ align:start position:0%
+own son. Had it been my fortune to have
+fathered an heir and live on in his
+
+ align:start position:0%
+fathered an heir and live on in his
+ 
+
+ align:start position:0%
+fathered an heir and live on in his
+flesh. For 50 years, I ruled this
+
+ align:start position:0%
+flesh. For 50 years, I ruled this
+ 
+
+ align:start position:0%
+flesh. For 50 years, I ruled this
+nation. No king of any neighboring clan
+
+ align:start position:0%
+nation. No king of any neighboring clan
+ 
+
+ align:start position:0%
+nation. No king of any neighboring clan
+would dare face me with troops, none had
+
+ align:start position:0%
+would dare face me with troops, none had
+ 
+
+ align:start position:0%
+would dare face me with troops, none had
+the power to intimidate me. I took what
+
+ align:start position:0%
+the power to intimidate me. I took what
+ 
+
+ align:start position:0%
+the power to intimidate me. I took what
+came, cared for and stood by things in
+
+ align:start position:0%
+came, cared for and stood by things in
+ 
+
+ align:start position:0%
+came, cared for and stood by things in
+my keeping, never foremented quarrels,
+
+ align:start position:0%
+my keeping, never foremented quarrels,
+ 
+
+ align:start position:0%
+my keeping, never foremented quarrels,
+never swore to a lie. All this consoles
+
+ align:start position:0%
+never swore to a lie. All this consoles
+ 
+
+ align:start position:0%
+never swore to a lie. All this consoles
+me, doomed as I am, and sickening for
+
+ align:start position:0%
+me, doomed as I am, and sickening for
+ 
+
+ align:start position:0%
+me, doomed as I am, and sickening for
+death. Because of my right ways, the
+
+ align:start position:0%
+death. Because of my right ways, the
+ 
+
+ align:start position:0%
+death. Because of my right ways, the
+ruler of mankind need never blame me
+
+ align:start position:0%
+ruler of mankind need never blame me
+ 
+
+ align:start position:0%
+ruler of mankind need never blame me
+when the breath leaves my body for
+
+ align:start position:0%
+when the breath leaves my body for
+ 
+
+ align:start position:0%
+when the breath leaves my body for
+murder of kinsmen. Go now quickly,
+
+ align:start position:0%
+murder of kinsmen. Go now quickly,
+ 
+
+ align:start position:0%
+murder of kinsmen. Go now quickly,
+dearest Wigloth, under the greystone
+
+ align:start position:0%
+dearest Wigloth, under the greystone
+ 
+
+ align:start position:0%
+dearest Wigloth, under the greystone
+where the dragon is laid out, lost to
+
+ align:start position:0%
+where the dragon is laid out, lost to
+ 
+
+ align:start position:0%
+where the dragon is laid out, lost to
+his treasure. Hurry to feast your eyes
+
+ align:start position:0%
+his treasure. Hurry to feast your eyes
+ 
+
+ align:start position:0%
+his treasure. Hurry to feast your eyes
+on the horde. Away you go. I want to
+
+ align:start position:0%
+on the horde. Away you go. I want to
+ 
+
+ align:start position:0%
+on the horde. Away you go. I want to
+examine that ancient gold. Gaze my fill
+
+ align:start position:0%
+examine that ancient gold. Gaze my fill
+ 
+
+ align:start position:0%
+examine that ancient gold. Gaze my fill
+on those garnered jewels. My going will
+
+ align:start position:0%
+on those garnered jewels. My going will
+ 
+
+ align:start position:0%
+on those garnered jewels. My going will
+be easier for having seen the treasure.
+
+ align:start position:0%
+be easier for having seen the treasure.
+ 
+
+ align:start position:0%
+be easier for having seen the treasure.
+A less troubled letting go of the life
+
+ align:start position:0%
+A less troubled letting go of the life
+ 
+
+ align:start position:0%
+A less troubled letting go of the life
+and lordship I have long maintained.
+
+ align:start position:0%
+and lordship I have long maintained.
+ 
+
+ align:start position:0%
+and lordship I have long maintained.
+Okay, so he's dying and he's worried one
+
+ align:start position:0%
+Okay, so he's dying and he's worried one
+ 
+
+ align:start position:0%
+Okay, so he's dying and he's worried one
+because he doesn't have a son. He was
+
+ align:start position:0%
+because he doesn't have a son. He was
+ 
+
+ align:start position:0%
+because he doesn't have a son. He was
+king for 50 years. Well, he could have
+
+ align:start position:0%
+king for 50 years. Well, he could have
+ 
+
+ align:start position:0%
+king for 50 years. Well, he could have
+done something about that presumably,
+
+ align:start position:0%
+done something about that presumably,
+ 
+
+ align:start position:0%
+done something about that presumably,
+but it didn't occur to him until this
+
+ align:start position:0%
+but it didn't occur to him until this
+ 
+
+ align:start position:0%
+but it didn't occur to him until this
+moment.
+
+ align:start position:0%
+moment.
+ 
+
+ align:start position:0%
+moment.
+And moreover, he wants Wigloff to quick
+
+ align:start position:0%
+And moreover, he wants Wigloff to quick
+ 
+
+ align:start position:0%
+And moreover, he wants Wigloff to quick
+run back to the dragon's lair and get
+
+ align:start position:0%
+run back to the dragon's lair and get
+ 
+
+ align:start position:0%
+run back to the dragon's lair and get
+some of the treasure and bring it back
+
+ align:start position:0%
+some of the treasure and bring it back
+ 
+
+ align:start position:0%
+some of the treasure and bring it back
+so he can see
+
+ align:start position:0%
+so he can see
+ 
+
+ align:start position:0%
+so he can see
+it. Seems maybe to be a silly way to us
+
+ align:start position:0%
+it. Seems maybe to be a silly way to us
+ 
+
+ align:start position:0%
+it. Seems maybe to be a silly way to us
+to spend your dying
+
+ align:start position:0%
+to spend your dying
+ 
+
+ align:start position:0%
+to spend your dying
+moments, right? But it's part of that
+
+ align:start position:0%
+moments, right? But it's part of that
+ 
+
+ align:start position:0%
+moments, right? But it's part of that
+it's part of that heroic mode, right?
+
+ align:start position:0%
+it's part of that heroic mode, right?
+ 
+
+ align:start position:0%
+it's part of that heroic mode, right?
+The whole point of of dying in this way,
+
+ align:start position:0%
+The whole point of of dying in this way,
+ 
+
+ align:start position:0%
+The whole point of of dying in this way,
+the whole point of it is that you've
+
+ align:start position:0%
+the whole point of it is that you've
+ 
+
+ align:start position:0%
+the whole point of it is that you've
+killed the dragon and you've in fact
+
+ align:start position:0%
+killed the dragon and you've in fact
+ 
+
+ align:start position:0%
+killed the dragon and you've in fact
+inherited his treasure. Now, it's true,
+
+ align:start position:0%
+inherited his treasure. Now, it's true,
+ 
+
+ align:start position:0%
+inherited his treasure. Now, it's true,
+you're going to die any moment. Um, but
+
+ align:start position:0%
+you're going to die any moment. Um, but
+ 
+
+ align:start position:0%
+you're going to die any moment. Um, but
+you've got the treasure, right? All of
+
+ align:start position:0%
+you've got the treasure, right? All of
+ 
+
+ align:start position:0%
+you've got the treasure, right? All of
+that fits perfectly into
+
+ align:start position:0%
+that fits perfectly into
+ 
+
+ align:start position:0%
+that fits perfectly into
+um into a, if you will, a classically
+
+ align:start position:0%
+um into a, if you will, a classically
+ 
+
+ align:start position:0%
+um into a, if you will, a classically
+heroic mode, right? And we and we know
+
+ align:start position:0%
+heroic mode, right? And we and we know
+ 
+
+ align:start position:0%
+heroic mode, right? And we and we know
+we know this kind of medieval literature
+
+ align:start position:0%
+we know this kind of medieval literature
+ 
+
+ align:start position:0%
+we know this kind of medieval literature
+and we're fairly comfortable with it.
+
+ align:start position:0%
+and we're fairly comfortable with it.
+ 
+
+ align:start position:0%
+and we're fairly comfortable with it.
+The movie industry is made up of this
+
+ align:start position:0%
+The movie industry is made up of this
+ 
+
+ align:start position:0%
+The movie industry is made up of this
+kind of medieval stuff, right? It's not
+
+ align:start position:0%
+kind of medieval stuff, right? It's not
+ 
+
+ align:start position:0%
+kind of medieval stuff, right? It's not
+made up of the Caroline Walker Binham
+
+ align:start position:0%
+made up of the Caroline Walker Binham
+ 
+
+ align:start position:0%
+made up of the Caroline Walker Binham
+kind of stuff, right? I mean, can you
+
+ align:start position:0%
+kind of stuff, right? I mean, can you
+ 
+
+ align:start position:0%
+kind of stuff, right? I mean, can you
+imagine the great movies of, you know,
+
+ align:start position:0%
+imagine the great movies of, you know,
+ 
+
+ align:start position:0%
+imagine the great movies of, you know,
+saintly women wasting away day by day
+
+ align:start position:0%
+saintly women wasting away day by day
+ 
+
+ align:start position:0%
+saintly women wasting away day by day
+slowly, you know, in penitence to God?
+
+ align:start position:0%
+slowly, you know, in penitence to God?
+ 
+
+ align:start position:0%
+slowly, you know, in penitence to God?
+It just, right? There's no plot, there's
+
+ align:start position:0%
+It just, right? There's no plot, there's
+ 
+
+ align:start position:0%
+It just, right? There's no plot, there's
+no excitement, there's no drama. Um,
+
+ align:start position:0%
+no excitement, there's no drama. Um,
+ 
+
+ align:start position:0%
+no excitement, there's no drama. Um,
+there would only be all of these
+
+ align:start position:0%
+there would only be all of these
+ 
+
+ align:start position:0%
+there would only be all of these
+disturbing questions and nobody would
+
+ align:start position:0%
+disturbing questions and nobody would
+ 
+
+ align:start position:0%
+disturbing questions and nobody would
+pay money to go see it for
+
+ align:start position:0%
+pay money to go see it for
+ 
+
+ align:start position:0%
+pay money to go see it for
+reconciliation with their husband. Stay
+
+ align:start position:0%
+reconciliation with their husband. Stay
+ 
+
+ align:start position:0%
+reconciliation with their husband. Stay
+tuned.
+
+ align:start position:0%
+tuned.
+ 
+
+ align:start position:0%
+tuned.
+The priest sake of communion. Yeah.
+
+ align:start position:0%
+The priest sake of communion. Yeah.
+ 
+
+ align:start position:0%
+The priest sake of communion. Yeah.
+There would be torture, right? There
+
+ align:start position:0%
+There would be torture, right? There
+ 
+
+ align:start position:0%
+There would be torture, right? There
+would be torture. That's true. And some
+
+ align:start position:0%
+would be torture. That's true. And some
+ 
+
+ align:start position:0%
+would be torture. That's true. And some
+people might go in for that, but it
+
+ align:start position:0%
+people might go in for that, but it
+ 
+
+ align:start position:0%
+people might go in for that, but it
+would be a small audience, right, of a
+
+ align:start position:0%
+would be a small audience, right, of a
+ 
+
+ align:start position:0%
+would be a small audience, right, of a
+very of a very particular kind of event.
+
+ align:start position:0%
+very of a very particular kind of event.
+ 
+
+ align:start position:0%
+very of a very particular kind of event.
+The Passion of the Christ is selling
+
+ align:start position:0%
+The Passion of the Christ is selling
+ 
+
+ align:start position:0%
+The Passion of the Christ is selling
+pretty well. Yeah. Passion of the
+
+ align:start position:0%
+pretty well. Yeah. Passion of the
+ 
+
+ align:start position:0%
+pretty well. Yeah. Passion of the
+Christ. I mean, Stigmata sold pretty
+
+ align:start position:0%
+Christ. I mean, Stigmata sold pretty
+ 
+
+ align:start position:0%
+Christ. I mean, Stigmata sold pretty
+good when it came through theaters. Oh,
+
+ align:start position:0%
+good when it came through theaters. Oh,
+ 
+
+ align:start position:0%
+good when it came through theaters. Oh,
+that was that was that was
+
+ align:start position:0%
+that was that was that was
+ 
+
+ align:start position:0%
+that was that was that was
+[Laughter]
+
+ align:start position:0%
+[Laughter]
+ 
+
+ align:start position:0%
+[Laughter]
+all right. All right. We don't want to
+
+ align:start position:0%
+all right. All right. We don't want to
+ 
+
+ align:start position:0%
+all right. All right. We don't want to
+overstate the case, but but
+
+ align:start position:0%
+overstate the case, but but
+ 
+
+ align:start position:0%
+overstate the case, but but
+but clearly there's still a difference
+
+ align:start position:0%
+but clearly there's still a difference
+ 
+
+ align:start position:0%
+but clearly there's still a difference
+in
+
+ align:start position:0%
+in
+ 
+
+ align:start position:0%
+in
+accessibility, right? Okay. But now
+
+ align:start position:0%
+accessibility, right? Okay. But now
+ 
+
+ align:start position:0%
+accessibility, right? Okay. But now
+let's think about the Lord of the
+
+ align:start position:0%
+let's think about the Lord of the
+ 
+
+ align:start position:0%
+let's think about the Lord of the
+Rings. If the heroic mode is part of
+
+ align:start position:0%
+Rings. If the heroic mode is part of
+ 
+
+ align:start position:0%
+Rings. If the heroic mode is part of
+what
+
+ align:start position:0%
+what
+ 
+
+ align:start position:0%
+what
+appeals, who is the hero in the Lord of
+
+ align:start position:0%
+appeals, who is the hero in the Lord of
+ 
+
+ align:start position:0%
+appeals, who is the hero in the Lord of
+the Rings?
+
+ align:start position:0%
+the Rings?
+ 
+
+ align:start position:0%
+the Rings?
+Froto
+
+ align:start position:0%
+Froto
+ 
+
+ align:start position:0%
+Froto
+and Sam, actually Sam is the hero. My
+
+ align:start position:0%
+and Sam, actually Sam is the hero. My
+ 
+
+ align:start position:0%
+and Sam, actually Sam is the hero. My
+bad. Okay. Okay. Anti-hero, so to speak.
+
+ align:start position:0%
+bad. Okay. Okay. Anti-hero, so to speak.
+ 
+
+ align:start position:0%
+bad. Okay. Okay. Anti-hero, so to speak.
+Yeah. What kind of heroes are they? I
+
+ align:start position:0%
+Yeah. What kind of heroes are they? I
+ 
+
+ align:start position:0%
+Yeah. What kind of heroes are they? I
+mean, how does the book end? I mean,
+
+ align:start position:0%
+mean, how does the book end? I mean,
+ 
+
+ align:start position:0%
+mean, how does the book end? I mean,
+there's there's Aragorn. Yeah, there is
+
+ align:start position:0%
+there's there's Aragorn. Yeah, there is
+ 
+
+ align:start position:0%
+there's there's Aragorn. Yeah, there is
+Aragorn. Who is it? Yeah, he gets the
+
+ align:start position:0%
+Aragorn. Who is it? Yeah, he gets the
+ 
+
+ align:start position:0%
+Aragorn. Who is it? Yeah, he gets the
+girl in the end. The girl in the
+
+ align:start position:0%
+girl in the end. The girl in the
+ 
+
+ align:start position:0%
+girl in the end. The girl in the
+kingdom. Okay, that's in the heroic
+
+ align:start position:0%
+kingdom. Okay, that's in the heroic
+ 
+
+ align:start position:0%
+kingdom. Okay, that's in the heroic
+mode. That girl's world is lost. Like he
+
+ align:start position:0%
+mode. That girl's world is lost. Like he
+ 
+
+ align:start position:0%
+mode. That girl's world is lost. Like he
+says it, some wounds never heal. Like he
+
+ align:start position:0%
+says it, some wounds never heal. Like he
+ 
+
+ align:start position:0%
+says it, some wounds never heal. Like he
+rescues the world for everyone else, but
+
+ align:start position:0%
+rescues the world for everyone else, but
+ 
+
+ align:start position:0%
+rescues the world for everyone else, but
+he couldn't rescue it for himself.
+
+ align:start position:0%
+he couldn't rescue it for himself.
+ 
+
+ align:start position:0%
+he couldn't rescue it for himself.
+So, so where should I mean if this book
+
+ align:start position:0%
+So, so where should I mean if this book
+ 
+
+ align:start position:0%
+So, so where should I mean if this book
+was in the heroic mode, shouldn't we
+
+ align:start position:0%
+was in the heroic mode, shouldn't we
+ 
+
+ align:start position:0%
+was in the heroic mode, shouldn't we
+have ended with Aragorn getting the girl
+
+ align:start position:0%
+have ended with Aragorn getting the girl
+ 
+
+ align:start position:0%
+have ended with Aragorn getting the girl
+in the kingdom? Well, how about how
+
+ align:start position:0%
+in the kingdom? Well, how about how
+ 
+
+ align:start position:0%
+in the kingdom? Well, how about how
+about like I mean Beaolf's death, right?
+
+ align:start position:0%
+about like I mean Beaolf's death, right?
+ 
+
+ align:start position:0%
+about like I mean Beaolf's death, right?
+That's that's Froto's Froto's dying in
+
+ align:start position:0%
+That's that's Froto's Froto's dying in
+ 
+
+ align:start position:0%
+That's that's Froto's Froto's dying in
+the in the sense that, you know, he's
+
+ align:start position:0%
+the in the sense that, you know, he's
+ 
+
+ align:start position:0%
+the in the sense that, you know, he's
+going on to the other land where he's
+
+ align:start position:0%
+going on to the other land where he's
+ 
+
+ align:start position:0%
+going on to the other land where he's
+going to die. He's just kind of giving
+
+ align:start position:0%
+going to die. He's just kind of giving
+ 
+
+ align:start position:0%
+going to die. He's just kind of giving
+up and moving on from this world, having
+
+ align:start position:0%
+up and moving on from this world, having
+ 
+
+ align:start position:0%
+up and moving on from this world, having
+performed this great deed, uh saved
+
+ align:start position:0%
+performed this great deed, uh saved
+ 
+
+ align:start position:0%
+performed this great deed, uh saved
+everything for for everyone else. But
+
+ align:start position:0%
+everything for for everyone else. But
+ 
+
+ align:start position:0%
+everything for for everyone else. But
+bewolf, I think, takes us as something
+
+ align:start position:0%
+bewolf, I think, takes us as something
+ 
+
+ align:start position:0%
+bewolf, I think, takes us as something
+where it's, you know, he's done this
+
+ align:start position:0%
+where it's, you know, he's done this
+ 
+
+ align:start position:0%
+where it's, you know, he's done this
+great deed and it's for other people
+
+ align:start position:0%
+great deed and it's for other people
+ 
+
+ align:start position:0%
+great deed and it's for other people
+also, but it's also for him. Like, he's
+
+ align:start position:0%
+also, but it's also for him. Like, he's
+ 
+
+ align:start position:0%
+also, but it's also for him. Like, he's
+done this and, you know, he gets the
+
+ align:start position:0%
+done this and, you know, he gets the
+ 
+
+ align:start position:0%
+done this and, you know, he gets the
+gold afterwards. So, he's gotten what
+
+ align:start position:0%
+gold afterwards. So, he's gotten what
+ 
+
+ align:start position:0%
+gold afterwards. So, he's gotten what
+he's wanted. You know, yeah, he's going
+
+ align:start position:0%
+he's wanted. You know, yeah, he's going
+ 
+
+ align:start position:0%
+he's wanted. You know, yeah, he's going
+to die, but he's gotten what he's
+
+ align:start position:0%
+to die, but he's gotten what he's
+ 
+
+ align:start position:0%
+to die, but he's gotten what he's
+wanted.
+
+ align:start position:0%
+wanted.
+ 
+
+ align:start position:0%
+wanted.
+He gets the praise. Well, you know,
+
+ align:start position:0%
+He gets the praise. Well, you know,
+ 
+
+ align:start position:0%
+He gets the praise. Well, you know,
+Froto's lost both what he wanted like he
+
+ align:start position:0%
+Froto's lost both what he wanted like he
+ 
+
+ align:start position:0%
+Froto's lost both what he wanted like he
+gets he saves the world, but he doesn't
+
+ align:start position:0%
+gets he saves the world, but he doesn't
+ 
+
+ align:start position:0%
+gets he saves the world, but he doesn't
+save, you know, what he really wanted to
+
+ align:start position:0%
+save, you know, what he really wanted to
+ 
+
+ align:start position:0%
+save, you know, what he really wanted to
+save and he didn't so he doesn't really
+
+ align:start position:0%
+save and he didn't so he doesn't really
+ 
+
+ align:start position:0%
+save and he didn't so he doesn't really
+get what he wants. He doesn't get really
+
+ align:start position:0%
+get what he wants. He doesn't get really
+ 
+
+ align:start position:0%
+get what he wants. He doesn't get really
+get the praise. Well, go ahead, Emily.
+
+ align:start position:0%
+get the praise. Well, go ahead, Emily.
+ 
+
+ align:start position:0%
+get the praise. Well, go ahead, Emily.
+But I think there's two really important
+
+ align:start position:0%
+But I think there's two really important
+ 
+
+ align:start position:0%
+But I think there's two really important
+distinctions to draw. Like first of all,
+
+ align:start position:0%
+distinctions to draw. Like first of all,
+ 
+
+ align:start position:0%
+distinctions to draw. Like first of all,
+Bearwolf gets the treasure, right? Froto
+
+ align:start position:0%
+Bearwolf gets the treasure, right? Froto
+ 
+
+ align:start position:0%
+Bearwolf gets the treasure, right? Froto
+spends the whole book trying to get rid
+
+ align:start position:0%
+spends the whole book trying to get rid
+ 
+
+ align:start position:0%
+spends the whole book trying to get rid
+of the treasure. Mhm. And secondly,
+
+ align:start position:0%
+of the treasure. Mhm. And secondly,
+ 
+
+ align:start position:0%
+of the treasure. Mhm. And secondly,
+Beaywolf is an aristocrat. Bearwolf is a
+
+ align:start position:0%
+Beaywolf is an aristocrat. Bearwolf is a
+ 
+
+ align:start position:0%
+Beaywolf is an aristocrat. Bearwolf is a
+king. He's a man of distinction. Frodo
+
+ align:start position:0%
+king. He's a man of distinction. Frodo
+ 
+
+ align:start position:0%
+king. He's a man of distinction. Frodo
+is a hobbit. He's he's of no importance
+
+ align:start position:0%
+is a hobbit. He's he's of no importance
+ 
+
+ align:start position:0%
+is a hobbit. He's he's of no importance
+at all in in global affairs. He has no
+
+ align:start position:0%
+at all in in global affairs. He has no
+ 
+
+ align:start position:0%
+at all in in global affairs. He has no
+family lineage. He's not he's not the
+
+ align:start position:0%
+family lineage. He's not he's not the
+ 
+
+ align:start position:0%
+family lineage. He's not he's not the
+archetypical medieval hero. He's he's no
+
+ align:start position:0%
+archetypical medieval hero. He's he's no
+ 
+
+ align:start position:0%
+archetypical medieval hero. He's he's no
+he's no blue blood. So I think it's
+
+ align:start position:0%
+he's no blue blood. So I think it's
+ 
+
+ align:start position:0%
+he's no blue blood. So I think it's
+there's some really important well
+
+ align:start position:0%
+there's some really important well
+ 
+
+ align:start position:0%
+there's some really important well
+that's where I think the Christian part
+
+ align:start position:0%
+that's where I think the Christian part
+ 
+
+ align:start position:0%
+that's where I think the Christian part
+comes in kind of. It's a like the whole
+
+ align:start position:0%
+comes in kind of. It's a like the whole
+ 
+
+ align:start position:0%
+comes in kind of. It's a like the whole
+like underdog, right? You have the
+
+ align:start position:0%
+like underdog, right? You have the
+ 
+
+ align:start position:0%
+like underdog, right? You have the
+person that no one else would choose
+
+ align:start position:0%
+person that no one else would choose
+ 
+
+ align:start position:0%
+person that no one else would choose
+taking on the task, right? Like Mary and
+
+ align:start position:0%
+taking on the task, right? Like Mary and
+ 
+
+ align:start position:0%
+taking on the task, right? Like Mary and
+Joseph like they get chosen even though
+
+ align:start position:0%
+Joseph like they get chosen even though
+ 
+
+ align:start position:0%
+Joseph like they get chosen even though
+they're at the bottom of the barrel, so
+
+ align:start position:0%
+they're at the bottom of the barrel, so
+ 
+
+ align:start position:0%
+they're at the bottom of the barrel, so
+to speak. And it's always the bottom of
+
+ align:start position:0%
+to speak. And it's always the bottom of
+ 
+
+ align:start position:0%
+to speak. And it's always the bottom of
+the barrel, right? That's like the theme
+
+ align:start position:0%
+the barrel, right? That's like the theme
+ 
+
+ align:start position:0%
+the barrel, right? That's like the theme
+throughout culture. That's our women,
+
+ align:start position:0%
+throughout culture. That's our women,
+ 
+
+ align:start position:0%
+throughout culture. That's our women,
+right, who are um engaged in these, if
+
+ align:start position:0%
+right, who are um engaged in these, if
+ 
+
+ align:start position:0%
+right, who are um engaged in these, if
+you will, anti-heroic feats of
+
+ align:start position:0%
+you will, anti-heroic feats of
+ 
+
+ align:start position:0%
+you will, anti-heroic feats of
+starvation and self mutilation and
+
+ align:start position:0%
+starvation and self mutilation and
+ 
+
+ align:start position:0%
+starvation and self mutilation and
+whatever else, right? They
+
+ align:start position:0%
+whatever else, right? They
+ 
+
+ align:start position:0%
+whatever else, right? They
+are they um are God's ultimate agents
+
+ align:start position:0%
+are they um are God's ultimate agents
+ 
+
+ align:start position:0%
+are they um are God's ultimate agents
+precisely because they are low and it's
+
+ align:start position:0%
+precisely because they are low and it's
+ 
+
+ align:start position:0%
+precisely because they are low and it's
+unexpected. Yeah, Ben, I don't I just
+
+ align:start position:0%
+unexpected. Yeah, Ben, I don't I just
+ 
+
+ align:start position:0%
+unexpected. Yeah, Ben, I don't I just
+wanted to say that uh like to me the
+
+ align:start position:0%
+wanted to say that uh like to me the
+ 
+
+ align:start position:0%
+wanted to say that uh like to me the
+Lord of the Rings isn't just like Froto
+
+ align:start position:0%
+Lord of the Rings isn't just like Froto
+ 
+
+ align:start position:0%
+Lord of the Rings isn't just like Froto
+isn't the main hero cuz like after uh
+
+ align:start position:0%
+isn't the main hero cuz like after uh
+ 
+
+ align:start position:0%
+isn't the main hero cuz like after uh
+the first book the fellowship it's all
+
+ align:start position:0%
+the first book the fellowship it's all
+ 
+
+ align:start position:0%
+the first book the fellowship it's all
+it like ever since I read it has always
+
+ align:start position:0%
+it like ever since I read it has always
+ 
+
+ align:start position:0%
+it like ever since I read it has always
+been two books like it was Froto and Sam
+
+ align:start position:0%
+been two books like it was Froto and Sam
+ 
+
+ align:start position:0%
+been two books like it was Froto and Sam
+like and they even split up into two
+
+ align:start position:0%
+like and they even split up into two
+ 
+
+ align:start position:0%
+like and they even split up into two
+books one's Froto and Sam and both and
+
+ align:start position:0%
+books one's Froto and Sam and both and
+ 
+
+ align:start position:0%
+books one's Froto and Sam and both and
+the other one's like Aragorn and Gimly
+
+ align:start position:0%
+the other one's like Aragorn and Gimly
+ 
+
+ align:start position:0%
+the other one's like Aragorn and Gimly
+and all the elves or everyone else and
+
+ align:start position:0%
+and all the elves or everyone else and
+ 
+
+ align:start position:0%
+and all the elves or everyone else and
+so it was always like yeah there was the
+
+ align:start position:0%
+so it was always like yeah there was the
+ 
+
+ align:start position:0%
+so it was always like yeah there was the
+anti-heroes Froto and him. But in the
+
+ align:start position:0%
+anti-heroes Froto and him. But in the
+ 
+
+ align:start position:0%
+anti-heroes Froto and him. But in the
+book there there was still an complete
+
+ align:start position:0%
+book there there was still an complete
+ 
+
+ align:start position:0%
+book there there was still an complete
+book that was made up of the heroes and
+
+ align:start position:0%
+book that was made up of the heroes and
+ 
+
+ align:start position:0%
+book that was made up of the heroes and
+all the hero quests and that sort of
+
+ align:start position:0%
+all the hero quests and that sort of
+ 
+
+ align:start position:0%
+all the hero quests and that sort of
+stuff. I agree with you. But Tolken puts
+
+ align:start position:0%
+stuff. I agree with you. But Tolken puts
+ 
+
+ align:start position:0%
+stuff. I agree with you. But Tolken puts
+his cards on the table by how he ends,
+
+ align:start position:0%
+his cards on the table by how he ends,
+ 
+
+ align:start position:0%
+his cards on the table by how he ends,
+right? I mean, when when
+
+ align:start position:0%
+right? I mean, when when
+ 
+
+ align:start position:0%
+right? I mean, when when
+when I first read this to um my own kids
+
+ align:start position:0%
+when I first read this to um my own kids
+ 
+
+ align:start position:0%
+when I first read this to um my own kids
+and and you know, of course, too young
+
+ align:start position:0%
+and and you know, of course, too young
+ 
+
+ align:start position:0%
+and and you know, of course, too young
+to properly appreciate it, but you know,
+
+ align:start position:0%
+to properly appreciate it, but you know,
+ 
+
+ align:start position:0%
+to properly appreciate it, but you know,
+couldn't wait.
+
+ align:start position:0%
+couldn't wait.
+ 
+
+ align:start position:0%
+couldn't wait.
+um they wanted more or less to stop
+
+ align:start position:0%
+um they wanted more or less to stop
+ 
+
+ align:start position:0%
+um they wanted more or less to stop
+reading when Aragorn gets crowned. And
+
+ align:start position:0%
+reading when Aragorn gets crowned. And
+ 
+
+ align:start position:0%
+reading when Aragorn gets crowned. And
+that going back to the Shire business,
+
+ align:start position:0%
+that going back to the Shire business,
+ 
+
+ align:start position:0%
+that going back to the Shire business,
+who even wants to read that? Could we
+
+ align:start position:0%
+who even wants to read that? Could we
+ 
+
+ align:start position:0%
+who even wants to read that? Could we
+just skip that part? Well, okay. But
+
+ align:start position:0%
+just skip that part? Well, okay. But
+ 
+
+ align:start position:0%
+just skip that part? Well, okay. But
+there's a totally different sensibility
+
+ align:start position:0%
+there's a totally different sensibility
+ 
+
+ align:start position:0%
+there's a totally different sensibility
+at that point, right? Um, but I think
+
+ align:start position:0%
+at that point, right? Um, but I think
+ 
+
+ align:start position:0%
+at that point, right? Um, but I think
+that I think that
+
+ align:start position:0%
+that I think that
+ 
+
+ align:start position:0%
+that I think that
+Tolken is, you know, when when you when
+
+ align:start position:0%
+Tolken is, you know, when when you when
+ 
+
+ align:start position:0%
+Tolken is, you know, when when you when
+you choose to have two stories running
+
+ align:start position:0%
+you choose to have two stories running
+ 
+
+ align:start position:0%
+you choose to have two stories running
+in parallel and you ultimately decide
+
+ align:start position:0%
+in parallel and you ultimately decide
+ 
+
+ align:start position:0%
+in parallel and you ultimately decide
+that one of them gets the last word,
+
+ align:start position:0%
+that one of them gets the last word,
+ 
+
+ align:start position:0%
+that one of them gets the last word,
+well, that's the one that gets the last
+
+ align:start position:0%
+well, that's the one that gets the last
+ 
+
+ align:start position:0%
+well, that's the one that gets the last
+word. I mean, I think you're I think
+
+ align:start position:0%
+word. I mean, I think you're I think
+ 
+
+ align:start position:0%
+word. I mean, I think you're I think
+you're making a powerful statement
+
+ align:start position:0%
+you're making a powerful statement
+ 
+
+ align:start position:0%
+you're making a powerful statement
+there. We could argue about it, but I
+
+ align:start position:0%
+there. We could argue about it, but I
+ 
+
+ align:start position:0%
+there. We could argue about it, but I
+mean, that's but that's how I would read
+
+ align:start position:0%
+mean, that's but that's how I would read
+ 
+
+ align:start position:0%
+mean, that's but that's how I would read
+that. I don't I don't know who was next.
+
+ align:start position:0%
+that. I don't I don't know who was next.
+ 
+
+ align:start position:0%
+that. I don't I don't know who was next.
+Miranda, I guess um well, two things. It
+
+ align:start position:0%
+Miranda, I guess um well, two things. It
+ 
+
+ align:start position:0%
+Miranda, I guess um well, two things. It
+was I think that what they said in the
+
+ align:start position:0%
+was I think that what they said in the
+ 
+
+ align:start position:0%
+was I think that what they said in the
+article fit more was the whole idea of
+
+ align:start position:0%
+article fit more was the whole idea of
+ 
+
+ align:start position:0%
+article fit more was the whole idea of
+the unsung hero of the World War I and
+
+ align:start position:0%
+the unsung hero of the World War I and
+ 
+
+ align:start position:0%
+the unsung hero of the World War I and
+how this sort of this person who you
+
+ align:start position:0%
+how this sort of this person who you
+ 
+
+ align:start position:0%
+how this sort of this person who you
+know has done a lot of this work just
+
+ align:start position:0%
+know has done a lot of this work just
+ 
+
+ align:start position:0%
+know has done a lot of this work just
+comes back and is you know going look
+
+ align:start position:0%
+comes back and is you know going look
+ 
+
+ align:start position:0%
+comes back and is you know going look
+what I've done and everyone's just so
+
+ align:start position:0%
+what I've done and everyone's just so
+ 
+
+ align:start position:0%
+what I've done and everyone's just so
+has just basically pushes any of this
+
+ align:start position:0%
+has just basically pushes any of this
+ 
+
+ align:start position:0%
+has just basically pushes any of this
+trying to push any of the thought away
+
+ align:start position:0%
+trying to push any of the thought away
+ 
+
+ align:start position:0%
+trying to push any of the thought away
+doesn't really give any of the praise.
+
+ align:start position:0%
+doesn't really give any of the praise.
+ 
+
+ align:start position:0%
+doesn't really give any of the praise.
+Mhm. I also trying to remember cuz I I'd
+
+ align:start position:0%
+Mhm. I also trying to remember cuz I I'd
+ 
+
+ align:start position:0%
+Mhm. I also trying to remember cuz I I'd
+heard I hadn't read the last one at all
+
+ align:start position:0%
+heard I hadn't read the last one at all
+ 
+
+ align:start position:0%
+heard I hadn't read the last one at all
+that in fact in the movie that they cut
+
+ align:start position:0%
+that in fact in the movie that they cut
+ 
+
+ align:start position:0%
+that in fact in the movie that they cut
+out a bunch where like someone had you
+
+ align:start position:0%
+out a bunch where like someone had you
+ 
+
+ align:start position:0%
+out a bunch where like someone had you
+know of going back to the Shire where he
+
+ align:start position:0%
+know of going back to the Shire where he
+ 
+
+ align:start position:0%
+know of going back to the Shire where he
+in
+
+ align:start position:0%
+in
+ 
+
+ align:start position:0%
+in
+fact Son had taken over the Shire and
+
+ align:start position:0%
+fact Son had taken over the Shire and
+ 
+
+ align:start position:0%
+fact Son had taken over the Shire and
+polluted it and stuff like that. Mhm.
+
+ align:start position:0%
+polluted it and stuff like that. Mhm.
+ 
+
+ align:start position:0%
+polluted it and stuff like that. Mhm.
+They've specifically cut that out of the
+
+ align:start position:0%
+They've specifically cut that out of the
+ 
+
+ align:start position:0%
+They've specifically cut that out of the
+movie because people would not be able
+
+ align:start position:0%
+movie because people would not be able
+ 
+
+ align:start position:0%
+movie because people would not be able
+to deal with something like, you know,
+
+ align:start position:0%
+to deal with something like, you know,
+ 
+
+ align:start position:0%
+to deal with something like, you know,
+that and it was already 3 and 1 half
+
+ align:start position:0%
+that and it was already 3 and 1 half
+ 
+
+ align:start position:0%
+that and it was already 3 and 1 half
+hours long or something like that. But
+
+ align:start position:0%
+hours long or something like that. But
+ 
+
+ align:start position:0%
+hours long or something like that. But
+yeah, they filmed that part. But the
+
+ align:start position:0%
+yeah, they filmed that part. But the
+ 
+
+ align:start position:0%
+yeah, they filmed that part. But the
+Shire got taken over in the very first
+
+ align:start position:0%
+Shire got taken over in the very first
+ 
+
+ align:start position:0%
+Shire got taken over in the very first
+book like when they left it. That was
+
+ align:start position:0%
+book like when they left it. That was
+ 
+
+ align:start position:0%
+book like when they left it. That was
+when they first all those
+
+ align:start position:0%
+when they first all those
+ 
+
+ align:start position:0%
+when they first all those
+scourging of
+
+ align:start position:0%
+scourging of
+ 
+
+ align:start position:0%
+scourging of
+the go ahead. But I think to get back to
+
+ align:start position:0%
+the go ahead. But I think to get back to
+ 
+
+ align:start position:0%
+the go ahead. But I think to get back to
+this like hero discussion. So this book
+
+ align:start position:0%
+this like hero discussion. So this book
+ 
+
+ align:start position:0%
+this like hero discussion. So this book
+had such a massive appeal in 40s or 50s
+
+ align:start position:0%
+had such a massive appeal in 40s or 50s
+ 
+
+ align:start position:0%
+had such a massive appeal in 40s or 50s
+or whenever it was published because it
+
+ align:start position:0%
+or whenever it was published because it
+ 
+
+ align:start position:0%
+or whenever it was published because it
+empathized with this unsung hero of
+
+ align:start position:0%
+empathized with this unsung hero of
+ 
+
+ align:start position:0%
+empathized with this unsung hero of
+World War I. Sure. But then why does it
+
+ align:start position:0%
+World War I. Sure. But then why does it
+ 
+
+ align:start position:0%
+World War I. Sure. But then why does it
+have such a wide appeal to us now? And I
+
+ align:start position:0%
+have such a wide appeal to us now? And I
+ 
+
+ align:start position:0%
+have such a wide appeal to us now? And I
+think I'd like to make the contention
+
+ align:start position:0%
+think I'd like to make the contention
+ 
+
+ align:start position:0%
+think I'd like to make the contention
+that it has such a wide appeal because
+
+ align:start position:0%
+that it has such a wide appeal because
+ 
+
+ align:start position:0%
+that it has such a wide appeal because
+like in today's society we don't really
+
+ align:start position:0%
+like in today's society we don't really
+ 
+
+ align:start position:0%
+like in today's society we don't really
+have heroes anymore. And we have to
+
+ align:start position:0%
+have heroes anymore. And we have to
+ 
+
+ align:start position:0%
+have heroes anymore. And we have to
+invent them either like you we we look
+
+ align:start position:0%
+invent them either like you we we look
+ 
+
+ align:start position:0%
+invent them either like you we we look
+for them in fiction because what's like
+
+ align:start position:0%
+for them in fiction because what's like
+ 
+
+ align:start position:0%
+for them in fiction because what's like
+the hero today like Michael Jordan you
+
+ align:start position:0%
+the hero today like Michael Jordan you
+ 
+
+ align:start position:0%
+the hero today like Michael Jordan you
+know like we it's athletes there's no
+
+ align:start position:0%
+know like we it's athletes there's no
+ 
+
+ align:start position:0%
+know like we it's athletes there's no
+what's a societal hero today like we
+
+ align:start position:0%
+what's a societal hero today like we
+ 
+
+ align:start position:0%
+what's a societal hero today like we
+really don't we don't really go around
+
+ align:start position:0%
+really don't we don't really go around
+ 
+
+ align:start position:0%
+really don't we don't really go around
+you said that with such contempt was
+
+ align:start position:0%
+you said that with such contempt was
+ 
+
+ align:start position:0%
+you said that with such contempt was
+wonderful
+
+ align:start position:0%
+wonderful
+ 
+
+ align:start position:0%
+wonderful
+like it's it's really striking like who
+
+ align:start position:0%
+like it's it's really striking like who
+ 
+
+ align:start position:0%
+like it's it's really striking like who
+do little children look up to I don't
+
+ align:start position:0%
+do little children look up to I don't
+ 
+
+ align:start position:0%
+do little children look up to I don't
+know I have no idea who was
+
+ align:start position:0%
+know I have no idea who was
+ 
+
+ align:start position:0%
+know I have no idea who was
+next Peter
+
+ align:start position:0%
+next Peter
+ 
+
+ align:start position:0%
+next Peter
+And how about that? I I do know my mom
+
+ align:start position:0%
+And how about that? I I do know my mom
+ 
+
+ align:start position:0%
+And how about that? I I do know my mom
+first read toolken and all those things
+
+ align:start position:0%
+first read toolken and all those things
+ 
+
+ align:start position:0%
+first read toolken and all those things
+like when she was in her 20s. Mhm. And
+
+ align:start position:0%
+like when she was in her 20s. Mhm. And
+ 
+
+ align:start position:0%
+like when she was in her 20s. Mhm. And
+when she first gave me the book, she was
+
+ align:start position:0%
+when she first gave me the book, she was
+ 
+
+ align:start position:0%
+when she first gave me the book, she was
+like, you know, when I first read these,
+
+ align:start position:0%
+like, you know, when I first read these,
+ 
+
+ align:start position:0%
+like, you know, when I first read these,
+I ended up living in Middle Earth for
+
+ align:start position:0%
+I ended up living in Middle Earth for
+ 
+
+ align:start position:0%
+I ended up living in Middle Earth for
+about 10 years.
+
+ align:start position:0%
+about 10 years.
+ 
+
+ align:start position:0%
+about 10 years.
+For for at least for that generation,
+
+ align:start position:0%
+For for at least for that generation,
+ 
+
+ align:start position:0%
+For for at least for that generation,
+for the 60s7s, their their the main
+
+ align:start position:0%
+for the 60s7s, their their the main
+ 
+
+ align:start position:0%
+for the 60s7s, their their the main
+appeal of the book was that he had
+
+ align:start position:0%
+appeal of the book was that he had
+ 
+
+ align:start position:0%
+appeal of the book was that he had
+created such a real world to them that
+
+ align:start position:0%
+created such a real world to them that
+ 
+
+ align:start position:0%
+created such a real world to them that
+they could actually imagine it being
+
+ align:start position:0%
+they could actually imagine it being
+ 
+
+ align:start position:0%
+they could actually imagine it being
+real, that it be that it became part of
+
+ align:start position:0%
+real, that it be that it became part of
+ 
+
+ align:start position:0%
+real, that it be that it became part of
+their lives. And that's why it it wasn't
+
+ align:start position:0%
+their lives. And that's why it it wasn't
+ 
+
+ align:start position:0%
+their lives. And that's why it it wasn't
+the heroes. It wasn't it wasn't the
+
+ align:start position:0%
+the heroes. It wasn't it wasn't the
+ 
+
+ align:start position:0%
+the heroes. It wasn't it wasn't the
+human part that made them that made them
+
+ align:start position:0%
+human part that made them that made them
+ 
+
+ align:start position:0%
+human part that made them that made them
+believe in that world so much. It was
+
+ align:start position:0%
+believe in that world so much. It was
+ 
+
+ align:start position:0%
+believe in that world so much. It was
+all the other it was all the things that
+
+ align:start position:0%
+all the other it was all the things that
+ 
+
+ align:start position:0%
+all the other it was all the things that
+weren't didn't don't actually exist. The
+
+ align:start position:0%
+weren't didn't don't actually exist. The
+ 
+
+ align:start position:0%
+weren't didn't don't actually exist. The
+hobbits and all these things
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+actually I know they don't really exist
+
+ align:start position:0%
+actually I know they don't really exist
+ 
+
+ align:start position:0%
+actually I know they don't really exist
+but they did exist in people's minds. He
+
+ align:start position:0%
+but they did exist in people's minds. He
+ 
+
+ align:start position:0%
+but they did exist in people's minds. He
+he created a history that may have been
+
+ align:start position:0%
+he created a history that may have been
+ 
+
+ align:start position:0%
+he created a history that may have been
+completely fiction, but it became but in
+
+ align:start position:0%
+completely fiction, but it became but in
+ 
+
+ align:start position:0%
+completely fiction, but it became but in
+a lot of people's minds it became true
+
+ align:start position:0%
+a lot of people's minds it became true
+ 
+
+ align:start position:0%
+a lot of people's minds it became true
+because it I think in part because when
+
+ align:start position:0%
+because it I think in part because when
+ 
+
+ align:start position:0%
+because it I think in part because when
+we went back earlier that he wrote it
+
+ align:start position:0%
+we went back earlier that he wrote it
+ 
+
+ align:start position:0%
+we went back earlier that he wrote it
+like a history text. Mhm.
+
+ align:start position:0%
+like a history text. Mhm.
+ 
+
+ align:start position:0%
+like a history text. Mhm.
+And I mean obviously one of the things
+
+ align:start position:0%
+And I mean obviously one of the things
+ 
+
+ align:start position:0%
+And I mean obviously one of the things
+that's going on here is the power of an
+
+ align:start position:0%
+that's going on here is the power of an
+ 
+
+ align:start position:0%
+that's going on here is the power of an
+exceedingly gifted writer. Oh, I I it's
+
+ align:start position:0%
+exceedingly gifted writer. Oh, I I it's
+ 
+
+ align:start position:0%
+exceedingly gifted writer. Oh, I I it's
+a contrast. Remember we read the unruded
+
+ align:start position:0%
+a contrast. Remember we read the unruded
+ 
+
+ align:start position:0%
+a contrast. Remember we read the unruded
+captive or Yeah. And I actually said
+
+ align:start position:0%
+captive or Yeah. And I actually said
+ 
+
+ align:start position:0%
+captive or Yeah. And I actually said
+then it was a fictional story that
+
+ align:start position:0%
+then it was a fictional story that
+ 
+
+ align:start position:0%
+then it was a fictional story that
+happened to be true in the way it was
+
+ align:start position:0%
+happened to be true in the way it was
+ 
+
+ align:start position:0%
+happened to be true in the way it was
+written. This is a this is a a fictional
+
+ align:start position:0%
+written. This is a this is a a fictional
+ 
+
+ align:start position:0%
+written. This is a this is a a fictional
+story. I mean this is a historical text
+
+ align:start position:0%
+story. I mean this is a historical text
+ 
+
+ align:start position:0%
+story. I mean this is a historical text
+that happens to be fiction, right? Okay.
+
+ align:start position:0%
+that happens to be fiction, right? Okay.
+ 
+
+ align:start position:0%
+that happens to be fiction, right? Okay.
+I mean I think that's actually I think
+
+ align:start position:0%
+I mean I think that's actually I think
+ 
+
+ align:start position:0%
+I mean I think that's actually I think
+that's actually something Tolken would
+
+ align:start position:0%
+that's actually something Tolken would
+ 
+
+ align:start position:0%
+that's actually something Tolken would
+have been very happy to hear. Um I don't
+
+ align:start position:0%
+have been very happy to hear. Um I don't
+ 
+
+ align:start position:0%
+have been very happy to hear. Um I don't
+even remember what I said. Peter, were
+
+ align:start position:0%
+even remember what I said. Peter, were
+ 
+
+ align:start position:0%
+even remember what I said. Peter, were
+you next? Okay. I can't really speak of
+
+ align:start position:0%
+you next? Okay. I can't really speak of
+ 
+
+ align:start position:0%
+you next? Okay. I can't really speak of
+Tolken as I said. But getting back to
+
+ align:start position:0%
+Tolken as I said. But getting back to
+ 
+
+ align:start position:0%
+Tolken as I said. But getting back to
+the hero discussion, I mean after World
+
+ align:start position:0%
+the hero discussion, I mean after World
+ 
+
+ align:start position:0%
+the hero discussion, I mean after World
+War I, you have you do have the
+
+ align:start position:0%
+War I, you have you do have the
+ 
+
+ align:start position:0%
+War I, you have you do have the
+invention of heroes. If you look at
+
+ align:start position:0%
+invention of heroes. If you look at
+ 
+
+ align:start position:0%
+invention of heroes. If you look at
+World War II, which is right before when
+
+ align:start position:0%
+World War II, which is right before when
+ 
+
+ align:start position:0%
+World War II, which is right before when
+I guess the Lord of the Rings comes out
+
+ align:start position:0%
+I guess the Lord of the Rings comes out
+ 
+
+ align:start position:0%
+I guess the Lord of the Rings comes out
+in the 50s, maybe. Yeah, early 50s. Um,
+
+ align:start position:0%
+in the 50s, maybe. Yeah, early 50s. Um,
+ 
+
+ align:start position:0%
+in the 50s, maybe. Yeah, early 50s. Um,
+who are the heroes on the Coppers of
+
+ align:start position:0%
+who are the heroes on the Coppers of
+ 
+
+ align:start position:0%
+who are the heroes on the Coppers of
+America, you have, you know, Rosie the
+
+ align:start position:0%
+America, you have, you know, Rosie the
+ 
+
+ align:start position:0%
+America, you have, you know, Rosie the
+Riveter? Is she a real person? No, she's
+
+ align:start position:0%
+Riveter? Is she a real person? No, she's
+ 
+
+ align:start position:0%
+Riveter? Is she a real person? No, she's
+this, you know, person that's been
+
+ align:start position:0%
+this, you know, person that's been
+ 
+
+ align:start position:0%
+this, you know, person that's been
+created as a as a sort of this is what
+
+ align:start position:0%
+created as a as a sort of this is what
+ 
+
+ align:start position:0%
+created as a as a sort of this is what
+you should be like. This is your hero.
+
+ align:start position:0%
+you should be like. This is your hero.
+ 
+
+ align:start position:0%
+you should be like. This is your hero.
+You don't you don't have real life
+
+ align:start position:0%
+You don't you don't have real life
+ 
+
+ align:start position:0%
+You don't you don't have real life
+heroes anymore. You have in the Soviet
+
+ align:start position:0%
+heroes anymore. You have in the Soviet
+ 
+
+ align:start position:0%
+heroes anymore. You have in the Soviet
+Union, you have people create I mean,
+
+ align:start position:0%
+Union, you have people create I mean,
+ 
+
+ align:start position:0%
+Union, you have people create I mean,
+it's a different culture. I mean it's a
+
+ align:start position:0%
+it's a different culture. I mean it's a
+ 
+
+ align:start position:0%
+it's a different culture. I mean it's a
+different political culture but you have
+
+ align:start position:0%
+different political culture but you have
+ 
+
+ align:start position:0%
+different political culture but you have
+um like an enemy at the gates which is
+
+ align:start position:0%
+um like an enemy at the gates which is
+ 
+
+ align:start position:0%
+um like an enemy at the gates which is
+based on a true story. You have I mean
+
+ align:start position:0%
+based on a true story. You have I mean
+ 
+
+ align:start position:0%
+based on a true story. You have I mean
+they really pump up Vitalisv as you know
+
+ align:start position:0%
+they really pump up Vitalisv as you know
+ 
+
+ align:start position:0%
+they really pump up Vitalisv as you know
+he is the hero of this war but nobody
+
+ align:start position:0%
+he is the hero of this war but nobody
+ 
+
+ align:start position:0%
+he is the hero of this war but nobody
+would have heard of him if he's not you
+
+ align:start position:0%
+would have heard of him if he's not you
+ 
+
+ align:start position:0%
+would have heard of him if he's not you
+know without propaganda. So I think that
+
+ align:start position:0%
+know without propaganda. So I think that
+ 
+
+ align:start position:0%
+know without propaganda. So I think that
+the creation of a hero in a society
+
+ align:start position:0%
+the creation of a hero in a society
+ 
+
+ align:start position:0%
+the creation of a hero in a society
+where the heroes are lacking is part of
+
+ align:start position:0%
+where the heroes are lacking is part of
+ 
+
+ align:start position:0%
+where the heroes are lacking is part of
+the appeal if I had read this book.
+
+ align:start position:0%
+the appeal if I had read this book.
+ 
+
+ align:start position:0%
+the appeal if I had read this book.
+Yeah. Okay. I it's a good point. The
+
+ align:start position:0%
+Yeah. Okay. I it's a good point. The
+ 
+
+ align:start position:0%
+Yeah. Okay. I it's a good point. The
+heroes are
+
+ align:start position:0%
+heroes are
+ 
+
+ align:start position:0%
+heroes are
+amalgams amalgamations. That's what I
+
+ align:start position:0%
+amalgams amalgamations. That's what I
+ 
+
+ align:start position:0%
+amalgams amalgamations. That's what I
+want to say of of lots of people who fit
+
+ align:start position:0%
+want to say of of lots of people who fit
+ 
+
+ align:start position:0%
+want to say of of lots of people who fit
+a type. And so in some sense, right,
+
+ align:start position:0%
+a type. And so in some sense, right,
+ 
+
+ align:start position:0%
+a type. And so in some sense, right,
+Froto and Sam are the quintessential
+
+ align:start position:0%
+Froto and Sam are the quintessential
+ 
+
+ align:start position:0%
+Froto and Sam are the quintessential
+friendship team. Honorable, true,
+
+ align:start position:0%
+friendship team. Honorable, true,
+ 
+
+ align:start position:0%
+friendship team. Honorable, true,
+steadfast, loyal. They don't have to be
+
+ align:start position:0%
+steadfast, loyal. They don't have to be
+ 
+
+ align:start position:0%
+steadfast, loyal. They don't have to be
+Froto and Sam real. They just have to be
+
+ align:start position:0%
+Froto and Sam real. They just have to be
+ 
+
+ align:start position:0%
+Froto and Sam real. They just have to be
+sort of the Froto Sam friendship type.
+
+ align:start position:0%
+sort of the Froto Sam friendship type.
+ 
+
+ align:start position:0%
+sort of the Froto Sam friendship type.
+And they can be heroic
+
+ align:start position:0%
+And they can be heroic
+ 
+
+ align:start position:0%
+And they can be heroic
+um without being
+
+ align:start position:0%
+um without being
+ 
+
+ align:start position:0%
+um without being
+individuated. I don't know if I'd want
+
+ align:start position:0%
+individuated. I don't know if I'd want
+ 
+
+ align:start position:0%
+individuated. I don't know if I'd want
+to stretch that too far. I think Ian,
+
+ align:start position:0%
+to stretch that too far. I think Ian,
+ 
+
+ align:start position:0%
+to stretch that too far. I think Ian,
+you were next. Um, I just want to make a
+
+ align:start position:0%
+you were next. Um, I just want to make a
+ 
+
+ align:start position:0%
+you were next. Um, I just want to make a
+comment. I think it's kind of funny that
+
+ align:start position:0%
+comment. I think it's kind of funny that
+ 
+
+ align:start position:0%
+comment. I think it's kind of funny that
+the part that he invented that that he
+
+ align:start position:0%
+the part that he invented that that he
+ 
+
+ align:start position:0%
+the part that he invented that that he
+didn't take from the medieval text was
+
+ align:start position:0%
+didn't take from the medieval text was
+ 
+
+ align:start position:0%
+didn't take from the medieval text was
+the the underdog, the unlikely hero.
+
+ align:start position:0%
+the the underdog, the unlikely hero.
+ 
+
+ align:start position:0%
+the the underdog, the unlikely hero.
+Mhm. And that's the part that that has
+
+ align:start position:0%
+Mhm. And that's the part that that has
+ 
+
+ align:start position:0%
+Mhm. And that's the part that that has
+lived on the most from his works cuz
+
+ align:start position:0%
+lived on the most from his works cuz
+ 
+
+ align:start position:0%
+lived on the most from his works cuz
+every sing I read so many fantasy books
+
+ align:start position:0%
+every sing I read so many fantasy books
+ 
+
+ align:start position:0%
+every sing I read so many fantasy books
+when I was when I was a kid and they're
+
+ align:start position:0%
+when I was when I was a kid and they're
+ 
+
+ align:start position:0%
+when I was when I was a kid and they're
+all about, you know, generally about
+
+ align:start position:0%
+all about, you know, generally about
+ 
+
+ align:start position:0%
+all about, you know, generally about
+when they're written for kids. Some
+
+ align:start position:0%
+when they're written for kids. Some
+ 
+
+ align:start position:0%
+when they're written for kids. Some
+young person who, you know, something
+
+ align:start position:0%
+young person who, you know, something
+ 
+
+ align:start position:0%
+young person who, you know, something
+something to do some extraordinary
+
+ align:start position:0%
+something to do some extraordinary
+ 
+
+ align:start position:0%
+something to do some extraordinary
+chance, you know, they save the world
+
+ align:start position:0%
+chance, you know, they save the world
+ 
+
+ align:start position:0%
+chance, you know, they save the world
+and that's what they're all about now.
+
+ align:start position:0%
+and that's what they're all about now.
+ 
+
+ align:start position:0%
+and that's what they're all about now.
+And because I mean I guess that that's I
+
+ align:start position:0%
+And because I mean I guess that that's I
+ 
+
+ align:start position:0%
+And because I mean I guess that that's I
+think part of why it has so much appeals
+
+ align:start position:0%
+think part of why it has so much appeals
+ 
+
+ align:start position:0%
+think part of why it has so much appeals
+because anyone can put themselves in
+
+ align:start position:0%
+because anyone can put themselves in
+ 
+
+ align:start position:0%
+because anyone can put themselves in
+their shoes. And it kind of makes me
+
+ align:start position:0%
+their shoes. And it kind of makes me
+ 
+
+ align:start position:0%
+their shoes. And it kind of makes me
+wonder why to the medievals that that
+
+ align:start position:0%
+wonder why to the medievals that that
+ 
+
+ align:start position:0%
+wonder why to the medievals that that
+didn't that didn't come about already.
+
+ align:start position:0%
+didn't that didn't come about already.
+ 
+
+ align:start position:0%
+didn't that didn't come about already.
+Why was Beaolf the to a peasant or I
+
+ align:start position:0%
+Why was Beaolf the to a peasant or I
+ 
+
+ align:start position:0%
+Why was Beaolf the to a peasant or I
+guess a peasant wouldn't be reading but
+
+ align:start position:0%
+guess a peasant wouldn't be reading but
+ 
+
+ align:start position:0%
+guess a peasant wouldn't be reading but
+even hearing it you know like even
+
+ align:start position:0%
+even hearing it you know like even
+ 
+
+ align:start position:0%
+even hearing it you know like even
+someone who would be told this story.
+
+ align:start position:0%
+someone who would be told this story.
+ 
+
+ align:start position:0%
+someone who would be told this story.
+Why is that so inspiring if you're never
+
+ align:start position:0%
+Why is that so inspiring if you're never
+ 
+
+ align:start position:0%
+Why is that so inspiring if you're never
+going to be able to do it? You know I'm
+
+ align:start position:0%
+going to be able to do it? You know I'm
+ 
+
+ align:start position:0%
+going to be able to do it? You know I'm
+never going to be like Beaolf because of
+
+ align:start position:0%
+never going to be like Beaolf because of
+ 
+
+ align:start position:0%
+never going to be like Beaolf because of
+who I am. Well, maybe your expectation
+
+ align:start position:0%
+who I am. Well, maybe your expectation
+ 
+
+ align:start position:0%
+who I am. Well, maybe your expectation
+isn't that you're the one who's going to
+
+ align:start position:0%
+isn't that you're the one who's going to
+ 
+
+ align:start position:0%
+isn't that you're the one who's going to
+do it. The story is appealing because
+
+ align:start position:0%
+do it. The story is appealing because
+ 
+
+ align:start position:0%
+do it. The story is appealing because
+somebody's going to take care of you.
+
+ align:start position:0%
+somebody's going to take care of you.
+ 
+
+ align:start position:0%
+somebody's going to take care of you.
+That's I mean I mean, why is Bea Wolf
+
+ align:start position:0%
+That's I mean I mean, why is Bea Wolf
+ 
+
+ align:start position:0%
+That's I mean I mean, why is Bea Wolf
+great, right? Okay. He goes first to um
+
+ align:start position:0%
+great, right? Okay. He goes first to um
+ 
+
+ align:start position:0%
+great, right? Okay. He goes first to um
+uh to the land of the Danes to rescue
+
+ align:start position:0%
+uh to the land of the Danes to rescue
+ 
+
+ align:start position:0%
+uh to the land of the Danes to rescue
+them from their little monster problem,
+
+ align:start position:0%
+them from their little monster problem,
+ 
+
+ align:start position:0%
+them from their little monster problem,
+kills Grenle. Then it turns out there's
+
+ align:start position:0%
+kills Grenle. Then it turns out there's
+ 
+
+ align:start position:0%
+kills Grenle. Then it turns out there's
+Grenle's mother, right? And she has to
+
+ align:start position:0%
+Grenle's mother, right? And she has to
+ 
+
+ align:start position:0%
+Grenle's mother, right? And she has to
+be dealt with. So he goes to the depths
+
+ align:start position:0%
+be dealt with. So he goes to the depths
+ 
+
+ align:start position:0%
+be dealt with. So he goes to the depths
+of the sea and fights Grenle's mother,
+
+ align:start position:0%
+of the sea and fights Grenle's mother,
+ 
+
+ align:start position:0%
+of the sea and fights Grenle's mother,
+right? Somehow amazingly not needing
+
+ align:start position:0%
+right? Somehow amazingly not needing
+ 
+
+ align:start position:0%
+right? Somehow amazingly not needing
+oxygen for an extended period of time
+
+ align:start position:0%
+oxygen for an extended period of time
+ 
+
+ align:start position:0%
+oxygen for an extended period of time
+while fighting and swinging a sword and
+
+ align:start position:0%
+while fighting and swinging a sword and
+ 
+
+ align:start position:0%
+while fighting and swinging a sword and
+swinging a club and all this other
+
+ align:start position:0%
+swinging a club and all this other
+ 
+
+ align:start position:0%
+swinging a club and all this other
+stuff. Okay. Right. And then he comes
+
+ align:start position:0%
+stuff. Okay. Right. And then he comes
+ 
+
+ align:start position:0%
+stuff. Okay. Right. And then he comes
+back to Rothgra and says, "Look, okay,
+
+ align:start position:0%
+back to Rothgra and says, "Look, okay,
+ 
+
+ align:start position:0%
+back to Rothgra and says, "Look, okay,
+monster problem solved." And he is he is
+
+ align:start position:0%
+monster problem solved." And he is he is
+ 
+
+ align:start position:0%
+monster problem solved." And he is he is
+gifted, right? that is the gifts of gold
+
+ align:start position:0%
+gifted, right? that is the gifts of gold
+ 
+
+ align:start position:0%
+gifted, right? that is the gifts of gold
+and so forth that are due to the warrior
+
+ align:start position:0%
+and so forth that are due to the warrior
+ 
+
+ align:start position:0%
+and so forth that are due to the warrior
+who has who has um proved himself in
+
+ align:start position:0%
+who has who has um proved himself in
+ 
+
+ align:start position:0%
+who has who has um proved himself in
+battle are all are all given and and
+
+ align:start position:0%
+battle are all are all given and and
+ 
+
+ align:start position:0%
+battle are all are all given and and
+Hothgar is actually a little nervous
+
+ align:start position:0%
+Hothgar is actually a little nervous
+ 
+
+ align:start position:0%
+Hothgar is actually a little nervous
+that Bale wolf's going to want more but
+
+ align:start position:0%
+that Bale wolf's going to want more but
+ 
+
+ align:start position:0%
+that Bale wolf's going to want more but
+he doesn't okay I'm ready to go now back
+
+ align:start position:0%
+he doesn't okay I'm ready to go now back
+ 
+
+ align:start position:0%
+he doesn't okay I'm ready to go now back
+to the land of the gats right he heads
+
+ align:start position:0%
+to the land of the gats right he heads
+ 
+
+ align:start position:0%
+to the land of the gats right he heads
+home and his uncle is still king and he
+
+ align:start position:0%
+home and his uncle is still king and he
+ 
+
+ align:start position:0%
+home and his uncle is still king and he
+reports what he's done and his uncle
+
+ align:start position:0%
+reports what he's done and his uncle
+ 
+
+ align:start position:0%
+reports what he's done and his uncle
+basically says says, "Excellent, right?
+
+ align:start position:0%
+basically says says, "Excellent, right?
+ 
+
+ align:start position:0%
+basically says says, "Excellent, right?
+That's what you should be doing." Um,
+
+ align:start position:0%
+That's what you should be doing." Um,
+ 
+
+ align:start position:0%
+That's what you should be doing." Um,
+and and sure enough, when his uncle
+
+ align:start position:0%
+and and sure enough, when his uncle
+ 
+
+ align:start position:0%
+and and sure enough, when his uncle
+passes on, Beaowolf is made king. Then
+
+ align:start position:0%
+passes on, Beaowolf is made king. Then
+ 
+
+ align:start position:0%
+passes on, Beaowolf is made king. Then
+we fast forward 50 years to the second
+
+ align:start position:0%
+we fast forward 50 years to the second
+ 
+
+ align:start position:0%
+we fast forward 50 years to the second
+main part of the narrative. And we have
+
+ align:start position:0%
+main part of the narrative. And we have
+ 
+
+ align:start position:0%
+main part of the narrative. And we have
+now Beaolf's little monster problem
+
+ align:start position:0%
+now Beaolf's little monster problem
+ 
+
+ align:start position:0%
+now Beaolf's little monster problem
+turns out to be the dragon, right? The
+
+ align:start position:0%
+turns out to be the dragon, right? The
+ 
+
+ align:start position:0%
+turns out to be the dragon, right? The
+dragon is disturbed because somebody
+
+ align:start position:0%
+dragon is disturbed because somebody
+ 
+
+ align:start position:0%
+dragon is disturbed because somebody
+steals a cup. some dingbat who doesn't
+
+ align:start position:0%
+steals a cup. some dingbat who doesn't
+ 
+
+ align:start position:0%
+steals a cup. some dingbat who doesn't
+know that, you know, you steal a dragon,
+
+ align:start position:0%
+know that, you know, you steal a dragon,
+ 
+
+ align:start position:0%
+know that, you know, you steal a dragon,
+a cup, excuse me, from a sleeping dragon
+
+ align:start position:0%
+a cup, excuse me, from a sleeping dragon
+ 
+
+ align:start position:0%
+a cup, excuse me, from a sleeping dragon
+and they're going to know about it,
+
+ align:start position:0%
+and they're going to know about it,
+ 
+
+ align:start position:0%
+and they're going to know about it,
+right? Because they know where every
+
+ align:start position:0%
+right? Because they know where every
+ 
+
+ align:start position:0%
+right? Because they know where every
+last piece of their horde is and what it
+
+ align:start position:0%
+last piece of their horde is and what it
+ 
+
+ align:start position:0%
+last piece of their horde is and what it
+looks like and what it smells like and
+
+ align:start position:0%
+looks like and what it smells like and
+ 
+
+ align:start position:0%
+looks like and what it smells like and
+what it feels like. And if you take
+
+ align:start position:0%
+what it feels like. And if you take
+ 
+
+ align:start position:0%
+what it feels like. And if you take
+something from a dragon, even if he
+
+ align:start position:0%
+something from a dragon, even if he
+ 
+
+ align:start position:0%
+something from a dragon, even if he
+doesn't see you do it, he's going to
+
+ align:start position:0%
+doesn't see you do it, he's going to
+ 
+
+ align:start position:0%
+doesn't see you do it, he's going to
+know all about it. And our friend, the
+
+ align:start position:0%
+know all about it. And our friend, the
+ 
+
+ align:start position:0%
+know all about it. And our friend, the
+peasant, who steals the cup from him,
+
+ align:start position:0%
+peasant, who steals the cup from him,
+ 
+
+ align:start position:0%
+peasant, who steals the cup from him,
+doesn't know this. And then he presents
+
+ align:start position:0%
+doesn't know this. And then he presents
+ 
+
+ align:start position:0%
+doesn't know this. And then he presents
+himself to Beaowolf and says, "Guess
+
+ align:start position:0%
+himself to Beaowolf and says, "Guess
+ 
+
+ align:start position:0%
+himself to Beaowolf and says, "Guess
+what? You have a problem. I've upset a
+
+ align:start position:0%
+what? You have a problem. I've upset a
+ 
+
+ align:start position:0%
+what? You have a problem. I've upset a
+dragon, right? And so Beaolf then has to
+
+ align:start position:0%
+dragon, right? And so Beaolf then has to
+ 
+
+ align:start position:0%
+dragon, right? And so Beaolf then has to
+go and fight the dragon.
+
+ align:start position:0%
+go and fight the dragon.
+ 
+
+ align:start position:0%
+go and fight the dragon.
+Um, if you're a
+
+ align:start position:0%
+Um, if you're a
+ 
+
+ align:start position:0%
+Um, if you're a
+peasant, you don't necessarily want to
+
+ align:start position:0%
+peasant, you don't necessarily want to
+ 
+
+ align:start position:0%
+peasant, you don't necessarily want to
+be
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Beaowolf, right? It's not a good job
+
+ align:start position:0%
+Beaowolf, right? It's not a good job
+ 
+
+ align:start position:0%
+Beaowolf, right? It's not a good job
+description. In fact, doom is certain.
+
+ align:start position:0%
+description. In fact, doom is certain.
+ 
+
+ align:start position:0%
+description. In fact, doom is certain.
+We know that from the very beginning of
+
+ align:start position:0%
+We know that from the very beginning of
+ 
+
+ align:start position:0%
+We know that from the very beginning of
+the poem, and we're told over and over
+
+ align:start position:0%
+the poem, and we're told over and over
+ 
+
+ align:start position:0%
+the poem, and we're told over and over
+and over and over again, right? Beaolf's
+
+ align:start position:0%
+and over and over again, right? Beaolf's
+ 
+
+ align:start position:0%
+and over and over again, right? Beaolf's
+day is coming. And and I actually want
+
+ align:start position:0%
+day is coming. And and I actually want
+ 
+
+ align:start position:0%
+day is coming. And and I actually want
+to read a little bit past that passage
+
+ align:start position:0%
+to read a little bit past that passage
+ 
+
+ align:start position:0%
+to read a little bit past that passage
+that I read to you before because
+
+ align:start position:0%
+that I read to you before because
+ 
+
+ align:start position:0%
+that I read to you before because
+because it's easy to think of Beaowolf
+
+ align:start position:0%
+because it's easy to think of Beaowolf
+ 
+
+ align:start position:0%
+because it's easy to think of Beaowolf
+as the hero, but the anti-hero is here
+
+ align:start position:0%
+as the hero, but the anti-hero is here
+ 
+
+ align:start position:0%
+as the hero, but the anti-hero is here
+also.
+
+ align:start position:0%
+also.
+ 
+
+ align:start position:0%
+also.
+Um what came about brought to nothing
+
+ align:start position:0%
+Um what came about brought to nothing
+ 
+
+ align:start position:0%
+Um what came about brought to nothing
+the hopes of the one who had wrongly
+
+ align:start position:0%
+the hopes of the one who had wrongly
+ 
+
+ align:start position:0%
+the hopes of the one who had wrongly
+hidden riches under the rockface. First,
+
+ align:start position:0%
+hidden riches under the rockface. First,
+ 
+
+ align:start position:0%
+hidden riches under the rockface. First,
+the dragon slew that man among men, who
+
+ align:start position:0%
+the dragon slew that man among men, who
+ 
+
+ align:start position:0%
+the dragon slew that man among men, who
+in turn made fearsome amends and settled
+
+ align:start position:0%
+in turn made fearsome amends and settled
+ 
+
+ align:start position:0%
+in turn made fearsome amends and settled
+the feud. Famous for his deeds, a
+
+ align:start position:0%
+the feud. Famous for his deeds, a
+ 
+
+ align:start position:0%
+the feud. Famous for his deeds, a
+warrior may be, but it remains a mystery
+
+ align:start position:0%
+warrior may be, but it remains a mystery
+ 
+
+ align:start position:0%
+warrior may be, but it remains a mystery
+where his life will end when he may no
+
+ align:start position:0%
+where his life will end when he may no
+ 
+
+ align:start position:0%
+where his life will end when he may no
+longer dwell in the meatall among his
+
+ align:start position:0%
+longer dwell in the meatall among his
+ 
+
+ align:start position:0%
+longer dwell in the meatall among his
+own. So it was with Beaolf, when he
+
+ align:start position:0%
+own. So it was with Beaolf, when he
+ 
+
+ align:start position:0%
+own. So it was with Beaolf, when he
+faced the cruelty and cunning of the
+
+ align:start position:0%
+faced the cruelty and cunning of the
+ 
+
+ align:start position:0%
+faced the cruelty and cunning of the
+mound guard, that's the dragon. He
+
+ align:start position:0%
+mound guard, that's the dragon. He
+ 
+
+ align:start position:0%
+mound guard, that's the dragon. He
+himself was ignorant of how his
+
+ align:start position:0%
+himself was ignorant of how his
+ 
+
+ align:start position:0%
+himself was ignorant of how his
+departure from the world would happen.
+
+ align:start position:0%
+departure from the world would happen.
+ 
+
+ align:start position:0%
+departure from the world would happen.
+The highborn chiefs who had buried the
+
+ align:start position:0%
+The highborn chiefs who had buried the
+ 
+
+ align:start position:0%
+The highborn chiefs who had buried the
+treasure declared it until doomsday so a
+
+ align:start position:0%
+treasure declared it until doomsday so a
+ 
+
+ align:start position:0%
+treasure declared it until doomsday so a
+cursed that whoever robbed it would be
+
+ align:start position:0%
+cursed that whoever robbed it would be
+ 
+
+ align:start position:0%
+cursed that whoever robbed it would be
+guilty of wrong and grimly punished for
+
+ align:start position:0%
+guilty of wrong and grimly punished for
+ 
+
+ align:start position:0%
+guilty of wrong and grimly punished for
+their transgression hasped in hell
+
+ align:start position:0%
+their transgression hasped in hell
+ 
+
+ align:start position:0%
+their transgression hasped in hell
+bounds in heathen shrines. Yet Baolf's
+
+ align:start position:0%
+bounds in heathen shrines. Yet Baolf's
+ 
+
+ align:start position:0%
+bounds in heathen shrines. Yet Baolf's
+gaze at the gold treasure when he first
+
+ align:start position:0%
+gaze at the gold treasure when he first
+ 
+
+ align:start position:0%
+gaze at the gold treasure when he first
+saw it had not been selfish.
+
+ align:start position:0%
+saw it had not been selfish.
+ 
+
+ align:start position:0%
+saw it had not been selfish.
+Um, there's a lot of complicated stuff
+
+ align:start position:0%
+Um, there's a lot of complicated stuff
+ 
+
+ align:start position:0%
+Um, there's a lot of complicated stuff
+going on in this passage, but the gist
+
+ align:start position:0%
+going on in this passage, but the gist
+ 
+
+ align:start position:0%
+going on in this passage, but the gist
+of it
+
+ align:start position:0%
+of it
+ 
+
+ align:start position:0%
+of it
+is it remains a mystery where Bea Wolf's
+
+ align:start position:0%
+is it remains a mystery where Bea Wolf's
+ 
+
+ align:start position:0%
+is it remains a mystery where Bea Wolf's
+life will end. This is a little bit
+
+ align:start position:0%
+life will end. This is a little bit
+ 
+
+ align:start position:0%
+life will end. This is a little bit
+anti-heroic. I mean, after
+
+ align:start position:0%
+anti-heroic. I mean, after
+ 
+
+ align:start position:0%
+anti-heroic. I mean, after
+all, he is going to die looking on that
+
+ align:start position:0%
+all, he is going to die looking on that
+ 
+
+ align:start position:0%
+all, he is going to die looking on that
+treasure. He's got the treasure, but not
+
+ align:start position:0%
+treasure. He's got the treasure, but not
+ 
+
+ align:start position:0%
+treasure. He's got the treasure, but not
+for long. And and in fact the whailing
+
+ align:start position:0%
+for long. And and in fact the whailing
+ 
+
+ align:start position:0%
+for long. And and in fact the whailing
+woman at the very end of the poem, her
+
+ align:start position:0%
+woman at the very end of the poem, her
+ 
+
+ align:start position:0%
+woman at the very end of the poem, her
+lamentation is we're
+
+ align:start position:0%
+lamentation is we're
+ 
+
+ align:start position:0%
+lamentation is we're
+doomed because now all the other feuds
+
+ align:start position:0%
+doomed because now all the other feuds
+ 
+
+ align:start position:0%
+doomed because now all the other feuds
+that have been kept at bay because
+
+ align:start position:0%
+that have been kept at bay because
+ 
+
+ align:start position:0%
+that have been kept at bay because
+Beaolf was so big and strong are now all
+
+ align:start position:0%
+Beaolf was so big and strong are now all
+ 
+
+ align:start position:0%
+Beaolf was so big and strong are now all
+going to resurface, right? The Swedes
+
+ align:start position:0%
+going to resurface, right? The Swedes
+ 
+
+ align:start position:0%
+going to resurface, right? The Swedes
+are going to be coming because of this
+
+ align:start position:0%
+are going to be coming because of this
+ 
+
+ align:start position:0%
+are going to be coming because of this
+old feud and the Danes are going to be
+
+ align:start position:0%
+old feud and the Danes are going to be
+ 
+
+ align:start position:0%
+old feud and the Danes are going to be
+coming because of that old feud, right?
+
+ align:start position:0%
+coming because of that old feud, right?
+ 
+
+ align:start position:0%
+coming because of that old feud, right?
+And we're doomed without Beaowolf. We're
+
+ align:start position:0%
+And we're doomed without Beaowolf. We're
+ 
+
+ align:start position:0%
+And we're doomed without Beaowolf. We're
+all going to die. So in fact the final
+
+ align:start position:0%
+all going to die. So in fact the final
+ 
+
+ align:start position:0%
+all going to die. So in fact the final
+note of this is I think ultimately much
+
+ align:start position:0%
+note of this is I think ultimately much
+ 
+
+ align:start position:0%
+note of this is I think ultimately much
+more depressing even than the final note
+
+ align:start position:0%
+more depressing even than the final note
+ 
+
+ align:start position:0%
+more depressing even than the final note
+of the Shire uh which is that Froto has
+
+ align:start position:0%
+of the Shire uh which is that Froto has
+ 
+
+ align:start position:0%
+of the Shire uh which is that Froto has
+to leave right but it has been saved for
+
+ align:start position:0%
+to leave right but it has been saved for
+ 
+
+ align:start position:0%
+to leave right but it has been saved for
+everybody else. Yeah Miranda I mean I
+
+ align:start position:0%
+everybody else. Yeah Miranda I mean I
+ 
+
+ align:start position:0%
+everybody else. Yeah Miranda I mean I
+understand the underdog thing with you
+
+ align:start position:0%
+understand the underdog thing with you
+ 
+
+ align:start position:0%
+understand the underdog thing with you
+know life there's a lot of fantasy stuff
+
+ align:start position:0%
+know life there's a lot of fantasy stuff
+ 
+
+ align:start position:0%
+know life there's a lot of fantasy stuff
+where you know there's the underdog and
+
+ align:start position:0%
+where you know there's the underdog and
+ 
+
+ align:start position:0%
+where you know there's the underdog and
+you want to be them but do you really
+
+ align:start position:0%
+you want to be them but do you really
+ 
+
+ align:start position:0%
+you want to be them but do you really
+want to be Frodo? I mean, you see what
+
+ align:start position:0%
+want to be Frodo? I mean, you see what
+ 
+
+ align:start position:0%
+want to be Frodo? I mean, you see what
+happens to him. Not just, you know, all
+
+ align:start position:0%
+happens to him. Not just, you know, all
+ 
+
+ align:start position:0%
+happens to him. Not just, you know, all
+he does is go, you know, he doesn't get
+
+ align:start position:0%
+he does is go, you know, he doesn't get
+ 
+
+ align:start position:0%
+he does is go, you know, he doesn't get
+anything good with, you know, all he
+
+ align:start position:0%
+anything good with, you know, all he
+ 
+
+ align:start position:0%
+anything good with, you know, all he
+does is go through torments, go through
+
+ align:start position:0%
+does is go through torments, go through
+ 
+
+ align:start position:0%
+does is go through torments, go through
+pain, go, you know, he doesn't have
+
+ align:start position:0%
+pain, go, you know, he doesn't have
+ 
+
+ align:start position:0%
+pain, go, you know, he doesn't have
+anything good among this at all. And so,
+
+ align:start position:0%
+anything good among this at all. And so,
+ 
+
+ align:start position:0%
+anything good among this at all. And so,
+it's sort of not really someone you want
+
+ align:start position:0%
+it's sort of not really someone you want
+ 
+
+ align:start position:0%
+it's sort of not really someone you want
+to be. The other problem I have is I've
+
+ align:start position:0%
+to be. The other problem I have is I've
+ 
+
+ align:start position:0%
+to be. The other problem I have is I've
+heard the story of, you know, well, we
+
+ align:start position:0%
+heard the story of, you know, well, we
+ 
+
+ align:start position:0%
+heard the story of, you know, well, we
+don't have heroes nowadays ever anymore.
+
+ align:start position:0%
+don't have heroes nowadays ever anymore.
+ 
+
+ align:start position:0%
+don't have heroes nowadays ever anymore.
+How much did they have heroes back then
+
+ align:start position:0%
+How much did they have heroes back then
+ 
+
+ align:start position:0%
+How much did they have heroes back then
+either? I mean there's you know God is
+
+ align:start position:0%
+either? I mean there's you know God is
+ 
+
+ align:start position:0%
+either? I mean there's you know God is
+the you know a hero but is it always you
+
+ align:start position:0%
+the you know a hero but is it always you
+ 
+
+ align:start position:0%
+the you know a hero but is it always you
+know the hero is something that's past
+
+ align:start position:0%
+know the hero is something that's past
+ 
+
+ align:start position:0%
+know the hero is something that's past
+you know is always something you know
+
+ align:start position:0%
+you know is always something you know
+ 
+
+ align:start position:0%
+you know is always something you know
+there's Beaolf as the hero is there
+
+ align:start position:0%
+there's Beaolf as the hero is there
+ 
+
+ align:start position:0%
+there's Beaolf as the hero is there
+really you know at the time of Beaolf
+
+ align:start position:0%
+really you know at the time of Beaolf
+ 
+
+ align:start position:0%
+really you know at the time of Beaolf
+were there you know kings that were
+
+ align:start position:0%
+were there you know kings that were
+ 
+
+ align:start position:0%
+were there you know kings that were
+thought of as you are the hero you're
+
+ align:start position:0%
+thought of as you are the hero you're
+ 
+
+ align:start position:0%
+thought of as you are the hero you're
+completely you know stuff like that like
+
+ align:start position:0%
+completely you know stuff like that like
+ 
+
+ align:start position:0%
+completely you know stuff like that like
+has there always been you know well
+
+ align:start position:0%
+has there always been you know well
+ 
+
+ align:start position:0%
+has there always been you know well
+there's no heroes of our time there's
+
+ align:start position:0%
+there's no heroes of our time there's
+ 
+
+ align:start position:0%
+there's no heroes of our time there's
+only fictional ones I mean the king used
+
+ align:start position:0%
+only fictional ones I mean the king used
+ 
+
+ align:start position:0%
+only fictional ones I mean the king used
+to get on his horse and lead his troops
+
+ align:start position:0%
+to get on his horse and lead his troops
+ 
+
+ align:start position:0%
+to get on his horse and lead his troops
+into battle in the 30 years war I mean
+
+ align:start position:0%
+into battle in the 30 years war I mean
+ 
+
+ align:start position:0%
+into battle in the 30 years war I mean
+Gustavos Adulus led the Swedish troops
+
+ align:start position:0%
+Gustavos Adulus led the Swedish troops
+ 
+
+ align:start position:0%
+Gustavos Adulus led the Swedish troops
+and he died, you know, in battle and he
+
+ align:start position:0%
+and he died, you know, in battle and he
+ 
+
+ align:start position:0%
+and he died, you know, in battle and he
+didn't die in battle.
+
+ align:start position:0%
+didn't die in battle.
+ 
+
+ align:start position:0%
+didn't die in battle.
+Wait, didn't he die in battle? No, he
+
+ align:start position:0%
+Wait, didn't he die in battle? No, he
+ 
+
+ align:start position:0%
+Wait, didn't he die in battle? No, he
+died. Well, he won. Let's see. He won
+
+ align:start position:0%
+died. Well, he won. Let's see. He won
+ 
+
+ align:start position:0%
+died. Well, he won. Let's see. He won
+his battle and then he sort of meandered
+
+ align:start position:0%
+his battle and then he sort of meandered
+ 
+
+ align:start position:0%
+his battle and then he sort of meandered
+off into the woods from the camp later
+
+ align:start position:0%
+off into the woods from the camp later
+ 
+
+ align:start position:0%
+off into the woods from the camp later
+that day and got killed in the woods.
+
+ align:start position:0%
+that day and got killed in the woods.
+ 
+
+ align:start position:0%
+that day and got killed in the woods.
+So, that's kind of like dying in battle,
+
+ align:start position:0%
+So, that's kind of like dying in battle,
+ 
+
+ align:start position:0%
+So, that's kind of like dying in battle,
+but not exactly. Well, I mean, he's I
+
+ align:start position:0%
+but not exactly. Well, I mean, he's I
+ 
+
+ align:start position:0%
+but not exactly. Well, I mean, he's I
+mean, I went to Sweden. There's statues
+
+ align:start position:0%
+mean, I went to Sweden. There's statues
+ 
+
+ align:start position:0%
+mean, I went to Sweden. There's statues
+of a metal. I mean, he's venerated.
+
+ align:start position:0%
+of a metal. I mean, he's venerated.
+ 
+
+ align:start position:0%
+of a metal. I mean, he's venerated.
+Absolutely. But, I mean, absolutely.
+
+ align:start position:0%
+Absolutely. But, I mean, absolutely.
+ 
+
+ align:start position:0%
+Absolutely. But, I mean, absolutely.
+during the warfare was different back
+
+ align:start position:0%
+during the warfare was different back
+ 
+
+ align:start position:0%
+during the warfare was different back
+when you know Kings League crusades um
+
+ align:start position:0%
+when you know Kings League crusades um
+ 
+
+ align:start position:0%
+when you know Kings League crusades um
+you know I'm going to you know the the
+
+ align:start position:0%
+you know I'm going to you know the the
+ 
+
+ align:start position:0%
+you know I'm going to you know the the
+War of the Roses you know you got No for
+
+ align:start position:0%
+War of the Roses you know you got No for
+ 
+
+ align:start position:0%
+War of the Roses you know you got No for
+sure I mean Charlemagne campaigned
+
+ align:start position:0%
+sure I mean Charlemagne campaigned
+ 
+
+ align:start position:0%
+sure I mean Charlemagne campaigned
+against the Saxons for 30 straight
+
+ align:start position:0%
+against the Saxons for 30 straight
+ 
+
+ align:start position:0%
+against the Saxons for 30 straight
+summers and he did it right for 30
+
+ align:start position:0%
+summers and he did it right for 30
+ 
+
+ align:start position:0%
+summers and he did it right for 30
+straight summers
+
+ align:start position:0%
+straight summers
+ 
+
+ align:start position:0%
+straight summers
+even as just a national guard so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and he was a tall guy too. Um there I
+
+ align:start position:0%
+and he was a tall guy too. Um there I
+ 
+
+ align:start position:0%
+and he was a tall guy too. Um there I
+mean this this I think Annie you made
+
+ align:start position:0%
+mean this this I think Annie you made
+ 
+
+ align:start position:0%
+mean this this I think Annie you made
+this point a little earlier but at some
+
+ align:start position:0%
+this point a little earlier but at some
+ 
+
+ align:start position:0%
+this point a little earlier but at some
+point we have to get the Christianity
+
+ align:start position:0%
+point we have to get the Christianity
+ 
+
+ align:start position:0%
+point we have to get the Christianity
+back in right because that mean
+
+ align:start position:0%
+back in right because that mean
+ 
+
+ align:start position:0%
+back in right because that mean
+obviously in in Beaowolf that's a
+
+ align:start position:0%
+obviously in in Beaowolf that's a
+ 
+
+ align:start position:0%
+obviously in in Beaowolf that's a
+critical piece right the author of the
+
+ align:start position:0%
+critical piece right the author of the
+ 
+
+ align:start position:0%
+critical piece right the author of the
+poem the text is
+
+ align:start position:0%
+poem the text is
+ 
+
+ align:start position:0%
+poem the text is
+Christian the text is um is a presumably
+
+ align:start position:0%
+Christian the text is um is a presumably
+ 
+
+ align:start position:0%
+Christian the text is um is a presumably
+oral tradition story that is not
+
+ align:start position:0%
+oral tradition story that is not
+ 
+
+ align:start position:0%
+oral tradition story that is not
+Christian. There's no ambiguity. Beyolf
+
+ align:start position:0%
+Christian. There's no ambiguity. Beyolf
+ 
+
+ align:start position:0%
+Christian. There's no ambiguity. Beyolf
+isn't ever um misunderstanding himself
+
+ align:start position:0%
+isn't ever um misunderstanding himself
+ 
+
+ align:start position:0%
+isn't ever um misunderstanding himself
+to be a Christian, right? He's very
+
+ align:start position:0%
+to be a Christian, right? He's very
+ 
+
+ align:start position:0%
+to be a Christian, right? He's very
+clear about who he is, but the author of
+
+ align:start position:0%
+clear about who he is, but the author of
+ 
+
+ align:start position:0%
+clear about who he is, but the author of
+the poem, our writer is a Christian. And
+
+ align:start position:0%
+the poem, our writer is a Christian. And
+ 
+
+ align:start position:0%
+the poem, our writer is a Christian. And
+so this tension is just present all the
+
+ align:start position:0%
+so this tension is just present all the
+ 
+
+ align:start position:0%
+so this tension is just present all the
+way throughout. uh and and clearly for
+
+ align:start position:0%
+way throughout. uh and and clearly for
+ 
+
+ align:start position:0%
+way throughout. uh and and clearly for
+Tolken and Lewis both
+
+ align:start position:0%
+Tolken and Lewis both
+ 
+
+ align:start position:0%
+Tolken and Lewis both
+they're they're
+
+ align:start position:0%
+they're they're
+ 
+
+ align:start position:0%
+they're they're
+intense experiences with Christian
+
+ align:start position:0%
+intense experiences with Christian
+ 
+
+ align:start position:0%
+intense experiences with Christian
+theology, right? And in Lewis's case, I
+
+ align:start position:0%
+theology, right? And in Lewis's case, I
+ 
+
+ align:start position:0%
+theology, right? And in Lewis's case, I
+mean really intense, you know, he's I
+
+ align:start position:0%
+mean really intense, you know, he's I
+ 
+
+ align:start position:0%
+mean really intense, you know, he's I
+mean half of his output is
+
+ align:start position:0%
+mean half of his output is
+ 
+
+ align:start position:0%
+mean half of his output is
+apologetics, right? He's not just a, you
+
+ align:start position:0%
+apologetics, right? He's not just a, you
+ 
+
+ align:start position:0%
+apologetics, right? He's not just a, you
+know, kind of an accidental Christian.
+
+ align:start position:0%
+know, kind of an accidental Christian.
+ 
+
+ align:start position:0%
+know, kind of an accidental Christian.
+He's a really serious serious one. And I
+
+ align:start position:0%
+He's a really serious serious one. And I
+ 
+
+ align:start position:0%
+He's a really serious serious one. And I
+mean, and so and so is Tolken, but but
+
+ align:start position:0%
+mean, and so and so is Tolken, but but
+ 
+
+ align:start position:0%
+mean, and so and so is Tolken, but but
+not in the sense that he's actually
+
+ align:start position:0%
+not in the sense that he's actually
+ 
+
+ align:start position:0%
+not in the sense that he's actually
+writing apologetics. Uh but but for both
+
+ align:start position:0%
+writing apologetics. Uh but but for both
+ 
+
+ align:start position:0%
+writing apologetics. Uh but but for both
+of these men uh whatever it was they
+
+ align:start position:0%
+of these men uh whatever it was they
+ 
+
+ align:start position:0%
+of these men uh whatever it was they
+were picking up from the past then had
+
+ align:start position:0%
+were picking up from the past then had
+ 
+
+ align:start position:0%
+were picking up from the past then had
+to be tempered by by what they believe
+
+ align:start position:0%
+to be tempered by by what they believe
+ 
+
+ align:start position:0%
+to be tempered by by what they believe
+to be truth, right? With a capital
+
+ align:start position:0%
+to be truth, right? With a capital
+ 
+
+ align:start position:0%
+to be truth, right? With a capital
+T, you know, getting back to that math
+
+ align:start position:0%
+T, you know, getting back to that math
+ 
+
+ align:start position:0%
+T, you know, getting back to that math
+problem. Um and and let me let me read
+
+ align:start position:0%
+problem. Um and and let me let me read
+ 
+
+ align:start position:0%
+problem. Um and and let me let me read
+you one other source that you probably
+
+ align:start position:0%
+you one other source that you probably
+ 
+
+ align:start position:0%
+you one other source that you probably
+don't just sort of have rolling around
+
+ align:start position:0%
+don't just sort of have rolling around
+ 
+
+ align:start position:0%
+don't just sort of have rolling around
+in your head.
+
+ align:start position:0%
+in your head.
+ 
+
+ align:start position:0%
+in your head.
+Um that has to do with this problem of
+
+ align:start position:0%
+Um that has to do with this problem of
+ 
+
+ align:start position:0%
+Um that has to do with this problem of
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+warrior. Um this is uh the venerable
+
+ align:start position:0%
+warrior. Um this is uh the venerable
+ 
+
+ align:start position:0%
+warrior. Um this is uh the venerable
+bead as they call him his ecclesiastical
+
+ align:start position:0%
+bead as they call him his ecclesiastical
+ 
+
+ align:start position:0%
+bead as they call him his ecclesiastical
+history of the English people. It's a um
+
+ align:start position:0%
+history of the English people. It's a um
+ 
+
+ align:start position:0%
+history of the English people. It's a um
+early 8th century text to be a little
+
+ align:start position:0%
+early 8th century text to be a little
+ 
+
+ align:start position:0%
+early 8th century text to be a little
+bit ahead of the probably depending on
+
+ align:start position:0%
+bit ahead of the probably depending on
+ 
+
+ align:start position:0%
+bit ahead of the probably depending on
+how we date beolf a little bit ahead of
+
+ align:start position:0%
+how we date beolf a little bit ahead of
+ 
+
+ align:start position:0%
+how we date beolf a little bit ahead of
+the writing of Beaolf but you know in
+
+ align:start position:0%
+the writing of Beaolf but you know in
+ 
+
+ align:start position:0%
+the writing of Beaolf but you know in
+that in that Anglo-Saxon world. And this
+
+ align:start position:0%
+that in that Anglo-Saxon world. And this
+ 
+
+ align:start position:0%
+that in that Anglo-Saxon world. And this
+is Bead's
+
+ align:start position:0%
+is Bead's
+ 
+
+ align:start position:0%
+is Bead's
+story about how Edwin of North Umbrea is
+
+ align:start position:0%
+story about how Edwin of North Umbrea is
+ 
+
+ align:start position:0%
+story about how Edwin of North Umbrea is
+converted to Christianity.
+
+ align:start position:0%
+converted to Christianity.
+ 
+
+ align:start position:0%
+converted to Christianity.
+Okay. So Edwin holds a council um the
+
+ align:start position:0%
+Okay. So Edwin holds a council um the
+ 
+
+ align:start position:0%
+Okay. So Edwin holds a council um the
+king answered when he's he's listening
+
+ align:start position:0%
+king answered when he's he's listening
+ 
+
+ align:start position:0%
+king answered when he's he's listening
+to a priest um that it was his will as
+
+ align:start position:0%
+to a priest um that it was his will as
+ 
+
+ align:start position:0%
+to a priest um that it was his will as
+well as his duty to accept the faith
+
+ align:start position:0%
+well as his duty to accept the faith
+ 
+
+ align:start position:0%
+well as his duty to accept the faith
+that Paulus that's the priest taught but
+
+ align:start position:0%
+that Paulus that's the priest taught but
+ 
+
+ align:start position:0%
+that Paulus that's the priest taught but
+said that he must first still discuss
+
+ align:start position:0%
+said that he must first still discuss
+ 
+
+ align:start position:0%
+said that he must first still discuss
+the matter with his principal adviserss
+
+ align:start position:0%
+the matter with his principal adviserss
+ 
+
+ align:start position:0%
+the matter with his principal adviserss
+and friends. Right? Right. So, this is
+
+ align:start position:0%
+and friends. Right? Right. So, this is
+ 
+
+ align:start position:0%
+and friends. Right? Right. So, this is
+the Anglo-Saxon mode. He's got to call
+
+ align:start position:0%
+the Anglo-Saxon mode. He's got to call
+ 
+
+ align:start position:0%
+the Anglo-Saxon mode. He's got to call
+his things together. They're going to
+
+ align:start position:0%
+his things together. They're going to
+ 
+
+ align:start position:0%
+his things together. They're going to
+talk about this. So, I'm persuaded
+
+ align:start position:0%
+talk about this. So, I'm persuaded
+ 
+
+ align:start position:0%
+talk about this. So, I'm persuaded
+that's all well and good, but we're not
+
+ align:start position:0%
+that's all well and good, but we're not
+ 
+
+ align:start position:0%
+that's all well and good, but we're not
+going to be Christians unless we're all
+
+ align:start position:0%
+going to be Christians unless we're all
+ 
+
+ align:start position:0%
+going to be Christians unless we're all
+going to do it together. The the Clovis
+
+ align:start position:0%
+going to do it together. The the Clovis
+ 
+
+ align:start position:0%
+going to do it together. The the Clovis
+conversion story is exactly the same.
+
+ align:start position:0%
+conversion story is exactly the same.
+ 
+
+ align:start position:0%
+conversion story is exactly the same.
+Um, if you've read Gregory of Tour's
+
+ align:start position:0%
+Um, if you've read Gregory of Tour's
+ 
+
+ align:start position:0%
+Um, if you've read Gregory of Tour's
+History of the Franks, okay? So, that if
+
+ align:start position:0%
+History of the Franks, okay? So, that if
+ 
+
+ align:start position:0%
+History of the Franks, okay? So, that if
+they were all in agreement, they might
+
+ align:start position:0%
+they were all in agreement, they might
+ 
+
+ align:start position:0%
+they were all in agreement, they might
+all be cleansed together in Christ. Paul
+
+ align:start position:0%
+all be cleansed together in Christ. Paul
+ 
+
+ align:start position:0%
+all be cleansed together in Christ. Paul
+agrees. The king keeps his promise. He
+
+ align:start position:0%
+agrees. The king keeps his promise. He
+ 
+
+ align:start position:0%
+agrees. The king keeps his promise. He
+summons the council. Okay? and he asks
+
+ align:start position:0%
+summons the council. Okay? and he asks
+ 
+
+ align:start position:0%
+summons the council. Okay? and he asks
+them, "What do you think of this strange
+
+ align:start position:0%
+them, "What do you think of this strange
+ 
+
+ align:start position:0%
+them, "What do you think of this strange
+doctrine and this new way of worshiping
+
+ align:start position:0%
+doctrine and this new way of worshiping
+ 
+
+ align:start position:0%
+doctrine and this new way of worshiping
+the godhead that is being proclaimed to
+
+ align:start position:0%
+the godhead that is being proclaimed to
+ 
+
+ align:start position:0%
+the godhead that is being proclaimed to
+us?" Kofi, the chief priest, replied
+
+ align:start position:0%
+us?" Kofi, the chief priest, replied
+ 
+
+ align:start position:0%
+us?" Kofi, the chief priest, replied
+without hesitation. Now, this is quite a
+
+ align:start position:0%
+without hesitation. Now, this is quite a
+ 
+
+ align:start position:0%
+without hesitation. Now, this is quite a
+wild speech, thinking this is the pagan
+
+ align:start position:0%
+wild speech, thinking this is the pagan
+ 
+
+ align:start position:0%
+wild speech, thinking this is the pagan
+chief priest, mind you. Your majesty,
+
+ align:start position:0%
+chief priest, mind you. Your majesty,
+ 
+
+ align:start position:0%
+chief priest, mind you. Your majesty,
+let us give careful consideration to
+
+ align:start position:0%
+let us give careful consideration to
+ 
+
+ align:start position:0%
+let us give careful consideration to
+this new teaching, for I frankly admit
+
+ align:start position:0%
+this new teaching, for I frankly admit
+ 
+
+ align:start position:0%
+this new teaching, for I frankly admit
+that in my experience, the religion that
+
+ align:start position:0%
+that in my experience, the religion that
+ 
+
+ align:start position:0%
+that in my experience, the religion that
+we have hitherto professed seems
+
+ align:start position:0%
+we have hitherto professed seems
+ 
+
+ align:start position:0%
+we have hitherto professed seems
+valueless and powerless. None of your
+
+ align:start position:0%
+valueless and powerless. None of your
+ 
+
+ align:start position:0%
+valueless and powerless. None of your
+subjects has been more devoted to the
+
+ align:start position:0%
+subjects has been more devoted to the
+ 
+
+ align:start position:0%
+subjects has been more devoted to the
+service of our gods than myself. Yet
+
+ align:start position:0%
+service of our gods than myself. Yet
+ 
+
+ align:start position:0%
+service of our gods than myself. Yet
+there are many to whom you show greater
+
+ align:start position:0%
+there are many to whom you show greater
+ 
+
+ align:start position:0%
+there are many to whom you show greater
+favor, who receive greater honors, and
+
+ align:start position:0%
+favor, who receive greater honors, and
+ 
+
+ align:start position:0%
+favor, who receive greater honors, and
+who are more successful. Now, if the
+
+ align:start position:0%
+who are more successful. Now, if the
+ 
+
+ align:start position:0%
+who are more successful. Now, if the
+gods had any power, they would surely
+
+ align:start position:0%
+gods had any power, they would surely
+ 
+
+ align:start position:0%
+gods had any power, they would surely
+have favored myself, who have been more
+
+ align:start position:0%
+have favored myself, who have been more
+ 
+
+ align:start position:0%
+have favored myself, who have been more
+zealous in their service. Therefore, I
+
+ align:start position:0%
+zealous in their service. Therefore, I
+ 
+
+ align:start position:0%
+zealous in their service. Therefore, I
+love the therefore, you know, it all
+
+ align:start position:0%
+love the therefore, you know, it all
+ 
+
+ align:start position:0%
+love the therefore, you know, it all
+just follows logically. If on
+
+ align:start position:0%
+just follows logically. If on
+ 
+
+ align:start position:0%
+just follows logically. If on
+examination you perceive that these new
+
+ align:start position:0%
+examination you perceive that these new
+ 
+
+ align:start position:0%
+examination you perceive that these new
+teachings are better and more effectual,
+
+ align:start position:0%
+teachings are better and more effectual,
+ 
+
+ align:start position:0%
+teachings are better and more effectual,
+let us not hesitate to accept
+
+ align:start position:0%
+let us not hesitate to accept
+ 
+
+ align:start position:0%
+let us not hesitate to accept
+them. Okay? You know, we're all
+
+ align:start position:0%
+them. Okay? You know, we're all
+ 
+
+ align:start position:0%
+them. Okay? You know, we're all
+thinking, "Yeah, that's a likely story."
+
+ align:start position:0%
+thinking, "Yeah, that's a likely story."
+ 
+
+ align:start position:0%
+thinking, "Yeah, that's a likely story."
+Okay. Another of the king's chief men
+
+ align:start position:0%
+Okay. Another of the king's chief men
+ 
+
+ align:start position:0%
+Okay. Another of the king's chief men
+signified his agreement with this
+
+ align:start position:0%
+signified his agreement with this
+ 
+
+ align:start position:0%
+signified his agreement with this
+prudent argument and went on to say,
+
+ align:start position:0%
+prudent argument and went on to say,
+ 
+
+ align:start position:0%
+prudent argument and went on to say,
+"Your majesty, when we compare the
+
+ align:start position:0%
+"Your majesty, when we compare the
+ 
+
+ align:start position:0%
+"Your majesty, when we compare the
+present life of man on earth with that
+
+ align:start position:0%
+present life of man on earth with that
+ 
+
+ align:start position:0%
+present life of man on earth with that
+time of which we have no knowledge, it
+
+ align:start position:0%
+time of which we have no knowledge, it
+ 
+
+ align:start position:0%
+time of which we have no knowledge, it
+seems to me like the swift flight of a
+
+ align:start position:0%
+seems to me like the swift flight of a
+ 
+
+ align:start position:0%
+seems to me like the swift flight of a
+single sparrow through the banqueting
+
+ align:start position:0%
+single sparrow through the banqueting
+ 
+
+ align:start position:0%
+single sparrow through the banqueting
+hall where you are sitting at dinner on
+
+ align:start position:0%
+hall where you are sitting at dinner on
+ 
+
+ align:start position:0%
+hall where you are sitting at dinner on
+a winter's day with your fangs and
+
+ align:start position:0%
+a winter's day with your fangs and
+ 
+
+ align:start position:0%
+a winter's day with your fangs and
+counselors. In the midst there is a
+
+ align:start position:0%
+counselors. In the midst there is a
+ 
+
+ align:start position:0%
+counselors. In the midst there is a
+comforting fire to warm the hall.
+
+ align:start position:0%
+comforting fire to warm the hall.
+ 
+
+ align:start position:0%
+comforting fire to warm the hall.
+Outside the storms of winter rain or
+
+ align:start position:0%
+Outside the storms of winter rain or
+ 
+
+ align:start position:0%
+Outside the storms of winter rain or
+snow are raging. The sparrow flies
+
+ align:start position:0%
+snow are raging. The sparrow flies
+ 
+
+ align:start position:0%
+snow are raging. The sparrow flies
+swiftly in through one door of the hall
+
+ align:start position:0%
+swiftly in through one door of the hall
+ 
+
+ align:start position:0%
+swiftly in through one door of the hall
+and out through another. While he is
+
+ align:start position:0%
+and out through another. While he is
+ 
+
+ align:start position:0%
+and out through another. While he is
+inside, he is safe from the winter
+
+ align:start position:0%
+inside, he is safe from the winter
+ 
+
+ align:start position:0%
+inside, he is safe from the winter
+storms. But after a few moments of
+
+ align:start position:0%
+storms. But after a few moments of
+ 
+
+ align:start position:0%
+storms. But after a few moments of
+comfort, he vanishes from sight into the
+
+ align:start position:0%
+comfort, he vanishes from sight into the
+ 
+
+ align:start position:0%
+comfort, he vanishes from sight into the
+wintry world from which he came. Even
+
+ align:start position:0%
+wintry world from which he came. Even
+ 
+
+ align:start position:0%
+wintry world from which he came. Even
+so, man appears on earth for a little
+
+ align:start position:0%
+so, man appears on earth for a little
+ 
+
+ align:start position:0%
+so, man appears on earth for a little
+while. But of what went before this life
+
+ align:start position:0%
+while. But of what went before this life
+ 
+
+ align:start position:0%
+while. But of what went before this life
+or of what follows, we know nothing.
+
+ align:start position:0%
+or of what follows, we know nothing.
+ 
+
+ align:start position:0%
+or of what follows, we know nothing.
+Therefore, again, the logic is
+
+ align:start position:0%
+Therefore, again, the logic is
+ 
+
+ align:start position:0%
+Therefore, again, the logic is
+impeccable. If this new teaching has
+
+ align:start position:0%
+impeccable. If this new teaching has
+ 
+
+ align:start position:0%
+impeccable. If this new teaching has
+brought any more certain knowledge, it
+
+ align:start position:0%
+brought any more certain knowledge, it
+ 
+
+ align:start position:0%
+brought any more certain knowledge, it
+seems only right that we should follow
+
+ align:start position:0%
+seems only right that we should follow
+ 
+
+ align:start position:0%
+seems only right that we should follow
+it. I mean, it's a it's a fabulous
+
+ align:start position:0%
+it. I mean, it's a it's a fabulous
+ 
+
+ align:start position:0%
+it. I mean, it's a it's a fabulous
+story. Whether you believe that Edwin
+
+ align:start position:0%
+story. Whether you believe that Edwin
+ 
+
+ align:start position:0%
+story. Whether you believe that Edwin
+really threw a council and this is what
+
+ align:start position:0%
+really threw a council and this is what
+ 
+
+ align:start position:0%
+really threw a council and this is what
+these guys just spontaneously said, I
+
+ align:start position:0%
+these guys just spontaneously said, I
+ 
+
+ align:start position:0%
+these guys just spontaneously said, I
+don't know. But it parallels the Beaalth
+
+ align:start position:0%
+don't know. But it parallels the Beaalth
+ 
+
+ align:start position:0%
+don't know. But it parallels the Beaalth
+ending really well, right? What's going
+
+ align:start position:0%
+ending really well, right? What's going
+ 
+
+ align:start position:0%
+ending really well, right? What's going
+to happen when you pass out of your meat
+
+ align:start position:0%
+to happen when you pass out of your meat
+ 
+
+ align:start position:0%
+to happen when you pass out of your meat
+hole and into the world you don't know
+
+ align:start position:0%
+hole and into the world you don't know
+ 
+
+ align:start position:0%
+hole and into the world you don't know
+about, right? And in that world,
+
+ align:start position:0%
+about, right? And in that world,
+ 
+
+ align:start position:0%
+about, right? And in that world,
+everything is uncertain and totally
+
+ align:start position:0%
+everything is uncertain and totally
+ 
+
+ align:start position:0%
+everything is uncertain and totally
+anti-heroic, right? Whatever you've
+
+ align:start position:0%
+anti-heroic, right? Whatever you've
+ 
+
+ align:start position:0%
+anti-heroic, right? Whatever you've
+achieved here, whatever monsters you've
+
+ align:start position:0%
+achieved here, whatever monsters you've
+ 
+
+ align:start position:0%
+achieved here, whatever monsters you've
+defeated, whatever dragons you've slain,
+
+ align:start position:0%
+defeated, whatever dragons you've slain,
+ 
+
+ align:start position:0%
+defeated, whatever dragons you've slain,
+ultimately they amount to nothing
+
+ align:start position:0%
+ultimately they amount to nothing
+ 
+
+ align:start position:0%
+ultimately they amount to nothing
+because you have no idea what's going to
+
+ align:start position:0%
+because you have no idea what's going to
+ 
+
+ align:start position:0%
+because you have no idea what's going to
+happen next. Now, think
+
+ align:start position:0%
+happen next. Now, think
+ 
+
+ align:start position:0%
+happen next. Now, think
+about think about these sort of, you
+
+ align:start position:0%
+about think about these sort of, you
+ 
+
+ align:start position:0%
+about think about these sort of, you
+know, these are proper historical
+
+ align:start position:0%
+know, these are proper historical
+ 
+
+ align:start position:0%
+know, these are proper historical
+documents, right? Written by
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Anglo-Saxons. Now, think about an
+
+ align:start position:0%
+Anglo-Saxons. Now, think about an
+ 
+
+ align:start position:0%
+Anglo-Saxons. Now, think about an
+improper historical document. Let's
+
+ align:start position:0%
+improper historical document. Let's
+ 
+
+ align:start position:0%
+improper historical document. Let's
+stick with Tolken for a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+moment. Where I mean where in his
+
+ align:start position:0%
+moment. Where I mean where in his
+ 
+
+ align:start position:0%
+moment. Where I mean where in his
+imaginative world do those kinds of
+
+ align:start position:0%
+imaginative world do those kinds of
+ 
+
+ align:start position:0%
+imaginative world do those kinds of
+Anglo-Saxon narratives fit?
+
+ align:start position:0%
+Anglo-Saxon narratives fit?
+ 
+
+ align:start position:0%
+Anglo-Saxon narratives fit?
+I mean for for men for for men and
+
+ align:start position:0%
+I mean for for men for for men and
+ 
+
+ align:start position:0%
+I mean for for men for for men and
+hobbits it's the same thing. They don't
+
+ align:start position:0%
+hobbits it's the same thing. They don't
+ 
+
+ align:start position:0%
+hobbits it's the same thing. They don't
+know really what happens after they die.
+
+ align:start position:0%
+know really what happens after they die.
+ 
+
+ align:start position:0%
+know really what happens after they die.
+I mean they and in the very same manner
+
+ align:start position:0%
+I mean they and in the very same manner
+ 
+
+ align:start position:0%
+I mean they and in the very same manner
+and and I think that that goes on with
+
+ align:start position:0%
+and and I think that that goes on with
+ 
+
+ align:start position:0%
+and and I think that that goes on with
+in
+
+ align:start position:0%
+in
+ 
+
+ align:start position:0%
+in
+after their, you know, after they didn't
+
+ align:start position:0%
+after their, you know, after they didn't
+ 
+
+ align:start position:0%
+after their, you know, after they didn't
+know what would happen after they
+
+ align:start position:0%
+know what would happen after they
+ 
+
+ align:start position:0%
+know what would happen after they
+defeated Thor, they had no idea what
+
+ align:start position:0%
+defeated Thor, they had no idea what
+ 
+
+ align:start position:0%
+defeated Thor, they had no idea what
+life would be like. And for Froto, what?
+
+ align:start position:0%
+life would be like. And for Froto, what?
+ 
+
+ align:start position:0%
+life would be like. And for Froto, what?
+Well, but what about for Frodo? What's
+
+ align:start position:0%
+Well, but what about for Frodo? What's
+ 
+
+ align:start position:0%
+Well, but what about for Frodo? What's
+different about Froto?
+
+ align:start position:0%
+different about Froto?
+ 
+
+ align:start position:0%
+different about Froto?
+I was going to say another Christian
+
+ align:start position:0%
+I was going to say another Christian
+ 
+
+ align:start position:0%
+I was going to say another Christian
+parallels. He gains the whole world and
+
+ align:start position:0%
+parallels. He gains the whole world and
+ 
+
+ align:start position:0%
+parallels. He gains the whole world and
+then like throws it away. The whole like
+
+ align:start position:0%
+then like throws it away. The whole like
+ 
+
+ align:start position:0%
+then like throws it away. The whole like
+all the power, gives it up for everyone
+
+ align:start position:0%
+all the power, gives it up for everyone
+ 
+
+ align:start position:0%
+all the power, gives it up for everyone
+else.
+
+ align:start position:0%
+else.
+ 
+
+ align:start position:0%
+else.
+Okay. That's not related to what we're
+
+ align:start position:0%
+Okay. That's not related to what we're
+ 
+
+ align:start position:0%
+Okay. That's not related to what we're
+talking about. Okay. But how does it
+
+ align:start position:0%
+talking about. Okay. But how does it
+ 
+
+ align:start position:0%
+talking about. Okay. But how does it
+end? Froto goes into the west. He goes
+
+ align:start position:0%
+end? Froto goes into the west. He goes
+ 
+
+ align:start position:0%
+end? Froto goes into the west. He goes
+into the west. This is where the elves
+
+ align:start position:0%
+into the west. This is where the elves
+ 
+
+ align:start position:0%
+into the west. This is where the elves
+came from. But is it is it really
+
+ align:start position:0%
+came from. But is it is it really
+ 
+
+ align:start position:0%
+came from. But is it is it really
+unknown? No. Is the west really? No,
+
+ align:start position:0%
+unknown? No. Is the west really? No,
+ 
+
+ align:start position:0%
+unknown? No. Is the west really? No,
+it's not unknown at all. But beyond it
+
+ align:start position:0%
+it's not unknown at all. But beyond it
+ 
+
+ align:start position:0%
+it's not unknown at all. But beyond it
+is is the thing because they go there
+
+ align:start position:0%
+is is the thing because they go there
+ 
+
+ align:start position:0%
+is is the thing because they go there
+and then but he's going to die there and
+
+ align:start position:0%
+and then but he's going to die there and
+ 
+
+ align:start position:0%
+and then but he's going to die there and
+then from there he where he goes from
+
+ align:start position:0%
+then from there he where he goes from
+ 
+
+ align:start position:0%
+then from there he where he goes from
+there they have no idea. They go to the
+
+ align:start position:0%
+there they have no idea. They go to the
+ 
+
+ align:start position:0%
+there they have no idea. They go to the
+halls. Well, but then from the halls of
+
+ align:start position:0%
+halls. Well, but then from the halls of
+ 
+
+ align:start position:0%
+halls. Well, but then from the halls of
+Mandos, the the humans and the hobbits
+
+ align:start position:0%
+Mandos, the the humans and the hobbits
+ 
+
+ align:start position:0%
+Mandos, the the humans and the hobbits
+go somewhere. Who's he going with? Who's
+
+ align:start position:0%
+go somewhere. Who's he going with? Who's
+ 
+
+ align:start position:0%
+go somewhere. Who's he going with? Who's
+he going with? Gandalf.
+
+ align:start position:0%
+he going with? Gandalf.
+ 
+
+ align:start position:0%
+he going with? Gandalf.
+The elves. Okay. He's going Yeah. And
+
+ align:start position:0%
+The elves. Okay. He's going Yeah. And
+ 
+
+ align:start position:0%
+The elves. Okay. He's going Yeah. And
+all the other people who are blessed.
+
+ align:start position:0%
+all the other people who are blessed.
+ 
+
+ align:start position:0%
+all the other people who are blessed.
+Okay. He's going with the elves
+
+ align:start position:0%
+Okay. He's going with the elves
+ 
+
+ align:start position:0%
+Okay. He's going with the elves
+to to
+
+ align:start position:0%
+to to
+ 
+
+ align:start position:0%
+to to
+to
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+what? What's the distinguishing hallmark
+
+ align:start position:0%
+what? What's the distinguishing hallmark
+ 
+
+ align:start position:0%
+what? What's the distinguishing hallmark
+of the elves? The undying limbs. They
+
+ align:start position:0%
+of the elves? The undying limbs. They
+ 
+
+ align:start position:0%
+of the elves? The undying limbs. They
+live forever forever.
+
+ align:start position:0%
+live forever forever.
+ 
+
+ align:start position:0%
+live forever forever.
+Yeah. He won't. That is not totally
+
+ align:start position:0%
+Yeah. He won't. That is not totally
+ 
+
+ align:start position:0%
+Yeah. He won't. That is not totally
+clear. Yeah. Actually, by the undying
+
+ align:start position:0%
+clear. Yeah. Actually, by the undying
+ 
+
+ align:start position:0%
+clear. Yeah. Actually, by the undying
+lens, there is an implication that he's
+
+ align:start position:0%
+lens, there is an implication that he's
+ 
+
+ align:start position:0%
+lens, there is an implication that he's
+not that he the reason he's going is
+
+ align:start position:0%
+not that he the reason he's going is
+ 
+
+ align:start position:0%
+not that he the reason he's going is
+that he doesn't have to die for the
+
+ align:start position:0%
+that he doesn't have to die for the
+ 
+
+ align:start position:0%
+that he doesn't have to die for the
+shadow. That's right.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+The first time my sister read it
+
+ align:start position:0%
+The first time my sister read it
+ 
+
+ align:start position:0%
+The first time my sister read it
+actually what she thought she came to me
+
+ align:start position:0%
+actually what she thought she came to me
+ 
+
+ align:start position:0%
+actually what she thought she came to me
+crying at the end of this book and she
+
+ align:start position:0%
+crying at the end of this book and she
+ 
+
+ align:start position:0%
+crying at the end of this book and she
+was in tears. She said, "Anmorry and I I
+
+ align:start position:0%
+was in tears. She said, "Anmorry and I I
+ 
+
+ align:start position:0%
+was in tears. She said, "Anmorry and I I
+hadn't read it." She said, "Any they all
+
+ align:start position:0%
+hadn't read it." She said, "Any they all
+ 
+
+ align:start position:0%
+hadn't read it." She said, "Any they all
+go to commit suicide.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+That's what that's what she understood
+
+ align:start position:0%
+That's what that's what she understood
+ 
+
+ align:start position:0%
+That's what that's what she understood
+from going into the boats and going out
+
+ align:start position:0%
+from going into the boats and going out
+ 
+
+ align:start position:0%
+from going into the boats and going out
+into the west to her. They can make the
+
+ align:start position:0%
+into the west to her. They can make the
+ 
+
+ align:start position:0%
+into the west to her. They can make the
+the analogy that it's it's like living
+
+ align:start position:0%
+the analogy that it's it's like living
+ 
+
+ align:start position:0%
+the analogy that it's it's like living
+living closer to the sun that that that
+
+ align:start position:0%
+living closer to the sun that that that
+ 
+
+ align:start position:0%
+living closer to the sun that that that
+you're going to that
+
+ align:start position:0%
+you're going to that
+ 
+
+ align:start position:0%
+you're going to that
+you're you're a candle living closer to
+
+ align:start position:0%
+you're you're a candle living closer to
+ 
+
+ align:start position:0%
+you're you're a candle living closer to
+the to the flame that you burn faster
+
+ align:start position:0%
+the to the flame that you burn faster
+ 
+
+ align:start position:0%
+the to the flame that you burn faster
+that you would even uh die that a mortal
+
+ align:start position:0%
+that you would even uh die that a mortal
+ 
+
+ align:start position:0%
+that you would even uh die that a mortal
+would would even Okay. But but Ian I I'm
+
+ align:start position:0%
+would would even Okay. But but Ian I I'm
+ 
+
+ align:start position:0%
+would would even Okay. But but Ian I I'm
+picking I'm picking at stupid little
+
+ align:start position:0%
+picking I'm picking at stupid little
+ 
+
+ align:start position:0%
+picking I'm picking at stupid little
+things. I don't know. No, no, no, no.
+
+ align:start position:0%
+things. I don't know. No, no, no, no.
+ 
+
+ align:start position:0%
+things. I don't know. No, no, no, no.
+Don't don't ever shut up. Um, just think
+
+ align:start position:0%
+Don't don't ever shut up. Um, just think
+ 
+
+ align:start position:0%
+Don't don't ever shut up. Um, just think
+before you talk,
+
+ align:start position:0%
+before you talk,
+ 
+
+ align:start position:0%
+before you talk,
+um,
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+if I'm going off admittedly into a kind
+
+ align:start position:0%
+if I'm going off admittedly into a kind
+ 
+
+ align:start position:0%
+if I'm going off admittedly into a kind
+of unknown, but I'm going with a group
+
+ align:start position:0%
+of unknown, but I'm going with a group
+ 
+
+ align:start position:0%
+of unknown, but I'm going with a group
+of people who are totally kind, nice,
+
+ align:start position:0%
+of people who are totally kind, nice,
+ 
+
+ align:start position:0%
+of people who are totally kind, nice,
+gentle, beautiful, right? Gorgeously,
+
+ align:start position:0%
+gentle, beautiful, right? Gorgeously,
+ 
+
+ align:start position:0%
+gentle, beautiful, right? Gorgeously,
+drop deadad beautiful.
+
+ align:start position:0%
+drop deadad beautiful.
+ 
+
+ align:start position:0%
+drop deadad beautiful.
+A lot of them have been there. And and
+
+ align:start position:0%
+A lot of them have been there. And and
+ 
+
+ align:start position:0%
+A lot of them have been there. And and
+they're not going to die. and they all
+
+ align:start position:0%
+they're not going to die. and they all
+ 
+
+ align:start position:0%
+they're not going to die. and they all
+sing beautiful music and play harps and
+
+ align:start position:0%
+sing beautiful music and play harps and
+ 
+
+ align:start position:0%
+sing beautiful music and play harps and
+right and I mean this isn't a scary
+
+ align:start position:0%
+right and I mean this isn't a scary
+ 
+
+ align:start position:0%
+right and I mean this isn't a scary
+prospect. No, I mean it's no scarier for
+
+ align:start position:0%
+prospect. No, I mean it's no scarier for
+ 
+
+ align:start position:0%
+prospect. No, I mean it's no scarier for
+instance than say being a Christian and
+
+ align:start position:0%
+instance than say being a Christian and
+ 
+
+ align:start position:0%
+instance than say being a Christian and
+not quite knowing what heaven is all
+
+ align:start position:0%
+not quite knowing what heaven is all
+ 
+
+ align:start position:0%
+not quite knowing what heaven is all
+about but knowing it's okay because I'm
+
+ align:start position:0%
+about but knowing it's okay because I'm
+ 
+
+ align:start position:0%
+about but knowing it's okay because I'm
+going there and God is there and God is
+
+ align:start position:0%
+going there and God is there and God is
+ 
+
+ align:start position:0%
+going there and God is there and God is
+purely good. So I'm okay. I don't have
+
+ align:start position:0%
+purely good. So I'm okay. I don't have
+ 
+
+ align:start position:0%
+purely good. So I'm okay. I don't have
+to know exactly what's going to happen
+
+ align:start position:0%
+to know exactly what's going to happen
+ 
+
+ align:start position:0%
+to know exactly what's going to happen
+because it's going to be pleasant
+
+ align:start position:0%
+because it's going to be pleasant
+ 
+
+ align:start position:0%
+because it's going to be pleasant
+because I'm in good company and wherever
+
+ align:start position:0%
+because I'm in good company and wherever
+ 
+
+ align:start position:0%
+because I'm in good company and wherever
+they're taking me, I'm gonna be okay.
+
+ align:start position:0%
+they're taking me, I'm gonna be okay.
+ 
+
+ align:start position:0%
+they're taking me, I'm gonna be okay.
+Okay, so let's go back and think again.
+
+ align:start position:0%
+Okay, so let's go back and think again.
+ 
+
+ align:start position:0%
+Okay, so let's go back and think again.
+Beaolf, he dies. He's got the chalice,
+
+ align:start position:0%
+Beaolf, he dies. He's got the chalice,
+ 
+
+ align:start position:0%
+Beaolf, he dies. He's got the chalice,
+you know, or whatever the bit of the
+
+ align:start position:0%
+you know, or whatever the bit of the
+ 
+
+ align:start position:0%
+you know, or whatever the bit of the
+treasure. He's looking on it. He's
+
+ align:start position:0%
+treasure. He's looking on it. He's
+ 
+
+ align:start position:0%
+treasure. He's looking on it. He's
+gazing on it. He's done all the things,
+
+ align:start position:0%
+gazing on it. He's done all the things,
+ 
+
+ align:start position:0%
+gazing on it. He's done all the things,
+right? He can't be accused of murdering
+
+ align:start position:0%
+right? He can't be accused of murdering
+ 
+
+ align:start position:0%
+right? He can't be accused of murdering
+a kinsman. And after all, 90% of these
+
+ align:start position:0%
+a kinsman. And after all, 90% of these
+ 
+
+ align:start position:0%
+a kinsman. And after all, 90% of these
+guys could be. though, right? He's, you
+
+ align:start position:0%
+guys could be. though, right? He's, you
+ 
+
+ align:start position:0%
+guys could be. though, right? He's, you
+know, he's going off with a clean
+
+ align:start position:0%
+know, he's going off with a clean
+ 
+
+ align:start position:0%
+know, he's going off with a clean
+conscience and yet and yet he has no
+
+ align:start position:0%
+conscience and yet and yet he has no
+ 
+
+ align:start position:0%
+conscience and yet and yet he has no
+idea where he's going or what's going to
+
+ align:start position:0%
+idea where he's going or what's going to
+ 
+
+ align:start position:0%
+idea where he's going or what's going to
+happen. Froto doesn't have that ending
+
+ align:start position:0%
+happen. Froto doesn't have that ending
+ 
+
+ align:start position:0%
+happen. Froto doesn't have that ending
+at all. Right. Yeah. Go ahead, Ben. But
+
+ align:start position:0%
+at all. Right. Yeah. Go ahead, Ben. But
+ 
+
+ align:start position:0%
+at all. Right. Yeah. Go ahead, Ben. But
+um you you said something I I haven't
+
+ align:start position:0%
+um you you said something I I haven't
+ 
+
+ align:start position:0%
+um you you said something I I haven't
+read be all the way through parts of it,
+
+ align:start position:0%
+read be all the way through parts of it,
+ 
+
+ align:start position:0%
+read be all the way through parts of it,
+but um you said something about uh the
+
+ align:start position:0%
+but um you said something about uh the
+ 
+
+ align:start position:0%
+but um you said something about uh the
+whailing woman at the end talking about
+
+ align:start position:0%
+whailing woman at the end talking about
+ 
+
+ align:start position:0%
+whailing woman at the end talking about
+how all this stuff can happen now. Isn't
+
+ align:start position:0%
+how all this stuff can happen now. Isn't
+ 
+
+ align:start position:0%
+how all this stuff can happen now. Isn't
+that sort of like how you know like all
+
+ align:start position:0%
+that sort of like how you know like all
+ 
+
+ align:start position:0%
+that sort of like how you know like all
+the heroes are leaving middle or like
+
+ align:start position:0%
+the heroes are leaving middle or like
+ 
+
+ align:start position:0%
+the heroes are leaving middle or like
+the elves are leaving Miller with
+
+ align:start position:0%
+the elves are leaving Miller with
+ 
+
+ align:start position:0%
+the elves are leaving Miller with
+Gandalf you know Frodo and isn't there
+
+ align:start position:0%
+Gandalf you know Frodo and isn't there
+ 
+
+ align:start position:0%
+Gandalf you know Frodo and isn't there
+still that uncertainty? I mean I know
+
+ align:start position:0%
+still that uncertainty? I mean I know
+ 
+
+ align:start position:0%
+still that uncertainty? I mean I know
+the bad guys are dead now but
+
+ align:start position:0%
+the bad guys are dead now but
+ 
+
+ align:start position:0%
+the bad guys are dead now but
+there's always more. Yeah, but there's
+
+ align:start position:0%
+there's always more. Yeah, but there's
+ 
+
+ align:start position:0%
+there's always more. Yeah, but there's
+that uncertainty for like the people
+
+ align:start position:0%
+that uncertainty for like the people
+ 
+
+ align:start position:0%
+that uncertainty for like the people
+that are left. Like you know how the
+
+ align:start position:0%
+that are left. Like you know how the
+ 
+
+ align:start position:0%
+that are left. Like you know how the
+book doesn't end just with them going
+
+ align:start position:0%
+book doesn't end just with them going
+ 
+
+ align:start position:0%
+book doesn't end just with them going
+off. It ends with Sam coming back and
+
+ align:start position:0%
+off. It ends with Sam coming back and
+ 
+
+ align:start position:0%
+off. It ends with Sam coming back and
+saying, "Well, I'm back." Except that
+
+ align:start position:0%
+saying, "Well, I'm back." Except that
+ 
+
+ align:start position:0%
+saying, "Well, I'm back." Except that
+Sam is what? Four-time mayor and he has
+
+ align:start position:0%
+Sam is what? Four-time mayor and he has
+ 
+
+ align:start position:0%
+Sam is what? Four-time mayor and he has
+children, right? You think it's
+
+ align:start position:0%
+children, right? You think it's
+ 
+
+ align:start position:0%
+children, right? You think it's
+unsignificant that Sam is busy getting
+
+ align:start position:0%
+unsignificant that Sam is busy getting
+ 
+
+ align:start position:0%
+unsignificant that Sam is busy getting
+married, having children, having
+
+ align:start position:0%
+married, having children, having
+ 
+
+ align:start position:0%
+married, having children, having
+grandchildren. No, we're supposed to
+
+ align:start position:0%
+grandchildren. No, we're supposed to
+ 
+
+ align:start position:0%
+grandchildren. No, we're supposed to
+feel good about that. I'm not saying
+
+ align:start position:0%
+feel good about that. I'm not saying
+ 
+
+ align:start position:0%
+feel good about that. I'm not saying
+we're we're not, but there's still and
+
+ align:start position:0%
+we're we're not, but there's still and
+ 
+
+ align:start position:0%
+we're we're not, but there's still and
+and Aragon is also he's going to die.
+
+ align:start position:0%
+and Aragon is also he's going to die.
+ 
+
+ align:start position:0%
+and Aragon is also he's going to die.
+Yes. And even Arwin is going to die
+
+ align:start position:0%
+Yes. And even Arwin is going to die
+ 
+
+ align:start position:0%
+Yes. And even Arwin is going to die
+because she's chosen that. But it's
+
+ align:start position:0%
+because she's chosen that. But it's
+ 
+
+ align:start position:0%
+because she's chosen that. But it's
+bittersweet, but it's not
+
+ align:start position:0%
+bittersweet, but it's not
+ 
+
+ align:start position:0%
+bittersweet, but it's not
+tragic. It's bittersweet. Right. And and
+
+ align:start position:0%
+tragic. It's bittersweet. Right. And and
+ 
+
+ align:start position:0%
+tragic. It's bittersweet. Right. And and
+yes, the the age of men that is being
+
+ align:start position:0%
+yes, the the age of men that is being
+ 
+
+ align:start position:0%
+yes, the the age of men that is being
+left behind by wizards and elves, yes,
+
+ align:start position:0%
+left behind by wizards and elves, yes,
+ 
+
+ align:start position:0%
+left behind by wizards and elves, yes,
+they're going to face perils.
+
+ align:start position:0%
+they're going to face perils.
+ 
+
+ align:start position:0%
+they're going to face perils.
+Absolutely, there will be dangers in the
+
+ align:start position:0%
+Absolutely, there will be dangers in the
+ 
+
+ align:start position:0%
+Absolutely, there will be dangers in the
+road ahead, but they are not doomed by
+
+ align:start position:0%
+road ahead, but they are not doomed by
+ 
+
+ align:start position:0%
+road ahead, but they are not doomed by
+any means, right? We can feel at the end
+
+ align:start position:0%
+any means, right? We can feel at the end
+ 
+
+ align:start position:0%
+any means, right? We can feel at the end
+like things are kind of in good hands,
+
+ align:start position:0%
+like things are kind of in good hands,
+ 
+
+ align:start position:0%
+like things are kind of in good hands,
+right? Mary and Pippen are going to live
+
+ align:start position:0%
+right? Mary and Pippen are going to live
+ 
+
+ align:start position:0%
+right? Mary and Pippen are going to live
+to a ripe old age. They're going to
+
+ align:start position:0%
+to a ripe old age. They're going to
+ 
+
+ align:start position:0%
+to a ripe old age. They're going to
+serve their respective feudal overlords
+
+ align:start position:0%
+serve their respective feudal overlords
+ 
+
+ align:start position:0%
+serve their respective feudal overlords
+as knights, basically, right? And the
+
+ align:start position:0%
+as knights, basically, right? And the
+ 
+
+ align:start position:0%
+as knights, basically, right? And the
+age of men will proceed with its ups and
+
+ align:start position:0%
+age of men will proceed with its ups and
+ 
+
+ align:start position:0%
+age of men will proceed with its ups and
+downs, but they're doing the right kinds
+
+ align:start position:0%
+downs, but they're doing the right kinds
+ 
+
+ align:start position:0%
+downs, but they're doing the right kinds
+of things. They're having children,
+
+ align:start position:0%
+of things. They're having children,
+ 
+
+ align:start position:0%
+of things. They're having children,
+right? Bailwolf again has no child.
+
+ align:start position:0%
+right? Bailwolf again has no child.
+ 
+
+ align:start position:0%
+right? Bailwolf again has no child.
+That's what he laments at the end. He's
+
+ align:start position:0%
+That's what he laments at the end. He's
+ 
+
+ align:start position:0%
+That's what he laments at the end. He's
+going into the unknown and he's not even
+
+ align:start position:0%
+going into the unknown and he's not even
+ 
+
+ align:start position:0%
+going into the unknown and he's not even
+leaving someone behind, right? It's a
+
+ align:start position:0%
+leaving someone behind, right? It's a
+ 
+
+ align:start position:0%
+leaving someone behind, right? It's a
+very, very different cast to the ending.
+
+ align:start position:0%
+very, very different cast to the ending.
+ 
+
+ align:start position:0%
+very, very different cast to the ending.
+Even though The Lord of the Rings feels
+
+ align:start position:0%
+Even though The Lord of the Rings feels
+ 
+
+ align:start position:0%
+Even though The Lord of the Rings feels
+kind of antilimatic at the end, I think
+
+ align:start position:0%
+kind of antilimatic at the end, I think
+ 
+
+ align:start position:0%
+kind of antilimatic at the end, I think
+to a lot of readers and obviously to
+
+ align:start position:0%
+to a lot of readers and obviously to
+ 
+
+ align:start position:0%
+to a lot of readers and obviously to
+movie makers.
+
+ align:start position:0%
+movie makers.
+ 
+
+ align:start position:0%
+movie makers.
+Um, but nonetheless, that that is a
+
+ align:start position:0%
+Um, but nonetheless, that that is a
+ 
+
+ align:start position:0%
+Um, but nonetheless, that that is a
+hopeful ending. Whereas the Beaolf
+
+ align:start position:0%
+hopeful ending. Whereas the Beaolf
+ 
+
+ align:start position:0%
+hopeful ending. Whereas the Beaolf
+ending, it is not a hopeful ending at
+
+ align:start position:0%
+ending, it is not a hopeful ending at
+ 
+
+ align:start position:0%
+ending, it is not a hopeful ending at
+all. It's not just that maybe the Swedes
+
+ align:start position:0%
+all. It's not just that maybe the Swedes
+ 
+
+ align:start position:0%
+all. It's not just that maybe the Swedes
+will come. For sure they're coming.
+
+ align:start position:0%
+will come. For sure they're coming.
+ 
+
+ align:start position:0%
+will come. For sure they're coming.
+They're in their boats already, right?
+
+ align:start position:0%
+They're in their boats already, right?
+ 
+
+ align:start position:0%
+They're in their boats already, right?
+They've heard the dragon has killed
+
+ align:start position:0%
+They've heard the dragon has killed
+ 
+
+ align:start position:0%
+They've heard the dragon has killed
+Beaowolf. Oh, excellent. Got rid of that
+
+ align:start position:0%
+Beaowolf. Oh, excellent. Got rid of that
+ 
+
+ align:start position:0%
+Beaowolf. Oh, excellent. Got rid of that
+guy. Um, we can go in now and and reopen
+
+ align:start position:0%
+guy. Um, we can go in now and and reopen
+ 
+
+ align:start position:0%
+guy. Um, we can go in now and and reopen
+that feud that we've had to put on hold
+
+ align:start position:0%
+that feud that we've had to put on hold
+ 
+
+ align:start position:0%
+that feud that we've had to put on hold
+for 50 long years because he was king
+
+ align:start position:0%
+for 50 long years because he was king
+ 
+
+ align:start position:0%
+for 50 long years because he was king
+and so powerful. It's certain that
+
+ align:start position:0%
+and so powerful. It's certain that
+ 
+
+ align:start position:0%
+and so powerful. It's certain that
+they're coming whereas you just don't
+
+ align:start position:0%
+they're coming whereas you just don't
+ 
+
+ align:start position:0%
+they're coming whereas you just don't
+have that kind of despair um at the end.
+
+ align:start position:0%
+have that kind of despair um at the end.
+ 
+
+ align:start position:0%
+have that kind of despair um at the end.
+Yeah. Go ahead, Mono. Before I start
+
+ align:start position:0%
+Yeah. Go ahead, Mono. Before I start
+ 
+
+ align:start position:0%
+Yeah. Go ahead, Mono. Before I start
+making a point, does is there any other
+
+ align:start position:0%
+making a point, does is there any other
+ 
+
+ align:start position:0%
+making a point, does is there any other
+fans of B5 here? Because if there isn't,
+
+ align:start position:0%
+fans of B5 here? Because if there isn't,
+ 
+
+ align:start position:0%
+fans of B5 here? Because if there isn't,
+my point will make no sense.
+
+ align:start position:0%
+my point will make no sense.
+ 
+
+ align:start position:0%
+my point will make no sense.
+B5. I have a friend. I already know.
+
+ align:start position:0%
+B5. I have a friend. I already know.
+ 
+
+ align:start position:0%
+B5. I have a friend. I already know.
+Okay, never mind. I won't make the
+
+ align:start position:0%
+Okay, never mind. I won't make the
+ 
+
+ align:start position:0%
+Okay, never mind. I won't make the
+point. We can move on. Okay. Talking of
+
+ align:start position:0%
+point. We can move on. Okay. Talking of
+ 
+
+ align:start position:0%
+point. We can move on. Okay. Talking of
+endings. Yes. Endings. Um, can we can we
+
+ align:start position:0%
+endings. Yes. Endings. Um, can we can we
+ 
+
+ align:start position:0%
+endings. Yes. Endings. Um, can we can we
+speak a little bit about the ending of
+
+ align:start position:0%
+speak a little bit about the ending of
+ 
+
+ align:start position:0%
+speak a little bit about the ending of
+this book? Absolutely. Where would you
+
+ align:start position:0%
+this book? Absolutely. Where would you
+ 
+
+ align:start position:0%
+this book? Absolutely. Where would you
+like to go? He says, "Are you in the
+
+ align:start position:0%
+like to go? He says, "Are you in the
+ 
+
+ align:start position:0%
+like to go? He says, "Are you in the
+epilogue or the influence?" And the
+
+ align:start position:0%
+epilogue or the influence?" And the
+ 
+
+ align:start position:0%
+epilogue or the influence?" And the
+influence. Page 215. Okay. There you go.
+
+ align:start position:0%
+influence. Page 215. Okay. There you go.
+ 
+
+ align:start position:0%
+influence. Page 215. Okay. There you go.
+Um, two last two sentences. And now in
+
+ align:start position:0%
+Um, two last two sentences. And now in
+ 
+
+ align:start position:0%
+Um, two last two sentences. And now in
+some extreme form of behaviorism, the
+
+ align:start position:0%
+some extreme form of behaviorism, the
+ 
+
+ align:start position:0%
+some extreme form of behaviorism, the
+subject himself is discounted as merely
+
+ align:start position:0%
+subject himself is discounted as merely
+ 
+
+ align:start position:0%
+subject himself is discounted as merely
+subjective. We only think that we think.
+
+ align:start position:0%
+subjective. We only think that we think.
+ 
+
+ align:start position:0%
+subjective. We only think that we think.
+Having eaten up everything else, he eats
+
+ align:start position:0%
+Having eaten up everything else, he eats
+ 
+
+ align:start position:0%
+Having eaten up everything else, he eats
+himself up too.
+
+ align:start position:0%
+himself up too.
+ 
+
+ align:start position:0%
+himself up too.
+I'm very confused. And where we go from
+
+ align:start position:0%
+I'm very confused. And where we go from
+ 
+
+ align:start position:0%
+I'm very confused. And where we go from
+that is a dark question. That's what
+
+ align:start position:0%
+that is a dark question. That's what
+ 
+
+ align:start position:0%
+that is a dark question. That's what
+that's what that's what Caner is
+
+ align:start position:0%
+that's what that's what Caner is
+ 
+
+ align:start position:0%
+that's what that's what Caner is
+rebelling against when he says Lewis is
+
+ align:start position:0%
+rebelling against when he says Lewis is
+ 
+
+ align:start position:0%
+rebelling against when he says Lewis is
+mopey and pessimistic and but really
+
+ align:start position:0%
+mopey and pessimistic and but really
+ 
+
+ align:start position:0%
+mopey and pessimistic and but really
+Caner's just jealous. Doesn't that I
+
+ align:start position:0%
+Caner's just jealous. Doesn't that I
+ 
+
+ align:start position:0%
+Caner's just jealous. Doesn't that I
+mean that really that reflects a lot on
+
+ align:start position:0%
+mean that really that reflects a lot on
+ 
+
+ align:start position:0%
+mean that really that reflects a lot on
+Louiswis's fictional writings. I mean
+
+ align:start position:0%
+Louiswis's fictional writings. I mean
+ 
+
+ align:start position:0%
+Louiswis's fictional writings. I mean
+lying witches the entire Narnia series
+
+ align:start position:0%
+lying witches the entire Narnia series
+ 
+
+ align:start position:0%
+lying witches the entire Narnia series
+has a really really dark overtones that
+
+ align:start position:0%
+has a really really dark overtones that
+ 
+
+ align:start position:0%
+has a really really dark overtones that
+are so nice. No no as says everyone and
+
+ align:start position:0%
+are so nice. No no as says everyone and
+ 
+
+ align:start position:0%
+are so nice. No no as says everyone and
+the end like the last book is really
+
+ align:start position:0%
+the end like the last book is really
+ 
+
+ align:start position:0%
+the end like the last book is really
+dark. It's both really dark orders.
+
+ align:start position:0%
+dark. It's both really dark orders.
+ 
+
+ align:start position:0%
+dark. It's both really dark orders.
+Yeah. It's really both really dark and
+
+ align:start position:0%
+Yeah. It's really both really dark and
+ 
+
+ align:start position:0%
+Yeah. It's really both really dark and
+yet it's also like it's it's the same
+
+ align:start position:0%
+yet it's also like it's it's the same
+ 
+
+ align:start position:0%
+yet it's also like it's it's the same
+sort of feeling of we don't know where
+
+ align:start position:0%
+sort of feeling of we don't know where
+ 
+
+ align:start position:0%
+sort of feeling of we don't know where
+we're going but we think it's going to
+
+ align:start position:0%
+we're going but we think it's going to
+ 
+
+ align:start position:0%
+we're going but we think it's going to
+be better. Like everyone all the good
+
+ align:start position:0%
+be better. Like everyone all the good
+ 
+
+ align:start position:0%
+be better. Like everyone all the good
+people are going there but we're not
+
+ align:start position:0%
+people are going there but we're not
+ 
+
+ align:start position:0%
+people are going there but we're not
+exactly sure where we're going. It's
+
+ align:start position:0%
+exactly sure where we're going. It's
+ 
+
+ align:start position:0%
+exactly sure where we're going. It's
+we're we're destroying something that's
+
+ align:start position:0%
+we're we're destroying something that's
+ 
+
+ align:start position:0%
+we're we're destroying something that's
+really wonderful. Narnia goes away.
+
+ align:start position:0%
+really wonderful. Narnia goes away.
+ 
+
+ align:start position:0%
+really wonderful. Narnia goes away.
+Yeah. but we're going to create sort of
+
+ align:start position:0%
+Yeah. but we're going to create sort of
+ 
+
+ align:start position:0%
+Yeah. but we're going to create sort of
+a new Narnia and the sequestion, but we
+
+ align:start position:0%
+a new Narnia and the sequestion, but we
+ 
+
+ align:start position:0%
+a new Narnia and the sequestion, but we
+don't exactly know for sure if this new
+
+ align:start position:0%
+don't exactly know for sure if this new
+ 
+
+ align:start position:0%
+don't exactly know for sure if this new
+Narnia is going to be that wonderful.
+
+ align:start position:0%
+Narnia is going to be that wonderful.
+ 
+
+ align:start position:0%
+Narnia is going to be that wonderful.
+And so, it's sort of a weird, it's the
+
+ align:start position:0%
+And so, it's sort of a weird, it's the
+ 
+
+ align:start position:0%
+And so, it's sort of a weird, it's the
+same sort of weirdness in the Beaolf
+
+ align:start position:0%
+same sort of weirdness in the Beaolf
+ 
+
+ align:start position:0%
+same sort of weirdness in the Beaolf
+type of feeling that destroying this old
+
+ align:start position:0%
+type of feeling that destroying this old
+ 
+
+ align:start position:0%
+type of feeling that destroying this old
+I mean, one thing has to be said, the
+
+ align:start position:0%
+I mean, one thing has to be said, the
+ 
+
+ align:start position:0%
+I mean, one thing has to be said, the
+seventh book in the Narnia series is by
+
+ align:start position:0%
+seventh book in the Narnia series is by
+ 
+
+ align:start position:0%
+seventh book in the Narnia series is by
+far the most poorly written. And I think
+
+ align:start position:0%
+far the most poorly written. And I think
+ 
+
+ align:start position:0%
+far the most poorly written. And I think
+that's part of the problem. And I'm I'm
+
+ align:start position:0%
+that's part of the problem. And I'm I'm
+ 
+
+ align:start position:0%
+that's part of the problem. And I'm I'm
+I'm I'm willing to uh say that the
+
+ align:start position:0%
+I'm I'm willing to uh say that the
+ 
+
+ align:start position:0%
+I'm I'm willing to uh say that the
+reason what was the title? The last
+
+ align:start position:0%
+reason what was the title? The last
+ 
+
+ align:start position:0%
+reason what was the title? The last
+battle. The last battle. It's by far the
+
+ align:start position:0%
+battle. The last battle. It's by far the
+ 
+
+ align:start position:0%
+battle. The last battle. It's by far the
+most poorly written. I mean, when Caner
+
+ align:start position:0%
+most poorly written. I mean, when Caner
+ 
+
+ align:start position:0%
+most poorly written. I mean, when Caner
+says that the Narnia series is uneven, I
+
+ align:start position:0%
+says that the Narnia series is uneven, I
+ 
+
+ align:start position:0%
+says that the Narnia series is uneven, I
+think that is fair. Um in a way that the
+
+ align:start position:0%
+think that is fair. Um in a way that the
+ 
+
+ align:start position:0%
+think that is fair. Um in a way that the
+Lord of the Rings is, you know, reliable
+
+ align:start position:0%
+Lord of the Rings is, you know, reliable
+ 
+
+ align:start position:0%
+Lord of the Rings is, you know, reliable
+from start to finish. Um, and if you
+
+ align:start position:0%
+from start to finish. Um, and if you
+ 
+
+ align:start position:0%
+from start to finish. Um, and if you
+read the Beaolf and the Critics and the
+
+ align:start position:0%
+read the Beaolf and the Critics and the
+ 
+
+ align:start position:0%
+read the Beaolf and the Critics and the
+Monsters and the Critics, you'll you'll
+
+ align:start position:0%
+Monsters and the Critics, you'll you'll
+ 
+
+ align:start position:0%
+Monsters and the Critics, you'll you'll
+see that same just sort of incredible
+
+ align:start position:0%
+see that same just sort of incredible
+ 
+
+ align:start position:0%
+see that same just sort of incredible
+penetrating um, pen um, at work. You
+
+ align:start position:0%
+penetrating um, pen um, at work. You
+ 
+
+ align:start position:0%
+penetrating um, pen um, at work. You
+know, every sentence is just packed. Um,
+
+ align:start position:0%
+know, every sentence is just packed. Um,
+ 
+
+ align:start position:0%
+know, every sentence is just packed. Um,
+but I want to come back to Ann Marie's
+
+ align:start position:0%
+but I want to come back to Ann Marie's
+ 
+
+ align:start position:0%
+but I want to come back to Ann Marie's
+question. What's going on here? Um, so
+
+ align:start position:0%
+question. What's going on here? Um, so
+ 
+
+ align:start position:0%
+question. What's going on here? Um, so
+let's put it into a context, right? And
+
+ align:start position:0%
+let's put it into a context, right? And
+ 
+
+ align:start position:0%
+let's put it into a context, right? And
+not just jump in at that last paragraph.
+
+ align:start position:0%
+not just jump in at that last paragraph.
+ 
+
+ align:start position:0%
+not just jump in at that last paragraph.
+He has made the argument that we're into
+
+ align:start position:0%
+He has made the argument that we're into
+ 
+
+ align:start position:0%
+He has made the argument that we're into
+originality and that distinguishes us
+
+ align:start position:0%
+originality and that distinguishes us
+ 
+
+ align:start position:0%
+originality and that distinguishes us
+from what came before us. And in fact,
+
+ align:start position:0%
+from what came before us. And in fact,
+ 
+
+ align:start position:0%
+from what came before us. And in fact,
+we're so into originality that we've
+
+ align:start position:0%
+we're so into originality that we've
+ 
+
+ align:start position:0%
+we're so into originality that we've
+gone even like a step beyond that,
+
+ align:start position:0%
+gone even like a step beyond that,
+ 
+
+ align:start position:0%
+gone even like a step beyond that,
+right? And so it's not just that we
+
+ align:start position:0%
+right? And so it's not just that we
+ 
+
+ align:start position:0%
+right? And so it's not just that we
+think we've added something, but maybe
+
+ align:start position:0%
+think we've added something, but maybe
+ 
+
+ align:start position:0%
+think we've added something, but maybe
+we're not even real. We only think we're
+
+ align:start position:0%
+we're not even real. We only think we're
+ 
+
+ align:start position:0%
+we're not even real. We only think we're
+real. Okay? So that as
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+as in the medieval mind he says nothing
+
+ align:start position:0%
+as in the medieval mind he says nothing
+ 
+
+ align:start position:0%
+as in the medieval mind he says nothing
+is subjective right I don't see the part
+
+ align:start position:0%
+is subjective right I don't see the part
+ 
+
+ align:start position:0%
+is subjective right I don't see the part
+I'm playing in this at
+
+ align:start position:0%
+I'm playing in this at
+ 
+
+ align:start position:0%
+I'm playing in this at
+all then some process of modernization
+
+ align:start position:0%
+all then some process of modernization
+ 
+
+ align:start position:0%
+all then some process of modernization
+happens right we'll pass over that
+
+ align:start position:0%
+happens right we'll pass over that
+ 
+
+ align:start position:0%
+happens right we'll pass over that
+without ex explicating it at all and in
+
+ align:start position:0%
+without ex explicating it at all and in
+ 
+
+ align:start position:0%
+without ex explicating it at all and in
+that process of modernization we become
+
+ align:start position:0%
+that process of modernization we become
+ 
+
+ align:start position:0%
+that process of modernization we become
+more cognizant of what we're
+
+ align:start position:0%
+more cognizant of what we're
+ 
+
+ align:start position:0%
+more cognizant of what we're
+adding but we become so cognizant of
+
+ align:start position:0%
+adding but we become so cognizant of
+ 
+
+ align:start position:0%
+adding but we become so cognizant of
+what we're adding
+
+ align:start position:0%
+what we're adding
+ 
+
+ align:start position:0%
+what we're adding
+that that we can actually become just
+
+ align:start position:0%
+that that we can actually become just
+ 
+
+ align:start position:0%
+that that we can actually become just
+um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh I think therefore I am is a stage in
+
+ align:start position:0%
+uh I think therefore I am is a stage in
+ 
+
+ align:start position:0%
+uh I think therefore I am is a stage in
+that process right and now
+
+ align:start position:0%
+that process right and now
+ 
+
+ align:start position:0%
+that process right and now
+it's I think I am so maybe I am right
+
+ align:start position:0%
+it's I think I am so maybe I am right
+ 
+
+ align:start position:0%
+it's I think I am so maybe I am right
+but only because I think I am there's
+
+ align:start position:0%
+but only because I think I am there's
+ 
+
+ align:start position:0%
+but only because I think I am there's
+something troubling about that and I
+
+ align:start position:0%
+something troubling about that and I
+ 
+
+ align:start position:0%
+something troubling about that and I
+don't think that Lewis's assessment of
+
+ align:start position:0%
+don't think that Lewis's assessment of
+ 
+
+ align:start position:0%
+don't think that Lewis's assessment of
+things is totally accurate. I think his
+
+ align:start position:0%
+things is totally accurate. I think his
+ 
+
+ align:start position:0%
+things is totally accurate. I think his
+reading of the Middle Ages is more
+
+ align:start position:0%
+reading of the Middle Ages is more
+ 
+
+ align:start position:0%
+reading of the Middle Ages is more
+reliable than his reading of his own
+
+ align:start position:0%
+reliable than his reading of his own
+ 
+
+ align:start position:0%
+reliable than his reading of his own
+times.
+
+ align:start position:0%
+times.
+ 
+
+ align:start position:0%
+times.
+Um, but what he's saying here at the end
+
+ align:start position:0%
+Um, but what he's saying here at the end
+ 
+
+ align:start position:0%
+Um, but what he's saying here at the end
+is if that's
+
+ align:start position:0%
+is if that's
+ 
+
+ align:start position:0%
+is if that's
+true, if that's true, we've eaten up
+
+ align:start position:0%
+true, if that's true, we've eaten up
+ 
+
+ align:start position:0%
+true, if that's true, we've eaten up
+everything else and all we have left is
+
+ align:start position:0%
+everything else and all we have left is
+ 
+
+ align:start position:0%
+everything else and all we have left is
+to eat ourselves, right? And and that is
+
+ align:start position:0%
+to eat ourselves, right? And and that is
+ 
+
+ align:start position:0%
+to eat ourselves, right? And and that is
+his dark question. And I think when
+
+ align:start position:0%
+his dark question. And I think when
+ 
+
+ align:start position:0%
+his dark question. And I think when
+Caner says that Lewis has this kind of
+
+ align:start position:0%
+Caner says that Lewis has this kind of
+ 
+
+ align:start position:0%
+Caner says that Lewis has this kind of
+despair, right, this dark cast to
+
+ align:start position:0%
+despair, right, this dark cast to
+ 
+
+ align:start position:0%
+despair, right, this dark cast to
+things, he's really picking up on the
+
+ align:start position:0%
+things, he's really picking up on the
+ 
+
+ align:start position:0%
+things, he's really picking up on the
+very end of this book.
+
+ align:start position:0%
+very end of this book.
+ 
+
+ align:start position:0%
+very end of this book.
+Um, but I think in general I don't agree
+
+ align:start position:0%
+Um, but I think in general I don't agree
+ 
+
+ align:start position:0%
+Um, but I think in general I don't agree
+with Caner's assessment. Um, there's
+
+ align:start position:0%
+with Caner's assessment. Um, there's
+ 
+
+ align:start position:0%
+with Caner's assessment. Um, there's
+there's one more thing that I that I
+
+ align:start position:0%
+there's one more thing that I that I
+ 
+
+ align:start position:0%
+there's one more thing that I that I
+absolutely want to do because I sent you
+
+ align:start position:0%
+absolutely want to do because I sent you
+ 
+
+ align:start position:0%
+absolutely want to do because I sent you
+these pages and of course I sent them to
+
+ align:start position:0%
+these pages and of course I sent them to
+ 
+
+ align:start position:0%
+these pages and of course I sent them to
+you in such a way that you could not
+
+ align:start position:0%
+you in such a way that you could not
+ 
+
+ align:start position:0%
+you in such a way that you could not
+read them. Um, but but there's but
+
+ align:start position:0%
+read them. Um, but but there's but
+ 
+
+ align:start position:0%
+read them. Um, but but there's but
+there's sort of one more piece to the
+
+ align:start position:0%
+there's sort of one more piece to the
+ 
+
+ align:start position:0%
+there's sort of one more piece to the
+Tolken story that I I want to go back to
+
+ align:start position:0%
+Tolken story that I I want to go back to
+ 
+
+ align:start position:0%
+Tolken story that I I want to go back to
+Broadell. I want to go back to World War
+
+ align:start position:0%
+Broadell. I want to go back to World War
+ 
+
+ align:start position:0%
+Broadell. I want to go back to World War
+II and what all these all these sort of
+
+ align:start position:0%
+II and what all these all these sort of
+ 
+
+ align:start position:0%
+II and what all these all these sort of
+cataclysmic political events that are
+
+ align:start position:0%
+cataclysmic political events that are
+ 
+
+ align:start position:0%
+cataclysmic political events that are
+happening. Okay, Miranda, you're going
+
+ align:start position:0%
+happening. Okay, Miranda, you're going
+ 
+
+ align:start position:0%
+happening. Okay, Miranda, you're going
+to derail me. Yeah. Yeah. I guess if you
+
+ align:start position:0%
+to derail me. Yeah. Yeah. I guess if you
+ 
+
+ align:start position:0%
+to derail me. Yeah. Yeah. I guess if you
+another derailing thing of of one of the
+
+ align:start position:0%
+another derailing thing of of one of the
+ 
+
+ align:start position:0%
+another derailing thing of of one of the
+things I'd always heard against Tolken
+
+ align:start position:0%
+things I'd always heard against Tolken
+ 
+
+ align:start position:0%
+things I'd always heard against Tolken
+is the whole, you know, well, is he
+
+ align:start position:0%
+is the whole, you know, well, is he
+ 
+
+ align:start position:0%
+is the whole, you know, well, is he
+sexist in terms of not having there's
+
+ align:start position:0%
+sexist in terms of not having there's
+ 
+
+ align:start position:0%
+sexist in terms of not having there's
+not a very very strong woman character
+
+ align:start position:0%
+not a very very strong woman character
+ 
+
+ align:start position:0%
+not a very very strong woman character
+or anything like that. But then, you
+
+ align:start position:0%
+or anything like that. But then, you
+ 
+
+ align:start position:0%
+or anything like that. But then, you
+know, you read, well, he had a wonderful
+
+ align:start position:0%
+know, you read, well, he had a wonderful
+ 
+
+ align:start position:0%
+know, you read, well, he had a wonderful
+wife that he loved dearly and children
+
+ align:start position:0%
+wife that he loved dearly and children
+ 
+
+ align:start position:0%
+wife that he loved dearly and children
+and stuff like that. And it's sort of,
+
+ align:start position:0%
+and stuff like that. And it's sort of,
+ 
+
+ align:start position:0%
+and stuff like that. And it's sort of,
+you know, he had four children
+
+ align:start position:0%
+you know, he had four children
+ 
+
+ align:start position:0%
+you know, he had four children
+incidentally, not the three that Caner
+
+ align:start position:0%
+incidentally, not the three that Caner
+ 
+
+ align:start position:0%
+incidentally, not the three that Caner
+says. I'm not sure which one of his
+
+ align:start position:0%
+says. I'm not sure which one of his
+ 
+
+ align:start position:0%
+says. I'm not sure which one of his
+children Caner got rid of,
+
+ align:start position:0%
+children Caner got rid of,
+ 
+
+ align:start position:0%
+children Caner got rid of,
+but it's kind of a serious flaw if
+
+ align:start position:0%
+but it's kind of a serious flaw if
+ 
+
+ align:start position:0%
+but it's kind of a serious flaw if
+you're writing a biography of someone, I
+
+ align:start position:0%
+you're writing a biography of someone, I
+ 
+
+ align:start position:0%
+you're writing a biography of someone, I
+think, to get rid of one of their
+
+ align:start position:0%
+think, to get rid of one of their
+ 
+
+ align:start position:0%
+think, to get rid of one of their
+children, but anyway, that's an aside.
+
+ align:start position:0%
+children, but anyway, that's an aside.
+ 
+
+ align:start position:0%
+children, but anyway, that's an aside.
+But that like I think I'm wondering if
+
+ align:start position:0%
+But that like I think I'm wondering if
+ 
+
+ align:start position:0%
+But that like I think I'm wondering if
+that's a lot more picking up on the
+
+ align:start position:0%
+that's a lot more picking up on the
+ 
+
+ align:start position:0%
+that's a lot more picking up on the
+medieval stuff that there would be you
+
+ align:start position:0%
+medieval stuff that there would be you
+ 
+
+ align:start position:0%
+medieval stuff that there would be you
+know there's women but they're sort of
+
+ align:start position:0%
+know there's women but they're sort of
+ 
+
+ align:start position:0%
+know there's women but they're sort of
+on the side type of they're not really
+
+ align:start position:0%
+on the side type of they're not really
+ 
+
+ align:start position:0%
+on the side type of they're not really
+at all part of like you know nowadays
+
+ align:start position:0%
+at all part of like you know nowadays
+ 
+
+ align:start position:0%
+at all part of like you know nowadays
+you're like well we need to have you
+
+ align:start position:0%
+you're like well we need to have you
+ 
+
+ align:start position:0%
+you're like well we need to have you
+know the woman the you know the guy the
+
+ align:start position:0%
+know the woman the you know the guy the
+ 
+
+ align:start position:0%
+know the woman the you know the guy the
+Yeah. Okay. There's a huge literature on
+
+ align:start position:0%
+Yeah. Okay. There's a huge literature on
+ 
+
+ align:start position:0%
+Yeah. Okay. There's a huge literature on
+this and we won't we won't go there
+
+ align:start position:0%
+this and we won't we won't go there
+ 
+
+ align:start position:0%
+this and we won't we won't go there
+because I actually have somewhere else I
+
+ align:start position:0%
+because I actually have somewhere else I
+ 
+
+ align:start position:0%
+because I actually have somewhere else I
+want to go and we don't have enough time
+
+ align:start position:0%
+want to go and we don't have enough time
+ 
+
+ align:start position:0%
+want to go and we don't have enough time
+to do both. Um, but let me just say
+
+ align:start position:0%
+to do both. Um, but let me just say
+ 
+
+ align:start position:0%
+to do both. Um, but let me just say
+this. Uh, Tolken's world is utterly a
+
+ align:start position:0%
+this. Uh, Tolken's world is utterly a
+ 
+
+ align:start position:0%
+this. Uh, Tolken's world is utterly a
+masculinist one. It is also a violent
+
+ align:start position:0%
+masculinist one. It is also a violent
+ 
+
+ align:start position:0%
+masculinist one. It is also a violent
+one. It is perfectly possible to write a
+
+ align:start position:0%
+one. It is perfectly possible to write a
+ 
+
+ align:start position:0%
+one. It is perfectly possible to write a
+good feminist critique of all of this
+
+ align:start position:0%
+good feminist critique of all of this
+ 
+
+ align:start position:0%
+good feminist critique of all of this
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+say, "Look at that masculinist world and
+
+ align:start position:0%
+say, "Look at that masculinist world and
+ 
+
+ align:start position:0%
+say, "Look at that masculinist world and
+how violent it is." Um, right. Tolken,
+
+ align:start position:0%
+how violent it is." Um, right. Tolken,
+ 
+
+ align:start position:0%
+how violent it is." Um, right. Tolken,
+if pressed on this, would say, "You're
+
+ align:start position:0%
+if pressed on this, would say, "You're
+ 
+
+ align:start position:0%
+if pressed on this, would say, "You're
+right. Absolutely. It's a violent world.
+
+ align:start position:0%
+right. Absolutely. It's a violent world.
+ 
+
+ align:start position:0%
+right. Absolutely. It's a violent world.
+That is the world that I know. This is
+
+ align:start position:0%
+That is the world that I know. This is
+ 
+
+ align:start position:0%
+That is the world that I know. This is
+in fact the world of sin, right? This is
+
+ align:start position:0%
+in fact the world of sin, right? This is
+ 
+
+ align:start position:0%
+in fact the world of sin, right? This is
+the fallen world. It is violent. And to
+
+ align:start position:0%
+the fallen world. It is violent. And to
+ 
+
+ align:start position:0%
+the fallen world. It is violent. And to
+the extent that we can mitigate that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+violence in whatever way, but maybe also
+
+ align:start position:0%
+violence in whatever way, but maybe also
+ 
+
+ align:start position:0%
+violence in whatever way, but maybe also
+in the way of of um female influence,
+
+ align:start position:0%
+in the way of of um female influence,
+ 
+
+ align:start position:0%
+in the way of of um female influence,
+that's a good thing. Now, if you've got
+
+ align:start position:0%
+that's a good thing. Now, if you've got
+ 
+
+ align:start position:0%
+that's a good thing. Now, if you've got
+sort of Beaolf running in your head from
+
+ align:start position:0%
+sort of Beaolf running in your head from
+ 
+
+ align:start position:0%
+sort of Beaolf running in your head from
+start to finish, you know that in that
+
+ align:start position:0%
+start to finish, you know that in that
+ 
+
+ align:start position:0%
+start to finish, you know that in that
+Anglo-Saxon world, female peacemaking
+
+ align:start position:0%
+Anglo-Saxon world, female peacemaking
+ 
+
+ align:start position:0%
+Anglo-Saxon world, female peacemaking
+doesn't work. We have at least three
+
+ align:start position:0%
+doesn't work. We have at least three
+ 
+
+ align:start position:0%
+doesn't work. We have at least three
+separate episodes in the Beaowolf larger
+
+ align:start position:0%
+separate episodes in the Beaowolf larger
+ 
+
+ align:start position:0%
+separate episodes in the Beaowolf larger
+narrative of specific references to
+
+ align:start position:0%
+narrative of specific references to
+ 
+
+ align:start position:0%
+narrative of specific references to
+attempts to use women. In fact, they're
+
+ align:start position:0%
+attempts to use women. In fact, they're
+ 
+
+ align:start position:0%
+attempts to use women. In fact, they're
+called like the queen, the Danish queen
+
+ align:start position:0%
+called like the queen, the Danish queen
+ 
+
+ align:start position:0%
+called like the queen, the Danish queen
+is called a peace weaver. Three or four
+
+ align:start position:0%
+is called a peace weaver. Three or four
+ 
+
+ align:start position:0%
+is called a peace weaver. Three or four
+times she's called that, a peacewaver.
+
+ align:start position:0%
+times she's called that, a peacewaver.
+ 
+
+ align:start position:0%
+times she's called that, a peacewaver.
+And yet we know it doesn't work because
+
+ align:start position:0%
+And yet we know it doesn't work because
+ 
+
+ align:start position:0%
+And yet we know it doesn't work because
+they're constantly feuding with each
+
+ align:start position:0%
+they're constantly feuding with each
+ 
+
+ align:start position:0%
+they're constantly feuding with each
+other. The lay of Ingeld which is
+
+ align:start position:0%
+other. The lay of Ingeld which is
+ 
+
+ align:start position:0%
+other. The lay of Ingeld which is
+embedded in there. Ingeld is married off
+
+ align:start position:0%
+embedded in there. Ingeld is married off
+ 
+
+ align:start position:0%
+embedded in there. Ingeld is married off
+to a woman who is the daughter of his
+
+ align:start position:0%
+to a woman who is the daughter of his
+ 
+
+ align:start position:0%
+to a woman who is the daughter of his
+enemy. And the idea is it's supposed to
+
+ align:start position:0%
+enemy. And the idea is it's supposed to
+ 
+
+ align:start position:0%
+enemy. And the idea is it's supposed to
+make peace. What does it do? Well, in
+
+ align:start position:0%
+make peace. What does it do? Well, in
+ 
+
+ align:start position:0%
+make peace. What does it do? Well, in
+fact, he ends up in the completely
+
+ align:start position:0%
+fact, he ends up in the completely
+ 
+
+ align:start position:0%
+fact, he ends up in the completely
+intractable situation of trying to
+
+ align:start position:0%
+intractable situation of trying to
+ 
+
+ align:start position:0%
+intractable situation of trying to
+decide whether he should kill his wife's
+
+ align:start position:0%
+decide whether he should kill his wife's
+ 
+
+ align:start position:0%
+decide whether he should kill his wife's
+father or his own brother, right? And
+
+ align:start position:0%
+father or his own brother, right? And
+ 
+
+ align:start position:0%
+father or his own brother, right? And
+you know, great, you lose both ways. So
+
+ align:start position:0%
+you know, great, you lose both ways. So
+ 
+
+ align:start position:0%
+you know, great, you lose both ways. So
+Tolken would acknowledge, I think,
+
+ align:start position:0%
+Tolken would acknowledge, I think,
+ 
+
+ align:start position:0%
+Tolken would acknowledge, I think,
+freely that his world is a totally
+
+ align:start position:0%
+freely that his world is a totally
+ 
+
+ align:start position:0%
+freely that his world is a totally
+masculineist one and that it's violent,
+
+ align:start position:0%
+masculineist one and that it's violent,
+ 
+
+ align:start position:0%
+masculineist one and that it's violent,
+but he would also say, "Look, read the
+
+ align:start position:0%
+but he would also say, "Look, read the
+ 
+
+ align:start position:0%
+but he would also say, "Look, read the
+sources. Read Beaolf. It'll tell you
+
+ align:start position:0%
+sources. Read Beaolf. It'll tell you
+ 
+
+ align:start position:0%
+sources. Read Beaolf. It'll tell you
+women aren't going to solve this
+
+ align:start position:0%
+women aren't going to solve this
+ 
+
+ align:start position:0%
+women aren't going to solve this
+problem." Okay? So I'm going to leave it
+
+ align:start position:0%
+problem." Okay? So I'm going to leave it
+ 
+
+ align:start position:0%
+problem." Okay? So I'm going to leave it
+at that. Okay? But I want I want to go
+
+ align:start position:0%
+at that. Okay? But I want I want to go
+ 
+
+ align:start position:0%
+at that. Okay? But I want I want to go
+back to war.
+
+ align:start position:0%
+back to war.
+ 
+
+ align:start position:0%
+back to war.
+Um, as you know, uh, Beaolf is a, um,
+
+ align:start position:0%
+Um, as you know, uh, Beaolf is a, um,
+ 
+
+ align:start position:0%
+Um, as you know, uh, Beaolf is a, um,
+uh, sort of a not about an Anglo-Saxon,
+
+ align:start position:0%
+uh, sort of a not about an Anglo-Saxon,
+ 
+
+ align:start position:0%
+uh, sort of a not about an Anglo-Saxon,
+but
+
+ align:start position:0%
+but
+ 
+
+ align:start position:0%
+but
+nonetheless speaks to, um, Anglo-Saxon
+
+ align:start position:0%
+nonetheless speaks to, um, Anglo-Saxon
+ 
+
+ align:start position:0%
+nonetheless speaks to, um, Anglo-Saxon
+culture. It is, after all, written by an
+
+ align:start position:0%
+culture. It is, after all, written by an
+ 
+
+ align:start position:0%
+culture. It is, after all, written by an
+Anglo-Saxon in the Anglo-Saxon language.
+
+ align:start position:0%
+Anglo-Saxon in the Anglo-Saxon language.
+ 
+
+ align:start position:0%
+Anglo-Saxon in the Anglo-Saxon language.
+Uh, and and Tolken specifically
+
+ align:start position:0%
+Uh, and and Tolken specifically
+ 
+
+ align:start position:0%
+Uh, and and Tolken specifically
+responded on numerous occasions to
+
+ align:start position:0%
+responded on numerous occasions to
+ 
+
+ align:start position:0%
+responded on numerous occasions to
+critics who poo pooed it. You may know
+
+ align:start position:0%
+critics who poo pooed it. You may know
+ 
+
+ align:start position:0%
+critics who poo pooed it. You may know
+that it was considered to be a totally
+
+ align:start position:0%
+that it was considered to be a totally
+ 
+
+ align:start position:0%
+that it was considered to be a totally
+inferior text for a long time basically
+
+ align:start position:0%
+inferior text for a long time basically
+ 
+
+ align:start position:0%
+inferior text for a long time basically
+because it had been written by some beer
+
+ align:start position:0%
+because it had been written by some beer
+ 
+
+ align:start position:0%
+because it had been written by some beer
+swilling
+
+ align:start position:0%
+swilling
+ 
+
+ align:start position:0%
+swilling
+Anglo-Saxon. Uh so this is this is this
+
+ align:start position:0%
+Anglo-Saxon. Uh so this is this is this
+ 
+
+ align:start position:0%
+Anglo-Saxon. Uh so this is this is this
+is um Tolken's response to this. This is
+
+ align:start position:0%
+is um Tolken's response to this. This is
+ 
+
+ align:start position:0%
+is um Tolken's response to this. This is
+from um um I actually let me let me read
+
+ align:start position:0%
+from um um I actually let me let me read
+ 
+
+ align:start position:0%
+from um um I actually let me let me read
+his actual response from from the the
+
+ align:start position:0%
+his actual response from from the the
+ 
+
+ align:start position:0%
+his actual response from from the the
+the essay Beaolf and the Critics and
+
+ align:start position:0%
+the essay Beaolf and the Critics and
+ 
+
+ align:start position:0%
+the essay Beaolf and the Critics and
+then I'm going to read you some some
+
+ align:start position:0%
+then I'm going to read you some some
+ 
+
+ align:start position:0%
+then I'm going to read you some some
+letters. All right.
+
+ align:start position:0%
+letters. All right.
+ 
+
+ align:start position:0%
+letters. All right.
+He's talking about a French critic,
+
+ align:start position:0%
+He's talking about a French critic,
+ 
+
+ align:start position:0%
+He's talking about a French critic,
+Yuserand. The strange poem of Beaowolf.
+
+ align:start position:0%
+Yuserand. The strange poem of Beaowolf.
+ 
+
+ align:start position:0%
+Yuserand. The strange poem of Beaowolf.
+He wanders on the most important
+
+ align:start position:0%
+He wanders on the most important
+ 
+
+ align:start position:0%
+He wanders on the most important
+monument of Anglo-Saxon literature and
+
+ align:start position:0%
+monument of Anglo-Saxon literature and
+ 
+
+ align:start position:0%
+monument of Anglo-Saxon literature and
+then in parenthesis talking has the poor
+
+ align:start position:0%
+then in parenthesis talking has the poor
+ 
+
+ align:start position:0%
+then in parenthesis talking has the poor
+poet lifts his nose out of his beerhorn
+
+ align:start position:0%
+poet lifts his nose out of his beerhorn
+ 
+
+ align:start position:0%
+poet lifts his nose out of his beerhorn
+and humbly acknowledges the gentleman's
+
+ align:start position:0%
+and humbly acknowledges the gentleman's
+ 
+
+ align:start position:0%
+and humbly acknowledges the gentleman's
+condescension. Like old Celtic tales is
+
+ align:start position:0%
+condescension. Like old Celtic tales is
+ 
+
+ align:start position:0%
+condescension. Like old Celtic tales is
+a medly of pagan legends which do not
+
+ align:start position:0%
+a medly of pagan legends which do not
+ 
+
+ align:start position:0%
+a medly of pagan legends which do not
+concern Beaolf the hero in particular
+
+ align:start position:0%
+concern Beaolf the hero in particular
+ 
+
+ align:start position:0%
+concern Beaolf the hero in particular
+and of historical facts. New discrepancy
+
+ align:start position:0%
+and of historical facts. New discrepancy
+ 
+
+ align:start position:0%
+and of historical facts. New discrepancy
+is introduced in trying to adapt the old
+
+ align:start position:0%
+is introduced in trying to adapt the old
+ 
+
+ align:start position:0%
+is introduced in trying to adapt the old
+tale to the faith of his the author's
+
+ align:start position:0%
+tale to the faith of his the author's
+ 
+
+ align:start position:0%
+tale to the faith of his the author's
+day. No need to expedate on the
+
+ align:start position:0%
+day. No need to expedate on the
+ 
+
+ align:start position:0%
+day. No need to expedate on the
+incoherence of a poem formed of such
+
+ align:start position:0%
+incoherence of a poem formed of such
+ 
+
+ align:start position:0%
+incoherence of a poem formed of such
+elements. Then in parenthesis, Tolken
+
+ align:start position:0%
+elements. Then in parenthesis, Tolken
+ 
+
+ align:start position:0%
+elements. Then in parenthesis, Tolken
+says, "The poor poet here hastily hides
+
+ align:start position:0%
+says, "The poor poet here hastily hides
+ 
+
+ align:start position:0%
+says, "The poor poet here hastily hides
+his blushes in the beer horn again. Its
+
+ align:start position:0%
+his blushes in the beer horn again. Its
+ 
+
+ align:start position:0%
+his blushes in the beer horn again. Its
+heroes, now we're back to the French
+
+ align:start position:0%
+heroes, now we're back to the French
+ 
+
+ align:start position:0%
+heroes, now we're back to the French
+critic, its heroes are at once pagan and
+
+ align:start position:0%
+critic, its heroes are at once pagan and
+ 
+
+ align:start position:0%
+critic, its heroes are at once pagan and
+Christian. They believe in Christ and we
+
+ align:start position:0%
+Christian. They believe in Christ and we
+ 
+
+ align:start position:0%
+Christian. They believe in Christ and we
+deathly and complicated flabbergasted
+
+ align:start position:0%
+deathly and complicated flabbergasted
+ 
+
+ align:start position:0%
+deathly and complicated flabbergasted
+silence throughout the hall while a
+
+ align:start position:0%
+silence throughout the hall while a
+ 
+
+ align:start position:0%
+silence throughout the hall while a
+horrible suspicion crosses the poet's
+
+ align:start position:0%
+horrible suspicion crosses the poet's
+ 
+
+ align:start position:0%
+horrible suspicion crosses the poet's
+mind that the magnificent gentleman is
+
+ align:start position:0%
+mind that the magnificent gentleman is
+ 
+
+ align:start position:0%
+mind that the magnificent gentleman is
+an
+
+ align:start position:0%
+an
+ 
+
+ align:start position:0%
+an
+idiot." Anyway, this whole essay is like
+
+ align:start position:0%
+idiot." Anyway, this whole essay is like
+ 
+
+ align:start position:0%
+idiot." Anyway, this whole essay is like
+this. you know, 70 pages of this kind of
+
+ align:start position:0%
+this. you know, 70 pages of this kind of
+ 
+
+ align:start position:0%
+this. you know, 70 pages of this kind of
+sort of very biting criticism, but the
+
+ align:start position:0%
+sort of very biting criticism, but the
+ 
+
+ align:start position:0%
+sort of very biting criticism, but the
+the racial issues that are implied in
+
+ align:start position:0%
+the racial issues that are implied in
+ 
+
+ align:start position:0%
+the racial issues that are implied in
+all of this, what it means to be
+
+ align:start position:0%
+all of this, what it means to be
+ 
+
+ align:start position:0%
+all of this, what it means to be
+Germanic, Tutonic, Norse, heroic, right,
+
+ align:start position:0%
+Germanic, Tutonic, Norse, heroic, right,
+ 
+
+ align:start position:0%
+Germanic, Tutonic, Norse, heroic, right,
+are fraught ones in the context of World
+
+ align:start position:0%
+are fraught ones in the context of World
+ 
+
+ align:start position:0%
+are fraught ones in the context of World
+War I and World War II, obviously,
+
+ align:start position:0%
+War I and World War II, obviously,
+ 
+
+ align:start position:0%
+War I and World War II, obviously,
+right? What does it mean to have a
+
+ align:start position:0%
+right? What does it mean to have a
+ 
+
+ align:start position:0%
+right? What does it mean to have a
+Germanic hero that kills dragons and
+
+ align:start position:0%
+Germanic hero that kills dragons and
+ 
+
+ align:start position:0%
+Germanic hero that kills dragons and
+goes to the bottom of the sea, right?
+
+ align:start position:0%
+goes to the bottom of the sea, right?
+ 
+
+ align:start position:0%
+goes to the bottom of the sea, right?
+especially if you're an Englishman
+
+ align:start position:0%
+especially if you're an Englishman
+ 
+
+ align:start position:0%
+especially if you're an Englishman
+writing about a monument of your English
+
+ align:start position:0%
+writing about a monument of your English
+ 
+
+ align:start position:0%
+writing about a monument of your English
+past, an Anglo-Saxon poem. Uh this is
+
+ align:start position:0%
+past, an Anglo-Saxon poem. Uh this is
+ 
+
+ align:start position:0%
+past, an Anglo-Saxon poem. Uh this is
+from a letter uh written in
+
+ align:start position:0%
+from a letter uh written in
+ 
+
+ align:start position:0%
+from a letter uh written in
+1941 to his son Michael. I have spent
+
+ align:start position:0%
+1941 to his son Michael. I have spent
+ 
+
+ align:start position:0%
+1941 to his son Michael. I have spent
+most of my life since I was your age
+
+ align:start position:0%
+most of my life since I was your age
+ 
+
+ align:start position:0%
+most of my life since I was your age
+studying Germanic matters in the general
+
+ align:start position:0%
+studying Germanic matters in the general
+ 
+
+ align:start position:0%
+studying Germanic matters in the general
+sense that includes England and
+
+ align:start position:0%
+sense that includes England and
+ 
+
+ align:start position:0%
+sense that includes England and
+Scandinavia. There is a great deal more
+
+ align:start position:0%
+Scandinavia. There is a great deal more
+ 
+
+ align:start position:0%
+Scandinavia. There is a great deal more
+force and truth than ignorant people
+
+ align:start position:0%
+force and truth than ignorant people
+ 
+
+ align:start position:0%
+force and truth than ignorant people
+imagine in the Germanic ideal. I was
+
+ align:start position:0%
+imagine in the Germanic ideal. I was
+ 
+
+ align:start position:0%
+imagine in the Germanic ideal. I was
+much attracted by it as an undergraduate
+
+ align:start position:0%
+much attracted by it as an undergraduate
+ 
+
+ align:start position:0%
+much attracted by it as an undergraduate
+when Hitler was, I suppose, dabbling in
+
+ align:start position:0%
+when Hitler was, I suppose, dabbling in
+ 
+
+ align:start position:0%
+when Hitler was, I suppose, dabbling in
+paint and had not heard of it in
+
+ align:start position:0%
+paint and had not heard of it in
+ 
+
+ align:start position:0%
+paint and had not heard of it in
+reaction against the classics, but no
+
+ align:start position:0%
+reaction against the classics, but no
+ 
+
+ align:start position:0%
+reaction against the classics, but no
+one ever calls on me to broadcast or to
+
+ align:start position:0%
+one ever calls on me to broadcast or to
+ 
+
+ align:start position:0%
+one ever calls on me to broadcast or to
+do a postcript. Yet, I suppose I know
+
+ align:start position:0%
+do a postcript. Yet, I suppose I know
+ 
+
+ align:start position:0%
+do a postcript. Yet, I suppose I know
+better than most what is the truth about
+
+ align:start position:0%
+better than most what is the truth about
+ 
+
+ align:start position:0%
+better than most what is the truth about
+this Nordic nonsense. Anyway, I have in
+
+ align:start position:0%
+this Nordic nonsense. Anyway, I have in
+ 
+
+ align:start position:0%
+this Nordic nonsense. Anyway, I have in
+this war, that would be World War II
+
+ align:start position:0%
+this war, that would be World War II
+ 
+
+ align:start position:0%
+this war, that would be World War II
+now, a burning private grudge which
+
+ align:start position:0%
+now, a burning private grudge which
+ 
+
+ align:start position:0%
+now, a burning private grudge which
+would probably make me a better soldier
+
+ align:start position:0%
+would probably make me a better soldier
+ 
+
+ align:start position:0%
+would probably make me a better soldier
+at 49 than I was at 22 against that
+
+ align:start position:0%
+at 49 than I was at 22 against that
+ 
+
+ align:start position:0%
+at 49 than I was at 22 against that
+ruddy little ignoramis Adolf Hitler.
+
+ align:start position:0%
+ruddy little ignoramis Adolf Hitler.
+ 
+
+ align:start position:0%
+ruddy little ignoramis Adolf Hitler.
+Ruining, perverting, misapplying, and
+
+ align:start position:0%
+Ruining, perverting, misapplying, and
+ 
+
+ align:start position:0%
+Ruining, perverting, misapplying, and
+making forever a cursed that noble
+
+ align:start position:0%
+making forever a cursed that noble
+ 
+
+ align:start position:0%
+making forever a cursed that noble
+northern spirit a supreme contribution
+
+ align:start position:0%
+northern spirit a supreme contribution
+ 
+
+ align:start position:0%
+northern spirit a supreme contribution
+to Europe which I have ever loved and
+
+ align:start position:0%
+to Europe which I have ever loved and
+ 
+
+ align:start position:0%
+to Europe which I have ever loved and
+tried to present in its true light.
+
+ align:start position:0%
+tried to present in its true light.
+ 
+
+ align:start position:0%
+tried to present in its true light.
+Nowhere, incidentally, was it nobler
+
+ align:start position:0%
+Nowhere, incidentally, was it nobler
+ 
+
+ align:start position:0%
+Nowhere, incidentally, was it nobler
+than in England, nor more early
+
+ align:start position:0%
+than in England, nor more early
+ 
+
+ align:start position:0%
+than in England, nor more early
+sanctified and Christianized. And this
+
+ align:start position:0%
+sanctified and Christianized. And this
+ 
+
+ align:start position:0%
+sanctified and Christianized. And this
+is a really powerful
+
+ align:start position:0%
+is a really powerful
+ 
+
+ align:start position:0%
+is a really powerful
+passage because Tolken with his German
+
+ align:start position:0%
+passage because Tolken with his German
+ 
+
+ align:start position:0%
+passage because Tolken with his German
+name, right, and his love of German
+
+ align:start position:0%
+name, right, and his love of German
+ 
+
+ align:start position:0%
+name, right, and his love of German
+Germanic lore and these heroes and this
+
+ align:start position:0%
+Germanic lore and these heroes and this
+ 
+
+ align:start position:0%
+Germanic lore and these heroes and this
+masculinist culture, right, which he
+
+ align:start position:0%
+masculinist culture, right, which he
+ 
+
+ align:start position:0%
+masculinist culture, right, which he
+freely partates
+
+ align:start position:0%
+freely partates
+ 
+
+ align:start position:0%
+freely partates
+in is feeling the tension of being alive
+
+ align:start position:0%
+in is feeling the tension of being alive
+ 
+
+ align:start position:0%
+in is feeling the tension of being alive
+in
+
+ align:start position:0%
+in
+ 
+
+ align:start position:0%
+in
+1941 and looking at what someone is
+
+ align:start position:0%
+1941 and looking at what someone is
+ 
+
+ align:start position:0%
+1941 and looking at what someone is
+doing with a quote Germanic ideal.
+
+ align:start position:0%
+doing with a quote Germanic ideal.
+ 
+
+ align:start position:0%
+doing with a quote Germanic ideal.
+Let me read one more from one more
+
+ align:start position:0%
+Let me read one more from one more
+ 
+
+ align:start position:0%
+Let me read one more from one more
+letter. This actually is dated in 1938.
+
+ align:start position:0%
+letter. This actually is dated in 1938.
+ 
+
+ align:start position:0%
+letter. This actually is dated in 1938.
+So before the Sudatan land, right back
+
+ align:start position:0%
+So before the Sudatan land, right back
+ 
+
+ align:start position:0%
+So before the Sudatan land, right back
+at a moment when people were still
+
+ align:start position:0%
+at a moment when people were still
+ 
+
+ align:start position:0%
+at a moment when people were still
+saying, "Hey, maybe we don't really know
+
+ align:start position:0%
+saying, "Hey, maybe we don't really know
+ 
+
+ align:start position:0%
+saying, "Hey, maybe we don't really know
+what's happening in Germany." I think
+
+ align:start position:0%
+what's happening in Germany." I think
+ 
+
+ align:start position:0%
+what's happening in Germany." I think
+it's very telling. Um this is a letter
+
+ align:start position:0%
+it's very telling. Um this is a letter
+ 
+
+ align:start position:0%
+it's very telling. Um this is a letter
+that was written to a German publishing
+
+ align:start position:0%
+that was written to a German publishing
+ 
+
+ align:start position:0%
+that was written to a German publishing
+house louning fell who were negotiating
+
+ align:start position:0%
+house louning fell who were negotiating
+ 
+
+ align:start position:0%
+house louning fell who were negotiating
+a publication of a German translation of
+
+ align:start position:0%
+a publication of a German translation of
+ 
+
+ align:start position:0%
+a publication of a German translation of
+the hobbit and they asked Tolken if he
+
+ align:start position:0%
+the hobbit and they asked Tolken if he
+ 
+
+ align:start position:0%
+the hobbit and they asked Tolken if he
+was Irish that is are you
+
+ align:start position:0%
+was Irish that is are you
+ 
+
+ align:start position:0%
+was Irish that is are you
+Aryan? He
+
+ align:start position:0%
+Aryan? He
+ 
+
+ align:start position:0%
+Aryan? He
+replied he was not aware sorry I am not
+
+ align:start position:0%
+replied he was not aware sorry I am not
+ 
+
+ align:start position:0%
+replied he was not aware sorry I am not
+aware that any of my ancestors spoke
+
+ align:start position:0%
+aware that any of my ancestors spoke
+ 
+
+ align:start position:0%
+aware that any of my ancestors spoke
+Hindustani Persian Gypsy or any related
+
+ align:start position:0%
+Hindustani Persian Gypsy or any related
+ 
+
+ align:start position:0%
+Hindustani Persian Gypsy or any related
+dialects and therefore cannot claim to
+
+ align:start position:0%
+dialects and therefore cannot claim to
+ 
+
+ align:start position:0%
+dialects and therefore cannot claim to
+be Aryan. However, if I am to understand
+
+ align:start position:0%
+be Aryan. However, if I am to understand
+ 
+
+ align:start position:0%
+be Aryan. However, if I am to understand
+that you are inquiring whether I am of
+
+ align:start position:0%
+that you are inquiring whether I am of
+ 
+
+ align:start position:0%
+that you are inquiring whether I am of
+Jewish origin, I can only reply that I
+
+ align:start position:0%
+Jewish origin, I can only reply that I
+ 
+
+ align:start position:0%
+Jewish origin, I can only reply that I
+regret that I appear to have no
+
+ align:start position:0%
+regret that I appear to have no
+ 
+
+ align:start position:0%
+regret that I appear to have no
+ancestors of that gifted people. The
+
+ align:start position:0%
+ancestors of that gifted people. The
+ 
+
+ align:start position:0%
+ancestors of that gifted people. The
+letter goes on for a space and then it
+
+ align:start position:0%
+letter goes on for a space and then it
+ 
+
+ align:start position:0%
+letter goes on for a space and then it
+ends like this. I have been accustomed
+
+ align:start position:0%
+ends like this. I have been accustomed
+ 
+
+ align:start position:0%
+ends like this. I have been accustomed
+to regard my German name with pride and
+
+ align:start position:0%
+to regard my German name with pride and
+ 
+
+ align:start position:0%
+to regard my German name with pride and
+continued to do so throughout the period
+
+ align:start position:0%
+continued to do so throughout the period
+ 
+
+ align:start position:0%
+continued to do so throughout the period
+of the late regrettable war. That would
+
+ align:start position:0%
+of the late regrettable war. That would
+ 
+
+ align:start position:0%
+of the late regrettable war. That would
+be World War I. I cannot, however,
+
+ align:start position:0%
+be World War I. I cannot, however,
+ 
+
+ align:start position:0%
+be World War I. I cannot, however,
+forebear to comment that if impertinent
+
+ align:start position:0%
+forebear to comment that if impertinent
+ 
+
+ align:start position:0%
+forebear to comment that if impertinent
+and irrelevant inquiries of this sort
+
+ align:start position:0%
+and irrelevant inquiries of this sort
+ 
+
+ align:start position:0%
+and irrelevant inquiries of this sort
+are to become the rule in matters of
+
+ align:start position:0%
+are to become the rule in matters of
+ 
+
+ align:start position:0%
+are to become the rule in matters of
+literature, then the time is not far
+
+ align:start position:0%
+literature, then the time is not far
+ 
+
+ align:start position:0%
+literature, then the time is not far
+distant when a German name will no
+
+ align:start position:0%
+distant when a German name will no
+ 
+
+ align:start position:0%
+distant when a German name will no
+longer be a source of pride.
+
+ align:start position:0%
+longer be a source of pride.
+ 
+
+ align:start position:0%
+longer be a source of pride.
+I just wanted you to have that because I
+
+ align:start position:0%
+I just wanted you to have that because I
+ 
+
+ align:start position:0%
+I just wanted you to have that because I
+mean such a powerful
+
+ align:start position:0%
+mean such a powerful
+ 
+
+ align:start position:0%
+mean such a powerful
+testimony to understanding
+
+ align:start position:0%
+testimony to understanding
+ 
+
+ align:start position:0%
+testimony to understanding
+um particularly particularly the letter
+
+ align:start position:0%
+um particularly particularly the letter
+ 
+
+ align:start position:0%
+um particularly particularly the letter
+written in
+
+ align:start position:0%
+written in
+ 
+
+ align:start position:0%
+written in
+1938 when
+
+ align:start position:0%
+1938 when
+ 
+
+ align:start position:0%
+1938 when
+um you know when lots of reasonable
+
+ align:start position:0%
+um you know when lots of reasonable
+ 
+
+ align:start position:0%
+um you know when lots of reasonable
+people said gosh we had no idea what was
+
+ align:start position:0%
+people said gosh we had no idea what was
+ 
+
+ align:start position:0%
+people said gosh we had no idea what was
+coming. Um how could we possibly have
+
+ align:start position:0%
+coming. Um how could we possibly have
+ 
+
+ align:start position:0%
+coming. Um how could we possibly have
+known right? Right. I mean, clearly
+
+ align:start position:0%
+known right? Right. I mean, clearly
+ 
+
+ align:start position:0%
+known right? Right. I mean, clearly
+Tolken has a pretty good sense um of
+
+ align:start position:0%
+Tolken has a pretty good sense um of
+ 
+
+ align:start position:0%
+Tolken has a pretty good sense um of
+what's happening, but I mean, I also
+
+ align:start position:0%
+what's happening, but I mean, I also
+ 
+
+ align:start position:0%
+what's happening, but I mean, I also
+wanted you to have that because it is
+
+ align:start position:0%
+wanted you to have that because it is
+ 
+
+ align:start position:0%
+wanted you to have that because it is
+easy to
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um it is easy to to um
+
+ align:start position:0%
+um it is easy to to um
+ 
+
+ align:start position:0%
+um it is easy to to um
+ridicule, right, the that Germanic
+
+ align:start position:0%
+ridicule, right, the that Germanic
+ 
+
+ align:start position:0%
+ridicule, right, the that Germanic
+ideal, which clearly I mean, which
+
+ align:start position:0%
+ideal, which clearly I mean, which
+ 
+
+ align:start position:0%
+ideal, which clearly I mean, which
+clearly he lived, breathed, died, right,
+
+ align:start position:0%
+clearly he lived, breathed, died, right,
+ 
+
+ align:start position:0%
+clearly he lived, breathed, died, right,
+and it informs his fiction
+
+ align:start position:0%
+and it informs his fiction
+ 
+
+ align:start position:0%
+and it informs his fiction
+utterly.
+
+ align:start position:0%
+utterly.
+ 
+
+ align:start position:0%
+utterly.
+Um, and given the context in which it
+
+ align:start position:0%
+Um, and given the context in which it
+ 
+
+ align:start position:0%
+Um, and given the context in which it
+was written could easily be
+
+ align:start position:0%
+was written could easily be
+ 
+
+ align:start position:0%
+was written could easily be
+misunderstood. And I and I and and I
+
+ align:start position:0%
+misunderstood. And I and I and and I
+ 
+
+ align:start position:0%
+misunderstood. And I and I and and I
+wanted to close with that because it
+
+ align:start position:0%
+wanted to close with that because it
+ 
+
+ align:start position:0%
+wanted to close with that because it
+takes us back one more time to Broadell,
+
+ align:start position:0%
+takes us back one more time to Broadell,
+ 
+
+ align:start position:0%
+takes us back one more time to Broadell,
+right, who also saw, if you will, the
+
+ align:start position:0%
+right, who also saw, if you will, the
+ 
+
+ align:start position:0%
+right, who also saw, if you will, the
+horrors of a particular way of thinking
+
+ align:start position:0%
+horrors of a particular way of thinking
+ 
+
+ align:start position:0%
+horrors of a particular way of thinking
+about
+
+ align:start position:0%
+about
+ 
+
+ align:start position:0%
+about
+race
+
+ align:start position:0%
+race
+ 
+
+ align:start position:0%
+race
+and and and he faces race. I mean, after
+
+ align:start position:0%
+and and and he faces race. I mean, after
+ 
+
+ align:start position:0%
+and and and he faces race. I mean, after
+all, Tolkien is celebrating race in many
+
+ align:start position:0%
+all, Tolkien is celebrating race in many
+ 
+
+ align:start position:0%
+all, Tolkien is celebrating race in many
+ways.
+
+ align:start position:0%
+ways.
+ 
+
+ align:start position:0%
+ways.
+Broadell is he facing it by saying you
+
+ align:start position:0%
+Broadell is he facing it by saying you
+ 
+
+ align:start position:0%
+Broadell is he facing it by saying you
+know no no what really matters is the
+
+ align:start position:0%
+know no no what really matters is the
+ 
+
+ align:start position:0%
+know no no what really matters is the
+mountains the air right the earth the
+
+ align:start position:0%
+mountains the air right the earth the
+ 
+
+ align:start position:0%
+mountains the air right the earth the
+camels right all these other things it's
+
+ align:start position:0%
+camels right all these other things it's
+ 
+
+ align:start position:0%
+camels right all these other things it's
+not race uh but both of them you can see
+
+ align:start position:0%
+not race uh but both of them you can see
+ 
+
+ align:start position:0%
+not race uh but both of them you can see
+I mean these are these are these are
+
+ align:start position:0%
+I mean these are these are these are
+ 
+
+ align:start position:0%
+I mean these are these are these are
+very intelligent men struggling with a
+
+ align:start position:0%
+very intelligent men struggling with a
+ 
+
+ align:start position:0%
+very intelligent men struggling with a
+world that is somewhat incomprehensible
+
+ align:start position:0%
+world that is somewhat incomprehensible
+ 
+
+ align:start position:0%
+world that is somewhat incomprehensible
+to them because it's gone mad right in
+
+ align:start position:0%
+to them because it's gone mad right in
+ 
+
+ align:start position:0%
+to them because it's gone mad right in
+some very real sense from the way they
+
+ align:start position:0%
+some very real sense from the way they
+ 
+
+ align:start position:0%
+some very real sense from the way they
+think about things and and what they
+
+ align:start position:0%
+think about things and and what they
+ 
+
+ align:start position:0%
+think about things and and what they
+write in Tolken it's fiction in broadell
+
+ align:start position:0%
+write in Tolken it's fiction in broadell
+ 
+
+ align:start position:0%
+write in Tolken it's fiction in broadell
+it's history but that line is a fine one
+
+ align:start position:0%
+it's history but that line is a fine one
+ 
+
+ align:start position:0%
+it's history but that line is a fine one
+as we've already said what they write
+
+ align:start position:0%
+as we've already said what they write
+ 
+
+ align:start position:0%
+as we've already said what they write
+then has to somehow deal with this
+
+ align:start position:0%
+then has to somehow deal with this
+ 
+
+ align:start position:0%
+then has to somehow deal with this
+problem that they're confronted with
+
+ align:start position:0%
+problem that they're confronted with
+ 
+
+ align:start position:0%
+problem that they're confronted with
+which is that they live in this world
+
+ align:start position:0%
+which is that they live in this world
+ 
+
+ align:start position:0%
+which is that they live in this world
+gone mad in particular over this
+
+ align:start position:0%
+gone mad in particular over this
+ 
+
+ align:start position:0%
+gone mad in particular over this
+question of race
+
+ align:start position:0%
+question of race
+ 
+
+ align:start position:0%
+question of race
+um and I just I wanted to close with
+
+ align:start position:0%
+um and I just I wanted to close with
+ 
+
+ align:start position:0%
+um and I just I wanted to close with
+that because I mean one uh you know
+
+ align:start position:0%
+that because I mean one uh you know
+ 
+
+ align:start position:0%
+that because I mean one uh you know
+clearly Tolken was a mench
+
+ align:start position:0%
+clearly Tolken was a mench
+ 
+
+ align:start position:0%
+clearly Tolken was a mench
+right in the truest sense of that word.
+
+ align:start position:0%
+right in the truest sense of that word.
+ 
+
+ align:start position:0%
+right in the truest sense of that word.
+Uh but but also because I I think it
+
+ align:start position:0%
+Uh but but also because I I think it
+ 
+
+ align:start position:0%
+Uh but but also because I I think it
+speaks to the kinds of intellectual
+
+ align:start position:0%
+speaks to the kinds of intellectual
+ 
+
+ align:start position:0%
+speaks to the kinds of intellectual
+influences that are in this case
+
+ align:start position:0%
+influences that are in this case
+ 
+
+ align:start position:0%
+influences that are in this case
+informing two very different genres,
+
+ align:start position:0%
+informing two very different genres,
+ 
+
+ align:start position:0%
+informing two very different genres,
+fantasy literature, right? And you know
+
+ align:start position:0%
+fantasy literature, right? And you know
+ 
+
+ align:start position:0%
+fantasy literature, right? And you know
+on the least history, could you possibly
+
+ align:start position:0%
+on the least history, could you possibly
+ 
+
+ align:start position:0%
+on the least history, could you possibly
+get two different genres, right? And yet
+
+ align:start position:0%
+get two different genres, right? And yet
+ 
+
+ align:start position:0%
+get two different genres, right? And yet
+um the the kind of intellectual millu
+
+ align:start position:0%
+um the the kind of intellectual millu
+ 
+
+ align:start position:0%
+um the the kind of intellectual millu
+that is motivating them is clearly very
+
+ align:start position:0%
+that is motivating them is clearly very
+ 
+
+ align:start position:0%
+that is motivating them is clearly very
+similar. Okay. End of sermon.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Do we have a rough sense of what we're
+
+ align:start position:0%
+Do we have a rough sense of what we're
+ 
+
+ align:start position:0%
+Do we have a rough sense of what we're
+doing for next week?
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Yeah. I don't mean I don't mean next
+
+ align:start position:0%
+Yeah. I don't mean I don't mean next
+ 
+
+ align:start position:0%
+Yeah. I don't mean I don't mean next
+week. Sorry.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Um Yes. And you know, it's not clear to
+
+ align:start position:0%
+Um Yes. And you know, it's not clear to
+ 
+
+ align:start position:0%
+Um Yes. And you know, it's not clear to
+me how you should be responsible for
+
+ align:start position:0%
+me how you should be responsible for
+ 
+
+ align:start position:0%
+me how you should be responsible for
+doing that, but you'll figure it out.
\ No newline at end of file
diff --git a/tl7q_VZ3eIQ.txt b/tl7q_VZ3eIQ.txt
new file mode 100644
index 0000000000000000000000000000000000000000..695c5030eb38347396f76997748dff19e61920a8
--- /dev/null
+++ b/tl7q_VZ3eIQ.txt
@@ -0,0 +1,2019 @@
+align:start position:0%
+ 
+all right so our next thing will be
+
+ align:start position:0%
+all right so our next thing will be
+ 
+
+ align:start position:0%
+all right so our next thing will be
+getting into the electron spin and I
+
+ align:start position:0%
+getting into the electron spin and I
+ 
+
+ align:start position:0%
+getting into the electron spin and I
+want to discuss two things a little bit
+
+ align:start position:0%
+want to discuss two things a little bit
+ 
+
+ align:start position:0%
+want to discuss two things a little bit
+of the Dirac equation and the paola
+
+ align:start position:0%
+of the Dirac equation and the paola
+ 
+
+ align:start position:0%
+of the Dirac equation and the paola
+equation for the electron we need to
+
+ align:start position:0%
+equation for the electron we need to
+ 
+
+ align:start position:0%
+equation for the electron we need to
+understand the electron a little better
+
+ align:start position:0%
+understand the electron a little better
+ 
+
+ align:start position:0%
+understand the electron a little better
+and understand the perturbations the
+
+ align:start position:0%
+and understand the perturbations the
+ 
+
+ align:start position:0%
+and understand the perturbations the
+relativistic Corrections so we will
+
+ align:start position:0%
+relativistic Corrections so we will
+ 
+
+ align:start position:0%
+relativistic Corrections so we will
+consider the power Li equation so how
+
+ align:start position:0%
+consider the power Li equation so how
+ 
+
+ align:start position:0%
+consider the power Li equation so how
+the equation is what we have to do now
+
+ align:start position:0%
+the equation is what we have to do now
+ 
+
+ align:start position:0%
+the equation is what we have to do now
+so what is the power equation it is the
+
+ align:start position:0%
+so what is the power equation it is the
+ 
+
+ align:start position:0%
+so what is the power equation it is the
+first attempt there was to figure out
+
+ align:start position:0%
+first attempt there was to figure out
+ 
+
+ align:start position:0%
+first attempt there was to figure out
+how the Schrodinger equation should be
+
+ align:start position:0%
+how the Schrodinger equation should be
+ 
+
+ align:start position:0%
+how the Schrodinger equation should be
+tailored for an electron so we can also
+
+ align:start position:0%
+tailored for an electron so we can also
+ 
+
+ align:start position:0%
+tailored for an electron so we can also
+think of the power equation as a baby
+
+ align:start position:0%
+think of the power equation as a baby
+ 
+
+ align:start position:0%
+think of the power equation as a baby
+version of the Dirac equation which is
+
+ align:start position:0%
+version of the Dirac equation which is
+ 
+
+ align:start position:0%
+version of the Dirac equation which is
+the complete equation for the electron
+
+ align:start position:0%
+the complete equation for the electron
+ 
+
+ align:start position:0%
+the complete equation for the electron
+so it all begins the motivations by
+
+ align:start position:0%
+so it all begins the motivations by
+ 
+
+ align:start position:0%
+so it all begins the motivations by
+considering what is the magnetic moment
+
+ align:start position:0%
+considering what is the magnetic moment
+ 
+
+ align:start position:0%
+considering what is the magnetic moment
+Natick moment of the of an electron so
+
+ align:start position:0%
+Natick moment of the of an electron so
+ 
+
+ align:start position:0%
+Natick moment of the of an electron so
+it's a question that you've been
+
+ align:start position:0%
+it's a question that you've been
+ 
+
+ align:start position:0%
+it's a question that you've been
+addressing in this course for a while
+
+ align:start position:0%
+addressing in this course for a while
+ 
+
+ align:start position:0%
+addressing in this course for a while
+you know stern-gerlach experiment and
+
+ align:start position:0%
+you know stern-gerlach experiment and
+ 
+
+ align:start position:0%
+you know stern-gerlach experiment and
+how magnetic fields interact with
+
+ align:start position:0%
+how magnetic fields interact with
+ 
+
+ align:start position:0%
+how magnetic fields interact with
+electron so classically we and in
+
+ align:start position:0%
+electron so classically we and in
+ 
+
+ align:start position:0%
+electron so classically we and in
+Gaussian units units if you have a
+
+ align:start position:0%
+Gaussian units units if you have a
+ 
+
+ align:start position:0%
+Gaussian units units if you have a
+current loop and an area a the magnetic
+
+ align:start position:0%
+current loop and an area a the magnetic
+ 
+
+ align:start position:0%
+current loop and an area a the magnetic
+moment is equal to I times the area
+
+ align:start position:0%
+moment is equal to I times the area
+ 
+
+ align:start position:0%
+moment is equal to I times the area
+vector divided by C
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+you can use that to imagine an object
+
+ align:start position:0%
+you can use that to imagine an object
+ 
+
+ align:start position:0%
+you can use that to imagine an object
+that is rotating and as the object
+
+ align:start position:0%
+that is rotating and as the object
+ 
+
+ align:start position:0%
+that is rotating and as the object
+rotates if it's charged it generates a
+
+ align:start position:0%
+rotates if it's charged it generates a
+ 
+
+ align:start position:0%
+rotates if it's charged it generates a
+magnetic moment and the magnetic moment
+
+ align:start position:0%
+magnetic moment and the magnetic moment
+ 
+
+ align:start position:0%
+magnetic moment and the magnetic moment
+depends on the amount of rotation of the
+
+ align:start position:0%
+depends on the amount of rotation of the
+ 
+
+ align:start position:0%
+depends on the amount of rotation of the
+orbit so it turns out that with a little
+
+ align:start position:0%
+orbit so it turns out that with a little
+ 
+
+ align:start position:0%
+orbit so it turns out that with a little
+classical argument you can derive that
+
+ align:start position:0%
+classical argument you can derive that
+ 
+
+ align:start position:0%
+classical argument you can derive that
+the magnetic moment is related to the
+
+ align:start position:0%
+the magnetic moment is related to the
+ 
+
+ align:start position:0%
+the magnetic moment is related to the
+angular momentum by a relation of the
+
+ align:start position:0%
+angular momentum by a relation of the
+ 
+
+ align:start position:0%
+angular momentum by a relation of the
+farm L so the charge of the object the
+
+ align:start position:0%
+farm L so the charge of the object the
+ 
+
+ align:start position:0%
+farm L so the charge of the object the
+mass of the object C and the angular
+
+ align:start position:0%
+mass of the object C and the angular
+ 
+
+ align:start position:0%
+mass of the object C and the angular
+momentum that's perfectly correct
+
+ align:start position:0%
+momentum that's perfectly correct
+ 
+
+ align:start position:0%
+momentum that's perfectly correct
+classically so people thought that
+
+ align:start position:0%
+classically so people thought that
+ 
+
+ align:start position:0%
+classically so people thought that
+quantum mechanically they expect that
+
+ align:start position:0%
+quantum mechanically they expect that
+ 
+
+ align:start position:0%
+quantum mechanically they expect that
+for an electron or for an elementary
+
+ align:start position:0%
+for an electron or for an elementary
+ 
+
+ align:start position:0%
+for an electron or for an elementary
+particle you would get Q times Q MC
+
+ align:start position:0%
+particle you would get Q times Q MC
+ 
+
+ align:start position:0%
+particle you would get Q times Q MC
+times the spin of the particle so this
+
+ align:start position:0%
+times the spin of the particle so this
+ 
+
+ align:start position:0%
+times the spin of the particle so this
+would be the intrinsic magnetic moment
+
+ align:start position:0%
+would be the intrinsic magnetic moment
+ 
+
+ align:start position:0%
+would be the intrinsic magnetic moment
+of an electron that it seems to have it
+
+ align:start position:0%
+of an electron that it seems to have it
+ 
+
+ align:start position:0%
+of an electron that it seems to have it
+times a fudge factor G that you would
+
+ align:start position:0%
+times a fudge factor G that you would
+ 
+
+ align:start position:0%
+times a fudge factor G that you would
+have to measure because after all the
+
+ align:start position:0%
+have to measure because after all the
+ 
+
+ align:start position:0%
+have to measure because after all the
+world is not classical there's no reason
+
+ align:start position:0%
+world is not classical there's no reason
+ 
+
+ align:start position:0%
+world is not classical there's no reason
+why a classical relation like that would
+
+ align:start position:0%
+why a classical relation like that would
+ 
+
+ align:start position:0%
+why a classical relation like that would
+give you the right exact value of the
+
+ align:start position:0%
+give you the right exact value of the
+ 
+
+ align:start position:0%
+give you the right exact value of the
+magnetic moment of the electron as it
+
+ align:start position:0%
+magnetic moment of the electron as it
+ 
+
+ align:start position:0%
+magnetic moment of the electron as it
+turns out this G happens to be equal to
+
+ align:start position:0%
+turns out this G happens to be equal to
+ 
+
+ align:start position:0%
+turns out this G happens to be equal to
+two
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and we get the following so four
+
+ align:start position:0%
+and we get the following so four
+ 
+
+ align:start position:0%
+and we get the following so four
+electrons G happens to be equal to two
+
+ align:start position:0%
+electrons G happens to be equal to two
+ 
+
+ align:start position:0%
+electrons G happens to be equal to two
+so mu is equal to two times minus e the
+
+ align:start position:0%
+so mu is equal to two times minus e the
+ 
+
+ align:start position:0%
+so mu is equal to two times minus e the
+charge of the electron is minus e to MC
+
+ align:start position:0%
+charge of the electron is minus e to MC
+ 
+
+ align:start position:0%
+charge of the electron is minus e to MC
+and the spin of the electron is h-bar
+
+ align:start position:0%
+and the spin of the electron is h-bar
+ 
+
+ align:start position:0%
+and the spin of the electron is h-bar
+over 2 times Sigma the Pauli matrices so
+
+ align:start position:0%
+over 2 times Sigma the Pauli matrices so
+ 
+
+ align:start position:0%
+over 2 times Sigma the Pauli matrices so
+this thing is minus e h-bar over 2 m C
+
+ align:start position:0%
+this thing is minus e h-bar over 2 m C
+ 
+
+ align:start position:0%
+this thing is minus e h-bar over 2 m C
+Sigma mu of the electron so if you have
+
+ align:start position:0%
+Sigma mu of the electron so if you have
+ 
+
+ align:start position:0%
+Sigma mu of the electron so if you have
+a magnetic field a be external the
+
+ align:start position:0%
+a magnetic field a be external the
+ 
+
+ align:start position:0%
+a magnetic field a be external the
+Hamiltonian that includes the energetics
+
+ align:start position:0%
+Hamiltonian that includes the energetics
+ 
+
+ align:start position:0%
+Hamiltonian that includes the energetics
+of the magnetic field interacting with
+
+ align:start position:0%
+of the magnetic field interacting with
+ 
+
+ align:start position:0%
+of the magnetic field interacting with
+the dipole moment is always minus mu dot
+
+ align:start position:0%
+the dipole moment is always minus mu dot
+ 
+
+ align:start position:0%
+the dipole moment is always minus mu dot
+B so in this case it would be e h-bar
+
+ align:start position:0%
+B so in this case it would be e h-bar
+ 
+
+ align:start position:0%
+B so in this case it would be e h-bar
+over 2 m C Sigma dot B that's a
+
+ align:start position:0%
+over 2 m C Sigma dot B that's a
+ 
+
+ align:start position:0%
+over 2 m C Sigma dot B that's a
+Hamiltonian for an electron in a
+
+ align:start position:0%
+Hamiltonian for an electron in a
+ 
+
+ align:start position:0%
+Hamiltonian for an electron in a
+magnetic field something you've used
+
+ align:start position:0%
+magnetic field something you've used
+ 
+
+ align:start position:0%
+magnetic field something you've used
+many many times the most unpleasant part
+
+ align:start position:0%
+many many times the most unpleasant part
+ 
+
+ align:start position:0%
+many many times the most unpleasant part
+of this thing is this G equal to why did
+
+ align:start position:0%
+of this thing is this G equal to why did
+ 
+
+ align:start position:0%
+of this thing is this G equal to why did
+it turn out to be G equal to people knew
+
+ align:start position:0%
+it turn out to be G equal to people knew
+ 
+
+ align:start position:0%
+it turn out to be G equal to people knew
+it was G equal to but why and here we're
+
+ align:start position:0%
+it was G equal to but why and here we're
+ 
+
+ align:start position:0%
+it was G equal to but why and here we're
+going to see the beginning of an
+
+ align:start position:0%
+going to see the beginning of an
+ 
+
+ align:start position:0%
+going to see the beginning of an
+explanation in fact it comes very close
+
+ align:start position:0%
+explanation in fact it comes very close
+ 
+
+ align:start position:0%
+explanation in fact it comes very close
+to an explanation of that through the
+
+ align:start position:0%
+to an explanation of that through the
+ 
+
+ align:start position:0%
+to an explanation of that through the
+power equation that is the power
+
+ align:start position:0%
+power equation that is the power
+ 
+
+ align:start position:0%
+power equation that is the power
+equation is a nice equation you can
+
+ align:start position:0%
+equation is a nice equation you can
+ 
+
+ align:start position:0%
+equation is a nice equation you can
+write and you can motivate and it
+
+ align:start position:0%
+write and you can motivate and it
+ 
+
+ align:start position:0%
+write and you can motivate and it
+predicts once you admit the power
+
+ align:start position:0%
+predicts once you admit the power
+ 
+
+ align:start position:0%
+predicts once you admit the power
+equation it predicts that G would be
+
+ align:start position:0%
+equation it predicts that G would be
+ 
+
+ align:start position:0%
+equation it predicts that G would be
+equal to 2 so that's and that of course
+
+ align:start position:0%
+equal to 2 so that's and that of course
+ 
+
+ align:start position:0%
+equal to 2 so that's and that of course
+happens also for the Dirac equation and
+
+ align:start position:0%
+happens also for the Dirac equation and
+ 
+
+ align:start position:0%
+happens also for the Dirac equation and
+Dirac note is
+
+ align:start position:0%
+Dirac note is
+ 
+
+ align:start position:0%
+Dirac note is
+that and he was very happy about it so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+it's quite remarkable how these things
+
+ align:start position:0%
+it's quite remarkable how these things
+ 
+
+ align:start position:0%
+it's quite remarkable how these things
+showed up and the G equal to two was
+
+ align:start position:0%
+showed up and the G equal to two was
+ 
+
+ align:start position:0%
+showed up and the G equal to two was
+perfectly natural so let's see this
+
+ align:start position:0%
+perfectly natural so let's see this
+ 
+
+ align:start position:0%
+perfectly natural so let's see this
+Dirac this pound equation first what is
+
+ align:start position:0%
+Dirac this pound equation first what is
+ 
+
+ align:start position:0%
+Dirac this pound equation first what is
+it well when you do the Schrodinger
+
+ align:start position:0%
+it well when you do the Schrodinger
+ 
+
+ align:start position:0%
+it well when you do the Schrodinger
+equation for a wavefunction you say P
+
+ align:start position:0%
+equation for a wavefunction you say P
+ 
+
+ align:start position:0%
+equation for a wavefunction you say P
+squared over 2m say a free particle free
+
+ align:start position:0%
+squared over 2m say a free particle free
+ 
+
+ align:start position:0%
+squared over 2m say a free particle free
+particle you would put a wave function
+
+ align:start position:0%
+particle you would put a wave function
+ 
+
+ align:start position:0%
+particle you would put a wave function
+is equal to energy systems the wave
+
+ align:start position:0%
+is equal to energy systems the wave
+ 
+
+ align:start position:0%
+is equal to energy systems the wave
+function H on the wave function is equal
+
+ align:start position:0%
+function H on the wave function is equal
+ 
+
+ align:start position:0%
+function H on the wave function is equal
+to the energy times the wave function so
+
+ align:start position:0%
+to the energy times the wave function so
+ 
+
+ align:start position:0%
+to the energy times the wave function so
+for us
+
+ align:start position:0%
+for us
+ 
+
+ align:start position:0%
+for us
+electrum you already know it's a two
+
+ align:start position:0%
+electrum you already know it's a two
+ 
+
+ align:start position:0%
+electrum you already know it's a two
+dimensional hilbert space the state
+
+ align:start position:0%
+dimensional hilbert space the state
+ 
+
+ align:start position:0%
+dimensional hilbert space the state
+space of the up-and-down so it's
+
+ align:start position:0%
+space of the up-and-down so it's
+ 
+
+ align:start position:0%
+space of the up-and-down so it's
+convenient to change this and to say you
+
+ align:start position:0%
+convenient to change this and to say you
+ 
+
+ align:start position:0%
+convenient to change this and to say you
+know what I'm gonna put here something L
+
+ align:start position:0%
+know what I'm gonna put here something L
+ 
+
+ align:start position:0%
+know what I'm gonna put here something L
+taller spinner Kai is a power Li has two
+
+ align:start position:0%
+taller spinner Kai is a power Li has two
+ 
+
+ align:start position:0%
+taller spinner Kai is a power Li has two
+things Taiwan and Akari - and it's a
+
+ align:start position:0%
+things Taiwan and Akari - and it's a
+ 
+
+ align:start position:0%
+things Taiwan and Akari - and it's a
+power Li spinner and this is reasonable
+
+ align:start position:0%
+power Li spinner and this is reasonable
+ 
+
+ align:start position:0%
+power Li spinner and this is reasonable
+so far the spin is defined by two
+
+ align:start position:0%
+so far the spin is defined by two
+ 
+
+ align:start position:0%
+so far the spin is defined by two
+degrees of freedom two basis vectors so
+
+ align:start position:0%
+degrees of freedom two basis vectors so
+ 
+
+ align:start position:0%
+degrees of freedom two basis vectors so
+you've done wave functions for spin and
+
+ align:start position:0%
+you've done wave functions for spin and
+ 
+
+ align:start position:0%
+you've done wave functions for spin and
+the wave functions for spin have these
+
+ align:start position:0%
+the wave functions for spin have these
+ 
+
+ align:start position:0%
+the wave functions for spin have these
+things and each themself can be a
+
+ align:start position:0%
+things and each themself can be a
+ 
+
+ align:start position:0%
+things and each themself can be a
+function of position so that's perfectly
+
+ align:start position:0%
+function of position so that's perfectly
+ 
+
+ align:start position:0%
+function of position so that's perfectly
+reasonable I don't think any one of you
+
+ align:start position:0%
+reasonable I don't think any one of you
+ 
+
+ align:start position:0%
+reasonable I don't think any one of you
+is not very impressed by this so far but
+
+ align:start position:0%
+is not very impressed by this so far but
+ 
+
+ align:start position:0%
+is not very impressed by this so far but
+here comes the funny thing in a sense
+
+ align:start position:0%
+here comes the funny thing in a sense
+ 
+
+ align:start position:0%
+here comes the funny thing in a sense
+here there is a a two by two identity
+
+ align:start position:0%
+here there is a a two by two identity
+ 
+
+ align:start position:0%
+here there is a a two by two identity
+matrix
+
+ align:start position:0%
+matrix
+ 
+
+ align:start position:0%
+matrix
+sitting here so Paola observes the
+
+ align:start position:0%
+sitting here so Paola observes the
+ 
+
+ align:start position:0%
+sitting here so Paola observes the
+following identity if you have Sigma dot
+
+ align:start position:0%
+following identity if you have Sigma dot
+ 
+
+ align:start position:0%
+following identity if you have Sigma dot
+8 and Sigma dot B is equal to a dot B
+
+ align:start position:0%
+8 and Sigma dot B is equal to a dot B
+ 
+
+ align:start position:0%
+8 and Sigma dot B is equal to a dot B
+times 1 plus I Sigma dot a cross B look
+
+ align:start position:0%
+times 1 plus I Sigma dot a cross B look
+ 
+
+ align:start position:0%
+times 1 plus I Sigma dot a cross B look
+these are two vectors a and B and if you
+
+ align:start position:0%
+these are two vectors a and B and if you
+ 
+
+ align:start position:0%
+these are two vectors a and B and if you
+multiply have this proud first this is a
+
+ align:start position:0%
+multiply have this proud first this is a
+ 
+
+ align:start position:0%
+multiply have this proud first this is a
+dot product means Sigma 1 times a 1
+
+ align:start position:0%
+dot product means Sigma 1 times a 1
+ 
+
+ align:start position:0%
+dot product means Sigma 1 times a 1
+Sigma 2 times a 2 Sigma 3 times a 3 so
+
+ align:start position:0%
+Sigma 2 times a 2 Sigma 3 times a 3 so
+ 
+
+ align:start position:0%
+Sigma 2 times a 2 Sigma 3 times a 3 so
+this is a dot product this product here
+
+ align:start position:0%
+this is a dot product this product here
+ 
+
+ align:start position:0%
+this is a dot product this product here
+is a matrix product because this is
+
+ align:start position:0%
+is a matrix product because this is
+ 
+
+ align:start position:0%
+is a matrix product because this is
+already a matrix this is a ready matrix
+
+ align:start position:0%
+already a matrix this is a ready matrix
+ 
+
+ align:start position:0%
+already a matrix this is a ready matrix
+so this is a matrix product and this is
+
+ align:start position:0%
+so this is a matrix product and this is
+ 
+
+ align:start position:0%
+so this is a matrix product and this is
+the result this comes from properties of
+
+ align:start position:0%
+the result this comes from properties of
+ 
+
+ align:start position:0%
+the result this comes from properties of
+the polymer matrices you already know in
+
+ align:start position:0%
+the polymer matrices you already know in
+ 
+
+ align:start position:0%
+the polymer matrices you already know in
+particular their commutator determines
+
+ align:start position:0%
+particular their commutator determines
+ 
+
+ align:start position:0%
+particular their commutator determines
+this piece and the anti commutator the
+
+ align:start position:0%
+this piece and the anti commutator the
+ 
+
+ align:start position:0%
+this piece and the anti commutator the
+term in this piece so here if you have
+
+ align:start position:0%
+term in this piece so here if you have
+ 
+
+ align:start position:0%
+term in this piece so here if you have
+for example Sigma dot P times Sigma dot
+
+ align:start position:0%
+for example Sigma dot P times Sigma dot
+ 
+
+ align:start position:0%
+for example Sigma dot P times Sigma dot
+P since these two vectors are the same
+
+ align:start position:0%
+P since these two vectors are the same
+ 
+
+ align:start position:0%
+P since these two vectors are the same
+in this case you'll get just P squared
+
+ align:start position:0%
+in this case you'll get just P squared
+ 
+
+ align:start position:0%
+in this case you'll get just P squared
+times 1 plus 0 because P times P those
+
+ align:start position:0%
+times 1 plus 0 because P times P those
+ 
+
+ align:start position:0%
+times 1 plus 0 because P times P those
+are two vectors 2 vector operators if
+
+ align:start position:0%
+are two vectors 2 vector operators if
+ 
+
+ align:start position:0%
+are two vectors 2 vector operators if
+you wish but still they commute so this
+
+ align:start position:0%
+you wish but still they commute so this
+ 
+
+ align:start position:0%
+you wish but still they commute so this
+is equal to 0 so your P squared can be
+
+ align:start position:0%
+is equal to 0 so your P squared can be
+ 
+
+ align:start position:0%
+is equal to 0 so your P squared can be
+replaced by Sigma dot P Sigma dot P so H
+
+ align:start position:0%
+replaced by Sigma dot P Sigma dot P so H
+ 
+
+ align:start position:0%
+replaced by Sigma dot P Sigma dot P so H
+the Hamiltonian that is P squared over
+
+ align:start position:0%
+the Hamiltonian that is P squared over
+ 
+
+ align:start position:0%
+the Hamiltonian that is P squared over
+2m times the identity matrix can be
+
+ align:start position:0%
+2m times the identity matrix can be
+ 
+
+ align:start position:0%
+2m times the identity matrix can be
+perhaps better thought a Sigma dot P
+
+ align:start position:0%
+perhaps better thought a Sigma dot P
+ 
+
+ align:start position:0%
+perhaps better thought a Sigma dot P
+then Sigma dot P divided by 2 n
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+but Sigma dot P so this is the the first
+
+ align:start position:0%
+but Sigma dot P so this is the the first
+ 
+
+ align:start position:0%
+but Sigma dot P so this is the the first
+step you haven't done really much but
+
+ align:start position:0%
+step you haven't done really much but
+ 
+
+ align:start position:0%
+step you haven't done really much but
+you've written the Hamiltonian with a
+
+ align:start position:0%
+you've written the Hamiltonian with a
+ 
+
+ align:start position:0%
+you've written the Hamiltonian with a
+unit matrix here perhaps in a somewhat
+
+ align:start position:0%
+unit matrix here perhaps in a somewhat
+ 
+
+ align:start position:0%
+unit matrix here perhaps in a somewhat
+provocative way in quantum mechanics
+
+ align:start position:0%
+provocative way in quantum mechanics
+ 
+
+ align:start position:0%
+provocative way in quantum mechanics
+when we coupled to electromagnetism
+
+ align:start position:0%
+when we coupled to electromagnetism
+ 
+
+ align:start position:0%
+when we coupled to electromagnetism
+there are simple changes we'd have to do
+
+ align:start position:0%
+there are simple changes we'd have to do
+ 
+
+ align:start position:0%
+there are simple changes we'd have to do
+and we will study that in detail in
+
+ align:start position:0%
+and we will study that in detail in
+ 
+
+ align:start position:0%
+and we will study that in detail in
+about three weeks but today I will just
+
+ align:start position:0%
+about three weeks but today I will just
+ 
+
+ align:start position:0%
+about three weeks but today I will just
+mention what you're supposed to do in
+
+ align:start position:0%
+mention what you're supposed to do in
+ 
+
+ align:start position:0%
+mention what you're supposed to do in
+order to couple to electromagnetism in
+
+ align:start position:0%
+order to couple to electromagnetism in
+ 
+
+ align:start position:0%
+order to couple to electromagnetism in
+order to couple the length of magnetism
+
+ align:start position:0%
+order to couple the length of magnetism
+ 
+
+ align:start position:0%
+order to couple the length of magnetism
+you're supposed to change P wherever you
+
+ align:start position:0%
+you're supposed to change P wherever you
+ 
+
+ align:start position:0%
+you're supposed to change P wherever you
+see by an object you can call pi is some
+
+ align:start position:0%
+see by an object you can call pi is some
+ 
+
+ align:start position:0%
+see by an object you can call pi is some
+sort of more canonical momentum in which
+
+ align:start position:0%
+sort of more canonical momentum in which
+ 
+
+ align:start position:0%
+sort of more canonical momentum in which
+it's equal to P minus Q over C the
+
+ align:start position:0%
+it's equal to P minus Q over C the
+ 
+
+ align:start position:0%
+it's equal to P minus Q over C the
+vector potential is a function of X well
+
+ align:start position:0%
+vector potential is a function of X well
+ 
+
+ align:start position:0%
+vector potential is a function of X well
+people write it like this Q P minus Q PC
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so you're supposed to do this
+
+ align:start position:0%
+so you're supposed to do this
+ 
+
+ align:start position:0%
+so you're supposed to do this
+replacement when you're dealing with a
+
+ align:start position:0%
+replacement when you're dealing with a
+ 
+
+ align:start position:0%
+replacement when you're dealing with a
+particle moving in some electromagnetic
+
+ align:start position:0%
+particle moving in some electromagnetic
+ 
+
+ align:start position:0%
+particle moving in some electromagnetic
+field that's the change you must do we
+
+ align:start position:0%
+field that's the change you must do we
+ 
+
+ align:start position:0%
+field that's the change you must do we
+will study that in detail but I think
+
+ align:start position:0%
+will study that in detail but I think
+ 
+
+ align:start position:0%
+will study that in detail but I think
+the obvious question and this moment is
+
+ align:start position:0%
+the obvious question and this moment is
+ 
+
+ align:start position:0%
+the obvious question and this moment is
+the following you say well I'm in
+
+ align:start position:0%
+the following you say well I'm in
+ 
+
+ align:start position:0%
+the following you say well I'm in
+quantum mechanics and I work with P and
+
+ align:start position:0%
+quantum mechanics and I work with P and
+ 
+
+ align:start position:0%
+quantum mechanics and I work with P and
+X those are my upper what is a it's an
+
+ align:start position:0%
+X those are my upper what is a it's an
+ 
+
+ align:start position:0%
+X those are my upper what is a it's an
+operator is it a vector is it what piece
+
+ align:start position:0%
+operator is it a vector is it what piece
+ 
+
+ align:start position:0%
+operator is it a vector is it what piece
+operator but what is a we should think
+
+ align:start position:0%
+operator but what is a we should think
+ 
+
+ align:start position:0%
+operator but what is a we should think
+of this vector potential in general this
+
+ align:start position:0%
+of this vector potential in general this
+ 
+
+ align:start position:0%
+of this vector potential in general this
+vector potential will depend on position
+
+ align:start position:0%
+vector potential will depend on position
+ 
+
+ align:start position:0%
+vector potential will depend on position
+so if you put a magnetic field you
+
+ align:start position:0%
+so if you put a magnetic field you
+ 
+
+ align:start position:0%
+so if you put a magnetic field you
+require a vector potential has some
+
+ align:start position:0%
+require a vector potential has some
+ 
+
+ align:start position:0%
+require a vector potential has some
+position dependence so actually this a
+
+ align:start position:0%
+position dependence so actually this a
+ 
+
+ align:start position:0%
+position dependence so actually this a
+here should be thought as a of X the
+
+ align:start position:0%
+here should be thought as a of X the
+ 
+
+ align:start position:0%
+here should be thought as a of X the
+same way as when you had a potential
+
+ align:start position:0%
+same way as when you had a potential
+ 
+
+ align:start position:0%
+same way as when you had a potential
+that depends on
+
+ align:start position:0%
+that depends on
+ 
+
+ align:start position:0%
+that depends on
+eggs in quantum mechanics we just think
+
+ align:start position:0%
+eggs in quantum mechanics we just think
+ 
+
+ align:start position:0%
+eggs in quantum mechanics we just think
+of that excess and operator so the a is
+
+ align:start position:0%
+of that excess and operator so the a is
+ 
+
+ align:start position:0%
+of that excess and operator so the a is
+an operator because X is an operator and
+
+ align:start position:0%
+an operator because X is an operator and
+ 
+
+ align:start position:0%
+an operator because X is an operator and
+a has X dependence so the Pauli
+
+ align:start position:0%
+a has X dependence so the Pauli
+ 
+
+ align:start position:0%
+a has X dependence so the Pauli
+Hamiltonian H poly H Powell E is nothing
+
+ align:start position:0%
+Hamiltonian H poly H Powell E is nothing
+ 
+
+ align:start position:0%
+Hamiltonian H poly H Powell E is nothing
+else that Sigma dot PI then Sigma dot PI
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+over 2 m because we said P must be
+
+ align:start position:0%
+over 2 m because we said P must be
+ 
+
+ align:start position:0%
+over 2 m because we said P must be
+replaced by PI so this is the poly
+
+ align:start position:0%
+replaced by PI so this is the poly
+ 
+
+ align:start position:0%
+replaced by PI so this is the poly
+Hamiltonian and it's equal to 1 over 2 M
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+PI squared PI dot pi times 1 plus I
+
+ align:start position:0%
+PI squared PI dot pi times 1 plus I
+ 
+
+ align:start position:0%
+PI squared PI dot pi times 1 plus I
+Sigma dotted with PI cross 5
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay here is the computation we need to
+
+ align:start position:0%
+okay here is the computation we need to
+ 
+
+ align:start position:0%
+okay here is the computation we need to
+do what is pi cross pi
+
+ align:start position:0%
+do what is pi cross pi
+ 
+
+ align:start position:0%
+do what is pi cross pi
+you know what PI is is given by this
+
+ align:start position:0%
+you know what PI is is given by this
+ 
+
+ align:start position:0%
+you know what PI is is given by this
+thing so how much is pi cross pi well it
+
+ align:start position:0%
+thing so how much is pi cross pi well it
+ 
+
+ align:start position:0%
+thing so how much is pi cross pi well it
+takes a little computation I'll tell you
+
+ align:start position:0%
+takes a little computation I'll tell you
+ 
+
+ align:start position:0%
+takes a little computation I'll tell you
+what you have to do it's a very
+
+ align:start position:0%
+what you have to do it's a very
+ 
+
+ align:start position:0%
+what you have to do it's a very
+interesting computation it's small it
+
+ align:start position:0%
+interesting computation it's small it
+ 
+
+ align:start position:0%
+interesting computation it's small it
+reminds you of this computation in
+
+ align:start position:0%
+reminds you of this computation in
+ 
+
+ align:start position:0%
+reminds you of this computation in
+angular momentum L cross L you've done
+
+ align:start position:0%
+angular momentum L cross L you've done
+ 
+
+ align:start position:0%
+angular momentum L cross L you've done
+maybe if we written the algebra of
+
+ align:start position:0%
+maybe if we written the algebra of
+ 
+
+ align:start position:0%
+maybe if we written the algebra of
+angular momentum in this language is
+
+ align:start position:0%
+angular momentum in this language is
+ 
+
+ align:start position:0%
+angular momentum in this language is
+equal to I h-bar L that's your
+
+ align:start position:0%
+equal to I h-bar L that's your
+ 
+
+ align:start position:0%
+equal to I h-bar L that's your
+commutation relations of angular
+
+ align:start position:0%
+commutation relations of angular
+ 
+
+ align:start position:0%
+commutation relations of angular
+momentum written like that so pi cross
+
+ align:start position:0%
+momentum written like that so pi cross
+ 
+
+ align:start position:0%
+momentum written like that so pi cross
+pi the caithe component is epsilon IJ k
+
+ align:start position:0%
+pi the caithe component is epsilon IJ k
+ 
+
+ align:start position:0%
+pi the caithe component is epsilon IJ k
+pi I PI J or 1/2 epsilon IJ K PI I
+
+ align:start position:0%
+pi I PI J or 1/2 epsilon IJ K PI I
+ 
+
+ align:start position:0%
+pi I PI J or 1/2 epsilon IJ K PI I
+commutator with PI J this last step it
+
+ align:start position:0%
+commutator with PI J this last step it
+ 
+
+ align:start position:0%
+commutator with PI J this last step it
+can be explained by writing out the
+
+ align:start position:0%
+can be explained by writing out the
+ 
+
+ align:start position:0%
+can be explained by writing out the
+commutator which is PI I PI J minus PI J
+
+ align:start position:0%
+commutator which is PI I PI J minus PI J
+ 
+
+ align:start position:0%
+commutator which is PI I PI J minus PI J
+PI I but with this epsilon those two
+
+ align:start position:0%
+PI I but with this epsilon those two
+ 
+
+ align:start position:0%
+PI I but with this epsilon those two
+terms are the same and it becomes this
+
+ align:start position:0%
+terms are the same and it becomes this
+ 
+
+ align:start position:0%
+terms are the same and it becomes this
+so how much is this thing I'll leave it
+
+ align:start position:0%
+so how much is this thing I'll leave it
+ 
+
+ align:start position:0%
+so how much is this thing I'll leave it
+for you to do it it's a simple thing you
+
+ align:start position:0%
+for you to do it it's a simple thing you
+ 
+
+ align:start position:0%
+for you to do it it's a simple thing you
+have to commute these things and you
+
+ align:start position:0%
+have to commute these things and you
+ 
+
+ align:start position:0%
+have to commute these things and you
+must think of P as derivatives so this
+
+ align:start position:0%
+must think of P as derivatives so this
+ 
+
+ align:start position:0%
+must think of P as derivatives so this
+pi I PI J is I h-bar Q over c di AJ
+
+ align:start position:0%
+pi I PI J is I h-bar Q over c di AJ
+ 
+
+ align:start position:0%
+pi I PI J is I h-bar Q over c di AJ
+minus DJ a I you can see it coming you
+
+ align:start position:0%
+minus DJ a I you can see it coming you
+ 
+
+ align:start position:0%
+minus DJ a I you can see it coming you
+see you have a commutator of two factors
+
+ align:start position:0%
+see you have a commutator of two factors
+ 
+
+ align:start position:0%
+see you have a commutator of two factors
+like that the a with a welcome
+
+ align:start position:0%
+like that the a with a welcome
+ 
+
+ align:start position:0%
+like that the a with a welcome
+the P with P will commute the cross
+
+ align:start position:0%
+the P with P will commute the cross
+ 
+
+ align:start position:0%
+the P with P will commute the cross
+products one but that's just derivatives
+
+ align:start position:0%
+products one but that's just derivatives
+ 
+
+ align:start position:0%
+products one but that's just derivatives
+so therefore you get derivatives of a
+
+ align:start position:0%
+so therefore you get derivatives of a
+ 
+
+ align:start position:0%
+so therefore you get derivatives of a
+anti symmetries and the relatives of a
+
+ align:start position:0%
+anti symmetries and the relatives of a
+ 
+
+ align:start position:0%
+anti symmetries and the relatives of a
+anti symmetries is the curl of a and the
+
+ align:start position:0%
+anti symmetries is the curl of a and the
+ 
+
+ align:start position:0%
+anti symmetries is the curl of a and the
+curl of a is the magnetic field so
+
+ align:start position:0%
+curl of a is the magnetic field so
+ 
+
+ align:start position:0%
+curl of a is the magnetic field so
+that's why this happens so at the end of
+
+ align:start position:0%
+that's why this happens so at the end of
+ 
+
+ align:start position:0%
+that's why this happens so at the end of
+the day when you'll finish this
+
+ align:start position:0%
+the day when you'll finish this
+ 
+
+ align:start position:0%
+the day when you'll finish this
+computational get that pie cross pi is
+
+ align:start position:0%
+computational get that pie cross pi is
+ 
+
+ align:start position:0%
+computational get that pie cross pi is
+just i q-- I H bar Q over Seaton's the
+
+ align:start position:0%
+just i q-- I H bar Q over Seaton's the
+ 
+
+ align:start position:0%
+just i q-- I H bar Q over Seaton's the
+magnetic field
+
+ align:start position:0%
+magnetic field
+ 
+
+ align:start position:0%
+magnetic field
+pretty nice equation so the Pauli
+
+ align:start position:0%
+pretty nice equation so the Pauli
+ 
+
+ align:start position:0%
+pretty nice equation so the Pauli
+Hamiltonian includes H Powell e includes
+
+ align:start position:0%
+Hamiltonian includes H Powell e includes
+ 
+
+ align:start position:0%
+Hamiltonian includes H Powell e includes
+this term which is I Sigma over 2m
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+dotted with I HQ over C B plus other
+
+ align:start position:0%
+dotted with I HQ over C B plus other
+ 
+
+ align:start position:0%
+dotted with I HQ over C B plus other
+terms I'm just looking at this term
+
+ align:start position:0%
+terms I'm just looking at this term
+ 
+
+ align:start position:0%
+terms I'm just looking at this term
+which has the magnetic field and
+
+ align:start position:0%
+which has the magnetic field and
+ 
+
+ align:start position:0%
+which has the magnetic field and
+therefore look this I with eyes minus
+
+ align:start position:0%
+therefore look this I with eyes minus
+ 
+
+ align:start position:0%
+therefore look this I with eyes minus
+one but Q is minus e so this is e h-bar
+
+ align:start position:0%
+one but Q is minus e so this is e h-bar
+ 
+
+ align:start position:0%
+one but Q is minus e so this is e h-bar
+over 2 m C Sigma dot B which is here
+
+ align:start position:0%
+over 2 m C Sigma dot B which is here
+ 
+
+ align:start position:0%
+over 2 m C Sigma dot B which is here
+which came from G equal to now where I
+
+ align:start position:0%
+which came from G equal to now where I
+ 
+
+ align:start position:0%
+which came from G equal to now where I
+had to say there that G is equal to 2 or
+
+ align:start position:0%
+had to say there that G is equal to 2 or
+ 
+
+ align:start position:0%
+had to say there that G is equal to 2 or
+it came out of out of this calculation
+
+ align:start position:0%
+it came out of out of this calculation
+ 
+
+ align:start position:0%
+it came out of out of this calculation
+the Pauli Hamiltonian knew of this and
+
+ align:start position:0%
+the Pauli Hamiltonian knew of this and
+ 
+
+ align:start position:0%
+the Pauli Hamiltonian knew of this and
+therefore it's great progress that Polly
+
+ align:start position:0%
+therefore it's great progress that Polly
+ 
+
+ align:start position:0%
+therefore it's great progress that Polly
+Hamiltonian but it suggests to us that
+
+ align:start position:0%
+Hamiltonian but it suggests to us that
+ 
+
+ align:start position:0%
+Hamiltonian but it suggests to us that
+we can do things still even better as
+
+ align:start position:0%
+we can do things still even better as
+ 
+
+ align:start position:0%
+we can do things still even better as
+Dirac did
\ No newline at end of file
diff --git a/uCK1z-h7Jbc.txt b/uCK1z-h7Jbc.txt
new file mode 100644
index 0000000000000000000000000000000000000000..fde6b3efd9a7d85c8078120dcf13d369ce115b53
--- /dev/null
+++ b/uCK1z-h7Jbc.txt
@@ -0,0 +1,2621 @@
+The following content is
+provided under a Creative
+
+Commons license.
+
+Your support will help MIT
+OpenCourseWare continue to
+
+offer high-quality educational
+resources for free.
+
+To make a donation or view
+additional materials from
+
+hundreds of MIT courses, visit
+MIT OpenCourseWare at
+
+ocw.mit.edu.
+
+PROFESSOR: Let's get
+right into it.
+
+So last day, we started looking
+at Roentgen again and
+
+the generation of x-rays, which
+we saw occurred when we
+
+operate the gas discharge tube
+at high voltage and low
+
+pressure and this is the
+image that we saw
+
+of his wife's hand.
+
+Birth of medical radiography.
+
+And we started looking at the
+origin of x-rays and we
+
+started looking at the energy
+level diagram of the target
+
+anode in the gas discharge tube
+and this is the energy
+
+level diagram of the target.
+
+So the ballistic electron--
+
+I'm calling it incident--
+
+this is the electron that's
+making its journey across the
+
+x-ray generating tube.
+
+It left the cathode and it's
+moving across and crashing
+
+into the anode.
+
+So this is the target
+or the anode.
+
+So let's label it as such.
+
+So we're looking at one of these
+mixed metaphors, where
+
+we've got both a Cartesian image
+here of the electron and
+
+we've got an energy image.
+
+So this is the target or it's
+the anode and it's charged
+
+positively and so the
+electrons are
+
+crashing into it.
+
+And we reason that what would
+happen is, if the electrons,
+
+the ballistic electrons, had
+high enough energy, they could
+
+actually dislodge 1s electrons
+and when they do so, they make
+
+the conditions for a cascade.
+
+So you can see electrons falling
+from n equals 2 to n
+
+equals 1 and when they do
+so, they emit radiation.
+
+They emit photons and these
+photons are called K alpha.
+
+K because the final shell
+number was n equals 1.
+
+And remember, the
+spectroscopists
+
+prefer to use letters.
+
+So when the electron ends at n
+equals 1, that's n final, we
+
+call it a K photon.
+
+And furthermore, the subscript
+alpha means that the delta,
+
+the n initial to n final
+is only one.
+
+So when you go from 2 to
+1, you get the K alpha.
+
+And less likely but still
+possible is the transition
+
+from 3 down to 1.
+
+So it's still called a K photon
+because the electron
+
+that generated the photon ended
+in the K shell, but it
+
+traveled from a delta n
+of 2, went from 3 to 1
+
+so that's a K beta.
+
+Over here, obviously if we have
+enough energy to kick out
+
+K shell electrons, we have
+enough energy to kick out L
+
+shell electrons.
+
+And so if we lose an L shell
+electron and we have a
+
+cascade, then anything that
+ends in n equals 2 will be
+
+called an L photon.
+
+If it comes from 3 to 2,
+that's a delta of 1.
+
+That's the L alpha.
+
+It it falls 4 to 2, that's
+a delta of 2.
+
+That's the L beta.
+
+And so you can see you
+get a set of lines.
+
+And that set of lines
+looks like this.
+
+We can plot a spectrum of this
+entire set of lines, which
+
+will be characteristic of the
+identity of the target.
+
+And I think I showed you last
+day that it's going to look
+
+like this, where we will plot
+intensity and the intensity on
+
+a spectrum is related to the
+frequency of occurrence and on
+
+the abscissa, we're going to
+have some kind of energy
+
+coordinate.
+
+We can put lambda increasing
+from left to right, which
+
+means energy increases
+from right to left.
+
+And we saw that we have this
+family of lines where we have
+
+a discrete line at the energy
+of K alpha and a second line
+
+at the energy associated with K
+beta and K beta has a higher
+
+energy, therefore, a lower
+wavelength, and the relative
+
+heights related to the relative
+frequency, again, not
+
+to scale, but still the general
+
+relationship is correct.
+
+The likelihood of falling from
+2 to 1 is higher than falling
+
+from 3 to 1 and so you'd expect
+to have the intensity
+
+of the K alpha line greater than
+the intensity of the K
+
+beta line and the L lines have
+to be of lower energy because
+
+transitions 3 to 2 are less
+energy than 2 to 1 so we
+
+expect those lines to be out
+here and again, a relative
+
+frequency where the L alpha has
+a slightly lower energy
+
+and L beta has a slightly lower
+frequency of a current.
+
+So that's the spectrum and this
+we call characteristic.
+
+Characteristic of what?
+
+Of the identity of the
+anode or the target.
+
+This is generating the x-rays.
+
+So if I want x-rays of this
+value of wavelength, I choose
+
+the target appropriately.
+
+That's why we have the
+relationship here.
+
+And then the other
+thing is that--
+
+it's obvious, but I just
+want to make sure that
+
+we put it up here--
+
+it's quantized because we're
+looking at the photons coming
+
+at discrete values of energy.
+
+So that's what we
+speculated on.
+
+Are there any data?
+
+The answer is yes and the data
+come from a young man by the
+
+name of Henry Moseley.
+
+He was doing his PhD
+up in Manchester.
+
+He was is working
+for Rutherford.
+
+Rutherford was his PhD thesis
+supervisor and 1913, 1914, he
+
+was making systematic
+measurements.
+
+He was conducting a systematic
+study of the characteristic
+
+spectra of no fewer than
+38 elements of
+
+the Periodic Table.
+
+And what did we learn from
+his measurements?
+
+Learned from his measurements
+that there's was a pattern
+
+here and here's what the pattern
+is that Moseley found.
+
+He found that if he took
+the value of--
+
+I'm going to just
+take one line.
+
+If he took all of the K alpha
+lines from 1K alpha per
+
+element and he plotted the value
+of the wave number of a
+
+particular line, he found that
+the value of the wave number
+
+of a particular line scaled
+with the identity of the
+
+element by the square of
+the proton number.
+
+So, for example, we would
+have, say here we
+
+started with aluminum.
+
+So aluminum proton numbers
+13 so 13 squared.
+
+And he went all the
+way up to gold.
+
+Didn't do all of them but
+he did, as I say, 38
+
+from one to the other.
+
+And these are discrete values.
+
+You have different elements here
+and gold is up here and
+
+he found that he could take the
+set of data for, say, all
+
+the K alphas and they
+lie on a line--
+
+new bar--
+
+as if proportional to the square
+of the proton number
+
+and he did the same
+with other lines--
+
+say, L alpha and so on--
+
+found that they lie on a line.
+
+So what does all of this mean?
+
+Well, let's take a look.
+
+Here's the image of the paper.
+
+High-frequency spectra
+elements.
+
+Henry Moseley, Master's degree,
+so he's working on his
+
+PhD, and the data were
+taken as follows in
+
+photographic plates.
+
+And so by trigonometry, you
+can figure out what the
+
+wavelength would be of the line
+that would go to this
+
+degree of distortion, et
+cetera, et cetera.
+
+It's a beautiful set of lines.
+
+Look at how these
+date are posed.
+
+So there's calcium.
+
+Scandium is frightfully
+expensive so you
+
+don't see it here.
+
+Then there's titanium, vanadium,
+chromium, manganese,
+
+and as you change the element,
+the wave number, the
+
+wavelength, the energy of all
+of these lines changes
+
+systematically in accordance
+with the square of the proton
+
+number, and we got over
+here to copper.
+
+Next one is zinc. Zinc melts at
+420 degrees Celsius, which
+
+is relatively low melting.
+
+And under the bombardment
+of electrons--
+
+the bombardment of zinc would
+cause it to melt and so rather
+
+than work with zinc, he instead
+worked with brass
+
+because brass is an alloy
+of copper and zinc--
+
+and look carefully.
+
+You can see that brass has
+four lines, two lines
+
+identical to the lines of copper
+and these two new lines
+
+are the lines associated with
+zinc. And I mentioned last day
+
+that you could actually
+deconvolve the complex spectra
+
+and identify the constituent
+elements.
+
+So this was really fantastic,
+really fantastic.
+
+Si what did we learn
+from all of this?
+
+What did we learn
+by these data?
+
+well, first of all, corrected
+Mendeleyev What
+
+do I mean by that?
+
+Not here to say bad things
+about Mendeleyev, but
+
+Mendeleyev had told us that
+periodicity is a function of
+
+the atomic mass.
+
+That's what Mendeleyev said.
+
+Periodicity is a function
+of atomic mass.
+
+And now Moseley says no.
+
+Moseley says that
+periodicity is a
+
+function of proton number.
+
+And you can see here--
+
+I wanted to show you the--
+
+this is an image taken
+from his paper.
+
+He worked for Rutherford.
+
+These people were brilliant
+experimentalists and
+
+so here he's got--
+
+the cathode is up
+here at the top.
+
+You see cathode of x-ray tube
+and the feed through and so
+
+on, so the anode is down here
+and it's connected and so on,
+
+and rather than take the x-ray
+tube apart in order to change
+
+the target, he went to the
+toy store and he bought--
+
+this is the train from the toy
+store and he's got different
+
+elements seated next to each
+other on the flat car of the
+
+train and he's got feedthroughs
+with silk fishing
+
+line so that after he's done
+the experiment with one
+
+element, he can pull the train
+car over and change the anode
+
+without having to take
+the apparatus apart.
+
+These guys were very, very
+good experimentalists.
+
+So here's from his paper.
+
+The author intends first to make
+a general survey of the
+
+principal types of
+high-frequency radiation and
+
+then to examine the spectra of
+a few elements in greater
+
+detail with greater accuracy.
+
+The results already obtained
+show that such data have an
+
+important bearing on the
+question of the internal
+
+structure of the atom and
+strongly support the views of
+
+Rutherford and Bohr.
+
+It's 1913.
+
+Remember, that's when
+Bohr paper came out.
+
+All these people were working
+in the lab at the same time,
+
+supporting each other.
+
+You see, this doesn't make any
+sense with a Plum Pudding
+
+Model, does it?
+
+See, he continues: "We have here
+a proof that there isn't
+
+the atom of fundamental
+quantity, which increases by
+
+regular steps as we pass from
+one element to the next.
+
+This quantity can only be the
+charge on the central positive
+
+nucleus on the existence of
+which we already have definite
+
+proof."
+
+See, not only-- remember, the
+Plum Pudding Model has this
+
+big blob of positive
+charge nests.
+
+There are no protons.
+
+In the nuclear model, we have
+a nucleus that has positive
+
+charge and he's saying, I know
+there's positive charge, and
+
+it increases as you go from
+one element to the next.
+
+We are therefore led by
+experiment to view that N-- we
+
+use the letter Z today.
+
+He's using capital N.
+
+N is the same as the number of
+the place occupied by the
+
+element in the periodic
+system.
+
+This atomic number-- for the
+first time, the term atomic
+
+number is used.
+
+That's why I was being coy here
+and I kept saying proton
+
+number, because that's
+the way they knew it.
+
+Now he's say, this is
+the social security
+
+number of the element.
+
+Proton number is then for
+hydrogen 1, helium 2, lithium
+
+3, calcium 20, zinc
+30, et cetera.
+
+We can confidently predict--
+
+look at-- this is the
+masters student and
+
+he's going on a limb.
+
+He says: "We can confidently
+predict that in the few cases
+
+in which the order of the atomic
+weights A clashes with
+
+the chemical order of the
+periodic system, the chemical
+
+properties are governed by N,
+while A itself is probably a
+
+complicated function
+of N." He's right.
+
+You look at the Periodic
+Table.
+
+You say, yeah, yeah, they just
+go in descending mass or
+
+ascending proton number.
+
+Look carefully.
+
+Potassium has a lower
+mass than argon.
+
+And nobody's to--
+
+well, if you were Mendeleyev,
+you'd say, go back
+
+and measure it again.
+
+Well, they have measured it.
+
+These are the accurate values
+and no one's going to put
+
+potassium underneath neon, but
+it comes next in the order of
+
+ascending atomic mass.
+
+Cobalt and nickel--
+nickel actually
+
+weighs less than cobalt.
+
+But they're transition elements
+so who cares if you
+
+get those two mixed up?
+
+You find them in stainless
+steel.
+
+It doesn't matter.
+
+This is a good one.
+
+Iodine is lower mass
+than tellurium.
+
+Iodine is a halogen.
+
+It belongs under fluorine,
+chlorine and bromine.
+
+You're not going
+to put it under
+
+oxygen, sulfur, selenium.
+
+But look, there's the data.
+
+And then last one that Moseley
+couldn't have known about is
+
+transuranic synthetic element,
+but that's just the fourth
+
+case in the periodic table.
+
+So that gets you the last wedge
+in Trivial Pursuit.
+
+What are the four pairs
+of elements
+
+that are out of sequence?
+
+OK.
+
+So now we can say that proton
+number is the atomic number.
+
+It's the identity.
+
+So that comes out of Moseley,
+comes out of his work.
+
+The second thing that he did as
+a result of his study of 38
+
+elements is he figured out
+what to do with the
+
+lanthanides.
+
+Remember our friends,
+the lanthanides.
+
+Place the lanthanides
+correctly in
+
+the Periodic Table.
+
+Many of the lanthanides have
+a valence 3 so people were
+
+struggling.
+
+They were putting them
+underneath aluminum.
+
+They didn't know what
+to do with them.
+
+He placed the lanthanides
+correctly in
+
+the Periodic Table.
+
+And it's not as though
+these were brand new.
+
+Lanthanum itself had been first
+isolated in 1839, and
+
+all through the 1800s, they
+were picking them up and
+
+finally, lutetium was the
+last one discovered,
+
+categorized in 1907.
+
+But people didn't know what to
+do with them and remember,
+
+they were obsessed with atomic
+mass measurements.
+
+So I'm going to give you this.
+
+I'll give you this piece
+of information.
+
+There's the atomic mass of
+lanthanum, and the atomic mass
+
+of lutetium is 174.97.
+
+So what?
+
+I don't know what to do
+with that information.
+
+That doesn't help me at all.
+
+But now comes Moseley and he
+says, we're not talking about
+
+atomic mass.
+
+We're talking about
+atomic number.
+
+So now I tell you this
+atomic number is 57.
+
+So where do you put it?
+
+Duh, you put it right
+next to barium.
+
+There's no debate.
+
+And furthermore, this
+one is 71--
+
+atomic number.
+
+Well, if this is 71 and
+this is 57, I can
+
+tell you with impunity--
+
+how many lanthanides
+are there?
+
+There's 14 of them from
+here to there.
+
+OK.
+
+14 elements, which makes sense
+because in s we've got one
+
+orbital, in p we've got three
+orbitals, and d we've got 5
+
+orbitals and these are f
+and there's 7 orbitals.
+
+7 times 2 is 14.
+
+Everything makes sense.
+
+And the last thing that's a
+corollary to the item two--
+
+we were able to give
+uranium its proper
+
+atomic number is 92.
+
+So now I ask you, how many
+elements are there up to
+
+uranium starting
+with hydrogen?
+
+92.
+
+All of this comes as the
+result of Moseley's
+
+experiments.
+
+But it's not over yet because he
+worked for Rutherford, and
+
+Rutherford pushed his
+people really hard.
+
+He wasn't abusive, but he
+brought out the best in them.
+
+So who else was in
+the building?
+
+Bohr, and what were
+they doing?
+
+They were doing theory and so
+he said, well, that's nice,
+
+but he says, I want those things
+fit to an equation.
+
+So Moseley said, all right.
+
+I'm going to use--
+
+there's already an equation in
+the building for a new bar.
+
+It's the Rydberg equation.
+
+So I'm going to use a
+Rydberg-like equation.
+
+So this is what he does.
+
+This is Moseley's fit.
+
+He goes the wave number of
+whatever the line is-- whether
+
+it's K alpha, L alpha, what have
+you-- is going to go as
+
+the product of the Rydberg
+constant--
+
+1/NF squared minus
+1/NI squared.
+
+So far that's just the
+Rydberg equation.
+
+But now comes Moseley's
+contribution.
+
+We're going to put z squared,
+but one more piece.
+
+Notice the way I've
+drawn those lines.
+
+They don't go through
+the origin, do they?
+
+There's an offset.
+
+So he said, let's allow
+for the offset--
+
+z minus sigma quantity square.
+
+And this is known as
+Moseley's Law.
+
+And you've got values
+for sigma.
+
+sigma for K alpha equals 1 and
+for L alpha equals 7.4.
+
+So now I can--
+
+with impunity, you give
+me the wavelength.
+
+I can get the wave number-- it's
+1 over the wavelength and
+
+I can plug into this equation
+and identify the element or
+
+turn it around if I want to get
+wavelength radiation of,
+
+say, 1.25 angstroms, I can plug
+into this equation and
+
+come up with the z, which will
+tell me what the target
+
+element choice should be.
+
+So let's go and plug this in
+because we're only going to
+
+look at these two.
+
+So we can say that the wave
+number for K alpha--
+
+it's always going to be 1/2
+squared minus 1/1 squared,
+
+which is always going
+to come up 3/4.
+
+So it's 3/4 times Rydberg
+z minus 1 squared.
+
+So this is for the 2:1 or, if
+you like, L to K transition
+
+and then the other one
+of interest here
+
+is nu bar of L alpha.
+
+nu bar of L alpha's going to
+be 1/3 squared minus 1/2
+
+squared, which becomes 536 times
+the Rydberg constant z
+
+minus 7.4 squared and this
+is for the transition 3:2
+
+or KLM, M to L.
+
+OK.
+
+So there it is.
+
+And now, what's the significance
+of all of this?
+
+I try to give a physical
+significance of this sigma,
+
+which is known as the
+screening factor.
+
+We're going to call sigma here
+the screening factor.
+
+You'll see why in a second.
+
+Why are we calling it the
+screening factor?
+
+So let's consider what's
+happening in the case of the K
+
+alpha lines.
+
+Let's look at K alpha
+generation.
+
+So not to scale.
+
+Let's draw--
+
+here's the nucleus with all of
+its z positive charges and
+
+then I'm going to draw the
+K shell, and its got two
+
+electrons in it, and I'm going
+to show there's a hole here.
+
+Because without this
+hole, there's no
+
+reason for the cascade.
+
+And then I'm going to draw the
+L shell and it's got-- what?
+
+There's 2 from the s, 2s,
+and then 6 from the 2p.
+
+At most. I know this is
+a terrible model.
+
+It violates all kinds of things,
+but it's as complex as
+
+it needs to be for the
+explanation I'm about to give
+
+and I don't want to load you
+down with a whole bunch of
+
+extraneous information.
+
+So consider the electrons
+in the L shell.
+
+They see the electron vacancy
+in the K shell and they're
+
+going to fall down.
+
+What's the Coulombic
+pull of the nucleus
+
+on the L shell electrons?
+
+Can you see that it's not z
+plus, but at z plus screened
+
+by 1 minus.
+
+So the nuclear charge
+is mediated--
+
+in other words, it's reduced by
+1 thanks to the presence of
+
+the one negative charge here.
+
+So these electrons in L shell
+feel z less 1 and hence, we
+
+get z minus 1 as screening
+factor.
+
+It's plausible.
+
+It's at least physically
+consistent.
+
+Now let's look at
+the next one.
+
+That's the transition
+from M to L.
+
+OK.
+
+So we get to M.
+
+We've got 18 electrons, up to
+maximum of 18, and if they're
+
+going to fall down to n equals
+2, there needs to be at least
+
+one vacancy here.
+
+So now let's use
+the same logic.
+
+So an electron in the m shell
+sees the positive charge of
+
+the nucleus mediated by the
+electrons between the shell n
+
+equals 3 and the nucleus.
+
+Now, I don't know how many
+electrons there are.
+
+What's the extreme case here?
+
+Two, four, six, seven,
+maybe eight, nine.
+
+Because this would still give me
+the conditions to generate
+
+the transition 3 to 2.
+
+I need a vacancy in two.
+
+I don't need a vacancy in one.
+
+So this is the maximum.
+
+so that would be two, four,
+six, eight, nine.
+
+So it could be z minus nine, but
+that would mean that all
+
+of these electrons are on the
+same side and I don't have any
+
+vacancies lower.
+
+I only have one vacancy here.
+
+That's an extreme.
+
+It's not observed.
+
+And the other extreme is, we
+blow away all the electrons.
+
+So somewhere in between 9 and
+0, it turns out it's 7.4.
+
+I can't predict that it's 7.4,
+but 7.4 makes sense.
+
+If the number were greater than
+9, I would be distressed.
+
+So it makes sense,
+rationalizes.
+
+OK.
+
+And by the way, if you use this
+formula, Moseley's Law--
+
+let's bring that back down.
+
+Remember, I told you I can still
+wake up in the middle of
+
+the night and quote you the
+wavelength of copper K alpha
+
+radiation of five significant
+figures.
+
+I had it drilled into me
+in my junior year.
+
+It's 1.5418 angstroms.
+That's the lambda.
+
+So you can use this formula for
+new bar and you know that
+
+new bar is equal to
+1 over lambda.
+
+So I can use Moseley's Law.
+
+But true value, lambda--
+
+I love this one.
+
+Watch.
+
+I'm going to do a triple
+subscript.
+
+Lambda of copper K alpha.
+
+Isn't that cool?
+
+Lambda of copper K alpha is
+equal to 1.5418 angstroms. And
+
+if you use Moseley's law, you
+get 1.546 and the delta here
+
+is 1/3 of 1%.
+
+This man was a positive
+genius.
+
+He was heading pell-mell for
+the Nobel Prize, but
+
+he never got it.
+
+Why not?
+
+World War I broke out in 1914
+and Moseley was passionately
+
+concerned about World War I.
+
+He wanted to fight.
+
+He wanted to fight for the
+Allied cause and he enlisted
+
+in the Army.
+
+Rutherford was furious.
+
+Rutherford called the Minister
+of War, which is analogous to
+
+the Secretary of Defense and
+said, give him a desk job.
+
+Put him up in Oxford at
+a military laboratory.
+
+And Moseley said,
+no, I refuse.
+
+I'm going to fight.
+
+And so he was sent
+to Gallipoli.
+
+Gallipoli, as you may know, was
+one of the bloodiest sites
+
+of World War I.
+
+A quarter of a million Allied
+troops and 1/3 sort of a
+
+million Turkish troops were
+killed at Gallipoli.
+
+Almost 2/3 of a million
+people died for that
+
+little piece of land.
+
+And on August 10th, 1915, at the
+age of 27, Henry Moseley
+
+was killed in the battle of
+Suvla Bay, and they don't give
+
+Nobel Prizes posthumously, and
+so that was the way it ended.
+
+There's a shot of Henry Moseley
+with one of his books.
+
+The tributes poured in from
+all over the world.
+
+The physics community was
+devastated because they knew
+
+all of this stuff.
+
+This is the one that really, I
+think, says it best. This was
+
+written by Robert Milliken,
+an American.
+
+He's the one that gave us the
+elementary charge of the
+
+electron, from the University
+of Chicago at the time.
+
+This is what Milliken wrote--
+wrote this to
+
+Rutherford to read.
+
+"In a research which is destined
+to rank as one of the
+
+dozen most brilliant in
+conception, skillful in
+
+execution, and illuminating in
+results, a young man 26 years
+
+old threw open the windows
+through which we can glimpse
+
+the subatomic world with a
+definiteness and a certainty
+
+never dreamed before.
+
+Had the European War no other
+result than the snuffing out
+
+of this young life, that alone
+would make it one of the most
+
+hideous and most irreparable
+crimes in history." That's
+
+when American scientists
+knew to write.
+
+It's beautiful writing.
+
+What a tribute.
+
+OK.
+
+So let's move on.
+
+Now that we've got Moseley's
+Law, we've straightened out
+
+the Periodic Table.
+
+So we keep moving.
+
+And I say, well, I gave you the
+drawing of the spectrum.
+
+Remember the spectrum?
+
+The spectrum was here.
+
+You see it?
+
+I'll put it up real
+quick again.
+
+This was the spectrum.
+
+OK.
+
+This is intensity and this is
+wavelength and this is K alpha
+
+and this is K beta and this is
+L alpha and this is L beta.
+
+These are the data coming
+from the x-ray tube.
+
+This happens to be a
+molybdenum target.
+
+Well, it doesn't quite look like
+what I've drawn, does it?
+
+It looks a little bit like
+it, but not quite.
+
+This is definitely there.
+
+You can see some of these lines
+so I'm going to call
+
+this spectrum A and it looks
+like spectrum A has been added
+
+on top of something else.
+
+I'm going to call the something
+else spectrum B and
+
+the spectrum B looks
+like this.
+
+And in New England--
+
+this curve has a shape because
+it's New England.
+
+This is called whale-shaped.
+
+I don't know what they call it
+in the rest of the country,
+
+but it even looks
+like a whale.
+
+So you can go on
+a whale watch.
+
+So it starts--
+
+it's a sharp front, goes
+straight up, hits the maximum
+
+and then-- are you
+ready for this?
+
+It tails off, all right?
+
+Whales have tails, yes.
+
+So what's the difference here?
+
+Well, the spectrum A, we already
+observed is quantized,
+
+whereas this one isn't.
+
+This one's continuous.
+
+It has continuous values up to
+this minimum value or, if you
+
+like, maximum value of energy,
+minimum value of wavelengths.
+
+So we got that.
+
+It's not quantized.
+
+And the other thing that's
+interesting is--
+
+spectrum A, we said, is a
+function of the identity of
+
+the target.
+
+z of the target, whereas this
+one, it's a function of the
+
+plate voltage.
+
+So you can see in the diagram
+I've shown you, as the plate
+
+voltage changes, we get a series
+of enveloping curves.
+
+So this is V1 and this is V2--
+
+greater than V1.
+
+So this whale-shaped
+thing is somehow
+
+related to plate voltage.
+
+And then beyond a certain
+critical value, can you see
+
+when you're down here at 15 or
+20,000 volts, all you got is
+
+the whale-shaped curve?
+
+But somewhere between 20 and
+25,000 volts, you hit a
+
+threshold and now you switch on
+the characteristic lines.
+
+So with low voltage, you don't
+get the characteristic lines.
+
+You only get the whale-shaped
+curve.
+
+And then beyond a certain
+critical value of V, it's as
+
+though all of a sudden
+these lines appear.
+
+Low voltage, no lines.
+
+High voltage, you get the
+characteristic lines.
+
+And what can we do here?
+
+Well, we can compute K alpha,
+L alpha by Moseley's Law.
+
+The continuous spectrum can't
+do anything with that, with
+
+one exception--
+
+here.
+
+So let's look inside and figure
+out what's going on.
+
+We have a proposal here of
+what's going on inside that
+
+target atom.
+
+So I'm going to make--
+
+this could be the molybdenum
+target up there.
+
+So these are molybdenum
+atoms. And just as
+
+in Moseley's figure--
+
+so this is body centered
+cubic--
+
+I can look that up on
+the Periodic Table.
+
+I know this is BCC crystal
+structure, molybdenum atom
+
+sitting here.
+
+This is the anode.
+
+It's charged positive and way
+up top, I get the cathode.
+
+So the cathode is shooting off
+ballistic electrons and they
+
+go zooming across the gap and
+crash into anode, but up until
+
+now, we've just said the
+anode is some material.
+
+Now we're going to take one more
+peel off the onion and
+
+say that these are discrete
+atoms. It's not continuous
+
+molybdenum.
+
+It's molybdenum atoms.
+
+And what do we know the
+molybdenum atom looks like?
+
+It's got a dense nucleus where
+all the positive charge
+
+resides and then there's this
+almost vacuum-like zone with
+
+the negative charge.
+
+So when the electron comes in,
+this electron sees the
+
+negative charge around
+the molybdenum atom.
+
+What happens?
+
+It's deflected.
+
+Maybe it comes in on a closer
+angle and it's scattered
+
+through a higher angle.
+
+Maybe it comes in almost
+in between and it
+
+hardly moves at all.
+
+Now can you see that when you
+have a charged species that
+
+changes direction, that's called
+an acceleration, and an
+
+acceleration gives rise to
+an emission of radiation?
+
+So because the angle
+of deflection--
+
+so this is low-angle deflection,
+this is high-angle
+
+deflection.
+
+So low-angle deflection means
+low energy emission.
+
+High angle means high-energy
+emission, and the result is
+
+this continue spectrum that
+I've shown you here.
+
+So this is the result of
+low-angle scattering of the
+
+ballistic electrons.
+
+This is the result of high-angle
+scattering of the
+
+ballistic electrons, and
+somewhere in the middle here
+
+is the dominant angle.
+
+I can't calculate this curve
+with one exception.
+
+Imagine the electron comes from
+the cathode, and with all
+
+of its energy is dead on and
+stops, gives up all of its
+
+kinetic energy to a photon.
+
+That's the maximum amount
+of energy possible.
+
+Let's look at that.
+
+That's the case where an
+electron comes in, stops dead
+
+here and then emits
+the photon.
+
+Sp the kinetic energy
+is translated
+
+into the photon energy.
+
+So we can do that one.
+
+That's a straightforward
+calculation.
+
+So the energy of the
+incident electron--
+
+E of the incident electron is
+equal to product of the charge
+
+on the electron and
+the plate voltage.
+
+Well, the charge on the electron
+is the elementary
+
+charge and the plate voltage
+is whatever it is, and I'm
+
+going to equate that with the
+energy of the emitted photon,
+
+and that's equal to
+hc over lambda.
+
+So now I can cross multiply and
+I can call this the lambda
+
+of the shortest wavelength.
+
+That's the shortest wavelength
+on the whale-shaped curve.
+
+So by algebra, you're going to
+get the product of the plane
+
+constant times the speed
+of light divided by the
+
+elementary charge times the
+plate voltage, which turns out
+
+to be 12,400 divided by plate
+voltage where the wavelength's
+
+given in angstroms.
+
+Just try it.
+
+If you put 10,000 volts, you're
+going to get 1.24
+
+angstroms, which is smack dab in
+the middle of the x-region
+
+of the spectrum, and this is
+called the Duane-Hunt Law.
+
+That's the only thing
+we can compute in
+
+the continuous spectrum.
+
+So I can get this one.
+
+Lambda shortest wavelength,
+because shortest wavelength is
+
+maximum energy.
+
+Now there's a fancier name for
+this whale-shaped curve, and
+
+it's the scientific community's
+term, and it's a
+
+German word.
+
+It's called bremsstrahlung.
+
+I love it.
+
+You need to know this.
+
+You can impress your
+friends at parties.
+
+What does bremsstrahlung mean?
+
+Brems is the German word for
+brake, as when you put on the
+
+brakes of a car.
+
+And strahl, strahl is
+the word for ray.
+
+And ung is like ing.
+
+So this is raying radiation
+and this is the
+
+radiation of braking.
+
+So the electrons are coming in
+and when they come up against
+
+the negative charge of the outer
+shell the target atom,
+
+they are slamming on the
+brakes and skidding
+
+everywhere.
+
+So this is what bremsstrahlung
+means: braking radiation.
+
+So we're going to call--
+
+I'm going to put a B here--
+
+see that?
+
+I was thinking ahead.
+
+B is bremsstrahlung.
+
+OK.
+
+So we've got a lot going
+here. for us.
+
+I think we've explained
+a fair bit.
+
+Now I want to talk about
+modern x-ray tubes.
+
+What do modern x-ray tubes have
+that these primitive ones
+
+that Moseley worked
+with and Roentgen
+
+worked with didn't have?
+
+So I want to show you that the
+modern x-ray tube is the
+
+result of improvements
+made by an MIT alum.
+
+His name was William Coolidge,
+and he's the class of '96--
+
+1896.
+
+And he made a number
+of improvements.
+
+He actually taught for awhile
+then eventually spent a good
+
+part of his professional career
+working as a research
+
+scientist at the General
+Electric Labs out in
+
+Schenectady.
+
+If you go down to the lobby of
+Building 6, on the south side
+
+of the lobby, there's
+a showcase.
+
+Look inside the showcase.
+
+You'll see there's a little
+display in honor of Coolidge.
+
+So what's the first thing
+Coolidge did?
+
+He was an engineer so he was
+thinking about making things
+
+more efficient.
+
+First thing he did is he turned
+the discharge tube into
+
+a vacuum tube.
+
+Remember, Roentgen worked at
+low pressure, but there was
+
+still gas, and he was blinded
+by the light and so on.
+
+This means you don't get any
+visible light, and secondly,
+
+it's more efficient because if
+you've got the tube like this
+
+with the two electrodes, the
+feedthroughs and you've got
+
+gas inside, some of the
+electrons are crashing into
+
+the gas molecules,
+and we don't care
+
+about the gas molecules.
+
+We want to get the electrons
+crashing into the target.
+
+So by going to vacuum, this
+improves the efficiency.
+
+No glow in the visible and
+higher energy efficiency.
+
+More x-rays out per
+unit power put in.
+
+What's the second
+thing he did?
+
+Second think he did
+was hot cathode.
+
+Remember, you're trying to rip
+the electrons out of the
+
+cathode and send them
+on their journey.
+
+So Coolidge reasoned that if you
+heated the cathode, you'd
+
+weaken the bonds, and the
+electrons would come off.
+
+They'd boil off much
+more readily, OK?
+
+Raise temperature to reduce bond
+energy, to reduce binding
+
+energy of the electrons.
+
+The electrons in the cathode
+makes them easier to boil off.
+
+Think I've got a cartoon
+of that.
+
+Yeah, here it is.
+
+So here's the tube lying
+on its side.
+
+So the cathode is over
+here to the left.
+
+It's negative.
+
+Here's the anode to the right.
+
+That's this purple thing here
+and the electrons are moving
+
+from left to right
+and so he's got--
+
+see, you can have multiple
+electrical signals going
+
+through the same conductor.
+
+It's not the same.
+
+You can't have an AC
+waveform and a DC
+
+waveform in the same conductor.
+
+So you've got a big DC voltage
+between the cathode and the
+
+anode and you'd got a separate
+little circuit going through
+
+the cathode, running almost
+like a toaster to
+
+make it super hot.
+
+So the potential between here
+and here is 35,000 volts.
+
+The potential along this stretch
+of real estate might
+
+be several hundred volts,
+and furthermore, this
+
+could be an AC signal.
+
+It's Coolidge.
+
+He was smart.
+
+So this makes this hot and now
+for per given voltage, you get
+
+much more yield of
+the electrons.
+
+So that was pretty good.
+
+I like that.
+
+Smart.
+
+Third thing he did was he heated
+the cathode and he
+
+cooled the anode.
+
+Water-cooled anode.
+
+Why?
+
+You got to dissipate the heat.
+
+All these electrons crashing
+into the anode.
+
+You raise the temperature of
+that anode so high you'll melt
+
+it and so they had to run the
+tubes intermittently.
+
+They just get a decent signal.
+
+You have to take these x-ray
+measurements over a long
+
+period of time because the
+amount of x-rays you get is
+
+small, but you have to keep
+shutting the thing down.
+
+Otherwise, you melt
+through the anode.
+
+So he put that on a water-cooled
+copper hearth and
+
+was able to run continuous.
+
+Continuous operation.
+
+No more pulse current.
+
+But sometimes when nature
+hands you a
+
+lemon, you make lemonade.
+
+So I'm going to turn
+this thing around.
+
+I'll say, hey, wait a minute.
+
+I don't want any water-cooled
+copper anode.
+
+Suppose I want to weld
+some titanium.
+
+Titanium melts at 1675 degrees
+Centigrade and it's got a
+
+voracious appetite for oxygen.
+
+Well, this thing's
+a vacuum tube.
+
+So what if I were to take my
+part and I put the two pieces
+
+of titanium in the path of an
+electron beam and I don't cool
+
+the titanium?
+
+Eventually, I get the
+temperature so high that I can
+
+weld titanium.
+
+This is the birth of electron
+beam welding.
+
+And that's how you weld
+refracting metals.
+
+You get one of those titanium
+bicycle frames
+
+that cost about $4,000.
+
+It might be tungsten
+inert gas.
+
+It might be electron
+beam, depending.
+
+So that's the flip side
+of the technology.
+
+By the way, if you were in
+attendance observing
+
+electronic beam welding, what
+do you think is being
+
+generated in the electron
+beam welding apparatus?
+
+X-rays, by the boatload
+
+So there's a fourth thing--
+maybe the most important thing
+
+that Coolidge came up
+with-- shielding.
+
+You see the yellow here?
+
+That's lead shielding.
+
+Why did he choose lead?
+
+Well, it's got a very high z.
+
+That means it's got many
+energy levels.
+
+So that if you start looking at
+the energy level diagram of
+
+lead, you've got lots of
+action up in here.
+
+So what can happen?
+
+When the x-rays come with their
+high energy, the x-rays
+
+from the tube on their way out
+to get you, and everybody
+
+standing observing
+this marvel.
+
+They excite electrons inside.
+
+So these x-rays are absorbed.
+
+The electrons inside the lead
+rise, cascade down and now
+
+they come out.
+
+And what's the difference
+in energy between
+
+the x-ray and these?
+
+The ones up here are
+much lower energy.
+
+So this is, if you like,
+a frequency shifter
+
+or an energy shifter.
+
+So now we're using
+photons to excite
+
+electrons to generate photons.
+
+And that's how the
+shielding works.
+
+So you want to absorb
+and re-emit.
+
+And while we're on the topic, he
+gave us lead shielding and
+
+he gave us beryllium windows
+because they were using
+
+silicate glass, just as you
+use in your home, but the
+
+silicate glass was absorbing
+some of the x-rays.
+
+So to get higher efficiency,
+he chose beryllium.
+
+Why did he choose beryllium?
+
+Well, it's got a low z.
+
+So that means it has
+few energy levels.
+
+So therefore, there's less
+absorption and re-emission--
+
+again, higher efficiency.
+
+I think this was taken from
+one of the other readings.
+
+So they flipped it around.
+
+See, here you can see the
+cathode here, the anode.
+
+That's one of these things.
+
+All right.
+
+So the window is up here.
+
+You don't use lithium because
+lithium is unstable in the air
+
+unless you had a giant room of
+humidity set at a dew point of
+
+minus 38 degrees, see,
+and then you can
+
+use a lithium window.
+
+Otherwise, you use beryllium
+and lead down here.
+
+Why'd he choose lead?
+
+Well, you're pretty much at the
+bottom of the naturally
+
+occurring elements in
+the Periodic Table.
+
+So it's the cheapest of
+all of these heavies.
+
+All right.
+
+So now let's take a few minutes
+and talk about the use
+
+of x-rays in characterizing
+art.
+
+So this painting here at once
+time was arguably one of the
+
+most recognizable paintings
+in the western world.
+
+It's The Angelus by
+Jean-Francois Millet.
+
+It was painted at 1857 to 1859
+on commission for an insurance
+
+company here in Boston.
+
+The Boston Brahmins loved BA's
+paintings of rural life in
+
+19th century France.
+
+And this is couple of peasants
+who are giving thanks to God.
+
+The Angelus is a prayer, and
+they're thanking God for this
+
+pitiful bounty of potatoes
+evident.
+
+Salvador Dali, as an art
+student, was required to paint
+
+this as part of training.
+
+You know how when you learn to
+play the piano, you reproduce
+
+the works of the
+Grand Masters.
+
+So when you go to art school,
+you have to paint.
+
+He hated this painting.
+
+For many years, it was here
+in Boston, and then it was
+
+repatriated around World War I,
+it hung in the Louvre, and
+
+then ultimately, now it's
+in the Musee d'Orsay.
+
+In 1963 when Dali was at the
+peak of his career, he asked
+
+the curator of the Louvre
+if she would have
+
+this painting x-rayed.
+
+He said this painting
+spooks him.
+
+He doesn't like this painting.
+
+And they x-rayed the painting.
+
+What did they find?
+
+They found that it had been
+painted over down here.
+
+Wasn't an art forgery, Millet
+himself had painted it over.
+
+You may have heard two years ago
+there was this art find.
+
+It was a van Gogh painting.
+
+They found that van Gogh had
+painted over one of his own
+
+paintings that had never been
+seen before even though the
+
+pencil sketches survived, so
+they assumed that maybe the
+
+painting was destroyed
+in World War II
+
+or some such thing.
+
+It turns out that van Gogh was
+so poor at one point that he
+
+valued the canvas over the art,
+and he took his previous
+
+painting, and he painted
+over it.
+
+OK.
+
+So this was going on here.
+
+This is the truth.
+
+Now my speculation begins.
+
+So what was underneath
+here initially?
+
+It was the casket of a baby.
+
+Look at the pose.
+
+These people don't look like
+they're happy with their
+
+bounty of harvest.
+They're grieving.
+
+This was this futility
+of peasant life.
+
+It was a hard life and
+they lost their baby.
+
+So imagine Millet paints this,
+puts it on a boat, it comes
+
+over to Boston, they unveil it,
+and the directors of the
+
+insurance company go, we can't
+hang this in the lobby of an
+
+insurance company.
+
+That's my speculation.
+
+It didn't take him three years
+to paint this thing.
+
+I think it spent most of
+its time on the boat.
+
+They sent it back
+and said fix it.
+
+So he put the basket
+of potatoes.
+
+That's my theory.
+
+All right, look at the pose.
+
+This is from the Galleria
+Borghese in Rome.
+
+I was there about two years
+ago and saw this and went,
+
+wow, referential.
+
+You see, everything's
+been said.
+
+All of art has been said.
+
+Now we're just recasting it.
+
+So now here's Dali's revenge.
+
+Now this is what he paints.
+
+You see the man is shorter
+than the woman.
+
+His hat is down a little bit
+below the waistline.
+
+There's all sorts of
+psychosexual things going on
+
+here, but we're running
+out of time.
+
+So here's Dali and his father
+and his dad is saying, see,
+
+this is life, et cetera,
+et cetera.
+
+So you can see the reference.
+
+See, man taller here, woman
+taller, et cetera, et cetera.
+
+Have you seen this one?
+
+The Hallucinogenic Toreador.
+
+OK, he went outside one day in
+Manhattan to buy some pencils.
+
+There was a company called the
+Venus Pencil Company, you see.
+
+And so he came back and made
+this trompe l'oeil.
+
+So this is the toreador.
+
+Do you see the breast
+here is the nose?
+
+There is the face.
+
+There are the flies of the
+Thames and here is
+
+the cape and so on.
+
+Symmetry plane-- all of those
+Venuses facing back, these
+
+Venuses facing forward.
+
+There's the bull.
+
+The life force of the
+bull is a crystal.
+
+What is the crystal structure?
+
+It's one of the 14
+Bravais lattices.
+
+If you ignore color, it's
+simple cubic, isn't it?
+
+And if you don't believe
+me, check.
+
+And if you don't appreciate
+it, study.
+
+Here's the symmetry plane.
+
+Atoms, atoms, fly, fly
+et cetera, et cetera.
+
+What else do we have here?
+
+Oh, this is the one he painted
+on the occasion of the
+
+revelation of the structure
+of DNA.
+
+It's hard to see, but
+over here is the
+
+double helix of DNA.
+
+This is his wife Gaia and here
+are people standing in cubic
+
+arrays with guns pointing
+at each other.
+
+And the point that he's making
+is that now that we've
+
+discovered the instruction set
+for reproduction of life, not
+
+just human life, but life, we
+are still at a point where we
+
+can't resist killing
+each other.
+
+So this was the point and he
+chose to use cubic arrays, and
+
+I would venture to say
+this is simple cubic.
+
+If you put a fifth person here,
+it would be-- are you
+
+ready for this?
+
+Body-centered cubic.
+
+Oh, yes!
+
+And there's more, but I think
+we're running out of time so I
+
+think at this point we will
+dismiss the class.
\ No newline at end of file
diff --git a/usMPXTDOIn0.txt b/usMPXTDOIn0.txt
new file mode 100644
index 0000000000000000000000000000000000000000..8aff98322cb916004c4cb49924205081bb6770a9
--- /dev/null
+++ b/usMPXTDOIn0.txt
@@ -0,0 +1,273 @@
+Another service provided by operating system
+is dealing properly with the attempt to execute
+
+instructions with "illegal" opcodes.
+
+Illegal is quotes because that just means
+opcodes whose operations aren't implemented
+
+directly by the hardware.
+
+As we'll see, it's possible extend the functionality
+of the hardware via software emulation.
+
+The action of the CPU upon encountering an
+illegal instruction (sometimes referred to
+
+as an unimplemented user operation or UUO)
+is very similar to how it processes interrupts.
+
+Think of illegal instructions as an interrupt
+caused directly by the CPU!
+
+As for interrupts, the execution of the current
+instruction is suspended and the control signals
+
+are set to values to capture PC+4 in the XP
+register and set the PC to, in this case,
+
+0x80000004.
+
+Note that bit 31 of the new PC, aka the supervisor
+bit, is set to 1, meaning that the OS handler
+
+will have access to the kernel-mode context.
+
+Here's some code similar to that found in
+the Tiny Operating System (TinyOS), which
+
+you'll be experimenting with in the final
+lab assignment.
+
+Let's do a quick walk-through of the code
+executed when an illegal instruction is executed.
+
+Starting at location 0, we see the branches
+to the handlers for the various interrupts
+
+and exceptions.
+
+In the case of an illegal instruction, the
+BR(I_IllOp) in location 4 will be executed.
+
+Immediately following is where the OS data
+structures are allocated.
+
+This includes space for the OS stack, UserMState
+where user-mode register values are stored
+
+during interrupts, and the process table,
+providing long-term storage for the complete
+
+state of each process while another process
+is executing.
+
+When writing in assembly language, it's convenient
+to define macros for operations that are used
+
+repeatedly.
+
+We can use a macro call whenever we want to
+perform the action and the assembler will
+
+insert the body of the macro in place of the
+macro call, performing a lexical substitution
+
+of the macro's arguments.
+
+Here's a macro for a two-instruction sequence
+that extracts a particular field of bits from
+
+a 32-bit value.
+
+M is the bit number of the left-most bit,
+N is the bit number of the right-most bit.
+
+Bits are numbered 0 through 31, where bit
+31 is the most-significant bit, i.e., the
+
+one at the left end of the 32-bit binary value.
+
+And here are some macros that expand into
+instruction sequences that save and restore
+
+the CPU registers to or from the UserMState
+temporary storage area.
+
+With those macros in hand, let's see how illegal
+opcodes are handled.
+
+Like all interrupt handlers, the first action
+is to save the user-mode registers in the
+
+temporary storage area and initialize the
+OS stack.
+
+Next, we fetch the illegal instruction from
+the user-mode program.
+
+Note that the saved PC+4 value is a virtual
+address in the context of the interrupted
+
+program.
+
+So we'll need to use the MMU routines to compute
+the correct physical address - more about
+
+this on the next slide.
+
+Then we'll use the opcode of the illegal instruction
+as an index into a table of subroutine addresses,
+
+one for each of the 64 possible opcodes.
+
+Once we have the address of the handler for
+this particular illegal opcode, we JMP there
+
+to deal with the situation.
+
+Selecting a destination from a table of addresses
+is called "dispatching" and the table is called
+
+the "dispatch table".
+
+If the dispatch table contains many different
+entries, dispatching is much more efficient
+
+in time and space than a long series of compares
+and branches.
+
+In this case, the table is indicating that
+the handler for most illegal opcodes is the
+
+UUOError routine,
+so it might have smaller and faster simply
+
+to test for the two illegal opcodes the OS
+is going to emulate.
+
+Illegal opcode 1 will be used to implement
+procedure calls from user-mode to the OS,
+
+which we call supervisor calls.
+
+More on this in the next segment.
+
+As an example of having the OS emulate an
+instruction, we'll use illegal opcode 2 as
+
+the opcode for the SWAPREG instruction, which
+we'll discuss now.
+
+But first just a quick look at how the OS
+converts user-mode virtual addresses into
+
+physical addresses it can use.
+
+We'll build on the MMU VtoP procedure, described
+in the previous lecture.
+
+This procedure expects as its arguments the
+virtual page number and offset fields of the
+
+virtual address, so,
+following our convention for passing arguments
+
+to C procedures, these are pushed onto the
+stack in reverse order.
+
+The corresponding physical address is returned
+in R0.
+
+We can then use the calculated physical address
+to read the desired location from physical
+
+memory.
+
+Okay, back to dealing with illegal opcodes.
+
+Here's the handler for opcodes that are truly
+illegal.
+
+In this case the OS uses various kernel routines
+to print out a helpful error message on the
+
+user's console, then crashes the system!
+
+You may have seen these "blue screens of death"
+if you run the Windows operating system, full
+
+of cryptic hex numbers.
+
+Actually, this wouldn't be the best approach
+to handling an illegal opcode in a user's
+
+program.
+
+In a real operating system, it would be better
+to save the state of the process in a special
+
+debugging file historically referred to as
+a "core dump"
+
+and then terminate this particular process,
+perhaps printing a short error message on
+
+the user's console to let them know what happened.
+
+Then later the user could start a debugging
+program to examine the dump file to see where
+
+their bug is.
+
+Finally, here's the handler that will emulate
+the actions of the SWAPREG instruction, after
+
+which program execution will resume as if
+the instruction had been implemented in hardware.
+
+SWAPREG is an instruction that swaps the values
+in the two specified registers.
+
+To define a new instruction, we'd first have
+to let the assembler know to convert the swapreg(ra,rc)
+
+assembly language statement into binary.
+
+In this case we'll use a binary format similar
+to the ADDC instruction, but setting the unused
+
+literal field to 0.
+
+The encoding for the RA and RC registers occur
+in their usual fields and the opcode field
+
+is set to 2.
+
+Emulation is surprisingly simple.
+
+First we extract the RA and RC fields from
+the binary for the swapreg instruction and
+
+convert those values into the appropriate
+byte offsets for accessing the temporary array
+
+of saved register values.
+
+Then we use RA and RC offsets to access the
+user-mode register values that have been saved
+
+in UserMState.
+
+We'll make the appropriate interchange, leaving
+the updated register values in UserMState,
+
+where they'll be loaded into the CPU registers
+upon returning from the illegal instruction
+
+interrupt handler.
+
+Finally, we'll branch to the kernel code that
+restores the process state and resumes execution.
+
+We'll see this code in the next segment.
\ No newline at end of file
diff --git a/vJnXKcHUzHM.txt b/vJnXKcHUzHM.txt
new file mode 100644
index 0000000000000000000000000000000000000000..e0384ede51e8707ea0b9811bed0463e6f76c2f45
--- /dev/null
+++ b/vJnXKcHUzHM.txt
@@ -0,0 +1,25363 @@
+align:start position:0%
+ 
+The following content is provided by MIT
+
+ align:start position:0%
+The following content is provided by MIT
+ 
+
+ align:start position:0%
+The following content is provided by MIT
+Open Courseware under a creative common
+
+ align:start position:0%
+Open Courseware under a creative common
+ 
+
+ align:start position:0%
+Open Courseware under a creative common
+license. Additional information about
+
+ align:start position:0%
+license. Additional information about
+ 
+
+ align:start position:0%
+license. Additional information about
+our license and MIT Open Courseware in
+
+ align:start position:0%
+our license and MIT Open Courseware in
+ 
+
+ align:start position:0%
+our license and MIT Open Courseware in
+general is available at ocw.mmit.edu.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Today is the last meeting of our class
+
+ align:start position:0%
+Today is the last meeting of our class
+ 
+
+ align:start position:0%
+Today is the last meeting of our class
+on the nature of creativity.
+
+ align:start position:0%
+on the nature of creativity.
+ 
+
+ align:start position:0%
+on the nature of creativity.
+And what I wanted to do were several
+
+ align:start position:0%
+And what I wanted to do were several
+ 
+
+ align:start position:0%
+And what I wanted to do were several
+things. First, I wanted to try to pull
+
+ align:start position:0%
+things. First, I wanted to try to pull
+ 
+
+ align:start position:0%
+things. First, I wanted to try to pull
+together the various threats that we've
+
+ align:start position:0%
+together the various threats that we've
+ 
+
+ align:start position:0%
+together the various threats that we've
+been investigating.
+
+ align:start position:0%
+been investigating.
+ 
+
+ align:start position:0%
+been investigating.
+Um, second, I wanted to
+
+ align:start position:0%
+Um, second, I wanted to
+ 
+
+ align:start position:0%
+Um, second, I wanted to
+continue with a little presentation of
+
+ align:start position:0%
+continue with a little presentation of
+ 
+
+ align:start position:0%
+continue with a little presentation of
+my own uh about uh creativity in in the
+
+ align:start position:0%
+my own uh about uh creativity in in the
+ 
+
+ align:start position:0%
+my own uh about uh creativity in in the
+western world and which is related to
+
+ align:start position:0%
+western world and which is related to
+ 
+
+ align:start position:0%
+western world and which is related to
+what we were talking about last time,
+
+ align:start position:0%
+what we were talking about last time,
+ 
+
+ align:start position:0%
+what we were talking about last time,
+creativity in science and technology.
+
+ align:start position:0%
+creativity in science and technology.
+ 
+
+ align:start position:0%
+creativity in science and technology.
+But mainly I eager to hear your ideas
+
+ align:start position:0%
+But mainly I eager to hear your ideas
+ 
+
+ align:start position:0%
+But mainly I eager to hear your ideas
+about the material of the course and um
+
+ align:start position:0%
+about the material of the course and um
+ 
+
+ align:start position:0%
+about the material of the course and um
+the course itself uh together with what
+
+ align:start position:0%
+the course itself uh together with what
+ 
+
+ align:start position:0%
+the course itself uh together with what
+you have in mind for the final paper
+
+ align:start position:0%
+you have in mind for the final paper
+ 
+
+ align:start position:0%
+you have in mind for the final paper
+which is theoretically due today but for
+
+ align:start position:0%
+which is theoretically due today but for
+ 
+
+ align:start position:0%
+which is theoretically due today but for
+which I told you all you could have an
+
+ align:start position:0%
+which I told you all you could have an
+ 
+
+ align:start position:0%
+which I told you all you could have an
+extension.
+
+ align:start position:0%
+extension.
+ 
+
+ align:start position:0%
+extension.
+And so what I would like you to do is to
+
+ align:start position:0%
+And so what I would like you to do is to
+ 
+
+ align:start position:0%
+And so what I would like you to do is to
+take over and talk about what you care
+
+ align:start position:0%
+take over and talk about what you care
+ 
+
+ align:start position:0%
+take over and talk about what you care
+about which is relevant to the course.
+
+ align:start position:0%
+about which is relevant to the course.
+ 
+
+ align:start position:0%
+about which is relevant to the course.
+um particularly in relation to the paper
+
+ align:start position:0%
+um particularly in relation to the paper
+ 
+
+ align:start position:0%
+um particularly in relation to the paper
+that you're going to turn into a
+
+ align:start position:0%
+that you're going to turn into a
+ 
+
+ align:start position:0%
+that you're going to turn into a
+masterpiece when it's handed in in a few
+
+ align:start position:0%
+masterpiece when it's handed in in a few
+ 
+
+ align:start position:0%
+masterpiece when it's handed in in a few
+days. Okay. Any question of that sort or
+
+ align:start position:0%
+days. Okay. Any question of that sort or
+ 
+
+ align:start position:0%
+days. Okay. Any question of that sort or
+business that you want to attend to? Now
+
+ align:start position:0%
+business that you want to attend to? Now
+ 
+
+ align:start position:0%
+business that you want to attend to? Now
+let me start then in reminding you that
+
+ align:start position:0%
+let me start then in reminding you that
+ 
+
+ align:start position:0%
+let me start then in reminding you that
+the course started out with um ideas of
+
+ align:start position:0%
+the course started out with um ideas of
+ 
+
+ align:start position:0%
+the course started out with um ideas of
+mine that I hope and that you
+
+ align:start position:0%
+mine that I hope and that you
+ 
+
+ align:start position:0%
+mine that I hope and that you
+contributed to in fact I'll say ideas of
+
+ align:start position:0%
+contributed to in fact I'll say ideas of
+ 
+
+ align:start position:0%
+contributed to in fact I'll say ideas of
+mine but throughout but each each week
+
+ align:start position:0%
+mine but throughout but each each week
+ 
+
+ align:start position:0%
+mine but throughout but each each week
+you all contributed a great deal um
+
+ align:start position:0%
+you all contributed a great deal um
+ 
+
+ align:start position:0%
+you all contributed a great deal um
+toward the subject that uh I was
+
+ align:start position:0%
+toward the subject that uh I was
+ 
+
+ align:start position:0%
+toward the subject that uh I was
+focusing the week on and um you your
+
+ align:start position:0%
+focusing the week on and um you your
+ 
+
+ align:start position:0%
+focusing the week on and um you your
+presentation ations were very valuable.
+
+ align:start position:0%
+presentation ations were very valuable.
+ 
+
+ align:start position:0%
+presentation ations were very valuable.
+Uh the first at the beginning it was um
+
+ align:start position:0%
+Uh the first at the beginning it was um
+ 
+
+ align:start position:0%
+Uh the first at the beginning it was um
+the relationship between the spiritual
+
+ align:start position:0%
+the relationship between the spiritual
+ 
+
+ align:start position:0%
+the relationship between the spiritual
+and the creative. My idea being that uh
+
+ align:start position:0%
+and the creative. My idea being that uh
+ 
+
+ align:start position:0%
+and the creative. My idea being that uh
+western philosophy in particular has uh
+
+ align:start position:0%
+western philosophy in particular has uh
+ 
+
+ align:start position:0%
+western philosophy in particular has uh
+western thought, theology has um put the
+
+ align:start position:0%
+western thought, theology has um put the
+ 
+
+ align:start position:0%
+western thought, theology has um put the
+cart before the horse in as much as they
+
+ align:start position:0%
+cart before the horse in as much as they
+ 
+
+ align:start position:0%
+cart before the horse in as much as they
+thought that um there was a spiritual
+
+ align:start position:0%
+thought that um there was a spiritual
+ 
+
+ align:start position:0%
+thought that um there was a spiritual
+basis to creativity and consequently
+
+ align:start position:0%
+basis to creativity and consequently
+ 
+
+ align:start position:0%
+basis to creativity and consequently
+human beings could be creative by
+
+ align:start position:0%
+human beings could be creative by
+ 
+
+ align:start position:0%
+human beings could be creative by
+emulating the spiritual source.
+
+ align:start position:0%
+emulating the spiritual source.
+ 
+
+ align:start position:0%
+emulating the spiritual source.
+as against that what I argued was um it
+
+ align:start position:0%
+as against that what I argued was um it
+ 
+
+ align:start position:0%
+as against that what I argued was um it
+is the creativity in human beings
+
+ align:start position:0%
+is the creativity in human beings
+ 
+
+ align:start position:0%
+is the creativity in human beings
+wherever it comes from that's to be
+
+ align:start position:0%
+wherever it comes from that's to be
+ 
+
+ align:start position:0%
+wherever it comes from that's to be
+determined um that gives rise to our
+
+ align:start position:0%
+determined um that gives rise to our
+ 
+
+ align:start position:0%
+determined um that gives rise to our
+ideas of what is spiritual at all so
+
+ align:start position:0%
+ideas of what is spiritual at all so
+ 
+
+ align:start position:0%
+ideas of what is spiritual at all so
+that the relationship should log
+
+ align:start position:0%
+that the relationship should log
+ 
+
+ align:start position:0%
+that the relationship should log
+logically be reversed
+
+ align:start position:0%
+logically be reversed
+ 
+
+ align:start position:0%
+logically be reversed
+after that um you read my book feeling
+
+ align:start position:0%
+after that um you read my book feeling
+ 
+
+ align:start position:0%
+after that um you read my book feeling
+and imagination
+
+ align:start position:0%
+and imagination
+ 
+
+ align:start position:0%
+and imagination
+and in for the next three weeks we
+
+ align:start position:0%
+and in for the next three weeks we
+ 
+
+ align:start position:0%
+and in for the next three weeks we
+discuss
+
+ align:start position:0%
+discuss
+ 
+
+ align:start position:0%
+discuss
+different aspects of it. Uh particularly
+
+ align:start position:0%
+different aspects of it. Uh particularly
+ 
+
+ align:start position:0%
+different aspects of it. Uh particularly
+the major chapters on the four modes of
+
+ align:start position:0%
+the major chapters on the four modes of
+ 
+
+ align:start position:0%
+the major chapters on the four modes of
+approach to uh questions related to
+
+ align:start position:0%
+approach to uh questions related to
+ 
+
+ align:start position:0%
+approach to uh questions related to
+creativity. Um
+
+ align:start position:0%
+creativity. Um
+ 
+
+ align:start position:0%
+creativity. Um
+even though none of them is adequate um
+
+ align:start position:0%
+even though none of them is adequate um
+ 
+
+ align:start position:0%
+even though none of them is adequate um
+for dealing with the nature of
+
+ align:start position:0%
+for dealing with the nature of
+ 
+
+ align:start position:0%
+for dealing with the nature of
+creativity itself. It was the point of
+
+ align:start position:0%
+creativity itself. It was the point of
+ 
+
+ align:start position:0%
+creativity itself. It was the point of
+development in myself. I couldn't carry
+
+ align:start position:0%
+development in myself. I couldn't carry
+ 
+
+ align:start position:0%
+development in myself. I couldn't carry
+out that mission as well as I would have
+
+ align:start position:0%
+out that mission as well as I would have
+ 
+
+ align:start position:0%
+out that mission as well as I would have
+liked to and would still would like to
+
+ align:start position:0%
+liked to and would still would like to
+ 
+
+ align:start position:0%
+liked to and would still would like to
+that is dealing directly frontly with
+
+ align:start position:0%
+that is dealing directly frontly with
+ 
+
+ align:start position:0%
+that is dealing directly frontly with
+creativity. Um but I saw these as
+
+ align:start position:0%
+creativity. Um but I saw these as
+ 
+
+ align:start position:0%
+creativity. Um but I saw these as
+different subsidiary categories uh that
+
+ align:start position:0%
+different subsidiary categories uh that
+ 
+
+ align:start position:0%
+different subsidiary categories uh that
+are relevant to that kind of question.
+
+ align:start position:0%
+are relevant to that kind of question.
+ 
+
+ align:start position:0%
+are relevant to that kind of question.
+Um one of them was imagination.
+
+ align:start position:0%
+Um one of them was imagination.
+ 
+
+ align:start position:0%
+Um one of them was imagination.
+Uh the second is idealization. The third
+
+ align:start position:0%
+Uh the second is idealization. The third
+ 
+
+ align:start position:0%
+Uh the second is idealization. The third
+is consummation
+
+ align:start position:0%
+is consummation
+ 
+
+ align:start position:0%
+is consummation
+and the fourth is the aesthetic. Um
+
+ align:start position:0%
+and the fourth is the aesthetic. Um
+ 
+
+ align:start position:0%
+and the fourth is the aesthetic. Um
+all of these I wanted to investigate
+
+ align:start position:0%
+all of these I wanted to investigate
+ 
+
+ align:start position:0%
+all of these I wanted to investigate
+because they were humanistic modes of
+
+ align:start position:0%
+because they were humanistic modes of
+ 
+
+ align:start position:0%
+because they were humanistic modes of
+thinking. Uh science has done very
+
+ align:start position:0%
+thinking. Uh science has done very
+ 
+
+ align:start position:0%
+thinking. Uh science has done very
+little with them and it's interesting in
+
+ align:start position:0%
+little with them and it's interesting in
+ 
+
+ align:start position:0%
+little with them and it's interesting in
+in the contemporary debates about uh
+
+ align:start position:0%
+in the contemporary debates about uh
+ 
+
+ align:start position:0%
+in the contemporary debates about uh
+brain science and uh the relationship
+
+ align:start position:0%
+brain science and uh the relationship
+ 
+
+ align:start position:0%
+brain science and uh the relationship
+between body and mind um very little is
+
+ align:start position:0%
+between body and mind um very little is
+ 
+
+ align:start position:0%
+between body and mind um very little is
+said. For instance, in Minsk's book that
+
+ align:start position:0%
+said. For instance, in Minsk's book that
+ 
+
+ align:start position:0%
+said. For instance, in Minsk's book that
+we got to later, I'll get to shortly uh
+
+ align:start position:0%
+we got to later, I'll get to shortly uh
+ 
+
+ align:start position:0%
+we got to later, I'll get to shortly uh
+the emotion machine, there's not uh much
+
+ align:start position:0%
+the emotion machine, there's not uh much
+ 
+
+ align:start position:0%
+the emotion machine, there's not uh much
+that I found found very fruitful on
+
+ align:start position:0%
+that I found found very fruitful on
+ 
+
+ align:start position:0%
+that I found found very fruitful on
+those subjects. Why? Because these are
+
+ align:start position:0%
+those subjects. Why? Because these are
+ 
+
+ align:start position:0%
+those subjects. Why? Because these are
+subjects that somehow have evaded the
+
+ align:start position:0%
+subjects that somehow have evaded the
+ 
+
+ align:start position:0%
+subjects that somehow have evaded the
+scientific net too hard for science to
+
+ align:start position:0%
+scientific net too hard for science to
+ 
+
+ align:start position:0%
+scientific net too hard for science to
+deal with with the precision and the um
+
+ align:start position:0%
+deal with with the precision and the um
+ 
+
+ align:start position:0%
+deal with with the precision and the um
+replica kind of replication that defines
+
+ align:start position:0%
+replica kind of replication that defines
+ 
+
+ align:start position:0%
+replica kind of replication that defines
+the nature of science and yet native to
+
+ align:start position:0%
+the nature of science and yet native to
+ 
+
+ align:start position:0%
+the nature of science and yet native to
+the humanities.
+
+ align:start position:0%
+the humanities.
+ 
+
+ align:start position:0%
+the humanities.
+Um and I was got to them myself because
+
+ align:start position:0%
+Um and I was got to them myself because
+ 
+
+ align:start position:0%
+Um and I was got to them myself because
+I am um a humanist. My training is in
+
+ align:start position:0%
+I am um a humanist. My training is in
+ 
+
+ align:start position:0%
+I am um a humanist. My training is in
+aesthetics and humanities general
+
+ align:start position:0%
+aesthetics and humanities general
+ 
+
+ align:start position:0%
+aesthetics and humanities general
+generally. Um, but that seemed to me now
+
+ align:start position:0%
+generally. Um, but that seemed to me now
+ 
+
+ align:start position:0%
+generally. Um, but that seemed to me now
+to be the thing that cognitive studies
+
+ align:start position:0%
+to be the thing that cognitive studies
+ 
+
+ align:start position:0%
+to be the thing that cognitive studies
+ought to be able to harmonize itself
+
+ align:start position:0%
+ought to be able to harmonize itself
+ 
+
+ align:start position:0%
+ought to be able to harmonize itself
+with. It's not a substitute for
+
+ align:start position:0%
+with. It's not a substitute for
+ 
+
+ align:start position:0%
+with. It's not a substitute for
+cognitive studies or brain science or
+
+ align:start position:0%
+cognitive studies or brain science or
+ 
+
+ align:start position:0%
+cognitive studies or brain science or
+any area of the sciences. And yet it
+
+ align:start position:0%
+any area of the sciences. And yet it
+ 
+
+ align:start position:0%
+any area of the sciences. And yet it
+seems to me to be um a new approach
+
+ align:start position:0%
+seems to me to be um a new approach
+ 
+
+ align:start position:0%
+seems to me to be um a new approach
+given the the way um the history of
+
+ align:start position:0%
+given the the way um the history of
+ 
+
+ align:start position:0%
+given the the way um the history of
+ideas has gone in recent years um that
+
+ align:start position:0%
+ideas has gone in recent years um that
+ 
+
+ align:start position:0%
+ideas has gone in recent years um that
+supplements the cognitive approach and
+
+ align:start position:0%
+supplements the cognitive approach and
+ 
+
+ align:start position:0%
+supplements the cognitive approach and
+the the challenge now uh for all of us
+
+ align:start position:0%
+the the challenge now uh for all of us
+ 
+
+ align:start position:0%
+the the challenge now uh for all of us
+particularly at MIT um is to find a way
+
+ align:start position:0%
+particularly at MIT um is to find a way
+ 
+
+ align:start position:0%
+particularly at MIT um is to find a way
+of harmonizing the two. I emphasize MIT
+
+ align:start position:0%
+of harmonizing the two. I emphasize MIT
+ 
+
+ align:start position:0%
+of harmonizing the two. I emphasize MIT
+because from the very its very
+
+ align:start position:0%
+because from the very its very
+ 
+
+ align:start position:0%
+because from the very its very
+beginnings as a university uh which
+
+ align:start position:0%
+beginnings as a university uh which
+ 
+
+ align:start position:0%
+beginnings as a university uh which
+dates back to just after the second
+
+ align:start position:0%
+dates back to just after the second
+ 
+
+ align:start position:0%
+dates back to just after the second
+world war as a university uh the ideal
+
+ align:start position:0%
+world war as a university uh the ideal
+ 
+
+ align:start position:0%
+world war as a university uh the ideal
+has been to harmonize humanities and
+
+ align:start position:0%
+has been to harmonize humanities and
+ 
+
+ align:start position:0%
+has been to harmonize humanities and
+science. It's an ideal in which science
+
+ align:start position:0%
+science. It's an ideal in which science
+ 
+
+ align:start position:0%
+science. It's an ideal in which science
+has done its share and and become uh
+
+ align:start position:0%
+has done its share and and become uh
+ 
+
+ align:start position:0%
+has done its share and and become uh
+very advanced and the humanities have
+
+ align:start position:0%
+very advanced and the humanities have
+ 
+
+ align:start position:0%
+very advanced and the humanities have
+not caught up but the blame is also on
+
+ align:start position:0%
+not caught up but the blame is also on
+ 
+
+ align:start position:0%
+not caught up but the blame is also on
+part of the scientists who have never
+
+ align:start position:0%
+part of the scientists who have never
+ 
+
+ align:start position:0%
+part of the scientists who have never
+known exactly what to do about the
+
+ align:start position:0%
+known exactly what to do about the
+ 
+
+ align:start position:0%
+known exactly what to do about the
+humanities. Well, that seemed to me the
+
+ align:start position:0%
+humanities. Well, that seemed to me the
+ 
+
+ align:start position:0%
+humanities. Well, that seemed to me the
+burden of the book feeling and
+
+ align:start position:0%
+burden of the book feeling and
+ 
+
+ align:start position:0%
+burden of the book feeling and
+imagination
+
+ align:start position:0%
+imagination
+ 
+
+ align:start position:0%
+imagination
+um as a kind of extended proposal uh
+
+ align:start position:0%
+um as a kind of extended proposal uh
+ 
+
+ align:start position:0%
+um as a kind of extended proposal uh
+through the analysis of those four
+
+ align:start position:0%
+through the analysis of those four
+ 
+
+ align:start position:0%
+through the analysis of those four
+categories imagination, idealization,
+
+ align:start position:0%
+categories imagination, idealization,
+ 
+
+ align:start position:0%
+categories imagination, idealization,
+consummation and the aesthetic
+
+ align:start position:0%
+consummation and the aesthetic
+ 
+
+ align:start position:0%
+consummation and the aesthetic
+um and especially relevant to any
+
+ align:start position:0%
+um and especially relevant to any
+ 
+
+ align:start position:0%
+um and especially relevant to any
+investigation about the nature of
+
+ align:start position:0%
+investigation about the nature of
+ 
+
+ align:start position:0%
+investigation about the nature of
+creativity.
+
+ align:start position:0%
+creativity.
+ 
+
+ align:start position:0%
+creativity.
+Uh we then went on to four three weeks
+
+ align:start position:0%
+Uh we then went on to four three weeks
+ 
+
+ align:start position:0%
+Uh we then went on to four three weeks
+uh discussing um chapters in David
+
+ align:start position:0%
+uh discussing um chapters in David
+ 
+
+ align:start position:0%
+uh discussing um chapters in David
+Boom's book on creativity and uh they
+
+ align:start position:0%
+Boom's book on creativity and uh they
+ 
+
+ align:start position:0%
+Boom's book on creativity and uh they
+were um uh dealt with in parallel with
+
+ align:start position:0%
+were um uh dealt with in parallel with
+ 
+
+ align:start position:0%
+were um uh dealt with in parallel with
+chapters out of the book I'm writing now
+
+ align:start position:0%
+chapters out of the book I'm writing now
+ 
+
+ align:start position:0%
+chapters out of the book I'm writing now
+on the nature of creativity. um two of
+
+ align:start position:0%
+on the nature of creativity. um two of
+ 
+
+ align:start position:0%
+on the nature of creativity. um two of
+those weeks on uh the creative
+
+ align:start position:0%
+those weeks on uh the creative
+ 
+
+ align:start position:0%
+those weeks on uh the creative
+experience and the third the first half
+
+ align:start position:0%
+experience and the third the first half
+ 
+
+ align:start position:0%
+experience and the third the first half
+of my chapter called the creative
+
+ align:start position:0%
+of my chapter called the creative
+ 
+
+ align:start position:0%
+of my chapter called the creative
+process. In talking about the creative
+
+ align:start position:0%
+process. In talking about the creative
+ 
+
+ align:start position:0%
+process. In talking about the creative
+experience you remember I emphasized
+
+ align:start position:0%
+experience you remember I emphasized
+ 
+
+ align:start position:0%
+experience you remember I emphasized
+that the experience itself doesn't
+
+ align:start position:0%
+that the experience itself doesn't
+ 
+
+ align:start position:0%
+that the experience itself doesn't
+explain creativity even though a great
+
+ align:start position:0%
+explain creativity even though a great
+ 
+
+ align:start position:0%
+explain creativity even though a great
+many writers have assumed that. So that
+
+ align:start position:0%
+many writers have assumed that. So that
+ 
+
+ align:start position:0%
+many writers have assumed that. So that
+Kekerlay's dream and Arimedes
+
+ align:start position:0%
+Kekerlay's dream and Arimedes
+ 
+
+ align:start position:0%
+Kekerlay's dream and Arimedes
+um uh eureka experience in bathtub
+
+ align:start position:0%
+um uh eureka experience in bathtub
+ 
+
+ align:start position:0%
+um uh eureka experience in bathtub
+getting out of the bathtub um are
+
+ align:start position:0%
+getting out of the bathtub um are
+ 
+
+ align:start position:0%
+getting out of the bathtub um are
+experiences that are usually used as
+
+ align:start position:0%
+experiences that are usually used as
+ 
+
+ align:start position:0%
+experiences that are usually used as
+paradigmatic for the nature of
+
+ align:start position:0%
+paradigmatic for the nature of
+ 
+
+ align:start position:0%
+paradigmatic for the nature of
+creativity. And what I was arguing was
+
+ align:start position:0%
+creativity. And what I was arguing was
+ 
+
+ align:start position:0%
+creativity. And what I was arguing was
+that no creativity invol can involve
+
+ align:start position:0%
+that no creativity invol can involve
+ 
+
+ align:start position:0%
+that no creativity invol can involve
+that and generally does but it involves
+
+ align:start position:0%
+that and generally does but it involves
+ 
+
+ align:start position:0%
+that and generally does but it involves
+so much more that the experience should
+
+ align:start position:0%
+so much more that the experience should
+ 
+
+ align:start position:0%
+so much more that the experience should
+be given a secondary place in uh after u
+
+ align:start position:0%
+be given a secondary place in uh after u
+ 
+
+ align:start position:0%
+be given a secondary place in uh after u
+the process the nature of the creative
+
+ align:start position:0%
+the process the nature of the creative
+ 
+
+ align:start position:0%
+the process the nature of the creative
+process. U we then turned to the
+
+ align:start position:0%
+process. U we then turned to the
+ 
+
+ align:start position:0%
+process. U we then turned to the
+creative process uh both parts uh the
+
+ align:start position:0%
+creative process uh both parts uh the
+ 
+
+ align:start position:0%
+creative process uh both parts uh the
+second part overlapping what you were
+
+ align:start position:0%
+second part overlapping what you were
+ 
+
+ align:start position:0%
+second part overlapping what you were
+reading uh about in the anthology
+
+ align:start position:0%
+reading uh about in the anthology
+ 
+
+ align:start position:0%
+reading uh about in the anthology
+creativity in the arts and then I went
+
+ align:start position:0%
+creativity in the arts and then I went
+ 
+
+ align:start position:0%
+creativity in the arts and then I went
+on to the the two parts of my chapter
+
+ align:start position:0%
+on to the the two parts of my chapter
+ 
+
+ align:start position:0%
+on to the the two parts of my chapter
+called aesthetic creativity uh which is
+
+ align:start position:0%
+called aesthetic creativity uh which is
+ 
+
+ align:start position:0%
+called aesthetic creativity uh which is
+all about creativity in the arts. Um
+
+ align:start position:0%
+all about creativity in the arts. Um
+ 
+
+ align:start position:0%
+all about creativity in the arts. Um
+after that um I asked you to read a
+
+ align:start position:0%
+after that um I asked you to read a
+ 
+
+ align:start position:0%
+after that um I asked you to read a
+chapter of mine from uh my book the
+
+ align:start position:0%
+chapter of mine from uh my book the
+ 
+
+ align:start position:0%
+chapter of mine from uh my book the
+harmony of nature and spirit called
+
+ align:start position:0%
+harmony of nature and spirit called
+ 
+
+ align:start position:0%
+harmony of nature and spirit called
+aesthetic foundations of ethics and
+
+ align:start position:0%
+aesthetic foundations of ethics and
+ 
+
+ align:start position:0%
+aesthetic foundations of ethics and
+religion. Uh and we uh discussed and I
+
+ align:start position:0%
+religion. Uh and we uh discussed and I
+ 
+
+ align:start position:0%
+religion. Uh and we uh discussed and I
+read new we discussed the new chapter of
+
+ align:start position:0%
+read new we discussed the new chapter of
+ 
+
+ align:start position:0%
+read new we discussed the new chapter of
+mine called creativity and practice. The
+
+ align:start position:0%
+mine called creativity and practice. The
+ 
+
+ align:start position:0%
+mine called creativity and practice. The
+burden of that being by taking a
+
+ align:start position:0%
+burden of that being by taking a
+ 
+
+ align:start position:0%
+burden of that being by taking a
+particular um practical problem uh one
+
+ align:start position:0%
+particular um practical problem uh one
+ 
+
+ align:start position:0%
+particular um practical problem uh one
+in the field of medicine um that deals
+
+ align:start position:0%
+in the field of medicine um that deals
+ 
+
+ align:start position:0%
+in the field of medicine um that deals
+with the question of doctor assisted
+
+ align:start position:0%
+with the question of doctor assisted
+ 
+
+ align:start position:0%
+with the question of doctor assisted
+suicide. uh to that from that I opened
+
+ align:start position:0%
+suicide. uh to that from that I opened
+ 
+
+ align:start position:0%
+suicide. uh to that from that I opened
+up the analysis and claimed as I have
+
+ align:start position:0%
+up the analysis and claimed as I have
+ 
+
+ align:start position:0%
+up the analysis and claimed as I have
+elsewhere
+
+ align:start position:0%
+elsewhere
+ 
+
+ align:start position:0%
+elsewhere
+uh that all of ethics is really uh a
+
+ align:start position:0%
+uh that all of ethics is really uh a
+ 
+
+ align:start position:0%
+uh that all of ethics is really uh a
+function of creativity that no rules no
+
+ align:start position:0%
+function of creativity that no rules no
+ 
+
+ align:start position:0%
+function of creativity that no rules no
+fixed principles whether they're
+
+ align:start position:0%
+fixed principles whether they're
+ 
+
+ align:start position:0%
+fixed principles whether they're
+contient are prioristic in terms of
+
+ align:start position:0%
+contient are prioristic in terms of
+ 
+
+ align:start position:0%
+contient are prioristic in terms of
+reason and respect for the personhood of
+
+ align:start position:0%
+reason and respect for the personhood of
+ 
+
+ align:start position:0%
+reason and respect for the personhood of
+other people or utilitarian in terms of
+
+ align:start position:0%
+other people or utilitarian in terms of
+ 
+
+ align:start position:0%
+other people or utilitarian in terms of
+the greatest good for the greatest
+
+ align:start position:0%
+the greatest good for the greatest
+ 
+
+ align:start position:0%
+the greatest good for the greatest
+number. None of them are adequate for
+
+ align:start position:0%
+number. None of them are adequate for
+ 
+
+ align:start position:0%
+number. None of them are adequate for
+explaining the actual practice of
+
+ align:start position:0%
+explaining the actual practice of
+ 
+
+ align:start position:0%
+explaining the actual practice of
+ethics, how people go about making
+
+ align:start position:0%
+ethics, how people go about making
+ 
+
+ align:start position:0%
+ethics, how people go about making
+ethical decisions and uh acting in ways
+
+ align:start position:0%
+ethical decisions and uh acting in ways
+ 
+
+ align:start position:0%
+ethical decisions and uh acting in ways
+that other people will consider to be
+
+ align:start position:0%
+that other people will consider to be
+ 
+
+ align:start position:0%
+that other people will consider to be
+ethical. And and the same I claim was
+
+ align:start position:0%
+ethical. And and the same I claim was
+ 
+
+ align:start position:0%
+ethical. And and the same I claim was
+true of religion. Now, in the last two
+
+ align:start position:0%
+true of religion. Now, in the last two
+ 
+
+ align:start position:0%
+true of religion. Now, in the last two
+weeks, we've been dealing with what I
+
+ align:start position:0%
+weeks, we've been dealing with what I
+ 
+
+ align:start position:0%
+weeks, we've been dealing with what I
+call you you will recall in my
+
+ align:start position:0%
+call you you will recall in my
+ 
+
+ align:start position:0%
+call you you will recall in my
+conclusion to feeling and imagination,
+
+ align:start position:0%
+conclusion to feeling and imagination,
+ 
+
+ align:start position:0%
+conclusion to feeling and imagination,
+the religion of science. The idea that
+
+ align:start position:0%
+the religion of science. The idea that
+ 
+
+ align:start position:0%
+the religion of science. The idea that
+science uh in principle should be able
+
+ align:start position:0%
+science uh in principle should be able
+ 
+
+ align:start position:0%
+science uh in principle should be able
+to tell us through its uh rational
+
+ align:start position:0%
+to tell us through its uh rational
+ 
+
+ align:start position:0%
+to tell us through its uh rational
+procedures, it special kind of
+
+ align:start position:0%
+procedures, it special kind of
+ 
+
+ align:start position:0%
+procedures, it special kind of
+rationality,
+
+ align:start position:0%
+rationality,
+ 
+
+ align:start position:0%
+rationality,
+the truth about everything, what the
+
+ align:start position:0%
+the truth about everything, what the
+ 
+
+ align:start position:0%
+the truth about everything, what the
+world is like. There's a world out
+
+ align:start position:0%
+world is like. There's a world out
+ 
+
+ align:start position:0%
+world is like. There's a world out
+there. science investigates it in
+
+ align:start position:0%
+there. science investigates it in
+ 
+
+ align:start position:0%
+there. science investigates it in
+principle at least given enough time
+
+ align:start position:0%
+principle at least given enough time
+ 
+
+ align:start position:0%
+principle at least given enough time
+maybe not only in principle but as a
+
+ align:start position:0%
+maybe not only in principle but as a
+ 
+
+ align:start position:0%
+maybe not only in principle but as a
+kind of program for the future given
+
+ align:start position:0%
+kind of program for the future given
+ 
+
+ align:start position:0%
+kind of program for the future given
+enough um decades centuries millennia
+
+ align:start position:0%
+enough um decades centuries millennia
+ 
+
+ align:start position:0%
+enough um decades centuries millennia
+eons nobody can say but the hope is the
+
+ align:start position:0%
+eons nobody can say but the hope is the
+ 
+
+ align:start position:0%
+eons nobody can say but the hope is the
+faith is that eventually science will
+
+ align:start position:0%
+faith is that eventually science will
+ 
+
+ align:start position:0%
+faith is that eventually science will
+put all the pieces of the p of the
+
+ align:start position:0%
+put all the pieces of the p of the
+ 
+
+ align:start position:0%
+put all the pieces of the p of the
+puzzle together um jigsaw puzzle
+
+ align:start position:0%
+puzzle together um jigsaw puzzle
+ 
+
+ align:start position:0%
+puzzle together um jigsaw puzzle
+together and then um that future future
+
+ align:start position:0%
+together and then um that future future
+ 
+
+ align:start position:0%
+together and then um that future future
+generation will um will know the truth
+
+ align:start position:0%
+generation will um will know the truth
+ 
+
+ align:start position:0%
+generation will um will know the truth
+about everything, right? Uh
+
+ align:start position:0%
+about everything, right? Uh
+ 
+
+ align:start position:0%
+about everything, right? Uh
+incidentally, I forgot to mention
+
+ align:start position:0%
+incidentally, I forgot to mention
+ 
+
+ align:start position:0%
+incidentally, I forgot to mention
+something that comes into
+
+ align:start position:0%
+something that comes into
+ 
+
+ align:start position:0%
+something that comes into
+other writings of mine um about the
+
+ align:start position:0%
+other writings of mine um about the
+ 
+
+ align:start position:0%
+other writings of mine um about the
+hitchhikers g uh hitchhikers guide to
+
+ align:start position:0%
+hitchhikers g uh hitchhikers guide to
+ 
+
+ align:start position:0%
+hitchhikers g uh hitchhikers guide to
+the galaxy. What to the galaxy? Guide.
+
+ align:start position:0%
+the galaxy. What to the galaxy? Guide.
+ 
+
+ align:start position:0%
+the galaxy. What to the galaxy? Guide.
+Guide to the galaxy. Right. You remember
+
+ align:start position:0%
+Guide to the galaxy. Right. You remember
+ 
+
+ align:start position:0%
+Guide to the galaxy. Right. You remember
+at the beginning the wise men uh ask um
+
+ align:start position:0%
+at the beginning the wise men uh ask um
+ 
+
+ align:start position:0%
+at the beginning the wise men uh ask um
+um deep deep mind is it the name of the
+
+ align:start position:0%
+um deep deep mind is it the name of the
+ 
+
+ align:start position:0%
+um deep deep mind is it the name of the
+computer? Deep. Deep thought. Deep
+
+ align:start position:0%
+computer? Deep. Deep thought. Deep
+ 
+
+ align:start position:0%
+computer? Deep. Deep thought. Deep
+thought right as a parody on deep throat
+
+ align:start position:0%
+thought right as a parody on deep throat
+ 
+
+ align:start position:0%
+thought right as a parody on deep throat
+to which something very different. Um
+
+ align:start position:0%
+to which something very different. Um
+ 
+
+ align:start position:0%
+to which something very different. Um
+the um the the problem they said him is
+
+ align:start position:0%
+the um the the problem they said him is
+ 
+
+ align:start position:0%
+the um the the problem they said him is
+what is the truth about everything? Uh
+
+ align:start position:0%
+what is the truth about everything? Uh
+ 
+
+ align:start position:0%
+what is the truth about everything? Uh
+the meaning of life, the meaning of
+
+ align:start position:0%
+the meaning of life, the meaning of
+ 
+
+ align:start position:0%
+the meaning of life, the meaning of
+everything. And after many many
+
+ align:start position:0%
+everything. And after many many
+ 
+
+ align:start position:0%
+everything. And after many many
+generations
+
+ align:start position:0%
+generations
+ 
+
+ align:start position:0%
+generations
+um uh it comes up it comes up with an
+
+ align:start position:0%
+um uh it comes up it comes up with an
+ 
+
+ align:start position:0%
+um uh it comes up it comes up with an
+answer for the elders of that time
+
+ align:start position:0%
+answer for the elders of that time
+ 
+
+ align:start position:0%
+answer for the elders of that time
+who've handed hand had had who who've
+
+ align:start position:0%
+who've handed hand had had who who've
+ 
+
+ align:start position:0%
+who've handed hand had had who who've
+handed out ideas about the the problem
+
+ align:start position:0%
+handed out ideas about the the problem
+ 
+
+ align:start position:0%
+handed out ideas about the the problem
+from generation to generation and it its
+
+ align:start position:0%
+from generation to generation and it its
+ 
+
+ align:start position:0%
+from generation to generation and it its
+answer is I don't have to tell you you
+
+ align:start position:0%
+answer is I don't have to tell you you
+ 
+
+ align:start position:0%
+answer is I don't have to tell you you
+all know this right Taz it's 42 42
+
+ align:start position:0%
+all know this right Taz it's 42 42
+ 
+
+ align:start position:0%
+all know this right Taz it's 42 42
+exactly that's the exact right answer
+
+ align:start position:0%
+exactly that's the exact right answer
+ 
+
+ align:start position:0%
+exactly that's the exact right answer
+and the old men are angry and say, "You
+
+ align:start position:0%
+and the old men are angry and say, "You
+ 
+
+ align:start position:0%
+and the old men are angry and say, "You
+mean all these centuries we've been
+
+ align:start position:0%
+mean all these centuries we've been
+ 
+
+ align:start position:0%
+mean all these centuries we've been
+waiting to get the answer and that's the
+
+ align:start position:0%
+waiting to get the answer and that's the
+ 
+
+ align:start position:0%
+waiting to get the answer and that's the
+best you can do?" And the computer says,
+
+ align:start position:0%
+best you can do?" And the computer says,
+ 
+
+ align:start position:0%
+best you can do?" And the computer says,
+"Well, I I checked it very carefully."
+
+ align:start position:0%
+"Well, I I checked it very carefully."
+ 
+
+ align:start position:0%
+"Well, I I checked it very carefully."
+And they're still annoyed. And and the
+
+ align:start position:0%
+And they're still annoyed. And and the
+ 
+
+ align:start position:0%
+And they're still annoyed. And and the
+the computer says, "Well, possibly you
+
+ align:start position:0%
+the computer says, "Well, possibly you
+ 
+
+ align:start position:0%
+the computer says, "Well, possibly you
+you didn't understand what you don't
+
+ align:start position:0%
+you didn't understand what you don't
+ 
+
+ align:start position:0%
+you didn't understand what you don't
+understand what the question is." And I
+
+ align:start position:0%
+understand what the question is." And I
+ 
+
+ align:start position:0%
+understand what the question is." And I
+think that's the most brilliant thing a
+
+ align:start position:0%
+think that's the most brilliant thing a
+ 
+
+ align:start position:0%
+think that's the most brilliant thing a
+computer could say. The crucial thing is
+
+ align:start position:0%
+computer could say. The crucial thing is
+ 
+
+ align:start position:0%
+computer could say. The crucial thing is
+to understand the question. That's the
+
+ align:start position:0%
+to understand the question. That's the
+ 
+
+ align:start position:0%
+to understand the question. That's the
+beginning of wisdom. That's what
+
+ align:start position:0%
+beginning of wisdom. That's what
+ 
+
+ align:start position:0%
+beginning of wisdom. That's what
+philosophy is really interested in. the
+
+ align:start position:0%
+philosophy is really interested in. the
+ 
+
+ align:start position:0%
+philosophy is really interested in. the
+giving of the answers even if they're
+
+ align:start position:0%
+giving of the answers even if they're
+ 
+
+ align:start position:0%
+giving of the answers even if they're
+purport to be scientific can be derived
+
+ align:start position:0%
+purport to be scientific can be derived
+ 
+
+ align:start position:0%
+purport to be scientific can be derived
+but the ability to understand the
+
+ align:start position:0%
+but the ability to understand the
+ 
+
+ align:start position:0%
+but the ability to understand the
+question that takes genius that I think
+
+ align:start position:0%
+question that takes genius that I think
+ 
+
+ align:start position:0%
+question that takes genius that I think
+is the highest creativity in any event
+
+ align:start position:0%
+is the highest creativity in any event
+ 
+
+ align:start position:0%
+is the highest creativity in any event
+um the u the present faith that I've
+
+ align:start position:0%
+um the u the present faith that I've
+ 
+
+ align:start position:0%
+um the u the present faith that I've
+started this little distraction on uh is
+
+ align:start position:0%
+started this little distraction on uh is
+ 
+
+ align:start position:0%
+started this little distraction on uh is
+that through brain uh studies through
+
+ align:start position:0%
+that through brain uh studies through
+ 
+
+ align:start position:0%
+that through brain uh studies through
+cognitive studies through the
+
+ align:start position:0%
+cognitive studies through the
+ 
+
+ align:start position:0%
+cognitive studies through the
+magnificent complex that MIT is now uh
+
+ align:start position:0%
+magnificent complex that MIT is now uh
+ 
+
+ align:start position:0%
+magnificent complex that MIT is now uh
+constructed. Uh in principle we should
+
+ align:start position:0%
+constructed. Uh in principle we should
+ 
+
+ align:start position:0%
+constructed. Uh in principle we should
+get to a point where all of these
+
+ align:start position:0%
+get to a point where all of these
+ 
+
+ align:start position:0%
+get to a point where all of these
+questions all of the questions about
+
+ align:start position:0%
+questions all of the questions about
+ 
+
+ align:start position:0%
+questions all of the questions about
+life and about um the world we live in
+
+ align:start position:0%
+life and about um the world we live in
+ 
+
+ align:start position:0%
+life and about um the world we live in
+about our reality the reality because
+
+ align:start position:0%
+about our reality the reality because
+ 
+
+ align:start position:0%
+about our reality the reality because
+what other one is there apart from the
+
+ align:start position:0%
+what other one is there apart from the
+ 
+
+ align:start position:0%
+what other one is there apart from the
+one we know will be solvable um and I
+
+ align:start position:0%
+one we know will be solvable um and I
+ 
+
+ align:start position:0%
+one we know will be solvable um and I
+think of that as a faith and that that
+
+ align:start position:0%
+think of that as a faith and that that
+ 
+
+ align:start position:0%
+think of that as a faith and that that
+was the argument of the conclusion to
+
+ align:start position:0%
+was the argument of the conclusion to
+ 
+
+ align:start position:0%
+was the argument of the conclusion to
+feeling and imagination. It's not that
+
+ align:start position:0%
+feeling and imagination. It's not that
+ 
+
+ align:start position:0%
+feeling and imagination. It's not that
+I'm opposed to people who have faith.
+
+ align:start position:0%
+I'm opposed to people who have faith.
+ 
+
+ align:start position:0%
+I'm opposed to people who have faith.
+What whatever the faith is, but it's
+
+ align:start position:0%
+What whatever the faith is, but it's
+ 
+
+ align:start position:0%
+What whatever the faith is, but it's
+merely a faith. And if you think that it
+
+ align:start position:0%
+merely a faith. And if you think that it
+ 
+
+ align:start position:0%
+merely a faith. And if you think that it
+itself is scientific, then I think that
+
+ align:start position:0%
+itself is scientific, then I think that
+ 
+
+ align:start position:0%
+itself is scientific, then I think that
+is a mistake that I was arguing against
+
+ align:start position:0%
+is a mistake that I was arguing against
+ 
+
+ align:start position:0%
+is a mistake that I was arguing against
+uh from my humanist philosophical point
+
+ align:start position:0%
+uh from my humanist philosophical point
+ 
+
+ align:start position:0%
+uh from my humanist philosophical point
+of view in the last chapter of that of
+
+ align:start position:0%
+of view in the last chapter of that of
+ 
+
+ align:start position:0%
+of view in the last chapter of that of
+that book. And I think it applies to um
+
+ align:start position:0%
+that book. And I think it applies to um
+ 
+
+ align:start position:0%
+that book. And I think it applies to um
+the um the the u
+
+ align:start position:0%
+the um the the u
+ 
+
+ align:start position:0%
+the um the the u
+prospect of the the new effort at MIT.
+
+ align:start position:0%
+prospect of the the new effort at MIT.
+ 
+
+ align:start position:0%
+prospect of the the new effort at MIT.
+I had when I was this is not a an
+
+ align:start position:0%
+I had when I was this is not a an
+ 
+
+ align:start position:0%
+I had when I was this is not a an
+autobiographical
+
+ align:start position:0%
+autobiographical
+ 
+
+ align:start position:0%
+autobiographical
+diversement but it's very relevant. When
+
+ align:start position:0%
+diversement but it's very relevant. When
+ 
+
+ align:start position:0%
+diversement but it's very relevant. When
+I was a an undergraduate, I had a friend
+
+ align:start position:0%
+I was a an undergraduate, I had a friend
+ 
+
+ align:start position:0%
+I was a an undergraduate, I had a friend
+in philosophy at Harvard and then we
+
+ align:start position:0%
+in philosophy at Harvard and then we
+ 
+
+ align:start position:0%
+in philosophy at Harvard and then we
+both went to graduate school in
+
+ align:start position:0%
+both went to graduate school in
+ 
+
+ align:start position:0%
+both went to graduate school in
+philosophy at Harvard and we talked a
+
+ align:start position:0%
+philosophy at Harvard and we talked a
+ 
+
+ align:start position:0%
+philosophy at Harvard and we talked a
+lot and uh the great man at that time
+
+ align:start position:0%
+lot and uh the great man at that time
+ 
+
+ align:start position:0%
+lot and uh the great man at that time
+was the philosopher and logician WV
+
+ align:start position:0%
+was the philosopher and logician WV
+ 
+
+ align:start position:0%
+was the philosopher and logician WV
+Quin. Have any of you read any of his
+
+ align:start position:0%
+Quin. Have any of you read any of his
+ 
+
+ align:start position:0%
+Quin. Have any of you read any of his
+works? In any event, he was he's he died
+
+ align:start position:0%
+works? In any event, he was he's he died
+ 
+
+ align:start position:0%
+works? In any event, he was he's he died
+maybe five years ago in a the memory of
+
+ align:start position:0%
+maybe five years ago in a the memory of
+ 
+
+ align:start position:0%
+maybe five years ago in a the memory of
+him seems to be fading already, but he
+
+ align:start position:0%
+him seems to be fading already, but he
+ 
+
+ align:start position:0%
+him seems to be fading already, but he
+was very he was the top of the heap at
+
+ align:start position:0%
+was very he was the top of the heap at
+ 
+
+ align:start position:0%
+was very he was the top of the heap at
+the time and had published an essay that
+
+ align:start position:0%
+the time and had published an essay that
+ 
+
+ align:start position:0%
+the time and had published an essay that
+we both had questions about and we my
+
+ align:start position:0%
+we both had questions about and we my
+ 
+
+ align:start position:0%
+we both had questions about and we my
+first paper was written with him and was
+
+ align:start position:0%
+first paper was written with him and was
+ 
+
+ align:start position:0%
+first paper was written with him and was
+published in the journal of philosophy
+
+ align:start position:0%
+published in the journal of philosophy
+ 
+
+ align:start position:0%
+published in the journal of philosophy
+when we were still first year graduate
+
+ align:start position:0%
+when we were still first year graduate
+ 
+
+ align:start position:0%
+when we were still first year graduate
+students and ever after that we've
+
+ align:start position:0%
+students and ever after that we've
+ 
+
+ align:start position:0%
+students and ever after that we've
+exchanged I we wrote another paper in
+
+ align:start position:0%
+exchanged I we wrote another paper in
+ 
+
+ align:start position:0%
+exchanged I we wrote another paper in
+jointly and then we've always been um
+
+ align:start position:0%
+jointly and then we've always been um
+ 
+
+ align:start position:0%
+jointly and then we've always been um
+exchanging um ideas. Now with the
+
+ align:start position:0%
+exchanging um ideas. Now with the
+ 
+
+ align:start position:0%
+exchanging um ideas. Now with the
+internet, we have a very voluminous
+
+ align:start position:0%
+internet, we have a very voluminous
+ 
+
+ align:start position:0%
+internet, we have a very voluminous
+correspondence back and forth on
+
+ align:start position:0%
+correspondence back and forth on
+ 
+
+ align:start position:0%
+correspondence back and forth on
+everything under the sun. He u uh took
+
+ align:start position:0%
+everything under the sun. He u uh took
+ 
+
+ align:start position:0%
+everything under the sun. He u uh took
+early retirement from the his
+
+ align:start position:0%
+early retirement from the his
+ 
+
+ align:start position:0%
+early retirement from the his
+professorship at the University of
+
+ align:start position:0%
+professorship at the University of
+ 
+
+ align:start position:0%
+professorship at the University of
+Maryland and moved to Florida and so we
+
+ align:start position:0%
+Maryland and moved to Florida and so we
+ 
+
+ align:start position:0%
+Maryland and moved to Florida and so we
+communicate through email mainly. Um he
+
+ align:start position:0%
+communicate through email mainly. Um he
+ 
+
+ align:start position:0%
+communicate through email mainly. Um he
+wrote a book um which is won uh a very
+
+ align:start position:0%
+wrote a book um which is won uh a very
+ 
+
+ align:start position:0%
+wrote a book um which is won uh a very
+uh prestigious award called the John
+
+ align:start position:0%
+uh prestigious award called the John
+ 
+
+ align:start position:0%
+uh prestigious award called the John
+Johnson Johnsonian prize given by the
+
+ align:start position:0%
+Johnson Johnsonian prize given by the
+ 
+
+ align:start position:0%
+Johnson Johnsonian prize given by the
+editors of the journal of philosophy and
+
+ align:start position:0%
+editors of the journal of philosophy and
+ 
+
+ align:start position:0%
+editors of the journal of philosophy and
+uh which came out maybe 20 years ago but
+
+ align:start position:0%
+uh which came out maybe 20 years ago but
+ 
+
+ align:start position:0%
+uh which came out maybe 20 years ago but
+is still remembered by analytical
+
+ align:start position:0%
+is still remembered by analytical
+ 
+
+ align:start position:0%
+is still remembered by analytical
+philosophers particularly the ones in my
+
+ align:start position:0%
+philosophers particularly the ones in my
+ 
+
+ align:start position:0%
+philosophers particularly the ones in my
+department who work along the lines that
+
+ align:start position:0%
+department who work along the lines that
+ 
+
+ align:start position:0%
+department who work along the lines that
+he had mapped out very early long before
+
+ align:start position:0%
+he had mapped out very early long before
+ 
+
+ align:start position:0%
+he had mapped out very early long before
+other people did. Uh the present uh
+
+ align:start position:0%
+other people did. Uh the present uh
+ 
+
+ align:start position:0%
+other people did. Uh the present uh
+version of that is what's called
+
+ align:start position:0%
+version of that is what's called
+ 
+
+ align:start position:0%
+version of that is what's called
+physicalism which I will explain in a
+
+ align:start position:0%
+physicalism which I will explain in a
+ 
+
+ align:start position:0%
+physicalism which I will explain in a
+moment. Um his name is Morland Perkins.
+
+ align:start position:0%
+moment. Um his name is Morland Perkins.
+ 
+
+ align:start position:0%
+moment. Um his name is Morland Perkins.
+Um and when I went to the inaugural
+
+ align:start position:0%
+Um and when I went to the inaugural
+ 
+
+ align:start position:0%
+Um and when I went to the inaugural
+proceedings at the Pikour um um center
+
+ align:start position:0%
+proceedings at the Pikour um um center
+ 
+
+ align:start position:0%
+proceedings at the Pikour um um center
+last week, I sent him uh a description
+
+ align:start position:0%
+last week, I sent him uh a description
+ 
+
+ align:start position:0%
+last week, I sent him uh a description
+of them and he he was interested. So I
+
+ align:start position:0%
+of them and he he was interested. So I
+ 
+
+ align:start position:0%
+of them and he he was interested. So I
+Xerox um what I could get uh which he
+
+ align:start position:0%
+Xerox um what I could get uh which he
+ 
+
+ align:start position:0%
+Xerox um what I could get uh which he
+could have got to off of the internet
+
+ align:start position:0%
+could have got to off of the internet
+ 
+
+ align:start position:0%
+could have got to off of the internet
+and I sent him a copy of tech talk which
+
+ align:start position:0%
+and I sent him a copy of tech talk which
+ 
+
+ align:start position:0%
+and I sent him a copy of tech talk which
+has several had several ar articles on
+
+ align:start position:0%
+has several had several ar articles on
+ 
+
+ align:start position:0%
+has several had several ar articles on
+on that in the last in the last issue.
+
+ align:start position:0%
+on that in the last in the last issue.
+ 
+
+ align:start position:0%
+on that in the last in the last issue.
+Um we in class at our last meeting you
+
+ align:start position:0%
+Um we in class at our last meeting you
+ 
+
+ align:start position:0%
+Um we in class at our last meeting you
+remember discussed the comment by one of
+
+ align:start position:0%
+remember discussed the comment by one of
+ 
+
+ align:start position:0%
+remember discussed the comment by one of
+the speakers um uh Patricia Churchland
+
+ align:start position:0%
+the speakers um uh Patricia Churchland
+ 
+
+ align:start position:0%
+the speakers um uh Patricia Churchland
+in which she said that
+
+ align:start position:0%
+in which she said that
+ 
+
+ align:start position:0%
+in which she said that
+mind uh so ideas of soul spirit mind
+
+ align:start position:0%
+mind uh so ideas of soul spirit mind
+ 
+
+ align:start position:0%
+mind uh so ideas of soul spirit mind
+consciousness
+
+ align:start position:0%
+consciousness
+ 
+
+ align:start position:0%
+consciousness
+are all simply
+
+ align:start position:0%
+are all simply
+ 
+
+ align:start position:0%
+are all simply
+illusions of the brain those were her
+
+ align:start position:0%
+illusions of the brain those were her
+ 
+
+ align:start position:0%
+illusions of the brain those were her
+words quote illusions of the brain and
+
+ align:start position:0%
+words quote illusions of the brain and
+ 
+
+ align:start position:0%
+words quote illusions of the brain and
+that's what we I question that I didn't
+
+ align:start position:0%
+that's what we I question that I didn't
+ 
+
+ align:start position:0%
+that's what we I question that I didn't
+see how that they could be illusions of
+
+ align:start position:0%
+see how that they could be illusions of
+ 
+
+ align:start position:0%
+see how that they could be illusions of
+the brain. They might somehow involve
+
+ align:start position:0%
+the brain. They might somehow involve
+ 
+
+ align:start position:0%
+the brain. They might somehow involve
+human illusions, but how could the brain
+
+ align:start position:0%
+human illusions, but how could the brain
+ 
+
+ align:start position:0%
+human illusions, but how could the brain
+have an illusion that my argument
+
+ align:start position:0%
+have an illusion that my argument
+ 
+
+ align:start position:0%
+have an illusion that my argument
+remember what I said that it's as if you
+
+ align:start position:0%
+remember what I said that it's as if you
+ 
+
+ align:start position:0%
+remember what I said that it's as if you
+thought that a hammer could have a
+
+ align:start position:0%
+thought that a hammer could have a
+ 
+
+ align:start position:0%
+thought that a hammer could have a
+headache or or
+
+ align:start position:0%
+headache or or
+ 
+
+ align:start position:0%
+headache or or
+be in a state of anxiety. Um,
+
+ align:start position:0%
+be in a state of anxiety. Um,
+ 
+
+ align:start position:0%
+be in a state of anxiety. Um,
+I discuss I discussed all that with
+
+ align:start position:0%
+I discuss I discussed all that with
+ 
+
+ align:start position:0%
+I discuss I discussed all that with
+Morland Perkins and um he he sent me
+
+ align:start position:0%
+Morland Perkins and um he he sent me
+ 
+
+ align:start position:0%
+Morland Perkins and um he he sent me
+back um an email in which he defended
+
+ align:start position:0%
+back um an email in which he defended
+ 
+
+ align:start position:0%
+back um an email in which he defended
+that view. Uh and his argument is that
+
+ align:start position:0%
+that view. Uh and his argument is that
+ 
+
+ align:start position:0%
+that view. Uh and his argument is that
+if uh what you're missing is that it's
+
+ align:start position:0%
+if uh what you're missing is that it's
+ 
+
+ align:start position:0%
+if uh what you're missing is that it's
+not a question merely of causation. It's
+
+ align:start position:0%
+not a question merely of causation. It's
+ 
+
+ align:start position:0%
+not a question merely of causation. It's
+not a question of whether the brain
+
+ align:start position:0%
+not a question of whether the brain
+ 
+
+ align:start position:0%
+not a question of whether the brain
+causes consciousness,
+
+ align:start position:0%
+causes consciousness,
+ 
+
+ align:start position:0%
+causes consciousness,
+which I don't question. I don't know who
+
+ align:start position:0%
+which I don't question. I don't know who
+ 
+
+ align:start position:0%
+which I don't question. I don't know who
+does question anymore. The question is
+
+ align:start position:0%
+does question anymore. The question is
+ 
+
+ align:start position:0%
+does question anymore. The question is
+whether consciousness
+
+ align:start position:0%
+whether consciousness
+ 
+
+ align:start position:0%
+whether consciousness
+is constituted by the brain
+
+ align:start position:0%
+is constituted by the brain
+ 
+
+ align:start position:0%
+is constituted by the brain
+um whether the two are somehow one and
+
+ align:start position:0%
+um whether the two are somehow one and
+ 
+
+ align:start position:0%
+um whether the two are somehow one and
+the same thing. uh and gave gave me a
+
+ align:start position:0%
+the same thing. uh and gave gave me a
+ 
+
+ align:start position:0%
+the same thing. uh and gave gave me a
+description. I wrote them back saying uh
+
+ align:start position:0%
+description. I wrote them back saying uh
+ 
+
+ align:start position:0%
+description. I wrote them back saying uh
+in class several of my bright students
+
+ align:start position:0%
+in class several of my bright students
+ 
+
+ align:start position:0%
+in class several of my bright students
+in this course uh held a similar view
+
+ align:start position:0%
+in this course uh held a similar view
+ 
+
+ align:start position:0%
+in this course uh held a similar view
+though they of course couldn't formulate
+
+ align:start position:0%
+though they of course couldn't formulate
+ 
+
+ align:start position:0%
+though they of course couldn't formulate
+it exact exactly or as well as as you
+
+ align:start position:0%
+it exact exactly or as well as as you
+ 
+
+ align:start position:0%
+it exact exactly or as well as as you
+can because here he is a
+
+ align:start position:0%
+can because here he is a
+ 
+
+ align:start position:0%
+can because here he is a
+an important philosopher. Um but it's a
+
+ align:start position:0%
+an important philosopher. Um but it's a
+ 
+
+ align:start position:0%
+an important philosopher. Um but it's a
+similar view to yours. And then I um I
+
+ align:start position:0%
+similar view to yours. And then I um I
+ 
+
+ align:start position:0%
+similar view to yours. And then I um I
+said to him um tell me if X constitutes
+
+ align:start position:0%
+said to him um tell me if X constitutes
+ 
+
+ align:start position:0%
+said to him um tell me if X constitutes
+Y, what does that mean? What does it
+
+ align:start position:0%
+Y, what does that mean? What does it
+ 
+
+ align:start position:0%
+Y, what does that mean? What does it
+mean for X to constitute Y? Because that
+
+ align:start position:0%
+mean for X to constitute Y? Because that
+ 
+
+ align:start position:0%
+mean for X to constitute Y? Because that
+seemed to be the view that he was
+
+ align:start position:0%
+seemed to be the view that he was
+ 
+
+ align:start position:0%
+seemed to be the view that he was
+defending. Uh I we I wasn't questioning
+
+ align:start position:0%
+defending. Uh I we I wasn't questioning
+ 
+
+ align:start position:0%
+defending. Uh I we I wasn't questioning
+um with him anymore than I did with you
+
+ align:start position:0%
+um with him anymore than I did with you
+ 
+
+ align:start position:0%
+um with him anymore than I did with you
+that the brain causes um um
+
+ align:start position:0%
+that the brain causes um um
+ 
+
+ align:start position:0%
+that the brain causes um um
+consciousness in the sense that unless
+
+ align:start position:0%
+consciousness in the sense that unless
+ 
+
+ align:start position:0%
+consciousness in the sense that unless
+there is a brain consciousness would not
+
+ align:start position:0%
+there is a brain consciousness would not
+ 
+
+ align:start position:0%
+there is a brain consciousness would not
+occur. Uh we could agree about that. uh
+
+ align:start position:0%
+occur. Uh we could agree about that. uh
+ 
+
+ align:start position:0%
+occur. Uh we could agree about that. uh
+but he and I gather you though you
+
+ align:start position:0%
+but he and I gather you though you
+ 
+
+ align:start position:0%
+but he and I gather you though you
+didn't carry it as far as he was uh were
+
+ align:start position:0%
+didn't carry it as far as he was uh were
+ 
+
+ align:start position:0%
+didn't carry it as far as he was uh were
+arguing that um the mo the consciousness
+
+ align:start position:0%
+arguing that um the mo the consciousness
+ 
+
+ align:start position:0%
+arguing that um the mo the consciousness
+is the brain con the consciousness
+
+ align:start position:0%
+is the brain con the consciousness
+ 
+
+ align:start position:0%
+is the brain con the consciousness
+is constituted by the brain or the brain
+
+ align:start position:0%
+is constituted by the brain or the brain
+ 
+
+ align:start position:0%
+is constituted by the brain or the brain
+constitutes
+
+ align:start position:0%
+constitutes
+ 
+
+ align:start position:0%
+constitutes
+no it has to be the other word I guess
+
+ align:start position:0%
+no it has to be the other word I guess
+ 
+
+ align:start position:0%
+no it has to be the other word I guess
+it was um uh the brain constitutes or
+
+ align:start position:0%
+it was um uh the brain constitutes or
+ 
+
+ align:start position:0%
+it was um uh the brain constitutes or
+could be either way a brain constitutes
+
+ align:start position:0%
+could be either way a brain constitutes
+ 
+
+ align:start position:0%
+could be either way a brain constitutes
+consciousness or consciousness is
+
+ align:start position:0%
+consciousness or consciousness is
+ 
+
+ align:start position:0%
+consciousness or consciousness is
+constituted by the brain. What does that
+
+ align:start position:0%
+constituted by the brain. What does that
+ 
+
+ align:start position:0%
+constituted by the brain. What does that
+mean? I want to read to you now
+
+ align:start position:0%
+mean? I want to read to you now
+ 
+
+ align:start position:0%
+mean? I want to read to you now
+um his email about that and um
+
+ align:start position:0%
+um his email about that and um
+ 
+
+ align:start position:0%
+um his email about that and um
+we can stop my part of the proceedings
+
+ align:start position:0%
+we can stop my part of the proceedings
+ 
+
+ align:start position:0%
+we can stop my part of the proceedings
+today with any kind of discussion about
+
+ align:start position:0%
+today with any kind of discussion about
+ 
+
+ align:start position:0%
+today with any kind of discussion about
+this that you want, but I do want to
+
+ align:start position:0%
+this that you want, but I do want to
+ 
+
+ align:start position:0%
+this that you want, but I do want to
+leave plenty of time for you
+
+ align:start position:0%
+leave plenty of time for you
+ 
+
+ align:start position:0%
+leave plenty of time for you
+talking about your papers and your ideas
+
+ align:start position:0%
+talking about your papers and your ideas
+ 
+
+ align:start position:0%
+talking about your papers and your ideas
+of everything in general. And this is
+
+ align:start position:0%
+of everything in general. And this is
+ 
+
+ align:start position:0%
+of everything in general. And this is
+Morland's reply in this context
+
+ align:start position:0%
+Morland's reply in this context
+ 
+
+ align:start position:0%
+Morland's reply in this context
+um constitutes
+
+ align:start position:0%
+um constitutes
+ 
+
+ align:start position:0%
+um constitutes
+uh is a way of signaling that there is
+
+ align:start position:0%
+uh is a way of signaling that there is
+ 
+
+ align:start position:0%
+uh is a way of signaling that there is
+nothing in the universe but physical
+
+ align:start position:0%
+nothing in the universe but physical
+ 
+
+ align:start position:0%
+nothing in the universe but physical
+stuff processes events and properties
+
+ align:start position:0%
+stuff processes events and properties
+ 
+
+ align:start position:0%
+stuff processes events and properties
+i.e
+
+ align:start position:0%
+i.e
+ 
+
+ align:start position:0%
+i.e
+that the mind, consciousness, moments,
+
+ align:start position:0%
+that the mind, consciousness, moments,
+ 
+
+ align:start position:0%
+that the mind, consciousness, moments,
+experience. Maybe it should be moments
+
+ align:start position:0%
+experience. Maybe it should be moments
+ 
+
+ align:start position:0%
+experience. Maybe it should be moments
+of experience. Um, or yeah, moments of
+
+ align:start position:0%
+of experience. Um, or yeah, moments of
+ 
+
+ align:start position:0%
+of experience. Um, or yeah, moments of
+experience, consciousness, mental
+
+ align:start position:0%
+experience, consciousness, mental
+ 
+
+ align:start position:0%
+experience, consciousness, mental
+events,
+
+ align:start position:0%
+events,
+ 
+
+ align:start position:0%
+events,
+thoughts, sensations, and so on are all
+
+ align:start position:0%
+thoughts, sensations, and so on are all
+ 
+
+ align:start position:0%
+thoughts, sensations, and so on are all
+brain structures. They are brain
+
+ align:start position:0%
+brain structures. They are brain
+ 
+
+ align:start position:0%
+brain structures. They are brain
+structures. That's the point. brain
+
+ align:start position:0%
+structures. That's the point. brain
+ 
+
+ align:start position:0%
+structures. That's the point. brain
+events, brain features, and so on
+
+ align:start position:0%
+events, brain features, and so on
+ 
+
+ align:start position:0%
+events, brain features, and so on
+through however many ways you want to
+
+ align:start position:0%
+through however many ways you want to
+ 
+
+ align:start position:0%
+through however many ways you want to
+specify that they are nothing but
+
+ align:start position:0%
+specify that they are nothing but
+ 
+
+ align:start position:0%
+specify that they are nothing but
+attributes of the human physical body.
+
+ align:start position:0%
+attributes of the human physical body.
+ 
+
+ align:start position:0%
+attributes of the human physical body.
+In other words, this expresses what used
+
+ align:start position:0%
+In other words, this expresses what used
+ 
+
+ align:start position:0%
+In other words, this expresses what used
+to be called a thoroughgoing
+
+ align:start position:0%
+to be called a thoroughgoing
+ 
+
+ align:start position:0%
+to be called a thoroughgoing
+metaphysical materialism,
+
+ align:start position:0%
+metaphysical materialism,
+ 
+
+ align:start position:0%
+metaphysical materialism,
+which is nowadays called physicalism,
+
+ align:start position:0%
+which is nowadays called physicalism,
+ 
+
+ align:start position:0%
+which is nowadays called physicalism,
+and which I would guess is the dominant
+
+ align:start position:0%
+and which I would guess is the dominant
+ 
+
+ align:start position:0%
+and which I would guess is the dominant
+belief about the nature of things among
+
+ align:start position:0%
+belief about the nature of things among
+ 
+
+ align:start position:0%
+belief about the nature of things among
+American analytical philosophers
+
+ align:start position:0%
+American analytical philosophers
+ 
+
+ align:start position:0%
+American analytical philosophers
+concerned with this sort of subject
+
+ align:start position:0%
+concerned with this sort of subject
+ 
+
+ align:start position:0%
+concerned with this sort of subject
+today.
+
+ align:start position:0%
+today.
+ 
+
+ align:start position:0%
+today.
+Though, of course, I could be wrong
+
+ align:start position:0%
+Though, of course, I could be wrong
+ 
+
+ align:start position:0%
+Though, of course, I could be wrong
+about the exact percentage.
+
+ align:start position:0%
+about the exact percentage.
+ 
+
+ align:start position:0%
+about the exact percentage.
+I personally adopted the physicalistic
+
+ align:start position:0%
+I personally adopted the physicalistic
+ 
+
+ align:start position:0%
+I personally adopted the physicalistic
+view in my doctoral thesis which uh was
+
+ align:start position:0%
+view in my doctoral thesis which uh was
+ 
+
+ align:start position:0%
+view in my doctoral thesis which uh was
+the origin of that prize-winning book of
+
+ align:start position:0%
+the origin of that prize-winning book of
+ 
+
+ align:start position:0%
+the origin of that prize-winning book of
+his that incidentally is called sens
+
+ align:start position:0%
+his that incidentally is called sens
+ 
+
+ align:start position:0%
+his that incidentally is called sens
+sensing the world
+
+ align:start position:0%
+sensing the world
+ 
+
+ align:start position:0%
+sensing the world
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+which was a physicalistic account of
+
+ align:start position:0%
+which was a physicalistic account of
+ 
+
+ align:start position:0%
+which was a physicalistic account of
+chiefly belief and secondarily drive or
+
+ align:start position:0%
+chiefly belief and secondarily drive or
+ 
+
+ align:start position:0%
+chiefly belief and secondarily drive or
+desire and tertiarily
+
+ align:start position:0%
+desire and tertiarily
+ 
+
+ align:start position:0%
+desire and tertiarily
+sense perception. Obviously, no one has
+
+ align:start position:0%
+sense perception. Obviously, no one has
+ 
+
+ align:start position:0%
+sense perception. Obviously, no one has
+proved this thesis. It's still an
+
+ align:start position:0%
+proved this thesis. It's still an
+ 
+
+ align:start position:0%
+proved this thesis. It's still an
+article of faith, if you like, as a kind
+
+ align:start position:0%
+article of faith, if you like, as a kind
+ 
+
+ align:start position:0%
+article of faith, if you like, as a kind
+of projection or prediction of how time,
+
+ align:start position:0%
+of projection or prediction of how time,
+ 
+
+ align:start position:0%
+of projection or prediction of how time,
+how over time the world will
+
+ align:start position:0%
+how over time the world will
+ 
+
+ align:start position:0%
+how over time the world will
+increasingly make itself visible as of
+
+ align:start position:0%
+increasingly make itself visible as of
+ 
+
+ align:start position:0%
+increasingly make itself visible as of
+this sort.
+
+ align:start position:0%
+this sort.
+ 
+
+ align:start position:0%
+this sort.
+So it's interesting because it talks
+
+ align:start position:0%
+So it's interesting because it talks
+ 
+
+ align:start position:0%
+So it's interesting because it talks
+about as an article of faith but it's an
+
+ align:start position:0%
+about as an article of faith but it's an
+ 
+
+ align:start position:0%
+about as an article of faith but it's an
+article of faith about discoveries that
+
+ align:start position:0%
+article of faith about discoveries that
+ 
+
+ align:start position:0%
+article of faith about discoveries that
+are not them themselves articles of
+
+ align:start position:0%
+are not them themselves articles of
+ 
+
+ align:start position:0%
+are not them themselves articles of
+faith but uh that will give concrete u
+
+ align:start position:0%
+faith but uh that will give concrete u
+ 
+
+ align:start position:0%
+faith but uh that will give concrete u
+proof scientific proof of the thesis of
+
+ align:start position:0%
+proof scientific proof of the thesis of
+ 
+
+ align:start position:0%
+proof scientific proof of the thesis of
+physicalism that he is uh defending.
+
+ align:start position:0%
+physicalism that he is uh defending.
+ 
+
+ align:start position:0%
+physicalism that he is uh defending.
+Next paragraph. However, there are
+
+ align:start position:0%
+Next paragraph. However, there are
+ 
+
+ align:start position:0%
+Next paragraph. However, there are
+certainly some very sharp and quite
+
+ align:start position:0%
+certainly some very sharp and quite
+ 
+
+ align:start position:0%
+certainly some very sharp and quite
+hard-headed analytic philosophers
+
+ align:start position:0%
+hard-headed analytic philosophers
+ 
+
+ align:start position:0%
+hard-headed analytic philosophers
+concerned with the subject who devote
+
+ align:start position:0%
+concerned with the subject who devote
+ 
+
+ align:start position:0%
+concerned with the subject who devote
+whole books still to showing that
+
+ align:start position:0%
+whole books still to showing that
+ 
+
+ align:start position:0%
+whole books still to showing that
+physicalism cannot be correct.
+
+ align:start position:0%
+physicalism cannot be correct.
+ 
+
+ align:start position:0%
+physicalism cannot be correct.
+So if your sentiments are this is me,
+
+ align:start position:0%
+So if your sentiments are this is me,
+ 
+
+ align:start position:0%
+So if your sentiments are this is me,
+you personally you not not you in
+
+ align:start position:0%
+you personally you not not you in
+ 
+
+ align:start position:0%
+you personally you not not you in
+general but me in particular. So if your
+
+ align:start position:0%
+general but me in particular. So if your
+ 
+
+ align:start position:0%
+general but me in particular. So if your
+if your own sentiments are dualistic or
+
+ align:start position:0%
+if your own sentiments are dualistic or
+ 
+
+ align:start position:0%
+if your own sentiments are dualistic or
+worse, you should feel free to continue
+
+ align:start position:0%
+worse, you should feel free to continue
+ 
+
+ align:start position:0%
+worse, you should feel free to continue
+to enjoy them with a good conscience.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+It's a wonderful it's a wonderful uh
+
+ align:start position:0%
+It's a wonderful it's a wonderful uh
+ 
+
+ align:start position:0%
+It's a wonderful it's a wonderful uh
+statement. I think now we can discuss it
+
+ align:start position:0%
+statement. I think now we can discuss it
+ 
+
+ align:start position:0%
+statement. I think now we can discuss it
+right now if any of you want to but
+
+ align:start position:0%
+right now if any of you want to but
+ 
+
+ align:start position:0%
+right now if any of you want to but
+thinking about it u I was a little taken
+
+ align:start position:0%
+thinking about it u I was a little taken
+ 
+
+ align:start position:0%
+thinking about it u I was a little taken
+aback that I should be accused of being
+
+ align:start position:0%
+aback that I should be accused of being
+ 
+
+ align:start position:0%
+aback that I should be accused of being
+a dualist because I've never thought of
+
+ align:start position:0%
+a dualist because I've never thought of
+ 
+
+ align:start position:0%
+a dualist because I've never thought of
+myself in that way and then it occurred
+
+ align:start position:0%
+myself in that way and then it occurred
+ 
+
+ align:start position:0%
+myself in that way and then it occurred
+to me
+
+ align:start position:0%
+to me
+ 
+
+ align:start position:0%
+to me
+um uh as I was walking over the bridge
+
+ align:start position:0%
+um uh as I was walking over the bridge
+ 
+
+ align:start position:0%
+um uh as I was walking over the bridge
+today thinking about the class um there
+
+ align:start position:0%
+today thinking about the class um there
+ 
+
+ align:start position:0%
+today thinking about the class um there
+are three kinds of dualists that one
+
+ align:start position:0%
+are three kinds of dualists that one
+ 
+
+ align:start position:0%
+are three kinds of dualists that one
+would have to consider. One kind of
+
+ align:start position:0%
+would have to consider. One kind of
+ 
+
+ align:start position:0%
+would have to consider. One kind of
+dualist um is uh the dualist of the
+
+ align:start position:0%
+dualist um is uh the dualist of the
+ 
+
+ align:start position:0%
+dualist um is uh the dualist of the
+traditional sort. Latin philosophy is
+
+ align:start position:0%
+traditional sort. Latin philosophy is
+ 
+
+ align:start position:0%
+traditional sort. Latin philosophy is
+supremely represented by uh Renee Deart.
+
+ align:start position:0%
+supremely represented by uh Renee Deart.
+ 
+
+ align:start position:0%
+supremely represented by uh Renee Deart.
+Decart believed that
+
+ align:start position:0%
+Decart believed that
+ 
+
+ align:start position:0%
+Decart believed that
+as a metaphysical principle there are
+
+ align:start position:0%
+as a metaphysical principle there are
+ 
+
+ align:start position:0%
+as a metaphysical principle there are
+two beings, two substances, one of which
+
+ align:start position:0%
+two beings, two substances, one of which
+ 
+
+ align:start position:0%
+two beings, two substances, one of which
+is matter, the other of which is mind.
+
+ align:start position:0%
+is matter, the other of which is mind.
+ 
+
+ align:start position:0%
+is matter, the other of which is mind.
+and that the two cannot cannot be
+
+ align:start position:0%
+and that the two cannot cannot be
+ 
+
+ align:start position:0%
+and that the two cannot cannot be
+confused one for the other and cannot be
+
+ align:start position:0%
+confused one for the other and cannot be
+ 
+
+ align:start position:0%
+confused one for the other and cannot be
+reduced to one another. Um now there are
+
+ align:start position:0%
+reduced to one another. Um now there are
+ 
+
+ align:start position:0%
+reduced to one another. Um now there are
+certain virtues for that that were
+
+ align:start position:0%
+certain virtues for that that were
+ 
+
+ align:start position:0%
+certain virtues for that that were
+capitalized on by uh Christianity and
+
+ align:start position:0%
+capitalized on by uh Christianity and
+ 
+
+ align:start position:0%
+capitalized on by uh Christianity and
+Decart was writing in a Catholic era uh
+
+ align:start position:0%
+Decart was writing in a Catholic era uh
+ 
+
+ align:start position:0%
+Decart was writing in a Catholic era uh
+when he could have got into a lot of
+
+ align:start position:0%
+when he could have got into a lot of
+ 
+
+ align:start position:0%
+when he could have got into a lot of
+trouble if he said uh things that were
+
+ align:start position:0%
+trouble if he said uh things that were
+ 
+
+ align:start position:0%
+trouble if he said uh things that were
+radically different. um Jordano Bruno,
+
+ align:start position:0%
+radically different. um Jordano Bruno,
+ 
+
+ align:start position:0%
+radically different. um Jordano Bruno,
+the great Italian um philosopher um of
+
+ align:start position:0%
+the great Italian um philosopher um of
+ 
+
+ align:start position:0%
+the great Italian um philosopher um of
+the previous century um or maybe less
+
+ align:start position:0%
+the previous century um or maybe less
+ 
+
+ align:start position:0%
+the previous century um or maybe less
+than a century from Decart um was burned
+
+ align:start position:0%
+than a century from Decart um was burned
+ 
+
+ align:start position:0%
+than a century from Decart um was burned
+at stake because he said that um that um
+
+ align:start position:0%
+at stake because he said that um that um
+ 
+
+ align:start position:0%
+at stake because he said that um that um
+um God and the world are the same. He
+
+ align:start position:0%
+um God and the world are the same. He
+ 
+
+ align:start position:0%
+um God and the world are the same. He
+was a radical pantheist. uh so uh I
+
+ align:start position:0%
+was a radical pantheist. uh so uh I
+ 
+
+ align:start position:0%
+was a radical pantheist. uh so uh I
+don't think Decart would have burned be
+
+ align:start position:0%
+don't think Decart would have burned be
+ 
+
+ align:start position:0%
+don't think Decart would have burned be
+burned the stake but he wanted to be
+
+ align:start position:0%
+burned the stake but he wanted to be
+ 
+
+ align:start position:0%
+burned the stake but he wanted to be
+acceptable to the Catholic theology that
+
+ align:start position:0%
+acceptable to the Catholic theology that
+ 
+
+ align:start position:0%
+acceptable to the Catholic theology that
+was the dominant force in French life at
+
+ align:start position:0%
+was the dominant force in French life at
+ 
+
+ align:start position:0%
+was the dominant force in French life at
+that time. Uh I mention that because um
+
+ align:start position:0%
+that time. Uh I mention that because um
+ 
+
+ align:start position:0%
+that time. Uh I mention that because um
+I can understand why religions would
+
+ align:start position:0%
+I can understand why religions would
+ 
+
+ align:start position:0%
+I can understand why religions would
+develop out of this attitude. Uh it's a
+
+ align:start position:0%
+develop out of this attitude. Uh it's a
+ 
+
+ align:start position:0%
+develop out of this attitude. Uh it's a
+very comforting one. It's one that
+
+ align:start position:0%
+very comforting one. It's one that
+ 
+
+ align:start position:0%
+very comforting one. It's one that
+speaks to the mentality of most people.
+
+ align:start position:0%
+speaks to the mentality of most people.
+ 
+
+ align:start position:0%
+speaks to the mentality of most people.
+All of us, I think, whether or not
+
+ align:start position:0%
+All of us, I think, whether or not
+ 
+
+ align:start position:0%
+All of us, I think, whether or not
+whatever whatever our religion is or if
+
+ align:start position:0%
+whatever whatever our religion is or if
+ 
+
+ align:start position:0%
+whatever whatever our religion is or if
+we even have a religion, we feel that we
+
+ align:start position:0%
+we even have a religion, we feel that we
+ 
+
+ align:start position:0%
+we even have a religion, we feel that we
+as conscious beings as ourselves are not
+
+ align:start position:0%
+as conscious beings as ourselves are not
+ 
+
+ align:start position:0%
+as conscious beings as ourselves are not
+reducible simply to our bodies.
+
+ align:start position:0%
+reducible simply to our bodies.
+ 
+
+ align:start position:0%
+reducible simply to our bodies.
+Um I Irving Singer identify with my
+
+ align:start position:0%
+Um I Irving Singer identify with my
+ 
+
+ align:start position:0%
+Um I Irving Singer identify with my
+consciousness, with my memories, with my
+
+ align:start position:0%
+consciousness, with my memories, with my
+ 
+
+ align:start position:0%
+consciousness, with my memories, with my
+experience, with my perception, my being
+
+ align:start position:0%
+experience, with my perception, my being
+ 
+
+ align:start position:0%
+experience, with my perception, my being
+here in front of you and not to what's
+
+ align:start position:0%
+here in front of you and not to what's
+ 
+
+ align:start position:0%
+here in front of you and not to what's
+happening in my uh organism, my body
+
+ align:start position:0%
+happening in my uh organism, my body
+ 
+
+ align:start position:0%
+happening in my uh organism, my body
+while I'm speaking. Um I'm not even
+
+ align:start position:0%
+while I'm speaking. Um I'm not even
+ 
+
+ align:start position:0%
+while I'm speaking. Um I'm not even
+aware of my digestive system at any time
+
+ align:start position:0%
+aware of my digestive system at any time
+ 
+
+ align:start position:0%
+aware of my digestive system at any time
+because uh it is it acts 24 hours a day
+
+ align:start position:0%
+because uh it is it acts 24 hours a day
+ 
+
+ align:start position:0%
+because uh it is it acts 24 hours a day
+uh without intruding very much into my
+
+ align:start position:0%
+uh without intruding very much into my
+ 
+
+ align:start position:0%
+uh without intruding very much into my
+consciousness. occasionally does if I
+
+ align:start position:0%
+consciousness. occasionally does if I
+ 
+
+ align:start position:0%
+consciousness. occasionally does if I
+have a belly ache but usually it's the
+
+ align:start position:0%
+have a belly ache but usually it's the
+ 
+
+ align:start position:0%
+have a belly ache but usually it's the
+body is performing its job as something
+
+ align:start position:0%
+body is performing its job as something
+ 
+
+ align:start position:0%
+body is performing its job as something
+separate from what I am aware of right
+
+ align:start position:0%
+separate from what I am aware of right
+ 
+
+ align:start position:0%
+separate from what I am aware of right
+and um I wouldn't mind if when my body
+
+ align:start position:0%
+and um I wouldn't mind if when my body
+ 
+
+ align:start position:0%
+and um I wouldn't mind if when my body
+dies which I have every reason to expect
+
+ align:start position:0%
+dies which I have every reason to expect
+ 
+
+ align:start position:0%
+dies which I have every reason to expect
+um my mind my consciousness kept on
+
+ align:start position:0%
+um my mind my consciousness kept on
+ 
+
+ align:start position:0%
+um my mind my consciousness kept on
+going
+
+ align:start position:0%
+going
+ 
+
+ align:start position:0%
+going
+um yes just as a little aside on this I
+
+ align:start position:0%
+um yes just as a little aside on this I
+ 
+
+ align:start position:0%
+um yes just as a little aside on this I
+showed an interview yesterday to my film
+
+ align:start position:0%
+showed an interview yesterday to my film
+ 
+
+ align:start position:0%
+showed an interview yesterday to my film
+class um with Ingmar Bergman who had um
+
+ align:start position:0%
+class um with Ingmar Bergman who had um
+ 
+
+ align:start position:0%
+class um with Ingmar Bergman who had um
+several of whose greatest movies are
+
+ align:start position:0%
+several of whose greatest movies are
+ 
+
+ align:start position:0%
+several of whose greatest movies are
+about religious themes and who was whose
+
+ align:start position:0%
+about religious themes and who was whose
+ 
+
+ align:start position:0%
+about religious themes and who was whose
+father was a parson in the um for the
+
+ align:start position:0%
+father was a parson in the um for the
+ 
+
+ align:start position:0%
+father was a parson in the um for the
+royal court and he was very troubled
+
+ align:start position:0%
+royal court and he was very troubled
+ 
+
+ align:start position:0%
+royal court and he was very troubled
+because he couldn't accept that faith
+
+ align:start position:0%
+because he couldn't accept that faith
+ 
+
+ align:start position:0%
+because he couldn't accept that faith
+and felt guilty and miserable and the
+
+ align:start position:0%
+and felt guilty and miserable and the
+ 
+
+ align:start position:0%
+and felt guilty and miserable and the
+movies as he says were ways of working
+
+ align:start position:0%
+movies as he says were ways of working
+ 
+
+ align:start position:0%
+movies as he says were ways of working
+out his fear of death and fear of um
+
+ align:start position:0%
+out his fear of death and fear of um
+ 
+
+ align:start position:0%
+out his fear of death and fear of um
+guilt and uh punishment because of his
+
+ align:start position:0%
+guilt and uh punishment because of his
+ 
+
+ align:start position:0%
+guilt and uh punishment because of his
+way of living. Um
+
+ align:start position:0%
+way of living. Um
+ 
+
+ align:start position:0%
+way of living. Um
+the um the in this interview made in his
+
+ align:start position:0%
+the um the in this interview made in his
+ 
+
+ align:start position:0%
+the um the in this interview made in his
+50s when he had gone through all of that
+
+ align:start position:0%
+50s when he had gone through all of that
+ 
+
+ align:start position:0%
+50s when he had gone through all of that
+he said um you know I'm happy to think
+
+ align:start position:0%
+he said um you know I'm happy to think
+ 
+
+ align:start position:0%
+he said um you know I'm happy to think
+that there is no God. I'm happy to think
+
+ align:start position:0%
+that there is no God. I'm happy to think
+ 
+
+ align:start position:0%
+that there is no God. I'm happy to think
+that when I die, it'll be like somebody
+
+ align:start position:0%
+that when I die, it'll be like somebody
+ 
+
+ align:start position:0%
+that when I die, it'll be like somebody
+turning off the light. And I would be
+
+ align:start position:0%
+turning off the light. And I would be
+ 
+
+ align:start position:0%
+turning off the light. And I would be
+very unhappy if that somebody came
+
+ align:start position:0%
+very unhappy if that somebody came
+ 
+
+ align:start position:0%
+very unhappy if that somebody came
+around and turned it back on and said,
+
+ align:start position:0%
+around and turned it back on and said,
+ 
+
+ align:start position:0%
+around and turned it back on and said,
+"You have to go here and there and be
+
+ align:start position:0%
+"You have to go here and there and be
+ 
+
+ align:start position:0%
+"You have to go here and there and be
+punished and you have guilts and we have
+
+ align:start position:0%
+punished and you have guilts and we have
+ 
+
+ align:start position:0%
+punished and you have guilts and we have
+to be cleansed and all of that." I'd
+
+ align:start position:0%
+to be cleansed and all of that." I'd
+ 
+
+ align:start position:0%
+to be cleansed and all of that." I'd
+rather I'm happy to think that this life
+
+ align:start position:0%
+rather I'm happy to think that this life
+ 
+
+ align:start position:0%
+rather I'm happy to think that this life
+is the only one. Um, well,
+
+ align:start position:0%
+is the only one. Um, well,
+ 
+
+ align:start position:0%
+is the only one. Um, well,
+I don't feel that way at all. I
+
+ align:start position:0%
+I don't feel that way at all. I
+ 
+
+ align:start position:0%
+I don't feel that way at all. I
+understand why he would because he was
+
+ align:start position:0%
+understand why he would because he was
+ 
+
+ align:start position:0%
+understand why he would because he was
+so guiltridden. I don't I I don't feel
+
+ align:start position:0%
+so guiltridden. I don't I I don't feel
+ 
+
+ align:start position:0%
+so guiltridden. I don't I I don't feel
+guiltridden. Uh what I want is to be
+
+ align:start position:0%
+guiltridden. Uh what I want is to be
+ 
+
+ align:start position:0%
+guiltridden. Uh what I want is to be
+able to go on even if it's only as a
+
+ align:start position:0%
+able to go on even if it's only as a
+ 
+
+ align:start position:0%
+able to go on even if it's only as a
+mind. I don't have that faith. But if
+
+ align:start position:0%
+mind. I don't have that faith. But if
+ 
+
+ align:start position:0%
+mind. I don't have that faith. But if
+that were turned out to be the reality,
+
+ align:start position:0%
+that were turned out to be the reality,
+ 
+
+ align:start position:0%
+that were turned out to be the reality,
+I think I I could like it very much more
+
+ align:start position:0%
+I think I I could like it very much more
+ 
+
+ align:start position:0%
+I think I I could like it very much more
+than Ingar Bergman thinks that he would
+
+ align:start position:0%
+than Ingar Bergman thinks that he would
+ 
+
+ align:start position:0%
+than Ingar Bergman thinks that he would
+like it if somebody turned on the lights
+
+ align:start position:0%
+like it if somebody turned on the lights
+ 
+
+ align:start position:0%
+like it if somebody turned on the lights
+for him. Um but all of us identify with
+
+ align:start position:0%
+for him. Um but all of us identify with
+ 
+
+ align:start position:0%
+for him. Um but all of us identify with
+our minds rather than our bodies. Uh, I
+
+ align:start position:0%
+our minds rather than our bodies. Uh, I
+ 
+
+ align:start position:0%
+our minds rather than our bodies. Uh, I
+had a friend who was dying of stomach
+
+ align:start position:0%
+had a friend who was dying of stomach
+ 
+
+ align:start position:0%
+had a friend who was dying of stomach
+cancer. Um, and I remember his saying to
+
+ align:start position:0%
+cancer. Um, and I remember his saying to
+ 
+
+ align:start position:0%
+cancer. Um, and I remember his saying to
+me, you know, there is in me a tumor as
+
+ align:start position:0%
+me, you know, there is in me a tumor as
+ 
+
+ align:start position:0%
+me, you know, there is in me a tumor as
+big as a grapefruit. What have I got to
+
+ align:start position:0%
+big as a grapefruit. What have I got to
+ 
+
+ align:start position:0%
+big as a grapefruit. What have I got to
+do with that? What what how how can I
+
+ align:start position:0%
+do with that? What what how how can I
+ 
+
+ align:start position:0%
+do with that? What what how how can I
+think of that as me? I'm totally
+
+ align:start position:0%
+think of that as me? I'm totally
+ 
+
+ align:start position:0%
+think of that as me? I'm totally
+different from that. We all And then and
+
+ align:start position:0%
+different from that. We all And then and
+ 
+
+ align:start position:0%
+different from that. We all And then and
+he knew he was going to kill him and it
+
+ align:start position:0%
+he knew he was going to kill him and it
+ 
+
+ align:start position:0%
+he knew he was going to kill him and it
+did kill him. Um, that's not what I am.
+
+ align:start position:0%
+did kill him. Um, that's not what I am.
+ 
+
+ align:start position:0%
+did kill him. Um, that's not what I am.
+Well, Deart's view about the
+
+ align:start position:0%
+Well, Deart's view about the
+ 
+
+ align:start position:0%
+Well, Deart's view about the
+relationship between mind and body makes
+
+ align:start position:0%
+relationship between mind and body makes
+ 
+
+ align:start position:0%
+relationship between mind and body makes
+sense and could could uh even possibly
+
+ align:start position:0%
+sense and could could uh even possibly
+ 
+
+ align:start position:0%
+sense and could could uh even possibly
+justify those who have the religious
+
+ align:start position:0%
+justify those who have the religious
+ 
+
+ align:start position:0%
+justify those who have the religious
+faith uh that after death the soul goes
+
+ align:start position:0%
+faith uh that after death the soul goes
+ 
+
+ align:start position:0%
+faith uh that after death the soul goes
+on and this is a good world with a good
+
+ align:start position:0%
+on and this is a good world with a good
+ 
+
+ align:start position:0%
+on and this is a good world with a good
+God and one way or another God will take
+
+ align:start position:0%
+God and one way or another God will take
+ 
+
+ align:start position:0%
+God and one way or another God will take
+care of it. That's one kind of dualism
+
+ align:start position:0%
+care of it. That's one kind of dualism
+ 
+
+ align:start position:0%
+care of it. That's one kind of dualism
+and in philosophy it's been the dominant
+
+ align:start position:0%
+and in philosophy it's been the dominant
+ 
+
+ align:start position:0%
+and in philosophy it's been the dominant
+one up until about the 20th century when
+
+ align:start position:0%
+one up until about the 20th century when
+ 
+
+ align:start position:0%
+one up until about the 20th century when
+there was great reaction against it. Um
+
+ align:start position:0%
+there was great reaction against it. Um
+ 
+
+ align:start position:0%
+there was great reaction against it. Um
+that's not the kind of dualism that
+
+ align:start position:0%
+that's not the kind of dualism that
+ 
+
+ align:start position:0%
+that's not the kind of dualism that
+applies to me because I don't have the
+
+ align:start position:0%
+applies to me because I don't have the
+ 
+
+ align:start position:0%
+applies to me because I don't have the
+metaphysical view that dayart has uh and
+
+ align:start position:0%
+metaphysical view that dayart has uh and
+ 
+
+ align:start position:0%
+metaphysical view that dayart has uh and
+don't espouse his philosophy.
+
+ align:start position:0%
+don't espouse his philosophy.
+ 
+
+ align:start position:0%
+don't espouse his philosophy.
+There's a second kind of dualism which
+
+ align:start position:0%
+There's a second kind of dualism which
+ 
+
+ align:start position:0%
+There's a second kind of dualism which
+um is um discussed by Minsky in the um
+
+ align:start position:0%
+um is um discussed by Minsky in the um
+ 
+
+ align:start position:0%
+um is um discussed by Minsky in the um
+in the um
+
+ align:start position:0%
+in the um
+ 
+
+ align:start position:0%
+in the um
+emotion machine. Uh that dualism
+
+ align:start position:0%
+emotion machine. Uh that dualism
+ 
+
+ align:start position:0%
+emotion machine. Uh that dualism
+argues um that um
+
+ align:start position:0%
+argues um that um
+ 
+
+ align:start position:0%
+argues um that um
+everything in the mind is caused by
+
+ align:start position:0%
+everything in the mind is caused by
+ 
+
+ align:start position:0%
+everything in the mind is caused by
+something happening in the brain. And
+
+ align:start position:0%
+something happening in the brain. And
+ 
+
+ align:start position:0%
+something happening in the brain. And
+therefore as Minsky says it in one place
+
+ align:start position:0%
+therefore as Minsky says it in one place
+ 
+
+ align:start position:0%
+therefore as Minsky says it in one place
+um our job in this book is to see how it
+
+ align:start position:0%
+um our job in this book is to see how it
+ 
+
+ align:start position:0%
+um our job in this book is to see how it
+is possible through what physical
+
+ align:start position:0%
+is possible through what physical
+ 
+
+ align:start position:0%
+is possible through what physical
+processes that we can investigate
+
+ align:start position:0%
+processes that we can investigate
+ 
+
+ align:start position:0%
+processes that we can investigate
+through artificial intelligence through
+
+ align:start position:0%
+through artificial intelligence through
+ 
+
+ align:start position:0%
+through artificial intelligence through
+brain brain uh science through uh
+
+ align:start position:0%
+brain brain uh science through uh
+ 
+
+ align:start position:0%
+brain brain uh science through uh
+physical uh psychology. How we can trace
+
+ align:start position:0%
+physical uh psychology. How we can trace
+ 
+
+ align:start position:0%
+physical uh psychology. How we can trace
+the origin of um our of our mental
+
+ align:start position:0%
+the origin of um our of our mental
+ 
+
+ align:start position:0%
+the origin of um our of our mental
+states to different states of the body.
+
+ align:start position:0%
+states to different states of the body.
+ 
+
+ align:start position:0%
+states to different states of the body.
+Now if by origin you mean that there is
+
+ align:start position:0%
+Now if by origin you mean that there is
+ 
+
+ align:start position:0%
+Now if by origin you mean that there is
+a causal relationship um I accept that
+
+ align:start position:0%
+a causal relationship um I accept that
+ 
+
+ align:start position:0%
+a causal relationship um I accept that
+and don't but wouldn't have thought of
+
+ align:start position:0%
+and don't but wouldn't have thought of
+ 
+
+ align:start position:0%
+and don't but wouldn't have thought of
+that as being a kind of dualism. Minsky
+
+ align:start position:0%
+that as being a kind of dualism. Minsky
+ 
+
+ align:start position:0%
+that as being a kind of dualism. Minsky
+himself offers it as a substitute for
+
+ align:start position:0%
+himself offers it as a substitute for
+ 
+
+ align:start position:0%
+himself offers it as a substitute for
+what he calls dear deart's
+
+ align:start position:0%
+what he calls dear deart's
+ 
+
+ align:start position:0%
+what he calls dear deart's
+theater of the mind as if it were
+
+ align:start position:0%
+theater of the mind as if it were
+ 
+
+ align:start position:0%
+theater of the mind as if it were
+totally independent of the body. Uh so
+
+ align:start position:0%
+totally independent of the body. Uh so
+ 
+
+ align:start position:0%
+totally independent of the body. Uh so
+that kind of dualism is not what is at
+
+ align:start position:0%
+that kind of dualism is not what is at
+ 
+
+ align:start position:0%
+that kind of dualism is not what is at
+stake in Morland Perkins rebuttal of my
+
+ align:start position:0%
+stake in Morland Perkins rebuttal of my
+ 
+
+ align:start position:0%
+stake in Morland Perkins rebuttal of my
+views. The third kind however is and
+
+ align:start position:0%
+views. The third kind however is and
+ 
+
+ align:start position:0%
+views. The third kind however is and
+it's also represented by um uh Minsky.
+
+ align:start position:0%
+it's also represented by um uh Minsky.
+ 
+
+ align:start position:0%
+it's also represented by um uh Minsky.
+Um you remember what I was calling your
+
+ align:start position:0%
+Um you remember what I was calling your
+ 
+
+ align:start position:0%
+Um you remember what I was calling your
+attention to last time uh in which
+
+ align:start position:0%
+attention to last time uh in which
+ 
+
+ align:start position:0%
+attention to last time uh in which
+Minsky says that feelings
+
+ align:start position:0%
+Minsky says that feelings
+ 
+
+ align:start position:0%
+Minsky says that feelings
+are simply uh attempts to think about
+
+ align:start position:0%
+are simply uh attempts to think about
+ 
+
+ align:start position:0%
+are simply uh attempts to think about
+something. So if the body the body has a
+
+ align:start position:0%
+something. So if the body the body has a
+ 
+
+ align:start position:0%
+something. So if the body the body has a
+problem which is how to survive under
+
+ align:start position:0%
+problem which is how to survive under
+ 
+
+ align:start position:0%
+problem which is how to survive under
+these perilous conditions of um of
+
+ align:start position:0%
+these perilous conditions of um of
+ 
+
+ align:start position:0%
+these perilous conditions of um of
+somebody pushing you to the edge of a
+
+ align:start position:0%
+somebody pushing you to the edge of a
+ 
+
+ align:start position:0%
+somebody pushing you to the edge of a
+cliff. um you're going to have a feeling
+
+ align:start position:0%
+cliff. um you're going to have a feeling
+ 
+
+ align:start position:0%
+cliff. um you're going to have a feeling
+of fear of desire to flee of whatever uh
+
+ align:start position:0%
+of fear of desire to flee of whatever uh
+ 
+
+ align:start position:0%
+of fear of desire to flee of whatever uh
+but the feeling is related to your
+
+ align:start position:0%
+but the feeling is related to your
+ 
+
+ align:start position:0%
+but the feeling is related to your
+thinking I may be killed or what should
+
+ align:start position:0%
+thinking I may be killed or what should
+ 
+
+ align:start position:0%
+thinking I may be killed or what should
+I do to escape u it's it's h the feeling
+
+ align:start position:0%
+I do to escape u it's it's h the feeling
+ 
+
+ align:start position:0%
+I do to escape u it's it's h the feeling
+is itself simply a part of the process
+
+ align:start position:0%
+is itself simply a part of the process
+ 
+
+ align:start position:0%
+is itself simply a part of the process
+of thinking
+
+ align:start position:0%
+of thinking
+ 
+
+ align:start position:0%
+of thinking
+right now that leads directly into the
+
+ align:start position:0%
+right now that leads directly into the
+ 
+
+ align:start position:0%
+right now that leads directly into the
+physicalism that Perkins and Mo's
+
+ align:start position:0%
+physicalism that Perkins and Mo's
+ 
+
+ align:start position:0%
+physicalism that Perkins and Mo's
+philosopher is if he's right and the
+
+ align:start position:0%
+philosopher is if he's right and the
+ 
+
+ align:start position:0%
+philosopher is if he's right and the
+people at the symposium uh are
+
+ align:start position:0%
+people at the symposium uh are
+ 
+
+ align:start position:0%
+people at the symposium uh are
+presupposed that the mind is simply a
+
+ align:start position:0%
+presupposed that the mind is simply a
+ 
+
+ align:start position:0%
+presupposed that the mind is simply a
+part of a physical process. My view is
+
+ align:start position:0%
+part of a physical process. My view is
+ 
+
+ align:start position:0%
+part of a physical process. My view is
+one could just as easily say the
+
+ align:start position:0%
+one could just as easily say the
+ 
+
+ align:start position:0%
+one could just as easily say the
+opposite that thinking is often uh a
+
+ align:start position:0%
+opposite that thinking is often uh a
+ 
+
+ align:start position:0%
+opposite that thinking is often uh a
+part of feeling uh that uh it isn't as
+
+ align:start position:0%
+part of feeling uh that uh it isn't as
+ 
+
+ align:start position:0%
+part of feeling uh that uh it isn't as
+if we only have we think about how to
+
+ align:start position:0%
+if we only have we think about how to
+ 
+
+ align:start position:0%
+if we only have we think about how to
+survive but also we are endowed with
+
+ align:start position:0%
+survive but also we are endowed with
+ 
+
+ align:start position:0%
+survive but also we are endowed with
+feelings which are therefore just as um
+
+ align:start position:0%
+feelings which are therefore just as um
+ 
+
+ align:start position:0%
+feelings which are therefore just as um
+highly programmed uh by nature as our
+
+ align:start position:0%
+highly programmed uh by nature as our
+ 
+
+ align:start position:0%
+highly programmed uh by nature as our
+ability to think and our uh the use of
+
+ align:start position:0%
+ability to think and our uh the use of
+ 
+
+ align:start position:0%
+ability to think and our uh the use of
+the brain for the sake of finding it
+
+ align:start position:0%
+the brain for the sake of finding it
+ 
+
+ align:start position:0%
+the brain for the sake of finding it
+means of of survival.
+
+ align:start position:0%
+means of of survival.
+ 
+
+ align:start position:0%
+means of of survival.
+we're endowed with these feelings that
+
+ align:start position:0%
+we're endowed with these feelings that
+ 
+
+ align:start position:0%
+we're endowed with these feelings that
+are useful to us and that it's the
+
+ align:start position:0%
+are useful to us and that it's the
+ 
+
+ align:start position:0%
+are useful to us and that it's the
+ignoring of of that part of the innate
+
+ align:start position:0%
+ignoring of of that part of the innate
+ 
+
+ align:start position:0%
+ignoring of of that part of the innate
+program which causes um the scientists
+
+ align:start position:0%
+program which causes um the scientists
+ 
+
+ align:start position:0%
+program which causes um the scientists
+I've been talking about and cognitive
+
+ align:start position:0%
+I've been talking about and cognitive
+ 
+
+ align:start position:0%
+I've been talking about and cognitive
+study people who do cognitive studies to
+
+ align:start position:0%
+study people who do cognitive studies to
+ 
+
+ align:start position:0%
+study people who do cognitive studies to
+shortch change the importance of
+
+ align:start position:0%
+shortch change the importance of
+ 
+
+ align:start position:0%
+shortch change the importance of
+phenomena like imagination,
+
+ align:start position:0%
+phenomena like imagination,
+ 
+
+ align:start position:0%
+phenomena like imagination,
+idealization, consummation and
+
+ align:start position:0%
+idealization, consummation and
+ 
+
+ align:start position:0%
+idealization, consummation and
+aesthetics. we're also programmed with
+
+ align:start position:0%
+aesthetics. we're also programmed with
+ 
+
+ align:start position:0%
+aesthetics. we're also programmed with
+them and they are not reducible to u
+
+ align:start position:0%
+them and they are not reducible to u
+ 
+
+ align:start position:0%
+them and they are not reducible to u
+patterns of cognition uh but rather are
+
+ align:start position:0%
+patterns of cognition uh but rather are
+ 
+
+ align:start position:0%
+patterns of cognition uh but rather are
+in interwoven with them they are in some
+
+ align:start position:0%
+in interwoven with them they are in some
+ 
+
+ align:start position:0%
+in interwoven with them they are in some
+kind of rich process so that to when
+
+ align:start position:0%
+kind of rich process so that to when
+ 
+
+ align:start position:0%
+kind of rich process so that to when
+when Minsky says what we're doing here
+
+ align:start position:0%
+when Minsky says what we're doing here
+ 
+
+ align:start position:0%
+when Minsky says what we're doing here
+is trying to to find the processes
+
+ align:start position:0%
+is trying to to find the processes
+ 
+
+ align:start position:0%
+is trying to to find the processes
+by which um the body uh contributes to
+
+ align:start position:0%
+by which um the body uh contributes to
+ 
+
+ align:start position:0%
+by which um the body uh contributes to
+our feelings things.
+
+ align:start position:0%
+our feelings things.
+ 
+
+ align:start position:0%
+our feelings things.
+I I want to say it's also a question of
+
+ align:start position:0%
+I I want to say it's also a question of
+ 
+
+ align:start position:0%
+I I want to say it's also a question of
+the processes by which our feelings
+
+ align:start position:0%
+the processes by which our feelings
+ 
+
+ align:start position:0%
+the processes by which our feelings
+interact with our thought and with other
+
+ align:start position:0%
+interact with our thought and with other
+ 
+
+ align:start position:0%
+interact with our thought and with other
+aspects that scientists uh in can easily
+
+ align:start position:0%
+aspects that scientists uh in can easily
+ 
+
+ align:start position:0%
+aspects that scientists uh in can easily
+investigate. It's just that these are
+
+ align:start position:0%
+investigate. It's just that these are
+ 
+
+ align:start position:0%
+investigate. It's just that these are
+more difficult parts of the program. And
+
+ align:start position:0%
+more difficult parts of the program. And
+ 
+
+ align:start position:0%
+more difficult parts of the program. And
+so in that sense, I both am a a dualist
+
+ align:start position:0%
+so in that sense, I both am a a dualist
+ 
+
+ align:start position:0%
+so in that sense, I both am a a dualist
+and I'm not. It's it's I don't in fact I
+
+ align:start position:0%
+and I'm not. It's it's I don't in fact I
+ 
+
+ align:start position:0%
+and I'm not. It's it's I don't in fact I
+don't like that distinction at all. Um
+
+ align:start position:0%
+don't like that distinction at all. Um
+ 
+
+ align:start position:0%
+don't like that distinction at all. Um
+the I don't want to reduce mind to body
+
+ align:start position:0%
+the I don't want to reduce mind to body
+ 
+
+ align:start position:0%
+the I don't want to reduce mind to body
+but I but I don't think that they are in
+
+ align:start position:0%
+but I but I don't think that they are in
+ 
+
+ align:start position:0%
+but I but I don't think that they are in
+principle totally independent of each
+
+ align:start position:0%
+principle totally independent of each
+ 
+
+ align:start position:0%
+principle totally independent of each
+other at least in principle as Decart
+
+ align:start position:0%
+other at least in principle as Decart
+ 
+
+ align:start position:0%
+other at least in principle as Decart
+does uh and uh thinkers and uh religious
+
+ align:start position:0%
+does uh and uh thinkers and uh religious
+ 
+
+ align:start position:0%
+does uh and uh thinkers and uh religious
+people of that sort.
+
+ align:start position:0%
+people of that sort.
+ 
+
+ align:start position:0%
+people of that sort.
+Um
+
+ align:start position:0%
+Um
+ 
+
+ align:start position:0%
+Um
+well there are various other things in
+
+ align:start position:0%
+well there are various other things in
+ 
+
+ align:start position:0%
+well there are various other things in
+Ninski which I was hoping to get to last
+
+ align:start position:0%
+Ninski which I was hoping to get to last
+ 
+
+ align:start position:0%
+Ninski which I was hoping to get to last
+time and maybe we can come back to them
+
+ align:start position:0%
+time and maybe we can come back to them
+ 
+
+ align:start position:0%
+time and maybe we can come back to them
+today but I think at this point I ought
+
+ align:start position:0%
+today but I think at this point I ought
+ 
+
+ align:start position:0%
+today but I think at this point I ought
+to turn things over to you. Um in terms
+
+ align:start position:0%
+to turn things over to you. Um in terms
+ 
+
+ align:start position:0%
+to turn things over to you. Um in terms
+of anything
+
+ align:start position:0%
+of anything
+ 
+
+ align:start position:0%
+of anything
+that you want to say in terms of where
+
+ align:start position:0%
+that you want to say in terms of where
+ 
+
+ align:start position:0%
+that you want to say in terms of where
+we were the discussion was going last
+
+ align:start position:0%
+we were the discussion was going last
+ 
+
+ align:start position:0%
+we were the discussion was going last
+time and above all and we can start with
+
+ align:start position:0%
+time and above all and we can start with
+ 
+
+ align:start position:0%
+time and above all and we can start with
+that if you want. um what you're doing
+
+ align:start position:0%
+that if you want. um what you're doing
+ 
+
+ align:start position:0%
+that if you want. um what you're doing
+in your papers to see how I can be of
+
+ align:start position:0%
+in your papers to see how I can be of
+ 
+
+ align:start position:0%
+in your papers to see how I can be of
+help to you with them.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Do you want to start Becken? Um with my
+
+ align:start position:0%
+Do you want to start Becken? Um with my
+ 
+
+ align:start position:0%
+Do you want to start Becken? Um with my
+paper or with a general question? Well,
+
+ align:start position:0%
+paper or with a general question? Well,
+ 
+
+ align:start position:0%
+paper or with a general question? Well,
+uh you also did the euro for me.
+
+ align:start position:0%
+uh you also did the euro for me.
+ 
+
+ align:start position:0%
+uh you also did the euro for me.
+Anything of that sort that you think
+
+ align:start position:0%
+Anything of that sort that you think
+ 
+
+ align:start position:0%
+Anything of that sort that you think
+might be of interest to the class and to
+
+ align:start position:0%
+might be of interest to the class and to
+ 
+
+ align:start position:0%
+might be of interest to the class and to
+the to the subject matter we're
+
+ align:start position:0%
+the to the subject matter we're
+ 
+
+ align:start position:0%
+the to the subject matter we're
+discussing?
+
+ align:start position:0%
+discussing?
+ 
+
+ align:start position:0%
+discussing?
+Well, I have a question I'd like to ask.
+
+ align:start position:0%
+Well, I have a question I'd like to ask.
+ 
+
+ align:start position:0%
+Well, I have a question I'd like to ask.
+Sure. in in response to um dualism.
+
+ align:start position:0%
+Sure. in in response to um dualism.
+ 
+
+ align:start position:0%
+Sure. in in response to um dualism.
+That's what I was looking up online. Um
+
+ align:start position:0%
+That's what I was looking up online. Um
+ 
+
+ align:start position:0%
+That's what I was looking up online. Um
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+you got the mind brain problem and I
+
+ align:start position:0%
+you got the mind brain problem and I
+ 
+
+ align:start position:0%
+you got the mind brain problem and I
+would assume you all would agree that we
+
+ align:start position:0%
+would assume you all would agree that we
+ 
+
+ align:start position:0%
+would assume you all would agree that we
+have an intellect that is
+
+ align:start position:0%
+have an intellect that is
+ 
+
+ align:start position:0%
+have an intellect that is
+I would say above that of animals. Would
+
+ align:start position:0%
+I would say above that of animals. Would
+ 
+
+ align:start position:0%
+I would say above that of animals. Would
+you all agree? Okay. So my question is
+
+ align:start position:0%
+you all agree? Okay. So my question is
+ 
+
+ align:start position:0%
+you all agree? Okay. So my question is
+why is that? Because if you look at the
+
+ align:start position:0%
+why is that? Because if you look at the
+ 
+
+ align:start position:0%
+why is that? Because if you look at the
+function of the brain among humans and
+
+ align:start position:0%
+function of the brain among humans and
+ 
+
+ align:start position:0%
+function of the brain among humans and
+animals, the neur the physiological
+
+ align:start position:0%
+animals, the neur the physiological
+ 
+
+ align:start position:0%
+animals, the neur the physiological
+function between species who have neural
+
+ align:start position:0%
+function between species who have neural
+ 
+
+ align:start position:0%
+function between species who have neural
+cortexes is still the same. So why is it
+
+ align:start position:0%
+cortexes is still the same. So why is it
+ 
+
+ align:start position:0%
+cortexes is still the same. So why is it
+we why is it that we are able this
+
+ align:start position:0%
+we why is it that we are able this
+ 
+
+ align:start position:0%
+we why is it that we are able this
+cognitive function and they are not and
+
+ align:start position:0%
+cognitive function and they are not and
+ 
+
+ align:start position:0%
+cognitive function and they are not and
+even though and some of these animals
+
+ align:start position:0%
+even though and some of these animals
+ 
+
+ align:start position:0%
+even though and some of these animals
+have bigger brains than us. Well, we
+
+ align:start position:0%
+have bigger brains than us. Well, we
+ 
+
+ align:start position:0%
+have bigger brains than us. Well, we
+assume it's rational. It's because it's
+
+ align:start position:0%
+assume it's rational. It's because it's
+ 
+
+ align:start position:0%
+assume it's rational. It's because it's
+rational. It may not be that it may not
+
+ align:start position:0%
+rational. It may not be that it may not
+ 
+
+ align:start position:0%
+rational. It may not be that it may not
+be particularly cognitive. It might be
+
+ align:start position:0%
+be particularly cognitive. It might be
+ 
+
+ align:start position:0%
+be particularly cognitive. It might be
+emotional or social in nature that
+
+ align:start position:0%
+emotional or social in nature that
+ 
+
+ align:start position:0%
+emotional or social in nature that
+there's something you know not logical
+
+ align:start position:0%
+there's something you know not logical
+ 
+
+ align:start position:0%
+there's something you know not logical
+that we do that other animals don't do.
+
+ align:start position:0%
+that we do that other animals don't do.
+ 
+
+ align:start position:0%
+that we do that other animals don't do.
+Are you asking like why it is that we
+
+ align:start position:0%
+Are you asking like why it is that we
+ 
+
+ align:start position:0%
+Are you asking like why it is that we
+can like like make tools and like why
+
+ align:start position:0%
+can like like make tools and like why
+ 
+
+ align:start position:0%
+can like like make tools and like why
+why is it that we have this intellect
+
+ align:start position:0%
+why is it that we have this intellect
+ 
+
+ align:start position:0%
+why is it that we have this intellect
+and they do not even though the brain
+
+ align:start position:0%
+and they do not even though the brain
+ 
+
+ align:start position:0%
+and they do not even though the brain
+function is remarkably
+
+ align:start position:0%
+function is remarkably
+ 
+
+ align:start position:0%
+function is remarkably
+and especially in comparison to
+
+ align:start position:0%
+and especially in comparison to
+ 
+
+ align:start position:0%
+and especially in comparison to
+chimpanzees
+
+ align:start position:0%
+chimpanzees
+ 
+
+ align:start position:0%
+chimpanzees
+98% exactly the same. I I think that uh
+
+ align:start position:0%
+98% exactly the same. I I think that uh
+ 
+
+ align:start position:0%
+98% exactly the same. I I think that uh
+like they've done studies where it's
+
+ align:start position:0%
+like they've done studies where it's
+ 
+
+ align:start position:0%
+like they've done studies where it's
+like our brains are significantly more
+
+ align:start position:0%
+like our brains are significantly more
+ 
+
+ align:start position:0%
+like our brains are significantly more
+complex like more wrinkles or whatever
+
+ align:start position:0%
+complex like more wrinkles or whatever
+ 
+
+ align:start position:0%
+complex like more wrinkles or whatever
+and it's so just there's like there's
+
+ align:start position:0%
+and it's so just there's like there's
+ 
+
+ align:start position:0%
+and it's so just there's like there's
+more stuff going on in it than like it
+
+ align:start position:0%
+more stuff going on in it than like it
+ 
+
+ align:start position:0%
+more stuff going on in it than like it
+can be. So one point to bring out is
+
+ align:start position:0%
+can be. So one point to bring out is
+ 
+
+ align:start position:0%
+can be. So one point to bring out is
+that even a very small change in a gene
+
+ align:start position:0%
+that even a very small change in a gene
+ 
+
+ align:start position:0%
+that even a very small change in a gene
+that regulates uh the function of for
+
+ align:start position:0%
+that regulates uh the function of for
+ 
+
+ align:start position:0%
+that regulates uh the function of for
+example the brain can make a very big
+
+ align:start position:0%
+example the brain can make a very big
+ 
+
+ align:start position:0%
+example the brain can make a very big
+difference. uh a few mutations in one
+
+ align:start position:0%
+difference. uh a few mutations in one
+ 
+
+ align:start position:0%
+difference. uh a few mutations in one
+gene, I don't remember which one
+
+ align:start position:0%
+gene, I don't remember which one
+ 
+
+ align:start position:0%
+gene, I don't remember which one
+anymore, uh can basically take you from
+
+ align:start position:0%
+anymore, uh can basically take you from
+ 
+
+ align:start position:0%
+anymore, uh can basically take you from
+full language skills to being unable to
+
+ align:start position:0%
+full language skills to being unable to
+ 
+
+ align:start position:0%
+full language skills to being unable to
+speak just by a recessive mutation and
+
+ align:start position:0%
+speak just by a recessive mutation and
+ 
+
+ align:start position:0%
+speak just by a recessive mutation and
+it's in a regulator gene of the brain.
+
+ align:start position:0%
+it's in a regulator gene of the brain.
+ 
+
+ align:start position:0%
+it's in a regulator gene of the brain.
+So it's not it the you can see it as the
+
+ align:start position:0%
+So it's not it the you can see it as the
+ 
+
+ align:start position:0%
+So it's not it the you can see it as the
+body is so complex that even small
+
+ align:start position:0%
+body is so complex that even small
+ 
+
+ align:start position:0%
+body is so complex that even small
+changes in some places can have drastic
+
+ align:start position:0%
+changes in some places can have drastic
+ 
+
+ align:start position:0%
+changes in some places can have drastic
+effects. So, okay, I can buy that. But
+
+ align:start position:0%
+effects. So, okay, I can buy that. But
+ 
+
+ align:start position:0%
+effects. So, okay, I can buy that. But
+there's there's also sort of a nature
+
+ align:start position:0%
+there's there's also sort of a nature
+ 
+
+ align:start position:0%
+there's there's also sort of a nature
+nurture problem which is, you know, if
+
+ align:start position:0%
+nurture problem which is, you know, if
+ 
+
+ align:start position:0%
+nurture problem which is, you know, if
+you if you well, human infants, for
+
+ align:start position:0%
+you if you well, human infants, for
+ 
+
+ align:start position:0%
+you if you well, human infants, for
+example, are are, I think, the most
+
+ align:start position:0%
+example, are are, I think, the most
+ 
+
+ align:start position:0%
+example, are are, I think, the most
+helpless among uh primates at least, if
+
+ align:start position:0%
+helpless among uh primates at least, if
+ 
+
+ align:start position:0%
+helpless among uh primates at least, if
+not mammals in general. Uh, and it's,
+
+ align:start position:0%
+not mammals in general. Uh, and it's,
+ 
+
+ align:start position:0%
+not mammals in general. Uh, and it's,
+you know, it's through the the
+
+ align:start position:0%
+you know, it's through the the
+ 
+
+ align:start position:0%
+you know, it's through the the
+environmental stimulation, uh, through
+
+ align:start position:0%
+environmental stimulation, uh, through
+ 
+
+ align:start position:0%
+environmental stimulation, uh, through
+their development and interaction um,
+
+ align:start position:0%
+their development and interaction um,
+ 
+
+ align:start position:0%
+their development and interaction um,
+with others in society that that really
+
+ align:start position:0%
+with others in society that that really
+ 
+
+ align:start position:0%
+with others in society that that really
+grows. If you take a child and isolate
+
+ align:start position:0%
+grows. If you take a child and isolate
+ 
+
+ align:start position:0%
+grows. If you take a child and isolate
+them from that, they, you know, they
+
+ align:start position:0%
+them from that, they, you know, they
+ 
+
+ align:start position:0%
+them from that, they, you know, they
+they grow into something very different
+
+ align:start position:0%
+they grow into something very different
+ 
+
+ align:start position:0%
+they grow into something very different
+than an average person.
+
+ align:start position:0%
+than an average person.
+ 
+
+ align:start position:0%
+than an average person.
+Something that is interesting to me is
+
+ align:start position:0%
+Something that is interesting to me is
+ 
+
+ align:start position:0%
+Something that is interesting to me is
+what what would the consequences be of
+
+ align:start position:0%
+what what would the consequences be of
+ 
+
+ align:start position:0%
+what what would the consequences be of
+consciousness being an illusion? I mean,
+
+ align:start position:0%
+consciousness being an illusion? I mean,
+ 
+
+ align:start position:0%
+consciousness being an illusion? I mean,
+what if if it's an illusion of the brain
+
+ align:start position:0%
+what if if it's an illusion of the brain
+ 
+
+ align:start position:0%
+what if if it's an illusion of the brain
+as we perceive things, what what does
+
+ align:start position:0%
+as we perceive things, what what does
+ 
+
+ align:start position:0%
+as we perceive things, what what does
+that mean to us? I mean, what what what
+
+ align:start position:0%
+that mean to us? I mean, what what what
+ 
+
+ align:start position:0%
+that mean to us? I mean, what what what
+are the consequences of that? Al also
+
+ align:start position:0%
+are the consequences of that? Al also
+ 
+
+ align:start position:0%
+are the consequences of that? Al also
+your questioning from the very start was
+
+ align:start position:0%
+your questioning from the very start was
+ 
+
+ align:start position:0%
+your questioning from the very start was
+that we are above the other animals.
+
+ align:start position:0%
+that we are above the other animals.
+ 
+
+ align:start position:0%
+that we are above the other animals.
+I mean see that's that's how I don't I
+
+ align:start position:0%
+I mean see that's that's how I don't I
+ 
+
+ align:start position:0%
+I mean see that's that's how I don't I
+don't feel that. Well see that's I say I
+
+ align:start position:0%
+don't feel that. Well see that's I say I
+ 
+
+ align:start position:0%
+don't feel that. Well see that's I say I
+was trying to say that carefully. I
+
+ align:start position:0%
+was trying to say that carefully. I
+ 
+
+ align:start position:0%
+was trying to say that carefully. I
+don't mean above but at the same time
+
+ align:start position:0%
+don't mean above but at the same time
+ 
+
+ align:start position:0%
+don't mean above but at the same time
+our cognitive abilities we possess
+
+ align:start position:0%
+our cognitive abilities we possess
+ 
+
+ align:start position:0%
+our cognitive abilities we possess
+cognitive abil abilities that animals do
+
+ align:start position:0%
+cognitive abil abilities that animals do
+ 
+
+ align:start position:0%
+cognitive abil abilities that animals do
+not. Well but that seems to because
+
+ align:start position:0%
+not. Well but that seems to because
+ 
+
+ align:start position:0%
+not. Well but that seems to because
+that's the kind of species we are.
+
+ align:start position:0%
+that's the kind of species we are.
+ 
+
+ align:start position:0%
+that's the kind of species we are.
+That's true. But why is it that we
+
+ align:start position:0%
+That's true. But why is it that we
+ 
+
+ align:start position:0%
+That's true. But why is it that we
+possess these cognitive abilities and
+
+ align:start position:0%
+possess these cognitive abilities and
+ 
+
+ align:start position:0%
+possess these cognitive abilities and
+they don't? Might be because of gene
+
+ align:start position:0%
+they don't? Might be because of gene
+ 
+
+ align:start position:0%
+they don't? Might be because of gene
+mutations or it might be that uh some
+
+ align:start position:0%
+mutations or it might be that uh some
+ 
+
+ align:start position:0%
+mutations or it might be that uh some
+animals simply evolve with that as their
+
+ align:start position:0%
+animals simply evolve with that as their
+ 
+
+ align:start position:0%
+animals simply evolve with that as their
+goal so to speak. Um whereas others did
+
+ align:start position:0%
+goal so to speak. Um whereas others did
+ 
+
+ align:start position:0%
+goal so to speak. Um whereas others did
+not. Uh and one could then say
+
+ align:start position:0%
+not. Uh and one could then say
+ 
+
+ align:start position:0%
+not. Uh and one could then say
+was it a good idea? Should they have if
+
+ align:start position:0%
+was it a good idea? Should they have if
+ 
+
+ align:start position:0%
+was it a good idea? Should they have if
+they could only realize what was going
+
+ align:start position:0%
+they could only realize what was going
+ 
+
+ align:start position:0%
+they could only realize what was going
+to happen, would they have persisted?
+
+ align:start position:0%
+to happen, would they have persisted?
+ 
+
+ align:start position:0%
+to happen, would they have persisted?
+And if they persisted, maybe it was
+
+ align:start position:0%
+And if they persisted, maybe it was
+ 
+
+ align:start position:0%
+And if they persisted, maybe it was
+because they were dumb or evil or
+
+ align:start position:0%
+because they were dumb or evil or
+ 
+
+ align:start position:0%
+because they were dumb or evil or
+somehow distorted, out of touch with
+
+ align:start position:0%
+somehow distorted, out of touch with
+ 
+
+ align:start position:0%
+somehow distorted, out of touch with
+with the possibilities of life, but they
+
+ align:start position:0%
+with the possibilities of life, but they
+ 
+
+ align:start position:0%
+with the possibilities of life, but they
+always had a need to exist. Like I mean
+
+ align:start position:0%
+always had a need to exist. Like I mean
+ 
+
+ align:start position:0%
+always had a need to exist. Like I mean
+that was No, but the point is all these
+
+ align:start position:0%
+that was No, but the point is all these
+ 
+
+ align:start position:0%
+that was No, but the point is all these
+other species do continue to exist and
+
+ align:start position:0%
+other species do continue to exist and
+ 
+
+ align:start position:0%
+other species do continue to exist and
+sometimes they do very well with their
+
+ align:start position:0%
+sometimes they do very well with their
+ 
+
+ align:start position:0%
+sometimes they do very well with their
+uh lesser. That's true. But see that's
+
+ align:start position:0%
+uh lesser. That's true. But see that's
+ 
+
+ align:start position:0%
+uh lesser. That's true. But see that's
+that's the question at hand. Why is it
+
+ align:start position:0%
+that's the question at hand. Why is it
+ 
+
+ align:start position:0%
+that's the question at hand. Why is it
+that we develop these cognitive
+
+ align:start position:0%
+that we develop these cognitive
+ 
+
+ align:start position:0%
+that we develop these cognitive
+abilities and they didn't but then but
+
+ align:start position:0%
+abilities and they didn't but then but
+ 
+
+ align:start position:0%
+abilities and they didn't but then but
+then then what I'm troubled by with the
+
+ align:start position:0%
+then then what I'm troubled by with the
+ 
+
+ align:start position:0%
+then then what I'm troubled by with the
+meaning of the word why. Why in what
+
+ align:start position:0%
+meaning of the word why. Why in what
+ 
+
+ align:start position:0%
+meaning of the word why. Why in what
+sense? Could it's like saying why am I
+
+ align:start position:0%
+sense? Could it's like saying why am I
+ 
+
+ align:start position:0%
+sense? Could it's like saying why am I
+here? It's because my parents and so on.
+
+ align:start position:0%
+here? It's because my parents and so on.
+ 
+
+ align:start position:0%
+here? It's because my parents and so on.
+Well, the reason the reason I say this
+
+ align:start position:0%
+Well, the reason the reason I say this
+ 
+
+ align:start position:0%
+Well, the reason the reason I say this
+is because different species of primates
+
+ align:start position:0%
+is because different species of primates
+ 
+
+ align:start position:0%
+is because different species of primates
+through evolution, you can see great
+
+ align:start position:0%
+through evolution, you can see great
+ 
+
+ align:start position:0%
+through evolution, you can see great
+similarities, but we are the only
+
+ align:start position:0%
+similarities, but we are the only
+ 
+
+ align:start position:0%
+similarities, but we are the only
+species out of the billions on this
+
+ align:start position:0%
+species out of the billions on this
+ 
+
+ align:start position:0%
+species out of the billions on this
+planet that has this cognitive
+
+ align:start position:0%
+planet that has this cognitive
+ 
+
+ align:start position:0%
+planet that has this cognitive
+abilities. Same thing with the cats.
+
+ align:start position:0%
+abilities. Same thing with the cats.
+ 
+
+ align:start position:0%
+abilities. Same thing with the cats.
+Like all of these cats, I mean, if you
+
+ align:start position:0%
+Like all of these cats, I mean, if you
+ 
+
+ align:start position:0%
+Like all of these cats, I mean, if you
+want to go by evolution, descended from
+
+ align:start position:0%
+want to go by evolution, descended from
+ 
+
+ align:start position:0%
+want to go by evolution, descended from
+one cat, which I don't believe, but at
+
+ align:start position:0%
+one cat, which I don't believe, but at
+ 
+
+ align:start position:0%
+one cat, which I don't believe, but at
+the same time, they all possess similar
+
+ align:start position:0%
+the same time, they all possess similar
+ 
+
+ align:start position:0%
+the same time, they all possess similar
+characteristics. There is yes they have
+
+ align:start position:0%
+characteristics. There is yes they have
+ 
+
+ align:start position:0%
+characteristics. There is yes they have
+vastly vastly different abilities in
+
+ align:start position:0%
+vastly vastly different abilities in
+ 
+
+ align:start position:0%
+vastly vastly different abilities in
+terms of speed, strength, agility but in
+
+ align:start position:0%
+terms of speed, strength, agility but in
+ 
+
+ align:start position:0%
+terms of speed, strength, agility but in
+terms of primates if you consider us
+
+ align:start position:0%
+terms of primates if you consider us
+ 
+
+ align:start position:0%
+terms of primates if you consider us
+primates we the way we have developed we
+
+ align:start position:0%
+primates we the way we have developed we
+ 
+
+ align:start position:0%
+primates we the way we have developed we
+have less fur and we have these
+
+ align:start position:0%
+have less fur and we have these
+ 
+
+ align:start position:0%
+have less fur and we have these
+cognitive abilities. Why is it that we
+
+ align:start position:0%
+cognitive abilities. Why is it that we
+ 
+
+ align:start position:0%
+cognitive abilities. Why is it that we
+out of the hundreds of species or
+
+ align:start position:0%
+out of the hundreds of species or
+ 
+
+ align:start position:0%
+out of the hundreds of species or
+thousands of species were the only ones
+
+ align:start position:0%
+thousands of species were the only ones
+ 
+
+ align:start position:0%
+thousands of species were the only ones
+to develop that? But either you're
+
+ align:start position:0%
+to develop that? But either you're
+ 
+
+ align:start position:0%
+to develop that? But either you're
+asking for details of evolutionary
+
+ align:start position:0%
+asking for details of evolutionary
+ 
+
+ align:start position:0%
+asking for details of evolutionary
+biology because at the theory of
+
+ align:start position:0%
+biology because at the theory of
+ 
+
+ align:start position:0%
+biology because at the theory of
+evolution is part of the attempt to give
+
+ align:start position:0%
+evolution is part of the attempt to give
+ 
+
+ align:start position:0%
+evolution is part of the attempt to give
+a scientific answer to that question or
+
+ align:start position:0%
+a scientific answer to that question or
+ 
+
+ align:start position:0%
+a scientific answer to that question or
+else you're using the word why in you
+
+ align:start position:0%
+else you're using the word why in you
+ 
+
+ align:start position:0%
+else you're using the word why in you
+know some more metaphysical or
+
+ align:start position:0%
+know some more metaphysical or
+ 
+
+ align:start position:0%
+know some more metaphysical or
+philosophical way and if it's the latter
+
+ align:start position:0%
+philosophical way and if it's the latter
+ 
+
+ align:start position:0%
+philosophical way and if it's the latter
+um I think I then want to open up and
+
+ align:start position:0%
+um I think I then want to open up and
+ 
+
+ align:start position:0%
+um I think I then want to open up and
+say u maybe we should it's unfortunate I
+
+ align:start position:0%
+say u maybe we should it's unfortunate I
+ 
+
+ align:start position:0%
+say u maybe we should it's unfortunate I
+mean maybe it would have been so much
+
+ align:start position:0%
+mean maybe it would have been so much
+ 
+
+ align:start position:0%
+mean maybe it would have been so much
+better if you add up all the goods in In
+
+ align:start position:0%
+better if you add up all the goods in In
+ 
+
+ align:start position:0%
+better if you add up all the goods in In
+this world, all the happiness, pleasure,
+
+ align:start position:0%
+this world, all the happiness, pleasure,
+ 
+
+ align:start position:0%
+this world, all the happiness, pleasure,
+all the positive things that we
+
+ align:start position:0%
+all the positive things that we
+ 
+
+ align:start position:0%
+all the positive things that we
+ourselves having evolved the way we have
+
+ align:start position:0%
+ourselves having evolved the way we have
+ 
+
+ align:start position:0%
+ourselves having evolved the way we have
+looking back over everything value.
+
+ align:start position:0%
+looking back over everything value.
+ 
+
+ align:start position:0%
+looking back over everything value.
+There may be more suffering
+
+ align:start position:0%
+There may be more suffering
+ 
+
+ align:start position:0%
+There may be more suffering
+than there is well-being. Think of all
+
+ align:start position:0%
+than there is well-being. Think of all
+ 
+
+ align:start position:0%
+than there is well-being. Think of all
+the animals that are slaughtered. All
+
+ align:start position:0%
+the animals that are slaughtered. All
+ 
+
+ align:start position:0%
+the animals that are slaughtered. All
+these millions and millions of people
+
+ align:start position:0%
+these millions and millions of people
+ 
+
+ align:start position:0%
+these millions and millions of people
+who's with these higher intellects who
+
+ align:start position:0%
+who's with these higher intellects who
+ 
+
+ align:start position:0%
+who's with these higher intellects who
+are killed for no good reason except
+
+ align:start position:0%
+are killed for no good reason except
+ 
+
+ align:start position:0%
+are killed for no good reason except
+because they belong uh in the wrong
+
+ align:start position:0%
+because they belong uh in the wrong
+ 
+
+ align:start position:0%
+because they belong uh in the wrong
+place at the wrong time with the wrong
+
+ align:start position:0%
+place at the wrong time with the wrong
+ 
+
+ align:start position:0%
+place at the wrong time with the wrong
+religion at the wrong time or the their
+
+ align:start position:0%
+religion at the wrong time or the their
+ 
+
+ align:start position:0%
+religion at the wrong time or the their
+race or whatever reason. All of this
+
+ align:start position:0%
+race or whatever reason. All of this
+ 
+
+ align:start position:0%
+race or whatever reason. All of this
+misery that we tend to ignore because
+
+ align:start position:0%
+misery that we tend to ignore because
+ 
+
+ align:start position:0%
+misery that we tend to ignore because
+it's just too painful to face up to
+
+ align:start position:0%
+it's just too painful to face up to
+ 
+
+ align:start position:0%
+it's just too painful to face up to
+them.
+
+ align:start position:0%
+them.
+ 
+
+ align:start position:0%
+them.
+In that sense, one could say why why
+
+ align:start position:0%
+In that sense, one could say why why
+ 
+
+ align:start position:0%
+In that sense, one could say why why
+couldn't we just be comfortable like
+
+ align:start position:0%
+couldn't we just be comfortable like
+ 
+
+ align:start position:0%
+couldn't we just be comfortable like
+pussycats and and domestic dogs? Why did
+
+ align:start position:0%
+pussycats and and domestic dogs? Why did
+ 
+
+ align:start position:0%
+pussycats and and domestic dogs? Why did
+we why do we need this extra intellect?
+
+ align:start position:0%
+we why do we need this extra intellect?
+ 
+
+ align:start position:0%
+we why do we need this extra intellect?
+Why Hamlet has it and a lot of freedom?
+
+ align:start position:0%
+Why Hamlet has it and a lot of freedom?
+ 
+
+ align:start position:0%
+Why Hamlet has it and a lot of freedom?
+Um you see so in that sense what you're
+
+ align:start position:0%
+Um you see so in that sense what you're
+ 
+
+ align:start position:0%
+Um you see so in that sense what you're
+asking now is a value question rather
+
+ align:start position:0%
+asking now is a value question rather
+ 
+
+ align:start position:0%
+asking now is a value question rather
+than a scientific one. If it's a
+
+ align:start position:0%
+than a scientific one. If it's a
+ 
+
+ align:start position:0%
+than a scientific one. If it's a
+scientific one, the answer is given by
+
+ align:start position:0%
+scientific one, the answer is given by
+ 
+
+ align:start position:0%
+scientific one, the answer is given by
+uh theories like the theory of
+
+ align:start position:0%
+uh theories like the theory of
+ 
+
+ align:start position:0%
+uh theories like the theory of
+evolution. If it's philosophical,
+
+ align:start position:0%
+evolution. If it's philosophical,
+ 
+
+ align:start position:0%
+evolution. If it's philosophical,
+then I myself say um it could all it
+
+ align:start position:0%
+then I myself say um it could all it
+ 
+
+ align:start position:0%
+then I myself say um it could all it
+could all have been a great big mistake.
+
+ align:start position:0%
+could all have been a great big mistake.
+ 
+
+ align:start position:0%
+could all have been a great big mistake.
+And that thinkers who said um the world
+
+ align:start position:0%
+And that thinkers who said um the world
+ 
+
+ align:start position:0%
+And that thinkers who said um the world
+was created by a cruel, angry, hateful
+
+ align:start position:0%
+was created by a cruel, angry, hateful
+ 
+
+ align:start position:0%
+was created by a cruel, angry, hateful
+god may very well be right. there's that
+
+ align:start position:0%
+god may very well be right. there's that
+ 
+
+ align:start position:0%
+god may very well be right. there's that
+much misery in the world that um one
+
+ align:start position:0%
+much misery in the world that um one
+ 
+
+ align:start position:0%
+much misery in the world that um one
+feels wouldn't exist if we didn't have
+
+ align:start position:0%
+feels wouldn't exist if we didn't have
+ 
+
+ align:start position:0%
+feels wouldn't exist if we didn't have
+these big intellects and and or the
+
+ align:start position:0%
+these big intellects and and or the
+ 
+
+ align:start position:0%
+these big intellects and and or the
+solution is yes u maybe that's true but
+
+ align:start position:0%
+solution is yes u maybe that's true but
+ 
+
+ align:start position:0%
+solution is yes u maybe that's true but
+that's how things are the we came came
+
+ align:start position:0%
+that's how things are the we came came
+ 
+
+ align:start position:0%
+that's how things are the we came came
+out of galactic dust and somehow it
+
+ align:start position:0%
+out of galactic dust and somehow it
+ 
+
+ align:start position:0%
+out of galactic dust and somehow it
+evolved into one species ourselves that
+
+ align:start position:0%
+evolved into one species ourselves that
+ 
+
+ align:start position:0%
+evolved into one species ourselves that
+then could conquer the world and in fact
+
+ align:start position:0%
+then could conquer the world and in fact
+ 
+
+ align:start position:0%
+then could conquer the world and in fact
+that's the reason why we have the
+
+ align:start position:0%
+that's the reason why we have the
+ 
+
+ align:start position:0%
+that's the reason why we have the
+intellect we do because it gives us that
+
+ align:start position:0%
+intellect we do because it gives us that
+ 
+
+ align:start position:0%
+intellect we do because it gives us that
+ability ability to conquer the world.
+
+ align:start position:0%
+ability ability to conquer the world.
+ 
+
+ align:start position:0%
+ability ability to conquer the world.
+You know, the insects still the last
+
+ align:start position:0%
+You know, the insects still the last
+ 
+
+ align:start position:0%
+You know, the insects still the last
+word isn't in. The jury is still out
+
+ align:start position:0%
+word isn't in. The jury is still out
+ 
+
+ align:start position:0%
+word isn't in. The jury is still out
+because the insects may eventually take
+
+ align:start position:0%
+because the insects may eventually take
+ 
+
+ align:start position:0%
+because the insects may eventually take
+over. But a short of that, that explains
+
+ align:start position:0%
+over. But a short of that, that explains
+ 
+
+ align:start position:0%
+over. But a short of that, that explains
+and why we have our intellect and one
+
+ align:start position:0%
+and why we have our intellect and one
+ 
+
+ align:start position:0%
+and why we have our intellect and one
+could say it's a pity. Who needed that?
+
+ align:start position:0%
+could say it's a pity. Who needed that?
+ 
+
+ align:start position:0%
+could say it's a pity. Who needed that?
+Who in the universe needs that? Now from
+
+ align:start position:0%
+Who in the universe needs that? Now from
+ 
+
+ align:start position:0%
+Who in the universe needs that? Now from
+the point of view of an individual who's
+
+ align:start position:0%
+the point of view of an individual who's
+ 
+
+ align:start position:0%
+the point of view of an individual who's
+interested in his own welfare
+
+ align:start position:0%
+interested in his own welfare
+ 
+
+ align:start position:0%
+interested in his own welfare
+and let's say he's an American bourgeoa
+
+ align:start position:0%
+and let's say he's an American bourgeoa
+ 
+
+ align:start position:0%
+and let's say he's an American bourgeoa
+who's been very lucky to have survived
+
+ align:start position:0%
+who's been very lucky to have survived
+ 
+
+ align:start position:0%
+who's been very lucky to have survived
+as long as he has and um sort of enjoys
+
+ align:start position:0%
+as long as he has and um sort of enjoys
+ 
+
+ align:start position:0%
+as long as he has and um sort of enjoys
+life. In other words, me um the question
+
+ align:start position:0%
+life. In other words, me um the question
+ 
+
+ align:start position:0%
+life. In other words, me um the question
+doesn't bother me very much. Well, you
+
+ align:start position:0%
+doesn't bother me very much. Well, you
+ 
+
+ align:start position:0%
+doesn't bother me very much. Well, you
+mean why? Well, I I I'm happy enough. I
+
+ align:start position:0%
+mean why? Well, I I I'm happy enough. I
+ 
+
+ align:start position:0%
+mean why? Well, I I I'm happy enough. I
+just want to live forever.
+
+ align:start position:0%
+just want to live forever.
+ 
+
+ align:start position:0%
+just want to live forever.
+um I'm not happy with the idea of giving
+
+ align:start position:0%
+um I'm not happy with the idea of giving
+ 
+
+ align:start position:0%
+um I'm not happy with the idea of giving
+up all these good things. But that's a
+
+ align:start position:0%
+up all these good things. But that's a
+ 
+
+ align:start position:0%
+up all these good things. But that's a
+different kind of attitude and different
+
+ align:start position:0%
+different kind of attitude and different
+ 
+
+ align:start position:0%
+different kind of attitude and different
+kind of question. If it's the kind that
+
+ align:start position:0%
+kind of question. If it's the kind that
+ 
+
+ align:start position:0%
+kind of question. If it's the kind that
+you were asking, then we're back to that
+
+ align:start position:0%
+you were asking, then we're back to that
+ 
+
+ align:start position:0%
+you were asking, then we're back to that
+same problem.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+I think the irony is that you're asking
+
+ align:start position:0%
+I think the irony is that you're asking
+ 
+
+ align:start position:0%
+I think the irony is that you're asking
+a question that requires us to
+
+ align:start position:0%
+a question that requires us to
+ 
+
+ align:start position:0%
+a question that requires us to
+understand our own brains. Yeah, that
+
+ align:start position:0%
+understand our own brains. Yeah, that
+ 
+
+ align:start position:0%
+understand our own brains. Yeah, that
+was actually I don't recall who said
+
+ align:start position:0%
+was actually I don't recall who said
+ 
+
+ align:start position:0%
+was actually I don't recall who said
+this statement but um
+
+ align:start position:0%
+this statement but um
+ 
+
+ align:start position:0%
+this statement but um
+the statement was the brain or the mind
+
+ align:start position:0%
+the statement was the brain or the mind
+ 
+
+ align:start position:0%
+the statement was the brain or the mind
+is the universe trying to understand
+
+ align:start position:0%
+is the universe trying to understand
+ 
+
+ align:start position:0%
+is the universe trying to understand
+itself. So just wanted to throw that out
+
+ align:start position:0%
+itself. So just wanted to throw that out
+ 
+
+ align:start position:0%
+itself. So just wanted to throw that out
+there. Well, George Bernard Saw said
+
+ align:start position:0%
+there. Well, George Bernard Saw said
+ 
+
+ align:start position:0%
+there. Well, George Bernard Saw said
+that the human brain is the attempt on
+
+ align:start position:0%
+that the human brain is the attempt on
+ 
+
+ align:start position:0%
+that the human brain is the attempt on
+the part of the universe to understand
+
+ align:start position:0%
+the part of the universe to understand
+ 
+
+ align:start position:0%
+the part of the universe to understand
+itself.
+
+ align:start position:0%
+itself.
+ 
+
+ align:start position:0%
+itself.
+That that we well you get the idea that
+
+ align:start position:0%
+That that we well you get the idea that
+ 
+
+ align:start position:0%
+That that we well you get the idea that
+we struggling for knowledge are the
+
+ align:start position:0%
+we struggling for knowledge are the
+ 
+
+ align:start position:0%
+we struggling for knowledge are the
+universe trying to make sense out of
+
+ align:start position:0%
+universe trying to make sense out of
+ 
+
+ align:start position:0%
+universe trying to make sense out of
+itself. But it was also in some of David
+
+ align:start position:0%
+itself. But it was also in some of David
+ 
+
+ align:start position:0%
+itself. But it was also in some of David
+Bow's writing when I was researching my
+
+ align:start position:0%
+Bow's writing when I was researching my
+ 
+
+ align:start position:0%
+Bow's writing when I was researching my
+first paper with his whole theory of
+
+ align:start position:0%
+first paper with his whole theory of
+ 
+
+ align:start position:0%
+first paper with his whole theory of
+infolding and the fact that the brain
+
+ align:start position:0%
+infolding and the fact that the brain
+ 
+
+ align:start position:0%
+infolding and the fact that the brain
+can't possibly actually understand
+
+ align:start position:0%
+can't possibly actually understand
+ 
+
+ align:start position:0%
+can't possibly actually understand
+anything cuz it is as much a part of the
+
+ align:start position:0%
+anything cuz it is as much a part of the
+ 
+
+ align:start position:0%
+anything cuz it is as much a part of the
+as anything else is as if without us.
+
+ align:start position:0%
+as anything else is as if without us.
+ 
+
+ align:start position:0%
+as anything else is as if without us.
+Yeah. Like well just that we are a part
+
+ align:start position:0%
+Yeah. Like well just that we are a part
+ 
+
+ align:start position:0%
+Yeah. Like well just that we are a part
+of it and therefore we cannot ever
+
+ align:start position:0%
+of it and therefore we cannot ever
+ 
+
+ align:start position:0%
+of it and therefore we cannot ever
+understand ourselves because it's
+
+ align:start position:0%
+understand ourselves because it's
+ 
+
+ align:start position:0%
+understand ourselves because it's
+trying. Yeah. It's it's circular. Yeah.
+
+ align:start position:0%
+trying. Yeah. It's it's circular. Yeah.
+ 
+
+ align:start position:0%
+trying. Yeah. It's it's circular. Yeah.
+The universe trying to understand. My
+
+ align:start position:0%
+The universe trying to understand. My
+ 
+
+ align:start position:0%
+The universe trying to understand. My
+view is even more radical and that is
+
+ align:start position:0%
+view is even more radical and that is
+ 
+
+ align:start position:0%
+view is even more radical and that is
+that I have none of the scientific faith
+
+ align:start position:0%
+that I have none of the scientific faith
+ 
+
+ align:start position:0%
+that I have none of the scientific faith
+that we can eventually understand
+
+ align:start position:0%
+that we can eventually understand
+ 
+
+ align:start position:0%
+that we can eventually understand
+everything else.
+
+ align:start position:0%
+everything else.
+ 
+
+ align:start position:0%
+everything else.
+But theoretically yourself as well
+
+ align:start position:0%
+But theoretically yourself as well
+ 
+
+ align:start position:0%
+But theoretically yourself as well
+because you are the universe. Um but um
+
+ align:start position:0%
+because you are the universe. Um but um
+ 
+
+ align:start position:0%
+because you are the universe. Um but um
+I I it's not just that we can't
+
+ align:start position:0%
+I I it's not just that we can't
+ 
+
+ align:start position:0%
+I I it's not just that we can't
+understand ourselves. I haven't any
+
+ align:start position:0%
+understand ourselves. I haven't any
+ 
+
+ align:start position:0%
+understand ourselves. I haven't any
+faith we can understand everything about
+
+ align:start position:0%
+faith we can understand everything about
+ 
+
+ align:start position:0%
+faith we can understand everything about
+everything else.
+
+ align:start position:0%
+everything else.
+ 
+
+ align:start position:0%
+everything else.
+So one thing I or or whether would be a
+
+ align:start position:0%
+So one thing I or or whether would be a
+ 
+
+ align:start position:0%
+So one thing I or or whether would be a
+good idea. Would would that make you
+
+ align:start position:0%
+good idea. Would would that make you
+ 
+
+ align:start position:0%
+good idea. Would would that make you
+happy? I don't know. Yeah. I think the
+
+ align:start position:0%
+happy? I don't know. Yeah. I think the
+ 
+
+ align:start position:0%
+happy? I don't know. Yeah. I think the
+uh example of Hamlet is that people who
+
+ align:start position:0%
+uh example of Hamlet is that people who
+ 
+
+ align:start position:0%
+uh example of Hamlet is that people who
+who think too much um often make
+
+ align:start position:0%
+who think too much um often make
+ 
+
+ align:start position:0%
+who think too much um often make
+themselves miserable and that the only
+
+ align:start position:0%
+themselves miserable and that the only
+ 
+
+ align:start position:0%
+themselves miserable and that the only
+happy ones are the ones who are very
+
+ align:start position:0%
+happy ones are the ones who are very
+ 
+
+ align:start position:0%
+happy ones are the ones who are very
+limited.
+
+ align:start position:0%
+limited.
+ 
+
+ align:start position:0%
+limited.
+Wow.
+
+ align:start position:0%
+Wow.
+ 
+
+ align:start position:0%
+Wow.
+One thing I ran across um in a book
+
+ align:start position:0%
+One thing I ran across um in a book
+ 
+
+ align:start position:0%
+One thing I ran across um in a book
+discussing entropy in art uh was the
+
+ align:start position:0%
+discussing entropy in art uh was the
+ 
+
+ align:start position:0%
+discussing entropy in art uh was the
+statement that creativity has a function
+
+ align:start position:0%
+statement that creativity has a function
+ 
+
+ align:start position:0%
+statement that creativity has a function
+and its function is to maintain a
+
+ align:start position:0%
+and its function is to maintain a
+ 
+
+ align:start position:0%
+and its function is to maintain a
+balance or homeostasis for a person in
+
+ align:start position:0%
+balance or homeostasis for a person in
+ 
+
+ align:start position:0%
+balance or homeostasis for a person in
+response to the destruction caused by
+
+ align:start position:0%
+response to the destruction caused by
+ 
+
+ align:start position:0%
+response to the destruction caused by
+entropy around them. What do you guys
+
+ align:start position:0%
+entropy around them. What do you guys
+ 
+
+ align:start position:0%
+entropy around them. What do you guys
+make of that? Do you think like do do
+
+ align:start position:0%
+make of that? Do you think like do do
+ 
+
+ align:start position:0%
+make of that? Do you think like do do
+you think creativity has a function and
+
+ align:start position:0%
+you think creativity has a function and
+ 
+
+ align:start position:0%
+you think creativity has a function and
+that's to it it's for the individual to
+
+ align:start position:0%
+that's to it it's for the individual to
+ 
+
+ align:start position:0%
+that's to it it's for the individual to
+respond to the random forces pushing
+
+ align:start position:0%
+respond to the random forces pushing
+ 
+
+ align:start position:0%
+respond to the random forces pushing
+against him or her in life.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+It's an interesting idea. Who who
+
+ align:start position:0%
+It's an interesting idea. Who who
+ 
+
+ align:start position:0%
+It's an interesting idea. Who who
+proposed that? I don't remember. It's in
+
+ align:start position:0%
+proposed that? I don't remember. It's in
+ 
+
+ align:start position:0%
+proposed that? I don't remember. It's in
+a book called Entropy and Art. I know
+
+ align:start position:0%
+a book called Entropy and Art. I know
+ 
+
+ align:start position:0%
+a book called Entropy and Art. I know
+that much. Do does it come into your
+
+ align:start position:0%
+that much. Do does it come into your
+ 
+
+ align:start position:0%
+that much. Do does it come into your
+paper? Uh possibly.
+
+ align:start position:0%
+paper? Uh possibly.
+ 
+
+ align:start position:0%
+paper? Uh possibly.
+I it started out great and then I didn't
+
+ align:start position:0%
+I it started out great and then I didn't
+ 
+
+ align:start position:0%
+I it started out great and then I didn't
+like the second half of it. So So you're
+
+ align:start position:0%
+like the second half of it. So So you're
+ 
+
+ align:start position:0%
+like the second half of it. So So you're
+working on something else related. Yes.
+
+ align:start position:0%
+working on something else related. Yes.
+ 
+
+ align:start position:0%
+working on something else related. Yes.
+Okay. Um
+
+ align:start position:0%
+Okay. Um
+ 
+
+ align:start position:0%
+Okay. Um
+Arnard
+
+ align:start position:0%
+Arnard
+ 
+
+ align:start position:0%
+Arnard
+possibly. I I
+
+ align:start position:0%
+possibly. I I
+ 
+
+ align:start position:0%
+possibly. I I
+What did you find? Actually, I just
+
+ align:start position:0%
+What did you find? Actually, I just
+ 
+
+ align:start position:0%
+What did you find? Actually, I just
+found an essay, not a book. Never mind.
+
+ align:start position:0%
+found an essay, not a book. Never mind.
+ 
+
+ align:start position:0%
+found an essay, not a book. Never mind.
+It Well, it's like 50 pages long. Yeah,
+
+ align:start position:0%
+It Well, it's like 50 pages long. Yeah,
+ 
+
+ align:start position:0%
+It Well, it's like 50 pages long. Yeah,
+it's an essay. Okay. uh Arnheim
+
+ align:start position:0%
+it's an essay. Okay. uh Arnheim
+ 
+
+ align:start position:0%
+it's an essay. Okay. uh Arnheim
+Arnheim he's a very important uh
+
+ align:start position:0%
+Arnheim he's a very important uh
+ 
+
+ align:start position:0%
+Arnheim he's a very important uh
+aesthetician who wrote a great deal
+
+ align:start position:0%
+aesthetician who wrote a great deal
+ 
+
+ align:start position:0%
+aesthetician who wrote a great deal
+particularly at the beginning about the
+
+ align:start position:0%
+particularly at the beginning about the
+ 
+
+ align:start position:0%
+particularly at the beginning about the
+aesthetics of film he's one of the you
+
+ align:start position:0%
+aesthetics of film he's one of the you
+ 
+
+ align:start position:0%
+aesthetics of film he's one of the you
+know icons of the development of film
+
+ align:start position:0%
+know icons of the development of film
+ 
+
+ align:start position:0%
+know icons of the development of film
+studies um and I think he died in the
+
+ align:start position:0%
+studies um and I think he died in the
+ 
+
+ align:start position:0%
+studies um and I think he died in the
+70s or 80s not too long ago
+
+ align:start position:0%
+70s or 80s not too long ago
+ 
+
+ align:start position:0%
+70s or 80s not too long ago
+Rudolfph Orinheim that's very
+
+ align:start position:0%
+Rudolfph Orinheim that's very
+ 
+
+ align:start position:0%
+Rudolfph Orinheim that's very
+interesting what's the book itself.
+
+ align:start position:0%
+interesting what's the book itself.
+ 
+
+ align:start position:0%
+interesting what's the book itself.
+Uh, Entropy and Art.
+
+ align:start position:0%
+Uh, Entropy and Art.
+ 
+
+ align:start position:0%
+Uh, Entropy and Art.
+And the essay is Entropy and Art? Yes.
+
+ align:start position:0%
+And the essay is Entropy and Art? Yes.
+ 
+
+ align:start position:0%
+And the essay is Entropy and Art? Yes.
+And he wrote the whole book or it's an
+
+ align:start position:0%
+And he wrote the whole book or it's an
+ 
+
+ align:start position:0%
+And he wrote the whole book or it's an
+anthology?
+
+ align:start position:0%
+anthology?
+ 
+
+ align:start position:0%
+anthology?
+It's a It's a 60page essay that he
+
+ align:start position:0%
+It's a It's a 60page essay that he
+ 
+
+ align:start position:0%
+It's a It's a 60page essay that he
+wrote. Uh, in his own book? Yes. Oh,
+
+ align:start position:0%
+wrote. Uh, in his own book? Yes. Oh,
+ 
+
+ align:start position:0%
+wrote. Uh, in his own book? Yes. Oh,
+okay. Yeah. And it looks like the entire
+
+ align:start position:0%
+okay. Yeah. And it looks like the entire
+ 
+
+ align:start position:0%
+okay. Yeah. And it looks like the entire
+thing is online. Cool.
+
+ align:start position:0%
+thing is online. Cool.
+ 
+
+ align:start position:0%
+thing is online. Cool.
+Yeah, it is. Okay. Well, that's Anything
+
+ align:start position:0%
+Yeah, it is. Okay. Well, that's Anything
+ 
+
+ align:start position:0%
+Yeah, it is. Okay. Well, that's Anything
+more you want to say about that? Well, I
+
+ align:start position:0%
+more you want to say about that? Well, I
+ 
+
+ align:start position:0%
+more you want to say about that? Well, I
+I just wanted to see what people think
+
+ align:start position:0%
+I just wanted to see what people think
+ 
+
+ align:start position:0%
+I just wanted to see what people think
+of the idea that uh I mean what what I'm
+
+ align:start position:0%
+of the idea that uh I mean what what I'm
+ 
+
+ align:start position:0%
+of the idea that uh I mean what what I'm
+tossing around in my head is that uh one
+
+ align:start position:0%
+tossing around in my head is that uh one
+ 
+
+ align:start position:0%
+tossing around in my head is that uh one
+an important part of scientific
+
+ align:start position:0%
+an important part of scientific
+ 
+
+ align:start position:0%
+an important part of scientific
+creativity is uh personal expression and
+
+ align:start position:0%
+creativity is uh personal expression and
+ 
+
+ align:start position:0%
+creativity is uh personal expression and
+that uh what you're expressing is your
+
+ align:start position:0%
+that uh what you're expressing is your
+ 
+
+ align:start position:0%
+that uh what you're expressing is your
+worldview and specific uh your belief
+
+ align:start position:0%
+worldview and specific uh your belief
+ 
+
+ align:start position:0%
+worldview and specific uh your belief
+about the nature of the world or the
+
+ align:start position:0%
+about the nature of the world or the
+ 
+
+ align:start position:0%
+about the nature of the world or the
+metaphysics of the world. And it seems
+
+ align:start position:0%
+metaphysics of the world. And it seems
+ 
+
+ align:start position:0%
+metaphysics of the world. And it seems
+to me that if you take scientific or if
+
+ align:start position:0%
+to me that if you take scientific or if
+ 
+
+ align:start position:0%
+to me that if you take scientific or if
+you take creativity in that way then it
+
+ align:start position:0%
+you take creativity in that way then it
+ 
+
+ align:start position:0%
+you take creativity in that way then it
+has a function that it it has a function
+
+ align:start position:0%
+has a function that it it has a function
+ 
+
+ align:start position:0%
+has a function that it it has a function
+that matches our intentions or our
+
+ align:start position:0%
+that matches our intentions or our
+ 
+
+ align:start position:0%
+that matches our intentions or our
+motivations in life. And you know
+
+ align:start position:0%
+motivations in life. And you know
+ 
+
+ align:start position:0%
+motivations in life. And you know
+Arnheim would say that function is to
+
+ align:start position:0%
+Arnheim would say that function is to
+ 
+
+ align:start position:0%
+Arnheim would say that function is to
+keep us balanced in the face of the
+
+ align:start position:0%
+keep us balanced in the face of the
+ 
+
+ align:start position:0%
+keep us balanced in the face of the
+destructive or or disordering influences
+
+ align:start position:0%
+destructive or or disordering influences
+ 
+
+ align:start position:0%
+destructive or or disordering influences
+of the world. And you know this is
+
+ align:start position:0%
+of the world. And you know this is
+ 
+
+ align:start position:0%
+of the world. And you know this is
+something that I just wanted to throw
+
+ align:start position:0%
+something that I just wanted to throw
+ 
+
+ align:start position:0%
+something that I just wanted to throw
+out see what people thought of it. It
+
+ align:start position:0%
+out see what people thought of it. It
+ 
+
+ align:start position:0%
+out see what people thought of it. It
+sort of makes I can sort of agree with
+
+ align:start position:0%
+sort of makes I can sort of agree with
+ 
+
+ align:start position:0%
+sort of makes I can sort of agree with
+that on a um everyday kind of scale just
+
+ align:start position:0%
+that on a um everyday kind of scale just
+ 
+
+ align:start position:0%
+that on a um everyday kind of scale just
+like simple problems like being on the
+
+ align:start position:0%
+like simple problems like being on the
+ 
+
+ align:start position:0%
+like simple problems like being on the
+highway and you ran out of and you run
+
+ align:start position:0%
+highway and you ran out of and you run
+ 
+
+ align:start position:0%
+highway and you ran out of and you run
+out of gas in your car. Well, you had to
+
+ align:start position:0%
+out of gas in your car. Well, you had to
+ 
+
+ align:start position:0%
+out of gas in your car. Well, you had to
+have a creative solution to solve that
+
+ align:start position:0%
+have a creative solution to solve that
+ 
+
+ align:start position:0%
+have a creative solution to solve that
+random event in order to make sense out
+
+ align:start position:0%
+random event in order to make sense out
+ 
+
+ align:start position:0%
+random event in order to make sense out
+of it. So, on a small scale, I can see
+
+ align:start position:0%
+of it. So, on a small scale, I can see
+ 
+
+ align:start position:0%
+of it. So, on a small scale, I can see
+that. But in terms of art and beauty, I
+
+ align:start position:0%
+that. But in terms of art and beauty, I
+ 
+
+ align:start position:0%
+that. But in terms of art and beauty, I
+don't know.
+
+ align:start position:0%
+don't know.
+ 
+
+ align:start position:0%
+don't know.
+So
+
+ align:start position:0%
+So
+ 
+
+ align:start position:0%
+So
+yeah, I mean it seems to me like from
+
+ align:start position:0%
+yeah, I mean it seems to me like from
+ 
+
+ align:start position:0%
+yeah, I mean it seems to me like from
+the way you describe it, it sounds like
+
+ align:start position:0%
+the way you describe it, it sounds like
+ 
+
+ align:start position:0%
+the way you describe it, it sounds like
+the level at which he's he's making this
+
+ align:start position:0%
+the level at which he's he's making this
+ 
+
+ align:start position:0%
+the level at which he's he's making this
+argument in sort of a, you know, big
+
+ align:start position:0%
+argument in sort of a, you know, big
+ 
+
+ align:start position:0%
+argument in sort of a, you know, big
+broad abstract sense of, you know, art
+
+ align:start position:0%
+broad abstract sense of, you know, art
+ 
+
+ align:start position:0%
+broad abstract sense of, you know, art
+helps us feel better about the world
+
+ align:start position:0%
+helps us feel better about the world
+ 
+
+ align:start position:0%
+helps us feel better about the world
+around us and whatnot. uh I don't think
+
+ align:start position:0%
+around us and whatnot. uh I don't think
+ 
+
+ align:start position:0%
+around us and whatnot. uh I don't think
+that that makes a whole lot of sense in
+
+ align:start position:0%
+that that makes a whole lot of sense in
+ 
+
+ align:start position:0%
+that that makes a whole lot of sense in
+terms of an evolutionary perspective if
+
+ align:start position:0%
+terms of an evolutionary perspective if
+ 
+
+ align:start position:0%
+terms of an evolutionary perspective if
+if you take that sort of view of of
+
+ align:start position:0%
+if you take that sort of view of of
+ 
+
+ align:start position:0%
+if you take that sort of view of of
+cognitive development and that things
+
+ align:start position:0%
+cognitive development and that things
+ 
+
+ align:start position:0%
+cognitive development and that things
+evolve or aspects of of cognition uh
+
+ align:start position:0%
+evolve or aspects of of cognition uh
+ 
+
+ align:start position:0%
+evolve or aspects of of cognition uh
+evolve to fit some uh evolutionary need.
+
+ align:start position:0%
+evolve to fit some uh evolutionary need.
+ 
+
+ align:start position:0%
+evolve to fit some uh evolutionary need.
+It makes a lot more sense that
+
+ align:start position:0%
+It makes a lot more sense that
+ 
+
+ align:start position:0%
+It makes a lot more sense that
+creativity would have to do with
+
+ align:start position:0%
+creativity would have to do with
+ 
+
+ align:start position:0%
+creativity would have to do with
+something a lot simpler where it's like
+
+ align:start position:0%
+something a lot simpler where it's like
+ 
+
+ align:start position:0%
+something a lot simpler where it's like
+you know pattern recognition or or you
+
+ align:start position:0%
+you know pattern recognition or or you
+ 
+
+ align:start position:0%
+you know pattern recognition or or you
+know such more more fundamental things
+
+ align:start position:0%
+know such more more fundamental things
+ 
+
+ align:start position:0%
+know such more more fundamental things
+like that um that would help our species
+
+ align:start position:0%
+like that um that would help our species
+ 
+
+ align:start position:0%
+like that um that would help our species
+survive um you know seeing new links
+
+ align:start position:0%
+survive um you know seeing new links
+ 
+
+ align:start position:0%
+survive um you know seeing new links
+between different things. Well, look,
+
+ align:start position:0%
+between different things. Well, look,
+ 
+
+ align:start position:0%
+between different things. Well, look,
+think of it this way. Uh, you're having
+
+ align:start position:0%
+think of it this way. Uh, you're having
+ 
+
+ align:start position:0%
+think of it this way. Uh, you're having
+a fight with your girlfriend and so you
+
+ align:start position:0%
+a fight with your girlfriend and so you
+ 
+
+ align:start position:0%
+a fight with your girlfriend and so you
+go to the movies and it really is a work
+
+ align:start position:0%
+go to the movies and it really is a work
+ 
+
+ align:start position:0%
+go to the movies and it really is a work
+of art that you whose beauty you can
+
+ align:start position:0%
+of art that you whose beauty you can
+ 
+
+ align:start position:0%
+of art that you whose beauty you can
+perceive and uh whose story is
+
+ align:start position:0%
+perceive and uh whose story is
+ 
+
+ align:start position:0%
+perceive and uh whose story is
+meaningful and you come out having had
+
+ align:start position:0%
+meaningful and you come out having had
+ 
+
+ align:start position:0%
+meaningful and you come out having had
+what John Dewey calls an experience. You
+
+ align:start position:0%
+what John Dewey calls an experience. You
+ 
+
+ align:start position:0%
+what John Dewey calls an experience. You
+remember I was discuss that
+
+ align:start position:0%
+remember I was discuss that
+ 
+
+ align:start position:0%
+remember I was discuss that
+the aesthetic is having an experience.
+
+ align:start position:0%
+the aesthetic is having an experience.
+ 
+
+ align:start position:0%
+the aesthetic is having an experience.
+You come out really is an experience.
+
+ align:start position:0%
+You come out really is an experience.
+ 
+
+ align:start position:0%
+You come out really is an experience.
+that might then cure your depression.
+
+ align:start position:0%
+that might then cure your depression.
+ 
+
+ align:start position:0%
+that might then cure your depression.
+That might enable you to go out and face
+
+ align:start position:0%
+That might enable you to go out and face
+ 
+
+ align:start position:0%
+That might enable you to go out and face
+the problems of the world and call up
+
+ align:start position:0%
+the problems of the world and call up
+ 
+
+ align:start position:0%
+the problems of the world and call up
+your girlfriend and settle your
+
+ align:start position:0%
+your girlfriend and settle your
+ 
+
+ align:start position:0%
+your girlfriend and settle your
+problems. I mean, I'm I'm not saying I'm
+
+ align:start position:0%
+problems. I mean, I'm I'm not saying I'm
+ 
+
+ align:start position:0%
+problems. I mean, I'm I'm not saying I'm
+not saying though that uh creative
+
+ align:start position:0%
+not saying though that uh creative
+ 
+
+ align:start position:0%
+not saying though that uh creative
+things can't do that. I'm saying that
+
+ align:start position:0%
+things can't do that. I'm saying that
+ 
+
+ align:start position:0%
+things can't do that. I'm saying that
+their primary function is something else
+
+ align:start position:0%
+their primary function is something else
+ 
+
+ align:start position:0%
+their primary function is something else
+and anything along those lines that is
+
+ align:start position:0%
+and anything along those lines that is
+ 
+
+ align:start position:0%
+and anything along those lines that is
+derived from it is secondary to its its
+
+ align:start position:0%
+derived from it is secondary to its its
+ 
+
+ align:start position:0%
+derived from it is secondary to its its
+fundamental purpose which exists. Is it
+
+ align:start position:0%
+fundamental purpose which exists. Is it
+ 
+
+ align:start position:0%
+fundamental purpose which exists. Is it
+there the the these other things the
+
+ align:start position:0%
+there the the these other things the
+ 
+
+ align:start position:0%
+there the the these other things the
+primary purpose or these the mechanisms
+
+ align:start position:0%
+primary purpose or these the mechanisms
+ 
+
+ align:start position:0%
+primary purpose or these the mechanisms
+by which it works? So it sounds like
+
+ align:start position:0%
+by which it works? So it sounds like
+ 
+
+ align:start position:0%
+by which it works? So it sounds like
+you're saying something interesting
+
+ align:start position:0%
+you're saying something interesting
+ 
+
+ align:start position:0%
+you're saying something interesting
+which is that you're making a
+
+ align:start position:0%
+which is that you're making a
+ 
+
+ align:start position:0%
+which is that you're making a
+distinction between uh function and
+
+ align:start position:0%
+distinction between uh function and
+ 
+
+ align:start position:0%
+distinction between uh function and
+evolutionary terms and I had sort of
+
+ align:start position:0%
+evolutionary terms and I had sort of
+ 
+
+ align:start position:0%
+evolutionary terms and I had sort of
+been thinking in terms of uh intention
+
+ align:start position:0%
+been thinking in terms of uh intention
+ 
+
+ align:start position:0%
+been thinking in terms of uh intention
+or motivation which when
+
+ align:start position:0%
+or motivation which when
+ 
+
+ align:start position:0%
+or motivation which when
+science does all and well until you
+
+ align:start position:0%
+science does all and well until you
+ 
+
+ align:start position:0%
+science does all and well until you
+start to have to deal with the question
+
+ align:start position:0%
+start to have to deal with the question
+ 
+
+ align:start position:0%
+start to have to deal with the question
+of why we do the things that we do and
+
+ align:start position:0%
+of why we do the things that we do and
+ 
+
+ align:start position:0%
+of why we do the things that we do and
+whether we are allowed to have such
+
+ align:start position:0%
+whether we are allowed to have such
+ 
+
+ align:start position:0%
+whether we are allowed to have such
+things as motivation and intention uh
+
+ align:start position:0%
+things as motivation and intention uh
+ 
+
+ align:start position:0%
+things as motivation and intention uh
+especially in the scientific
+
+ align:start position:0%
+especially in the scientific
+ 
+
+ align:start position:0%
+especially in the scientific
+description. So wait, hang on. Why would
+
+ align:start position:0%
+description. So wait, hang on. Why would
+ 
+
+ align:start position:0%
+description. So wait, hang on. Why would
+you not be allowed to have motivation
+
+ align:start position:0%
+you not be allowed to have motivation
+ 
+
+ align:start position:0%
+you not be allowed to have motivation
+and intention? Surely that's kind of the
+
+ align:start position:0%
+and intention? Surely that's kind of the
+ 
+
+ align:start position:0%
+and intention? Surely that's kind of the
+basis of why you're doing science.
+
+ align:start position:0%
+basis of why you're doing science.
+ 
+
+ align:start position:0%
+basis of why you're doing science.
+Well, so but the question is can you
+
+ align:start position:0%
+Well, so but the question is can you
+ 
+
+ align:start position:0%
+Well, so but the question is can you
+does that fit within a scientific
+
+ align:start position:0%
+does that fit within a scientific
+ 
+
+ align:start position:0%
+does that fit within a scientific
+theory? I mean the
+
+ align:start position:0%
+theory? I mean the
+ 
+
+ align:start position:0%
+theory? I mean the
+see if I can explain this. Uh it
+
+ align:start position:0%
+see if I can explain this. Uh it
+ 
+
+ align:start position:0%
+see if I can explain this. Uh it
+revolves around the question of free
+
+ align:start position:0%
+revolves around the question of free
+ 
+
+ align:start position:0%
+revolves around the question of free
+will.
+
+ align:start position:0%
+will.
+ 
+
+ align:start position:0%
+will.
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+primarily in terms of uh taking human
+
+ align:start position:0%
+primarily in terms of uh taking human
+ 
+
+ align:start position:0%
+primarily in terms of uh taking human
+behavior down to the lowest level, the
+
+ align:start position:0%
+behavior down to the lowest level, the
+ 
+
+ align:start position:0%
+behavior down to the lowest level, the
+most fundamental theory of science which
+
+ align:start position:0%
+most fundamental theory of science which
+ 
+
+ align:start position:0%
+most fundamental theory of science which
+has its own problems. But it trying to
+
+ align:start position:0%
+has its own problems. But it trying to
+ 
+
+ align:start position:0%
+has its own problems. But it trying to
+reduce things that we claim we do
+
+ align:start position:0%
+reduce things that we claim we do
+ 
+
+ align:start position:0%
+reduce things that we claim we do
+because of emotions or desires down to
+
+ align:start position:0%
+because of emotions or desires down to
+ 
+
+ align:start position:0%
+because of emotions or desires down to
+atoms or quantum mechanics at that
+
+ align:start position:0%
+atoms or quantum mechanics at that
+ 
+
+ align:start position:0%
+atoms or quantum mechanics at that
+level. You know, previously it was to
+
+ align:start position:0%
+level. You know, previously it was to
+ 
+
+ align:start position:0%
+level. You know, previously it was to
+classical mechanics where Newton said
+
+ align:start position:0%
+classical mechanics where Newton said
+ 
+
+ align:start position:0%
+classical mechanics where Newton said
+the world is I don't know if the claim
+
+ align:start position:0%
+the world is I don't know if the claim
+ 
+
+ align:start position:0%
+the world is I don't know if the claim
+was that the world is clockwork and it's
+
+ align:start position:0%
+was that the world is clockwork and it's
+ 
+
+ align:start position:0%
+was that the world is clockwork and it's
+deterministic. And that was a real
+
+ align:start position:0%
+deterministic. And that was a real
+ 
+
+ align:start position:0%
+deterministic. And that was a real
+problem for intentionality and free will
+
+ align:start position:0%
+problem for intentionality and free will
+ 
+
+ align:start position:0%
+problem for intentionality and free will
+because then if you just knew enough all
+
+ align:start position:0%
+because then if you just knew enough all
+ 
+
+ align:start position:0%
+because then if you just knew enough all
+of human action would be derable by
+
+ align:start position:0%
+of human action would be derable by
+ 
+
+ align:start position:0%
+of human action would be derable by
+logic. When you get to quantum
+
+ align:start position:0%
+logic. When you get to quantum
+ 
+
+ align:start position:0%
+logic. When you get to quantum
+mechanics, if you take quantum mechanics
+
+ align:start position:0%
+mechanics, if you take quantum mechanics
+ 
+
+ align:start position:0%
+mechanics, if you take quantum mechanics
+as true, then suddenly it's
+
+ align:start position:0%
+as true, then suddenly it's
+ 
+
+ align:start position:0%
+as true, then suddenly it's
+probabilistic, but it's still governed
+
+ align:start position:0%
+probabilistic, but it's still governed
+ 
+
+ align:start position:0%
+probabilistic, but it's still governed
+by laws. And so you still don't get the
+
+ align:start position:0%
+by laws. And so you still don't get the
+ 
+
+ align:start position:0%
+by laws. And so you still don't get the
+same kind of uh I actually am a person
+
+ align:start position:0%
+same kind of uh I actually am a person
+ 
+
+ align:start position:0%
+same kind of uh I actually am a person
+and I have emotions that I can take as
+
+ align:start position:0%
+and I have emotions that I can take as
+ 
+
+ align:start position:0%
+and I have emotions that I can take as
+holes. I have
+
+ align:start position:0%
+holes. I have
+ 
+
+ align:start position:0%
+holes. I have
+because the claim of science is that no
+
+ align:start position:0%
+because the claim of science is that no
+ 
+
+ align:start position:0%
+because the claim of science is that no
+what you want to phrase as emotions need
+
+ align:start position:0%
+what you want to phrase as emotions need
+ 
+
+ align:start position:0%
+what you want to phrase as emotions need
+to be or are better expressed as laws of
+
+ align:start position:0%
+to be or are better expressed as laws of
+ 
+
+ align:start position:0%
+to be or are better expressed as laws of
+quantum mechanics. So they want to
+
+ align:start position:0%
+quantum mechanics. So they want to
+ 
+
+ align:start position:0%
+quantum mechanics. So they want to
+replace emotions with quantum mechanics
+
+ align:start position:0%
+replace emotions with quantum mechanics
+ 
+
+ align:start position:0%
+replace emotions with quantum mechanics
+and at that level the human
+
+ align:start position:0%
+and at that level the human
+ 
+
+ align:start position:0%
+and at that level the human
+intentionality goes away. I don't think
+
+ align:start position:0%
+intentionality goes away. I don't think
+ 
+
+ align:start position:0%
+intentionality goes away. I don't think
+I don't think they're trying to replace
+
+ align:start position:0%
+I don't think they're trying to replace
+ 
+
+ align:start position:0%
+I don't think they're trying to replace
+Yeah. I mean there are many people who
+
+ align:start position:0%
+Yeah. I mean there are many people who
+ 
+
+ align:start position:0%
+Yeah. I mean there are many people who
+don't there are many people who don't
+
+ align:start position:0%
+don't there are many people who don't
+ 
+
+ align:start position:0%
+don't there are many people who don't
+agree with that. So it's not universal
+
+ align:start position:0%
+agree with that. So it's not universal
+ 
+
+ align:start position:0%
+agree with that. So it's not universal
+but it is a real it is a real it's
+
+ align:start position:0%
+but it is a real it is a real it's
+ 
+
+ align:start position:0%
+but it is a real it is a real it's
+reductionism scientific reductionism and
+
+ align:start position:0%
+reductionism scientific reductionism and
+ 
+
+ align:start position:0%
+reductionism scientific reductionism and
+philosophy. So it I'm not making it up
+
+ align:start position:0%
+philosophy. So it I'm not making it up
+ 
+
+ align:start position:0%
+philosophy. So it I'm not making it up
+but I agree that not everybody goes
+
+ align:start position:0%
+but I agree that not everybody goes
+ 
+
+ align:start position:0%
+but I agree that not everybody goes
+along with that. Just know how to think.
+
+ align:start position:0%
+along with that. Just know how to think.
+ 
+
+ align:start position:0%
+along with that. Just know how to think.
+So anyway the the distinction that I was
+
+ align:start position:0%
+So anyway the the distinction that I was
+ 
+
+ align:start position:0%
+So anyway the the distinction that I was
+you know when I was throwing function
+
+ align:start position:0%
+you know when I was throwing function
+ 
+
+ align:start position:0%
+you know when I was throwing function
+and I actually meant in a in a
+
+ align:start position:0%
+and I actually meant in a in a
+ 
+
+ align:start position:0%
+and I actually meant in a in a
+intentional sort of way. So it's
+
+ align:start position:0%
+intentional sort of way. So it's
+ 
+
+ align:start position:0%
+intentional sort of way. So it's
+interesting to then think of it in terms
+
+ align:start position:0%
+interesting to then think of it in terms
+ 
+
+ align:start position:0%
+interesting to then think of it in terms
+of an evolutionary sense.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+I don't know whether there's room for
+
+ align:start position:0%
+I don't know whether there's room for
+ 
+
+ align:start position:0%
+I don't know whether there's room for
+both of them at the same time or what
+
+ align:start position:0%
+both of them at the same time or what
+ 
+
+ align:start position:0%
+both of them at the same time or what
+you think about them.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Do you want a paper? Well, did you have
+
+ align:start position:0%
+Do you want a paper? Well, did you have
+ 
+
+ align:start position:0%
+Do you want a paper? Well, did you have
+I was thinking they both sort of they
+
+ align:start position:0%
+I was thinking they both sort of they
+ 
+
+ align:start position:0%
+I was thinking they both sort of they
+can fit together. I mean they're just
+
+ align:start position:0%
+can fit together. I mean they're just
+ 
+
+ align:start position:0%
+can fit together. I mean they're just
+different meanings of the same sort of
+
+ align:start position:0%
+different meanings of the same sort of
+ 
+
+ align:start position:0%
+different meanings of the same sort of
+terminology and that I mean it's I think
+
+ align:start position:0%
+terminology and that I mean it's I think
+ 
+
+ align:start position:0%
+terminology and that I mean it's I think
+uh a lot I mean a lot of times actually
+
+ align:start position:0%
+uh a lot I mean a lot of times actually
+ 
+
+ align:start position:0%
+uh a lot I mean a lot of times actually
+in evolution they things evolve for one
+
+ align:start position:0%
+in evolution they things evolve for one
+ 
+
+ align:start position:0%
+in evolution they things evolve for one
+purpose and than used for another. I
+
+ align:start position:0%
+purpose and than used for another. I
+ 
+
+ align:start position:0%
+purpose and than used for another. I
+mean uh kind of what we were talking
+
+ align:start position:0%
+mean uh kind of what we were talking
+ 
+
+ align:start position:0%
+mean uh kind of what we were talking
+about earlier where human intelligence
+
+ align:start position:0%
+about earlier where human intelligence
+ 
+
+ align:start position:0%
+about earlier where human intelligence
+general evolved to help us survive. It
+
+ align:start position:0%
+general evolved to help us survive. It
+ 
+
+ align:start position:0%
+general evolved to help us survive. It
+didn't evolve for us to say you know sit
+
+ align:start position:0%
+didn't evolve for us to say you know sit
+ 
+
+ align:start position:0%
+didn't evolve for us to say you know sit
+around in a classroom and discuss
+
+ align:start position:0%
+around in a classroom and discuss
+ 
+
+ align:start position:0%
+around in a classroom and discuss
+philosophy. Nevertheless, we use it for
+
+ align:start position:0%
+philosophy. Nevertheless, we use it for
+ 
+
+ align:start position:0%
+philosophy. Nevertheless, we use it for
+that. Um and so there are those two sort
+
+ align:start position:0%
+that. Um and so there are those two sort
+ 
+
+ align:start position:0%
+that. Um and so there are those two sort
+of different types of function.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+So then my sense what would be the
+
+ align:start position:0%
+So then my sense what would be the
+ 
+
+ align:start position:0%
+So then my sense what would be the
+purpose of intellect
+
+ align:start position:0%
+purpose of intellect
+ 
+
+ align:start position:0%
+purpose of intellect
+to help us survive. It's our you know at
+
+ align:start position:0%
+to help us survive. It's our you know at
+ 
+
+ align:start position:0%
+to help us survive. It's our you know at
+the same time the animals are surviving
+
+ align:start position:0%
+the same time the animals are surviving
+ 
+
+ align:start position:0%
+the same time the animals are surviving
+just as well.
+
+ align:start position:0%
+just as well.
+ 
+
+ align:start position:0%
+just as well.
+They have different adaptations,
+
+ align:start position:0%
+They have different adaptations,
+ 
+
+ align:start position:0%
+They have different adaptations,
+multiple solutions to the same problem
+
+ align:start position:0%
+multiple solutions to the same problem
+ 
+
+ align:start position:0%
+multiple solutions to the same problem
+of survival,
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+but the simplest solution tends to be
+
+ align:start position:0%
+but the simplest solution tends to be
+ 
+
+ align:start position:0%
+but the simplest solution tends to be
+the more right one.
+
+ align:start position:0%
+the more right one.
+ 
+
+ align:start position:0%
+the more right one.
+That assumes somebody sitting there
+
+ align:start position:0%
+That assumes somebody sitting there
+ 
+
+ align:start position:0%
+That assumes somebody sitting there
+designing it, but let's not get into
+
+ align:start position:0%
+designing it, but let's not get into
+ 
+
+ align:start position:0%
+designing it, but let's not get into
+that. Okay.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um the way human nature seems to be
+
+ align:start position:0%
+um the way human nature seems to be
+ 
+
+ align:start position:0%
+um the way human nature seems to be
+evolving
+
+ align:start position:0%
+evolving
+ 
+
+ align:start position:0%
+evolving
+more and there'll be more and more
+
+ align:start position:0%
+more and there'll be more and more
+ 
+
+ align:start position:0%
+more and there'll be more and more
+people harder and harder to deal with
+
+ align:start position:0%
+people harder and harder to deal with
+ 
+
+ align:start position:0%
+people harder and harder to deal with
+them and therefore probably more chaos
+
+ align:start position:0%
+them and therefore probably more chaos
+ 
+
+ align:start position:0%
+them and therefore probably more chaos
+in political and social structures. Um
+
+ align:start position:0%
+in political and social structures. Um
+ 
+
+ align:start position:0%
+in political and social structures. Um
+and one one way of dealing with that is
+
+ align:start position:0%
+and one one way of dealing with that is
+ 
+
+ align:start position:0%
+and one one way of dealing with that is
+by destroying them in bigger and bigger
+
+ align:start position:0%
+by destroying them in bigger and bigger
+ 
+
+ align:start position:0%
+by destroying them in bigger and bigger
+nuclear explosions. of the world that in
+
+ align:start position:0%
+nuclear explosions. of the world that in
+ 
+
+ align:start position:0%
+nuclear explosions. of the world that in
+other words that the nature given the
+
+ align:start position:0%
+other words that the nature given the
+ 
+
+ align:start position:0%
+other words that the nature given the
+intellect we have given the slowness at
+
+ align:start position:0%
+intellect we have given the slowness at
+ 
+
+ align:start position:0%
+intellect we have given the slowness at
+which evolution works. There may be no
+
+ align:start position:0%
+which evolution works. There may be no
+ 
+
+ align:start position:0%
+which evolution works. There may be no
+way in which we can ever cope with
+
+ align:start position:0%
+way in which we can ever cope with
+ 
+
+ align:start position:0%
+way in which we can ever cope with
+fundamental problems of a small planet
+
+ align:start position:0%
+fundamental problems of a small planet
+ 
+
+ align:start position:0%
+fundamental problems of a small planet
+overpop populated and with uh creatures
+
+ align:start position:0%
+overpop populated and with uh creatures
+ 
+
+ align:start position:0%
+overpop populated and with uh creatures
+dominating it who have so many
+
+ align:start position:0%
+dominating it who have so many
+ 
+
+ align:start position:0%
+dominating it who have so many
+antisocial attitudes and feelings.
+
+ align:start position:0%
+antisocial attitudes and feelings.
+ 
+
+ align:start position:0%
+antisocial attitudes and feelings.
+If you take that point of view and then
+
+ align:start position:0%
+If you take that point of view and then
+ 
+
+ align:start position:0%
+If you take that point of view and then
+compare the state of animals in the
+
+ align:start position:0%
+compare the state of animals in the
+ 
+
+ align:start position:0%
+compare the state of animals in the
+rainforest who are not troubled by human
+
+ align:start position:0%
+rainforest who are not troubled by human
+ 
+
+ align:start position:0%
+rainforest who are not troubled by human
+beings uh al and particular species like
+
+ align:start position:0%
+beings uh al and particular species like
+ 
+
+ align:start position:0%
+beings uh al and particular species like
+the bonos
+
+ align:start position:0%
+the bonos
+ 
+
+ align:start position:0%
+the bonos
+um who are so similar to us or sort of
+
+ align:start position:0%
+um who are so similar to us or sort of
+ 
+
+ align:start position:0%
+um who are so similar to us or sort of
+variation of chimpanzees.
+
+ align:start position:0%
+variation of chimpanzees.
+ 
+
+ align:start position:0%
+variation of chimpanzees.
+Um you might say you know why uh why be
+
+ align:start position:0%
+Um you might say you know why uh why be
+ 
+
+ align:start position:0%
+Um you might say you know why uh why be
+human? Why who needs all of this? the
+
+ align:start position:0%
+human? Why who needs all of this? the
+ 
+
+ align:start position:0%
+human? Why who needs all of this? the
+bonos. Um I mean chimpanzees have many
+
+ align:start position:0%
+bonos. Um I mean chimpanzees have many
+ 
+
+ align:start position:0%
+bonos. Um I mean chimpanzees have many
+of our aggressive
+
+ align:start position:0%
+of our aggressive
+ 
+
+ align:start position:0%
+of our aggressive
+and violent traits
+
+ align:start position:0%
+and violent traits
+ 
+
+ align:start position:0%
+and violent traits
+because we share so many so many genes.
+
+ align:start position:0%
+because we share so many so many genes.
+ 
+
+ align:start position:0%
+because we share so many so many genes.
+But the bonos for some reason have a
+
+ align:start position:0%
+But the bonos for some reason have a
+ 
+
+ align:start position:0%
+But the bonos for some reason have a
+slightly different program
+
+ align:start position:0%
+slightly different program
+ 
+
+ align:start position:0%
+slightly different program
+and they don't fight. They just make
+
+ align:start position:0%
+and they don't fight. They just make
+ 
+
+ align:start position:0%
+and they don't fight. They just make
+love all the time and they seem to have
+
+ align:start position:0%
+love all the time and they seem to have
+ 
+
+ align:start position:0%
+love all the time and they seem to have
+a very pleasant existence except when
+
+ align:start position:0%
+a very pleasant existence except when
+ 
+
+ align:start position:0%
+a very pleasant existence except when
+the others kill them for reasons of
+
+ align:start position:0%
+the others kill them for reasons of
+ 
+
+ align:start position:0%
+the others kill them for reasons of
+their own. But if thinking of the state
+
+ align:start position:0%
+their own. But if thinking of the state
+ 
+
+ align:start position:0%
+their own. But if thinking of the state
+of the species independent of their
+
+ align:start position:0%
+of the species independent of their
+ 
+
+ align:start position:0%
+of the species independent of their
+interaction with one another, one might
+
+ align:start position:0%
+interaction with one another, one might
+ 
+
+ align:start position:0%
+interaction with one another, one might
+say how much better it would be to be a
+
+ align:start position:0%
+say how much better it would be to be a
+ 
+
+ align:start position:0%
+say how much better it would be to be a
+bono than a human being.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+And if that's true, then we could start
+
+ align:start position:0%
+And if that's true, then we could start
+ 
+
+ align:start position:0%
+And if that's true, then we could start
+finding other species that one would be
+
+ align:start position:0%
+finding other species that one would be
+ 
+
+ align:start position:0%
+finding other species that one would be
+better off being.
+
+ align:start position:0%
+better off being.
+ 
+
+ align:start position:0%
+better off being.
+I mean,
+
+ align:start position:0%
+I mean,
+ 
+
+ align:start position:0%
+I mean,
+that seems to me similar to the claim of
+
+ align:start position:0%
+that seems to me similar to the claim of
+ 
+
+ align:start position:0%
+that seems to me similar to the claim of
+the noble savage
+
+ align:start position:0%
+the noble savage
+ 
+
+ align:start position:0%
+the noble savage
+who was the primitive state of man that
+
+ align:start position:0%
+who was the primitive state of man that
+ 
+
+ align:start position:0%
+who was the primitive state of man that
+lived in harmony with nature and uh had
+
+ align:start position:0%
+lived in harmony with nature and uh had
+ 
+
+ align:start position:0%
+lived in harmony with nature and uh had
+a small tight-knit social group and you
+
+ align:start position:0%
+a small tight-knit social group and you
+ 
+
+ align:start position:0%
+a small tight-knit social group and you
+know lived off the land and sort of the
+
+ align:start position:0%
+know lived off the land and sort of the
+ 
+
+ align:start position:0%
+know lived off the land and sort of the
+pure natural state that
+
+ align:start position:0%
+pure natural state that
+ 
+
+ align:start position:0%
+pure natural state that
+was best for humankind. Well, there's a
+
+ align:start position:0%
+was best for humankind. Well, there's a
+ 
+
+ align:start position:0%
+was best for humankind. Well, there's a
+confusion in that because we live close
+
+ align:start position:0%
+confusion in that because we live close
+ 
+
+ align:start position:0%
+confusion in that because we live close
+to nature
+
+ align:start position:0%
+to nature
+ 
+
+ align:start position:0%
+to nature
+where all what we do is natural and it's
+
+ align:start position:0%
+where all what we do is natural and it's
+ 
+
+ align:start position:0%
+where all what we do is natural and it's
+all a function of natural impulses in
+
+ align:start position:0%
+all a function of natural impulses in
+ 
+
+ align:start position:0%
+all a function of natural impulses in
+us. It's just that the consequences
+
+ align:start position:0%
+us. It's just that the consequences
+ 
+
+ align:start position:0%
+us. It's just that the consequences
+um don't conduce to the system of values
+
+ align:start position:0%
+um don't conduce to the system of values
+ 
+
+ align:start position:0%
+um don't conduce to the system of values
+that we've also acquired and they don't
+
+ align:start position:0%
+that we've also acquired and they don't
+ 
+
+ align:start position:0%
+that we've also acquired and they don't
+bring about a kind of
+
+ align:start position:0%
+bring about a kind of
+ 
+
+ align:start position:0%
+bring about a kind of
+brute happiness that everybody would
+
+ align:start position:0%
+brute happiness that everybody would
+ 
+
+ align:start position:0%
+brute happiness that everybody would
+like to have. So it isn't as if the
+
+ align:start position:0%
+like to have. So it isn't as if the
+ 
+
+ align:start position:0%
+like to have. So it isn't as if the
+Bonos are closer to nature. It's just
+
+ align:start position:0%
+Bonos are closer to nature. It's just
+ 
+
+ align:start position:0%
+Bonos are closer to nature. It's just
+that they have a a better relationship
+
+ align:start position:0%
+that they have a a better relationship
+ 
+
+ align:start position:0%
+that they have a a better relationship
+to nature than we do. Both of us being
+
+ align:start position:0%
+to nature than we do. Both of us being
+ 
+
+ align:start position:0%
+to nature than we do. Both of us being
+uh in doing what comes naturally. But
+
+ align:start position:0%
+uh in doing what comes naturally. But
+ 
+
+ align:start position:0%
+uh in doing what comes naturally. But
+I'm not convinced that the noble savage
+
+ align:start position:0%
+I'm not convinced that the noble savage
+ 
+
+ align:start position:0%
+I'm not convinced that the noble savage
+ever existed. I think it's that's
+
+ align:start position:0%
+ever existed. I think it's that's
+ 
+
+ align:start position:0%
+ever existed. I think it's that's
+because of the contradiction in the
+
+ align:start position:0%
+because of the contradiction in the
+ 
+
+ align:start position:0%
+because of the contradiction in the
+terms. If he's noble, he's not going to
+
+ align:start position:0%
+terms. If he's noble, he's not going to
+ 
+
+ align:start position:0%
+terms. If he's noble, he's not going to
+be a savage. And if he's a savage
+
+ align:start position:0%
+be a savage. And if he's a savage
+ 
+
+ align:start position:0%
+be a savage. And if he's a savage
+savage, he's not going to be noble. But
+
+ align:start position:0%
+savage, he's not going to be noble. But
+ 
+
+ align:start position:0%
+savage, he's not going to be noble. But
+um eliminating all of that romantic
+
+ align:start position:0%
+um eliminating all of that romantic
+ 
+
+ align:start position:0%
+um eliminating all of that romantic
+verbiage of one might say uh there are
+
+ align:start position:0%
+verbiage of one might say uh there are
+ 
+
+ align:start position:0%
+verbiage of one might say uh there are
+species we name them um who uh are
+
+ align:start position:0%
+species we name them um who uh are
+ 
+
+ align:start position:0%
+species we name them um who uh are
+better off in the world would be better
+
+ align:start position:0%
+better off in the world would be better
+ 
+
+ align:start position:0%
+better off in the world would be better
+off if they were the dominant creatures
+
+ align:start position:0%
+off if they were the dominant creatures
+ 
+
+ align:start position:0%
+off if they were the dominant creatures
+rather than us. You see so I'm you get
+
+ align:start position:0%
+rather than us. You see so I'm you get
+ 
+
+ align:start position:0%
+rather than us. You see so I'm you get
+my idea I I don't want to pursue the
+
+ align:start position:0%
+my idea I I don't want to pursue the
+ 
+
+ align:start position:0%
+my idea I I don't want to pursue the
+question about the noble savage or I
+
+ align:start position:0%
+question about the noble savage or I
+ 
+
+ align:start position:0%
+question about the noble savage or I
+encourage you maybe to think beyond
+
+ align:start position:0%
+encourage you maybe to think beyond
+ 
+
+ align:start position:0%
+encourage you maybe to think beyond
+that.
+
+ align:start position:0%
+that.
+ 
+
+ align:start position:0%
+that.
+Well it's just a question of
+
+ align:start position:0%
+Well it's just a question of
+ 
+
+ align:start position:0%
+Well it's just a question of
+It it's somewhat ironic to say uh the
+
+ align:start position:0%
+It it's somewhat ironic to say uh the
+ 
+
+ align:start position:0%
+It it's somewhat ironic to say uh the
+world would be better off put these
+
+ align:start position:0%
+world would be better off put these
+ 
+
+ align:start position:0%
+world would be better off put these
+species in charge given that it's us
+
+ align:start position:0%
+species in charge given that it's us
+ 
+
+ align:start position:0%
+species in charge given that it's us
+making the value decision
+
+ align:start position:0%
+making the value decision
+ 
+
+ align:start position:0%
+making the value decision
+that and no no no not no that's
+
+ align:start position:0%
+that and no no no not no that's
+ 
+
+ align:start position:0%
+that and no no no not no that's
+contradictory. If we make the value
+
+ align:start position:0%
+contradictory. If we make the value
+ 
+
+ align:start position:0%
+contradictory. If we make the value
+decisions we're already separating
+
+ align:start position:0%
+decisions we're already separating
+ 
+
+ align:start position:0%
+decisions we're already separating
+ourselves from them and assuming that we
+
+ align:start position:0%
+ourselves from them and assuming that we
+ 
+
+ align:start position:0%
+ourselves from them and assuming that we
+have a superiority. I'm saying uh if you
+
+ align:start position:0%
+have a superiority. I'm saying uh if you
+ 
+
+ align:start position:0%
+have a superiority. I'm saying uh if you
+accept our value
+
+ align:start position:0%
+accept our value
+ 
+
+ align:start position:0%
+accept our value
+system of values and there is a certain
+
+ align:start position:0%
+system of values and there is a certain
+ 
+
+ align:start position:0%
+system of values and there is a certain
+degree of agreement uh about the
+
+ align:start position:0%
+degree of agreement uh about the
+ 
+
+ align:start position:0%
+degree of agreement uh about the
+goodness of happiness, the goodness of
+
+ align:start position:0%
+goodness of happiness, the goodness of
+ 
+
+ align:start position:0%
+goodness of happiness, the goodness of
+being peaceful and getting along with
+
+ align:start position:0%
+being peaceful and getting along with
+ 
+
+ align:start position:0%
+being peaceful and getting along with
+your roommates uh and so on. uh
+
+ align:start position:0%
+your roommates uh and so on. uh
+ 
+
+ align:start position:0%
+your roommates uh and so on. uh
+you can then say given those values
+
+ align:start position:0%
+you can then say given those values
+ 
+
+ align:start position:0%
+you can then say given those values
+um there are other other species who
+
+ align:start position:0%
+um there are other other species who
+ 
+
+ align:start position:0%
+um there are other other species who
+would do a better job of living up to
+
+ align:start position:0%
+would do a better job of living up to
+ 
+
+ align:start position:0%
+would do a better job of living up to
+them if only we didn't have our
+
+ align:start position:0%
+them if only we didn't have our
+ 
+
+ align:start position:0%
+them if only we didn't have our
+dominance over those. But but I mean it
+
+ align:start position:0%
+dominance over those. But but I mean it
+ 
+
+ align:start position:0%
+dominance over those. But but I mean it
+could be that the the whole reason that
+
+ align:start position:0%
+could be that the the whole reason that
+ 
+
+ align:start position:0%
+could be that the the whole reason that
+these species aren't dominant is because
+
+ align:start position:0%
+these species aren't dominant is because
+ 
+
+ align:start position:0%
+these species aren't dominant is because
+of those very traits that make them sort
+
+ align:start position:0%
+of those very traits that make them sort
+ 
+
+ align:start position:0%
+of those very traits that make them sort
+of you know work well with their
+
+ align:start position:0%
+of you know work well with their
+ 
+
+ align:start position:0%
+of you know work well with their
+environment. they they tend to be a
+
+ align:start position:0%
+environment. they they tend to be a
+ 
+
+ align:start position:0%
+environment. they they tend to be a
+little bit more passive and it's it's
+
+ align:start position:0%
+little bit more passive and it's it's
+ 
+
+ align:start position:0%
+little bit more passive and it's it's
+our sort of destructive dominant nature
+
+ align:start position:0%
+our sort of destructive dominant nature
+ 
+
+ align:start position:0%
+our sort of destructive dominant nature
+uh that is the reason we're dominant.
+
+ align:start position:0%
+uh that is the reason we're dominant.
+ 
+
+ align:start position:0%
+uh that is the reason we're dominant.
+And so you can argue theoretically,
+
+ align:start position:0%
+And so you can argue theoretically,
+ 
+
+ align:start position:0%
+And so you can argue theoretically,
+yeah, it might be better if some other
+
+ align:start position:0%
+yeah, it might be better if some other
+ 
+
+ align:start position:0%
+yeah, it might be better if some other
+species were in charge, but it's it's
+
+ align:start position:0%
+species were in charge, but it's it's
+ 
+
+ align:start position:0%
+species were in charge, but it's it's
+not something that could ever actually
+
+ align:start position:0%
+not something that could ever actually
+ 
+
+ align:start position:0%
+not something that could ever actually
+occur because of the actual uh because
+
+ align:start position:0%
+occur because of the actual uh because
+ 
+
+ align:start position:0%
+occur because of the actual uh because
+of the because the happiness comes from
+
+ align:start position:0%
+of the because the happiness comes from
+ 
+
+ align:start position:0%
+of the because the happiness comes from
+not being in charge. Yeah, something
+
+ align:start position:0%
+not being in charge. Yeah, something
+ 
+
+ align:start position:0%
+not being in charge. Yeah, something
+like that, right? Or I mean there's I I
+
+ align:start position:0%
+like that, right? Or I mean there's I I
+ 
+
+ align:start position:0%
+like that, right? Or I mean there's I I
+I also think there's a problem with
+
+ align:start position:0%
+I also think there's a problem with
+ 
+
+ align:start position:0%
+I also think there's a problem with
+trying to say what would be better with
+
+ align:start position:0%
+trying to say what would be better with
+ 
+
+ align:start position:0%
+trying to say what would be better with
+than us given that we're judging as us.
+
+ align:start position:0%
+than us given that we're judging as us.
+ 
+
+ align:start position:0%
+than us given that we're judging as us.
+You know if if if humans are so flawed
+
+ align:start position:0%
+You know if if if humans are so flawed
+ 
+
+ align:start position:0%
+You know if if if humans are so flawed
+that they would be better replaced by
+
+ align:start position:0%
+that they would be better replaced by
+ 
+
+ align:start position:0%
+that they would be better replaced by
+something else then it seems strange to
+
+ align:start position:0%
+something else then it seems strange to
+ 
+
+ align:start position:0%
+something else then it seems strange to
+judge what should be replaced you know
+
+ align:start position:0%
+judge what should be replaced you know
+ 
+
+ align:start position:0%
+judge what should be replaced you know
+what what should replace humans as
+
+ align:start position:0%
+what what should replace humans as
+ 
+
+ align:start position:0%
+what what should replace humans as
+humans. That might be the flaw in the
+
+ align:start position:0%
+humans. That might be the flaw in the
+ 
+
+ align:start position:0%
+humans. That might be the flaw in the
+first place. It could be an inescapable
+
+ align:start position:0%
+first place. It could be an inescapable
+ 
+
+ align:start position:0%
+first place. It could be an inescapable
+problem. Um, that may be an interesting
+
+ align:start position:0%
+problem. Um, that may be an interesting
+ 
+
+ align:start position:0%
+problem. Um, that may be an interesting
+insight into the flaw in all morality
+
+ align:start position:0%
+insight into the flaw in all morality
+ 
+
+ align:start position:0%
+insight into the flaw in all morality
+because if if you're going to be moral,
+
+ align:start position:0%
+because if if you're going to be moral,
+ 
+
+ align:start position:0%
+because if if you're going to be moral,
+you have to have a system of values and
+
+ align:start position:0%
+you have to have a system of values and
+ 
+
+ align:start position:0%
+you have to have a system of values and
+standards, right? Uh, but having them
+
+ align:start position:0%
+standards, right? Uh, but having them
+ 
+
+ align:start position:0%
+standards, right? Uh, but having them
+might already disqualify you from living
+
+ align:start position:0%
+might already disqualify you from living
+ 
+
+ align:start position:0%
+might already disqualify you from living
+up to them.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+I think I think there are lots of flaws
+
+ align:start position:0%
+I think I think there are lots of flaws
+ 
+
+ align:start position:0%
+I think I think there are lots of flaws
+of that sort in human nature.
+
+ align:start position:0%
+of that sort in human nature.
+ 
+
+ align:start position:0%
+of that sort in human nature.
+So, I don't I'm just sort of reluctant
+
+ align:start position:0%
+So, I don't I'm just sort of reluctant
+ 
+
+ align:start position:0%
+So, I don't I'm just sort of reluctant
+to to uh believe that other species are
+
+ align:start position:0%
+to to uh believe that other species are
+ 
+
+ align:start position:0%
+to to uh believe that other species are
+uh in fact better than we are because
+
+ align:start position:0%
+uh in fact better than we are because
+ 
+
+ align:start position:0%
+uh in fact better than we are because
+the assumption requires us to judge
+
+ align:start position:0%
+the assumption requires us to judge
+ 
+
+ align:start position:0%
+the assumption requires us to judge
+ourselves as so terrible that uh we
+
+ align:start position:0%
+ourselves as so terrible that uh we
+ 
+
+ align:start position:0%
+ourselves as so terrible that uh we
+would be replaced by them. But in fact,
+
+ align:start position:0%
+would be replaced by them. But in fact,
+ 
+
+ align:start position:0%
+would be replaced by them. But in fact,
+we're not fit to make that judgment in
+
+ align:start position:0%
+we're not fit to make that judgment in
+ 
+
+ align:start position:0%
+we're not fit to make that judgment in
+the first place if we are so terrible.
+
+ align:start position:0%
+the first place if we are so terrible.
+ 
+
+ align:start position:0%
+the first place if we are so terrible.
+All right. No. Uh I I would be willing
+
+ align:start position:0%
+All right. No. Uh I I would be willing
+ 
+
+ align:start position:0%
+All right. No. Uh I I would be willing
+to yield that generalization I made if
+
+ align:start position:0%
+to yield that generalization I made if
+ 
+
+ align:start position:0%
+to yield that generalization I made if
+it were agreed that um there is
+
+ align:start position:0%
+it were agreed that um there is
+ 
+
+ align:start position:0%
+it were agreed that um there is
+something radically flawed in our very
+
+ align:start position:0%
+something radically flawed in our very
+ 
+
+ align:start position:0%
+something radically flawed in our very
+being. Now that of course is the view of
+
+ align:start position:0%
+being. Now that of course is the view of
+ 
+
+ align:start position:0%
+being. Now that of course is the view of
+great many religions
+
+ align:start position:0%
+great many religions
+ 
+
+ align:start position:0%
+great many religions
+that man human nature is evil and that
+
+ align:start position:0%
+that man human nature is evil and that
+ 
+
+ align:start position:0%
+that man human nature is evil and that
+um uh there's original sin and therefore
+
+ align:start position:0%
+um uh there's original sin and therefore
+ 
+
+ align:start position:0%
+um uh there's original sin and therefore
+the most you can do is to throw yourself
+
+ align:start position:0%
+the most you can do is to throw yourself
+ 
+
+ align:start position:0%
+the most you can do is to throw yourself
+at the mercy of loving God. Right. So
+
+ align:start position:0%
+at the mercy of loving God. Right. So
+ 
+
+ align:start position:0%
+at the mercy of loving God. Right. So
+that there may be a great deal of
+
+ align:start position:0%
+that there may be a great deal of
+ 
+
+ align:start position:0%
+that there may be a great deal of
+consensus about that. The question is
+
+ align:start position:0%
+consensus about that. The question is
+ 
+
+ align:start position:0%
+consensus about that. The question is
+the idea of flaw what what
+
+ align:start position:0%
+the idea of flaw what what
+ 
+
+ align:start position:0%
+the idea of flaw what what
+interpretation you lay upon it. And that
+
+ align:start position:0%
+interpretation you lay upon it. And that
+ 
+
+ align:start position:0%
+interpretation you lay upon it. And that
+doesn't have to be the same as what it
+
+ align:start position:0%
+doesn't have to be the same as what it
+ 
+
+ align:start position:0%
+doesn't have to be the same as what it
+is in most religions.
+
+ align:start position:0%
+is in most religions.
+ 
+
+ align:start position:0%
+is in most religions.
+Um, in the case of the bonos or the
+
+ align:start position:0%
+Um, in the case of the bonos or the
+ 
+
+ align:start position:0%
+Um, in the case of the bonos or the
+other instinct, other in animals who
+
+ align:start position:0%
+other instinct, other in animals who
+ 
+
+ align:start position:0%
+other instinct, other in animals who
+seem to have a happier relationship with
+
+ align:start position:0%
+seem to have a happier relationship with
+ 
+
+ align:start position:0%
+seem to have a happier relationship with
+their own instincts, we may be
+
+ align:start position:0%
+their own instincts, we may be
+ 
+
+ align:start position:0%
+their own instincts, we may be
+romanticizing them. They're all sorts of
+
+ align:start position:0%
+romanticizing them. They're all sorts of
+ 
+
+ align:start position:0%
+romanticizing them. They're all sorts of
+problems they might have that we never
+
+ align:start position:0%
+problems they might have that we never
+ 
+
+ align:start position:0%
+problems they might have that we never
+know anything about. In fact, I think we
+
+ align:start position:0%
+know anything about. In fact, I think we
+ 
+
+ align:start position:0%
+know anything about. In fact, I think we
+know very little about what it is to be
+
+ align:start position:0%
+know very little about what it is to be
+ 
+
+ align:start position:0%
+know very little about what it is to be
+another member of another species. We
+
+ align:start position:0%
+another member of another species. We
+ 
+
+ align:start position:0%
+another member of another species. We
+don't know what their minds are. um you
+
+ align:start position:0%
+don't know what their minds are. um you
+ 
+
+ align:start position:0%
+don't know what their minds are. um you
+know in the um the um u insects in um in
+
+ align:start position:0%
+know in the um the um u insects in um in
+ 
+
+ align:start position:0%
+know in the um the um u insects in um in
+a colony where there's a queen and
+
+ align:start position:0%
+a colony where there's a queen and
+ 
+
+ align:start position:0%
+a colony where there's a queen and
+there's that class stratification and
+
+ align:start position:0%
+there's that class stratification and
+ 
+
+ align:start position:0%
+there's that class stratification and
+the workers do all the work. Um we don't
+
+ align:start position:0%
+the workers do all the work. Um we don't
+ 
+
+ align:start position:0%
+the workers do all the work. Um we don't
+know how they feel about that. Uh, do
+
+ align:start position:0%
+know how they feel about that. Uh, do
+ 
+
+ align:start position:0%
+know how they feel about that. Uh, do
+they when they pass each other, do they
+
+ align:start position:0%
+they when they pass each other, do they
+ 
+
+ align:start position:0%
+they when they pass each other, do they
+nudge them on the elbow and enjoy their
+
+ align:start position:0%
+nudge them on the elbow and enjoy their
+ 
+
+ align:start position:0%
+nudge them on the elbow and enjoy their
+company and and have a or compete to see
+
+ align:start position:0%
+company and and have a or compete to see
+ 
+
+ align:start position:0%
+company and and have a or compete to see
+who can bring the most food to the to
+
+ align:start position:0%
+who can bring the most food to the to
+ 
+
+ align:start position:0%
+who can bring the most food to the to
+the queen? We have no idea whatsoever
+
+ align:start position:0%
+the queen? We have no idea whatsoever
+ 
+
+ align:start position:0%
+the queen? We have no idea whatsoever
+what's going on in these other other
+
+ align:start position:0%
+what's going on in these other other
+ 
+
+ align:start position:0%
+what's going on in these other other
+species, particularly the insect
+
+ align:start position:0%
+species, particularly the insect
+ 
+
+ align:start position:0%
+species, particularly the insect
+species, but it also would be true of
+
+ align:start position:0%
+species, but it also would be true of
+ 
+
+ align:start position:0%
+species, but it also would be true of
+underground molds and and other animals
+
+ align:start position:0%
+underground molds and and other animals
+ 
+
+ align:start position:0%
+underground molds and and other animals
+that we never try to make sense of.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+What about your paper?
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Um,
+
+ align:start position:0%
+Um,
+ 
+
+ align:start position:0%
+Um,
+okay. So,
+
+ align:start position:0%
+okay. So,
+ 
+
+ align:start position:0%
+okay. So,
+like I said, I'm kicking around the idea
+
+ align:start position:0%
+like I said, I'm kicking around the idea
+ 
+
+ align:start position:0%
+like I said, I'm kicking around the idea
+of uh scientific creativity being a
+
+ align:start position:0%
+of uh scientific creativity being a
+ 
+
+ align:start position:0%
+of uh scientific creativity being a
+personal expression of what the
+
+ align:start position:0%
+personal expression of what the
+ 
+
+ align:start position:0%
+personal expression of what the
+scientist believes the nature of the
+
+ align:start position:0%
+scientist believes the nature of the
+ 
+
+ align:start position:0%
+scientist believes the nature of the
+world is. Uh, so in other words, the
+
+ align:start position:0%
+world is. Uh, so in other words, the
+ 
+
+ align:start position:0%
+world is. Uh, so in other words, the
+metaphysics of the world. uh one example
+
+ align:start position:0%
+metaphysics of the world. uh one example
+ 
+
+ align:start position:0%
+metaphysics of the world. uh one example
+might be how
+
+ align:start position:0%
+might be how
+ 
+
+ align:start position:0%
+might be how
+uh early mechanics arose from capernicus
+
+ align:start position:0%
+uh early mechanics arose from capernicus
+ 
+
+ align:start position:0%
+uh early mechanics arose from capernicus
+to Kepler to Newton and then uh sort of
+
+ align:start position:0%
+to Kepler to Newton and then uh sort of
+ 
+
+ align:start position:0%
+to Kepler to Newton and then uh sort of
+in contradiction with Einstein by a
+
+ align:start position:0%
+in contradiction with Einstein by a
+ 
+
+ align:start position:0%
+in contradiction with Einstein by a
+statement of God's presence in the
+
+ align:start position:0%
+statement of God's presence in the
+ 
+
+ align:start position:0%
+statement of God's presence in the
+universe and that leading to harmonious
+
+ align:start position:0%
+universe and that leading to harmonious
+ 
+
+ align:start position:0%
+universe and that leading to harmonious
+relationships between uh the heavenly
+
+ align:start position:0%
+relationships between uh the heavenly
+ 
+
+ align:start position:0%
+relationships between uh the heavenly
+bodies
+
+ align:start position:0%
+bodies
+ 
+
+ align:start position:0%
+bodies
+and it was you know specifically a
+
+ align:start position:0%
+and it was you know specifically a
+ 
+
+ align:start position:0%
+and it was you know specifically a
+belief that uh if God is existent and
+
+ align:start position:0%
+belief that uh if God is existent and
+ 
+
+ align:start position:0%
+belief that uh if God is existent and
+present in the universe, then the
+
+ align:start position:0%
+present in the universe, then the
+ 
+
+ align:start position:0%
+present in the universe, then the
+relationships of objects in nature must
+
+ align:start position:0%
+relationships of objects in nature must
+ 
+
+ align:start position:0%
+relationships of objects in nature must
+be harmonious or beautiful or somehow
+
+ align:start position:0%
+be harmonious or beautiful or somehow
+ 
+
+ align:start position:0%
+be harmonious or beautiful or somehow
+representative of the great nature of
+
+ align:start position:0%
+representative of the great nature of
+ 
+
+ align:start position:0%
+representative of the great nature of
+God. And for example, Kepler
+
+ align:start position:0%
+God. And for example, Kepler
+ 
+
+ align:start position:0%
+God. And for example, Kepler
+uh was
+
+ align:start position:0%
+uh was
+ 
+
+ align:start position:0%
+uh was
+in part so pleased with his theory that
+
+ align:start position:0%
+in part so pleased with his theory that
+ 
+
+ align:start position:0%
+in part so pleased with his theory that
+uh gave the motions of the planets
+
+ align:start position:0%
+uh gave the motions of the planets
+ 
+
+ align:start position:0%
+uh gave the motions of the planets
+ellypoid form because it finally let him
+
+ align:start position:0%
+ellypoid form because it finally let him
+ 
+
+ align:start position:0%
+ellypoid form because it finally let him
+put the sun back at the center of the
+
+ align:start position:0%
+put the sun back at the center of the
+ 
+
+ align:start position:0%
+put the sun back at the center of the
+solar system where at at that time the
+
+ align:start position:0%
+solar system where at at that time the
+ 
+
+ align:start position:0%
+solar system where at at that time the
+universe which meant that the sun uh
+
+ align:start position:0%
+universe which meant that the sun uh
+ 
+
+ align:start position:0%
+universe which meant that the sun uh
+which he saw as the center of or the
+
+ align:start position:0%
+which he saw as the center of or the
+ 
+
+ align:start position:0%
+which he saw as the center of or the
+temple of God in some ways uh of the
+
+ align:start position:0%
+temple of God in some ways uh of the
+ 
+
+ align:start position:0%
+temple of God in some ways uh of the
+heavenly bodies was then in its rightful
+
+ align:start position:0%
+heavenly bodies was then in its rightful
+ 
+
+ align:start position:0%
+heavenly bodies was then in its rightful
+place in the universe. And that was
+
+ align:start position:0%
+place in the universe. And that was
+ 
+
+ align:start position:0%
+place in the universe. And that was
+beautiful to him and was something he
+
+ align:start position:0%
+beautiful to him and was something he
+ 
+
+ align:start position:0%
+beautiful to him and was something he
+actually
+
+ align:start position:0%
+actually
+ 
+
+ align:start position:0%
+actually
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+used as or was an expression of what he
+
+ align:start position:0%
+used as or was an expression of what he
+ 
+
+ align:start position:0%
+used as or was an expression of what he
+believed in his science and that's
+
+ align:start position:0%
+believed in his science and that's
+ 
+
+ align:start position:0%
+believed in his science and that's
+something that guided him in creating
+
+ align:start position:0%
+something that guided him in creating
+ 
+
+ align:start position:0%
+something that guided him in creating
+the science. He was looking for a
+
+ align:start position:0%
+the science. He was looking for a
+ 
+
+ align:start position:0%
+the science. He was looking for a
+beautiful relationship between the
+
+ align:start position:0%
+beautiful relationship between the
+ 
+
+ align:start position:0%
+beautiful relationship between the
+heavenly bodies. Now it's balanced by
+
+ align:start position:0%
+heavenly bodies. Now it's balanced by
+ 
+
+ align:start position:0%
+heavenly bodies. Now it's balanced by
+the fact that uh the relationships have
+
+ align:start position:0%
+the fact that uh the relationships have
+ 
+
+ align:start position:0%
+the fact that uh the relationships have
+to be in accordance with observation.
+
+ align:start position:0%
+to be in accordance with observation.
+ 
+
+ align:start position:0%
+to be in accordance with observation.
+And so Kepler struggled with the fact
+
+ align:start position:0%
+And so Kepler struggled with the fact
+ 
+
+ align:start position:0%
+And so Kepler struggled with the fact
+that in fact the heavenly bodies were
+
+ align:start position:0%
+that in fact the heavenly bodies were
+ 
+
+ align:start position:0%
+that in fact the heavenly bodies were
+not did not have uh circular orbits but
+
+ align:start position:0%
+not did not have uh circular orbits but
+ 
+
+ align:start position:0%
+not did not have uh circular orbits but
+were ellip ellipses. But it's kind of
+
+ align:start position:0%
+were ellip ellipses. But it's kind of
+ 
+
+ align:start position:0%
+were ellip ellipses. But it's kind of
+interesting to see that when he did
+
+ align:start position:0%
+interesting to see that when he did
+ 
+
+ align:start position:0%
+interesting to see that when he did
+finally accept that they were ellipses,
+
+ align:start position:0%
+finally accept that they were ellipses,
+ 
+
+ align:start position:0%
+finally accept that they were ellipses,
+there were other beauties that he found
+
+ align:start position:0%
+there were other beauties that he found
+ 
+
+ align:start position:0%
+there were other beauties that he found
+to replace them which is that oh
+
+ align:start position:0%
+to replace them which is that oh
+ 
+
+ align:start position:0%
+to replace them which is that oh
+suddenly the sun is in the center of the
+
+ align:start position:0%
+suddenly the sun is in the center of the
+ 
+
+ align:start position:0%
+suddenly the sun is in the center of the
+the solar system. Uh Einstein kind of
+
+ align:start position:0%
+the solar system. Uh Einstein kind of
+ 
+
+ align:start position:0%
+the solar system. Uh Einstein kind of
+threw this out in some ways because he
+
+ align:start position:0%
+threw this out in some ways because he
+ 
+
+ align:start position:0%
+threw this out in some ways because he
+uh early on accepted uh the metaphysics
+
+ align:start position:0%
+uh early on accepted uh the metaphysics
+ 
+
+ align:start position:0%
+uh early on accepted uh the metaphysics
+of mock as in the uh speed of sound and
+
+ align:start position:0%
+of mock as in the uh speed of sound and
+ 
+
+ align:start position:0%
+of mock as in the uh speed of sound and
+who held that the primary
+
+ align:start position:0%
+who held that the primary
+ 
+
+ align:start position:0%
+who held that the primary
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+I guess origin of knowledge was the
+
+ align:start position:0%
+I guess origin of knowledge was the
+ 
+
+ align:start position:0%
+I guess origin of knowledge was the
+senses and the senses uh told you
+
+ align:start position:0%
+senses and the senses uh told you
+ 
+
+ align:start position:0%
+senses and the senses uh told you
+nothing about what is in fact there. uh
+
+ align:start position:0%
+nothing about what is in fact there. uh
+ 
+
+ align:start position:0%
+nothing about what is in fact there. uh
+rather that all you could all you could
+
+ align:start position:0%
+rather that all you could all you could
+ 
+
+ align:start position:0%
+rather that all you could all you could
+build your your theories off of or your
+
+ align:start position:0%
+build your your theories off of or your
+ 
+
+ align:start position:0%
+build your your theories off of or your
+understanding of the of nature off of
+
+ align:start position:0%
+understanding of the of nature off of
+ 
+
+ align:start position:0%
+understanding of the of nature off of
+was were empirical measurements and that
+
+ align:start position:0%
+was were empirical measurements and that
+ 
+
+ align:start position:0%
+was were empirical measurements and that
+that they were observer centered and
+
+ align:start position:0%
+that they were observer centered and
+ 
+
+ align:start position:0%
+that they were observer centered and
+this fits nicely in with Einstein's
+
+ align:start position:0%
+this fits nicely in with Einstein's
+ 
+
+ align:start position:0%
+this fits nicely in with Einstein's
+theory of relativity because he what
+
+ align:start position:0%
+theory of relativity because he what
+ 
+
+ align:start position:0%
+theory of relativity because he what
+Einstein what the theory depends upon
+
+ align:start position:0%
+Einstein what the theory depends upon
+ 
+
+ align:start position:0%
+Einstein what the theory depends upon
+are the uh observable clocks and
+
+ align:start position:0%
+are the uh observable clocks and
+ 
+
+ align:start position:0%
+are the uh observable clocks and
+observable rulers that are dependent or
+
+ align:start position:0%
+observable rulers that are dependent or
+ 
+
+ align:start position:0%
+observable rulers that are dependent or
+whose measurements change based bas on
+
+ align:start position:0%
+whose measurements change based bas on
+ 
+
+ align:start position:0%
+whose measurements change based bas on
+where they are in space to the observer.
+
+ align:start position:0%
+where they are in space to the observer.
+ 
+
+ align:start position:0%
+where they are in space to the observer.
+And so in this way uh under the notion
+
+ align:start position:0%
+And so in this way uh under the notion
+ 
+
+ align:start position:0%
+And so in this way uh under the notion
+that the observer's measurements are
+
+ align:start position:0%
+that the observer's measurements are
+ 
+
+ align:start position:0%
+that the observer's measurements are
+primary, Einstein undercut the uh source
+
+ align:start position:0%
+primary, Einstein undercut the uh source
+ 
+
+ align:start position:0%
+primary, Einstein undercut the uh source
+of harmony in the universe from one god.
+
+ align:start position:0%
+of harmony in the universe from one god.
+ 
+
+ align:start position:0%
+of harmony in the universe from one god.
+It became observer oriented rather than
+
+ align:start position:0%
+It became observer oriented rather than
+ 
+
+ align:start position:0%
+It became observer oriented rather than
+uh some sort of absolute relationship
+
+ align:start position:0%
+uh some sort of absolute relationship
+ 
+
+ align:start position:0%
+uh some sort of absolute relationship
+between the different objects.
+
+ align:start position:0%
+between the different objects.
+ 
+
+ align:start position:0%
+between the different objects.
+Um so I have a few other examples but
+
+ align:start position:0%
+Um so I have a few other examples but
+ 
+
+ align:start position:0%
+Um so I have a few other examples but
+that's the basic idea in terms of uh how
+
+ align:start position:0%
+that's the basic idea in terms of uh how
+ 
+
+ align:start position:0%
+that's the basic idea in terms of uh how
+your worldview or your metaphysics on
+
+ align:start position:0%
+your worldview or your metaphysics on
+ 
+
+ align:start position:0%
+your worldview or your metaphysics on
+the nature of the universe are in fact
+
+ align:start position:0%
+the nature of the universe are in fact
+ 
+
+ align:start position:0%
+the nature of the universe are in fact
+or are what you express when you create
+
+ align:start position:0%
+or are what you express when you create
+ 
+
+ align:start position:0%
+or are what you express when you create
+a theory. Um when you create a theory
+
+ align:start position:0%
+a theory. Um when you create a theory
+ 
+
+ align:start position:0%
+a theory. Um when you create a theory
+what is the create element of creativity
+
+ align:start position:0%
+what is the create element of creativity
+ 
+
+ align:start position:0%
+what is the create element of creativity
+in this?
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+what makes one theory more creative than
+
+ align:start position:0%
+what makes one theory more creative than
+ 
+
+ align:start position:0%
+what makes one theory more creative than
+another.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+So in his book the structure of
+
+ align:start position:0%
+So in his book the structure of
+ 
+
+ align:start position:0%
+So in his book the structure of
+scientific revolutions draws a
+
+ align:start position:0%
+scientific revolutions draws a
+ 
+
+ align:start position:0%
+scientific revolutions draws a
+distinction between extraordinary and
+
+ align:start position:0%
+distinction between extraordinary and
+ 
+
+ align:start position:0%
+distinction between extraordinary and
+normal science uh where extraordinary
+
+ align:start position:0%
+normal science uh where extraordinary
+ 
+
+ align:start position:0%
+normal science uh where extraordinary
+science creates uh a
+
+ align:start position:0%
+science creates uh a
+ 
+
+ align:start position:0%
+science creates uh a
+sort of new
+
+ align:start position:0%
+sort of new
+ 
+
+ align:start position:0%
+sort of new
+paradigm paradigm. Yeah. uh that is no
+
+ align:start position:0%
+paradigm paradigm. Yeah. uh that is no
+ 
+
+ align:start position:0%
+paradigm paradigm. Yeah. uh that is no
+is not commensurable is not logically
+
+ align:start position:0%
+is not commensurable is not logically
+ 
+
+ align:start position:0%
+is not commensurable is not logically
+connectable perfectly back to the
+
+ align:start position:0%
+connectable perfectly back to the
+ 
+
+ align:start position:0%
+connectable perfectly back to the
+previous paradigm. So going from
+
+ align:start position:0%
+previous paradigm. So going from
+ 
+
+ align:start position:0%
+previous paradigm. So going from
+classical mechanics to quantum mechanics
+
+ align:start position:0%
+classical mechanics to quantum mechanics
+ 
+
+ align:start position:0%
+classical mechanics to quantum mechanics
+would be a paradigm shift and and that
+
+ align:start position:0%
+would be a paradigm shift and and that
+ 
+
+ align:start position:0%
+would be a paradigm shift and and that
+is that is extraordinary science now. So
+
+ align:start position:0%
+is that is extraordinary science now. So
+ 
+
+ align:start position:0%
+is that is extraordinary science now. So
+um so that that so in extraordinary
+
+ align:start position:0%
+um so that that so in extraordinary
+ 
+
+ align:start position:0%
+um so that that so in extraordinary
+science the creativity is exactly the
+
+ align:start position:0%
+science the creativity is exactly the
+ 
+
+ align:start position:0%
+science the creativity is exactly the
+expression of a new metaphysics a new um
+
+ align:start position:0%
+expression of a new metaphysics a new um
+ 
+
+ align:start position:0%
+expression of a new metaphysics a new um
+well a new perspective right and but is
+
+ align:start position:0%
+well a new perspective right and but is
+ 
+
+ align:start position:0%
+well a new perspective right and but is
+that the meaning of creativity or is
+
+ align:start position:0%
+that the meaning of creativity or is
+ 
+
+ align:start position:0%
+that the meaning of creativity or is
+there creativity in normal science so in
+
+ align:start position:0%
+there creativity in normal science so in
+ 
+
+ align:start position:0%
+there creativity in normal science so in
+normal science I think the creativity is
+
+ align:start position:0%
+normal science I think the creativity is
+ 
+
+ align:start position:0%
+normal science I think the creativity is
+different um and I haven't delved into
+
+ align:start position:0%
+different um and I haven't delved into
+ 
+
+ align:start position:0%
+different um and I haven't delved into
+this part as deeply but uh the idea I'm
+
+ align:start position:0%
+this part as deeply but uh the idea I'm
+ 
+
+ align:start position:0%
+this part as deeply but uh the idea I'm
+playing around with is in fact that uh
+
+ align:start position:0%
+playing around with is in fact that uh
+ 
+
+ align:start position:0%
+playing around with is in fact that uh
+the I mean what what calls that
+
+ align:start position:0%
+the I mean what what calls that
+ 
+
+ align:start position:0%
+the I mean what what calls that
+normal science is basically problem
+
+ align:start position:0%
+normal science is basically problem
+ 
+
+ align:start position:0%
+normal science is basically problem
+solving. uh you have some paradigm, you
+
+ align:start position:0%
+solving. uh you have some paradigm, you
+ 
+
+ align:start position:0%
+solving. uh you have some paradigm, you
+have a problem that because you accept
+
+ align:start position:0%
+have a problem that because you accept
+ 
+
+ align:start position:0%
+have a problem that because you accept
+the paradigm, you know must be solvable.
+
+ align:start position:0%
+the paradigm, you know must be solvable.
+ 
+
+ align:start position:0%
+the paradigm, you know must be solvable.
+So therefore, you must solve the problem
+
+ align:start position:0%
+So therefore, you must solve the problem
+ 
+
+ align:start position:0%
+So therefore, you must solve the problem
+and if you don't, it's your failure, not
+
+ align:start position:0%
+and if you don't, it's your failure, not
+ 
+
+ align:start position:0%
+and if you don't, it's your failure, not
+the paradigms. Now, of course, that
+
+ align:start position:0%
+the paradigms. Now, of course, that
+ 
+
+ align:start position:0%
+the paradigms. Now, of course, that
+breaks down when you actually get to the
+
+ align:start position:0%
+breaks down when you actually get to the
+ 
+
+ align:start position:0%
+breaks down when you actually get to the
+point where the paradigm really does
+
+ align:start position:0%
+point where the paradigm really does
+ 
+
+ align:start position:0%
+point where the paradigm really does
+fail. But if you're working within the
+
+ align:start position:0%
+fail. But if you're working within the
+ 
+
+ align:start position:0%
+fail. But if you're working within the
+paradigm, then you must be able to solve
+
+ align:start position:0%
+paradigm, then you must be able to solve
+ 
+
+ align:start position:0%
+paradigm, then you must be able to solve
+the problem. And
+
+ align:start position:0%
+the problem. And
+ 
+
+ align:start position:0%
+the problem. And
+I think the creativity there is to find
+
+ align:start position:0%
+I think the creativity there is to find
+ 
+
+ align:start position:0%
+I think the creativity there is to find
+how the
+
+ align:start position:0%
+how the
+ 
+
+ align:start position:0%
+how the
+structure of the solution fits with the
+
+ align:start position:0%
+structure of the solution fits with the
+ 
+
+ align:start position:0%
+structure of the solution fits with the
+structure of the paradigm. Uh which in
+
+ align:start position:0%
+structure of the paradigm. Uh which in
+ 
+
+ align:start position:0%
+structure of the paradigm. Uh which in
+some in some ways is a a design problem.
+
+ align:start position:0%
+some in some ways is a a design problem.
+ 
+
+ align:start position:0%
+some in some ways is a a design problem.
+Uh you're looking to uh on some level
+
+ align:start position:0%
+Uh you're looking to uh on some level
+ 
+
+ align:start position:0%
+Uh you're looking to uh on some level
+construct consciously and on some level
+
+ align:start position:0%
+construct consciously and on some level
+ 
+
+ align:start position:0%
+construct consciously and on some level
+uh intuitively understand the uh correct
+
+ align:start position:0%
+uh intuitively understand the uh correct
+ 
+
+ align:start position:0%
+uh intuitively understand the uh correct
+design that fits the given structure of
+
+ align:start position:0%
+design that fits the given structure of
+ 
+
+ align:start position:0%
+design that fits the given structure of
+the theory. Um
+
+ align:start position:0%
+the theory. Um
+ 
+
+ align:start position:0%
+the theory. Um
+what I would sort of throw out there
+
+ align:start position:0%
+what I would sort of throw out there
+ 
+
+ align:start position:0%
+what I would sort of throw out there
+which may be nonsense but
+
+ align:start position:0%
+which may be nonsense but
+ 
+
+ align:start position:0%
+which may be nonsense but
+um is that what is beautiful about
+
+ align:start position:0%
+um is that what is beautiful about
+ 
+
+ align:start position:0%
+um is that what is beautiful about
+problem solving is exactly how it fits
+
+ align:start position:0%
+problem solving is exactly how it fits
+ 
+
+ align:start position:0%
+problem solving is exactly how it fits
+the metaphysics of the paradigm. So that
+
+ align:start position:0%
+the metaphysics of the paradigm. So that
+ 
+
+ align:start position:0%
+the metaphysics of the paradigm. So that
+if it's an expression of the basic
+
+ align:start position:0%
+if it's an expression of the basic
+ 
+
+ align:start position:0%
+if it's an expression of the basic
+perspectives such as uh God is the
+
+ align:start position:0%
+perspectives such as uh God is the
+ 
+
+ align:start position:0%
+perspectives such as uh God is the
+origin of harmony in the heavenly bodies
+
+ align:start position:0%
+origin of harmony in the heavenly bodies
+ 
+
+ align:start position:0%
+origin of harmony in the heavenly bodies
+then that is a beautiful solution in
+
+ align:start position:0%
+then that is a beautiful solution in
+ 
+
+ align:start position:0%
+then that is a beautiful solution in
+science.
+
+ align:start position:0%
+science.
+ 
+
+ align:start position:0%
+science.
+Now that may not be the the same uh
+
+ align:start position:0%
+Now that may not be the the same uh
+ 
+
+ align:start position:0%
+Now that may not be the the same uh
+aesthetic pleasure or beauty that we
+
+ align:start position:0%
+aesthetic pleasure or beauty that we
+ 
+
+ align:start position:0%
+aesthetic pleasure or beauty that we
+brought up earlier in terms of doing lab
+
+ align:start position:0%
+brought up earlier in terms of doing lab
+ 
+
+ align:start position:0%
+brought up earlier in terms of doing lab
+work but in terms of a theoretical uh
+
+ align:start position:0%
+work but in terms of a theoretical uh
+ 
+
+ align:start position:0%
+work but in terms of a theoretical uh
+origin that would be
+
+ align:start position:0%
+origin that would be
+ 
+
+ align:start position:0%
+origin that would be
+a possible explanation for what is
+
+ align:start position:0%
+a possible explanation for what is
+ 
+
+ align:start position:0%
+a possible explanation for what is
+beautiful in science.
+
+ align:start position:0%
+beautiful in science.
+ 
+
+ align:start position:0%
+beautiful in science.
+You can think it's totally nonsense.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+You look like you're thinking about
+
+ align:start position:0%
+You look like you're thinking about
+ 
+
+ align:start position:0%
+You look like you're thinking about
+something. Is that true? No. Okay.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Should we go on to another paper?
+
+ align:start position:0%
+Should we go on to another paper?
+ 
+
+ align:start position:0%
+Should we go on to another paper?
+Another This This is the basis of your
+
+ align:start position:0%
+Another This This is the basis of your
+ 
+
+ align:start position:0%
+Another This This is the basis of your
+paper, right? Yeah. My paper is going to
+
+ align:start position:0%
+paper, right? Yeah. My paper is going to
+ 
+
+ align:start position:0%
+paper, right? Yeah. My paper is going to
+be a subset of that because How far is
+
+ align:start position:0%
+be a subset of that because How far is
+ 
+
+ align:start position:0%
+be a subset of that because How far is
+it to being being complete? Not far
+
+ align:start position:0%
+it to being being complete? Not far
+ 
+
+ align:start position:0%
+it to being being complete? Not far
+enough.
+
+ align:start position:0%
+enough.
+ 
+
+ align:start position:0%
+enough.
+It It's too large. I'm going to take a
+
+ align:start position:0%
+It It's too large. I'm going to take a
+ 
+
+ align:start position:0%
+It It's too large. I'm going to take a
+small part of it. Well, we'll we'll talk
+
+ align:start position:0%
+small part of it. Well, we'll we'll talk
+ 
+
+ align:start position:0%
+small part of it. Well, we'll we'll talk
+about that later on about when the
+
+ align:start position:0%
+about that later on about when the
+ 
+
+ align:start position:0%
+about that later on about when the
+papers are going to be handed in and
+
+ align:start position:0%
+papers are going to be handed in and
+ 
+
+ align:start position:0%
+papers are going to be handed in and
+just what state they're in. Um,
+
+ align:start position:0%
+just what state they're in. Um,
+ 
+
+ align:start position:0%
+just what state they're in. Um,
+which way should we go? Eric, I mean,
+
+ align:start position:0%
+which way should we go? Eric, I mean,
+ 
+
+ align:start position:0%
+which way should we go? Eric, I mean,
+um, Alec, are you ready? Sure, why not?
+
+ align:start position:0%
+um, Alec, are you ready? Sure, why not?
+ 
+
+ align:start position:0%
+um, Alec, are you ready? Sure, why not?
+Uh, okay. So, I'm I'm kind of doing uh
+
+ align:start position:0%
+Uh, okay. So, I'm I'm kind of doing uh
+ 
+
+ align:start position:0%
+Uh, okay. So, I'm I'm kind of doing uh
+kind of like what I talked about last
+
+ align:start position:0%
+kind of like what I talked about last
+ 
+
+ align:start position:0%
+kind of like what I talked about last
+week where um I'm interested in looking
+
+ align:start position:0%
+week where um I'm interested in looking
+ 
+
+ align:start position:0%
+week where um I'm interested in looking
+at uh the idea of free will and uh
+
+ align:start position:0%
+at uh the idea of free will and uh
+ 
+
+ align:start position:0%
+at uh the idea of free will and uh
+determinism. And actually I guess we
+
+ align:start position:0%
+determinism. And actually I guess we
+ 
+
+ align:start position:0%
+determinism. And actually I guess we
+talked about this briefly earlier uh
+
+ align:start position:0%
+talked about this briefly earlier uh
+ 
+
+ align:start position:0%
+talked about this briefly earlier uh
+today. Um and what the implications are
+
+ align:start position:0%
+today. Um and what the implications are
+ 
+
+ align:start position:0%
+today. Um and what the implications are
+uh for creativity where if well for
+
+ align:start position:0%
+uh for creativity where if well for
+ 
+
+ align:start position:0%
+uh for creativity where if well for
+example if you look at it in one way
+
+ align:start position:0%
+example if you look at it in one way
+ 
+
+ align:start position:0%
+example if you look at it in one way
+from in the sort of uh uh mind body
+
+ align:start position:0%
+from in the sort of uh uh mind body
+ 
+
+ align:start position:0%
+from in the sort of uh uh mind body
+problem. If creativity is something that
+
+ align:start position:0%
+problem. If creativity is something that
+ 
+
+ align:start position:0%
+problem. If creativity is something that
+arises out of mind and mind is something
+
+ align:start position:0%
+arises out of mind and mind is something
+ 
+
+ align:start position:0%
+arises out of mind and mind is something
+that arises out of the brain and the
+
+ align:start position:0%
+that arises out of the brain and the
+ 
+
+ align:start position:0%
+that arises out of the brain and the
+brain is governed by physical laws um in
+
+ align:start position:0%
+brain is governed by physical laws um in
+ 
+
+ align:start position:0%
+brain is governed by physical laws um in
+some deterministic
+
+ align:start position:0%
+some deterministic
+ 
+
+ align:start position:0%
+some deterministic
+nature of or of some deterministic
+
+ align:start position:0%
+nature of or of some deterministic
+ 
+
+ align:start position:0%
+nature of or of some deterministic
+nature rather uh then is creativity
+
+ align:start position:0%
+nature rather uh then is creativity
+ 
+
+ align:start position:0%
+nature rather uh then is creativity
+itself you know deterministic i.e. If
+
+ align:start position:0%
+itself you know deterministic i.e. If
+ 
+
+ align:start position:0%
+itself you know deterministic i.e. If
+you could know everything uh about the
+
+ align:start position:0%
+you could know everything uh about the
+ 
+
+ align:start position:0%
+you could know everything uh about the
+you know all the states of all the
+
+ align:start position:0%
+you know all the states of all the
+ 
+
+ align:start position:0%
+you know all the states of all the
+particles and everything in the early
+
+ align:start position:0%
+particles and everything in the early
+ 
+
+ align:start position:0%
+particles and everything in the early
+universe and what they were doing at any
+
+ align:start position:0%
+universe and what they were doing at any
+ 
+
+ align:start position:0%
+universe and what they were doing at any
+given moment you would be able to sort
+
+ align:start position:0%
+given moment you would be able to sort
+ 
+
+ align:start position:0%
+given moment you would be able to sort
+of uh calculate out all creativity that
+
+ align:start position:0%
+of uh calculate out all creativity that
+ 
+
+ align:start position:0%
+of uh calculate out all creativity that
+would happen um from that point forward
+
+ align:start position:0%
+would happen um from that point forward
+ 
+
+ align:start position:0%
+would happen um from that point forward
+or sort of back calculate anything that
+
+ align:start position:0%
+or sort of back calculate anything that
+ 
+
+ align:start position:0%
+or sort of back calculate anything that
+had happened before that. um is
+
+ align:start position:0%
+had happened before that. um is
+ 
+
+ align:start position:0%
+had happened before that. um is
+creativity truly creative or is it
+
+ align:start position:0%
+creativity truly creative or is it
+ 
+
+ align:start position:0%
+creativity truly creative or is it
+simply something that uh
+
+ align:start position:0%
+simply something that uh
+ 
+
+ align:start position:0%
+simply something that uh
+follows from physical laws and it's it's
+
+ align:start position:0%
+follows from physical laws and it's it's
+ 
+
+ align:start position:0%
+follows from physical laws and it's it's
+its sort of independent nature is an
+
+ align:start position:0%
+its sort of independent nature is an
+ 
+
+ align:start position:0%
+its sort of independent nature is an
+illusion kind of thing. So um there is
+
+ align:start position:0%
+illusion kind of thing. So um there is
+ 
+
+ align:start position:0%
+illusion kind of thing. So um there is
+for you the question it involves a
+
+ align:start position:0%
+for you the question it involves a
+ 
+
+ align:start position:0%
+for you the question it involves a
+paradox maybe it's a paradox that um if
+
+ align:start position:0%
+paradox maybe it's a paradox that um if
+ 
+
+ align:start position:0%
+paradox maybe it's a paradox that um if
+something is really creative then it's
+
+ align:start position:0%
+something is really creative then it's
+ 
+
+ align:start position:0%
+something is really creative then it's
+not creative because it carries out
+
+ align:start position:0%
+not creative because it carries out
+ 
+
+ align:start position:0%
+not creative because it carries out
+those laws. Right. Right. So the
+
+ align:start position:0%
+those laws. Right. Right. So the
+ 
+
+ align:start position:0%
+those laws. Right. Right. So the
+question is is there anything that is
+
+ align:start position:0%
+question is is there anything that is
+ 
+
+ align:start position:0%
+question is is there anything that is
+truly paradoxical? That's your
+
+ align:start position:0%
+truly paradoxical? That's your
+ 
+
+ align:start position:0%
+truly paradoxical? That's your
+fundamental question. Am I right? Uh
+
+ align:start position:0%
+fundamental question. Am I right? Uh
+ 
+
+ align:start position:0%
+fundamental question. Am I right? Uh
+how do you mean in terms of what you
+
+ align:start position:0%
+how do you mean in terms of what you
+ 
+
+ align:start position:0%
+how do you mean in terms of what you
+were just now saying? I wasn't adding
+
+ align:start position:0%
+were just now saying? I wasn't adding
+ 
+
+ align:start position:0%
+were just now saying? I wasn't adding
+anything. I was trying to reformulate
+
+ align:start position:0%
+anything. I was trying to reformulate
+ 
+
+ align:start position:0%
+anything. I was trying to reformulate
+it. Uh where does where does where's the
+
+ align:start position:0%
+it. Uh where does where does where's the
+ 
+
+ align:start position:0%
+it. Uh where does where does where's the
+paradoxical come in? That to be creative
+
+ align:start position:0%
+paradoxical come in? That to be creative
+ 
+
+ align:start position:0%
+paradoxical come in? That to be creative
+seems to be not derivative merely from
+
+ align:start position:0%
+seems to be not derivative merely from
+ 
+
+ align:start position:0%
+seems to be not derivative merely from
+pre-established laws. then we would say,
+
+ align:start position:0%
+pre-established laws. then we would say,
+ 
+
+ align:start position:0%
+pre-established laws. then we would say,
+"Oh, no. It's not create it's not really
+
+ align:start position:0%
+"Oh, no. It's not create it's not really
+ 
+
+ align:start position:0%
+"Oh, no. It's not create it's not really
+creative because it's been determined."
+
+ align:start position:0%
+creative because it's been determined."
+ 
+
+ align:start position:0%
+creative because it's been determined."
+Well, no, not not so much in that sense.
+
+ align:start position:0%
+Well, no, not not so much in that sense.
+ 
+
+ align:start position:0%
+Well, no, not not so much in that sense.
+I mean, it would it would require a
+
+ align:start position:0%
+I mean, it would it would require a
+ 
+
+ align:start position:0%
+I mean, it would it would require a
+little bit of a redefinition of the
+
+ align:start position:0%
+little bit of a redefinition of the
+ 
+
+ align:start position:0%
+little bit of a redefinition of the
+understanding of creativity, but just
+
+ align:start position:0%
+understanding of creativity, but just
+ 
+
+ align:start position:0%
+understanding of creativity, but just
+just because, you know, creativity
+
+ align:start position:0%
+just because, you know, creativity
+ 
+
+ align:start position:0%
+just because, you know, creativity
+doesn't actually come out of some
+
+ align:start position:0%
+doesn't actually come out of some
+ 
+
+ align:start position:0%
+doesn't actually come out of some
+something external to the physical
+
+ align:start position:0%
+something external to the physical
+ 
+
+ align:start position:0%
+something external to the physical
+world. Doesn't mean that it's anything
+
+ align:start position:0%
+world. Doesn't mean that it's anything
+ 
+
+ align:start position:0%
+world. Doesn't mean that it's anything
+different. It's just, you know,
+
+ align:start position:0%
+different. It's just, you know,
+ 
+
+ align:start position:0%
+different. It's just, you know,
+understanding that at its most
+
+ align:start position:0%
+understanding that at its most
+ 
+
+ align:start position:0%
+understanding that at its most
+fundamental level, it's that. Um now one
+
+ align:start position:0%
+fundamental level, it's that. Um now one
+ 
+
+ align:start position:0%
+fundamental level, it's that. Um now one
+of the things I'm I'm thinking along
+
+ align:start position:0%
+of the things I'm I'm thinking along
+ 
+
+ align:start position:0%
+of the things I'm I'm thinking along
+these lines is h how it has to do with
+
+ align:start position:0%
+these lines is h how it has to do with
+ 
+
+ align:start position:0%
+these lines is h how it has to do with
+free will um where the two would sort of
+
+ align:start position:0%
+free will um where the two would sort of
+ 
+
+ align:start position:0%
+free will um where the two would sort of
+seem to be linked um in that if
+
+ align:start position:0%
+seem to be linked um in that if
+ 
+
+ align:start position:0%
+seem to be linked um in that if
+creativity is truly creative in in the
+
+ align:start position:0%
+creativity is truly creative in in the
+ 
+
+ align:start position:0%
+creativity is truly creative in in the
+original sense then there's some element
+
+ align:start position:0%
+original sense then there's some element
+ 
+
+ align:start position:0%
+original sense then there's some element
+of free will involved um if there is no
+
+ align:start position:0%
+of free will involved um if there is no
+ 
+
+ align:start position:0%
+of free will involved um if there is no
+free will there is no you know
+
+ align:start position:0%
+free will there is no you know
+ 
+
+ align:start position:0%
+free will there is no you know
+creativity in that sense and the
+
+ align:start position:0%
+creativity in that sense and the
+ 
+
+ align:start position:0%
+creativity in that sense and the
+interesting thing about it is that if
+
+ align:start position:0%
+interesting thing about it is that if
+ 
+
+ align:start position:0%
+interesting thing about it is that if
+you have a totally deter deterministic
+
+ align:start position:0%
+you have a totally deter deterministic
+ 
+
+ align:start position:0%
+you have a totally deter deterministic
+universe and uh and again this is I
+
+ align:start position:0%
+universe and uh and again this is I
+ 
+
+ align:start position:0%
+universe and uh and again this is I
+briefly mentioned this last week. Uh if
+
+ align:start position:0%
+briefly mentioned this last week. Uh if
+ 
+
+ align:start position:0%
+briefly mentioned this last week. Uh if
+you have a totally deterministic
+
+ align:start position:0%
+you have a totally deterministic
+ 
+
+ align:start position:0%
+you have a totally deterministic
+universe and you know the human mind is
+
+ align:start position:0%
+universe and you know the human mind is
+ 
+
+ align:start position:0%
+universe and you know the human mind is
+simply just this sort of big complex
+
+ align:start position:0%
+simply just this sort of big complex
+ 
+
+ align:start position:0%
+simply just this sort of big complex
+calculator uh where if you know what's
+
+ align:start position:0%
+calculator uh where if you know what's
+ 
+
+ align:start position:0%
+calculator uh where if you know what's
+going on with all the elements inside
+
+ align:start position:0%
+going on with all the elements inside
+ 
+
+ align:start position:0%
+going on with all the elements inside
+it, you can figure out what it's going
+
+ align:start position:0%
+it, you can figure out what it's going
+ 
+
+ align:start position:0%
+it, you can figure out what it's going
+to do. Um you know does that mean that
+
+ align:start position:0%
+to do. Um you know does that mean that
+ 
+
+ align:start position:0%
+to do. Um you know does that mean that
+there's no free will? Uh but the trick
+
+ align:start position:0%
+there's no free will? Uh but the trick
+ 
+
+ align:start position:0%
+there's no free will? Uh but the trick
+to that is is that uh such a system can
+
+ align:start position:0%
+to that is is that uh such a system can
+ 
+
+ align:start position:0%
+to that is is that uh such a system can
+have a set of beliefs independent of
+
+ align:start position:0%
+have a set of beliefs independent of
+ 
+
+ align:start position:0%
+have a set of beliefs independent of
+free will. A system can have a belief
+
+ align:start position:0%
+free will. A system can have a belief
+ 
+
+ align:start position:0%
+free will. A system can have a belief
+about things. uh for example a
+
+ align:start position:0%
+about things. uh for example a
+ 
+
+ align:start position:0%
+about things. uh for example a
+thermostat can believe that the
+
+ align:start position:0%
+thermostat can believe that the
+ 
+
+ align:start position:0%
+thermostat can believe that the
+temperature in the room is something it
+
+ align:start position:0%
+temperature in the room is something it
+ 
+
+ align:start position:0%
+temperature in the room is something it
+has nothing to do with free will and if
+
+ align:start position:0%
+has nothing to do with free will and if
+ 
+
+ align:start position:0%
+has nothing to do with free will and if
+the the system that is the human brain
+
+ align:start position:0%
+the the system that is the human brain
+ 
+
+ align:start position:0%
+the the system that is the human brain
+or the human mind um if that system
+
+ align:start position:0%
+or the human mind um if that system
+ 
+
+ align:start position:0%
+or the human mind um if that system
+actually itself has the belief in free
+
+ align:start position:0%
+actually itself has the belief in free
+ 
+
+ align:start position:0%
+actually itself has the belief in free
+will it has the belief that it has the
+
+ align:start position:0%
+will it has the belief that it has the
+ 
+
+ align:start position:0%
+will it has the belief that it has the
+capacity to make these decisions that
+
+ align:start position:0%
+capacity to make these decisions that
+ 
+
+ align:start position:0%
+capacity to make these decisions that
+actually changes the calculus that
+
+ align:start position:0%
+actually changes the calculus that
+ 
+
+ align:start position:0%
+actually changes the calculus that
+occurs um uh when that system you know
+
+ align:start position:0%
+occurs um uh when that system you know
+ 
+
+ align:start position:0%
+occurs um uh when that system you know
+calculates what to do next or decides
+
+ align:start position:0%
+calculates what to do next or decides
+ 
+
+ align:start position:0%
+calculates what to do next or decides
+what to do um depending on whether or
+
+ align:start position:0%
+what to do um depending on whether or
+ 
+
+ align:start position:0%
+what to do um depending on whether or
+not it believes that it has the capacity
+
+ align:start position:0%
+not it believes that it has the capacity
+ 
+
+ align:start position:0%
+not it believes that it has the capacity
+for free Well, but aren't these two
+
+ align:start position:0%
+for free Well, but aren't these two
+ 
+
+ align:start position:0%
+for free Well, but aren't these two
+different questions? One about the
+
+ align:start position:0%
+different questions? One about the
+ 
+
+ align:start position:0%
+different questions? One about the
+nature of creativity and second the
+
+ align:start position:0%
+nature of creativity and second the
+ 
+
+ align:start position:0%
+nature of creativity and second the
+question of whether there is free will.
+
+ align:start position:0%
+question of whether there is free will.
+ 
+
+ align:start position:0%
+question of whether there is free will.
+Uh because even if there is free will,
+
+ align:start position:0%
+Uh because even if there is free will,
+ 
+
+ align:start position:0%
+Uh because even if there is free will,
+there might be a world in which there is
+
+ align:start position:0%
+there might be a world in which there is
+ 
+
+ align:start position:0%
+there might be a world in which there is
+no creativity. No real that's called
+
+ align:start position:0%
+no creativity. No real that's called
+ 
+
+ align:start position:0%
+no creativity. No real that's called
+true creativity. That's true. But and
+
+ align:start position:0%
+true creativity. That's true. But and
+ 
+
+ align:start position:0%
+true creativity. That's true. But and
+second, if even if the world is
+
+ align:start position:0%
+second, if even if the world is
+ 
+
+ align:start position:0%
+second, if even if the world is
+determined, we could say in in some
+
+ align:start position:0%
+determined, we could say in in some
+ 
+
+ align:start position:0%
+determined, we could say in in some
+areas of determin determination there is
+
+ align:start position:0%
+areas of determin determination there is
+ 
+
+ align:start position:0%
+areas of determin determination there is
+creativity and others not. So maybe the
+
+ align:start position:0%
+creativity and others not. So maybe the
+ 
+
+ align:start position:0%
+creativity and others not. So maybe the
+two problems are but I think unrelated I
+
+ align:start position:0%
+two problems are but I think unrelated I
+ 
+
+ align:start position:0%
+two problems are but I think unrelated I
+mean the way I see it I think free will
+
+ align:start position:0%
+mean the way I see it I think free will
+ 
+
+ align:start position:0%
+mean the way I see it I think free will
+is a necessary condition for I guess
+
+ align:start position:0%
+is a necessary condition for I guess
+ 
+
+ align:start position:0%
+is a necessary condition for I guess
+what we'll call true creativity in an
+
+ align:start position:0%
+what we'll call true creativity in an
+ 
+
+ align:start position:0%
+what we'll call true creativity in an
+original sense where if there is no free
+
+ align:start position:0%
+original sense where if there is no free
+ 
+
+ align:start position:0%
+original sense where if there is no free
+will then you know what would the
+
+ align:start position:0%
+will then you know what would the
+ 
+
+ align:start position:0%
+will then you know what would the
+creativity be coming out of um if if you
+
+ align:start position:0%
+creativity be coming out of um if if you
+ 
+
+ align:start position:0%
+creativity be coming out of um if if you
+have this true creativity wherein it is
+
+ align:start position:0%
+have this true creativity wherein it is
+ 
+
+ align:start position:0%
+have this true creativity wherein it is
+something coming in external uh from
+
+ align:start position:0%
+something coming in external uh from
+ 
+
+ align:start position:0%
+something coming in external uh from
+from external to the system then that in
+
+ align:start position:0%
+from external to the system then that in
+ 
+
+ align:start position:0%
+from external to the system then that in
+itself could be considered a form of
+
+ align:start position:0%
+itself could be considered a form of
+ 
+
+ align:start position:0%
+itself could be considered a form of
+free will and so if there is no free
+
+ align:start position:0%
+free will and so if there is no free
+ 
+
+ align:start position:0%
+free will and so if there is no free
+will there can be no true creativity in
+
+ align:start position:0%
+will there can be no true creativity in
+ 
+
+ align:start position:0%
+will there can be no true creativity in
+that but that's because of the
+
+ align:start position:0%
+that but that's because of the
+ 
+
+ align:start position:0%
+that but that's because of the
+definition you're given giving to the
+
+ align:start position:0%
+definition you're given giving to the
+ 
+
+ align:start position:0%
+definition you're given giving to the
+word true in ordinary language someone
+
+ align:start position:0%
+word true in ordinary language someone
+ 
+
+ align:start position:0%
+word true in ordinary language someone
+might say of of Picasso he really was
+
+ align:start position:0%
+might say of of Picasso he really was
+ 
+
+ align:start position:0%
+might say of of Picasso he really was
+very creative look at all of these
+
+ align:start position:0%
+very creative look at all of these
+ 
+
+ align:start position:0%
+very creative look at all of these
+different stages and different works
+
+ align:start position:0%
+different stages and different works
+ 
+
+ align:start position:0%
+different stages and different works
+that he produced um and um this that and
+
+ align:start position:0%
+that he produced um and um this that and
+ 
+
+ align:start position:0%
+that he produced um and um this that and
+someone would say yes that really is an
+
+ align:start position:0%
+someone would say yes that really is an
+ 
+
+ align:start position:0%
+someone would say yes that really is an
+example of creativity but it would apply
+
+ align:start position:0%
+example of creativity but it would apply
+ 
+
+ align:start position:0%
+example of creativity but it would apply
+even whether the world is free or
+
+ align:start position:0%
+even whether the world is free or
+ 
+
+ align:start position:0%
+even whether the world is free or
+determined that seems to be a
+
+ align:start position:0%
+determined that seems to be a
+ 
+
+ align:start position:0%
+determined that seems to be a
+metaphysical question of a different
+
+ align:start position:0%
+metaphysical question of a different
+ 
+
+ align:start position:0%
+metaphysical question of a different
+sort
+
+ align:start position:0%
+sort
+ 
+
+ align:start position:0%
+sort
+Unless you defy true creativity as not
+
+ align:start position:0%
+Unless you defy true creativity as not
+ 
+
+ align:start position:0%
+Unless you defy true creativity as not
+being deterministic.
+
+ align:start position:0%
+being deterministic.
+ 
+
+ align:start position:0%
+being deterministic.
+Um, well, yeah. I mean, I mean, that's
+
+ align:start position:0%
+Um, well, yeah. I mean, I mean, that's
+ 
+
+ align:start position:0%
+Um, well, yeah. I mean, I mean, that's
+that's sort of what I'm getting at is
+
+ align:start position:0%
+that's sort of what I'm getting at is
+ 
+
+ align:start position:0%
+that's sort of what I'm getting at is
+trying to explore, you know, I mean, I
+
+ align:start position:0%
+trying to explore, you know, I mean, I
+ 
+
+ align:start position:0%
+trying to explore, you know, I mean, I
+don't I don't think this this
+
+ align:start position:0%
+don't I don't think this this
+ 
+
+ align:start position:0%
+don't I don't think this this
+necessarily
+
+ align:start position:0%
+necessarily
+ 
+
+ align:start position:0%
+necessarily
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+it doesn't, you know, it doesn't change
+
+ align:start position:0%
+it doesn't, you know, it doesn't change
+ 
+
+ align:start position:0%
+it doesn't, you know, it doesn't change
+the fact that we'll look at something
+
+ align:start position:0%
+the fact that we'll look at something
+ 
+
+ align:start position:0%
+the fact that we'll look at something
+that Picasso did or whatever and say,
+
+ align:start position:0%
+that Picasso did or whatever and say,
+ 
+
+ align:start position:0%
+that Picasso did or whatever and say,
+"Yes, that's creative." But then the
+
+ align:start position:0%
+"Yes, that's creative." But then the
+ 
+
+ align:start position:0%
+"Yes, that's creative." But then the
+question is uh is that something that
+
+ align:start position:0%
+question is uh is that something that
+ 
+
+ align:start position:0%
+question is uh is that something that
+simply arose because of the physical
+
+ align:start position:0%
+simply arose because of the physical
+ 
+
+ align:start position:0%
+simply arose because of the physical
+nature of his brain at that time in that
+
+ align:start position:0%
+nature of his brain at that time in that
+ 
+
+ align:start position:0%
+nature of his brain at that time in that
+environment or is it did it come from
+
+ align:start position:0%
+environment or is it did it come from
+ 
+
+ align:start position:0%
+environment or is it did it come from
+something external to the whole system?
+
+ align:start position:0%
+something external to the whole system?
+ 
+
+ align:start position:0%
+something external to the whole system?
+Um, and I think I think again though
+
+ align:start position:0%
+Um, and I think I think again though
+ 
+
+ align:start position:0%
+Um, and I think I think again though
+that uh there and I I haven't fully
+
+ align:start position:0%
+that uh there and I I haven't fully
+ 
+
+ align:start position:0%
+that uh there and I I haven't fully
+worked out this part of my argument yet,
+
+ align:start position:0%
+worked out this part of my argument yet,
+ 
+
+ align:start position:0%
+worked out this part of my argument yet,
+but um as I argued for the thing of free
+
+ align:start position:0%
+but um as I argued for the thing of free
+ 
+
+ align:start position:0%
+but um as I argued for the thing of free
+will where if if the system of the human
+
+ align:start position:0%
+will where if if the system of the human
+ 
+
+ align:start position:0%
+will where if if the system of the human
+brain uh or mind does in fact believe
+
+ align:start position:0%
+brain uh or mind does in fact believe
+ 
+
+ align:start position:0%
+brain uh or mind does in fact believe
+that it has free will that actually
+
+ align:start position:0%
+that it has free will that actually
+ 
+
+ align:start position:0%
+that it has free will that actually
+changes what it will do so that it will
+
+ align:start position:0%
+changes what it will do so that it will
+ 
+
+ align:start position:0%
+changes what it will do so that it will
+behave as though it has uh some sort of
+
+ align:start position:0%
+behave as though it has uh some sort of
+ 
+
+ align:start position:0%
+behave as though it has uh some sort of
+free will. I think a similar argument
+
+ align:start position:0%
+free will. I think a similar argument
+ 
+
+ align:start position:0%
+free will. I think a similar argument
+may apply to creativity where if uh
+
+ align:start position:0%
+may apply to creativity where if uh
+ 
+
+ align:start position:0%
+may apply to creativity where if uh
+someone believes if if if if one of the
+
+ align:start position:0%
+someone believes if if if if one of the
+ 
+
+ align:start position:0%
+someone believes if if if if one of the
+if if a brain or system believes it that
+
+ align:start position:0%
+if if a brain or system believes it that
+ 
+
+ align:start position:0%
+if if a brain or system believes it that
+it is creative that it has capacity for
+
+ align:start position:0%
+it is creative that it has capacity for
+ 
+
+ align:start position:0%
+it is creative that it has capacity for
+creativity that that actually changes um
+
+ align:start position:0%
+creativity that that actually changes um
+ 
+
+ align:start position:0%
+creativity that that actually changes um
+what that system will produce and you
+
+ align:start position:0%
+what that system will produce and you
+ 
+
+ align:start position:0%
+what that system will produce and you
+know therein sort of paradoxically
+
+ align:start position:0%
+know therein sort of paradoxically
+ 
+
+ align:start position:0%
+know therein sort of paradoxically
+creates uh the creative process out of
+
+ align:start position:0%
+creates uh the creative process out of
+ 
+
+ align:start position:0%
+creates uh the creative process out of
+that. But somebody might believe that he
+
+ align:start position:0%
+that. But somebody might believe that he
+ 
+
+ align:start position:0%
+that. But somebody might believe that he
+has no free will and yet go on and be
+
+ align:start position:0%
+has no free will and yet go on and be
+ 
+
+ align:start position:0%
+has no free will and yet go on and be
+very creative. What would you say to
+
+ align:start position:0%
+very creative. What would you say to
+ 
+
+ align:start position:0%
+very creative. What would you say to
+him? Oh, you're deliluding yourself
+
+ align:start position:0%
+him? Oh, you're deliluding yourself
+ 
+
+ align:start position:0%
+him? Oh, you're deliluding yourself
+because uh you're contradicting yourself
+
+ align:start position:0%
+because uh you're contradicting yourself
+ 
+
+ align:start position:0%
+because uh you're contradicting yourself
+because if there is you have no free
+
+ align:start position:0%
+because if there is you have no free
+ 
+
+ align:start position:0%
+because if there is you have no free
+will, then how can you be creative?
+
+ align:start position:0%
+will, then how can you be creative?
+ 
+
+ align:start position:0%
+will, then how can you be creative?
+You're just doing things that come out
+
+ align:start position:0%
+You're just doing things that come out
+ 
+
+ align:start position:0%
+You're just doing things that come out
+of you. But every to the rest of us
+
+ align:start position:0%
+of you. But every to the rest of us
+ 
+
+ align:start position:0%
+of you. But every to the rest of us
+there these astonishing things would be
+
+ align:start position:0%
+there these astonishing things would be
+ 
+
+ align:start position:0%
+there these astonishing things would be
+what we mean by creativity. Yes. But
+
+ align:start position:0%
+what we mean by creativity. Yes. But
+ 
+
+ align:start position:0%
+what we mean by creativity. Yes. But
+those those predetermined. Yeah. They
+
+ align:start position:0%
+those those predetermined. Yeah. They
+ 
+
+ align:start position:0%
+those those predetermined. Yeah. They
+were all predetermined is what the
+
+ align:start position:0%
+were all predetermined is what the
+ 
+
+ align:start position:0%
+were all predetermined is what the
+argument would be. If if you know if
+
+ align:start position:0%
+argument would be. If if you know if
+ 
+
+ align:start position:0%
+argument would be. If if you know if
+this free will if this this source of uh
+
+ align:start position:0%
+this free will if this this source of uh
+ 
+
+ align:start position:0%
+this free will if this this source of uh
+mental things external to physical
+
+ align:start position:0%
+mental things external to physical
+ 
+
+ align:start position:0%
+mental things external to physical
+reality exists um that's one thing. If
+
+ align:start position:0%
+reality exists um that's one thing. If
+ 
+
+ align:start position:0%
+reality exists um that's one thing. If
+it doesn't exist then all of these
+
+ align:start position:0%
+it doesn't exist then all of these
+ 
+
+ align:start position:0%
+it doesn't exist then all of these
+things uh follow from physical laws. Uh
+
+ align:start position:0%
+things uh follow from physical laws. Uh
+ 
+
+ align:start position:0%
+things uh follow from physical laws. Uh
+unless you don't necessarily believe in
+
+ align:start position:0%
+unless you don't necessarily believe in
+ 
+
+ align:start position:0%
+unless you don't necessarily believe in
+a deterministic universe which is a bit
+
+ align:start position:0%
+a deterministic universe which is a bit
+ 
+
+ align:start position:0%
+a deterministic universe which is a bit
+more of a problem for physics. Um,
+
+ align:start position:0%
+more of a problem for physics. Um,
+ 
+
+ align:start position:0%
+more of a problem for physics. Um,
+quantum mechanics does open the door to
+
+ align:start position:0%
+quantum mechanics does open the door to
+ 
+
+ align:start position:0%
+quantum mechanics does open the door to
+possibility of a universe that's not
+
+ align:start position:0%
+possibility of a universe that's not
+ 
+
+ align:start position:0%
+possibility of a universe that's not
+deterministic. Um, but you know, again,
+
+ align:start position:0%
+deterministic. Um, but you know, again,
+ 
+
+ align:start position:0%
+deterministic. Um, but you know, again,
+that's sort of a bit of a physical
+
+ align:start position:0%
+that's sort of a bit of a physical
+ 
+
+ align:start position:0%
+that's sort of a bit of a physical
+question. Could we take a break at this
+
+ align:start position:0%
+question. Could we take a break at this
+ 
+
+ align:start position:0%
+question. Could we take a break at this
+point? I'd like to continue with Eric
+
+ align:start position:0%
+point? I'd like to continue with Eric
+ 
+
+ align:start position:0%
+point? I'd like to continue with Eric
+and the rest of you. Now, we've got one
+
+ align:start position:0%
+and the rest of you. Now, we've got one
+ 
+
+ align:start position:0%
+and the rest of you. Now, we've got one
+and a half papers discussed and I do
+
+ align:start position:0%
+and a half papers discussed and I do
+ 
+
+ align:start position:0%
+and a half papers discussed and I do
+want to hear from all of you, but could
+
+ align:start position:0%
+want to hear from all of you, but could
+ 
+
+ align:start position:0%
+want to hear from all of you, but could
+we take a short break, please?
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+All right. Um, why don't you start?
+
+ align:start position:0%
+All right. Um, why don't you start?
+ 
+
+ align:start position:0%
+All right. Um, why don't you start?
+Okay, where are we? Um, tell me how far
+
+ align:start position:0%
+Okay, where are we? Um, tell me how far
+ 
+
+ align:start position:0%
+Okay, where are we? Um, tell me how far
+along the paper is. Uh, it's getting
+
+ align:start position:0%
+along the paper is. Uh, it's getting
+ 
+
+ align:start position:0%
+along the paper is. Uh, it's getting
+there. Uh, I'm still digging through
+
+ align:start position:0%
+there. Uh, I'm still digging through
+ 
+
+ align:start position:0%
+there. Uh, I'm still digging through
+some of my research, but I'm I'm I've
+
+ align:start position:0%
+some of my research, but I'm I'm I've
+ 
+
+ align:start position:0%
+some of my research, but I'm I'm I've
+got a
+
+ align:start position:0%
+got a
+ 
+
+ align:start position:0%
+got a
+I guess my my argument's formulating
+
+ align:start position:0%
+I guess my my argument's formulating
+ 
+
+ align:start position:0%
+I guess my my argument's formulating
+fairly well in my head and I'm pretty
+
+ align:start position:0%
+fairly well in my head and I'm pretty
+ 
+
+ align:start position:0%
+fairly well in my head and I'm pretty
+comfortable with where I am. Uh like I
+
+ align:start position:0%
+comfortable with where I am. Uh like I
+ 
+
+ align:start position:0%
+comfortable with where I am. Uh like I
+said, the one thing that I'm still just
+
+ align:start position:0%
+said, the one thing that I'm still just
+ 
+
+ align:start position:0%
+said, the one thing that I'm still just
+a bit uncertain of is uh I'm I'm working
+
+ align:start position:0%
+a bit uncertain of is uh I'm I'm working
+ 
+
+ align:start position:0%
+a bit uncertain of is uh I'm I'm working
+on tying in the argument that I said
+
+ align:start position:0%
+on tying in the argument that I said
+ 
+
+ align:start position:0%
+on tying in the argument that I said
+about uh free will and the belief in
+
+ align:start position:0%
+about uh free will and the belief in
+ 
+
+ align:start position:0%
+about uh free will and the belief in
+such thing uh changing the outcome to uh
+
+ align:start position:0%
+such thing uh changing the outcome to uh
+ 
+
+ align:start position:0%
+such thing uh changing the outcome to uh
+the same sort of argument about
+
+ align:start position:0%
+the same sort of argument about
+ 
+
+ align:start position:0%
+the same sort of argument about
+creativity where uh the belief in a a
+
+ align:start position:0%
+creativity where uh the belief in a a
+ 
+
+ align:start position:0%
+creativity where uh the belief in a a
+capacity for original creativity uh
+
+ align:start position:0%
+capacity for original creativity uh
+ 
+
+ align:start position:0%
+capacity for original creativity uh
+actually changes the outcome in a
+
+ align:start position:0%
+actually changes the outcome in a
+ 
+
+ align:start position:0%
+actually changes the outcome in a
+deterministic system. Uh and that's the
+
+ align:start position:0%
+deterministic system. Uh and that's the
+ 
+
+ align:start position:0%
+deterministic system. Uh and that's the
+last little bit I'm kind of working
+
+ align:start position:0%
+last little bit I'm kind of working
+ 
+
+ align:start position:0%
+last little bit I'm kind of working
+through there.
+
+ align:start position:0%
+through there.
+ 
+
+ align:start position:0%
+through there.
+Um, what's the outside research? Uh,
+
+ align:start position:0%
+Um, what's the outside research? Uh,
+ 
+
+ align:start position:0%
+Um, what's the outside research? Uh,
+I've got a number of, uh,
+
+ align:start position:0%
+I've got a number of, uh,
+ 
+
+ align:start position:0%
+I've got a number of, uh,
+things I pull together here. Um, one of
+
+ align:start position:0%
+things I pull together here. Um, one of
+ 
+
+ align:start position:0%
+things I pull together here. Um, one of
+them is,
+
+ align:start position:0%
+them is,
+ 
+
+ align:start position:0%
+them is,
+uh, free will as creativity. It's from
+
+ align:start position:0%
+uh, free will as creativity. It's from
+ 
+
+ align:start position:0%
+uh, free will as creativity. It's from
+this, uh, online, uh, philosophy
+
+ align:start position:0%
+this, uh, online, uh, philosophy
+ 
+
+ align:start position:0%
+this, uh, online, uh, philosophy
+journal. It's saying, oh, it's about
+
+ align:start position:0%
+journal. It's saying, oh, it's about
+ 
+
+ align:start position:0%
+journal. It's saying, oh, it's about
+creativity. I see. Uh, this one's more
+
+ align:start position:0%
+creativity. I see. Uh, this one's more
+ 
+
+ align:start position:0%
+creativity. I see. Uh, this one's more
+about free will and the terminal. I
+
+ align:start position:0%
+about free will and the terminal. I
+ 
+
+ align:start position:0%
+about free will and the terminal. I
+mean, I did all these. The way I found
+
+ align:start position:0%
+mean, I did all these. The way I found
+ 
+
+ align:start position:0%
+mean, I did all these. The way I found
+them was by searching for the real
+
+ align:start position:0%
+them was by searching for the real
+ 
+
+ align:start position:0%
+them was by searching for the real
+creativity. So these all have something
+
+ align:start position:0%
+creativity. So these all have something
+ 
+
+ align:start position:0%
+creativity. So these all have something
+to do with um creativity. Okay. Um you
+
+ align:start position:0%
+to do with um creativity. Okay. Um you
+ 
+
+ align:start position:0%
+to do with um creativity. Okay. Um you
+remember that I gave you two pages of
+
+ align:start position:0%
+remember that I gave you two pages of
+ 
+
+ align:start position:0%
+remember that I gave you two pages of
+uh research material outside partial
+
+ align:start position:0%
+uh research material outside partial
+ 
+
+ align:start position:0%
+uh research material outside partial
+lists. I said um I mean that could be of
+
+ align:start position:0%
+lists. I said um I mean that could be of
+ 
+
+ align:start position:0%
+lists. I said um I mean that could be of
+help depending on what you want to do in
+
+ align:start position:0%
+help depending on what you want to do in
+ 
+
+ align:start position:0%
+help depending on what you want to do in
+your paper. Um do you you feel
+
+ align:start position:0%
+your paper. Um do you you feel
+ 
+
+ align:start position:0%
+your paper. Um do you you feel
+comfortable about it? Yeah. Okay. You
+
+ align:start position:0%
+comfortable about it? Yeah. Okay. You
+ 
+
+ align:start position:0%
+comfortable about it? Yeah. Okay. You
+you Beckard, you are too. You know what
+
+ align:start position:0%
+you Beckard, you are too. You know what
+ 
+
+ align:start position:0%
+you Beckard, you are too. You know what
+you're doing. Um Tom. All right. I'm uh
+
+ align:start position:0%
+you're doing. Um Tom. All right. I'm uh
+ 
+
+ align:start position:0%
+you're doing. Um Tom. All right. I'm uh
+mostly looking at um creative artificial
+
+ align:start position:0%
+mostly looking at um creative artificial
+ 
+
+ align:start position:0%
+mostly looking at um creative artificial
+intelligence. So uh I've got a couple
+
+ align:start position:0%
+intelligence. So uh I've got a couple
+ 
+
+ align:start position:0%
+intelligence. So uh I've got a couple
+examples of uh I'm trying to figure out
+
+ align:start position:0%
+examples of uh I'm trying to figure out
+ 
+
+ align:start position:0%
+examples of uh I'm trying to figure out
+like what has to be done to create
+
+ align:start position:0%
+like what has to be done to create
+ 
+
+ align:start position:0%
+like what has to be done to create
+artificial intelligence that is
+
+ align:start position:0%
+artificial intelligence that is
+ 
+
+ align:start position:0%
+artificial intelligence that is
+creative. What about the Minsk's book?
+
+ align:start position:0%
+creative. What about the Minsk's book?
+ 
+
+ align:start position:0%
+creative. What about the Minsk's book?
+Uh the emotion machine. Pardon? I mean
+
+ align:start position:0%
+Uh the emotion machine. Pardon? I mean
+ 
+
+ align:start position:0%
+Uh the emotion machine. Pardon? I mean
+have you been using that? Uh I've read
+
+ align:start position:0%
+have you been using that? Uh I've read
+ 
+
+ align:start position:0%
+have you been using that? Uh I've read
+it. I don't know. Uh you have read it
+
+ align:start position:0%
+it. I don't know. Uh you have read it
+ 
+
+ align:start position:0%
+it. I don't know. Uh you have read it
+all. Gone through it all. I've read most
+
+ align:start position:0%
+all. Gone through it all. I've read most
+ 
+
+ align:start position:0%
+all. Gone through it all. I've read most
+of it like the first part of it. Um I
+
+ align:start position:0%
+of it like the first part of it. Um I
+ 
+
+ align:start position:0%
+of it like the first part of it. Um I
+I'm not sure how much of it really
+
+ align:start position:0%
+I'm not sure how much of it really
+ 
+
+ align:start position:0%
+I'm not sure how much of it really
+applies to this. I thought uh something
+
+ align:start position:0%
+applies to this. I thought uh something
+ 
+
+ align:start position:0%
+applies to this. I thought uh something
+that was more applicable was uh a paper
+
+ align:start position:0%
+that was more applicable was uh a paper
+ 
+
+ align:start position:0%
+that was more applicable was uh a paper
+by uh Margaret Bone which was uh talking
+
+ align:start position:0%
+by uh Margaret Bone which was uh talking
+ 
+
+ align:start position:0%
+by uh Margaret Bone which was uh talking
+about like conceptual spaces and how
+
+ align:start position:0%
+about like conceptual spaces and how
+ 
+
+ align:start position:0%
+about like conceptual spaces and how
+like uh how that would affect it. I
+
+ align:start position:0%
+like uh how that would affect it. I
+ 
+
+ align:start position:0%
+like uh how that would affect it. I
+think uh like the stuff that Minsky did
+
+ align:start position:0%
+think uh like the stuff that Minsky did
+ 
+
+ align:start position:0%
+think uh like the stuff that Minsky did
+on like uh neural networks and like
+
+ align:start position:0%
+on like uh neural networks and like
+ 
+
+ align:start position:0%
+on like uh neural networks and like
+randomly wired neural networks is pretty
+
+ align:start position:0%
+randomly wired neural networks is pretty
+ 
+
+ align:start position:0%
+randomly wired neural networks is pretty
+uh pretty important to it in terms of
+
+ align:start position:0%
+uh pretty important to it in terms of
+ 
+
+ align:start position:0%
+uh pretty important to it in terms of
+finding like um computers that can like
+
+ align:start position:0%
+finding like um computers that can like
+ 
+
+ align:start position:0%
+finding like um computers that can like
+that's the paper you mentioned last
+
+ align:start position:0%
+that's the paper you mentioned last
+ 
+
+ align:start position:0%
+that's the paper you mentioned last
+week, right? That's true. Okay. And then
+
+ align:start position:0%
+week, right? That's true. Okay. And then
+ 
+
+ align:start position:0%
+week, right? That's true. Okay. And then
+uh I also wanted to look at like um
+
+ align:start position:0%
+uh I also wanted to look at like um
+ 
+
+ align:start position:0%
+uh I also wanted to look at like um
+uh the program Aaron which was uh
+
+ align:start position:0%
+uh the program Aaron which was uh
+ 
+
+ align:start position:0%
+uh the program Aaron which was uh
+written by Harold Cohen and it's like a
+
+ align:start position:0%
+written by Harold Cohen and it's like a
+ 
+
+ align:start position:0%
+written by Harold Cohen and it's like a
+uh like an art making uh program that uh
+
+ align:start position:0%
+uh like an art making uh program that uh
+ 
+
+ align:start position:0%
+uh like an art making uh program that uh
+it's like I guess like uh written in
+
+ align:start position:0%
+it's like I guess like uh written in
+ 
+
+ align:start position:0%
+it's like I guess like uh written in
+lisp and uh it's been it's been given
+
+ align:start position:0%
+lisp and uh it's been it's been given
+ 
+
+ align:start position:0%
+lisp and uh it's been it's been given
+like a lot of uh public attention for
+
+ align:start position:0%
+like a lot of uh public attention for
+ 
+
+ align:start position:0%
+like a lot of uh public attention for
+being like this like creative um like uh
+
+ align:start position:0%
+being like this like creative um like uh
+ 
+
+ align:start position:0%
+being like this like creative um like uh
+like artificial artificial intelligence.
+
+ align:start position:0%
+like artificial artificial intelligence.
+ 
+
+ align:start position:0%
+like artificial artificial intelligence.
+But uh my argument is that it's not in
+
+ align:start position:0%
+But uh my argument is that it's not in
+ 
+
+ align:start position:0%
+But uh my argument is that it's not in
+fact creative because um what it does is
+
+ align:start position:0%
+fact creative because um what it does is
+ 
+
+ align:start position:0%
+fact creative because um what it does is
+it kind of mimics like uh the art style
+
+ align:start position:0%
+it kind of mimics like uh the art style
+ 
+
+ align:start position:0%
+it kind of mimics like uh the art style
+of Harold Cohen. So in the in like in as
+
+ align:start position:0%
+of Harold Cohen. So in the in like in as
+ 
+
+ align:start position:0%
+of Harold Cohen. So in the in like in as
+much as Harold Con's like his art style
+
+ align:start position:0%
+much as Harold Con's like his art style
+ 
+
+ align:start position:0%
+much as Harold Con's like his art style
+would be creative then I guess it would
+
+ align:start position:0%
+would be creative then I guess it would
+ 
+
+ align:start position:0%
+would be creative then I guess it would
+be but like all it can really do is uh
+
+ align:start position:0%
+be but like all it can really do is uh
+ 
+
+ align:start position:0%
+be but like all it can really do is uh
+that one style like there's nothing that
+
+ align:start position:0%
+that one style like there's nothing that
+ 
+
+ align:start position:0%
+that one style like there's nothing that
+it can like it can't like start like a
+
+ align:start position:0%
+it can like it can't like start like a
+ 
+
+ align:start position:0%
+it can like it can't like start like a
+new style or like change like I guess
+
+ align:start position:0%
+new style or like change like I guess
+ 
+
+ align:start position:0%
+new style or like change like I guess
+the conceptual like boundaries that is
+
+ align:start position:0%
+the conceptual like boundaries that is
+ 
+
+ align:start position:0%
+the conceptual like boundaries that is
+what is necessary for like actual
+
+ align:start position:0%
+what is necessary for like actual
+ 
+
+ align:start position:0%
+what is necessary for like actual
+creative act. Um
+
+ align:start position:0%
+creative act. Um
+ 
+
+ align:start position:0%
+creative act. Um
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+in the def in the book on creativ the
+
+ align:start position:0%
+in the def in the book on creativ the
+ 
+
+ align:start position:0%
+in the def in the book on creativ the
+definition of creativity I think is that
+
+ align:start position:0%
+definition of creativity I think is that
+ 
+
+ align:start position:0%
+definition of creativity I think is that
+the name of the anthology that that
+
+ align:start position:0%
+the name of the anthology that that
+ 
+
+ align:start position:0%
+the name of the anthology that that
+Bowden edited and there's an article of
+
+ align:start position:0%
+Bowden edited and there's an article of
+ 
+
+ align:start position:0%
+Bowden edited and there's an article of
+hers in that
+
+ align:start position:0%
+hers in that
+ 
+
+ align:start position:0%
+hers in that
+uh in which she distinguishes between
+
+ align:start position:0%
+uh in which she distinguishes between
+ 
+
+ align:start position:0%
+uh in which she distinguishes between
+the sort of minor and the major kind of
+
+ align:start position:0%
+the sort of minor and the major kind of
+ 
+
+ align:start position:0%
+the sort of minor and the major kind of
+creativity. That's the same idea. She
+
+ align:start position:0%
+creativity. That's the same idea. She
+ 
+
+ align:start position:0%
+creativity. That's the same idea. She
+develops it further or have you not
+
+ align:start position:0%
+develops it further or have you not
+ 
+
+ align:start position:0%
+develops it further or have you not
+looked at that other essay? Um, what's
+
+ align:start position:0%
+looked at that other essay? Um, what's
+ 
+
+ align:start position:0%
+looked at that other essay? Um, what's
+the name of that essay? Uh, the
+
+ align:start position:0%
+the name of that essay? Uh, the
+ 
+
+ align:start position:0%
+the name of that essay? Uh, the
+definition of creativity. Definition of
+
+ align:start position:0%
+definition of creativity. Definition of
+ 
+
+ align:start position:0%
+definition of creativity. Definition of
+creativity. I'll read that, I guess. Um,
+
+ align:start position:0%
+creativity. I'll read that, I guess. Um,
+ 
+
+ align:start position:0%
+creativity. I'll read that, I guess. Um,
+it's conceivable that I have the library
+
+ align:start position:0%
+it's conceivable that I have the library
+ 
+
+ align:start position:0%
+it's conceivable that I have the library
+copy,
+
+ align:start position:0%
+copy,
+ 
+
+ align:start position:0%
+copy,
+but um, yeah, somebody has most of
+
+ align:start position:0%
+but um, yeah, somebody has most of
+ 
+
+ align:start position:0%
+but um, yeah, somebody has most of
+Bowden's books out of the library. I
+
+ align:start position:0%
+Bowden's books out of the library. I
+ 
+
+ align:start position:0%
+Bowden's books out of the library. I
+looked and all the ones dealing with
+
+ align:start position:0%
+looked and all the ones dealing with
+ 
+
+ align:start position:0%
+looked and all the ones dealing with
+creativity are not there. Well, there's
+
+ align:start position:0%
+creativity are not there. Well, there's
+ 
+
+ align:start position:0%
+creativity are not there. Well, there's
+only one of hers that I have and that's
+
+ align:start position:0%
+only one of hers that I have and that's
+ 
+
+ align:start position:0%
+only one of hers that I have and that's
+the book that she edited.
+
+ align:start position:0%
+the book that she edited.
+ 
+
+ align:start position:0%
+the book that she edited.
+But uh possibly you don't need that
+
+ align:start position:0%
+But uh possibly you don't need that
+ 
+
+ align:start position:0%
+But uh possibly you don't need that
+essay of hers because it's all in that
+
+ align:start position:0%
+essay of hers because it's all in that
+ 
+
+ align:start position:0%
+essay of hers because it's all in that
+book that you of hers that you do have.
+
+ align:start position:0%
+book that you of hers that you do have.
+ 
+
+ align:start position:0%
+book that you of hers that you do have.
+Right. Um in terms of your concern,
+
+ align:start position:0%
+Right. Um in terms of your concern,
+ 
+
+ align:start position:0%
+Right. Um in terms of your concern,
+Megan, maybe you ought to try to
+
+ align:start position:0%
+Megan, maybe you ought to try to
+ 
+
+ align:start position:0%
+Megan, maybe you ought to try to
+cooperate with Tom, see what he has out.
+
+ align:start position:0%
+cooperate with Tom, see what he has out.
+ 
+
+ align:start position:0%
+cooperate with Tom, see what he has out.
+Well, I was able to find plenty. I You
+
+ align:start position:0%
+Well, I was able to find plenty. I You
+ 
+
+ align:start position:0%
+Well, I was able to find plenty. I You
+don't need it. Was specifically looking
+
+ align:start position:0%
+don't need it. Was specifically looking
+ 
+
+ align:start position:0%
+don't need it. Was specifically looking
+for those out. Okay. In general, keep in
+
+ align:start position:0%
+for those out. Okay. In general, keep in
+ 
+
+ align:start position:0%
+for those out. Okay. In general, keep in
+mind what you're learning right now
+
+ align:start position:0%
+mind what you're learning right now
+ 
+
+ align:start position:0%
+mind what you're learning right now
+about who has which books out so that
+
+ align:start position:0%
+about who has which books out so that
+ 
+
+ align:start position:0%
+about who has which books out so that
+you can talk to each other and share
+
+ align:start position:0%
+you can talk to each other and share
+ 
+
+ align:start position:0%
+you can talk to each other and share
+them. The one I'm uh like the article I
+
+ align:start position:0%
+them. The one I'm uh like the article I
+ 
+
+ align:start position:0%
+them. The one I'm uh like the article I
+was using was a constructions of the
+
+ align:start position:0%
+was using was a constructions of the
+ 
+
+ align:start position:0%
+was using was a constructions of the
+mind by her. Yeah, I don't know anything
+
+ align:start position:0%
+mind by her. Yeah, I don't know anything
+ 
+
+ align:start position:0%
+mind by her. Yeah, I don't know anything
+about that.
+
+ align:start position:0%
+about that.
+ 
+
+ align:start position:0%
+about that.
+Okay. there um is um somebody whom I
+
+ align:start position:0%
+Okay. there um is um somebody whom I
+ 
+
+ align:start position:0%
+Okay. there um is um somebody whom I
+learned about this weekend who is a
+
+ align:start position:0%
+learned about this weekend who is a
+ 
+
+ align:start position:0%
+learned about this weekend who is a
+professor at Georgia Institute of
+
+ align:start position:0%
+professor at Georgia Institute of
+ 
+
+ align:start position:0%
+professor at Georgia Institute of
+Technology
+
+ align:start position:0%
+Technology
+ 
+
+ align:start position:0%
+Technology
+and uh she has an NE grant this year and
+
+ align:start position:0%
+and uh she has an NE grant this year and
+ 
+
+ align:start position:0%
+and uh she has an NE grant this year and
+is spending her time in Rat at the
+
+ align:start position:0%
+is spending her time in Rat at the
+ 
+
+ align:start position:0%
+is spending her time in Rat at the
+Ratcliffe Institute and the topic of her
+
+ align:start position:0%
+Ratcliffe Institute and the topic of her
+ 
+
+ align:start position:0%
+Ratcliffe Institute and the topic of her
+project is creativity and science.
+
+ align:start position:0%
+project is creativity and science.
+ 
+
+ align:start position:0%
+project is creativity and science.
+um her you might want to I don't know if
+
+ align:start position:0%
+um her you might want to I don't know if
+ 
+
+ align:start position:0%
+um her you might want to I don't know if
+there's time for you to even think of
+
+ align:start position:0%
+there's time for you to even think of
+ 
+
+ align:start position:0%
+there's time for you to even think of
+getting in touch with her if she's right
+
+ align:start position:0%
+getting in touch with her if she's right
+ 
+
+ align:start position:0%
+getting in touch with her if she's right
+in her office or anything but um her
+
+ align:start position:0%
+in her office or anything but um her
+ 
+
+ align:start position:0%
+in her office or anything but um her
+name is um Nancy Nuressian.
+
+ align:start position:0%
+name is um Nancy Nuressian.
+ 
+
+ align:start position:0%
+name is um Nancy Nuressian.
+Well, no actually
+
+ align:start position:0%
+Well, no actually
+ 
+
+ align:start position:0%
+Well, no actually
+look why don't you proceed this way? Um
+
+ align:start position:0%
+look why don't you proceed this way? Um
+ 
+
+ align:start position:0%
+look why don't you proceed this way? Um
+get on to Google and track down Nancy
+
+ align:start position:0%
+get on to Google and track down Nancy
+ 
+
+ align:start position:0%
+get on to Google and track down Nancy
+Nessian. Uh Mikuel is very good about
+
+ align:start position:0%
+Nessian. Uh Mikuel is very good about
+ 
+
+ align:start position:0%
+Nessian. Uh Mikuel is very good about
+doing that on the spot and uh see if
+
+ align:start position:0%
+doing that on the spot and uh see if
+ 
+
+ align:start position:0%
+doing that on the spot and uh see if
+there are any any um extracts from her
+
+ align:start position:0%
+there are any any um extracts from her
+ 
+
+ align:start position:0%
+there are any any um extracts from her
+writings about creativity and science on
+
+ align:start position:0%
+writings about creativity and science on
+ 
+
+ align:start position:0%
+writings about creativity and science on
+the on the internet. You got her
+
+ align:start position:0%
+the on the internet. You got her
+ 
+
+ align:start position:0%
+the on the internet. You got her
+already. Well, it says her research
+
+ align:start position:0%
+already. Well, it says her research
+ 
+
+ align:start position:0%
+already. Well, it says her research
+focuses on human creativity and science.
+
+ align:start position:0%
+focuses on human creativity and science.
+ 
+
+ align:start position:0%
+focuses on human creativity and science.
+The major theme of this research is
+
+ align:start position:0%
+The major theme of this research is
+ 
+
+ align:start position:0%
+The major theme of this research is
+conceptual and innovation and change in
+
+ align:start position:0%
+conceptual and innovation and change in
+ 
+
+ align:start position:0%
+conceptual and innovation and change in
+physics and and physics education.
+
+ align:start position:0%
+physics and and physics education.
+ 
+
+ align:start position:0%
+physics and and physics education.
+specifically the role of analogical and
+
+ align:start position:0%
+specifically the role of analogical and
+ 
+
+ align:start position:0%
+specifically the role of analogical and
+visual modeling and thought
+
+ align:start position:0%
+visual modeling and thought
+ 
+
+ align:start position:0%
+visual modeling and thought
+experimenting simulative modeling. Her
+
+ align:start position:0%
+experimenting simulative modeling. Her
+ 
+
+ align:start position:0%
+experimenting simulative modeling. Her
+current research include investigative
+
+ align:start position:0%
+current research include investigative
+ 
+
+ align:start position:0%
+current research include investigative
+reasoning and representational
+
+ align:start position:0%
+reasoning and representational
+ 
+
+ align:start position:0%
+reasoning and representational
+procedures in interdisciplinary research
+
+ align:start position:0%
+procedures in interdisciplinary research
+ 
+
+ align:start position:0%
+procedures in interdisciplinary research
+laboratories and blah blah blah blah.
+
+ align:start position:0%
+laboratories and blah blah blah blah.
+ 
+
+ align:start position:0%
+laboratories and blah blah blah blah.
+Does that interest any of you?
+
+ align:start position:0%
+Does that interest any of you?
+ 
+
+ align:start position:0%
+Does that interest any of you?
+Okay, then don't worry about it. Uh you
+
+ align:start position:0%
+Okay, then don't worry about it. Uh you
+ 
+
+ align:start position:0%
+Okay, then don't worry about it. Uh you
+have plenty of sources with Bowden's
+
+ align:start position:0%
+have plenty of sources with Bowden's
+ 
+
+ align:start position:0%
+have plenty of sources with Bowden's
+writings. So yeah. Um one other thing
+
+ align:start position:0%
+writings. So yeah. Um one other thing
+ 
+
+ align:start position:0%
+writings. So yeah. Um one other thing
+that was interesting uh interesting to
+
+ align:start position:0%
+that was interesting uh interesting to
+ 
+
+ align:start position:0%
+that was interesting uh interesting to
+me was uh I was looking up like uh like
+
+ align:start position:0%
+me was uh I was looking up like uh like
+ 
+
+ align:start position:0%
+me was uh I was looking up like uh like
+alternate means of like creating uh like
+
+ align:start position:0%
+alternate means of like creating uh like
+ 
+
+ align:start position:0%
+alternate means of like creating uh like
+creative artificial intelligence and I
+
+ align:start position:0%
+creative artificial intelligence and I
+ 
+
+ align:start position:0%
+creative artificial intelligence and I
+came across like the uh the touring uh
+
+ align:start position:0%
+came across like the uh the touring uh
+ 
+
+ align:start position:0%
+came across like the uh the touring uh
+touring test which I guess is
+
+ align:start position:0%
+touring test which I guess is
+ 
+
+ align:start position:0%
+touring test which I guess is
+pardon which I guess is like a way of uh
+
+ align:start position:0%
+pardon which I guess is like a way of uh
+ 
+
+ align:start position:0%
+pardon which I guess is like a way of uh
+trying to make uh artificial
+
+ align:start position:0%
+trying to make uh artificial
+ 
+
+ align:start position:0%
+trying to make uh artificial
+intelligence that could communicate like
+
+ align:start position:0%
+intelligence that could communicate like
+ 
+
+ align:start position:0%
+intelligence that could communicate like
+with a human and the human wouldn't be
+
+ align:start position:0%
+with a human and the human wouldn't be
+ 
+
+ align:start position:0%
+with a human and the human wouldn't be
+able to tell the difference. So, uh,
+
+ align:start position:0%
+able to tell the difference. So, uh,
+ 
+
+ align:start position:0%
+able to tell the difference. So, uh,
+this is just a a label, isn't it? Alan
+
+ align:start position:0%
+this is just a a label, isn't it? Alan
+ 
+
+ align:start position:0%
+this is just a a label, isn't it? Alan
+Turing didn't come up with this, did he?
+
+ align:start position:0%
+Turing didn't come up with this, did he?
+ 
+
+ align:start position:0%
+Turing didn't come up with this, did he?
+He was one of the great, uh, founding
+
+ align:start position:0%
+He was one of the great, uh, founding
+ 
+
+ align:start position:0%
+He was one of the great, uh, founding
+fathers of of artificial intelligence
+
+ align:start position:0%
+fathers of of artificial intelligence
+ 
+
+ align:start position:0%
+fathers of of artificial intelligence
+and apparently a a very very brilliant
+
+ align:start position:0%
+and apparently a a very very brilliant
+ 
+
+ align:start position:0%
+and apparently a a very very brilliant
+and tragic figure in the 1940s.
+
+ align:start position:0%
+and tragic figure in the 1940s.
+ 
+
+ align:start position:0%
+and tragic figure in the 1940s.
+But he didn't himself to do with the
+
+ align:start position:0%
+But he didn't himself to do with the
+ 
+
+ align:start position:0%
+But he didn't himself to do with the
+Turing test, did was he? Did he? I
+
+ align:start position:0%
+Turing test, did was he? Did he? I
+ 
+
+ align:start position:0%
+Turing test, did was he? Did he? I
+thought he I thought he did. Oh, he did.
+
+ align:start position:0%
+thought he I thought he did. Oh, he did.
+ 
+
+ align:start position:0%
+thought he I thought he did. Oh, he did.
+I thought I thought I could written
+
+ align:start position:0%
+I thought I thought I could written
+ 
+
+ align:start position:0%
+I thought I thought I could written
+about Oh, he's written about it, but he
+
+ align:start position:0%
+about Oh, he's written about it, but he
+ 
+
+ align:start position:0%
+about Oh, he's written about it, but he
+didn't set up the the um competition.
+
+ align:start position:0%
+didn't set up the the um competition.
+ 
+
+ align:start position:0%
+didn't set up the the um competition.
+Well, I guess it's like a hypothetical
+
+ align:start position:0%
+Well, I guess it's like a hypothetical
+ 
+
+ align:start position:0%
+Well, I guess it's like a hypothetical
+test. I don't think has it I don't Okay.
+
+ align:start position:0%
+test. I don't think has it I don't Okay.
+ 
+
+ align:start position:0%
+test. I don't think has it I don't Okay.
+Yes, it does. It has been. All right.
+
+ align:start position:0%
+Yes, it does. It has been. All right.
+ 
+
+ align:start position:0%
+Yes, it does. It has been. All right.
+How how
+
+ align:start position:0%
+How how
+ 
+
+ align:start position:0%
+How how
+it's about how is it related to
+
+ align:start position:0%
+it's about how is it related to
+ 
+
+ align:start position:0%
+it's about how is it related to
+creativity? Well, uh like there one of
+
+ align:start position:0%
+creativity? Well, uh like there one of
+ 
+
+ align:start position:0%
+creativity? Well, uh like there one of
+the uh uh one of the ideas for like a
+
+ align:start position:0%
+the uh uh one of the ideas for like a
+ 
+
+ align:start position:0%
+the uh uh one of the ideas for like a
+computer that could be put into it was
+
+ align:start position:0%
+computer that could be put into it was
+ 
+
+ align:start position:0%
+computer that could be put into it was
+uh this one by uh Ned Block, I think.
+
+ align:start position:0%
+uh this one by uh Ned Block, I think.
+ 
+
+ align:start position:0%
+uh this one by uh Ned Block, I think.
+And uh it's like the uh the block head
+
+ align:start position:0%
+And uh it's like the uh the block head
+ 
+
+ align:start position:0%
+And uh it's like the uh the block head
+computer which is a hypothetical
+
+ align:start position:0%
+computer which is a hypothetical
+ 
+
+ align:start position:0%
+computer which is a hypothetical
+computer which would have like uh all
+
+ align:start position:0%
+computer which would have like uh all
+ 
+
+ align:start position:0%
+computer which would have like uh all
+the possible like opening like
+
+ align:start position:0%
+the possible like opening like
+ 
+
+ align:start position:0%
+the possible like opening like
+statements or like beginning uh ways of
+
+ align:start position:0%
+statements or like beginning uh ways of
+ 
+
+ align:start position:0%
+statements or like beginning uh ways of
+like starting the conversation and then
+
+ align:start position:0%
+like starting the conversation and then
+ 
+
+ align:start position:0%
+like starting the conversation and then
+would also have programmed in it like
+
+ align:start position:0%
+would also have programmed in it like
+ 
+
+ align:start position:0%
+would also have programmed in it like
+every uh like correct grammatical
+
+ align:start position:0%
+every uh like correct grammatical
+ 
+
+ align:start position:0%
+every uh like correct grammatical
+response to that um to to any statement
+
+ align:start position:0%
+response to that um to to any statement
+ 
+
+ align:start position:0%
+response to that um to to any statement
+that like the person would get back to
+
+ align:start position:0%
+that like the person would get back to
+ 
+
+ align:start position:0%
+that like the person would get back to
+it. So then uh the idea would be like if
+
+ align:start position:0%
+it. So then uh the idea would be like if
+ 
+
+ align:start position:0%
+it. So then uh the idea would be like if
+it had all of those programmed into it,
+
+ align:start position:0%
+it had all of those programmed into it,
+ 
+
+ align:start position:0%
+it had all of those programmed into it,
+it could have like a uh like a
+
+ align:start position:0%
+it could have like a uh like a
+ 
+
+ align:start position:0%
+it could have like a uh like a
+contextually and a grammatically correct
+
+ align:start position:0%
+contextually and a grammatically correct
+ 
+
+ align:start position:0%
+contextually and a grammatically correct
+response to anything that you might say
+
+ align:start position:0%
+response to anything that you might say
+ 
+
+ align:start position:0%
+response to anything that you might say
+to it. So it would be just like it was a
+
+ align:start position:0%
+to it. So it would be just like it was a
+ 
+
+ align:start position:0%
+to it. So it would be just like it was a
+person like in every way. So is is it is
+
+ align:start position:0%
+person like in every way. So is is it is
+ 
+
+ align:start position:0%
+person like in every way. So is is it is
+basically like Eliza with a very large
+
+ align:start position:0%
+basically like Eliza with a very large
+ 
+
+ align:start position:0%
+basically like Eliza with a very large
+database, right? with like an infinitely
+
+ align:start position:0%
+database, right? with like an infinitely
+ 
+
+ align:start position:0%
+database, right? with like an infinitely
+large database or something because I
+
+ align:start position:0%
+large database or something because I
+ 
+
+ align:start position:0%
+large database or something because I
+guess there's like there are there's
+
+ align:start position:0%
+guess there's like there are there's
+ 
+
+ align:start position:0%
+guess there's like there are there's
+like a uh
+
+ align:start position:0%
+like a uh
+ 
+
+ align:start position:0%
+like a uh
+uh there's like a limited number of
+
+ align:start position:0%
+uh there's like a limited number of
+ 
+
+ align:start position:0%
+uh there's like a limited number of
+possible like uh statements that you
+
+ align:start position:0%
+possible like uh statements that you
+ 
+
+ align:start position:0%
+possible like uh statements that you
+could say. So I I was talking I was kind
+
+ align:start position:0%
+could say. So I I was talking I was kind
+ 
+
+ align:start position:0%
+could say. So I I was talking I was kind
+of thinking about like whether or not
+
+ align:start position:0%
+of thinking about like whether or not
+ 
+
+ align:start position:0%
+of thinking about like whether or not
+that would be something that would be
+
+ align:start position:0%
+that would be something that would be
+ 
+
+ align:start position:0%
+that would be something that would be
+creative then because it would act
+
+ align:start position:0%
+creative then because it would act
+ 
+
+ align:start position:0%
+creative then because it would act
+exactly like a person would in the
+
+ align:start position:0%
+exactly like a person would in the
+ 
+
+ align:start position:0%
+exactly like a person would in the
+situation or whether or not that would
+
+ align:start position:0%
+situation or whether or not that would
+ 
+
+ align:start position:0%
+situation or whether or not that would
+just be like just the sum of its
+
+ align:start position:0%
+just be like just the sum of its
+ 
+
+ align:start position:0%
+just be like just the sum of its
+components. Anybody
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+want to say anything about this?
+
+ align:start position:0%
+want to say anything about this?
+ 
+
+ align:start position:0%
+want to say anything about this?
+Well, keep working. You seem to know
+
+ align:start position:0%
+Well, keep working. You seem to know
+ 
+
+ align:start position:0%
+Well, keep working. You seem to know
+what you're doing really well. Is there
+
+ align:start position:0%
+what you're doing really well. Is there
+ 
+
+ align:start position:0%
+what you're doing really well. Is there
+any way you can think that I can be
+
+ align:start position:0%
+any way you can think that I can be
+ 
+
+ align:start position:0%
+any way you can think that I can be
+helpful?
+
+ align:start position:0%
+helpful?
+ 
+
+ align:start position:0%
+helpful?
+Um, I think I'm Is this a good moment to
+
+ align:start position:0%
+Um, I think I'm Is this a good moment to
+ 
+
+ align:start position:0%
+Um, I think I'm Is this a good moment to
+come back to a discussion of um of um
+
+ align:start position:0%
+come back to a discussion of um of um
+ 
+
+ align:start position:0%
+come back to a discussion of um of um
+the emotion machine of Minsky's?
+
+ align:start position:0%
+the emotion machine of Minsky's?
+ 
+
+ align:start position:0%
+the emotion machine of Minsky's?
+Let me let me take over for just a few
+
+ align:start position:0%
+Let me let me take over for just a few
+ 
+
+ align:start position:0%
+Let me let me take over for just a few
+minutes. But I mean, it turns out that I
+
+ align:start position:0%
+minutes. But I mean, it turns out that I
+ 
+
+ align:start position:0%
+minutes. But I mean, it turns out that I
+can stay until 5 instead of returning to
+
+ align:start position:0%
+can stay until 5 instead of returning to
+ 
+
+ align:start position:0%
+can stay until 5 instead of returning to
+my
+
+ align:start position:0%
+my
+ 
+
+ align:start position:0%
+my
+emergency.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh but and I do but there and there
+
+ align:start position:0%
+uh but and I do but there and there
+ 
+
+ align:start position:0%
+uh but and I do but there and there
+should be enough time for everybody. Um
+
+ align:start position:0%
+should be enough time for everybody. Um
+ 
+
+ align:start position:0%
+should be enough time for everybody. Um
+I wrote down a number of questions
+
+ align:start position:0%
+I wrote down a number of questions
+ 
+
+ align:start position:0%
+I wrote down a number of questions
+relevant to the emotion machine that
+
+ align:start position:0%
+relevant to the emotion machine that
+ 
+
+ align:start position:0%
+relevant to the emotion machine that
+might interest you.
+
+ align:start position:0%
+might interest you.
+ 
+
+ align:start position:0%
+might interest you.
+The first is um what is it that um
+
+ align:start position:0%
+The first is um what is it that um
+ 
+
+ align:start position:0%
+The first is um what is it that um
+Minsky is trying to do at all? And the
+
+ align:start position:0%
+Minsky is trying to do at all? And the
+ 
+
+ align:start position:0%
+Minsky is trying to do at all? And the
+one would be how to construct a humanoid
+
+ align:start position:0%
+one would be how to construct a humanoid
+ 
+
+ align:start position:0%
+one would be how to construct a humanoid
+machine naturally. I mean everybody with
+
+ align:start position:0%
+machine naturally. I mean everybody with
+ 
+
+ align:start position:0%
+machine naturally. I mean everybody with
+in artificial intelligence has that in
+
+ align:start position:0%
+in artificial intelligence has that in
+ 
+
+ align:start position:0%
+in artificial intelligence has that in
+mind. But second is how to make uh
+
+ align:start position:0%
+mind. But second is how to make uh
+ 
+
+ align:start position:0%
+mind. But second is how to make uh
+computers that are sensitive to human
+
+ align:start position:0%
+computers that are sensitive to human
+ 
+
+ align:start position:0%
+computers that are sensitive to human
+feelings. And that's where the work of
+
+ align:start position:0%
+feelings. And that's where the work of
+ 
+
+ align:start position:0%
+feelings. And that's where the work of
+Rosalind Picard comes in. She's here uh
+
+ align:start position:0%
+Rosalind Picard comes in. She's here uh
+ 
+
+ align:start position:0%
+Rosalind Picard comes in. She's here uh
+at the um media lab and there's a book
+
+ align:start position:0%
+at the um media lab and there's a book
+ 
+
+ align:start position:0%
+at the um media lab and there's a book
+of hers um affective computing that
+
+ align:start position:0%
+of hers um affective computing that
+ 
+
+ align:start position:0%
+of hers um affective computing that
+deals directly with that. So that you
+
+ align:start position:0%
+deals directly with that. So that you
+ 
+
+ align:start position:0%
+deals directly with that. So that you
+might want to look at that. Uh but third
+
+ align:start position:0%
+might want to look at that. Uh but third
+ 
+
+ align:start position:0%
+might want to look at that. Uh but third
+what interests me most and which I think
+
+ align:start position:0%
+what interests me most and which I think
+ 
+
+ align:start position:0%
+what interests me most and which I think
+Minsky is also interested in is what are
+
+ align:start position:0%
+Minsky is also interested in is what are
+ 
+
+ align:start position:0%
+Minsky is also interested in is what are
+the relationship
+
+ align:start position:0%
+the relationship
+ 
+
+ align:start position:0%
+the relationship
+uh between mind and matter meaning by
+
+ align:start position:0%
+uh between mind and matter meaning by
+ 
+
+ align:start position:0%
+uh between mind and matter meaning by
+mind feeling including feelings in what
+
+ align:start position:0%
+mind feeling including feelings in what
+ 
+
+ align:start position:0%
+mind feeling including feelings in what
+we mean by mind. what is the interaction
+
+ align:start position:0%
+we mean by mind. what is the interaction
+ 
+
+ align:start position:0%
+we mean by mind. what is the interaction
+between um the two of them and out of
+
+ align:start position:0%
+between um the two of them and out of
+ 
+
+ align:start position:0%
+between um the two of them and out of
+that uh how can affective and and
+
+ align:start position:0%
+that uh how can affective and and
+ 
+
+ align:start position:0%
+that uh how can affective and and
+cognitive approaches
+
+ align:start position:0%
+cognitive approaches
+ 
+
+ align:start position:0%
+cognitive approaches
+uh be related to each other. Now the um
+
+ align:start position:0%
+uh be related to each other. Now the um
+ 
+
+ align:start position:0%
+uh be related to each other. Now the um
+effort that Minsky makes is very
+
+ align:start position:0%
+effort that Minsky makes is very
+ 
+
+ align:start position:0%
+effort that Minsky makes is very
+interesting to me because he's obvious I
+
+ align:start position:0%
+interesting to me because he's obvious I
+ 
+
+ align:start position:0%
+interesting to me because he's obvious I
+don't know him very well though
+
+ align:start position:0%
+don't know him very well though
+ 
+
+ align:start position:0%
+don't know him very well though
+apparently we over overlapped in various
+
+ align:start position:0%
+apparently we over overlapped in various
+ 
+
+ align:start position:0%
+apparently we over overlapped in various
+ways. Uh but I I can't say that he's a
+
+ align:start position:0%
+ways. Uh but I I can't say that he's a
+ 
+
+ align:start position:0%
+ways. Uh but I I can't say that he's a
+friend of mine or that I've had a really
+
+ align:start position:0%
+friend of mine or that I've had a really
+ 
+
+ align:start position:0%
+friend of mine or that I've had a really
+serious discussion with him. But I find
+
+ align:start position:0%
+serious discussion with him. But I find
+ 
+
+ align:start position:0%
+serious discussion with him. But I find
+uh his writing very impressive once he
+
+ align:start position:0%
+uh his writing very impressive once he
+ 
+
+ align:start position:0%
+uh his writing very impressive once he
+steps back from the official program of
+
+ align:start position:0%
+steps back from the official program of
+ 
+
+ align:start position:0%
+steps back from the official program of
+what he's doing as one of the founders
+
+ align:start position:0%
+what he's doing as one of the founders
+ 
+
+ align:start position:0%
+what he's doing as one of the founders
+of artificial intelligence and talks
+
+ align:start position:0%
+of artificial intelligence and talks
+ 
+
+ align:start position:0%
+of artificial intelligence and talks
+about the world about life about the way
+
+ align:start position:0%
+about the world about life about the way
+ 
+
+ align:start position:0%
+about the world about life about the way
+a moralist would uh the way somebody in
+
+ align:start position:0%
+a moralist would uh the way somebody in
+ 
+
+ align:start position:0%
+a moralist would uh the way somebody in
+literature or humanistic philosophy
+
+ align:start position:0%
+literature or humanistic philosophy
+ 
+
+ align:start position:0%
+literature or humanistic philosophy
+would the way I try to do only he does
+
+ align:start position:0%
+would the way I try to do only he does
+ 
+
+ align:start position:0%
+would the way I try to do only he does
+it better from his own point of view and
+
+ align:start position:0%
+it better from his own point of view and
+ 
+
+ align:start position:0%
+it better from his own point of view and
+totally ignores what I'm doing which I'm
+
+ align:start position:0%
+totally ignores what I'm doing which I'm
+ 
+
+ align:start position:0%
+totally ignores what I'm doing which I'm
+used to but what he does seems to me
+
+ align:start position:0%
+used to but what he does seems to me
+ 
+
+ align:start position:0%
+used to but what he does seems to me
+very attractive and very indicates that
+
+ align:start position:0%
+very attractive and very indicates that
+ 
+
+ align:start position:0%
+very attractive and very indicates that
+he's a brilliant man but I don't see the
+
+ align:start position:0%
+he's a brilliant man but I don't see the
+ 
+
+ align:start position:0%
+he's a brilliant man but I don't see the
+connection with the rest as being
+
+ align:start position:0%
+connection with the rest as being
+ 
+
+ align:start position:0%
+connection with the rest as being
+established in the hope in the way that
+
+ align:start position:0%
+established in the hope in the way that
+ 
+
+ align:start position:0%
+established in the hope in the way that
+he hopes um he he hopes that by talking
+
+ align:start position:0%
+he hopes um he he hopes that by talking
+ 
+
+ align:start position:0%
+he hopes um he he hopes that by talking
+about um the body the brain artificial
+
+ align:start position:0%
+about um the body the brain artificial
+ 
+
+ align:start position:0%
+about um the body the brain artificial
+intelligence on a mechanistic ma basis
+
+ align:start position:0%
+intelligence on a mechanistic ma basis
+ 
+
+ align:start position:0%
+intelligence on a mechanistic ma basis
+will explain all of these other insights
+
+ align:start position:0%
+will explain all of these other insights
+ 
+
+ align:start position:0%
+will explain all of these other insights
+that he has about human nature and about
+
+ align:start position:0%
+that he has about human nature and about
+ 
+
+ align:start position:0%
+that he has about human nature and about
+life and I don't fe find that I find
+
+ align:start position:0%
+life and I don't fe find that I find
+ 
+
+ align:start position:0%
+life and I don't fe find that I find
+these two different compartments uh in
+
+ align:start position:0%
+these two different compartments uh in
+ 
+
+ align:start position:0%
+these two different compartments uh in
+his mind maybe that is enough maybe
+
+ align:start position:0%
+his mind maybe that is enough maybe
+ 
+
+ align:start position:0%
+his mind maybe that is enough maybe
+that's all that anybody can do nowadays
+
+ align:start position:0%
+that's all that anybody can do nowadays
+ 
+
+ align:start position:0%
+that's all that anybody can do nowadays
+but that perception uh is strong me and
+
+ align:start position:0%
+but that perception uh is strong me and
+ 
+
+ align:start position:0%
+but that perception uh is strong me and
+possibly I'm right possibly I'm wrong uh
+
+ align:start position:0%
+possibly I'm right possibly I'm wrong uh
+ 
+
+ align:start position:0%
+possibly I'm right possibly I'm wrong uh
+at the beginning of the first chapter
+
+ align:start position:0%
+at the beginning of the first chapter
+ 
+
+ align:start position:0%
+at the beginning of the first chapter
+um he talks right you know right throws
+
+ align:start position:0%
+um he talks right you know right throws
+ 
+
+ align:start position:0%
+um he talks right you know right throws
+it in your face he talks about the
+
+ align:start position:0%
+it in your face he talks about the
+ 
+
+ align:start position:0%
+it in your face he talks about the
+nature of love uh which doesn't sound
+
+ align:start position:0%
+nature of love uh which doesn't sound
+ 
+
+ align:start position:0%
+nature of love uh which doesn't sound
+very much like artificial intelligence
+
+ align:start position:0%
+very much like artificial intelligence
+ 
+
+ align:start position:0%
+very much like artificial intelligence
+uh and quotes I don't know how many of
+
+ align:start position:0%
+uh and quotes I don't know how many of
+ 
+
+ align:start position:0%
+uh and quotes I don't know how many of
+you noticed this uh from Darthothy
+
+ align:start position:0%
+you noticed this uh from Darthothy
+ 
+
+ align:start position:0%
+you noticed this uh from Darthothy
+Parker who was a very important not
+
+ align:start position:0%
+Parker who was a very important not
+ 
+
+ align:start position:0%
+Parker who was a very important not
+quite a great writer but a very
+
+ align:start position:0%
+quite a great writer but a very
+ 
+
+ align:start position:0%
+quite a great writer but a very
+outstanding writer of the 1920s and 30s
+
+ align:start position:0%
+outstanding writer of the 1920s and 30s
+ 
+
+ align:start position:0%
+outstanding writer of the 1920s and 30s
+who published in poems in the New Yorker
+
+ align:start position:0%
+who published in poems in the New Yorker
+ 
+
+ align:start position:0%
+who published in poems in the New Yorker
+um and was extremely witty but uh in a
+
+ align:start position:0%
+um and was extremely witty but uh in a
+ 
+
+ align:start position:0%
+um and was extremely witty but uh in a
+kind of disillusioned embittered sort of
+
+ align:start position:0%
+kind of disillusioned embittered sort of
+ 
+
+ align:start position:0%
+kind of disillusioned embittered sort of
+way. Uh I don't know whether any of you
+
+ align:start position:0%
+way. Uh I don't know whether any of you
+ 
+
+ align:start position:0%
+way. Uh I don't know whether any of you
+have read anything by her but the poem
+
+ align:start position:0%
+have read anything by her but the poem
+ 
+
+ align:start position:0%
+have read anything by her but the poem
+that Minsky starts with uh is
+
+ align:start position:0%
+that Minsky starts with uh is
+ 
+
+ align:start position:0%
+that Minsky starts with uh is
+characteristic of her. He gives only the
+
+ align:start position:0%
+characteristic of her. He gives only the
+ 
+
+ align:start position:0%
+characteristic of her. He gives only the
+first four lines or or maybe I can't
+
+ align:start position:0%
+first four lines or or maybe I can't
+ 
+
+ align:start position:0%
+first four lines or or maybe I can't
+remember now maybe this is the whole
+
+ align:start position:0%
+remember now maybe this is the whole
+ 
+
+ align:start position:0%
+remember now maybe this is the whole
+poem and let me read it to you. Oh, life
+
+ align:start position:0%
+poem and let me read it to you. Oh, life
+ 
+
+ align:start position:0%
+poem and let me read it to you. Oh, life
+is a glorious
+
+ align:start position:0%
+is a glorious
+ 
+
+ align:start position:0%
+is a glorious
+cycle of song, a medley of
+
+ align:start position:0%
+cycle of song, a medley of
+ 
+
+ align:start position:0%
+cycle of song, a medley of
+extemporaneia,
+
+ align:start position:0%
+extemporaneia,
+ 
+
+ align:start position:0%
+extemporaneia,
+and love is a thing that can never go
+
+ align:start position:0%
+and love is a thing that can never go
+ 
+
+ align:start position:0%
+and love is a thing that can never go
+wrong. And I am Marie of Romania. Uh,
+
+ align:start position:0%
+wrong. And I am Marie of Romania. Uh,
+ 
+
+ align:start position:0%
+wrong. And I am Marie of Romania. Uh,
+Marie of Marie of Romania was a queen at
+
+ align:start position:0%
+Marie of Marie of Romania was a queen at
+ 
+
+ align:start position:0%
+Marie of Marie of Romania was a queen at
+that point. So the poet is obviously
+
+ align:start position:0%
+that point. So the poet is obviously
+ 
+
+ align:start position:0%
+that point. So the poet is obviously
+insane
+
+ align:start position:0%
+insane
+ 
+
+ align:start position:0%
+insane
+and and that explains this gush of
+
+ align:start position:0%
+and and that explains this gush of
+ 
+
+ align:start position:0%
+and and that explains this gush of
+enthusiasm about love. Um now it's very
+
+ align:start position:0%
+enthusiasm about love. Um now it's very
+ 
+
+ align:start position:0%
+enthusiasm about love. Um now it's very
+witty and um um
+
+ align:start position:0%
+witty and um um
+ 
+
+ align:start position:0%
+witty and um um
+um Minsky
+
+ align:start position:0%
+um Minsky
+ 
+
+ align:start position:0%
+um Minsky
+um used to uh I mean um uses it very
+
+ align:start position:0%
+um used to uh I mean um uses it very
+ 
+
+ align:start position:0%
+um used to uh I mean um uses it very
+effectively to make his points about
+
+ align:start position:0%
+effectively to make his points about
+ 
+
+ align:start position:0%
+effectively to make his points about
+love. They boil down to uh his saying
+
+ align:start position:0%
+love. They boil down to uh his saying
+ 
+
+ align:start position:0%
+love. They boil down to uh his saying
+that by studying where is it? Um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+I guess it's on another maybe no it's on
+
+ align:start position:0%
+I guess it's on another maybe no it's on
+ 
+
+ align:start position:0%
+I guess it's on another maybe no it's on
+another page in which he says throughout
+
+ align:start position:0%
+another page in which he says throughout
+ 
+
+ align:start position:0%
+another page in which he says throughout
+this book what we're going to do is to
+
+ align:start position:0%
+this book what we're going to do is to
+ 
+
+ align:start position:0%
+this book what we're going to do is to
+show how it is that people given their
+
+ align:start position:0%
+show how it is that people given their
+ 
+
+ align:start position:0%
+show how it is that people given their
+bodily equipment and their brains um
+
+ align:start position:0%
+bodily equipment and their brains um
+ 
+
+ align:start position:0%
+bodily equipment and their brains um
+their hard wiring which would be
+
+ align:start position:0%
+their hard wiring which would be
+ 
+
+ align:start position:0%
+their hard wiring which would be
+relevant to the work of artificial
+
+ align:start position:0%
+relevant to the work of artificial
+ 
+
+ align:start position:0%
+relevant to the work of artificial
+intelligence the making of robots how
+
+ align:start position:0%
+intelligence the making of robots how
+ 
+
+ align:start position:0%
+intelligence the making of robots how
+they're capable even of having
+
+ align:start position:0%
+they're capable even of having
+ 
+
+ align:start position:0%
+they're capable even of having
+experiences of love, whatever love may
+
+ align:start position:0%
+experiences of love, whatever love may
+ 
+
+ align:start position:0%
+experiences of love, whatever love may
+be. And he gives a kind of analysis of
+
+ align:start position:0%
+be. And he gives a kind of analysis of
+ 
+
+ align:start position:0%
+be. And he gives a kind of analysis of
+it, which is not very advanced and you
+
+ align:start position:0%
+it, which is not very advanced and you
+ 
+
+ align:start position:0%
+it, which is not very advanced and you
+know, since I've spent so much of my
+
+ align:start position:0%
+know, since I've spent so much of my
+ 
+
+ align:start position:0%
+know, since I've spent so much of my
+life on this uh sort of amateurish, but
+
+ align:start position:0%
+life on this uh sort of amateurish, but
+ 
+
+ align:start position:0%
+life on this uh sort of amateurish, but
+utterly respectable and I wouldn't
+
+ align:start position:0%
+utterly respectable and I wouldn't
+ 
+
+ align:start position:0%
+utterly respectable and I wouldn't
+demean his um you doing what he's done
+
+ align:start position:0%
+demean his um you doing what he's done
+ 
+
+ align:start position:0%
+demean his um you doing what he's done
+about love. Um but the point is that
+
+ align:start position:0%
+about love. Um but the point is that
+ 
+
+ align:start position:0%
+about love. Um but the point is that
+what I focus on is the fact that we he's
+
+ align:start position:0%
+what I focus on is the fact that we he's
+ 
+
+ align:start position:0%
+what I focus on is the fact that we he's
+offering um a mechanistic analysis of
+
+ align:start position:0%
+offering um a mechanistic analysis of
+ 
+
+ align:start position:0%
+offering um a mechanistic analysis of
+the body as a way of explaining
+
+ align:start position:0%
+the body as a way of explaining
+ 
+
+ align:start position:0%
+the body as a way of explaining
+something that most people have never
+
+ align:start position:0%
+something that most people have never
+ 
+
+ align:start position:0%
+something that most people have never
+thought cannot be explained that is not
+
+ align:start position:0%
+thought cannot be explained that is not
+ 
+
+ align:start position:0%
+thought cannot be explained that is not
+reducible merely to physiological or um
+
+ align:start position:0%
+reducible merely to physiological or um
+ 
+
+ align:start position:0%
+reducible merely to physiological or um
+other bodily um explorations. In other
+
+ align:start position:0%
+other bodily um explorations. In other
+ 
+
+ align:start position:0%
+other bodily um explorations. In other
+words, he he rejects a Freudian
+
+ align:start position:0%
+words, he he rejects a Freudian
+ 
+
+ align:start position:0%
+words, he he rejects a Freudian
+reduction of love to sex or any any
+
+ align:start position:0%
+reduction of love to sex or any any
+ 
+
+ align:start position:0%
+reduction of love to sex or any any
+statement of it in terms of chemistry or
+
+ align:start position:0%
+statement of it in terms of chemistry or
+ 
+
+ align:start position:0%
+statement of it in terms of chemistry or
+or
+
+ align:start position:0%
+or
+ 
+
+ align:start position:0%
+or
+hormones um in order to give his own
+
+ align:start position:0%
+hormones um in order to give his own
+ 
+
+ align:start position:0%
+hormones um in order to give his own
+idea of what he's talking about and that
+
+ align:start position:0%
+idea of what he's talking about and that
+ 
+
+ align:start position:0%
+idea of what he's talking about and that
+uh studying artificial intelligence will
+
+ align:start position:0%
+uh studying artificial intelligence will
+ 
+
+ align:start position:0%
+uh studying artificial intelligence will
+help us to understand what brings it
+
+ align:start position:0%
+help us to understand what brings it
+ 
+
+ align:start position:0%
+help us to understand what brings it
+about. Okay. on in page in the third
+
+ align:start position:0%
+about. Okay. on in page in the third
+ 
+
+ align:start position:0%
+about. Okay. on in page in the third
+chapter. However,
+
+ align:start position:0%
+chapter. However,
+ 
+
+ align:start position:0%
+chapter. However,
+um he then takes another tact which is
+
+ align:start position:0%
+um he then takes another tact which is
+ 
+
+ align:start position:0%
+um he then takes another tact which is
+the one that I was talking about last
+
+ align:start position:0%
+the one that I was talking about last
+ 
+
+ align:start position:0%
+the one that I was talking about last
+time that that I mentioned today uh
+
+ align:start position:0%
+time that that I mentioned today uh
+ 
+
+ align:start position:0%
+time that that I mentioned today uh
+briefly. I will argue that each of our
+
+ align:start position:0%
+briefly. I will argue that each of our
+ 
+
+ align:start position:0%
+briefly. I will argue that each of our
+various each of our various mental
+
+ align:start position:0%
+various each of our various mental
+ 
+
+ align:start position:0%
+various each of our various mental
+states so that would include our
+
+ align:start position:0%
+states so that would include our
+ 
+
+ align:start position:0%
+states so that would include our
+feelings is a different pattern of ways
+
+ align:start position:0%
+feelings is a different pattern of ways
+ 
+
+ align:start position:0%
+feelings is a different pattern of ways
+to think and that what we call feelings
+
+ align:start position:0%
+to think and that what we call feelings
+ 
+
+ align:start position:0%
+to think and that what we call feelings
+could be attempts by some parts of a of
+
+ align:start position:0%
+could be attempts by some parts of a of
+ 
+
+ align:start position:0%
+could be attempts by some parts of a of
+a mind to describe some aspects of those
+
+ align:start position:0%
+a mind to describe some aspects of those
+ 
+
+ align:start position:0%
+a mind to describe some aspects of those
+conditions. Now that's a contradiction I
+
+ align:start position:0%
+conditions. Now that's a contradiction I
+ 
+
+ align:start position:0%
+conditions. Now that's a contradiction I
+think to the first view and the
+
+ align:start position:0%
+think to the first view and the
+ 
+
+ align:start position:0%
+think to the first view and the
+fluctuates back and forth. Uh and that I
+
+ align:start position:0%
+fluctuates back and forth. Uh and that I
+ 
+
+ align:start position:0%
+fluctuates back and forth. Uh and that I
+think is a problem uh with much of what
+
+ align:start position:0%
+think is a problem uh with much of what
+ 
+
+ align:start position:0%
+think is a problem uh with much of what
+he has to say. Um let let's go back now
+
+ align:start position:0%
+he has to say. Um let let's go back now
+ 
+
+ align:start position:0%
+he has to say. Um let let's go back now
+to um uh Tom if he wants or if you've
+
+ align:start position:0%
+to um uh Tom if he wants or if you've
+ 
+
+ align:start position:0%
+to um uh Tom if he wants or if you've
+exhausted your ideas. I mean if if if
+
+ align:start position:0%
+exhausted your ideas. I mean if if if
+ 
+
+ align:start position:0%
+exhausted your ideas. I mean if if if
+you have said as much as about your use
+
+ align:start position:0%
+you have said as much as about your use
+ 
+
+ align:start position:0%
+you have said as much as about your use
+of artificial intelligence as you want
+
+ align:start position:0%
+of artificial intelligence as you want
+ 
+
+ align:start position:0%
+of artificial intelligence as you want
+to we can go further. Do you want it to
+
+ align:start position:0%
+to we can go further. Do you want it to
+ 
+
+ align:start position:0%
+to we can go further. Do you want it to
+go? You don't want you don't feel any
+
+ align:start position:0%
+go? You don't want you don't feel any
+ 
+
+ align:start position:0%
+go? You don't want you don't feel any
+need. Yeah. All right. With all of you
+
+ align:start position:0%
+need. Yeah. All right. With all of you
+ 
+
+ align:start position:0%
+need. Yeah. All right. With all of you
+please read carefully the paragraph at
+
+ align:start position:0%
+please read carefully the paragraph at
+ 
+
+ align:start position:0%
+please read carefully the paragraph at
+the bottom of the syllabus.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Um Amy
+
+ align:start position:0%
+Um Amy
+ 
+
+ align:start position:0%
+Um Amy
+Um I read the from the related resources
+
+ align:start position:0%
+Um I read the from the related resources
+ 
+
+ align:start position:0%
+Um I read the from the related resources
+the nature of creativity by Sternberg.
+
+ align:start position:0%
+the nature of creativity by Sternberg.
+ 
+
+ align:start position:0%
+the nature of creativity by Sternberg.
+It's a collection of essays and I talked
+
+ align:start position:0%
+It's a collection of essays and I talked
+ 
+
+ align:start position:0%
+It's a collection of essays and I talked
+about last week I'm going to talk about
+
+ align:start position:0%
+about last week I'm going to talk about
+ 
+
+ align:start position:0%
+about last week I'm going to talk about
+the investment theory of creativity
+
+ align:start position:0%
+the investment theory of creativity
+ 
+
+ align:start position:0%
+the investment theory of creativity
+which asserts that creative thinkers are
+
+ align:start position:0%
+which asserts that creative thinkers are
+ 
+
+ align:start position:0%
+which asserts that creative thinkers are
+like good investors who buy low and sell
+
+ align:start position:0%
+like good investors who buy low and sell
+ 
+
+ align:start position:0%
+like good investors who buy low and sell
+high and basically want to generate
+
+ align:start position:0%
+high and basically want to generate
+ 
+
+ align:start position:0%
+high and basically want to generate
+ideas. Okay. That's that's what you
+
+ align:start position:0%
+ideas. Okay. That's that's what you
+ 
+
+ align:start position:0%
+ideas. Okay. That's that's what you
+mentioned last time. Have you progressed
+
+ align:start position:0%
+mentioned last time. Have you progressed
+ 
+
+ align:start position:0%
+mentioned last time. Have you progressed
+further? Yeah. So basically what I'm
+
+ align:start position:0%
+further? Yeah. So basically what I'm
+ 
+
+ align:start position:0%
+further? Yeah. So basically what I'm
+going to do is they
+
+ align:start position:0%
+going to do is they
+ 
+
+ align:start position:0%
+going to do is they
+divide up creativity like make an effort
+
+ align:start position:0%
+divide up creativity like make an effort
+ 
+
+ align:start position:0%
+divide up creativity like make an effort
+to define it into different categories.
+
+ align:start position:0%
+to define it into different categories.
+ 
+
+ align:start position:0%
+to define it into different categories.
+Those being um in terms of creative
+
+ align:start position:0%
+Those being um in terms of creative
+ 
+
+ align:start position:0%
+Those being um in terms of creative
+leadership um say more more um they're
+
+ align:start position:0%
+leadership um say more more um they're
+ 
+
+ align:start position:0%
+leadership um say more more um they're
+dividing slowly at the crucial points
+
+ align:start position:0%
+dividing slowly at the crucial points
+ 
+
+ align:start position:0%
+dividing slowly at the crucial points
+they're dividing
+
+ align:start position:0%
+they're dividing
+ 
+
+ align:start position:0%
+they're dividing
+um different types of creativity into
+
+ align:start position:0%
+um different types of creativity into
+ 
+
+ align:start position:0%
+um different types of creativity into
+different categories. Those being Go
+
+ align:start position:0%
+different categories. Those being Go
+ 
+
+ align:start position:0%
+different categories. Those being Go
+ahead. Right. Those being um leadership
+
+ align:start position:0%
+ahead. Right. Those being um leadership
+ 
+
+ align:start position:0%
+ahead. Right. Those being um leadership
+that accepts existing ways of doing
+
+ align:start position:0%
+that accepts existing ways of doing
+ 
+
+ align:start position:0%
+that accepts existing ways of doing
+leadership that accepts existing ways of
+
+ align:start position:0%
+leadership that accepts existing ways of
+ 
+
+ align:start position:0%
+leadership that accepts existing ways of
+doing things
+
+ align:start position:0%
+doing things
+ 
+
+ align:start position:0%
+doing things
+um which could include replication,
+
+ align:start position:0%
+um which could include replication,
+ 
+
+ align:start position:0%
+um which could include replication,
+redefination,
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+either trying to advance an existing
+
+ align:start position:0%
+either trying to advance an existing
+ 
+
+ align:start position:0%
+either trying to advance an existing
+idea a little bit or trying to advance
+
+ align:start position:0%
+idea a little bit or trying to advance
+ 
+
+ align:start position:0%
+idea a little bit or trying to advance
+an existing idea. That sounds like the
+
+ align:start position:0%
+an existing idea. That sounds like the
+ 
+
+ align:start position:0%
+an existing idea. That sounds like the
+second of Bowden's categories
+
+ align:start position:0%
+second of Bowden's categories
+ 
+
+ align:start position:0%
+second of Bowden's categories
+where um if it's creative it's at a
+
+ align:start position:0%
+where um if it's creative it's at a
+ 
+
+ align:start position:0%
+where um if it's creative it's at a
+lesser level or to a lesser lesser
+
+ align:start position:0%
+lesser level or to a lesser lesser
+ 
+
+ align:start position:0%
+lesser level or to a lesser lesser
+degree. uh in that uh chapter that
+
+ align:start position:0%
+degree. uh in that uh chapter that
+ 
+
+ align:start position:0%
+degree. uh in that uh chapter that
+called the definition of creativity that
+
+ align:start position:0%
+called the definition of creativity that
+ 
+
+ align:start position:0%
+called the definition of creativity that
+I mentioned uh she contrasts Mozart and
+
+ align:start position:0%
+I mentioned uh she contrasts Mozart and
+ 
+
+ align:start position:0%
+I mentioned uh she contrasts Mozart and
+Beetho and Heiden in that respect that
+
+ align:start position:0%
+Beetho and Heiden in that respect that
+ 
+
+ align:start position:0%
+Beetho and Heiden in that respect that
+what Heiden does is creative but within
+
+ align:start position:0%
+what Heiden does is creative but within
+ 
+
+ align:start position:0%
+what Heiden does is creative but within
+limits set by the musical tradition what
+
+ align:start position:0%
+limits set by the musical tradition what
+ 
+
+ align:start position:0%
+limits set by the musical tradition what
+we call classical music which he was one
+
+ align:start position:0%
+we call classical music which he was one
+ 
+
+ align:start position:0%
+we call classical music which he was one
+of the founders of but that he had
+
+ align:start position:0%
+of the founders of but that he had
+ 
+
+ align:start position:0%
+of the founders of but that he had
+somehow to a large extent some degree
+
+ align:start position:0%
+somehow to a large extent some degree
+ 
+
+ align:start position:0%
+somehow to a large extent some degree
+had inherited from the way music was
+
+ align:start position:0%
+had inherited from the way music was
+ 
+
+ align:start position:0%
+had inherited from the way music was
+being done at that time in the early
+
+ align:start position:0%
+being done at that time in the early
+ 
+
+ align:start position:0%
+being done at that time in the early
+18th century.
+
+ align:start position:0%
+18th century.
+ 
+
+ align:start position:0%
+18th century.
+That's to be contrasted with Mozart who
+
+ align:start position:0%
+That's to be contrasted with Mozart who
+ 
+
+ align:start position:0%
+That's to be contrasted with Mozart who
+um digests all of that. But then he does
+
+ align:start position:0%
+um digests all of that. But then he does
+ 
+
+ align:start position:0%
+um digests all of that. But then he does
+these very different
+
+ align:start position:0%
+these very different
+ 
+
+ align:start position:0%
+these very different
+basically extensively different kinds of
+
+ align:start position:0%
+basically extensively different kinds of
+ 
+
+ align:start position:0%
+basically extensively different kinds of
+uses of the accepted rules.
+
+ align:start position:0%
+uses of the accepted rules.
+ 
+
+ align:start position:0%
+uses of the accepted rules.
+Um and as I think I mentioned in the
+
+ align:start position:0%
+Um and as I think I mentioned in the
+ 
+
+ align:start position:0%
+Um and as I think I mentioned in the
+first class of the course, I myself
+
+ align:start position:0%
+first class of the course, I myself
+ 
+
+ align:start position:0%
+first class of the course, I myself
+would then contrast Mozart with
+
+ align:start position:0%
+would then contrast Mozart with
+ 
+
+ align:start position:0%
+would then contrast Mozart with
+Beethoven because Mozart was a great
+
+ align:start position:0%
+Beethoven because Mozart was a great
+ 
+
+ align:start position:0%
+Beethoven because Mozart was a great
+genius who knew how to invent he in a
+
+ align:start position:0%
+genius who knew how to invent he in a
+ 
+
+ align:start position:0%
+genius who knew how to invent he in a
+sense one might even this I don't know
+
+ align:start position:0%
+sense one might even this I don't know
+ 
+
+ align:start position:0%
+sense one might even this I don't know
+if this is uh going to make much sense
+
+ align:start position:0%
+if this is uh going to make much sense
+ 
+
+ align:start position:0%
+if this is uh going to make much sense
+but let's try it out. uh that Mozart was
+
+ align:start position:0%
+but let's try it out. uh that Mozart was
+ 
+
+ align:start position:0%
+but let's try it out. uh that Mozart was
+not creative in his genius so much as
+
+ align:start position:0%
+not creative in his genius so much as
+ 
+
+ align:start position:0%
+not creative in his genius so much as
+inventive. Um that he would invent new
+
+ align:start position:0%
+inventive. Um that he would invent new
+ 
+
+ align:start position:0%
+inventive. Um that he would invent new
+melodies. He would turn on the faucet
+
+ align:start position:0%
+melodies. He would turn on the faucet
+ 
+
+ align:start position:0%
+melodies. He would turn on the faucet
+and out would come all of these
+
+ align:start position:0%
+and out would come all of these
+ 
+
+ align:start position:0%
+and out would come all of these
+different possibilities, but that they
+
+ align:start position:0%
+different possibilities, but that they
+ 
+
+ align:start position:0%
+different possibilities, but that they
+were not based on some fundamental
+
+ align:start position:0%
+were not based on some fundamental
+ 
+
+ align:start position:0%
+were not based on some fundamental
+construction of new rules uh for doing
+
+ align:start position:0%
+construction of new rules uh for doing
+ 
+
+ align:start position:0%
+construction of new rules uh for doing
+music or new forms of music. Whereas
+
+ align:start position:0%
+music or new forms of music. Whereas
+ 
+
+ align:start position:0%
+music or new forms of music. Whereas
+Beethoven
+
+ align:start position:0%
+Beethoven
+ 
+
+ align:start position:0%
+Beethoven
+uh was creative in that respect that uh
+
+ align:start position:0%
+uh was creative in that respect that uh
+ 
+
+ align:start position:0%
+uh was creative in that respect that uh
+he did invent those
+
+ align:start position:0%
+he did invent those
+ 
+
+ align:start position:0%
+he did invent those
+new new ways of doing things. He
+
+ align:start position:0%
+new new ways of doing things. He
+ 
+
+ align:start position:0%
+new new ways of doing things. He
+experimented with them and and when he
+
+ align:start position:0%
+experimented with them and and when he
+ 
+
+ align:start position:0%
+experimented with them and and when he
+did them uh people thought they were
+
+ align:start position:0%
+did them uh people thought they were
+ 
+
+ align:start position:0%
+did them uh people thought they were
+very strange and wild. Um I was reading
+
+ align:start position:0%
+very strange and wild. Um I was reading
+ 
+
+ align:start position:0%
+very strange and wild. Um I was reading
+a biography of Mendlesson uh who was
+
+ align:start position:0%
+a biography of Mendlesson uh who was
+ 
+
+ align:start position:0%
+a biography of Mendlesson uh who was
+himself a genius and whose father um um
+
+ align:start position:0%
+himself a genius and whose father um um
+ 
+
+ align:start position:0%
+himself a genius and whose father um um
+um was uh great lover of music and very
+
+ align:start position:0%
+um was uh great lover of music and very
+ 
+
+ align:start position:0%
+um was uh great lover of music and very
+very knowledgeable. Um and the father uh
+
+ align:start position:0%
+very knowledgeable. Um and the father uh
+ 
+
+ align:start position:0%
+very knowledgeable. Um and the father uh
+didn't think much of Beethoven. This
+
+ align:start position:0%
+didn't think much of Beethoven. This
+ 
+
+ align:start position:0%
+didn't think much of Beethoven. This
+would be in the early 19th century maybe
+
+ align:start position:0%
+would be in the early 19th century maybe
+ 
+
+ align:start position:0%
+would be in the early 19th century maybe
+couple of decades after Beethoven died.
+
+ align:start position:0%
+couple of decades after Beethoven died.
+ 
+
+ align:start position:0%
+couple of decades after Beethoven died.
+And uh he said all this you know the
+
+ align:start position:0%
+And uh he said all this you know the
+ 
+
+ align:start position:0%
+And uh he said all this you know the
+last quartets they're just sort of
+
+ align:start position:0%
+last quartets they're just sort of
+ 
+
+ align:start position:0%
+last quartets they're just sort of
+formless and wild and unprincipled and
+
+ align:start position:0%
+formless and wild and unprincipled and
+ 
+
+ align:start position:0%
+formless and wild and unprincipled and
+he didn't think much of Beethoven. The
+
+ align:start position:0%
+he didn't think much of Beethoven. The
+ 
+
+ align:start position:0%
+he didn't think much of Beethoven. The
+truth is that Beethoven was
+
+ align:start position:0%
+truth is that Beethoven was
+ 
+
+ align:start position:0%
+truth is that Beethoven was
+experimenting with new forms in such an
+
+ align:start position:0%
+experimenting with new forms in such an
+ 
+
+ align:start position:0%
+experimenting with new forms in such an
+original way that many people couldn't
+
+ align:start position:0%
+original way that many people couldn't
+ 
+
+ align:start position:0%
+original way that many people couldn't
+quite even practice uh sympathetic
+
+ align:start position:0%
+quite even practice uh sympathetic
+ 
+
+ align:start position:0%
+quite even practice uh sympathetic
+musicians couldn't understand what he
+
+ align:start position:0%
+musicians couldn't understand what he
+ 
+
+ align:start position:0%
+musicians couldn't understand what he
+was doing. Well that would be a
+
+ align:start position:0%
+was doing. Well that would be a
+ 
+
+ align:start position:0%
+was doing. Well that would be a
+different mode of creativity. So you
+
+ align:start position:0%
+different mode of creativity. So you
+ 
+
+ align:start position:0%
+different mode of creativity. So you
+would have if you want to explore this
+
+ align:start position:0%
+would have if you want to explore this
+ 
+
+ align:start position:0%
+would have if you want to explore this
+let's go back to the Bowden chapter uh
+
+ align:start position:0%
+let's go back to the Bowden chapter uh
+ 
+
+ align:start position:0%
+let's go back to the Bowden chapter uh
+but from Tom I gather maybe you don't
+
+ align:start position:0%
+but from Tom I gather maybe you don't
+ 
+
+ align:start position:0%
+but from Tom I gather maybe you don't
+have to go there anything in Bodance
+
+ align:start position:0%
+have to go there anything in Bodance
+ 
+
+ align:start position:0%
+have to go there anything in Bodance
+will give you the same um explore these
+
+ align:start position:0%
+will give you the same um explore these
+ 
+
+ align:start position:0%
+will give you the same um explore these
+as three different possibilities okay
+
+ align:start position:0%
+as three different possibilities okay
+ 
+
+ align:start position:0%
+as three different possibilities okay
+that's all under the first category now
+
+ align:start position:0%
+that's all under the first category now
+ 
+
+ align:start position:0%
+that's all under the first category now
+go on yeah so I was going to say the
+
+ align:start position:0%
+go on yeah so I was going to say the
+ 
+
+ align:start position:0%
+go on yeah so I was going to say the
+second category is creativity that
+
+ align:start position:0%
+second category is creativity that
+ 
+
+ align:start position:0%
+second category is creativity that
+challenges existing ways of doing things
+
+ align:start position:0%
+challenges existing ways of doing things
+ 
+
+ align:start position:0%
+challenges existing ways of doing things
+or if you think about it um more of
+
+ align:start position:0%
+or if you think about it um more of
+ 
+
+ align:start position:0%
+or if you think about it um more of
+inventiveness opposed to well the word
+
+ align:start position:0%
+inventiveness opposed to well the word
+ 
+
+ align:start position:0%
+inventiveness opposed to well the word
+again yeah that now we're getting into
+
+ align:start position:0%
+again yeah that now we're getting into
+ 
+
+ align:start position:0%
+again yeah that now we're getting into
+the terminological problem about word
+
+ align:start position:0%
+the terminological problem about word
+ 
+
+ align:start position:0%
+the terminological problem about word
+what the word inventiveness means as
+
+ align:start position:0%
+what the word inventiveness means as
+ 
+
+ align:start position:0%
+what the word inventiveness means as
+opposed to uh creativity um um
+
+ align:start position:0%
+opposed to uh creativity um um
+ 
+
+ align:start position:0%
+opposed to uh creativity um um
+Kesler distinguishes between creativity
+
+ align:start position:0%
+Kesler distinguishes between creativity
+ 
+
+ align:start position:0%
+Kesler distinguishes between creativity
+and inventiveness too um also what
+
+ align:start position:0%
+and inventiveness too um also what
+ 
+
+ align:start position:0%
+and inventiveness too um also what
+you're saying about the um
+
+ align:start position:0%
+you're saying about the um
+ 
+
+ align:start position:0%
+you're saying about the um
+third the third the second category
+
+ align:start position:0%
+third the third the second category
+ 
+
+ align:start position:0%
+third the third the second category
+seems to the the definition that Kesler
+
+ align:start position:0%
+seems to the the definition that Kesler
+ 
+
+ align:start position:0%
+seems to the the definition that Kesler
+gives for all creativity that all
+
+ align:start position:0%
+gives for all creativity that all
+ 
+
+ align:start position:0%
+gives for all creativity that all
+creativity is the reaction against
+
+ align:start position:0%
+creativity is the reaction against
+ 
+
+ align:start position:0%
+creativity is the reaction against
+established ways of doing things. That
+
+ align:start position:0%
+established ways of doing things. That
+ 
+
+ align:start position:0%
+established ways of doing things. That
+the creativity consists in that by
+
+ align:start position:0%
+the creativity consists in that by
+ 
+
+ align:start position:0%
+the creativity consists in that by
+association. You remember that Kesla
+
+ align:start position:0%
+association. You remember that Kesla
+ 
+
+ align:start position:0%
+association. You remember that Kesla
+talks about where you take two separated
+
+ align:start position:0%
+talks about where you take two separated
+ 
+
+ align:start position:0%
+talks about where you take two separated
+methods of thinking and of and of
+
+ align:start position:0%
+methods of thinking and of and of
+ 
+
+ align:start position:0%
+methods of thinking and of and of
+imagination and you combine them two.
+
+ align:start position:0%
+imagination and you combine them two.
+ 
+
+ align:start position:0%
+imagination and you combine them two.
+you you unite them in a way that nobody
+
+ align:start position:0%
+you you unite them in a way that nobody
+ 
+
+ align:start position:0%
+you you unite them in a way that nobody
+else has done. So that would seem to fit
+
+ align:start position:0%
+else has done. So that would seem to fit
+ 
+
+ align:start position:0%
+else has done. So that would seem to fit
+the second category. Yeah. I guess that
+
+ align:start position:0%
+the second category. Yeah. I guess that
+ 
+
+ align:start position:0%
+the second category. Yeah. I guess that
+um Sternberg is more saying that um a
+
+ align:start position:0%
+um Sternberg is more saying that um a
+ 
+
+ align:start position:0%
+um Sternberg is more saying that um a
+credifying type of creativity might be
+
+ align:start position:0%
+credifying type of creativity might be
+ 
+
+ align:start position:0%
+credifying type of creativity might be
+something that's reconstructed from a
+
+ align:start position:0%
+something that's reconstructed from a
+ 
+
+ align:start position:0%
+something that's reconstructed from a
+point in the past but might not be
+
+ align:start position:0%
+point in the past but might not be
+ 
+
+ align:start position:0%
+point in the past but might not be
+something that's used in the present.
+
+ align:start position:0%
+something that's used in the present.
+ 
+
+ align:start position:0%
+something that's used in the present.
+And one of the examples that he brings
+
+ align:start position:0%
+And one of the examples that he brings
+ 
+
+ align:start position:0%
+And one of the examples that he brings
+up is the Clinton administration
+
+ align:start position:0%
+up is the Clinton administration
+ 
+
+ align:start position:0%
+up is the Clinton administration
+um trying to achieve a balanced budget,
+
+ align:start position:0%
+um trying to achieve a balanced budget,
+ 
+
+ align:start position:0%
+um trying to achieve a balanced budget,
+which although it might not seem
+
+ align:start position:0%
+which although it might not seem
+ 
+
+ align:start position:0%
+which although it might not seem
+creative, was something that hadn't been
+
+ align:start position:0%
+creative, was something that hadn't been
+ 
+
+ align:start position:0%
+creative, was something that hadn't been
+done in a long time. And basically he's
+
+ align:start position:0%
+done in a long time. And basically he's
+ 
+
+ align:start position:0%
+done in a long time. And basically he's
+arguing that that is in a sense creative
+
+ align:start position:0%
+arguing that that is in a sense creative
+ 
+
+ align:start position:0%
+arguing that that is in a sense creative
+because they were able to redirect
+
+ align:start position:0%
+because they were able to redirect
+ 
+
+ align:start position:0%
+because they were able to redirect
+um basically the direction of the
+
+ align:start position:0%
+um basically the direction of the
+ 
+
+ align:start position:0%
+um basically the direction of the
+financial state. Is this the third
+
+ align:start position:0%
+financial state. Is this the third
+ 
+
+ align:start position:0%
+financial state. Is this the third
+category? No, it's under like saying
+
+ align:start position:0%
+category? No, it's under like saying
+ 
+
+ align:start position:0%
+category? No, it's under like saying
+that this is like a crowd-defying type
+
+ align:start position:0%
+that this is like a crowd-defying type
+ 
+
+ align:start position:0%
+that this is like a crowd-defying type
+of creativity
+
+ align:start position:0%
+of creativity
+ 
+
+ align:start position:0%
+of creativity
+and he's just trying to use a lot of
+
+ align:start position:0%
+and he's just trying to use a lot of
+ 
+
+ align:start position:0%
+and he's just trying to use a lot of
+different examples. Sternberg talks
+
+ align:start position:0%
+different examples. Sternberg talks
+ 
+
+ align:start position:0%
+different examples. Sternberg talks
+about businesses. He talks about product
+
+ align:start position:0%
+about businesses. He talks about product
+ 
+
+ align:start position:0%
+about businesses. He talks about product
+design. He talks about the government.
+
+ align:start position:0%
+design. He talks about the government.
+ 
+
+ align:start position:0%
+design. He talks about the government.
+So, he's just trying to say that
+
+ align:start position:0%
+So, he's just trying to say that
+ 
+
+ align:start position:0%
+So, he's just trying to say that
+basically they were a new like their
+
+ align:start position:0%
+basically they were a new like their
+ 
+
+ align:start position:0%
+basically they were a new like their
+administration was using a new type
+
+ align:start position:0%
+administration was using a new type
+ 
+
+ align:start position:0%
+administration was using a new type
+their leadership was exemplifying a new
+
+ align:start position:0%
+their leadership was exemplifying a new
+ 
+
+ align:start position:0%
+their leadership was exemplifying a new
+type of creativity since they went back
+
+ align:start position:0%
+type of creativity since they went back
+ 
+
+ align:start position:0%
+type of creativity since they went back
+to um the era of actually making balance
+
+ align:start position:0%
+to um the era of actually making balance
+ 
+
+ align:start position:0%
+to um the era of actually making balance
+budget and that that isn't what after
+
+ align:start position:0%
+budget and that that isn't what after
+ 
+
+ align:start position:0%
+budget and that that isn't what after
+all I may have misunderstood what you're
+
+ align:start position:0%
+all I may have misunderstood what you're
+ 
+
+ align:start position:0%
+all I may have misunderstood what you're
+saying that isn't what Kesler had in
+
+ align:start position:0%
+saying that isn't what Kesler had in
+ 
+
+ align:start position:0%
+saying that isn't what Kesler had in
+mind. This is a a redirection whereas
+
+ align:start position:0%
+mind. This is a a redirection whereas
+ 
+
+ align:start position:0%
+mind. This is a a redirection whereas
+Tesla's idea is that it's a a kind of
+
+ align:start position:0%
+Tesla's idea is that it's a a kind of
+ 
+
+ align:start position:0%
+Tesla's idea is that it's a a kind of
+radical a logically radical way of
+
+ align:start position:0%
+radical a logically radical way of
+ 
+
+ align:start position:0%
+radical a logically radical way of
+combining what everyone else would have
+
+ align:start position:0%
+combining what everyone else would have
+ 
+
+ align:start position:0%
+combining what everyone else would have
+thought would be um irreconcilable
+
+ align:start position:0%
+thought would be um irreconcilable
+ 
+
+ align:start position:0%
+thought would be um irreconcilable
+differences opposites. Yeah, I was going
+
+ align:start position:0%
+differences opposites. Yeah, I was going
+ 
+
+ align:start position:0%
+differences opposites. Yeah, I was going
+to say Sternberg's third idea is
+
+ align:start position:0%
+to say Sternberg's third idea is
+ 
+
+ align:start position:0%
+to say Sternberg's third idea is
+synthesis
+
+ align:start position:0%
+synthesis
+ 
+
+ align:start position:0%
+synthesis
+and that would be more that is that
+
+ align:start position:0%
+and that would be more that is that
+ 
+
+ align:start position:0%
+and that would be more that is that
+would be what that would be more like
+
+ align:start position:0%
+would be what that would be more like
+ 
+
+ align:start position:0%
+would be what that would be more like
+what Kesler was saying is is there a
+
+ align:start position:0%
+what Kesler was saying is is there a
+ 
+
+ align:start position:0%
+what Kesler was saying is is there a
+category for that? Yeah, his third
+
+ align:start position:0%
+category for that? Yeah, his third
+ 
+
+ align:start position:0%
+category for that? Yeah, his third
+category is synthesis and that's the one
+
+ align:start position:0%
+category is synthesis and that's the one
+ 
+
+ align:start position:0%
+category is synthesis and that's the one
+that's least described obviously but a
+
+ align:start position:0%
+that's least described obviously but a
+ 
+
+ align:start position:0%
+that's least described obviously but a
+synthesis uh among uh what seemed to be
+
+ align:start position:0%
+synthesis uh among uh what seemed to be
+ 
+
+ align:start position:0%
+synthesis uh among uh what seemed to be
+irreconcilable opposites not just a
+
+ align:start position:0%
+irreconcilable opposites not just a
+ 
+
+ align:start position:0%
+irreconcilable opposites not just a
+synthesis but that particular one
+
+ align:start position:0%
+synthesis but that particular one
+ 
+
+ align:start position:0%
+synthesis but that particular one
+otherwise everyone would have thought
+
+ align:start position:0%
+otherwise everyone would have thought
+ 
+
+ align:start position:0%
+otherwise everyone would have thought
+about it but it's because it's the
+
+ align:start position:0%
+about it but it's because it's the
+ 
+
+ align:start position:0%
+about it but it's because it's the
+components seem to be irreconcilable the
+
+ align:start position:0%
+components seem to be irreconcilable the
+ 
+
+ align:start position:0%
+components seem to be irreconcilable the
+synthesis is created
+
+ align:start position:0%
+synthesis is created
+ 
+
+ align:start position:0%
+synthesis is created
+okay now okay now uh do you want to go
+
+ align:start position:0%
+okay now okay now uh do you want to go
+ 
+
+ align:start position:0%
+okay now okay now uh do you want to go
+through all of them or Uh, I mean I
+
+ align:start position:0%
+through all of them or Uh, I mean I
+ 
+
+ align:start position:0%
+through all of them or Uh, I mean I
+there should probably be enough time. I
+
+ align:start position:0%
+there should probably be enough time. I
+ 
+
+ align:start position:0%
+there should probably be enough time. I
+don't know if other people want to know.
+
+ align:start position:0%
+don't know if other people want to know.
+ 
+
+ align:start position:0%
+don't know if other people want to know.
+And um you you're you're in control. I
+
+ align:start position:0%
+And um you you're you're in control. I
+ 
+
+ align:start position:0%
+And um you you're you're in control. I
+mean you don't have any problems with
+
+ align:start position:0%
+mean you don't have any problems with
+ 
+
+ align:start position:0%
+mean you don't have any problems with
+the writing of the papers. Uh I think
+
+ align:start position:0%
+the writing of the papers. Uh I think
+ 
+
+ align:start position:0%
+the writing of the papers. Uh I think
+I'm okay. So is is there any way that we
+
+ align:start position:0%
+I'm okay. So is is there any way that we
+ 
+
+ align:start position:0%
+I'm okay. So is is there any way that we
+could be of help?
+
+ align:start position:0%
+could be of help?
+ 
+
+ align:start position:0%
+could be of help?
+Um
+
+ align:start position:0%
+Um
+ 
+
+ align:start position:0%
+Um
+I think I'm okay. Okay. Uh Mel.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+All right. So
+
+ align:start position:0%
+All right. So
+ 
+
+ align:start position:0%
+All right. So
+hi.
+
+ align:start position:0%
+hi.
+ 
+
+ align:start position:0%
+hi.
+So um as I stated before last week, I
+
+ align:start position:0%
+So um as I stated before last week, I
+ 
+
+ align:start position:0%
+So um as I stated before last week, I
+will be writing about creativity and
+
+ align:start position:0%
+will be writing about creativity and
+ 
+
+ align:start position:0%
+will be writing about creativity and
+intelligence and what role creativity
+
+ align:start position:0%
+intelligence and what role creativity
+ 
+
+ align:start position:0%
+intelligence and what role creativity
+plays in the development of intelligence
+
+ align:start position:0%
+plays in the development of intelligence
+ 
+
+ align:start position:0%
+plays in the development of intelligence
+and how that leads to creative
+
+ align:start position:0%
+and how that leads to creative
+ 
+
+ align:start position:0%
+and how that leads to creative
+intellectuals.
+
+ align:start position:0%
+intellectuals.
+ 
+
+ align:start position:0%
+intellectuals.
+And so what I'm basing I'm basing a lot
+
+ align:start position:0%
+And so what I'm basing I'm basing a lot
+ 
+
+ align:start position:0%
+And so what I'm basing I'm basing a lot
+of this on on previous research that
+
+ align:start position:0%
+of this on on previous research that
+ 
+
+ align:start position:0%
+of this on on previous research that
+I've done in the past and how the mind
+
+ align:start position:0%
+I've done in the past and how the mind
+ 
+
+ align:start position:0%
+I've done in the past and how the mind
+develops especially in infants and
+
+ align:start position:0%
+develops especially in infants and
+ 
+
+ align:start position:0%
+develops especially in infants and
+adulthood. And so one of my one of my
+
+ align:start position:0%
+adulthood. And so one of my one of my
+ 
+
+ align:start position:0%
+adulthood. And so one of my one of my
+claims which is actually I would say the
+
+ align:start position:0%
+claims which is actually I would say the
+ 
+
+ align:start position:0%
+claims which is actually I would say the
+most important claim that I make is that
+
+ align:start position:0%
+most important claim that I make is that
+ 
+
+ align:start position:0%
+most important claim that I make is that
+creativity is a native function to all
+
+ align:start position:0%
+creativity is a native function to all
+ 
+
+ align:start position:0%
+creativity is a native function to all
+humans and that in order for any type of
+
+ align:start position:0%
+humans and that in order for any type of
+ 
+
+ align:start position:0%
+humans and that in order for any type of
+intellectual development to take place
+
+ align:start position:0%
+intellectual development to take place
+ 
+
+ align:start position:0%
+intellectual development to take place
+creativity must be an innate ability of
+
+ align:start position:0%
+creativity must be an innate ability of
+ 
+
+ align:start position:0%
+creativity must be an innate ability of
+our mind. And the reason I say this is
+
+ align:start position:0%
+our mind. And the reason I say this is
+ 
+
+ align:start position:0%
+our mind. And the reason I say this is
+because
+
+ align:start position:0%
+because
+ 
+
+ align:start position:0%
+because
+it is defined by James Russell L that
+
+ align:start position:0%
+it is defined by James Russell L that
+ 
+
+ align:start position:0%
+it is defined by James Russell L that
+creativity is not the finding of a thing
+
+ align:start position:0%
+creativity is not the finding of a thing
+ 
+
+ align:start position:0%
+creativity is not the finding of a thing
+but the making something out of it after
+
+ align:start position:0%
+but the making something out of it after
+ 
+
+ align:start position:0%
+but the making something out of it after
+it is found. And so from that I'm going
+
+ align:start position:0%
+it is found. And so from that I'm going
+ 
+
+ align:start position:0%
+it is found. And so from that I'm going
+to use that definition as the basis for
+
+ align:start position:0%
+to use that definition as the basis for
+ 
+
+ align:start position:0%
+to use that definition as the basis for
+the creating of new concepts that a
+
+ align:start position:0%
+the creating of new concepts that a
+ 
+
+ align:start position:0%
+the creating of new concepts that a
+person will go through throughout life
+
+ align:start position:0%
+person will go through throughout life
+ 
+
+ align:start position:0%
+person will go through throughout life
+making sense of the world from his or
+
+ align:start position:0%
+making sense of the world from his or
+ 
+
+ align:start position:0%
+making sense of the world from his or
+her experiences. Um let me interrupt
+
+ align:start position:0%
+her experiences. Um let me interrupt
+ 
+
+ align:start position:0%
+her experiences. Um let me interrupt
+you. Uh, Lel F that Lel was a poet and
+
+ align:start position:0%
+you. Uh, Lel F that Lel was a poet and
+ 
+
+ align:start position:0%
+you. Uh, Lel F that Lel was a poet and
+it's a poetic statement. Uh, I don't
+
+ align:start position:0%
+it's a poetic statement. Uh, I don't
+ 
+
+ align:start position:0%
+it's a poetic statement. Uh, I don't
+know exactly what it means and I don't
+
+ align:start position:0%
+know exactly what it means and I don't
+ 
+
+ align:start position:0%
+know exactly what it means and I don't
+have to and you don't have to, but
+
+ align:start position:0%
+have to and you don't have to, but
+ 
+
+ align:start position:0%
+have to and you don't have to, but
+putting too much weight on it. Do you
+
+ align:start position:0%
+putting too much weight on it. Do you
+ 
+
+ align:start position:0%
+putting too much weight on it. Do you
+Well, no, no, no. That's not that's not
+
+ align:start position:0%
+Well, no, no, no. That's not that's not
+ 
+
+ align:start position:0%
+Well, no, no, no. That's not that's not
+what I was basing it off of. I'm just
+
+ align:start position:0%
+what I was basing it off of. I'm just
+ 
+
+ align:start position:0%
+what I was basing it off of. I'm just
+That's I found that actually I just
+
+ align:start position:0%
+That's I found that actually I just
+ 
+
+ align:start position:0%
+That's I found that actually I just
+found that earlier today that actually
+
+ align:start position:0%
+found that earlier today that actually
+ 
+
+ align:start position:0%
+found that earlier today that actually
+supports. Okay, that's fine. But um
+
+ align:start position:0%
+supports. Okay, that's fine. But um
+ 
+
+ align:start position:0%
+supports. Okay, that's fine. But um
+also I was going like I said I was using
+
+ align:start position:0%
+also I was going like I said I was using
+ 
+
+ align:start position:0%
+also I was going like I said I was using
+creativity as an innate ability of all
+
+ align:start position:0%
+creativity as an innate ability of all
+ 
+
+ align:start position:0%
+creativity as an innate ability of all
+human beings and it's from this innate
+
+ align:start position:0%
+human beings and it's from this innate
+ 
+
+ align:start position:0%
+human beings and it's from this innate
+ability we're able to conceptualize and
+
+ align:start position:0%
+ability we're able to conceptualize and
+ 
+
+ align:start position:0%
+ability we're able to conceptualize and
+thus
+
+ align:start position:0%
+thus
+ 
+
+ align:start position:0%
+thus
+form our mental cognition
+
+ align:start position:0%
+form our mental cognition
+ 
+
+ align:start position:0%
+form our mental cognition
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+I have some sources and also I've known
+
+ align:start position:0%
+I have some sources and also I've known
+ 
+
+ align:start position:0%
+I have some sources and also I've known
+this from past research is that
+
+ align:start position:0%
+this from past research is that
+ 
+
+ align:start position:0%
+this from past research is that
+it is seems to be the case that more
+
+ align:start position:0%
+it is seems to be the case that more
+ 
+
+ align:start position:0%
+it is seems to be the case that more
+intellectual ual people tend to be more
+
+ align:start position:0%
+intellectual ual people tend to be more
+ 
+
+ align:start position:0%
+intellectual ual people tend to be more
+creative than well, let me phrase that.
+
+ align:start position:0%
+creative than well, let me phrase that.
+ 
+
+ align:start position:0%
+creative than well, let me phrase that.
+Above average intellect persons tend to
+
+ align:start position:0%
+Above average intellect persons tend to
+ 
+
+ align:start position:0%
+Above average intellect persons tend to
+be more creative than average intellect
+
+ align:start position:0%
+be more creative than average intellect
+ 
+
+ align:start position:0%
+be more creative than average intellect
+persons. Now, I'm still looking digging
+
+ align:start position:0%
+persons. Now, I'm still looking digging
+ 
+
+ align:start position:0%
+persons. Now, I'm still looking digging
+into what that's based off of, but there
+
+ align:start position:0%
+into what that's based off of, but there
+ 
+
+ align:start position:0%
+into what that's based off of, but there
+is a correlation between creativity and
+
+ align:start position:0%
+is a correlation between creativity and
+ 
+
+ align:start position:0%
+is a correlation between creativity and
+intelligence. And so from that I deduced
+
+ align:start position:0%
+intelligence. And so from that I deduced
+ 
+
+ align:start position:0%
+intelligence. And so from that I deduced
+that creativity
+
+ align:start position:0%
+that creativity
+ 
+
+ align:start position:0%
+that creativity
+is not is as stated an innate ability
+
+ align:start position:0%
+is not is as stated an innate ability
+ 
+
+ align:start position:0%
+is not is as stated an innate ability
+such as language and can be practiced.
+
+ align:start position:0%
+such as language and can be practiced.
+ 
+
+ align:start position:0%
+such as language and can be practiced.
+And from that I deduced that everyone
+
+ align:start position:0%
+And from that I deduced that everyone
+ 
+
+ align:start position:0%
+And from that I deduced that everyone
+has the potential to be a genius because
+
+ align:start position:0%
+has the potential to be a genius because
+ 
+
+ align:start position:0%
+has the potential to be a genius because
+as life goes on you keep practicing this
+
+ align:start position:0%
+as life goes on you keep practicing this
+ 
+
+ align:start position:0%
+as life goes on you keep practicing this
+create this creative process and
+
+ align:start position:0%
+create this creative process and
+ 
+
+ align:start position:0%
+create this creative process and
+creating new concepts. And so from that
+
+ align:start position:0%
+creating new concepts. And so from that
+ 
+
+ align:start position:0%
+creating new concepts. And so from that
+I argue that the uh disparity between
+
+ align:start position:0%
+I argue that the uh disparity between
+ 
+
+ align:start position:0%
+I argue that the uh disparity between
+intellectuals and non-intellectuals
+
+ align:start position:0%
+intellectuals and non-intellectuals
+ 
+
+ align:start position:0%
+intellectuals and non-intellectuals
+is not the basis of genetics but more of
+
+ align:start position:0%
+is not the basis of genetics but more of
+ 
+
+ align:start position:0%
+is not the basis of genetics but more of
+nurturing because of that creative
+
+ align:start position:0%
+nurturing because of that creative
+ 
+
+ align:start position:0%
+nurturing because of that creative
+process has not been nurtured as much as
+
+ align:start position:0%
+process has not been nurtured as much as
+ 
+
+ align:start position:0%
+process has not been nurtured as much as
+someone else who has had who has a
+
+ align:start position:0%
+someone else who has had who has a
+ 
+
+ align:start position:0%
+someone else who has had who has a
+higher IQ. So I would say that a person,
+
+ align:start position:0%
+higher IQ. So I would say that a person,
+ 
+
+ align:start position:0%
+higher IQ. So I would say that a person,
+let's say you have two children, for
+
+ align:start position:0%
+let's say you have two children, for
+ 
+
+ align:start position:0%
+let's say you have two children, for
+example, two children in a neighborhood
+
+ align:start position:0%
+example, two children in a neighborhood
+ 
+
+ align:start position:0%
+example, two children in a neighborhood
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+at the age of eight, they're roughly the
+
+ align:start position:0%
+at the age of eight, they're roughly the
+ 
+
+ align:start position:0%
+at the age of eight, they're roughly the
+same intelligence, but one grows up to
+
+ align:start position:0%
+same intelligence, but one grows up to
+ 
+
+ align:start position:0%
+same intelligence, but one grows up to
+be a professor and the other grows up to
+
+ align:start position:0%
+be a professor and the other grows up to
+ 
+
+ align:start position:0%
+be a professor and the other grows up to
+be a manager of McDonald's. And I would
+
+ align:start position:0%
+be a manager of McDonald's. And I would
+ 
+
+ align:start position:0%
+be a manager of McDonald's. And I would
+argue that the reason why this one grew
+
+ align:start position:0%
+argue that the reason why this one grew
+ 
+
+ align:start position:0%
+argue that the reason why this one grew
+up into being a professor is because he
+
+ align:start position:0%
+up into being a professor is because he
+ 
+
+ align:start position:0%
+up into being a professor is because he
+had more practice in creating new
+
+ align:start position:0%
+had more practice in creating new
+ 
+
+ align:start position:0%
+had more practice in creating new
+concepts. he was exposed to more things
+
+ align:start position:0%
+concepts. he was exposed to more things
+ 
+
+ align:start position:0%
+concepts. he was exposed to more things
+that caused that forced him in order to
+
+ align:start position:0%
+that caused that forced him in order to
+ 
+
+ align:start position:0%
+that caused that forced him in order to
+make sense of the world to be more
+
+ align:start position:0%
+make sense of the world to be more
+ 
+
+ align:start position:0%
+make sense of the world to be more
+creative than the person who was a
+
+ align:start position:0%
+creative than the person who was a
+ 
+
+ align:start position:0%
+creative than the person who was a
+manager at McDonald's. And so from that
+
+ align:start position:0%
+manager at McDonald's. And so from that
+ 
+
+ align:start position:0%
+manager at McDonald's. And so from that
+I go into one of the main questions that
+
+ align:start position:0%
+I go into one of the main questions that
+ 
+
+ align:start position:0%
+I go into one of the main questions that
+has bothered me for a long time is why
+
+ align:start position:0%
+has bothered me for a long time is why
+ 
+
+ align:start position:0%
+has bothered me for a long time is why
+is there such a disparity between
+
+ align:start position:0%
+is there such a disparity between
+ 
+
+ align:start position:0%
+is there such a disparity between
+geniuses and mentally people?
+
+ align:start position:0%
+geniuses and mentally people?
+ 
+
+ align:start position:0%
+geniuses and mentally people?
+And the reason I asked this is because
+
+ align:start position:0%
+And the reason I asked this is because
+ 
+
+ align:start position:0%
+And the reason I asked this is because
+if what I'm saying is true such that
+
+ align:start position:0%
+if what I'm saying is true such that
+ 
+
+ align:start position:0%
+if what I'm saying is true such that
+creativity is an innate ability that can
+
+ align:start position:0%
+creativity is an innate ability that can
+ 
+
+ align:start position:0%
+creativity is an innate ability that can
+be practiced practiced and strengthened
+
+ align:start position:0%
+be practiced practiced and strengthened
+ 
+
+ align:start position:0%
+be practiced practiced and strengthened
+just as language or any other ability or
+
+ align:start position:0%
+just as language or any other ability or
+ 
+
+ align:start position:0%
+just as language or any other ability or
+kinesthetic intelligence it can be
+
+ align:start position:0%
+kinesthetic intelligence it can be
+ 
+
+ align:start position:0%
+kinesthetic intelligence it can be
+strengthened with practice and
+
+ align:start position:0%
+strengthened with practice and
+ 
+
+ align:start position:0%
+strengthened with practice and
+repetition. Why is it that for mentally
+
+ align:start position:0%
+repetition. Why is it that for mentally
+ 
+
+ align:start position:0%
+repetition. Why is it that for mentally
+ persons that even with
+
+ align:start position:0%
+ persons that even with
+ 
+
+ align:start position:0%
+ persons that even with
+extensive extensive practice and
+
+ align:start position:0%
+extensive extensive practice and
+ 
+
+ align:start position:0%
+extensive extensive practice and
+repetition it is still the process of
+
+ align:start position:0%
+repetition it is still the process of
+ 
+
+ align:start position:0%
+repetition it is still the process of
+creating new concept is still slow. is
+
+ align:start position:0%
+creating new concept is still slow. is
+ 
+
+ align:start position:0%
+creating new concept is still slow. is
+still delayed and they never seem to be
+
+ align:start position:0%
+still delayed and they never seem to be
+ 
+
+ align:start position:0%
+still delayed and they never seem to be
+able to reach that level of even average
+
+ align:start position:0%
+able to reach that level of even average
+ 
+
+ align:start position:0%
+able to reach that level of even average
+intellect. And so that's what I'm going
+
+ align:start position:0%
+intellect. And so that's what I'm going
+ 
+
+ align:start position:0%
+intellect. And so that's what I'm going
+into. Well, the point are you starting
+
+ align:start position:0%
+into. Well, the point are you starting
+ 
+
+ align:start position:0%
+into. Well, the point are you starting
+out with the premise that it is innate
+
+ align:start position:0%
+out with the premise that it is innate
+ 
+
+ align:start position:0%
+out with the premise that it is innate
+in the sense that in it's innate to the
+
+ align:start position:0%
+in the sense that in it's innate to the
+ 
+
+ align:start position:0%
+in the sense that in it's innate to the
+human race and everybody is equally
+
+ align:start position:0%
+human race and everybody is equally
+ 
+
+ align:start position:0%
+human race and everybody is equally
+endowed.
+
+ align:start position:0%
+endowed.
+ 
+
+ align:start position:0%
+endowed.
+That's part of my arguments. Yeah. I
+
+ align:start position:0%
+That's part of my arguments. Yeah. I
+ 
+
+ align:start position:0%
+That's part of my arguments. Yeah. I
+would say I would say with the
+
+ align:start position:0%
+would say I would say with the
+ 
+
+ align:start position:0%
+would say I would say with the
+exceptions of born geniuses and mentally
+
+ align:start position:0%
+exceptions of born geniuses and mentally
+ 
+
+ align:start position:0%
+exceptions of born geniuses and mentally
+ people, I would say yes. Okay.
+
+ align:start position:0%
+ people, I would say yes. Okay.
+ 
+
+ align:start position:0%
+ people, I would say yes. Okay.
+Now, how do you explain those those two
+
+ align:start position:0%
+Now, how do you explain those those two
+ 
+
+ align:start position:0%
+Now, how do you explain those those two
+two kinds of of exceptions? That's what
+
+ align:start position:0%
+two kinds of of exceptions? That's what
+ 
+
+ align:start position:0%
+two kinds of of exceptions? That's what
+I'm researching right now. Also, if um
+
+ align:start position:0%
+I'm researching right now. Also, if um
+ 
+
+ align:start position:0%
+I'm researching right now. Also, if um
+as we know in many areas there are
+
+ align:start position:0%
+as we know in many areas there are
+ 
+
+ align:start position:0%
+as we know in many areas there are
+talents, aptitudes talk about that as
+
+ align:start position:0%
+talents, aptitudes talk about that as
+ 
+
+ align:start position:0%
+talents, aptitudes talk about that as
+well as that come from the genes. That's
+
+ align:start position:0%
+well as that come from the genes. That's
+ 
+
+ align:start position:0%
+well as that come from the genes. That's
+what I mean. Well, why wouldn't the
+
+ align:start position:0%
+what I mean. Well, why wouldn't the
+ 
+
+ align:start position:0%
+what I mean. Well, why wouldn't the
+creativity also be limited by the genes
+
+ align:start position:0%
+creativity also be limited by the genes
+ 
+
+ align:start position:0%
+creativity also be limited by the genes
+that we inherit? That's true. But at the
+
+ align:start position:0%
+that we inherit? That's true. But at the
+ 
+
+ align:start position:0%
+that we inherit? That's true. But at the
+same time it I may be genetically predis
+
+ align:start position:0%
+same time it I may be genetically predis
+ 
+
+ align:start position:0%
+same time it I may be genetically predis
+I may be genetically disposed and predis
+
+ align:start position:0%
+I may be genetically disposed and predis
+ 
+
+ align:start position:0%
+I may be genetically disposed and predis
+what is that predisposed there we go um
+
+ align:start position:0%
+what is that predisposed there we go um
+ 
+
+ align:start position:0%
+what is that predisposed there we go um
+I may be genetically predisposed to have
+
+ align:start position:0%
+I may be genetically predisposed to have
+ 
+
+ align:start position:0%
+I may be genetically predisposed to have
+a knack for physics but that does not
+
+ align:start position:0%
+a knack for physics but that does not
+ 
+
+ align:start position:0%
+a knack for physics but that does not
+mean that I cannot develop other mental
+
+ align:start position:0%
+mean that I cannot develop other mental
+ 
+
+ align:start position:0%
+mean that I cannot develop other mental
+faculties to that same level now wait a
+
+ align:start position:0%
+faculties to that same level now wait a
+ 
+
+ align:start position:0%
+faculties to that same level now wait a
+minute a knack is what you're
+
+ align:start position:0%
+minute a knack is what you're
+ 
+
+ align:start position:0%
+minute a knack is what you're
+predisposed to that's genetic genetic
+
+ align:start position:0%
+predisposed to that's genetic genetic
+ 
+
+ align:start position:0%
+predisposed to that's genetic genetic
+now What what does that knock? No, I
+
+ align:start position:0%
+now What what does that knock? No, I
+ 
+
+ align:start position:0%
+now What what does that knock? No, I
+mean genetically I'm predisposed to have
+
+ align:start position:0%
+mean genetically I'm predisposed to have
+ 
+
+ align:start position:0%
+mean genetically I'm predisposed to have
+a gift in physics. No, but that I mean
+
+ align:start position:0%
+a gift in physics. No, but that I mean
+ 
+
+ align:start position:0%
+a gift in physics. No, but that I mean
+what goes into that? Why I mean that
+
+ align:start position:0%
+what goes into that? Why I mean that
+ 
+
+ align:start position:0%
+what goes into that? Why I mean that
+seems very high level to choose physics?
+
+ align:start position:0%
+seems very high level to choose physics?
+ 
+
+ align:start position:0%
+seems very high level to choose physics?
+What I mean what do you have to be in
+
+ align:start position:0%
+What I mean what do you have to be in
+ 
+
+ align:start position:0%
+What I mean what do you have to be in
+order to be a physicist? Why know take
+
+ align:start position:0%
+order to be a physicist? Why know take
+ 
+
+ align:start position:0%
+order to be a physicist? Why know take
+make it a little easier or more obvious.
+
+ align:start position:0%
+make it a little easier or more obvious.
+ 
+
+ align:start position:0%
+make it a little easier or more obvious.
+Um let's say that you have a knack to be
+
+ align:start position:0%
+Um let's say that you have a knack to be
+ 
+
+ align:start position:0%
+Um let's say that you have a knack to be
+a pianist.
+
+ align:start position:0%
+a pianist.
+ 
+
+ align:start position:0%
+a pianist.
+Now what does that mean? Means I would
+
+ align:start position:0%
+Now what does that mean? Means I would
+ 
+
+ align:start position:0%
+Now what does that mean? Means I would
+interpret that as genetically you have
+
+ align:start position:0%
+interpret that as genetically you have
+ 
+
+ align:start position:0%
+interpret that as genetically you have
+the qualities and abilities in order so
+
+ align:start position:0%
+the qualities and abilities in order so
+ 
+
+ align:start position:0%
+the qualities and abilities in order so
+such that the act of playing a piano is
+
+ align:start position:0%
+such that the act of playing a piano is
+ 
+
+ align:start position:0%
+such that the act of playing a piano is
+more natural for you than that of
+
+ align:start position:0%
+more natural for you than that of
+ 
+
+ align:start position:0%
+more natural for you than that of
+another. Now would that be true of
+
+ align:start position:0%
+another. Now would that be true of
+ 
+
+ align:start position:0%
+another. Now would that be true of
+everybody? No. But what I'm saying is
+
+ align:start position:0%
+everybody? No. But what I'm saying is
+ 
+
+ align:start position:0%
+everybody? No. But what I'm saying is
+because of this inability to create new
+
+ align:start position:0%
+because of this inability to create new
+ 
+
+ align:start position:0%
+because of this inability to create new
+concepts that everyone given sufficient
+
+ align:start position:0%
+concepts that everyone given sufficient
+ 
+
+ align:start position:0%
+concepts that everyone given sufficient
+repetition at work can work up to that
+
+ align:start position:0%
+repetition at work can work up to that
+ 
+
+ align:start position:0%
+repetition at work can work up to that
+level. Everyone could. Yes. That's
+
+ align:start position:0%
+level. Everyone could. Yes. That's
+ 
+
+ align:start position:0%
+level. Everyone could. Yes. That's
+that's what I'm saying. you're you're
+
+ align:start position:0%
+that's what I'm saying. you're you're
+ 
+
+ align:start position:0%
+that's what I'm saying. you're you're
+putting creativity as an independent
+
+ align:start position:0%
+putting creativity as an independent
+ 
+
+ align:start position:0%
+putting creativity as an independent
+sort of function of the brain as opposed
+
+ align:start position:0%
+sort of function of the brain as opposed
+ 
+
+ align:start position:0%
+sort of function of the brain as opposed
+to learning or uh that there there is in
+
+ align:start position:0%
+to learning or uh that there there is in
+ 
+
+ align:start position:0%
+to learning or uh that there there is in
+every area of life
+
+ align:start position:0%
+every area of life
+ 
+
+ align:start position:0%
+every area of life
+um that innate potentiality. I would say
+
+ align:start position:0%
+um that innate potentiality. I would say
+ 
+
+ align:start position:0%
+um that innate potentiality. I would say
+yes because I would say that there I
+
+ align:start position:0%
+yes because I would say that there I
+ 
+
+ align:start position:0%
+yes because I would say that there I
+would say that the there is no mental
+
+ align:start position:0%
+would say that the there is no mental
+ 
+
+ align:start position:0%
+would say that the there is no mental
+limit to what a person is capable of
+
+ align:start position:0%
+limit to what a person is capable of
+ 
+
+ align:start position:0%
+limit to what a person is capable of
+doing. I mean, I would say that the
+
+ align:start position:0%
+doing. I mean, I would say that the
+ 
+
+ align:start position:0%
+doing. I mean, I would say that the
+reason like I play the saxophone. The
+
+ align:start position:0%
+reason like I play the saxophone. The
+ 
+
+ align:start position:0%
+reason like I play the saxophone. The
+reason why I would never ever be as
+
+ align:start position:0%
+reason why I would never ever be as
+ 
+
+ align:start position:0%
+reason why I would never ever be as
+great as say Charlie Parker is because I
+
+ align:start position:0%
+great as say Charlie Parker is because I
+ 
+
+ align:start position:0%
+great as say Charlie Parker is because I
+don't play as much as he does. Charlie
+
+ align:start position:0%
+don't play as much as he does. Charlie
+ 
+
+ align:start position:0%
+don't play as much as he does. Charlie
+Parker played from every waking moment
+
+ align:start position:0%
+Parker played from every waking moment
+ 
+
+ align:start position:0%
+Parker played from every waking moment
+of of his life. The time he woke up to
+
+ align:start position:0%
+of of his life. The time he woke up to
+ 
+
+ align:start position:0%
+of of his life. The time he woke up to
+the time he went to sleep, unless he was
+
+ align:start position:0%
+the time he went to sleep, unless he was
+ 
+
+ align:start position:0%
+the time he went to sleep, unless he was
+doing drugs, but all the time he was
+
+ align:start position:0%
+doing drugs, but all the time he was
+ 
+
+ align:start position:0%
+doing drugs, but all the time he was
+playing. As with I I play maybe an hour,
+
+ align:start position:0%
+playing. As with I I play maybe an hour,
+ 
+
+ align:start position:0%
+playing. As with I I play maybe an hour,
+a week or two. So because if if I were
+
+ align:start position:0%
+a week or two. So because if if I were
+ 
+
+ align:start position:0%
+a week or two. So because if if I were
+to play that intensely as Charlie
+
+ align:start position:0%
+to play that intensely as Charlie
+ 
+
+ align:start position:0%
+to play that intensely as Charlie
+Parker, I do not feel that there's any
+
+ align:start position:0%
+Parker, I do not feel that there's any
+ 
+
+ align:start position:0%
+Parker, I do not feel that there's any
+reason why I would not be able to get to
+
+ align:start position:0%
+reason why I would not be able to get to
+ 
+
+ align:start position:0%
+reason why I would not be able to get to
+that level. I wouldn't question that for
+
+ align:start position:0%
+that level. I wouldn't question that for
+ 
+
+ align:start position:0%
+that level. I wouldn't question that for
+a moment about you because I don't know.
+
+ align:start position:0%
+a moment about you because I don't know.
+ 
+
+ align:start position:0%
+a moment about you because I don't know.
+But uh I can't believe that that would
+
+ align:start position:0%
+But uh I can't believe that that would
+ 
+
+ align:start position:0%
+But uh I can't believe that that would
+be true of everybody that if only you
+
+ align:start position:0%
+be true of everybody that if only you
+ 
+
+ align:start position:0%
+be true of everybody that if only you
+know somebody
+
+ align:start position:0%
+know somebody
+ 
+
+ align:start position:0%
+know somebody
+in the population were picked up and
+
+ align:start position:0%
+in the population were picked up and
+ 
+
+ align:start position:0%
+in the population were picked up and
+forced or encouraged and who liked even
+
+ align:start position:0%
+forced or encouraged and who liked even
+ 
+
+ align:start position:0%
+forced or encouraged and who liked even
+to play as much as Charlie Parker did
+
+ align:start position:0%
+to play as much as Charlie Parker did
+ 
+
+ align:start position:0%
+to play as much as Charlie Parker did
+that he would ever play as well. So in
+
+ align:start position:0%
+that he would ever play as well. So in
+ 
+
+ align:start position:0%
+that he would ever play as well. So in
+that sense that's that's like the
+
+ align:start position:0%
+that sense that's that's like the
+ 
+
+ align:start position:0%
+that sense that's that's like the
+monkeys uh being put into the typewriter
+
+ align:start position:0%
+monkeys uh being put into the typewriter
+ 
+
+ align:start position:0%
+monkeys uh being put into the typewriter
+and ending up with the works of
+
+ align:start position:0%
+and ending up with the works of
+ 
+
+ align:start position:0%
+and ending up with the works of
+Shakespeare. I mean, you have it has to
+
+ align:start position:0%
+Shakespeare. I mean, you have it has to
+ 
+
+ align:start position:0%
+Shakespeare. I mean, you have it has to
+be more than just this application of
+
+ align:start position:0%
+be more than just this application of
+ 
+
+ align:start position:0%
+be more than just this application of
+the seat of the pants to the seat of the
+
+ align:start position:0%
+the seat of the pants to the seat of the
+ 
+
+ align:start position:0%
+the seat of the pants to the seat of the
+of the of the chair. That actually gives
+
+ align:start position:0%
+of the of the chair. That actually gives
+ 
+
+ align:start position:0%
+of the of the chair. That actually gives
+me a good argument for why it was
+
+ align:start position:0%
+me a good argument for why it was
+ 
+
+ align:start position:0%
+me a good argument for why it was
+genetic as well. How well you're able to
+
+ align:start position:0%
+genetic as well. How well you're able to
+ 
+
+ align:start position:0%
+genetic as well. How well you're able to
+create these new the concepts. Yes.
+
+ align:start position:0%
+create these new the concepts. Yes.
+ 
+
+ align:start position:0%
+create these new the concepts. Yes.
+What's what's the concept?
+
+ align:start position:0%
+What's what's the concept?
+ 
+
+ align:start position:0%
+What's what's the concept?
+I would say these concepts of these
+
+ align:start position:0%
+I would say these concepts of these
+ 
+
+ align:start position:0%
+I would say these concepts of these
+practices, these abilities. Oh, that
+
+ align:start position:0%
+practices, these abilities. Oh, that
+ 
+
+ align:start position:0%
+practices, these abilities. Oh, that
+they're different from concepts. Your
+
+ align:start position:0%
+they're different from concepts. Your
+ 
+
+ align:start position:0%
+they're different from concepts. Your
+ability to be creative in these was in
+
+ align:start position:0%
+ability to be creative in these was in
+ 
+
+ align:start position:0%
+ability to be creative in these was in
+these abilities, right? Well, when I say
+
+ align:start position:0%
+these abilities, right? Well, when I say
+ 
+
+ align:start position:0%
+these abilities, right? Well, when I say
+creative, I'm not strictly prevent I'm
+
+ align:start position:0%
+creative, I'm not strictly prevent I'm
+ 
+
+ align:start position:0%
+creative, I'm not strictly prevent I'm
+not strictly speaking about the arts.
+
+ align:start position:0%
+not strictly speaking about the arts.
+ 
+
+ align:start position:0%
+not strictly speaking about the arts.
+I'm speaking about like everyday life
+
+ align:start position:0%
+I'm speaking about like everyday life
+ 
+
+ align:start position:0%
+I'm speaking about like everyday life
+and particularly intelligence, the
+
+ align:start position:0%
+and particularly intelligence, the
+ 
+
+ align:start position:0%
+and particularly intelligence, the
+different faculties of intelligence. So
+
+ align:start position:0%
+different faculties of intelligence. So
+ 
+
+ align:start position:0%
+different faculties of intelligence. So
+it's just like some people
+
+ align:start position:0%
+it's just like some people
+ 
+
+ align:start position:0%
+it's just like some people
+I would argue that some people I would
+
+ align:start position:0%
+I would argue that some people I would
+ 
+
+ align:start position:0%
+I would argue that some people I would
+argue that everyone has the ability to
+
+ align:start position:0%
+argue that everyone has the ability to
+ 
+
+ align:start position:0%
+argue that everyone has the ability to
+create innately but I would say that for
+
+ align:start position:0%
+create innately but I would say that for
+ 
+
+ align:start position:0%
+create innately but I would say that for
+some people that ability is stronger
+
+ align:start position:0%
+some people that ability is stronger
+ 
+
+ align:start position:0%
+some people that ability is stronger
+than others and their lives that
+
+ align:start position:0%
+than others and their lives that
+ 
+
+ align:start position:0%
+than others and their lives that
+disparity between those strengths is the
+
+ align:start position:0%
+disparity between those strengths is the
+ 
+
+ align:start position:0%
+disparity between those strengths is the
+disparity between genius and mentally
+
+ align:start position:0%
+disparity between genius and mentally
+ 
+
+ align:start position:0%
+disparity between genius and mentally
+ But it it looks if you it
+
+ align:start position:0%
+ But it it looks if you it
+ 
+
+ align:start position:0%
+ But it it looks if you it
+seems like a truism if all you're saying
+
+ align:start position:0%
+seems like a truism if all you're saying
+ 
+
+ align:start position:0%
+seems like a truism if all you're saying
+is to some degree however slight
+
+ align:start position:0%
+is to some degree however slight
+ 
+
+ align:start position:0%
+is to some degree however slight
+everybody can be creative because that
+
+ align:start position:0%
+everybody can be creative because that
+ 
+
+ align:start position:0%
+everybody can be creative because that
+is sort of innocuous. You could say that
+
+ align:start position:0%
+is sort of innocuous. You could say that
+ 
+
+ align:start position:0%
+is sort of innocuous. You could say that
+because it doesn't matter. You know he
+
+ align:start position:0%
+because it doesn't matter. You know he
+ 
+
+ align:start position:0%
+because it doesn't matter. You know he
+has a little ability but he isn't a
+
+ align:start position:0%
+has a little ability but he isn't a
+ 
+
+ align:start position:0%
+has a little ability but he isn't a
+creative person because that amount is
+
+ align:start position:0%
+creative person because that amount is
+ 
+
+ align:start position:0%
+creative person because that amount is
+so small. No, I would say the
+
+ align:start position:0%
+so small. No, I would say the
+ 
+
+ align:start position:0%
+so small. No, I would say the
+interesting question would be if
+
+ align:start position:0%
+interesting question would be if
+ 
+
+ align:start position:0%
+interesting question would be if
+everybody has a comparable ability. I
+
+ align:start position:0%
+everybody has a comparable ability. I
+ 
+
+ align:start position:0%
+everybody has a comparable ability. I
+would say everyone of average intellect
+
+ align:start position:0%
+would say everyone of average intellect
+ 
+
+ align:start position:0%
+would say everyone of average intellect
+has a comparable ability because it
+
+ align:start position:0%
+has a comparable ability because it
+ 
+
+ align:start position:0%
+has a comparable ability because it
+requires based on my claim that
+
+ align:start position:0%
+requires based on my claim that
+ 
+
+ align:start position:0%
+requires based on my claim that
+creativity is required for intellectual
+
+ align:start position:0%
+creativity is required for intellectual
+ 
+
+ align:start position:0%
+creativity is required for intellectual
+development. In order to get to a point
+
+ align:start position:0%
+development. In order to get to a point
+ 
+
+ align:start position:0%
+development. In order to get to a point
+of self being able to live in this world
+
+ align:start position:0%
+of self being able to live in this world
+ 
+
+ align:start position:0%
+of self being able to live in this world
+self- sustained, you have to have a
+
+ align:start position:0%
+self- sustained, you have to have a
+ 
+
+ align:start position:0%
+self- sustained, you have to have a
+certain level of intelligence and from
+
+ align:start position:0%
+certain level of intelligence and from
+ 
+
+ align:start position:0%
+certain level of intelligence and from
+that creativity you are born with. You
+
+ align:start position:0%
+that creativity you are born with. You
+ 
+
+ align:start position:0%
+that creativity you are born with. You
+create the concepts required or create
+
+ align:start position:0%
+create the concepts required or create
+ 
+
+ align:start position:0%
+create the concepts required or create
+abilities or intelligence whatever part
+
+ align:start position:0%
+abilities or intelligence whatever part
+ 
+
+ align:start position:0%
+abilities or intelligence whatever part
+whatever faculty of life required in
+
+ align:start position:0%
+whatever faculty of life required in
+ 
+
+ align:start position:0%
+whatever faculty of life required in
+order to live your life at the bare at
+
+ align:start position:0%
+order to live your life at the bare at
+ 
+
+ align:start position:0%
+order to live your life at the bare at
+the bare minimum. It does. Well, I I I
+
+ align:start position:0%
+the bare minimum. It does. Well, I I I
+ 
+
+ align:start position:0%
+the bare minimum. It does. Well, I I I
+think I understand what you're saying,
+
+ align:start position:0%
+think I understand what you're saying,
+ 
+
+ align:start position:0%
+think I understand what you're saying,
+but it seems strange to
+
+ align:start position:0%
+but it seems strange to
+ 
+
+ align:start position:0%
+but it seems strange to
+treat the great j gen geniuses of this
+
+ align:start position:0%
+treat the great j gen geniuses of this
+ 
+
+ align:start position:0%
+treat the great j gen geniuses of this
+world in any field uh as sort of being
+
+ align:start position:0%
+world in any field uh as sort of being
+ 
+
+ align:start position:0%
+world in any field uh as sort of being
+um on the same level or on a par with
+
+ align:start position:0%
+um on the same level or on a par with
+ 
+
+ align:start position:0%
+um on the same level or on a par with
+ordinary mortals like ordinary mortals
+
+ align:start position:0%
+ordinary mortals like ordinary mortals
+ 
+
+ align:start position:0%
+ordinary mortals like ordinary mortals
+like most of us. You know, when I think
+
+ align:start position:0%
+like most of us. You know, when I think
+ 
+
+ align:start position:0%
+like most of us. You know, when I think
+of um people like Johan Sebastian Bach
+
+ align:start position:0%
+of um people like Johan Sebastian Bach
+ 
+
+ align:start position:0%
+of um people like Johan Sebastian Bach
+or um uh uh Emanuel Kant
+
+ align:start position:0%
+or um uh uh Emanuel Kant
+ 
+
+ align:start position:0%
+or um uh uh Emanuel Kant
+or Vitkinstein or any number of great
+
+ align:start position:0%
+or Vitkinstein or any number of great
+ 
+
+ align:start position:0%
+or Vitkinstein or any number of great
+philosophers
+
+ align:start position:0%
+philosophers
+ 
+
+ align:start position:0%
+philosophers
+or um um people like Picasso,
+
+ align:start position:0%
+or um um people like Picasso,
+ 
+
+ align:start position:0%
+or um um people like Picasso,
+there's something more that they their
+
+ align:start position:0%
+there's something more that they their
+ 
+
+ align:start position:0%
+there's something more that they their
+genius sort of exceeds anything I could
+
+ align:start position:0%
+genius sort of exceeds anything I could
+ 
+
+ align:start position:0%
+genius sort of exceeds anything I could
+ever approximate. I stand in awe of them
+
+ align:start position:0%
+ever approximate. I stand in awe of them
+ 
+
+ align:start position:0%
+ever approximate. I stand in awe of them
+and it's not because I don't want to be
+
+ align:start position:0%
+and it's not because I don't want to be
+ 
+
+ align:start position:0%
+and it's not because I don't want to be
+one of them or apply myself. It's
+
+ align:start position:0%
+one of them or apply myself. It's
+ 
+
+ align:start position:0%
+one of them or apply myself. It's
+because there is something in their
+
+ align:start position:0%
+because there is something in their
+ 
+
+ align:start position:0%
+because there is something in their
+powers of perception, something in maybe
+
+ align:start position:0%
+powers of perception, something in maybe
+ 
+
+ align:start position:0%
+powers of perception, something in maybe
+the genes, something in their very
+
+ align:start position:0%
+the genes, something in their very
+ 
+
+ align:start position:0%
+the genes, something in their very
+unique
+
+ align:start position:0%
+unique
+ 
+
+ align:start position:0%
+unique
+lifyle
+
+ align:start position:0%
+lifyle
+ 
+
+ align:start position:0%
+lifyle
+that I can't approximate no matter if
+
+ align:start position:0%
+that I can't approximate no matter if
+ 
+
+ align:start position:0%
+that I can't approximate no matter if
+any more than I could run a four mile uh
+
+ align:start position:0%
+any more than I could run a four mile uh
+ 
+
+ align:start position:0%
+any more than I could run a four mile uh
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+the mile in four minutes. Um, it's
+
+ align:start position:0%
+the mile in four minutes. Um, it's
+ 
+
+ align:start position:0%
+the mile in four minutes. Um, it's
+simply not in my reperatory. I'm not
+
+ align:start position:0%
+simply not in my reperatory. I'm not
+ 
+
+ align:start position:0%
+simply not in my reperatory. I'm not
+programmed for that to be a possibility.
+
+ align:start position:0%
+programmed for that to be a possibility.
+ 
+
+ align:start position:0%
+programmed for that to be a possibility.
+So, it is the idea of dragging them down
+
+ align:start position:0%
+So, it is the idea of dragging them down
+ 
+
+ align:start position:0%
+So, it is the idea of dragging them down
+to my level. Well, seems seems very
+
+ align:start position:0%
+to my level. Well, seems seems very
+ 
+
+ align:start position:0%
+to my level. Well, seems seems very
+questionable. I'm not dragging them
+
+ align:start position:0%
+questionable. I'm not dragging them
+ 
+
+ align:start position:0%
+questionable. I'm not dragging them
+down. I'm actually It's those people
+
+ align:start position:0%
+down. I'm actually It's those people
+ 
+
+ align:start position:0%
+down. I'm actually It's those people
+that I'm those are the anomalies and
+
+ align:start position:0%
+that I'm those are the anomalies and
+ 
+
+ align:start position:0%
+that I'm those are the anomalies and
+that's what I'm trying to explain. The
+
+ align:start position:0%
+that's what I'm trying to explain. The
+ 
+
+ align:start position:0%
+that's what I'm trying to explain. The
+geniuses and the mentally
+
+ align:start position:0%
+geniuses and the mentally
+ 
+
+ align:start position:0%
+geniuses and the mentally
+Those are the anomalies to those to that
+
+ align:start position:0%
+Those are the anomalies to those to that
+ 
+
+ align:start position:0%
+Those are the anomalies to those to that
+innate ability that we all share. But
+
+ align:start position:0%
+innate ability that we all share. But
+ 
+
+ align:start position:0%
+innate ability that we all share. But
+but I also don't think that we have I
+
+ align:start position:0%
+but I also don't think that we have I
+ 
+
+ align:start position:0%
+but I also don't think that we have I
+mean it's not clear to me that the
+
+ align:start position:0%
+mean it's not clear to me that the
+ 
+
+ align:start position:0%
+mean it's not clear to me that the
+difference between uh me and Picasso is
+
+ align:start position:0%
+difference between uh me and Picasso is
+ 
+
+ align:start position:0%
+difference between uh me and Picasso is
+one that's actually objective. Uh I I
+
+ align:start position:0%
+one that's actually objective. Uh I I
+ 
+
+ align:start position:0%
+one that's actually objective. Uh I I
+think it's much fuzzier than that. So it
+
+ align:start position:0%
+think it's much fuzzier than that. So it
+ 
+
+ align:start position:0%
+think it's much fuzzier than that. So it
+it it
+
+ align:start position:0%
+it it
+ 
+
+ align:start position:0%
+it it
+depends a lot on how much weight you put
+
+ align:start position:0%
+depends a lot on how much weight you put
+ 
+
+ align:start position:0%
+depends a lot on how much weight you put
+on, for example, whether Picasso
+
+ align:start position:0%
+on, for example, whether Picasso
+ 
+
+ align:start position:0%
+on, for example, whether Picasso
+actually, you know, deserves credit for
+
+ align:start position:0%
+actually, you know, deserves credit for
+ 
+
+ align:start position:0%
+actually, you know, deserves credit for
+it or whether it was simply his
+
+ align:start position:0%
+it or whether it was simply his
+ 
+
+ align:start position:0%
+it or whether it was simply his
+environment that produced it. It those
+
+ align:start position:0%
+environment that produced it. It those
+ 
+
+ align:start position:0%
+environment that produced it. It those
+sorts of questions, I think, undermine
+
+ align:start position:0%
+sorts of questions, I think, undermine
+ 
+
+ align:start position:0%
+sorts of questions, I think, undermine
+the the guaranteed value of that kind of
+
+ align:start position:0%
+the the guaranteed value of that kind of
+ 
+
+ align:start position:0%
+the the guaranteed value of that kind of
+differentiation and an argument. So I
+
+ align:start position:0%
+differentiation and an argument. So I
+ 
+
+ align:start position:0%
+differentiation and an argument. So I
+wouldn't say that it's clear how
+
+ align:start position:0%
+wouldn't say that it's clear how
+ 
+
+ align:start position:0%
+wouldn't say that it's clear how
+different Picasso is from me on some,
+
+ align:start position:0%
+different Picasso is from me on some,
+ 
+
+ align:start position:0%
+different Picasso is from me on some,
+you know, clear standard. I think he's
+
+ align:start position:0%
+you know, clear standard. I think he's
+ 
+
+ align:start position:0%
+you know, clear standard. I think he's
+done very different things than me. But
+
+ align:start position:0%
+done very different things than me. But
+ 
+
+ align:start position:0%
+done very different things than me. But
+it it's not I I don't feel like you can
+
+ align:start position:0%
+it it's not I I don't feel like you can
+ 
+
+ align:start position:0%
+it it's not I I don't feel like you can
+say he's just simply qualitatively
+
+ align:start position:0%
+say he's just simply qualitatively
+ 
+
+ align:start position:0%
+say he's just simply qualitatively
+different from me based on, you know, on
+
+ align:start position:0%
+different from me based on, you know, on
+ 
+
+ align:start position:0%
+different from me based on, you know, on
+this well-reasoned argument because we
+
+ align:start position:0%
+this well-reasoned argument because we
+ 
+
+ align:start position:0%
+this well-reasoned argument because we
+have no way of actually measuring that
+
+ align:start position:0%
+have no way of actually measuring that
+ 
+
+ align:start position:0%
+have no way of actually measuring that
+outside of the the social values and and
+
+ align:start position:0%
+outside of the the social values and and
+ 
+
+ align:start position:0%
+outside of the the social values and and
+culture that we bring to the the
+
+ align:start position:0%
+culture that we bring to the the
+ 
+
+ align:start position:0%
+culture that we bring to the the
+exercise.
+
+ align:start position:0%
+exercise.
+ 
+
+ align:start position:0%
+exercise.
+I don't know if that made sense.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+I'm guessing not.
+
+ align:start position:0%
+I'm guessing not.
+ 
+
+ align:start position:0%
+I'm guessing not.
+Basically, I well, I'm having a hard
+
+ align:start position:0%
+Basically, I well, I'm having a hard
+ 
+
+ align:start position:0%
+Basically, I well, I'm having a hard
+time believing that we can say how like
+
+ align:start position:0%
+time believing that we can say how like
+ 
+
+ align:start position:0%
+time believing that we can say how like
+whether creativity is democratic in
+
+ align:start position:0%
+whether creativity is democratic in
+ 
+
+ align:start position:0%
+whether creativity is democratic in
+distribution or whether it has some, you
+
+ align:start position:0%
+distribution or whether it has some, you
+ 
+
+ align:start position:0%
+distribution or whether it has some, you
+know, elite or or uh, you know, nonflat
+
+ align:start position:0%
+know, elite or or uh, you know, nonflat
+ 
+
+ align:start position:0%
+know, elite or or uh, you know, nonflat
+distribution to it on any rational basis
+
+ align:start position:0%
+distribution to it on any rational basis
+ 
+
+ align:start position:0%
+distribution to it on any rational basis
+because
+
+ align:start position:0%
+because
+ 
+
+ align:start position:0%
+because
+so much of our discussion of what
+
+ align:start position:0%
+so much of our discussion of what
+ 
+
+ align:start position:0%
+so much of our discussion of what
+creativity is and how we value it is not
+
+ align:start position:0%
+creativity is and how we value it is not
+ 
+
+ align:start position:0%
+creativity is and how we value it is not
+rational. So
+
+ align:start position:0%
+rational. So
+ 
+
+ align:start position:0%
+rational. So
+there there's there's something else
+
+ align:start position:0%
+there there's there's something else
+ 
+
+ align:start position:0%
+there there's there's something else
+going on here than that that needs to be
+
+ align:start position:0%
+going on here than that that needs to be
+ 
+
+ align:start position:0%
+going on here than that that needs to be
+discussed if we're going to try and say
+
+ align:start position:0%
+discussed if we're going to try and say
+ 
+
+ align:start position:0%
+discussed if we're going to try and say
+that geniuses are qualitatively
+
+ align:start position:0%
+that geniuses are qualitatively
+ 
+
+ align:start position:0%
+that geniuses are qualitatively
+different than average.
+
+ align:start position:0%
+different than average.
+ 
+
+ align:start position:0%
+different than average.
+One thing you can say which the all of
+
+ align:start position:0%
+One thing you can say which the all of
+ 
+
+ align:start position:0%
+One thing you can say which the all of
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+totalitarian countries have capitalized
+
+ align:start position:0%
+totalitarian countries have capitalized
+ 
+
+ align:start position:0%
+totalitarian countries have capitalized
+on is that if you sort of regiment large
+
+ align:start position:0%
+on is that if you sort of regiment large
+ 
+
+ align:start position:0%
+on is that if you sort of regiment large
+enough members of the population
+
+ align:start position:0%
+enough members of the population
+ 
+
+ align:start position:0%
+enough members of the population
+to be
+
+ align:start position:0%
+to be
+ 
+
+ align:start position:0%
+to be
+pole vaultters or athletes or musicians
+
+ align:start position:0%
+pole vaultters or athletes or musicians
+ 
+
+ align:start position:0%
+pole vaultters or athletes or musicians
+or anything
+
+ align:start position:0%
+or anything
+ 
+
+ align:start position:0%
+or anything
+you're going out of that there will come
+
+ align:start position:0%
+you're going out of that there will come
+ 
+
+ align:start position:0%
+you're going out of that there will come
+a few geniuses who would otherwise not
+
+ align:start position:0%
+a few geniuses who would otherwise not
+ 
+
+ align:start position:0%
+a few geniuses who would otherwise not
+have been noticed.
+
+ align:start position:0%
+have been noticed.
+ 
+
+ align:start position:0%
+have been noticed.
+I mean that that was the reason why the
+
+ align:start position:0%
+I mean that that was the reason why the
+ 
+
+ align:start position:0%
+I mean that that was the reason why the
+Soviet Union continued for 70 years.
+
+ align:start position:0%
+Soviet Union continued for 70 years.
+ 
+
+ align:start position:0%
+Soviet Union continued for 70 years.
+Everybody I as I mentioned knew it was a
+
+ align:start position:0%
+Everybody I as I mentioned knew it was a
+ 
+
+ align:start position:0%
+Everybody I as I mentioned knew it was a
+a bad system that it wouldn't work but
+
+ align:start position:0%
+a bad system that it wouldn't work but
+ 
+
+ align:start position:0%
+a bad system that it wouldn't work but
+um everybody wasn't equally encouraged
+
+ align:start position:0%
+um everybody wasn't equally encouraged
+ 
+
+ align:start position:0%
+um everybody wasn't equally encouraged
+and so they had these masses of young
+
+ align:start position:0%
+and so they had these masses of young
+ 
+
+ align:start position:0%
+and so they had these masses of young
+people marching together and doing
+
+ align:start position:0%
+people marching together and doing
+ 
+
+ align:start position:0%
+people marching together and doing
+athletics together and a few of them
+
+ align:start position:0%
+athletics together and a few of them
+ 
+
+ align:start position:0%
+athletics together and a few of them
+really were geniuses and that seemed to
+
+ align:start position:0%
+really were geniuses and that seemed to
+ 
+
+ align:start position:0%
+really were geniuses and that seemed to
+compensate for all the failures of the
+
+ align:start position:0%
+compensate for all the failures of the
+ 
+
+ align:start position:0%
+compensate for all the failures of the
+system. In our in democratic worlds,
+
+ align:start position:0%
+system. In our in democratic worlds,
+ 
+
+ align:start position:0%
+system. In our in democratic worlds,
+things are less well organized. But the
+
+ align:start position:0%
+things are less well organized. But the
+ 
+
+ align:start position:0%
+things are less well organized. But the
+fact remains that um it isn't just a
+
+ align:start position:0%
+fact remains that um it isn't just a
+ 
+
+ align:start position:0%
+fact remains that um it isn't just a
+question of nurturing and it isn't some
+
+ align:start position:0%
+question of nurturing and it isn't some
+ 
+
+ align:start position:0%
+question of nurturing and it isn't some
+innate ability that we know about. But
+
+ align:start position:0%
+innate ability that we know about. But
+ 
+
+ align:start position:0%
+innate ability that we know about. But
+you know,
+
+ align:start position:0%
+you know,
+ 
+
+ align:start position:0%
+you know,
+just encouraging people think they're
+
+ align:start position:0%
+just encouraging people think they're
+ 
+
+ align:start position:0%
+just encouraging people think they're
+all creative doesn't make them all
+
+ align:start position:0%
+all creative doesn't make them all
+ 
+
+ align:start position:0%
+all creative doesn't make them all
+creative. only there's still going to be
+
+ align:start position:0%
+creative. only there's still going to be
+ 
+
+ align:start position:0%
+creative. only there's still going to be
+that handful who really stand out
+
+ align:start position:0%
+that handful who really stand out
+ 
+
+ align:start position:0%
+that handful who really stand out
+and those are the geniuses and or near
+
+ align:start position:0%
+and those are the geniuses and or near
+ 
+
+ align:start position:0%
+and those are the geniuses and or near
+geniuses and the question is how to
+
+ align:start position:0%
+geniuses and the question is how to
+ 
+
+ align:start position:0%
+geniuses and the question is how to
+explain them
+
+ align:start position:0%
+explain them
+ 
+
+ align:start position:0%
+explain them
+but maybe you'll do that in the paper I
+
+ align:start position:0%
+but maybe you'll do that in the paper I
+ 
+
+ align:start position:0%
+but maybe you'll do that in the paper I
+don't know
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+you you can and can any of us help
+
+ align:start position:0%
+you you can and can any of us help
+ 
+
+ align:start position:0%
+you you can and can any of us help
+Harold no Harold go ahead uh I was
+
+ align:start position:0%
+Harold no Harold go ahead uh I was
+ 
+
+ align:start position:0%
+Harold no Harold go ahead uh I was
+wondering how you deal with the cases of
+
+ align:start position:0%
+wondering how you deal with the cases of
+ 
+
+ align:start position:0%
+wondering how you deal with the cases of
+like like autistic sants. Yeah, I was
+
+ align:start position:0%
+like like autistic sants. Yeah, I was
+ 
+
+ align:start position:0%
+like like autistic sants. Yeah, I was
+actually just researching him today.
+
+ align:start position:0%
+actually just researching him today.
+ 
+
+ align:start position:0%
+actually just researching him today.
+Haven't really dived into that just yet.
+
+ align:start position:0%
+Haven't really dived into that just yet.
+ 
+
+ align:start position:0%
+Haven't really dived into that just yet.
+So, that's definitely to be considered.
+
+ align:start position:0%
+So, that's definitely to be considered.
+ 
+
+ align:start position:0%
+So, that's definitely to be considered.
+I really don't know what to think of
+
+ align:start position:0%
+I really don't know what to think of
+ 
+
+ align:start position:0%
+I really don't know what to think of
+that just yet. Yeah, because my mom's a
+
+ align:start position:0%
+that just yet. Yeah, because my mom's a
+ 
+
+ align:start position:0%
+that just yet. Yeah, because my mom's a
+neurologist and she's worked with kids
+
+ align:start position:0%
+neurologist and she's worked with kids
+ 
+
+ align:start position:0%
+neurologist and she's worked with kids
+who are, you know, you can't communicate
+
+ align:start position:0%
+who are, you know, you can't communicate
+ 
+
+ align:start position:0%
+who are, you know, you can't communicate
+with them, but they could, you know,
+
+ align:start position:0%
+with them, but they could, you know,
+ 
+
+ align:start position:0%
+with them, but they could, you know,
+draw these amazing paintings and, you
+
+ align:start position:0%
+draw these amazing paintings and, you
+ 
+
+ align:start position:0%
+draw these amazing paintings and, you
+know, do all this, you know, perform
+
+ align:start position:0%
+know, do all this, you know, perform
+ 
+
+ align:start position:0%
+know, do all this, you know, perform
+great pieces. I'm not sure they can.
+
+ align:start position:0%
+great pieces. I'm not sure they can.
+ 
+
+ align:start position:0%
+great pieces. I'm not sure they can.
+Actually, I think they do construct
+
+ align:start position:0%
+Actually, I think they do construct
+ 
+
+ align:start position:0%
+Actually, I think they do construct
+their own pieces. Some of them do. So,
+
+ align:start position:0%
+their own pieces. Some of them do. So,
+ 
+
+ align:start position:0%
+their own pieces. Some of them do. So,
+that is creative. Like playing someone
+
+ align:start position:0%
+that is creative. Like playing someone
+ 
+
+ align:start position:0%
+that is creative. Like playing someone
+else's piece may not be considered
+
+ align:start position:0%
+else's piece may not be considered
+ 
+
+ align:start position:0%
+else's piece may not be considered
+creative, but I mean it depends
+
+ align:start position:0%
+creative, but I mean it depends
+ 
+
+ align:start position:0%
+creative, but I mean it depends
+how where you're going with the argument
+
+ align:start position:0%
+how where you're going with the argument
+ 
+
+ align:start position:0%
+how where you're going with the argument
+in your paper. Another
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+just quick question is your argument
+
+ align:start position:0%
+just quick question is your argument
+ 
+
+ align:start position:0%
+just quick question is your argument
+that there's sort of a Gaussian
+
+ align:start position:0%
+that there's sort of a Gaussian
+ 
+
+ align:start position:0%
+that there's sort of a Gaussian
+distribution and everything in the
+
+ align:start position:0%
+distribution and everything in the
+ 
+
+ align:start position:0%
+distribution and everything in the
+middle is kind of interchangeable and
+
+ align:start position:0%
+middle is kind of interchangeable and
+ 
+
+ align:start position:0%
+middle is kind of interchangeable and
+then once you get out like say two
+
+ align:start position:0%
+then once you get out like say two
+ 
+
+ align:start position:0%
+then once you get out like say two
+standard deviations it's this weird
+
+ align:start position:0%
+standard deviations it's this weird
+ 
+
+ align:start position:0%
+standard deviations it's this weird
+conflicting point or is it that like you
+
+ align:start position:0%
+conflicting point or is it that like you
+ 
+
+ align:start position:0%
+conflicting point or is it that like you
+know basically there's every most people
+
+ align:start position:0%
+know basically there's every most people
+ 
+
+ align:start position:0%
+know basically there's every most people
+are in the middle and there's a little
+
+ align:start position:0%
+are in the middle and there's a little
+ 
+
+ align:start position:0%
+are in the middle and there's a little
+spike out at one end and a little spike
+
+ align:start position:0%
+spike out at one end and a little spike
+ 
+
+ align:start position:0%
+spike out at one end and a little spike
+out at that end and there's nothing
+
+ align:start position:0%
+out at that end and there's nothing
+ 
+
+ align:start position:0%
+out at that end and there's nothing
+really in between more of a Gian
+
+ align:start position:0%
+really in between more of a Gian
+ 
+
+ align:start position:0%
+really in between more of a Gian
+distribution
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+of course I mean that was the whole
+
+ align:start position:0%
+of course I mean that was the whole
+ 
+
+ align:start position:0%
+of course I mean that was the whole
+thing I was sort of trying to undermine
+
+ align:start position:0%
+thing I was sort of trying to undermine
+ 
+
+ align:start position:0%
+thing I was sort of trying to undermine
+but that that you can even put it in a
+
+ align:start position:0%
+but that that you can even put it in a
+ 
+
+ align:start position:0%
+but that that you can even put it in a
+distribution. Uh I don't see why that
+
+ align:start position:0%
+distribution. Uh I don't see why that
+ 
+
+ align:start position:0%
+distribution. Uh I don't see why that
+though. I don't see how. So if you have
+
+ align:start position:0%
+though. I don't see how. So if you have
+ 
+
+ align:start position:0%
+though. I don't see how. So if you have
+a Gaussian distribution then
+
+ align:start position:0%
+a Gaussian distribution then
+ 
+
+ align:start position:0%
+a Gaussian distribution then
+and you want it to mean something then
+
+ align:start position:0%
+and you want it to mean something then
+ 
+
+ align:start position:0%
+and you want it to mean something then
+you need to have some uh objective
+
+ align:start position:0%
+you need to have some uh objective
+ 
+
+ align:start position:0%
+you need to have some uh objective
+meaning attached to the variable that
+
+ align:start position:0%
+meaning attached to the variable that
+ 
+
+ align:start position:0%
+meaning attached to the variable that
+your distribution is over.
+
+ align:start position:0%
+your distribution is over.
+ 
+
+ align:start position:0%
+your distribution is over.
+Otherwise I mean then then it might mean
+
+ align:start position:0%
+Otherwise I mean then then it might mean
+ 
+
+ align:start position:0%
+Otherwise I mean then then it might mean
+something to you because it's subjective
+
+ align:start position:0%
+something to you because it's subjective
+ 
+
+ align:start position:0%
+something to you because it's subjective
+you know and say well this is how
+
+ align:start position:0%
+you know and say well this is how
+ 
+
+ align:start position:0%
+you know and say well this is how
+creative people are. but it's not going
+
+ align:start position:0%
+creative people are. but it's not going
+ 
+
+ align:start position:0%
+creative people are. but it's not going
+to mean much to everybody else because
+
+ align:start position:0%
+to mean much to everybody else because
+ 
+
+ align:start position:0%
+to mean much to everybody else because
+they don't know they can't hold your
+
+ align:start position:0%
+they don't know they can't hold your
+ 
+
+ align:start position:0%
+they don't know they can't hold your
+meaning of creativity. So that that
+
+ align:start position:0%
+meaning of creativity. So that that
+ 
+
+ align:start position:0%
+meaning of creativity. So that that
+that's what I think the challenge I
+
+ align:start position:0%
+that's what I think the challenge I
+ 
+
+ align:start position:0%
+that's what I think the challenge I
+would pose is well I think I don't know
+
+ align:start position:0%
+would pose is well I think I don't know
+ 
+
+ align:start position:0%
+would pose is well I think I don't know
+if I made this clear or not but when I
+
+ align:start position:0%
+if I made this clear or not but when I
+ 
+
+ align:start position:0%
+if I made this clear or not but when I
+say people are creative I I mean that in
+
+ align:start position:0%
+say people are creative I I mean that in
+ 
+
+ align:start position:0%
+say people are creative I I mean that in
+a sense we are all creative like we had
+
+ align:start position:0%
+a sense we are all creative like we had
+ 
+
+ align:start position:0%
+a sense we are all creative like we had
+to be creative in order to get where we
+
+ align:start position:0%
+to be creative in order to get where we
+ 
+
+ align:start position:0%
+to be creative in order to get where we
+are today. in order when we experience a
+
+ align:start position:0%
+are today. in order when we experience a
+ 
+
+ align:start position:0%
+are today. in order when we experience a
+new concept or when we experience an
+
+ align:start position:0%
+new concept or when we experience an
+ 
+
+ align:start position:0%
+new concept or when we experience an
+event in the world, we must create a
+
+ align:start position:0%
+event in the world, we must create a
+ 
+
+ align:start position:0%
+event in the world, we must create a
+concept that makes sense of that
+
+ align:start position:0%
+concept that makes sense of that
+ 
+
+ align:start position:0%
+concept that makes sense of that
+experience. And that's that's what I'm
+
+ align:start position:0%
+experience. And that's that's what I'm
+ 
+
+ align:start position:0%
+experience. And that's that's what I'm
+saying. In that sense, we are all
+
+ align:start position:0%
+saying. In that sense, we are all
+ 
+
+ align:start position:0%
+saying. In that sense, we are all
+creative. But then there are these
+
+ align:start position:0%
+creative. But then there are these
+ 
+
+ align:start position:0%
+creative. But then there are these
+anomalies, those two standard deviations
+
+ align:start position:0%
+anomalies, those two standard deviations
+ 
+
+ align:start position:0%
+anomalies, those two standard deviations
+to the right or left where this ability
+
+ align:start position:0%
+to the right or left where this ability
+ 
+
+ align:start position:0%
+to the right or left where this ability
+seems to be overdeveloped, either
+
+ align:start position:0%
+seems to be overdeveloped, either
+ 
+
+ align:start position:0%
+seems to be overdeveloped, either
+overdeveloped or
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+overdeveloped, underdeveloped. That's by
+
+ align:start position:0%
+overdeveloped, underdeveloped. That's by
+ 
+
+ align:start position:0%
+overdeveloped, underdeveloped. That's by
+the nurture or by nature. Genetically,
+
+ align:start position:0%
+the nurture or by nature. Genetically,
+ 
+
+ align:start position:0%
+the nurture or by nature. Genetically,
+they just have this ability that's far
+
+ align:start position:0%
+they just have this ability that's far
+ 
+
+ align:start position:0%
+they just have this ability that's far
+that is far superior than that of the
+
+ align:start position:0%
+that is far superior than that of the
+ 
+
+ align:start position:0%
+that is far superior than that of the
+average person.
+
+ align:start position:0%
+average person.
+ 
+
+ align:start position:0%
+average person.
+at at the Pikau inaugural there was some
+
+ align:start position:0%
+at at the Pikau inaugural there was some
+ 
+
+ align:start position:0%
+at at the Pikau inaugural there was some
+discussion about nature and nurture that
+
+ align:start position:0%
+discussion about nature and nurture that
+ 
+
+ align:start position:0%
+discussion about nature and nurture that
+came from questions from the floor and
+
+ align:start position:0%
+came from questions from the floor and
+ 
+
+ align:start position:0%
+came from questions from the floor and
+um in the panel of the five Nobel
+
+ align:start position:0%
+um in the panel of the five Nobel
+ 
+
+ align:start position:0%
+um in the panel of the five Nobel
+laureates they all agreed that that's
+
+ align:start position:0%
+laureates they all agreed that that's
+ 
+
+ align:start position:0%
+laureates they all agreed that that's
+not an interesting scientific question
+
+ align:start position:0%
+not an interesting scientific question
+ 
+
+ align:start position:0%
+not an interesting scientific question
+anymore before people used to think in
+
+ align:start position:0%
+anymore before people used to think in
+ 
+
+ align:start position:0%
+anymore before people used to think in
+terms of these alternatives but what
+
+ align:start position:0%
+terms of these alternatives but what
+ 
+
+ align:start position:0%
+terms of these alternatives but what
+we've learned is that it's all a
+
+ align:start position:0%
+we've learned is that it's all a
+ 
+
+ align:start position:0%
+we've learned is that it's all a
+combination of both. Mhm. I don't know
+
+ align:start position:0%
+combination of both. Mhm. I don't know
+ 
+
+ align:start position:0%
+combination of both. Mhm. I don't know
+if that's of any help to you. Yeah,
+
+ align:start position:0%
+if that's of any help to you. Yeah,
+ 
+
+ align:start position:0%
+if that's of any help to you. Yeah,
+that's what I'm going to go into. It's
+
+ align:start position:0%
+that's what I'm going to go into. It's
+ 
+
+ align:start position:0%
+that's what I'm going to go into. It's
+com definitely a combination of both.
+
+ align:start position:0%
+com definitely a combination of both.
+ 
+
+ align:start position:0%
+com definitely a combination of both.
+All right. So, the if that's true, then
+
+ align:start position:0%
+All right. So, the if that's true, then
+ 
+
+ align:start position:0%
+All right. So, the if that's true, then
+what the job for the creative thinker in
+
+ align:start position:0%
+what the job for the creative thinker in
+ 
+
+ align:start position:0%
+what the job for the creative thinker in
+science and about the life in general
+
+ align:start position:0%
+science and about the life in general
+ 
+
+ align:start position:0%
+science and about the life in general
+would be just how do the two enter in?
+
+ align:start position:0%
+would be just how do the two enter in?
+ 
+
+ align:start position:0%
+would be just how do the two enter in?
+Just how in clear cases does one find
+
+ align:start position:0%
+Just how in clear cases does one find
+ 
+
+ align:start position:0%
+Just how in clear cases does one find
+the effect of both of them? and they're
+
+ align:start position:0%
+the effect of both of them? and they're
+ 
+
+ align:start position:0%
+the effect of both of them? and they're
+responding to each other in some kind of
+
+ align:start position:0%
+responding to each other in some kind of
+ 
+
+ align:start position:0%
+responding to each other in some kind of
+ricochet. I think that would be very
+
+ align:start position:0%
+ricochet. I think that would be very
+ 
+
+ align:start position:0%
+ricochet. I think that would be very
+useful in writing your papers on I think
+
+ align:start position:0%
+useful in writing your papers on I think
+ 
+
+ align:start position:0%
+useful in writing your papers on I think
+in philosophy in general but in
+
+ align:start position:0%
+in philosophy in general but in
+ 
+
+ align:start position:0%
+in philosophy in general but in
+something as obscure as the topic of
+
+ align:start position:0%
+something as obscure as the topic of
+ 
+
+ align:start position:0%
+something as obscure as the topic of
+this course.
+
+ align:start position:0%
+this course.
+ 
+
+ align:start position:0%
+this course.
+try very very hard to focus on
+
+ align:start position:0%
+try very very hard to focus on
+ 
+
+ align:start position:0%
+try very very hard to focus on
+clear cases and analyze them in terms of
+
+ align:start position:0%
+clear cases and analyze them in terms of
+ 
+
+ align:start position:0%
+clear cases and analyze them in terms of
+something details that you can clarify
+
+ align:start position:0%
+something details that you can clarify
+ 
+
+ align:start position:0%
+something details that you can clarify
+rather than feeling any need to create a
+
+ align:start position:0%
+rather than feeling any need to create a
+ 
+
+ align:start position:0%
+rather than feeling any need to create a
+grand new metaphysics of any sort or
+
+ align:start position:0%
+grand new metaphysics of any sort or
+ 
+
+ align:start position:0%
+grand new metaphysics of any sort or
+even uh a solution to whatever problem
+
+ align:start position:0%
+even uh a solution to whatever problem
+ 
+
+ align:start position:0%
+even uh a solution to whatever problem
+you're concerned about. It's the
+
+ align:start position:0%
+you're concerned about. It's the
+ 
+
+ align:start position:0%
+you're concerned about. It's the
+analysis. It's the focusing upon details
+
+ align:start position:0%
+analysis. It's the focusing upon details
+ 
+
+ align:start position:0%
+analysis. It's the focusing upon details
+within a complicated system as a way of
+
+ align:start position:0%
+within a complicated system as a way of
+ 
+
+ align:start position:0%
+within a complicated system as a way of
+revealing their importance for each
+
+ align:start position:0%
+revealing their importance for each
+ 
+
+ align:start position:0%
+revealing their importance for each
+other. That that I think is crucial. Um
+
+ align:start position:0%
+other. That that I think is crucial. Um
+ 
+
+ align:start position:0%
+other. That that I think is crucial. Um
+I say that for this paper because that's
+
+ align:start position:0%
+I say that for this paper because that's
+ 
+
+ align:start position:0%
+I say that for this paper because that's
+what's hardest for people at at the
+
+ align:start position:0%
+what's hardest for people at at the
+ 
+
+ align:start position:0%
+what's hardest for people at at the
+beginning of their philosophical
+
+ align:start position:0%
+beginning of their philosophical
+ 
+
+ align:start position:0%
+beginning of their philosophical
+training to realize that that's really
+
+ align:start position:0%
+training to realize that that's really
+ 
+
+ align:start position:0%
+training to realize that that's really
+what matters.
+
+ align:start position:0%
+what matters.
+ 
+
+ align:start position:0%
+what matters.
+But as a matter of fact, I I myself
+
+ align:start position:0%
+But as a matter of fact, I I myself
+ 
+
+ align:start position:0%
+But as a matter of fact, I I myself
+believe that for me at least that's the
+
+ align:start position:0%
+believe that for me at least that's the
+ 
+
+ align:start position:0%
+believe that for me at least that's the
+best way to do philosophy. It's the only
+
+ align:start position:0%
+best way to do philosophy. It's the only
+ 
+
+ align:start position:0%
+best way to do philosophy. It's the only
+way I can do philosophy. Otherwise, uh I
+
+ align:start position:0%
+way I can do philosophy. Otherwise, uh I
+ 
+
+ align:start position:0%
+way I can do philosophy. Otherwise, uh I
+find that the generalizations and or
+
+ align:start position:0%
+find that the generalizations and or
+ 
+
+ align:start position:0%
+find that the generalizations and or
+platitudes and that I'm not creative. If
+
+ align:start position:0%
+platitudes and that I'm not creative. If
+ 
+
+ align:start position:0%
+platitudes and that I'm not creative. If
+I have any creativity myself, it's by
+
+ align:start position:0%
+I have any creativity myself, it's by
+ 
+
+ align:start position:0%
+I have any creativity myself, it's by
+having perceptions that other people
+
+ align:start position:0%
+having perceptions that other people
+ 
+
+ align:start position:0%
+having perceptions that other people
+don't. and then the ability to reveal
+
+ align:start position:0%
+don't. and then the ability to reveal
+ 
+
+ align:start position:0%
+don't. and then the ability to reveal
+the content of those perceptions and
+
+ align:start position:0%
+the content of those perceptions and
+ 
+
+ align:start position:0%
+the content of those perceptions and
+show how they're relevant to to whatever
+
+ align:start position:0%
+show how they're relevant to to whatever
+ 
+
+ align:start position:0%
+show how they're relevant to to whatever
+it is I'm trying to explain. Um, but it
+
+ align:start position:0%
+it is I'm trying to explain. Um, but it
+ 
+
+ align:start position:0%
+it is I'm trying to explain. Um, but it
+doesn't matter about me. I think that's
+
+ align:start position:0%
+doesn't matter about me. I think that's
+ 
+
+ align:start position:0%
+doesn't matter about me. I think that's
+advice I'd offer to all of you for the
+
+ align:start position:0%
+advice I'd offer to all of you for the
+ 
+
+ align:start position:0%
+advice I'd offer to all of you for the
+writing of papers.
+
+ align:start position:0%
+writing of papers.
+ 
+
+ align:start position:0%
+writing of papers.
+Thomas, um, okay. So um I was initially
+
+ align:start position:0%
+Thomas, um, okay. So um I was initially
+ 
+
+ align:start position:0%
+Thomas, um, okay. So um I was initially
+going to write on the necessity of
+
+ align:start position:0%
+going to write on the necessity of
+ 
+
+ align:start position:0%
+going to write on the necessity of
+creativity but um when I was doing my
+
+ align:start position:0%
+creativity but um when I was doing my
+ 
+
+ align:start position:0%
+creativity but um when I was doing my
+research I couldn't really find anything
+
+ align:start position:0%
+research I couldn't really find anything
+ 
+
+ align:start position:0%
+research I couldn't really find anything
+on it. I actually switched to creativity
+
+ align:start position:0%
+on it. I actually switched to creativity
+ 
+
+ align:start position:0%
+on it. I actually switched to creativity
+versus intelligence. Um and I also used
+
+ align:start position:0%
+versus intelligence. Um and I also used
+ 
+
+ align:start position:0%
+versus intelligence. Um and I also used
+a lot of Sternberg's work. Um and
+
+ align:start position:0%
+a lot of Sternberg's work. Um and
+ 
+
+ align:start position:0%
+a lot of Sternberg's work. Um and
+basically what I'm going to look at is
+
+ align:start position:0%
+basically what I'm going to look at is
+ 
+
+ align:start position:0%
+basically what I'm going to look at is
+um looking at kind of the definitions of
+
+ align:start position:0%
+um looking at kind of the definitions of
+ 
+
+ align:start position:0%
+um looking at kind of the definitions of
+creativity and intelligence and see
+
+ align:start position:0%
+creativity and intelligence and see
+ 
+
+ align:start position:0%
+creativity and intelligence and see
+whether you can actually have one
+
+ align:start position:0%
+whether you can actually have one
+ 
+
+ align:start position:0%
+whether you can actually have one
+without the other. say can you be
+
+ align:start position:0%
+without the other. say can you be
+ 
+
+ align:start position:0%
+without the other. say can you be
+creative but not necessarily always
+
+ align:start position:0%
+creative but not necessarily always
+ 
+
+ align:start position:0%
+creative but not necessarily always
+deemed to be as intelligent by like say
+
+ align:start position:0%
+deemed to be as intelligent by like say
+ 
+
+ align:start position:0%
+deemed to be as intelligent by like say
+the standard tests or whatever. Um or um
+
+ align:start position:0%
+the standard tests or whatever. Um or um
+ 
+
+ align:start position:0%
+the standard tests or whatever. Um or um
+what I found is that a lot of people
+
+ align:start position:0%
+what I found is that a lot of people
+ 
+
+ align:start position:0%
+what I found is that a lot of people
+argue that creativity is actually a
+
+ align:start position:0%
+argue that creativity is actually a
+ 
+
+ align:start position:0%
+argue that creativity is actually a
+subset of intelligence and that or
+
+ align:start position:0%
+subset of intelligence and that or
+ 
+
+ align:start position:0%
+subset of intelligence and that or
+actually what a subset of intelligence
+
+ align:start position:0%
+actually what a subset of intelligence
+ 
+
+ align:start position:0%
+actually what a subset of intelligence
+and that without intelligence you can't
+
+ align:start position:0%
+and that without intelligence you can't
+ 
+
+ align:start position:0%
+and that without intelligence you can't
+have creativity. How much intelligence?
+
+ align:start position:0%
+have creativity. How much intelligence?
+ 
+
+ align:start position:0%
+have creativity. How much intelligence?
+Well see that's thing it's what kind of
+
+ align:start position:0%
+Well see that's thing it's what kind of
+ 
+
+ align:start position:0%
+Well see that's thing it's what kind of
+intelligence are you talking about? So
+
+ align:start position:0%
+intelligence are you talking about? So
+ 
+
+ align:start position:0%
+intelligence are you talking about? So
+are you talking about the kind of
+
+ align:start position:0%
+are you talking about the kind of
+ 
+
+ align:start position:0%
+are you talking about the kind of
+intelligence which is proven by your
+
+ align:start position:0%
+intelligence which is proven by your
+ 
+
+ align:start position:0%
+intelligence which is proven by your
+standards IQ test. So um someone is seen
+
+ align:start position:0%
+standards IQ test. So um someone is seen
+ 
+
+ align:start position:0%
+standards IQ test. So um someone is seen
+to be or deemed to be intelligent
+
+ align:start position:0%
+to be or deemed to be intelligent
+ 
+
+ align:start position:0%
+to be or deemed to be intelligent
+because they're able to pass XY Z like
+
+ align:start position:0%
+because they're able to pass XY Z like
+ 
+
+ align:start position:0%
+because they're able to pass XY Z like
+with amazingly good results compared to
+
+ align:start position:0%
+with amazingly good results compared to
+ 
+
+ align:start position:0%
+with amazingly good results compared to
+the average person or um something which
+
+ align:start position:0%
+the average person or um something which
+ 
+
+ align:start position:0%
+the average person or um something which
+I think has cropped up once or twice in
+
+ align:start position:0%
+I think has cropped up once or twice in
+ 
+
+ align:start position:0%
+I think has cropped up once or twice in
+class is um what we call your everyday
+
+ align:start position:0%
+class is um what we call your everyday
+ 
+
+ align:start position:0%
+class is um what we call your everyday
+common sense. And is that more
+
+ align:start position:0%
+common sense. And is that more
+ 
+
+ align:start position:0%
+common sense. And is that more
+intelligent because you're taking a
+
+ align:start position:0%
+intelligent because you're taking a
+ 
+
+ align:start position:0%
+intelligent because you're taking a
+problem and you're you're seeing like
+
+ align:start position:0%
+problem and you're you're seeing like
+ 
+
+ align:start position:0%
+problem and you're you're seeing like
+you know, you're looking in a in a
+
+ align:start position:0%
+you know, you're looking in a in a
+ 
+
+ align:start position:0%
+you know, you're looking in a in a
+practical way and actually being able to
+
+ align:start position:0%
+practical way and actually being able to
+ 
+
+ align:start position:0%
+practical way and actually being able to
+solve it. And that is uh but that isn't
+
+ align:start position:0%
+solve it. And that is uh but that isn't
+ 
+
+ align:start position:0%
+solve it. And that is uh but that isn't
+prerequisite for all creativity.
+
+ align:start position:0%
+prerequisite for all creativity.
+ 
+
+ align:start position:0%
+prerequisite for all creativity.
+Well, maybe excuse me, what maybe or
+
+ align:start position:0%
+Well, maybe excuse me, what maybe or
+ 
+
+ align:start position:0%
+Well, maybe excuse me, what maybe or
+maybe not. Like that's what I'm trying
+
+ align:start position:0%
+maybe not. Like that's what I'm trying
+ 
+
+ align:start position:0%
+maybe not. Like that's what I'm trying
+to decide because very often the people
+
+ align:start position:0%
+to decide because very often the people
+ 
+
+ align:start position:0%
+to decide because very often the people
+we think of as creative, particularly
+
+ align:start position:0%
+we think of as creative, particularly
+ 
+
+ align:start position:0%
+we think of as creative, particularly
+the geniuses, don't have good common
+
+ align:start position:0%
+the geniuses, don't have good common
+ 
+
+ align:start position:0%
+the geniuses, don't have good common
+sense. Exactly. But because they don't
+
+ align:start position:0%
+sense. Exactly. But because they don't
+ 
+
+ align:start position:0%
+sense. Exactly. But because they don't
+live in that domain, it doesn't matter
+
+ align:start position:0%
+live in that domain, it doesn't matter
+ 
+
+ align:start position:0%
+live in that domain, it doesn't matter
+to them. Yeah. But then is it can you
+
+ align:start position:0%
+to them. Yeah. But then is it can you
+ 
+
+ align:start position:0%
+to them. Yeah. But then is it can you
+actually say then that they're really
+
+ align:start position:0%
+actually say then that they're really
+ 
+
+ align:start position:0%
+actually say then that they're really
+that intelligent because okay so a story
+
+ align:start position:0%
+that intelligent because okay so a story
+ 
+
+ align:start position:0%
+that intelligent because okay so a story
+for if for their for their purposes they
+
+ align:start position:0%
+for if for their for their purposes they
+ 
+
+ align:start position:0%
+for if for their for their purposes they
+don't they might not be as good but like
+
+ align:start position:0%
+don't they might not be as good but like
+ 
+
+ align:start position:0%
+don't they might not be as good but like
+okay so a a story Sternberg and Lubbert
+
+ align:start position:0%
+okay so a a story Sternberg and Lubbert
+ 
+
+ align:start position:0%
+okay so a a story Sternberg and Lubbert
+I think in a book which they both wrote
+
+ align:start position:0%
+I think in a book which they both wrote
+ 
+
+ align:start position:0%
+I think in a book which they both wrote
+together called define the crowd um they
+
+ align:start position:0%
+together called define the crowd um they
+ 
+
+ align:start position:0%
+together called define the crowd um they
+talk about um these two boys and they're
+
+ align:start position:0%
+talk about um these two boys and they're
+ 
+
+ align:start position:0%
+talk about um these two boys and they're
+in the they're in the woods
+
+ align:start position:0%
+in the they're in the woods
+ 
+
+ align:start position:0%
+in the they're in the woods
+and um there's this bear that's running
+
+ align:start position:0%
+and um there's this bear that's running
+ 
+
+ align:start position:0%
+and um there's this bear that's running
+after them. And then he says, "Well, to
+
+ align:start position:0%
+after them. And then he says, "Well, to
+ 
+
+ align:start position:0%
+after them. And then he says, "Well, to
+make this story to make more sense, you
+
+ align:start position:0%
+make this story to make more sense, you
+ 
+
+ align:start position:0%
+make this story to make more sense, you
+need to understand the background of
+
+ align:start position:0%
+need to understand the background of
+ 
+
+ align:start position:0%
+need to understand the background of
+these two boys." Now, one of these boys
+
+ align:start position:0%
+these two boys." Now, one of these boys
+ 
+
+ align:start position:0%
+these two boys." Now, one of these boys
+is really, really intelligent. Like he's
+
+ align:start position:0%
+is really, really intelligent. Like he's
+ 
+
+ align:start position:0%
+is really, really intelligent. Like he's
+got really high marks and all his like
+
+ align:start position:0%
+got really high marks and all his like
+ 
+
+ align:start position:0%
+got really high marks and all his like
+IQ tests. He's got really good
+
+ align:start position:0%
+IQ tests. He's got really good
+ 
+
+ align:start position:0%
+IQ tests. He's got really good
+commendations from teachers and his
+
+ align:start position:0%
+commendations from teachers and his
+ 
+
+ align:start position:0%
+commendations from teachers and his
+parents think he's intelligent and like
+
+ align:start position:0%
+parents think he's intelligent and like
+ 
+
+ align:start position:0%
+parents think he's intelligent and like
+um with a lot of arrogance, he kind of
+
+ align:start position:0%
+um with a lot of arrogance, he kind of
+ 
+
+ align:start position:0%
+um with a lot of arrogance, he kind of
+says, "Well, and the boy pretty much
+
+ align:start position:0%
+says, "Well, and the boy pretty much
+ 
+
+ align:start position:0%
+says, "Well, and the boy pretty much
+thinks he's pretty intelligent, too."
+
+ align:start position:0%
+thinks he's pretty intelligent, too."
+ 
+
+ align:start position:0%
+thinks he's pretty intelligent, too."
+Um, but then there's this other kid
+
+ align:start position:0%
+Um, but then there's this other kid
+ 
+
+ align:start position:0%
+Um, but then there's this other kid
+there and he doesn't have such good
+
+ align:start position:0%
+there and he doesn't have such good
+ 
+
+ align:start position:0%
+there and he doesn't have such good
+grades or whatever. And um, he doesn't
+
+ align:start position:0%
+grades or whatever. And um, he doesn't
+ 
+
+ align:start position:0%
+grades or whatever. And um, he doesn't
+have as good commendations and he's not
+
+ align:start position:0%
+have as good commendations and he's not
+ 
+
+ align:start position:0%
+have as good commendations and he's not
+deemed to be as intelligent, but they're
+
+ align:start position:0%
+deemed to be as intelligent, but they're
+ 
+
+ align:start position:0%
+deemed to be as intelligent, but they're
+both in this in this wood um, in these
+
+ align:start position:0%
+both in this in this wood um, in these
+ 
+
+ align:start position:0%
+both in this in this wood um, in these
+woods and there's this grizzly bear
+
+ align:start position:0%
+woods and there's this grizzly bear
+ 
+
+ align:start position:0%
+woods and there's this grizzly bear
+really angry. He's running after them.
+
+ align:start position:0%
+really angry. He's running after them.
+ 
+
+ align:start position:0%
+really angry. He's running after them.
+And the intelligent boy is able to stand
+
+ align:start position:0%
+And the intelligent boy is able to stand
+ 
+
+ align:start position:0%
+And the intelligent boy is able to stand
+there and calculate the speed at which
+
+ align:start position:0%
+there and calculate the speed at which
+ 
+
+ align:start position:0%
+there and calculate the speed at which
+the bear is
+
+ align:start position:0%
+the bear is
+ 
+
+ align:start position:0%
+the bear is
+the speed at which like the bear is like
+
+ align:start position:0%
+the speed at which like the bear is like
+ 
+
+ align:start position:0%
+the speed at which like the bear is like
+running towards him and realizes there
+
+ align:start position:0%
+running towards him and realizes there
+ 
+
+ align:start position:0%
+running towards him and realizes there
+something like 17 seconds before the
+
+ align:start position:0%
+something like 17 seconds before the
+ 
+
+ align:start position:0%
+something like 17 seconds before the
+bear is going to get to them. But
+
+ align:start position:0%
+bear is going to get to them. But
+ 
+
+ align:start position:0%
+bear is going to get to them. But
+there's no way that they're going to be
+
+ align:start position:0%
+there's no way that they're going to be
+ 
+
+ align:start position:0%
+there's no way that they're going to be
+able to run away because there's too
+
+ align:start position:0%
+able to run away because there's too
+ 
+
+ align:start position:0%
+able to run away because there's too
+short a time for both of them to get
+
+ align:start position:0%
+short a time for both of them to get
+ 
+
+ align:start position:0%
+short a time for both of them to get
+away. And the story goes that the other
+
+ align:start position:0%
+away. And the story goes that the other
+ 
+
+ align:start position:0%
+away. And the story goes that the other
+boy in the meantime is busy changing
+
+ align:start position:0%
+boy in the meantime is busy changing
+ 
+
+ align:start position:0%
+boy in the meantime is busy changing
+from his hiking shoes to his jogging
+
+ align:start position:0%
+from his hiking shoes to his jogging
+ 
+
+ align:start position:0%
+from his hiking shoes to his jogging
+shoes. And the intelligent boy kind of
+
+ align:start position:0%
+shoes. And the intelligent boy kind of
+ 
+
+ align:start position:0%
+shoes. And the intelligent boy kind of
+looks at this like other guy and he's
+
+ align:start position:0%
+looks at this like other guy and he's
+ 
+
+ align:start position:0%
+looks at this like other guy and he's
+like, "What are you doing? We're never
+
+ align:start position:0%
+like, "What are you doing? We're never
+ 
+
+ align:start position:0%
+like, "What are you doing? We're never
+gonna get away." And the other guy says,
+
+ align:start position:0%
+gonna get away." And the other guy says,
+ 
+
+ align:start position:0%
+gonna get away." And the other guy says,
+"Well, yeah, but that doesn't really
+
+ align:start position:0%
+"Well, yeah, but that doesn't really
+ 
+
+ align:start position:0%
+"Well, yeah, but that doesn't really
+matter because all that matters is that
+
+ align:start position:0%
+matter because all that matters is that
+ 
+
+ align:start position:0%
+matter because all that matters is that
+um I get further away than you."
+
+ align:start position:0%
+um I get further away than you."
+ 
+
+ align:start position:0%
+um I get further away than you."
+So, is it really that this intelligent
+
+ align:start position:0%
+So, is it really that this intelligent
+ 
+
+ align:start position:0%
+So, is it really that this intelligent
+boy was really that intelligent? because
+
+ align:start position:0%
+boy was really that intelligent? because
+ 
+
+ align:start position:0%
+boy was really that intelligent? because
+he clearly can't have been that
+
+ align:start position:0%
+he clearly can't have been that
+ 
+
+ align:start position:0%
+he clearly can't have been that
+intelligent cuz maybe it would have been
+
+ align:start position:0%
+intelligent cuz maybe it would have been
+ 
+
+ align:start position:0%
+intelligent cuz maybe it would have been
+better instead of him sitting there and
+
+ align:start position:0%
+better instead of him sitting there and
+ 
+
+ align:start position:0%
+better instead of him sitting there and
+calculating the speed at which this bear
+
+ align:start position:0%
+calculating the speed at which this bear
+ 
+
+ align:start position:0%
+calculating the speed at which this bear
+was going to get to them if he thought
+
+ align:start position:0%
+was going to get to them if he thought
+ 
+
+ align:start position:0%
+was going to get to them if he thought
+of a better way of actually being able
+
+ align:start position:0%
+of a better way of actually being able
+ 
+
+ align:start position:0%
+of a better way of actually being able
+to get away. Um whereas obviously this
+
+ align:start position:0%
+to get away. Um whereas obviously this
+ 
+
+ align:start position:0%
+to get away. Um whereas obviously this
+so-called not so intelligent guy
+
+ align:start position:0%
+so-called not so intelligent guy
+ 
+
+ align:start position:0%
+so-called not so intelligent guy
+actually, you know, did manage to run to
+
+ align:start position:0%
+actually, you know, did manage to run to
+ 
+
+ align:start position:0%
+actually, you know, did manage to run to
+safety because the other guy got killed
+
+ align:start position:0%
+safety because the other guy got killed
+ 
+
+ align:start position:0%
+safety because the other guy got killed
+because the bear got him first. But do
+
+ align:start position:0%
+because the bear got him first. But do
+ 
+
+ align:start position:0%
+because the bear got him first. But do
+you see? So there is that kind of slight
+
+ align:start position:0%
+you see? So there is that kind of slight
+ 
+
+ align:start position:0%
+you see? So there is that kind of slight
+dis this kind of really blurry line
+
+ align:start position:0%
+dis this kind of really blurry line
+ 
+
+ align:start position:0%
+dis this kind of really blurry line
+between what you can say is like really
+
+ align:start position:0%
+between what you can say is like really
+ 
+
+ align:start position:0%
+between what you can say is like really
+intelligent or what is really creative
+
+ align:start position:0%
+intelligent or what is really creative
+ 
+
+ align:start position:0%
+intelligent or what is really creative
+because in that kind of situation you
+
+ align:start position:0%
+because in that kind of situation you
+ 
+
+ align:start position:0%
+because in that kind of situation you
+would say that the second boy the
+
+ align:start position:0%
+would say that the second boy the
+ 
+
+ align:start position:0%
+would say that the second boy the
+technically not so intelligent boy was
+
+ align:start position:0%
+technically not so intelligent boy was
+ 
+
+ align:start position:0%
+technically not so intelligent boy was
+actually far more intelligent or was it
+
+ align:start position:0%
+actually far more intelligent or was it
+ 
+
+ align:start position:0%
+actually far more intelligent or was it
+yeah so another thing that I've come up
+
+ align:start position:0%
+yeah so another thing that I've come up
+ 
+
+ align:start position:0%
+yeah so another thing that I've come up
+with so the first um so I've almost
+
+ align:start position:0%
+with so the first um so I've almost
+ 
+
+ align:start position:0%
+with so the first um so I've almost
+finished my paper but the the first
+
+ align:start position:0%
+finished my paper but the the first
+ 
+
+ align:start position:0%
+finished my paper but the the first
+thing I kind of set about doing which I
+
+ align:start position:0%
+thing I kind of set about doing which I
+ 
+
+ align:start position:0%
+thing I kind of set about doing which I
+don't think I did very well in my my
+
+ align:start position:0%
+don't think I did very well in my my
+ 
+
+ align:start position:0%
+don't think I did very well in my my
+first essay is to try and define
+
+ align:start position:0%
+first essay is to try and define
+ 
+
+ align:start position:0%
+first essay is to try and define
+creativity and try and define what is
+
+ align:start position:0%
+creativity and try and define what is
+ 
+
+ align:start position:0%
+creativity and try and define what is
+meant by intelligence. And I found like
+
+ align:start position:0%
+meant by intelligence. And I found like
+ 
+
+ align:start position:0%
+meant by intelligence. And I found like
+one or two models that other people have
+
+ align:start position:0%
+one or two models that other people have
+ 
+
+ align:start position:0%
+one or two models that other people have
+come up with and I discussed those a
+
+ align:start position:0%
+come up with and I discussed those a
+ 
+
+ align:start position:0%
+come up with and I discussed those a
+bit. Um, and something that's come up in
+
+ align:start position:0%
+bit. Um, and something that's come up in
+ 
+
+ align:start position:0%
+bit. Um, and something that's come up in
+the definition of what is considered
+
+ align:start position:0%
+the definition of what is considered
+ 
+
+ align:start position:0%
+the definition of what is considered
+creative is not that it's just novel,
+
+ align:start position:0%
+creative is not that it's just novel,
+ 
+
+ align:start position:0%
+creative is not that it's just novel,
+but like you said is whether it's
+
+ align:start position:0%
+but like you said is whether it's
+ 
+
+ align:start position:0%
+but like you said is whether it's
+actually appropriate or not. Whether
+
+ align:start position:0%
+actually appropriate or not. Whether
+ 
+
+ align:start position:0%
+actually appropriate or not. Whether
+it's what appropriate appropriate. So um
+
+ align:start position:0%
+it's what appropriate appropriate. So um
+ 
+
+ align:start position:0%
+it's what appropriate appropriate. So um
+something might be creative but just not
+
+ align:start position:0%
+something might be creative but just not
+ 
+
+ align:start position:0%
+something might be creative but just not
+deemed socially appropriate. And an
+
+ align:start position:0%
+deemed socially appropriate. And an
+ 
+
+ align:start position:0%
+deemed socially appropriate. And an
+example which Sternberg actually gives
+
+ align:start position:0%
+example which Sternberg actually gives
+ 
+
+ align:start position:0%
+example which Sternberg actually gives
+is um the artist Damian Hurst. I don't
+
+ align:start position:0%
+is um the artist Damian Hurst. I don't
+ 
+
+ align:start position:0%
+is um the artist Damian Hurst. I don't
+know if you guys have heard of him. He
+
+ align:start position:0%
+know if you guys have heard of him. He
+ 
+
+ align:start position:0%
+know if you guys have heard of him. He
+basically one of his pieces of art he um
+
+ align:start position:0%
+basically one of his pieces of art he um
+ 
+
+ align:start position:0%
+basically one of his pieces of art he um
+cut up animal um frag um cut up animals
+
+ align:start position:0%
+cut up animal um frag um cut up animals
+ 
+
+ align:start position:0%
+cut up animal um frag um cut up animals
+into fragments and put them on display
+
+ align:start position:0%
+into fragments and put them on display
+ 
+
+ align:start position:0%
+into fragments and put them on display
+and that's what he called art. And I
+
+ align:start position:0%
+and that's what he called art. And I
+ 
+
+ align:start position:0%
+and that's what he called art. And I
+mean it received a lot of criticism
+
+ align:start position:0%
+mean it received a lot of criticism
+ 
+
+ align:start position:0%
+mean it received a lot of criticism
+because a lot of people said well you
+
+ align:start position:0%
+because a lot of people said well you
+ 
+
+ align:start position:0%
+because a lot of people said well you
+know obviously that's not art that's
+
+ align:start position:0%
+know obviously that's not art that's
+ 
+
+ align:start position:0%
+know obviously that's not art that's
+just complete butchery. But can you not
+
+ align:start position:0%
+just complete butchery. But can you not
+ 
+
+ align:start position:0%
+just complete butchery. But can you not
+I mean you explain this to me. He he
+
+ align:start position:0%
+I mean you explain this to me. He he
+ 
+
+ align:start position:0%
+I mean you explain this to me. He he
+live he would kill animals and then
+
+ align:start position:0%
+live he would kill animals and then
+ 
+
+ align:start position:0%
+live he would kill animals and then
+rearrange the parts. He literally um
+
+ align:start position:0%
+rearrange the parts. He literally um
+ 
+
+ align:start position:0%
+rearrange the parts. He literally um
+like you would get them in like a
+
+ align:start position:0%
+like you would get them in like a
+ 
+
+ align:start position:0%
+like you would get them in like a
+slicing machine basically. You take you
+
+ align:start position:0%
+slicing machine basically. You take you
+ 
+
+ align:start position:0%
+slicing machine basically. You take you
+literally slice the Yeah, that guy he
+
+ align:start position:0%
+literally slice the Yeah, that guy he
+ 
+
+ align:start position:0%
+literally slice the Yeah, that guy he
+he's literally like sliced the animal
+
+ align:start position:0%
+he's literally like sliced the animal
+ 
+
+ align:start position:0%
+he's literally like sliced the animal
+into pieces and he didn't rearrange
+
+ align:start position:0%
+into pieces and he didn't rearrange
+ 
+
+ align:start position:0%
+into pieces and he didn't rearrange
+them, but he put these pieces in like
+
+ align:start position:0%
+them, but he put these pieces in like
+ 
+
+ align:start position:0%
+them, but he put these pieces in like
+preservatives and stuff and he put them
+
+ align:start position:0%
+preservatives and stuff and he put them
+ 
+
+ align:start position:0%
+preservatives and stuff and he put them
+in like double-sided glass um cabinets,
+
+ align:start position:0%
+in like double-sided glass um cabinets,
+ 
+
+ align:start position:0%
+in like double-sided glass um cabinets,
+whatever. So you can see like either
+
+ align:start position:0%
+whatever. So you can see like either
+ 
+
+ align:start position:0%
+whatever. So you can see like either
+side of basically like all the different
+
+ align:start position:0%
+side of basically like all the different
+ 
+
+ align:start position:0%
+side of basically like all the different
+organs and where they would be etc.
+
+ align:start position:0%
+organs and where they would be etc.
+ 
+
+ align:start position:0%
+organs and where they would be etc.
+Exactly as it would be in the live
+
+ align:start position:0%
+Exactly as it would be in the live
+ 
+
+ align:start position:0%
+Exactly as it would be in the live
+animal. And it was called art. But
+
+ align:start position:0%
+animal. And it was called art. But
+ 
+
+ align:start position:0%
+animal. And it was called art. But
+that's a that's exactly what people
+
+ align:start position:0%
+that's a that's exactly what people
+ 
+
+ align:start position:0%
+that's a that's exactly what people
+said. They said it was cruel, right?
+
+ align:start position:0%
+said. They said it was cruel, right?
+ 
+
+ align:start position:0%
+said. They said it was cruel, right?
+Because like
+
+ align:start position:0%
+Because like
+ 
+
+ align:start position:0%
+Because like
+well you can say it's cruel but it's I
+
+ align:start position:0%
+well you can say it's cruel but it's I
+ 
+
+ align:start position:0%
+well you can say it's cruel but it's I
+mean a lot of people said well is it
+
+ align:start position:0%
+mean a lot of people said well is it
+ 
+
+ align:start position:0%
+mean a lot of people said well is it
+complete butchery or whatever? And um I
+
+ align:start position:0%
+complete butchery or whatever? And um I
+ 
+
+ align:start position:0%
+complete butchery or whatever? And um I
+haven't heard of that. But if you um I
+
+ align:start position:0%
+haven't heard of that. But if you um I
+ 
+
+ align:start position:0%
+haven't heard of that. But if you um I
+think he was an English artist.
+
+ align:start position:0%
+think he was an English artist.
+ 
+
+ align:start position:0%
+think he was an English artist.
+No, this guy I'm sorry just to throw in
+
+ align:start position:0%
+No, this guy I'm sorry just to throw in
+ 
+
+ align:start position:0%
+No, this guy I'm sorry just to throw in
+one of an athlete had died and donated
+
+ align:start position:0%
+one of an athlete had died and donated
+ 
+
+ align:start position:0%
+one of an athlete had died and donated
+his body to him and h Damian H I guess I
+
+ align:start position:0%
+his body to him and h Damian H I guess I
+ 
+
+ align:start position:0%
+his body to him and h Damian H I guess I
+don't remember the names but what he did
+
+ align:start position:0%
+don't remember the names but what he did
+ 
+
+ align:start position:0%
+don't remember the names but what he did
+the um the artist guy skinned him
+
+ align:start position:0%
+the um the artist guy skinned him
+ 
+
+ align:start position:0%
+the um the artist guy skinned him
+skinned his body. I think he you said an
+
+ align:start position:0%
+skinned his body. I think he you said an
+ 
+
+ align:start position:0%
+skinned his body. I think he you said an
+athlete first. Yeah an athlete. He after
+
+ align:start position:0%
+athlete first. Yeah an athlete. He after
+ 
+
+ align:start position:0%
+athlete first. Yeah an athlete. He after
+he died he donated his body to the
+
+ align:start position:0%
+he died he donated his body to the
+ 
+
+ align:start position:0%
+he died he donated his body to the
+artist. Right. To the artist. The artist
+
+ align:start position:0%
+artist. Right. To the artist. The artist
+ 
+
+ align:start position:0%
+artist. Right. To the artist. The artist
+skinned his body and what he did is that
+
+ align:start position:0%
+skinned his body and what he did is that
+ 
+
+ align:start position:0%
+skinned his body and what he did is that
+he peeled back every all the muscles and
+
+ align:start position:0%
+he peeled back every all the muscles and
+ 
+
+ align:start position:0%
+he peeled back every all the muscles and
+like peeled like so you could see the
+
+ align:start position:0%
+like peeled like so you could see the
+ 
+
+ align:start position:0%
+like peeled like so you could see the
+different layers of muscles and then
+
+ align:start position:0%
+different layers of muscles and then
+ 
+
+ align:start position:0%
+different layers of muscles and then
+they put them on display where he's
+
+ align:start position:0%
+they put them on display where he's
+ 
+
+ align:start position:0%
+they put them on display where he's
+running like this but you can see all of
+
+ align:start position:0%
+running like this but you can see all of
+ 
+
+ align:start position:0%
+running like this but you can see all of
+his muscles peeled back and you can see
+
+ align:start position:0%
+his muscles peeled back and you can see
+ 
+
+ align:start position:0%
+his muscles peeled back and you can see
+all all the entire muscular structure of
+
+ align:start position:0%
+all all the entire muscular structure of
+ 
+
+ align:start position:0%
+all all the entire muscular structure of
+the body. That's um I actually thought
+
+ align:start position:0%
+the body. That's um I actually thought
+ 
+
+ align:start position:0%
+the body. That's um I actually thought
+that was pretty cool. That's another guy
+
+ align:start position:0%
+that was pretty cool. That's another guy
+ 
+
+ align:start position:0%
+that was pretty cool. That's another guy
+here and he displayed it. I mean that
+
+ align:start position:0%
+here and he displayed it. I mean that
+ 
+
+ align:start position:0%
+here and he displayed it. I mean that
+was that was his work of art
+
+ align:start position:0%
+was that was his work of art
+ 
+
+ align:start position:0%
+was that was his work of art
+becoming more popular. Yeah, it was
+
+ align:start position:0%
+becoming more popular. Yeah, it was
+ 
+
+ align:start position:0%
+becoming more popular. Yeah, it was
+called the I actually saw that
+
+ align:start position:0%
+called the I actually saw that
+ 
+
+ align:start position:0%
+called the I actually saw that
+exhibition. It was called Body Welds.
+
+ align:start position:0%
+exhibition. It was called Body Welds.
+ 
+
+ align:start position:0%
+exhibition. It was called Body Welds.
+Who was his name? Um Dr. Gunther
+
+ align:start position:0%
+Who was his name? Um Dr. Gunther
+ 
+
+ align:start position:0%
+Who was his name? Um Dr. Gunther
+Hunter I think or something like it's
+
+ align:start position:0%
+Hunter I think or something like it's
+ 
+
+ align:start position:0%
+Hunter I think or something like it's
+Gunther Body W. That was the name of the
+
+ align:start position:0%
+Gunther Body W. That was the name of the
+ 
+
+ align:start position:0%
+Gunther Body W. That was the name of the
+exhibition. It was really really
+
+ align:start position:0%
+exhibition. It was really really
+ 
+
+ align:start position:0%
+exhibition. It was really really
+popular. Um I don't know whether it was
+
+ align:start position:0%
+popular. Um I don't know whether it was
+ 
+
+ align:start position:0%
+popular. Um I don't know whether it was
+just popular in England but I think it
+
+ align:start position:0%
+just popular in England but I think it
+ 
+
+ align:start position:0%
+just popular in England but I think it
+went touring around Europe as well. He
+
+ align:start position:0%
+went touring around Europe as well. He
+ 
+
+ align:start position:0%
+went touring around Europe as well. He
+actually also did something really
+
+ align:start position:0%
+actually also did something really
+ 
+
+ align:start position:0%
+actually also did something really
+controversial. Yeah, that's the one. Um
+
+ align:start position:0%
+controversial. Yeah, that's the one. Um
+ 
+
+ align:start position:0%
+controversial. Yeah, that's the one. Um
+where he did a live um
+
+ align:start position:0%
+where he did a live um
+ 
+
+ align:start position:0%
+where he did a live um
+dissection of a human being um and it
+
+ align:start position:0%
+dissection of a human being um and it
+ 
+
+ align:start position:0%
+dissection of a human being um and it
+was all do you remember hearing that?
+
+ align:start position:0%
+was all do you remember hearing that?
+ 
+
+ align:start position:0%
+was all do you remember hearing that?
+Yeah. Come to the point.
+
+ align:start position:0%
+Yeah. Come to the point.
+ 
+
+ align:start position:0%
+Yeah. Come to the point.
+So again it's the idea of whether
+
+ align:start position:0%
+So again it's the idea of whether
+ 
+
+ align:start position:0%
+So again it's the idea of whether
+whether you can say admittedly it's not
+
+ align:start position:0%
+whether you can say admittedly it's not
+ 
+
+ align:start position:0%
+whether you can say admittedly it's not
+socially appropriate and but does that
+
+ align:start position:0%
+socially appropriate and but does that
+ 
+
+ align:start position:0%
+socially appropriate and but does that
+does that detract from it being
+
+ align:start position:0%
+does that detract from it being
+ 
+
+ align:start position:0%
+does that detract from it being
+creative? Because one of part of the
+
+ align:start position:0%
+creative? Because one of part of the
+ 
+
+ align:start position:0%
+creative? Because one of part of the
+definition of creative is that it's
+
+ align:start position:0%
+definition of creative is that it's
+ 
+
+ align:start position:0%
+definition of creative is that it's
+novel. So it's the use of maybe ordinary
+
+ align:start position:0%
+novel. So it's the use of maybe ordinary
+ 
+
+ align:start position:0%
+novel. So it's the use of maybe ordinary
+tools in a different way. So is that
+
+ align:start position:0%
+tools in a different way. So is that
+ 
+
+ align:start position:0%
+tools in a different way. So is that
+saying is it really fair to say
+
+ align:start position:0%
+saying is it really fair to say
+ 
+
+ align:start position:0%
+saying is it really fair to say
+objectively that what these people did
+
+ align:start position:0%
+objectively that what these people did
+ 
+
+ align:start position:0%
+objectively that what these people did
+is actually not created just because we
+
+ align:start position:0%
+is actually not created just because we
+ 
+
+ align:start position:0%
+is actually not created just because we
+deem it socially unacceptable
+
+ align:start position:0%
+deem it socially unacceptable
+ 
+
+ align:start position:0%
+deem it socially unacceptable
+do you see? So I mean there's that kind
+
+ align:start position:0%
+do you see? So I mean there's that kind
+ 
+
+ align:start position:0%
+do you see? So I mean there's that kind
+of fine I mean that's another bit of the
+
+ align:start position:0%
+of fine I mean that's another bit of the
+ 
+
+ align:start position:0%
+of fine I mean that's another bit of the
+discussion I go into when I go into kind
+
+ align:start position:0%
+discussion I go into when I go into kind
+ 
+
+ align:start position:0%
+discussion I go into when I go into kind
+of trying to define creativity and then
+
+ align:start position:0%
+of trying to define creativity and then
+ 
+
+ align:start position:0%
+of trying to define creativity and then
+the idea is basically I have the
+
+ align:start position:0%
+the idea is basically I have the
+ 
+
+ align:start position:0%
+the idea is basically I have the
+definition of creativity and like there
+
+ align:start position:0%
+definition of creativity and like there
+ 
+
+ align:start position:0%
+definition of creativity and like there
+are different models for intelligence
+
+ align:start position:0%
+are different models for intelligence
+ 
+
+ align:start position:0%
+are different models for intelligence
+and trying to see how interrelated the
+
+ align:start position:0%
+and trying to see how interrelated the
+ 
+
+ align:start position:0%
+and trying to see how interrelated the
+two are and whether you can have one
+
+ align:start position:0%
+two are and whether you can have one
+ 
+
+ align:start position:0%
+two are and whether you can have one
+without the other. Well I I would have
+
+ align:start position:0%
+without the other. Well I I would have
+ 
+
+ align:start position:0%
+without the other. Well I I would have
+thought in this case the socially
+
+ align:start position:0%
+thought in this case the socially
+ 
+
+ align:start position:0%
+thought in this case the socially
+inappropriate would be less important
+
+ align:start position:0%
+inappropriate would be less important
+ 
+
+ align:start position:0%
+inappropriate would be less important
+than the question of what he actually
+
+ align:start position:0%
+than the question of what he actually
+ 
+
+ align:start position:0%
+than the question of what he actually
+did with the material that he was
+
+ align:start position:0%
+did with the material that he was
+ 
+
+ align:start position:0%
+did with the material that he was
+presenting. uh artists, Michelangelo for
+
+ align:start position:0%
+presenting. uh artists, Michelangelo for
+ 
+
+ align:start position:0%
+presenting. uh artists, Michelangelo for
+instance, used to go um to study
+
+ align:start position:0%
+instance, used to go um to study
+ 
+
+ align:start position:0%
+instance, used to go um to study
+cadaavvers
+
+ align:start position:0%
+cadaavvers
+ 
+
+ align:start position:0%
+cadaavvers
+in order to learn about um the muscles
+
+ align:start position:0%
+in order to learn about um the muscles
+ 
+
+ align:start position:0%
+in order to learn about um the muscles
+and the structure of the of the anatomy.
+
+ align:start position:0%
+and the structure of the of the anatomy.
+ 
+
+ align:start position:0%
+and the structure of the of the anatomy.
+Um now, one might say uh that this
+
+ align:start position:0%
+Um now, one might say uh that this
+ 
+
+ align:start position:0%
+Um now, one might say uh that this
+artist was doing something comparable
+
+ align:start position:0%
+artist was doing something comparable
+ 
+
+ align:start position:0%
+artist was doing something comparable
+does doesn't yet prove to us how that
+
+ align:start position:0%
+does doesn't yet prove to us how that
+ 
+
+ align:start position:0%
+does doesn't yet prove to us how that
+he's very uh creative. He might have
+
+ align:start position:0%
+he's very uh creative. He might have
+ 
+
+ align:start position:0%
+he's very uh creative. He might have
+been a showman who was charging money
+
+ align:start position:0%
+been a showman who was charging money
+ 
+
+ align:start position:0%
+been a showman who was charging money
+and there's nothing creative unless
+
+ align:start position:0%
+and there's nothing creative unless
+ 
+
+ align:start position:0%
+and there's nothing creative unless
+there was a way in which he presented it
+
+ align:start position:0%
+there was a way in which he presented it
+ 
+
+ align:start position:0%
+there was a way in which he presented it
+under the circumstances of this being an
+
+ align:start position:0%
+under the circumstances of this being an
+ 
+
+ align:start position:0%
+under the circumstances of this being an
+art gallery or something like that that
+
+ align:start position:0%
+art gallery or something like that that
+ 
+
+ align:start position:0%
+art gallery or something like that that
+might make it creative. Yeah. So this
+
+ align:start position:0%
+might make it creative. Yeah. So this
+ 
+
+ align:start position:0%
+might make it creative. Yeah. So this
+this guy who did the body worlds
+
+ align:start position:0%
+this guy who did the body worlds
+ 
+
+ align:start position:0%
+this guy who did the body worlds
+exhibition um I mean it was very very
+
+ align:start position:0%
+exhibition um I mean it was very very
+ 
+
+ align:start position:0%
+exhibition um I mean it was very very
+controversial at the time but very
+
+ align:start position:0%
+controversial at the time but very
+ 
+
+ align:start position:0%
+controversial at the time but very
+popular like everyone was running to see
+
+ align:start position:0%
+popular like everyone was running to see
+ 
+
+ align:start position:0%
+popular like everyone was running to see
+it. Um, and he actually managed to get
+
+ align:start position:0%
+it. Um, and he actually managed to get
+ 
+
+ align:start position:0%
+it. Um, and he actually managed to get
+all the bodies he put on display because
+
+ align:start position:0%
+all the bodies he put on display because
+ 
+
+ align:start position:0%
+all the bodies he put on display because
+he um went through and got a grant and
+
+ align:start position:0%
+he um went through and got a grant and
+ 
+
+ align:start position:0%
+he um went through and got a grant and
+basically said he was trying to teach
+
+ align:start position:0%
+basically said he was trying to teach
+ 
+
+ align:start position:0%
+basically said he was trying to teach
+science. And the idea was is that
+
+ align:start position:0%
+science. And the idea was is that
+ 
+
+ align:start position:0%
+science. And the idea was is that
+basically he was putting out all this
+
+ align:start position:0%
+basically he was putting out all this
+ 
+
+ align:start position:0%
+basically he was putting out all this
+anatomy and he developed a very okay
+
+ align:start position:0%
+anatomy and he developed a very okay
+ 
+
+ align:start position:0%
+anatomy and he developed a very okay
+very interesting system where you could
+
+ align:start position:0%
+very interesting system where you could
+ 
+
+ align:start position:0%
+very interesting system where you could
+preserve um like body material using
+
+ align:start position:0%
+preserve um like body material using
+ 
+
+ align:start position:0%
+preserve um like body material using
+some sort of plastic which you can
+
+ align:start position:0%
+some sort of plastic which you can
+ 
+
+ align:start position:0%
+some sort of plastic which you can
+inject into material or whatever. So he
+
+ align:start position:0%
+inject into material or whatever. So he
+ 
+
+ align:start position:0%
+inject into material or whatever. So he
+had these really amazing displays where
+
+ align:start position:0%
+had these really amazing displays where
+ 
+
+ align:start position:0%
+had these really amazing displays where
+um he'd injected a a dye and it had gone
+
+ align:start position:0%
+um he'd injected a a dye and it had gone
+ 
+
+ align:start position:0%
+um he'd injected a a dye and it had gone
+into every single blood vessel and then
+
+ align:start position:0%
+into every single blood vessel and then
+ 
+
+ align:start position:0%
+into every single blood vessel and then
+dissolved away all the tissue, the bone,
+
+ align:start position:0%
+dissolved away all the tissue, the bone,
+ 
+
+ align:start position:0%
+dissolved away all the tissue, the bone,
+the muscle and everything. And all you
+
+ align:start position:0%
+the muscle and everything. And all you
+ 
+
+ align:start position:0%
+the muscle and everything. And all you
+had left standing was all the veins and
+
+ align:start position:0%
+had left standing was all the veins and
+ 
+
+ align:start position:0%
+had left standing was all the veins and
+arteries and everything and that's all
+
+ align:start position:0%
+arteries and everything and that's all
+ 
+
+ align:start position:0%
+arteries and everything and that's all
+you had. But you it was amazing. It was
+
+ align:start position:0%
+you had. But you it was amazing. It was
+ 
+
+ align:start position:0%
+you had. But you it was amazing. It was
+absolutely amazing. And that was what he
+
+ align:start position:0%
+absolutely amazing. And that was what he
+ 
+
+ align:start position:0%
+absolutely amazing. And that was what he
+put on display. But he was it wasn't
+
+ align:start position:0%
+put on display. But he was it wasn't
+ 
+
+ align:start position:0%
+put on display. But he was it wasn't
+supposed to be some sort of freak show
+
+ align:start position:0%
+supposed to be some sort of freak show
+ 
+
+ align:start position:0%
+supposed to be some sort of freak show
+which it really turned out to be. um or
+
+ align:start position:0%
+which it really turned out to be. um or
+ 
+
+ align:start position:0%
+which it really turned out to be. um or
+however I've perceived it, but it was
+
+ align:start position:0%
+however I've perceived it, but it was
+ 
+
+ align:start position:0%
+however I've perceived it, but it was
+supposed to kind of be a teaching a kind
+
+ align:start position:0%
+supposed to kind of be a teaching a kind
+ 
+
+ align:start position:0%
+supposed to kind of be a teaching a kind
+of science and art merging and teaching
+
+ align:start position:0%
+of science and art merging and teaching
+ 
+
+ align:start position:0%
+of science and art merging and teaching
+you about science and that kind of
+
+ align:start position:0%
+you about science and that kind of
+ 
+
+ align:start position:0%
+you about science and that kind of
+letting you see how everything's
+
+ align:start position:0%
+letting you see how everything's
+ 
+
+ align:start position:0%
+letting you see how everything's
+interrelated and that kind of thing. So,
+
+ align:start position:0%
+interrelated and that kind of thing. So,
+ 
+
+ align:start position:0%
+interrelated and that kind of thing. So,
+let me see if there's time
+
+ align:start position:0%
+let me see if there's time
+ 
+
+ align:start position:0%
+let me see if there's time
+for
+
+ align:start position:0%
+for
+ 
+
+ align:start position:0%
+for
+Harold and Megan. We never got to you.
+
+ align:start position:0%
+Harold and Megan. We never got to you.
+ 
+
+ align:start position:0%
+Harold and Megan. We never got to you.
+Can we stay a little longer? Not not
+
+ align:start position:0%
+Can we stay a little longer? Not not
+ 
+
+ align:start position:0%
+Can we stay a little longer? Not not
+much. Okay. Why don't Taz, do you mind
+
+ align:start position:0%
+much. Okay. Why don't Taz, do you mind
+ 
+
+ align:start position:0%
+much. Okay. Why don't Taz, do you mind
+if we move on? Nope. That's Harold. It's
+
+ align:start position:0%
+if we move on? Nope. That's Harold. It's
+ 
+
+ align:start position:0%
+if we move on? Nope. That's Harold. It's
+35.
+
+ align:start position:0%
+35.
+ 
+
+ align:start position:0%
+35.
+35 of five. That's 505. Five after.
+
+ align:start position:0%
+35 of five. That's 505. Five after.
+ 
+
+ align:start position:0%
+35 of five. That's 505. Five after.
+Yeah. Or 52. Five after. All right. Then
+
+ align:start position:0%
+Yeah. Or 52. Five after. All right. Then
+ 
+
+ align:start position:0%
+Yeah. Or 52. Five after. All right. Then
+why do And you've got to leave. Or are
+
+ align:start position:0%
+why do And you've got to leave. Or are
+ 
+
+ align:start position:0%
+why do And you've got to leave. Or are
+you thinking of the filming? No, no, no.
+
+ align:start position:0%
+you thinking of the filming? No, no, no.
+ 
+
+ align:start position:0%
+you thinking of the filming? No, no, no.
+I have to I may have to go in a little
+
+ align:start position:0%
+I have to I may have to go in a little
+ 
+
+ align:start position:0%
+I have to I may have to go in a little
+bit. No. Just tell me in 30 seconds what
+
+ align:start position:0%
+bit. No. Just tell me in 30 seconds what
+ 
+
+ align:start position:0%
+bit. No. Just tell me in 30 seconds what
+state your paper is in. Okay. I've been
+
+ align:start position:0%
+state your paper is in. Okay. I've been
+ 
+
+ align:start position:0%
+state your paper is in. Okay. I've been
+looking for other sources to read about.
+
+ align:start position:0%
+looking for other sources to read about.
+ 
+
+ align:start position:0%
+looking for other sources to read about.
+The idea was to do creativity and
+
+ align:start position:0%
+The idea was to do creativity and
+ 
+
+ align:start position:0%
+The idea was to do creativity and
+software development. And I started
+
+ align:start position:0%
+software development. And I started
+ 
+
+ align:start position:0%
+software development. And I started
+thinking about relating it to writing a
+
+ align:start position:0%
+thinking about relating it to writing a
+ 
+
+ align:start position:0%
+thinking about relating it to writing a
+poem. I was talking about that. And I
+
+ align:start position:0%
+poem. I was talking about that. And I
+ 
+
+ align:start position:0%
+poem. I was talking about that. And I
+also started thinking about how, you
+
+ align:start position:0%
+also started thinking about how, you
+ 
+
+ align:start position:0%
+also started thinking about how, you
+know, software engineers tend to not do
+
+ align:start position:0%
+know, software engineers tend to not do
+ 
+
+ align:start position:0%
+know, software engineers tend to not do
+other forms of art generally. Like you
+
+ align:start position:0%
+other forms of art generally. Like you
+ 
+
+ align:start position:0%
+other forms of art generally. Like you
+think of them as like a, you know,
+
+ align:start position:0%
+think of them as like a, you know,
+ 
+
+ align:start position:0%
+think of them as like a, you know,
+software dork at first, you know, a
+
+ align:start position:0%
+software dork at first, you know, a
+ 
+
+ align:start position:0%
+software dork at first, you know, a
+software nerd. And then they don't
+
+ align:start position:0%
+software nerd. And then they don't
+ 
+
+ align:start position:0%
+software nerd. And then they don't
+usually do like the painting and stuff,
+
+ align:start position:0%
+usually do like the painting and stuff,
+ 
+
+ align:start position:0%
+usually do like the painting and stuff,
+but it's a very, very few people
+
+ align:start position:0%
+but it's a very, very few people
+ 
+
+ align:start position:0%
+but it's a very, very few people
+actually do both. I wanted to evaluate
+
+ align:start position:0%
+actually do both. I wanted to evaluate
+ 
+
+ align:start position:0%
+actually do both. I wanted to evaluate
+why that was. You know, if if
+
+ align:start position:0%
+why that was. You know, if if
+ 
+
+ align:start position:0%
+why that was. You know, if if
+programming is created, why don't they
+
+ align:start position:0%
+programming is created, why don't they
+ 
+
+ align:start position:0%
+programming is created, why don't they
+engage in, you know, the standard
+
+ align:start position:0%
+engage in, you know, the standard
+ 
+
+ align:start position:0%
+engage in, you know, the standard
+classical creative acts? Are you in any
+
+ align:start position:0%
+classical creative acts? Are you in any
+ 
+
+ align:start position:0%
+classical creative acts? Are you in any
+danger? Are you in control of the
+
+ align:start position:0%
+danger? Are you in control of the
+ 
+
+ align:start position:0%
+danger? Are you in control of the
+material? Uh, yeah. And you've written
+
+ align:start position:0%
+material? Uh, yeah. And you've written
+ 
+
+ align:start position:0%
+material? Uh, yeah. And you've written
+it and got it going. Yeah. All right.
+
+ align:start position:0%
+it and got it going. Yeah. All right.
+ 
+
+ align:start position:0%
+it and got it going. Yeah. All right.
+So, you'll get it in on time and be
+
+ align:start position:0%
+So, you'll get it in on time and be
+ 
+
+ align:start position:0%
+So, you'll get it in on time and be
+satisfied. Yeah. Hope so. All right.
+
+ align:start position:0%
+satisfied. Yeah. Hope so. All right.
+ 
+
+ align:start position:0%
+satisfied. Yeah. Hope so. All right.
+Megan, the same with you. Um, I'm
+
+ align:start position:0%
+Megan, the same with you. Um, I'm
+ 
+
+ align:start position:0%
+Megan, the same with you. Um, I'm
+writing partially on what I talked about
+
+ align:start position:0%
+writing partially on what I talked about
+ 
+
+ align:start position:0%
+writing partially on what I talked about
+last week, which is creativity and
+
+ align:start position:0%
+last week, which is creativity and
+ 
+
+ align:start position:0%
+last week, which is creativity and
+everyday life. Mostly in an attempt, um,
+
+ align:start position:0%
+everyday life. Mostly in an attempt, um,
+ 
+
+ align:start position:0%
+everyday life. Mostly in an attempt, um,
+in my research, like I find that there's
+
+ align:start position:0%
+in my research, like I find that there's
+ 
+
+ align:start position:0%
+in my research, like I find that there's
+two different ways of looking at
+
+ align:start position:0%
+two different ways of looking at
+ 
+
+ align:start position:0%
+two different ways of looking at
+creativity. There's the the artistic
+
+ align:start position:0%
+creativity. There's the the artistic
+ 
+
+ align:start position:0%
+creativity. There's the the artistic
+sort that refers to what we talk about
+
+ align:start position:0%
+sort that refers to what we talk about
+ 
+
+ align:start position:0%
+sort that refers to what we talk about
+most in this class, and then creativity
+
+ align:start position:0%
+most in this class, and then creativity
+ 
+
+ align:start position:0%
+most in this class, and then creativity
+in like the kid that's putting his toys
+
+ align:start position:0%
+in like the kid that's putting his toys
+ 
+
+ align:start position:0%
+in like the kid that's putting his toys
+away and wants to put the block on the
+
+ align:start position:0%
+away and wants to put the block on the
+ 
+
+ align:start position:0%
+away and wants to put the block on the
+top shelf and finds a way to do it
+
+ align:start position:0%
+top shelf and finds a way to do it
+ 
+
+ align:start position:0%
+top shelf and finds a way to do it
+without any help. even though you know
+
+ align:start position:0%
+without any help. even though you know
+ 
+
+ align:start position:0%
+without any help. even though you know
+his little brother or his older brother
+
+ align:start position:0%
+his little brother or his older brother
+ 
+
+ align:start position:0%
+his little brother or his older brother
+learned to do the same thing, it's still
+
+ align:start position:0%
+learned to do the same thing, it's still
+ 
+
+ align:start position:0%
+learned to do the same thing, it's still
+creative because the kid didn't know
+
+ align:start position:0%
+creative because the kid didn't know
+ 
+
+ align:start position:0%
+creative because the kid didn't know
+that. You know, we don't discuss that
+
+ align:start position:0%
+that. You know, we don't discuss that
+ 
+
+ align:start position:0%
+that. You know, we don't discuss that
+kind of creativity much in this class.
+
+ align:start position:0%
+kind of creativity much in this class.
+ 
+
+ align:start position:0%
+kind of creativity much in this class.
+So, sort of an attempt to to
+
+ align:start position:0%
+So, sort of an attempt to to
+ 
+
+ align:start position:0%
+So, sort of an attempt to to
+link together the two different kinds of
+
+ align:start position:0%
+link together the two different kinds of
+ 
+
+ align:start position:0%
+link together the two different kinds of
+creativity and then um second part of my
+
+ align:start position:0%
+creativity and then um second part of my
+ 
+
+ align:start position:0%
+creativity and then um second part of my
+paper is going to be on creativity and
+
+ align:start position:0%
+paper is going to be on creativity and
+ 
+
+ align:start position:0%
+paper is going to be on creativity and
+intuition.
+
+ align:start position:0%
+intuition.
+ 
+
+ align:start position:0%
+intuition.
+I found two different definitions of
+
+ align:start position:0%
+I found two different definitions of
+ 
+
+ align:start position:0%
+I found two different definitions of
+intuition that support the two different
+
+ align:start position:0%
+intuition that support the two different
+ 
+
+ align:start position:0%
+intuition that support the two different
+definitions of creativity. But in both
+
+ align:start position:0%
+definitions of creativity. But in both
+ 
+
+ align:start position:0%
+definitions of creativity. But in both
+senses intuition is directly linked to
+
+ align:start position:0%
+senses intuition is directly linked to
+ 
+
+ align:start position:0%
+senses intuition is directly linked to
+creativity and okay. So well uh
+
+ align:start position:0%
+creativity and okay. So well uh
+ 
+
+ align:start position:0%
+creativity and okay. So well uh
+particularly for you too if you send me
+
+ align:start position:0%
+particularly for you too if you send me
+ 
+
+ align:start position:0%
+particularly for you too if you send me
+emails
+
+ align:start position:0%
+emails
+ 
+
+ align:start position:0%
+emails
+at any point I mean right immediately or
+
+ align:start position:0%
+at any point I mean right immediately or
+ 
+
+ align:start position:0%
+at any point I mean right immediately or
+tomorrow I'll I'll try to help you
+
+ align:start position:0%
+tomorrow I'll I'll try to help you
+ 
+
+ align:start position:0%
+tomorrow I'll I'll try to help you
+further
+
+ align:start position:0%
+further
+ 
+
+ align:start position:0%
+further
+and in fact that's true of all of you.
+
+ align:start position:0%
+and in fact that's true of all of you.
+ 
+
+ align:start position:0%
+and in fact that's true of all of you.
+Don't despair of uh getting my help up
+
+ align:start position:0%
+Don't despair of uh getting my help up
+ 
+
+ align:start position:0%
+Don't despair of uh getting my help up
+to the very last minute.
+
+ align:start position:0%
+to the very last minute.
+ 
+
+ align:start position:0%
+to the very last minute.
+Good night.
\ No newline at end of file
diff --git a/wH9nO8_aDSI.txt b/wH9nO8_aDSI.txt
new file mode 100644
index 0000000000000000000000000000000000000000..58ba973609f527b397d9ed39bbb9b4c2c52945f8
--- /dev/null
+++ b/wH9nO8_aDSI.txt
@@ -0,0 +1,18768 @@
+align:start position:0%
+ 
+the following content is provided under
+
+ align:start position:0%
+the following content is provided under
+ 
+
+ align:start position:0%
+the following content is provided under
+a creative commons license your support
+
+ align:start position:0%
+a creative commons license your support
+ 
+
+ align:start position:0%
+a creative commons license your support
+will help mit opencourseware continue to
+
+ align:start position:0%
+will help mit opencourseware continue to
+ 
+
+ align:start position:0%
+will help mit opencourseware continue to
+offer high quality educational resources
+
+ align:start position:0%
+offer high quality educational resources
+ 
+
+ align:start position:0%
+offer high quality educational resources
+for free
+
+ align:start position:0%
+for free
+ 
+
+ align:start position:0%
+for free
+to make a donation or to view additional
+
+ align:start position:0%
+to make a donation or to view additional
+ 
+
+ align:start position:0%
+to make a donation or to view additional
+materials from hundreds of mit courses
+
+ align:start position:0%
+materials from hundreds of mit courses
+ 
+
+ align:start position:0%
+materials from hundreds of mit courses
+visit mit opencourseware at ocw.mit.edu
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so today we're going to do our last uh
+
+ align:start position:0%
+so today we're going to do our last uh
+ 
+
+ align:start position:0%
+so today we're going to do our last uh
+lecture on scattering in quantum
+
+ align:start position:0%
+lecture on scattering in quantum
+ 
+
+ align:start position:0%
+lecture on scattering in quantum
+mechanics in 1d quantum mechanics and
+
+ align:start position:0%
+mechanics in 1d quantum mechanics and
+ 
+
+ align:start position:0%
+mechanics in 1d quantum mechanics and
+we're going to introduce some powerful
+
+ align:start position:0%
+we're going to introduce some powerful
+ 
+
+ align:start position:0%
+we're going to introduce some powerful
+ideas in particular the phase shift and
+
+ align:start position:0%
+ideas in particular the phase shift and
+ 
+
+ align:start position:0%
+ideas in particular the phase shift and
+the s matrix and they're cool we'll use
+
+ align:start position:0%
+the s matrix and they're cool we'll use
+ 
+
+ align:start position:0%
+the s matrix and they're cool we'll use
+them for good before we get started
+
+ align:start position:0%
+them for good before we get started
+ 
+
+ align:start position:0%
+them for good before we get started
+questions
+
+ align:start position:0%
+questions
+ 
+
+ align:start position:0%
+questions
+from last time
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+just now it's a band called saint
+
+ align:start position:0%
+just now it's a band called saint
+ 
+
+ align:start position:0%
+just now it's a band called saint
+germain um
+
+ align:start position:0%
+germain um
+ 
+
+ align:start position:0%
+germain um
+it's actually a guy
+
+ align:start position:0%
+it's actually a guy
+ 
+
+ align:start position:0%
+it's actually a guy
+but he's refers to himself as a band
+
+ align:start position:0%
+but he's refers to himself as a band
+ 
+
+ align:start position:0%
+but he's refers to himself as a band
+called cengermain anyway it's from an
+
+ align:start position:0%
+called cengermain anyway it's from an
+ 
+
+ align:start position:0%
+called cengermain anyway it's from an
+album i think called traveler
+
+ align:start position:0%
+album i think called traveler
+ 
+
+ align:start position:0%
+album i think called traveler
+physics questions
+
+ align:start position:0%
+physics questions
+ 
+
+ align:start position:0%
+physics questions
+[Music]
+
+ align:start position:0%
+[Music]
+ 
+
+ align:start position:0%
+[Music]
+anyone
+
+ align:start position:0%
+anyone
+ 
+
+ align:start position:0%
+anyone
+okay good um well bad actually i'd much
+
+ align:start position:0%
+okay good um well bad actually i'd much
+ 
+
+ align:start position:0%
+okay good um well bad actually i'd much
+referred if you had questions but i'll
+
+ align:start position:0%
+referred if you had questions but i'll
+ 
+
+ align:start position:0%
+referred if you had questions but i'll
+take that as a sign of of knowledge
+
+ align:start position:0%
+take that as a sign of of knowledge
+ 
+
+ align:start position:0%
+take that as a sign of of knowledge
+competence and mastery
+
+ align:start position:0%
+competence and mastery
+ 
+
+ align:start position:0%
+competence and mastery
+okay so
+
+ align:start position:0%
+okay so
+ 
+
+ align:start position:0%
+okay so
+yeah so
+
+ align:start position:0%
+yeah so
+ 
+
+ align:start position:0%
+yeah so
+so last time we talked about uh
+
+ align:start position:0%
+so last time we talked about uh
+ 
+
+ align:start position:0%
+so last time we talked about uh
+scattering past a barrier with some
+
+ align:start position:0%
+scattering past a barrier with some
+ 
+
+ align:start position:0%
+scattering past a barrier with some
+height l and some height v which i think
+
+ align:start position:0%
+height l and some height v which i think
+ 
+
+ align:start position:0%
+height l and some height v which i think
+we called v naught
+
+ align:start position:0%
+we called v naught
+ 
+
+ align:start position:0%
+we called v naught
+and we observed a bunch of nice things
+
+ align:start position:0%
+and we observed a bunch of nice things
+ 
+
+ align:start position:0%
+and we observed a bunch of nice things
+about this first off we computed the
+
+ align:start position:0%
+about this first off we computed the
+ 
+
+ align:start position:0%
+about this first off we computed the
+probability of transmission across this
+
+ align:start position:0%
+probability of transmission across this
+ 
+
+ align:start position:0%
+probability of transmission across this
+barrier oops the probability of
+
+ align:start position:0%
+barrier oops the probability of
+ 
+
+ align:start position:0%
+barrier oops the probability of
+transmission across this barrier as a
+
+ align:start position:0%
+transmission across this barrier as a
+ 
+
+ align:start position:0%
+transmission across this barrier as a
+function of the energy and it had a
+
+ align:start position:0%
+function of the energy and it had a
+ 
+
+ align:start position:0%
+function of the energy and it had a
+bunch of nice features first off um it
+
+ align:start position:0%
+bunch of nice features first off um it
+ 
+
+ align:start position:0%
+bunch of nice features first off um it
+asymptoted to one at high energies which
+
+ align:start position:0%
+asymptoted to one at high energies which
+ 
+
+ align:start position:0%
+asymptoted to one at high energies which
+makes sense things shouldn't really care
+
+ align:start position:0%
+makes sense things shouldn't really care
+ 
+
+ align:start position:0%
+makes sense things shouldn't really care
+if you have a little tiny barrier
+
+ align:start position:0%
+if you have a little tiny barrier
+ 
+
+ align:start position:0%
+if you have a little tiny barrier
+it went to zero at zero energy uh that i
+
+ align:start position:0%
+it went to zero at zero energy uh that i
+ 
+
+ align:start position:0%
+it went to zero at zero energy uh that i
+don't know how uh i think we should all
+
+ align:start position:0%
+don't know how uh i think we should all
+ 
+
+ align:start position:0%
+don't know how uh i think we should all
+find that obviously if you have
+
+ align:start position:0%
+find that obviously if you have
+ 
+
+ align:start position:0%
+find that obviously if you have
+extremely low energy you're just going
+
+ align:start position:0%
+extremely low energy you're just going
+ 
+
+ align:start position:0%
+extremely low energy you're just going
+to bounce off this very hard wall
+
+ align:start position:0%
+to bounce off this very hard wall
+ 
+
+ align:start position:0%
+to bounce off this very hard wall
+in between though there's some structure
+
+ align:start position:0%
+in between though there's some structure
+ 
+
+ align:start position:0%
+in between though there's some structure
+and in particular uh at certain values
+
+ align:start position:0%
+and in particular uh at certain values
+ 
+
+ align:start position:0%
+and in particular uh at certain values
+of the energy corresponding to certain
+
+ align:start position:0%
+of the energy corresponding to certain
+ 
+
+ align:start position:0%
+of the energy corresponding to certain
+values of the wave number in the barrier
+
+ align:start position:0%
+values of the wave number in the barrier
+ 
+
+ align:start position:0%
+values of the wave number in the barrier
+region at certain values of the energy
+
+ align:start position:0%
+region at certain values of the energy
+ 
+
+ align:start position:0%
+region at certain values of the energy
+we saw that the transmission was perfect
+
+ align:start position:0%
+we saw that the transmission was perfect
+ 
+
+ align:start position:0%
+we saw that the transmission was perfect
+oops this should have been here sorry
+
+ align:start position:0%
+oops this should have been here sorry
+ 
+
+ align:start position:0%
+oops this should have been here sorry
+the transmission was perfect
+
+ align:start position:0%
+the transmission was perfect
+ 
+
+ align:start position:0%
+the transmission was perfect
+at special values of the energy
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and that the reflection
+
+ align:start position:0%
+and that the reflection
+ 
+
+ align:start position:0%
+and that the reflection
+at those points was zero you transmitted
+
+ align:start position:0%
+at those points was zero you transmitted
+ 
+
+ align:start position:0%
+at those points was zero you transmitted
+perfectly
+
+ align:start position:0%
+perfectly
+ 
+
+ align:start position:0%
+perfectly
+but meanwhile the reflection which is
+
+ align:start position:0%
+but meanwhile the reflection which is
+ 
+
+ align:start position:0%
+but meanwhile the reflection which is
+one minus the transmission hit maxima at
+
+ align:start position:0%
+one minus the transmission hit maxima at
+ 
+
+ align:start position:0%
+one minus the transmission hit maxima at
+special points and those special points
+
+ align:start position:0%
+special points and those special points
+ 
+
+ align:start position:0%
+special points and those special points
+turn out to be
+
+ align:start position:0%
+turn out to be
+ 
+
+ align:start position:0%
+turn out to be
+half integer shifted away from the
+
+ align:start position:0%
+half integer shifted away from the
+ 
+
+ align:start position:0%
+half integer shifted away from the
+special points for perfect transmission
+
+ align:start position:0%
+special points for perfect transmission
+ 
+
+ align:start position:0%
+special points for perfect transmission
+so at certain points we have perfect
+
+ align:start position:0%
+so at certain points we have perfect
+ 
+
+ align:start position:0%
+so at certain points we have perfect
+transmission at certain points we have
+
+ align:start position:0%
+transmission at certain points we have
+ 
+
+ align:start position:0%
+transmission at certain points we have
+extremely efficient reflection
+
+ align:start position:0%
+extremely efficient reflection
+ 
+
+ align:start position:0%
+extremely efficient reflection
+and so one of our goals today is going
+
+ align:start position:0%
+and so one of our goals today is going
+ 
+
+ align:start position:0%
+and so one of our goals today is going
+to be to understand
+
+ align:start position:0%
+to be to understand
+ 
+
+ align:start position:0%
+to be to understand
+this physics the physics of resonance in
+
+ align:start position:0%
+this physics the physics of resonance in
+ 
+
+ align:start position:0%
+this physics the physics of resonance in
+scattering off of a potential okay
+
+ align:start position:0%
+scattering off of a potential okay
+ 
+
+ align:start position:0%
+scattering off of a potential okay
+so the asymptotes we understand
+
+ align:start position:0%
+so the asymptotes we understand
+ 
+
+ align:start position:0%
+so the asymptotes we understand
+classically that makes sense classically
+
+ align:start position:0%
+classically that makes sense classically
+ 
+
+ align:start position:0%
+classically that makes sense classically
+that makes sense but classically this is
+
+ align:start position:0%
+that makes sense but classically this is
+ 
+
+ align:start position:0%
+that makes sense but classically this is
+a really weird structure to see
+
+ align:start position:0%
+a really weird structure to see
+ 
+
+ align:start position:0%
+a really weird structure to see
+and notice that it's also not something
+
+ align:start position:0%
+and notice that it's also not something
+ 
+
+ align:start position:0%
+and notice that it's also not something
+that we saw when we looked at scattering
+
+ align:start position:0%
+that we saw when we looked at scattering
+ 
+
+ align:start position:0%
+that we saw when we looked at scattering
+off of a simple step when we looked at a
+
+ align:start position:0%
+off of a simple step when we looked at a
+ 
+
+ align:start position:0%
+off of a simple step when we looked at a
+simple step what we got was something
+
+ align:start position:0%
+simple step what we got was something
+ 
+
+ align:start position:0%
+simple step what we got was something
+that looked like zero
+
+ align:start position:0%
+that looked like zero
+ 
+
+ align:start position:0%
+that looked like zero
+and then
+
+ align:start position:0%
+and then
+ 
+
+ align:start position:0%
+and then
+this
+
+ align:start position:0%
+this
+ 
+
+ align:start position:0%
+this
+right there was no structure it was just
+
+ align:start position:0%
+right there was no structure it was just
+ 
+
+ align:start position:0%
+right there was no structure it was just
+a nice simple curve
+
+ align:start position:0%
+a nice simple curve
+ 
+
+ align:start position:0%
+a nice simple curve
+so something is happening when we have a
+
+ align:start position:0%
+so something is happening when we have a
+ 
+
+ align:start position:0%
+so something is happening when we have a
+barrier as opposed to a step
+
+ align:start position:0%
+barrier as opposed to a step
+ 
+
+ align:start position:0%
+barrier as opposed to a step
+so our job is going to be in some sense
+
+ align:start position:0%
+so our job is going to be in some sense
+ 
+
+ align:start position:0%
+so our job is going to be in some sense
+to answer why are they so different
+
+ align:start position:0%
+to answer why are they so different
+ 
+
+ align:start position:0%
+to answer why are they so different
+before i get going questions about
+
+ align:start position:0%
+before i get going questions about
+ 
+
+ align:start position:0%
+before i get going questions about
+the step
+
+ align:start position:0%
+the step
+ 
+
+ align:start position:0%
+the step
+barrier yeah
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+is that just scale
+
+ align:start position:0%
+is that just scale
+ 
+
+ align:start position:0%
+is that just scale
+oh sorry um
+
+ align:start position:0%
+oh sorry um
+ 
+
+ align:start position:0%
+oh sorry um
+this one
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this that was the transmission sorry i
+
+ align:start position:0%
+this that was the transmission sorry i
+ 
+
+ align:start position:0%
+this that was the transmission sorry i
+should have drawn it separately that was
+
+ align:start position:0%
+should have drawn it separately that was
+ 
+
+ align:start position:0%
+should have drawn it separately that was
+the transmission as um as a function of
+
+ align:start position:0%
+the transmission as um as a function of
+ 
+
+ align:start position:0%
+the transmission as um as a function of
+energy
+
+ align:start position:0%
+energy
+ 
+
+ align:start position:0%
+energy
+across a single step
+
+ align:start position:0%
+across a single step
+ 
+
+ align:start position:0%
+across a single step
+and so that looked like this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+exactly oh oh sorry so so i just meant
+
+ align:start position:0%
+exactly oh oh sorry so so i just meant
+ 
+
+ align:start position:0%
+exactly oh oh sorry so so i just meant
+to compare the two i just want to think
+
+ align:start position:0%
+to compare the two i just want to think
+ 
+
+ align:start position:0%
+to compare the two i just want to think
+of them as two different systems in this
+
+ align:start position:0%
+of them as two different systems in this
+ 
+
+ align:start position:0%
+of them as two different systems in this
+system we have
+
+ align:start position:0%
+system we have
+ 
+
+ align:start position:0%
+system we have
+the transmission curve is a nice simple
+
+ align:start position:0%
+the transmission curve is a nice simple
+ 
+
+ align:start position:0%
+the transmission curve is a nice simple
+curve it has no structure in the case of
+
+ align:start position:0%
+curve it has no structure in the case of
+ 
+
+ align:start position:0%
+curve it has no structure in the case of
+a step barrier we get non-zero
+
+ align:start position:0%
+a step barrier we get non-zero
+ 
+
+ align:start position:0%
+a step barrier we get non-zero
+transmission at low energies instead of
+
+ align:start position:0%
+transmission at low energies instead of
+ 
+
+ align:start position:0%
+transmission at low energies instead of
+going to zero and we get this resonant
+
+ align:start position:0%
+going to zero and we get this resonant
+ 
+
+ align:start position:0%
+going to zero and we get this resonant
+structure
+
+ align:start position:0%
+structure
+ 
+
+ align:start position:0%
+structure
+so it's just for contrast
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+so before before going into that in
+
+ align:start position:0%
+so before before going into that in
+ 
+
+ align:start position:0%
+so before before going into that in
+detail i wanna do one slight variation
+
+ align:start position:0%
+detail i wanna do one slight variation
+ 
+
+ align:start position:0%
+detail i wanna do one slight variation
+of this problem and i'm not going to do
+
+ align:start position:0%
+of this problem and i'm not going to do
+ 
+
+ align:start position:0%
+of this problem and i'm not going to do
+any of the computations i'm just going
+
+ align:start position:0%
+any of the computations i'm just going
+ 
+
+ align:start position:0%
+any of the computations i'm just going
+to tell you how to get the answer from
+
+ align:start position:0%
+to tell you how to get the answer from
+ 
+
+ align:start position:0%
+to tell you how to get the answer from
+the answers we've already computed
+
+ align:start position:0%
+the answers we've already computed
+ 
+
+ align:start position:0%
+the answers we've already computed
+so consider a barrier a square well you
+
+ align:start position:0%
+so consider a barrier a square well you
+ 
+
+ align:start position:0%
+so consider a barrier a square well you
+guys have solved the finite square well
+
+ align:start position:0%
+guys have solved the finite square well
+ 
+
+ align:start position:0%
+guys have solved the finite square well
+in your problem sets consider finding
+
+ align:start position:0%
+in your problem sets consider finding
+ 
+
+ align:start position:0%
+in your problem sets consider finding
+square well again of width l and of
+
+ align:start position:0%
+square well again of width l and of
+ 
+
+ align:start position:0%
+square well again of width l and of
+depth now minus v naught so it's the
+
+ align:start position:0%
+depth now minus v naught so it's the
+ 
+
+ align:start position:0%
+depth now minus v naught so it's the
+same thing with v goes to minus v
+
+ align:start position:0%
+same thing with v goes to minus v
+ 
+
+ align:start position:0%
+same thing with v goes to minus v
+okay and again i want to consider
+
+ align:start position:0%
+okay and again i want to consider
+ 
+
+ align:start position:0%
+okay and again i want to consider
+scattering states so i want to consider
+
+ align:start position:0%
+scattering states so i want to consider
+ 
+
+ align:start position:0%
+scattering states so i want to consider
+states with positive energy energy above
+
+ align:start position:0%
+states with positive energy energy above
+ 
+
+ align:start position:0%
+states with positive energy energy above
+the asymptotic potential
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+now at this point by now we all know how
+
+ align:start position:0%
+now at this point by now we all know how
+ 
+
+ align:start position:0%
+now at this point by now we all know how
+to solve this we write plane waves here
+
+ align:start position:0%
+to solve this we write plane waves here
+ 
+
+ align:start position:0%
+to solve this we write plane waves here
+plane waves here we solve and plane
+
+ align:start position:0%
+plane waves here we solve and plane
+ 
+
+ align:start position:0%
+plane waves here we solve and plane
+waves in between we solve the potential
+
+ align:start position:0%
+waves in between we solve the potential
+ 
+
+ align:start position:0%
+waves in between we solve the potential
+in each region where it's constant and
+
+ align:start position:0%
+in each region where it's constant and
+ 
+
+ align:start position:0%
+in each region where it's constant and
+then we impose p uh continuity
+
+ align:start position:0%
+then we impose p uh continuity
+ 
+
+ align:start position:0%
+then we impose p uh continuity
+and of the wave function and continuity
+
+ align:start position:0%
+and of the wave function and continuity
+ 
+
+ align:start position:0%
+and of the wave function and continuity
+the derivative of the wave function at
+
+ align:start position:0%
+the derivative of the wave function at
+ 
+
+ align:start position:0%
+the derivative of the wave function at
+the matching points right so we know how
+
+ align:start position:0%
+the matching points right so we know how
+ 
+
+ align:start position:0%
+the matching points right so we know how
+to solve this problem and deduce the
+
+ align:start position:0%
+to solve this problem and deduce the
+ 
+
+ align:start position:0%
+to solve this problem and deduce the
+transmission reflection coefficients
+
+ align:start position:0%
+transmission reflection coefficients
+ 
+
+ align:start position:0%
+transmission reflection coefficients
+we've done it for this problem and it's
+
+ align:start position:0%
+we've done it for this problem and it's
+ 
+
+ align:start position:0%
+we've done it for this problem and it's
+exactly the same algebra and in fact
+
+ align:start position:0%
+exactly the same algebra and in fact
+ 
+
+ align:start position:0%
+exactly the same algebra and in fact
+it's so exactly the same algebra that we
+
+ align:start position:0%
+it's so exactly the same algebra that we
+ 
+
+ align:start position:0%
+it's so exactly the same algebra that we
+can just take the results from this one
+
+ align:start position:0%
+can just take the results from this one
+ 
+
+ align:start position:0%
+can just take the results from this one
+and take v to minus v and we'll get the
+
+ align:start position:0%
+and take v to minus v and we'll get the
+ 
+
+ align:start position:0%
+and take v to minus v and we'll get the
+right answer
+
+ align:start position:0%
+right answer
+ 
+
+ align:start position:0%
+right answer
+you kind of have to so
+
+ align:start position:0%
+you kind of have to so
+ 
+
+ align:start position:0%
+you kind of have to so
+if we do
+
+ align:start position:0%
+if we do
+ 
+
+ align:start position:0%
+if we do
+what we get for the transmission
+
+ align:start position:0%
+what we get for the transmission
+ 
+
+ align:start position:0%
+what we get for the transmission
+probability
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and now this is the transmission
+
+ align:start position:0%
+and now this is the transmission
+ 
+
+ align:start position:0%
+and now this is the transmission
+probability for a square well
+
+ align:start position:0%
+probability for a square well
+ 
+
+ align:start position:0%
+probability for a square well
+and again i'm going to use the same
+
+ align:start position:0%
+and again i'm going to use the same
+ 
+
+ align:start position:0%
+and again i'm going to use the same
+dimensionless constants g naught squared
+
+ align:start position:0%
+dimensionless constants g naught squared
+ 
+
+ align:start position:0%
+dimensionless constants g naught squared
+is equal to
+
+ align:start position:0%
+is equal to
+ 
+
+ align:start position:0%
+is equal to
+2m l squared over h bar squared times v
+
+ align:start position:0%
+2m l squared over h bar squared times v
+ 
+
+ align:start position:0%
+2m l squared over h bar squared times v
+naught this is 1 over an energy this is
+
+ align:start position:0%
+naught this is 1 over an energy this is
+ 
+
+ align:start position:0%
+naught this is 1 over an energy this is
+an energy this is dimensionless and the
+
+ align:start position:0%
+an energy this is dimensionless and the
+ 
+
+ align:start position:0%
+an energy this is dimensionless and the
+dimensionless energy epsilon is equal to
+
+ align:start position:0%
+dimensionless energy epsilon is equal to
+ 
+
+ align:start position:0%
+dimensionless energy epsilon is equal to
+e over v to express my transmission
+
+ align:start position:0%
+e over v to express my transmission
+ 
+
+ align:start position:0%
+e over v to express my transmission
+probability life is better when it's
+
+ align:start position:0%
+probability life is better when it's
+ 
+
+ align:start position:0%
+probability life is better when it's
+dimensionless
+
+ align:start position:0%
+dimensionless
+ 
+
+ align:start position:0%
+dimensionless
+so t the transmission probability is
+
+ align:start position:0%
+so t the transmission probability is
+ 
+
+ align:start position:0%
+so t the transmission probability is
+again it's one of these horrible one
+
+ align:start position:0%
+again it's one of these horrible one
+ 
+
+ align:start position:0%
+again it's one of these horrible one
+overs one over 1 plus
+
+ align:start position:0%
+overs one over 1 plus
+ 
+
+ align:start position:0%
+overs one over 1 plus
+1 over 4 epsilon epsilon
+
+ align:start position:0%
+1 over 4 epsilon epsilon
+ 
+
+ align:start position:0%
+1 over 4 epsilon epsilon
+plus 1.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+good sine squared of g naught
+
+ align:start position:0%
+good sine squared of g naught
+ 
+
+ align:start position:0%
+good sine squared of g naught
+square root of epsilon plus 1.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+this is again the same so if you
+
+ align:start position:0%
+this is again the same so if you
+ 
+
+ align:start position:0%
+this is again the same so if you
+remember last time
+
+ align:start position:0%
+remember last time
+ 
+
+ align:start position:0%
+remember last time
+you can see what we got last time by now
+
+ align:start position:0%
+you can see what we got last time by now
+ 
+
+ align:start position:0%
+you can see what we got last time by now
+taking v to minus v again that takes
+
+ align:start position:0%
+taking v to minus v again that takes
+ 
+
+ align:start position:0%
+taking v to minus v again that takes
+epsilon to minus epsilon so we get out
+
+ align:start position:0%
+epsilon to minus epsilon so we get out
+ 
+
+ align:start position:0%
+epsilon to minus epsilon so we get out
+epsilon a one minus epsilon or epsilon
+
+ align:start position:0%
+epsilon a one minus epsilon or epsilon
+ 
+
+ align:start position:0%
+epsilon a one minus epsilon or epsilon
+minus one picking up the minus sign from
+
+ align:start position:0%
+minus one picking up the minus sign from
+ 
+
+ align:start position:0%
+minus one picking up the minus sign from
+this epsilon
+
+ align:start position:0%
+this epsilon
+ 
+
+ align:start position:0%
+this epsilon
+um and here we get a one minus epsilon
+
+ align:start position:0%
+um and here we get a one minus epsilon
+ 
+
+ align:start position:0%
+um and here we get a one minus epsilon
+instead of one plus epsilon that's
+
+ align:start position:0%
+instead of one plus epsilon that's
+ 
+
+ align:start position:0%
+instead of one plus epsilon that's
+precisely what we got last time
+
+ align:start position:0%
+precisely what we got last time
+ 
+
+ align:start position:0%
+precisely what we got last time
+so if you're feeling punchy at home
+
+ align:start position:0%
+so if you're feeling punchy at home
+ 
+
+ align:start position:0%
+so if you're feeling punchy at home
+tonight
+
+ align:start position:0%
+tonight
+ 
+
+ align:start position:0%
+tonight
+check this
+
+ align:start position:0%
+check this
+ 
+
+ align:start position:0%
+check this
+in some sense you're going to rederive
+
+ align:start position:0%
+in some sense you're going to rederive
+ 
+
+ align:start position:0%
+in some sense you're going to rederive
+it on the problem set
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so
+
+ align:start position:0%
+okay so
+ 
+
+ align:start position:0%
+okay so
+it looks basically the same as before we
+
+ align:start position:0%
+it looks basically the same as before we
+ 
+
+ align:start position:0%
+it looks basically the same as before we
+have a sine function downstairs which
+
+ align:start position:0%
+have a sine function downstairs which
+ 
+
+ align:start position:0%
+have a sine function downstairs which
+again will sometimes be zero the sine
+
+ align:start position:0%
+again will sometimes be zero the sine
+ 
+
+ align:start position:0%
+again will sometimes be zero the sine
+will occasionally be b0 when it's
+
+ align:start position:0%
+will occasionally be b0 when it's
+ 
+
+ align:start position:0%
+will occasionally be b0 when it's
+argument is a multiple of pi and when
+
+ align:start position:0%
+argument is a multiple of pi and when
+ 
+
+ align:start position:0%
+argument is a multiple of pi and when
+that sine function is zero then the
+
+ align:start position:0%
+that sine function is zero then the
+ 
+
+ align:start position:0%
+that sine function is zero then the
+transmission probability is one over one
+
+ align:start position:0%
+transmission probability is one over one
+ 
+
+ align:start position:0%
+transmission probability is one over one
+plus zero it's also known as one
+
+ align:start position:0%
+plus zero it's also known as one
+ 
+
+ align:start position:0%
+plus zero it's also known as one
+transmission is perfect so we again get
+
+ align:start position:0%
+transmission is perfect so we again get
+ 
+
+ align:start position:0%
+transmission is perfect so we again get
+a resonant structure and it's in fact
+
+ align:start position:0%
+a resonant structure and it's in fact
+ 
+
+ align:start position:0%
+a resonant structure and it's in fact
+exactly the same plot or almost exactly
+
+ align:start position:0%
+exactly the same plot or almost exactly
+ 
+
+ align:start position:0%
+exactly the same plot or almost exactly
+the same plot so um i'm going to plot
+
+ align:start position:0%
+the same plot so um i'm going to plot
+ 
+
+ align:start position:0%
+the same plot so um i'm going to plot
+transmission
+
+ align:start position:0%
+transmission
+ 
+
+ align:start position:0%
+transmission
+let's go ahead and do this transmission
+
+ align:start position:0%
+let's go ahead and do this transmission
+ 
+
+ align:start position:0%
+let's go ahead and do this transmission
+probability as a function again of the
+
+ align:start position:0%
+probability as a function again of the
+ 
+
+ align:start position:0%
+probability as a function again of the
+dimensionless energy
+
+ align:start position:0%
+dimensionless energy
+ 
+
+ align:start position:0%
+dimensionless energy
+and what we get
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+is again oops
+
+ align:start position:0%
+is again oops
+ 
+
+ align:start position:0%
+is again oops
+not very well drawn
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+resonances
+
+ align:start position:0%
+resonances
+ 
+
+ align:start position:0%
+resonances
+where transmission goes to one
+
+ align:start position:0%
+where transmission goes to one
+ 
+
+ align:start position:0%
+where transmission goes to one
+thanks to my beautiful artistic skills
+
+ align:start position:0%
+thanks to my beautiful artistic skills
+ 
+
+ align:start position:0%
+thanks to my beautiful artistic skills
+points where the resonance or the where
+
+ align:start position:0%
+points where the resonance or the where
+ 
+
+ align:start position:0%
+points where the resonance or the where
+the reflection hits a local maximum
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+but we know one more thing about this
+
+ align:start position:0%
+but we know one more thing about this
+ 
+
+ align:start position:0%
+but we know one more thing about this
+system which is that in addition to
+
+ align:start position:0%
+system which is that in addition to
+ 
+
+ align:start position:0%
+system which is that in addition to
+having scattering states
+
+ align:start position:0%
+having scattering states
+ 
+
+ align:start position:0%
+having scattering states
+whose transmission probability are
+
+ align:start position:0%
+whose transmission probability are
+ 
+
+ align:start position:0%
+whose transmission probability are
+indicated by this plot we know we also
+
+ align:start position:0%
+indicated by this plot we know we also
+ 
+
+ align:start position:0%
+indicated by this plot we know we also
+have for negative energy bound states
+
+ align:start position:0%
+have for negative energy bound states
+ 
+
+ align:start position:0%
+have for negative energy bound states
+right unlike the step barrier for the
+
+ align:start position:0%
+right unlike the step barrier for the
+ 
+
+ align:start position:0%
+right unlike the step barrier for the
+step well we also have bound states so
+
+ align:start position:0%
+step well we also have bound states so
+ 
+
+ align:start position:0%
+step well we also have bound states so
+here's the transmission curve but i just
+
+ align:start position:0%
+here's the transmission curve but i just
+ 
+
+ align:start position:0%
+here's the transmission curve but i just
+want to remind you that we have energies
+
+ align:start position:0%
+want to remind you that we have energies
+ 
+
+ align:start position:0%
+want to remind you that we have energies
+at special values of energies we also
+
+ align:start position:0%
+at special values of energies we also
+ 
+
+ align:start position:0%
+at special values of energies we also
+have
+
+ align:start position:0%
+have
+ 
+
+ align:start position:0%
+have
+bound states
+
+ align:start position:0%
+bound states
+ 
+
+ align:start position:0%
+bound states
+and precisely what energies depends on
+
+ align:start position:0%
+and precisely what energies depends on
+ 
+
+ align:start position:0%
+and precisely what energies depends on
+the structure of the well and the depth
+
+ align:start position:0%
+the structure of the well and the depth
+ 
+
+ align:start position:0%
+the structure of the well and the depth
+but if the depth of the well is say v
+
+ align:start position:0%
+but if the depth of the well is say v
+ 
+
+ align:start position:0%
+but if the depth of the well is say v
+naught
+
+ align:start position:0%
+naught
+ 
+
+ align:start position:0%
+naught
+so this is minus one
+
+ align:start position:0%
+so this is minus one
+ 
+
+ align:start position:0%
+so this is minus one
+we know that the lowest bound state is
+
+ align:start position:0%
+we know that the lowest bound state is
+ 
+
+ align:start position:0%
+we know that the lowest bound state is
+always greater energy than the bottom of
+
+ align:start position:0%
+always greater energy than the bottom of
+ 
+
+ align:start position:0%
+always greater energy than the bottom of
+the well
+
+ align:start position:0%
+the well
+ 
+
+ align:start position:0%
+the well
+cool
+
+ align:start position:0%
+cool
+ 
+
+ align:start position:0%
+cool
+so epsilon remember is e over v naught
+
+ align:start position:0%
+so epsilon remember is e over v naught
+ 
+
+ align:start position:0%
+so epsilon remember is e over v naught
+and in the square well of depth v naught
+
+ align:start position:0%
+and in the square well of depth v naught
+ 
+
+ align:start position:0%
+and in the square well of depth v naught
+the lowest bound state cannot possibly
+
+ align:start position:0%
+the lowest bound state cannot possibly
+ 
+
+ align:start position:0%
+the lowest bound state cannot possibly
+have energy lower than the bottom of the
+
+ align:start position:0%
+have energy lower than the bottom of the
+ 
+
+ align:start position:0%
+have energy lower than the bottom of the
+well so its epsilon must have epsilon
+
+ align:start position:0%
+well so its epsilon must have epsilon
+ 
+
+ align:start position:0%
+well so its epsilon must have epsilon
+greater than one or minus one
+
+ align:start position:0%
+greater than one or minus one
+ 
+
+ align:start position:0%
+greater than one or minus one
+cool anyway this is just to remind you
+
+ align:start position:0%
+cool anyway this is just to remind you
+ 
+
+ align:start position:0%
+cool anyway this is just to remind you
+that there are bound states
+
+ align:start position:0%
+that there are bound states
+ 
+
+ align:start position:0%
+that there are bound states
+and um
+
+ align:start position:0%
+and um
+ 
+
+ align:start position:0%
+and um
+think of this like a gun put down on a
+
+ align:start position:0%
+think of this like a gun put down on a
+ 
+
+ align:start position:0%
+think of this like a gun put down on a
+table in a play in act one
+
+ align:start position:0%
+table in a play in act one
+ 
+
+ align:start position:0%
+table in a play in act one
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+it's that dramatic
+
+ align:start position:0%
+it's that dramatic
+ 
+
+ align:start position:0%
+it's that dramatic
+so it will show up again it will come
+
+ align:start position:0%
+so it will show up again it will come
+ 
+
+ align:start position:0%
+so it will show up again it will come
+back
+
+ align:start position:0%
+back
+ 
+
+ align:start position:0%
+back
+and play well with us so
+
+ align:start position:0%
+and play well with us so
+ 
+
+ align:start position:0%
+and play well with us so
+i want to talk about these residences so
+
+ align:start position:0%
+i want to talk about these residences so
+ 
+
+ align:start position:0%
+i want to talk about these residences so
+let's understand why they're there
+
+ align:start position:0%
+let's understand why they're there
+ 
+
+ align:start position:0%
+let's understand why they're there
+so there are a bunch of ways of
+
+ align:start position:0%
+so there are a bunch of ways of
+ 
+
+ align:start position:0%
+so there are a bunch of ways of
+understanding why these resonances are
+
+ align:start position:0%
+understanding why these resonances are
+ 
+
+ align:start position:0%
+understanding why these resonances are
+present
+
+ align:start position:0%
+present
+ 
+
+ align:start position:0%
+present
+and let me just
+
+ align:start position:0%
+and let me just
+ 
+
+ align:start position:0%
+and let me just
+give you a couple
+
+ align:start position:0%
+give you a couple
+ 
+
+ align:start position:0%
+give you a couple
+so first a heuristic picture and then i
+
+ align:start position:0%
+so first a heuristic picture and then i
+ 
+
+ align:start position:0%
+so first a heuristic picture and then i
+want to give you a very precise
+
+ align:start position:0%
+want to give you a very precise
+ 
+
+ align:start position:0%
+want to give you a very precise
+computational picture of why these
+
+ align:start position:0%
+computational picture of why these
+ 
+
+ align:start position:0%
+computational picture of why these
+resonances are happening so the first is
+
+ align:start position:0%
+resonances are happening so the first is
+ 
+
+ align:start position:0%
+resonances are happening so the first is
+imagine we have a state where the
+
+ align:start position:0%
+imagine we have a state where the
+ 
+
+ align:start position:0%
+imagine we have a state where the
+transmission is perfect what that tells
+
+ align:start position:0%
+transmission is perfect what that tells
+ 
+
+ align:start position:0%
+transmission is perfect what that tells
+you is kl is a multiple of pi
+
+ align:start position:0%
+you is kl is a multiple of pi
+ 
+
+ align:start position:0%
+you is kl is a multiple of pi
+so in here
+
+ align:start position:0%
+so in here
+ 
+
+ align:start position:0%
+so in here
+so if this is the distance l of the well
+
+ align:start position:0%
+so if this is the distance l of the well
+ 
+
+ align:start position:0%
+so if this is the distance l of the well
+in here the wave is exactly one period
+
+ align:start position:0%
+in here the wave is exactly one period
+ 
+
+ align:start position:0%
+in here the wave is exactly one period
+or if it's kale is equal to
+
+ align:start position:0%
+or if it's kale is equal to
+ 
+
+ align:start position:0%
+or if it's kale is equal to
+two to a multiple of pi um so if kl is
+
+ align:start position:0%
+two to a multiple of pi um so if kl is
+ 
+
+ align:start position:0%
+two to a multiple of pi um so if kl is
+pi
+
+ align:start position:0%
+pi
+ 
+
+ align:start position:0%
+pi
+whoops i think i want do i want two
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+good let me simplify my life and
+
+ align:start position:0%
+good let me simplify my life and
+ 
+
+ align:start position:0%
+good let me simplify my life and
+consider the case kale is two pie so
+
+ align:start position:0%
+consider the case kale is two pie so
+ 
+
+ align:start position:0%
+consider the case kale is two pie so
+when the wave comes through and becomes
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+oh i know why shoot so for this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+sorry
+
+ align:start position:0%
+sorry
+ 
+
+ align:start position:0%
+sorry
+four pi so um i switched notations for
+
+ align:start position:0%
+four pi so um i switched notations for
+ 
+
+ align:start position:0%
+four pi so um i switched notations for
+you i was using in my head uh and or
+
+ align:start position:0%
+you i was using in my head uh and or
+ 
+
+ align:start position:0%
+you i was using in my head uh and or
+rather in my notes uh width of the well
+
+ align:start position:0%
+rather in my notes uh width of the well
+ 
+
+ align:start position:0%
+rather in my notes uh width of the well
+is 2l from
+
+ align:start position:0%
+is 2l from
+ 
+
+ align:start position:0%
+is 2l from
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+for reasons you'll see on the notes if
+
+ align:start position:0%
+for reasons you'll see on the notes if
+ 
+
+ align:start position:0%
+for reasons you'll see on the notes if
+you look at the notes but let's ignore
+
+ align:start position:0%
+you look at the notes but let's ignore
+ 
+
+ align:start position:0%
+you look at the notes but let's ignore
+that let's focus on these guys so
+
+ align:start position:0%
+that let's focus on these guys so
+ 
+
+ align:start position:0%
+that let's focus on these guys so
+consider the state
+
+ align:start position:0%
+consider the state
+ 
+
+ align:start position:0%
+consider the state
+a configuration in energy such that in
+
+ align:start position:0%
+a configuration in energy such that in
+ 
+
+ align:start position:0%
+a configuration in energy such that in
+the well we have exactly one period of
+
+ align:start position:0%
+the well we have exactly one period of
+ 
+
+ align:start position:0%
+the well we have exactly one period of
+the wave function that means that the
+
+ align:start position:0%
+the wave function that means that the
+ 
+
+ align:start position:0%
+the wave function that means that the
+value of the wave function at the two
+
+ align:start position:0%
+value of the wave function at the two
+ 
+
+ align:start position:0%
+value of the wave function at the two
+ends is the same and the slope is the
+
+ align:start position:0%
+ends is the same and the slope is the
+ 
+
+ align:start position:0%
+ends is the same and the slope is the
+same
+
+ align:start position:0%
+same
+ 
+
+ align:start position:0%
+same
+so whatever the energy is out here
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+if it matches smoothly continuously and
+
+ align:start position:0%
+if it matches smoothly continuously and
+ 
+
+ align:start position:0%
+if it matches smoothly continuously and
+its derivative is continuous here it
+
+ align:start position:0%
+its derivative is continuous here it
+ 
+
+ align:start position:0%
+its derivative is continuous here it
+will match smoothly and continuously out
+
+ align:start position:0%
+will match smoothly and continuously out
+ 
+
+ align:start position:0%
+will match smoothly and continuously out
+here as well with the same
+
+ align:start position:0%
+here as well with the same
+ 
+
+ align:start position:0%
+here as well with the same
+amplitude and the same
+
+ align:start position:0%
+amplitude and the same
+ 
+
+ align:start position:0%
+amplitude and the same
+period inside and outside
+
+ align:start position:0%
+period inside and outside
+ 
+
+ align:start position:0%
+period inside and outside
+right the amplitude is the same in the
+
+ align:start position:0%
+right the amplitude is the same in the
+ 
+
+ align:start position:0%
+right the amplitude is the same in the
+phases the same that means this wave
+
+ align:start position:0%
+phases the same that means this wave
+ 
+
+ align:start position:0%
+phases the same that means this wave
+must have the same amplitude in the same
+
+ align:start position:0%
+must have the same amplitude in the same
+ 
+
+ align:start position:0%
+must have the same amplitude in the same
+period well it has to have the same
+
+ align:start position:0%
+period well it has to have the same
+ 
+
+ align:start position:0%
+period well it has to have the same
+period is the same energy but must have
+
+ align:start position:0%
+period is the same energy but must have
+ 
+
+ align:start position:0%
+period is the same energy but must have
+the same amplitude and the same slope at
+
+ align:start position:0%
+the same amplitude and the same slope at
+ 
+
+ align:start position:0%
+the same amplitude and the same slope at
+that point
+
+ align:start position:0%
+that point
+ 
+
+ align:start position:0%
+that point
+and that means that this wave has the
+
+ align:start position:0%
+and that means that this wave has the
+ 
+
+ align:start position:0%
+and that means that this wave has the
+same amplitude as this wave the norm
+
+ align:start position:0%
+same amplitude as this wave the norm
+ 
+
+ align:start position:0%
+same amplitude as this wave the norm
+squared
+
+ align:start position:0%
+squared
+ 
+
+ align:start position:0%
+squared
+is the transmission probability norm
+
+ align:start position:0%
+is the transmission probability norm
+ 
+
+ align:start position:0%
+is the transmission probability norm
+squared of this divided by the normal
+
+ align:start position:0%
+squared of this divided by the normal
+ 
+
+ align:start position:0%
+squared of this divided by the normal
+square of this that means the
+
+ align:start position:0%
+square of this that means the
+ 
+
+ align:start position:0%
+square of this that means the
+transmission probability has to be one
+
+ align:start position:0%
+transmission probability has to be one
+ 
+
+ align:start position:0%
+transmission probability has to be one
+what would have happened had the system
+
+ align:start position:0%
+what would have happened had the system
+ 
+
+ align:start position:0%
+what would have happened had the system
+instead of being perfectly periodic
+
+ align:start position:0%
+instead of being perfectly periodic
+ 
+
+ align:start position:0%
+instead of being perfectly periodic
+inside the well well let me actually let
+
+ align:start position:0%
+inside the well well let me actually let
+ 
+
+ align:start position:0%
+inside the well well let me actually let
+me leave that up
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so we
+
+ align:start position:0%
+so we
+ 
+
+ align:start position:0%
+so we
+have let's do it as this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+oh shoot i'm even getting my qualitative
+
+ align:start position:0%
+oh shoot i'm even getting my qualitative
+ 
+
+ align:start position:0%
+oh shoot i'm even getting my qualitative
+wave functions wrong let's try this
+
+ align:start position:0%
+wave functions wrong let's try this
+ 
+
+ align:start position:0%
+wave functions wrong let's try this
+again
+
+ align:start position:0%
+again
+ 
+
+ align:start position:0%
+again
+okay start at the top go down and then
+
+ align:start position:0%
+okay start at the top go down and then
+ 
+
+ align:start position:0%
+okay start at the top go down and then
+it's got a lower uh uh it's deeper
+
+ align:start position:0%
+it's got a lower uh uh it's deeper
+ 
+
+ align:start position:0%
+it's got a lower uh uh it's deeper
+inside the well so the amplitude out
+
+ align:start position:0%
+inside the well so the amplitude out
+ 
+
+ align:start position:0%
+inside the well so the amplitude out
+here the the potent the difference in
+
+ align:start position:0%
+here the the potent the difference in
+ 
+
+ align:start position:0%
+here the the potent the difference in
+energy between the energy and the
+
+ align:start position:0%
+energy between the energy and the
+ 
+
+ align:start position:0%
+energy between the energy and the
+potential is less which means the period
+
+ align:start position:0%
+potential is less which means the period
+ 
+
+ align:start position:0%
+potential is less which means the period
+is longer and the amplitude is greater
+
+ align:start position:0%
+is longer and the amplitude is greater
+ 
+
+ align:start position:0%
+is longer and the amplitude is greater
+but it's the way i've drawn it it's got
+
+ align:start position:0%
+but it's the way i've drawn it it's got
+ 
+
+ align:start position:0%
+but it's the way i've drawn it it's got
+a particular value it's got zero
+
+ align:start position:0%
+a particular value it's got zero
+ 
+
+ align:start position:0%
+a particular value it's got zero
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+zero uh
+
+ align:start position:0%
+zero uh
+ 
+
+ align:start position:0%
+zero uh
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+derivative at this point
+
+ align:start position:0%
+derivative at this point
+ 
+
+ align:start position:0%
+derivative at this point
+so it's got two
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay good so there's our wavefunction
+
+ align:start position:0%
+okay good so there's our wavefunction
+ 
+
+ align:start position:0%
+okay good so there's our wavefunction
+same thing out here
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+but the important thing is the amplitude
+
+ align:start position:0%
+but the important thing is the amplitude
+ 
+
+ align:start position:0%
+but the important thing is the amplitude
+here has to be the same as the amplitude
+
+ align:start position:0%
+here has to be the same as the amplitude
+ 
+
+ align:start position:0%
+here has to be the same as the amplitude
+here because the amplitude and the
+
+ align:start position:0%
+here because the amplitude and the
+ 
+
+ align:start position:0%
+here because the amplitude and the
+amplitude in the phase were exactly as
+
+ align:start position:0%
+amplitude in the phase were exactly as
+ 
+
+ align:start position:0%
+amplitude in the phase were exactly as
+if there had been no intervening region
+
+ align:start position:0%
+if there had been no intervening region
+ 
+
+ align:start position:0%
+if there had been no intervening region
+wouldn't agree with that
+
+ align:start position:0%
+wouldn't agree with that
+ 
+
+ align:start position:0%
+wouldn't agree with that
+by contrast if we had looked at a
+
+ align:start position:0%
+by contrast if we had looked at a
+ 
+
+ align:start position:0%
+by contrast if we had looked at a
+situation where inside the well
+
+ align:start position:0%
+situation where inside the well
+ 
+
+ align:start position:0%
+situation where inside the well
+it was not the same amplitude so for
+
+ align:start position:0%
+it was not the same amplitude so for
+ 
+
+ align:start position:0%
+it was not the same amplitude so for
+example
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+something like this
+
+ align:start position:0%
+something like this
+ 
+
+ align:start position:0%
+something like this
+came up with some slope which is
+
+ align:start position:0%
+came up with some slope which is
+ 
+
+ align:start position:0%
+came up with some slope which is
+different in a value which was different
+
+ align:start position:0%
+different in a value which was different
+ 
+
+ align:start position:0%
+different in a value which was different
+then this is going to match onto
+
+ align:start position:0%
+then this is going to match onto
+ 
+
+ align:start position:0%
+then this is going to match onto
+something with the same period but with
+
+ align:start position:0%
+something with the same period but with
+ 
+
+ align:start position:0%
+something with the same period but with
+a different amplitude
+
+ align:start position:0%
+a different amplitude
+ 
+
+ align:start position:0%
+a different amplitude
+than it would have
+
+ align:start position:0%
+than it would have
+ 
+
+ align:start position:0%
+than it would have
+over here
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+same period because it's got the same
+
+ align:start position:0%
+same period because it's got the same
+ 
+
+ align:start position:0%
+same period because it's got the same
+energy but a different amplitude because
+
+ align:start position:0%
+energy but a different amplitude because
+ 
+
+ align:start position:0%
+energy but a different amplitude because
+it has to match on with the value and
+
+ align:start position:0%
+it has to match on with the value and
+ 
+
+ align:start position:0%
+it has to match on with the value and
+the derivative
+
+ align:start position:0%
+the derivative
+ 
+
+ align:start position:0%
+the derivative
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+you can think through this and pretty
+
+ align:start position:0%
+you can think through this and pretty
+ 
+
+ align:start position:0%
+you can think through this and pretty
+quickly convince yourself of
+
+ align:start position:0%
+quickly convince yourself of
+ 
+
+ align:start position:0%
+quickly convince yourself of
+the necessity of the transmission
+
+ align:start position:0%
+the necessity of the transmission
+ 
+
+ align:start position:0%
+the necessity of the transmission
+amplitude being one if this is exactly
+
+ align:start position:0%
+amplitude being one if this is exactly
+ 
+
+ align:start position:0%
+amplitude being one if this is exactly
+periodic
+
+ align:start position:0%
+periodic
+ 
+
+ align:start position:0%
+periodic
+again if this is exactly one period
+
+ align:start position:0%
+again if this is exactly one period
+ 
+
+ align:start position:0%
+again if this is exactly one period
+inside you can just imagine this is gone
+
+ align:start position:0%
+inside you can just imagine this is gone
+ 
+
+ align:start position:0%
+inside you can just imagine this is gone
+and you get a continuous wave function
+
+ align:start position:0%
+and you get a continuous wave function
+ 
+
+ align:start position:0%
+and you get a continuous wave function
+so the amplitude and the derivative must
+
+ align:start position:0%
+so the amplitude and the derivative must
+ 
+
+ align:start position:0%
+so the amplitude and the derivative must
+be the same on both sides
+
+ align:start position:0%
+be the same on both sides
+ 
+
+ align:start position:0%
+be the same on both sides
+as if there is no barrier there and when
+
+ align:start position:0%
+as if there is no barrier there and when
+ 
+
+ align:start position:0%
+as if there is no barrier there and when
+the phases uh when the phase is not same
+
+ align:start position:0%
+the phases uh when the phase is not same
+ 
+
+ align:start position:0%
+the phases uh when the phase is not same
+here when the wave function doesn't have
+
+ align:start position:0%
+here when the wave function doesn't have
+ 
+
+ align:start position:0%
+here when the wave function doesn't have
+exactly one period inside the well you
+
+ align:start position:0%
+exactly one period inside the well you
+ 
+
+ align:start position:0%
+exactly one period inside the well you
+can't do that
+
+ align:start position:0%
+can't do that
+ 
+
+ align:start position:0%
+can't do that
+so the amplitudes can't be the same on
+
+ align:start position:0%
+so the amplitudes can't be the same on
+ 
+
+ align:start position:0%
+so the amplitudes can't be the same on
+both sides
+
+ align:start position:0%
+both sides
+ 
+
+ align:start position:0%
+both sides
+okay but that's not a very satisfying
+
+ align:start position:0%
+okay but that's not a very satisfying
+ 
+
+ align:start position:0%
+okay but that's not a very satisfying
+explanation that's really an explanation
+
+ align:start position:0%
+explanation that's really an explanation
+ 
+
+ align:start position:0%
+explanation that's really an explanation
+about solutions to the differential
+
+ align:start position:0%
+about solutions to the differential
+ 
+
+ align:start position:0%
+about solutions to the differential
+equation i'm just telling you properties
+
+ align:start position:0%
+equation i'm just telling you properties
+ 
+
+ align:start position:0%
+equation i'm just telling you properties
+of second-order differential equations
+
+ align:start position:0%
+of second-order differential equations
+ 
+
+ align:start position:0%
+of second-order differential equations
+let's think of a more physical more
+
+ align:start position:0%
+let's think of a more physical more
+ 
+
+ align:start position:0%
+let's think of a more physical more
+quantum mechanical explanation why are
+
+ align:start position:0%
+quantum mechanical explanation why are
+ 
+
+ align:start position:0%
+quantum mechanical explanation why are
+we getting these resonances
+
+ align:start position:0%
+we getting these resonances
+ 
+
+ align:start position:0%
+we getting these resonances
+well i want to think about this in the
+
+ align:start position:0%
+well i want to think about this in the
+ 
+
+ align:start position:0%
+well i want to think about this in the
+same way as we thought about the boxes
+
+ align:start position:0%
+same way as we thought about the boxes
+ 
+
+ align:start position:0%
+same way as we thought about the boxes
+in the very first lecture
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+suppose
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+we have this square well
+
+ align:start position:0%
+we have this square well
+ 
+
+ align:start position:0%
+we have this square well
+and i know i have some amplitude here
+
+ align:start position:0%
+and i know i have some amplitude here
+ 
+
+ align:start position:0%
+and i know i have some amplitude here
+and i want to know with some i've got a
+
+ align:start position:0%
+and i want to know with some i've got a
+ 
+
+ align:start position:0%
+and i want to know with some i've got a
+wave function it's got some amplitude
+
+ align:start position:0%
+wave function it's got some amplitude
+ 
+
+ align:start position:0%
+wave function it's got some amplitude
+here it's got some momentum going this
+
+ align:start position:0%
+here it's got some momentum going this
+ 
+
+ align:start position:0%
+here it's got some momentum going this
+way some positive momentum and i want to
+
+ align:start position:0%
+way some positive momentum and i want to
+ 
+
+ align:start position:0%
+way some positive momentum and i want to
+ask
+
+ align:start position:0%
+ask
+ 
+
+ align:start position:0%
+ask
+what's the probability that i will
+
+ align:start position:0%
+what's the probability that i will
+ 
+
+ align:start position:0%
+what's the probability that i will
+scatter past the potential let's say to
+
+ align:start position:0%
+scatter past the potential let's say to
+ 
+
+ align:start position:0%
+scatter past the potential let's say to
+this point right here just on the other
+
+ align:start position:0%
+this point right here just on the other
+ 
+
+ align:start position:0%
+this point right here just on the other
+side of the potential what's the
+
+ align:start position:0%
+side of the potential what's the
+ 
+
+ align:start position:0%
+side of the potential what's the
+probability that i will scatter across
+
+ align:start position:0%
+probability that i will scatter across
+ 
+
+ align:start position:0%
+probability that i will scatter across
+well you say we've done this calculation
+
+ align:start position:0%
+well you say we've done this calculation
+ 
+
+ align:start position:0%
+well you say we've done this calculation
+we know the probability to transmit
+
+ align:start position:0%
+we know the probability to transmit
+ 
+
+ align:start position:0%
+we know the probability to transmit
+across this step potential we did that
+
+ align:start position:0%
+across this step potential we did that
+ 
+
+ align:start position:0%
+across this step potential we did that
+last time
+
+ align:start position:0%
+last time
+ 
+
+ align:start position:0%
+last time
+so that's t step
+
+ align:start position:0%
+so that's t step
+ 
+
+ align:start position:0%
+so that's t step
+and we know the probability we know what
+
+ align:start position:0%
+and we know the probability we know what
+ 
+
+ align:start position:0%
+and we know the probability we know what
+happens to the phase of the wave
+
+ align:start position:0%
+happens to the phase of the wave
+ 
+
+ align:start position:0%
+happens to the phase of the wave
+function or sorry we know the
+
+ align:start position:0%
+function or sorry we know the
+ 
+
+ align:start position:0%
+function or sorry we know the
+probability of scattering across this
+
+ align:start position:0%
+probability of scattering across this
+ 
+
+ align:start position:0%
+probability of scattering across this
+potential step
+
+ align:start position:0%
+potential step
+ 
+
+ align:start position:0%
+potential step
+and that's transmission uh
+
+ align:start position:0%
+and that's transmission uh
+ 
+
+ align:start position:0%
+and that's transmission uh
+up
+
+ align:start position:0%
+up
+ 
+
+ align:start position:0%
+up
+and so the probability that you transmit
+
+ align:start position:0%
+and so the probability that you transmit
+ 
+
+ align:start position:0%
+and so the probability that you transmit
+from here to here is the probability you
+
+ align:start position:0%
+from here to here is the probability you
+ 
+
+ align:start position:0%
+from here to here is the probability you
+transmit here first and then the
+
+ align:start position:0%
+transmit here first and then the
+ 
+
+ align:start position:0%
+transmit here first and then the
+probability that you transmit here right
+
+ align:start position:0%
+probability that you transmit here right
+ 
+
+ align:start position:0%
+probability that you transmit here right
+the product of the probabilities
+
+ align:start position:0%
+the product of the probabilities
+ 
+
+ align:start position:0%
+the product of the probabilities
+sound reasonable
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay let's vote how many people think
+
+ align:start position:0%
+okay let's vote how many people think
+ 
+
+ align:start position:0%
+okay let's vote how many people think
+that this is equal to the transmission
+
+ align:start position:0%
+that this is equal to the transmission
+ 
+
+ align:start position:0%
+that this is equal to the transmission
+probability
+
+ align:start position:0%
+probability
+ 
+
+ align:start position:0%
+probability
+across the potential well
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+any votes you have to vote one way or
+
+ align:start position:0%
+any votes you have to vote one way or
+ 
+
+ align:start position:0%
+any votes you have to vote one way or
+the other no it is not how many people
+
+ align:start position:0%
+the other no it is not how many people
+ 
+
+ align:start position:0%
+the other no it is not how many people
+vote
+
+ align:start position:0%
+vote
+ 
+
+ align:start position:0%
+vote
+okay yes it is
+
+ align:start position:0%
+okay yes it is
+ 
+
+ align:start position:0%
+okay yes it is
+okay the nose have it and that's not
+
+ align:start position:0%
+okay the nose have it and that's not
+ 
+
+ align:start position:0%
+okay the nose have it and that's not
+terribly surprising uh because of course
+
+ align:start position:0%
+terribly surprising uh because of course
+ 
+
+ align:start position:0%
+terribly surprising uh because of course
+these have no resonance structure so
+
+ align:start position:0%
+these have no resonance structure so
+ 
+
+ align:start position:0%
+these have no resonance structure so
+where did that come from if it's just
+
+ align:start position:0%
+where did that come from if it's just
+ 
+
+ align:start position:0%
+where did that come from if it's just
+that thing squared
+
+ align:start position:0%
+that thing squared
+ 
+
+ align:start position:0%
+that thing squared
+right so that probably can't be it but
+
+ align:start position:0%
+right so that probably can't be it but
+ 
+
+ align:start position:0%
+right so that probably can't be it but
+here's the better here's the the bigger
+
+ align:start position:0%
+here's the better here's the the bigger
+ 
+
+ align:start position:0%
+here's the better here's the the bigger
+problem why is this the wrong argument
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+because there's reflection yeah exactly
+
+ align:start position:0%
+because there's reflection yeah exactly
+ 
+
+ align:start position:0%
+because there's reflection yeah exactly
+there's reflection but that's only one
+
+ align:start position:0%
+there's reflection but that's only one
+ 
+
+ align:start position:0%
+there's reflection but that's only one
+step in the answer of why it's the wrong
+
+ align:start position:0%
+step in the answer of why it's the wrong
+ 
+
+ align:start position:0%
+step in the answer of why it's the wrong
+answer why else
+
+ align:start position:0%
+answer why else
+ 
+
+ align:start position:0%
+answer why else
+uh your transmission definitions have to
+
+ align:start position:0%
+uh your transmission definitions have to
+ 
+
+ align:start position:0%
+uh your transmission definitions have to
+do far away that's true but i just want
+
+ align:start position:0%
+do far away that's true but i just want
+ 
+
+ align:start position:0%
+do far away that's true but i just want
+the probability if i got here with
+
+ align:start position:0%
+the probability if i got here with
+ 
+
+ align:start position:0%
+the probability if i got here with
+positive momentum i'm eventually going
+
+ align:start position:0%
+positive momentum i'm eventually going
+ 
+
+ align:start position:0%
+positive momentum i'm eventually going
+to get out to infinity so it's the same
+
+ align:start position:0%
+to get out to infinity so it's the same
+ 
+
+ align:start position:0%
+to get out to infinity so it's the same
+probability
+
+ align:start position:0%
+probability
+ 
+
+ align:start position:0%
+probability
+because it's just an e to the ik x out
+
+ align:start position:0%
+because it's just an e to the ik x out
+ 
+
+ align:start position:0%
+because it's just an e to the ik x out
+here the wave function is just e to the
+
+ align:start position:0%
+here the wave function is just e to the
+ 
+
+ align:start position:0%
+here the wave function is just e to the
+ikx
+
+ align:start position:0%
+ikx
+ 
+
+ align:start position:0%
+ikx
+so the probability is going to be the
+
+ align:start position:0%
+so the probability is going to be the
+ 
+
+ align:start position:0%
+so the probability is going to be the
+same
+
+ align:start position:0%
+same
+ 
+
+ align:start position:0%
+same
+other
+
+ align:start position:0%
+other
+ 
+
+ align:start position:0%
+other
+well the reasons of the well is very
+
+ align:start position:0%
+well the reasons of the well is very
+ 
+
+ align:start position:0%
+well the reasons of the well is very
+important but the first argument ignores
+
+ align:start position:0%
+important but the first argument ignores
+ 
+
+ align:start position:0%
+important but the first argument ignores
+that exactly that's also true so far the
+
+ align:start position:0%
+that exactly that's also true so far the
+ 
+
+ align:start position:0%
+that exactly that's also true so far the
+reasons we have are we need the width of
+
+ align:start position:0%
+reasons we have are we need the width of
+ 
+
+ align:start position:0%
+reasons we have are we need the width of
+the well doesn't appear
+
+ align:start position:0%
+the well doesn't appear
+ 
+
+ align:start position:0%
+the well doesn't appear
+that seems probably wrong
+
+ align:start position:0%
+that seems probably wrong
+ 
+
+ align:start position:0%
+that seems probably wrong
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+uh the second is it's possible that you
+
+ align:start position:0%
+uh the second is it's possible that you
+ 
+
+ align:start position:0%
+uh the second is it's possible that you
+could have reflected we haven't really
+
+ align:start position:0%
+could have reflected we haven't really
+ 
+
+ align:start position:0%
+could have reflected we haven't really
+incorporated that in any sort of elegant
+
+ align:start position:0%
+incorporated that in any sort of elegant
+ 
+
+ align:start position:0%
+incorporated that in any sort of elegant
+way what's there other ways
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that's absolutely true there are other
+
+ align:start position:0%
+that's absolutely true there are other
+ 
+
+ align:start position:0%
+that's absolutely true there are other
+ways to transmit so you could transmit
+
+ align:start position:0%
+ways to transmit so you could transmit
+ 
+
+ align:start position:0%
+ways to transmit so you could transmit
+then you could reflect so we could
+
+ align:start position:0%
+then you could reflect so we could
+ 
+
+ align:start position:0%
+then you could reflect so we could
+transmit then reflect and reflect again
+
+ align:start position:0%
+transmit then reflect and reflect again
+ 
+
+ align:start position:0%
+transmit then reflect and reflect again
+and then transmit so we could transmit
+
+ align:start position:0%
+and then transmit so we could transmit
+ 
+
+ align:start position:0%
+and then transmit so we could transmit
+reflect reflect transmit
+
+ align:start position:0%
+reflect reflect transmit
+ 
+
+ align:start position:0%
+reflect reflect transmit
+what else
+
+ align:start position:0%
+what else
+ 
+
+ align:start position:0%
+what else
+do probabilities add in quantum
+
+ align:start position:0%
+do probabilities add in quantum
+ 
+
+ align:start position:0%
+do probabilities add in quantum
+mechanics
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and when you have products of events do
+
+ align:start position:0%
+and when you have products of events do
+ 
+
+ align:start position:0%
+and when you have products of events do
+your probabilities multiply
+
+ align:start position:0%
+your probabilities multiply
+ 
+
+ align:start position:0%
+your probabilities multiply
+what adds in quantum mechanics
+
+ align:start position:0%
+what adds in quantum mechanics
+ 
+
+ align:start position:0%
+what adds in quantum mechanics
+the amplitude the wave function we do
+
+ align:start position:0%
+the amplitude the wave function we do
+ 
+
+ align:start position:0%
+the amplitude the wave function we do
+not take the product of probabilities
+
+ align:start position:0%
+not take the product of probabilities
+ 
+
+ align:start position:0%
+not take the product of probabilities
+what we do is we ask what's the
+
+ align:start position:0%
+what we do is we ask what's the
+ 
+
+ align:start position:0%
+what we do is we ask what's the
+amplitude to get here from there
+
+ align:start position:0%
+amplitude to get here from there
+ 
+
+ align:start position:0%
+amplitude to get here from there
+and we take the amplitude norm squared
+
+ align:start position:0%
+and we take the amplitude norm squared
+ 
+
+ align:start position:0%
+and we take the amplitude norm squared
+to get the probability
+
+ align:start position:0%
+to get the probability
+ 
+
+ align:start position:0%
+to get the probability
+right
+
+ align:start position:0%
+right
+ 
+
+ align:start position:0%
+right
+so the correct
+
+ align:start position:0%
+so the correct
+ 
+
+ align:start position:0%
+so the correct
+question is what's the amplitude to get
+
+ align:start position:0%
+question is what's the amplitude to get
+ 
+
+ align:start position:0%
+question is what's the amplitude to get
+from here to here how does bless you how
+
+ align:start position:0%
+from here to here how does bless you how
+ 
+
+ align:start position:0%
+from here to here how does bless you how
+does the wave function of the amplitude
+
+ align:start position:0%
+does the wave function of the amplitude
+ 
+
+ align:start position:0%
+does the wave function of the amplitude
+change as you get as you move from here
+
+ align:start position:0%
+change as you get as you move from here
+ 
+
+ align:start position:0%
+change as you get as you move from here
+to here
+
+ align:start position:0%
+to here
+ 
+
+ align:start position:0%
+to here
+and for that
+
+ align:start position:0%
+and for that
+ 
+
+ align:start position:0%
+and for that
+think back to the two-slit experiment or
+
+ align:start position:0%
+think back to the two-slit experiment or
+ 
+
+ align:start position:0%
+think back to the two-slit experiment or
+think back to the boxes we asked the
+
+ align:start position:0%
+think back to the boxes we asked the
+ 
+
+ align:start position:0%
+think back to the boxes we asked the
+following question
+
+ align:start position:0%
+following question
+ 
+
+ align:start position:0%
+following question
+the transit the amplitude that you
+
+ align:start position:0%
+the transit the amplitude that you
+ 
+
+ align:start position:0%
+the transit the amplitude that you
+should transmit across this well
+
+ align:start position:0%
+should transmit across this well
+ 
+
+ align:start position:0%
+should transmit across this well
+has a bunch of
+
+ align:start position:0%
+has a bunch of
+ 
+
+ align:start position:0%
+has a bunch of
+components is a sum of a bunch of terms
+
+ align:start position:0%
+components is a sum of a bunch of terms
+ 
+
+ align:start position:0%
+components is a sum of a bunch of terms
+you could transmit down this well
+
+ align:start position:0%
+you could transmit down this well
+ 
+
+ align:start position:0%
+you could transmit down this well
+transmit down the down as well inside
+
+ align:start position:0%
+transmit down the down as well inside
+ 
+
+ align:start position:0%
+transmit down the down as well inside
+here you know your wavefunction is e to
+
+ align:start position:0%
+here you know your wavefunction is e to
+ 
+
+ align:start position:0%
+here you know your wavefunction is e to
+the i k prime l or i think i'm calling
+
+ align:start position:0%
+the i k prime l or i think i'm calling
+ 
+
+ align:start position:0%
+the i k prime l or i think i'm calling
+this k2 l
+
+ align:start position:0%
+this k2 l
+ 
+
+ align:start position:0%
+this k2 l
+uh yes key2 x
+
+ align:start position:0%
+uh yes key2 x
+ 
+
+ align:start position:0%
+uh yes key2 x
+and in moving across the well your wave
+
+ align:start position:0%
+and in moving across the well your wave
+ 
+
+ align:start position:0%
+and in moving across the well your wave
+function evolves by an e to the i k 2 l
+
+ align:start position:0%
+function evolves by an e to the i k 2 l
+ 
+
+ align:start position:0%
+function evolves by an e to the i k 2 l
+and then you could transmit again with
+
+ align:start position:0%
+and then you could transmit again with
+ 
+
+ align:start position:0%
+and then you could transmit again with
+some transmission amplitude so this
+
+ align:start position:0%
+some transmission amplitude so this
+ 
+
+ align:start position:0%
+some transmission amplitude so this
+would be the transmission down times e
+
+ align:start position:0%
+would be the transmission down times e
+ 
+
+ align:start position:0%
+would be the transmission down times e
+to the i k 2 l
+
+ align:start position:0%
+to the i k 2 l
+ 
+
+ align:start position:0%
+to the i k 2 l
+times the transmit
+
+ align:start position:0%
+times the transmit
+ 
+
+ align:start position:0%
+times the transmit
+up
+
+ align:start position:0%
+up
+ 
+
+ align:start position:0%
+up
+as we saw last time these are the same
+
+ align:start position:0%
+as we saw last time these are the same
+ 
+
+ align:start position:0%
+as we saw last time these are the same
+but i just want to keep them separate so
+
+ align:start position:0%
+but i just want to keep them separate so
+ 
+
+ align:start position:0%
+but i just want to keep them separate so
+you know which one i'm talking about so
+
+ align:start position:0%
+you know which one i'm talking about so
+ 
+
+ align:start position:0%
+you know which one i'm talking about so
+this is a contribution this is something
+
+ align:start position:0%
+this is a contribution this is something
+ 
+
+ align:start position:0%
+this is a contribution this is something
+that could contribute to the amplitude
+
+ align:start position:0%
+that could contribute to the amplitude
+ 
+
+ align:start position:0%
+that could contribute to the amplitude
+is it the only thing that could
+
+ align:start position:0%
+is it the only thing that could
+ 
+
+ align:start position:0%
+is it the only thing that could
+contribute to the amplitude no what else
+
+ align:start position:0%
+contribute to the amplitude no what else
+ 
+
+ align:start position:0%
+contribute to the amplitude no what else
+could contribute
+
+ align:start position:0%
+could contribute
+ 
+
+ align:start position:0%
+could contribute
+bounce right so to get from here to here
+
+ align:start position:0%
+bounce right so to get from here to here
+ 
+
+ align:start position:0%
+bounce right so to get from here to here
+i could transmit
+
+ align:start position:0%
+i could transmit
+ 
+
+ align:start position:0%
+i could transmit
+evolve transmit i could also transmit
+
+ align:start position:0%
+evolve transmit i could also transmit
+ 
+
+ align:start position:0%
+evolve transmit i could also transmit
+evolve
+
+ align:start position:0%
+evolve
+ 
+
+ align:start position:0%
+evolve
+reflect
+
+ align:start position:0%
+reflect
+ 
+
+ align:start position:0%
+reflect
+evolve reflect evolve transmit so
+
+ align:start position:0%
+evolve reflect evolve transmit so
+ 
+
+ align:start position:0%
+evolve reflect evolve transmit so
+there's also a term that's t
+
+ align:start position:0%
+there's also a term that's t
+ 
+
+ align:start position:0%
+there's also a term that's t
+e to the i k l
+
+ align:start position:0%
+e to the i k l
+ 
+
+ align:start position:0%
+e to the i k l
+r
+
+ align:start position:0%
+r
+ 
+
+ align:start position:0%
+r
+e to the minus i k l
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+r e to the i k l
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+sorry e either the plus ical because
+
+ align:start position:0%
+sorry e either the plus ical because
+ 
+
+ align:start position:0%
+sorry e either the plus ical because
+we're increasing the evolution of the
+
+ align:start position:0%
+we're increasing the evolution of the
+ 
+
+ align:start position:0%
+we're increasing the evolution of the
+phase um and then transmit finally at
+
+ align:start position:0%
+phase um and then transmit finally at
+ 
+
+ align:start position:0%
+phase um and then transmit finally at
+the end
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and these k's are all k2s k2 p2 but i
+
+ align:start position:0%
+and these k's are all k2s k2 p2 but i
+ 
+
+ align:start position:0%
+and these k's are all k2s k2 p2 but i
+could have done that many times
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+but notice that each time what i'm going
+
+ align:start position:0%
+but notice that each time what i'm going
+ 
+
+ align:start position:0%
+but notice that each time what i'm going
+to do is i'm going to
+
+ align:start position:0%
+to do is i'm going to
+ 
+
+ align:start position:0%
+to do is i'm going to
+transmit reflect reflect transmit or
+
+ align:start position:0%
+transmit reflect reflect transmit or
+ 
+
+ align:start position:0%
+transmit reflect reflect transmit or
+transmit reflect reflect reflect reflect
+
+ align:start position:0%
+transmit reflect reflect reflect reflect
+ 
+
+ align:start position:0%
+transmit reflect reflect reflect reflect
+transmit so i'm always going to do this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+some even number of some number of times
+
+ align:start position:0%
+some even number of some number of times
+ 
+
+ align:start position:0%
+some even number of some number of times
+i do this once i do this twice i do it
+
+ align:start position:0%
+i do this once i do this twice i do it
+ 
+
+ align:start position:0%
+i do this once i do this twice i do it
+thrice this gives me a geometric series
+
+ align:start position:0%
+thrice this gives me a geometric series
+ 
+
+ align:start position:0%
+thrice this gives me a geometric series
+this is t
+
+ align:start position:0%
+this is t
+ 
+
+ align:start position:0%
+this is t
+e to the i k 2 x
+
+ align:start position:0%
+e to the i k 2 x
+ 
+
+ align:start position:0%
+e to the i k 2 x
+t
+
+ align:start position:0%
+t
+ 
+
+ align:start position:0%
+t
+times
+
+ align:start position:0%
+times
+ 
+
+ align:start position:0%
+times
+1 plus
+
+ align:start position:0%
+1 plus
+ 
+
+ align:start position:0%
+1 plus
+this quantity plus this quantity squared
+
+ align:start position:0%
+this quantity plus this quantity squared
+ 
+
+ align:start position:0%
+this quantity plus this quantity squared
+that's a geometric series 1 over 1 plus
+
+ align:start position:0%
+that's a geometric series 1 over 1 plus
+ 
+
+ align:start position:0%
+that's a geometric series 1 over 1 plus
+this quantity squared
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+or sorry 1 minus because it's a
+
+ align:start position:0%
+or sorry 1 minus because it's a
+ 
+
+ align:start position:0%
+or sorry 1 minus because it's a
+geometric sum and what is this quantity
+
+ align:start position:0%
+geometric sum and what is this quantity
+ 
+
+ align:start position:0%
+geometric sum and what is this quantity
+well it's r squared and remember the r's
+
+ align:start position:0%
+well it's r squared and remember the r's
+ 
+
+ align:start position:0%
+well it's r squared and remember the r's
+in both directions are the same so i'm
+
+ align:start position:0%
+in both directions are the same so i'm
+ 
+
+ align:start position:0%
+in both directions are the same so i'm
+just going to write it as r squared
+
+ align:start position:0%
+just going to write it as r squared
+ 
+
+ align:start position:0%
+just going to write it as r squared
+e to the 2i
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+well
+
+ align:start position:0%
+well
+ 
+
+ align:start position:0%
+well
+r squared it's a real number but i'm
+
+ align:start position:0%
+r squared it's a real number but i'm
+ 
+
+ align:start position:0%
+r squared it's a real number but i'm
+going to put the
+
+ align:start position:0%
+going to put the
+ 
+
+ align:start position:0%
+going to put the
+abs on absolute value on anyway it's
+
+ align:start position:0%
+abs on absolute value on anyway it's
+ 
+
+ align:start position:0%
+abs on absolute value on anyway it's
+going to simplify my life you need the
+
+ align:start position:0%
+going to simplify my life you need the
+ 
+
+ align:start position:0%
+going to simplify my life you need the
+2i k2l
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+so this is our prediction from multiple
+
+ align:start position:0%
+so this is our prediction from multiple
+ 
+
+ align:start position:0%
+so this is our prediction from multiple
+bounces
+
+ align:start position:0%
+bounces
+ 
+
+ align:start position:0%
+bounces
+what we're doing here is we're taking
+
+ align:start position:0%
+what we're doing here is we're taking
+ 
+
+ align:start position:0%
+what we're doing here is we're taking
+seriously the superposition principle
+
+ align:start position:0%
+seriously the superposition principle
+ 
+
+ align:start position:0%
+seriously the superposition principle
+that says given any process any way that
+
+ align:start position:0%
+that says given any process any way that
+ 
+
+ align:start position:0%
+that says given any process any way that
+that process could happen you sum up the
+
+ align:start position:0%
+that process could happen you sum up the
+ 
+
+ align:start position:0%
+that process could happen you sum up the
+amplitudes and the probability is the
+
+ align:start position:0%
+amplitudes and the probability is the
+ 
+
+ align:start position:0%
+amplitudes and the probability is the
+norm squared if we have a source and we
+
+ align:start position:0%
+norm squared if we have a source and we
+ 
+
+ align:start position:0%
+norm squared if we have a source and we
+have two slits
+
+ align:start position:0%
+have two slits
+ 
+
+ align:start position:0%
+have two slits
+and i ask you what's the probability
+
+ align:start position:0%
+and i ask you what's the probability
+ 
+
+ align:start position:0%
+and i ask you what's the probability
+that you land here the probability is
+
+ align:start position:0%
+that you land here the probability is
+ 
+
+ align:start position:0%
+that you land here the probability is
+not the sum of the probabilities for
+
+ align:start position:0%
+not the sum of the probabilities for
+ 
+
+ align:start position:0%
+not the sum of the probabilities for
+each individual transit the probability
+
+ align:start position:0%
+each individual transit the probability
+ 
+
+ align:start position:0%
+each individual transit the probability
+is the square of the amplitude where the
+
+ align:start position:0%
+is the square of the amplitude where the
+ 
+
+ align:start position:0%
+is the square of the amplitude where the
+amplitude is the sum amplitude top plus
+
+ align:start position:0%
+amplitude is the sum amplitude top plus
+ 
+
+ align:start position:0%
+amplitude is the sum amplitude top plus
+amplitude bottom
+
+ align:start position:0%
+amplitude bottom
+ 
+
+ align:start position:0%
+amplitude bottom
+here there are many many slits there are
+
+ align:start position:0%
+here there are many many slits there are
+ 
+
+ align:start position:0%
+here there are many many slits there are
+many different ways this could happen
+
+ align:start position:0%
+many different ways this could happen
+ 
+
+ align:start position:0%
+many different ways this could happen
+you could reflect multiple times
+
+ align:start position:0%
+you could reflect multiple times
+ 
+
+ align:start position:0%
+you could reflect multiple times
+ever cool with that
+
+ align:start position:0%
+ever cool with that
+ 
+
+ align:start position:0%
+ever cool with that
+no by the same token we could have done
+
+ align:start position:0%
+no by the same token we could have done
+ 
+
+ align:start position:0%
+no by the same token we could have done
+the same thing for reflection but let's
+
+ align:start position:0%
+the same thing for reflection but let's
+ 
+
+ align:start position:0%
+the same thing for reflection but let's
+stick with transmission for the moment
+
+ align:start position:0%
+stick with transmission for the moment
+ 
+
+ align:start position:0%
+stick with transmission for the moment
+this is what we get for the transmission
+
+ align:start position:0%
+this is what we get for the transmission
+ 
+
+ align:start position:0%
+this is what we get for the transmission
+and again the transmission amplitudes
+
+ align:start position:0%
+and again the transmission amplitudes
+ 
+
+ align:start position:0%
+and again the transmission amplitudes
+across the step as we saw last time are
+
+ align:start position:0%
+across the step as we saw last time are
+ 
+
+ align:start position:0%
+across the step as we saw last time are
+the same so this is in fact t squared
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and this gives us
+
+ align:start position:0%
+and this gives us
+ 
+
+ align:start position:0%
+and this gives us
+a result
+
+ align:start position:0%
+a result
+ 
+
+ align:start position:0%
+a result
+for transmission down the potential well
+
+ align:start position:0%
+for transmission down the potential well
+ 
+
+ align:start position:0%
+for transmission down the potential well
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+if we put in the factors of if we use
+
+ align:start position:0%
+if we put in the factors of if we use
+ 
+
+ align:start position:0%
+if we put in the factors of if we use
+what uh the trench sorry if we use what
+
+ align:start position:0%
+what uh the trench sorry if we use what
+ 
+
+ align:start position:0%
+what uh the trench sorry if we use what
+the reflection
+
+ align:start position:0%
+the reflection
+ 
+
+ align:start position:0%
+the reflection
+and transmission
+
+ align:start position:0%
+and transmission
+ 
+
+ align:start position:0%
+and transmission
+amplitudes were
+
+ align:start position:0%
+amplitudes were
+ 
+
+ align:start position:0%
+amplitudes were
+for our stepwells the answer that this
+
+ align:start position:0%
+for our stepwells the answer that this
+ 
+
+ align:start position:0%
+for our stepwells the answer that this
+gives is 1 over
+
+ align:start position:0%
+gives is 1 over
+ 
+
+ align:start position:0%
+gives is 1 over
+e to the i k2l
+
+ align:start position:0%
+e to the i k2l
+ 
+
+ align:start position:0%
+e to the i k2l
+minus 2i upon the transmission
+
+ align:start position:0%
+minus 2i upon the transmission
+ 
+
+ align:start position:0%
+minus 2i upon the transmission
+for a step
+
+ align:start position:0%
+for a step
+ 
+
+ align:start position:0%
+for a step
+times
+
+ align:start position:0%
+times
+ 
+
+ align:start position:0%
+times
+sine of k prime l or sorry k2l
+
+ align:start position:0%
+sine of k prime l or sorry k2l
+ 
+
+ align:start position:0%
+sine of k prime l or sorry k2l
+now this isn't the same
+
+ align:start position:0%
+now this isn't the same
+ 
+
+ align:start position:0%
+now this isn't the same
+as the
+
+ align:start position:0%
+as the
+ 
+
+ align:start position:0%
+as the
+probability that we derived over here
+
+ align:start position:0%
+probability that we derived over here
+ 
+
+ align:start position:0%
+probability that we derived over here
+but that's because this isn't the
+
+ align:start position:0%
+but that's because this isn't the
+ 
+
+ align:start position:0%
+but that's because this isn't the
+probability this was the amplitude we
+
+ align:start position:0%
+probability this was the amplitude we
+ 
+
+ align:start position:0%
+probability this was the amplitude we
+just computed the total amplitude to get
+
+ align:start position:0%
+just computed the total amplitude to get
+ 
+
+ align:start position:0%
+just computed the total amplitude to get
+the probability we have to take the norm
+
+ align:start position:0%
+the probability we have to take the norm
+ 
+
+ align:start position:0%
+the probability we have to take the norm
+squared of the amplitude
+
+ align:start position:0%
+squared of the amplitude
+ 
+
+ align:start position:0%
+squared of the amplitude
+and when we take the norm squared
+
+ align:start position:0%
+and when we take the norm squared
+ 
+
+ align:start position:0%
+and when we take the norm squared
+what we get is 1 upon 1 plus 1 over 4
+
+ align:start position:0%
+what we get is 1 upon 1 plus 1 over 4
+ 
+
+ align:start position:0%
+what we get is 1 upon 1 plus 1 over 4
+epsilon epsilon minus 1 or plus 1.
+
+ align:start position:0%
+epsilon epsilon minus 1 or plus 1.
+ 
+
+ align:start position:0%
+epsilon epsilon minus 1 or plus 1.
+sine squared
+
+ align:start position:0%
+sine squared
+ 
+
+ align:start position:0%
+sine squared
+of g naught
+
+ align:start position:0%
+of g naught
+ 
+
+ align:start position:0%
+of g naught
+root epsilon plus one
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+we get the same answer
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+sorry
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this is inequality
+
+ align:start position:0%
+this is inequality
+ 
+
+ align:start position:0%
+this is inequality
+oh sorry sorry
+
+ align:start position:0%
+oh sorry sorry
+ 
+
+ align:start position:0%
+oh sorry sorry
+sorry
+
+ align:start position:0%
+sorry
+ 
+
+ align:start position:0%
+sorry
+thank you martin
+
+ align:start position:0%
+thank you martin
+ 
+
+ align:start position:0%
+thank you martin
+we get that the transmission probability
+
+ align:start position:0%
+we get that the transmission probability
+ 
+
+ align:start position:0%
+we get that the transmission probability
+when we take the norm square of the
+
+ align:start position:0%
+when we take the norm square of the
+ 
+
+ align:start position:0%
+when we take the norm square of the
+amplitude thank you is equal to this
+
+ align:start position:0%
+amplitude thank you is equal to this
+ 
+
+ align:start position:0%
+amplitude thank you is equal to this
+which is the same as we got before
+
+ align:start position:0%
+which is the same as we got before
+ 
+
+ align:start position:0%
+which is the same as we got before
+thanks
+
+ align:start position:0%
+thanks
+ 
+
+ align:start position:0%
+thanks
+okay so this is to me this is very sad
+
+ align:start position:0%
+okay so this is to me this is very sad
+ 
+
+ align:start position:0%
+okay so this is to me this is very sad
+yeah please
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+kl equals pi doesn't work it does you
+
+ align:start position:0%
+kl equals pi doesn't work it does you
+ 
+
+ align:start position:0%
+kl equals pi doesn't work it does you
+just have to be careful what kl
+
+ align:start position:0%
+just have to be careful what kl
+ 
+
+ align:start position:0%
+just have to be careful what kl
+expressing it sorry
+
+ align:start position:0%
+expressing it sorry
+ 
+
+ align:start position:0%
+expressing it sorry
+what am i
+
+ align:start position:0%
+what am i
+ 
+
+ align:start position:0%
+what am i
+um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+because i'm an idiot because i got a
+
+ align:start position:0%
+because i'm an idiot because i got a
+ 
+
+ align:start position:0%
+because i'm an idiot because i got a
+factor of two wrong thank you
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+thank you matt
+
+ align:start position:0%
+thank you matt
+ 
+
+ align:start position:0%
+thank you matt
+thank you
+
+ align:start position:0%
+thank you
+ 
+
+ align:start position:0%
+thank you
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+answer analysis it's a wonderful thing
+
+ align:start position:0%
+answer analysis it's a wonderful thing
+ 
+
+ align:start position:0%
+answer analysis it's a wonderful thing
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so this gives us this has something
+
+ align:start position:0%
+so this gives us this has something
+ 
+
+ align:start position:0%
+so this gives us this has something
+really nice for us
+
+ align:start position:0%
+really nice for us
+ 
+
+ align:start position:0%
+really nice for us
+why are we getting a resonance at
+
+ align:start position:0%
+why are we getting a resonance at
+ 
+
+ align:start position:0%
+why are we getting a resonance at
+special values
+
+ align:start position:0%
+special values
+ 
+
+ align:start position:0%
+special values
+why are we getting a resonance of
+
+ align:start position:0%
+why are we getting a resonance of
+ 
+
+ align:start position:0%
+why are we getting a resonance of
+special values of the energy
+
+ align:start position:0%
+special values of the energy
+ 
+
+ align:start position:0%
+special values of the energy
+what's happening
+
+ align:start position:0%
+what's happening
+ 
+
+ align:start position:0%
+what's happening
+well in this process in this quantum
+
+ align:start position:0%
+well in this process in this quantum
+ 
+
+ align:start position:0%
+well in this process in this quantum
+mechanical process
+
+ align:start position:0%
+mechanical process
+ 
+
+ align:start position:0%
+mechanical process
+of multiple interactions multiple
+
+ align:start position:0%
+of multiple interactions multiple
+ 
+
+ align:start position:0%
+of multiple interactions multiple
+scatterings there are many terms in the
+
+ align:start position:0%
+scatterings there are many terms in the
+ 
+
+ align:start position:0%
+scatterings there are many terms in the
+amplitude for transmitting
+
+ align:start position:0%
+amplitude for transmitting
+ 
+
+ align:start position:0%
+amplitude for transmitting
+there are terms that involve no
+
+ align:start position:0%
+there are terms that involve no
+ 
+
+ align:start position:0%
+there are terms that involve no
+reflection there are terms that involve
+
+ align:start position:0%
+reflection there are terms that involve
+ 
+
+ align:start position:0%
+reflection there are terms that involve
+two reflections they're terms that
+
+ align:start position:0%
+two reflections they're terms that
+ 
+
+ align:start position:0%
+two reflections they're terms that
+involve four reflections
+
+ align:start position:0%
+involve four reflections
+ 
+
+ align:start position:0%
+involve four reflections
+and they all come with an actual
+
+ align:start position:0%
+and they all come with an actual
+ 
+
+ align:start position:0%
+and they all come with an actual
+magnitude and a phase
+
+ align:start position:0%
+magnitude and a phase
+ 
+
+ align:start position:0%
+magnitude and a phase
+and when the phase
+
+ align:start position:0%
+and when the phase
+ 
+
+ align:start position:0%
+and when the phase
+is the same
+
+ align:start position:0%
+is the same
+ 
+
+ align:start position:0%
+is the same
+they add constructively
+
+ align:start position:0%
+they add constructively
+ 
+
+ align:start position:0%
+they add constructively
+and when the phases are not the same
+
+ align:start position:0%
+and when the phases are not the same
+ 
+
+ align:start position:0%
+and when the phases are not the same
+they interfere and when the phases are
+
+ align:start position:0%
+they interfere and when the phases are
+ 
+
+ align:start position:0%
+they interfere and when the phases are
+exactly off they interfere destructively
+
+ align:start position:0%
+exactly off they interfere destructively
+ 
+
+ align:start position:0%
+exactly off they interfere destructively
+and that is why you're getting a
+
+ align:start position:0%
+and that is why you're getting a
+ 
+
+ align:start position:0%
+and that is why you're getting a
+resonance
+
+ align:start position:0%
+resonance
+ 
+
+ align:start position:0%
+resonance
+multiple terms in your superposition
+
+ align:start position:0%
+multiple terms in your superposition
+ 
+
+ align:start position:0%
+multiple terms in your superposition
+interfere with each other something that
+
+ align:start position:0%
+interfere with each other something that
+ 
+
+ align:start position:0%
+interfere with each other something that
+does not happen classically classically
+
+ align:start position:0%
+does not happen classically classically
+ 
+
+ align:start position:0%
+does not happen classically classically
+the probabilities are products quantum
+
+ align:start position:0%
+the probabilities are products quantum
+ 
+
+ align:start position:0%
+the probabilities are products quantum
+mechanically we have superposition and
+
+ align:start position:0%
+mechanically we have superposition and
+ 
+
+ align:start position:0%
+mechanically we have superposition and
+probabilities are the squares of the
+
+ align:start position:0%
+probabilities are the squares of the
+ 
+
+ align:start position:0%
+probabilities are the squares of the
+amplitude and we get interference
+
+ align:start position:0%
+amplitude and we get interference
+ 
+
+ align:start position:0%
+amplitude and we get interference
+effects and the probabilities
+
+ align:start position:0%
+effects and the probabilities
+ 
+
+ align:start position:0%
+effects and the probabilities
+cool
+
+ align:start position:0%
+cool
+ 
+
+ align:start position:0%
+cool
+so to me this is a nice
+
+ align:start position:0%
+so to me this is a nice
+ 
+
+ align:start position:0%
+so to me this is a nice
+sort of glorious version of the two-slit
+
+ align:start position:0%
+sort of glorious version of the two-slit
+ 
+
+ align:start position:0%
+sort of glorious version of the two-slit
+experiment um and we're gonna bump up
+
+ align:start position:0%
+experiment um and we're gonna bump up
+ 
+
+ align:start position:0%
+experiment um and we're gonna bump up
+again into it later when we talk about
+
+ align:start position:0%
+again into it later when we talk about
+ 
+
+ align:start position:0%
+again into it later when we talk about
+the physics of solids uh
+
+ align:start position:0%
+the physics of solids uh
+ 
+
+ align:start position:0%
+the physics of solids uh
+in the real world
+
+ align:start position:0%
+in the real world
+ 
+
+ align:start position:0%
+in the real world
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+questions at this point
+
+ align:start position:0%
+questions at this point
+ 
+
+ align:start position:0%
+questions at this point
+yeah
+
+ align:start position:0%
+yeah
+ 
+
+ align:start position:0%
+yeah
+you said earlier
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah what's special about that so what's
+
+ align:start position:0%
+yeah what's special about that so what's
+ 
+
+ align:start position:0%
+yeah what's special about that so what's
+special about that is so at this point
+
+ align:start position:0%
+special about that is so at this point
+ 
+
+ align:start position:0%
+special about that is so at this point
+where kale is in pi
+
+ align:start position:0%
+where kale is in pi
+ 
+
+ align:start position:0%
+where kale is in pi
+when kale is is n pi we get perfect
+
+ align:start position:0%
+when kale is is n pi we get perfect
+ 
+
+ align:start position:0%
+when kale is is n pi we get perfect
+transmission
+
+ align:start position:0%
+transmission
+ 
+
+ align:start position:0%
+transmission
+when kl is equal to n plus one half pi
+
+ align:start position:0%
+when kl is equal to n plus one half pi
+ 
+
+ align:start position:0%
+when kl is equal to n plus one half pi
+the reflection is as good as it gets
+
+ align:start position:0%
+the reflection is as good as it gets
+ 
+
+ align:start position:0%
+the reflection is as good as it gets
+okay so what that's really doing is it's
+
+ align:start position:0%
+okay so what that's really doing is it's
+ 
+
+ align:start position:0%
+okay so what that's really doing is it's
+saying when is this largest
+
+ align:start position:0%
+saying when is this largest
+ 
+
+ align:start position:0%
+saying when is this largest
+locally largest okay so that's these
+
+ align:start position:0%
+locally largest okay so that's these
+ 
+
+ align:start position:0%
+locally largest okay so that's these
+special points when we're the
+
+ align:start position:0%
+special points when we're the
+ 
+
+ align:start position:0%
+special points when we're the
+transmission is as small as possible
+
+ align:start position:0%
+transmission is as small as possible
+ 
+
+ align:start position:0%
+transmission is as small as possible
+which means the reflection which is one
+
+ align:start position:0%
+which means the reflection which is one
+ 
+
+ align:start position:0%
+which means the reflection which is one
+minus the transmission probabilities as
+
+ align:start position:0%
+minus the transmission probabilities as
+ 
+
+ align:start position:0%
+minus the transmission probabilities as
+large as possible
+
+ align:start position:0%
+large as possible
+ 
+
+ align:start position:0%
+large as possible
+and you can get that again from from
+
+ align:start position:0%
+and you can get that again from from
+ 
+
+ align:start position:0%
+and you can get that again from from
+these expressions
+
+ align:start position:0%
+these expressions
+ 
+
+ align:start position:0%
+these expressions
+other questions
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+stopping
+
+ align:start position:0%
+stopping
+ 
+
+ align:start position:0%
+stopping
+so i want to think a little more about
+
+ align:start position:0%
+so i want to think a little more about
+ 
+
+ align:start position:0%
+so i want to think a little more about
+these square barriers and in particular
+
+ align:start position:0%
+these square barriers and in particular
+ 
+
+ align:start position:0%
+these square barriers and in particular
+in thinking about the square well
+
+ align:start position:0%
+in thinking about the square well
+ 
+
+ align:start position:0%
+in thinking about the square well
+barrier
+
+ align:start position:0%
+barrier
+ 
+
+ align:start position:0%
+barrier
+what we've been talking about all along
+
+ align:start position:0%
+what we've been talking about all along
+ 
+
+ align:start position:0%
+what we've been talking about all along
+are monochromatic
+
+ align:start position:0%
+are monochromatic
+ 
+
+ align:start position:0%
+are monochromatic
+wave packers we've been talking about
+
+ align:start position:0%
+wave packers we've been talking about
+ 
+
+ align:start position:0%
+wave packers we've been talking about
+plane waves just simple e to the ikx
+
+ align:start position:0%
+plane waves just simple e to the ikx
+ 
+
+ align:start position:0%
+plane waves just simple e to the ikx
+but you can't actually build
+
+ align:start position:0%
+but you can't actually build
+ 
+
+ align:start position:0%
+but you can't actually build
+uh you can't put a single particle in a
+
+ align:start position:0%
+uh you can't put a single particle in a
+ 
+
+ align:start position:0%
+uh you can't put a single particle in a
+state
+
+ align:start position:0%
+state
+ 
+
+ align:start position:0%
+state
+which is
+
+ align:start position:0%
+which is
+ 
+
+ align:start position:0%
+which is
+a plane wave right it's not normalizable
+
+ align:start position:0%
+a plane wave right it's not normalizable
+ 
+
+ align:start position:0%
+a plane wave right it's not normalizable
+what we really mean at the end of the
+
+ align:start position:0%
+what we really mean at the end of the
+ 
+
+ align:start position:0%
+what we really mean at the end of the
+day when we talk about single particles
+
+ align:start position:0%
+day when we talk about single particles
+ 
+
+ align:start position:0%
+day when we talk about single particles
+is we put them in some well localized
+
+ align:start position:0%
+is we put them in some well localized
+ 
+
+ align:start position:0%
+is we put them in some well localized
+wave packet
+
+ align:start position:0%
+wave packet
+ 
+
+ align:start position:0%
+wave packet
+which at time zero let's say is at
+
+ align:start position:0%
+which at time zero let's say is at
+ 
+
+ align:start position:0%
+which at time zero let's say is at
+position x naught or maybe
+
+ align:start position:0%
+position x naught or maybe
+ 
+
+ align:start position:0%
+position x naught or maybe
+well x naught which in this case is
+
+ align:start position:0%
+well x naught which in this case is
+ 
+
+ align:start position:0%
+well x naught which in this case is
+negative and which has some
+
+ align:start position:0%
+negative and which has some
+ 
+
+ align:start position:0%
+negative and which has some
+well-defined average momentum cannot
+
+ align:start position:0%
+well-defined average momentum cannot
+ 
+
+ align:start position:0%
+well-defined average momentum cannot
+i'll say it's the expectation value of
+
+ align:start position:0%
+i'll say it's the expectation value of
+ 
+
+ align:start position:0%
+i'll say it's the expectation value of
+momentum in this wave package
+
+ align:start position:0%
+momentum in this wave package
+ 
+
+ align:start position:0%
+momentum in this wave package
+and the question we really want to ask
+
+ align:start position:0%
+and the question we really want to ask
+ 
+
+ align:start position:0%
+and the question we really want to ask
+when we talk about scattering is what
+
+ align:start position:0%
+when we talk about scattering is what
+ 
+
+ align:start position:0%
+when we talk about scattering is what
+happens to this beast as it
+
+ align:start position:0%
+happens to this beast as it
+ 
+
+ align:start position:0%
+happens to this beast as it
+hits the weight as it hits the barrier
+
+ align:start position:0%
+hits the weight as it hits the barrier
+ 
+
+ align:start position:0%
+hits the weight as it hits the barrier
+which i'm going to put the left-hand
+
+ align:start position:0%
+which i'm going to put the left-hand
+ 
+
+ align:start position:0%
+which i'm going to put the left-hand
+side at zero on the right-hand side at l
+
+ align:start position:0%
+side at zero on the right-hand side at l
+ 
+
+ align:start position:0%
+side at zero on the right-hand side at l
+and let the depth be minus v-naught
+
+ align:start position:0%
+and let the depth be minus v-naught
+ 
+
+ align:start position:0%
+and let the depth be minus v-naught
+again
+
+ align:start position:0%
+again
+ 
+
+ align:start position:0%
+again
+what happens is this incident wave
+
+ align:start position:0%
+what happens is this incident wave
+ 
+
+ align:start position:0%
+what happens is this incident wave
+packet hits the barrier
+
+ align:start position:0%
+packet hits the barrier
+ 
+
+ align:start position:0%
+packet hits the barrier
+and then scatters off
+
+ align:start position:0%
+and then scatters off
+ 
+
+ align:start position:0%
+and then scatters off
+well we know what would happen if it was
+
+ align:start position:0%
+well we know what would happen if it was
+ 
+
+ align:start position:0%
+well we know what would happen if it was
+a plane wave but a plane wave wouldn't
+
+ align:start position:0%
+a plane wave but a plane wave wouldn't
+ 
+
+ align:start position:0%
+a plane wave but a plane wave wouldn't
+be localized so this is the question i
+
+ align:start position:0%
+be localized so this is the question i
+ 
+
+ align:start position:0%
+be localized so this is the question i
+want to ask and i want to use the
+
+ align:start position:0%
+want to ask and i want to use the
+ 
+
+ align:start position:0%
+want to ask and i want to use the
+results we already have
+
+ align:start position:0%
+results we already have
+ 
+
+ align:start position:0%
+results we already have
+now here's the key thing
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+if we had consider for to begin with
+
+ align:start position:0%
+if we had consider for to begin with
+ 
+
+ align:start position:0%
+if we had consider for to begin with
+just a wave packet
+
+ align:start position:0%
+just a wave packet
+ 
+
+ align:start position:0%
+just a wave packet
+for a free particle centered at x naught
+
+ align:start position:0%
+for a free particle centered at x naught
+ 
+
+ align:start position:0%
+for a free particle centered at x naught
+and with momentum k naught
+
+ align:start position:0%
+and with momentum k naught
+ 
+
+ align:start position:0%
+and with momentum k naught
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+just for a free particle
+
+ align:start position:0%
+just for a free particle
+ 
+
+ align:start position:0%
+just for a free particle
+we know how to write this and if this is
+
+ align:start position:0%
+we know how to write this and if this is
+ 
+
+ align:start position:0%
+we know how to write this and if this is
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+we can put the system for example we can
+
+ align:start position:0%
+we can put the system for example we can
+ 
+
+ align:start position:0%
+we can put the system for example we can
+take our wave function at time 0 to be
+
+ align:start position:0%
+take our wave function at time 0 to be
+ 
+
+ align:start position:0%
+take our wave function at time 0 to be
+a gaussian some normalization times e to
+
+ align:start position:0%
+a gaussian some normalization times e to
+ 
+
+ align:start position:0%
+a gaussian some normalization times e to
+the minus x minus x naught
+
+ align:start position:0%
+the minus x minus x naught
+ 
+
+ align:start position:0%
+the minus x minus x naught
+squared
+
+ align:start position:0%
+squared
+ 
+
+ align:start position:0%
+squared
+over 2a squared
+
+ align:start position:0%
+over 2a squared
+ 
+
+ align:start position:0%
+over 2a squared
+and we want to give it some momentum k
+
+ align:start position:0%
+and we want to give it some momentum k
+ 
+
+ align:start position:0%
+and we want to give it some momentum k
+naught and you know how to do that after
+
+ align:start position:0%
+naught and you know how to do that after
+ 
+
+ align:start position:0%
+naught and you know how to do that after
+the last problem set e to the i k naught
+
+ align:start position:0%
+the last problem set e to the i k naught
+ 
+
+ align:start position:0%
+the last problem set e to the i k naught
+x
+
+ align:start position:0%
+x
+ 
+
+ align:start position:0%
+x
+everyone call that
+
+ align:start position:0%
+everyone call that
+ 
+
+ align:start position:0%
+everyone call that
+so there's our initial wave function
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and we want to know how it evolves with
+
+ align:start position:0%
+and we want to know how it evolves with
+ 
+
+ align:start position:0%
+and we want to know how it evolves with
+time and we know how to do that to
+
+ align:start position:0%
+time and we know how to do that to
+ 
+
+ align:start position:0%
+time and we know how to do that to
+evolve in time we first expand it in
+
+ align:start position:0%
+evolve in time we first expand it in
+ 
+
+ align:start position:0%
+evolve in time we first expand it in
+energy eigenstates
+
+ align:start position:0%
+energy eigenstates
+ 
+
+ align:start position:0%
+energy eigenstates
+so psi
+
+ align:start position:0%
+so psi
+ 
+
+ align:start position:0%
+so psi
+of x naught
+
+ align:start position:0%
+of x naught
+ 
+
+ align:start position:0%
+of x naught
+is equal to well the energy i can states
+
+ align:start position:0%
+is equal to well the energy i can states
+ 
+
+ align:start position:0%
+is equal to well the energy i can states
+in this case are plane waves dk
+
+ align:start position:0%
+in this case are plane waves dk
+ 
+
+ align:start position:0%
+in this case are plane waves dk
+e to the ikx
+
+ align:start position:0%
+e to the ikx
+ 
+
+ align:start position:0%
+e to the ikx
+over root 2 pi
+
+ align:start position:0%
+over root 2 pi
+ 
+
+ align:start position:0%
+over root 2 pi
+times some coefficients f of k the
+
+ align:start position:0%
+times some coefficients f of k the
+ 
+
+ align:start position:0%
+times some coefficients f of k the
+expansion coefficients but these are
+
+ align:start position:0%
+expansion coefficients but these are
+ 
+
+ align:start position:0%
+expansion coefficients but these are
+just the fourier transform
+
+ align:start position:0%
+just the fourier transform
+ 
+
+ align:start position:0%
+just the fourier transform
+of
+
+ align:start position:0%
+of
+ 
+
+ align:start position:0%
+of
+our initial gaussian wave packet and we
+
+ align:start position:0%
+our initial gaussian wave packet and we
+ 
+
+ align:start position:0%
+our initial gaussian wave packet and we
+know what the form of f 0 is f 0 or
+
+ align:start position:0%
+know what the form of f 0 is f 0 or
+ 
+
+ align:start position:0%
+know what the form of f 0 is f 0 or
+sorry f
+
+ align:start position:0%
+sorry f
+ 
+
+ align:start position:0%
+sorry f
+of k
+
+ align:start position:0%
+of k
+ 
+
+ align:start position:0%
+of k
+is equal to well it's a gaussian of
+
+ align:start position:0%
+is equal to well it's a gaussian of
+ 
+
+ align:start position:0%
+is equal to well it's a gaussian of
+width 1 upon alpha
+
+ align:start position:0%
+width 1 upon alpha
+ 
+
+ align:start position:0%
+width 1 upon alpha
+e to the minus
+
+ align:start position:0%
+e to the minus
+ 
+
+ align:start position:0%
+e to the minus
+k minus k naught because it has momentum
+
+ align:start position:0%
+k minus k naught because it has momentum
+ 
+
+ align:start position:0%
+k minus k naught because it has momentum
+k naught so it's centered around k
+
+ align:start position:0%
+k naught so it's centered around k
+ 
+
+ align:start position:0%
+k naught so it's centered around k
+naught squared over 2 times a squared
+
+ align:start position:0%
+naught squared over 2 times a squared
+ 
+
+ align:start position:0%
+naught squared over 2 times a squared
+and the a goes upstairs
+
+ align:start position:0%
+and the a goes upstairs
+ 
+
+ align:start position:0%
+and the a goes upstairs
+and the position
+
+ align:start position:0%
+and the position
+ 
+
+ align:start position:0%
+and the position
+of the fourier of the uh the initial
+
+ align:start position:0%
+of the fourier of the uh the initial
+ 
+
+ align:start position:0%
+of the fourier of the uh the initial
+wave packet is encoded in the fourier
+
+ align:start position:0%
+wave packet is encoded in the fourier
+ 
+
+ align:start position:0%
+wave packet is encoded in the fourier
+transform and i'm going to put a
+
+ align:start position:0%
+transform and i'm going to put a
+ 
+
+ align:start position:0%
+transform and i'm going to put a
+normalization here which i'm not going
+
+ align:start position:0%
+normalization here which i'm not going
+ 
+
+ align:start position:0%
+normalization here which i'm not going
+to worry about
+
+ align:start position:0%
+to worry about
+ 
+
+ align:start position:0%
+to worry about
+with an overall phase e to the i um
+
+ align:start position:0%
+with an overall phase e to the i um
+ 
+
+ align:start position:0%
+with an overall phase e to the i um
+minus i
+
+ align:start position:0%
+minus i
+ 
+
+ align:start position:0%
+minus i
+k x naught
+
+ align:start position:0%
+k x naught
+ 
+
+ align:start position:0%
+k x naught
+so in just the same way that adding on a
+
+ align:start position:0%
+so in just the same way that adding on a
+ 
+
+ align:start position:0%
+so in just the same way that adding on a
+phase e to the aik not x in the position
+
+ align:start position:0%
+phase e to the aik not x in the position
+ 
+
+ align:start position:0%
+phase e to the aik not x in the position
+space wave function tells you what the
+
+ align:start position:0%
+space wave function tells you what the
+ 
+
+ align:start position:0%
+space wave function tells you what the
+expectation value of momentum is tacking
+
+ align:start position:0%
+expectation value of momentum is tacking
+ 
+
+ align:start position:0%
+expectation value of momentum is tacking
+on the phase and we can get this from
+
+ align:start position:0%
+on the phase and we can get this from
+ 
+
+ align:start position:0%
+on the phase and we can get this from
+just fourier transform attacking on the
+
+ align:start position:0%
+just fourier transform attacking on the
+ 
+
+ align:start position:0%
+just fourier transform attacking on the
+phase e to the ik x naught tells you in
+
+ align:start position:0%
+phase e to the ik x naught tells you in
+ 
+
+ align:start position:0%
+phase e to the ik x naught tells you in
+the fourier transform tells you the
+
+ align:start position:0%
+the fourier transform tells you the
+ 
+
+ align:start position:0%
+the fourier transform tells you the
+center point the central position of the
+
+ align:start position:0%
+center point the central position of the
+ 
+
+ align:start position:0%
+center point the central position of the
+wave pack okay so this you did on the
+
+ align:start position:0%
+wave pack okay so this you did on the
+ 
+
+ align:start position:0%
+wave pack okay so this you did on the
+problem set and this is a trivial
+
+ align:start position:0%
+problem set and this is a trivial
+ 
+
+ align:start position:0%
+problem set and this is a trivial
+momentum space version of the same thing
+
+ align:start position:0%
+momentum space version of the same thing
+ 
+
+ align:start position:0%
+momentum space version of the same thing
+so here's our wave packet expanded in
+
+ align:start position:0%
+so here's our wave packet expanded in
+ 
+
+ align:start position:0%
+so here's our wave packet expanded in
+plane waves which are energy eigenstates
+
+ align:start position:0%
+plane waves which are energy eigenstates
+ 
+
+ align:start position:0%
+plane waves which are energy eigenstates
+and the statement that these are energy
+
+ align:start position:0%
+and the statement that these are energy
+ 
+
+ align:start position:0%
+and the statement that these are energy
+eigenstates is equivalent to the
+
+ align:start position:0%
+eigenstates is equivalent to the
+ 
+
+ align:start position:0%
+eigenstates is equivalent to the
+statement that under time evolution they
+
+ align:start position:0%
+statement that under time evolution they
+ 
+
+ align:start position:0%
+statement that under time evolution they
+do nothing but rotate by a phase
+
+ align:start position:0%
+do nothing but rotate by a phase
+ 
+
+ align:start position:0%
+do nothing but rotate by a phase
+so if we want to know what the wave
+
+ align:start position:0%
+so if we want to know what the wave
+ 
+
+ align:start position:0%
+so if we want to know what the wave
+function is a function of time psi of x
+
+ align:start position:0%
+function is a function of time psi of x
+ 
+
+ align:start position:0%
+function is a function of time psi of x
+and t
+
+ align:start position:0%
+and t
+ 
+
+ align:start position:0%
+and t
+is equal to the integral dk
+
+ align:start position:0%
+is equal to the integral dk
+ 
+
+ align:start position:0%
+is equal to the integral dk
+the fourier mode
+
+ align:start position:0%
+the fourier mode
+ 
+
+ align:start position:0%
+the fourier mode
+uh f of k
+
+ align:start position:0%
+uh f of k
+ 
+
+ align:start position:0%
+uh f of k
+i'll write it out
+
+ align:start position:0%
+i'll write it out
+ 
+
+ align:start position:0%
+i'll write it out
+actually i'm going to write this out
+
+ align:start position:0%
+actually i'm going to write this out
+ 
+
+ align:start position:0%
+actually i'm going to write this out
+explicitly f of k
+
+ align:start position:0%
+explicitly f of k
+ 
+
+ align:start position:0%
+explicitly f of k
+1 over root 2 pi
+
+ align:start position:0%
+1 over root 2 pi
+ 
+
+ align:start position:0%
+1 over root 2 pi
+e to the i k x minus omega t
+
+ align:start position:0%
+e to the i k x minus omega t
+ 
+
+ align:start position:0%
+e to the i k x minus omega t
+where omega of course is a function of k
+
+ align:start position:0%
+where omega of course is a function of k
+ 
+
+ align:start position:0%
+where omega of course is a function of k
+it's a free particle so for our free
+
+ align:start position:0%
+it's a free particle so for our free
+ 
+
+ align:start position:0%
+it's a free particle so for our free
+particle uh h bar squared omega squared
+
+ align:start position:0%
+particle uh h bar squared omega squared
+ 
+
+ align:start position:0%
+particle uh h bar squared omega squared
+oh sorry h bar squared k squared
+
+ align:start position:0%
+oh sorry h bar squared k squared
+ 
+
+ align:start position:0%
+oh sorry h bar squared k squared
+upon 2m
+
+ align:start position:0%
+upon 2m
+ 
+
+ align:start position:0%
+upon 2m
+is equal to uh h bar omega
+
+ align:start position:0%
+is equal to uh h bar omega
+ 
+
+ align:start position:0%
+is equal to uh h bar omega
+okay so this is we've done this before
+
+ align:start position:0%
+okay so this is we've done this before
+ 
+
+ align:start position:0%
+okay so this is we've done this before
+but now what i want to do is i'm going
+
+ align:start position:0%
+but now what i want to do is i'm going
+ 
+
+ align:start position:0%
+but now what i want to do is i'm going
+to take exactly the same system and i
+
+ align:start position:0%
+to take exactly the same system and i
+ 
+
+ align:start position:0%
+to take exactly the same system and i
+want to add at position 0 a well of
+
+ align:start position:0%
+want to add at position 0 a well of
+ 
+
+ align:start position:0%
+want to add at position 0 a well of
+depth v naught and width l
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+how is our story going to change
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+well we want our initial wave packet
+
+ align:start position:0%
+well we want our initial wave packet
+ 
+
+ align:start position:0%
+well we want our initial wave packet
+which is you know up to us to choose we
+
+ align:start position:0%
+which is you know up to us to choose we
+ 
+
+ align:start position:0%
+which is you know up to us to choose we
+want our initial wave packet to be the
+
+ align:start position:0%
+want our initial wave packet to be the
+ 
+
+ align:start position:0%
+want our initial wave packet to be the
+same we want to start with the gaussian
+
+ align:start position:0%
+same we want to start with the gaussian
+ 
+
+ align:start position:0%
+same we want to start with the gaussian
+far far far away from the barrier
+
+ align:start position:0%
+far far far away from the barrier
+ 
+
+ align:start position:0%
+far far far away from the barrier
+we want it to be well localized in
+
+ align:start position:0%
+we want it to be well localized in
+ 
+
+ align:start position:0%
+we want it to be well localized in
+position and well localized in momentum
+
+ align:start position:0%
+position and well localized in momentum
+ 
+
+ align:start position:0%
+position and well localized in momentum
+space not perfectly localized of course
+
+ align:start position:0%
+space not perfectly localized of course
+ 
+
+ align:start position:0%
+space not perfectly localized of course
+it's a finite gaussian to satisfy the
+
+ align:start position:0%
+it's a finite gaussian to satisfy the
+ 
+
+ align:start position:0%
+it's a finite gaussian to satisfy the
+uncertainty principle but it's well
+
+ align:start position:0%
+uncertainty principle but it's well
+ 
+
+ align:start position:0%
+uncertainty principle but it's well
+localized so how does the story change
+
+ align:start position:0%
+localized so how does the story change
+ 
+
+ align:start position:0%
+localized so how does the story change
+well this doesn't change at all it's the
+
+ align:start position:0%
+well this doesn't change at all it's the
+ 
+
+ align:start position:0%
+well this doesn't change at all it's the
+same wave function
+
+ align:start position:0%
+same wave function
+ 
+
+ align:start position:0%
+same wave function
+however when we expand in energy
+
+ align:start position:0%
+however when we expand in energy
+ 
+
+ align:start position:0%
+however when we expand in energy
+eigenstates the energy eigenstates are
+
+ align:start position:0%
+eigenstates the energy eigenstates are
+ 
+
+ align:start position:0%
+eigenstates the energy eigenstates are
+no longer
+
+ align:start position:0%
+no longer
+ 
+
+ align:start position:0%
+no longer
+the energy eigenstates are no longer
+
+ align:start position:0%
+the energy eigenstates are no longer
+ 
+
+ align:start position:0%
+the energy eigenstates are no longer
+simple plane waves
+
+ align:start position:0%
+simple plane waves
+ 
+
+ align:start position:0%
+simple plane waves
+the energy eigen states as we know
+
+ align:start position:0%
+the energy eigen states as we know
+ 
+
+ align:start position:0%
+the energy eigen states as we know
+for the system take a different form
+
+ align:start position:0%
+for the system take a different form
+ 
+
+ align:start position:0%
+for the system take a different form
+for the square well
+
+ align:start position:0%
+for the square well
+ 
+
+ align:start position:0%
+for the square well
+and positive energy scattering states
+
+ align:start position:0%
+and positive energy scattering states
+ 
+
+ align:start position:0%
+and positive energy scattering states
+the plane wave or the energy eigenstates
+
+ align:start position:0%
+the plane wave or the energy eigenstates
+ 
+
+ align:start position:0%
+the plane wave or the energy eigenstates
+which i will label by k
+
+ align:start position:0%
+which i will label by k
+ 
+
+ align:start position:0%
+which i will label by k
+just because i'm going to call e is
+
+ align:start position:0%
+just because i'm going to call e is
+ 
+
+ align:start position:0%
+just because i'm going to call e is
+equal to h bar squared k squared upon 2
+
+ align:start position:0%
+equal to h bar squared k squared upon 2
+ 
+
+ align:start position:0%
+equal to h bar squared k squared upon 2
+m
+
+ align:start position:0%
+m
+ 
+
+ align:start position:0%
+m
+which is the energy
+
+ align:start position:0%
+which is the energy
+ 
+
+ align:start position:0%
+which is the energy
+well the energy is constant which is the
+
+ align:start position:0%
+well the energy is constant which is the
+ 
+
+ align:start position:0%
+well the energy is constant which is the
+k asymptotically far away from the
+
+ align:start position:0%
+k asymptotically far away from the
+ 
+
+ align:start position:0%
+k asymptotically far away from the
+potential
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the wave function i can write as 1 over
+
+ align:start position:0%
+the wave function i can write as 1 over
+ 
+
+ align:start position:0%
+the wave function i can write as 1 over
+root 2 pi
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+times e to the ikx
+
+ align:start position:0%
+times e to the ikx
+ 
+
+ align:start position:0%
+times e to the ikx
+when we're on the left hand side
+
+ align:start position:0%
+when we're on the left hand side
+ 
+
+ align:start position:0%
+when we're on the left hand side
+but left being on the left-hand side is
+
+ align:start position:0%
+but left being on the left-hand side is
+ 
+
+ align:start position:0%
+but left being on the left-hand side is
+equivalent to multiplying by a theta
+
+ align:start position:0%
+equivalent to multiplying by a theta
+ 
+
+ align:start position:0%
+equivalent to multiplying by a theta
+function of minus x minus x this is the
+
+ align:start position:0%
+function of minus x minus x this is the
+ 
+
+ align:start position:0%
+function of minus x minus x this is the
+function which is zero when its argument
+
+ align:start position:0%
+function which is zero when its argument
+ 
+
+ align:start position:0%
+function which is zero when its argument
+is negative and positive when its um
+
+ align:start position:0%
+is negative and positive when its um
+ 
+
+ align:start position:0%
+is negative and positive when its um
+argument is
+
+ align:start position:0%
+argument is
+ 
+
+ align:start position:0%
+argument is
+and one when its argument is positive
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+plus
+
+ align:start position:0%
+plus
+ 
+
+ align:start position:0%
+plus
+we have the reflected term
+
+ align:start position:0%
+we have the reflected term
+ 
+
+ align:start position:0%
+we have the reflected term
+which has an amplitude r which is again
+
+ align:start position:0%
+which has an amplitude r which is again
+ 
+
+ align:start position:0%
+which has an amplitude r which is again
+a function of k this is the reflection
+
+ align:start position:0%
+a function of k this is the reflection
+ 
+
+ align:start position:0%
+a function of k this is the reflection
+amplitude also known as c upon a
+
+ align:start position:0%
+amplitude also known as c upon a
+ 
+
+ align:start position:0%
+amplitude also known as c upon a
+e to the minus psi kx
+
+ align:start position:0%
+e to the minus psi kx
+ 
+
+ align:start position:0%
+e to the minus psi kx
+again on the left hand side theta of
+
+ align:start position:0%
+again on the left hand side theta of
+ 
+
+ align:start position:0%
+again on the left hand side theta of
+minus x
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+plus
+
+ align:start position:0%
+plus
+ 
+
+ align:start position:0%
+plus
+a transmission amplitude whose norm
+
+ align:start position:0%
+a transmission amplitude whose norm
+ 
+
+ align:start position:0%
+a transmission amplitude whose norm
+squared is transmission probability e to
+
+ align:start position:0%
+squared is transmission probability e to
+ 
+
+ align:start position:0%
+squared is transmission probability e to
+the ikx when we're on the right
+
+ align:start position:0%
+the ikx when we're on the right
+ 
+
+ align:start position:0%
+the ikx when we're on the right
+uh x whoops
+
+ align:start position:0%
+uh x whoops
+ 
+
+ align:start position:0%
+uh x whoops
+theta of x
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+so this is just a slightly different
+
+ align:start position:0%
+so this is just a slightly different
+ 
+
+ align:start position:0%
+so this is just a slightly different
+notation
+
+ align:start position:0%
+notation
+ 
+
+ align:start position:0%
+notation
+than what we usually write
+
+ align:start position:0%
+than what we usually write
+ 
+
+ align:start position:0%
+than what we usually write
+with left and right separated
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so what we want to do now is we want to
+
+ align:start position:0%
+so what we want to do now is we want to
+ 
+
+ align:start position:0%
+so what we want to do now is we want to
+decompose our wavefunction in terms of
+
+ align:start position:0%
+decompose our wavefunction in terms of
+ 
+
+ align:start position:0%
+decompose our wavefunction in terms of
+the actual energy eigenstates
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and so
+
+ align:start position:0%
+and so
+ 
+
+ align:start position:0%
+and so
+the way we're going to do that
+
+ align:start position:0%
+the way we're going to do that
+ 
+
+ align:start position:0%
+the way we're going to do that
+and having done that having expanded our
+
+ align:start position:0%
+and having done that having expanded our
+ 
+
+ align:start position:0%
+and having done that having expanded our
+wave function in this eigens in this
+
+ align:start position:0%
+wave function in this eigens in this
+ 
+
+ align:start position:0%
+wave function in this eigens in this
+basis
+
+ align:start position:0%
+basis
+ 
+
+ align:start position:0%
+basis
+um we can determine the time evolution
+
+ align:start position:0%
+um we can determine the time evolution
+ 
+
+ align:start position:0%
+um we can determine the time evolution
+in the following way first we compute we
+
+ align:start position:0%
+in the following way first we compute we
+ 
+
+ align:start position:0%
+in the following way first we compute we
+expand the wave function at time 0 as an
+
+ align:start position:0%
+expand the wave function at time 0 as an
+ 
+
+ align:start position:0%
+expand the wave function at time 0 as an
+integral dk
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and i'm going to pull the root 2 pi out
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and we have some for a transform which
+
+ align:start position:0%
+and we have some for a transform which
+ 
+
+ align:start position:0%
+and we have some for a transform which
+i'm not going to call f tilde because
+
+ align:start position:0%
+i'm not going to call f tilde because
+ 
+
+ align:start position:0%
+i'm not going to call f tilde because
+it's slightly different than the f we
+
+ align:start position:0%
+it's slightly different than the f we
+ 
+
+ align:start position:0%
+it's slightly different than the f we
+used before but it's what it's what the
+
+ align:start position:0%
+used before but it's what it's what the
+ 
+
+ align:start position:0%
+used before but it's what it's what the
+expansion coefficients have to be f
+
+ align:start position:0%
+expansion coefficients have to be f
+ 
+
+ align:start position:0%
+expansion coefficients have to be f
+tilde of um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah sorry f tilde of k times this beast
+
+ align:start position:0%
+yeah sorry f tilde of k times this beast
+ 
+
+ align:start position:0%
+yeah sorry f tilde of k times this beast
+phi sub k
+
+ align:start position:0%
+phi sub k
+ 
+
+ align:start position:0%
+phi sub k
+5k
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+good and let me actually write this out
+
+ align:start position:0%
+good and let me actually write this out
+ 
+
+ align:start position:0%
+good and let me actually write this out
+in terms of the let me actually take
+
+ align:start position:0%
+in terms of the let me actually take
+ 
+
+ align:start position:0%
+in terms of the let me actually take
+this product and write it out in terms
+
+ align:start position:0%
+this product and write it out in terms
+ 
+
+ align:start position:0%
+this product and write it out in terms
+of the three terms so those three terms
+
+ align:start position:0%
+of the three terms so those three terms
+ 
+
+ align:start position:0%
+of the three terms so those three terms
+are going to be
+
+ align:start position:0%
+are going to be
+ 
+
+ align:start position:0%
+are going to be
+f of k
+
+ align:start position:0%
+f of k
+ 
+
+ align:start position:0%
+f of k
+again tilde e to the i kx
+
+ align:start position:0%
+again tilde e to the i kx
+ 
+
+ align:start position:0%
+again tilde e to the i kx
+theta minus x
+
+ align:start position:0%
+theta minus x
+ 
+
+ align:start position:0%
+theta minus x
+plus f tilde
+
+ align:start position:0%
+plus f tilde
+ 
+
+ align:start position:0%
+plus f tilde
+r
+
+ align:start position:0%
+r
+ 
+
+ align:start position:0%
+r
+e to the minus ikx
+
+ align:start position:0%
+e to the minus ikx
+ 
+
+ align:start position:0%
+e to the minus ikx
+theta minus x
+
+ align:start position:0%
+theta minus x
+ 
+
+ align:start position:0%
+theta minus x
+plus f tilde
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh t
+
+ align:start position:0%
+uh t
+ 
+
+ align:start position:0%
+uh t
+e to the i k x
+
+ align:start position:0%
+e to the i k x
+ 
+
+ align:start position:0%
+e to the i k x
+theta of x
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+let's look at these terms this is this
+
+ align:start position:0%
+let's look at these terms this is this
+ 
+
+ align:start position:0%
+let's look at these terms this is this
+wave function now oh and sorry
+
+ align:start position:0%
+wave function now oh and sorry
+ 
+
+ align:start position:0%
+wave function now oh and sorry
+finally we want to look at the time
+
+ align:start position:0%
+finally we want to look at the time
+ 
+
+ align:start position:0%
+finally we want to look at the time
+evolution but this we started out as a
+
+ align:start position:0%
+evolution but this we started out as a
+ 
+
+ align:start position:0%
+evolution but this we started out as a
+superposition of states with definite
+
+ align:start position:0%
+superposition of states with definite
+ 
+
+ align:start position:0%
+superposition of states with definite
+energy labeled by k so we know the time
+
+ align:start position:0%
+energy labeled by k so we know the time
+ 
+
+ align:start position:0%
+energy labeled by k so we know the time
+evolution is e to the i k x minus omega
+
+ align:start position:0%
+evolution is e to the i k x minus omega
+ 
+
+ align:start position:0%
+evolution is e to the i k x minus omega
+t
+
+ align:start position:0%
+t
+ 
+
+ align:start position:0%
+t
+e to the i minus i k x plus omega t
+
+ align:start position:0%
+e to the i minus i k x plus omega t
+ 
+
+ align:start position:0%
+e to the i minus i k x plus omega t
+that's minus i omega t and k x minus
+
+ align:start position:0%
+that's minus i omega t and k x minus
+ 
+
+ align:start position:0%
+that's minus i omega t and k x minus
+omega t
+
+ align:start position:0%
+omega t
+ 
+
+ align:start position:0%
+omega t
+so we can immediately from
+
+ align:start position:0%
+so we can immediately from
+ 
+
+ align:start position:0%
+so we can immediately from
+from this time evolving wave function
+
+ align:start position:0%
+from this time evolving wave function
+ 
+
+ align:start position:0%
+from this time evolving wave function
+identify these two terms as terms with
+
+ align:start position:0%
+identify these two terms as terms with
+ 
+
+ align:start position:0%
+identify these two terms as terms with
+with
+
+ align:start position:0%
+with
+ 
+
+ align:start position:0%
+with
+a central peak moving to the right and
+
+ align:start position:0%
+a central peak moving to the right and
+ 
+
+ align:start position:0%
+a central peak moving to the right and
+this a central peak moving to the left
+
+ align:start position:0%
+this a central peak moving to the left
+ 
+
+ align:start position:0%
+this a central peak moving to the left
+kx plus omega t
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+everyone cool with that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+questions
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+or just where this came from
+
+ align:start position:0%
+or just where this came from
+ 
+
+ align:start position:0%
+or just where this came from
+oh good good good okay so this is just a
+
+ align:start position:0%
+oh good good good okay so this is just a
+ 
+
+ align:start position:0%
+oh good good good okay so this is just a
+notational thing so usually when i say a
+
+ align:start position:0%
+notational thing so usually when i say a
+ 
+
+ align:start position:0%
+notational thing so usually when i say a
+uh phi sub k is equal to
+
+ align:start position:0%
+uh phi sub k is equal to
+ 
+
+ align:start position:0%
+uh phi sub k is equal to
+on the left
+
+ align:start position:0%
+on the left
+ 
+
+ align:start position:0%
+on the left
+e to the ikx uh with some overall
+
+ align:start position:0%
+e to the ikx uh with some overall
+ 
+
+ align:start position:0%
+e to the ikx uh with some overall
+amplitude a
+
+ align:start position:0%
+amplitude a
+ 
+
+ align:start position:0%
+amplitude a
+let's say 1 over root 2 pi
+
+ align:start position:0%
+let's say 1 over root 2 pi
+ 
+
+ align:start position:0%
+let's say 1 over root 2 pi
+e to the ikx
+
+ align:start position:0%
+e to the ikx
+ 
+
+ align:start position:0%
+e to the ikx
+plus
+
+ align:start position:0%
+plus
+ 
+
+ align:start position:0%
+plus
+c over a
+
+ align:start position:0%
+c over a
+ 
+
+ align:start position:0%
+c over a
+e to the minus ikx
+
+ align:start position:0%
+e to the minus ikx
+ 
+
+ align:start position:0%
+e to the minus ikx
+right on the left and i'm just going to
+
+ align:start position:0%
+right on the left and i'm just going to
+ 
+
+ align:start position:0%
+right on the left and i'm just going to
+call this because this is the reflected
+
+ align:start position:0%
+call this because this is the reflected
+ 
+
+ align:start position:0%
+call this because this is the reflected
+wave i'm just going to call this r
+
+ align:start position:0%
+wave i'm just going to call this r
+ 
+
+ align:start position:0%
+wave i'm just going to call this r
+okay and then on the right
+
+ align:start position:0%
+okay and then on the right
+ 
+
+ align:start position:0%
+okay and then on the right
+we have e to the ikx
+
+ align:start position:0%
+we have e to the ikx
+ 
+
+ align:start position:0%
+we have e to the ikx
+there's only a wave traveling to the
+
+ align:start position:0%
+there's only a wave traveling to the
+ 
+
+ align:start position:0%
+there's only a wave traveling to the
+right and the coefficient is the
+
+ align:start position:0%
+right and the coefficient is the
+ 
+
+ align:start position:0%
+right and the coefficient is the
+transmission amplitude so this is what
+
+ align:start position:0%
+transmission amplitude so this is what
+ 
+
+ align:start position:0%
+transmission amplitude so this is what
+we normally write but then i'm using the
+
+ align:start position:0%
+we normally write but then i'm using the
+ 
+
+ align:start position:0%
+we normally write but then i'm using the
+function the theta function so called
+
+ align:start position:0%
+function the theta function so called
+ 
+
+ align:start position:0%
+function the theta function so called
+theta function theta of x is defined as
+
+ align:start position:0%
+theta function theta of x is defined as
+ 
+
+ align:start position:0%
+theta function theta of x is defined as
+zero when x is less than zero and one
+
+ align:start position:0%
+zero when x is less than zero and one
+ 
+
+ align:start position:0%
+zero when x is less than zero and one
+when x is greater than zero
+
+ align:start position:0%
+when x is greater than zero
+ 
+
+ align:start position:0%
+when x is greater than zero
+okay so this is a function one so this
+
+ align:start position:0%
+okay so this is a function one so this
+ 
+
+ align:start position:0%
+okay so this is a function one so this
+allows me using theta function allows me
+
+ align:start position:0%
+allows me using theta function allows me
+ 
+
+ align:start position:0%
+allows me using theta function allows me
+to write this thing as a single function
+
+ align:start position:0%
+to write this thing as a single function
+ 
+
+ align:start position:0%
+to write this thing as a single function
+without having to goose around with lots
+
+ align:start position:0%
+without having to goose around with lots
+ 
+
+ align:start position:0%
+without having to goose around with lots
+of terms is that cool
+
+ align:start position:0%
+of terms is that cool
+ 
+
+ align:start position:0%
+of terms is that cool
+great
+
+ align:start position:0%
+great
+ 
+
+ align:start position:0%
+great
+i will just take into account
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+because otherwise we should have
+
+ align:start position:0%
+because otherwise we should have
+ 
+
+ align:start position:0%
+because otherwise we should have
+something
+
+ align:start position:0%
+something
+ 
+
+ align:start position:0%
+something
+excellent excellent thank you so much so
+
+ align:start position:0%
+excellent excellent thank you so much so
+ 
+
+ align:start position:0%
+excellent excellent thank you so much so
+here what i want to do is
+
+ align:start position:0%
+here what i want to do is
+ 
+
+ align:start position:0%
+here what i want to do is
+thank you what i want to do is i want to
+
+ align:start position:0%
+thank you what i want to do is i want to
+ 
+
+ align:start position:0%
+thank you what i want to do is i want to
+think of the wave function
+
+ align:start position:0%
+think of the wave function
+ 
+
+ align:start position:0%
+think of the wave function
+so this is a good description when the
+
+ align:start position:0%
+so this is a good description when the
+ 
+
+ align:start position:0%
+so this is a good description when the
+particle is far far away
+
+ align:start position:0%
+particle is far far away
+ 
+
+ align:start position:0%
+particle is far far away
+and this is a good description when the
+
+ align:start position:0%
+and this is a good description when the
+ 
+
+ align:start position:0%
+and this is a good description when the
+particle is not in the potential so i
+
+ align:start position:0%
+particle is not in the potential so i
+ 
+
+ align:start position:0%
+particle is not in the potential so i
+want to just imagine this sorry thank
+
+ align:start position:0%
+want to just imagine this sorry thank
+ 
+
+ align:start position:0%
+want to just imagine this sorry thank
+you i totally glossed over this step i
+
+ align:start position:0%
+you i totally glossed over this step i
+ 
+
+ align:start position:0%
+you i totally glossed over this step i
+want to imagine this as a potential
+
+ align:start position:0%
+want to imagine this as a potential
+ 
+
+ align:start position:0%
+want to imagine this as a potential
+where all of the matching is implemented
+
+ align:start position:0%
+where all of the matching is implemented
+ 
+
+ align:start position:0%
+where all of the matching is implemented
+at x equals zero
+
+ align:start position:0%
+at x equals zero
+ 
+
+ align:start position:0%
+at x equals zero
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+so when i write it in this fashion
+
+ align:start position:0%
+so when i write it in this fashion
+ 
+
+ align:start position:0%
+so when i write it in this fashion
+but the better way to another equivalent
+
+ align:start position:0%
+but the better way to another equivalent
+ 
+
+ align:start position:0%
+but the better way to another equivalent
+way to think about this is this is a
+
+ align:start position:0%
+way to think about this is this is a
+ 
+
+ align:start position:0%
+way to think about this is this is a
+good description of the wave function
+
+ align:start position:0%
+good description of the wave function
+ 
+
+ align:start position:0%
+good description of the wave function
+when we're not inside the well
+
+ align:start position:0%
+when we're not inside the well
+ 
+
+ align:start position:0%
+when we're not inside the well
+so for the purposes of the rest of the
+
+ align:start position:0%
+so for the purposes of the rest of the
+ 
+
+ align:start position:0%
+so for the purposes of the rest of the
+analysis that i'm going to do this is
+
+ align:start position:0%
+analysis that i'm going to do this is
+ 
+
+ align:start position:0%
+analysis that i'm going to do this is
+exactly what the form of the wave
+
+ align:start position:0%
+exactly what the form of the wave
+ 
+
+ align:start position:0%
+exactly what the form of the wave
+function is when we're not inside the
+
+ align:start position:0%
+function is when we're not inside the
+ 
+
+ align:start position:0%
+function is when we're not inside the
+well
+
+ align:start position:0%
+well
+ 
+
+ align:start position:0%
+well
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+and then let's just not use this to ask
+
+ align:start position:0%
+and then let's just not use this to ask
+ 
+
+ align:start position:0%
+and then let's just not use this to ask
+about questions inside the well
+
+ align:start position:0%
+about questions inside the well
+ 
+
+ align:start position:0%
+about questions inside the well
+when i write it in this theta form or
+
+ align:start position:0%
+when i write it in this theta form or
+ 
+
+ align:start position:0%
+when i write it in this theta form or
+for that matter when i write it in this
+
+ align:start position:0%
+for that matter when i write it in this
+ 
+
+ align:start position:0%
+for that matter when i write it in this
+form this is not the the form what i
+
+ align:start position:0%
+form this is not the the form what i
+ 
+
+ align:start position:0%
+form this is not the the form what i
+mean is left of the well
+
+ align:start position:0%
+mean is left of the well
+ 
+
+ align:start position:0%
+mean is left of the well
+and right of the well
+
+ align:start position:0%
+and right of the well
+ 
+
+ align:start position:0%
+and right of the well
+and inside
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+t e to the ikx
+
+ align:start position:0%
+t e to the ikx
+ 
+
+ align:start position:0%
+t e to the ikx
+inside it's doing something else
+
+ align:start position:0%
+inside it's doing something else
+ 
+
+ align:start position:0%
+inside it's doing something else
+but we don't want to ask questions about
+
+ align:start position:0%
+but we don't want to ask questions about
+ 
+
+ align:start position:0%
+but we don't want to ask questions about
+it okay
+
+ align:start position:0%
+it okay
+ 
+
+ align:start position:0%
+it okay
+cool that's just going to simplify my
+
+ align:start position:0%
+cool that's just going to simplify my
+ 
+
+ align:start position:0%
+cool that's just going to simplify my
+life
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+root of capital yeah
+
+ align:start position:0%
+root of capital yeah
+ 
+
+ align:start position:0%
+root of capital yeah
+it's the square root of capital t but
+
+ align:start position:0%
+it's the square root of capital t but
+ 
+
+ align:start position:0%
+it's the square root of capital t but
+you've got to be careful because there
+
+ align:start position:0%
+you've got to be careful because there
+ 
+
+ align:start position:0%
+you've got to be careful because there
+can be a phase
+
+ align:start position:0%
+can be a phase
+ 
+
+ align:start position:0%
+can be a phase
+remember this is the amplitude and what
+
+ align:start position:0%
+remember this is the amplitude and what
+ 
+
+ align:start position:0%
+remember this is the amplitude and what
+it really is is this reflection is b
+
+ align:start position:0%
+it really is is this reflection is b
+ 
+
+ align:start position:0%
+it really is is this reflection is b
+over a
+
+ align:start position:0%
+over a
+ 
+
+ align:start position:0%
+over a
+and these guys are complex numbers and
+
+ align:start position:0%
+and these guys are complex numbers and
+ 
+
+ align:start position:0%
+and these guys are complex numbers and
+it's true that b over a norm squared is
+
+ align:start position:0%
+it's true that b over a norm squared is
+ 
+
+ align:start position:0%
+it's true that b over a norm squared is
+the transmission probability
+
+ align:start position:0%
+the transmission probability
+ 
+
+ align:start position:0%
+the transmission probability
+but b over a has a phase and that
+
+ align:start position:0%
+but b over a has a phase and that
+ 
+
+ align:start position:0%
+but b over a has a phase and that
+quantity i'm going to call t and we'll
+
+ align:start position:0%
+quantity i'm going to call t and we'll
+ 
+
+ align:start position:0%
+quantity i'm going to call t and we'll
+interpret that in more detail in a few
+
+ align:start position:0%
+interpret that in more detail in a few
+ 
+
+ align:start position:0%
+interpret that in more detail in a few
+minutes
+
+ align:start position:0%
+minutes
+ 
+
+ align:start position:0%
+minutes
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+so it's of this form
+
+ align:start position:0%
+so it's of this form
+ 
+
+ align:start position:0%
+so it's of this form
+and i just want to look at each of these
+
+ align:start position:0%
+and i just want to look at each of these
+ 
+
+ align:start position:0%
+and i just want to look at each of these
+three terms
+
+ align:start position:0%
+three terms
+ 
+
+ align:start position:0%
+three terms
+and in particular i want to focus on
+
+ align:start position:0%
+and in particular i want to focus on
+ 
+
+ align:start position:0%
+and in particular i want to focus on
+them at time 0.
+
+ align:start position:0%
+them at time 0.
+ 
+
+ align:start position:0%
+them at time 0.
+so at t equals 0 what does this look
+
+ align:start position:0%
+so at t equals 0 what does this look
+ 
+
+ align:start position:0%
+so at t equals 0 what does this look
+like well that first term is integral dk
+
+ align:start position:0%
+like well that first term is integral dk
+ 
+
+ align:start position:0%
+like well that first term is integral dk
+of f of k
+
+ align:start position:0%
+of f of k
+ 
+
+ align:start position:0%
+of f of k
+e to the ikx
+
+ align:start position:0%
+e to the ikx
+ 
+
+ align:start position:0%
+e to the ikx
+minus omega t
+
+ align:start position:0%
+minus omega t
+ 
+
+ align:start position:0%
+minus omega t
+okay theta minus x
+
+ align:start position:0%
+okay theta minus x
+ 
+
+ align:start position:0%
+okay theta minus x
+notice that theta minus x is independent
+
+ align:start position:0%
+notice that theta minus x is independent
+ 
+
+ align:start position:0%
+notice that theta minus x is independent
+of
+
+ align:start position:0%
+of
+ 
+
+ align:start position:0%
+of
+k it's independent of the integral so
+
+ align:start position:0%
+k it's independent of the integral so
+ 
+
+ align:start position:0%
+k it's independent of the integral so
+this is just a function times theta of
+
+ align:start position:0%
+this is just a function times theta of
+ 
+
+ align:start position:0%
+this is just a function times theta of
+minus x
+
+ align:start position:0%
+minus x
+ 
+
+ align:start position:0%
+minus x
+okay and this function was constructed
+
+ align:start position:0%
+okay and this function was constructed
+ 
+
+ align:start position:0%
+okay and this function was constructed
+to give us the initial gaussian
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so this is just oh sorry and this was at
+
+ align:start position:0%
+so this is just oh sorry and this was at
+ 
+
+ align:start position:0%
+so this is just oh sorry and this was at
+t equals 0. so this is just our gaussian
+
+ align:start position:0%
+t equals 0. so this is just our gaussian
+ 
+
+ align:start position:0%
+t equals 0. so this is just our gaussian
+at position x naught
+
+ align:start position:0%
+at position x naught
+ 
+
+ align:start position:0%
+at position x naught
+centered around value k naught
+
+ align:start position:0%
+centered around value k naught
+ 
+
+ align:start position:0%
+centered around value k naught
+at time equals zero
+
+ align:start position:0%
+at time equals zero
+ 
+
+ align:start position:0%
+at time equals zero
+theta of minus x
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay this is just saying that um sorry
+
+ align:start position:0%
+okay this is just saying that um sorry
+ 
+
+ align:start position:0%
+okay this is just saying that um sorry
+at x at position x sorry of x naught
+
+ align:start position:0%
+at x at position x sorry of x naught
+ 
+
+ align:start position:0%
+at x at position x sorry of x naught
+so this all this function is is the this
+
+ align:start position:0%
+so this all this function is is the this
+ 
+
+ align:start position:0%
+so this all this function is is the this
+is the fourier transform of our gaussian
+
+ align:start position:0%
+is the fourier transform of our gaussian
+ 
+
+ align:start position:0%
+is the fourier transform of our gaussian
+and we're undoing the fourier transform
+
+ align:start position:0%
+and we're undoing the fourier transform
+ 
+
+ align:start position:0%
+and we're undoing the fourier transform
+so this is just giving us our gaussian
+
+ align:start position:0%
+so this is just giving us our gaussian
+ 
+
+ align:start position:0%
+so this is just giving us our gaussian
+back
+
+ align:start position:0%
+back
+ 
+
+ align:start position:0%
+back
+and as long as the particle is far away
+
+ align:start position:0%
+and as long as the particle is far away
+ 
+
+ align:start position:0%
+and as long as the particle is far away
+from the well so here's the well and
+
+ align:start position:0%
+from the well so here's the well and
+ 
+
+ align:start position:0%
+from the well so here's the well and
+here's our wave packet uh that theta
+
+ align:start position:0%
+here's our wave packet uh that theta
+ 
+
+ align:start position:0%
+here's our wave packet uh that theta
+function is totally irrelevant because
+
+ align:start position:0%
+function is totally irrelevant because
+ 
+
+ align:start position:0%
+function is totally irrelevant because
+the gaussian makes it zero away from the
+
+ align:start position:0%
+the gaussian makes it zero away from the
+ 
+
+ align:start position:0%
+the gaussian makes it zero away from the
+center of the gaussian anyway
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and so just as a quick question if we
+
+ align:start position:0%
+and so just as a quick question if we
+ 
+
+ align:start position:0%
+and so just as a quick question if we
+look at this as a function of t so we
+
+ align:start position:0%
+look at this as a function of t so we
+ 
+
+ align:start position:0%
+look at this as a function of t so we
+put back in the minus omega t
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so if we put back in the time dependence
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this is a wave
+
+ align:start position:0%
+this is a wave
+ 
+
+ align:start position:0%
+this is a wave
+that's moving to the right and we need
+
+ align:start position:0%
+that's moving to the right and we need
+ 
+
+ align:start position:0%
+that's moving to the right and we need
+to make to be more precise about that
+
+ align:start position:0%
+to make to be more precise about that
+ 
+
+ align:start position:0%
+to make to be more precise about that
+what does it mean to say it's a wave
+
+ align:start position:0%
+what does it mean to say it's a wave
+ 
+
+ align:start position:0%
+what does it mean to say it's a wave
+moving to the right
+
+ align:start position:0%
+moving to the right
+ 
+
+ align:start position:0%
+moving to the right
+well this is an envelope
+
+ align:start position:0%
+well this is an envelope
+ 
+
+ align:start position:0%
+well this is an envelope
+on this
+
+ align:start position:0%
+on this
+ 
+
+ align:start position:0%
+on this
+set of plane waves and the envelope by
+
+ align:start position:0%
+set of plane waves and the envelope by
+ 
+
+ align:start position:0%
+set of plane waves and the envelope by
+construction
+
+ align:start position:0%
+construction
+ 
+
+ align:start position:0%
+construction
+was well localized around position x but
+
+ align:start position:0%
+was well localized around position x but
+ 
+
+ align:start position:0%
+was well localized around position x but
+it was also well localized in momentum
+
+ align:start position:0%
+it was also well localized in momentum
+ 
+
+ align:start position:0%
+it was also well localized in momentum
+and in particular the fourier transform
+
+ align:start position:0%
+and in particular the fourier transform
+ 
+
+ align:start position:0%
+and in particular the fourier transform
+is well localized around the momentum
+
+ align:start position:0%
+is well localized around the momentum
+ 
+
+ align:start position:0%
+is well localized around the momentum
+k naught
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and so using using the method of
+
+ align:start position:0%
+and so using using the method of
+ 
+
+ align:start position:0%
+and so using using the method of
+stationary phase or just asking where is
+
+ align:start position:0%
+stationary phase or just asking where is
+ 
+
+ align:start position:0%
+stationary phase or just asking where is
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+where is the phase constant stationary
+
+ align:start position:0%
+where is the phase constant stationary
+ 
+
+ align:start position:0%
+where is the phase constant stationary
+we get that the center of the the
+
+ align:start position:0%
+we get that the center of the the
+ 
+
+ align:start position:0%
+we get that the center of the the
+peaks the the central peak of the wave
+
+ align:start position:0%
+peaks the the central peak of the wave
+ 
+
+ align:start position:0%
+peaks the the central peak of the wave
+function
+
+ align:start position:0%
+function
+ 
+
+ align:start position:0%
+function
+satisfies the equation ddk naught
+
+ align:start position:0%
+satisfies the equation ddk naught
+ 
+
+ align:start position:0%
+satisfies the equation ddk naught
+if you're not familiar with stationary
+
+ align:start position:0%
+if you're not familiar with stationary
+ 
+
+ align:start position:0%
+if you're not familiar with stationary
+phase let the
+
+ align:start position:0%
+phase let the
+ 
+
+ align:start position:0%
+phase let the
+restoration instructors uh know and they
+
+ align:start position:0%
+restoration instructors uh know and they
+ 
+
+ align:start position:0%
+restoration instructors uh know and they
+will discuss it for you um
+
+ align:start position:0%
+will discuss it for you um
+ 
+
+ align:start position:0%
+will discuss it for you um
+so this the the
+
+ align:start position:0%
+so this the the
+ 
+
+ align:start position:0%
+so this the the
+points of stationary phase of this uh
+
+ align:start position:0%
+points of stationary phase of this uh
+ 
+
+ align:start position:0%
+points of stationary phase of this uh
+this superposition of this wave packet
+
+ align:start position:0%
+this superposition of this wave packet
+ 
+
+ align:start position:0%
+this superposition of this wave packet
+lie at the position ddk naught of kx
+
+ align:start position:0%
+lie at the position ddk naught of kx
+ 
+
+ align:start position:0%
+lie at the position ddk naught of kx
+sorry ddk of kx minus omega of kt
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+evaluated at the peak k naught
+
+ align:start position:0%
+evaluated at the peak k naught
+ 
+
+ align:start position:0%
+evaluated at the peak k naught
+of the distribution
+
+ align:start position:0%
+of the distribution
+ 
+
+ align:start position:0%
+of the distribution
+but ddk of kx minus omega t is for the
+
+ align:start position:0%
+but ddk of kx minus omega t is for the
+ 
+
+ align:start position:0%
+but ddk of kx minus omega t is for the
+first term x and for the second term ddk
+
+ align:start position:0%
+first term x and for the second term ddk
+ 
+
+ align:start position:0%
+first term x and for the second term ddk
+of omega well we know that omega we're
+
+ align:start position:0%
+of omega well we know that omega we're
+ 
+
+ align:start position:0%
+of omega well we know that omega we're
+in the free particle regime
+
+ align:start position:0%
+in the free particle regime
+ 
+
+ align:start position:0%
+in the free particle regime
+um omega where did it go um well we all
+
+ align:start position:0%
+um omega where did it go um well we all
+ 
+
+ align:start position:0%
+um omega where did it go um well we all
+know what it is it's h bar h bar k
+
+ align:start position:0%
+know what it is it's h bar h bar k
+ 
+
+ align:start position:0%
+know what it is it's h bar h bar k
+squared upon 2 m we take a derivative
+
+ align:start position:0%
+squared upon 2 m we take a derivative
+ 
+
+ align:start position:0%
+squared upon 2 m we take a derivative
+with respect to k we get h bar k over m
+
+ align:start position:0%
+with respect to k we get h bar k over m
+ 
+
+ align:start position:0%
+with respect to k we get h bar k over m
+the twos cancel so x minus
+
+ align:start position:0%
+the twos cancel so x minus
+ 
+
+ align:start position:0%
+the twos cancel so x minus
+h bar k
+
+ align:start position:0%
+h bar k
+ 
+
+ align:start position:0%
+h bar k
+over m
+
+ align:start position:0%
+over m
+ 
+
+ align:start position:0%
+over m
+t
+
+ align:start position:0%
+t
+ 
+
+ align:start position:0%
+t
+and a place where this point where this
+
+ align:start position:0%
+and a place where this point where this
+ 
+
+ align:start position:0%
+and a place where this point where this
+phase is zero
+
+ align:start position:0%
+phase is zero
+ 
+
+ align:start position:0%
+phase is zero
+where the phase is stationary
+
+ align:start position:0%
+where the phase is stationary
+ 
+
+ align:start position:0%
+where the phase is stationary
+moves over time as x is equal to h bar k
+
+ align:start position:0%
+moves over time as x is equal to h bar k
+ 
+
+ align:start position:0%
+moves over time as x is equal to h bar k
+over m
+
+ align:start position:0%
+over m
+ 
+
+ align:start position:0%
+over m
+t
+
+ align:start position:0%
+t
+ 
+
+ align:start position:0%
+t
+but h bar k over m that's the class
+
+ align:start position:0%
+but h bar k over m that's the class
+ 
+
+ align:start position:0%
+but h bar k over m that's the class
+that's the momentum
+
+ align:start position:0%
+that's the momentum
+ 
+
+ align:start position:0%
+that's the momentum
+p over m that's the classical velocity
+
+ align:start position:0%
+p over m that's the classical velocity
+ 
+
+ align:start position:0%
+p over m that's the classical velocity
+so this is v naught t
+
+ align:start position:0%
+so this is v naught t
+ 
+
+ align:start position:0%
+so this is v naught t
+the velocity associated with that
+
+ align:start position:0%
+the velocity associated with that
+ 
+
+ align:start position:0%
+the velocity associated with that
+momentum
+
+ align:start position:0%
+momentum
+ 
+
+ align:start position:0%
+momentum
+so this is good we've done the right job
+
+ align:start position:0%
+so this is good we've done the right job
+ 
+
+ align:start position:0%
+so this is good we've done the right job
+of setting up our wave packet we built a
+
+ align:start position:0%
+of setting up our wave packet we built a
+ 
+
+ align:start position:0%
+of setting up our wave packet we built a
+gaussian that was far away that was
+
+ align:start position:0%
+gaussian that was far away that was
+ 
+
+ align:start position:0%
+gaussian that was far away that was
+moving in with a fixed velocity towards
+
+ align:start position:0%
+moving in with a fixed velocity towards
+ 
+
+ align:start position:0%
+moving in with a fixed velocity towards
+the barrier and now we want to know what
+
+ align:start position:0%
+the barrier and now we want to know what
+ 
+
+ align:start position:0%
+the barrier and now we want to know what
+happens after it collides off the
+
+ align:start position:0%
+happens after it collides off the
+ 
+
+ align:start position:0%
+happens after it collides off the
+barrier
+
+ align:start position:0%
+barrier
+ 
+
+ align:start position:0%
+barrier
+cool
+
+ align:start position:0%
+cool
+ 
+
+ align:start position:0%
+cool
+so what we really want to ask is that
+
+ align:start position:0%
+so what we really want to ask is that
+ 
+
+ align:start position:0%
+so what we really want to ask is that
+late times what does the wave function
+
+ align:start position:0%
+late times what does the wave function
+ 
+
+ align:start position:0%
+late times what does the wave function
+look like well at late times the
+
+ align:start position:0%
+look like well at late times the
+ 
+
+ align:start position:0%
+look like well at late times the
+position of this so again we're focusing
+
+ align:start position:0%
+position of this so again we're focusing
+ 
+
+ align:start position:0%
+position of this so again we're focusing
+on the first term the position of this
+
+ align:start position:0%
+on the first term the position of this
+ 
+
+ align:start position:0%
+on the first term the position of this
+wave packet at late times at positive t
+
+ align:start position:0%
+wave packet at late times at positive t
+ 
+
+ align:start position:0%
+wave packet at late times at positive t
+is positive
+
+ align:start position:0%
+is positive
+ 
+
+ align:start position:0%
+is positive
+and when it's positive then this theta
+
+ align:start position:0%
+and when it's positive then this theta
+ 
+
+ align:start position:0%
+and when it's positive then this theta
+function kills its contribution to the
+
+ align:start position:0%
+function kills its contribution to the
+ 
+
+ align:start position:0%
+function kills its contribution to the
+overall wave function
+
+ align:start position:0%
+overall wave function
+ 
+
+ align:start position:0%
+overall wave function
+right
+
+ align:start position:0%
+right
+ 
+
+ align:start position:0%
+right
+this theta is now theta of minus a
+
+ align:start position:0%
+this theta is now theta of minus a
+ 
+
+ align:start position:0%
+this theta is now theta of minus a
+positive number and this gaussian is
+
+ align:start position:0%
+positive number and this gaussian is
+ 
+
+ align:start position:0%
+positive number and this gaussian is
+gone
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+what is it replaced by well these two
+
+ align:start position:0%
+what is it replaced by well these two
+ 
+
+ align:start position:0%
+what is it replaced by well these two
+terms aren't necessarily zero in
+
+ align:start position:0%
+terms aren't necessarily zero in
+ 
+
+ align:start position:0%
+terms aren't necessarily zero in
+particular this one is moving to the
+
+ align:start position:0%
+particular this one is moving to the
+ 
+
+ align:start position:0%
+particular this one is moving to the
+left so x is as time goes forward x is
+
+ align:start position:0%
+left so x is as time goes forward x is
+ 
+
+ align:start position:0%
+left so x is as time goes forward x is
+moving further and further to the left
+
+ align:start position:0%
+moving further and further to the left
+ 
+
+ align:start position:0%
+moving further and further to the left
+and so this theta function starts
+
+ align:start position:0%
+and so this theta function starts
+ 
+
+ align:start position:0%
+and so this theta function starts
+turning on
+
+ align:start position:0%
+turning on
+ 
+
+ align:start position:0%
+turning on
+and similarly as x goes positive this
+
+ align:start position:0%
+and similarly as x goes positive this
+ 
+
+ align:start position:0%
+and similarly as x goes positive this
+theta function starts turning on as well
+
+ align:start position:0%
+theta function starts turning on as well
+ 
+
+ align:start position:0%
+theta function starts turning on as well
+let's focus on this third term
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+transmitted term
+
+ align:start position:0%
+transmitted term
+ 
+
+ align:start position:0%
+transmitted term
+so let's focus on this third term
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+in particular that term looks like
+
+ align:start position:0%
+in particular that term looks like
+ 
+
+ align:start position:0%
+in particular that term looks like
+integral dk over root 2 pi
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+f
+
+ align:start position:0%
+f
+ 
+
+ align:start position:0%
+f
+times the transmission amplitude times e
+
+ align:start position:0%
+times the transmission amplitude times e
+ 
+
+ align:start position:0%
+times the transmission amplitude times e
+to the i kx
+
+ align:start position:0%
+to the i kx
+ 
+
+ align:start position:0%
+to the i kx
+minus uh omega t
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay and there's an overall theta of x
+
+ align:start position:0%
+okay and there's an overall theta of x
+ 
+
+ align:start position:0%
+okay and there's an overall theta of x
+outside but for late times where the
+
+ align:start position:0%
+outside but for late times where the
+ 
+
+ align:start position:0%
+outside but for late times where the
+center of the wave packet for the
+
+ align:start position:0%
+center of the wave packet for the
+ 
+
+ align:start position:0%
+center of the wave packet for the
+transmitted wave packet should be
+
+ align:start position:0%
+transmitted wave packet should be
+ 
+
+ align:start position:0%
+transmitted wave packet should be
+positive the state is just going to be
+
+ align:start position:0%
+positive the state is just going to be
+ 
+
+ align:start position:0%
+positive the state is just going to be
+one so we can safely ignore it
+
+ align:start position:0%
+one so we can safely ignore it
+ 
+
+ align:start position:0%
+one so we can safely ignore it
+it's just saying we're far off to the
+
+ align:start position:0%
+it's just saying we're far off to the
+ 
+
+ align:start position:0%
+it's just saying we're far off to the
+right
+
+ align:start position:0%
+right
+ 
+
+ align:start position:0%
+right
+and now i want to i want to do one last
+
+ align:start position:0%
+and now i want to i want to do one last
+ 
+
+ align:start position:0%
+and now i want to i want to do one last
+thing this was an overall
+
+ align:start position:0%
+thing this was an overall
+ 
+
+ align:start position:0%
+thing this was an overall
+this was an overall
+
+ align:start position:0%
+this was an overall
+ 
+
+ align:start position:0%
+this was an overall
+envelope
+
+ align:start position:0%
+envelope
+ 
+
+ align:start position:0%
+envelope
+this t was our scattering amplitude and
+
+ align:start position:0%
+this t was our scattering amplitude and
+ 
+
+ align:start position:0%
+this t was our scattering amplitude and
+i want to write it in the following form
+
+ align:start position:0%
+i want to write it in the following form
+ 
+
+ align:start position:0%
+i want to write it in the following form
+i want to write it as root t
+
+ align:start position:0%
+i want to write it as root t
+ 
+
+ align:start position:0%
+i want to write it as root t
+e to the minus i phi
+
+ align:start position:0%
+e to the minus i phi
+ 
+
+ align:start position:0%
+e to the minus i phi
+where phi is okay so what this is saying
+
+ align:start position:0%
+where phi is okay so what this is saying
+ 
+
+ align:start position:0%
+where phi is okay so what this is saying
+is that indeed as was pointed out
+
+ align:start position:0%
+is that indeed as was pointed out
+ 
+
+ align:start position:0%
+is that indeed as was pointed out
+earlier the norm squared of this
+
+ align:start position:0%
+earlier the norm squared of this
+ 
+
+ align:start position:0%
+earlier the norm squared of this
+coefficient t is the transmission
+
+ align:start position:0%
+coefficient t is the transmission
+ 
+
+ align:start position:0%
+coefficient t is the transmission
+probability
+
+ align:start position:0%
+probability
+ 
+
+ align:start position:0%
+probability
+but it has a phase and what i want to
+
+ align:start position:0%
+but it has a phase and what i want to
+ 
+
+ align:start position:0%
+but it has a phase and what i want to
+know is what does this phase mean
+
+ align:start position:0%
+know is what does this phase mean
+ 
+
+ align:start position:0%
+know is what does this phase mean
+what information is contained in this
+
+ align:start position:0%
+what information is contained in this
+ 
+
+ align:start position:0%
+what information is contained in this
+phase and that's what we're about to
+
+ align:start position:0%
+phase and that's what we're about to
+ 
+
+ align:start position:0%
+phase and that's what we're about to
+find
+
+ align:start position:0%
+find
+ 
+
+ align:start position:0%
+find
+so let's put that in here we have root t
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and minus phi
+
+ align:start position:0%
+and minus phi
+ 
+
+ align:start position:0%
+and minus phi
+okay where omega and k and phi are both
+
+ align:start position:0%
+okay where omega and k and phi are both
+ 
+
+ align:start position:0%
+okay where omega and k and phi are both
+functions of k
+
+ align:start position:0%
+functions of k
+ 
+
+ align:start position:0%
+functions of k
+because the transmission amplitudes
+
+ align:start position:0%
+because the transmission amplitudes
+ 
+
+ align:start position:0%
+because the transmission amplitudes
+depend on
+
+ align:start position:0%
+depend on
+ 
+
+ align:start position:0%
+depend on
+the momentum or the energy
+
+ align:start position:0%
+the momentum or the energy
+ 
+
+ align:start position:0%
+the momentum or the energy
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+and now i again want to know
+
+ align:start position:0%
+and now i again want to know
+ 
+
+ align:start position:0%
+and now i again want to know
+how does this wave packet move if i look
+
+ align:start position:0%
+how does this wave packet move if i look
+ 
+
+ align:start position:0%
+how does this wave packet move if i look
+at this wave packet how does it move on
+
+ align:start position:0%
+at this wave packet how does it move on
+ 
+
+ align:start position:0%
+at this wave packet how does it move on
+mass how does it has a group of waves
+
+ align:start position:0%
+mass how does it has a group of waves
+ 
+
+ align:start position:0%
+mass how does it has a group of waves
+how does this wave packet move
+
+ align:start position:0%
+how does this wave packet move
+ 
+
+ align:start position:0%
+how does this wave packet move
+in particular with y velocity
+
+ align:start position:0%
+in particular with y velocity
+ 
+
+ align:start position:0%
+in particular with y velocity
+so i'll do again make an argument by
+
+ align:start position:0%
+so i'll do again make an argument by
+ 
+
+ align:start position:0%
+so i'll do again make an argument by
+stationary phase i'll look at a point of
+
+ align:start position:0%
+stationary phase i'll look at a point of
+ 
+
+ align:start position:0%
+stationary phase i'll look at a point of
+of phase equals 0 and ask how it moves
+
+ align:start position:0%
+of phase equals 0 and ask how it moves
+ 
+
+ align:start position:0%
+of phase equals 0 and ask how it moves
+over time and the point of stationary
+
+ align:start position:0%
+over time and the point of stationary
+ 
+
+ align:start position:0%
+over time and the point of stationary
+phase is again given by ddk of the phase
+
+ align:start position:0%
+phase is again given by ddk of the phase
+ 
+
+ align:start position:0%
+phase is again given by ddk of the phase
+kx
+
+ align:start position:0%
+kx
+ 
+
+ align:start position:0%
+kx
+minus omega of kt
+
+ align:start position:0%
+minus omega of kt
+ 
+
+ align:start position:0%
+minus omega of kt
+minus 5k
+
+ align:start position:0%
+minus 5k
+ 
+
+ align:start position:0%
+minus 5k
+is equal to zero evaluated at k0 which
+
+ align:start position:0%
+is equal to zero evaluated at k0 which
+ 
+
+ align:start position:0%
+is equal to zero evaluated at k0 which
+is where our envelope is sharply peaked
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+this expression is equal to this is
+
+ align:start position:0%
+this expression is equal to this is
+ 
+
+ align:start position:0%
+this expression is equal to this is
+again x
+
+ align:start position:0%
+again x
+ 
+
+ align:start position:0%
+again x
+minus d omega dk that's the classical
+
+ align:start position:0%
+minus d omega dk that's the classical
+ 
+
+ align:start position:0%
+minus d omega dk that's the classical
+velocity v naught t
+
+ align:start position:0%
+velocity v naught t
+ 
+
+ align:start position:0%
+velocity v naught t
+minus
+
+ align:start position:0%
+minus
+ 
+
+ align:start position:0%
+minus
+d phi
+
+ align:start position:0%
+d phi
+ 
+
+ align:start position:0%
+d phi
+d k
+
+ align:start position:0%
+d k
+ 
+
+ align:start position:0%
+d k
+but just as a note d phi
+
+ align:start position:0%
+but just as a note d phi
+ 
+
+ align:start position:0%
+but just as a note d phi
+d k
+
+ align:start position:0%
+d k
+ 
+
+ align:start position:0%
+d k
+is equal to d omega d k
+
+ align:start position:0%
+is equal to d omega d k
+ 
+
+ align:start position:0%
+is equal to d omega d k
+d phi
+
+ align:start position:0%
+d phi
+ 
+
+ align:start position:0%
+d phi
+d omega
+
+ align:start position:0%
+d omega
+ 
+
+ align:start position:0%
+d omega
+but this is equal to this is just the
+
+ align:start position:0%
+but this is equal to this is just the
+ 
+
+ align:start position:0%
+but this is equal to this is just the
+chain rule the omega dk that's the
+
+ align:start position:0%
+chain rule the omega dk that's the
+ 
+
+ align:start position:0%
+chain rule the omega dk that's the
+classical velocity d omega or defined
+
+ align:start position:0%
+classical velocity d omega or defined
+ 
+
+ align:start position:0%
+classical velocity d omega or defined
+the omega
+
+ align:start position:0%
+the omega
+ 
+
+ align:start position:0%
+the omega
+that's d phi
+
+ align:start position:0%
+that's d phi
+ 
+
+ align:start position:0%
+that's d phi
+d e
+
+ align:start position:0%
+d e
+ 
+
+ align:start position:0%
+d e
+times h bar i just multiplied by h bar
+
+ align:start position:0%
+times h bar i just multiplied by h bar
+ 
+
+ align:start position:0%
+times h bar i just multiplied by h bar
+on the top and bottom
+
+ align:start position:0%
+on the top and bottom
+ 
+
+ align:start position:0%
+on the top and bottom
+so this is equal to
+
+ align:start position:0%
+so this is equal to
+ 
+
+ align:start position:0%
+so this is equal to
+x minus v naught
+
+ align:start position:0%
+x minus v naught
+ 
+
+ align:start position:0%
+x minus v naught
+t
+
+ align:start position:0%
+t
+ 
+
+ align:start position:0%
+t
+plus
+
+ align:start position:0%
+plus
+ 
+
+ align:start position:0%
+plus
+h bar
+
+ align:start position:0%
+h bar
+ 
+
+ align:start position:0%
+h bar
+d phi d e
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so first off let's just make sure that
+
+ align:start position:0%
+so first off let's just make sure that
+ 
+
+ align:start position:0%
+so first off let's just make sure that
+the units make sense
+
+ align:start position:0%
+the units make sense
+ 
+
+ align:start position:0%
+the units make sense
+that's a length that's a velocity so
+
+ align:start position:0%
+that's a length that's a velocity so
+ 
+
+ align:start position:0%
+that's a length that's a velocity so
+they said better have units of time time
+
+ align:start position:0%
+they said better have units of time time
+ 
+
+ align:start position:0%
+they said better have units of time time
+that's good so h bar times d phase over
+
+ align:start position:0%
+that's good so h bar times d phase over
+ 
+
+ align:start position:0%
+that's good so h bar times d phase over
+d e well a phase is dimensionless energy
+
+ align:start position:0%
+d e well a phase is dimensionless energy
+ 
+
+ align:start position:0%
+d e well a phase is dimensionless energy
+is units of energy h is energy times
+
+ align:start position:0%
+is units of energy h is energy times
+ 
+
+ align:start position:0%
+is units of energy h is energy times
+time so this dimensionally works out so
+
+ align:start position:0%
+time so this dimensionally works out so
+ 
+
+ align:start position:0%
+time so this dimensionally works out so
+this is zero so the claim is that the
+
+ align:start position:0%
+this is zero so the claim is that the
+ 
+
+ align:start position:0%
+this is zero so the claim is that the
+point of stationary phase has this
+
+ align:start position:0%
+point of stationary phase has this
+ 
+
+ align:start position:0%
+point of stationary phase has this
+derivative equal to zero so setting this
+
+ align:start position:0%
+derivative equal to zero so setting this
+ 
+
+ align:start position:0%
+derivative equal to zero so setting this
+equal to zero tells us that the the peak
+
+ align:start position:0%
+equal to zero tells us that the the peak
+ 
+
+ align:start position:0%
+equal to zero tells us that the the peak
+of the wave function moves
+
+ align:start position:0%
+of the wave function moves
+ 
+
+ align:start position:0%
+of the wave function moves
+according to this equation
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and so now so this is really satisfying
+
+ align:start position:0%
+and so now so this is really satisfying
+ 
+
+ align:start position:0%
+and so now so this is really satisfying
+this should be really satisfying for a
+
+ align:start position:0%
+this should be really satisfying for a
+ 
+
+ align:start position:0%
+this should be really satisfying for a
+couple of reasons first off it tells you
+
+ align:start position:0%
+couple of reasons first off it tells you
+ 
+
+ align:start position:0%
+couple of reasons first off it tells you
+that the peak of the transmitted wave
+
+ align:start position:0%
+that the peak of the transmitted wave
+ 
+
+ align:start position:0%
+that the peak of the transmitted wave
+the peak of the transmitted wave packet
+
+ align:start position:0%
+the peak of the transmitted wave packet
+ 
+
+ align:start position:0%
+the peak of the transmitted wave packet
+not just a plane wave the peak of the
+
+ align:start position:0%
+not just a plane wave the peak of the
+ 
+
+ align:start position:0%
+not just a plane wave the peak of the
+actual wave packet well localized moves
+
+ align:start position:0%
+actual wave packet well localized moves
+ 
+
+ align:start position:0%
+actual wave packet well localized moves
+with overall velocity v naught the
+
+ align:start position:0%
+with overall velocity v naught the
+ 
+
+ align:start position:0%
+with overall velocity v naught the
+constant velocity that we started with
+
+ align:start position:0%
+constant velocity that we started with
+ 
+
+ align:start position:0%
+constant velocity that we started with
+and that's good if it was moving with
+
+ align:start position:0%
+and that's good if it was moving with
+ 
+
+ align:start position:0%
+and that's good if it was moving with
+some other velocity we would have lost
+
+ align:start position:0%
+some other velocity we would have lost
+ 
+
+ align:start position:0%
+some other velocity we would have lost
+energy somehow that would be
+
+ align:start position:0%
+energy somehow that would be
+ 
+
+ align:start position:0%
+energy somehow that would be
+not so sensible
+
+ align:start position:0%
+not so sensible
+ 
+
+ align:start position:0%
+not so sensible
+so this wave packet is moving with an
+
+ align:start position:0%
+so this wave packet is moving with an
+ 
+
+ align:start position:0%
+so this wave packet is moving with an
+overall velocity v naught however
+
+ align:start position:0%
+overall velocity v naught however
+ 
+
+ align:start position:0%
+overall velocity v naught however
+it doesn't
+
+ align:start position:0%
+it doesn't
+ 
+
+ align:start position:0%
+it doesn't
+move
+
+ align:start position:0%
+move
+ 
+
+ align:start position:0%
+move
+uh at the same it doesn't move along
+
+ align:start position:0%
+uh at the same it doesn't move along
+ 
+
+ align:start position:0%
+uh at the same it doesn't move along
+just as the original wave packet's peak
+
+ align:start position:0%
+just as the original wave packet's peak
+ 
+
+ align:start position:0%
+just as the original wave packet's peak
+had
+
+ align:start position:0%
+had
+ 
+
+ align:start position:0%
+had
+it moves as if shifted in time
+
+ align:start position:0%
+it moves as if shifted in time
+ 
+
+ align:start position:0%
+it moves as if shifted in time
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+so the phase and more to the point the
+
+ align:start position:0%
+so the phase and more to the point the
+ 
+
+ align:start position:0%
+so the phase and more to the point the
+gradient of the phase with respect to
+
+ align:start position:0%
+gradient of the phase with respect to
+ 
+
+ align:start position:0%
+gradient of the phase with respect to
+energy the rate of change with energy of
+
+ align:start position:0%
+energy the rate of change with energy of
+ 
+
+ align:start position:0%
+energy the rate of change with energy of
+the phase
+
+ align:start position:0%
+the phase
+ 
+
+ align:start position:0%
+the phase
+times h-bar
+
+ align:start position:0%
+times h-bar
+ 
+
+ align:start position:0%
+times h-bar
+is giving us a phase a shift in the time
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+of where the wave packet is so what does
+
+ align:start position:0%
+of where the wave packet is so what does
+ 
+
+ align:start position:0%
+of where the wave packet is so what does
+that mean
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so let's be precise about this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so let's interpret this
+
+ align:start position:0%
+so let's interpret this
+ 
+
+ align:start position:0%
+so let's interpret this
+and here's the interpretation i want to
+
+ align:start position:0%
+and here's the interpretation i want to
+ 
+
+ align:start position:0%
+and here's the interpretation i want to
+give you
+
+ align:start position:0%
+give you
+ 
+
+ align:start position:0%
+give you
+so in the absence so consider it
+
+ align:start position:0%
+so in the absence so consider it
+ 
+
+ align:start position:0%
+so in the absence so consider it
+classically consider classically the
+
+ align:start position:0%
+classically consider classically the
+ 
+
+ align:start position:0%
+classically consider classically the
+system classically we have
+
+ align:start position:0%
+system classically we have
+ 
+
+ align:start position:0%
+system classically we have
+an object
+
+ align:start position:0%
+an object
+ 
+
+ align:start position:0%
+an object
+with some energy and it comes along it
+
+ align:start position:0%
+with some energy and it comes along it
+ 
+
+ align:start position:0%
+with some energy and it comes along it
+rolls along and it finds a barrier a
+
+ align:start position:0%
+rolls along and it finds a barrier a
+ 
+
+ align:start position:0%
+rolls along and it finds a barrier a
+potential well and what happens when it
+
+ align:start position:0%
+potential well and what happens when it
+ 
+
+ align:start position:0%
+potential well and what happens when it
+gets into the potential well
+
+ align:start position:0%
+gets into the potential well
+ 
+
+ align:start position:0%
+gets into the potential well
+it speeds up
+
+ align:start position:0%
+it speeds up
+ 
+
+ align:start position:0%
+it speeds up
+right because it's got a lot more energy
+
+ align:start position:0%
+right because it's got a lot more energy
+ 
+
+ align:start position:0%
+right because it's got a lot more energy
+relative to the potential so it goes
+
+ align:start position:0%
+relative to the potential so it goes
+ 
+
+ align:start position:0%
+relative to the potential so it goes
+much faster in here and it gets to the
+
+ align:start position:0%
+much faster in here and it gets to the
+ 
+
+ align:start position:0%
+much faster in here and it gets to the
+other side it slows down again
+
+ align:start position:0%
+other side it slows down again
+ 
+
+ align:start position:0%
+other side it slows down again
+so if i had taken a particle with
+
+ align:start position:0%
+so if i had taken a particle with
+ 
+
+ align:start position:0%
+so if i had taken a particle with
+velocity and so let's call this position
+
+ align:start position:0%
+velocity and so let's call this position
+ 
+
+ align:start position:0%
+velocity and so let's call this position
+zero let's say it gets to this wall at
+
+ align:start position:0%
+zero let's say it gets to this wall at
+ 
+
+ align:start position:0%
+zero let's say it gets to this wall at
+time zero so it's moving with x is equal
+
+ align:start position:0%
+time zero so it's moving with x is equal
+ 
+
+ align:start position:0%
+time zero so it's moving with x is equal
+to v naught t
+
+ align:start position:0%
+to v naught t
+ 
+
+ align:start position:0%
+to v naught t
+if there had been no barrier there then
+
+ align:start position:0%
+if there had been no barrier there then
+ 
+
+ align:start position:0%
+if there had been no barrier there then
+at subsequent times it would get out
+
+ align:start position:0%
+at subsequent times it would get out
+ 
+
+ align:start position:0%
+at subsequent times it would get out
+here in a time
+
+ align:start position:0%
+here in a time
+ 
+
+ align:start position:0%
+here in a time
+x that distance over v naught right
+
+ align:start position:0%
+x that distance over v naught right
+ 
+
+ align:start position:0%
+x that distance over v naught right
+however imagine this well was
+
+ align:start position:0%
+however imagine this well was
+ 
+
+ align:start position:0%
+however imagine this well was
+extraordinarily deep
+
+ align:start position:0%
+extraordinarily deep
+ 
+
+ align:start position:0%
+extraordinarily deep
+if this well were extraordinarily deep
+
+ align:start position:0%
+if this well were extraordinarily deep
+ 
+
+ align:start position:0%
+if this well were extraordinarily deep
+what would happen
+
+ align:start position:0%
+what would happen
+ 
+
+ align:start position:0%
+what would happen
+well basically in here its velocity is
+
+ align:start position:0%
+well basically in here its velocity is
+ 
+
+ align:start position:0%
+well basically in here its velocity is
+arbitrarily large
+
+ align:start position:0%
+arbitrarily large
+ 
+
+ align:start position:0%
+arbitrarily large
+and it would just immediately jump
+
+ align:start position:0%
+and it would just immediately jump
+ 
+
+ align:start position:0%
+and it would just immediately jump
+across
+
+ align:start position:0%
+across
+ 
+
+ align:start position:0%
+across
+this well yeah
+
+ align:start position:0%
+this well yeah
+ 
+
+ align:start position:0%
+this well yeah
+so its velocity so this would be a
+
+ align:start position:0%
+so its velocity so this would be a
+ 
+
+ align:start position:0%
+so its velocity so this would be a
+perfectly good description of the of the
+
+ align:start position:0%
+perfectly good description of the of the
+ 
+
+ align:start position:0%
+perfectly good description of the of the
+motion before it gets to the well but
+
+ align:start position:0%
+motion before it gets to the well but
+ 
+
+ align:start position:0%
+motion before it gets to the well but
+after it leaves the well the position is
+
+ align:start position:0%
+after it leaves the well the position is
+ 
+
+ align:start position:0%
+after it leaves the well the position is
+going to be
+
+ align:start position:0%
+going to be
+ 
+
+ align:start position:0%
+going to be
+v naught t
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+plus well what's the time shift it the
+
+ align:start position:0%
+plus well what's the time shift it the
+ 
+
+ align:start position:0%
+plus well what's the time shift it the
+time shift is the time that we didn't
+
+ align:start position:0%
+time shift is the time that we didn't
+ 
+
+ align:start position:0%
+time shift is the time that we didn't
+need to cross this gap
+
+ align:start position:0%
+need to cross this gap
+ 
+
+ align:start position:0%
+need to cross this gap
+and how much would that time have been
+
+ align:start position:0%
+and how much would that time have been
+ 
+
+ align:start position:0%
+and how much would that time have been
+that time would have been well it's the
+
+ align:start position:0%
+that time would have been well it's the
+ 
+
+ align:start position:0%
+that time would have been well it's the
+distance divided by the velocity
+
+ align:start position:0%
+distance divided by the velocity
+ 
+
+ align:start position:0%
+distance divided by the velocity
+right so that's the time we didn't need
+
+ align:start position:0%
+right so that's the time we didn't need
+ 
+
+ align:start position:0%
+right so that's the time we didn't need
+so t plus it moves as if it's at a later
+
+ align:start position:0%
+so t plus it moves as if it's at a later
+ 
+
+ align:start position:0%
+so t plus it moves as if it's at a later
+time t plus l over v naught
+
+ align:start position:0%
+time t plus l over v naught
+ 
+
+ align:start position:0%
+time t plus l over v naught
+cool
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so if we had a really deep well and we
+
+ align:start position:0%
+so if we had a really deep well and we
+ 
+
+ align:start position:0%
+so if we had a really deep well and we
+watched a particle move we would watch
+
+ align:start position:0%
+watched a particle move we would watch
+ 
+
+ align:start position:0%
+watched a particle move we would watch
+it move x naught x is v not t v not t v
+
+ align:start position:0%
+it move x naught x is v not t v not t v
+ 
+
+ align:start position:0%
+it move x naught x is v not t v not t v
+not t v naught t plus l over v v naught
+
+ align:start position:0%
+not t v naught t plus l over v v naught
+ 
+
+ align:start position:0%
+not t v naught t plus l over v v naught
+t plus over v okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so it's the time that we made up by
+
+ align:start position:0%
+so it's the time that we made up by
+ 
+
+ align:start position:0%
+so it's the time that we made up by
+being deep in the well so there's a
+
+ align:start position:0%
+being deep in the well so there's a
+ 
+
+ align:start position:0%
+being deep in the well so there's a
+classical picture because it goes faster
+
+ align:start position:0%
+classical picture because it goes faster
+ 
+
+ align:start position:0%
+classical picture because it goes faster
+inside
+
+ align:start position:0%
+inside
+ 
+
+ align:start position:0%
+inside
+so comparing these
+
+ align:start position:0%
+so comparing these
+ 
+
+ align:start position:0%
+so comparing these
+here we've done a calculation of the
+
+ align:start position:0%
+here we've done a calculation of the
+ 
+
+ align:start position:0%
+here we've done a calculation of the
+time shift due to
+
+ align:start position:0%
+time shift due to
+ 
+
+ align:start position:0%
+time shift due to
+the quantum particle quantum
+
+ align:start position:0%
+the quantum particle quantum
+ 
+
+ align:start position:0%
+the quantum particle quantum
+mechanically
+
+ align:start position:0%
+mechanically
+ 
+
+ align:start position:0%
+mechanically
+transverse transiting the potential well
+
+ align:start position:0%
+transverse transiting the potential well
+ 
+
+ align:start position:0%
+transverse transiting the potential well
+yeah so let's compare these
+
+ align:start position:0%
+yeah so let's compare these
+ 
+
+ align:start position:0%
+yeah so let's compare these
+the classical prediction this says the
+
+ align:start position:0%
+the classical prediction this says the
+ 
+
+ align:start position:0%
+the classical prediction this says the
+classical prediction is um the
+
+ align:start position:0%
+classical prediction is um the
+ 
+
+ align:start position:0%
+classical prediction is um the
+time it took delta t classical
+
+ align:start position:0%
+time it took delta t classical
+ 
+
+ align:start position:0%
+time it took delta t classical
+is equal to l over v naught
+
+ align:start position:0%
+is equal to l over v naught
+ 
+
+ align:start position:0%
+is equal to l over v naught
+and the question is is this the same so
+
+ align:start position:0%
+and the question is is this the same so
+ 
+
+ align:start position:0%
+and the question is is this the same so
+one way to phrase this question is is
+
+ align:start position:0%
+one way to phrase this question is is
+ 
+
+ align:start position:0%
+one way to phrase this question is is
+the same as h bar d phi d e
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+evaluated at uh
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+k naught
+
+ align:start position:0%
+k naught
+ 
+
+ align:start position:0%
+k naught
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+and
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+from our results last time
+
+ align:start position:0%
+from our results last time
+ 
+
+ align:start position:0%
+from our results last time
+for the amplitude c over a
+
+ align:start position:0%
+for the amplitude c over a
+ 
+
+ align:start position:0%
+for the amplitude c over a
+we get that phi
+
+ align:start position:0%
+we get that phi
+ 
+
+ align:start position:0%
+we get that phi
+is equal to which is just the minus the
+
+ align:start position:0%
+is equal to which is just the minus the
+ 
+
+ align:start position:0%
+is equal to which is just the minus the
+uh the argument or the phase of c over a
+
+ align:start position:0%
+uh the argument or the phase of c over a
+ 
+
+ align:start position:0%
+uh the argument or the phase of c over a
+or of the transmission coefficient
+
+ align:start position:0%
+or of the transmission coefficient
+ 
+
+ align:start position:0%
+or of the transmission coefficient
+little transition amplitude little t
+
+ align:start position:0%
+little transition amplitude little t
+ 
+
+ align:start position:0%
+little transition amplitude little t
+phi turns out to be equal to k2 l
+
+ align:start position:0%
+phi turns out to be equal to k2 l
+ 
+
+ align:start position:0%
+phi turns out to be equal to k2 l
+minus arctan
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+of k1 squared plus k2 squared
+
+ align:start position:0%
+of k1 squared plus k2 squared
+ 
+
+ align:start position:0%
+of k1 squared plus k2 squared
+over 2 k1 k2
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+tan
+
+ align:start position:0%
+tan
+ 
+
+ align:start position:0%
+tan
+of k2l okay
+
+ align:start position:0%
+of k2l okay
+ 
+
+ align:start position:0%
+of k2l okay
+i look at this and it doesn't tell me
+
+ align:start position:0%
+i look at this and it doesn't tell me
+ 
+
+ align:start position:0%
+i look at this and it doesn't tell me
+all that much it's a little bit
+
+ align:start position:0%
+all that much it's a little bit
+ 
+
+ align:start position:0%
+all that much it's a little bit
+bewildering so let's unpack this
+
+ align:start position:0%
+bewildering so let's unpack this
+ 
+
+ align:start position:0%
+bewildering so let's unpack this
+what we really want to know is is this
+
+ align:start position:0%
+what we really want to know is is this
+ 
+
+ align:start position:0%
+what we really want to know is is this
+close to the classical result
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+here's a quick way to check
+
+ align:start position:0%
+here's a quick way to check
+ 
+
+ align:start position:0%
+here's a quick way to check
+this is we know this expression is going
+
+ align:start position:0%
+this is we know this expression is going
+ 
+
+ align:start position:0%
+this is we know this expression is going
+to simplify near resonance where the
+
+ align:start position:0%
+to simplify near resonance where the
+ 
+
+ align:start position:0%
+to simplify near resonance where the
+sign vanishes so let's look just for
+
+ align:start position:0%
+sign vanishes so let's look just for
+ 
+
+ align:start position:0%
+sign vanishes so let's look just for
+simplicity near the resonance
+
+ align:start position:0%
+simplicity near the resonance
+ 
+
+ align:start position:0%
+simplicity near the resonance
+and in particular let's look near the
+
+ align:start position:0%
+and in particular let's look near the
+ 
+
+ align:start position:0%
+and in particular let's look near the
+resonance k2 l
+
+ align:start position:0%
+resonance k2 l
+ 
+
+ align:start position:0%
+resonance k2 l
+is equal to n pi
+
+ align:start position:0%
+is equal to n pi
+ 
+
+ align:start position:0%
+is equal to n pi
+then it turns out that a quick
+
+ align:start position:0%
+then it turns out that a quick
+ 
+
+ align:start position:0%
+then it turns out that a quick
+calculation gives you that h bar d phi d
+
+ align:start position:0%
+calculation gives you that h bar d phi d
+ 
+
+ align:start position:0%
+calculation gives you that h bar d phi d
+e
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+at this value of k at that value of the
+
+ align:start position:0%
+at this value of k at that value of the
+ 
+
+ align:start position:0%
+at this value of k at that value of the
+energy
+
+ align:start position:0%
+energy
+ 
+
+ align:start position:0%
+energy
+goes as l
+
+ align:start position:0%
+goes as l
+ 
+
+ align:start position:0%
+goes as l
+over 2 v naught times 1 plus whoops 1
+
+ align:start position:0%
+over 2 v naught times 1 plus whoops 1
+ 
+
+ align:start position:0%
+over 2 v naught times 1 plus whoops 1
+plus
+
+ align:start position:0%
+plus
+ 
+
+ align:start position:0%
+plus
+the energy
+
+ align:start position:0%
+the energy
+ 
+
+ align:start position:0%
+the energy
+over the depth of the well v naught now
+
+ align:start position:0%
+over the depth of the well v naught now
+ 
+
+ align:start position:0%
+over the depth of the well v naught now
+remember the classical approximation was
+
+ align:start position:0%
+remember the classical approximation was
+ 
+
+ align:start position:0%
+remember the classical approximation was
+l over v naught we just did this very
+
+ align:start position:0%
+l over v naught we just did this very
+ 
+
+ align:start position:0%
+l over v naught we just did this very
+quickly we did it assuming an
+
+ align:start position:0%
+quickly we did it assuming an
+ 
+
+ align:start position:0%
+quickly we did it assuming an
+arbitrarily deep well so v naught is
+
+ align:start position:0%
+arbitrarily deep well so v naught is
+ 
+
+ align:start position:0%
+arbitrarily deep well so v naught is
+arbitrarily larger in magnitude than e
+
+ align:start position:0%
+arbitrarily larger in magnitude than e
+ 
+
+ align:start position:0%
+arbitrarily larger in magnitude than e
+so this term is negligible so where we
+
+ align:start position:0%
+so this term is negligible so where we
+ 
+
+ align:start position:0%
+so this term is negligible so where we
+should compare that very simple naive
+
+ align:start position:0%
+should compare that very simple naive
+ 
+
+ align:start position:0%
+should compare that very simple naive
+classical result is here l over two v
+
+ align:start position:0%
+classical result is here l over two v
+ 
+
+ align:start position:0%
+classical result is here l over two v
+naught and what we see is that the
+
+ align:start position:0%
+naught and what we see is that the
+ 
+
+ align:start position:0%
+naught and what we see is that the
+quantum mechanical result
+
+ align:start position:0%
+quantum mechanical result
+ 
+
+ align:start position:0%
+quantum mechanical result
+gives a time shift which is down by a
+
+ align:start position:0%
+gives a time shift which is down by a
+ 
+
+ align:start position:0%
+gives a time shift which is down by a
+factor of two
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+so what's going on well apparently the
+
+ align:start position:0%
+so what's going on well apparently the
+ 
+
+ align:start position:0%
+so what's going on well apparently the
+things slowed down inside
+
+ align:start position:0%
+things slowed down inside
+ 
+
+ align:start position:0%
+things slowed down inside
+the time the time that it's that it took
+
+ align:start position:0%
+the time the time that it's that it took
+ 
+
+ align:start position:0%
+the time the time that it's that it took
+us to cross was greater than you would
+
+ align:start position:0%
+us to cross was greater than you would
+ 
+
+ align:start position:0%
+us to cross was greater than you would
+have naively guessed by making it
+
+ align:start position:0%
+have naively guessed by making it
+ 
+
+ align:start position:0%
+have naively guessed by making it
+arbitrarily deep
+
+ align:start position:0%
+arbitrarily deep
+ 
+
+ align:start position:0%
+arbitrarily deep
+and we can
+
+ align:start position:0%
+and we can
+ 
+
+ align:start position:0%
+and we can
+make that a little more sharp by
+
+ align:start position:0%
+make that a little more sharp by
+ 
+
+ align:start position:0%
+make that a little more sharp by
+plotting as a function of e
+
+ align:start position:0%
+plotting as a function of e
+ 
+
+ align:start position:0%
+plotting as a function of e
+over v naught
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the uh the actual phase shift so the
+
+ align:start position:0%
+the uh the actual phase shift so the
+ 
+
+ align:start position:0%
+the uh the actual phase shift so the
+classical prediction if you do better
+
+ align:start position:0%
+classical prediction if you do better
+ 
+
+ align:start position:0%
+classical prediction if you do better
+job than saying it's infinitely deep the
+
+ align:start position:0%
+job than saying it's infinitely deep the
+ 
+
+ align:start position:0%
+job than saying it's infinitely deep the
+classical prediction looks something
+
+ align:start position:0%
+classical prediction looks something
+ 
+
+ align:start position:0%
+classical prediction looks something
+like this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay and this is for
+
+ align:start position:0%
+okay and this is for
+ 
+
+ align:start position:0%
+okay and this is for
+delta t
+
+ align:start position:0%
+delta t
+ 
+
+ align:start position:0%
+delta t
+the time shift classical
+
+ align:start position:0%
+the time shift classical
+ 
+
+ align:start position:0%
+the time shift classical
+when you look at the correct quantum
+
+ align:start position:0%
+when you look at the correct quantum
+ 
+
+ align:start position:0%
+when you look at the correct quantum
+mechanical result here's what you find
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+oops
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+where
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+difference is a factor of two
+
+ align:start position:0%
+difference is a factor of two
+ 
+
+ align:start position:0%
+difference is a factor of two
+one-half the height down and again
+
+ align:start position:0%
+one-half the height down and again
+ 
+
+ align:start position:0%
+one-half the height down and again
+one-half a height down so this is that
+
+ align:start position:0%
+one-half a height down so this is that
+ 
+
+ align:start position:0%
+one-half a height down so this is that
+factor of two downstairs
+
+ align:start position:0%
+factor of two downstairs
+ 
+
+ align:start position:0%
+factor of two downstairs
+so the wave packet goes actually a
+
+ align:start position:0%
+so the wave packet goes actually a
+ 
+
+ align:start position:0%
+so the wave packet goes actually a
+little bit faster than it would than the
+
+ align:start position:0%
+little bit faster than it would than the
+ 
+
+ align:start position:0%
+little bit faster than it would than the
+classical prediction would guess except
+
+ align:start position:0%
+classical prediction would guess except
+ 
+
+ align:start position:0%
+classical prediction would guess except
+near resonance and these are at the
+
+ align:start position:0%
+near resonance and these are at the
+ 
+
+ align:start position:0%
+near resonance and these are at the
+resonant values of the momentum
+
+ align:start position:0%
+resonant values of the momentum
+ 
+
+ align:start position:0%
+resonant values of the momentum
+at the resonant values of the momentum
+
+ align:start position:0%
+at the resonant values of the momentum
+ 
+
+ align:start position:0%
+at the resonant values of the momentum
+it takes much longer to get across
+
+ align:start position:0%
+it takes much longer to get across
+ 
+
+ align:start position:0%
+it takes much longer to get across
+instead of going a little bit faster
+
+ align:start position:0%
+instead of going a little bit faster
+ 
+
+ align:start position:0%
+instead of going a little bit faster
+than the classic result it goes a factor
+
+ align:start position:0%
+than the classic result it goes a factor
+ 
+
+ align:start position:0%
+than the classic result it goes a factor
+of two slower than the classical result
+
+ align:start position:0%
+of two slower than the classical result
+ 
+
+ align:start position:0%
+of two slower than the classical result
+and so now i ask you the question why is
+
+ align:start position:0%
+and so now i ask you the question why is
+ 
+
+ align:start position:0%
+and so now i ask you the question why is
+it going more slowly why does it spend
+
+ align:start position:0%
+it going more slowly why does it spend
+ 
+
+ align:start position:0%
+it going more slowly why does it spend
+so much more time inside the well
+
+ align:start position:0%
+so much more time inside the well
+ 
+
+ align:start position:0%
+so much more time inside the well
+quantum mechanically than it would have
+
+ align:start position:0%
+quantum mechanically than it would have
+ 
+
+ align:start position:0%
+quantum mechanically than it would have
+classically
+
+ align:start position:0%
+classically
+ 
+
+ align:start position:0%
+classically
+why is the particle effectively taking
+
+ align:start position:0%
+why is the particle effectively taking
+ 
+
+ align:start position:0%
+why is the particle effectively taking
+so much longer to transit the well near
+
+ align:start position:0%
+so much longer to transit the well near
+ 
+
+ align:start position:0%
+so much longer to transit the well near
+resonance
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah exactly so the classical particle
+
+ align:start position:0%
+yeah exactly so the classical particle
+ 
+
+ align:start position:0%
+yeah exactly so the classical particle
+just goes across the quantum mechanical
+
+ align:start position:0%
+just goes across the quantum mechanical
+ 
+
+ align:start position:0%
+just goes across the quantum mechanical
+particle has a superposition of
+
+ align:start position:0%
+particle has a superposition of
+ 
+
+ align:start position:0%
+particle has a superposition of
+contributions to its amplitude where it
+
+ align:start position:0%
+contributions to its amplitude where it
+ 
+
+ align:start position:0%
+contributions to its amplitude where it
+transits
+
+ align:start position:0%
+transits
+ 
+
+ align:start position:0%
+transits
+transit bounce bounce transit transit
+
+ align:start position:0%
+transit bounce bounce transit transit
+ 
+
+ align:start position:0%
+transit bounce bounce transit transit
+bounce bounce bounce bounce transit
+
+ align:start position:0%
+bounce bounce bounce bounce transit
+ 
+
+ align:start position:0%
+bounce bounce bounce bounce transit
+and now you can ask how much time was
+
+ align:start position:0%
+and now you can ask how much time was
+ 
+
+ align:start position:0%
+and now you can ask how much time was
+spent by each of those imaginary
+
+ align:start position:0%
+spent by each of those imaginary
+ 
+
+ align:start position:0%
+spent by each of those imaginary
+particles imaginarily moving across
+
+ align:start position:0%
+particles imaginarily moving across
+ 
+
+ align:start position:0%
+particles imaginarily moving across
+and if you're careful about how you set
+
+ align:start position:0%
+and if you're careful about how you set
+ 
+
+ align:start position:0%
+and if you're careful about how you set
+up that question you can recover this
+
+ align:start position:0%
+up that question you can recover this
+ 
+
+ align:start position:0%
+up that question you can recover this
+factor of two
+
+ align:start position:0%
+factor of two
+ 
+
+ align:start position:0%
+factor of two
+which is kind of beautiful
+
+ align:start position:0%
+which is kind of beautiful
+ 
+
+ align:start position:0%
+which is kind of beautiful
+but the important thing here is when
+
+ align:start position:0%
+but the important thing here is when
+ 
+
+ align:start position:0%
+but the important thing here is when
+you're hitting resonance the multiple
+
+ align:start position:0%
+you're hitting resonance the multiple
+ 
+
+ align:start position:0%
+you're hitting resonance the multiple
+scattering processes are important
+
+ align:start position:0%
+scattering processes are important
+ 
+
+ align:start position:0%
+scattering processes are important
+they're not canceling out they're not at
+
+ align:start position:0%
+they're not canceling out they're not at
+ 
+
+ align:start position:0%
+they're not canceling out they're not at
+random phase they're not interfering
+
+ align:start position:0%
+random phase they're not interfering
+ 
+
+ align:start position:0%
+random phase they're not interfering
+destructively with each other they're
+
+ align:start position:0%
+destructively with each other they're
+ 
+
+ align:start position:0%
+destructively with each other they're
+interfering constructively and you get
+
+ align:start position:0%
+interfering constructively and you get
+ 
+
+ align:start position:0%
+interfering constructively and you get
+perfect transmission precisely because
+
+ align:start position:0%
+perfect transmission precisely because
+ 
+
+ align:start position:0%
+perfect transmission precisely because
+of the
+
+ align:start position:0%
+of the
+ 
+
+ align:start position:0%
+of the
+constructive interference of an infinite
+
+ align:start position:0%
+constructive interference of an infinite
+ 
+
+ align:start position:0%
+constructive interference of an infinite
+number of contributions to the quantum
+
+ align:start position:0%
+number of contributions to the quantum
+ 
+
+ align:start position:0%
+number of contributions to the quantum
+mechanical amplitude okay and this is
+
+ align:start position:0%
+mechanical amplitude okay and this is
+ 
+
+ align:start position:0%
+mechanical amplitude okay and this is
+again we're seeing the same thing in
+
+ align:start position:0%
+again we're seeing the same thing in
+ 
+
+ align:start position:0%
+again we're seeing the same thing in
+this annoying slowdown
+
+ align:start position:0%
+this annoying slowdown
+ 
+
+ align:start position:0%
+this annoying slowdown
+and this tells us another thing though
+
+ align:start position:0%
+and this tells us another thing though
+ 
+
+ align:start position:0%
+and this tells us another thing though
+which is that the phase the scattering
+
+ align:start position:0%
+which is that the phase the scattering
+ 
+
+ align:start position:0%
+which is that the phase the scattering
+phase the phase in the transmission
+
+ align:start position:0%
+phase the phase in the transmission
+ 
+
+ align:start position:0%
+phase the phase in the transmission
+amplitude
+
+ align:start position:0%
+amplitude
+ 
+
+ align:start position:0%
+amplitude
+contains an awful lot of the physics of
+
+ align:start position:0%
+contains an awful lot of the physics of
+ 
+
+ align:start position:0%
+contains an awful lot of the physics of
+the system it's telling us about
+
+ align:start position:0%
+the system it's telling us about
+ 
+
+ align:start position:0%
+the system it's telling us about
+how long it takes for the wave packet to
+
+ align:start position:0%
+how long it takes for the wave packet to
+ 
+
+ align:start position:0%
+how long it takes for the wave packet to
+transit across the potential effectively
+
+ align:start position:0%
+transit across the potential effectively
+ 
+
+ align:start position:0%
+transit across the potential effectively
+yeah
+
+ align:start position:0%
+yeah
+ 
+
+ align:start position:0%
+yeah
+sorry the vertical axis here is the time
+
+ align:start position:0%
+sorry the vertical axis here is the time
+ 
+
+ align:start position:0%
+sorry the vertical axis here is the time
+that it takes the the shift in the time
+
+ align:start position:0%
+that it takes the the shift in the time
+ 
+
+ align:start position:0%
+that it takes the the shift in the time
+due to the fact that it went across this
+
+ align:start position:0%
+due to the fact that it went across this
+ 
+
+ align:start position:0%
+due to the fact that it went across this
+well and went a little bit faster inside
+
+ align:start position:0%
+well and went a little bit faster inside
+ 
+
+ align:start position:0%
+well and went a little bit faster inside
+okay so empirically what it means is
+
+ align:start position:0%
+okay so empirically what it means is
+ 
+
+ align:start position:0%
+okay so empirically what it means is
+when you get out very far away
+
+ align:start position:0%
+when you get out very far away
+ 
+
+ align:start position:0%
+when you get out very far away
+and you watch the velocity the motion of
+
+ align:start position:0%
+and you watch the velocity the motion of
+ 
+
+ align:start position:0%
+and you watch the velocity the motion of
+the wave packet and you ask how long has
+
+ align:start position:0%
+the wave packet and you ask how long has
+ 
+
+ align:start position:0%
+the wave packet and you ask how long has
+it been since it
+
+ align:start position:0%
+it been since it
+ 
+
+ align:start position:0%
+it been since it
+got to the barrier in the first place it
+
+ align:start position:0%
+got to the barrier in the first place it
+ 
+
+ align:start position:0%
+got to the barrier in the first place it
+took less time than you would have
+
+ align:start position:0%
+took less time than you would have
+ 
+
+ align:start position:0%
+took less time than you would have
+guessed by knowing that its velocity is
+
+ align:start position:0%
+guessed by knowing that its velocity is
+ 
+
+ align:start position:0%
+guessed by knowing that its velocity is
+v naught and the amount of time less is
+
+ align:start position:0%
+v naught and the amount of time less is
+ 
+
+ align:start position:0%
+v naught and the amount of time less is
+this much time
+
+ align:start position:0%
+this much time
+ 
+
+ align:start position:0%
+this much time
+that answer your question good
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+of uh one yeah
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+it bounces around twice
+
+ align:start position:0%
+it bounces around twice
+ 
+
+ align:start position:0%
+it bounces around twice
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+uh so so the the classical amplitude is
+
+ align:start position:0%
+uh so so the the classical amplitude is
+ 
+
+ align:start position:0%
+uh so so the the classical amplitude is
+so when we compare the classical length
+
+ align:start position:0%
+so when we compare the classical length
+ 
+
+ align:start position:0%
+so when we compare the classical length
+to the limit that v naught goes to
+
+ align:start position:0%
+to the limit that v naught goes to
+ 
+
+ align:start position:0%
+to the limit that v naught goes to
+infinity
+
+ align:start position:0%
+infinity
+ 
+
+ align:start position:0%
+infinity
+so the the comparison is just a factor
+
+ align:start position:0%
+so the the comparison is just a factor
+ 
+
+ align:start position:0%
+so the the comparison is just a factor
+of two
+
+ align:start position:0%
+of two
+ 
+
+ align:start position:0%
+of two
+okay it's more complicated out here and
+
+ align:start position:0%
+okay it's more complicated out here and
+ 
+
+ align:start position:0%
+okay it's more complicated out here and
+i guess it's not it's it in the limit
+
+ align:start position:0%
+i guess it's not it's it in the limit
+ 
+
+ align:start position:0%
+i guess it's not it's it in the limit
+that v naught is large this is exactly
+
+ align:start position:0%
+that v naught is large this is exactly
+ 
+
+ align:start position:0%
+that v naught is large this is exactly
+one half
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+well it's got the yeah it's got the the
+
+ align:start position:0%
+well it's got the yeah it's got the the
+ 
+
+ align:start position:0%
+well it's got the yeah it's got the the
+resonances are leading to this extra
+
+ align:start position:0%
+resonances are leading to this extra
+ 
+
+ align:start position:0%
+resonances are leading to this extra
+factor of one half um and so as you i i
+
+ align:start position:0%
+factor of one half um and so as you i i
+ 
+
+ align:start position:0%
+factor of one half um and so as you i i
+don't i have to say i don't remember
+
+ align:start position:0%
+don't i have to say i don't remember
+ 
+
+ align:start position:0%
+don't i have to say i don't remember
+exactly whether as you um include the
+
+ align:start position:0%
+exactly whether as you um include the
+ 
+
+ align:start position:0%
+exactly whether as you um include the
+the subleading terms of one over v
+
+ align:start position:0%
+the subleading terms of one over v
+ 
+
+ align:start position:0%
+the subleading terms of one over v
+naught whether it stays one half or
+
+ align:start position:0%
+naught whether it stays one half or
+ 
+
+ align:start position:0%
+naught whether it stays one half or
+whether it doesn't but in the limit that
+
+ align:start position:0%
+whether it doesn't but in the limit that
+ 
+
+ align:start position:0%
+whether it doesn't but in the limit that
+v naught is large it remains either
+
+ align:start position:0%
+v naught is large it remains either
+ 
+
+ align:start position:0%
+v naught is large it remains either
+close to one half or exactly one if i
+
+ align:start position:0%
+close to one half or exactly one if i
+ 
+
+ align:start position:0%
+close to one half or exactly one if i
+just don't remember exactly the
+
+ align:start position:0%
+just don't remember exactly the
+ 
+
+ align:start position:0%
+just don't remember exactly the
+important thing is that there's a sharp
+
+ align:start position:0%
+important thing is that there's a sharp
+ 
+
+ align:start position:0%
+important thing is that there's a sharp
+dip
+
+ align:start position:0%
+dip
+ 
+
+ align:start position:0%
+dip
+it takes much longer to transit and so
+
+ align:start position:0%
+it takes much longer to transit and so
+ 
+
+ align:start position:0%
+it takes much longer to transit and so
+you get less
+
+ align:start position:0%
+you get less
+ 
+
+ align:start position:0%
+you get less
+bonus time as it were
+
+ align:start position:0%
+bonus time as it were
+ 
+
+ align:start position:0%
+bonus time as it were
+uh you've you've gained less time in the
+
+ align:start position:0%
+uh you've you've gained less time in the
+ 
+
+ align:start position:0%
+uh you've you've gained less time in the
+quantum mechanical model than the
+
+ align:start position:0%
+quantum mechanical model than the
+ 
+
+ align:start position:0%
+quantum mechanical model than the
+classical model
+
+ align:start position:0%
+classical model
+ 
+
+ align:start position:0%
+classical model
+and when you do the experiment you get
+
+ align:start position:0%
+and when you do the experiment you get
+ 
+
+ align:start position:0%
+and when you do the experiment you get
+the quantum result right so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that's uh that's the crucial point
+
+ align:start position:0%
+that's uh that's the crucial point
+ 
+
+ align:start position:0%
+that's uh that's the crucial point
+other questions
+
+ align:start position:0%
+other questions
+ 
+
+ align:start position:0%
+other questions
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+so the phase contains an awful lot of
+
+ align:start position:0%
+so the phase contains an awful lot of
+ 
+
+ align:start position:0%
+so the phase contains an awful lot of
+the physics
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so i want to generalize this whole story
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+in a very particular way
+
+ align:start position:0%
+in a very particular way
+ 
+
+ align:start position:0%
+in a very particular way
+and this way of reorganizing the
+
+ align:start position:0%
+and this way of reorganizing the
+ 
+
+ align:start position:0%
+and this way of reorganizing the
+scattering in 1d so what we're doing
+
+ align:start position:0%
+scattering in 1d so what we're doing
+ 
+
+ align:start position:0%
+scattering in 1d so what we're doing
+right now is we're studying scattering
+
+ align:start position:0%
+right now is we're studying scattering
+ 
+
+ align:start position:0%
+right now is we're studying scattering
+problems in one dimension but we live in
+
+ align:start position:0%
+problems in one dimension but we live in
+ 
+
+ align:start position:0%
+problems in one dimension but we live in
+three dimensions the story's going to be
+
+ align:start position:0%
+three dimensions the story's going to be
+ 
+
+ align:start position:0%
+three dimensions the story's going to be
+more complicated in three dimensions
+
+ align:start position:0%
+more complicated in three dimensions
+ 
+
+ align:start position:0%
+more complicated in three dimensions
+it's going to be more complicated in two
+
+ align:start position:0%
+it's going to be more complicated in two
+ 
+
+ align:start position:0%
+it's going to be more complicated in two
+dimensions but the basic ideas are all
+
+ align:start position:0%
+dimensions but the basic ideas are all
+ 
+
+ align:start position:0%
+dimensions but the basic ideas are all
+the same
+
+ align:start position:0%
+the same
+ 
+
+ align:start position:0%
+the same
+it's just the details are going to be
+
+ align:start position:0%
+it's just the details are going to be
+ 
+
+ align:start position:0%
+it's just the details are going to be
+different and one thing that turns out
+
+ align:start position:0%
+different and one thing that turns out
+ 
+
+ align:start position:0%
+different and one thing that turns out
+to be very useful in organizing
+
+ align:start position:0%
+to be very useful in organizing
+ 
+
+ align:start position:0%
+to be very useful in organizing
+scattering both in
+
+ align:start position:0%
+scattering both in
+ 
+
+ align:start position:0%
+scattering both in
+in one dimension and in three dimensions
+
+ align:start position:0%
+in one dimension and in three dimensions
+ 
+
+ align:start position:0%
+in one dimension and in three dimensions
+something called the scattering matrix
+
+ align:start position:0%
+something called the scattering matrix
+ 
+
+ align:start position:0%
+something called the scattering matrix
+and i'm going to talk about that now
+
+ align:start position:0%
+and i'm going to talk about that now
+ 
+
+ align:start position:0%
+and i'm going to talk about that now
+in three dimensions it's almost i mean
+
+ align:start position:0%
+in three dimensions it's almost i mean
+ 
+
+ align:start position:0%
+in three dimensions it's almost i mean
+it's essential
+
+ align:start position:0%
+it's essential
+ 
+
+ align:start position:0%
+it's essential
+but even in one dimensions where it's
+
+ align:start position:0%
+but even in one dimensions where it's
+ 
+
+ align:start position:0%
+but even in one dimensions where it's
+usually not used it's a very powerful
+
+ align:start position:0%
+usually not used it's a very powerful
+ 
+
+ align:start position:0%
+usually not used it's a very powerful
+way to organize our knowledge of the
+
+ align:start position:0%
+way to organize our knowledge of the
+ 
+
+ align:start position:0%
+way to organize our knowledge of the
+system as encoded by the scattering data
+
+ align:start position:0%
+system as encoded by the scattering data
+ 
+
+ align:start position:0%
+system as encoded by the scattering data
+so here's the basic idea
+
+ align:start position:0%
+so here's the basic idea
+ 
+
+ align:start position:0%
+so here's the basic idea
+as we discussed before what we really
+
+ align:start position:0%
+as we discussed before what we really
+ 
+
+ align:start position:0%
+as we discussed before what we really
+want to do in the ideal world is take
+
+ align:start position:0%
+want to do in the ideal world is take
+ 
+
+ align:start position:0%
+want to do in the ideal world is take
+some unknown potential in some bounded
+
+ align:start position:0%
+some unknown potential in some bounded
+ 
+
+ align:start position:0%
+some unknown potential in some bounded
+region
+
+ align:start position:0%
+region
+ 
+
+ align:start position:0%
+region
+some region and outside we have the
+
+ align:start position:0%
+some region and outside we have the
+ 
+
+ align:start position:0%
+some region and outside we have the
+potential is constant
+
+ align:start position:0%
+potential is constant
+ 
+
+ align:start position:0%
+potential is constant
+modula my bad artistic skills so
+
+ align:start position:0%
+modula my bad artistic skills so
+ 
+
+ align:start position:0%
+modula my bad artistic skills so
+potential is constant out here
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and the potential could be some horrible
+
+ align:start position:0%
+and the potential could be some horrible
+ 
+
+ align:start position:0%
+and the potential could be some horrible
+thing in here that we don't happen to
+
+ align:start position:0%
+thing in here that we don't happen to
+ 
+
+ align:start position:0%
+thing in here that we don't happen to
+know and we want to read off of the
+
+ align:start position:0%
+know and we want to read off of the
+ 
+
+ align:start position:0%
+know and we want to read off of the
+scattering process we want to be able to
+
+ align:start position:0%
+scattering process we want to be able to
+ 
+
+ align:start position:0%
+scattering process we want to be able to
+do something about the potential so for
+
+ align:start position:0%
+do something about the potential so for
+ 
+
+ align:start position:0%
+do something about the potential so for
+example we can deduce the um the uh the
+
+ align:start position:0%
+example we can deduce the um the uh the
+ 
+
+ align:start position:0%
+example we can deduce the um the uh the
+energy of our step
+
+ align:start position:0%
+energy of our step
+ 
+
+ align:start position:0%
+energy of our step
+um or
+
+ align:start position:0%
+um or
+ 
+
+ align:start position:0%
+um or
+we can deduce the energy by looking so
+
+ align:start position:0%
+we can deduce the energy by looking so
+ 
+
+ align:start position:0%
+we can deduce the energy by looking so
+good we can reduce the energy by looking
+
+ align:start position:0%
+good we can reduce the energy by looking
+ 
+
+ align:start position:0%
+good we can reduce the energy by looking
+at the um
+
+ align:start position:0%
+at the um
+ 
+
+ align:start position:0%
+at the um
+the position of the barriers and we can
+
+ align:start position:0%
+the position of the barriers and we can
+ 
+
+ align:start position:0%
+the position of the barriers and we can
+disentangle the position of the energy
+
+ align:start position:0%
+disentangle the position of the energy
+ 
+
+ align:start position:0%
+disentangle the position of the energy
+and the uh the width the depth and the
+
+ align:start position:0%
+and the uh the width the depth and the
+ 
+
+ align:start position:0%
+and the uh the width the depth and the
+width by looking at the phase shift by
+
+ align:start position:0%
+width by looking at the phase shift by
+ 
+
+ align:start position:0%
+width by looking at the phase shift by
+looking at the time delay so we can
+
+ align:start position:0%
+looking at the time delay so we can
+ 
+
+ align:start position:0%
+looking at the time delay so we can
+deduce all the parameters of our
+
+ align:start position:0%
+deduce all the parameters of our
+ 
+
+ align:start position:0%
+deduce all the parameters of our
+potential by looking at the resonance
+
+ align:start position:0%
+potential by looking at the resonance
+ 
+
+ align:start position:0%
+potential by looking at the resonance
+points and the phase shifts i want to do
+
+ align:start position:0%
+points and the phase shifts i want to do
+ 
+
+ align:start position:0%
+points and the phase shifts i want to do
+this more generally for a general
+
+ align:start position:0%
+this more generally for a general
+ 
+
+ align:start position:0%
+this more generally for a general
+potential
+
+ align:start position:0%
+potential
+ 
+
+ align:start position:0%
+potential
+and to set that up we need to be a bit
+
+ align:start position:0%
+and to set that up we need to be a bit
+ 
+
+ align:start position:0%
+and to set that up we need to be a bit
+more general than than we've been
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+so in general if we solve this potential
+
+ align:start position:0%
+so in general if we solve this potential
+ 
+
+ align:start position:0%
+so in general if we solve this potential
+as we talked about before we have a and
+
+ align:start position:0%
+as we talked about before we have a and
+ 
+
+ align:start position:0%
+as we talked about before we have a and
+d oh sorry a plus b
+
+ align:start position:0%
+d oh sorry a plus b
+ 
+
+ align:start position:0%
+d oh sorry a plus b
+i e to the i k x
+
+ align:start position:0%
+i e to the i k x
+ 
+
+ align:start position:0%
+i e to the i k x
+minus i k x out here
+
+ align:start position:0%
+minus i k x out here
+ 
+
+ align:start position:0%
+minus i k x out here
+and out here we have c e to the i k x
+
+ align:start position:0%
+and out here we have c e to the i k x
+ 
+
+ align:start position:0%
+and out here we have c e to the i k x
+and d e to the minus sign
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and i'm not going to ask what happens
+
+ align:start position:0%
+and i'm not going to ask what happens
+ 
+
+ align:start position:0%
+and i'm not going to ask what happens
+inside
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+now we can do as discuss two kinds of
+
+ align:start position:0%
+now we can do as discuss two kinds of
+ 
+
+ align:start position:0%
+now we can do as discuss two kinds of
+scattering experiments we can send
+
+ align:start position:0%
+scattering experiments we can send
+ 
+
+ align:start position:0%
+scattering experiments we can send
+things in from the left in which case a
+
+ align:start position:0%
+things in from the left in which case a
+ 
+
+ align:start position:0%
+things in from the left in which case a
+is non-zero and then things can either
+
+ align:start position:0%
+is non-zero and then things can either
+ 
+
+ align:start position:0%
+is non-zero and then things can either
+transmit or reflect but nothing's going
+
+ align:start position:0%
+transmit or reflect but nothing's going
+ 
+
+ align:start position:0%
+transmit or reflect but nothing's going
+to come in from infinity so d is zero or
+
+ align:start position:0%
+to come in from infinity so d is zero or
+ 
+
+ align:start position:0%
+to come in from infinity so d is zero or
+we could do the same in reverse send
+
+ align:start position:0%
+we could do the same in reverse send
+ 
+
+ align:start position:0%
+we could do the same in reverse send
+things in from here and that corresponds
+
+ align:start position:0%
+things in from here and that corresponds
+ 
+
+ align:start position:0%
+things in from here and that corresponds
+to a zero nothing coming in this way
+
+ align:start position:0%
+to a zero nothing coming in this way
+ 
+
+ align:start position:0%
+to a zero nothing coming in this way
+but d non-zero
+
+ align:start position:0%
+but d non-zero
+ 
+
+ align:start position:0%
+but d non-zero
+and more generally we can ask the
+
+ align:start position:0%
+and more generally we can ask the
+ 
+
+ align:start position:0%
+and more generally we can ask the
+following question look suppose i send
+
+ align:start position:0%
+following question look suppose i send
+ 
+
+ align:start position:0%
+following question look suppose i send
+some amount of stuff in from the left
+
+ align:start position:0%
+some amount of stuff in from the left
+ 
+
+ align:start position:0%
+some amount of stuff in from the left
+and i send some amount of stuff in from
+
+ align:start position:0%
+and i send some amount of stuff in from
+ 
+
+ align:start position:0%
+and i send some amount of stuff in from
+the right d
+
+ align:start position:0%
+the right d
+ 
+
+ align:start position:0%
+the right d
+then that will tell me how much stuff
+
+ align:start position:0%
+then that will tell me how much stuff
+ 
+
+ align:start position:0%
+then that will tell me how much stuff
+will be going out to the right and how
+
+ align:start position:0%
+will be going out to the right and how
+ 
+
+ align:start position:0%
+will be going out to the right and how
+much stuff will be going out to the left
+
+ align:start position:0%
+much stuff will be going out to the left
+ 
+
+ align:start position:0%
+much stuff will be going out to the left
+yeah
+
+ align:start position:0%
+yeah
+ 
+
+ align:start position:0%
+yeah
+if you tell me how much is coming in i
+
+ align:start position:0%
+if you tell me how much is coming in i
+ 
+
+ align:start position:0%
+if you tell me how much is coming in i
+will tell you how much is coming out
+
+ align:start position:0%
+will tell you how much is coming out
+ 
+
+ align:start position:0%
+will tell you how much is coming out
+bc
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so if you could solve this problem
+
+ align:start position:0%
+so if you could solve this problem
+ 
+
+ align:start position:0%
+so if you could solve this problem
+the answer is just some relation some
+
+ align:start position:0%
+the answer is just some relation some
+ 
+
+ align:start position:0%
+the answer is just some relation some
+pair of linear relations between these
+
+ align:start position:0%
+pair of linear relations between these
+ 
+
+ align:start position:0%
+pair of linear relations between these
+and we can write this as a matrix which
+
+ align:start position:0%
+and we can write this as a matrix which
+ 
+
+ align:start position:0%
+and we can write this as a matrix which
+i will call s11 s12 s21
+
+ align:start position:0%
+i will call s11 s12 s21
+ 
+
+ align:start position:0%
+i will call s11 s12 s21
+s22
+
+ align:start position:0%
+s22
+ 
+
+ align:start position:0%
+s22
+okay what this matrix is doing is it
+
+ align:start position:0%
+okay what this matrix is doing is it
+ 
+
+ align:start position:0%
+okay what this matrix is doing is it
+takes the amplitude you're sending in
+
+ align:start position:0%
+takes the amplitude you're sending in
+ 
+
+ align:start position:0%
+takes the amplitude you're sending in
+from the left or right and tells you the
+
+ align:start position:0%
+from the left or right and tells you the
+ 
+
+ align:start position:0%
+from the left or right and tells you the
+amplitude coming out to the left or to
+
+ align:start position:0%
+amplitude coming out to the left or to
+ 
+
+ align:start position:0%
+amplitude coming out to the left or to
+the right yes
+
+ align:start position:0%
+the right yes
+ 
+
+ align:start position:0%
+the right yes
+how would we know this relation is
+
+ align:start position:0%
+how would we know this relation is
+ 
+
+ align:start position:0%
+how would we know this relation is
+linear
+
+ align:start position:0%
+linear
+ 
+
+ align:start position:0%
+linear
+uh if you double the amount of stuff
+
+ align:start position:0%
+uh if you double the amount of stuff
+ 
+
+ align:start position:0%
+uh if you double the amount of stuff
+coming in
+
+ align:start position:0%
+coming in
+ 
+
+ align:start position:0%
+coming in
+then you must double the amount of stuff
+
+ align:start position:0%
+then you must double the amount of stuff
+ 
+
+ align:start position:0%
+then you must double the amount of stuff
+going out or probability is not
+
+ align:start position:0%
+going out or probability is not
+ 
+
+ align:start position:0%
+going out or probability is not
+conserved
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+also we've derived these relations you
+
+ align:start position:0%
+also we've derived these relations you
+ 
+
+ align:start position:0%
+also we've derived these relations you
+know how the relations work the
+
+ align:start position:0%
+know how the relations work the
+ 
+
+ align:start position:0%
+know how the relations work the
+relations work by satisfying a series of
+
+ align:start position:0%
+relations work by satisfying a series of
+ 
+
+ align:start position:0%
+relations work by satisfying a series of
+linear equations uh
+
+ align:start position:0%
+linear equations uh
+ 
+
+ align:start position:0%
+linear equations uh
+between the various coefficients such
+
+ align:start position:0%
+between the various coefficients such
+ 
+
+ align:start position:0%
+between the various coefficients such
+that you have continuity and
+
+ align:start position:0%
+that you have continuity and
+ 
+
+ align:start position:0%
+that you have continuity and
+differentiability at all the matching
+
+ align:start position:0%
+differentiability at all the matching
+ 
+
+ align:start position:0%
+differentiability at all the matching
+points
+
+ align:start position:0%
+points
+ 
+
+ align:start position:0%
+points
+but the crucial thing of linearity is
+
+ align:start position:0%
+but the crucial thing of linearity is
+ 
+
+ align:start position:0%
+but the crucial thing of linearity is
+you need probabilities conserved and
+
+ align:start position:0%
+you need probabilities conserved and
+ 
+
+ align:start position:0%
+you need probabilities conserved and
+time evolution is linear so
+
+ align:start position:0%
+time evolution is linear so
+ 
+
+ align:start position:0%
+time evolution is linear so
+other questions
+
+ align:start position:0%
+other questions
+ 
+
+ align:start position:0%
+other questions
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+so this is just some stupid matrix and
+
+ align:start position:0%
+so this is just some stupid matrix and
+ 
+
+ align:start position:0%
+so this is just some stupid matrix and
+we call it not surprisingly the s matrix
+
+ align:start position:0%
+we call it not surprisingly the s matrix
+ 
+
+ align:start position:0%
+we call it not surprisingly the s matrix
+in all of its majesty um
+
+ align:start position:0%
+in all of its majesty um
+ 
+
+ align:start position:0%
+in all of its majesty um
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+the basic idea is this for scattering
+
+ align:start position:0%
+the basic idea is this for scattering
+ 
+
+ align:start position:0%
+the basic idea is this for scattering
+problems if you if someone tells you the
+
+ align:start position:0%
+problems if you if someone tells you the
+ 
+
+ align:start position:0%
+problems if you if someone tells you the
+s matrix and in particular if someone
+
+ align:start position:0%
+s matrix and in particular if someone
+ 
+
+ align:start position:0%
+s matrix and in particular if someone
+tells you how all the coefficients of
+
+ align:start position:0%
+tells you how all the coefficients of
+ 
+
+ align:start position:0%
+tells you how all the coefficients of
+the s matrix vary with energy
+
+ align:start position:0%
+the s matrix vary with energy
+ 
+
+ align:start position:0%
+the s matrix vary with energy
+then you've completely solved any
+
+ align:start position:0%
+then you've completely solved any
+ 
+
+ align:start position:0%
+then you've completely solved any
+scattering problem you tell me what a
+
+ align:start position:0%
+scattering problem you tell me what a
+ 
+
+ align:start position:0%
+scattering problem you tell me what a
+and d are great i'll tell you exactly
+
+ align:start position:0%
+and d are great i'll tell you exactly
+ 
+
+ align:start position:0%
+and d are great i'll tell you exactly
+what b and c are mode by mode and i can
+
+ align:start position:0%
+what b and c are mode by mode and i can
+ 
+
+ align:start position:0%
+what b and c are mode by mode and i can
+do this for a superposition so this
+
+ align:start position:0%
+do this for a superposition so this
+ 
+
+ align:start position:0%
+do this for a superposition so this
+allows you to completely solve
+
+ align:start position:0%
+allows you to completely solve
+ 
+
+ align:start position:0%
+allows you to completely solve
+any scattering problem in quantum
+
+ align:start position:0%
+any scattering problem in quantum
+ 
+
+ align:start position:0%
+any scattering problem in quantum
+mechanics once you know it so it
+
+ align:start position:0%
+mechanics once you know it so it
+ 
+
+ align:start position:0%
+mechanics once you know it so it
+suffices to know s to solve all
+
+ align:start position:0%
+suffices to know s to solve all
+ 
+
+ align:start position:0%
+suffices to know s to solve all
+scattering problems
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so let's i want to now spend just a
+
+ align:start position:0%
+so let's i want to now spend just a
+ 
+
+ align:start position:0%
+so let's i want to now spend just a
+little bit of time thinking about what
+
+ align:start position:0%
+little bit of time thinking about what
+ 
+
+ align:start position:0%
+little bit of time thinking about what
+properties the s matrix and its
+
+ align:start position:0%
+properties the s matrix and its
+ 
+
+ align:start position:0%
+properties the s matrix and its
+components must satisfy
+
+ align:start position:0%
+components must satisfy
+ 
+
+ align:start position:0%
+components must satisfy
+what things what properties must the s
+
+ align:start position:0%
+what things what properties must the s
+ 
+
+ align:start position:0%
+what things what properties must the s
+matrix satisfy in order to uh
+
+ align:start position:0%
+matrix satisfy in order to uh
+ 
+
+ align:start position:0%
+matrix satisfy in order to uh
+you know jive well with the rest of the
+
+ align:start position:0%
+you know jive well with the rest of the
+ 
+
+ align:start position:0%
+you know jive well with the rest of the
+rules of quantum mechanics
+
+ align:start position:0%
+rules of quantum mechanics
+ 
+
+ align:start position:0%
+rules of quantum mechanics
+and i'm not going to study any
+
+ align:start position:0%
+and i'm not going to study any
+ 
+
+ align:start position:0%
+and i'm not going to study any
+particular system i just want to ask
+
+ align:start position:0%
+particular system i just want to ask
+ 
+
+ align:start position:0%
+particular system i just want to ask
+general questions
+
+ align:start position:0%
+general questions
+ 
+
+ align:start position:0%
+general questions
+so the first thing that must be true is
+
+ align:start position:0%
+so the first thing that must be true is
+ 
+
+ align:start position:0%
+so the first thing that must be true is
+that stuff
+
+ align:start position:0%
+that stuff
+ 
+
+ align:start position:0%
+that stuff
+doesn't just doesn't disappear
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+i guess disapperate it's probably the
+
+ align:start position:0%
+i guess disapperate it's probably the
+ 
+
+ align:start position:0%
+i guess disapperate it's probably the
+appropriate
+
+ align:start position:0%
+appropriate
+ 
+
+ align:start position:0%
+appropriate
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+stuff doesn't
+
+ align:start position:0%
+stuff doesn't
+ 
+
+ align:start position:0%
+stuff doesn't
+leak out of the world so whatever goes
+
+ align:start position:0%
+leak out of the world so whatever goes
+ 
+
+ align:start position:0%
+leak out of the world so whatever goes
+in must come out so what that means is
+
+ align:start position:0%
+in must come out so what that means is
+ 
+
+ align:start position:0%
+in must come out so what that means is
+norm of a squared plus norm of d squared
+
+ align:start position:0%
+norm of a squared plus norm of d squared
+ 
+
+ align:start position:0%
+norm of a squared plus norm of d squared
+which is the probability density in
+
+ align:start position:0%
+which is the probability density in
+ 
+
+ align:start position:0%
+which is the probability density in
+probe and probability density out must
+
+ align:start position:0%
+probe and probability density out must
+ 
+
+ align:start position:0%
+probe and probability density out must
+be equal to
+
+ align:start position:0%
+be equal to
+ 
+
+ align:start position:0%
+be equal to
+b squared plus c squared
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+everyone agree with that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+why can't stuff stay in the potential
+
+ align:start position:0%
+why can't stuff stay in the potential
+ 
+
+ align:start position:0%
+why can't stuff stay in the potential
+that's a good ques so um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so yeah it's so it's a stationary state
+
+ align:start position:0%
+so yeah it's so it's a stationary state
+ 
+
+ align:start position:0%
+so yeah it's so it's a stationary state
+is so if we're looking at at fixed
+
+ align:start position:0%
+is so if we're looking at at fixed
+ 
+
+ align:start position:0%
+is so if we're looking at at fixed
+energy eigenstates we know that we're in
+
+ align:start position:0%
+energy eigenstates we know that we're in
+ 
+
+ align:start position:0%
+energy eigenstates we know that we're in
+a stationary state so whatever the
+
+ align:start position:0%
+a stationary state so whatever the
+ 
+
+ align:start position:0%
+a stationary state so whatever the
+amplitude um going into the middle is it
+
+ align:start position:0%
+amplitude um going into the middle is it
+ 
+
+ align:start position:0%
+amplitude um going into the middle is it
+must also be coming out of the middle
+
+ align:start position:0%
+must also be coming out of the middle
+ 
+
+ align:start position:0%
+must also be coming out of the middle
+right so there's another way to say this
+
+ align:start position:0%
+right so there's another way to say this
+ 
+
+ align:start position:0%
+right so there's another way to say this
+which is that um let's think about it
+
+ align:start position:0%
+which is that um let's think about it
+ 
+
+ align:start position:0%
+which is that um let's think about it
+not in terms of energy individual energy
+
+ align:start position:0%
+not in terms of energy individual energy
+ 
+
+ align:start position:0%
+not in terms of energy individual energy
+i can say so let's think about it in
+
+ align:start position:0%
+i can say so let's think about it in
+ 
+
+ align:start position:0%
+i can say so let's think about it in
+terms of wave packets so if we take a
+
+ align:start position:0%
+terms of wave packets so if we take a
+ 
+
+ align:start position:0%
+terms of wave packets so if we take a
+wave packet of stuff and we send in that
+
+ align:start position:0%
+wave packet of stuff and we send in that
+ 
+
+ align:start position:0%
+wave packet of stuff and we send in that
+wave packet it has some momentum right
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um oh this is going to get delicate
+
+ align:start position:0%
+um oh this is going to get delicate
+ 
+
+ align:start position:0%
+um oh this is going to get delicate
+technical let me just stick with the
+
+ align:start position:0%
+technical let me just stick with the
+ 
+
+ align:start position:0%
+technical let me just stick with the
+first
+
+ align:start position:0%
+first
+ 
+
+ align:start position:0%
+first
+the first statement which is that if
+
+ align:start position:0%
+the first statement which is that if
+ 
+
+ align:start position:0%
+the first statement which is that if
+stuff is going in then it has to also be
+
+ align:start position:0%
+stuff is going in then it has to also be
+ 
+
+ align:start position:0%
+stuff is going in then it has to also be
+coming out
+
+ align:start position:0%
+coming out
+ 
+
+ align:start position:0%
+coming out
+by the fact that this is an energy
+
+ align:start position:0%
+by the fact that this is an energy
+ 
+
+ align:start position:0%
+by the fact that this is an energy
+eigenstate
+
+ align:start position:0%
+eigenstate
+ 
+
+ align:start position:0%
+eigenstate
+the overall probability distribution is
+
+ align:start position:0%
+the overall probability distribution is
+ 
+
+ align:start position:0%
+the overall probability distribution is
+not changing in time
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so if if stuff went in and it didn't
+
+ align:start position:0%
+so if if stuff went in and it didn't
+ 
+
+ align:start position:0%
+so if if stuff went in and it didn't
+come out that would mean it's staying
+
+ align:start position:0%
+come out that would mean it's staying
+ 
+
+ align:start position:0%
+come out that would mean it's staying
+there that would mean that the
+
+ align:start position:0%
+there that would mean that the
+ 
+
+ align:start position:0%
+there that would mean that the
+probability density is changing in time
+
+ align:start position:0%
+probability density is changing in time
+ 
+
+ align:start position:0%
+probability density is changing in time
+that's not what happens in an energy
+
+ align:start position:0%
+that's not what happens in an energy
+ 
+
+ align:start position:0%
+that's not what happens in an energy
+eigenstate the probability distribution
+
+ align:start position:0%
+eigenstate the probability distribution
+ 
+
+ align:start position:0%
+eigenstate the probability distribution
+is time independent
+
+ align:start position:0%
+is time independent
+ 
+
+ align:start position:0%
+is time independent
+everyone call that
+
+ align:start position:0%
+everyone call that
+ 
+
+ align:start position:0%
+everyone call that
+okay so
+
+ align:start position:0%
+okay so
+ 
+
+ align:start position:0%
+okay so
+um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+good so uh so let's think though about
+
+ align:start position:0%
+good so uh so let's think though about
+ 
+
+ align:start position:0%
+good so uh so let's think though about
+what this is i can write this in the
+
+ align:start position:0%
+what this is i can write this in the
+ 
+
+ align:start position:0%
+what this is i can write this in the
+following nice way
+
+ align:start position:0%
+following nice way
+ 
+
+ align:start position:0%
+following nice way
+i can write this as uh a complex
+
+ align:start position:0%
+i can write this as uh a complex
+ 
+
+ align:start position:0%
+i can write this as uh a complex
+conjugate
+
+ align:start position:0%
+conjugate
+ 
+
+ align:start position:0%
+conjugate
+d complex con whoops d complex conjugate
+
+ align:start position:0%
+d complex con whoops d complex conjugate
+ 
+
+ align:start position:0%
+d complex con whoops d complex conjugate
+a d
+
+ align:start position:0%
+a d
+ 
+
+ align:start position:0%
+a d
+and on the right hand side this is equal
+
+ align:start position:0%
+and on the right hand side this is equal
+ 
+
+ align:start position:0%
+and on the right hand side this is equal
+to uh b complex conjugate c complex
+
+ align:start position:0%
+to uh b complex conjugate c complex
+ 
+
+ align:start position:0%
+to uh b complex conjugate c complex
+conjugate
+
+ align:start position:0%
+conjugate
+ 
+
+ align:start position:0%
+conjugate
+bc
+
+ align:start position:0%
+bc
+ 
+
+ align:start position:0%
+bc
+i have done nothing other than write
+
+ align:start position:0%
+i have done nothing other than write
+ 
+
+ align:start position:0%
+i have done nothing other than write
+this out in some suggested form
+
+ align:start position:0%
+this out in some suggested form
+ 
+
+ align:start position:0%
+this out in some suggested form
+but
+
+ align:start position:0%
+but
+ 
+
+ align:start position:0%
+but
+b and c are equal to the s matrix so bc
+
+ align:start position:0%
+b and c are equal to the s matrix so bc
+ 
+
+ align:start position:0%
+b and c are equal to the s matrix so bc
+is the s matrix times a
+
+ align:start position:0%
+is the s matrix times a
+ 
+
+ align:start position:0%
+is the s matrix times a
+and b comics conjugate c complex
+
+ align:start position:0%
+and b comics conjugate c complex
+ 
+
+ align:start position:0%
+and b comics conjugate c complex
+conjugate is the transpose complex
+
+ align:start position:0%
+conjugate is the transpose complex
+ 
+
+ align:start position:0%
+conjugate is the transpose complex
+conjugate so this is equal to
+
+ align:start position:0%
+conjugate so this is equal to
+ 
+
+ align:start position:0%
+conjugate so this is equal to
+a complex conjugate d complex conjugate
+
+ align:start position:0%
+a complex conjugate d complex conjugate
+ 
+
+ align:start position:0%
+a complex conjugate d complex conjugate
+s transpose complex conjugate also known
+
+ align:start position:0%
+s transpose complex conjugate also known
+ 
+
+ align:start position:0%
+s transpose complex conjugate also known
+as adjoint and this is s on a d
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah
+
+ align:start position:0%
+yeah
+ 
+
+ align:start position:0%
+yeah
+but this has to be equal to this
+
+ align:start position:0%
+but this has to be equal to this
+ 
+
+ align:start position:0%
+but this has to be equal to this
+for any a and d
+
+ align:start position:0%
+for any a and d
+ 
+
+ align:start position:0%
+for any a and d
+so what must be true of s dagger s as a
+
+ align:start position:0%
+so what must be true of s dagger s as a
+ 
+
+ align:start position:0%
+so what must be true of s dagger s as a
+matrix
+
+ align:start position:0%
+matrix
+ 
+
+ align:start position:0%
+matrix
+it's got to be the identity
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+as a matrix in order for this to be true
+
+ align:start position:0%
+as a matrix in order for this to be true
+ 
+
+ align:start position:0%
+as a matrix in order for this to be true
+for all a and e
+
+ align:start position:0%
+for all a and e
+ 
+
+ align:start position:0%
+for all a and e
+ah that's cool stuff doesn't disappear s
+
+ align:start position:0%
+ah that's cool stuff doesn't disappear s
+ 
+
+ align:start position:0%
+ah that's cool stuff doesn't disappear s
+is a unitary matrix
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so s is unitary matrix
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+its inverse is its adjoint
+
+ align:start position:0%
+its inverse is its adjoint
+ 
+
+ align:start position:0%
+its inverse is its adjoint
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+and you'll prove this in a little more
+
+ align:start position:0%
+and you'll prove this in a little more
+ 
+
+ align:start position:0%
+and you'll prove this in a little more
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+uh elegance um
+
+ align:start position:0%
+uh elegance um
+ 
+
+ align:start position:0%
+uh elegance um
+you'll
+
+ align:start position:0%
+you'll
+ 
+
+ align:start position:0%
+you'll
+you'll study this in a little more
+
+ align:start position:0%
+you'll study this in a little more
+ 
+
+ align:start position:0%
+you'll study this in a little more
+detail on the problem set you showed uh
+
+ align:start position:0%
+detail on the problem set you showed uh
+ 
+
+ align:start position:0%
+detail on the problem set you showed uh
+the definition of unitary you studied
+
+ align:start position:0%
+the definition of unitary you studied
+ 
+
+ align:start position:0%
+the definition of unitary you studied
+the definition of unitary and the last
+
+ align:start position:0%
+the definition of unitary and the last
+ 
+
+ align:start position:0%
+the definition of unitary and the last
+problem is that
+
+ align:start position:0%
+problem is that
+ 
+
+ align:start position:0%
+problem is that
+okay so that's the first thing about s
+
+ align:start position:0%
+okay so that's the first thing about s
+ 
+
+ align:start position:0%
+okay so that's the first thing about s
+and it turns out to be completely
+
+ align:start position:0%
+and it turns out to be completely
+ 
+
+ align:start position:0%
+and it turns out to be completely
+general any time whether you're in one
+
+ align:start position:0%
+general any time whether you're in one
+ 
+
+ align:start position:0%
+general any time whether you're in one
+dimension or two dimension or three if
+
+ align:start position:0%
+dimension or two dimension or three if
+ 
+
+ align:start position:0%
+dimension or two dimension or three if
+you send stuff in it should not get
+
+ align:start position:0%
+you send stuff in it should not get
+ 
+
+ align:start position:0%
+you send stuff in it should not get
+stuck it should come out
+
+ align:start position:0%
+stuck it should come out
+ 
+
+ align:start position:0%
+stuck it should come out
+and when it does come out
+
+ align:start position:0%
+and when it does come out
+ 
+
+ align:start position:0%
+and when it does come out
+uh the statement that it comes out for
+
+ align:start position:0%
+uh the statement that it comes out for
+ 
+
+ align:start position:0%
+uh the statement that it comes out for
+energy eigenstates is the statement that
+
+ align:start position:0%
+energy eigenstates is the statement that
+ 
+
+ align:start position:0%
+energy eigenstates is the statement that
+s is unitary matrix
+
+ align:start position:0%
+s is unitary matrix
+ 
+
+ align:start position:0%
+s is unitary matrix
+questions on that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+a consequence of that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+is that the the eigenvalues
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+of s
+
+ align:start position:0%
+of s
+ 
+
+ align:start position:0%
+of s
+are phases
+
+ align:start position:0%
+are phases
+ 
+
+ align:start position:0%
+are phases
+pure phases
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so i can write s
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+i'll write them as
+
+ align:start position:0%
+i'll write them as
+ 
+
+ align:start position:0%
+i'll write them as
+s1
+
+ align:start position:0%
+s1
+ 
+
+ align:start position:0%
+s1
+e to the i uh phi 1 and
+
+ align:start position:0%
+e to the i uh phi 1 and
+ 
+
+ align:start position:0%
+e to the i uh phi 1 and
+s2 is equal to i phi 2.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+the statement that s is a unitary matrix
+
+ align:start position:0%
+the statement that s is a unitary matrix
+ 
+
+ align:start position:0%
+the statement that s is a unitary matrix
+leads to constraints on the coefficients
+
+ align:start position:0%
+leads to constraints on the coefficients
+ 
+
+ align:start position:0%
+leads to constraints on the coefficients
+okay and you're going to derive these on
+
+ align:start position:0%
+okay and you're going to derive these on
+ 
+
+ align:start position:0%
+okay and you're going to derive these on
+your problem set i'm just going to list
+
+ align:start position:0%
+your problem set i'm just going to list
+ 
+
+ align:start position:0%
+your problem set i'm just going to list
+them now so the first is that the
+
+ align:start position:0%
+them now so the first is that the
+ 
+
+ align:start position:0%
+them now so the first is that the
+magnitude of s1
+
+ align:start position:0%
+magnitude of s1
+ 
+
+ align:start position:0%
+magnitude of s1
+1 is equal to the magnitude of s22
+
+ align:start position:0%
+1 is equal to the magnitude of s22
+ 
+
+ align:start position:0%
+1 is equal to the magnitude of s22
+the magnitude of s12 is equal to the
+
+ align:start position:0%
+the magnitude of s12 is equal to the
+ 
+
+ align:start position:0%
+the magnitude of s12 is equal to the
+magnitude of s21
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+oops
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+good
+
+ align:start position:0%
+good
+ 
+
+ align:start position:0%
+good
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+more importantly s12 norm squared plus s
+
+ align:start position:0%
+more importantly s12 norm squared plus s
+ 
+
+ align:start position:0%
+more importantly s12 norm squared plus s
+one one squared
+
+ align:start position:0%
+one one squared
+ 
+
+ align:start position:0%
+one one squared
+is equal to one
+
+ align:start position:0%
+is equal to one
+ 
+
+ align:start position:0%
+is equal to one
+and finally s11
+
+ align:start position:0%
+and finally s11
+ 
+
+ align:start position:0%
+and finally s11
+s2 s12
+
+ align:start position:0%
+s2 s12
+ 
+
+ align:start position:0%
+s2 s12
+complex conjugate plus
+
+ align:start position:0%
+complex conjugate plus
+ 
+
+ align:start position:0%
+complex conjugate plus
+two one s two two complex conjugate uh
+
+ align:start position:0%
+two one s two two complex conjugate uh
+ 
+
+ align:start position:0%
+two one s two two complex conjugate uh
+is equal to zero
+
+ align:start position:0%
+is equal to zero
+ 
+
+ align:start position:0%
+is equal to zero
+so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+what do these mean what are these
+
+ align:start position:0%
+what do these mean what are these
+ 
+
+ align:start position:0%
+what do these mean what are these
+conditions telling us
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+what are these can so they're they're
+
+ align:start position:0%
+what are these can so they're they're
+ 
+
+ align:start position:0%
+what are these can so they're they're
+telling us of course they're a
+
+ align:start position:0%
+telling us of course they're a
+ 
+
+ align:start position:0%
+telling us of course they're a
+consequence of conservation of
+
+ align:start position:0%
+consequence of conservation of
+ 
+
+ align:start position:0%
+consequence of conservation of
+probability but they have another
+
+ align:start position:0%
+probability but they have another
+ 
+
+ align:start position:0%
+probability but they have another
+meaning and let's to get that other
+
+ align:start position:0%
+meaning and let's to get that other
+ 
+
+ align:start position:0%
+meaning and let's to get that other
+meaning let's look at the definition of
+
+ align:start position:0%
+meaning let's look at the definition of
+ 
+
+ align:start position:0%
+meaning let's look at the definition of
+of
+
+ align:start position:0%
+of
+ 
+
+ align:start position:0%
+of
+uh the transmission amplitudes so in
+
+ align:start position:0%
+uh the transmission amplitudes so in
+ 
+
+ align:start position:0%
+uh the transmission amplitudes so in
+particular consider the case that we
+
+ align:start position:0%
+particular consider the case that we
+ 
+
+ align:start position:0%
+particular consider the case that we
+send stuff in from the left
+
+ align:start position:0%
+send stuff in from the left
+ 
+
+ align:start position:0%
+send stuff in from the left
+and nothing in from the right so that
+
+ align:start position:0%
+and nothing in from the right so that
+ 
+
+ align:start position:0%
+and nothing in from the right so that
+corresponds to d equals zero so when d
+
+ align:start position:0%
+corresponds to d equals zero so when d
+ 
+
+ align:start position:0%
+corresponds to d equals zero so when d
+equals zero what does this tell us it
+
+ align:start position:0%
+equals zero what does this tell us it
+ 
+
+ align:start position:0%
+equals zero what does this tell us it
+tells us that b
+
+ align:start position:0%
+tells us that b
+ 
+
+ align:start position:0%
+tells us that b
+is equal to and a equals one for
+
+ align:start position:0%
+is equal to and a equals one for
+ 
+
+ align:start position:0%
+is equal to and a equals one for
+normalization so
+
+ align:start position:0%
+normalization so
+ 
+
+ align:start position:0%
+normalization so
+b is equal to
+
+ align:start position:0%
+b is equal to
+ 
+
+ align:start position:0%
+b is equal to
+well d is equal to zero so it's just s11
+
+ align:start position:0%
+well d is equal to zero so it's just s11
+ 
+
+ align:start position:0%
+well d is equal to zero so it's just s11
+a
+
+ align:start position:0%
+a
+ 
+
+ align:start position:0%
+a
+so b over a
+
+ align:start position:0%
+so b over a
+ 
+
+ align:start position:0%
+so b over a
+is s11
+
+ align:start position:0%
+is s11
+ 
+
+ align:start position:0%
+is s11
+and similarly c over a
+
+ align:start position:0%
+and similarly c over a
+ 
+
+ align:start position:0%
+and similarly c over a
+is s21
+
+ align:start position:0%
+is s21
+ 
+
+ align:start position:0%
+is s21
+but c over a is the thing that we've
+
+ align:start position:0%
+but c over a is the thing that we've
+ 
+
+ align:start position:0%
+but c over a is the thing that we've
+been calling
+
+ align:start position:0%
+been calling
+ 
+
+ align:start position:0%
+been calling
+the transmission amplitude little t
+
+ align:start position:0%
+the transmission amplitude little t
+ 
+
+ align:start position:0%
+the transmission amplitude little t
+and this is the reflection amplitude
+
+ align:start position:0%
+and this is the reflection amplitude
+ 
+
+ align:start position:0%
+and this is the reflection amplitude
+little r so this is the reflection
+
+ align:start position:0%
+little r so this is the reflection
+ 
+
+ align:start position:0%
+little r so this is the reflection
+amplitude if we send in stuff and
+
+ align:start position:0%
+amplitude if we send in stuff and
+ 
+
+ align:start position:0%
+amplitude if we send in stuff and
+bounces off reflex to the left
+
+ align:start position:0%
+bounces off reflex to the left
+ 
+
+ align:start position:0%
+bounces off reflex to the left
+and this is the transmission amplitude
+
+ align:start position:0%
+and this is the transmission amplitude
+ 
+
+ align:start position:0%
+and this is the transmission amplitude
+for transmitting to the right
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+everyone cool with that
+
+ align:start position:0%
+everyone cool with that
+ 
+
+ align:start position:0%
+everyone cool with that
+and by the same token so this is
+
+ align:start position:0%
+and by the same token so this is
+ 
+
+ align:start position:0%
+and by the same token so this is
+reflection to the left this is
+
+ align:start position:0%
+reflection to the left this is
+ 
+
+ align:start position:0%
+reflection to the left this is
+transmission to the right
+
+ align:start position:0%
+transmission to the right
+ 
+
+ align:start position:0%
+transmission to the right
+by the same token this is going to be
+
+ align:start position:0%
+by the same token this is going to be
+ 
+
+ align:start position:0%
+by the same token this is going to be
+transmission to the left and reflection
+
+ align:start position:0%
+transmission to the left and reflection
+ 
+
+ align:start position:0%
+transmission to the left and reflection
+to the right
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so now let's look at these conditions
+
+ align:start position:0%
+so now let's look at these conditions
+ 
+
+ align:start position:0%
+so now let's look at these conditions
+s11 is reflection this is going to be
+
+ align:start position:0%
+s11 is reflection this is going to be
+ 
+
+ align:start position:0%
+s11 is reflection this is going to be
+reflection this says that the reflection
+
+ align:start position:0%
+reflection this says that the reflection
+ 
+
+ align:start position:0%
+reflection this says that the reflection
+to the left is equal to the reflection
+
+ align:start position:0%
+to the left is equal to the reflection
+ 
+
+ align:start position:0%
+to the left is equal to the reflection
+to the right
+
+ align:start position:0%
+to the right
+ 
+
+ align:start position:0%
+to the right
+in magnitude
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+before what we saw was for the simple
+
+ align:start position:0%
+before what we saw was for the simple
+ 
+
+ align:start position:0%
+before what we saw was for the simple
+step the reflection was equal to the
+
+ align:start position:0%
+step the reflection was equal to the
+ 
+
+ align:start position:0%
+step the reflection was equal to the
+reflection the reflection amplitude was
+
+ align:start position:0%
+reflection the reflection amplitude was
+ 
+
+ align:start position:0%
+reflection the reflection amplitude was
+equal from left to right not just the
+
+ align:start position:0%
+equal from left to right not just the
+ 
+
+ align:start position:0%
+equal from left to right not just the
+magnitude but the actual value was equal
+
+ align:start position:0%
+magnitude but the actual value was equal
+ 
+
+ align:start position:0%
+magnitude but the actual value was equal
+from the left and the right it was a
+
+ align:start position:0%
+from the left and the right it was a
+ 
+
+ align:start position:0%
+from the left and the right it was a
+little bit of a cheat because they were
+
+ align:start position:0%
+little bit of a cheat because they were
+ 
+
+ align:start position:0%
+little bit of a cheat because they were
+real
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and we saw that that was a consequence
+
+ align:start position:0%
+and we saw that that was a consequence
+ 
+
+ align:start position:0%
+and we saw that that was a consequence
+of just being the step we didn't know
+
+ align:start position:0%
+of just being the step we didn't know
+ 
+
+ align:start position:0%
+of just being the step we didn't know
+anything more about it but now we see
+
+ align:start position:0%
+anything more about it but now we see
+ 
+
+ align:start position:0%
+anything more about it but now we see
+that on general grounds on conservation
+
+ align:start position:0%
+that on general grounds on conservation
+ 
+
+ align:start position:0%
+that on general grounds on conservation
+and probability grounds
+
+ align:start position:0%
+and probability grounds
+ 
+
+ align:start position:0%
+and probability grounds
+the magnitude of the reflection to the
+
+ align:start position:0%
+the magnitude of the reflection to the
+ 
+
+ align:start position:0%
+the magnitude of the reflection to the
+left and to the right for any potential
+
+ align:start position:0%
+left and to the right for any potential
+ 
+
+ align:start position:0%
+left and to the right for any potential
+had better be equal and similarly the
+
+ align:start position:0%
+had better be equal and similarly the
+ 
+
+ align:start position:0%
+had better be equal and similarly the
+magnitude of the transmission for the
+
+ align:start position:0%
+magnitude of the transmission for the
+ 
+
+ align:start position:0%
+magnitude of the transmission for the
+left
+
+ align:start position:0%
+left
+ 
+
+ align:start position:0%
+left
+and the transmission to the right
+
+ align:start position:0%
+and the transmission to the right
+ 
+
+ align:start position:0%
+and the transmission to the right
+had better be equal
+
+ align:start position:0%
+had better be equal
+ 
+
+ align:start position:0%
+had better be equal
+all other things being
+
+ align:start position:0%
+all other things being
+ 
+
+ align:start position:0%
+all other things being
+uh you know if you're sending in from
+
+ align:start position:0%
+uh you know if you're sending in from
+ 
+
+ align:start position:0%
+uh you know if you're sending in from
+the left and then transmitting to the
+
+ align:start position:0%
+the left and then transmitting to the
+ 
+
+ align:start position:0%
+the left and then transmitting to the
+left or sending in from the right and
+
+ align:start position:0%
+left or sending in from the right and
+ 
+
+ align:start position:0%
+left or sending in from the right and
+transmitting to the right and what does
+
+ align:start position:0%
+transmitting to the right and what does
+ 
+
+ align:start position:0%
+transmitting to the right and what does
+this one tell us
+
+ align:start position:0%
+this one tell us
+ 
+
+ align:start position:0%
+this one tell us
+well s12 and s11
+
+ align:start position:0%
+well s12 and s11
+ 
+
+ align:start position:0%
+well s12 and s11
+that tells us that t squared little t
+
+ align:start position:0%
+that tells us that t squared little t
+ 
+
+ align:start position:0%
+that tells us that t squared little t
+squared which is
+
+ align:start position:0%
+squared which is
+ 
+
+ align:start position:0%
+squared which is
+the total probability trans to transmit
+
+ align:start position:0%
+the total probability trans to transmit
+ 
+
+ align:start position:0%
+the total probability trans to transmit
+plus little r squared norm squared is
+
+ align:start position:0%
+plus little r squared norm squared is
+ 
+
+ align:start position:0%
+plus little r squared norm squared is
+the total probability to reflect is
+
+ align:start position:0%
+the total probability to reflect is
+ 
+
+ align:start position:0%
+the total probability to reflect is
+equal to one and we saw this last time
+
+ align:start position:0%
+equal to one and we saw this last time
+ 
+
+ align:start position:0%
+equal to one and we saw this last time
+too
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and this was the earlier definition of
+
+ align:start position:0%
+and this was the earlier definition of
+ 
+
+ align:start position:0%
+and this was the earlier definition of
+nothing gets stuck
+
+ align:start position:0%
+nothing gets stuck
+ 
+
+ align:start position:0%
+nothing gets stuck
+and this one
+
+ align:start position:0%
+and this one
+ 
+
+ align:start position:0%
+and this one
+you'll study on your problem set
+
+ align:start position:0%
+you'll study on your problem set
+ 
+
+ align:start position:0%
+you'll study on your problem set
+it's a little more subtle
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay questions
+
+ align:start position:0%
+okay questions
+ 
+
+ align:start position:0%
+okay questions
+yeah
+
+ align:start position:0%
+yeah
+ 
+
+ align:start position:0%
+yeah
+one more time
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah i got s's okay good so the way we
+
+ align:start position:0%
+yeah i got s's okay good so the way we
+ 
+
+ align:start position:0%
+yeah i got s's okay good so the way we
+got s was unitary first off this is just
+
+ align:start position:0%
+got s was unitary first off this is just
+ 
+
+ align:start position:0%
+got s was unitary first off this is just
+the definition of s s is the matrix that
+
+ align:start position:0%
+the definition of s s is the matrix that
+ 
+
+ align:start position:0%
+the definition of s s is the matrix that
+g for any energy relates a and d the in
+
+ align:start position:0%
+g for any energy relates a and d the in
+ 
+
+ align:start position:0%
+g for any energy relates a and d the in
+going amplitudes to the outgoing
+
+ align:start position:0%
+going amplitudes to the outgoing
+ 
+
+ align:start position:0%
+going amplitudes to the outgoing
+amplitudes b and c just the definition
+
+ align:start position:0%
+amplitudes b and c just the definition
+ 
+
+ align:start position:0%
+amplitudes b and c just the definition
+meanwhile i claim that stuff doesn't go
+
+ align:start position:0%
+meanwhile i claim that stuff doesn't go
+ 
+
+ align:start position:0%
+meanwhile i claim that stuff doesn't go
+away nothing gets stuck nothing gets
+
+ align:start position:0%
+away nothing gets stuck nothing gets
+ 
+
+ align:start position:0%
+away nothing gets stuck nothing gets
+nothing disappears so the total
+
+ align:start position:0%
+nothing disappears so the total
+ 
+
+ align:start position:0%
+nothing disappears so the total
+probability density of stuff going in
+
+ align:start position:0%
+probability density of stuff going in
+ 
+
+ align:start position:0%
+probability density of stuff going in
+must be equal to the total probability
+
+ align:start position:0%
+must be equal to the total probability
+ 
+
+ align:start position:0%
+must be equal to the total probability
+density of stuff going out
+
+ align:start position:0%
+density of stuff going out
+ 
+
+ align:start position:0%
+density of stuff going out
+but the probability this
+
+ align:start position:0%
+but the probability this
+ 
+
+ align:start position:0%
+but the probability this
+the probability of stuff going in can be
+
+ align:start position:0%
+the probability of stuff going in can be
+ 
+
+ align:start position:0%
+the probability of stuff going in can be
+expressed as this
+
+ align:start position:0%
+expressed as this
+ 
+
+ align:start position:0%
+expressed as this
+row vector times this column vector and
+
+ align:start position:0%
+row vector times this column vector and
+ 
+
+ align:start position:0%
+row vector times this column vector and
+on the out this row vector times this
+
+ align:start position:0%
+on the out this row vector times this
+ 
+
+ align:start position:0%
+on the out this row vector times this
+column vector and now we use the
+
+ align:start position:0%
+column vector and now we use the
+ 
+
+ align:start position:0%
+column vector and now we use the
+definition of the s matrix this column
+
+ align:start position:0%
+definition of the s matrix this column
+ 
+
+ align:start position:0%
+definition of the s matrix this column
+vector is equal to s times this row
+
+ align:start position:0%
+vector is equal to s times this row
+ 
+
+ align:start position:0%
+vector is equal to s times this row
+vector
+
+ align:start position:0%
+vector
+ 
+
+ align:start position:0%
+vector
+yeah
+
+ align:start position:0%
+yeah
+ 
+
+ align:start position:0%
+yeah
+b c is equal to s times a d
+
+ align:start position:0%
+b c is equal to s times a d
+ 
+
+ align:start position:0%
+b c is equal to s times a d
+and when i take the transpose complex
+
+ align:start position:0%
+and when i take the transpose complex
+ 
+
+ align:start position:0%
+and when i take the transpose complex
+conjugate i get a d transpose complex
+
+ align:start position:0%
+conjugate i get a d transpose complex
+ 
+
+ align:start position:0%
+conjugate i get a d transpose complex
+conjugate s transpose complex conjugate
+
+ align:start position:0%
+conjugate s transpose complex conjugate
+ 
+
+ align:start position:0%
+conjugate s transpose complex conjugate
+but that's yes adjoint
+
+ align:start position:0%
+but that's yes adjoint
+ 
+
+ align:start position:0%
+but that's yes adjoint
+but in order for this to be true for any
+
+ align:start position:0%
+but in order for this to be true for any
+ 
+
+ align:start position:0%
+but in order for this to be true for any
+matrix any vectors a and d
+
+ align:start position:0%
+matrix any vectors a and d
+ 
+
+ align:start position:0%
+matrix any vectors a and d
+this must be it must be that as stagger
+
+ align:start position:0%
+this must be it must be that as stagger
+ 
+
+ align:start position:0%
+this must be it must be that as stagger
+s is the unitary is the identity but
+
+ align:start position:0%
+s is the unitary is the identity but
+ 
+
+ align:start position:0%
+s is the unitary is the identity but
+that's the definition of a unitary
+
+ align:start position:0%
+that's the definition of a unitary
+ 
+
+ align:start position:0%
+that's the definition of a unitary
+matrix
+
+ align:start position:0%
+matrix
+ 
+
+ align:start position:0%
+matrix
+cool
+
+ align:start position:0%
+cool
+ 
+
+ align:start position:0%
+cool
+others
+
+ align:start position:0%
+others
+ 
+
+ align:start position:0%
+others
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+you're going to prove a variety of
+
+ align:start position:0%
+you're going to prove a variety of
+ 
+
+ align:start position:0%
+you're going to prove a variety of
+things on the problem set
+
+ align:start position:0%
+things on the problem set
+ 
+
+ align:start position:0%
+things on the problem set
+about
+
+ align:start position:0%
+about
+ 
+
+ align:start position:0%
+about
+the um
+
+ align:start position:0%
+the um
+ 
+
+ align:start position:0%
+the um
+about the scattering matrix and its
+
+ align:start position:0%
+about the scattering matrix and its
+ 
+
+ align:start position:0%
+about the scattering matrix and its
+coefficients but i want to show you two
+
+ align:start position:0%
+coefficients but i want to show you two
+ 
+
+ align:start position:0%
+coefficients but i want to show you two
+properties of it
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the first
+
+ align:start position:0%
+the first
+ 
+
+ align:start position:0%
+the first
+is
+
+ align:start position:0%
+is
+ 
+
+ align:start position:0%
+is
+reasonably tame
+
+ align:start position:0%
+reasonably tame
+ 
+
+ align:start position:0%
+reasonably tame
+and it'll make a little sharper the step
+
+ align:start position:0%
+and it'll make a little sharper the step
+ 
+
+ align:start position:0%
+and it'll make a little sharper the step
+result we got earlier that the
+
+ align:start position:0%
+result we got earlier that the
+ 
+
+ align:start position:0%
+result we got earlier that the
+reflection in both directions off the
+
+ align:start position:0%
+reflection in both directions off the
+ 
+
+ align:start position:0%
+reflection in both directions off the
+step potential is in fact exactly the
+
+ align:start position:0%
+step potential is in fact exactly the
+ 
+
+ align:start position:0%
+step potential is in fact exactly the
+same
+
+ align:start position:0%
+same
+ 
+
+ align:start position:0%
+same
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+where did i put this
+
+ align:start position:0%
+where did i put this
+ 
+
+ align:start position:0%
+where did i put this
+good so suppose
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+suppose our system is time reversal
+
+ align:start position:0%
+suppose our system is time reversal
+ 
+
+ align:start position:0%
+suppose our system is time reversal
+invariant
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so if t goes to minus t nothing changes
+
+ align:start position:0%
+so if t goes to minus t nothing changes
+ 
+
+ align:start position:0%
+so if t goes to minus t nothing changes
+this would not be true for example if we
+
+ align:start position:0%
+this would not be true for example if we
+ 
+
+ align:start position:0%
+this would not be true for example if we
+had electric currents in our system
+
+ align:start position:0%
+had electric currents in our system
+ 
+
+ align:start position:0%
+had electric currents in our system
+because as we take t to minus t then the
+
+ align:start position:0%
+because as we take t to minus t then the
+ 
+
+ align:start position:0%
+because as we take t to minus t then the
+current reverses so if their current
+
+ align:start position:0%
+current reverses so if their current
+ 
+
+ align:start position:0%
+current reverses so if their current
+shows up in the potential or if a
+
+ align:start position:0%
+shows up in the potential or if a
+ 
+
+ align:start position:0%
+shows up in the potential or if a
+magnetic field due to a current shows up
+
+ align:start position:0%
+magnetic field due to a current shows up
+ 
+
+ align:start position:0%
+magnetic field due to a current shows up
+in the potential energy then as we
+
+ align:start position:0%
+in the potential energy then as we
+ 
+
+ align:start position:0%
+in the potential energy then as we
+change t to minus t we change the
+
+ align:start position:0%
+change t to minus t we change the
+ 
+
+ align:start position:0%
+change t to minus t we change the
+direction of the current we change the
+
+ align:start position:0%
+direction of the current we change the
+ 
+
+ align:start position:0%
+direction of the current we change the
+direction of the magnetic field
+
+ align:start position:0%
+direction of the magnetic field
+ 
+
+ align:start position:0%
+direction of the magnetic field
+so in simple systems where we have time
+
+ align:start position:0%
+so in simple systems where we have time
+ 
+
+ align:start position:0%
+so in simple systems where we have time
+reversal invariants
+
+ align:start position:0%
+reversal invariants
+ 
+
+ align:start position:0%
+reversal invariants
+for example electrostatics but not for
+
+ align:start position:0%
+for example electrostatics but not for
+ 
+
+ align:start position:0%
+for example electrostatics but not for
+example magnetostatics suppose we have
+
+ align:start position:0%
+example magnetostatics suppose we have
+ 
+
+ align:start position:0%
+example magnetostatics suppose we have
+time reversal and variance
+
+ align:start position:0%
+time reversal and variance
+ 
+
+ align:start position:0%
+time reversal and variance
+then
+
+ align:start position:0%
+then
+ 
+
+ align:start position:0%
+then
+what you've shown on a previous problem
+
+ align:start position:0%
+what you've shown on a previous problem
+ 
+
+ align:start position:0%
+what you've shown on a previous problem
+set is that psi is a solution
+
+ align:start position:0%
+set is that psi is a solution
+ 
+
+ align:start position:0%
+set is that psi is a solution
+then psi star psi complex conjugate is
+
+ align:start position:0%
+then psi star psi complex conjugate is
+ 
+
+ align:start position:0%
+then psi star psi complex conjugate is
+also a solution
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and using these
+
+ align:start position:0%
+and using these
+ 
+
+ align:start position:0%
+and using these
+what you'll what you can show and i'm
+
+ align:start position:0%
+what you'll what you can show and i'm
+ 
+
+ align:start position:0%
+what you'll what you can show and i'm
+not going to go through the steps for
+
+ align:start position:0%
+not going to go through the steps for
+ 
+
+ align:start position:0%
+not going to go through the steps for
+this
+
+ align:start position:0%
+this
+ 
+
+ align:start position:0%
+this
+well okay that's easy so
+
+ align:start position:0%
+well okay that's easy so
+ 
+
+ align:start position:0%
+well okay that's easy so
+if we do the time reversal the wave
+
+ align:start position:0%
+if we do the time reversal the wave
+ 
+
+ align:start position:0%
+if we do the time reversal the wave
+function
+
+ align:start position:0%
+function
+ 
+
+ align:start position:0%
+function
+on looking on the left or on the right
+
+ align:start position:0%
+on looking on the left or on the right
+ 
+
+ align:start position:0%
+on looking on the left or on the right
+so comparing these guys um so what
+
+ align:start position:0%
+so comparing these guys um so what
+ 
+
+ align:start position:0%
+so comparing these guys um so what
+changes
+
+ align:start position:0%
+changes
+ 
+
+ align:start position:0%
+changes
+well under time reversal
+
+ align:start position:0%
+well under time reversal
+ 
+
+ align:start position:0%
+well under time reversal
+we get a solution so given this solution
+
+ align:start position:0%
+we get a solution so given this solution
+ 
+
+ align:start position:0%
+we get a solution so given this solution
+we have another solution a star e to the
+
+ align:start position:0%
+we have another solution a star e to the
+ 
+
+ align:start position:0%
+we have another solution a star e to the
+minus i k x b star e to the plus i k x
+
+ align:start position:0%
+minus i k x b star e to the plus i k x
+ 
+
+ align:start position:0%
+minus i k x b star e to the plus i k x
+see minus
+
+ align:start position:0%
+see minus
+ 
+
+ align:start position:0%
+see minus
+star
+
+ align:start position:0%
+star
+ 
+
+ align:start position:0%
+star
+star
+
+ align:start position:0%
+star
+ 
+
+ align:start position:0%
+star
+plus
+
+ align:start position:0%
+plus
+ 
+
+ align:start position:0%
+plus
+okay so we can run exactly the same game
+
+ align:start position:0%
+okay so we can run exactly the same game
+ 
+
+ align:start position:0%
+okay so we can run exactly the same game
+now with this
+
+ align:start position:0%
+now with this
+ 
+
+ align:start position:0%
+now with this
+amplitude
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and when you put these conditions when
+
+ align:start position:0%
+and when you put these conditions when
+ 
+
+ align:start position:0%
+and when you put these conditions when
+you put the conditions together which
+
+ align:start position:0%
+you put the conditions together which
+ 
+
+ align:start position:0%
+you put the conditions together which
+you'll do on the problem set um so this
+
+ align:start position:0%
+you'll do on the problem set um so this
+ 
+
+ align:start position:0%
+you'll do on the problem set um so this
+another way to say this is the same
+
+ align:start position:0%
+another way to say this is the same
+ 
+
+ align:start position:0%
+another way to say this is the same
+solution with k to minus k and with a
+
+ align:start position:0%
+solution with k to minus k and with a
+ 
+
+ align:start position:0%
+solution with k to minus k and with a
+and b ex replaced by their complex
+
+ align:start position:0%
+and b ex replaced by their complex
+ 
+
+ align:start position:0%
+and b ex replaced by their complex
+conjugates and c and d replaced by each
+
+ align:start position:0%
+conjugates and c and d replaced by each
+ 
+
+ align:start position:0%
+conjugates and c and d replaced by each
+other's complex conjugates
+
+ align:start position:0%
+other's complex conjugates
+ 
+
+ align:start position:0%
+other's complex conjugates
+then this implies that it must be true
+
+ align:start position:0%
+then this implies that it must be true
+ 
+
+ align:start position:0%
+then this implies that it must be true
+that
+
+ align:start position:0%
+that
+ 
+
+ align:start position:0%
+that
+a
+
+ align:start position:0%
+a
+ 
+
+ align:start position:0%
+a
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+and d which are now the outgoing guys
+
+ align:start position:0%
+and d which are now the outgoing guys
+ 
+
+ align:start position:0%
+and d which are now the outgoing guys
+because we've time reversed is equal to
+
+ align:start position:0%
+because we've time reversed is equal to
+ 
+
+ align:start position:0%
+because we've time reversed is equal to
+s and i'll write this out explicitly
+
+ align:start position:0%
+s and i'll write this out explicitly
+ 
+
+ align:start position:0%
+s and i'll write this out explicitly
+s11 s12 s21 s22
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+b star
+
+ align:start position:0%
+b star
+ 
+
+ align:start position:0%
+b star
+and c star
+
+ align:start position:0%
+and c star
+ 
+
+ align:start position:0%
+and c star
+okay and so these together give you that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+i should have done this over here
+
+ align:start position:0%
+i should have done this over here
+ 
+
+ align:start position:0%
+i should have done this over here
+therefore
+
+ align:start position:0%
+therefore
+ 
+
+ align:start position:0%
+therefore
+s complex conjugate s
+
+ align:start position:0%
+s complex conjugate s
+ 
+
+ align:start position:0%
+s complex conjugate s
+is equal to one
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so if s complex conjugate s is
+
+ align:start position:0%
+okay so if s complex conjugate s is
+ 
+
+ align:start position:0%
+okay so if s complex conjugate s is
+equal to one then s inverse is equal to
+
+ align:start position:0%
+equal to one then s inverse is equal to
+ 
+
+ align:start position:0%
+equal to one then s inverse is equal to
+s transpose
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+just putting this on the right
+
+ align:start position:0%
+just putting this on the right
+ 
+
+ align:start position:0%
+just putting this on the right
+so s transpose is equal to s inverse
+
+ align:start position:0%
+so s transpose is equal to s inverse
+ 
+
+ align:start position:0%
+so s transpose is equal to s inverse
+is equal to s adjoint
+
+ align:start position:0%
+is equal to s adjoint
+ 
+
+ align:start position:0%
+is equal to s adjoint
+because s is also unitary
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so time reversal and variance
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+implies for example that s is equal to
+
+ align:start position:0%
+implies for example that s is equal to
+ 
+
+ align:start position:0%
+implies for example that s is equal to
+whoops um
+
+ align:start position:0%
+whoops um
+ 
+
+ align:start position:0%
+whoops um
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+that s dagger is equal to s r s is equal
+
+ align:start position:0%
+that s dagger is equal to s r s is equal
+ 
+
+ align:start position:0%
+that s dagger is equal to s r s is equal
+to s transpose
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+stem reverse
+
+ align:start position:0%
+stem reverse
+ 
+
+ align:start position:0%
+stem reverse
+this is what i wanted to write here it
+
+ align:start position:0%
+this is what i wanted to write here it
+ 
+
+ align:start position:0%
+this is what i wanted to write here it
+gives us that s is equal to s transpose
+
+ align:start position:0%
+gives us that s is equal to s transpose
+ 
+
+ align:start position:0%
+gives us that s is equal to s transpose
+and in particular this tells us that s21
+
+ align:start position:0%
+and in particular this tells us that s21
+ 
+
+ align:start position:0%
+and in particular this tells us that s21
+is equal to s12
+
+ align:start position:0%
+is equal to s12
+ 
+
+ align:start position:0%
+is equal to s12
+the off diagonal terms are
+
+ align:start position:0%
+the off diagonal terms are
+ 
+
+ align:start position:0%
+the off diagonal terms are
+equal
+
+ align:start position:0%
+equal
+ 
+
+ align:start position:0%
+equal
+not just in magnitude which was insured
+
+ align:start position:0%
+not just in magnitude which was insured
+ 
+
+ align:start position:0%
+not just in magnitude which was insured
+by unitarity but if in addition to uh to
+
+ align:start position:0%
+by unitarity but if in addition to uh to
+ 
+
+ align:start position:0%
+by unitarity but if in addition to uh to
+being a unitary system which of course
+
+ align:start position:0%
+being a unitary system which of course
+ 
+
+ align:start position:0%
+being a unitary system which of course
+it should be if in addition it's time
+
+ align:start position:0%
+it should be if in addition it's time
+ 
+
+ align:start position:0%
+it should be if in addition it's time
+reversal invariant then we see that the
+
+ align:start position:0%
+reversal invariant then we see that the
+ 
+
+ align:start position:0%
+reversal invariant then we see that the
+off-diagonal terms are equal not just in
+
+ align:start position:0%
+off-diagonal terms are equal not just in
+ 
+
+ align:start position:0%
+off-diagonal terms are equal not just in
+magnitude but also in phase and as you
+
+ align:start position:0%
+magnitude but also in phase and as you
+ 
+
+ align:start position:0%
+magnitude but also in phase and as you
+know the phase is important the phase
+
+ align:start position:0%
+know the phase is important the phase
+ 
+
+ align:start position:0%
+know the phase is important the phase
+contains physics it tells you about time
+
+ align:start position:0%
+contains physics it tells you about time
+ 
+
+ align:start position:0%
+contains physics it tells you about time
+delays and shifts on in the scattering
+
+ align:start position:0%
+delays and shifts on in the scattering
+ 
+
+ align:start position:0%
+delays and shifts on in the scattering
+process so the phases are the same that
+
+ align:start position:0%
+process so the phases are the same that
+ 
+
+ align:start position:0%
+process so the phases are the same that
+statement is not a trivial one it
+
+ align:start position:0%
+statement is not a trivial one it
+ 
+
+ align:start position:0%
+statement is not a trivial one it
+contains physics
+
+ align:start position:0%
+contains physics
+ 
+
+ align:start position:0%
+contains physics
+so when the system is time reversal
+
+ align:start position:0%
+so when the system is time reversal
+ 
+
+ align:start position:0%
+so when the system is time reversal
+invariant the phases are the the phases
+
+ align:start position:0%
+invariant the phases are the the phases
+ 
+
+ align:start position:0%
+invariant the phases are the the phases
+as well as the amplitudes are the same
+
+ align:start position:0%
+as well as the amplitudes are the same
+ 
+
+ align:start position:0%
+as well as the amplitudes are the same
+and you'll derive a series of related
+
+ align:start position:0%
+and you'll derive a series of related
+ 
+
+ align:start position:0%
+and you'll derive a series of related
+conditions or consequences
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+for the s matrix from various properties
+
+ align:start position:0%
+for the s matrix from various properties
+ 
+
+ align:start position:0%
+for the s matrix from various properties
+of the system for example parity if you
+
+ align:start position:0%
+of the system for example parity if you
+ 
+
+ align:start position:0%
+of the system for example parity if you
+can if you have a symmetric potential
+
+ align:start position:0%
+can if you have a symmetric potential
+ 
+
+ align:start position:0%
+can if you have a symmetric potential
+but now i want to in the last few
+
+ align:start position:0%
+but now i want to in the last few
+ 
+
+ align:start position:0%
+but now i want to in the last few
+minutes i just want to tell you a really
+
+ align:start position:0%
+minutes i just want to tell you a really
+ 
+
+ align:start position:0%
+minutes i just want to tell you a really
+lovely thing
+
+ align:start position:0%
+lovely thing
+ 
+
+ align:start position:0%
+lovely thing
+so it should be pretty clear at this
+
+ align:start position:0%
+so it should be pretty clear at this
+ 
+
+ align:start position:0%
+so it should be pretty clear at this
+point that all the information about
+
+ align:start position:0%
+point that all the information about
+ 
+
+ align:start position:0%
+point that all the information about
+scattering is contained in the s matrix
+
+ align:start position:0%
+scattering is contained in the s matrix
+ 
+
+ align:start position:0%
+scattering is contained in the s matrix
+and its dependence on the energy if you
+
+ align:start position:0%
+and its dependence on the energy if you
+ 
+
+ align:start position:0%
+and its dependence on the energy if you
+know what the incident amplitudes are
+
+ align:start position:0%
+know what the incident amplitudes are
+ 
+
+ align:start position:0%
+know what the incident amplitudes are
+you know what the outgoing amplitudes
+
+ align:start position:0%
+you know what the outgoing amplitudes
+ 
+
+ align:start position:0%
+you know what the outgoing amplitudes
+are
+
+ align:start position:0%
+are
+ 
+
+ align:start position:0%
+are
+and that's cool because you can measure
+
+ align:start position:0%
+and that's cool because you can measure
+ 
+
+ align:start position:0%
+and that's cool because you can measure
+this right you can take a potential you
+
+ align:start position:0%
+this right you can take a potential you
+ 
+
+ align:start position:0%
+this right you can take a potential you
+can literally just send in a beam of
+
+ align:start position:0%
+can literally just send in a beam of
+ 
+
+ align:start position:0%
+can literally just send in a beam of
+particles you can ask how likely are
+
+ align:start position:0%
+particles you can ask how likely are
+ 
+
+ align:start position:0%
+particles you can ask how likely are
+they to get out and more importantly if
+
+ align:start position:0%
+they to get out and more importantly if
+ 
+
+ align:start position:0%
+they to get out and more importantly if
+i build a wave packet
+
+ align:start position:0%
+i build a wave packet
+ 
+
+ align:start position:0%
+i build a wave packet
+on average what's the time delay or
+
+ align:start position:0%
+on average what's the time delay or
+ 
+
+ align:start position:0%
+on average what's the time delay or
+acceleration of the transmitted wave
+
+ align:start position:0%
+acceleration of the transmitted wave
+ 
+
+ align:start position:0%
+acceleration of the transmitted wave
+pack and that way i can measure the
+
+ align:start position:0%
+pack and that way i can measure the
+ 
+
+ align:start position:0%
+pack and that way i can measure the
+phase as well i can measure both the
+
+ align:start position:0%
+phase as well i can measure both the
+ 
+
+ align:start position:0%
+phase as well i can measure both the
+transmission probabilities and the
+
+ align:start position:0%
+transmission probabilities and the
+ 
+
+ align:start position:0%
+transmission probabilities and the
+phases release the gradient to the phase
+
+ align:start position:0%
+phases release the gradient to the phase
+ 
+
+ align:start position:0%
+phases release the gradient to the phase
+with energy hold on
+
+ align:start position:0%
+with energy hold on
+ 
+
+ align:start position:0%
+with energy hold on
+go ahead is there a special condition
+
+ align:start position:0%
+go ahead is there a special condition
+ 
+
+ align:start position:0%
+go ahead is there a special condition
+that we can impose to see the resonance
+
+ align:start position:0%
+that we can impose to see the resonance
+ 
+
+ align:start position:0%
+that we can impose to see the resonance
+excellent question hold on to your
+
+ align:start position:0%
+excellent question hold on to your
+ 
+
+ align:start position:0%
+excellent question hold on to your
+question for a second
+
+ align:start position:0%
+question for a second
+ 
+
+ align:start position:0%
+question for a second
+yeah so there's an enormous amount of
+
+ align:start position:0%
+yeah so there's an enormous amount of
+ 
+
+ align:start position:0%
+yeah so there's an enormous amount of
+the physics of scattering contained in
+
+ align:start position:0%
+the physics of scattering contained in
+ 
+
+ align:start position:0%
+the physics of scattering contained in
+the s matrix and you can measure the s
+
+ align:start position:0%
+the s matrix and you can measure the s
+ 
+
+ align:start position:0%
+the s matrix and you can measure the s
+matrix and you can measure its
+
+ align:start position:0%
+matrix and you can measure its
+ 
+
+ align:start position:0%
+matrix and you can measure its
+dependence on the energy you can measure
+
+ align:start position:0%
+dependence on the energy you can measure
+ 
+
+ align:start position:0%
+dependence on the energy you can measure
+the coefficients s12 and s22 their
+
+ align:start position:0%
+the coefficients s12 and s22 their
+ 
+
+ align:start position:0%
+the coefficients s12 and s22 their
+phases and their amplitudes as a
+
+ align:start position:0%
+phases and their amplitudes as a
+ 
+
+ align:start position:0%
+phases and their amplitudes as a
+function of energy and you can plot them
+
+ align:start position:0%
+function of energy and you can plot them
+ 
+
+ align:start position:0%
+function of energy and you can plot them
+and here's what i want to convince you
+
+ align:start position:0%
+and here's what i want to convince you
+ 
+
+ align:start position:0%
+and here's what i want to convince you
+of
+
+ align:start position:0%
+of
+ 
+
+ align:start position:0%
+of
+if you plot those
+
+ align:start position:0%
+if you plot those
+ 
+
+ align:start position:0%
+if you plot those
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+look at how the functions behave as
+
+ align:start position:0%
+look at how the functions behave as
+ 
+
+ align:start position:0%
+look at how the functions behave as
+functions of energy and ask how do those
+
+ align:start position:0%
+functions of energy and ask how do those
+ 
+
+ align:start position:0%
+functions of energy and ask how do those
+functions extend
+
+ align:start position:0%
+functions extend
+ 
+
+ align:start position:0%
+functions extend
+to negative energy
+
+ align:start position:0%
+to negative energy
+ 
+
+ align:start position:0%
+to negative energy
+by just drawing the line continuing the
+
+ align:start position:0%
+by just drawing the line continuing the
+ 
+
+ align:start position:0%
+by just drawing the line continuing the
+lines
+
+ align:start position:0%
+lines
+ 
+
+ align:start position:0%
+lines
+you can derive the energy of any bound
+
+ align:start position:0%
+you can derive the energy of any bound
+ 
+
+ align:start position:0%
+you can derive the energy of any bound
+states in the system too
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+knowledge of the scattering
+
+ align:start position:0%
+knowledge of the scattering
+ 
+
+ align:start position:0%
+knowledge of the scattering
+is enough to determine
+
+ align:start position:0%
+is enough to determine
+ 
+
+ align:start position:0%
+is enough to determine
+the bound state energies of a system and
+
+ align:start position:0%
+the bound state energies of a system and
+ 
+
+ align:start position:0%
+the bound state energies of a system and
+let me show you that
+
+ align:start position:0%
+let me show you that
+ 
+
+ align:start position:0%
+let me show you that
+and this is one of the coolest things in
+
+ align:start position:0%
+and this is one of the coolest things in
+ 
+
+ align:start position:0%
+and this is one of the coolest things in
+quantum mechanics so here's how this
+
+ align:start position:0%
+quantum mechanics so here's how this
+ 
+
+ align:start position:0%
+quantum mechanics so here's how this
+works
+
+ align:start position:0%
+works
+ 
+
+ align:start position:0%
+works
+we have from the definition of the s
+
+ align:start position:0%
+we have from the definition of the s
+ 
+
+ align:start position:0%
+we have from the definition of the s
+matrix that bc is equal to the s matrix
+
+ align:start position:0%
+matrix that bc is equal to the s matrix
+ 
+
+ align:start position:0%
+matrix that bc is equal to the s matrix
+on a d
+
+ align:start position:0%
+on a d
+ 
+
+ align:start position:0%
+on a d
+right where the wave function let me
+
+ align:start position:0%
+right where the wave function let me
+ 
+
+ align:start position:0%
+right where the wave function let me
+just put this back in the original form
+
+ align:start position:0%
+just put this back in the original form
+ 
+
+ align:start position:0%
+just put this back in the original form
+is c d
+
+ align:start position:0%
+is c d
+ 
+
+ align:start position:0%
+is c d
+a b
+
+ align:start position:0%
+a b
+ 
+
+ align:start position:0%
+a b
+e to the i k x e to the minus i k x
+
+ align:start position:0%
+e to the i k x e to the minus i k x
+ 
+
+ align:start position:0%
+e to the i k x e to the minus i k x
+and e to the plus i k x e to the minus i
+
+ align:start position:0%
+and e to the plus i k x e to the minus i
+ 
+
+ align:start position:0%
+and e to the plus i k x e to the minus i
+k x yeah so that's the definition of the
+
+ align:start position:0%
+k x yeah so that's the definition of the
+ 
+
+ align:start position:0%
+k x yeah so that's the definition of the
+s matrix the s matrix at a given energy
+
+ align:start position:0%
+s matrix the s matrix at a given energy
+ 
+
+ align:start position:0%
+s matrix the s matrix at a given energy
+e is this relation is a coefficient
+
+ align:start position:0%
+e is this relation is a coefficient
+ 
+
+ align:start position:0%
+e is this relation is a coefficient
+relation matrix between the in-going
+
+ align:start position:0%
+relation matrix between the in-going
+ 
+
+ align:start position:0%
+relation matrix between the in-going
+outgoing or more to the point a and d
+
+ align:start position:0%
+outgoing or more to the point a and d
+ 
+
+ align:start position:0%
+outgoing or more to the point a and d
+and in all of this i've assumed that the
+
+ align:start position:0%
+and in all of this i've assumed that the
+ 
+
+ align:start position:0%
+and in all of this i've assumed that the
+energy was positive that the k1 and k2
+
+ align:start position:0%
+energy was positive that the k1 and k2
+ 
+
+ align:start position:0%
+energy was positive that the k1 and k2
+are are positive and real but now let's
+
+ align:start position:0%
+are are positive and real but now let's
+ 
+
+ align:start position:0%
+are are positive and real but now let's
+ask the question what would have
+
+ align:start position:0%
+ask the question what would have
+ 
+
+ align:start position:0%
+ask the question what would have
+happened if in the whole process i had
+
+ align:start position:0%
+happened if in the whole process i had
+ 
+
+ align:start position:0%
+happened if in the whole process i had
+taken um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+take
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the energy less than zero so if the
+
+ align:start position:0%
+the energy less than zero so if the
+ 
+
+ align:start position:0%
+the energy less than zero so if the
+energy were less than zero instead of k
+
+ align:start position:0%
+energy were less than zero instead of k
+ 
+
+ align:start position:0%
+energy were less than zero instead of k
+k would be replaced by i alpha let's
+
+ align:start position:0%
+k would be replaced by i alpha let's
+ 
+
+ align:start position:0%
+k would be replaced by i alpha let's
+think about what that does
+
+ align:start position:0%
+think about what that does
+ 
+
+ align:start position:0%
+think about what that does
+if k is i alpha
+
+ align:start position:0%
+if k is i alpha
+ 
+
+ align:start position:0%
+if k is i alpha
+this is e to the i k is minus alpha
+
+ align:start position:0%
+this is e to the i k is minus alpha
+ 
+
+ align:start position:0%
+this is e to the i k is minus alpha
+and minus ik is plus alpha plus alpha
+
+ align:start position:0%
+and minus ik is plus alpha plus alpha
+ 
+
+ align:start position:0%
+and minus ik is plus alpha plus alpha
+similarly i k times i that gives me a
+
+ align:start position:0%
+similarly i k times i that gives me a
+ 
+
+ align:start position:0%
+similarly i k times i that gives me a
+minus alpha
+
+ align:start position:0%
+minus alpha
+ 
+
+ align:start position:0%
+minus alpha
+and this gives me a plus alpha
+
+ align:start position:0%
+and this gives me a plus alpha
+ 
+
+ align:start position:0%
+and this gives me a plus alpha
+yeah
+
+ align:start position:0%
+yeah
+ 
+
+ align:start position:0%
+yeah
+so as equations they're the same
+
+ align:start position:0%
+so as equations they're the same
+ 
+
+ align:start position:0%
+so as equations they're the same
+equations with k replaced by
+
+ align:start position:0%
+equations with k replaced by
+ 
+
+ align:start position:0%
+equations with k replaced by
+i alpha
+
+ align:start position:0%
+i alpha
+ 
+
+ align:start position:0%
+i alpha
+yeah
+
+ align:start position:0%
+yeah
+ 
+
+ align:start position:0%
+yeah
+and now what must be true for this state
+
+ align:start position:0%
+and now what must be true for this state
+ 
+
+ align:start position:0%
+and now what must be true for this state
+for these states to be normalizable
+
+ align:start position:0%
+for these states to be normalizable
+ 
+
+ align:start position:0%
+for these states to be normalizable
+what must be true for example of a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+a must be zero because at minus infinity
+
+ align:start position:0%
+a must be zero because at minus infinity
+ 
+
+ align:start position:0%
+a must be zero because at minus infinity
+this diverges it's not normalizable
+
+ align:start position:0%
+this diverges it's not normalizable
+ 
+
+ align:start position:0%
+this diverges it's not normalizable
+so in order to be a bouncy in order to
+
+ align:start position:0%
+so in order to be a bouncy in order to
+ 
+
+ align:start position:0%
+so in order to be a bouncy in order to
+have a physical state a must be zero
+
+ align:start position:0%
+have a physical state a must be zero
+ 
+
+ align:start position:0%
+have a physical state a must be zero
+what about d
+
+ align:start position:0%
+what about d
+ 
+
+ align:start position:0%
+what about d
+same reason it's got to be zero at
+
+ align:start position:0%
+same reason it's got to be zero at
+ 
+
+ align:start position:0%
+same reason it's got to be zero at
+positive infinity these guys are
+
+ align:start position:0%
+positive infinity these guys are
+ 
+
+ align:start position:0%
+positive infinity these guys are
+convergent so c and b can be non-zero so
+
+ align:start position:0%
+convergent so c and b can be non-zero so
+ 
+
+ align:start position:0%
+convergent so c and b can be non-zero so
+now here's my question can i scatter a
+
+ align:start position:0%
+now here's my question can i scatter a
+ 
+
+ align:start position:0%
+now here's my question can i scatter a
+state from a b we know that these
+
+ align:start position:0%
+state from a b we know that these
+ 
+
+ align:start position:0%
+state from a b we know that these
+relations must be true because all these
+
+ align:start position:0%
+relations must be true because all these
+ 
+
+ align:start position:0%
+relations must be true because all these
+relations are encoding all these
+
+ align:start position:0%
+relations are encoding all these
+ 
+
+ align:start position:0%
+relations are encoding all these
+relations are encoding is how a solution
+
+ align:start position:0%
+relations are encoding is how a solution
+ 
+
+ align:start position:0%
+relations are encoding is how a solution
+here matches to a solution here through
+
+ align:start position:0%
+here matches to a solution here through
+ 
+
+ align:start position:0%
+here matches to a solution here through
+a potential in between with continuity
+
+ align:start position:0%
+a potential in between with continuity
+ 
+
+ align:start position:0%
+a potential in between with continuity
+continuity of the derivative and
+
+ align:start position:0%
+continuity of the derivative and
+ 
+
+ align:start position:0%
+continuity of the derivative and
+anything else that's true of that
+
+ align:start position:0%
+anything else that's true of that
+ 
+
+ align:start position:0%
+anything else that's true of that
+potential inside all that s is doing
+
+ align:start position:0%
+potential inside all that s is doing
+ 
+
+ align:start position:0%
+potential inside all that s is doing
+from that point of view is telling me
+
+ align:start position:0%
+from that point of view is telling me
+ 
+
+ align:start position:0%
+from that point of view is telling me
+how these coefficients match onto these
+
+ align:start position:0%
+how these coefficients match onto these
+ 
+
+ align:start position:0%
+how these coefficients match onto these
+coefficients yes now what for a bound
+
+ align:start position:0%
+coefficients yes now what for a bound
+ 
+
+ align:start position:0%
+coefficients yes now what for a bound
+state so if we have e less than zero
+
+ align:start position:0%
+state so if we have e less than zero
+ 
+
+ align:start position:0%
+state so if we have e less than zero
+what must be true we must be true that a
+
+ align:start position:0%
+what must be true we must be true that a
+ 
+
+ align:start position:0%
+what must be true we must be true that a
+d is equal to
+
+ align:start position:0%
+d is equal to
+ 
+
+ align:start position:0%
+d is equal to
+zero and in particular zero zero right
+
+ align:start position:0%
+zero and in particular zero zero right
+ 
+
+ align:start position:0%
+zero and in particular zero zero right
+so what are b and c
+
+ align:start position:0%
+so what are b and c
+ 
+
+ align:start position:0%
+so what are b and c
+oh well a matrix times 0 is equal to
+
+ align:start position:0%
+oh well a matrix times 0 is equal to
+ 
+
+ align:start position:0%
+oh well a matrix times 0 is equal to
+unless
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+unless the matrix itself is diverging
+
+ align:start position:0%
+unless the matrix itself is diverging
+ 
+
+ align:start position:0%
+unless the matrix itself is diverging
+and then you have to be more careful but
+
+ align:start position:0%
+and then you have to be more careful but
+ 
+
+ align:start position:0%
+and then you have to be more careful but
+let's be naive for the moment
+
+ align:start position:0%
+let's be naive for the moment
+ 
+
+ align:start position:0%
+let's be naive for the moment
+if a is 0 0 then in order for b and c to
+
+ align:start position:0%
+if a is 0 0 then in order for b and c to
+ 
+
+ align:start position:0%
+if a is 0 0 then in order for b and c to
+be non-zero
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+s must have a pole
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+s must go like one over zero
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+s must diverge at some special value of
+
+ align:start position:0%
+s must diverge at some special value of
+ 
+
+ align:start position:0%
+s must diverge at some special value of
+the energy
+
+ align:start position:0%
+the energy
+ 
+
+ align:start position:0%
+the energy
+okay well that's easy that tells you
+
+ align:start position:0%
+okay well that's easy that tells you
+ 
+
+ align:start position:0%
+okay well that's easy that tells you
+that if you look at any particular
+
+ align:start position:0%
+that if you look at any particular
+ 
+
+ align:start position:0%
+that if you look at any particular
+coefficient in s
+
+ align:start position:0%
+coefficient in s
+ 
+
+ align:start position:0%
+coefficient in s
+any of the matrix elements of s
+
+ align:start position:0%
+any of the matrix elements of s
+ 
+
+ align:start position:0%
+any of the matrix elements of s
+the numerator can be whatever you want
+
+ align:start position:0%
+the numerator can be whatever you want
+ 
+
+ align:start position:0%
+the numerator can be whatever you want
+some finite number but the denominator
+
+ align:start position:0%
+some finite number but the denominator
+ 
+
+ align:start position:0%
+some finite number but the denominator
+had better be
+
+ align:start position:0%
+had better be
+ 
+
+ align:start position:0%
+had better be
+zero
+
+ align:start position:0%
+zero
+ 
+
+ align:start position:0%
+zero
+so let's look at the denominator
+
+ align:start position:0%
+so let's look at the denominator
+ 
+
+ align:start position:0%
+so let's look at the denominator
+if i compute s21
+
+ align:start position:0%
+if i compute s21
+ 
+
+ align:start position:0%
+if i compute s21
+oh actually let me do this over here
+
+ align:start position:0%
+oh actually let me do this over here
+ 
+
+ align:start position:0%
+oh actually let me do this over here
+let's compute
+
+ align:start position:0%
+let's compute
+ 
+
+ align:start position:0%
+let's compute
+ah no it's all filled damn
+
+ align:start position:0%
+ah no it's all filled damn
+ 
+
+ align:start position:0%
+ah no it's all filled damn
+let's do it over here
+
+ align:start position:0%
+let's do it over here
+ 
+
+ align:start position:0%
+let's do it over here
+so if i look at s21 for the barrier or
+
+ align:start position:0%
+so if i look at s21 for the barrier or
+ 
+
+ align:start position:0%
+so if i look at s21 for the barrier or
+for the potential well scattering off
+
+ align:start position:0%
+for the potential well scattering off
+ 
+
+ align:start position:0%
+for the potential well scattering off
+the potential well that we looked at at
+
+ align:start position:0%
+the potential well that we looked at at
+ 
+
+ align:start position:0%
+the potential well that we looked at at
+the beginning of today's lecture
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this guy
+
+ align:start position:0%
+this guy
+ 
+
+ align:start position:0%
+this guy
+and now i'm going to look at
+
+ align:start position:0%
+and now i'm going to look at
+ 
+
+ align:start position:0%
+and now i'm going to look at
+s21
+
+ align:start position:0%
+s21
+ 
+
+ align:start position:0%
+s21
+one of the coefficients of this guys
+
+ align:start position:0%
+one of the coefficients of this guys
+ 
+
+ align:start position:0%
+one of the coefficients of this guys
+also known as the scattering amplitude t
+
+ align:start position:0%
+also known as the scattering amplitude t
+ 
+
+ align:start position:0%
+also known as the scattering amplitude t
+for the well
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this is equal to
+
+ align:start position:0%
+this is equal to
+ 
+
+ align:start position:0%
+this is equal to
+and it's got awful expression
+
+ align:start position:0%
+and it's got awful expression
+ 
+
+ align:start position:0%
+and it's got awful expression
+2 k1 k2
+
+ align:start position:0%
+2 k1 k2
+ 
+
+ align:start position:0%
+2 k1 k2
+e to the ik k2 l
+
+ align:start position:0%
+e to the ik k2 l
+ 
+
+ align:start position:0%
+e to the ik k2 l
+over
+
+ align:start position:0%
+over
+ 
+
+ align:start position:0%
+over
+
+ align:start position:0%
+ 
+
+ align:start position:0%
+1 k 2
+
+ align:start position:0%
+1 k 2
+ 
+
+ align:start position:0%
+1 k 2
+cos
+
+ align:start position:0%
+cos
+ 
+
+ align:start position:0%
+cos
+of k prime l
+
+ align:start position:0%
+of k prime l
+ 
+
+ align:start position:0%
+of k prime l
+minus i
+
+ align:start position:0%
+minus i
+ 
+
+ align:start position:0%
+minus i
+k squared plus k 1 squared plus k 2
+
+ align:start position:0%
+k squared plus k 1 squared plus k 2
+ 
+
+ align:start position:0%
+k squared plus k 1 squared plus k 2
+squared
+
+ align:start position:0%
+squared
+ 
+
+ align:start position:0%
+squared
+times sine
+
+ align:start position:0%
+times sine
+ 
+
+ align:start position:0%
+times sine
+of k
+
+ align:start position:0%
+of k
+ 
+
+ align:start position:0%
+of k
+2 l
+
+ align:start position:0%
+2 l
+ 
+
+ align:start position:0%
+2 l
+okay this is some horrible thing but now
+
+ align:start position:0%
+okay this is some horrible thing but now
+ 
+
+ align:start position:0%
+okay this is some horrible thing but now
+i ask the condition look when does this
+
+ align:start position:0%
+i ask the condition look when does this
+ 
+
+ align:start position:0%
+i ask the condition look when does this
+have a pole for what values of the
+
+ align:start position:0%
+have a pole for what values of the
+ 
+
+ align:start position:0%
+have a pole for what values of the
+energy does this when the energy is
+
+ align:start position:0%
+energy does this when the energy is
+ 
+
+ align:start position:0%
+energy does this when the energy is
+continued to be negative
+
+ align:start position:0%
+continued to be negative
+ 
+
+ align:start position:0%
+continued to be negative
+for what values does this have a pole or
+
+ align:start position:0%
+for what values does this have a pole or
+ 
+
+ align:start position:0%
+for what values does this have a pole or
+does the denominator have a zero and the
+
+ align:start position:0%
+does the denominator have a zero and the
+ 
+
+ align:start position:0%
+does the denominator have a zero and the
+answer is if you take this and you
+
+ align:start position:0%
+answer is if you take this and you
+ 
+
+ align:start position:0%
+answer is if you take this and you
+massage the equation this is equal to 0
+
+ align:start position:0%
+massage the equation this is equal to 0
+ 
+
+ align:start position:0%
+massage the equation this is equal to 0
+a little bit you get the following
+
+ align:start position:0%
+a little bit you get the following
+ 
+
+ align:start position:0%
+a little bit you get the following
+expression
+
+ align:start position:0%
+expression
+ 
+
+ align:start position:0%
+expression
+k2 l upon 2
+
+ align:start position:0%
+k2 l upon 2
+ 
+
+ align:start position:0%
+k2 l upon 2
+tangent
+
+ align:start position:0%
+tangent
+ 
+
+ align:start position:0%
+tangent
+of k2 l
+
+ align:start position:0%
+of k2 l
+ 
+
+ align:start position:0%
+of k2 l
+upon 2 is equal to k1 l upon 2. this is
+
+ align:start position:0%
+upon 2 is equal to k1 l upon 2. this is
+ 
+
+ align:start position:0%
+upon 2 is equal to k1 l upon 2. this is
+the condition for the bound state
+
+ align:start position:0%
+the condition for the bound state
+ 
+
+ align:start position:0%
+the condition for the bound state
+energies of the square well and we've
+
+ align:start position:0%
+energies of the square well and we've
+ 
+
+ align:start position:0%
+energies of the square well and we've
+computed it using knowledge only of the
+
+ align:start position:0%
+computed it using knowledge only of the
+ 
+
+ align:start position:0%
+computed it using knowledge only of the
+scattering states if you took particles
+
+ align:start position:0%
+scattering states if you took particles
+ 
+
+ align:start position:0%
+scattering states if you took particles
+and a square well and roll the particles
+
+ align:start position:0%
+and a square well and roll the particles
+ 
+
+ align:start position:0%
+and a square well and roll the particles
+across the square well potential and
+
+ align:start position:0%
+across the square well potential and
+ 
+
+ align:start position:0%
+across the square well potential and
+measured as a function of energy
+
+ align:start position:0%
+measured as a function of energy
+ 
+
+ align:start position:0%
+measured as a function of energy
+the scattering amplitude the
+
+ align:start position:0%
+the scattering amplitude the
+ 
+
+ align:start position:0%
+the scattering amplitude the
+transmission amplitude in particular s21
+
+ align:start position:0%
+transmission amplitude in particular s21
+ 
+
+ align:start position:0%
+transmission amplitude in particular s21
+an element to the s matrix and you
+
+ align:start position:0%
+an element to the s matrix and you
+ 
+
+ align:start position:0%
+an element to the s matrix and you
+plotted it as a function of energy and
+
+ align:start position:0%
+plotted it as a function of energy and
+ 
+
+ align:start position:0%
+plotted it as a function of energy and
+then you approximated that by
+
+ align:start position:0%
+then you approximated that by
+ 
+
+ align:start position:0%
+then you approximated that by
+a function of energy that satisfies the
+
+ align:start position:0%
+a function of energy that satisfies the
+ 
+
+ align:start position:0%
+a function of energy that satisfies the
+basic properties of unitarity
+
+ align:start position:0%
+basic properties of unitarity
+ 
+
+ align:start position:0%
+basic properties of unitarity
+what you would find is that when you
+
+ align:start position:0%
+what you would find is that when you
+ 
+
+ align:start position:0%
+what you would find is that when you
+then extend that function in mathematica
+
+ align:start position:0%
+then extend that function in mathematica
+ 
+
+ align:start position:0%
+then extend that function in mathematica
+to minus a particular value of the
+
+ align:start position:0%
+to minus a particular value of the
+ 
+
+ align:start position:0%
+to minus a particular value of the
+energy the denominator diverges at that
+
+ align:start position:0%
+energy the denominator diverges at that
+ 
+
+ align:start position:0%
+energy the denominator diverges at that
+energy
+
+ align:start position:0%
+energy
+ 
+
+ align:start position:0%
+energy
+you know that there will be a bound
+
+ align:start position:0%
+you know that there will be a bound
+ 
+
+ align:start position:0%
+you know that there will be a bound
+state
+
+ align:start position:0%
+state
+ 
+
+ align:start position:0%
+state
+and so from scattering you've determined
+
+ align:start position:0%
+and so from scattering you've determined
+ 
+
+ align:start position:0%
+and so from scattering you've determined
+the existence of a bound state and this
+
+ align:start position:0%
+the existence of a bound state and this
+ 
+
+ align:start position:0%
+the existence of a bound state and this
+is how we find an awful lot of the
+
+ align:start position:0%
+is how we find an awful lot of the
+ 
+
+ align:start position:0%
+is how we find an awful lot of the
+particles that we actually deduce must
+
+ align:start position:0%
+particles that we actually deduce must
+ 
+
+ align:start position:0%
+particles that we actually deduce must
+exist in the real world
+
+ align:start position:0%
+exist in the real world
+ 
+
+ align:start position:0%
+exist in the real world
+we'll pick up next time
+
+ align:start position:0%
+we'll pick up next time
+ 
+
+ align:start position:0%
+we'll pick up next time
+[Applause]
\ No newline at end of file
diff --git a/xqmEuE97KzI.txt b/xqmEuE97KzI.txt
new file mode 100644
index 0000000000000000000000000000000000000000..c8dc72c28c45574bdf43fdae86062473a97526fa
--- /dev/null
+++ b/xqmEuE97KzI.txt
@@ -0,0 +1,483 @@
+align:start position:0%
+ 
+you have another sheet of paper
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+now we want to be able to communicate
+
+ align:start position:0%
+now we want to be able to communicate
+ 
+
+ align:start position:0%
+now we want to be able to communicate
+with the local people
+
+ align:start position:0%
+with the local people
+ 
+
+ align:start position:0%
+with the local people
+and ask for directions
+
+ align:start position:0%
+and ask for directions
+ 
+
+ align:start position:0%
+and ask for directions
+so you see that there are numbers close
+
+ align:start position:0%
+so you see that there are numbers close
+ 
+
+ align:start position:0%
+so you see that there are numbers close
+to each sentence okay so you should
+
+ align:start position:0%
+to each sentence okay so you should
+ 
+
+ align:start position:0%
+to each sentence okay so you should
+choose the number
+
+ align:start position:0%
+choose the number
+ 
+
+ align:start position:0%
+choose the number
+so try zero
+
+ align:start position:0%
+so try zero
+ 
+
+ align:start position:0%
+so try zero
+Mario Uno Anita
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so Circle your number so that you know
+
+ align:start position:0%
+so Circle your number so that you know
+ 
+
+ align:start position:0%
+so Circle your number so that you know
+when it's your turn so we first read it
+
+ align:start position:0%
+when it's your turn so we first read it
+ 
+
+ align:start position:0%
+when it's your turn so we first read it
+and then we try to understand and follow
+
+ align:start position:0%
+and then we try to understand and follow
+ 
+
+ align:start position:0%
+and then we try to understand and follow
+la cartina
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay here zero
+
+ align:start position:0%
+okay here zero
+ 
+
+ align:start position:0%
+okay here zero
+Uno
+
+ align:start position:0%
+Uno
+ 
+
+ align:start position:0%
+Uno
+Gomez
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+let's see what we're saying here we are
+
+ align:start position:0%
+let's see what we're saying here we are
+ 
+
+ align:start position:0%
+let's see what we're saying here we are
+having a formal conversation so we are
+
+ align:start position:0%
+having a formal conversation so we are
+ 
+
+ align:start position:0%
+having a formal conversation so we are
+using always the third person singular
+
+ align:start position:0%
+using always the third person singular
+ 
+
+ align:start position:0%
+using always the third person singular
+we're saying
+
+ align:start position:0%
+we're saying
+ 
+
+ align:start position:0%
+we're saying
+instead of scuza and we're saying
+
+ align:start position:0%
+instead of scuza and we're saying
+ 
+
+ align:start position:0%
+instead of scuza and we're saying
+instead of poi that we were using it for
+
+ align:start position:0%
+instead of poi that we were using it for
+ 
+
+ align:start position:0%
+instead of poi that we were using it for
+so first sentence is Miss Koozie
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+what does it means
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+excuse me
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+foreign
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+foreign
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+try again
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+I wanna hear your voice
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and now you should look at the map
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+but where the train station is
+
+ align:start position:0%
+but where the train station is
+ 
+
+ align:start position:0%
+but where the train station is
+so he says
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so what does it means
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that is left
+
+ align:start position:0%
+that is left
+ 
+
+ align:start position:0%
+that is left
+foreign
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so what are we doing now
+
+ align:start position:0%
+so what are we doing now
+ 
+
+ align:start position:0%
+so what are we doing now
+yes we're making a rice
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that means
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+40.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+foreign
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+intersections
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+we should say
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+a small thing in crochet
+
+ align:start position:0%
+a small thing in crochet
+ 
+
+ align:start position:0%
+a small thing in crochet
+okay so we have to pass many craft
+
+ align:start position:0%
+okay so we have to pass many craft
+ 
+
+ align:start position:0%
+okay so we have to pass many craft
+things and that's the jiri at sinistra
+
+ align:start position:0%
+things and that's the jiri at sinistra
+ 
+
+ align:start position:0%
+things and that's the jiri at sinistra
+so which one is
+
+ align:start position:0%
+so which one is
+ 
+
+ align:start position:0%
+so which one is
+to the left so we turn left
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+they're saying dogs
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+to the left
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+is very long and I couldn't take notes
+
+ align:start position:0%
+is very long and I couldn't take notes
+ 
+
+ align:start position:0%
+is very long and I couldn't take notes
+so that kind of fell asleep so
+
+ align:start position:0%
+so that kind of fell asleep so
+ 
+
+ align:start position:0%
+so that kind of fell asleep so
+I may ask
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yes
+
+ align:start position:0%
+yes
+ 
+
+ align:start position:0%
+yes
+because I'm talking about La Fontana
+
+ align:start position:0%
+because I'm talking about La Fontana
+ 
+
+ align:start position:0%
+because I'm talking about La Fontana
+which is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+because otherwise you're saying it's not
+
+ align:start position:0%
+because otherwise you're saying it's not
+ 
+
+ align:start position:0%
+because otherwise you're saying it's not
+funny
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+to run
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+there is a song
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+thank you
\ No newline at end of file
diff --git a/xvUz7P-DjhI.txt b/xvUz7P-DjhI.txt
new file mode 100644
index 0000000000000000000000000000000000000000..31b9c4bc1d070a92b27b38d492b8661cd1e3645a
--- /dev/null
+++ b/xvUz7P-DjhI.txt
@@ -0,0 +1,10477 @@
+align:start position:0%
+ 
+the following content is provided under
+
+ align:start position:0%
+the following content is provided under
+ 
+
+ align:start position:0%
+the following content is provided under
+a creative commons license
+
+ align:start position:0%
+a creative commons license
+ 
+
+ align:start position:0%
+a creative commons license
+your support will help mit
+
+ align:start position:0%
+your support will help mit
+ 
+
+ align:start position:0%
+your support will help mit
+opencourseware continue to offer high
+
+ align:start position:0%
+opencourseware continue to offer high
+ 
+
+ align:start position:0%
+opencourseware continue to offer high
+quality educational resources for free
+
+ align:start position:0%
+quality educational resources for free
+ 
+
+ align:start position:0%
+quality educational resources for free
+to make a donation or view additional
+
+ align:start position:0%
+to make a donation or view additional
+ 
+
+ align:start position:0%
+to make a donation or view additional
+materials from hundreds of mit courses
+
+ align:start position:0%
+materials from hundreds of mit courses
+ 
+
+ align:start position:0%
+materials from hundreds of mit courses
+visit mit open courseware at ocw.mit.edu
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so we're going to be talking about
+
+ align:start position:0%
+so we're going to be talking about
+ 
+
+ align:start position:0%
+so we're going to be talking about
+normal modes
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and you've already done a normal mode
+
+ align:start position:0%
+and you've already done a normal mode
+ 
+
+ align:start position:0%
+and you've already done a normal mode
+calculation on trans assist acetylene so
+
+ align:start position:0%
+calculation on trans assist acetylene so
+ 
+
+ align:start position:0%
+calculation on trans assist acetylene so
+you know most of this stuff
+
+ align:start position:0%
+you know most of this stuff
+ 
+
+ align:start position:0%
+you know most of this stuff
+but the notes contain
+
+ align:start position:0%
+but the notes contain
+ 
+
+ align:start position:0%
+but the notes contain
+a lot of
+
+ align:start position:0%
+a lot of
+ 
+
+ align:start position:0%
+a lot of
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+stuff worked out completely on water
+
+ align:start position:0%
+stuff worked out completely on water
+ 
+
+ align:start position:0%
+stuff worked out completely on water
+which is simpler than the case you did
+
+ align:start position:0%
+which is simpler than the case you did
+ 
+
+ align:start position:0%
+which is simpler than the case you did
+but it's also there's more here than
+
+ align:start position:0%
+but it's also there's more here than
+ 
+
+ align:start position:0%
+but it's also there's more here than
+what you did
+
+ align:start position:0%
+what you did
+ 
+
+ align:start position:0%
+what you did
+and
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+we will
+
+ align:start position:0%
+we will
+ 
+
+ align:start position:0%
+we will
+deal with the vibrational normal modes
+
+ align:start position:0%
+deal with the vibrational normal modes
+ 
+
+ align:start position:0%
+deal with the vibrational normal modes
+of water and then make some comments
+
+ align:start position:0%
+of water and then make some comments
+ 
+
+ align:start position:0%
+of water and then make some comments
+about why are certain internal
+
+ align:start position:0%
+about why are certain internal
+ 
+
+ align:start position:0%
+about why are certain internal
+coordinates mixed and others not
+
+ align:start position:0%
+coordinates mixed and others not
+ 
+
+ align:start position:0%
+coordinates mixed and others not
+and that brings up the concept of
+
+ align:start position:0%
+and that brings up the concept of
+ 
+
+ align:start position:0%
+and that brings up the concept of
+symmetry making symmetrized normal modes
+
+ align:start position:0%
+symmetry making symmetrized normal modes
+ 
+
+ align:start position:0%
+symmetry making symmetrized normal modes
+which block diagonalizes both f and g
+
+ align:start position:0%
+which block diagonalizes both f and g
+ 
+
+ align:start position:0%
+which block diagonalizes both f and g
+matrices
+
+ align:start position:0%
+matrices
+ 
+
+ align:start position:0%
+matrices
+and
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+then a more general or
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+discussion once you have symmetrized you
+
+ align:start position:0%
+discussion once you have symmetrized you
+ 
+
+ align:start position:0%
+discussion once you have symmetrized you
+might have a mixture you have might have
+
+ align:start position:0%
+might have a mixture you have might have
+ 
+
+ align:start position:0%
+might have a mixture you have might have
+states of the same symmetry species
+
+ align:start position:0%
+states of the same symmetry species
+ 
+
+ align:start position:0%
+states of the same symmetry species
+abandon a stretch
+
+ align:start position:0%
+abandon a stretch
+ 
+
+ align:start position:0%
+abandon a stretch
+and what makes them mix or not
+
+ align:start position:0%
+and what makes them mix or not
+ 
+
+ align:start position:0%
+and what makes them mix or not
+and so so some discussion of how do you
+
+ align:start position:0%
+and so so some discussion of how do you
+ 
+
+ align:start position:0%
+and so so some discussion of how do you
+read these matrices
+
+ align:start position:0%
+read these matrices
+ 
+
+ align:start position:0%
+read these matrices
+and infer causality for
+
+ align:start position:0%
+and infer causality for
+ 
+
+ align:start position:0%
+and infer causality for
+mixing of different kinds of internal
+
+ align:start position:0%
+mixing of different kinds of internal
+ 
+
+ align:start position:0%
+mixing of different kinds of internal
+motions so
+
+ align:start position:0%
+motions so
+ 
+
+ align:start position:0%
+motions so
+uh
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+read f
+
+ align:start position:0%
+read f
+ 
+
+ align:start position:0%
+read f
+and g matrices
+
+ align:start position:0%
+and g matrices
+ 
+
+ align:start position:0%
+and g matrices
+and there'll be some discussion of
+
+ align:start position:0%
+and there'll be some discussion of
+ 
+
+ align:start position:0%
+and there'll be some discussion of
+kinetic energy coupling and potential
+
+ align:start position:0%
+kinetic energy coupling and potential
+ 
+
+ align:start position:0%
+kinetic energy coupling and potential
+energy coupling
+
+ align:start position:0%
+energy coupling
+ 
+
+ align:start position:0%
+energy coupling
+and then
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+a refuge for
+
+ align:start position:0%
+a refuge for
+ 
+
+ align:start position:0%
+a refuge for
+the ill-prepared i go to something that
+
+ align:start position:0%
+the ill-prepared i go to something that
+ 
+
+ align:start position:0%
+the ill-prepared i go to something that
+i know very well uh pollyanne so if we
+
+ align:start position:0%
+i know very well uh pollyanne so if we
+ 
+
+ align:start position:0%
+i know very well uh pollyanne so if we
+get through all of the notes we'll end
+
+ align:start position:0%
+get through all of the notes we'll end
+ 
+
+ align:start position:0%
+get through all of the notes we'll end
+with with
+
+ align:start position:0%
+with with
+ 
+
+ align:start position:0%
+with with
+uh a description of
+
+ align:start position:0%
+uh a description of
+ 
+
+ align:start position:0%
+uh a description of
+the coupling among many systematically
+
+ align:start position:0%
+the coupling among many systematically
+ 
+
+ align:start position:0%
+the coupling among many systematically
+near degenerate levels
+
+ align:start position:0%
+near degenerate levels
+ 
+
+ align:start position:0%
+near degenerate levels
+and that's the menu
+
+ align:start position:0%
+and that's the menu
+ 
+
+ align:start position:0%
+and that's the menu
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+we have
+
+ align:start position:0%
+we have
+ 
+
+ align:start position:0%
+we have
+a whole bunch of
+
+ align:start position:0%
+a whole bunch of
+ 
+
+ align:start position:0%
+a whole bunch of
+transformations we start out with
+
+ align:start position:0%
+transformations we start out with
+ 
+
+ align:start position:0%
+transformations we start out with
+cartesian displacements we do mass
+
+ align:start position:0%
+cartesian displacements we do mass
+ 
+
+ align:start position:0%
+cartesian displacements we do mass
+weighted cartesians then we go to
+
+ align:start position:0%
+weighted cartesians then we go to
+ 
+
+ align:start position:0%
+weighted cartesians then we go to
+internal coordinates
+
+ align:start position:0%
+internal coordinates
+ 
+
+ align:start position:0%
+internal coordinates
+and then we uh get to the normal
+
+ align:start position:0%
+and then we uh get to the normal
+ 
+
+ align:start position:0%
+and then we uh get to the normal
+coordinates and we have some
+
+ align:start position:0%
+coordinates and we have some
+ 
+
+ align:start position:0%
+coordinates and we have some
+equations like this
+
+ align:start position:0%
+equations like this
+ 
+
+ align:start position:0%
+equations like this
+this relates
+
+ align:start position:0%
+this relates
+ 
+
+ align:start position:0%
+this relates
+the internal displacements to the normal
+
+ align:start position:0%
+the internal displacements to the normal
+ 
+
+ align:start position:0%
+the internal displacements to the normal
+displacements this is
+
+ align:start position:0%
+displacements this is
+ 
+
+ align:start position:0%
+displacements this is
+this looks like quantum mechanics but
+
+ align:start position:0%
+this looks like quantum mechanics but
+ 
+
+ align:start position:0%
+this looks like quantum mechanics but
+it's just a
+
+ align:start position:0%
+it's just a
+ 
+
+ align:start position:0%
+it's just a
+form of
+
+ align:start position:0%
+form of
+ 
+
+ align:start position:0%
+form of
+a shorthand
+
+ align:start position:0%
+a shorthand
+ 
+
+ align:start position:0%
+a shorthand
+and it says okay
+
+ align:start position:0%
+and it says okay
+ 
+
+ align:start position:0%
+and it says okay
+the jth
+
+ align:start position:0%
+the jth
+ 
+
+ align:start position:0%
+the jth
+normal
+
+ align:start position:0%
+normal
+ 
+
+ align:start position:0%
+normal
+displacement is given by the rules of
+
+ align:start position:0%
+displacement is given by the rules of
+ 
+
+ align:start position:0%
+displacement is given by the rules of
+matrix multiplication so we would have a
+
+ align:start position:0%
+matrix multiplication so we would have a
+ 
+
+ align:start position:0%
+matrix multiplication so we would have a
+sum over i
+
+ align:start position:0%
+sum over i
+ 
+
+ align:start position:0%
+sum over i
+of l minus 1 i j s
+
+ align:start position:0%
+of l minus 1 i j s
+ 
+
+ align:start position:0%
+of l minus 1 i j s
+j
+
+ align:start position:0%
+j
+ 
+
+ align:start position:0%
+j
+except that i did it wrong
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+no i did it
+
+ align:start position:0%
+no i did it
+ 
+
+ align:start position:0%
+no i did it
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+well
+
+ align:start position:0%
+well
+ 
+
+ align:start position:0%
+well
+s sub i j i
+
+ align:start position:0%
+s sub i j i
+ 
+
+ align:start position:0%
+s sub i j i
+that good that's good okay
+
+ align:start position:0%
+that good that's good okay
+ 
+
+ align:start position:0%
+that good that's good okay
+um this is the rules for
+
+ align:start position:0%
+um this is the rules for
+ 
+
+ align:start position:0%
+um this is the rules for
+who's beeping
+
+ align:start position:0%
+who's beeping
+ 
+
+ align:start position:0%
+who's beeping
+outside
+
+ align:start position:0%
+outside
+ 
+
+ align:start position:0%
+outside
+okay all right so this is the rules for
+
+ align:start position:0%
+okay all right so this is the rules for
+ 
+
+ align:start position:0%
+okay all right so this is the rules for
+matrix multiplication and this is
+
+ align:start position:0%
+matrix multiplication and this is
+ 
+
+ align:start position:0%
+matrix multiplication and this is
+telling us that if we had this l inverse
+
+ align:start position:0%
+telling us that if we had this l inverse
+ 
+
+ align:start position:0%
+telling us that if we had this l inverse
+matrix
+
+ align:start position:0%
+matrix
+ 
+
+ align:start position:0%
+matrix
+what would we do well we would take the
+
+ align:start position:0%
+what would we do well we would take the
+ 
+
+ align:start position:0%
+what would we do well we would take the
+jth row
+
+ align:start position:0%
+jth row
+ 
+
+ align:start position:0%
+jth row
+of the l inverse matrix and that would
+
+ align:start position:0%
+of the l inverse matrix and that would
+ 
+
+ align:start position:0%
+of the l inverse matrix and that would
+give us the information that we need to
+
+ align:start position:0%
+give us the information that we need to
+ 
+
+ align:start position:0%
+give us the information that we need to
+construct
+
+ align:start position:0%
+construct
+ 
+
+ align:start position:0%
+construct
+the jth
+
+ align:start position:0%
+the jth
+ 
+
+ align:start position:0%
+the jth
+normal mode from all of the internal
+
+ align:start position:0%
+normal mode from all of the internal
+ 
+
+ align:start position:0%
+normal mode from all of the internal
+displacements and i've always i'm always
+
+ align:start position:0%
+displacements and i've always i'm always
+ 
+
+ align:start position:0%
+displacements and i've always i'm always
+troubled or confused about do we want
+
+ align:start position:0%
+troubled or confused about do we want
+ 
+
+ align:start position:0%
+troubled or confused about do we want
+the the row or the column
+
+ align:start position:0%
+the the row or the column
+ 
+
+ align:start position:0%
+the the row or the column
+do we want the inverse matrix or the
+
+ align:start position:0%
+do we want the inverse matrix or the
+ 
+
+ align:start position:0%
+do we want the inverse matrix or the
+non-inverse matrix
+
+ align:start position:0%
+non-inverse matrix
+ 
+
+ align:start position:0%
+non-inverse matrix
+and there's only one correct answer
+
+ align:start position:0%
+and there's only one correct answer
+ 
+
+ align:start position:0%
+and there's only one correct answer
+and this is it
+
+ align:start position:0%
+and this is it
+ 
+
+ align:start position:0%
+and this is it
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+we describe
+
+ align:start position:0%
+we describe
+ 
+
+ align:start position:0%
+we describe
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+internal displacements using these
+
+ align:start position:0%
+internal displacements using these
+ 
+
+ align:start position:0%
+internal displacements using these
+st alpha
+
+ align:start position:0%
+st alpha
+ 
+
+ align:start position:0%
+st alpha
+u
+
+ align:start position:0%
+u
+ 
+
+ align:start position:0%
+u
+matrices
+
+ align:start position:0%
+matrices
+ 
+
+ align:start position:0%
+matrices
+displacement vectors alpha refers to the
+
+ align:start position:0%
+displacement vectors alpha refers to the
+ 
+
+ align:start position:0%
+displacement vectors alpha refers to the
+atom t refers to a particular internal
+
+ align:start position:0%
+atom t refers to a particular internal
+ 
+
+ align:start position:0%
+atom t refers to a particular internal
+displacement
+
+ align:start position:0%
+displacement
+ 
+
+ align:start position:0%
+displacement
+and these things are vectors
+
+ align:start position:0%
+and these things are vectors
+ 
+
+ align:start position:0%
+and these things are vectors
+of length one
+
+ align:start position:0%
+of length one
+ 
+
+ align:start position:0%
+of length one
+pointing in the direction where a
+
+ align:start position:0%
+pointing in the direction where a
+ 
+
+ align:start position:0%
+pointing in the direction where a
+displacement of one causes the maximum
+
+ align:start position:0%
+displacement of one causes the maximum
+ 
+
+ align:start position:0%
+displacement of one causes the maximum
+increase in the specified internal
+
+ align:start position:0%
+increase in the specified internal
+ 
+
+ align:start position:0%
+increase in the specified internal
+coordinate
+
+ align:start position:0%
+coordinate
+ 
+
+ align:start position:0%
+coordinate
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+a normal normal
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+a normal mode would involve harmonic
+
+ align:start position:0%
+a normal mode would involve harmonic
+ 
+
+ align:start position:0%
+a normal mode would involve harmonic
+motion of all of the atoms at the same
+
+ align:start position:0%
+motion of all of the atoms at the same
+ 
+
+ align:start position:0%
+motion of all of the atoms at the same
+frequency
+
+ align:start position:0%
+frequency
+ 
+
+ align:start position:0%
+frequency
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+okay so
+
+ align:start position:0%
+okay so
+ 
+
+ align:start position:0%
+okay so
+that's the review which you
+
+ align:start position:0%
+that's the review which you
+ 
+
+ align:start position:0%
+that's the review which you
+the stuff you know
+
+ align:start position:0%
+the stuff you know
+ 
+
+ align:start position:0%
+the stuff you know
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+now
+
+ align:start position:0%
+now
+ 
+
+ align:start position:0%
+now
+let's talk about water so we have a
+
+ align:start position:0%
+let's talk about water so we have a
+ 
+
+ align:start position:0%
+let's talk about water so we have a
+structure of water uh
+
+ align:start position:0%
+structure of water uh
+ 
+
+ align:start position:0%
+structure of water uh
+we'll call this one there's two this is
+
+ align:start position:0%
+we'll call this one there's two this is
+ 
+
+ align:start position:0%
+we'll call this one there's two this is
+and three this is conventional
+
+ align:start position:0%
+and three this is conventional
+ 
+
+ align:start position:0%
+and three this is conventional
+uh you would think one two three but
+
+ align:start position:0%
+uh you would think one two three but
+ 
+
+ align:start position:0%
+uh you would think one two three but
+this is the way it's most often labeled
+
+ align:start position:0%
+this is the way it's most often labeled
+ 
+
+ align:start position:0%
+this is the way it's most often labeled
+we have an angle and we have two
+
+ align:start position:0%
+we have an angle and we have two
+ 
+
+ align:start position:0%
+we have an angle and we have two
+bond lengths
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay and what we want to do is describe
+
+ align:start position:0%
+okay and what we want to do is describe
+ 
+
+ align:start position:0%
+okay and what we want to do is describe
+all of the internal displacement
+
+ align:start position:0%
+all of the internal displacement
+ 
+
+ align:start position:0%
+all of the internal displacement
+coordinates
+
+ align:start position:0%
+coordinates
+ 
+
+ align:start position:0%
+coordinates
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+build up the f and g matrices with which
+
+ align:start position:0%
+build up the f and g matrices with which
+ 
+
+ align:start position:0%
+build up the f and g matrices with which
+we can solve for all of the problems so
+
+ align:start position:0%
+we can solve for all of the problems so
+ 
+
+ align:start position:0%
+we can solve for all of the problems so
+by uh
+
+ align:start position:0%
+by uh
+ 
+
+ align:start position:0%
+by uh
+we we can we know that there are
+
+ align:start position:0%
+we we can we know that there are
+ 
+
+ align:start position:0%
+we we can we know that there are
+uh three n minus six or three
+
+ align:start position:0%
+uh three n minus six or three
+ 
+
+ align:start position:0%
+uh three n minus six or three
+normal modes there'll be three linearly
+
+ align:start position:0%
+normal modes there'll be three linearly
+ 
+
+ align:start position:0%
+normal modes there'll be three linearly
+independent
+
+ align:start position:0%
+independent
+ 
+
+ align:start position:0%
+independent
+internal displacements
+
+ align:start position:0%
+internal displacements
+ 
+
+ align:start position:0%
+internal displacements
+these three
+
+ align:start position:0%
+these three
+ 
+
+ align:start position:0%
+these three
+are
+
+ align:start position:0%
+are
+ 
+
+ align:start position:0%
+are
+a linearly independent set
+
+ align:start position:0%
+a linearly independent set
+ 
+
+ align:start position:0%
+a linearly independent set
+we can call one of them
+
+ align:start position:0%
+we can call one of them
+ 
+
+ align:start position:0%
+we can call one of them
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+there's no reason to worry about the
+
+ align:start position:0%
+there's no reason to worry about the
+ 
+
+ align:start position:0%
+there's no reason to worry about the
+numbering of the internal displacements
+
+ align:start position:0%
+numbering of the internal displacements
+ 
+
+ align:start position:0%
+numbering of the internal displacements
+but there is a reason to worry about the
+
+ align:start position:0%
+but there is a reason to worry about the
+ 
+
+ align:start position:0%
+but there is a reason to worry about the
+numbering of the normal modes
+
+ align:start position:0%
+numbering of the normal modes
+ 
+
+ align:start position:0%
+numbering of the normal modes
+and so we can choose whatever or we can
+
+ align:start position:0%
+and so we can choose whatever or we can
+ 
+
+ align:start position:0%
+and so we can choose whatever or we can
+call this uh we can call
+
+ align:start position:0%
+call this uh we can call
+ 
+
+ align:start position:0%
+call this uh we can call
+the stretch of
+
+ align:start position:0%
+the stretch of
+ 
+
+ align:start position:0%
+the stretch of
+the three one bond s1 the stretch
+
+ align:start position:0%
+the three one bond s1 the stretch
+ 
+
+ align:start position:0%
+the three one bond s1 the stretch
+of the
+
+ align:start position:0%
+of the
+ 
+
+ align:start position:0%
+of the
+three two bond s2 and the bend
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+s3
+
+ align:start position:0%
+s3
+ 
+
+ align:start position:0%
+s3
+and we then do the problem okay so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+in order to express these internal
+
+ align:start position:0%
+in order to express these internal
+ 
+
+ align:start position:0%
+in order to express these internal
+displacements which are motions of two
+
+ align:start position:0%
+displacements which are motions of two
+ 
+
+ align:start position:0%
+displacements which are motions of two
+or three atoms
+
+ align:start position:0%
+or three atoms
+ 
+
+ align:start position:0%
+or three atoms
+subject to the constraints that we don't
+
+ align:start position:0%
+subject to the constraints that we don't
+ 
+
+ align:start position:0%
+subject to the constraints that we don't
+want to move
+
+ align:start position:0%
+want to move
+ 
+
+ align:start position:0%
+want to move
+the molecule
+
+ align:start position:0%
+the molecule
+ 
+
+ align:start position:0%
+the molecule
+and we don't want to cause rotation
+
+ align:start position:0%
+and we don't want to cause rotation
+ 
+
+ align:start position:0%
+and we don't want to cause rotation
+we go through some
+
+ align:start position:0%
+we go through some
+ 
+
+ align:start position:0%
+we go through some
+vector analysis and we get the
+
+ align:start position:0%
+vector analysis and we get the
+ 
+
+ align:start position:0%
+vector analysis and we get the
+expressions
+
+ align:start position:0%
+expressions
+ 
+
+ align:start position:0%
+expressions
+for the
+
+ align:start position:0%
+for the
+ 
+
+ align:start position:0%
+for the
+little st alphas for the three atoms and
+
+ align:start position:0%
+little st alphas for the three atoms and
+ 
+
+ align:start position:0%
+little st alphas for the three atoms and
+the three internal displacements and
+
+ align:start position:0%
+the three internal displacements and
+ 
+
+ align:start position:0%
+the three internal displacements and
+that's
+
+ align:start position:0%
+that's
+ 
+
+ align:start position:0%
+that's
+a beautiful bit of vector analysis which
+
+ align:start position:0%
+a beautiful bit of vector analysis which
+ 
+
+ align:start position:0%
+a beautiful bit of vector analysis which
+i will not do
+
+ align:start position:0%
+i will not do
+ 
+
+ align:start position:0%
+i will not do
+and it's in the notes
+
+ align:start position:0%
+and it's in the notes
+ 
+
+ align:start position:0%
+and it's in the notes
+and the important thing
+
+ align:start position:0%
+and the important thing
+ 
+
+ align:start position:0%
+and the important thing
+is that
+
+ align:start position:0%
+is that
+ 
+
+ align:start position:0%
+is that
+you take this example
+
+ align:start position:0%
+you take this example
+ 
+
+ align:start position:0%
+you take this example
+and you apply it to a problem
+
+ align:start position:0%
+and you apply it to a problem
+ 
+
+ align:start position:0%
+and you apply it to a problem
+which is not too complicated and you get
+
+ align:start position:0%
+which is not too complicated and you get
+ 
+
+ align:start position:0%
+which is not too complicated and you get
+this you know you get the same results
+
+ align:start position:0%
+this you know you get the same results
+ 
+
+ align:start position:0%
+this you know you get the same results
+so i mean i ideally you'd apply it to
+
+ align:start position:0%
+so i mean i ideally you'd apply it to
+ 
+
+ align:start position:0%
+so i mean i ideally you'd apply it to
+water or d2o
+
+ align:start position:0%
+water or d2o
+ 
+
+ align:start position:0%
+water or d2o
+and see if you get
+
+ align:start position:0%
+and see if you get
+ 
+
+ align:start position:0%
+and see if you get
+if all the analysis is correct now one
+
+ align:start position:0%
+if all the analysis is correct now one
+ 
+
+ align:start position:0%
+if all the analysis is correct now one
+of the things about these guys
+
+ align:start position:0%
+of the things about these guys
+ 
+
+ align:start position:0%
+of the things about these guys
+is there are no
+
+ align:start position:0%
+is there are no
+ 
+
+ align:start position:0%
+is there are no
+masses involved
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and that's always bothered me because
+
+ align:start position:0%
+and that's always bothered me because
+ 
+
+ align:start position:0%
+and that's always bothered me because
+you would think that you'd describe the
+
+ align:start position:0%
+you would think that you'd describe the
+ 
+
+ align:start position:0%
+you would think that you'd describe the
+internal displacements in a way where
+
+ align:start position:0%
+internal displacements in a way where
+ 
+
+ align:start position:0%
+internal displacements in a way where
+you don't move the center mass
+
+ align:start position:0%
+you don't move the center mass
+ 
+
+ align:start position:0%
+you don't move the center mass
+but that's not it you're not you're
+
+ align:start position:0%
+but that's not it you're not you're
+ 
+
+ align:start position:0%
+but that's not it you're not you're
+you're
+
+ align:start position:0%
+you're
+ 
+
+ align:start position:0%
+you're
+uh you're moving the two atoms
+
+ align:start position:0%
+uh you're moving the two atoms
+ 
+
+ align:start position:0%
+uh you're moving the two atoms
+equal and opposite amounts
+
+ align:start position:0%
+equal and opposite amounts
+ 
+
+ align:start position:0%
+equal and opposite amounts
+uh in a bond stretch
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that's wonderful
+
+ align:start position:0%
+that's wonderful
+ 
+
+ align:start position:0%
+that's wonderful
+yes they are so that takes care of that
+
+ align:start position:0%
+yes they are so that takes care of that
+ 
+
+ align:start position:0%
+yes they are so that takes care of that
+completely fantastic
+
+ align:start position:0%
+completely fantastic
+ 
+
+ align:start position:0%
+completely fantastic
+i didn't understand that thank you
+
+ align:start position:0%
+i didn't understand that thank you
+ 
+
+ align:start position:0%
+i didn't understand that thank you
+i mean it really it's always bothered me
+
+ align:start position:0%
+i mean it really it's always bothered me
+ 
+
+ align:start position:0%
+i mean it really it's always bothered me
+i every time i go through this i see no
+
+ align:start position:0%
+i every time i go through this i see no
+ 
+
+ align:start position:0%
+i every time i go through this i see no
+masses
+
+ align:start position:0%
+masses
+ 
+
+ align:start position:0%
+masses
+they're already in there
+
+ align:start position:0%
+they're already in there
+ 
+
+ align:start position:0%
+they're already in there
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+see
+
+ align:start position:0%
+see
+ 
+
+ align:start position:0%
+see
+we we all learn here
+
+ align:start position:0%
+we we all learn here
+ 
+
+ align:start position:0%
+we we all learn here
+okay so
+
+ align:start position:0%
+okay so
+ 
+
+ align:start position:0%
+okay so
+we derive these uh
+
+ align:start position:0%
+we derive these uh
+ 
+
+ align:start position:0%
+we derive these uh
+little
+
+ align:start position:0%
+little
+ 
+
+ align:start position:0%
+little
+s vectors
+
+ align:start position:0%
+s vectors
+ 
+
+ align:start position:0%
+s vectors
+and we can build up each of the internal
+
+ align:start position:0%
+and we can build up each of the internal
+ 
+
+ align:start position:0%
+and we can build up each of the internal
+displacements
+
+ align:start position:0%
+displacements
+ 
+
+ align:start position:0%
+displacements
+subject to the constraints
+
+ align:start position:0%
+subject to the constraints
+ 
+
+ align:start position:0%
+subject to the constraints
+now one of the things you find is that
+
+ align:start position:0%
+now one of the things you find is that
+ 
+
+ align:start position:0%
+now one of the things you find is that
+here we have two stretches and these
+
+ align:start position:0%
+here we have two stretches and these
+ 
+
+ align:start position:0%
+here we have two stretches and these
+have units of length and here we have a
+
+ align:start position:0%
+have units of length and here we have a
+ 
+
+ align:start position:0%
+have units of length and here we have a
+bend which has a unit of angle and these
+
+ align:start position:0%
+bend which has a unit of angle and these
+ 
+
+ align:start position:0%
+bend which has a unit of angle and these
+don't have the same dimensionality
+
+ align:start position:0%
+don't have the same dimensionality
+ 
+
+ align:start position:0%
+don't have the same dimensionality
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+if you don't like that you can define
+
+ align:start position:0%
+if you don't like that you can define
+ 
+
+ align:start position:0%
+if you don't like that you can define
+a different
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+bend
+
+ align:start position:0%
+bend
+ 
+
+ align:start position:0%
+bend
+internal displacement simply by
+
+ align:start position:0%
+internal displacement simply by
+ 
+
+ align:start position:0%
+internal displacement simply by
+weighting the change in angle by
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the equilibrium bond lengths of the two
+
+ align:start position:0%
+the equilibrium bond lengths of the two
+ 
+
+ align:start position:0%
+the equilibrium bond lengths of the two
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+bonds
+
+ align:start position:0%
+bonds
+ 
+
+ align:start position:0%
+bonds
+and then all of the internal
+
+ align:start position:0%
+and then all of the internal
+ 
+
+ align:start position:0%
+and then all of the internal
+displacements have the same
+
+ align:start position:0%
+displacements have the same
+ 
+
+ align:start position:0%
+displacements have the same
+dimensionality this actually makes you
+
+ align:start position:0%
+dimensionality this actually makes you
+ 
+
+ align:start position:0%
+dimensionality this actually makes you
+feel better because the matrices we're
+
+ align:start position:0%
+feel better because the matrices we're
+ 
+
+ align:start position:0%
+feel better because the matrices we're
+going to develop the f and g matrices
+
+ align:start position:0%
+going to develop the f and g matrices
+ 
+
+ align:start position:0%
+going to develop the f and g matrices
+they also have elements that have
+
+ align:start position:0%
+they also have elements that have
+ 
+
+ align:start position:0%
+they also have elements that have
+different dimensionality
+
+ align:start position:0%
+different dimensionality
+ 
+
+ align:start position:0%
+different dimensionality
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+that goes away if you make all the
+
+ align:start position:0%
+that goes away if you make all the
+ 
+
+ align:start position:0%
+that goes away if you make all the
+internal displacements have the same
+
+ align:start position:0%
+internal displacements have the same
+ 
+
+ align:start position:0%
+internal displacements have the same
+dimensionality however
+
+ align:start position:0%
+dimensionality however
+ 
+
+ align:start position:0%
+dimensionality however
+even though
+
+ align:start position:0%
+even though
+ 
+
+ align:start position:0%
+even though
+these matrices have elements with
+
+ align:start position:0%
+these matrices have elements with
+ 
+
+ align:start position:0%
+these matrices have elements with
+different units or different
+
+ align:start position:0%
+different units or different
+ 
+
+ align:start position:0%
+different units or different
+dimensionality when you expand the
+
+ align:start position:0%
+dimensionality when you expand the
+ 
+
+ align:start position:0%
+dimensionality when you expand the
+matrix to get the you know to evaluate
+
+ align:start position:0%
+matrix to get the you know to evaluate
+ 
+
+ align:start position:0%
+matrix to get the you know to evaluate
+when you expand the determinant that's
+
+ align:start position:0%
+when you expand the determinant that's
+ 
+
+ align:start position:0%
+when you expand the determinant that's
+supposed to be a number
+
+ align:start position:0%
+supposed to be a number
+ 
+
+ align:start position:0%
+supposed to be a number
+and in that expansion of the determinant
+
+ align:start position:0%
+and in that expansion of the determinant
+ 
+
+ align:start position:0%
+and in that expansion of the determinant
+you're multiplying a whole bunch of
+
+ align:start position:0%
+you're multiplying a whole bunch of
+ 
+
+ align:start position:0%
+you're multiplying a whole bunch of
+numbers and every term in that sum of
+
+ align:start position:0%
+numbers and every term in that sum of
+ 
+
+ align:start position:0%
+numbers and every term in that sum of
+products
+
+ align:start position:0%
+products
+ 
+
+ align:start position:0%
+products
+has the same dimensionality whether you
+
+ align:start position:0%
+has the same dimensionality whether you
+ 
+
+ align:start position:0%
+has the same dimensionality whether you
+do this or not
+
+ align:start position:0%
+do this or not
+ 
+
+ align:start position:0%
+do this or not
+but it's a good way of checking to see
+
+ align:start position:0%
+but it's a good way of checking to see
+ 
+
+ align:start position:0%
+but it's a good way of checking to see
+whether you've made a mistake
+
+ align:start position:0%
+whether you've made a mistake
+ 
+
+ align:start position:0%
+whether you've made a mistake
+if
+
+ align:start position:0%
+if
+ 
+
+ align:start position:0%
+if
+you know some
+
+ align:start position:0%
+you know some
+ 
+
+ align:start position:0%
+you know some
+element in your in one of the matrices
+
+ align:start position:0%
+element in your in one of the matrices
+ 
+
+ align:start position:0%
+element in your in one of the matrices
+has the wrong dimensionality okay so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+we can do this or we cannot do that as
+
+ align:start position:0%
+we can do this or we cannot do that as
+ 
+
+ align:start position:0%
+we can do this or we cannot do that as
+you wish
+
+ align:start position:0%
+you wish
+ 
+
+ align:start position:0%
+you wish
+okay so
+
+ align:start position:0%
+okay so
+ 
+
+ align:start position:0%
+okay so
+first step was
+
+ align:start position:0%
+first step was
+ 
+
+ align:start position:0%
+first step was
+figuring out these little st alphas
+
+ align:start position:0%
+figuring out these little st alphas
+ 
+
+ align:start position:0%
+figuring out these little st alphas
+because we want to draw pictures of the
+
+ align:start position:0%
+because we want to draw pictures of the
+ 
+
+ align:start position:0%
+because we want to draw pictures of the
+displacements
+
+ align:start position:0%
+displacements
+ 
+
+ align:start position:0%
+displacements
+the next step is to
+
+ align:start position:0%
+the next step is to
+ 
+
+ align:start position:0%
+the next step is to
+compute
+
+ align:start position:0%
+compute
+ 
+
+ align:start position:0%
+compute
+what's called the g matrix
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and this is a matrix that contains
+
+ align:start position:0%
+and this is a matrix that contains
+ 
+
+ align:start position:0%
+and this is a matrix that contains
+masses and geometry
+
+ align:start position:0%
+masses and geometry
+ 
+
+ align:start position:0%
+masses and geometry
+and it's used to uh
+
+ align:start position:0%
+and it's used to uh
+ 
+
+ align:start position:0%
+and it's used to uh
+evaluate the contribution of the kinetic
+
+ align:start position:0%
+evaluate the contribution of the kinetic
+ 
+
+ align:start position:0%
+evaluate the contribution of the kinetic
+energy to the total hamiltonian
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+now
+
+ align:start position:0%
+now
+ 
+
+ align:start position:0%
+now
+there are a limited this is so beautiful
+
+ align:start position:0%
+there are a limited this is so beautiful
+ 
+
+ align:start position:0%
+there are a limited this is so beautiful
+i get i get a little thrill every time i
+
+ align:start position:0%
+i get i get a little thrill every time i
+ 
+
+ align:start position:0%
+i get i get a little thrill every time i
+look at this when we're worried about
+
+ align:start position:0%
+look at this when we're worried about
+ 
+
+ align:start position:0%
+look at this when we're worried about
+the vibrations of polyatomic molecules
+
+ align:start position:0%
+the vibrations of polyatomic molecules
+ 
+
+ align:start position:0%
+the vibrations of polyatomic molecules
+when we talk about internal
+
+ align:start position:0%
+when we talk about internal
+ 
+
+ align:start position:0%
+when we talk about internal
+displacements they involve a very small
+
+ align:start position:0%
+displacements they involve a very small
+ 
+
+ align:start position:0%
+displacements they involve a very small
+number of atoms two first stretch three
+
+ align:start position:0%
+number of atoms two first stretch three
+ 
+
+ align:start position:0%
+number of atoms two first stretch three
+for a bend
+
+ align:start position:0%
+for a bend
+ 
+
+ align:start position:0%
+for a bend
+uh four for a torsion
+
+ align:start position:0%
+uh four for a torsion
+ 
+
+ align:start position:0%
+uh four for a torsion
+uh and then that's you could have much
+
+ align:start position:0%
+uh and then that's you could have much
+ 
+
+ align:start position:0%
+uh and then that's you could have much
+much bigger molecules than that
+
+ align:start position:0%
+much bigger molecules than that
+ 
+
+ align:start position:0%
+much bigger molecules than that
+yet
+
+ align:start position:0%
+yet
+ 
+
+ align:start position:0%
+yet
+uh there is a limited number of
+
+ align:start position:0%
+uh there is a limited number of
+ 
+
+ align:start position:0%
+uh there is a limited number of
+topological cases and if you're clever
+
+ align:start position:0%
+topological cases and if you're clever
+ 
+
+ align:start position:0%
+topological cases and if you're clever
+with vector analysis you can work out
+
+ align:start position:0%
+with vector analysis you can work out
+ 
+
+ align:start position:0%
+with vector analysis you can work out
+all of them
+
+ align:start position:0%
+all of them
+ 
+
+ align:start position:0%
+all of them
+and some of them are pretty evil the
+
+ align:start position:0%
+and some of them are pretty evil the
+ 
+
+ align:start position:0%
+and some of them are pretty evil the
+torsions are terrible
+
+ align:start position:0%
+torsions are terrible
+ 
+
+ align:start position:0%
+torsions are terrible
+especially torsions combined with other
+
+ align:start position:0%
+especially torsions combined with other
+ 
+
+ align:start position:0%
+especially torsions combined with other
+things but it can be done and that has
+
+ align:start position:0%
+things but it can be done and that has
+ 
+
+ align:start position:0%
+things but it can be done and that has
+been done
+
+ align:start position:0%
+been done
+ 
+
+ align:start position:0%
+been done
+and so
+
+ align:start position:0%
+and so
+ 
+
+ align:start position:0%
+and so
+the papers by
+
+ align:start position:0%
+the papers by
+ 
+
+ align:start position:0%
+the papers by
+theseus and the book by wilson deceased
+
+ align:start position:0%
+theseus and the book by wilson deceased
+ 
+
+ align:start position:0%
+theseus and the book by wilson deceased
+and cross it's all done there
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and so
+
+ align:start position:0%
+and so
+ 
+
+ align:start position:0%
+and so
+then you don't want to have to do this
+
+ align:start position:0%
+then you don't want to have to do this
+ 
+
+ align:start position:0%
+then you don't want to have to do this
+you want to be able to look up
+
+ align:start position:0%
+you want to be able to look up
+ 
+
+ align:start position:0%
+you want to be able to look up
+all of the relevant elements of this g
+
+ align:start position:0%
+all of the relevant elements of this g
+ 
+
+ align:start position:0%
+all of the relevant elements of this g
+matrix
+
+ align:start position:0%
+matrix
+ 
+
+ align:start position:0%
+matrix
+expressed in terms of the things you
+
+ align:start position:0%
+expressed in terms of the things you
+ 
+
+ align:start position:0%
+expressed in terms of the things you
+know
+
+ align:start position:0%
+know
+ 
+
+ align:start position:0%
+know
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+because it's a little bit complicated in
+
+ align:start position:0%
+because it's a little bit complicated in
+ 
+
+ align:start position:0%
+because it's a little bit complicated in
+general the
+
+ align:start position:0%
+general the
+ 
+
+ align:start position:0%
+general the
+matrix the elements of this g matrix are
+
+ align:start position:0%
+matrix the elements of this g matrix are
+ 
+
+ align:start position:0%
+matrix the elements of this g matrix are
+tabulated
+
+ align:start position:0%
+tabulated
+ 
+
+ align:start position:0%
+tabulated
+in a kind of code
+
+ align:start position:0%
+in a kind of code
+ 
+
+ align:start position:0%
+in a kind of code
+it's a very elegant code
+
+ align:start position:0%
+it's a very elegant code
+ 
+
+ align:start position:0%
+it's a very elegant code
+uh but it's it it's it's easy to make
+
+ align:start position:0%
+uh but it's it it's it's easy to make
+ 
+
+ align:start position:0%
+uh but it's it it's it's easy to make
+mistakes in interpreting those elements
+
+ align:start position:0%
+mistakes in interpreting those elements
+ 
+
+ align:start position:0%
+mistakes in interpreting those elements
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+there are more than four types of uh
+
+ align:start position:0%
+there are more than four types of uh
+ 
+
+ align:start position:0%
+there are more than four types of uh
+elements of the g matrix the simplest
+
+ align:start position:0%
+elements of the g matrix the simplest
+ 
+
+ align:start position:0%
+elements of the g matrix the simplest
+one is
+
+ align:start position:0%
+one is
+ 
+
+ align:start position:0%
+one is
+something that's done like this
+
+ align:start position:0%
+something that's done like this
+ 
+
+ align:start position:0%
+something that's done like this
+rr just means two stretches
+
+ align:start position:0%
+rr just means two stretches
+ 
+
+ align:start position:0%
+rr just means two stretches
+now
+
+ align:start position:0%
+now
+ 
+
+ align:start position:0%
+now
+the elements are not tabulated with r
+
+ align:start position:0%
+the elements are not tabulated with r
+ 
+
+ align:start position:0%
+the elements are not tabulated with r
+and r prime it just means it's a stretch
+
+ align:start position:0%
+and r prime it just means it's a stretch
+ 
+
+ align:start position:0%
+and r prime it just means it's a stretch
+stretch interaction it could be diagonal
+
+ align:start position:0%
+stretch interaction it could be diagonal
+ 
+
+ align:start position:0%
+stretch interaction it could be diagonal
+could be off diagonal and two means two
+
+ align:start position:0%
+could be off diagonal and two means two
+ 
+
+ align:start position:0%
+could be off diagonal and two means two
+atoms that means it's the the element
+
+ align:start position:0%
+atoms that means it's the the element
+ 
+
+ align:start position:0%
+atoms that means it's the the element
+involving the same two atoms
+
+ align:start position:0%
+involving the same two atoms
+ 
+
+ align:start position:0%
+involving the same two atoms
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+twice and there is a diagram
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that
+
+ align:start position:0%
+that
+ 
+
+ align:start position:0%
+that
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+goes with this symbol
+
+ align:start position:0%
+goes with this symbol
+ 
+
+ align:start position:0%
+goes with this symbol
+and this just says okay we have atom one
+
+ align:start position:0%
+and this just says okay we have atom one
+ 
+
+ align:start position:0%
+and this just says okay we have atom one
+and atom two and two circles are on atom
+
+ align:start position:0%
+and atom two and two circles are on atom
+ 
+
+ align:start position:0%
+and atom two and two circles are on atom
+one two circles around atom two means
+
+ align:start position:0%
+one two circles around atom two means
+ 
+
+ align:start position:0%
+one two circles around atom two means
+that
+
+ align:start position:0%
+that
+ 
+
+ align:start position:0%
+that
+this is a matrix element between two
+
+ align:start position:0%
+this is a matrix element between two
+ 
+
+ align:start position:0%
+this is a matrix element between two
+internal displacements the same two
+
+ align:start position:0%
+internal displacements the same two
+ 
+
+ align:start position:0%
+internal displacements the same two
+atoms are involved in both
+
+ align:start position:0%
+atoms are involved in both
+ 
+
+ align:start position:0%
+atoms are involved in both
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+are the
+
+ align:start position:0%
+are the
+ 
+
+ align:start position:0%
+are the
+involved here and here now we could
+
+ align:start position:0%
+involved here and here now we could
+ 
+
+ align:start position:0%
+involved here and here now we could
+uh if we had something where
+
+ align:start position:0%
+uh if we had something where
+ 
+
+ align:start position:0%
+uh if we had something where
+we had
+
+ align:start position:0%
+we had
+ 
+
+ align:start position:0%
+we had
+three atoms
+
+ align:start position:0%
+three atoms
+ 
+
+ align:start position:0%
+three atoms
+and two circles around one
+
+ align:start position:0%
+and two circles around one
+ 
+
+ align:start position:0%
+and two circles around one
+that would be an interaction between one
+
+ align:start position:0%
+that would be an interaction between one
+ 
+
+ align:start position:0%
+that would be an interaction between one
+stretch here and one stretch here
+
+ align:start position:0%
+stretch here and one stretch here
+ 
+
+ align:start position:0%
+stretch here and one stretch here
+that would still
+
+ align:start position:0%
+that would still
+ 
+
+ align:start position:0%
+that would still
+be
+
+ align:start position:0%
+be
+ 
+
+ align:start position:0%
+be
+rr but it would have a one up there
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and so it could be straight straight it
+
+ align:start position:0%
+and so it could be straight straight it
+ 
+
+ align:start position:0%
+and so it could be straight straight it
+could be bent and we
+
+ align:start position:0%
+could be bent and we
+ 
+
+ align:start position:0%
+could be bent and we
+these things tend to have
+
+ align:start position:0%
+these things tend to have
+ 
+
+ align:start position:0%
+these things tend to have
+numbers on them because the elements
+
+ align:start position:0%
+numbers on them because the elements
+ 
+
+ align:start position:0%
+numbers on them because the elements
+that are tabulated
+
+ align:start position:0%
+that are tabulated
+ 
+
+ align:start position:0%
+that are tabulated
+uh make use of those numbers and so it's
+
+ align:start position:0%
+uh make use of those numbers and so it's
+ 
+
+ align:start position:0%
+uh make use of those numbers and so it's
+a good thing
+
+ align:start position:0%
+a good thing
+ 
+
+ align:start position:0%
+a good thing
+to
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+exploit the numbers
+
+ align:start position:0%
+exploit the numbers
+ 
+
+ align:start position:0%
+exploit the numbers
+we could have
+
+ align:start position:0%
+we could have
+ 
+
+ align:start position:0%
+we could have
+three
+
+ align:start position:0%
+three
+ 
+
+ align:start position:0%
+three
+atoms
+
+ align:start position:0%
+atoms
+ 
+
+ align:start position:0%
+atoms
+connected
+
+ align:start position:0%
+connected
+ 
+
+ align:start position:0%
+connected
+circles
+
+ align:start position:0%
+circles
+ 
+
+ align:start position:0%
+circles
+like that
+
+ align:start position:0%
+like that
+ 
+
+ align:start position:0%
+like that
+and you know immediately that the only
+
+ align:start position:0%
+and you know immediately that the only
+ 
+
+ align:start position:0%
+and you know immediately that the only
+way three atoms could be involved in
+
+ align:start position:0%
+way three atoms could be involved in
+ 
+
+ align:start position:0%
+way three atoms could be involved in
+both motions would be for a diagonal
+
+ align:start position:0%
+both motions would be for a diagonal
+ 
+
+ align:start position:0%
+both motions would be for a diagonal
+bend bend interaction and that would
+
+ align:start position:0%
+bend bend interaction and that would
+ 
+
+ align:start position:0%
+bend bend interaction and that would
+correspond to three atoms
+
+ align:start position:0%
+correspond to three atoms
+ 
+
+ align:start position:0%
+correspond to three atoms
+and uh
+
+ align:start position:0%
+and uh
+ 
+
+ align:start position:0%
+and uh
+phi five
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and again
+
+ align:start position:0%
+and again
+ 
+
+ align:start position:0%
+and again
+they should be numbered three
+
+ align:start position:0%
+they should be numbered three
+ 
+
+ align:start position:0%
+they should be numbered three
+now i don't know why
+
+ align:start position:0%
+now i don't know why
+ 
+
+ align:start position:0%
+now i don't know why
+the numbering is topologically different
+
+ align:start position:0%
+the numbering is topologically different
+ 
+
+ align:start position:0%
+the numbering is topologically different
+for this and it's possible that i
+
+ align:start position:0%
+for this and it's possible that i
+ 
+
+ align:start position:0%
+for this and it's possible that i
+screwed up on one of them
+
+ align:start position:0%
+screwed up on one of them
+ 
+
+ align:start position:0%
+screwed up on one of them
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+we could have a bend stretch interaction
+
+ align:start position:0%
+we could have a bend stretch interaction
+ 
+
+ align:start position:0%
+we could have a bend stretch interaction
+where we'd have three
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+so here we have a bending motion
+
+ align:start position:0%
+so here we have a bending motion
+ 
+
+ align:start position:0%
+so here we have a bending motion
+between these three involving these
+
+ align:start position:0%
+between these three involving these
+ 
+
+ align:start position:0%
+between these three involving these
+three atoms and a stretch involving two
+
+ align:start position:0%
+three atoms and a stretch involving two
+ 
+
+ align:start position:0%
+three atoms and a stretch involving two
+and so
+
+ align:start position:0%
+and so
+ 
+
+ align:start position:0%
+and so
+that would be a g2
+
+ align:start position:0%
+that would be a g2
+ 
+
+ align:start position:0%
+that would be a g2
+because there's two atoms in common
+
+ align:start position:0%
+because there's two atoms in common
+ 
+
+ align:start position:0%
+because there's two atoms in common
+and it would be in our
+
+ align:start position:0%
+and it would be in our
+ 
+
+ align:start position:0%
+and it would be in our
+whoops an r5
+
+ align:start position:0%
+whoops an r5
+ 
+
+ align:start position:0%
+whoops an r5
+okay so there are more symbols than this
+
+ align:start position:0%
+okay so there are more symbols than this
+ 
+
+ align:start position:0%
+okay so there are more symbols than this
+in the
+
+ align:start position:0%
+in the
+ 
+
+ align:start position:0%
+in the
+table tables but uh i think this is so
+
+ align:start position:0%
+table tables but uh i think this is so
+ 
+
+ align:start position:0%
+table tables but uh i think this is so
+beautiful
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+it's even worse uh because
+
+ align:start position:0%
+it's even worse uh because
+ 
+
+ align:start position:0%
+it's even worse uh because
+then when you go
+
+ align:start position:0%
+then when you go
+ 
+
+ align:start position:0%
+then when you go
+to look up
+
+ align:start position:0%
+to look up
+ 
+
+ align:start position:0%
+to look up
+the elements g11
+
+ align:start position:0%
+the elements g11
+ 
+
+ align:start position:0%
+the elements g11
+or well g one one
+
+ align:start position:0%
+or well g one one
+ 
+
+ align:start position:0%
+or well g one one
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+uh suppose we have uh
+
+ align:start position:0%
+uh suppose we have uh
+ 
+
+ align:start position:0%
+uh suppose we have uh
+uh the one internal coordinate is a
+
+ align:start position:0%
+uh the one internal coordinate is a
+ 
+
+ align:start position:0%
+uh the one internal coordinate is a
+stretch well g one one
+
+ align:start position:0%
+stretch well g one one
+ 
+
+ align:start position:0%
+stretch well g one one
+is then equal to
+
+ align:start position:0%
+is then equal to
+ 
+
+ align:start position:0%
+is then equal to
+g
+
+ align:start position:0%
+g
+ 
+
+ align:start position:0%
+g
+
+ align:start position:0%
+ 
+
+ align:start position:0%
+r 3 1 r
+
+ align:start position:0%
+r 3 1 r
+ 
+
+ align:start position:0%
+r 3 1 r
+3 1.
+
+ align:start position:0%
+3 1.
+ 
+
+ align:start position:0%
+3 1.
+in other words it's two identical
+
+ align:start position:0%
+in other words it's two identical
+ 
+
+ align:start position:0%
+in other words it's two identical
+stretches
+
+ align:start position:0%
+stretches
+ 
+
+ align:start position:0%
+stretches
+and then you're told to to write mu 1
+
+ align:start position:0%
+and then you're told to to write mu 1
+ 
+
+ align:start position:0%
+and then you're told to to write mu 1
+plus u2
+
+ align:start position:0%
+plus u2
+ 
+
+ align:start position:0%
+plus u2
+and this is 1 over the mass of atom one
+
+ align:start position:0%
+and this is 1 over the mass of atom one
+ 
+
+ align:start position:0%
+and this is 1 over the mass of atom one
+and this is one over the mass of atom
+
+ align:start position:0%
+and this is one over the mass of atom
+ 
+
+ align:start position:0%
+and this is one over the mass of atom
+two one place where you make mistakes mu
+
+ align:start position:0%
+two one place where you make mistakes mu
+ 
+
+ align:start position:0%
+two one place where you make mistakes mu
+sounds like mass
+
+ align:start position:0%
+sounds like mass
+ 
+
+ align:start position:0%
+sounds like mass
+but it's one reciprocal mess
+
+ align:start position:0%
+but it's one reciprocal mess
+ 
+
+ align:start position:0%
+but it's one reciprocal mess
+it's easy to screw up
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+anyway i'm not going to write more of
+
+ align:start position:0%
+anyway i'm not going to write more of
+ 
+
+ align:start position:0%
+anyway i'm not going to write more of
+them another place where you screw up is
+
+ align:start position:0%
+them another place where you screw up is
+ 
+
+ align:start position:0%
+them another place where you screw up is
+often distances appear and they appear
+
+ align:start position:0%
+often distances appear and they appear
+ 
+
+ align:start position:0%
+often distances appear and they appear
+with the symbol rho rather than r
+
+ align:start position:0%
+with the symbol rho rather than r
+ 
+
+ align:start position:0%
+with the symbol rho rather than r
+and those are reciprocal distances
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so there are two places where you could
+
+ align:start position:0%
+so there are two places where you could
+ 
+
+ align:start position:0%
+so there are two places where you could
+be led to think you understand
+
+ align:start position:0%
+be led to think you understand
+ 
+
+ align:start position:0%
+be led to think you understand
+especially if you're using a table you
+
+ align:start position:0%
+especially if you're using a table you
+ 
+
+ align:start position:0%
+especially if you're using a table you
+didn't make
+
+ align:start position:0%
+didn't make
+ 
+
+ align:start position:0%
+didn't make
+but
+
+ align:start position:0%
+but
+ 
+
+ align:start position:0%
+but
+once you have
+
+ align:start position:0%
+once you have
+ 
+
+ align:start position:0%
+once you have
+considered that it's done
+
+ align:start position:0%
+considered that it's done
+ 
+
+ align:start position:0%
+considered that it's done
+okay so
+
+ align:start position:0%
+okay so
+ 
+
+ align:start position:0%
+okay so
+you have this
+
+ align:start position:0%
+you have this
+ 
+
+ align:start position:0%
+you have this
+g matrix which you need to describe the
+
+ align:start position:0%
+g matrix which you need to describe the
+ 
+
+ align:start position:0%
+g matrix which you need to describe the
+kinetic energy of the vibrating molecule
+
+ align:start position:0%
+kinetic energy of the vibrating molecule
+ 
+
+ align:start position:0%
+kinetic energy of the vibrating molecule
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+uh once you have it in symbolic form you
+
+ align:start position:0%
+uh once you have it in symbolic form you
+ 
+
+ align:start position:0%
+uh once you have it in symbolic form you
+can put in the masses and the distances
+
+ align:start position:0%
+can put in the masses and the distances
+ 
+
+ align:start position:0%
+can put in the masses and the distances
+and the angles and you can make this a
+
+ align:start position:0%
+and the angles and you can make this a
+ 
+
+ align:start position:0%
+and the angles and you can make this a
+numerical matrix
+
+ align:start position:0%
+numerical matrix
+ 
+
+ align:start position:0%
+numerical matrix
+and so
+
+ align:start position:0%
+and so
+ 
+
+ align:start position:0%
+and so
+you can derive
+
+ align:start position:0%
+you can derive
+ 
+
+ align:start position:0%
+you can derive
+the numerical g matrix
+
+ align:start position:0%
+the numerical g matrix
+ 
+
+ align:start position:0%
+the numerical g matrix
+and for water it's a three by three
+
+ align:start position:0%
+and for water it's a three by three
+ 
+
+ align:start position:0%
+and for water it's a three by three
+matrix the elements have different units
+
+ align:start position:0%
+matrix the elements have different units
+ 
+
+ align:start position:0%
+matrix the elements have different units
+and the elements not only have different
+
+ align:start position:0%
+and the elements not only have different
+ 
+
+ align:start position:0%
+and the elements not only have different
+units i'm using forbidden units of
+
+ align:start position:0%
+units i'm using forbidden units of
+ 
+
+ align:start position:0%
+units i'm using forbidden units of
+nines milodynes most of you don't even
+
+ align:start position:0%
+nines milodynes most of you don't even
+ 
+
+ align:start position:0%
+nines milodynes most of you don't even
+know i gave a lecture in france a few
+
+ align:start position:0%
+know i gave a lecture in france a few
+ 
+
+ align:start position:0%
+know i gave a lecture in france a few
+years ago and i was nearly killed when i
+
+ align:start position:0%
+years ago and i was nearly killed when i
+ 
+
+ align:start position:0%
+years ago and i was nearly killed when i
+started talking about dines
+
+ align:start position:0%
+started talking about dines
+ 
+
+ align:start position:0%
+started talking about dines
+and
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and ergs rather than
+
+ align:start position:0%
+and ergs rather than
+ 
+
+ align:start position:0%
+and ergs rather than
+newtons and jewels and
+
+ align:start position:0%
+newtons and jewels and
+ 
+
+ align:start position:0%
+newtons and jewels and
+but
+
+ align:start position:0%
+but
+ 
+
+ align:start position:0%
+but
+anyway
+
+ align:start position:0%
+anyway
+ 
+
+ align:start position:0%
+anyway
+this is an old subject and i learned it
+
+ align:start position:0%
+this is an old subject and i learned it
+ 
+
+ align:start position:0%
+this is an old subject and i learned it
+a long time ago my notes are have dines
+
+ align:start position:0%
+a long time ago my notes are have dines
+ 
+
+ align:start position:0%
+a long time ago my notes are have dines
+but the important thing is that you can
+
+ align:start position:0%
+but the important thing is that you can
+ 
+
+ align:start position:0%
+but the important thing is that you can
+convert the uh
+
+ align:start position:0%
+convert the uh
+ 
+
+ align:start position:0%
+convert the uh
+units to something uh uh
+
+ align:start position:0%
+units to something uh uh
+ 
+
+ align:start position:0%
+units to something uh uh
+more universal and uh
+
+ align:start position:0%
+more universal and uh
+ 
+
+ align:start position:0%
+more universal and uh
+so anyway you you you get the g matrix
+
+ align:start position:0%
+so anyway you you you get the g matrix
+ 
+
+ align:start position:0%
+so anyway you you you get the g matrix
+and the
+
+ align:start position:0%
+and the
+ 
+
+ align:start position:0%
+and the
+f matrix now the f matrix is the matrix
+
+ align:start position:0%
+f matrix now the f matrix is the matrix
+ 
+
+ align:start position:0%
+f matrix now the f matrix is the matrix
+of force constants
+
+ align:start position:0%
+of force constants
+ 
+
+ align:start position:0%
+of force constants
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+what are the
+
+ align:start position:0%
+what are the
+ 
+
+ align:start position:0%
+what are the
+um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+what force does it take
+
+ align:start position:0%
+what force does it take
+ 
+
+ align:start position:0%
+what force does it take
+to stretch the ver to change the various
+
+ align:start position:0%
+to stretch the ver to change the various
+ 
+
+ align:start position:0%
+to stretch the ver to change the various
+internal coordinates
+
+ align:start position:0%
+internal coordinates
+ 
+
+ align:start position:0%
+internal coordinates
+and one can get these
+
+ align:start position:0%
+and one can get these
+ 
+
+ align:start position:0%
+and one can get these
+uh elements of the force constant matrix
+
+ align:start position:0%
+uh elements of the force constant matrix
+ 
+
+ align:start position:0%
+uh elements of the force constant matrix
+by fitting a lot of spectra
+
+ align:start position:0%
+by fitting a lot of spectra
+ 
+
+ align:start position:0%
+by fitting a lot of spectra
+or by doing an initial calculation but
+
+ align:start position:0%
+or by doing an initial calculation but
+ 
+
+ align:start position:0%
+or by doing an initial calculation but
+when you do and i've initial calculation
+
+ align:start position:0%
+when you do and i've initial calculation
+ 
+
+ align:start position:0%
+when you do and i've initial calculation
+what you get
+
+ align:start position:0%
+what you get
+ 
+
+ align:start position:0%
+what you get
+is not a
+
+ align:start position:0%
+is not a
+ 
+
+ align:start position:0%
+is not a
+three n minus six by three n minus six
+
+ align:start position:0%
+three n minus six by three n minus six
+ 
+
+ align:start position:0%
+three n minus six by three n minus six
+dimensional force constant matrix you
+
+ align:start position:0%
+dimensional force constant matrix you
+ 
+
+ align:start position:0%
+dimensional force constant matrix you
+get a three n by three n matrix and you
+
+ align:start position:0%
+get a three n by three n matrix and you
+ 
+
+ align:start position:0%
+get a three n by three n matrix and you
+have to do a transformation to reduce it
+
+ align:start position:0%
+have to do a transformation to reduce it
+ 
+
+ align:start position:0%
+have to do a transformation to reduce it
+to this
+
+ align:start position:0%
+to this
+ 
+
+ align:start position:0%
+to this
+okay but that's if you have the s's then
+
+ align:start position:0%
+okay but that's if you have the s's then
+ 
+
+ align:start position:0%
+okay but that's if you have the s's then
+you can do that i'm just not going to
+
+ align:start position:0%
+you can do that i'm just not going to
+ 
+
+ align:start position:0%
+you can do that i'm just not going to
+talk about it
+
+ align:start position:0%
+talk about it
+ 
+
+ align:start position:0%
+talk about it
+now in this case for water we have three
+
+ align:start position:0%
+now in this case for water we have three
+ 
+
+ align:start position:0%
+now in this case for water we have three
+normal mode frequencies
+
+ align:start position:0%
+normal mode frequencies
+ 
+
+ align:start position:0%
+normal mode frequencies
+and it's a three by three matrix and so
+
+ align:start position:0%
+and it's a three by three matrix and so
+ 
+
+ align:start position:0%
+and it's a three by three matrix and so
+uh in this three by three matrix we have
+
+ align:start position:0%
+uh in this three by three matrix we have
+ 
+
+ align:start position:0%
+uh in this three by three matrix we have
+six linearly independent elements
+
+ align:start position:0%
+six linearly independent elements
+ 
+
+ align:start position:0%
+six linearly independent elements
+not uh and that's too many
+
+ align:start position:0%
+not uh and that's too many
+ 
+
+ align:start position:0%
+not uh and that's too many
+well g and f are both symmetric matrices
+
+ align:start position:0%
+well g and f are both symmetric matrices
+ 
+
+ align:start position:0%
+well g and f are both symmetric matrices
+and so
+
+ align:start position:0%
+and so
+ 
+
+ align:start position:0%
+and so
+how do you get all six
+
+ align:start position:0%
+how do you get all six
+ 
+
+ align:start position:0%
+how do you get all six
+uh elements of the force constant matrix
+
+ align:start position:0%
+uh elements of the force constant matrix
+ 
+
+ align:start position:0%
+uh elements of the force constant matrix
+uh well you fit isotopic spectra or you
+
+ align:start position:0%
+uh well you fit isotopic spectra or you
+ 
+
+ align:start position:0%
+uh well you fit isotopic spectra or you
+do complicated stuff and but you can do
+
+ align:start position:0%
+do complicated stuff and but you can do
+ 
+
+ align:start position:0%
+do complicated stuff and but you can do
+that you can eventually get six elements
+
+ align:start position:0%
+that you can eventually get six elements
+ 
+
+ align:start position:0%
+that you can eventually get six elements
+it's not as trivial as you might think
+
+ align:start position:0%
+it's not as trivial as you might think
+ 
+
+ align:start position:0%
+it's not as trivial as you might think
+because
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+what you want is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+is
+
+ align:start position:0%
+is
+ 
+
+ align:start position:0%
+is
+the harmonic
+
+ align:start position:0%
+the harmonic
+ 
+
+ align:start position:0%
+the harmonic
+force constant
+
+ align:start position:0%
+force constant
+ 
+
+ align:start position:0%
+force constant
+and what you get in the spectrum is a
+
+ align:start position:0%
+and what you get in the spectrum is a
+ 
+
+ align:start position:0%
+and what you get in the spectrum is a
+difference in energy between v equals
+
+ align:start position:0%
+difference in energy between v equals
+ 
+
+ align:start position:0%
+difference in energy between v equals
+zero and v equals one
+
+ align:start position:0%
+zero and v equals one
+ 
+
+ align:start position:0%
+zero and v equals one
+and if it's a polyatomic if it's not a
+
+ align:start position:0%
+and if it's a polyatomic if it's not a
+ 
+
+ align:start position:0%
+and if it's a polyatomic if it's not a
+diatomic molecule there's cross and
+
+ align:start position:0%
+diatomic molecule there's cross and
+ 
+
+ align:start position:0%
+diatomic molecule there's cross and
+harmonicities between all the modes and
+
+ align:start position:0%
+harmonicities between all the modes and
+ 
+
+ align:start position:0%
+harmonicities between all the modes and
+somehow you have to back that all out
+
+ align:start position:0%
+somehow you have to back that all out
+ 
+
+ align:start position:0%
+somehow you have to back that all out
+and it's not so trivial to do it to get
+
+ align:start position:0%
+and it's not so trivial to do it to get
+ 
+
+ align:start position:0%
+and it's not so trivial to do it to get
+this from the spectrum but in principle
+
+ align:start position:0%
+this from the spectrum but in principle
+ 
+
+ align:start position:0%
+this from the spectrum but in principle
+you could imagine you could get that
+
+ align:start position:0%
+you could imagine you could get that
+ 
+
+ align:start position:0%
+you could imagine you could get that
+experimentally
+
+ align:start position:0%
+experimentally
+ 
+
+ align:start position:0%
+experimentally
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+so this is a symmetric matrix and this
+
+ align:start position:0%
+so this is a symmetric matrix and this
+ 
+
+ align:start position:0%
+so this is a symmetric matrix and this
+is a symmetric matrix
+
+ align:start position:0%
+is a symmetric matrix
+ 
+
+ align:start position:0%
+is a symmetric matrix
+what we want is this combination of g
+
+ align:start position:0%
+what we want is this combination of g
+ 
+
+ align:start position:0%
+what we want is this combination of g
+and f
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and this is the matrix
+
+ align:start position:0%
+and this is the matrix
+ 
+
+ align:start position:0%
+and this is the matrix
+whose eigenvalues we want in order to
+
+ align:start position:0%
+whose eigenvalues we want in order to
+ 
+
+ align:start position:0%
+whose eigenvalues we want in order to
+determine the normal mode frequencies
+
+ align:start position:0%
+determine the normal mode frequencies
+ 
+
+ align:start position:0%
+determine the normal mode frequencies
+and whose eigenvectors we want in order
+
+ align:start position:0%
+and whose eigenvectors we want in order
+ 
+
+ align:start position:0%
+and whose eigenvectors we want in order
+to determine the forms of the normal
+
+ align:start position:0%
+to determine the forms of the normal
+ 
+
+ align:start position:0%
+to determine the forms of the normal
+modes
+
+ align:start position:0%
+modes
+ 
+
+ align:start position:0%
+modes
+so if we have these two matrices
+
+ align:start position:0%
+so if we have these two matrices
+ 
+
+ align:start position:0%
+so if we have these two matrices
+evaluate expressed in numerical form
+
+ align:start position:0%
+evaluate expressed in numerical form
+ 
+
+ align:start position:0%
+evaluate expressed in numerical form
+it's trivial to multiply them
+
+ align:start position:0%
+it's trivial to multiply them
+ 
+
+ align:start position:0%
+it's trivial to multiply them
+symmetric matrix symmetric matrix
+
+ align:start position:0%
+symmetric matrix symmetric matrix
+ 
+
+ align:start position:0%
+symmetric matrix symmetric matrix
+not a symmetric matrix
+
+ align:start position:0%
+not a symmetric matrix
+ 
+
+ align:start position:0%
+not a symmetric matrix
+that's a
+
+ align:start position:0%
+that's a
+ 
+
+ align:start position:0%
+that's a
+surprise
+
+ align:start position:0%
+surprise
+ 
+
+ align:start position:0%
+surprise
+but you can prove that it's not
+
+ align:start position:0%
+but you can prove that it's not
+ 
+
+ align:start position:0%
+but you can prove that it's not
+symmetric just by taking two symmetric
+
+ align:start position:0%
+symmetric just by taking two symmetric
+ 
+
+ align:start position:0%
+symmetric just by taking two symmetric
+two by twos and multiplying them you
+
+ align:start position:0%
+two by twos and multiplying them you
+ 
+
+ align:start position:0%
+two by twos and multiplying them you
+discover
+
+ align:start position:0%
+discover
+ 
+
+ align:start position:0%
+discover
+you're not guaranteed and
+
+ align:start position:0%
+you're not guaranteed and
+ 
+
+ align:start position:0%
+you're not guaranteed and
+when you have a not symmetric matrix
+
+ align:start position:0%
+when you have a not symmetric matrix
+ 
+
+ align:start position:0%
+when you have a not symmetric matrix
+you cannot diagonalize that by a unitary
+
+ align:start position:0%
+you cannot diagonalize that by a unitary
+ 
+
+ align:start position:0%
+you cannot diagonalize that by a unitary
+transformation
+
+ align:start position:0%
+transformation
+ 
+
+ align:start position:0%
+transformation
+you diagonalize it by a similarity
+
+ align:start position:0%
+you diagonalize it by a similarity
+ 
+
+ align:start position:0%
+you diagonalize it by a similarity
+transformation
+
+ align:start position:0%
+transformation
+ 
+
+ align:start position:0%
+transformation
+the computer does it you don't care how
+
+ align:start position:0%
+the computer does it you don't care how
+ 
+
+ align:start position:0%
+the computer does it you don't care how
+it does it you just have to instruct it
+
+ align:start position:0%
+it does it you just have to instruct it
+ 
+
+ align:start position:0%
+it does it you just have to instruct it
+slightly differently and you want to
+
+ align:start position:0%
+slightly differently and you want to
+ 
+
+ align:start position:0%
+slightly differently and you want to
+know what transformation it used to find
+
+ align:start position:0%
+know what transformation it used to find
+ 
+
+ align:start position:0%
+know what transformation it used to find
+the eigenvalues of this matrix because
+
+ align:start position:0%
+the eigenvalues of this matrix because
+ 
+
+ align:start position:0%
+the eigenvalues of this matrix because
+you're going to use them
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+for the water example we have the
+
+ align:start position:0%
+for the water example we have the
+ 
+
+ align:start position:0%
+for the water example we have the
+numerical g and f matrices we have gf
+
+ align:start position:0%
+numerical g and f matrices we have gf
+ 
+
+ align:start position:0%
+numerical g and f matrices we have gf
+and
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+as soon as we have this we can write the
+
+ align:start position:0%
+as soon as we have this we can write the
+ 
+
+ align:start position:0%
+as soon as we have this we can write the
+secular equation and the the
+
+ align:start position:0%
+secular equation and the the
+ 
+
+ align:start position:0%
+secular equation and the the
+roots of the secular equation are three
+
+ align:start position:0%
+roots of the secular equation are three
+ 
+
+ align:start position:0%
+roots of the secular equation are three
+numbers also with three different units
+
+ align:start position:0%
+numbers also with three different units
+ 
+
+ align:start position:0%
+numbers also with three different units
+well that's that's not true no there are
+
+ align:start position:0%
+well that's that's not true no there are
+ 
+
+ align:start position:0%
+well that's that's not true no there are
+three numbers with the same units
+
+ align:start position:0%
+three numbers with the same units
+ 
+
+ align:start position:0%
+three numbers with the same units
+and converting
+
+ align:start position:0%
+and converting
+ 
+
+ align:start position:0%
+and converting
+to useful units they all have units of
+
+ align:start position:0%
+to useful units they all have units of
+ 
+
+ align:start position:0%
+to useful units they all have units of
+seconds and minus two
+
+ align:start position:0%
+seconds and minus two
+ 
+
+ align:start position:0%
+seconds and minus two
+and what we want so we we have three
+
+ align:start position:0%
+and what we want so we we have three
+ 
+
+ align:start position:0%
+and what we want so we we have three
+eigenvalues
+
+ align:start position:0%
+eigenvalues
+ 
+
+ align:start position:0%
+eigenvalues
+lambda one lambda two lambda three
+
+ align:start position:0%
+lambda one lambda two lambda three
+ 
+
+ align:start position:0%
+lambda one lambda two lambda three
+and what we want is the square roots of
+
+ align:start position:0%
+and what we want is the square roots of
+ 
+
+ align:start position:0%
+and what we want is the square roots of
+these things because those will be
+
+ align:start position:0%
+these things because those will be
+ 
+
+ align:start position:0%
+these things because those will be
+frequencies
+
+ align:start position:0%
+frequencies
+ 
+
+ align:start position:0%
+frequencies
+and but we're spectroscopists and so we
+
+ align:start position:0%
+and but we're spectroscopists and so we
+ 
+
+ align:start position:0%
+and but we're spectroscopists and so we
+don't want frequencies we want
+
+ align:start position:0%
+don't want frequencies we want
+ 
+
+ align:start position:0%
+don't want frequencies we want
+reciprocal centimeters and so we divide
+
+ align:start position:0%
+reciprocal centimeters and so we divide
+ 
+
+ align:start position:0%
+reciprocal centimeters and so we divide
+by the speed of light
+
+ align:start position:0%
+by the speed of light
+ 
+
+ align:start position:0%
+by the speed of light
+so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+we get
+
+ align:start position:0%
+we get
+ 
+
+ align:start position:0%
+we get
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+three eigenvalues and the three
+
+ align:start position:0%
+three eigenvalues and the three
+ 
+
+ align:start position:0%
+three eigenvalues and the three
+eigenvectors that correspond to these
+
+ align:start position:0%
+eigenvectors that correspond to these
+ 
+
+ align:start position:0%
+eigenvectors that correspond to these
+eigenvalues
+
+ align:start position:0%
+eigenvalues
+ 
+
+ align:start position:0%
+eigenvalues
+and they have the frequencies
+
+ align:start position:0%
+and they have the frequencies
+ 
+
+ align:start position:0%
+and they have the frequencies
+uh 39
+
+ align:start position:0%
+uh 39
+ 
+
+ align:start position:0%
+uh 39
+
+ align:start position:0%
+ 
+
+ align:start position:0%
+reciprocal centimeters
+
+ align:start position:0%
+reciprocal centimeters
+ 
+
+ align:start position:0%
+reciprocal centimeters
+
+ align:start position:0%
+ 
+
+ align:start position:0%
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and 1648
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so that's what comes out
+
+ align:start position:0%
+okay so that's what comes out
+ 
+
+ align:start position:0%
+okay so that's what comes out
+and these are in fact the normal mode
+
+ align:start position:0%
+and these are in fact the normal mode
+ 
+
+ align:start position:0%
+and these are in fact the normal mode
+frequencies of water
+
+ align:start position:0%
+frequencies of water
+ 
+
+ align:start position:0%
+frequencies of water
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+but there's one thing that's wrong
+
+ align:start position:0%
+but there's one thing that's wrong
+ 
+
+ align:start position:0%
+but there's one thing that's wrong
+they're numbered wrong
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the computer solves this problem
+
+ align:start position:0%
+the computer solves this problem
+ 
+
+ align:start position:0%
+the computer solves this problem
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+it numbers or
+
+ align:start position:0%
+it numbers or
+ 
+
+ align:start position:0%
+it numbers or
+it gives you a list of eigenvalues in
+
+ align:start position:0%
+it gives you a list of eigenvalues in
+ 
+
+ align:start position:0%
+it gives you a list of eigenvalues in
+some order and you might call them one
+
+ align:start position:0%
+some order and you might call them one
+ 
+
+ align:start position:0%
+some order and you might call them one
+two three
+
+ align:start position:0%
+two three
+ 
+
+ align:start position:0%
+two three
+it doesn't know anything about
+
+ align:start position:0%
+it doesn't know anything about
+ 
+
+ align:start position:0%
+it doesn't know anything about
+spectroscopic conventions because it's
+
+ align:start position:0%
+spectroscopic conventions because it's
+ 
+
+ align:start position:0%
+spectroscopic conventions because it's
+it's it's not a it's a it's a computer
+
+ align:start position:0%
+it's it's not a it's a it's a computer
+ 
+
+ align:start position:0%
+it's it's not a it's a it's a computer
+it's not an insane person
+
+ align:start position:0%
+it's not an insane person
+ 
+
+ align:start position:0%
+it's not an insane person
+there is a spectroscopic convention for
+
+ align:start position:0%
+there is a spectroscopic convention for
+ 
+
+ align:start position:0%
+there is a spectroscopic convention for
+numbering the normal modes of any
+
+ align:start position:0%
+numbering the normal modes of any
+ 
+
+ align:start position:0%
+numbering the normal modes of any
+molecule
+
+ align:start position:0%
+molecule
+ 
+
+ align:start position:0%
+molecule
+and i should talk about that for a
+
+ align:start position:0%
+and i should talk about that for a
+ 
+
+ align:start position:0%
+and i should talk about that for a
+moment
+
+ align:start position:0%
+moment
+ 
+
+ align:start position:0%
+moment
+if you're a spectroscopist
+
+ align:start position:0%
+if you're a spectroscopist
+ 
+
+ align:start position:0%
+if you're a spectroscopist
+and you say i have a molecule say
+
+ align:start position:0%
+and you say i have a molecule say
+ 
+
+ align:start position:0%
+and you say i have a molecule say
+benzene
+
+ align:start position:0%
+benzene
+ 
+
+ align:start position:0%
+benzene
+and i say okay nu18 of benzene is
+
+ align:start position:0%
+and i say okay nu18 of benzene is
+ 
+
+ align:start position:0%
+and i say okay nu18 of benzene is
+something you immediately can figure out
+
+ align:start position:0%
+something you immediately can figure out
+ 
+
+ align:start position:0%
+something you immediately can figure out
+what that
+
+ align:start position:0%
+what that
+ 
+
+ align:start position:0%
+what that
+uh which
+
+ align:start position:0%
+uh which
+ 
+
+ align:start position:0%
+uh which
+uh symmetry species that normal mode has
+
+ align:start position:0%
+uh symmetry species that normal mode has
+ 
+
+ align:start position:0%
+uh symmetry species that normal mode has
+and whether it's predominantly a bend or
+
+ align:start position:0%
+and whether it's predominantly a bend or
+ 
+
+ align:start position:0%
+and whether it's predominantly a bend or
+a stretch
+
+ align:start position:0%
+a stretch
+ 
+
+ align:start position:0%
+a stretch
+maybe not immediately but there is no
+
+ align:start position:0%
+maybe not immediately but there is no
+ 
+
+ align:start position:0%
+maybe not immediately but there is no
+possibility for disagreement
+
+ align:start position:0%
+possibility for disagreement
+ 
+
+ align:start position:0%
+possibility for disagreement
+because the the agree the international
+
+ align:start position:0%
+because the the agree the international
+ 
+
+ align:start position:0%
+because the the agree the international
+convention on how you number the modes
+
+ align:start position:0%
+convention on how you number the modes
+ 
+
+ align:start position:0%
+convention on how you number the modes
+is well established what do you do
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+well
+
+ align:start position:0%
+well
+ 
+
+ align:start position:0%
+well
+the high the the
+
+ align:start position:0%
+the high the the
+ 
+
+ align:start position:0%
+the high the the
+we have two different things we have
+
+ align:start position:0%
+we have two different things we have
+ 
+
+ align:start position:0%
+we have two different things we have
+frequency
+
+ align:start position:0%
+frequency
+ 
+
+ align:start position:0%
+frequency
+and symmetry
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+it would be a child child's play if we
+
+ align:start position:0%
+it would be a child child's play if we
+ 
+
+ align:start position:0%
+it would be a child child's play if we
+just took all the eigenvalues of this
+
+ align:start position:0%
+just took all the eigenvalues of this
+ 
+
+ align:start position:0%
+just took all the eigenvalues of this
+matrix
+
+ align:start position:0%
+matrix
+ 
+
+ align:start position:0%
+matrix
+and listed them in numerical order and
+
+ align:start position:0%
+and listed them in numerical order and
+ 
+
+ align:start position:0%
+and listed them in numerical order and
+say the largest one is
+
+ align:start position:0%
+say the largest one is
+ 
+
+ align:start position:0%
+say the largest one is
+mode one and the smallest one is mode
+
+ align:start position:0%
+mode one and the smallest one is mode
+ 
+
+ align:start position:0%
+mode one and the smallest one is mode
+three n minus six
+
+ align:start position:0%
+three n minus six
+ 
+
+ align:start position:0%
+three n minus six
+and that would be a correct thing to do
+
+ align:start position:0%
+and that would be a correct thing to do
+ 
+
+ align:start position:0%
+and that would be a correct thing to do
+for a molecule that has no symmetry
+
+ align:start position:0%
+for a molecule that has no symmetry
+ 
+
+ align:start position:0%
+for a molecule that has no symmetry
+but when there is symmetry
+
+ align:start position:0%
+but when there is symmetry
+ 
+
+ align:start position:0%
+but when there is symmetry
+as there is in water water has uh c2
+
+ align:start position:0%
+as there is in water water has uh c2
+ 
+
+ align:start position:0%
+as there is in water water has uh c2
+symmetry it has reflection planes and
+
+ align:start position:0%
+symmetry it has reflection planes and
+ 
+
+ align:start position:0%
+symmetry it has reflection planes and
+all that sort of good stuff it belongs
+
+ align:start position:0%
+all that sort of good stuff it belongs
+ 
+
+ align:start position:0%
+all that sort of good stuff it belongs
+to what point group
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+right and c2v has
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+symmetry species for symmetry species
+
+ align:start position:0%
+symmetry species for symmetry species
+ 
+
+ align:start position:0%
+symmetry species for symmetry species
+and so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+what you do
+
+ align:start position:0%
+what you do
+ 
+
+ align:start position:0%
+what you do
+is you first
+
+ align:start position:0%
+is you first
+ 
+
+ align:start position:0%
+is you first
+number the totally symmetric modes in
+
+ align:start position:0%
+number the totally symmetric modes in
+ 
+
+ align:start position:0%
+number the totally symmetric modes in
+order
+
+ align:start position:0%
+order
+ 
+
+ align:start position:0%
+order
+and then you go to the next
+
+ align:start position:0%
+and then you go to the next
+ 
+
+ align:start position:0%
+and then you go to the next
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+there is a convention for which one you
+
+ align:start position:0%
+there is a convention for which one you
+ 
+
+ align:start position:0%
+there is a convention for which one you
+do which you do second it's this one
+
+ align:start position:0%
+do which you do second it's this one
+ 
+
+ align:start position:0%
+do which you do second it's this one
+character no the character is going to
+
+ align:start position:0%
+character no the character is going to
+ 
+
+ align:start position:0%
+character no the character is going to
+be a1 a2
+
+ align:start position:0%
+be a1 a2
+ 
+
+ align:start position:0%
+be a1 a2
+it might be uh and then you would go
+
+ align:start position:0%
+it might be uh and then you would go
+ 
+
+ align:start position:0%
+it might be uh and then you would go
+down the character table but it's a one
+
+ align:start position:0%
+down the character table but it's a one
+ 
+
+ align:start position:0%
+down the character table but it's a one
+then a2 then b1 then b2
+
+ align:start position:0%
+then a2 then b1 then b2
+ 
+
+ align:start position:0%
+then a2 then b1 then b2
+and if we're in c2h it would be a g then
+
+ align:start position:0%
+and if we're in c2h it would be a g then
+ 
+
+ align:start position:0%
+and if we're in c2h it would be a g then
+a u b g then b u there's lots of but
+
+ align:start position:0%
+a u b g then b u there's lots of but
+ 
+
+ align:start position:0%
+a u b g then b u there's lots of but
+once you see what the the idea is you
+
+ align:start position:0%
+once you see what the the idea is you
+ 
+
+ align:start position:0%
+once you see what the the idea is you
+can figure out how
+
+ align:start position:0%
+can figure out how
+ 
+
+ align:start position:0%
+can figure out how
+you
+
+ align:start position:0%
+you
+ 
+
+ align:start position:0%
+you
+uh assign modes to symmetry now you
+
+ align:start position:0%
+uh assign modes to symmetry now you
+ 
+
+ align:start position:0%
+uh assign modes to symmetry now you
+don't know
+
+ align:start position:0%
+don't know
+ 
+
+ align:start position:0%
+don't know
+at the present time for an arbitrary
+
+ align:start position:0%
+at the present time for an arbitrary
+ 
+
+ align:start position:0%
+at the present time for an arbitrary
+molecule how many modes there are
+
+ align:start position:0%
+molecule how many modes there are
+ 
+
+ align:start position:0%
+molecule how many modes there are
+in each symmetry species
+
+ align:start position:0%
+in each symmetry species
+ 
+
+ align:start position:0%
+in each symmetry species
+that is a fairly beautiful and standard
+
+ align:start position:0%
+that is a fairly beautiful and standard
+ 
+
+ align:start position:0%
+that is a fairly beautiful and standard
+problem which i probably well i don't
+
+ align:start position:0%
+problem which i probably well i don't
+ 
+
+ align:start position:0%
+problem which i probably well i don't
+know if i run out of things to talk
+
+ align:start position:0%
+know if i run out of things to talk
+ 
+
+ align:start position:0%
+know if i run out of things to talk
+about i'll do it but it's too easy
+
+ align:start position:0%
+about i'll do it but it's too easy
+ 
+
+ align:start position:0%
+about i'll do it but it's too easy
+and there's also a simple group
+
+ align:start position:0%
+and there's also a simple group
+ 
+
+ align:start position:0%
+and there's also a simple group
+theoretical thing method for deciding
+
+ align:start position:0%
+theoretical thing method for deciding
+ 
+
+ align:start position:0%
+theoretical thing method for deciding
+whether a particular mode is
+
+ align:start position:0%
+whether a particular mode is
+ 
+
+ align:start position:0%
+whether a particular mode is
+predominantly stretch or bend or a
+
+ align:start position:0%
+predominantly stretch or bend or a
+ 
+
+ align:start position:0%
+predominantly stretch or bend or a
+mixture and what kind of stretch or
+
+ align:start position:0%
+mixture and what kind of stretch or
+ 
+
+ align:start position:0%
+mixture and what kind of stretch or
+bends so there's some very nice stuff
+
+ align:start position:0%
+bends so there's some very nice stuff
+ 
+
+ align:start position:0%
+bends so there's some very nice stuff
+that you can do just with group theory
+
+ align:start position:0%
+that you can do just with group theory
+ 
+
+ align:start position:0%
+that you can do just with group theory
+to describe the essential
+
+ align:start position:0%
+to describe the essential
+ 
+
+ align:start position:0%
+to describe the essential
+characteristics of all of the normal
+
+ align:start position:0%
+characteristics of all of the normal
+ 
+
+ align:start position:0%
+characteristics of all of the normal
+modes and so if someone tells you the
+
+ align:start position:0%
+modes and so if someone tells you the
+ 
+
+ align:start position:0%
+modes and so if someone tells you the
+mode number
+
+ align:start position:0%
+mode number
+ 
+
+ align:start position:0%
+mode number
+without too much work all the hard
+
+ align:start position:0%
+without too much work all the hard
+ 
+
+ align:start position:0%
+without too much work all the hard
+all the hard work has been done getting
+
+ align:start position:0%
+all the hard work has been done getting
+ 
+
+ align:start position:0%
+all the hard work has been done getting
+these frequencies
+
+ align:start position:0%
+these frequencies
+ 
+
+ align:start position:0%
+these frequencies
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+if if then that person knows the rules
+
+ align:start position:0%
+if if then that person knows the rules
+ 
+
+ align:start position:0%
+if if then that person knows the rules
+and says this is new 18
+
+ align:start position:0%
+and says this is new 18
+ 
+
+ align:start position:0%
+and says this is new 18
+then you can do the group theory and
+
+ align:start position:0%
+then you can do the group theory and
+ 
+
+ align:start position:0%
+then you can do the group theory and
+figure out what is the essential
+
+ align:start position:0%
+figure out what is the essential
+ 
+
+ align:start position:0%
+figure out what is the essential
+characteristic of that mode
+
+ align:start position:0%
+characteristic of that mode
+ 
+
+ align:start position:0%
+characteristic of that mode
+and that's really very wonderful okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+we diagonalize we get the eigenvalues of
+
+ align:start position:0%
+we diagonalize we get the eigenvalues of
+ 
+
+ align:start position:0%
+we diagonalize we get the eigenvalues of
+the gf matrix and
+
+ align:start position:0%
+the gf matrix and
+ 
+
+ align:start position:0%
+the gf matrix and
+we also get the l matrix and the l
+
+ align:start position:0%
+we also get the l matrix and the l
+ 
+
+ align:start position:0%
+we also get the l matrix and the l
+matrix is a bunch of numbers
+
+ align:start position:0%
+matrix is a bunch of numbers
+ 
+
+ align:start position:0%
+matrix is a bunch of numbers
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+in order to
+
+ align:start position:0%
+in order to
+ 
+
+ align:start position:0%
+in order to
+go from
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the simple things
+
+ align:start position:0%
+the simple things
+ 
+
+ align:start position:0%
+the simple things
+the internal displacements to the things
+
+ align:start position:0%
+the internal displacements to the things
+ 
+
+ align:start position:0%
+the internal displacements to the things
+we want the normal displacements
+
+ align:start position:0%
+we want the normal displacements
+ 
+
+ align:start position:0%
+we want the normal displacements
+we need the inverse l matrix and there's
+
+ align:start position:0%
+we need the inverse l matrix and there's
+ 
+
+ align:start position:0%
+we need the inverse l matrix and there's
+two ways of getting that one is you have
+
+ align:start position:0%
+two ways of getting that one is you have
+ 
+
+ align:start position:0%
+two ways of getting that one is you have
+a numerically defined matrix you can
+
+ align:start position:0%
+a numerically defined matrix you can
+ 
+
+ align:start position:0%
+a numerically defined matrix you can
+tell the computer
+
+ align:start position:0%
+tell the computer
+ 
+
+ align:start position:0%
+tell the computer
+symbolically because it knows linear
+
+ align:start position:0%
+symbolically because it knows linear
+ 
+
+ align:start position:0%
+symbolically because it knows linear
+algebra better than you do how to find
+
+ align:start position:0%
+algebra better than you do how to find
+ 
+
+ align:start position:0%
+algebra better than you do how to find
+the the inverse matrix
+
+ align:start position:0%
+the the inverse matrix
+ 
+
+ align:start position:0%
+the the inverse matrix
+there is also another relationship that
+
+ align:start position:0%
+there is also another relationship that
+ 
+
+ align:start position:0%
+there is also another relationship that
+came
+
+ align:start position:0%
+came
+ 
+
+ align:start position:0%
+came
+as when we were dealing with the uh
+
+ align:start position:0%
+as when we were dealing with the uh
+ 
+
+ align:start position:0%
+as when we were dealing with the uh
+analysis of the vibrational problem we
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+saw that this
+
+ align:start position:0%
+saw that this
+ 
+
+ align:start position:0%
+saw that this
+had to be true
+
+ align:start position:0%
+had to be true
+ 
+
+ align:start position:0%
+had to be true
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+l matrix
+
+ align:start position:0%
+l matrix
+ 
+
+ align:start position:0%
+l matrix
+multiplied b inverse of the g matrix
+
+ align:start position:0%
+multiplied b inverse of the g matrix
+ 
+
+ align:start position:0%
+multiplied b inverse of the g matrix
+multiplied by the conjugate transpose of
+
+ align:start position:0%
+multiplied by the conjugate transpose of
+ 
+
+ align:start position:0%
+multiplied by the conjugate transpose of
+the l matrix and since these matrices
+
+ align:start position:0%
+the l matrix and since these matrices
+ 
+
+ align:start position:0%
+the l matrix and since these matrices
+are real conjugate transpose is just
+
+ align:start position:0%
+are real conjugate transpose is just
+ 
+
+ align:start position:0%
+are real conjugate transpose is just
+transpose
+
+ align:start position:0%
+transpose
+ 
+
+ align:start position:0%
+transpose
+we could get the inverse
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah that's right we could get the uh
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+inverse l matrix simply by multiplying
+
+ align:start position:0%
+inverse l matrix simply by multiplying
+ 
+
+ align:start position:0%
+inverse l matrix simply by multiplying
+this on the left on the right by the
+
+ align:start position:0%
+this on the left on the right by the
+ 
+
+ align:start position:0%
+this on the left on the right by the
+inverse so we have l dagger g minus 1 l
+
+ align:start position:0%
+inverse so we have l dagger g minus 1 l
+ 
+
+ align:start position:0%
+inverse so we have l dagger g minus 1 l
+l minus 1.
+
+ align:start position:0%
+l minus 1.
+ 
+
+ align:start position:0%
+l minus 1.
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+symbolically the inverse l matrix is
+
+ align:start position:0%
+symbolically the inverse l matrix is
+ 
+
+ align:start position:0%
+symbolically the inverse l matrix is
+just l dagger which you know
+
+ align:start position:0%
+just l dagger which you know
+ 
+
+ align:start position:0%
+just l dagger which you know
+and g inverse which you don't know you
+
+ align:start position:0%
+and g inverse which you don't know you
+ 
+
+ align:start position:0%
+and g inverse which you don't know you
+have to invert g
+
+ align:start position:0%
+have to invert g
+ 
+
+ align:start position:0%
+have to invert g
+so some matrix is going to have to be
+
+ align:start position:0%
+so some matrix is going to have to be
+ 
+
+ align:start position:0%
+so some matrix is going to have to be
+inverted
+
+ align:start position:0%
+inverted
+ 
+
+ align:start position:0%
+inverted
+either allergy
+
+ align:start position:0%
+either allergy
+ 
+
+ align:start position:0%
+either allergy
+doesn't matter
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so
+
+ align:start position:0%
+okay so
+ 
+
+ align:start position:0%
+okay so
+once you now have the eigenvectors once
+
+ align:start position:0%
+once you now have the eigenvectors once
+ 
+
+ align:start position:0%
+once you now have the eigenvectors once
+you have
+
+ align:start position:0%
+you have
+ 
+
+ align:start position:0%
+you have
+uh this l major this l inverse matrix
+
+ align:start position:0%
+uh this l major this l inverse matrix
+ 
+
+ align:start position:0%
+uh this l major this l inverse matrix
+you can write what each of the normal
+
+ align:start position:0%
+you can write what each of the normal
+ 
+
+ align:start position:0%
+you can write what each of the normal
+modes
+
+ align:start position:0%
+modes
+ 
+
+ align:start position:0%
+modes
+is in terms of the internal
+
+ align:start position:0%
+is in terms of the internal
+ 
+
+ align:start position:0%
+is in terms of the internal
+displacements
+
+ align:start position:0%
+displacements
+ 
+
+ align:start position:0%
+displacements
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+when you do that
+
+ align:start position:0%
+when you do that
+ 
+
+ align:start position:0%
+when you do that
+you can begin to draw pictures of what
+
+ align:start position:0%
+you can begin to draw pictures of what
+ 
+
+ align:start position:0%
+you can begin to draw pictures of what
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+motions of the individual atoms in the
+
+ align:start position:0%
+motions of the individual atoms in the
+ 
+
+ align:start position:0%
+motions of the individual atoms in the
+molecule look like
+
+ align:start position:0%
+molecule look like
+ 
+
+ align:start position:0%
+molecule look like
+and from those pictures you can
+
+ align:start position:0%
+and from those pictures you can
+ 
+
+ align:start position:0%
+and from those pictures you can
+say what the
+
+ align:start position:0%
+say what the
+ 
+
+ align:start position:0%
+say what the
+name of the mode is symmetric stretch
+
+ align:start position:0%
+name of the mode is symmetric stretch
+ 
+
+ align:start position:0%
+name of the mode is symmetric stretch
+and asymmetric stretch bend simply by
+
+ align:start position:0%
+and asymmetric stretch bend simply by
+ 
+
+ align:start position:0%
+and asymmetric stretch bend simply by
+seeing how these vectors
+
+ align:start position:0%
+seeing how these vectors
+ 
+
+ align:start position:0%
+seeing how these vectors
+look
+
+ align:start position:0%
+look
+ 
+
+ align:start position:0%
+look
+and so uh
+
+ align:start position:0%
+and so uh
+ 
+
+ align:start position:0%
+and so uh
+the l inverse matrix tells you how to
+
+ align:start position:0%
+the l inverse matrix tells you how to
+ 
+
+ align:start position:0%
+the l inverse matrix tells you how to
+build this out of the
+
+ align:start position:0%
+build this out of the
+ 
+
+ align:start position:0%
+build this out of the
+uh internal displacements and then you
+
+ align:start position:0%
+uh internal displacements and then you
+ 
+
+ align:start position:0%
+uh internal displacements and then you
+just draw vectors
+
+ align:start position:0%
+just draw vectors
+ 
+
+ align:start position:0%
+just draw vectors
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+of
+
+ align:start position:0%
+of
+ 
+
+ align:start position:0%
+of
+uh in the appropriate directions and
+
+ align:start position:0%
+uh in the appropriate directions and
+ 
+
+ align:start position:0%
+uh in the appropriate directions and
+lengths
+
+ align:start position:0%
+lengths
+ 
+
+ align:start position:0%
+lengths
+and you can see what the
+
+ align:start position:0%
+and you can see what the
+ 
+
+ align:start position:0%
+and you can see what the
+matrices look like now on page five of
+
+ align:start position:0%
+matrices look like now on page five of
+ 
+
+ align:start position:0%
+matrices look like now on page five of
+the notes uh
+
+ align:start position:0%
+the notes uh
+ 
+
+ align:start position:0%
+the notes uh
+q1 and q2 the co
+
+ align:start position:0%
+q1 and q2 the co
+ 
+
+ align:start position:0%
+q1 and q2 the co
+the indices are reversed
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+because these are
+
+ align:start position:0%
+because these are
+ 
+
+ align:start position:0%
+because these are
+this is a combination of notes written
+
+ align:start position:0%
+this is a combination of notes written
+ 
+
+ align:start position:0%
+this is a combination of notes written
+years apart and
+
+ align:start position:0%
+years apart and
+ 
+
+ align:start position:0%
+years apart and
+i discovered only after combining them
+
+ align:start position:0%
+i discovered only after combining them
+ 
+
+ align:start position:0%
+i discovered only after combining them
+that i used a different convention okay
+
+ align:start position:0%
+that i used a different convention okay
+ 
+
+ align:start position:0%
+that i used a different convention okay
+so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+by looking at
+
+ align:start position:0%
+by looking at
+ 
+
+ align:start position:0%
+by looking at
+the eigenvectors you can just say that
+
+ align:start position:0%
+the eigenvectors you can just say that
+ 
+
+ align:start position:0%
+the eigenvectors you can just say that
+q1
+
+ align:start position:0%
+q1
+ 
+
+ align:start position:0%
+q1
+the the one with the frequency of 38
+
+ align:start position:0%
+the the one with the frequency of 38
+ 
+
+ align:start position:0%
+the the one with the frequency of 38
+
+ align:start position:0%
+ 
+
+ align:start position:0%
+is a symmetric
+
+ align:start position:0%
+is a symmetric
+ 
+
+ align:start position:0%
+is a symmetric
+stretch
+
+ align:start position:0%
+stretch
+ 
+
+ align:start position:0%
+stretch
+because
+
+ align:start position:0%
+because
+ 
+
+ align:start position:0%
+because
+the two identical bonds
+
+ align:start position:0%
+the two identical bonds
+ 
+
+ align:start position:0%
+the two identical bonds
+are oscillating in phase
+
+ align:start position:0%
+are oscillating in phase
+ 
+
+ align:start position:0%
+are oscillating in phase
+and they're oscillating by the same
+
+ align:start position:0%
+and they're oscillating by the same
+ 
+
+ align:start position:0%
+and they're oscillating by the same
+amount
+
+ align:start position:0%
+amount
+ 
+
+ align:start position:0%
+amount
+and we can call this thing
+
+ align:start position:0%
+and we can call this thing
+ 
+
+ align:start position:0%
+and we can call this thing
+the one with
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+39 42
+
+ align:start position:0%
+39 42
+ 
+
+ align:start position:0%
+39 42
+the anti-symmetric
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+stretch
+
+ align:start position:0%
+stretch
+ 
+
+ align:start position:0%
+stretch
+now i have a little bit of a
+
+ align:start position:0%
+now i have a little bit of a
+ 
+
+ align:start position:0%
+now i have a little bit of a
+anal compulsive streak in me that when
+
+ align:start position:0%
+anal compulsive streak in me that when
+ 
+
+ align:start position:0%
+anal compulsive streak in me that when
+you have two
+
+ align:start position:0%
+you have two
+ 
+
+ align:start position:0%
+you have two
+uh identical bonds
+
+ align:start position:0%
+uh identical bonds
+ 
+
+ align:start position:0%
+uh identical bonds
+there are symmetric and antisymmetric
+
+ align:start position:0%
+there are symmetric and antisymmetric
+ 
+
+ align:start position:0%
+there are symmetric and antisymmetric
+stretches
+
+ align:start position:0%
+stretches
+ 
+
+ align:start position:0%
+stretches
+from other cases it's okay to talk about
+
+ align:start position:0%
+from other cases it's okay to talk about
+ 
+
+ align:start position:0%
+from other cases it's okay to talk about
+asymmetric stretches but when there's
+
+ align:start position:0%
+asymmetric stretches but when there's
+ 
+
+ align:start position:0%
+asymmetric stretches but when there's
+two
+
+ align:start position:0%
+two
+ 
+
+ align:start position:0%
+two
+and you can have them symmetra you can
+
+ align:start position:0%
+and you can have them symmetra you can
+ 
+
+ align:start position:0%
+and you can have them symmetra you can
+have them with the same phase or
+
+ align:start position:0%
+have them with the same phase or
+ 
+
+ align:start position:0%
+have them with the same phase or
+opposite phase it's symmetric and
+
+ align:start position:0%
+opposite phase it's symmetric and
+ 
+
+ align:start position:0%
+opposite phase it's symmetric and
+antisymmetric
+
+ align:start position:0%
+antisymmetric
+ 
+
+ align:start position:0%
+antisymmetric
+and i'm sure that you'll have a laugh
+
+ align:start position:0%
+and i'm sure that you'll have a laugh
+ 
+
+ align:start position:0%
+and i'm sure that you'll have a laugh
+about that and then this other one the
+
+ align:start position:0%
+about that and then this other one the
+ 
+
+ align:start position:0%
+about that and then this other one the
+low frequency guy is the bend
+
+ align:start position:0%
+low frequency guy is the bend
+ 
+
+ align:start position:0%
+low frequency guy is the bend
+and the vectors tell you all about that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+now
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+in describing
+
+ align:start position:0%
+in describing
+ 
+
+ align:start position:0%
+in describing
+the various
+
+ align:start position:0%
+the various
+ 
+
+ align:start position:0%
+the various
+normal modes
+
+ align:start position:0%
+normal modes
+ 
+
+ align:start position:0%
+normal modes
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+q1
+
+ align:start position:0%
+q1
+ 
+
+ align:start position:0%
+q1
+is written as minus o6a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+s1
+
+ align:start position:0%
+s1
+ 
+
+ align:start position:0%
+s1
+plus
+
+ align:start position:0%
+plus
+ 
+
+ align:start position:0%
+plus
+0.685
+
+ align:start position:0%
+0.685
+ 
+
+ align:start position:0%
+0.685
+s2
+
+ align:start position:0%
+s2
+ 
+
+ align:start position:0%
+s2
+two internal stretches
+
+ align:start position:0%
+two internal stretches
+ 
+
+ align:start position:0%
+two internal stretches
+and q2
+
+ align:start position:0%
+and q2
+ 
+
+ align:start position:0%
+and q2
+is written as
+
+ align:start position:0%
+is written as
+ 
+
+ align:start position:0%
+is written as
+0.695
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+s1
+
+ align:start position:0%
+s1
+ 
+
+ align:start position:0%
+s1
+plus
+
+ align:start position:0%
+plus
+ 
+
+ align:start position:0%
+plus
+0.695
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+s2
+
+ align:start position:0%
+s2
+ 
+
+ align:start position:0%
+s2
+plus 0.037
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+s3
+
+ align:start position:0%
+s3
+ 
+
+ align:start position:0%
+s3
+notice we have two equal numbers
+
+ align:start position:0%
+notice we have two equal numbers
+ 
+
+ align:start position:0%
+notice we have two equal numbers
+of opposite signs here we have two
+
+ align:start position:0%
+of opposite signs here we have two
+ 
+
+ align:start position:0%
+of opposite signs here we have two
+equal numbers of the same sign and a
+
+ align:start position:0%
+equal numbers of the same sign and a
+ 
+
+ align:start position:0%
+equal numbers of the same sign and a
+little bit of this bet so these are two
+
+ align:start position:0%
+little bit of this bet so these are two
+ 
+
+ align:start position:0%
+little bit of this bet so these are two
+stretches in out of phase and in phase
+
+ align:start position:0%
+stretches in out of phase and in phase
+ 
+
+ align:start position:0%
+stretches in out of phase and in phase
+and a straight and a bend
+
+ align:start position:0%
+and a straight and a bend
+ 
+
+ align:start position:0%
+and a straight and a bend
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+uh q3
+
+ align:start position:0%
+uh q3
+ 
+
+ align:start position:0%
+uh q3
+is just oh 6 5 5
+
+ align:start position:0%
+is just oh 6 5 5
+ 
+
+ align:start position:0%
+is just oh 6 5 5
+s3
+
+ align:start position:0%
+s3
+ 
+
+ align:start position:0%
+s3
+so the three normal modes
+
+ align:start position:0%
+so the three normal modes
+ 
+
+ align:start position:0%
+so the three normal modes
+have this form
+
+ align:start position:0%
+have this form
+ 
+
+ align:start position:0%
+have this form
+notice there's no s3
+
+ align:start position:0%
+notice there's no s3
+ 
+
+ align:start position:0%
+notice there's no s3
+in
+
+ align:start position:0%
+in
+ 
+
+ align:start position:0%
+in
+q1
+
+ align:start position:0%
+q1
+ 
+
+ align:start position:0%
+q1
+there's s3 and these two
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+s3 is the bend
+
+ align:start position:0%
+s3 is the bend
+ 
+
+ align:start position:0%
+s3 is the bend
+and somehow this guy
+
+ align:start position:0%
+and somehow this guy
+ 
+
+ align:start position:0%
+and somehow this guy
+doesn't have now
+
+ align:start position:0%
+doesn't have now
+ 
+
+ align:start position:0%
+doesn't have now
+this these numbers come out equal
+
+ align:start position:0%
+this these numbers come out equal
+ 
+
+ align:start position:0%
+this these numbers come out equal
+because
+
+ align:start position:0%
+because
+ 
+
+ align:start position:0%
+because
+uh the eigenvectors of a matrix said
+
+ align:start position:0%
+uh the eigenvectors of a matrix said
+ 
+
+ align:start position:0%
+uh the eigenvectors of a matrix said
+they're equal we're not imposing any
+
+ align:start position:0%
+they're equal we're not imposing any
+ 
+
+ align:start position:0%
+they're equal we're not imposing any
+symmetry these numbers came out equal
+
+ align:start position:0%
+symmetry these numbers came out equal
+ 
+
+ align:start position:0%
+symmetry these numbers came out equal
+and opposite these numbers came out to
+
+ align:start position:0%
+and opposite these numbers came out to
+ 
+
+ align:start position:0%
+and opposite these numbers came out to
+be the same
+
+ align:start position:0%
+be the same
+ 
+
+ align:start position:0%
+be the same
+again because of the structure of the
+
+ align:start position:0%
+again because of the structure of the
+ 
+
+ align:start position:0%
+again because of the structure of the
+matrix these two numbers
+
+ align:start position:0%
+matrix these two numbers
+ 
+
+ align:start position:0%
+matrix these two numbers
+are very different and different in
+
+ align:start position:0%
+are very different and different in
+ 
+
+ align:start position:0%
+are very different and different in
+magnitude this guy
+
+ align:start position:0%
+magnitude this guy
+ 
+
+ align:start position:0%
+magnitude this guy
+uh is predominantly a bend it has a
+
+ align:start position:0%
+uh is predominantly a bend it has a
+ 
+
+ align:start position:0%
+uh is predominantly a bend it has a
+little bit
+
+ align:start position:0%
+little bit
+ 
+
+ align:start position:0%
+little bit
+uh whoops
+
+ align:start position:0%
+uh whoops
+ 
+
+ align:start position:0%
+uh whoops
+um i'm sorry
+
+ align:start position:0%
+um i'm sorry
+ 
+
+ align:start position:0%
+um i'm sorry
+this guy is
+
+ align:start position:0%
+this guy is
+ 
+
+ align:start position:0%
+this guy is
+basically a pure bend this is
+
+ align:start position:0%
+basically a pure bend this is
+ 
+
+ align:start position:0%
+basically a pure bend this is
+predominantly a symmetric stretch and
+
+ align:start position:0%
+predominantly a symmetric stretch and
+ 
+
+ align:start position:0%
+predominantly a symmetric stretch and
+has a little bit of uh bend in it
+
+ align:start position:0%
+has a little bit of uh bend in it
+ 
+
+ align:start position:0%
+has a little bit of uh bend in it
+why just a little bit
+
+ align:start position:0%
+why just a little bit
+ 
+
+ align:start position:0%
+why just a little bit
+how do the g and f matrices tell us
+
+ align:start position:0%
+how do the g and f matrices tell us
+ 
+
+ align:start position:0%
+how do the g and f matrices tell us
+about the mixing of the internal
+
+ align:start position:0%
+about the mixing of the internal
+ 
+
+ align:start position:0%
+about the mixing of the internal
+coordinates
+
+ align:start position:0%
+coordinates
+ 
+
+ align:start position:0%
+coordinates
+so you look at these and you see oh yeah
+
+ align:start position:0%
+so you look at these and you see oh yeah
+ 
+
+ align:start position:0%
+so you look at these and you see oh yeah
+it's obviously antisymmetric symmetric
+
+ align:start position:0%
+it's obviously antisymmetric symmetric
+ 
+
+ align:start position:0%
+it's obviously antisymmetric symmetric
+and this is obviously
+
+ align:start position:0%
+and this is obviously
+ 
+
+ align:start position:0%
+and this is obviously
+a bend and this is a stretch with a
+
+ align:start position:0%
+a bend and this is a stretch with a
+ 
+
+ align:start position:0%
+a bend and this is a stretch with a
+little bit of bend in it
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so what do we do
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+what are the rules that you use for
+
+ align:start position:0%
+what are the rules that you use for
+ 
+
+ align:start position:0%
+what are the rules that you use for
+normalization
+
+ align:start position:0%
+normalization
+ 
+
+ align:start position:0%
+normalization
+there's no normalization
+
+ align:start position:0%
+there's no normalization
+ 
+
+ align:start position:0%
+there's no normalization
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+i mean you started with normalized
+
+ align:start position:0%
+i mean you started with normalized
+ 
+
+ align:start position:0%
+i mean you started with normalized
+quantities
+
+ align:start position:0%
+quantities
+ 
+
+ align:start position:0%
+quantities
+somewhere over here
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the little stl
+
+ align:start position:0%
+the little stl
+ 
+
+ align:start position:0%
+the little stl
+that's right
+
+ align:start position:0%
+that's right
+ 
+
+ align:start position:0%
+that's right
+and so you're building you start with
+
+ align:start position:0%
+and so you're building you start with
+ 
+
+ align:start position:0%
+and so you're building you start with
+normal you know the you start with unit
+
+ align:start position:0%
+normal you know the you start with unit
+ 
+
+ align:start position:0%
+normal you know the you start with unit
+vectors
+
+ align:start position:0%
+vectors
+ 
+
+ align:start position:0%
+vectors
+and so everything then is normalized in
+
+ align:start position:0%
+and so everything then is normalized in
+ 
+
+ align:start position:0%
+and so everything then is normalized in
+that sense
+
+ align:start position:0%
+that sense
+ 
+
+ align:start position:0%
+that sense
+so you're mixing these st alphas
+
+ align:start position:0%
+so you're mixing these st alphas
+ 
+
+ align:start position:0%
+so you're mixing these st alphas
+and all this is just several steps of
+
+ align:start position:0%
+and all this is just several steps of
+ 
+
+ align:start position:0%
+and all this is just several steps of
+transformations of the st alphas so
+
+ align:start position:0%
+transformations of the st alphas so
+ 
+
+ align:start position:0%
+transformations of the st alphas so
+these
+
+ align:start position:0%
+these
+ 
+
+ align:start position:0%
+these
+uh there's no normalization at all
+
+ align:start position:0%
+uh there's no normalization at all
+ 
+
+ align:start position:0%
+uh there's no normalization at all
+i've often thought about that what do
+
+ align:start position:0%
+i've often thought about that what do
+ 
+
+ align:start position:0%
+i've often thought about that what do
+these numbers mean
+
+ align:start position:0%
+these numbers mean
+ 
+
+ align:start position:0%
+these numbers mean
+is there some
+
+ align:start position:0%
+is there some
+ 
+
+ align:start position:0%
+is there some
+you know it's so close to
+
+ align:start position:0%
+you know it's so close to
+ 
+
+ align:start position:0%
+you know it's so close to
+this is very close to one over the
+
+ align:start position:0%
+this is very close to one over the
+ 
+
+ align:start position:0%
+this is very close to one over the
+square root of two but it's not and this
+
+ align:start position:0%
+square root of two but it's not and this
+ 
+
+ align:start position:0%
+square root of two but it's not and this
+is also very close to one over n squared
+
+ align:start position:0%
+is also very close to one over n squared
+ 
+
+ align:start position:0%
+is also very close to one over n squared
+it's closer but it's not and you know
+
+ align:start position:0%
+it's closer but it's not and you know
+ 
+
+ align:start position:0%
+it's closer but it's not and you know
+and this one is just an orphan
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and you would expect in fact i'm a
+
+ align:start position:0%
+and you would expect in fact i'm a
+ 
+
+ align:start position:0%
+and you would expect in fact i'm a
+little puzzled at whether there should
+
+ align:start position:0%
+little puzzled at whether there should
+ 
+
+ align:start position:0%
+little puzzled at whether there should
+have been some more stuff here or not
+
+ align:start position:0%
+have been some more stuff here or not
+ 
+
+ align:start position:0%
+have been some more stuff here or not
+but
+
+ align:start position:0%
+but
+ 
+
+ align:start position:0%
+but
+anyway
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+it is reasonable to ask
+
+ align:start position:0%
+it is reasonable to ask
+ 
+
+ align:start position:0%
+it is reasonable to ask
+can we
+
+ align:start position:0%
+can we
+ 
+
+ align:start position:0%
+can we
+by looking at the f and g
+
+ align:start position:0%
+by looking at the f and g
+ 
+
+ align:start position:0%
+by looking at the f and g
+oh i'm getting ahead of myself can we by
+
+ align:start position:0%
+oh i'm getting ahead of myself can we by
+ 
+
+ align:start position:0%
+oh i'm getting ahead of myself can we by
+looking at the f and g matrices
+
+ align:start position:0%
+looking at the f and g matrices
+ 
+
+ align:start position:0%
+looking at the f and g matrices
+understand
+
+ align:start position:0%
+understand
+ 
+
+ align:start position:0%
+understand
+the specific or at least the qualitative
+
+ align:start position:0%
+the specific or at least the qualitative
+ 
+
+ align:start position:0%
+the specific or at least the qualitative
+things that determine how much
+
+ align:start position:0%
+things that determine how much
+ 
+
+ align:start position:0%
+things that determine how much
+stretch
+
+ align:start position:0%
+stretch
+ 
+
+ align:start position:0%
+stretch
+how much bend is mixed into a
+
+ align:start position:0%
+how much bend is mixed into a
+ 
+
+ align:start position:0%
+how much bend is mixed into a
+predominantly stretch
+
+ align:start position:0%
+predominantly stretch
+ 
+
+ align:start position:0%
+predominantly stretch
+when you have normal modes
+
+ align:start position:0%
+when you have normal modes
+ 
+
+ align:start position:0%
+when you have normal modes
+of the same symmetry
+
+ align:start position:0%
+of the same symmetry
+ 
+
+ align:start position:0%
+of the same symmetry
+they are going to be mixtures of the
+
+ align:start position:0%
+they are going to be mixtures of the
+ 
+
+ align:start position:0%
+they are going to be mixtures of the
+of combinations of internal coordinates
+
+ align:start position:0%
+of combinations of internal coordinates
+ 
+
+ align:start position:0%
+of combinations of internal coordinates
+of similar of the same symmetry but what
+
+ align:start position:0%
+of similar of the same symmetry but what
+ 
+
+ align:start position:0%
+of similar of the same symmetry but what
+is the
+
+ align:start position:0%
+is the
+ 
+
+ align:start position:0%
+is the
+detail of that mixing can you by looking
+
+ align:start position:0%
+detail of that mixing can you by looking
+ 
+
+ align:start position:0%
+detail of that mixing can you by looking
+at the f matrix and the g matrix say yes
+
+ align:start position:0%
+at the f matrix and the g matrix say yes
+ 
+
+ align:start position:0%
+at the f matrix and the g matrix say yes
+there ought to be a lot of mixing of
+
+ align:start position:0%
+there ought to be a lot of mixing of
+ 
+
+ align:start position:0%
+there ought to be a lot of mixing of
+bend with stretch or no there shouldn't
+
+ align:start position:0%
+bend with stretch or no there shouldn't
+ 
+
+ align:start position:0%
+bend with stretch or no there shouldn't
+be what are the dynamical factors but i
+
+ align:start position:0%
+be what are the dynamical factors but i
+ 
+
+ align:start position:0%
+be what are the dynamical factors but i
+got ahead of myself and so i'm going to
+
+ align:start position:0%
+got ahead of myself and so i'm going to
+ 
+
+ align:start position:0%
+got ahead of myself and so i'm going to
+take a brief
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah so if those like q3 that number
+
+ align:start position:0%
+yeah so if those like q3 that number
+ 
+
+ align:start position:0%
+yeah so if those like q3 that number
+seems like anomalously small right does
+
+ align:start position:0%
+seems like anomalously small right does
+ 
+
+ align:start position:0%
+seems like anomalously small right does
+that really tell you that the magnitude
+
+ align:start position:0%
+that really tell you that the magnitude
+ 
+
+ align:start position:0%
+that really tell you that the magnitude
+of the motion
+
+ align:start position:0%
+of the motion
+ 
+
+ align:start position:0%
+of the motion
+if you have
+
+ align:start position:0%
+if you have
+ 
+
+ align:start position:0%
+if you have
+uh like one quantum of band that like
+
+ align:start position:0%
+uh like one quantum of band that like
+ 
+
+ align:start position:0%
+uh like one quantum of band that like
+the atoms don't move as much no i think
+
+ align:start position:0%
+the atoms don't move as much no i think
+ 
+
+ align:start position:0%
+the atoms don't move as much no i think
+it's just that three atoms are moving
+
+ align:start position:0%
+it's just that three atoms are moving
+ 
+
+ align:start position:0%
+it's just that three atoms are moving
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+i think that uh
+
+ align:start position:0%
+i think that uh
+ 
+
+ align:start position:0%
+i think that uh
+that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah s3 involves three atoms moving
+
+ align:start position:0%
+yeah s3 involves three atoms moving
+ 
+
+ align:start position:0%
+yeah s3 involves three atoms moving
+whereas s one and two have two atoms
+
+ align:start position:0%
+whereas s one and two have two atoms
+ 
+
+ align:start position:0%
+whereas s one and two have two atoms
+moving okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+you can put big s3 into the little st
+
+ align:start position:0%
+you can put big s3 into the little st
+ 
+
+ align:start position:0%
+you can put big s3 into the little st
+alphas that comprise it and that's right
+
+ align:start position:0%
+alphas that comprise it and that's right
+ 
+
+ align:start position:0%
+alphas that comprise it and that's right
+then you could tell
+
+ align:start position:0%
+then you could tell
+ 
+
+ align:start position:0%
+then you could tell
+yes in fact when you draw these famous
+
+ align:start position:0%
+yes in fact when you draw these famous
+ 
+
+ align:start position:0%
+yes in fact when you draw these famous
+pictures of arrows
+
+ align:start position:0%
+pictures of arrows
+ 
+
+ align:start position:0%
+pictures of arrows
+uh pointing in of definite lengths
+
+ align:start position:0%
+uh pointing in of definite lengths
+ 
+
+ align:start position:0%
+uh pointing in of definite lengths
+and definite directions uh
+
+ align:start position:0%
+and definite directions uh
+ 
+
+ align:start position:0%
+and definite directions uh
+those you know those comes from the st
+
+ align:start position:0%
+those you know those comes from the st
+ 
+
+ align:start position:0%
+those you know those comes from the st
+alphas
+
+ align:start position:0%
+alphas
+ 
+
+ align:start position:0%
+alphas
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+and so you know what they are and that's
+
+ align:start position:0%
+and so you know what they are and that's
+ 
+
+ align:start position:0%
+and so you know what they are and that's
+what the normal modes are said to look
+
+ align:start position:0%
+what the normal modes are said to look
+ 
+
+ align:start position:0%
+what the normal modes are said to look
+like
+
+ align:start position:0%
+like
+ 
+
+ align:start position:0%
+like
+and so those vectors aren't arbitrary
+
+ align:start position:0%
+and so those vectors aren't arbitrary
+ 
+
+ align:start position:0%
+and so those vectors aren't arbitrary
+objects although frequently you draw
+
+ align:start position:0%
+objects although frequently you draw
+ 
+
+ align:start position:0%
+objects although frequently you draw
+them in a symmetry sense as opposed to a
+
+ align:start position:0%
+them in a symmetry sense as opposed to a
+ 
+
+ align:start position:0%
+them in a symmetry sense as opposed to a
+numerical sense but that's always close
+
+ align:start position:0%
+numerical sense but that's always close
+ 
+
+ align:start position:0%
+numerical sense but that's always close
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+suppose
+
+ align:start position:0%
+suppose
+ 
+
+ align:start position:0%
+suppose
+we have
+
+ align:start position:0%
+we have
+ 
+
+ align:start position:0%
+we have
+two or more identical bond lengths or
+
+ align:start position:0%
+two or more identical bond lengths or
+ 
+
+ align:start position:0%
+two or more identical bond lengths or
+two identical
+
+ align:start position:0%
+two identical
+ 
+
+ align:start position:0%
+two identical
+our or more identical
+
+ align:start position:0%
+our or more identical
+ 
+
+ align:start position:0%
+our or more identical
+internal coordinates in a molecule
+
+ align:start position:0%
+internal coordinates in a molecule
+ 
+
+ align:start position:0%
+internal coordinates in a molecule
+in water there's two identical bond
+
+ align:start position:0%
+in water there's two identical bond
+ 
+
+ align:start position:0%
+in water there's two identical bond
+stretches
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+in other molecules you might have more
+
+ align:start position:0%
+in other molecules you might have more
+ 
+
+ align:start position:0%
+in other molecules you might have more
+than uh
+
+ align:start position:0%
+than uh
+ 
+
+ align:start position:0%
+than uh
+two in benzene you have
+
+ align:start position:0%
+two in benzene you have
+ 
+
+ align:start position:0%
+two in benzene you have
+six identical chs
+
+ align:start position:0%
+six identical chs
+ 
+
+ align:start position:0%
+six identical chs
+but in toluene it's not that you have
+
+ align:start position:0%
+but in toluene it's not that you have
+ 
+
+ align:start position:0%
+but in toluene it's not that you have
+five identical chs of one flavor and
+
+ align:start position:0%
+five identical chs of one flavor and
+ 
+
+ align:start position:0%
+five identical chs of one flavor and
+three of another you have five and they
+
+ align:start position:0%
+three of another you have five and they
+ 
+
+ align:start position:0%
+three of another you have five and they
+come in
+
+ align:start position:0%
+come in
+ 
+
+ align:start position:0%
+come in
+uh or two ortho two pair two meta and
+
+ align:start position:0%
+uh or two ortho two pair two meta and
+ 
+
+ align:start position:0%
+uh or two ortho two pair two meta and
+one para so
+
+ align:start position:0%
+one para so
+ 
+
+ align:start position:0%
+one para so
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+so you can symmetrize you can build
+
+ align:start position:0%
+so you can symmetrize you can build
+ 
+
+ align:start position:0%
+so you can symmetrize you can build
+linear combinations
+
+ align:start position:0%
+linear combinations
+ 
+
+ align:start position:0%
+linear combinations
+of
+
+ align:start position:0%
+of
+ 
+
+ align:start position:0%
+of
+identical internal coordinates
+
+ align:start position:0%
+identical internal coordinates
+ 
+
+ align:start position:0%
+identical internal coordinates
+for example
+
+ align:start position:0%
+for example
+ 
+
+ align:start position:0%
+for example
+so here is what's called a symmetrized
+
+ align:start position:0%
+so here is what's called a symmetrized
+ 
+
+ align:start position:0%
+so here is what's called a symmetrized
+internal coordinate now people use
+
+ align:start position:0%
+internal coordinate now people use
+ 
+
+ align:start position:0%
+internal coordinate now people use
+different notations because
+
+ align:start position:0%
+different notations because
+ 
+
+ align:start position:0%
+different notations because
+they like to use s
+
+ align:start position:0%
+they like to use s
+ 
+
+ align:start position:0%
+they like to use s
+for symmetrized internal coordinates
+
+ align:start position:0%
+for symmetrized internal coordinates
+ 
+
+ align:start position:0%
+for symmetrized internal coordinates
+but s has been taken
+
+ align:start position:0%
+but s has been taken
+ 
+
+ align:start position:0%
+but s has been taken
+and so what do they do well some people
+
+ align:start position:0%
+and so what do they do well some people
+ 
+
+ align:start position:0%
+and so what do they do well some people
+use s for symmetrized internal
+
+ align:start position:0%
+use s for symmetrized internal
+ 
+
+ align:start position:0%
+use s for symmetrized internal
+coordinates and then they pretend that
+
+ align:start position:0%
+coordinates and then they pretend that
+ 
+
+ align:start position:0%
+coordinates and then they pretend that
+the it hasn't so you have some matrix
+
+ align:start position:0%
+the it hasn't so you have some matrix
+ 
+
+ align:start position:0%
+the it hasn't so you have some matrix
+that combines the individual
+
+ align:start position:0%
+that combines the individual
+ 
+
+ align:start position:0%
+that combines the individual
+non-symmetrized internal coordinates
+
+ align:start position:0%
+non-symmetrized internal coordinates
+ 
+
+ align:start position:0%
+non-symmetrized internal coordinates
+and so if in the case of water this
+
+ align:start position:0%
+and so if in the case of water this
+ 
+
+ align:start position:0%
+and so if in the case of water this
+matrix would have the form
+
+ align:start position:0%
+matrix would have the form
+ 
+
+ align:start position:0%
+matrix would have the form
+1 over square root of 2
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+1 over square root of 2
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+over square root of 2
+
+ align:start position:0%
+over square root of 2
+ 
+
+ align:start position:0%
+over square root of 2
+minus 1 over square root of two
+
+ align:start position:0%
+minus 1 over square root of two
+ 
+
+ align:start position:0%
+minus 1 over square root of two
+zero zero zero one
+
+ align:start position:0%
+zero zero zero one
+ 
+
+ align:start position:0%
+zero zero zero one
+i mean it's really easy if there's only
+
+ align:start position:0%
+i mean it's really easy if there's only
+ 
+
+ align:start position:0%
+i mean it's really easy if there's only
+two objects you you
+
+ align:start position:0%
+two objects you you
+ 
+
+ align:start position:0%
+two objects you you
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+you just have a normalized thing and
+
+ align:start position:0%
+you just have a normalized thing and
+ 
+
+ align:start position:0%
+you just have a normalized thing and
+then
+
+ align:start position:0%
+then
+ 
+
+ align:start position:0%
+then
+that's easy so
+
+ align:start position:0%
+that's easy so
+ 
+
+ align:start position:0%
+that's easy so
+we define the symmetrized uh
+
+ align:start position:0%
+we define the symmetrized uh
+ 
+
+ align:start position:0%
+we define the symmetrized uh
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+coordinates by
+
+ align:start position:0%
+coordinates by
+ 
+
+ align:start position:0%
+coordinates by
+uh applying this transformation to the
+
+ align:start position:0%
+uh applying this transformation to the
+ 
+
+ align:start position:0%
+uh applying this transformation to the
+non-symmetrized things the f matrix
+
+ align:start position:0%
+non-symmetrized things the f matrix
+ 
+
+ align:start position:0%
+non-symmetrized things the f matrix
+elements are given by this
+
+ align:start position:0%
+elements are given by this
+ 
+
+ align:start position:0%
+elements are given by this
+so these are the non-symmetrized things
+
+ align:start position:0%
+so these are the non-symmetrized things
+ 
+
+ align:start position:0%
+so these are the non-symmetrized things
+this is the
+
+ align:start position:0%
+this is the
+ 
+
+ align:start position:0%
+this is the
+okay and now we can
+
+ align:start position:0%
+okay and now we can
+ 
+
+ align:start position:0%
+okay and now we can
+insert
+
+ align:start position:0%
+insert
+ 
+
+ align:start position:0%
+insert
+one
+
+ align:start position:0%
+one
+ 
+
+ align:start position:0%
+one
+this is a unitary matrix as opposed to
+
+ align:start position:0%
+this is a unitary matrix as opposed to
+ 
+
+ align:start position:0%
+this is a unitary matrix as opposed to
+just a
+
+ align:start position:0%
+just a
+ 
+
+ align:start position:0%
+just a
+matrix it's a
+
+ align:start position:0%
+matrix it's a
+ 
+
+ align:start position:0%
+matrix it's a
+normalization preserving matrix we can
+
+ align:start position:0%
+normalization preserving matrix we can
+ 
+
+ align:start position:0%
+normalization preserving matrix we can
+rewrite this as
+
+ align:start position:0%
+rewrite this as
+ 
+
+ align:start position:0%
+rewrite this as
+u dagger u
+
+ align:start position:0%
+u dagger u
+ 
+
+ align:start position:0%
+u dagger u
+uh f
+
+ align:start position:0%
+uh f
+ 
+
+ align:start position:0%
+uh f
+u dagger
+
+ align:start position:0%
+u dagger
+ 
+
+ align:start position:0%
+u dagger
+u
+
+ align:start position:0%
+u
+ 
+
+ align:start position:0%
+u
+s
+
+ align:start position:0%
+s
+ 
+
+ align:start position:0%
+s
+we've just inserted one
+
+ align:start position:0%
+we've just inserted one
+ 
+
+ align:start position:0%
+we've just inserted one
+into this formula twice
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and i did it right
+
+ align:start position:0%
+and i did it right
+ 
+
+ align:start position:0%
+and i did it right
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+so we can then rewrite this and say s
+
+ align:start position:0%
+so we can then rewrite this and say s
+ 
+
+ align:start position:0%
+so we can then rewrite this and say s
+twiddle f
+
+ align:start position:0%
+twiddle f
+ 
+
+ align:start position:0%
+twiddle f
+twiddle
+
+ align:start position:0%
+twiddle
+ 
+
+ align:start position:0%
+twiddle
+s twiddle
+
+ align:start position:0%
+s twiddle
+ 
+
+ align:start position:0%
+s twiddle
+this transformation takes this
+
+ align:start position:0%
+this transformation takes this
+ 
+
+ align:start position:0%
+this transformation takes this
+to this and so this is the symmetrized
+
+ align:start position:0%
+to this and so this is the symmetrized
+ 
+
+ align:start position:0%
+to this and so this is the symmetrized
+force constant matrix and these are the
+
+ align:start position:0%
+force constant matrix and these are the
+ 
+
+ align:start position:0%
+force constant matrix and these are the
+symmetrized functions
+
+ align:start position:0%
+symmetrized functions
+ 
+
+ align:start position:0%
+symmetrized functions
+in that representation
+
+ align:start position:0%
+in that representation
+ 
+
+ align:start position:0%
+in that representation
+what we find
+
+ align:start position:0%
+what we find
+ 
+
+ align:start position:0%
+what we find
+is that
+
+ align:start position:0%
+is that
+ 
+
+ align:start position:0%
+is that
+the force constant matrix is block
+
+ align:start position:0%
+the force constant matrix is block
+ 
+
+ align:start position:0%
+the force constant matrix is block
+diagonalized
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and it's block diagonalized in the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+in the representation i've been using
+
+ align:start position:0%
+in the representation i've been using
+ 
+
+ align:start position:0%
+in the representation i've been using
+it's block diagonalized in the sense
+
+ align:start position:0%
+it's block diagonalized in the sense
+ 
+
+ align:start position:0%
+it's block diagonalized in the sense
+where we have zero here here here and
+
+ align:start position:0%
+where we have zero here here here and
+ 
+
+ align:start position:0%
+where we have zero here here here and
+here
+
+ align:start position:0%
+here
+ 
+
+ align:start position:0%
+here
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+and uh
+
+ align:start position:0%
+and uh
+ 
+
+ align:start position:0%
+and uh
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+numbers
+
+ align:start position:0%
+numbers
+ 
+
+ align:start position:0%
+numbers
+here and here and that's awkward and so
+
+ align:start position:0%
+here and here and that's awkward and so
+ 
+
+ align:start position:0%
+here and here and that's awkward and so
+you simply rearrange rows and columns
+
+ align:start position:0%
+you simply rearrange rows and columns
+ 
+
+ align:start position:0%
+you simply rearrange rows and columns
+and you end up having
+
+ align:start position:0%
+and you end up having
+ 
+
+ align:start position:0%
+and you end up having
+the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+force constant matrix
+
+ align:start position:0%
+force constant matrix
+ 
+
+ align:start position:0%
+force constant matrix
+with numbers
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+it becomes a symmetric matrix
+
+ align:start position:0%
+it becomes a symmetric matrix
+ 
+
+ align:start position:0%
+it becomes a symmetric matrix
+there's a two by two symmetric matrix
+
+ align:start position:0%
+there's a two by two symmetric matrix
+ 
+
+ align:start position:0%
+there's a two by two symmetric matrix
+and a one by one
+
+ align:start position:0%
+and a one by one
+ 
+
+ align:start position:0%
+and a one by one
+it has block diagonalized so
+
+ align:start position:0%
+it has block diagonalized so
+ 
+
+ align:start position:0%
+it has block diagonalized so
+this transformation
+
+ align:start position:0%
+this transformation
+ 
+
+ align:start position:0%
+this transformation
+where all you do is you say i have two
+
+ align:start position:0%
+where all you do is you say i have two
+ 
+
+ align:start position:0%
+where all you do is you say i have two
+identical internal displacements i don't
+
+ align:start position:0%
+identical internal displacements i don't
+ 
+
+ align:start position:0%
+identical internal displacements i don't
+know about group theory
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+it has transformed this three by three
+
+ align:start position:0%
+it has transformed this three by three
+ 
+
+ align:start position:0%
+it has transformed this three by three
+matrix into a two by two and a one by
+
+ align:start position:0%
+matrix into a two by two and a one by
+ 
+
+ align:start position:0%
+matrix into a two by two and a one by
+one
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and amazingly it does the same thing to
+
+ align:start position:0%
+and amazingly it does the same thing to
+ 
+
+ align:start position:0%
+and amazingly it does the same thing to
+the g matrix
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and so
+
+ align:start position:0%
+and so
+ 
+
+ align:start position:0%
+and so
+you can
+
+ align:start position:0%
+you can
+ 
+
+ align:start position:0%
+you can
+uh factor
+
+ align:start position:0%
+uh factor
+ 
+
+ align:start position:0%
+uh factor
+the f matrix and the g matrix both into
+
+ align:start position:0%
+the f matrix and the g matrix both into
+ 
+
+ align:start position:0%
+the f matrix and the g matrix both into
+two by twos and one by ones and when you
+
+ align:start position:0%
+two by twos and one by ones and when you
+ 
+
+ align:start position:0%
+two by twos and one by ones and when you
+do that the gf matrix is also of this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+form
+
+ align:start position:0%
+form
+ 
+
+ align:start position:0%
+form
+where you have a two by two and a one by
+
+ align:start position:0%
+where you have a two by two and a one by
+ 
+
+ align:start position:0%
+where you have a two by two and a one by
+one
+
+ align:start position:0%
+one
+ 
+
+ align:start position:0%
+one
+and this
+
+ align:start position:0%
+and this
+ 
+
+ align:start position:0%
+and this
+is the this block is associated with the
+
+ align:start position:0%
+is the this block is associated with the
+ 
+
+ align:start position:0%
+is the this block is associated with the
+totally symmetric levels
+
+ align:start position:0%
+totally symmetric levels
+ 
+
+ align:start position:0%
+totally symmetric levels
+the bend and the symmetric stretch and
+
+ align:start position:0%
+the bend and the symmetric stretch and
+ 
+
+ align:start position:0%
+the bend and the symmetric stretch and
+this block is associated with the
+
+ align:start position:0%
+this block is associated with the
+ 
+
+ align:start position:0%
+this block is associated with the
+antisymmetric level
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so now
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+we've discovered that no
+
+ align:start position:0%
+we've discovered that no
+ 
+
+ align:start position:0%
+we've discovered that no
+even though you don't start out by using
+
+ align:start position:0%
+even though you don't start out by using
+ 
+
+ align:start position:0%
+even though you don't start out by using
+group theory
+
+ align:start position:0%
+group theory
+ 
+
+ align:start position:0%
+group theory
+you can
+
+ align:start position:0%
+you can
+ 
+
+ align:start position:0%
+you can
+factor this problem in uh into
+
+ align:start position:0%
+factor this problem in uh into
+ 
+
+ align:start position:0%
+factor this problem in uh into
+the simpler
+
+ align:start position:0%
+the simpler
+ 
+
+ align:start position:0%
+the simpler
+units and that's wonderful
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and does geez quickly up quickly
+
+ align:start position:0%
+and does geez quickly up quickly
+ 
+
+ align:start position:0%
+and does geez quickly up quickly
+diagonalize to give you an else quickly
+
+ align:start position:0%
+diagonalize to give you an else quickly
+ 
+
+ align:start position:0%
+diagonalize to give you an else quickly
+yes i believe so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so
+
+ align:start position:0%
+okay so
+ 
+
+ align:start position:0%
+okay so
+now
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+what
+
+ align:start position:0%
+what
+ 
+
+ align:start position:0%
+what
+actually can can one look at i mean when
+
+ align:start position:0%
+actually can can one look at i mean when
+ 
+
+ align:start position:0%
+actually can can one look at i mean when
+you have a hamiltonian you can look at
+
+ align:start position:0%
+you have a hamiltonian you can look at
+ 
+
+ align:start position:0%
+you have a hamiltonian you can look at
+the make the form of the matrix and you
+
+ align:start position:0%
+the make the form of the matrix and you
+ 
+
+ align:start position:0%
+the make the form of the matrix and you
+could say there are off-diagonal
+
+ align:start position:0%
+could say there are off-diagonal
+ 
+
+ align:start position:0%
+could say there are off-diagonal
+elements that are there are diagonal
+
+ align:start position:0%
+elements that are there are diagonal
+ 
+
+ align:start position:0%
+elements that are there are diagonal
+elements that are very different and
+
+ align:start position:0%
+elements that are very different and
+ 
+
+ align:start position:0%
+elements that are very different and
+there's an off-diagonal element coupling
+
+ align:start position:0%
+there's an off-diagonal element coupling
+ 
+
+ align:start position:0%
+there's an off-diagonal element coupling
+those two diagonal
+
+ align:start position:0%
+those two diagonal
+ 
+
+ align:start position:0%
+those two diagonal
+things which is small compared to the
+
+ align:start position:0%
+things which is small compared to the
+ 
+
+ align:start position:0%
+things which is small compared to the
+difference in the diagonal element and
+
+ align:start position:0%
+difference in the diagonal element and
+ 
+
+ align:start position:0%
+difference in the diagonal element and
+when that happens
+
+ align:start position:0%
+when that happens
+ 
+
+ align:start position:0%
+when that happens
+the off diagonal element has a
+
+ align:start position:0%
+the off diagonal element has a
+ 
+
+ align:start position:0%
+the off diagonal element has a
+negligible effect on the problem
+
+ align:start position:0%
+negligible effect on the problem
+ 
+
+ align:start position:0%
+negligible effect on the problem
+and so one is always interested in
+
+ align:start position:0%
+and so one is always interested in
+ 
+
+ align:start position:0%
+and so one is always interested in
+making a comparison of the off diagonal
+
+ align:start position:0%
+making a comparison of the off diagonal
+ 
+
+ align:start position:0%
+making a comparison of the off diagonal
+element to the difference in diagonal so
+
+ align:start position:0%
+element to the difference in diagonal so
+ 
+
+ align:start position:0%
+element to the difference in diagonal so
+in this case we have g13 twiddle
+
+ align:start position:0%
+in this case we have g13 twiddle
+ 
+
+ align:start position:0%
+in this case we have g13 twiddle
+and we have g11 twiddle minus g33
+
+ align:start position:0%
+and we have g11 twiddle minus g33
+ 
+
+ align:start position:0%
+and we have g11 twiddle minus g33
+twiddle
+
+ align:start position:0%
+twiddle
+ 
+
+ align:start position:0%
+twiddle
+and we'd like to compare them
+
+ align:start position:0%
+and we'd like to compare them
+ 
+
+ align:start position:0%
+and we'd like to compare them
+and we'd also
+
+ align:start position:0%
+and we'd also
+ 
+
+ align:start position:0%
+and we'd also
+we have f13
+
+ align:start position:0%
+we have f13
+ 
+
+ align:start position:0%
+we have f13
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+f11 twiddle minus f33 twiddle
+
+ align:start position:0%
+f11 twiddle minus f33 twiddle
+ 
+
+ align:start position:0%
+f11 twiddle minus f33 twiddle
+and so even though gf is not a symmetric
+
+ align:start position:0%
+and so even though gf is not a symmetric
+ 
+
+ align:start position:0%
+and so even though gf is not a symmetric
+matrix
+
+ align:start position:0%
+matrix
+ 
+
+ align:start position:0%
+matrix
+we can use some of the same ideas we use
+
+ align:start position:0%
+we can use some of the same ideas we use
+ 
+
+ align:start position:0%
+we can use some of the same ideas we use
+for reading symmetric matrices
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+and so i
+
+ align:start position:0%
+and so i
+ 
+
+ align:start position:0%
+and so i
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+the off diagonal elements
+
+ align:start position:0%
+the off diagonal elements
+ 
+
+ align:start position:0%
+the off diagonal elements
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+g one three and g three one
+
+ align:start position:0%
+g one three and g three one
+ 
+
+ align:start position:0%
+g one three and g three one
+yes don't you care about the diagonal
+
+ align:start position:0%
+yes don't you care about the diagonal
+ 
+
+ align:start position:0%
+yes don't you care about the diagonal
+and off diagonal elements of g f not of
+
+ align:start position:0%
+and off diagonal elements of g f not of
+ 
+
+ align:start position:0%
+and off diagonal elements of g f not of
+g and f individually you do but you can
+
+ align:start position:0%
+g and f individually you do but you can
+ 
+
+ align:start position:0%
+g and f individually you do but you can
+you can you can build it up i mean
+
+ align:start position:0%
+you can you can build it up i mean
+ 
+
+ align:start position:0%
+you can you can build it up i mean
+yes you care about gf
+
+ align:start position:0%
+yes you care about gf
+ 
+
+ align:start position:0%
+yes you care about gf
+but if there's big differences here or
+
+ align:start position:0%
+but if there's big differences here or
+ 
+
+ align:start position:0%
+but if there's big differences here or
+here that will
+
+ align:start position:0%
+here that will
+ 
+
+ align:start position:0%
+here that will
+carry over into
+
+ align:start position:0%
+carry over into
+ 
+
+ align:start position:0%
+carry over into
+the big differences in gf
+
+ align:start position:0%
+the big differences in gf
+ 
+
+ align:start position:0%
+the big differences in gf
+and can they cancel out also
+
+ align:start position:0%
+and can they cancel out also
+ 
+
+ align:start position:0%
+and can they cancel out also
+yeah there's lots of problems but what
+
+ align:start position:0%
+yeah there's lots of problems but what
+ 
+
+ align:start position:0%
+yeah there's lots of problems but what
+you want is some qualitative rules
+
+ align:start position:0%
+you want is some qualitative rules
+ 
+
+ align:start position:0%
+you want is some qualitative rules
+for
+
+ align:start position:0%
+for
+ 
+
+ align:start position:0%
+for
+deciding by looking at masses or
+
+ align:start position:0%
+deciding by looking at masses or
+ 
+
+ align:start position:0%
+deciding by looking at masses or
+adjusting masses or designing a molecule
+
+ align:start position:0%
+adjusting masses or designing a molecule
+ 
+
+ align:start position:0%
+adjusting masses or designing a molecule
+to say i want to
+
+ align:start position:0%
+to say i want to
+ 
+
+ align:start position:0%
+to say i want to
+minimize the mixing of two different
+
+ align:start position:0%
+minimize the mixing of two different
+ 
+
+ align:start position:0%
+minimize the mixing of two different
+kinds of internal coordinates
+
+ align:start position:0%
+kinds of internal coordinates
+ 
+
+ align:start position:0%
+kinds of internal coordinates
+how do i do that what
+
+ align:start position:0%
+how do i do that what
+ 
+
+ align:start position:0%
+how do i do that what
+causes that to happen
+
+ align:start position:0%
+causes that to happen
+ 
+
+ align:start position:0%
+causes that to happen
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+you
+
+ align:start position:0%
+you
+ 
+
+ align:start position:0%
+you
+there's
+
+ align:start position:0%
+there's
+ 
+
+ align:start position:0%
+there's
+kinetic energy coupling
+
+ align:start position:0%
+kinetic energy coupling
+ 
+
+ align:start position:0%
+kinetic energy coupling
+uh which is expressed by examining the g
+
+ align:start position:0%
+uh which is expressed by examining the g
+ 
+
+ align:start position:0%
+uh which is expressed by examining the g
+matrix and there's potential energy
+
+ align:start position:0%
+matrix and there's potential energy
+ 
+
+ align:start position:0%
+matrix and there's potential energy
+coupling which is obtained by
+
+ align:start position:0%
+coupling which is obtained by
+ 
+
+ align:start position:0%
+coupling which is obtained by
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+examining the f matrix and so you can
+
+ align:start position:0%
+examining the f matrix and so you can
+ 
+
+ align:start position:0%
+examining the f matrix and so you can
+look at both
+
+ align:start position:0%
+look at both
+ 
+
+ align:start position:0%
+look at both
+and you can draw conclusions so on page
+
+ align:start position:0%
+and you can draw conclusions so on page
+ 
+
+ align:start position:0%
+and you can draw conclusions so on page
+10 of my notes i have a formula
+
+ align:start position:0%
+10 of my notes i have a formula
+ 
+
+ align:start position:0%
+10 of my notes i have a formula
+expressing g13 in terms of a bond length
+
+ align:start position:0%
+expressing g13 in terms of a bond length
+ 
+
+ align:start position:0%
+expressing g13 in terms of a bond length
+and an angle and a mass
+
+ align:start position:0%
+and an angle and a mass
+ 
+
+ align:start position:0%
+and an angle and a mass
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+this is
+
+ align:start position:0%
+this is
+ 
+
+ align:start position:0%
+this is
+this is a fairly famous
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+brooks pate
+
+ align:start position:0%
+brooks pate
+ 
+
+ align:start position:0%
+brooks pate
+and kevin lehman
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+idea
+
+ align:start position:0%
+idea
+ 
+
+ align:start position:0%
+idea
+that
+
+ align:start position:0%
+that
+ 
+
+ align:start position:0%
+that
+if you want to
+
+ align:start position:0%
+if you want to
+ 
+
+ align:start position:0%
+if you want to
+minimize coupling
+
+ align:start position:0%
+minimize coupling
+ 
+
+ align:start position:0%
+minimize coupling
+between two
+
+ align:start position:0%
+between two
+ 
+
+ align:start position:0%
+between two
+halves of a molecule if you put a heavy
+
+ align:start position:0%
+halves of a molecule if you put a heavy
+ 
+
+ align:start position:0%
+halves of a molecule if you put a heavy
+atom between them it
+
+ align:start position:0%
+atom between them it
+ 
+
+ align:start position:0%
+atom between them it
+will shut that down and
+
+ align:start position:0%
+will shut that down and
+ 
+
+ align:start position:0%
+will shut that down and
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+in this g13 there is a one over
+
+ align:start position:0%
+in this g13 there is a one over
+ 
+
+ align:start position:0%
+in this g13 there is a one over
+m
+
+ align:start position:0%
+m
+ 
+
+ align:start position:0%
+m
+three which was the center
+
+ align:start position:0%
+three which was the center
+ 
+
+ align:start position:0%
+three which was the center
+atom heavy makes the g13 the coupling
+
+ align:start position:0%
+atom heavy makes the g13 the coupling
+ 
+
+ align:start position:0%
+atom heavy makes the g13 the coupling
+matrix element small
+
+ align:start position:0%
+matrix element small
+ 
+
+ align:start position:0%
+matrix element small
+and so that
+
+ align:start position:0%
+and so that
+ 
+
+ align:start position:0%
+and so that
+shuts down the kinetic energy coupling
+
+ align:start position:0%
+shuts down the kinetic energy coupling
+ 
+
+ align:start position:0%
+shuts down the kinetic energy coupling
+now
+
+ align:start position:0%
+now
+ 
+
+ align:start position:0%
+now
+this difference
+
+ align:start position:0%
+this difference
+ 
+
+ align:start position:0%
+this difference
+would be
+
+ align:start position:0%
+would be
+ 
+
+ align:start position:0%
+would be
+these numbers are small if the
+
+ align:start position:0%
+these numbers are small if the
+ 
+
+ align:start position:0%
+these numbers are small if the
+end atoms are heavy and are large if the
+
+ align:start position:0%
+end atoms are heavy and are large if the
+ 
+
+ align:start position:0%
+end atoms are heavy and are large if the
+end atoms are light
+
+ align:start position:0%
+end atoms are light
+ 
+
+ align:start position:0%
+end atoms are light
+and so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+you can look at
+
+ align:start position:0%
+you can look at
+ 
+
+ align:start position:0%
+you can look at
+the structure of the g matrix and you
+
+ align:start position:0%
+the structure of the g matrix and you
+ 
+
+ align:start position:0%
+the structure of the g matrix and you
+can design a molecule either by isotopic
+
+ align:start position:0%
+can design a molecule either by isotopic
+ 
+
+ align:start position:0%
+can design a molecule either by isotopic
+substitution or replacing carbon with
+
+ align:start position:0%
+substitution or replacing carbon with
+ 
+
+ align:start position:0%
+substitution or replacing carbon with
+germanium
+
+ align:start position:0%
+germanium
+ 
+
+ align:start position:0%
+germanium
+that's what they did
+
+ align:start position:0%
+that's what they did
+ 
+
+ align:start position:0%
+that's what they did
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+and you could
+
+ align:start position:0%
+and you could
+ 
+
+ align:start position:0%
+and you could
+try to minimize the communication
+
+ align:start position:0%
+try to minimize the communication
+ 
+
+ align:start position:0%
+try to minimize the communication
+between the different parts of the
+
+ align:start position:0%
+between the different parts of the
+ 
+
+ align:start position:0%
+between the different parts of the
+molecule
+
+ align:start position:0%
+molecule
+ 
+
+ align:start position:0%
+molecule
+and
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the this
+
+ align:start position:0%
+the this
+ 
+
+ align:start position:0%
+the this
+the force constant matrix is similar
+
+ align:start position:0%
+the force constant matrix is similar
+ 
+
+ align:start position:0%
+the force constant matrix is similar
+okay one of the things that
+
+ align:start position:0%
+okay one of the things that
+ 
+
+ align:start position:0%
+okay one of the things that
+you discover is force constants
+
+ align:start position:0%
+you discover is force constants
+ 
+
+ align:start position:0%
+you discover is force constants
+for
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+stretch
+
+ align:start position:0%
+stretch
+ 
+
+ align:start position:0%
+stretch
+stretch force constants
+
+ align:start position:0%
+stretch force constants
+ 
+
+ align:start position:0%
+stretch force constants
+or stretching force constants
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+are
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+much larger than
+
+ align:start position:0%
+much larger than
+ 
+
+ align:start position:0%
+much larger than
+bending force constants
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and because of that suppose in the case
+
+ align:start position:0%
+and because of that suppose in the case
+ 
+
+ align:start position:0%
+and because of that suppose in the case
+of water you have a symmetric stretch
+
+ align:start position:0%
+of water you have a symmetric stretch
+ 
+
+ align:start position:0%
+of water you have a symmetric stretch
+and a symmetric bend
+
+ align:start position:0%
+and a symmetric bend
+ 
+
+ align:start position:0%
+and a symmetric bend
+they belong to the same symmetry species
+
+ align:start position:0%
+they belong to the same symmetry species
+ 
+
+ align:start position:0%
+they belong to the same symmetry species
+but there's a huge difference between
+
+ align:start position:0%
+but there's a huge difference between
+ 
+
+ align:start position:0%
+but there's a huge difference between
+the force constant for the ben the
+
+ align:start position:0%
+the force constant for the ben the
+ 
+
+ align:start position:0%
+the force constant for the ben the
+stretch and the bend
+
+ align:start position:0%
+stretch and the bend
+ 
+
+ align:start position:0%
+stretch and the bend
+and as a result
+
+ align:start position:0%
+and as a result
+ 
+
+ align:start position:0%
+and as a result
+you have built into the f matrix a big
+
+ align:start position:0%
+you have built into the f matrix a big
+ 
+
+ align:start position:0%
+you have built into the f matrix a big
+difference in diagonal elements that
+
+ align:start position:0%
+difference in diagonal elements that
+ 
+
+ align:start position:0%
+difference in diagonal elements that
+fights this the small coupling between
+
+ align:start position:0%
+fights this the small coupling between
+ 
+
+ align:start position:0%
+fights this the small coupling between
+the stretch and the bend and this is the
+
+ align:start position:0%
+the stretch and the bend and this is the
+ 
+
+ align:start position:0%
+the stretch and the bend and this is the
+the physical basis for the distinction
+
+ align:start position:0%
+the physical basis for the distinction
+ 
+
+ align:start position:0%
+the physical basis for the distinction
+between bending modes and stretching
+
+ align:start position:0%
+between bending modes and stretching
+ 
+
+ align:start position:0%
+between bending modes and stretching
+modes
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+occasionally you have an irreducible
+
+ align:start position:0%
+occasionally you have an irreducible
+ 
+
+ align:start position:0%
+occasionally you have an irreducible
+representation a symmetry where there's
+
+ align:start position:0%
+representation a symmetry where there's
+ 
+
+ align:start position:0%
+representation a symmetry where there's
+only
+
+ align:start position:0%
+only
+ 
+
+ align:start position:0%
+only
+a stretch or only a bend
+
+ align:start position:0%
+a stretch or only a bend
+ 
+
+ align:start position:0%
+a stretch or only a bend
+for example in formaldehyde
+
+ align:start position:0%
+for example in formaldehyde
+ 
+
+ align:start position:0%
+for example in formaldehyde
+the a2
+
+ align:start position:0%
+the a2
+ 
+
+ align:start position:0%
+the a2
+symmetry is unique for outer plane bend
+
+ align:start position:0%
+symmetry is unique for outer plane bend
+ 
+
+ align:start position:0%
+symmetry is unique for outer plane bend
+and so that's a pure
+
+ align:start position:0%
+and so that's a pure
+ 
+
+ align:start position:0%
+and so that's a pure
+outer plane bend there isn't any stretch
+
+ align:start position:0%
+outer plane bend there isn't any stretch
+ 
+
+ align:start position:0%
+outer plane bend there isn't any stretch
+but there's uh but there are
+
+ align:start position:0%
+but there's uh but there are
+ 
+
+ align:start position:0%
+but there's uh but there are
+often a stretch and a bend or maybe two
+
+ align:start position:0%
+often a stretch and a bend or maybe two
+ 
+
+ align:start position:0%
+often a stretch and a bend or maybe two
+different classes of bends or two
+
+ align:start position:0%
+different classes of bends or two
+ 
+
+ align:start position:0%
+different classes of bends or two
+different classes of stretch and as long
+
+ align:start position:0%
+different classes of stretch and as long
+ 
+
+ align:start position:0%
+different classes of stretch and as long
+as they belong to the same symmetry
+
+ align:start position:0%
+as they belong to the same symmetry
+ 
+
+ align:start position:0%
+as they belong to the same symmetry
+species they'll mix and you can make
+
+ align:start position:0%
+species they'll mix and you can make
+ 
+
+ align:start position:0%
+species they'll mix and you can make
+judgments about what causes the mixing
+
+ align:start position:0%
+judgments about what causes the mixing
+ 
+
+ align:start position:0%
+judgments about what causes the mixing
+based on masses and about these
+
+ align:start position:0%
+based on masses and about these
+ 
+
+ align:start position:0%
+based on masses and about these
+qualitative things and because bending
+
+ align:start position:0%
+qualitative things and because bending
+ 
+
+ align:start position:0%
+qualitative things and because bending
+is it's easier to bend than to stretch
+
+ align:start position:0%
+is it's easier to bend than to stretch
+ 
+
+ align:start position:0%
+is it's easier to bend than to stretch
+there's usually very little bend
+
+ align:start position:0%
+there's usually very little bend
+ 
+
+ align:start position:0%
+there's usually very little bend
+character in stretches
+
+ align:start position:0%
+character in stretches
+ 
+
+ align:start position:0%
+character in stretches
+and you call things stretches and bends
+
+ align:start position:0%
+and you call things stretches and bends
+ 
+
+ align:start position:0%
+and you call things stretches and bends
+what time is it have i talked too long
+
+ align:start position:0%
+what time is it have i talked too long
+ 
+
+ align:start position:0%
+what time is it have i talked too long
+no
+
+ align:start position:0%
+no
+ 
+
+ align:start position:0%
+no
+um okay so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so i haven't gotten to page 11 and 12
+
+ align:start position:0%
+so i haven't gotten to page 11 and 12
+ 
+
+ align:start position:0%
+so i haven't gotten to page 11 and 12
+and i'll probably begin my lecture i
+
+ align:start position:0%
+and i'll probably begin my lecture i
+ 
+
+ align:start position:0%
+and i'll probably begin my lecture i
+mean so there's some
+
+ align:start position:0%
+mean so there's some
+ 
+
+ align:start position:0%
+mean so there's some
+virtue in this because i'm not going to
+
+ align:start position:0%
+virtue in this because i'm not going to
+ 
+
+ align:start position:0%
+virtue in this because i'm not going to
+have any time to prepare for tomorrow
+
+ align:start position:0%
+have any time to prepare for tomorrow
+ 
+
+ align:start position:0%
+have any time to prepare for tomorrow
+morning's lecture so i'll start with
+
+ align:start position:0%
+morning's lecture so i'll start with
+ 
+
+ align:start position:0%
+morning's lecture so i'll start with
+something i really know
+
+ align:start position:0%
+something i really know
+ 
+
+ align:start position:0%
+something i really know
+for tomorrow morning
+
+ align:start position:0%
+for tomorrow morning
+ 
+
+ align:start position:0%
+for tomorrow morning
+okay so that's that's it
\ No newline at end of file
diff --git a/y1bnBxfNVkU.txt b/y1bnBxfNVkU.txt
new file mode 100644
index 0000000000000000000000000000000000000000..5ec882406f93522abf0e5d619fc51a88df5f802f
--- /dev/null
+++ b/y1bnBxfNVkU.txt
@@ -0,0 +1,8984 @@
+align:start position:0%
+ 
+So today we're going to continue our
+
+ align:start position:0%
+So today we're going to continue our
+ 
+
+ align:start position:0%
+So today we're going to continue our
+discussion of uh producer Theory
+
+ align:start position:0%
+discussion of uh producer Theory
+ 
+
+ align:start position:0%
+discussion of uh producer Theory
+remember the first few lectures we
+
+ align:start position:0%
+remember the first few lectures we
+ 
+
+ align:start position:0%
+remember the first few lectures we
+developed consumer Theory and where the
+
+ align:start position:0%
+developed consumer Theory and where the
+ 
+
+ align:start position:0%
+developed consumer Theory and where the
+demain curve came from now we're turning
+
+ align:start position:0%
+demain curve came from now we're turning
+ 
+
+ align:start position:0%
+demain curve came from now we're turning
+to producer Theory and where the supply
+
+ align:start position:0%
+to producer Theory and where the supply
+ 
+
+ align:start position:0%
+to producer Theory and where the supply
+curve comes from drawing on a lot of
+
+ align:start position:0%
+curve comes from drawing on a lot of
+ 
+
+ align:start position:0%
+curve comes from drawing on a lot of
+parallels from the math and techniques
+
+ align:start position:0%
+parallels from the math and techniques
+ 
+
+ align:start position:0%
+parallels from the math and techniques
+that we use for Consumer Theory so we're
+
+ align:start position:0%
+that we use for Consumer Theory so we're
+ 
+
+ align:start position:0%
+that we use for Consumer Theory so we're
+going to start today by talking about
+
+ align:start position:0%
+going to start today by talking about
+ 
+
+ align:start position:0%
+going to start today by talking about
+the key construct a key construct of
+
+ align:start position:0%
+the key construct a key construct of
+ 
+
+ align:start position:0%
+the key construct a key construct of
+producer Theory which is short run cost
+
+ align:start position:0%
+producer Theory which is short run cost
+ 
+
+ align:start position:0%
+producer Theory which is short run cost
+curves remember the short run is the
+
+ align:start position:0%
+curves remember the short run is the
+ 
+
+ align:start position:0%
+curves remember the short run is the
+period of time over which some inputs
+
+ align:start position:0%
+period of time over which some inputs
+ 
+
+ align:start position:0%
+period of time over which some inputs
+are fixed in our case capital and other
+
+ align:start position:0%
+are fixed in our case capital and other
+ 
+
+ align:start position:0%
+are fixed in our case capital and other
+inputs are variable in our case labor
+
+ align:start position:0%
+inputs are variable in our case labor
+ 
+
+ align:start position:0%
+inputs are variable in our case labor
+okay so basically we last time developed
+
+ align:start position:0%
+okay so basically we last time developed
+ 
+
+ align:start position:0%
+okay so basically we last time developed
+a firm production
+
+ align:start position:0%
+a firm production
+ 
+
+ align:start position:0%
+a firm production
+function now I want to translate that
+
+ align:start position:0%
+function now I want to translate that
+ 
+
+ align:start position:0%
+function now I want to translate that
+production function into costs and why
+
+ align:start position:0%
+production function into costs and why
+ 
+
+ align:start position:0%
+production function into costs and why
+do we want to do that because remember
+
+ align:start position:0%
+do we want to do that because remember
+ 
+
+ align:start position:0%
+do we want to do that because remember
+the way firms maximize profits is by
+
+ align:start position:0%
+the way firms maximize profits is by
+ 
+
+ align:start position:0%
+the way firms maximize profits is by
+minimizing costs by producing Goods as
+
+ align:start position:0%
+minimizing costs by producing Goods as
+ 
+
+ align:start position:0%
+minimizing costs by producing Goods as
+efficiently as possible at minimum costs
+
+ align:start position:0%
+efficiently as possible at minimum costs
+ 
+
+ align:start position:0%
+efficiently as possible at minimum costs
+remember a production function from last
+
+ align:start position:0%
+remember a production function from last
+ 
+
+ align:start position:0%
+remember a production function from last
+time was little Q equals the square root
+
+ align:start position:0%
+time was little Q equals the square root
+ 
+
+ align:start position:0%
+time was little Q equals the square root
+of L * K
+
+ align:start position:0%
+of L * K
+ 
+
+ align:start position:0%
+of L * K
+okay that was our production function
+
+ align:start position:0%
+okay that was our production function
+ 
+
+ align:start position:0%
+okay that was our production function
+now what we want to do today is write
+
+ align:start position:0%
+now what we want to do today is write
+ 
+
+ align:start position:0%
+now what we want to do today is write
+down a new function which is what does
+
+ align:start position:0%
+down a new function which is what does
+ 
+
+ align:start position:0%
+down a new function which is what does
+it cost to produce little Q for any
+
+ align:start position:0%
+it cost to produce little Q for any
+ 
+
+ align:start position:0%
+it cost to produce little Q for any
+given L and K what's it cost well the
+
+ align:start position:0%
+given L and K what's it cost well the
+ 
+
+ align:start position:0%
+given L and K what's it cost well the
+cost of producing producing little Q
+
+ align:start position:0%
+cost of producing producing little Q
+ 
+
+ align:start position:0%
+cost of producing producing little Q
+which is a function of Q is equal to the
+
+ align:start position:0%
+which is a function of Q is equal to the
+ 
+
+ align:start position:0%
+which is a function of Q is equal to the
+amount of capital you have which is
+
+ align:start position:0%
+amount of capital you have which is
+ 
+
+ align:start position:0%
+amount of capital you have which is
+fixed which is I'm sorry which is fixed
+
+ align:start position:0%
+fixed which is I'm sorry which is fixed
+ 
+
+ align:start position:0%
+fixed which is I'm sorry which is fixed
+times the rental rate of capital
+
+ align:start position:0%
+times the rental rate of capital
+ 
+
+ align:start position:0%
+times the rental rate of capital
+remember that's the price of machines is
+
+ align:start position:0%
+remember that's the price of machines is
+ 
+
+ align:start position:0%
+remember that's the price of machines is
+their rental rate plus the amount of
+
+ align:start position:0%
+their rental rate plus the amount of
+ 
+
+ align:start position:0%
+their rental rate plus the amount of
+Labor which is a function of Q times the
+
+ align:start position:0%
+Labor which is a function of Q times the
+ 
+
+ align:start position:0%
+Labor which is a function of Q times the
+wage so basically your choice variable
+
+ align:start position:0%
+wage so basically your choice variable
+ 
+
+ align:start position:0%
+wage so basically your choice variable
+is how many workers you want to have to
+
+ align:start position:0%
+is how many workers you want to have to
+ 
+
+ align:start position:0%
+is how many workers you want to have to
+decide how much Q you want to produce
+
+ align:start position:0%
+decide how much Q you want to produce
+ 
+
+ align:start position:0%
+decide how much Q you want to produce
+you're going to decide how many hours of
+
+ align:start position:0%
+you're going to decide how many hours of
+ 
+
+ align:start position:0%
+you're going to decide how many hours of
+Labor or workers you want to employ by
+
+ align:start position:0%
+Labor or workers you want to employ by
+ 
+
+ align:start position:0%
+Labor or workers you want to employ by
+the way I will talk
+
+ align:start position:0%
+the way I will talk
+ 
+
+ align:start position:0%
+the way I will talk
+interchangeably between hours of Labor
+
+ align:start position:0%
+interchangeably between hours of Labor
+ 
+
+ align:start position:0%
+interchangeably between hours of Labor
+and workers there's no right measure of
+
+ align:start position:0%
+and workers there's no right measure of
+ 
+
+ align:start position:0%
+and workers there's no right measure of
+L it depends on the context Etc so don't
+
+ align:start position:0%
+L it depends on the context Etc so don't
+ 
+
+ align:start position:0%
+L it depends on the context Etc so don't
+feel like it's just two different ways
+
+ align:start position:0%
+feel like it's just two different ways
+ 
+
+ align:start position:0%
+feel like it's just two different ways
+of measuring the L input so uh it
+
+ align:start position:0%
+of measuring the L input so uh it
+ 
+
+ align:start position:0%
+of measuring the L input so uh it
+matters less when I say hours of work
+
+ align:start position:0%
+matters less when I say hours of work
+ 
+
+ align:start position:0%
+matters less when I say hours of work
+versus workers if it's an important
+
+ align:start position:0%
+versus workers if it's an important
+ 
+
+ align:start position:0%
+versus workers if it's an important
+distinction I'll tell you but right now
+
+ align:start position:0%
+distinction I'll tell you but right now
+ 
+
+ align:start position:0%
+distinction I'll tell you but right now
+I'm using two different ways of
+
+ align:start position:0%
+I'm using two different ways of
+ 
+
+ align:start position:0%
+I'm using two different ways of
+measuring L the bottom line is it's a
+
+ align:start position:0%
+measuring L the bottom line is it's a
+ 
+
+ align:start position:0%
+measuring L the bottom line is it's a
+labor
+
+ align:start position:0%
+labor
+ 
+
+ align:start position:0%
+labor
+input okay so now
+
+ align:start position:0%
+input okay so now
+ 
+
+ align:start position:0%
+input okay so now
+we want to um say what is the explicit
+
+ align:start position:0%
+we want to um say what is the explicit
+ 
+
+ align:start position:0%
+we want to um say what is the explicit
+expression for the cost function well in
+
+ align:start position:0%
+expression for the cost function well in
+ 
+
+ align:start position:0%
+expression for the cost function well in
+fact if we know a production function
+
+ align:start position:0%
+fact if we know a production function
+ 
+
+ align:start position:0%
+fact if we know a production function
+and we know W and R we can write down a
+
+ align:start position:0%
+and we know W and R we can write down a
+ 
+
+ align:start position:0%
+and we know W and R we can write down a
+cost function so we know this production
+
+ align:start position:0%
+cost function so we know this production
+ 
+
+ align:start position:0%
+cost function so we know this production
+function and let's assume for this case
+
+ align:start position:0%
+function and let's assume for this case
+ 
+
+ align:start position:0%
+function and let's assume for this case
+let's assume W equals 5 and R equals 10
+
+ align:start position:0%
+let's assume W equals 5 and R equals 10
+ 
+
+ align:start position:0%
+let's assume W equals 5 and R equals 10
+okay where those come from I'll teach
+
+ align:start position:0%
+okay where those come from I'll teach
+ 
+
+ align:start position:0%
+okay where those come from I'll teach
+you that in a few lectures remember we
+
+ align:start position:0%
+you that in a few lectures remember we
+ 
+
+ align:start position:0%
+you that in a few lectures remember we
+sort of peeled the onion in this class
+
+ align:start position:0%
+sort of peeled the onion in this class
+ 
+
+ align:start position:0%
+sort of peeled the onion in this class
+we're kind of revealing the m slowly
+
+ align:start position:0%
+we're kind of revealing the m slowly
+ 
+
+ align:start position:0%
+we're kind of revealing the m slowly
+right now just take those as given in a
+
+ align:start position:0%
+right now just take those as given in a
+ 
+
+ align:start position:0%
+right now just take those as given in a
+few lect I'll tell you where they come
+
+ align:start position:0%
+few lect I'll tell you where they come
+ 
+
+ align:start position:0%
+few lect I'll tell you where they come
+from okay so we know the production
+
+ align:start position:0%
+from okay so we know the production
+ 
+
+ align:start position:0%
+from okay so we know the production
+function is qal squ of L * K so we can
+
+ align:start position:0%
+function is qal squ of L * K so we can
+ 
+
+ align:start position:0%
+function is qal squ of L * K so we can
+take that from that production function
+
+ align:start position:0%
+take that from that production function
+ 
+
+ align:start position:0%
+take that from that production function
+we can just flip it and say Lal Q ^2
+
+ align:start position:0%
+we can just flip it and say Lal Q ^2
+ 
+
+ align:start position:0%
+we can just flip it and say Lal Q ^2
+over K bar right just squaring that
+
+ align:start position:0%
+over K bar right just squaring that
+ 
+
+ align:start position:0%
+over K bar right just squaring that
+moving to the other side okay so then we
+
+ align:start position:0%
+moving to the other side okay so then we
+ 
+
+ align:start position:0%
+moving to the other side okay so then we
+could say that we can rewrite the cost
+
+ align:start position:0%
+could say that we can rewrite the cost
+ 
+
+ align:start position:0%
+could say that we can rewrite the cost
+function as C equals 10 K
+
+ align:start position:0%
+function as C equals 10 K
+ 
+
+ align:start position:0%
+function as C equals 10 K
+Bar okay because 10 is the rental
+
+ align:start position:0%
+Bar okay because 10 is the rental
+ 
+
+ align:start position:0%
+Bar okay because 10 is the rental
+rate plus five q^2 over K Bar because
+
+ align:start position:0%
+rate plus five q^2 over K Bar because
+ 
+
+ align:start position:0%
+rate plus five q^2 over K Bar because
+plug in from this equation five is the
+
+ align:start position:0%
+plug in from this equation five is the
+ 
+
+ align:start position:0%
+plug in from this equation five is the
+wage
+
+ align:start position:0%
+wage
+ 
+
+ align:start position:0%
+wage
+rate okay now K bar is a fixed number to
+
+ align:start position:0%
+rate okay now K bar is a fixed number to
+ 
+
+ align:start position:0%
+rate okay now K bar is a fixed number to
+make life easy let's just assume K Bar
+
+ align:start position:0%
+make life easy let's just assume K Bar
+ 
+
+ align:start position:0%
+make life easy let's just assume K Bar
+equals one it could be any fixed number
+
+ align:start position:0%
+equals one it could be any fixed number
+ 
+
+ align:start position:0%
+equals one it could be any fixed number
+in the short run let's assume K bar is
+
+ align:start position:0%
+in the short run let's assume K bar is
+ 
+
+ align:start position:0%
+in the short run let's assume K bar is
+one to make life easy so that says that
+
+ align:start position:0%
+one to make life easy so that says that
+ 
+
+ align:start position:0%
+one to make life easy so that says that
+the cost function we could simply write
+
+ align:start position:0%
+the cost function we could simply write
+ 
+
+ align:start position:0%
+the cost function we could simply write
+as 10 + 5
+
+ align:start position:0%
+as 10 + 5
+ 
+
+ align:start position:0%
+as 10 + 5
+q^2 that's our cost function to get that
+
+ align:start position:0%
+q^2 that's our cost function to get that
+ 
+
+ align:start position:0%
+q^2 that's our cost function to get that
+cost
+
+ align:start position:0%
+cost
+ 
+
+ align:start position:0%
+cost
+function which is a relationship between
+
+ align:start position:0%
+function which is a relationship between
+ 
+
+ align:start position:0%
+function which is a relationship between
+the cost of the firm and the quantity
+
+ align:start position:0%
+the cost of the firm and the quantity
+ 
+
+ align:start position:0%
+the cost of the firm and the quantity
+they produce okay the cost function
+
+ align:start position:0%
+they produce okay the cost function
+ 
+
+ align:start position:0%
+they produce okay the cost function
+relates the quantity produced to the
+
+ align:start position:0%
+relates the quantity produced to the
+ 
+
+ align:start position:0%
+relates the quantity produced to the
+cost all we do is start with the
+
+ align:start position:0%
+cost all we do is start with the
+ 
+
+ align:start position:0%
+cost all we do is start with the
+production function plug in these
+
+ align:start position:0%
+production function plug in these
+ 
+
+ align:start position:0%
+production function plug in these
+parameters and we end up with a cost
+
+ align:start position:0%
+parameters and we end up with a cost
+ 
+
+ align:start position:0%
+parameters and we end up with a cost
+function okay so that's how you
+
+ align:start position:0%
+function okay so that's how you
+ 
+
+ align:start position:0%
+function okay so that's how you
+translate production to
+
+ align:start position:0%
+translate production to
+ 
+
+ align:start position:0%
+translate production to
+cost okay
+
+ align:start position:0%
+cost okay
+ 
+
+ align:start position:0%
+cost okay
+now let's look at this cost function for
+
+ align:start position:0%
+now let's look at this cost function for
+ 
+
+ align:start position:0%
+now let's look at this cost function for
+a second and and I want to give you some
+
+ align:start position:0%
+a second and and I want to give you some
+ 
+
+ align:start position:0%
+a second and and I want to give you some
+key definitions that we'll be using
+
+ align:start position:0%
+key definitions that we'll be using
+ 
+
+ align:start position:0%
+key definitions that we'll be using
+throughout this
+
+ align:start position:0%
+throughout this
+ 
+
+ align:start position:0%
+throughout this
+course okay we are going to
+
+ align:start position:0%
+course okay we are going to
+ 
+
+ align:start position:0%
+course okay we are going to
+call fixed
+
+ align:start position:0%
+call fixed
+ 
+
+ align:start position:0%
+call fixed
+costs fixed
+
+ align:start position:0%
+costs fixed
+ 
+
+ align:start position:0%
+costs fixed
+costs are going to be costs which are
+
+ align:start position:0%
+costs are going to be costs which are
+ 
+
+ align:start position:0%
+costs are going to be costs which are
+not variable in the short
+
+ align:start position:0%
+not variable in the short
+ 
+
+ align:start position:0%
+not variable in the short
+run fixed costs are costs which are not
+
+ align:start position:0%
+run fixed costs are costs which are not
+ 
+
+ align:start position:0%
+run fixed costs are costs which are not
+variable in the short run here it's 10
+
+ align:start position:0%
+variable in the short run here it's 10
+ 
+
+ align:start position:0%
+variable in the short run here it's 10
+the fixed cost in this example is 10
+
+ align:start position:0%
+the fixed cost in this example is 10
+ 
+
+ align:start position:0%
+the fixed cost in this example is 10
+there's nothing you can do in the short
+
+ align:start position:0%
+there's nothing you can do in the short
+ 
+
+ align:start position:0%
+there's nothing you can do in the short
+run to change your fixed cost because
+
+ align:start position:0%
+run to change your fixed cost because
+ 
+
+ align:start position:0%
+run to change your fixed cost because
+capital's
+
+ align:start position:0%
+capital's
+ 
+
+ align:start position:0%
+capital's
+fixed variable
+
+ align:start position:0%
+fixed variable
+ 
+
+ align:start position:0%
+fixed variable
+costs are the costs that can be varied
+
+ align:start position:0%
+costs are the costs that can be varied
+ 
+
+ align:start position:0%
+costs are the costs that can be varied
+in the short run in our case variable
+
+ align:start position:0%
+in the short run in our case variable
+ 
+
+ align:start position:0%
+in the short run in our case variable
+costs are 5
+
+ align:start position:0%
+costs are 5
+ 
+
+ align:start position:0%
+costs are 5
+q^2 so your variable costs are 5 q^ squ
+
+ align:start position:0%
+q^2 so your variable costs are 5 q^ squ
+ 
+
+ align:start position:0%
+q^2 so your variable costs are 5 q^ squ
+that's the part of cost that you can
+
+ align:start position:0%
+that's the part of cost that you can
+ 
+
+ align:start position:0%
+that's the part of cost that you can
+move in the short
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+run and total costs is the sum of those
+
+ align:start position:0%
+run and total costs is the sum of those
+ 
+
+ align:start position:0%
+run and total costs is the sum of those
+two as expressed there total cost is the
+
+ align:start position:0%
+two as expressed there total cost is the
+ 
+
+ align:start position:0%
+two as expressed there total cost is the
+sum of fixed and variable
+
+ align:start position:0%
+sum of fixed and variable
+ 
+
+ align:start position:0%
+sum of fixed and variable
+costs now the
+
+ align:start position:0%
+costs now the
+ 
+
+ align:start position:0%
+costs now the
+key the the single key that will drive
+
+ align:start position:0%
+key the the single key that will drive
+ 
+
+ align:start position:0%
+key the the single key that will drive
+production theory is what we're going to
+
+ align:start position:0%
+production theory is what we're going to
+ 
+
+ align:start position:0%
+production theory is what we're going to
+call marginal costs marginal costs is
+
+ align:start position:0%
+call marginal costs marginal costs is
+ 
+
+ align:start position:0%
+call marginal costs marginal costs is
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+differential of total costs with respect
+
+ align:start position:0%
+differential of total costs with respect
+ 
+
+ align:start position:0%
+differential of total costs with respect
+to
+
+ align:start position:0%
+to
+ 
+
+ align:start position:0%
+to
+quantity okay so marginal cost is DC
+
+ align:start position:0%
+quantity okay so marginal cost is DC
+ 
+
+ align:start position:0%
+quantity okay so marginal cost is DC
+DQ which G given that fixed costs are
+
+ align:start position:0%
+DQ which G given that fixed costs are
+ 
+
+ align:start position:0%
+DQ which G given that fixed costs are
+fixed in the short run it's the same as
+
+ align:start position:0%
+fixed in the short run it's the same as
+ 
+
+ align:start position:0%
+fixed in the short run it's the same as
+saying D variable cost
+
+ align:start position:0%
+saying D variable cost
+ 
+
+ align:start position:0%
+saying D variable cost
+DQ okay in the short run D total cost DQ
+
+ align:start position:0%
+DQ okay in the short run D total cost DQ
+ 
+
+ align:start position:0%
+DQ okay in the short run D total cost DQ
+is the same as D variable cost DQ
+
+ align:start position:0%
+is the same as D variable cost DQ
+ 
+
+ align:start position:0%
+is the same as D variable cost DQ
+because fixed costs are
+
+ align:start position:0%
+because fixed costs are
+ 
+
+ align:start position:0%
+because fixed costs are
+fixed okay so marginal costs are the
+
+ align:start position:0%
+fixed okay so marginal costs are the
+ 
+
+ align:start position:0%
+fixed okay so marginal costs are the
+marginal cost of producing the next unit
+
+ align:start position:0%
+marginal cost of producing the next unit
+ 
+
+ align:start position:0%
+marginal cost of producing the next unit
+what is the cost to produ of the next
+
+ align:start position:0%
+what is the cost to produ of the next
+ 
+
+ align:start position:0%
+what is the cost to produ of the next
+unit it's the change in variable costs
+
+ align:start position:0%
+unit it's the change in variable costs
+ 
+
+ align:start position:0%
+unit it's the change in variable costs
+for the next unit
+
+ align:start position:0%
+for the next unit
+ 
+
+ align:start position:0%
+for the next unit
+produced and then finally we'll Define
+
+ align:start position:0%
+produced and then finally we'll Define
+ 
+
+ align:start position:0%
+produced and then finally we'll Define
+average cost is what they sound like
+
+ align:start position:0%
+average cost is what they sound like
+ 
+
+ align:start position:0%
+average cost is what they sound like
+which is C over Q total cost over
+
+ align:start position:0%
+which is C over Q total cost over
+ 
+
+ align:start position:0%
+which is C over Q total cost over
+quantity produced that's average
+
+ align:start position:0%
+quantity produced that's average
+ 
+
+ align:start position:0%
+quantity produced that's average
+cost we can graph these various cost
+
+ align:start position:0%
+cost we can graph these various cost
+ 
+
+ align:start position:0%
+cost we can graph these various cost
+Curves in figure
+
+ align:start position:0%
+Curves in figure
+ 
+
+ align:start position:0%
+Curves in figure
+61 so figure 61 in your handout shows
+
+ align:start position:0%
+61 so figure 61 in your handout shows
+ 
+
+ align:start position:0%
+61 so figure 61 in your handout shows
+the cost curves for our sample cost
+
+ align:start position:0%
+the cost curves for our sample cost
+ 
+
+ align:start position:0%
+the cost curves for our sample cost
+function which remember is really our
+
+ align:start position:0%
+function which remember is really our
+ 
+
+ align:start position:0%
+function which remember is really our
+example production function given in RW
+
+ align:start position:0%
+example production function given in RW
+ 
+
+ align:start position:0%
+example production function given in RW
+and K Bar what you see here is the
+
+ align:start position:0%
+and K Bar what you see here is the
+ 
+
+ align:start position:0%
+and K Bar what you see here is the
+marginal
+
+ align:start position:0%
+marginal
+ 
+
+ align:start position:0%
+marginal
+cost that is D variable cost DQ
+
+ align:start position:0%
+cost that is D variable cost DQ
+ 
+
+ align:start position:0%
+cost that is D variable cost DQ
+is equal in our example to 10 Q just
+
+ align:start position:0%
+is equal in our example to 10 Q just
+ 
+
+ align:start position:0%
+is equal in our example to 10 Q just
+differentiating that with respect to Q
+
+ align:start position:0%
+differentiating that with respect to Q
+ 
+
+ align:start position:0%
+differentiating that with respect to Q
+is 10 Q our marginal costs are are the
+
+ align:start position:0%
+is 10 Q our marginal costs are are the
+ 
+
+ align:start position:0%
+is 10 Q our marginal costs are are the
+line with the equation 10
+
+ align:start position:0%
+line with the equation 10
+ 
+
+ align:start position:0%
+line with the equation 10
+Q our average
+
+ align:start position:0%
+Q our average
+ 
+
+ align:start position:0%
+Q our average
+costs are this expression over Q so it's
+
+ align:start position:0%
+costs are this expression over Q so it's
+ 
+
+ align:start position:0%
+costs are this expression over Q so it's
+10 over Q + 5
+
+ align:start position:0%
+10 over Q + 5
+ 
+
+ align:start position:0%
+10 over Q + 5
+Q 10 over Q + 5 q is average cost
+
+ align:start position:0%
+Q 10 over Q + 5 q is average cost
+ 
+
+ align:start position:0%
+Q 10 over Q + 5 q is average cost
+okay how did I get that it's divide the
+
+ align:start position:0%
+okay how did I get that it's divide the
+ 
+
+ align:start position:0%
+okay how did I get that it's divide the
+cost by Q okay also on this graph you
+
+ align:start position:0%
+cost by Q okay also on this graph you
+ 
+
+ align:start position:0%
+cost by Q okay also on this graph you
+can see average variable costs and
+
+ align:start position:0%
+can see average variable costs and
+ 
+
+ align:start position:0%
+can see average variable costs and
+average fixed cost so you can see that
+
+ align:start position:0%
+average fixed cost so you can see that
+ 
+
+ align:start position:0%
+average fixed cost so you can see that
+the average cost line is a combination
+
+ align:start position:0%
+the average cost line is a combination
+ 
+
+ align:start position:0%
+the average cost line is a combination
+of two pieces an average variable cost
+
+ align:start position:0%
+of two pieces an average variable cost
+ 
+
+ align:start position:0%
+of two pieces an average variable cost
+which is everywhere up sloping upward
+
+ align:start position:0%
+which is everywhere up sloping upward
+ 
+
+ align:start position:0%
+which is everywhere up sloping upward
+sloping and average fixed cost which is
+
+ align:start position:0%
+sloping and average fixed cost which is
+ 
+
+ align:start position:0%
+sloping and average fixed cost which is
+everywhere fall which is everywhere
+
+ align:start position:0%
+everywhere fall which is everywhere
+ 
+
+ align:start position:0%
+everywhere fall which is everywhere
+falling okay so average costs themselves
+
+ align:start position:0%
+falling okay so average costs themselves
+ 
+
+ align:start position:0%
+falling okay so average costs themselves
+first fall then rise
+
+ align:start position:0%
+first fall then rise
+ 
+
+ align:start position:0%
+first fall then rise
+PR average cost First fall then rise why
+
+ align:start position:0%
+PR average cost First fall then rise why
+ 
+
+ align:start position:0%
+PR average cost First fall then rise why
+is that well that's because at first you
+
+ align:start position:0%
+is that well that's because at first you
+ 
+
+ align:start position:0%
+is that well that's because at first you
+have these big fixed costs you have to
+
+ align:start position:0%
+have these big fixed costs you have to
+ 
+
+ align:start position:0%
+have these big fixed costs you have to
+sort of pay off but over time the fixed
+
+ align:start position:0%
+sort of pay off but over time the fixed
+ 
+
+ align:start position:0%
+sort of pay off but over time the fixed
+cost gets small well the variable cost
+
+ align:start position:0%
+cost gets small well the variable cost
+ 
+
+ align:start position:0%
+cost gets small well the variable cost
+so over time it
+
+ align:start position:0%
+so over time it
+ 
+
+ align:start position:0%
+so over time it
+rises okay so average costs are the
+
+ align:start position:0%
+rises okay so average costs are the
+ 
+
+ align:start position:0%
+rises okay so average costs are the
+first fall because the first couple
+
+ align:start position:0%
+first fall because the first couple
+ 
+
+ align:start position:0%
+first fall because the first couple
+units your costs are very high your
+
+ align:start position:0%
+units your costs are very high your
+ 
+
+ align:start position:0%
+units your costs are very high your
+costs are super high at the start
+
+ align:start position:0%
+costs are super high at the start
+ 
+
+ align:start position:0%
+costs are super high at the start
+because you got all these fixed costs
+
+ align:start position:0%
+because you got all these fixed costs
+ 
+
+ align:start position:0%
+because you got all these fixed costs
+each unit you those fixed costs per unit
+
+ align:start position:0%
+each unit you those fixed costs per unit
+ 
+
+ align:start position:0%
+each unit you those fixed costs per unit
+fall and fall and fall that's the AFC
+
+ align:start position:0%
+fall and fall and fall that's the AFC
+ 
+
+ align:start position:0%
+fall and fall and fall that's the AFC
+loan
+
+ align:start position:0%
+loan
+ 
+
+ align:start position:0%
+loan
+fixed cost per unit fall and fall and
+
+ align:start position:0%
+fixed cost per unit fall and fall and
+ 
+
+ align:start position:0%
+fixed cost per unit fall and fall and
+fall whereas Mar variable cost per unit
+
+ align:start position:0%
+fall whereas Mar variable cost per unit
+ 
+
+ align:start position:0%
+fall whereas Mar variable cost per unit
+rise and rise and rise and the
+
+ align:start position:0%
+rise and rise and rise and the
+ 
+
+ align:start position:0%
+rise and rise and rise and the
+minimum of average cost is where it
+
+ align:start position:0%
+minimum of average cost is where it
+ 
+
+ align:start position:0%
+minimum of average cost is where it
+crosses the marginal cost curve it's
+
+ align:start position:0%
+crosses the marginal cost curve it's
+ 
+
+ align:start position:0%
+crosses the marginal cost curve it's
+just mathematical the minimum if you
+
+ align:start position:0%
+just mathematical the minimum if you
+ 
+
+ align:start position:0%
+just mathematical the minimum if you
+take a function the minimum of the
+
+ align:start position:0%
+take a function the minimum of the
+ 
+
+ align:start position:0%
+take a function the minimum of the
+average is going to be where it
+
+ align:start position:0%
+average is going to be where it
+ 
+
+ align:start position:0%
+average is going to be where it
+intersects the margin okay because
+
+ align:start position:0%
+intersects the margin okay because
+ 
+
+ align:start position:0%
+intersects the margin okay because
+wherever the average cost is wherever
+
+ align:start position:0%
+wherever the average cost is wherever
+ 
+
+ align:start position:0%
+wherever the average cost is wherever
+the marginal cost is above the average
+
+ align:start position:0%
+the marginal cost is above the average
+ 
+
+ align:start position:0%
+the marginal cost is above the average
+cost the average cost is rising wherever
+
+ align:start position:0%
+cost the average cost is rising wherever
+ 
+
+ align:start position:0%
+cost the average cost is rising wherever
+the marginal cost is below the average
+
+ align:start position:0%
+the marginal cost is below the average
+ 
+
+ align:start position:0%
+the marginal cost is below the average
+cost that's falling therefore marginal
+
+ align:start position:0%
+cost that's falling therefore marginal
+ 
+
+ align:start position:0%
+cost that's falling therefore marginal
+cost intersects average costs at the
+
+ align:start position:0%
+cost intersects average costs at the
+ 
+
+ align:start position:0%
+cost intersects average costs at the
+minimum okay in other words if average
+
+ align:start position:0%
+minimum okay in other words if average
+ 
+
+ align:start position:0%
+minimum okay in other words if average
+cost if you're to the point to the left
+
+ align:start position:0%
+cost if you're to the point to the left
+ 
+
+ align:start position:0%
+cost if you're to the point to the left
+of
+
+ align:start position:0%
+of
+ 
+
+ align:start position:0%
+of
+1.5 if you're Rising less than 1.5 units
+
+ align:start position:0%
+1.5 if you're Rising less than 1.5 units
+ 
+
+ align:start position:0%
+1.5 if you're Rising less than 1.5 units
+marginal cost is below average
+
+ align:start position:0%
+marginal cost is below average
+ 
+
+ align:start position:0%
+marginal cost is below average
+costs okay so by producing more you
+
+ align:start position:0%
+costs okay so by producing more you
+ 
+
+ align:start position:0%
+costs okay so by producing more you
+drive average cost down because the
+
+ align:start position:0%
+drive average cost down because the
+ 
+
+ align:start position:0%
+drive average cost down because the
+marginal cost is less than the average
+
+ align:start position:0%
+marginal cost is less than the average
+ 
+
+ align:start position:0%
+marginal cost is less than the average
+cost so as you increase production from
+
+ align:start position:0%
+cost so as you increase production from
+ 
+
+ align:start position:0%
+cost so as you increase production from
+one unit to one and a half unit you
+
+ align:start position:0%
+one unit to one and a half unit you
+ 
+
+ align:start position:0%
+one unit to one and a half unit you
+drive average cost down but once
+
+ align:start position:0%
+drive average cost down but once
+ 
+
+ align:start position:0%
+drive average cost down but once
+marginal cost is above average cost
+
+ align:start position:0%
+marginal cost is above average cost
+ 
+
+ align:start position:0%
+marginal cost is above average cost
+increasing production drives average
+
+ align:start position:0%
+increasing production drives average
+ 
+
+ align:start position:0%
+increasing production drives average
+cost up and that's why marginal cost
+
+ align:start position:0%
+cost up and that's why marginal cost
+ 
+
+ align:start position:0%
+cost up and that's why marginal cost
+hits average cost at the
+
+ align:start position:0%
+hits average cost at the
+ 
+
+ align:start position:0%
+hits average cost at the
+minimum okay questions about those
+
+ align:start position:0%
+minimum okay questions about those
+ 
+
+ align:start position:0%
+minimum okay questions about those
+relationships are those
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+graphs okay so
+
+ align:start position:0%
+graphs okay so
+ 
+
+ align:start position:0%
+graphs okay so
+now let's go back and note a key
+
+ align:start position:0%
+now let's go back and note a key
+ 
+
+ align:start position:0%
+now let's go back and note a key
+relationship between marginal cost and
+
+ align:start position:0%
+relationship between marginal cost and
+ 
+
+ align:start position:0%
+relationship between marginal cost and
+something we discussed last time the
+
+ align:start position:0%
+something we discussed last time the
+ 
+
+ align:start position:0%
+something we discussed last time the
+marginal product of
+
+ align:start position:0%
+marginal product of
+ 
+
+ align:start position:0%
+marginal product of
+labor okay remember
+
+ align:start position:0%
+labor okay remember
+ 
+
+ align:start position:0%
+labor okay remember
+cost
+
+ align:start position:0%
+cost
+ 
+
+ align:start position:0%
+cost
+equals uh K Bar * r+ L *
+
+ align:start position:0%
+equals uh K Bar * r+ L *
+ 
+
+ align:start position:0%
+equals uh K Bar * r+ L *
+W if you differentiate this with respect
+
+ align:start position:0%
+W if you differentiate this with respect
+ 
+
+ align:start position:0%
+W if you differentiate this with respect
+to Q to get the marginal cost you get
+
+ align:start position:0%
+to Q to get the marginal cost you get
+ 
+
+ align:start position:0%
+to Q to get the marginal cost you get
+marginal
+
+ align:start position:0%
+marginal
+ 
+
+ align:start position:0%
+marginal
+cost equals W * DL DQ okay because this
+
+ align:start position:0%
+cost equals W * DL DQ okay because this
+ 
+
+ align:start position:0%
+cost equals W * DL DQ okay because this
+term drops out and so you just
+
+ align:start position:0%
+term drops out and so you just
+ 
+
+ align:start position:0%
+term drops out and so you just
+differentiate differentiate by the law
+
+ align:start position:0%
+differentiate differentiate by the law
+ 
+
+ align:start position:0%
+differentiate differentiate by the law
+of of you get W time dld
+
+ align:start position:0%
+of of you get W time dld
+ 
+
+ align:start position:0%
+of of you get W time dld
+DQ okay so the marginal cost of
+
+ align:start position:0%
+DQ okay so the marginal cost of
+ 
+
+ align:start position:0%
+DQ okay so the marginal cost of
+producing the next unit is the price per
+
+ align:start position:0%
+producing the next unit is the price per
+ 
+
+ align:start position:0%
+producing the next unit is the price per
+unit of
+
+ align:start position:0%
+unit of
+ 
+
+ align:start position:0%
+unit of
+Labor times how many units of Labor it
+
+ align:start position:0%
+Labor times how many units of Labor it
+ 
+
+ align:start position:0%
+Labor times how many units of Labor it
+takes to make the next unit this is the
+
+ align:start position:0%
+takes to make the next unit this is the
+ 
+
+ align:start position:0%
+takes to make the next unit this is the
+price per unit of Labor W this is how
+
+ align:start position:0%
+price per unit of Labor W this is how
+ 
+
+ align:start position:0%
+price per unit of Labor W this is how
+much labor takes to make the next unit
+
+ align:start position:0%
+much labor takes to make the next unit
+ 
+
+ align:start position:0%
+much labor takes to make the next unit
+so the marginal cost of the next unit is
+
+ align:start position:0%
+so the marginal cost of the next unit is
+ 
+
+ align:start position:0%
+so the marginal cost of the next unit is
+the product of those
+
+ align:start position:0%
+the product of those
+ 
+
+ align:start position:0%
+the product of those
+but we also know from last
+
+ align:start position:0%
+but we also know from last
+ 
+
+ align:start position:0%
+but we also know from last
+lecture we know from last lecture that
+
+ align:start position:0%
+lecture we know from last lecture that
+ 
+
+ align:start position:0%
+lecture we know from last lecture that
+DQ DL we had a name for that we called
+
+ align:start position:0%
+DQ DL we had a name for that we called
+ 
+
+ align:start position:0%
+DQ DL we had a name for that we called
+that the marginal product of labor we
+
+ align:start position:0%
+that the marginal product of labor we
+ 
+
+ align:start position:0%
+that the marginal product of labor we
+defined that last lecture how productive
+
+ align:start position:0%
+defined that last lecture how productive
+ 
+
+ align:start position:0%
+defined that last lecture how productive
+the next unit of Labor is was
+
+ align:start position:0%
+the next unit of Labor is was
+ 
+
+ align:start position:0%
+the next unit of Labor is was
+dql so we can substitute in to write we
+
+ align:start position:0%
+dql so we can substitute in to write we
+ 
+
+ align:start position:0%
+dql so we can substitute in to write we
+can substitute that in to write that
+
+ align:start position:0%
+can substitute that in to write that
+ 
+
+ align:start position:0%
+can substitute that in to write that
+marginal cost equals W over the marginal
+
+ align:start position:0%
+marginal cost equals W over the marginal
+ 
+
+ align:start position:0%
+marginal cost equals W over the marginal
+product of labor
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that is the marginal cost producing the
+
+ align:start position:0%
+that is the marginal cost producing the
+ 
+
+ align:start position:0%
+that is the marginal cost producing the
+next unit of the good is higher the more
+
+ align:start position:0%
+next unit of the good is higher the more
+ 
+
+ align:start position:0%
+next unit of the good is higher the more
+you have to pay each worker and lower
+
+ align:start position:0%
+you have to pay each worker and lower
+ 
+
+ align:start position:0%
+you have to pay each worker and lower
+the more productive each worker
+
+ align:start position:0%
+the more productive each worker
+ 
+
+ align:start position:0%
+the more productive each worker
+is okay so as marginal product of labor
+
+ align:start position:0%
+is okay so as marginal product of labor
+ 
+
+ align:start position:0%
+is okay so as marginal product of labor
+is very high unless wages very high
+
+ align:start position:0%
+is very high unless wages very high
+ 
+
+ align:start position:0%
+is very high unless wages very high
+marginal cost is going to be
+
+ align:start position:0%
+marginal cost is going to be
+ 
+
+ align:start position:0%
+marginal cost is going to be
+low okay so basically what's going to
+
+ align:start position:0%
+low okay so basically what's going to
+ 
+
+ align:start position:0%
+low okay so basically what's going to
+matter is the marginal uh the
+
+ align:start position:0%
+matter is the marginal uh the
+ 
+
+ align:start position:0%
+matter is the marginal uh the
+marginal product of each unit of Labor
+
+ align:start position:0%
+marginal product of each unit of Labor
+ 
+
+ align:start position:0%
+marginal product of each unit of Labor
+and the wage of to pay for that
+
+ align:start position:0%
+and the wage of to pay for that
+ 
+
+ align:start position:0%
+and the wage of to pay for that
+unit okay now last point I want to make
+
+ align:start position:0%
+unit okay now last point I want to make
+ 
+
+ align:start position:0%
+unit okay now last point I want to make
+here on on definitions I want about
+
+ align:start position:0%
+here on on definitions I want about
+ 
+
+ align:start position:0%
+here on on definitions I want about
+something called sunk
+
+ align:start position:0%
+something called sunk
+ 
+
+ align:start position:0%
+something called sunk
+costs I'm gonna I'm GNA already
+
+ align:start position:0%
+costs I'm gonna I'm GNA already
+ 
+
+ align:start position:0%
+costs I'm gonna I'm GNA already
+contradict something I said last lecture
+
+ align:start position:0%
+contradict something I said last lecture
+ 
+
+ align:start position:0%
+contradict something I said last lecture
+last lecture I said in the long run all
+
+ align:start position:0%
+last lecture I said in the long run all
+ 
+
+ align:start position:0%
+last lecture I said in the long run all
+inputs are variable in the short run
+
+ align:start position:0%
+inputs are variable in the short run
+ 
+
+ align:start position:0%
+inputs are variable in the short run
+only some inputs are variable we have
+
+ align:start position:0%
+only some inputs are variable we have
+ 
+
+ align:start position:0%
+only some inputs are variable we have
+some costs which in the we have some
+
+ align:start position:0%
+some costs which in the we have some
+ 
+
+ align:start position:0%
+some costs which in the we have some
+costs which in the long run are not
+
+ align:start position:0%
+costs which in the long run are not
+ 
+
+ align:start position:0%
+costs which in the long run are not
+variable those are called sunk costs
+
+ align:start position:0%
+variable those are called sunk costs
+ 
+
+ align:start position:0%
+variable those are called sunk costs
+those are costs where once you make them
+
+ align:start position:0%
+those are costs where once you make them
+ 
+
+ align:start position:0%
+those are costs where once you make them
+you can never get them
+
+ align:start position:0%
+you can never get them
+ 
+
+ align:start position:0%
+you can never get them
+back a fixed cost is something like a
+
+ align:start position:0%
+back a fixed cost is something like a
+ 
+
+ align:start position:0%
+back a fixed cost is something like a
+machine if you buy a machine and you
+
+ align:start position:0%
+machine if you buy a machine and you
+ 
+
+ align:start position:0%
+machine if you buy a machine and you
+want to get rid of it you can sell that
+
+ align:start position:0%
+want to get rid of it you can sell that
+ 
+
+ align:start position:0%
+want to get rid of it you can sell that
+machine or a building if you buy a
+
+ align:start position:0%
+machine or a building if you buy a
+ 
+
+ align:start position:0%
+machine or a building if you buy a
+building and you want rid of it you can
+
+ align:start position:0%
+building and you want rid of it you can
+ 
+
+ align:start position:0%
+building and you want rid of it you can
+sell that building a sun cost is
+
+ align:start position:0%
+sell that building a sun cost is
+ 
+
+ align:start position:0%
+sell that building a sun cost is
+something you can't ever get rid of or
+
+ align:start position:0%
+something you can't ever get rid of or
+ 
+
+ align:start position:0%
+something you can't ever get rid of or
+sell the best example would be med
+
+ align:start position:0%
+sell the best example would be med
+ 
+
+ align:start position:0%
+sell the best example would be med
+school if you want to be a doctor you
+
+ align:start position:0%
+school if you want to be a doctor you
+ 
+
+ align:start position:0%
+school if you want to be a doctor you
+have to go to med
+
+ align:start position:0%
+have to go to med
+ 
+
+ align:start position:0%
+have to go to med
+school having gone to med school school
+
+ align:start position:0%
+school having gone to med school school
+ 
+
+ align:start position:0%
+school having gone to med school school
+you can't ever ungo to med school you
+
+ align:start position:0%
+you can't ever ungo to med school you
+ 
+
+ align:start position:0%
+you can't ever ungo to med school you
+have paid that cost of time and money
+
+ align:start position:0%
+have paid that cost of time and money
+ 
+
+ align:start position:0%
+have paid that cost of time and money
+and you're done it's
+
+ align:start position:0%
+and you're done it's
+ 
+
+ align:start position:0%
+and you're done it's
+sunk a sunk cost is essentially a long
+
+ align:start position:0%
+sunk a sunk cost is essentially a long
+ 
+
+ align:start position:0%
+sunk a sunk cost is essentially a long
+run fixed cost it's something where once
+
+ align:start position:0%
+run fixed cost it's something where once
+ 
+
+ align:start position:0%
+run fixed cost it's something where once
+you make that investment you never get
+
+ align:start position:0%
+you make that investment you never get
+ 
+
+ align:start position:0%
+you make that investment you never get
+it there's no way to get it back now you
+
+ align:start position:0%
+it there's no way to get it back now you
+ 
+
+ align:start position:0%
+it there's no way to get it back now you
+can get benefits from it I'm not saying
+
+ align:start position:0%
+can get benefits from it I'm not saying
+ 
+
+ align:start position:0%
+can get benefits from it I'm not saying
+it's not a good idea I'm just saying
+
+ align:start position:0%
+it's not a good idea I'm just saying
+ 
+
+ align:start position:0%
+it's not a good idea I'm just saying
+unlike a building which you could sell
+
+ align:start position:0%
+unlike a building which you could sell
+ 
+
+ align:start position:0%
+unlike a building which you could sell
+or a machine which you could sell med
+
+ align:start position:0%
+or a machine which you could sell med
+ 
+
+ align:start position:0%
+or a machine which you could sell med
+school you can't sell your med school
+
+ align:start position:0%
+school you can't sell your med school
+ 
+
+ align:start position:0%
+school you can't sell your med school
+experience okay and this is very
+
+ align:start position:0%
+experience okay and this is very
+ 
+
+ align:start position:0%
+experience okay and this is very
+important important because it leads to
+
+ align:start position:0%
+important important because it leads to
+ 
+
+ align:start position:0%
+important important because it leads to
+a very
+
+ align:start position:0%
+a very
+ 
+
+ align:start position:0%
+a very
+counterintuitive difference between sunk
+
+ align:start position:0%
+counterintuitive difference between sunk
+ 
+
+ align:start position:0%
+counterintuitive difference between sunk
+costs and fixed costs something that
+
+ align:start position:0%
+costs and fixed costs something that
+ 
+
+ align:start position:0%
+costs and fixed costs something that
+trips people up all the
+
+ align:start position:0%
+trips people up all the
+ 
+
+ align:start position:0%
+trips people up all the
+time which is that sunk costs are
+
+ align:start position:0%
+time which is that sunk costs are
+ 
+
+ align:start position:0%
+time which is that sunk costs are
+irrelevant to decision making once
+
+ align:start position:0%
+irrelevant to decision making once
+ 
+
+ align:start position:0%
+irrelevant to decision making once
+they're
+
+ align:start position:0%
+they're
+ 
+
+ align:start position:0%
+they're
+paid once you've paid your sunk costs
+
+ align:start position:0%
+paid once you've paid your sunk costs
+ 
+
+ align:start position:0%
+paid once you've paid your sunk costs
+they are relevant because you can't get
+
+ align:start position:0%
+they are relevant because you can't get
+ 
+
+ align:start position:0%
+they are relevant because you can't get
+them back anyway it's done or does The
+
+ align:start position:0%
+them back anyway it's done or does The
+ 
+
+ align:start position:0%
+them back anyway it's done or does The
+Economist say sunk costs or sunk doesn't
+
+ align:start position:0%
+Economist say sunk costs or sunk doesn't
+ 
+
+ align:start position:0%
+Economist say sunk costs or sunk doesn't
+matter it's
+
+ align:start position:0%
+matter it's
+ 
+
+ align:start position:0%
+matter it's
+irrelevant now here's why that matters
+
+ align:start position:0%
+irrelevant now here's why that matters
+ 
+
+ align:start position:0%
+irrelevant now here's why that matters
+in real life
+
+ align:start position:0%
+in real life
+ 
+
+ align:start position:0%
+in real life
+let me talk about a simple example many
+
+ align:start position:0%
+let me talk about a simple example many
+ 
+
+ align:start position:0%
+let me talk about a simple example many
+of you have heard of the band Journey
+
+ align:start position:0%
+of you have heard of the band Journey
+ 
+
+ align:start position:0%
+of you have heard of the band Journey
+classic 80s band a few years ago Journey
+
+ align:start position:0%
+classic 80s band a few years ago Journey
+ 
+
+ align:start position:0%
+classic 80s band a few years ago Journey
+was touring and they have a new lead
+
+ align:start position:0%
+was touring and they have a new lead
+ 
+
+ align:start position:0%
+was touring and they have a new lead
+singer this guy they fat actually
+
+ align:start position:0%
+singer this guy they fat actually
+ 
+
+ align:start position:0%
+singer this guy they fat actually
+through YouTube who sounds he's from the
+
+ align:start position:0%
+through YouTube who sounds he's from the
+ 
+
+ align:start position:0%
+through YouTube who sounds he's from the
+Philippines sounds just like the old
+
+ align:start position:0%
+Philippines sounds just like the old
+ 
+
+ align:start position:0%
+Philippines sounds just like the old
+lead singer it's kind of cool so uh they
+
+ align:start position:0%
+lead singer it's kind of cool so uh they
+ 
+
+ align:start position:0%
+lead singer it's kind of cool so uh they
+were playing down in uh uh Mansfield
+
+ align:start position:0%
+were playing down in uh uh Mansfield
+ 
+
+ align:start position:0%
+were playing down in uh uh Mansfield
+Mass and I bought a couple of tickets
+
+ align:start position:0%
+Mass and I bought a couple of tickets
+ 
+
+ align:start position:0%
+Mass and I bought a couple of tickets
+for my wife and I for 125 bucks each
+
+ align:start position:0%
+for my wife and I for 125 bucks each
+ 
+
+ align:start position:0%
+for my wife and I for 125 bucks each
+good
+
+ align:start position:0%
+good
+ 
+
+ align:start position:0%
+good
+seats then I looked at the set list and
+
+ align:start position:0%
+seats then I looked at the set list and
+ 
+
+ align:start position:0%
+seats then I looked at the set list and
+I thought you know I don't actually like
+
+ align:start position:0%
+I thought you know I don't actually like
+ 
+
+ align:start position:0%
+I thought you know I don't actually like
+that many Journey songs M there's hour
+
+ align:start position:0%
+that many Journey songs M there's hour
+ 
+
+ align:start position:0%
+that many Journey songs M there's hour
+and a half concert for like the three
+
+ align:start position:0%
+and a half concert for like the three
+ 
+
+ align:start position:0%
+and a half concert for like the three
+songs as I like it doesn't really seem
+
+ align:start position:0%
+songs as I like it doesn't really seem
+ 
+
+ align:start position:0%
+songs as I like it doesn't really seem
+worth it I don't think I want to go I
+
+ align:start position:0%
+worth it I don't think I want to go I
+ 
+
+ align:start position:0%
+worth it I don't think I want to go I
+think I'm going to try to sell these
+
+ align:start position:0%
+think I'm going to try to sell these
+ 
+
+ align:start position:0%
+think I'm going to try to sell these
+tickets on the secondary market so I can
+
+ align:start position:0%
+tickets on the secondary market so I can
+ 
+
+ align:start position:0%
+tickets on the secondary market so I can
+go to Stubhub and sell the tickets the
+
+ align:start position:0%
+go to Stubhub and sell the tickets the
+ 
+
+ align:start position:0%
+go to Stubhub and sell the tickets the
+question
+
+ align:start position:0%
+question
+ 
+
+ align:start position:0%
+question
+is I had paid $250 for those tickets how
+
+ align:start position:0%
+is I had paid $250 for those tickets how
+ 
+
+ align:start position:0%
+is I had paid $250 for those tickets how
+should that impact the price I set on
+
+ align:start position:0%
+should that impact the price I set on
+ 
+
+ align:start position:0%
+should that impact the price I set on
+StubHub the money I paid for those
+
+ align:start position:0%
+StubHub the money I paid for those
+ 
+
+ align:start position:0%
+StubHub the money I paid for those
+tickets how should it that money forget
+
+ align:start position:0%
+tickets how should it that money forget
+ 
+
+ align:start position:0%
+tickets how should it that money forget
+everything else just the money I paid
+
+ align:start position:0%
+everything else just the money I paid
+ 
+
+ align:start position:0%
+everything else just the money I paid
+how should it impact the price I set on
+
+ align:start position:0%
+how should it impact the price I set on
+ 
+
+ align:start position:0%
+how should it impact the price I set on
+StubHub
+
+ align:start position:0%
+StubHub
+ 
+
+ align:start position:0%
+StubHub
+yeah it shouldn't why
+
+ align:start position:0%
+yeah it shouldn't why
+ 
+
+ align:start position:0%
+yeah it shouldn't why
+not it's a some cost I paid it already
+
+ align:start position:0%
+not it's a some cost I paid it already
+ 
+
+ align:start position:0%
+not it's a some cost I paid it already
+it's
+
+ align:start position:0%
+it's
+ 
+
+ align:start position:0%
+it's
+irrelevant it's done I already paid the
+
+ align:start position:0%
+irrelevant it's done I already paid the
+ 
+
+ align:start position:0%
+irrelevant it's done I already paid the
+250 it's gone I might feel sad but it's
+
+ align:start position:0%
+250 it's gone I might feel sad but it's
+ 
+
+ align:start position:0%
+250 it's gone I might feel sad but it's
+gone how should I decide what to put the
+
+ align:start position:0%
+gone how should I decide what to put the
+ 
+
+ align:start position:0%
+gone how should I decide what to put the
+tickets on salale for subhub well it's a
+
+ align:start position:0%
+tickets on salale for subhub well it's a
+ 
+
+ align:start position:0%
+tickets on salale for subhub well it's a
+function of two factors first is I can
+
+ align:start position:0%
+function of two factors first is I can
+ 
+
+ align:start position:0%
+function of two factors first is I can
+look at what things are selling for and
+
+ align:start position:0%
+look at what things are selling for and
+ 
+
+ align:start position:0%
+look at what things are selling for and
+try to use the
+
+ align:start position:0%
+try to use the
+ 
+
+ align:start position:0%
+try to use the
+market that's one thing but let's add no
+
+ align:start position:0%
+market that's one thing but let's add no
+ 
+
+ align:start position:0%
+market that's one thing but let's add no
+information let's add no information on
+
+ align:start position:0%
+information let's add no information on
+ 
+
+ align:start position:0%
+information let's add no information on
+the market leave that aside it's just an
+
+ align:start position:0%
+the market leave that aside it's just an
+ 
+
+ align:start position:0%
+the market leave that aside it's just an
+internal decision decision on what what
+
+ align:start position:0%
+internal decision decision on what what
+ 
+
+ align:start position:0%
+internal decision decision on what what
+I'm willing to sell the tickets for how
+
+ align:start position:0%
+I'm willing to sell the tickets for how
+ 
+
+ align:start position:0%
+I'm willing to sell the tickets for how
+should I
+
+ align:start position:0%
+should I
+ 
+
+ align:start position:0%
+should I
+decide
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah you well that's one way to think
+
+ align:start position:0%
+yeah you well that's one way to think
+ 
+
+ align:start position:0%
+yeah you well that's one way to think
+about it you'd not be a to pay the buy
+
+ align:start position:0%
+about it you'd not be a to pay the buy
+ 
+
+ align:start position:0%
+about it you'd not be a to pay the buy
+tickets that's one way but there's sort
+
+ align:start position:0%
+tickets that's one way but there's sort
+ 
+
+ align:start position:0%
+tickets that's one way but there's sort
+of a that's sort of a confusing way
+
+ align:start position:0%
+of a that's sort of a confusing way
+ 
+
+ align:start position:0%
+of a that's sort of a confusing way
+there's another way to think about it
+
+ align:start position:0%
+there's another way to think about it
+ 
+
+ align:start position:0%
+there's another way to think about it
+what's another way to think about it's
+
+ align:start position:0%
+what's another way to think about it's
+ 
+
+ align:start position:0%
+what's another way to think about it's
+related to that sort the flip of what
+
+ align:start position:0%
+related to that sort the flip of what
+ 
+
+ align:start position:0%
+related to that sort the flip of what
+you
+
+ align:start position:0%
+you
+ 
+
+ align:start position:0%
+you
+said how should I think about how much
+
+ align:start position:0%
+said how should I think about how much
+ 
+
+ align:start position:0%
+said how should I think about how much
+I'm willing to I'm willing to how much
+
+ align:start position:0%
+I'm willing to I'm willing to how much
+ 
+
+ align:start position:0%
+I'm willing to I'm willing to how much
+am I willing forget the price that I set
+
+ align:start position:0%
+am I willing forget the price that I set
+ 
+
+ align:start position:0%
+am I willing forget the price that I set
+which is a function of what I think the
+
+ align:start position:0%
+which is a function of what I think the
+ 
+
+ align:start position:0%
+which is a function of what I think the
+market is my willingness how much should
+
+ align:start position:0%
+market is my willingness how much should
+ 
+
+ align:start position:0%
+market is my willingness how much should
+I you willing to sell those tickets
+
+ align:start position:0%
+I you willing to sell those tickets
+ 
+
+ align:start position:0%
+I you willing to sell those tickets
+for well think about it if I if I sell
+
+ align:start position:0%
+for well think about it if I if I sell
+ 
+
+ align:start position:0%
+for well think about it if I if I sell
+the tickets what am I not
+
+ align:start position:0%
+the tickets what am I not
+ 
+
+ align:start position:0%
+the tickets what am I not
+doing I'm not going to the
+
+ align:start position:0%
+doing I'm not going to the
+ 
+
+ align:start position:0%
+doing I'm not going to the
+concert so how much should I be willing
+
+ align:start position:0%
+concert so how much should I be willing
+ 
+
+ align:start position:0%
+concert so how much should I be willing
+to sell the tickets
+
+ align:start position:0%
+to sell the tickets
+ 
+
+ align:start position:0%
+to sell the tickets
+for yeah yeah go ahead white shirt you
+
+ align:start position:0%
+for yeah yeah go ahead white shirt you
+ 
+
+ align:start position:0%
+for yeah yeah go ahead white shirt you
+had your hand up
+
+ align:start position:0%
+had your hand up
+ 
+
+ align:start position:0%
+had your hand up
+yeah yeah basically I should sell them
+
+ align:start position:0%
+yeah yeah basically I should sell them
+ 
+
+ align:start position:0%
+yeah yeah basically I should sell them
+for how much I'm willing to pay to go to
+
+ align:start position:0%
+for how much I'm willing to pay to go to
+ 
+
+ align:start position:0%
+for how much I'm willing to pay to go to
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+show if
+
+ align:start position:0%
+show if
+ 
+
+ align:start position:0%
+show if
+literally I don't want to go that I
+
+ align:start position:0%
+literally I don't want to go that I
+ 
+
+ align:start position:0%
+literally I don't want to go that I
+should be willing to sell them for zero
+
+ align:start position:0%
+should be willing to sell them for zero
+ 
+
+ align:start position:0%
+should be willing to sell them for zero
+I should willing to give them away not
+
+ align:start position:0%
+I should willing to give them away not
+ 
+
+ align:start position:0%
+I should willing to give them away not
+saying I will sell them for zero because
+
+ align:start position:0%
+saying I will sell them for zero because
+ 
+
+ align:start position:0%
+saying I will sell them for zero because
+I might make money on it but there's a
+
+ align:start position:0%
+I might make money on it but there's a
+ 
+
+ align:start position:0%
+I might make money on it but there's a
+my underlying opportunity cost at zero
+
+ align:start position:0%
+my underlying opportunity cost at zero
+ 
+
+ align:start position:0%
+my underlying opportunity cost at zero
+because I literally would rather sit at
+
+ align:start position:0%
+because I literally would rather sit at
+ 
+
+ align:start position:0%
+because I literally would rather sit at
+home if I say yeah I don't want to pay
+
+ align:start position:0%
+home if I say yeah I don't want to pay
+ 
+
+ align:start position:0%
+home if I say yeah I don't want to pay
+250 but if you said you get Journey
+
+ align:start position:0%
+250 but if you said you get Journey
+ 
+
+ align:start position:0%
+250 but if you said you get Journey
+tickets for 50 bucks each I'd go then I
+
+ align:start position:0%
+tickets for 50 bucks each I'd go then I
+ 
+
+ align:start position:0%
+tickets for 50 bucks each I'd go then I
+should set the price at 50 bucks each if
+
+ align:start position:0%
+should set the price at 50 bucks each if
+ 
+
+ align:start position:0%
+should set the price at 50 bucks each if
+someone will pay me more than 50 I sell
+
+ align:start position:0%
+someone will pay me more than 50 I sell
+ 
+
+ align:start position:0%
+someone will pay me more than 50 I sell
+them if they'll pay me less than 50 I go
+
+ align:start position:0%
+them if they'll pay me less than 50 I go
+ 
+
+ align:start position:0%
+them if they'll pay me less than 50 I go
+so the amount I should will be willing
+
+ align:start position:0%
+so the amount I should will be willing
+ 
+
+ align:start position:0%
+so the amount I should will be willing
+to get should be determined by the
+
+ align:start position:0%
+to get should be determined by the
+ 
+
+ align:start position:0%
+to get should be determined by the
+opportunity cost of going not by what I
+
+ align:start position:0%
+opportunity cost of going not by what I
+ 
+
+ align:start position:0%
+opportunity cost of going not by what I
+paid for them that is a very confusing
+
+ align:start position:0%
+paid for them that is a very confusing
+ 
+
+ align:start position:0%
+paid for them that is a very confusing
+logic
+
+ align:start position:0%
+logic
+ 
+
+ align:start position:0%
+logic
+yeah but
+
+ align:start position:0%
+yeah but
+ 
+
+ align:start position:0%
+yeah but
+some like
+
+ align:start position:0%
+some like
+ 
+
+ align:start position:0%
+some like
+think you would because that's the way
+
+ align:start position:0%
+think you would because that's the way
+ 
+
+ align:start position:0%
+think you would because that's the way
+humans think but it's
+
+ align:start position:0%
+humans think but it's
+ 
+
+ align:start position:0%
+humans think but it's
+wrong it's not a real
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+thing but it doesn't matter they're
+
+ align:start position:0%
+thing but it doesn't matter they're
+ 
+
+ align:start position:0%
+thing but it doesn't matter they're
+already gone so once again let me think
+
+ align:start position:0%
+already gone so once again let me think
+ 
+
+ align:start position:0%
+already gone so once again let me think
+of it this way let's say that um you
+
+ align:start position:0%
+of it this way let's say that um you
+ 
+
+ align:start position:0%
+of it this way let's say that um you
+the fact you've paid the costs makes you
+
+ align:start position:0%
+the fact you've paid the costs makes you
+ 
+
+ align:start position:0%
+the fact you've paid the costs makes you
+sad you've you've paid those costs you
+
+ align:start position:0%
+sad you've you've paid those costs you
+ 
+
+ align:start position:0%
+sad you've you've paid those costs you
+made them sad but right now if you
+
+ align:start position:0%
+made them sad but right now if you
+ 
+
+ align:start position:0%
+made them sad but right now if you
+whatever you sell them for okay that's
+
+ align:start position:0%
+whatever you sell them for okay that's
+ 
+
+ align:start position:0%
+whatever you sell them for okay that's
+all you can get back so let's say let me
+
+ align:start position:0%
+all you can get back so let's say let me
+ 
+
+ align:start position:0%
+all you can get back so let's say let me
+put this way let's say I can go online
+
+ align:start position:0%
+put this way let's say I can go online
+ 
+
+ align:start position:0%
+put this way let's say I can go online
+and sell them for 500 bucks each should
+
+ align:start position:0%
+and sell them for 500 bucks each should
+ 
+
+ align:start position:0%
+and sell them for 500 bucks each should
+I only sell them for 250 because that's
+
+ align:start position:0%
+I only sell them for 250 because that's
+ 
+
+ align:start position:0%
+I only sell them for 250 because that's
+what I paid for him no sell them for 500
+
+ align:start position:0%
+what I paid for him no sell them for 500
+ 
+
+ align:start position:0%
+what I paid for him no sell them for 500
+so it's irrelevant that I paid 250 if I
+
+ align:start position:0%
+so it's irrelevant that I paid 250 if I
+ 
+
+ align:start position:0%
+so it's irrelevant that I paid 250 if I
+only sell them for 50 I sell them for 50
+
+ align:start position:0%
+only sell them for 50 I sell them for 50
+ 
+
+ align:start position:0%
+only sell them for 50 I sell them for 50
+I've sell them for 500 sell them for 500
+
+ align:start position:0%
+I've sell them for 500 sell them for 500
+ 
+
+ align:start position:0%
+I've sell them for 500 sell them for 500
+what I paid is some amount I paid in the
+
+ align:start position:0%
+what I paid is some amount I paid in the
+ 
+
+ align:start position:0%
+what I paid is some amount I paid in the
+past I may be sad about it and look let
+
+ align:start position:0%
+past I may be sad about it and look let
+ 
+
+ align:start position:0%
+past I may be sad about it and look let
+me be clear the way you're thinking
+
+ align:start position:0%
+me be clear the way you're thinking
+ 
+
+ align:start position:0%
+me be clear the way you're thinking
+about is the way that the world thinks
+
+ align:start position:0%
+about is the way that the world thinks
+ 
+
+ align:start position:0%
+about is the way that the world thinks
+about it and it's wrong okay um you know
+
+ align:start position:0%
+about it and it's wrong okay um you know
+ 
+
+ align:start position:0%
+about it and it's wrong okay um you know
+I got chastised by my advisor in
+
+ align:start position:0%
+I got chastised by my advisor in
+ 
+
+ align:start position:0%
+I got chastised by my advisor in
+graduate school because I had plane
+
+ align:start position:0%
+graduate school because I had plane
+ 
+
+ align:start position:0%
+graduate school because I had plane
+tickets that I was going to cancel and I
+
+ align:start position:0%
+tickets that I was going to cancel and I
+ 
+
+ align:start position:0%
+tickets that I was going to cancel and I
+was suffering from the Sun cost Val I
+
+ align:start position:0%
+was suffering from the Sun cost Val I
+ 
+
+ align:start position:0%
+was suffering from the Sun cost Val I
+was going to say well I paid this much
+
+ align:start position:0%
+was going to say well I paid this much
+ 
+
+ align:start position:0%
+was going to say well I paid this much
+for him and he said doesn't matter what
+
+ align:start position:0%
+for him and he said doesn't matter what
+ 
+
+ align:start position:0%
+for him and he said doesn't matter what
+you paid for him what matters is the
+
+ align:start position:0%
+you paid for him what matters is the
+ 
+
+ align:start position:0%
+you paid for him what matters is the
+value to you of flying
+
+ align:start position:0%
+value to you of flying
+ 
+
+ align:start position:0%
+value to you of flying
+home okay the sun costs are
+
+ align:start position:0%
+home okay the sun costs are
+ 
+
+ align:start position:0%
+home okay the sun costs are
+gone okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah s selling what
+
+ align:start position:0%
+yeah s selling what
+ 
+
+ align:start position:0%
+yeah s selling what
+build oh so the difference that's a
+
+ align:start position:0%
+build oh so the difference that's a
+ 
+
+ align:start position:0%
+build oh so the difference that's a
+great point the difference is um with
+
+ align:start position:0%
+great point the difference is um with
+ 
+
+ align:start position:0%
+great point the difference is um with
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+building when
+
+ align:start position:0%
+building when
+ 
+
+ align:start position:0%
+building when
+I the difference is um with with the
+
+ align:start position:0%
+I the difference is um with with the
+ 
+
+ align:start position:0%
+I the difference is um with with the
+building I buy it as an investment that
+
+ align:start position:0%
+building I buy it as an investment that
+ 
+
+ align:start position:0%
+building I buy it as an investment that
+I intend to use for a while and then
+
+ align:start position:0%
+I intend to use for a while and then
+ 
+
+ align:start position:0%
+I intend to use for a while and then
+sell with the tickets I just bought that
+
+ align:start position:0%
+sell with the tickets I just bought that
+ 
+
+ align:start position:0%
+sell with the tickets I just bought that
+I wasn't thinking about selling them I
+
+ align:start position:0%
+I wasn't thinking about selling them I
+ 
+
+ align:start position:0%
+I wasn't thinking about selling them I
+was thinking about buying them I mean
+
+ align:start position:0%
+was thinking about buying them I mean
+ 
+
+ align:start position:0%
+was thinking about buying them I mean
+for example I could have bought the
+
+ align:start position:0%
+for example I could have bought the
+ 
+
+ align:start position:0%
+for example I could have bought the
+Journey tickets as an investment like a
+
+ align:start position:0%
+Journey tickets as an investment like a
+ 
+
+ align:start position:0%
+Journey tickets as an investment like a
+building I could have bought the Journey
+
+ align:start position:0%
+building I could have bought the Journey
+ 
+
+ align:start position:0%
+building I could have bought the Journey
+tickets and said well look I'm going to
+
+ align:start position:0%
+tickets and said well look I'm going to
+ 
+
+ align:start position:0%
+tickets and said well look I'm going to
+pay this for them because I at that form
+
+ align:start position:0%
+pay this for them because I at that form
+ 
+
+ align:start position:0%
+pay this for them because I at that form
+I plan to sell them but I wasn't plan to
+
+ align:start position:0%
+I plan to sell them but I wasn't plan to
+ 
+
+ align:start position:0%
+I plan to sell them but I wasn't plan to
+sell them I just bought them I thought I
+
+ align:start position:0%
+sell them I just bought them I thought I
+ 
+
+ align:start position:0%
+sell them I just bought them I thought I
+was done then things changed so from my
+
+ align:start position:0%
+was done then things changed so from my
+ 
+
+ align:start position:0%
+was done then things changed so from my
+new perspective they were
+
+ align:start position:0%
+new perspective they were
+ 
+
+ align:start position:0%
+new perspective they were
+sunk It's a good question good questions
+
+ align:start position:0%
+sunk It's a good question good questions
+ 
+
+ align:start position:0%
+sunk It's a good question good questions
+yeah some costs are basically Goods that
+
+ align:start position:0%
+yeah some costs are basically Goods that
+ 
+
+ align:start position:0%
+yeah some costs are basically Goods that
+you didn't want to sell in the first
+
+ align:start position:0%
+you didn't want to sell in the first
+ 
+
+ align:start position:0%
+you didn't want to sell in the first
+place some costs are things Investments
+
+ align:start position:0%
+place some costs are things Investments
+ 
+
+ align:start position:0%
+place some costs are things Investments
+you
+
+ align:start position:0%
+you
+ 
+
+ align:start position:0%
+you
+make you decide I want to go to med
+
+ align:start position:0%
+make you decide I want to go to med
+ 
+
+ align:start position:0%
+make you decide I want to go to med
+school I want to go to Journey okay and
+
+ align:start position:0%
+school I want to go to Journey okay and
+ 
+
+ align:start position:0%
+school I want to go to Journey okay and
+you make and you make those decisions
+
+ align:start position:0%
+you make and you make those decisions
+ 
+
+ align:start position:0%
+you make and you make those decisions
+and then things change and you may or or
+
+ align:start position:0%
+and then things change and you may or or
+ 
+
+ align:start position:0%
+and then things change and you may or or
+they don't change but the point is
+
+ align:start position:0%
+they don't change but the point is
+ 
+
+ align:start position:0%
+they don't change but the point is
+whatever you want to do next it's
+
+ align:start position:0%
+whatever you want to do next it's
+ 
+
+ align:start position:0%
+whatever you want to do next it's
+irrelevant that you made that decision
+
+ align:start position:0%
+irrelevant that you made that decision
+ 
+
+ align:start position:0%
+irrelevant that you made that decision
+you already made it now the question is
+
+ align:start position:0%
+you already made it now the question is
+ 
+
+ align:start position:0%
+you already made it now the question is
+what to do next it's it's it's it's not
+
+ align:start position:0%
+what to do next it's it's it's it's not
+ 
+
+ align:start position:0%
+what to do next it's it's it's it's not
+it's not an easy concept but it's an
+
+ align:start position:0%
+it's not an easy concept but it's an
+ 
+
+ align:start position:0%
+it's not an easy concept but it's an
+important one
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah oh you use it and journey buy joury
+
+ align:start position:0%
+yeah oh you use it and journey buy joury
+ 
+
+ align:start position:0%
+yeah oh you use it and journey buy joury
+tickets was the kind of investment that
+
+ align:start position:0%
+tickets was the kind of investment that
+ 
+
+ align:start position:0%
+tickets was the kind of investment that
+I would have used to go to Journey the
+
+ align:start position:0%
+I would have used to go to Journey the
+ 
+
+ align:start position:0%
+I would have used to go to Journey the
+difference if I decide I don't want to
+
+ align:start position:0%
+difference if I decide I don't want to
+ 
+
+ align:start position:0%
+difference if I decide I don't want to
+be a
+
+ align:start position:0%
+be a
+ 
+
+ align:start position:0%
+be a
+doctor let's say being a doctor is
+
+ align:start position:0%
+doctor let's say being a doctor is
+ 
+
+ align:start position:0%
+doctor let's say being a doctor is
+composed to three things going to med
+
+ align:start position:0%
+composed to three things going to med
+ 
+
+ align:start position:0%
+composed to three things going to med
+school buying an office and working
+
+ align:start position:0%
+school buying an office and working
+ 
+
+ align:start position:0%
+school buying an office and working
+every day if I decide I want to be aor
+
+ align:start position:0%
+every day if I decide I want to be aor
+ 
+
+ align:start position:0%
+every day if I decide I want to be aor
+doctor I can stop working every day I
+
+ align:start position:0%
+doctor I can stop working every day I
+ 
+
+ align:start position:0%
+doctor I can stop working every day I
+can sell the office but I can't ungo to
+
+ align:start position:0%
+can sell the office but I can't ungo to
+ 
+
+ align:start position:0%
+can sell the office but I can't ungo to
+med school it's
+
+ align:start position:0%
+med school it's
+ 
+
+ align:start position:0%
+med school it's
+done so my decision tomorrow do I want
+
+ align:start position:0%
+done so my decision tomorrow do I want
+ 
+
+ align:start position:0%
+done so my decision tomorrow do I want
+to stay being a doctor it's irrelevant
+
+ align:start position:0%
+to stay being a doctor it's irrelevant
+ 
+
+ align:start position:0%
+to stay being a doctor it's irrelevant
+if I went to med school I just say well
+
+ align:start position:0%
+if I went to med school I just say well
+ 
+
+ align:start position:0%
+if I went to med school I just say well
+how much do I like it how much money I'm
+
+ align:start position:0%
+how much do I like it how much money I'm
+ 
+
+ align:start position:0%
+how much do I like it how much money I'm
+making Rel to the cost of the office and
+
+ align:start position:0%
+making Rel to the cost of the office and
+ 
+
+ align:start position:0%
+making Rel to the cost of the office and
+the cost of what I have of my time and
+
+ align:start position:0%
+the cost of what I have of my time and
+ 
+
+ align:start position:0%
+the cost of what I have of my time and
+working every
+
+ align:start position:0%
+working every
+ 
+
+ align:start position:0%
+working every
+day
+
+ align:start position:0%
+day
+ 
+
+ align:start position:0%
+day
+okay that these are great questions
+
+ align:start position:0%
+okay that these are great questions
+ 
+
+ align:start position:0%
+okay that these are great questions
+because this is exactly kind of concept
+
+ align:start position:0%
+because this is exactly kind of concept
+ 
+
+ align:start position:0%
+because this is exactly kind of concept
+that I want you to be able to think
+
+ align:start position:0%
+that I want you to be able to think
+ 
+
+ align:start position:0%
+that I want you to be able to think
+differently about coming out of this
+
+ align:start position:0%
+differently about coming out of this
+ 
+
+ align:start position:0%
+differently about coming out of this
+course yeah
+
+ align:start position:0%
+course yeah
+ 
+
+ align:start position:0%
+course yeah
+or at least for some cost does intent
+
+ align:start position:0%
+or at least for some cost does intent
+ 
+
+ align:start position:0%
+or at least for some cost does intent
+matter what's that intent matter well
+
+ align:start position:0%
+matter what's that intent matter well
+ 
+
+ align:start position:0%
+matter what's that intent matter well
+it's it intent matters and whether we
+
+ align:start position:0%
+it's it intent matters and whether we
+ 
+
+ align:start position:0%
+it's it intent matters and whether we
+label it fixed or sunk that was the
+
+ align:start position:0%
+label it fixed or sunk that was the
+ 
+
+ align:start position:0%
+label it fixed or sunk that was the
+question here intent matters if you
+
+ align:start position:0%
+question here intent matters if you
+ 
+
+ align:start position:0%
+question here intent matters if you
+intend to eventually use it and sell it
+
+ align:start position:0%
+intend to eventually use it and sell it
+ 
+
+ align:start position:0%
+intend to eventually use it and sell it
+then it's fixed if you intend if it
+
+ align:start position:0%
+then it's fixed if you intend if it
+ 
+
+ align:start position:0%
+then it's fixed if you intend if it
+can't be sold or you don't intend to
+
+ align:start position:0%
+can't be sold or you don't intend to
+ 
+
+ align:start position:0%
+can't be sold or you don't intend to
+sell it then it's sunk but that that's a
+
+ align:start position:0%
+sell it then it's sunk but that that's a
+ 
+
+ align:start position:0%
+sell it then it's sunk but that that's a
+fuzzy
+
+ align:start position:0%
+fuzzy
+ 
+
+ align:start position:0%
+fuzzy
+line okay all right great discussion
+
+ align:start position:0%
+line okay all right great discussion
+ 
+
+ align:start position:0%
+line okay all right great discussion
+let's go on so now let's talk talk about
+
+ align:start position:0%
+let's go on so now let's talk talk about
+ 
+
+ align:start position:0%
+let's go on so now let's talk talk about
+the long run versus the short
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+run the long run versus the short
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+run the difference in the long run let's
+
+ align:start position:0%
+run the difference in the long run let's
+ 
+
+ align:start position:0%
+run the difference in the long run let's
+put Sun cost aside now how many choose
+
+ align:start position:0%
+put Sun cost aside now how many choose
+ 
+
+ align:start position:0%
+put Sun cost aside now how many choose
+let's put them aside okay that's more
+
+ align:start position:0%
+let's put them aside okay that's more
+ 
+
+ align:start position:0%
+let's put them aside okay that's more
+just sort of a fun thing for you to be
+
+ align:start position:0%
+just sort of a fun thing for you to be
+ 
+
+ align:start position:0%
+just sort of a fun thing for you to be
+thinking about in your life but for but
+
+ align:start position:0%
+thinking about in your life but for but
+ 
+
+ align:start position:0%
+thinking about in your life but for but
+for the rest for most of us class we'll
+
+ align:start position:0%
+for the rest for most of us class we'll
+ 
+
+ align:start position:0%
+for the rest for most of us class we'll
+talk about cost being fixed or variable
+
+ align:start position:0%
+talk about cost being fixed or variable
+ 
+
+ align:start position:0%
+talk about cost being fixed or variable
+not sunk so let's go back to where we
+
+ align:start position:0%
+not sunk so let's go back to where we
+ 
+
+ align:start position:0%
+not sunk so let's go back to where we
+just fixed and variable costs and we
+
+ align:start position:0%
+just fixed and variable costs and we
+ 
+
+ align:start position:0%
+just fixed and variable costs and we
+want to ask how do costs differ in the
+
+ align:start position:0%
+want to ask how do costs differ in the
+ 
+
+ align:start position:0%
+want to ask how do costs differ in the
+long run to short run and here there's a
+
+ align:start position:0%
+long run to short run and here there's a
+ 
+
+ align:start position:0%
+long run to short run and here there's a
+relatively simple but important
+
+ align:start position:0%
+relatively simple but important
+ 
+
+ align:start position:0%
+relatively simple but important
+intuition which is that long run
+
+ align:start position:0%
+intuition which is that long run
+ 
+
+ align:start position:0%
+intuition which is that long run
+costs will always
+
+ align:start position:0%
+costs will always
+ 
+
+ align:start position:0%
+costs will always
+be at the lower bound of short run
+
+ align:start position:0%
+be at the lower bound of short run
+ 
+
+ align:start position:0%
+be at the lower bound of short run
+costs the cost of production in Long Run
+
+ align:start position:0%
+costs the cost of production in Long Run
+ 
+
+ align:start position:0%
+costs the cost of production in Long Run
+are always the same or lower than the
+
+ align:start position:0%
+are always the same or lower than the
+ 
+
+ align:start position:0%
+are always the same or lower than the
+cost of production in the short run to
+
+ align:start position:0%
+cost of production in the short run to
+ 
+
+ align:start position:0%
+cost of production in the short run to
+see this let's go to figure 62 this is
+
+ align:start position:0%
+see this let's go to figure 62 this is
+ 
+
+ align:start position:0%
+see this let's go to figure 62 this is
+sort of a hard intuition let's go figure
+
+ align:start position:0%
+sort of a hard intuition let's go figure
+ 
+
+ align:start position:0%
+sort of a hard intuition let's go figure
+62 in this figure there's a firm that
+
+ align:start position:0%
+62 in this figure there's a firm that
+ 
+
+ align:start position:0%
+62 in this figure there's a firm that
+has three possible scales of production
+
+ align:start position:0%
+has three possible scales of production
+ 
+
+ align:start position:0%
+has three possible scales of production
+think of this is three different K bars
+
+ align:start position:0%
+think of this is three different K bars
+ 
+
+ align:start position:0%
+think of this is three different K bars
+they can
+
+ align:start position:0%
+they can
+ 
+
+ align:start position:0%
+they can
+choose and the way production work is in
+
+ align:start position:0%
+choose and the way production work is in
+ 
+
+ align:start position:0%
+choose and the way production work is in
+the short run you choose a k
+
+ align:start position:0%
+the short run you choose a k
+ 
+
+ align:start position:0%
+the short run you choose a k
+bar you then decide how much l to use
+
+ align:start position:0%
+bar you then decide how much l to use
+ 
+
+ align:start position:0%
+bar you then decide how much l to use
+and that's what you produce but in the
+
+ align:start position:0%
+and that's what you produce but in the
+ 
+
+ align:start position:0%
+and that's what you produce but in the
+long run you can change your K bar so
+
+ align:start position:0%
+long run you can change your K bar so
+ 
+
+ align:start position:0%
+long run you can change your K bar so
+think of a firm who has three different
+
+ align:start position:0%
+think of a firm who has three different
+ 
+
+ align:start position:0%
+think of a firm who has three different
+K bar options and those three different
+
+ align:start position:0%
+K bar options and those three different
+ 
+
+ align:start position:0%
+K bar options and those three different
+K bar options give three different
+
+ align:start position:0%
+K bar options give three different
+ 
+
+ align:start position:0%
+K bar options give three different
+average cost curves because you can see
+
+ align:start position:0%
+average cost curves because you can see
+ 
+
+ align:start position:0%
+average cost curves because you can see
+if I change K bar from one to two my
+
+ align:start position:0%
+if I change K bar from one to two my
+ 
+
+ align:start position:0%
+if I change K bar from one to two my
+average cost would change my average
+
+ align:start position:0%
+average cost would change my average
+ 
+
+ align:start position:0%
+average cost would change my average
+cost would no longer
+
+ align:start position:0%
+cost would no longer
+ 
+
+ align:start position:0%
+cost would no longer
+be uh would no longer be 10 over Q + 5 q
+
+ align:start position:0%
+be uh would no longer be 10 over Q + 5 q
+ 
+
+ align:start position:0%
+be uh would no longer be 10 over Q + 5 q
+okay my average cost would be 20 over Q
+
+ align:start position:0%
+okay my average cost would be 20 over Q
+ 
+
+ align:start position:0%
+okay my average cost would be 20 over Q
++ 5 q okay if Kar changed so think of
+
+ align:start position:0%
++ 5 q okay if Kar changed so think of
+ 
+
+ align:start position:0%
++ 5 q okay if Kar changed so think of
+these three curves as three different K
+
+ align:start position:0%
+these three curves as three different K
+ 
+
+ align:start position:0%
+these three curves as three different K
+bars now the firm in the short run has
+
+ align:start position:0%
+bars now the firm in the short run has
+ 
+
+ align:start position:0%
+bars now the firm in the short run has
+to choose which one it wants so for
+
+ align:start position:0%
+to choose which one it wants so for
+ 
+
+ align:start position:0%
+to choose which one it wants so for
+example
+
+ align:start position:0%
+example
+ 
+
+ align:start position:0%
+example
+sr1 that short run AC cost curve one
+
+ align:start position:0%
+sr1 that short run AC cost curve one
+ 
+
+ align:start position:0%
+sr1 that short run AC cost curve one
+that would be the average cost curve
+
+ align:start position:0%
+that would be the average cost curve
+ 
+
+ align:start position:0%
+that would be the average cost curve
+they choose if they think they're not
+
+ align:start position:0%
+they choose if they think they're not
+ 
+
+ align:start position:0%
+they choose if they think they're not
+going to produce that much they think
+
+ align:start position:0%
+going to produce that much they think
+ 
+
+ align:start position:0%
+going to produce that much they think
+they don't have much demand for their
+
+ align:start position:0%
+they don't have much demand for their
+ 
+
+ align:start position:0%
+they don't have much demand for their
+good as opposed to src3 that's the cost
+
+ align:start position:0%
+good as opposed to src3 that's the cost
+ 
+
+ align:start position:0%
+good as opposed to src3 that's the cost
+curve they choose they think there's
+
+ align:start position:0%
+curve they choose they think there's
+ 
+
+ align:start position:0%
+curve they choose they think there's
+going to be a lot of production they
+
+ align:start position:0%
+going to be a lot of production they
+ 
+
+ align:start position:0%
+going to be a lot of production they
+think there going be a lot of demand for
+
+ align:start position:0%
+think there going be a lot of demand for
+ 
+
+ align:start position:0%
+think there going be a lot of demand for
+the good so think of this about how big
+
+ align:start position:0%
+the good so think of this about how big
+ 
+
+ align:start position:0%
+the good so think of this about how big
+you build the plant if you think people
+
+ align:start position:0%
+you build the plant if you think people
+ 
+
+ align:start position:0%
+you build the plant if you think people
+are going to want much of your good you
+
+ align:start position:0%
+are going to want much of your good you
+ 
+
+ align:start position:0%
+are going to want much of your good you
+build a small plant think they're going
+
+ align:start position:0%
+build a small plant think they're going
+ 
+
+ align:start position:0%
+build a small plant think they're going
+want want to want want a lot of your
+
+ align:start position:0%
+want want to want want a lot of your
+ 
+
+ align:start position:0%
+want want to want want a lot of your
+good you build a big plant and sr2 is in
+
+ align:start position:0%
+good you build a big plant and sr2 is in
+ 
+
+ align:start position:0%
+good you build a big plant and sr2 is in
+between okay so in other words if the
+
+ align:start position:0%
+between okay so in other words if the
+ 
+
+ align:start position:0%
+between okay so in other words if the
+firm wants to produce the amount little
+
+ align:start position:0%
+firm wants to produce the amount little
+ 
+
+ align:start position:0%
+firm wants to produce the amount little
+q1 the most efficient K Bar to choose is
+
+ align:start position:0%
+q1 the most efficient K Bar to choose is
+ 
+
+ align:start position:0%
+q1 the most efficient K Bar to choose is
+the K Bar that yields
+
+ align:start position:0%
+the K Bar that yields
+ 
+
+ align:start position:0%
+the K Bar that yields
+sr1 right if the firm wants to produce
+
+ align:start position:0%
+sr1 right if the firm wants to produce
+ 
+
+ align:start position:0%
+sr1 right if the firm wants to produce
+little Q Q3 the most
+
+ align:start position:0%
+little Q Q3 the most
+ 
+
+ align:start position:0%
+little Q Q3 the most
+efficient K Bar to choose is the K Bar
+
+ align:start position:0%
+efficient K Bar to choose is the K Bar
+ 
+
+ align:start position:0%
+efficient K Bar to choose is the K Bar
+that yields
+
+ align:start position:0%
+that yields
+ 
+
+ align:start position:0%
+that yields
+sr3 but in the long run no matter what
+
+ align:start position:0%
+sr3 but in the long run no matter what
+ 
+
+ align:start position:0%
+sr3 but in the long run no matter what
+since it can reoptimize over K it can
+
+ align:start position:0%
+since it can reoptimize over K it can
+ 
+
+ align:start position:0%
+since it can reoptimize over K it can
+always do better than the short run it
+
+ align:start position:0%
+always do better than the short run it
+ 
+
+ align:start position:0%
+always do better than the short run it
+could do or at least no worse so if it
+
+ align:start position:0%
+could do or at least no worse so if it
+ 
+
+ align:start position:0%
+could do or at least no worse so if it
+turns out that in the long run demand is
+
+ align:start position:0%
+turns out that in the long run demand is
+ 
+
+ align:start position:0%
+turns out that in the long run demand is
+q1 and you chose src1 great the long run
+
+ align:start position:0%
+q1 and you chose src1 great the long run
+ 
+
+ align:start position:0%
+q1 and you chose src1 great the long run
+cost is the same as a short run costs
+
+ align:start position:0%
+cost is the same as a short run costs
+ 
+
+ align:start position:0%
+cost is the same as a short run costs
+but if by mistake you chose
+
+ align:start position:0%
+but if by mistake you chose
+ 
+
+ align:start position:0%
+but if by mistake you chose
+sr3 you can do better in the long run by
+
+ align:start position:0%
+sr3 you can do better in the long run by
+ 
+
+ align:start position:0%
+sr3 you can do better in the long run by
+reoptimizing your Capital it's just like
+
+ align:start position:0%
+reoptimizing your Capital it's just like
+ 
+
+ align:start position:0%
+reoptimizing your Capital it's just like
+any general scientific rule the more
+
+ align:start position:0%
+any general scientific rule the more
+ 
+
+ align:start position:0%
+any general scientific rule the more
+variables you have to toy with the more
+
+ align:start position:0%
+variables you have to toy with the more
+ 
+
+ align:start position:0%
+variables you have to toy with the more
+you can optimize okay here you can toy
+
+ align:start position:0%
+you can optimize okay here you can toy
+ 
+
+ align:start position:0%
+you can optimize okay here you can toy
+with two variables labor and capital so
+
+ align:start position:0%
+with two variables labor and capital so
+ 
+
+ align:start position:0%
+with two variables labor and capital so
+you can do better in terms of minimizing
+
+ align:start position:0%
+you can do better in terms of minimizing
+ 
+
+ align:start position:0%
+you can do better in terms of minimizing
+costs this is is not just a theoretical
+
+ align:start position:0%
+costs this is is not just a theoretical
+ 
+
+ align:start position:0%
+costs this is is not just a theoretical
+concept let's talk about one of the most
+
+ align:start position:0%
+concept let's talk about one of the most
+ 
+
+ align:start position:0%
+concept let's talk about one of the most
+important uh companies in America today
+
+ align:start position:0%
+important uh companies in America today
+ 
+
+ align:start position:0%
+important uh companies in America today
+which is
+
+ align:start position:0%
+which is
+ 
+
+ align:start position:0%
+which is
+Tesla when Tesla was founded in
+
+ align:start position:0%
+Tesla when Tesla was founded in
+ 
+
+ align:start position:0%
+Tesla when Tesla was founded in
+2013 Elon Musk had to decide how large a
+
+ align:start position:0%
+2013 Elon Musk had to decide how large a
+ 
+
+ align:start position:0%
+2013 Elon Musk had to decide how large a
+battery production plant to
+
+ align:start position:0%
+battery production plant to
+ 
+
+ align:start position:0%
+battery production plant to
+build he built a plant which was the
+
+ align:start position:0%
+build he built a plant which was the
+ 
+
+ align:start position:0%
+build he built a plant which was the
+size such that he would sell 20,000 cars
+
+ align:start position:0%
+size such that he would sell 20,000 cars
+ 
+
+ align:start position:0%
+size such that he would sell 20,000 cars
+in 2017 he figured his demand be 20,000
+
+ align:start position:0%
+in 2017 he figured his demand be 20,000
+ 
+
+ align:start position:0%
+in 2017 he figured his demand be 20,000
+cars in 2017 so he buil a plant let's
+
+ align:start position:0%
+cars in 2017 so he buil a plant let's
+ 
+
+ align:start position:0%
+cars in 2017 so he buil a plant let's
+call src1 cuz he expect Ed Q little
+
+ align:start position:0%
+call src1 cuz he expect Ed Q little
+ 
+
+ align:start position:0%
+call src1 cuz he expect Ed Q little
+1 what happened was he got Q Little
+
+ align:start position:0%
+1 what happened was he got Q Little
+ 
+
+ align:start position:0%
+1 what happened was he got Q Little
+3 by 2017 there was a 200,000 200,000
+
+ align:start position:0%
+3 by 2017 there was a 200,000 200,000
+ 
+
+ align:start position:0%
+3 by 2017 there was a 200,000 200,000
+person waiting list for Teslas because
+
+ align:start position:0%
+person waiting list for Teslas because
+ 
+
+ align:start position:0%
+person waiting list for Teslas because
+they couldn't produce the batteries fast
+
+ align:start position:0%
+they couldn't produce the batteries fast
+ 
+
+ align:start position:0%
+they couldn't produce the batteries fast
+enough so Elon Musk realized he'd built
+
+ align:start position:0%
+enough so Elon Musk realized he'd built
+ 
+
+ align:start position:0%
+enough so Elon Musk realized he'd built
+too small a plant so he then has built
+
+ align:start position:0%
+too small a plant so he then has built
+ 
+
+ align:start position:0%
+too small a plant so he then has built
+the largest electric battery plant in
+
+ align:start position:0%
+the largest electric battery plant in
+ 
+
+ align:start position:0%
+the largest electric battery plant in
+the world in Nevada he's gone from src1
+
+ align:start position:0%
+the world in Nevada he's gone from src1
+ 
+
+ align:start position:0%
+the world in Nevada he's gone from src1
+to
+
+ align:start position:0%
+to
+ 
+
+ align:start position:0%
+to
+src3 this clant can produce 500,000 cars
+
+ align:start position:0%
+src3 this clant can produce 500,000 cars
+ 
+
+ align:start position:0%
+src3 this clant can produce 500,000 cars
+a year
+
+ align:start position:0%
+a year
+ 
+
+ align:start position:0%
+a year
+but what if people decide Elon Musk is
+
+ align:start position:0%
+but what if people decide Elon Musk is
+ 
+
+ align:start position:0%
+but what if people decide Elon Musk is
+an idiot and they don't want to buy
+
+ align:start position:0%
+an idiot and they don't want to buy
+ 
+
+ align:start position:0%
+an idiot and they don't want to buy
+Teslas anymore okay and all of a sudden
+
+ align:start position:0%
+Teslas anymore okay and all of a sudden
+ 
+
+ align:start position:0%
+Teslas anymore okay and all of a sudden
+Tesla sales Fall well that one could be
+
+ align:start position:0%
+Tesla sales Fall well that one could be
+ 
+
+ align:start position:0%
+Tesla sales Fall well that one could be
+too big and maybe next time he'll sell
+
+ align:start position:0%
+too big and maybe next time he'll sell
+ 
+
+ align:start position:0%
+too big and maybe next time he'll sell
+that plant and build one in
+
+ align:start position:0%
+that plant and build one in
+ 
+
+ align:start position:0%
+that plant and build one in
+between the point is he can always
+
+ align:start position:0%
+between the point is he can always
+ 
+
+ align:start position:0%
+between the point is he can always
+reoptimize depending on how demand turns
+
+ align:start position:0%
+reoptimize depending on how demand turns
+ 
+
+ align:start position:0%
+reoptimize depending on how demand turns
+out to be so you can always do better
+
+ align:start position:0%
+out to be so you can always do better
+ 
+
+ align:start position:0%
+out to be so you can always do better
+Elon Musk did not produce most
+
+ align:start position:0%
+Elon Musk did not produce most
+ 
+
+ align:start position:0%
+Elon Musk did not produce most
+efficiently in the short run so he built
+
+ align:start position:0%
+efficiently in the short run so he built
+ 
+
+ align:start position:0%
+efficiently in the short run so he built
+a bigger plant will he now produce most
+
+ align:start position:0%
+a bigger plant will he now produce most
+ 
+
+ align:start position:0%
+a bigger plant will he now produce most
+efficiently it depends when the demands
+
+ align:start position:0%
+efficiently it depends when the demands
+ 
+
+ align:start position:0%
+efficiently it depends when the demands
+set up a Q3 or somewhere else
+
+ align:start position:0%
+set up a Q3 or somewhere else
+ 
+
+ align:start position:0%
+set up a Q3 or somewhere else
+okay questions about
+
+ align:start position:0%
+okay questions about
+ 
+
+ align:start position:0%
+okay questions about
+that so basically the point is in the
+
+ align:start position:0%
+that so basically the point is in the
+ 
+
+ align:start position:0%
+that so basically the point is in the
+long run it's just like the short run
+
+ align:start position:0%
+long run it's just like the short run
+ 
+
+ align:start position:0%
+long run it's just like the short run
+except you get to choose K bar which
+
+ align:start position:0%
+except you get to choose K bar which
+ 
+
+ align:start position:0%
+except you get to choose K bar which
+means you take multiple shots at what
+
+ align:start position:0%
+means you take multiple shots at what
+ 
+
+ align:start position:0%
+means you take multiple shots at what
+average but having chosen K Bar you're
+
+ align:start position:0%
+average but having chosen K Bar you're
+ 
+
+ align:start position:0%
+average but having chosen K Bar you're
+back in the short run all you can do is
+
+ align:start position:0%
+back in the short run all you can do is
+ 
+
+ align:start position:0%
+back in the short run all you can do is
+value the number of
+
+ align:start position:0%
+value the number of
+ 
+
+ align:start position:0%
+value the number of
+workers okay so think of the long run is
+
+ align:start position:0%
+workers okay so think of the long run is
+ 
+
+ align:start position:0%
+workers okay so think of the long run is
+a set of Short Run games in the each
+
+ align:start position:0%
+a set of Short Run games in the each
+ 
+
+ align:start position:0%
+a set of Short Run games in the each
+short run you choose K Bar you produce
+
+ align:start position:0%
+short run you choose K Bar you produce
+ 
+
+ align:start position:0%
+short run you choose K Bar you produce
+as efficiently as
+
+ align:start position:0%
+as efficiently as
+ 
+
+ align:start position:0%
+as efficiently as
+possible okay if if you turns out you've
+
+ align:start position:0%
+possible okay if if you turns out you've
+ 
+
+ align:start position:0%
+possible okay if if you turns out you've
+chosen the wrong K Bar you then choose a
+
+ align:start position:0%
+chosen the wrong K Bar you then choose a
+ 
+
+ align:start position:0%
+chosen the wrong K Bar you then choose a
+different on the next period the next
+
+ align:start position:0%
+different on the next period the next
+ 
+
+ align:start position:0%
+different on the next period the next
+long run
+
+ align:start position:0%
+long run
+ 
+
+ align:start position:0%
+long run
+period
+
+ align:start position:0%
+period
+ 
+
+ align:start position:0%
+period
+okay so now let's talk about long run
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+costs let's talk about how we think
+
+ align:start position:0%
+costs let's talk about how we think
+ 
+
+ align:start position:0%
+costs let's talk about how we think
+about firm production decisions and
+
+ align:start position:0%
+about firm production decisions and
+ 
+
+ align:start position:0%
+about firm production decisions and
+costs in a world where both labor and
+
+ align:start position:0%
+costs in a world where both labor and
+ 
+
+ align:start position:0%
+costs in a world where both labor and
+capital is
+
+ align:start position:0%
+capital is
+ 
+
+ align:start position:0%
+capital is
+variable okay so remember last time we
+
+ align:start position:0%
+variable okay so remember last time we
+ 
+
+ align:start position:0%
+variable okay so remember last time we
+developed an ISO
+
+ align:start position:0%
+developed an ISO
+ 
+
+ align:start position:0%
+developed an ISO
+Quant the isoquant was the choice of all
+
+ align:start position:0%
+Quant the isoquant was the choice of all
+ 
+
+ align:start position:0%
+Quant the isoquant was the choice of all
+L and K that give the same same little
+
+ align:start position:0%
+L and K that give the same same little
+ 
+
+ align:start position:0%
+L and K that give the same same little
+Q the choice of all L and K that give
+
+ align:start position:0%
+Q the choice of all L and K that give
+ 
+
+ align:start position:0%
+Q the choice of all L and K that give
+the same little Q was the
+
+ align:start position:0%
+the same little Q was the
+ 
+
+ align:start position:0%
+the same little Q was the
+isoquant and you could
+
+ align:start position:0%
+isoquant and you could
+ 
+
+ align:start position:0%
+isoquant and you could
+choose um and basically the point was
+
+ align:start position:0%
+choose um and basically the point was
+ 
+
+ align:start position:0%
+choose um and basically the point was
+along any given isoquant there are
+
+ align:start position:0%
+along any given isoquant there are
+ 
+
+ align:start position:0%
+along any given isoquant there are
+different combinations of L and K that
+
+ align:start position:0%
+different combinations of L and K that
+ 
+
+ align:start position:0%
+different combinations of L and K that
+can give you a little Q just like along
+
+ align:start position:0%
+can give you a little Q just like along
+ 
+
+ align:start position:0%
+can give you a little Q just like along
+an ISO just along an indifference curve
+
+ align:start position:0%
+an ISO just along an indifference curve
+ 
+
+ align:start position:0%
+an ISO just along an indifference curve
+there are many combinations of pizza and
+
+ align:start position:0%
+there are many combinations of pizza and
+ 
+
+ align:start position:0%
+there are many combinations of pizza and
+cookies that make you equally happy so
+
+ align:start position:0%
+cookies that make you equally happy so
+ 
+
+ align:start position:0%
+cookies that make you equally happy so
+the question is how do you decide which
+
+ align:start position:0%
+the question is how do you decide which
+ 
+
+ align:start position:0%
+the question is how do you decide which
+combination to use well to do so
+
+ align:start position:0%
+combination to use well to do so
+ 
+
+ align:start position:0%
+combination to use well to do so
+we create just like in consumer Theory
+
+ align:start position:0%
+we create just like in consumer Theory
+ 
+
+ align:start position:0%
+we create just like in consumer Theory
+we solve the problem by creating a
+
+ align:start position:0%
+we solve the problem by creating a
+ 
+
+ align:start position:0%
+we solve the problem by creating a
+budget constraint in producer Theory we
+
+ align:start position:0%
+budget constraint in producer Theory we
+ 
+
+ align:start position:0%
+budget constraint in producer Theory we
+solve the problem by creating an ISO
+
+ align:start position:0%
+solve the problem by creating an ISO
+ 
+
+ align:start position:0%
+solve the problem by creating an ISO
+cost
+
+ align:start position:0%
+cost
+ 
+
+ align:start position:0%
+cost
+line the iso cost line which is
+
+ align:start position:0%
+line the iso cost line which is
+ 
+
+ align:start position:0%
+line the iso cost line which is
+basically the firm's budget constraint
+
+ align:start position:0%
+basically the firm's budget constraint
+ 
+
+ align:start position:0%
+basically the firm's budget constraint
+if you will isoc cost line is the line
+
+ align:start position:0%
+if you will isoc cost line is the line
+ 
+
+ align:start position:0%
+if you will isoc cost line is the line
+which gives you the cost of Labor and
+
+ align:start position:0%
+which gives you the cost of Labor and
+ 
+
+ align:start position:0%
+which gives you the cost of Labor and
+capital uh that help you choose which
+
+ align:start position:0%
+capital uh that help you choose which
+ 
+
+ align:start position:0%
+capital uh that help you choose which
+combination you'd like to choose so I'm
+
+ align:start position:0%
+combination you'd like to choose so I'm
+ 
+
+ align:start position:0%
+combination you'd like to choose so I'm
+not saying it well in words let's go to
+
+ align:start position:0%
+not saying it well in words let's go to
+ 
+
+ align:start position:0%
+not saying it well in words let's go to
+the graphs okay here's some isocost
+
+ align:start position:0%
+the graphs okay here's some isocost
+ 
+
+ align:start position:0%
+the graphs okay here's some isocost
+lines remember I assumed that the wage
+
+ align:start position:0%
+lines remember I assumed that the wage
+ 
+
+ align:start position:0%
+lines remember I assumed that the wage
+was five and the renovated Capital was
+
+ align:start position:0%
+was five and the renovated Capital was
+ 
+
+ align:start position:0%
+was five and the renovated Capital was
+10 okay so basically these lines are
+
+ align:start position:0%
+10 okay so basically these lines are
+ 
+
+ align:start position:0%
+10 okay so basically these lines are
+combinations of capital and labor that
+
+ align:start position:0%
+combinations of capital and labor that
+ 
+
+ align:start position:0%
+combinations of capital and labor that
+yield the same total level of costs the
+
+ align:start position:0%
+yield the same total level of costs the
+ 
+
+ align:start position:0%
+yield the same total level of costs the
+combination of capital and labor that
+
+ align:start position:0%
+combination of capital and labor that
+ 
+
+ align:start position:0%
+combination of capital and labor that
+yield the same total level of costs so
+
+ align:start position:0%
+yield the same total level of costs so
+ 
+
+ align:start position:0%
+yield the same total level of costs so
+you see the $50 Isa cost says if you
+
+ align:start position:0%
+you see the $50 Isa cost says if you
+ 
+
+ align:start position:0%
+you see the $50 Isa cost says if you
+want to spend $50 you could either have
+
+ align:start position:0%
+want to spend $50 you could either have
+ 
+
+ align:start position:0%
+want to spend $50 you could either have
+10 units of Labor
+
+ align:start position:0%
+10 units of Labor
+ 
+
+ align:start position:0%
+10 units of Labor
+and no Capital five units of capital and
+
+ align:start position:0%
+and no Capital five units of capital and
+ 
+
+ align:start position:0%
+and no Capital five units of capital and
+no labor some combination in
+
+ align:start position:0%
+no labor some combination in
+ 
+
+ align:start position:0%
+no labor some combination in
+between but if you want to spend
+
+ align:start position:0%
+between but if you want to spend
+ 
+
+ align:start position:0%
+between but if you want to spend
+$150 you could then have 30 units of
+
+ align:start position:0%
+$150 you could then have 30 units of
+ 
+
+ align:start position:0%
+$150 you could then have 30 units of
+Labor and no capital or 15 units of
+
+ align:start position:0%
+Labor and no capital or 15 units of
+ 
+
+ align:start position:0%
+Labor and no capital or 15 units of
+capital no labor or some combination in
+
+ align:start position:0%
+capital no labor or some combination in
+ 
+
+ align:start position:0%
+capital no labor or some combination in
+between so it's basically the
+
+ align:start position:0%
+between so it's basically the
+ 
+
+ align:start position:0%
+between so it's basically the
+combination of capital and labor that
+
+ align:start position:0%
+combination of capital and labor that
+ 
+
+ align:start position:0%
+combination of capital and labor that
+yield the same total
+
+ align:start position:0%
+yield the same total
+ 
+
+ align:start position:0%
+yield the same total
+cost okay and what is the slope of the
+
+ align:start position:0%
+cost okay and what is the slope of the
+ 
+
+ align:start position:0%
+cost okay and what is the slope of the
+isocost line well the slope is minus W
+
+ align:start position:0%
+isocost line well the slope is minus W
+ 
+
+ align:start position:0%
+isocost line well the slope is minus W
+over
+
+ align:start position:0%
+over
+ 
+
+ align:start position:0%
+over
+R minus the ratio of the price of Labor
+
+ align:start position:0%
+R minus the ratio of the price of Labor
+ 
+
+ align:start position:0%
+R minus the ratio of the price of Labor
+to the price of
+
+ align:start position:0%
+to the price of
+ 
+
+ align:start position:0%
+to the price of
+capital okay what does this say this
+
+ align:start position:0%
+capital okay what does this say this
+ 
+
+ align:start position:0%
+capital okay what does this say this
+says that you have to give up half a
+
+ align:start position:0%
+says that you have to give up half a
+ 
+
+ align:start position:0%
+says that you have to give up half a
+unit of capital to get a unit of Labor
+
+ align:start position:0%
+unit of capital to get a unit of Labor
+ 
+
+ align:start position:0%
+unit of capital to get a unit of Labor
+it's back to opportunity costs for a
+
+ align:start position:0%
+it's back to opportunity costs for a
+ 
+
+ align:start position:0%
+it's back to opportunity costs for a
+given total cost of production if you
+
+ align:start position:0%
+given total cost of production if you
+ 
+
+ align:start position:0%
+given total cost of production if you
+want one more worker you're gonna have
+
+ align:start position:0%
+want one more worker you're gonna have
+ 
+
+ align:start position:0%
+want one more worker you're gonna have
+to give up half a
+
+ align:start position:0%
+to give up half a
+ 
+
+ align:start position:0%
+to give up half a
+machine okay for a given total cost of
+
+ align:start position:0%
+machine okay for a given total cost of
+ 
+
+ align:start position:0%
+machine okay for a given total cost of
+Productions that's the slope of the
+
+ align:start position:0%
+Productions that's the slope of the
+ 
+
+ align:start position:0%
+Productions that's the slope of the
+isocost line so then we say the firm to
+
+ align:start position:0%
+isocost line so then we say the firm to
+ 
+
+ align:start position:0%
+isocost line so then we say the firm to
+minimize
+
+ align:start position:0%
+minimize
+ 
+
+ align:start position:0%
+minimize
+costs will use the efficient
+
+ align:start position:0%
+costs will use the efficient
+ 
+
+ align:start position:0%
+costs will use the efficient
+combination of Labor and capital to
+
+ align:start position:0%
+combination of Labor and capital to
+ 
+
+ align:start position:0%
+combination of Labor and capital to
+produce any level of goods and how do we
+
+ align:start position:0%
+produce any level of goods and how do we
+ 
+
+ align:start position:0%
+produce any level of goods and how do we
+get that we get that by the tangency
+
+ align:start position:0%
+get that we get that by the tangency
+ 
+
+ align:start position:0%
+get that we get that by the tangency
+between the isoquant and the iso cost
+
+ align:start position:0%
+between the isoquant and the iso cost
+ 
+
+ align:start position:0%
+between the isoquant and the iso cost
+the tangency between the iso Quant and
+
+ align:start position:0%
+the tangency between the iso Quant and
+ 
+
+ align:start position:0%
+the tangency between the iso Quant and
+the iso cost gives us the efficient
+
+ align:start position:0%
+the iso cost gives us the efficient
+ 
+
+ align:start position:0%
+the iso cost gives us the efficient
+combination of capital and labor for any
+
+ align:start position:0%
+combination of capital and labor for any
+ 
+
+ align:start position:0%
+combination of capital and labor for any
+level of production little Q so so for
+
+ align:start position:0%
+level of production little Q so so for
+ 
+
+ align:start position:0%
+level of production little Q so so for
+example going back keeping these isocost
+
+ align:start position:0%
+example going back keeping these isocost
+ 
+
+ align:start position:0%
+example going back keeping these isocost
+lines and going back to our production
+
+ align:start position:0%
+lines and going back to our production
+ 
+
+ align:start position:0%
+lines and going back to our production
+function and our therefore cost
+
+ align:start position:0%
+function and our therefore cost
+ 
+
+ align:start position:0%
+function and our therefore cost
+function we can draw the
+
+ align:start position:0%
+function we can draw the
+ 
+
+ align:start position:0%
+function we can draw the
+isoquant okay uh for production okay so
+
+ align:start position:0%
+isoquant okay uh for production okay so
+ 
+
+ align:start position:0%
+isoquant okay uh for production okay so
+we start with the production function we
+
+ align:start position:0%
+we start with the production function we
+ 
+
+ align:start position:0%
+we start with the production function we
+start with our production function qal
+
+ align:start position:0%
+start with our production function qal
+ 
+
+ align:start position:0%
+start with our production function qal
+of L * K okay we know that the slope of
+
+ align:start position:0%
+of L * K okay we know that the slope of
+ 
+
+ align:start position:0%
+of L * K okay we know that the slope of
+the isoquant the isoquant slope we
+
+ align:start position:0%
+the isoquant the isoquant slope we
+ 
+
+ align:start position:0%
+the isoquant the isoquant slope we
+defined last time is minus MP L over
+
+ align:start position:0%
+defined last time is minus MP L over
+ 
+
+ align:start position:0%
+defined last time is minus MP L over
+mpk MPL over
+
+ align:start position:0%
+mpk MPL over
+ 
+
+ align:start position:0%
+mpk MPL over
+mpk so at the tangency we set these two
+
+ align:start position:0%
+mpk so at the tangency we set these two
+ 
+
+ align:start position:0%
+mpk so at the tangency we set these two
+things
+
+ align:start position:0%
+things
+ 
+
+ align:start position:0%
+things
+equal we set npl over mpk equal to W
+
+ align:start position:0%
+equal we set npl over mpk equal to W
+ 
+
+ align:start position:0%
+equal we set npl over mpk equal to W
+over
+
+ align:start position:0%
+over
+ 
+
+ align:start position:0%
+over
+r that is in the optimum with this
+
+ align:start position:0%
+r that is in the optimum with this
+ 
+
+ align:start position:0%
+r that is in the optimum with this
+example okay you set these things equal
+
+ align:start position:0%
+example okay you set these things equal
+ 
+
+ align:start position:0%
+example okay you set these things equal
+you you always set the slope of the
+
+ align:start position:0%
+you you always set the slope of the
+ 
+
+ align:start position:0%
+you you always set the slope of the
+isocost line equal to slope of the
+
+ align:start position:0%
+isocost line equal to slope of the
+ 
+
+ align:start position:0%
+isocost line equal to slope of the
+isoquant but in this example that is
+
+ align:start position:0%
+isoquant but in this example that is
+ 
+
+ align:start position:0%
+isoquant but in this example that is
+such that you want to use half as much
+
+ align:start position:0%
+such that you want to use half as much
+ 
+
+ align:start position:0%
+such that you want to use half as much
+Capital as labor you want to basically
+
+ align:start position:0%
+Capital as labor you want to basically
+ 
+
+ align:start position:0%
+Capital as labor you want to basically
+use because basically if you look at um
+
+ align:start position:0%
+use because basically if you look at um
+ 
+
+ align:start position:0%
+use because basically if you look at um
+MPL if you use our example we defined
+
+ align:start position:0%
+MPL if you use our example we defined
+ 
+
+ align:start position:0%
+MPL if you use our example we defined
+last time set these equal says remember
+
+ align:start position:0%
+last time set these equal says remember
+ 
+
+ align:start position:0%
+last time set these equal says remember
+from last time the MPL was minus L over
+
+ align:start position:0%
+from last time the MPL was minus L over
+ 
+
+ align:start position:0%
+from last time the MPL was minus L over
+K here we're saying to equal to minus W
+
+ align:start position:0%
+K here we're saying to equal to minus W
+ 
+
+ align:start position:0%
+K here we're saying to equal to minus W
+over R okay if you remember last time we
+
+ align:start position:0%
+over R okay if you remember last time we
+ 
+
+ align:start position:0%
+over R okay if you remember last time we
+solved for the marginal the mrts I'm
+
+ align:start position:0%
+solved for the marginal the mrts I'm
+ 
+
+ align:start position:0%
+solved for the marginal the mrts I'm
+sorry K Over
+
+ align:start position:0%
+sorry K Over
+ 
+
+ align:start position:0%
+sorry K Over
+l k over
+
+ align:start position:0%
+l k over
+ 
+
+ align:start position:0%
+l k over
+l k over l so minus k lus w Rus k l we
+
+ align:start position:0%
+l k over l so minus k lus w Rus k l we
+ 
+
+ align:start position:0%
+l k over l so minus k lus w Rus k l we
+defined last time as the marginal rate
+
+ align:start position:0%
+defined last time as the marginal rate
+ 
+
+ align:start position:0%
+defined last time as the marginal rate
+of technical
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+substitution okay which is generally
+
+ align:start position:0%
+substitution okay which is generally
+ 
+
+ align:start position:0%
+substitution okay which is generally
+this formula but in our specific case
+
+ align:start position:0%
+this formula but in our specific case
+ 
+
+ align:start position:0%
+this formula but in our specific case
+it's that minus WR is the price ratio
+
+ align:start position:0%
+it's that minus WR is the price ratio
+ 
+
+ align:start position:0%
+it's that minus WR is the price ratio
+the the margin rate of technical
+
+ align:start position:0%
+the the margin rate of technical
+ 
+
+ align:start position:0%
+the the margin rate of technical
+substitution is the slope of the
+
+ align:start position:0%
+substitution is the slope of the
+ 
+
+ align:start position:0%
+substitution is the slope of the
+isoquant minus W over R is the slope of
+
+ align:start position:0%
+isoquant minus W over R is the slope of
+ 
+
+ align:start position:0%
+isoquant minus W over R is the slope of
+the price ratio here in our example
+
+ align:start position:0%
+the price ratio here in our example
+ 
+
+ align:start position:0%
+the price ratio here in our example
+example we know that equals minus a half
+
+ align:start position:0%
+example we know that equals minus a half
+ 
+
+ align:start position:0%
+example we know that equals minus a half
+so in this example you want to set K L
+
+ align:start position:0%
+so in this example you want to set K L
+ 
+
+ align:start position:0%
+so in this example you want to set K L
+equal to minus a half you want half as
+
+ align:start position:0%
+equal to minus a half you want half as
+ 
+
+ align:start position:0%
+equal to minus a half you want half as
+much Capital as
+
+ align:start position:0%
+much Capital as
+ 
+
+ align:start position:0%
+much Capital as
+labor okay why is that well same
+
+ align:start position:0%
+labor okay why is that well same
+ 
+
+ align:start position:0%
+labor okay why is that well same
+intuitions with
+
+ align:start position:0%
+intuitions with
+ 
+
+ align:start position:0%
+intuitions with
+consumers okay you can the market is
+
+ align:start position:0%
+consumers okay you can the market is
+ 
+
+ align:start position:0%
+consumers okay you can the market is
+telling you it's going to cost half as
+
+ align:start position:0%
+telling you it's going to cost half as
+ 
+
+ align:start position:0%
+telling you it's going to cost half as
+much to have a worker as a
+
+ align:start position:0%
+much to have a worker as a
+ 
+
+ align:start position:0%
+much to have a worker as a
+machine your technology is telling you
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay that you are you're basically
+
+ align:start position:0%
+okay that you are you're basically
+ 
+
+ align:start position:0%
+okay that you are you're basically
+indifferent that basically you at the
+
+ align:start position:0%
+indifferent that basically you at the
+ 
+
+ align:start position:0%
+indifferent that basically you at the
+point you're at you are um you're
+
+ align:start position:0%
+point you're at you are um you're
+ 
+
+ align:start position:0%
+point you're at you are um you're
+basically the tradeoff between workers
+
+ align:start position:0%
+basically the tradeoff between workers
+ 
+
+ align:start position:0%
+basically the tradeoff between workers
+and machines is K Over l so you set
+
+ align:start position:0%
+and machines is K Over l so you set
+ 
+
+ align:start position:0%
+and machines is K Over l so you set
+those equal and that gives you the rule
+
+ align:start position:0%
+those equal and that gives you the rule
+ 
+
+ align:start position:0%
+those equal and that gives you the rule
+that you want to set in our particular
+
+ align:start position:0%
+that you want to set in our particular
+ 
+
+ align:start position:0%
+that you want to set in our particular
+example K Over L equal to minus W over2
+
+ align:start position:0%
+example K Over L equal to minus W over2
+ 
+
+ align:start position:0%
+example K Over L equal to minus W over2
+so let me review again a the isoquant
+
+ align:start position:0%
+so let me review again a the isoquant
+ 
+
+ align:start position:0%
+so let me review again a the isoquant
+Curve comes from production function and
+
+ align:start position:0%
+Curve comes from production function and
+ 
+
+ align:start position:0%
+Curve comes from production function and
+delivers the marginal rate of technical
+
+ align:start position:0%
+delivers the marginal rate of technical
+ 
+
+ align:start position:0%
+delivers the marginal rate of technical
+substitution which is this step one okay
+
+ align:start position:0%
+substitution which is this step one okay
+ 
+
+ align:start position:0%
+substitution which is this step one okay
+step two the iso cost has a slope of
+
+ align:start position:0%
+step two the iso cost has a slope of
+ 
+
+ align:start position:0%
+step two the iso cost has a slope of
+this step three you set them equal so
+
+ align:start position:0%
+this step three you set them equal so
+ 
+
+ align:start position:0%
+this step three you set them equal so
+you get minus K Over L which is what
+
+ align:start position:0%
+you get minus K Over L which is what
+ 
+
+ align:start position:0%
+you get minus K Over L which is what
+this is equals minus a half which is
+
+ align:start position:0%
+this is equals minus a half which is
+ 
+
+ align:start position:0%
+this is equals minus a half which is
+what that is so use capital and labor
+
+ align:start position:0%
+what that is so use capital and labor
+ 
+
+ align:start position:0%
+what that is so use capital and labor
+until using half as much Capital as
+
+ align:start position:0%
+until using half as much Capital as
+ 
+
+ align:start position:0%
+until using half as much Capital as
+labor and once again you can use the
+
+ align:start position:0%
+labor and once again you can use the
+ 
+
+ align:start position:0%
+labor and once again you can use the
+same kind of examples we use for
+
+ align:start position:0%
+same kind of examples we use for
+ 
+
+ align:start position:0%
+same kind of examples we use for
+Consumer Theory to show you why if you
+
+ align:start position:0%
+Consumer Theory to show you why if you
+ 
+
+ align:start position:0%
+Consumer Theory to show you why if you
+weren't using half as much Capital as
+
+ align:start position:0%
+weren't using half as much Capital as
+ 
+
+ align:start position:0%
+weren't using half as much Capital as
+labor you'd be getting it wrong should s
+
+ align:start position:0%
+labor you'd be getting it wrong should s
+ 
+
+ align:start position:0%
+labor you'd be getting it wrong should s
+yourself at home remember last time we
+
+ align:start position:0%
+yourself at home remember last time we
+ 
+
+ align:start position:0%
+yourself at home remember last time we
+had points on we had points where the
+
+ align:start position:0%
+had points on we had points where the
+ 
+
+ align:start position:0%
+had points on we had points where the
+where the indifference curve wasn't
+
+ align:start position:0%
+where the indifference curve wasn't
+ 
+
+ align:start position:0%
+where the indifference curve wasn't
+tangent to the budget constraint we show
+
+ align:start position:0%
+tangent to the budget constraint we show
+ 
+
+ align:start position:0%
+tangent to the budget constraint we show
+why they were wrong you can do the same
+
+ align:start position:0%
+why they were wrong you can do the same
+ 
+
+ align:start position:0%
+why they were wrong you can do the same
+thing here you can draw points where the
+
+ align:start position:0%
+thing here you can draw points where the
+ 
+
+ align:start position:0%
+thing here you can draw points where the
+isoquant is not tangent to the isocost
+
+ align:start position:0%
+isoquant is not tangent to the isocost
+ 
+
+ align:start position:0%
+isoquant is not tangent to the isocost
+and show you why that's inefficient why
+
+ align:start position:0%
+and show you why that's inefficient why
+ 
+
+ align:start position:0%
+and show you why that's inefficient why
+it's inefficient
+
+ align:start position:0%
+it's inefficient
+ 
+
+ align:start position:0%
+it's inefficient
+production okay now questions about
+
+ align:start position:0%
+production okay now questions about
+ 
+
+ align:start position:0%
+production okay now questions about
+that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah oh that's a okay oh Jesus that's
+
+ align:start position:0%
+yeah oh that's a okay oh Jesus that's
+ 
+
+ align:start position:0%
+yeah oh that's a okay oh Jesus that's
+that the uh let me make sure I I get the
+
+ align:start position:0%
+that the uh let me make sure I I get the
+ 
+
+ align:start position:0%
+that the uh let me make sure I I get the
+uh get the inversion right it's
+
+ align:start position:0%
+uh get the inversion right it's
+ 
+
+ align:start position:0%
+uh get the inversion right it's
+MPL over mpk sorry about that that's not
+
+ align:start position:0%
+MPL over mpk sorry about that that's not
+ 
+
+ align:start position:0%
+MPL over mpk sorry about that that's not
+any better mpk MPL mpk thank you for
+
+ align:start position:0%
+any better mpk MPL mpk thank you for
+ 
+
+ align:start position:0%
+any better mpk MPL mpk thank you for
+asking once again 70% of the class had
+
+ align:start position:0%
+asking once again 70% of the class had
+ 
+
+ align:start position:0%
+asking once again 70% of the class had
+no idea what those were so you did a
+
+ align:start position:0%
+no idea what those were so you did a
+ 
+
+ align:start position:0%
+no idea what those were so you did a
+good service yeah go
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+ahead for this example yes the general
+
+ align:start position:0%
+ahead for this example yes the general
+ 
+
+ align:start position:0%
+ahead for this example yes the general
+formula is that the mrts equal to the
+
+ align:start position:0%
+formula is that the mrts equal to the
+ 
+
+ align:start position:0%
+formula is that the mrts equal to the
+input price ratio
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that's the general formula so general
+
+ align:start position:0%
+that's the general formula so general
+ 
+
+ align:start position:0%
+that's the general formula so general
+formula is you set minus m
+
+ align:start position:0%
+formula is you set minus m
+ 
+
+ align:start position:0%
+formula is you set minus m
+l over
+
+ align:start position:0%
+l over
+ 
+
+ align:start position:0%
+l over
+mpk equal to minus W over R that's the
+
+ align:start position:0%
+mpk equal to minus W over R that's the
+ 
+
+ align:start position:0%
+mpk equal to minus W over R that's the
+general formula in our particular case
+
+ align:start position:0%
+general formula in our particular case
+ 
+
+ align:start position:0%
+general formula in our particular case
+that amounts to K Over L equals a
+
+ align:start position:0%
+that amounts to K Over L equals a
+ 
+
+ align:start position:0%
+that amounts to K Over L equals a
+half yeah
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+is there
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+version that's a really interesting
+
+ align:start position:0%
+version that's a really interesting
+ 
+
+ align:start position:0%
+version that's a really interesting
+question um that we won't really get
+
+ align:start position:0%
+question um that we won't really get
+ 
+
+ align:start position:0%
+question um that we won't really get
+into I think the difference is actually
+
+ align:start position:0%
+into I think the difference is actually
+ 
+
+ align:start position:0%
+into I think the difference is actually
+I will teach you why I won't get into it
+
+ align:start position:0%
+I will teach you why I won't get into it
+ 
+
+ align:start position:0%
+I will teach you why I won't get into it
+because firms you're it's a good segue
+
+ align:start position:0%
+because firms you're it's a good segue
+ 
+
+ align:start position:0%
+because firms you're it's a good segue
+to why firms are not the same as
+
+ align:start position:0%
+to why firms are not the same as
+ 
+
+ align:start position:0%
+to why firms are not the same as
+consumers and I'll talk about that in a
+
+ align:start position:0%
+consumers and I'll talk about that in a
+ 
+
+ align:start position:0%
+consumers and I'll talk about that in a
+minute other questions okay well that's
+
+ align:start position:0%
+minute other questions okay well that's
+ 
+
+ align:start position:0%
+minute other questions okay well that's
+a great segue which is when we did
+
+ align:start position:0%
+a great segue which is when we did
+ 
+
+ align:start position:0%
+a great segue which is when we did
+consumer Theory we were done here we
+
+ align:start position:0%
+consumer Theory we were done here we
+ 
+
+ align:start position:0%
+consumer Theory we were done here we
+said well I just find the point where
+
+ align:start position:0%
+said well I just find the point where
+ 
+
+ align:start position:0%
+said well I just find the point where
+this is true
+
+ align:start position:0%
+this is true
+ 
+
+ align:start position:0%
+this is true
+that's the optimal
+
+ align:start position:0%
+that's the optimal
+ 
+
+ align:start position:0%
+that's the optimal
+bundle then I think comes substitution
+
+ align:start position:0%
+bundle then I think comes substitution
+ 
+
+ align:start position:0%
+bundle then I think comes substitution
+effects and all that as was pointed
+
+ align:start position:0%
+effects and all that as was pointed
+ 
+
+ align:start position:0%
+effects and all that as was pointed
+out this is why producer theory is
+
+ align:start position:0%
+out this is why producer theory is
+ 
+
+ align:start position:0%
+out this is why producer theory is
+harder because we're not done why aren't
+
+ align:start position:0%
+harder because we're not done why aren't
+ 
+
+ align:start position:0%
+harder because we're not done why aren't
+we done because I didn't tell you the
+
+ align:start position:0%
+we done because I didn't tell you the
+ 
+
+ align:start position:0%
+we done because I didn't tell you the
+Right iso
+
+ align:start position:0%
+Right iso
+ 
+
+ align:start position:0%
+Right iso
+cost with per consumer Theory I gave you
+
+ align:start position:0%
+cost with per consumer Theory I gave you
+ 
+
+ align:start position:0%
+cost with per consumer Theory I gave you
+a budget
+
+ align:start position:0%
+a budget
+ 
+
+ align:start position:0%
+a budget
+constraint I'm not giving you an ISO
+
+ align:start position:0%
+constraint I'm not giving you an ISO
+ 
+
+ align:start position:0%
+constraint I'm not giving you an ISO
+cost here I'm just saying there are
+
+ align:start position:0%
+cost here I'm just saying there are
+ 
+
+ align:start position:0%
+cost here I'm just saying there are
+multiple possible ISO costs therefore
+
+ align:start position:0%
+multiple possible ISO costs therefore
+ 
+
+ align:start position:0%
+multiple possible ISO costs therefore
+there are multiple possible
+
+ align:start position:0%
+there are multiple possible
+ 
+
+ align:start position:0%
+there are multiple possible
+tangencies so with consumer Theory I
+
+ align:start position:0%
+tangencies so with consumer Theory I
+ 
+
+ align:start position:0%
+tangencies so with consumer Theory I
+gave you a budget constraint and
+
+ align:start position:0%
+gave you a budget constraint and
+ 
+
+ align:start position:0%
+gave you a budget constraint and
+therefore I told you two equations and
+
+ align:start position:0%
+therefore I told you two equations and
+ 
+
+ align:start position:0%
+therefore I told you two equations and
+two unknowns gives you the answer here
+
+ align:start position:0%
+two unknowns gives you the answer here
+ 
+
+ align:start position:0%
+two unknowns gives you the answer here
+two equations two unknowns does not give
+
+ align:start position:0%
+two equations two unknowns does not give
+ 
+
+ align:start position:0%
+two equations two unknowns does not give
+you the answer it just gives you a
+
+ align:start position:0%
+you the answer it just gives you a
+ 
+
+ align:start position:0%
+you the answer it just gives you a
+formula but how you apply that formula
+
+ align:start position:0%
+formula but how you apply that formula
+ 
+
+ align:start position:0%
+formula but how you apply that formula
+is going to depend on how big you want
+
+ align:start position:0%
+is going to depend on how big you want
+ 
+
+ align:start position:0%
+is going to depend on how big you want
+your firm to be which isocost you want
+
+ align:start position:0%
+your firm to be which isocost you want
+ 
+
+ align:start position:0%
+your firm to be which isocost you want
+to choose well how the hell you going to
+
+ align:start position:0%
+to choose well how the hell you going to
+ 
+
+ align:start position:0%
+to choose well how the hell you going to
+choose that that's where we have to add
+
+ align:start position:0%
+choose that that's where we have to add
+ 
+
+ align:start position:0%
+choose that that's where we have to add
+one more step that's where producer
+
+ align:start position:0%
+one more step that's where producer
+ 
+
+ align:start position:0%
+one more step that's where producer
+Theory gets one step
+
+ align:start position:0%
+Theory gets one step
+ 
+
+ align:start position:0%
+Theory gets one step
+harder to see that let's look at figure
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+65a figure
+
+ align:start position:0%
+65a figure
+ 
+
+ align:start position:0%
+65a figure
+65a shows for different ISO
+
+ align:start position:0%
+65a shows for different ISO
+ 
+
+ align:start position:0%
+65a shows for different ISO
+cost how much capital and labor we want
+
+ align:start position:0%
+cost how much capital and labor we want
+ 
+
+ align:start position:0%
+cost how much capital and labor we want
+to use for our example so the previous
+
+ align:start position:0%
+to use for our example so the previous
+ 
+
+ align:start position:0%
+to use for our example so the previous
+example we were at Point a we were
+
+ align:start position:0%
+example we were at Point a we were
+ 
+
+ align:start position:0%
+example we were at Point a we were
+choosing to spend
+
+ align:start position:0%
+choosing to spend
+ 
+
+ align:start position:0%
+choosing to spend
+$50 that allowed us to produce square
+
+ align:start position:0%
+$50 that allowed us to produce square
+ 
+
+ align:start position:0%
+$50 that allowed us to produce square
+root of 12.5
+
+ align:start position:0%
+root of 12.5
+ 
+
+ align:start position:0%
+root of 12.5
+units okay at a tangency of five units
+
+ align:start position:0%
+units okay at a tangency of five units
+ 
+
+ align:start position:0%
+units okay at a tangency of five units
+of cap labor and two and a half units of
+
+ align:start position:0%
+of cap labor and two and a half units of
+ 
+
+ align:start position:0%
+of cap labor and two and a half units of
+capital okay flip back and forth to
+
+ align:start position:0%
+capital okay flip back and forth to
+ 
+
+ align:start position:0%
+capital okay flip back and forth to
+figure 64 you'll see that's where we
+
+ align:start position:0%
+figure 64 you'll see that's where we
+ 
+
+ align:start position:0%
+figure 64 you'll see that's where we
+were
+
+ align:start position:0%
+were
+ 
+
+ align:start position:0%
+were
+right however I could have said instead
+
+ align:start position:0%
+right however I could have said instead
+ 
+
+ align:start position:0%
+right however I could have said instead
+no I want to be bigger I want to make
+
+ align:start position:0%
+no I want to be bigger I want to make
+ 
+
+ align:start position:0%
+no I want to be bigger I want to make
+more I'm going to choose to spend 100
+
+ align:start position:0%
+more I'm going to choose to spend 100
+ 
+
+ align:start position:0%
+more I'm going to choose to spend 100
+then I would be at point B where I could
+
+ align:start position:0%
+then I would be at point B where I could
+ 
+
+ align:start position:0%
+then I would be at point B where I could
+have 20 units not 100 square of 50 it's
+
+ align:start position:0%
+have 20 units not 100 square of 50 it's
+ 
+
+ align:start position:0%
+have 20 units not 100 square of 50 it's
+uh four times yeah yeah I'm going to
+
+ align:start position:0%
+uh four times yeah yeah I'm going to
+ 
+
+ align:start position:0%
+uh four times yeah yeah I'm going to
+spend 200 okay so basically here if I
+
+ align:start position:0%
+spend 200 okay so basically here if I
+ 
+
+ align:start position:0%
+spend 200 okay so basically here if I
+spend 200 I can have 20 workers and 10
+
+ align:start position:0%
+spend 200 I can have 20 workers and 10
+ 
+
+ align:start position:0%
+spend 200 I can have 20 workers and 10
+machines I I spend 200 have 20 workers
+
+ align:start position:0%
+machines I I spend 200 have 20 workers
+ 
+
+ align:start position:0%
+machines I I spend 200 have 20 workers
+of 10 machines and then I'll produce
+
+ align:start position:0%
+of 10 machines and then I'll produce
+ 
+
+ align:start position:0%
+of 10 machines and then I'll produce
+square root of 50 which is right I don't
+
+ align:start position:0%
+square root of 50 which is right I don't
+ 
+
+ align:start position:0%
+square root of 50 which is right I don't
+know I haven't told you yet how do you
+
+ align:start position:0%
+know I haven't told you yet how do you
+ 
+
+ align:start position:0%
+know I haven't told you yet how do you
+choose as a boss remember capital's
+
+ align:start position:0%
+choose as a boss remember capital's
+ 
+
+ align:start position:0%
+choose as a boss remember capital's
+fixed I'm talking about this is not the
+
+ align:start position:0%
+fixed I'm talking about this is not the
+ 
+
+ align:start position:0%
+fixed I'm talking about this is not the
+Elon Musk example it's not Capital this
+
+ align:start position:0%
+Elon Musk example it's not Capital this
+ 
+
+ align:start position:0%
+Elon Musk example it's not Capital this
+is within the short run this is how many
+
+ align:start position:0%
+is within the short run this is how many
+ 
+
+ align:start position:0%
+is within the short run this is how many
+workers do you
+
+ align:start position:0%
+workers do you
+ 
+
+ align:start position:0%
+workers do you
+hire well you don't know you could hire
+
+ align:start position:0%
+hire well you don't know you could hire
+ 
+
+ align:start position:0%
+hire well you don't know you could hire
+10 workers 20 workers 30 workers it
+
+ align:start position:0%
+10 workers 20 workers 30 workers it
+ 
+
+ align:start position:0%
+10 workers 20 workers 30 workers it
+depends how much you want to
+
+ align:start position:0%
+depends how much you want to
+ 
+
+ align:start position:0%
+depends how much you want to
+produce how much you want to produce
+
+ align:start position:0%
+produce how much you want to produce
+ 
+
+ align:start position:0%
+produce how much you want to produce
+that is the extra step we have to add
+
+ align:start position:0%
+that is the extra step we have to add
+ 
+
+ align:start position:0%
+that is the extra step we have to add
+for Consumer for producer Theory
+
+ align:start position:0%
+for Consumer for producer Theory
+ 
+
+ align:start position:0%
+for Consumer for producer Theory
+we call this the long run expansion
+
+ align:start position:0%
+we call this the long run expansion
+ 
+
+ align:start position:0%
+we call this the long run expansion
+path this is
+
+ align:start position:0%
+path this is
+ 
+
+ align:start position:0%
+path this is
+essentially the combinations of Labor
+
+ align:start position:0%
+essentially the combinations of Labor
+ 
+
+ align:start position:0%
+essentially the combinations of Labor
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+capital at every single Quee that you
+
+ align:start position:0%
+capital at every single Quee that you
+ 
+
+ align:start position:0%
+capital at every single Quee that you
+would choose in other words you can map
+
+ align:start position:0%
+would choose in other words you can map
+ 
+
+ align:start position:0%
+would choose in other words you can map
+out I haven't yet to told you which
+
+ align:start position:0%
+out I haven't yet to told you which
+ 
+
+ align:start position:0%
+out I haven't yet to told you which
+queue you're going to choose but I've
+
+ align:start position:0%
+queue you're going to choose but I've
+ 
+
+ align:start position:0%
+queue you're going to choose but I've
+told you how to map out for each Q how
+
+ align:start position:0%
+told you how to map out for each Q how
+ 
+
+ align:start position:0%
+told you how to map out for each Q how
+much Ln K you want to
+
+ align:start position:0%
+much Ln K you want to
+ 
+
+ align:start position:0%
+much Ln K you want to
+use if you decide the que you want a
+
+ align:start position:0%
+use if you decide the que you want a
+ 
+
+ align:start position:0%
+use if you decide the que you want a
+square of 12 A2 you choose 10 workers
+
+ align:start position:0%
+square of 12 A2 you choose 10 workers
+ 
+
+ align:start position:0%
+square of 12 A2 you choose 10 workers
+and five machines if you decide it's a
+
+ align:start position:0%
+and five machines if you decide it's a
+ 
+
+ align:start position:0%
+and five machines if you decide it's a
+square 112 A2 you choose 30 workers and
+
+ align:start position:0%
+square 112 A2 you choose 30 workers and
+ 
+
+ align:start position:0%
+square 112 A2 you choose 30 workers and
+
+ align:start position:0%
+ 
+
+ align:start position:0%
+machines ultimately the question is how
+
+ align:start position:0%
+machines ultimately the question is how
+ 
+
+ align:start position:0%
+machines ultimately the question is how
+much you want to
+
+ align:start position:0%
+much you want to
+ 
+
+ align:start position:0%
+much you want to
+produce now in this example the long run
+
+ align:start position:0%
+produce now in this example the long run
+ 
+
+ align:start position:0%
+produce now in this example the long run
+expansion path is linear but it doesn't
+
+ align:start position:0%
+expansion path is linear but it doesn't
+ 
+
+ align:start position:0%
+expansion path is linear but it doesn't
+have to be for example consider figure
+
+ align:start position:0%
+have to be for example consider figure
+ 
+
+ align:start position:0%
+have to be for example consider figure
+65b this is a long run expansion path
+
+ align:start position:0%
+65b this is a long run expansion path
+ 
+
+ align:start position:0%
+65b this is a long run expansion path
+where capital is is becoming less
+
+ align:start position:0%
+where capital is is becoming less
+ 
+
+ align:start position:0%
+where capital is is becoming less
+productive as you produce
+
+ align:start position:0%
+productive as you produce
+ 
+
+ align:start position:0%
+productive as you produce
+more okay in 65a no matter how much you
+
+ align:start position:0%
+more okay in 65a no matter how much you
+ 
+
+ align:start position:0%
+more okay in 65a no matter how much you
+produce you always want to use half as
+
+ align:start position:0%
+produce you always want to use half as
+ 
+
+ align:start position:0%
+produce you always want to use half as
+much Capital as labor that ratio never
+
+ align:start position:0%
+much Capital as labor that ratio never
+ 
+
+ align:start position:0%
+much Capital as labor that ratio never
+changes in 65b it does change that means
+
+ align:start position:0%
+changes in 65b it does change that means
+ 
+
+ align:start position:0%
+changes in 65b it does change that means
+it's a different production
+
+ align:start position:0%
+it's a different production
+ 
+
+ align:start position:0%
+it's a different production
+function I haven't written down the
+
+ align:start position:0%
+function I haven't written down the
+ 
+
+ align:start position:0%
+function I haven't written down the
+underlying production function for 65b
+
+ align:start position:0%
+underlying production function for 65b
+ 
+
+ align:start position:0%
+underlying production function for 65b
+but it's a different production function
+
+ align:start position:0%
+but it's a different production function
+ 
+
+ align:start position:0%
+but it's a different production function
+the iso costs are the same the cost of
+
+ align:start position:0%
+the iso costs are the same the cost of
+ 
+
+ align:start position:0%
+the iso costs are the same the cost of
+Labor and capital labor is always TW
+
+ align:start position:0%
+Labor and capital labor is always TW
+ 
+
+ align:start position:0%
+Labor and capital labor is always TW
+half the price of capital but it's a
+
+ align:start position:0%
+half the price of capital but it's a
+ 
+
+ align:start position:0%
+half the price of capital but it's a
+different production function which has
+
+ align:start position:0%
+different production function which has
+ 
+
+ align:start position:0%
+different production function which has
+the feature that as you produce more and
+
+ align:start position:0%
+the feature that as you produce more and
+ 
+
+ align:start position:0%
+the feature that as you produce more and
+more Capital becomes less productive you
+
+ align:start position:0%
+more Capital becomes less productive you
+ 
+
+ align:start position:0%
+more Capital becomes less productive you
+might think of this as something like a
+
+ align:start position:0%
+might think of this as something like a
+ 
+
+ align:start position:0%
+might think of this as something like a
+McDonald's long run expansion path once
+
+ align:start position:0%
+McDonald's long run expansion path once
+ 
+
+ align:start position:0%
+McDonald's long run expansion path once
+they' got the fryolator and the
+
+ align:start position:0%
+they' got the fryolator and the
+ 
+
+ align:start position:0%
+they' got the fryolator and the
+building then what really matters is how
+
+ align:start position:0%
+building then what really matters is how
+ 
+
+ align:start position:0%
+building then what really matters is how
+many more workers you have you employ
+
+ align:start position:0%
+many more workers you have you employ
+ 
+
+ align:start position:0%
+many more workers you have you employ
+there cranking stuff through so that's a
+
+ align:start position:0%
+there cranking stuff through so that's a
+ 
+
+ align:start position:0%
+there cranking stuff through so that's a
+case where in some sense each additional
+
+ align:start position:0%
+case where in some sense each additional
+ 
+
+ align:start position:0%
+case where in some sense each additional
+unit of capital the fry later isn't that
+
+ align:start position:0%
+unit of capital the fry later isn't that
+ 
+
+ align:start position:0%
+unit of capital the fry later isn't that
+productive okay it's really labor which
+
+ align:start position:0%
+productive okay it's really labor which
+ 
+
+ align:start position:0%
+productive okay it's really labor which
+is really the thing which you want more
+
+ align:start position:0%
+is really the thing which you want more
+ 
+
+ align:start position:0%
+is really the thing which you want more
+and more of as you
+
+ align:start position:0%
+and more of as you
+ 
+
+ align:start position:0%
+and more of as you
+expand alternatively you could have
+
+ align:start position:0%
+expand alternatively you could have
+ 
+
+ align:start position:0%
+expand alternatively you could have
+something like figure 65
+
+ align:start position:0%
+something like figure 65
+ 
+
+ align:start position:0%
+something like figure 65
+C which is an expansion path where
+
+ align:start position:0%
+C which is an expansion path where
+ 
+
+ align:start position:0%
+C which is an expansion path where
+Capital becomes more productive and
+
+ align:start position:0%
+Capital becomes more productive and
+ 
+
+ align:start position:0%
+Capital becomes more productive and
+labor becomes less
+
+ align:start position:0%
+labor becomes less
+ 
+
+ align:start position:0%
+labor becomes less
+productive that is so that is you are
+
+ align:start position:0%
+productive that is so that is you are
+ 
+
+ align:start position:0%
+productive that is so that is you are
+choosing relatively more and
+
+ align:start position:0%
+choosing relatively more and
+ 
+
+ align:start position:0%
+choosing relatively more and
+more Capital compared to labor so let's
+
+ align:start position:0%
+more Capital compared to labor so let's
+ 
+
+ align:start position:0%
+more Capital compared to labor so let's
+compare 65b to 65c in
+
+ align:start position:0%
+compare 65b to 65c in
+ 
+
+ align:start position:0%
+compare 65b to 65c in
+65b when you go from point A to point C
+
+ align:start position:0%
+65b when you go from point A to point C
+ 
+
+ align:start position:0%
+65b when you go from point A to point C
+you go from four workers to 15 workers
+
+ align:start position:0%
+you go from four workers to 15 workers
+ 
+
+ align:start position:0%
+you go from four workers to 15 workers
+but only three machine to S and a half
+
+ align:start position:0%
+but only three machine to S and a half
+ 
+
+ align:start position:0%
+but only three machine to S and a half
+machines okay go from point A to C and
+
+ align:start position:0%
+machines okay go from point A to C and
+ 
+
+ align:start position:0%
+machines okay go from point A to C and
+65b the number of workers goes up almost
+
+ align:start position:0%
+65b the number of workers goes up almost
+ 
+
+ align:start position:0%
+65b the number of workers goes up almost
+four times the number of machines only
+
+ align:start position:0%
+four times the number of machines only
+ 
+
+ align:start position:0%
+four times the number of machines only
+goes up two and a half
+
+ align:start position:0%
+goes up two and a half
+ 
+
+ align:start position:0%
+goes up two and a half
+times on the other hand with figure
+
+ align:start position:0%
+times on the other hand with figure
+ 
+
+ align:start position:0%
+times on the other hand with figure
+65c the number of workers going from a
+
+ align:start position:0%
+65c the number of workers going from a
+ 
+
+ align:start position:0%
+65c the number of workers going from a
+to c goes from 7 to 16 which is a little
+
+ align:start position:0%
+to c goes from 7 to 16 which is a little
+ 
+
+ align:start position:0%
+to c goes from 7 to 16 which is a little
+more than twice the of machines goes
+
+ align:start position:0%
+more than twice the of machines goes
+ 
+
+ align:start position:0%
+more than twice the of machines goes
+from 1.5 to 7 which is almost five times
+
+ align:start position:0%
+from 1.5 to 7 which is almost five times
+ 
+
+ align:start position:0%
+from 1.5 to 7 which is almost five times
+as
+
+ align:start position:0%
+as
+ 
+
+ align:start position:0%
+as
+much capital's becoming more productive
+
+ align:start position:0%
+much capital's becoming more productive
+ 
+
+ align:start position:0%
+much capital's becoming more productive
+workers becom less productive in 65c
+
+ align:start position:0%
+workers becom less productive in 65c
+ 
+
+ align:start position:0%
+workers becom less productive in 65c
+this might be something might Happ for
+
+ align:start position:0%
+this might be something might Happ for
+ 
+
+ align:start position:0%
+this might be something might Happ for
+like a heavy machinery
+
+ align:start position:0%
+like a heavy machinery
+ 
+
+ align:start position:0%
+like a heavy machinery
+plant okay where over time more you want
+
+ align:start position:0%
+plant okay where over time more you want
+ 
+
+ align:start position:0%
+plant okay where over time more you want
+more and more machines and you fur and
+
+ align:start position:0%
+more and more machines and you fur and
+ 
+
+ align:start position:0%
+more and more machines and you fur and
+fewer workers to run
+
+ align:start position:0%
+fewer workers to run
+ 
+
+ align:start position:0%
+fewer workers to run
+them the point of this is not to say
+
+ align:start position:0%
+them the point of this is not to say
+ 
+
+ align:start position:0%
+them the point of this is not to say
+that I can tell you what these speciic
+
+ align:start position:0%
+that I can tell you what these speciic
+ 
+
+ align:start position:0%
+that I can tell you what these speciic
+examples are and each of these obviously
+
+ align:start position:0%
+examples are and each of these obviously
+ 
+
+ align:start position:0%
+examples are and each of these obviously
+have different production functions
+
+ align:start position:0%
+have different production functions
+ 
+
+ align:start position:0%
+have different production functions
+under them it's just to show you that
+
+ align:start position:0%
+under them it's just to show you that
+ 
+
+ align:start position:0%
+under them it's just to show you that
+long run expansion paths can vary in the
+
+ align:start position:0%
+long run expansion paths can vary in the
+ 
+
+ align:start position:0%
+long run expansion paths can vary in the
+real world it's basically a question of
+
+ align:start position:0%
+real world it's basically a question of
+ 
+
+ align:start position:0%
+real world it's basically a question of
+as you want to produce
+
+ align:start position:0%
+as you want to produce
+ 
+
+ align:start position:0%
+as you want to produce
+more does labor and capital become
+
+ align:start position:0%
+more does labor and capital become
+ 
+
+ align:start position:0%
+more does labor and capital become
+equally more
+
+ align:start position:0%
+equally more
+ 
+
+ align:start position:0%
+equally more
+productive okay questions about
+
+ align:start position:0%
+productive okay questions about
+ 
+
+ align:start position:0%
+productive okay questions about
+that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah down if I can't I haven't got
+
+ align:start position:0%
+yeah down if I can't I haven't got
+ 
+
+ align:start position:0%
+yeah down if I can't I haven't got
+talked about shutdown yet you're you're
+
+ align:start position:0%
+talked about shutdown yet you're you're
+ 
+
+ align:start position:0%
+talked about shutdown yet you're you're
+a bit ahead of me that that is related
+
+ align:start position:0%
+a bit ahead of me that that is related
+ 
+
+ align:start position:0%
+a bit ahead of me that that is related
+to how you're going to decide on your
+
+ align:start position:0%
+to how you're going to decide on your
+ 
+
+ align:start position:0%
+to how you're going to decide on your
+que and I'm gonna get to that next
+
+ align:start position:0%
+que and I'm gonna get to that next
+ 
+
+ align:start position:0%
+que and I'm gonna get to that next
+lecture okay so next lecture I haven't
+
+ align:start position:0%
+lecture okay so next lecture I haven't
+ 
+
+ align:start position:0%
+lecture okay so next lecture I haven't
+told you how you choose q but next
+
+ align:start position:0%
+told you how you choose q but next
+ 
+
+ align:start position:0%
+told you how you choose q but next
+lecture I will I'm going to choose the
+
+ align:start position:0%
+lecture I will I'm going to choose the
+ 
+
+ align:start position:0%
+lecture I will I'm going to choose the
+one extra step that lets you choose q
+
+ align:start position:0%
+one extra step that lets you choose q
+ 
+
+ align:start position:0%
+one extra step that lets you choose q
+but before I do I want to ask a sort of
+
+ align:start position:0%
+but before I do I want to ask a sort of
+ 
+
+ align:start position:0%
+but before I do I want to ask a sort of
+existential question which is how do we
+
+ align:start position:0%
+existential question which is how do we
+ 
+
+ align:start position:0%
+existential question which is how do we
+actually measure
+
+ align:start position:0%
+actually measure
+ 
+
+ align:start position:0%
+actually measure
+costs in the real world step four
+
+ align:start position:0%
+costs in the real world step four
+ 
+
+ align:start position:0%
+costs in the real world step four
+measuring
+
+ align:start position:0%
+measuring
+ 
+
+ align:start position:0%
+measuring
+costs and this is where I get to tell
+
+ align:start position:0%
+costs and this is where I get to tell
+ 
+
+ align:start position:0%
+costs and this is where I get to tell
+you that economics is just cooler than
+
+ align:start position:0%
+you that economics is just cooler than
+ 
+
+ align:start position:0%
+you that economics is just cooler than
+accounting and let me explain why
+
+ align:start position:0%
+accounting and let me explain why
+ 
+
+ align:start position:0%
+accounting and let me explain why
+okay accounting only considers the cash
+
+ align:start position:0%
+okay accounting only considers the cash
+ 
+
+ align:start position:0%
+okay accounting only considers the cash
+flow costs that you that you have when
+
+ align:start position:0%
+flow costs that you that you have when
+ 
+
+ align:start position:0%
+flow costs that you that you have when
+you start a firm economics more
+
+ align:start position:0%
+you start a firm economics more
+ 
+
+ align:start position:0%
+you start a firm economics more
+appropriately considers opportunity
+
+ align:start position:0%
+appropriately considers opportunity
+ 
+
+ align:start position:0%
+appropriately considers opportunity
+costs as
+
+ align:start position:0%
+costs as
+ 
+
+ align:start position:0%
+costs as
+well okay so
+
+ align:start position:0%
+well okay so
+ 
+
+ align:start position:0%
+well okay so
+profits is revenue Minus cost we're
+
+ align:start position:0%
+profits is revenue Minus cost we're
+ 
+
+ align:start position:0%
+profits is revenue Minus cost we're
+going to focus on the costs here costs
+
+ align:start position:0%
+going to focus on the costs here costs
+ 
+
+ align:start position:0%
+going to focus on the costs here costs
+and accounting are literally what you
+
+ align:start position:0%
+and accounting are literally what you
+ 
+
+ align:start position:0%
+and accounting are literally what you
+spend in economics they're what your
+
+ align:start position:0%
+spend in economics they're what your
+ 
+
+ align:start position:0%
+spend in economics they're what your
+opportunity cost is and those could
+
+ align:start position:0%
+opportunity cost is and those could
+ 
+
+ align:start position:0%
+opportunity cost is and those could
+differ so let me give you a simple
+
+ align:start position:0%
+differ so let me give you a simple
+ 
+
+ align:start position:0%
+differ so let me give you a simple
+example you're going to start a website
+
+ align:start position:0%
+example you're going to start a website
+ 
+
+ align:start position:0%
+example you're going to start a website
+design firm when you gradu that's kind
+
+ align:start position:0%
+design firm when you gradu that's kind
+ 
+
+ align:start position:0%
+design firm when you gradu that's kind
+of out of date but you know whatever
+
+ align:start position:0%
+of out of date but you know whatever
+ 
+
+ align:start position:0%
+of out of date but you know whatever
+okay you going to start a website design
+
+ align:start position:0%
+okay you going to start a website design
+ 
+
+ align:start position:0%
+okay you going to start a website design
+firm when you graduate okay and that
+
+ align:start position:0%
+firm when you graduate okay and that
+ 
+
+ align:start position:0%
+firm when you graduate okay and that
+involves you working
+
+ align:start position:0%
+involves you working
+ 
+
+ align:start position:0%
+involves you working
+full-time plus some slave programmer you
+
+ align:start position:0%
+full-time plus some slave programmer you
+ 
+
+ align:start position:0%
+full-time plus some slave programmer you
+can hire for $40,000 a year okay so
+
+ align:start position:0%
+can hire for $40,000 a year okay so
+ 
+
+ align:start position:0%
+can hire for $40,000 a year okay so
+you're going to work full-time and hire
+
+ align:start position:0%
+you're going to work full-time and hire
+ 
+
+ align:start position:0%
+you're going to work full-time and hire
+the program for $40,000 a year moreover
+
+ align:start position:0%
+the program for $40,000 a year moreover
+ 
+
+ align:start position:0%
+the program for $40,000 a year moreover
+you the program you don't even need to
+
+ align:start position:0%
+you the program you don't even need to
+ 
+
+ align:start position:0%
+you the program you don't even need to
+buy a computer for the programmer
+
+ align:start position:0%
+buy a computer for the programmer
+ 
+
+ align:start position:0%
+buy a computer for the programmer
+because you have an extra computer
+
+ align:start position:0%
+because you have an extra computer
+ 
+
+ align:start position:0%
+because you have an extra computer
+that's got one more year before it
+
+ align:start position:0%
+that's got one more year before it
+ 
+
+ align:start position:0%
+that's got one more year before it
+becomes useless so you can give that
+
+ align:start position:0%
+becomes useless so you can give that
+ 
+
+ align:start position:0%
+becomes useless so you can give that
+computer to the programmer and they can
+
+ align:start position:0%
+computer to the programmer and they can
+ 
+
+ align:start position:0%
+computer to the programmer and they can
+use that for the year so you're going
+
+ align:start position:0%
+use that for the year so you're going
+ 
+
+ align:start position:0%
+use that for the year so you're going
+have a one-year company okay you're
+
+ align:start position:0%
+have a one-year company okay you're
+ 
+
+ align:start position:0%
+have a one-year company okay you're
+going to pay it's you're going to work
+
+ align:start position:0%
+going to pay it's you're going to work
+ 
+
+ align:start position:0%
+going to pay it's you're going to work
+full-time you're going to pay your
+
+ align:start position:0%
+full-time you're going to pay your
+ 
+
+ align:start position:0%
+full-time you're going to pay your
+programmer $40,000 and you give your
+
+ align:start position:0%
+programmer $40,000 and you give your
+ 
+
+ align:start position:0%
+programmer $40,000 and you give your
+program or this computer you have that
+
+ align:start position:0%
+program or this computer you have that
+ 
+
+ align:start position:0%
+program or this computer you have that
+one more year to work and let's say your
+
+ align:start position:0%
+one more year to work and let's say your
+ 
+
+ align:start position:0%
+one more year to work and let's say your
+goal is by the end of year one I want to
+
+ align:start position:0%
+goal is by the end of year one I want to
+ 
+
+ align:start position:0%
+goal is by the end of year one I want to
+be making a profit okay my parents will
+
+ align:start position:0%
+be making a profit okay my parents will
+ 
+
+ align:start position:0%
+be making a profit okay my parents will
+be mad at me if I take more than one
+
+ align:start position:0%
+be mad at me if I take more than one
+ 
+
+ align:start position:0%
+be mad at me if I take more than one
+year with this by the end of year one I
+
+ align:start position:0%
+year with this by the end of year one I
+ 
+
+ align:start position:0%
+year with this by the end of year one I
+want to make a profit and let's say at
+
+ align:start position:0%
+want to make a profit and let's say at
+ 
+
+ align:start position:0%
+want to make a profit and let's say at
+the end of year one your revenues are
+
+ align:start position:0%
+the end of year one your revenues are
+ 
+
+ align:start position:0%
+the end of year one your revenues are
+$660,000
+
+ align:start position:0%
+$660,000
+ 
+
+ align:start position:0%
+$660,000
+we could say to your parents who are
+
+ align:start position:0%
+we could say to your parents who are
+ 
+
+ align:start position:0%
+we could say to your parents who are
+accountants well gee I earned
+
+ align:start position:0%
+accountants well gee I earned
+ 
+
+ align:start position:0%
+accountants well gee I earned
+$60,000 I paid my programmer
+
+ align:start position:0%
+$60,000 I paid my programmer
+ 
+
+ align:start position:0%
+$60,000 I paid my programmer
+$40,000 that's my cost so I made profit
+
+ align:start position:0%
+$40,000 that's my cost so I made profit
+ 
+
+ align:start position:0%
+$40,000 that's my cost so I made profit
+of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+$220,000 see my company's great your
+
+ align:start position:0%
+$220,000 see my company's great your
+ 
+
+ align:start position:0%
+$220,000 see my company's great your
+accounting parents we's say an
+
+ align:start position:0%
+accounting parents we's say an
+ 
+
+ align:start position:0%
+accounting parents we's say an
+accounting mom and economics dad the
+
+ align:start position:0%
+accounting mom and economics dad the
+ 
+
+ align:start position:0%
+accounting mom and economics dad the
+accounting mom is fool but the economics
+
+ align:start position:0%
+accounting mom is fool but the economics
+ 
+
+ align:start position:0%
+accounting mom is fool but the economics
+dad is not because what does the
+
+ align:start position:0%
+dad is not because what does the
+ 
+
+ align:start position:0%
+dad is not because what does the
+economics dad point
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+out
+
+ align:start position:0%
+out
+ 
+
+ align:start position:0%
+out
+yeah yeah well go on what about let's
+
+ align:start position:0%
+yeah yeah well go on what about let's
+ 
+
+ align:start position:0%
+yeah yeah well go on what about let's
+talk about your
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+time there's an opportunity cost of the
+
+ align:start position:0%
+time there's an opportunity cost of the
+ 
+
+ align:start position:0%
+time there's an opportunity cost of the
+year you spent with this firm and you're
+
+ align:start position:0%
+year you spent with this firm and you're
+ 
+
+ align:start position:0%
+year you spent with this firm and you're
+an MIT graduate for God's sake who knows
+
+ align:start position:0%
+an MIT graduate for God's sake who knows
+ 
+
+ align:start position:0%
+an MIT graduate for God's sake who knows
+you could have made like I don't know
+
+ align:start position:0%
+you could have made like I don't know
+ 
+
+ align:start position:0%
+you could have made like I don't know
+100K 200k who knows what you guys make
+
+ align:start position:0%
+100K 200k who knows what you guys make
+ 
+
+ align:start position:0%
+100K 200k who knows what you guys make
+these days okay let's say you could have
+
+ align:start position:0%
+these days okay let's say you could have
+ 
+
+ align:start position:0%
+these days okay let's say you could have
+made
+
+ align:start position:0%
+made
+ 
+
+ align:start position:0%
+made
+100K you did not make 100K by starting
+
+ align:start position:0%
+100K you did not make 100K by starting
+ 
+
+ align:start position:0%
+100K you did not make 100K by starting
+this firm that is a true economic cost
+
+ align:start position:0%
+this firm that is a true economic cost
+ 
+
+ align:start position:0%
+this firm that is a true economic cost
+it's not an accounting cost but it's a
+
+ align:start position:0%
+it's not an accounting cost but it's a
+ 
+
+ align:start position:0%
+it's not an accounting cost but it's a
+true economic cost it's an opportunity
+
+ align:start position:0%
+true economic cost it's an opportunity
+ 
+
+ align:start position:0%
+true economic cost it's an opportunity
+cost you gave up 100K to do this
+
+ align:start position:0%
+cost you gave up 100K to do this
+ 
+
+ align:start position:0%
+cost you gave up 100K to do this
+moreover that computer is still one year
+
+ align:start position:0%
+moreover that computer is still one year
+ 
+
+ align:start position:0%
+moreover that computer is still one year
+left you could have sold it for
+
+ align:start position:0%
+left you could have sold it for
+ 
+
+ align:start position:0%
+left you could have sold it for
+something there's an opportunity cost
+
+ align:start position:0%
+something there's an opportunity cost
+ 
+
+ align:start position:0%
+something there's an opportunity cost
+giving to this guy you could have sold
+
+ align:start position:0%
+giving to this guy you could have sold
+ 
+
+ align:start position:0%
+giving to this guy you could have sold
+it let's say you could have sold it for
+
+ align:start position:0%
+it let's say you could have sold it for
+ 
+
+ align:start position:0%
+it let's say you could have sold it for
+,000
+
+ align:start position:0%
+,000
+ 
+
+ align:start position:0%
+,000
+bucks so your opportunity costs are
+
+ align:start position:0%
+bucks so your opportunity costs are
+ 
+
+ align:start position:0%
+bucks so your opportunity costs are
+101,000 plus the 40 your total costs are
+
+ align:start position:0%
+101,000 plus the 40 your total costs are
+ 
+
+ align:start position:0%
+101,000 plus the 40 your total costs are
+141,000 this was a terrible
+
+ align:start position:0%
+141,000 this was a terrible
+ 
+
+ align:start position:0%
+141,000 this was a terrible
+idea okay your total cost of $141,000
+
+ align:start position:0%
+idea okay your total cost of $141,000
+ 
+
+ align:start position:0%
+idea okay your total cost of $141,000
+you've lost
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+$81,000 okay opportunity costs are real
+
+ align:start position:0%
+$81,000 okay opportunity costs are real
+ 
+
+ align:start position:0%
+$81,000 okay opportunity costs are real
+costs opportunity
+
+ align:start position:0%
+costs opportunity
+ 
+
+ align:start position:0%
+costs opportunity
+costs are the value of the best NE the
+
+ align:start position:0%
+costs are the value of the best NE the
+ 
+
+ align:start position:0%
+costs are the value of the best NE the
+next best forone alternative remember
+
+ align:start position:0%
+next best forone alternative remember
+ 
+
+ align:start position:0%
+next best forone alternative remember
+that's why we call economics to dismal
+
+ align:start position:0%
+that's why we call economics to dismal
+ 
+
+ align:start position:0%
+that's why we call economics to dismal
+science we point out nothing's free your
+
+ align:start position:0%
+science we point out nothing's free your
+ 
+
+ align:start position:0%
+science we point out nothing's free your
+time wasn't free the time you dedicated
+
+ align:start position:0%
+time wasn't free the time you dedicated
+ 
+
+ align:start position:0%
+time wasn't free the time you dedicated
+to this firm meant you could have been
+
+ align:start position:0%
+to this firm meant you could have been
+ 
+
+ align:start position:0%
+to this firm meant you could have been
+doing something else and that's not free
+
+ align:start position:0%
+doing something else and that's not free
+ 
+
+ align:start position:0%
+doing something else and that's not free
+okay and as a result you are not making
+
+ align:start position:0%
+okay and as a result you are not making
+ 
+
+ align:start position:0%
+okay and as a result you are not making
+money in this company even if you think
+
+ align:start position:0%
+money in this company even if you think
+ 
+
+ align:start position:0%
+money in this company even if you think
+they are you are okay it's not saying we
+
+ align:start position:0%
+they are you are okay it's not saying we
+ 
+
+ align:start position:0%
+they are you are okay it's not saying we
+shouldn't do startups that lose money in
+
+ align:start position:0%
+shouldn't do startups that lose money in
+ 
+
+ align:start position:0%
+shouldn't do startups that lose money in
+the first year obviously most startups
+
+ align:start position:0%
+the first year obviously most startups
+ 
+
+ align:start position:0%
+the first year obviously most startups
+lose money in the first year okay we get
+
+ align:start position:0%
+lose money in the first year okay we get
+ 
+
+ align:start position:0%
+lose money in the first year okay we get
+to that later in the semester about how
+
+ align:start position:0%
+to that later in the semester about how
+ 
+
+ align:start position:0%
+to that later in the semester about how
+you think about money companies that
+
+ align:start position:0%
+you think about money companies that
+ 
+
+ align:start position:0%
+you think about money companies that
+lose money in the first year and make
+
+ align:start position:0%
+lose money in the first year and make
+ 
+
+ align:start position:0%
+lose money in the first year and make
+money in the second year we'll come back
+
+ align:start position:0%
+money in the second year we'll come back
+ 
+
+ align:start position:0%
+money in the second year we'll come back
+to that but in this simple example you
+
+ align:start position:0%
+to that but in this simple example you
+ 
+
+ align:start position:0%
+to that but in this simple example you
+shouldn't fool yourself to think that
+
+ align:start position:0%
+shouldn't fool yourself to think that
+ 
+
+ align:start position:0%
+shouldn't fool yourself to think that
+you actually made money because of the
+
+ align:start position:0%
+you actually made money because of the
+ 
+
+ align:start position:0%
+you actually made money because of the
+opportunity costs okay questions about
+
+ align:start position:0%
+opportunity costs okay questions about
+ 
+
+ align:start position:0%
+opportunity costs okay questions about
+that all right let's stop there thanks
+
+ align:start position:0%
+that all right let's stop there thanks
+ 
+
+ align:start position:0%
+that all right let's stop there thanks
+again for all the great questions today
+
+ align:start position:0%
+again for all the great questions today
+ 
+
+ align:start position:0%
+again for all the great questions today
+and we'll come back Wednesday and figure
+
+ align:start position:0%
+and we'll come back Wednesday and figure
+ 
+
+ align:start position:0%
+and we'll come back Wednesday and figure
+out how we pick our queue
\ No newline at end of file
diff --git a/yK5SA6HngCY.txt b/yK5SA6HngCY.txt
new file mode 100644
index 0000000000000000000000000000000000000000..afc3a7a099091cdb560a62ff560ccd2485f19ed9
--- /dev/null
+++ b/yK5SA6HngCY.txt
@@ -0,0 +1,12067 @@
+align:start position:0%
+ 
+The following content is provided under
+
+ align:start position:0%
+The following content is provided under
+ 
+
+ align:start position:0%
+The following content is provided under
+a Creative Common License. Your support
+
+ align:start position:0%
+a Creative Common License. Your support
+ 
+
+ align:start position:0%
+a Creative Common License. Your support
+will help MIT Open Courseware continue
+
+ align:start position:0%
+will help MIT Open Courseware continue
+ 
+
+ align:start position:0%
+will help MIT Open Courseware continue
+to offer high-quality educational
+
+ align:start position:0%
+to offer high-quality educational
+ 
+
+ align:start position:0%
+to offer high-quality educational
+resources for free. To make a donation
+
+ align:start position:0%
+resources for free. To make a donation
+ 
+
+ align:start position:0%
+resources for free. To make a donation
+or view additional materials from
+
+ align:start position:0%
+or view additional materials from
+ 
+
+ align:start position:0%
+or view additional materials from
+hundreds of MIT courses, visit MIT Open
+
+ align:start position:0%
+hundreds of MIT courses, visit MIT Open
+ 
+
+ align:start position:0%
+hundreds of MIT courses, visit MIT Open
+Courseware at ocw.mmit.edu.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+All right. So last time we started
+
+ align:start position:0%
+All right. So last time we started
+ 
+
+ align:start position:0%
+All right. So last time we started
+talking about energy absorption and I
+
+ align:start position:0%
+talking about energy absorption and I
+ 
+
+ align:start position:0%
+talking about energy absorption and I
+wanted to try to finish that up today
+
+ align:start position:0%
+wanted to try to finish that up today
+ 
+
+ align:start position:0%
+wanted to try to finish that up today
+and then next week we would talk about
+
+ align:start position:0%
+and then next week we would talk about
+ 
+
+ align:start position:0%
+and then next week we would talk about
+sandwich panels and using honeycombs and
+
+ align:start position:0%
+sandwich panels and using honeycombs and
+ 
+
+ align:start position:0%
+sandwich panels and using honeycombs and
+foams in sandwich panels. So I think we
+
+ align:start position:0%
+foams in sandwich panels. So I think we
+ 
+
+ align:start position:0%
+foams in sandwich panels. So I think we
+got as far as the idea of introducing
+
+ align:start position:0%
+got as far as the idea of introducing
+ 
+
+ align:start position:0%
+got as far as the idea of introducing
+what these energy absorption diagrams
+
+ align:start position:0%
+what these energy absorption diagrams
+ 
+
+ align:start position:0%
+what these energy absorption diagrams
+are. So let me run through this little
+
+ align:start position:0%
+are. So let me run through this little
+ 
+
+ align:start position:0%
+are. So let me run through this little
+sequence again and then I'll put the
+
+ align:start position:0%
+sequence again and then I'll put the
+ 
+
+ align:start position:0%
+sequence again and then I'll put the
+notes up on the board. So the idea is is
+
+ align:start position:0%
+notes up on the board. So the idea is is
+ 
+
+ align:start position:0%
+notes up on the board. So the idea is is
+that you have uh your compressive stress
+
+ align:start position:0%
+that you have uh your compressive stress
+ 
+
+ align:start position:0%
+that you have uh your compressive stress
+strain curve. So here's a series of
+
+ align:start position:0%
+strain curve. So here's a series of
+ 
+
+ align:start position:0%
+strain curve. So here's a series of
+curves for different densities of a
+
+ align:start position:0%
+curves for different densities of a
+ 
+
+ align:start position:0%
+curves for different densities of a
+foam. And we would do these all at the
+
+ align:start position:0%
+foam. And we would do these all at the
+ 
+
+ align:start position:0%
+foam. And we would do these all at the
+same strain rate and temperature so that
+
+ align:start position:0%
+same strain rate and temperature so that
+ 
+
+ align:start position:0%
+same strain rate and temperature so that
+those aren't variables. And then what we
+
+ align:start position:0%
+those aren't variables. And then what we
+ 
+
+ align:start position:0%
+those aren't variables. And then what we
+would do is we could turn those into
+
+ align:start position:0%
+would do is we could turn those into
+ 
+
+ align:start position:0%
+would do is we could turn those into
+energy absorption diagrams. So notice
+
+ align:start position:0%
+energy absorption diagrams. So notice
+ 
+
+ align:start position:0%
+energy absorption diagrams. So notice
+here, this is a log log plot. So here's
+
+ align:start position:0%
+here, this is a log log plot. So here's
+ 
+
+ align:start position:0%
+here, this is a log log plot. So here's
+the energy absorption here. Here's the
+
+ align:start position:0%
+the energy absorption here. Here's the
+ 
+
+ align:start position:0%
+the energy absorption here. Here's the
+peak stress here. So that's the peak
+
+ align:start position:0%
+peak stress here. So that's the peak
+ 
+
+ align:start position:0%
+peak stress here. So that's the peak
+stress up to some level of energy that
+
+ align:start position:0%
+stress up to some level of energy that
+ 
+
+ align:start position:0%
+stress up to some level of energy that
+you've absorbed. And we've normalized
+
+ align:start position:0%
+you've absorbed. And we've normalized
+ 
+
+ align:start position:0%
+you've absorbed. And we've normalized
+both of those by the solid modulus. So
+
+ align:start position:0%
+both of those by the solid modulus. So
+ 
+
+ align:start position:0%
+both of those by the solid modulus. So
+say we look at one density here. Say we
+
+ align:start position:0%
+say we look at one density here. Say we
+ 
+
+ align:start position:0%
+say we look at one density here. Say we
+look at the lowest density 0.01. So
+
+ align:start position:0%
+look at the lowest density 0.01. So
+ 
+
+ align:start position:0%
+look at the lowest density 0.01. So
+here's our curve here for the for the
+
+ align:start position:0%
+here's our curve here for the for the
+ 
+
+ align:start position:0%
+here's our curve here for the for the
+test. Uh if I go up to some stress level
+
+ align:start position:0%
+test. Uh if I go up to some stress level
+ 
+
+ align:start position:0%
+test. Uh if I go up to some stress level
+that's still in the linear elastic
+
+ align:start position:0%
+that's still in the linear elastic
+ 
+
+ align:start position:0%
+that's still in the linear elastic
+region, then that's going to translate
+
+ align:start position:0%
+region, then that's going to translate
+ 
+
+ align:start position:0%
+region, then that's going to translate
+into somewhere along here on the energy
+
+ align:start position:0%
+into somewhere along here on the energy
+ 
+
+ align:start position:0%
+into somewhere along here on the energy
+absorption curve. And one of the things
+
+ align:start position:0%
+absorption curve. And one of the things
+ 
+
+ align:start position:0%
+absorption curve. And one of the things
+we're going to do today, I'm going to
+
+ align:start position:0%
+we're going to do today, I'm going to
+ 
+
+ align:start position:0%
+we're going to do today, I'm going to
+just show you how you draw these and how
+
+ align:start position:0%
+just show you how you draw these and how
+ 
+
+ align:start position:0%
+just show you how you draw these and how
+you can sort of set them up. And you can
+
+ align:start position:0%
+you can sort of set them up. And you can
+ 
+
+ align:start position:0%
+you can sort of set them up. And you can
+either get them from experiments. So
+
+ align:start position:0%
+either get them from experiments. So
+ 
+
+ align:start position:0%
+either get them from experiments. So
+this is kind of say the top curve or
+
+ align:start position:0%
+this is kind of say the top curve or
+ 
+
+ align:start position:0%
+this is kind of say the top curve or
+experiments doing it from experiments or
+
+ align:start position:0%
+experiments doing it from experiments or
+ 
+
+ align:start position:0%
+experiments doing it from experiments or
+you can use the models for the um foams
+
+ align:start position:0%
+you can use the models for the um foams
+ 
+
+ align:start position:0%
+you can use the models for the um foams
+to do it as well. So we'll see how you
+
+ align:start position:0%
+to do it as well. So we'll see how you
+ 
+
+ align:start position:0%
+to do it as well. So we'll see how you
+can do it from both ways. So this would
+
+ align:start position:0%
+can do it from both ways. So this would
+ 
+
+ align:start position:0%
+can do it from both ways. So this would
+be the linear elastic bit here. This
+
+ align:start position:0%
+be the linear elastic bit here. This
+ 
+
+ align:start position:0%
+be the linear elastic bit here. This
+vertical part where the energy is
+
+ align:start position:0%
+vertical part where the energy is
+ 
+
+ align:start position:0%
+vertical part where the energy is
+increasing but the peak stress isn't
+
+ align:start position:0%
+increasing but the peak stress isn't
+ 
+
+ align:start position:0%
+increasing but the peak stress isn't
+increasing that corresponds to the
+
+ align:start position:0%
+increasing that corresponds to the
+ 
+
+ align:start position:0%
+increasing that corresponds to the
+plateau here. And then this part here
+
+ align:start position:0%
+plateau here. And then this part here
+ 
+
+ align:start position:0%
+plateau here. And then this part here
+where the energy is not increasing very
+
+ align:start position:0%
+where the energy is not increasing very
+ 
+
+ align:start position:0%
+where the energy is not increasing very
+much but the stress increases a lot that
+
+ align:start position:0%
+much but the stress increases a lot that
+ 
+
+ align:start position:0%
+much but the stress increases a lot that
+corresponds to the densification part
+
+ align:start position:0%
+corresponds to the densification part
+ 
+
+ align:start position:0%
+corresponds to the densification part
+over there. Okay. So what you would do
+
+ align:start position:0%
+over there. Okay. So what you would do
+ 
+
+ align:start position:0%
+over there. Okay. So what you would do
+is you would do tests on foams of
+
+ align:start position:0%
+is you would do tests on foams of
+ 
+
+ align:start position:0%
+is you would do tests on foams of
+different densities and from the test
+
+ align:start position:0%
+different densities and from the test
+ 
+
+ align:start position:0%
+different densities and from the test
+data you could draw an energy absorption
+
+ align:start position:0%
+data you could draw an energy absorption
+ 
+
+ align:start position:0%
+data you could draw an energy absorption
+curve for each density. So you plot you
+
+ align:start position:0%
+curve for each density. So you plot you
+ 
+
+ align:start position:0%
+curve for each density. So you plot you
+know there's four different densities
+
+ align:start position:0%
+know there's four different densities
+ 
+
+ align:start position:0%
+know there's four different densities
+here. So it's sort of forms a family of
+
+ align:start position:0%
+here. So it's sort of forms a family of
+ 
+
+ align:start position:0%
+here. So it's sort of forms a family of
+these curves and then what you do is you
+
+ align:start position:0%
+these curves and then what you do is you
+ 
+
+ align:start position:0%
+these curves and then what you do is you
+say and I think we talked about this
+
+ align:start position:0%
+say and I think we talked about this
+ 
+
+ align:start position:0%
+say and I think we talked about this
+last time that the the place you want to
+
+ align:start position:0%
+last time that the the place you want to
+ 
+
+ align:start position:0%
+last time that the the place you want to
+be is at this shoulder point. You want
+
+ align:start position:0%
+be is at this shoulder point. You want
+ 
+
+ align:start position:0%
+be is at this shoulder point. You want
+to be absorbing as much energy as
+
+ align:start position:0%
+to be absorbing as much energy as
+ 
+
+ align:start position:0%
+to be absorbing as much energy as
+possible at that plateau stress. So you
+
+ align:start position:0%
+possible at that plateau stress. So you
+ 
+
+ align:start position:0%
+possible at that plateau stress. So you
+want to be at the point just before it
+
+ align:start position:0%
+want to be at the point just before it
+ 
+
+ align:start position:0%
+want to be at the point just before it
+kind of turns around to the
+
+ align:start position:0%
+kind of turns around to the
+ 
+
+ align:start position:0%
+kind of turns around to the
+densification regime. So you can mark uh
+
+ align:start position:0%
+densification regime. So you can mark uh
+ 
+
+ align:start position:0%
+densification regime. So you can mark uh
+that little shoulder point for each
+
+ align:start position:0%
+that little shoulder point for each
+ 
+
+ align:start position:0%
+that little shoulder point for each
+density. So here's like 0.01, here's 03,
+
+ align:start position:0%
+density. So here's like 0.01, here's 03,
+ 
+
+ align:start position:0%
+density. So here's like 0.01, here's 03,
+and then so on. And then those points
+
+ align:start position:0%
+and then so on. And then those points
+ 
+
+ align:start position:0%
+and then so on. And then those points
+can be connected by a line. So that
+
+ align:start position:0%
+can be connected by a line. So that
+ 
+
+ align:start position:0%
+can be connected by a line. So that
+heavy line then connects those sort of
+
+ align:start position:0%
+heavy line then connects those sort of
+ 
+
+ align:start position:0%
+heavy line then connects those sort of
+shoulder points or those optimum points.
+
+ align:start position:0%
+shoulder points or those optimum points.
+ 
+
+ align:start position:0%
+shoulder points or those optimum points.
+And then what you can do is then repeat
+
+ align:start position:0%
+And then what you can do is then repeat
+ 
+
+ align:start position:0%
+And then what you can do is then repeat
+this whole process for different strain
+
+ align:start position:0%
+this whole process for different strain
+ 
+
+ align:start position:0%
+this whole process for different strain
+rates. So this family of lines here is
+
+ align:start position:0%
+rates. So this family of lines here is
+ 
+
+ align:start position:0%
+rates. So this family of lines here is
+at different strain rates. So these
+
+ align:start position:0%
+at different strain rates. So these
+ 
+
+ align:start position:0%
+at different strain rates. So these
+lines, this set that goes this way
+
+ align:start position:0%
+lines, this set that goes this way
+ 
+
+ align:start position:0%
+lines, this set that goes this way
+corresponds to this line here. And if
+
+ align:start position:0%
+corresponds to this line here. And if
+ 
+
+ align:start position:0%
+corresponds to this line here. And if
+you do them at different strain rates,
+
+ align:start position:0%
+you do them at different strain rates,
+ 
+
+ align:start position:0%
+you do them at different strain rates,
+where the shoulder is appears at a
+
+ align:start position:0%
+where the shoulder is appears at a
+ 
+
+ align:start position:0%
+where the shoulder is appears at a
+slightly different point. And so if you
+
+ align:start position:0%
+slightly different point. And so if you
+ 
+
+ align:start position:0%
+slightly different point. And so if you
+mark those shoulder points, you can draw
+
+ align:start position:0%
+mark those shoulder points, you can draw
+ 
+
+ align:start position:0%
+mark those shoulder points, you can draw
+these lines here that connect up for one
+
+ align:start position:0%
+these lines here that connect up for one
+ 
+
+ align:start position:0%
+these lines here that connect up for one
+relative density. So this uh line on the
+
+ align:start position:0%
+relative density. So this uh line on the
+ 
+
+ align:start position:0%
+relative density. So this uh line on the
+left hand side here, these are all
+
+ align:start position:0%
+left hand side here, these are all
+ 
+
+ align:start position:0%
+left hand side here, these are all
+relative densities of 0.01. These ones
+
+ align:start position:0%
+relative densities of 0.01. These ones
+ 
+
+ align:start position:0%
+relative densities of 0.01. These ones
+are all relative densities of 0.03. So
+
+ align:start position:0%
+are all relative densities of 0.03. So
+ 
+
+ align:start position:0%
+are all relative densities of 0.03. So
+this diagram down here, you know, it
+
+ align:start position:0%
+this diagram down here, you know, it
+ 
+
+ align:start position:0%
+this diagram down here, you know, it
+doesn't really look like this at all. It
+
+ align:start position:0%
+doesn't really look like this at all. It
+ 
+
+ align:start position:0%
+doesn't really look like this at all. It
+doesn't look like the basic energy
+
+ align:start position:0%
+doesn't look like the basic energy
+ 
+
+ align:start position:0%
+doesn't look like the basic energy
+absorption diagram, but it actually has
+
+ align:start position:0%
+absorption diagram, but it actually has
+ 
+
+ align:start position:0%
+absorption diagram, but it actually has
+information for what the optimum would
+
+ align:start position:0%
+information for what the optimum would
+ 
+
+ align:start position:0%
+information for what the optimum would
+be for a range of densities and a range
+
+ align:start position:0%
+be for a range of densities and a range
+ 
+
+ align:start position:0%
+be for a range of densities and a range
+of strain rates. Okay, so typically
+
+ align:start position:0%
+of strain rates. Okay, so typically
+ 
+
+ align:start position:0%
+of strain rates. Okay, so typically
+these foams are visco elastic and they
+
+ align:start position:0%
+these foams are visco elastic and they
+ 
+
+ align:start position:0%
+these foams are visco elastic and they
+have some strain rate sensitivity. So
+
+ align:start position:0%
+have some strain rate sensitivity. So
+ 
+
+ align:start position:0%
+have some strain rate sensitivity. So
+you'd like to get the strain rate
+
+ align:start position:0%
+you'd like to get the strain rate
+ 
+
+ align:start position:0%
+you'd like to get the strain rate
+sensitivity into it. And it's not shown
+
+ align:start position:0%
+sensitivity into it. And it's not shown
+ 
+
+ align:start position:0%
+sensitivity into it. And it's not shown
+here, but you could do the same thing at
+
+ align:start position:0%
+here, but you could do the same thing at
+ 
+
+ align:start position:0%
+here, but you could do the same thing at
+a constant strain rate and varying the
+
+ align:start position:0%
+a constant strain rate and varying the
+ 
+
+ align:start position:0%
+a constant strain rate and varying the
+temperature, too. So if you had things
+
+ align:start position:0%
+temperature, too. So if you had things
+ 
+
+ align:start position:0%
+temperature, too. So if you had things
+at different temperatures, you could do
+
+ align:start position:0%
+at different temperatures, you could do
+ 
+
+ align:start position:0%
+at different temperatures, you could do
+the same kind of idea. Okay. So are we
+
+ align:start position:0%
+the same kind of idea. Okay. So are we
+ 
+
+ align:start position:0%
+the same kind of idea. Okay. So are we
+good with how this works? because I'm
+
+ align:start position:0%
+good with how this works? because I'm
+ 
+
+ align:start position:0%
+good with how this works? because I'm
+now I'm going to write some stuff notes
+
+ align:start position:0%
+now I'm going to write some stuff notes
+ 
+
+ align:start position:0%
+now I'm going to write some stuff notes
+on the board so you can kind of have it
+
+ align:start position:0%
+on the board so you can kind of have it
+ 
+
+ align:start position:0%
+on the board so you can kind of have it
+in your notes. Okay.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+So the idea is that you turn your stress
+
+ align:start position:0%
+So the idea is that you turn your stress
+ 
+
+ align:start position:0%
+So the idea is that you turn your stress
+strain curve that looks something like
+
+ align:start position:0%
+strain curve that looks something like
+ 
+
+ align:start position:0%
+strain curve that looks something like
+that into an energy absorption diagram.
+
+ align:start position:0%
+that into an energy absorption diagram.
+ 
+
+ align:start position:0%
+that into an energy absorption diagram.
+And
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+you can plot
+
+ align:start position:0%
+you can plot
+ 
+
+ align:start position:0%
+you can plot
+on log log scales the energy versus the
+
+ align:start position:0%
+on log log scales the energy versus the
+ 
+
+ align:start position:0%
+on log log scales the energy versus the
+peak stress and you get something like
+
+ align:start position:0%
+peak stress and you get something like
+ 
+
+ align:start position:0%
+peak stress and you get something like
+that. And this point here, I'm going to
+
+ align:start position:0%
+that. And this point here, I'm going to
+ 
+
+ align:start position:0%
+that. And this point here, I'm going to
+call the shoulder point.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+And that would use the material in the
+
+ align:start position:0%
+And that would use the material in the
+ 
+
+ align:start position:0%
+And that would use the material in the
+most efficient way. You get the most
+
+ align:start position:0%
+most efficient way. You get the most
+ 
+
+ align:start position:0%
+most efficient way. You get the most
+energy absorption without getting higher
+
+ align:start position:0%
+energy absorption without getting higher
+ 
+
+ align:start position:0%
+energy absorption without getting higher
+than that plateau stress.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+So we can say at the stress plateau,
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the energy increases without much
+
+ align:start position:0%
+the energy increases without much
+ 
+
+ align:start position:0%
+the energy increases without much
+increase in the peak stress.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+And then as the foam densifies
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+then you get an increase
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+in that peak stress with little increase
+
+ align:start position:0%
+in that peak stress with little increase
+ 
+
+ align:start position:0%
+in that peak stress with little increase
+in and the energy absorbed.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+And so ideally you want to be at that
+
+ align:start position:0%
+And so ideally you want to be at that
+ 
+
+ align:start position:0%
+And so ideally you want to be at that
+shoulder point.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+So to construct these energy diagrams,
+
+ align:start position:0%
+So to construct these energy diagrams,
+ 
+
+ align:start position:0%
+So to construct these energy diagrams,
+you can test a series of foams at
+
+ align:start position:0%
+you can test a series of foams at
+ 
+
+ align:start position:0%
+you can test a series of foams at
+different relative densities and
+
+ align:start position:0%
+different relative densities and
+ 
+
+ align:start position:0%
+different relative densities and
+constant strain rate and temperature.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+And then you make that plot of the
+
+ align:start position:0%
+And then you make that plot of the
+ 
+
+ align:start position:0%
+And then you make that plot of the
+energy absorbed normalized by the
+
+ align:start position:0%
+energy absorbed normalized by the
+ 
+
+ align:start position:0%
+energy absorbed normalized by the
+solid modulus versus the peak stress
+
+ align:start position:0%
+solid modulus versus the peak stress
+ 
+
+ align:start position:0%
+solid modulus versus the peak stress
+normalized by the solid modulus for each
+
+ align:start position:0%
+normalized by the solid modulus for each
+ 
+
+ align:start position:0%
+normalized by the solid modulus for each
+curve.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+And typically what people do is they
+
+ align:start position:0%
+And typically what people do is they
+ 
+
+ align:start position:0%
+And typically what people do is they
+would take the solid modulus at a
+
+ align:start position:0%
+would take the solid modulus at a
+ 
+
+ align:start position:0%
+would take the solid modulus at a
+constant strain rate and temperature. So
+
+ align:start position:0%
+constant strain rate and temperature. So
+ 
+
+ align:start position:0%
+constant strain rate and temperature. So
+you don't have to introduce that as
+
+ align:start position:0%
+you don't have to introduce that as
+ 
+
+ align:start position:0%
+you don't have to introduce that as
+well.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Then you would mark the density for each
+
+ align:start position:0%
+Then you would mark the density for each
+ 
+
+ align:start position:0%
+Then you would mark the density for each
+of those shoulder points.
+
+ align:start position:0%
+of those shoulder points.
+ 
+
+ align:start position:0%
+of those shoulder points.
+And then you would connect them.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+And then you could repeat this whole
+
+ align:start position:0%
+And then you could repeat this whole
+ 
+
+ align:start position:0%
+And then you could repeat this whole
+process for different strain rates.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+And then you would draw the final
+
+ align:start position:0%
+And then you would draw the final
+ 
+
+ align:start position:0%
+And then you would draw the final
+diagram at the bottom where you have
+
+ align:start position:0%
+diagram at the bottom where you have
+ 
+
+ align:start position:0%
+diagram at the bottom where you have
+this family of lines that describes the
+
+ align:start position:0%
+this family of lines that describes the
+ 
+
+ align:start position:0%
+this family of lines that describes the
+shoulder points for different densities
+
+ align:start position:0%
+shoulder points for different densities
+ 
+
+ align:start position:0%
+shoulder points for different densities
+and different strain rates.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+And you could treat different
+
+ align:start position:0%
+And you could treat different
+ 
+
+ align:start position:0%
+And you could treat different
+temperatures in the same way if you
+
+ align:start position:0%
+temperatures in the same way if you
+ 
+
+ align:start position:0%
+temperatures in the same way if you
+wanted to. you would hold the strain
+
+ align:start position:0%
+wanted to. you would hold the strain
+ 
+
+ align:start position:0%
+wanted to. you would hold the strain
+rate constant and vary the temperature.
+
+ align:start position:0%
+rate constant and vary the temperature.
+ 
+
+ align:start position:0%
+rate constant and vary the temperature.
+Okay, so it's kind of a nice way of just
+
+ align:start position:0%
+Okay, so it's kind of a nice way of just
+ 
+
+ align:start position:0%
+Okay, so it's kind of a nice way of just
+putting a lot of information on one
+
+ align:start position:0%
+putting a lot of information on one
+ 
+
+ align:start position:0%
+putting a lot of information on one
+diagram.
+
+ align:start position:0%
+diagram.
+ 
+
+ align:start position:0%
+diagram.
+So one of the things about this is that
+
+ align:start position:0%
+So one of the things about this is that
+ 
+
+ align:start position:0%
+So one of the things about this is that
+because we're normalizing by ES and if
+
+ align:start position:0%
+because we're normalizing by ES and if
+ 
+
+ align:start position:0%
+because we're normalizing by ES and if
+you think of elasttoic foams, elasttoic
+
+ align:start position:0%
+you think of elasttoic foams, elasttoic
+ 
+
+ align:start position:0%
+you think of elasttoic foams, elasttoic
+foams both the Young's modulus depends
+
+ align:start position:0%
+foams both the Young's modulus depends
+ 
+
+ align:start position:0%
+foams both the Young's modulus depends
+on ES and the plateau stress depends on
+
+ align:start position:0%
+on ES and the plateau stress depends on
+ 
+
+ align:start position:0%
+on ES and the plateau stress depends on
+ES. So the the Young's modulus depends
+
+ align:start position:0%
+ES. So the the Young's modulus depends
+ 
+
+ align:start position:0%
+ES. So the the Young's modulus depends
+on the stiffness of the solid and also
+
+ align:start position:0%
+on the stiffness of the solid and also
+ 
+
+ align:start position:0%
+on the stiffness of the solid and also
+because the plateau stress is related to
+
+ align:start position:0%
+because the plateau stress is related to
+ 
+
+ align:start position:0%
+because the plateau stress is related to
+elastic buckling it also depends on the
+
+ align:start position:0%
+elastic buckling it also depends on the
+ 
+
+ align:start position:0%
+elastic buckling it also depends on the
+modulus of the solid. So for elastoic
+
+ align:start position:0%
+modulus of the solid. So for elastoic
+ 
+
+ align:start position:0%
+modulus of the solid. So for elastoic
+foams you can really if because you
+
+ align:start position:0%
+foams you can really if because you
+ 
+
+ align:start position:0%
+foams you can really if because you
+normalize it with respect to es one of
+
+ align:start position:0%
+normalize it with respect to es one of
+ 
+
+ align:start position:0%
+normalize it with respect to es one of
+these diagrams will represent all
+
+ align:start position:0%
+these diagrams will represent all
+ 
+
+ align:start position:0%
+these diagrams will represent all
+elasttoic foams. Okay so that's rather a
+
+ align:start position:0%
+elasttoic foams. Okay so that's rather a
+ 
+
+ align:start position:0%
+elasttoic foams. Okay so that's rather a
+nice thing. So you can have different
+
+ align:start position:0%
+nice thing. So you can have different
+ 
+
+ align:start position:0%
+nice thing. So you can have different
+elasttoic foams but one of those
+
+ align:start position:0%
+elasttoic foams but one of those
+ 
+
+ align:start position:0%
+elasttoic foams but one of those
+diagrams is going to represent all of
+
+ align:start position:0%
+diagrams is going to represent all of
+ 
+
+ align:start position:0%
+diagrams is going to represent all of
+them.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+So we can say elastoic foams can all be
+
+ align:start position:0%
+So we can say elastoic foams can all be
+ 
+
+ align:start position:0%
+So we can say elastoic foams can all be
+plotted on one plot or one curve since
+
+ align:start position:0%
+plotted on one plot or one curve since
+ 
+
+ align:start position:0%
+plotted on one plot or one curve since
+both the modulus and the plateau stress
+
+ align:start position:0%
+both the modulus and the plateau stress
+ 
+
+ align:start position:0%
+both the modulus and the plateau stress
+are related to ES. Yes.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+So if we look at this next figure here,
+
+ align:start position:0%
+So if we look at this next figure here,
+ 
+
+ align:start position:0%
+So if we look at this next figure here,
+maybe I'll just wait a minute for people
+
+ align:start position:0%
+maybe I'll just wait a minute for people
+ 
+
+ align:start position:0%
+maybe I'll just wait a minute for people
+to stop writing.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Yep. Some people write faster than
+
+ align:start position:0%
+Yep. Some people write faster than
+ 
+
+ align:start position:0%
+Yep. Some people write faster than
+others.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay. So, if we look at this next plot
+
+ align:start position:0%
+Okay. So, if we look at this next plot
+ 
+
+ align:start position:0%
+Okay. So, if we look at this next plot
+here, here's uh compressive stress and
+
+ align:start position:0%
+here, here's uh compressive stress and
+ 
+
+ align:start position:0%
+here, here's uh compressive stress and
+strain. These tests are done for one
+
+ align:start position:0%
+strain. These tests are done for one
+ 
+
+ align:start position:0%
+strain. These tests are done for one
+density but a different strain rate. So,
+
+ align:start position:0%
+density but a different strain rate. So,
+ 
+
+ align:start position:0%
+density but a different strain rate. So,
+it's kind of the other other version of
+
+ align:start position:0%
+it's kind of the other other version of
+ 
+
+ align:start position:0%
+it's kind of the other other version of
+this. But here's the stress strain
+
+ align:start position:0%
+this. But here's the stress strain
+ 
+
+ align:start position:0%
+this. But here's the stress strain
+curves here. And here's the energy
+
+ align:start position:0%
+curves here. And here's the energy
+ 
+
+ align:start position:0%
+curves here. And here's the energy
+absorption diagram that's derived from
+
+ align:start position:0%
+absorption diagram that's derived from
+ 
+
+ align:start position:0%
+absorption diagram that's derived from
+those. And then here's a sort of a
+
+ align:start position:0%
+those. And then here's a sort of a
+ 
+
+ align:start position:0%
+those. And then here's a sort of a
+summary diagram uh that has the
+
+ align:start position:0%
+summary diagram uh that has the
+ 
+
+ align:start position:0%
+summary diagram uh that has the
+different strain rates and that would
+
+ align:start position:0%
+different strain rates and that would
+ 
+
+ align:start position:0%
+different strain rates and that would
+have different densities here. And the
+
+ align:start position:0%
+have different densities here. And the
+ 
+
+ align:start position:0%
+have different densities here. And the
+idea is this diagram here could
+
+ align:start position:0%
+idea is this diagram here could
+ 
+
+ align:start position:0%
+idea is this diagram here could
+represent all elasttoic foam. So this
+
+ align:start position:0%
+represent all elasttoic foam. So this
+ 
+
+ align:start position:0%
+represent all elasttoic foam. So this
+has been put together for polyurethane
+
+ align:start position:0%
+has been put together for polyurethane
+ 
+
+ align:start position:0%
+has been put together for polyurethane
+but it could have been you know it
+
+ align:start position:0%
+but it could have been you know it
+ 
+
+ align:start position:0%
+but it could have been you know it
+should be able to represent other sorts
+
+ align:start position:0%
+should be able to represent other sorts
+ 
+
+ align:start position:0%
+should be able to represent other sorts
+of flexible um elasttoic foams.
+
+ align:start position:0%
+of flexible um elasttoic foams.
+ 
+
+ align:start position:0%
+of flexible um elasttoic foams.
+Sorry. diagrams then the
+
+ align:start position:0%
+Sorry. diagrams then the
+ 
+
+ align:start position:0%
+Sorry. diagrams then the
+intersection of the strain rate line and
+
+ align:start position:0%
+intersection of the strain rate line and
+ 
+
+ align:start position:0%
+intersection of the strain rate line and
+your relative density line should be the
+
+ align:start position:0%
+your relative density line should be the
+ 
+
+ align:start position:0%
+your relative density line should be the
+shoulder position.
+
+ align:start position:0%
+shoulder position.
+ 
+
+ align:start position:0%
+shoulder position.
+Yeah, exactly. And so like so this line
+
+ align:start position:0%
+Yeah, exactly. And so like so this line
+ 
+
+ align:start position:0%
+Yeah, exactly. And so like so this line
+here is for 01 and that one's for 003.
+
+ align:start position:0%
+here is for 01 and that one's for 003.
+ 
+
+ align:start position:0%
+here is for 01 and that one's for 003.
+So 0.02 is going to be you know you'd
+
+ align:start position:0%
+So 0.02 is going to be you know you'd
+ 
+
+ align:start position:0%
+So 0.02 is going to be you know you'd
+have to kind of interpolate somewhere in
+
+ align:start position:0%
+have to kind of interpolate somewhere in
+ 
+
+ align:start position:0%
+have to kind of interpolate somewhere in
+between there. Okay. So so we've just
+
+ align:start position:0%
+between there. Okay. So so we've just
+ 
+
+ align:start position:0%
+between there. Okay. So so we've just
+put on certain values because we're not
+
+ align:start position:0%
+put on certain values because we're not
+ 
+
+ align:start position:0%
+put on certain values because we're not
+going to put on a million values. So you
+
+ align:start position:0%
+going to put on a million values. So you
+ 
+
+ align:start position:0%
+going to put on a million values. So you
+just put on certain ones and then
+
+ align:start position:0%
+just put on certain ones and then
+ 
+
+ align:start position:0%
+just put on certain ones and then
+and then you can sort of estimate where
+
+ align:start position:0%
+and then you can sort of estimate where
+ 
+
+ align:start position:0%
+and then you can sort of estimate where
+other densities would appear on there.
+
+ align:start position:0%
+other densities would appear on there.
+ 
+
+ align:start position:0%
+other densities would appear on there.
+Okay. Uh so here's another example here.
+
+ align:start position:0%
+Okay. Uh so here's another example here.
+ 
+
+ align:start position:0%
+Okay. Uh so here's another example here.
+These are curves for two different foam.
+
+ align:start position:0%
+These are curves for two different foam.
+ 
+
+ align:start position:0%
+These are curves for two different foam.
+So here's a polyurethane and a
+
+ align:start position:0%
+So here's a polyurethane and a
+ 
+
+ align:start position:0%
+So here's a polyurethane and a
+polyethylene. So these are both
+
+ align:start position:0%
+polyethylene. So these are both
+ 
+
+ align:start position:0%
+polyethylene. So these are both
+elastimemers and one is the dashed line
+
+ align:start position:0%
+elastimemers and one is the dashed line
+ 
+
+ align:start position:0%
+elastimemers and one is the dashed line
+and one's the solid line. And you can
+
+ align:start position:0%
+and one's the solid line. And you can
+ 
+
+ align:start position:0%
+and one's the solid line. And you can
+kind of see how the lines um kind of
+
+ align:start position:0%
+kind of see how the lines um kind of
+ 
+
+ align:start position:0%
+kind of see how the lines um kind of
+mesh up. So here's a density of 0.01 for
+
+ align:start position:0%
+mesh up. So here's a density of 0.01 for
+ 
+
+ align:start position:0%
+mesh up. So here's a density of 0.01 for
+the polyurethane. Here's 0.05 05 for the
+
+ align:start position:0%
+the polyurethane. Here's 0.05 05 for the
+ 
+
+ align:start position:0%
+the polyurethane. Here's 0.05 05 for the
+polyurethane. And here's 006 for the
+
+ align:start position:0%
+polyurethane. And here's 006 for the
+ 
+
+ align:start position:0%
+polyurethane. And here's 006 for the
+polyethylene. And you can see how the
+
+ align:start position:0%
+polyethylene. And you can see how the
+ 
+
+ align:start position:0%
+polyethylene. And you can see how the
+006 and the 0.05, they're not quite on
+
+ align:start position:0%
+006 and the 0.05, they're not quite on
+ 
+
+ align:start position:0%
+006 and the 0.05, they're not quite on
+top of each other, but they're pretty
+
+ align:start position:0%
+top of each other, but they're pretty
+ 
+
+ align:start position:0%
+top of each other, but they're pretty
+close to coming on top of each other.
+
+ align:start position:0%
+close to coming on top of each other.
+ 
+
+ align:start position:0%
+close to coming on top of each other.
+And then 0.12. And so you get sort of a
+
+ align:start position:0%
+And then 0.12. And so you get sort of a
+ 
+
+ align:start position:0%
+And then 0.12. And so you get sort of a
+family of them for the different
+
+ align:start position:0%
+family of them for the different
+ 
+
+ align:start position:0%
+family of them for the different
+densities. Okay? And you can also do
+
+ align:start position:0%
+densities. Okay? And you can also do
+ 
+
+ align:start position:0%
+densities. Okay? And you can also do
+this for materials that have a yield
+
+ align:start position:0%
+this for materials that have a yield
+ 
+
+ align:start position:0%
+this for materials that have a yield
+point. So polymethacry liid has a yield
+
+ align:start position:0%
+point. So polymethacry liid has a yield
+ 
+
+ align:start position:0%
+point. So polymethacry liid has a yield
+point. So you do exactly the same kind
+
+ align:start position:0%
+point. So you do exactly the same kind
+ 
+
+ align:start position:0%
+point. So you do exactly the same kind
+of thing. Uh so here's the energy
+
+ align:start position:0%
+of thing. Uh so here's the energy
+ 
+
+ align:start position:0%
+of thing. Uh so here's the energy
+absorption diagram that's been developed
+
+ align:start position:0%
+absorption diagram that's been developed
+ 
+
+ align:start position:0%
+absorption diagram that's been developed
+from the stress strain curves. But now
+
+ align:start position:0%
+from the stress strain curves. But now
+ 
+
+ align:start position:0%
+from the stress strain curves. But now
+this curve here or this set of curves
+
+ align:start position:0%
+this curve here or this set of curves
+ 
+
+ align:start position:0%
+this curve here or this set of curves
+here is really just valid for one ratio
+
+ align:start position:0%
+here is really just valid for one ratio
+ 
+
+ align:start position:0%
+here is really just valid for one ratio
+of sigma to ES. So the solid module or
+
+ align:start position:0%
+of sigma to ES. So the solid module or
+ 
+
+ align:start position:0%
+of sigma to ES. So the solid module or
+solid yield strength to the solid
+
+ align:start position:0%
+solid yield strength to the solid
+ 
+
+ align:start position:0%
+solid yield strength to the solid
+modulus. So it's valid for whatever it
+
+ align:start position:0%
+modulus. So it's valid for whatever it
+ 
+
+ align:start position:0%
+modulus. So it's valid for whatever it
+was for that particular type of um foam
+
+ align:start position:0%
+was for that particular type of um foam
+ 
+
+ align:start position:0%
+was for that particular type of um foam
+the polymethyl
+
+ align:start position:0%
+the polymethyl
+ 
+
+ align:start position:0%
+the polymethyl
+methylacrimid.
+
+ align:start position:0%
+methylacrimid.
+ 
+
+ align:start position:0%
+methylacrimid.
+Um,
+
+ align:start position:0%
+Um,
+ 
+
+ align:start position:0%
+Um,
+so I'll just say if we have foams
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that are made from a material with a
+
+ align:start position:0%
+that are made from a material with a
+ 
+
+ align:start position:0%
+that are made from a material with a
+yield point and so they have a a plastic
+
+ align:start position:0%
+yield point and so they have a a plastic
+ 
+
+ align:start position:0%
+yield point and so they have a a plastic
+collapse stress
+
+ align:start position:0%
+collapse stress
+ 
+
+ align:start position:0%
+collapse stress
+then the curve
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+will be valid
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+for foams with the same ratio of sigma
+
+ align:start position:0%
+for foams with the same ratio of sigma
+ 
+
+ align:start position:0%
+for foams with the same ratio of sigma
+ys to Yes.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+So in that case there for the poly m the
+
+ align:start position:0%
+So in that case there for the poly m the
+ 
+
+ align:start position:0%
+So in that case there for the poly m the
+facral limit that ratio is about equal
+
+ align:start position:0%
+facral limit that ratio is about equal
+ 
+
+ align:start position:0%
+facral limit that ratio is about equal
+to 1 over 30.
+
+ align:start position:0%
+to 1 over 30.
+ 
+
+ align:start position:0%
+to 1 over 30.
+So that plot would probably give not a
+
+ align:start position:0%
+So that plot would probably give not a
+ 
+
+ align:start position:0%
+So that plot would probably give not a
+bad description of other foams with the
+
+ align:start position:0%
+bad description of other foams with the
+ 
+
+ align:start position:0%
+bad description of other foams with the
+same value of sigma ys over
+
+ align:start position:0%
+same value of sigma ys over
+ 
+
+ align:start position:0%
+same value of sigma ys over
+es.
+
+ align:start position:0%
+es.
+ 
+
+ align:start position:0%
+es.
+So the idea here is we can generate
+
+ align:start position:0%
+So the idea here is we can generate
+ 
+
+ align:start position:0%
+So the idea here is we can generate
+these diagrams
+
+ align:start position:0%
+these diagrams
+ 
+
+ align:start position:0%
+these diagrams
+either from data the way those ones have
+
+ align:start position:0%
+either from data the way those ones have
+ 
+
+ align:start position:0%
+either from data the way those ones have
+been done or from the models.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+So another way to generate these is to
+
+ align:start position:0%
+So another way to generate these is to
+ 
+
+ align:start position:0%
+So another way to generate these is to
+think about the models that we have for
+
+ align:start position:0%
+think about the models that we have for
+ 
+
+ align:start position:0%
+think about the models that we have for
+the foams and the foam behavior. So we
+
+ align:start position:0%
+the foams and the foam behavior. So we
+ 
+
+ align:start position:0%
+the foams and the foam behavior. So we
+have an equation that describes the
+
+ align:start position:0%
+have an equation that describes the
+ 
+
+ align:start position:0%
+have an equation that describes the
+Young's modulus. We have equations that
+
+ align:start position:0%
+Young's modulus. We have equations that
+ 
+
+ align:start position:0%
+Young's modulus. We have equations that
+describe the plateau stresses. We have
+
+ align:start position:0%
+describe the plateau stresses. We have
+ 
+
+ align:start position:0%
+describe the plateau stresses. We have
+an empirical equation for the
+
+ align:start position:0%
+an empirical equation for the
+ 
+
+ align:start position:0%
+an empirical equation for the
+densification strain and we can use
+
+ align:start position:0%
+densification strain and we can use
+ 
+
+ align:start position:0%
+densification strain and we can use
+those to generate these diagrams and
+
+ align:start position:0%
+those to generate these diagrams and
+ 
+
+ align:start position:0%
+those to generate these diagrams and
+they're kind of useful because they kind
+
+ align:start position:0%
+they're kind of useful because they kind
+ 
+
+ align:start position:0%
+they're kind of useful because they kind
+of show you what's going on on a sort of
+
+ align:start position:0%
+of show you what's going on on a sort of
+ 
+
+ align:start position:0%
+of show you what's going on on a sort of
+mechanis mechanistic basis. So this is a
+
+ align:start position:0%
+mechanis mechanistic basis. So this is a
+ 
+
+ align:start position:0%
+mechanis mechanistic basis. So this is a
+diagram here that's been generated for
+
+ align:start position:0%
+diagram here that's been generated for
+ 
+
+ align:start position:0%
+diagram here that's been generated for
+open cell elastoic foams. Here's our
+
+ align:start position:0%
+open cell elastoic foams. Here's our
+ 
+
+ align:start position:0%
+open cell elastoic foams. Here's our
+energy absorbed. Here's our peak stress
+
+ align:start position:0%
+energy absorbed. Here's our peak stress
+ 
+
+ align:start position:0%
+energy absorbed. Here's our peak stress
+down here. This little inset is sort of
+
+ align:start position:0%
+down here. This little inset is sort of
+ 
+
+ align:start position:0%
+down here. This little inset is sort of
+a schematic of the idealized foam
+
+ align:start position:0%
+a schematic of the idealized foam
+ 
+
+ align:start position:0%
+a schematic of the idealized foam
+behavior. So here's the Young's modulus.
+
+ align:start position:0%
+behavior. So here's the Young's modulus.
+ 
+
+ align:start position:0%
+behavior. So here's the Young's modulus.
+Here's the elastic collapse stress.
+
+ align:start position:0%
+Here's the elastic collapse stress.
+ 
+
+ align:start position:0%
+Here's the elastic collapse stress.
+Here's the densification over here. So
+
+ align:start position:0%
+Here's the densification over here. So
+ 
+
+ align:start position:0%
+Here's the densification over here. So
+obviously it's kind of a very idealized
+
+ align:start position:0%
+obviously it's kind of a very idealized
+ 
+
+ align:start position:0%
+obviously it's kind of a very idealized
+setup. Um but we can generate this
+
+ align:start position:0%
+setup. Um but we can generate this
+ 
+
+ align:start position:0%
+setup. Um but we can generate this
+diagram and I'm going to go through the
+
+ align:start position:0%
+diagram and I'm going to go through the
+ 
+
+ align:start position:0%
+diagram and I'm going to go through the
+equations that'll let us do that. So,
+
+ align:start position:0%
+equations that'll let us do that. So,
+ 
+
+ align:start position:0%
+equations that'll let us do that. So,
+um, one thing to note is here's the sort
+
+ align:start position:0%
+um, one thing to note is here's the sort
+ 
+
+ align:start position:0%
+um, one thing to note is here's the sort
+of curves for each density. Here's this
+
+ align:start position:0%
+of curves for each density. Here's this
+ 
+
+ align:start position:0%
+of curves for each density. Here's this
+line that connects the shoulder points.
+
+ align:start position:0%
+line that connects the shoulder points.
+ 
+
+ align:start position:0%
+line that connects the shoulder points.
+There's a couple of other lines on here
+
+ align:start position:0%
+There's a couple of other lines on here
+ 
+
+ align:start position:0%
+There's a couple of other lines on here
+that I just wanted to mention something
+
+ align:start position:0%
+that I just wanted to mention something
+ 
+
+ align:start position:0%
+that I just wanted to mention something
+about. If you think about the densities,
+
+ align:start position:0%
+about. If you think about the densities,
+ 
+
+ align:start position:0%
+about. If you think about the densities,
+like that's 0.01, this is 0.03, that's
+
+ align:start position:0%
+like that's 0.01, this is 0.03, that's
+ 
+
+ align:start position:0%
+like that's 0.01, this is 0.03, that's
+0.1. If you had a fully dense solid that
+
+ align:start position:0%
+0.1. If you had a fully dense solid that
+ 
+
+ align:start position:0%
+0.1. If you had a fully dense solid that
+was made of the same elastimer, you
+
+ align:start position:0%
+was made of the same elastimer, you
+ 
+
+ align:start position:0%
+was made of the same elastimer, you
+could plot the curve for that, and that
+
+ align:start position:0%
+could plot the curve for that, and that
+ 
+
+ align:start position:0%
+could plot the curve for that, and that
+is going to show up over here. So, this
+
+ align:start position:0%
+is going to show up over here. So, this
+ 
+
+ align:start position:0%
+is going to show up over here. So, this
+is kind of an upper bound. It can't get
+
+ align:start position:0%
+is kind of an upper bound. It can't get
+ 
+
+ align:start position:0%
+is kind of an upper bound. It can't get
+any more than that, right? Or uh and
+
+ align:start position:0%
+any more than that, right? Or uh and
+ 
+
+ align:start position:0%
+any more than that, right? Or uh and
+we've also got a dotted line here which
+
+ align:start position:0%
+we've also got a dotted line here which
+ 
+
+ align:start position:0%
+we've also got a dotted line here which
+takes into account fluid flow within the
+
+ align:start position:0%
+takes into account fluid flow within the
+ 
+
+ align:start position:0%
+takes into account fluid flow within the
+cells. So there can be some fluid flow
+
+ align:start position:0%
+cells. So there can be some fluid flow
+ 
+
+ align:start position:0%
+cells. So there can be some fluid flow
+and because we haven't talked about
+
+ align:start position:0%
+and because we haven't talked about
+ 
+
+ align:start position:0%
+and because we haven't talked about
+that, we're not going to go into that.
+
+ align:start position:0%
+that, we're not going to go into that.
+ 
+
+ align:start position:0%
+that, we're not going to go into that.
+So we can just ignore that dotted line
+
+ align:start position:0%
+So we can just ignore that dotted line
+ 
+
+ align:start position:0%
+So we can just ignore that dotted line
+for now. Okay. Okay. So let me let me go
+
+ align:start position:0%
+for now. Okay. Okay. So let me let me go
+ 
+
+ align:start position:0%
+for now. Okay. Okay. So let me let me go
+through how we can do the modeling.
+
+ align:start position:0%
+through how we can do the modeling.
+ 
+
+ align:start position:0%
+through how we can do the modeling.
+So, we're going to divide the stress
+
+ align:start position:0%
+So, we're going to divide the stress
+ 
+
+ align:start position:0%
+So, we're going to divide the stress
+strain curve up into bits, and I'm going
+
+ align:start position:0%
+strain curve up into bits, and I'm going
+ 
+
+ align:start position:0%
+strain curve up into bits, and I'm going
+to write equations for the energy
+
+ align:start position:0%
+to write equations for the energy
+ 
+
+ align:start position:0%
+to write equations for the energy
+absorbed for each bit. So, we're going
+
+ align:start position:0%
+absorbed for each bit. So, we're going
+ 
+
+ align:start position:0%
+absorbed for each bit. So, we're going
+to start
+
+ align:start position:0%
+to start
+ 
+
+ align:start position:0%
+to start
+with a linear elastic behavior.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+And I'm going to
+
+ align:start position:0%
+And I'm going to
+ 
+
+ align:start position:0%
+And I'm going to
+let's see uh yeah, so let me just note
+
+ align:start position:0%
+let's see uh yeah, so let me just note
+ 
+
+ align:start position:0%
+let's see uh yeah, so let me just note
+here that this is the densification
+
+ align:start position:0%
+here that this is the densification
+ 
+
+ align:start position:0%
+here that this is the densification
+strain out here. And this strain epsilon
+
+ align:start position:0%
+strain out here. And this strain epsilon
+ 
+
+ align:start position:0%
+strain out here. And this strain epsilon
+kn corresponds to the strain at which we
+
+ align:start position:0%
+kn corresponds to the strain at which we
+ 
+
+ align:start position:0%
+kn corresponds to the strain at which we
+first reach the stress plateau. So here
+
+ align:start position:0%
+first reach the stress plateau. So here
+ 
+
+ align:start position:0%
+first reach the stress plateau. So here
+for the linear elastic part I'm going to
+
+ align:start position:0%
+for the linear elastic part I'm going to
+ 
+
+ align:start position:0%
+for the linear elastic part I'm going to
+say that the strain is less than that.
+
+ align:start position:0%
+say that the strain is less than that.
+ 
+
+ align:start position:0%
+say that the strain is less than that.
+So the strain is less than epsilon kn
+
+ align:start position:0%
+So the strain is less than epsilon kn
+ 
+
+ align:start position:0%
+So the strain is less than epsilon kn
+and then I can say
+
+ align:start position:0%
+and then I can say
+ 
+
+ align:start position:0%
+and then I can say
+the energy absorbed.
+
+ align:start position:0%
+the energy absorbed.
+ 
+
+ align:start position:0%
+the energy absorbed.
+So if you just remember from hook's law
+
+ align:start position:0%
+So if you just remember from hook's law
+ 
+
+ align:start position:0%
+So if you just remember from hook's law
+and linear elasticity energy under the
+
+ align:start position:0%
+and linear elasticity energy under the
+ 
+
+ align:start position:0%
+and linear elasticity energy under the
+stress strain curve for the linear
+
+ align:start position:0%
+stress strain curve for the linear
+ 
+
+ align:start position:0%
+stress strain curve for the linear
+elastic part is 12 of sigma squar over
+
+ align:start position:0%
+elastic part is 12 of sigma squar over
+ 
+
+ align:start position:0%
+elastic part is 12 of sigma squar over
+e. So I'm going to call sigma the
+
+ align:start position:0%
+e. So I'm going to call sigma the
+ 
+
+ align:start position:0%
+e. So I'm going to call sigma the
+whatever the stress is going to be the
+
+ align:start position:0%
+whatever the stress is going to be the
+ 
+
+ align:start position:0%
+whatever the stress is going to be the
+peak stress that we get to. And now
+
+ align:start position:0%
+peak stress that we get to. And now
+ 
+
+ align:start position:0%
+peak stress that we get to. And now
+we're going to divide by E of the foam
+
+ align:start position:0%
+we're going to divide by E of the foam
+ 
+
+ align:start position:0%
+we're going to divide by E of the foam
+because these are our foams here. And I
+
+ align:start position:0%
+because these are our foams here. And I
+ 
+
+ align:start position:0%
+because these are our foams here. And I
+can use our model here to say
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and then I got to divide that by ES
+
+ align:start position:0%
+and then I got to divide that by ES
+ 
+
+ align:start position:0%
+and then I got to divide that by ES
+because I've normalized here.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+So, because I know from my modeling that
+
+ align:start position:0%
+So, because I know from my modeling that
+ 
+
+ align:start position:0%
+So, because I know from my modeling that
+the Young's modulus of the foam is just
+
+ align:start position:0%
+the Young's modulus of the foam is just
+ 
+
+ align:start position:0%
+the Young's modulus of the foam is just
+equal to ES times the relative density
+
+ align:start position:0%
+equal to ES times the relative density
+ 
+
+ align:start position:0%
+equal to ES times the relative density
+squared for the open cell foam, that
+
+ align:start position:0%
+squared for the open cell foam, that
+ 
+
+ align:start position:0%
+squared for the open cell foam, that
+means I've now got an ES squared in the
+
+ align:start position:0%
+means I've now got an ES squared in the
+ 
+
+ align:start position:0%
+means I've now got an ES squared in the
+denominator. So, I've got sigma P over
+
+ align:start position:0%
+denominator. So, I've got sigma P over
+ 
+
+ align:start position:0%
+denominator. So, I've got sigma P over
+ES^2 and then I've got a one over the
+
+ align:start position:0%
+ES^2 and then I've got a one over the
+ 
+
+ align:start position:0%
+ES^2 and then I've got a one over the
+relative density squared term. Okay,
+
+ align:start position:0%
+relative density squared term. Okay,
+ 
+
+ align:start position:0%
+relative density squared term. Okay,
+so that uh factor there, that equation
+
+ align:start position:0%
+so that uh factor there, that equation
+ 
+
+ align:start position:0%
+so that uh factor there, that equation
+there gives you these first set of lines
+
+ align:start position:0%
+there gives you these first set of lines
+ 
+
+ align:start position:0%
+there gives you these first set of lines
+here. Gives you that bit and this bit
+
+ align:start position:0%
+here. Gives you that bit and this bit
+ 
+
+ align:start position:0%
+here. Gives you that bit and this bit
+and that bit. Okay, so it gives you
+
+ align:start position:0%
+and that bit. Okay, so it gives you
+ 
+
+ align:start position:0%
+and that bit. Okay, so it gives you
+those first parts of the energy
+
+ align:start position:0%
+those first parts of the energy
+ 
+
+ align:start position:0%
+those first parts of the energy
+absorption diagram.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+And then if we look at the stress
+
+ align:start position:0%
+And then if we look at the stress
+ 
+
+ align:start position:0%
+And then if we look at the stress
+plateau, so here we're going to say that
+
+ align:start position:0%
+plateau, so here we're going to say that
+ 
+
+ align:start position:0%
+plateau, so here we're going to say that
+epsilon kn is less than epsilon is less
+
+ align:start position:0%
+epsilon kn is less than epsilon is less
+ 
+
+ align:start position:0%
+epsilon kn is less than epsilon is less
+than the densification strain. So we're
+
+ align:start position:0%
+than the densification strain. So we're
+ 
+
+ align:start position:0%
+than the densification strain. So we're
+on the plateau somewhere. And now the
+
+ align:start position:0%
+on the plateau somewhere. And now the
+ 
+
+ align:start position:0%
+on the plateau somewhere. And now the
+energy absorbed is just going to be our
+
+ align:start position:0%
+energy absorbed is just going to be our
+ 
+
+ align:start position:0%
+energy absorbed is just going to be our
+plateau stress times the amount of
+
+ align:start position:0%
+plateau stress times the amount of
+ 
+
+ align:start position:0%
+plateau stress times the amount of
+strain we've got.
+
+ align:start position:0%
+strain we've got.
+ 
+
+ align:start position:0%
+strain we've got.
+So that's epsilon minus epsilon kn. And
+
+ align:start position:0%
+So that's epsilon minus epsilon kn. And
+ 
+
+ align:start position:0%
+So that's epsilon minus epsilon kn. And
+if I normalize with respect to the solid
+
+ align:start position:0%
+if I normalize with respect to the solid
+ 
+
+ align:start position:0%
+if I normalize with respect to the solid
+modulus, I can write down that my
+
+ align:start position:0%
+modulus, I can write down that my
+ 
+
+ align:start position:0%
+modulus, I can write down that my
+plateau stress is 0.05 005
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+time the relative density squared and
+
+ align:start position:0%
+time the relative density squared and
+ 
+
+ align:start position:0%
+time the relative density squared and
+then multiply that times
+
+ align:start position:0%
+then multiply that times
+ 
+
+ align:start position:0%
+then multiply that times
+epsilon minus epsilon kn. Okay.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+So that equation then corresponds to
+
+ align:start position:0%
+So that equation then corresponds to
+ 
+
+ align:start position:0%
+So that equation then corresponds to
+these vertical parts. So this part here,
+
+ align:start position:0%
+these vertical parts. So this part here,
+ 
+
+ align:start position:0%
+these vertical parts. So this part here,
+that part there, this part here, it
+
+ align:start position:0%
+that part there, this part here, it
+ 
+
+ align:start position:0%
+that part there, this part here, it
+corresponds to those vertical lines on
+
+ align:start position:0%
+corresponds to those vertical lines on
+ 
+
+ align:start position:0%
+corresponds to those vertical lines on
+the figure.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+vertical lines on the diagram. And then
+
+ align:start position:0%
+vertical lines on the diagram. And then
+ 
+
+ align:start position:0%
+vertical lines on the diagram. And then
+the plateau stress is going to end at
+
+ align:start position:0%
+the plateau stress is going to end at
+ 
+
+ align:start position:0%
+the plateau stress is going to end at
+the densification strain.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+And at that point, the energy diagram is
+
+ align:start position:0%
+And at that point, the energy diagram is
+ 
+
+ align:start position:0%
+And at that point, the energy diagram is
+just going to become vertical.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay. And then the last part. Let me try
+
+ align:start position:0%
+Okay. And then the last part. Let me try
+ 
+
+ align:start position:0%
+Okay. And then the last part. Let me try
+and rub this off a little better.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+And then the last part is when we're at
+
+ align:start position:0%
+And then the last part is when we're at
+ 
+
+ align:start position:0%
+And then the last part is when we're at
+the end of the stress plateau
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and the strain is equal to that
+
+ align:start position:0%
+and the strain is equal to that
+ 
+
+ align:start position:0%
+and the strain is equal to that
+densification strain.
+
+ align:start position:0%
+densification strain.
+ 
+
+ align:start position:0%
+densification strain.
+And so the amount of energy we absorb
+
+ align:start position:0%
+And so the amount of energy we absorb
+ 
+
+ align:start position:0%
+And so the amount of energy we absorb
+here is really going to be the maximum
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+So this is the energy that's going to
+
+ align:start position:0%
+So this is the energy that's going to
+ 
+
+ align:start position:0%
+So this is the energy that's going to
+correspond to that shoulder point that
+
+ align:start position:0%
+correspond to that shoulder point that
+ 
+
+ align:start position:0%
+correspond to that shoulder point that
+I've been talking about. So I'm going to
+
+ align:start position:0%
+I've been talking about. So I'm going to
+ 
+
+ align:start position:0%
+I've been talking about. So I'm going to
+call that W max
+
+ align:start position:0%
+call that W max
+ 
+
+ align:start position:0%
+call that W max
+and normalize that with respect to ES.
+
+ align:start position:0%
+and normalize that with respect to ES.
+ 
+
+ align:start position:0%
+and normalize that with respect to ES.
+And that's then going to be
+
+ align:start position:0%
+And that's then going to be
+ 
+
+ align:start position:0%
+And that's then going to be
+our plateau stress times the
+
+ align:start position:0%
+our plateau stress times the
+ 
+
+ align:start position:0%
+our plateau stress times the
+densification strain.
+
+ align:start position:0%
+densification strain.
+ 
+
+ align:start position:0%
+densification strain.
+And the densification strain
+
+ align:start position:0%
+And the densification strain
+ 
+
+ align:start position:0%
+And the densification strain
+was just 1 minus 1.4 times the relative
+
+ align:start position:0%
+was just 1 minus 1.4 times the relative
+ 
+
+ align:start position:0%
+was just 1 minus 1.4 times the relative
+density.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+So here I'm assuming
+
+ align:start position:0%
+So here I'm assuming
+ 
+
+ align:start position:0%
+So here I'm assuming
+that the densification strain is very
+
+ align:start position:0%
+that the densification strain is very
+ 
+
+ align:start position:0%
+that the densification strain is very
+much bigger than the strain at which the
+
+ align:start position:0%
+much bigger than the strain at which the
+ 
+
+ align:start position:0%
+much bigger than the strain at which the
+buckling first occurs. And I'm
+
+ align:start position:0%
+buckling first occurs. And I'm
+ 
+
+ align:start position:0%
+buckling first occurs. And I'm
+neglecting that linear elastic part.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+So then we could say the optimum foam
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+is at that shoulder point
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and I can say that the peak stress at
+
+ align:start position:0%
+and I can say that the peak stress at
+ 
+
+ align:start position:0%
+and I can say that the peak stress at
+that point is just equal to the plateau
+
+ align:start position:0%
+that point is just equal to the plateau
+ 
+
+ align:start position:0%
+that point is just equal to the plateau
+stress.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+And I can what I want to do is get an
+
+ align:start position:0%
+And I can what I want to do is get an
+ 
+
+ align:start position:0%
+And I can what I want to do is get an
+equation for that um solid line up here
+
+ align:start position:0%
+equation for that um solid line up here
+ 
+
+ align:start position:0%
+equation for that um solid line up here
+that connects all those shoulder points.
+
+ align:start position:0%
+that connects all those shoulder points.
+ 
+
+ align:start position:0%
+that connects all those shoulder points.
+So I want an equation in terms of the
+
+ align:start position:0%
+So I want an equation in terms of the
+ 
+
+ align:start position:0%
+So I want an equation in terms of the
+energy and the peak stress instead of in
+
+ align:start position:0%
+energy and the peak stress instead of in
+ 
+
+ align:start position:0%
+energy and the peak stress instead of in
+terms of the density. So what I'm going
+
+ align:start position:0%
+terms of the density. So what I'm going
+ 
+
+ align:start position:0%
+terms of the density. So what I'm going
+to do is solve this for the density and
+
+ align:start position:0%
+to do is solve this for the density and
+ 
+
+ align:start position:0%
+to do is solve this for the density and
+then plug that back into there.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+So that's
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so I get that the relative density is
+
+ align:start position:0%
+so I get that the relative density is
+ 
+
+ align:start position:0%
+so I get that the relative density is
+then 20 times the peak stress over the
+
+ align:start position:0%
+then 20 times the peak stress over the
+ 
+
+ align:start position:0%
+then 20 times the peak stress over the
+solid modulus and I take the square root
+
+ align:start position:0%
+solid modulus and I take the square root
+ 
+
+ align:start position:0%
+solid modulus and I take the square root
+of that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and now I can substitute this up here
+
+ align:start position:0%
+and now I can substitute this up here
+ 
+
+ align:start position:0%
+and now I can substitute this up here
+for the relative density.
+
+ align:start position:0%
+for the relative density.
+ 
+
+ align:start position:0%
+for the relative density.
+I think I need another board.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+So then I've got this is my my peak
+
+ align:start position:0%
+So then I've got this is my my peak
+ 
+
+ align:start position:0%
+So then I've got this is my my peak
+stress or my plateau stress over ES and
+
+ align:start position:0%
+stress or my plateau stress over ES and
+ 
+
+ align:start position:0%
+stress or my plateau stress over ES and
+this is all just the densification or
+
+ align:start position:0%
+this is all just the densification or
+ 
+
+ align:start position:0%
+this is all just the densification or
+one yeah this is all just the
+
+ align:start position:0%
+one yeah this is all just the
+ 
+
+ align:start position:0%
+one yeah this is all just the
+densification strain and that's just 1 -
+
+ align:start position:0%
+densification strain and that's just 1 -
+ 
+
+ align:start position:0%
+densification strain and that's just 1 -
+1.4 four times the relative density. But
+
+ align:start position:0%
+1.4 four times the relative density. But
+ 
+
+ align:start position:0%
+1.4 four times the relative density. But
+now I'm putting the relative density in
+
+ align:start position:0%
+now I'm putting the relative density in
+ 
+
+ align:start position:0%
+now I'm putting the relative density in
+terms of the peak stress or the plateau
+
+ align:start position:0%
+terms of the peak stress or the plateau
+ 
+
+ align:start position:0%
+terms of the peak stress or the plateau
+stress.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+So if I just simplify that slightly with
+
+ align:start position:0%
+So if I just simplify that slightly with
+ 
+
+ align:start position:0%
+So if I just simplify that slightly with
+the constant,
+
+ align:start position:0%
+the constant,
+ 
+
+ align:start position:0%
+the constant,
+it's 1 - 6.26
+
+ align:start position:0%
+it's 1 - 6.26
+ 
+
+ align:start position:0%
+it's 1 - 6.26
+* sigma p over e s
+
+ align:start position:0%
+* sigma p over e s
+ 
+
+ align:start position:0%
+* sigma p over e s
+to the 1/2 power.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+So that equation there describes the
+
+ align:start position:0%
+So that equation there describes the
+ 
+
+ align:start position:0%
+So that equation there describes the
+Oops. Oops. Oh, come on. No more
+
+ align:start position:0%
+Oops. Oops. Oh, come on. No more
+ 
+
+ align:start position:0%
+Oops. Oops. Oh, come on. No more
+updates. No updates. Go away.
+
+ align:start position:0%
+updates. No updates. Go away.
+ 
+
+ align:start position:0%
+updates. No updates. Go away.
+Ah. So that equation there describes
+
+ align:start position:0%
+Ah. So that equation there describes
+ 
+
+ align:start position:0%
+Ah. So that equation there describes
+this line here that connects those
+
+ align:start position:0%
+this line here that connects those
+ 
+
+ align:start position:0%
+this line here that connects those
+shoulder points. Okay. And that's the
+
+ align:start position:0%
+shoulder points. Okay. And that's the
+ 
+
+ align:start position:0%
+shoulder points. Okay. And that's the
+line you're sort of the most interested
+
+ align:start position:0%
+line you're sort of the most interested
+ 
+
+ align:start position:0%
+line you're sort of the most interested
+in because each of those shoulder points
+
+ align:start position:0%
+in because each of those shoulder points
+ 
+
+ align:start position:0%
+in because each of those shoulder points
+is a point where the foam is being used
+
+ align:start position:0%
+is a point where the foam is being used
+ 
+
+ align:start position:0%
+is a point where the foam is being used
+in the most efficient way or the optimum
+
+ align:start position:0%
+in the most efficient way or the optimum
+ 
+
+ align:start position:0%
+in the most efficient way or the optimum
+way. Okay.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+And then let's see. Is that going to
+
+ align:start position:0%
+And then let's see. Is that going to
+ 
+
+ align:start position:0%
+And then let's see. Is that going to
+fit? Let me try the other board.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+And then the last thing we can do is
+
+ align:start position:0%
+And then the last thing we can do is
+ 
+
+ align:start position:0%
+And then the last thing we can do is
+calculate that line that corresponds to
+
+ align:start position:0%
+calculate that line that corresponds to
+ 
+
+ align:start position:0%
+calculate that line that corresponds to
+the dense solid. Yeah.
+
+ align:start position:0%
+the dense solid. Yeah.
+ 
+
+ align:start position:0%
+the dense solid. Yeah.
+On that it says it corresponds to the
+
+ align:start position:0%
+On that it says it corresponds to the
+ 
+
+ align:start position:0%
+On that it says it corresponds to the
+vertical lines on the diagram. And then
+
+ align:start position:0%
+vertical lines on the diagram. And then
+ 
+
+ align:start position:0%
+vertical lines on the diagram. And then
+later it says then it becomes vertical.
+
+ align:start position:0%
+later it says then it becomes vertical.
+ 
+
+ align:start position:0%
+later it says then it becomes vertical.
+Is that referring to two different
+
+ align:start position:0%
+Is that referring to two different
+ 
+
+ align:start position:0%
+Is that referring to two different
+diagrams?
+
+ align:start position:0%
+diagrams?
+ 
+
+ align:start position:0%
+diagrams?
+Um, so this stress plateau equation here
+
+ align:start position:0%
+Um, so this stress plateau equation here
+ 
+
+ align:start position:0%
+Um, so this stress plateau equation here
+corresponds to these vertical lines
+
+ align:start position:0%
+corresponds to these vertical lines
+ 
+
+ align:start position:0%
+corresponds to these vertical lines
+here. So for for a relative density of
+
+ align:start position:0%
+here. So for for a relative density of
+ 
+
+ align:start position:0%
+here. So for for a relative density of
+0.01 it corresponds to that part and for
+
+ align:start position:0%
+0.01 it corresponds to that part and for
+ 
+
+ align:start position:0%
+0.01 it corresponds to that part and for
+03 it's this part and for 01 it's that
+
+ align:start position:0%
+03 it's this part and for 01 it's that
+ 
+
+ align:start position:0%
+03 it's this part and for 01 it's that
+part. Okay.
+
+ align:start position:0%
+part. Okay.
+ 
+
+ align:start position:0%
+part. Okay.
+But then the third point then w versus
+
+ align:start position:0%
+But then the third point then w versus
+ 
+
+ align:start position:0%
+But then the third point then w versus
+sigma becomes vertical.
+
+ align:start position:0%
+sigma becomes vertical.
+ 
+
+ align:start position:0%
+sigma becomes vertical.
+Oh so well the plateau stress ends at
+
+ align:start position:0%
+Oh so well the plateau stress ends at
+ 
+
+ align:start position:0%
+Oh so well the plateau stress ends at
+the densification strain. So the plateau
+
+ align:start position:0%
+the densification strain. So the plateau
+ 
+
+ align:start position:0%
+the densification strain. So the plateau
+stress ends here. Oh, let's see. And
+
+ align:start position:0%
+stress ends here. Oh, let's see. And
+ 
+
+ align:start position:0%
+stress ends here. Oh, let's see. And
+then it becomes should be horizontal.
+
+ align:start position:0%
+then it becomes should be horizontal.
+ 
+
+ align:start position:0%
+then it becomes should be horizontal.
+Sorry, sorry. Sorry.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay. Sorry. Happy.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Now I'm going to rub that all off.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay, everybody get this. Rub it off.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay.
+
+ align:start position:0%
+Okay.
+ 
+
+ align:start position:0%
+Okay.
+So then the last part
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+is what happens when the foam is
+
+ align:start position:0%
+is what happens when the foam is
+ 
+
+ align:start position:0%
+is what happens when the foam is
+densified. And if it was fully dense,
+
+ align:start position:0%
+densified. And if it was fully dense,
+ 
+
+ align:start position:0%
+densified. And if it was fully dense,
+and you never really can get to this
+
+ align:start position:0%
+and you never really can get to this
+ 
+
+ align:start position:0%
+and you never really can get to this
+point, but if it was fully dense, you
+
+ align:start position:0%
+point, but if it was fully dense, you
+ 
+
+ align:start position:0%
+point, but if it was fully dense, you
+would get rid of all the pores and it
+
+ align:start position:0%
+would get rid of all the pores and it
+ 
+
+ align:start position:0%
+would get rid of all the pores and it
+would just be a solid. And then the
+
+ align:start position:0%
+would just be a solid. And then the
+ 
+
+ align:start position:0%
+would just be a solid. And then the
+energy absorption curve would be this
+
+ align:start position:0%
+energy absorption curve would be this
+ 
+
+ align:start position:0%
+energy absorption curve would be this
+curve for the solid.
+
+ align:start position:0%
+curve for the solid.
+ 
+
+ align:start position:0%
+curve for the solid.
+So I'll just say when fully densified,
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+We'll just say the curve approaches
+
+ align:start position:0%
+We'll just say the curve approaches
+ 
+
+ align:start position:0%
+We'll just say the curve approaches
+that for the solid.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Then for the solid you would just have
+
+ align:start position:0%
+Then for the solid you would just have
+ 
+
+ align:start position:0%
+Then for the solid you would just have
+that W over E S is equal to 12
+
+ align:start position:0%
+that W over E S is equal to 12
+ 
+
+ align:start position:0%
+that W over E S is equal to 12
+the peak stress squared over ES. Okay.
+
+ align:start position:0%
+the peak stress squared over ES. Okay.
+ 
+
+ align:start position:0%
+the peak stress squared over ES. Okay.
+So the this model curve the curves have
+
+ align:start position:0%
+So the this model curve the curves have
+ 
+
+ align:start position:0%
+So the this model curve the curves have
+the same shape as when you get the
+
+ align:start position:0%
+the same shape as when you get the
+ 
+
+ align:start position:0%
+the same shape as when you get the
+diagrams from the experiments and you
+
+ align:start position:0%
+diagrams from the experiments and you
+ 
+
+ align:start position:0%
+diagrams from the experiments and you
+can kind of see how the different
+
+ align:start position:0%
+can kind of see how the different
+ 
+
+ align:start position:0%
+can kind of see how the different
+mechanisms of deformation and failure
+
+ align:start position:0%
+mechanisms of deformation and failure
+ 
+
+ align:start position:0%
+mechanisms of deformation and failure
+kind of contribute to the diagram where
+
+ align:start position:0%
+kind of contribute to the diagram where
+ 
+
+ align:start position:0%
+kind of contribute to the diagram where
+the diagram comes from. Okay.
+
+ align:start position:0%
+the diagram comes from. Okay.
+ 
+
+ align:start position:0%
+the diagram comes from. Okay.
+Um and I guess one other point is you
+
+ align:start position:0%
+Um and I guess one other point is you
+ 
+
+ align:start position:0%
+Um and I guess one other point is you
+can see that the foams are always going
+
+ align:start position:0%
+can see that the foams are always going
+ 
+
+ align:start position:0%
+can see that the foams are always going
+to be a lot better than the solid. And
+
+ align:start position:0%
+to be a lot better than the solid. And
+ 
+
+ align:start position:0%
+to be a lot better than the solid. And
+remember this is a log log curve. So
+
+ align:start position:0%
+remember this is a log log curve. So
+ 
+
+ align:start position:0%
+remember this is a log log curve. So
+that you know a foam that's like uh has
+
+ align:start position:0%
+that you know a foam that's like uh has
+ 
+
+ align:start position:0%
+that you know a foam that's like uh has
+a density of 3% here there's a huge
+
+ align:start position:0%
+a density of 3% here there's a huge
+ 
+
+ align:start position:0%
+a density of 3% here there's a huge
+difference in the peak stress. So say
+
+ align:start position:0%
+difference in the peak stress. So say
+ 
+
+ align:start position:0%
+difference in the peak stress. So say
+say you wanted to absorb this amount of
+
+ align:start position:0%
+say you wanted to absorb this amount of
+ 
+
+ align:start position:0%
+say you wanted to absorb this amount of
+energy up here. Uh for a foam that was
+
+ align:start position:0%
+energy up here. Uh for a foam that was
+ 
+
+ align:start position:0%
+energy up here. Uh for a foam that was
+003 dense the peak stress would be a
+
+ align:start position:0%
+003 dense the peak stress would be a
+ 
+
+ align:start position:0%
+003 dense the peak stress would be a
+little less than 10us4 normalized by the
+
+ align:start position:0%
+little less than 10us4 normalized by the
+ 
+
+ align:start position:0%
+little less than 10us4 normalized by the
+modulus and for the solid it'd be like
+
+ align:start position:0%
+modulus and for the solid it'd be like
+ 
+
+ align:start position:0%
+modulus and for the solid it'd be like
+10us2. So it's orders of magnitude
+
+ align:start position:0%
+10us2. So it's orders of magnitude
+ 
+
+ align:start position:0%
+10us2. So it's orders of magnitude
+better to have the foam rather than the
+
+ align:start position:0%
+better to have the foam rather than the
+ 
+
+ align:start position:0%
+better to have the foam rather than the
+solid. Okay. All right.
+
+ align:start position:0%
+solid. Okay. All right.
+ 
+
+ align:start position:0%
+solid. Okay. All right.
+Now let's see what else we have. So we
+
+ align:start position:0%
+Now let's see what else we have. So we
+ 
+
+ align:start position:0%
+Now let's see what else we have. So we
+we could do a similar thing for closed
+
+ align:start position:0%
+we could do a similar thing for closed
+ 
+
+ align:start position:0%
+we could do a similar thing for closed
+cell foams and you get diagrams that
+
+ align:start position:0%
+cell foams and you get diagrams that
+ 
+
+ align:start position:0%
+cell foams and you get diagrams that
+look like this. Uh one of the
+
+ align:start position:0%
+look like this. Uh one of the
+ 
+
+ align:start position:0%
+look like this. Uh one of the
+differences with the closed cell foams
+
+ align:start position:0%
+differences with the closed cell foams
+ 
+
+ align:start position:0%
+differences with the closed cell foams
+if you assume that the faces don't
+
+ align:start position:0%
+if you assume that the faces don't
+ 
+
+ align:start position:0%
+if you assume that the faces don't
+rupture the the plateau stresses and
+
+ align:start position:0%
+rupture the the plateau stresses and
+ 
+
+ align:start position:0%
+rupture the the plateau stresses and
+horizontals. You know remember we had
+
+ align:start position:0%
+horizontals. You know remember we had
+ 
+
+ align:start position:0%
+horizontals. You know remember we had
+that gas contribution and you can take
+
+ align:start position:0%
+that gas contribution and you can take
+ 
+
+ align:start position:0%
+that gas contribution and you can take
+that into account. So I'm I'm not going
+
+ align:start position:0%
+that into account. So I'm I'm not going
+ 
+
+ align:start position:0%
+that into account. So I'm I'm not going
+to go over the details of that. Um the
+
+ align:start position:0%
+to go over the details of that. Um the
+ 
+
+ align:start position:0%
+to go over the details of that. Um the
+next one I wanted to talk about was uh
+
+ align:start position:0%
+next one I wanted to talk about was uh
+ 
+
+ align:start position:0%
+next one I wanted to talk about was uh
+looking at foams that have a yield
+
+ align:start position:0%
+looking at foams that have a yield
+ 
+
+ align:start position:0%
+looking at foams that have a yield
+point. And again you can generate a
+
+ align:start position:0%
+point. And again you can generate a
+ 
+
+ align:start position:0%
+point. And again you can generate a
+similar kind of diagram but now instead
+
+ align:start position:0%
+similar kind of diagram but now instead
+ 
+
+ align:start position:0%
+similar kind of diagram but now instead
+of having an elastic failure here you've
+
+ align:start position:0%
+of having an elastic failure here you've
+ 
+
+ align:start position:0%
+of having an elastic failure here you've
+got a plastic failure you form plastic
+
+ align:start position:0%
+got a plastic failure you form plastic
+ 
+
+ align:start position:0%
+got a plastic failure you form plastic
+hinges. And then again this diagram is
+
+ align:start position:0%
+hinges. And then again this diagram is
+ 
+
+ align:start position:0%
+hinges. And then again this diagram is
+less general than the one for elastoic
+
+ align:start position:0%
+less general than the one for elastoic
+ 
+
+ align:start position:0%
+less general than the one for elastoic
+foams. So this diagram would be valid
+
+ align:start position:0%
+foams. So this diagram would be valid
+ 
+
+ align:start position:0%
+foams. So this diagram would be valid
+for whatever ratio of sigma ys over es
+
+ align:start position:0%
+for whatever ratio of sigma ys over es
+ 
+
+ align:start position:0%
+for whatever ratio of sigma ys over es
+you've done the calculation for. So this
+
+ align:start position:0%
+you've done the calculation for. So this
+ 
+
+ align:start position:0%
+you've done the calculation for. So this
+one here it's for 001. Okay. So let me
+
+ align:start position:0%
+one here it's for 001. Okay. So let me
+ 
+
+ align:start position:0%
+one here it's for 001. Okay. So let me
+just run through the same kind of
+
+ align:start position:0%
+just run through the same kind of
+ 
+
+ align:start position:0%
+just run through the same kind of
+calculation for for the plastic foams.
+
+ align:start position:0%
+calculation for for the plastic foams.
+ 
+
+ align:start position:0%
+calculation for for the plastic foams.
+Um,
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+can I rub this off? Then I can use this
+
+ align:start position:0%
+can I rub this off? Then I can use this
+ 
+
+ align:start position:0%
+can I rub this off? Then I can use this
+board right here. Yeah.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+So the linear elastic part is just the
+
+ align:start position:0%
+So the linear elastic part is just the
+ 
+
+ align:start position:0%
+So the linear elastic part is just the
+same as for the elastoic foams.
+
+ align:start position:0%
+same as for the elastoic foams.
+ 
+
+ align:start position:0%
+same as for the elastoic foams.
+So you get W over E S is a half
+
+ align:start position:0%
+So you get W over E S is a half
+ 
+
+ align:start position:0%
+So you get W over E S is a half
+sigma P over E S squared
+
+ align:start position:0%
+sigma P over E S squared
+ 
+
+ align:start position:0%
+sigma P over E S squared
+* 1 over the relative density squared.
+
+ align:start position:0%
+* 1 over the relative density squared.
+ 
+
+ align:start position:0%
+* 1 over the relative density squared.
+So it's just the same thing.
+
+ align:start position:0%
+So it's just the same thing.
+ 
+
+ align:start position:0%
+So it's just the same thing.
+Then the stress plateau
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+get W over E S is just the uh plastic
+
+ align:start position:0%
+get W over E S is just the uh plastic
+ 
+
+ align:start position:0%
+get W over E S is just the uh plastic
+collapse strength
+
+ align:start position:0%
+collapse strength
+ 
+
+ align:start position:0%
+collapse strength
+times
+
+ align:start position:0%
+times
+ 
+
+ align:start position:0%
+times
+the strain range that you go up to. So
+
+ align:start position:0%
+the strain range that you go up to. So
+ 
+
+ align:start position:0%
+the strain range that you go up to. So
+if you remember the plastic collapse
+
+ align:start position:0%
+if you remember the plastic collapse
+ 
+
+ align:start position:0%
+if you remember the plastic collapse
+strength was.3
+
+ align:start position:0%
+strength was.3
+ 
+
+ align:start position:0%
+strength was.3
+sigma ys
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+times the relative density to the three
+
+ align:start position:0%
+times the relative density to the three
+ 
+
+ align:start position:0%
+times the relative density to the three
+halves power and then times the strain
+
+ align:start position:0%
+halves power and then times the strain
+ 
+
+ align:start position:0%
+halves power and then times the strain
+range and then
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and then at the end of the stress
+
+ align:start position:0%
+and then at the end of the stress
+ 
+
+ align:start position:0%
+and then at the end of the stress
+plateau you've got the maximum energy
+
+ align:start position:0%
+plateau you've got the maximum energy
+ 
+
+ align:start position:0%
+plateau you've got the maximum energy
+absorbed.
+
+ align:start position:0%
+absorbed.
+ 
+
+ align:start position:0%
+absorbed.
+So normalize that by ES
+
+ align:start position:0%
+So normalize that by ES
+ 
+
+ align:start position:0%
+So normalize that by ES
+and that's going to be your peak stress
+
+ align:start position:0%
+and that's going to be your peak stress
+ 
+
+ align:start position:0%
+and that's going to be your peak stress
+over ES times the densification strain
+
+ align:start position:0%
+over ES times the densification strain
+ 
+
+ align:start position:0%
+over ES times the densification strain
+again.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+So this bit here
+
+ align:start position:0%
+So this bit here
+ 
+
+ align:start position:0%
+So this bit here
+is the densification strain.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+And then you can do a similar thing to
+
+ align:start position:0%
+And then you can do a similar thing to
+ 
+
+ align:start position:0%
+And then you can do a similar thing to
+figure out the equation of that line
+
+ align:start position:0%
+figure out the equation of that line
+ 
+
+ align:start position:0%
+figure out the equation of that line
+that joins the shoulder points.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+So the first step is to solve for the
+
+ align:start position:0%
+So the first step is to solve for the
+ 
+
+ align:start position:0%
+So the first step is to solve for the
+relative density there.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Um, so that's
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so if this part here.3 sigma ys times
+
+ align:start position:0%
+so if this part here.3 sigma ys times
+ 
+
+ align:start position:0%
+so if this part here.3 sigma ys times
+the relative density to the three halves
+
+ align:start position:0%
+the relative density to the three halves
+ 
+
+ align:start position:0%
+the relative density to the three halves
+power is the plastic collapse stress,
+
+ align:start position:0%
+power is the plastic collapse stress,
+ 
+
+ align:start position:0%
+power is the plastic collapse stress,
+then at the densification point the
+
+ align:start position:0%
+then at the densification point the
+ 
+
+ align:start position:0%
+then at the densification point the
+relative density you can just rewrite
+
+ align:start position:0%
+relative density you can just rewrite
+ 
+
+ align:start position:0%
+relative density you can just rewrite
+that and it comes out to the 2/3 power
+
+ align:start position:0%
+that and it comes out to the 2/3 power
+ 
+
+ align:start position:0%
+that and it comes out to the 2/3 power
+because you turn the power around. And
+
+ align:start position:0%
+because you turn the power around. And
+ 
+
+ align:start position:0%
+because you turn the power around. And
+then you just substitute this up in
+
+ align:start position:0%
+then you just substitute this up in
+ 
+
+ align:start position:0%
+then you just substitute this up in
+here.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+So you get that the maximum energy
+
+ align:start position:0%
+So you get that the maximum energy
+ 
+
+ align:start position:0%
+So you get that the maximum energy
+absorbed normalized by the solid modulus
+
+ align:start position:0%
+absorbed normalized by the solid modulus
+ 
+
+ align:start position:0%
+absorbed normalized by the solid modulus
+is your peak stress time 1 - 1.4 * this
+
+ align:start position:0%
+is your peak stress time 1 - 1.4 * this
+ 
+
+ align:start position:0%
+is your peak stress time 1 - 1.4 * this
+thing in brackets to the 2/3 power the
+
+ align:start position:0%
+thing in brackets to the 2/3 power the
+ 
+
+ align:start position:0%
+thing in brackets to the 2/3 power the
+3.3 times the peak stress over the yield
+
+ align:start position:0%
+3.3 times the peak stress over the yield
+ 
+
+ align:start position:0%
+3.3 times the peak stress over the yield
+strength of the solid. And then if I
+
+ align:start position:0%
+strength of the solid. And then if I
+ 
+
+ align:start position:0%
+strength of the solid. And then if I
+just rearrange that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and get the constants,
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+it's 1 minus 3.1
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+times our ratio of the stresses there.
+
+ align:start position:0%
+times our ratio of the stresses there.
+ 
+
+ align:start position:0%
+times our ratio of the stresses there.
+Okay.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+So maybe I'll just put over here. The
+
+ align:start position:0%
+So maybe I'll just put over here. The
+ 
+
+ align:start position:0%
+So maybe I'll just put over here. The
+curves are less general than for
+
+ align:start position:0%
+curves are less general than for
+ 
+
+ align:start position:0%
+curves are less general than for
+elastimeic
+
+ align:start position:0%
+elastimeic
+ 
+
+ align:start position:0%
+elastimeic
+foams.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay. So each sort of family of curves
+
+ align:start position:0%
+Okay. So each sort of family of curves
+ 
+
+ align:start position:0%
+Okay. So each sort of family of curves
+would be for a particular ratio of the
+
+ align:start position:0%
+would be for a particular ratio of the
+ 
+
+ align:start position:0%
+would be for a particular ratio of the
+solid yield strength to the solid
+
+ align:start position:0%
+solid yield strength to the solid
+ 
+
+ align:start position:0%
+solid yield strength to the solid
+modulus. Okay.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+[Applause]
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+So you get the idea. It's fairly
+
+ align:start position:0%
+So you get the idea. It's fairly
+ 
+
+ align:start position:0%
+So you get the idea. It's fairly
+straightforward. So I wanted to finish
+
+ align:start position:0%
+straightforward. So I wanted to finish
+ 
+
+ align:start position:0%
+straightforward. So I wanted to finish
+up this topic by giving you a few
+
+ align:start position:0%
+up this topic by giving you a few
+ 
+
+ align:start position:0%
+up this topic by giving you a few
+examples of how you can use these
+
+ align:start position:0%
+examples of how you can use these
+ 
+
+ align:start position:0%
+examples of how you can use these
+curves. So the next thing is to look at
+
+ align:start position:0%
+curves. So the next thing is to look at
+ 
+
+ align:start position:0%
+curves. So the next thing is to look at
+the selection of foams for impact
+
+ align:start position:0%
+the selection of foams for impact
+ 
+
+ align:start position:0%
+the selection of foams for impact
+protection. And typically you're given
+
+ align:start position:0%
+protection. And typically you're given
+ 
+
+ align:start position:0%
+protection. And typically you're given
+some information about the object. So
+
+ align:start position:0%
+some information about the object. So
+ 
+
+ align:start position:0%
+some information about the object. So
+typically you want to protect some
+
+ align:start position:0%
+typically you want to protect some
+ 
+
+ align:start position:0%
+typically you want to protect some
+object. It could be a computer. It could
+
+ align:start position:0%
+object. It could be a computer. It could
+ 
+
+ align:start position:0%
+object. It could be a computer. It could
+be your head, some part of your body.
+
+ align:start position:0%
+be your head, some part of your body.
+ 
+
+ align:start position:0%
+be your head, some part of your body.
+So, typically, you know something about
+
+ align:start position:0%
+So, typically, you know something about
+ 
+
+ align:start position:0%
+So, typically, you know something about
+the object you want to protect. So, you
+
+ align:start position:0%
+the object you want to protect. So, you
+ 
+
+ align:start position:0%
+the object you want to protect. So, you
+might know its mass. You might know the
+
+ align:start position:0%
+might know its mass. You might know the
+ 
+
+ align:start position:0%
+might know its mass. You might know the
+area of contact. You might say, well, if
+
+ align:start position:0%
+area of contact. You might say, well, if
+ 
+
+ align:start position:0%
+area of contact. You might say, well, if
+it's my computer, I want to make sure it
+
+ align:start position:0%
+it's my computer, I want to make sure it
+ 
+
+ align:start position:0%
+it's my computer, I want to make sure it
+doesn't break if I drop it from a height
+
+ align:start position:0%
+doesn't break if I drop it from a height
+ 
+
+ align:start position:0%
+doesn't break if I drop it from a height
+of a meter or, you know, you could say
+
+ align:start position:0%
+of a meter or, you know, you could say
+ 
+
+ align:start position:0%
+of a meter or, you know, you could say
+whatever it is, 2 meters, but you pick
+
+ align:start position:0%
+whatever it is, 2 meters, but you pick
+ 
+
+ align:start position:0%
+whatever it is, 2 meters, but you pick
+something. Uh, and so there's a certain
+
+ align:start position:0%
+something. Uh, and so there's a certain
+ 
+
+ align:start position:0%
+something. Uh, and so there's a certain
+amount of energy, you know, that you
+
+ align:start position:0%
+amount of energy, you know, that you
+ 
+
+ align:start position:0%
+amount of energy, you know, that you
+need to absorb. And you may know that
+
+ align:start position:0%
+need to absorb. And you may know that
+ 
+
+ align:start position:0%
+need to absorb. And you may know that
+the whatever the component is or the
+
+ align:start position:0%
+the whatever the component is or the
+ 
+
+ align:start position:0%
+the whatever the component is or the
+body part or whatever, there's some
+
+ align:start position:0%
+body part or whatever, there's some
+ 
+
+ align:start position:0%
+body part or whatever, there's some
+maximum acceleration you can tolerate.
+
+ align:start position:0%
+maximum acceleration you can tolerate.
+ 
+
+ align:start position:0%
+maximum acceleration you can tolerate.
+So you might say, well, I want to make
+
+ align:start position:0%
+So you might say, well, I want to make
+ 
+
+ align:start position:0%
+So you might say, well, I want to make
+sure my computer doesn't break under an
+
+ align:start position:0%
+sure my computer doesn't break under an
+ 
+
+ align:start position:0%
+sure my computer doesn't break under an
+acceleration of so much. So you're given
+
+ align:start position:0%
+acceleration of so much. So you're given
+ 
+
+ align:start position:0%
+acceleration of so much. So you're given
+the acceleration. Um, and so if you know
+
+ align:start position:0%
+the acceleration. Um, and so if you know
+ 
+
+ align:start position:0%
+the acceleration. Um, and so if you know
+the mass and the acceleration and you
+
+ align:start position:0%
+the mass and the acceleration and you
+ 
+
+ align:start position:0%
+the mass and the acceleration and you
+know the area of contact, you can figure
+
+ align:start position:0%
+know the area of contact, you can figure
+ 
+
+ align:start position:0%
+know the area of contact, you can figure
+out a force over an area and that gives
+
+ align:start position:0%
+out a force over an area and that gives
+ 
+
+ align:start position:0%
+out a force over an area and that gives
+you the peak stress. So typically you
+
+ align:start position:0%
+you the peak stress. So typically you
+ 
+
+ align:start position:0%
+you the peak stress. So typically you
+know those things in the problem and
+
+ align:start position:0%
+know those things in the problem and
+ 
+
+ align:start position:0%
+know those things in the problem and
+typically the problem involves choosing
+
+ align:start position:0%
+typically the problem involves choosing
+ 
+
+ align:start position:0%
+typically the problem involves choosing
+a material or choosing like choosing
+
+ align:start position:0%
+a material or choosing like choosing
+ 
+
+ align:start position:0%
+a material or choosing like choosing
+what kind of material do you want to
+
+ align:start position:0%
+what kind of material do you want to
+ 
+
+ align:start position:0%
+what kind of material do you want to
+make the foam out of, what density of
+
+ align:start position:0%
+make the foam out of, what density of
+ 
+
+ align:start position:0%
+make the foam out of, what density of
+foam do you want to use, what thickness
+
+ align:start position:0%
+foam do you want to use, what thickness
+ 
+
+ align:start position:0%
+foam do you want to use, what thickness
+of foam do you want to use. So, I've got
+
+ align:start position:0%
+of foam do you want to use. So, I've got
+ 
+
+ align:start position:0%
+of foam do you want to use. So, I've got
+a couple of examples uh just to show you
+
+ align:start position:0%
+a couple of examples uh just to show you
+ 
+
+ align:start position:0%
+a couple of examples uh just to show you
+how this works. So, uh let me just write
+
+ align:start position:0%
+how this works. So, uh let me just write
+ 
+
+ align:start position:0%
+how this works. So, uh let me just write
+down a couple notes and then the rest of
+
+ align:start position:0%
+down a couple notes and then the rest of
+ 
+
+ align:start position:0%
+down a couple notes and then the rest of
+it I think is I'm just going to take
+
+ align:start position:0%
+it I think is I'm just going to take
+ 
+
+ align:start position:0%
+it I think is I'm just going to take
+from the slides.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+So typically you know what it is you
+
+ align:start position:0%
+So typically you know what it is you
+ 
+
+ align:start position:0%
+So typically you know what it is you
+want to protect and you know something
+
+ align:start position:0%
+want to protect and you know something
+ 
+
+ align:start position:0%
+want to protect and you know something
+about it.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+So if you know what it is typically you
+
+ align:start position:0%
+So if you know what it is typically you
+ 
+
+ align:start position:0%
+So if you know what it is typically you
+know what the mass is.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Uh you might know what the contact area
+
+ align:start position:0%
+Uh you might know what the contact area
+ 
+
+ align:start position:0%
+Uh you might know what the contact area
+would be.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+say a maximum drop height,
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+maximum tolerable acceleration.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+So say if you're worried about brain
+
+ align:start position:0%
+So say if you're worried about brain
+ 
+
+ align:start position:0%
+So say if you're worried about brain
+injury and making a helmet, you might
+
+ align:start position:0%
+injury and making a helmet, you might
+ 
+
+ align:start position:0%
+injury and making a helmet, you might
+know what the maximum tolerable
+
+ align:start position:0%
+know what the maximum tolerable
+ 
+
+ align:start position:0%
+know what the maximum tolerable
+acceleration would be.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+So typically you know what the peak
+
+ align:start position:0%
+So typically you know what the peak
+ 
+
+ align:start position:0%
+So typically you know what the peak
+allowable stress is just from whatever
+
+ align:start position:0%
+allowable stress is just from whatever
+ 
+
+ align:start position:0%
+allowable stress is just from whatever
+the object itself is. And the variables
+
+ align:start position:0%
+the object itself is. And the variables
+ 
+
+ align:start position:0%
+the object itself is. And the variables
+that you have to play around with
+
+ align:start position:0%
+that you have to play around with
+ 
+
+ align:start position:0%
+that you have to play around with
+variables
+
+ align:start position:0%
+variables
+ 
+
+ align:start position:0%
+variables
+are things like the foam material
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the foam density
+
+ align:start position:0%
+the foam density
+ 
+
+ align:start position:0%
+the foam density
+and the foam thickness.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+So I have a couple of examples that have
+
+ align:start position:0%
+So I have a couple of examples that have
+ 
+
+ align:start position:0%
+So I have a couple of examples that have
+um sort of different setups here and
+
+ align:start position:0%
+um sort of different setups here and
+ 
+
+ align:start position:0%
+um sort of different setups here and
+we'll just see how the thing works out
+
+ align:start position:0%
+we'll just see how the thing works out
+ 
+
+ align:start position:0%
+we'll just see how the thing works out
+here. So the first example uh we're told
+
+ align:start position:0%
+here. So the first example uh we're told
+ 
+
+ align:start position:0%
+here. So the first example uh we're told
+the mass of the packaged object is half
+
+ align:start position:0%
+the mass of the packaged object is half
+ 
+
+ align:start position:0%
+the mass of the packaged object is half
+a kilogram. We're told the area of
+
+ align:start position:0%
+a kilogram. We're told the area of
+ 
+
+ align:start position:0%
+a kilogram. We're told the area of
+contact is between the foam and the
+
+ align:start position:0%
+contact is between the foam and the
+ 
+
+ align:start position:0%
+contact is between the foam and the
+object is going to be 0.01 of a meter
+
+ align:start position:0%
+object is going to be 0.01 of a meter
+ 
+
+ align:start position:0%
+object is going to be 0.01 of a meter
+squared. And we're told that it it's
+
+ align:start position:0%
+squared. And we're told that it it's
+ 
+
+ align:start position:0%
+squared. And we're told that it it's
+supposed to be designed to withstand a
+
+ align:start position:0%
+supposed to be designed to withstand a
+ 
+
+ align:start position:0%
+supposed to be designed to withstand a
+drop of 1 meter. So if the drop height
+
+ align:start position:0%
+drop of 1 meter. So if the drop height
+ 
+
+ align:start position:0%
+drop of 1 meter. So if the drop height
+is 1 meter, then the velocity is just
+
+ align:start position:0%
+is 1 meter, then the velocity is just
+ 
+
+ align:start position:0%
+is 1 meter, then the velocity is just
+the square<unk> of 2 GH. So G is
+
+ align:start position:0%
+the square<unk> of 2 GH. So G is
+ 
+
+ align:start position:0%
+the square<unk> of 2 GH. So G is
+gravity. So you can work out the
+
+ align:start position:0%
+gravity. So you can work out the
+ 
+
+ align:start position:0%
+gravity. So you can work out the
+velocity on impact would be 4.5 m/s. And
+
+ align:start position:0%
+velocity on impact would be 4.5 m/s. And
+ 
+
+ align:start position:0%
+velocity on impact would be 4.5 m/s. And
+if you have the velocity on impact and
+
+ align:start position:0%
+if you have the velocity on impact and
+ 
+
+ align:start position:0%
+if you have the velocity on impact and
+the mass, you can figure out the energy
+
+ align:start position:0%
+the mass, you can figure out the energy
+ 
+
+ align:start position:0%
+the mass, you can figure out the energy
+to be absorbed. You can say mv^2 over
+
+ align:start position:0%
+to be absorbed. You can say mv^2 over
+ 
+
+ align:start position:0%
+to be absorbed. You can say mv^2 over
+two or you could say it's mgh either
+
+ align:start position:0%
+two or you could say it's mgh either
+ 
+
+ align:start position:0%
+two or you could say it's mgh either
+way. So here it's going to work out to 5
+
+ align:start position:0%
+way. So here it's going to work out to 5
+ 
+
+ align:start position:0%
+way. So here it's going to work out to 5
+jewels.
+
+ align:start position:0%
+jewels.
+ 
+
+ align:start position:0%
+jewels.
+And in this case uh we're told that the
+
+ align:start position:0%
+And in this case uh we're told that the
+ 
+
+ align:start position:0%
+And in this case uh we're told that the
+uh the maximum deceleration is 10 g. So
+
+ align:start position:0%
+uh the maximum deceleration is 10 g. So
+ 
+
+ align:start position:0%
+uh the maximum deceleration is 10 g. So
+then if that's 10 g, the maximum force
+
+ align:start position:0%
+then if that's 10 g, the maximum force
+ 
+
+ align:start position:0%
+then if that's 10 g, the maximum force
+is the mass times the acceleration that
+
+ align:start position:0%
+is the mass times the acceleration that
+ 
+
+ align:start position:0%
+is the mass times the acceleration that
+we're set to 50 newtons. And then that
+
+ align:start position:0%
+we're set to 50 newtons. And then that
+ 
+
+ align:start position:0%
+we're set to 50 newtons. And then that
+gives us a peak stress. The maximum
+
+ align:start position:0%
+gives us a peak stress. The maximum
+ 
+
+ align:start position:0%
+gives us a peak stress. The maximum
+allowable peak stress of the force over
+
+ align:start position:0%
+allowable peak stress of the force over
+ 
+
+ align:start position:0%
+allowable peak stress of the force over
+the area is 5 kons per meter squared.
+
+ align:start position:0%
+the area is 5 kons per meter squared.
+ 
+
+ align:start position:0%
+the area is 5 kons per meter squared.
+And in this case, we're told that the
+
+ align:start position:0%
+And in this case, we're told that the
+ 
+
+ align:start position:0%
+And in this case, we're told that the
+foam is going to be a flexible
+
+ align:start position:0%
+foam is going to be a flexible
+ 
+
+ align:start position:0%
+foam is going to be a flexible
+polyurethane and it has a solid modulus
+
+ align:start position:0%
+polyurethane and it has a solid modulus
+ 
+
+ align:start position:0%
+polyurethane and it has a solid modulus
+of 50 megapascals. And so we can
+
+ align:start position:0%
+of 50 megapascals. And so we can
+ 
+
+ align:start position:0%
+of 50 megapascals. And so we can
+calculate this normalized peak stress.
+
+ align:start position:0%
+calculate this normalized peak stress.
+ 
+
+ align:start position:0%
+calculate this normalized peak stress.
+So the normalized peak stress here is
+
+ align:start position:0%
+So the normalized peak stress here is
+ 
+
+ align:start position:0%
+So the normalized peak stress here is
+10us4.
+
+ align:start position:0%
+10us4.
+ 
+
+ align:start position:0%
+10us4.
+So in this pro problem here, we need to
+
+ align:start position:0%
+So in this pro problem here, we need to
+ 
+
+ align:start position:0%
+So in this pro problem here, we need to
+figure out what's the foam density and
+
+ align:start position:0%
+figure out what's the foam density and
+ 
+
+ align:start position:0%
+figure out what's the foam density and
+what's the thickness of the foam to
+
+ align:start position:0%
+what's the thickness of the foam to
+ 
+
+ align:start position:0%
+what's the thickness of the foam to
+protect the object. And um so that the
+
+ align:start position:0%
+protect the object. And um so that the
+ 
+
+ align:start position:0%
+protect the object. And um so that the
+last slide is just sum summarized here.
+
+ align:start position:0%
+last slide is just sum summarized here.
+ 
+
+ align:start position:0%
+last slide is just sum summarized here.
+And I realized that when I was going to
+
+ align:start position:0%
+And I realized that when I was going to
+ 
+
+ align:start position:0%
+And I realized that when I was going to
+put this up, the font is going to be
+
+ align:start position:0%
+put this up, the font is going to be
+ 
+
+ align:start position:0%
+put this up, the font is going to be
+kind of small. So I blew it up a little.
+
+ align:start position:0%
+kind of small. So I blew it up a little.
+ 
+
+ align:start position:0%
+kind of small. So I blew it up a little.
+So we have figured out that we're at
+
+ align:start position:0%
+So we have figured out that we're at
+ 
+
+ align:start position:0%
+So we have figured out that we're at
+sigma P over ES. The peak stress
+
+ align:start position:0%
+sigma P over ES. The peak stress
+ 
+
+ align:start position:0%
+sigma P over ES. The peak stress
+normalized by the solid modulus is 10
+
+ align:start position:0%
+normalized by the solid modulus is 10
+ 
+
+ align:start position:0%
+normalized by the solid modulus is 10
+the minus 4. And we know that we're
+
+ align:start position:0%
+the minus 4. And we know that we're
+ 
+
+ align:start position:0%
+the minus 4. And we know that we're
+going to use a flexible elastoic
+
+ align:start position:0%
+going to use a flexible elastoic
+ 
+
+ align:start position:0%
+going to use a flexible elastoic
+polyurethane. So we pull out our diagram
+
+ align:start position:0%
+polyurethane. So we pull out our diagram
+ 
+
+ align:start position:0%
+polyurethane. So we pull out our diagram
+for elastoic foams. And this sort of
+
+ align:start position:0%
+for elastoic foams. And this sort of
+ 
+
+ align:start position:0%
+for elastoic foams. And this sort of
+hashed band here corresponds to all the
+
+ align:start position:0%
+hashed band here corresponds to all the
+ 
+
+ align:start position:0%
+hashed band here corresponds to all the
+different strain rates and all the
+
+ align:start position:0%
+different strain rates and all the
+ 
+
+ align:start position:0%
+different strain rates and all the
+different densities. So I haven't
+
+ align:start position:0%
+different densities. So I haven't
+ 
+
+ align:start position:0%
+different densities. So I haven't
+plotted each individual line. We've just
+
+ align:start position:0%
+plotted each individual line. We've just
+ 
+
+ align:start position:0%
+plotted each individual line. We've just
+got this kind of band that represents
+
+ align:start position:0%
+got this kind of band that represents
+ 
+
+ align:start position:0%
+got this kind of band that represents
+the whole thing. So we know that our
+
+ align:start position:0%
+the whole thing. So we know that our
+ 
+
+ align:start position:0%
+the whole thing. So we know that our
+normalized peak stress is going to be
+
+ align:start position:0%
+normalized peak stress is going to be
+ 
+
+ align:start position:0%
+normalized peak stress is going to be
+somewhere along this line here. Okay,
+
+ align:start position:0%
+somewhere along this line here. Okay,
+ 
+
+ align:start position:0%
+somewhere along this line here. Okay,
+that's that's from everything that's
+
+ align:start position:0%
+that's that's from everything that's
+ 
+
+ align:start position:0%
+that's that's from everything that's
+given and what we can calculate. And we
+
+ align:start position:0%
+given and what we can calculate. And we
+ 
+
+ align:start position:0%
+given and what we can calculate. And we
+want to know what density of foam to use
+
+ align:start position:0%
+want to know what density of foam to use
+ 
+
+ align:start position:0%
+want to know what density of foam to use
+and what thickness. So the way you
+
+ align:start position:0%
+and what thickness. So the way you
+ 
+
+ align:start position:0%
+and what thickness. So the way you
+approach this is the thickness is going
+
+ align:start position:0%
+approach this is the thickness is going
+ 
+
+ align:start position:0%
+approach this is the thickness is going
+to affect the strain rate. So the strain
+
+ align:start position:0%
+to affect the strain rate. So the strain
+ 
+
+ align:start position:0%
+to affect the strain rate. So the strain
+rate is just going to be the velocity on
+
+ align:start position:0%
+rate is just going to be the velocity on
+ 
+
+ align:start position:0%
+rate is just going to be the velocity on
+impact divided by the thickness or it's
+
+ align:start position:0%
+impact divided by the thickness or it's
+ 
+
+ align:start position:0%
+impact divided by the thickness or it's
+an approximation for the strain rate. So
+
+ align:start position:0%
+an approximation for the strain rate. So
+ 
+
+ align:start position:0%
+an approximation for the strain rate. So
+we don't know if we're sort of at this
+
+ align:start position:0%
+we don't know if we're sort of at this
+ 
+
+ align:start position:0%
+we don't know if we're sort of at this
+point down here or if we're at this
+
+ align:start position:0%
+point down here or if we're at this
+ 
+
+ align:start position:0%
+point down here or if we're at this
+point up there because we don't know
+
+ align:start position:0%
+point up there because we don't know
+ 
+
+ align:start position:0%
+point up there because we don't know
+where we are in the strain rate end of
+
+ align:start position:0%
+where we are in the strain rate end of
+ 
+
+ align:start position:0%
+where we are in the strain rate end of
+things. So the way you solve this is you
+
+ align:start position:0%
+things. So the way you solve this is you
+ 
+
+ align:start position:0%
+things. So the way you solve this is you
+just guess a thickness. And if you guess
+
+ align:start position:0%
+just guess a thickness. And if you guess
+ 
+
+ align:start position:0%
+just guess a thickness. And if you guess
+a thickness, you can calculate a strain
+
+ align:start position:0%
+a thickness, you can calculate a strain
+ 
+
+ align:start position:0%
+a thickness, you can calculate a strain
+rate. Then if you calculate the strain
+
+ align:start position:0%
+rate. Then if you calculate the strain
+ 
+
+ align:start position:0%
+rate. Then if you calculate the strain
+rate, you know where in this band you
+
+ align:start position:0%
+rate, you know where in this band you
+ 
+
+ align:start position:0%
+rate, you know where in this band you
+are. You can figure out a value of w
+
+ align:start position:0%
+are. You can figure out a value of w
+ 
+
+ align:start position:0%
+are. You can figure out a value of w
+over es. And you can use an iterative
+
+ align:start position:0%
+over es. And you can use an iterative
+ 
+
+ align:start position:0%
+over es. And you can use an iterative
+process. And the way this is set up is
+
+ align:start position:0%
+process. And the way this is set up is
+ 
+
+ align:start position:0%
+process. And the way this is set up is
+we've chosen two very different initial
+
+ align:start position:0%
+we've chosen two very different initial
+ 
+
+ align:start position:0%
+we've chosen two very different initial
+thicknesses. And the point of doing that
+
+ align:start position:0%
+thicknesses. And the point of doing that
+ 
+
+ align:start position:0%
+thicknesses. And the point of doing that
+is to show you that it converges very
+
+ align:start position:0%
+is to show you that it converges very
+ 
+
+ align:start position:0%
+is to show you that it converges very
+quickly. So the first iteration on this
+
+ align:start position:0%
+quickly. So the first iteration on this
+ 
+
+ align:start position:0%
+quickly. So the first iteration on this
+side here, we've chosen a thickness of a
+
+ align:start position:0%
+side here, we've chosen a thickness of a
+ 
+
+ align:start position:0%
+side here, we've chosen a thickness of a
+meter, which is probably unlikely that
+
+ align:start position:0%
+meter, which is probably unlikely that
+ 
+
+ align:start position:0%
+meter, which is probably unlikely that
+we need a meter of foam. And on this
+
+ align:start position:0%
+we need a meter of foam. And on this
+ 
+
+ align:start position:0%
+we need a meter of foam. And on this
+side here, we've chosen a millimeter,
+
+ align:start position:0%
+side here, we've chosen a millimeter,
+ 
+
+ align:start position:0%
+side here, we've chosen a millimeter,
+0.001 meters. So probably we need more
+
+ align:start position:0%
+0.001 meters. So probably we need more
+ 
+
+ align:start position:0%
+0.001 meters. So probably we need more
+than that. So we probably need to be
+
+ align:start position:0%
+than that. So we probably need to be
+ 
+
+ align:start position:0%
+than that. So we probably need to be
+somewhere between those two bounds. So
+
+ align:start position:0%
+somewhere between those two bounds. So
+ 
+
+ align:start position:0%
+somewhere between those two bounds. So
+if the thickness was a meter, then the
+
+ align:start position:0%
+if the thickness was a meter, then the
+ 
+
+ align:start position:0%
+if the thickness was a meter, then the
+strain rate turns out to be 4.5 per
+
+ align:start position:0%
+strain rate turns out to be 4.5 per
+ 
+
+ align:start position:0%
+strain rate turns out to be 4.5 per
+second. And then we know where we are on
+
+ align:start position:0%
+second. And then we know where we are on
+ 
+
+ align:start position:0%
+second. And then we know where we are on
+this diagram. And we can read off a
+
+ align:start position:0%
+this diagram. And we can read off a
+ 
+
+ align:start position:0%
+this diagram. And we can read off a
+value of W over ES. So we know we're on
+
+ align:start position:0%
+value of W over ES. So we know we're on
+ 
+
+ align:start position:0%
+value of W over ES. So we know we're on
+this line here. And for a particular
+
+ align:start position:0%
+this line here. And for a particular
+ 
+
+ align:start position:0%
+this line here. And for a particular
+strain rate, we can read off the W over
+
+ align:start position:0%
+strain rate, we can read off the W over
+ 
+
+ align:start position:0%
+strain rate, we can read off the W over
+ES. So here's the value 5.25* 10us 5.
+
+ align:start position:0%
+ES. So here's the value 5.25* 10us 5.
+ 
+
+ align:start position:0%
+ES. So here's the value 5.25* 10us 5.
+And if we know ES which we do, we can
+
+ align:start position:0%
+And if we know ES which we do, we can
+ 
+
+ align:start position:0%
+And if we know ES which we do, we can
+then u calculate the actual energy
+
+ align:start position:0%
+then u calculate the actual energy
+ 
+
+ align:start position:0%
+then u calculate the actual energy
+absorbed per unit volume and get W. So
+
+ align:start position:0%
+absorbed per unit volume and get W. So
+ 
+
+ align:start position:0%
+absorbed per unit volume and get W. So
+W's 2620 JUW per cubic meter and we can
+
+ align:start position:0%
+W's 2620 JUW per cubic meter and we can
+ 
+
+ align:start position:0%
+W's 2620 JUW per cubic meter and we can
+use that value that's an energy per unit
+
+ align:start position:0%
+use that value that's an energy per unit
+ 
+
+ align:start position:0%
+use that value that's an energy per unit
+volume. We know the area of contact and
+
+ align:start position:0%
+volume. We know the area of contact and
+ 
+
+ align:start position:0%
+volume. We know the area of contact and
+we can use that to get another value of
+
+ align:start position:0%
+we can use that to get another value of
+ 
+
+ align:start position:0%
+we can use that to get another value of
+the thickness. So we we use that to
+
+ align:start position:0%
+the thickness. So we we use that to
+ 
+
+ align:start position:0%
+the thickness. So we we use that to
+calculate the next iteration of the
+
+ align:start position:0%
+calculate the next iteration of the
+ 
+
+ align:start position:0%
+calculate the next iteration of the
+thickness. So U is the total energy in
+
+ align:start position:0%
+thickness. So U is the total energy in
+ 
+
+ align:start position:0%
+thickness. So U is the total energy in
+jewels and W is the energy per unit
+
+ align:start position:0%
+jewels and W is the energy per unit
+ 
+
+ align:start position:0%
+jewels and W is the energy per unit
+volume. So u the energy in jewels is
+
+ align:start position:0%
+volume. So u the energy in jewels is
+ 
+
+ align:start position:0%
+volume. So u the energy in jewels is
+going to equal the energy unit volume
+
+ align:start position:0%
+going to equal the energy unit volume
+ 
+
+ align:start position:0%
+going to equal the energy unit volume
+time the area time the thickness. So we
+
+ align:start position:0%
+time the area time the thickness. So we
+ 
+
+ align:start position:0%
+time the area time the thickness. So we
+know what the area is 2. We can then
+
+ align:start position:0%
+know what the area is 2. We can then
+ 
+
+ align:start position:0%
+know what the area is 2. We can then
+calculate a new thickness. So now our
+
+ align:start position:0%
+calculate a new thickness. So now our
+ 
+
+ align:start position:0%
+calculate a new thickness. So now our
+new thickness is.19 m. We can use that
+
+ align:start position:0%
+new thickness is.19 m. We can use that
+ 
+
+ align:start position:0%
+new thickness is.19 m. We can use that
+to get a new strain rate that's 24/
+
+ align:start position:0%
+to get a new strain rate that's 24/
+ 
+
+ align:start position:0%
+to get a new strain rate that's 24/
+And go through the whole thing again and
+
+ align:start position:0%
+And go through the whole thing again and
+ 
+
+ align:start position:0%
+And go through the whole thing again and
+we end up with a revised energy of 3300
+
+ align:start position:0%
+we end up with a revised energy of 3300
+ 
+
+ align:start position:0%
+we end up with a revised energy of 3300
+jew peric meter. Now if we started at
+
+ align:start position:0%
+jew peric meter. Now if we started at
+ 
+
+ align:start position:0%
+jew peric meter. Now if we started at
+the other end if we started with the
+
+ align:start position:0%
+the other end if we started with the
+ 
+
+ align:start position:0%
+the other end if we started with the
+first guess was a millimeter
+
+ align:start position:0%
+first guess was a millimeter
+ 
+
+ align:start position:0%
+first guess was a millimeter
+then the strain rate is 4.5 * 10us 3/s
+
+ align:start position:0%
+then the strain rate is 4.5 * 10us 3/s
+ 
+
+ align:start position:0%
+then the strain rate is 4.5 * 10us 3/s
+uh that gives us a different value that
+
+ align:start position:0%
+uh that gives us a different value that
+ 
+
+ align:start position:0%
+uh that gives us a different value that
+we read off here for w over es and a
+
+ align:start position:0%
+we read off here for w over es and a
+ 
+
+ align:start position:0%
+we read off here for w over es and a
+different value for w and then we use
+
+ align:start position:0%
+different value for w and then we use
+ 
+
+ align:start position:0%
+different value for w and then we use
+this value here for w to make another
+
+ align:start position:0%
+this value here for w to make another
+ 
+
+ align:start position:0%
+this value here for w to make another
+guess for the thickness. So that value
+
+ align:start position:0%
+guess for the thickness. So that value
+ 
+
+ align:start position:0%
+guess for the thickness. So that value
+is 0.14. And then we go through the
+
+ align:start position:0%
+is 0.14. And then we go through the
+ 
+
+ align:start position:0%
+is 0.14. And then we go through the
+whole thing again. We get a revised
+
+ align:start position:0%
+whole thing again. We get a revised
+ 
+
+ align:start position:0%
+whole thing again. We get a revised
+strain rate, a revised W over ES and a
+
+ align:start position:0%
+strain rate, a revised W over ES and a
+ 
+
+ align:start position:0%
+strain rate, a revised W over ES and a
+revised W. And you can see after just
+
+ align:start position:0%
+revised W. And you can see after just
+ 
+
+ align:start position:0%
+revised W. And you can see after just
+two iterations, these two things are
+
+ align:start position:0%
+two iterations, these two things are
+ 
+
+ align:start position:0%
+two iterations, these two things are
+almost exactly the same. And then on the
+
+ align:start position:0%
+almost exactly the same. And then on the
+ 
+
+ align:start position:0%
+almost exactly the same. And then on the
+third iteration, they both would give
+
+ align:start position:0%
+third iteration, they both would give
+ 
+
+ align:start position:0%
+third iteration, they both would give
+you a thickness of 0.15 m. Okay? So even
+
+ align:start position:0%
+you a thickness of 0.15 m. Okay? So even
+ 
+
+ align:start position:0%
+you a thickness of 0.15 m. Okay? So even
+though you can pick, you know, wildly
+
+ align:start position:0%
+though you can pick, you know, wildly
+ 
+
+ align:start position:0%
+though you can pick, you know, wildly
+wrong first iterations, it it converges
+
+ align:start position:0%
+wrong first iterations, it it converges
+ 
+
+ align:start position:0%
+wrong first iterations, it it converges
+very quickly. And it's sort of a fairly
+
+ align:start position:0%
+very quickly. And it's sort of a fairly
+ 
+
+ align:start position:0%
+very quickly. And it's sort of a fairly
+simple calculation to do. Um so you know
+
+ align:start position:0%
+simple calculation to do. Um so you know
+ 
+
+ align:start position:0%
+simple calculation to do. Um so you know
+the thickness that you want is in here
+
+ align:start position:0%
+the thickness that you want is in here
+ 
+
+ align:start position:0%
+the thickness that you want is in here
+and then you can get the optimum density
+
+ align:start position:0%
+and then you can get the optimum density
+ 
+
+ align:start position:0%
+and then you can get the optimum density
+here. So you know uh that your sigma P
+
+ align:start position:0%
+here. So you know uh that your sigma P
+ 
+
+ align:start position:0%
+here. So you know uh that your sigma P
+over ES is along this line of 10us 4
+
+ align:start position:0%
+over ES is along this line of 10us 4
+ 
+
+ align:start position:0%
+over ES is along this line of 10us 4
+were somewhere in here. Uh these two
+
+ align:start position:0%
+were somewhere in here. Uh these two
+ 
+
+ align:start position:0%
+were somewhere in here. Uh these two
+strain rates here one was 24 one was 32.
+
+ align:start position:0%
+strain rates here one was 24 one was 32.
+ 
+
+ align:start position:0%
+strain rates here one was 24 one was 32.
+So the the final value is going to be
+
+ align:start position:0%
+So the the final value is going to be
+ 
+
+ align:start position:0%
+So the the final value is going to be
+somewhere around 30. And if you look on
+
+ align:start position:0%
+somewhere around 30. And if you look on
+ 
+
+ align:start position:0%
+somewhere around 30. And if you look on
+this thing here you can see there's a
+
+ align:start position:0%
+this thing here you can see there's a
+ 
+
+ align:start position:0%
+this thing here you can see there's a
+line that corresponds to 10 there's a
+
+ align:start position:0%
+line that corresponds to 10 there's a
+ 
+
+ align:start position:0%
+line that corresponds to 10 there's a
+line that corresponds to 100. We're
+
+ align:start position:0%
+line that corresponds to 100. We're
+ 
+
+ align:start position:0%
+line that corresponds to 100. We're
+going to be right around in there. So
+
+ align:start position:0%
+going to be right around in there. So
+ 
+
+ align:start position:0%
+going to be right around in there. So
+the relative density is going to be
+
+ align:start position:0%
+the relative density is going to be
+ 
+
+ align:start position:0%
+the relative density is going to be
+right around 0.01. Okay. So you can use
+
+ align:start position:0%
+right around 0.01. Okay. So you can use
+ 
+
+ align:start position:0%
+right around 0.01. Okay. So you can use
+the diagram to get the thickness and to
+
+ align:start position:0%
+the diagram to get the thickness and to
+ 
+
+ align:start position:0%
+the diagram to get the thickness and to
+get the density. Okay. Are we good?
+
+ align:start position:0%
+get the density. Okay. Are we good?
+ 
+
+ align:start position:0%
+get the density. Okay. Are we good?
+We're good. Okay. Um so I've written
+
+ align:start position:0%
+We're good. Okay. Um so I've written
+ 
+
+ align:start position:0%
+We're good. Okay. Um so I've written
+some notes and I'll just scan those and
+
+ align:start position:0%
+some notes and I'll just scan those and
+ 
+
+ align:start position:0%
+some notes and I'll just scan those and
+I'll put them in the stellar site.
+
+ align:start position:0%
+I'll put them in the stellar site.
+ 
+
+ align:start position:0%
+I'll put them in the stellar site.
+Uh so here's another example here. And
+
+ align:start position:0%
+Uh so here's another example here. And
+ 
+
+ align:start position:0%
+Uh so here's another example here. And
+in this example it's set up a little bit
+
+ align:start position:0%
+in this example it's set up a little bit
+ 
+
+ align:start position:0%
+in this example it's set up a little bit
+differently. So in this example here, uh
+
+ align:start position:0%
+differently. So in this example here, uh
+ 
+
+ align:start position:0%
+differently. So in this example here, uh
+we're not told the material, but we're
+
+ align:start position:0%
+we're not told the material, but we're
+ 
+
+ align:start position:0%
+we're not told the material, but we're
+told the thickness of the foam. So this
+
+ align:start position:0%
+told the thickness of the foam. So this
+ 
+
+ align:start position:0%
+told the thickness of the foam. So this
+time we want to get the material and we
+
+ align:start position:0%
+time we want to get the material and we
+ 
+
+ align:start position:0%
+time we want to get the material and we
+want to get the density of the foam. So
+
+ align:start position:0%
+want to get the density of the foam. So
+ 
+
+ align:start position:0%
+want to get the density of the foam. So
+here we've got um the specification.
+
+ align:start position:0%
+here we've got um the specification.
+ 
+
+ align:start position:0%
+here we've got um the specification.
+We're told the mass is 2 1/2 kg. The
+
+ align:start position:0%
+We're told the mass is 2 1/2 kg. The
+ 
+
+ align:start position:0%
+We're told the mass is 2 1/2 kg. The
+area of contact is 0025 m squared. We're
+
+ align:start position:0%
+area of contact is 0025 m squared. We're
+ 
+
+ align:start position:0%
+area of contact is 0025 m squared. We're
+told the thickness here. The thickness
+
+ align:start position:0%
+told the thickness here. The thickness
+ 
+
+ align:start position:0%
+told the thickness here. The thickness
+is 20 mm. We've got a drop height of 1
+
+ align:start position:0%
+is 20 mm. We've got a drop height of 1
+ 
+
+ align:start position:0%
+is 20 mm. We've got a drop height of 1
+meter again. The velocity of impact is
+
+ align:start position:0%
+meter again. The velocity of impact is
+ 
+
+ align:start position:0%
+meter again. The velocity of impact is
+then going to be 4.5 m/s again. And
+
+ align:start position:0%
+then going to be 4.5 m/s again. And
+ 
+
+ align:start position:0%
+then going to be 4.5 m/s again. And
+since we know t, we know that the strain
+
+ align:start position:0%
+since we know t, we know that the strain
+ 
+
+ align:start position:0%
+since we know t, we know that the strain
+rate is going to be around 225 per
+
+ align:start position:0%
+rate is going to be around 225 per
+ 
+
+ align:start position:0%
+rate is going to be around 225 per
+second. Okay.
+
+ align:start position:0%
+second. Okay.
+ 
+
+ align:start position:0%
+second. Okay.
+Uh we can calculate the energy absorbed
+
+ align:start position:0%
+Uh we can calculate the energy absorbed
+ 
+
+ align:start position:0%
+Uh we can calculate the energy absorbed
+mgh uh 25 jewels. Uh we can calculate
+
+ align:start position:0%
+mgh uh 25 jewels. Uh we can calculate
+ 
+
+ align:start position:0%
+mgh uh 25 jewels. Uh we can calculate
+the energy absorbed per unit volume
+
+ align:start position:0%
+the energy absorbed per unit volume
+ 
+
+ align:start position:0%
+the energy absorbed per unit volume
+because we've got the area and the
+
+ align:start position:0%
+because we've got the area and the
+ 
+
+ align:start position:0%
+because we've got the area and the
+thickness. So we just divide that by the
+
+ align:start position:0%
+thickness. So we just divide that by the
+ 
+
+ align:start position:0%
+thickness. So we just divide that by the
+area and the thickness. And we have 5 or
+
+ align:start position:0%
+area and the thickness. And we have 5 or
+ 
+
+ align:start position:0%
+area and the thickness. And we have 5 or
+5 * 10 4th jewels per cubic meter. And
+
+ align:start position:0%
+5 * 10 4th jewels per cubic meter. And
+ 
+
+ align:start position:0%
+5 * 10 4th jewels per cubic meter. And
+we're told that we're supposed to design
+
+ align:start position:0%
+we're told that we're supposed to design
+ 
+
+ align:start position:0%
+we're told that we're supposed to design
+it so the package can withstand a
+
+ align:start position:0%
+it so the package can withstand a
+ 
+
+ align:start position:0%
+it so the package can withstand a
+deceleration of 100 g. And so that gives
+
+ align:start position:0%
+deceleration of 100 g. And so that gives
+ 
+
+ align:start position:0%
+deceleration of 100 g. And so that gives
+you a maximum force. And here we've got
+
+ align:start position:0%
+you a maximum force. And here we've got
+ 
+
+ align:start position:0%
+you a maximum force. And here we've got
+a maximum allowable peak stress of 10 5
+
+ align:start position:0%
+a maximum allowable peak stress of 10 5
+ 
+
+ align:start position:0%
+a maximum allowable peak stress of 10 5
+newtons per meter squared. So here we
+
+ align:start position:0%
+newtons per meter squared. So here we
+ 
+
+ align:start position:0%
+newtons per meter squared. So here we
+have our curve for the elastic foams.
+
+ align:start position:0%
+have our curve for the elastic foams.
+ 
+
+ align:start position:0%
+have our curve for the elastic foams.
+Again, let's assume it's going to be an
+
+ align:start position:0%
+Again, let's assume it's going to be an
+ 
+
+ align:start position:0%
+Again, let's assume it's going to be an
+elastic foam, but we don't know what
+
+ align:start position:0%
+elastic foam, but we don't know what
+ 
+
+ align:start position:0%
+elastic foam, but we don't know what
+kind of foam.
+
+ align:start position:0%
+kind of foam.
+ 
+
+ align:start position:0%
+kind of foam.
+So the way you solve this problem is
+
+ align:start position:0%
+So the way you solve this problem is
+ 
+
+ align:start position:0%
+So the way you solve this problem is
+that you make a guess for what ES is. So
+
+ align:start position:0%
+that you make a guess for what ES is. So
+ 
+
+ align:start position:0%
+that you make a guess for what ES is. So
+remember these diagrams are all
+
+ align:start position:0%
+remember these diagrams are all
+ 
+
+ align:start position:0%
+remember these diagrams are all
+normalized by ES. So to plot a point on
+
+ align:start position:0%
+normalized by ES. So to plot a point on
+ 
+
+ align:start position:0%
+normalized by ES. So to plot a point on
+there, we need to know what ES is. So
+
+ align:start position:0%
+there, we need to know what ES is. So
+ 
+
+ align:start position:0%
+there, we need to know what ES is. So
+here we're going to make a guess and
+
+ align:start position:0%
+here we're going to make a guess and
+ 
+
+ align:start position:0%
+here we're going to make a guess and
+we're going to assume that ES is 100
+
+ align:start position:0%
+we're going to assume that ES is 100
+ 
+
+ align:start position:0%
+we're going to assume that ES is 100
+megapascals to start. And if we had that
+
+ align:start position:0%
+megapascals to start. And if we had that
+ 
+
+ align:start position:0%
+megapascals to start. And if we had that
+value of ES, we know W up here and we
+
+ align:start position:0%
+value of ES, we know W up here and we
+ 
+
+ align:start position:0%
+value of ES, we know W up here and we
+know sigma P there. So we just divide
+
+ align:start position:0%
+know sigma P there. So we just divide
+ 
+
+ align:start position:0%
+know sigma P there. So we just divide
+those values of W and sigma P by ES and
+
+ align:start position:0%
+those values of W and sigma P by ES and
+ 
+
+ align:start position:0%
+those values of W and sigma P by ES and
+we get these two values here and we plot
+
+ align:start position:0%
+we get these two values here and we plot
+ 
+
+ align:start position:0%
+we get these two values here and we plot
+those two values on the thing here. So
+
+ align:start position:0%
+those two values on the thing here. So
+ 
+
+ align:start position:0%
+those two values on the thing here. So
+here's our point A and that corresponds
+
+ align:start position:0%
+here's our point A and that corresponds
+ 
+
+ align:start position:0%
+here's our point A and that corresponds
+to that first guess of 100 megapascals
+
+ align:start position:0%
+to that first guess of 100 megapascals
+ 
+
+ align:start position:0%
+to that first guess of 100 megapascals
+for the modulus of the solid. So that's
+
+ align:start position:0%
+for the modulus of the solid. So that's
+ 
+
+ align:start position:0%
+for the modulus of the solid. So that's
+that's not necessarily the final answer.
+
+ align:start position:0%
+that's not necessarily the final answer.
+ 
+
+ align:start position:0%
+that's not necessarily the final answer.
+That's not the right answer. That's just
+
+ align:start position:0%
+That's not the right answer. That's just
+ 
+
+ align:start position:0%
+That's not the right answer. That's just
+somewhere to start. So the thing to
+
+ align:start position:0%
+somewhere to start. So the thing to
+ 
+
+ align:start position:0%
+somewhere to start. So the thing to
+notice is if we have that point there,
+
+ align:start position:0%
+notice is if we have that point there,
+ 
+
+ align:start position:0%
+notice is if we have that point there,
+um the strain rate there is probably not
+
+ align:start position:0%
+um the strain rate there is probably not
+ 
+
+ align:start position:0%
+um the strain rate there is probably not
+quite right. This upper bound here is um
+
+ align:start position:0%
+quite right. This upper bound here is um
+ 
+
+ align:start position:0%
+quite right. This upper bound here is um
+let's see got to get closer. Oh, let's
+
+ align:start position:0%
+let's see got to get closer. Oh, let's
+ 
+
+ align:start position:0%
+let's see got to get closer. Oh, let's
+see. That's 10 to the minus two. That's
+
+ align:start position:0%
+see. That's 10 to the minus two. That's
+ 
+
+ align:start position:0%
+see. That's 10 to the minus two. That's
+10 to the two. So the strain rate we
+
+ align:start position:0%
+10 to the two. So the strain rate we
+ 
+
+ align:start position:0%
+10 to the two. So the strain rate we
+want to be is closer up to here. It's
+
+ align:start position:0%
+want to be is closer up to here. It's
+ 
+
+ align:start position:0%
+want to be is closer up to here. It's
+not quite down there. Um, so we're not
+
+ align:start position:0%
+not quite down there. Um, so we're not
+ 
+
+ align:start position:0%
+not quite down there. Um, so we're not
+at the right strain rate. But the thing
+
+ align:start position:0%
+at the right strain rate. But the thing
+ 
+
+ align:start position:0%
+at the right strain rate. But the thing
+to notice is that if we draw a line of
+
+ align:start position:0%
+to notice is that if we draw a line of
+ 
+
+ align:start position:0%
+to notice is that if we draw a line of
+slope one, so there's this dashed line
+
+ align:start position:0%
+slope one, so there's this dashed line
+ 
+
+ align:start position:0%
+slope one, so there's this dashed line
+of slope one. When we move up and down
+
+ align:start position:0%
+of slope one. When we move up and down
+ 
+
+ align:start position:0%
+of slope one. When we move up and down
+that line, we're just changing ES,
+
+ align:start position:0%
+that line, we're just changing ES,
+ 
+
+ align:start position:0%
+that line, we're just changing ES,
+right? Because everything's normalized
+
+ align:start position:0%
+right? Because everything's normalized
+ 
+
+ align:start position:0%
+right? Because everything's normalized
+with respect to ES. If that line has a
+
+ align:start position:0%
+with respect to ES. If that line has a
+ 
+
+ align:start position:0%
+with respect to ES. If that line has a
+slope of one, then we're just kind of
+
+ align:start position:0%
+slope of one, then we're just kind of
+ 
+
+ align:start position:0%
+slope of one, then we're just kind of
+moving up and down with respect to ES.
+
+ align:start position:0%
+moving up and down with respect to ES.
+ 
+
+ align:start position:0%
+moving up and down with respect to ES.
+So what we do is we scoot up the line to
+
+ align:start position:0%
+So what we do is we scoot up the line to
+ 
+
+ align:start position:0%
+So what we do is we scoot up the line to
+get to the point that's on the uh right
+
+ align:start position:0%
+get to the point that's on the uh right
+ 
+
+ align:start position:0%
+get to the point that's on the uh right
+strain rate. So if this is a strain rate
+
+ align:start position:0%
+strain rate. So if this is a strain rate
+ 
+
+ align:start position:0%
+strain rate. So if this is a strain rate
+of 100 or around 200, we want to be at
+
+ align:start position:0%
+of 100 or around 200, we want to be at
+ 
+
+ align:start position:0%
+of 100 or around 200, we want to be at
+point B. And then from point B, we can
+
+ align:start position:0%
+point B. And then from point B, we can
+ 
+
+ align:start position:0%
+point B. And then from point B, we can
+read off what's the value of W over ES
+
+ align:start position:0%
+read off what's the value of W over ES
+ 
+
+ align:start position:0%
+read off what's the value of W over ES
+and sigma P over ES. And from that, we
+
+ align:start position:0%
+and sigma P over ES. And from that, we
+ 
+
+ align:start position:0%
+and sigma P over ES. And from that, we
+can back out what the solid modulus we
+
+ align:start position:0%
+can back out what the solid modulus we
+ 
+
+ align:start position:0%
+can back out what the solid modulus we
+want is. So these are the values that we
+
+ align:start position:0%
+want is. So these are the values that we
+ 
+
+ align:start position:0%
+want is. So these are the values that we
+read off the chart. This gives us an ES
+
+ align:start position:0%
+read off the chart. This gives us an ES
+ 
+
+ align:start position:0%
+read off the chart. This gives us an ES
+of 28 megapascals. And again, you can go
+
+ align:start position:0%
+of 28 megapascals. And again, you can go
+ 
+
+ align:start position:0%
+of 28 megapascals. And again, you can go
+to this more detailed diagram here. And
+
+ align:start position:0%
+to this more detailed diagram here. And
+ 
+
+ align:start position:0%
+to this more detailed diagram here. And
+if you read off the sigma P over ES and
+
+ align:start position:0%
+if you read off the sigma P over ES and
+ 
+
+ align:start position:0%
+if you read off the sigma P over ES and
+the W over E S, the density you want is
+
+ align:start position:0%
+the W over E S, the density you want is
+ 
+
+ align:start position:0%
+the W over E S, the density you want is
+about 0.1. So it tells you the modulus
+
+ align:start position:0%
+about 0.1. So it tells you the modulus
+ 
+
+ align:start position:0%
+about 0.1. So it tells you the modulus
+of the solid and from that you can pick
+
+ align:start position:0%
+of the solid and from that you can pick
+ 
+
+ align:start position:0%
+of the solid and from that you can pick
+a solid and it tells you the density.
+
+ align:start position:0%
+a solid and it tells you the density.
+ 
+
+ align:start position:0%
+a solid and it tells you the density.
+Okay. Are we good? No. Okay. So I have
+
+ align:start position:0%
+Okay. Are we good? No. Okay. So I have
+ 
+
+ align:start position:0%
+Okay. Are we good? No. Okay. So I have
+one more. So there's there's a slightly
+
+ align:start position:0%
+one more. So there's there's a slightly
+ 
+
+ align:start position:0%
+one more. So there's there's a slightly
+different way you can do it too. Um so
+
+ align:start position:0%
+different way you can do it too. Um so
+ 
+
+ align:start position:0%
+different way you can do it too. Um so
+now I want to talk about bicycle
+
+ align:start position:0%
+now I want to talk about bicycle
+ 
+
+ align:start position:0%
+now I want to talk about bicycle
+helmets. Who's not you're my bicycle
+
+ align:start position:0%
+helmets. Who's not you're my bicycle
+ 
+
+ align:start position:0%
+helmets. Who's not you're my bicycle
+helmet person?
+
+ align:start position:0%
+helmet person?
+ 
+
+ align:start position:0%
+helmet person?
+So um so this is another little case
+
+ align:start position:0%
+So um so this is another little case
+ 
+
+ align:start position:0%
+So um so this is another little case
+study that involves a slightly different
+
+ align:start position:0%
+study that involves a slightly different
+ 
+
+ align:start position:0%
+study that involves a slightly different
+way to do this. Uh, and this involves a
+
+ align:start position:0%
+way to do this. Uh, and this involves a
+ 
+
+ align:start position:0%
+way to do this. Uh, and this involves a
+slightly different diagram. So, the idea
+
+ align:start position:0%
+slightly different diagram. So, the idea
+ 
+
+ align:start position:0%
+slightly different diagram. So, the idea
+here is to choose a material for a
+
+ align:start position:0%
+here is to choose a material for a
+ 
+
+ align:start position:0%
+here is to choose a material for a
+bicycle helmet. And as you probably all
+
+ align:start position:0%
+bicycle helmet. And as you probably all
+ 
+
+ align:start position:0%
+bicycle helmet. And as you probably all
+know, the bicycle helmets have a hard
+
+ align:start position:0%
+know, the bicycle helmets have a hard
+ 
+
+ align:start position:0%
+know, the bicycle helmets have a hard
+shell and they have some sort of foamy
+
+ align:start position:0%
+shell and they have some sort of foamy
+ 
+
+ align:start position:0%
+shell and they have some sort of foamy
+liner. And the foam's usually around 20
+
+ align:start position:0%
+liner. And the foam's usually around 20
+ 
+
+ align:start position:0%
+liner. And the foam's usually around 20
+mm thick. And you want something that's
+
+ align:start position:0%
+mm thick. And you want something that's
+ 
+
+ align:start position:0%
+mm thick. And you want something that's
+light because you don't want your helmet
+
+ align:start position:0%
+light because you don't want your helmet
+ 
+
+ align:start position:0%
+light because you don't want your helmet
+to be too heavy, but you want something
+
+ align:start position:0%
+to be too heavy, but you want something
+ 
+
+ align:start position:0%
+to be too heavy, but you want something
+that'll absorb the energy from the
+
+ align:start position:0%
+that'll absorb the energy from the
+ 
+
+ align:start position:0%
+that'll absorb the energy from the
+impact. So, um, I've set this up here.
+
+ align:start position:0%
+impact. So, um, I've set this up here.
+ 
+
+ align:start position:0%
+impact. So, um, I've set this up here.
+So we assume the mass of the head is
+
+ align:start position:0%
+So we assume the mass of the head is
+ 
+
+ align:start position:0%
+So we assume the mass of the head is
+about 3 kg and we assume that it could
+
+ align:start position:0%
+about 3 kg and we assume that it could
+ 
+
+ align:start position:0%
+about 3 kg and we assume that it could
+withstand a deceleration of something
+
+ align:start position:0%
+withstand a deceleration of something
+ 
+
+ align:start position:0%
+withstand a deceleration of something
+like 300g.
+
+ align:start position:0%
+like 300g.
+ 
+
+ align:start position:0%
+like 300g.
+And so then you can get a force mass
+
+ align:start position:0%
+And so then you can get a force mass
+ 
+
+ align:start position:0%
+And so then you can get a force mass
+times the acceleration gives you the
+
+ align:start position:0%
+times the acceleration gives you the
+ 
+
+ align:start position:0%
+times the acceleration gives you the
+force. And I've assumed an area of
+
+ align:start position:0%
+force. And I've assumed an area of
+ 
+
+ align:start position:0%
+force. And I've assumed an area of
+contact of something like 1.01
+
+ align:start position:0%
+contact of something like 1.01
+ 
+
+ align:start position:0%
+contact of something like 1.01
+meters squared. So that gives you a peak
+
+ align:start position:0%
+meters squared. So that gives you a peak
+ 
+
+ align:start position:0%
+meters squared. So that gives you a peak
+stress. So this uh method here is based
+
+ align:start position:0%
+stress. So this uh method here is based
+ 
+
+ align:start position:0%
+stress. So this uh method here is based
+on the idea that you have these um
+
+ align:start position:0%
+on the idea that you have these um
+ 
+
+ align:start position:0%
+on the idea that you have these um
+material selection charts for foams.
+
+ align:start position:0%
+material selection charts for foams.
+ 
+
+ align:start position:0%
+material selection charts for foams.
+Remember we talked about that earlier.
+
+ align:start position:0%
+Remember we talked about that earlier.
+ 
+
+ align:start position:0%
+Remember we talked about that earlier.
+And this is the compressive stress at
+
+ align:start position:0%
+And this is the compressive stress at
+ 
+
+ align:start position:0%
+And this is the compressive stress at
+25% strain. So the idea is that axis
+
+ align:start position:0%
+25% strain. So the idea is that axis
+ 
+
+ align:start position:0%
+25% strain. So the idea is that axis
+there is meant to represent the plateau
+
+ align:start position:0%
+there is meant to represent the plateau
+ 
+
+ align:start position:0%
+there is meant to represent the plateau
+stress. And this axis here represents
+
+ align:start position:0%
+stress. And this axis here represents
+ 
+
+ align:start position:0%
+stress. And this axis here represents
+the densification strain. And these
+
+ align:start position:0%
+the densification strain. And these
+ 
+
+ align:start position:0%
+the densification strain. And these
+dashed lines here correspond to
+
+ align:start position:0%
+dashed lines here correspond to
+ 
+
+ align:start position:0%
+dashed lines here correspond to
+basically a value of w an energy
+
+ align:start position:0%
+basically a value of w an energy
+ 
+
+ align:start position:0%
+basically a value of w an energy
+absorbed per unit volume. So this is an
+
+ align:start position:0%
+absorbed per unit volume. So this is an
+ 
+
+ align:start position:0%
+absorbed per unit volume. So this is an
+energy absorbed per unit volume of 0.01
+
+ align:start position:0%
+energy absorbed per unit volume of 0.01
+ 
+
+ align:start position:0%
+energy absorbed per unit volume of 0.01
+mega per cubic meter 0.01 and so on.
+
+ align:start position:0%
+mega per cubic meter 0.01 and so on.
+ 
+
+ align:start position:0%
+mega per cubic meter 0.01 and so on.
+So if you know the uh peak stress that
+
+ align:start position:0%
+So if you know the uh peak stress that
+ 
+
+ align:start position:0%
+So if you know the uh peak stress that
+you can tolerate uh for the numbers I
+
+ align:start position:0%
+you can tolerate uh for the numbers I
+ 
+
+ align:start position:0%
+you can tolerate uh for the numbers I
+gave you it works out to be 0.9
+
+ align:start position:0%
+gave you it works out to be 0.9
+ 
+
+ align:start position:0%
+gave you it works out to be 0.9
+megapascals. So here is just a little
+
+ align:start position:0%
+megapascals. So here is just a little
+ 
+
+ align:start position:0%
+megapascals. So here is just a little
+less than one. So that's the peak stress
+
+ align:start position:0%
+less than one. So that's the peak stress
+ 
+
+ align:start position:0%
+less than one. So that's the peak stress
+that you can tolerate there. And uh you
+
+ align:start position:0%
+that you can tolerate there. And uh you
+ 
+
+ align:start position:0%
+that you can tolerate there. And uh you
+can see that the material that's going
+
+ align:start position:0%
+can see that the material that's going
+ 
+
+ align:start position:0%
+can see that the material that's going
+to absorb the most energy. So you're
+
+ align:start position:0%
+to absorb the most energy. So you're
+ 
+
+ align:start position:0%
+to absorb the most energy. So you're
+absorbing more energy as you move over
+
+ align:start position:0%
+absorbing more energy as you move over
+ 
+
+ align:start position:0%
+absorbing more energy as you move over
+kind of this way on the curve um on the
+
+ align:start position:0%
+kind of this way on the curve um on the
+ 
+
+ align:start position:0%
+kind of this way on the curve um on the
+plot. So the material that's going to do
+
+ align:start position:0%
+plot. So the material that's going to do
+ 
+
+ align:start position:0%
+plot. So the material that's going to do
+the best is something like an expanded
+
+ align:start position:0%
+the best is something like an expanded
+ 
+
+ align:start position:0%
+the best is something like an expanded
+polystyrene that's 5% dense. So I've
+
+ align:start position:0%
+polystyrene that's 5% dense. So I've
+ 
+
+ align:start position:0%
+polystyrene that's 5% dense. So I've
+highlighted that in red. Expanded
+
+ align:start position:0%
+highlighted that in red. Expanded
+ 
+
+ align:start position:0%
+highlighted that in red. Expanded
+polystyrene that's 5% dense. And then
+
+ align:start position:0%
+polystyrene that's 5% dense. And then
+ 
+
+ align:start position:0%
+polystyrene that's 5% dense. And then
+this is the the densification strain
+
+ align:start position:0%
+this is the the densification strain
+ 
+
+ align:start position:0%
+this is the the densification strain
+here. And you know the the the lines of
+
+ align:start position:0%
+here. And you know the the the lines of
+ 
+
+ align:start position:0%
+here. And you know the the the lines of
+the energy absorption are just the
+
+ align:start position:0%
+the energy absorption are just the
+ 
+
+ align:start position:0%
+the energy absorption are just the
+stress times the strain. So you can
+
+ align:start position:0%
+stress times the strain. So you can
+ 
+
+ align:start position:0%
+stress times the strain. So you can
+basically just read off from here that
+
+ align:start position:0%
+basically just read off from here that
+ 
+
+ align:start position:0%
+basically just read off from here that
+expanded polystyrene that was 5% dense
+
+ align:start position:0%
+expanded polystyrene that was 5% dense
+ 
+
+ align:start position:0%
+expanded polystyrene that was 5% dense
+would be a good choice for a bicycle
+
+ align:start position:0%
+would be a good choice for a bicycle
+ 
+
+ align:start position:0%
+would be a good choice for a bicycle
+helmet foam. Okay. Would you like to add
+
+ align:start position:0%
+helmet foam. Okay. Would you like to add
+ 
+
+ align:start position:0%
+helmet foam. Okay. Would you like to add
+anything about bicycle helmet foams?
+
+ align:start position:0%
+anything about bicycle helmet foams?
+ 
+
+ align:start position:0%
+anything about bicycle helmet foams?
+Exactly what they use.
+
+ align:start position:0%
+Exactly what they use.
+ 
+
+ align:start position:0%
+Exactly what they use.
+I think that is exactly what they use.
+
+ align:start position:0%
+I think that is exactly what they use.
+ 
+
+ align:start position:0%
+I think that is exactly what they use.
+Yes. So um so this is just another way
+
+ align:start position:0%
+Yes. So um so this is just another way
+ 
+
+ align:start position:0%
+Yes. So um so this is just another way
+to do this kind of thing. And I did one
+
+ align:start position:0%
+to do this kind of thing. And I did one
+ 
+
+ align:start position:0%
+to do this kind of thing. And I did one
+more little calculation here. You can if
+
+ align:start position:0%
+more little calculation here. You can if
+ 
+
+ align:start position:0%
+more little calculation here. You can if
+you know um the thickness of the foam is
+
+ align:start position:0%
+you know um the thickness of the foam is
+ 
+
+ align:start position:0%
+you know um the thickness of the foam is
+say 20 millimeters and we've estimated
+
+ align:start position:0%
+say 20 millimeters and we've estimated
+ 
+
+ align:start position:0%
+say 20 millimeters and we've estimated
+the area of the contact. Uh you can
+
+ align:start position:0%
+the area of the contact. Uh you can
+ 
+
+ align:start position:0%
+the area of the contact. Uh you can
+figure out what the energy absorbed is
+
+ align:start position:0%
+figure out what the energy absorbed is
+ 
+
+ align:start position:0%
+figure out what the energy absorbed is
+per unit volume and from that you can
+
+ align:start position:0%
+per unit volume and from that you can
+ 
+
+ align:start position:0%
+per unit volume and from that you can
+back out the energy in terms of jewels
+
+ align:start position:0%
+back out the energy in terms of jewels
+ 
+
+ align:start position:0%
+back out the energy in terms of jewels
+and from that you can back out the the
+
+ align:start position:0%
+and from that you can back out the the
+ 
+
+ align:start position:0%
+and from that you can back out the the
+velocity. That's the maximum speed that
+
+ align:start position:0%
+velocity. That's the maximum speed that
+ 
+
+ align:start position:0%
+velocity. That's the maximum speed that
+one would want to get binged at on your
+
+ align:start position:0%
+one would want to get binged at on your
+ 
+
+ align:start position:0%
+one would want to get binged at on your
+bicycle. And the maximum speed works out
+
+ align:start position:0%
+bicycle. And the maximum speed works out
+ 
+
+ align:start position:0%
+bicycle. And the maximum speed works out
+to about 22 miles an hour. So, so that's
+
+ align:start position:0%
+to about 22 miles an hour. So, so that's
+ 
+
+ align:start position:0%
+to about 22 miles an hour. So, so that's
+just another example. Okay. Are we good?
+
+ align:start position:0%
+just another example. Okay. Are we good?
+ 
+
+ align:start position:0%
+just another example. Okay. Are we good?
+Okay.
+
+ align:start position:0%
+Okay.
+ 
+
+ align:start position:0%
+Okay.
+Yeah, exactly. Your head would be
+
+ align:start position:0%
+Yeah, exactly. Your head would be
+ 
+
+ align:start position:0%
+Yeah, exactly. Your head would be
+hitting the ground at 22 miles an hour,
+
+ align:start position:0%
+hitting the ground at 22 miles an hour,
+ 
+
+ align:start position:0%
+hitting the ground at 22 miles an hour,
+which would be ouchy. Which is why you
+
+ align:start position:0%
+which would be ouchy. Which is why you
+ 
+
+ align:start position:0%
+which would be ouchy. Which is why you
+want to wear your helmet because your
+
+ align:start position:0%
+want to wear your helmet because your
+ 
+
+ align:start position:0%
+want to wear your helmet because your
+skull will not be happy if that happens
+
+ align:start position:0%
+skull will not be happy if that happens
+ 
+
+ align:start position:0%
+skull will not be happy if that happens
+and your brain will not be happy and you
+
+ align:start position:0%
+and your brain will not be happy and you
+ 
+
+ align:start position:0%
+and your brain will not be happy and you
+will not be happy and your mom and dad
+
+ align:start position:0%
+will not be happy and your mom and dad
+ 
+
+ align:start position:0%
+will not be happy and your mom and dad
+will be really, really, really unhappy.
+
+ align:start position:0%
+will be really, really, really unhappy.
+ 
+
+ align:start position:0%
+will be really, really, really unhappy.
+So, you don't want that to happen. Okay.
+
+ align:start position:0%
+So, you don't want that to happen. Okay.
+ 
+
+ align:start position:0%
+So, you don't want that to happen. Okay.
+So, I have a few minutes left and I know
+
+ align:start position:0%
+So, I have a few minutes left and I know
+ 
+
+ align:start position:0%
+So, I have a few minutes left and I know
+I've done this for the people in 3032,
+
+ align:start position:0%
+I've done this for the people in 3032,
+ 
+
+ align:start position:0%
+I've done this for the people in 3032,
+but I was going to do by Woodpecker talk
+
+ align:start position:0%
+but I was going to do by Woodpecker talk
+ 
+
+ align:start position:0%
+but I was going to do by Woodpecker talk
+because it's about energy absorption.
+
+ align:start position:0%
+because it's about energy absorption.
+ 
+
+ align:start position:0%
+because it's about energy absorption.
+So, I mean, if you don't if you don't
+
+ align:start position:0%
+So, I mean, if you don't if you don't
+ 
+
+ align:start position:0%
+So, I mean, if you don't if you don't
+want to watch it, if you already seen
+
+ align:start position:0%
+want to watch it, if you already seen
+ 
+
+ align:start position:0%
+want to watch it, if you already seen
+it, you can go. But there's some people
+
+ align:start position:0%
+it, you can go. But there's some people
+ 
+
+ align:start position:0%
+it, you can go. But there's some people
+you guys haven't seen it and you haven't
+
+ align:start position:0%
+you guys haven't seen it and you haven't
+ 
+
+ align:start position:0%
+you guys haven't seen it and you haven't
+seen it. There's a few people haven't
+
+ align:start position:0%
+seen it. There's a few people haven't
+ 
+
+ align:start position:0%
+seen it. There's a few people haven't
+seen and it's cute. It involves birds.
+
+ align:start position:0%
+seen and it's cute. It involves birds.
+ 
+
+ align:start position:0%
+seen and it's cute. It involves birds.
+So, and it involves energy absorption.
+
+ align:start position:0%
+So, and it involves energy absorption.
+ 
+
+ align:start position:0%
+So, and it involves energy absorption.
+So, I thought I would do the woodpecker
+
+ align:start position:0%
+So, I thought I would do the woodpecker
+ 
+
+ align:start position:0%
+So, I thought I would do the woodpecker
+talk.
+
+ align:start position:0%
+talk.
+ 
+
+ align:start position:0%
+talk.
+Okay.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+So, Barry, this is all just slides. I
+
+ align:start position:0%
+So, Barry, this is all just slides. I
+ 
+
+ align:start position:0%
+So, Barry, this is all just slides. I
+don't know if you want to do the lights
+
+ align:start position:0%
+don't know if you want to do the lights
+ 
+
+ align:start position:0%
+don't know if you want to do the lights
+differently or I'm not going to write
+
+ align:start position:0%
+differently or I'm not going to write
+ 
+
+ align:start position:0%
+differently or I'm not going to write
+anything on the board. I'm just going to
+
+ align:start position:0%
+anything on the board. I'm just going to
+ 
+
+ align:start position:0%
+anything on the board. I'm just going to
+talk.
+
+ align:start position:0%
+talk.
+ 
+
+ align:start position:0%
+talk.
+Yeah. I think maybe we could turn the
+
+ align:start position:0%
+Yeah. I think maybe we could turn the
+ 
+
+ align:start position:0%
+Yeah. I think maybe we could turn the
+lights down a little, please.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Let's try this one.
+
+ align:start position:0%
+Let's try this one.
+ 
+
+ align:start position:0%
+Let's try this one.
+Oh, there we go. That's good. Yeah. And
+
+ align:start position:0%
+Oh, there we go. That's good. Yeah. And
+ 
+
+ align:start position:0%
+Oh, there we go. That's good. Yeah. And
+I don't feel like I'm looking in the
+
+ align:start position:0%
+I don't feel like I'm looking in the
+ 
+
+ align:start position:0%
+I don't feel like I'm looking in the
+spotlight so much. That's good. Okay.
+
+ align:start position:0%
+spotlight so much. That's good. Okay.
+ 
+
+ align:start position:0%
+spotlight so much. That's good. Okay.
+So, you guys know that I like to watch
+
+ align:start position:0%
+So, you guys know that I like to watch
+ 
+
+ align:start position:0%
+So, you guys know that I like to watch
+birds. And you know that I work on
+
+ align:start position:0%
+birds. And you know that I work on
+ 
+
+ align:start position:0%
+birds. And you know that I work on
+foams. And if you look at bird books,
+
+ align:start position:0%
+foams. And if you look at bird books,
+ 
+
+ align:start position:0%
+foams. And if you look at bird books,
+sometimes the bird books say that
+
+ align:start position:0%
+sometimes the bird books say that
+ 
+
+ align:start position:0%
+sometimes the bird books say that
+woodpeckers can withstand the impact
+
+ align:start position:0%
+woodpeckers can withstand the impact
+ 
+
+ align:start position:0%
+woodpeckers can withstand the impact
+from pecking because they have a special
+
+ align:start position:0%
+from pecking because they have a special
+ 
+
+ align:start position:0%
+from pecking because they have a special
+material between their skulls and their
+
+ align:start position:0%
+material between their skulls and their
+ 
+
+ align:start position:0%
+material between their skulls and their
+brains. And I thought, oh well, I study
+
+ align:start position:0%
+brains. And I thought, oh well, I study
+ 
+
+ align:start position:0%
+brains. And I thought, oh well, I study
+foams and I'm interested in woodpeckers.
+
+ align:start position:0%
+foams and I'm interested in woodpeckers.
+ 
+
+ align:start position:0%
+foams and I'm interested in woodpeckers.
+I should find out what this special
+
+ align:start position:0%
+I should find out what this special
+ 
+
+ align:start position:0%
+I should find out what this special
+material is. So I started looking into
+
+ align:start position:0%
+material is. So I started looking into
+ 
+
+ align:start position:0%
+material is. So I started looking into
+this and it turns out there is no
+
+ align:start position:0%
+this and it turns out there is no
+ 
+
+ align:start position:0%
+this and it turns out there is no
+special material. People have looked at
+
+ align:start position:0%
+special material. People have looked at
+ 
+
+ align:start position:0%
+special material. People have looked at
+the anatomy of woodpecker brains and
+
+ align:start position:0%
+the anatomy of woodpecker brains and
+ 
+
+ align:start position:0%
+the anatomy of woodpecker brains and
+skulls and there is no special material.
+
+ align:start position:0%
+skulls and there is no special material.
+ 
+
+ align:start position:0%
+skulls and there is no special material.
+But it turns out there were also a group
+
+ align:start position:0%
+But it turns out there were also a group
+ 
+
+ align:start position:0%
+But it turns out there were also a group
+of neurologists in the late 1970s who
+
+ align:start position:0%
+of neurologists in the late 1970s who
+ 
+
+ align:start position:0%
+of neurologists in the late 1970s who
+got interested in why woodpeckers don't
+
+ align:start position:0%
+got interested in why woodpeckers don't
+ 
+
+ align:start position:0%
+got interested in why woodpeckers don't
+get brain injury. And they took
+
+ align:start position:0%
+get brain injury. And they took
+ 
+
+ align:start position:0%
+get brain injury. And they took
+high-speed video of a woodpecker
+
+ align:start position:0%
+high-speed video of a woodpecker
+ 
+
+ align:start position:0%
+high-speed video of a woodpecker
+pecking. And it was kind of amazing what
+
+ align:start position:0%
+pecking. And it was kind of amazing what
+ 
+
+ align:start position:0%
+pecking. And it was kind of amazing what
+they found out. So it turns out the
+
+ align:start position:0%
+they found out. So it turns out the
+ 
+
+ align:start position:0%
+they found out. So it turns out the
+woodpeckers can withstand incredibly
+
+ align:start position:0%
+woodpeckers can withstand incredibly
+ 
+
+ align:start position:0%
+woodpeckers can withstand incredibly
+high decelerations, much higher than our
+
+ align:start position:0%
+high decelerations, much higher than our
+ 
+
+ align:start position:0%
+high decelerations, much higher than our
+brains could withstand. And so I kind of
+
+ align:start position:0%
+brains could withstand. And so I kind of
+ 
+
+ align:start position:0%
+brains could withstand. And so I kind of
+got interested in this and I um decided
+
+ align:start position:0%
+got interested in this and I um decided
+ 
+
+ align:start position:0%
+got interested in this and I um decided
+to try to figure out how it works. So
+
+ align:start position:0%
+to try to figure out how it works. So
+ 
+
+ align:start position:0%
+to try to figure out how it works. So
+here's an acorn woodpecker.
+
+ align:start position:0%
+here's an acorn woodpecker.
+ 
+
+ align:start position:0%
+here's an acorn woodpecker.
+And uh let's see. I got a little video
+
+ align:start position:0%
+And uh let's see. I got a little video
+ 
+
+ align:start position:0%
+And uh let's see. I got a little video
+here so we can see little Wait a minute.
+
+ align:start position:0%
+here so we can see little Wait a minute.
+ 
+
+ align:start position:0%
+here so we can see little Wait a minute.
+Where's my There we go.
+
+ align:start position:0%
+Where's my There we go.
+ 
+
+ align:start position:0%
+Where's my There we go.
+There we go. So, here's our little acorn
+
+ align:start position:0%
+There we go. So, here's our little acorn
+ 
+
+ align:start position:0%
+There we go. So, here's our little acorn
+woodpecker. These live in California.
+
+ align:start position:0%
+woodpecker. These live in California.
+ 
+
+ align:start position:0%
+woodpecker. These live in California.
+Anybody from California? Yeah. Have you
+
+ align:start position:0%
+Anybody from California? Yeah. Have you
+ 
+
+ align:start position:0%
+Anybody from California? Yeah. Have you
+seen them?
+
+ align:start position:0%
+seen them?
+ 
+
+ align:start position:0%
+seen them?
+No. Okay. Well, you have not been
+
+ align:start position:0%
+No. Okay. Well, you have not been
+ 
+
+ align:start position:0%
+No. Okay. Well, you have not been
+looking carefully. So, here's our little
+
+ align:start position:0%
+looking carefully. So, here's our little
+ 
+
+ align:start position:0%
+looking carefully. So, here's our little
+acorn. And you can see they peck. Oh,
+
+ align:start position:0%
+acorn. And you can see they peck. Oh,
+ 
+
+ align:start position:0%
+acorn. And you can see they peck. Oh,
+like around San Francisco.
+
+ align:start position:0%
+like around San Francisco.
+ 
+
+ align:start position:0%
+like around San Francisco.
+[Laughter]
+
+ align:start position:0%
+[Laughter]
+ 
+
+ align:start position:0%
+[Laughter]
+So, so they're pecking and when they're
+
+ align:start position:0%
+So, so they're pecking and when they're
+ 
+
+ align:start position:0%
+So, so they're pecking and when they're
+pecking, you know, they don't just go
+
+ align:start position:0%
+pecking, you know, they don't just go
+ 
+
+ align:start position:0%
+pecking, you know, they don't just go
+bonk. They they do this repeatedly,
+
+ align:start position:0%
+bonk. They they do this repeatedly,
+ 
+
+ align:start position:0%
+bonk. They they do this repeatedly,
+right? They can peck at it 10 or 20
+
+ align:start position:0%
+right? They can peck at it 10 or 20
+ 
+
+ align:start position:0%
+right? They can peck at it 10 or 20
+times per second. So, the question is,
+
+ align:start position:0%
+times per second. So, the question is,
+ 
+
+ align:start position:0%
+times per second. So, the question is,
+why don't they um get brain injury?
+
+ align:start position:0%
+why don't they um get brain injury?
+ 
+
+ align:start position:0%
+why don't they um get brain injury?
+So, first of all, why do they peck? So,
+
+ align:start position:0%
+So, first of all, why do they peck? So,
+ 
+
+ align:start position:0%
+So, first of all, why do they peck? So,
+as we saw in that little video, that
+
+ align:start position:0%
+as we saw in that little video, that
+ 
+
+ align:start position:0%
+as we saw in that little video, that
+woodpecker was foraging. It was trying
+
+ align:start position:0%
+woodpecker was foraging. It was trying
+ 
+
+ align:start position:0%
+woodpecker was foraging. It was trying
+to get little things out of the bark.
+
+ align:start position:0%
+to get little things out of the bark.
+ 
+
+ align:start position:0%
+to get little things out of the bark.
+And they insect or woodpeckers eat
+
+ align:start position:0%
+And they insect or woodpeckers eat
+ 
+
+ align:start position:0%
+And they insect or woodpeckers eat
+insects. Uh, and so they the bird books
+
+ align:start position:0%
+insects. Uh, and so they the bird books
+ 
+
+ align:start position:0%
+insects. Uh, and so they the bird books
+say that they can actually hear insects
+
+ align:start position:0%
+say that they can actually hear insects
+ 
+
+ align:start position:0%
+say that they can actually hear insects
+scurrying around under the bark and
+
+ align:start position:0%
+scurrying around under the bark and
+ 
+
+ align:start position:0%
+scurrying around under the bark and
+they'll peck at the bark and forage to
+
+ align:start position:0%
+they'll peck at the bark and forage to
+ 
+
+ align:start position:0%
+they'll peck at the bark and forage to
+try to get insects. And there's one
+
+ align:start position:0%
+try to get insects. And there's one
+ 
+
+ align:start position:0%
+try to get insects. And there's one
+other anatomical feature of woodpeckers
+
+ align:start position:0%
+other anatomical feature of woodpeckers
+ 
+
+ align:start position:0%
+other anatomical feature of woodpeckers
+which is kind of amazing. So, and you
+
+ align:start position:0%
+which is kind of amazing. So, and you
+ 
+
+ align:start position:0%
+which is kind of amazing. So, and you
+can see it in this picture here. So,
+
+ align:start position:0%
+can see it in this picture here. So,
+ 
+
+ align:start position:0%
+can see it in this picture here. So,
+this is the woodpecker tongue. And the
+
+ align:start position:0%
+this is the woodpecker tongue. And the
+ 
+
+ align:start position:0%
+this is the woodpecker tongue. And the
+tongue is connected to something called
+
+ align:start position:0%
+tongue is connected to something called
+ 
+
+ align:start position:0%
+tongue is connected to something called
+the hyoid process. And the hyoid process
+
+ align:start position:0%
+the hyoid process. And the hyoid process
+ 
+
+ align:start position:0%
+the hyoid process. And the hyoid process
+wraps around their eyeballs. And then
+
+ align:start position:0%
+wraps around their eyeballs. And then
+ 
+
+ align:start position:0%
+wraps around their eyeballs. And then
+when they peck, I mean, the idea is
+
+ align:start position:0%
+when they peck, I mean, the idea is
+ 
+
+ align:start position:0%
+when they peck, I mean, the idea is
+they're making a hole in the in the tree
+
+ align:start position:0%
+they're making a hole in the in the tree
+ 
+
+ align:start position:0%
+they're making a hole in the in the tree
+and they got to get their tongue into
+
+ align:start position:0%
+and they got to get their tongue into
+ 
+
+ align:start position:0%
+and they got to get their tongue into
+the hole to get the bug. And their end
+
+ align:start position:0%
+the hole to get the bug. And their end
+ 
+
+ align:start position:0%
+the hole to get the bug. And their end
+of their tongue has little barbs on it.
+
+ align:start position:0%
+of their tongue has little barbs on it.
+ 
+
+ align:start position:0%
+of their tongue has little barbs on it.
+And when they contract this thing here,
+
+ align:start position:0%
+And when they contract this thing here,
+ 
+
+ align:start position:0%
+And when they contract this thing here,
+their tongue scoots out and gets the
+
+ align:start position:0%
+their tongue scoots out and gets the
+ 
+
+ align:start position:0%
+their tongue scoots out and gets the
+little bugs. So they they peck partly to
+
+ align:start position:0%
+little bugs. So they they peck partly to
+ 
+
+ align:start position:0%
+little bugs. So they they peck partly to
+forage. They also build something called
+
+ align:start position:0%
+forage. They also build something called
+ 
+
+ align:start position:0%
+forage. They also build something called
+cavity nests. So they'll find a tree
+
+ align:start position:0%
+cavity nests. So they'll find a tree
+ 
+
+ align:start position:0%
+cavity nests. So they'll find a tree
+that's, you know, started to rot and
+
+ align:start position:0%
+that's, you know, started to rot and
+ 
+
+ align:start position:0%
+that's, you know, started to rot and
+they'll drill a sort of horizontal hole
+
+ align:start position:0%
+they'll drill a sort of horizontal hole
+ 
+
+ align:start position:0%
+they'll drill a sort of horizontal hole
+and then they'll drill a cup underneath
+
+ align:start position:0%
+and then they'll drill a cup underneath
+ 
+
+ align:start position:0%
+and then they'll drill a cup underneath
+that and they lay the eggs and have
+
+ align:start position:0%
+that and they lay the eggs and have
+ 
+
+ align:start position:0%
+that and they lay the eggs and have
+their nest at the bottom of the cup. And
+
+ align:start position:0%
+their nest at the bottom of the cup. And
+ 
+
+ align:start position:0%
+their nest at the bottom of the cup. And
+then they also, especially at this time
+
+ align:start position:0%
+then they also, especially at this time
+ 
+
+ align:start position:0%
+then they also, especially at this time
+of year, in fact, today I heard
+
+ align:start position:0%
+of year, in fact, today I heard
+ 
+
+ align:start position:0%
+of year, in fact, today I heard
+woodpeckers drumming. So it's kind of a
+
+ align:start position:0%
+woodpeckers drumming. So it's kind of a
+ 
+
+ align:start position:0%
+woodpeckers drumming. So it's kind of a
+uh, you know, one of these mating
+
+ align:start position:0%
+uh, you know, one of these mating
+ 
+
+ align:start position:0%
+uh, you know, one of these mating
+things, one of these courtship things.
+
+ align:start position:0%
+things, one of these courtship things.
+ 
+
+ align:start position:0%
+things, one of these courtship things.
+So woodpeckers will peck on a hollow
+
+ align:start position:0%
+So woodpeckers will peck on a hollow
+ 
+
+ align:start position:0%
+So woodpeckers will peck on a hollow
+branch or a hollow tree just to make a
+
+ align:start position:0%
+branch or a hollow tree just to make a
+ 
+
+ align:start position:0%
+branch or a hollow tree just to make a
+big loud noise to say, "Here I am
+
+ align:start position:0%
+big loud noise to say, "Here I am
+ 
+
+ align:start position:0%
+big loud noise to say, "Here I am
+looking for sex. I'm ready. You know,
+
+ align:start position:0%
+looking for sex. I'm ready. You know,
+ 
+
+ align:start position:0%
+looking for sex. I'm ready. You know,
+this is my territory. Uh, and so in the
+
+ align:start position:0%
+this is my territory. Uh, and so in the
+ 
+
+ align:start position:0%
+this is my territory. Uh, and so in the
+spring, so this time of year, you hear
+
+ align:start position:0%
+spring, so this time of year, you hear
+ 
+
+ align:start position:0%
+spring, so this time of year, you hear
+woodpeckers drumming. And I think
+
+ align:start position:0%
+woodpeckers drumming. And I think
+ 
+
+ align:start position:0%
+woodpeckers drumming. And I think
+naturally they do this on hollow trees
+
+ align:start position:0%
+naturally they do this on hollow trees
+ 
+
+ align:start position:0%
+naturally they do this on hollow trees
+to try to make a big sound, but they
+
+ align:start position:0%
+to try to make a big sound, but they
+ 
+
+ align:start position:0%
+to try to make a big sound, but they
+have adapted to um metal downspouts,
+
+ align:start position:0%
+have adapted to um metal downspouts,
+ 
+
+ align:start position:0%
+have adapted to um metal downspouts,
+which are also very effective for making
+
+ align:start position:0%
+which are also very effective for making
+ 
+
+ align:start position:0%
+which are also very effective for making
+this loud noise. And people who've I
+
+ align:start position:0%
+this loud noise. And people who've I
+ 
+
+ align:start position:0%
+this loud noise. And people who've I
+wrote a paper on this. People who've
+
+ align:start position:0%
+wrote a paper on this. People who've
+ 
+
+ align:start position:0%
+wrote a paper on this. People who've
+read my paper sometimes email me and
+
+ align:start position:0%
+read my paper sometimes email me and
+ 
+
+ align:start position:0%
+read my paper sometimes email me and
+say, "Oh, I heard you know about
+
+ align:start position:0%
+say, "Oh, I heard you know about
+ 
+
+ align:start position:0%
+say, "Oh, I heard you know about
+woodpecker pecking. How can I get them
+
+ align:start position:0%
+woodpecker pecking. How can I get them
+ 
+
+ align:start position:0%
+woodpecker pecking. How can I get them
+to stop drumming on my downspout?"
+
+ align:start position:0%
+to stop drumming on my downspout?"
+ 
+
+ align:start position:0%
+to stop drumming on my downspout?"
+Because it's kind of annoying if you're
+
+ align:start position:0%
+Because it's kind of annoying if you're
+ 
+
+ align:start position:0%
+Because it's kind of annoying if you're
+the human inside the house. So anyway,
+
+ align:start position:0%
+the human inside the house. So anyway,
+ 
+
+ align:start position:0%
+the human inside the house. So anyway,
+they they peck for these reasons. And
+
+ align:start position:0%
+they they peck for these reasons. And
+ 
+
+ align:start position:0%
+they they peck for these reasons. And
+then acorn woodpeckers are special.
+
+ align:start position:0%
+then acorn woodpeckers are special.
+ 
+
+ align:start position:0%
+then acorn woodpeckers are special.
+Acorn woodpeckers are what I think of as
+
+ align:start position:0%
+Acorn woodpeckers are what I think of as
+ 
+
+ align:start position:0%
+Acorn woodpeckers are what I think of as
+the champions of pecking. And they do
+
+ align:start position:0%
+the champions of pecking. And they do
+ 
+
+ align:start position:0%
+the champions of pecking. And they do
+one more behavior. So here's from David
+
+ align:start position:0%
+one more behavior. So here's from David
+ 
+
+ align:start position:0%
+one more behavior. So here's from David
+Sibli's beautiful uh guide to birds.
+
+ align:start position:0%
+Sibli's beautiful uh guide to birds.
+ 
+
+ align:start position:0%
+Sibli's beautiful uh guide to birds.
+Here's the acorn woodpecker. They store
+
+ align:start position:0%
+Here's the acorn woodpecker. They store
+ 
+
+ align:start position:0%
+Here's the acorn woodpecker. They store
+acorns in what's called a granary. And
+
+ align:start position:0%
+acorns in what's called a granary. And
+ 
+
+ align:start position:0%
+acorns in what's called a granary. And
+they get they look at old uh kind of old
+
+ align:start position:0%
+they get they look at old uh kind of old
+ 
+
+ align:start position:0%
+they get they look at old uh kind of old
+tree trunks that are beginning to rot
+
+ align:start position:0%
+tree trunks that are beginning to rot
+ 
+
+ align:start position:0%
+tree trunks that are beginning to rot
+and they peck holes in the tree trunk
+
+ align:start position:0%
+and they peck holes in the tree trunk
+ 
+
+ align:start position:0%
+and they peck holes in the tree trunk
+and they store the acorns in the holes.
+
+ align:start position:0%
+and they store the acorns in the holes.
+ 
+
+ align:start position:0%
+and they store the acorns in the holes.
+So see all those little like dark dots
+
+ align:start position:0%
+So see all those little like dark dots
+ 
+
+ align:start position:0%
+So see all those little like dark dots
+on that trunk? Those are all holes that
+
+ align:start position:0%
+on that trunk? Those are all holes that
+ 
+
+ align:start position:0%
+on that trunk? Those are all holes that
+the acorn woodpecker has pecked. And
+
+ align:start position:0%
+the acorn woodpecker has pecked. And
+ 
+
+ align:start position:0%
+the acorn woodpecker has pecked. And
+they'll do this in they live in social
+
+ align:start position:0%
+they'll do this in they live in social
+ 
+
+ align:start position:0%
+they'll do this in they live in social
+groups. So there might be like 10 or 20
+
+ align:start position:0%
+groups. So there might be like 10 or 20
+ 
+
+ align:start position:0%
+groups. So there might be like 10 or 20
+of them living together.
+
+ align:start position:0%
+of them living together.
+ 
+
+ align:start position:0%
+of them living together.
+And they'll peck like 10,000 holes into
+
+ align:start position:0%
+And they'll peck like 10,000 holes into
+ 
+
+ align:start position:0%
+And they'll peck like 10,000 holes into
+their granary. There'll be thousands and
+
+ align:start position:0%
+their granary. There'll be thousands and
+ 
+
+ align:start position:0%
+their granary. There'll be thousands and
+thousands of these holes. And here we
+
+ align:start position:0%
+thousands of these holes. And here we
+ 
+
+ align:start position:0%
+thousands of these holes. And here we
+have the acorn woodpecker with the acorn
+
+ align:start position:0%
+have the acorn woodpecker with the acorn
+ 
+
+ align:start position:0%
+have the acorn woodpecker with the acorn
+in its beak. And you can see there's
+
+ align:start position:0%
+in its beak. And you can see there's
+ 
+
+ align:start position:0%
+in its beak. And you can see there's
+some of these holes have acorns and some
+
+ align:start position:0%
+some of these holes have acorns and some
+ 
+
+ align:start position:0%
+some of these holes have acorns and some
+of them are empty. So here's the acorn
+
+ align:start position:0%
+of them are empty. So here's the acorn
+ 
+
+ align:start position:0%
+of them are empty. So here's the acorn
+woodpecker in action. And here's the
+
+ align:start position:0%
+woodpecker in action. And here's the
+ 
+
+ align:start position:0%
+woodpecker in action. And here's the
+little video again. I won't play the
+
+ align:start position:0%
+little video again. I won't play the
+ 
+
+ align:start position:0%
+little video again. I won't play the
+video. So I I often give this talk for
+
+ align:start position:0%
+video. So I I often give this talk for
+ 
+
+ align:start position:0%
+video. So I I often give this talk for
+non-engineers. So I'm going to explain
+
+ align:start position:0%
+non-engineers. So I'm going to explain
+ 
+
+ align:start position:0%
+non-engineers. So I'm going to explain
+some things that you know there's going
+
+ align:start position:0%
+some things that you know there's going
+ 
+
+ align:start position:0%
+some things that you know there's going
+to be some writing on the slides that
+
+ align:start position:0%
+to be some writing on the slides that
+ 
+
+ align:start position:0%
+to be some writing on the slides that
+you guys already know. So the impact
+
+ align:start position:0%
+you guys already know. So the impact
+ 
+
+ align:start position:0%
+you guys already know. So the impact
+force depends on the deceleration, how
+
+ align:start position:0%
+force depends on the deceleration, how
+ 
+
+ align:start position:0%
+force depends on the deceleration, how
+quickly the brain stops when the beak
+
+ align:start position:0%
+quickly the brain stops when the beak
+ 
+
+ align:start position:0%
+quickly the brain stops when the beak
+hits the tree. And I should mention
+
+ align:start position:0%
+hits the tree. And I should mention
+ 
+
+ align:start position:0%
+hits the tree. And I should mention
+these videos are from the Cornell Lab of
+
+ align:start position:0%
+these videos are from the Cornell Lab of
+ 
+
+ align:start position:0%
+these videos are from the Cornell Lab of
+Ornithology. They have an amazing
+
+ align:start position:0%
+Ornithology. They have an amazing
+ 
+
+ align:start position:0%
+Ornithology. They have an amazing
+collection of bird audio, like bird
+
+ align:start position:0%
+collection of bird audio, like bird
+ 
+
+ align:start position:0%
+collection of bird audio, like bird
+calls, bird songs, and bird photographs
+
+ align:start position:0%
+calls, bird songs, and bird photographs
+ 
+
+ align:start position:0%
+calls, bird songs, and bird photographs
+and videos. It's it's incredible the
+
+ align:start position:0%
+and videos. It's it's incredible the
+ 
+
+ align:start position:0%
+and videos. It's it's incredible the
+collection that they've got. Um, and
+
+ align:start position:0%
+collection that they've got. Um, and
+ 
+
+ align:start position:0%
+collection that they've got. Um, and
+then I explain what acceleration is. So,
+
+ align:start position:0%
+then I explain what acceleration is. So,
+ 
+
+ align:start position:0%
+then I explain what acceleration is. So,
+I'm going to put acceleration in terms
+
+ align:start position:0%
+I'm going to put acceleration in terms
+ 
+
+ align:start position:0%
+I'm going to put acceleration in terms
+of gravity. And when the when the beak
+
+ align:start position:0%
+of gravity. And when the when the beak
+ 
+
+ align:start position:0%
+of gravity. And when the when the beak
+hits the tree, there's going to be a
+
+ align:start position:0%
+hits the tree, there's going to be a
+ 
+
+ align:start position:0%
+hits the tree, there's going to be a
+deceleration on impact. And just as a
+
+ align:start position:0%
+deceleration on impact. And just as a
+ 
+
+ align:start position:0%
+deceleration on impact. And just as a
+comparison, human brain injury occurs
+
+ align:start position:0%
+comparison, human brain injury occurs
+ 
+
+ align:start position:0%
+comparison, human brain injury occurs
+roughly at about 100g. Uh, and so the
+
+ align:start position:0%
+roughly at about 100g. Uh, and so the
+ 
+
+ align:start position:0%
+roughly at about 100g. Uh, and so the
+question is, how much deceleration can
+
+ align:start position:0%
+question is, how much deceleration can
+ 
+
+ align:start position:0%
+question is, how much deceleration can
+the woodpecker brain take? And that's
+
+ align:start position:0%
+the woodpecker brain take? And that's
+ 
+
+ align:start position:0%
+the woodpecker brain take? And that's
+where the neurologists in the Bay Area
+
+ align:start position:0%
+where the neurologists in the Bay Area
+ 
+
+ align:start position:0%
+where the neurologists in the Bay Area
+come into the picture. They uh found out
+
+ align:start position:0%
+come into the picture. They uh found out
+ 
+
+ align:start position:0%
+come into the picture. They uh found out
+that there was a park ranger I think um
+
+ align:start position:0%
+that there was a park ranger I think um
+ 
+
+ align:start position:0%
+that there was a park ranger I think um
+maybe at Point Race just north of San
+
+ align:start position:0%
+maybe at Point Race just north of San
+ 
+
+ align:start position:0%
+maybe at Point Race just north of San
+Francisco and he had an acorn woodpecker
+
+ align:start position:0%
+Francisco and he had an acorn woodpecker
+ 
+
+ align:start position:0%
+Francisco and he had an acorn woodpecker
+that I don't know had an injured wing or
+
+ align:start position:0%
+that I don't know had an injured wing or
+ 
+
+ align:start position:0%
+that I don't know had an injured wing or
+something. Anyway, he had this acorn
+
+ align:start position:0%
+something. Anyway, he had this acorn
+ 
+
+ align:start position:0%
+something. Anyway, he had this acorn
+woodpecker that he kept um and they were
+
+ align:start position:0%
+woodpecker that he kept um and they were
+ 
+
+ align:start position:0%
+woodpecker that he kept um and they were
+able to use this acorn woodpecker and
+
+ align:start position:0%
+able to use this acorn woodpecker and
+ 
+
+ align:start position:0%
+able to use this acorn woodpecker and
+they took high-speed video of the pe
+
+ align:start position:0%
+they took high-speed video of the pe
+ 
+
+ align:start position:0%
+they took high-speed video of the pe
+woodpecker pecking. So from the
+
+ align:start position:0%
+woodpecker pecking. So from the
+ 
+
+ align:start position:0%
+woodpecker pecking. So from the
+high-speed video, the video that they
+
+ align:start position:0%
+high-speed video, the video that they
+ 
+
+ align:start position:0%
+high-speed video, the video that they
+took went at something like uh 2,000
+
+ align:start position:0%
+took went at something like uh 2,000
+ 
+
+ align:start position:0%
+took went at something like uh 2,000
+frames a second. So they have a picture
+
+ align:start position:0%
+frames a second. So they have a picture
+ 
+
+ align:start position:0%
+frames a second. So they have a picture
+of where the head is every 2,000th of a
+
+ align:start position:0%
+of where the head is every 2,000th of a
+ 
+
+ align:start position:0%
+of where the head is every 2,000th of a
+second. So if you know the position at
+
+ align:start position:0%
+second. So if you know the position at
+ 
+
+ align:start position:0%
+second. So if you know the position at
+these times, you can get the velocity
+
+ align:start position:0%
+these times, you can get the velocity
+ 
+
+ align:start position:0%
+these times, you can get the velocity
+and you can get the deceleration, right?
+
+ align:start position:0%
+and you can get the deceleration, right?
+ 
+
+ align:start position:0%
+and you can get the deceleration, right?
+So they measured the deceleration and
+
+ align:start position:0%
+So they measured the deceleration and
+ 
+
+ align:start position:0%
+So they measured the deceleration and
+they measured some amazing things. So
+
+ align:start position:0%
+they measured some amazing things. So
+ 
+
+ align:start position:0%
+they measured some amazing things. So
+they measured that on impact the
+
+ align:start position:0%
+they measured that on impact the
+ 
+
+ align:start position:0%
+they measured that on impact the
+woodpecker's bill was going something
+
+ align:start position:0%
+woodpecker's bill was going something
+ 
+
+ align:start position:0%
+woodpecker's bill was going something
+like 15 miles an hour and the
+
+ align:start position:0%
+like 15 miles an hour and the
+ 
+
+ align:start position:0%
+like 15 miles an hour and the
+decelerations were up to 1500g. So many
+
+ align:start position:0%
+decelerations were up to 1500g. So many
+ 
+
+ align:start position:0%
+decelerations were up to 1500g. So many
+times more than what we can withstand.
+
+ align:start position:0%
+times more than what we can withstand.
+ 
+
+ align:start position:0%
+times more than what we can withstand.
+And they also measured the stopping time
+
+ align:start position:0%
+And they also measured the stopping time
+ 
+
+ align:start position:0%
+And they also measured the stopping time
+and they they thought it was between
+
+ align:start position:0%
+and they they thought it was between
+ 
+
+ align:start position:0%
+and they they thought it was between
+about 1/500th to 1/ 1,000th of a second.
+
+ align:start position:0%
+about 1/500th to 1/ 1,000th of a second.
+ 
+
+ align:start position:0%
+about 1/500th to 1/ 1,000th of a second.
+And that's going to be important later
+
+ align:start position:0%
+And that's going to be important later
+ 
+
+ align:start position:0%
+And that's going to be important later
+on. So one of the interesting things
+
+ align:start position:0%
+on. So one of the interesting things
+ 
+
+ align:start position:0%
+on. So one of the interesting things
+about this was how they got this whole
+
+ align:start position:0%
+about this was how they got this whole
+ 
+
+ align:start position:0%
+about this was how they got this whole
+thing set up. So I don't know how many
+
+ align:start position:0%
+thing set up. So I don't know how many
+ 
+
+ align:start position:0%
+thing set up. So I don't know how many
+of you do eur ops, but you know part of
+
+ align:start position:0%
+of you do eur ops, but you know part of
+ 
+
+ align:start position:0%
+of you do eur ops, but you know part of
+the thing in doing europs and doing
+
+ align:start position:0%
+the thing in doing europs and doing
+ 
+
+ align:start position:0%
+the thing in doing europs and doing
+experiments in labs, just how do you do
+
+ align:start position:0%
+experiments in labs, just how do you do
+ 
+
+ align:start position:0%
+experiments in labs, just how do you do
+the experiment? So you know the park
+
+ align:start position:0%
+the experiment? So you know the park
+ 
+
+ align:start position:0%
+the experiment? So you know the park
+rangers got the acorn woodpecker. That's
+
+ align:start position:0%
+rangers got the acorn woodpecker. That's
+ 
+
+ align:start position:0%
+rangers got the acorn woodpecker. That's
+all very good, but they have to get the
+
+ align:start position:0%
+all very good, but they have to get the
+ 
+
+ align:start position:0%
+all very good, but they have to get the
+woodpecker to peck in front of the
+
+ align:start position:0%
+woodpecker to peck in front of the
+ 
+
+ align:start position:0%
+woodpecker to peck in front of the
+camera, right? They have to get the
+
+ align:start position:0%
+camera, right? They have to get the
+ 
+
+ align:start position:0%
+camera, right? They have to get the
+camera to turn on as it's pecking and
+
+ align:start position:0%
+camera to turn on as it's pecking and
+ 
+
+ align:start position:0%
+camera to turn on as it's pecking and
+all this. there's some experimental
+
+ align:start position:0%
+all this. there's some experimental
+ 
+
+ align:start position:0%
+all this. there's some experimental
+challenges. So the important thing, the
+
+ align:start position:0%
+challenges. So the important thing, the
+ 
+
+ align:start position:0%
+challenges. So the important thing, the
+critical thing is the date of the paper.
+
+ align:start position:0%
+critical thing is the date of the paper.
+ 
+
+ align:start position:0%
+critical thing is the date of the paper.
+This was written in 1979, which meant
+
+ align:start position:0%
+This was written in 1979, which meant
+ 
+
+ align:start position:0%
+This was written in 1979, which meant
+they probably did the experiments in
+
+ align:start position:0%
+they probably did the experiments in
+ 
+
+ align:start position:0%
+they probably did the experiments in
+1978 and I was a graduate student in
+
+ align:start position:0%
+1978 and I was a graduate student in
+ 
+
+ align:start position:0%
+1978 and I was a graduate student in
+1978. And I can report there were no
+
+ align:start position:0%
+1978. And I can report there were no
+ 
+
+ align:start position:0%
+1978. And I can report there were no
+Apple computers in 1978. There were no
+
+ align:start position:0%
+Apple computers in 1978. There were no
+ 
+
+ align:start position:0%
+Apple computers in 1978. There were no
+laptops. You couldn't just kind of do
+
+ align:start position:0%
+laptops. You couldn't just kind of do
+ 
+
+ align:start position:0%
+laptops. You couldn't just kind of do
+your little PowerPoint slides. And most
+
+ align:start position:0%
+your little PowerPoint slides. And most
+ 
+
+ align:start position:0%
+your little PowerPoint slides. And most
+offices had something called an IBM
+
+ align:start position:0%
+offices had something called an IBM
+ 
+
+ align:start position:0%
+offices had something called an IBM
+select electric typewriter. I don't know
+
+ align:start position:0%
+select electric typewriter. I don't know
+ 
+
+ align:start position:0%
+select electric typewriter. I don't know
+if you've ever seen the old IBM
+
+ align:start position:0%
+if you've ever seen the old IBM
+ 
+
+ align:start position:0%
+if you've ever seen the old IBM
+typewriters, but the typewriters when
+
+ align:start position:0%
+typewriters, but the typewriters when
+ 
+
+ align:start position:0%
+typewriters, but the typewriters when
+you typed on the typewriters, they made
+
+ align:start position:0%
+you typed on the typewriters, they made
+ 
+
+ align:start position:0%
+you typed on the typewriters, they made
+these noises and it sounded kind of like
+
+ align:start position:0%
+these noises and it sounded kind of like
+ 
+
+ align:start position:0%
+these noises and it sounded kind of like
+a woodpecker pecking. And the ranger had
+
+ align:start position:0%
+a woodpecker pecking. And the ranger had
+ 
+
+ align:start position:0%
+a woodpecker pecking. And the ranger had
+one of these typewriters in his office.
+
+ align:start position:0%
+one of these typewriters in his office.
+ 
+
+ align:start position:0%
+one of these typewriters in his office.
+And he had discovered that if he typed
+
+ align:start position:0%
+And he had discovered that if he typed
+ 
+
+ align:start position:0%
+And he had discovered that if he typed
+on the typewriter, the woodpecker
+
+ align:start position:0%
+on the typewriter, the woodpecker
+ 
+
+ align:start position:0%
+on the typewriter, the woodpecker
+thought, "Oh, there's another
+
+ align:start position:0%
+thought, "Oh, there's another
+ 
+
+ align:start position:0%
+thought, "Oh, there's another
+woodpecker. I'll start pecking." And so
+
+ align:start position:0%
+woodpecker. I'll start pecking." And so
+ 
+
+ align:start position:0%
+woodpecker. I'll start pecking." And so
+they used the typewriter as a way to get
+
+ align:start position:0%
+they used the typewriter as a way to get
+ 
+
+ align:start position:0%
+they used the typewriter as a way to get
+the woodpeckers to peck. And I think
+
+ align:start position:0%
+the woodpeckers to peck. And I think
+ 
+
+ align:start position:0%
+the woodpeckers to peck. And I think
+they had some old stump and they put I
+
+ align:start position:0%
+they had some old stump and they put I
+ 
+
+ align:start position:0%
+they had some old stump and they put I
+don't know if they put nuts or peanut
+
+ align:start position:0%
+don't know if they put nuts or peanut
+ 
+
+ align:start position:0%
+don't know if they put nuts or peanut
+butter or something into the stump to
+
+ align:start position:0%
+butter or something into the stump to
+ 
+
+ align:start position:0%
+butter or something into the stump to
+get the woodpecker to peck at it because
+
+ align:start position:0%
+get the woodpecker to peck at it because
+ 
+
+ align:start position:0%
+get the woodpecker to peck at it because
+they needed to peck at a particular
+
+ align:start position:0%
+they needed to peck at a particular
+ 
+
+ align:start position:0%
+they needed to peck at a particular
+spot. So they have the camera all set
+
+ align:start position:0%
+spot. So they have the camera all set
+ 
+
+ align:start position:0%
+spot. So they have the camera all set
+up. So anyway, they had this whole kind
+
+ align:start position:0%
+up. So anyway, they had this whole kind
+ 
+
+ align:start position:0%
+up. So anyway, they had this whole kind
+of arrangement to um to do this
+
+ align:start position:0%
+of arrangement to um to do this
+ 
+
+ align:start position:0%
+of arrangement to um to do this
+high-speed video of the woodpecker
+
+ align:start position:0%
+high-speed video of the woodpecker
+ 
+
+ align:start position:0%
+high-speed video of the woodpecker
+pecking. Okay, so it goes at up to
+
+ align:start position:0%
+pecking. Okay, so it goes at up to
+ 
+
+ align:start position:0%
+pecking. Okay, so it goes at up to
+1500g, which is kind of amazing. And
+
+ align:start position:0%
+1500g, which is kind of amazing. And
+ 
+
+ align:start position:0%
+1500g, which is kind of amazing. And
+then, you know, remember also they do
+
+ align:start position:0%
+then, you know, remember also they do
+ 
+
+ align:start position:0%
+then, you know, remember also they do
+this repeatedly. They do it at like 10
+
+ align:start position:0%
+this repeatedly. They do it at like 10
+ 
+
+ align:start position:0%
+this repeatedly. They do it at like 10
+or 20 times a second. Um then this is
+
+ align:start position:0%
+or 20 times a second. Um then this is
+ 
+
+ align:start position:0%
+or 20 times a second. Um then this is
+just explaining what stress is, but you
+
+ align:start position:0%
+just explaining what stress is, but you
+ 
+
+ align:start position:0%
+just explaining what stress is, but you
+already know what stress is, so I'm
+
+ align:start position:0%
+already know what stress is, so I'm
+ 
+
+ align:start position:0%
+already know what stress is, so I'm
+going to skip over that. And so the way
+
+ align:start position:0%
+going to skip over that. And so the way
+ 
+
+ align:start position:0%
+going to skip over that. And so the way
+you can think about this is to think
+
+ align:start position:0%
+you can think about this is to think
+ 
+
+ align:start position:0%
+you can think about this is to think
+about it in terms of a scaling argument.
+
+ align:start position:0%
+about it in terms of a scaling argument.
+ 
+
+ align:start position:0%
+about it in terms of a scaling argument.
+So imagine there's the brain and there's
+
+ align:start position:0%
+So imagine there's the brain and there's
+ 
+
+ align:start position:0%
+So imagine there's the brain and there's
+the skull. And when the head hits the
+
+ align:start position:0%
+the skull. And when the head hits the
+ 
+
+ align:start position:0%
+the skull. And when the head hits the
+tree, the brain's going to accelerate
+
+ align:start position:0%
+tree, the brain's going to accelerate
+ 
+
+ align:start position:0%
+tree, the brain's going to accelerate
+and the skull or the brain and the skull
+
+ align:start position:0%
+and the skull or the brain and the skull
+ 
+
+ align:start position:0%
+and the skull or the brain and the skull
+are both going to decelerate. And you
+
+ align:start position:0%
+are both going to decelerate. And you
+ 
+
+ align:start position:0%
+are both going to decelerate. And you
+can think of the stress as the force
+
+ align:start position:0%
+can think of the stress as the force
+ 
+
+ align:start position:0%
+can think of the stress as the force
+over the area. So the force is the mass
+
+ align:start position:0%
+over the area. So the force is the mass
+ 
+
+ align:start position:0%
+over the area. So the force is the mass
+times the deceleration over the area. So
+
+ align:start position:0%
+times the deceleration over the area. So
+ 
+
+ align:start position:0%
+times the deceleration over the area. So
+that value for the woodpecker you can
+
+ align:start position:0%
+that value for the woodpecker you can
+ 
+
+ align:start position:0%
+that value for the woodpecker you can
+say is roughly equal to the same values
+
+ align:start position:0%
+say is roughly equal to the same values
+ 
+
+ align:start position:0%
+say is roughly equal to the same values
+but for the human. So what that sort of
+
+ align:start position:0%
+but for the human. So what that sort of
+ 
+
+ align:start position:0%
+but for the human. So what that sort of
+argument relies on is the idea that the
+
+ align:start position:0%
+argument relies on is the idea that the
+ 
+
+ align:start position:0%
+argument relies on is the idea that the
+stress to cause damage in the woodpecker
+
+ align:start position:0%
+stress to cause damage in the woodpecker
+ 
+
+ align:start position:0%
+stress to cause damage in the woodpecker
+brain is similar to to the stress to
+
+ align:start position:0%
+brain is similar to to the stress to
+ 
+
+ align:start position:0%
+brain is similar to to the stress to
+cause damage in the human brain. And
+
+ align:start position:0%
+cause damage in the human brain. And
+ 
+
+ align:start position:0%
+cause damage in the human brain. And
+that's not totally unre unreasonable. So
+
+ align:start position:0%
+that's not totally unre unreasonable. So
+ 
+
+ align:start position:0%
+that's not totally unre unreasonable. So
+if you if you look at bone for example
+
+ align:start position:0%
+if you if you look at bone for example
+ 
+
+ align:start position:0%
+if you if you look at bone for example
+like when you measure the strength of
+
+ align:start position:0%
+like when you measure the strength of
+ 
+
+ align:start position:0%
+like when you measure the strength of
+the whale bones it's not going to be
+
+ align:start position:0%
+the whale bones it's not going to be
+ 
+
+ align:start position:0%
+the whale bones it's not going to be
+that different from what you would
+
+ align:start position:0%
+that different from what you would
+ 
+
+ align:start position:0%
+that different from what you would
+measure from human bones. So when you
+
+ align:start position:0%
+measure from human bones. So when you
+ 
+
+ align:start position:0%
+measure from human bones. So when you
+look at a particular type of tissue and
+
+ align:start position:0%
+look at a particular type of tissue and
+ 
+
+ align:start position:0%
+look at a particular type of tissue and
+you look at the strength of it in
+
+ align:start position:0%
+you look at the strength of it in
+ 
+
+ align:start position:0%
+you look at the strength of it in
+different species, the properties aren't
+
+ align:start position:0%
+different species, the properties aren't
+ 
+
+ align:start position:0%
+different species, the properties aren't
+that different from one species to
+
+ align:start position:0%
+that different from one species to
+ 
+
+ align:start position:0%
+that different from one species to
+another. So let's say the brain tissue
+
+ align:start position:0%
+another. So let's say the brain tissue
+ 
+
+ align:start position:0%
+another. So let's say the brain tissue
+has gets damaged at the same stress in
+
+ align:start position:0%
+has gets damaged at the same stress in
+ 
+
+ align:start position:0%
+has gets damaged at the same stress in
+the two species. So we can write this
+
+ align:start position:0%
+the two species. So we can write this
+ 
+
+ align:start position:0%
+the two species. So we can write this
+sort of equation down. Uh and then the
+
+ align:start position:0%
+sort of equation down. Uh and then the
+ 
+
+ align:start position:0%
+sort of equation down. Uh and then the
+mass oops see there we go. The mass is
+
+ align:start position:0%
+mass oops see there we go. The mass is
+ 
+
+ align:start position:0%
+mass oops see there we go. The mass is
+going to depend on the density of the
+
+ align:start position:0%
+going to depend on the density of the
+ 
+
+ align:start position:0%
+going to depend on the density of the
+brain tissue times the volume. And the
+
+ align:start position:0%
+brain tissue times the volume. And the
+ 
+
+ align:start position:0%
+brain tissue times the volume. And the
+volume goes as the radius cubed. And the
+
+ align:start position:0%
+volume goes as the radius cubed. And the
+ 
+
+ align:start position:0%
+volume goes as the radius cubed. And the
+density is going to be the same for the
+
+ align:start position:0%
+density is going to be the same for the
+ 
+
+ align:start position:0%
+density is going to be the same for the
+woodpecker or for the human. So assume
+
+ align:start position:0%
+woodpecker or for the human. So assume
+ 
+
+ align:start position:0%
+woodpecker or for the human. So assume
+the brain tissue has the same kind of
+
+ align:start position:0%
+the brain tissue has the same kind of
+ 
+
+ align:start position:0%
+the brain tissue has the same kind of
+basic stuff. So the mass goes as the
+
+ align:start position:0%
+basic stuff. So the mass goes as the
+ 
+
+ align:start position:0%
+basic stuff. So the mass goes as the
+radius cubed and the area of contact is
+
+ align:start position:0%
+radius cubed and the area of contact is
+ 
+
+ align:start position:0%
+radius cubed and the area of contact is
+going to go as the radius squared. And
+
+ align:start position:0%
+going to go as the radius squared. And
+ 
+
+ align:start position:0%
+going to go as the radius squared. And
+so there's a a radius term. So you can
+
+ align:start position:0%
+so there's a a radius term. So you can
+ 
+
+ align:start position:0%
+so there's a a radius term. So you can
+say the radius times the deceleration in
+
+ align:start position:0%
+say the radius times the deceleration in
+ 
+
+ align:start position:0%
+say the radius times the deceleration in
+the woodpecker should be equal to the
+
+ align:start position:0%
+the woodpecker should be equal to the
+ 
+
+ align:start position:0%
+the woodpecker should be equal to the
+radius times the deceleration in the
+
+ align:start position:0%
+radius times the deceleration in the
+ 
+
+ align:start position:0%
+radius times the deceleration in the
+human. And obviously the woodpecker
+
+ align:start position:0%
+human. And obviously the woodpecker
+ 
+
+ align:start position:0%
+human. And obviously the woodpecker
+radius is going to be a lot smaller. So
+
+ align:start position:0%
+radius is going to be a lot smaller. So
+ 
+
+ align:start position:0%
+radius is going to be a lot smaller. So
+that woodpecker deceleration is going to
+
+ align:start position:0%
+that woodpecker deceleration is going to
+ 
+
+ align:start position:0%
+that woodpecker deceleration is going to
+be a lot bigger. So part of the thing is
+
+ align:start position:0%
+be a lot bigger. So part of the thing is
+ 
+
+ align:start position:0%
+be a lot bigger. So part of the thing is
+the brain is just a lot smaller. Then
+
+ align:start position:0%
+the brain is just a lot smaller. Then
+ 
+
+ align:start position:0%
+the brain is just a lot smaller. Then
+there's there's another factor that
+
+ align:start position:0%
+there's there's another factor that
+ 
+
+ align:start position:0%
+there's there's another factor that
+comes into it. These are um photographs
+
+ align:start position:0%
+comes into it. These are um photographs
+ 
+
+ align:start position:0%
+comes into it. These are um photographs
+of of a acorn woodpecker skull and a
+
+ align:start position:0%
+of of a acorn woodpecker skull and a
+ 
+
+ align:start position:0%
+of of a acorn woodpecker skull and a
+human skull that I got from the Museum
+
+ align:start position:0%
+human skull that I got from the Museum
+ 
+
+ align:start position:0%
+human skull that I got from the Museum
+of Comparative Zoolology at Harvard. So
+
+ align:start position:0%
+of Comparative Zoolology at Harvard. So
+ 
+
+ align:start position:0%
+of Comparative Zoolology at Harvard. So
+this is looking down on the top and this
+
+ align:start position:0%
+this is looking down on the top and this
+ 
+
+ align:start position:0%
+this is looking down on the top and this
+is sort of an elevation view. And if you
+
+ align:start position:0%
+is sort of an elevation view. And if you
+ 
+
+ align:start position:0%
+is sort of an elevation view. And if you
+think of the brain as roughly a
+
+ align:start position:0%
+think of the brain as roughly a
+ 
+
+ align:start position:0%
+think of the brain as roughly a
+hemisphere, I mean obviously it's not a
+
+ align:start position:0%
+hemisphere, I mean obviously it's not a
+ 
+
+ align:start position:0%
+hemisphere, I mean obviously it's not a
+perfect hemisphere but let's say it's
+
+ align:start position:0%
+perfect hemisphere but let's say it's
+ 
+
+ align:start position:0%
+perfect hemisphere but let's say it's
+roughly a hemisphere. The orientation of
+
+ align:start position:0%
+roughly a hemisphere. The orientation of
+ 
+
+ align:start position:0%
+roughly a hemisphere. The orientation of
+the brain in the skull is slightly
+
+ align:start position:0%
+the brain in the skull is slightly
+ 
+
+ align:start position:0%
+the brain in the skull is slightly
+different in the birds and in the human.
+
+ align:start position:0%
+different in the birds and in the human.
+ 
+
+ align:start position:0%
+different in the birds and in the human.
+So if you think of it as being this way
+
+ align:start position:0%
+So if you think of it as being this way
+ 
+
+ align:start position:0%
+So if you think of it as being this way
+on in the woodpecker, it's turned
+
+ align:start position:0%
+on in the woodpecker, it's turned
+ 
+
+ align:start position:0%
+on in the woodpecker, it's turned
+roughly this way on and the contact
+
+ align:start position:0%
+roughly this way on and the contact
+ 
+
+ align:start position:0%
+roughly this way on and the contact
+area, think of this as the contact area,
+
+ align:start position:0%
+area, think of this as the contact area,
+ 
+
+ align:start position:0%
+area, think of this as the contact area,
+sort of projected area would be a full
+
+ align:start position:0%
+sort of projected area would be a full
+ 
+
+ align:start position:0%
+sort of projected area would be a full
+circle. And in the human, the brain is
+
+ align:start position:0%
+circle. And in the human, the brain is
+ 
+
+ align:start position:0%
+circle. And in the human, the brain is
+more this way on. And then the sort of
+
+ align:start position:0%
+more this way on. And then the sort of
+ 
+
+ align:start position:0%
+more this way on. And then the sort of
+projected contact area is a semicircle.
+
+ align:start position:0%
+projected contact area is a semicircle.
+ 
+
+ align:start position:0%
+projected contact area is a semicircle.
+So there's a factor of two difference
+
+ align:start position:0%
+So there's a factor of two difference
+ 
+
+ align:start position:0%
+So there's a factor of two difference
+just because of the orientation of the
+
+ align:start position:0%
+just because of the orientation of the
+ 
+
+ align:start position:0%
+just because of the orientation of the
+brain. And so I've I put the factor of
+
+ align:start position:0%
+brain. And so I've I put the factor of
+ 
+
+ align:start position:0%
+brain. And so I've I put the factor of
+two that accounts for that. So then I
+
+ align:start position:0%
+two that accounts for that. So then I
+ 
+
+ align:start position:0%
+two that accounts for that. So then I
+could say the deceleration that the
+
+ align:start position:0%
+could say the deceleration that the
+ 
+
+ align:start position:0%
+could say the deceleration that the
+woodpecker can take is twice the ratio
+
+ align:start position:0%
+woodpecker can take is twice the ratio
+ 
+
+ align:start position:0%
+woodpecker can take is twice the ratio
+of the radi of the human and the
+
+ align:start position:0%
+of the radi of the human and the
+ 
+
+ align:start position:0%
+of the radi of the human and the
+woodpecker brain times the deceleration
+
+ align:start position:0%
+woodpecker brain times the deceleration
+ 
+
+ align:start position:0%
+woodpecker brain times the deceleration
+the human can take. And this was around
+
+ align:start position:0%
+the human can take. And this was around
+ 
+
+ align:start position:0%
+the human can take. And this was around
+100g, remember? So then I wanted to know
+
+ align:start position:0%
+100g, remember? So then I wanted to know
+ 
+
+ align:start position:0%
+100g, remember? So then I wanted to know
+what the ratio of the sizes was. And I
+
+ align:start position:0%
+what the ratio of the sizes was. And I
+ 
+
+ align:start position:0%
+what the ratio of the sizes was. And I
+thought, "Oh geez, I'm going to have to,
+
+ align:start position:0%
+thought, "Oh geez, I'm going to have to,
+ 
+
+ align:start position:0%
+thought, "Oh geez, I'm going to have to,
+you know, mess around with skulls and
+
+ align:start position:0%
+you know, mess around with skulls and
+ 
+
+ align:start position:0%
+you know, mess around with skulls and
+try to make some sort of measurements
+
+ align:start position:0%
+try to make some sort of measurements
+ 
+
+ align:start position:0%
+try to make some sort of measurements
+and this is going to be a drag." And
+
+ align:start position:0%
+and this is going to be a drag." And
+ 
+
+ align:start position:0%
+and this is going to be a drag." And
+then I found this paper. I couldn't
+
+ align:start position:0%
+then I found this paper. I couldn't
+ 
+
+ align:start position:0%
+then I found this paper. I couldn't
+believe it. I found this paper called
+
+ align:start position:0%
+believe it. I found this paper called
+ 
+
+ align:start position:0%
+believe it. I found this paper called
+brain size in birds. And this guy had
+
+ align:start position:0%
+brain size in birds. And this guy had
+ 
+
+ align:start position:0%
+brain size in birds. And this guy had
+table after table after table of the
+
+ align:start position:0%
+table after table after table of the
+ 
+
+ align:start position:0%
+table after table after table of the
+mass of the brain in different birds.
+
+ align:start position:0%
+mass of the brain in different birds.
+ 
+
+ align:start position:0%
+mass of the brain in different birds.
+And he had the acorn woodpecker, lucky
+
+ align:start position:0%
+And he had the acorn woodpecker, lucky
+ 
+
+ align:start position:0%
+And he had the acorn woodpecker, lucky
+for me. So if you just assume that the
+
+ align:start position:0%
+for me. So if you just assume that the
+ 
+
+ align:start position:0%
+for me. So if you just assume that the
+the brain is roughly a hemisphere, if
+
+ align:start position:0%
+the brain is roughly a hemisphere, if
+ 
+
+ align:start position:0%
+the brain is roughly a hemisphere, if
+you have the mass, you can work out
+
+ align:start position:0%
+you have the mass, you can work out
+ 
+
+ align:start position:0%
+you have the mass, you can work out
+roughly what the radius is. So it turns
+
+ align:start position:0%
+roughly what the radius is. So it turns
+ 
+
+ align:start position:0%
+roughly what the radius is. So it turns
+out there's a factor of eight difference
+
+ align:start position:0%
+out there's a factor of eight difference
+ 
+
+ align:start position:0%
+out there's a factor of eight difference
+between the radi. And so uh the human
+
+ align:start position:0%
+between the radi. And so uh the human
+ 
+
+ align:start position:0%
+between the radi. And so uh the human
+brain's about eight times the size of
+
+ align:start position:0%
+brain's about eight times the size of
+ 
+
+ align:start position:0%
+brain's about eight times the size of
+the woodpecker. And then if you take
+
+ align:start position:0%
+the woodpecker. And then if you take
+ 
+
+ align:start position:0%
+the woodpecker. And then if you take
+into account this factor of two, that
+
+ align:start position:0%
+into account this factor of two, that
+ 
+
+ align:start position:0%
+into account this factor of two, that
+means the woodpecker should be able to
+
+ align:start position:0%
+means the woodpecker should be able to
+ 
+
+ align:start position:0%
+means the woodpecker should be able to
+tolerate a deceleration of 16 times what
+
+ align:start position:0%
+tolerate a deceleration of 16 times what
+ 
+
+ align:start position:0%
+tolerate a deceleration of 16 times what
+the human can. So remember I said the
+
+ align:start position:0%
+the human can. So remember I said the
+ 
+
+ align:start position:0%
+the human can. So remember I said the
+human can take about 100. So this would
+
+ align:start position:0%
+human can take about 100. So this would
+ 
+
+ align:start position:0%
+human can take about 100. So this would
+get the woodpecker up to 1600, but they
+
+ align:start position:0%
+get the woodpecker up to 1600, but they
+ 
+
+ align:start position:0%
+get the woodpecker up to 1600, but they
+measured 1500. And I'm a civil engineer.
+
+ align:start position:0%
+measured 1500. And I'm a civil engineer.
+ 
+
+ align:start position:0%
+measured 1500. And I'm a civil engineer.
+Originally, I like big factors of
+
+ align:start position:0%
+Originally, I like big factors of
+ 
+
+ align:start position:0%
+Originally, I like big factors of
+safety. That's a little too close for
+
+ align:start position:0%
+safety. That's a little too close for
+ 
+
+ align:start position:0%
+safety. That's a little too close for
+comfort for me. Uh and so it turns out
+
+ align:start position:0%
+comfort for me. Uh and so it turns out
+ 
+
+ align:start position:0%
+comfort for me. Uh and so it turns out
+there's one more factor that that
+
+ align:start position:0%
+there's one more factor that that
+ 
+
+ align:start position:0%
+there's one more factor that that
+matters. Uh people have studied human
+
+ align:start position:0%
+matters. Uh people have studied human
+ 
+
+ align:start position:0%
+matters. Uh people have studied human
+brain injury pretty extensively. And one
+
+ align:start position:0%
+brain injury pretty extensively. And one
+ 
+
+ align:start position:0%
+brain injury pretty extensively. And one
+of the things they've looked at is how
+
+ align:start position:0%
+of the things they've looked at is how
+ 
+
+ align:start position:0%
+of the things they've looked at is how
+much acceleration you can tolerate
+
+ align:start position:0%
+much acceleration you can tolerate
+ 
+
+ align:start position:0%
+much acceleration you can tolerate
+without injury uh relative to the
+
+ align:start position:0%
+without injury uh relative to the
+ 
+
+ align:start position:0%
+without injury uh relative to the
+duration of the impact. So this is from
+
+ align:start position:0%
+duration of the impact. So this is from
+ 
+
+ align:start position:0%
+duration of the impact. So this is from
+a car crash conference. Uh so here's the
+
+ align:start position:0%
+a car crash conference. Uh so here's the
+ 
+
+ align:start position:0%
+a car crash conference. Uh so here's the
+tolerable acceleration and here's the
+
+ align:start position:0%
+tolerable acceleration and here's the
+ 
+
+ align:start position:0%
+tolerable acceleration and here's the
+duration of the impact. And typically
+
+ align:start position:0%
+duration of the impact. And typically
+ 
+
+ align:start position:0%
+duration of the impact. And typically
+for human head impacts the deceleration
+
+ align:start position:0%
+for human head impacts the deceleration
+ 
+
+ align:start position:0%
+for human head impacts the deceleration
+occurs over a few milliseconds like over
+
+ align:start position:0%
+occurs over a few milliseconds like over
+ 
+
+ align:start position:0%
+occurs over a few milliseconds like over
+3 to 10 milliseconds. So if this is the
+
+ align:start position:0%
+3 to 10 milliseconds. So if this is the
+ 
+
+ align:start position:0%
+3 to 10 milliseconds. So if this is the
+duration of the typical head impact for
+
+ align:start position:0%
+duration of the typical head impact for
+ 
+
+ align:start position:0%
+duration of the typical head impact for
+a human, here's the range of the
+
+ align:start position:0%
+a human, here's the range of the
+ 
+
+ align:start position:0%
+a human, here's the range of the
+tolerable accelerations between about 80
+
+ align:start position:0%
+tolerable accelerations between about 80
+ 
+
+ align:start position:0%
+tolerable accelerations between about 80
+and 160 g. So you know I said around
+
+ align:start position:0%
+and 160 g. So you know I said around
+ 
+
+ align:start position:0%
+and 160 g. So you know I said around
+100. So we can take this curve and now
+
+ align:start position:0%
+100. So we can take this curve and now
+ 
+
+ align:start position:0%
+100. So we can take this curve and now
+we have this factor of 16 and we can
+
+ align:start position:0%
+we have this factor of 16 and we can
+ 
+
+ align:start position:0%
+we have this factor of 16 and we can
+just scale it up by our factor of 16 for
+
+ align:start position:0%
+just scale it up by our factor of 16 for
+ 
+
+ align:start position:0%
+just scale it up by our factor of 16 for
+the woodpecker. So if I scale it up by
+
+ align:start position:0%
+the woodpecker. So if I scale it up by
+ 
+
+ align:start position:0%
+the woodpecker. So if I scale it up by
+the factor of 16, we're there. But the
+
+ align:start position:0%
+the factor of 16, we're there. But the
+ 
+
+ align:start position:0%
+the factor of 16, we're there. But the
+the duration of the impacts was more
+
+ align:start position:0%
+the duration of the impacts was more
+ 
+
+ align:start position:0%
+the duration of the impacts was more
+around a half a millisecond to a
+
+ align:start position:0%
+around a half a millisecond to a
+ 
+
+ align:start position:0%
+around a half a millisecond to a
+millisecond. So I've extrapolated this a
+
+ align:start position:0%
+millisecond. So I've extrapolated this a
+ 
+
+ align:start position:0%
+millisecond. So I've extrapolated this a
+little bit and the duration of them is
+
+ align:start position:0%
+little bit and the duration of them is
+ 
+
+ align:start position:0%
+little bit and the duration of them is
+is up in here. So this is saying the
+
+ align:start position:0%
+is up in here. So this is saying the
+ 
+
+ align:start position:0%
+is up in here. So this is saying the
+woodpecker can take uh these sorts of
+
+ align:start position:0%
+woodpecker can take uh these sorts of
+ 
+
+ align:start position:0%
+woodpecker can take uh these sorts of
+decelerations here and that adds on
+
+ align:start position:0%
+decelerations here and that adds on
+ 
+
+ align:start position:0%
+decelerations here and that adds on
+another factor of four and these were
+
+ align:start position:0%
+another factor of four and these were
+ 
+
+ align:start position:0%
+another factor of four and these were
+the measured decelerations. They were
+
+ align:start position:0%
+the measured decelerations. They were
+ 
+
+ align:start position:0%
+the measured decelerations. They were
+sort of in 1500 was about the biggest
+
+ align:start position:0%
+sort of in 1500 was about the biggest
+ 
+
+ align:start position:0%
+sort of in 1500 was about the biggest
+and I think it went down to about few
+
+ align:start position:0%
+and I think it went down to about few
+ 
+
+ align:start position:0%
+and I think it went down to about few
+hundred g. So there's really three
+
+ align:start position:0%
+hundred g. So there's really three
+ 
+
+ align:start position:0%
+hundred g. So there's really three
+factors. One is the small brain size. So
+
+ align:start position:0%
+factors. One is the small brain size. So
+ 
+
+ align:start position:0%
+factors. One is the small brain size. So
+there's this sort of scaling factor. One
+
+ align:start position:0%
+there's this sort of scaling factor. One
+ 
+
+ align:start position:0%
+there's this sort of scaling factor. One
+is the orientation of the brain. That
+
+ align:start position:0%
+is the orientation of the brain. That
+ 
+
+ align:start position:0%
+is the orientation of the brain. That
+was another factor of two. And then
+
+ align:start position:0%
+was another factor of two. And then
+ 
+
+ align:start position:0%
+was another factor of two. And then
+there's this duration of impact which is
+
+ align:start position:0%
+there's this duration of impact which is
+ 
+
+ align:start position:0%
+there's this duration of impact which is
+a factor of four. And so that's how you
+
+ align:start position:0%
+a factor of four. And so that's how you
+ 
+
+ align:start position:0%
+a factor of four. And so that's how you
+can get this huge decelerations that
+
+ align:start position:0%
+can get this huge decelerations that
+ 
+
+ align:start position:0%
+can get this huge decelerations that
+they've measured in the woodpecker when
+
+ align:start position:0%
+they've measured in the woodpecker when
+ 
+
+ align:start position:0%
+they've measured in the woodpecker when
+they're pecking. Um so now I have just a
+
+ align:start position:0%
+they're pecking. Um so now I have just a
+ 
+
+ align:start position:0%
+they're pecking. Um so now I have just a
+couple more slides. So woodpeckers have
+
+ align:start position:0%
+couple more slides. So woodpeckers have
+ 
+
+ align:start position:0%
+couple more slides. So woodpeckers have
+various adaptations to pecking too. So
+
+ align:start position:0%
+various adaptations to pecking too. So
+ 
+
+ align:start position:0%
+various adaptations to pecking too. So
+one of the things is they have amazingly
+
+ align:start position:0%
+one of the things is they have amazingly
+ 
+
+ align:start position:0%
+one of the things is they have amazingly
+stiff tail feathers. You see the tails
+
+ align:start position:0%
+stiff tail feathers. You see the tails
+ 
+
+ align:start position:0%
+stiff tail feathers. You see the tails
+here? You can't quite see it because
+
+ align:start position:0%
+here? You can't quite see it because
+ 
+
+ align:start position:0%
+here? You can't quite see it because
+this didn't reproduce quite properly,
+
+ align:start position:0%
+this didn't reproduce quite properly,
+ 
+
+ align:start position:0%
+this didn't reproduce quite properly,
+but the the woodpecker is perched on a
+
+ align:start position:0%
+but the the woodpecker is perched on a
+ 
+
+ align:start position:0%
+but the the woodpecker is perched on a
+tree here and the tail is pressed up
+
+ align:start position:0%
+tree here and the tail is pressed up
+ 
+
+ align:start position:0%
+tree here and the tail is pressed up
+against the tree. And if you think about
+
+ align:start position:0%
+against the tree. And if you think about
+ 
+
+ align:start position:0%
+against the tree. And if you think about
+pecking, like imagine if its tail was
+
+ align:start position:0%
+pecking, like imagine if its tail was
+ 
+
+ align:start position:0%
+pecking, like imagine if its tail was
+not pressed up against the tree. It
+
+ align:start position:0%
+not pressed up against the tree. It
+ 
+
+ align:start position:0%
+not pressed up against the tree. It
+would be kind of grabbing on with its
+
+ align:start position:0%
+would be kind of grabbing on with its
+ 
+
+ align:start position:0%
+would be kind of grabbing on with its
+feet and it'd be trying to peck and it
+
+ align:start position:0%
+feet and it'd be trying to peck and it
+ 
+
+ align:start position:0%
+feet and it'd be trying to peck and it
+would be kind of hard to push. You know,
+
+ align:start position:0%
+would be kind of hard to push. You know,
+ 
+
+ align:start position:0%
+would be kind of hard to push. You know,
+you need something to push against. And
+
+ align:start position:0%
+you need something to push against. And
+ 
+
+ align:start position:0%
+you need something to push against. And
+so it's got these stiff tail feathers
+
+ align:start position:0%
+so it's got these stiff tail feathers
+ 
+
+ align:start position:0%
+so it's got these stiff tail feathers
+which make it easier to um to push
+
+ align:start position:0%
+which make it easier to um to push
+ 
+
+ align:start position:0%
+which make it easier to um to push
+against the tree. And so here's stiff
+
+ align:start position:0%
+against the tree. And so here's stiff
+ 
+
+ align:start position:0%
+against the tree. And so here's stiff
+tail feathers here. It's also got um
+
+ align:start position:0%
+tail feathers here. It's also got um
+ 
+
+ align:start position:0%
+tail feathers here. It's also got um
+kind of unusual feet for birds. It's got
+
+ align:start position:0%
+kind of unusual feet for birds. It's got
+ 
+
+ align:start position:0%
+kind of unusual feet for birds. It's got
+two toes forward and two toes back. And
+
+ align:start position:0%
+two toes forward and two toes back. And
+ 
+
+ align:start position:0%
+two toes forward and two toes back. And
+again, if it's grabbing with its feet,
+
+ align:start position:0%
+again, if it's grabbing with its feet,
+ 
+
+ align:start position:0%
+again, if it's grabbing with its feet,
+that helps it kind of get some perches
+
+ align:start position:0%
+that helps it kind of get some perches
+ 
+
+ align:start position:0%
+that helps it kind of get some perches
+to kind of push against. That's called
+
+ align:start position:0%
+to kind of push against. That's called
+ 
+
+ align:start position:0%
+to kind of push against. That's called
+zygodactyl in the bird world. So, it's
+
+ align:start position:0%
+zygodactyl in the bird world. So, it's
+ 
+
+ align:start position:0%
+zygodactyl in the bird world. So, it's
+got these adaptations to pecking. And
+
+ align:start position:0%
+got these adaptations to pecking. And
+ 
+
+ align:start position:0%
+got these adaptations to pecking. And
+then finally, I just like this slide
+
+ align:start position:0%
+then finally, I just like this slide
+ 
+
+ align:start position:0%
+then finally, I just like this slide
+here from the New Yorker because it's a
+
+ align:start position:0%
+here from the New Yorker because it's a
+ 
+
+ align:start position:0%
+here from the New Yorker because it's a
+woodpecker pecking out a woodpecker. So,
+
+ align:start position:0%
+woodpecker pecking out a woodpecker. So,
+ 
+
+ align:start position:0%
+woodpecker pecking out a woodpecker. So,
+it seemed kind of cute. And there's
+
+ align:start position:0%
+it seemed kind of cute. And there's
+ 
+
+ align:start position:0%
+it seemed kind of cute. And there's
+there's several people help me with this
+
+ align:start position:0%
+there's several people help me with this
+ 
+
+ align:start position:0%
+there's several people help me with this
+project. Trey Krisco studies head injury
+
+ align:start position:0%
+project. Trey Krisco studies head injury
+ 
+
+ align:start position:0%
+project. Trey Krisco studies head injury
+at Brown. He he actually does uh work
+
+ align:start position:0%
+at Brown. He he actually does uh work
+ 
+
+ align:start position:0%
+at Brown. He he actually does uh work
+for the NFL on football um brain
+
+ align:start position:0%
+for the NFL on football um brain
+ 
+
+ align:start position:0%
+for the NFL on football um brain
+injuries and looks at football helmets.
+
+ align:start position:0%
+injuries and looks at football helmets.
+ 
+
+ align:start position:0%
+injuries and looks at football helmets.
+Sharon Schwarz is a friend of mine at
+
+ align:start position:0%
+Sharon Schwarz is a friend of mine at
+ 
+
+ align:start position:0%
+Sharon Schwarz is a friend of mine at
+Brown who's a biologist. She studies bat
+
+ align:start position:0%
+Brown who's a biologist. She studies bat
+ 
+
+ align:start position:0%
+Brown who's a biologist. She studies bat
+flight and she just thought this was
+
+ align:start position:0%
+flight and she just thought this was
+ 
+
+ align:start position:0%
+flight and she just thought this was
+kind of a cool project. So, in fact, I
+
+ align:start position:0%
+kind of a cool project. So, in fact, I
+ 
+
+ align:start position:0%
+kind of a cool project. So, in fact, I
+was walking the dog last week, a few
+
+ align:start position:0%
+was walking the dog last week, a few
+ 
+
+ align:start position:0%
+was walking the dog last week, a few
+days ago, and I saw bats flying around
+
+ align:start position:0%
+days ago, and I saw bats flying around
+ 
+
+ align:start position:0%
+days ago, and I saw bats flying around
+overhead at night, and it was so great
+
+ align:start position:0%
+overhead at night, and it was so great
+ 
+
+ align:start position:0%
+overhead at night, and it was so great
+to see the little bats. Um, so I had to
+
+ align:start position:0%
+to see the little bats. Um, so I had to
+ 
+
+ align:start position:0%
+to see the little bats. Um, so I had to
+immediately email Sharon and say, "Bats,
+
+ align:start position:0%
+immediately email Sharon and say, "Bats,
+ 
+
+ align:start position:0%
+immediately email Sharon and say, "Bats,
+there's bats in my neighborhood." Andy
+
+ align:start position:0%
+there's bats in my neighborhood." Andy
+ 
+
+ align:start position:0%
+there's bats in my neighborhood." Andy
+Beewiner runs the um Conquered Field
+
+ align:start position:0%
+Beewiner runs the um Conquered Field
+ 
+
+ align:start position:0%
+Beewiner runs the um Conquered Field
+Station and studies animal locomotion,
+
+ align:start position:0%
+Station and studies animal locomotion,
+ 
+
+ align:start position:0%
+Station and studies animal locomotion,
+and I talked to him about it. Jeremy
+
+ align:start position:0%
+and I talked to him about it. Jeremy
+ 
+
+ align:start position:0%
+and I talked to him about it. Jeremy
+Trimble was the one who gave me the
+
+ align:start position:0%
+Trimble was the one who gave me the
+ 
+
+ align:start position:0%
+Trimble was the one who gave me the
+skull pictures, and Matt Dawson was a
+
+ align:start position:0%
+skull pictures, and Matt Dawson was a
+ 
+
+ align:start position:0%
+skull pictures, and Matt Dawson was a
+student who helped me do some of the
+
+ align:start position:0%
+student who helped me do some of the
+ 
+
+ align:start position:0%
+student who helped me do some of the
+images. So, that's my woodpecker talk.
+
+ align:start position:0%
+images. So, that's my woodpecker talk.
+ 
+
+ align:start position:0%
+images. So, that's my woodpecker talk.
+So, that's the end of energy absorption.
+
+ align:start position:0%
+So, that's the end of energy absorption.
+ 
+
+ align:start position:0%
+So, that's the end of energy absorption.
+I just thought that was kind of amusing.
+
+ align:start position:0%
+I just thought that was kind of amusing.
+ 
+
+ align:start position:0%
+I just thought that was kind of amusing.
+So, next time we'll start talking about
+
+ align:start position:0%
+So, next time we'll start talking about
+ 
+
+ align:start position:0%
+So, next time we'll start talking about
+sandwich panels. So, uh let's see.
+
+ align:start position:0%
+sandwich panels. So, uh let's see.
+ 
+
+ align:start position:0%
+sandwich panels. So, uh let's see.
+Monday's a holiday. I will be in Toronto
+
+ align:start position:0%
+Monday's a holiday. I will be in Toronto
+ 
+
+ align:start position:0%
+Monday's a holiday. I will be in Toronto
+on Monday seeing my family. In fact, I'm
+
+ align:start position:0%
+on Monday seeing my family. In fact, I'm
+ 
+
+ align:start position:0%
+on Monday seeing my family. In fact, I'm
+going to see one of my old professors.
+
+ align:start position:0%
+going to see one of my old professors.
+ 
+
+ align:start position:0%
+going to see one of my old professors.
+I'm going to see my old fluid mechanics
+
+ align:start position:0%
+I'm going to see my old fluid mechanics
+ 
+
+ align:start position:0%
+I'm going to see my old fluid mechanics
+professor on Monday and have lunch. See
+
+ align:start position:0%
+professor on Monday and have lunch. See
+ 
+
+ align:start position:0%
+professor on Monday and have lunch. See
+my family on the weekend. And uh so
+
+ align:start position:0%
+my family on the weekend. And uh so
+ 
+
+ align:start position:0%
+my family on the weekend. And uh so
+we'll meet Wednesday next week and I'll
+
+ align:start position:0%
+we'll meet Wednesday next week and I'll
+ 
+
+ align:start position:0%
+we'll meet Wednesday next week and I'll
+start the bit on sandwich panels. So I
+
+ align:start position:0%
+start the bit on sandwich panels. So I
+ 
+
+ align:start position:0%
+start the bit on sandwich panels. So I
+think there's two lectures on sort of
+
+ align:start position:0%
+think there's two lectures on sort of
+ 
+
+ align:start position:0%
+think there's two lectures on sort of
+engineering sandwich panels and then
+
+ align:start position:0%
+engineering sandwich panels and then
+ 
+
+ align:start position:0%
+engineering sandwich panels and then
+there's a lecture on natural sandwich
+
+ align:start position:0%
+there's a lecture on natural sandwich
+ 
+
+ align:start position:0%
+there's a lecture on natural sandwich
+panels. Uh so bird skulls for example or
+
+ align:start position:0%
+panels. Uh so bird skulls for example or
+ 
+
+ align:start position:0%
+panels. Uh so bird skulls for example or
+natural sandwich panels. So I'll talk
+
+ align:start position:0%
+natural sandwich panels. So I'll talk
+ 
+
+ align:start position:0%
+natural sandwich panels. So I'll talk
+about that and then I think the last
+
+ align:start position:0%
+about that and then I think the last
+ 
+
+ align:start position:0%
+about that and then I think the last
+lecture we're getting like there's only
+
+ align:start position:0%
+lecture we're getting like there's only
+ 
+
+ align:start position:0%
+lecture we're getting like there's only
+a handful of lectures left. The last one
+
+ align:start position:0%
+a handful of lectures left. The last one
+ 
+
+ align:start position:0%
+a handful of lectures left. The last one
+I think I talk about natural materials
+
+ align:start position:0%
+I think I talk about natural materials
+ 
+
+ align:start position:0%
+I think I talk about natural materials
+because you know I like that so I just
+
+ align:start position:0%
+because you know I like that so I just
+ 
+
+ align:start position:0%
+because you know I like that so I just
+do that for fun.
\ No newline at end of file
diff --git a/ymsbTVLbyN4.txt b/ymsbTVLbyN4.txt
new file mode 100644
index 0000000000000000000000000000000000000000..1ad99e8750768d665356ec3e695a5b02a137fd60
--- /dev/null
+++ b/ymsbTVLbyN4.txt
@@ -0,0 +1,13891 @@
+align:start position:0%
+ 
+[Music]
+
+ align:start position:0%
+[Music]
+ 
+
+ align:start position:0%
+[Music]
+Well, so far in this course we've been
+
+ align:start position:0%
+Well, so far in this course we've been
+ 
+
+ align:start position:0%
+Well, so far in this course we've been
+talking about procedures
+
+ align:start position:0%
+talking about procedures
+ 
+
+ align:start position:0%
+talking about procedures
+and then just to remind you of this
+
+ align:start position:0%
+and then just to remind you of this
+ 
+
+ align:start position:0%
+and then just to remind you of this
+framework that that we introduced for
+
+ align:start position:0%
+framework that that we introduced for
+ 
+
+ align:start position:0%
+framework that that we introduced for
+talking about languages. We talked about
+
+ align:start position:0%
+talking about languages. We talked about
+ 
+
+ align:start position:0%
+talking about languages. We talked about
+the primitive things that are built into
+
+ align:start position:0%
+the primitive things that are built into
+ 
+
+ align:start position:0%
+the primitive things that are built into
+the system. Uh we mentioned some means
+
+ align:start position:0%
+the system. Uh we mentioned some means
+ 
+
+ align:start position:0%
+the system. Uh we mentioned some means
+of combination
+
+ align:start position:0%
+of combination
+ 
+
+ align:start position:0%
+of combination
+by which you take the primitive things
+
+ align:start position:0%
+by which you take the primitive things
+ 
+
+ align:start position:0%
+by which you take the primitive things
+and you make more complicated things.
+
+ align:start position:0%
+and you make more complicated things.
+ 
+
+ align:start position:0%
+and you make more complicated things.
+And then we talked about the means of
+
+ align:start position:0%
+And then we talked about the means of
+ 
+
+ align:start position:0%
+And then we talked about the means of
+abstraction. How you can take those
+
+ align:start position:0%
+abstraction. How you can take those
+ 
+
+ align:start position:0%
+abstraction. How you can take those
+complicated things and name them. So you
+
+ align:start position:0%
+complicated things and name them. So you
+ 
+
+ align:start position:0%
+complicated things and name them. So you
+can use them as simple building blocks.
+
+ align:start position:0%
+can use them as simple building blocks.
+ 
+
+ align:start position:0%
+can use them as simple building blocks.
+And then last time you saw we went even
+
+ align:start position:0%
+And then last time you saw we went even
+ 
+
+ align:start position:0%
+And then last time you saw we went even
+beyond that. We saw that by using higher
+
+ align:start position:0%
+beyond that. We saw that by using higher
+ 
+
+ align:start position:0%
+beyond that. We saw that by using higher
+order procedures,
+
+ align:start position:0%
+order procedures,
+ 
+
+ align:start position:0%
+order procedures,
+you can actually express general methods
+
+ align:start position:0%
+you can actually express general methods
+ 
+
+ align:start position:0%
+you can actually express general methods
+for computing things like the method of
+
+ align:start position:0%
+for computing things like the method of
+ 
+
+ align:start position:0%
+for computing things like the method of
+doing something by fixed points or
+
+ align:start position:0%
+doing something by fixed points or
+ 
+
+ align:start position:0%
+doing something by fixed points or
+Newton's method. And so the the
+
+ align:start position:0%
+Newton's method. And so the the
+ 
+
+ align:start position:0%
+Newton's method. And so the the
+incredible expressive power you can get
+
+ align:start position:0%
+incredible expressive power you can get
+ 
+
+ align:start position:0%
+incredible expressive power you can get
+just by combining these these means of
+
+ align:start position:0%
+just by combining these these means of
+ 
+
+ align:start position:0%
+just by combining these these means of
+abstraction. And the crucial idea in all
+
+ align:start position:0%
+abstraction. And the crucial idea in all
+ 
+
+ align:start position:0%
+abstraction. And the crucial idea in all
+of this is the one that we build a
+
+ align:start position:0%
+of this is the one that we build a
+ 
+
+ align:start position:0%
+of this is the one that we build a
+layered system. So for instance if we're
+
+ align:start position:0%
+layered system. So for instance if we're
+ 
+
+ align:start position:0%
+layered system. So for instance if we're
+writing the square root procedure
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+somewhere the square root procedure uses
+
+ align:start position:0%
+somewhere the square root procedure uses
+ 
+
+ align:start position:0%
+somewhere the square root procedure uses
+a procedure called good enough
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and between those there's some sort of
+
+ align:start position:0%
+and between those there's some sort of
+ 
+
+ align:start position:0%
+and between those there's some sort of
+abstraction boundary.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+It's almost as if uh we go out and in
+
+ align:start position:0%
+It's almost as if uh we go out and in
+ 
+
+ align:start position:0%
+It's almost as if uh we go out and in
+writing square root, we go and make a
+
+ align:start position:0%
+writing square root, we go and make a
+ 
+
+ align:start position:0%
+writing square root, we go and make a
+contract with uh with George and tell
+
+ align:start position:0%
+contract with uh with George and tell
+ 
+
+ align:start position:0%
+contract with uh with George and tell
+George that his job is to write good
+
+ align:start position:0%
+George that his job is to write good
+ 
+
+ align:start position:0%
+George that his job is to write good
+enough.
+
+ align:start position:0%
+enough.
+ 
+
+ align:start position:0%
+enough.
+And so long as good enough works, we
+
+ align:start position:0%
+And so long as good enough works, we
+ 
+
+ align:start position:0%
+And so long as good enough works, we
+don't care what it does. We don't care
+
+ align:start position:0%
+don't care what it does. We don't care
+ 
+
+ align:start position:0%
+don't care what it does. We don't care
+exactly how it's implemented. There are
+
+ align:start position:0%
+exactly how it's implemented. There are
+ 
+
+ align:start position:0%
+exactly how it's implemented. There are
+levels of detail here that are George's
+
+ align:start position:0%
+levels of detail here that are George's
+ 
+
+ align:start position:0%
+levels of detail here that are George's
+concern and not ours.
+
+ align:start position:0%
+concern and not ours.
+ 
+
+ align:start position:0%
+concern and not ours.
+So for instance, George might use uh an
+
+ align:start position:0%
+So for instance, George might use uh an
+ 
+
+ align:start position:0%
+So for instance, George might use uh an
+absolute value procedure that's written
+
+ align:start position:0%
+absolute value procedure that's written
+ 
+
+ align:start position:0%
+absolute value procedure that's written
+by Harry and we don't much care about
+
+ align:start position:0%
+by Harry and we don't much care about
+ 
+
+ align:start position:0%
+by Harry and we don't much care about
+that or even know that that maybe Harry
+
+ align:start position:0%
+that or even know that that maybe Harry
+ 
+
+ align:start position:0%
+that or even know that that maybe Harry
+exists.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+So the crucial idea is that when we're
+
+ align:start position:0%
+So the crucial idea is that when we're
+ 
+
+ align:start position:0%
+So the crucial idea is that when we're
+building things, we divorce the task of
+
+ align:start position:0%
+building things, we divorce the task of
+ 
+
+ align:start position:0%
+building things, we divorce the task of
+building things
+
+ align:start position:0%
+building things
+ 
+
+ align:start position:0%
+building things
+from the task of implementing the parts.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+It's as if and then in a large system of
+
+ align:start position:0%
+It's as if and then in a large system of
+ 
+
+ align:start position:0%
+It's as if and then in a large system of
+course we have abstraction barriers like
+
+ align:start position:0%
+course we have abstraction barriers like
+ 
+
+ align:start position:0%
+course we have abstraction barriers like
+this at lots and lots and lots of levels
+
+ align:start position:0%
+this at lots and lots and lots of levels
+ 
+
+ align:start position:0%
+this at lots and lots and lots of levels
+and that's the idea that we've been
+
+ align:start position:0%
+and that's the idea that we've been
+ 
+
+ align:start position:0%
+and that's the idea that we've been
+using so far over and over in
+
+ align:start position:0%
+using so far over and over in
+ 
+
+ align:start position:0%
+using so far over and over in
+implementing procedures. Well, now what
+
+ align:start position:0%
+implementing procedures. Well, now what
+ 
+
+ align:start position:0%
+implementing procedures. Well, now what
+we're going to do is look at the same
+
+ align:start position:0%
+we're going to do is look at the same
+ 
+
+ align:start position:0%
+we're going to do is look at the same
+issues for data.
+
+ align:start position:0%
+issues for data.
+ 
+
+ align:start position:0%
+issues for data.
+We're going to see that the system has
+
+ align:start position:0%
+We're going to see that the system has
+ 
+
+ align:start position:0%
+We're going to see that the system has
+primitive data. In fact, we've already
+
+ align:start position:0%
+primitive data. In fact, we've already
+ 
+
+ align:start position:0%
+primitive data. In fact, we've already
+seen that. We've talked about numbers as
+
+ align:start position:0%
+seen that. We've talked about numbers as
+ 
+
+ align:start position:0%
+seen that. We've talked about numbers as
+primitive data. And then we're going to
+
+ align:start position:0%
+primitive data. And then we're going to
+ 
+
+ align:start position:0%
+primitive data. And then we're going to
+see their means of combination for data.
+
+ align:start position:0%
+see their means of combination for data.
+ 
+
+ align:start position:0%
+see their means of combination for data.
+There's glue that allows you to put
+
+ align:start position:0%
+There's glue that allows you to put
+ 
+
+ align:start position:0%
+There's glue that allows you to put
+primitive data together to make more
+
+ align:start position:0%
+primitive data together to make more
+ 
+
+ align:start position:0%
+primitive data together to make more
+complicated kind of compound data. And
+
+ align:start position:0%
+complicated kind of compound data. And
+ 
+
+ align:start position:0%
+complicated kind of compound data. And
+then we're going to see a methodology
+
+ align:start position:0%
+then we're going to see a methodology
+ 
+
+ align:start position:0%
+then we're going to see a methodology
+for abstraction.
+
+ align:start position:0%
+for abstraction.
+ 
+
+ align:start position:0%
+for abstraction.
+That's a very good thing to use when you
+
+ align:start position:0%
+That's a very good thing to use when you
+ 
+
+ align:start position:0%
+That's a very good thing to use when you
+start building up data in terms of
+
+ align:start position:0%
+start building up data in terms of
+ 
+
+ align:start position:0%
+start building up data in terms of
+simpler data. And again, the key idea is
+
+ align:start position:0%
+simpler data. And again, the key idea is
+ 
+
+ align:start position:0%
+simpler data. And again, the key idea is
+that you're going to build this system
+
+ align:start position:0%
+that you're going to build this system
+ 
+
+ align:start position:0%
+that you're going to build this system
+in layers and set up abstraction
+
+ align:start position:0%
+in layers and set up abstraction
+ 
+
+ align:start position:0%
+in layers and set up abstraction
+barriers that isolate the details at the
+
+ align:start position:0%
+barriers that isolate the details at the
+ 
+
+ align:start position:0%
+barriers that isolate the details at the
+lower layers
+
+ align:start position:0%
+lower layers
+ 
+
+ align:start position:0%
+lower layers
+from the thing that's going on at the
+
+ align:start position:0%
+from the thing that's going on at the
+ 
+
+ align:start position:0%
+from the thing that's going on at the
+upper layers. the details at the lower
+
+ align:start position:0%
+upper layers. the details at the lower
+ 
+
+ align:start position:0%
+upper layers. the details at the lower
+layers, the idea is they won't matter.
+
+ align:start position:0%
+layers, the idea is they won't matter.
+ 
+
+ align:start position:0%
+layers, the idea is they won't matter.
+They're going to be George's concern
+
+ align:start position:0%
+They're going to be George's concern
+ 
+
+ align:start position:0%
+They're going to be George's concern
+because he signed this contract with us
+
+ align:start position:0%
+because he signed this contract with us
+ 
+
+ align:start position:0%
+because he signed this contract with us
+for how the stuff that he implements
+
+ align:start position:0%
+for how the stuff that he implements
+ 
+
+ align:start position:0%
+for how the stuff that he implements
+behaves. And how he implements the thing
+
+ align:start position:0%
+behaves. And how he implements the thing
+ 
+
+ align:start position:0%
+behaves. And how he implements the thing
+is his problem.
+
+ align:start position:0%
+is his problem.
+ 
+
+ align:start position:0%
+is his problem.
+All right. Well, let's look at an
+
+ align:start position:0%
+All right. Well, let's look at an
+ 
+
+ align:start position:0%
+All right. Well, let's look at an
+example. And the example I'm going to
+
+ align:start position:0%
+example. And the example I'm going to
+ 
+
+ align:start position:0%
+example. And the example I'm going to
+talk about is a system that does
+
+ align:start position:0%
+talk about is a system that does
+ 
+
+ align:start position:0%
+talk about is a system that does
+arithmetic on rational numbers. And what
+
+ align:start position:0%
+arithmetic on rational numbers. And what
+ 
+
+ align:start position:0%
+arithmetic on rational numbers. And what
+I have in mind is that we should have
+
+ align:start position:0%
+I have in mind is that we should have
+ 
+
+ align:start position:0%
+I have in mind is that we should have
+something in the computer that allows us
+
+ align:start position:0%
+something in the computer that allows us
+ 
+
+ align:start position:0%
+something in the computer that allows us
+to
+
+ align:start position:0%
+to
+ 
+
+ align:start position:0%
+to
+ask it like u what's the sum of a half
+
+ align:start position:0%
+ask it like u what's the sum of a half
+ 
+
+ align:start position:0%
+ask it like u what's the sum of a half
+and a fourth and somehow the system
+
+ align:start position:0%
+and a fourth and somehow the system
+ 
+
+ align:start position:0%
+and a fourth and somehow the system
+should say
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+say yeah that's 3/4s
+
+ align:start position:0%
+say yeah that's 3/4s
+ 
+
+ align:start position:0%
+say yeah that's 3/4s
+or uh we should be able to say what's
+
+ align:start position:0%
+or uh we should be able to say what's
+ 
+
+ align:start position:0%
+or uh we should be able to say what's
+3/4s
+
+ align:start position:0%
+3/4s
+ 
+
+ align:start position:0%
+3/4s
+times
+
+ align:start position:0%
+times
+ 
+
+ align:start position:0%
+times
+2/3
+
+ align:start position:0%
+2/3
+ 
+
+ align:start position:0%
+2/3
+and the system should be able to say,
+
+ align:start position:0%
+and the system should be able to say,
+ 
+
+ align:start position:0%
+and the system should be able to say,
+"Yeah, that's a half,
+
+ align:start position:0%
+"Yeah, that's a half,
+ 
+
+ align:start position:0%
+"Yeah, that's a half,
+right?" And you know what I have in
+
+ align:start position:0%
+right?" And you know what I have in
+ 
+
+ align:start position:0%
+right?" And you know what I have in
+mind, and you also know how to do this
+
+ align:start position:0%
+mind, and you also know how to do this
+ 
+
+ align:start position:0%
+mind, and you also know how to do this
+from uh I don't know, fifth grade or
+
+ align:start position:0%
+from uh I don't know, fifth grade or
+ 
+
+ align:start position:0%
+from uh I don't know, fifth grade or
+sixth grade. There are these formulas
+
+ align:start position:0%
+sixth grade. There are these formulas
+ 
+
+ align:start position:0%
+sixth grade. There are these formulas
+that say if I have some fraction
+
+ align:start position:0%
+that say if I have some fraction
+ 
+
+ align:start position:0%
+that say if I have some fraction
+which is a numerator over a denominator
+
+ align:start position:0%
+which is a numerator over a denominator
+ 
+
+ align:start position:0%
+which is a numerator over a denominator
+and I want to add that to some other
+
+ align:start position:0%
+and I want to add that to some other
+ 
+
+ align:start position:0%
+and I want to add that to some other
+fraction which is another numerator over
+
+ align:start position:0%
+fraction which is another numerator over
+ 
+
+ align:start position:0%
+fraction which is another numerator over
+another denominator. Then the answer is
+
+ align:start position:0%
+another denominator. Then the answer is
+ 
+
+ align:start position:0%
+another denominator. Then the answer is
+the numerator of the first time the
+
+ align:start position:0%
+the numerator of the first time the
+ 
+
+ align:start position:0%
+the numerator of the first time the
+denominator of the second plus the uh
+
+ align:start position:0%
+denominator of the second plus the uh
+ 
+
+ align:start position:0%
+denominator of the second plus the uh
+numerator of the second time the
+
+ align:start position:0%
+numerator of the second time the
+ 
+
+ align:start position:0%
+numerator of the second time the
+denominator of the first.
+
+ align:start position:0%
+denominator of the first.
+ 
+
+ align:start position:0%
+denominator of the first.
+That's the numerator of the answer and
+
+ align:start position:0%
+That's the numerator of the answer and
+ 
+
+ align:start position:0%
+That's the numerator of the answer and
+the denominator is the product of the
+
+ align:start position:0%
+the denominator is the product of the
+ 
+
+ align:start position:0%
+the denominator is the product of the
+two denominators. Right? So there's
+
+ align:start position:0%
+two denominators. Right? So there's
+ 
+
+ align:start position:0%
+two denominators. Right? So there's
+something from fifth or sixth grade
+
+ align:start position:0%
+something from fifth or sixth grade
+ 
+
+ align:start position:0%
+something from fifth or sixth grade
+fraction arithmetic. And then similarly,
+
+ align:start position:0%
+fraction arithmetic. And then similarly,
+ 
+
+ align:start position:0%
+fraction arithmetic. And then similarly,
+if I want to multiply two things, n1
+
+ align:start position:0%
+if I want to multiply two things, n1
+ 
+
+ align:start position:0%
+if I want to multiply two things, n1
+over d1 multiplied by n2 over d2 is the
+
+ align:start position:0%
+over d1 multiplied by n2 over d2 is the
+ 
+
+ align:start position:0%
+over d1 multiplied by n2 over d2 is the
+product of the numerators
+
+ align:start position:0%
+product of the numerators
+ 
+
+ align:start position:0%
+product of the numerators
+over the product of the denominators.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+So it's no problem at all, but it's
+
+ align:start position:0%
+So it's no problem at all, but it's
+ 
+
+ align:start position:0%
+So it's no problem at all, but it's
+absolutely no problem to to think about
+
+ align:start position:0%
+absolutely no problem to to think about
+ 
+
+ align:start position:0%
+absolutely no problem to to think about
+what computation you want to make in
+
+ align:start position:0%
+what computation you want to make in
+ 
+
+ align:start position:0%
+what computation you want to make in
+adding and multiplying these fractions.
+
+ align:start position:0%
+adding and multiplying these fractions.
+ 
+
+ align:start position:0%
+adding and multiplying these fractions.
+But as soon as we go to implement it, we
+
+ align:start position:0%
+But as soon as we go to implement it, we
+ 
+
+ align:start position:0%
+But as soon as we go to implement it, we
+run up across something. We don't have
+
+ align:start position:0%
+run up across something. We don't have
+ 
+
+ align:start position:0%
+run up across something. We don't have
+what a rational number is.
+
+ align:start position:0%
+what a rational number is.
+ 
+
+ align:start position:0%
+what a rational number is.
+See, we've said that the system gives us
+
+ align:start position:0%
+See, we've said that the system gives us
+ 
+
+ align:start position:0%
+See, we've said that the system gives us
+individual numbers. So we can have five
+
+ align:start position:0%
+individual numbers. So we can have five
+ 
+
+ align:start position:0%
+individual numbers. So we can have five
+and three, but but somehow we don't have
+
+ align:start position:0%
+and three, but but somehow we don't have
+ 
+
+ align:start position:0%
+and three, but but somehow we don't have
+a way of of saying there's a thing that
+
+ align:start position:0%
+a way of of saying there's a thing that
+ 
+
+ align:start position:0%
+a way of of saying there's a thing that
+has, you know, both a three and a four
+
+ align:start position:0%
+has, you know, both a three and a four
+ 
+
+ align:start position:0%
+has, you know, both a three and a four
+in it or both a both a two and a three.
+
+ align:start position:0%
+in it or both a both a two and a three.
+ 
+
+ align:start position:0%
+in it or both a both a two and a three.
+It's almost as if
+
+ align:start position:0%
+It's almost as if
+ 
+
+ align:start position:0%
+It's almost as if
+we'd like to imagine that somehow there
+
+ align:start position:0%
+we'd like to imagine that somehow there
+ 
+
+ align:start position:0%
+we'd like to imagine that somehow there
+are these clouds
+
+ align:start position:0%
+are these clouds
+ 
+
+ align:start position:0%
+are these clouds
+and a cloud somehow has both a numerator
+
+ align:start position:0%
+and a cloud somehow has both a numerator
+ 
+
+ align:start position:0%
+and a cloud somehow has both a numerator
+and a denominator in it. And that's what
+
+ align:start position:0%
+and a denominator in it. And that's what
+ 
+
+ align:start position:0%
+and a denominator in it. And that's what
+we'd like to work in terms of.
+
+ align:start position:0%
+we'd like to work in terms of.
+ 
+
+ align:start position:0%
+we'd like to work in terms of.
+Well, how are we going to solve that
+
+ align:start position:0%
+Well, how are we going to solve that
+ 
+
+ align:start position:0%
+Well, how are we going to solve that
+problem? We're going to solve that
+
+ align:start position:0%
+problem? We're going to solve that
+ 
+
+ align:start position:0%
+problem? We're going to solve that
+problem by using this incredibly
+
+ align:start position:0%
+problem by using this incredibly
+ 
+
+ align:start position:0%
+problem by using this incredibly
+powerful design strategy that you've
+
+ align:start position:0%
+powerful design strategy that you've
+ 
+
+ align:start position:0%
+powerful design strategy that you've
+already seen us use over and over. And
+
+ align:start position:0%
+already seen us use over and over. And
+ 
+
+ align:start position:0%
+already seen us use over and over. And
+that's the strategy of wishful thinking.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Just like before when we didn't have a
+
+ align:start position:0%
+Just like before when we didn't have a
+ 
+
+ align:start position:0%
+Just like before when we didn't have a
+procedure, we said, well, let's imagine
+
+ align:start position:0%
+procedure, we said, well, let's imagine
+ 
+
+ align:start position:0%
+procedure, we said, well, let's imagine
+that that procedure already exists.
+
+ align:start position:0%
+that that procedure already exists.
+ 
+
+ align:start position:0%
+that that procedure already exists.
+We'll say well let's imagine that we
+
+ align:start position:0%
+We'll say well let's imagine that we
+ 
+
+ align:start position:0%
+We'll say well let's imagine that we
+have these clouds
+
+ align:start position:0%
+have these clouds
+ 
+
+ align:start position:0%
+have these clouds
+now more precisely what I mean is
+
+ align:start position:0%
+now more precisely what I mean is
+ 
+
+ align:start position:0%
+now more precisely what I mean is
+let's imagine that we have three
+
+ align:start position:0%
+let's imagine that we have three
+ 
+
+ align:start position:0%
+let's imagine that we have three
+procedures
+
+ align:start position:0%
+procedures
+ 
+
+ align:start position:0%
+procedures
+one called makerat
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+makerat is going to take as arguments
+
+ align:start position:0%
+makerat is going to take as arguments
+ 
+
+ align:start position:0%
+makerat is going to take as arguments
+two numbers
+
+ align:start position:0%
+two numbers
+ 
+
+ align:start position:0%
+two numbers
+which I'll call numerator and
+
+ align:start position:0%
+which I'll call numerator and
+ 
+
+ align:start position:0%
+which I'll call numerator and
+denominator
+
+ align:start position:0%
+denominator
+ 
+
+ align:start position:0%
+denominator
+and it'll return for us
+
+ align:start position:0%
+and it'll return for us
+ 
+
+ align:start position:0%
+and it'll return for us
+a cloud,
+
+ align:start position:0%
+a cloud,
+ 
+
+ align:start position:0%
+a cloud,
+right? One of these clouds.
+
+ align:start position:0%
+right? One of these clouds.
+ 
+
+ align:start position:0%
+right? One of these clouds.
+I don't really know what a cloud is.
+
+ align:start position:0%
+I don't really know what a cloud is.
+ 
+
+ align:start position:0%
+I don't really know what a cloud is.
+It's whatever Makeat returns. That's its
+
+ align:start position:0%
+It's whatever Makeat returns. That's its
+ 
+
+ align:start position:0%
+It's whatever Makeat returns. That's its
+business.
+
+ align:start position:0%
+business.
+ 
+
+ align:start position:0%
+business.
+And then we're going to say suppose
+
+ align:start position:0%
+And then we're going to say suppose
+ 
+
+ align:start position:0%
+And then we're going to say suppose
+we've got one of these clouds. We have a
+
+ align:start position:0%
+we've got one of these clouds. We have a
+ 
+
+ align:start position:0%
+we've got one of these clouds. We have a
+procedure called numer
+
+ align:start position:0%
+procedure called numer
+ 
+
+ align:start position:0%
+procedure called numer
+which takes in a cloud that has an n and
+
+ align:start position:0%
+which takes in a cloud that has an n and
+ 
+
+ align:start position:0%
+which takes in a cloud that has an n and
+a d in it. Whatever a cloud is and I
+
+ align:start position:0%
+a d in it. Whatever a cloud is and I
+ 
+
+ align:start position:0%
+a d in it. Whatever a cloud is and I
+don't know what it is, and returns for
+
+ align:start position:0%
+don't know what it is, and returns for
+ 
+
+ align:start position:0%
+don't know what it is, and returns for
+us the numerator part.
+
+ align:start position:0%
+us the numerator part.
+ 
+
+ align:start position:0%
+us the numerator part.
+And then we'll assume we have a
+
+ align:start position:0%
+And then we'll assume we have a
+ 
+
+ align:start position:0%
+And then we'll assume we have a
+procedure denom
+
+ align:start position:0%
+procedure denom
+ 
+
+ align:start position:0%
+procedure denom
+which again takes in a cloud whatever a
+
+ align:start position:0%
+which again takes in a cloud whatever a
+ 
+
+ align:start position:0%
+which again takes in a cloud whatever a
+cloud is
+
+ align:start position:0%
+cloud is
+ 
+
+ align:start position:0%
+cloud is
+and returns for us the denominator
+
+ align:start position:0%
+and returns for us the denominator
+ 
+
+ align:start position:0%
+and returns for us the denominator
+report. This is just like before when if
+
+ align:start position:0%
+report. This is just like before when if
+ 
+
+ align:start position:0%
+report. This is just like before when if
+we're building a square root, we assume
+
+ align:start position:0%
+we're building a square root, we assume
+ 
+
+ align:start position:0%
+we're building a square root, we assume
+that we have good enough, right? And
+
+ align:start position:0%
+that we have good enough, right? And
+ 
+
+ align:start position:0%
+that we have good enough, right? And
+what we'll say is we'll go find George.
+
+ align:start position:0%
+what we'll say is we'll go find George.
+ 
+
+ align:start position:0%
+what we'll say is we'll go find George.
+We'll say to George, well, it's your
+
+ align:start position:0%
+We'll say to George, well, it's your
+ 
+
+ align:start position:0%
+We'll say to George, well, it's your
+business to make us these procedures
+
+ align:start position:0%
+business to make us these procedures
+ 
+
+ align:start position:0%
+business to make us these procedures
+and how you choose to implement these
+
+ align:start position:0%
+and how you choose to implement these
+ 
+
+ align:start position:0%
+and how you choose to implement these
+clouds, that's your problem. We don't
+
+ align:start position:0%
+clouds, that's your problem. We don't
+ 
+
+ align:start position:0%
+clouds, that's your problem. We don't
+want to know.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Well, having pushed this task off onto
+
+ align:start position:0%
+Well, having pushed this task off onto
+ 
+
+ align:start position:0%
+Well, having pushed this task off onto
+George, then it's pretty easy to do the
+
+ align:start position:0%
+George, then it's pretty easy to do the
+ 
+
+ align:start position:0%
+George, then it's pretty easy to do the
+other part. Once we've got the clouds,
+
+ align:start position:0%
+other part. Once we've got the clouds,
+ 
+
+ align:start position:0%
+other part. Once we've got the clouds,
+it's pretty easy to write the thing that
+
+ align:start position:0%
+it's pretty easy to write the thing that
+ 
+
+ align:start position:0%
+it's pretty easy to write the thing that
+does say addition of rational numbers
+
+ align:start position:0%
+does say addition of rational numbers
+ 
+
+ align:start position:0%
+does say addition of rational numbers
+can just say define
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+well let's say uh plus rat
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+define plus rat which will take in two
+
+ align:start position:0%
+define plus rat which will take in two
+ 
+
+ align:start position:0%
+define plus rat which will take in two
+rational numbers
+
+ align:start position:0%
+rational numbers
+ 
+
+ align:start position:0%
+rational numbers
+x and y x and y are each these clouds
+
+ align:start position:0%
+x and y x and y are each these clouds
+ 
+
+ align:start position:0%
+x and y x and y are each these clouds
+and what does it do? Well, it's going to
+
+ align:start position:0%
+and what does it do? Well, it's going to
+ 
+
+ align:start position:0%
+and what does it do? Well, it's going to
+return for us a rational number.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+What rational number is it? Well, we've
+
+ align:start position:0%
+What rational number is it? Well, we've
+ 
+
+ align:start position:0%
+What rational number is it? Well, we've
+got the formulas there. The numerator of
+
+ align:start position:0%
+got the formulas there. The numerator of
+ 
+
+ align:start position:0%
+got the formulas there. The numerator of
+it is the sum of
+
+ align:start position:0%
+it is the sum of
+ 
+
+ align:start position:0%
+it is the sum of
+the product
+
+ align:start position:0%
+the product
+ 
+
+ align:start position:0%
+the product
+of the numerator
+
+ align:start position:0%
+of the numerator
+ 
+
+ align:start position:0%
+of the numerator
+of x
+
+ align:start position:0%
+of x
+ 
+
+ align:start position:0%
+of x
+and the denominator of y.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+It's one thing in the sum and the other
+
+ align:start position:0%
+It's one thing in the sum and the other
+ 
+
+ align:start position:0%
+It's one thing in the sum and the other
+thing in the numerator is the product of
+
+ align:start position:0%
+thing in the numerator is the product of
+ 
+
+ align:start position:0%
+thing in the numerator is the product of
+the numerator
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+of y
+
+ align:start position:0%
+of y
+ 
+
+ align:start position:0%
+of y
+and the denominator
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+of x
+
+ align:start position:0%
+of x
+ 
+
+ align:start position:0%
+of x
+close the star close the plus right
+
+ align:start position:0%
+close the star close the plus right
+ 
+
+ align:start position:0%
+close the star close the plus right
+that's the the first argument to make
+
+ align:start position:0%
+that's the the first argument to make
+ 
+
+ align:start position:0%
+that's the the first argument to make
+which is the numerator of the thing I'm
+
+ align:start position:0%
+which is the numerator of the thing I'm
+ 
+
+ align:start position:0%
+which is the numerator of the thing I'm
+constructing and then the rest of the
+
+ align:start position:0%
+constructing and then the rest of the
+ 
+
+ align:start position:0%
+constructing and then the rest of the
+thing goes into makerat is the denom
+
+ align:start position:0%
+thing goes into makerat is the denom
+ 
+
+ align:start position:0%
+thing goes into makerat is the denom
+denominator of the answer which is the
+
+ align:start position:0%
+denominator of the answer which is the
+ 
+
+ align:start position:0%
+denominator of the answer which is the
+product of the denominator
+
+ align:start position:0%
+product of the denominator
+ 
+
+ align:start position:0%
+product of the denominator
+of x and the denominator
+
+ align:start position:0%
+of x and the denominator
+ 
+
+ align:start position:0%
+of x and the denominator
+of y
+
+ align:start position:0%
+of y
+ 
+
+ align:start position:0%
+of y
+like that.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay, so there is there's the analog of
+
+ align:start position:0%
+Okay, so there is there's the analog of
+ 
+
+ align:start position:0%
+Okay, so there is there's the analog of
+of doing rational number addition and
+
+ align:start position:0%
+of doing rational number addition and
+ 
+
+ align:start position:0%
+of doing rational number addition and
+it's no problem at all assuming that we
+
+ align:start position:0%
+it's no problem at all assuming that we
+ 
+
+ align:start position:0%
+it's no problem at all assuming that we
+have these clouds
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and of course we can do uh
+
+ align:start position:0%
+and of course we can do uh
+ 
+
+ align:start position:0%
+and of course we can do uh
+multiplication in the same way
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+I define
+
+ align:start position:0%
+I define
+ 
+
+ align:start position:0%
+I define
+how to get the product of two rational
+
+ align:start position:0%
+how to get the product of two rational
+ 
+
+ align:start position:0%
+how to get the product of two rational
+numbers call it star rat takes in two of
+
+ align:start position:0%
+numbers call it star rat takes in two of
+ 
+
+ align:start position:0%
+numbers call it star rat takes in two of
+these clouds x and y.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+It returns a rational number make rat
+
+ align:start position:0%
+It returns a rational number make rat
+ 
+
+ align:start position:0%
+It returns a rational number make rat
+whose numerator is the product of the
+
+ align:start position:0%
+whose numerator is the product of the
+ 
+
+ align:start position:0%
+whose numerator is the product of the
+numerators
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+numerator at x times the numerator
+
+ align:start position:0%
+numerator at x times the numerator
+ 
+
+ align:start position:0%
+numerator at x times the numerator
+of y.
+
+ align:start position:0%
+of y.
+ 
+
+ align:start position:0%
+of y.
+And the denominator of the thing it's
+
+ align:start position:0%
+And the denominator of the thing it's
+ 
+
+ align:start position:0%
+And the denominator of the thing it's
+going to return is the product of the
+
+ align:start position:0%
+going to return is the product of the
+ 
+
+ align:start position:0%
+going to return is the product of the
+denominators.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay. Well,
+
+ align:start position:0%
+Okay. Well,
+ 
+
+ align:start position:0%
+Okay. Well,
+except that I haven't told you what
+
+ align:start position:0%
+except that I haven't told you what
+ 
+
+ align:start position:0%
+except that I haven't told you what
+these clouds are. That's all there is to
+
+ align:start position:0%
+these clouds are. That's all there is to
+ 
+
+ align:start position:0%
+these clouds are. That's all there is to
+it. See, what did I do? I assumed by
+
+ align:start position:0%
+it. See, what did I do? I assumed by
+ 
+
+ align:start position:0%
+it. See, what did I do? I assumed by
+wishful thinking that I had a new kind
+
+ align:start position:0%
+wishful thinking that I had a new kind
+ 
+
+ align:start position:0%
+wishful thinking that I had a new kind
+of data object and in particular I
+
+ align:start position:0%
+of data object and in particular I
+ 
+
+ align:start position:0%
+of data object and in particular I
+assumed I had ways of creating these
+
+ align:start position:0%
+assumed I had ways of creating these
+ 
+
+ align:start position:0%
+assumed I had ways of creating these
+data objects. Make rat creates one of
+
+ align:start position:0%
+data objects. Make rat creates one of
+ 
+
+ align:start position:0%
+data objects. Make rat creates one of
+these things. This is called a
+
+ align:start position:0%
+these things. This is called a
+ 
+
+ align:start position:0%
+these things. This is called a
+constructor.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+I had a thing that that constructs such
+
+ align:start position:0%
+I had a thing that that constructs such
+ 
+
+ align:start position:0%
+I had a thing that that constructs such
+data objects and then I assume I have
+
+ align:start position:0%
+data objects and then I assume I have
+ 
+
+ align:start position:0%
+data objects and then I assume I have
+things that having made these things I
+
+ align:start position:0%
+things that having made these things I
+ 
+
+ align:start position:0%
+things that having made these things I
+have ways of getting the parts out.
+
+ align:start position:0%
+have ways of getting the parts out.
+ 
+
+ align:start position:0%
+have ways of getting the parts out.
+Those are called selectors.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Right? So formally what I said is I
+
+ align:start position:0%
+Right? So formally what I said is I
+ 
+
+ align:start position:0%
+Right? So formally what I said is I
+assumed I had procedures that are
+
+ align:start position:0%
+assumed I had procedures that are
+ 
+
+ align:start position:0%
+assumed I had procedures that are
+constructors and selectors for these
+
+ align:start position:0%
+constructors and selectors for these
+ 
+
+ align:start position:0%
+constructors and selectors for these
+data objects and then I went off and
+
+ align:start position:0%
+data objects and then I went off and
+ 
+
+ align:start position:0%
+data objects and then I went off and
+used them.
+
+ align:start position:0%
+used them.
+ 
+
+ align:start position:0%
+used them.
+And that's no different in kind from
+
+ align:start position:0%
+And that's no different in kind from
+ 
+
+ align:start position:0%
+And that's no different in kind from
+saying I assume I have a procedure good
+
+ align:start position:0%
+saying I assume I have a procedure good
+ 
+
+ align:start position:0%
+saying I assume I have a procedure good
+enough and I go use it to implement
+
+ align:start position:0%
+enough and I go use it to implement
+ 
+
+ align:start position:0%
+enough and I go use it to implement
+square root.
+
+ align:start position:0%
+square root.
+ 
+
+ align:start position:0%
+square root.
+Okay. Well, before we go on,
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+let's ask the question of why we want to
+
+ align:start position:0%
+let's ask the question of why we want to
+ 
+
+ align:start position:0%
+let's ask the question of why we want to
+why we want to do this in the first
+
+ align:start position:0%
+why we want to do this in the first
+ 
+
+ align:start position:0%
+why we want to do this in the first
+place. See, why do we want a procedure
+
+ align:start position:0%
+place. See, why do we want a procedure
+ 
+
+ align:start position:0%
+place. See, why do we want a procedure
+like uh like plus rat that takes in two
+
+ align:start position:0%
+like uh like plus rat that takes in two
+ 
+
+ align:start position:0%
+like uh like plus rat that takes in two
+rational numbers and returns a rational
+
+ align:start position:0%
+rational numbers and returns a rational
+ 
+
+ align:start position:0%
+rational numbers and returns a rational
+number. See, another way to think about
+
+ align:start position:0%
+number. See, another way to think about
+ 
+
+ align:start position:0%
+number. See, another way to think about
+this is well, here's this formula.
+
+ align:start position:0%
+this is well, here's this formula.
+ 
+
+ align:start position:0%
+this is well, here's this formula.
+And what I if I was going to implement,
+
+ align:start position:0%
+And what I if I was going to implement,
+ 
+
+ align:start position:0%
+And what I if I was going to implement,
+you know, something that adds rational
+
+ align:start position:0%
+you know, something that adds rational
+ 
+
+ align:start position:0%
+you know, something that adds rational
+numbers, one other way to think about it
+
+ align:start position:0%
+numbers, one other way to think about it
+ 
+
+ align:start position:0%
+numbers, one other way to think about it
+is, well, there's this thing, and I type
+
+ align:start position:0%
+is, well, there's this thing, and I type
+ 
+
+ align:start position:0%
+is, well, there's this thing, and I type
+in four numbers, an n1 and a d1 and an
+
+ align:start position:0%
+in four numbers, an n1 and a d1 and an
+ 
+
+ align:start position:0%
+in four numbers, an n1 and a d1 and an
+n2 and a d2, and it sets some registers
+
+ align:start position:0%
+n2 and a d2, and it sets some registers
+ 
+
+ align:start position:0%
+n2 and a d2, and it sets some registers
+in the machine to uh
+
+ align:start position:0%
+in the machine to uh
+ 
+
+ align:start position:0%
+in the machine to uh
+this numerator and this denominator. So
+
+ align:start position:0%
+this numerator and this denominator. So
+ 
+
+ align:start position:0%
+this numerator and this denominator. So
+I might say, well, why don't I just add
+
+ align:start position:0%
+I might say, well, why don't I just add
+ 
+
+ align:start position:0%
+I might say, well, why don't I just add
+rational numbers by I type in four
+
+ align:start position:0%
+rational numbers by I type in four
+ 
+
+ align:start position:0%
+rational numbers by I type in four
+numbers, numerators and denominators,
+
+ align:start position:0%
+numbers, numerators and denominators,
+ 
+
+ align:start position:0%
+numbers, numerators and denominators,
+and get out two numbers, which is a
+
+ align:start position:0%
+and get out two numbers, which is a
+ 
+
+ align:start position:0%
+and get out two numbers, which is a
+numerator and a denominator,
+
+ align:start position:0%
+numerator and a denominator,
+ 
+
+ align:start position:0%
+numerator and a denominator,
+right? Why why are we worrying about
+
+ align:start position:0%
+right? Why why are we worrying about
+ 
+
+ align:start position:0%
+right? Why why are we worrying about
+building things like this anyway?
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Well, the answer is suppose you want to
+
+ align:start position:0%
+Well, the answer is suppose you want to
+ 
+
+ align:start position:0%
+Well, the answer is suppose you want to
+think about expressing something like uh
+
+ align:start position:0%
+think about expressing something like uh
+ 
+
+ align:start position:0%
+think about expressing something like uh
+like this. Suppose I'd like to express
+
+ align:start position:0%
+like this. Suppose I'd like to express
+ 
+
+ align:start position:0%
+like this. Suppose I'd like to express
+the idea of taking two rational numbers
+
+ align:start position:0%
+the idea of taking two rational numbers
+ 
+
+ align:start position:0%
+the idea of taking two rational numbers
+x + y say and multiplying that by the
+
+ align:start position:0%
+x + y say and multiplying that by the
+ 
+
+ align:start position:0%
+x + y say and multiplying that by the
+sum
+
+ align:start position:0%
+sum
+ 
+
+ align:start position:0%
+sum
+of two other rational numbers.
+
+ align:start position:0%
+of two other rational numbers.
+ 
+
+ align:start position:0%
+of two other rational numbers.
+Well, the way I do it having things like
+
+ align:start position:0%
+Well, the way I do it having things like
+ 
+
+ align:start position:0%
+Well, the way I do it having things like
+plus rat and star rat is I'd say oh yeah
+
+ align:start position:0%
+plus rat and star rat is I'd say oh yeah
+ 
+
+ align:start position:0%
+plus rat and star rat is I'd say oh yeah
+what that is is is just the uh the
+
+ align:start position:0%
+what that is is is just the uh the
+ 
+
+ align:start position:0%
+what that is is is just the uh the
+product that's star rat
+
+ align:start position:0%
+product that's star rat
+ 
+
+ align:start position:0%
+product that's star rat
+of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the sum of x and y
+
+ align:start position:0%
+the sum of x and y
+ 
+
+ align:start position:0%
+the sum of x and y
+and the sum
+
+ align:start position:0%
+and the sum
+ 
+
+ align:start position:0%
+and the sum
+of s and t.
+
+ align:start position:0%
+of s and t.
+ 
+
+ align:start position:0%
+of s and t.
+So except for syntax,
+
+ align:start position:0%
+So except for syntax,
+ 
+
+ align:start position:0%
+So except for syntax,
+I get an expression that looks like the
+
+ align:start position:0%
+I get an expression that looks like the
+ 
+
+ align:start position:0%
+I get an expression that looks like the
+way I want to think about it
+
+ align:start position:0%
+way I want to think about it
+ 
+
+ align:start position:0%
+way I want to think about it
+mathematically. I want to say there's
+
+ align:start position:0%
+mathematically. I want to say there's
+ 
+
+ align:start position:0%
+mathematically. I want to say there's
+there are two numbers. There's a thing
+
+ align:start position:0%
+there are two numbers. There's a thing
+ 
+
+ align:start position:0%
+there are two numbers. There's a thing
+which is the sum of them
+
+ align:start position:0%
+which is the sum of them
+ 
+
+ align:start position:0%
+which is the sum of them
+and there's a thing which is the sum of
+
+ align:start position:0%
+and there's a thing which is the sum of
+ 
+
+ align:start position:0%
+and there's a thing which is the sum of
+these two. That's that's this
+
+ align:start position:0%
+these two. That's that's this
+ 
+
+ align:start position:0%
+these two. That's that's this
+and this. And then I multiply them. So I
+
+ align:start position:0%
+and this. And then I multiply them. So I
+ 
+
+ align:start position:0%
+and this. And then I multiply them. So I
+get an expression that matches this
+
+ align:start position:0%
+get an expression that matches this
+ 
+
+ align:start position:0%
+get an expression that matches this
+expression. If I did the other thing, if
+
+ align:start position:0%
+expression. If I did the other thing, if
+ 
+
+ align:start position:0%
+expression. If I did the other thing, if
+I said, well, the way I want to think
+
+ align:start position:0%
+I said, well, the way I want to think
+ 
+
+ align:start position:0%
+I said, well, the way I want to think
+about this is I type into my machine
+
+ align:start position:0%
+about this is I type into my machine
+ 
+
+ align:start position:0%
+about this is I type into my machine
+four numbers, which are the numerators
+
+ align:start position:0%
+four numbers, which are the numerators
+ 
+
+ align:start position:0%
+four numbers, which are the numerators
+and denominators of X and Y, and then
+
+ align:start position:0%
+and denominators of X and Y, and then
+ 
+
+ align:start position:0%
+and denominators of X and Y, and then
+four more numbers, which are the
+
+ align:start position:0%
+four more numbers, which are the
+ 
+
+ align:start position:0%
+four more numbers, which are the
+numerators and denominators of X, S, and
+
+ align:start position:0%
+numerators and denominators of X, S, and
+ 
+
+ align:start position:0%
+numerators and denominators of X, S, and
+T. And then what I'd be sitting with is,
+
+ align:start position:0%
+T. And then what I'd be sitting with is,
+ 
+
+ align:start position:0%
+T. And then what I'd be sitting with is,
+well, what would I do? I'd add these,
+
+ align:start position:0%
+well, what would I do? I'd add these,
+ 
+
+ align:start position:0%
+well, what would I do? I'd add these,
+and somehow I'd have to have two
+
+ align:start position:0%
+and somehow I'd have to have two
+ 
+
+ align:start position:0%
+and somehow I'd have to have two
+temporary variables, which are the
+
+ align:start position:0%
+temporary variables, which are the
+ 
+
+ align:start position:0%
+temporary variables, which are the
+numerators and denominators of this sum.
+
+ align:start position:0%
+numerators and denominators of this sum.
+ 
+
+ align:start position:0%
+numerators and denominators of this sum.
+And I'd go off and store them someplace.
+
+ align:start position:0%
+And I'd go off and store them someplace.
+ 
+
+ align:start position:0%
+And I'd go off and store them someplace.
+And then I'd go over here. I'd type in
+
+ align:start position:0%
+And then I'd go over here. I'd type in
+ 
+
+ align:start position:0%
+And then I'd go over here. I'd type in
+four more numbers. I get two more
+
+ align:start position:0%
+four more numbers. I get two more
+ 
+
+ align:start position:0%
+four more numbers. I get two more
+temporary variables which are the
+
+ align:start position:0%
+temporary variables which are the
+ 
+
+ align:start position:0%
+temporary variables which are the
+numerators and denominators of S&T and
+
+ align:start position:0%
+numerators and denominators of S&T and
+ 
+
+ align:start position:0%
+numerators and denominators of S&T and
+T. And then finally I put those together
+
+ align:start position:0%
+T. And then finally I put those together
+ 
+
+ align:start position:0%
+T. And then finally I put those together
+by multiplying them.
+
+ align:start position:0%
+by multiplying them.
+ 
+
+ align:start position:0%
+by multiplying them.
+You see what's what's starting to
+
+ align:start position:0%
+You see what's what's starting to
+ 
+
+ align:start position:0%
+You see what's what's starting to
+happen? There are all these temporary
+
+ align:start position:0%
+happen? There are all these temporary
+ 
+
+ align:start position:0%
+happen? There are all these temporary
+variables which are which are sort of
+
+ align:start position:0%
+variables which are which are sort of
+ 
+
+ align:start position:0%
+variables which are which are sort of
+the guts of the internals of these
+
+ align:start position:0%
+the guts of the internals of these
+ 
+
+ align:start position:0%
+the guts of the internals of these
+rational numbers that start hanging out
+
+ align:start position:0%
+rational numbers that start hanging out
+ 
+
+ align:start position:0%
+rational numbers that start hanging out
+all over the system. And of course, if I
+
+ align:start position:0%
+all over the system. And of course, if I
+ 
+
+ align:start position:0%
+all over the system. And of course, if I
+had more and more complicated
+
+ align:start position:0%
+had more and more complicated
+ 
+
+ align:start position:0%
+had more and more complicated
+expressions, there'd be more and more
+
+ align:start position:0%
+expressions, there'd be more and more
+ 
+
+ align:start position:0%
+expressions, there'd be more and more
+guts hanging out that confused my
+
+ align:start position:0%
+guts hanging out that confused my
+ 
+
+ align:start position:0%
+guts hanging out that confused my
+programming.
+
+ align:start position:0%
+programming.
+ 
+
+ align:start position:0%
+programming.
+And those of you who sort of programmed
+
+ align:start position:0%
+And those of you who sort of programmed
+ 
+
+ align:start position:0%
+And those of you who sort of programmed
+things like that where you're just uh
+
+ align:start position:0%
+things like that where you're just uh
+ 
+
+ align:start position:0%
+things like that where you're just uh
+adding numbers in assembly language, you
+
+ align:start position:0%
+adding numbers in assembly language, you
+ 
+
+ align:start position:0%
+adding numbers in assembly language, you
+sort of see you have to suddenly be
+
+ align:start position:0%
+sort of see you have to suddenly be
+ 
+
+ align:start position:0%
+sort of see you have to suddenly be
+concerned with these temporary
+
+ align:start position:0%
+concerned with these temporary
+ 
+
+ align:start position:0%
+concerned with these temporary
+variables.
+
+ align:start position:0%
+variables.
+ 
+
+ align:start position:0%
+variables.
+But more more importantly, they they're
+
+ align:start position:0%
+But more more importantly, they they're
+ 
+
+ align:start position:0%
+But more more importantly, they they're
+gonna not more importantly than
+
+ align:start position:0%
+gonna not more importantly than
+ 
+
+ align:start position:0%
+gonna not more importantly than
+confusing my programming, they're going
+
+ align:start position:0%
+confusing my programming, they're going
+ 
+
+ align:start position:0%
+confusing my programming, they're going
+to confuse my mind because the whole
+
+ align:start position:0%
+to confuse my mind because the whole
+ 
+
+ align:start position:0%
+to confuse my mind because the whole
+name of this game
+
+ align:start position:0%
+name of this game
+ 
+
+ align:start position:0%
+name of this game
+is that we'd like the programming
+
+ align:start position:0%
+is that we'd like the programming
+ 
+
+ align:start position:0%
+is that we'd like the programming
+language
+
+ align:start position:0%
+language
+ 
+
+ align:start position:0%
+language
+to express the concepts that we have in
+
+ align:start position:0%
+to express the concepts that we have in
+ 
+
+ align:start position:0%
+to express the concepts that we have in
+our heads like rational numbers are
+
+ align:start position:0%
+our heads like rational numbers are
+ 
+
+ align:start position:0%
+our heads like rational numbers are
+things that you can add and then take
+
+ align:start position:0%
+things that you can add and then take
+ 
+
+ align:start position:0%
+things that you can add and then take
+that result and multiply them.
+
+ align:start position:0%
+that result and multiply them.
+ 
+
+ align:start position:0%
+that result and multiply them.
+Okay, let's break for questions.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Yeah,
+
+ align:start position:0%
+Yeah,
+ 
+
+ align:start position:0%
+Yeah,
+I don't quite see the need where we had
+
+ align:start position:0%
+I don't quite see the need where we had
+ 
+
+ align:start position:0%
+I don't quite see the need where we had
+make rat with a numerator and
+
+ align:start position:0%
+make rat with a numerator and
+ 
+
+ align:start position:0%
+make rat with a numerator and
+denominator. We had to have the
+
+ align:start position:0%
+denominator. We had to have the
+ 
+
+ align:start position:0%
+denominator. We had to have the
+numerator and denominator to passes
+
+ align:start position:0%
+numerator and denominator to passes
+ 
+
+ align:start position:0%
+numerator and denominator to passes
+parameters to create the cloud. That's
+
+ align:start position:0%
+parameters to create the cloud. That's
+ 
+
+ align:start position:0%
+parameters to create the cloud. That's
+right. And then we extracted to get back
+
+ align:start position:0%
+right. And then we extracted to get back
+ 
+
+ align:start position:0%
+right. And then we extracted to get back
+what we had to have originally.
+
+ align:start position:0%
+what we had to have originally.
+ 
+
+ align:start position:0%
+what we had to have originally.
+That's right.
+
+ align:start position:0%
+That's right.
+ 
+
+ align:start position:0%
+That's right.
+Right. So the question is I sort of have
+
+ align:start position:0%
+Right. So the question is I sort of have
+ 
+
+ align:start position:0%
+Right. So the question is I sort of have
+the numerator and denominator. Why am I
+
+ align:start position:0%
+the numerator and denominator. Why am I
+ 
+
+ align:start position:0%
+the numerator and denominator. Why am I
+why am I worrying about having the cloud
+
+ align:start position:0%
+why am I worrying about having the cloud
+ 
+
+ align:start position:0%
+why am I worrying about having the cloud
+given that I have to get the pieces out?
+
+ align:start position:0%
+given that I have to get the pieces out?
+ 
+
+ align:start position:0%
+given that I have to get the pieces out?
+That's sort of what I tried to say at
+
+ align:start position:0%
+That's sort of what I tried to say at
+ 
+
+ align:start position:0%
+That's sort of what I tried to say at
+the end, but let me let me try and say
+
+ align:start position:0%
+the end, but let me let me try and say
+ 
+
+ align:start position:0%
+the end, but let me let me try and say
+it again because that's really the
+
+ align:start position:0%
+it again because that's really the
+ 
+
+ align:start position:0%
+it again because that's really the
+crucial question. The point is I want to
+
+ align:start position:0%
+crucial question. The point is I want to
+ 
+
+ align:start position:0%
+crucial question. The point is I want to
+carry this numerator and denominator
+
+ align:start position:0%
+carry this numerator and denominator
+ 
+
+ align:start position:0%
+carry this numerator and denominator
+around
+
+ align:start position:0%
+around
+ 
+
+ align:start position:0%
+around
+together all the time.
+
+ align:start position:0%
+together all the time.
+ 
+
+ align:start position:0%
+together all the time.
+And it's almost as if I I want to know
+
+ align:start position:0%
+And it's almost as if I I want to know
+ 
+
+ align:start position:0%
+And it's almost as if I I want to know
+yeah there's a numerator and denominator
+
+ align:start position:0%
+yeah there's a numerator and denominator
+ 
+
+ align:start position:0%
+yeah there's a numerator and denominator
+in there but also I would like to to say
+
+ align:start position:0%
+in there but also I would like to to say
+ 
+
+ align:start position:0%
+in there but also I would like to to say
+fine but from another point of view
+
+ align:start position:0%
+fine but from another point of view
+ 
+
+ align:start position:0%
+fine but from another point of view
+that's x and I carry x around and I name
+
+ align:start position:0%
+that's x and I carry x around and I name
+ 
+
+ align:start position:0%
+that's x and I carry x around and I name
+it as x and I hold it and I can say
+
+ align:start position:0%
+it as x and I hold it and I can say
+ 
+
+ align:start position:0%
+it as x and I hold it and I can say
+things like the sum of x and y rather
+
+ align:start position:0%
+things like the sum of x and y rather
+ 
+
+ align:start position:0%
+things like the sum of x and y rather
+than just have see it's not so bad when
+
+ align:start position:0%
+than just have see it's not so bad when
+ 
+
+ align:start position:0%
+than just have see it's not so bad when
+I only think about x but if I have a
+
+ align:start position:0%
+I only think about x but if I have a
+ 
+
+ align:start position:0%
+I only think about x but if I have a
+system with 10 rational numbers suddenly
+
+ align:start position:0%
+system with 10 rational numbers suddenly
+ 
+
+ align:start position:0%
+system with 10 rational numbers suddenly
+I have 20 numerators and denominators
+
+ align:start position:0%
+I have 20 numerators and denominators
+ 
+
+ align:start position:0%
+I have 20 numerators and denominators
+which are not necessarily if I don't
+
+ align:start position:0%
+which are not necessarily if I don't
+ 
+
+ align:start position:0%
+which are not necessarily if I don't
+link them then It's just 20 arbitrary
+
+ align:start position:0%
+link them then It's just 20 arbitrary
+ 
+
+ align:start position:0%
+link them then It's just 20 arbitrary
+numbers that are not linked in any
+
+ align:start position:0%
+numbers that are not linked in any
+ 
+
+ align:start position:0%
+numbers that are not linked in any
+particular way. It's I mean it's a lot
+
+ align:start position:0%
+particular way. It's I mean it's a lot
+ 
+
+ align:start position:0%
+particular way. It's I mean it's a lot
+like saying well I have these
+
+ align:start position:0%
+like saying well I have these
+ 
+
+ align:start position:0%
+like saying well I have these
+instructions that are the body of the
+
+ align:start position:0%
+instructions that are the body of the
+ 
+
+ align:start position:0%
+instructions that are the body of the
+procedures. Why do I want to package
+
+ align:start position:0%
+procedures. Why do I want to package
+ 
+
+ align:start position:0%
+procedures. Why do I want to package
+them and say it's the procedure? It's
+
+ align:start position:0%
+them and say it's the procedure? It's
+ 
+
+ align:start position:0%
+them and say it's the procedure? It's
+exactly the same idea. Okay.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay.
+
+ align:start position:0%
+Okay.
+ 
+
+ align:start position:0%
+Okay.
+with just stretch and get somebody to
+
+ align:start position:0%
+with just stretch and get somebody to
+ 
+
+ align:start position:0%
+with just stretch and get somebody to
+[Music]
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+[Music]
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay. Well, we've been working on this
+
+ align:start position:0%
+Okay. Well, we've been working on this
+ 
+
+ align:start position:0%
+Okay. Well, we've been working on this
+rational number arithmetic system.
+
+ align:start position:0%
+rational number arithmetic system.
+ 
+
+ align:start position:0%
+rational number arithmetic system.
+And then what we did, right, the
+
+ align:start position:0%
+And then what we did, right, the
+ 
+
+ align:start position:0%
+And then what we did, right, the
+important thing about what we did is we
+
+ align:start position:0%
+important thing about what we did is we
+ 
+
+ align:start position:0%
+important thing about what we did is we
+thought about the problem by breaking it
+
+ align:start position:0%
+thought about the problem by breaking it
+ 
+
+ align:start position:0%
+thought about the problem by breaking it
+into two pieces,
+
+ align:start position:0%
+into two pieces,
+ 
+
+ align:start position:0%
+into two pieces,
+right? We said assume there's this
+
+ align:start position:0%
+right? We said assume there's this
+ 
+
+ align:start position:0%
+right? We said assume there's this
+contract with George and George has
+
+ align:start position:0%
+contract with George and George has
+ 
+
+ align:start position:0%
+contract with George and George has
+figured out the way to how to construct
+
+ align:start position:0%
+figured out the way to how to construct
+ 
+
+ align:start position:0%
+figured out the way to how to construct
+these clouds
+
+ align:start position:0%
+these clouds
+ 
+
+ align:start position:0%
+these clouds
+provided us procedures make rat which
+
+ align:start position:0%
+provided us procedures make rat which
+ 
+
+ align:start position:0%
+provided us procedures make rat which
+was a constructor and selectors which
+
+ align:start position:0%
+was a constructor and selectors which
+ 
+
+ align:start position:0%
+was a constructor and selectors which
+are numer and denominator and then in
+
+ align:start position:0%
+are numer and denominator and then in
+ 
+
+ align:start position:0%
+are numer and denominator and then in
+terms of that we went off and
+
+ align:start position:0%
+terms of that we went off and
+ 
+
+ align:start position:0%
+terms of that we went off and
+implemented addition and multiplication
+
+ align:start position:0%
+implemented addition and multiplication
+ 
+
+ align:start position:0%
+implemented addition and multiplication
+of rational numbers.
+
+ align:start position:0%
+of rational numbers.
+ 
+
+ align:start position:0%
+of rational numbers.
+Well, now let's go look at George's
+
+ align:start position:0%
+Well, now let's go look at George's
+ 
+
+ align:start position:0%
+Well, now let's go look at George's
+problem, right? How can we go and
+
+ align:start position:0%
+problem, right? How can we go and
+ 
+
+ align:start position:0%
+problem, right? How can we go and
+package together a numerator and a and a
+
+ align:start position:0%
+package together a numerator and a and a
+ 
+
+ align:start position:0%
+package together a numerator and a and a
+denominator to actually make one of
+
+ align:start position:0%
+denominator to actually make one of
+ 
+
+ align:start position:0%
+denominator to actually make one of
+these clouds? See, what we need is a
+
+ align:start position:0%
+these clouds? See, what we need is a
+ 
+
+ align:start position:0%
+these clouds? See, what we need is a
+kind of glue
+
+ align:start position:0%
+kind of glue
+ 
+
+ align:start position:0%
+kind of glue
+kind of glue that a glue for data
+
+ align:start position:0%
+kind of glue that a glue for data
+ 
+
+ align:start position:0%
+kind of glue that a glue for data
+objects that allows us to put things
+
+ align:start position:0%
+objects that allows us to put things
+ 
+
+ align:start position:0%
+objects that allows us to put things
+together and uh list provides such a
+
+ align:start position:0%
+together and uh list provides such a
+ 
+
+ align:start position:0%
+together and uh list provides such a
+glue.
+
+ align:start position:0%
+glue.
+ 
+
+ align:start position:0%
+glue.
+That glue is is called list structure.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that list structure is a way of gluing
+
+ align:start position:0%
+that list structure is a way of gluing
+ 
+
+ align:start position:0%
+that list structure is a way of gluing
+things together
+
+ align:start position:0%
+things together
+ 
+
+ align:start position:0%
+things together
+and more precisely list provides a way
+
+ align:start position:0%
+and more precisely list provides a way
+ 
+
+ align:start position:0%
+and more precisely list provides a way
+of constructing things called pairs.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay, there's a there's a primitive
+
+ align:start position:0%
+Okay, there's a there's a primitive
+ 
+
+ align:start position:0%
+Okay, there's a there's a primitive
+operator in lisp called cons.
+
+ align:start position:0%
+operator in lisp called cons.
+ 
+
+ align:start position:0%
+operator in lisp called cons.
+You can take a look at it.
+
+ align:start position:0%
+You can take a look at it.
+ 
+
+ align:start position:0%
+You can take a look at it.
+There's a thing called called cons,
+
+ align:start position:0%
+There's a thing called called cons,
+ 
+
+ align:start position:0%
+There's a thing called called cons,
+right? Conce is an operator which takes
+
+ align:start position:0%
+right? Conce is an operator which takes
+ 
+
+ align:start position:0%
+right? Conce is an operator which takes
+in two arguments called x and y
+
+ align:start position:0%
+in two arguments called x and y
+ 
+
+ align:start position:0%
+in two arguments called x and y
+and it returns for us a thing called a
+
+ align:start position:0%
+and it returns for us a thing called a
+ 
+
+ align:start position:0%
+and it returns for us a thing called a
+pair,
+
+ align:start position:0%
+pair,
+ 
+
+ align:start position:0%
+pair,
+right? Things called it's a thing called
+
+ align:start position:0%
+right? Things called it's a thing called
+ 
+
+ align:start position:0%
+right? Things called it's a thing called
+a pair,
+
+ align:start position:0%
+a pair,
+ 
+
+ align:start position:0%
+a pair,
+right? That has a first part and a
+
+ align:start position:0%
+right? That has a first part and a
+ 
+
+ align:start position:0%
+right? That has a first part and a
+second part,
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+right? So K takes two objects.
+
+ align:start position:0%
+right? So K takes two objects.
+ 
+
+ align:start position:0%
+right? So K takes two objects.
+There's a thing called a pair. The first
+
+ align:start position:0%
+There's a thing called a pair. The first
+ 
+
+ align:start position:0%
+There's a thing called a pair. The first
+part of the con is X and the second part
+
+ align:start position:0%
+part of the con is X and the second part
+ 
+
+ align:start position:0%
+part of the con is X and the second part
+of the con is Y. And that's what it
+
+ align:start position:0%
+of the con is Y. And that's what it
+ 
+
+ align:start position:0%
+of the con is Y. And that's what it
+builds.
+
+ align:start position:0%
+builds.
+ 
+
+ align:start position:0%
+builds.
+And then we also assume we have ways of
+
+ align:start position:0%
+And then we also assume we have ways of
+ 
+
+ align:start position:0%
+And then we also assume we have ways of
+getting things out. If you're given a
+
+ align:start position:0%
+getting things out. If you're given a
+ 
+
+ align:start position:0%
+getting things out. If you're given a
+pair, there's a thing called car.
+
+ align:start position:0%
+pair, there's a thing called car.
+ 
+
+ align:start position:0%
+pair, there's a thing called car.
+And car of a pair P gives you out the
+
+ align:start position:0%
+And car of a pair P gives you out the
+ 
+
+ align:start position:0%
+And car of a pair P gives you out the
+first part of the pair P. And there's a
+
+ align:start position:0%
+first part of the pair P. And there's a
+ 
+
+ align:start position:0%
+first part of the pair P. And there's a
+thing called cutter. the coder of the
+
+ align:start position:0%
+thing called cutter. the coder of the
+ 
+
+ align:start position:0%
+thing called cutter. the coder of the
+pair P gives you the the second part of
+
+ align:start position:0%
+pair P gives you the the second part of
+ 
+
+ align:start position:0%
+pair P gives you the the second part of
+the pair P.
+
+ align:start position:0%
+the pair P.
+ 
+
+ align:start position:0%
+the pair P.
+Okay, so that's how we construct things.
+
+ align:start position:0%
+Okay, so that's how we construct things.
+ 
+
+ align:start position:0%
+Okay, so that's how we construct things.
+There's also a uh conventional way of of
+
+ align:start position:0%
+There's also a uh conventional way of of
+ 
+
+ align:start position:0%
+There's also a uh conventional way of of
+drawing pictures of these things just
+
+ align:start position:0%
+drawing pictures of these things just
+ 
+
+ align:start position:0%
+drawing pictures of these things just
+like we write down uh
+
+ align:start position:0%
+like we write down uh
+ 
+
+ align:start position:0%
+like we write down uh
+just as we write down that as the
+
+ align:start position:0%
+just as we write down that as the
+ 
+
+ align:start position:0%
+just as we write down that as the
+conventional way of writing Plato's idea
+
+ align:start position:0%
+conventional way of writing Plato's idea
+ 
+
+ align:start position:0%
+conventional way of writing Plato's idea
+of two.
+
+ align:start position:0%
+of two.
+ 
+
+ align:start position:0%
+of two.
+The way we would we could
+
+ align:start position:0%
+The way we would we could
+ 
+
+ align:start position:0%
+The way we would we could
+draw a diagram to represent con of two
+
+ align:start position:0%
+draw a diagram to represent con of two
+ 
+
+ align:start position:0%
+draw a diagram to represent con of two
+and three is like this. We draw a little
+
+ align:start position:0%
+and three is like this. We draw a little
+ 
+
+ align:start position:0%
+and three is like this. We draw a little
+box
+
+ align:start position:0%
+box
+ 
+
+ align:start position:0%
+box
+and say here's the box we're talking
+
+ align:start position:0%
+and say here's the box we're talking
+ 
+
+ align:start position:0%
+and say here's the box we're talking
+about. And this box has two arrows
+
+ align:start position:0%
+about. And this box has two arrows
+ 
+
+ align:start position:0%
+about. And this box has two arrows
+coming out of it.
+
+ align:start position:0%
+coming out of it.
+ 
+
+ align:start position:0%
+coming out of it.
+Let's say the first
+
+ align:start position:0%
+Let's say the first
+ 
+
+ align:start position:0%
+Let's say the first
+part of this this pair is two. And the
+
+ align:start position:0%
+part of this this pair is two. And the
+ 
+
+ align:start position:0%
+part of this this pair is two. And the
+second part of this pair is three.
+
+ align:start position:0%
+second part of this pair is three.
+ 
+
+ align:start position:0%
+second part of this pair is three.
+And this notation has a name. It's
+
+ align:start position:0%
+And this notation has a name. It's
+ 
+
+ align:start position:0%
+And this notation has a name. It's
+called box.
+
+ align:start position:0%
+called box.
+ 
+
+ align:start position:0%
+called box.
+It's called box and pointer notation.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay, by the way, let me say right now
+
+ align:start position:0%
+Okay, by the way, let me say right now
+ 
+
+ align:start position:0%
+Okay, by the way, let me say right now
+that a lot of people get confused that
+
+ align:start position:0%
+that a lot of people get confused that
+ 
+
+ align:start position:0%
+that a lot of people get confused that
+there's some significance to the
+
+ align:start position:0%
+there's some significance to the
+ 
+
+ align:start position:0%
+there's some significance to the
+geometric way I drew these pointers, the
+
+ align:start position:0%
+geometric way I drew these pointers, the
+ 
+
+ align:start position:0%
+geometric way I drew these pointers, the
+directions. Like some people think it'd
+
+ align:start position:0%
+directions. Like some people think it'd
+ 
+
+ align:start position:0%
+directions. Like some people think it'd
+be different if I took this pointer and
+
+ align:start position:0%
+be different if I took this pointer and
+ 
+
+ align:start position:0%
+be different if I took this pointer and
+turned it up here and put the three out
+
+ align:start position:0%
+turned it up here and put the three out
+ 
+
+ align:start position:0%
+turned it up here and put the three out
+here. That has no significance, right?
+
+ align:start position:0%
+here. That has no significance, right?
+ 
+
+ align:start position:0%
+here. That has no significance, right?
+It's it's merely you have a bunch of
+
+ align:start position:0%
+It's it's merely you have a bunch of
+ 
+
+ align:start position:0%
+It's it's merely you have a bunch of
+arrows, these pointers, right? and the
+
+ align:start position:0%
+arrows, these pointers, right? and the
+ 
+
+ align:start position:0%
+arrows, these pointers, right? and the
+boxes. And the only issue is the is how
+
+ align:start position:0%
+boxes. And the only issue is the is how
+ 
+
+ align:start position:0%
+boxes. And the only issue is the is how
+they're connected, not the the geometric
+
+ align:start position:0%
+they're connected, not the the geometric
+ 
+
+ align:start position:0%
+they're connected, not the the geometric
+arrangement of whether I write the
+
+ align:start position:0%
+arrangement of whether I write the
+ 
+
+ align:start position:0%
+arrangement of whether I write the
+pointer across or up or down.
+
+ align:start position:0%
+pointer across or up or down.
+ 
+
+ align:start position:0%
+pointer across or up or down.
+Now, it's completely unobvious
+
+ align:start position:0%
+Now, it's completely unobvious
+ 
+
+ align:start position:0%
+Now, it's completely unobvious
+probably why that's called list
+
+ align:start position:0%
+probably why that's called list
+ 
+
+ align:start position:0%
+probably why that's called list
+structure. We're not actually going to
+
+ align:start position:0%
+structure. We're not actually going to
+ 
+
+ align:start position:0%
+structure. We're not actually going to
+talk about that today. We'll we'll see
+
+ align:start position:0%
+talk about that today. We'll we'll see
+ 
+
+ align:start position:0%
+talk about that today. We'll we'll see
+that next time.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay. So, those are pairs. There's K
+
+ align:start position:0%
+Okay. So, those are pairs. There's K
+ 
+
+ align:start position:0%
+Okay. So, those are pairs. There's K
+that constructs them. And what I'm going
+
+ align:start position:0%
+that constructs them. And what I'm going
+ 
+
+ align:start position:0%
+that constructs them. And what I'm going
+to know about Kant and K and Cutter is
+
+ align:start position:0%
+to know about Kant and K and Cutter is
+ 
+
+ align:start position:0%
+to know about Kant and K and Cutter is
+precisely that if I give if I have any X
+
+ align:start position:0%
+precisely that if I give if I have any X
+ 
+
+ align:start position:0%
+precisely that if I give if I have any X
+and Y right if I'm going to say if I
+
+ align:start position:0%
+and Y right if I'm going to say if I
+ 
+
+ align:start position:0%
+and Y right if I'm going to say if I
+have anything X and Y
+
+ align:start position:0%
+have anything X and Y
+ 
+
+ align:start position:0%
+have anything X and Y
+and I use cons to construct a pair
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+then the car of that pair is going to be
+
+ align:start position:0%
+then the car of that pair is going to be
+ 
+
+ align:start position:0%
+then the car of that pair is going to be
+X the thing I put in and the critter of
+
+ align:start position:0%
+X the thing I put in and the critter of
+ 
+
+ align:start position:0%
+X the thing I put in and the critter of
+that pair is going to be Y
+
+ align:start position:0%
+that pair is going to be Y
+ 
+
+ align:start position:0%
+that pair is going to be Y
+right that's the that's the behavior of
+
+ align:start position:0%
+right that's the that's the behavior of
+ 
+
+ align:start position:0%
+right that's the that's the behavior of
+these operators const car and citter
+
+ align:start position:0%
+these operators const car and citter
+ 
+
+ align:start position:0%
+these operators const car and citter
+given them it's pretty clear how George
+
+ align:start position:0%
+given them it's pretty clear how George
+ 
+
+ align:start position:0%
+given them it's pretty clear how George
+can go off and construct his rational
+
+ align:start position:0%
+can go off and construct his rational
+ 
+
+ align:start position:0%
+can go off and construct his rational
+numbers
+
+ align:start position:0%
+numbers
+ 
+
+ align:start position:0%
+numbers
+after all he has to do remember George's
+
+ align:start position:0%
+after all he has to do remember George's
+ 
+
+ align:start position:0%
+after all he has to do remember George's
+problem was to implement make rat
+
+ align:start position:0%
+problem was to implement make rat
+ 
+
+ align:start position:0%
+problem was to implement make rat
+numerator and denom so all George has to
+
+ align:start position:0%
+numerator and denom so all George has to
+ 
+
+ align:start position:0%
+numerator and denom so all George has to
+do is say define
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+make rat
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+of some n and a g well all I have to do
+
+ align:start position:0%
+of some n and a g well all I have to do
+ 
+
+ align:start position:0%
+of some n and a g well all I have to do
+is constant
+
+ align:start position:0%
+is constant
+ 
+
+ align:start position:0%
+is constant
+That's constant of n to d
+
+ align:start position:0%
+That's constant of n to d
+ 
+
+ align:start position:0%
+That's constant of n to d
+and then if I want to get the numerator
+
+ align:start position:0%
+and then if I want to get the numerator
+ 
+
+ align:start position:0%
+and then if I want to get the numerator
+out I can say define
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the numerator numer
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+of some rational number x. If the
+
+ align:start position:0%
+of some rational number x. If the
+ 
+
+ align:start position:0%
+of some rational number x. If the
+rational number is implemented as a pair
+
+ align:start position:0%
+rational number is implemented as a pair
+ 
+
+ align:start position:0%
+rational number is implemented as a pair
+then all I have to do is get out the car
+
+ align:start position:0%
+then all I have to do is get out the car
+ 
+
+ align:start position:0%
+then all I have to do is get out the car
+of x
+
+ align:start position:0%
+of x
+ 
+
+ align:start position:0%
+of x
+and then similarly
+
+ align:start position:0%
+and then similarly
+ 
+
+ align:start position:0%
+and then similarly
+define
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the denom
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+is going to be the critter the other
+
+ align:start position:0%
+is going to be the critter the other
+ 
+
+ align:start position:0%
+is going to be the critter the other
+thing I put into the pair.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Well, now we're in business, right?
+
+ align:start position:0%
+Well, now we're in business, right?
+ 
+
+ align:start position:0%
+Well, now we're in business, right?
+That's the
+
+ align:start position:0%
+That's the
+ 
+
+ align:start position:0%
+That's the
+that's a complete implementation of
+
+ align:start position:0%
+that's a complete implementation of
+ 
+
+ align:start position:0%
+that's a complete implementation of
+rational numbers. Let's use it. Suppose
+
+ align:start position:0%
+rational numbers. Let's use it. Suppose
+ 
+
+ align:start position:0%
+rational numbers. Let's use it. Suppose
+I want to say so I want to think about
+
+ align:start position:0%
+I want to say so I want to think about
+ 
+
+ align:start position:0%
+I want to say so I want to think about
+how to add 1/2 + 1/4
+
+ align:start position:0%
+how to add 1/2 + 1/4
+ 
+
+ align:start position:0%
+how to add 1/2 + 1/4
+and see watch the system work. Well, the
+
+ align:start position:0%
+and see watch the system work. Well, the
+ 
+
+ align:start position:0%
+and see watch the system work. Well, the
+way I'd use that is I'd say well maybe
+
+ align:start position:0%
+way I'd use that is I'd say well maybe
+ 
+
+ align:start position:0%
+way I'd use that is I'd say well maybe
+define
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+define a I have to make a 1/2.
+
+ align:start position:0%
+define a I have to make a 1/2.
+ 
+
+ align:start position:0%
+define a I have to make a 1/2.
+Well, that's a rational number with
+
+ align:start position:0%
+Well, that's a rational number with
+ 
+
+ align:start position:0%
+Well, that's a rational number with
+numerator one and denominator two.
+
+ align:start position:0%
+numerator one and denominator two.
+ 
+
+ align:start position:0%
+numerator one and denominator two.
+So a will be make rat of one and two
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and then I'll construct the 1/4. I'll
+
+ align:start position:0%
+and then I'll construct the 1/4. I'll
+ 
+
+ align:start position:0%
+and then I'll construct the 1/4. I'll
+say define
+
+ align:start position:0%
+say define
+ 
+
+ align:start position:0%
+say define
+d
+
+ align:start position:0%
+d
+ 
+
+ align:start position:0%
+d
+to be
+
+ align:start position:0%
+to be
+ 
+
+ align:start position:0%
+to be
+make rat
+
+ align:start position:0%
+make rat
+ 
+
+ align:start position:0%
+make rat
+of uh
+
+ align:start position:0%
+of uh
+ 
+
+ align:start position:0%
+of uh
+1 and four.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+And if I'd like to look at the answer,
+
+ align:start position:0%
+And if I'd like to look at the answer,
+ 
+
+ align:start position:0%
+And if I'd like to look at the answer,
+well, assuming I don't have a special
+
+ align:start position:0%
+well, assuming I don't have a special
+ 
+
+ align:start position:0%
+well, assuming I don't have a special
+thing that prints rational numbers or I
+
+ align:start position:0%
+thing that prints rational numbers or I
+ 
+
+ align:start position:0%
+thing that prints rational numbers or I
+could make one, I could say, for
+
+ align:start position:0%
+could make one, I could say, for
+ 
+
+ align:start position:0%
+could make one, I could say, for
+instance, define
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the answer
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+to be plus rat
+
+ align:start position:0%
+to be plus rat
+ 
+
+ align:start position:0%
+to be plus rat
+of a and b.
+
+ align:start position:0%
+of a and b.
+ 
+
+ align:start position:0%
+of a and b.
+And now I can say what's the answer?
+
+ align:start position:0%
+And now I can say what's the answer?
+ 
+
+ align:start position:0%
+And now I can say what's the answer?
+What's the what are the numerators and
+
+ align:start position:0%
+What's the what are the numerators and
+ 
+
+ align:start position:0%
+What's the what are the numerators and
+denominators of the answer? So if I'm
+
+ align:start position:0%
+denominators of the answer? So if I'm
+ 
+
+ align:start position:0%
+denominators of the answer? So if I'm
+adding 1/2 and 1/4,
+
+ align:start position:0%
+adding 1/2 and 1/4,
+ 
+
+ align:start position:0%
+adding 1/2 and 1/4,
+I'll say what is the numerator
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+of the answer
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and the system is going to type out
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+well six. Bad news.
+
+ align:start position:0%
+well six. Bad news.
+ 
+
+ align:start position:0%
+well six. Bad news.
+And if I say what's the denominator of
+
+ align:start position:0%
+And if I say what's the denominator of
+ 
+
+ align:start position:0%
+And if I say what's the denominator of
+the answer,
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the system's going to type out eight.
+
+ align:start position:0%
+the system's going to type out eight.
+ 
+
+ align:start position:0%
+the system's going to type out eight.
+So instead of what I would really like,
+
+ align:start position:0%
+So instead of what I would really like,
+ 
+
+ align:start position:0%
+So instead of what I would really like,
+which is for it to say that 1/2 and 1/4
+
+ align:start position:0%
+which is for it to say that 1/2 and 1/4
+ 
+
+ align:start position:0%
+which is for it to say that 1/2 and 1/4
+is 3/4s,
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this foolish machine is going to say,
+
+ align:start position:0%
+this foolish machine is going to say,
+ 
+
+ align:start position:0%
+this foolish machine is going to say,
+"No, it's 68."
+
+ align:start position:0%
+"No, it's 68."
+ 
+
+ align:start position:0%
+"No, it's 68."
+You know, that's that's sort of bad
+
+ align:start position:0%
+You know, that's that's sort of bad
+ 
+
+ align:start position:0%
+You know, that's that's sort of bad
+news.
+
+ align:start position:0%
+news.
+ 
+
+ align:start position:0%
+news.
+Where's the bug?
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Why does it do that after all? Well,
+
+ align:start position:0%
+Why does it do that after all? Well,
+ 
+
+ align:start position:0%
+Why does it do that after all? Well,
+it's the way that we just had plus rat.
+
+ align:start position:0%
+it's the way that we just had plus rat.
+ 
+
+ align:start position:0%
+it's the way that we just had plus rat.
+Plus rat just took the right. It said
+
+ align:start position:0%
+Plus rat just took the right. It said
+ 
+
+ align:start position:0%
+Plus rat just took the right. It said
+you add the the numerator times the
+
+ align:start position:0%
+you add the the numerator times the
+ 
+
+ align:start position:0%
+you add the the numerator times the
+denominator.
+
+ align:start position:0%
+denominator.
+ 
+
+ align:start position:0%
+denominator.
+You add that to the numerator times the
+
+ align:start position:0%
+You add that to the numerator times the
+ 
+
+ align:start position:0%
+You add that to the numerator times the
+denominator and put that over the
+
+ align:start position:0%
+denominator and put that over the
+ 
+
+ align:start position:0%
+denominator and put that over the
+product of the two denominators and
+
+ align:start position:0%
+product of the two denominators and
+ 
+
+ align:start position:0%
+product of the two denominators and
+that's why you get 68.
+
+ align:start position:0%
+that's why you get 68.
+ 
+
+ align:start position:0%
+that's why you get 68.
+So what was wrong with our
+
+ align:start position:0%
+So what was wrong with our
+ 
+
+ align:start position:0%
+So what was wrong with our
+implementation of plus rad? What's wrong
+
+ align:start position:0%
+implementation of plus rad? What's wrong
+ 
+
+ align:start position:0%
+implementation of plus rad? What's wrong
+with that rational number arithmetic
+
+ align:start position:0%
+with that rational number arithmetic
+ 
+
+ align:start position:0%
+with that rational number arithmetic
+stuff that we did before the break?
+
+ align:start position:0%
+stuff that we did before the break?
+ 
+
+ align:start position:0%
+stuff that we did before the break?
+Well, the answer is one way to look at
+
+ align:start position:0%
+Well, the answer is one way to look at
+ 
+
+ align:start position:0%
+Well, the answer is one way to look at
+it is absolutely nothing's wrong with
+
+ align:start position:0%
+it is absolutely nothing's wrong with
+ 
+
+ align:start position:0%
+it is absolutely nothing's wrong with
+it. That's perfectly good
+
+ align:start position:0%
+it. That's perfectly good
+ 
+
+ align:start position:0%
+it. That's perfectly good
+implementation. Follows the right
+
+ align:start position:0%
+implementation. Follows the right
+ 
+
+ align:start position:0%
+implementation. Follows the right
+follows the the sixth grade, fifth grade
+
+ align:start position:0%
+follows the the sixth grade, fifth grade
+ 
+
+ align:start position:0%
+follows the the sixth grade, fifth grade
+mathematics for adding fractions.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+One thing we can say is, well, that's
+
+ align:start position:0%
+One thing we can say is, well, that's
+ 
+
+ align:start position:0%
+One thing we can say is, well, that's
+George's problem, right? Boy, wasn't
+
+ align:start position:0%
+George's problem, right? Boy, wasn't
+ 
+
+ align:start position:0%
+George's problem, right? Boy, wasn't
+George dumb to say that he can make a
+
+ align:start position:0%
+George dumb to say that he can make a
+ 
+
+ align:start position:0%
+George dumb to say that he can make a
+rational number simply by sticking
+
+ align:start position:0%
+rational number simply by sticking
+ 
+
+ align:start position:0%
+rational number simply by sticking
+together the numerator and denominator,
+
+ align:start position:0%
+together the numerator and denominator,
+ 
+
+ align:start position:0%
+together the numerator and denominator,
+right? Wouldn't it be better for George
+
+ align:start position:0%
+right? Wouldn't it be better for George
+ 
+
+ align:start position:0%
+right? Wouldn't it be better for George
+when he made a rational number to reduce
+
+ align:start position:0%
+when he made a rational number to reduce
+ 
+
+ align:start position:0%
+when he made a rational number to reduce
+the stuff to lowest terms?
+
+ align:start position:0%
+the stuff to lowest terms?
+ 
+
+ align:start position:0%
+the stuff to lowest terms?
+And what I mean is, wouldn't it be
+
+ align:start position:0%
+And what I mean is, wouldn't it be
+ 
+
+ align:start position:0%
+And what I mean is, wouldn't it be
+better
+
+ align:start position:0%
+better
+ 
+
+ align:start position:0%
+better
+for George instead of using this version
+
+ align:start position:0%
+for George instead of using this version
+ 
+
+ align:start position:0%
+for George instead of using this version
+of Maker
+
+ align:start position:0%
+of Maker
+ 
+
+ align:start position:0%
+of Maker
+to use this one on the slide
+
+ align:start position:0%
+to use this one on the slide
+ 
+
+ align:start position:0%
+to use this one on the slide
+where instead of just saying const
+
+ align:start position:0%
+where instead of just saying const
+ 
+
+ align:start position:0%
+where instead of just saying const
+together N and D, what you do is compute
+
+ align:start position:0%
+together N and D, what you do is compute
+ 
+
+ align:start position:0%
+together N and D, what you do is compute
+the greatest common divisor of N and D
+
+ align:start position:0%
+the greatest common divisor of N and D
+ 
+
+ align:start position:0%
+the greatest common divisor of N and D
+and GCD is a procedure which well for
+
+ align:start position:0%
+and GCD is a procedure which well for
+ 
+
+ align:start position:0%
+and GCD is a procedure which well for
+all we care is a primitive which
+
+ align:start position:0%
+all we care is a primitive which
+ 
+
+ align:start position:0%
+all we care is a primitive which
+computes the greatest common divisor of
+
+ align:start position:0%
+computes the greatest common divisor of
+ 
+
+ align:start position:0%
+computes the greatest common divisor of
+two numbers.
+
+ align:start position:0%
+two numbers.
+ 
+
+ align:start position:0%
+two numbers.
+So the way I can construct a rational
+
+ align:start position:0%
+So the way I can construct a rational
+ 
+
+ align:start position:0%
+So the way I can construct a rational
+number is
+
+ align:start position:0%
+number is
+ 
+
+ align:start position:0%
+number is
+get the greatest common divisor of the
+
+ align:start position:0%
+get the greatest common divisor of the
+ 
+
+ align:start position:0%
+get the greatest common divisor of the
+two numbers and I'm going to call that
+
+ align:start position:0%
+two numbers and I'm going to call that
+ 
+
+ align:start position:0%
+two numbers and I'm going to call that
+G.
+
+ align:start position:0%
+G.
+ 
+
+ align:start position:0%
+G.
+And then instead of constanting together
+
+ align:start position:0%
+And then instead of constanting together
+ 
+
+ align:start position:0%
+And then instead of constanting together
+N and D, I'll divide them through. I'll
+
+ align:start position:0%
+N and D, I'll divide them through. I'll
+ 
+
+ align:start position:0%
+N and D, I'll divide them through. I'll
+constant together the quotient of the N
+
+ align:start position:0%
+constant together the quotient of the N
+ 
+
+ align:start position:0%
+constant together the quotient of the N
+by the the GCD and the quotient of D by
+
+ align:start position:0%
+by the the GCD and the quotient of D by
+ 
+
+ align:start position:0%
+by the the GCD and the quotient of D by
+the GCD
+
+ align:start position:0%
+the GCD
+ 
+
+ align:start position:0%
+the GCD
+and that'll reduce a rational number to
+
+ align:start position:0%
+and that'll reduce a rational number to
+ 
+
+ align:start position:0%
+and that'll reduce a rational number to
+lowest terms.
+
+ align:start position:0%
+lowest terms.
+ 
+
+ align:start position:0%
+lowest terms.
+So that when
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+right so when I do this addition when
+
+ align:start position:0%
+right so when I do this addition when
+ 
+
+ align:start position:0%
+right so when I do this addition when
+this when plus rat calls
+
+ align:start position:0%
+this when plus rat calls
+ 
+
+ align:start position:0%
+this when plus rat calls
+nrat remember the definition of plus rat
+
+ align:start position:0%
+nrat remember the definition of plus rat
+ 
+
+ align:start position:0%
+nrat remember the definition of plus rat
+it have a nrat in there just by the fact
+
+ align:start position:0%
+it have a nrat in there just by the fact
+ 
+
+ align:start position:0%
+it have a nrat in there just by the fact
+that it's constructing that the thing
+
+ align:start position:0%
+that it's constructing that the thing
+ 
+
+ align:start position:0%
+that it's constructing that the thing
+will get reduced to lowest terms
+
+ align:start position:0%
+will get reduced to lowest terms
+ 
+
+ align:start position:0%
+will get reduced to lowest terms
+automatically
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay that
+
+ align:start position:0%
+okay that
+ 
+
+ align:start position:0%
+okay that
+that is a complete system,
+
+ align:start position:0%
+that is a complete system,
+ 
+
+ align:start position:0%
+that is a complete system,
+right? For rational number arithmetic.
+
+ align:start position:0%
+right? For rational number arithmetic.
+ 
+
+ align:start position:0%
+right? For rational number arithmetic.
+Let's look at what we've done,
+
+ align:start position:0%
+Let's look at what we've done,
+ 
+
+ align:start position:0%
+Let's look at what we've done,
+right? We said we want to build rational
+
+ align:start position:0%
+right? We said we want to build rational
+ 
+
+ align:start position:0%
+right? We said we want to build rational
+number arithmetic
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and we had a thing called plus rat. We
+
+ align:start position:0%
+and we had a thing called plus rat. We
+ 
+
+ align:start position:0%
+and we had a thing called plus rat. We
+implemented that
+
+ align:start position:0%
+implemented that
+ 
+
+ align:start position:0%
+implemented that
+and uh showed you multiplying rational
+
+ align:start position:0%
+and uh showed you multiplying rational
+ 
+
+ align:start position:0%
+and uh showed you multiplying rational
+numbers and although I didn't put them
+
+ align:start position:0%
+numbers and although I didn't put them
+ 
+
+ align:start position:0%
+numbers and although I didn't put them
+up there presumably we'd like to have
+
+ align:start position:0%
+up there presumably we'd like to have
+ 
+
+ align:start position:0%
+up there presumably we'd like to have
+something that subtracts rational
+
+ align:start position:0%
+something that subtracts rational
+ 
+
+ align:start position:0%
+something that subtracts rational
+numbers and I don't know all sorts of
+
+ align:start position:0%
+numbers and I don't know all sorts of
+ 
+
+ align:start position:0%
+numbers and I don't know all sorts of
+things things that test equality and
+
+ align:start position:0%
+things things that test equality and
+ 
+
+ align:start position:0%
+things things that test equality and
+division and maybe things that print
+
+ align:start position:0%
+division and maybe things that print
+ 
+
+ align:start position:0%
+division and maybe things that print
+rational numbers in some particular way
+
+ align:start position:0%
+rational numbers in some particular way
+ 
+
+ align:start position:0%
+rational numbers in some particular way
+and we implemented those
+
+ align:start position:0%
+and we implemented those
+ 
+
+ align:start position:0%
+and we implemented those
+in terms of pairs
+
+ align:start position:0%
+in terms of pairs
+ 
+
+ align:start position:0%
+in terms of pairs
+these pairs conar and critter that are
+
+ align:start position:0%
+these pairs conar and critter that are
+ 
+
+ align:start position:0%
+these pairs conar and critter that are
+built into lisp but the important thing
+
+ align:start position:0%
+built into lisp but the important thing
+ 
+
+ align:start position:0%
+built into lisp but the important thing
+is that between
+
+ align:start position:0%
+is that between
+ 
+
+ align:start position:0%
+is that between
+these
+
+ align:start position:0%
+these
+ 
+
+ align:start position:0%
+these
+and these we set up an abstraction
+
+ align:start position:0%
+and these we set up an abstraction
+ 
+
+ align:start position:0%
+and these we set up an abstraction
+barrier. We set up a layer of
+
+ align:start position:0%
+barrier. We set up a layer of
+ 
+
+ align:start position:0%
+barrier. We set up a layer of
+abstraction.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+And what was that layer of abstraction?
+
+ align:start position:0%
+And what was that layer of abstraction?
+ 
+
+ align:start position:0%
+And what was that layer of abstraction?
+That layer abstraction was precisely the
+
+ align:start position:0%
+That layer abstraction was precisely the
+ 
+
+ align:start position:0%
+That layer abstraction was precisely the
+constructor and the selectors.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+This layer was mrat
+
+ align:start position:0%
+This layer was mrat
+ 
+
+ align:start position:0%
+This layer was mrat
+and numer
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and denom
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this methodology
+
+ align:start position:0%
+this methodology
+ 
+
+ align:start position:0%
+this methodology
+right this methodology another way to
+
+ align:start position:0%
+right this methodology another way to
+ 
+
+ align:start position:0%
+right this methodology another way to
+say what it's doing is that we are
+
+ align:start position:0%
+say what it's doing is that we are
+ 
+
+ align:start position:0%
+say what it's doing is that we are
+separating
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+we're separating the way something is
+
+ align:start position:0%
+we're separating the way something is
+ 
+
+ align:start position:0%
+we're separating the way something is
+used
+
+ align:start position:0%
+used
+ 
+
+ align:start position:0%
+used
+separating the use of data object
+
+ align:start position:0%
+separating the use of data object
+ 
+
+ align:start position:0%
+separating the use of data object
+objects from the representation of data
+
+ align:start position:0%
+objects from the representation of data
+ 
+
+ align:start position:0%
+objects from the representation of data
+objects.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Right? So up here we have the way that
+
+ align:start position:0%
+Right? So up here we have the way that
+ 
+
+ align:start position:0%
+Right? So up here we have the way that
+rational numbers are used do arithmetic
+
+ align:start position:0%
+rational numbers are used do arithmetic
+ 
+
+ align:start position:0%
+rational numbers are used do arithmetic
+on them. Down here we have the way that
+
+ align:start position:0%
+on them. Down here we have the way that
+ 
+
+ align:start position:0%
+on them. Down here we have the way that
+they're represented and they're
+
+ align:start position:0%
+they're represented and they're
+ 
+
+ align:start position:0%
+they're represented and they're
+separated by this boundary. The boundary
+
+ align:start position:0%
+separated by this boundary. The boundary
+ 
+
+ align:start position:0%
+separated by this boundary. The boundary
+is the constructors and selectors.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay. And this this methodology has a
+
+ align:start position:0%
+Okay. And this this methodology has a
+ 
+
+ align:start position:0%
+Okay. And this this methodology has a
+name. This is called data abstraction.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Data abstraction is sort of the
+
+ align:start position:0%
+Data abstraction is sort of the
+ 
+
+ align:start position:0%
+Data abstraction is sort of the
+programming methodology of setting up
+
+ align:start position:0%
+programming methodology of setting up
+ 
+
+ align:start position:0%
+programming methodology of setting up
+data objects by postulating constructors
+
+ align:start position:0%
+data objects by postulating constructors
+ 
+
+ align:start position:0%
+data objects by postulating constructors
+and selectors to isolate use from
+
+ align:start position:0%
+and selectors to isolate use from
+ 
+
+ align:start position:0%
+and selectors to isolate use from
+representation.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Well, so what? I mean, after all, we
+
+ align:start position:0%
+Well, so what? I mean, after all, we
+ 
+
+ align:start position:0%
+Well, so what? I mean, after all, we
+didn't have to do it this way. It's
+
+ align:start position:0%
+didn't have to do it this way. It's
+ 
+
+ align:start position:0%
+didn't have to do it this way. It's
+perfectly possible to do rational number
+
+ align:start position:0%
+perfectly possible to do rational number
+ 
+
+ align:start position:0%
+perfectly possible to do rational number
+addition without having any compound
+
+ align:start position:0%
+addition without having any compound
+ 
+
+ align:start position:0%
+addition without having any compound
+data objects. And here on this slide is
+
+ align:start position:0%
+data objects. And here on this slide is
+ 
+
+ align:start position:0%
+data objects. And here on this slide is
+one example. We certainly could have
+
+ align:start position:0%
+one example. We certainly could have
+ 
+
+ align:start position:0%
+one example. We certainly could have
+defined plus rat which takes in
+
+ align:start position:0%
+defined plus rat which takes in
+ 
+
+ align:start position:0%
+defined plus rat which takes in
+things x and y. And we'll say well what
+
+ align:start position:0%
+things x and y. And we'll say well what
+ 
+
+ align:start position:0%
+things x and y. And we'll say well what
+are these rational numbers really?
+
+ align:start position:0%
+are these rational numbers really?
+ 
+
+ align:start position:0%
+are these rational numbers really?
+Right? We'll say well really they're
+
+ align:start position:0%
+Right? We'll say well really they're
+ 
+
+ align:start position:0%
+Right? We'll say well really they're
+just pairs and the numerator is the car
+
+ align:start position:0%
+just pairs and the numerator is the car
+ 
+
+ align:start position:0%
+just pairs and the numerator is the car
+and the denominator is the cutter. So
+
+ align:start position:0%
+and the denominator is the cutter. So
+ 
+
+ align:start position:0%
+and the denominator is the cutter. So
+what we'll do is we'll take the car of X
+
+ align:start position:0%
+what we'll do is we'll take the car of X
+ 
+
+ align:start position:0%
+what we'll do is we'll take the car of X
+times the cooter of Y,
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+multiply them. Take the car of Y times
+
+ align:start position:0%
+multiply them. Take the car of Y times
+ 
+
+ align:start position:0%
+multiply them. Take the car of Y times
+the coder of X, multiply them, add them.
+
+ align:start position:0%
+the coder of X, multiply them, add them.
+ 
+
+ align:start position:0%
+the coder of X, multiply them, add them.
+Take the cooter of X and the CER of Y,
+
+ align:start position:0%
+Take the cooter of X and the CER of Y,
+ 
+
+ align:start position:0%
+Take the cooter of X and the CER of Y,
+multiply them, and then const the two
+
+ align:start position:0%
+multiply them, and then const the two
+ 
+
+ align:start position:0%
+multiply them, and then const the two
+together.
+
+ align:start position:0%
+together.
+ 
+
+ align:start position:0%
+together.
+And that well that sort of does the same
+
+ align:start position:0%
+And that well that sort of does the same
+ 
+
+ align:start position:0%
+And that well that sort of does the same
+thing,
+
+ align:start position:0%
+thing,
+ 
+
+ align:start position:0%
+thing,
+right?
+
+ align:start position:0%
+right?
+ 
+
+ align:start position:0%
+right?
+This ignores the problem of reducing
+
+ align:start position:0%
+This ignores the problem of reducing
+ 
+
+ align:start position:0%
+This ignores the problem of reducing
+things to lowest terms. But let's let's
+
+ align:start position:0%
+things to lowest terms. But let's let's
+ 
+
+ align:start position:0%
+things to lowest terms. But let's let's
+not worry about that for a minute. Well,
+
+ align:start position:0%
+not worry about that for a minute. Well,
+ 
+
+ align:start position:0%
+not worry about that for a minute. Well,
+so what why don't we do it that way?
+
+ align:start position:0%
+so what why don't we do it that way?
+ 
+
+ align:start position:0%
+so what why don't we do it that way?
+Right? After all, there there sort of
+
+ align:start position:0%
+Right? After all, there there sort of
+ 
+
+ align:start position:0%
+Right? After all, there there sort of
+fewer procedures to define and it's a
+
+ align:start position:0%
+fewer procedures to define and it's a
+ 
+
+ align:start position:0%
+fewer procedures to define and it's a
+lot more straightforward.
+
+ align:start position:0%
+lot more straightforward.
+ 
+
+ align:start position:0%
+lot more straightforward.
+Uh
+
+ align:start position:0%
+Uh
+ 
+
+ align:start position:0%
+Uh
+saves all this self-righteous BS about
+
+ align:start position:0%
+saves all this self-righteous BS about
+ 
+
+ align:start position:0%
+saves all this self-righteous BS about
+talking about data abstraction. We just
+
+ align:start position:0%
+talking about data abstraction. We just
+ 
+
+ align:start position:0%
+talking about data abstraction. We just
+sort of do it. I mean, who knows? Maybe
+
+ align:start position:0%
+sort of do it. I mean, who knows? Maybe
+ 
+
+ align:start position:0%
+sort of do it. I mean, who knows? Maybe
+it's even marginally more efficient
+
+ align:start position:0%
+it's even marginally more efficient
+ 
+
+ align:start position:0%
+it's even marginally more efficient
+depending on whatever compiler we're
+
+ align:start position:0%
+depending on whatever compiler we're
+ 
+
+ align:start position:0%
+depending on whatever compiler we're
+using for this, right? What's the what's
+
+ align:start position:0%
+using for this, right? What's the what's
+ 
+
+ align:start position:0%
+using for this, right? What's the what's
+the point of isolating the youth from
+
+ align:start position:0%
+the point of isolating the youth from
+ 
+
+ align:start position:0%
+the point of isolating the youth from
+the representation?
+
+ align:start position:0%
+the representation?
+ 
+
+ align:start position:0%
+the representation?
+Well, goes back to this notion of
+
+ align:start position:0%
+Well, goes back to this notion of
+ 
+
+ align:start position:0%
+Well, goes back to this notion of
+naming. Remember the one of the most
+
+ align:start position:0%
+naming. Remember the one of the most
+ 
+
+ align:start position:0%
+naming. Remember the one of the most
+important principles in programming is
+
+ align:start position:0%
+important principles in programming is
+ 
+
+ align:start position:0%
+important principles in programming is
+the same as one of the most important
+
+ align:start position:0%
+the same as one of the most important
+ 
+
+ align:start position:0%
+the same as one of the most important
+principles in sorcery, right? That's if
+
+ align:start position:0%
+principles in sorcery, right? That's if
+ 
+
+ align:start position:0%
+principles in sorcery, right? That's if
+you have the name of a spirit, you get
+
+ align:start position:0%
+you have the name of a spirit, you get
+ 
+
+ align:start position:0%
+you have the name of a spirit, you get
+control over it. And if you go back and
+
+ align:start position:0%
+control over it. And if you go back and
+ 
+
+ align:start position:0%
+control over it. And if you go back and
+look at this slide,
+
+ align:start position:0%
+look at this slide,
+ 
+
+ align:start position:0%
+look at this slide,
+you see what's in there is we have this
+
+ align:start position:0%
+you see what's in there is we have this
+ 
+
+ align:start position:0%
+you see what's in there is we have this
+thing plus rat, but nowhere in this
+
+ align:start position:0%
+thing plus rat, but nowhere in this
+ 
+
+ align:start position:0%
+thing plus rat, but nowhere in this
+system, if I have a plus rat and a minus
+
+ align:start position:0%
+system, if I have a plus rat and a minus
+ 
+
+ align:start position:0%
+system, if I have a plus rat and a minus
+rat and a star rat and things that look
+
+ align:start position:0%
+rat and a star rat and things that look
+ 
+
+ align:start position:0%
+rat and a star rat and things that look
+like that, nowhere in this system do I
+
+ align:start position:0%
+like that, nowhere in this system do I
+ 
+
+ align:start position:0%
+like that, nowhere in this system do I
+have a thing that I can point at
+
+ align:start position:0%
+have a thing that I can point at
+ 
+
+ align:start position:0%
+have a thing that I can point at
+thing that I can point at which is a
+
+ align:start position:0%
+thing that I can point at which is a
+ 
+
+ align:start position:0%
+thing that I can point at which is a
+rational number.
+
+ align:start position:0%
+rational number.
+ 
+
+ align:start position:0%
+rational number.
+Right? I don't have in a system like
+
+ align:start position:0%
+Right? I don't have in a system like
+ 
+
+ align:start position:0%
+Right? I don't have in a system like
+that the no idea of rational number as a
+
+ align:start position:0%
+that the no idea of rational number as a
+ 
+
+ align:start position:0%
+that the no idea of rational number as a
+conceptual entity.
+
+ align:start position:0%
+conceptual entity.
+ 
+
+ align:start position:0%
+conceptual entity.
+Well, what's the advantage of that?
+
+ align:start position:0%
+Well, what's the advantage of that?
+ 
+
+ align:start position:0%
+Well, what's the advantage of that?
+What's the advantage of of isolating the
+
+ align:start position:0%
+What's the advantage of of isolating the
+ 
+
+ align:start position:0%
+What's the advantage of of isolating the
+idea of rational number as a conceptual
+
+ align:start position:0%
+idea of rational number as a conceptual
+ 
+
+ align:start position:0%
+idea of rational number as a conceptual
+entity and really naming it with mrat
+
+ align:start position:0%
+entity and really naming it with mrat
+ 
+
+ align:start position:0%
+entity and really naming it with mrat
+numerator and denominator?
+
+ align:start position:0%
+numerator and denominator?
+ 
+
+ align:start position:0%
+numerator and denominator?
+Well, one advantage is you might want to
+
+ align:start position:0%
+Well, one advantage is you might want to
+ 
+
+ align:start position:0%
+Well, one advantage is you might want to
+you might want to have alternative
+
+ align:start position:0%
+you might want to have alternative
+ 
+
+ align:start position:0%
+you might want to have alternative
+representations.
+
+ align:start position:0%
+representations.
+ 
+
+ align:start position:0%
+representations.
+See before I showed you that one way
+
+ align:start position:0%
+See before I showed you that one way
+ 
+
+ align:start position:0%
+See before I showed you that one way
+George could solve this this uh things
+
+ align:start position:0%
+George could solve this this uh things
+ 
+
+ align:start position:0%
+George could solve this this uh things
+not reduced to lowered terms problem is
+
+ align:start position:0%
+not reduced to lowered terms problem is
+ 
+
+ align:start position:0%
+not reduced to lowered terms problem is
+when you build a rational number you
+
+ align:start position:0%
+when you build a rational number you
+ 
+
+ align:start position:0%
+when you build a rational number you
+divide out by the greatest common
+
+ align:start position:0%
+divide out by the greatest common
+ 
+
+ align:start position:0%
+divide out by the greatest common
+denominator. Another way to do that
+
+ align:start position:0%
+denominator. Another way to do that
+ 
+
+ align:start position:0%
+denominator. Another way to do that
+is uh shown over here I can have an
+
+ align:start position:0%
+is uh shown over here I can have an
+ 
+
+ align:start position:0%
+is uh shown over here I can have an
+alternative representation for rational
+
+ align:start position:0%
+alternative representation for rational
+ 
+
+ align:start position:0%
+alternative representation for rational
+numbers where when you make a rational
+
+ align:start position:0%
+numbers where when you make a rational
+ 
+
+ align:start position:0%
+numbers where when you make a rational
+number you just const them.
+
+ align:start position:0%
+number you just const them.
+ 
+
+ align:start position:0%
+number you just const them.
+However, when you go to select out the
+
+ align:start position:0%
+However, when you go to select out the
+ 
+
+ align:start position:0%
+However, when you go to select out the
+numerator at that point, you compute the
+
+ align:start position:0%
+numerator at that point, you compute the
+ 
+
+ align:start position:0%
+numerator at that point, you compute the
+GCD of the stuff that's sitting in that
+
+ align:start position:0%
+GCD of the stuff that's sitting in that
+ 
+
+ align:start position:0%
+GCD of the stuff that's sitting in that
+pair and divide out by the GCD.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Right? And similarly, when I get the
+
+ align:start position:0%
+Right? And similarly, when I get the
+ 
+
+ align:start position:0%
+Right? And similarly, when I get the
+denominator
+
+ align:start position:0%
+denominator
+ 
+
+ align:start position:0%
+denominator
+at that point when I go to get the
+
+ align:start position:0%
+at that point when I go to get the
+ 
+
+ align:start position:0%
+at that point when I go to get the
+denominator, I'll divide out by the GCD.
+
+ align:start position:0%
+denominator, I'll divide out by the GCD.
+ 
+
+ align:start position:0%
+denominator, I'll divide out by the GCD.
+So, the difference would be in the old
+
+ align:start position:0%
+So, the difference would be in the old
+ 
+
+ align:start position:0%
+So, the difference would be in the old
+representation
+
+ align:start position:0%
+representation
+ 
+
+ align:start position:0%
+representation
+when ants was constructed here say with
+
+ align:start position:0%
+when ants was constructed here say with
+ 
+
+ align:start position:0%
+when ants was constructed here say with
+six and eight In the first way, the six
+
+ align:start position:0%
+six and eight In the first way, the six
+ 
+
+ align:start position:0%
+six and eight In the first way, the six
+and eight would have got reduced when
+
+ align:start position:0%
+and eight would have got reduced when
+ 
+
+ align:start position:0%
+and eight would have got reduced when
+they got stuck into that pair and
+
+ align:start position:0%
+they got stuck into that pair and
+ 
+
+ align:start position:0%
+they got stuck into that pair and
+numerator would select out three.
+
+ align:start position:0%
+numerator would select out three.
+ 
+
+ align:start position:0%
+numerator would select out three.
+And in the way I just showed you, well,
+
+ align:start position:0%
+And in the way I just showed you, well,
+ 
+
+ align:start position:0%
+And in the way I just showed you, well,
+ants would get six and eight put in. And
+
+ align:start position:0%
+ants would get six and eight put in. And
+ 
+
+ align:start position:0%
+ants would get six and eight put in. And
+then at the point where I said
+
+ align:start position:0%
+then at the point where I said
+ 
+
+ align:start position:0%
+then at the point where I said
+numerator, some computation would get
+
+ align:start position:0%
+numerator, some computation would get
+ 
+
+ align:start position:0%
+numerator, some computation would get
+done to put out three instead of six.
+
+ align:start position:0%
+done to put out three instead of six.
+ 
+
+ align:start position:0%
+done to put out three instead of six.
+So those are two different ways I might
+
+ align:start position:0%
+So those are two different ways I might
+ 
+
+ align:start position:0%
+So those are two different ways I might
+do it. Which one's better?
+
+ align:start position:0%
+do it. Which one's better?
+ 
+
+ align:start position:0%
+do it. Which one's better?
+Well, it depends, right? If I'm making a
+
+ align:start position:0%
+Well, it depends, right? If I'm making a
+ 
+
+ align:start position:0%
+Well, it depends, right? If I'm making a
+system where I am mostly constructing
+
+ align:start position:0%
+system where I am mostly constructing
+ 
+
+ align:start position:0%
+system where I am mostly constructing
+rational numbers and hardly ever looking
+
+ align:start position:0%
+rational numbers and hardly ever looking
+ 
+
+ align:start position:0%
+rational numbers and hardly ever looking
+at them, then it's probably better not
+
+ align:start position:0%
+at them, then it's probably better not
+ 
+
+ align:start position:0%
+at them, then it's probably better not
+to do that that GCD computation when I
+
+ align:start position:0%
+to do that that GCD computation when I
+ 
+
+ align:start position:0%
+to do that that GCD computation when I
+construct them. If I'm doing a system
+
+ align:start position:0%
+construct them. If I'm doing a system
+ 
+
+ align:start position:0%
+construct them. If I'm doing a system
+where I look at a look at things a lot
+
+ align:start position:0%
+where I look at a look at things a lot
+ 
+
+ align:start position:0%
+where I look at a look at things a lot
+more than I construct them, then it's
+
+ align:start position:0%
+more than I construct them, then it's
+ 
+
+ align:start position:0%
+more than I construct them, then it's
+probably better to to do the work when I
+
+ align:start position:0%
+probably better to to do the work when I
+ 
+
+ align:start position:0%
+probably better to to do the work when I
+construct them.
+
+ align:start position:0%
+construct them.
+ 
+
+ align:start position:0%
+construct them.
+So there's there's a choice there. But
+
+ align:start position:0%
+So there's there's a choice there. But
+ 
+
+ align:start position:0%
+So there's there's a choice there. But
+the real issue is that you might not be
+
+ align:start position:0%
+the real issue is that you might not be
+ 
+
+ align:start position:0%
+the real issue is that you might not be
+able to decide
+
+ align:start position:0%
+able to decide
+ 
+
+ align:start position:0%
+able to decide
+at the moment you're worrying about
+
+ align:start position:0%
+at the moment you're worrying about
+ 
+
+ align:start position:0%
+at the moment you're worrying about
+these rational numbers. See, in general,
+
+ align:start position:0%
+these rational numbers. See, in general,
+ 
+
+ align:start position:0%
+these rational numbers. See, in general,
+as systems designers,
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+you're forced with the necessity to make
+
+ align:start position:0%
+you're forced with the necessity to make
+ 
+
+ align:start position:0%
+you're forced with the necessity to make
+decisions about how you're going to do
+
+ align:start position:0%
+decisions about how you're going to do
+ 
+
+ align:start position:0%
+decisions about how you're going to do
+things. And in general, the way you'd
+
+ align:start position:0%
+things. And in general, the way you'd
+ 
+
+ align:start position:0%
+things. And in general, the way you'd
+like to retain flexibility is to never
+
+ align:start position:0%
+like to retain flexibility is to never
+ 
+
+ align:start position:0%
+like to retain flexibility is to never
+make up your mind about anything until
+
+ align:start position:0%
+make up your mind about anything until
+ 
+
+ align:start position:0%
+make up your mind about anything until
+you're forced to do it.
+
+ align:start position:0%
+you're forced to do it.
+ 
+
+ align:start position:0%
+you're forced to do it.
+And the problem is there's a a very,
+
+ align:start position:0%
+And the problem is there's a a very,
+ 
+
+ align:start position:0%
+And the problem is there's a a very,
+very narrow line between deferring
+
+ align:start position:0%
+very narrow line between deferring
+ 
+
+ align:start position:0%
+very narrow line between deferring
+decisions and outright procrastination.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+So you'd like to make progress.
+
+ align:start position:0%
+So you'd like to make progress.
+ 
+
+ align:start position:0%
+So you'd like to make progress.
+You'd like to make progress but also at
+
+ align:start position:0%
+You'd like to make progress but also at
+ 
+
+ align:start position:0%
+You'd like to make progress but also at
+the same time never be bound by the
+
+ align:start position:0%
+the same time never be bound by the
+ 
+
+ align:start position:0%
+the same time never be bound by the
+consequences of your decisions.
+
+ align:start position:0%
+consequences of your decisions.
+ 
+
+ align:start position:0%
+consequences of your decisions.
+Data abstraction is one way of doing
+
+ align:start position:0%
+Data abstraction is one way of doing
+ 
+
+ align:start position:0%
+Data abstraction is one way of doing
+this. What we did is we used wishful
+
+ align:start position:0%
+this. What we did is we used wishful
+ 
+
+ align:start position:0%
+this. What we did is we used wishful
+thinking.
+
+ align:start position:0%
+thinking.
+ 
+
+ align:start position:0%
+thinking.
+See we gave a name to the decision. We
+
+ align:start position:0%
+See we gave a name to the decision. We
+ 
+
+ align:start position:0%
+See we gave a name to the decision. We
+said make rat numerator and denominator
+
+ align:start position:0%
+said make rat numerator and denominator
+ 
+
+ align:start position:0%
+said make rat numerator and denominator
+will stand for however it's going to be
+
+ align:start position:0%
+will stand for however it's going to be
+ 
+
+ align:start position:0%
+will stand for however it's going to be
+done. And however it's going to be done
+
+ align:start position:0%
+done. And however it's going to be done
+ 
+
+ align:start position:0%
+done. And however it's going to be done
+it's George's problem. Really what that
+
+ align:start position:0%
+it's George's problem. Really what that
+ 
+
+ align:start position:0%
+it's George's problem. Really what that
+was doing is giving a name to the
+
+ align:start position:0%
+was doing is giving a name to the
+ 
+
+ align:start position:0%
+was doing is giving a name to the
+decision of how we're going to do it
+
+ align:start position:0%
+decision of how we're going to do it
+ 
+
+ align:start position:0%
+decision of how we're going to do it
+and then continuing as if we'd made the
+
+ align:start position:0%
+and then continuing as if we'd made the
+ 
+
+ align:start position:0%
+and then continuing as if we'd made the
+decision come and then eventually when
+
+ align:start position:0%
+decision come and then eventually when
+ 
+
+ align:start position:0%
+decision come and then eventually when
+we really wanted it to work coming back
+
+ align:start position:0%
+we really wanted it to work coming back
+ 
+
+ align:start position:0%
+we really wanted it to work coming back
+and facing what we really had to do
+
+ align:start position:0%
+and facing what we really had to do
+ 
+
+ align:start position:0%
+and facing what we really had to do
+and in fact we'll see a couple of times
+
+ align:start position:0%
+and in fact we'll see a couple of times
+ 
+
+ align:start position:0%
+and in fact we'll see a couple of times
+from now that you may never have to
+
+ align:start position:0%
+from now that you may never have to
+ 
+
+ align:start position:0%
+from now that you may never have to
+choose any particular representation
+
+ align:start position:0%
+choose any particular representation
+ 
+
+ align:start position:0%
+choose any particular representation
+ever ever.
+
+ align:start position:0%
+ever ever.
+ 
+
+ align:start position:0%
+ever ever.
+Anyway, that's a very powerful design
+
+ align:start position:0%
+Anyway, that's a very powerful design
+ 
+
+ align:start position:0%
+Anyway, that's a very powerful design
+technique. It's the key to the reason
+
+ align:start position:0%
+technique. It's the key to the reason
+ 
+
+ align:start position:0%
+technique. It's the key to the reason
+people use data abstraction.
+
+ align:start position:0%
+people use data abstraction.
+ 
+
+ align:start position:0%
+people use data abstraction.
+And we're going to see that idea again
+
+ align:start position:0%
+And we're going to see that idea again
+ 
+
+ align:start position:0%
+And we're going to see that idea again
+and again.
+
+ align:start position:0%
+and again.
+ 
+
+ align:start position:0%
+and again.
+Let's stop for questions.
+
+ align:start position:0%
+Let's stop for questions.
+ 
+
+ align:start position:0%
+Let's stop for questions.
+What does this um decision making
+
+ align:start position:0%
+What does this um decision making
+ 
+
+ align:start position:0%
+What does this um decision making
+through abstraction layers do to the
+
+ align:start position:0%
+through abstraction layers do to the
+ 
+
+ align:start position:0%
+through abstraction layers do to the
+maximum of do all your design before any
+
+ align:start position:0%
+maximum of do all your design before any
+ 
+
+ align:start position:0%
+maximum of do all your design before any
+of your code?
+
+ align:start position:0%
+of your code?
+ 
+
+ align:start position:0%
+of your code?
+Well, that's someone's axiom and I bet
+
+ align:start position:0%
+Well, that's someone's axiom and I bet
+ 
+
+ align:start position:0%
+Well, that's someone's axiom and I bet
+that's the axiom of someone who hasn't
+
+ align:start position:0%
+that's the axiom of someone who hasn't
+ 
+
+ align:start position:0%
+that's the axiom of someone who hasn't
+implemented very large computer systems
+
+ align:start position:0%
+implemented very large computer systems
+ 
+
+ align:start position:0%
+implemented very large computer systems
+very much.
+
+ align:start position:0%
+very much.
+ 
+
+ align:start position:0%
+very much.
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+said that computer science is a lot like
+
+ align:start position:0%
+said that computer science is a lot like
+ 
+
+ align:start position:0%
+said that computer science is a lot like
+magic and it's sort of good that it's
+
+ align:start position:0%
+magic and it's sort of good that it's
+ 
+
+ align:start position:0%
+magic and it's sort of good that it's
+like magic. There's a bad part of
+
+ align:start position:0%
+like magic. There's a bad part of
+ 
+
+ align:start position:0%
+like magic. There's a bad part of
+computer science that's a lot like
+
+ align:start position:0%
+computer science that's a lot like
+ 
+
+ align:start position:0%
+computer science that's a lot like
+religion and uh
+
+ align:start position:0%
+religion and uh
+ 
+
+ align:start position:0%
+religion and uh
+but uh in general I think people who
+
+ align:start position:0%
+but uh in general I think people who
+ 
+
+ align:start position:0%
+but uh in general I think people who
+really believe that you design
+
+ align:start position:0%
+really believe that you design
+ 
+
+ align:start position:0%
+really believe that you design
+everything before you implement it
+
+ align:start position:0%
+everything before you implement it
+ 
+
+ align:start position:0%
+everything before you implement it
+basically are people who haven't
+
+ align:start position:0%
+basically are people who haven't
+ 
+
+ align:start position:0%
+basically are people who haven't
+designed very many things.
+
+ align:start position:0%
+designed very many things.
+ 
+
+ align:start position:0%
+designed very many things.
+The real the real power is that you can
+
+ align:start position:0%
+The real the real power is that you can
+ 
+
+ align:start position:0%
+The real the real power is that you can
+pretend that you've made the decision
+
+ align:start position:0%
+pretend that you've made the decision
+ 
+
+ align:start position:0%
+pretend that you've made the decision
+and then later on figure out which one
+
+ align:start position:0%
+and then later on figure out which one
+ 
+
+ align:start position:0%
+and then later on figure out which one
+is right, which decision you ought to
+
+ align:start position:0%
+is right, which decision you ought to
+ 
+
+ align:start position:0%
+is right, which decision you ought to
+have made. And when you can do that, you
+
+ align:start position:0%
+have made. And when you can do that, you
+ 
+
+ align:start position:0%
+have made. And when you can do that, you
+have the best of both worlds.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Can you explain the difference between
+
+ align:start position:0%
+Can you explain the difference between
+ 
+
+ align:start position:0%
+Can you explain the difference between
+let and define?
+
+ align:start position:0%
+let and define?
+ 
+
+ align:start position:0%
+let and define?
+Oh, okay. Uh,
+
+ align:start position:0%
+Oh, okay. Uh,
+ 
+
+ align:start position:0%
+Oh, okay. Uh,
+let is
+
+ align:start position:0%
+let is
+ 
+
+ align:start position:0%
+let is
+let is a way to to establish local
+
+ align:start position:0%
+let is a way to to establish local
+ 
+
+ align:start position:0%
+let is a way to to establish local
+names.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay. So there let me give you sort of
+
+ align:start position:0%
+Okay. So there let me give you sort of
+ 
+
+ align:start position:0%
+Okay. So there let me give you sort of
+the half answer and I'll say maybe we
+
+ align:start position:0%
+the half answer and I'll say maybe we
+ 
+
+ align:start position:0%
+the half answer and I'll say maybe we
+later on we can talk about the whole
+
+ align:start position:0%
+later on we can talk about the whole
+ 
+
+ align:start position:0%
+later on we can talk about the whole
+very complicated thing but the big
+
+ align:start position:0%
+very complicated thing but the big
+ 
+
+ align:start position:0%
+very complicated thing but the big
+difference for now is that see when
+
+ align:start position:0%
+difference for now is that see when
+ 
+
+ align:start position:0%
+difference for now is that see when
+you're typing at lisp you're typing in
+
+ align:start position:0%
+you're typing at lisp you're typing in
+ 
+
+ align:start position:0%
+you're typing at lisp you're typing in
+this this environment where you're
+
+ align:start position:0%
+this this environment where you're
+ 
+
+ align:start position:0%
+this this environment where you're
+making definitions and when you say
+
+ align:start position:0%
+making definitions and when you say
+ 
+
+ align:start position:0%
+making definitions and when you say
+define a to be five
+
+ align:start position:0%
+define a to be five
+ 
+
+ align:start position:0%
+define a to be five
+if I say define
+
+ align:start position:0%
+if I say define
+ 
+
+ align:start position:0%
+if I say define
+a to be five
+
+ align:start position:0%
+a to be five
+ 
+
+ align:start position:0%
+a to be five
+then from then on the thing will
+
+ align:start position:0%
+then from then on the thing will
+ 
+
+ align:start position:0%
+then from then on the thing will
+remember that a is five.
+
+ align:start position:0%
+remember that a is five.
+ 
+
+ align:start position:0%
+remember that a is five.
+Okay, let is a way to set up a local
+
+ align:start position:0%
+Okay, let is a way to set up a local
+ 
+
+ align:start position:0%
+Okay, let is a way to set up a local
+context where there's a definition. So
+
+ align:start position:0%
+context where there's a definition. So
+ 
+
+ align:start position:0%
+context where there's a definition. So
+if I type something like saying let
+
+ align:start position:0%
+if I type something like saying let
+ 
+
+ align:start position:0%
+if I type something like saying let
+um let A no I shouldn't say A.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+If I said let let Z be tan
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and within that context tell me what the
+
+ align:start position:0%
+and within that context tell me what the
+ 
+
+ align:start position:0%
+and within that context tell me what the
+sum of Z and Z is. So if I typed in this
+
+ align:start position:0%
+sum of Z and Z is. So if I typed in this
+ 
+
+ align:start position:0%
+sum of Z and Z is. So if I typed in this
+expression to lisp
+
+ align:start position:0%
+expression to lisp
+ 
+
+ align:start position:0%
+expression to lisp
+and then this would put out 20. However,
+
+ align:start position:0%
+and then this would put out 20. However,
+ 
+
+ align:start position:0%
+and then this would put out 20. However,
+then if I said what's Z, the computer
+
+ align:start position:0%
+then if I said what's Z, the computer
+ 
+
+ align:start position:0%
+then if I said what's Z, the computer
+would say that's an unbound variable.
+
+ align:start position:0%
+would say that's an unbound variable.
+ 
+
+ align:start position:0%
+would say that's an unbound variable.
+So let is a way of setting up a context
+
+ align:start position:0%
+So let is a way of setting up a context
+ 
+
+ align:start position:0%
+So let is a way of setting up a context
+where you can make definitions,
+
+ align:start position:0%
+where you can make definitions,
+ 
+
+ align:start position:0%
+where you can make definitions,
+but those definitions are local to this
+
+ align:start position:0%
+but those definitions are local to this
+ 
+
+ align:start position:0%
+but those definitions are local to this
+context. And of course, if I'd said a in
+
+ align:start position:0%
+context. And of course, if I'd said a in
+ 
+
+ align:start position:0%
+context. And of course, if I'd said a in
+here,
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+I'd still get 20. But this A
+
+ align:start position:0%
+I'd still get 20. But this A
+ 
+
+ align:start position:0%
+I'd still get 20. But this A
+would not interfere at all with this
+
+ align:start position:0%
+would not interfere at all with this
+ 
+
+ align:start position:0%
+would not interfere at all with this
+one.
+
+ align:start position:0%
+one.
+ 
+
+ align:start position:0%
+one.
+So if I type this and then type this and
+
+ align:start position:0%
+So if I type this and then type this and
+ 
+
+ align:start position:0%
+So if I type this and then type this and
+then say what's a, a will still be five.
+
+ align:start position:0%
+then say what's a, a will still be five.
+ 
+
+ align:start position:0%
+then say what's a, a will still be five.
+So that's there's some other subtle
+
+ align:start position:0%
+So that's there's some other subtle
+ 
+
+ align:start position:0%
+So that's there's some other subtle
+differences between let and define, but
+
+ align:start position:0%
+differences between let and define, but
+ 
+
+ align:start position:0%
+differences between let and define, but
+that's the the most important one.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+[Music]
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+All right. Well, we've looked at
+
+ align:start position:0%
+All right. Well, we've looked at
+ 
+
+ align:start position:0%
+All right. Well, we've looked at
+implementing this this little system for
+
+ align:start position:0%
+implementing this this little system for
+ 
+
+ align:start position:0%
+implementing this this little system for
+doing arithmetic on rational numbers as
+
+ align:start position:0%
+doing arithmetic on rational numbers as
+ 
+
+ align:start position:0%
+doing arithmetic on rational numbers as
+an example of this methodology of data
+
+ align:start position:0%
+an example of this methodology of data
+ 
+
+ align:start position:0%
+an example of this methodology of data
+abstraction.
+
+ align:start position:0%
+abstraction.
+ 
+
+ align:start position:0%
+abstraction.
+And that's a way of controlling
+
+ align:start position:0%
+And that's a way of controlling
+ 
+
+ align:start position:0%
+And that's a way of controlling
+complexity in large systems.
+
+ align:start position:0%
+complexity in large systems.
+ 
+
+ align:start position:0%
+complexity in large systems.
+But see like procedure definition and
+
+ align:start position:0%
+But see like procedure definition and
+ 
+
+ align:start position:0%
+But see like procedure definition and
+like all the ways we're going to talk
+
+ align:start position:0%
+like all the ways we're going to talk
+ 
+
+ align:start position:0%
+like all the ways we're going to talk
+about for controlling complexity the
+
+ align:start position:0%
+about for controlling complexity the
+ 
+
+ align:start position:0%
+about for controlling complexity the
+real power of these things show up not
+
+ align:start position:0%
+real power of these things show up not
+ 
+
+ align:start position:0%
+real power of these things show up not
+when you sort of do these things in
+
+ align:start position:0%
+when you sort of do these things in
+ 
+
+ align:start position:0%
+when you sort of do these things in
+themselves like it's you know it's not
+
+ align:start position:0%
+themselves like it's you know it's not
+ 
+
+ align:start position:0%
+themselves like it's you know it's not
+such a great thing that we've done
+
+ align:start position:0%
+such a great thing that we've done
+ 
+
+ align:start position:0%
+such a great thing that we've done
+rational number arithmetic
+
+ align:start position:0%
+rational number arithmetic
+ 
+
+ align:start position:0%
+rational number arithmetic
+it's that you can use these as building
+
+ align:start position:0%
+it's that you can use these as building
+ 
+
+ align:start position:0%
+it's that you can use these as building
+blocks for making more complicated
+
+ align:start position:0%
+blocks for making more complicated
+ 
+
+ align:start position:0%
+blocks for making more complicated
+things.
+
+ align:start position:0%
+things.
+ 
+
+ align:start position:0%
+things.
+Right? So it's no wonderful idea that
+
+ align:start position:0%
+Right? So it's no wonderful idea that
+ 
+
+ align:start position:0%
+Right? So it's no wonderful idea that
+you can just put two numbers together to
+
+ align:start position:0%
+you can just put two numbers together to
+ 
+
+ align:start position:0%
+you can just put two numbers together to
+form a pair if that's all you ever
+
+ align:start position:0%
+form a pair if that's all you ever
+ 
+
+ align:start position:0%
+form a pair if that's all you ever
+wanted to do. There are tons of ways
+
+ align:start position:0%
+wanted to do. There are tons of ways
+ 
+
+ align:start position:0%
+wanted to do. There are tons of ways
+that you can do that. The real issue is
+
+ align:start position:0%
+that you can do that. The real issue is
+ 
+
+ align:start position:0%
+that you can do that. The real issue is
+can you do that in such a way so that
+
+ align:start position:0%
+can you do that in such a way so that
+ 
+
+ align:start position:0%
+can you do that in such a way so that
+the things that you build become
+
+ align:start position:0%
+the things that you build become
+ 
+
+ align:start position:0%
+the things that you build become
+building blocks for doing something even
+
+ align:start position:0%
+building blocks for doing something even
+ 
+
+ align:start position:0%
+building blocks for doing something even
+even more complex. So whenever someone
+
+ align:start position:0%
+even more complex. So whenever someone
+ 
+
+ align:start position:0%
+even more complex. So whenever someone
+shows you a method for controlling
+
+ align:start position:0%
+shows you a method for controlling
+ 
+
+ align:start position:0%
+shows you a method for controlling
+complexity, you should say, "Yeah,
+
+ align:start position:0%
+complexity, you should say, "Yeah,
+ 
+
+ align:start position:0%
+complexity, you should say, "Yeah,
+that's great, but what can I build with
+
+ align:start position:0%
+that's great, but what can I build with
+ 
+
+ align:start position:0%
+that's great, but what can I build with
+it?"
+
+ align:start position:0%
+it?"
+ 
+
+ align:start position:0%
+it?"
+Okay, so for example,
+
+ align:start position:0%
+Okay, so for example,
+ 
+
+ align:start position:0%
+Okay, so for example,
+let's do a let me just run through
+
+ align:start position:0%
+let's do a let me just run through
+ 
+
+ align:start position:0%
+let's do a let me just run through
+another thing that's a lot like the
+
+ align:start position:0%
+another thing that's a lot like the
+ 
+
+ align:start position:0%
+another thing that's a lot like the
+rational number one. Suppose we would
+
+ align:start position:0%
+rational number one. Suppose we would
+ 
+
+ align:start position:0%
+rational number one. Suppose we would
+like to represent uh you know points in
+
+ align:start position:0%
+like to represent uh you know points in
+ 
+
+ align:start position:0%
+like to represent uh you know points in
+the plane. you sort of say, well,
+
+ align:start position:0%
+the plane. you sort of say, well,
+ 
+
+ align:start position:0%
+the plane. you sort of say, well,
+there's a point and we're going to call
+
+ align:start position:0%
+there's a point and we're going to call
+ 
+
+ align:start position:0%
+there's a point and we're going to call
+that point P
+
+ align:start position:0%
+that point P
+ 
+
+ align:start position:0%
+that point P
+and uh
+
+ align:start position:0%
+and uh
+ 
+
+ align:start position:0%
+and uh
+that that point might have coordinates
+
+ align:start position:0%
+that that point might have coordinates
+ 
+
+ align:start position:0%
+that that point might have coordinates
+like uh this might be the point one
+
+ align:start position:0%
+like uh this might be the point one
+ 
+
+ align:start position:0%
+like uh this might be the point one
+comma 2. Its x coordinate might be one
+
+ align:start position:0%
+comma 2. Its x coordinate might be one
+ 
+
+ align:start position:0%
+comma 2. Its x coordinate might be one
+and its ycoordinate might be two. And
+
+ align:start position:0%
+and its ycoordinate might be two. And
+ 
+
+ align:start position:0%
+and its ycoordinate might be two. And
+then we'll make a little system for for
+
+ align:start position:0%
+then we'll make a little system for for
+ 
+
+ align:start position:0%
+then we'll make a little system for for
+manipulating points in the plane.
+
+ align:start position:0%
+manipulating points in the plane.
+ 
+
+ align:start position:0%
+manipulating points in the plane.
+And again, we can do that. Here's a
+
+ align:start position:0%
+And again, we can do that. Here's a
+ 
+
+ align:start position:0%
+And again, we can do that. Here's a
+here's a little example of that.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+can represent vectors that's the same as
+
+ align:start position:0%
+can represent vectors that's the same as
+ 
+
+ align:start position:0%
+can represent vectors that's the same as
+points in the plane. And we'll say, yep,
+
+ align:start position:0%
+points in the plane. And we'll say, yep,
+ 
+
+ align:start position:0%
+points in the plane. And we'll say, yep,
+there's a
+
+ align:start position:0%
+there's a
+ 
+
+ align:start position:0%
+there's a
+there's a constructor
+
+ align:start position:0%
+there's a constructor
+ 
+
+ align:start position:0%
+there's a constructor
+called make vector. Make vector is going
+
+ align:start position:0%
+called make vector. Make vector is going
+ 
+
+ align:start position:0%
+called make vector. Make vector is going
+to take two coordinates.
+
+ align:start position:0%
+to take two coordinates.
+ 
+
+ align:start position:0%
+to take two coordinates.
+And here we can implement them if we
+
+ align:start position:0%
+And here we can implement them if we
+ 
+
+ align:start position:0%
+And here we can implement them if we
+like as pairs. But the important thing
+
+ align:start position:0%
+like as pairs. But the important thing
+ 
+
+ align:start position:0%
+like as pairs. But the important thing
+is that there's a constructor.
+
+ align:start position:0%
+is that there's a constructor.
+ 
+
+ align:start position:0%
+is that there's a constructor.
+And then given some vector p, we can
+
+ align:start position:0%
+And then given some vector p, we can
+ 
+
+ align:start position:0%
+And then given some vector p, we can
+find its x coordinate
+
+ align:start position:0%
+find its x coordinate
+ 
+
+ align:start position:0%
+find its x coordinate
+or we can get its ycoordinate. So
+
+ align:start position:0%
+or we can get its ycoordinate. So
+ 
+
+ align:start position:0%
+or we can get its ycoordinate. So
+there's a constructor and selectors for
+
+ align:start position:0%
+there's a constructor and selectors for
+ 
+
+ align:start position:0%
+there's a constructor and selectors for
+points on the plane.
+
+ align:start position:0%
+points on the plane.
+ 
+
+ align:start position:0%
+points on the plane.
+Well, given points in the plane, we
+
+ align:start position:0%
+Well, given points in the plane, we
+ 
+
+ align:start position:0%
+Well, given points in the plane, we
+might want to use them to build
+
+ align:start position:0%
+might want to use them to build
+ 
+
+ align:start position:0%
+might want to use them to build
+something. So for instance, we might
+
+ align:start position:0%
+something. So for instance, we might
+ 
+
+ align:start position:0%
+something. So for instance, we might
+want to talk about we might have a point
+
+ align:start position:0%
+want to talk about we might have a point
+ 
+
+ align:start position:0%
+want to talk about we might have a point
+P and a point Q. So P might be the point
+
+ align:start position:0%
+P and a point Q. So P might be the point
+ 
+
+ align:start position:0%
+P and a point Q. So P might be the point
+one, two, and Q might be the point 23.
+
+ align:start position:0%
+one, two, and Q might be the point 23.
+ 
+
+ align:start position:0%
+one, two, and Q might be the point 23.
+And we might want to talk about the line
+
+ align:start position:0%
+And we might want to talk about the line
+ 
+
+ align:start position:0%
+And we might want to talk about the line
+segment that starts at P and ends at Q,
+
+ align:start position:0%
+segment that starts at P and ends at Q,
+ 
+
+ align:start position:0%
+segment that starts at P and ends at Q,
+right? Right? And that might be the
+
+ align:start position:0%
+right? Right? And that might be the
+ 
+
+ align:start position:0%
+right? Right? And that might be the
+segment S.
+
+ align:start position:0%
+segment S.
+ 
+
+ align:start position:0%
+segment S.
+So we might want to build points in
+
+ align:start position:0%
+So we might want to build points in
+ 
+
+ align:start position:0%
+So we might want to build points in
+terms of numbers and segments in terms
+
+ align:start position:0%
+terms of numbers and segments in terms
+ 
+
+ align:start position:0%
+terms of numbers and segments in terms
+we might want to build points or vectors
+
+ align:start position:0%
+we might want to build points or vectors
+ 
+
+ align:start position:0%
+we might want to build points or vectors
+in terms of numbers and segments in
+
+ align:start position:0%
+in terms of numbers and segments in
+ 
+
+ align:start position:0%
+in terms of numbers and segments in
+terms of vectors.
+
+ align:start position:0%
+terms of vectors.
+ 
+
+ align:start position:0%
+terms of vectors.
+So we can represent line segments in
+
+ align:start position:0%
+So we can represent line segments in
+ 
+
+ align:start position:0%
+So we can represent line segments in
+exactly the same way. Right? So the line
+
+ align:start position:0%
+exactly the same way. Right? So the line
+ 
+
+ align:start position:0%
+exactly the same way. Right? So the line
+segment from P to Q. We'll say there's a
+
+ align:start position:0%
+segment from P to Q. We'll say there's a
+ 
+
+ align:start position:0%
+segment from P to Q. We'll say there's a
+constructor make segment
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and there's make up names for the
+
+ align:start position:0%
+and there's make up names for the
+ 
+
+ align:start position:0%
+and there's make up names for the
+selectors. starting point of the segment
+
+ align:start position:0%
+selectors. starting point of the segment
+ 
+
+ align:start position:0%
+selectors. starting point of the segment
+and the ending point of the segment. And
+
+ align:start position:0%
+and the ending point of the segment. And
+ 
+
+ align:start position:0%
+and the ending point of the segment. And
+again, we can implement a segment using
+
+ align:start position:0%
+again, we can implement a segment using
+ 
+
+ align:start position:0%
+again, we can implement a segment using
+con as a pair of points
+
+ align:start position:0%
+con as a pair of points
+ 
+
+ align:start position:0%
+con as a pair of points
+and car and cooter get out the two
+
+ align:start position:0%
+and car and cooter get out the two
+ 
+
+ align:start position:0%
+and car and cooter get out the two
+points that we put together to get the
+
+ align:start position:0%
+points that we put together to get the
+ 
+
+ align:start position:0%
+points that we put together to get the
+segment.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Well, now having done that,
+
+ align:start position:0%
+Well, now having done that,
+ 
+
+ align:start position:0%
+Well, now having done that,
+we can have some operations on them,
+
+ align:start position:0%
+we can have some operations on them,
+ 
+
+ align:start position:0%
+we can have some operations on them,
+right? Like we could say what's the
+
+ align:start position:0%
+right? Like we could say what's the
+ 
+
+ align:start position:0%
+right? Like we could say what's the
+what's the midpoint of a line segment?
+
+ align:start position:0%
+what's the midpoint of a line segment?
+ 
+
+ align:start position:0%
+what's the midpoint of a line segment?
+So here's the midpoint of a line
+
+ align:start position:0%
+So here's the midpoint of a line
+ 
+
+ align:start position:0%
+So here's the midpoint of a line
+segment. That's going to be the point
+
+ align:start position:0%
+segment. That's going to be the point
+ 
+
+ align:start position:0%
+segment. That's going to be the point
+that well the points whose coordinates
+
+ align:start position:0%
+that well the points whose coordinates
+ 
+
+ align:start position:0%
+that well the points whose coordinates
+are the averages of the coordinates of
+
+ align:start position:0%
+are the averages of the coordinates of
+ 
+
+ align:start position:0%
+are the averages of the coordinates of
+the end points. There's the midpoint.
+
+ align:start position:0%
+the end points. There's the midpoint.
+ 
+
+ align:start position:0%
+the end points. There's the midpoint.
+So to get the midpoint of a line segment
+
+ align:start position:0%
+So to get the midpoint of a line segment
+ 
+
+ align:start position:0%
+So to get the midpoint of a line segment
+S,
+
+ align:start position:0%
+S,
+ 
+
+ align:start position:0%
+S,
+we'll just say grab the starting point
+
+ align:start position:0%
+we'll just say grab the starting point
+ 
+
+ align:start position:0%
+we'll just say grab the starting point
+of the segment, grab the ending point of
+
+ align:start position:0%
+of the segment, grab the ending point of
+ 
+
+ align:start position:0%
+of the segment, grab the ending point of
+the segment,
+
+ align:start position:0%
+the segment,
+ 
+
+ align:start position:0%
+the segment,
+and now make a vector, right? make a
+
+ align:start position:0%
+and now make a vector, right? make a
+ 
+
+ align:start position:0%
+and now make a vector, right? make a
+point whose coordinates are the average
+
+ align:start position:0%
+point whose coordinates are the average
+ 
+
+ align:start position:0%
+point whose coordinates are the average
+of the x coordinate of the first point
+
+ align:start position:0%
+of the x coordinate of the first point
+ 
+
+ align:start position:0%
+of the x coordinate of the first point
+and the x coordinate of the second point
+
+ align:start position:0%
+and the x coordinate of the second point
+ 
+
+ align:start position:0%
+and the x coordinate of the second point
+and whose y-coordinate is the average of
+
+ align:start position:0%
+and whose y-coordinate is the average of
+ 
+
+ align:start position:0%
+and whose y-coordinate is the average of
+the y-coordinates.
+
+ align:start position:0%
+the y-coordinates.
+ 
+
+ align:start position:0%
+the y-coordinates.
+So there's an implementation of midpoint
+
+ align:start position:0%
+So there's an implementation of midpoint
+ 
+
+ align:start position:0%
+So there's an implementation of midpoint
+and then and then similarly
+
+ align:start position:0%
+and then and then similarly
+ 
+
+ align:start position:0%
+and then and then similarly
+we can build something like the length
+
+ align:start position:0%
+we can build something like the length
+ 
+
+ align:start position:0%
+we can build something like the length
+of a segment right the length of a
+
+ align:start position:0%
+of a segment right the length of a
+ 
+
+ align:start position:0%
+of a segment right the length of a
+segment is a thing whose
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+right we use use Pythagoras's rule the
+
+ align:start position:0%
+right we use use Pythagoras's rule the
+ 
+
+ align:start position:0%
+right we use use Pythagoras's rule the
+length of the segment is a square root
+
+ align:start position:0%
+length of the segment is a square root
+ 
+
+ align:start position:0%
+length of the segment is a square root
+of dx^2 plus dy^2 we'll say to get the
+
+ align:start position:0%
+of dx^2 plus dy^2 we'll say to get the
+ 
+
+ align:start position:0%
+of dx^2 plus dy^2 we'll say to get the
+length of a line segment well we'll let
+
+ align:start position:0%
+length of a line segment well we'll let
+ 
+
+ align:start position:0%
+length of a line segment well we'll let
+dx be the difference of the xcoordinate
+
+ align:start position:0%
+dx be the difference of the xcoordinate
+ 
+
+ align:start position:0%
+dx be the difference of the xcoordinate
+of one endpoint
+
+ align:start position:0%
+of one endpoint
+ 
+
+ align:start position:0%
+of one endpoint
+and the x coordinate of the other end
+
+ align:start position:0%
+and the x coordinate of the other end
+ 
+
+ align:start position:0%
+and the x coordinate of the other end
+point and we'll let dy be the difference
+
+ align:start position:0%
+point and we'll let dy be the difference
+ 
+
+ align:start position:0%
+point and we'll let dy be the difference
+of the ycoordinates
+
+ align:start position:0%
+of the ycoordinates
+ 
+
+ align:start position:0%
+of the ycoordinates
+and then we'll take the square root of
+
+ align:start position:0%
+and then we'll take the square root of
+ 
+
+ align:start position:0%
+and then we'll take the square root of
+the sum of the squares of dx and dy.
+
+ align:start position:0%
+the sum of the squares of dx and dy.
+ 
+
+ align:start position:0%
+the sum of the squares of dx and dy.
+That's what this says, right? So there's
+
+ align:start position:0%
+That's what this says, right? So there's
+ 
+
+ align:start position:0%
+That's what this says, right? So there's
+an implementation of length
+
+ align:start position:0%
+an implementation of length
+ 
+
+ align:start position:0%
+an implementation of length
+and again
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+what we built is a layered system
+
+ align:start position:0%
+what we built is a layered system
+ 
+
+ align:start position:0%
+what we built is a layered system
+right we built a system which has well
+
+ align:start position:0%
+right we built a system which has well
+ 
+
+ align:start position:0%
+right we built a system which has well
+say up here there are segments
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and then there's an abstraction barrier
+
+ align:start position:0%
+and then there's an abstraction barrier
+ 
+
+ align:start position:0%
+and then there's an abstraction barrier
+right the abstraction barrier barrier
+
+ align:start position:0%
+right the abstraction barrier barrier
+ 
+
+ align:start position:0%
+right the abstraction barrier barrier
+separates
+
+ align:start position:0%
+separates
+ 
+
+ align:start position:0%
+separates
+the implementation
+
+ align:start position:0%
+the implementation
+ 
+
+ align:start position:0%
+the implementation
+of segments from the implementation of
+
+ align:start position:0%
+of segments from the implementation of
+ 
+
+ align:start position:0%
+of segments from the implementation of
+vectors and points. And what that
+
+ align:start position:0%
+vectors and points. And what that
+ 
+
+ align:start position:0%
+vectors and points. And what that
+abstraction barrier is
+
+ align:start position:0%
+abstraction barrier is
+ 
+
+ align:start position:0%
+abstraction barrier is
+are the constructors and selectors. It's
+
+ align:start position:0%
+are the constructors and selectors. It's
+ 
+
+ align:start position:0%
+are the constructors and selectors. It's
+make segment
+
+ align:start position:0%
+make segment
+ 
+
+ align:start position:0%
+make segment
+and segment start
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and segment end,
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+right? And then there are vectors. And
+
+ align:start position:0%
+right? And then there are vectors. And
+ 
+
+ align:start position:0%
+right? And then there are vectors. And
+then vectors in turn are built on top of
+
+ align:start position:0%
+then vectors in turn are built on top of
+ 
+
+ align:start position:0%
+then vectors in turn are built on top of
+pairs and numbers. So let's say pairs
+
+ align:start position:0%
+pairs and numbers. So let's say pairs
+ 
+
+ align:start position:0%
+pairs and numbers. So let's say pairs
+and numbers. And that has its own
+
+ align:start position:0%
+and numbers. And that has its own
+ 
+
+ align:start position:0%
+and numbers. And that has its own
+abstraction barrier, right? Which is
+
+ align:start position:0%
+abstraction barrier, right? Which is
+ 
+
+ align:start position:0%
+abstraction barrier, right? Which is
+make vector
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and x coordinate
+
+ align:start position:0%
+and x coordinate
+ 
+
+ align:start position:0%
+and x coordinate
+and ycoordinate.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Right? So we have again a layered
+
+ align:start position:0%
+Right? So we have again a layered
+ 
+
+ align:start position:0%
+Right? So we have again a layered
+system. You're starting to see that
+
+ align:start position:0%
+system. You're starting to see that
+ 
+
+ align:start position:0%
+system. You're starting to see that
+there are layers here. I ought to
+
+ align:start position:0%
+there are layers here. I ought to
+ 
+
+ align:start position:0%
+there are layers here. I ought to
+mention there's a very important thing
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that I kind of took for granted
+
+ align:start position:0%
+that I kind of took for granted
+ 
+
+ align:start position:0%
+that I kind of took for granted
+and it's
+
+ align:start position:0%
+and it's
+ 
+
+ align:start position:0%
+and it's
+it's sort of so natural. On the other
+
+ align:start position:0%
+it's sort of so natural. On the other
+ 
+
+ align:start position:0%
+it's sort of so natural. On the other
+hand, it's it's one it's a very
+
+ align:start position:0%
+hand, it's it's one it's a very
+ 
+
+ align:start position:0%
+hand, it's it's one it's a very
+important thing. Notice that in order to
+
+ align:start position:0%
+important thing. Notice that in order to
+ 
+
+ align:start position:0%
+important thing. Notice that in order to
+represent the segment S,
+
+ align:start position:0%
+represent the segment S,
+ 
+
+ align:start position:0%
+represent the segment S,
+I said this segment is a pair of points
+
+ align:start position:0%
+I said this segment is a pair of points
+ 
+
+ align:start position:0%
+I said this segment is a pair of points
+and a point is a pair of numbers. And if
+
+ align:start position:0%
+and a point is a pair of numbers. And if
+ 
+
+ align:start position:0%
+and a point is a pair of numbers. And if
+I were going to draw the box and
+
+ align:start position:0%
+I were going to draw the box and
+ 
+
+ align:start position:0%
+I were going to draw the box and
+pointers structure for that, I would
+
+ align:start position:0%
+pointers structure for that, I would
+ 
+
+ align:start position:0%
+pointers structure for that, I would
+say, oh, the segment is given those
+
+ align:start position:0%
+say, oh, the segment is given those
+ 
+
+ align:start position:0%
+say, oh, the segment is given those
+particular representations that I showed
+
+ align:start position:0%
+particular representations that I showed
+ 
+
+ align:start position:0%
+particular representations that I showed
+you, I'd say this segment S is a pair.
+
+ align:start position:0%
+you, I'd say this segment S is a pair.
+ 
+
+ align:start position:0%
+you, I'd say this segment S is a pair.
+And the first thing in the pair is
+
+ align:start position:0%
+And the first thing in the pair is
+ 
+
+ align:start position:0%
+And the first thing in the pair is
+a vector.
+
+ align:start position:0%
+a vector.
+ 
+
+ align:start position:0%
+a vector.
+And the vector is
+
+ align:start position:0%
+And the vector is
+ 
+
+ align:start position:0%
+And the vector is
+a pair of numbers.
+
+ align:start position:0%
+a pair of numbers.
+ 
+
+ align:start position:0%
+a pair of numbers.
+That's this. That's P.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+And the other thing in the segment is Q
+
+ align:start position:0%
+And the other thing in the segment is Q
+ 
+
+ align:start position:0%
+And the other thing in the segment is Q
+which is itself a pair
+
+ align:start position:0%
+which is itself a pair
+ 
+
+ align:start position:0%
+which is itself a pair
+of numbers.
+
+ align:start position:0%
+of numbers.
+ 
+
+ align:start position:0%
+of numbers.
+So I almost took it for granted when I
+
+ align:start position:0%
+So I almost took it for granted when I
+ 
+
+ align:start position:0%
+So I almost took it for granted when I
+said that Kant allows you to put things
+
+ align:start position:0%
+said that Kant allows you to put things
+ 
+
+ align:start position:0%
+said that Kant allows you to put things
+together.
+
+ align:start position:0%
+together.
+ 
+
+ align:start position:0%
+together.
+But it's very easy to not appreciate
+
+ align:start position:0%
+But it's very easy to not appreciate
+ 
+
+ align:start position:0%
+But it's very easy to not appreciate
+that because notice I can put some of
+
+ align:start position:0%
+that because notice I can put some of
+ 
+
+ align:start position:0%
+that because notice I can put some of
+the things I can put together can
+
+ align:start position:0%
+the things I can put together can
+ 
+
+ align:start position:0%
+the things I can put together can
+themselves be pairs.
+
+ align:start position:0%
+themselves be pairs.
+ 
+
+ align:start position:0%
+themselves be pairs.
+And let me introduce a word that I'll
+
+ align:start position:0%
+And let me introduce a word that I'll
+ 
+
+ align:start position:0%
+And let me introduce a word that I'll
+talk about more next time. It's one of
+
+ align:start position:0%
+talk about more next time. It's one of
+ 
+
+ align:start position:0%
+talk about more next time. It's one of
+my my favorite words called closure.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+And by closure I mean that the means of
+
+ align:start position:0%
+And by closure I mean that the means of
+ 
+
+ align:start position:0%
+And by closure I mean that the means of
+combination in your system are such that
+
+ align:start position:0%
+combination in your system are such that
+ 
+
+ align:start position:0%
+combination in your system are such that
+when you put things together using them
+
+ align:start position:0%
+when you put things together using them
+ 
+
+ align:start position:0%
+when you put things together using them
+like you make a pair
+
+ align:start position:0%
+like you make a pair
+ 
+
+ align:start position:0%
+like you make a pair
+you can then put those together with the
+
+ align:start position:0%
+you can then put those together with the
+ 
+
+ align:start position:0%
+you can then put those together with the
+same means of combination. So I can have
+
+ align:start position:0%
+same means of combination. So I can have
+ 
+
+ align:start position:0%
+same means of combination. So I can have
+not only a pair of numbers but I can
+
+ align:start position:0%
+not only a pair of numbers but I can
+ 
+
+ align:start position:0%
+not only a pair of numbers but I can
+have a pair of pairs.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+So for instance uh
+
+ align:start position:0%
+So for instance uh
+ 
+
+ align:start position:0%
+So for instance uh
+making arrays in a language like forran
+
+ align:start position:0%
+making arrays in a language like forran
+ 
+
+ align:start position:0%
+making arrays in a language like forran
+is not a closed means of combination
+
+ align:start position:0%
+is not a closed means of combination
+ 
+
+ align:start position:0%
+is not a closed means of combination
+because I can make an array of numbers
+
+ align:start position:0%
+because I can make an array of numbers
+ 
+
+ align:start position:0%
+because I can make an array of numbers
+but I can't make an array of arrays
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and one of the things that you should
+
+ align:start position:0%
+and one of the things that you should
+ 
+
+ align:start position:0%
+and one of the things that you should
+ask one of your one of your tests of
+
+ align:start position:0%
+ask one of your one of your tests of
+ 
+
+ align:start position:0%
+ask one of your one of your tests of
+quality for a means of combination that
+
+ align:start position:0%
+quality for a means of combination that
+ 
+
+ align:start position:0%
+quality for a means of combination that
+someone shows you is gee are the things
+
+ align:start position:0%
+someone shows you is gee are the things
+ 
+
+ align:start position:0%
+someone shows you is gee are the things
+you make closed under that means of
+
+ align:start position:0%
+you make closed under that means of
+ 
+
+ align:start position:0%
+you make closed under that means of
+combination so it's not so Paris would
+
+ align:start position:0%
+combination so it's not so Paris would
+ 
+
+ align:start position:0%
+combination so it's not so Paris would
+not be nearly so interesting if all I
+
+ align:start position:0%
+not be nearly so interesting if all I
+ 
+
+ align:start position:0%
+not be nearly so interesting if all I
+could do was make a pair of numbers. I
+
+ align:start position:0%
+could do was make a pair of numbers. I
+ 
+
+ align:start position:0%
+could do was make a pair of numbers. I
+couldn't build very much structure at
+
+ align:start position:0%
+couldn't build very much structure at
+ 
+
+ align:start position:0%
+couldn't build very much structure at
+all.
+
+ align:start position:0%
+all.
+ 
+
+ align:start position:0%
+all.
+Okay. Well, we'll come back to that. I
+
+ align:start position:0%
+Okay. Well, we'll come back to that. I
+ 
+
+ align:start position:0%
+Okay. Well, we'll come back to that. I
+just wanted to mention it now. You'll
+
+ align:start position:0%
+just wanted to mention it now. You'll
+ 
+
+ align:start position:0%
+just wanted to mention it now. You'll
+hear a lot about closure later on. You
+
+ align:start position:0%
+hear a lot about closure later on. You
+ 
+
+ align:start position:0%
+hear a lot about closure later on. You
+can also see
+
+ align:start position:0%
+can also see
+ 
+
+ align:start position:0%
+can also see
+the potential for losing control of
+
+ align:start position:0%
+the potential for losing control of
+ 
+
+ align:start position:0%
+the potential for losing control of
+complexity as soon as you have a layered
+
+ align:start position:0%
+complexity as soon as you have a layered
+ 
+
+ align:start position:0%
+complexity as soon as you have a layered
+system if you don't use data
+
+ align:start position:0%
+system if you don't use data
+ 
+
+ align:start position:0%
+system if you don't use data
+abstraction.
+
+ align:start position:0%
+abstraction.
+ 
+
+ align:start position:0%
+abstraction.
+See, let's go back and let's go back and
+
+ align:start position:0%
+See, let's go back and let's go back and
+ 
+
+ align:start position:0%
+See, let's go back and let's go back and
+look at this slide for length. See,
+
+ align:start position:0%
+look at this slide for length. See,
+ 
+
+ align:start position:0%
+look at this slide for length. See,
+length length works and is a simple
+
+ align:start position:0%
+length length works and is a simple
+ 
+
+ align:start position:0%
+length length works and is a simple
+thing.
+
+ align:start position:0%
+thing.
+ 
+
+ align:start position:0%
+thing.
+Because I can say when I want to get
+
+ align:start position:0%
+Because I can say when I want to get
+ 
+
+ align:start position:0%
+Because I can say when I want to get
+this value I can say oh that is the
+
+ align:start position:0%
+this value I can say oh that is the
+ 
+
+ align:start position:0%
+this value I can say oh that is the
+x-coordinate
+
+ align:start position:0%
+x-coordinate
+ 
+
+ align:start position:0%
+x-coordinate
+of the first endpoint of the segment
+
+ align:start position:0%
+of the first endpoint of the segment
+ 
+
+ align:start position:0%
+of the first endpoint of the segment
+and each of these things each of these
+
+ align:start position:0%
+and each of these things each of these
+ 
+
+ align:start position:0%
+and each of these things each of these
+selectors x-coordinate and endpoint
+
+ align:start position:0%
+selectors x-coordinate and endpoint
+ 
+
+ align:start position:0%
+selectors x-coordinate and endpoint
+stand for a decision choice whose
+
+ align:start position:0%
+stand for a decision choice whose
+ 
+
+ align:start position:0%
+stand for a decision choice whose
+details I don't have to look at. See, I
+
+ align:start position:0%
+details I don't have to look at. See, I
+ 
+
+ align:start position:0%
+details I don't have to look at. See, I
+could perfectly well, again, just like
+
+ align:start position:0%
+could perfectly well, again, just like
+ 
+
+ align:start position:0%
+could perfectly well, again, just like
+rational numbers I do before, I could
+
+ align:start position:0%
+rational numbers I do before, I could
+ 
+
+ align:start position:0%
+rational numbers I do before, I could
+say, "Oh, well, gee, a segment really is
+
+ align:start position:0%
+say, "Oh, well, gee, a segment really is
+ 
+
+ align:start position:0%
+say, "Oh, well, gee, a segment really is
+a pair of pairs." And the uh the
+
+ align:start position:0%
+a pair of pairs." And the uh the
+ 
+
+ align:start position:0%
+a pair of pairs." And the uh the
+xcoordinate of the first end point of
+
+ align:start position:0%
+xcoordinate of the first end point of
+ 
+
+ align:start position:0%
+xcoordinate of the first end point of
+the segment really is the well, what is
+
+ align:start position:0%
+the segment really is the well, what is
+ 
+
+ align:start position:0%
+the segment really is the well, what is
+it? It's the car
+
+ align:start position:0%
+it? It's the car
+ 
+
+ align:start position:0%
+it? It's the car
+of the car of the segment. So, I could
+
+ align:start position:0%
+of the car of the segment. So, I could
+ 
+
+ align:start position:0%
+of the car of the segment. So, I could
+perfectly well go and redefine length. I
+
+ align:start position:0%
+perfectly well go and redefine length. I
+ 
+
+ align:start position:0%
+perfectly well go and redefine length. I
+could say define
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the length
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+of some segment s
+
+ align:start position:0%
+of some segment s
+ 
+
+ align:start position:0%
+of some segment s
+and I could start off writing something
+
+ align:start position:0%
+and I could start off writing something
+ 
+
+ align:start position:0%
+and I could start off writing something
+like well we well let
+
+ align:start position:0%
+like well we well let
+ 
+
+ align:start position:0%
+like well we well let
+dx
+
+ align:start position:0%
+dx
+ 
+
+ align:start position:0%
+dx
+be well what's got be it's got to be the
+
+ align:start position:0%
+be well what's got be it's got to be the
+ 
+
+ align:start position:0%
+be well what's got be it's got to be the
+difference of the two coordinates so
+
+ align:start position:0%
+difference of the two coordinates so
+ 
+
+ align:start position:0%
+difference of the two coordinates so
+that's the difference of the first one
+
+ align:start position:0%
+that's the difference of the first one
+ 
+
+ align:start position:0%
+that's the difference of the first one
+is the car
+
+ align:start position:0%
+is the car
+ 
+
+ align:start position:0%
+is the car
+of
+
+ align:start position:0%
+of
+ 
+
+ align:start position:0%
+of
+the car of s
+
+ align:start position:0%
+the car of s
+ 
+
+ align:start position:0%
+the car of s
+subtracted from The X the first one the
+
+ align:start position:0%
+subtracted from The X the first one the
+ 
+
+ align:start position:0%
+subtracted from The X the first one the
+car of the other half of it the cooter
+
+ align:start position:0%
+car of the other half of it the cooter
+ 
+
+ align:start position:0%
+car of the other half of it the cooter
+of S
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+right and then dy would be
+
+ align:start position:0%
+right and then dy would be
+ 
+
+ align:start position:0%
+right and then dy would be
+well let's see it' be I'd get the
+
+ align:start position:0%
+well let's see it' be I'd get the
+ 
+
+ align:start position:0%
+well let's see it' be I'd get the
+ycoordinate so it' be the difference of
+
+ align:start position:0%
+ycoordinate so it' be the difference of
+ 
+
+ align:start position:0%
+ycoordinate so it' be the difference of
+the cooter
+
+ align:start position:0%
+the cooter
+ 
+
+ align:start position:0%
+the cooter
+of the car of S and the cter
+
+ align:start position:0%
+of the car of S and the cter
+ 
+
+ align:start position:0%
+of the car of S and the cter
+of the cter of this
+
+ align:start position:0%
+of the cter of this
+ 
+
+ align:start position:0%
+of the cter of this
+sort of go on.
+
+ align:start position:0%
+sort of go on.
+ 
+
+ align:start position:0%
+sort of go on.
+You can see that's that's much harder to
+
+ align:start position:0%
+You can see that's that's much harder to
+ 
+
+ align:start position:0%
+You can see that's that's much harder to
+read than the program I had before. But
+
+ align:start position:0%
+read than the program I had before. But
+ 
+
+ align:start position:0%
+read than the program I had before. But
+uh but worse than that, I mean suppose
+
+ align:start position:0%
+uh but worse than that, I mean suppose
+ 
+
+ align:start position:0%
+uh but worse than that, I mean suppose
+you'd gone and implemented length.
+
+ align:start position:0%
+you'd gone and implemented length.
+ 
+
+ align:start position:0%
+you'd gone and implemented length.
+You come
+
+ align:start position:0%
+You come
+ 
+
+ align:start position:0%
+You come
+and then the next day George comes to
+
+ align:start position:0%
+and then the next day George comes to
+ 
+
+ align:start position:0%
+and then the next day George comes to
+you and said, "I'm sorry, I changed my
+
+ align:start position:0%
+you and said, "I'm sorry, I changed my
+ 
+
+ align:start position:0%
+you and said, "I'm sorry, I changed my
+mind. I want to write points with the
+
+ align:start position:0%
+mind. I want to write points with the
+ 
+
+ align:start position:0%
+mind. I want to write points with the
+with the x coordinate first." So you
+
+ align:start position:0%
+with the x coordinate first." So you
+ 
+
+ align:start position:0%
+with the x coordinate first." So you
+come back and you stare at this code and
+
+ align:start position:0%
+come back and you stare at this code and
+ 
+
+ align:start position:0%
+come back and you stare at this code and
+say, "Oh, gee, what was that? That was
+
+ align:start position:0%
+say, "Oh, gee, what was that? That was
+ 
+
+ align:start position:0%
+say, "Oh, gee, what was that? That was
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+oh the car. So I have to change this to
+
+ align:start position:0%
+oh the car. So I have to change this to
+ 
+
+ align:start position:0%
+oh the car. So I have to change this to
+cter
+
+ align:start position:0%
+cter
+ 
+
+ align:start position:0%
+cter
+and uh this is cooter
+
+ align:start position:0%
+and uh this is cooter
+ 
+
+ align:start position:0%
+and uh this is cooter
+and this now has to be car
+
+ align:start position:0%
+and this now has to be car
+ 
+
+ align:start position:0%
+and this now has to be car
+and this has to be car
+
+ align:start position:0%
+and this has to be car
+ 
+
+ align:start position:0%
+and this has to be car
+and you sort of do that and then the
+
+ align:start position:0%
+and you sort of do that and then the
+ 
+
+ align:start position:0%
+and you sort of do that and then the
+next day George comes back and says
+
+ align:start position:0%
+next day George comes back and says
+ 
+
+ align:start position:0%
+next day George comes back and says
+sorry uh
+
+ align:start position:0%
+sorry uh
+ 
+
+ align:start position:0%
+sorry uh
+the guys designing the display would
+
+ align:start position:0%
+the guys designing the display would
+ 
+
+ align:start position:0%
+the guys designing the display would
+like you know would like lines to be
+
+ align:start position:0%
+like you know would like lines to be
+ 
+
+ align:start position:0%
+like you know would like lines to be
+painted in the opposite direction. So I
+
+ align:start position:0%
+painted in the opposite direction. So I
+ 
+
+ align:start position:0%
+painted in the opposite direction. So I
+have to write the end point first in the
+
+ align:start position:0%
+have to write the end point first in the
+ 
+
+ align:start position:0%
+have to write the end point first in the
+order and then you come back and you
+
+ align:start position:0%
+order and then you come back and you
+ 
+
+ align:start position:0%
+order and then you come back and you
+stare at this code and say gee what was
+
+ align:start position:0%
+stare at this code and say gee what was
+ 
+
+ align:start position:0%
+stare at this code and say gee what was
+it you know what was it talking about?
+
+ align:start position:0%
+it you know what was it talking about?
+ 
+
+ align:start position:0%
+it you know what was it talking about?
+Oh yeah well I got to change this one to
+
+ align:start position:0%
+Oh yeah well I got to change this one to
+ 
+
+ align:start position:0%
+Oh yeah well I got to change this one to
+cter and this one becomes car and this
+
+ align:start position:0%
+cter and this one becomes car and this
+ 
+
+ align:start position:0%
+cter and this one becomes car and this
+one becomes car and this becomes critter
+
+ align:start position:0%
+one becomes car and this becomes critter
+ 
+
+ align:start position:0%
+one becomes car and this becomes critter
+and you go off and do that and then the
+
+ align:start position:0%
+and you go off and do that and then the
+ 
+
+ align:start position:0%
+and you go off and do that and then the
+next day George comes back to you. I'm
+
+ align:start position:0%
+next day George comes back to you. I'm
+ 
+
+ align:start position:0%
+next day George comes back to you. I'm
+sorry what I really meant is that the
+
+ align:start position:0%
+sorry what I really meant is that the
+ 
+
+ align:start position:0%
+sorry what I really meant is that the
+segments always have to go be painted
+
+ align:start position:0%
+segments always have to go be painted
+ 
+
+ align:start position:0%
+segments always have to go be painted
+from left to right on the screen and
+
+ align:start position:0%
+from left to right on the screen and
+ 
+
+ align:start position:0%
+from left to right on the screen and
+then you sort of you know it's clear you
+
+ align:start position:0%
+then you sort of you know it's clear you
+ 
+
+ align:start position:0%
+then you sort of you know it's clear you
+just go and punch George in the mouth at
+
+ align:start position:0%
+just go and punch George in the mouth at
+ 
+
+ align:start position:0%
+just go and punch George in the mouth at
+that point. But uh
+
+ align:start position:0%
+that point. But uh
+ 
+
+ align:start position:0%
+that point. But uh
+right but you see as soon as we have you
+
+ align:start position:0%
+right but you see as soon as we have you
+ 
+
+ align:start position:0%
+right but you see as soon as we have you
+know a 10 layer system you see how that
+
+ align:start position:0%
+know a 10 layer system you see how that
+ 
+
+ align:start position:0%
+know a 10 layer system you see how that
+complexity immediately builds up to the
+
+ align:start position:0%
+complexity immediately builds up to the
+ 
+
+ align:start position:0%
+complexity immediately builds up to the
+point where where even something like
+
+ align:start position:0%
+point where where even something like
+ 
+
+ align:start position:0%
+point where where even something like
+this gets out of control.
+
+ align:start position:0%
+this gets out of control.
+ 
+
+ align:start position:0%
+this gets out of control.
+Right? So again the way we've gotten out
+
+ align:start position:0%
+Right? So again the way we've gotten out
+ 
+
+ align:start position:0%
+Right? So again the way we've gotten out
+of that is we've named that spirit. See,
+
+ align:start position:0%
+of that is we've named that spirit. See,
+ 
+
+ align:start position:0%
+of that is we've named that spirit. See,
+we've built we've built a system where
+
+ align:start position:0%
+we've built we've built a system where
+ 
+
+ align:start position:0%
+we've built we've built a system where
+there is a thing which is the
+
+ align:start position:0%
+there is a thing which is the
+ 
+
+ align:start position:0%
+there is a thing which is the
+representation choice for how you're
+
+ align:start position:0%
+representation choice for how you're
+ 
+
+ align:start position:0%
+representation choice for how you're
+going to talk about vectors and choices
+
+ align:start position:0%
+going to talk about vectors and choices
+ 
+
+ align:start position:0%
+going to talk about vectors and choices
+about that representation are localized
+
+ align:start position:0%
+about that representation are localized
+ 
+
+ align:start position:0%
+about that representation are localized
+right there. They don't have their guts
+
+ align:start position:0%
+right there. They don't have their guts
+ 
+
+ align:start position:0%
+right there. They don't have their guts
+spilling over into things like how you
+
+ align:start position:0%
+spilling over into things like how you
+ 
+
+ align:start position:0%
+spilling over into things like how you
+compute the length or how you compute
+
+ align:start position:0%
+compute the length or how you compute
+ 
+
+ align:start position:0%
+compute the length or how you compute
+the midpoint.
+
+ align:start position:0%
+the midpoint.
+ 
+
+ align:start position:0%
+the midpoint.
+Right? And that's the real that's the
+
+ align:start position:0%
+Right? And that's the real that's the
+ 
+
+ align:start position:0%
+Right? And that's the real that's the
+real power of this system.
+
+ align:start position:0%
+real power of this system.
+ 
+
+ align:start position:0%
+real power of this system.
+Okay? We're explicit about them so that
+
+ align:start position:0%
+Okay? We're explicit about them so that
+ 
+
+ align:start position:0%
+Okay? We're explicit about them so that
+we have control over them.
+
+ align:start position:0%
+we have control over them.
+ 
+
+ align:start position:0%
+we have control over them.
+Great questions. What happens in the
+
+ align:start position:0%
+Great questions. What happens in the
+ 
+
+ align:start position:0%
+Great questions. What happens in the
+case where you're you don't want to be
+
+ align:start position:0%
+case where you're you don't want to be
+ 
+
+ align:start position:0%
+case where you're you don't want to be
+treating objects in terms of pairs for
+
+ align:start position:0%
+treating objects in terms of pairs for
+ 
+
+ align:start position:0%
+treating objects in terms of pairs for
+instance that in three-dimensional space
+
+ align:start position:0%
+instance that in three-dimensional space
+ 
+
+ align:start position:0%
+instance that in three-dimensional space
+you'd have three coordinates or even in
+
+ align:start position:0%
+you'd have three coordinates or even in
+ 
+
+ align:start position:0%
+you'd have three coordinates or even in
+the case where you have n dimensional
+
+ align:start position:0%
+the case where you have n dimensional
+ 
+
+ align:start position:0%
+the case where you have n dimensional
+space
+
+ align:start position:0%
+space
+ 
+
+ align:start position:0%
+space
+right what happens
+
+ align:start position:0%
+right what happens
+ 
+
+ align:start position:0%
+right what happens
+okay well this is this is a preview of
+
+ align:start position:0%
+okay well this is this is a preview of
+ 
+
+ align:start position:0%
+okay well this is this is a preview of
+what I'll say tomorrow but uh
+
+ align:start position:0%
+what I'll say tomorrow but uh
+ 
+
+ align:start position:0%
+what I'll say tomorrow but uh
+the point is once you have once you have
+
+ align:start position:0%
+the point is once you have once you have
+ 
+
+ align:start position:0%
+the point is once you have once you have
+two things you have as many things as
+
+ align:start position:0%
+two things you have as many things as
+ 
+
+ align:start position:0%
+two things you have as many things as
+you want right because if I want to make
+
+ align:start position:0%
+you want right because if I want to make
+ 
+
+ align:start position:0%
+you want right because if I want to make
+three things I could start making things
+
+ align:start position:0%
+three things I could start making things
+ 
+
+ align:start position:0%
+three things I could start making things
+like a pair
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+whose first thing is one and whose
+
+ align:start position:0%
+whose first thing is one and whose
+ 
+
+ align:start position:0%
+whose first thing is one and whose
+second thing is another pair
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that say has two and three in it.
+
+ align:start position:0%
+that say has two and three in it.
+ 
+
+ align:start position:0%
+that say has two and three in it.
+So I wanted 100 things. I can nest them
+
+ align:start position:0%
+So I wanted 100 things. I can nest them
+ 
+
+ align:start position:0%
+So I wanted 100 things. I can nest them
+out of pairs. Here I made a pretty
+
+ align:start position:0%
+out of pairs. Here I made a pretty
+ 
+
+ align:start position:0%
+out of pairs. Here I made a pretty
+arbitrary decision about how to do it.
+
+ align:start position:0%
+arbitrary decision about how to do it.
+ 
+
+ align:start position:0%
+arbitrary decision about how to do it.
+And you can immediately see there are
+
+ align:start position:0%
+And you can immediately see there are
+ 
+
+ align:start position:0%
+And you can immediately see there are
+lots of ways to do that. We'll start
+
+ align:start position:0%
+lots of ways to do that. We'll start
+ 
+
+ align:start position:0%
+lots of ways to do that. We'll start
+talking about next time are conventions
+
+ align:start position:0%
+talking about next time are conventions
+ 
+
+ align:start position:0%
+talking about next time are conventions
+for how to do things like that.
+
+ align:start position:0%
+for how to do things like that.
+ 
+
+ align:start position:0%
+for how to do things like that.
+But notice that what this really depends
+
+ align:start position:0%
+But notice that what this really depends
+ 
+
+ align:start position:0%
+But notice that what this really depends
+on is I can make pairs of pairs.
+
+ align:start position:0%
+on is I can make pairs of pairs.
+ 
+
+ align:start position:0%
+on is I can make pairs of pairs.
+If all I could do was make pairs of
+
+ align:start position:0%
+If all I could do was make pairs of
+ 
+
+ align:start position:0%
+If all I could do was make pairs of
+numbers, I'd be stuck.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay,
+
+ align:start position:0%
+Okay,
+ 
+
+ align:start position:0%
+Okay,
+let's break.
+
+ align:start position:0%
+let's break.
+ 
+
+ align:start position:0%
+let's break.
+[Music]
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+[Music]
+
+ align:start position:0%
+[Music]
+ 
+
+ align:start position:0%
+[Music]
+All right. Well, we've just gone off and
+
+ align:start position:0%
+All right. Well, we've just gone off and
+ 
+
+ align:start position:0%
+All right. Well, we've just gone off and
+done
+
+ align:start position:0%
+done
+ 
+
+ align:start position:0%
+done
+a couple of simple examples of data
+
+ align:start position:0%
+a couple of simple examples of data
+ 
+
+ align:start position:0%
+a couple of simple examples of data
+abstraction.
+
+ align:start position:0%
+abstraction.
+ 
+
+ align:start position:0%
+abstraction.
+Now, I'm going to do something more
+
+ align:start position:0%
+Now, I'm going to do something more
+ 
+
+ align:start position:0%
+Now, I'm going to do something more
+complicated. We're going to talk about
+
+ align:start position:0%
+complicated. We're going to talk about
+ 
+
+ align:start position:0%
+complicated. We're going to talk about
+what it means. And this will be harder
+
+ align:start position:0%
+what it means. And this will be harder
+ 
+
+ align:start position:0%
+what it means. And this will be harder
+because it's always It's always much
+
+ align:start position:0%
+because it's always It's always much
+ 
+
+ align:start position:0%
+because it's always It's always much
+harder to in computer programming to
+
+ align:start position:0%
+harder to in computer programming to
+ 
+
+ align:start position:0%
+harder to in computer programming to
+talk about what something means than to
+
+ align:start position:0%
+talk about what something means than to
+ 
+
+ align:start position:0%
+talk about what something means than to
+go off and do it. But uh let's go back
+
+ align:start position:0%
+go off and do it. But uh let's go back
+ 
+
+ align:start position:0%
+go off and do it. But uh let's go back
+to almost the very beginning. Let's go
+
+ align:start position:0%
+to almost the very beginning. Let's go
+ 
+
+ align:start position:0%
+to almost the very beginning. Let's go
+back to the point where I said we just
+
+ align:start position:0%
+back to the point where I said we just
+ 
+
+ align:start position:0%
+back to the point where I said we just
+assumed that there were procedures
+
+ align:start position:0%
+assumed that there were procedures
+ 
+
+ align:start position:0%
+assumed that there were procedures
+make
+
+ align:start position:0%
+make
+ 
+
+ align:start position:0%
+make
+and numer
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and denom.
+
+ align:start position:0%
+and denom.
+ 
+
+ align:start position:0%
+and denom.
+Let's go back to where we had those at
+
+ align:start position:0%
+Let's go back to where we had those at
+ 
+
+ align:start position:0%
+Let's go back to where we had those at
+the very beginning constructors and
+
+ align:start position:0%
+the very beginning constructors and
+ 
+
+ align:start position:0%
+the very beginning constructors and
+selectors and went off and defined the
+
+ align:start position:0%
+selectors and went off and defined the
+ 
+
+ align:start position:0%
+selectors and went off and defined the
+rational number arithmetic. And I
+
+ align:start position:0%
+rational number arithmetic. And I
+ 
+
+ align:start position:0%
+rational number arithmetic. And I
+remember I said at that point we were
+
+ align:start position:0%
+remember I said at that point we were
+ 
+
+ align:start position:0%
+remember I said at that point we were
+sort of done except for George.
+
+ align:start position:0%
+sort of done except for George.
+ 
+
+ align:start position:0%
+sort of done except for George.
+Well, but what is it that we'd actually
+
+ align:start position:0%
+Well, but what is it that we'd actually
+ 
+
+ align:start position:0%
+Well, but what is it that we'd actually
+done at that point? What was it that was
+
+ align:start position:0%
+done at that point? What was it that was
+ 
+
+ align:start position:0%
+done at that point? What was it that was
+done?
+
+ align:start position:0%
+done?
+ 
+
+ align:start position:0%
+done?
+Well, what I want to say is what was
+
+ align:start position:0%
+Well, what I want to say is what was
+ 
+
+ align:start position:0%
+Well, what I want to say is what was
+done after we'd implemented the
+
+ align:start position:0%
+done after we'd implemented the
+ 
+
+ align:start position:0%
+done after we'd implemented the
+operations in terms of these was that we
+
+ align:start position:0%
+operations in terms of these was that we
+ 
+
+ align:start position:0%
+operations in terms of these was that we
+had defined our rational number
+
+ align:start position:0%
+had defined our rational number
+ 
+
+ align:start position:0%
+had defined our rational number
+representation in terms of abstract
+
+ align:start position:0%
+representation in terms of abstract
+ 
+
+ align:start position:0%
+representation in terms of abstract
+data.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+What do I mean by abstract data?
+
+ align:start position:0%
+What do I mean by abstract data?
+ 
+
+ align:start position:0%
+What do I mean by abstract data?
+Well, the idea is that
+
+ align:start position:0%
+Well, the idea is that
+ 
+
+ align:start position:0%
+Well, the idea is that
+at that point when we had our plus rat
+
+ align:start position:0%
+at that point when we had our plus rat
+ 
+
+ align:start position:0%
+at that point when we had our plus rat
+and our star rat
+
+ align:start position:0%
+and our star rat
+ 
+
+ align:start position:0%
+and our star rat
+that any implementation of make rat and
+
+ align:start position:0%
+that any implementation of make rat and
+ 
+
+ align:start position:0%
+that any implementation of make rat and
+numerator and denominator
+
+ align:start position:0%
+numerator and denominator
+ 
+
+ align:start position:0%
+numerator and denominator
+that George supplied us with
+
+ align:start position:0%
+that George supplied us with
+ 
+
+ align:start position:0%
+that George supplied us with
+could be the basis for a rational number
+
+ align:start position:0%
+could be the basis for a rational number
+ 
+
+ align:start position:0%
+could be the basis for a rational number
+representation like it wasn't our
+
+ align:start position:0%
+representation like it wasn't our
+ 
+
+ align:start position:0%
+representation like it wasn't our
+concern where you where you uh divide it
+
+ align:start position:0%
+concern where you where you uh divide it
+ 
+
+ align:start position:0%
+concern where you where you uh divide it
+through to get the greatest common
+
+ align:start position:0%
+through to get the greatest common
+ 
+
+ align:start position:0%
+through to get the greatest common
+denominator or any of that.
+
+ align:start position:0%
+denominator or any of that.
+ 
+
+ align:start position:0%
+denominator or any of that.
+Right? So the idea is that what we built
+
+ align:start position:0%
+Right? So the idea is that what we built
+ 
+
+ align:start position:0%
+Right? So the idea is that what we built
+is a rational arithmetic system that
+
+ align:start position:0%
+is a rational arithmetic system that
+ 
+
+ align:start position:0%
+is a rational arithmetic system that
+would sit on top of any representation.
+
+ align:start position:0%
+would sit on top of any representation.
+ 
+
+ align:start position:0%
+would sit on top of any representation.
+But what do I mean by any
+
+ align:start position:0%
+But what do I mean by any
+ 
+
+ align:start position:0%
+But what do I mean by any
+representation?
+
+ align:start position:0%
+representation?
+ 
+
+ align:start position:0%
+representation?
+I mean certainly it can't be the case
+
+ align:start position:0%
+I mean certainly it can't be the case
+ 
+
+ align:start position:0%
+I mean certainly it can't be the case
+that all I mean is George can reach in a
+
+ align:start position:0%
+that all I mean is George can reach in a
+ 
+
+ align:start position:0%
+that all I mean is George can reach in a
+bag and pull out three arbitrary
+
+ align:start position:0%
+bag and pull out three arbitrary
+ 
+
+ align:start position:0%
+bag and pull out three arbitrary
+procedures
+
+ align:start position:0%
+procedures
+ 
+
+ align:start position:0%
+procedures
+and say well fine now you now that's the
+
+ align:start position:0%
+and say well fine now you now that's the
+ 
+
+ align:start position:0%
+and say well fine now you now that's the
+implementation right that can't be what
+
+ align:start position:0%
+implementation right that can't be what
+ 
+
+ align:start position:0%
+implementation right that can't be what
+I mean right what I've got to mean is
+
+ align:start position:0%
+I mean right what I've got to mean is
+ 
+
+ align:start position:0%
+I mean right what I've got to mean is
+that there's
+
+ align:start position:0%
+that there's
+ 
+
+ align:start position:0%
+that there's
+some way of saying whether
+
+ align:start position:0%
+some way of saying whether
+ 
+
+ align:start position:0%
+some way of saying whether
+three procedures are going to be
+
+ align:start position:0%
+three procedures are going to be
+ 
+
+ align:start position:0%
+three procedures are going to be
+suitable as a basis for rational number
+
+ align:start position:0%
+suitable as a basis for rational number
+ 
+
+ align:start position:0%
+suitable as a basis for rational number
+representation if we if we think about
+
+ align:start position:0%
+representation if we if we think about
+ 
+
+ align:start position:0%
+representation if we if we think about
+it what's suitable might mean is is if I
+
+ align:start position:0%
+it what's suitable might mean is is if I
+ 
+
+ align:start position:0%
+it what's suitable might mean is is if I
+have to assume something like this. So I
+
+ align:start position:0%
+have to assume something like this. So I
+ 
+
+ align:start position:0%
+have to assume something like this. So I
+have to say that if
+
+ align:start position:0%
+have to say that if
+ 
+
+ align:start position:0%
+have to say that if
+X is the result of
+
+ align:start position:0%
+X is the result of
+ 
+
+ align:start position:0%
+X is the result of
+say doing make rat
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+of N and D
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+then
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the numerator
+
+ align:start position:0%
+the numerator
+ 
+
+ align:start position:0%
+the numerator
+of X
+
+ align:start position:0%
+of X
+ 
+
+ align:start position:0%
+of X
+divided by the denominator of X
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+is equal to N /d D.
+
+ align:start position:0%
+is equal to N /d D.
+ 
+
+ align:start position:0%
+is equal to N /d D.
+See what that is is that's George's
+
+ align:start position:0%
+See what that is is that's George's
+ 
+
+ align:start position:0%
+See what that is is that's George's
+contract.
+
+ align:start position:0%
+contract.
+ 
+
+ align:start position:0%
+contract.
+What we mean by writing a contract for
+
+ align:start position:0%
+What we mean by writing a contract for
+ 
+
+ align:start position:0%
+What we mean by writing a contract for
+rational numbers, if you think about it,
+
+ align:start position:0%
+rational numbers, if you think about it,
+ 
+
+ align:start position:0%
+rational numbers, if you think about it,
+this is the right thing. And the two the
+
+ align:start position:0%
+this is the right thing. And the two the
+ 
+
+ align:start position:0%
+this is the right thing. And the two the
+two ones we showed do do the right
+
+ align:start position:0%
+two ones we showed do do the right
+ 
+
+ align:start position:0%
+two ones we showed do do the right
+thing. You see, if I'm taking out
+
+ align:start position:0%
+thing. You see, if I'm taking out
+ 
+
+ align:start position:0%
+thing. You see, if I'm taking out
+greatest common divisors,
+
+ align:start position:0%
+greatest common divisors,
+ 
+
+ align:start position:0%
+greatest common divisors,
+doesn't matter whether I take them out
+
+ align:start position:0%
+doesn't matter whether I take them out
+ 
+
+ align:start position:0%
+doesn't matter whether I take them out
+or not or the place where I take them
+
+ align:start position:0%
+or not or the place where I take them
+ 
+
+ align:start position:0%
+or not or the place where I take them
+out because the idea is I'm going to
+
+ align:start position:0%
+out because the idea is I'm going to
+ 
+
+ align:start position:0%
+out because the idea is I'm going to
+divide through.
+
+ align:start position:0%
+divide through.
+ 
+
+ align:start position:0%
+divide through.
+But see, this is George's contract. So,
+
+ align:start position:0%
+But see, this is George's contract. So,
+ 
+
+ align:start position:0%
+But see, this is George's contract. So,
+what we really say to George is what
+
+ align:start position:0%
+what we really say to George is what
+ 
+
+ align:start position:0%
+what we really say to George is what
+your your business is to go off and find
+
+ align:start position:0%
+your your business is to go off and find
+ 
+
+ align:start position:0%
+your your business is to go off and find
+us three procedures make numerator and
+
+ align:start position:0%
+us three procedures make numerator and
+ 
+
+ align:start position:0%
+us three procedures make numerator and
+denominator that fulfill this contract
+
+ align:start position:0%
+denominator that fulfill this contract
+ 
+
+ align:start position:0%
+denominator that fulfill this contract
+for any choice of N and D. And that's
+
+ align:start position:0%
+for any choice of N and D. And that's
+ 
+
+ align:start position:0%
+for any choice of N and D. And that's
+what we mean by we can use that as the
+
+ align:start position:0%
+what we mean by we can use that as the
+ 
+
+ align:start position:0%
+what we mean by we can use that as the
+basis for a rational number
+
+ align:start position:0%
+basis for a rational number
+ 
+
+ align:start position:0%
+basis for a rational number
+representation.
+
+ align:start position:0%
+representation.
+ 
+
+ align:start position:0%
+representation.
+And other than that, it fulfills this
+
+ align:start position:0%
+And other than that, it fulfills this
+ 
+
+ align:start position:0%
+And other than that, it fulfills this
+contract. We don't care how he does it.
+
+ align:start position:0%
+contract. We don't care how he does it.
+ 
+
+ align:start position:0%
+contract. We don't care how he does it.
+It's not our business. It's below the
+
+ align:start position:0%
+It's not our business. It's below the
+ 
+
+ align:start position:0%
+It's not our business. It's below the
+layer of abstraction.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+In fact, if we want to say what is a
+
+ align:start position:0%
+In fact, if we want to say what is a
+ 
+
+ align:start position:0%
+In fact, if we want to say what is a
+rational number really,
+
+ align:start position:0%
+rational number really,
+ 
+
+ align:start position:0%
+rational number really,
+see what's it really without having to
+
+ align:start position:0%
+see what's it really without having to
+ 
+
+ align:start position:0%
+see what's it really without having to
+talk about going below the layer of
+
+ align:start position:0%
+talk about going below the layer of
+ 
+
+ align:start position:0%
+talk about going below the layer of
+abstraction. What we're forced into
+
+ align:start position:0%
+abstraction. What we're forced into
+ 
+
+ align:start position:0%
+abstraction. What we're forced into
+saying is a rational number really
+
+ align:start position:0%
+saying is a rational number really
+ 
+
+ align:start position:0%
+saying is a rational number really
+is sort of this axiom is three
+
+ align:start position:0%
+is sort of this axiom is three
+ 
+
+ align:start position:0%
+is sort of this axiom is three
+procedures make numerator and
+
+ align:start position:0%
+procedures make numerator and
+ 
+
+ align:start position:0%
+procedures make numerator and
+denominator that satisfy this axiom.
+
+ align:start position:0%
+denominator that satisfy this axiom.
+ 
+
+ align:start position:0%
+denominator that satisfy this axiom.
+in some in some sense abstractly that's
+
+ align:start position:0%
+in some in some sense abstractly that's
+ 
+
+ align:start position:0%
+in some in some sense abstractly that's
+what a rational number is really right
+
+ align:start position:0%
+what a rational number is really right
+ 
+
+ align:start position:0%
+what a rational number is really right
+so we that's
+
+ align:start position:0%
+so we that's
+ 
+
+ align:start position:0%
+so we that's
+that's sort of easy that's sort of easy
+
+ align:start position:0%
+that's sort of easy that's sort of easy
+ 
+
+ align:start position:0%
+that's sort of easy that's sort of easy
+words to listen to because what you have
+
+ align:start position:0%
+words to listen to because what you have
+ 
+
+ align:start position:0%
+words to listen to because what you have
+in your head of course is well for all
+
+ align:start position:0%
+in your head of course is well for all
+ 
+
+ align:start position:0%
+in your head of course is well for all
+this thing about saying that's what a
+
+ align:start position:0%
+this thing about saying that's what a
+ 
+
+ align:start position:0%
+this thing about saying that's what a
+rational number is really you actually
+
+ align:start position:0%
+rational number is really you actually
+ 
+
+ align:start position:0%
+rational number is really you actually
+just saw that we built rational numbers
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+what we really did is we built rational
+
+ align:start position:0%
+what we really did is we built rational
+ 
+
+ align:start position:0%
+what we really did is we built rational
+numbers
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+on top of pairs.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+So for all I'm saying abstractly, we can
+
+ align:start position:0%
+So for all I'm saying abstractly, we can
+ 
+
+ align:start position:0%
+So for all I'm saying abstractly, we can
+say a rational number really is just
+
+ align:start position:0%
+say a rational number really is just
+ 
+
+ align:start position:0%
+say a rational number really is just
+this axiom.
+
+ align:start position:0%
+this axiom.
+ 
+
+ align:start position:0%
+this axiom.
+You can listen to that comfortably
+
+ align:start position:0%
+You can listen to that comfortably
+ 
+
+ align:start position:0%
+You can listen to that comfortably
+because you're saying, "Well, yeah, but
+
+ align:start position:0%
+because you're saying, "Well, yeah, but
+ 
+
+ align:start position:0%
+because you're saying, "Well, yeah, but
+really it's actually pairs and I'm just
+
+ align:start position:0%
+really it's actually pairs and I'm just
+ 
+
+ align:start position:0%
+really it's actually pairs and I'm just
+annoying you by trying to be abstract."
+
+ align:start position:0%
+annoying you by trying to be abstract."
+ 
+
+ align:start position:0%
+annoying you by trying to be abstract."
+Well, let me as an antidote for that,
+
+ align:start position:0%
+Well, let me as an antidote for that,
+ 
+
+ align:start position:0%
+Well, let me as an antidote for that,
+let me do something that I think is
+
+ align:start position:0%
+let me do something that I think is
+ 
+
+ align:start position:0%
+let me do something that I think is
+really going to terrify you and is
+
+ align:start position:0%
+really going to terrify you and is
+ 
+
+ align:start position:0%
+really going to terrify you and is
+really going to bring you, you know,
+
+ align:start position:0%
+really going to bring you, you know,
+ 
+
+ align:start position:0%
+really going to bring you, you know,
+face to face with the the sort of uh
+
+ align:start position:0%
+face to face with the the sort of uh
+ 
+
+ align:start position:0%
+face to face with the the sort of uh
+existential reality of this abstraction
+
+ align:start position:0%
+existential reality of this abstraction
+ 
+
+ align:start position:0%
+existential reality of this abstraction
+that we're talking about. And what I'm
+
+ align:start position:0%
+that we're talking about. And what I'm
+ 
+
+ align:start position:0%
+that we're talking about. And what I'm
+going to talk about is what are pairs
+
+ align:start position:0%
+going to talk about is what are pairs
+ 
+
+ align:start position:0%
+going to talk about is what are pairs
+really?
+
+ align:start position:0%
+really?
+ 
+
+ align:start position:0%
+really?
+See, what did I tell you about pairs?
+
+ align:start position:0%
+See, what did I tell you about pairs?
+ 
+
+ align:start position:0%
+See, what did I tell you about pairs?
+I tricked you, right? I said that list
+
+ align:start position:0%
+I tricked you, right? I said that list
+ 
+
+ align:start position:0%
+I tricked you, right? I said that list
+well list has this primitive called con
+
+ align:start position:0%
+well list has this primitive called con
+ 
+
+ align:start position:0%
+well list has this primitive called con
+that builds pairs. But what did I really
+
+ align:start position:0%
+that builds pairs. But what did I really
+ 
+
+ align:start position:0%
+that builds pairs. But what did I really
+tell you about them? If you go back and
+
+ align:start position:0%
+tell you about them? If you go back and
+ 
+
+ align:start position:0%
+tell you about them? If you go back and
+said, let's look on this slide, all I
+
+ align:start position:0%
+said, let's look on this slide, all I
+ 
+
+ align:start position:0%
+said, let's look on this slide, all I
+really told you about pairs is that
+
+ align:start position:0%
+really told you about pairs is that
+ 
+
+ align:start position:0%
+really told you about pairs is that
+there happens to be this properties,
+
+ align:start position:0%
+there happens to be this properties,
+ 
+
+ align:start position:0%
+there happens to be this properties,
+these properties of K, car, and CERT.
+
+ align:start position:0%
+these properties of K, car, and CERT.
+ 
+
+ align:start position:0%
+these properties of K, car, and CERT.
+And all I really said about pairs is
+
+ align:start position:0%
+And all I really said about pairs is
+ 
+
+ align:start position:0%
+And all I really said about pairs is
+that there's a thing called cons and a
+
+ align:start position:0%
+that there's a thing called cons and a
+ 
+
+ align:start position:0%
+that there's a thing called cons and a
+thing called car and a thing called
+
+ align:start position:0%
+thing called car and a thing called
+ 
+
+ align:start position:0%
+thing called car and a thing called
+curter.
+
+ align:start position:0%
+curter.
+ 
+
+ align:start position:0%
+curter.
+And it is the case that if I build const
+
+ align:start position:0%
+And it is the case that if I build const
+ 
+
+ align:start position:0%
+And it is the case that if I build const
+of xy and take car of it, I get x.
+
+ align:start position:0%
+of xy and take car of it, I get x.
+ 
+
+ align:start position:0%
+of xy and take car of it, I get x.
+And if I build cter if I build concept
+
+ align:start position:0%
+And if I build cter if I build concept
+ 
+
+ align:start position:0%
+And if I build cter if I build concept
+xy and get cer of it I get y
+
+ align:start position:0%
+xy and get cer of it I get y
+ 
+
+ align:start position:0%
+xy and get cer of it I get y
+and that
+
+ align:start position:0%
+and that
+ 
+
+ align:start position:0%
+and that
+right even though I even though I lulled
+
+ align:start position:0%
+right even though I even though I lulled
+ 
+
+ align:start position:0%
+right even though I even though I lulled
+you into thinking that there's something
+
+ align:start position:0%
+you into thinking that there's something
+ 
+
+ align:start position:0%
+you into thinking that there's something
+in lisp that does that so you pretended
+
+ align:start position:0%
+in lisp that does that so you pretended
+ 
+
+ align:start position:0%
+in lisp that does that so you pretended
+you knew what it was in fact I didn't
+
+ align:start position:0%
+you knew what it was in fact I didn't
+ 
+
+ align:start position:0%
+you knew what it was in fact I didn't
+tell you any more about pairs than this
+
+ align:start position:0%
+tell you any more about pairs than this
+ 
+
+ align:start position:0%
+tell you any more about pairs than this
+tells you about rational numbers it's
+
+ align:start position:0%
+tells you about rational numbers it's
+ 
+
+ align:start position:0%
+tells you about rational numbers it's
+just some axiom for pairs
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+well
+
+ align:start position:0%
+well
+ 
+
+ align:start position:0%
+well
+to drive that home let me really scare
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and show you what we might build pairs
+
+ align:start position:0%
+and show you what we might build pairs
+ 
+
+ align:start position:0%
+and show you what we might build pairs
+in terms of
+
+ align:start position:0%
+in terms of
+ 
+
+ align:start position:0%
+in terms of
+what you're going to see is that we can
+
+ align:start position:0%
+what you're going to see is that we can
+ 
+
+ align:start position:0%
+what you're going to see is that we can
+build right rational numbers and line
+
+ align:start position:0%
+build right rational numbers and line
+ 
+
+ align:start position:0%
+build right rational numbers and line
+segments and vectors and all of this
+
+ align:start position:0%
+segments and vectors and all of this
+ 
+
+ align:start position:0%
+segments and vectors and all of this
+stuff in terms of pairs. And we're going
+
+ align:start position:0%
+stuff in terms of pairs. And we're going
+ 
+
+ align:start position:0%
+stuff in terms of pairs. And we're going
+to see below here that pairs can be
+
+ align:start position:0%
+to see below here that pairs can be
+ 
+
+ align:start position:0%
+to see below here that pairs can be
+built out of nothing at all.
+
+ align:start position:0%
+built out of nothing at all.
+ 
+
+ align:start position:0%
+built out of nothing at all.
+Right? Pure abstraction. So what let me
+
+ align:start position:0%
+Right? Pure abstraction. So what let me
+ 
+
+ align:start position:0%
+Right? Pure abstraction. So what let me
+show you on this slide
+
+ align:start position:0%
+show you on this slide
+ 
+
+ align:start position:0%
+show you on this slide
+an implementation of constar encoder
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and we'll look at it again in a second
+
+ align:start position:0%
+and we'll look at it again in a second
+ 
+
+ align:start position:0%
+and we'll look at it again in a second
+but notice that their procedure
+
+ align:start position:0%
+but notice that their procedure
+ 
+
+ align:start position:0%
+but notice that their procedure
+definition of const
+
+ align:start position:0%
+definition of const
+ 
+
+ align:start position:0%
+definition of const
+you don't see any data in there what you
+
+ align:start position:0%
+you don't see any data in there what you
+ 
+
+ align:start position:0%
+you don't see any data in there what you
+see is
+
+ align:start position:0%
+see is
+ 
+
+ align:start position:0%
+see is
+is a lambda
+
+ align:start position:0%
+is a lambda
+ 
+
+ align:start position:0%
+is a lambda
+right con so conce here is going to
+
+ align:start position:0%
+right con so conce here is going to
+ 
+
+ align:start position:0%
+right con so conce here is going to
+return is a procedure that returns a
+
+ align:start position:0%
+return is a procedure that returns a
+ 
+
+ align:start position:0%
+return is a procedure that returns a
+procedure just like uh average n
+
+ align:start position:0%
+procedure just like uh average n
+ 
+
+ align:start position:0%
+procedure just like uh average n
+con a and b returns a procedure
+
+ align:start position:0%
+con a and b returns a procedure
+ 
+
+ align:start position:0%
+con a and b returns a procedure
+of an argument called pick
+
+ align:start position:0%
+of an argument called pick
+ 
+
+ align:start position:0%
+of an argument called pick
+and it says if p is equal to one I'm
+
+ align:start position:0%
+and it says if p is equal to one I'm
+ 
+
+ align:start position:0%
+and it says if p is equal to one I'm
+going to return a and if p is equal to
+
+ align:start position:0%
+going to return a and if p is equal to
+ 
+
+ align:start position:0%
+going to return a and if p is equal to
+two I'm going to return b and that's
+
+ align:start position:0%
+two I'm going to return b and that's
+ 
+
+ align:start position:0%
+two I'm going to return b and that's
+what con is going to be
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+car of
+
+ align:start position:0%
+car of
+ 
+
+ align:start position:0%
+car of
+a thing x car of a pair x is going to be
+
+ align:start position:0%
+a thing x car of a pair x is going to be
+ 
+
+ align:start position:0%
+a thing x car of a pair x is going to be
+x applied to one and notice that makes
+
+ align:start position:0%
+x applied to one and notice that makes
+ 
+
+ align:start position:0%
+x applied to one and notice that makes
+sense. You may not understand why or how
+
+ align:start position:0%
+sense. You may not understand why or how
+ 
+
+ align:start position:0%
+sense. You may not understand why or how
+I'm doing such a thing, but at least it
+
+ align:start position:0%
+I'm doing such a thing, but at least it
+ 
+
+ align:start position:0%
+I'm doing such a thing, but at least it
+makes sense because the thing
+
+ align:start position:0%
+makes sense because the thing
+ 
+
+ align:start position:0%
+makes sense because the thing
+constructed by con is a procedure and
+
+ align:start position:0%
+constructed by con is a procedure and
+ 
+
+ align:start position:0%
+constructed by con is a procedure and
+car applies that to one
+
+ align:start position:0%
+car applies that to one
+ 
+
+ align:start position:0%
+car applies that to one
+and similarly cooter applies that thing
+
+ align:start position:0%
+and similarly cooter applies that thing
+ 
+
+ align:start position:0%
+and similarly cooter applies that thing
+to two.
+
+ align:start position:0%
+to two.
+ 
+
+ align:start position:0%
+to two.
+Okay, now I claim that this is a
+
+ align:start position:0%
+Okay, now I claim that this is a
+ 
+
+ align:start position:0%
+Okay, now I claim that this is a
+representation of concar and cter. And
+
+ align:start position:0%
+representation of concar and cter. And
+ 
+
+ align:start position:0%
+representation of concar and cter. And
+notice there's no data in it, right?
+
+ align:start position:0%
+notice there's no data in it, right?
+ 
+
+ align:start position:0%
+notice there's no data in it, right?
+It's built out of air. It's just
+
+ align:start position:0%
+It's built out of air. It's just
+ 
+
+ align:start position:0%
+It's built out of air. It's just
+procedures,
+
+ align:start position:0%
+procedures,
+ 
+
+ align:start position:0%
+procedures,
+right? There's no data objects at all in
+
+ align:start position:0%
+right? There's no data objects at all in
+ 
+
+ align:start position:0%
+right? There's no data objects at all in
+that representation.
+
+ align:start position:0%
+that representation.
+ 
+
+ align:start position:0%
+that representation.
+Well, what could that possibly mean,
+
+ align:start position:0%
+Well, what could that possibly mean,
+ 
+
+ align:start position:0%
+Well, what could that possibly mean,
+right?
+
+ align:start position:0%
+right?
+ 
+
+ align:start position:0%
+right?
+Well, if you really believe this stuff,
+
+ align:start position:0%
+Well, if you really believe this stuff,
+ 
+
+ align:start position:0%
+Well, if you really believe this stuff,
+then you have to believe that in order
+
+ align:start position:0%
+then you have to believe that in order
+ 
+
+ align:start position:0%
+then you have to believe that in order
+to show that that's a representation for
+
+ align:start position:0%
+to show that that's a representation for
+ 
+
+ align:start position:0%
+to show that that's a representation for
+K's current critter, all I have to do is
+
+ align:start position:0%
+K's current critter, all I have to do is
+ 
+
+ align:start position:0%
+K's current critter, all I have to do is
+show that it satisfies the axiom. See,
+
+ align:start position:0%
+show that it satisfies the axiom. See,
+ 
+
+ align:start position:0%
+show that it satisfies the axiom. See,
+all I should have to convince you of is
+
+ align:start position:0%
+all I should have to convince you of is
+ 
+
+ align:start position:0%
+all I should have to convince you of is
+for example that uh
+
+ align:start position:0%
+for example that uh
+ 
+
+ align:start position:0%
+for example that uh
+gee that car
+
+ align:start position:0%
+gee that car
+ 
+
+ align:start position:0%
+gee that car
+of cons of 37 and 49,
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+right? Is 37, right? For arbitrary
+
+ align:start position:0%
+right? Is 37, right? For arbitrary
+ 
+
+ align:start position:0%
+right? Is 37, right? For arbitrary
+values of 37 and 49, right? See if I
+
+ align:start position:0%
+values of 37 and 49, right? See if I
+ 
+
+ align:start position:0%
+values of 37 and 49, right? See if I
+really can and could the same way,
+
+ align:start position:0%
+really can and could the same way,
+ 
+
+ align:start position:0%
+really can and could the same way,
+right? See, if I really can can
+
+ align:start position:0%
+right? See, if I really can can
+ 
+
+ align:start position:0%
+right? See, if I really can can
+demonstrate to you that that weird
+
+ align:start position:0%
+demonstrate to you that that weird
+ 
+
+ align:start position:0%
+demonstrate to you that that weird
+procedure definition in terms of air has
+
+ align:start position:0%
+procedure definition in terms of air has
+ 
+
+ align:start position:0%
+procedure definition in terms of air has
+the property that it satisfies this,
+
+ align:start position:0%
+the property that it satisfies this,
+ 
+
+ align:start position:0%
+the property that it satisfies this,
+then you just have to grant me that that
+
+ align:start position:0%
+then you just have to grant me that that
+ 
+
+ align:start position:0%
+then you just have to grant me that that
+is a rep that is a possible
+
+ align:start position:0%
+is a rep that is a possible
+ 
+
+ align:start position:0%
+is a rep that is a possible
+implementation of const which I can
+
+ align:start position:0%
+implementation of const which I can
+ 
+
+ align:start position:0%
+implementation of const which I can
+build everything else. Well, let's look
+
+ align:start position:0%
+build everything else. Well, let's look
+ 
+
+ align:start position:0%
+build everything else. Well, let's look
+at that. This will be practice in in the
+
+ align:start position:0%
+at that. This will be practice in in the
+ 
+
+ align:start position:0%
+at that. This will be practice in in the
+substitution model. How would I actually
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+right how could we check this? So we
+
+ align:start position:0%
+right how could we check this? So we
+ 
+
+ align:start position:0%
+right how could we check this? So we
+sort of know how to do that. It's just
+
+ align:start position:0%
+sort of know how to do that. It's just
+ 
+
+ align:start position:0%
+sort of know how to do that. It's just
+the same substitution model,
+
+ align:start position:0%
+the same substitution model,
+ 
+
+ align:start position:0%
+the same substitution model,
+right? Let's let's look. We start out
+
+ align:start position:0%
+right? Let's let's look. We start out
+ 
+
+ align:start position:0%
+right? Let's let's look. We start out
+and we say what's car of con of 37 and
+
+ align:start position:0%
+and we say what's car of con of 37 and
+ 
+
+ align:start position:0%
+and we say what's car of con of 37 and
+49.
+
+ align:start position:0%
+49.
+ 
+
+ align:start position:0%
+49.
+What do we do? Conce is some procedure.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Its value is cons was a procedure of a
+
+ align:start position:0%
+Its value is cons was a procedure of a
+ 
+
+ align:start position:0%
+Its value is cons was a procedure of a
+and b. The thing returned by k is its
+
+ align:start position:0%
+and b. The thing returned by k is its
+ 
+
+ align:start position:0%
+and b. The thing returned by k is its
+procedure body with 37 sub and 49
+
+ align:start position:0%
+procedure body with 37 sub and 49
+ 
+
+ align:start position:0%
+procedure body with 37 sub and 49
+substituted for the parameters. namely
+
+ align:start position:0%
+substituted for the parameters. namely
+ 
+
+ align:start position:0%
+substituted for the parameters. namely
+37 substituted for a and 49 substituted
+
+ align:start position:0%
+37 substituted for a and 49 substituted
+ 
+
+ align:start position:0%
+37 substituted for a and 49 substituted
+for b.
+
+ align:start position:0%
+for b.
+ 
+
+ align:start position:0%
+for b.
+So this expression has the same meaning
+
+ align:start position:0%
+So this expression has the same meaning
+ 
+
+ align:start position:0%
+So this expression has the same meaning
+as this expression. And it's car of and
+
+ align:start position:0%
+as this expression. And it's car of and
+ 
+
+ align:start position:0%
+as this expression. And it's car of and
+the body of const was this thing that
+
+ align:start position:0%
+the body of const was this thing that
+ 
+
+ align:start position:0%
+the body of const was this thing that
+started with lambda
+
+ align:start position:0%
+started with lambda
+ 
+
+ align:start position:0%
+started with lambda
+and says so if p is equal to one where p
+
+ align:start position:0%
+and says so if p is equal to one where p
+ 
+
+ align:start position:0%
+and says so if p is equal to one where p
+is this other argument if p is equal to
+
+ align:start position:0%
+is this other argument if p is equal to
+ 
+
+ align:start position:0%
+is this other argument if p is equal to
+1 it's 37 that's where a was and if p is
+
+ align:start position:0%
+1 it's 37 that's where a was and if p is
+ 
+
+ align:start position:0%
+1 it's 37 that's where a was and if p is
+equal to two it's 49
+
+ align:start position:0%
+equal to two it's 49
+ 
+
+ align:start position:0%
+equal to two it's 49
+right so that's the first step and I'm
+
+ align:start position:0%
+right so that's the first step and I'm
+ 
+
+ align:start position:0%
+right so that's the first step and I'm
+just going through mechanical
+
+ align:start position:0%
+just going through mechanical
+ 
+
+ align:start position:0%
+just going through mechanical
+substitution and remember at this point
+
+ align:start position:0%
+substitution and remember at this point
+ 
+
+ align:start position:0%
+substitution and remember at this point
+in the course if you're confused about
+
+ align:start position:0%
+in the course if you're confused about
+ 
+
+ align:start position:0%
+in the course if you're confused about
+what things mean go mechanically through
+
+ align:start position:0%
+what things mean go mechanically through
+ 
+
+ align:start position:0%
+what things mean go mechanically through
+the substitution model. Well, what does
+
+ align:start position:0%
+the substitution model. Well, what does
+ 
+
+ align:start position:0%
+the substitution model. Well, what does
+this reduced to?
+
+ align:start position:0%
+this reduced to?
+ 
+
+ align:start position:0%
+this reduced to?
+Carr said take your
+
+ align:start position:0%
+Carr said take your
+ 
+
+ align:start position:0%
+Carr said take your
+take your argument which in this case is
+
+ align:start position:0%
+take your argument which in this case is
+ 
+
+ align:start position:0%
+take your argument which in this case is
+this and apply it to one. That was the
+
+ align:start position:0%
+this and apply it to one. That was the
+ 
+
+ align:start position:0%
+this and apply it to one. That was the
+definition of car. So if I look at car
+
+ align:start position:0%
+definition of car. So if I look at car
+ 
+
+ align:start position:0%
+definition of car. So if I look at car
+if I do that the answer is well it's
+
+ align:start position:0%
+if I do that the answer is well it's
+ 
+
+ align:start position:0%
+if I do that the answer is well it's
+that argument. This was the argument to
+
+ align:start position:0%
+that argument. This was the argument to
+ 
+
+ align:start position:0%
+that argument. This was the argument to
+car applied to one.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Well what does that mean? I take one and
+
+ align:start position:0%
+Well what does that mean? I take one and
+ 
+
+ align:start position:0%
+Well what does that mean? I take one and
+I substitute it in the body here for
+
+ align:start position:0%
+I substitute it in the body here for
+ 
+
+ align:start position:0%
+I substitute it in the body here for
+this value of pick which is the name of
+
+ align:start position:0%
+this value of pick which is the name of
+ 
+
+ align:start position:0%
+this value of pick which is the name of
+the argument and what do I get? Well, I
+
+ align:start position:0%
+the argument and what do I get? Well, I
+ 
+
+ align:start position:0%
+the argument and what do I get? Well, I
+get the thing that says if one equals to
+
+ align:start position:0%
+get the thing that says if one equals to
+ 
+
+ align:start position:0%
+get the thing that says if one equals to
+equals 1, it's 37 and if one equals 2,
+
+ align:start position:0%
+equals 1, it's 37 and if one equals 2,
+ 
+
+ align:start position:0%
+equals 1, it's 37 and if one equals 2,
+it's 49. So the answer is 37. And
+
+ align:start position:0%
+it's 49. So the answer is 37. And
+ 
+
+ align:start position:0%
+it's 49. So the answer is 37. And
+similarly, if I'd applied it if I'd
+
+ align:start position:0%
+similarly, if I'd applied it if I'd
+ 
+
+ align:start position:0%
+similarly, if I'd applied it if I'd
+taken cter that would apply it to two
+
+ align:start position:0%
+taken cter that would apply it to two
+ 
+
+ align:start position:0%
+taken cter that would apply it to two
+and I'd get 49. So you see what I've
+
+ align:start position:0%
+and I'd get 49. So you see what I've
+ 
+
+ align:start position:0%
+and I'd get 49. So you see what I've
+demonstrated is that that completely
+
+ align:start position:0%
+demonstrated is that that completely
+ 
+
+ align:start position:0%
+demonstrated is that that completely
+weird implementation of K's current
+
+ align:start position:0%
+weird implementation of K's current
+ 
+
+ align:start position:0%
+weird implementation of K's current
+satisfies the axioms. So it's a
+
+ align:start position:0%
+satisfies the axioms. So it's a
+ 
+
+ align:start position:0%
+satisfies the axioms. So it's a
+perfectly valid way of building in fact
+
+ align:start position:0%
+perfectly valid way of building in fact
+ 
+
+ align:start position:0%
+perfectly valid way of building in fact
+all of the data objects we're going to
+
+ align:start position:0%
+all of the data objects we're going to
+ 
+
+ align:start position:0%
+all of the data objects we're going to
+see in lisp. So they all if you like can
+
+ align:start position:0%
+see in lisp. So they all if you like can
+ 
+
+ align:start position:0%
+see in lisp. So they all if you like can
+be built on on sort of existential
+
+ align:start position:0%
+be built on on sort of existential
+ 
+
+ align:start position:0%
+be built on on sort of existential
+nothing and as far as you know that's
+
+ align:start position:0%
+nothing and as far as you know that's
+ 
+
+ align:start position:0%
+nothing and as far as you know that's
+how it works.
+
+ align:start position:0%
+how it works.
+ 
+
+ align:start position:0%
+how it works.
+You couldn't tell if all you're ever
+
+ align:start position:0%
+You couldn't tell if all you're ever
+ 
+
+ align:start position:0%
+You couldn't tell if all you're ever
+going to do with pairs is construct them
+
+ align:start position:0%
+going to do with pairs is construct them
+ 
+
+ align:start position:0%
+going to do with pairs is construct them
+with consonant look at them with car and
+
+ align:start position:0%
+with consonant look at them with car and
+ 
+
+ align:start position:0%
+with consonant look at them with car and
+curter. You couldn't possibly tell how
+
+ align:start position:0%
+curter. You couldn't possibly tell how
+ 
+
+ align:start position:0%
+curter. You couldn't possibly tell how
+this thing works.
+
+ align:start position:0%
+this thing works.
+ 
+
+ align:start position:0%
+this thing works.
+Now it might give you a sort of warm
+
+ align:start position:0%
+Now it might give you a sort of warm
+ 
+
+ align:start position:0%
+Now it might give you a sort of warm
+feeling inside if I say well yeah in
+
+ align:start position:0%
+feeling inside if I say well yeah in
+ 
+
+ align:start position:0%
+feeling inside if I say well yeah in
+fact for various reasons there happens
+
+ align:start position:0%
+fact for various reasons there happens
+ 
+
+ align:start position:0%
+fact for various reasons there happens
+to be a primitive called conscar and
+
+ align:start position:0%
+to be a primitive called conscar and
+ 
+
+ align:start position:0%
+to be a primitive called conscar and
+citterter and you know if it's too scary
+
+ align:start position:0%
+citterter and you know if it's too scary
+ 
+
+ align:start position:0%
+citterter and you know if it's too scary
+if this kind of stuff is too scary you
+
+ align:start position:0%
+if this kind of stuff is too scary you
+ 
+
+ align:start position:0%
+if this kind of stuff is too scary you
+don't have to look inside of it so that
+
+ align:start position:0%
+don't have to look inside of it so that
+ 
+
+ align:start position:0%
+don't have to look inside of it so that
+might make you feel better but the point
+
+ align:start position:0%
+might make you feel better but the point
+ 
+
+ align:start position:0%
+might make you feel better but the point
+is it it really could work this way and
+
+ align:start position:0%
+is it it really could work this way and
+ 
+
+ align:start position:0%
+is it it really could work this way and
+it wouldn't make any difference to the
+
+ align:start position:0%
+it wouldn't make any difference to the
+ 
+
+ align:start position:0%
+it wouldn't make any difference to the
+system at all
+
+ align:start position:0%
+system at all
+ 
+
+ align:start position:0%
+system at all
+so in some sense we don't need data at
+
+ align:start position:0%
+so in some sense we don't need data at
+ 
+
+ align:start position:0%
+so in some sense we don't need data at
+all to build these data abstractions
+
+ align:start position:0%
+all to build these data abstractions
+ 
+
+ align:start position:0%
+all to build these data abstractions
+because we can do everything in terms of
+
+ align:start position:0%
+because we can do everything in terms of
+ 
+
+ align:start position:0%
+because we can do everything in terms of
+procedures
+
+ align:start position:0%
+procedures
+ 
+
+ align:start position:0%
+procedures
+Okay. Well, why did I terrify you in
+
+ align:start position:0%
+Okay. Well, why did I terrify you in
+ 
+
+ align:start position:0%
+Okay. Well, why did I terrify you in
+this way? First, I really want to
+
+ align:start position:0%
+this way? First, I really want to
+ 
+
+ align:start position:0%
+this way? First, I really want to
+reinforce this idea of abstraction
+
+ align:start position:0%
+reinforce this idea of abstraction
+ 
+
+ align:start position:0%
+reinforce this idea of abstraction
+that you really can do these things
+
+ align:start position:0%
+that you really can do these things
+ 
+
+ align:start position:0%
+that you really can do these things
+abstractly.
+
+ align:start position:0%
+abstractly.
+ 
+
+ align:start position:0%
+abstractly.
+Secondly, I want to introduce
+
+ align:start position:0%
+Secondly, I want to introduce
+ 
+
+ align:start position:0%
+Secondly, I want to introduce
+an idea we're going to see more and more
+
+ align:start position:0%
+an idea we're going to see more and more
+ 
+
+ align:start position:0%
+an idea we're going to see more and more
+of in this course,
+
+ align:start position:0%
+of in this course,
+ 
+
+ align:start position:0%
+of in this course,
+which is we're going to blur the line
+
+ align:start position:0%
+which is we're going to blur the line
+ 
+
+ align:start position:0%
+which is we're going to blur the line
+between what's data and what's a
+
+ align:start position:0%
+between what's data and what's a
+ 
+
+ align:start position:0%
+between what's data and what's a
+procedure.
+
+ align:start position:0%
+procedure.
+ 
+
+ align:start position:0%
+procedure.
+See in this funny implementation it
+
+ align:start position:0%
+See in this funny implementation it
+ 
+
+ align:start position:0%
+See in this funny implementation it
+turned out that that con of something
+
+ align:start position:0%
+turned out that that con of something
+ 
+
+ align:start position:0%
+turned out that that con of something
+happened to be represented in terms of a
+
+ align:start position:0%
+happened to be represented in terms of a
+ 
+
+ align:start position:0%
+happened to be represented in terms of a
+procedure even though we think of it as
+
+ align:start position:0%
+procedure even though we think of it as
+ 
+
+ align:start position:0%
+procedure even though we think of it as
+data.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Well here that's sort of a mathematical
+
+ align:start position:0%
+Well here that's sort of a mathematical
+ 
+
+ align:start position:0%
+Well here that's sort of a mathematical
+trick. But one of the things we'll see
+
+ align:start position:0%
+trick. But one of the things we'll see
+ 
+
+ align:start position:0%
+trick. But one of the things we'll see
+is that a lot of the very important
+
+ align:start position:0%
+is that a lot of the very important
+ 
+
+ align:start position:0%
+is that a lot of the very important
+programming techniques that we're going
+
+ align:start position:0%
+programming techniques that we're going
+ 
+
+ align:start position:0%
+programming techniques that we're going
+to get to refer sort of depend very
+
+ align:start position:0%
+to get to refer sort of depend very
+ 
+
+ align:start position:0%
+to get to refer sort of depend very
+crucially on blurring this this
+
+ align:start position:0%
+crucially on blurring this this
+ 
+
+ align:start position:0%
+crucially on blurring this this
+traditional line between what you
+
+ align:start position:0%
+traditional line between what you
+ 
+
+ align:start position:0%
+traditional line between what you
+consider a procedure and what you
+
+ align:start position:0%
+consider a procedure and what you
+ 
+
+ align:start position:0%
+consider a procedure and what you
+consider data. We're going to see more
+
+ align:start position:0%
+consider data. We're going to see more
+ 
+
+ align:start position:0%
+consider data. We're going to see more
+and more of that especially next time.
+
+ align:start position:0%
+and more of that especially next time.
+ 
+
+ align:start position:0%
+and more of that especially next time.
+Okay, questions.
+
+ align:start position:0%
+Okay, questions.
+ 
+
+ align:start position:0%
+Okay, questions.
+If
+
+ align:start position:0%
+If
+ 
+
+ align:start position:0%
+If
+you asked uh the system to print a what
+
+ align:start position:0%
+you asked uh the system to print a what
+ 
+
+ align:start position:0%
+you asked uh the system to print a what
+would be the result? Uh the question is
+
+ align:start position:0%
+would be the result? Uh the question is
+ 
+
+ align:start position:0%
+would be the result? Uh the question is
+what?
+
+ align:start position:0%
+what?
+ 
+
+ align:start position:0%
+what?
+The question is what would happen if I
+
+ align:start position:0%
+The question is what would happen if I
+ 
+
+ align:start position:0%
+The question is what would happen if I
+asked the system to print a given this
+
+ align:start position:0%
+asked the system to print a given this
+ 
+
+ align:start position:0%
+asked the system to print a given this
+representation? You already know the
+
+ align:start position:0%
+representation? You already know the
+ 
+
+ align:start position:0%
+representation? You already know the
+answer.
+
+ align:start position:0%
+answer.
+ 
+
+ align:start position:0%
+answer.
+Right? The answer is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+compound procedure A. Just like last
+
+ align:start position:0%
+compound procedure A. Just like last
+ 
+
+ align:start position:0%
+compound procedure A. Just like last
+time
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+we say compound procedure
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+might say a little bit more. I might say
+
+ align:start position:0%
+might say a little bit more. I might say
+ 
+
+ align:start position:0%
+might say a little bit more. I might say
+compound procedure lambda something or
+
+ align:start position:0%
+compound procedure lambda something or
+ 
+
+ align:start position:0%
+compound procedure lambda something or
+other depending on details of how I
+
+ align:start position:0%
+other depending on details of how I
+ 
+
+ align:start position:0%
+other depending on details of how I
+named it but it's a procedure and the
+
+ align:start position:0%
+named it but it's a procedure and the
+ 
+
+ align:start position:0%
+named it but it's a procedure and the
+only reason for that is I haven't told
+
+ align:start position:0%
+only reason for that is I haven't told
+ 
+
+ align:start position:0%
+only reason for that is I haven't told
+the system anything special about how to
+
+ align:start position:0%
+the system anything special about how to
+ 
+
+ align:start position:0%
+the system anything special about how to
+print such things now it's in fact true
+
+ align:start position:0%
+print such things now it's in fact true
+ 
+
+ align:start position:0%
+print such things now it's in fact true
+that with the actual implementation of
+
+ align:start position:0%
+that with the actual implementation of
+ 
+
+ align:start position:0%
+that with the actual implementation of
+con that happens to be built in the
+
+ align:start position:0%
+con that happens to be built in the
+ 
+
+ align:start position:0%
+con that happens to be built in the
+system it would print something else it
+
+ align:start position:0%
+system it would print something else it
+ 
+
+ align:start position:0%
+system it would print something else it
+would print say this is a pair
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um when you define cons
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+And then you pass it in two values.
+
+ align:start position:0%
+And then you pass it in two values.
+ 
+
+ align:start position:0%
+And then you pass it in two values.
+How does it know where to look for the
+
+ align:start position:0%
+How does it know where to look for the
+ 
+
+ align:start position:0%
+How does it know where to look for the
+cons? Because you can use cons over and
+
+ align:start position:0%
+cons? Because you can use cons over and
+ 
+
+ align:start position:0%
+cons? Because you can use cons over and
+over again. So how does it know where to
+
+ align:start position:0%
+over again. So how does it know where to
+ 
+
+ align:start position:0%
+over again. So how does it know where to
+look to know which A and B it's supposed
+
+ align:start position:0%
+look to know which A and B it's supposed
+ 
+
+ align:start position:0%
+look to know which A and B it's supposed
+to pull back out. I don't know if that
+
+ align:start position:0%
+to pull back out. I don't know if that
+ 
+
+ align:start position:0%
+to pull back out. I don't know if that
+expressing that quite right.
+
+ align:start position:0%
+expressing that quite right.
+ 
+
+ align:start position:0%
+expressing that quite right.
+Okay. The question is
+
+ align:start position:0%
+Okay. The question is
+ 
+
+ align:start position:0%
+Okay. The question is
+where is it stored?
+
+ align:start position:0%
+where is it stored?
+ 
+
+ align:start position:0%
+where is it stored?
+Okay. The question is
+
+ align:start position:0%
+Okay. The question is
+ 
+
+ align:start position:0%
+Okay. The question is
+I sort of have a conce with a with a 37
+
+ align:start position:0%
+I sort of have a conce with a with a 37
+ 
+
+ align:start position:0%
+I sort of have a conce with a with a 37
+and a 49 and I might make another con
+
+ align:start position:0%
+and a 49 and I might make another con
+ 
+
+ align:start position:0%
+and a 49 and I might make another con
+with a one and a two and I might have
+
+ align:start position:0%
+with a one and a two and I might have
+ 
+
+ align:start position:0%
+with a one and a two and I might have
+one called A and might have one called B
+
+ align:start position:0%
+one called A and might have one called B
+ 
+
+ align:start position:0%
+one called A and might have one called B
+and the question is how does it know and
+
+ align:start position:0%
+and the question is how does it know and
+ 
+
+ align:start position:0%
+and the question is how does it know and
+why don't they get confused and that's a
+
+ align:start position:0%
+why don't they get confused and that's a
+ 
+
+ align:start position:0%
+why don't they get confused and that's a
+very that's a very good question.
+
+ align:start position:0%
+very that's a very good question.
+ 
+
+ align:start position:0%
+very that's a very good question.
+What it see you have to really believe
+
+ align:start position:0%
+What it see you have to really believe
+ 
+
+ align:start position:0%
+What it see you have to really believe
+that the procedures are objects.
+
+ align:start position:0%
+that the procedures are objects.
+ 
+
+ align:start position:0%
+that the procedures are objects.
+See it's sort of it's sort of like
+
+ align:start position:0%
+See it's sort of it's sort of like
+ 
+
+ align:start position:0%
+See it's sort of it's sort of like
+saying let's try another simpler
+
+ align:start position:0%
+saying let's try another simpler
+ 
+
+ align:start position:0%
+saying let's try another simpler
+example.
+
+ align:start position:0%
+example.
+ 
+
+ align:start position:0%
+example.
+Suppose I ask for the square root of
+
+ align:start position:0%
+Suppose I ask for the square root of
+ 
+
+ align:start position:0%
+Suppose I ask for the square root of
+three.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+So I ask for the square root of five and
+
+ align:start position:0%
+So I ask for the square root of five and
+ 
+
+ align:start position:0%
+So I ask for the square root of five and
+then I ask for the square root
+
+ align:start position:0%
+then I ask for the square root
+ 
+
+ align:start position:0%
+then I ask for the square root
+of 20.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+You're probably not the least bit
+
+ align:start position:0%
+You're probably not the least bit
+ 
+
+ align:start position:0%
+You're probably not the least bit
+bothered like I that I can take square
+
+ align:start position:0%
+bothered like I that I can take square
+ 
+
+ align:start position:0%
+bothered like I that I can take square
+root and apply it to five and then I can
+
+ align:start position:0%
+root and apply it to five and then I can
+ 
+
+ align:start position:0%
+root and apply it to five and then I can
+take square root and apply it to 20
+
+ align:start position:0%
+take square root and apply it to 20
+ 
+
+ align:start position:0%
+take square root and apply it to 20
+and there's sort of no issue. Doesn't it
+
+ align:start position:0%
+and there's sort of no issue. Doesn't it
+ 
+
+ align:start position:0%
+and there's sort of no issue. Doesn't it
+get confused about whether it's working
+
+ align:start position:0%
+get confused about whether it's working
+ 
+
+ align:start position:0%
+get confused about whether it's working
+on five or 20? There's no issue about
+
+ align:start position:0%
+on five or 20? There's no issue about
+ 
+
+ align:start position:0%
+on five or 20? There's no issue about
+that because you're thinking of a
+
+ align:start position:0%
+that because you're thinking of a
+ 
+
+ align:start position:0%
+that because you're thinking of a
+procedure which goes off and and does
+
+ align:start position:0%
+procedure which goes off and and does
+ 
+
+ align:start position:0%
+procedure which goes off and and does
+something.
+
+ align:start position:0%
+something.
+ 
+
+ align:start position:0%
+something.
+Now, in some sense, you're asking me the
+
+ align:start position:0%
+Now, in some sense, you're asking me the
+ 
+
+ align:start position:0%
+Now, in some sense, you're asking me the
+same question,
+
+ align:start position:0%
+same question,
+ 
+
+ align:start position:0%
+same question,
+but it's really bothering you and it's
+
+ align:start position:0%
+but it's really bothering you and it's
+ 
+
+ align:start position:0%
+but it's really bothering you and it's
+bothering you for a really good reason
+
+ align:start position:0%
+bothering you for a really good reason
+ 
+
+ align:start position:0%
+bothering you for a really good reason
+because when I write that you're saying,
+
+ align:start position:0%
+because when I write that you're saying,
+ 
+
+ align:start position:0%
+because when I write that you're saying,
+gee, this is I know sort of a procedure,
+
+ align:start position:0%
+gee, this is I know sort of a procedure,
+ 
+
+ align:start position:0%
+gee, this is I know sort of a procedure,
+but it's not a procedure that's just
+
+ align:start position:0%
+but it's not a procedure that's just
+ 
+
+ align:start position:0%
+but it's not a procedure that's just
+running. It's just sort of a procedure
+
+ align:start position:0%
+running. It's just sort of a procedure
+ 
+
+ align:start position:0%
+running. It's just sort of a procedure
+sitting there. And how can it be that
+
+ align:start position:0%
+sitting there. And how can it be that
+ 
+
+ align:start position:0%
+sitting there. And how can it be that
+sometimes this procedure has 37 and 49
+
+ align:start position:0%
+sometimes this procedure has 37 and 49
+ 
+
+ align:start position:0%
+sometimes this procedure has 37 and 49
+and there might be another one which has
+
+ align:start position:0%
+and there might be another one which has
+ 
+
+ align:start position:0%
+and there might be another one which has
+uh five and six in there and why don't
+
+ align:start position:0%
+uh five and six in there and why don't
+ 
+
+ align:start position:0%
+uh five and six in there and why don't
+they get confused?
+
+ align:start position:0%
+they get confused?
+ 
+
+ align:start position:0%
+they get confused?
+See, so you're really there's something
+
+ align:start position:0%
+See, so you're really there's something
+ 
+
+ align:start position:0%
+See, so you're really there's something
+very very important that's bothering you
+
+ align:start position:0%
+very very important that's bothering you
+ 
+
+ align:start position:0%
+very very important that's bothering you
+and it's really crucial to what's going
+
+ align:start position:0%
+and it's really crucial to what's going
+ 
+
+ align:start position:0%
+and it's really crucial to what's going
+on. It's we're suddenly saying that
+
+ align:start position:0%
+on. It's we're suddenly saying that
+ 
+
+ align:start position:0%
+on. It's we're suddenly saying that
+procedures are not just
+
+ align:start position:0%
+procedures are not just
+ 
+
+ align:start position:0%
+procedures are not just
+the act of doing something.
+
+ align:start position:0%
+the act of doing something.
+ 
+
+ align:start position:0%
+the act of doing something.
+Procedures are conceptual entities,
+
+ align:start position:0%
+Procedures are conceptual entities,
+ 
+
+ align:start position:0%
+Procedures are conceptual entities,
+objects. And if I build and if I build
+
+ align:start position:0%
+objects. And if I build and if I build
+ 
+
+ align:start position:0%
+objects. And if I build and if I build
+cons of 37 and 49 that's a particular
+
+ align:start position:0%
+cons of 37 and 49 that's a particular
+ 
+
+ align:start position:0%
+cons of 37 and 49 that's a particular
+procedure that sits there
+
+ align:start position:0%
+procedure that sits there
+ 
+
+ align:start position:0%
+procedure that sits there
+and it's different from car
+
+ align:start position:0%
+and it's different from car
+ 
+
+ align:start position:0%
+and it's different from car
+and it's different from cons of three
+
+ align:start position:0%
+and it's different from cons of three
+ 
+
+ align:start position:0%
+and it's different from cons of three
+and four that's another procedure that
+
+ align:start position:0%
+and four that's another procedure that
+ 
+
+ align:start position:0%
+and four that's another procedure that
+sits there
+
+ align:start position:0%
+sits there
+ 
+
+ align:start position:0%
+sits there
+exists independently
+
+ align:start position:0%
+exists independently
+ 
+
+ align:start position:0%
+exists independently
+and exists independently
+
+ align:start position:0%
+and exists independently
+ 
+
+ align:start position:0%
+and exists independently
+and they both can be referenced by car
+
+ align:start position:0%
+and they both can be referenced by car
+ 
+
+ align:start position:0%
+and they both can be referenced by car
+and cter
+
+ align:start position:0%
+and cter
+ 
+
+ align:start position:0%
+and cter
+and they both would be referenced by car
+
+ align:start position:0%
+and they both would be referenced by car
+ 
+
+ align:start position:0%
+and they both would be referenced by car
+and cuddter just like I could you know
+
+ align:start position:0%
+and cuddter just like I could you know
+ 
+
+ align:start position:0%
+and cuddter just like I could you know
+just like I could increment this and I
+
+ align:start position:0%
+just like I could increment this and I
+ 
+
+ align:start position:0%
+just like I could increment this and I
+could increment increment that they're
+
+ align:start position:0%
+could increment increment that they're
+ 
+
+ align:start position:0%
+could increment increment that they're
+objects and that's that's sort of where
+
+ align:start position:0%
+objects and that's that's sort of where
+ 
+
+ align:start position:0%
+objects and that's that's sort of where
+we're going. See, the fact that you're
+
+ align:start position:0%
+we're going. See, the fact that you're
+ 
+
+ align:start position:0%
+we're going. See, the fact that you're
+asking the question shows that you're
+
+ align:start position:0%
+asking the question shows that you're
+ 
+
+ align:start position:0%
+asking the question shows that you're
+really starting to think about the
+
+ align:start position:0%
+really starting to think about the
+ 
+
+ align:start position:0%
+really starting to think about the
+implications of of what's going on. It's
+
+ align:start position:0%
+implications of of what's going on. It's
+ 
+
+ align:start position:0%
+implications of of what's going on. It's
+the difference between saying a
+
+ align:start position:0%
+the difference between saying a
+ 
+
+ align:start position:0%
+the difference between saying a
+procedure is just the act of doing
+
+ align:start position:0%
+procedure is just the act of doing
+ 
+
+ align:start position:0%
+procedure is just the act of doing
+something and a procedure is a real
+
+ align:start position:0%
+something and a procedure is a real
+ 
+
+ align:start position:0%
+something and a procedure is a real
+object that has existence.
+
+ align:start position:0%
+object that has existence.
+ 
+
+ align:start position:0%
+object that has existence.
+So when the procedure gets built, the
+
+ align:start position:0%
+So when the procedure gets built, the
+ 
+
+ align:start position:0%
+So when the procedure gets built, the
+actual values are now substituted for A
+
+ align:start position:0%
+actual values are now substituted for A
+ 
+
+ align:start position:0%
+actual values are now substituted for A
+and B and that procedure exists as a
+
+ align:start position:0%
+and B and that procedure exists as a
+ 
+
+ align:start position:0%
+and B and that procedure exists as a
+lambda and is what's actually passed in.
+
+ align:start position:0%
+lambda and is what's actually passed in.
+ 
+
+ align:start position:0%
+lambda and is what's actually passed in.
+Yes. when when cons gets called and the
+
+ align:start position:0%
+Yes. when when cons gets called and the
+ 
+
+ align:start position:0%
+Yes. when when cons gets called and the
+result of cons is a new procedure that's
+
+ align:start position:0%
+result of cons is a new procedure that's
+ 
+
+ align:start position:0%
+result of cons is a new procedure that's
+constructed that new procedure has an
+
+ align:start position:0%
+constructed that new procedure has an
+ 
+
+ align:start position:0%
+constructed that new procedure has an
+argument that's called pick
+
+ align:start position:0%
+argument that's called pick
+ 
+
+ align:start position:0%
+argument that's called pick
+but it no longer has an A and B the A
+
+ align:start position:0%
+but it no longer has an A and B the A
+ 
+
+ align:start position:0%
+but it no longer has an A and B the A
+and B are the actual values that were
+
+ align:start position:0%
+and B are the actual values that were
+ 
+
+ align:start position:0%
+and B are the actual values that were
+passed
+
+ align:start position:0%
+passed
+ 
+
+ align:start position:0%
+passed
+and it has right according to the
+
+ align:start position:0%
+and it has right according to the
+ 
+
+ align:start position:0%
+and it has right according to the
+substitution model what it now has is
+
+ align:start position:0%
+substitution model what it now has is
+ 
+
+ align:start position:0%
+substitution model what it now has is
+not those arbitrary names A and B it
+
+ align:start position:0%
+not those arbitrary names A and B it
+ 
+
+ align:start position:0%
+not those arbitrary names A and B it
+somehow has that 37 and 49 in there
+
+ align:start position:0%
+somehow has that 37 and 49 in there
+ 
+
+ align:start position:0%
+somehow has that 37 and 49 in there
+but you're right that's a hard thing to
+
+ align:start position:0%
+but you're right that's a hard thing to
+ 
+
+ align:start position:0%
+but you're right that's a hard thing to
+think about and it's different from the
+
+ align:start position:0%
+think about and it's different from the
+ 
+
+ align:start position:0%
+think about and it's different from the
+way you've been thinking about
+
+ align:start position:0%
+way you've been thinking about
+ 
+
+ align:start position:0%
+way you've been thinking about
+procedures
+
+ align:start position:0%
+procedures
+ 
+
+ align:start position:0%
+procedures
+and if I have again con of 37 and 49
+
+ align:start position:0%
+and if I have again con of 37 and 49
+ 
+
+ align:start position:0%
+and if I have again con of 37 and 49
+it's a different option
+
+ align:start position:0%
+it's a different option
+ 
+
+ align:start position:0%
+it's a different option
+and if you make
+
+ align:start position:0%
+and if you make
+ 
+
+ align:start position:0%
+and if you make
+and if you
+
+ align:start position:0%
+and if you
+ 
+
+ align:start position:0%
+and if you
+make another con of 37 and 49
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+you're into a wonderful philosophical
+
+ align:start position:0%
+you're into a wonderful philosophical
+ 
+
+ align:start position:0%
+you're into a wonderful philosophical
+problem which is going to be what the
+
+ align:start position:0%
+problem which is going to be what the
+ 
+
+ align:start position:0%
+problem which is going to be what the
+lecture about halfway through this
+
+ align:start position:0%
+lecture about halfway through this
+ 
+
+ align:start position:0%
+lecture about halfway through this
+course is about
+
+ align:start position:0%
+course is about
+ 
+
+ align:start position:0%
+course is about
+which is if I con 37 and 49 and I do it
+
+ align:start position:0%
+which is if I con 37 and 49 and I do it
+ 
+
+ align:start position:0%
+which is if I con 37 and 49 and I do it
+again is that the same thing or is it a
+
+ align:start position:0%
+again is that the same thing or is it a
+ 
+
+ align:start position:0%
+again is that the same thing or is it a
+different thing and how could you tell
+
+ align:start position:0%
+different thing and how could you tell
+ 
+
+ align:start position:0%
+different thing and how could you tell
+and when could it possibly matter? And
+
+ align:start position:0%
+and when could it possibly matter? And
+ 
+
+ align:start position:0%
+and when could it possibly matter? And
+that's like saying is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that's sort of like saying is
+
+ align:start position:0%
+that's sort of like saying is
+ 
+
+ align:start position:0%
+that's sort of like saying is
+is that the same thing as as this
+
+ align:start position:0%
+is that the same thing as as this
+ 
+
+ align:start position:0%
+is that the same thing as as this
+or is this the same thing as that? It's
+
+ align:start position:0%
+or is this the same thing as that? It's
+ 
+
+ align:start position:0%
+or is this the same thing as that? It's
+the same kind of question and that's a
+
+ align:start position:0%
+the same kind of question and that's a
+ 
+
+ align:start position:0%
+the same kind of question and that's a
+very that's a very very deep question
+
+ align:start position:0%
+very that's a very very deep question
+ 
+
+ align:start position:0%
+very that's a very very deep question
+and I can't answer it in less than an
+
+ align:start position:0%
+and I can't answer it in less than an
+ 
+
+ align:start position:0%
+and I can't answer it in less than an
+hour but we will
+
+ align:start position:0%
+hour but we will
+ 
+
+ align:start position:0%
+hour but we will
+[Music]
\ No newline at end of file
diff --git a/zI9cSV3QKz0.txt b/zI9cSV3QKz0.txt
new file mode 100644
index 0000000000000000000000000000000000000000..a7ea783ffdeb2e4fcb3384cdd08d78ff4c68372d
--- /dev/null
+++ b/zI9cSV3QKz0.txt
@@ -0,0 +1,7851 @@
+align:start position:0%
+ 
+the following content is provided under
+
+ align:start position:0%
+the following content is provided under
+ 
+
+ align:start position:0%
+the following content is provided under
+a Creative Commons license your support
+
+ align:start position:0%
+a Creative Commons license your support
+ 
+
+ align:start position:0%
+a Creative Commons license your support
+will help MIT open courseware continue
+
+ align:start position:0%
+will help MIT open courseware continue
+ 
+
+ align:start position:0%
+will help MIT open courseware continue
+to offer highquality educational
+
+ align:start position:0%
+to offer highquality educational
+ 
+
+ align:start position:0%
+to offer highquality educational
+resources for free to make a donation or
+
+ align:start position:0%
+resources for free to make a donation or
+ 
+
+ align:start position:0%
+resources for free to make a donation or
+to view additional materials from
+
+ align:start position:0%
+to view additional materials from
+ 
+
+ align:start position:0%
+to view additional materials from
+hundreds of MIT courses visit MIT open
+
+ align:start position:0%
+hundreds of MIT courses visit MIT open
+ 
+
+ align:start position:0%
+hundreds of MIT courses visit MIT open
+courseware at ocw.mit.edu
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so I'm ready for anything as as or hope
+
+ align:start position:0%
+so I'm ready for anything as as or hope
+ 
+
+ align:start position:0%
+so I'm ready for anything as as or hope
+I am uh questions about any topics yes
+
+ align:start position:0%
+I am uh questions about any topics yes
+ 
+
+ align:start position:0%
+I am uh questions about any topics yes
+okay so I feel there's is like a White
+
+ align:start position:0%
+okay so I feel there's is like a White
+ 
+
+ align:start position:0%
+okay so I feel there's is like a White
+House Press Conference I think there's
+
+ align:start position:0%
+House Press Conference I think there's
+ 
+
+ align:start position:0%
+House Press Conference I think there's
+always somebody in the front row who who
+
+ align:start position:0%
+always somebody in the front row who who
+ 
+
+ align:start position:0%
+always somebody in the front row who who
+who who gets to ask the first question
+
+ align:start position:0%
+who who gets to ask the first question
+ 
+
+ align:start position:0%
+who who gets to ask the first question
+and then gets to say Thank you Mr
+
+ align:start position:0%
+and then gets to say Thank you Mr
+ 
+
+ align:start position:0%
+and then gets to say Thank you Mr
+President at the end and then I'm off uh
+
+ align:start position:0%
+President at the end and then I'm off uh
+ 
+
+ align:start position:0%
+President at the end and then I'm off uh
+but I don't
+
+ align:start position:0%
+but I don't
+ 
+
+ align:start position:0%
+but I don't
+yes
+
+ align:start position:0%
+yes
+ 
+
+ align:start position:0%
+yes
+yeah this has I'm tempted by the way to
+
+ align:start position:0%
+yeah this has I'm tempted by the way to
+ 
+
+ align:start position:0%
+yeah this has I'm tempted by the way to
+ask you all are you going to vote next
+
+ align:start position:0%
+ask you all are you going to vote next
+ 
+
+ align:start position:0%
+ask you all are you going to vote next
+Tuesday and of course I'd like to know
+
+ align:start position:0%
+Tuesday and of course I'd like to know
+ 
+
+ align:start position:0%
+Tuesday and of course I'd like to know
+who you vote for and I'd like to give
+
+ align:start position:0%
+who you vote for and I'd like to give
+ 
+
+ align:start position:0%
+who you vote for and I'd like to give
+you my advice but uh I don't know that
+
+ align:start position:0%
+you my advice but uh I don't know that
+ 
+
+ align:start position:0%
+you my advice but uh I don't know that
+that's proper if anybody wants advice
+
+ align:start position:0%
+that's proper if anybody wants advice
+ 
+
+ align:start position:0%
+that's proper if anybody wants advice
+they can email but but please vote
+
+ align:start position:0%
+they can email but but please vote
+ 
+
+ align:start position:0%
+they can email but but please vote
+please vote yeah yeah all right question
+
+ align:start position:0%
+please vote yeah yeah all right question
+ 
+
+ align:start position:0%
+please vote yeah yeah all right question
+here and then we'll have
+
+ align:start position:0%
+here and then we'll have
+ 
+
+ align:start position:0%
+here and then we'll have
+yeah um so I looked online and I started
+
+ align:start position:0%
+yeah um so I looked online and I started
+ 
+
+ align:start position:0%
+yeah um so I looked online and I started
+with
+
+ align:start position:0%
+with
+ 
+
+ align:start position:0%
+with
+number two oh okay so those were just
+
+ align:start position:0%
+number two oh okay so those were just
+ 
+
+ align:start position:0%
+number two oh okay so those were just
+posted like yeah I see okay 3.3 number
+
+ align:start position:0%
+posted like yeah I see okay 3.3 number
+ 
+
+ align:start position:0%
+posted like yeah I see okay 3.3 number
+two it seems like it should be a very
+
+ align:start position:0%
+two it seems like it should be a very
+ 
+
+ align:start position:0%
+two it seems like it should be a very
+straight question not finding aall
+
+ align:start position:0%
+straight question not finding aall
+ 
+
+ align:start position:0%
+straight question not finding aall
+to W I'm finding okay so that this was a
+
+ align:start position:0%
+to W I'm finding okay so that this was a
+ 
+
+ align:start position:0%
+to W I'm finding okay so that this was a
+a case yeah right uh oh okay it could be
+
+ align:start position:0%
+a case yeah right uh oh okay it could be
+ 
+
+ align:start position:0%
+a case yeah right uh oh okay it could be
+wrong so let's just so that's a a so so
+
+ align:start position:0%
+wrong so let's just so that's a a so so
+ 
+
+ align:start position:0%
+wrong so let's just so that's a a so so
+this is 3.3 number two asks you about
+
+ align:start position:0%
+this is 3.3 number two asks you about
+ 
+
+ align:start position:0%
+this is 3.3 number two asks you about
+the uh flow field
+
+ align:start position:0%
+the uh flow field
+ 
+
+ align:start position:0%
+the uh flow field
+uh which is has no flow in the X
+
+ align:start position:0%
+uh which is has no flow in the X
+ 
+
+ align:start position:0%
+uh which is has no flow in the X
+Direction
+
+ align:start position:0%
+Direction
+ 
+
+ align:start position:0%
+Direction
+the Velocity in the X direction is zero
+
+ align:start position:0%
+the Velocity in the X direction is zero
+ 
+
+ align:start position:0%
+the Velocity in the X direction is zero
+the Velocity in the y direction is X
+
+ align:start position:0%
+the Velocity in the y direction is X
+ 
+
+ align:start position:0%
+the Velocity in the y direction is X
+okay so suppose we just take that as a a
+
+ align:start position:0%
+okay so suppose we just take that as a a
+ 
+
+ align:start position:0%
+okay so suppose we just take that as a a
+flow field and try to understand is it a
+
+ align:start position:0%
+flow field and try to understand is it a
+ 
+
+ align:start position:0%
+flow field and try to understand is it a
+gradient I mean so what are the
+
+ align:start position:0%
+gradient I mean so what are the
+ 
+
+ align:start position:0%
+gradient I mean so what are the
+questions I would ask is it a gradient
+
+ align:start position:0%
+questions I would ask is it a gradient
+ 
+
+ align:start position:0%
+questions I would ask is it a gradient
+of anything because as we're we're now
+
+ align:start position:0%
+of anything because as we're we're now
+ 
+
+ align:start position:0%
+of anything because as we're we're now
+thinking V and W are pretty much the
+
+ align:start position:0%
+thinking V and W are pretty much the
+ 
+
+ align:start position:0%
+thinking V and W are pretty much the
+same guy so is it a gradient yes or no
+
+ align:start position:0%
+same guy so is it a gradient yes or no
+ 
+
+ align:start position:0%
+same guy so is it a gradient yes or no
+if so what's the potential is it does is
+
+ align:start position:0%
+if so what's the potential is it does is
+ 
+
+ align:start position:0%
+if so what's the potential is it does is
+it diver free yes or no if it is what's
+
+ align:start position:0%
+it diver free yes or no if it is what's
+ 
+
+ align:start position:0%
+it diver free yes or no if it is what's
+the stream function and of course if it
+
+ align:start position:0%
+the stream function and of course if it
+ 
+
+ align:start position:0%
+the stream function and of course if it
+if the answer to both tests was yes then
+
+ align:start position:0%
+if the answer to both tests was yes then
+ 
+
+ align:start position:0%
+if the answer to both tests was yes then
+we would be talking about lass's
+
+ align:start position:0%
+we would be talking about lass's
+ 
+
+ align:start position:0%
+we would be talking about lass's
+equation I suspect for this example the
+
+ align:start position:0%
+equation I suspect for this example the
+ 
+
+ align:start position:0%
+equation I suspect for this example the
+answers to answer at least to one of the
+
+ align:start position:0%
+answers to answer at least to one of the
+ 
+
+ align:start position:0%
+answers to answer at least to one of the
+two questions will be no so we're not
+
+ align:start position:0%
+two questions will be no so we're not
+ 
+
+ align:start position:0%
+two questions will be no so we're not
+we're not we won't have the two pieces
+
+ align:start position:0%
+we're not we won't have the two pieces
+ 
+
+ align:start position:0%
+we're not we won't have the two pieces
+coming together into La PL okay so first
+
+ align:start position:0%
+coming together into La PL okay so first
+ 
+
+ align:start position:0%
+coming together into La PL okay so first
+of all is it a gradient what's the test
+
+ align:start position:0%
+of all is it a gradient what's the test
+ 
+
+ align:start position:0%
+of all is it a gradient what's the test
+for is this the gradient so is this so
+
+ align:start position:0%
+for is this the gradient so is this so
+ 
+
+ align:start position:0%
+for is this the gradient so is this so
+the my two questions are uh is V the
+
+ align:start position:0%
+the my two questions are uh is V the
+ 
+
+ align:start position:0%
+the my two questions are uh is V the
+gradient of some U
+
+ align:start position:0%
+gradient of some U
+ 
+
+ align:start position:0%
+gradient of some U
+and what's the test for that
+
+ align:start position:0%
+and what's the test for that
+ 
+
+ align:start position:0%
+and what's the test for that
+uh you remember if it is the gradient
+
+ align:start position:0%
+uh you remember if it is the gradient
+ 
+
+ align:start position:0%
+uh you remember if it is the gradient
+see I could remember myself if it is a
+
+ align:start position:0%
+see I could remember myself if it is a
+ 
+
+ align:start position:0%
+see I could remember myself if it is a
+gradient then this is dudx and this is
+
+ align:start position:0%
+gradient then this is dudx and this is
+ 
+
+ align:start position:0%
+gradient then this is dudx and this is
+dudy
+
+ align:start position:0%
+dudy
+ 
+
+ align:start position:0%
+dudy
+and the condition that V1 and V2 would
+
+ align:start position:0%
+and the condition that V1 and V2 would
+ 
+
+ align:start position:0%
+and the condition that V1 and V2 would
+have to satisfy is that the Y derivative
+
+ align:start position:0%
+have to satisfy is that the Y derivative
+ 
+
+ align:start position:0%
+have to satisfy is that the Y derivative
+of that would have to equal the X
+
+ align:start position:0%
+of that would have to equal the X
+ 
+
+ align:start position:0%
+of that would have to equal the X
+derivative of that because on the right
+
+ align:start position:0%
+derivative of that because on the right
+ 
+
+ align:start position:0%
+derivative of that because on the right
+hand side they are the same uxy is the
+
+ align:start position:0%
+hand side they are the same uxy is the
+ 
+
+ align:start position:0%
+hand side they are the same uxy is the
+same as uyx so I would look at at at uh
+
+ align:start position:0%
+same as uyx so I would look at at at uh
+ 
+
+ align:start position:0%
+same as uyx so I would look at at at uh
+so I need so let me write that again I
+
+ align:start position:0%
+so I need so let me write that again I
+ 
+
+ align:start position:0%
+so I need so let me write that again I
+need
+
+ align:start position:0%
+need
+ 
+
+ align:start position:0%
+need
+dv1
+
+ align:start position:0%
+dv1
+ 
+
+ align:start position:0%
+dv1
+Dy
+
+ align:start position:0%
+Dy
+ 
+
+ align:start position:0%
+Dy
+to equal dv2 DX and is that true in this
+
+ align:start position:0%
+to equal dv2 DX and is that true in this
+ 
+
+ align:start position:0%
+to equal dv2 DX and is that true in this
+in this example
+
+ align:start position:0%
+in this example
+ 
+
+ align:start position:0%
+in this example
+what's what's dv1 Dy
+
+ align:start position:0%
+what's what's dv1 Dy
+ 
+
+ align:start position:0%
+what's what's dv1 Dy
+zero what's dv2 DX
+
+ align:start position:0%
+zero what's dv2 DX
+ 
+
+ align:start position:0%
+zero what's dv2 DX
+one so the answer is no okay so test
+
+ align:start position:0%
+one so the answer is no okay so test
+ 
+
+ align:start position:0%
+one so the answer is no okay so test
+failed
+
+ align:start position:0%
+failed
+ 
+
+ align:start position:0%
+failed
+all right the second question is
+
+ align:start position:0%
+all right the second question is
+ 
+
+ align:start position:0%
+all right the second question is
+is it does it possibly play sit over in
+
+ align:start position:0%
+is it does it possibly play sit over in
+ 
+
+ align:start position:0%
+is it does it possibly play sit over in
+the Divergence free world is the
+
+ align:start position:0%
+the Divergence free world is the
+ 
+
+ align:start position:0%
+the Divergence free world is the
+Divergence of and now I'll call it w
+
+ align:start position:0%
+Divergence of and now I'll call it w
+ 
+
+ align:start position:0%
+Divergence of and now I'll call it w
+equals z so I take the so the answer was
+
+ align:start position:0%
+equals z so I take the so the answer was
+ 
+
+ align:start position:0%
+equals z so I take the so the answer was
+no to that question but now I think the
+
+ align:start position:0%
+no to that question but now I think the
+ 
+
+ align:start position:0%
+no to that question but now I think the
+answer to this question will be yes
+
+ align:start position:0%
+answer to this question will be yes
+ 
+
+ align:start position:0%
+answer to this question will be yes
+because the what's the Divergence of
+
+ align:start position:0%
+because the what's the Divergence of
+ 
+
+ align:start position:0%
+because the what's the Divergence of
+this thing the it's the X derivative of
+
+ align:start position:0%
+this thing the it's the X derivative of
+ 
+
+ align:start position:0%
+this thing the it's the X derivative of
+that which is certainly zero plus the Y
+
+ align:start position:0%
+that which is certainly zero plus the Y
+ 
+
+ align:start position:0%
+that which is certainly zero plus the Y
+derivative of that which is certainly
+
+ align:start position:0%
+derivative of that which is certainly
+ 
+
+ align:start position:0%
+derivative of that which is certainly
+zero so the answer is yes so it is so so
+
+ align:start position:0%
+zero so the answer is yes so it is so so
+ 
+
+ align:start position:0%
+zero so the answer is yes so it is so so
+there's no potential but there is a
+
+ align:start position:0%
+there's no potential but there is a
+ 
+
+ align:start position:0%
+there's no potential but there is a
+stream function right because the stream
+
+ align:start position:0%
+stream function right because the stream
+ 
+
+ align:start position:0%
+stream function right because the stream
+function comes in with this test so
+
+ align:start position:0%
+function comes in with this test so
+ 
+
+ align:start position:0%
+function comes in with this test so
+let's remember what just just from
+
+ align:start position:0%
+let's remember what just just from
+ 
+
+ align:start position:0%
+let's remember what just just from
+today's lecture what was the stream
+
+ align:start position:0%
+today's lecture what was the stream
+ 
+
+ align:start position:0%
+today's lecture what was the stream
+function when when the D from dw1 DX
+
+ align:start position:0%
+function when when the D from dw1 DX
+ 
+
+ align:start position:0%
+function when when the D from dw1 DX
+plus dw2 Dy equals z that will be
+
+ align:start position:0%
+plus dw2 Dy equals z that will be
+ 
+
+ align:start position:0%
+plus dw2 Dy equals z that will be
+satisfied if W1 is the Y derivative of
+
+ align:start position:0%
+satisfied if W1 is the Y derivative of
+ 
+
+ align:start position:0%
+satisfied if W1 is the Y derivative of
+the stream function and W2 is minus the
+
+ align:start position:0%
+the stream function and W2 is minus the
+ 
+
+ align:start position:0%
+the stream function and W2 is minus the
+X derivative
+
+ align:start position:0%
+X derivative
+ 
+
+ align:start position:0%
+X derivative
+because if I if then the this matches
+
+ align:start position:0%
+because if I if then the this matches
+ 
+
+ align:start position:0%
+because if I if then the this matches
+the X derivative of this plus the Y
+
+ align:start position:0%
+the X derivative of this plus the Y
+ 
+
+ align:start position:0%
+the X derivative of this plus the Y
+derivative of this which is the
+
+ align:start position:0%
+derivative of this which is the
+ 
+
+ align:start position:0%
+derivative of this which is the
+Divergence on the right hand side I
+
+ align:start position:0%
+Divergence on the right hand side I
+ 
+
+ align:start position:0%
+Divergence on the right hand side I
+would get zero so there's got to be an S
+
+ align:start position:0%
+would get zero so there's got to be an S
+ 
+
+ align:start position:0%
+would get zero so there's got to be an S
+and what is it probably not hard to find
+
+ align:start position:0%
+and what is it probably not hard to find
+ 
+
+ align:start position:0%
+and what is it probably not hard to find
+let's see
+
+ align:start position:0%
+let's see
+ 
+
+ align:start position:0%
+let's see
+here W1 is zero so that tells me S
+
+ align:start position:0%
+here W1 is zero so that tells me S
+ 
+
+ align:start position:0%
+here W1 is zero so that tells me S
+doesn't depend on Y at all
+
+ align:start position:0%
+doesn't depend on Y at all
+ 
+
+ align:start position:0%
+doesn't depend on Y at all
+W2 is X so X is supposed to be minus the
+
+ align:start position:0%
+W2 is X so X is supposed to be minus the
+ 
+
+ align:start position:0%
+W2 is X so X is supposed to be minus the
+X derivative of the stream function so
+
+ align:start position:0%
+X derivative of the stream function so
+ 
+
+ align:start position:0%
+X derivative of the stream function so
+what's what is the stream function then
+
+ align:start position:0%
+what's what is the stream function then
+ 
+
+ align:start position:0%
+what's what is the stream function then
+have I got room to put it here
+
+ align:start position:0%
+have I got room to put it here
+ 
+
+ align:start position:0%
+have I got room to put it here
+just about what will work
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+it's so again here's W1 the Y derivative
+
+ align:start position:0%
+it's so again here's W1 the Y derivative
+ 
+
+ align:start position:0%
+it's so again here's W1 the Y derivative
+of s is zero W2 tells me that the X
+
+ align:start position:0%
+of s is zero W2 tells me that the X
+ 
+
+ align:start position:0%
+of s is zero W2 tells me that the X
+derivative of s is minus X so all I'm
+
+ align:start position:0%
+derivative of s is minus X so all I'm
+ 
+
+ align:start position:0%
+derivative of s is minus X so all I'm
+looking for is a function that only
+
+ align:start position:0%
+looking for is a function that only
+ 
+
+ align:start position:0%
+looking for is a function that only
+depends on X has no dependence on Y and
+
+ align:start position:0%
+depends on X has no dependence on Y and
+ 
+
+ align:start position:0%
+depends on X has no dependence on Y and
+its derivative should be minus X so
+
+ align:start position:0%
+its derivative should be minus X so
+ 
+
+ align:start position:0%
+its derivative should be minus X so
+what's the function
+
+ align:start position:0%
+what's the function
+ 
+
+ align:start position:0%
+what's the function
+minus
+
+ align:start position:0%
+minus
+ 
+
+ align:start position:0%
+minus
+minus a half of x s yeah let me let me
+
+ align:start position:0%
+minus a half of x s yeah let me let me
+ 
+
+ align:start position:0%
+minus a half of x s yeah let me let me
+so so so this gives me S = minus a half
+
+ align:start position:0%
+so so so this gives me S = minus a half
+ 
+
+ align:start position:0%
+so so so this gives me S = minus a half
+of x^2
+
+ align:start position:0%
+of x^2
+ 
+
+ align:start position:0%
+of x^2
+okay all right so you're saying that
+
+ align:start position:0%
+okay all right so you're saying that
+ 
+
+ align:start position:0%
+okay all right so you're saying that
+yeah so uh so there is a string function
+
+ align:start position:0%
+yeah so uh so there is a string function
+ 
+
+ align:start position:0%
+yeah so uh so there is a string function
+right and what does that travel along
+
+ align:start position:0%
+right and what does that travel along
+ 
+
+ align:start position:0%
+right and what does that travel along
+that travels along stream that means
+
+ align:start position:0%
+that travels along stream that means
+ 
+
+ align:start position:0%
+that travels along stream that means
+that the flow buzzes along stream lines
+
+ align:start position:0%
+that the flow buzzes along stream lines
+ 
+
+ align:start position:0%
+that the flow buzzes along stream lines
+and what are the stream lines they're
+
+ align:start position:0%
+and what are the stream lines they're
+ 
+
+ align:start position:0%
+and what are the stream lines they're
+the lines where s is constant
+
+ align:start position:0%
+the lines where s is constant
+ 
+
+ align:start position:0%
+the lines where s is constant
+equip potentials were the lines where U
+
+ align:start position:0%
+equip potentials were the lines where U
+ 
+
+ align:start position:0%
+equip potentials were the lines where U
+was constant but here we don't have a u
+
+ align:start position:0%
+was constant but here we don't have a u
+ 
+
+ align:start position:0%
+was constant but here we don't have a u
+in this problem stream lines are lines
+
+ align:start position:0%
+in this problem stream lines are lines
+ 
+
+ align:start position:0%
+in this problem stream lines are lines
+where the S is constant so - half x^2 is
+
+ align:start position:0%
+where the S is constant so - half x^2 is
+ 
+
+ align:start position:0%
+where the S is constant so - half x^2 is
+constant what what's the picture look
+
+ align:start position:0%
+constant what what's the picture look
+ 
+
+ align:start position:0%
+constant what what's the picture look
+like
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the picture then for that
+
+ align:start position:0%
+the picture then for that
+ 
+
+ align:start position:0%
+the picture then for that
+well and you you know where where what
+
+ align:start position:0%
+well and you you know where where what
+ 
+
+ align:start position:0%
+well and you you know where where what
+the flow is doing at a typical Point
+
+ align:start position:0%
+the flow is doing at a typical Point
+ 
+
+ align:start position:0%
+the flow is doing at a typical Point
+here say x = 3 y = 1 what let me draw
+
+ align:start position:0%
+here say x = 3 y = 1 what let me draw
+ 
+
+ align:start position:0%
+here say x = 3 y = 1 what let me draw
+the little arrow uh with a big chalk
+
+ align:start position:0%
+the little arrow uh with a big chalk
+ 
+
+ align:start position:0%
+the little arrow uh with a big chalk
+uh which way is the flow going well no
+
+ align:start position:0%
+uh which way is the flow going well no
+ 
+
+ align:start position:0%
+uh which way is the flow going well no
+flow if the X component is zero the Y
+
+ align:start position:0%
+flow if the X component is zero the Y
+ 
+
+ align:start position:0%
+flow if the X component is zero the Y
+component is X so if that so that the
+
+ align:start position:0%
+component is X so if that so that the
+ 
+
+ align:start position:0%
+component is X so if that so that the
+flow is going up there right
+
+ align:start position:0%
+flow is going up there right
+ 
+
+ align:start position:0%
+flow is going up there right
+here
+
+ align:start position:0%
+here
+ 
+
+ align:start position:0%
+here
+uh yeah here are the Y component is X
+
+ align:start position:0%
+uh yeah here are the Y component is X
+ 
+
+ align:start position:0%
+uh yeah here are the Y component is X
+this whole line is all traveling up with
+
+ align:start position:0%
+this whole line is all traveling up with
+ 
+
+ align:start position:0%
+this whole line is all traveling up with
+the same
+
+ align:start position:0%
+the same
+ 
+
+ align:start position:0%
+the same
+velocity if I drop a leaf there it
+
+ align:start position:0%
+velocity if I drop a leaf there it
+ 
+
+ align:start position:0%
+velocity if I drop a leaf there it
+buzzes up that straight line so that's
+
+ align:start position:0%
+buzzes up that straight line so that's
+ 
+
+ align:start position:0%
+buzzes up that straight line so that's
+the Streamline and uh it's velocity is
+
+ align:start position:0%
+the Streamline and uh it's velocity is
+ 
+
+ align:start position:0%
+the Streamline and uh it's velocity is
+uh if if that's x equal if say the
+
+ align:start position:0%
+uh if if that's x equal if say the
+ 
+
+ align:start position:0%
+uh if if that's x equal if say the
+velocity is three then these this this
+
+ align:start position:0%
+velocity is three then these this this
+ 
+
+ align:start position:0%
+velocity is three then these this this
+uh speed is three it's going up that
+
+ align:start position:0%
+uh speed is three it's going up that
+ 
+
+ align:start position:0%
+uh speed is three it's going up that
+line so that's a that's a streamline and
+
+ align:start position:0%
+line so that's a that's a streamline and
+ 
+
+ align:start position:0%
+line so that's a that's a streamline and
+sure enough on that line minus a half
+
+ align:start position:0%
+sure enough on that line minus a half
+ 
+
+ align:start position:0%
+sure enough on that line minus a half
+x^2 is a constant so you see it's we're
+
+ align:start position:0%
+x^2 is a constant so you see it's we're
+ 
+
+ align:start position:0%
+x^2 is a constant so you see it's we're
+not talking parabas here because we're
+
+ align:start position:0%
+not talking parabas here because we're
+ 
+
+ align:start position:0%
+not talking parabas here because we're
+not our our curve is not y equal - half
+
+ align:start position:0%
+not our our curve is not y equal - half
+ 
+
+ align:start position:0%
+not our our curve is not y equal - half
+x^2 it's - half x^2 equal constant yeah
+
+ align:start position:0%
+x^2 it's - half x^2 equal constant yeah
+ 
+
+ align:start position:0%
+x^2 it's - half x^2 equal constant yeah
+that's what we want so but now having
+
+ align:start position:0%
+that's what we want so but now having
+ 
+
+ align:start position:0%
+that's what we want so but now having
+got so far let me go let me take xal 1
+
+ align:start position:0%
+got so far let me go let me take xal 1
+ 
+
+ align:start position:0%
+got so far let me go let me take xal 1
+say what what's the flow like on that so
+
+ align:start position:0%
+say what what's the flow like on that so
+ 
+
+ align:start position:0%
+say what what's the flow like on that so
+there's a streamline
+
+ align:start position:0%
+there's a streamline
+ 
+
+ align:start position:0%
+there's a streamline
+with s equal constant and the velocity
+
+ align:start position:0%
+with s equal constant and the velocity
+ 
+
+ align:start position:0%
+with s equal constant and the velocity
+on that is zero so nothing's going in
+
+ align:start position:0%
+on that is zero so nothing's going in
+ 
+
+ align:start position:0%
+on that is zero so nothing's going in
+the in in that horizontally and now it's
+
+ align:start position:0%
+the in in that horizontally and now it's
+ 
+
+ align:start position:0%
+the in in that horizontally and now it's
+one so these the flow is slower up this
+
+ align:start position:0%
+one so these the flow is slower up this
+ 
+
+ align:start position:0%
+one so these the flow is slower up this
+line
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay slower flow this was faster flow
+
+ align:start position:0%
+okay slower flow this was faster flow
+ 
+
+ align:start position:0%
+okay slower flow this was faster flow
+and then the the question that's in that
+
+ align:start position:0%
+and then the the question that's in that
+ 
+
+ align:start position:0%
+and then the the question that's in that
+homework problem is is there any
+
+ align:start position:0%
+homework problem is is there any
+ 
+
+ align:start position:0%
+homework problem is is there any
+rotation in this flow
+
+ align:start position:0%
+rotation in this flow
+ 
+
+ align:start position:0%
+rotation in this flow
+you know we think about rotation we have
+
+ align:start position:0%
+you know we think about rotation we have
+ 
+
+ align:start position:0%
+you know we think about rotation we have
+an we have an image of rotational flow
+
+ align:start position:0%
+an we have an image of rotational flow
+ 
+
+ align:start position:0%
+an we have an image of rotational flow
+like in and that could be the next
+
+ align:start position:0%
+like in and that could be the next
+ 
+
+ align:start position:0%
+like in and that could be the next
+example we we could figure out what what
+
+ align:start position:0%
+example we we could figure out what what
+ 
+
+ align:start position:0%
+example we we could figure out what what
+a a flow that goes around in circles
+
+ align:start position:0%
+a a flow that goes around in circles
+ 
+
+ align:start position:0%
+a a flow that goes around in circles
+right we well those would be the
+
+ align:start position:0%
+right we well those would be the
+ 
+
+ align:start position:0%
+right we well those would be the
+streamlines so this would be like pure
+
+ align:start position:0%
+streamlines so this would be like pure
+ 
+
+ align:start position:0%
+streamlines so this would be like pure
+rotation shall I call it
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+but I don't have that there I just want
+
+ align:start position:0%
+but I don't have that there I just want
+ 
+
+ align:start position:0%
+but I don't have that there I just want
+to draw the other picture in which the
+
+ align:start position:0%
+to draw the other picture in which the
+ 
+
+ align:start position:0%
+to draw the other picture in which the
+streamlines
+
+ align:start position:0%
+streamlines
+ 
+
+ align:start position:0%
+streamlines
+are circles
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+to have another nice clean beautiful
+
+ align:start position:0%
+to have another nice clean beautiful
+ 
+
+ align:start position:0%
+to have another nice clean beautiful
+example okay but here we don't have our
+
+ align:start position:0%
+example okay but here we don't have our
+ 
+
+ align:start position:0%
+example okay but here we don't have our
+streamlines are straight lines and yet
+
+ align:start position:0%
+streamlines are straight lines and yet
+ 
+
+ align:start position:0%
+streamlines are straight lines and yet
+we have rotation that's the point here
+
+ align:start position:0%
+we have rotation that's the point here
+ 
+
+ align:start position:0%
+we have rotation that's the point here
+why do we have what's why do I say we
+
+ align:start position:0%
+why do we have what's why do I say we
+ 
+
+ align:start position:0%
+why do we have what's why do I say we
+have rotation because the test for
+
+ align:start position:0%
+have rotation because the test for
+ 
+
+ align:start position:0%
+have rotation because the test for
+rotation was that original test of
+
+ align:start position:0%
+rotation was that original test of
+ 
+
+ align:start position:0%
+rotation was that original test of
+looking that which I just wrote the
+
+ align:start position:0%
+looking that which I just wrote the
+ 
+
+ align:start position:0%
+looking that which I just wrote the
+answer to be no here
+
+ align:start position:0%
+answer to be no here
+ 
+
+ align:start position:0%
+answer to be no here
+it's not the great so if it's not the
+
+ align:start position:0%
+it's not the great so if it's not the
+ 
+
+ align:start position:0%
+it's not the great so if it's not the
+gradient the reason is there's some
+
+ align:start position:0%
+gradient the reason is there's some
+ 
+
+ align:start position:0%
+gradient the reason is there's some
+rotation gradient Fields don't have any
+
+ align:start position:0%
+rotation gradient Fields don't have any
+ 
+
+ align:start position:0%
+rotation gradient Fields don't have any
+rotation the the rotation is this is
+
+ align:start position:0%
+rotation the the rotation is this is
+ 
+
+ align:start position:0%
+rotation the the rotation is this is
+this uh du is this thing that comes out
+
+ align:start position:0%
+this uh du is this thing that comes out
+ 
+
+ align:start position:0%
+this uh du is this thing that comes out
+yeah it's this difference dv2 DX it's
+
+ align:start position:0%
+yeah it's this difference dv2 DX it's
+ 
+
+ align:start position:0%
+yeah it's this difference dv2 DX it's
+the difference between those that tells
+
+ align:start position:0%
+the difference between those that tells
+ 
+
+ align:start position:0%
+the difference between those that tells
+us the rotation and that was not zero
+
+ align:start position:0%
+us the rotation and that was not zero
+ 
+
+ align:start position:0%
+us the rotation and that was not zero
+right that for for this example dv1 Dy
+
+ align:start position:0%
+right that for for this example dv1 Dy
+ 
+
+ align:start position:0%
+right that for for this example dv1 Dy
+was Zero because V1 is zero dv2 DX was
+
+ align:start position:0%
+was Zero because V1 is zero dv2 DX was
+ 
+
+ align:start position:0%
+was Zero because V1 is zero dv2 DX was
+one because V2 is X so there's some
+
+ align:start position:0%
+one because V2 is X so there's some
+ 
+
+ align:start position:0%
+one because V2 is X so there's some
+rotation here and that's that's in other
+
+ align:start position:0%
+rotation here and that's that's in other
+ 
+
+ align:start position:0%
+rotation here and that's that's in other
+words the test being a gradient is no
+
+ align:start position:0%
+words the test being a gradient is no
+ 
+
+ align:start position:0%
+words the test being a gradient is no
+rotation this fails that test so but how
+
+ align:start position:0%
+rotation this fails that test so but how
+ 
+
+ align:start position:0%
+rotation this fails that test so but how
+is it rotating how how can it how can it
+
+ align:start position:0%
+is it rotating how how can it how can it
+ 
+
+ align:start position:0%
+is it rotating how how can it how can it
+be rotating when the all the flow is
+
+ align:start position:0%
+be rotating when the all the flow is
+ 
+
+ align:start position:0%
+be rotating when the all the flow is
+just traveling vertically do do you I I
+
+ align:start position:0%
+just traveling vertically do do you I I
+ 
+
+ align:start position:0%
+just traveling vertically do do you I I
+guess I give you this example because it
+
+ align:start position:0%
+guess I give you this example because it
+ 
+
+ align:start position:0%
+guess I give you this example because it
+meant something to me I didn't you know
+
+ align:start position:0%
+meant something to me I didn't you know
+ 
+
+ align:start position:0%
+meant something to me I didn't you know
+my image of rotation was this
+
+ align:start position:0%
+my image of rotation was this
+ 
+
+ align:start position:0%
+my image of rotation was this
+simple-minded type of flow you know like
+
+ align:start position:0%
+simple-minded type of flow you know like
+ 
+
+ align:start position:0%
+simple-minded type of flow you know like
+a phonograph record or something this
+
+ align:start position:0%
+a phonograph record or something this
+ 
+
+ align:start position:0%
+a phonograph record or something this
+would be called a sheer flow and there's
+
+ align:start position:0%
+would be called a sheer flow and there's
+ 
+
+ align:start position:0%
+would be called a sheer flow and there's
+a very important type of flow
+
+ align:start position:0%
+a very important type of flow
+ 
+
+ align:start position:0%
+a very important type of flow
+and and actually you you realize that if
+
+ align:start position:0%
+and and actually you you realize that if
+ 
+
+ align:start position:0%
+and and actually you you realize that if
+if x is negative then the the flow in
+
+ align:start position:0%
+if x is negative then the the flow in
+ 
+
+ align:start position:0%
+if x is negative then the the flow in
+the the second component of the Velocity
+
+ align:start position:0%
+the the second component of the Velocity
+ 
+
+ align:start position:0%
+the the second component of the Velocity
+is now negative so it would be the
+
+ align:start position:0%
+is now negative so it would be the
+ 
+
+ align:start position:0%
+is now negative so it would be the
+Streamline the flow would be going down
+
+ align:start position:0%
+Streamline the flow would be going down
+ 
+
+ align:start position:0%
+Streamline the flow would be going down
+this way and this point wouldn't move at
+
+ align:start position:0%
+this way and this point wouldn't move at
+ 
+
+ align:start position:0%
+this way and this point wouldn't move at
+all these guy this would be well I don't
+
+ align:start position:0%
+all these guy this would be well I don't
+ 
+
+ align:start position:0%
+all these guy this would be well I don't
+know if it's a streamline it's a
+
+ align:start position:0%
+know if it's a streamline it's a
+ 
+
+ align:start position:0%
+know if it's a streamline it's a
+stagnant streamline right x equal x
+
+ align:start position:0%
+stagnant streamline right x equal x
+ 
+
+ align:start position:0%
+stagnant streamline right x equal x
+equals z on that line there's no
+
+ align:start position:0%
+equals z on that line there's no
+ 
+
+ align:start position:0%
+equals z on that line there's no
+velocity z0 so this is this is all just
+
+ align:start position:0%
+velocity z0 so this is this is all just
+ 
+
+ align:start position:0%
+velocity z0 so this is this is all just
+staying there these lines are moving
+
+ align:start position:0%
+staying there these lines are moving
+ 
+
+ align:start position:0%
+staying there these lines are moving
+this Line's moving faster this line will
+
+ align:start position:0%
+this Line's moving faster this line will
+ 
+
+ align:start position:0%
+this Line's moving faster this line will
+be moving even faster this Line's going
+
+ align:start position:0%
+be moving even faster this Line's going
+ 
+
+ align:start position:0%
+be moving even faster this Line's going
+the other way
+
+ align:start position:0%
+the other way
+ 
+
+ align:start position:0%
+the other way
+faster and faster the other way it's a
+
+ align:start position:0%
+faster and faster the other way it's a
+ 
+
+ align:start position:0%
+faster and faster the other way it's a
+important flow you know in in
+
+ align:start position:0%
+important flow you know in in
+ 
+
+ align:start position:0%
+important flow you know in in
+earthquakes and things like that this
+
+ align:start position:0%
+earthquakes and things like that this
+ 
+
+ align:start position:0%
+earthquakes and things like that this
+this is this happens when one plate
+
+ align:start position:0%
+this is this happens when one plate
+ 
+
+ align:start position:0%
+this is this happens when one plate
+shears with respect to another
+
+ align:start position:0%
+shears with respect to another
+ 
+
+ align:start position:0%
+shears with respect to another
+so that's shear ing shearing is that
+
+ align:start position:0%
+so that's shear ing shearing is that
+ 
+
+ align:start position:0%
+so that's shear ing shearing is that
+that word shearing means that that the a
+
+ align:start position:0%
+that word shearing means that that the a
+ 
+
+ align:start position:0%
+that word shearing means that that the a
+line that was you know that line after a
+
+ align:start position:0%
+line that was you know that line after a
+ 
+
+ align:start position:0%
+line that was you know that line after a
+while is tilted yeah th this is going
+
+ align:start position:0%
+while is tilted yeah th this is going
+ 
+
+ align:start position:0%
+while is tilted yeah th this is going
+faster than this yes
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+right being a constant
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh that's true
+
+ align:start position:0%
+uh that's true
+ 
+
+ align:start position:0%
+uh that's true
+ah well okay uh let's see
+
+ align:start position:0%
+ah well okay uh let's see
+ 
+
+ align:start position:0%
+ah well okay uh let's see
+yeah what okay well how do I fix that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yes yeah so that's a good question
+
+ align:start position:0%
+yes yeah so that's a good question
+ 
+
+ align:start position:0%
+yes yeah so that's a good question
+should I have allowed
+
+ align:start position:0%
+should I have allowed
+ 
+
+ align:start position:0%
+should I have allowed
+in my stream function
+
+ align:start position:0%
+in my stream function
+ 
+
+ align:start position:0%
+in my stream function
+I mean that's a stream function because
+
+ align:start position:0%
+I mean that's a stream function because
+ 
+
+ align:start position:0%
+I mean that's a stream function because
+it satisfies the equations that stream
+
+ align:start position:0%
+it satisfies the equations that stream
+ 
+
+ align:start position:0%
+it satisfies the equations that stream
+functions are so I could have thrown in
+
+ align:start position:0%
+functions are so I could have thrown in
+ 
+
+ align:start position:0%
+functions are so I could have thrown in
+a constant yeah so you're pointing out a
+
+ align:start position:0%
+a constant yeah so you're pointing out a
+ 
+
+ align:start position:0%
+a constant yeah so you're pointing out a
+difficulty makes me think I should have
+
+ align:start position:0%
+difficulty makes me think I should have
+ 
+
+ align:start position:0%
+difficulty makes me think I should have
+thrown in a constant yeah yeah so if I
+
+ align:start position:0%
+thrown in a constant yeah yeah so if I
+ 
+
+ align:start position:0%
+thrown in a constant yeah yeah so if I
+throw in constants then I could get
+
+ align:start position:0%
+throw in constants then I could get
+ 
+
+ align:start position:0%
+throw in constants then I could get
+other lines yeah yeah thanks that's a
+
+ align:start position:0%
+other lines yeah yeah thanks that's a
+ 
+
+ align:start position:0%
+other lines yeah yeah thanks that's a
+good point I just want to see do you see
+
+ align:start position:0%
+good point I just want to see do you see
+ 
+
+ align:start position:0%
+good point I just want to see do you see
+rotation in this flow in this sheer flow
+
+ align:start position:0%
+rotation in this flow in this sheer flow
+ 
+
+ align:start position:0%
+rotation in this flow in this sheer flow
+and I think you do if you think about it
+
+ align:start position:0%
+and I think you do if you think about it
+ 
+
+ align:start position:0%
+and I think you do if you think about it
+suppose you put a little leaf or a or a
+
+ align:start position:0%
+suppose you put a little leaf or a or a
+ 
+
+ align:start position:0%
+suppose you put a little leaf or a or a
+little Penny or something right there
+
+ align:start position:0%
+little Penny or something right there
+ 
+
+ align:start position:0%
+little Penny or something right there
+okay is it going to turn it'll flow
+
+ align:start position:0%
+okay is it going to turn it'll flow
+ 
+
+ align:start position:0%
+okay is it going to turn it'll flow
+along but as it flows
+
+ align:start position:0%
+along but as it flows
+ 
+
+ align:start position:0%
+along but as it flows
+is it going to turn in other words is
+
+ align:start position:0%
+is it going to turn in other words is
+ 
+
+ align:start position:0%
+is it going to turn in other words is
+there some
+
+ align:start position:0%
+there some
+ 
+
+ align:start position:0%
+there some
+uh is there some difference in the in
+
+ align:start position:0%
+uh is there some difference in the in
+ 
+
+ align:start position:0%
+uh is there some difference in the in
+the um speed on one side compared to the
+
+ align:start position:0%
+the um speed on one side compared to the
+ 
+
+ align:start position:0%
+the um speed on one side compared to the
+other I mean it's what makes a curveball
+
+ align:start position:0%
+other I mean it's what makes a curveball
+ 
+
+ align:start position:0%
+other I mean it's what makes a curveball
+curve right you when the pitcher throws
+
+ align:start position:0%
+curve right you when the pitcher throws
+ 
+
+ align:start position:0%
+curve right you when the pitcher throws
+the ball he imparts a spin to it and
+
+ align:start position:0%
+the ball he imparts a spin to it and
+ 
+
+ align:start position:0%
+the ball he imparts a spin to it and
+that and that gives a different pressure
+
+ align:start position:0%
+that and that gives a different pressure
+ 
+
+ align:start position:0%
+that and that gives a different pressure
+on the two sides of the ball and it
+
+ align:start position:0%
+on the two sides of the ball and it
+ 
+
+ align:start position:0%
+on the two sides of the ball and it
+moves the ball moves okay I think that's
+
+ align:start position:0%
+moves the ball moves okay I think that's
+ 
+
+ align:start position:0%
+moves the ball moves okay I think that's
+going to happen here
+
+ align:start position:0%
+going to happen here
+ 
+
+ align:start position:0%
+going to happen here
+maybe you see it and I'm just talking uh
+
+ align:start position:0%
+maybe you see it and I'm just talking uh
+ 
+
+ align:start position:0%
+maybe you see it and I'm just talking uh
+I mean this side is going faster than
+
+ align:start position:0%
+I mean this side is going faster than
+ 
+
+ align:start position:0%
+I mean this side is going faster than
+this side so the net result is that that
+
+ align:start position:0%
+this side so the net result is that that
+ 
+
+ align:start position:0%
+this side so the net result is that that
+even though the the thing is traveling
+
+ align:start position:0%
+even though the the thing is traveling
+ 
+
+ align:start position:0%
+even though the the thing is traveling
+up and down it's
+
+ align:start position:0%
+up and down it's
+ 
+
+ align:start position:0%
+up and down it's
+turning it's it's turning because the
+
+ align:start position:0%
+turning it's it's turning because the
+ 
+
+ align:start position:0%
+turning it's it's turning because the
+right hand side is is going faster than
+
+ align:start position:0%
+right hand side is is going faster than
+ 
+
+ align:start position:0%
+right hand side is is going faster than
+the left hand side so it has a it does
+
+ align:start position:0%
+the left hand side so it has a it does
+ 
+
+ align:start position:0%
+the left hand side so it has a it does
+have a rotation this this quantity this
+
+ align:start position:0%
+have a rotation this this quantity this
+ 
+
+ align:start position:0%
+have a rotation this this quantity this
+difference between dv1 Dy and dv2 DX
+
+ align:start position:0%
+difference between dv1 Dy and dv2 DX
+ 
+
+ align:start position:0%
+difference between dv1 Dy and dv2 DX
+which is is the component of the curl
+
+ align:start position:0%
+which is is the component of the curl
+ 
+
+ align:start position:0%
+which is is the component of the curl
+maybe the sign it should be the opposite
+
+ align:start position:0%
+maybe the sign it should be the opposite
+ 
+
+ align:start position:0%
+maybe the sign it should be the opposite
+maybe I think it should be minus this
+
+ align:start position:0%
+maybe I think it should be minus this
+ 
+
+ align:start position:0%
+maybe I think it should be minus this
+plus this or something point is that
+
+ align:start position:0%
+plus this or something point is that
+ 
+
+ align:start position:0%
+plus this or something point is that
+it's not zero so there is curl there is
+
+ align:start position:0%
+it's not zero so there is curl there is
+ 
+
+ align:start position:0%
+it's not zero so there is curl there is
+rotation okay I was going to ask about
+
+ align:start position:0%
+rotation okay I was going to ask about
+ 
+
+ align:start position:0%
+rotation okay I was going to ask about
+this picture too but then and then I'll
+
+ align:start position:0%
+this picture too but then and then I'll
+ 
+
+ align:start position:0%
+this picture too but then and then I'll
+open to more examples I I I just feel
+
+ align:start position:0%
+open to more examples I I I just feel
+ 
+
+ align:start position:0%
+open to more examples I I I just feel
+examples are good simple velocity Fields
+
+ align:start position:0%
+examples are good simple velocity Fields
+ 
+
+ align:start position:0%
+examples are good simple velocity Fields
+like 0x
+
+ align:start position:0%
+like 0x
+ 
+
+ align:start position:0%
+like 0x
+uh just to Think Through okay what does
+
+ align:start position:0%
+uh just to Think Through okay what does
+ 
+
+ align:start position:0%
+uh just to Think Through okay what does
+that mean what's the does is it curlf
+
+ align:start position:0%
+that mean what's the does is it curlf
+ 
+
+ align:start position:0%
+that mean what's the does is it curlf
+free another way of saying is it a
+
+ align:start position:0%
+free another way of saying is it a
+ 
+
+ align:start position:0%
+free another way of saying is it a
+gradient field would be to say is it
+
+ align:start position:0%
+gradient field would be to say is it
+ 
+
+ align:start position:0%
+gradient field would be to say is it
+curlf free rot not irrotational is the
+
+ align:start position:0%
+curlf free rot not irrotational is the
+ 
+
+ align:start position:0%
+curlf free rot not irrotational is the
+right word here test one is it
+
+ align:start position:0%
+right word here test one is it
+ 
+
+ align:start position:0%
+right word here test one is it
+irrotational answer no is it Divergence
+
+ align:start position:0%
+irrotational answer no is it Divergence
+ 
+
+ align:start position:0%
+irrotational answer no is it Divergence
+free is it Source free answer was yes
+
+ align:start position:0%
+free is it Source free answer was yes
+ 
+
+ align:start position:0%
+free is it Source free answer was yes
+for this example if we pick another
+
+ align:start position:0%
+for this example if we pick another
+ 
+
+ align:start position:0%
+for this example if we pick another
+example I could reverse those or another
+
+ align:start position:0%
+example I could reverse those or another
+ 
+
+ align:start position:0%
+example I could reverse those or another
+example I can probably come up with an
+
+ align:start position:0%
+example I can probably come up with an
+ 
+
+ align:start position:0%
+example I can probably come up with an
+example here let's see what what should
+
+ align:start position:0%
+example here let's see what what should
+ 
+
+ align:start position:0%
+example here let's see what what should
+be the if I wanted the streamlines to be
+
+ align:start position:0%
+be the if I wanted the streamlines to be
+ 
+
+ align:start position:0%
+be the if I wanted the streamlines to be
+circles what would be a good velocity
+
+ align:start position:0%
+circles what would be a good velocity
+ 
+
+ align:start position:0%
+circles what would be a good velocity
+field that goes in circles
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+let's see at a typical point
+
+ align:start position:0%
+let's see at a typical point
+ 
+
+ align:start position:0%
+let's see at a typical point
+if I want the velocity to be going that
+
+ align:start position:0%
+if I want the velocity to be going that
+ 
+
+ align:start position:0%
+if I want the velocity to be going that
+way here's the here's the vector the
+
+ align:start position:0%
+way here's the here's the vector the
+ 
+
+ align:start position:0%
+way here's the here's the vector the
+position Vector the radius Vector that
+
+ align:start position:0%
+position Vector the radius Vector that
+ 
+
+ align:start position:0%
+position Vector the radius Vector that
+goes so what are the components of this
+
+ align:start position:0%
+goes so what are the components of this
+ 
+
+ align:start position:0%
+goes so what are the components of this
+Vector just XY
+
+ align:start position:0%
+Vector just XY
+ 
+
+ align:start position:0%
+Vector just XY
+so now if I want the velocity field to
+
+ align:start position:0%
+so now if I want the velocity field to
+ 
+
+ align:start position:0%
+so now if I want the velocity field to
+go
+
+ align:start position:0%
+go
+ 
+
+ align:start position:0%
+go
+other way which what would be a good Vel
+
+ align:start position:0%
+other way which what would be a good Vel
+ 
+
+ align:start position:0%
+other way which what would be a good Vel
+what would be a good thing with
+
+ align:start position:0%
+what would be a good thing with
+ 
+
+ align:start position:0%
+what would be a good thing with
+with rotation
+
+ align:start position:0%
+with rotation
+ 
+
+ align:start position:0%
+with rotation
+minus YX would sound good V equal minus
+
+ align:start position:0%
+minus YX would sound good V equal minus
+ 
+
+ align:start position:0%
+minus YX would sound good V equal minus
+YX
+
+ align:start position:0%
+YX
+ 
+
+ align:start position:0%
+YX
+so are we expecting this to be a
+
+ align:start position:0%
+so are we expecting this to be a
+ 
+
+ align:start position:0%
+so are we expecting this to be a
+gradient of anything
+
+ align:start position:0%
+gradient of anything
+ 
+
+ align:start position:0%
+gradient of anything
+I'm not
+
+ align:start position:0%
+I'm not
+ 
+
+ align:start position:0%
+I'm not
+this is uh we've built in rotation here
+
+ align:start position:0%
+this is uh we've built in rotation here
+ 
+
+ align:start position:0%
+this is uh we've built in rotation here
+I'm expecting the curl of this thing
+
+ align:start position:0%
+I'm expecting the curl of this thing
+ 
+
+ align:start position:0%
+I'm expecting the curl of this thing
+this quantity I think it's I take the X
+
+ align:start position:0%
+this quantity I think it's I take the X
+ 
+
+ align:start position:0%
+this quantity I think it's I take the X
+derivative I take the X derivative of I
+
+ align:start position:0%
+derivative I take the X derivative of I
+ 
+
+ align:start position:0%
+derivative I take the X derivative of I
+I look at the the Y derivative of this
+
+ align:start position:0%
+I look at the the Y derivative of this
+ 
+
+ align:start position:0%
+I look at the the Y derivative of this
+and compare it with the X derivative of
+
+ align:start position:0%
+and compare it with the X derivative of
+ 
+
+ align:start position:0%
+and compare it with the X derivative of
+that and they're not the same in fact
+
+ align:start position:0%
+that and they're not the same in fact
+ 
+
+ align:start position:0%
+that and they're not the same in fact
+one is minus one and the other is plus
+
+ align:start position:0%
+one is minus one and the other is plus
+ 
+
+ align:start position:0%
+one is minus one and the other is plus
+one so I've got rotation here I've got
+
+ align:start position:0%
+one so I've got rotation here I've got
+ 
+
+ align:start position:0%
+one so I've got rotation here I've got
+sort of two is the the the the the
+
+ align:start position:0%
+sort of two is the the the the the
+ 
+
+ align:start position:0%
+sort of two is the the the the the
+measure of is is that component of the
+
+ align:start position:0%
+measure of is is that component of the
+ 
+
+ align:start position:0%
+measure of is is that component of the
+curl so so let me let's just write it
+
+ align:start position:0%
+curl so so let me let's just write it
+ 
+
+ align:start position:0%
+curl so so let me let's just write it
+down dv2 DX
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this vorticity
+
+ align:start position:0%
+this vorticity
+ 
+
+ align:start position:0%
+this vorticity
+that that measures the Turning speed is
+
+ align:start position:0%
+that that measures the Turning speed is
+ 
+
+ align:start position:0%
+that that measures the Turning speed is
+1 from dv2 DX minus minus one is 2
+
+ align:start position:0%
+1 from dv2 DX minus minus one is 2
+ 
+
+ align:start position:0%
+1 from dv2 DX minus minus one is 2
+so it's not a gradient of anything
+
+ align:start position:0%
+so it's not a gradient of anything
+ 
+
+ align:start position:0%
+so it's not a gradient of anything
+if the X derivative of U is minus y then
+
+ align:start position:0%
+if the X derivative of U is minus y then
+ 
+
+ align:start position:0%
+if the X derivative of U is minus y then
+the Y derivative can't be plus x no good
+
+ align:start position:0%
+the Y derivative can't be plus x no good
+ 
+
+ align:start position:0%
+the Y derivative can't be plus x no good
+okay what about does it have is it
+
+ align:start position:0%
+okay what about does it have is it
+ 
+
+ align:start position:0%
+okay what about does it have is it
+Divergence free is it is it do I need a
+
+ align:start position:0%
+Divergence free is it is it do I need a
+ 
+
+ align:start position:0%
+Divergence free is it is it do I need a
+source to keep this flow going well
+
+ align:start position:0%
+source to keep this flow going well
+ 
+
+ align:start position:0%
+source to keep this flow going well
+what's the test in other words is there
+
+ align:start position:0%
+what's the test in other words is there
+ 
+
+ align:start position:0%
+what's the test in other words is there
+a stream function for this guy
+
+ align:start position:0%
+a stream function for this guy
+ 
+
+ align:start position:0%
+a stream function for this guy
+I I think probably there is
+
+ align:start position:0%
+I I think probably there is
+ 
+
+ align:start position:0%
+I I think probably there is
+what's the test to to know if there is a
+
+ align:start position:0%
+what's the test to to know if there is a
+ 
+
+ align:start position:0%
+what's the test to to know if there is a
+stream function I take the Divergence
+
+ align:start position:0%
+stream function I take the Divergence
+ 
+
+ align:start position:0%
+stream function I take the Divergence
+I'm over on the right hand side of my my
+
+ align:start position:0%
+I'm over on the right hand side of my my
+ 
+
+ align:start position:0%
+I'm over on the right hand side of my my
+picture now I take the Divergence
+
+ align:start position:0%
+picture now I take the Divergence
+ 
+
+ align:start position:0%
+picture now I take the Divergence
+Divergence of this V is the X derivative
+
+ align:start position:0%
+Divergence of this V is the X derivative
+ 
+
+ align:start position:0%
+Divergence of this V is the X derivative
+of that plus the Y derivative of that
+
+ align:start position:0%
+of that plus the Y derivative of that
+ 
+
+ align:start position:0%
+of that plus the Y derivative of that
+good zero so there is a stream function
+
+ align:start position:0%
+good zero so there is a stream function
+ 
+
+ align:start position:0%
+good zero so there is a stream function
+and what is it
+
+ align:start position:0%
+and what is it
+ 
+
+ align:start position:0%
+and what is it
+well I'm pretty darn sure that the these
+
+ align:start position:0%
+well I'm pretty darn sure that the these
+ 
+
+ align:start position:0%
+well I'm pretty darn sure that the these
+stream lines are circles I think the
+
+ align:start position:0%
+stream lines are circles I think the
+ 
+
+ align:start position:0%
+stream lines are circles I think the
+stream function is going to be X2 + y^2
+
+ align:start position:0%
+stream function is going to be X2 + y^2
+ 
+
+ align:start position:0%
+stream function is going to be X2 + y^2
+yeah yeah
+
+ align:start position:0%
+yeah yeah
+ 
+
+ align:start position:0%
+yeah yeah
+then am I right that the Y derivative of
+
+ align:start position:0%
+then am I right that the Y derivative of
+ 
+
+ align:start position:0%
+then am I right that the Y derivative of
+that will be 2x sorry the Y derivative
+
+ align:start position:0%
+that will be 2x sorry the Y derivative
+ 
+
+ align:start position:0%
+that will be 2x sorry the Y derivative
+of that will be 2 y who it's not not
+
+ align:start position:0%
+of that will be 2 y who it's not not
+ 
+
+ align:start position:0%
+of that will be 2 y who it's not not
+looking too good what do I want here
+
+ align:start position:0%
+looking too good what do I want here
+ 
+
+ align:start position:0%
+looking too good what do I want here
+here's my V which is the same as W and
+
+ align:start position:0%
+here's my V which is the same as W and
+ 
+
+ align:start position:0%
+here's my V which is the same as W and
+what I'm looking for is to get these
+
+ align:start position:0%
+what I'm looking for is to get these
+ 
+
+ align:start position:0%
+what I'm looking for is to get these
+guys correct so so and I'm should be
+
+ align:start position:0%
+guys correct so so and I'm should be
+ 
+
+ align:start position:0%
+guys correct so so and I'm should be
+able to do it and what What Would S be I
+
+ align:start position:0%
+able to do it and what What Would S be I
+ 
+
+ align:start position:0%
+able to do it and what What Would S be I
+haven't got s quite right
+
+ align:start position:0%
+haven't got s quite right
+ 
+
+ align:start position:0%
+haven't got s quite right
+I think if I multiply by negative a half
+
+ align:start position:0%
+I think if I multiply by negative a half
+ 
+
+ align:start position:0%
+I think if I multiply by negative a half
+that might have done it yeah because now
+
+ align:start position:0%
+that might have done it yeah because now
+ 
+
+ align:start position:0%
+that might have done it yeah because now
+the Y derivative is now
+
+ align:start position:0%
+the Y derivative is now
+ 
+
+ align:start position:0%
+the Y derivative is now
+minus y great and the X derivative of s
+
+ align:start position:0%
+minus y great and the X derivative of s
+ 
+
+ align:start position:0%
+minus y great and the X derivative of s
+is min - x and then I should take a
+
+ align:start position:0%
+is min - x and then I should take a
+ 
+
+ align:start position:0%
+is min - x and then I should take a
+minus that so I should want a plus X
+
+ align:start position:0%
+minus that so I should want a plus X
+ 
+
+ align:start position:0%
+minus that so I should want a plus X
+which is what I've got yeah so those are
+
+ align:start position:0%
+which is what I've got yeah so those are
+ 
+
+ align:start position:0%
+which is what I've got yeah so those are
+the streamlines C CES
+
+ align:start position:0%
+the streamlines C CES
+ 
+
+ align:start position:0%
+the streamlines C CES
+so I have Circle the flow is going
+
+ align:start position:0%
+so I have Circle the flow is going
+ 
+
+ align:start position:0%
+so I have Circle the flow is going
+around in a circle
+
+ align:start position:0%
+around in a circle
+ 
+
+ align:start position:0%
+around in a circle
+I don't have to I don't need any source
+
+ align:start position:0%
+I don't have to I don't need any source
+ 
+
+ align:start position:0%
+I don't have to I don't need any source
+to keep it going
+
+ align:start position:0%
+to keep it going
+ 
+
+ align:start position:0%
+to keep it going
+but it's not uh it's not a gradient
+
+ align:start position:0%
+but it's not uh it's not a gradient
+ 
+
+ align:start position:0%
+but it's not uh it's not a gradient
+field right it's not it's not a gradient
+
+ align:start position:0%
+field right it's not it's not a gradient
+ 
+
+ align:start position:0%
+field right it's not it's not a gradient
+field so those are the this is like
+
+ align:start position:0%
+field so those are the this is like
+ 
+
+ align:start position:0%
+field so those are the this is like
+sample tests to to take a a simple flow
+
+ align:start position:0%
+sample tests to to take a a simple flow
+ 
+
+ align:start position:0%
+sample tests to to take a a simple flow
+field apply the two tests and I guess we
+
+ align:start position:0%
+field apply the two tests and I guess we
+ 
+
+ align:start position:0%
+field apply the two tests and I guess we
+should complete with an example that
+
+ align:start position:0%
+should complete with an example that
+ 
+
+ align:start position:0%
+should complete with an example that
+passes both tests
+
+ align:start position:0%
+passes both tests
+ 
+
+ align:start position:0%
+passes both tests
+right un this let me open to any other
+
+ align:start position:0%
+right un this let me open to any other
+ 
+
+ align:start position:0%
+right un this let me open to any other
+question and then I'll we could cook up
+
+ align:start position:0%
+question and then I'll we could cook up
+ 
+
+ align:start position:0%
+question and then I'll we could cook up
+an example that passes both tests before
+
+ align:start position:0%
+an example that passes both tests before
+ 
+
+ align:start position:0%
+an example that passes both tests before
+we stop I'll stop talking first though
+
+ align:start position:0%
+we stop I'll stop talking first though
+ 
+
+ align:start position:0%
+we stop I'll stop talking first though
+and just listen for a question on any
+
+ align:start position:0%
+and just listen for a question on any
+ 
+
+ align:start position:0%
+and just listen for a question on any
+topic or or is it useful just to take
+
+ align:start position:0%
+topic or or is it useful just to take
+ 
+
+ align:start position:0%
+topic or or is it useful just to take
+Fields like this and go through those
+
+ align:start position:0%
+Fields like this and go through those
+ 
+
+ align:start position:0%
+Fields like this and go through those
+steps to probably is certainly good for
+
+ align:start position:0%
+steps to probably is certainly good for
+ 
+
+ align:start position:0%
+steps to probably is certainly good for
+me
+
+ align:start position:0%
+me
+ 
+
+ align:start position:0%
+me
+okay what's a field that will satisfy
+
+ align:start position:0%
+okay what's a field that will satisfy
+ 
+
+ align:start position:0%
+okay what's a field that will satisfy
+everybody that will be a gradient field
+
+ align:start position:0%
+everybody that will be a gradient field
+ 
+
+ align:start position:0%
+everybody that will be a gradient field
+and also Divergence free so that it'll
+
+ align:start position:0%
+and also Divergence free so that it'll
+ 
+
+ align:start position:0%
+and also Divergence free so that it'll
+be a it'll we'll have solution to llaus
+
+ align:start position:0%
+be a it'll we'll have solution to llaus
+ 
+
+ align:start position:0%
+be a it'll we'll have solution to llaus
+equation
+
+ align:start position:0%
+equation
+ 
+
+ align:start position:0%
+equation
+uh let's see well we had some solutions
+
+ align:start position:0%
+uh let's see well we had some solutions
+ 
+
+ align:start position:0%
+uh let's see well we had some solutions
+to lus equation
+
+ align:start position:0%
+to lus equation
+ 
+
+ align:start position:0%
+to lus equation
+there how do we get yeah do want
+
+ align:start position:0%
+there how do we get yeah do want
+ 
+
+ align:start position:0%
+there how do we get yeah do want
+you know if I make it linear it's real
+
+ align:start position:0%
+you know if I make it linear it's real
+ 
+
+ align:start position:0%
+you know if I make it linear it's real
+easy
+
+ align:start position:0%
+easy
+ 
+
+ align:start position:0%
+easy
+should I if I make it quadratic we huh
+
+ align:start position:0%
+should I if I make it quadratic we huh
+ 
+
+ align:start position:0%
+should I if I make it quadratic we huh
+let me
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+can can I anticipate a little what's
+
+ align:start position:0%
+can can I anticipate a little what's
+ 
+
+ align:start position:0%
+can can I anticipate a little what's
+coming Friday
+
+ align:start position:0%
+coming Friday
+ 
+
+ align:start position:0%
+coming Friday
+I I still recommend to come to Friday's
+
+ align:start position:0%
+I I still recommend to come to Friday's
+ 
+
+ align:start position:0%
+I I still recommend to come to Friday's
+lecture but uh here here so what's
+
+ align:start position:0%
+lecture but uh here here so what's
+ 
+
+ align:start position:0%
+lecture but uh here here so what's
+coming what did we do today we
+
+ align:start position:0%
+coming what did we do today we
+ 
+
+ align:start position:0%
+coming what did we do today we
+discovered that we got solutions to the
+
+ align:start position:0%
+discovered that we got solutions to the
+ 
+
+ align:start position:0%
+discovered that we got solutions to the
+ples equation from all by real and
+
+ align:start position:0%
+ples equation from all by real and
+ 
+
+ align:start position:0%
+ples equation from all by real and
+imaginary parts of all these guys th
+
+ align:start position:0%
+imaginary parts of all these guys th
+ 
+
+ align:start position:0%
+imaginary parts of all these guys th
+those were terrific
+
+ align:start position:0%
+those were terrific
+ 
+
+ align:start position:0%
+those were terrific
+and then we could take combinations of
+
+ align:start position:0%
+and then we could take combinations of
+ 
+
+ align:start position:0%
+and then we could take combinations of
+those so here's what's coming Friday
+
+ align:start position:0%
+those so here's what's coming Friday
+ 
+
+ align:start position:0%
+those so here's what's coming Friday
+when I take combinations of these guys
+
+ align:start position:0%
+when I take combinations of these guys
+ 
+
+ align:start position:0%
+when I take combinations of these guys
+I get some some function of this magic
+
+ align:start position:0%
+I get some some function of this magic
+ 
+
+ align:start position:0%
+I get some some function of this magic
+complex
+
+ align:start position:0%
+complex
+ 
+
+ align:start position:0%
+complex
+of this magic combination X Plus i y
+
+ align:start position:0%
+of this magic combination X Plus i y
+ 
+
+ align:start position:0%
+of this magic combination X Plus i y
+some function any function any
+
+ align:start position:0%
+some function any function any
+ 
+
+ align:start position:0%
+some function any function any
+reasonable function and we'll say what
+
+ align:start position:0%
+reasonable function and we'll say what
+ 
+
+ align:start position:0%
+reasonable function and we'll say what
+reasonable means of X Plus i y its real
+
+ align:start position:0%
+reasonable means of X Plus i y its real
+ 
+
+ align:start position:0%
+reasonable means of X Plus i y its real
+part and its imaginary part are going to
+
+ align:start position:0%
+part and its imaginary part are going to
+ 
+
+ align:start position:0%
+part and its imaginary part are going to
+be great this is like the center of a
+
+ align:start position:0%
+be great this is like the center of a
+ 
+
+ align:start position:0%
+be great this is like the center of a
+big big part of mathematics functions of
+
+ align:start position:0%
+big big part of mathematics functions of
+ 
+
+ align:start position:0%
+big big part of mathematics functions of
+X Plus i y
+
+ align:start position:0%
+X Plus i y
+ 
+
+ align:start position:0%
+X Plus i y
+and I if by nice I mean that there these
+
+ align:start position:0%
+and I if by nice I mean that there these
+ 
+
+ align:start position:0%
+and I if by nice I mean that there these
+series converge so that we have really a
+
+ align:start position:0%
+series converge so that we have really a
+ 
+
+ align:start position:0%
+series converge so that we have really a
+nice function let me take the first
+
+ align:start position:0%
+nice function let me take the first
+ 
+
+ align:start position:0%
+nice function let me take the first
+function that comes to mind e to the X
+
+ align:start position:0%
+function that comes to mind e to the X
+ 
+
+ align:start position:0%
+function that comes to mind e to the X
+Plus iy so so let me let me take this to
+
+ align:start position:0%
+Plus iy so so let me let me take this to
+ 
+
+ align:start position:0%
+Plus iy so so let me let me take this to
+be e to the x + i y
+
+ align:start position:0%
+be e to the x + i y
+ 
+
+ align:start position:0%
+be e to the x + i y
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+all right so you remember I'm aiming to
+
+ align:start position:0%
+all right so you remember I'm aiming to
+ 
+
+ align:start position:0%
+all right so you remember I'm aiming to
+get solutions to the ples equation
+
+ align:start position:0%
+get solutions to the ples equation
+ 
+
+ align:start position:0%
+get solutions to the ples equation
+because that will give me automatically
+
+ align:start position:0%
+because that will give me automatically
+ 
+
+ align:start position:0%
+because that will give me automatically
+the two pieces both working so I claim
+
+ align:start position:0%
+the two pieces both working so I claim
+ 
+
+ align:start position:0%
+the two pieces both working so I claim
+that the real part of that and the
+
+ align:start position:0%
+that the real part of that and the
+ 
+
+ align:start position:0%
+that the real part of that and the
+imagin part those are my twins U and S
+
+ align:start position:0%
+imagin part those are my twins U and S
+ 
+
+ align:start position:0%
+imagin part those are my twins U and S
+both solve so U is going to be the real
+
+ align:start position:0%
+both solve so U is going to be the real
+ 
+
+ align:start position:0%
+both solve so U is going to be the real
+part of this function and S is going to
+
+ align:start position:0%
+part of this function and S is going to
+ 
+
+ align:start position:0%
+part of this function and S is going to
+be the imaginary part of it and I claim
+
+ align:start position:0%
+be the imaginary part of it and I claim
+ 
+
+ align:start position:0%
+be the imaginary part of it and I claim
+that those will both solve theosis
+
+ align:start position:0%
+that those will both solve theosis
+ 
+
+ align:start position:0%
+that those will both solve theosis
+equation we can plug it in and see that
+
+ align:start position:0%
+equation we can plug it in and see that
+ 
+
+ align:start position:0%
+equation we can plug it in and see that
+it does and that they will have they'll
+
+ align:start position:0%
+it does and that they will have they'll
+ 
+
+ align:start position:0%
+it does and that they will have they'll
+they'll they're twinned by the Koshi
+
+ align:start position:0%
+they'll they're twinned by the Koshi
+ 
+
+ align:start position:0%
+they'll they're twinned by the Koshi
+remon equations so how am I going to
+
+ align:start position:0%
+remon equations so how am I going to
+ 
+
+ align:start position:0%
+remon equations so how am I going to
+simplify that so that I can identify the
+
+ align:start position:0%
+simplify that so that I can identify the
+ 
+
+ align:start position:0%
+simplify that so that I can identify the
+what's the real part of that thing and
+
+ align:start position:0%
+what's the real part of that thing and
+ 
+
+ align:start position:0%
+what's the real part of that thing and
+what's the imaginary part this is
+
+ align:start position:0%
+what's the imaginary part this is
+ 
+
+ align:start position:0%
+what's the imaginary part this is
+actually that's a good question question
+
+ align:start position:0%
+actually that's a good question question
+ 
+
+ align:start position:0%
+actually that's a good question question
+do you we I don't know how many how much
+
+ align:start position:0%
+do you we I don't know how many how much
+ 
+
+ align:start position:0%
+do you we I don't know how many how much
+you've run into I in the past are you
+
+ align:start position:0%
+you've run into I in the past are you
+ 
+
+ align:start position:0%
+you've run into I in the past are you
+happy with
+
+ align:start position:0%
+happy with
+ 
+
+ align:start position:0%
+happy with
+something like that how could you find
+
+ align:start position:0%
+something like that how could you find
+ 
+
+ align:start position:0%
+something like that how could you find
+the real part of it how could you
+
+ align:start position:0%
+the real part of it how could you
+ 
+
+ align:start position:0%
+the real part of it how could you
+simplify it how else could I write e to
+
+ align:start position:0%
+simplify it how else could I write e to
+ 
+
+ align:start position:0%
+simplify it how else could I write e to
+the something
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+what
+
+ align:start position:0%
+what
+ 
+
+ align:start position:0%
+what
+I exactly right it think of it as the
+
+ align:start position:0%
+I exactly right it think of it as the
+ 
+
+ align:start position:0%
+I exactly right it think of it as the
+product of two so the key fact about
+
+ align:start position:0%
+product of two so the key fact about
+ 
+
+ align:start position:0%
+product of two so the key fact about
+exponentials is that that's the same as
+
+ align:start position:0%
+exponentials is that that's the same as
+ 
+
+ align:start position:0%
+exponentials is that that's the same as
+e to the x * e to the i y right that's
+
+ align:start position:0%
+e to the x * e to the i y right that's
+ 
+
+ align:start position:0%
+e to the x * e to the i y right that's
+the exponents add so that's the first
+
+ align:start position:0%
+the exponents add so that's the first
+ 
+
+ align:start position:0%
+the exponents add so that's the first
+thing always to think about as a
+
+ align:start position:0%
+thing always to think about as a
+ 
+
+ align:start position:0%
+thing always to think about as a
+possibility now what am I going to do I
+
+ align:start position:0%
+possibility now what am I going to do I
+ 
+
+ align:start position:0%
+possibility now what am I going to do I
+still want to get a real part this is
+
+ align:start position:0%
+still want to get a real part this is
+ 
+
+ align:start position:0%
+still want to get a real part this is
+clearly all real right e to the x is
+
+ align:start position:0%
+clearly all real right e to the x is
+ 
+
+ align:start position:0%
+clearly all real right e to the x is
+real so it's it's this part that's got
+
+ align:start position:0%
+real so it's it's this part that's got
+ 
+
+ align:start position:0%
+real so it's it's this part that's got
+it's going to give me the two pieces so
+
+ align:start position:0%
+it's going to give me the two pieces so
+ 
+
+ align:start position:0%
+it's going to give me the two pieces so
+it's going to be e to the x times now
+
+ align:start position:0%
+it's going to be e to the x times now
+ 
+
+ align:start position:0%
+it's going to be e to the x times now
+what is what do I put for e to the i y
+
+ align:start position:0%
+what is what do I put for e to the i y
+ 
+
+ align:start position:0%
+what is what do I put for e to the i y
+y cos y good
+
+ align:start position:0%
+y cos y good
+ 
+
+ align:start position:0%
+y cos y good
+plus I sin y good and now I can read off
+
+ align:start position:0%
+plus I sin y good and now I can read off
+ 
+
+ align:start position:0%
+plus I sin y good and now I can read off
+no problem what is this real part that I
+
+ align:start position:0%
+no problem what is this real part that I
+ 
+
+ align:start position:0%
+no problem what is this real part that I
+was looking for
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+E to X cos Y
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and the imaginary part is just the
+
+ align:start position:0%
+and the imaginary part is just the
+ 
+
+ align:start position:0%
+and the imaginary part is just the
+what's multiplying the I it's the e to
+
+ align:start position:0%
+what's multiplying the I it's the e to
+ 
+
+ align:start position:0%
+what's multiplying the I it's the e to
+the X sin y
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+so what's my claim I claim that that
+
+ align:start position:0%
+so what's my claim I claim that that
+ 
+
+ align:start position:0%
+so what's my claim I claim that that
+function solves the ploes equation
+
+ align:start position:0%
+function solves the ploes equation
+ 
+
+ align:start position:0%
+function solves the ploes equation
+and this one too
+
+ align:start position:0%
+and this one too
+ 
+
+ align:start position:0%
+and this one too
+and that they're twinned and that
+
+ align:start position:0%
+and that they're twinned and that
+ 
+
+ align:start position:0%
+and that they're twinned and that
+they're they give streamlines and equip
+
+ align:start position:0%
+they're they give streamlines and equip
+ 
+
+ align:start position:0%
+they're they give streamlines and equip
+potentials that meet at right angles
+
+ align:start position:0%
+potentials that meet at right angles
+ 
+
+ align:start position:0%
+potentials that meet at right angles
+it's it's uh another another pair
+
+ align:start position:0%
+it's it's uh another another pair
+ 
+
+ align:start position:0%
+it's it's uh another another pair
+uh can we plug that into ll's equation
+
+ align:start position:0%
+uh can we plug that into ll's equation
+ 
+
+ align:start position:0%
+uh can we plug that into ll's equation
+so that's so let me do uxx X Plus uy y
+
+ align:start position:0%
+so that's so let me do uxx X Plus uy y
+ 
+
+ align:start position:0%
+so that's so let me do uxx X Plus uy y
+just to satisfy that it is going to come
+
+ align:start position:0%
+just to satisfy that it is going to come
+ 
+
+ align:start position:0%
+just to satisfy that it is going to come
+out zero so what's the XX derivative the
+
+ align:start position:0%
+out zero so what's the XX derivative the
+ 
+
+ align:start position:0%
+out zero so what's the XX derivative the
+second X derivative of that function
+
+ align:start position:0%
+second X derivative of that function
+ 
+
+ align:start position:0%
+second X derivative of that function
+say take its derivative respect to X and
+
+ align:start position:0%
+say take its derivative respect to X and
+ 
+
+ align:start position:0%
+say take its derivative respect to X and
+then do it again and what do you have
+
+ align:start position:0%
+then do it again and what do you have
+ 
+
+ align:start position:0%
+then do it again and what do you have
+same didn't change e to the x is just
+
+ align:start position:0%
+same didn't change e to the x is just
+ 
+
+ align:start position:0%
+same didn't change e to the x is just
+and and now what about the second y
+
+ align:start position:0%
+and and now what about the second y
+ 
+
+ align:start position:0%
+and and now what about the second y
+derivative
+
+ align:start position:0%
+derivative
+ 
+
+ align:start position:0%
+derivative
+so now e to the x is just a constant
+
+ align:start position:0%
+so now e to the x is just a constant
+ 
+
+ align:start position:0%
+so now e to the x is just a constant
+what's the second derivative of cos y
+
+ align:start position:0%
+what's the second derivative of cos y
+ 
+
+ align:start position:0%
+what's the second derivative of cos y
+negative cos y right because the first
+
+ align:start position:0%
+negative cos y right because the first
+ 
+
+ align:start position:0%
+negative cos y right because the first
+derivative is negative s and the second
+
+ align:start position:0%
+derivative is negative s and the second
+ 
+
+ align:start position:0%
+derivative is negative s and the second
+derivative is negative cosine so it's
+
+ align:start position:0%
+derivative is negative cosine so it's
+ 
+
+ align:start position:0%
+derivative is negative cosine so it's
+the second derivative is this e to the x
+
+ align:start position:0%
+the second derivative is this e to the x
+ 
+
+ align:start position:0%
+the second derivative is this e to the x
+that didn't change times cos y with the
+
+ align:start position:0%
+that didn't change times cos y with the
+ 
+
+ align:start position:0%
+that didn't change times cos y with the
+minus sign and you see what what
+
+ align:start position:0%
+minus sign and you see what what
+ 
+
+ align:start position:0%
+minus sign and you see what what
+did I write S I meant to write cosine
+
+ align:start position:0%
+did I write S I meant to write cosine
+ 
+
+ align:start position:0%
+did I write S I meant to write cosine
+cancel that from the tape okay right
+
+ align:start position:0%
+cancel that from the tape okay right
+ 
+
+ align:start position:0%
+cancel that from the tape okay right
+yeah so the second X derivative was just
+
+ align:start position:0%
+yeah so the second X derivative was just
+ 
+
+ align:start position:0%
+yeah so the second X derivative was just
+e the x e to the X cos y didn't move
+
+ align:start position:0%
+e the x e to the X cos y didn't move
+ 
+
+ align:start position:0%
+e the x e to the X cos y didn't move
+sorry that was frightening okay and then
+
+ align:start position:0%
+sorry that was frightening okay and then
+ 
+
+ align:start position:0%
+sorry that was frightening okay and then
+now here's the second second y
+
+ align:start position:0%
+now here's the second second y
+ 
+
+ align:start position:0%
+now here's the second second y
+derivative in other words it gives zero
+
+ align:start position:0%
+derivative in other words it gives zero
+ 
+
+ align:start position:0%
+derivative in other words it gives zero
+give zero and this one would too yeah so
+
+ align:start position:0%
+give zero and this one would too yeah so
+ 
+
+ align:start position:0%
+give zero and this one would too yeah so
+those are two now I will not do I don't
+
+ align:start position:0%
+those are two now I will not do I don't
+ 
+
+ align:start position:0%
+those are two now I will not do I don't
+really have an idea of what those what
+
+ align:start position:0%
+really have an idea of what those what
+ 
+
+ align:start position:0%
+really have an idea of what those what
+the picture is like
+
+ align:start position:0%
+the picture is like
+ 
+
+ align:start position:0%
+the picture is like
+uh but
+
+ align:start position:0%
+uh but
+ 
+
+ align:start position:0%
+uh but
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+it it's important we've got a flow field
+
+ align:start position:0%
+it it's important we've got a flow field
+ 
+
+ align:start position:0%
+it it's important we've got a flow field
+here and and it's from e to the z e to
+
+ align:start position:0%
+here and and it's from e to the z e to
+ 
+
+ align:start position:0%
+here and and it's from e to the z e to
+the X Plus i y exponential is a got to
+
+ align:start position:0%
+the X Plus i y exponential is a got to
+ 
+
+ align:start position:0%
+the X Plus i y exponential is a got to
+be an important function so it's got to
+
+ align:start position:0%
+be an important function so it's got to
+ 
+
+ align:start position:0%
+be an important function so it's got to
+be somehow interesting what do you think
+
+ align:start position:0%
+be somehow interesting what do you think
+ 
+
+ align:start position:0%
+be somehow interesting what do you think
+so what would the uh
+
+ align:start position:0%
+so what would the uh
+ 
+
+ align:start position:0%
+so what would the uh
+what would the ex equip potential lines
+
+ align:start position:0%
+what would the ex equip potential lines
+ 
+
+ align:start position:0%
+what would the ex equip potential lines
+look like oh boy e to X cos yal constant
+
+ align:start position:0%
+look like oh boy e to X cos yal constant
+ 
+
+ align:start position:0%
+look like oh boy e to X cos yal constant
+my gosh e to X cos y so let's see
+
+ align:start position:0%
+my gosh e to X cos y so let's see
+ 
+
+ align:start position:0%
+my gosh e to X cos y so let's see
+I I don't know how to draw this picture
+
+ align:start position:0%
+I I don't know how to draw this picture
+ 
+
+ align:start position:0%
+I I don't know how to draw this picture
+but I but one thing I know
+
+ align:start position:0%
+but I but one thing I know
+ 
+
+ align:start position:0%
+but I but one thing I know
+is that if I changed y by 2 pi I would
+
+ align:start position:0%
+is that if I changed y by 2 pi I would
+ 
+
+ align:start position:0%
+is that if I changed y by 2 pi I would
+get another copy of of this curve right
+
+ align:start position:0%
+get another copy of of this curve right
+ 
+
+ align:start position:0%
+get another copy of of this curve right
+if I changed y by every time you see
+
+ align:start position:0%
+if I changed y by every time you see
+ 
+
+ align:start position:0%
+if I changed y by every time you see
+cosine or S you think hey that's
+
+ align:start position:0%
+cosine or S you think hey that's
+ 
+
+ align:start position:0%
+cosine or S you think hey that's
+periodic if I change it by 2 pi so I'm
+
+ align:start position:0%
+periodic if I change it by 2 pi so I'm
+ 
+
+ align:start position:0%
+periodic if I change it by 2 pi so I'm
+thinking that the I'm thinking that say
+
+ align:start position:0%
+thinking that the I'm thinking that say
+ 
+
+ align:start position:0%
+thinking that the I'm thinking that say
+why from I I'm thinking that y between Z
+
+ align:start position:0%
+why from I I'm thinking that y between Z
+ 
+
+ align:start position:0%
+why from I I'm thinking that y between Z
+and 2 pi so here's yal 0
+
+ align:start position:0%
+and 2 pi so here's yal 0
+ 
+
+ align:start position:0%
+and 2 pi so here's yal 0
+and yal 2 pi I'm thinking that my flow
+
+ align:start position:0%
+and yal 2 pi I'm thinking that my flow
+ 
+
+ align:start position:0%
+and yal 2 pi I'm thinking that my flow
+probably
+
+ align:start position:0%
+probably
+ 
+
+ align:start position:0%
+probably
+somehow is stays in a strip
+
+ align:start position:0%
+somehow is stays in a strip
+ 
+
+ align:start position:0%
+somehow is stays in a strip
+like that and then the whole thing just
+
+ align:start position:0%
+like that and then the whole thing just
+ 
+
+ align:start position:0%
+like that and then the whole thing just
+repeats and repeats and repeats so I I'm
+
+ align:start position:0%
+repeats and repeats and repeats so I I'm
+ 
+
+ align:start position:0%
+repeats and repeats and repeats so I I'm
+thinking really this is flow in an
+
+ align:start position:0%
+thinking really this is flow in an
+ 
+
+ align:start position:0%
+thinking really this is flow in an
+infinite strip infinite pipe or
+
+ align:start position:0%
+infinite strip infinite pipe or
+ 
+
+ align:start position:0%
+infinite strip infinite pipe or
+something like that you can imagine that
+
+ align:start position:0%
+something like that you can imagine that
+ 
+
+ align:start position:0%
+something like that you can imagine that
+that could be there could be
+
+ align:start position:0%
+that could be there could be
+ 
+
+ align:start position:0%
+that could be there could be
+applications so I but I still haven't
+
+ align:start position:0%
+applications so I but I still haven't
+ 
+
+ align:start position:0%
+applications so I but I still haven't
+drawn the curve I just think uh let's
+
+ align:start position:0%
+drawn the curve I just think uh let's
+ 
+
+ align:start position:0%
+drawn the curve I just think uh let's
+see what what would it look like when Y
+
+ align:start position:0%
+see what what would it look like when Y
+ 
+
+ align:start position:0%
+see what what would it look like when Y
+is a little
+
+ align:start position:0%
+is a little
+ 
+
+ align:start position:0%
+is a little
+suppose I'm trying to draw the picture
+
+ align:start position:0%
+suppose I'm trying to draw the picture
+ 
+
+ align:start position:0%
+suppose I'm trying to draw the picture
+of e to the X cos yal
+
+ align:start position:0%
+of e to the X cos yal
+ 
+
+ align:start position:0%
+of e to the X cos yal
+1 whatever okay
+
+ align:start position:0%
+1 whatever okay
+ 
+
+ align:start position:0%
+1 whatever okay
+let me try to I'll just attempt to draw
+
+ align:start position:0%
+let me try to I'll just attempt to draw
+ 
+
+ align:start position:0%
+let me try to I'll just attempt to draw
+that curve just just
+
+ align:start position:0%
+that curve just just
+ 
+
+ align:start position:0%
+that curve just just
+so if y was a little bit just a little
+
+ align:start position:0%
+so if y was a little bit just a little
+ 
+
+ align:start position:0%
+so if y was a little bit just a little
+bit off of zero the cosine would be
+
+ align:start position:0%
+bit off of zero the cosine would be
+ 
+
+ align:start position:0%
+bit off of zero the cosine would be
+yeah how's it going to go if Y is just a
+
+ align:start position:0%
+yeah how's it going to go if Y is just a
+ 
+
+ align:start position:0%
+yeah how's it going to go if Y is just a
+little off zero
+
+ align:start position:0%
+little off zero
+ 
+
+ align:start position:0%
+little off zero
+uh
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+well can are tell me any points on this
+
+ align:start position:0%
+well can are tell me any points on this
+ 
+
+ align:start position:0%
+well can are tell me any points on this
+curve
+
+ align:start position:0%
+curve
+ 
+
+ align:start position:0%
+curve
+uh yeah
+
+ align:start position:0%
+uh yeah
+ 
+
+ align:start position:0%
+uh yeah
+I I can see that my yeah e to the x is
+
+ align:start position:0%
+I I can see that my yeah e to the x is
+ 
+
+ align:start position:0%
+I I can see that my yeah e to the x is
+going to be a big number if if x
+
+ align:start position:0%
+going to be a big number if if x
+ 
+
+ align:start position:0%
+going to be a big number if if x
+yeah is z z on the curve good got one
+
+ align:start position:0%
+yeah is z z on the curve good got one
+ 
+
+ align:start position:0%
+yeah is z z on the curve good got one
+point all right got got the easier now
+
+ align:start position:0%
+point all right got got the easier now
+ 
+
+ align:start position:0%
+point all right got got the easier now
+all right uh now suppose Y is a little
+
+ align:start position:0%
+all right uh now suppose Y is a little
+ 
+
+ align:start position:0%
+all right uh now suppose Y is a little
+bit more than zero so suppose I go up a
+
+ align:start position:0%
+bit more than zero so suppose I go up a
+ 
+
+ align:start position:0%
+bit more than zero so suppose I go up a
+little bit then what one Z or something
+
+ align:start position:0%
+little bit then what one Z or something
+ 
+
+ align:start position:0%
+little bit then what one Z or something
+yeah suppose
+
+ align:start position:0%
+yeah suppose
+ 
+
+ align:start position:0%
+yeah suppose
+one zero no no uh yeah so so if y goes
+
+ align:start position:0%
+one zero no no uh yeah so so if y goes
+ 
+
+ align:start position:0%
+one zero no no uh yeah so so if y goes
+up a little
+
+ align:start position:0%
+up a little
+ 
+
+ align:start position:0%
+up a little
+uh then X would go out a little bit I I
+
+ align:start position:0%
+uh then X would go out a little bit I I
+ 
+
+ align:start position:0%
+uh then X would go out a little bit I I
+think you think so what's happening so
+
+ align:start position:0%
+think you think so what's happening so
+ 
+
+ align:start position:0%
+think you think so what's happening so
+cosine of Y so what's the cosine of Y is
+
+ align:start position:0%
+cosine of Y so what's the cosine of Y is
+ 
+
+ align:start position:0%
+cosine of Y so what's the cosine of Y is
+the cosine of Y is going to drop from
+
+ align:start position:0%
+the cosine of Y is going to drop from
+ 
+
+ align:start position:0%
+the cosine of Y is going to drop from
+one to zero right
+
+ align:start position:0%
+one to zero right
+ 
+
+ align:start position:0%
+one to zero right
+to start with then if this cosine of Y
+
+ align:start position:0%
+to start with then if this cosine of Y
+ 
+
+ align:start position:0%
+to start with then if this cosine of Y
+is dropping from one to zero then this e
+
+ align:start position:0%
+is dropping from one to zero then this e
+ 
+
+ align:start position:0%
+is dropping from one to zero then this e
+to the X has got to climb up
+
+ align:start position:0%
+to the X has got to climb up
+ 
+
+ align:start position:0%
+to the X has got to climb up
+to to keep the product one so I'll move
+
+ align:start position:0%
+to to keep the product one so I'll move
+ 
+
+ align:start position:0%
+to to keep the product one so I'll move
+out so somehow it'll move out I I don't
+
+ align:start position:0%
+out so somehow it'll move out I I don't
+ 
+
+ align:start position:0%
+out so somehow it'll move out I I don't
+know what the
+
+ align:start position:0%
+know what the
+ 
+
+ align:start position:0%
+know what the
+this is at well yeah that's really at pi
+
+ align:start position:0%
+this is at well yeah that's really at pi
+ 
+
+ align:start position:0%
+this is at well yeah that's really at pi
+over two when
+
+ align:start position:0%
+over two when
+ 
+
+ align:start position:0%
+over two when
+maybe I think it's I think maybe at that
+
+ align:start position:0%
+maybe I think it's I think maybe at that
+ 
+
+ align:start position:0%
+maybe I think it's I think maybe at that
+point Pi when when y reaches Pi / 2 then
+
+ align:start position:0%
+point Pi when when y reaches Pi / 2 then
+ 
+
+ align:start position:0%
+point Pi when when y reaches Pi / 2 then
+the cosine has got down to zero
+
+ align:start position:0%
+the cosine has got down to zero
+ 
+
+ align:start position:0%
+the cosine has got down to zero
+you know
+
+ align:start position:0%
+you know
+ 
+
+ align:start position:0%
+you know
+we could we could work on this for a
+
+ align:start position:0%
+we could we could work on this for a
+ 
+
+ align:start position:0%
+we could we could work on this for a
+while or or we could let mat lab draw it
+
+ align:start position:0%
+while or or we could let mat lab draw it
+ 
+
+ align:start position:0%
+while or or we could let mat lab draw it
+but I think that we would see these uh
+
+ align:start position:0%
+but I think that we would see these uh
+ 
+
+ align:start position:0%
+but I think that we would see these uh
+and I I could do better I'm feeling
+
+ align:start position:0%
+and I I could do better I'm feeling
+ 
+
+ align:start position:0%
+and I I could do better I'm feeling
+pretty humiliated to not have a better
+
+ align:start position:0%
+pretty humiliated to not have a better
+ 
+
+ align:start position:0%
+pretty humiliated to not have a better
+picture here suppose Y is a little less
+
+ align:start position:0%
+picture here suppose Y is a little less
+ 
+
+ align:start position:0%
+picture here suppose Y is a little less
+than zero do we get anything interesting
+
+ align:start position:0%
+than zero do we get anything interesting
+ 
+
+ align:start position:0%
+than zero do we get anything interesting
+there oh well the cosine is an even
+
+ align:start position:0%
+there oh well the cosine is an even
+ 
+
+ align:start position:0%
+there oh well the cosine is an even
+function so I think the thing might is
+
+ align:start position:0%
+function so I think the thing might is
+ 
+
+ align:start position:0%
+function so I think the thing might is
+it just going to turn around like that
+
+ align:start position:0%
+it just going to turn around like that
+ 
+
+ align:start position:0%
+it just going to turn around like that
+I mean so that Y and minus y for this
+
+ align:start position:0%
+I mean so that Y and minus y for this
+ 
+
+ align:start position:0%
+I mean so that Y and minus y for this
+for a certain X the Y value and the
+
+ align:start position:0%
+for a certain X the Y value and the
+ 
+
+ align:start position:0%
+for a certain X the Y value and the
+minus y will both be on the curve
+
+ align:start position:0%
+minus y will both be on the curve
+ 
+
+ align:start position:0%
+minus y will both be on the curve
+because the cosine doesn't know whether
+
+ align:start position:0%
+because the cosine doesn't know whether
+ 
+
+ align:start position:0%
+because the cosine doesn't know whether
+it's the cosine of a plus or a minus
+
+ align:start position:0%
+it's the cosine of a plus or a minus
+ 
+
+ align:start position:0%
+it's the cosine of a plus or a minus
+yeah I I think we would get curves of
+
+ align:start position:0%
+yeah I I think we would get curves of
+ 
+
+ align:start position:0%
+yeah I I think we would get curves of
+that sort yeah yeah
+
+ align:start position:0%
+that sort yeah yeah
+ 
+
+ align:start position:0%
+that sort yeah yeah
+and then the uh the other the curves
+
+ align:start position:0%
+and then the uh the other the curves
+ 
+
+ align:start position:0%
+and then the uh the other the curves
+seal constant the streamlines will
+
+ align:start position:0%
+seal constant the streamlines will
+ 
+
+ align:start position:0%
+seal constant the streamlines will
+somehow go vertically yeah I maybe I'll
+
+ align:start position:0%
+somehow go vertically yeah I maybe I'll
+ 
+
+ align:start position:0%
+somehow go vertically yeah I maybe I'll
+just not use the whole time to
+
+ align:start position:0%
+just not use the whole time to
+ 
+
+ align:start position:0%
+just not use the whole time to
+to uh work on that particular curve I
+
+ align:start position:0%
+to uh work on that particular curve I
+ 
+
+ align:start position:0%
+to uh work on that particular curve I
+would have to prepare it but the point
+
+ align:start position:0%
+would have to prepare it but the point
+ 
+
+ align:start position:0%
+would have to prepare it but the point
+is you see how incredibly easily we
+
+ align:start position:0%
+is you see how incredibly easily we
+ 
+
+ align:start position:0%
+is you see how incredibly easily we
+produce solutions that lasses equation
+
+ align:start position:0%
+produce solutions that lasses equation
+ 
+
+ align:start position:0%
+produce solutions that lasses equation
+that you wouldn't have thought of and I
+
+ align:start position:0%
+that you wouldn't have thought of and I
+ 
+
+ align:start position:0%
+that you wouldn't have thought of and I
+wouldn't have thought of so that would
+
+ align:start position:0%
+wouldn't have thought of so that would
+ 
+
+ align:start position:0%
+wouldn't have thought of so that would
+be one way to produce Solutions I I'll I
+
+ align:start position:0%
+be one way to produce Solutions I I'll I
+ 
+
+ align:start position:0%
+be one way to produce Solutions I I'll I
+might even repeat this one in class uh
+
+ align:start position:0%
+might even repeat this one in class uh
+ 
+
+ align:start position:0%
+might even repeat this one in class uh
+Friday or I might not let me suggest
+
+ align:start position:0%
+Friday or I might not let me suggest
+ 
+
+ align:start position:0%
+Friday or I might not let me suggest
+another couple of possibilities that I
+
+ align:start position:0%
+another couple of possibilities that I
+ 
+
+ align:start position:0%
+another couple of possibilities that I
+will do in class uh can I just give you
+
+ align:start position:0%
+will do in class uh can I just give you
+ 
+
+ align:start position:0%
+will do in class uh can I just give you
+a couple of other functions F
+
+ align:start position:0%
+a couple of other functions F
+ 
+
+ align:start position:0%
+a couple of other functions F
+in fact I'll just erase that one and put
+
+ align:start position:0%
+in fact I'll just erase that one and put
+ 
+
+ align:start position:0%
+in fact I'll just erase that one and put
+in some other ones suppose I took the
+
+ align:start position:0%
+in some other ones suppose I took the
+ 
+
+ align:start position:0%
+in some other ones suppose I took the
+function
+
+ align:start position:0%
+function
+ 
+
+ align:start position:0%
+function
+1 over x + i y
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+what's its so that's a function of this
+
+ align:start position:0%
+what's its so that's a function of this
+ 
+
+ align:start position:0%
+what's its so that's a function of this
+magic combination X Plus i y what's its
+
+ align:start position:0%
+magic combination X Plus i y what's its
+ 
+
+ align:start position:0%
+magic combination X Plus i y what's its
+real part and what's its imaginary part
+
+ align:start position:0%
+real part and what's its imaginary part
+ 
+
+ align:start position:0%
+real part and what's its imaginary part
+can you do you know how to split that
+
+ align:start position:0%
+can you do you know how to split that
+ 
+
+ align:start position:0%
+can you do you know how to split that
+guy into real and imaginary there a
+
+ align:start position:0%
+guy into real and imaginary there a
+ 
+
+ align:start position:0%
+guy into real and imaginary there a
+there's a little trick if you remember
+
+ align:start position:0%
+there's a little trick if you remember
+ 
+
+ align:start position:0%
+there's a little trick if you remember
+from learning complex numbers
+
+ align:start position:0%
+from learning complex numbers
+ 
+
+ align:start position:0%
+from learning complex numbers
+do you remember the trick the is that
+
+ align:start position:0%
+do you remember the trick the is that
+ 
+
+ align:start position:0%
+do you remember the trick the is that
+that this thing is down in the
+
+ align:start position:0%
+that this thing is down in the
+ 
+
+ align:start position:0%
+that this thing is down in the
+denominator right we don't want it there
+
+ align:start position:0%
+denominator right we don't want it there
+ 
+
+ align:start position:0%
+denominator right we don't want it there
+because we can't split the real
+
+ align:start position:0%
+because we can't split the real
+ 
+
+ align:start position:0%
+because we can't split the real
+imaginary Parts down there so I would
+
+ align:start position:0%
+imaginary Parts down there so I would
+ 
+
+ align:start position:0%
+imaginary Parts down there so I would
+like to rewrite it in a way that gets
+
+ align:start position:0%
+like to rewrite it in a way that gets
+ 
+
+ align:start position:0%
+like to rewrite it in a way that gets
+something real down the denominator
+
+ align:start position:0%
+something real down the denominator
+ 
+
+ align:start position:0%
+something real down the denominator
+moves all the i stuff up in the
+
+ align:start position:0%
+moves all the i stuff up in the
+ 
+
+ align:start position:0%
+moves all the i stuff up in the
+numerator where I can separate do how do
+
+ align:start position:0%
+numerator where I can separate do how do
+ 
+
+ align:start position:0%
+numerator where I can separate do how do
+I do it
+
+ align:start position:0%
+I do it
+ 
+
+ align:start position:0%
+I do it
+good multiply both sides by both top and
+
+ align:start position:0%
+good multiply both sides by both top and
+ 
+
+ align:start position:0%
+good multiply both sides by both top and
+bottom by
+
+ align:start position:0%
+bottom by
+ 
+
+ align:start position:0%
+bottom by
+by x minus iy good
+
+ align:start position:0%
+by x minus iy good
+ 
+
+ align:start position:0%
+by x minus iy good
+that that that trick puts so what does
+
+ align:start position:0%
+that that that trick puts so what does
+ 
+
+ align:start position:0%
+that that that trick puts so what does
+that put down here now that's a number
+
+ align:start position:0%
+that put down here now that's a number
+ 
+
+ align:start position:0%
+that put down here now that's a number
+times its conjugate and that's going to
+
+ align:start position:0%
+times its conjugate and that's going to
+ 
+
+ align:start position:0%
+times its conjugate and that's going to
+produce
+
+ align:start position:0%
+produce
+ 
+
+ align:start position:0%
+produce
+X2
+
+ align:start position:0%
+X2
+ 
+
+ align:start position:0%
+X2
+minus or plus
+
+ align:start position:0%
+minus or plus
+ 
+
+ align:start position:0%
+minus or plus
+plus y^2 right the number times its
+
+ align:start position:0%
+plus y^2 right the number times its
+ 
+
+ align:start position:0%
+plus y^2 right the number times its
+conjugate is the length squared and now
+
+ align:start position:0%
+conjugate is the length squared and now
+ 
+
+ align:start position:0%
+conjugate is the length squared and now
+we just have x - i y and now it's
+
+ align:start position:0%
+we just have x - i y and now it's
+ 
+
+ align:start position:0%
+we just have x - i y and now it's
+obvious what the U is
+
+ align:start position:0%
+obvious what the U is
+ 
+
+ align:start position:0%
+obvious what the U is
+the real part this is real now so the U
+
+ align:start position:0%
+the real part this is real now so the U
+ 
+
+ align:start position:0%
+the real part this is real now so the U
+is just X over x^2 + y^2 and the and the
+
+ align:start position:0%
+is just X over x^2 + y^2 and the and the
+ 
+
+ align:start position:0%
+is just X over x^2 + y^2 and the and the
+S is the minus y over x^2 + y^2
+
+ align:start position:0%
+S is the minus y over x^2 + y^2
+ 
+
+ align:start position:0%
+S is the minus y over x^2 + y^2
+that's a very interesting flow that's an
+
+ align:start position:0%
+that's a very interesting flow that's an
+ 
+
+ align:start position:0%
+that's a very interesting flow that's an
+interesting flow and and we could do its
+
+ align:start position:0%
+interesting flow and and we could do its
+ 
+
+ align:start position:0%
+interesting flow and and we could do its
+picture and so on in fact it would be a
+
+ align:start position:0%
+picture and so on in fact it would be a
+ 
+
+ align:start position:0%
+picture and so on in fact it would be a
+nicer picture than the one we stopped on
+
+ align:start position:0%
+nicer picture than the one we stopped on
+ 
+
+ align:start position:0%
+nicer picture than the one we stopped on
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+what what you what should I notice about
+
+ align:start position:0%
+what what you what should I notice about
+ 
+
+ align:start position:0%
+what what you what should I notice about
+this flow it yeah of course the flow is
+
+ align:start position:0%
+this flow it yeah of course the flow is
+ 
+
+ align:start position:0%
+this flow it yeah of course the flow is
+automatically
+
+ align:start position:0%
+automatically
+ 
+
+ align:start position:0%
+automatically
+um IR rotational the curl is zero
+
+ align:start position:0%
+um IR rotational the curl is zero
+ 
+
+ align:start position:0%
+um IR rotational the curl is zero
+because there is a there is a potential
+
+ align:start position:0%
+because there is a there is a potential
+ 
+
+ align:start position:0%
+because there is a there is a potential
+the gradient of a potential the gradient
+
+ align:start position:0%
+the gradient of a potential the gradient
+ 
+
+ align:start position:0%
+the gradient of a potential the gradient
+of of a potential is going to be uh free
+
+ align:start position:0%
+of of a potential is going to be uh free
+ 
+
+ align:start position:0%
+of of a potential is going to be uh free
+of rotation and there will be
+
+ align:start position:0%
+of rotation and there will be
+ 
+
+ align:start position:0%
+of rotation and there will be
+streamlines all those good things there
+
+ align:start position:0%
+streamlines all those good things there
+ 
+
+ align:start position:0%
+streamlines all those good things there
+so what
+
+ align:start position:0%
+so what
+ 
+
+ align:start position:0%
+so what
+there's one bad point about the flow
+
+ align:start position:0%
+there's one bad point about the flow
+ 
+
+ align:start position:0%
+there's one bad point about the flow
+though
+
+ align:start position:0%
+though
+ 
+
+ align:start position:0%
+though
+which is where at Z 0 the whole thing
+
+ align:start position:0%
+which is where at Z 0 the whole thing
+ 
+
+ align:start position:0%
+which is where at Z 0 the whole thing
+falls apart right if at the origin This
+
+ align:start position:0%
+falls apart right if at the origin This
+ 
+
+ align:start position:0%
+falls apart right if at the origin This
+falls apart so this is a great flow
+
+ align:start position:0%
+falls apart so this is a great flow
+ 
+
+ align:start position:0%
+falls apart so this is a great flow
+except at the origin it's uh it's very
+
+ align:start position:0%
+except at the origin it's uh it's very
+ 
+
+ align:start position:0%
+except at the origin it's uh it's very
+problematic it's singular at the origin
+
+ align:start position:0%
+problematic it's singular at the origin
+ 
+
+ align:start position:0%
+problematic it's singular at the origin
+so yeah so if we drew the pictures we
+
+ align:start position:0%
+so yeah so if we drew the pictures we
+ 
+
+ align:start position:0%
+so yeah so if we drew the pictures we
+would see you know something strange
+
+ align:start position:0%
+would see you know something strange
+ 
+
+ align:start position:0%
+would see you know something strange
+this is is this is going to zero at the
+
+ align:start position:0%
+this is is this is going to zero at the
+ 
+
+ align:start position:0%
+this is is this is going to zero at the
+origin so yeah we have trouble at the
+
+ align:start position:0%
+origin so yeah we have trouble at the
+ 
+
+ align:start position:0%
+origin so yeah we have trouble at the
+origin but an important flow otherwise
+
+ align:start position:0%
+origin but an important flow otherwise
+ 
+
+ align:start position:0%
+origin but an important flow otherwise
+yeah and I'll just mention the third but
+
+ align:start position:0%
+yeah and I'll just mention the third but
+ 
+
+ align:start position:0%
+yeah and I'll just mention the third but
+I won't do anything with it because I
+
+ align:start position:0%
+I won't do anything with it because I
+ 
+
+ align:start position:0%
+I won't do anything with it because I
+because it's such a neat one that I have
+
+ align:start position:0%
+because it's such a neat one that I have
+ 
+
+ align:start position:0%
+because it's such a neat one that I have
+to save it for uh Friday it's the other
+
+ align:start position:0%
+to save it for uh Friday it's the other
+ 
+
+ align:start position:0%
+to save it for uh Friday it's the other
+natural function to think of is the
+
+ align:start position:0%
+natural function to think of is the
+ 
+
+ align:start position:0%
+natural function to think of is the
+logarithm the logarithm of X+ iy
+
+ align:start position:0%
+logarithm the logarithm of X+ iy
+ 
+
+ align:start position:0%
+logarithm the logarithm of X+ iy
+split that into U and a yes
+
+ align:start position:0%
+split that into U and a yes
+ 
+
+ align:start position:0%
+split that into U and a yes
+what kind of thing do we have here what
+
+ align:start position:0%
+what kind of thing do we have here what
+ 
+
+ align:start position:0%
+what kind of thing do we have here what
+kind of Singularity I mean yeah let me
+
+ align:start position:0%
+kind of Singularity I mean yeah let me
+ 
+
+ align:start position:0%
+kind of Singularity I mean yeah let me
+just do two moments on this example and
+
+ align:start position:0%
+just do two moments on this example and
+ 
+
+ align:start position:0%
+just do two moments on this example and
+then leave it for Friday because it's
+
+ align:start position:0%
+then leave it for Friday because it's
+ 
+
+ align:start position:0%
+then leave it for Friday because it's
+the whole class has to see it uh is
+
+ align:start position:0%
+the whole class has to see it uh is
+ 
+
+ align:start position:0%
+the whole class has to see it uh is
+there a singularity for this guy
+
+ align:start position:0%
+there a singularity for this guy
+ 
+
+ align:start position:0%
+there a singularity for this guy
+is there a point XY where the logorithm
+
+ align:start position:0%
+is there a point XY where the logorithm
+ 
+
+ align:start position:0%
+is there a point XY where the logorithm
+is not uh great
+
+ align:start position:0%
+is not uh great
+ 
+
+ align:start position:0%
+is not uh great
+at the the origin again the or this will
+
+ align:start position:0%
+at the the origin again the or this will
+ 
+
+ align:start position:0%
+at the the origin again the or this will
+again have a singularity at the origin
+
+ align:start position:0%
+again have a singularity at the origin
+ 
+
+ align:start position:0%
+again have a singularity at the origin
+something strange is happening at the
+
+ align:start position:0%
+something strange is happening at the
+ 
+
+ align:start position:0%
+something strange is happening at the
+origin and and what we'll find is
+
+ align:start position:0%
+origin and and what we'll find is
+ 
+
+ align:start position:0%
+origin and and what we'll find is
+there's a Delta function there the we're
+
+ align:start position:0%
+there's a Delta function there the we're
+ 
+
+ align:start position:0%
+there's a Delta function there the we're
+feeding in uh we we have a source right
+
+ align:start position:0%
+feeding in uh we we have a source right
+ 
+
+ align:start position:0%
+feeding in uh we we have a source right
+at the origin and then it's flowing out
+
+ align:start position:0%
+at the origin and then it's flowing out
+ 
+
+ align:start position:0%
+at the origin and then it's flowing out
+uh on uh I think on radial lines I think
+
+ align:start position:0%
+uh on uh I think on radial lines I think
+ 
+
+ align:start position:0%
+uh on uh I think on radial lines I think
+the streamlines go out from the origin
+
+ align:start position:0%
+the streamlines go out from the origin
+ 
+
+ align:start position:0%
+the streamlines go out from the origin
+and the equip potentials go around the
+
+ align:start position:0%
+and the equip potentials go around the
+ 
+
+ align:start position:0%
+and the equip potentials go around the
+origin yeah it's a great example so
+
+ align:start position:0%
+origin yeah it's a great example so
+ 
+
+ align:start position:0%
+origin yeah it's a great example so
+that's another another one to come okay
+
+ align:start position:0%
+that's another another one to come okay
+ 
+
+ align:start position:0%
+that's another another one to come okay
+so examples like these are
+
+ align:start position:0%
+so examples like these are
+ 
+
+ align:start position:0%
+so examples like these are
+I mean
+
+ align:start position:0%
+I mean
+ 
+
+ align:start position:0%
+I mean
+generations of thinking went into uh
+
+ align:start position:0%
+generations of thinking went into uh
+ 
+
+ align:start position:0%
+generations of thinking went into uh
+Solutions of Thea equation yeah and in
+
+ align:start position:0%
+Solutions of Thea equation yeah and in
+ 
+
+ align:start position:0%
+Solutions of Thea equation yeah and in
+and 2D particularly where we have this
+
+ align:start position:0%
+and 2D particularly where we have this
+ 
+
+ align:start position:0%
+and 2D particularly where we have this
+special uh combination I'm I wish we had
+
+ align:start position:0%
+special uh combination I'm I wish we had
+ 
+
+ align:start position:0%
+special uh combination I'm I wish we had
+such a combination in 3D but we simply
+
+ align:start position:0%
+such a combination in 3D but we simply
+ 
+
+ align:start position:0%
+such a combination in 3D but we simply
+don't you know we can discuss the
+
+ align:start position:0%
+don't you know we can discuss the
+ 
+
+ align:start position:0%
+don't you know we can discuss the
+equation in 3D of course very important
+
+ align:start position:0%
+equation in 3D of course very important
+ 
+
+ align:start position:0%
+equation in 3D of course very important
+but I mean wave equation this the fact
+
+ align:start position:0%
+but I mean wave equation this the fact
+ 
+
+ align:start position:0%
+but I mean wave equation this the fact
+we're talking to each other is is uh got
+
+ align:start position:0%
+we're talking to each other is is uh got
+ 
+
+ align:start position:0%
+we're talking to each other is is uh got
+the lassan in 3D but
+
+ align:start position:0%
+the lassan in 3D but
+ 
+
+ align:start position:0%
+the lassan in 3D but
+it uh that there's no exp plus iy magic
+
+ align:start position:0%
+it uh that there's no exp plus iy magic
+ 
+
+ align:start position:0%
+it uh that there's no exp plus iy magic
+right okay that's some U's and S's and
+
+ align:start position:0%
+right okay that's some U's and S's and
+ 
+
+ align:start position:0%
+right okay that's some U's and S's and
+and v's and W's what else is on your
+
+ align:start position:0%
+and v's and W's what else is on your
+ 
+
+ align:start position:0%
+and v's and W's what else is on your
+mind
+
+ align:start position:0%
+mind
+ 
+
+ align:start position:0%
+mind
+question
+
+ align:start position:0%
+question
+ 
+
+ align:start position:0%
+question
+shall I
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+I could ask this question oh here's
+
+ align:start position:0%
+I could ask this question oh here's
+ 
+
+ align:start position:0%
+I could ask this question oh here's
+something I did not do in class
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+I I think I wrote down the Divergence
+
+ align:start position:0%
+I I think I wrote down the Divergence
+ 
+
+ align:start position:0%
+I I think I wrote down the Divergence
+Theorem so can we start by doing that
+
+ align:start position:0%
+Theorem so can we start by doing that
+ 
+
+ align:start position:0%
+Theorem so can we start by doing that
+let me write down the Divergence Theorem
+
+ align:start position:0%
+let me write down the Divergence Theorem
+ 
+
+ align:start position:0%
+let me write down the Divergence Theorem
+or let with your help
+
+ align:start position:0%
+or let with your help
+ 
+
+ align:start position:0%
+or let with your help
+and then uh use it
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so what does the Divergence theorem
+
+ align:start position:0%
+so what does the Divergence theorem
+ 
+
+ align:start position:0%
+so what does the Divergence theorem
+we're in 2D so this is 2D
+
+ align:start position:0%
+we're in 2D so this is 2D
+ 
+
+ align:start position:0%
+we're in 2D so this is 2D
+just a similar theorem and so what's the
+
+ align:start position:0%
+just a similar theorem and so what's the
+ 
+
+ align:start position:0%
+just a similar theorem and so what's the
+what is the theorem say
+
+ align:start position:0%
+what is the theorem say
+ 
+
+ align:start position:0%
+what is the theorem say
+that if I take the Divergence of some W
+
+ align:start position:0%
+that if I take the Divergence of some W
+ 
+
+ align:start position:0%
+that if I take the Divergence of some W
+some Vector field
+
+ align:start position:0%
+some Vector field
+ 
+
+ align:start position:0%
+some Vector field
+then and if I integrate that
+
+ align:start position:0%
+then and if I integrate that
+ 
+
+ align:start position:0%
+then and if I integrate that
+over some region so I have some region
+
+ align:start position:0%
+over some region so I have some region
+ 
+
+ align:start position:0%
+over some region so I have some region
+here and at every Point there's a flow
+
+ align:start position:0%
+here and at every Point there's a flow
+ 
+
+ align:start position:0%
+here and at every Point there's a flow
+W and I look at the Divergence of w and
+
+ align:start position:0%
+W and I look at the Divergence of w and
+ 
+
+ align:start position:0%
+W and I look at the Divergence of w and
+I integrate that dxdy
+
+ align:start position:0%
+I integrate that dxdy
+ 
+
+ align:start position:0%
+I integrate that dxdy
+so that's inte it's a double integral
+
+ align:start position:0%
+so that's inte it's a double integral
+ 
+
+ align:start position:0%
+so that's inte it's a double integral
+over a region
+
+ align:start position:0%
+over a region
+ 
+
+ align:start position:0%
+over a region
+I will get what what's the what is
+
+ align:start position:0%
+I will get what what's the what is
+ 
+
+ align:start position:0%
+I will get what what's the what is
+what's the right hand side
+
+ align:start position:0%
+what's the right hand side
+ 
+
+ align:start position:0%
+what's the right hand side
+what what is the Divergence measure
+
+ align:start position:0%
+what what is the Divergence measure
+ 
+
+ align:start position:0%
+what what is the Divergence measure
+so I'm really asking you like just
+
+ align:start position:0%
+so I'm really asking you like just
+ 
+
+ align:start position:0%
+so I'm really asking you like just
+memory what's the what is the Divergence
+
+ align:start position:0%
+memory what's the what is the Divergence
+ 
+
+ align:start position:0%
+memory what's the what is the Divergence
+what's it's an identity it's it's
+
+ align:start position:0%
+what's it's an identity it's it's
+ 
+
+ align:start position:0%
+what's it's an identity it's it's
+integration by Parts in some way as as
+
+ align:start position:0%
+integration by Parts in some way as as
+ 
+
+ align:start position:0%
+integration by Parts in some way as as
+we'll see uh but what do you remember
+
+ align:start position:0%
+we'll see uh but what do you remember
+ 
+
+ align:start position:0%
+we'll see uh but what do you remember
+for the Divergence Theorem
+
+ align:start position:0%
+for the Divergence Theorem
+ 
+
+ align:start position:0%
+for the Divergence Theorem
+you get what you get it measures how
+
+ align:start position:0%
+you get what you get it measures how
+ 
+
+ align:start position:0%
+you get what you get it measures how
+much
+
+ align:start position:0%
+much
+ 
+
+ align:start position:0%
+much
+flux out right so when we measure the
+
+ align:start position:0%
+flux out right so when we measure the
+ 
+
+ align:start position:0%
+flux out right so when we measure the
+flux out by integrating around the
+
+ align:start position:0%
+flux out by integrating around the
+ 
+
+ align:start position:0%
+flux out by integrating around the
+boundary how much is getting through the
+
+ align:start position:0%
+boundary how much is getting through the
+ 
+
+ align:start position:0%
+boundary how much is getting through the
+boundary and what's the flow through the
+
+ align:start position:0%
+boundary and what's the flow through the
+ 
+
+ align:start position:0%
+boundary and what's the flow through the
+boundary
+
+ align:start position:0%
+boundary
+ 
+
+ align:start position:0%
+boundary
+I take w but that's a vector and I'm
+
+ align:start position:0%
+I take w but that's a vector and I'm
+ 
+
+ align:start position:0%
+I take w but that's a vector and I'm
+looking for what component of w
+
+ align:start position:0%
+looking for what component of w
+ 
+
+ align:start position:0%
+looking for what component of w
+the normal component the component of w
+
+ align:start position:0%
+the normal component the component of w
+ 
+
+ align:start position:0%
+the normal component the component of w
+w.n the component of w that's headed out
+
+ align:start position:0%
+w.n the component of w that's headed out
+ 
+
+ align:start position:0%
+w.n the component of w that's headed out
+N is a is defined to be where whatever
+
+ align:start position:0%
+N is a is defined to be where whatever
+ 
+
+ align:start position:0%
+N is a is defined to be where whatever
+the boundary is here I made it look like
+
+ align:start position:0%
+the boundary is here I made it look like
+ 
+
+ align:start position:0%
+the boundary is here I made it look like
+a circle but I didn't shouldn't have let
+
+ align:start position:0%
+a circle but I didn't shouldn't have let
+ 
+
+ align:start position:0%
+a circle but I didn't shouldn't have let
+me let me make it a little wobbler or
+
+ align:start position:0%
+me let me make it a little wobbler or
+ 
+
+ align:start position:0%
+me let me make it a little wobbler or
+something uh yeah so the B the the
+
+ align:start position:0%
+something uh yeah so the B the the
+ 
+
+ align:start position:0%
+something uh yeah so the B the the
+normal component at any there look at
+
+ align:start position:0%
+normal component at any there look at
+ 
+
+ align:start position:0%
+normal component at any there look at
+that point
+
+ align:start position:0%
+that point
+ 
+
+ align:start position:0%
+that point
+the normal Direction Through The
+
+ align:start position:0%
+the normal Direction Through The
+ 
+
+ align:start position:0%
+the normal Direction Through The
+Boundary down in that crazy point is
+
+ align:start position:0%
+Boundary down in that crazy point is
+ 
+
+ align:start position:0%
+Boundary down in that crazy point is
+this way yeah so this the normal is
+
+ align:start position:0%
+this way yeah so this the normal is
+ 
+
+ align:start position:0%
+this way yeah so this the normal is
+going this way here here it's going over
+
+ align:start position:0%
+going this way here here it's going over
+ 
+
+ align:start position:0%
+going this way here here it's going over
+this way it's perpendicular to the
+
+ align:start position:0%
+this way it's perpendicular to the
+ 
+
+ align:start position:0%
+this way it's perpendicular to the
+boundary okay and then we integrate
+
+ align:start position:0%
+boundary okay and then we integrate
+ 
+
+ align:start position:0%
+boundary okay and then we integrate
+around the boundary all right
+
+ align:start position:0%
+around the boundary all right
+ 
+
+ align:start position:0%
+around the boundary all right
+yeah yeah so that's the identity of that
+
+ align:start position:0%
+yeah yeah so that's the identity of that
+ 
+
+ align:start position:0%
+yeah yeah so that's the identity of that
+that's the Divergence Theorem right
+
+ align:start position:0%
+that's the Divergence Theorem right
+ 
+
+ align:start position:0%
+that's the Divergence Theorem right
+now let's see
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+could you yeah so here here's a we have
+
+ align:start position:0%
+could you yeah so here here's a we have
+ 
+
+ align:start position:0%
+could you yeah so here here's a we have
+a minute shall I do you want to give me
+
+ align:start position:0%
+a minute shall I do you want to give me
+ 
+
+ align:start position:0%
+a minute shall I do you want to give me
+a particular take a particular W and see
+
+ align:start position:0%
+a particular take a particular W and see
+ 
+
+ align:start position:0%
+a particular take a particular W and see
+if this would be correct
+
+ align:start position:0%
+if this would be correct
+ 
+
+ align:start position:0%
+if this would be correct
+huh how about W equal 0x our first
+
+ align:start position:0%
+huh how about W equal 0x our first
+ 
+
+ align:start position:0%
+huh how about W equal 0x our first
+example
+
+ align:start position:0%
+example
+ 
+
+ align:start position:0%
+example
+suppose I tried wals ZX I I just want to
+
+ align:start position:0%
+suppose I tried wals ZX I I just want to
+ 
+
+ align:start position:0%
+suppose I tried wals ZX I I just want to
+see if the Divergence
+
+ align:start position:0%
+see if the Divergence
+ 
+
+ align:start position:0%
+see if the Divergence
+what the flux is through the boundary
+
+ align:start position:0%
+what the flux is through the boundary
+ 
+
+ align:start position:0%
+what the flux is through the boundary
+what what region shall I take for the
+
+ align:start position:0%
+what what region shall I take for the
+ 
+
+ align:start position:0%
+what what region shall I take for the
+so so the Divergence Theorem has two
+
+ align:start position:0%
+so so the Divergence Theorem has two
+ 
+
+ align:start position:0%
+so so the Divergence Theorem has two
+inputs it has a flow field and let me
+
+ align:start position:0%
+inputs it has a flow field and let me
+ 
+
+ align:start position:0%
+inputs it has a flow field and let me
+take W to be 0x as just so it's a shear
+
+ align:start position:0%
+take W to be 0x as just so it's a shear
+ 
+
+ align:start position:0%
+take W to be 0x as just so it's a shear
+and a region
+
+ align:start position:0%
+and a region
+ 
+
+ align:start position:0%
+and a region
+and of course the integral might not be
+
+ align:start position:0%
+and of course the integral might not be
+ 
+
+ align:start position:0%
+and of course the integral might not be
+that much fun to do unless we make the
+
+ align:start position:0%
+that much fun to do unless we make the
+ 
+
+ align:start position:0%
+that much fun to do unless we make the
+region nice what do you take as a nice
+
+ align:start position:0%
+region nice what do you take as a nice
+ 
+
+ align:start position:0%
+region nice what do you take as a nice
+region for uh
+
+ align:start position:0%
+region for uh
+ 
+
+ align:start position:0%
+region for uh
+oh
+
+ align:start position:0%
+oh
+ 
+
+ align:start position:0%
+oh
+actually it doesn't matter what the
+
+ align:start position:0%
+actually it doesn't matter what the
+ 
+
+ align:start position:0%
+actually it doesn't matter what the
+region is take any old region for the
+
+ align:start position:0%
+region is take any old region for the
+ 
+
+ align:start position:0%
+region is take any old region for the
+moment
+
+ align:start position:0%
+moment
+ 
+
+ align:start position:0%
+moment
+what's the answer for for this
+
+ align:start position:0%
+what's the answer for for this
+ 
+
+ align:start position:0%
+what's the answer for for this
+particular flow W equals 0x
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+zero
+
+ align:start position:0%
+zero
+ 
+
+ align:start position:0%
+zero
+that's the right that's the cool part if
+
+ align:start position:0%
+that's the right that's the cool part if
+ 
+
+ align:start position:0%
+that's the right that's the cool part if
+they answer zero then like you know work
+
+ align:start position:0%
+they answer zero then like you know work
+ 
+
+ align:start position:0%
+they answer zero then like you know work
+is suspended
+
+ align:start position:0%
+is suspended
+ 
+
+ align:start position:0%
+is suspended
+and why is it zero
+
+ align:start position:0%
+and why is it zero
+ 
+
+ align:start position:0%
+and why is it zero
+because the Divergence of this
+
+ align:start position:0%
+because the Divergence of this
+ 
+
+ align:start position:0%
+because the Divergence of this
+particular W the X derivative of that
+
+ align:start position:0%
+particular W the X derivative of that
+ 
+
+ align:start position:0%
+particular W the X derivative of that
+plus the Y derivative of that is zero
+
+ align:start position:0%
+plus the Y derivative of that is zero
+ 
+
+ align:start position:0%
+plus the Y derivative of that is zero
+this has Divergence Z everywhere zero
+
+ align:start position:0%
+this has Divergence Z everywhere zero
+ 
+
+ align:start position:0%
+this has Divergence Z everywhere zero
+so integrating is no problem at all so
+
+ align:start position:0%
+so integrating is no problem at all so
+ 
+
+ align:start position:0%
+so integrating is no problem at all so
+the so that would be zero for this flow
+
+ align:start position:0%
+the so that would be zero for this flow
+ 
+
+ align:start position:0%
+the so that would be zero for this flow
+field for for this Divergence free field
+
+ align:start position:0%
+field for for this Divergence free field
+ 
+
+ align:start position:0%
+field for for this Divergence free field
+zero for that because
+
+ align:start position:0%
+zero for that because
+ 
+
+ align:start position:0%
+zero for that because
+div W is zero
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+but is that correct what does that tell
+
+ align:start position:0%
+but is that correct what does that tell
+ 
+
+ align:start position:0%
+but is that correct what does that tell
+me this these flows are we saw what the
+
+ align:start position:0%
+me this these flows are we saw what the
+ 
+
+ align:start position:0%
+me this these flows are we saw what the
+flow was like here's say there's the
+
+ align:start position:0%
+flow was like here's say there's the
+ 
+
+ align:start position:0%
+flow was like here's say there's the
+origin it doesn't have to be a circle it
+
+ align:start position:0%
+origin it doesn't have to be a circle it
+ 
+
+ align:start position:0%
+origin it doesn't have to be a circle it
+looks like a circle
+
+ align:start position:0%
+looks like a circle
+ 
+
+ align:start position:0%
+looks like a circle
+do you see why the flux is zero there is
+
+ align:start position:0%
+do you see why the flux is zero there is
+ 
+
+ align:start position:0%
+do you see why the flux is zero there is
+there is flow through the boundary right
+
+ align:start position:0%
+there is flow through the boundary right
+ 
+
+ align:start position:0%
+there is flow through the boundary right
+flow is going buzz buzz buzz up this
+
+ align:start position:0%
+flow is going buzz buzz buzz up this
+ 
+
+ align:start position:0%
+flow is going buzz buzz buzz up this
+line and out
+
+ align:start position:0%
+line and out
+ 
+
+ align:start position:0%
+line and out
+and and it's coming in here so the right
+
+ align:start position:0%
+and and it's coming in here so the right
+ 
+
+ align:start position:0%
+and and it's coming in here so the right
+that that's what we discovered the this
+
+ align:start position:0%
+that that's what we discovered the this
+ 
+
+ align:start position:0%
+that that's what we discovered the this
+ZX is vertical flow
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+it hasn't got any horizontal component
+
+ align:start position:0%
+it hasn't got any horizontal component
+ 
+
+ align:start position:0%
+it hasn't got any horizontal component
+it's vertical it's got a vertical
+
+ align:start position:0%
+it's vertical it's got a vertical
+ 
+
+ align:start position:0%
+it's vertical it's got a vertical
+component it's going out and would we
+
+ align:start position:0%
+component it's going out and would we
+ 
+
+ align:start position:0%
+component it's going out and would we
+want to do this right hand side I don't
+
+ align:start position:0%
+want to do this right hand side I don't
+ 
+
+ align:start position:0%
+want to do this right hand side I don't
+think so right this right hand side is
+
+ align:start position:0%
+think so right this right hand side is
+ 
+
+ align:start position:0%
+think so right this right hand side is
+asking me what I have to find the normal
+
+ align:start position:0%
+asking me what I have to find the normal
+ 
+
+ align:start position:0%
+asking me what I have to find the normal
+Direction on this whatever curve that is
+
+ align:start position:0%
+Direction on this whatever curve that is
+ 
+
+ align:start position:0%
+Direction on this whatever curve that is
+I have to take its dotproduct with the
+
+ align:start position:0%
+I have to take its dotproduct with the
+ 
+
+ align:start position:0%
+I have to take its dotproduct with the
+flow 0x so this is the this is uh some
+
+ align:start position:0%
+flow 0x so this is the this is uh some
+ 
+
+ align:start position:0%
+flow 0x so this is the this is uh some
+quantity and then I have to do this DS
+
+ align:start position:0%
+quantity and then I have to do this DS
+ 
+
+ align:start position:0%
+quantity and then I have to do this DS
+which I haven't even mentioned DS is Arc
+
+ align:start position:0%
+which I haven't even mentioned DS is Arc
+ 
+
+ align:start position:0%
+which I haven't even mentioned DS is Arc
+Length around I'm integrating around
+
+ align:start position:0%
+Length around I'm integrating around
+ 
+
+ align:start position:0%
+Length around I'm integrating around
+these pieces but but yet
+
+ align:start position:0%
+these pieces but but yet
+ 
+
+ align:start position:0%
+these pieces but but yet
+somehow we have some idea that the from
+
+ align:start position:0%
+somehow we have some idea that the from
+ 
+
+ align:start position:0%
+somehow we have some idea that the from
+that picture that the total flux is zero
+
+ align:start position:0%
+that picture that the total flux is zero
+ 
+
+ align:start position:0%
+that picture that the total flux is zero
+what how would you say it in words if I
+
+ align:start position:0%
+what how would you say it in words if I
+ 
+
+ align:start position:0%
+what how would you say it in words if I
+say here's the flow field there's a
+
+ align:start position:0%
+say here's the flow field there's a
+ 
+
+ align:start position:0%
+say here's the flow field there's a
+region funny shape
+
+ align:start position:0%
+region funny shape
+ 
+
+ align:start position:0%
+region funny shape
+the flux is zero through that boundary
+
+ align:start position:0%
+the flux is zero through that boundary
+ 
+
+ align:start position:0%
+the flux is zero through that boundary
+and and if I asked you why what would
+
+ align:start position:0%
+and and if I asked you why what would
+ 
+
+ align:start position:0%
+and and if I asked you why what would
+you say you I mean a math answer would
+
+ align:start position:0%
+you say you I mean a math answer would
+ 
+
+ align:start position:0%
+you say you I mean a math answer would
+be use the Divergence Theorem but okay
+
+ align:start position:0%
+be use the Divergence Theorem but okay
+ 
+
+ align:start position:0%
+be use the Divergence Theorem but okay
+but why from this picture does it look
+
+ align:start position:0%
+but why from this picture does it look
+ 
+
+ align:start position:0%
+but why from this picture does it look
+like we have zero flux
+
+ align:start position:0%
+like we have zero flux
+ 
+
+ align:start position:0%
+like we have zero flux
+what comes in goes out yeah what's
+
+ align:start position:0%
+what comes in goes out yeah what's
+ 
+
+ align:start position:0%
+what comes in goes out yeah what's
+coming in the bottom here is going out
+
+ align:start position:0%
+coming in the bottom here is going out
+ 
+
+ align:start position:0%
+coming in the bottom here is going out
+the top yeah yeah that's that's
+
+ align:start position:0%
+the top yeah yeah that's that's
+ 
+
+ align:start position:0%
+the top yeah yeah that's that's
+basically it right right yeah yeah so we
+
+ align:start position:0%
+basically it right right yeah yeah so we
+ 
+
+ align:start position:0%
+basically it right right yeah yeah so we
+would get zero for that one so I'm
+
+ align:start position:0%
+would get zero for that one so I'm
+ 
+
+ align:start position:0%
+would get zero for that one so I'm
+you if if if I think the homework the
+
+ align:start position:0%
+you if if if I think the homework the
+ 
+
+ align:start position:0%
+you if if if I think the homework the
+suggested homework maybe includes an
+
+ align:start position:0%
+suggested homework maybe includes an
+ 
+
+ align:start position:0%
+suggested homework maybe includes an
+example where the Divergence isn't zero
+
+ align:start position:0%
+example where the Divergence isn't zero
+ 
+
+ align:start position:0%
+example where the Divergence isn't zero
+and then you actually have to do these
+
+ align:start position:0%
+and then you actually have to do these
+ 
+
+ align:start position:0%
+and then you actually have to do these
+integrals just as like practice for what
+
+ align:start position:0%
+integrals just as like practice for what
+ 
+
+ align:start position:0%
+integrals just as like practice for what
+do those integrals mean yeah maybe I
+
+ align:start position:0%
+do those integrals mean yeah maybe I
+ 
+
+ align:start position:0%
+do those integrals mean yeah maybe I
+won't go through one now but that's good
+
+ align:start position:0%
+won't go through one now but that's good
+ 
+
+ align:start position:0%
+won't go through one now but that's good
+practice is take a some simple W but one
+
+ align:start position:0%
+practice is take a some simple W but one
+ 
+
+ align:start position:0%
+practice is take a some simple W but one
+with
+
+ align:start position:0%
+with
+ 
+
+ align:start position:0%
+with
+with with with a nonzero Divergence and
+
+ align:start position:0%
+with with with a nonzero Divergence and
+ 
+
+ align:start position:0%
+with with with a nonzero Divergence and
+then see if you can do either or both of
+
+ align:start position:0%
+then see if you can do either or both of
+ 
+
+ align:start position:0%
+then see if you can do either or both of
+the integrals that are supposed to come
+
+ align:start position:0%
+the integrals that are supposed to come
+ 
+
+ align:start position:0%
+the integrals that are supposed to come
+out equal yeah yeah that's a that's a
+
+ align:start position:0%
+out equal yeah yeah that's a that's a
+ 
+
+ align:start position:0%
+out equal yeah yeah that's a that's a
+good one
+
+ align:start position:0%
+good one
+ 
+
+ align:start position:0%
+good one
+now there's one thing I could any
+
+ align:start position:0%
+now there's one thing I could any
+ 
+
+ align:start position:0%
+now there's one thing I could any
+question or discussion yeah it's you
+
+ align:start position:0%
+question or discussion yeah it's you
+ 
+
+ align:start position:0%
+question or discussion yeah it's you
+guys are seeing these uh
+
+ align:start position:0%
+guys are seeing these uh
+ 
+
+ align:start position:0%
+guys are seeing these uh
+examples come up it's the only way I
+
+ align:start position:0%
+examples come up it's the only way I
+ 
+
+ align:start position:0%
+examples come up it's the only way I
+would know to learn this subject is take
+
+ align:start position:0%
+would know to learn this subject is take
+ 
+
+ align:start position:0%
+would know to learn this subject is take
+simple v's and ws and uh um see what you
+
+ align:start position:0%
+simple v's and ws and uh um see what you
+ 
+
+ align:start position:0%
+simple v's and ws and uh um see what you
+can do with them
+
+ align:start position:0%
+can do with them
+ 
+
+ align:start position:0%
+can do with them
+uh we've got the general principles but
+
+ align:start position:0%
+uh we've got the general principles but
+ 
+
+ align:start position:0%
+uh we've got the general principles but
+then apply them to specific flows
+
+ align:start position:0%
+then apply them to specific flows
+ 
+
+ align:start position:0%
+then apply them to specific flows
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+yes thanks that app for
+
+ align:start position:0%
+yes thanks that app for
+ 
+
+ align:start position:0%
+yes thanks that app for
+nonre
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh this theorem
+
+ align:start position:0%
+uh this theorem
+ 
+
+ align:start position:0%
+uh this theorem
+right the flow in flow out but if it was
+
+ align:start position:0%
+right the flow in flow out but if it was
+ 
+
+ align:start position:0%
+right the flow in flow out but if it was
+like
+
+ align:start position:0%
+like
+ 
+
+ align:start position:0%
+like
+yeah if it was well let's draw a funny
+
+ align:start position:0%
+yeah if it was well let's draw a funny
+ 
+
+ align:start position:0%
+yeah if it was well let's draw a funny
+shape
+
+ align:start position:0%
+shape
+ 
+
+ align:start position:0%
+shape
+see what we think I mean let's with this
+
+ align:start position:0%
+see what we think I mean let's with this
+ 
+
+ align:start position:0%
+see what we think I mean let's with this
+flow right uh I mean if the
+
+ align:start position:0%
+flow right uh I mean if the
+ 
+
+ align:start position:0%
+flow right uh I mean if the
+if let me just say if the flow is not if
+
+ align:start position:0%
+if let me just say if the flow is not if
+ 
+
+ align:start position:0%
+if let me just say if the flow is not if
+it has some difficult Divergence and the
+
+ align:start position:0%
+it has some difficult Divergence and the
+ 
+
+ align:start position:0%
+it has some difficult Divergence and the
+and the region is some mess nobody's
+
+ align:start position:0%
+and the region is some mess nobody's
+ 
+
+ align:start position:0%
+and the region is some mess nobody's
+going to be able to do it right I mean
+
+ align:start position:0%
+going to be able to do it right I mean
+ 
+
+ align:start position:0%
+going to be able to do it right I mean
+yeah so don't think that these can all
+
+ align:start position:0%
+yeah so don't think that these can all
+ 
+
+ align:start position:0%
+yeah so don't think that these can all
+be done the the equ quality is it's like
+
+ align:start position:0%
+be done the the equ quality is it's like
+ 
+
+ align:start position:0%
+be done the the equ quality is it's like
+integrals in calculus
+
+ align:start position:0%
+integrals in calculus
+ 
+
+ align:start position:0%
+integrals in calculus
+no problem to think of Integrations that
+
+ align:start position:0%
+no problem to think of Integrations that
+ 
+
+ align:start position:0%
+no problem to think of Integrations that
+are just beyond human capacity but the
+
+ align:start position:0%
+are just beyond human capacity but the
+ 
+
+ align:start position:0%
+are just beyond human capacity but the
+formulas still hold suppose my region
+
+ align:start position:0%
+formulas still hold suppose my region
+ 
+
+ align:start position:0%
+formulas still hold suppose my region
+was even like this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+would that still be would it do we still
+
+ align:start position:0%
+would that still be would it do we still
+ 
+
+ align:start position:0%
+would that still be would it do we still
+see flow in equals flow out for this
+
+ align:start position:0%
+see flow in equals flow out for this
+ 
+
+ align:start position:0%
+see flow in equals flow out for this
+particular flow I I think yeah the flow
+
+ align:start position:0%
+particular flow I I think yeah the flow
+ 
+
+ align:start position:0%
+particular flow I I think yeah the flow
+is going this way so it's coming in here
+
+ align:start position:0%
+is going this way so it's coming in here
+ 
+
+ align:start position:0%
+is going this way so it's coming in here
+it's going out out again that
+
+ align:start position:0%
+it's going out out again that
+ 
+
+ align:start position:0%
+it's going out out again that
+contributes back in again here and out
+
+ align:start position:0%
+contributes back in again here and out
+ 
+
+ align:start position:0%
+contributes back in again here and out
+again here yeah I think uh I think our
+
+ align:start position:0%
+again here yeah I think uh I think our
+ 
+
+ align:start position:0%
+again here yeah I think uh I think our
+our uh Instinct would be correct there
+
+ align:start position:0%
+our uh Instinct would be correct there
+ 
+
+ align:start position:0%
+our uh Instinct would be correct there
+yeah yeah yeah all all sorts of examples
+
+ align:start position:0%
+yeah yeah yeah all all sorts of examples
+ 
+
+ align:start position:0%
+yeah yeah yeah all all sorts of examples
+I I was going to well I'll maybe do it
+
+ align:start position:0%
+I I was going to well I'll maybe do it
+ 
+
+ align:start position:0%
+I I was going to well I'll maybe do it
+in class um yeah this this Divergent
+
+ align:start position:0%
+in class um yeah this this Divergent
+ 
+
+ align:start position:0%
+in class um yeah this this Divergent
+theem is is like it's the fundamental
+
+ align:start position:0%
+theem is is like it's the fundamental
+ 
+
+ align:start position:0%
+theem is is like it's the fundamental
+theorem of 2D calculus you could say or
+
+ align:start position:0%
+theorem of 2D calculus you could say or
+ 
+
+ align:start position:0%
+theorem of 2D calculus you could say or
+one of them and uh um
+
+ align:start position:0%
+one of them and uh um
+ 
+
+ align:start position:0%
+one of them and uh um
+yeah and and to see what these uh
+
+ align:start position:0%
+yeah and and to see what these uh
+ 
+
+ align:start position:0%
+yeah and and to see what these uh
+yeah to to to write these things and and
+
+ align:start position:0%
+yeah to to to write these things and and
+ 
+
+ align:start position:0%
+yeah to to to write these things and and
+and and see what they what they lead to
+
+ align:start position:0%
+and and see what they what they lead to
+ 
+
+ align:start position:0%
+and and see what they what they lead to
+yeah may maybe I'll I won't what I'll
+
+ align:start position:0%
+yeah may maybe I'll I won't what I'll
+ 
+
+ align:start position:0%
+yeah may maybe I'll I won't what I'll
+tell you what I was going to do I was
+
+ align:start position:0%
+tell you what I was going to do I was
+ 
+
+ align:start position:0%
+tell you what I was going to do I was
+going to apply this to the to a vector
+
+ align:start position:0%
+going to apply this to the to a vector
+ 
+
+ align:start position:0%
+going to apply this to the to a vector
+field U * W so U is a scaler W is a
+
+ align:start position:0%
+field U * W so U is a scaler W is a
+ 
+
+ align:start position:0%
+field U * W so U is a scaler W is a
+vector and and and therefore UW is a
+
+ align:start position:0%
+vector and and and therefore UW is a
+ 
+
+ align:start position:0%
+vector and and and therefore UW is a
+vector it's got two components uw1 and
+
+ align:start position:0%
+vector it's got two components uw1 and
+ 
+
+ align:start position:0%
+vector it's got two components uw1 and
+so sh are you willing to do that one
+
+ align:start position:0%
+so sh are you willing to do that one
+ 
+
+ align:start position:0%
+so sh are you willing to do that one
+so I apply it to apply it to apply this
+
+ align:start position:0%
+so I apply it to apply it to apply this
+ 
+
+ align:start position:0%
+so I apply it to apply it to apply this
+to not to W itself but to U * W which is
+
+ align:start position:0%
+to not to W itself but to U * W which is
+ 
+
+ align:start position:0%
+to not to W itself but to U * W which is
+has two components U W1 and uw2
+
+ align:start position:0%
+has two components U W1 and uw2
+ 
+
+ align:start position:0%
+has two components U W1 and uw2
+okay so I should take the Divergence of
+
+ align:start position:0%
+okay so I should take the Divergence of
+ 
+
+ align:start position:0%
+okay so I should take the Divergence of
+UW
+
+ align:start position:0%
+UW
+ 
+
+ align:start position:0%
+UW
+I mean that's that's a vector field UW
+
+ align:start position:0%
+I mean that's that's a vector field UW
+ 
+
+ align:start position:0%
+I mean that's that's a vector field UW
+this guy and I'll get the U.N
+
+ align:start position:0%
+this guy and I'll get the U.N
+ 
+
+ align:start position:0%
+this guy and I'll get the U.N
+and it just turns out that this is the
+
+ align:start position:0%
+and it just turns out that this is the
+ 
+
+ align:start position:0%
+and it just turns out that this is the
+right way to do it
+
+ align:start position:0%
+right way to do it
+ 
+
+ align:start position:0%
+right way to do it
+um to see the fact that gradient and
+
+ align:start position:0%
+um to see the fact that gradient and
+ 
+
+ align:start position:0%
+um to see the fact that gradient and
+Divergence are transposes of each other
+
+ align:start position:0%
+Divergence are transposes of each other
+ 
+
+ align:start position:0%
+Divergence are transposes of each other
+yeah yeah maybe I won't do that
+
+ align:start position:0%
+yeah yeah maybe I won't do that
+ 
+
+ align:start position:0%
+yeah yeah maybe I won't do that
+calculation now I'll just say that if if
+
+ align:start position:0%
+calculation now I'll just say that if if
+ 
+
+ align:start position:0%
+calculation now I'll just say that if if
+you take the Divergence Theorem and you
+
+ align:start position:0%
+you take the Divergence Theorem and you
+ 
+
+ align:start position:0%
+you take the Divergence Theorem and you
+apply it to this guy uw1 uw2
+
+ align:start position:0%
+apply it to this guy uw1 uw2
+ 
+
+ align:start position:0%
+apply it to this guy uw1 uw2
+then you and write out what it means you
+
+ align:start position:0%
+then you and write out what it means you
+ 
+
+ align:start position:0%
+then you and write out what it means you
+you get a very in interesting formula
+
+ align:start position:0%
+you get a very in interesting formula
+ 
+
+ align:start position:0%
+you get a very in interesting formula
+yeah yeah yeah that's
+
+ align:start position:0%
+yeah yeah yeah that's
+ 
+
+ align:start position:0%
+yeah yeah yeah that's
+I I'll just leave that there so I'm
+
+ align:start position:0%
+I I'll just leave that there so I'm
+ 
+
+ align:start position:0%
+I I'll just leave that there so I'm
+ready for a final question if there is
+
+ align:start position:0%
+ready for a final question if there is
+ 
+
+ align:start position:0%
+ready for a final question if there is
+one or otherwise keep going Friday with
+
+ align:start position:0%
+one or otherwise keep going Friday with
+ 
+
+ align:start position:0%
+one or otherwise keep going Friday with
+the uh with these laass equation
+
+ align:start position:0%
+the uh with these laass equation
+ 
+
+ align:start position:0%
+the uh with these laass equation
+Solutions play with some play with some
+
+ align:start position:0%
+Solutions play with some play with some
+ 
+
+ align:start position:0%
+Solutions play with some play with some
+Vector fields that that's my best advice
+
+ align:start position:0%
+Vector fields that that's my best advice
+ 
+
+ align:start position:0%
+Vector fields that that's my best advice
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+and uh
+
+ align:start position:0%
+and uh
+ 
+
+ align:start position:0%
+and uh
+and I'll see you Friday
\ No newline at end of file
diff --git a/zmzyW1rP-hk.txt b/zmzyW1rP-hk.txt
new file mode 100644
index 0000000000000000000000000000000000000000..4e6253abde78bba1ba52b6c7f038c774e24cf729
--- /dev/null
+++ b/zmzyW1rP-hk.txt
@@ -0,0 +1,2115 @@
+align:start position:0%
+ 
+Welcome to this recitation on a face
+
+ align:start position:0%
+Welcome to this recitation on a face
+ 
+
+ align:start position:0%
+Welcome to this recitation on a face
+portrait. So you're given matrix A, a
+
+ align:start position:0%
+portrait. So you're given matrix A, a
+ 
+
+ align:start position:0%
+portrait. So you're given matrix A, a
+2x2 matrix with entries minus one, minus
+
+ align:start position:0%
+2x2 matrix with entries minus one, minus
+ 
+
+ align:start position:0%
+2x2 matrix with entries minus one, minus
+one, one minus C, where C is a constant,
+
+ align:start position:0%
+one, one minus C, where C is a constant,
+ 
+
+ align:start position:0%
+one, one minus C, where C is a constant,
+we will be varying and minus one. As C
+
+ align:start position:0%
+we will be varying and minus one. As C
+ 
+
+ align:start position:0%
+we will be varying and minus one. As C
+increases from zero to other positive
+
+ align:start position:0%
+increases from zero to other positive
+ 
+
+ align:start position:0%
+increases from zero to other positive
+values, determine the path of the system
+
+ align:start position:0%
+values, determine the path of the system
+ 
+
+ align:start position:0%
+values, determine the path of the system
+on the trace determinant diagram that we
+
+ align:start position:0%
+on the trace determinant diagram that we
+ 
+
+ align:start position:0%
+on the trace determinant diagram that we
+saw in previous recitations and draw the
+
+ align:start position:0%
+saw in previous recitations and draw the
+ 
+
+ align:start position:0%
+saw in previous recitations and draw the
+face portraits that corresponds to uh
+
+ align:start position:0%
+face portraits that corresponds to uh
+ 
+
+ align:start position:0%
+face portraits that corresponds to uh
+the critical points uh and the nature of
+
+ align:start position:0%
+the critical points uh and the nature of
+ 
+
+ align:start position:0%
+the critical points uh and the nature of
+the critical points. So here we're
+
+ align:start position:0%
+the critical points. So here we're
+ 
+
+ align:start position:0%
+the critical points. So here we're
+basically talking of a system that would
+
+ align:start position:0%
+basically talking of a system that would
+ 
+
+ align:start position:0%
+basically talking of a system that would
+be a 2x two
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+system where we have derivative of
+
+ align:start position:0%
+system where we have derivative of
+ 
+
+ align:start position:0%
+system where we have derivative of
+entries xy for vector equals to this
+
+ align:start position:0%
+entries xy for vector equals to this
+ 
+
+ align:start position:0%
+entries xy for vector equals to this
+matrix a c multiplying the unknown uh
+
+ align:start position:0%
+matrix a c multiplying the unknown uh
+ 
+
+ align:start position:0%
+matrix a c multiplying the unknown uh
+vector x c. So take a few minutes and
+
+ align:start position:0%
+vector x c. So take a few minutes and
+ 
+
+ align:start position:0%
+vector x c. So take a few minutes and
+work out through this problem and I'll
+
+ align:start position:0%
+work out through this problem and I'll
+ 
+
+ align:start position:0%
+work out through this problem and I'll
+be right back.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Welcome back. Okay, so I already
+
+ align:start position:0%
+Welcome back. Okay, so I already
+ 
+
+ align:start position:0%
+Welcome back. Okay, so I already
+prepared the trace diagram uh the the
+
+ align:start position:0%
+prepared the trace diagram uh the the
+ 
+
+ align:start position:0%
+prepared the trace diagram uh the the
+trace determined diagram for you. So
+
+ align:start position:0%
+trace determined diagram for you. So
+ 
+
+ align:start position:0%
+trace determined diagram for you. So
+here as a reminder, this is the uh
+
+ align:start position:0%
+here as a reminder, this is the uh
+ 
+
+ align:start position:0%
+here as a reminder, this is the uh
+parabola that determines whether we're
+
+ align:start position:0%
+parabola that determines whether we're
+ 
+
+ align:start position:0%
+parabola that determines whether we're
+going to have repeated a values or not.
+
+ align:start position:0%
+going to have repeated a values or not.
+ 
+
+ align:start position:0%
+going to have repeated a values or not.
+Above this parabola, we have two real
+
+ align:start position:0%
+Above this parabola, we have two real
+ 
+
+ align:start position:0%
+Above this parabola, we have two real
+two complex conjugate values. Below this
+
+ align:start position:0%
+two complex conjugate values. Below this
+ 
+
+ align:start position:0%
+two complex conjugate values. Below this
+parabola we have real values either of
+
+ align:start position:0%
+parabola we have real values either of
+ 
+
+ align:start position:0%
+parabola we have real values either of
+the same signs positive or negative or
+
+ align:start position:0%
+the same signs positive or negative or
+ 
+
+ align:start position:0%
+the same signs positive or negative or
+of different signs. And then we have the
+
+ align:start position:0%
+of different signs. And then we have the
+ 
+
+ align:start position:0%
+of different signs. And then we have the
+borderline cases. In our case here we're
+
+ align:start position:0%
+borderline cases. In our case here we're
+ 
+
+ align:start position:0%
+borderline cases. In our case here we're
+looking at a matrix A
+
+ align:start position:0%
+looking at a matrix A
+ 
+
+ align:start position:0%
+looking at a matrix A
+with a trace equals to -1 + -1 - 1. So
+
+ align:start position:0%
+with a trace equals to -1 + -1 - 1. So
+ 
+
+ align:start position:0%
+with a trace equals to -1 + -1 - 1. So
+it's minus2 and a determinant
+
+ align:start position:0%
+it's minus2 and a determinant
+ 
+
+ align:start position:0%
+it's minus2 and a determinant
+that is equal to 2 - c. So here we are
+
+ align:start position:0%
+that is equal to 2 - c. So here we are
+ 
+
+ align:start position:0%
+that is equal to 2 - c. So here we are
+basically along this dotted line where
+
+ align:start position:0%
+basically along this dotted line where
+ 
+
+ align:start position:0%
+basically along this dotted line where
+the trace equals to minus2. So either
+
+ align:start position:0%
+the trace equals to minus2. So either
+ 
+
+ align:start position:0%
+the trace equals to minus2. So either
+we're going to have complex values with
+
+ align:start position:0%
+we're going to have complex values with
+ 
+
+ align:start position:0%
+we're going to have complex values with
+negative real parts or uh negative agon
+
+ align:start position:0%
+negative real parts or uh negative agon
+ 
+
+ align:start position:0%
+negative real parts or uh negative agon
+value. So we're in stable
+
+ align:start position:0%
+value. So we're in stable
+ 
+
+ align:start position:0%
+value. So we're in stable
+configurations. So we're going to be
+
+ align:start position:0%
+configurations. So we're going to be
+ 
+
+ align:start position:0%
+configurations. So we're going to be
+moving at C equal to zero from a case
+
+ align:start position:0%
+moving at C equal to zero from a case
+ 
+
+ align:start position:0%
+moving at C equal to zero from a case
+where
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+I'm just going to label this point one
+
+ align:start position:0%
+I'm just going to label this point one
+ 
+
+ align:start position:0%
+I'm just going to label this point one
+from for example we have the matrix
+
+ align:start position:0%
+from for example we have the matrix
+ 
+
+ align:start position:0%
+from for example we have the matrix
+minus one one one minus one with the
+
+ align:start position:0%
+minus one one one minus one with the
+ 
+
+ align:start position:0%
+minus one one one minus one with the
+trace equals to minus2 and the
+
+ align:start position:0%
+trace equals to minus2 and the
+ 
+
+ align:start position:0%
+trace equals to minus2 and the
+determinant equals to two.
+
+ align:start position:0%
+determinant equals to two.
+ 
+
+ align:start position:0%
+determinant equals to two.
+So clearly we're at this point and we
+
+ align:start position:0%
+So clearly we're at this point and we
+ 
+
+ align:start position:0%
+So clearly we're at this point and we
+were we are just going to be increasing
+
+ align:start position:0%
+were we are just going to be increasing
+ 
+
+ align:start position:0%
+were we are just going to be increasing
+the value of C and moving along this
+
+ align:start position:0%
+the value of C and moving along this
+ 
+
+ align:start position:0%
+the value of C and moving along this
+line crossing this first boundary case
+
+ align:start position:0%
+line crossing this first boundary case
+ 
+
+ align:start position:0%
+line crossing this first boundary case
+where we will have uh either defective
+
+ align:start position:0%
+where we will have uh either defective
+ 
+
+ align:start position:0%
+where we will have uh either defective
+or or not case and I'll discuss very
+
+ align:start position:0%
+or or not case and I'll discuss very
+ 
+
+ align:start position:0%
+or or not case and I'll discuss very
+briefly uh what we have and then we have
+
+ align:start position:0%
+briefly uh what we have and then we have
+ 
+
+ align:start position:0%
+briefly uh what we have and then we have
+other value where we are basically in
+
+ align:start position:0%
+other value where we are basically in
+ 
+
+ align:start position:0%
+other value where we are basically in
+this area where we have real values both
+
+ align:start position:0%
+this area where we have real values both
+ 
+
+ align:start position:0%
+this area where we have real values both
+of them negative so we have stability
+
+ align:start position:0%
+of them negative so we have stability
+ 
+
+ align:start position:0%
+of them negative so we have stability
+and it would basically be a sync and
+
+ align:start position:0%
+and it would basically be a sync and
+ 
+
+ align:start position:0%
+and it would basically be a sync and
+then we cross this uh other border line
+
+ align:start position:0%
+then we cross this uh other border line
+ 
+
+ align:start position:0%
+then we cross this uh other border line
+case where the determinant is equal to
+
+ align:start position:0%
+case where the determinant is equal to
+ 
+
+ align:start position:0%
+case where the determinant is equal to
+zero. And here we have one egg value
+
+ align:start position:0%
+zero. And here we have one egg value
+ 
+
+ align:start position:0%
+zero. And here we have one egg value
+that is equal to zero and one that is
+
+ align:start position:0%
+that is equal to zero and one that is
+ 
+
+ align:start position:0%
+that is equal to zero and one that is
+negative and then we get to the the part
+
+ align:start position:0%
+negative and then we get to the the part
+ 
+
+ align:start position:0%
+negative and then we get to the the part
+of the diagram where the determinant is
+
+ align:start position:0%
+of the diagram where the determinant is
+ 
+
+ align:start position:0%
+of the diagram where the determinant is
+negative and the trace is negative and
+
+ align:start position:0%
+negative and the trace is negative and
+ 
+
+ align:start position:0%
+negative and the trace is negative and
+we basically have a saddle uh a saddle
+
+ align:start position:0%
+we basically have a saddle uh a saddle
+ 
+
+ align:start position:0%
+we basically have a saddle uh a saddle
+uh structure where we have one egg in
+
+ align:start position:0%
+uh structure where we have one egg in
+ 
+
+ align:start position:0%
+uh structure where we have one egg in
+value that is negative and another egg
+
+ align:start position:0%
+value that is negative and another egg
+ 
+
+ align:start position:0%
+value that is negative and another egg
+in value that is positive. So let's get
+
+ align:start position:0%
+in value that is positive. So let's get
+ 
+
+ align:start position:0%
+in value that is positive. So let's get
+through these uh five cases and I'll
+
+ align:start position:0%
+through these uh five cases and I'll
+ 
+
+ align:start position:0%
+through these uh five cases and I'll
+just do more detailed picture
+
+ align:start position:0%
+just do more detailed picture
+ 
+
+ align:start position:0%
+just do more detailed picture
+illustrating what I just said.
+
+ align:start position:0%
+illustrating what I just said.
+ 
+
+ align:start position:0%
+illustrating what I just said.
+So I'll just uh write down a bit more in
+
+ align:start position:0%
+So I'll just uh write down a bit more in
+ 
+
+ align:start position:0%
+So I'll just uh write down a bit more in
+detail the first case here. So we have
+
+ align:start position:0%
+detail the first case here. So we have
+ 
+
+ align:start position:0%
+detail the first case here. So we have
+the case where the the the uh the aen
+
+ align:start position:0%
+the case where the the the uh the aen
+ 
+
+ align:start position:0%
+the case where the the the uh the aen
+values are both
+
+ align:start position:0%
+values are both
+ 
+
+ align:start position:0%
+values are both
+complex conjugate and we have their real
+
+ align:start position:0%
+complex conjugate and we have their real
+ 
+
+ align:start position:0%
+complex conjugate and we have their real
+part being negative. So basically we
+
+ align:start position:0%
+part being negative. So basically we
+ 
+
+ align:start position:0%
+part being negative. So basically we
+have spirals, right?
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+asmtotically
+
+ align:start position:0%
+asmtotically
+ 
+
+ align:start position:0%
+asmtotically
+stable
+
+ align:start position:0%
+stable
+ 
+
+ align:start position:0%
+stable
+spirals and the spirals could be either
+
+ align:start position:0%
+spirals and the spirals could be either
+ 
+
+ align:start position:0%
+spirals and the spirals could be either
+clockwise or counterclockwise. And one
+
+ align:start position:0%
+clockwise or counterclockwise. And one
+ 
+
+ align:start position:0%
+clockwise or counterclockwise. And one
+way of determining
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the direction of these spirals is to
+
+ align:start position:0%
+the direction of these spirals is to
+ 
+
+ align:start position:0%
+the direction of these spirals is to
+look at the sign of the velocity vector
+
+ align:start position:0%
+look at the sign of the velocity vector
+ 
+
+ align:start position:0%
+look at the sign of the velocity vector
+of the trajectories in the face. So the
+
+ align:start position:0%
+of the trajectories in the face. So the
+ 
+
+ align:start position:0%
+of the trajectories in the face. So the
+face base basically diagram here where
+
+ align:start position:0%
+face base basically diagram here where
+ 
+
+ align:start position:0%
+face base basically diagram here where
+we have x and y as the axis of the of
+
+ align:start position:0%
+we have x and y as the axis of the of
+ 
+
+ align:start position:0%
+we have x and y as the axis of the of
+this space. So let's look at
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+oops
+
+ align:start position:0%
+oops
+ 
+
+ align:start position:0%
+oops
+let's look for example at a particular
+
+ align:start position:0%
+let's look for example at a particular
+ 
+
+ align:start position:0%
+let's look for example at a particular
+point here that would be veloc
+
+ align:start position:0%
+point here that would be veloc
+ 
+
+ align:start position:0%
+point here that would be veloc
+and this uh position vector 1 z would
+
+ align:start position:0%
+and this uh position vector 1 z would
+ 
+
+ align:start position:0%
+and this uh position vector 1 z would
+give us a velocity vector uh of minus1
+
+ align:start position:0%
+give us a velocity vector uh of minus1
+ 
+
+ align:start position:0%
+give us a velocity vector uh of minus1
+and plus one. So basically this vector
+
+ align:start position:0%
+and plus one. So basically this vector
+ 
+
+ align:start position:0%
+and plus one. So basically this vector
+would be directed upward which means
+
+ align:start position:0%
+would be directed upward which means
+ 
+
+ align:start position:0%
+would be directed upward which means
+that we are in the case where we would
+
+ align:start position:0%
+that we are in the case where we would
+ 
+
+ align:start position:0%
+that we are in the case where we would
+have a spiral
+
+ align:start position:0%
+have a spiral
+ 
+
+ align:start position:0%
+have a spiral
+coming this way
+
+ align:start position:0%
+coming this way
+ 
+
+ align:start position:0%
+coming this way
+toward
+
+ align:start position:0%
+toward
+ 
+
+ align:start position:0%
+toward
+the critical point and basically with
+
+ align:start position:0%
+the critical point and basically with
+ 
+
+ align:start position:0%
+the critical point and basically with
+the velocity vector here going this way.
+
+ align:start position:0%
+the velocity vector here going this way.
+ 
+
+ align:start position:0%
+the velocity vector here going this way.
+You don't have to actually do all this
+
+ align:start position:0%
+You don't have to actually do all this
+ 
+
+ align:start position:0%
+You don't have to actually do all this
+to figure out which direction of the
+
+ align:start position:0%
+to figure out which direction of the
+ 
+
+ align:start position:0%
+to figure out which direction of the
+spiral you should choose. You can just
+
+ align:start position:0%
+spiral you should choose. You can just
+ 
+
+ align:start position:0%
+spiral you should choose. You can just
+look for these cases 2 x2 matrices at
+
+ align:start position:0%
+look for these cases 2 x2 matrices at
+ 
+
+ align:start position:0%
+look for these cases 2 x2 matrices at
+the entry at the lower left part of your
+
+ align:start position:0%
+the entry at the lower left part of your
+ 
+
+ align:start position:0%
+the entry at the lower left part of your
+matrix and if the coefficient here is
+
+ align:start position:0%
+matrix and if the coefficient here is
+ 
+
+ align:start position:0%
+matrix and if the coefficient here is
+positive then it will determine the
+
+ align:start position:0%
+positive then it will determine the
+ 
+
+ align:start position:0%
+positive then it will determine the
+direction of the uh of the velocity
+
+ align:start position:0%
+direction of the uh of the velocity
+ 
+
+ align:start position:0%
+direction of the uh of the velocity
+vector at this point. So if it's
+
+ align:start position:0%
+vector at this point. So if it's
+ 
+
+ align:start position:0%
+vector at this point. So if it's
+positive in this case you would have
+
+ align:start position:0%
+positive in this case you would have
+ 
+
+ align:start position:0%
+positive in this case you would have
+this counterclockwise uh direction of
+
+ align:start position:0%
+this counterclockwise uh direction of
+ 
+
+ align:start position:0%
+this counterclockwise uh direction of
+rotation of the spiral. Okay. So now we
+
+ align:start position:0%
+rotation of the spiral. Okay. So now we
+ 
+
+ align:start position:0%
+rotation of the spiral. Okay. So now we
+can move on and do the second the
+
+ align:start position:0%
+can move on and do the second the
+ 
+
+ align:start position:0%
+can move on and do the second the
+following cases a bit faster. So the
+
+ align:start position:0%
+following cases a bit faster. So the
+ 
+
+ align:start position:0%
+following cases a bit faster. So the
+second case we are in the case where we
+
+ align:start position:0%
+second case we are in the case where we
+ 
+
+ align:start position:0%
+second case we are in the case where we
+now have two repeated egg values. both
+
+ align:start position:0%
+now have two repeated egg values. both
+ 
+
+ align:start position:0%
+now have two repeated egg values. both
+of them are negative. So we can have
+
+ align:start position:0%
+of them are negative. So we can have
+ 
+
+ align:start position:0%
+of them are negative. So we can have
+either uh a complete case. If we had a
+
+ align:start position:0%
+either uh a complete case. If we had a
+ 
+
+ align:start position:0%
+either uh a complete case. If we had a
+matrix that was diagonal, we would have
+
+ align:start position:0%
+matrix that was diagonal, we would have
+ 
+
+ align:start position:0%
+matrix that was diagonal, we would have
+basically a star. But that's not the
+
+ align:start position:0%
+basically a star. But that's not the
+ 
+
+ align:start position:0%
+basically a star. But that's not the
+case because if we pick for example the
+
+ align:start position:0%
+case because if we pick for example the
+ 
+
+ align:start position:0%
+case because if we pick for example the
+value C equals to one, that puts us on
+
+ align:start position:0%
+value C equals to one, that puts us on
+ 
+
+ align:start position:0%
+value C equals to one, that puts us on
+the parabola. We can see that the matrix
+
+ align:start position:0%
+the parabola. We can see that the matrix
+ 
+
+ align:start position:0%
+the parabola. We can see that the matrix
+AC is not diagonal. So we are in a
+
+ align:start position:0%
+AC is not diagonal. So we are in a
+ 
+
+ align:start position:0%
+AC is not diagonal. So we are in a
+defective case. The defective case
+
+ align:start position:0%
+defective case. The defective case
+ 
+
+ align:start position:0%
+defective case. The defective case
+uh if you compute the AEN uh values in
+
+ align:start position:0%
+uh if you compute the AEN uh values in
+ 
+
+ align:start position:0%
+uh if you compute the AEN uh values in
+AEN vector would give you something that
+
+ align:start position:0%
+AEN vector would give you something that
+ 
+
+ align:start position:0%
+AEN vector would give you something that
+looks like that. The first ray of the
+
+ align:start position:0%
+looks like that. The first ray of the
+ 
+
+ align:start position:0%
+looks like that. The first ray of the
+agon vector corresponding to your uh
+
+ align:start position:0%
+agon vector corresponding to your uh
+ 
+
+ align:start position:0%
+agon vector corresponding to your uh
+agon values would be uh in the direction
+
+ align:start position:0%
+agon values would be uh in the direction
+ 
+
+ align:start position:0%
+agon values would be uh in the direction
+of one zero. We have negative aen
+
+ align:start position:0%
+of one zero. We have negative aen
+ 
+
+ align:start position:0%
+of one zero. We have negative aen
+values. So it's going to zero. And
+
+ align:start position:0%
+values. So it's going to zero. And
+ 
+
+ align:start position:0%
+values. So it's going to zero. And
+basically to determine the direction you
+
+ align:start position:0%
+basically to determine the direction you
+ 
+
+ align:start position:0%
+basically to determine the direction you
+have to see that we're also following a
+
+ align:start position:0%
+have to see that we're also following a
+ 
+
+ align:start position:0%
+have to see that we're also following a
+transition here on the determinant on
+
+ align:start position:0%
+transition here on the determinant on
+ 
+
+ align:start position:0%
+transition here on the determinant on
+the on the trace determinant diagram.
+
+ align:start position:0%
+the on the trace determinant diagram.
+ 
+
+ align:start position:0%
+the on the trace determinant diagram.
+And so basically we will have um a
+
+ align:start position:0%
+And so basically we will have um a
+ 
+
+ align:start position:0%
+And so basically we will have um a
+spiral that would look like this. Um
+
+ align:start position:0%
+spiral that would look like this. Um
+ 
+
+ align:start position:0%
+spiral that would look like this. Um
+yep.
+
+ align:start position:0%
+yep.
+ 
+
+ align:start position:0%
+yep.
+What am I doing? Am I doing the same
+
+ align:start position:0%
+What am I doing? Am I doing the same
+ 
+
+ align:start position:0%
+What am I doing? Am I doing the same
+thing? Yeah.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+And it would basically rotate
+
+ align:start position:0%
+And it would basically rotate
+ 
+
+ align:start position:0%
+And it would basically rotate
+as you can see here
+
+ align:start position:0%
+as you can see here
+ 
+
+ align:start position:0%
+as you can see here
+in the same
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+direction
+
+ align:start position:0%
+direction
+ 
+
+ align:start position:0%
+direction
+as the case that we had just before
+
+ align:start position:0%
+as the case that we had just before
+ 
+
+ align:start position:0%
+as the case that we had just before
+because we basically have the transition
+
+ align:start position:0%
+because we basically have the transition
+ 
+
+ align:start position:0%
+because we basically have the transition
+of the structure of the critical point.
+
+ align:start position:0%
+of the structure of the critical point.
+ 
+
+ align:start position:0%
+of the structure of the critical point.
+Okay. And the arrows are pointing toward
+
+ align:start position:0%
+Okay. And the arrows are pointing toward
+ 
+
+ align:start position:0%
+Okay. And the arrows are pointing toward
+the critical point again because our two
+
+ align:start position:0%
+the critical point again because our two
+ 
+
+ align:start position:0%
+the critical point again because our two
+aen values are uh uh are basically here
+
+ align:start position:0%
+aen values are uh uh are basically here
+ 
+
+ align:start position:0%
+aen values are uh uh are basically here
+negative. which is just a repeated egg
+
+ align:start position:0%
+negative. which is just a repeated egg
+ 
+
+ align:start position:0%
+negative. which is just a repeated egg
+value that is negative. Okay. So now we
+
+ align:start position:0%
+value that is negative. Okay. So now we
+ 
+
+ align:start position:0%
+value that is negative. Okay. So now we
+can move on to a third case where here
+
+ align:start position:0%
+can move on to a third case where here
+ 
+
+ align:start position:0%
+can move on to a third case where here
+we move into the wedge area where we
+
+ align:start position:0%
+we move into the wedge area where we
+ 
+
+ align:start position:0%
+we move into the wedge area where we
+have the two aen values now being real
+
+ align:start position:0%
+have the two aen values now being real
+ 
+
+ align:start position:0%
+have the two aen values now being real
+and uh both of them are negative.
+
+ align:start position:0%
+and uh both of them are negative.
+ 
+
+ align:start position:0%
+and uh both of them are negative.
+So for example
+
+ align:start position:0%
+So for example
+ 
+
+ align:start position:0%
+So for example
+we would have two egg values that would
+
+ align:start position:0%
+we would have two egg values that would
+ 
+
+ align:start position:0%
+we would have two egg values that would
+give us two egg vectors that are
+
+ align:start position:0%
+give us two egg vectors that are
+ 
+
+ align:start position:0%
+give us two egg vectors that are
+basically the rays. The direction of the
+
+ align:start position:0%
+basically the rays. The direction of the
+ 
+
+ align:start position:0%
+basically the rays. The direction of the
+trajectories on these two rays would be
+
+ align:start position:0%
+trajectories on these two rays would be
+ 
+
+ align:start position:0%
+trajectories on these two rays would be
+toward the critical point because we
+
+ align:start position:0%
+toward the critical point because we
+ 
+
+ align:start position:0%
+toward the critical point because we
+have again negative uh a values and uh
+
+ align:start position:0%
+have again negative uh a values and uh
+ 
+
+ align:start position:0%
+have again negative uh a values and uh
+the trajectories then would be following
+
+ align:start position:0%
+the trajectories then would be following
+ 
+
+ align:start position:0%
+the trajectories then would be following
+the uh lambda. So if I for example pick
+
+ align:start position:0%
+the uh lambda. So if I for example pick
+ 
+
+ align:start position:0%
+the uh lambda. So if I for example pick
+lambda one less than lambda 2
+
+ align:start position:0%
+lambda one less than lambda 2
+ 
+
+ align:start position:0%
+lambda one less than lambda 2
+then I would have something like this
+
+ align:start position:0%
+then I would have something like this
+ 
+
+ align:start position:0%
+then I would have something like this
+going to zero
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and we would have this trajectory
+
+ align:start position:0%
+and we would have this trajectory
+ 
+
+ align:start position:0%
+and we would have this trajectory
+corresponding
+
+ align:start position:0%
+corresponding
+ 
+
+ align:start position:0%
+corresponding
+to the value that is the closer to zero.
+
+ align:start position:0%
+to the value that is the closer to zero.
+ 
+
+ align:start position:0%
+to the value that is the closer to zero.
+Okay. And again the arrows would be
+
+ align:start position:0%
+Okay. And again the arrows would be
+ 
+
+ align:start position:0%
+Okay. And again the arrows would be
+going toward this critical point. So we
+
+ align:start position:0%
+going toward this critical point. So we
+ 
+
+ align:start position:0%
+going toward this critical point. So we
+can now move on and if we keep
+
+ align:start position:0%
+can now move on and if we keep
+ 
+
+ align:start position:0%
+can now move on and if we keep
+increasing C uh we reach now the point
+
+ align:start position:0%
+increasing C uh we reach now the point
+ 
+
+ align:start position:0%
+increasing C uh we reach now the point
+four where we are in the special case
+
+ align:start position:0%
+four where we are in the special case
+ 
+
+ align:start position:0%
+four where we are in the special case
+again a boundary case where the
+
+ align:start position:0%
+again a boundary case where the
+ 
+
+ align:start position:0%
+again a boundary case where the
+determinant is zero but the trace is non
+
+ align:start position:0%
+determinant is zero but the trace is non
+ 
+
+ align:start position:0%
+determinant is zero but the trace is non
+zero. If the terminant is zero which is
+
+ align:start position:0%
+zero. If the terminant is zero which is
+ 
+
+ align:start position:0%
+zero. If the terminant is zero which is
+the product of the two aen values it
+
+ align:start position:0%
+the product of the two aen values it
+ 
+
+ align:start position:0%
+the product of the two aen values it
+means that we have one a value that is
+
+ align:start position:0%
+means that we have one a value that is
+ 
+
+ align:start position:0%
+means that we have one a value that is
+equal to zero
+
+ align:start position:0%
+equal to zero
+ 
+
+ align:start position:0%
+equal to zero
+and another aen value that is actually
+
+ align:start position:0%
+and another aen value that is actually
+ 
+
+ align:start position:0%
+and another aen value that is actually
+in this case minus two. So just
+
+ align:start position:0%
+in this case minus two. So just
+ 
+
+ align:start position:0%
+in this case minus two. So just
+negative. So what happens here? uh what
+
+ align:start position:0%
+negative. So what happens here? uh what
+ 
+
+ align:start position:0%
+negative. So what happens here? uh what
+happens is that we have now
+
+ align:start position:0%
+happens is that we have now
+ 
+
+ align:start position:0%
+happens is that we have now
+the aen vector that corresponds to the
+
+ align:start position:0%
+the aen vector that corresponds to the
+ 
+
+ align:start position:0%
+the aen vector that corresponds to the
+egg value equals to zero is basically
+
+ align:start position:0%
+egg value equals to zero is basically
+ 
+
+ align:start position:0%
+egg value equals to zero is basically
+just defining a whole line of critical
+
+ align:start position:0%
+just defining a whole line of critical
+ 
+
+ align:start position:0%
+just defining a whole line of critical
+points. So all the points on this line
+
+ align:start position:0%
+points. So all the points on this line
+ 
+
+ align:start position:0%
+points. So all the points on this line
+that would correspond so for example to
+
+ align:start position:0%
+that would correspond so for example to
+ 
+
+ align:start position:0%
+that would correspond so for example to
+lambda zero are all critical points. So
+
+ align:start position:0%
+lambda zero are all critical points. So
+ 
+
+ align:start position:0%
+lambda zero are all critical points. So
+we don't need to actually draw arrows
+
+ align:start position:0%
+we don't need to actually draw arrows
+ 
+
+ align:start position:0%
+we don't need to actually draw arrows
+here. All the points would be critical
+
+ align:start position:0%
+here. All the points would be critical
+ 
+
+ align:start position:0%
+here. All the points would be critical
+points. And another direction or ray
+
+ align:start position:0%
+points. And another direction or ray
+ 
+
+ align:start position:0%
+points. And another direction or ray
+would be determined by the second egg
+
+ align:start position:0%
+would be determined by the second egg
+ 
+
+ align:start position:0%
+would be determined by the second egg
+value lambda 2. And uh we would have for
+
+ align:start position:0%
+value lambda 2. And uh we would have for
+ 
+
+ align:start position:0%
+value lambda 2. And uh we would have for
+example
+
+ align:start position:0%
+example
+ 
+
+ align:start position:0%
+example
+directions
+
+ align:start position:0%
+directions
+ 
+
+ align:start position:0%
+directions
+uh in this way that would correspond to
+
+ align:start position:0%
+uh in this way that would correspond to
+ 
+
+ align:start position:0%
+uh in this way that would correspond to
+direction of v2. So all these would be
+
+ align:start position:0%
+direction of v2. So all these would be
+ 
+
+ align:start position:0%
+direction of v2. So all these would be
+parallel to v2 and we would have the
+
+ align:start position:0%
+parallel to v2 and we would have the
+ 
+
+ align:start position:0%
+parallel to v2 and we would have the
+trajectories
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+going toward all the critical points on
+
+ align:start position:0%
+going toward all the critical points on
+ 
+
+ align:start position:0%
+going toward all the critical points on
+this line. So in this case we're in a
+
+ align:start position:0%
+this line. So in this case we're in a
+ 
+
+ align:start position:0%
+this line. So in this case we're in a
+case where we actually don't have one
+
+ align:start position:0%
+case where we actually don't have one
+ 
+
+ align:start position:0%
+case where we actually don't have one
+localized critical points like in the
+
+ align:start position:0%
+localized critical points like in the
+ 
+
+ align:start position:0%
+localized critical points like in the
+previous case that we saw we actually
+
+ align:start position:0%
+previous case that we saw we actually
+ 
+
+ align:start position:0%
+previous case that we saw we actually
+have a full a whole line of critical
+
+ align:start position:0%
+have a full a whole line of critical
+ 
+
+ align:start position:0%
+have a full a whole line of critical
+points. Okay. So let's move one more
+
+ align:start position:0%
+points. Okay. So let's move one more
+ 
+
+ align:start position:0%
+points. Okay. So let's move one more
+point down. So here for another value of
+
+ align:start position:0%
+point down. So here for another value of
+ 
+
+ align:start position:0%
+point down. So here for another value of
+C. We now are in the lower part of the
+
+ align:start position:0%
+C. We now are in the lower part of the
+ 
+
+ align:start position:0%
+C. We now are in the lower part of the
+diagram where we now have two values are
+
+ align:start position:0%
+diagram where we now have two values are
+ 
+
+ align:start position:0%
+diagram where we now have two values are
+again real but now the determinant is
+
+ align:start position:0%
+again real but now the determinant is
+ 
+
+ align:start position:0%
+again real but now the determinant is
+negative. Determinant is the product of
+
+ align:start position:0%
+negative. Determinant is the product of
+ 
+
+ align:start position:0%
+negative. Determinant is the product of
+the two. So basically you know that one
+
+ align:start position:0%
+the two. So basically you know that one
+ 
+
+ align:start position:0%
+the two. So basically you know that one
+is positive and the other one is
+
+ align:start position:0%
+is positive and the other one is
+ 
+
+ align:start position:0%
+is positive and the other one is
+negative. Okay. So for example here we
+
+ align:start position:0%
+negative. Okay. So for example here we
+ 
+
+ align:start position:0%
+negative. Okay. So for example here we
+would have
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh one positive
+
+ align:start position:0%
+uh one positive
+ 
+
+ align:start position:0%
+uh one positive
+the negative aen uh value.
+
+ align:start position:0%
+the negative aen uh value.
+ 
+
+ align:start position:0%
+the negative aen uh value.
+Oops sorry. Thank you.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+So we would have the positive aen value
+
+ align:start position:0%
+So we would have the positive aen value
+ 
+
+ align:start position:0%
+So we would have the positive aen value
+and the negative aen value here. So here
+
+ align:start position:0%
+and the negative aen value here. So here
+ 
+
+ align:start position:0%
+and the negative aen value here. So here
+again we're just moving in the structure
+
+ align:start position:0%
+again we're just moving in the structure
+ 
+
+ align:start position:0%
+again we're just moving in the structure
+of the a of the uh critical point. So we
+
+ align:start position:0%
+of the a of the uh critical point. So we
+ 
+
+ align:start position:0%
+of the a of the uh critical point. So we
+should have a smooth transition between
+
+ align:start position:0%
+should have a smooth transition between
+ 
+
+ align:start position:0%
+should have a smooth transition between
+the diagrams going one to five. And so
+
+ align:start position:0%
+the diagrams going one to five. And so
+ 
+
+ align:start position:0%
+the diagrams going one to five. And so
+here what we see is that we actually
+
+ align:start position:0%
+here what we see is that we actually
+ 
+
+ align:start position:0%
+here what we see is that we actually
+have uh the array that is basically the
+
+ align:start position:0%
+have uh the array that is basically the
+ 
+
+ align:start position:0%
+have uh the array that is basically the
+stable the spa stable space here that
+
+ align:start position:0%
+stable the spa stable space here that
+ 
+
+ align:start position:0%
+stable the spa stable space here that
+would uh give us the trajectories going
+
+ align:start position:0%
+would uh give us the trajectories going
+ 
+
+ align:start position:0%
+would uh give us the trajectories going
+to zero. But it's the only air region
+
+ align:start position:0%
+to zero. But it's the only air region
+ 
+
+ align:start position:0%
+to zero. But it's the only air region
+where we have stability and all the
+
+ align:start position:0%
+where we have stability and all the
+ 
+
+ align:start position:0%
+where we have stability and all the
+trajectories would just then be
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+tangent in minus infinity to the the
+
+ align:start position:0%
+tangent in minus infinity to the the
+ 
+
+ align:start position:0%
+tangent in minus infinity to the the
+array v1 corresponding to uh the
+
+ align:start position:0%
+array v1 corresponding to uh the
+ 
+
+ align:start position:0%
+array v1 corresponding to uh the
+negative aen value and going toward the
+
+ align:start position:0%
+negative aen value and going toward the
+ 
+
+ align:start position:0%
+negative aen value and going toward the
+direction of the ray with the positive
+
+ align:start position:0%
+direction of the ray with the positive
+ 
+
+ align:start position:0%
+direction of the ray with the positive
+aen uh value at plus infinity. Okay. So
+
+ align:start position:0%
+aen uh value at plus infinity. Okay. So
+ 
+
+ align:start position:0%
+aen uh value at plus infinity. Okay. So
+we would have
+
+ align:start position:0%
+we would have
+ 
+
+ align:start position:0%
+we would have
+something like that that would
+
+ align:start position:0%
+something like that that would
+ 
+
+ align:start position:0%
+something like that that would
+correspond to a saddle.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+This would be a comp.
+
+ align:start position:0%
+This would be a comp.
+ 
+
+ align:start position:0%
+This would be a comp.
+This is basically a sink
+
+ align:start position:0%
+This is basically a sink
+ 
+
+ align:start position:0%
+This is basically a sink
+or basically a stable node. This would
+
+ align:start position:0%
+or basically a stable node. This would
+ 
+
+ align:start position:0%
+or basically a stable node. This would
+be defective
+
+ align:start position:0%
+be defective
+ 
+
+ align:start position:0%
+be defective
+stable node.
+
+ align:start position:0%
+stable node.
+ 
+
+ align:start position:0%
+stable node.
+And here we just have a astoically
+
+ align:start position:0%
+And here we just have a astoically
+ 
+
+ align:start position:0%
+And here we just have a astoically
+stable
+
+ align:start position:0%
+stable
+ 
+
+ align:start position:0%
+stable
+spiral. So uh basically here what you
+
+ align:start position:0%
+spiral. So uh basically here what you
+ 
+
+ align:start position:0%
+spiral. So uh basically here what you
+could see is that we have uh by just
+
+ align:start position:0%
+could see is that we have uh by just
+ 
+
+ align:start position:0%
+could see is that we have uh by just
+changing the value of the constant C had
+
+ align:start position:0%
+changing the value of the constant C had
+ 
+
+ align:start position:0%
+changing the value of the constant C had
+um moved this the the structure of the
+
+ align:start position:0%
+um moved this the the structure of the
+ 
+
+ align:start position:0%
+um moved this the the structure of the
+critical point for the of the system
+
+ align:start position:0%
+critical point for the of the system
+ 
+
+ align:start position:0%
+critical point for the of the system
+from the phase diagrams one to five and
+
+ align:start position:0%
+from the phase diagrams one to five and
+ 
+
+ align:start position:0%
+from the phase diagrams one to five and
+the transitions can be seen to be smooth
+
+ align:start position:0%
+the transitions can be seen to be smooth
+ 
+
+ align:start position:0%
+the transitions can be seen to be smooth
+if you had a continuum of values of for
+
+ align:start position:0%
+if you had a continuum of values of for
+ 
+
+ align:start position:0%
+if you had a continuum of values of for
+C. So that ends this recitation.
\ No newline at end of file
diff --git a/zsxqmbdUXuo.txt b/zsxqmbdUXuo.txt
new file mode 100644
index 0000000000000000000000000000000000000000..41ddf6397ddc5e83f588ff7bdf9d5c8ff242018d
--- /dev/null
+++ b/zsxqmbdUXuo.txt
@@ -0,0 +1,10200 @@
+align:start position:0%
+ 
+the following content is provided under
+
+ align:start position:0%
+the following content is provided under
+ 
+
+ align:start position:0%
+the following content is provided under
+a Creative Commons license your support
+
+ align:start position:0%
+a Creative Commons license your support
+ 
+
+ align:start position:0%
+a Creative Commons license your support
+will help MIT OpenCourseWare continue to
+
+ align:start position:0%
+will help MIT OpenCourseWare continue to
+ 
+
+ align:start position:0%
+will help MIT OpenCourseWare continue to
+offer high quality educational resources
+
+ align:start position:0%
+offer high quality educational resources
+ 
+
+ align:start position:0%
+offer high quality educational resources
+for free to make a donation or view
+
+ align:start position:0%
+for free to make a donation or view
+ 
+
+ align:start position:0%
+for free to make a donation or view
+additional materials from hundreds of
+
+ align:start position:0%
+additional materials from hundreds of
+ 
+
+ align:start position:0%
+additional materials from hundreds of
+MIT courses visit MIT opencourseware at
+
+ align:start position:0%
+MIT courses visit MIT opencourseware at
+ 
+
+ align:start position:0%
+MIT courses visit MIT opencourseware at
+ocw.mit.edu
+
+ align:start position:0%
+ocw.mit.edu
+ 
+
+ align:start position:0%
+ocw.mit.edu
+ok
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+one
+
+ align:start position:0%
+one
+ 
+
+ align:start position:0%
+one
+of the really important things in this
+
+ align:start position:0%
+of the really important things in this
+ 
+
+ align:start position:0%
+of the really important things in this
+course on spectroscopy is being able to
+
+ align:start position:0%
+course on spectroscopy is being able to
+ 
+
+ align:start position:0%
+course on spectroscopy is being able to
+write effective hamiltonians to describe
+
+ align:start position:0%
+write effective hamiltonians to describe
+ 
+
+ align:start position:0%
+write effective hamiltonians to describe
+the problem that you're going to be
+
+ align:start position:0%
+the problem that you're going to be
+ 
+
+ align:start position:0%
+the problem that you're going to be
+solving and so at the beginning I'm
+
+ align:start position:0%
+solving and so at the beginning I'm
+ 
+
+ align:start position:0%
+solving and so at the beginning I'm
+doing an exercise and I in two versions
+
+ align:start position:0%
+doing an exercise and I in two versions
+ 
+
+ align:start position:0%
+doing an exercise and I in two versions
+of effective Hamiltonian before starting
+
+ align:start position:0%
+of effective Hamiltonian before starting
+ 
+
+ align:start position:0%
+of effective Hamiltonian before starting
+to pick up the material of spectroscopy
+
+ align:start position:0%
+to pick up the material of spectroscopy
+ 
+
+ align:start position:0%
+to pick up the material of spectroscopy
+in a logical order and so it's it's
+
+ align:start position:0%
+in a logical order and so it's it's
+ 
+
+ align:start position:0%
+in a logical order and so it's it's
+a taste of what's to come it's an
+
+ align:start position:0%
+a taste of what's to come it's an
+ 
+
+ align:start position:0%
+a taste of what's to come it's an
+example of the kind of problems I hope
+
+ align:start position:0%
+example of the kind of problems I hope
+ 
+
+ align:start position:0%
+example of the kind of problems I hope
+you'll be able to to solve and like
+
+ align:start position:0%
+you'll be able to to solve and like
+ 
+
+ align:start position:0%
+you'll be able to to solve and like
+solving and I said there was a problem
+
+ align:start position:0%
+solving and I said there was a problem
+ 
+
+ align:start position:0%
+solving and I said there was a problem
+last time the problem is described at
+
+ align:start position:0%
+last time the problem is described at
+ 
+
+ align:start position:0%
+last time the problem is described at
+the top of the first page now probably
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the best thing would be for you to
+
+ align:start position:0%
+the best thing would be for you to
+ 
+
+ align:start position:0%
+the best thing would be for you to
+submit that answer to me on Friday on
+
+ align:start position:0%
+submit that answer to me on Friday on
+ 
+
+ align:start position:0%
+submit that answer to me on Friday on
+Thursday or to one of the members of my
+
+ align:start position:0%
+Thursday or to one of the members of my
+ 
+
+ align:start position:0%
+Thursday or to one of the members of my
+group if you're and but I'm mostly going
+
+ align:start position:0%
+group if you're and but I'm mostly going
+ 
+
+ align:start position:0%
+group if you're and but I'm mostly going
+to look at this just to say oh yeah you
+
+ align:start position:0%
+to look at this just to say oh yeah you
+ 
+
+ align:start position:0%
+to look at this just to say oh yeah you
+did it and I my idea is that you're
+
+ align:start position:0%
+did it and I my idea is that you're
+ 
+
+ align:start position:0%
+did it and I my idea is that you're
+going to do these problems just to sort
+
+ align:start position:0%
+going to do these problems just to sort
+ 
+
+ align:start position:0%
+going to do these problems just to sort
+of refresh
+
+ align:start position:0%
+of refresh
+ 
+
+ align:start position:0%
+of refresh
+your memory of perturbation theory and
+
+ align:start position:0%
+your memory of perturbation theory and
+ 
+
+ align:start position:0%
+your memory of perturbation theory and
+get a little bit insane
+
+ align:start position:0%
+get a little bit insane
+ 
+
+ align:start position:0%
+get a little bit insane
+with the awful algebra that ensues okay
+
+ align:start position:0%
+with the awful algebra that ensues okay
+ 
+
+ align:start position:0%
+with the awful algebra that ensues okay
+so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+the problem that I wanted you to do is a
+
+ align:start position:0%
+the problem that I wanted you to do is a
+ 
+
+ align:start position:0%
+the problem that I wanted you to do is a
+diatomic molecule and
+
+ align:start position:0%
+diatomic molecule and
+ 
+
+ align:start position:0%
+diatomic molecule and
+it's a vibrating
+
+ align:start position:0%
+it's a vibrating
+ 
+
+ align:start position:0%
+it's a vibrating
+rotor
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+we have a potential and
+
+ align:start position:0%
+we have a potential and
+ 
+
+ align:start position:0%
+we have a potential and
+the potential is got the harmonic term I
+
+ align:start position:0%
+the potential is got the harmonic term I
+ 
+
+ align:start position:0%
+the potential is got the harmonic term I
+just
+
+ align:start position:0%
+just
+ 
+
+ align:start position:0%
+just
+want to make sure and then
+
+ align:start position:0%
+want to make sure and then
+ 
+
+ align:start position:0%
+want to make sure and then
+a cubic
+
+ align:start position:0%
+a cubic
+ 
+
+ align:start position:0%
+a cubic
+term and
+
+ align:start position:0%
+term and
+ 
+
+ align:start position:0%
+term and
+a quartic term so
+
+ align:start position:0%
+a quartic term so
+ 
+
+ align:start position:0%
+a quartic term so
+these are the operators that you're
+
+ align:start position:0%
+these are the operators that you're
+ 
+
+ align:start position:0%
+these are the operators that you're
+going to be dealing with using
+
+ align:start position:0%
+going to be dealing with using
+ 
+
+ align:start position:0%
+going to be dealing with using
+perturbation theory and we
+
+ align:start position:0%
+perturbation theory and we
+ 
+
+ align:start position:0%
+perturbation theory and we
+also have the rotational operator which
+
+ align:start position:0%
+also have the rotational operator which
+ 
+
+ align:start position:0%
+also have the rotational operator which
+is the moment of inertia operator and
+
+ align:start position:0%
+is the moment of inertia operator and
+ 
+
+ align:start position:0%
+is the moment of inertia operator and
+that's H bar squared over H see that's
+
+ align:start position:0%
+that's H bar squared over H see that's
+ 
+
+ align:start position:0%
+that's H bar squared over H see that's
+just because if the units were using and
+
+ align:start position:0%
+just because if the units were using and
+ 
+
+ align:start position:0%
+just because if the units were using and
+it's 1 over 2 mu R
+
+ align:start position:0%
+it's 1 over 2 mu R
+ 
+
+ align:start position:0%
+it's 1 over 2 mu R
+squared and I'm going to convert our
+
+ align:start position:0%
+squared and I'm going to convert our
+ 
+
+ align:start position:0%
+squared and I'm going to convert our
+into Q in a moment but this is just
+
+ align:start position:0%
+into Q in a moment but this is just
+ 
+
+ align:start position:0%
+into Q in a moment but this is just
+analogous to the the kinetic energy
+
+ align:start position:0%
+analogous to the the kinetic energy
+ 
+
+ align:start position:0%
+analogous to the the kinetic energy
+operator 1 over 2m a
+
+ align:start position:0%
+operator 1 over 2m a
+ 
+
+ align:start position:0%
+operator 1 over 2m a
+P
+
+ align:start position:0%
+P
+ 
+
+ align:start position:0%
+P
+squared over 2m and the the we get a J
+
+ align:start position:0%
+squared over 2m and the the we get a J
+ 
+
+ align:start position:0%
+squared over 2m and the the we get a J
+squared here okay so we
+
+ align:start position:0%
+squared here okay so we
+ 
+
+ align:start position:0%
+squared here okay so we
+we write B of our by saying r
+
+ align:start position:0%
+we write B of our by saying r
+ 
+
+ align:start position:0%
+we write B of our by saying r
+minus r e SQ rewrite be of our and we do
+
+ align:start position:0%
+minus r e SQ rewrite be of our and we do
+ 
+
+ align:start position:0%
+minus r e SQ rewrite be of our and we do
+a power series expansion and we get the
+
+ align:start position:0%
+a power series expansion and we get the
+ 
+
+ align:start position:0%
+a power series expansion and we get the
+e1
+
+ align:start position:0%
+e1
+ 
+
+ align:start position:0%
+e1
+minus 2q
+
+ align:start position:0%
+minus 2q
+ 
+
+ align:start position:0%
+minus 2q
+over r-e + 3
+
+ align:start position:0%
+over r-e + 3
+ 
+
+ align:start position:0%
+over r-e + 3
+q / r e squared so the problem we're
+
+ align:start position:0%
+q / r e squared so the problem we're
+ 
+
+ align:start position:0%
+q / r e squared so the problem we're
+going to solve that you're going to
+
+ align:start position:0%
+going to solve that you're going to
+ 
+
+ align:start position:0%
+going to solve that you're going to
+solve involves cute squared QQQ fourth
+
+ align:start position:0%
+solve involves cute squared QQQ fourth
+ 
+
+ align:start position:0%
+solve involves cute squared QQQ fourth
+and cue to the one Q squared and we're
+
+ align:start position:0%
+and cue to the one Q squared and we're
+ 
+
+ align:start position:0%
+and cue to the one Q squared and we're
+going to put that all together in a way
+
+ align:start position:0%
+going to put that all together in a way
+ 
+
+ align:start position:0%
+going to put that all together in a way
+that relay gives you something thats
+
+ align:start position:0%
+that relay gives you something thats
+ 
+
+ align:start position:0%
+that relay gives you something thats
+related to the energy levels of
+
+ align:start position:0%
+related to the energy levels of
+ 
+
+ align:start position:0%
+related to the energy levels of
+a diatomic molecule so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the energy levels for a diatomic
+
+ align:start position:0%
+the energy levels for a diatomic
+ 
+
+ align:start position:0%
+the energy levels for a diatomic
+molecule they
+
+ align:start position:0%
+molecule they
+ 
+
+ align:start position:0%
+molecule they
+have two quantum numbers v + j actually
+
+ align:start position:0%
+have two quantum numbers v + j actually
+ 
+
+ align:start position:0%
+have two quantum numbers v + j actually
+you'll see that they have omega and
+
+ align:start position:0%
+you'll see that they have omega and
+ 
+
+ align:start position:0%
+you'll see that they have omega and
+lambda s and sigma and other things
+
+ align:start position:0%
+lambda s and sigma and other things
+ 
+
+ align:start position:0%
+lambda s and sigma and other things
+later but for an ordinary molecule
+
+ align:start position:0%
+later but for an ordinary molecule
+ 
+
+ align:start position:0%
+later but for an ordinary molecule
+without any angular momenta any
+
+ align:start position:0%
+without any angular momenta any
+ 
+
+ align:start position:0%
+without any angular momenta any
+electronic an angular momentum we
+
+ align:start position:0%
+electronic an angular momentum we
+ 
+
+ align:start position:0%
+electronic an angular momentum we
+write the energy levels in a in a naive
+
+ align:start position:0%
+write the energy levels in a in a naive
+ 
+
+ align:start position:0%
+write the energy levels in a in a naive
+way I got
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this wrong last yesterday and then we
+
+ align:start position:0%
+this wrong last yesterday and then we
+ 
+
+ align:start position:0%
+this wrong last yesterday and then we
+have plus j j plus 1 times B times okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+sorry ve minus
+
+ align:start position:0%
+sorry ve minus
+ 
+
+ align:start position:0%
+sorry ve minus
+alpha e e plus a half plus
+
+ align:start position:0%
+alpha e e plus a half plus
+ 
+
+ align:start position:0%
+alpha e e plus a half plus
+gamma e a plus a half squared and
+
+ align:start position:0%
+gamma e a plus a half squared and
+ 
+
+ align:start position:0%
+gamma e a plus a half squared and
+continues
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and then we have plus minus J a square
+
+ align:start position:0%
+and then we have plus minus J a square
+ 
+
+ align:start position:0%
+and then we have plus minus J a square
+J plus 1 squared d
+
+ align:start position:0%
+J plus 1 squared d
+ 
+
+ align:start position:0%
+J plus 1 squared d
+e plus beta e plus
+
+ align:start position:0%
+e plus beta e plus
+ 
+
+ align:start position:0%
+e plus beta e plus
+a half so you see what we have is a
+
+ align:start position:0%
+a half so you see what we have is a
+ 
+
+ align:start position:0%
+a half so you see what we have is a
+bunch of expansions and powers of e plus
+
+ align:start position:0%
+bunch of expansions and powers of e plus
+ 
+
+ align:start position:0%
+bunch of expansions and powers of e plus
+a half and JJ
+
+ align:start position:0%
+a half and JJ
+ 
+
+ align:start position:0%
+a half and JJ
++ 1 and so
+
+ align:start position:0%
++ 1 and so
+ 
+
+ align:start position:0%
++ 1 and so
+in order to describe the energy levels
+
+ align:start position:0%
+in order to describe the energy levels
+ 
+
+ align:start position:0%
+in order to describe the energy levels
+of a molecule or
+
+ align:start position:0%
+of a molecule or
+ 
+
+ align:start position:0%
+of a molecule or
+the problem that I've asked you to solve
+
+ align:start position:0%
+the problem that I've asked you to solve
+ 
+
+ align:start position:0%
+the problem that I've asked you to solve
+you want to get omega omega XE be alpha
+
+ align:start position:0%
+you want to get omega omega XE be alpha
+ 
+
+ align:start position:0%
+you want to get omega omega XE be alpha
+e and de from the
+
+ align:start position:0%
+e and de from the
+ 
+
+ align:start position:0%
+e and de from the
+quantities k ay B
+
+ align:start position:0%
+quantities k ay B
+ 
+
+ align:start position:0%
+quantities k ay B
+mu
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so we
+
+ align:start position:0%
+so we
+ 
+
+ align:start position:0%
+so we
+we
+
+ align:start position:0%
+we
+ 
+
+ align:start position:0%
+we
+have the harmonic the cubic the quartic
+
+ align:start position:0%
+have the harmonic the cubic the quartic
+ 
+
+ align:start position:0%
+have the harmonic the cubic the quartic
+and the mass and that will enable you to
+
+ align:start position:0%
+and the mass and that will enable you to
+ 
+
+ align:start position:0%
+and the mass and that will enable you to
+derive values for the things that you'd
+
+ align:start position:0%
+derive values for the things that you'd
+ 
+
+ align:start position:0%
+derive values for the things that you'd
+actually observe in the spectrum you
+
+ align:start position:0%
+actually observe in the spectrum you
+ 
+
+ align:start position:0%
+actually observe in the spectrum you
+could carry this further and get ye and
+
+ align:start position:0%
+could carry this further and get ye and
+ 
+
+ align:start position:0%
+could carry this further and get ye and
+gamma e but I'm not too cruel and so
+
+ align:start position:0%
+gamma e but I'm not too cruel and so
+ 
+
+ align:start position:0%
+gamma e but I'm not too cruel and so
+that's the problem and okay
+
+ align:start position:0%
+that's the problem and okay
+ 
+
+ align:start position:0%
+that's the problem and okay
+so let me go the other board so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+what do we do how do we use perturbation
+
+ align:start position:0%
+what do we do how do we use perturbation
+ 
+
+ align:start position:0%
+what do we do how do we use perturbation
+theory now this is really a lengthy
+
+ align:start position:0%
+theory now this is really a lengthy
+ 
+
+ align:start position:0%
+theory now this is really a lengthy
+review of what we did last time but it's
+
+ align:start position:0%
+review of what we did last time but it's
+ 
+
+ align:start position:0%
+review of what we did last time but it's
+still better to see it we
+
+ align:start position:0%
+still better to see it we
+ 
+
+ align:start position:0%
+still better to see it we
+expanded the Hamiltonian into a zero
+
+ align:start position:0%
+expanded the Hamiltonian into a zero
+ 
+
+ align:start position:0%
+expanded the Hamiltonian into a zero
+order part and a perturbation part we'd
+
+ align:start position:0%
+order part and a perturbation part we'd
+ 
+
+ align:start position:0%
+order part and a perturbation part we'd
+expended the energy into a zero order
+
+ align:start position:0%
+expended the energy into a zero order
+ 
+
+ align:start position:0%
+expended the energy into a zero order
+part which is I ghen values of H 0 and
+
+ align:start position:0%
+part which is I ghen values of H 0 and
+ 
+
+ align:start position:0%
+part which is I ghen values of H 0 and
+first order and second order etc and so
+
+ align:start position:0%
+first order and second order etc and so
+ 
+
+ align:start position:0%
+first order and second order etc and so
+we got zero
+
+ align:start position:0%
+we got zero
+ 
+
+ align:start position:0%
+we got zero
+order equation
+
+ align:start position:0%
+order equation
+ 
+
+ align:start position:0%
+order equation
+and
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this is what we use to describe to
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+define our wave functions our wave
+
+ align:start position:0%
+define our wave functions our wave
+ 
+
+ align:start position:0%
+define our wave functions our wave
+functions are eigenfunctions of the
+
+ align:start position:0%
+functions are eigenfunctions of the
+ 
+
+ align:start position:0%
+functions are eigenfunctions of the
+hamel the zero-order hamiltonian the
+
+ align:start position:0%
+hamel the zero-order hamiltonian the
+ 
+
+ align:start position:0%
+hamel the zero-order hamiltonian the
+energy levels are the eigenvalues and
+
+ align:start position:0%
+energy levels are the eigenvalues and
+ 
+
+ align:start position:0%
+energy levels are the eigenvalues and
+there are many choices of h0 it's
+
+ align:start position:0%
+there are many choices of h0 it's
+ 
+
+ align:start position:0%
+there are many choices of h0 it's
+usually not necessary to make your
+
+ align:start position:0%
+usually not necessary to make your
+ 
+
+ align:start position:0%
+usually not necessary to make your
+choice of h0 read the mind of the
+
+ align:start position:0%
+choice of h0 read the mind of the
+ 
+
+ align:start position:0%
+choice of h0 read the mind of the
+molecule it's just usually you tues 80
+
+ align:start position:0%
+molecule it's just usually you tues 80
+ 
+
+ align:start position:0%
+molecule it's just usually you tues 80
+because it gives you things that you can
+
+ align:start position:0%
+because it gives you things that you can
+ 
+
+ align:start position:0%
+because it gives you things that you can
+do without breaking a sweat as far as
+
+ align:start position:0%
+do without breaking a sweat as far as
+ 
+
+ align:start position:0%
+do without breaking a sweat as far as
+writing down values of matrix elements
+
+ align:start position:0%
+writing down values of matrix elements
+ 
+
+ align:start position:0%
+writing down values of matrix elements
+once you've written down values of
+
+ align:start position:0%
+once you've written down values of
+ 
+
+ align:start position:0%
+once you've written down values of
+matrix elements the computer does all
+
+ align:start position:0%
+matrix elements the computer does all
+ 
+
+ align:start position:0%
+matrix elements the computer does all
+the work and it's nice to be able to
+
+ align:start position:0%
+the work and it's nice to be able to
+ 
+
+ align:start position:0%
+the work and it's nice to be able to
+have a way of writing the matrix
+
+ align:start position:0%
+have a way of writing the matrix
+ 
+
+ align:start position:0%
+have a way of writing the matrix
+elements which really don't even require
+
+ align:start position:0%
+elements which really don't even require
+ 
+
+ align:start position:0%
+elements which really don't even require
+you to write them you say mr. computer
+
+ align:start position:0%
+you to write them you say mr. computer
+ 
+
+ align:start position:0%
+you to write them you say mr. computer
+you write them because they are gotten
+
+ align:start position:0%
+you write them because they are gotten
+ 
+
+ align:start position:0%
+you write them because they are gotten
+by this simple formula
+
+ align:start position:0%
+by this simple formula
+ 
+
+ align:start position:0%
+by this simple formula
+so but
+
+ align:start position:0%
+so but
+ 
+
+ align:start position:0%
+so but
+you don't have to do that this h0 is
+
+ align:start position:0%
+you don't have to do that this h0 is
+ 
+
+ align:start position:0%
+you don't have to do that this h0 is
+whatever you like but it and it provides
+
+ align:start position:0%
+whatever you like but it and it provides
+ 
+
+ align:start position:0%
+whatever you like but it and it provides
+the words you use and the images you use
+
+ align:start position:0%
+the words you use and the images you use
+ 
+
+ align:start position:0%
+the words you use and the images you use
+to describe what you're seeing in the
+
+ align:start position:0%
+to describe what you're seeing in the
+ 
+
+ align:start position:0%
+to describe what you're seeing in the
+experiment and sometimes
+
+ align:start position:0%
+experiment and sometimes
+ 
+
+ align:start position:0%
+experiment and sometimes
+that's valuable it also provides you
+
+ align:start position:0%
+that's valuable it also provides you
+ 
+
+ align:start position:0%
+that's valuable it also provides you
+with a starting point when you start out
+
+ align:start position:0%
+with a starting point when you start out
+ 
+
+ align:start position:0%
+with a starting point when you start out
+in interpreting an experiment you have
+
+ align:start position:0%
+in interpreting an experiment you have
+ 
+
+ align:start position:0%
+in interpreting an experiment you have
+energy levels and they don't come with
+
+ align:start position:0%
+energy levels and they don't come with
+ 
+
+ align:start position:0%
+energy levels and they don't come with
+any hints on them about well they
+
+ align:start position:0%
+any hints on them about well they
+ 
+
+ align:start position:0%
+any hints on them about well they
+usually don't come with many hints on
+
+ align:start position:0%
+usually don't come with many hints on
+ 
+
+ align:start position:0%
+usually don't come with many hints on
+them what they mean and your
+
+ align:start position:0%
+them what they mean and your
+ 
+
+ align:start position:0%
+them what they mean and your
+job is to somehow recognize the patterns
+
+ align:start position:0%
+job is to somehow recognize the patterns
+ 
+
+ align:start position:0%
+job is to somehow recognize the patterns
+in the real spectrum and relate those
+
+ align:start position:0%
+in the real spectrum and relate those
+ 
+
+ align:start position:0%
+in the real spectrum and relate those
+patterns to the
+
+ align:start position:0%
+patterns to the
+ 
+
+ align:start position:0%
+patterns to the
+truth and that's a non trivial matter
+
+ align:start position:0%
+truth and that's a non trivial matter
+ 
+
+ align:start position:0%
+truth and that's a non trivial matter
+and so if you have a good 801 that does
+
+ align:start position:0%
+and so if you have a good 801 that does
+ 
+
+ align:start position:0%
+and so if you have a good 801 that does
+mimic what the molecule the way the
+
+ align:start position:0%
+mimic what the molecule the way the
+ 
+
+ align:start position:0%
+mimic what the molecule the way the
+molecule things you will have a much
+
+ align:start position:0%
+molecule things you will have a much
+ 
+
+ align:start position:0%
+molecule things you will have a much
+easier job of making sense of the
+
+ align:start position:0%
+easier job of making sense of the
+ 
+
+ align:start position:0%
+easier job of making sense of the
+experiment then if you have a bad one
+
+ align:start position:0%
+experiment then if you have a bad one
+ 
+
+ align:start position:0%
+experiment then if you have a bad one
+but that's counterbalanced by wanting to
+
+ align:start position:0%
+but that's counterbalanced by wanting to
+ 
+
+ align:start position:0%
+but that's counterbalanced by wanting to
+have the computer essentially
+
+ align:start position:0%
+have the computer essentially
+ 
+
+ align:start position:0%
+have the computer essentially
+do all the work so you have to make a
+
+ align:start position:0%
+do all the work so you have to make a
+ 
+
+ align:start position:0%
+do all the work so you have to make a
+compromise ok so we choose this that
+
+ align:start position:0%
+compromise ok so we choose this that
+ 
+
+ align:start position:0%
+compromise ok so we choose this that
+defines basis States the
+
+ align:start position:0%
+defines basis States the
+ 
+
+ align:start position:0%
+defines basis States the
+h0 for a diatomic molecule is a harmonic
+
+ align:start position:0%
+h0 for a diatomic molecule is a harmonic
+ 
+
+ align:start position:0%
+h0 for a diatomic molecule is a harmonic
+oscillator plus
+
+ align:start position:0%
+oscillator plus
+ 
+
+ align:start position:0%
+oscillator plus
+a rigid rotor and so 80 is I
+
+ align:start position:0%
+a rigid rotor and so 80 is I
+ 
+
+ align:start position:0%
+a rigid rotor and so 80 is I
+can
+
+ align:start position:0%
+can
+ 
+
+ align:start position:0%
+can
+never remember where the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that's the zero-order Hamiltonian rigid
+
+ align:start position:0%
+that's the zero-order Hamiltonian rigid
+ 
+
+ align:start position:0%
+that's the zero-order Hamiltonian rigid
+rotor because it's a constant and
+
+ align:start position:0%
+rotor because it's a constant and
+ 
+
+ align:start position:0%
+rotor because it's a constant and
+harmonic oscillator and so
+
+ align:start position:0%
+harmonic oscillator and so
+ 
+
+ align:start position:0%
+harmonic oscillator and so
+the zero-order energy levels r omega e
+
+ align:start position:0%
+the zero-order energy levels r omega e
+ 
+
+ align:start position:0%
+the zero-order energy levels r omega e
+EV + f plus
+
+ align:start position:0%
+EV + f plus
+ 
+
+ align:start position:0%
+EV + f plus
+de JJ + 1 well
+
+ align:start position:0%
+de JJ + 1 well
+ 
+
+ align:start position:0%
+de JJ + 1 well
+gives
+
+ align:start position:0%
+gives
+ 
+
+ align:start position:0%
+gives
+you ev0
+
+ align:start position:0%
+you ev0
+ 
+
+ align:start position:0%
+you ev0
+j
+
+ align:start position:0%
+j
+ 
+
+ align:start position:0%
+j
+is equal to that and you get I ghen
+
+ align:start position:0%
+is equal to that and you get I ghen
+ 
+
+ align:start position:0%
+is equal to that and you get I ghen
+functions which are the and j
+
+ align:start position:0%
+functions which are the and j
+ 
+
+ align:start position:0%
+functions which are the and j
+MJ and those
+
+ align:start position:0%
+MJ and those
+ 
+
+ align:start position:0%
+MJ and those
+are your those are the things that you
+
+ align:start position:0%
+are your those are the things that you
+ 
+
+ align:start position:0%
+are your those are the things that you
+manipulate but one of the things about
+
+ align:start position:0%
+manipulate but one of the things about
+ 
+
+ align:start position:0%
+manipulate but one of the things about
+matrix mechanics which is making it
+
+ align:start position:0%
+matrix mechanics which is making it
+ 
+
+ align:start position:0%
+matrix mechanics which is making it
+really beautiful is that you never
+
+ align:start position:0%
+really beautiful is that you never
+ 
+
+ align:start position:0%
+really beautiful is that you never
+unpack these things you never asked well
+
+ align:start position:0%
+unpack these things you never asked well
+ 
+
+ align:start position:0%
+unpack these things you never asked well
+what are these functions these are
+
+ align:start position:0%
+what are these functions these are
+ 
+
+ align:start position:0%
+what are these functions these are
+labels of states in some abstract space
+
+ align:start position:0%
+labels of states in some abstract space
+ 
+
+ align:start position:0%
+labels of states in some abstract space
+and they have certain properties that
+
+ align:start position:0%
+and they have certain properties that
+ 
+
+ align:start position:0%
+and they have certain properties that
+you can write down there matrix elements
+
+ align:start position:0%
+you can write down there matrix elements
+ 
+
+ align:start position:0%
+you can write down there matrix elements
+without thinking about them and you
+
+ align:start position:0%
+without thinking about them and you
+ 
+
+ align:start position:0%
+without thinking about them and you
+almost never look at what the functions
+
+ align:start position:0%
+almost never look at what the functions
+ 
+
+ align:start position:0%
+almost never look at what the functions
+are in fact this is actually not a
+
+ align:start position:0%
+are in fact this is actually not a
+ 
+
+ align:start position:0%
+are in fact this is actually not a
+function to make this a function you
+
+ align:start position:0%
+function to make this a function you
+ 
+
+ align:start position:0%
+function to make this a function you
+have to write this quantity here but
+
+ align:start position:0%
+have to write this quantity here but
+ 
+
+ align:start position:0%
+have to write this quantity here but
+it is wonderful one of the wonderful
+
+ align:start position:0%
+it is wonderful one of the wonderful
+ 
+
+ align:start position:0%
+it is wonderful one of the wonderful
+things about matrix mechanics is you're
+
+ align:start position:0%
+things about matrix mechanics is you're
+ 
+
+ align:start position:0%
+things about matrix mechanics is you're
+dealing with vectors and you're dealing
+
+ align:start position:0%
+dealing with vectors and you're dealing
+ 
+
+ align:start position:0%
+dealing with vectors and you're dealing
+you're not looking at the differential
+
+ align:start position:0%
+you're not looking at the differential
+ 
+
+ align:start position:0%
+you're not looking at the differential
+operators and you you get to do things
+
+ align:start position:0%
+operators and you you get to do things
+ 
+
+ align:start position:0%
+operators and you you get to do things
+that are terribly profound without doing
+
+ align:start position:0%
+that are terribly profound without doing
+ 
+
+ align:start position:0%
+that are terribly profound without doing
+very much work okay so we have 80 now we
+
+ align:start position:0%
+very much work okay so we have 80 now we
+ 
+
+ align:start position:0%
+very much work okay so we have 80 now we
+have the perturbation term and since
+
+ align:start position:0%
+have the perturbation term and since
+ 
+
+ align:start position:0%
+have the perturbation term and since
+we're dealing with an harmonic
+
+ align:start position:0%
+we're dealing with an harmonic
+ 
+
+ align:start position:0%
+we're dealing with an harmonic
+oscillators we'd like to be able to say
+
+ align:start position:0%
+oscillators we'd like to be able to say
+ 
+
+ align:start position:0%
+oscillators we'd like to be able to say
+something Universal about the coordinate
+
+ align:start position:0%
+something Universal about the coordinate
+ 
+
+ align:start position:0%
+something Universal about the coordinate
+displacement and the momentum which is
+
+ align:start position:0%
+displacement and the momentum which is
+ 
+
+ align:start position:0%
+displacement and the momentum which is
+conjugate and so
+
+ align:start position:0%
+conjugate and so
+ 
+
+ align:start position:0%
+conjugate and so
+it's a wonderful thing to replace a cool
+
+ align:start position:0%
+it's a wonderful thing to replace a cool
+ 
+
+ align:start position:0%
+it's a wonderful thing to replace a cool
+ordinate that depends on all sorts of
+
+ align:start position:0%
+ordinate that depends on all sorts of
+ 
+
+ align:start position:0%
+ordinate that depends on all sorts of
+things like what system of masses you're
+
+ align:start position:0%
+things like what system of masses you're
+ 
+
+ align:start position:0%
+things like what system of masses you're
+using and what what
+
+ align:start position:0%
+using and what what
+ 
+
+ align:start position:0%
+using and what what
+coordinates
+
+ align:start position:0%
+coordinates
+ 
+
+ align:start position:0%
+coordinates
+you're using to replace them by a
+
+ align:start position:0%
+you're using to replace them by a
+ 
+
+ align:start position:0%
+you're using to replace them by a
+dimensionless quantity so we have this
+
+ align:start position:0%
+dimensionless quantity so we have this
+ 
+
+ align:start position:0%
+dimensionless quantity so we have this
+scale factor 2 pi c mu
+
+ align:start position:0%
+scale factor 2 pi c mu
+ 
+
+ align:start position:0%
+scale factor 2 pi c mu
+0 maybeee right this
+
+ align:start position:0%
+0 maybeee right this
+ 
+
+ align:start position:0%
+0 maybeee right this
+is a dimensionless quantity and
+
+ align:start position:0%
+is a dimensionless quantity and
+ 
+
+ align:start position:0%
+is a dimensionless quantity and
+so that makes it universal and so if you
+
+ align:start position:0%
+so that makes it universal and so if you
+ 
+
+ align:start position:0%
+so that makes it universal and so if you
+not a strip out the specific molecule
+
+ align:start position:0%
+not a strip out the specific molecule
+ 
+
+ align:start position:0%
+not a strip out the specific molecule
+specific things the reduced mass and the
+
+ align:start position:0%
+specific things the reduced mass and the
+ 
+
+ align:start position:0%
+specific things the reduced mass and the
+fourth constants I guess know it's there
+
+ align:start position:0%
+fourth constants I guess know it's there
+ 
+
+ align:start position:0%
+fourth constants I guess know it's there
+okay if you strip out the molecule
+
+ align:start position:0%
+okay if you strip out the molecule
+ 
+
+ align:start position:0%
+okay if you strip out the molecule
+specific stuff then you're going to be
+
+ align:start position:0%
+specific stuff then you're going to be
+ 
+
+ align:start position:0%
+specific stuff then you're going to be
+dealing with universal things and you
+
+ align:start position:0%
+dealing with universal things and you
+ 
+
+ align:start position:0%
+dealing with universal things and you
+solve problems once and then you just
+
+ align:start position:0%
+solve problems once and then you just
+ 
+
+ align:start position:0%
+solve problems once and then you just
+know how to scale them okay
+
+ align:start position:0%
+know how to scale them okay
+ 
+
+ align:start position:0%
+know how to scale them okay
+and the same is true for P the factor
+
+ align:start position:0%
+and the same is true for P the factor
+ 
+
+ align:start position:0%
+and the same is true for P the factor
+here is you
+
+ align:start position:0%
+here is you
+ 
+
+ align:start position:0%
+here is you
+see I don't even I have to look at my
+
+ align:start position:0%
+see I don't even I have to look at my
+ 
+
+ align:start position:0%
+see I don't even I have to look at my
+notes because I don't know what the
+
+ align:start position:0%
+notes because I don't know what the
+ 
+
+ align:start position:0%
+notes because I don't know what the
+factor is but I only have to do it once
+
+ align:start position:0%
+factor is but I only have to do it once
+ 
+
+ align:start position:0%
+factor is but I only have to do it once
+dupuy
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+c mu omega e spero
+
+ align:start position:0%
+c mu omega e spero
+ 
+
+ align:start position:0%
+c mu omega e spero
+p hat
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and then there's a further reduction q
+
+ align:start position:0%
+and then there's a further reduction q
+ 
+
+ align:start position:0%
+and then there's a further reduction q
+now
+
+ align:start position:0%
+now
+ 
+
+ align:start position:0%
+now
+if I tell you what are in the basis set
+
+ align:start position:0%
+if I tell you what are in the basis set
+ 
+
+ align:start position:0%
+if I tell you what are in the basis set
+of the harmonic oscillator where we have
+
+ align:start position:0%
+of the harmonic oscillator where we have
+ 
+
+ align:start position:0%
+of the harmonic oscillator where we have
+these kinds of functions v what are what
+
+ align:start position:0%
+these kinds of functions v what are what
+ 
+
+ align:start position:0%
+these kinds of functions v what are what
+is the selection rule for matrix
+
+ align:start position:0%
+is the selection rule for matrix
+ 
+
+ align:start position:0%
+is the selection rule for matrix
+elements of q most of you know that most
+
+ align:start position:0%
+elements of q most of you know that most
+ 
+
+ align:start position:0%
+elements of q most of you know that most
+of you know that from the Schrodinger
+
+ align:start position:0%
+of you know that from the Schrodinger
+ 
+
+ align:start position:0%
+of you know that from the Schrodinger
+picture from a first course in quantum
+
+ align:start position:0%
+picture from a first course in quantum
+ 
+
+ align:start position:0%
+picture from a first course in quantum
+mechanics you know that the coordinate
+
+ align:start position:0%
+mechanics you know that the coordinate
+ 
+
+ align:start position:0%
+mechanics you know that the coordinate
+changes the quantum number x plus or
+
+ align:start position:0%
+changes the quantum number x plus or
+ 
+
+ align:start position:0%
+changes the quantum number x plus or
+minus one okay
+
+ align:start position:0%
+minus one okay
+ 
+
+ align:start position:0%
+minus one okay
+and so the matrix elements of Q are
+
+ align:start position:0%
+and so the matrix elements of Q are
+ 
+
+ align:start position:0%
+and so the matrix elements of Q are
+going to be Delta V of plus and minus
+
+ align:start position:0%
+going to be Delta V of plus and minus
+ 
+
+ align:start position:0%
+going to be Delta V of plus and minus
+one and many
+
+ align:start position:0%
+one and many
+ 
+
+ align:start position:0%
+one and many
+of you also probably know what the
+
+ align:start position:0%
+of you also probably know what the
+ 
+
+ align:start position:0%
+of you also probably know what the
+actual value is but you don't really you
+
+ align:start position:0%
+actual value is but you don't really you
+ 
+
+ align:start position:0%
+actual value is but you don't really you
+know but you don't know how to dig it
+
+ align:start position:0%
+know but you don't know how to dig it
+ 
+
+ align:start position:0%
+know but you don't know how to dig it
+out because it's entangled with all this
+
+ align:start position:0%
+out because it's entangled with all this
+ 
+
+ align:start position:0%
+out because it's entangled with all this
+garbage and factor a square root of two
+
+ align:start position:0%
+garbage and factor a square root of two
+ 
+
+ align:start position:0%
+garbage and factor a square root of two
+and so it doesn't look memorable so if
+
+ align:start position:0%
+and so it doesn't look memorable so if
+ 
+
+ align:start position:0%
+and so it doesn't look memorable so if
+we replace this by 1 over square root of
+
+ align:start position:0%
+we replace this by 1 over square root of
+ 
+
+ align:start position:0%
+we replace this by 1 over square root of
+two times a plus a dagger
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+then we now have simplified q in terms
+
+ align:start position:0%
+then we now have simplified q in terms
+ 
+
+ align:start position:0%
+then we now have simplified q in terms
+of operators which have two
+
+ align:start position:0%
+of operators which have two
+ 
+
+ align:start position:0%
+of operators which have two
+wonderfully convenient properties a
+
+ align:start position:0%
+wonderfully convenient properties a
+ 
+
+ align:start position:0%
+wonderfully convenient properties a
+decreases
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the number of quanta of the thing on its
+
+ align:start position:0%
+the number of quanta of the thing on its
+ 
+
+ align:start position:0%
+the number of quanta of the thing on its
+right by one a dagger increases the
+
+ align:start position:0%
+right by one a dagger increases the
+ 
+
+ align:start position:0%
+right by one a dagger increases the
+number of quanta of the thing that's
+
+ align:start position:0%
+number of quanta of the thing that's
+ 
+
+ align:start position:0%
+number of quanta of the thing that's
+right and it gives you a number they
+
+ align:start position:0%
+right and it gives you a number they
+ 
+
+ align:start position:0%
+right and it gives you a number they
+both give you a number and so if you
+
+ align:start position:0%
+both give you a number and so if you
+ 
+
+ align:start position:0%
+both give you a number and so if you
+write it this way a V
+
+ align:start position:0%
+write it this way a V
+ 
+
+ align:start position:0%
+write it this way a V
+plus 1 B you
+
+ align:start position:0%
+plus 1 B you
+ 
+
+ align:start position:0%
+plus 1 B you
+get D plus 1 square root and it's right
+
+ align:start position:0%
+get D plus 1 square root and it's right
+ 
+
+ align:start position:0%
+get D plus 1 square root and it's right
+be
+
+ align:start position:0%
+be
+ 
+
+ align:start position:0%
+be
+a dagger
+
+ align:start position:0%
+a dagger
+ 
+
+ align:start position:0%
+a dagger
+B minus 1 you get V so
+
+ align:start position:0%
+B minus 1 you get V so
+ 
+
+ align:start position:0%
+B minus 1 you get V so
+there's only one non zero matrix element
+
+ align:start position:0%
+there's only one non zero matrix element
+ 
+
+ align:start position:0%
+there's only one non zero matrix element
+at a and a dagger q
+
+ align:start position:0%
+at a and a dagger q
+ 
+
+ align:start position:0%
+at a and a dagger q
+has two non zero matrix elements because
+
+ align:start position:0%
+has two non zero matrix elements because
+ 
+
+ align:start position:0%
+has two non zero matrix elements because
+it's a sum of a and a dagger this
+
+ align:start position:0%
+it's a sum of a and a dagger this
+ 
+
+ align:start position:0%
+it's a sum of a and a dagger this
+is simpler and this is wonderful because
+
+ align:start position:0%
+is simpler and this is wonderful because
+ 
+
+ align:start position:0%
+is simpler and this is wonderful because
+suppose I tell you that I have some
+
+ align:start position:0%
+suppose I tell you that I have some
+ 
+
+ align:start position:0%
+suppose I tell you that I have some
+operator that's q1 q2 q3 squared
+
+ align:start position:0%
+operator that's q1 q2 q3 squared
+ 
+
+ align:start position:0%
+operator that's q1 q2 q3 squared
+and I ask you well what's the matrix
+
+ align:start position:0%
+and I ask you well what's the matrix
+ 
+
+ align:start position:0%
+and I ask you well what's the matrix
+element between this number of
+
+ align:start position:0%
+element between this number of
+ 
+
+ align:start position:0%
+element between this number of
+vibrational this combination of
+
+ align:start position:0%
+vibrational this combination of
+ 
+
+ align:start position:0%
+vibrational this combination of
+vibrational quantum / than that and as
+
+ align:start position:0%
+vibrational quantum / than that and as
+ 
+
+ align:start position:0%
+vibrational quantum / than that and as
+soon as I tell you that I you know
+
+ align:start position:0%
+soon as I tell you that I you know
+ 
+
+ align:start position:0%
+soon as I tell you that I you know
+exactly how many a's and a daggers to
+
+ align:start position:0%
+exactly how many a's and a daggers to
+ 
+
+ align:start position:0%
+exactly how many a's and a daggers to
+pull out and then you know exactly how
+
+ align:start position:0%
+pull out and then you know exactly how
+ 
+
+ align:start position:0%
+pull out and then you know exactly how
+to evaluate all the matrix elements so
+
+ align:start position:0%
+to evaluate all the matrix elements so
+ 
+
+ align:start position:0%
+to evaluate all the matrix elements so
+this simple thing is saying whether it's
+
+ align:start position:0%
+this simple thing is saying whether it's
+ 
+
+ align:start position:0%
+this simple thing is saying whether it's
+a or a dagger doesn't
+
+ align:start position:0%
+a or a dagger doesn't
+ 
+
+ align:start position:0%
+a or a dagger doesn't
+matter you just take the larger of the
+
+ align:start position:0%
+matter you just take the larger of the
+ 
+
+ align:start position:0%
+matter you just take the larger of the
+two quantum numbers and take the square
+
+ align:start position:0%
+two quantum numbers and take the square
+ 
+
+ align:start position:0%
+two quantum numbers and take the square
+root that's
+
+ align:start position:0%
+root that's
+ 
+
+ align:start position:0%
+root that's
+all you ever have to remember for
+
+ align:start position:0%
+all you ever have to remember for
+ 
+
+ align:start position:0%
+all you ever have to remember for
+harmonic oscillator matrix elements the
+
+ align:start position:0%
+harmonic oscillator matrix elements the
+ 
+
+ align:start position:0%
+harmonic oscillator matrix elements the
+larger of the two and you you also
+
+ align:start position:0%
+larger of the two and you you also
+ 
+
+ align:start position:0%
+larger of the two and you you also
+recognize
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+missing the plus and that's decreasing
+
+ align:start position:0%
+missing the plus and that's decreasing
+ 
+
+ align:start position:0%
+missing the plus and that's decreasing
+and that's all there is and so you can
+
+ align:start position:0%
+and that's all there is and so you can
+ 
+
+ align:start position:0%
+and that's all there is and so you can
+remember then all the matrix elements of
+
+ align:start position:0%
+remember then all the matrix elements of
+ 
+
+ align:start position:0%
+remember then all the matrix elements of
+Q and P and integer power of Q and P and
+
+ align:start position:0%
+Q and P and integer power of Q and P and
+ 
+
+ align:start position:0%
+Q and P and integer power of Q and P and
+if you're clever any non integer power
+
+ align:start position:0%
+if you're clever any non integer power
+ 
+
+ align:start position:0%
+if you're clever any non integer power
+of cumin p that's later okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so absolutely
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+it's
+
+ align:start position:0%
+it's
+ 
+
+ align:start position:0%
+it's
+wrong on the lecture notes holy mackerel
+
+ align:start position:0%
+wrong on the lecture notes holy mackerel
+ 
+
+ align:start position:0%
+wrong on the lecture notes holy mackerel
+what's mine well it's factor too in
+
+ align:start position:0%
+what's mine well it's factor too in
+ 
+
+ align:start position:0%
+what's mine well it's factor too in
+this case okay well sorry about that I I
+
+ align:start position:0%
+this case okay well sorry about that I I
+ 
+
+ align:start position:0%
+this case okay well sorry about that I I
+don't know what I say I don't know what
+
+ align:start position:0%
+don't know what I say I don't know what
+ 
+
+ align:start position:0%
+don't know what I say I don't know what
+I right I don't know what's in my notes
+
+ align:start position:0%
+I right I don't know what's in my notes
+ 
+
+ align:start position:0%
+I right I don't know what's in my notes
+I mean there's the you know and two out
+
+ align:start position:0%
+I mean there's the you know and two out
+ 
+
+ align:start position:0%
+I mean there's the you know and two out
+of three is not good enough oh ok well
+
+ align:start position:0%
+of three is not good enough oh ok well
+ 
+
+ align:start position:0%
+of three is not good enough oh ok well
+that's okay well that's good alright so
+
+ align:start position:0%
+that's okay well that's good alright so
+ 
+
+ align:start position:0%
+that's okay well that's good alright so
+now
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+there are some other things and last
+
+ align:start position:0%
+there are some other things and last
+ 
+
+ align:start position:0%
+there are some other things and last
+time when I went through the beginning
+
+ align:start position:0%
+time when I went through the beginning
+ 
+
+ align:start position:0%
+time when I went through the beginning
+of this I decided not to introduce these
+
+ align:start position:0%
+of this I decided not to introduce these
+ 
+
+ align:start position:0%
+of this I decided not to introduce these
+other simplifying factors but it turns
+
+ align:start position:0%
+other simplifying factors but it turns
+ 
+
+ align:start position:0%
+other simplifying factors but it turns
+out you really want them so we have a
+
+ align:start position:0%
+out you really want them so we have a
+ 
+
+ align:start position:0%
+out you really want them so we have a
+couple of other ways in which you deal
+
+ align:start position:0%
+couple of other ways in which you deal
+ 
+
+ align:start position:0%
+couple of other ways in which you deal
+with strings of A's and a daggers and
+
+ align:start position:0%
+with strings of A's and a daggers and
+ 
+
+ align:start position:0%
+with strings of A's and a daggers and
+one is the number operator which is a
+
+ align:start position:0%
+one is the number operator which is a
+ 
+
+ align:start position:0%
+one is the number operator which is a
+dagger a we
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+want something which will return the
+
+ align:start position:0%
+want something which will return the
+ 
+
+ align:start position:0%
+want something which will return the
+number of quanta so if we write n on V
+
+ align:start position:0%
+number of quanta so if we write n on V
+ 
+
+ align:start position:0%
+number of quanta so if we write n on V
+we want V B and
+
+ align:start position:0%
+we want V B and
+ 
+
+ align:start position:0%
+we want V B and
+C a lowers
+
+ align:start position:0%
+C a lowers
+ 
+
+ align:start position:0%
+C a lowers
+V a dagger raises it so if we have an
+
+ align:start position:0%
+V a dagger raises it so if we have an
+ 
+
+ align:start position:0%
+V a dagger raises it so if we have an
+equal number of A's and a daggers the
+
+ align:start position:0%
+equal number of A's and a daggers the
+ 
+
+ align:start position:0%
+equal number of A's and a daggers the
+matrix element in question is diagonal
+
+ align:start position:0%
+matrix element in question is diagonal
+ 
+
+ align:start position:0%
+matrix element in question is diagonal
+and V so
+
+ align:start position:0%
+and V so
+ 
+
+ align:start position:0%
+and V so
+but now you look at this and you say
+
+ align:start position:0%
+but now you look at this and you say
+ 
+
+ align:start position:0%
+but now you look at this and you say
+well i'm going to apply this to the V
+
+ align:start position:0%
+well i'm going to apply this to the V
+ 
+
+ align:start position:0%
+well i'm going to apply this to the V
+state and I'm going to decrease p by one
+
+ align:start position:0%
+state and I'm going to decrease p by one
+ 
+
+ align:start position:0%
+state and I'm going to decrease p by one
+but the larger of the two quantum
+
+ align:start position:0%
+but the larger of the two quantum
+ 
+
+ align:start position:0%
+but the larger of the two quantum
+numbers is where you start it's that's
+
+ align:start position:0%
+numbers is where you start it's that's
+ 
+
+ align:start position:0%
+numbers is where you start it's that's
+square root of V and I'm going to III
+
+ align:start position:0%
+square root of V and I'm going to III
+ 
+
+ align:start position:0%
+square root of V and I'm going to III
+increase it again back to V and so we
+
+ align:start position:0%
+increase it again back to V and so we
+ 
+
+ align:start position:0%
+increase it again back to V and so we
+get a factor of square root square root
+
+ align:start position:0%
+get a factor of square root square root
+ 
+
+ align:start position:0%
+get a factor of square root square root
+of V from both of these and that's what
+
+ align:start position:0%
+of V from both of these and that's what
+ 
+
+ align:start position:0%
+of V from both of these and that's what
+we get this so that's the number
+
+ align:start position:0%
+we get this so that's the number
+ 
+
+ align:start position:0%
+we get this so that's the number
+operator and that's convenient and then
+
+ align:start position:0%
+operator and that's convenient and then
+ 
+
+ align:start position:0%
+operator and that's convenient and then
+we have some commutation rules
+
+ align:start position:0%
+we have some commutation rules
+ 
+
+ align:start position:0%
+we have some commutation rules
+and so
+
+ align:start position:0%
+and so
+ 
+
+ align:start position:0%
+and so
+that's just a dagger a minus
+
+ align:start position:0%
+that's just a dagger a minus
+ 
+
+ align:start position:0%
+that's just a dagger a minus
+a dagger and so
+
+ align:start position:0%
+a dagger and so
+ 
+
+ align:start position:0%
+a dagger and so
+you can figure out what that is by
+
+ align:start position:0%
+you can figure out what that is by
+ 
+
+ align:start position:0%
+you can figure out what that is by
+applying this to V but
+
+ align:start position:0%
+applying this to V but
+ 
+
+ align:start position:0%
+applying this to V but
+i'm
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+just going to tell you it's minus 1 and
+
+ align:start position:0%
+just going to tell you it's minus 1 and
+ 
+
+ align:start position:0%
+just going to tell you it's minus 1 and
+if you do it the other order a a dagger
+
+ align:start position:0%
+if you do it the other order a a dagger
+ 
+
+ align:start position:0%
+if you do it the other order a a dagger
+its plus 1 and then there is commutation
+
+ align:start position:0%
+its plus 1 and then there is commutation
+ 
+
+ align:start position:0%
+its plus 1 and then there is commutation
+rules involving m and a dagger this
+
+ align:start position:0%
+rules involving m and a dagger this
+ 
+
+ align:start position:0%
+rules involving m and a dagger this
+is quantum mechanics so you have to
+
+ align:start position:0%
+is quantum mechanics so you have to
+ 
+
+ align:start position:0%
+is quantum mechanics so you have to
+watch out the order in which things
+
+ align:start position:0%
+watch out the order in which things
+ 
+
+ align:start position:0%
+watch out the order in which things
+appear and one
+
+ align:start position:0%
+appear and one
+ 
+
+ align:start position:0%
+appear and one
+of the beautiful things when you have n
+
+ align:start position:0%
+of the beautiful things when you have n
+ 
+
+ align:start position:0%
+of the beautiful things when you have n
+with a dagger is you just get a dagger
+
+ align:start position:0%
+with a dagger is you just get a dagger
+ 
+
+ align:start position:0%
+with a dagger is you just get a dagger
+back when you have n with a you just get
+
+ align:start position:0%
+back when you have n with a you just get
+ 
+
+ align:start position:0%
+back when you have n with a you just get
+a back but it's a minus sign
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so these little tricks enable you to
+
+ align:start position:0%
+so these little tricks enable you to
+ 
+
+ align:start position:0%
+so these little tricks enable you to
+make tremendous simplifications and so
+
+ align:start position:0%
+make tremendous simplifications and so
+ 
+
+ align:start position:0%
+make tremendous simplifications and so
+now let's look at Q squared well Q
+
+ align:start position:0%
+now let's look at Q squared well Q
+ 
+
+ align:start position:0%
+now let's look at Q squared well Q
+squared is one-half a plus a dagger
+
+ align:start position:0%
+squared is one-half a plus a dagger
+ 
+
+ align:start position:0%
+squared is one-half a plus a dagger
+square
+
+ align:start position:0%
+square
+ 
+
+ align:start position:0%
+square
+and so we immediately know we got a
+
+ align:start position:0%
+and so we immediately know we got a
+ 
+
+ align:start position:0%
+and so we immediately know we got a
+squared a dagger squared and then we get
+
+ align:start position:0%
+squared a dagger squared and then we get
+ 
+
+ align:start position:0%
+squared a dagger squared and then we get
+a a dagger plus a dagger a so
+
+ align:start position:0%
+a a dagger plus a dagger a so
+ 
+
+ align:start position:0%
+a a dagger plus a dagger a so
+that's the number operator and this is
+
+ align:start position:0%
+that's the number operator and this is
+ 
+
+ align:start position:0%
+that's the number operator and this is
+the number operator written in the wrong
+
+ align:start position:0%
+the number operator written in the wrong
+ 
+
+ align:start position:0%
+the number operator written in the wrong
+order until you can you can permute
+
+ align:start position:0%
+order until you can you can permute
+ 
+
+ align:start position:0%
+order until you can you can permute
+these so suppose you have a a dagger you
+
+ align:start position:0%
+these so suppose you have a a dagger you
+ 
+
+ align:start position:0%
+these so suppose you have a a dagger you
+can write that as a a dagger plus
+
+ align:start position:0%
+can write that as a a dagger plus
+ 
+
+ align:start position:0%
+can write that as a a dagger plus
+a dagger a minus a dagger a and then you
+
+ align:start position:0%
+a dagger a minus a dagger a and then you
+ 
+
+ align:start position:0%
+a dagger a minus a dagger a and then you
+combine these two terms and those two
+
+ align:start position:0%
+combine these two terms and those two
+ 
+
+ align:start position:0%
+combine these two terms and those two
+terms are the commutator a a dagger and
+
+ align:start position:0%
+terms are the commutator a a dagger and
+ 
+
+ align:start position:0%
+terms are the commutator a a dagger and
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+commutator a a dagger is one so
+
+ align:start position:0%
+commutator a a dagger is one so
+ 
+
+ align:start position:0%
+commutator a a dagger is one so
+we take these two terms combined them
+
+ align:start position:0%
+we take these two terms combined them
+ 
+
+ align:start position:0%
+we take these two terms combined them
+they're just one and this is the number
+
+ align:start position:0%
+they're just one and this is the number
+ 
+
+ align:start position:0%
+they're just one and this is the number
+operator and so
+
+ align:start position:0%
+operator and so
+ 
+
+ align:start position:0%
+operator and so
+to
+
+ align:start position:0%
+to
+ 
+
+ align:start position:0%
+to
+to take a term which is written not in
+
+ align:start position:0%
+to take a term which is written not in
+ 
+
+ align:start position:0%
+to take a term which is written not in
+the order of the number operator and
+
+ align:start position:0%
+the order of the number operator and
+ 
+
+ align:start position:0%
+the order of the number operator and
+reduce it to the number operator you ask
+
+ align:start position:0%
+reduce it to the number operator you ask
+ 
+
+ align:start position:0%
+reduce it to the number operator you ask
+how many times do I have to permute in a
+
+ align:start position:0%
+how many times do I have to permute in a
+ 
+
+ align:start position:0%
+how many times do I have to permute in a
+dagger plastic past a and so
+
+ align:start position:0%
+dagger plastic past a and so
+ 
+
+ align:start position:0%
+dagger plastic past a and so
+each time you have a term like a a
+
+ align:start position:0%
+each time you have a term like a a
+ 
+
+ align:start position:0%
+each time you have a term like a a
+dagger or a dagger a you're going to get
+
+ align:start position:0%
+dagger or a dagger a you're going to get
+ 
+
+ align:start position:0%
+dagger or a dagger a you're going to get
+a number operator but you're going to
+
+ align:start position:0%
+a number operator but you're going to
+ 
+
+ align:start position:0%
+a number operator but you're going to
+get something extra from this one
+
+ align:start position:0%
+get something extra from this one
+ 
+
+ align:start position:0%
+get something extra from this one
+because you had up in route / mute okay
+
+ align:start position:0%
+because you had up in route / mute okay
+ 
+
+ align:start position:0%
+because you had up in route / mute okay
+and so it
+
+ align:start position:0%
+and so it
+ 
+
+ align:start position:0%
+and so it
+turns out you can very quickly look at
+
+ align:start position:0%
+turns out you can very quickly look at
+ 
+
+ align:start position:0%
+turns out you can very quickly look at
+these sorts of things and write down
+
+ align:start position:0%
+these sorts of things and write down
+ 
+
+ align:start position:0%
+these sorts of things and write down
+what
+
+ align:start position:0%
+what
+ 
+
+ align:start position:0%
+what
+they are in terms of the most compact
+
+ align:start position:0%
+they are in terms of the most compact
+ 
+
+ align:start position:0%
+they are in terms of the most compact
+form and so we
+
+ align:start position:0%
+form and so we
+ 
+
+ align:start position:0%
+form and so we
+get one
+
+ align:start position:0%
+get one
+ 
+
+ align:start position:0%
+get one
+half a squared
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+a dagger squared plus 2n plus one so
+
+ align:start position:0%
+a dagger squared plus 2n plus one so
+ 
+
+ align:start position:0%
+a dagger squared plus 2n plus one so
+this is this is the number operator it's
+
+ align:start position:0%
+this is this is the number operator it's
+ 
+
+ align:start position:0%
+this is this is the number operator it's
+not a constant if you multiply it on v
+
+ align:start position:0%
+not a constant if you multiply it on v
+ 
+
+ align:start position:0%
+not a constant if you multiply it on v
+plus one you get v plus 1 not be okay
+
+ align:start position:0%
+plus one you get v plus 1 not be okay
+ 
+
+ align:start position:0%
+plus one you get v plus 1 not be okay
+so this is how you reduce a Q squared
+
+ align:start position:0%
+so this is how you reduce a Q squared
+ 
+
+ align:start position:0%
+so this is how you reduce a Q squared
+you
+
+ align:start position:0%
+you
+ 
+
+ align:start position:0%
+you
+can reduce p squared similarly
+
+ align:start position:0%
+can reduce p squared similarly
+ 
+
+ align:start position:0%
+can reduce p squared similarly
+I'm not going to do it it's in the notes
+
+ align:start position:0%
+I'm not going to do it it's in the notes
+ 
+
+ align:start position:0%
+I'm not going to do it it's in the notes
+when
+
+ align:start position:0%
+when
+ 
+
+ align:start position:0%
+when
+you do Q squared plus B squared you
+
+ align:start position:0%
+you do Q squared plus B squared you
+ 
+
+ align:start position:0%
+you do Q squared plus B squared you
+discover from the definition of P which
+
+ align:start position:0%
+discover from the definition of P which
+ 
+
+ align:start position:0%
+discover from the definition of P which
+I didn't write down today which has a
+
+ align:start position:0%
+I didn't write down today which has a
+ 
+
+ align:start position:0%
+I didn't write down today which has a
+minus we have a dagger minus a but
+
+ align:start position:0%
+minus we have a dagger minus a but
+ 
+
+ align:start position:0%
+minus we have a dagger minus a but
+there's a I in front you end up having
+
+ align:start position:0%
+there's a I in front you end up having
+ 
+
+ align:start position:0%
+there's a I in front you end up having
+these raising
+
+ align:start position:0%
+these raising
+ 
+
+ align:start position:0%
+these raising
+and lowering operators squared cancel
+
+ align:start position:0%
+and lowering operators squared cancel
+ 
+
+ align:start position:0%
+and lowering operators squared cancel
+giving
+
+ align:start position:0%
+giving
+ 
+
+ align:start position:0%
+giving
+back giving you 2 n plus 1 times a half
+
+ align:start position:0%
+back giving you 2 n plus 1 times a half
+ 
+
+ align:start position:0%
+back giving you 2 n plus 1 times a half
+from from
+
+ align:start position:0%
+from from
+ 
+
+ align:start position:0%
+from from
+each and the overall matrix element if a
+
+ align:start position:0%
+each and the overall matrix element if a
+ 
+
+ align:start position:0%
+each and the overall matrix element if a
+0 comes out to be just n plus a half
+
+ align:start position:0%
+0 comes out to be just n plus a half
+ 
+
+ align:start position:0%
+0 comes out to be just n plus a half
+it's
+
+ align:start position:0%
+it's
+ 
+
+ align:start position:0%
+it's
+you
+
+ align:start position:0%
+you
+ 
+
+ align:start position:0%
+you
+have 2n plus 1 1
+
+ align:start position:0%
+have 2n plus 1 1
+ 
+
+ align:start position:0%
+have 2n plus 1 1
+half Omega E is what you get by adding
+
+ align:start position:0%
+half Omega E is what you get by adding
+ 
+
+ align:start position:0%
+half Omega E is what you get by adding
+the the one half P squared plus one-half
+
+ align:start position:0%
+the the one half P squared plus one-half
+ 
+
+ align:start position:0%
+the the one half P squared plus one-half
+Q squared stuff so so that you
+
+ align:start position:0%
+Q squared stuff so so that you
+ 
+
+ align:start position:0%
+Q squared stuff so so that you
+you discover the Q squared is not
+
+ align:start position:0%
+you discover the Q squared is not
+ 
+
+ align:start position:0%
+you discover the Q squared is not
+diagonal p squared is not diagonal but
+
+ align:start position:0%
+diagonal p squared is not diagonal but
+ 
+
+ align:start position:0%
+diagonal p squared is not diagonal but
+their sum is that's
+
+ align:start position:0%
+their sum is that's
+ 
+
+ align:start position:0%
+their sum is that's
+good you want it to be diagonal because
+
+ align:start position:0%
+good you want it to be diagonal because
+ 
+
+ align:start position:0%
+good you want it to be diagonal because
+you wanted those to be eigenfunctions of
+
+ align:start position:0%
+you wanted those to be eigenfunctions of
+ 
+
+ align:start position:0%
+you wanted those to be eigenfunctions of
+you
+
+ align:start position:0%
+you
+ 
+
+ align:start position:0%
+you
+wanted to have harmonic oscillator
+
+ align:start position:0%
+wanted to have harmonic oscillator
+ 
+
+ align:start position:0%
+wanted to have harmonic oscillator
+eigenfunctions okay so now the next
+
+ align:start position:0%
+eigenfunctions okay so now the next
+ 
+
+ align:start position:0%
+eigenfunctions okay so now the next
+blackboard do over here suppose
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+we want Q to
+
+ align:start position:0%
+we want Q to
+ 
+
+ align:start position:0%
+we want Q to
+the third power well
+
+ align:start position:0%
+the third power well
+ 
+
+ align:start position:0%
+the third power well
+we know when we left the Hat we know
+
+ align:start position:0%
+we know when we left the Hat we know
+ 
+
+ align:start position:0%
+we know when we left the Hat we know
+that we're going to have 1 over square
+
+ align:start position:0%
+that we're going to have 1 over square
+ 
+
+ align:start position:0%
+that we're going to have 1 over square
+root of two three times so it's to the
+
+ align:start position:0%
+root of two three times so it's to the
+ 
+
+ align:start position:0%
+root of two three times so it's to the
+minus three halves and we know we're
+
+ align:start position:0%
+minus three halves and we know we're
+ 
+
+ align:start position:0%
+minus three halves and we know we're
+going to have a dagger cubed and we know
+
+ align:start position:0%
+going to have a dagger cubed and we know
+ 
+
+ align:start position:0%
+going to have a dagger cubed and we know
+we're going to have a a cube and then we
+
+ align:start position:0%
+we're going to have a a cube and then we
+ 
+
+ align:start position:0%
+we're going to have a a cube and then we
+know we're going to have three terms
+
+ align:start position:0%
+know we're going to have three terms
+ 
+
+ align:start position:0%
+know we're going to have three terms
+that have a a dagger a in
+
+ align:start position:0%
+that have a a dagger a in
+ 
+
+ align:start position:0%
+that have a a dagger a in
+the various orders and we're going to
+
+ align:start position:0%
+the various orders and we're going to
+ 
+
+ align:start position:0%
+the various orders and we're going to
+have three terms involving a a a dagger
+
+ align:start position:0%
+have three terms involving a a a dagger
+ 
+
+ align:start position:0%
+have three terms involving a a a dagger
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+so that the trick before one gets into
+
+ align:start position:0%
+so that the trick before one gets into
+ 
+
+ align:start position:0%
+so that the trick before one gets into
+heavy duty perturbation theory is to
+
+ align:start position:0%
+heavy duty perturbation theory is to
+ 
+
+ align:start position:0%
+heavy duty perturbation theory is to
+simplify these things and so because
+
+ align:start position:0%
+simplify these things and so because
+ 
+
+ align:start position:0%
+simplify these things and so because
+there's three terms we know we're going
+
+ align:start position:0%
+there's three terms we know we're going
+ 
+
+ align:start position:0%
+there's three terms we know we're going
+to get three times some simple thing a
+
+ align:start position:0%
+to get three times some simple thing a
+ 
+
+ align:start position:0%
+to get three times some simple thing a
+number operate well first of all a
+
+ align:start position:0%
+number operate well first of all a
+ 
+
+ align:start position:0%
+number operate well first of all a
+dagger we've got to a daggers in 1a so
+
+ align:start position:0%
+dagger we've got to a daggers in 1a so
+ 
+
+ align:start position:0%
+dagger we've got to a daggers in 1a so
+the overall thing is going to change
+
+ align:start position:0%
+the overall thing is going to change
+ 
+
+ align:start position:0%
+the overall thing is going to change
+increase v by one so it's going to look
+
+ align:start position:0%
+increase v by one so it's going to look
+ 
+
+ align:start position:0%
+increase v by one so it's going to look
+something like n a dagger so let's
+
+ align:start position:0%
+something like n a dagger so let's
+ 
+
+ align:start position:0%
+something like n a dagger so let's
+extract from these three terms three
+
+ align:start position:0%
+extract from these three terms three
+ 
+
+ align:start position:0%
+extract from these three terms three
+times a diagram and
+
+ align:start position:0%
+times a diagram and
+ 
+
+ align:start position:0%
+times a diagram and
+so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+what
+
+ align:start position:0%
+what
+ 
+
+ align:start position:0%
+what
+does that look like a dagger n looks
+
+ align:start position:0%
+does that look like a dagger n looks
+ 
+
+ align:start position:0%
+does that look like a dagger n looks
+like that
+
+ align:start position:0%
+like that
+ 
+
+ align:start position:0%
+like that
+so that's one of the three terms we have
+
+ align:start position:0%
+so that's one of the three terms we have
+ 
+
+ align:start position:0%
+so that's one of the three terms we have
+a dagger a a dagger and we have a a
+
+ align:start position:0%
+a dagger a a dagger and we have a a
+ 
+
+ align:start position:0%
+a dagger a a dagger and we have a a
+dagger a dagger okay
+
+ align:start position:0%
+dagger a dagger okay
+ 
+
+ align:start position:0%
+dagger a dagger okay
+so this is right this one we have to
+
+ align:start position:0%
+so this is right this one we have to
+ 
+
+ align:start position:0%
+so this is right this one we have to
+permute the a past the a dagger so
+
+ align:start position:0%
+permute the a past the a dagger so
+ 
+
+ align:start position:0%
+permute the a past the a dagger so
+we have to do one permutation this
+
+ align:start position:0%
+we have to do one permutation this
+ 
+
+ align:start position:0%
+we have to do one permutation this
+one we have to do one permutation than
+
+ align:start position:0%
+one we have to do one permutation than
+ 
+
+ align:start position:0%
+one we have to do one permutation than
+one more so
+
+ align:start position:0%
+one more so
+ 
+
+ align:start position:0%
+one more so
+when you do that you discover that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+we get three
+
+ align:start position:0%
+we get three
+ 
+
+ align:start position:0%
+we get three
+times a dagger
+
+ align:start position:0%
+times a dagger
+ 
+
+ align:start position:0%
+times a dagger
+n plus
+
+ align:start position:0%
+n plus
+ 
+
+ align:start position:0%
+n plus
+1 or we get 3 a daggers and three a
+
+ align:start position:0%
+1 or we get 3 a daggers and three a
+ 
+
+ align:start position:0%
+1 or we get 3 a daggers and three a
+dagger ends notice
+
+ align:start position:0%
+dagger ends notice
+ 
+
+ align:start position:0%
+dagger ends notice
+that all of these terms change the
+
+ align:start position:0%
+that all of these terms change the
+ 
+
+ align:start position:0%
+that all of these terms change the
+vibrational quantum number up by one so
+
+ align:start position:0%
+vibrational quantum number up by one so
+ 
+
+ align:start position:0%
+vibrational quantum number up by one so
+there's a beauty to this algebra because
+
+ align:start position:0%
+there's a beauty to this algebra because
+ 
+
+ align:start position:0%
+there's a beauty to this algebra because
+you know what you're going to get you
+
+ align:start position:0%
+you know what you're going to get you
+ 
+
+ align:start position:0%
+you know what you're going to get you
+have to do a little work to massage the
+
+ align:start position:0%
+have to do a little work to massage the
+ 
+
+ align:start position:0%
+have to do a little work to massage the
+terms to all come out you know in this
+
+ align:start position:0%
+terms to all come out you know in this
+ 
+
+ align:start position:0%
+terms to all come out you know in this
+form but and you know you're going to
+
+ align:start position:0%
+form but and you know you're going to
+ 
+
+ align:start position:0%
+form but and you know you're going to
+have a term that changes the vibrational
+
+ align:start position:0%
+have a term that changes the vibrational
+ 
+
+ align:start position:0%
+have a term that changes the vibrational
+quantum number by one or in this from
+
+ align:start position:0%
+quantum number by one or in this from
+ 
+
+ align:start position:0%
+quantum number by one or in this from
+this you're going to have a term that
+
+ align:start position:0%
+this you're going to have a term that
+ 
+
+ align:start position:0%
+this you're going to have a term that
+decreases the vibrational quantum number
+
+ align:start position:0%
+decreases the vibrational quantum number
+ 
+
+ align:start position:0%
+decreases the vibrational quantum number
+by one and so these three terms are
+
+ align:start position:0%
+by one and so these three terms are
+ 
+
+ align:start position:0%
+by one and so these three terms are
+going to give you in just three a n and
+
+ align:start position:0%
+going to give you in just three a n and
+ 
+
+ align:start position:0%
+going to give you in just three a n and
+so you should go through this because
+
+ align:start position:0%
+so you should go through this because
+ 
+
+ align:start position:0%
+so you should go through this because
+you can fill sheets of paper doing the
+
+ align:start position:0%
+you can fill sheets of paper doing the
+ 
+
+ align:start position:0%
+you can fill sheets of paper doing the
+algebra subtracting
+
+ align:start position:0%
+algebra subtracting
+ 
+
+ align:start position:0%
+algebra subtracting
+and adding terms or you can just say oh
+
+ align:start position:0%
+and adding terms or you can just say oh
+ 
+
+ align:start position:0%
+and adding terms or you can just say oh
+yeah I want to rearrange the order by
+
+ align:start position:0%
+yeah I want to rearrange the order by
+ 
+
+ align:start position:0%
+yeah I want to rearrange the order by
+doing a series of binary binary
+
+ align:start position:0%
+doing a series of binary binary
+ 
+
+ align:start position:0%
+doing a series of binary binary
+permutations and once
+
+ align:start position:0%
+permutations and once
+ 
+
+ align:start position:0%
+permutations and once
+you've got the hang of that then you
+
+ align:start position:0%
+you've got the hang of that then you
+ 
+
+ align:start position:0%
+you've got the hang of that then you
+just count the number of binary
+
+ align:start position:0%
+just count the number of binary
+ 
+
+ align:start position:0%
+just count the number of binary
+permutations and you multiply the the
+
+ align:start position:0%
+permutations and you multiply the the
+ 
+
+ align:start position:0%
+permutations and you multiply the the
+orphan
+
+ align:start position:0%
+orphan
+ 
+
+ align:start position:0%
+orphan
+term and you've got it and so similarly
+
+ align:start position:0%
+term and you've got it and so similarly
+ 
+
+ align:start position:0%
+term and you've got it and so similarly
+for q4 for q4 one has 14 times a diagram
+
+ align:start position:0%
+for q4 for q4 one has 14 times a diagram
+ 
+
+ align:start position:0%
+for q4 for q4 one has 14 times a diagram
+the fourth a the fourth and then we're
+
+ align:start position:0%
+the fourth a the fourth and then we're
+ 
+
+ align:start position:0%
+the fourth a the fourth and then we're
+going to have one term that has one more
+
+ align:start position:0%
+going to have one term that has one more
+ 
+
+ align:start position:0%
+going to have one term that has one more
+dagger than not and
+
+ align:start position:0%
+dagger than not and
+ 
+
+ align:start position:0%
+dagger than not and
+what one term that has I'm
+
+ align:start position:0%
+what one term that has I'm
+ 
+
+ align:start position:0%
+what one term that has I'm
+sorry we're going to have a dagger a
+
+ align:start position:0%
+sorry we're going to have a dagger a
+ 
+
+ align:start position:0%
+sorry we're going to have a dagger a
+dagger a dagger a 2 more daggers than
+
+ align:start position:0%
+dagger a dagger a 2 more daggers than
+ 
+
+ align:start position:0%
+dagger a dagger a 2 more daggers than
+not and we're going to have one term
+
+ align:start position:0%
+not and we're going to have one term
+ 
+
+ align:start position:0%
+not and we're going to have one term
+that's a a
+
+ align:start position:0%
+that's a a
+ 
+
+ align:start position:0%
+that's a a
+a dagger and we'll have other terms that
+
+ align:start position:0%
+a dagger and we'll have other terms that
+ 
+
+ align:start position:0%
+a dagger and we'll have other terms that
+have this combination so these are going
+
+ align:start position:0%
+have this combination so these are going
+ 
+
+ align:start position:0%
+have this combination so these are going
+to change the vibrational quantum number
+
+ align:start position:0%
+to change the vibrational quantum number
+ 
+
+ align:start position:0%
+to change the vibrational quantum number
+by to increase it by two these are going
+
+ align:start position:0%
+by to increase it by two these are going
+ 
+
+ align:start position:0%
+by to increase it by two these are going
+to decrease it by two and these are not
+
+ align:start position:0%
+to decrease it by two and these are not
+ 
+
+ align:start position:0%
+to decrease it by two and these are not
+going to change it we already know from
+
+ align:start position:0%
+going to change it we already know from
+ 
+
+ align:start position:0%
+going to change it we already know from
+what you know from however you saw
+
+ align:start position:0%
+what you know from however you saw
+ 
+
+ align:start position:0%
+what you know from however you saw
+matrix elements of Q in your previous
+
+ align:start position:0%
+matrix elements of Q in your previous
+ 
+
+ align:start position:0%
+matrix elements of Q in your previous
+life you know that there's going to be
+
+ align:start position:0%
+life you know that there's going to be
+ 
+
+ align:start position:0%
+life you know that there's going to be
+Delta V of for delta v of 2 delta v of 0
+
+ align:start position:0%
+Delta V of for delta v of 2 delta v of 0
+ 
+
+ align:start position:0%
+Delta V of for delta v of 2 delta v of 0
+delta v of minus 2 delta v of minus 4
+
+ align:start position:0%
+delta v of minus 2 delta v of minus 4
+ 
+
+ align:start position:0%
+delta v of minus 2 delta v of minus 4
+and it's nice to be able to get them
+
+ align:start position:0%
+and it's nice to be able to get them
+ 
+
+ align:start position:0%
+and it's nice to be able to get them
+without having to do an awful lot of
+
+ align:start position:0%
+without having to do an awful lot of
+ 
+
+ align:start position:0%
+without having to do an awful lot of
+work now
+
+ align:start position:0%
+work now
+ 
+
+ align:start position:0%
+work now
+you can also have a computer set up the
+
+ align:start position:0%
+you can also have a computer set up the
+ 
+
+ align:start position:0%
+you can also have a computer set up the
+matrix for Q and then
+
+ align:start position:0%
+matrix for Q and then
+ 
+
+ align:start position:0%
+matrix for Q and then
+do matrix multiplication of those things
+
+ align:start position:0%
+do matrix multiplication of those things
+ 
+
+ align:start position:0%
+do matrix multiplication of those things
+and that's easy to instruct a computer
+
+ align:start position:0%
+and that's easy to instruct a computer
+ 
+
+ align:start position:0%
+and that's easy to instruct a computer
+to do too but this is nice because you
+
+ align:start position:0%
+to do too but this is nice because you
+ 
+
+ align:start position:0%
+to do too but this is nice because you
+you actually arrange things and you
+
+ align:start position:0%
+you actually arrange things and you
+ 
+
+ align:start position:0%
+you actually arrange things and you
+discover how to put things together
+
+ align:start position:0%
+discover how to put things together
+ 
+
+ align:start position:0%
+discover how to put things together
+without doing a lot of work okay
+
+ align:start position:0%
+without doing a lot of work okay
+ 
+
+ align:start position:0%
+without doing a lot of work okay
+so with
+
+ align:start position:0%
+so with
+ 
+
+ align:start position:0%
+so with
+this algebra you're really in a position
+
+ align:start position:0%
+this algebra you're really in a position
+ 
+
+ align:start position:0%
+this algebra you're really in a position
+now to write down all of the necessary
+
+ align:start position:0%
+now to write down all of the necessary
+ 
+
+ align:start position:0%
+now to write down all of the necessary
+perturbation
+
+ align:start position:0%
+perturbation
+ 
+
+ align:start position:0%
+perturbation
+theory to solve the problem and in
+
+ align:start position:0%
+theory to solve the problem and in
+ 
+
+ align:start position:0%
+theory to solve the problem and in
+addition you've got to hand out with
+
+ align:start position:0%
+addition you've got to hand out with
+ 
+
+ align:start position:0%
+addition you've got to hand out with
+this lecture which actually does it so
+
+ align:start position:0%
+this lecture which actually does it so
+ 
+
+ align:start position:0%
+this lecture which actually does it so
+there's not too much trouble actually
+
+ align:start position:0%
+there's not too much trouble actually
+ 
+
+ align:start position:0%
+there's not too much trouble actually
+doing this problem but i think you know
+
+ align:start position:0%
+doing this problem but i think you know
+ 
+
+ align:start position:0%
+doing this problem but i think you know
+you really want to go through the paces
+
+ align:start position:0%
+you really want to go through the paces
+ 
+
+ align:start position:0%
+you really want to go through the paces
+using this stuff okay so now I you
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+know I don't think many of you are
+
+ align:start position:0%
+know I don't think many of you are
+ 
+
+ align:start position:0%
+know I don't think many of you are
+interested in making a career doing
+
+ align:start position:0%
+interested in making a career doing
+ 
+
+ align:start position:0%
+interested in making a career doing
+spectroscopy on diatomic molecules but
+
+ align:start position:0%
+spectroscopy on diatomic molecules but
+ 
+
+ align:start position:0%
+spectroscopy on diatomic molecules but
+one of the nice things about diatomic
+
+ align:start position:0%
+one of the nice things about diatomic
+ 
+
+ align:start position:0%
+one of the nice things about diatomic
+molecules is everything
+
+ align:start position:0%
+molecules is everything
+ 
+
+ align:start position:0%
+molecules is everything
+we can almost
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+everything we can do for diatomic
+
+ align:start position:0%
+everything we can do for diatomic
+ 
+
+ align:start position:0%
+everything we can do for diatomic
+molecules we can do for polyatomic
+
+ align:start position:0%
+molecules we can do for polyatomic
+ 
+
+ align:start position:0%
+molecules we can do for polyatomic
+molecules and the things we can't do for
+
+ align:start position:0%
+molecules and the things we can't do for
+ 
+
+ align:start position:0%
+molecules and the things we can't do for
+polyatomic molecules like get a
+
+ align:start position:0%
+polyatomic molecules like get a
+ 
+
+ align:start position:0%
+polyatomic molecules like get a
+potential energy curve by the rid
+
+ align:start position:0%
+potential energy curve by the rid
+ 
+
+ align:start position:0%
+potential energy curve by the rid
+berkline Reese method which
+
+ align:start position:0%
+berkline Reese method which
+ 
+
+ align:start position:0%
+berkline Reese method which
+you can do for diatomics well you can't
+
+ align:start position:0%
+you can do for diatomics well you can't
+ 
+
+ align:start position:0%
+you can do for diatomics well you can't
+do that for polyatomic so you have to
+
+ align:start position:0%
+do that for polyatomic so you have to
+ 
+
+ align:start position:0%
+do that for polyatomic so you have to
+take something from diatomics and extend
+
+ align:start position:0%
+take something from diatomics and extend
+ 
+
+ align:start position:0%
+take something from diatomics and extend
+so suppose we have this triatomic
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+molecule a bet triatomic molecule and
+
+ align:start position:0%
+molecule a bet triatomic molecule and
+ 
+
+ align:start position:0%
+molecule a bet triatomic molecule and
+we
+
+ align:start position:0%
+we
+ 
+
+ align:start position:0%
+we
+know that it belongs to the c2v point
+
+ align:start position:0%
+know that it belongs to the c2v point
+ 
+
+ align:start position:0%
+know that it belongs to the c2v point
+group the point group has four
+
+ align:start position:0%
+group the point group has four
+ 
+
+ align:start position:0%
+group the point group has four
+irreducible representations and
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+we
+
+ align:start position:0%
+we
+ 
+
+ align:start position:0%
+we
+it's a try atomic you don't really need
+
+ align:start position:0%
+it's a try atomic you don't really need
+ 
+
+ align:start position:0%
+it's a try atomic you don't really need
+fancy techniques there's going to be a
+
+ align:start position:0%
+fancy techniques there's going to be a
+ 
+
+ align:start position:0%
+fancy techniques there's going to be a
+symmetric stretch is going to be a band
+
+ align:start position:0%
+symmetric stretch is going to be a band
+ 
+
+ align:start position:0%
+symmetric stretch is going to be a band
+and there's going to be an
+
+ align:start position:0%
+and there's going to be an
+ 
+
+ align:start position:0%
+and there's going to be an
+anti-symmetric stretch so we have the
+
+ align:start position:0%
+anti-symmetric stretch so we have the
+ 
+
+ align:start position:0%
+anti-symmetric stretch so we have the
+symmetric stretch that's
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+new one and LBA one and we have a bend
+
+ align:start position:0%
+new one and LBA one and we have a bend
+ 
+
+ align:start position:0%
+new one and LBA one and we have a bend
+and that
+
+ align:start position:0%
+and that
+ 
+
+ align:start position:0%
+and that
+will be called new two and then
+
+ align:start position:0%
+will be called new two and then
+ 
+
+ align:start position:0%
+will be called new two and then
+we have and
+
+ align:start position:0%
+we have and
+ 
+
+ align:start position:0%
+we have and
+that's a one also and then we have the
+
+ align:start position:0%
+that's a one also and then we have the
+ 
+
+ align:start position:0%
+that's a one also and then we have the
+anti-symmetric stretch and that's be one
+
+ align:start position:0%
+anti-symmetric stretch and that's be one
+ 
+
+ align:start position:0%
+anti-symmetric stretch and that's be one
+that's
+
+ align:start position:0%
+that's
+ 
+
+ align:start position:0%
+that's
+next week okay
+
+ align:start position:0%
+next week okay
+ 
+
+ align:start position:0%
+next week okay
+so if you don't know group theory you
+
+ align:start position:0%
+so if you don't know group theory you
+ 
+
+ align:start position:0%
+so if you don't know group theory you
+will you will learn it but the important
+
+ align:start position:0%
+will you will learn it but the important
+ 
+
+ align:start position:0%
+will you will learn it but the important
+thing is this is called the totally
+
+ align:start position:0%
+thing is this is called the totally
+ 
+
+ align:start position:0%
+thing is this is called the totally
+symmetric representation the hamiltonian
+
+ align:start position:0%
+symmetric representation the hamiltonian
+ 
+
+ align:start position:0%
+symmetric representation the hamiltonian
+is totally symmetric if a hamiltonian is
+
+ align:start position:0%
+is totally symmetric if a hamiltonian is
+ 
+
+ align:start position:0%
+is totally symmetric if a hamiltonian is
+three a product of three things we
+
+ align:start position:0%
+three a product of three things we
+ 
+
+ align:start position:0%
+three a product of three things we
+function operator wave function and
+
+ align:start position:0%
+function operator wave function and
+ 
+
+ align:start position:0%
+function operator wave function and
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+operator in the hamiltonian has to
+
+ align:start position:0%
+operator in the hamiltonian has to
+ 
+
+ align:start position:0%
+operator in the hamiltonian has to
+belong to let
+
+ align:start position:0%
+belong to let
+ 
+
+ align:start position:0%
+belong to let
+me back up
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+hamiltonian itself belongs to the
+
+ align:start position:0%
+hamiltonian itself belongs to the
+ 
+
+ align:start position:0%
+hamiltonian itself belongs to the
+totally symmetric representation one
+
+ align:start position:0%
+totally symmetric representation one
+ 
+
+ align:start position:0%
+totally symmetric representation one
+can have off diagonal matrix elements of
+
+ align:start position:0%
+can have off diagonal matrix elements of
+ 
+
+ align:start position:0%
+can have off diagonal matrix elements of
+the hamiltonian but those are terms in
+
+ align:start position:0%
+the hamiltonian but those are terms in
+ 
+
+ align:start position:0%
+the hamiltonian but those are terms in
+the hamiltonian which combined
+
+ align:start position:0%
+the hamiltonian which combined
+ 
+
+ align:start position:0%
+the hamiltonian which combined
+with other terms of the hamiltonian to
+
+ align:start position:0%
+with other terms of the hamiltonian to
+ 
+
+ align:start position:0%
+with other terms of the hamiltonian to
+leave the thing being totally symmetric
+
+ align:start position:0%
+leave the thing being totally symmetric
+ 
+
+ align:start position:0%
+leave the thing being totally symmetric
+so the
+
+ align:start position:0%
+so the
+ 
+
+ align:start position:0%
+so the
+thing that I got wrong in writing
+
+ align:start position:0%
+thing that I got wrong in writing
+ 
+
+ align:start position:0%
+thing that I got wrong in writing
+lecture notes two and three previously
+
+ align:start position:0%
+lecture notes two and three previously
+ 
+
+ align:start position:0%
+lecture notes two and three previously
+was I said we're going to have a linear
+
+ align:start position:0%
+was I said we're going to have a linear
+ 
+
+ align:start position:0%
+was I said we're going to have a linear
+molecule and we have the x-band and the
+
+ align:start position:0%
+molecule and we have the x-band and the
+ 
+
+ align:start position:0%
+molecule and we have the x-band and the
+y bed and the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+problem is the way I've formulated the
+
+ align:start position:0%
+problem is the way I've formulated the
+ 
+
+ align:start position:0%
+problem is the way I've formulated the
+problem the
+
+ align:start position:0%
+problem the
+ 
+
+ align:start position:0%
+problem the
+matrix elements are the terms that I
+
+ align:start position:0%
+matrix elements are the terms that I
+ 
+
+ align:start position:0%
+matrix elements are the terms that I
+used in the Hamiltonian were not totally
+
+ align:start position:0%
+used in the Hamiltonian were not totally
+ 
+
+ align:start position:0%
+used in the Hamiltonian were not totally
+symmetric they didn't respect
+
+ align:start position:0%
+symmetric they didn't respect
+ 
+
+ align:start position:0%
+symmetric they didn't respect
+cylindrical symmetry and so that was all
+
+ align:start position:0%
+cylindrical symmetry and so that was all
+ 
+
+ align:start position:0%
+cylindrical symmetry and so that was all
+completely crazy so now I've careful to
+
+ align:start position:0%
+completely crazy so now I've careful to
+ 
+
+ align:start position:0%
+completely crazy so now I've careful to
+choose a bent molecule will
+
+ align:start position:0%
+choose a bent molecule will
+ 
+
+ align:start position:0%
+choose a bent molecule will
+come back to linear molecules eventually
+
+ align:start position:0%
+come back to linear molecules eventually
+ 
+
+ align:start position:0%
+come back to linear molecules eventually
+but the important thing is that the
+
+ align:start position:0%
+but the important thing is that the
+ 
+
+ align:start position:0%
+but the important thing is that the
+Hamiltonian if you write down something
+
+ align:start position:0%
+Hamiltonian if you write down something
+ 
+
+ align:start position:0%
+Hamiltonian if you write down something
+that thing
+
+ align:start position:0%
+that thing
+ 
+
+ align:start position:0%
+that thing
+is going to connect basis
+
+ align:start position:0%
+is going to connect basis
+ 
+
+ align:start position:0%
+is going to connect basis
+functions that belong to the same
+
+ align:start position:0%
+functions that belong to the same
+ 
+
+ align:start position:0%
+functions that belong to the same
+irreducible representation okay
+
+ align:start position:0%
+irreducible representation okay
+ 
+
+ align:start position:0%
+irreducible representation okay
+so what we want to do is take what we
+
+ align:start position:0%
+so what we want to do is take what we
+ 
+
+ align:start position:0%
+so what we want to do is take what we
+learn from allowing
+
+ align:start position:0%
+learn from allowing
+ 
+
+ align:start position:0%
+learn from allowing
+a diatomic rotating molecule and
+
+ align:start position:0%
+a diatomic rotating molecule and
+ 
+
+ align:start position:0%
+a diatomic rotating molecule and
+vibrating molecule to be an harmonic to
+
+ align:start position:0%
+vibrating molecule to be an harmonic to
+ 
+
+ align:start position:0%
+vibrating molecule to be an harmonic to
+extend that to the vibrational levels of
+
+ align:start position:0%
+extend that to the vibrational levels of
+ 
+
+ align:start position:0%
+extend that to the vibrational levels of
+a try atomic and so
+
+ align:start position:0%
+a try atomic and so
+ 
+
+ align:start position:0%
+a try atomic and so
+we're going to have diagonal and hominis
+
+ align:start position:0%
+we're going to have diagonal and hominis
+ 
+
+ align:start position:0%
+we're going to have diagonal and hominis
+in each of these modes just like what we
+
+ align:start position:0%
+in each of these modes just like what we
+ 
+
+ align:start position:0%
+in each of these modes just like what we
+did for a diatomic but while also going
+
+ align:start position:0%
+did for a diatomic but while also going
+ 
+
+ align:start position:0%
+did for a diatomic but while also going
+to allow these modes to couple to each
+
+ align:start position:0%
+to allow these modes to couple to each
+ 
+
+ align:start position:0%
+to allow these modes to couple to each
+other involving terms like q1 q2
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+say
+
+ align:start position:0%
+say
+ 
+
+ align:start position:0%
+say
+Q 2 squared or Q 1 squared cubed
+
+ align:start position:0%
+Q 2 squared or Q 1 squared cubed
+ 
+
+ align:start position:0%
+Q 2 squared or Q 1 squared cubed
+three squared
+
+ align:start position:0%
+three squared
+ 
+
+ align:start position:0%
+three squared
+okay a1 a1 b1 so we can have any powers
+
+ align:start position:0%
+okay a1 a1 b1 so we can have any powers
+ 
+
+ align:start position:0%
+okay a1 a1 b1 so we can have any powers
+of modes one and two but
+
+ align:start position:0%
+of modes one and two but
+ 
+
+ align:start position:0%
+of modes one and two but
+if we have mode 3 they have to we have
+
+ align:start position:0%
+if we have mode 3 they have to we have
+ 
+
+ align:start position:0%
+if we have mode 3 they have to we have
+to have even powers of mode 3 for
+
+ align:start position:0%
+to have even powers of mode 3 for
+ 
+
+ align:start position:0%
+to have even powers of mode 3 for
+the cup like legal coupling terms
+
+ align:start position:0%
+the cup like legal coupling terms
+ 
+
+ align:start position:0%
+the cup like legal coupling terms
+involving mode 3 so we're going to want
+
+ align:start position:0%
+involving mode 3 so we're going to want
+ 
+
+ align:start position:0%
+involving mode 3 so we're going to want
+to deal with the energy vibrational
+
+ align:start position:0%
+to deal with the energy vibrational
+ 
+
+ align:start position:0%
+to deal with the energy vibrational
+energy levels of a molecule with both
+
+ align:start position:0%
+energy levels of a molecule with both
+ 
+
+ align:start position:0%
+energy levels of a molecule with both
+diagonal and off-diagonal at Harmon
+
+ align:start position:0%
+diagonal and off-diagonal at Harmon
+ 
+
+ align:start position:0%
+diagonal and off-diagonal at Harmon
+icity and we'd like to relate the the
+
+ align:start position:0%
+icity and we'd like to relate the the
+ 
+
+ align:start position:0%
+icity and we'd like to relate the the
+things that we measure in the spectrum
+
+ align:start position:0%
+things that we measure in the spectrum
+ 
+
+ align:start position:0%
+things that we measure in the spectrum
+from differences between energy levels
+
+ align:start position:0%
+from differences between energy levels
+ 
+
+ align:start position:0%
+from differences between energy levels
+to things that are constants in the
+
+ align:start position:0%
+to things that are constants in the
+ 
+
+ align:start position:0%
+to things that are constants in the
+potential like k12
+
+ align:start position:0%
+potential like k12
+ 
+
+ align:start position:0%
+potential like k12
+too because one of these two of these k
+
+ align:start position:0%
+too because one of these two of these k
+ 
+
+ align:start position:0%
+too because one of these two of these k
+1 to 2 or this k 1 133 so these are the
+
+ align:start position:0%
+1 to 2 or this k 1 133 so these are the
+ 
+
+ align:start position:0%
+1 to 2 or this k 1 133 so these are the
+new things that we want to bring into
+
+ align:start position:0%
+new things that we want to bring into
+ 
+
+ align:start position:0%
+new things that we want to bring into
+explaining
+
+ align:start position:0%
+explaining
+ 
+
+ align:start position:0%
+explaining
+the molecular energy levels are
+
+ align:start position:0%
+the molecular energy levels are
+ 
+
+ align:start position:0%
+the molecular energy levels are
+we all okay I haven't had any questions
+
+ align:start position:0%
+we all okay I haven't had any questions
+ 
+
+ align:start position:0%
+we all okay I haven't had any questions
+I have seen some responses and so
+
+ align:start position:0%
+I have seen some responses and so
+ 
+
+ align:start position:0%
+I have seen some responses and so
+I think most of you are semi
+
+ align:start position:0%
+I think most of you are semi
+ 
+
+ align:start position:0%
+I think most of you are semi
+ok here we are you all right okay
+
+ align:start position:0%
+ok here we are you all right okay
+ 
+
+ align:start position:0%
+ok here we are you all right okay
+so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+I want
+
+ align:start position:0%
+I want
+ 
+
+ align:start position:0%
+I want
+to enter illustrate the
+
+ align:start position:0%
+to enter illustrate the
+ 
+
+ align:start position:0%
+to enter illustrate the
+use of perturbation theory and Lou and
+
+ align:start position:0%
+use of perturbation theory and Lou and
+ 
+
+ align:start position:0%
+use of perturbation theory and Lou and
+the use of judgment so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+what I'm going to do is say okay omega
+
+ align:start position:0%
+what I'm going to do is say okay omega
+ 
+
+ align:start position:0%
+what I'm going to do is say okay omega
+one happens to be almost exactly 2 Omega
+
+ align:start position:0%
+one happens to be almost exactly 2 Omega
+ 
+
+ align:start position:0%
+one happens to be almost exactly 2 Omega
+2 and
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Omega 3 is approximately
+
+ align:start position:0%
+Omega 3 is approximately
+ 
+
+ align:start position:0%
+Omega 3 is approximately
+1.2 Omega 1 so
+
+ align:start position:0%
+1.2 Omega 1 so
+ 
+
+ align:start position:0%
+1.2 Omega 1 so
+this is telling you that Omega 1 and
+
+ align:start position:0%
+this is telling you that Omega 1 and
+ 
+
+ align:start position:0%
+this is telling you that Omega 1 and
+Omega 2 are resonant that
+
+ align:start position:0%
+Omega 2 are resonant that
+ 
+
+ align:start position:0%
+Omega 2 are resonant that
+we're going to get when we do
+
+ align:start position:0%
+we're going to get when we do
+ 
+
+ align:start position:0%
+we're going to get when we do
+perturbation theory we're going to get
+
+ align:start position:0%
+perturbation theory we're going to get
+ 
+
+ align:start position:0%
+perturbation theory we're going to get
+an energy denominator
+
+ align:start position:0%
+an energy denominator
+ 
+
+ align:start position:0%
+an energy denominator
+it's near zero for certain terms
+
+ align:start position:0%
+it's near zero for certain terms
+ 
+
+ align:start position:0%
+it's near zero for certain terms
+coupling the
+
+ align:start position:0%
+coupling the
+ 
+
+ align:start position:0%
+coupling the
+normal
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+mode one with normal 02 but normal mode
+
+ align:start position:0%
+mode one with normal 02 but normal mode
+ 
+
+ align:start position:0%
+mode one with normal 02 but normal mode
+3 is not going to have surprising
+
+ align:start position:0%
+3 is not going to have surprising
+ 
+
+ align:start position:0%
+3 is not going to have surprising
+denominators with either mode 1 or mode
+
+ align:start position:0%
+denominators with either mode 1 or mode
+ 
+
+ align:start position:0%
+denominators with either mode 1 or mode
+2 so that means that the coupling
+
+ align:start position:0%
+2 so that means that the coupling
+ 
+
+ align:start position:0%
+2 so that means that the coupling
+between modes three two and two and
+
+ align:start position:0%
+between modes three two and two and
+ 
+
+ align:start position:0%
+between modes three two and two and
+three and one can be handled by ordinary
+
+ align:start position:0%
+three and one can be handled by ordinary
+ 
+
+ align:start position:0%
+three and one can be handled by ordinary
+non degenerate perturbation theory but
+
+ align:start position:0%
+non degenerate perturbation theory but
+ 
+
+ align:start position:0%
+non degenerate perturbation theory but
+the coupling between modes one and two
+
+ align:start position:0%
+the coupling between modes one and two
+ 
+
+ align:start position:0%
+the coupling between modes one and two
+we have to be careful so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+let us write the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+perturbation term and the
+
+ align:start position:0%
+perturbation term and the
+ 
+
+ align:start position:0%
+perturbation term and the
+perturbation term contains terms like
+
+ align:start position:0%
+perturbation term contains terms like
+ 
+
+ align:start position:0%
+perturbation term contains terms like
+this k12 to q1
+
+ align:start position:0%
+this k12 to q1
+ 
+
+ align:start position:0%
+this k12 to q1
+cube 2 squared this
+
+ align:start position:0%
+cube 2 squared this
+ 
+
+ align:start position:0%
+cube 2 squared this
+just tells you what exponents to write
+
+ align:start position:0%
+just tells you what exponents to write
+ 
+
+ align:start position:0%
+just tells you what exponents to write
+up here and as soon as you know what
+
+ align:start position:0%
+up here and as soon as you know what
+ 
+
+ align:start position:0%
+up here and as soon as you know what
+exponents are right up here you know the
+
+ align:start position:0%
+exponents are right up here you know the
+ 
+
+ align:start position:0%
+exponents are right up here you know the
+matrix elements okay
+
+ align:start position:0%
+matrix elements okay
+ 
+
+ align:start position:0%
+matrix elements okay
+and then there's another term 140 k 1
+
+ align:start position:0%
+and then there's another term 140 k 1
+ 
+
+ align:start position:0%
+and then there's another term 140 k 1
+133 k q1 squared q 3 square and then
+
+ align:start position:0%
+133 k q1 squared q 3 square and then
+ 
+
+ align:start position:0%
+133 k q1 squared q 3 square and then
+let's write a third term 112 k
+
+ align:start position:0%
+let's write a third term 112 k
+ 
+
+ align:start position:0%
+let's write a third term 112 k
+2 2 2 3 3 q 2 q q 3 squared so
+
+ align:start position:0%
+2 2 2 3 3 q 2 q q 3 squared so
+ 
+
+ align:start position:0%
+2 2 2 3 3 q 2 q q 3 squared so
+here is a cubic term a quartic term and
+
+ align:start position:0%
+here is a cubic term a quartic term and
+ 
+
+ align:start position:0%
+here is a cubic term a quartic term and
+a quintic term why
+
+ align:start position:0%
+a quintic term why
+ 
+
+ align:start position:0%
+a quintic term why
+did we stop why
+
+ align:start position:0%
+did we stop why
+ 
+
+ align:start position:0%
+did we stop why
+not write more there's
+
+ align:start position:0%
+not write more there's
+ 
+
+ align:start position:0%
+not write more there's
+no reason why we have to stop with
+
+ align:start position:0%
+no reason why we have to stop with
+ 
+
+ align:start position:0%
+no reason why we have to stop with
+quintic terms and there are perhaps
+
+ align:start position:0%
+quintic terms and there are perhaps
+ 
+
+ align:start position:0%
+quintic terms and there are perhaps
+cubic and quartic terms that I haven't
+
+ align:start position:0%
+cubic and quartic terms that I haven't
+ 
+
+ align:start position:0%
+cubic and quartic terms that I haven't
+included here why didn't I write them
+
+ align:start position:0%
+included here why didn't I write them
+ 
+
+ align:start position:0%
+included here why didn't I write them
+well
+
+ align:start position:0%
+well
+ 
+
+ align:start position:0%
+well
+we want the simplest possible
+
+ align:start position:0%
+we want the simplest possible
+ 
+
+ align:start position:0%
+we want the simplest possible
+representation and
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+mode
+
+ align:start position:0%
+mode
+ 
+
+ align:start position:0%
+mode
+3 is not totally symmetric so
+
+ align:start position:0%
+3 is not totally symmetric so
+ 
+
+ align:start position:0%
+3 is not totally symmetric so
+anytime we're coupling to mode 3 we have
+
+ align:start position:0%
+anytime we're coupling to mode 3 we have
+ 
+
+ align:start position:0%
+anytime we're coupling to mode 3 we have
+to have two of them so
+
+ align:start position:0%
+to have two of them so
+ 
+
+ align:start position:0%
+to have two of them so
+we could conceivably have q1
+
+ align:start position:0%
+we could conceivably have q1
+ 
+
+ align:start position:0%
+we could conceivably have q1
+q3 squared we could have q2 q3 squared
+
+ align:start position:0%
+q3 squared we could have q2 q3 squared
+ 
+
+ align:start position:0%
+q3 squared we could have q2 q3 squared
+but what you see here is that the
+
+ align:start position:0%
+but what you see here is that the
+ 
+
+ align:start position:0%
+but what you see here is that the
+frequencies for modes one and three are
+
+ align:start position:0%
+frequencies for modes one and three are
+ 
+
+ align:start position:0%
+frequencies for modes one and three are
+nearly
+
+ align:start position:0%
+nearly
+ 
+
+ align:start position:0%
+nearly
+the same but they're not resonant and so
+
+ align:start position:0%
+the same but they're not resonant and so
+ 
+
+ align:start position:0%
+the same but they're not resonant and so
+if you change v1 down and v3 up your
+
+ align:start position:0%
+if you change v1 down and v3 up your
+ 
+
+ align:start position:0%
+if you change v1 down and v3 up your
+you're not going to be near resonant
+
+ align:start position:0%
+you're not going to be near resonant
+ 
+
+ align:start position:0%
+you're not going to be near resonant
+you're not going to have trouble so you
+
+ align:start position:0%
+you're not going to have trouble so you
+ 
+
+ align:start position:0%
+you're not going to have trouble so you
+don't really need these terms this one
+
+ align:start position:0%
+don't really need these terms this one
+ 
+
+ align:start position:0%
+don't really need these terms this one
+though because mode 1 is roughly twice
+
+ align:start position:0%
+though because mode 1 is roughly twice
+ 
+
+ align:start position:0%
+though because mode 1 is roughly twice
+the frequency of Mo to this is a
+
+ align:start position:0%
+the frequency of Mo to this is a
+ 
+
+ align:start position:0%
+the frequency of Mo to this is a
+resonant term this is very important
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+there is this one where we have modes
+
+ align:start position:0%
+there is this one where we have modes
+ 
+
+ align:start position:0%
+there is this one where we have modes
+one and three to the same power and
+
+ align:start position:0%
+one and three to the same power and
+ 
+
+ align:start position:0%
+one and three to the same power and
+they're similar in frequency they're not
+
+ align:start position:0%
+they're similar in frequency they're not
+ 
+
+ align:start position:0%
+they're similar in frequency they're not
+resonant but it's the it's the lowest
+
+ align:start position:0%
+resonant but it's the it's the lowest
+ 
+
+ align:start position:0%
+resonant but it's the it's the lowest
+ordered near resonant erm and you're
+
+ align:start position:0%
+ordered near resonant erm and you're
+ 
+
+ align:start position:0%
+ordered near resonant erm and you're
+going to have a relative you going to
+
+ align:start position:0%
+going to have a relative you going to
+ 
+
+ align:start position:0%
+going to have a relative you going to
+have some relatively small energy
+
+ align:start position:0%
+have some relatively small energy
+ 
+
+ align:start position:0%
+have some relatively small energy
+denominators will which will make this
+
+ align:start position:0%
+denominators will which will make this
+ 
+
+ align:start position:0%
+denominators will which will make this
+one import this is quintic okay but
+
+ align:start position:0%
+one import this is quintic okay but
+ 
+
+ align:start position:0%
+one import this is quintic okay but
+doesn't that resonance depend on how big
+
+ align:start position:0%
+doesn't that resonance depend on how big
+ 
+
+ align:start position:0%
+doesn't that resonance depend on how big
+say omega one is because yes so if your
+
+ align:start position:0%
+say omega one is because yes so if your
+ 
+
+ align:start position:0%
+say omega one is because yes so if your
+energy difference is lodged then that
+
+ align:start position:0%
+energy difference is lodged then that
+ 
+
+ align:start position:0%
+energy difference is lodged then that
+residents may not necessarily be right
+
+ align:start position:0%
+residents may not necessarily be right
+ 
+
+ align:start position:0%
+residents may not necessarily be right
+yellow ones that's right okay so but
+
+ align:start position:0%
+yellow ones that's right okay so but
+ 
+
+ align:start position:0%
+yellow ones that's right okay so but
+what I wanted to point out is that the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+quintic terms I think the cubic terms
+
+ align:start position:0%
+quintic terms I think the cubic terms
+ 
+
+ align:start position:0%
+quintic terms I think the cubic terms
+make generally a factor of ten larger
+
+ align:start position:0%
+make generally a factor of ten larger
+ 
+
+ align:start position:0%
+make generally a factor of ten larger
+contribution to the energy than the
+
+ align:start position:0%
+contribution to the energy than the
+ 
+
+ align:start position:0%
+contribution to the energy than the
+quartic terms and these factor 10 larger
+
+ align:start position:0%
+quartic terms and these factor 10 larger
+ 
+
+ align:start position:0%
+quartic terms and these factor 10 larger
+the de quintic terms there's more stuff
+
+ align:start position:0%
+the de quintic terms there's more stuff
+ 
+
+ align:start position:0%
+the de quintic terms there's more stuff
+that actually so
+
+ align:start position:0%
+that actually so
+ 
+
+ align:start position:0%
+that actually so
+part of that came from that scaling
+
+ align:start position:0%
+part of that came from that scaling
+ 
+
+ align:start position:0%
+part of that came from that scaling
+which I think we've lost by now Thea the
+
+ align:start position:0%
+which I think we've lost by now Thea the
+ 
+
+ align:start position:0%
+which I think we've lost by now Thea the
+fact is that I pulled out of of Q and so
+
+ align:start position:0%
+fact is that I pulled out of of Q and so
+ 
+
+ align:start position:0%
+fact is that I pulled out of of Q and so
+because each of those factors had won
+
+ align:start position:0%
+because each of those factors had won
+ 
+
+ align:start position:0%
+because each of those factors had won
+over the spirit of Omega in it and so
+
+ align:start position:0%
+over the spirit of Omega in it and so
+ 
+
+ align:start position:0%
+over the spirit of Omega in it and so
+each time you have another Q you get
+
+ align:start position:0%
+each time you have another Q you get
+ 
+
+ align:start position:0%
+each time you have another Q you get
+another factor 1 over square root of
+
+ align:start position:0%
+another factor 1 over square root of
+ 
+
+ align:start position:0%
+another factor 1 over square root of
+Omega mega is usually a thousand so you
+
+ align:start position:0%
+Omega mega is usually a thousand so you
+ 
+
+ align:start position:0%
+Omega mega is usually a thousand so you
+know square root of that is 30 and so
+
+ align:start position:0%
+know square root of that is 30 and so
+ 
+
+ align:start position:0%
+know square root of that is 30 and so
+just that factor kills you by a factor
+
+ align:start position:0%
+just that factor kills you by a factor
+ 
+
+ align:start position:0%
+just that factor kills you by a factor
+30 / q and there are other factors so
+
+ align:start position:0%
+30 / q and there are other factors so
+ 
+
+ align:start position:0%
+30 / q and there are other factors so
+you get roughly a factor of 10 / power
+
+ align:start position:0%
+you get roughly a factor of 10 / power
+ 
+
+ align:start position:0%
+you get roughly a factor of 10 / power
+of the coordinate and that means you you
+
+ align:start position:0%
+of the coordinate and that means you you
+ 
+
+ align:start position:0%
+of the coordinate and that means you you
+generally want to look very carefully at
+
+ align:start position:0%
+generally want to look very carefully at
+ 
+
+ align:start position:0%
+generally want to look very carefully at
+the cubic ones you
+
+ align:start position:0%
+the cubic ones you
+ 
+
+ align:start position:0%
+the cubic ones you
+look very careful at the quartic ones
+
+ align:start position:0%
+look very careful at the quartic ones
+ 
+
+ align:start position:0%
+look very careful at the quartic ones
+because the aquatic ones remember in
+
+ align:start position:0%
+because the aquatic ones remember in
+ 
+
+ align:start position:0%
+because the aquatic ones remember in
+perturbation theory we have energy which
+
+ align:start position:0%
+perturbation theory we have energy which
+ 
+
+ align:start position:0%
+perturbation theory we have energy which
+is for the ice level is
+
+ align:start position:0%
+is for the ice level is
+ 
+
+ align:start position:0%
+is for the ice level is
+zero + e i1
+
+ align:start position:0%
+zero + e i1
+ 
+
+ align:start position:0%
+zero + e i1
+plus i2 and
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this guy comes from just H I i won it
+
+ align:start position:0%
+this guy comes from just H I i won it
+ 
+
+ align:start position:0%
+this guy comes from just H I i won it
+comes from a diagonal matrix element of
+
+ align:start position:0%
+comes from a diagonal matrix element of
+ 
+
+ align:start position:0%
+comes from a diagonal matrix element of
+the perturbation term no energy
+
+ align:start position:0%
+the perturbation term no energy
+ 
+
+ align:start position:0%
+the perturbation term no energy
+denominator and so
+
+ align:start position:0%
+denominator and so
+ 
+
+ align:start position:0%
+denominator and so
+if there is a quartic term if there is a
+
+ align:start position:0%
+if there is a quartic term if there is a
+ 
+
+ align:start position:0%
+if there is a quartic term if there is a
+term that can have a diagonal element of
+
+ align:start position:0%
+term that can have a diagonal element of
+ 
+
+ align:start position:0%
+term that can have a diagonal element of
+one of the perturbation terms that's
+
+ align:start position:0%
+one of the perturbation terms that's
+ 
+
+ align:start position:0%
+one of the perturbation terms that's
+going to be important and
+
+ align:start position:0%
+going to be important and
+ 
+
+ align:start position:0%
+going to be important and
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+we
+
+ align:start position:0%
+we
+ 
+
+ align:start position:0%
+we
+look for things where we have 11
+
+ align:start position:0%
+look for things where we have 11
+ 
+
+ align:start position:0%
+look for things where we have 11
+33 or 1122 because
+
+ align:start position:0%
+33 or 1122 because
+ 
+
+ align:start position:0%
+33 or 1122 because
+as q squared has matrix element Delta V
+
+ align:start position:0%
+as q squared has matrix element Delta V
+ 
+
+ align:start position:0%
+as q squared has matrix element Delta V
+of 0 and plus and minus 2 and so you can
+
+ align:start position:0%
+of 0 and plus and minus 2 and so you can
+ 
+
+ align:start position:0%
+of 0 and plus and minus 2 and so you can
+get to Delta V sub 0 and that's the same
+
+ align:start position:0%
+get to Delta V sub 0 and that's the same
+ 
+
+ align:start position:0%
+get to Delta V sub 0 and that's the same
+thing as saying okay this is you're
+
+ align:start position:0%
+thing as saying okay this is you're
+ 
+
+ align:start position:0%
+thing as saying okay this is you're
+going to have some diagonal matrix
+
+ align:start position:0%
+going to have some diagonal matrix
+ 
+
+ align:start position:0%
+going to have some diagonal matrix
+elements of the perturbation operator
+
+ align:start position:0%
+elements of the perturbation operator
+ 
+
+ align:start position:0%
+elements of the perturbation operator
+and they become really important yes it
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+isn't it
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+isn't it's just you know I just wanted
+
+ align:start position:0%
+isn't it's just you know I just wanted
+ 
+
+ align:start position:0%
+isn't it's just you know I just wanted
+to include a quintic term because we
+
+ align:start position:0%
+to include a quintic term because we
+ 
+
+ align:start position:0%
+to include a quintic term because we
+want to kill it okay
+
+ align:start position:0%
+want to kill it okay
+ 
+
+ align:start position:0%
+want to kill it okay
+all right so
+
+ align:start position:0%
+all right so
+ 
+
+ align:start position:0%
+all right so
+you know that's all you know it just had
+
+ align:start position:0%
+you know that's all you know it just had
+ 
+
+ align:start position:0%
+you know that's all you know it just had
+to have an example and there's
+
+ align:start position:0%
+to have an example and there's
+ 
+
+ align:start position:0%
+to have an example and there's
+another thing that happens when
+
+ align:start position:0%
+another thing that happens when
+ 
+
+ align:start position:0%
+another thing that happens when
+you just look at the magnitudes of these
+
+ align:start position:0%
+you just look at the magnitudes of these
+ 
+
+ align:start position:0%
+you just look at the magnitudes of these
+terms they decrease by roughly a factor
+
+ align:start position:0%
+terms they decrease by roughly a factor
+ 
+
+ align:start position:0%
+terms they decrease by roughly a factor
+10 / power but the the even powers
+
+ align:start position:0%
+10 / power but the the even powers
+ 
+
+ align:start position:0%
+10 / power but the the even powers
+appear in first order and the
+
+ align:start position:0%
+appear in first order and the
+ 
+
+ align:start position:0%
+appear in first order and the
+odd powers appear only in second order
+
+ align:start position:0%
+odd powers appear only in second order
+ 
+
+ align:start position:0%
+odd powers appear only in second order
+and so it turns out that quintic and
+
+ align:start position:0%
+and so it turns out that quintic and
+ 
+
+ align:start position:0%
+and so it turns out that quintic and
+second or a cubic and second order is
+
+ align:start position:0%
+second or a cubic and second order is
+ 
+
+ align:start position:0%
+second or a cubic and second order is
+roughly the same order of magnitude as
+
+ align:start position:0%
+roughly the same order of magnitude as
+ 
+
+ align:start position:0%
+roughly the same order of magnitude as
+quartic
+
+ align:start position:0%
+quartic
+ 
+
+ align:start position:0%
+quartic
+in first order and quintic is just out
+
+ align:start position:0%
+in first order and quintic is just out
+ 
+
+ align:start position:0%
+in first order and quintic is just out
+of business because there's no quintic
+
+ align:start position:0%
+of business because there's no quintic
+ 
+
+ align:start position:0%
+of business because there's no quintic
+and first-order there's quintic only in
+
+ align:start position:0%
+and first-order there's quintic only in
+ 
+
+ align:start position:0%
+and first-order there's quintic only in
+second order that makes it roughly the
+
+ align:start position:0%
+second order that makes it roughly the
+ 
+
+ align:start position:0%
+second order that makes it roughly the
+same magnitude as sexting in zeroth
+
+ align:start position:0%
+same magnitude as sexting in zeroth
+ 
+
+ align:start position:0%
+same magnitude as sexting in zeroth
+order in first order and so you know
+
+ align:start position:0%
+order in first order and so you know
+ 
+
+ align:start position:0%
+order in first order and so you know
+this is why we stopped here we don't
+
+ align:start position:0%
+this is why we stopped here we don't
+ 
+
+ align:start position:0%
+this is why we stopped here we don't
+generally want to look at quintic terms
+
+ align:start position:0%
+generally want to look at quintic terms
+ 
+
+ align:start position:0%
+generally want to look at quintic terms
+because they're really small and they
+
+ align:start position:0%
+because they're really small and they
+ 
+
+ align:start position:0%
+because they're really small and they
+only appear squared over an energy
+
+ align:start position:0%
+only appear squared over an energy
+ 
+
+ align:start position:0%
+only appear squared over an energy
+difference okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+[Music]
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+we're going to want to get
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+from perturbation theory the
+
+ align:start position:0%
+from perturbation theory the
+ 
+
+ align:start position:0%
+from perturbation theory the
+expressions in this general energy
+
+ align:start position:0%
+expressions in this general energy
+ 
+
+ align:start position:0%
+expressions in this general energy
+expression i just use a bold v to
+
+ align:start position:0%
+expression i just use a bold v to
+ 
+
+ align:start position:0%
+expression i just use a bold v to
+indicate all the vibrational modes
+
+ align:start position:0%
+indicate all the vibrational modes
+ 
+
+ align:start position:0%
+indicate all the vibrational modes
+instead of having to write e v1
+
+ align:start position:0%
+instead of having to write e v1
+ 
+
+ align:start position:0%
+instead of having to write e v1
+v2 v3 but that's what this means and so
+
+ align:start position:0%
+v2 v3 but that's what this means and so
+ 
+
+ align:start position:0%
+v2 v3 but that's what this means and so
+we're going to have omega
+
+ align:start position:0%
+we're going to have omega
+ 
+
+ align:start position:0%
+we're going to have omega
+i VI plus a half plus
+
+ align:start position:0%
+i VI plus a half plus
+ 
+
+ align:start position:0%
+i VI plus a half plus
+i J
+
+ align:start position:0%
+i J
+ 
+
+ align:start position:0%
+i J
+I greater
+
+ align:start position:0%
+I greater
+ 
+
+ align:start position:0%
+I greater
+than or equal to j x
+
+ align:start position:0%
+than or equal to j x
+ 
+
+ align:start position:0%
+than or equal to j x
+i J VI plus
+
+ align:start position:0%
+i J VI plus
+ 
+
+ align:start position:0%
+i J VI plus
+a half be J
+
+ align:start position:0%
+a half be J
+ 
+
+ align:start position:0%
+a half be J
+okay right VJ plus a half and
+
+ align:start position:0%
+okay right VJ plus a half and
+ 
+
+ align:start position:0%
+okay right VJ plus a half and
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+we're going to have three omegas we're
+
+ align:start position:0%
+we're going to have three omegas we're
+ 
+
+ align:start position:0%
+we're going to have three omegas we're
+going to have 6
+
+ align:start position:0%
+going to have 6
+ 
+
+ align:start position:0%
+going to have 6
+x's and we're going to want to get the
+
+ align:start position:0%
+x's and we're going to want to get the
+ 
+
+ align:start position:0%
+x's and we're going to want to get the
+three omegas and the 6 x's out of the
+
+ align:start position:0%
+three omegas and the 6 x's out of the
+ 
+
+ align:start position:0%
+three omegas and the 6 x's out of the
+put
+
+ align:start position:0%
+put
+ 
+
+ align:start position:0%
+put
+the expression for H prime we have these
+
+ align:start position:0%
+the expression for H prime we have these
+ 
+
+ align:start position:0%
+the expression for H prime we have these
+this we don't have that and we have the
+
+ align:start position:0%
+this we don't have that and we have the
+ 
+
+ align:start position:0%
+this we don't have that and we have the
+the mass factors and the force constants
+
+ align:start position:0%
+the mass factors and the force constants
+ 
+
+ align:start position:0%
+the mass factors and the force constants
+so we're
+
+ align:start position:0%
+so we're
+ 
+
+ align:start position:0%
+so we're
+going to use perturbation theory to get
+
+ align:start position:0%
+going to use perturbation theory to get
+ 
+
+ align:start position:0%
+going to use perturbation theory to get
+all that information
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay now
+
+ align:start position:0%
+okay now
+ 
+
+ align:start position:0%
+okay now
+it doesn't really matter if I don't
+
+ align:start position:0%
+it doesn't really matter if I don't
+ 
+
+ align:start position:0%
+it doesn't really matter if I don't
+finish these notes I won't because I've
+
+ align:start position:0%
+finish these notes I won't because I've
+ 
+
+ align:start position:0%
+finish these notes I won't because I've
+already done the important stuff you
+
+ align:start position:0%
+already done the important stuff you
+ 
+
+ align:start position:0%
+already done the important stuff you
+know the important thing is that we're
+
+ align:start position:0%
+know the important thing is that we're
+ 
+
+ align:start position:0%
+know the important thing is that we're
+going to use perturbation theory we have
+
+ align:start position:0%
+going to use perturbation theory we have
+ 
+
+ align:start position:0%
+going to use perturbation theory we have
+a trick for simplifying all of the
+
+ align:start position:0%
+a trick for simplifying all of the
+ 
+
+ align:start position:0%
+a trick for simplifying all of the
+matrix elements we have a way of telling
+
+ align:start position:0%
+matrix elements we have a way of telling
+ 
+
+ align:start position:0%
+matrix elements we have a way of telling
+a computer how to evaluate all the
+
+ align:start position:0%
+a computer how to evaluate all the
+ 
+
+ align:start position:0%
+a computer how to evaluate all the
+matrix elements and how to assemble them
+
+ align:start position:0%
+matrix elements and how to assemble them
+ 
+
+ align:start position:0%
+matrix elements and how to assemble them
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+but there are some more really beautiful
+
+ align:start position:0%
+but there are some more really beautiful
+ 
+
+ align:start position:0%
+but there are some more really beautiful
+stuff here that I want to talk
+
+ align:start position:0%
+stuff here that I want to talk
+ 
+
+ align:start position:0%
+stuff here that I want to talk
+about a little bit
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+you know the formula for the first order
+
+ align:start position:0%
+you know the formula for the first order
+ 
+
+ align:start position:0%
+you know the formula for the first order
+correction that to the energy that's the
+
+ align:start position:0%
+correction that to the energy that's the
+ 
+
+ align:start position:0%
+correction that to the energy that's the
+diagonal element of the perturbation
+
+ align:start position:0%
+diagonal element of the perturbation
+ 
+
+ align:start position:0%
+diagonal element of the perturbation
+term you know the formula for second
+
+ align:start position:0%
+term you know the formula for second
+ 
+
+ align:start position:0%
+term you know the formula for second
+order correction we have e to I is going
+
+ align:start position:0%
+order correction we have e to I is going
+ 
+
+ align:start position:0%
+order correction we have e to I is going
+to be the sum over j not equal to i h i
+
+ align:start position:0%
+to be the sum over j not equal to i h i
+ 
+
+ align:start position:0%
+to be the sum over j not equal to i h i
+j HJ
+
+ align:start position:0%
+j HJ
+ 
+
+ align:start position:0%
+j HJ
+I /
+
+ align:start position:0%
+I /
+ 
+
+ align:start position:0%
+I /
+e I 0 minus e j you know these things
+
+ align:start position:0%
+e I 0 minus e j you know these things
+ 
+
+ align:start position:0%
+e I 0 minus e j you know these things
+are just combinations of omegas so
+
+ align:start position:0%
+are just combinations of omegas so
+ 
+
+ align:start position:0%
+are just combinations of omegas so
+the energy nominees are really easy to
+
+ align:start position:0%
+the energy nominees are really easy to
+ 
+
+ align:start position:0%
+the energy nominees are really easy to
+write because it's basically you know
+
+ align:start position:0%
+write because it's basically you know
+ 
+
+ align:start position:0%
+write because it's basically you know
+you have energy levels which are
+
+ align:start position:0%
+you have energy levels which are
+ 
+
+ align:start position:0%
+you have energy levels which are
+expressed as you know three quantum mode
+
+ align:start position:0%
+expressed as you know three quantum mode
+ 
+
+ align:start position:0%
+expressed as you know three quantum mode
+1 plus 2 of mode 2 etc and you take
+
+ align:start position:0%
+1 plus 2 of mode 2 etc and you take
+ 
+
+ align:start position:0%
+1 plus 2 of mode 2 etc and you take
+those differences it's just some number
+
+ align:start position:0%
+those differences it's just some number
+ 
+
+ align:start position:0%
+those differences it's just some number
+times
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the different values of Omega so this is
+
+ align:start position:0%
+the different values of Omega so this is
+ 
+
+ align:start position:0%
+the different values of Omega so this is
+easy these are easy to because they're
+
+ align:start position:0%
+easy these are easy to because they're
+ 
+
+ align:start position:0%
+easy these are easy to because they're
+matrix elements of things like q1 q2
+
+ align:start position:0%
+matrix elements of things like q1 q2
+ 
+
+ align:start position:0%
+matrix elements of things like q1 q2
+squared so you could you write these
+
+ align:start position:0%
+squared so you could you write these
+ 
+
+ align:start position:0%
+squared so you could you write these
+things down and generally
+
+ align:start position:0%
+things down and generally
+ 
+
+ align:start position:0%
+things down and generally
+their matrix element squared so you get
+
+ align:start position:0%
+their matrix element squared so you get
+ 
+
+ align:start position:0%
+their matrix element squared so you get
+square roots of things from this and you
+
+ align:start position:0%
+square roots of things from this and you
+ 
+
+ align:start position:0%
+square roots of things from this and you
+just kill the square roots okay
+
+ align:start position:0%
+just kill the square roots okay
+ 
+
+ align:start position:0%
+just kill the square roots okay
+and so there's all sorts of very
+
+ align:start position:0%
+and so there's all sorts of very
+ 
+
+ align:start position:0%
+and so there's all sorts of very
+wonderful things but now again
+
+ align:start position:0%
+wonderful things but now again
+ 
+
+ align:start position:0%
+wonderful things but now again
+suppose you had q1 q2 squared you want
+
+ align:start position:0%
+suppose you had q1 q2 squared you want
+ 
+
+ align:start position:0%
+suppose you had q1 q2 squared you want
+to you want to make a list of all of the
+
+ align:start position:0%
+to you want to make a list of all of the
+ 
+
+ align:start position:0%
+to you want to make a list of all of the
+possible non zero matrix elements so we
+
+ align:start position:0%
+possible non zero matrix elements so we
+ 
+
+ align:start position:0%
+possible non zero matrix elements so we
+have Delta v1 plus and minus 1 we have
+
+ align:start position:0%
+have Delta v1 plus and minus 1 we have
+ 
+
+ align:start position:0%
+have Delta v1 plus and minus 1 we have
+Delta V 2 of 0 plus or minus 2 and so
+
+ align:start position:0%
+Delta V 2 of 0 plus or minus 2 and so
+ 
+
+ align:start position:0%
+Delta V 2 of 0 plus or minus 2 and so
+there are there
+
+ align:start position:0%
+there are there
+ 
+
+ align:start position:0%
+there are there
+are if
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+we write Delta V 1 Delta V 2 for
+
+ align:start position:0%
+we write Delta V 1 Delta V 2 for
+ 
+
+ align:start position:0%
+we write Delta V 1 Delta V 2 for
+the possible selection rules we have
+
+ align:start position:0%
+the possible selection rules we have
+ 
+
+ align:start position:0%
+the possible selection rules we have
+plus 1 plus 2
+
+ align:start position:0%
+plus 1 plus 2
+ 
+
+ align:start position:0%
+plus 1 plus 2
+minus
+
+ align:start position:0%
+minus
+ 
+
+ align:start position:0%
+minus
+one plus two plus one
+
+ align:start position:0%
+one plus two plus one
+ 
+
+ align:start position:0%
+one plus two plus one
+minus
+
+ align:start position:0%
+minus
+ 
+
+ align:start position:0%
+minus
+two minus
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+one minus two so
+
+ align:start position:0%
+one minus two so
+ 
+
+ align:start position:0%
+one minus two so
+there are four possible combinations of
+
+ align:start position:0%
+there are four possible combinations of
+ 
+
+ align:start position:0%
+there are four possible combinations of
+not dial matrix' now as soon as you
+
+ align:start position:0%
+not dial matrix' now as soon as you
+ 
+
+ align:start position:0%
+not dial matrix' now as soon as you
+write this you know oh well my goodness
+
+ align:start position:0%
+write this you know oh well my goodness
+ 
+
+ align:start position:0%
+write this you know oh well my goodness
+a 1
+
+ align:start position:0%
+a 1
+ 
+
+ align:start position:0%
+a 1
+dagger a 2 dagger squared the the term
+
+ align:start position:0%
+dagger a 2 dagger squared the the term
+ 
+
+ align:start position:0%
+dagger a 2 dagger squared the the term
+that you want that that multiple that
+
+ align:start position:0%
+that you want that that multiple that
+ 
+
+ align:start position:0%
+that you want that that multiple that
+controls this guy is that the term that
+
+ align:start position:0%
+controls this guy is that the term that
+ 
+
+ align:start position:0%
+controls this guy is that the term that
+you want for this is a 1 a 2 dagger
+
+ align:start position:0%
+you want for this is a 1 a 2 dagger
+ 
+
+ align:start position:0%
+you want for this is a 1 a 2 dagger
+squared so all of the possible non zero
+
+ align:start position:0%
+squared so all of the possible non zero
+ 
+
+ align:start position:0%
+squared so all of the possible non zero
+matrix elements tell you go and get this
+
+ align:start position:0%
+matrix elements tell you go and get this
+ 
+
+ align:start position:0%
+matrix elements tell you go and get this
+combination of a Zen a daggers and what
+
+ align:start position:0%
+combination of a Zen a daggers and what
+ 
+
+ align:start position:0%
+combination of a Zen a daggers and what
+was the number in front of that that you
+
+ align:start position:0%
+was the number in front of that that you
+ 
+
+ align:start position:0%
+was the number in front of that that you
+got when you expand it cute this
+
+ align:start position:0%
+got when you expand it cute this
+ 
+
+ align:start position:0%
+got when you expand it cute this
+is very easy to tell the computer what
+
+ align:start position:0%
+is very easy to tell the computer what
+ 
+
+ align:start position:0%
+is very easy to tell the computer what
+to do and so you
+
+ align:start position:0%
+to do and so you
+ 
+
+ align:start position:0%
+to do and so you
+write down an operator that expresses
+
+ align:start position:0%
+write down an operator that expresses
+ 
+
+ align:start position:0%
+write down an operator that expresses
+the an ominous City you break it up into
+
+ align:start position:0%
+the an ominous City you break it up into
+ 
+
+ align:start position:0%
+the an ominous City you break it up into
+selection rules the selection rules
+
+ align:start position:0%
+selection rules the selection rules
+ 
+
+ align:start position:0%
+selection rules the selection rules
+tells you which combination of a Zen a
+
+ align:start position:0%
+tells you which combination of a Zen a
+ 
+
+ align:start position:0%
+tells you which combination of a Zen a
+daggers and then the little algebra you
+
+ align:start position:0%
+daggers and then the little algebra you
+ 
+
+ align:start position:0%
+daggers and then the little algebra you
+did at the beginning and the cue to the
+
+ align:start position:0%
+did at the beginning and the cue to the
+ 
+
+ align:start position:0%
+did at the beginning and the cue to the
+what enables you to finish the job the
+
+ align:start position:0%
+what enables you to finish the job the
+ 
+
+ align:start position:0%
+what enables you to finish the job the
+rest is awful because you're
+
+ align:start position:0%
+rest is awful because you're
+ 
+
+ align:start position:0%
+rest is awful because you're
+manipulating these huge sums of things
+
+ align:start position:0%
+manipulating these huge sums of things
+ 
+
+ align:start position:0%
+manipulating these huge sums of things
+which involve matrix
+
+ align:start position:0%
+which involve matrix
+ 
+
+ align:start position:0%
+which involve matrix
+elements of lots of constants in the
+
+ align:start position:0%
+elements of lots of constants in the
+ 
+
+ align:start position:0%
+elements of lots of constants in the
+numerator and in the denominator you
+
+ align:start position:0%
+numerator and in the denominator you
+ 
+
+ align:start position:0%
+numerator and in the denominator you
+have differences in omega ones and Omega
+
+ align:start position:0%
+have differences in omega ones and Omega
+ 
+
+ align:start position:0%
+have differences in omega ones and Omega
+2 s or sums it will make a ones in omega
+
+ align:start position:0%
+2 s or sums it will make a ones in omega
+ 
+
+ align:start position:0%
+2 s or sums it will make a ones in omega
+two but it's all automatic and you can
+
+ align:start position:0%
+two but it's all automatic and you can
+ 
+
+ align:start position:0%
+two but it's all automatic and you can
+work that out okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+you're proceeding along here you're
+
+ align:start position:0%
+you're proceeding along here you're
+ 
+
+ align:start position:0%
+you're proceeding along here you're
+systematically writing down all the
+
+ align:start position:0%
+systematically writing down all the
+ 
+
+ align:start position:0%
+systematically writing down all the
+terms in the perturbation expansion the
+
+ align:start position:0%
+terms in the perturbation expansion the
+ 
+
+ align:start position:0%
+terms in the perturbation expansion the
+second-order perturbation expansion and
+
+ align:start position:0%
+second-order perturbation expansion and
+ 
+
+ align:start position:0%
+second-order perturbation expansion and
+all of a sudden you get some number / 0
+
+ align:start position:0%
+all of a sudden you get some number / 0
+ 
+
+ align:start position:0%
+all of a sudden you get some number / 0
+and you
+
+ align:start position:0%
+and you
+ 
+
+ align:start position:0%
+and you
+know that this is bed and
+
+ align:start position:0%
+know that this is bed and
+ 
+
+ align:start position:0%
+know that this is bed and
+that
+
+ align:start position:0%
+that
+ 
+
+ align:start position:0%
+that
+corresponds to a resonance you know as
+
+ align:start position:0%
+corresponds to a resonance you know as
+ 
+
+ align:start position:0%
+corresponds to a resonance you know as
+soon as i wrote Omega 1 is approximately
+
+ align:start position:0%
+soon as i wrote Omega 1 is approximately
+ 
+
+ align:start position:0%
+soon as i wrote Omega 1 is approximately
+equal to Omega 2 2 Omega 2 we're going
+
+ align:start position:0%
+equal to Omega 2 2 Omega 2 we're going
+ 
+
+ align:start position:0%
+equal to Omega 2 2 Omega 2 we're going
+to have a resonance whenever we have
+
+ align:start position:0%
+to have a resonance whenever we have
+ 
+
+ align:start position:0%
+to have a resonance whenever we have
+Delta V 1 is equal to minus Delta V
+
+ align:start position:0%
+Delta V 1 is equal to minus Delta V
+ 
+
+ align:start position:0%
+Delta V 1 is equal to minus Delta V
+minus 2 Delta V 2 and so we can do this
+
+ align:start position:0%
+minus 2 Delta V 2 and so we can do this
+ 
+
+ align:start position:0%
+minus 2 Delta V 2 and so we can do this
+two different ways so they're going to
+
+ align:start position:0%
+two different ways so they're going to
+ 
+
+ align:start position:0%
+two different ways so they're going to
+be two different resonance terms and as
+
+ align:start position:0%
+be two different resonance terms and as
+ 
+
+ align:start position:0%
+be two different resonance terms and as
+long as we stay away from those
+
+ align:start position:0%
+long as we stay away from those
+ 
+
+ align:start position:0%
+long as we stay away from those
+resonance terms second order
+
+ align:start position:0%
+resonance terms second order
+ 
+
+ align:start position:0%
+resonance terms second order
+perturbation theory is fine but we have
+
+ align:start position:0%
+perturbation theory is fine but we have
+ 
+
+ align:start position:0%
+perturbation theory is fine but we have
+to do something that respects
+
+ align:start position:0%
+to do something that respects
+ 
+
+ align:start position:0%
+to do something that respects
+these resonant terms so what do you do
+
+ align:start position:0%
+these resonant terms so what do you do
+ 
+
+ align:start position:0%
+these resonant terms so what do you do
+we have non degenerate perturbation
+
+ align:start position:0%
+we have non degenerate perturbation
+ 
+
+ align:start position:0%
+we have non degenerate perturbation
+theory that means not degenerate well
+
+ align:start position:0%
+theory that means not degenerate well
+ 
+
+ align:start position:0%
+theory that means not degenerate well
+if you have degeneracy you have to say
+
+ align:start position:0%
+if you have degeneracy you have to say
+ 
+
+ align:start position:0%
+if you have degeneracy you have to say
+all forget order sorting I have to solve
+
+ align:start position:0%
+all forget order sorting I have to solve
+ 
+
+ align:start position:0%
+all forget order sorting I have to solve
+a secular equation I have to write down
+
+ align:start position:0%
+a secular equation I have to write down
+ 
+
+ align:start position:0%
+a secular equation I have to write down
+a block
+
+ align:start position:0%
+a block
+ 
+
+ align:start position:0%
+a block
+of the Hamiltonian which I find the
+
+ align:start position:0%
+of the Hamiltonian which I find the
+ 
+
+ align:start position:0%
+of the Hamiltonian which I find the
+eigenvalues and eigenvectors of and that
+
+ align:start position:0%
+eigenvalues and eigenvectors of and that
+ 
+
+ align:start position:0%
+eigenvalues and eigenvectors of and that
+deals with the residents and so it just
+
+ align:start position:0%
+deals with the residents and so it just
+ 
+
+ align:start position:0%
+deals with the residents and so it just
+tells okay so suppose we have what we
+
+ align:start position:0%
+tells okay so suppose we have what we
+ 
+
+ align:start position:0%
+tells okay so suppose we have what we
+call a poly add quantum number this is
+
+ align:start position:0%
+call a poly add quantum number this is
+ 
+
+ align:start position:0%
+call a poly add quantum number this is
+just a way of saying well
+
+ align:start position:0%
+just a way of saying well
+ 
+
+ align:start position:0%
+just a way of saying well
+what's resonant suppo and that is to v1
+
+ align:start position:0%
+what's resonant suppo and that is to v1
+ 
+
+ align:start position:0%
+what's resonant suppo and that is to v1
+plus v2 okay
+
+ align:start position:0%
+plus v2 okay
+ 
+
+ align:start position:0%
+plus v2 okay
+and so this is a little code that says I
+
+ align:start position:0%
+and so this is a little code that says I
+ 
+
+ align:start position:0%
+and so this is a little code that says I
+suppose I have the tenth p equals 10 I
+
+ align:start position:0%
+suppose I have the tenth p equals 10 I
+ 
+
+ align:start position:0%
+suppose I have the tenth p equals 10 I
+can
+
+ align:start position:0%
+can
+ 
+
+ align:start position:0%
+can
+then write down for p equals 10 all of
+
+ align:start position:0%
+then write down for p equals 10 all of
+ 
+
+ align:start position:0%
+then write down for p equals 10 all of
+the zero order states that are resonant
+
+ align:start position:0%
+the zero order states that are resonant
+ 
+
+ align:start position:0%
+the zero order states that are resonant
+let's just do it you know I don't have P
+
+ align:start position:0%
+let's just do it you know I don't have P
+ 
+
+ align:start position:0%
+let's just do it you know I don't have P
+equals 10 in the notes so i know that to
+
+ align:start position:0%
+equals 10 in the notes so i know that to
+ 
+
+ align:start position:0%
+equals 10 in the notes so i know that to
+get p equals 10 i can do that with zero
+
+ align:start position:0%
+get p equals 10 i can do that with zero
+ 
+
+ align:start position:0%
+get p equals 10 i can do that with zero
+right
+
+ align:start position:0%
+right
+ 
+
+ align:start position:0%
+right
+I can get that with 18 I can 2634
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+to
+
+ align:start position:0%
+to
+ 
+
+ align:start position:0%
+to
+oops
+
+ align:start position:0%
+oops
+ 
+
+ align:start position:0%
+oops
+
+ align:start position:0%
+ 
+
+ align:start position:0%
+and 50
+
+ align:start position:0%
+and 50
+ 
+
+ align:start position:0%
+and 50
+one two three four five six so there's
+
+ align:start position:0%
+one two three four five six so there's
+ 
+
+ align:start position:0%
+one two three four five six so there's
+60 order states in this Holly ad which
+
+ align:start position:0%
+60 order states in this Holly ad which
+ 
+
+ align:start position:0%
+60 order states in this Holly ad which
+with p equals 10 so that's a scaling
+
+ align:start position:0%
+with p equals 10 so that's a scaling
+ 
+
+ align:start position:0%
+with p equals 10 so that's a scaling
+rule for membership that's a rule that's
+
+ align:start position:0%
+rule for membership that's a rule that's
+ 
+
+ align:start position:0%
+rule for membership that's a rule that's
+okay I've recognized what is the
+
+ align:start position:0%
+okay I've recognized what is the
+ 
+
+ align:start position:0%
+okay I've recognized what is the
+resonance condition that combining
+
+ align:start position:0%
+resonance condition that combining
+ 
+
+ align:start position:0%
+resonance condition that combining
+things this way and so since Omega 1 is
+
+ align:start position:0%
+things this way and so since Omega 1 is
+ 
+
+ align:start position:0%
+things this way and so since Omega 1 is
+twice as big as Omega 2 for each quantum
+
+ align:start position:0%
+twice as big as Omega 2 for each quantum
+ 
+
+ align:start position:0%
+twice as big as Omega 2 for each quantum
+in omega 1 I get two points for each
+
+ align:start position:0%
+in omega 1 I get two points for each
+ 
+
+ align:start position:0%
+in omega 1 I get two points for each
+quantum and Omega 1 I get one point
+
+ align:start position:0%
+quantum and Omega 1 I get one point
+ 
+
+ align:start position:0%
+quantum and Omega 1 I get one point
+that's where these polyethers come from
+
+ align:start position:0%
+that's where these polyethers come from
+ 
+
+ align:start position:0%
+that's where these polyethers come from
+and then as soon as I say what this is I
+
+ align:start position:0%
+and then as soon as I say what this is I
+ 
+
+ align:start position:0%
+and then as soon as I say what this is I
+discover that i have a six by six or
+
+ align:start position:0%
+discover that i have a six by six or
+ 
+
+ align:start position:0%
+discover that i have a six by six or
+whatever matrix that I have to
+
+ align:start position:0%
+whatever matrix that I have to
+ 
+
+ align:start position:0%
+whatever matrix that I have to
+diagonalize and then I recognize that i
+
+ align:start position:0%
+diagonalize and then I recognize that i
+ 
+
+ align:start position:0%
+diagonalize and then I recognize that i
+only have couplings between successive
+
+ align:start position:0%
+only have couplings between successive
+ 
+
+ align:start position:0%
+only have couplings between successive
+members in this list and so
+
+ align:start position:0%
+members in this list and so
+ 
+
+ align:start position:0%
+members in this list and so
+i can write the matrix and it's going to
+
+ align:start position:0%
+i can write the matrix and it's going to
+ 
+
+ align:start position:0%
+i can write the matrix and it's going to
+have the form of in
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this particular one zeros numbers
+
+ align:start position:0%
+this particular one zeros numbers
+ 
+
+ align:start position:0%
+this particular one zeros numbers
+zeros
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and so then the job is just to fill out
+
+ align:start position:0%
+and so then the job is just to fill out
+ 
+
+ align:start position:0%
+and so then the job is just to fill out
+these numbers and the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+nice thing about this is all the trash
+
+ align:start position:0%
+nice thing about this is all the trash
+ 
+
+ align:start position:0%
+nice thing about this is all the trash
+comes out in front and these are just
+
+ align:start position:0%
+comes out in front and these are just
+ 
+
+ align:start position:0%
+comes out in front and these are just
+square roots of integers and
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so you all of a sudden you get an
+
+ align:start position:0%
+so you all of a sudden you get an
+ 
+
+ align:start position:0%
+so you all of a sudden you get an
+effective Hamiltonian with trash which
+
+ align:start position:0%
+effective Hamiltonian with trash which
+ 
+
+ align:start position:0%
+effective Hamiltonian with trash which
+you can or cannot if you choose to deal
+
+ align:start position:0%
+you can or cannot if you choose to deal
+ 
+
+ align:start position:0%
+you can or cannot if you choose to deal
+with and then the critical structure
+
+ align:start position:0%
+with and then the critical structure
+ 
+
+ align:start position:0%
+with and then the critical structure
+which is universal along
+
+ align:start position:0%
+which is universal along
+ 
+
+ align:start position:0%
+which is universal along
+the diagonal and depending on which
+
+ align:start position:0%
+the diagonal and depending on which
+ 
+
+ align:start position:0%
+the diagonal and depending on which
+value of P you get a different matrix
+
+ align:start position:0%
+value of P you get a different matrix
+ 
+
+ align:start position:0%
+value of P you get a different matrix
+but
+
+ align:start position:0%
+but
+ 
+
+ align:start position:0%
+but
+it's got the same structure and so
+
+ align:start position:0%
+it's got the same structure and so
+ 
+
+ align:start position:0%
+it's got the same structure and so
+and there's only one thing that controls
+
+ align:start position:0%
+and there's only one thing that controls
+ 
+
+ align:start position:0%
+and there's only one thing that controls
+the energy levels and that's this trash
+
+ align:start position:0%
+the energy levels and that's this trash
+ 
+
+ align:start position:0%
+the energy levels and that's this trash
+out here and
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so what you've done is you've dealt with
+
+ align:start position:0%
+so what you've done is you've dealt with
+ 
+
+ align:start position:0%
+so what you've done is you've dealt with
+a resonance that's a classical resonance
+
+ align:start position:0%
+a resonance that's a classical resonance
+ 
+
+ align:start position:0%
+a resonance that's a classical resonance
+because you've got two things that
+
+ align:start position:0%
+because you've got two things that
+ 
+
+ align:start position:0%
+because you've got two things that
+oscillate it integer multiples it's a
+
+ align:start position:0%
+oscillate it integer multiples it's a
+ 
+
+ align:start position:0%
+oscillate it integer multiples it's a
+quantum mechanical resonance and you
+
+ align:start position:0%
+quantum mechanical resonance and you
+ 
+
+ align:start position:0%
+quantum mechanical resonance and you
+just wrote down some thing some problem
+
+ align:start position:0%
+just wrote down some thing some problem
+ 
+
+ align:start position:0%
+just wrote down some thing some problem
+that you have to solve to get the
+
+ align:start position:0%
+that you have to solve to get the
+ 
+
+ align:start position:0%
+that you have to solve to get the
+correct linear combination of states
+
+ align:start position:0%
+correct linear combination of states
+ 
+
+ align:start position:0%
+correct linear combination of states
+that deal with that resonance now the
+
+ align:start position:0%
+that deal with that resonance now the
+ 
+
+ align:start position:0%
+that deal with that resonance now the
+next thing you have to do is to say well
+
+ align:start position:0%
+next thing you have to do is to say well
+ 
+
+ align:start position:0%
+next thing you have to do is to say well
+hold your horses we could do this but
+
+ align:start position:0%
+hold your horses we could do this but
+ 
+
+ align:start position:0%
+hold your horses we could do this but
+there are and
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this is the last thing I'm going to say
+
+ align:start position:0%
+this is the last thing I'm going to say
+ 
+
+ align:start position:0%
+this is the last thing I'm going to say
+so you don't have to get impatient i'm
+
+ align:start position:0%
+so you don't have to get impatient i'm
+ 
+
+ align:start position:0%
+so you don't have to get impatient i'm
+not going to cheat this again we're done
+
+ align:start position:0%
+not going to cheat this again we're done
+ 
+
+ align:start position:0%
+not going to cheat this again we're done
+but so the hamiltonian is arranged in
+
+ align:start position:0%
+but so the hamiltonian is arranged in
+ 
+
+ align:start position:0%
+but so the hamiltonian is arranged in
+the form of blocks along the diagonal
+
+ align:start position:0%
+the form of blocks along the diagonal
+ 
+
+ align:start position:0%
+the form of blocks along the diagonal
+and as you go down the block get bigger
+
+ align:start position:0%
+and as you go down the block get bigger
+ 
+
+ align:start position:0%
+and as you go down the block get bigger
+and bigger each of these blocks is
+
+ align:start position:0%
+and bigger each of these blocks is
+ 
+
+ align:start position:0%
+and bigger each of these blocks is
+generated by the same constants in the
+
+ align:start position:0%
+generated by the same constants in the
+ 
+
+ align:start position:0%
+generated by the same constants in the
+previous one and so there's nothing new
+
+ align:start position:0%
+previous one and so there's nothing new
+ 
+
+ align:start position:0%
+previous one and so there's nothing new
+except that you have to write them down
+
+ align:start position:0%
+except that you have to write them down
+ 
+
+ align:start position:0%
+except that you have to write them down
+but sometimes there are matrix elements
+
+ align:start position:0%
+but sometimes there are matrix elements
+ 
+
+ align:start position:0%
+but sometimes there are matrix elements
+outside of blocks and you have to fold
+
+ align:start position:0%
+outside of blocks and you have to fold
+ 
+
+ align:start position:0%
+outside of blocks and you have to fold
+them into the blocks before you
+
+ align:start position:0%
+them into the blocks before you
+ 
+
+ align:start position:0%
+them into the blocks before you
+diagonalize them that's
+
+ align:start position:0%
+diagonalize them that's
+ 
+
+ align:start position:0%
+diagonalize them that's
+called a van vleck transformation it's a
+
+ align:start position:0%
+called a van vleck transformation it's a
+ 
+
+ align:start position:0%
+called a van vleck transformation it's a
+fancy kind of second order perturbation
+
+ align:start position:0%
+fancy kind of second order perturbation
+ 
+
+ align:start position:0%
+fancy kind of second order perturbation
+theory and so what you do is you
+
+ align:start position:0%
+theory and so what you do is you
+ 
+
+ align:start position:0%
+theory and so what you do is you
+say okay if there is an out of block
+
+ align:start position:0%
+say okay if there is an out of block
+ 
+
+ align:start position:0%
+say okay if there is an out of block
+state that interact strongly between
+
+ align:start position:0%
+state that interact strongly between
+ 
+
+ align:start position:0%
+state that interact strongly between
+these
+
+ align:start position:0%
+these
+ 
+
+ align:start position:0%
+these
+it has a strong enough interaction
+
+ align:start position:0%
+it has a strong enough interaction
+ 
+
+ align:start position:0%
+it has a strong enough interaction
+between these two that could mess up the
+
+ align:start position:0%
+between these two that could mess up the
+ 
+
+ align:start position:0%
+between these two that could mess up the
+the detailed structure in here we fold
+
+ align:start position:0%
+the detailed structure in here we fold
+ 
+
+ align:start position:0%
+the detailed structure in here we fold
+the effect of this dated here and so
+
+ align:start position:0%
+the effect of this dated here and so
+ 
+
+ align:start position:0%
+the effect of this dated here and so
+what do you do you say the
+
+ align:start position:0%
+what do you do you say the
+ 
+
+ align:start position:0%
+what do you do you say the
+transformed
+
+ align:start position:0%
+transformed
+ 
+
+ align:start position:0%
+transformed
+Hamiltonian correcting for out of block
+
+ align:start position:0%
+Hamiltonian correcting for out of block
+ 
+
+ align:start position:0%
+Hamiltonian correcting for out of block
+States so here we have the IJ element in
+
+ align:start position:0%
+States so here we have the IJ element in
+ 
+
+ align:start position:0%
+States so here we have the IJ element in
+a block we
+
+ align:start position:0%
+a block we
+ 
+
+ align:start position:0%
+a block we
+write that as I que
+
+ align:start position:0%
+write that as I que
+ 
+
+ align:start position:0%
+write that as I que
+que je and these are perturbation terms
+
+ align:start position:0%
+que je and these are perturbation terms
+ 
+
+ align:start position:0%
+que je and these are perturbation terms
+sum over K and we have e i0
+
+ align:start position:0%
+sum over K and we have e i0
+ 
+
+ align:start position:0%
+sum over K and we have e i0
+plus e j 0 over 2 minus e k 0 now this
+
+ align:start position:0%
+plus e j 0 over 2 minus e k 0 now this
+ 
+
+ align:start position:0%
+plus e j 0 over 2 minus e k 0 now this
+is a formula that was proposed by Van
+
+ align:start position:0%
+is a formula that was proposed by Van
+ 
+
+ align:start position:0%
+is a formula that was proposed by Van
+Vleck and you
+
+ align:start position:0%
+Vleck and you
+ 
+
+ align:start position:0%
+Vleck and you
+know it looks just like second-order
+
+ align:start position:0%
+know it looks just like second-order
+ 
+
+ align:start position:0%
+know it looks just like second-order
+perturbation theory we have a product of
+
+ align:start position:0%
+perturbation theory we have a product of
+ 
+
+ align:start position:0%
+perturbation theory we have a product of
+off diagonal matrix elements but it's a
+
+ align:start position:0%
+off diagonal matrix elements but it's a
+ 
+
+ align:start position:0%
+off diagonal matrix elements but it's a
+product where the initial and final
+
+ align:start position:0%
+product where the initial and final
+ 
+
+ align:start position:0%
+product where the initial and final
+index is different and this
+
+ align:start position:0%
+index is different and this
+ 
+
+ align:start position:0%
+index is different and this
+is an average over the initial and final
+
+ align:start position:0%
+is an average over the initial and final
+ 
+
+ align:start position:0%
+is an average over the initial and final
+zero order states within the block and
+
+ align:start position:0%
+zero order states within the block and
+ 
+
+ align:start position:0%
+zero order states within the block and
+that's not a big deal because the energy
+
+ align:start position:0%
+that's not a big deal because the energy
+ 
+
+ align:start position:0%
+that's not a big deal because the energy
+difference within a block is small
+
+ align:start position:0%
+difference within a block is small
+ 
+
+ align:start position:0%
+difference within a block is small
+compared to the difference between
+
+ align:start position:0%
+compared to the difference between
+ 
+
+ align:start position:0%
+compared to the difference between
+states in the block and outside the
+
+ align:start position:0%
+states in the block and outside the
+ 
+
+ align:start position:0%
+states in the block and outside the
+block and so basically this is just a
+
+ align:start position:0%
+block and so basically this is just a
+ 
+
+ align:start position:0%
+block and so basically this is just a
+computational
+
+ align:start position:0%
+computational
+ 
+
+ align:start position:0%
+computational
+simplification and so we have energy
+
+ align:start position:0%
+simplification and so we have energy
+ 
+
+ align:start position:0%
+simplification and so we have energy
+differences we have matrix elements and
+
+ align:start position:0%
+differences we have matrix elements and
+ 
+
+ align:start position:0%
+differences we have matrix elements and
+that provides us with a way of
+
+ align:start position:0%
+that provides us with a way of
+ 
+
+ align:start position:0%
+that provides us with a way of
+compensating for the effect of out of
+
+ align:start position:0%
+compensating for the effect of out of
+ 
+
+ align:start position:0%
+compensating for the effect of out of
+block not resonant terms on the intra
+
+ align:start position:0%
+block not resonant terms on the intra
+ 
+
+ align:start position:0%
+block not resonant terms on the intra
+block energies and that improves the
+
+ align:start position:0%
+block energies and that improves the
+ 
+
+ align:start position:0%
+block energies and that improves the
+accuracy of the calculation and that's
+
+ align:start position:0%
+accuracy of the calculation and that's
+ 
+
+ align:start position:0%
+accuracy of the calculation and that's
+really the whole story and so
+
+ align:start position:0%
+really the whole story and so
+ 
+
+ align:start position:0%
+really the whole story and so
+I don't want to say any more this
+
+ align:start position:0%
+I don't want to say any more this
+ 
+
+ align:start position:0%
+I don't want to say any more this
+algebraically
+
+ align:start position:0%
+algebraically
+ 
+
+ align:start position:0%
+algebraically
+is awful but again you know once you've
+
+ align:start position:0%
+is awful but again you know once you've
+ 
+
+ align:start position:0%
+is awful but again you know once you've
+taught your computer the other stuff you
+
+ align:start position:0%
+taught your computer the other stuff you
+ 
+
+ align:start position:0%
+taught your computer the other stuff you
+can teach the computer this too because
+
+ align:start position:0%
+can teach the computer this too because
+ 
+
+ align:start position:0%
+can teach the computer this too because
+there's nothing new here and
+
+ align:start position:0%
+there's nothing new here and
+ 
+
+ align:start position:0%
+there's nothing new here and
+there's nothing new here
+
+ align:start position:0%
+there's nothing new here
+ 
+
+ align:start position:0%
+there's nothing new here
+and just integers times trash and
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so so
+
+ align:start position:0%
+so so
+ 
+
+ align:start position:0%
+so so
+that's it I this is an example of you
+
+ align:start position:0%
+that's it I this is an example of you
+ 
+
+ align:start position:0%
+that's it I this is an example of you
+know you start with the effective
+
+ align:start position:0%
+know you start with the effective
+ 
+
+ align:start position:0%
+know you start with the effective
+Hamiltonian for a one-dimensional system
+
+ align:start position:0%
+Hamiltonian for a one-dimensional system
+ 
+
+ align:start position:0%
+Hamiltonian for a one-dimensional system
+and you deal with that are Missy you
+
+ align:start position:0%
+and you deal with that are Missy you
+ 
+
+ align:start position:0%
+and you deal with that are Missy you
+discover that you simplify the coupling
+
+ align:start position:0%
+discover that you simplify the coupling
+ 
+
+ align:start position:0%
+discover that you simplify the coupling
+terms in to a form that's really really
+
+ align:start position:0%
+terms in to a form that's really really
+ 
+
+ align:start position:0%
+terms in to a form that's really really
+convenient for sticking it to mr.
+
+ align:start position:0%
+convenient for sticking it to mr.
+ 
+
+ align:start position:0%
+convenient for sticking it to mr.
+computer and then you say okay well now
+
+ align:start position:0%
+computer and then you say okay well now
+ 
+
+ align:start position:0%
+computer and then you say okay well now
+we have several oscillators and we have
+
+ align:start position:0%
+we have several oscillators and we have
+ 
+
+ align:start position:0%
+we have several oscillators and we have
+the diagonal anharmonicity we know about
+
+ align:start position:0%
+the diagonal anharmonicity we know about
+ 
+
+ align:start position:0%
+the diagonal anharmonicity we know about
+that and we have the cross an ominous
+
+ align:start position:0%
+that and we have the cross an ominous
+ 
+
+ align:start position:0%
+that and we have the cross an ominous
+ease between the different modes and we
+
+ align:start position:0%
+ease between the different modes and we
+ 
+
+ align:start position:0%
+ease between the different modes and we
+just represent them phenomenologically
+
+ align:start position:0%
+just represent them phenomenologically
+ 
+
+ align:start position:0%
+just represent them phenomenologically
+as coupling terms and we have a sense
+
+ align:start position:0%
+as coupling terms and we have a sense
+ 
+
+ align:start position:0%
+as coupling terms and we have a sense
+for which are the important ones and
+
+ align:start position:0%
+for which are the important ones and
+ 
+
+ align:start position:0%
+for which are the important ones and
+then we say be careful of residence and
+
+ align:start position:0%
+then we say be careful of residence and
+ 
+
+ align:start position:0%
+then we say be careful of residence and
+we have a way of fixing residents and
+
+ align:start position:0%
+we have a way of fixing residents and
+ 
+
+ align:start position:0%
+we have a way of fixing residents and
+then we're done we we have a machine
+
+ align:start position:0%
+then we're done we we have a machine
+ 
+
+ align:start position:0%
+then we're done we we have a machine
+that can represent the energy levels it
+
+ align:start position:0%
+that can represent the energy levels it
+ 
+
+ align:start position:0%
+that can represent the energy levels it
+will not only represent the energy
+
+ align:start position:0%
+will not only represent the energy
+ 
+
+ align:start position:0%
+will not only represent the energy
+levels it will give you things that are
+
+ align:start position:0%
+levels it will give you things that are
+ 
+
+ align:start position:0%
+levels it will give you things that are
+almost like wave functions with which
+
+ align:start position:0%
+almost like wave functions with which
+ 
+
+ align:start position:0%
+almost like wave functions with which
+you can calculate properties other than
+
+ align:start position:0%
+you can calculate properties other than
+ 
+
+ align:start position:0%
+you can calculate properties other than
+the energy but you have to be careful
+
+ align:start position:0%
+the energy but you have to be careful
+ 
+
+ align:start position:0%
+the energy but you have to be careful
+but
+
+ align:start position:0%
+but
+ 
+
+ align:start position:0%
+but
+you only have to be careful because of
+
+ align:start position:0%
+you only have to be careful because of
+ 
+
+ align:start position:0%
+you only have to be careful because of
+these out of block things and that's a
+
+ align:start position:0%
+these out of block things and that's a
+ 
+
+ align:start position:0%
+these out of block things and that's a
+subtle thing and most people can go
+
+ align:start position:0%
+subtle thing and most people can go
+ 
+
+ align:start position:0%
+subtle thing and most people can go
+through their life without worrying
+
+ align:start position:0%
+through their life without worrying
+ 
+
+ align:start position:0%
+through their life without worrying
+about that but there is a subtle
+
+ align:start position:0%
+about that but there is a subtle
+ 
+
+ align:start position:0%
+about that but there is a subtle
+business here and if you're a quantum
+
+ align:start position:0%
+business here and if you're a quantum
+ 
+
+ align:start position:0%
+business here and if you're a quantum
+chemist you need to know about that
+
+ align:start position:0%
+chemist you need to know about that
+ 
+
+ align:start position:0%
+chemist you need to know about that
+because you're going to be comparing
+
+ align:start position:0%
+because you're going to be comparing
+ 
+
+ align:start position:0%
+because you're going to be comparing
+what you calculate against experiment
+
+ align:start position:0%
+what you calculate against experiment
+ 
+
+ align:start position:0%
+what you calculate against experiment
+and it'll be apples and oranges but
+
+ align:start position:0%
+and it'll be apples and oranges but
+ 
+
+ align:start position:0%
+and it'll be apples and oranges but
+for experimental lists you don't really
+
+ align:start position:0%
+for experimental lists you don't really
+ 
+
+ align:start position:0%
+for experimental lists you don't really
+too worried about that too much so what
+
+ align:start position:0%
+too worried about that too much so what
+ 
+
+ align:start position:0%
+too worried about that too much so what
+we're going to start doing next lecture
+
+ align:start position:0%
+we're going to start doing next lecture
+ 
+
+ align:start position:0%
+we're going to start doing next lecture
+is start dealing with many electron
+
+ align:start position:0%
+is start dealing with many electron
+ 
+
+ align:start position:0%
+is start dealing with many electron
+atoms and what I want to do is I'm not
+
+ align:start position:0%
+atoms and what I want to do is I'm not
+ 
+
+ align:start position:0%
+atoms and what I want to do is I'm not
+going to teach you how to do quantum
+
+ align:start position:0%
+going to teach you how to do quantum
+ 
+
+ align:start position:0%
+going to teach you how to do quantum
+chemistry but I'm going to teach you how
+
+ align:start position:0%
+chemistry but I'm going to teach you how
+ 
+
+ align:start position:0%
+chemistry but I'm going to teach you how
+you can see the periodic structure the
+
+ align:start position:0%
+you can see the periodic structure the
+ 
+
+ align:start position:0%
+you can see the periodic structure the
+periodic table in the the control
+
+ align:start position:0%
+periodic table in the the control
+ 
+
+ align:start position:0%
+periodic table in the the control
+parameters that you use to build the
+
+ align:start position:0%
+parameters that you use to build the
+ 
+
+ align:start position:0%
+parameters that you use to build the
+energy levels of atoms out of and that
+
+ align:start position:0%
+energy levels of atoms out of and that
+ 
+
+ align:start position:0%
+energy levels of atoms out of and that
+then provides us with a rep a machinery
+
+ align:start position:0%
+then provides us with a rep a machinery
+ 
+
+ align:start position:0%
+then provides us with a rep a machinery
+that enables us to understand something
+
+ align:start position:0%
+that enables us to understand something
+ 
+
+ align:start position:0%
+that enables us to understand something
+about the energy levels of molecules and
+
+ align:start position:0%
+about the energy levels of molecules and
+ 
+
+ align:start position:0%
+about the energy levels of molecules and
+so it's when I started teaching this at
+
+ align:start position:0%
+so it's when I started teaching this at
+ 
+
+ align:start position:0%
+so it's when I started teaching this at
+MIT actually I I felt I have to show how
+
+ align:start position:0%
+MIT actually I I felt I have to show how
+ 
+
+ align:start position:0%
+MIT actually I I felt I have to show how
+the periodic table enters into the
+
+ align:start position:0%
+the periodic table enters into the
+ 
+
+ align:start position:0%
+the periodic table enters into the
+spectra of things and
+
+ align:start position:0%
+spectra of things and
+ 
+
+ align:start position:0%
+spectra of things and
+really a tremendous battle it's not so
+
+ align:start position:0%
+really a tremendous battle it's not so
+ 
+
+ align:start position:0%
+really a tremendous battle it's not so
+hard for atoms but it's really hard for
+
+ align:start position:0%
+hard for atoms but it's really hard for
+ 
+
+ align:start position:0%
+hard for atoms but it's really hard for
+molecules because you lose the spherical
+
+ align:start position:0%
+molecules because you lose the spherical
+ 
+
+ align:start position:0%
+molecules because you lose the spherical
+symmetry but there's still ways to make
+
+ align:start position:0%
+symmetry but there's still ways to make
+ 
+
+ align:start position:0%
+symmetry but there's still ways to make
+contact with periodicity and this is one
+
+ align:start position:0%
+contact with periodicity and this is one
+ 
+
+ align:start position:0%
+contact with periodicity and this is one
+of our central concepts shell structure
+
+ align:start position:0%
+of our central concepts shell structure
+ 
+
+ align:start position:0%
+of our central concepts shell structure
+and you know or but certain orbitals are
+
+ align:start position:0%
+and you know or but certain orbitals are
+ 
+
+ align:start position:0%
+and you know or but certain orbitals are
+small and shields well and other or
+
+ align:start position:0%
+small and shields well and other or
+ 
+
+ align:start position:0%
+small and shields well and other or
+below big and don't shield and all these
+
+ align:start position:0%
+below big and don't shield and all these
+ 
+
+ align:start position:0%
+below big and don't shield and all these
+concepts you know we learn as freshmen
+
+ align:start position:0%
+concepts you know we learn as freshmen
+ 
+
+ align:start position:0%
+concepts you know we learn as freshmen
+and it's
+
+ align:start position:0%
+and it's
+ 
+
+ align:start position:0%
+and it's
+certainly why I became a chemist and and
+
+ align:start position:0%
+certainly why I became a chemist and and
+ 
+
+ align:start position:0%
+certainly why I became a chemist and and
+so as a spectroscopy I want to do more
+
+ align:start position:0%
+so as a spectroscopy I want to do more
+ 
+
+ align:start position:0%
+so as a spectroscopy I want to do more
+than lip service to that and so we're
+
+ align:start position:0%
+than lip service to that and so we're
+ 
+
+ align:start position:0%
+than lip service to that and so we're
+going to go through some fairly
+
+ align:start position:0%
+going to go through some fairly
+ 
+
+ align:start position:0%
+going to go through some fairly
+elementary stuff on many electron atoms
+
+ align:start position:0%
+elementary stuff on many electron atoms
+ 
+
+ align:start position:0%
+elementary stuff on many electron atoms
+and then get into molecules and I think
+
+ align:start position:0%
+and then get into molecules and I think
+ 
+
+ align:start position:0%
+and then get into molecules and I think
+then it'll be a more traditional
+
+ align:start position:0%
+then it'll be a more traditional
+ 
+
+ align:start position:0%
+then it'll be a more traditional
+trajectory
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+through the relevant spectroscopic
+
+ align:start position:0%
+through the relevant spectroscopic
+ 
+
+ align:start position:0%
+through the relevant spectroscopic
+theory and but
+
+ align:start position:0%
+theory and but
+ 
+
+ align:start position:0%
+theory and but
+i do love atoms and you you'll probably
+
+ align:start position:0%
+i do love atoms and you you'll probably
+ 
+
+ align:start position:0%
+i do love atoms and you you'll probably
+say enough Adams already okay see you
+
+ align:start position:0%
+say enough Adams already okay see you
+ 
+
+ align:start position:0%
+say enough Adams already okay see you
+Wednesday oh yeah the
+
+ align:start position:0%
+Wednesday oh yeah the
+ 
+
+ align:start position:0%
+Wednesday oh yeah the
+kind of business that you show there
+
+ align:start position:0%
+kind of business that you show there
+ 
+
+ align:start position:0%
+kind of business that you show there
+where the omega 1.is proximately is
+
+ align:start position:0%
+where the omega 1.is proximately is
+ 
+
+ align:start position:0%
+where the omega 1.is proximately is
+that classical an analog to classical
+
+ align:start position:0%
+that classical an analog to classical
+ 
+
+ align:start position:0%
+that classical an analog to classical
+references p.s letters that are
+
+ align:start position:0%
+references p.s letters that are
+ 
+
+ align:start position:0%
+references p.s letters that are
+oscillating your mobile yes so two
+
+ align:start position:0%
+oscillating your mobile yes so two
+ 
+
+ align:start position:0%
+oscillating your mobile yes so two
+questions first of all how close do they
+
+ align:start position:0%
+questions first of all how close do they
+ 
+
+ align:start position:0%
+questions first of all how close do they
+have to be before you start caring well
+
+ align:start position:0%
+have to be before you start caring well
+ 
+
+ align:start position:0%
+have to be before you start caring well
+in is there some other kind of resonance
+
+ align:start position:0%
+in is there some other kind of resonance
+ 
+
+ align:start position:0%
+in is there some other kind of resonance
+that also comes up that somehow
+
+ align:start position:0%
+that also comes up that somehow
+ 
+
+ align:start position:0%
+that also comes up that somehow
+inherently
+
+ align:start position:0%
+inherently
+ 
+
+ align:start position:0%
+inherently
+no or what do you mean when you call it
+
+ align:start position:0%
+no or what do you mean when you call it
+ 
+
+ align:start position:0%
+no or what do you mean when you call it
+a classical both you've been in your car
+
+ align:start position:0%
+a classical both you've been in your car
+ 
+
+ align:start position:0%
+a classical both you've been in your car
+and its wheels aren't quite aligned and
+
+ align:start position:0%
+and its wheels aren't quite aligned and
+ 
+
+ align:start position:0%
+and its wheels aren't quite aligned and
+you're going over some road that has
+
+ align:start position:0%
+you're going over some road that has
+ 
+
+ align:start position:0%
+you're going over some road that has
+periodic structure and at a certain
+
+ align:start position:0%
+periodic structure and at a certain
+ 
+
+ align:start position:0%
+periodic structure and at a certain
+velocity you discover you bitter slow to
+
+ align:start position:0%
+velocity you discover you bitter slow to
+ 
+
+ align:start position:0%
+velocity you discover you bitter slow to
+slow down or speed up and that's a
+
+ align:start position:0%
+slow down or speed up and that's a
+ 
+
+ align:start position:0%
+slow down or speed up and that's a
+resonance because there's a natural
+
+ align:start position:0%
+resonance because there's a natural
+ 
+
+ align:start position:0%
+resonance because there's a natural
+mechanical resonance in the car and
+
+ align:start position:0%
+mechanical resonance in the car and
+ 
+
+ align:start position:0%
+mechanical resonance in the car and
+you're you're you're perturbing your
+
+ align:start position:0%
+you're you're you're perturbing your
+ 
+
+ align:start position:0%
+you're you're you're perturbing your
+system at an integer multiple or sub
+
+ align:start position:0%
+system at an integer multiple or sub
+ 
+
+ align:start position:0%
+system at an integer multiple or sub
+multiple of that and it gets it's a
+
+ align:start position:0%
+multiple of that and it gets it's a
+ 
+
+ align:start position:0%
+multiple of that and it gets it's a
+starts absorbing energy and resonance is
+
+ align:start position:0%
+starts absorbing energy and resonance is
+ 
+
+ align:start position:0%
+starts absorbing energy and resonance is
+what leads to energy moving from one
+
+ align:start position:0%
+what leads to energy moving from one
+ 
+
+ align:start position:0%
+what leads to energy moving from one
+part of the molecule to another it's
+
+ align:start position:0%
+part of the molecule to another it's
+ 
+
+ align:start position:0%
+part of the molecule to another it's
+always resonance that controls most of
+
+ align:start position:0%
+always resonance that controls most of
+ 
+
+ align:start position:0%
+always resonance that controls most of
+the dynamics that we can understand now
+
+ align:start position:0%
+the dynamics that we can understand now
+ 
+
+ align:start position:0%
+the dynamics that we can understand now
+when is it big enough well the coupling
+
+ align:start position:0%
+when is it big enough well the coupling
+ 
+
+ align:start position:0%
+when is it big enough well the coupling
+terms grow as the
+
+ align:start position:0%
+terms grow as the
+ 
+
+ align:start position:0%
+terms grow as the
+quantum numbers go up they go up as the
+
+ align:start position:0%
+quantum numbers go up they go up as the
+ 
+
+ align:start position:0%
+quantum numbers go up they go up as the
+square root or the square root to
+
+ align:start position:0%
+square root or the square root to
+ 
+
+ align:start position:0%
+square root or the square root to
+certain power of the quantum numbers and
+
+ align:start position:0%
+certain power of the quantum numbers and
+ 
+
+ align:start position:0%
+certain power of the quantum numbers and
+the energy defect doesn't grow and so a
+
+ align:start position:0%
+the energy defect doesn't grow and so a
+ 
+
+ align:start position:0%
+the energy defect doesn't grow and so a
+resonance will generally make itself
+
+ align:start position:0%
+resonance will generally make itself
+ 
+
+ align:start position:0%
+resonance will generally make itself
+felt eventually as you go up in energy
+
+ align:start position:0%
+felt eventually as you go up in energy
+ 
+
+ align:start position:0%
+felt eventually as you go up in energy
+conversely
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+if it happens it won't go away the
+
+ align:start position:0%
+if it happens it won't go away the
+ 
+
+ align:start position:0%
+if it happens it won't go away the
+there is a special situation where you
+
+ align:start position:0%
+there is a special situation where you
+ 
+
+ align:start position:0%
+there is a special situation where you
+can tune into resonance very early we're
+
+ align:start position:0%
+can tune into resonance very early we're
+ 
+
+ align:start position:0%
+can tune into resonance very early we're
+at a very sharp angle of attack on the
+
+ align:start position:0%
+at a very sharp angle of attack on the
+ 
+
+ align:start position:0%
+at a very sharp angle of attack on the
+energy levels and then you
+
+ align:start position:0%
+energy levels and then you
+ 
+
+ align:start position:0%
+energy levels and then you
+can detune from resonance because the
+
+ align:start position:0%
+can detune from resonance because the
+ 
+
+ align:start position:0%
+can detune from resonance because the
+levels move apart faster than the matrix
+
+ align:start position:0%
+levels move apart faster than the matrix
+ 
+
+ align:start position:0%
+levels move apart faster than the matrix
+elements can grow but that's very hard
+
+ align:start position:0%
+elements can grow but that's very hard
+ 
+
+ align:start position:0%
+elements can grow but that's very hard
+to cook up and so
+
+ align:start position:0%
+to cook up and so
+ 
+
+ align:start position:0%
+to cook up and so
+it's very typical that if there is a
+
+ align:start position:0%
+it's very typical that if there is a
+ 
+
+ align:start position:0%
+it's very typical that if there is a
+resonance it just gets worse or and
+
+ align:start position:0%
+resonance it just gets worse or and
+ 
+
+ align:start position:0%
+resonance it just gets worse or and
+Mercer but
+
+ align:start position:0%
+Mercer but
+ 
+
+ align:start position:0%
+Mercer but
+you know you know once you once you've
+
+ align:start position:0%
+you know you know once you once you've
+ 
+
+ align:start position:0%
+you know you know once you once you've
+solved the problem of the residents it
+
+ align:start position:0%
+solved the problem of the residents it
+ 
+
+ align:start position:0%
+solved the problem of the residents it
+doesn't matter because you're smarter
+
+ align:start position:0%
+doesn't matter because you're smarter
+ 
+
+ align:start position:0%
+doesn't matter because you're smarter
+than it and all it does is scale and so
+
+ align:start position:0%
+than it and all it does is scale and so
+ 
+
+ align:start position:0%
+than it and all it does is scale and so
+you know it scales in the number of
+
+ align:start position:0%
+you know it scales in the number of
+ 
+
+ align:start position:0%
+you know it scales in the number of
+resonance states and the strength of the
+
+ align:start position:0%
+resonance states and the strength of the
+ 
+
+ align:start position:0%
+resonance states and the strength of the
+resonance but everything has been
+
+ align:start position:0%
+resonance but everything has been
+ 
+
+ align:start position:0%
+resonance but everything has been
+determined from the first appearance you
+
+ align:start position:0%
+determined from the first appearance you
+ 
+
+ align:start position:0%
+determined from the first appearance you
+know what you need is the coupling term
+
+ align:start position:0%
+know what you need is the coupling term
+ 
+
+ align:start position:0%
+know what you need is the coupling term
+and the energy defect and once you know
+
+ align:start position:0%
+and the energy defect and once you know
+ 
+
+ align:start position:0%
+and the energy defect and once you know
+those it's it's all over for the
+
+ align:start position:0%
+those it's it's all over for the
+ 
+
+ align:start position:0%
+those it's it's all over for the
+molecules who is the first type of
+
+ align:start position:0%
+molecules who is the first type of
+ 
+
+ align:start position:0%
+molecules who is the first type of
+residence type in a very steep angle
+
+ align:start position:0%
+residence type in a very steep angle
+ 
+
+ align:start position:0%
+residence type in a very steep angle
+diagonally peers and energy is you call
+
+ align:start position:0%
+diagonally peers and energy is you call
+ 
+
+ align:start position:0%
+diagonally peers and energy is you call
+that accidental residence yes I would
+
+ align:start position:0%
+that accidental residence yes I would
+ 
+
+ align:start position:0%
+that accidental residence yes I would
+call it accidental in the other side is
+
+ align:start position:0%
+call it accidental in the other side is
+ 
+
+ align:start position:0%
+call it accidental in the other side is
+a because matica yes or global and
+
+ align:start position:0%
+a because matica yes or global and
+ 
+
+ align:start position:0%
+a because matica yes or global and
+it turns out that you
+
+ align:start position:0%
+it turns out that you
+ 
+
+ align:start position:0%
+it turns out that you
+can have a very high order resonance
+
+ align:start position:0%
+can have a very high order resonance
+ 
+
+ align:start position:0%
+can have a very high order resonance
+like you have 124 or something like that
+
+ align:start position:0%
+like you have 124 or something like that
+ 
+
+ align:start position:0%
+like you have 124 or something like that
+then the one doesn't scale the floor
+
+ align:start position:0%
+then the one doesn't scale the floor
+ 
+
+ align:start position:0%
+then the one doesn't scale the floor
+does scale but they can crash through
+
+ align:start position:0%
+does scale but they can crash through
+ 
+
+ align:start position:0%
+does scale but they can crash through
+each other really fast when it's a 222
+
+ align:start position:0%
+each other really fast when it's a 222
+ 
+
+ align:start position:0%
+each other really fast when it's a 222
+it's really hard to to cook up a problem
+
+ align:start position:0%
+it's really hard to to cook up a problem
+ 
+
+ align:start position:0%
+it's really hard to to cook up a problem
+that dtunes from residents no matter
+
+ align:start position:0%
+that dtunes from residents no matter
+ 
+
+ align:start position:0%
+that dtunes from residents no matter
+what and I found the algebra that to do
+
+ align:start position:0%
+what and I found the algebra that to do
+ 
+
+ align:start position:0%
+what and I found the algebra that to do
+that but I chose the wrong one in the a
+
+ align:start position:0%
+that but I chose the wrong one in the a
+ 
+
+ align:start position:0%
+that but I chose the wrong one in the a
+privet there is going to be a paper on
+
+ align:start position:0%
+privet there is going to be a paper on
+ 
+
+ align:start position:0%
+privet there is going to be a paper on
+effective Hamiltonians which I will
+
+ align:start position:0%
+effective Hamiltonians which I will
+ 
+
+ align:start position:0%
+effective Hamiltonians which I will
+distribute to the class at some point
+
+ align:start position:0%
+distribute to the class at some point
+ 
+
+ align:start position:0%
+distribute to the class at some point
+which is sort of my magnum opus you know
+
+ align:start position:0%
+which is sort of my magnum opus you know
+ 
+
+ align:start position:0%
+which is sort of my magnum opus you know
+what I've been working on all my
+
+ align:start position:0%
+what I've been working on all my
+ 
+
+ align:start position:0%
+what I've been working on all my
+scientific career and so
+
+ align:start position:0%
+scientific career and so
+ 
+
+ align:start position:0%
+scientific career and so
+there will be something that I will
+
+ align:start position:0%
+there will be something that I will
+ 
+
+ align:start position:0%
+there will be something that I will
+share with you but that's neither here
+
+ align:start position:0%
+share with you but that's neither here
+ 
+
+ align:start position:0%
+share with you but that's neither here
+nor there right now so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+thank you
\ No newline at end of file